diff --git a/assets/avatar/avatar_yuyanhuang.jpg b/assets/avatar/avatar_yuyanhuang.jpg
new file mode 100644
index 000000000..55bbb528a
Binary files /dev/null and b/assets/avatar/avatar_yuyanhuang.jpg differ
diff --git a/assets/javascripts/bundle.c2b142ea.min.js b/assets/javascripts/bundle.c2b142ea.min.js
index cb5773b85..02158b76a 100644
--- a/assets/javascripts/bundle.c2b142ea.min.js
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rect{fill:var(--md-mermaid-edge-color)!important;stroke:none!important}.statediagram-cluster.statediagram-cluster .inner{fill:var(--md-default-bg-color)}.statediagram-cluster rect{fill:var(--md-mermaid-node-bg-color);stroke:var(--md-mermaid-node-fg-color)}.statediagram-state rect.divider{fill:var(--md-default-fg-color--lightest);stroke:var(--md-default-fg-color--lighter)}defs #statediagram-barbEnd{stroke:var(--md-mermaid-edge-color)}[id^=entity] path,[id^=entity] rect{fill:var(--md-default-bg-color)}.relationshipLine{stroke:var(--md-mermaid-edge-color)}defs .marker.oneOrMore.er *,defs .marker.onlyOne.er *,defs .marker.zeroOrMore.er *,defs .marker.zeroOrOne.er 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t.pipe(g(r=>R(Y(!0),Y(!1).pipe(It(2e3))).pipe(f(n=>({message:r,active:n})))))}function Fs(e,t){let r=G(".md-typeset",e);return j(()=>{let n=new I;return n.subscribe(({message:o,active:i})=>{e.classList.toggle("md-dialog--active",i),r.textContent=o}),dp(e,t).pipe($(o=>n.next(o)),V(()=>n.complete()),f(o=>H({ref:e},o)))})}function hp({viewport$:e}){if(!X("header.autohide"))return Y(!1);let t=e.pipe(f(({offset:{y:o}})=>o),Pt(2,1),f(([o,i])=>[o<i,i]),fe(0)),r=re([e,t]).pipe(L(([{offset:o},[,i]])=>Math.abs(i-o.y)>100),f(([,[o]])=>o),ie()),n=Tn("search");return re([e,n]).pipe(f(([{offset:o},i])=>o.y>400&&!i),ie(),g(o=>o?r:Y(!1)),J(!1))}function Us(e,t){return j(()=>re([Re(e),hp(t)])).pipe(f(([{height:r},n])=>({height:r,hidden:n})),ie((r,n)=>r.height===n.height&&r.hidden===n.hidden),se(1))}function Ns(e,{viewport$:t,header$:r,main$:n}){return j(()=>{let o=new 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Lt=Us(ht("header"),{viewport$:ze}),Fr=vt.pipe(f(()=>ht("main")),g(e=>Ws(e,{viewport$:ze,header$:Lt})),se(1)),Pp=R(...Ee("consent").map(e=>us(e,{target$:hr})),...Ee("dialog").map(e=>Fs(e,{alert$:Po})),...Ee("palette").map(e=>Vs(e)),...Ee("progress").map(e=>zs(e,{progress$:Io})),...Ee("search").map(e=>Ks(e,{index$:gc})),...Ee("source").map(e=>Zs(e))),Ip=j(()=>R(...Ee("announce").map(e=>ls(e)),...Ee("content").map(e=>js(e,{sitemap$:_c,viewport$:ze,target$:hr,print$:bc})),...Ee("content").map(e=>X("search.highlight")?Ys(e,{index$:gc,location$:Ur}):y),...Ee("header").map(e=>Ns(e,{viewport$:ze,header$:Lt,main$:Fr})),...Ee("header-title").map(e=>Ds(e,{viewport$:ze,header$:Lt})),...Ee("sidebar").map(e=>e.getAttribute("data-md-type")==="navigation"?yo(vc,()=>Ao(e,{viewport$:ze,header$:Lt,main$:Fr})):yo($o,()=>Ao(e,{viewport$:ze,header$:Lt,main$:Fr}))),...Ee("tabs").map(e=>Qs(e,{viewport$:ze,header$:Lt})),...Ee("toc").map(e=>ec(e,{viewport$:ze,header$:Lt,main$:Fr,target$:hr})),...Ee("top").map(e=>tc(e,{viewport$:ze,header$:Lt,main$:Fr,target$:hr})))),yc=vt.pipe(g(()=>Ip),Rt(Pp),se(1));yc.subscribe();window.document$=vt;window.location$=Ur;window.target$=hr;window.keyboard$=hc;window.viewport$=ze;window.tablet$=$o;window.screen$=vc;window.print$=bc;window.alert$=Po;window.progress$=Io;window.component$=yc;})();
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+/*! update cache: 20260330081538 */
diff --git a/en/404.html b/en/404.html
index dffc401e1..26452ec4b 100644
--- a/en/404.html
+++ b/en/404.html
@@ -59,8 +59,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Lato:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Lato";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Inter:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Inter";--md-code-font:"JetBrains Mono"}</style>
       
     
     
diff --git a/en/assets/javascripts/bundle.c2b142ea.min.js b/en/assets/javascripts/bundle.c2b142ea.min.js
index 8c73d00f8..2404a9147 100644
--- a/en/assets/javascripts/bundle.c2b142ea.min.js
+++ b/en/assets/javascripts/bundle.c2b142ea.min.js
@@ -1,4 +1,4 @@
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index d78f22221..237a15069 100644
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index a53d60ea6..e7676a453 100644
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diff --git a/en/chapter_sorting/radix_sort/index.html b/en/chapter_sorting/radix_sort/index.html
index 8cbb059eb..d0d307f20 100644
--- a/en/chapter_sorting/radix_sort/index.html
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diff --git a/en/chapter_sorting/selection_sort/index.html b/en/chapter_sorting/selection_sort/index.html
index dfcda7323..7360d0ac5 100644
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+        <style>:root{--md-text-font:"Inter";--md-code-font:"JetBrains Mono"}</style>
       
     
     
diff --git a/en/chapter_sorting/sorting_algorithm/index.html b/en/chapter_sorting/sorting_algorithm/index.html
index 948ada92f..b7534553c 100644
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+        <style>:root{--md-text-font:"Inter";--md-code-font:"JetBrains Mono"}</style>
       
     
     
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index 6dc4209cf..6d6e42a57 100644
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-        <style>:root{--md-text-font:"Lato";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Inter:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Inter";--md-code-font:"JetBrains Mono"}</style>
       
     
     
diff --git a/en/chapter_stack_and_queue/deque/index.html b/en/chapter_stack_and_queue/deque/index.html
index 93b7f5dff..db52a2be7 100644
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-        <style>:root{--md-text-font:"Lato";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Inter:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Inter";--md-code-font:"JetBrains Mono"}</style>
       
     
     
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index d7ea9a6e3..479e802ab 100644
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-        <style>:root{--md-text-font:"Lato";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Inter:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Inter";--md-code-font:"JetBrains Mono"}</style>
       
     
     
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index 27d2d53a1..a1819f9c8 100644
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-        <style>:root{--md-text-font:"Lato";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Inter:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Inter";--md-code-font:"JetBrains Mono"}</style>
       
     
     
diff --git a/en/chapter_stack_and_queue/stack/index.html b/en/chapter_stack_and_queue/stack/index.html
index 32043a0cc..d26f40b97 100644
--- a/en/chapter_stack_and_queue/stack/index.html
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@@ -65,8 +65,8 @@
         
         
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-        <style>:root{--md-text-font:"Lato";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Inter:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Inter";--md-code-font:"JetBrains Mono"}</style>
       
     
     
diff --git a/en/chapter_stack_and_queue/summary/index.html b/en/chapter_stack_and_queue/summary/index.html
index a37b2a813..e484de749 100644
--- a/en/chapter_stack_and_queue/summary/index.html
+++ b/en/chapter_stack_and_queue/summary/index.html
@@ -65,8 +65,8 @@
         
         
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-        <style>:root{--md-text-font:"Lato";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Inter:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Inter";--md-code-font:"JetBrains Mono"}</style>
       
     
     
diff --git a/en/chapter_tree/array_representation_of_tree/index.html b/en/chapter_tree/array_representation_of_tree/index.html
index f7d0c1c32..e327bce2c 100644
--- a/en/chapter_tree/array_representation_of_tree/index.html
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-        <style>:root{--md-text-font:"Lato";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Inter:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Inter";--md-code-font:"JetBrains Mono"}</style>
       
     
     
diff --git a/en/chapter_tree/avl_tree/index.html b/en/chapter_tree/avl_tree/index.html
index 06e1cb5cf..8360fbaee 100644
--- a/en/chapter_tree/avl_tree/index.html
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@@ -65,8 +65,8 @@
         
         
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-        <style>:root{--md-text-font:"Lato";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Inter:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Inter";--md-code-font:"JetBrains Mono"}</style>
       
     
     
diff --git a/en/chapter_tree/binary_search_tree/index.html b/en/chapter_tree/binary_search_tree/index.html
index 6c153ebe8..a0b8a20a3 100644
--- a/en/chapter_tree/binary_search_tree/index.html
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@@ -65,8 +65,8 @@
         
         
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-        <style>:root{--md-text-font:"Lato";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Inter:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Inter";--md-code-font:"JetBrains Mono"}</style>
       
     
     
diff --git a/en/chapter_tree/binary_tree/index.html b/en/chapter_tree/binary_tree/index.html
index 88333d1d8..4a00b4f93 100644
--- a/en/chapter_tree/binary_tree/index.html
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-        <style>:root{--md-text-font:"Lato";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Inter:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Inter";--md-code-font:"JetBrains Mono"}</style>
       
     
     
diff --git a/en/chapter_tree/binary_tree_traversal/index.html b/en/chapter_tree/binary_tree_traversal/index.html
index b73c5ff0b..45222d559 100644
--- a/en/chapter_tree/binary_tree_traversal/index.html
+++ b/en/chapter_tree/binary_tree_traversal/index.html
@@ -65,8 +65,8 @@
         
         
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-        <style>:root{--md-text-font:"Lato";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Inter:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Inter";--md-code-font:"JetBrains Mono"}</style>
       
     
     
diff --git a/en/chapter_tree/index.html b/en/chapter_tree/index.html
index 391d4bf72..e9299245b 100644
--- a/en/chapter_tree/index.html
+++ b/en/chapter_tree/index.html
@@ -65,8 +65,8 @@
         
         
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-        <style>:root{--md-text-font:"Lato";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Inter:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Inter";--md-code-font:"JetBrains Mono"}</style>
       
     
     
diff --git a/en/chapter_tree/summary/index.html b/en/chapter_tree/summary/index.html
index d6ec82d79..58af139ec 100644
--- a/en/chapter_tree/summary/index.html
+++ b/en/chapter_tree/summary/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Lato:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Lato";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Inter:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Inter";--md-code-font:"JetBrains Mono"}</style>
       
     
     
diff --git a/en/index.html b/en/index.html
index e33689fd3..a23952a92 100644
--- a/en/index.html
+++ b/en/index.html
@@ -19,9 +19,9 @@
     <link href="./assets/stylesheets/modern/main.6f2fbb28.min.css" rel="stylesheet"/>
     <link href="./assets/stylesheets/modern/palette.dfe2e883.min.css" rel="stylesheet"/>
     <link crossorigin="" href="https://fonts.gstatic.com" rel="preconnect"/>
-    <link href="https://fonts.googleapis.com/css?family=Lato:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&amp;display=fallback" rel="stylesheet"/>
+    <link href="https://fonts.googleapis.com/css?family=Inter:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&amp;display=fallback" rel="stylesheet"/>
     <style>
-      :root{--md-text-font:"Lato";--md-code-font:"JetBrains Mono"}
+      :root{--md-text-font:"Inter";--md-code-font:"JetBrains Mono"}
     </style>
     <link href="./stylesheets/extra.css" rel="stylesheet"/>
     <script>
@@ -129,7 +129,7 @@
           <div class="starfield-origin">
           </div>
         </div>
-        <div class="hero-div">
+        <div class="hero-div hero-div--en">
           <img alt="" src="../assets/hero/ground.png" style="position: absolute; width: auto; height: 26.445%; left: 28.211%; top: 54.145%;"/>
           <img alt="" src="../assets/hero/links.png" style="position: absolute; width: auto; height: 78.751%; left: 10.545%; top: 7.326%;"/>
           <a href="chapter_introduction/">
diff --git a/en/javascripts/katex.js b/en/javascripts/katex.js
index c94c87c33..5095e0f41 100644
--- a/en/javascripts/katex.js
+++ b/en/javascripts/katex.js
@@ -8,4 +8,4 @@ document$.subscribe(({ body }) => {
     ],
   });
 });
-/*! update cache: 20260329054745 */
+/*! update cache: 20260330081601 */
diff --git a/en/javascripts/mathjax.js b/en/javascripts/mathjax.js
index b40332047..0e27a72e8 100644
--- a/en/javascripts/mathjax.js
+++ b/en/javascripts/mathjax.js
@@ -15,4 +15,4 @@ window.MathJax = {
 document$.subscribe(() => {
   MathJax.typesetPromise();
 });
-/*! update cache: 20260329054745 */
+/*! update cache: 20260330081601 */
diff --git a/en/javascripts/starfield.js b/en/javascripts/starfield.js
index 4b35fe18b..746823bdd 100644
--- a/en/javascripts/starfield.js
+++ b/en/javascripts/starfield.js
@@ -469,4 +469,4 @@
 
   return Starfield;
 });
-/*! update cache: 20260329054745 */
+/*! update cache: 20260330081601 */
diff --git a/en/stylesheets/extra.css b/en/stylesheets/extra.css
index 4a8a625ab..b5c83f9f9 100644
--- a/en/stylesheets/extra.css
+++ b/en/stylesheets/extra.css
@@ -375,6 +375,14 @@ a:hover .text-button span {
   font-weight: normal;
 }
 
+.hero-div--en {
+  font-size: min(1.65vh, 2.3vw);
+}
+
+.hero-div--ru {
+  font-size: min(1.45vh, 2vw);
+}
+
 .hero-bg {
   height: 100%;
   width: 100%;
@@ -487,6 +495,11 @@ a:hover .text-button span {
   text-align: center;
 }
 
+.profile-cell a:hover b,
+.profile-cell a:focus-visible b {
+  text-decoration: underline;
+}
+
 .profile-img {
   width: 5em;
   border-radius: 50%;
@@ -768,4 +781,4 @@ html:has(body[data-md-color-scheme="default"]) {
 .md-typeset a:not(.md-button):focus-visible {
   text-decoration: underline;
 }
-/*! update cache: 20260329054745 */
+/*! update cache: 20260330081601 */
diff --git a/ja/404.html b/ja/404.html
index fb7fa6a3a..0616dc3a9 100644
--- a/ja/404.html
+++ b/ja/404.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -110,7 +110,7 @@
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -334,7 +334,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -351,7 +351,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -611,7 +611,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -639,7 +639,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -776,7 +776,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1053,7 +1053,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1081,7 +1081,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1584,7 +1584,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1606,7 +1606,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1628,7 +1628,7 @@
   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1935,7 +1935,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2098,7 +2098,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2484,7 +2484,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2540,7 +2540,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2568,7 +2568,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3106,7 +3106,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3162,7 +3162,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3190,7 +3190,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3383,7 +3383,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3411,7 +3411,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3552,7 +3552,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3580,7 +3580,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3608,7 +3608,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3636,7 +3636,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3829,7 +3829,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4074,7 +4074,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
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rect{fill:var(--md-mermaid-edge-color)!important;stroke:none!important}.statediagram-cluster.statediagram-cluster .inner{fill:var(--md-default-bg-color)}.statediagram-cluster rect{fill:var(--md-mermaid-node-bg-color);stroke:var(--md-mermaid-node-fg-color)}.statediagram-state rect.divider{fill:var(--md-default-fg-color--lightest);stroke:var(--md-default-fg-color--lighter)}defs #statediagram-barbEnd{stroke:var(--md-mermaid-edge-color)}[id^=entity] path,[id^=entity] rect{fill:var(--md-default-bg-color)}.relationshipLine{stroke:var(--md-mermaid-edge-color)}defs .marker.oneOrMore.er *,defs .marker.onlyOne.er *,defs .marker.zeroOrMore.er *,defs .marker.zeroOrOne.er 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t});Object.values||(Object.values=function(e){let t=[];for(let r of Object.keys(e))t.push(e[r]);return t});typeof Element!="undefined"&&(Element.prototype.scrollTo||(Element.prototype.scrollTo=function(e,t){typeof e=="object"?(this.scrollLeft=e.left,this.scrollTop=e.top):(this.scrollLeft=e,this.scrollTop=t)}),Element.prototype.replaceWith||(Element.prototype.replaceWith=function(...e){let t=this.parentNode;if(t){e.length===0&&t.removeChild(this);for(let r=e.length-1;r>=0;r--){let n=e[r];typeof n=="string"?n=document.createTextNode(n):n.parentNode&&n.parentNode.removeChild(n),r?t.insertBefore(this.previousSibling,n):t.replaceChild(n,this)}}}));function $p(){return location.protocol==="file:"?ar(`${new URL("search.js",Mn.base)}`).pipe(f(()=>__index),_e(()=>Ke),se(1)):et(new URL("search.json",Mn.base))}document.documentElement.classList.remove("no-js");document.documentElement.classList.add("js");var vt=Si(),Ur=Za(),hr=ts(Ur),hc=Xa(),ze=cs(),$o=Ir("(min-width: 60em)"),vc=Ir("(min-width: 76.25em)"),bc=rs(),Mn=Ue(),gc=Le(".md-search")?$p():Ke,Po=new I;oc({alert$:Po});nc({document$:vt});var Io=new I,_c=dr(Mn.base);X("navigation.instant")&&cc({sitemap$:_c,location$:Ur,viewport$:ze,progress$:Io}).subscribe(vt);var dc;((dc=Mn.version)==null?void 0:dc.provider)==="mike"&&uc({document$:vt});R(Ur,hr).pipe(It(125)).subscribe(()=>{Eo("drawer",!1),Eo("search",!1)});hc.pipe(L(({mode:e,meta:t})=>e==="global"&&!t)).subscribe(e=>{switch(e.type){case",":case"p":let t=document.querySelector("link[rel=prev]");t instanceof HTMLLinkElement&&dt(t);break;case".":case"n":let r=document.querySelector("link[rel=next]");r instanceof HTMLLinkElement&&dt(r);break;case"/":let n=document.querySelector("[data-md-component=search] button");n instanceof HTMLButtonElement&&n.click();break;case"Enter":let o=xt();o instanceof HTMLLabelElement&&o.click()}});pc({viewport$:ze,document$:vt});fc({document$:vt,tablet$:$o});mc({document$:vt});var Lt=Us(ht("header"),{viewport$:ze}),Fr=vt.pipe(f(()=>ht("main")),g(e=>Ws(e,{viewport$:ze,header$:Lt})),se(1)),Pp=R(...Ee("consent").map(e=>us(e,{target$:hr})),...Ee("dialog").map(e=>Fs(e,{alert$:Po})),...Ee("palette").map(e=>Vs(e)),...Ee("progress").map(e=>zs(e,{progress$:Io})),...Ee("search").map(e=>Ks(e,{index$:gc})),...Ee("source").map(e=>Zs(e))),Ip=j(()=>R(...Ee("announce").map(e=>ls(e)),...Ee("content").map(e=>js(e,{sitemap$:_c,viewport$:ze,target$:hr,print$:bc})),...Ee("content").map(e=>X("search.highlight")?Ys(e,{index$:gc,location$:Ur}):y),...Ee("header").map(e=>Ns(e,{viewport$:ze,header$:Lt,main$:Fr})),...Ee("header-title").map(e=>Ds(e,{viewport$:ze,header$:Lt})),...Ee("sidebar").map(e=>e.getAttribute("data-md-type")==="navigation"?yo(vc,()=>Ao(e,{viewport$:ze,header$:Lt,main$:Fr})):yo($o,()=>Ao(e,{viewport$:ze,header$:Lt,main$:Fr}))),...Ee("tabs").map(e=>Qs(e,{viewport$:ze,header$:Lt})),...Ee("toc").map(e=>ec(e,{viewport$:ze,header$:Lt,main$:Fr,target$:hr})),...Ee("top").map(e=>tc(e,{viewport$:ze,header$:Lt,main$:Fr,target$:hr})))),yc=vt.pipe(g(()=>Ip),Rt(Pp),se(1));yc.subscribe();window.document$=vt;window.location$=Ur;window.target$=hr;window.keyboard$=hc;window.viewport$=ze;window.tablet$=$o;window.screen$=vc;window.print$=bc;window.alert$=Po;window.progress$=Io;window.component$=yc;})();
-/*! update cache: 20260329054750 */
+/*! update cache: 20260330081613 */
diff --git a/ja/chapter_appendix/contribution/index.html b/ja/chapter_appendix/contribution/index.html
index 4b5216382..e0eeac003 100644
--- a/ja/chapter_appendix/contribution/index.html
+++ b/ja/chapter_appendix/contribution/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -39,7 +39,7 @@
     
     
       
-        <title>16.2 コントリビューション - Hello アルゴリズム</title>
+        <title>16.2 一緒に制作に参加しましょう - Hello アルゴリズム</title>
       
     
     
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -152,7 +152,7 @@
         <div class="md-header__topic" data-md-component="header-topic">
           <span class="md-ellipsis">
             
-              16.2 &nbsp; コントリビューション
+              16.2 &nbsp; 一緒に制作に参加しましょう
             
           </span>
         </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1635,7 +1635,7 @@
   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1942,7 +1942,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2105,7 +2105,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2491,7 +2491,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2547,7 +2547,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2575,7 +2575,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3113,7 +3113,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3169,7 +3169,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3197,7 +3197,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3390,7 +3390,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3418,7 +3418,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3559,7 +3559,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3587,7 +3587,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3615,7 +3615,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3643,7 +3643,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3836,7 +3836,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4092,7 +4092,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4110,7 +4110,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4151,7 +4151,7 @@
   <a href="#2" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2. &nbsp; 内容の作成
+        2. &nbsp; コンテンツ制作
       
     </span>
   </a>
@@ -4162,7 +4162,7 @@
   <a href="#3-docker" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3. &nbsp; Dockerデプロイメント
+        3. &nbsp; Docker デプロイ
       
     </span>
   </a>
@@ -4321,7 +4321,7 @@
   <a href="#2" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2. &nbsp; 内容の作成
+        2. &nbsp; コンテンツ制作
       
     </span>
   </a>
@@ -4332,7 +4332,7 @@
   <a href="#3-docker" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3. &nbsp; Dockerデプロイメント
+        3. &nbsp; Docker デプロイ
       
     </span>
   </a>
@@ -4376,39 +4376,39 @@
 
 
 <!-- Page content -->
-<h1 id="162">16.2 &nbsp; コントリビューション<a class="headerlink" href="#162" title="Permanent link">&para;</a></h1>
-<p>著者の能力に限りがあるため、本書にはいくつかの省略や誤りが避けられません。ご理解をお願いします。誤字、リンク切れ、内容の欠落、文章の曖昧さ、説明の不明確さ、または不合理な文章構造を発見された場合は、読者により良質な学習リソースを提供するため、修正にご協力ください。</p>
-<p>すべての<a href="https://github.com/krahets/hello-algo/graphs/contributors">コントリビューター</a>のGitHub IDは、本書のリポジトリ、ウェブ、PDFバージョンのホームページに表示され、オープンソースコミュニティへの無私の貢献に感謝いたします。</p>
+<h1 id="162">16.2 &nbsp; 一緒に制作に参加しましょう<a class="headerlink" href="#162" title="Permanent link">&para;</a></h1>
+<p>著者の力には限りがあるため、本書にはどうしても一部の漏れや誤りが含まれる可能性があります。ご了承ください。誤字、リンク切れ、内容の欠落、表現の曖昧さ、説明の不明瞭さ、文章構成の不適切さなどの問題を見つけた場合は、ぜひ修正にご協力ください。読者により良い学習リソースを提供できます。</p>
+<p>すべての<a href="https://github.com/krahets/hello-algo/graphs/contributors">寄稿者</a>の GitHub ID は、本書のリポジトリ、Web 版、PDF 版のホームページに掲載され、オープンソースコミュニティへの惜しみない貢献に感謝を表します。</p>
 <div class="admonition success">
 <p class="admonition-title">オープンソースの魅力</p>
-<p>紙の本の2つの印刷版の間隔はしばしば長く、内容の更新が非常に不便です。</p>
-<p>しかし、このオープンソースの本では、内容の更新サイクルは数日、さらには数時間に短縮されます。</p>
+<p>紙の書籍では、2 回の増刷の間隔が長くなりがちで、内容更新は非常に不便です。</p>
+<p>一方、このオープンソース書籍では、内容更新のサイクルは数日、場合によっては数時間にまで短縮されています。</p>
 </div>
 <h3 id="1">1. &nbsp; 内容の微調整<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>下の図に示すように、各ページの右上角に「編集アイコン」があります。以下の手順に従ってテキストやコードを修正できます。</p>
+<p>以下の図のように、各ページの右上には「編集アイコン」があります。次の手順で本文やコードを修正できます。</p>
 <ol>
-<li>「編集アイコン」をクリックします。「このリポジトリをフォークしますか」と促された場合は、同意してください。</li>
-<li>Markdownソースファイルの内容を修正し、内容の正確性を確認し、フォーマットの一貫性を保つようにしてください。</li>
-<li>ページの下部で修正説明を記入し、「Propose file change」ボタンをクリックします。ページがリダイレクトされた後、「Create pull request」ボタンをクリックしてプルリクエストを開始します。</li>
+<li>「編集アイコン」をクリックし、「このリポジトリを Fork する必要があります」と表示された場合は、その操作を承認してください。</li>
+<li>Markdown のソースファイルを修正し、内容が正しいことを確認したうえで、できるだけ書式の統一を保ってください。</li>
+<li>ページ下部に修正内容の説明を入力し、その後「Propose file change」ボタンをクリックします。ページ遷移後、「Create pull request」ボタンをクリックするとプルリクエストを作成できます。</li>
 </ol>
 <p><img alt="ページ編集ボタン" class="animation-figure" src="../contribution.assets/edit_markdown.png" /></p>
 <p align="center"> 図 16-3 &nbsp; ページ編集ボタン </p>
 
-<p>図は直接修正できないため、新しい<a href="https://github.com/krahets/hello-algo/issues">Issue</a>を作成するか、問題を説明するコメントが必要です。できるだけ早く図を再描画して置き換えます。</p>
-<h3 id="2">2. &nbsp; 内容の作成<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>このオープンソースプロジェクトへの参加に興味がある場合、コードを他のプログラミング言語に翻訳したり、記事の内容を拡張したりすることを含めて、以下のプルリクエストワークフローを実装する必要があります。</p>
+<p>画像は直接修正できないため、新しい <a href="https://github.com/krahets/hello-algo/issues">Issue</a> を作成するかコメントで問題を説明してください。できるだけ早く描き直して差し替えます。</p>
+<h3 id="2">2. &nbsp; コンテンツ制作<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>コードを他のプログラミング言語へ翻訳することや、記事内容を拡充することなど、このオープンソースプロジェクトへの参加に興味がある場合は、以下の Pull Request ワークフローに従ってください。</p>
 <ol>
-<li>GitHubにログインし、本書の<a href="https://github.com/krahets/hello-algo">コードリポジトリ</a>を個人アカウントにフォークします。</li>
-<li>フォークしたリポジトリのウェブページに移動し、<code>git clone</code>コマンドを使用してリポジトリをローカルマシンにクローンします。</li>
-<li>ローカルで内容を作成し、完全なテストを実行してコードの正確性を検証します。</li>
-<li>ローカルで行った変更をコミットし、リモートリポジトリにプッシュします。</li>
-<li>リポジトリのウェブページを更新し、「Create pull request」ボタンをクリックしてプルリクエストを開始します。</li>
+<li>GitHub にログインし、本書の<a href="https://github.com/krahets/hello-algo">コードリポジトリ</a>を個人アカウントに Fork します。</li>
+<li>Fork したリポジトリのページに入り、<code>git clone</code> コマンドを使ってリポジトリをローカルにクローンします。</li>
+<li>ローカルでコンテンツを作成し、完全なテストを行ってコードの正しさを確認します。</li>
+<li>ローカルで行った変更を Commit し、その後リモートリポジトリへ Push します。</li>
+<li>リポジトリのページを更新し、「Create pull request」ボタンをクリックするとプルリクエストを作成できます。</li>
 </ol>
-<h3 id="3-docker">3. &nbsp; Dockerデプロイメント<a class="headerlink" href="#3-docker" title="Permanent link">&para;</a></h3>
-<p><code>hello-algo</code>ルートディレクトリで、以下のDockerスクリプトを実行して<code>http://localhost:8000</code>でプロジェクトにアクセスします：</p>
+<h3 id="3-docker">3. &nbsp; Docker デプロイ<a class="headerlink" href="#3-docker" title="Permanent link">&para;</a></h3>
+<p><code>hello-algo</code> のルートディレクトリで以下の Docker スクリプトを実行すると、<code>http://localhost:8000</code> で本プロジェクトにアクセスできます。</p>
 <div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a>docker-compose<span class="w"> </span>up<span class="w"> </span>-d
 </code></pre></div>
-<p>以下のコマンドを使用してデプロイメントを削除します：</p>
+<p>以下のコマンドでデプロイを削除できます。</p>
 <div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a>docker-compose<span class="w"> </span>down
 </code></pre></div>
 
diff --git a/ja/chapter_appendix/index.html b/ja/chapter_appendix/index.html
index 0743fe880..32980937f 100644
--- a/ja/chapter_appendix/index.html
+++ b/ja/chapter_appendix/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1635,7 +1635,7 @@
   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1942,7 +1942,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2105,7 +2105,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2491,7 +2491,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2547,7 +2547,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2575,7 +2575,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3113,7 +3113,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3169,7 +3169,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3197,7 +3197,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3390,7 +3390,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3418,7 +3418,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3559,7 +3559,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3587,7 +3587,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3615,7 +3615,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3643,7 +3643,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3836,7 +3836,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4083,7 +4083,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4278,7 +4278,7 @@
 <h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
 <li><a href="installation/">16.1 &nbsp; プログラミング環境のインストール</a></li>
-<li><a href="contribution/">16.2 &nbsp; 一緒に創作に参加する</a></li>
+<li><a href="contribution/">16.2 &nbsp; 一緒に制作に参加しましょう</a></li>
 <li><a href="terminology/">16.3 &nbsp; 用語集</a></li>
 </ul>
 
diff --git a/ja/chapter_appendix/installation/index.html b/ja/chapter_appendix/installation/index.html
index 26f43b00b..9e6163415 100644
--- a/ja/chapter_appendix/installation/index.html
+++ b/ja/chapter_appendix/installation/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -39,7 +39,7 @@
     
     
       
-        <title>16.1 インストール - Hello アルゴリズム</title>
+        <title>16.1 プログラミング環境のインストール - Hello アルゴリズム</title>
       
     
     
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -152,7 +152,7 @@
         <div class="md-header__topic" data-md-component="header-topic">
           <span class="md-ellipsis">
             
-              16.1 &nbsp; インストール
+              16.1 &nbsp; プログラミング環境のインストール
             
           </span>
         </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1635,7 +1635,7 @@
   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1942,7 +1942,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2105,7 +2105,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2491,7 +2491,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2547,7 +2547,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2575,7 +2575,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3113,7 +3113,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3169,7 +3169,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3197,7 +3197,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3390,7 +3390,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3418,7 +3418,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3559,7 +3559,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3587,7 +3587,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3615,7 +3615,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3643,7 +3643,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3836,7 +3836,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4112,7 +4112,7 @@
   <a href="#1611-ide" class="md-nav__link">
     <span class="md-ellipsis">
       
-        16.1.1 &nbsp; IDEのインストール
+        16.1.1 &nbsp; IDE のインストール
       
     </span>
   </a>
@@ -4135,7 +4135,7 @@
   <a href="#1-python" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; Python環境
+        1. &nbsp; Python 環境
       
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@@ -4146,7 +4146,7 @@
   <a href="#2-cc" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2. &nbsp; C/C++環境
+        2. &nbsp; C/C++ 環境
       
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   </a>
@@ -4157,7 +4157,7 @@
   <a href="#3-java" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3. &nbsp; Java環境
+        3. &nbsp; Java 環境
       
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@@ -4168,7 +4168,7 @@
   <a href="#4-c" class="md-nav__link">
     <span class="md-ellipsis">
       
-        4. &nbsp; C#環境
+        4. &nbsp; C# 環境
       
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@@ -4179,7 +4179,7 @@
   <a href="#5-go" class="md-nav__link">
     <span class="md-ellipsis">
       
-        5. &nbsp; Go環境
+        5. &nbsp; Go 環境
       
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@@ -4190,7 +4190,7 @@
   <a href="#6-swift" class="md-nav__link">
     <span class="md-ellipsis">
       
-        6. &nbsp; Swift環境
+        6. &nbsp; Swift 環境
       
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@@ -4201,7 +4201,7 @@
   <a href="#7-javascript" class="md-nav__link">
     <span class="md-ellipsis">
       
-        7. &nbsp; JavaScript環境
+        7. &nbsp; JavaScript 環境
       
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@@ -4212,7 +4212,7 @@
   <a href="#8-typescript" class="md-nav__link">
     <span class="md-ellipsis">
       
-        8. &nbsp; TypeScript環境
+        8. &nbsp; TypeScript 環境
       
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@@ -4223,7 +4223,7 @@
   <a href="#9-dart" class="md-nav__link">
     <span class="md-ellipsis">
       
-        9. &nbsp; Dart環境
+        9. &nbsp; Dart 環境
       
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@@ -4234,7 +4234,7 @@
   <a href="#10-rust" class="md-nav__link">
     <span class="md-ellipsis">
       
-        10. &nbsp; Rust環境
+        10. &nbsp; Rust 環境
       
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@@ -4269,7 +4269,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4415,7 +4415,7 @@
   <a href="#1611-ide" class="md-nav__link">
     <span class="md-ellipsis">
       
-        16.1.1 &nbsp; IDEのインストール
+        16.1.1 &nbsp; IDE のインストール
       
     </span>
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@@ -4438,7 +4438,7 @@
   <a href="#1-python" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; Python環境
+        1. &nbsp; Python 環境
       
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@@ -4449,7 +4449,7 @@
   <a href="#2-cc" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2. &nbsp; C/C++環境
+        2. &nbsp; C/C++ 環境
       
     </span>
   </a>
@@ -4460,7 +4460,7 @@
   <a href="#3-java" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3. &nbsp; Java環境
+        3. &nbsp; Java 環境
       
     </span>
   </a>
@@ -4471,7 +4471,7 @@
   <a href="#4-c" class="md-nav__link">
     <span class="md-ellipsis">
       
-        4. &nbsp; C#環境
+        4. &nbsp; C# 環境
       
     </span>
   </a>
@@ -4482,7 +4482,7 @@
   <a href="#5-go" class="md-nav__link">
     <span class="md-ellipsis">
       
-        5. &nbsp; Go環境
+        5. &nbsp; Go 環境
       
     </span>
   </a>
@@ -4493,7 +4493,7 @@
   <a href="#6-swift" class="md-nav__link">
     <span class="md-ellipsis">
       
-        6. &nbsp; Swift環境
+        6. &nbsp; Swift 環境
       
     </span>
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@@ -4504,7 +4504,7 @@
   <a href="#7-javascript" class="md-nav__link">
     <span class="md-ellipsis">
       
-        7. &nbsp; JavaScript環境
+        7. &nbsp; JavaScript 環境
       
     </span>
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@@ -4515,7 +4515,7 @@
   <a href="#8-typescript" class="md-nav__link">
     <span class="md-ellipsis">
       
-        8. &nbsp; TypeScript環境
+        8. &nbsp; TypeScript 環境
       
     </span>
   </a>
@@ -4526,7 +4526,7 @@
   <a href="#9-dart" class="md-nav__link">
     <span class="md-ellipsis">
       
-        9. &nbsp; Dart環境
+        9. &nbsp; Dart 環境
       
     </span>
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@@ -4537,7 +4537,7 @@
   <a href="#10-rust" class="md-nav__link">
     <span class="md-ellipsis">
       
-        10. &nbsp; Rust環境
+        10. &nbsp; Rust 環境
       
     </span>
   </a>
@@ -4586,71 +4586,71 @@
 
 
 <!-- Page content -->
-<h1 id="161">16.1 &nbsp; インストール<a class="headerlink" href="#161" title="Permanent link">&para;</a></h1>
-<h2 id="1611-ide">16.1.1 &nbsp; IDEのインストール<a class="headerlink" href="#1611-ide" title="Permanent link">&para;</a></h2>
-<p>ローカルの統合開発環境（IDE）として、オープンソースで軽量なVS Codeを使用することをお勧めします。<a href="https://code.visualstudio.com/">VS Code公式ウェブサイト</a>にアクセスし、お使いのオペレーティングシステムに適したVS Codeのバージョンを選択してダウンロードし、インストールしてください。</p>
-<p><img alt="公式ウェブサイトからVS Codeをダウンロード" class="animation-figure" src="../installation.assets/vscode_installation.png" /></p>
-<p align="center"> 図 16-1 &nbsp; 公式ウェブサイトからVS Codeをダウンロード </p>
+<h1 id="161">16.1 &nbsp; プログラミング環境のインストール<a class="headerlink" href="#161" title="Permanent link">&para;</a></h1>
+<h2 id="1611-ide">16.1.1 &nbsp; IDE のインストール<a class="headerlink" href="#1611-ide" title="Permanent link">&para;</a></h2>
+<p>オープンソースで軽量な VS Code をローカルの統合開発環境（IDE）として使用することを推奨します。<a href="https://code.visualstudio.com/">VS Code 公式サイト</a> にアクセスし、使用している OS に応じたバージョンの VS Code をダウンロードしてインストールしてください。</p>
+<p><img alt="公式サイトから VS Code をダウンロード" class="animation-figure" src="../installation.assets/vscode_installation.png" /></p>
+<p align="center"> 図 16-1 &nbsp; 公式サイトから VS Code をダウンロード </p>
 
-<p>VS Codeには強力な拡張機能エコシステムがあり、ほとんどのプログラミング言語の実行とデバッグをサポートしています。例えば、「Python Extension Pack」をインストールした後、Pythonコードをデバッグできます。インストール手順を下の図に示します。</p>
-<p><img alt="VS Code拡張機能パックのインストール" class="animation-figure" src="../installation.assets/vscode_extension_installation.png" /></p>
-<p align="center"> 図 16-2 &nbsp; VS Code拡張機能パックのインストール </p>
+<p>VS Code には強力な拡張機能のエコシステムがあり、ほとんどのプログラミング言語の実行とデバッグをサポートしています。Python を例にすると、「Python Extension Pack」拡張機能をインストールした後、Python コードをデバッグできるようになります。インストール手順を以下に示します。</p>
+<p><img alt="VS Code 拡張機能のインストール" class="animation-figure" src="../installation.assets/vscode_extension_installation.png" /></p>
+<p align="center"> 図 16-2 &nbsp; VS Code 拡張機能のインストール </p>
 
 <h2 id="1612">16.1.2 &nbsp; 言語環境のインストール<a class="headerlink" href="#1612" title="Permanent link">&para;</a></h2>
-<h3 id="1-python">1. &nbsp; Python環境<a class="headerlink" href="#1-python" title="Permanent link">&para;</a></h3>
+<h3 id="1-python">1. &nbsp; Python 環境<a class="headerlink" href="#1-python" title="Permanent link">&para;</a></h3>
 <ol>
-<li><a href="https://docs.conda.io/en/latest/miniconda.html">Miniconda3</a>をダウンロードしてインストールします。Python 3.10以降が必要です。</li>
-<li>VS Code拡張機能マーケットプレイスで<code>python</code>を検索し、Python Extension Packをインストールします。</li>
-<li>（オプション）コマンドラインで<code>pip install black</code>を入力して、コードフォーマッティングツールをインストールします。</li>
+<li><a href="https://docs.conda.io/en/latest/miniconda.html">Miniconda3</a> をダウンロードしてインストールします。Python 3.10 以降が必要です。</li>
+<li>VS Code の拡張機能マーケットプレイスで <code>python</code> を検索し、Python Extension Pack をインストールします。</li>
+<li>（任意）コマンドラインで <code>pip install black</code> を入力し、コード整形ツールをインストールします。</li>
 </ol>
-<h3 id="2-cc">2. &nbsp; C/C++環境<a class="headerlink" href="#2-cc" title="Permanent link">&para;</a></h3>
+<h3 id="2-cc">2. &nbsp; C/C++ 環境<a class="headerlink" href="#2-cc" title="Permanent link">&para;</a></h3>
 <ol>
-<li>Windowsシステムでは<a href="https://sourceforge.net/projects/mingw-w64/files/">MinGW</a>をインストールする必要があります（<a href="https://blog.csdn.net/qq_33698226/article/details/129031241">設定チュートリアル</a>）。MacOSにはClangが付属しているため、インストールは不要です。</li>
-<li>VS Code拡張機能マーケットプレイスで<code>c++</code>を検索し、C/C++ Extension Packをインストールします。</li>
-<li>（オプション）設定ページを開き、<code>Clang_format_fallback Style</code>コードフォーマッティングオプションを検索し、<code>{ BasedOnStyle: Microsoft, BreakBeforeBraces: Attach }</code>に設定します。</li>
+<li>Windows システムでは <a href="https://sourceforge.net/projects/mingw-w64/files/">MinGW</a> をインストールする必要があります（<a href="https://blog.csdn.net/qq_33698226/article/details/129031241">設定チュートリアル</a>）。MacOS には Clang が標準搭載されているため、追加インストールは不要です。</li>
+<li>VS Code の拡張機能マーケットプレイスで <code>c++</code> を検索し、C/C++ Extension Pack をインストールします。</li>
+<li>（任意）Settings ページを開き、コード整形オプション <code>Clang_format_fallback Style</code> を検索して、<code>{ BasedOnStyle: Microsoft, BreakBeforeBraces: Attach }</code> に設定します。</li>
 </ol>
-<h3 id="3-java">3. &nbsp; Java環境<a class="headerlink" href="#3-java" title="Permanent link">&para;</a></h3>
+<h3 id="3-java">3. &nbsp; Java 環境<a class="headerlink" href="#3-java" title="Permanent link">&para;</a></h3>
 <ol>
-<li><a href="https://jdk.java.net/18/">OpenJDK</a>をダウンロードしてインストールします（バージョンはJDK 9より新しい必要があります）。</li>
-<li>VS Code拡張機能マーケットプレイスで<code>java</code>を検索し、Extension Pack for Javaをインストールします。</li>
+<li><a href="https://jdk.java.net/18/">OpenJDK</a> をダウンロードしてインストールします（バージョンは JDK 9 より新しい必要があります）。</li>
+<li>VS Code の拡張機能マーケットプレイスで <code>java</code> を検索し、Extension Pack for Java をインストールします。</li>
 </ol>
-<h3 id="4-c">4. &nbsp; C#環境<a class="headerlink" href="#4-c" title="Permanent link">&para;</a></h3>
+<h3 id="4-c">4. &nbsp; C# 環境<a class="headerlink" href="#4-c" title="Permanent link">&para;</a></h3>
 <ol>
-<li><a href="https://dotnet.microsoft.com/en-us/download">.Net 8.0</a>をダウンロードしてインストールします。</li>
-<li>VS Code拡張機能マーケットプレイスで<code>C# Dev Kit</code>を検索し、C# Dev Kitをインストールします（<a href="https://code.visualstudio.com/docs/csharp/get-started">設定チュートリアル</a>）。</li>
-<li>Visual Studioを使用することもできます（<a href="https://learn.microsoft.com/zh-cn/visualstudio/install/install-visual-studio?view=vs-2022">インストールチュートリアル</a>）。</li>
+<li><a href="https://dotnet.microsoft.com/en-us/download">.Net 8.0</a> をダウンロードしてインストールします。</li>
+<li>VS Code の拡張機能マーケットプレイスで <code>C# Dev Kit</code> を検索し、C# Dev Kit をインストールします（<a href="https://code.visualstudio.com/docs/csharp/get-started">設定チュートリアル</a>）。</li>
+<li>Visual Studio を使用することもできます（<a href="https://learn.microsoft.com/zh-cn/visualstudio/install/install-visual-studio?view=vs-2022">インストール手順</a>）。</li>
 </ol>
-<h3 id="5-go">5. &nbsp; Go環境<a class="headerlink" href="#5-go" title="Permanent link">&para;</a></h3>
+<h3 id="5-go">5. &nbsp; Go 環境<a class="headerlink" href="#5-go" title="Permanent link">&para;</a></h3>
 <ol>
-<li><a href="https://go.dev/dl/">go</a>をダウンロードしてインストールします。</li>
-<li>VS Code拡張機能マーケットプレイスで<code>go</code>を検索し、Goをインストールします。</li>
-<li><code>Ctrl + Shift + P</code>を押してコマンドバーを呼び出し、goと入力し、<code>Go: Install/Update Tools</code>を選択し、すべてを選択してインストールします。</li>
+<li><a href="https://go.dev/dl/">go</a> をダウンロードしてインストールします。</li>
+<li>VS Code の拡張機能マーケットプレイスで <code>go</code> を検索し、Go をインストールします。</li>
+<li>ショートカットキー <code>Ctrl + Shift + P</code> を押してコマンドパレットを開き、go と入力して <code>Go: Install/Update Tools</code> を選択し、すべてにチェックを入れてインストールします。</li>
 </ol>
-<h3 id="6-swift">6. &nbsp; Swift環境<a class="headerlink" href="#6-swift" title="Permanent link">&para;</a></h3>
+<h3 id="6-swift">6. &nbsp; Swift 環境<a class="headerlink" href="#6-swift" title="Permanent link">&para;</a></h3>
 <ol>
-<li><a href="https://www.swift.org/download/">Swift</a>をダウンロードしてインストールします。</li>
-<li>VS Code拡張機能マーケットプレイスで<code>swift</code>を検索し、<a href="https://marketplace.visualstudio.com/items?itemName=sswg.swift-lang">Swift for Visual Studio Code</a>をインストールします。</li>
+<li><a href="https://www.swift.org/download/">Swift</a> をダウンロードしてインストールします。</li>
+<li>VS Code の拡張機能マーケットプレイスで <code>swift</code> を検索し、<a href="https://marketplace.visualstudio.com/items?itemName=sswg.swift-lang">Swift for Visual Studio Code</a> をインストールします。</li>
 </ol>
-<h3 id="7-javascript">7. &nbsp; JavaScript環境<a class="headerlink" href="#7-javascript" title="Permanent link">&para;</a></h3>
+<h3 id="7-javascript">7. &nbsp; JavaScript 環境<a class="headerlink" href="#7-javascript" title="Permanent link">&para;</a></h3>
 <ol>
-<li><a href="https://nodejs.org/en/">Node.js</a>をダウンロードしてインストールします。</li>
-<li>（オプション）VS Code拡張機能マーケットプレイスで<code>Prettier</code>を検索し、コードフォーマッティングツールをインストールします。</li>
+<li><a href="https://nodejs.org/en/">Node.js</a> をダウンロードしてインストールします。</li>
+<li>（任意）VS Code の拡張機能マーケットプレイスで <code>Prettier</code> を検索し、コード整形ツールをインストールします。</li>
 </ol>
-<h3 id="8-typescript">8. &nbsp; TypeScript環境<a class="headerlink" href="#8-typescript" title="Permanent link">&para;</a></h3>
+<h3 id="8-typescript">8. &nbsp; TypeScript 環境<a class="headerlink" href="#8-typescript" title="Permanent link">&para;</a></h3>
 <ol>
-<li>JavaScript環境と同じインストール手順に従います。</li>
-<li><a href="https://github.com/privatenumber/tsx?tab=readme-ov-file#global-installation">TypeScript Execute (tsx)</a>をインストールします。</li>
-<li>VS Code拡張機能マーケットプレイスで<code>typescript</code>を検索し、<a href="https://marketplace.visualstudio.com/items?itemName=yoavbls.pretty-ts-errors">Pretty TypeScript Errors</a>をインストールします。</li>
+<li>JavaScript 環境と同じ手順でインストールします。</li>
+<li><a href="https://github.com/privatenumber/tsx?tab=readme-ov-file#global-installation">TypeScript Execute (tsx)</a> をインストールします。</li>
+<li>VS Code の拡張機能マーケットプレイスで <code>typescript</code> を検索し、<a href="https://marketplace.visualstudio.com/items?itemName=yoavbls.pretty-ts-errors">Pretty TypeScript Errors</a> をインストールします。</li>
 </ol>
-<h3 id="9-dart">9. &nbsp; Dart環境<a class="headerlink" href="#9-dart" title="Permanent link">&para;</a></h3>
+<h3 id="9-dart">9. &nbsp; Dart 環境<a class="headerlink" href="#9-dart" title="Permanent link">&para;</a></h3>
 <ol>
-<li><a href="https://dart.dev/get-dart">Dart</a>をダウンロードしてインストールします。</li>
-<li>VS Code拡張機能マーケットプレイスで<code>dart</code>を検索し、<a href="https://marketplace.visualstudio.com/items?itemName=Dart-Code.dart-code">Dart</a>をインストールします。</li>
+<li><a href="https://dart.dev/get-dart">Dart</a> をダウンロードしてインストールします。</li>
+<li>VS Code の拡張機能マーケットプレイスで <code>dart</code> を検索し、<a href="https://marketplace.visualstudio.com/items?itemName=Dart-Code.dart-code">Dart</a> をインストールします。</li>
 </ol>
-<h3 id="10-rust">10. &nbsp; Rust環境<a class="headerlink" href="#10-rust" title="Permanent link">&para;</a></h3>
+<h3 id="10-rust">10. &nbsp; Rust 環境<a class="headerlink" href="#10-rust" title="Permanent link">&para;</a></h3>
 <ol>
-<li><a href="https://www.rust-lang.org/tools/install">Rust</a>をダウンロードしてインストールします。</li>
-<li>VS Code拡張機能マーケットプレイスで<code>rust</code>を検索し、<a href="https://marketplace.visualstudio.com/items?itemName=rust-lang.rust-analyzer">rust-analyzer</a>をインストールします。</li>
+<li><a href="https://www.rust-lang.org/tools/install">Rust</a> をダウンロードしてインストールします。</li>
+<li>VS Code の拡張機能マーケットプレイスで <code>rust</code> を検索し、<a href="https://marketplace.visualstudio.com/items?itemName=rust-lang.rust-analyzer">rust-analyzer</a> をインストールします。</li>
 </ol>
 
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     class="md-footer__link md-footer__link--next"
-    aria-label="次: 16.2 &amp;nbsp; 一緒に創作に参加する"
+    aria-label="次: 16.2 &amp;nbsp; 一緒に制作に参加しましょう"
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       </span>
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@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
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-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
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-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
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 <!-- Page content -->
 <h1 id="163">16.3 &nbsp; 用語集<a class="headerlink" href="#163" title="Permanent link">&para;</a></h1>
-<p>下の表は本書に登場する重要な用語をリストアップしており、以下の点に注意する価値があります。</p>
+<p>以下の表は、本書に登場する重要な用語を一覧にしたものです。特に次の点に注意してください。</p>
 <ul>
-<li>英語文献を読みやすくするため、用語の英語名を覚えることをお勧めします。</li>
-<li>一部の用語は簡体字中国語と繁体字中国語で異なる名前を持ちます。</li>
+<li>名詞の英語表現も覚えておくと、英語文献を読む際に役立ちます。</li>
+<li>一部の名詞は、簡体字中国語と繁体字中国語で呼び方が異なります。</li>
 </ul>
 <p align="center"> 表 16-1 &nbsp; データ構造とアルゴリズムの重要用語 </p>
 
@@ -4278,766 +4278,639 @@
 <tr>
 <th>English</th>
 <th>日本語</th>
-<th>简体中文</th>
-<th>繁体中文</th>
+<th>日本語</th>
 </tr>
 </thead>
 <tbody>
 <tr>
 <td>algorithm</td>
 <td>アルゴリズム</td>
-<td>算法</td>
-<td>演算法</td>
+<td>アルゴリズム</td>
 </tr>
 <tr>
 <td>data structure</td>
 <td>データ構造</td>
-<td>数据结构</td>
-<td>資料結構</td>
+<td>データ構造</td>
 </tr>
 <tr>
 <td>code</td>
 <td>コード</td>
-<td>代码</td>
-<td>程式碼</td>
+<td>コード</td>
 </tr>
 <tr>
 <td>file</td>
 <td>ファイル</td>
-<td>文件</td>
-<td>檔案</td>
+<td>ファイル</td>
 </tr>
 <tr>
 <td>function</td>
 <td>関数</td>
-<td>函数</td>
-<td>函式</td>
+<td>関数</td>
 </tr>
 <tr>
 <td>method</td>
 <td>メソッド</td>
-<td>方法</td>
-<td>方法</td>
+<td>メソッド</td>
 </tr>
 <tr>
 <td>variable</td>
 <td>変数</td>
-<td>变量</td>
-<td>變數</td>
+<td>変数</td>
 </tr>
 <tr>
 <td>asymptotic complexity analysis</td>
 <td>漸近計算量解析</td>
-<td>渐近复杂度分析</td>
-<td>漸近複雜度分析</td>
+<td>漸近計算量解析</td>
 </tr>
 <tr>
 <td>time complexity</td>
 <td>時間計算量</td>
-<td>时间复杂度</td>
-<td>時間複雜度</td>
+<td>時間計算量</td>
 </tr>
 <tr>
 <td>space complexity</td>
 <td>空間計算量</td>
-<td>空间复杂度</td>
-<td>空間複雜度</td>
+<td>空間計算量</td>
 </tr>
 <tr>
 <td>loop</td>
 <td>ループ</td>
-<td>循环</td>
-<td>迴圈</td>
+<td>ループ</td>
 </tr>
 <tr>
 <td>iteration</td>
 <td>反復</td>
-<td>迭代</td>
-<td>迭代</td>
+<td>反復</td>
 </tr>
 <tr>
 <td>recursion</td>
 <td>再帰</td>
-<td>递归</td>
-<td>遞迴</td>
+<td>再帰</td>
 </tr>
 <tr>
 <td>tail recursion</td>
 <td>末尾再帰</td>
-<td>尾递归</td>
-<td>尾遞迴</td>
+<td>末尾再帰</td>
 </tr>
 <tr>
 <td>recursion tree</td>
 <td>再帰木</td>
-<td>递归树</td>
-<td>遞迴樹</td>
+<td>再帰木</td>
 </tr>
 <tr>
 <td>big-<span class="arithmatex">\(O\)</span> notation</td>
-<td>ビッグO記法</td>
-<td>大 <span class="arithmatex">\(O\)</span> 记号</td>
-<td>大 <span class="arithmatex">\(O\)</span> 記號</td>
+<td>ビッグオー記法</td>
+<td>ビッグオー記法</td>
 </tr>
 <tr>
 <td>asymptotic upper bound</td>
 <td>漸近上界</td>
-<td>渐近上界</td>
 <td>漸近上界</td>
 </tr>
 <tr>
 <td>sign-magnitude</td>
-<td>符号と絶対値</td>
-<td>原码</td>
-<td>原碼</td>
+<td>符号絶対値表現</td>
+<td>符号絶対値表現</td>
 </tr>
 <tr>
-<td>1's complement</td>
+<td>1’s complement</td>
+<td>1の補数</td>
 <td>1の補数</td>
-<td>反码</td>
-<td>一補數</td>
 </tr>
 <tr>
-<td>2's complement</td>
+<td>2’s complement</td>
+<td>2の補数</td>
 <td>2の補数</td>
-<td>补码</td>
-<td>二補數</td>
 </tr>
 <tr>
 <td>array</td>
 <td>配列</td>
-<td>数组</td>
-<td>陣列</td>
+<td>配列</td>
 </tr>
 <tr>
 <td>index</td>
 <td>インデックス</td>
-<td>索引</td>
-<td>索引</td>
+<td>インデックス</td>
 </tr>
 <tr>
 <td>linked list</td>
 <td>連結リスト</td>
-<td>链表</td>
-<td>鏈結串列</td>
+<td>連結リスト</td>
 </tr>
 <tr>
 <td>linked list node, list node</td>
 <td>連結リストノード</td>
-<td>链表节点</td>
-<td>鏈結串列節點</td>
+<td>連結リストノード</td>
 </tr>
 <tr>
 <td>head node</td>
 <td>先頭ノード</td>
-<td>头节点</td>
-<td>頭節點</td>
+<td>先頭ノード</td>
 </tr>
 <tr>
 <td>tail node</td>
 <td>末尾ノード</td>
-<td>尾节点</td>
-<td>尾節點</td>
+<td>末尾ノード</td>
 </tr>
 <tr>
 <td>list</td>
 <td>リスト</td>
-<td>列表</td>
-<td>串列</td>
+<td>リスト</td>
 </tr>
 <tr>
 <td>dynamic array</td>
 <td>動的配列</td>
-<td>动态数组</td>
-<td>動態陣列</td>
+<td>動的配列</td>
 </tr>
 <tr>
 <td>hard disk</td>
 <td>ハードディスク</td>
-<td>硬盘</td>
-<td>硬碟</td>
+<td>ハードディスク</td>
 </tr>
 <tr>
 <td>random-access memory (RAM)</td>
 <td>メモリ</td>
-<td>内存</td>
-<td>記憶體</td>
+<td>メモリ</td>
 </tr>
 <tr>
 <td>cache memory</td>
-<td>キャッシュメモリ</td>
-<td>缓存</td>
-<td>快取</td>
+<td>キャッシュ</td>
+<td>キャッシュ</td>
 </tr>
 <tr>
 <td>cache miss</td>
 <td>キャッシュミス</td>
-<td>缓存未命中</td>
-<td>快取未命中</td>
+<td>キャッシュミス</td>
 </tr>
 <tr>
 <td>cache hit rate</td>
 <td>キャッシュヒット率</td>
-<td>缓存命中率</td>
-<td>快取命中率</td>
+<td>キャッシュヒット率</td>
 </tr>
 <tr>
 <td>stack</td>
 <td>スタック</td>
-<td>栈</td>
-<td>堆疊</td>
+<td>スタック</td>
 </tr>
 <tr>
 <td>top of the stack</td>
 <td>スタックトップ</td>
-<td>栈顶</td>
-<td>堆疊頂</td>
+<td>スタックトップ</td>
 </tr>
 <tr>
 <td>bottom of the stack</td>
 <td>スタックボトム</td>
-<td>栈底</td>
-<td>堆疊底</td>
+<td>スタックボトム</td>
 </tr>
 <tr>
 <td>queue</td>
 <td>キュー</td>
-<td>队列</td>
-<td>佇列</td>
+<td>キュー</td>
 </tr>
 <tr>
 <td>double-ended queue</td>
 <td>両端キュー</td>
-<td>双向队列</td>
-<td>雙向佇列</td>
+<td>両端キュー</td>
 </tr>
 <tr>
 <td>front of the queue</td>
-<td>キューの先頭</td>
-<td>队首</td>
-<td>佇列首</td>
+<td>キュー先頭</td>
+<td>キュー先頭</td>
 </tr>
 <tr>
 <td>rear of the queue</td>
-<td>キューの末尾</td>
-<td>队尾</td>
-<td>佇列尾</td>
+<td>キュー末尾</td>
+<td>キュー末尾</td>
 </tr>
 <tr>
 <td>hash table</td>
 <td>ハッシュテーブル</td>
-<td>哈希表</td>
-<td>雜湊表</td>
+<td>ハッシュテーブル</td>
 </tr>
 <tr>
 <td>hash set</td>
-<td>ハッシュセット</td>
-<td>哈希集合</td>
-<td>雜湊集合</td>
+<td>ハッシュ集合</td>
+<td>ハッシュ集合</td>
 </tr>
 <tr>
 <td>bucket</td>
 <td>バケット</td>
-<td>桶</td>
-<td>桶</td>
+<td>バケット</td>
 </tr>
 <tr>
 <td>hash function</td>
 <td>ハッシュ関数</td>
-<td>哈希函数</td>
-<td>雜湊函式</td>
+<td>ハッシュ関数</td>
 </tr>
 <tr>
 <td>hash collision</td>
 <td>ハッシュ衝突</td>
-<td>哈希冲突</td>
-<td>雜湊衝突</td>
+<td>ハッシュ衝突</td>
 </tr>
 <tr>
 <td>load factor</td>
 <td>負荷率</td>
-<td>负载因子</td>
-<td>負載因子</td>
+<td>負荷率</td>
 </tr>
 <tr>
 <td>separate chaining</td>
-<td>チェイン法</td>
-<td>链式地址</td>
-<td>鏈結位址</td>
+<td>連鎖アドレス法</td>
+<td>連鎖アドレス法</td>
 </tr>
 <tr>
 <td>open addressing</td>
 <td>オープンアドレス法</td>
-<td>开放寻址</td>
-<td>開放定址</td>
+<td>オープンアドレス法</td>
 </tr>
 <tr>
 <td>linear probing</td>
-<td>線形プローブ法</td>
-<td>线性探测</td>
-<td>線性探查</td>
+<td>線形探索</td>
+<td>線形探索</td>
 </tr>
 <tr>
 <td>lazy deletion</td>
 <td>遅延削除</td>
-<td>懒删除</td>
-<td>懶刪除</td>
+<td>遅延削除</td>
 </tr>
 <tr>
 <td>binary tree</td>
 <td>二分木</td>
-<td>二叉树</td>
-<td>二元樹</td>
+<td>二分木</td>
 </tr>
 <tr>
 <td>tree node</td>
-<td>木のノード</td>
-<td>树节点</td>
-<td>樹節點</td>
+<td>ノード</td>
+<td>ノード</td>
 </tr>
 <tr>
 <td>left-child node</td>
-<td>左の子ノード</td>
-<td>左子节点</td>
-<td>左子節點</td>
+<td>左子ノード</td>
+<td>左子ノード</td>
 </tr>
 <tr>
 <td>right-child node</td>
-<td>右の子ノード</td>
-<td>右子节点</td>
-<td>右子節點</td>
+<td>右子ノード</td>
+<td>右子ノード</td>
 </tr>
 <tr>
 <td>parent node</td>
 <td>親ノード</td>
-<td>父节点</td>
-<td>父節點</td>
+<td>親ノード</td>
 </tr>
 <tr>
 <td>left subtree</td>
-<td>左の部分木</td>
-<td>左子树</td>
-<td>左子樹</td>
+<td>左部分木</td>
+<td>左部分木</td>
 </tr>
 <tr>
 <td>right subtree</td>
-<td>右の部分木</td>
-<td>右子树</td>
-<td>右子樹</td>
+<td>右部分木</td>
+<td>右部分木</td>
 </tr>
 <tr>
 <td>root node</td>
-<td>ルートノード</td>
-<td>根节点</td>
-<td>根節點</td>
+<td>根ノード</td>
+<td>根ノード</td>
 </tr>
 <tr>
 <td>leaf node</td>
 <td>葉ノード</td>
-<td>叶节点</td>
-<td>葉節點</td>
+<td>葉ノード</td>
 </tr>
 <tr>
 <td>edge</td>
-<td>エッジ</td>
-<td>边</td>
-<td>邊</td>
+<td>辺</td>
+<td>辺</td>
 </tr>
 <tr>
 <td>level</td>
 <td>レベル</td>
-<td>层</td>
-<td>層</td>
+<td>レベル</td>
 </tr>
 <tr>
 <td>degree</td>
 <td>次数</td>
-<td>度</td>
-<td>度</td>
+<td>次数</td>
 </tr>
 <tr>
 <td>height</td>
 <td>高さ</td>
-<td>高度</td>
-<td>高度</td>
+<td>高さ</td>
 </tr>
 <tr>
 <td>depth</td>
 <td>深さ</td>
-<td>深度</td>
-<td>深度</td>
+<td>深さ</td>
 </tr>
 <tr>
 <td>perfect binary tree</td>
-<td>完全二分木</td>
-<td>完美二叉树</td>
-<td>完美二元樹</td>
+<td>完備二分木</td>
+<td>完備二分木</td>
 </tr>
 <tr>
 <td>complete binary tree</td>
 <td>完全二分木</td>
-<td>完全二叉树</td>
-<td>完全二元樹</td>
+<td>完全二分木</td>
 </tr>
 <tr>
 <td>full binary tree</td>
 <td>満二分木</td>
-<td>完满二叉树</td>
-<td>完滿二元樹</td>
+<td>満二分木</td>
 </tr>
 <tr>
 <td>balanced binary tree</td>
 <td>平衡二分木</td>
-<td>平衡二叉树</td>
-<td>平衡二元樹</td>
+<td>平衡二分木</td>
 </tr>
 <tr>
 <td>binary search tree</td>
 <td>二分探索木</td>
-<td>二叉搜索树</td>
-<td>二元搜尋樹</td>
+<td>二分探索木</td>
 </tr>
 <tr>
 <td>AVL tree</td>
-<td>AVL木</td>
-<td>AVL 树</td>
-<td>AVL 樹</td>
+<td>AVL 木</td>
+<td>AVL 木</td>
 </tr>
 <tr>
 <td>red-black tree</td>
 <td>赤黒木</td>
-<td>红黑树</td>
-<td>紅黑樹</td>
+<td>赤黒木</td>
 </tr>
 <tr>
 <td>level-order traversal</td>
 <td>レベル順走査</td>
-<td>层序遍历</td>
-<td>層序走訪</td>
+<td>レベル順走査</td>
 </tr>
 <tr>
 <td>breadth-first traversal</td>
 <td>幅優先走査</td>
-<td>广度优先遍历</td>
-<td>廣度優先走訪</td>
+<td>幅優先走査</td>
 </tr>
 <tr>
 <td>depth-first traversal</td>
 <td>深さ優先走査</td>
-<td>深度优先遍历</td>
-<td>深度優先走訪</td>
+<td>深さ優先走査</td>
 </tr>
 <tr>
 <td>binary search tree</td>
 <td>二分探索木</td>
-<td>二叉搜索树</td>
-<td>二元搜尋樹</td>
+<td>二分探索木</td>
 </tr>
 <tr>
 <td>balanced binary search tree</td>
 <td>平衡二分探索木</td>
-<td>平衡二叉搜索树</td>
-<td>平衡二元搜尋樹</td>
+<td>平衡二分探索木</td>
 </tr>
 <tr>
 <td>balance factor</td>
-<td>平衡因子</td>
-<td>平衡因子</td>
-<td>平衡因子</td>
+<td>平衡係数</td>
+<td>平衡係数</td>
 </tr>
 <tr>
 <td>heap</td>
 <td>ヒープ</td>
-<td>堆</td>
-<td>堆積</td>
+<td>ヒープ</td>
 </tr>
 <tr>
 <td>max heap</td>
 <td>最大ヒープ</td>
-<td>大顶堆</td>
-<td>大頂堆積</td>
+<td>最大ヒープ</td>
 </tr>
 <tr>
 <td>min heap</td>
 <td>最小ヒープ</td>
-<td>小顶堆</td>
-<td>小頂堆積</td>
+<td>最小ヒープ</td>
 </tr>
 <tr>
 <td>priority queue</td>
-<td>優先度キュー</td>
-<td>优先队列</td>
-<td>優先佇列</td>
+<td>優先度付きキュー</td>
+<td>優先度付きキュー</td>
 </tr>
 <tr>
 <td>heapify</td>
 <td>ヒープ化</td>
-<td>堆化</td>
-<td>堆積化</td>
+<td>ヒープ化</td>
 </tr>
 <tr>
 <td>top-<span class="arithmatex">\(k\)</span> problem</td>
 <td>Top-<span class="arithmatex">\(k\)</span> 問題</td>
-<td>Top-<span class="arithmatex">\(k\)</span> 问题</td>
 <td>Top-<span class="arithmatex">\(k\)</span> 問題</td>
 </tr>
 <tr>
 <td>graph</td>
 <td>グラフ</td>
-<td>图</td>
-<td>圖</td>
+<td>グラフ</td>
 </tr>
 <tr>
 <td>vertex</td>
 <td>頂点</td>
-<td>顶点</td>
-<td>頂點</td>
+<td>頂点</td>
 </tr>
 <tr>
 <td>undirected graph</td>
 <td>無向グラフ</td>
-<td>无向图</td>
-<td>無向圖</td>
+<td>無向グラフ</td>
 </tr>
 <tr>
 <td>directed graph</td>
 <td>有向グラフ</td>
-<td>有向图</td>
-<td>有向圖</td>
+<td>有向グラフ</td>
 </tr>
 <tr>
 <td>connected graph</td>
 <td>連結グラフ</td>
-<td>连通图</td>
-<td>連通圖</td>
+<td>連結グラフ</td>
 </tr>
 <tr>
 <td>disconnected graph</td>
 <td>非連結グラフ</td>
-<td>非连通图</td>
-<td>非連通圖</td>
+<td>非連結グラフ</td>
 </tr>
 <tr>
 <td>weighted graph</td>
 <td>重み付きグラフ</td>
-<td>有权图</td>
-<td>有權圖</td>
+<td>重み付きグラフ</td>
 </tr>
 <tr>
 <td>adjacency</td>
 <td>隣接</td>
-<td>邻接</td>
-<td>鄰接</td>
+<td>隣接</td>
 </tr>
 <tr>
 <td>path</td>
-<td>パス</td>
-<td>路径</td>
-<td>路徑</td>
+<td>経路</td>
+<td>経路</td>
 </tr>
 <tr>
 <td>in-degree</td>
 <td>入次数</td>
-<td>入度</td>
-<td>入度</td>
+<td>入次数</td>
 </tr>
 <tr>
 <td>out-degree</td>
 <td>出次数</td>
-<td>出度</td>
-<td>出度</td>
+<td>出次数</td>
 </tr>
 <tr>
 <td>adjacency matrix</td>
 <td>隣接行列</td>
-<td>邻接矩阵</td>
-<td>鄰接矩陣</td>
+<td>隣接行列</td>
 </tr>
 <tr>
 <td>adjacency list</td>
 <td>隣接リスト</td>
-<td>邻接表</td>
-<td>鄰接表</td>
+<td>隣接リスト</td>
 </tr>
 <tr>
 <td>breadth-first search</td>
 <td>幅優先探索</td>
-<td>广度优先搜索</td>
-<td>廣度優先搜尋</td>
+<td>幅優先探索</td>
 </tr>
 <tr>
 <td>depth-first search</td>
 <td>深さ優先探索</td>
-<td>深度优先搜索</td>
-<td>深度優先搜尋</td>
+<td>深さ優先探索</td>
 </tr>
 <tr>
 <td>binary search</td>
 <td>二分探索</td>
-<td>二分查找</td>
-<td>二分搜尋</td>
+<td>二分探索</td>
 </tr>
 <tr>
 <td>searching algorithm</td>
 <td>探索アルゴリズム</td>
-<td>搜索算法</td>
-<td>搜尋演算法</td>
+<td>探索アルゴリズム</td>
 </tr>
 <tr>
 <td>sorting algorithm</td>
 <td>ソートアルゴリズム</td>
-<td>排序算法</td>
-<td>排序演算法</td>
+<td>ソートアルゴリズム</td>
 </tr>
 <tr>
 <td>selection sort</td>
 <td>選択ソート</td>
-<td>选择排序</td>
-<td>選擇排序</td>
+<td>選択ソート</td>
 </tr>
 <tr>
 <td>bubble sort</td>
 <td>バブルソート</td>
-<td>冒泡排序</td>
-<td>泡沫排序</td>
+<td>バブルソート</td>
 </tr>
 <tr>
 <td>insertion sort</td>
 <td>挿入ソート</td>
-<td>插入排序</td>
-<td>插入排序</td>
+<td>挿入ソート</td>
 </tr>
 <tr>
 <td>quick sort</td>
 <td>クイックソート</td>
-<td>快速排序</td>
-<td>快速排序</td>
+<td>クイックソート</td>
 </tr>
 <tr>
 <td>merge sort</td>
 <td>マージソート</td>
-<td>归并排序</td>
-<td>合併排序</td>
+<td>マージソート</td>
 </tr>
 <tr>
 <td>heap sort</td>
 <td>ヒープソート</td>
-<td>堆排序</td>
-<td>堆積排序</td>
+<td>ヒープソート</td>
 </tr>
 <tr>
 <td>bucket sort</td>
 <td>バケットソート</td>
-<td>桶排序</td>
-<td>桶排序</td>
+<td>バケットソート</td>
 </tr>
 <tr>
 <td>counting sort</td>
 <td>計数ソート</td>
-<td>计数排序</td>
-<td>計數排序</td>
+<td>計数ソート</td>
 </tr>
 <tr>
 <td>radix sort</td>
 <td>基数ソート</td>
-<td>基数排序</td>
-<td>基數排序</td>
+<td>基数ソート</td>
 </tr>
 <tr>
 <td>divide and conquer</td>
-<td>分割統治法</td>
-<td>分治</td>
-<td>分治</td>
+<td>分割統治</td>
+<td>分割統治</td>
 </tr>
 <tr>
 <td>hanota problem</td>
 <td>ハノイの塔問題</td>
-<td>汉诺塔问题</td>
-<td>河內塔問題</td>
+<td>ハノイの塔問題</td>
 </tr>
 <tr>
 <td>backtracking algorithm</td>
-<td>バックトラッキング</td>
-<td>回溯算法</td>
-<td>回溯演算法</td>
+<td>バックトラッキングアルゴリズム</td>
+<td>バックトラッキングアルゴリズム</td>
 </tr>
 <tr>
 <td>constraint</td>
 <td>制約</td>
-<td>约束</td>
-<td>約束</td>
+<td>制約</td>
 </tr>
 <tr>
 <td>solution</td>
 <td>解</td>
 <td>解</td>
-<td>解</td>
 </tr>
 <tr>
 <td>state</td>
 <td>状態</td>
-<td>状态</td>
-<td>狀態</td>
+<td>状態</td>
 </tr>
 <tr>
 <td>pruning</td>
 <td>枝刈り</td>
-<td>剪枝</td>
-<td>剪枝</td>
+<td>枝刈り</td>
 </tr>
 <tr>
 <td>permutations problem</td>
-<td>順列問題</td>
-<td>全排列问题</td>
-<td>全排列問題</td>
+<td>全順列問題</td>
+<td>全順列問題</td>
 </tr>
 <tr>
 <td>subset-sum problem</td>
-<td>部分集合和問題</td>
-<td>子集和问题</td>
-<td>子集合問題</td>
+<td>部分和問題</td>
+<td>部分和問題</td>
 </tr>
 <tr>
 <td><span class="arithmatex">\(n\)</span>-queens problem</td>
 <td><span class="arithmatex">\(n\)</span> クイーン問題</td>
-<td><span class="arithmatex">\(n\)</span> 皇后问题</td>
-<td><span class="arithmatex">\(n\)</span> 皇后問題</td>
+<td><span class="arithmatex">\(n\)</span> クイーン問題</td>
 </tr>
 <tr>
 <td>dynamic programming</td>
-<td>動的プログラミング</td>
-<td>动态规划</td>
-<td>動態規劃</td>
+<td>動的計画法</td>
+<td>動的計画法</td>
 </tr>
 <tr>
 <td>initial state</td>
 <td>初期状態</td>
-<td>初始状态</td>
-<td>初始狀態</td>
+<td>初期状態</td>
 </tr>
 <tr>
 <td>state-transition equation</td>
 <td>状態遷移方程式</td>
-<td>状态转移方程</td>
-<td>狀態轉移方程</td>
+<td>状態遷移方程式</td>
 </tr>
 <tr>
 <td>knapsack problem</td>
 <td>ナップサック問題</td>
-<td>背包问题</td>
-<td>背包問題</td>
+<td>ナップサック問題</td>
 </tr>
 <tr>
 <td>edit distance problem</td>
 <td>編集距離問題</td>
-<td>编辑距离问题</td>
-<td>編輯距離問題</td>
+<td>編集距離問題</td>
 </tr>
 <tr>
 <td>greedy algorithm</td>
-<td>貪欲アルゴリズム</td>
-<td>贪心算法</td>
-<td>貪婪演算法</td>
+<td>貪欲法</td>
+<td>貪欲法</td>
 </tr>
 </tbody>
 </table>
@@ -5064,7 +4937,7 @@ aria-label="フッター"
   <a
     href="../contribution/"
     class="md-footer__link md-footer__link--prev"
-    aria-label="前: 16.2 &amp;nbsp; 一緒に創作に参加する"
+    aria-label="前: 16.2 &amp;nbsp; 一緒に制作に参加しましょう"
     rel="prev"
   >
     <div class="md-footer__button md-icon">
@@ -5076,7 +4949,7 @@ aria-label="フッター"
         前
       </span>
       <div class="md-ellipsis">
-        16.2 &nbsp; 一緒に創作に参加する
+        16.2 &nbsp; 一緒に制作に参加しましょう
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     </div>
   </a>
diff --git a/ja/chapter_array_and_linkedlist/array/index.html b/ja/chapter_array_and_linkedlist/array/index.html
index f904e73e0..a3e1d1187 100644
--- a/ja/chapter_array_and_linkedlist/array/index.html
+++ b/ja/chapter_array_and_linkedlist/array/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
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-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
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-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
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-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
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-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
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   <a href="#412" class="md-nav__link">
     <span class="md-ellipsis">
       
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   <a href="#412" class="md-nav__link">
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+        4.1.2 &nbsp; 配列の利点と限界
       
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@@ -4543,626 +4543,1190 @@
 
 <!-- Page content -->
 <h1 id="41">4.1 &nbsp; 配列<a class="headerlink" href="#41" title="Permanent link">&para;</a></h1>
-<p><u>配列</u>は線形データ構造で、同じような項目が並んでいるようなもので、コンピュータのメモリ内の連続した空間に一緒に格納されます。これは整理された格納を維持するシーケンスのようなものです。この並びの各項目には、<u>インデックス</u>として知られる独自の「位置」があります。以下の図を参照して、配列の動作を観察し、これらの重要な用語を理解してください。</p>
-<p><img alt="配列の定義と格納方法" class="animation-figure" src="../array.assets/array_definition.png" /></p>
-<p align="center"> 図 4-1 &nbsp; 配列の定義と格納方法 </p>
+<p><u>配列（array）</u>は線形データ構造の一種であり、同じ型の要素を連続したメモリ領域に格納します。要素が配列内にある位置を、その要素の<u>インデックス（index）</u>と呼びます。下図は、配列の主要な概念と格納方式を示しています。</p>
+<p><img alt="配列の定義と格納方式" class="animation-figure" src="../array.assets/array_definition.png" /></p>
+<p align="center"> 図 4-1 &nbsp; 配列の定義と格納方式 </p>
 
 <h2 id="411">4.1.1 &nbsp; 配列の一般的な操作<a class="headerlink" href="#411" title="Permanent link">&para;</a></h2>
 <h3 id="1">1. &nbsp; 配列の初期化<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>配列は必要に応じて2つの方法で初期化できます：初期値なしまたは指定された初期値付きです。初期値が指定されていない場合、ほとんどのプログラミング言語は配列要素を<span class="arithmatex">\(0\)</span>に設定します：</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="1:12"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label></div>
+<p>必要に応じて、配列の初期化方法として初期値なしと初期値ありの 2 種類を使い分けられます。初期値を指定しない場合、多くのプログラミング言語では配列要素は <span class="arithmatex">\(0\)</span> に初期化されます。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 配列を初期化</span>
+<div class="highlight"><span class="filename">array.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 配列を初期化する</span>
 <a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="n">arr</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">5</span>  <span class="c1"># [ 0, 0, 0, 0, 0 ]</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">4</span><span class="p">]</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 配列を初期化 */</span>
-<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// スタックに格納</span>
+<div class="highlight"><span class="filename">array.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 配列を初期化する */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// スタック上に格納</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="kt">int</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="w"> </span><span class="p">};</span>
-<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="c1">// ヒープに格納（手動でのメモリ解放が必要）</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="c1">// ヒープ上に格納（手動で領域を解放する必要がある）</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="kt">int</span><span class="o">*</span><span class="w"> </span><span class="n">arr1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="kt">int</span><span class="o">*</span><span class="w"> </span><span class="n">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="w"> </span><span class="p">};</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 配列を初期化 */</span>
+<div class="highlight"><span class="filename">array.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 配列を初期化する */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="mi">5</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="c1">// { 0, 0, 0, 0, 0 }</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="w"> </span><span class="p">};</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 配列を初期化 */</span>
+<div class="highlight"><span class="filename">array.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 配列を初期化する */</span>
 <a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span><span class="w"> </span><span class="c1">// [ 0, 0, 0, 0, 0 ]</span>
 <a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">];</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 配列を初期化 */</span>
+<div class="highlight"><span class="filename">array.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 配列を初期化する */</span>
 <a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">var</span><span class="w"> </span><span class="nx">arr</span><span class="w"> </span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="kt">int</span>
-<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="c1">// Goでは、長さを指定（[5]int）すると配列を示し、指定しない（[]int）とスライスを示します。</span>
-<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="c1">// Goの配列はコンパイル時に固定長を持つよう設計されているため、長さの指定には定数のみ使用できます。</span>
-<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="c1">// extend()メソッドの実装の便宜上、ここではSliceを配列として扱います。</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="c1">// Go では、長さを指定する場合（[5]int）は配列であり、長さを指定しない場合（[]int）はスライス</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="c1">// Go の配列はコンパイル時に長さが確定するよう設計されているため、長さの指定には定数しか使用できない</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="c1">// 拡張 extend() メソッドを実装しやすくするため、以下ではスライス（Slice）を配列（Array）として扱う</span>
 <a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="nx">nums</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 配列を初期化 */</span>
+<div class="highlight"><span class="filename">array.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 配列を初期化する */</span>
 <a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">let</span><span class="w"> </span><span class="nv">arr</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span><span class="w"> </span><span class="c1">// [0, 0, 0, 0, 0]</span>
 <a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">let</span><span class="w"> </span><span class="nv">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">]</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 配列を初期化 */</span>
+<div class="highlight"><span class="filename">array.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 配列を初期化する */</span>
 <a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">var</span><span class="w"> </span><span class="nx">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mf">5</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
 <a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="kd">var</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span><span class="w"> </span><span class="mf">5</span><span class="p">,</span><span class="w"> </span><span class="mf">4</span><span class="p">];</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 配列を初期化 */</span>
+<div class="highlight"><span class="filename">array.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 配列を初期化する */</span>
 <a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">let</span><span class="w"> </span><span class="nx">arr</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mf">5</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
 <a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="kd">let</span><span class="w"> </span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span><span class="w"> </span><span class="mf">5</span><span class="p">,</span><span class="w"> </span><span class="mf">4</span><span class="p">];</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 配列を初期化 */</span>
+<div class="highlight"><span class="filename">array.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 配列を初期化する */</span>
 <a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// [0, 0, 0, 0, 0]</span>
 <a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">];</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 配列を初期化 */</span>
+<div class="highlight"><span class="filename">array.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 配列を初期化する */</span>
 <a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="kd">let</span><span class="w"> </span><span class="n">arr</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">;</span><span class="w"> </span><span class="mi">5</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="mi">5</span><span class="p">];</span><span class="w"> </span><span class="c1">// [0, 0, 0, 0, 0]</span>
 <a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="kd">let</span><span class="w"> </span><span class="n">slice</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">&amp;</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="mi">5</span><span class="p">];</span>
-<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="c1">// Rustでは、長さを指定（[i32; 5]）すると配列を示し、指定しない（&amp;[i32]）とスライスを示します。</span>
-<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="c1">// Rustの配列はコンパイル時に固定長を持つよう設計されているため、長さの指定には定数のみ使用できます。</span>
-<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="c1">// 一般的にRustでは動的配列としてVectorが使用されます。</span>
-<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="c1">// extend()メソッドの実装の便宜上、ここではベクターを配列として扱います。</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="c1">// Rust では、長さを指定する場合（[i32; 5]）は配列であり、長さを指定しない場合（&amp;[i32]）はスライス</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="c1">// Rust の配列はコンパイル時に長さが確定するよう設計されているため、長さの指定には定数しか使用できない</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="c1">// Vector は Rust で一般に動的配列として使われる型</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="c1">// 拡張 extend() メソッドを実装しやすくするため、以下では vector を配列（array）として扱う</span>
 <a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="kd">let</span><span class="w"> </span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">];</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 配列を初期化 */</span>
+<div class="highlight"><span class="filename">array.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 配列を初期化する */</span>
 <a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">};</span><span class="w"> </span><span class="c1">// { 0, 0, 0, 0, 0 }</span>
 <a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="w"> </span><span class="p">};</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
+<div class="highlight"><span class="filename">array.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 配列を初期化する */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">var</span><span class="w"> </span><span class="nv">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="m">5</span><span class="p">)</span><span class="w"> </span><span class="c1">// { 0, 0, 0, 0, 0 }</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="kd">var</span><span class="w"> </span><span class="nv">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">intArrayOf</span><span class="p">(</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1"># 配列を初期化する</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="o">]</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>実行の可視化</summary>
+<p>https://pythontutor.com/render.html#code=%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E6%95%B0%E7%BB%84%0Aarr%20%3D%20%5B0%5D%20*%205%20%20%23%20%5B%200,%200,%200,%200,%200%20%5D%0Anums%20%3D%20%5B1,%203,%202,%205,%204%5D&amp;cumulative=false&amp;curInstr=0&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>
+</details>
 <h3 id="2">2. &nbsp; 要素へのアクセス<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>配列内の要素は連続したメモリ空間に格納されるため、各要素のメモリアドレスを計算することが簡単になります。以下の図に示されている公式は、配列のメモリアドレス（特に、最初の要素のアドレス）と要素のインデックスを利用して、要素のメモリアドレスを決定するのに役立ちます。この計算により、目的の要素への直接アクセスが合理化されます。</p>
-<p><img alt="配列要素のメモリアドレス計算" class="animation-figure" src="../array.assets/array_memory_location_calculation.png" /></p>
-<p align="center"> 図 4-2 &nbsp; 配列要素のメモリアドレス計算 </p>
+<p>配列要素は連続したメモリ領域に格納されるため、要素のメモリアドレスの計算は非常に容易です。配列のメモリアドレス（先頭要素のメモリアドレス）とある要素のインデックスが与えられれば、下図の式を使ってその要素のメモリアドレスを計算でき、直接その要素にアクセスできます。</p>
+<p><img alt="配列要素のメモリアドレスの計算" class="animation-figure" src="../array.assets/array_memory_location_calculation.png" /></p>
+<p align="center"> 図 4-2 &nbsp; 配列要素のメモリアドレスの計算 </p>
 
-<p>上の図で観察されるように、配列のインデックスは慣例的に<span class="arithmatex">\(0\)</span>から始まります。これは直感に反するように見えるかもしれません。数を数えるのは通常<span class="arithmatex">\(1\)</span>から始まるためですが、アドレス計算公式内では、**インデックスは本質的にメモリアドレスからのオフセット**です。最初の要素のアドレスでは、このオフセットは<span class="arithmatex">\(0\)</span>で、そのインデックスが<span class="arithmatex">\(0\)</span>であることを検証しています。</p>
-<p>配列内の要素へのアクセスは非常に効率的で、<span class="arithmatex">\(O(1)\)</span>時間で任意の要素にランダムアクセスできます。</p>
+<p>上図を見ると、配列の最初の要素のインデックスは <span class="arithmatex">\(0\)</span> であり、これは少し直感に反するように思えます。というのも、<span class="arithmatex">\(1\)</span> から数え始めるほうが自然だからです。しかし、アドレス計算式の観点では、**インデックスの本質はメモリアドレスのオフセット**です。先頭要素のアドレスのオフセットは <span class="arithmatex">\(0\)</span> であるため、そのインデックスが <span class="arithmatex">\(0\)</span> なのは妥当です。</p>
+<p>配列では要素へのアクセスは非常に効率的であり、<span class="arithmatex">\(O(1)\)</span> 時間で任意の要素にランダムアクセスできます。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.py</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">random_access</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;要素へのランダムアクセス&quot;&quot;&quot;</span>
-<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a>    <span class="c1"># 区間 [0, len(nums)-1] から数値をランダムに選択</span>
-<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>    <span class="n">random_index</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a>    <span class="c1"># ランダムな要素を取得して返す</span>
-<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a>    <span class="n">random_num</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">random_index</span><span class="p">]</span>
-<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a>    <span class="k">return</span> <span class="n">random_num</span>
+<div class="highlight"><span class="filename">array.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">random_access</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;要素へランダムアクセス&quot;&quot;&quot;</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="c1"># 区間 [0, len(nums)-1] からランダムに数字を 1 つ選ぶ</span>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="n">random_index</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># ランダムな要素を取得して返す</span>
+<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>    <span class="n">random_num</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">random_index</span><span class="p">]</span>
+<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>    <span class="k">return</span> <span class="n">random_num</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.cpp</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="cm">/* 要素への乱数アクセス */</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">randomAccess</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="w">    </span><span class="c1">// [0, size)の範囲で乱数を選択</span>
-<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">randomIndex</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rand</span><span class="p">()</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">size</span><span class="p">;</span>
-<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="w">    </span><span class="c1">// 乱数要素を取得して返却</span>
-<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">randomNum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">randomIndex</span><span class="p">];</span>
-<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">randomNum</span><span class="p">;</span>
-<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">array.java</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 要素へのランダムアクセス */</span>
-<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">randomAccess</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="c1">// 区間 [0, nums.length) からランダムに数を選択</span>
-<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">randomIndex</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ThreadLocalRandom</span><span class="p">.</span><span class="na">current</span><span class="p">().</span><span class="na">nextInt</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">);</span>
-<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="c1">// ランダム要素を取得して返す</span>
-<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">randomNum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">randomIndex</span><span class="o">]</span><span class="p">;</span>
+<div class="highlight"><span class="filename">array.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 要素へランダムアクセス */</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">randomAccess</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="c1">// 区間 [0, size) からランダムに 1 つの数を選ぶ</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">randomIndex</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rand</span><span class="p">()</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">size</span><span class="p">;</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="c1">// ランダムな要素を取得して返す</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">randomNum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">randomIndex</span><span class="p">];</span>
 <a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">randomNum</span><span class="p">;</span>
 <a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.cs</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">array</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">RandomAccess</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 要素へランダムアクセス */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">randomAccess</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 区間 [0, nums.length) からランダムに 1 つの数を選ぶ</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">randomIndex</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ThreadLocalRandom</span><span class="p">.</span><span class="na">current</span><span class="p">().</span><span class="na">nextInt</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">);</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="c1">// ランダムな要素を取得して返す</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">randomNum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">randomIndex</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">randomNum</span><span class="p">;</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.go</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">randomAccess</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 要素へランダムアクセス */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">RandomAccess</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="n">Random</span><span class="w"> </span><span class="n">random</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">();</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="c1">// 区間 [0, nums.Length) からランダムに数字を 1 つ選ぶ</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">randomIndex</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">random</span><span class="p">.</span><span class="n">Next</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">);</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="c1">// ランダムな要素を取得して返す</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">randomNum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">randomIndex</span><span class="p">];</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">randomNum</span><span class="p">;</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.swift</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">randomAccess</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 要素へランダムアクセス */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">randomAccess</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">(</span><span class="nx">randomNum</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="c1">// 区間 [0, nums.length) からランダムに 1 つの数を選ぶ</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="nx">randomIndex</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">rand</span><span class="p">.</span><span class="nx">Intn</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">))</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">    </span><span class="c1">// ランダムな要素を取得して返す</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">    </span><span class="nx">randomNum</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">randomIndex</span><span class="p">]</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">    </span><span class="k">return</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.js</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">randomAccess</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 要素へランダムアクセス */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">randomAccess</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="c1">// 区間 [0, nums.count) からランダムに数字を 1 つ選ぶ</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">randomIndex</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="p">.</span><span class="n">randomElement</span><span class="p">()</span><span class="o">!</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">    </span><span class="c1">// ランダムな要素を取得して返す</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">randomNum</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">randomIndex</span><span class="p">]</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">randomNum</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.ts</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">randomAccess</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 要素へランダムアクセス */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">randomAccess</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="c1">// 区間 [0, nums.length) からランダムに 1 つの数を選ぶ</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">random_index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nb">Math</span><span class="p">.</span><span class="nx">random</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">);</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">    </span><span class="c1">// ランダムな要素を取得して返す</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">random_num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">random_index</span><span class="p">];</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">random_num</span><span class="p">;</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.dart</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">randomAccess</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 要素へランダムアクセス */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">randomAccess</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="c1">// 区間 [0, nums.length) からランダムに 1 つの数を選ぶ</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">random_index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nb">Math</span><span class="p">.</span><span class="nx">random</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">);</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">    </span><span class="c1">// ランダムな要素を取得して返す</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">random_num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">random_index</span><span class="p">];</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">random_num</span><span class="p">;</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.rs</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">random_access</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 要素へランダムアクセス */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">randomAccess</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="c1">// 区間 [0, nums.length) からランダムに 1 つの数を選ぶ</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">randomIndex</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Random</span><span class="p">().</span><span class="n">nextInt</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="p">);</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">  </span><span class="c1">// ランダムな要素を取得して返す</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">randomNum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">randomIndex</span><span class="p">];</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">randomNum</span><span class="p">;</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.c</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">randomAccess</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 要素へランダムアクセス */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">random_access</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="c1">// 区間 [0, nums.len()) からランダムに数字を 1 つ選ぶ</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">random_index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rand</span><span class="p">::</span><span class="n">thread_rng</span><span class="p">().</span><span class="n">gen_range</span><span class="p">(</span><span class="mi">0</span><span class="o">..</span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">());</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">    </span><span class="c1">// ランダムな要素を取得して返す</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">random_num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">random_index</span><span class="p">];</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">    </span><span class="n">random_num</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.kt</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">randomAccess</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 要素へランダムアクセス */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">randomAccess</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="c1">// 区間 [0, size) からランダムに 1 つの数を選ぶ</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">randomIndex</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rand</span><span class="p">()</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">size</span><span class="p">;</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">    </span><span class="c1">// ランダムな要素を取得して返す</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">randomNum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">randomIndex</span><span class="p">];</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">randomNum</span><span class="p">;</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.rb</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">random_access</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 要素へランダムアクセス */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">randomAccess</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="c1">// 区間 [0, nums.size) からランダムに数字を 1 つ選ぶ</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">randomIndex</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ThreadLocalRandom</span><span class="p">.</span><span class="na">current</span><span class="p">().</span><span class="na">nextInt</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span><span class="p">)</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">    </span><span class="c1">// ランダムな要素を取得して返す</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">randomNum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">randomIndex</span><span class="o">]</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">randomNum</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### 要素にランダムアクセス ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">random_access</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="c1"># 区間 [0, nums.length) からランダムに 1 つの数を選ぶ</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">  </span><span class="n">random_index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">Random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="p">)</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">  </span><span class="c1"># ランダムな要素を取得して返す</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">  </span><span class="n">nums</span><span class="o">[</span><span class="n">random_index</span><span class="o">]</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 513px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=import%20random%0A%0Adef%20random_access%28nums%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E8%A6%81%E7%B4%A0%E3%81%B8%E3%83%A9%E3%83%B3%E3%83%80%E3%83%A0%E3%82%A2%E3%82%AF%E3%82%BB%E3%82%B9%22%22%22%0A%20%20%20%20%23%20%E5%8C%BA%E9%96%93%20%5B0%2C%20len%28nums%29-1%5D%20%E3%81%8B%E3%82%89%E3%83%A9%E3%83%B3%E3%83%80%E3%83%A0%E3%81%AB%E6%95%B0%E5%AD%97%E3%82%92%201%20%E3%81%A4%E9%81%B8%E3%81%B6%0A%20%20%20%20random_index%20%3D%20random.randint%280%2C%20len%28nums%29%20-%201%29%0A%20%20%20%20%23%20%E3%83%A9%E3%83%B3%E3%83%80%E3%83%A0%E3%81%AA%E8%A6%81%E7%B4%A0%E3%82%92%E5%8F%96%E5%BE%97%E3%81%97%E3%81%A6%E8%BF%94%E3%81%99%0A%20%20%20%20random_num%20%3D%20nums%5Brandom_index%5D%0A%20%20%20%20return%20random_num%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%85%8D%E5%88%97%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20print%28%22%E9%85%8D%E5%88%97%20nums%20%3D%22%2C%20nums%29%0A%0A%20%20%20%20%23%20%E3%83%A9%E3%83%B3%E3%83%80%E3%83%A0%E3%82%A2%E3%82%AF%E3%82%BB%E3%82%B9%0A%20%20%20%20random_num%3A%20int%20%3D%20random_access%28nums%29%0A%20%20%20%20print%28%22nums%20%E3%81%8B%E3%82%89%E3%83%A9%E3%83%B3%E3%83%80%E3%83%A0%E3%81%AA%E8%A6%81%E7%B4%A0%E3%82%92%E5%8F%96%E5%BE%97%22%2C%20random_num%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=7&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=import%20random%0A%0Adef%20random_access%28nums%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E8%A6%81%E7%B4%A0%E3%81%B8%E3%83%A9%E3%83%B3%E3%83%80%E3%83%A0%E3%82%A2%E3%82%AF%E3%82%BB%E3%82%B9%22%22%22%0A%20%20%20%20%23%20%E5%8C%BA%E9%96%93%20%5B0%2C%20len%28nums%29-1%5D%20%E3%81%8B%E3%82%89%E3%83%A9%E3%83%B3%E3%83%80%E3%83%A0%E3%81%AB%E6%95%B0%E5%AD%97%E3%82%92%201%20%E3%81%A4%E9%81%B8%E3%81%B6%0A%20%20%20%20random_index%20%3D%20random.randint%280%2C%20len%28nums%29%20-%201%29%0A%20%20%20%20%23%20%E3%83%A9%E3%83%B3%E3%83%80%E3%83%A0%E3%81%AA%E8%A6%81%E7%B4%A0%E3%82%92%E5%8F%96%E5%BE%97%E3%81%97%E3%81%A6%E8%BF%94%E3%81%99%0A%20%20%20%20random_num%20%3D%20nums%5Brandom_index%5D%0A%20%20%20%20return%20random_num%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%85%8D%E5%88%97%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20print%28%22%E9%85%8D%E5%88%97%20nums%20%3D%22%2C%20nums%29%0A%0A%20%20%20%20%23%20%E3%83%A9%E3%83%B3%E3%83%80%E3%83%A0%E3%82%A2%E3%82%AF%E3%82%BB%E3%82%B9%0A%20%20%20%20random_num%3A%20int%20%3D%20random_access%28nums%29%0A%20%20%20%20print%28%22nums%20%E3%81%8B%E3%82%89%E3%83%A9%E3%83%B3%E3%83%80%E3%83%A0%E3%81%AA%E8%A6%81%E7%B4%A0%E3%82%92%E5%8F%96%E5%BE%97%22%2C%20random_num%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=7&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 <h3 id="3">3. &nbsp; 要素の挿入<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
-<p>配列要素はメモリ内で密に詰まっており、それらの間に追加データを収容するための空間はありません。以下の図に示すように、配列の中央に要素を挿入するには、後続のすべての要素を1つずつ後ろにシフトして、新しい要素のための空間を作る必要があります。</p>
-<p><img alt="配列要素挿入の例" class="animation-figure" src="../array.assets/array_insert_element.png" /></p>
-<p align="center"> 図 4-3 &nbsp; 配列要素挿入の例 </p>
+<p>配列要素はメモリ内で「ぴったり隣接して」おり、その間にほかのデータを格納する余地はありません。下図のように、配列の途中に要素を挿入したい場合は、その要素より後ろにあるすべての要素を 1 つずつ後ろへずらし、その後でそのインデックスに要素を代入する必要があります。</p>
+<p><img alt="配列への要素挿入の例" class="animation-figure" src="../array.assets/array_insert_element.png" /></p>
+<p align="center"> 図 4-3 &nbsp; 配列への要素挿入の例 </p>
 
-<p>配列の長さが固定されているため、要素を挿入すると必然的に配列の最後の要素が失われることに注意することが重要です。この問題を解決する方法は「リスト」の章で探求されます。</p>
+<p>注意すべき点として、配列の長さは固定であるため、要素を 1 つ挿入すると配列末尾の要素が必ず「失われ」ます。この問題の解決策は「リスト」の章で扱います。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.py</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;インデックス index に要素 num を挿入&quot;&quot;&quot;</span>
-<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a>    <span class="c1"># インデックス index より後のすべての要素を1つ後ろに移動</span>
-<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">index</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
-<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a>        <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span>
-<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a>    <span class="c1"># num を index の位置の要素に代入</span>
-<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a>    <span class="n">nums</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>
+<div class="highlight"><span class="filename">array.py</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;配列の index 番目に要素 num を挿入&quot;&quot;&quot;</span>
+<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>    <span class="c1"># インデックス index 以降の全要素を 1 つ後ろへ移動する</span>
+<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">index</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a>        <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a>    <span class="c1"># index の要素に num を代入する</span>
+<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a>    <span class="n">nums</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.cpp</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="cm">/* `index`に要素numを挿入 */</span>
-<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w">    </span><span class="c1">// `index`より後のすべての要素を1つ後ろに移動</span>
-<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
-<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="w">    </span><span class="c1">// indexの位置にnumを代入</span>
-<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="w">    </span><span class="n">nums</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">array.java</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* `index` に要素 num を挿入 */</span>
-<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="c1">// `index` より後のすべての要素を1つ後ろに移動</span>
-<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<div class="highlight"><span class="filename">array.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* 配列の index 番目に要素 num を挿入 */</span>
+<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="c1">// インデックス index 以降の全要素を 1 つ後ろへ移動する</span>
+<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
 <a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">    </span><span class="c1">// index の要素に num を代入</span>
-<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w">    </span><span class="n">nums</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">    </span><span class="c1">// index の要素に num を代入する</span>
+<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w">    </span><span class="n">nums</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
 <a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.cs</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">array</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 配列の index 番目に要素 num を挿入 */</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="c1">// インデックス index 以降の全要素を 1 つ後ろへ移動する</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">    </span><span class="c1">// index の要素に num を代入する</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">    </span><span class="n">nums</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.go</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 配列の index 番目に要素 num を挿入 */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Insert</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="c1">// インデックス index 以降の全要素を 1 つ後ろへ移動する</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="c1">// index の要素に num を代入する</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">    </span><span class="n">nums</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.swift</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="bp">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 配列の index 番目に要素 num を挿入 */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">insert</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="c1">// インデックス index 以降の全要素を 1 つ後ろへ移動する</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">index</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">    </span><span class="c1">// index の要素に num を代入する</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">    </span><span class="nx">nums</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">num</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.js</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* 配列の index 番目に要素 num を挿入 */</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">index</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w">    </span><span class="c1">// インデックス index 以降の全要素を 1 つ後ろへ移動する</span>
+<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="p">.</span><span class="bp">dropFirst</span><span class="p">(</span><span class="n">index</span><span class="p">).</span><span class="n">reversed</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w">    </span><span class="c1">// index の要素に num を代入する</span>
+<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w">    </span><span class="n">nums</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.ts</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* 配列の index 番目に要素 num を挿入 */</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">insert</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">num</span><span class="p">,</span><span class="w"> </span><span class="nx">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w">    </span><span class="c1">// インデックス index 以降の全要素を 1 つ後ろへ移動する</span>
+<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">index</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="w">    </span><span class="c1">// index の要素に num を代入する</span>
+<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w">    </span><span class="nx">nums</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.dart</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* 配列の index 番目に要素 num を挿入 */</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">insert</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">num</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">index</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w">    </span><span class="c1">// インデックス index 以降の全要素を 1 つ後ろへ移動する</span>
+<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">index</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w">    </span><span class="c1">// index の要素に num を代入する</span>
+<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w">    </span><span class="nx">nums</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.rs</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* 配列の添字 index に要素 _num を挿入 */</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">insert</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w">  </span><span class="c1">// インデックス index 以降の全要素を 1 つ後ろへ移動する</span>
+<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w">    </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">];</span>
+<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w">  </span><span class="c1">// _num を index の位置の要素に代入</span>
+<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w">  </span><span class="n">nums</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_num</span><span class="p">;</span>
+<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.c</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* 配列の index 番目に要素 num を挿入 */</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">index</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w">    </span><span class="c1">// インデックス index 以降の全要素を 1 つ後ろへ移動する</span>
+<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">..</span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()).</span><span class="n">rev</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="w">    </span><span class="c1">// index の要素に num を代入する</span>
+<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="w">    </span><span class="n">nums</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.kt</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* 配列の index 番目に要素 num を挿入 */</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w">    </span><span class="c1">// インデックス index 以降の全要素を 1 つ後ろへ移動する</span>
+<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="w">    </span><span class="c1">// index の要素に num を代入する</span>
+<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="w">    </span><span class="n">nums</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.rb</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* 配列の index 番目に要素 num を挿入 */</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">index</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w">    </span><span class="c1">// インデックス index 以降の全要素を 1 つ後ろへ移動する</span>
+<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="n">downTo</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span>
+<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w">    </span><span class="c1">// index の要素に num を代入する</span>
+<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="w">    </span><span class="n">nums</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="c1">### 配列のインデックス index に要素 num を挿入 ###</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="n">index</span><span class="p">)</span>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w">  </span><span class="c1"># インデックス index 以降の全要素を 1 つ後ろへ移動する</span>
+<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="w">    </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
+<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a>
+<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="w">  </span><span class="c1"># index の要素に num を代入する</span>
+<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="w">  </span><span class="n">nums</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 477px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20insert%28nums%3A%20list%5Bint%5D%2C%20num%3A%20int%2C%20index%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E9%85%8D%E5%88%97%E3%81%AE%20index%20%E7%95%AA%E7%9B%AE%E3%81%AB%E8%A6%81%E7%B4%A0%20num%20%E3%82%92%E6%8C%BF%E5%85%A5%22%22%22%0A%20%20%20%20%23%20%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20index%20%E4%BB%A5%E9%99%8D%E3%81%AE%E5%85%A8%E8%A6%81%E7%B4%A0%E3%82%92%201%20%E3%81%A4%E5%BE%8C%E3%82%8D%E3%81%B8%E7%A7%BB%E5%8B%95%E3%81%99%E3%82%8B%0A%20%20%20%20for%20i%20in%20range%28len%28nums%29%20-%201%2C%20index%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20nums%5Bi%5D%20%3D%20nums%5Bi%20-%201%5D%0A%20%20%20%20%23%20index%20%E3%81%AE%E8%A6%81%E7%B4%A0%E3%81%AB%20num%20%E3%82%92%E4%BB%A3%E5%85%A5%E3%81%99%E3%82%8B%0A%20%20%20%20nums%5Bindex%5D%20%3D%20num%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%85%8D%E5%88%97%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20print%28%22%E9%85%8D%E5%88%97%20nums%20%3D%22%2C%20nums%29%0A%0A%20%20%20%20%23%20%E8%A6%81%E7%B4%A0%E3%82%92%E6%8C%BF%E5%85%A5%E3%81%99%E3%82%8B%0A%20%20%20%20insert%28nums%2C%206%2C%203%29%0A%20%20%20%20print%28%22%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%203%20%E3%81%AB%E6%95%B0%E5%80%A4%206%20%E3%82%92%E6%8C%BF%E5%85%A5%E3%81%97%E3%80%81nums%20%3D%22%2C%20nums%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20insert%28nums%3A%20list%5Bint%5D%2C%20num%3A%20int%2C%20index%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E9%85%8D%E5%88%97%E3%81%AE%20index%20%E7%95%AA%E7%9B%AE%E3%81%AB%E8%A6%81%E7%B4%A0%20num%20%E3%82%92%E6%8C%BF%E5%85%A5%22%22%22%0A%20%20%20%20%23%20%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20index%20%E4%BB%A5%E9%99%8D%E3%81%AE%E5%85%A8%E8%A6%81%E7%B4%A0%E3%82%92%201%20%E3%81%A4%E5%BE%8C%E3%82%8D%E3%81%B8%E7%A7%BB%E5%8B%95%E3%81%99%E3%82%8B%0A%20%20%20%20for%20i%20in%20range%28len%28nums%29%20-%201%2C%20index%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20nums%5Bi%5D%20%3D%20nums%5Bi%20-%201%5D%0A%20%20%20%20%23%20index%20%E3%81%AE%E8%A6%81%E7%B4%A0%E3%81%AB%20num%20%E3%82%92%E4%BB%A3%E5%85%A5%E3%81%99%E3%82%8B%0A%20%20%20%20nums%5Bindex%5D%20%3D%20num%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%85%8D%E5%88%97%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20print%28%22%E9%85%8D%E5%88%97%20nums%20%3D%22%2C%20nums%29%0A%0A%20%20%20%20%23%20%E8%A6%81%E7%B4%A0%E3%82%92%E6%8C%BF%E5%85%A5%E3%81%99%E3%82%8B%0A%20%20%20%20insert%28nums%2C%206%2C%203%29%0A%20%20%20%20print%28%22%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%203%20%E3%81%AB%E6%95%B0%E5%80%A4%206%20%E3%82%92%E6%8C%BF%E5%85%A5%E3%81%97%E3%80%81nums%20%3D%22%2C%20nums%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 <h3 id="4">4. &nbsp; 要素の削除<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
-<p>同様に、以下の図に示すように、インデックス<span class="arithmatex">\(i\)</span>の要素を削除するには、インデックス<span class="arithmatex">\(i\)</span>に続くすべての要素を1つずつ前に移動する必要があります。</p>
-<p><img alt="配列要素削除の例" class="animation-figure" src="../array.assets/array_remove_element.png" /></p>
-<p align="center"> 図 4-4 &nbsp; 配列要素削除の例 </p>
+<p>同様に、下図のように、インデックス <span class="arithmatex">\(i\)</span> の要素を削除したい場合は、インデックス <span class="arithmatex">\(i\)</span> より後ろの要素をすべて 1 つずつ前へずらす必要があります。</p>
+<p><img alt="配列からの要素削除の例" class="animation-figure" src="../array.assets/array_remove_element.png" /></p>
+<p align="center"> 図 4-4 &nbsp; 配列からの要素削除の例 </p>
 
-<p>削除後、元の最後の要素は「意味がない」ものになるため、特定の修正は必要ないことに注意してください。</p>
+<p>注意してください。要素の削除が完了すると、もともとの末尾要素は「意味を持たない」状態になるため、わざわざ変更する必要はありません。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="4:13"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.py</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;インデックス index の要素を削除&quot;&quot;&quot;</span>
-<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a>    <span class="c1"># インデックス index より後のすべての要素を1つ前に移動</span>
-<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">index</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
-<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a>        <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span>
+<div class="highlight"><span class="filename">array.py</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;index の要素を削除する&quot;&quot;&quot;</span>
+<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a>    <span class="c1"># インデックス index より後ろの全要素を 1 つ前へ移動する</span>
+<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">index</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a>        <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.cpp</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="cm">/* `index`の要素を削除 */</span>
-<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="w">    </span><span class="c1">// `index`より後のすべての要素を1つ前に移動</span>
-<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
-<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">array.java</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* `index` の要素を削除 */</span>
-<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w">    </span><span class="c1">// `index` より後のすべての要素を1つ前に移動</span>
-<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<div class="highlight"><span class="filename">array.cpp</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* index の要素を削除する */</span>
+<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w">    </span><span class="c1">// インデックス index より後ろの全要素を 1 つ前へ移動する</span>
+<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
 <a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.cs</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">array</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.java</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* index の要素を削除する */</span>
+<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w">    </span><span class="c1">// インデックス index より後ろの全要素を 1 つ前へ移動する</span>
+<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.go</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.cs</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="cm">/* index の要素を削除する */</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Remove</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="w">    </span><span class="c1">// インデックス index より後ろの全要素を 1 つ前へ移動する</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.swift</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.go</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* index の要素を削除する */</span>
+<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">remove</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w">    </span><span class="c1">// インデックス index より後ろの全要素を 1 つ前へ移動する</span>
+<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">index</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.js</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.swift</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* index の要素を削除する */</span>
+<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">index</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w">    </span><span class="c1">// インデックス index より後ろの全要素を 1 つ前へ移動する</span>
+<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="p">.</span><span class="bp">dropFirst</span><span class="p">(</span><span class="n">index</span><span class="p">).</span><span class="bp">dropLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.ts</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.js</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="cm">/* index の要素を削除する */</span>
+<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">remove</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w">    </span><span class="c1">// インデックス index より後ろの全要素を 1 つ前へ移動する</span>
+<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">index</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.dart</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.ts</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="cm">/* index の要素を削除する */</span>
+<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">remove</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">index</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w">    </span><span class="c1">// インデックス index より後ろの全要素を 1 つ前へ移動する</span>
+<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">index</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.rs</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.dart</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* index の要素を削除する */</span>
+<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w">  </span><span class="c1">// インデックス index より後ろの全要素を 1 つ前へ移動する</span>
+<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="w">    </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">];</span>
+<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.c</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">removeItem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.rs</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="cm">/* index の要素を削除する */</span>
+<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">index</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="w">    </span><span class="c1">// インデックス index より後ろの全要素を 1 つ前へ移動する</span>
+<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">index</span><span class="o">..</span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.kt</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.c</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* index の要素を削除する */</span>
+<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="c1">// 注意: stdio.h が remove 識別子を使用している</span>
+<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="kt">void</span><span class="w"> </span><span class="nf">removeItem</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w">    </span><span class="c1">// インデックス index より後ろの全要素を 1 つ前へ移動する</span>
+<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.rb</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.kt</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* index の要素を削除する */</span>
+<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">index</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w">    </span><span class="c1">// インデックス index より後ろの全要素を 1 つ前へ移動する</span>
+<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">index</span><span class="p">..</span><span class="o">&lt;</span><span class="n">nums</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="o">]</span>
+<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.rb</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="c1">### インデックス index の要素を削除 ###</span>
+<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">index</span><span class="p">)</span>
+<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w">  </span><span class="c1"># インデックス index より後ろの全要素を 1 つ前へ移動する</span>
+<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">index</span><span class="o">...</span><span class="p">(</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w">    </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
+<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>要約すると、配列の挿入と削除操作には以下の欠点があります：</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 441px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20remove%28nums%3A%20list%5Bint%5D%2C%20index%3A%20int%29%3A%0A%20%20%20%20%22%22%22index%20%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E5%89%8A%E9%99%A4%E3%81%99%E3%82%8B%22%22%22%0A%20%20%20%20%23%20%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20index%20%E3%82%88%E3%82%8A%E5%BE%8C%E3%82%8D%E3%81%AE%E5%85%A8%E8%A6%81%E7%B4%A0%E3%82%92%201%20%E3%81%A4%E5%89%8D%E3%81%B8%E7%A7%BB%E5%8B%95%E3%81%99%E3%82%8B%0A%20%20%20%20for%20i%20in%20range%28index%2C%20len%28nums%29%20-%201%29%3A%0A%20%20%20%20%20%20%20%20nums%5Bi%5D%20%3D%20nums%5Bi%20%2B%201%5D%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%85%8D%E5%88%97%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20print%28%22%E9%85%8D%E5%88%97%20nums%20%3D%22%2C%20nums%29%0A%0A%20%20%20%20%23%20%E8%A6%81%E7%B4%A0%E3%82%92%E5%89%8A%E9%99%A4%0A%20%20%20%20remove%28nums%2C%202%29%0A%20%20%20%20print%28%22%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%202%20%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E5%89%8A%E9%99%A4%E3%81%97%E3%80%81nums%20%3D%22%2C%20nums%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20remove%28nums%3A%20list%5Bint%5D%2C%20index%3A%20int%29%3A%0A%20%20%20%20%22%22%22index%20%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E5%89%8A%E9%99%A4%E3%81%99%E3%82%8B%22%22%22%0A%20%20%20%20%23%20%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20index%20%E3%82%88%E3%82%8A%E5%BE%8C%E3%82%8D%E3%81%AE%E5%85%A8%E8%A6%81%E7%B4%A0%E3%82%92%201%20%E3%81%A4%E5%89%8D%E3%81%B8%E7%A7%BB%E5%8B%95%E3%81%99%E3%82%8B%0A%20%20%20%20for%20i%20in%20range%28index%2C%20len%28nums%29%20-%201%29%3A%0A%20%20%20%20%20%20%20%20nums%5Bi%5D%20%3D%20nums%5Bi%20%2B%201%5D%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%85%8D%E5%88%97%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20print%28%22%E9%85%8D%E5%88%97%20nums%20%3D%22%2C%20nums%29%0A%0A%20%20%20%20%23%20%E8%A6%81%E7%B4%A0%E3%82%92%E5%89%8A%E9%99%A4%0A%20%20%20%20remove%28nums%2C%202%29%0A%20%20%20%20print%28%22%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%202%20%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E5%89%8A%E9%99%A4%E3%81%97%E3%80%81nums%20%3D%22%2C%20nums%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>全体として見ると、配列の挿入と削除には次の欠点があります。</p>
 <ul>
-<li><strong>高い時間計算量</strong>：配列の挿入と削除の両方の平均時間計算量は<span class="arithmatex">\(O(n)\)</span>で、ここで<span class="arithmatex">\(n\)</span>は配列の長さです。</li>
-<li><strong>要素の損失</strong>：配列の長さが固定されているため、挿入時に配列の容量を超える要素は失われます。</li>
-<li><strong>メモリの無駄</strong>：より長い配列を初期化して前部分のみを利用すると、挿入時に「意味のない」末尾要素が生じ、メモリ空間の無駄につながります。</li>
+<li><strong>時間計算量が高い</strong>：配列の挿入と削除の平均時間計算量はいずれも <span class="arithmatex">\(O(n)\)</span> であり、ここで <span class="arithmatex">\(n\)</span> は配列長です。</li>
+<li><strong>要素が失われる</strong>：配列の長さは不変であるため、要素を挿入すると配列長の範囲を超えた要素は失われます。</li>
+<li><strong>メモリの浪費</strong>：やや長めの配列を初期化して先頭部分だけを使うこともでき、この場合データ挿入時に失われる末尾要素はすべて「無意味」ですが、その代わり一部のメモリ領域が無駄になります。</li>
 </ul>
 <h3 id="5">5. &nbsp; 配列の走査<a class="headerlink" href="#5" title="Permanent link">&para;</a></h3>
-<p>ほとんどのプログラミング言語では、インデックスを使用するか、各要素を直接反復することで配列を走査できます：</p>
+<p>ほとんどのプログラミング言語では、インデックスを使って配列を走査することも、各要素を直接取り出しながら走査することもできます。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="5:13"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.py</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">traverse</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
-<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;配列の走査&quot;&quot;&quot;</span>
-<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
-<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a>    <span class="c1"># インデックスによる配列の走査</span>
-<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
-<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
-<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a>    <span class="c1"># 配列要素の走査</span>
-<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a>    <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">nums</span><span class="p">:</span>
-<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="n">num</span>
-<a id="__codelineno-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></a>    <span class="c1"># データのインデックスと要素の両方を走査</span>
-<a id="__codelineno-51-11" name="__codelineno-51-11" href="#__codelineno-51-11"></a>    <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">num</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">nums</span><span class="p">):</span>
-<a id="__codelineno-51-12" name="__codelineno-51-12" href="#__codelineno-51-12"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
-<a id="__codelineno-51-13" name="__codelineno-51-13" href="#__codelineno-51-13"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="n">num</span>
+<div class="highlight"><span class="filename">array.py</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">traverse</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
+<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;配列を走査&quot;&quot;&quot;</span>
+<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a>    <span class="c1"># インデックスで配列を走査</span>
+<a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
+<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></a>    <span class="c1"># 配列要素を直接走査</span>
+<a id="__codelineno-52-8" name="__codelineno-52-8" href="#__codelineno-52-8"></a>    <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">nums</span><span class="p">:</span>
+<a id="__codelineno-52-9" name="__codelineno-52-9" href="#__codelineno-52-9"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="n">num</span>
+<a id="__codelineno-52-10" name="__codelineno-52-10" href="#__codelineno-52-10"></a>    <span class="c1"># データのインデックスと要素を同時に走査する</span>
+<a id="__codelineno-52-11" name="__codelineno-52-11" href="#__codelineno-52-11"></a>    <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">num</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">nums</span><span class="p">):</span>
+<a id="__codelineno-52-12" name="__codelineno-52-12" href="#__codelineno-52-12"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-52-13" name="__codelineno-52-13" href="#__codelineno-52-13"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="n">num</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.cpp</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="cm">/* 配列の走査 */</span>
-<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">traverse</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a><span class="w">    </span><span class="c1">// インデックスによる配列の走査</span>
-<a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
-<a id="__codelineno-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-52-8" name="__codelineno-52-8" href="#__codelineno-52-8"></a><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">array.java</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 配列を走査 */</span>
-<a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">traverse</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<div class="highlight"><span class="filename">array.cpp</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 配列を走査 */</span>
+<a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">traverse</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a><span class="w">    </span><span class="c1">// インデックスによる配列の走査</span>
-<a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a><span class="w">    </span><span class="c1">// インデックスで配列を走査</span>
+<a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
 <a id="__codelineno-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a><span class="w">    </span><span class="c1">// 配列要素の走査</span>
-<a id="__codelineno-53-9" name="__codelineno-53-9" href="#__codelineno-53-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-53-10" name="__codelineno-53-10" href="#__codelineno-53-10"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-53-11" name="__codelineno-53-11" href="#__codelineno-53-11"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-53-12" name="__codelineno-53-12" href="#__codelineno-53-12"></a><span class="p">}</span>
+<a id="__codelineno-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.cs</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">array</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Traverse</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.java</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="cm">/* 配列を走査 */</span>
+<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">traverse</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w">    </span><span class="c1">// インデックスで配列を走査</span>
+<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w">    </span><span class="c1">// 配列要素を直接走査</span>
+<a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-54-10" name="__codelineno-54-10" href="#__codelineno-54-10"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.go</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">traverse</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.cs</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="cm">/* 配列を走査 */</span>
+<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Traverse</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-55-4" name="__codelineno-55-4" href="#__codelineno-55-4"></a><span class="w">    </span><span class="c1">// インデックスで配列を走査</span>
+<a id="__codelineno-55-5" name="__codelineno-55-5" href="#__codelineno-55-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-6" name="__codelineno-55-6" href="#__codelineno-55-6"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-55-7" name="__codelineno-55-7" href="#__codelineno-55-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-55-8" name="__codelineno-55-8" href="#__codelineno-55-8"></a><span class="w">    </span><span class="c1">// 配列要素を直接走査</span>
+<a id="__codelineno-55-9" name="__codelineno-55-9" href="#__codelineno-55-9"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-10" name="__codelineno-55-10" href="#__codelineno-55-10"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-55-11" name="__codelineno-55-11" href="#__codelineno-55-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-55-12" name="__codelineno-55-12" href="#__codelineno-55-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.swift</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">traverse</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.go</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="cm">/* 配列を走査 */</span>
+<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">traverse</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a><span class="w">    </span><span class="c1">// インデックスで配列を走査</span>
+<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a><span class="w">        </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
+<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></a><span class="w">    </span><span class="c1">// 配列要素を直接走査</span>
+<a id="__codelineno-56-10" name="__codelineno-56-10" href="#__codelineno-56-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-11" name="__codelineno-56-11" href="#__codelineno-56-11"></a><span class="w">        </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">num</span>
+<a id="__codelineno-56-12" name="__codelineno-56-12" href="#__codelineno-56-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-56-13" name="__codelineno-56-13" href="#__codelineno-56-13"></a><span class="w">    </span><span class="c1">// データのインデックスと要素を同時に走査する</span>
+<a id="__codelineno-56-14" name="__codelineno-56-14" href="#__codelineno-56-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-15" name="__codelineno-56-15" href="#__codelineno-56-15"></a><span class="w">        </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
+<a id="__codelineno-56-16" name="__codelineno-56-16" href="#__codelineno-56-16"></a><span class="w">        </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">num</span>
+<a id="__codelineno-56-17" name="__codelineno-56-17" href="#__codelineno-56-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-56-18" name="__codelineno-56-18" href="#__codelineno-56-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.js</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">traverse</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.swift</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 配列を走査 */</span>
+<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">traverse</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="w">    </span><span class="c1">// インデックスで配列を走査</span>
+<a id="__codelineno-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a><span class="w">        </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w">    </span><span class="c1">// 配列要素を直接走査</span>
+<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-10" name="__codelineno-57-10" href="#__codelineno-57-10"></a><span class="w">        </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-57-11" name="__codelineno-57-11" href="#__codelineno-57-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-57-12" name="__codelineno-57-12" href="#__codelineno-57-12"></a><span class="w">    </span><span class="c1">// データのインデックスと要素を同時に走査する</span>
+<a id="__codelineno-57-13" name="__codelineno-57-13" href="#__codelineno-57-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">enumerated</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-14" name="__codelineno-57-14" href="#__codelineno-57-14"></a><span class="w">        </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-57-15" name="__codelineno-57-15" href="#__codelineno-57-15"></a><span class="w">        </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-57-16" name="__codelineno-57-16" href="#__codelineno-57-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-57-17" name="__codelineno-57-17" href="#__codelineno-57-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.ts</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">traverse</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.js</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 配列を走査 */</span>
+<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">traverse</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><span class="w">    </span><span class="c1">// インデックスで配列を走査</span>
+<a id="__codelineno-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a><span class="w">        </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></a><span class="w">    </span><span class="c1">// 配列要素を直接走査</span>
+<a id="__codelineno-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-10" name="__codelineno-58-10" href="#__codelineno-58-10"></a><span class="w">        </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-58-11" name="__codelineno-58-11" href="#__codelineno-58-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-58-12" name="__codelineno-58-12" href="#__codelineno-58-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.dart</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">traverse</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.ts</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="cm">/* 配列を走査 */</span>
+<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">traverse</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-59-4" name="__codelineno-59-4" href="#__codelineno-59-4"></a><span class="w">    </span><span class="c1">// インデックスで配列を走査</span>
+<a id="__codelineno-59-5" name="__codelineno-59-5" href="#__codelineno-59-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-6" name="__codelineno-59-6" href="#__codelineno-59-6"></a><span class="w">        </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-59-7" name="__codelineno-59-7" href="#__codelineno-59-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-59-8" name="__codelineno-59-8" href="#__codelineno-59-8"></a><span class="w">    </span><span class="c1">// 配列要素を直接走査</span>
+<a id="__codelineno-59-9" name="__codelineno-59-9" href="#__codelineno-59-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-10" name="__codelineno-59-10" href="#__codelineno-59-10"></a><span class="w">        </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-59-11" name="__codelineno-59-11" href="#__codelineno-59-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-59-12" name="__codelineno-59-12" href="#__codelineno-59-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.rs</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">traverse</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.dart</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="cm">/* 配列要素を走査する */</span>
+<a id="__codelineno-60-2" name="__codelineno-60-2" href="#__codelineno-60-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">traverse</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-3" name="__codelineno-60-3" href="#__codelineno-60-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-60-4" name="__codelineno-60-4" href="#__codelineno-60-4"></a><span class="w">  </span><span class="c1">// インデックスで配列を走査</span>
+<a id="__codelineno-60-5" name="__codelineno-60-5" href="#__codelineno-60-5"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-6" name="__codelineno-60-6" href="#__codelineno-60-6"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-60-7" name="__codelineno-60-7" href="#__codelineno-60-7"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-60-8" name="__codelineno-60-8" href="#__codelineno-60-8"></a><span class="w">  </span><span class="c1">// 配列要素を直接走査</span>
+<a id="__codelineno-60-9" name="__codelineno-60-9" href="#__codelineno-60-9"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-10" name="__codelineno-60-10" href="#__codelineno-60-10"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">_num</span><span class="p">;</span>
+<a id="__codelineno-60-11" name="__codelineno-60-11" href="#__codelineno-60-11"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-60-12" name="__codelineno-60-12" href="#__codelineno-60-12"></a><span class="w">  </span><span class="c1">// forEach メソッドで配列を走査する</span>
+<a id="__codelineno-60-13" name="__codelineno-60-13" href="#__codelineno-60-13"></a><span class="w">  </span><span class="n">nums</span><span class="p">.</span><span class="n">forEach</span><span class="p">((</span><span class="n">_num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-14" name="__codelineno-60-14" href="#__codelineno-60-14"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">_num</span><span class="p">;</span>
+<a id="__codelineno-60-15" name="__codelineno-60-15" href="#__codelineno-60-15"></a><span class="w">  </span><span class="p">});</span>
+<a id="__codelineno-60-16" name="__codelineno-60-16" href="#__codelineno-60-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.c</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">traverse</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.rs</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="cm">/* 配列を走査 */</span>
+<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">traverse</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-3" name="__codelineno-61-3" href="#__codelineno-61-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">_count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-61-4" name="__codelineno-61-4" href="#__codelineno-61-4"></a><span class="w">    </span><span class="c1">// インデックスで配列を走査</span>
+<a id="__codelineno-61-5" name="__codelineno-61-5" href="#__codelineno-61-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-6" name="__codelineno-61-6" href="#__codelineno-61-6"></a><span class="w">        </span><span class="n">_count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-61-7" name="__codelineno-61-7" href="#__codelineno-61-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-61-8" name="__codelineno-61-8" href="#__codelineno-61-8"></a><span class="w">    </span><span class="c1">// 配列要素を直接走査</span>
+<a id="__codelineno-61-9" name="__codelineno-61-9" href="#__codelineno-61-9"></a><span class="w">    </span><span class="n">_count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-61-10" name="__codelineno-61-10" href="#__codelineno-61-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="o">&amp;</span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-11" name="__codelineno-61-11" href="#__codelineno-61-11"></a><span class="w">        </span><span class="n">_count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-61-12" name="__codelineno-61-12" href="#__codelineno-61-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-61-13" name="__codelineno-61-13" href="#__codelineno-61-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.kt</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">traverse</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.c</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="cm">/* 配列を走査 */</span>
+<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">traverse</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-62-4" name="__codelineno-62-4" href="#__codelineno-62-4"></a><span class="w">    </span><span class="c1">// インデックスで配列を走査</span>
+<a id="__codelineno-62-5" name="__codelineno-62-5" href="#__codelineno-62-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-6" name="__codelineno-62-6" href="#__codelineno-62-6"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-62-7" name="__codelineno-62-7" href="#__codelineno-62-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-62-8" name="__codelineno-62-8" href="#__codelineno-62-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.rb</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">traverse</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.kt</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="cm">/* 配列を走査 */</span>
+<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">traverse</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-63-4" name="__codelineno-63-4" href="#__codelineno-63-4"></a><span class="w">    </span><span class="c1">// インデックスで配列を走査</span>
+<a id="__codelineno-63-5" name="__codelineno-63-5" href="#__codelineno-63-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">indices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-6" name="__codelineno-63-6" href="#__codelineno-63-6"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-63-8" name="__codelineno-63-8" href="#__codelineno-63-8"></a><span class="w">    </span><span class="c1">// 配列要素を直接走査</span>
+<a id="__codelineno-63-9" name="__codelineno-63-9" href="#__codelineno-63-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-10" name="__codelineno-63-10" href="#__codelineno-63-10"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">j</span>
+<a id="__codelineno-63-11" name="__codelineno-63-11" href="#__codelineno-63-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-63-12" name="__codelineno-63-12" href="#__codelineno-63-12"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.rb</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="c1">### 配列を走査 ###</span>
+<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">traverse</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a><span class="w">  </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-64-4" name="__codelineno-64-4" href="#__codelineno-64-4"></a>
+<a id="__codelineno-64-5" name="__codelineno-64-5" href="#__codelineno-64-5"></a><span class="w">  </span><span class="c1"># インデックスで配列を走査</span>
+<a id="__codelineno-64-6" name="__codelineno-64-6" href="#__codelineno-64-6"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-64-7" name="__codelineno-64-7" href="#__codelineno-64-7"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-64-8" name="__codelineno-64-8" href="#__codelineno-64-8"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-64-9" name="__codelineno-64-9" href="#__codelineno-64-9"></a>
+<a id="__codelineno-64-10" name="__codelineno-64-10" href="#__codelineno-64-10"></a><span class="w">  </span><span class="c1"># 配列要素を直接走査</span>
+<a id="__codelineno-64-11" name="__codelineno-64-11" href="#__codelineno-64-11"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span>
+<a id="__codelineno-64-12" name="__codelineno-64-12" href="#__codelineno-64-12"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-64-13" name="__codelineno-64-13" href="#__codelineno-64-13"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-64-14" name="__codelineno-64-14" href="#__codelineno-64-14"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20traverse%28nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%22%22%22%E9%85%8D%E5%88%97%E3%82%92%E8%B5%B0%E6%9F%BB%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%A7%E9%85%8D%E5%88%97%E3%82%92%E8%B5%B0%E6%9F%BB%0A%20%20%20%20for%20i%20in%20range%28len%28nums%29%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%20nums%5Bi%5D%0A%20%20%20%20%23%20%E9%85%8D%E5%88%97%E8%A6%81%E7%B4%A0%E3%82%92%E7%9B%B4%E6%8E%A5%E8%B5%B0%E6%9F%BB%0A%20%20%20%20for%20num%20in%20nums%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%20num%0A%20%20%20%20%23%20%E3%83%87%E3%83%BC%E3%82%BF%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%A8%E8%A6%81%E7%B4%A0%E3%82%92%E5%90%8C%E6%99%82%E3%81%AB%E8%B5%B0%E6%9F%BB%E3%81%99%E3%82%8B%0A%20%20%20%20for%20i%2C%20num%20in%20enumerate%28nums%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%20nums%5Bi%5D%0A%20%20%20%20%20%20%20%20count%20%2B%3D%20num%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%85%8D%E5%88%97%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20print%28%22%E9%85%8D%E5%88%97%20nums%20%3D%22%2C%20nums%29%0A%0A%20%20%20%20%23%20%E9%85%8D%E5%88%97%E3%82%92%E8%B5%B0%E6%9F%BB%0A%20%20%20%20traverse%28nums%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20traverse%28nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%22%22%22%E9%85%8D%E5%88%97%E3%82%92%E8%B5%B0%E6%9F%BB%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%A7%E9%85%8D%E5%88%97%E3%82%92%E8%B5%B0%E6%9F%BB%0A%20%20%20%20for%20i%20in%20range%28len%28nums%29%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%20nums%5Bi%5D%0A%20%20%20%20%23%20%E9%85%8D%E5%88%97%E8%A6%81%E7%B4%A0%E3%82%92%E7%9B%B4%E6%8E%A5%E8%B5%B0%E6%9F%BB%0A%20%20%20%20for%20num%20in%20nums%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%20num%0A%20%20%20%20%23%20%E3%83%87%E3%83%BC%E3%82%BF%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%A8%E8%A6%81%E7%B4%A0%E3%82%92%E5%90%8C%E6%99%82%E3%81%AB%E8%B5%B0%E6%9F%BB%E3%81%99%E3%82%8B%0A%20%20%20%20for%20i%2C%20num%20in%20enumerate%28nums%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%20nums%5Bi%5D%0A%20%20%20%20%20%20%20%20count%20%2B%3D%20num%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%85%8D%E5%88%97%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20print%28%22%E9%85%8D%E5%88%97%20nums%20%3D%22%2C%20nums%29%0A%0A%20%20%20%20%23%20%E9%85%8D%E5%88%97%E3%82%92%E8%B5%B0%E6%9F%BB%0A%20%20%20%20traverse%28nums%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 <h3 id="6">6. &nbsp; 要素の検索<a class="headerlink" href="#6" title="Permanent link">&para;</a></h3>
-<p>配列内の特定の要素を見つけることは、配列を反復し、各要素をチェックして目的の値と一致するかどうかを決定することを含みます。</p>
-<p>配列は線形データ構造であるため、この操作は一般的に「線形探索」と呼ばれます。</p>
+<p>配列内で指定した要素を探すには、配列を走査し、各反復で要素値が一致するかを判定し、一致したら対応するインデックスを出力します。</p>
+<p>配列は線形データ構造であるため、上記の検索操作は「線形探索」と呼ばれます。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="6:13"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><input id="__tabbed_6_13" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Kotlin</label><label for="__tabbed_6_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.py</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;配列内の指定された要素を検索&quot;&quot;&quot;</span>
-<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
-<a id="__codelineno-64-4" name="__codelineno-64-4" href="#__codelineno-64-4"></a>        <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">==</span> <span class="n">target</span><span class="p">:</span>
-<a id="__codelineno-64-5" name="__codelineno-64-5" href="#__codelineno-64-5"></a>            <span class="k">return</span> <span class="n">i</span>
-<a id="__codelineno-64-6" name="__codelineno-64-6" href="#__codelineno-64-6"></a>    <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>
+<div class="highlight"><span class="filename">array.py</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;配列内で指定要素を探す&quot;&quot;&quot;</span>
+<a id="__codelineno-65-3" name="__codelineno-65-3" href="#__codelineno-65-3"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
+<a id="__codelineno-65-4" name="__codelineno-65-4" href="#__codelineno-65-4"></a>        <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">==</span> <span class="n">target</span><span class="p">:</span>
+<a id="__codelineno-65-5" name="__codelineno-65-5" href="#__codelineno-65-5"></a>            <span class="k">return</span> <span class="n">i</span>
+<a id="__codelineno-65-6" name="__codelineno-65-6" href="#__codelineno-65-6"></a>    <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.cpp</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="cm">/* 配列内の指定要素を検索 */</span>
-<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-65-3" name="__codelineno-65-3" href="#__codelineno-65-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-65-4" name="__codelineno-65-4" href="#__codelineno-65-4"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
-<a id="__codelineno-65-5" name="__codelineno-65-5" href="#__codelineno-65-5"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
-<a id="__codelineno-65-6" name="__codelineno-65-6" href="#__codelineno-65-6"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-65-7" name="__codelineno-65-7" href="#__codelineno-65-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
-<a id="__codelineno-65-8" name="__codelineno-65-8" href="#__codelineno-65-8"></a><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">array.java</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="cm">/* 配列内で指定された要素を検索 */</span>
-<a id="__codelineno-66-2" name="__codelineno-66-2" href="#__codelineno-66-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-66-3" name="__codelineno-66-3" href="#__codelineno-66-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-66-4" name="__codelineno-66-4" href="#__codelineno-66-4"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<div class="highlight"><span class="filename">array.cpp</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="cm">/* 配列内で指定要素を探す */</span>
+<a id="__codelineno-66-2" name="__codelineno-66-2" href="#__codelineno-66-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-66-3" name="__codelineno-66-3" href="#__codelineno-66-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-66-4" name="__codelineno-66-4" href="#__codelineno-66-4"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
 <a id="__codelineno-66-5" name="__codelineno-66-5" href="#__codelineno-66-5"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
 <a id="__codelineno-66-6" name="__codelineno-66-6" href="#__codelineno-66-6"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-66-7" name="__codelineno-66-7" href="#__codelineno-66-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-66-7" name="__codelineno-66-7" href="#__codelineno-66-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
 <a id="__codelineno-66-8" name="__codelineno-66-8" href="#__codelineno-66-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.cs</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">array</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Find</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.java</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="cm">/* 配列内で指定要素を探す */</span>
+<a id="__codelineno-67-2" name="__codelineno-67-2" href="#__codelineno-67-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-67-3" name="__codelineno-67-3" href="#__codelineno-67-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-67-4" name="__codelineno-67-4" href="#__codelineno-67-4"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-67-5" name="__codelineno-67-5" href="#__codelineno-67-5"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-67-6" name="__codelineno-67-6" href="#__codelineno-67-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-67-7" name="__codelineno-67-7" href="#__codelineno-67-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-67-8" name="__codelineno-67-8" href="#__codelineno-67-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.go</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">find</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.cs</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="cm">/* 配列内で指定要素を探す */</span>
+<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Find</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-68-3" name="__codelineno-68-3" href="#__codelineno-68-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-68-4" name="__codelineno-68-4" href="#__codelineno-68-4"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-68-5" name="__codelineno-68-5" href="#__codelineno-68-5"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-68-6" name="__codelineno-68-6" href="#__codelineno-68-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-68-7" name="__codelineno-68-7" href="#__codelineno-68-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-68-8" name="__codelineno-68-8" href="#__codelineno-68-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.swift</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="bp">find</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.go</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="cm">/* 配列内で指定要素を探す */</span>
+<a id="__codelineno-69-2" name="__codelineno-69-2" href="#__codelineno-69-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">find</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">(</span><span class="nx">index</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-3" name="__codelineno-69-3" href="#__codelineno-69-3"></a><span class="w">    </span><span class="nx">index</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-69-4" name="__codelineno-69-4" href="#__codelineno-69-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-5" name="__codelineno-69-5" href="#__codelineno-69-5"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-6" name="__codelineno-69-6" href="#__codelineno-69-6"></a><span class="w">            </span><span class="nx">index</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">i</span>
+<a id="__codelineno-69-7" name="__codelineno-69-7" href="#__codelineno-69-7"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-69-8" name="__codelineno-69-8" href="#__codelineno-69-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-69-9" name="__codelineno-69-9" href="#__codelineno-69-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-69-10" name="__codelineno-69-10" href="#__codelineno-69-10"></a><span class="w">    </span><span class="k">return</span>
+<a id="__codelineno-69-11" name="__codelineno-69-11" href="#__codelineno-69-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.js</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">find</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.swift</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="cm">/* 配列内で指定要素を探す */</span>
+<a id="__codelineno-70-2" name="__codelineno-70-2" href="#__codelineno-70-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-3" name="__codelineno-70-3" href="#__codelineno-70-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-4" name="__codelineno-70-4" href="#__codelineno-70-4"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-5" name="__codelineno-70-5" href="#__codelineno-70-5"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-70-6" name="__codelineno-70-6" href="#__codelineno-70-6"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-70-7" name="__codelineno-70-7" href="#__codelineno-70-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-70-8" name="__codelineno-70-8" href="#__codelineno-70-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-70-9" name="__codelineno-70-9" href="#__codelineno-70-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.ts</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">find</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.js</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="cm">/* 配列内で指定要素を探す */</span>
+<a id="__codelineno-71-2" name="__codelineno-71-2" href="#__codelineno-71-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">find</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-3" name="__codelineno-71-3" href="#__codelineno-71-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-4" name="__codelineno-71-4" href="#__codelineno-71-4"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-71-5" name="__codelineno-71-5" href="#__codelineno-71-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-71-6" name="__codelineno-71-6" href="#__codelineno-71-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-71-7" name="__codelineno-71-7" href="#__codelineno-71-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.dart</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">find</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.ts</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="cm">/* 配列内で指定要素を探す */</span>
+<a id="__codelineno-72-2" name="__codelineno-72-2" href="#__codelineno-72-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">find</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">target</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-3" name="__codelineno-72-3" href="#__codelineno-72-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-4" name="__codelineno-72-4" href="#__codelineno-72-4"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-5" name="__codelineno-72-5" href="#__codelineno-72-5"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-72-6" name="__codelineno-72-6" href="#__codelineno-72-6"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-72-7" name="__codelineno-72-7" href="#__codelineno-72-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-72-8" name="__codelineno-72-8" href="#__codelineno-72-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-72-9" name="__codelineno-72-9" href="#__codelineno-72-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.rs</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">find</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.dart</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="cm">/* 配列内で指定要素を探す */</span>
+<a id="__codelineno-73-2" name="__codelineno-73-2" href="#__codelineno-73-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">find</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-73-3" name="__codelineno-73-3" href="#__codelineno-73-3"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-73-4" name="__codelineno-73-4" href="#__codelineno-73-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-73-5" name="__codelineno-73-5" href="#__codelineno-73-5"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-73-6" name="__codelineno-73-6" href="#__codelineno-73-6"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-73-7" name="__codelineno-73-7" href="#__codelineno-73-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.c</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">find</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.rs</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="cm">/* 配列内で指定要素を探す */</span>
+<a id="__codelineno-74-2" name="__codelineno-74-2" href="#__codelineno-74-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="kt">usize</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-3" name="__codelineno-74-3" href="#__codelineno-74-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-4" name="__codelineno-74-4" href="#__codelineno-74-4"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-5" name="__codelineno-74-5" href="#__codelineno-74-5"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-74-6" name="__codelineno-74-6" href="#__codelineno-74-6"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-74-7" name="__codelineno-74-7" href="#__codelineno-74-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-74-8" name="__codelineno-74-8" href="#__codelineno-74-8"></a><span class="w">    </span><span class="nb">None</span>
+<a id="__codelineno-74-9" name="__codelineno-74-9" href="#__codelineno-74-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.kt</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">find</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.c</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="cm">/* 配列内で指定要素を探す */</span>
+<a id="__codelineno-75-2" name="__codelineno-75-2" href="#__codelineno-75-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-75-3" name="__codelineno-75-3" href="#__codelineno-75-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-75-4" name="__codelineno-75-4" href="#__codelineno-75-4"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-75-5" name="__codelineno-75-5" href="#__codelineno-75-5"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-75-6" name="__codelineno-75-6" href="#__codelineno-75-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-75-7" name="__codelineno-75-7" href="#__codelineno-75-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-75-8" name="__codelineno-75-8" href="#__codelineno-75-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.rb</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">find</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.kt</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="cm">/* 配列内で指定要素を探す */</span>
+<a id="__codelineno-76-2" name="__codelineno-76-2" href="#__codelineno-76-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-76-3" name="__codelineno-76-3" href="#__codelineno-76-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">indices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-76-4" name="__codelineno-76-4" href="#__codelineno-76-4"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-76-5" name="__codelineno-76-5" href="#__codelineno-76-5"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-76-6" name="__codelineno-76-6" href="#__codelineno-76-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-76-7" name="__codelineno-76-7" href="#__codelineno-76-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="m">1</span>
+<a id="__codelineno-76-8" name="__codelineno-76-8" href="#__codelineno-76-8"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.rb</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="c1">### 配列内の指定要素を検索 ###</span>
+<a id="__codelineno-77-2" name="__codelineno-77-2" href="#__codelineno-77-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-77-3" name="__codelineno-77-3" href="#__codelineno-77-3"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-77-4" name="__codelineno-77-4" href="#__codelineno-77-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span>
+<a id="__codelineno-77-5" name="__codelineno-77-5" href="#__codelineno-77-5"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-77-6" name="__codelineno-77-6" href="#__codelineno-77-6"></a>
+<a id="__codelineno-77-7" name="__codelineno-77-7" href="#__codelineno-77-7"></a><span class="w">  </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-77-8" name="__codelineno-77-8" href="#__codelineno-77-8"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 459px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20find%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%85%8D%E5%88%97%E5%86%85%E3%81%A7%E6%8C%87%E5%AE%9A%E8%A6%81%E7%B4%A0%E3%82%92%E6%8E%A2%E3%81%99%22%22%22%0A%20%20%20%20for%20i%20in%20range%28len%28nums%29%29%3A%0A%20%20%20%20%20%20%20%20if%20nums%5Bi%5D%20%3D%3D%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20i%0A%20%20%20%20return%20-1%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%85%8D%E5%88%97%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20print%28%22%E9%85%8D%E5%88%97%20nums%20%3D%22%2C%20nums%29%0A%0A%20%20%20%20%23%20%E8%A6%81%E7%B4%A0%E3%82%92%E6%8E%A2%E7%B4%A2%E3%81%99%E3%82%8B%0A%20%20%20%20index%3A%20int%20%3D%20find%28nums%2C%203%29%0A%20%20%20%20print%28%22nums%20%E3%81%A7%E8%A6%81%E7%B4%A0%203%20%E3%82%92%E6%A4%9C%E7%B4%A2%E3%81%97%E3%80%81%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20%3D%22%2C%20index%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20find%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%85%8D%E5%88%97%E5%86%85%E3%81%A7%E6%8C%87%E5%AE%9A%E8%A6%81%E7%B4%A0%E3%82%92%E6%8E%A2%E3%81%99%22%22%22%0A%20%20%20%20for%20i%20in%20range%28len%28nums%29%29%3A%0A%20%20%20%20%20%20%20%20if%20nums%5Bi%5D%20%3D%3D%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20i%0A%20%20%20%20return%20-1%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%85%8D%E5%88%97%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20print%28%22%E9%85%8D%E5%88%97%20nums%20%3D%22%2C%20nums%29%0A%0A%20%20%20%20%23%20%E8%A6%81%E7%B4%A0%E3%82%92%E6%8E%A2%E7%B4%A2%E3%81%99%E3%82%8B%0A%20%20%20%20index%3A%20int%20%3D%20find%28nums%2C%203%29%0A%20%20%20%20print%28%22nums%20%E3%81%A7%E8%A6%81%E7%B4%A0%203%20%E3%82%92%E6%A4%9C%E7%B4%A2%E3%81%97%E3%80%81%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20%3D%22%2C%20index%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 <h3 id="7">7. &nbsp; 配列の拡張<a class="headerlink" href="#7" title="Permanent link">&para;</a></h3>
-<p>複雑なシステム環境では、安全な容量拡張のために配列の後にメモリ空間の可用性を確保することが困難になります。その結果、ほとんどのプログラミング言語では、**配列の長さは不変**です。</p>
-<p>配列を拡張するには、より大きな配列を作成し、元の配列から要素をコピーする必要があります。この操作の時間計算量は<span class="arithmatex">\(O(n)\)</span>で、大きな配列では時間がかかる可能性があります。コードは以下の通りです：</p>
+<p>複雑なシステム環境では、配列の後方にあるメモリ領域が利用可能であることをプログラム側で保証できず、そのため安全に配列容量を拡張できません。したがって、ほとんどのプログラミング言語では、<strong>配列の長さは不変です</strong>。</p>
+<p>配列を拡張したい場合は、より大きな新しい配列を作り、元の配列の要素を順に新配列へコピーする必要があります。これは <span class="arithmatex">\(O(n)\)</span> の操作であり、配列が大きい場合は非常に時間がかかります。コードは次のとおりです。</p>
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 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.py</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">extend</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">enlarge</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
-<a id="__codelineno-77-2" name="__codelineno-77-2" href="#__codelineno-77-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;配列の長さを拡張&quot;&quot;&quot;</span>
-<a id="__codelineno-77-3" name="__codelineno-77-3" href="#__codelineno-77-3"></a>    <span class="c1"># 拡張された長さの配列を初期化</span>
-<a id="__codelineno-77-4" name="__codelineno-77-4" href="#__codelineno-77-4"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">+</span> <span class="n">enlarge</span><span class="p">)</span>
-<a id="__codelineno-77-5" name="__codelineno-77-5" href="#__codelineno-77-5"></a>    <span class="c1"># 元の配列のすべての要素を新しい配列にコピー</span>
-<a id="__codelineno-77-6" name="__codelineno-77-6" href="#__codelineno-77-6"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
-<a id="__codelineno-77-7" name="__codelineno-77-7" href="#__codelineno-77-7"></a>        <span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
-<a id="__codelineno-77-8" name="__codelineno-77-8" href="#__codelineno-77-8"></a>    <span class="c1"># 拡張後の新しい配列を返す</span>
-<a id="__codelineno-77-9" name="__codelineno-77-9" href="#__codelineno-77-9"></a>    <span class="k">return</span> <span class="n">res</span>
+<div class="highlight"><span class="filename">array.py</span><pre><span></span><code><a id="__codelineno-78-1" name="__codelineno-78-1" href="#__codelineno-78-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">extend</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">enlarge</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-78-2" name="__codelineno-78-2" href="#__codelineno-78-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;配列長を拡張する&quot;&quot;&quot;</span>
+<a id="__codelineno-78-3" name="__codelineno-78-3" href="#__codelineno-78-3"></a>    <span class="c1"># 拡張後の長さを持つ配列を初期化する</span>
+<a id="__codelineno-78-4" name="__codelineno-78-4" href="#__codelineno-78-4"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">+</span> <span class="n">enlarge</span><span class="p">)</span>
+<a id="__codelineno-78-5" name="__codelineno-78-5" href="#__codelineno-78-5"></a>    <span class="c1"># 元の配列の全要素を新しい配列にコピー</span>
+<a id="__codelineno-78-6" name="__codelineno-78-6" href="#__codelineno-78-6"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
+<a id="__codelineno-78-7" name="__codelineno-78-7" href="#__codelineno-78-7"></a>        <span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-78-8" name="__codelineno-78-8" href="#__codelineno-78-8"></a>    <span class="c1"># 拡張後の新しい配列を返す</span>
+<a id="__codelineno-78-9" name="__codelineno-78-9" href="#__codelineno-78-9"></a>    <span class="k">return</span> <span class="n">res</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.cpp</span><pre><span></span><code><a id="__codelineno-78-1" name="__codelineno-78-1" href="#__codelineno-78-1"></a><span class="cm">/* 配列長の拡張 */</span>
-<a id="__codelineno-78-2" name="__codelineno-78-2" href="#__codelineno-78-2"></a><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="nf">extend</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">enlarge</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-78-3" name="__codelineno-78-3" href="#__codelineno-78-3"></a><span class="w">    </span><span class="c1">// 拡張された長さの配列を初期化</span>
-<a id="__codelineno-78-4" name="__codelineno-78-4" href="#__codelineno-78-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">size</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">enlarge</span><span class="p">];</span>
-<a id="__codelineno-78-5" name="__codelineno-78-5" href="#__codelineno-78-5"></a><span class="w">    </span><span class="c1">// 元の配列の全要素を新しい配列にコピー</span>
-<a id="__codelineno-78-6" name="__codelineno-78-6" href="#__codelineno-78-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-78-7" name="__codelineno-78-7" href="#__codelineno-78-7"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
-<a id="__codelineno-78-8" name="__codelineno-78-8" href="#__codelineno-78-8"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-78-9" name="__codelineno-78-9" href="#__codelineno-78-9"></a><span class="w">    </span><span class="c1">// メモリを解放</span>
-<a id="__codelineno-78-10" name="__codelineno-78-10" href="#__codelineno-78-10"></a><span class="w">    </span><span class="k">delete</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
-<a id="__codelineno-78-11" name="__codelineno-78-11" href="#__codelineno-78-11"></a><span class="w">    </span><span class="c1">// 拡張後の新しい配列を返却</span>
-<a id="__codelineno-78-12" name="__codelineno-78-12" href="#__codelineno-78-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
-<a id="__codelineno-78-13" name="__codelineno-78-13" href="#__codelineno-78-13"></a><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">array.java</span><pre><span></span><code><a id="__codelineno-79-1" name="__codelineno-79-1" href="#__codelineno-79-1"></a><span class="cm">/* 配列長の拡張 */</span>
-<a id="__codelineno-79-2" name="__codelineno-79-2" href="#__codelineno-79-2"></a><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">extend</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">enlarge</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-79-3" name="__codelineno-79-3" href="#__codelineno-79-3"></a><span class="w">    </span><span class="c1">// 拡張された長さの配列を初期化</span>
-<a id="__codelineno-79-4" name="__codelineno-79-4" href="#__codelineno-79-4"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">enlarge</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-79-5" name="__codelineno-79-5" href="#__codelineno-79-5"></a><span class="w">    </span><span class="c1">// 元の配列のすべての要素を新しい配列にコピー</span>
-<a id="__codelineno-79-6" name="__codelineno-79-6" href="#__codelineno-79-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-79-7" name="__codelineno-79-7" href="#__codelineno-79-7"></a><span class="w">        </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
+<div class="highlight"><span class="filename">array.cpp</span><pre><span></span><code><a id="__codelineno-79-1" name="__codelineno-79-1" href="#__codelineno-79-1"></a><span class="cm">/* 配列長を拡張する */</span>
+<a id="__codelineno-79-2" name="__codelineno-79-2" href="#__codelineno-79-2"></a><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="nf">extend</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">enlarge</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-3" name="__codelineno-79-3" href="#__codelineno-79-3"></a><span class="w">    </span><span class="c1">// 拡張後の長さを持つ配列を初期化する</span>
+<a id="__codelineno-79-4" name="__codelineno-79-4" href="#__codelineno-79-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">size</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">enlarge</span><span class="p">];</span>
+<a id="__codelineno-79-5" name="__codelineno-79-5" href="#__codelineno-79-5"></a><span class="w">    </span><span class="c1">// 元の配列の全要素を新しい配列にコピー</span>
+<a id="__codelineno-79-6" name="__codelineno-79-6" href="#__codelineno-79-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-7" name="__codelineno-79-7" href="#__codelineno-79-7"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
 <a id="__codelineno-79-8" name="__codelineno-79-8" href="#__codelineno-79-8"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-79-9" name="__codelineno-79-9" href="#__codelineno-79-9"></a><span class="w">    </span><span class="c1">// 拡張後の新しい配列を返す</span>
-<a id="__codelineno-79-10" name="__codelineno-79-10" href="#__codelineno-79-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
-<a id="__codelineno-79-11" name="__codelineno-79-11" href="#__codelineno-79-11"></a><span class="p">}</span>
+<a id="__codelineno-79-9" name="__codelineno-79-9" href="#__codelineno-79-9"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-79-10" name="__codelineno-79-10" href="#__codelineno-79-10"></a><span class="w">    </span><span class="k">delete</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
+<a id="__codelineno-79-11" name="__codelineno-79-11" href="#__codelineno-79-11"></a><span class="w">    </span><span class="c1">// 拡張後の新しい配列を返す</span>
+<a id="__codelineno-79-12" name="__codelineno-79-12" href="#__codelineno-79-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-79-13" name="__codelineno-79-13" href="#__codelineno-79-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.cs</span><pre><span></span><code><a id="__codelineno-80-1" name="__codelineno-80-1" href="#__codelineno-80-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">array</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Extend</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.java</span><pre><span></span><code><a id="__codelineno-80-1" name="__codelineno-80-1" href="#__codelineno-80-1"></a><span class="cm">/* 配列長を拡張する */</span>
+<a id="__codelineno-80-2" name="__codelineno-80-2" href="#__codelineno-80-2"></a><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">extend</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">enlarge</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-3" name="__codelineno-80-3" href="#__codelineno-80-3"></a><span class="w">    </span><span class="c1">// 拡張後の長さを持つ配列を初期化する</span>
+<a id="__codelineno-80-4" name="__codelineno-80-4" href="#__codelineno-80-4"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">enlarge</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-80-5" name="__codelineno-80-5" href="#__codelineno-80-5"></a><span class="w">    </span><span class="c1">// 元の配列の全要素を新しい配列にコピー</span>
+<a id="__codelineno-80-6" name="__codelineno-80-6" href="#__codelineno-80-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-7" name="__codelineno-80-7" href="#__codelineno-80-7"></a><span class="w">        </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-80-8" name="__codelineno-80-8" href="#__codelineno-80-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-80-9" name="__codelineno-80-9" href="#__codelineno-80-9"></a><span class="w">    </span><span class="c1">// 拡張後の新しい配列を返す</span>
+<a id="__codelineno-80-10" name="__codelineno-80-10" href="#__codelineno-80-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-80-11" name="__codelineno-80-11" href="#__codelineno-80-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.go</span><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">extend</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.cs</span><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="cm">/* 配列長を拡張する */</span>
+<a id="__codelineno-81-2" name="__codelineno-81-2" href="#__codelineno-81-2"></a><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="nf">Extend</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">enlarge</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-3" name="__codelineno-81-3" href="#__codelineno-81-3"></a><span class="w">    </span><span class="c1">// 拡張後の長さを持つ配列を初期化する</span>
+<a id="__codelineno-81-4" name="__codelineno-81-4" href="#__codelineno-81-4"></a><span class="w">    </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">enlarge</span><span class="p">];</span>
+<a id="__codelineno-81-5" name="__codelineno-81-5" href="#__codelineno-81-5"></a><span class="w">    </span><span class="c1">// 元の配列の全要素を新しい配列にコピー</span>
+<a id="__codelineno-81-6" name="__codelineno-81-6" href="#__codelineno-81-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-7" name="__codelineno-81-7" href="#__codelineno-81-7"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-81-8" name="__codelineno-81-8" href="#__codelineno-81-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-81-9" name="__codelineno-81-9" href="#__codelineno-81-9"></a><span class="w">    </span><span class="c1">// 拡張後の新しい配列を返す</span>
+<a id="__codelineno-81-10" name="__codelineno-81-10" href="#__codelineno-81-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-81-11" name="__codelineno-81-11" href="#__codelineno-81-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.swift</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="bp">extend</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.go</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="cm">/* 配列長を拡張する */</span>
+<a id="__codelineno-82-2" name="__codelineno-82-2" href="#__codelineno-82-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">extend</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">enlarge</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-3" name="__codelineno-82-3" href="#__codelineno-82-3"></a><span class="w">    </span><span class="c1">// 拡張後の長さを持つ配列を初期化する</span>
+<a id="__codelineno-82-4" name="__codelineno-82-4" href="#__codelineno-82-4"></a><span class="w">    </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="o">+</span><span class="nx">enlarge</span><span class="p">)</span>
+<a id="__codelineno-82-5" name="__codelineno-82-5" href="#__codelineno-82-5"></a><span class="w">    </span><span class="c1">// 元の配列の全要素を新しい配列にコピー</span>
+<a id="__codelineno-82-6" name="__codelineno-82-6" href="#__codelineno-82-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-7" name="__codelineno-82-7" href="#__codelineno-82-7"></a><span class="w">        </span><span class="nx">res</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">num</span>
+<a id="__codelineno-82-8" name="__codelineno-82-8" href="#__codelineno-82-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-82-9" name="__codelineno-82-9" href="#__codelineno-82-9"></a><span class="w">    </span><span class="c1">// 拡張後の新しい配列を返す</span>
+<a id="__codelineno-82-10" name="__codelineno-82-10" href="#__codelineno-82-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
+<a id="__codelineno-82-11" name="__codelineno-82-11" href="#__codelineno-82-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.js</span><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">extend</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.swift</span><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="cm">/* 配列長を拡張する */</span>
+<a id="__codelineno-83-2" name="__codelineno-83-2" href="#__codelineno-83-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">extend</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">enlarge</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-3" name="__codelineno-83-3" href="#__codelineno-83-3"></a><span class="w">    </span><span class="c1">// 拡張後の長さを持つ配列を初期化する</span>
+<a id="__codelineno-83-4" name="__codelineno-83-4" href="#__codelineno-83-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">count</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">enlarge</span><span class="p">)</span>
+<a id="__codelineno-83-5" name="__codelineno-83-5" href="#__codelineno-83-5"></a><span class="w">    </span><span class="c1">// 元の配列の全要素を新しい配列にコピー</span>
+<a id="__codelineno-83-6" name="__codelineno-83-6" href="#__codelineno-83-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-7" name="__codelineno-83-7" href="#__codelineno-83-7"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-83-8" name="__codelineno-83-8" href="#__codelineno-83-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-83-9" name="__codelineno-83-9" href="#__codelineno-83-9"></a><span class="w">    </span><span class="c1">// 拡張後の新しい配列を返す</span>
+<a id="__codelineno-83-10" name="__codelineno-83-10" href="#__codelineno-83-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-83-11" name="__codelineno-83-11" href="#__codelineno-83-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.ts</span><pre><span></span><code><a id="__codelineno-84-1" name="__codelineno-84-1" href="#__codelineno-84-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">extend</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.js</span><pre><span></span><code><a id="__codelineno-84-1" name="__codelineno-84-1" href="#__codelineno-84-1"></a><span class="cm">/* 配列長を拡張する */</span>
+<a id="__codelineno-84-2" name="__codelineno-84-2" href="#__codelineno-84-2"></a><span class="c1">// JavaScript の Array は動的配列であり、直接拡張できます</span>
+<a id="__codelineno-84-3" name="__codelineno-84-3" href="#__codelineno-84-3"></a><span class="c1">// 学習しやすいよう、本関数では Array を長さ不変の配列として扱います</span>
+<a id="__codelineno-84-4" name="__codelineno-84-4" href="#__codelineno-84-4"></a><span class="kd">function</span><span class="w"> </span><span class="nx">extend</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">enlarge</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-5" name="__codelineno-84-5" href="#__codelineno-84-5"></a><span class="w">    </span><span class="c1">// 拡張後の長さを持つ配列を初期化する</span>
+<a id="__codelineno-84-6" name="__codelineno-84-6" href="#__codelineno-84-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">enlarge</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-84-7" name="__codelineno-84-7" href="#__codelineno-84-7"></a><span class="w">    </span><span class="c1">// 元の配列の全要素を新しい配列にコピー</span>
+<a id="__codelineno-84-8" name="__codelineno-84-8" href="#__codelineno-84-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-9" name="__codelineno-84-9" href="#__codelineno-84-9"></a><span class="w">        </span><span class="nx">res</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-84-10" name="__codelineno-84-10" href="#__codelineno-84-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-84-11" name="__codelineno-84-11" href="#__codelineno-84-11"></a><span class="w">    </span><span class="c1">// 拡張後の新しい配列を返す</span>
+<a id="__codelineno-84-12" name="__codelineno-84-12" href="#__codelineno-84-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-84-13" name="__codelineno-84-13" href="#__codelineno-84-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.dart</span><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">extend</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.ts</span><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="cm">/* 配列長を拡張する */</span>
+<a id="__codelineno-85-2" name="__codelineno-85-2" href="#__codelineno-85-2"></a><span class="c1">// TypeScript の Array は動的配列であり、直接拡張できます</span>
+<a id="__codelineno-85-3" name="__codelineno-85-3" href="#__codelineno-85-3"></a><span class="c1">// 学習しやすいよう、本関数では Array を長さ不変の配列として扱います</span>
+<a id="__codelineno-85-4" name="__codelineno-85-4" href="#__codelineno-85-4"></a><span class="kd">function</span><span class="w"> </span><span class="nx">extend</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">enlarge</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-5" name="__codelineno-85-5" href="#__codelineno-85-5"></a><span class="w">    </span><span class="c1">// 拡張後の長さを持つ配列を初期化する</span>
+<a id="__codelineno-85-6" name="__codelineno-85-6" href="#__codelineno-85-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">enlarge</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-85-7" name="__codelineno-85-7" href="#__codelineno-85-7"></a><span class="w">    </span><span class="c1">// 元の配列の全要素を新しい配列にコピー</span>
+<a id="__codelineno-85-8" name="__codelineno-85-8" href="#__codelineno-85-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-9" name="__codelineno-85-9" href="#__codelineno-85-9"></a><span class="w">        </span><span class="nx">res</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-85-10" name="__codelineno-85-10" href="#__codelineno-85-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-85-11" name="__codelineno-85-11" href="#__codelineno-85-11"></a><span class="w">    </span><span class="c1">// 拡張後の新しい配列を返す</span>
+<a id="__codelineno-85-12" name="__codelineno-85-12" href="#__codelineno-85-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-85-13" name="__codelineno-85-13" href="#__codelineno-85-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.rs</span><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">extend</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.dart</span><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="cm">/* 配列長を拡張する */</span>
+<a id="__codelineno-86-2" name="__codelineno-86-2" href="#__codelineno-86-2"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">extend</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">enlarge</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-3" name="__codelineno-86-3" href="#__codelineno-86-3"></a><span class="w">  </span><span class="c1">// 拡張後の長さを持つ配列を初期化する</span>
+<a id="__codelineno-86-4" name="__codelineno-86-4" href="#__codelineno-86-4"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">enlarge</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-86-5" name="__codelineno-86-5" href="#__codelineno-86-5"></a><span class="w">  </span><span class="c1">// 元の配列の全要素を新しい配列にコピー</span>
+<a id="__codelineno-86-6" name="__codelineno-86-6" href="#__codelineno-86-6"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-7" name="__codelineno-86-7" href="#__codelineno-86-7"></a><span class="w">    </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-86-8" name="__codelineno-86-8" href="#__codelineno-86-8"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-86-9" name="__codelineno-86-9" href="#__codelineno-86-9"></a><span class="w">  </span><span class="c1">// 拡張後の新しい配列を返す</span>
+<a id="__codelineno-86-10" name="__codelineno-86-10" href="#__codelineno-86-10"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-86-11" name="__codelineno-86-11" href="#__codelineno-86-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.c</span><pre><span></span><code><a id="__codelineno-87-1" name="__codelineno-87-1" href="#__codelineno-87-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">extend</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.rs</span><pre><span></span><code><a id="__codelineno-87-1" name="__codelineno-87-1" href="#__codelineno-87-1"></a><span class="cm">/* 配列長を拡張する */</span>
+<a id="__codelineno-87-2" name="__codelineno-87-2" href="#__codelineno-87-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">extend</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">enlarge</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-3" name="__codelineno-87-3" href="#__codelineno-87-3"></a><span class="w">    </span><span class="c1">// 拡張後の長さを持つ配列を初期化する</span>
+<a id="__codelineno-87-4" name="__codelineno-87-4" href="#__codelineno-87-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">enlarge</span><span class="p">];</span>
+<a id="__codelineno-87-5" name="__codelineno-87-5" href="#__codelineno-87-5"></a><span class="w">    </span><span class="c1">// 元の配列の全要素を新しい配列にコピー</span>
+<a id="__codelineno-87-6" name="__codelineno-87-6" href="#__codelineno-87-6"></a><span class="w">    </span><span class="n">res</span><span class="p">[</span><span class="mi">0</span><span class="o">..</span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()].</span><span class="n">copy_from_slice</span><span class="p">(</span><span class="n">nums</span><span class="p">);</span>
+<a id="__codelineno-87-7" name="__codelineno-87-7" href="#__codelineno-87-7"></a>
+<a id="__codelineno-87-8" name="__codelineno-87-8" href="#__codelineno-87-8"></a><span class="w">    </span><span class="c1">// 拡張後の新しい配列を返す</span>
+<a id="__codelineno-87-9" name="__codelineno-87-9" href="#__codelineno-87-9"></a><span class="w">    </span><span class="n">res</span>
+<a id="__codelineno-87-10" name="__codelineno-87-10" href="#__codelineno-87-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.kt</span><pre><span></span><code><a id="__codelineno-88-1" name="__codelineno-88-1" href="#__codelineno-88-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">extend</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.c</span><pre><span></span><code><a id="__codelineno-88-1" name="__codelineno-88-1" href="#__codelineno-88-1"></a><span class="cm">/* 配列長を拡張する */</span>
+<a id="__codelineno-88-2" name="__codelineno-88-2" href="#__codelineno-88-2"></a><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="nf">extend</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">enlarge</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-3" name="__codelineno-88-3" href="#__codelineno-88-3"></a><span class="w">    </span><span class="c1">// 拡張後の長さを持つ配列を初期化する</span>
+<a id="__codelineno-88-4" name="__codelineno-88-4" href="#__codelineno-88-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">enlarge</span><span class="p">));</span>
+<a id="__codelineno-88-5" name="__codelineno-88-5" href="#__codelineno-88-5"></a><span class="w">    </span><span class="c1">// 元の配列の全要素を新しい配列にコピー</span>
+<a id="__codelineno-88-6" name="__codelineno-88-6" href="#__codelineno-88-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-7" name="__codelineno-88-7" href="#__codelineno-88-7"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-88-8" name="__codelineno-88-8" href="#__codelineno-88-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-88-9" name="__codelineno-88-9" href="#__codelineno-88-9"></a><span class="w">    </span><span class="c1">// 拡張後の領域を初期化する</span>
+<a id="__codelineno-88-10" name="__codelineno-88-10" href="#__codelineno-88-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">enlarge</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-11" name="__codelineno-88-11" href="#__codelineno-88-11"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-88-12" name="__codelineno-88-12" href="#__codelineno-88-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-88-13" name="__codelineno-88-13" href="#__codelineno-88-13"></a><span class="w">    </span><span class="c1">// 拡張後の新しい配列を返す</span>
+<a id="__codelineno-88-14" name="__codelineno-88-14" href="#__codelineno-88-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-88-15" name="__codelineno-88-15" href="#__codelineno-88-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array.rb</span><pre><span></span><code><a id="__codelineno-89-1" name="__codelineno-89-1" href="#__codelineno-89-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="kp">extend</span><span class="p">}</span>
+<div class="highlight"><span class="filename">array.kt</span><pre><span></span><code><a id="__codelineno-89-1" name="__codelineno-89-1" href="#__codelineno-89-1"></a><span class="cm">/* 配列長を拡張する */</span>
+<a id="__codelineno-89-2" name="__codelineno-89-2" href="#__codelineno-89-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">extend</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">enlarge</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="n">IntArray</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-89-3" name="__codelineno-89-3" href="#__codelineno-89-3"></a><span class="w">    </span><span class="c1">// 拡張後の長さを持つ配列を初期化する</span>
+<a id="__codelineno-89-4" name="__codelineno-89-4" href="#__codelineno-89-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">enlarge</span><span class="p">)</span>
+<a id="__codelineno-89-5" name="__codelineno-89-5" href="#__codelineno-89-5"></a><span class="w">    </span><span class="c1">// 元の配列の全要素を新しい配列にコピー</span>
+<a id="__codelineno-89-6" name="__codelineno-89-6" href="#__codelineno-89-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">indices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-89-7" name="__codelineno-89-7" href="#__codelineno-89-7"></a><span class="w">        </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-89-8" name="__codelineno-89-8" href="#__codelineno-89-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-89-9" name="__codelineno-89-9" href="#__codelineno-89-9"></a><span class="w">    </span><span class="c1">// 拡張後の新しい配列を返す</span>
+<a id="__codelineno-89-10" name="__codelineno-89-10" href="#__codelineno-89-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-89-11" name="__codelineno-89-11" href="#__codelineno-89-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.rb</span><pre><span></span><code><a id="__codelineno-90-1" name="__codelineno-90-1" href="#__codelineno-90-1"></a><span class="c1">### 配列長を拡張 ###</span>
+<a id="__codelineno-90-2" name="__codelineno-90-2" href="#__codelineno-90-2"></a><span class="c1"># Ruby の Array は動的配列であり、直接拡張できます</span>
+<a id="__codelineno-90-3" name="__codelineno-90-3" href="#__codelineno-90-3"></a><span class="c1"># 学習しやすいよう、本関数では Array を長さ不変の配列として扱います</span>
+<a id="__codelineno-90-4" name="__codelineno-90-4" href="#__codelineno-90-4"></a><span class="k">def</span><span class="w"> </span><span class="nf">extend</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">enlarge</span><span class="p">)</span>
+<a id="__codelineno-90-5" name="__codelineno-90-5" href="#__codelineno-90-5"></a><span class="w">  </span><span class="c1"># 拡張後の長さを持つ配列を初期化する</span>
+<a id="__codelineno-90-6" name="__codelineno-90-6" href="#__codelineno-90-6"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">enlarge</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-90-7" name="__codelineno-90-7" href="#__codelineno-90-7"></a>
+<a id="__codelineno-90-8" name="__codelineno-90-8" href="#__codelineno-90-8"></a><span class="w">  </span><span class="c1"># 元の配列の全要素を新しい配列にコピー</span>
+<a id="__codelineno-90-9" name="__codelineno-90-9" href="#__codelineno-90-9"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-90-10" name="__codelineno-90-10" href="#__codelineno-90-10"></a><span class="w">    </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-90-11" name="__codelineno-90-11" href="#__codelineno-90-11"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-90-12" name="__codelineno-90-12" href="#__codelineno-90-12"></a>
+<a id="__codelineno-90-13" name="__codelineno-90-13" href="#__codelineno-90-13"></a><span class="w">  </span><span class="c1"># 拡張後の新しい配列を返す</span>
+<a id="__codelineno-90-14" name="__codelineno-90-14" href="#__codelineno-90-14"></a><span class="w">  </span><span class="n">res</span>
+<a id="__codelineno-90-15" name="__codelineno-90-15" href="#__codelineno-90-15"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h2 id="412">4.1.2 &nbsp; 配列の利点と制限<a class="headerlink" href="#412" title="Permanent link">&para;</a></h2>
-<p>配列は連続したメモリ空間に格納され、同じ型の要素で構成されます。このアプローチは、システムがデータ構造操作の効率を最適化するために活用できる実質的な事前情報を提供します。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=%23%20Python%20%E3%81%AE%20list%20%E3%81%AF%E5%8B%95%E7%9A%84%E9%85%8D%E5%88%97%E3%81%A7%E3%81%82%E3%82%8A%E3%80%81%E7%9B%B4%E6%8E%A5%E6%8B%A1%E5%BC%B5%E3%81%A7%E3%81%8D%E3%81%BE%E3%81%99%0A%23%20%E5%AD%A6%E7%BF%92%E3%81%97%E3%82%84%E3%81%99%E3%81%84%E3%82%88%E3%81%86%E3%80%81%E6%9C%AC%E9%96%A2%E6%95%B0%E3%81%A7%E3%81%AF%20list%20%E3%82%92%E9%95%B7%E3%81%95%E4%B8%8D%E5%A4%89%E3%81%AE%E9%85%8D%E5%88%97%E3%81%A8%E3%81%97%E3%81%A6%E6%89%B1%E3%81%84%E3%81%BE%E3%81%99%0Adef%20extend%28nums%3A%20list%5Bint%5D%2C%20enlarge%3A%20int%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%22%22%22%E9%85%8D%E5%88%97%E9%95%B7%E3%82%92%E6%8B%A1%E5%BC%B5%E3%81%99%E3%82%8B%22%22%22%0A%20%20%20%20%23%20%E6%8B%A1%E5%BC%B5%E5%BE%8C%E3%81%AE%E9%95%B7%E3%81%95%E3%82%92%E6%8C%81%E3%81%A4%E9%85%8D%E5%88%97%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20res%20%3D%20%5B0%5D%20%2A%20%28len%28nums%29%20%2B%20enlarge%29%0A%20%20%20%20%23%20%E5%85%83%E3%81%AE%E9%85%8D%E5%88%97%E3%81%AE%E5%85%A8%E8%A6%81%E7%B4%A0%E3%82%92%E6%96%B0%E3%81%97%E3%81%84%E9%85%8D%E5%88%97%E3%81%AB%E3%82%B3%E3%83%94%E3%83%BC%0A%20%20%20%20for%20i%20in%20range%28len%28nums%29%29%3A%0A%20%20%20%20%20%20%20%20res%5Bi%5D%20%3D%20nums%5Bi%5D%0A%20%20%20%20%23%20%E6%8B%A1%E5%BC%B5%E5%BE%8C%E3%81%AE%E6%96%B0%E3%81%97%E3%81%84%E9%85%8D%E5%88%97%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20res%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%85%8D%E5%88%97%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20print%28%22%E9%85%8D%E5%88%97%20nums%20%3D%22%2C%20nums%29%0A%0A%20%20%20%20%23%20%E9%95%B7%E3%81%95%E3%82%92%E6%8B%A1%E5%BC%B5%0A%20%20%20%20nums%20%3D%20extend%28nums%2C%203%29%0A%20%20%20%20print%28%22%E9%85%8D%E5%88%97%E3%81%AE%E9%95%B7%E3%81%95%E3%82%92%208%20%E3%81%AB%E6%8B%A1%E5%BC%B5%E3%81%97%E3%80%81nums%20%3D%22%2C%20nums%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=%23%20Python%20%E3%81%AE%20list%20%E3%81%AF%E5%8B%95%E7%9A%84%E9%85%8D%E5%88%97%E3%81%A7%E3%81%82%E3%82%8A%E3%80%81%E7%9B%B4%E6%8E%A5%E6%8B%A1%E5%BC%B5%E3%81%A7%E3%81%8D%E3%81%BE%E3%81%99%0A%23%20%E5%AD%A6%E7%BF%92%E3%81%97%E3%82%84%E3%81%99%E3%81%84%E3%82%88%E3%81%86%E3%80%81%E6%9C%AC%E9%96%A2%E6%95%B0%E3%81%A7%E3%81%AF%20list%20%E3%82%92%E9%95%B7%E3%81%95%E4%B8%8D%E5%A4%89%E3%81%AE%E9%85%8D%E5%88%97%E3%81%A8%E3%81%97%E3%81%A6%E6%89%B1%E3%81%84%E3%81%BE%E3%81%99%0Adef%20extend%28nums%3A%20list%5Bint%5D%2C%20enlarge%3A%20int%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%22%22%22%E9%85%8D%E5%88%97%E9%95%B7%E3%82%92%E6%8B%A1%E5%BC%B5%E3%81%99%E3%82%8B%22%22%22%0A%20%20%20%20%23%20%E6%8B%A1%E5%BC%B5%E5%BE%8C%E3%81%AE%E9%95%B7%E3%81%95%E3%82%92%E6%8C%81%E3%81%A4%E9%85%8D%E5%88%97%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20res%20%3D%20%5B0%5D%20%2A%20%28len%28nums%29%20%2B%20enlarge%29%0A%20%20%20%20%23%20%E5%85%83%E3%81%AE%E9%85%8D%E5%88%97%E3%81%AE%E5%85%A8%E8%A6%81%E7%B4%A0%E3%82%92%E6%96%B0%E3%81%97%E3%81%84%E9%85%8D%E5%88%97%E3%81%AB%E3%82%B3%E3%83%94%E3%83%BC%0A%20%20%20%20for%20i%20in%20range%28len%28nums%29%29%3A%0A%20%20%20%20%20%20%20%20res%5Bi%5D%20%3D%20nums%5Bi%5D%0A%20%20%20%20%23%20%E6%8B%A1%E5%BC%B5%E5%BE%8C%E3%81%AE%E6%96%B0%E3%81%97%E3%81%84%E9%85%8D%E5%88%97%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20res%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%85%8D%E5%88%97%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20print%28%22%E9%85%8D%E5%88%97%20nums%20%3D%22%2C%20nums%29%0A%0A%20%20%20%20%23%20%E9%95%B7%E3%81%95%E3%82%92%E6%8B%A1%E5%BC%B5%0A%20%20%20%20nums%20%3D%20extend%28nums%2C%203%29%0A%20%20%20%20print%28%22%E9%85%8D%E5%88%97%E3%81%AE%E9%95%B7%E3%81%95%E3%82%92%208%20%E3%81%AB%E6%8B%A1%E5%BC%B5%E3%81%97%E3%80%81nums%20%3D%22%2C%20nums%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h2 id="412">4.1.2 &nbsp; 配列の利点と限界<a class="headerlink" href="#412" title="Permanent link">&para;</a></h2>
+<p>配列は連続したメモリ領域に格納され、要素の型も同一です。この方法には豊富な事前情報が含まれており、システムはそれらを利用してデータ構造の操作効率を最適化できます。</p>
 <ul>
-<li><strong>高い空間効率</strong>：配列はデータのための連続したメモリブロックを割り当て、追加の構造的オーバーヘッドの必要性を排除します。</li>
-<li><strong>ランダムアクセスのサポート</strong>：配列は任意の要素への<span class="arithmatex">\(O(1)\)</span>時間アクセスを可能にします。</li>
-<li><strong>キャッシュ局所性</strong>：配列要素にアクセスするとき、コンピュータはそれらを読み込むだけでなく、周囲のデータもキャッシュし、高速キャッシュを利用して後続の操作速度を向上させます。</li>
+<li><strong>空間効率が高い</strong>：配列はデータに連続したメモリブロックを割り当てるため、追加の構造オーバーヘッドが不要です。</li>
+<li><strong>ランダムアクセスをサポートする</strong>：配列では任意の要素に <span class="arithmatex">\(O(1)\)</span> 時間でアクセスできます。</li>
+<li><strong>キャッシュ局所性</strong>：配列要素にアクセスする際、コンピュータはその要素だけでなく周囲のデータもキャッシュするため、高速キャッシュを利用して後続操作の実行速度を高められます。</li>
 </ul>
-<p>しかし、連続空間格納は諸刃の剣で、以下の制限があります：</p>
+<p>連続領域への格納は諸刃の剣であり、次のような制約があります。</p>
 <ul>
-<li><strong>挿入と削除の効率が低い</strong>：配列に多くの要素が蓄積されると、要素の挿入や削除には大量の要素をシフトする必要があります。</li>
-<li><strong>固定長</strong>：配列の長さは初期化後に固定されます。配列を拡張するには、すべてのデータを新しい配列にコピーする必要があり、大きなコストがかかります。</li>
-<li><strong>空間の無駄</strong>：割り当てられた配列サイズが必要以上に大きい場合、余分な空間が無駄になります。</li>
+<li><strong>挿入と削除の効率が低い</strong>：配列内の要素が多い場合、挿入や削除では大量の要素を移動する必要があります。</li>
+<li><strong>長さが不変</strong>：配列は初期化後に長さが固定され、拡張するにはすべてのデータを新しい配列へコピーする必要があり、コストが大きくなります。</li>
+<li><strong>空間の浪費</strong>：配列に割り当てたサイズが実際の必要量を上回る場合、余分な領域は無駄になります。</li>
 </ul>
 <h2 id="413">4.1.3 &nbsp; 配列の典型的な応用<a class="headerlink" href="#413" title="Permanent link">&para;</a></h2>
-<p>配列は基本的で広く使用されるデータ構造です。様々なアルゴリズムで頻繁に応用され、複雑なデータ構造の実装に役立ちます。</p>
+<p>配列は基礎的で一般的なデータ構造であり、さまざまなアルゴリズムで頻繁に使われるだけでなく、多様な複雑データ構造の実装にも利用できます。</p>
 <ul>
-<li><strong>ランダムアクセス</strong>：配列はランダムサンプリングが必要なときのデータ格納に理想的です。インデックスに基づいてランダムシーケンスを生成することで、効率的にランダムサンプリングを実現できます。</li>
-<li><strong>ソートと検索</strong>：配列はソートと検索アルゴリズムで最も一般的に使用されるデータ構造です。クイックソート、マージソート、二分探索などの技術は主に配列で動作します。</li>
-<li><strong>ルックアップテーブル</strong>：配列は迅速な要素や関係の取得のための効率的なルックアップテーブルとして機能します。例えば、文字をASCIIコードにマッピングすることは、ASCIIコード値をインデックスとして使用し、対応する要素を配列に格納することで簡単になります。</li>
-<li><strong>機械学習</strong>：ニューラルネットワークの領域では、配列はベクトル、行列、テンソルを含む重要な線形代数演算の実行において重要な役割を果たします。配列はニューラルネットワークプログラミングにおいて主要かつ最も広範囲に使用されるデータ構造として機能します。</li>
-<li><strong>データ構造の実装</strong>：配列は、スタック、キュー、ハッシュ表、ヒープ、グラフなど、様々なデータ構造を実装するための構成要素として機能します。例えば、グラフの隣接行列表現は本質的に二次元配列です。</li>
+<li><strong>ランダムアクセス</strong>：いくつかのサンプルをランダムに抽出したい場合、配列に格納してランダムな系列を生成し、インデックスに基づいてランダムサンプリングを行えます。</li>
+<li><strong>ソートと探索</strong>：配列はソートアルゴリズムと探索アルゴリズムで最もよく使われるデータ構造です。クイックソート、マージソート、二分探索などは主に配列上で行われます。</li>
+<li><strong>ルックアップテーブル</strong>：ある要素やその対応関係を高速に調べる必要がある場合、配列をルックアップテーブルとして使えます。たとえば文字から ASCII コードへの対応を実装したいなら、文字の ASCII コード値をインデックスとし、対応する要素を配列の対応位置に格納できます。</li>
+<li><strong>機械学習</strong>：ニューラルネットワークでは、ベクトル、行列、テンソル間の線形代数演算が大量に使われ、これらのデータはいずれも配列の形で構築されます。配列はニューラルネットワークプログラミングで最もよく使われるデータ構造です。</li>
+<li><strong>データ構造の実装</strong>：配列はスタック、キュー、ハッシュテーブル、ヒープ、グラフなどのデータ構造の実装に利用できます。たとえば、グラフの隣接行列表現は実際には 2 次元配列です。</li>
 </ul>
 
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@@ -6,7 +6,7 @@
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       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
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+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
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 <p><img alt="配列と連結リスト" class="cover-image" src="../assets/covers/chapter_array_and_linkedlist.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>データ構造の世界は頑丈なレンガの壁に似ています。</p>
-<p>配列では、レンガがぴったりと整列し、それぞれが次のものと継ぎ目なく隣り合って、統一された形成を作っている姿を想像してください。一方、連結リストでは、これらのレンガが自由に散らばり、それらの間を優雅に編み込む蔦に抱かれています。</p>
+<p>データ構造の世界は、まるで重厚なれんがの壁のようです。</p>
+<p>配列のれんがは整然と並び、一つひとつがぴったりと接しています。連結リストのれんがはあちこちに分散し、それらをつなぐつるがれんがのすき間を自由に行き交います。</p>
 </div>
 <h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
diff --git a/ja/chapter_array_and_linkedlist/linked_list/index.html b/ja/chapter_array_and_linkedlist/linked_list/index.html
index ec936df15..5b9d3f3df 100644
--- a/ja/chapter_array_and_linkedlist/linked_list/index.html
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@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
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             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
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-    <nav class="md-nav" aria-label="4.2.1 連結リストの一般的な操作">
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 <!-- Page content -->
 <h1 id="42">4.2 &nbsp; 連結リスト<a class="headerlink" href="#42" title="Permanent link">&para;</a></h1>
-<p>メモリ空間は、すべてのプログラム間で共有されるリソースです。複雑なシステム環境では、使用可能なメモリがメモリ空間全体に分散している可能性があります。配列に割り当てられるメモリは連続している必要があることを理解していますが、非常に大きな配列の場合、十分な大きさの連続メモリ空間を見つけるのは困難な場合があります。ここで、連結リストの柔軟な利点が明らかになります。</p>
-<p><u>連結リスト</u>は線形データ構造であり、各要素はノードオブジェクトで、ノードは「参照」を通じて相互接続されています。これらの参照は後続ノードのメモリアドレスを保持し、1つのノードから次のノードへのナビゲーションを可能にします。</p>
-<p>連結リストの設計では、ノードを連続するメモリアドレスを必要とせずに、メモリ位置全体に分散配置することができます。</p>
-<p><img alt="連結リストの定義と格納方法" class="animation-figure" src="../linked_list.assets/linkedlist_definition.png" /></p>
-<p align="center"> 図 4-5 &nbsp; 連結リストの定義と格納方法 </p>
+<p>メモリ空間はすべてのプログラムに共通の資源であり、複雑なシステム実行環境では、空きメモリがメモリの各所に散在している可能性があります。配列を格納するメモリ空間は連続していなければなりませんが、配列が非常に大きい場合、メモリはそのような大きな連続領域を提供できないことがあります。このとき、連結リストの柔軟性という利点が現れます。</p>
+<p><u>連結リスト（linked list）</u>は線形データ構造の一種であり、各要素はノードオブジェクトです。各ノードは「参照」によって接続されます。参照には次のノードのメモリアドレスが記録されており、これによって現在のノードから次のノードへアクセスできます。</p>
+<p>連結リストの設計では、各ノードをメモリの各所に分散して格納でき、それらのメモリアドレスは連続している必要がありません。</p>
+<p><img alt="連結リストの定義と格納方式" class="animation-figure" src="../linked_list.assets/linkedlist_definition.png" /></p>
+<p align="center"> 図 4-5 &nbsp; 連結リストの定義と格納方式 </p>
 
-<p>上図に示すように、連結リストの基本的な構成要素は<u>ノード</u>オブジェクトです。各ノードは2つの主要なコンポーネントで構成されています：ノードの「値」と次のノードへの「参照」です。</p>
+<p>上図を見ると、連結リストの構成単位は<u>ノード（node）</u>オブジェクトです。各ノードは 2 つのデータ、すなわちノードの「値」と次のノードを指す「参照」を含みます。</p>
 <ul>
-<li>連結リストの最初のノードは「ヘッドノード」、最後のノードは「テールノード」です。</li>
-<li>テールノードは「null」を指し、Javaでは<code>null</code>、C++では<code>nullptr</code>、Pythonでは<code>None</code>として指定されます。</li>
-<li>C、C++、Go、Rustなどのポインタをサポートする言語では、この「参照」は通常「ポインタ」として実装されます。</li>
+<li>連結リストの最初のノードを「先頭ノード」、最後のノードを「末尾ノード」と呼びます。</li>
+<li>末尾ノードが指す先は「空」であり、Java、C++、Python ではそれぞれ <code>null</code>、<code>nullptr</code>、<code>None</code> と表記します。</li>
+<li>C、C++、Go、Rust などポインタをサポートする言語では、上記の「参照」は「ポインタ」に置き換えるべきです。</li>
 </ul>
-<p>以下のコードが示すように、連結リストの<code>ListNode</code>は値を保持するだけでなく、追加の参照（またはポインタ）も維持する必要があります。したがって、<strong>連結リストは同じ量のデータを格納する場合、配列よりも多くのメモリ空間を占有します</strong>。</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="1:12"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label></div>
+<p>以下のコードが示すように、連結リストノード <code>ListNode</code> は値のほかに、追加で 1 つの参照（ポインタ）を保持する必要があります。そのため、同じデータ量であれば、<strong>連結リストは配列より多くのメモリ空間を消費します</strong>。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">ListNode</span><span class="p">:</span>
 <a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;連結リストノードクラス&quot;&quot;&quot;</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">val</span>               <span class="c1"># ノード値</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">val</span>               <span class="c1"># ノードの値</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">next</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 次のノードへの参照</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 連結リストノード構造体 */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">         </span><span class="c1">// ノード値</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">         </span><span class="c1">// ノードの値</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">next</span><span class="p">;</span><span class="w">  </span><span class="c1">// 次のノードへのポインタ</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="n">ListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">x</span><span class="p">),</span><span class="w"> </span><span class="n">next</span><span class="p">(</span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{}</span><span class="w">  </span><span class="c1">// コンストラクタ</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="p">};</span>
@@ -4556,7 +4556,7 @@
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 連結リストノードクラス */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kd">class</span> <span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">        </span><span class="c1">// ノード値</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">        </span><span class="c1">// ノードの値</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">next</span><span class="p">;</span><span class="w">  </span><span class="c1">// 次のノードへの参照</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="n">ListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w"> </span><span class="p">}</span><span class="w">  </span><span class="c1">// コンストラクタ</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="p">}</span>
@@ -4564,8 +4564,8 @@
 </div>
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 連結リストノードクラス */</span>
-<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">class</span><span class="w"> </span><span class="nf">ListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// コンストラクタ</span>
-<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w">         </span><span class="c1">// ノード値</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">class</span><span class="w"> </span><span class="nf">ListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">//コンストラクタ</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w">         </span><span class="c1">// ノードの値</span>
 <a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">next</span><span class="p">;</span><span class="w">      </span><span class="c1">// 次のノードへの参照</span>
 <a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="p">}</span>
 </code></pre></div>
@@ -4573,11 +4573,11 @@
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 連結リストノード構造体 */</span>
 <a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">ListNode</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="nx">Val</span><span class="w">  </span><span class="kt">int</span><span class="w">       </span><span class="c1">// ノード値</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="nx">Val</span><span class="w">  </span><span class="kt">int</span><span class="w">       </span><span class="c1">// ノードの値</span>
 <a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">Next</span><span class="w"> </span><span class="o">*</span><span class="nx">ListNode</span><span class="w"> </span><span class="c1">// 次のノードへのポインタ</span>
 <a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="p">}</span>
 <a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a>
-<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="c1">// NewListNode コンストラクタ、新しい連結リストを作成</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="c1">// NewListNode コンストラクタ。新しい連結リストを作成する</span>
 <a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="kd">func</span><span class="w"> </span><span class="nx">NewListNode</span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">ListNode</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">ListNode</span><span class="p">{</span>
 <a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">        </span><span class="nx">Val</span><span class="p">:</span><span class="w">  </span><span class="nx">val</span><span class="p">,</span>
@@ -4589,7 +4589,7 @@
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 連結リストノードクラス */</span>
 <a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">val</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// ノード値</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">val</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// ノードの値</span>
 <a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">next</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 次のノードへの参照</span>
 <a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a>
 <a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="kd">init</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// コンストラクタ</span>
@@ -4602,7 +4602,7 @@
 <div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 連結リストノードクラス */</span>
 <a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">ListNode</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">next</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">val</span><span class="p">);</span><span class="w">       </span><span class="c1">// ノード値</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">val</span><span class="p">);</span><span class="w">       </span><span class="c1">// ノードの値</span>
 <a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="nx">next</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">next</span><span class="p">);</span><span class="w"> </span><span class="c1">// 次のノードへの参照</span>
 <a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="p">}</span>
@@ -4614,7 +4614,7 @@
 <a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span>
 <a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="nx">next</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
 <a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val?</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">next?</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">val</span><span class="p">;</span><span class="w">        </span><span class="c1">// ノード値</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">val</span><span class="p">;</span><span class="w">        </span><span class="c1">// ノードの値</span>
 <a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">next</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">next</span><span class="p">;</span><span class="w">  </span><span class="c1">// 次のノードへの参照</span>
 <a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="p">}</span>
@@ -4623,7 +4623,7 @@
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 連結リストノードクラス */</span>
 <a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// ノード値</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// ノードの値</span>
 <a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">next</span><span class="p">;</span><span class="w"> </span><span class="c1">// 次のノードへの参照</span>
 <a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="n">ListNode</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="k">this</span><span class="p">.</span><span class="n">next</span><span class="p">]);</span><span class="w"> </span><span class="c1">// コンストラクタ</span>
 <a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="p">}</span>
@@ -4635,7 +4635,7 @@
 <a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="cm">/* 連結リストノードクラス */</span>
 <a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="cp">#[derive(Debug)]</span>
 <a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="k">struct</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="c1">// ノード値</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="c1">// ノードの値</span>
 <a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="c1">// 次のノードへのポインタ</span>
 <a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="p">}</span>
 </code></pre></div>
@@ -4643,7 +4643,7 @@
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 連結リストノード構造体 */</span>
 <a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">               </span><span class="c1">// ノード値</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">               </span><span class="c1">// ノードの値</span>
 <a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="k">struct</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">next</span><span class="p">;</span><span class="w"> </span><span class="c1">// 次のノードへのポインタ</span>
 <a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="p">}</span><span class="w"> </span><span class="n">ListNode</span><span class="p">;</span>
 <a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a>
@@ -4658,123 +4658,126 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 連結リストノードクラス */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="c1">// コンストラクタ</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">_val</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="w">          </span><span class="c1">// ノードの値</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">next</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="c1">// 次のノードへの参照</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1"># 連結リストノードクラス</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ListNode</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:val</span><span class="w">  </span><span class="c1"># ノードの値</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:next</span><span class="w"> </span><span class="c1"># 次のノードへの参照</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">val</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">next_node</span><span class="o">=</span><span class="kp">nil</span><span class="p">)</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">    </span><span class="vi">@val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">    </span><span class="vi">@next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">next_node</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h2 id="421">4.2.1 &nbsp; 連結リストの一般的な操作<a class="headerlink" href="#421" title="Permanent link">&para;</a></h2>
+<h2 id="421">4.2.1 &nbsp; 連結リストの基本操作<a class="headerlink" href="#421" title="Permanent link">&para;</a></h2>
 <h3 id="1">1. &nbsp; 連結リストの初期化<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>連結リストの構築は2段階のプロセスです：まず各ノードオブジェクトを初期化し、次にノード間の参照リンクを形成します。初期化後、ヘッドノードから<code>next</code>参照をたどってすべてのノードを順次巡回できます。</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="2:12"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label></div>
+<p>連結リストの構築は 2 つの手順に分かれます。第 1 に各ノードオブジェクトを初期化し、第 2 にノード間の参照関係を構築します。初期化が完了したら、連結リストの先頭ノードから出発し、参照で <code>next</code> をたどってすべてのノードに順にアクセスできます。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.py</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1"># 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4</span>
-<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="c1"># 各ノードを初期化</span>
-<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="n">n0</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="n">n1</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
-<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="n">n2</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
-<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="n">n3</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
-<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="n">n4</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
-<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="c1"># ノード間の参照を構築</span>
-<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="n">n0</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">n1</span>
-<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="n">n1</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">n2</span>
-<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="n">n2</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">n3</span>
-<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="n">n3</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">n4</span>
+<div class="highlight"><span class="filename">linked_list.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="c1"># 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="c1"># 各ノードを初期化</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="n">n0</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="n">n1</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="n">n2</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="n">n3</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="n">n4</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="c1"># ノード間の参照を構築</span>
+<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="n">n0</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">n1</span>
+<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a><span class="n">n1</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">n2</span>
+<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="n">n2</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">n3</span>
+<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a><span class="n">n3</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">n4</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.cpp</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="cm">/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="c1">// 各ノードを初期化</span>
-<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
-<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
-<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
-<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
-<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="c1">// ノード間の参照を構築</span>
-<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
-<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a><span class="n">n1</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
-<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="n">n2</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
-<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a><span class="n">n3</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.java</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */</span>
+<div class="highlight"><span class="filename">linked_list.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化 */</span>
 <a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="c1">// 各ノードを初期化</span>
-<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
-<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
-<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
-<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
 <a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="c1">// ノード間の参照を構築</span>
-<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="n">n0</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
-<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="n">n1</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
-<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="n">n2</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
-<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="n">n3</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="n">n1</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="n">n2</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="n">n3</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.cs</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */</span>
+<div class="highlight"><span class="filename">linked_list.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化 */</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="c1">// 各ノードを初期化</span>
-<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
-<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
-<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
-<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
 <a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="c1">// ノード間の参照を構築</span>
-<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="n">n0</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
-<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="n">n1</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
-<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="n">n2</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
-<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="n">n3</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="n">n0</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="n">n1</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="n">n2</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="n">n3</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.go</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */</span>
+<div class="highlight"><span class="filename">linked_list.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化 */</span>
 <a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="c1">// 各ノードを初期化</span>
-<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="nx">n0</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewListNode</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="nx">n1</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewListNode</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
-<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="nx">n2</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewListNode</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
-<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="nx">n3</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewListNode</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
-<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="nx">n4</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewListNode</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
 <a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="c1">// ノード間の参照を構築</span>
-<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="nx">n0</span><span class="p">.</span><span class="nx">Next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n1</span>
-<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">Next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n2</span>
-<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="nx">n2</span><span class="p">.</span><span class="nx">Next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n3</span>
-<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="nx">n3</span><span class="p">.</span><span class="nx">Next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n4</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="n">n0</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="n">n1</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="n">n2</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="n">n3</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.swift</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */</span>
+<div class="highlight"><span class="filename">linked_list.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化 */</span>
 <a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="c1">// 各ノードを初期化</span>
-<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="kd">let</span><span class="w"> </span><span class="nv">n0</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="kd">let</span><span class="w"> </span><span class="nv">n1</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span>
-<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="kd">let</span><span class="w"> </span><span class="nv">n2</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
-<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="kd">let</span><span class="w"> </span><span class="nv">n3</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span>
-<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="kd">let</span><span class="w"> </span><span class="nv">n4</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="nx">n0</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewListNode</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="nx">n1</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewListNode</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="nx">n2</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewListNode</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="nx">n3</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewListNode</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="nx">n4</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewListNode</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
 <a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="c1">// ノード間の参照を構築</span>
-<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="n">n0</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n1</span>
-<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="n">n1</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n2</span>
-<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="n">n2</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n3</span>
-<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="n">n3</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n4</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="nx">n0</span><span class="p">.</span><span class="nx">Next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n1</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">Next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n2</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="nx">n2</span><span class="p">.</span><span class="nx">Next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n3</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="nx">n3</span><span class="p">.</span><span class="nx">Next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n4</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.js</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */</span>
+<div class="highlight"><span class="filename">linked_list.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化 */</span>
 <a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="c1">// 各ノードを初期化</span>
-<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="kd">const</span><span class="w"> </span><span class="nx">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">1</span><span class="p">);</span>
-<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="kd">const</span><span class="w"> </span><span class="nx">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">3</span><span class="p">);</span>
-<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="kd">const</span><span class="w"> </span><span class="nx">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">2</span><span class="p">);</span>
-<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="kd">const</span><span class="w"> </span><span class="nx">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
-<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="kd">const</span><span class="w"> </span><span class="nx">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">4</span><span class="p">);</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="kd">let</span><span class="w"> </span><span class="nv">n0</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="kd">let</span><span class="w"> </span><span class="nv">n1</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="kd">let</span><span class="w"> </span><span class="nv">n2</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="kd">let</span><span class="w"> </span><span class="nv">n3</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="kd">let</span><span class="w"> </span><span class="nv">n4</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span>
 <a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="c1">// ノード間の参照を構築</span>
-<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="nx">n0</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n1</span><span class="p">;</span>
-<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n2</span><span class="p">;</span>
-<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="nx">n2</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n3</span><span class="p">;</span>
-<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="nx">n3</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n4</span><span class="p">;</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="n">n0</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n1</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="n">n1</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n2</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="n">n2</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n3</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="n">n3</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n4</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.ts</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */</span>
+<div class="highlight"><span class="filename">linked_list.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化 */</span>
 <a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="c1">// 各ノードを初期化</span>
 <a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="kd">const</span><span class="w"> </span><span class="nx">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">1</span><span class="p">);</span>
 <a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="kd">const</span><span class="w"> </span><span class="nx">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">3</span><span class="p">);</span>
@@ -4789,389 +4792,797 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.dart</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */</span>
+<div class="highlight"><span class="filename">linked_list.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化 */</span>
 <a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="c1">// 各ノードを初期化</span>
-<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">1</span><span class="p">);</span>
-<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">3</span><span class="p">);</span>
-<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">2</span><span class="p">);</span>
-<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">5</span><span class="p">);</span>
-<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">4</span><span class="p">);</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="kd">const</span><span class="w"> </span><span class="nx">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="kd">const</span><span class="w"> </span><span class="nx">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">3</span><span class="p">);</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="kd">const</span><span class="w"> </span><span class="nx">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">2</span><span class="p">);</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="kd">const</span><span class="w"> </span><span class="nx">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="kd">const</span><span class="w"> </span><span class="nx">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">4</span><span class="p">);</span>
 <a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="c1">// ノード間の参照を構築</span>
-<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="n">n0</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
-<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="n">n1</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
-<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="n">n2</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
-<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="n">n3</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="nx">n0</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n1</span><span class="p">;</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n2</span><span class="p">;</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="nx">n2</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n3</span><span class="p">;</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="nx">n3</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n4</span><span class="p">;</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.rs</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */</span>
+<div class="highlight"><span class="filename">linked_list.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化 */</span><span class="err">\</span>
 <a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="c1">// 各ノードを初期化</span>
-<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="kd">let</span><span class="w"> </span><span class="n">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Rc</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">RefCell</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="p">}));</span>
-<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="kd">let</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Rc</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">RefCell</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="p">}));</span>
-<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="kd">let</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Rc</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">RefCell</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="p">}));</span>
-<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="kd">let</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Rc</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">RefCell</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="p">}));</span>
-<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="kd">let</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Rc</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">RefCell</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="p">}));</span>
-<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a>
-<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="c1">// ノード間の参照を構築</span>
-<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="n">n0</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">n1</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
-<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="n">n1</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">n2</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
-<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="n">n2</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">n3</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
-<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="n">n3</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">n4</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">3</span><span class="p">);</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">2</span><span class="p">);</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">5</span><span class="p">);</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">4</span><span class="p">);</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="c1">// ノード間の参照を構築</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="n">n0</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="n">n1</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="n">n2</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="n">n3</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.c</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */</span>
+<div class="highlight"><span class="filename">linked_list.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化 */</span>
 <a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="c1">// 各ノードを初期化</span>
-<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newListNode</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newListNode</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
-<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newListNode</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
-<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newListNode</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
-<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newListNode</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
-<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="c1">// ノード間の参照を構築</span>
-<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
-<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="n">n1</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
-<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="n">n2</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
-<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="n">n3</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="kd">let</span><span class="w"> </span><span class="n">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Rc</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">RefCell</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="p">}));</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="kd">let</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Rc</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">RefCell</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="p">}));</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="kd">let</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Rc</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">RefCell</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="p">}));</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="kd">let</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Rc</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">RefCell</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="p">}));</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="kd">let</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Rc</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">RefCell</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="p">}));</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="c1">// ノード間の参照を構築</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="n">n0</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">n1</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="n">n1</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">n2</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="n">n2</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">n3</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="n">n3</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">n4</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.kt</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a>
+<div class="highlight"><span class="filename">linked_list.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化 */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="c1">// 各ノードを初期化</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newListNode</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newListNode</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newListNode</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newListNode</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newListNode</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="c1">// ノード間の参照を構築</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="n">n1</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="n">n2</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="n">n3</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化 */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="c1">// 各ノードを初期化</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="kd">val</span><span class="w"> </span><span class="nv">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="kd">val</span><span class="w"> </span><span class="nv">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">3</span><span class="p">)</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="kd">val</span><span class="w"> </span><span class="nv">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">2</span><span class="p">)</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="kd">val</span><span class="w"> </span><span class="nv">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">5</span><span class="p">)</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="kd">val</span><span class="w"> </span><span class="nv">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">4</span><span class="p">)</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="c1">// ノード間の参照を構築</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="n">n0</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="n">n1</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="n">n2</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="n">n3</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1"># 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="c1"># 各ノードを初期化</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="n">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">ListNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">ListNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">ListNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">ListNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">ListNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="c1"># ノード間の参照を構築</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="n">n0</span><span class="o">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="n">n1</span><span class="o">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="n">n2</span><span class="o">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="n">n3</span><span class="o">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>配列全体は1つの変数です。例えば、配列<code>nums</code>には<code>nums[0]</code>、<code>nums[1]</code>などの要素が含まれますが、連結リストは複数の異なるノードオブジェクトで構成されています。<strong>通常、連結リストはそのヘッドノードで参照されます</strong>。例えば、前のコードスニペットの連結リストは<code>n0</code>として参照されます。</p>
+<details class="pythontutor">
+<summary>可視化実行</summary>
+<p>https://pythontutor.com/render.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%E9%93%BE%E8%A1%A8%E8%8A%82%E7%82%B9%E7%B1%BB%22%22%22%0A%20%20%20%20def%20__init__%28self,%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E8%8A%82%E7%82%B9%E5%80%BC%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%90%8E%E7%BB%A7%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E9%93%BE%E8%A1%A8%201%20-%3E%203%20-%3E%202%20-%3E%205%20-%3E%204%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%90%84%E4%B8%AA%E8%8A%82%E7%82%B9%0A%20%20%20%20n0%20%3D%20ListNode%281%29%0A%20%20%20%20n1%20%3D%20ListNode%283%29%0A%20%20%20%20n2%20%3D%20ListNode%282%29%0A%20%20%20%20n3%20%3D%20ListNode%285%29%0A%20%20%20%20n4%20%3D%20ListNode%284%29%0A%20%20%20%20%23%20%E6%9E%84%E5%BB%BA%E8%8A%82%E7%82%B9%E4%B9%8B%E9%97%B4%E7%9A%84%E5%BC%95%E7%94%A8%0A%20%20%20%20n0.next%20%3D%20n1%0A%20%20%20%20n1.next%20%3D%20n2%0A%20%20%20%20n2.next%20%3D%20n3%0A%20%20%20%20n3.next%20%3D%20n4&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>
+</details>
+<p>配列全体は 1 つの変数であり、たとえば配列 <code>nums</code> には <code>nums[0]</code> や <code>nums[1]</code> などの要素が含まれます。一方、連結リストは複数の独立したノードオブジェクトで構成されます。<strong>通常、先頭ノードを連結リストの代名詞として扱います</strong>。たとえば上記のコードの連結リストは <code>n0</code> と表せます。</p>
 <h3 id="2">2. &nbsp; ノードの挿入<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>連結リストにノードを挿入するのは非常に簡単です。下図に示すように、隣接する2つのノード<code>n0</code>と<code>n1</code>の間に新しいノード<code>P</code>を挿入することを目指すとします。<strong>これは2つのノード参照（ポインタ）を変更するだけで実現でき</strong>、時間計算量は<span class="arithmatex">\(O(1)\)</span>です。</p>
-<p>比較すると、配列に要素を挿入する時間計算量は<span class="arithmatex">\(O(n)\)</span>であり、大量のデータを扱う場合には効率が悪くなります。</p>
-<p><img alt="連結リストノード挿入の例" class="animation-figure" src="../linked_list.assets/linkedlist_insert_node.png" /></p>
-<p align="center"> 図 4-6 &nbsp; 連結リストノード挿入の例 </p>
+<p>連結リストへのノード挿入は非常に簡単です。下図に示すように、隣り合う 2 つのノード <code>n0</code> と <code>n1</code> の間に新しいノード <code>P</code> を挿入したいとします。<strong>このとき 2 つのノードの参照（ポインタ）を変更するだけでよく</strong>、時間計算量は <span class="arithmatex">\(O(1)\)</span> です。</p>
+<p>これに対して、配列に要素を挿入する時間計算量は <span class="arithmatex">\(O(n)\)</span> であり、データ量が大きい場合の効率は低くなります。</p>
+<p><img alt="連結リストへのノード挿入例" class="animation-figure" src="../linked_list.assets/linkedlist_insert_node.png" /></p>
+<p align="center"> 図 4-6 &nbsp; 連結リストへのノード挿入例 </p>
 
 <div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.py</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">n0</span><span class="p">:</span> <span class="n">ListNode</span><span class="p">,</span> <span class="n">P</span><span class="p">:</span> <span class="n">ListNode</span><span class="p">):</span>
-<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;連結リストのノード n0 の後にノード P を挿入&quot;&quot;&quot;</span>
-<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a>    <span class="n">n1</span> <span class="o">=</span> <span class="n">n0</span><span class="o">.</span><span class="n">next</span>
-<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a>    <span class="n">P</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">n1</span>
-<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a>    <span class="n">n0</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">P</span>
+<div class="highlight"><span class="filename">linked_list.py</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">n0</span><span class="p">:</span> <span class="n">ListNode</span><span class="p">,</span> <span class="n">P</span><span class="p">:</span> <span class="n">ListNode</span><span class="p">):</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;連結リストでノード n0 の後ろにノード P を挿入する&quot;&quot;&quot;</span>
+<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>    <span class="n">n1</span> <span class="o">=</span> <span class="n">n0</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>    <span class="n">P</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">n1</span>
+<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a>    <span class="n">n0</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">P</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.cpp</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="cm">/* 連結リストのノードn0の後にノードPを挿入 */</span>
-<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">n0</span><span class="p">,</span><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">P</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
-<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">    </span><span class="n">P</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
-<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">    </span><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="p">;</span>
-<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* 連結リストでノード n0 の後ろにノード P を挿入する */</span>
+<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">n0</span><span class="p">,</span><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">P</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">    </span><span class="n">P</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">    </span><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="p">;</span>
+<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.java</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="cm">/* 連結リストでノード n0 の後にノード P を挿入 */</span>
-<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="n">n0</span><span class="p">,</span><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="n">P</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n0</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
-<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w">    </span><span class="n">P</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
-<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w">    </span><span class="n">n0</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="p">;</span>
-<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 連結リストでノード n0 の後ろにノード P を挿入する */</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="n">n0</span><span class="p">,</span><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="n">P</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n0</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="n">P</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">    </span><span class="n">n0</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="p">;</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.cs</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">linked_list</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 連結リストでノード n0 の後ろにノード P を挿入する */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Insert</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="n">n0</span><span class="p">,</span><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="n">P</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n0</span><span class="p">.</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="n">P</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">    </span><span class="n">n0</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="p">;</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.go</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">insertNode</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 連結リストでノード n0 の後ろにノード P を挿入する */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">insertNode</span><span class="p">(</span><span class="nx">n0</span><span class="w"> </span><span class="o">*</span><span class="nx">ListNode</span><span class="p">,</span><span class="w"> </span><span class="nx">P</span><span class="w"> </span><span class="o">*</span><span class="nx">ListNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="nx">n1</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">n0</span><span class="p">.</span><span class="nx">Next</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="nx">P</span><span class="p">.</span><span class="nx">Next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n1</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">    </span><span class="nx">n0</span><span class="p">.</span><span class="nx">Next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">P</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.swift</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="bp">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* 連結リストでノード n0 の後ろにノード P を挿入する */</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">n0</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode</span><span class="p">,</span><span class="w"> </span><span class="n">P</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">n1</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n0</span><span class="p">.</span><span class="n">next</span>
+<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w">    </span><span class="n">P</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n1</span>
+<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w">    </span><span class="n">n0</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">P</span>
+<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.js</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* 連結リストでノード n0 の後ろにノード P を挿入する */</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">insert</span><span class="p">(</span><span class="nx">n0</span><span class="p">,</span><span class="w"> </span><span class="nx">P</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n0</span><span class="p">.</span><span class="nx">next</span><span class="p">;</span>
+<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="w">    </span><span class="nx">P</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n1</span><span class="p">;</span>
+<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="w">    </span><span class="nx">n0</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">P</span><span class="p">;</span>
+<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.ts</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* 連結リストでノード n0 の後ろにノード P を挿入する */</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">insert</span><span class="p">(</span><span class="nx">n0</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="p">,</span><span class="w"> </span><span class="nx">P</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n0</span><span class="p">.</span><span class="nx">next</span><span class="p">;</span>
+<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w">    </span><span class="nx">P</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n1</span><span class="p">;</span>
+<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w">    </span><span class="nx">n0</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">P</span><span class="p">;</span>
+<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.dart</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* 連結リストでノード n0 の後ろにノード P を挿入する */</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">insert</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="n">n0</span><span class="p">,</span><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="n">P</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w">  </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n0</span><span class="p">.</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w">  </span><span class="n">P</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w">  </span><span class="n">n0</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="p">;</span>
+<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.rs</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* 連結リストでノード n0 の後ろにノード P を挿入する */</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="cp">#[allow(non_snake_case)]</span>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">insert</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">n0</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">P</span><span class="p">:</span><span class="w"> </span><span class="nc">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n0</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="p">.</span><span class="n">take</span><span class="p">();</span>
+<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="w">    </span><span class="n">P</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="w">    </span><span class="n">n0</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">P</span><span class="p">);</span>
+<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.c</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* 連結リストでノード n0 の後ろにノード P を挿入する */</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">n0</span><span class="p">,</span><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">P</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w">    </span><span class="n">P</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w">    </span><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="p">;</span>
+<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.kt</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* 連結リストでノード n0 の後ろにノード P を挿入する */</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">n0</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode?,</span><span class="w"> </span><span class="n">p</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode?)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n0</span><span class="o">?.</span><span class="na">next</span>
+<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w">    </span><span class="n">p</span><span class="o">?.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span>
+<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w">    </span><span class="n">n0</span><span class="o">?.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span>
+<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.rb</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="c1">### 連結リストのノード n0 の後にノード _p を挿入 ###</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="c1"># Ruby の `p` は組み込み関数で、`P` は定数なので、代わりに `_p` を使える</span>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">n0</span><span class="p">,</span><span class="w"> </span><span class="n">_p</span><span class="p">)</span>
+<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w">  </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n0</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="w">  </span><span class="n">_p</span><span class="o">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span>
+<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w">  </span><span class="n">n0</span><span class="o">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_p</span>
+<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E5%80%A4%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%BE%8C%E7%B6%9A%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%0Adef%20insert%28n0%3A%20ListNode%2C%20P%3A%20ListNode%29%3A%0A%20%20%20%20%22%22%22%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%81%A7%E3%83%8E%E3%83%BC%E3%83%89%20n0%20%E3%81%AE%E5%BE%8C%E3%82%8D%E3%81%AB%E3%83%8E%E3%83%BC%E3%83%89%20P%20%E3%82%92%E6%8C%BF%E5%85%A5%E3%81%99%E3%82%8B%22%22%22%0A%20%20%20%20n1%20%3D%20n0.next%0A%20%20%20%20P.next%20%3D%20n1%0A%20%20%20%20n0.next%20%3D%20P%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20%23%20%E5%90%84%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20n0%20%3D%20ListNode%281%29%0A%20%20%20%20n1%20%3D%20ListNode%283%29%0A%20%20%20%20n2%20%3D%20ListNode%282%29%0A%20%20%20%20n3%20%3D%20ListNode%285%29%0A%20%20%20%20n4%20%3D%20ListNode%284%29%0A%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E9%96%93%E3%81%AE%E5%8F%82%E7%85%A7%E3%82%92%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20n0.next%20%3D%20n1%0A%20%20%20%20n1.next%20%3D%20n2%0A%20%20%20%20n2.next%20%3D%20n3%0A%20%20%20%20n3.next%20%3D%20n4%0A%0A%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%8C%BF%E5%85%A5%0A%20%20%20%20p%20%3D%20ListNode%280%29%0A%20%20%20%20insert%28n0%2C%20p%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=39&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E5%80%A4%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%BE%8C%E7%B6%9A%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%0Adef%20insert%28n0%3A%20ListNode%2C%20P%3A%20ListNode%29%3A%0A%20%20%20%20%22%22%22%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%81%A7%E3%83%8E%E3%83%BC%E3%83%89%20n0%20%E3%81%AE%E5%BE%8C%E3%82%8D%E3%81%AB%E3%83%8E%E3%83%BC%E3%83%89%20P%20%E3%82%92%E6%8C%BF%E5%85%A5%E3%81%99%E3%82%8B%22%22%22%0A%20%20%20%20n1%20%3D%20n0.next%0A%20%20%20%20P.next%20%3D%20n1%0A%20%20%20%20n0.next%20%3D%20P%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20%23%20%E5%90%84%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20n0%20%3D%20ListNode%281%29%0A%20%20%20%20n1%20%3D%20ListNode%283%29%0A%20%20%20%20n2%20%3D%20ListNode%282%29%0A%20%20%20%20n3%20%3D%20ListNode%285%29%0A%20%20%20%20n4%20%3D%20ListNode%284%29%0A%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E9%96%93%E3%81%AE%E5%8F%82%E7%85%A7%E3%82%92%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20n0.next%20%3D%20n1%0A%20%20%20%20n1.next%20%3D%20n2%0A%20%20%20%20n2.next%20%3D%20n3%0A%20%20%20%20n3.next%20%3D%20n4%0A%0A%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%8C%BF%E5%85%A5%0A%20%20%20%20p%20%3D%20ListNode%280%29%0A%20%20%20%20insert%28n0%2C%20p%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=39&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 <h3 id="3">3. &nbsp; ノードの削除<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
-<p>下図に示すように、連結リストからノードを削除することも非常に簡単で、<strong>1つのノードの参照（ポインタ）を変更するだけです</strong>。</p>
-<p>重要な点は、ノード<code>P</code>が削除された後も<code>n1</code>を指し続けていることですが、連結リストの巡回中にはアクセスできなくなることです。これは事実上、<code>P</code>が連結リストの一部ではなくなったことを意味します。</p>
-<p><img alt="連結リストノードの削除" class="animation-figure" src="../linked_list.assets/linkedlist_remove_node.png" /></p>
-<p align="center"> 図 4-7 &nbsp; 連結リストノードの削除 </p>
+<p>下図に示すように、連結リストでのノード削除も非常に簡単で、<strong>1 つのノードの参照（ポインタ）を変更するだけで済みます</strong>。</p>
+<p>なお、削除操作が完了した後もノード <code>P</code> は依然として <code>n1</code> を指していますが、実際にはこの連結リストをたどっても <code>P</code> へはアクセスできません。つまり、<code>P</code> はすでにこの連結リストには属していません。</p>
+<p><img alt="連結リストのノード削除" class="animation-figure" src="../linked_list.assets/linkedlist_remove_node.png" /></p>
+<p align="center"> 図 4-7 &nbsp; 連結リストのノード削除 </p>
 
 <div class="tabbed-set tabbed-alternate" data-tabs="4:13"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.py</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">n0</span><span class="p">:</span> <span class="n">ListNode</span><span class="p">):</span>
-<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;連結リストのノード n0 の後の最初のノードを削除&quot;&quot;&quot;</span>
-<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a>    <span class="k">if</span> <span class="ow">not</span> <span class="n">n0</span><span class="o">.</span><span class="n">next</span><span class="p">:</span>
-<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a>        <span class="k">return</span>
-<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a>    <span class="c1"># n0 -&gt; P -&gt; n1</span>
-<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a>    <span class="n">P</span> <span class="o">=</span> <span class="n">n0</span><span class="o">.</span><span class="n">next</span>
-<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a>    <span class="n">n1</span> <span class="o">=</span> <span class="n">P</span><span class="o">.</span><span class="n">next</span>
-<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a>    <span class="n">n0</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">n1</span>
+<div class="highlight"><span class="filename">linked_list.py</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">n0</span><span class="p">:</span> <span class="n">ListNode</span><span class="p">):</span>
+<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;連結リストでノード n0 の直後のノードを削除する&quot;&quot;&quot;</span>
+<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a>    <span class="k">if</span> <span class="ow">not</span> <span class="n">n0</span><span class="o">.</span><span class="n">next</span><span class="p">:</span>
+<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a>        <span class="k">return</span>
+<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a>    <span class="c1"># n0 -&gt; P -&gt; n1</span>
+<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a>    <span class="n">P</span> <span class="o">=</span> <span class="n">n0</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a>    <span class="n">n1</span> <span class="o">=</span> <span class="n">P</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a>    <span class="n">n0</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">n1</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.cpp</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="cm">/* 連結リストのノードn0の後の最初のノードを削除 */</span>
-<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">n0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
-<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="w">    </span><span class="c1">// n0 -&gt; P -&gt; n1</span>
-<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
-<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
-<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="w">    </span><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
-<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="w">    </span><span class="c1">// メモリを解放</span>
-<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a><span class="w">    </span><span class="k">delete</span><span class="w"> </span><span class="n">P</span><span class="p">;</span>
-<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.cpp</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* 連結リストでノード n0 の直後のノードを削除する */</span>
+<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">n0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
+<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w">    </span><span class="c1">// n0 -&gt; P -&gt; n1</span>
+<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w">    </span><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w">    </span><span class="k">delete</span><span class="w"> </span><span class="n">P</span><span class="p">;</span>
+<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.java</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="cm">/* 連結リストでノード n0 の後の最初のノードを削除 */</span>
-<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="n">n0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n0</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
-<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a><span class="w">    </span><span class="c1">// n0 -&gt; P -&gt; n1</span>
-<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n0</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
-<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
-<a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a><span class="w">    </span><span class="n">n0</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
-<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.java</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 連結リストでノード n0 の直後のノードを削除する */</span>
+<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="n">n0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n0</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="w">    </span><span class="c1">// n0 -&gt; P -&gt; n1</span>
+<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n0</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
+<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
+<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a><span class="w">    </span><span class="n">n0</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.cs</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">linked_list</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.cs</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="cm">/* 連結リストでノード n0 の直後のノードを削除する */</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Remove</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="n">n0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n0</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="w">    </span><span class="c1">// n0 -&gt; P -&gt; n1</span>
+<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n0</span><span class="p">.</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="w">    </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="p">.</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a><span class="w">    </span><span class="n">n0</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.go</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">removeItem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.go</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* 連結リストでノード n0 の直後のノードを削除する */</span>
+<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">removeItem</span><span class="p">(</span><span class="nx">n0</span><span class="w"> </span><span class="o">*</span><span class="nx">ListNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">n0</span><span class="p">.</span><span class="nx">Next</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w">    </span><span class="c1">// n0 -&gt; P -&gt; n1</span>
+<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="w">    </span><span class="nx">P</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">n0</span><span class="p">.</span><span class="nx">Next</span>
+<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w">    </span><span class="nx">n1</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">P</span><span class="p">.</span><span class="nx">Next</span>
+<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w">    </span><span class="nx">n0</span><span class="p">.</span><span class="nx">Next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n1</span>
+<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.swift</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.swift</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* 連結リストでノード n0 の直後のノードを削除する */</span>
+<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">n0</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n0</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w">    </span><span class="c1">// n0 -&gt; P -&gt; n1</span>
+<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">P</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n0</span><span class="p">.</span><span class="n">next</span>
+<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">n1</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">P</span><span class="p">?.</span><span class="n">next</span>
+<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w">    </span><span class="n">n0</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n1</span>
+<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.js</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.js</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="cm">/* 連結リストでノード n0 の直後のノードを削除する */</span>
+<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">remove</span><span class="p">(</span><span class="nx">n0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="nx">n0</span><span class="p">.</span><span class="nx">next</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w">    </span><span class="c1">// n0 -&gt; P -&gt; n1</span>
+<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n0</span><span class="p">.</span><span class="nx">next</span><span class="p">;</span>
+<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">P</span><span class="p">.</span><span class="nx">next</span><span class="p">;</span>
+<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="w">    </span><span class="nx">n0</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n1</span><span class="p">;</span>
+<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.ts</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.ts</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="cm">/* 連結リストでノード n0 の直後のノードを削除する */</span>
+<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">remove</span><span class="p">(</span><span class="nx">n0</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="nx">n0</span><span class="p">.</span><span class="nx">next</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a><span class="w">    </span><span class="c1">// n0 -&gt; P -&gt; n1</span>
+<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n0</span><span class="p">.</span><span class="nx">next</span><span class="p">;</span>
+<a id="__codelineno-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">P</span><span class="p">.</span><span class="nx">next</span><span class="p">;</span>
+<a id="__codelineno-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></a><span class="w">    </span><span class="nx">n0</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n1</span><span class="p">;</span>
+<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.dart</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.dart</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* 連結リストでノード n0 の直後のノードを削除する */</span>
+<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="n">n0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n0</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w">  </span><span class="c1">// n0 -&gt; P -&gt; n1</span>
+<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="w">  </span><span class="n">ListNode</span><span class="w"> </span><span class="n">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n0</span><span class="p">.</span><span class="n">next</span><span class="o">!</span><span class="p">;</span>
+<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a><span class="w">  </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="p">.</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="w">  </span><span class="n">n0</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.rs</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.rs</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="cm">/* 連結リストでノード n0 の直後のノードを削除する */</span>
+<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="cp">#[allow(non_snake_case)]</span>
+<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">remove</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">n0</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a><span class="w">    </span><span class="c1">// n0 -&gt; P -&gt; n1</span>
+<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n0</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="p">.</span><span class="n">take</span><span class="p">();</span>
+<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="p">.</span><span class="n">take</span><span class="p">();</span>
+<a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a><span class="w">        </span><span class="n">n0</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.c</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">removeItem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.c</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* 連結リストでノード n0 の直後のノードを削除する */</span>
+<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="c1">// 注意: stdio.h が remove 識別子を使用している</span>
+<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="kt">void</span><span class="w"> </span><span class="nf">removeItem</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">n0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">)</span>
+<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a><span class="w">    </span><span class="c1">// n0 -&gt; P -&gt; n1</span>
+<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-49-9" name="__codelineno-49-9" href="#__codelineno-49-9"></a><span class="w">    </span><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-49-10" name="__codelineno-49-10" href="#__codelineno-49-10"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-49-11" name="__codelineno-49-11" href="#__codelineno-49-11"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">P</span><span class="p">);</span>
+<a id="__codelineno-49-12" name="__codelineno-49-12" href="#__codelineno-49-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.kt</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.kt</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* 連結リストでノード n0 の直後のノードを削除する */</span>
+<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">n0</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode?)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n0</span><span class="o">?.</span><span class="na">next</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="w">    </span><span class="c1">// n0 -&gt; P -&gt; n1</span>
+<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n0</span><span class="p">.</span><span class="na">next</span>
+<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="o">?.</span><span class="na">next</span>
+<a id="__codelineno-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a><span class="w">    </span><span class="n">n0</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span>
+<a id="__codelineno-50-9" name="__codelineno-50-9" href="#__codelineno-50-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.rb</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.rb</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="c1">### 連結リストのノード n0 の直後のノードを削除 ###</span>
+<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">n0</span><span class="p">)</span>
+<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n0</span><span class="o">.</span><span class="n">next</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a>
+<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w">  </span><span class="c1"># n0 -&gt; remove_node -&gt; n1</span>
+<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a><span class="w">  </span><span class="n">remove_node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n0</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="w">  </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">remove_node</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="w">  </span><span class="n">n0</span><span class="o">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span>
+<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E5%80%A4%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%BE%8C%E7%B6%9A%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%0Adef%20remove%28n0%3A%20ListNode%29%3A%0A%20%20%20%20%22%22%22%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%81%A7%E3%83%8E%E3%83%BC%E3%83%89%20n0%20%E3%81%AE%E7%9B%B4%E5%BE%8C%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E5%89%8A%E9%99%A4%E3%81%99%E3%82%8B%22%22%22%0A%20%20%20%20if%20not%20n0.next%3A%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20%23%20n0%20-%3E%20P%20-%3E%20n1%0A%20%20%20%20P%20%3D%20n0.next%0A%20%20%20%20n1%20%3D%20P.next%0A%20%20%20%20n0.next%20%3D%20n1%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20%23%20%E5%90%84%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20n0%20%3D%20ListNode%281%29%0A%20%20%20%20n1%20%3D%20ListNode%283%29%0A%20%20%20%20n2%20%3D%20ListNode%282%29%0A%20%20%20%20n3%20%3D%20ListNode%285%29%0A%20%20%20%20n4%20%3D%20ListNode%284%29%0A%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E9%96%93%E3%81%AE%E5%8F%82%E7%85%A7%E3%82%92%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20n0.next%20%3D%20n1%0A%20%20%20%20n1.next%20%3D%20n2%0A%20%20%20%20n2.next%20%3D%20n3%0A%20%20%20%20n3.next%20%3D%20n4%0A%0A%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E5%89%8A%E9%99%A4%0A%20%20%20%20remove%28n0%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=34&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E5%80%A4%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%BE%8C%E7%B6%9A%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%0Adef%20remove%28n0%3A%20ListNode%29%3A%0A%20%20%20%20%22%22%22%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%81%A7%E3%83%8E%E3%83%BC%E3%83%89%20n0%20%E3%81%AE%E7%9B%B4%E5%BE%8C%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E5%89%8A%E9%99%A4%E3%81%99%E3%82%8B%22%22%22%0A%20%20%20%20if%20not%20n0.next%3A%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20%23%20n0%20-%3E%20P%20-%3E%20n1%0A%20%20%20%20P%20%3D%20n0.next%0A%20%20%20%20n1%20%3D%20P.next%0A%20%20%20%20n0.next%20%3D%20n1%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20%23%20%E5%90%84%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20n0%20%3D%20ListNode%281%29%0A%20%20%20%20n1%20%3D%20ListNode%283%29%0A%20%20%20%20n2%20%3D%20ListNode%282%29%0A%20%20%20%20n3%20%3D%20ListNode%285%29%0A%20%20%20%20n4%20%3D%20ListNode%284%29%0A%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E9%96%93%E3%81%AE%E5%8F%82%E7%85%A7%E3%82%92%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20n0.next%20%3D%20n1%0A%20%20%20%20n1.next%20%3D%20n2%0A%20%20%20%20n2.next%20%3D%20n3%0A%20%20%20%20n3.next%20%3D%20n4%0A%0A%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E5%89%8A%E9%99%A4%0A%20%20%20%20remove%28n0%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=34&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 <h3 id="4">4. &nbsp; ノードへのアクセス<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
-<p><strong>連結リストでのノードへのアクセスは効率が悪いです</strong>。前述したように、配列の任意の要素には<span class="arithmatex">\(O(1)\)</span>時間でアクセスできます。対照的に、連結リストでは、プログラムはヘッドノードから開始して目的のノードが見つかるまで順次ノードを巡回する必要があります。つまり、連結リストの<span class="arithmatex">\(i\)</span>番目のノードにアクセスするには、プログラムは<span class="arithmatex">\(i - 1\)</span>個のノードを反復処理する必要があり、時間計算量は<span class="arithmatex">\(O(n)\)</span>になります。</p>
+<p>**連結リストでノードにアクセスする効率は低い**です。前節で述べたように、配列では任意の要素へ <span class="arithmatex">\(O(1)\)</span> 時間でアクセスできます。これに対して連結リストでは、プログラムは先頭ノードから出発し、1 つずつ後ろへたどって目的のノードを見つける必要があります。つまり、連結リストの第 <span class="arithmatex">\(i\)</span> ノードにアクセスするには <span class="arithmatex">\(i - 1\)</span> 回のループが必要であり、時間計算量は <span class="arithmatex">\(O(n)\)</span> です。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="5:13"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.py</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">access</span><span class="p">(</span><span class="n">head</span><span class="p">:</span> <span class="n">ListNode</span><span class="p">,</span> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;連結リストのインデックス index のノードにアクセス&quot;&quot;&quot;</span>
-<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">index</span><span class="p">):</span>
-<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a>        <span class="k">if</span> <span class="ow">not</span> <span class="n">head</span><span class="p">:</span>
-<a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a>            <span class="k">return</span> <span class="kc">None</span>
-<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a>        <span class="n">head</span> <span class="o">=</span> <span class="n">head</span><span class="o">.</span><span class="n">next</span>
-<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a>    <span class="k">return</span> <span class="n">head</span>
+<div class="highlight"><span class="filename">linked_list.py</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">access</span><span class="p">(</span><span class="n">head</span><span class="p">:</span> <span class="n">ListNode</span><span class="p">,</span> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;連結リスト内で index 番目のノードにアクセス&quot;&quot;&quot;</span>
+<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">index</span><span class="p">):</span>
+<a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a>        <span class="k">if</span> <span class="ow">not</span> <span class="n">head</span><span class="p">:</span>
+<a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a>            <span class="k">return</span> <span class="kc">None</span>
+<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a>        <span class="n">head</span> <span class="o">=</span> <span class="n">head</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></a>    <span class="k">return</span> <span class="n">head</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.cpp</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="cm">/* 連結リストの`index`番目のノードにアクセス */</span>
-<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="nf">access</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">head</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
-<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
-<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a><span class="w">        </span><span class="n">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
-<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">head</span><span class="p">;</span>
-<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.cpp</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 連結リスト内で index 番目のノードにアクセス */</span>
+<a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="nf">access</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">head</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
+<a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
+<a id="__codelineno-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></a><span class="w">        </span><span class="n">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">head</span><span class="p">;</span>
+<a id="__codelineno-53-9" name="__codelineno-53-9" href="#__codelineno-53-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.java</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="cm">/* 連結リストの `index` のノードにアクセス */</span>
-<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="n">ListNode</span><span class="w"> </span><span class="nf">access</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="n">head</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
-<a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
-<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a><span class="w">        </span><span class="n">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
-<a id="__codelineno-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-52-8" name="__codelineno-52-8" href="#__codelineno-52-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">head</span><span class="p">;</span>
-<a id="__codelineno-52-9" name="__codelineno-52-9" href="#__codelineno-52-9"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.java</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="cm">/* 連結リスト内で index 番目のノードにアクセス */</span>
+<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="n">ListNode</span><span class="w"> </span><span class="nf">access</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="n">head</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w">        </span><span class="n">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
+<a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">head</span><span class="p">;</span>
+<a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.cs</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">linked_list</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Access</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.cs</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="cm">/* 連結リスト内で index 番目のノードにアクセス */</span>
+<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">Access</span><span class="p">(</span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">head</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-4" name="__codelineno-55-4" href="#__codelineno-55-4"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span>
+<a id="__codelineno-55-5" name="__codelineno-55-5" href="#__codelineno-55-5"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
+<a id="__codelineno-55-6" name="__codelineno-55-6" href="#__codelineno-55-6"></a><span class="w">        </span><span class="n">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="p">.</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-55-7" name="__codelineno-55-7" href="#__codelineno-55-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-55-8" name="__codelineno-55-8" href="#__codelineno-55-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">head</span><span class="p">;</span>
+<a id="__codelineno-55-9" name="__codelineno-55-9" href="#__codelineno-55-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.go</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">access</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.go</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="cm">/* 連結リスト内で index 番目のノードにアクセス */</span>
+<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">access</span><span class="p">(</span><span class="nx">head</span><span class="w"> </span><span class="o">*</span><span class="nx">ListNode</span><span class="p">,</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">index</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">head</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a><span class="w">        </span><span class="nx">head</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">head</span><span class="p">.</span><span class="nx">Next</span>
+<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">head</span>
+<a id="__codelineno-56-10" name="__codelineno-56-10" href="#__codelineno-56-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.swift</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">access</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.swift</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 連結リスト内で index 番目のノードにアクセス */</span>
+<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">access</span><span class="p">(</span><span class="n">head</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode</span><span class="p">,</span><span class="w"> </span><span class="n">index</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">ListNode</span><span class="p">?</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">head</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode</span><span class="p">?</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">head</span>
+<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">head</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w">        </span><span class="n">head</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">head</span><span class="p">?.</span><span class="n">next</span>
+<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-57-10" name="__codelineno-57-10" href="#__codelineno-57-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">head</span>
+<a id="__codelineno-57-11" name="__codelineno-57-11" href="#__codelineno-57-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.js</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">access</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.js</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 連結リスト内で index 番目のノードにアクセス */</span>
+<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">access</span><span class="p">(</span><span class="nx">head</span><span class="p">,</span><span class="w"> </span><span class="nx">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">index</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="nx">head</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></a><span class="w">        </span><span class="nx">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">head</span><span class="p">.</span><span class="nx">next</span><span class="p">;</span>
+<a id="__codelineno-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">head</span><span class="p">;</span>
+<a id="__codelineno-58-10" name="__codelineno-58-10" href="#__codelineno-58-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.ts</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">access</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.ts</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="cm">/* 連結リスト内で index 番目のノードにアクセス */</span>
+<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">access</span><span class="p">(</span><span class="nx">head</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="nx">index</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="nx">ListNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">index</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-4" name="__codelineno-59-4" href="#__codelineno-59-4"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="nx">head</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-5" name="__codelineno-59-5" href="#__codelineno-59-5"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-59-6" name="__codelineno-59-6" href="#__codelineno-59-6"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-59-7" name="__codelineno-59-7" href="#__codelineno-59-7"></a><span class="w">        </span><span class="nx">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">head</span><span class="p">.</span><span class="nx">next</span><span class="p">;</span>
+<a id="__codelineno-59-8" name="__codelineno-59-8" href="#__codelineno-59-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-59-9" name="__codelineno-59-9" href="#__codelineno-59-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">head</span><span class="p">;</span>
+<a id="__codelineno-59-10" name="__codelineno-59-10" href="#__codelineno-59-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.dart</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">access</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.dart</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="cm">/* 連結リスト内で index 番目のノードにアクセス */</span>
+<a id="__codelineno-60-2" name="__codelineno-60-2" href="#__codelineno-60-2"></a><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">access</span><span class="p">(</span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">head</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-3" name="__codelineno-60-3" href="#__codelineno-60-3"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-4" name="__codelineno-60-4" href="#__codelineno-60-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-60-5" name="__codelineno-60-5" href="#__codelineno-60-5"></a><span class="w">    </span><span class="n">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="p">.</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-60-6" name="__codelineno-60-6" href="#__codelineno-60-6"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-60-7" name="__codelineno-60-7" href="#__codelineno-60-7"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">head</span><span class="p">;</span>
+<a id="__codelineno-60-8" name="__codelineno-60-8" href="#__codelineno-60-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.rs</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">access</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.rs</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="cm">/* 連結リスト内で index 番目のノードにアクセス */</span>
+<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">access</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">head</span><span class="p">:</span><span class="w"> </span><span class="nc">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">index</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-3" name="__codelineno-61-3" href="#__codelineno-61-3"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">dfs</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="p">(</span>
+<a id="__codelineno-61-4" name="__codelineno-61-4" href="#__codelineno-61-4"></a><span class="w">        </span><span class="n">head</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-61-5" name="__codelineno-61-5" href="#__codelineno-61-5"></a><span class="w">        </span><span class="n">index</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span>
+<a id="__codelineno-61-6" name="__codelineno-61-6" href="#__codelineno-61-6"></a><span class="w">    </span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-7" name="__codelineno-61-7" href="#__codelineno-61-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-8" name="__codelineno-61-8" href="#__codelineno-61-8"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">head</span><span class="p">.</span><span class="n">cloned</span><span class="p">();</span>
+<a id="__codelineno-61-9" name="__codelineno-61-9" href="#__codelineno-61-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-61-10" name="__codelineno-61-10" href="#__codelineno-61-10"></a>
+<a id="__codelineno-61-11" name="__codelineno-61-11" href="#__codelineno-61-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-12" name="__codelineno-61-12" href="#__codelineno-61-12"></a><span class="w">            </span><span class="n">dfs</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">next</span><span class="p">.</span><span class="n">as_ref</span><span class="p">(),</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-61-13" name="__codelineno-61-13" href="#__codelineno-61-13"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-14" name="__codelineno-61-14" href="#__codelineno-61-14"></a><span class="w">            </span><span class="nb">None</span>
+<a id="__codelineno-61-15" name="__codelineno-61-15" href="#__codelineno-61-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-61-16" name="__codelineno-61-16" href="#__codelineno-61-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-61-17" name="__codelineno-61-17" href="#__codelineno-61-17"></a>
+<a id="__codelineno-61-18" name="__codelineno-61-18" href="#__codelineno-61-18"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">head</span><span class="p">).</span><span class="n">as_ref</span><span class="p">(),</span><span class="w"> </span><span class="n">index</span><span class="p">)</span>
+<a id="__codelineno-61-19" name="__codelineno-61-19" href="#__codelineno-61-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.c</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">access</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.c</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="cm">/* 連結リスト内で index 番目のノードにアクセス */</span>
+<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="nf">access</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">head</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-4" name="__codelineno-62-4" href="#__codelineno-62-4"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span>
+<a id="__codelineno-62-5" name="__codelineno-62-5" href="#__codelineno-62-5"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-62-6" name="__codelineno-62-6" href="#__codelineno-62-6"></a><span class="w">        </span><span class="n">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-62-7" name="__codelineno-62-7" href="#__codelineno-62-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-62-8" name="__codelineno-62-8" href="#__codelineno-62-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">head</span><span class="p">;</span>
+<a id="__codelineno-62-9" name="__codelineno-62-9" href="#__codelineno-62-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.kt</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">access</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.kt</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="cm">/* 連結リスト内で index 番目のノードにアクセス */</span>
+<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">access</span><span class="p">(</span><span class="n">head</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode?,</span><span class="w"> </span><span class="n">index</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="n">ListNode? </span><span class="p">{</span>
+<a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">h</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span>
+<a id="__codelineno-63-4" name="__codelineno-63-4" href="#__codelineno-63-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-5" name="__codelineno-63-5" href="#__codelineno-63-5"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">h</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-63-6" name="__codelineno-63-6" href="#__codelineno-63-6"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span>
+<a id="__codelineno-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></a><span class="w">        </span><span class="n">h</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">h</span><span class="p">.</span><span class="na">next</span>
+<a id="__codelineno-63-8" name="__codelineno-63-8" href="#__codelineno-63-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-63-9" name="__codelineno-63-9" href="#__codelineno-63-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">h</span>
+<a id="__codelineno-63-10" name="__codelineno-63-10" href="#__codelineno-63-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.rb</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">access</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.rb</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="c1">### 連結リスト内の index 番目のノードにアクセス ###</span>
+<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">access</span><span class="p">(</span><span class="n">head</span><span class="p">,</span><span class="w"> </span><span class="n">index</span><span class="p">)</span>
+<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">index</span>
+<a id="__codelineno-64-4" name="__codelineno-64-4" href="#__codelineno-64-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="kp">nil</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">head</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-64-5" name="__codelineno-64-5" href="#__codelineno-64-5"></a><span class="w">    </span><span class="n">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-64-6" name="__codelineno-64-6" href="#__codelineno-64-6"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-64-7" name="__codelineno-64-7" href="#__codelineno-64-7"></a>
+<a id="__codelineno-64-8" name="__codelineno-64-8" href="#__codelineno-64-8"></a><span class="w">  </span><span class="n">head</span>
+<a id="__codelineno-64-9" name="__codelineno-64-9" href="#__codelineno-64-9"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h3 id="5">5. &nbsp; ノードの検索<a class="headerlink" href="#5" title="Permanent link">&para;</a></h3>
-<p>連結リストを巡回して、値が<code>target</code>に一致するノードを見つけ、連結リスト内でのそのノードのインデックスを出力します。この手順も線形検索の例です。対応するコードは以下のとおりです：</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E5%80%A4%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%BE%8C%E7%B6%9A%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%0Adef%20access%28head%3A%20ListNode%2C%20index%3A%20int%29%20-%3E%20ListNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E5%86%85%E3%81%A7%20index%20%E7%95%AA%E7%9B%AE%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AB%E3%82%A2%E3%82%AF%E3%82%BB%E3%82%B9%22%22%22%0A%20%20%20%20for%20_%20in%20range%28index%29%3A%0A%20%20%20%20%20%20%20%20if%20not%20head%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%20%20%20%20head%20%3D%20head.next%0A%20%20%20%20return%20head%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20%23%20%E5%90%84%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20n0%20%3D%20ListNode%281%29%0A%20%20%20%20n1%20%3D%20ListNode%283%29%0A%20%20%20%20n2%20%3D%20ListNode%282%29%0A%20%20%20%20n3%20%3D%20ListNode%285%29%0A%20%20%20%20n4%20%3D%20ListNode%284%29%0A%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E9%96%93%E3%81%AE%E5%8F%82%E7%85%A7%E3%82%92%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20n0.next%20%3D%20n1%0A%20%20%20%20n1.next%20%3D%20n2%0A%20%20%20%20n2.next%20%3D%20n3%0A%20%20%20%20n3.next%20%3D%20n4%0A%0A%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AB%E3%82%A2%E3%82%AF%E3%82%BB%E3%82%B9%0A%20%20%20%20node%20%3D%20access%28n0%2C%203%29%0A%20%20%20%20print%28%22%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%203%20%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AE%E5%80%A4%20%3D%20%7B%7D%22.format%28node.val%29%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=34&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E5%80%A4%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%BE%8C%E7%B6%9A%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%0Adef%20access%28head%3A%20ListNode%2C%20index%3A%20int%29%20-%3E%20ListNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E5%86%85%E3%81%A7%20index%20%E7%95%AA%E7%9B%AE%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AB%E3%82%A2%E3%82%AF%E3%82%BB%E3%82%B9%22%22%22%0A%20%20%20%20for%20_%20in%20range%28index%29%3A%0A%20%20%20%20%20%20%20%20if%20not%20head%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%20%20%20%20head%20%3D%20head.next%0A%20%20%20%20return%20head%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20%23%20%E5%90%84%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20n0%20%3D%20ListNode%281%29%0A%20%20%20%20n1%20%3D%20ListNode%283%29%0A%20%20%20%20n2%20%3D%20ListNode%282%29%0A%20%20%20%20n3%20%3D%20ListNode%285%29%0A%20%20%20%20n4%20%3D%20ListNode%284%29%0A%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E9%96%93%E3%81%AE%E5%8F%82%E7%85%A7%E3%82%92%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20n0.next%20%3D%20n1%0A%20%20%20%20n1.next%20%3D%20n2%0A%20%20%20%20n2.next%20%3D%20n3%0A%20%20%20%20n3.next%20%3D%20n4%0A%0A%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AB%E3%82%A2%E3%82%AF%E3%82%BB%E3%82%B9%0A%20%20%20%20node%20%3D%20access%28n0%2C%203%29%0A%20%20%20%20print%28%22%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%203%20%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AE%E5%80%A4%20%3D%20%7B%7D%22.format%28node.val%29%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=34&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h3 id="5">5. &nbsp; ノードの探索<a class="headerlink" href="#5" title="Permanent link">&para;</a></h3>
+<p>連結リストを走査し、その中から値が <code>target</code> のノードを探し、そのノードの連結リスト内でのインデックスを出力します。この処理も線形探索に属します。コードは次のとおりです。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="6:13"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><input id="__tabbed_6_13" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Kotlin</label><label for="__tabbed_6_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.py</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="n">head</span><span class="p">:</span> <span class="n">ListNode</span><span class="p">,</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;連結リストで値 target を持つ最初のノードを検索&quot;&quot;&quot;</span>
-<a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a>    <span class="n">index</span> <span class="o">=</span> <span class="mi">0</span>
-<a id="__codelineno-63-4" name="__codelineno-63-4" href="#__codelineno-63-4"></a>    <span class="k">while</span> <span class="n">head</span><span class="p">:</span>
-<a id="__codelineno-63-5" name="__codelineno-63-5" href="#__codelineno-63-5"></a>        <span class="k">if</span> <span class="n">head</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="n">target</span><span class="p">:</span>
-<a id="__codelineno-63-6" name="__codelineno-63-6" href="#__codelineno-63-6"></a>            <span class="k">return</span> <span class="n">index</span>
-<a id="__codelineno-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></a>        <span class="n">head</span> <span class="o">=</span> <span class="n">head</span><span class="o">.</span><span class="n">next</span>
-<a id="__codelineno-63-8" name="__codelineno-63-8" href="#__codelineno-63-8"></a>        <span class="n">index</span> <span class="o">+=</span> <span class="mi">1</span>
-<a id="__codelineno-63-9" name="__codelineno-63-9" href="#__codelineno-63-9"></a>    <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>
+<div class="highlight"><span class="filename">linked_list.py</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="n">head</span><span class="p">:</span> <span class="n">ListNode</span><span class="p">,</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;連結リストで値が target の最初のノードを探す&quot;&quot;&quot;</span>
+<a id="__codelineno-65-3" name="__codelineno-65-3" href="#__codelineno-65-3"></a>    <span class="n">index</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-65-4" name="__codelineno-65-4" href="#__codelineno-65-4"></a>    <span class="k">while</span> <span class="n">head</span><span class="p">:</span>
+<a id="__codelineno-65-5" name="__codelineno-65-5" href="#__codelineno-65-5"></a>        <span class="k">if</span> <span class="n">head</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="n">target</span><span class="p">:</span>
+<a id="__codelineno-65-6" name="__codelineno-65-6" href="#__codelineno-65-6"></a>            <span class="k">return</span> <span class="n">index</span>
+<a id="__codelineno-65-7" name="__codelineno-65-7" href="#__codelineno-65-7"></a>        <span class="n">head</span> <span class="o">=</span> <span class="n">head</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-65-8" name="__codelineno-65-8" href="#__codelineno-65-8"></a>        <span class="n">index</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-65-9" name="__codelineno-65-9" href="#__codelineno-65-9"></a>    <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.cpp</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="cm">/* 連結リストで値がtargetの最初のノードを検索 */</span>
-<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">head</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-64-4" name="__codelineno-64-4" href="#__codelineno-64-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-64-5" name="__codelineno-64-5" href="#__codelineno-64-5"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
-<a id="__codelineno-64-6" name="__codelineno-64-6" href="#__codelineno-64-6"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
-<a id="__codelineno-64-7" name="__codelineno-64-7" href="#__codelineno-64-7"></a><span class="w">        </span><span class="n">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
-<a id="__codelineno-64-8" name="__codelineno-64-8" href="#__codelineno-64-8"></a><span class="w">        </span><span class="n">index</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-64-9" name="__codelineno-64-9" href="#__codelineno-64-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-64-10" name="__codelineno-64-10" href="#__codelineno-64-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
-<a id="__codelineno-64-11" name="__codelineno-64-11" href="#__codelineno-64-11"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.cpp</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="cm">/* 連結リストで値が target の最初のノードを探す */</span>
+<a id="__codelineno-66-2" name="__codelineno-66-2" href="#__codelineno-66-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">head</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-66-3" name="__codelineno-66-3" href="#__codelineno-66-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-66-4" name="__codelineno-66-4" href="#__codelineno-66-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-66-5" name="__codelineno-66-5" href="#__codelineno-66-5"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-66-6" name="__codelineno-66-6" href="#__codelineno-66-6"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
+<a id="__codelineno-66-7" name="__codelineno-66-7" href="#__codelineno-66-7"></a><span class="w">        </span><span class="n">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-66-8" name="__codelineno-66-8" href="#__codelineno-66-8"></a><span class="w">        </span><span class="n">index</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-66-9" name="__codelineno-66-9" href="#__codelineno-66-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-66-10" name="__codelineno-66-10" href="#__codelineno-66-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-66-11" name="__codelineno-66-11" href="#__codelineno-66-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.java</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="cm">/* 連結リストで値 target を持つ最初のノードを検索 */</span>
-<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="n">head</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-65-3" name="__codelineno-65-3" href="#__codelineno-65-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-65-4" name="__codelineno-65-4" href="#__codelineno-65-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-65-5" name="__codelineno-65-5" href="#__codelineno-65-5"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
-<a id="__codelineno-65-6" name="__codelineno-65-6" href="#__codelineno-65-6"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
-<a id="__codelineno-65-7" name="__codelineno-65-7" href="#__codelineno-65-7"></a><span class="w">        </span><span class="n">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
-<a id="__codelineno-65-8" name="__codelineno-65-8" href="#__codelineno-65-8"></a><span class="w">        </span><span class="n">index</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-65-9" name="__codelineno-65-9" href="#__codelineno-65-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-65-10" name="__codelineno-65-10" href="#__codelineno-65-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-65-11" name="__codelineno-65-11" href="#__codelineno-65-11"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.java</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="cm">/* 連結リストで値が target の最初のノードを探す */</span>
+<a id="__codelineno-67-2" name="__codelineno-67-2" href="#__codelineno-67-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="n">head</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-67-3" name="__codelineno-67-3" href="#__codelineno-67-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-67-4" name="__codelineno-67-4" href="#__codelineno-67-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-67-5" name="__codelineno-67-5" href="#__codelineno-67-5"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-67-6" name="__codelineno-67-6" href="#__codelineno-67-6"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
+<a id="__codelineno-67-7" name="__codelineno-67-7" href="#__codelineno-67-7"></a><span class="w">        </span><span class="n">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
+<a id="__codelineno-67-8" name="__codelineno-67-8" href="#__codelineno-67-8"></a><span class="w">        </span><span class="n">index</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-67-9" name="__codelineno-67-9" href="#__codelineno-67-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-67-10" name="__codelineno-67-10" href="#__codelineno-67-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-67-11" name="__codelineno-67-11" href="#__codelineno-67-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.cs</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">linked_list</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Find</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.cs</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="cm">/* 連結リストで値が target の最初のノードを探す */</span>
+<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Find</span><span class="p">(</span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">head</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-68-3" name="__codelineno-68-3" href="#__codelineno-68-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-68-4" name="__codelineno-68-4" href="#__codelineno-68-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-68-5" name="__codelineno-68-5" href="#__codelineno-68-5"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-68-6" name="__codelineno-68-6" href="#__codelineno-68-6"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
+<a id="__codelineno-68-7" name="__codelineno-68-7" href="#__codelineno-68-7"></a><span class="w">        </span><span class="n">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="p">.</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-68-8" name="__codelineno-68-8" href="#__codelineno-68-8"></a><span class="w">        </span><span class="n">index</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-68-9" name="__codelineno-68-9" href="#__codelineno-68-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-68-10" name="__codelineno-68-10" href="#__codelineno-68-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-68-11" name="__codelineno-68-11" href="#__codelineno-68-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.go</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">findNode</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.go</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="cm">/* 連結リストで値が target の最初のノードを探す */</span>
+<a id="__codelineno-69-2" name="__codelineno-69-2" href="#__codelineno-69-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">findNode</span><span class="p">(</span><span class="nx">head</span><span class="w"> </span><span class="o">*</span><span class="nx">ListNode</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-3" name="__codelineno-69-3" href="#__codelineno-69-3"></a><span class="w">    </span><span class="nx">index</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-69-4" name="__codelineno-69-4" href="#__codelineno-69-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">head</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-5" name="__codelineno-69-5" href="#__codelineno-69-5"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">head</span><span class="p">.</span><span class="nx">Val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-6" name="__codelineno-69-6" href="#__codelineno-69-6"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nx">index</span>
+<a id="__codelineno-69-7" name="__codelineno-69-7" href="#__codelineno-69-7"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-69-8" name="__codelineno-69-8" href="#__codelineno-69-8"></a><span class="w">        </span><span class="nx">head</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">head</span><span class="p">.</span><span class="nx">Next</span>
+<a id="__codelineno-69-9" name="__codelineno-69-9" href="#__codelineno-69-9"></a><span class="w">        </span><span class="nx">index</span><span class="o">++</span>
+<a id="__codelineno-69-10" name="__codelineno-69-10" href="#__codelineno-69-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-69-11" name="__codelineno-69-11" href="#__codelineno-69-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-69-12" name="__codelineno-69-12" href="#__codelineno-69-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.swift</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="bp">find</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.swift</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="cm">/* 連結リストで値が target の最初のノードを探す */</span>
+<a id="__codelineno-70-2" name="__codelineno-70-2" href="#__codelineno-70-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="n">head</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-3" name="__codelineno-70-3" href="#__codelineno-70-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">head</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode</span><span class="p">?</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">head</span>
+<a id="__codelineno-70-4" name="__codelineno-70-4" href="#__codelineno-70-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">index</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-70-5" name="__codelineno-70-5" href="#__codelineno-70-5"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">head</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-6" name="__codelineno-70-6" href="#__codelineno-70-6"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">head</span><span class="p">?.</span><span class="n">val</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-7" name="__codelineno-70-7" href="#__codelineno-70-7"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">index</span>
+<a id="__codelineno-70-8" name="__codelineno-70-8" href="#__codelineno-70-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-70-9" name="__codelineno-70-9" href="#__codelineno-70-9"></a><span class="w">        </span><span class="n">head</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">head</span><span class="p">?.</span><span class="n">next</span>
+<a id="__codelineno-70-10" name="__codelineno-70-10" href="#__codelineno-70-10"></a><span class="w">        </span><span class="n">index</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-70-11" name="__codelineno-70-11" href="#__codelineno-70-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-70-12" name="__codelineno-70-12" href="#__codelineno-70-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-70-13" name="__codelineno-70-13" href="#__codelineno-70-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.js</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">find</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.js</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="cm">/* 連結リストで値が target の最初のノードを探す */</span>
+<a id="__codelineno-71-2" name="__codelineno-71-2" href="#__codelineno-71-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">find</span><span class="p">(</span><span class="nx">head</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-3" name="__codelineno-71-3" href="#__codelineno-71-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-71-4" name="__codelineno-71-4" href="#__codelineno-71-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">head</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-5" name="__codelineno-71-5" href="#__codelineno-71-5"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">head</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-6" name="__codelineno-71-6" href="#__codelineno-71-6"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nx">index</span><span class="p">;</span>
+<a id="__codelineno-71-7" name="__codelineno-71-7" href="#__codelineno-71-7"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-71-8" name="__codelineno-71-8" href="#__codelineno-71-8"></a><span class="w">        </span><span class="nx">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">head</span><span class="p">.</span><span class="nx">next</span><span class="p">;</span>
+<a id="__codelineno-71-9" name="__codelineno-71-9" href="#__codelineno-71-9"></a><span class="w">        </span><span class="nx">index</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-71-10" name="__codelineno-71-10" href="#__codelineno-71-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-71-11" name="__codelineno-71-11" href="#__codelineno-71-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-71-12" name="__codelineno-71-12" href="#__codelineno-71-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.ts</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">find</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.ts</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="cm">/* 連結リストで値が target の最初のノードを探す */</span>
+<a id="__codelineno-72-2" name="__codelineno-72-2" href="#__codelineno-72-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">find</span><span class="p">(</span><span class="nx">head</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-3" name="__codelineno-72-3" href="#__codelineno-72-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-72-4" name="__codelineno-72-4" href="#__codelineno-72-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">head</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-5" name="__codelineno-72-5" href="#__codelineno-72-5"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">head</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-6" name="__codelineno-72-6" href="#__codelineno-72-6"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nx">index</span><span class="p">;</span>
+<a id="__codelineno-72-7" name="__codelineno-72-7" href="#__codelineno-72-7"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-72-8" name="__codelineno-72-8" href="#__codelineno-72-8"></a><span class="w">        </span><span class="nx">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">head</span><span class="p">.</span><span class="nx">next</span><span class="p">;</span>
+<a id="__codelineno-72-9" name="__codelineno-72-9" href="#__codelineno-72-9"></a><span class="w">        </span><span class="nx">index</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-72-10" name="__codelineno-72-10" href="#__codelineno-72-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-72-11" name="__codelineno-72-11" href="#__codelineno-72-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-72-12" name="__codelineno-72-12" href="#__codelineno-72-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.dart</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">find</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.dart</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="cm">/* 連結リストで値が target の最初のノードを探す */</span>
+<a id="__codelineno-73-2" name="__codelineno-73-2" href="#__codelineno-73-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">find</span><span class="p">(</span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">head</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-73-3" name="__codelineno-73-3" href="#__codelineno-73-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-73-4" name="__codelineno-73-4" href="#__codelineno-73-4"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-73-5" name="__codelineno-73-5" href="#__codelineno-73-5"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-73-6" name="__codelineno-73-6" href="#__codelineno-73-6"></a><span class="w">      </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
+<a id="__codelineno-73-7" name="__codelineno-73-7" href="#__codelineno-73-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-73-8" name="__codelineno-73-8" href="#__codelineno-73-8"></a><span class="w">    </span><span class="n">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="p">.</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-73-9" name="__codelineno-73-9" href="#__codelineno-73-9"></a><span class="w">    </span><span class="n">index</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-73-10" name="__codelineno-73-10" href="#__codelineno-73-10"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-73-11" name="__codelineno-73-11" href="#__codelineno-73-11"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-73-12" name="__codelineno-73-12" href="#__codelineno-73-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.rs</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">find</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.rs</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="cm">/* 連結リストで値が target の最初のノードを探す */</span>
+<a id="__codelineno-74-2" name="__codelineno-74-2" href="#__codelineno-74-2"></a><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">find</span><span class="o">&lt;</span><span class="n">T</span><span class="p">:</span><span class="w"> </span><span class="nb">PartialEq</span><span class="o">&gt;</span><span class="p">(</span><span class="n">head</span><span class="p">:</span><span class="w"> </span><span class="nc">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="nc">T</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-3" name="__codelineno-74-3" href="#__codelineno-74-3"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">find</span><span class="o">&lt;</span><span class="n">T</span><span class="p">:</span><span class="w"> </span><span class="nb">PartialEq</span><span class="o">&gt;</span><span class="p">(</span><span class="n">head</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="nc">T</span><span class="p">,</span><span class="w"> </span><span class="n">idx</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-4" name="__codelineno-74-4" href="#__codelineno-74-4"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-5" name="__codelineno-74-5" href="#__codelineno-74-5"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-6" name="__codelineno-74-6" href="#__codelineno-74-6"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="n">idx</span><span class="p">;</span>
+<a id="__codelineno-74-7" name="__codelineno-74-7" href="#__codelineno-74-7"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-74-8" name="__codelineno-74-8" href="#__codelineno-74-8"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">find</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">next</span><span class="p">.</span><span class="n">as_ref</span><span class="p">(),</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">idx</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-74-9" name="__codelineno-74-9" href="#__codelineno-74-9"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-10" name="__codelineno-74-10" href="#__codelineno-74-10"></a><span class="w">            </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-74-11" name="__codelineno-74-11" href="#__codelineno-74-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-74-12" name="__codelineno-74-12" href="#__codelineno-74-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-74-13" name="__codelineno-74-13" href="#__codelineno-74-13"></a>
+<a id="__codelineno-74-14" name="__codelineno-74-14" href="#__codelineno-74-14"></a><span class="w">    </span><span class="n">find</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">head</span><span class="p">).</span><span class="n">as_ref</span><span class="p">(),</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-74-15" name="__codelineno-74-15" href="#__codelineno-74-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.c</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">find</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.c</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="cm">/* 連結リストで値が target の最初のノードを探す */</span>
+<a id="__codelineno-75-2" name="__codelineno-75-2" href="#__codelineno-75-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">head</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-75-3" name="__codelineno-75-3" href="#__codelineno-75-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-75-4" name="__codelineno-75-4" href="#__codelineno-75-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-75-5" name="__codelineno-75-5" href="#__codelineno-75-5"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-75-6" name="__codelineno-75-6" href="#__codelineno-75-6"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
+<a id="__codelineno-75-7" name="__codelineno-75-7" href="#__codelineno-75-7"></a><span class="w">        </span><span class="n">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-75-8" name="__codelineno-75-8" href="#__codelineno-75-8"></a><span class="w">        </span><span class="n">index</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-75-9" name="__codelineno-75-9" href="#__codelineno-75-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-75-10" name="__codelineno-75-10" href="#__codelineno-75-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-75-11" name="__codelineno-75-11" href="#__codelineno-75-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.kt</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">find</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.kt</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="cm">/* 連結リストで値が target の最初のノードを探す */</span>
+<a id="__codelineno-76-2" name="__codelineno-76-2" href="#__codelineno-76-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="n">head</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode?,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-76-3" name="__codelineno-76-3" href="#__codelineno-76-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-76-4" name="__codelineno-76-4" href="#__codelineno-76-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">h</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span>
+<a id="__codelineno-76-5" name="__codelineno-76-5" href="#__codelineno-76-5"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">h</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-76-6" name="__codelineno-76-6" href="#__codelineno-76-6"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">h</span><span class="p">.</span><span class="na">_val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-76-7" name="__codelineno-76-7" href="#__codelineno-76-7"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">index</span>
+<a id="__codelineno-76-8" name="__codelineno-76-8" href="#__codelineno-76-8"></a><span class="w">        </span><span class="n">h</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">h</span><span class="p">.</span><span class="na">next</span>
+<a id="__codelineno-76-9" name="__codelineno-76-9" href="#__codelineno-76-9"></a><span class="w">        </span><span class="n">index</span><span class="o">++</span>
+<a id="__codelineno-76-10" name="__codelineno-76-10" href="#__codelineno-76-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-76-11" name="__codelineno-76-11" href="#__codelineno-76-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="m">1</span>
+<a id="__codelineno-76-12" name="__codelineno-76-12" href="#__codelineno-76-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linked_list.rb</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">find</span><span class="p">}</span>
+<div class="highlight"><span class="filename">linked_list.rb</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="c1">### 連結リストで値が target の最初のノードを探す ###</span>
+<a id="__codelineno-77-2" name="__codelineno-77-2" href="#__codelineno-77-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="n">head</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-77-3" name="__codelineno-77-3" href="#__codelineno-77-3"></a><span class="w">  </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-77-4" name="__codelineno-77-4" href="#__codelineno-77-4"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="n">head</span>
+<a id="__codelineno-77-5" name="__codelineno-77-5" href="#__codelineno-77-5"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">head</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span>
+<a id="__codelineno-77-6" name="__codelineno-77-6" href="#__codelineno-77-6"></a><span class="w">    </span><span class="n">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-77-7" name="__codelineno-77-7" href="#__codelineno-77-7"></a><span class="w">    </span><span class="n">index</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-77-8" name="__codelineno-77-8" href="#__codelineno-77-8"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-77-9" name="__codelineno-77-9" href="#__codelineno-77-9"></a>
+<a id="__codelineno-77-10" name="__codelineno-77-10" href="#__codelineno-77-10"></a><span class="w">  </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-77-11" name="__codelineno-77-11" href="#__codelineno-77-11"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E5%80%A4%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%BE%8C%E7%B6%9A%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%0Adef%20find%28head%3A%20ListNode%2C%20target%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%81%A7%E5%80%A4%E3%81%8C%20target%20%E3%81%AE%E6%9C%80%E5%88%9D%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%8E%A2%E3%81%99%22%22%22%0A%20%20%20%20index%20%3D%200%0A%20%20%20%20while%20head%3A%0A%20%20%20%20%20%20%20%20if%20head.val%20%3D%3D%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20index%0A%20%20%20%20%20%20%20%20head%20%3D%20head.next%0A%20%20%20%20%20%20%20%20index%20%2B%3D%201%0A%20%20%20%20return%20-1%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20%23%20%E5%90%84%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20n0%20%3D%20ListNode%281%29%0A%20%20%20%20n1%20%3D%20ListNode%283%29%0A%20%20%20%20n2%20%3D%20ListNode%282%29%0A%20%20%20%20n3%20%3D%20ListNode%285%29%0A%20%20%20%20n4%20%3D%20ListNode%284%29%0A%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E9%96%93%E3%81%AE%E5%8F%82%E7%85%A7%E3%82%92%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20n0.next%20%3D%20n1%0A%20%20%20%20n1.next%20%3D%20n2%0A%20%20%20%20n2.next%20%3D%20n3%0A%20%20%20%20n3.next%20%3D%20n4%0A%0A%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%8E%A2%E7%B4%A2%0A%20%20%20%20index%20%3D%20find%28n0%2C%202%29%0A%20%20%20%20print%28%22%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E5%86%85%E3%81%A7%E5%80%A4%E3%81%8C%202%20%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20%3D%20%7B%7D%22.format%28index%29%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=34&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E5%80%A4%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%BE%8C%E7%B6%9A%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%0Adef%20find%28head%3A%20ListNode%2C%20target%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%81%A7%E5%80%A4%E3%81%8C%20target%20%E3%81%AE%E6%9C%80%E5%88%9D%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%8E%A2%E3%81%99%22%22%22%0A%20%20%20%20index%20%3D%200%0A%20%20%20%20while%20head%3A%0A%20%20%20%20%20%20%20%20if%20head.val%20%3D%3D%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20index%0A%20%20%20%20%20%20%20%20head%20%3D%20head.next%0A%20%20%20%20%20%20%20%20index%20%2B%3D%201%0A%20%20%20%20return%20-1%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20%23%20%E5%90%84%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20n0%20%3D%20ListNode%281%29%0A%20%20%20%20n1%20%3D%20ListNode%283%29%0A%20%20%20%20n2%20%3D%20ListNode%282%29%0A%20%20%20%20n3%20%3D%20ListNode%285%29%0A%20%20%20%20n4%20%3D%20ListNode%284%29%0A%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E9%96%93%E3%81%AE%E5%8F%82%E7%85%A7%E3%82%92%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20n0.next%20%3D%20n1%0A%20%20%20%20n1.next%20%3D%20n2%0A%20%20%20%20n2.next%20%3D%20n3%0A%20%20%20%20n3.next%20%3D%20n4%0A%0A%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%8E%A2%E7%B4%A2%0A%20%20%20%20index%20%3D%20find%28n0%2C%202%29%0A%20%20%20%20print%28%22%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E5%86%85%E3%81%A7%E5%80%A4%E3%81%8C%202%20%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20%3D%20%7B%7D%22.format%28index%29%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=34&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 <h2 id="422-vs">4.2.2 &nbsp; 配列 vs. 連結リスト<a class="headerlink" href="#422-vs" title="Permanent link">&para;</a></h2>
-<p>下表は配列と連結リストの特性をまとめ、様々な操作における効率も比較しています。それぞれが対照的な格納戦略を使用するため、それぞれの特性と操作効率は明確に対比されています。</p>
+<p>次の表は、配列と連結リストの各種特徴と操作効率をまとめたものです。両者は互いに逆の格納戦略を採用しているため、各種性質や操作効率にも対照的な特徴が現れます。</p>
 <p align="center"> 表 4-1 &nbsp; 配列と連結リストの効率比較 </p>
 
 <div class="center-table">
@@ -5186,18 +5597,18 @@
 <tbody>
 <tr>
 <td>格納方式</td>
-<td>連続メモリ空間</td>
-<td>分散メモリ空間</td>
+<td>連続したメモリ空間</td>
+<td>分散したメモリ空間</td>
 </tr>
 <tr>
 <td>容量拡張</td>
-<td>固定長</td>
-<td>柔軟な拡張</td>
+<td>長さは不変</td>
+<td>柔軟に拡張可能</td>
 </tr>
 <tr>
 <td>メモリ効率</td>
-<td>要素あたりのメモリ少、潜在的な空間の無駄</td>
-<td>要素あたりのメモリ多</td>
+<td>要素のメモリ消費は少ないが、空間を無駄にする可能性がある</td>
+<td>要素のメモリ消費が多い</td>
 </tr>
 <tr>
 <td>要素へのアクセス</td>
@@ -5217,188 +5628,209 @@
 </tbody>
 </table>
 </div>
-<h2 id="423">4.2.3 &nbsp; 連結リストの一般的な種類<a class="headerlink" href="#423" title="Permanent link">&para;</a></h2>
-<p>下図に示すように、連結リストには3つの一般的な種類があります。</p>
+<h2 id="423">4.2.3 &nbsp; 一般的な連結リストの種類<a class="headerlink" href="#423" title="Permanent link">&para;</a></h2>
+<p>下図に示すように、一般的な連結リストの種類は 3 つあります。</p>
 <ul>
-<li><strong>単方向連結リスト</strong>：これは前述した標準的な連結リストです。単方向連結リストのノードには値と次のノードへの参照が含まれます。最初のノードはヘッドノードと呼ばれ、null（<code>None</code>）を指す最後のノードはテールノードです。</li>
-<li><strong>循環連結リスト</strong>：これは単方向連結リストのテールノードがヘッドノードを指してループを作ることで形成されます。循環連結リストでは、任意のノードがヘッドノードとして機能できます。</li>
-<li><strong>双方向連結リスト</strong>：単方向連結リストとは対照的に、双方向連結リストは2つの方向で参照を維持します。各ノードには後続者（次のノード）と前任者（前のノード）の両方への参照（ポインタ）が含まれます。双方向連結リストはどちらの方向にも巡回できるより多くの柔軟性を提供しますが、より多くのメモリ空間も消費します。</li>
+<li><strong>単方向連結リスト</strong>：前述した通常の連結リストのことです。単方向連結リストのノードは、値と次のノードを指す参照の 2 つのデータを含みます。最初のノードを先頭ノード、最後のノードを末尾ノードと呼び、末尾ノードは空 <code>None</code> を指します。</li>
+<li><strong>循環連結リスト</strong>：単方向連結リストの末尾ノードを先頭ノードへ向けると（先頭と末尾をつなぐと）、循環連結リストが得られます。循環連結リストでは、任意のノードを先頭ノードとみなせます。</li>
+<li><strong>双方向連結リスト</strong>：単方向連結リストと比べて、双方向連結リストは 2 方向の参照を記録します。双方向連結リストのノード定義には、後続ノード（次のノード）と前駆ノード（前のノード）を指す参照（ポインタ）が含まれます。単方向連結リストより柔軟で、2 方向に連結リストを走査できますが、そのぶん多くのメモリ空間を必要とします。</li>
 </ul>
-<div class="tabbed-set tabbed-alternate" data-tabs="7:12"><input checked="checked" id="__tabbed_7_1" name="__tabbed_7" type="radio" /><input id="__tabbed_7_2" name="__tabbed_7" type="radio" /><input id="__tabbed_7_3" name="__tabbed_7" type="radio" /><input id="__tabbed_7_4" name="__tabbed_7" type="radio" /><input id="__tabbed_7_5" name="__tabbed_7" type="radio" /><input id="__tabbed_7_6" name="__tabbed_7" type="radio" /><input id="__tabbed_7_7" name="__tabbed_7" type="radio" /><input id="__tabbed_7_8" name="__tabbed_7" type="radio" /><input id="__tabbed_7_9" name="__tabbed_7" type="radio" /><input id="__tabbed_7_10" name="__tabbed_7" type="radio" /><input id="__tabbed_7_11" name="__tabbed_7" type="radio" /><input id="__tabbed_7_12" name="__tabbed_7" type="radio" /><div class="tabbed-labels"><label for="__tabbed_7_1">Python</label><label for="__tabbed_7_2">C++</label><label for="__tabbed_7_3">Java</label><label for="__tabbed_7_4">C#</label><label for="__tabbed_7_5">Go</label><label for="__tabbed_7_6">Swift</label><label for="__tabbed_7_7">JS</label><label for="__tabbed_7_8">TS</label><label for="__tabbed_7_9">Dart</label><label for="__tabbed_7_10">Rust</label><label for="__tabbed_7_11">C</label><label for="__tabbed_7_12">Kotlin</label></div>
+<div class="tabbed-set tabbed-alternate" data-tabs="7:13"><input checked="checked" id="__tabbed_7_1" name="__tabbed_7" type="radio" /><input id="__tabbed_7_2" name="__tabbed_7" type="radio" /><input id="__tabbed_7_3" name="__tabbed_7" type="radio" /><input id="__tabbed_7_4" name="__tabbed_7" type="radio" /><input id="__tabbed_7_5" name="__tabbed_7" type="radio" /><input id="__tabbed_7_6" name="__tabbed_7" type="radio" /><input id="__tabbed_7_7" name="__tabbed_7" type="radio" /><input id="__tabbed_7_8" name="__tabbed_7" type="radio" /><input id="__tabbed_7_9" name="__tabbed_7" type="radio" /><input id="__tabbed_7_10" name="__tabbed_7" type="radio" /><input id="__tabbed_7_11" name="__tabbed_7" type="radio" /><input id="__tabbed_7_12" name="__tabbed_7" type="radio" /><input id="__tabbed_7_13" name="__tabbed_7" type="radio" /><div class="tabbed-labels"><label for="__tabbed_7_1">Python</label><label for="__tabbed_7_2">C++</label><label for="__tabbed_7_3">Java</label><label for="__tabbed_7_4">C#</label><label for="__tabbed_7_5">Go</label><label for="__tabbed_7_6">Swift</label><label for="__tabbed_7_7">JS</label><label for="__tabbed_7_8">TS</label><label for="__tabbed_7_9">Dart</label><label for="__tabbed_7_10">Rust</label><label for="__tabbed_7_11">C</label><label for="__tabbed_7_12">Kotlin</label><label for="__tabbed_7_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">ListNode</span><span class="p">:</span>
-<a id="__codelineno-76-2" name="__codelineno-76-2" href="#__codelineno-76-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;双方向連結リストノードクラス&quot;&quot;&quot;</span>
-<a id="__codelineno-76-3" name="__codelineno-76-3" href="#__codelineno-76-3"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-76-4" name="__codelineno-76-4" href="#__codelineno-76-4"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">val</span>                <span class="c1"># ノード値</span>
-<a id="__codelineno-76-5" name="__codelineno-76-5" href="#__codelineno-76-5"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">next</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># 後続ノードへの参照</span>
-<a id="__codelineno-76-6" name="__codelineno-76-6" href="#__codelineno-76-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">prev</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># 前任ノードへの参照</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-78-1" name="__codelineno-78-1" href="#__codelineno-78-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">ListNode</span><span class="p">:</span>
+<a id="__codelineno-78-2" name="__codelineno-78-2" href="#__codelineno-78-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;双方向連結リストノードクラス&quot;&quot;&quot;</span>
+<a id="__codelineno-78-3" name="__codelineno-78-3" href="#__codelineno-78-3"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-78-4" name="__codelineno-78-4" href="#__codelineno-78-4"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">val</span>                <span class="c1"># ノードの値</span>
+<a id="__codelineno-78-5" name="__codelineno-78-5" href="#__codelineno-78-5"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">next</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># 後続ノードへの参照</span>
+<a id="__codelineno-78-6" name="__codelineno-78-6" href="#__codelineno-78-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">prev</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># 前駆ノードへの参照</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="cm">/* 双方向連結リストノード構造体 */</span>
-<a id="__codelineno-77-2" name="__codelineno-77-2" href="#__codelineno-77-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-77-3" name="__codelineno-77-3" href="#__codelineno-77-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">         </span><span class="c1">// ノード値</span>
-<a id="__codelineno-77-4" name="__codelineno-77-4" href="#__codelineno-77-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">next</span><span class="p">;</span><span class="w">  </span><span class="c1">// 後続ノードへのポインタ</span>
-<a id="__codelineno-77-5" name="__codelineno-77-5" href="#__codelineno-77-5"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">prev</span><span class="p">;</span><span class="w">  </span><span class="c1">// 前任ノードへのポインタ</span>
-<a id="__codelineno-77-6" name="__codelineno-77-6" href="#__codelineno-77-6"></a><span class="w">    </span><span class="n">ListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">x</span><span class="p">),</span><span class="w"> </span><span class="n">next</span><span class="p">(</span><span class="k">nullptr</span><span class="p">),</span><span class="w"> </span><span class="n">prev</span><span class="p">(</span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{}</span><span class="w">  </span><span class="c1">// コンストラクタ</span>
-<a id="__codelineno-77-7" name="__codelineno-77-7" href="#__codelineno-77-7"></a><span class="p">};</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-79-1" name="__codelineno-79-1" href="#__codelineno-79-1"></a><span class="cm">/* 双方向連結リストノード構造体 */</span>
+<a id="__codelineno-79-2" name="__codelineno-79-2" href="#__codelineno-79-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-3" name="__codelineno-79-3" href="#__codelineno-79-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">         </span><span class="c1">// ノードの値</span>
+<a id="__codelineno-79-4" name="__codelineno-79-4" href="#__codelineno-79-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">next</span><span class="p">;</span><span class="w">  </span><span class="c1">// 後続ノードへのポインタ</span>
+<a id="__codelineno-79-5" name="__codelineno-79-5" href="#__codelineno-79-5"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">prev</span><span class="p">;</span><span class="w">  </span><span class="c1">// 前駆ノードへのポインタ</span>
+<a id="__codelineno-79-6" name="__codelineno-79-6" href="#__codelineno-79-6"></a><span class="w">    </span><span class="n">ListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">x</span><span class="p">),</span><span class="w"> </span><span class="n">next</span><span class="p">(</span><span class="k">nullptr</span><span class="p">),</span><span class="w"> </span><span class="n">prev</span><span class="p">(</span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{}</span><span class="w">  </span><span class="c1">// コンストラクタ</span>
+<a id="__codelineno-79-7" name="__codelineno-79-7" href="#__codelineno-79-7"></a><span class="p">};</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-78-1" name="__codelineno-78-1" href="#__codelineno-78-1"></a><span class="cm">/* 双方向連結リストノードクラス */</span>
-<a id="__codelineno-78-2" name="__codelineno-78-2" href="#__codelineno-78-2"></a><span class="kd">class</span> <span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-78-3" name="__codelineno-78-3" href="#__codelineno-78-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">        </span><span class="c1">// ノード値</span>
-<a id="__codelineno-78-4" name="__codelineno-78-4" href="#__codelineno-78-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">next</span><span class="p">;</span><span class="w">  </span><span class="c1">// 次のノードへの参照</span>
-<a id="__codelineno-78-5" name="__codelineno-78-5" href="#__codelineno-78-5"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">prev</span><span class="p">;</span><span class="w">  </span><span class="c1">// 前任ノードへの参照</span>
-<a id="__codelineno-78-6" name="__codelineno-78-6" href="#__codelineno-78-6"></a><span class="w">    </span><span class="n">ListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w"> </span><span class="p">}</span><span class="w">  </span><span class="c1">// コンストラクタ</span>
-<a id="__codelineno-78-7" name="__codelineno-78-7" href="#__codelineno-78-7"></a><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-79-1" name="__codelineno-79-1" href="#__codelineno-79-1"></a><span class="cm">/* 双方向連結リストノードクラス */</span>
-<a id="__codelineno-79-2" name="__codelineno-79-2" href="#__codelineno-79-2"></a><span class="k">class</span><span class="w"> </span><span class="nf">ListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// コンストラクタ</span>
-<a id="__codelineno-79-3" name="__codelineno-79-3" href="#__codelineno-79-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w">    </span><span class="c1">// ノード値</span>
-<a id="__codelineno-79-4" name="__codelineno-79-4" href="#__codelineno-79-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">next</span><span class="p">;</span><span class="w">  </span><span class="c1">// 次のノードへの参照</span>
-<a id="__codelineno-79-5" name="__codelineno-79-5" href="#__codelineno-79-5"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">prev</span><span class="p">;</span><span class="w">  </span><span class="c1">// 前任ノードへの参照</span>
-<a id="__codelineno-79-6" name="__codelineno-79-6" href="#__codelineno-79-6"></a><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-80-1" name="__codelineno-80-1" href="#__codelineno-80-1"></a><span class="cm">/* 双方向連結リストノード構造体 */</span>
-<a id="__codelineno-80-2" name="__codelineno-80-2" href="#__codelineno-80-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">DoublyListNode</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-80-3" name="__codelineno-80-3" href="#__codelineno-80-3"></a><span class="w">    </span><span class="nx">Val</span><span class="w">  </span><span class="kt">int</span><span class="w">             </span><span class="c1">// ノード値</span>
-<a id="__codelineno-80-4" name="__codelineno-80-4" href="#__codelineno-80-4"></a><span class="w">    </span><span class="nx">Next</span><span class="w"> </span><span class="o">*</span><span class="nx">DoublyListNode</span><span class="w"> </span><span class="c1">// 後続ノードへのポインタ</span>
-<a id="__codelineno-80-5" name="__codelineno-80-5" href="#__codelineno-80-5"></a><span class="w">    </span><span class="nx">Prev</span><span class="w"> </span><span class="o">*</span><span class="nx">DoublyListNode</span><span class="w"> </span><span class="c1">// 前任ノードへのポインタ</span>
-<a id="__codelineno-80-6" name="__codelineno-80-6" href="#__codelineno-80-6"></a><span class="p">}</span>
-<a id="__codelineno-80-7" name="__codelineno-80-7" href="#__codelineno-80-7"></a>
-<a id="__codelineno-80-8" name="__codelineno-80-8" href="#__codelineno-80-8"></a><span class="c1">// NewDoublyListNode 初期化</span>
-<a id="__codelineno-80-9" name="__codelineno-80-9" href="#__codelineno-80-9"></a><span class="kd">func</span><span class="w"> </span><span class="nx">NewDoublyListNode</span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">DoublyListNode</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-80-10" name="__codelineno-80-10" href="#__codelineno-80-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">DoublyListNode</span><span class="p">{</span>
-<a id="__codelineno-80-11" name="__codelineno-80-11" href="#__codelineno-80-11"></a><span class="w">        </span><span class="nx">Val</span><span class="p">:</span><span class="w">  </span><span class="nx">val</span><span class="p">,</span>
-<a id="__codelineno-80-12" name="__codelineno-80-12" href="#__codelineno-80-12"></a><span class="w">        </span><span class="nx">Next</span><span class="p">:</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span>
-<a id="__codelineno-80-13" name="__codelineno-80-13" href="#__codelineno-80-13"></a><span class="w">        </span><span class="nx">Prev</span><span class="p">:</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span>
-<a id="__codelineno-80-14" name="__codelineno-80-14" href="#__codelineno-80-14"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-80-15" name="__codelineno-80-15" href="#__codelineno-80-15"></a><span class="p">}</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-80-1" name="__codelineno-80-1" href="#__codelineno-80-1"></a><span class="cm">/* 双方向連結リストノードクラス */</span>
+<a id="__codelineno-80-2" name="__codelineno-80-2" href="#__codelineno-80-2"></a><span class="kd">class</span> <span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-3" name="__codelineno-80-3" href="#__codelineno-80-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">        </span><span class="c1">// ノードの値</span>
+<a id="__codelineno-80-4" name="__codelineno-80-4" href="#__codelineno-80-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">next</span><span class="p">;</span><span class="w">  </span><span class="c1">// 後続ノードへの参照</span>
+<a id="__codelineno-80-5" name="__codelineno-80-5" href="#__codelineno-80-5"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">prev</span><span class="p">;</span><span class="w">  </span><span class="c1">// 前駆ノードへの参照</span>
+<a id="__codelineno-80-6" name="__codelineno-80-6" href="#__codelineno-80-6"></a><span class="w">    </span><span class="n">ListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w"> </span><span class="p">}</span><span class="w">  </span><span class="c1">// コンストラクタ</span>
+<a id="__codelineno-80-7" name="__codelineno-80-7" href="#__codelineno-80-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="cm">/* 双方向連結リストノードクラス */</span>
-<a id="__codelineno-81-2" name="__codelineno-81-2" href="#__codelineno-81-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-81-3" name="__codelineno-81-3" href="#__codelineno-81-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">val</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// ノード値</span>
-<a id="__codelineno-81-4" name="__codelineno-81-4" href="#__codelineno-81-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">next</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 次のノードへの参照</span>
-<a id="__codelineno-81-5" name="__codelineno-81-5" href="#__codelineno-81-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">prev</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 前任ノードへの参照</span>
-<a id="__codelineno-81-6" name="__codelineno-81-6" href="#__codelineno-81-6"></a>
-<a id="__codelineno-81-7" name="__codelineno-81-7" href="#__codelineno-81-7"></a><span class="w">    </span><span class="kd">init</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// コンストラクタ</span>
-<a id="__codelineno-81-8" name="__codelineno-81-8" href="#__codelineno-81-8"></a><span class="w">        </span><span class="n">val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">x</span>
-<a id="__codelineno-81-9" name="__codelineno-81-9" href="#__codelineno-81-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-81-10" name="__codelineno-81-10" href="#__codelineno-81-10"></a><span class="p">}</span>
+<a id="__codelineno-81-2" name="__codelineno-81-2" href="#__codelineno-81-2"></a><span class="k">class</span><span class="w"> </span><span class="nf">ListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// コンストラクタ</span>
+<a id="__codelineno-81-3" name="__codelineno-81-3" href="#__codelineno-81-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w">    </span><span class="c1">// ノードの値</span>
+<a id="__codelineno-81-4" name="__codelineno-81-4" href="#__codelineno-81-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">next</span><span class="p">;</span><span class="w">  </span><span class="c1">// 後続ノードへの参照</span>
+<a id="__codelineno-81-5" name="__codelineno-81-5" href="#__codelineno-81-5"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">prev</span><span class="p">;</span><span class="w">  </span><span class="c1">// 前駆ノードへの参照</span>
+<a id="__codelineno-81-6" name="__codelineno-81-6" href="#__codelineno-81-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="cm">/* 双方向連結リストノードクラス */</span>
-<a id="__codelineno-82-2" name="__codelineno-82-2" href="#__codelineno-82-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">ListNode</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-82-3" name="__codelineno-82-3" href="#__codelineno-82-3"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">next</span><span class="p">,</span><span class="w"> </span><span class="nx">prev</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-82-4" name="__codelineno-82-4" href="#__codelineno-82-4"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w">  </span><span class="o">===</span><span class="w">  </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span><span class="w">        </span><span class="c1">// ノード値</span>
-<a id="__codelineno-82-5" name="__codelineno-82-5" href="#__codelineno-82-5"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">next</span><span class="w">  </span><span class="o">===</span><span class="w">  </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">next</span><span class="p">;</span><span class="w">  </span><span class="c1">// 後続ノードへの参照</span>
-<a id="__codelineno-82-6" name="__codelineno-82-6" href="#__codelineno-82-6"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">prev</span><span class="w">  </span><span class="o">===</span><span class="w">  </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">prev</span><span class="p">;</span><span class="w">  </span><span class="c1">// 前任ノードへの参照</span>
-<a id="__codelineno-82-7" name="__codelineno-82-7" href="#__codelineno-82-7"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-82-8" name="__codelineno-82-8" href="#__codelineno-82-8"></a><span class="p">}</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="cm">/* 双方向連結リストノード構造体 */</span>
+<a id="__codelineno-82-2" name="__codelineno-82-2" href="#__codelineno-82-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">DoublyListNode</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-3" name="__codelineno-82-3" href="#__codelineno-82-3"></a><span class="w">    </span><span class="nx">Val</span><span class="w">  </span><span class="kt">int</span><span class="w">             </span><span class="c1">// ノードの値</span>
+<a id="__codelineno-82-4" name="__codelineno-82-4" href="#__codelineno-82-4"></a><span class="w">    </span><span class="nx">Next</span><span class="w"> </span><span class="o">*</span><span class="nx">DoublyListNode</span><span class="w"> </span><span class="c1">// 後続ノードへのポインタ</span>
+<a id="__codelineno-82-5" name="__codelineno-82-5" href="#__codelineno-82-5"></a><span class="w">    </span><span class="nx">Prev</span><span class="w"> </span><span class="o">*</span><span class="nx">DoublyListNode</span><span class="w"> </span><span class="c1">// 前駆ノードへのポインタ</span>
+<a id="__codelineno-82-6" name="__codelineno-82-6" href="#__codelineno-82-6"></a><span class="p">}</span>
+<a id="__codelineno-82-7" name="__codelineno-82-7" href="#__codelineno-82-7"></a>
+<a id="__codelineno-82-8" name="__codelineno-82-8" href="#__codelineno-82-8"></a><span class="c1">// NewDoublyListNode の初期化</span>
+<a id="__codelineno-82-9" name="__codelineno-82-9" href="#__codelineno-82-9"></a><span class="kd">func</span><span class="w"> </span><span class="nx">NewDoublyListNode</span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">DoublyListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-10" name="__codelineno-82-10" href="#__codelineno-82-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">DoublyListNode</span><span class="p">{</span>
+<a id="__codelineno-82-11" name="__codelineno-82-11" href="#__codelineno-82-11"></a><span class="w">        </span><span class="nx">Val</span><span class="p">:</span><span class="w">  </span><span class="nx">val</span><span class="p">,</span>
+<a id="__codelineno-82-12" name="__codelineno-82-12" href="#__codelineno-82-12"></a><span class="w">        </span><span class="nx">Next</span><span class="p">:</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span>
+<a id="__codelineno-82-13" name="__codelineno-82-13" href="#__codelineno-82-13"></a><span class="w">        </span><span class="nx">Prev</span><span class="p">:</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span>
+<a id="__codelineno-82-14" name="__codelineno-82-14" href="#__codelineno-82-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-82-15" name="__codelineno-82-15" href="#__codelineno-82-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="cm">/* 双方向連結リストノードクラス */</span>
-<a id="__codelineno-83-2" name="__codelineno-83-2" href="#__codelineno-83-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">ListNode</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-83-3" name="__codelineno-83-3" href="#__codelineno-83-3"></a><span class="w">    </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span>
-<a id="__codelineno-83-4" name="__codelineno-83-4" href="#__codelineno-83-4"></a><span class="w">    </span><span class="nx">next</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
-<a id="__codelineno-83-5" name="__codelineno-83-5" href="#__codelineno-83-5"></a><span class="w">    </span><span class="nx">prev</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
-<a id="__codelineno-83-6" name="__codelineno-83-6" href="#__codelineno-83-6"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val?</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">next?</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="nx">prev?</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-83-7" name="__codelineno-83-7" href="#__codelineno-83-7"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w">  </span><span class="o">===</span><span class="w">  </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">val</span><span class="p">;</span><span class="w">        </span><span class="c1">// ノード値</span>
-<a id="__codelineno-83-8" name="__codelineno-83-8" href="#__codelineno-83-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">next</span><span class="w">  </span><span class="o">===</span><span class="w">  </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">next</span><span class="p">;</span><span class="w">  </span><span class="c1">// 後続ノードへの参照</span>
-<a id="__codelineno-83-9" name="__codelineno-83-9" href="#__codelineno-83-9"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">prev</span><span class="w">  </span><span class="o">===</span><span class="w">  </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">prev</span><span class="p">;</span><span class="w">  </span><span class="c1">// 前任ノードへの参照</span>
-<a id="__codelineno-83-10" name="__codelineno-83-10" href="#__codelineno-83-10"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-83-11" name="__codelineno-83-11" href="#__codelineno-83-11"></a><span class="p">}</span>
+<a id="__codelineno-83-2" name="__codelineno-83-2" href="#__codelineno-83-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-3" name="__codelineno-83-3" href="#__codelineno-83-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">val</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// ノードの値</span>
+<a id="__codelineno-83-4" name="__codelineno-83-4" href="#__codelineno-83-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">next</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 後続ノードへの参照</span>
+<a id="__codelineno-83-5" name="__codelineno-83-5" href="#__codelineno-83-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">prev</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 前駆ノードへの参照</span>
+<a id="__codelineno-83-6" name="__codelineno-83-6" href="#__codelineno-83-6"></a>
+<a id="__codelineno-83-7" name="__codelineno-83-7" href="#__codelineno-83-7"></a><span class="w">    </span><span class="kd">init</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// コンストラクタ</span>
+<a id="__codelineno-83-8" name="__codelineno-83-8" href="#__codelineno-83-8"></a><span class="w">        </span><span class="n">val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">x</span>
+<a id="__codelineno-83-9" name="__codelineno-83-9" href="#__codelineno-83-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-83-10" name="__codelineno-83-10" href="#__codelineno-83-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-84-1" name="__codelineno-84-1" href="#__codelineno-84-1"></a><span class="cm">/* 双方向連結リストノードクラス */</span>
-<a id="__codelineno-84-2" name="__codelineno-84-2" href="#__codelineno-84-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-84-3" name="__codelineno-84-3" href="#__codelineno-84-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">        </span><span class="c1">// ノード値</span>
-<a id="__codelineno-84-4" name="__codelineno-84-4" href="#__codelineno-84-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">next</span><span class="p">;</span><span class="w">  </span><span class="c1">// 次のノードへの参照</span>
-<a id="__codelineno-84-5" name="__codelineno-84-5" href="#__codelineno-84-5"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">prev</span><span class="p">;</span><span class="w">  </span><span class="c1">// 前任ノードへの参照</span>
-<a id="__codelineno-84-6" name="__codelineno-84-6" href="#__codelineno-84-6"></a><span class="w">    </span><span class="n">ListNode</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="k">this</span><span class="p">.</span><span class="n">next</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">prev</span><span class="p">]);</span><span class="w">  </span><span class="c1">// コンストラクタ</span>
-<a id="__codelineno-84-7" name="__codelineno-84-7" href="#__codelineno-84-7"></a><span class="p">}</span>
+<a id="__codelineno-84-2" name="__codelineno-84-2" href="#__codelineno-84-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-3" name="__codelineno-84-3" href="#__codelineno-84-3"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">next</span><span class="p">,</span><span class="w"> </span><span class="nx">prev</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-4" name="__codelineno-84-4" href="#__codelineno-84-4"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w">  </span><span class="o">===</span><span class="w">  </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span><span class="w">        </span><span class="c1">// ノードの値</span>
+<a id="__codelineno-84-5" name="__codelineno-84-5" href="#__codelineno-84-5"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">next</span><span class="w">  </span><span class="o">===</span><span class="w">  </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">next</span><span class="p">;</span><span class="w">  </span><span class="c1">// 後続ノードへの参照</span>
+<a id="__codelineno-84-6" name="__codelineno-84-6" href="#__codelineno-84-6"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">prev</span><span class="w">  </span><span class="o">===</span><span class="w">  </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">prev</span><span class="p">;</span><span class="w">  </span><span class="c1">// 前駆ノードへの参照</span>
+<a id="__codelineno-84-7" name="__codelineno-84-7" href="#__codelineno-84-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-84-8" name="__codelineno-84-8" href="#__codelineno-84-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">rc</span><span class="p">::</span><span class="n">Rc</span><span class="p">;</span>
-<a id="__codelineno-85-2" name="__codelineno-85-2" href="#__codelineno-85-2"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cell</span><span class="p">::</span><span class="n">RefCell</span><span class="p">;</span>
-<a id="__codelineno-85-3" name="__codelineno-85-3" href="#__codelineno-85-3"></a>
-<a id="__codelineno-85-4" name="__codelineno-85-4" href="#__codelineno-85-4"></a><span class="cm">/* 双方向連結リストノード型 */</span>
-<a id="__codelineno-85-5" name="__codelineno-85-5" href="#__codelineno-85-5"></a><span class="cp">#[derive(Debug)]</span>
-<a id="__codelineno-85-6" name="__codelineno-85-6" href="#__codelineno-85-6"></a><span class="k">struct</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-85-7" name="__codelineno-85-7" href="#__codelineno-85-7"></a><span class="w">    </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="c1">// ノード値</span>
-<a id="__codelineno-85-8" name="__codelineno-85-8" href="#__codelineno-85-8"></a><span class="w">    </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="c1">// 後続ノードへのポインタ</span>
-<a id="__codelineno-85-9" name="__codelineno-85-9" href="#__codelineno-85-9"></a><span class="w">    </span><span class="n">prev</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="c1">// 前任ノードへのポインタ</span>
-<a id="__codelineno-85-10" name="__codelineno-85-10" href="#__codelineno-85-10"></a><span class="p">}</span>
-<a id="__codelineno-85-11" name="__codelineno-85-11" href="#__codelineno-85-11"></a>
-<a id="__codelineno-85-12" name="__codelineno-85-12" href="#__codelineno-85-12"></a><span class="cm">/* コンストラクタ */</span>
-<a id="__codelineno-85-13" name="__codelineno-85-13" href="#__codelineno-85-13"></a><span class="k">impl</span><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-85-14" name="__codelineno-85-14" href="#__codelineno-85-14"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">new</span><span class="p">(</span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">Self</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-85-15" name="__codelineno-85-15" href="#__codelineno-85-15"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-85-16" name="__codelineno-85-16" href="#__codelineno-85-16"></a><span class="w">            </span><span class="n">val</span><span class="p">,</span>
-<a id="__codelineno-85-17" name="__codelineno-85-17" href="#__codelineno-85-17"></a><span class="w">            </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span>
-<a id="__codelineno-85-18" name="__codelineno-85-18" href="#__codelineno-85-18"></a><span class="w">            </span><span class="n">prev</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span>
-<a id="__codelineno-85-19" name="__codelineno-85-19" href="#__codelineno-85-19"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-85-20" name="__codelineno-85-20" href="#__codelineno-85-20"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-85-21" name="__codelineno-85-21" href="#__codelineno-85-21"></a><span class="p">}</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="cm">/* 双方向連結リストノードクラス */</span>
+<a id="__codelineno-85-2" name="__codelineno-85-2" href="#__codelineno-85-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-3" name="__codelineno-85-3" href="#__codelineno-85-3"></a><span class="w">    </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span>
+<a id="__codelineno-85-4" name="__codelineno-85-4" href="#__codelineno-85-4"></a><span class="w">    </span><span class="nx">next</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-85-5" name="__codelineno-85-5" href="#__codelineno-85-5"></a><span class="w">    </span><span class="nx">prev</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-85-6" name="__codelineno-85-6" href="#__codelineno-85-6"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val?</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">next?</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="nx">prev?</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-7" name="__codelineno-85-7" href="#__codelineno-85-7"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w">  </span><span class="o">===</span><span class="w">  </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">val</span><span class="p">;</span><span class="w">        </span><span class="c1">// ノードの値</span>
+<a id="__codelineno-85-8" name="__codelineno-85-8" href="#__codelineno-85-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">next</span><span class="w">  </span><span class="o">===</span><span class="w">  </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">next</span><span class="p">;</span><span class="w">  </span><span class="c1">// 後続ノードへの参照</span>
+<a id="__codelineno-85-9" name="__codelineno-85-9" href="#__codelineno-85-9"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">prev</span><span class="w">  </span><span class="o">===</span><span class="w">  </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">prev</span><span class="p">;</span><span class="w">  </span><span class="c1">// 前駆ノードへの参照</span>
+<a id="__codelineno-85-10" name="__codelineno-85-10" href="#__codelineno-85-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-85-11" name="__codelineno-85-11" href="#__codelineno-85-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="cm">/* 双方向連結リストノード構造体 */</span>
-<a id="__codelineno-86-2" name="__codelineno-86-2" href="#__codelineno-86-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-86-3" name="__codelineno-86-3" href="#__codelineno-86-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">               </span><span class="c1">// ノード値</span>
-<a id="__codelineno-86-4" name="__codelineno-86-4" href="#__codelineno-86-4"></a><span class="w">    </span><span class="k">struct</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">next</span><span class="p">;</span><span class="w"> </span><span class="c1">// 後続ノードへのポインタ</span>
-<a id="__codelineno-86-5" name="__codelineno-86-5" href="#__codelineno-86-5"></a><span class="w">    </span><span class="k">struct</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">prev</span><span class="p">;</span><span class="w"> </span><span class="c1">// 前任ノードへのポインタ</span>
-<a id="__codelineno-86-6" name="__codelineno-86-6" href="#__codelineno-86-6"></a><span class="p">}</span><span class="w"> </span><span class="n">ListNode</span><span class="p">;</span>
-<a id="__codelineno-86-7" name="__codelineno-86-7" href="#__codelineno-86-7"></a>
-<a id="__codelineno-86-8" name="__codelineno-86-8" href="#__codelineno-86-8"></a><span class="cm">/* コンストラクタ */</span>
-<a id="__codelineno-86-9" name="__codelineno-86-9" href="#__codelineno-86-9"></a><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="nf">newListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-86-10" name="__codelineno-86-10" href="#__codelineno-86-10"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">next</span><span class="p">;</span>
-<a id="__codelineno-86-11" name="__codelineno-86-11" href="#__codelineno-86-11"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">ListNode</span><span class="p">));</span>
-<a id="__codelineno-86-12" name="__codelineno-86-12" href="#__codelineno-86-12"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
-<a id="__codelineno-86-13" name="__codelineno-86-13" href="#__codelineno-86-13"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
-<a id="__codelineno-86-14" name="__codelineno-86-14" href="#__codelineno-86-14"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
-<a id="__codelineno-86-15" name="__codelineno-86-15" href="#__codelineno-86-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
-<a id="__codelineno-86-16" name="__codelineno-86-16" href="#__codelineno-86-16"></a><span class="p">}</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="cm">/* 双方向連結リストノードクラス */</span>
+<a id="__codelineno-86-2" name="__codelineno-86-2" href="#__codelineno-86-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-3" name="__codelineno-86-3" href="#__codelineno-86-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">        </span><span class="c1">// ノードの値</span>
+<a id="__codelineno-86-4" name="__codelineno-86-4" href="#__codelineno-86-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">next</span><span class="p">;</span><span class="w">  </span><span class="c1">// 後続ノードへの参照</span>
+<a id="__codelineno-86-5" name="__codelineno-86-5" href="#__codelineno-86-5"></a><span class="w">    </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">prev</span><span class="p">;</span><span class="w">  </span><span class="c1">// 前駆ノードへの参照</span>
+<a id="__codelineno-86-6" name="__codelineno-86-6" href="#__codelineno-86-6"></a><span class="w">    </span><span class="n">ListNode</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="k">this</span><span class="p">.</span><span class="n">next</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">prev</span><span class="p">]);</span><span class="w">  </span><span class="c1">// コンストラクタ</span>
+<a id="__codelineno-86-7" name="__codelineno-86-7" href="#__codelineno-86-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-87-1" name="__codelineno-87-1" href="#__codelineno-87-1"></a>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-87-1" name="__codelineno-87-1" href="#__codelineno-87-1"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">rc</span><span class="p">::</span><span class="n">Rc</span><span class="p">;</span>
+<a id="__codelineno-87-2" name="__codelineno-87-2" href="#__codelineno-87-2"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cell</span><span class="p">::</span><span class="n">RefCell</span><span class="p">;</span>
+<a id="__codelineno-87-3" name="__codelineno-87-3" href="#__codelineno-87-3"></a>
+<a id="__codelineno-87-4" name="__codelineno-87-4" href="#__codelineno-87-4"></a><span class="cm">/* 双方向連結リストノード型 */</span>
+<a id="__codelineno-87-5" name="__codelineno-87-5" href="#__codelineno-87-5"></a><span class="cp">#[derive(Debug)]</span>
+<a id="__codelineno-87-6" name="__codelineno-87-6" href="#__codelineno-87-6"></a><span class="k">struct</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-7" name="__codelineno-87-7" href="#__codelineno-87-7"></a><span class="w">    </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="c1">// ノードの値</span>
+<a id="__codelineno-87-8" name="__codelineno-87-8" href="#__codelineno-87-8"></a><span class="w">    </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="c1">// 後続ノードへのポインタ</span>
+<a id="__codelineno-87-9" name="__codelineno-87-9" href="#__codelineno-87-9"></a><span class="w">    </span><span class="n">prev</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="c1">// 前駆ノードへのポインタ</span>
+<a id="__codelineno-87-10" name="__codelineno-87-10" href="#__codelineno-87-10"></a><span class="p">}</span>
+<a id="__codelineno-87-11" name="__codelineno-87-11" href="#__codelineno-87-11"></a>
+<a id="__codelineno-87-12" name="__codelineno-87-12" href="#__codelineno-87-12"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-87-13" name="__codelineno-87-13" href="#__codelineno-87-13"></a><span class="k">impl</span><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-14" name="__codelineno-87-14" href="#__codelineno-87-14"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">new</span><span class="p">(</span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-15" name="__codelineno-87-15" href="#__codelineno-87-15"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-16" name="__codelineno-87-16" href="#__codelineno-87-16"></a><span class="w">            </span><span class="n">val</span><span class="p">,</span>
+<a id="__codelineno-87-17" name="__codelineno-87-17" href="#__codelineno-87-17"></a><span class="w">            </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span>
+<a id="__codelineno-87-18" name="__codelineno-87-18" href="#__codelineno-87-18"></a><span class="w">            </span><span class="n">prev</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span>
+<a id="__codelineno-87-19" name="__codelineno-87-19" href="#__codelineno-87-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-87-20" name="__codelineno-87-20" href="#__codelineno-87-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-87-21" name="__codelineno-87-21" href="#__codelineno-87-21"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-88-1" name="__codelineno-88-1" href="#__codelineno-88-1"></a><span class="cm">/* 双方向連結リストノード構造体 */</span>
+<a id="__codelineno-88-2" name="__codelineno-88-2" href="#__codelineno-88-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-3" name="__codelineno-88-3" href="#__codelineno-88-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">               </span><span class="c1">// ノードの値</span>
+<a id="__codelineno-88-4" name="__codelineno-88-4" href="#__codelineno-88-4"></a><span class="w">    </span><span class="k">struct</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">next</span><span class="p">;</span><span class="w"> </span><span class="c1">// 後続ノードへのポインタ</span>
+<a id="__codelineno-88-5" name="__codelineno-88-5" href="#__codelineno-88-5"></a><span class="w">    </span><span class="k">struct</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">prev</span><span class="p">;</span><span class="w"> </span><span class="c1">// 前駆ノードへのポインタ</span>
+<a id="__codelineno-88-6" name="__codelineno-88-6" href="#__codelineno-88-6"></a><span class="p">}</span><span class="w"> </span><span class="n">ListNode</span><span class="p">;</span>
+<a id="__codelineno-88-7" name="__codelineno-88-7" href="#__codelineno-88-7"></a>
+<a id="__codelineno-88-8" name="__codelineno-88-8" href="#__codelineno-88-8"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-88-9" name="__codelineno-88-9" href="#__codelineno-88-9"></a><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="nf">newListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-10" name="__codelineno-88-10" href="#__codelineno-88-10"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-88-11" name="__codelineno-88-11" href="#__codelineno-88-11"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">ListNode</span><span class="p">));</span>
+<a id="__codelineno-88-12" name="__codelineno-88-12" href="#__codelineno-88-12"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-88-13" name="__codelineno-88-13" href="#__codelineno-88-13"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-88-14" name="__codelineno-88-14" href="#__codelineno-88-14"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-88-15" name="__codelineno-88-15" href="#__codelineno-88-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-88-16" name="__codelineno-88-16" href="#__codelineno-88-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-89-1" name="__codelineno-89-1" href="#__codelineno-89-1"></a><span class="cm">/* 双方向連結リストノードクラス */</span>
+<a id="__codelineno-89-2" name="__codelineno-89-2" href="#__codelineno-89-2"></a><span class="c1">// コンストラクタ</span>
+<a id="__codelineno-89-3" name="__codelineno-89-3" href="#__codelineno-89-3"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-89-4" name="__codelineno-89-4" href="#__codelineno-89-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">_val</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="w">           </span><span class="c1">// ノードの値</span>
+<a id="__codelineno-89-5" name="__codelineno-89-5" href="#__codelineno-89-5"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">next</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="w">  </span><span class="c1">// 後続ノードへの参照</span>
+<a id="__codelineno-89-6" name="__codelineno-89-6" href="#__codelineno-89-6"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">prev</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="w">  </span><span class="c1">// 前駆ノードへの参照</span>
+<a id="__codelineno-89-7" name="__codelineno-89-7" href="#__codelineno-89-7"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-90-1" name="__codelineno-90-1" href="#__codelineno-90-1"></a><span class="c1"># 双方向連結リストノードクラス</span>
+<a id="__codelineno-90-2" name="__codelineno-90-2" href="#__codelineno-90-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ListNode</span>
+<a id="__codelineno-90-3" name="__codelineno-90-3" href="#__codelineno-90-3"></a><span class="w">  </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:val</span><span class="w">    </span><span class="c1"># ノードの値</span>
+<a id="__codelineno-90-4" name="__codelineno-90-4" href="#__codelineno-90-4"></a><span class="w">  </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:next</span><span class="w">   </span><span class="c1"># 後続ノードへの参照</span>
+<a id="__codelineno-90-5" name="__codelineno-90-5" href="#__codelineno-90-5"></a><span class="w">  </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:prev</span><span class="w">   </span><span class="c1"># 前駆ノードへの参照</span>
+<a id="__codelineno-90-6" name="__codelineno-90-6" href="#__codelineno-90-6"></a>
+<a id="__codelineno-90-7" name="__codelineno-90-7" href="#__codelineno-90-7"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">val</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">next_node</span><span class="o">=</span><span class="kp">nil</span><span class="p">,</span><span class="w"> </span><span class="n">prev_node</span><span class="o">=</span><span class="kp">nil</span><span class="p">)</span>
+<a id="__codelineno-90-8" name="__codelineno-90-8" href="#__codelineno-90-8"></a><span class="w">    </span><span class="vi">@val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span>
+<a id="__codelineno-90-9" name="__codelineno-90-9" href="#__codelineno-90-9"></a><span class="w">    </span><span class="vi">@next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">next_node</span>
+<a id="__codelineno-90-10" name="__codelineno-90-10" href="#__codelineno-90-10"></a><span class="w">    </span><span class="vi">@prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">prev_node</span>
+<a id="__codelineno-90-11" name="__codelineno-90-11" href="#__codelineno-90-11"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-90-12" name="__codelineno-90-12" href="#__codelineno-90-12"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p><img alt="連結リストの一般的な種類" class="animation-figure" src="../linked_list.assets/linkedlist_common_types.png" /></p>
-<p align="center"> 図 4-8 &nbsp; 連結リストの一般的な種類 </p>
+<p><img alt="一般的な連結リストの種類" class="animation-figure" src="../linked_list.assets/linkedlist_common_types.png" /></p>
+<p align="center"> 図 4-8 &nbsp; 一般的な連結リストの種類 </p>
 
 <h2 id="424">4.2.4 &nbsp; 連結リストの典型的な応用<a class="headerlink" href="#424" title="Permanent link">&para;</a></h2>
-<p>単方向連結リストは、スタック、キュー、ハッシュ表、グラフの実装によく使用されます。</p>
+<p>単方向連結リストは、スタック、キュー、ハッシュテーブル、グラフなどのデータ構造の実装によく用いられます。</p>
 <ul>
-<li><strong>スタックとキュー</strong>：単方向連結リストで、挿入と削除が同じ端で行われる場合、スタック（後入先出）のように動作します。逆に、挿入が一方の端で、削除がもう一方の端で行われる場合、キュー（先入先出）のように機能します。</li>
-<li><strong>ハッシュ表</strong>：連結リストは、ハッシュ衝突を解決する人気の方法である連鎖法で使用されます。ここでは、すべての衝突した要素が連結リストにグループ化されます。</li>
-<li><strong>グラフ</strong>：グラフ表現の標準的な方法である隣接リストは、各グラフ頂点を連結リストに関連付けます。このリストには、対応する頂点に接続された頂点を表す要素が含まれます。</li>
+<li><strong>スタックとキュー</strong>：挿入と削除の両方の操作を連結リストの一端で行うと、その性質は後入れ先出しとなり、スタックに対応します。挿入を連結リストの一端で行い、削除をもう一端で行うと、その性質は先入れ先出しとなり、キューに対応します。</li>
+<li><strong>ハッシュテーブル</strong>：連鎖アドレス法はハッシュ衝突を解決する主流の方式の 1 つであり、この方式では、衝突したすべての要素が 1 つの連結リストに格納されます。</li>
+<li><strong>グラフ</strong>：隣接リストはグラフを表現する一般的な方法の 1 つであり、グラフの各頂点は 1 つの連結リストに関連付けられます。連結リスト内の各要素は、その頂点に接続されたほかの頂点を表します。</li>
 </ul>
-<p>双方向連結リストは、前後の要素への高速アクセスが必要なシナリオに最適です。</p>
+<p>双方向連結リストは、前後の要素をすばやく見つける必要がある場面でよく用いられます。</p>
 <ul>
-<li><strong>高度なデータ構造</strong>：赤黒木やB木などの構造では、ノードの親へのアクセスが重要です。これは各ノードに親ノードへの参照を組み込むことで実現され、双方向連結リストに似ています。</li>
-<li><strong>ブラウザ履歴</strong>：Webブラウザでは、双方向連結リストにより、ユーザーが前進または後退ボタンをクリックしたときの訪問ページの履歴ナビゲーションが容易になります。</li>
-<li><strong>LRUアルゴリズム</strong>：双方向連結リストは、最近最少使用（LRU）キャッシュ削除アルゴリズムに適しており、最近最少使用データの迅速な識別と、高速なノード追加・削除を可能にします。</li>
+<li><strong>高度なデータ構造</strong>：たとえば赤黒木や B 木では、ノードの親ノードへアクセスする必要があります。これは、ノード内に親ノードを指す参照を保持することで実現でき、双方向連結リストに似ています。</li>
+<li><strong>ブラウザ履歴</strong>：Web ブラウザでユーザーが進むボタンや戻るボタンをクリックしたとき、ブラウザはユーザーが訪れた前後のページを知る必要があります。双方向連結リストの性質によって、この操作は簡単になります。</li>
+<li><strong>LRU アルゴリズム</strong>：キャッシュ淘汰（LRU）アルゴリズムでは、最近最も使用されていないデータをすばやく見つける必要があり、さらにノードの高速な追加と削除も必要です。そのため、双方向連結リストが非常に適しています。</li>
 </ul>
-<p>循環連結リストは、オペレーティングシステムでのリソーススケジューリングなど、周期的な操作が必要なアプリケーションに最適です。</p>
+<p>循環連結リストは、オペレーティングシステムのリソーススケジューリングのように、周期的な操作が必要な場面でよく用いられます。</p>
 <ul>
-<li><strong>ラウンドロビンスケジューリングアルゴリズム</strong>：オペレーティングシステムでは、ラウンドロビンスケジューリングアルゴリズムは一般的なCPUスケジューリング方法であり、プロセスのグループを循環する必要があります。各プロセスにはタイムスライスが割り当てられ、期限切れになるとCPUは次のプロセスに回転します。この循環操作は循環連結リストを使用して効率的に実現でき、すべてのプロセス間で公平かつ時分割システムを可能にします。</li>
-<li><strong>データバッファ</strong>：循環連結リストは、オーディオやビデオプレーヤーなどのデータバッファでも使用され、データストリームが複数のバッファブロックに分割され、シームレスな再生のために循環方式で配置されます。</li>
+<li><strong>ラウンドロビン時間片スケジューリングアルゴリズム</strong>：オペレーティングシステムにおいて、ラウンドロビン時間片スケジューリングは一般的な CPU スケジューリングアルゴリズムであり、一連のプロセスを循環的に処理する必要があります。各プロセスには 1 つの時間片が割り当てられ、その時間片を使い切ると、CPU は次のプロセスへ切り替わります。この循環操作は、循環連結リストで実現できます。</li>
+<li><strong>データバッファ</strong>：一部のデータバッファ実装でも、循環連結リストが使われることがあります。たとえば音声・動画プレーヤーでは、データストリームを複数のバッファブロックに分割して循環連結リストへ格納し、シームレス再生を実現できます。</li>
 </ul>
 
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@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
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-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1340,12 +1340,12 @@
   <a href="#431" class="md-nav__link">
     <span class="md-ellipsis">
       
-        4.3.1 &nbsp; リストの一般的な操作
+        4.3.1 &nbsp; リストの基本操作
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="4.3.1 リストの一般的な操作">
+    <nav class="md-nav" aria-label="4.3.1 リストの基本操作">
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@@ -1385,7 +1385,7 @@
   <a href="#4" class="md-nav__link">
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-        4. &nbsp; リストの反復
+        4. &nbsp; リストの走査
       
     </span>
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@@ -1407,7 +1407,7 @@
   <a href="#6" class="md-nav__link">
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-        6. &nbsp; リストのソート
+        6. &nbsp; リストをソート
       
     </span>
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@@ -1735,7 +1735,7 @@
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
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-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
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-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
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-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
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-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
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-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
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-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
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-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
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-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
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-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3980,7 +3980,7 @@
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4225,7 +4225,7 @@
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4371,12 +4371,12 @@
   <a href="#431" class="md-nav__link">
     <span class="md-ellipsis">
       
-        4.3.1 &nbsp; リストの一般的な操作
+        4.3.1 &nbsp; リストの基本操作
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="4.3.1 リストの一般的な操作">
+    <nav class="md-nav" aria-label="4.3.1 リストの基本操作">
       <ul class="md-nav__list">
         
           <li class="md-nav__item">
@@ -4416,7 +4416,7 @@
   <a href="#4" class="md-nav__link">
     <span class="md-ellipsis">
       
-        4. &nbsp; リストの反復
+        4. &nbsp; リストの走査
       
     </span>
   </a>
@@ -4438,7 +4438,7 @@
   <a href="#6" class="md-nav__link">
     <span class="md-ellipsis">
       
-        6. &nbsp; リストのソート
+        6. &nbsp; リストをソート
       
     </span>
   </a>
@@ -4499,18 +4499,18 @@
 
 <!-- Page content -->
 <h1 id="43">4.3 &nbsp; リスト<a class="headerlink" href="#43" title="Permanent link">&para;</a></h1>
-<p><u>リスト</u>は、要素へのアクセス、変更、追加、削除、走査などの操作をサポートする、順序付けられた要素のコレクションを表す抽象的なデータ構造の概念であり、ユーザーが容量制限を考慮する必要がありません。リストは連結リストまたは配列に基づいて実装できます。</p>
+<p><u>リスト（list）</u>は抽象的なデータ構造の概念であり、要素の順序付き集合を表す。要素のアクセス、更新、追加、削除、走査などの操作をサポートし、利用者は容量制限の問題を考慮する必要がない。リストは連結リストまたは配列に基づいて実装できる。</p>
 <ul>
-<li>連結リストは本質的にリストとして機能し、要素の追加、削除、検索、変更の操作をサポートし、サイズを動的に調整する柔軟性があります。</li>
-<li>配列もこれらの操作をサポートしますが、長さが不変であるため、長さ制限のあるリストと考えることができます。</li>
+<li>連結リストは本質的にリストと見なすことができ、要素の追加・削除・参照・更新をサポートし、柔軟に動的拡張できる。</li>
+<li>配列も要素の追加・削除・参照・更新をサポートするが、長さが不変であるため、長さ制限のあるリストとしか見なせない。</li>
 </ul>
-<p>配列を使用してリストを実装する場合、<strong>長さの不変性によりリストの実用性が低下します</strong>。これは、事前に格納するデータ量を予測することが困難な場合が多く、適切なリスト長を選択することが困難であるためです。長さが小さすぎると要件を満たさない可能性があり、大きすぎるとメモリ空間を無駄にする可能性があります。</p>
-<p>この問題を解決するために、<u>動的配列</u>を使用してリストを実装できます。これは配列の利点を継承し、プログラム実行中に動的に拡張できます。</p>
-<p>実際、<strong>多くのプログラミング言語の標準ライブラリは動的配列を使用してリストを実装しています</strong>。例えば、Pythonの<code>list</code>、Javaの<code>ArrayList</code>、C++の<code>vector</code>、C#の<code>List</code>などです。以下の議論では、「リスト」と「動的配列」を同義の概念として扱います。</p>
-<h2 id="431">4.3.1 &nbsp; リストの一般的な操作<a class="headerlink" href="#431" title="Permanent link">&para;</a></h2>
+<p>配列でリストを実装する場合、<strong>長さが不変である性質によってリストの実用性が低下する</strong>。これは、通常は事前にどれだけのデータを格納する必要があるかを決められず、適切なリスト長を選びにくいためである。長さが小さすぎると利用要件を満たせない可能性が高く、大きすぎるとメモリ空間の浪費を招く。</p>
+<p>この問題を解決するために、<u>動的配列（dynamic array）</u>を用いてリストを実装できる。これは配列の各種利点を引き継ぎつつ、プログラム実行中に動的な拡張を行える。</p>
+<p>実際には、<strong>多くのプログラミング言語の標準ライブラリが提供するリストは動的配列に基づいて実装されている</strong>。たとえば、Python の <code>list</code> 、Java の <code>ArrayList</code> 、C++ の <code>vector</code> 、C# の <code>List</code> などである。以降の議論では、「リスト」と「動的配列」を同じ概念として扱う。</p>
+<h2 id="431">4.3.1 &nbsp; リストの基本操作<a class="headerlink" href="#431" title="Permanent link">&para;</a></h2>
 <h3 id="1">1. &nbsp; リストの初期化<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>通常、「初期値なし」と「初期値あり」の2つの初期化方法を使用します。</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="1:12"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label></div>
+<p>通常は「初期値なし」と「初期値あり」の 2 つの初期化方法を用いる。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">list.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># リストを初期化</span>
@@ -4522,7 +4522,7 @@
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">list.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* リストを初期化 */</span>
-<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// 注意: C++では、vectorがここで説明されているnumsに相当します</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// なお、C++ では vector が本稿でいう nums に相当する</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="c1">// 初期値なし</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums1</span><span class="p">;</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="c1">// 初期値あり</span>
@@ -4533,7 +4533,7 @@
 <div class="highlight"><span class="filename">list.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* リストを初期化 */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="c1">// 初期値なし</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
-<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="c1">// 初期値あり（要素型はint[]のラッパークラスInteger[]である必要があります）</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="c1">// 初期値あり（配列の要素型は int[] のラッパークラスである Integer[] である必要があることに注意）</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="n">Integer</span><span class="o">[]</span><span class="w"> </span><span class="n">numbers</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Integer</span><span class="o">[]</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="w"> </span><span class="p">};</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">Arrays</span><span class="p">.</span><span class="na">asList</span><span class="p">(</span><span class="n">numbers</span><span class="p">));</span>
 </code></pre></div>
@@ -4596,935 +4596,2027 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// Cは組み込みの動的配列を提供していません</span>
+<div class="highlight"><span class="filename">list.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// C には組み込みの動的配列がない</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
+<div class="highlight"><span class="filename">list.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* リストを初期化 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="c1">// 初期値なし</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="kd">var</span><span class="w"> </span><span class="nv">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">listOf</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="c1">// 初期値あり</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="kd">var</span><span class="w"> </span><span class="nv">numbers</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arrayOf</span><span class="p">(</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">)</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="kd">var</span><span class="w"> </span><span class="nv">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">numbers</span><span class="p">.</span><span class="na">toMutableList</span><span class="p">()</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1"># リストを初期化</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="c1"># 初期値なし</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="n">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="c1"># 初期値あり</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="o">]</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>可視化実行</summary>
+<p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%88%97%E8%A1%A8%0A%20%20%20%20%23%20%E6%97%A0%E5%88%9D%E5%A7%8B%E5%80%BC%0A%20%20%20%20nums1%20%3D%20%5B%5D%0A%20%20%20%20%23%20%E6%9C%89%E5%88%9D%E5%A7%8B%E5%80%BC%0A%20%20%20%20nums%20%3D%20%5B1,%203,%202,%205,%204%5D&amp;cumulative=false&amp;curInstr=4&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>
+</details>
 <h3 id="2">2. &nbsp; 要素へのアクセス<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>リストは本質的に配列であるため、<span class="arithmatex">\(O(1)\)</span>時間で要素にアクセスし更新することができ、非常に効率的です。</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="2:12"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label></div>
+<p>リストの本質は配列であるため、要素へのアクセスと更新は <span class="arithmatex">\(O(1)\)</span> 時間で行え、効率が高い。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.py</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1"># 要素にアクセス</span>
-<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="n">num</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>  <span class="c1"># インデックス1の要素にアクセス</span>
-<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a>
-<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="c1"># 要素を更新</span>
-<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>    <span class="c1"># インデックス1の要素を0に更新</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">list.cpp</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="cm">/* 要素にアクセス */</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">];</span><span class="w">  </span><span class="c1">// インデックス1の要素にアクセス</span>
+<div class="highlight"><span class="filename">list.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="c1"># 要素にアクセス</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="n">num</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>  <span class="c1"># インデックス 1 の要素にアクセス</span>
 <a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>
-<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="cm">/* 要素を更新 */</span>
-<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">  </span><span class="c1">// インデックス1の要素を0に更新</span>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="c1"># 要素を更新</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>    <span class="c1"># インデックス 1 の要素を 0 に更新</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.java</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 要素にアクセス */</span>
-<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span><span class="w">  </span><span class="c1">// インデックス1の要素にアクセス</span>
+<div class="highlight"><span class="filename">list.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">];</span><span class="w">  </span><span class="c1">// インデックス 1 の要素にアクセス</span>
 <a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a>
 <a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="cm">/* 要素を更新 */</span>
-<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="n">nums</span><span class="p">.</span><span class="na">set</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span><span class="w">  </span><span class="c1">// インデックス1の要素を0に更新</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">  </span><span class="c1">// インデックス 1 の要素を 0 に更新</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.cs</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 要素にアクセス */</span>
-<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">];</span><span class="w">  </span><span class="c1">// インデックス1の要素にアクセス</span>
+<div class="highlight"><span class="filename">list.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span><span class="w">  </span><span class="c1">// インデックス 1 の要素にアクセス</span>
 <a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a>
 <a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="cm">/* 要素を更新 */</span>
-<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">  </span><span class="c1">// インデックス1の要素を0に更新</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="n">nums</span><span class="p">.</span><span class="na">set</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span><span class="w">  </span><span class="c1">// インデックス 1 の要素を 0 に更新</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list_test.go</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 要素にアクセス */</span>
-<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="nx">num</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w">  </span><span class="c1">// インデックス1の要素にアクセス</span>
+<div class="highlight"><span class="filename">list.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">];</span><span class="w">  </span><span class="c1">// インデックス 1 の要素にアクセス</span>
 <a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a>
 <a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="cm">/* 要素を更新 */</span>
-<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="nx">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span><span class="w">     </span><span class="c1">// インデックス1の要素を0に更新</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">  </span><span class="c1">// インデックス 1 の要素を 0 に更新</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.swift</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 要素にアクセス */</span>
-<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">let</span><span class="w"> </span><span class="nv">num</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="c1">// インデックス1の要素にアクセス</span>
+<div class="highlight"><span class="filename">list_test.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="nx">num</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w">  </span><span class="c1">// インデックス 1 の要素にアクセス</span>
 <a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a>
 <a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="cm">/* 要素を更新 */</span>
-<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1">// インデックス1の要素を0に更新</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="nx">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span><span class="w">     </span><span class="c1">// インデックス 1 の要素を 0 に更新</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.js</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 要素にアクセス */</span>
-<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="mf">1</span><span class="p">];</span><span class="w">  </span><span class="c1">// インデックス1の要素にアクセス</span>
+<div class="highlight"><span class="filename">list.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">let</span><span class="w"> </span><span class="nv">num</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="c1">// インデックス 1 の要素にアクセス</span>
 <a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a>
 <a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="cm">/* 要素を更新 */</span>
-<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="nx">nums</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w">  </span><span class="c1">// インデックス1の要素を0に更新</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1">// インデックス 1 の要素を 0 に更新</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.ts</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 要素にアクセス */</span>
-<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="mf">1</span><span class="p">];</span><span class="w">  </span><span class="c1">// インデックス1の要素にアクセス</span>
+<div class="highlight"><span class="filename">list.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="mf">1</span><span class="p">];</span><span class="w">  </span><span class="c1">// インデックス 1 の要素にアクセス</span>
 <a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a>
 <a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="cm">/* 要素を更新 */</span>
-<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="nx">nums</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w">  </span><span class="c1">// インデックス1の要素を0に更新</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="nx">nums</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w">  </span><span class="c1">// インデックス 1 の要素を 0 に更新</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.dart</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 要素にアクセス */</span>
-<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kt">int</span><span class="w"> </span><span class="kt">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="m">1</span><span class="p">];</span><span class="w">  </span><span class="c1">// インデックス1の要素にアクセス</span>
+<div class="highlight"><span class="filename">list.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="mf">1</span><span class="p">];</span><span class="w">  </span><span class="c1">// インデックス 1 の要素にアクセス</span>
 <a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a>
 <a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="cm">/* 要素を更新 */</span>
-<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="n">nums</span><span class="p">[</span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w">  </span><span class="c1">// インデックス1の要素を0に更新</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="nx">nums</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w">  </span><span class="c1">// インデックス 1 の要素を 0 に更新</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.rs</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 要素にアクセス */</span>
-<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kd">let</span><span class="w"> </span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">];</span><span class="w">  </span><span class="c1">// インデックス1の要素にアクセス</span>
-<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="cm">/* 要素を更新 */</span>
-<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">             </span><span class="c1">// インデックス1の要素を0に更新</span>
+<div class="highlight"><span class="filename">list.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">int</span><span class="w"> </span><span class="kt">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="m">1</span><span class="p">];</span><span class="w">  </span><span class="c1">// インデックス 1 の要素にアクセス</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="cm">/* 要素を更新 */</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="n">nums</span><span class="p">[</span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w">  </span><span class="c1">// インデックス 1 の要素を 0 に更新</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.c</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="c1">// Cは組み込みの動的配列を提供していません</span>
+<div class="highlight"><span class="filename">list.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="kd">let</span><span class="w"> </span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">];</span><span class="w">  </span><span class="c1">// インデックス 1 の要素にアクセス</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="cm">/* 要素を更新 */</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">             </span><span class="c1">// インデックス 1 の要素を 0 に更新</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.kt</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a>
+<div class="highlight"><span class="filename">list.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="c1">// C には組み込みの動的配列がない</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">val</span><span class="w"> </span><span class="nv">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="m">1</span><span class="o">]</span><span class="w">       </span><span class="c1">// インデックス 1 の要素にアクセス</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="cm">/* 要素を更新 */</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="n">nums</span><span class="o">[</span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="w">             </span><span class="c1">// インデックス 1 の要素を 0 に更新</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1"># 要素にアクセス</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="c1"># インデックス 1 の要素にアクセス</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="c1"># 要素を更新</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="n">nums</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1"># インデックス 1 の要素を 0 に更新</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>可視化実行</summary>
+<p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%88%97%E8%A1%A8%0A%20%20%20%20nums%20%3D%20%5B1,%203,%202,%205,%204%5D%0A%0A%20%20%20%20%23%20%E8%AE%BF%E9%97%AE%E5%85%83%E7%B4%A0%0A%20%20%20%20num%20%3D%20nums%5B1%5D%20%20%23%20%E8%AE%BF%E9%97%AE%E7%B4%A2%E5%BC%95%201%20%E5%A4%84%E7%9A%84%E5%85%83%E7%B4%A0%0A%0A%20%20%20%20%23%20%E6%9B%B4%E6%96%B0%E5%85%83%E7%B4%A0%0A%20%20%20%20nums%5B1%5D%20%3D%200%20%20%20%20%23%20%E5%B0%86%E7%B4%A2%E5%BC%95%201%20%E5%A4%84%E7%9A%84%E5%85%83%E7%B4%A0%E6%9B%B4%E6%96%B0%E4%B8%BA%200&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>
+</details>
 <h3 id="3">3. &nbsp; 要素の挿入と削除<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
-<p>配列と比較して、リストは要素の追加と削除においてより柔軟性を提供します。リストの末尾への要素追加は<span class="arithmatex">\(O(1)\)</span>操作ですが、リストの他の場所での要素の挿入と削除の効率は配列と同じままで、時間計算量は<span class="arithmatex">\(O(n)\)</span>です。</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="3:12"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label></div>
+<p>配列と比べて、リストでは要素を自由に追加・削除できる。リスト末尾への要素追加の時間計算量は <span class="arithmatex">\(O(1)\)</span> だが、要素の挿入と削除の効率は依然として配列と同じで、時間計算量は <span class="arithmatex">\(O(n)\)</span> である。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.py</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="c1"># リストをクリア</span>
-<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="n">nums</span><span class="o">.</span><span class="n">clear</span><span class="p">()</span>
-<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a>
-<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="c1"># 末尾に要素を追加</span>
-<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="n">nums</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="n">nums</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
-<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="n">nums</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
-<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="n">nums</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
-<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="n">nums</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
-<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a>
-<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="c1"># 中間に要素を挿入</span>
-<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="n">nums</span><span class="o">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">6</span><span class="p">)</span>  <span class="c1"># インデックス3に数値6を挿入</span>
-<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a>
-<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="c1"># 要素を削除</span>
-<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="n">nums</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>        <span class="c1"># インデックス3の要素を削除</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">list.cpp</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="cm">/* リストをクリア */</span>
-<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="n">nums</span><span class="p">.</span><span class="n">clear</span><span class="p">();</span>
-<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a>
-<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="cm">/* 末尾に要素を追加 */</span>
-<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="n">nums</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="n">nums</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
-<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="n">nums</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
-<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="n">nums</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
-<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="n">nums</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
-<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a>
-<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="cm">/* 中間に要素を挿入 */</span>
-<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="n">nums</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">);</span><span class="w">  </span><span class="c1">// インデックス3に数値6を挿入</span>
-<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a>
-<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="cm">/* 要素を削除 */</span>
-<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="n">nums</span><span class="p">.</span><span class="n">erase</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">3</span><span class="p">);</span><span class="w">      </span><span class="c1">// インデックス3の要素を削除</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">list.java</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="cm">/* リストをクリア */</span>
-<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="n">nums</span><span class="p">.</span><span class="na">clear</span><span class="p">();</span>
+<div class="highlight"><span class="filename">list.py</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1"># リストをクリア</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="n">nums</span><span class="o">.</span><span class="n">clear</span><span class="p">()</span>
 <a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>
-<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="cm">/* 末尾に要素を追加 */</span>
-<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="n">nums</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="n">nums</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
-<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="n">nums</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
-<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="n">nums</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
-<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="n">nums</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="c1"># 末尾に要素を追加</span>
+<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="n">nums</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="n">nums</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="n">nums</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="n">nums</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="n">nums</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
 <a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a>
-<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="cm">/* 中間に要素を挿入 */</span>
-<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="n">nums</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">);</span><span class="w">  </span><span class="c1">// インデックス3に数値6を挿入</span>
+<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="c1"># 途中に要素を挿入</span>
+<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="n">nums</span><span class="o">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">6</span><span class="p">)</span>  <span class="c1"># インデックス 3 に数値 6 を挿入</span>
 <a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a>
-<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a><span class="cm">/* 要素を削除 */</span>
-<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="n">nums</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span><span class="w">  </span><span class="c1">// インデックス3の要素を削除</span>
+<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a><span class="c1"># 要素を削除</span>
+<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="n">nums</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>        <span class="c1"># インデックス 3 の要素を削除</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.cs</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* リストをクリア */</span>
-<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="n">nums</span><span class="p">.</span><span class="n">Clear</span><span class="p">();</span>
+<div class="highlight"><span class="filename">list.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* リストをクリア */</span>
+<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="n">nums</span><span class="p">.</span><span class="n">clear</span><span class="p">();</span>
 <a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a>
 <a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="cm">/* 末尾に要素を追加 */</span>
-<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="n">nums</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="n">nums</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
-<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="n">nums</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
-<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="n">nums</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
-<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="n">nums</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="n">nums</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="n">nums</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="n">nums</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="n">nums</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="n">nums</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
 <a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a>
-<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="cm">/* 中間に要素を挿入 */</span>
-<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="n">nums</span><span class="p">.</span><span class="n">Insert</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">);</span>
+<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="cm">/* 途中に要素を挿入 */</span>
+<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="n">nums</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">);</span><span class="w">  </span><span class="c1">// インデックス 3 に数値 6 を挿入</span>
 <a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a>
 <a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a><span class="cm">/* 要素を削除 */</span>
-<a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="n">nums</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="n">nums</span><span class="p">.</span><span class="n">erase</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">3</span><span class="p">);</span><span class="w">      </span><span class="c1">// インデックス 3 の要素を削除</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list_test.go</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* リストをクリア */</span>
-<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">nil</span>
+<div class="highlight"><span class="filename">list.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* リストをクリア */</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="n">nums</span><span class="p">.</span><span class="na">clear</span><span class="p">();</span>
 <a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a>
 <a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="cm">/* 末尾に要素を追加 */</span>
-<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span>
-<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
-<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span>
-<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="n">nums</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="n">nums</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="n">nums</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="n">nums</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="n">nums</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
 <a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a>
-<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="cm">/* 中間に要素を挿入 */</span>
-<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">[:</span><span class="mi">3</span><span class="p">],</span><span class="w"> </span><span class="nb">append</span><span class="p">([]</span><span class="kt">int</span><span class="p">{</span><span class="mi">6</span><span class="p">},</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="mi">3</span><span class="p">:]</span><span class="o">...</span><span class="p">)</span><span class="o">...</span><span class="p">)</span><span class="w"> </span><span class="c1">// インデックス3に数値6を挿入</span>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="cm">/* 途中に要素を挿入 */</span>
+<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a><span class="n">nums</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">);</span><span class="w">  </span><span class="c1">// インデックス 3 に数値 6 を挿入</span>
 <a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a>
 <a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a><span class="cm">/* 要素を削除 */</span>
-<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">[:</span><span class="mi">3</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="mi">4</span><span class="p">:]</span><span class="o">...</span><span class="p">)</span><span class="w"> </span><span class="c1">// インデックス3の要素を削除</span>
+<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="n">nums</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span><span class="w">  </span><span class="c1">// インデックス 3 の要素を削除</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.swift</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* リストをクリア */</span>
-<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="n">nums</span><span class="p">.</span><span class="bp">removeAll</span><span class="p">()</span>
+<div class="highlight"><span class="filename">list.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* リストをクリア */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="n">nums</span><span class="p">.</span><span class="n">Clear</span><span class="p">();</span>
 <a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a>
 <a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="cm">/* 末尾に要素を追加 */</span>
-<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="n">nums</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="n">nums</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
-<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="n">nums</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
-<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="n">nums</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
-<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="n">nums</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="n">nums</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="n">nums</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="n">nums</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="n">nums</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="n">nums</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
 <a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a>
-<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="cm">/* 中間に要素を挿入 */</span>
-<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="n">nums</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="n">at</span><span class="p">:</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="c1">// インデックス3に数値6を挿入</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="cm">/* 途中に要素を挿入 */</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="n">nums</span><span class="p">.</span><span class="n">Insert</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">);</span><span class="w">  </span><span class="c1">// インデックス 3 に数値 6 を挿入</span>
 <a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a>
 <a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="cm">/* 要素を削除 */</span>
-<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="n">nums</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">at</span><span class="p">:</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="c1">// インデックス3の要素を削除</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="n">nums</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span><span class="w">  </span><span class="c1">// インデックス 3 の要素を削除</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.js</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* リストをクリア */</span>
-<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<div class="highlight"><span class="filename">list_test.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* リストをクリア */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">nil</span>
 <a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a>
 <a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="cm">/* 末尾に要素を追加 */</span>
-<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">1</span><span class="p">);</span>
-<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">3</span><span class="p">);</span>
-<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">2</span><span class="p">);</span>
-<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
-<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">4</span><span class="p">);</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span>
 <a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a>
-<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="cm">/* 中間に要素を挿入 */</span>
-<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">splice</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="mf">6</span><span class="p">);</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="cm">/* 途中に要素を挿入 */</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">[:</span><span class="mi">3</span><span class="p">],</span><span class="w"> </span><span class="nb">append</span><span class="p">([]</span><span class="kt">int</span><span class="p">{</span><span class="mi">6</span><span class="p">},</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="mi">3</span><span class="p">:]</span><span class="o">...</span><span class="p">)</span><span class="o">...</span><span class="p">)</span><span class="w"> </span><span class="c1">// インデックス 3 に数値 6 を挿入</span>
 <a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a>
 <a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="cm">/* 要素を削除 */</span>
-<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">splice</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">[:</span><span class="mi">3</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="mi">4</span><span class="p">:]</span><span class="o">...</span><span class="p">)</span><span class="w"> </span><span class="c1">// インデックス 3 の要素を削除</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.ts</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* リストをクリア */</span>
-<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<div class="highlight"><span class="filename">list.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* リストをクリア */</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="n">nums</span><span class="p">.</span><span class="bp">removeAll</span><span class="p">()</span>
 <a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a>
 <a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="cm">/* 末尾に要素を追加 */</span>
-<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">1</span><span class="p">);</span>
-<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">3</span><span class="p">);</span>
-<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">2</span><span class="p">);</span>
-<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
-<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">4</span><span class="p">);</span>
+<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="n">nums</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="n">nums</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="n">nums</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="n">nums</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="n">nums</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
 <a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a>
-<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="cm">/* 中間に要素を挿入 */</span>
-<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">splice</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="mf">6</span><span class="p">);</span>
+<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="cm">/* 途中に要素を挿入 */</span>
+<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="n">nums</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="n">at</span><span class="p">:</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="c1">// インデックス 3 に数値 6 を挿入</span>
 <a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a>
 <a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a><span class="cm">/* 要素を削除 */</span>
-<a id="__codelineno-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">splice</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></a><span class="n">nums</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">at</span><span class="p">:</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="c1">// インデックス 3 の要素を削除</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.dart</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* リストをクリア */</span>
-<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="n">nums</span><span class="p">.</span><span class="n">clear</span><span class="p">();</span>
+<div class="highlight"><span class="filename">list.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* リストをクリア */</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
 <a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a>
 <a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="cm">/* 末尾に要素を追加 */</span>
-<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="n">nums</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">1</span><span class="p">);</span>
-<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="n">nums</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">3</span><span class="p">);</span>
-<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="n">nums</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">2</span><span class="p">);</span>
-<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="n">nums</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">5</span><span class="p">);</span>
-<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="n">nums</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">4</span><span class="p">);</span>
+<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">3</span><span class="p">);</span>
+<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">2</span><span class="p">);</span>
+<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
+<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">4</span><span class="p">);</span>
 <a id="__codelineno-32-10" name="__codelineno-32-10" href="#__codelineno-32-10"></a>
-<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a><span class="cm">/* 中間に要素を挿入 */</span>
-<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a><span class="n">nums</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">6</span><span class="p">);</span><span class="w"> </span><span class="c1">// インデックス3に数値6を挿入</span>
+<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a><span class="cm">/* 途中に要素を挿入 */</span>
+<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">splice</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="mf">6</span><span class="p">);</span><span class="w"> </span><span class="c1">// インデックス 3 に数値 6 を挿入</span>
 <a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a>
 <a id="__codelineno-32-14" name="__codelineno-32-14" href="#__codelineno-32-14"></a><span class="cm">/* 要素を削除 */</span>
-<a id="__codelineno-32-15" name="__codelineno-32-15" href="#__codelineno-32-15"></a><span class="n">nums</span><span class="p">.</span><span class="n">removeAt</span><span class="p">(</span><span class="m">3</span><span class="p">);</span><span class="w"> </span><span class="c1">// インデックス3の要素を削除</span>
+<a id="__codelineno-32-15" name="__codelineno-32-15" href="#__codelineno-32-15"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">splice</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span><span class="w">  </span><span class="c1">// インデックス 3 の要素を削除</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.rs</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* リストをクリア */</span>
-<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="n">nums</span><span class="p">.</span><span class="n">clear</span><span class="p">();</span>
+<div class="highlight"><span class="filename">list.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* リストをクリア */</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
 <a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a>
 <a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="cm">/* 末尾に要素を追加 */</span>
-<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="n">nums</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="n">nums</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
-<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="n">nums</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
-<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="n">nums</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
-<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="n">nums</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">3</span><span class="p">);</span>
+<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">2</span><span class="p">);</span>
+<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
+<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">4</span><span class="p">);</span>
 <a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a>
-<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="cm">/* 中間に要素を挿入 */</span>
-<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="n">nums</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">);</span><span class="w">  </span><span class="c1">// インデックス3に数値6を挿入</span>
+<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="cm">/* 途中に要素を挿入 */</span>
+<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">splice</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="mf">6</span><span class="p">);</span><span class="w"> </span><span class="c1">// インデックス 3 に数値 6 を挿入</span>
 <a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a>
 <a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a><span class="cm">/* 要素を削除 */</span>
-<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a><span class="n">nums</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span><span class="w">    </span><span class="c1">// インデックス3の要素を削除</span>
+<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">splice</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span><span class="w">  </span><span class="c1">// インデックス 3 の要素を削除</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.c</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="c1">// Cは組み込みの動的配列を提供していません</span>
+<div class="highlight"><span class="filename">list.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* リストをクリア */</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="n">nums</span><span class="p">.</span><span class="n">clear</span><span class="p">();</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a>
+<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="cm">/* 末尾に要素を追加 */</span>
+<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="n">nums</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="n">nums</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">3</span><span class="p">);</span>
+<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="n">nums</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">2</span><span class="p">);</span>
+<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="n">nums</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">5</span><span class="p">);</span>
+<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="n">nums</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">4</span><span class="p">);</span>
+<a id="__codelineno-34-10" name="__codelineno-34-10" href="#__codelineno-34-10"></a>
+<a id="__codelineno-34-11" name="__codelineno-34-11" href="#__codelineno-34-11"></a><span class="cm">/* 途中に要素を挿入 */</span>
+<a id="__codelineno-34-12" name="__codelineno-34-12" href="#__codelineno-34-12"></a><span class="n">nums</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">6</span><span class="p">);</span><span class="w"> </span><span class="c1">// インデックス 3 に数値 6 を挿入</span>
+<a id="__codelineno-34-13" name="__codelineno-34-13" href="#__codelineno-34-13"></a>
+<a id="__codelineno-34-14" name="__codelineno-34-14" href="#__codelineno-34-14"></a><span class="cm">/* 要素を削除 */</span>
+<a id="__codelineno-34-15" name="__codelineno-34-15" href="#__codelineno-34-15"></a><span class="n">nums</span><span class="p">.</span><span class="n">removeAt</span><span class="p">(</span><span class="m">3</span><span class="p">);</span><span class="w"> </span><span class="c1">// インデックス 3 の要素を削除</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.kt</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a>
+<div class="highlight"><span class="filename">list.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* リストをクリア */</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="n">nums</span><span class="p">.</span><span class="n">clear</span><span class="p">();</span>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a>
+<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="cm">/* 末尾に要素を追加 */</span>
+<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="n">nums</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="n">nums</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="n">nums</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="n">nums</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="n">nums</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a>
+<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a><span class="cm">/* 途中に要素を挿入 */</span>
+<a id="__codelineno-35-12" name="__codelineno-35-12" href="#__codelineno-35-12"></a><span class="n">nums</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">);</span><span class="w">  </span><span class="c1">// インデックス 3 に数値 6 を挿入</span>
+<a id="__codelineno-35-13" name="__codelineno-35-13" href="#__codelineno-35-13"></a>
+<a id="__codelineno-35-14" name="__codelineno-35-14" href="#__codelineno-35-14"></a><span class="cm">/* 要素を削除 */</span>
+<a id="__codelineno-35-15" name="__codelineno-35-15" href="#__codelineno-35-15"></a><span class="n">nums</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span><span class="w">    </span><span class="c1">// インデックス 3 の要素を削除</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="c1">// C には組み込みの動的配列がない</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* リストをクリア */</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="n">nums</span><span class="p">.</span><span class="na">clear</span><span class="p">();</span>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a>
+<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="cm">/* 末尾に要素を追加 */</span>
+<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="n">nums</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="n">nums</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="m">3</span><span class="p">);</span>
+<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="n">nums</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="m">2</span><span class="p">);</span>
+<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="n">nums</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="m">5</span><span class="p">);</span>
+<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="n">nums</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="m">4</span><span class="p">);</span>
+<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a>
+<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a><span class="cm">/* 途中に要素を挿入 */</span>
+<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a><span class="n">nums</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">6</span><span class="p">);</span><span class="w">  </span><span class="c1">// インデックス 3 に数値 6 を挿入</span>
+<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a>
+<a id="__codelineno-37-14" name="__codelineno-37-14" href="#__codelineno-37-14"></a><span class="cm">/* 要素を削除 */</span>
+<a id="__codelineno-37-15" name="__codelineno-37-15" href="#__codelineno-37-15"></a><span class="n">nums</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="m">3</span><span class="p">);</span><span class="w">  </span><span class="c1">// インデックス 3 の要素を削除</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="c1"># リストをクリア</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="n">nums</span><span class="o">.</span><span class="n">clear</span>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a>
+<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="c1"># 末尾に要素を追加</span>
+<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="n">nums</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="n">nums</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">3</span>
+<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="n">nums</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="n">nums</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">5</span>
+<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="n">nums</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">4</span>
+<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a>
+<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a><span class="c1"># 途中に要素を挿入</span>
+<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a><span class="n">nums</span><span class="o">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">)</span><span class="w"> </span><span class="c1"># インデックス 3 に数値 6 を挿入</span>
+<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a>
+<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a><span class="c1"># 要素を削除</span>
+<a id="__codelineno-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a><span class="n">nums</span><span class="o">.</span><span class="n">delete_at</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="c1"># インデックス 3 の要素を削除</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h3 id="4">4. &nbsp; リストの反復<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
-<p>配列と同様に、リストはインデックスを使用して反復することも、各要素を直接反復することもできます。</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="4:12"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label></div>
+<details class="pythontutor">
+<summary>可視化実行</summary>
+<p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E6%9C%89%E5%88%9D%E5%A7%8B%E5%80%BC%0A%20%20%20%20nums%20%3D%20%5B1,%203,%202,%205,%204%5D%0A%20%20%20%20%0A%20%20%20%20%23%20%E6%B8%85%E7%A9%BA%E5%88%97%E8%A1%A8%0A%20%20%20%20nums.clear%28%29%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%9C%A8%E5%B0%BE%E9%83%A8%E6%B7%BB%E5%8A%A0%E5%85%83%E7%B4%A0%0A%20%20%20%20nums.append%281%29%0A%20%20%20%20nums.append%283%29%0A%20%20%20%20nums.append%282%29%0A%20%20%20%20nums.append%285%29%0A%20%20%20%20nums.append%284%29%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%9C%A8%E4%B8%AD%E9%97%B4%E6%8F%92%E5%85%A5%E5%85%83%E7%B4%A0%0A%20%20%20%20nums.insert%283,%206%29%20%20%23%20%E5%9C%A8%E7%B4%A2%E5%BC%95%203%20%E5%A4%84%E6%8F%92%E5%85%A5%E6%95%B0%E5%AD%97%206%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%88%A0%E9%99%A4%E5%85%83%E7%B4%A0%0A%20%20%20%20nums.pop%283%29%20%20%20%20%20%20%20%20%23%20%E5%88%A0%E9%99%A4%E7%B4%A2%E5%BC%95%203%20%E5%A4%84%E7%9A%84%E5%85%83%E7%B4%A0&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>
+</details>
+<h3 id="4">4. &nbsp; リストの走査<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
+<p>配列と同様に、リストもインデックスに基づいて走査することも、各要素を直接走査することもできる。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="4:13"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.py</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="c1"># インデックスでリストを反復</span>
-<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
-<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
-<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a>    <span class="n">count</span> <span class="o">+=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
-<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a>
-<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="c1"># リスト要素を直接反復</span>
-<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">nums</span><span class="p">:</span>
-<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a>    <span class="n">count</span> <span class="o">+=</span> <span class="n">num</span>
+<div class="highlight"><span class="filename">list.py</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="c1"># インデックスでリストを走査</span>
+<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
+<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a>    <span class="n">count</span> <span class="o">+=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a>
+<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a><span class="c1"># リストの要素を直接走査</span>
+<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a><span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">nums</span><span class="p">:</span>
+<a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a>    <span class="n">count</span> <span class="o">+=</span> <span class="n">num</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.cpp</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* インデックスでリストを反復 */</span>
-<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
-<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="p">}</span>
-<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a>
-<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="cm">/* リスト要素を直接反復 */</span>
-<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">list.java</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="cm">/* インデックスでリストを反復 */</span>
-<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
-<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="p">}</span>
-<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a>
-<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="cm">/* リスト要素を直接反復 */</span>
-<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">list.cs</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="cm">/* インデックスでリストを反復 */</span>
-<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Count</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
-<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a><span class="p">}</span>
-<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a>
-<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a><span class="cm">/* リスト要素を直接反復 */</span>
-<a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-39-11" name="__codelineno-39-11" href="#__codelineno-39-11"></a><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">list_test.go</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* インデックスでリストを反復 */</span>
-<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
-<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
+<div class="highlight"><span class="filename">list.cpp</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* インデックスでリストを走査 */</span>
+<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
 <a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="p">}</span>
 <a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a>
-<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="cm">/* リスト要素を直接反復 */</span>
-<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="nx">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
-<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">num</span>
+<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="cm">/* リストの要素を直接走査 */</span>
+<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
 <a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.swift</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* インデックスでリストを反復 */</span>
-<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
-<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w">    </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<div class="highlight"><span class="filename">list.java</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* インデックスでリストを走査 */</span>
+<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
 <a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="p">}</span>
 <a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a>
-<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="cm">/* リスト要素を直接反復 */</span>
-<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a><span class="bp">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
-<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="w">    </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span>
-<a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a><span class="p">}</span>
+<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="cm">/* リストの要素を直接走査 */</span>
+<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.js</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="cm">/* インデックスでリストを反復 */</span>
-<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
-<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<div class="highlight"><span class="filename">list.cs</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="cm">/* インデックスでリストを走査 */</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Count</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
 <a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="p">}</span>
 <a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a>
-<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="cm">/* リスト要素を直接反復 */</span>
-<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
-<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="cm">/* リストの要素を直接走査 */</span>
+<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
 <a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.ts</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* インデックスでリストを反復 */</span>
-<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
-<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<div class="highlight"><span class="filename">list_test.go</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* インデックスでリストを走査 */</span>
+<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
 <a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="p">}</span>
 <a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a>
-<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="cm">/* リスト要素を直接反復 */</span>
-<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
-<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="cm">/* リストの要素を直接走査 */</span>
+<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="nx">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">num</span>
 <a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.dart</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* インデックスでリストを反復 */</span>
-<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
-<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<div class="highlight"><span class="filename">list.swift</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* インデックスでリストを走査 */</span>
+<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">    </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
 <a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="p">}</span>
 <a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a>
-<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="cm">/* リスト要素を直接反復 */</span>
-<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
-<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="kt">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="kt">num</span><span class="p">;</span>
+<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="cm">/* リストの要素を直接走査 */</span>
+<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="bp">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w">    </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span>
 <a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.rs</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="c1">// インデックスでリストを反復</span>
-<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">_count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w">    </span><span class="n">_count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<div class="highlight"><span class="filename">list.js</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="cm">/* インデックスでリストを走査 */</span>
+<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
 <a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="p">}</span>
 <a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a>
-<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="c1">// リスト要素を直接反復</span>
-<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="n">_count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="w">    </span><span class="n">_count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="cm">/* リストの要素を直接走査 */</span>
+<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
 <a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.c</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="c1">// Cは組み込みの動的配列を提供していません</span>
+<div class="highlight"><span class="filename">list.ts</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="cm">/* インデックスでリストを走査 */</span>
+<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="p">}</span>
+<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a>
+<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></a><span class="cm">/* リストの要素を直接走査 */</span>
+<a id="__codelineno-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.kt</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a>
+<div class="highlight"><span class="filename">list.dart</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* インデックスでリストを走査 */</span>
+<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="p">}</span>
+<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a>
+<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="cm">/* リストの要素を直接走査 */</span>
+<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="kt">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="kt">num</span><span class="p">;</span>
+<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.rs</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="c1">// インデックスでリストを走査</span>
+<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">_count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a><span class="w">    </span><span class="n">_count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a><span class="p">}</span>
+<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a>
+<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a><span class="c1">// リストの要素を直接走査</span>
+<a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a><span class="n">_count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a><span class="w">    </span><span class="n">_count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-48-11" name="__codelineno-48-11" href="#__codelineno-48-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.c</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="c1">// C には組み込みの動的配列がない</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.kt</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* インデックスでリストを走査 */</span>
+<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">indices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="p">}</span>
+<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a>
+<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="cm">/* リストの要素を直接走査 */</span>
+<a id="__codelineno-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-9" name="__codelineno-50-9" href="#__codelineno-50-9"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-50-10" name="__codelineno-50-10" href="#__codelineno-50-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.rb</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="c1"># インデックスでリストを走査</span>
+<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="k">end</span>
+<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a>
+<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="c1"># リストの要素を直接走査</span>
+<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span>
+<a id="__codelineno-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-51-11" name="__codelineno-51-11" href="#__codelineno-51-11"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>可視化実行</summary>
+<p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%88%97%E8%A1%A8%0A%20%20%20%20nums%20%3D%20%5B1,%203,%202,%205,%204%5D%0A%20%20%20%20%0A%20%20%20%20%23%20%E9%80%9A%E8%BF%87%E7%B4%A2%E5%BC%95%E9%81%8D%E5%8E%86%E5%88%97%E8%A1%A8%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20for%20i%20in%20range%28len%28nums%29%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%20nums%5Bi%5D%0A%0A%20%20%20%20%23%20%E7%9B%B4%E6%8E%A5%E9%81%8D%E5%8E%86%E5%88%97%E8%A1%A8%E5%85%83%E7%B4%A0%0A%20%20%20%20for%20num%20in%20nums%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%20num&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>
+</details>
 <h3 id="5">5. &nbsp; リストの連結<a class="headerlink" href="#5" title="Permanent link">&para;</a></h3>
-<p>新しいリスト<code>nums1</code>が与えられたとき、それを元のリストの末尾に追加できます。</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="5:12"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label></div>
+<p>新しいリスト <code>nums1</code> が与えられたとき、それを元のリストの末尾に連結できる。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="5:13"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.py</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="c1"># 2つのリストを連結</span>
-<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="n">nums1</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">6</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">9</span><span class="p">]</span>
-<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="n">nums</span> <span class="o">+=</span> <span class="n">nums1</span>  <span class="c1"># nums1をnumsの末尾に連結</span>
+<div class="highlight"><span class="filename">list.py</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="c1"># 2 つのリストを連結</span>
+<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="n">nums1</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">6</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">9</span><span class="p">]</span>
+<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a><span class="n">nums</span> <span class="o">+=</span> <span class="n">nums1</span>  <span class="c1"># リスト nums1 を nums の後ろに連結</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.cpp</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* 2つのリストを連結 */</span>
-<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="w"> </span><span class="p">};</span>
-<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="c1">// nums1をnumsの末尾に連結</span>
-<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="n">nums</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">end</span><span class="p">(),</span><span class="w"> </span><span class="n">nums1</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">nums1</span><span class="p">.</span><span class="n">end</span><span class="p">());</span>
+<div class="highlight"><span class="filename">list.cpp</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 2 つのリストを連結 */</span>
+<a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="w"> </span><span class="p">};</span>
+<a id="__codelineno-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a><span class="c1">// リスト nums1 を nums の後ろに連結</span>
+<a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a><span class="n">nums</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">end</span><span class="p">(),</span><span class="w"> </span><span class="n">nums1</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">nums1</span><span class="p">.</span><span class="n">end</span><span class="p">());</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.java</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* 2つのリストを連結 */</span>
-<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">Arrays</span><span class="p">.</span><span class="na">asList</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">Integer</span><span class="o">[]</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="w"> </span><span class="p">}));</span>
-<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="n">nums</span><span class="p">.</span><span class="na">addAll</span><span class="p">(</span><span class="n">nums1</span><span class="p">);</span><span class="w">  </span><span class="c1">// nums1をnumsの末尾に連結</span>
+<div class="highlight"><span class="filename">list.java</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="cm">/* 2 つのリストを連結 */</span>
+<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">Arrays</span><span class="p">.</span><span class="na">asList</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">Integer</span><span class="o">[]</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="w"> </span><span class="p">}));</span>
+<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="n">nums</span><span class="p">.</span><span class="na">addAll</span><span class="p">(</span><span class="n">nums1</span><span class="p">);</span><span class="w">  </span><span class="c1">// リスト nums1 を nums の後ろに連結</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.cs</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="cm">/* 2つのリストを連結 */</span>
-<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">];</span>
-<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="n">nums</span><span class="p">.</span><span class="n">AddRange</span><span class="p">(</span><span class="n">nums1</span><span class="p">);</span><span class="w">  </span><span class="c1">// nums1をnumsの末尾に連結</span>
+<div class="highlight"><span class="filename">list.cs</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="cm">/* 2 つのリストを連結 */</span>
+<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">];</span>
+<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="n">nums</span><span class="p">.</span><span class="n">AddRange</span><span class="p">(</span><span class="n">nums1</span><span class="p">);</span><span class="w">  </span><span class="c1">// リスト nums1 を nums の後ろに連結</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list_test.go</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="cm">/* 2つのリストを連結 */</span>
-<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="nx">nums1</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">{</span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">}</span>
-<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">nums1</span><span class="o">...</span><span class="p">)</span><span class="w">  </span><span class="c1">// nums1をnumsの末尾に連結</span>
+<div class="highlight"><span class="filename">list_test.go</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="cm">/* 2 つのリストを連結 */</span>
+<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="nx">nums1</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">{</span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">}</span>
+<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">nums1</span><span class="o">...</span><span class="p">)</span><span class="w">  </span><span class="c1">// リスト nums1 を nums の後ろに連結</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.swift</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 2つのリストを連結 */</span>
-<a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a><span class="kd">let</span><span class="w"> </span><span class="nv">nums1</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">]</span>
-<a id="__codelineno-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a><span class="n">nums</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">contentsOf</span><span class="p">:</span><span class="w"> </span><span class="n">nums1</span><span class="p">)</span><span class="w"> </span><span class="c1">// nums1をnumsの末尾に連結</span>
+<div class="highlight"><span class="filename">list.swift</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 2 つのリストを連結 */</span>
+<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="kd">let</span><span class="w"> </span><span class="nv">nums1</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">]</span>
+<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="n">nums</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">contentsOf</span><span class="p">:</span><span class="w"> </span><span class="n">nums1</span><span class="p">)</span><span class="w"> </span><span class="c1">// リスト nums1 を nums の後ろに連結</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.js</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="cm">/* 2つのリストを連結 */</span>
-<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">6</span><span class="p">,</span><span class="w"> </span><span class="mf">8</span><span class="p">,</span><span class="w"> </span><span class="mf">7</span><span class="p">,</span><span class="w"> </span><span class="mf">10</span><span class="p">,</span><span class="w"> </span><span class="mf">9</span><span class="p">];</span>
-<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(...</span><span class="nx">nums1</span><span class="p">);</span><span class="w">  </span><span class="c1">// nums1をnumsの末尾に連結</span>
+<div class="highlight"><span class="filename">list.js</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 2 つのリストを連結 */</span>
+<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">6</span><span class="p">,</span><span class="w"> </span><span class="mf">8</span><span class="p">,</span><span class="w"> </span><span class="mf">7</span><span class="p">,</span><span class="w"> </span><span class="mf">10</span><span class="p">,</span><span class="w"> </span><span class="mf">9</span><span class="p">];</span>
+<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(...</span><span class="nx">nums1</span><span class="p">);</span><span class="w">  </span><span class="c1">// リスト nums1 を nums の後ろに連結</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.ts</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="cm">/* 2つのリストを連結 */</span>
-<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">nums1</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">6</span><span class="p">,</span><span class="w"> </span><span class="mf">8</span><span class="p">,</span><span class="w"> </span><span class="mf">7</span><span class="p">,</span><span class="w"> </span><span class="mf">10</span><span class="p">,</span><span class="w"> </span><span class="mf">9</span><span class="p">];</span>
-<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(...</span><span class="nx">nums1</span><span class="p">);</span><span class="w">  </span><span class="c1">// nums1をnumsの末尾に連結</span>
+<div class="highlight"><span class="filename">list.ts</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="cm">/* 2 つのリストを連結 */</span>
+<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">nums1</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">6</span><span class="p">,</span><span class="w"> </span><span class="mf">8</span><span class="p">,</span><span class="w"> </span><span class="mf">7</span><span class="p">,</span><span class="w"> </span><span class="mf">10</span><span class="p">,</span><span class="w"> </span><span class="mf">9</span><span class="p">];</span>
+<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(...</span><span class="nx">nums1</span><span class="p">);</span><span class="w">  </span><span class="c1">// リスト nums1 を nums の後ろに連結</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.dart</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="cm">/* 2つのリストを連結 */</span>
-<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="m">6</span><span class="p">,</span><span class="w"> </span><span class="m">8</span><span class="p">,</span><span class="w"> </span><span class="m">7</span><span class="p">,</span><span class="w"> </span><span class="m">10</span><span class="p">,</span><span class="w"> </span><span class="m">9</span><span class="p">];</span>
-<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a><span class="n">nums</span><span class="p">.</span><span class="n">addAll</span><span class="p">(</span><span class="n">nums1</span><span class="p">);</span><span class="w">  </span><span class="c1">// nums1をnumsの末尾に連結</span>
+<div class="highlight"><span class="filename">list.dart</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="cm">/* 2 つのリストを連結 */</span>
+<a id="__codelineno-60-2" name="__codelineno-60-2" href="#__codelineno-60-2"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="m">6</span><span class="p">,</span><span class="w"> </span><span class="m">8</span><span class="p">,</span><span class="w"> </span><span class="m">7</span><span class="p">,</span><span class="w"> </span><span class="m">10</span><span class="p">,</span><span class="w"> </span><span class="m">9</span><span class="p">];</span>
+<a id="__codelineno-60-3" name="__codelineno-60-3" href="#__codelineno-60-3"></a><span class="n">nums</span><span class="p">.</span><span class="n">addAll</span><span class="p">(</span><span class="n">nums1</span><span class="p">);</span><span class="w">  </span><span class="c1">// リスト nums1 を nums の後ろに連結</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.rs</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 2つのリストを連結 */</span>
-<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="kd">let</span><span class="w"> </span><span class="n">nums1</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">];</span>
-<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="n">nums</span><span class="p">.</span><span class="n">extend</span><span class="p">(</span><span class="n">nums1</span><span class="p">);</span>
+<div class="highlight"><span class="filename">list.rs</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="cm">/* 2 つのリストを連結 */</span>
+<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a><span class="kd">let</span><span class="w"> </span><span class="n">nums1</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">];</span>
+<a id="__codelineno-61-3" name="__codelineno-61-3" href="#__codelineno-61-3"></a><span class="n">nums</span><span class="p">.</span><span class="n">extend</span><span class="p">(</span><span class="n">nums1</span><span class="p">);</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.c</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="c1">// Cは組み込みの動的配列を提供していません</span>
+<div class="highlight"><span class="filename">list.c</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="c1">// C には組み込みの動的配列がない</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.kt</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a>
+<div class="highlight"><span class="filename">list.kt</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="cm">/* 2 つのリストを連結 */</span>
+<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a><span class="kd">val</span><span class="w"> </span><span class="nv">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">intArrayOf</span><span class="p">(</span><span class="m">6</span><span class="p">,</span><span class="w"> </span><span class="m">8</span><span class="p">,</span><span class="w"> </span><span class="m">7</span><span class="p">,</span><span class="w"> </span><span class="m">10</span><span class="p">,</span><span class="w"> </span><span class="m">9</span><span class="p">).</span><span class="na">toMutableList</span><span class="p">()</span>
+<a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a><span class="n">nums</span><span class="p">.</span><span class="na">addAll</span><span class="p">(</span><span class="n">nums1</span><span class="p">)</span><span class="w">  </span><span class="c1">// リスト nums1 を nums の後ろに連結</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.rb</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="c1"># 2 つのリストを連結</span>
+<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a><span class="n">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="o">]</span>
+<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a><span class="n">nums</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums1</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h3 id="6">6. &nbsp; リストのソート<a class="headerlink" href="#6" title="Permanent link">&para;</a></h3>
-<p>リストがソートされると、「二分探索」や「双ポインタ」アルゴリズムなど、配列関連のアルゴリズム問題でよく使用されるアルゴリズムを使用できます。</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="6:12"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Kotlin</label></div>
+<details class="pythontutor">
+<summary>可視化実行</summary>
+<p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%88%97%E8%A1%A8%0A%20%20%20%20nums%20%3D%20%5B1,%203,%202,%205,%204%5D%0A%20%20%20%20%0A%20%20%20%20%23%20%E6%8B%BC%E6%8E%A5%E4%B8%A4%E4%B8%AA%E5%88%97%E8%A1%A8%0A%20%20%20%20nums1%20%3D%20%5B6,%208,%207,%2010,%209%5D%0A%20%20%20%20nums%20%2B%3D%20nums1%20%20%23%20%E5%B0%86%E5%88%97%E8%A1%A8%20nums1%20%E6%8B%BC%E6%8E%A5%E5%88%B0%20nums%20%E4%B9%8B%E5%90%8E&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>
+</details>
+<h3 id="6">6. &nbsp; リストをソート<a class="headerlink" href="#6" title="Permanent link">&para;</a></h3>
+<p>リストのソートが完了すると、配列系アルゴリズム問題でよく問われる「二分探索」や「両ポインタ」アルゴリズムを使えるようになる。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="6:13"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><input id="__tabbed_6_13" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Kotlin</label><label for="__tabbed_6_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.py</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="c1"># リストをソート</span>
-<a id="__codelineno-60-2" name="__codelineno-60-2" href="#__codelineno-60-2"></a><span class="n">nums</span><span class="o">.</span><span class="n">sort</span><span class="p">()</span>  <span class="c1"># ソート後、リスト要素は昇順になります</span>
+<div class="highlight"><span class="filename">list.py</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="c1"># リストをソート</span>
+<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></a><span class="n">nums</span><span class="o">.</span><span class="n">sort</span><span class="p">()</span>  <span class="c1"># ソート後、リスト要素は小さい順に並ぶ</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.cpp</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="cm">/* リストをソート */</span>
-<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a><span class="n">sort</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">end</span><span class="p">());</span><span class="w">  </span><span class="c1">// ソート後、リスト要素は昇順になります</span>
+<div class="highlight"><span class="filename">list.cpp</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="cm">/* リストをソート */</span>
+<a id="__codelineno-66-2" name="__codelineno-66-2" href="#__codelineno-66-2"></a><span class="n">sort</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">end</span><span class="p">());</span><span class="w">  </span><span class="c1">// ソート後、リスト要素は小さい順に並ぶ</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.java</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="cm">/* リストをソート */</span>
-<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a><span class="n">Collections</span><span class="p">.</span><span class="na">sort</span><span class="p">(</span><span class="n">nums</span><span class="p">);</span><span class="w">  </span><span class="c1">// ソート後、リスト要素は昇順になります</span>
+<div class="highlight"><span class="filename">list.java</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="cm">/* リストをソート */</span>
+<a id="__codelineno-67-2" name="__codelineno-67-2" href="#__codelineno-67-2"></a><span class="n">Collections</span><span class="p">.</span><span class="na">sort</span><span class="p">(</span><span class="n">nums</span><span class="p">);</span><span class="w">  </span><span class="c1">// ソート後、リスト要素は小さい順に並ぶ</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.cs</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="cm">/* リストをソート */</span>
-<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a><span class="n">nums</span><span class="p">.</span><span class="n">Sort</span><span class="p">();</span><span class="w"> </span><span class="c1">// ソート後、リスト要素は昇順になります</span>
+<div class="highlight"><span class="filename">list.cs</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="cm">/* リストをソート */</span>
+<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a><span class="n">nums</span><span class="p">.</span><span class="n">Sort</span><span class="p">();</span><span class="w"> </span><span class="c1">// ソート後、リスト要素は小さい順に並ぶ</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list_test.go</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="cm">/* リストをソート */</span>
-<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a><span class="nx">sort</span><span class="p">.</span><span class="nx">Ints</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w">  </span><span class="c1">// ソート後、リスト要素は昇順になります</span>
+<div class="highlight"><span class="filename">list_test.go</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="cm">/* リストをソート */</span>
+<a id="__codelineno-69-2" name="__codelineno-69-2" href="#__codelineno-69-2"></a><span class="nx">sort</span><span class="p">.</span><span class="nx">Ints</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w">  </span><span class="c1">// ソート後、リスト要素は小さい順に並ぶ</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.swift</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="cm">/* リストをソート */</span>
-<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></a><span class="n">nums</span><span class="p">.</span><span class="bp">sort</span><span class="p">()</span><span class="w"> </span><span class="c1">// ソート後、リスト要素は昇順になります</span>
+<div class="highlight"><span class="filename">list.swift</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="cm">/* リストをソート */</span>
+<a id="__codelineno-70-2" name="__codelineno-70-2" href="#__codelineno-70-2"></a><span class="n">nums</span><span class="p">.</span><span class="bp">sort</span><span class="p">()</span><span class="w"> </span><span class="c1">// ソート後、リスト要素は小さい順に並ぶ</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.js</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="cm">/* リストをソート */</span>
-<a id="__codelineno-66-2" name="__codelineno-66-2" href="#__codelineno-66-2"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">sort</span><span class="p">((</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">b</span><span class="p">);</span><span class="w">  </span><span class="c1">// ソート後、リスト要素は昇順になります</span>
+<div class="highlight"><span class="filename">list.js</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="cm">/* リストをソート */</span>
+<a id="__codelineno-71-2" name="__codelineno-71-2" href="#__codelineno-71-2"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">sort</span><span class="p">((</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">b</span><span class="p">);</span><span class="w">  </span><span class="c1">// ソート後、リスト要素は小さい順に並ぶ</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.ts</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="cm">/* リストをソート */</span>
-<a id="__codelineno-67-2" name="__codelineno-67-2" href="#__codelineno-67-2"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">sort</span><span class="p">((</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">b</span><span class="p">);</span><span class="w">  </span><span class="c1">// ソート後、リスト要素は昇順になります</span>
+<div class="highlight"><span class="filename">list.ts</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="cm">/* リストをソート */</span>
+<a id="__codelineno-72-2" name="__codelineno-72-2" href="#__codelineno-72-2"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">sort</span><span class="p">((</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">b</span><span class="p">);</span><span class="w">  </span><span class="c1">// ソート後、リスト要素は小さい順に並ぶ</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.dart</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="cm">/* リストをソート */</span>
-<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a><span class="n">nums</span><span class="p">.</span><span class="n">sort</span><span class="p">();</span><span class="w"> </span><span class="c1">// ソート後、リスト要素は昇順になります</span>
+<div class="highlight"><span class="filename">list.dart</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="cm">/* リストをソート */</span>
+<a id="__codelineno-73-2" name="__codelineno-73-2" href="#__codelineno-73-2"></a><span class="n">nums</span><span class="p">.</span><span class="n">sort</span><span class="p">();</span><span class="w"> </span><span class="c1">// ソート後、リスト要素は小さい順に並ぶ</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.rs</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="cm">/* リストをソート */</span>
-<a id="__codelineno-69-2" name="__codelineno-69-2" href="#__codelineno-69-2"></a><span class="n">nums</span><span class="p">.</span><span class="n">sort</span><span class="p">();</span><span class="w"> </span><span class="c1">// ソート後、リスト要素は昇順になります</span>
+<div class="highlight"><span class="filename">list.rs</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="cm">/* リストをソート */</span>
+<a id="__codelineno-74-2" name="__codelineno-74-2" href="#__codelineno-74-2"></a><span class="n">nums</span><span class="p">.</span><span class="n">sort</span><span class="p">();</span><span class="w"> </span><span class="c1">// ソート後、リスト要素は小さい順に並ぶ</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.c</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="c1">// Cは組み込みの動的配列を提供していません</span>
+<div class="highlight"><span class="filename">list.c</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="c1">// C には組み込みの動的配列がない</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">list.kt</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a>
+<div class="highlight"><span class="filename">list.kt</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="cm">/* リストをソート */</span>
+<a id="__codelineno-76-2" name="__codelineno-76-2" href="#__codelineno-76-2"></a><span class="n">nums</span><span class="p">.</span><span class="na">sort</span><span class="p">()</span><span class="w"> </span><span class="c1">// ソート後、リスト要素は小さい順に並ぶ</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.rb</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="c1"># リストをソート</span>
+<a id="__codelineno-77-2" name="__codelineno-77-2" href="#__codelineno-77-2"></a><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">.</span><span class="n">sort</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="o">|</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=&gt;</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="c1"># ソート後、リスト要素は小さい順に並ぶ</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>可視化実行</summary>
+<p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%88%97%E8%A1%A8%0A%20%20%20%20nums%20%3D%20%5B1,%203,%202,%205,%204%5D%0A%20%20%20%20%0A%20%20%20%20%23%20%E6%8E%92%E5%BA%8F%E5%88%97%E8%A1%A8%0A%20%20%20%20nums.sort%28%29%20%20%23%20%E6%8E%92%E5%BA%8F%E5%90%8E%EF%BC%8C%E5%88%97%E8%A1%A8%E5%85%83%E7%B4%A0%E4%BB%8E%E5%B0%8F%E5%88%B0%E5%A4%A7%E6%8E%92%E5%88%97&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>
+</details>
 <h2 id="432">4.3.2 &nbsp; リストの実装<a class="headerlink" href="#432" title="Permanent link">&para;</a></h2>
-<p>多くのプログラミング言語には、Java、C++、Pythonなどを含む組み込みリストが付属しています。それらの実装は、初期容量や拡張係数などの様々なパラメータを慎重に考慮した設定で、複雑になりがちです。興味のある読者は、さらなる学習のためにソースコードを調べることができます。</p>
-<p>リストがどのように動作するかの理解を深めるために、3つの重要な設計側面に焦点を当てて、簡略化されたリストの実装を試みます：</p>
+<p>多くのプログラミング言語にはリストが組み込まれており、たとえば Java、C++、Python などがある。それらの実装は比較的複雑で、初期容量や拡張倍率など各種パラメータの設定もよく考えられている。興味があればソースコードを参照して学べる。</p>
+<p>リストの動作原理への理解を深めるため、ここでは簡易版のリストを実装し、以下の 3 つの設計ポイントを含める。</p>
 <ul>
-<li><strong>初期容量</strong>：配列に合理的な初期容量を選択します。この例では、初期容量として10を選択します。</li>
-<li><strong>サイズ記録</strong>：リスト内の現在の要素数を記録する変数<code>size</code>を宣言し、要素の挿入と削除でリアルタイムに更新します。この変数により、リストの末尾を特定し、拡張が必要かどうかを判断できます。</li>
-<li><strong>拡張メカニズム</strong>：要素挿入時にリストが満杯に達した場合、拡張プロセスが必要です。これには拡張係数に基づいてより大きな配列を作成し、現在の配列からすべての要素を新しい配列に転送することが含まれます。この例では、拡張のたびに配列サイズを2倍にすることを規定します。</li>
+<li><strong>初期容量</strong>：妥当な配列の初期容量を選ぶ。この例では 10 を初期容量として選ぶ。</li>
+<li><strong>要素数の記録</strong>：<code>size</code> という変数を宣言して、現在のリスト要素数を記録し、要素の挿入と削除に応じてリアルタイムに更新する。この変数により、リスト末尾の位置を特定し、拡張が必要かどうかを判断できる。</li>
+<li><strong>拡張機構</strong>：要素を挿入する時点でリスト容量がいっぱいなら、拡張が必要になる。まず拡張倍率に応じてより大きな配列を作成し、次に現在の配列の全要素を順に新しい配列へ移す。この例では、配列を毎回以前の 2 倍に拡張する。</li>
 </ul>
 <div class="tabbed-set tabbed-alternate" data-tabs="7:13"><input checked="checked" id="__tabbed_7_1" name="__tabbed_7" type="radio" /><input id="__tabbed_7_2" name="__tabbed_7" type="radio" /><input id="__tabbed_7_3" name="__tabbed_7" type="radio" /><input id="__tabbed_7_4" name="__tabbed_7" type="radio" /><input id="__tabbed_7_5" name="__tabbed_7" type="radio" /><input id="__tabbed_7_6" name="__tabbed_7" type="radio" /><input id="__tabbed_7_7" name="__tabbed_7" type="radio" /><input id="__tabbed_7_8" name="__tabbed_7" type="radio" /><input id="__tabbed_7_9" name="__tabbed_7" type="radio" /><input id="__tabbed_7_10" name="__tabbed_7" type="radio" /><input id="__tabbed_7_11" name="__tabbed_7" type="radio" /><input id="__tabbed_7_12" name="__tabbed_7" type="radio" /><input id="__tabbed_7_13" name="__tabbed_7" type="radio" /><div class="tabbed-labels"><label for="__tabbed_7_1">Python</label><label for="__tabbed_7_2">C++</label><label for="__tabbed_7_3">Java</label><label for="__tabbed_7_4">C#</label><label for="__tabbed_7_5">Go</label><label for="__tabbed_7_6">Swift</label><label for="__tabbed_7_7">JS</label><label for="__tabbed_7_8">TS</label><label for="__tabbed_7_9">Dart</label><label for="__tabbed_7_10">Rust</label><label for="__tabbed_7_11">C</label><label for="__tabbed_7_12">Kotlin</label><label for="__tabbed_7_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_list.py</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">MyList</span><span class="p">:</span>
-<a id="__codelineno-72-2" name="__codelineno-72-2" href="#__codelineno-72-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;リストクラス&quot;&quot;&quot;</span>
-<a id="__codelineno-72-3" name="__codelineno-72-3" href="#__codelineno-72-3"></a>
-<a id="__codelineno-72-4" name="__codelineno-72-4" href="#__codelineno-72-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<a id="__codelineno-72-5" name="__codelineno-72-5" href="#__codelineno-72-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
-<a id="__codelineno-72-6" name="__codelineno-72-6" href="#__codelineno-72-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_capacity</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">10</span>  <span class="c1"># リストの容量</span>
-<a id="__codelineno-72-7" name="__codelineno-72-7" href="#__codelineno-72-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">_capacity</span>  <span class="c1"># 配列（リスト要素を格納）</span>
-<a id="__codelineno-72-8" name="__codelineno-72-8" href="#__codelineno-72-8"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># リストの長さ（現在の要素数）</span>
-<a id="__codelineno-72-9" name="__codelineno-72-9" href="#__codelineno-72-9"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_extend_ratio</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">2</span>  <span class="c1"># 各リスト拡張の倍数</span>
-<a id="__codelineno-72-10" name="__codelineno-72-10" href="#__codelineno-72-10"></a>
-<a id="__codelineno-72-11" name="__codelineno-72-11" href="#__codelineno-72-11"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-72-12" name="__codelineno-72-12" href="#__codelineno-72-12"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;リストの長さ（現在の要素数）を取得&quot;&quot;&quot;</span>
-<a id="__codelineno-72-13" name="__codelineno-72-13" href="#__codelineno-72-13"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span>
-<a id="__codelineno-72-14" name="__codelineno-72-14" href="#__codelineno-72-14"></a>
-<a id="__codelineno-72-15" name="__codelineno-72-15" href="#__codelineno-72-15"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">capacity</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-72-16" name="__codelineno-72-16" href="#__codelineno-72-16"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;リストの容量を取得&quot;&quot;&quot;</span>
-<a id="__codelineno-72-17" name="__codelineno-72-17" href="#__codelineno-72-17"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_capacity</span>
-<a id="__codelineno-72-18" name="__codelineno-72-18" href="#__codelineno-72-18"></a>
-<a id="__codelineno-72-19" name="__codelineno-72-19" href="#__codelineno-72-19"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-72-20" name="__codelineno-72-20" href="#__codelineno-72-20"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;要素にアクセス&quot;&quot;&quot;</span>
-<a id="__codelineno-72-21" name="__codelineno-72-21" href="#__codelineno-72-21"></a>        <span class="c1"># インデックスが範囲外の場合、以下のように例外をスロー</span>
-<a id="__codelineno-72-22" name="__codelineno-72-22" href="#__codelineno-72-22"></a>        <span class="k">if</span> <span class="n">index</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">index</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span>
-<a id="__codelineno-72-23" name="__codelineno-72-23" href="#__codelineno-72-23"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Index out of bounds&quot;</span><span class="p">)</span>
-<a id="__codelineno-72-24" name="__codelineno-72-24" href="#__codelineno-72-24"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
-<a id="__codelineno-72-25" name="__codelineno-72-25" href="#__codelineno-72-25"></a>
-<a id="__codelineno-72-26" name="__codelineno-72-26" href="#__codelineno-72-26"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">set</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-72-27" name="__codelineno-72-27" href="#__codelineno-72-27"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;要素を更新&quot;&quot;&quot;</span>
-<a id="__codelineno-72-28" name="__codelineno-72-28" href="#__codelineno-72-28"></a>        <span class="k">if</span> <span class="n">index</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">index</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span>
-<a id="__codelineno-72-29" name="__codelineno-72-29" href="#__codelineno-72-29"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Index out of bounds&quot;</span><span class="p">)</span>
-<a id="__codelineno-72-30" name="__codelineno-72-30" href="#__codelineno-72-30"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>
-<a id="__codelineno-72-31" name="__codelineno-72-31" href="#__codelineno-72-31"></a>
-<a id="__codelineno-72-32" name="__codelineno-72-32" href="#__codelineno-72-32"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">add</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-72-33" name="__codelineno-72-33" href="#__codelineno-72-33"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;末尾に要素を追加&quot;&quot;&quot;</span>
-<a id="__codelineno-72-34" name="__codelineno-72-34" href="#__codelineno-72-34"></a>        <span class="c1"># 要素数が容量を超える場合、拡張メカニズムをトリガー</span>
-<a id="__codelineno-72-35" name="__codelineno-72-35" href="#__codelineno-72-35"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">():</span>
-<a id="__codelineno-72-36" name="__codelineno-72-36" href="#__codelineno-72-36"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">extend_capacity</span><span class="p">()</span>
-<a id="__codelineno-72-37" name="__codelineno-72-37" href="#__codelineno-72-37"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>
-<a id="__codelineno-72-38" name="__codelineno-72-38" href="#__codelineno-72-38"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">+=</span> <span class="mi">1</span>
-<a id="__codelineno-72-39" name="__codelineno-72-39" href="#__codelineno-72-39"></a>
-<a id="__codelineno-72-40" name="__codelineno-72-40" href="#__codelineno-72-40"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-72-41" name="__codelineno-72-41" href="#__codelineno-72-41"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;中間に要素を挿入&quot;&quot;&quot;</span>
-<a id="__codelineno-72-42" name="__codelineno-72-42" href="#__codelineno-72-42"></a>        <span class="k">if</span> <span class="n">index</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">index</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span>
-<a id="__codelineno-72-43" name="__codelineno-72-43" href="#__codelineno-72-43"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Index out of bounds&quot;</span><span class="p">)</span>
-<a id="__codelineno-72-44" name="__codelineno-72-44" href="#__codelineno-72-44"></a>        <span class="c1"># 要素数が容量を超える場合、拡張メカニズムをトリガー</span>
-<a id="__codelineno-72-45" name="__codelineno-72-45" href="#__codelineno-72-45"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">():</span>
-<a id="__codelineno-72-46" name="__codelineno-72-46" href="#__codelineno-72-46"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">extend_capacity</span><span class="p">()</span>
-<a id="__codelineno-72-47" name="__codelineno-72-47" href="#__codelineno-72-47"></a>        <span class="c1"># インデックス index より後のすべての要素を1つ後ろに移動</span>
-<a id="__codelineno-72-48" name="__codelineno-72-48" href="#__codelineno-72-48"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">index</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
-<a id="__codelineno-72-49" name="__codelineno-72-49" href="#__codelineno-72-49"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
-<a id="__codelineno-72-50" name="__codelineno-72-50" href="#__codelineno-72-50"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>
-<a id="__codelineno-72-51" name="__codelineno-72-51" href="#__codelineno-72-51"></a>        <span class="c1"># 要素数を更新</span>
-<a id="__codelineno-72-52" name="__codelineno-72-52" href="#__codelineno-72-52"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">+=</span> <span class="mi">1</span>
-<a id="__codelineno-72-53" name="__codelineno-72-53" href="#__codelineno-72-53"></a>
-<a id="__codelineno-72-54" name="__codelineno-72-54" href="#__codelineno-72-54"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-72-55" name="__codelineno-72-55" href="#__codelineno-72-55"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;要素を削除&quot;&quot;&quot;</span>
-<a id="__codelineno-72-56" name="__codelineno-72-56" href="#__codelineno-72-56"></a>        <span class="k">if</span> <span class="n">index</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">index</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span>
-<a id="__codelineno-72-57" name="__codelineno-72-57" href="#__codelineno-72-57"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Index out of bounds&quot;</span><span class="p">)</span>
-<a id="__codelineno-72-58" name="__codelineno-72-58" href="#__codelineno-72-58"></a>        <span class="n">num</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
-<a id="__codelineno-72-59" name="__codelineno-72-59" href="#__codelineno-72-59"></a>        <span class="c1"># インデックス index より後のすべての要素を1つ前に移動</span>
-<a id="__codelineno-72-60" name="__codelineno-72-60" href="#__codelineno-72-60"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">index</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
-<a id="__codelineno-72-61" name="__codelineno-72-61" href="#__codelineno-72-61"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span>
-<a id="__codelineno-72-62" name="__codelineno-72-62" href="#__codelineno-72-62"></a>        <span class="c1"># 要素数を更新</span>
-<a id="__codelineno-72-63" name="__codelineno-72-63" href="#__codelineno-72-63"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-=</span> <span class="mi">1</span>
-<a id="__codelineno-72-64" name="__codelineno-72-64" href="#__codelineno-72-64"></a>        <span class="c1"># 削除された要素を返す</span>
-<a id="__codelineno-72-65" name="__codelineno-72-65" href="#__codelineno-72-65"></a>        <span class="k">return</span> <span class="n">num</span>
-<a id="__codelineno-72-66" name="__codelineno-72-66" href="#__codelineno-72-66"></a>
-<a id="__codelineno-72-67" name="__codelineno-72-67" href="#__codelineno-72-67"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">extend_capacity</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<a id="__codelineno-72-68" name="__codelineno-72-68" href="#__codelineno-72-68"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;リストを拡張&quot;&quot;&quot;</span>
-<a id="__codelineno-72-69" name="__codelineno-72-69" href="#__codelineno-72-69"></a>        <span class="c1"># 元の配列の _extend_ratio 倍の長さの新しい配列を作成し、元の配列を新しい配列にコピー</span>
-<a id="__codelineno-72-70" name="__codelineno-72-70" href="#__codelineno-72-70"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span> <span class="o">+</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">()</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_extend_ratio</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-72-71" name="__codelineno-72-71" href="#__codelineno-72-71"></a>        <span class="c1"># リストの容量を更新</span>
-<a id="__codelineno-72-72" name="__codelineno-72-72" href="#__codelineno-72-72"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_capacity</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">)</span>
-<a id="__codelineno-72-73" name="__codelineno-72-73" href="#__codelineno-72-73"></a>
-<a id="__codelineno-72-74" name="__codelineno-72-74" href="#__codelineno-72-74"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">to_array</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
-<a id="__codelineno-72-75" name="__codelineno-72-75" href="#__codelineno-72-75"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;有効な長さのリストを返す&quot;&quot;&quot;</span>
-<a id="__codelineno-72-76" name="__codelineno-72-76" href="#__codelineno-72-76"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[:</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">]</span>
+<div class="highlight"><span class="filename">my_list.py</span><pre><span></span><code><a id="__codelineno-78-1" name="__codelineno-78-1" href="#__codelineno-78-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">MyList</span><span class="p">:</span>
+<a id="__codelineno-78-2" name="__codelineno-78-2" href="#__codelineno-78-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;リストクラス&quot;&quot;&quot;</span>
+<a id="__codelineno-78-3" name="__codelineno-78-3" href="#__codelineno-78-3"></a>
+<a id="__codelineno-78-4" name="__codelineno-78-4" href="#__codelineno-78-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<a id="__codelineno-78-5" name="__codelineno-78-5" href="#__codelineno-78-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
+<a id="__codelineno-78-6" name="__codelineno-78-6" href="#__codelineno-78-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_capacity</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">10</span>  <span class="c1"># リスト容量</span>
+<a id="__codelineno-78-7" name="__codelineno-78-7" href="#__codelineno-78-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">_capacity</span>  <span class="c1"># 配列（リスト要素を格納）</span>
+<a id="__codelineno-78-8" name="__codelineno-78-8" href="#__codelineno-78-8"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># リストの長さ（現在の要素数）</span>
+<a id="__codelineno-78-9" name="__codelineno-78-9" href="#__codelineno-78-9"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_extend_ratio</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">2</span>  <span class="c1"># リスト拡張時の増加倍率</span>
+<a id="__codelineno-78-10" name="__codelineno-78-10" href="#__codelineno-78-10"></a>
+<a id="__codelineno-78-11" name="__codelineno-78-11" href="#__codelineno-78-11"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-78-12" name="__codelineno-78-12" href="#__codelineno-78-12"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;リストの長さを取得（現在の要素数）&quot;&quot;&quot;</span>
+<a id="__codelineno-78-13" name="__codelineno-78-13" href="#__codelineno-78-13"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span>
+<a id="__codelineno-78-14" name="__codelineno-78-14" href="#__codelineno-78-14"></a>
+<a id="__codelineno-78-15" name="__codelineno-78-15" href="#__codelineno-78-15"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">capacity</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-78-16" name="__codelineno-78-16" href="#__codelineno-78-16"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;リスト容量を取得する&quot;&quot;&quot;</span>
+<a id="__codelineno-78-17" name="__codelineno-78-17" href="#__codelineno-78-17"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_capacity</span>
+<a id="__codelineno-78-18" name="__codelineno-78-18" href="#__codelineno-78-18"></a>
+<a id="__codelineno-78-19" name="__codelineno-78-19" href="#__codelineno-78-19"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-78-20" name="__codelineno-78-20" href="#__codelineno-78-20"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;要素にアクセス&quot;&quot;&quot;</span>
+<a id="__codelineno-78-21" name="__codelineno-78-21" href="#__codelineno-78-21"></a>        <span class="c1"># インデックスが範囲外なら例外を送出する。以下同様</span>
+<a id="__codelineno-78-22" name="__codelineno-78-22" href="#__codelineno-78-22"></a>        <span class="k">if</span> <span class="n">index</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">index</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span>
+<a id="__codelineno-78-23" name="__codelineno-78-23" href="#__codelineno-78-23"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;インデックスが範囲外です&quot;</span><span class="p">)</span>
+<a id="__codelineno-78-24" name="__codelineno-78-24" href="#__codelineno-78-24"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
+<a id="__codelineno-78-25" name="__codelineno-78-25" href="#__codelineno-78-25"></a>
+<a id="__codelineno-78-26" name="__codelineno-78-26" href="#__codelineno-78-26"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">set</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-78-27" name="__codelineno-78-27" href="#__codelineno-78-27"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;要素を更新&quot;&quot;&quot;</span>
+<a id="__codelineno-78-28" name="__codelineno-78-28" href="#__codelineno-78-28"></a>        <span class="k">if</span> <span class="n">index</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">index</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span>
+<a id="__codelineno-78-29" name="__codelineno-78-29" href="#__codelineno-78-29"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;インデックスが範囲外です&quot;</span><span class="p">)</span>
+<a id="__codelineno-78-30" name="__codelineno-78-30" href="#__codelineno-78-30"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>
+<a id="__codelineno-78-31" name="__codelineno-78-31" href="#__codelineno-78-31"></a>
+<a id="__codelineno-78-32" name="__codelineno-78-32" href="#__codelineno-78-32"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">add</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-78-33" name="__codelineno-78-33" href="#__codelineno-78-33"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;末尾に要素を追加&quot;&quot;&quot;</span>
+<a id="__codelineno-78-34" name="__codelineno-78-34" href="#__codelineno-78-34"></a>        <span class="c1"># 要素数が容量を超えると、拡張機構が発動する</span>
+<a id="__codelineno-78-35" name="__codelineno-78-35" href="#__codelineno-78-35"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">():</span>
+<a id="__codelineno-78-36" name="__codelineno-78-36" href="#__codelineno-78-36"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">extend_capacity</span><span class="p">()</span>
+<a id="__codelineno-78-37" name="__codelineno-78-37" href="#__codelineno-78-37"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>
+<a id="__codelineno-78-38" name="__codelineno-78-38" href="#__codelineno-78-38"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-78-39" name="__codelineno-78-39" href="#__codelineno-78-39"></a>
+<a id="__codelineno-78-40" name="__codelineno-78-40" href="#__codelineno-78-40"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-78-41" name="__codelineno-78-41" href="#__codelineno-78-41"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;中間に要素を挿入&quot;&quot;&quot;</span>
+<a id="__codelineno-78-42" name="__codelineno-78-42" href="#__codelineno-78-42"></a>        <span class="k">if</span> <span class="n">index</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">index</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span>
+<a id="__codelineno-78-43" name="__codelineno-78-43" href="#__codelineno-78-43"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;インデックスが範囲外です&quot;</span><span class="p">)</span>
+<a id="__codelineno-78-44" name="__codelineno-78-44" href="#__codelineno-78-44"></a>        <span class="c1"># 要素数が容量を超えると、拡張機構が発動する</span>
+<a id="__codelineno-78-45" name="__codelineno-78-45" href="#__codelineno-78-45"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">():</span>
+<a id="__codelineno-78-46" name="__codelineno-78-46" href="#__codelineno-78-46"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">extend_capacity</span><span class="p">()</span>
+<a id="__codelineno-78-47" name="__codelineno-78-47" href="#__codelineno-78-47"></a>        <span class="c1"># index 以降の要素をすべて 1 つ後ろへずらす</span>
+<a id="__codelineno-78-48" name="__codelineno-78-48" href="#__codelineno-78-48"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">index</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-78-49" name="__codelineno-78-49" href="#__codelineno-78-49"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-78-50" name="__codelineno-78-50" href="#__codelineno-78-50"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>
+<a id="__codelineno-78-51" name="__codelineno-78-51" href="#__codelineno-78-51"></a>        <span class="c1"># 要素数を更新</span>
+<a id="__codelineno-78-52" name="__codelineno-78-52" href="#__codelineno-78-52"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-78-53" name="__codelineno-78-53" href="#__codelineno-78-53"></a>
+<a id="__codelineno-78-54" name="__codelineno-78-54" href="#__codelineno-78-54"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-78-55" name="__codelineno-78-55" href="#__codelineno-78-55"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;要素を削除&quot;&quot;&quot;</span>
+<a id="__codelineno-78-56" name="__codelineno-78-56" href="#__codelineno-78-56"></a>        <span class="k">if</span> <span class="n">index</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">index</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span>
+<a id="__codelineno-78-57" name="__codelineno-78-57" href="#__codelineno-78-57"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;インデックスが範囲外です&quot;</span><span class="p">)</span>
+<a id="__codelineno-78-58" name="__codelineno-78-58" href="#__codelineno-78-58"></a>        <span class="n">num</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
+<a id="__codelineno-78-59" name="__codelineno-78-59" href="#__codelineno-78-59"></a>        <span class="c1"># インデックス index より後の要素をすべて 1 つ前に移動する</span>
+<a id="__codelineno-78-60" name="__codelineno-78-60" href="#__codelineno-78-60"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">index</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-78-61" name="__codelineno-78-61" href="#__codelineno-78-61"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-78-62" name="__codelineno-78-62" href="#__codelineno-78-62"></a>        <span class="c1"># 要素数を更新</span>
+<a id="__codelineno-78-63" name="__codelineno-78-63" href="#__codelineno-78-63"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-=</span> <span class="mi">1</span>
+<a id="__codelineno-78-64" name="__codelineno-78-64" href="#__codelineno-78-64"></a>        <span class="c1"># 削除された要素を返す</span>
+<a id="__codelineno-78-65" name="__codelineno-78-65" href="#__codelineno-78-65"></a>        <span class="k">return</span> <span class="n">num</span>
+<a id="__codelineno-78-66" name="__codelineno-78-66" href="#__codelineno-78-66"></a>
+<a id="__codelineno-78-67" name="__codelineno-78-67" href="#__codelineno-78-67"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">extend_capacity</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<a id="__codelineno-78-68" name="__codelineno-78-68" href="#__codelineno-78-68"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;リストの拡張&quot;&quot;&quot;</span>
+<a id="__codelineno-78-69" name="__codelineno-78-69" href="#__codelineno-78-69"></a>        <span class="c1"># 元の配列の `_extend_ratio` 倍の長さを持つ新しい配列を作成し、元の配列を新しい配列にコピーする</span>
+<a id="__codelineno-78-70" name="__codelineno-78-70" href="#__codelineno-78-70"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span> <span class="o">+</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">()</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_extend_ratio</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-78-71" name="__codelineno-78-71" href="#__codelineno-78-71"></a>        <span class="c1"># リストの容量を更新</span>
+<a id="__codelineno-78-72" name="__codelineno-78-72" href="#__codelineno-78-72"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_capacity</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">)</span>
+<a id="__codelineno-78-73" name="__codelineno-78-73" href="#__codelineno-78-73"></a>
+<a id="__codelineno-78-74" name="__codelineno-78-74" href="#__codelineno-78-74"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">to_array</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-78-75" name="__codelineno-78-75" href="#__codelineno-78-75"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;有効長のリストを返す&quot;&quot;&quot;</span>
+<a id="__codelineno-78-76" name="__codelineno-78-76" href="#__codelineno-78-76"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[:</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">]</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_list.cpp</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="cm">/* リストクラス */</span>
-<a id="__codelineno-73-2" name="__codelineno-73-2" href="#__codelineno-73-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">MyList</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-73-3" name="__codelineno-73-3" href="#__codelineno-73-3"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
-<a id="__codelineno-73-4" name="__codelineno-73-4" href="#__codelineno-73-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">arr</span><span class="p">;</span><span class="w">             </span><span class="c1">// 配列（リスト要素を格納）</span>
-<a id="__codelineno-73-5" name="__codelineno-73-5" href="#__codelineno-73-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">arrCapacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">10</span><span class="p">;</span><span class="w"> </span><span class="c1">// リストの容量</span>
-<a id="__codelineno-73-6" name="__codelineno-73-6" href="#__codelineno-73-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">arrSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">      </span><span class="c1">// リストの長さ（現在の要素数）</span>
-<a id="__codelineno-73-7" name="__codelineno-73-7" href="#__codelineno-73-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">   </span><span class="c1">// リスト拡張時の倍率</span>
-<a id="__codelineno-73-8" name="__codelineno-73-8" href="#__codelineno-73-8"></a>
-<a id="__codelineno-73-9" name="__codelineno-73-9" href="#__codelineno-73-9"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
-<a id="__codelineno-73-10" name="__codelineno-73-10" href="#__codelineno-73-10"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
-<a id="__codelineno-73-11" name="__codelineno-73-11" href="#__codelineno-73-11"></a><span class="w">    </span><span class="n">MyList</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-73-12" name="__codelineno-73-12" href="#__codelineno-73-12"></a><span class="w">        </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">arrCapacity</span><span class="p">];</span>
-<a id="__codelineno-73-13" name="__codelineno-73-13" href="#__codelineno-73-13"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-73-14" name="__codelineno-73-14" href="#__codelineno-73-14"></a>
-<a id="__codelineno-73-15" name="__codelineno-73-15" href="#__codelineno-73-15"></a><span class="w">    </span><span class="cm">/* デストラクタ */</span>
-<a id="__codelineno-73-16" name="__codelineno-73-16" href="#__codelineno-73-16"></a><span class="w">    </span><span class="o">~</span><span class="n">MyList</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-73-17" name="__codelineno-73-17" href="#__codelineno-73-17"></a><span class="w">        </span><span class="k">delete</span><span class="p">[]</span><span class="w"> </span><span class="n">arr</span><span class="p">;</span>
-<a id="__codelineno-73-18" name="__codelineno-73-18" href="#__codelineno-73-18"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-73-19" name="__codelineno-73-19" href="#__codelineno-73-19"></a>
-<a id="__codelineno-73-20" name="__codelineno-73-20" href="#__codelineno-73-20"></a><span class="w">    </span><span class="cm">/* リストの長さを取得（現在の要素数）*/</span>
-<a id="__codelineno-73-21" name="__codelineno-73-21" href="#__codelineno-73-21"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-73-22" name="__codelineno-73-22" href="#__codelineno-73-22"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">arrSize</span><span class="p">;</span>
-<a id="__codelineno-73-23" name="__codelineno-73-23" href="#__codelineno-73-23"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-73-24" name="__codelineno-73-24" href="#__codelineno-73-24"></a>
-<a id="__codelineno-73-25" name="__codelineno-73-25" href="#__codelineno-73-25"></a><span class="w">    </span><span class="cm">/* リストの容量を取得 */</span>
-<a id="__codelineno-73-26" name="__codelineno-73-26" href="#__codelineno-73-26"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-73-27" name="__codelineno-73-27" href="#__codelineno-73-27"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">arrCapacity</span><span class="p">;</span>
-<a id="__codelineno-73-28" name="__codelineno-73-28" href="#__codelineno-73-28"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-73-29" name="__codelineno-73-29" href="#__codelineno-73-29"></a>
-<a id="__codelineno-73-30" name="__codelineno-73-30" href="#__codelineno-73-30"></a><span class="w">    </span><span class="cm">/* 要素にアクセス */</span>
-<a id="__codelineno-73-31" name="__codelineno-73-31" href="#__codelineno-73-31"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-73-32" name="__codelineno-73-32" href="#__codelineno-73-32"></a><span class="w">        </span><span class="c1">// インデックスが範囲外の場合、例外をスロー（以下同様）</span>
-<a id="__codelineno-73-33" name="__codelineno-73-33" href="#__codelineno-73-33"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
-<a id="__codelineno-73-34" name="__codelineno-73-34" href="#__codelineno-73-34"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Index out of bounds&quot;</span><span class="p">);</span>
-<a id="__codelineno-73-35" name="__codelineno-73-35" href="#__codelineno-73-35"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
-<a id="__codelineno-73-36" name="__codelineno-73-36" href="#__codelineno-73-36"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-73-37" name="__codelineno-73-37" href="#__codelineno-73-37"></a>
-<a id="__codelineno-73-38" name="__codelineno-73-38" href="#__codelineno-73-38"></a><span class="w">    </span><span class="cm">/* 要素を更新 */</span>
-<a id="__codelineno-73-39" name="__codelineno-73-39" href="#__codelineno-73-39"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">set</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-73-40" name="__codelineno-73-40" href="#__codelineno-73-40"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
-<a id="__codelineno-73-41" name="__codelineno-73-41" href="#__codelineno-73-41"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Index out of bounds&quot;</span><span class="p">);</span>
-<a id="__codelineno-73-42" name="__codelineno-73-42" href="#__codelineno-73-42"></a><span class="w">        </span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-73-43" name="__codelineno-73-43" href="#__codelineno-73-43"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-73-44" name="__codelineno-73-44" href="#__codelineno-73-44"></a>
-<a id="__codelineno-73-45" name="__codelineno-73-45" href="#__codelineno-73-45"></a><span class="w">    </span><span class="cm">/* 末尾に要素を追加 */</span>
-<a id="__codelineno-73-46" name="__codelineno-73-46" href="#__codelineno-73-46"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">add</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-73-47" name="__codelineno-73-47" href="#__codelineno-73-47"></a><span class="w">        </span><span class="c1">// 要素数が容量を超えた場合、拡張メカニズムをトリガー</span>
-<a id="__codelineno-73-48" name="__codelineno-73-48" href="#__codelineno-73-48"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span>
-<a id="__codelineno-73-49" name="__codelineno-73-49" href="#__codelineno-73-49"></a><span class="w">            </span><span class="n">extendCapacity</span><span class="p">();</span>
-<a id="__codelineno-73-50" name="__codelineno-73-50" href="#__codelineno-73-50"></a><span class="w">        </span><span class="n">arr</span><span class="p">[</span><span class="n">size</span><span class="p">()]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-73-51" name="__codelineno-73-51" href="#__codelineno-73-51"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
-<a id="__codelineno-73-52" name="__codelineno-73-52" href="#__codelineno-73-52"></a><span class="w">        </span><span class="n">arrSize</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-73-53" name="__codelineno-73-53" href="#__codelineno-73-53"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-73-54" name="__codelineno-73-54" href="#__codelineno-73-54"></a>
-<a id="__codelineno-73-55" name="__codelineno-73-55" href="#__codelineno-73-55"></a><span class="w">    </span><span class="cm">/* 中間に要素を挿入 */</span>
-<a id="__codelineno-73-56" name="__codelineno-73-56" href="#__codelineno-73-56"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">insert</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-73-57" name="__codelineno-73-57" href="#__codelineno-73-57"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
-<a id="__codelineno-73-58" name="__codelineno-73-58" href="#__codelineno-73-58"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Index out of bounds&quot;</span><span class="p">);</span>
-<a id="__codelineno-73-59" name="__codelineno-73-59" href="#__codelineno-73-59"></a><span class="w">        </span><span class="c1">// 要素数が容量を超えた場合、拡張メカニズムをトリガー</span>
-<a id="__codelineno-73-60" name="__codelineno-73-60" href="#__codelineno-73-60"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span>
-<a id="__codelineno-73-61" name="__codelineno-73-61" href="#__codelineno-73-61"></a><span class="w">            </span><span class="n">extendCapacity</span><span class="p">();</span>
-<a id="__codelineno-73-62" name="__codelineno-73-62" href="#__codelineno-73-62"></a><span class="w">        </span><span class="c1">// `index`より後のすべての要素を1つ後ろに移動</span>
-<a id="__codelineno-73-63" name="__codelineno-73-63" href="#__codelineno-73-63"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-73-64" name="__codelineno-73-64" href="#__codelineno-73-64"></a><span class="w">            </span><span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
-<a id="__codelineno-73-65" name="__codelineno-73-65" href="#__codelineno-73-65"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-73-66" name="__codelineno-73-66" href="#__codelineno-73-66"></a><span class="w">        </span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-73-67" name="__codelineno-73-67" href="#__codelineno-73-67"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
-<a id="__codelineno-73-68" name="__codelineno-73-68" href="#__codelineno-73-68"></a><span class="w">        </span><span class="n">arrSize</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-73-69" name="__codelineno-73-69" href="#__codelineno-73-69"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-73-70" name="__codelineno-73-70" href="#__codelineno-73-70"></a>
-<a id="__codelineno-73-71" name="__codelineno-73-71" href="#__codelineno-73-71"></a><span class="w">    </span><span class="cm">/* 要素を削除 */</span>
-<a id="__codelineno-73-72" name="__codelineno-73-72" href="#__codelineno-73-72"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-73-73" name="__codelineno-73-73" href="#__codelineno-73-73"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
-<a id="__codelineno-73-74" name="__codelineno-73-74" href="#__codelineno-73-74"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Index out of bounds&quot;</span><span class="p">);</span>
-<a id="__codelineno-73-75" name="__codelineno-73-75" href="#__codelineno-73-75"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
-<a id="__codelineno-73-76" name="__codelineno-73-76" href="#__codelineno-73-76"></a><span class="w">        </span><span class="c1">// `index`より後のすべての要素を1つ前に移動</span>
-<a id="__codelineno-73-77" name="__codelineno-73-77" href="#__codelineno-73-77"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-73-78" name="__codelineno-73-78" href="#__codelineno-73-78"></a><span class="w">            </span><span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
-<a id="__codelineno-73-79" name="__codelineno-73-79" href="#__codelineno-73-79"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-73-80" name="__codelineno-73-80" href="#__codelineno-73-80"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
-<a id="__codelineno-73-81" name="__codelineno-73-81" href="#__codelineno-73-81"></a><span class="w">        </span><span class="n">arrSize</span><span class="o">--</span><span class="p">;</span>
-<a id="__codelineno-73-82" name="__codelineno-73-82" href="#__codelineno-73-82"></a><span class="w">        </span><span class="c1">// 削除された要素を返却</span>
-<a id="__codelineno-73-83" name="__codelineno-73-83" href="#__codelineno-73-83"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-73-84" name="__codelineno-73-84" href="#__codelineno-73-84"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-73-85" name="__codelineno-73-85" href="#__codelineno-73-85"></a>
-<a id="__codelineno-73-86" name="__codelineno-73-86" href="#__codelineno-73-86"></a><span class="w">    </span><span class="cm">/* リストを拡張 */</span>
-<a id="__codelineno-73-87" name="__codelineno-73-87" href="#__codelineno-73-87"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">extendCapacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-73-88" name="__codelineno-73-88" href="#__codelineno-73-88"></a><span class="w">        </span><span class="c1">// 元の配列のextendRatio倍の長さで新しい配列を作成</span>
-<a id="__codelineno-73-89" name="__codelineno-73-89" href="#__codelineno-73-89"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">newCapacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span>
-<a id="__codelineno-73-90" name="__codelineno-73-90" href="#__codelineno-73-90"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">;</span>
-<a id="__codelineno-73-91" name="__codelineno-73-91" href="#__codelineno-73-91"></a><span class="w">        </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">newCapacity</span><span class="p">];</span>
-<a id="__codelineno-73-92" name="__codelineno-73-92" href="#__codelineno-73-92"></a><span class="w">        </span><span class="c1">// 元の配列のすべての要素を新しい配列にコピー</span>
-<a id="__codelineno-73-93" name="__codelineno-73-93" href="#__codelineno-73-93"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-73-94" name="__codelineno-73-94" href="#__codelineno-73-94"></a><span class="w">            </span><span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
-<a id="__codelineno-73-95" name="__codelineno-73-95" href="#__codelineno-73-95"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-73-96" name="__codelineno-73-96" href="#__codelineno-73-96"></a><span class="w">        </span><span class="c1">// メモリを解放</span>
-<a id="__codelineno-73-97" name="__codelineno-73-97" href="#__codelineno-73-97"></a><span class="w">        </span><span class="k">delete</span><span class="p">[]</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
-<a id="__codelineno-73-98" name="__codelineno-73-98" href="#__codelineno-73-98"></a><span class="w">        </span><span class="n">arrCapacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newCapacity</span><span class="p">;</span>
-<a id="__codelineno-73-99" name="__codelineno-73-99" href="#__codelineno-73-99"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-73-100" name="__codelineno-73-100" href="#__codelineno-73-100"></a>
-<a id="__codelineno-73-101" name="__codelineno-73-101" href="#__codelineno-73-101"></a><span class="w">    </span><span class="cm">/* リストをVectorに変換して印刷用に使用 */</span>
-<a id="__codelineno-73-102" name="__codelineno-73-102" href="#__codelineno-73-102"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toVector</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-73-103" name="__codelineno-73-103" href="#__codelineno-73-103"></a><span class="w">        </span><span class="c1">// 有効な長さ範囲内の要素のみを変換</span>
-<a id="__codelineno-73-104" name="__codelineno-73-104" href="#__codelineno-73-104"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">vec</span><span class="p">(</span><span class="n">size</span><span class="p">());</span>
-<a id="__codelineno-73-105" name="__codelineno-73-105" href="#__codelineno-73-105"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-73-106" name="__codelineno-73-106" href="#__codelineno-73-106"></a><span class="w">            </span><span class="n">vec</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
-<a id="__codelineno-73-107" name="__codelineno-73-107" href="#__codelineno-73-107"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-73-108" name="__codelineno-73-108" href="#__codelineno-73-108"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">vec</span><span class="p">;</span>
-<a id="__codelineno-73-109" name="__codelineno-73-109" href="#__codelineno-73-109"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-73-110" name="__codelineno-73-110" href="#__codelineno-73-110"></a><span class="p">};</span>
+<div class="highlight"><span class="filename">my_list.cpp</span><pre><span></span><code><a id="__codelineno-79-1" name="__codelineno-79-1" href="#__codelineno-79-1"></a><span class="cm">/* リストクラス */</span>
+<a id="__codelineno-79-2" name="__codelineno-79-2" href="#__codelineno-79-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">MyList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-3" name="__codelineno-79-3" href="#__codelineno-79-3"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
+<a id="__codelineno-79-4" name="__codelineno-79-4" href="#__codelineno-79-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">arr</span><span class="p">;</span><span class="w">             </span><span class="c1">// 配列（リスト要素を格納）</span>
+<a id="__codelineno-79-5" name="__codelineno-79-5" href="#__codelineno-79-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">arrCapacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">10</span><span class="p">;</span><span class="w"> </span><span class="c1">// リスト容量</span>
+<a id="__codelineno-79-6" name="__codelineno-79-6" href="#__codelineno-79-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">arrSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">      </span><span class="c1">// リストの長さ（現在の要素数）</span>
+<a id="__codelineno-79-7" name="__codelineno-79-7" href="#__codelineno-79-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">   </span><span class="c1">// リスト拡張時の増加倍率</span>
+<a id="__codelineno-79-8" name="__codelineno-79-8" href="#__codelineno-79-8"></a>
+<a id="__codelineno-79-9" name="__codelineno-79-9" href="#__codelineno-79-9"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
+<a id="__codelineno-79-10" name="__codelineno-79-10" href="#__codelineno-79-10"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-79-11" name="__codelineno-79-11" href="#__codelineno-79-11"></a><span class="w">    </span><span class="n">MyList</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-12" name="__codelineno-79-12" href="#__codelineno-79-12"></a><span class="w">        </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">arrCapacity</span><span class="p">];</span>
+<a id="__codelineno-79-13" name="__codelineno-79-13" href="#__codelineno-79-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-79-14" name="__codelineno-79-14" href="#__codelineno-79-14"></a>
+<a id="__codelineno-79-15" name="__codelineno-79-15" href="#__codelineno-79-15"></a><span class="w">    </span><span class="cm">/* デストラクタメソッド */</span>
+<a id="__codelineno-79-16" name="__codelineno-79-16" href="#__codelineno-79-16"></a><span class="w">    </span><span class="o">~</span><span class="n">MyList</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-17" name="__codelineno-79-17" href="#__codelineno-79-17"></a><span class="w">        </span><span class="k">delete</span><span class="p">[]</span><span class="w"> </span><span class="n">arr</span><span class="p">;</span>
+<a id="__codelineno-79-18" name="__codelineno-79-18" href="#__codelineno-79-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-79-19" name="__codelineno-79-19" href="#__codelineno-79-19"></a>
+<a id="__codelineno-79-20" name="__codelineno-79-20" href="#__codelineno-79-20"></a><span class="w">    </span><span class="cm">/* リストの長さを取得（現在の要素数） */</span>
+<a id="__codelineno-79-21" name="__codelineno-79-21" href="#__codelineno-79-21"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-22" name="__codelineno-79-22" href="#__codelineno-79-22"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">arrSize</span><span class="p">;</span>
+<a id="__codelineno-79-23" name="__codelineno-79-23" href="#__codelineno-79-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-79-24" name="__codelineno-79-24" href="#__codelineno-79-24"></a>
+<a id="__codelineno-79-25" name="__codelineno-79-25" href="#__codelineno-79-25"></a><span class="w">    </span><span class="cm">/* リスト容量を取得する */</span>
+<a id="__codelineno-79-26" name="__codelineno-79-26" href="#__codelineno-79-26"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-27" name="__codelineno-79-27" href="#__codelineno-79-27"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">arrCapacity</span><span class="p">;</span>
+<a id="__codelineno-79-28" name="__codelineno-79-28" href="#__codelineno-79-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-79-29" name="__codelineno-79-29" href="#__codelineno-79-29"></a>
+<a id="__codelineno-79-30" name="__codelineno-79-30" href="#__codelineno-79-30"></a><span class="w">    </span><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-79-31" name="__codelineno-79-31" href="#__codelineno-79-31"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-32" name="__codelineno-79-32" href="#__codelineno-79-32"></a><span class="w">        </span><span class="c1">// インデックスが範囲外なら例外を送出する。以下同様</span>
+<a id="__codelineno-79-33" name="__codelineno-79-33" href="#__codelineno-79-33"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
+<a id="__codelineno-79-34" name="__codelineno-79-34" href="#__codelineno-79-34"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外&quot;</span><span class="p">);</span>
+<a id="__codelineno-79-35" name="__codelineno-79-35" href="#__codelineno-79-35"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-79-36" name="__codelineno-79-36" href="#__codelineno-79-36"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-79-37" name="__codelineno-79-37" href="#__codelineno-79-37"></a>
+<a id="__codelineno-79-38" name="__codelineno-79-38" href="#__codelineno-79-38"></a><span class="w">    </span><span class="cm">/* 要素を更新 */</span>
+<a id="__codelineno-79-39" name="__codelineno-79-39" href="#__codelineno-79-39"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">set</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-40" name="__codelineno-79-40" href="#__codelineno-79-40"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
+<a id="__codelineno-79-41" name="__codelineno-79-41" href="#__codelineno-79-41"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外&quot;</span><span class="p">);</span>
+<a id="__codelineno-79-42" name="__codelineno-79-42" href="#__codelineno-79-42"></a><span class="w">        </span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-79-43" name="__codelineno-79-43" href="#__codelineno-79-43"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-79-44" name="__codelineno-79-44" href="#__codelineno-79-44"></a>
+<a id="__codelineno-79-45" name="__codelineno-79-45" href="#__codelineno-79-45"></a><span class="w">    </span><span class="cm">/* 末尾に要素を追加 */</span>
+<a id="__codelineno-79-46" name="__codelineno-79-46" href="#__codelineno-79-46"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">add</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-47" name="__codelineno-79-47" href="#__codelineno-79-47"></a><span class="w">        </span><span class="c1">// 要素数が容量を超えると、拡張機構が発動する</span>
+<a id="__codelineno-79-48" name="__codelineno-79-48" href="#__codelineno-79-48"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span>
+<a id="__codelineno-79-49" name="__codelineno-79-49" href="#__codelineno-79-49"></a><span class="w">            </span><span class="n">extendCapacity</span><span class="p">();</span>
+<a id="__codelineno-79-50" name="__codelineno-79-50" href="#__codelineno-79-50"></a><span class="w">        </span><span class="n">arr</span><span class="p">[</span><span class="n">size</span><span class="p">()]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-79-51" name="__codelineno-79-51" href="#__codelineno-79-51"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-79-52" name="__codelineno-79-52" href="#__codelineno-79-52"></a><span class="w">        </span><span class="n">arrSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-79-53" name="__codelineno-79-53" href="#__codelineno-79-53"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-79-54" name="__codelineno-79-54" href="#__codelineno-79-54"></a>
+<a id="__codelineno-79-55" name="__codelineno-79-55" href="#__codelineno-79-55"></a><span class="w">    </span><span class="cm">/* 中間に要素を挿入 */</span>
+<a id="__codelineno-79-56" name="__codelineno-79-56" href="#__codelineno-79-56"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">insert</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-57" name="__codelineno-79-57" href="#__codelineno-79-57"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
+<a id="__codelineno-79-58" name="__codelineno-79-58" href="#__codelineno-79-58"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外&quot;</span><span class="p">);</span>
+<a id="__codelineno-79-59" name="__codelineno-79-59" href="#__codelineno-79-59"></a><span class="w">        </span><span class="c1">// 要素数が容量を超えると、拡張機構が発動する</span>
+<a id="__codelineno-79-60" name="__codelineno-79-60" href="#__codelineno-79-60"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span>
+<a id="__codelineno-79-61" name="__codelineno-79-61" href="#__codelineno-79-61"></a><span class="w">            </span><span class="n">extendCapacity</span><span class="p">();</span>
+<a id="__codelineno-79-62" name="__codelineno-79-62" href="#__codelineno-79-62"></a><span class="w">        </span><span class="c1">// index 以降の要素をすべて 1 つ後ろへずらす</span>
+<a id="__codelineno-79-63" name="__codelineno-79-63" href="#__codelineno-79-63"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-64" name="__codelineno-79-64" href="#__codelineno-79-64"></a><span class="w">            </span><span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-79-65" name="__codelineno-79-65" href="#__codelineno-79-65"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-79-66" name="__codelineno-79-66" href="#__codelineno-79-66"></a><span class="w">        </span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-79-67" name="__codelineno-79-67" href="#__codelineno-79-67"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-79-68" name="__codelineno-79-68" href="#__codelineno-79-68"></a><span class="w">        </span><span class="n">arrSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-79-69" name="__codelineno-79-69" href="#__codelineno-79-69"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-79-70" name="__codelineno-79-70" href="#__codelineno-79-70"></a>
+<a id="__codelineno-79-71" name="__codelineno-79-71" href="#__codelineno-79-71"></a><span class="w">    </span><span class="cm">/* 要素を削除 */</span>
+<a id="__codelineno-79-72" name="__codelineno-79-72" href="#__codelineno-79-72"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-73" name="__codelineno-79-73" href="#__codelineno-79-73"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
+<a id="__codelineno-79-74" name="__codelineno-79-74" href="#__codelineno-79-74"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外&quot;</span><span class="p">);</span>
+<a id="__codelineno-79-75" name="__codelineno-79-75" href="#__codelineno-79-75"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-79-76" name="__codelineno-79-76" href="#__codelineno-79-76"></a><span class="w">        </span><span class="c1">// インデックス index より後の要素をすべて 1 つ前に移動する</span>
+<a id="__codelineno-79-77" name="__codelineno-79-77" href="#__codelineno-79-77"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-78" name="__codelineno-79-78" href="#__codelineno-79-78"></a><span class="w">            </span><span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-79-79" name="__codelineno-79-79" href="#__codelineno-79-79"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-79-80" name="__codelineno-79-80" href="#__codelineno-79-80"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-79-81" name="__codelineno-79-81" href="#__codelineno-79-81"></a><span class="w">        </span><span class="n">arrSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-79-82" name="__codelineno-79-82" href="#__codelineno-79-82"></a><span class="w">        </span><span class="c1">// 削除された要素を返す</span>
+<a id="__codelineno-79-83" name="__codelineno-79-83" href="#__codelineno-79-83"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-79-84" name="__codelineno-79-84" href="#__codelineno-79-84"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-79-85" name="__codelineno-79-85" href="#__codelineno-79-85"></a>
+<a id="__codelineno-79-86" name="__codelineno-79-86" href="#__codelineno-79-86"></a><span class="w">    </span><span class="cm">/* リストの拡張 */</span>
+<a id="__codelineno-79-87" name="__codelineno-79-87" href="#__codelineno-79-87"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">extendCapacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-88" name="__codelineno-79-88" href="#__codelineno-79-88"></a><span class="w">        </span><span class="c1">// 元の配列の `extendRatio` 倍の長さを持つ新しい配列を作成する</span>
+<a id="__codelineno-79-89" name="__codelineno-79-89" href="#__codelineno-79-89"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">newCapacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span>
+<a id="__codelineno-79-90" name="__codelineno-79-90" href="#__codelineno-79-90"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">;</span>
+<a id="__codelineno-79-91" name="__codelineno-79-91" href="#__codelineno-79-91"></a><span class="w">        </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">newCapacity</span><span class="p">];</span>
+<a id="__codelineno-79-92" name="__codelineno-79-92" href="#__codelineno-79-92"></a><span class="w">        </span><span class="c1">// 元の配列の全要素を新しい配列にコピー</span>
+<a id="__codelineno-79-93" name="__codelineno-79-93" href="#__codelineno-79-93"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-94" name="__codelineno-79-94" href="#__codelineno-79-94"></a><span class="w">            </span><span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-79-95" name="__codelineno-79-95" href="#__codelineno-79-95"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-79-96" name="__codelineno-79-96" href="#__codelineno-79-96"></a><span class="w">        </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-79-97" name="__codelineno-79-97" href="#__codelineno-79-97"></a><span class="w">        </span><span class="k">delete</span><span class="p">[]</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-79-98" name="__codelineno-79-98" href="#__codelineno-79-98"></a><span class="w">        </span><span class="n">arrCapacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newCapacity</span><span class="p">;</span>
+<a id="__codelineno-79-99" name="__codelineno-79-99" href="#__codelineno-79-99"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-79-100" name="__codelineno-79-100" href="#__codelineno-79-100"></a>
+<a id="__codelineno-79-101" name="__codelineno-79-101" href="#__codelineno-79-101"></a><span class="w">    </span><span class="cm">/* 出力用にリストを Vector に変換 */</span>
+<a id="__codelineno-79-102" name="__codelineno-79-102" href="#__codelineno-79-102"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toVector</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-103" name="__codelineno-79-103" href="#__codelineno-79-103"></a><span class="w">        </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-79-104" name="__codelineno-79-104" href="#__codelineno-79-104"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">vec</span><span class="p">(</span><span class="n">size</span><span class="p">());</span>
+<a id="__codelineno-79-105" name="__codelineno-79-105" href="#__codelineno-79-105"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-106" name="__codelineno-79-106" href="#__codelineno-79-106"></a><span class="w">            </span><span class="n">vec</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-79-107" name="__codelineno-79-107" href="#__codelineno-79-107"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-79-108" name="__codelineno-79-108" href="#__codelineno-79-108"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">vec</span><span class="p">;</span>
+<a id="__codelineno-79-109" name="__codelineno-79-109" href="#__codelineno-79-109"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-79-110" name="__codelineno-79-110" href="#__codelineno-79-110"></a><span class="p">};</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_list.java</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="cm">/* リストクラス */</span>
-<a id="__codelineno-74-2" name="__codelineno-74-2" href="#__codelineno-74-2"></a><span class="kd">class</span> <span class="nc">MyList</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-74-3" name="__codelineno-74-3" href="#__codelineno-74-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">arr</span><span class="p">;</span><span class="w"> </span><span class="c1">// 配列（リスト要素を格納）</span>
-<a id="__codelineno-74-4" name="__codelineno-74-4" href="#__codelineno-74-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">10</span><span class="p">;</span><span class="w"> </span><span class="c1">// リスト容量</span>
-<a id="__codelineno-74-5" name="__codelineno-74-5" href="#__codelineno-74-5"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// リスト長（現在の要素数）</span>
-<a id="__codelineno-74-6" name="__codelineno-74-6" href="#__codelineno-74-6"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// リストの各拡張倍率</span>
-<a id="__codelineno-74-7" name="__codelineno-74-7" href="#__codelineno-74-7"></a>
-<a id="__codelineno-74-8" name="__codelineno-74-8" href="#__codelineno-74-8"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
-<a id="__codelineno-74-9" name="__codelineno-74-9" href="#__codelineno-74-9"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">MyList</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-74-10" name="__codelineno-74-10" href="#__codelineno-74-10"></a><span class="w">        </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">capacity</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-74-11" name="__codelineno-74-11" href="#__codelineno-74-11"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-74-12" name="__codelineno-74-12" href="#__codelineno-74-12"></a>
-<a id="__codelineno-74-13" name="__codelineno-74-13" href="#__codelineno-74-13"></a><span class="w">    </span><span class="cm">/* リスト長を取得（現在の要素数） */</span>
-<a id="__codelineno-74-14" name="__codelineno-74-14" href="#__codelineno-74-14"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-74-15" name="__codelineno-74-15" href="#__codelineno-74-15"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">;</span>
-<a id="__codelineno-74-16" name="__codelineno-74-16" href="#__codelineno-74-16"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-74-17" name="__codelineno-74-17" href="#__codelineno-74-17"></a>
-<a id="__codelineno-74-18" name="__codelineno-74-18" href="#__codelineno-74-18"></a><span class="w">    </span><span class="cm">/* リスト容量を取得 */</span>
-<a id="__codelineno-74-19" name="__codelineno-74-19" href="#__codelineno-74-19"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-74-20" name="__codelineno-74-20" href="#__codelineno-74-20"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
-<a id="__codelineno-74-21" name="__codelineno-74-21" href="#__codelineno-74-21"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-74-22" name="__codelineno-74-22" href="#__codelineno-74-22"></a>
-<a id="__codelineno-74-23" name="__codelineno-74-23" href="#__codelineno-74-23"></a><span class="w">    </span><span class="cm">/* 要素へのアクセス */</span>
-<a id="__codelineno-74-24" name="__codelineno-74-24" href="#__codelineno-74-24"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-74-25" name="__codelineno-74-25" href="#__codelineno-74-25"></a><span class="w">        </span><span class="c1">// インデックスが範囲外の場合、以下のように例外をスロー</span>
-<a id="__codelineno-74-26" name="__codelineno-74-26" href="#__codelineno-74-26"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">)</span>
-<a id="__codelineno-74-27" name="__codelineno-74-27" href="#__codelineno-74-27"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外です&quot;</span><span class="p">);</span>
-<a id="__codelineno-74-28" name="__codelineno-74-28" href="#__codelineno-74-28"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">arr</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-74-29" name="__codelineno-74-29" href="#__codelineno-74-29"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-74-30" name="__codelineno-74-30" href="#__codelineno-74-30"></a>
-<a id="__codelineno-74-31" name="__codelineno-74-31" href="#__codelineno-74-31"></a><span class="w">    </span><span class="cm">/* 要素の更新 */</span>
-<a id="__codelineno-74-32" name="__codelineno-74-32" href="#__codelineno-74-32"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">set</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-74-33" name="__codelineno-74-33" href="#__codelineno-74-33"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">)</span>
-<a id="__codelineno-74-34" name="__codelineno-74-34" href="#__codelineno-74-34"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外です&quot;</span><span class="p">);</span>
-<a id="__codelineno-74-35" name="__codelineno-74-35" href="#__codelineno-74-35"></a><span class="w">        </span><span class="n">arr</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-74-36" name="__codelineno-74-36" href="#__codelineno-74-36"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-74-37" name="__codelineno-74-37" href="#__codelineno-74-37"></a>
-<a id="__codelineno-74-38" name="__codelineno-74-38" href="#__codelineno-74-38"></a><span class="w">    </span><span class="cm">/* 末尾に要素を追加 */</span>
-<a id="__codelineno-74-39" name="__codelineno-74-39" href="#__codelineno-74-39"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">add</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-74-40" name="__codelineno-74-40" href="#__codelineno-74-40"></a><span class="w">        </span><span class="c1">// 要素数が容量を超える場合、拡張メカニズムを実行</span>
-<a id="__codelineno-74-41" name="__codelineno-74-41" href="#__codelineno-74-41"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span>
-<a id="__codelineno-74-42" name="__codelineno-74-42" href="#__codelineno-74-42"></a><span class="w">            </span><span class="n">extendCapacity</span><span class="p">();</span>
-<a id="__codelineno-74-43" name="__codelineno-74-43" href="#__codelineno-74-43"></a><span class="w">        </span><span class="n">arr</span><span class="o">[</span><span class="n">size</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-74-44" name="__codelineno-74-44" href="#__codelineno-74-44"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
-<a id="__codelineno-74-45" name="__codelineno-74-45" href="#__codelineno-74-45"></a><span class="w">        </span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-74-46" name="__codelineno-74-46" href="#__codelineno-74-46"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-74-47" name="__codelineno-74-47" href="#__codelineno-74-47"></a>
-<a id="__codelineno-74-48" name="__codelineno-74-48" href="#__codelineno-74-48"></a><span class="w">    </span><span class="cm">/* 中間に要素を挿入 */</span>
-<a id="__codelineno-74-49" name="__codelineno-74-49" href="#__codelineno-74-49"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-74-50" name="__codelineno-74-50" href="#__codelineno-74-50"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">)</span>
-<a id="__codelineno-74-51" name="__codelineno-74-51" href="#__codelineno-74-51"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外です&quot;</span><span class="p">);</span>
-<a id="__codelineno-74-52" name="__codelineno-74-52" href="#__codelineno-74-52"></a><span class="w">        </span><span class="c1">// 要素数が容量を超える場合、拡張メカニズムを実行</span>
-<a id="__codelineno-74-53" name="__codelineno-74-53" href="#__codelineno-74-53"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span>
-<a id="__codelineno-74-54" name="__codelineno-74-54" href="#__codelineno-74-54"></a><span class="w">            </span><span class="n">extendCapacity</span><span class="p">();</span>
-<a id="__codelineno-74-55" name="__codelineno-74-55" href="#__codelineno-74-55"></a><span class="w">        </span><span class="c1">// `index` より後のすべての要素を1つ後ろに移動</span>
-<a id="__codelineno-74-56" name="__codelineno-74-56" href="#__codelineno-74-56"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-74-57" name="__codelineno-74-57" href="#__codelineno-74-57"></a><span class="w">            </span><span class="n">arr</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-74-58" name="__codelineno-74-58" href="#__codelineno-74-58"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-74-59" name="__codelineno-74-59" href="#__codelineno-74-59"></a><span class="w">        </span><span class="n">arr</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-74-60" name="__codelineno-74-60" href="#__codelineno-74-60"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
-<a id="__codelineno-74-61" name="__codelineno-74-61" href="#__codelineno-74-61"></a><span class="w">        </span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-74-62" name="__codelineno-74-62" href="#__codelineno-74-62"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-74-63" name="__codelineno-74-63" href="#__codelineno-74-63"></a>
-<a id="__codelineno-74-64" name="__codelineno-74-64" href="#__codelineno-74-64"></a><span class="w">    </span><span class="cm">/* 要素の削除 */</span>
-<a id="__codelineno-74-65" name="__codelineno-74-65" href="#__codelineno-74-65"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-74-66" name="__codelineno-74-66" href="#__codelineno-74-66"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">)</span>
-<a id="__codelineno-74-67" name="__codelineno-74-67" href="#__codelineno-74-67"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外です&quot;</span><span class="p">);</span>
-<a id="__codelineno-74-68" name="__codelineno-74-68" href="#__codelineno-74-68"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-74-69" name="__codelineno-74-69" href="#__codelineno-74-69"></a><span class="w">        </span><span class="c1">// `index` より後のすべての要素を1つ前に移動</span>
-<a id="__codelineno-74-70" name="__codelineno-74-70" href="#__codelineno-74-70"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-74-71" name="__codelineno-74-71" href="#__codelineno-74-71"></a><span class="w">            </span><span class="n">arr</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-74-72" name="__codelineno-74-72" href="#__codelineno-74-72"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-74-73" name="__codelineno-74-73" href="#__codelineno-74-73"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
-<a id="__codelineno-74-74" name="__codelineno-74-74" href="#__codelineno-74-74"></a><span class="w">        </span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
-<a id="__codelineno-74-75" name="__codelineno-74-75" href="#__codelineno-74-75"></a><span class="w">        </span><span class="c1">// 削除された要素を返す</span>
-<a id="__codelineno-74-76" name="__codelineno-74-76" href="#__codelineno-74-76"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-74-77" name="__codelineno-74-77" href="#__codelineno-74-77"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-74-78" name="__codelineno-74-78" href="#__codelineno-74-78"></a>
-<a id="__codelineno-74-79" name="__codelineno-74-79" href="#__codelineno-74-79"></a><span class="w">    </span><span class="cm">/* リストを拡張 */</span>
-<a id="__codelineno-74-80" name="__codelineno-74-80" href="#__codelineno-74-80"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">extendCapacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-74-81" name="__codelineno-74-81" href="#__codelineno-74-81"></a><span class="w">        </span><span class="c1">// 元の配列の長さを extendRatio 倍した新しい配列を作成し、元の配列を新しい配列にコピー</span>
-<a id="__codelineno-74-82" name="__codelineno-74-82" href="#__codelineno-74-82"></a><span class="w">        </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Arrays</span><span class="p">.</span><span class="na">copyOf</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">);</span>
-<a id="__codelineno-74-83" name="__codelineno-74-83" href="#__codelineno-74-83"></a><span class="w">        </span><span class="c1">// リスト容量を更新</span>
-<a id="__codelineno-74-84" name="__codelineno-74-84" href="#__codelineno-74-84"></a><span class="w">        </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
-<a id="__codelineno-74-85" name="__codelineno-74-85" href="#__codelineno-74-85"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-74-86" name="__codelineno-74-86" href="#__codelineno-74-86"></a>
-<a id="__codelineno-74-87" name="__codelineno-74-87" href="#__codelineno-74-87"></a><span class="w">    </span><span class="cm">/* リストを配列に変換 */</span>
-<a id="__codelineno-74-88" name="__codelineno-74-88" href="#__codelineno-74-88"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-74-89" name="__codelineno-74-89" href="#__codelineno-74-89"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="p">();</span>
-<a id="__codelineno-74-90" name="__codelineno-74-90" href="#__codelineno-74-90"></a><span class="w">        </span><span class="c1">// 有効な長さ範囲内の要素のみを変換</span>
-<a id="__codelineno-74-91" name="__codelineno-74-91" href="#__codelineno-74-91"></a><span class="w">        </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">size</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-74-92" name="__codelineno-74-92" href="#__codelineno-74-92"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-74-93" name="__codelineno-74-93" href="#__codelineno-74-93"></a><span class="w">            </span><span class="n">arr</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">get</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
-<a id="__codelineno-74-94" name="__codelineno-74-94" href="#__codelineno-74-94"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-74-95" name="__codelineno-74-95" href="#__codelineno-74-95"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">arr</span><span class="p">;</span>
-<a id="__codelineno-74-96" name="__codelineno-74-96" href="#__codelineno-74-96"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-74-97" name="__codelineno-74-97" href="#__codelineno-74-97"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">my_list.java</span><pre><span></span><code><a id="__codelineno-80-1" name="__codelineno-80-1" href="#__codelineno-80-1"></a><span class="cm">/* リストクラス */</span>
+<a id="__codelineno-80-2" name="__codelineno-80-2" href="#__codelineno-80-2"></a><span class="kd">class</span> <span class="nc">MyList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-3" name="__codelineno-80-3" href="#__codelineno-80-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">arr</span><span class="p">;</span><span class="w"> </span><span class="c1">// 配列（リスト要素を格納）</span>
+<a id="__codelineno-80-4" name="__codelineno-80-4" href="#__codelineno-80-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">10</span><span class="p">;</span><span class="w"> </span><span class="c1">// リスト容量</span>
+<a id="__codelineno-80-5" name="__codelineno-80-5" href="#__codelineno-80-5"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// リストの長さ（現在の要素数）</span>
+<a id="__codelineno-80-6" name="__codelineno-80-6" href="#__codelineno-80-6"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// リスト拡張時の増加倍率</span>
+<a id="__codelineno-80-7" name="__codelineno-80-7" href="#__codelineno-80-7"></a>
+<a id="__codelineno-80-8" name="__codelineno-80-8" href="#__codelineno-80-8"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-80-9" name="__codelineno-80-9" href="#__codelineno-80-9"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">MyList</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-10" name="__codelineno-80-10" href="#__codelineno-80-10"></a><span class="w">        </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">capacity</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-80-11" name="__codelineno-80-11" href="#__codelineno-80-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-80-12" name="__codelineno-80-12" href="#__codelineno-80-12"></a>
+<a id="__codelineno-80-13" name="__codelineno-80-13" href="#__codelineno-80-13"></a><span class="w">    </span><span class="cm">/* リストの長さを取得（現在の要素数） */</span>
+<a id="__codelineno-80-14" name="__codelineno-80-14" href="#__codelineno-80-14"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-15" name="__codelineno-80-15" href="#__codelineno-80-15"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">;</span>
+<a id="__codelineno-80-16" name="__codelineno-80-16" href="#__codelineno-80-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-80-17" name="__codelineno-80-17" href="#__codelineno-80-17"></a>
+<a id="__codelineno-80-18" name="__codelineno-80-18" href="#__codelineno-80-18"></a><span class="w">    </span><span class="cm">/* リスト容量を取得する */</span>
+<a id="__codelineno-80-19" name="__codelineno-80-19" href="#__codelineno-80-19"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-20" name="__codelineno-80-20" href="#__codelineno-80-20"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-80-21" name="__codelineno-80-21" href="#__codelineno-80-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-80-22" name="__codelineno-80-22" href="#__codelineno-80-22"></a>
+<a id="__codelineno-80-23" name="__codelineno-80-23" href="#__codelineno-80-23"></a><span class="w">    </span><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-80-24" name="__codelineno-80-24" href="#__codelineno-80-24"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-25" name="__codelineno-80-25" href="#__codelineno-80-25"></a><span class="w">        </span><span class="c1">// インデックスが範囲外なら例外を送出する。以下同様</span>
+<a id="__codelineno-80-26" name="__codelineno-80-26" href="#__codelineno-80-26"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">)</span>
+<a id="__codelineno-80-27" name="__codelineno-80-27" href="#__codelineno-80-27"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外です&quot;</span><span class="p">);</span>
+<a id="__codelineno-80-28" name="__codelineno-80-28" href="#__codelineno-80-28"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">arr</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-80-29" name="__codelineno-80-29" href="#__codelineno-80-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-80-30" name="__codelineno-80-30" href="#__codelineno-80-30"></a>
+<a id="__codelineno-80-31" name="__codelineno-80-31" href="#__codelineno-80-31"></a><span class="w">    </span><span class="cm">/* 要素を更新 */</span>
+<a id="__codelineno-80-32" name="__codelineno-80-32" href="#__codelineno-80-32"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">set</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-33" name="__codelineno-80-33" href="#__codelineno-80-33"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">)</span>
+<a id="__codelineno-80-34" name="__codelineno-80-34" href="#__codelineno-80-34"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外です&quot;</span><span class="p">);</span>
+<a id="__codelineno-80-35" name="__codelineno-80-35" href="#__codelineno-80-35"></a><span class="w">        </span><span class="n">arr</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-80-36" name="__codelineno-80-36" href="#__codelineno-80-36"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-80-37" name="__codelineno-80-37" href="#__codelineno-80-37"></a>
+<a id="__codelineno-80-38" name="__codelineno-80-38" href="#__codelineno-80-38"></a><span class="w">    </span><span class="cm">/* 末尾に要素を追加 */</span>
+<a id="__codelineno-80-39" name="__codelineno-80-39" href="#__codelineno-80-39"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">add</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-40" name="__codelineno-80-40" href="#__codelineno-80-40"></a><span class="w">        </span><span class="c1">// 要素数が容量を超えると、拡張機構が発動する</span>
+<a id="__codelineno-80-41" name="__codelineno-80-41" href="#__codelineno-80-41"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span>
+<a id="__codelineno-80-42" name="__codelineno-80-42" href="#__codelineno-80-42"></a><span class="w">            </span><span class="n">extendCapacity</span><span class="p">();</span>
+<a id="__codelineno-80-43" name="__codelineno-80-43" href="#__codelineno-80-43"></a><span class="w">        </span><span class="n">arr</span><span class="o">[</span><span class="n">size</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-80-44" name="__codelineno-80-44" href="#__codelineno-80-44"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-80-45" name="__codelineno-80-45" href="#__codelineno-80-45"></a><span class="w">        </span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-80-46" name="__codelineno-80-46" href="#__codelineno-80-46"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-80-47" name="__codelineno-80-47" href="#__codelineno-80-47"></a>
+<a id="__codelineno-80-48" name="__codelineno-80-48" href="#__codelineno-80-48"></a><span class="w">    </span><span class="cm">/* 中間に要素を挿入 */</span>
+<a id="__codelineno-80-49" name="__codelineno-80-49" href="#__codelineno-80-49"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-50" name="__codelineno-80-50" href="#__codelineno-80-50"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">)</span>
+<a id="__codelineno-80-51" name="__codelineno-80-51" href="#__codelineno-80-51"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外です&quot;</span><span class="p">);</span>
+<a id="__codelineno-80-52" name="__codelineno-80-52" href="#__codelineno-80-52"></a><span class="w">        </span><span class="c1">// 要素数が容量を超えると、拡張機構が発動する</span>
+<a id="__codelineno-80-53" name="__codelineno-80-53" href="#__codelineno-80-53"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span>
+<a id="__codelineno-80-54" name="__codelineno-80-54" href="#__codelineno-80-54"></a><span class="w">            </span><span class="n">extendCapacity</span><span class="p">();</span>
+<a id="__codelineno-80-55" name="__codelineno-80-55" href="#__codelineno-80-55"></a><span class="w">        </span><span class="c1">// index 以降の要素をすべて 1 つ後ろへずらす</span>
+<a id="__codelineno-80-56" name="__codelineno-80-56" href="#__codelineno-80-56"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-57" name="__codelineno-80-57" href="#__codelineno-80-57"></a><span class="w">            </span><span class="n">arr</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-80-58" name="__codelineno-80-58" href="#__codelineno-80-58"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-80-59" name="__codelineno-80-59" href="#__codelineno-80-59"></a><span class="w">        </span><span class="n">arr</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-80-60" name="__codelineno-80-60" href="#__codelineno-80-60"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-80-61" name="__codelineno-80-61" href="#__codelineno-80-61"></a><span class="w">        </span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-80-62" name="__codelineno-80-62" href="#__codelineno-80-62"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-80-63" name="__codelineno-80-63" href="#__codelineno-80-63"></a>
+<a id="__codelineno-80-64" name="__codelineno-80-64" href="#__codelineno-80-64"></a><span class="w">    </span><span class="cm">/* 要素を削除 */</span>
+<a id="__codelineno-80-65" name="__codelineno-80-65" href="#__codelineno-80-65"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-66" name="__codelineno-80-66" href="#__codelineno-80-66"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">)</span>
+<a id="__codelineno-80-67" name="__codelineno-80-67" href="#__codelineno-80-67"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外です&quot;</span><span class="p">);</span>
+<a id="__codelineno-80-68" name="__codelineno-80-68" href="#__codelineno-80-68"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-80-69" name="__codelineno-80-69" href="#__codelineno-80-69"></a><span class="w">        </span><span class="c1">// インデックス index より後の要素をすべて 1 つ前に移動する</span>
+<a id="__codelineno-80-70" name="__codelineno-80-70" href="#__codelineno-80-70"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-71" name="__codelineno-80-71" href="#__codelineno-80-71"></a><span class="w">            </span><span class="n">arr</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-80-72" name="__codelineno-80-72" href="#__codelineno-80-72"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-80-73" name="__codelineno-80-73" href="#__codelineno-80-73"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-80-74" name="__codelineno-80-74" href="#__codelineno-80-74"></a><span class="w">        </span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-80-75" name="__codelineno-80-75" href="#__codelineno-80-75"></a><span class="w">        </span><span class="c1">// 削除された要素を返す</span>
+<a id="__codelineno-80-76" name="__codelineno-80-76" href="#__codelineno-80-76"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-80-77" name="__codelineno-80-77" href="#__codelineno-80-77"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-80-78" name="__codelineno-80-78" href="#__codelineno-80-78"></a>
+<a id="__codelineno-80-79" name="__codelineno-80-79" href="#__codelineno-80-79"></a><span class="w">    </span><span class="cm">/* リストの拡張 */</span>
+<a id="__codelineno-80-80" name="__codelineno-80-80" href="#__codelineno-80-80"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">extendCapacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-81" name="__codelineno-80-81" href="#__codelineno-80-81"></a><span class="w">        </span><span class="c1">// 元の配列の extendRatio 倍の長さを持つ新しい配列を作成し、元の配列をコピーする</span>
+<a id="__codelineno-80-82" name="__codelineno-80-82" href="#__codelineno-80-82"></a><span class="w">        </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Arrays</span><span class="p">.</span><span class="na">copyOf</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">);</span>
+<a id="__codelineno-80-83" name="__codelineno-80-83" href="#__codelineno-80-83"></a><span class="w">        </span><span class="c1">// リストの容量を更新</span>
+<a id="__codelineno-80-84" name="__codelineno-80-84" href="#__codelineno-80-84"></a><span class="w">        </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
+<a id="__codelineno-80-85" name="__codelineno-80-85" href="#__codelineno-80-85"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-80-86" name="__codelineno-80-86" href="#__codelineno-80-86"></a>
+<a id="__codelineno-80-87" name="__codelineno-80-87" href="#__codelineno-80-87"></a><span class="w">    </span><span class="cm">/* リストを配列に変換する */</span>
+<a id="__codelineno-80-88" name="__codelineno-80-88" href="#__codelineno-80-88"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-89" name="__codelineno-80-89" href="#__codelineno-80-89"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-80-90" name="__codelineno-80-90" href="#__codelineno-80-90"></a><span class="w">        </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-80-91" name="__codelineno-80-91" href="#__codelineno-80-91"></a><span class="w">        </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">size</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-80-92" name="__codelineno-80-92" href="#__codelineno-80-92"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-93" name="__codelineno-80-93" href="#__codelineno-80-93"></a><span class="w">            </span><span class="n">arr</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">get</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-80-94" name="__codelineno-80-94" href="#__codelineno-80-94"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-80-95" name="__codelineno-80-95" href="#__codelineno-80-95"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">arr</span><span class="p">;</span>
+<a id="__codelineno-80-96" name="__codelineno-80-96" href="#__codelineno-80-96"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-80-97" name="__codelineno-80-97" href="#__codelineno-80-97"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_list.cs</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">MyList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">my_list.cs</span><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="cm">/* リストクラス */</span>
+<a id="__codelineno-81-2" name="__codelineno-81-2" href="#__codelineno-81-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">MyList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-3" name="__codelineno-81-3" href="#__codelineno-81-3"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">arr</span><span class="p">;</span><span class="w">           </span><span class="c1">// 配列（リスト要素を格納）</span>
+<a id="__codelineno-81-4" name="__codelineno-81-4" href="#__codelineno-81-4"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">arrCapacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">10</span><span class="p">;</span><span class="w">    </span><span class="c1">// リスト容量</span>
+<a id="__codelineno-81-5" name="__codelineno-81-5" href="#__codelineno-81-5"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">arrSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">         </span><span class="c1">// リストの長さ（現在の要素数）</span>
+<a id="__codelineno-81-6" name="__codelineno-81-6" href="#__codelineno-81-6"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="k">readonly</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// リスト拡張時の増加倍率</span>
+<a id="__codelineno-81-7" name="__codelineno-81-7" href="#__codelineno-81-7"></a>
+<a id="__codelineno-81-8" name="__codelineno-81-8" href="#__codelineno-81-8"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-81-9" name="__codelineno-81-9" href="#__codelineno-81-9"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nf">MyList</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-10" name="__codelineno-81-10" href="#__codelineno-81-10"></a><span class="w">        </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">arrCapacity</span><span class="p">];</span>
+<a id="__codelineno-81-11" name="__codelineno-81-11" href="#__codelineno-81-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-81-12" name="__codelineno-81-12" href="#__codelineno-81-12"></a>
+<a id="__codelineno-81-13" name="__codelineno-81-13" href="#__codelineno-81-13"></a><span class="w">    </span><span class="cm">/* リストの長さを取得（現在の要素数） */</span>
+<a id="__codelineno-81-14" name="__codelineno-81-14" href="#__codelineno-81-14"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-15" name="__codelineno-81-15" href="#__codelineno-81-15"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">arrSize</span><span class="p">;</span>
+<a id="__codelineno-81-16" name="__codelineno-81-16" href="#__codelineno-81-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-81-17" name="__codelineno-81-17" href="#__codelineno-81-17"></a>
+<a id="__codelineno-81-18" name="__codelineno-81-18" href="#__codelineno-81-18"></a><span class="w">    </span><span class="cm">/* リスト容量を取得する */</span>
+<a id="__codelineno-81-19" name="__codelineno-81-19" href="#__codelineno-81-19"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-20" name="__codelineno-81-20" href="#__codelineno-81-20"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">arrCapacity</span><span class="p">;</span>
+<a id="__codelineno-81-21" name="__codelineno-81-21" href="#__codelineno-81-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-81-22" name="__codelineno-81-22" href="#__codelineno-81-22"></a>
+<a id="__codelineno-81-23" name="__codelineno-81-23" href="#__codelineno-81-23"></a><span class="w">    </span><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-81-24" name="__codelineno-81-24" href="#__codelineno-81-24"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-25" name="__codelineno-81-25" href="#__codelineno-81-25"></a><span class="w">        </span><span class="c1">// インデックスが範囲外なら例外を送出する。以下同様</span>
+<a id="__codelineno-81-26" name="__codelineno-81-26" href="#__codelineno-81-26"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">arrSize</span><span class="p">)</span>
+<a id="__codelineno-81-27" name="__codelineno-81-27" href="#__codelineno-81-27"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="nf">IndexOutOfRangeException</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外です&quot;</span><span class="p">);</span>
+<a id="__codelineno-81-28" name="__codelineno-81-28" href="#__codelineno-81-28"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-81-29" name="__codelineno-81-29" href="#__codelineno-81-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-81-30" name="__codelineno-81-30" href="#__codelineno-81-30"></a>
+<a id="__codelineno-81-31" name="__codelineno-81-31" href="#__codelineno-81-31"></a><span class="w">    </span><span class="cm">/* 要素を更新 */</span>
+<a id="__codelineno-81-32" name="__codelineno-81-32" href="#__codelineno-81-32"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">Set</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-33" name="__codelineno-81-33" href="#__codelineno-81-33"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">arrSize</span><span class="p">)</span>
+<a id="__codelineno-81-34" name="__codelineno-81-34" href="#__codelineno-81-34"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="nf">IndexOutOfRangeException</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外です&quot;</span><span class="p">);</span>
+<a id="__codelineno-81-35" name="__codelineno-81-35" href="#__codelineno-81-35"></a><span class="w">        </span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-81-36" name="__codelineno-81-36" href="#__codelineno-81-36"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-81-37" name="__codelineno-81-37" href="#__codelineno-81-37"></a>
+<a id="__codelineno-81-38" name="__codelineno-81-38" href="#__codelineno-81-38"></a><span class="w">    </span><span class="cm">/* 末尾に要素を追加 */</span>
+<a id="__codelineno-81-39" name="__codelineno-81-39" href="#__codelineno-81-39"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">Add</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-40" name="__codelineno-81-40" href="#__codelineno-81-40"></a><span class="w">        </span><span class="c1">// 要素数が容量を超えると、拡張機構が発動する</span>
+<a id="__codelineno-81-41" name="__codelineno-81-41" href="#__codelineno-81-41"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">arrSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">arrCapacity</span><span class="p">)</span>
+<a id="__codelineno-81-42" name="__codelineno-81-42" href="#__codelineno-81-42"></a><span class="w">            </span><span class="n">ExtendCapacity</span><span class="p">();</span>
+<a id="__codelineno-81-43" name="__codelineno-81-43" href="#__codelineno-81-43"></a><span class="w">        </span><span class="n">arr</span><span class="p">[</span><span class="n">arrSize</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-81-44" name="__codelineno-81-44" href="#__codelineno-81-44"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-81-45" name="__codelineno-81-45" href="#__codelineno-81-45"></a><span class="w">        </span><span class="n">arrSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-81-46" name="__codelineno-81-46" href="#__codelineno-81-46"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-81-47" name="__codelineno-81-47" href="#__codelineno-81-47"></a>
+<a id="__codelineno-81-48" name="__codelineno-81-48" href="#__codelineno-81-48"></a><span class="w">    </span><span class="cm">/* 中間に要素を挿入 */</span>
+<a id="__codelineno-81-49" name="__codelineno-81-49" href="#__codelineno-81-49"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">Insert</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-50" name="__codelineno-81-50" href="#__codelineno-81-50"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">arrSize</span><span class="p">)</span>
+<a id="__codelineno-81-51" name="__codelineno-81-51" href="#__codelineno-81-51"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="nf">IndexOutOfRangeException</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外です&quot;</span><span class="p">);</span>
+<a id="__codelineno-81-52" name="__codelineno-81-52" href="#__codelineno-81-52"></a><span class="w">        </span><span class="c1">// 要素数が容量を超えると、拡張機構が発動する</span>
+<a id="__codelineno-81-53" name="__codelineno-81-53" href="#__codelineno-81-53"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">arrSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">arrCapacity</span><span class="p">)</span>
+<a id="__codelineno-81-54" name="__codelineno-81-54" href="#__codelineno-81-54"></a><span class="w">            </span><span class="n">ExtendCapacity</span><span class="p">();</span>
+<a id="__codelineno-81-55" name="__codelineno-81-55" href="#__codelineno-81-55"></a><span class="w">        </span><span class="c1">// index 以降の要素をすべて 1 つ後ろへずらす</span>
+<a id="__codelineno-81-56" name="__codelineno-81-56" href="#__codelineno-81-56"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arrSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-57" name="__codelineno-81-57" href="#__codelineno-81-57"></a><span class="w">            </span><span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-81-58" name="__codelineno-81-58" href="#__codelineno-81-58"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-81-59" name="__codelineno-81-59" href="#__codelineno-81-59"></a><span class="w">        </span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-81-60" name="__codelineno-81-60" href="#__codelineno-81-60"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-81-61" name="__codelineno-81-61" href="#__codelineno-81-61"></a><span class="w">        </span><span class="n">arrSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-81-62" name="__codelineno-81-62" href="#__codelineno-81-62"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-81-63" name="__codelineno-81-63" href="#__codelineno-81-63"></a>
+<a id="__codelineno-81-64" name="__codelineno-81-64" href="#__codelineno-81-64"></a><span class="w">    </span><span class="cm">/* 要素を削除 */</span>
+<a id="__codelineno-81-65" name="__codelineno-81-65" href="#__codelineno-81-65"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-66" name="__codelineno-81-66" href="#__codelineno-81-66"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">arrSize</span><span class="p">)</span>
+<a id="__codelineno-81-67" name="__codelineno-81-67" href="#__codelineno-81-67"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="nf">IndexOutOfRangeException</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外です&quot;</span><span class="p">);</span>
+<a id="__codelineno-81-68" name="__codelineno-81-68" href="#__codelineno-81-68"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-81-69" name="__codelineno-81-69" href="#__codelineno-81-69"></a><span class="w">        </span><span class="c1">// インデックス index より後の要素をすべて 1 つ前に移動する</span>
+<a id="__codelineno-81-70" name="__codelineno-81-70" href="#__codelineno-81-70"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">arrSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-71" name="__codelineno-81-71" href="#__codelineno-81-71"></a><span class="w">            </span><span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-81-72" name="__codelineno-81-72" href="#__codelineno-81-72"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-81-73" name="__codelineno-81-73" href="#__codelineno-81-73"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-81-74" name="__codelineno-81-74" href="#__codelineno-81-74"></a><span class="w">        </span><span class="n">arrSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-81-75" name="__codelineno-81-75" href="#__codelineno-81-75"></a><span class="w">        </span><span class="c1">// 削除された要素を返す</span>
+<a id="__codelineno-81-76" name="__codelineno-81-76" href="#__codelineno-81-76"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-81-77" name="__codelineno-81-77" href="#__codelineno-81-77"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-81-78" name="__codelineno-81-78" href="#__codelineno-81-78"></a>
+<a id="__codelineno-81-79" name="__codelineno-81-79" href="#__codelineno-81-79"></a><span class="w">    </span><span class="cm">/* リストの拡張 */</span>
+<a id="__codelineno-81-80" name="__codelineno-81-80" href="#__codelineno-81-80"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">ExtendCapacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-81" name="__codelineno-81-81" href="#__codelineno-81-81"></a><span class="w">        </span><span class="c1">// `arrCapacity * extendRatio` の長さを持つ配列を新規作成し、元の配列を新しい配列にコピーする</span>
+<a id="__codelineno-81-82" name="__codelineno-81-82" href="#__codelineno-81-82"></a><span class="w">        </span><span class="n">Array</span><span class="p">.</span><span class="n">Resize</span><span class="p">(</span><span class="k">ref</span><span class="w"> </span><span class="n">arr</span><span class="p">,</span><span class="w"> </span><span class="n">arrCapacity</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">);</span>
+<a id="__codelineno-81-83" name="__codelineno-81-83" href="#__codelineno-81-83"></a><span class="w">        </span><span class="c1">// リストの容量を更新</span>
+<a id="__codelineno-81-84" name="__codelineno-81-84" href="#__codelineno-81-84"></a><span class="w">        </span><span class="n">arrCapacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
+<a id="__codelineno-81-85" name="__codelineno-81-85" href="#__codelineno-81-85"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-81-86" name="__codelineno-81-86" href="#__codelineno-81-86"></a>
+<a id="__codelineno-81-87" name="__codelineno-81-87" href="#__codelineno-81-87"></a><span class="w">    </span><span class="cm">/* リストを配列に変換する */</span>
+<a id="__codelineno-81-88" name="__codelineno-81-88" href="#__codelineno-81-88"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="nf">ToArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-89" name="__codelineno-81-89" href="#__codelineno-81-89"></a><span class="w">        </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-81-90" name="__codelineno-81-90" href="#__codelineno-81-90"></a><span class="w">        </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">arrSize</span><span class="p">];</span>
+<a id="__codelineno-81-91" name="__codelineno-81-91" href="#__codelineno-81-91"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">arrSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-92" name="__codelineno-81-92" href="#__codelineno-81-92"></a><span class="w">            </span><span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Get</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-81-93" name="__codelineno-81-93" href="#__codelineno-81-93"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-81-94" name="__codelineno-81-94" href="#__codelineno-81-94"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">arr</span><span class="p">;</span>
+<a id="__codelineno-81-95" name="__codelineno-81-95" href="#__codelineno-81-95"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-81-96" name="__codelineno-81-96" href="#__codelineno-81-96"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_list.go</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">myList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">my_list.go</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="cm">/* リストクラス */</span>
+<a id="__codelineno-82-2" name="__codelineno-82-2" href="#__codelineno-82-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">myList</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-3" name="__codelineno-82-3" href="#__codelineno-82-3"></a><span class="w">    </span><span class="nx">arrCapacity</span><span class="w"> </span><span class="kt">int</span>
+<a id="__codelineno-82-4" name="__codelineno-82-4" href="#__codelineno-82-4"></a><span class="w">    </span><span class="nx">arr</span><span class="w">         </span><span class="p">[]</span><span class="kt">int</span>
+<a id="__codelineno-82-5" name="__codelineno-82-5" href="#__codelineno-82-5"></a><span class="w">    </span><span class="nx">arrSize</span><span class="w">     </span><span class="kt">int</span>
+<a id="__codelineno-82-6" name="__codelineno-82-6" href="#__codelineno-82-6"></a><span class="w">    </span><span class="nx">extendRatio</span><span class="w"> </span><span class="kt">int</span>
+<a id="__codelineno-82-7" name="__codelineno-82-7" href="#__codelineno-82-7"></a><span class="p">}</span>
+<a id="__codelineno-82-8" name="__codelineno-82-8" href="#__codelineno-82-8"></a>
+<a id="__codelineno-82-9" name="__codelineno-82-9" href="#__codelineno-82-9"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-82-10" name="__codelineno-82-10" href="#__codelineno-82-10"></a><span class="kd">func</span><span class="w"> </span><span class="nx">newMyList</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="nx">myList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-11" name="__codelineno-82-11" href="#__codelineno-82-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">myList</span><span class="p">{</span>
+<a id="__codelineno-82-12" name="__codelineno-82-12" href="#__codelineno-82-12"></a><span class="w">        </span><span class="nx">arrCapacity</span><span class="p">:</span><span class="w"> </span><span class="mi">10</span><span class="p">,</span><span class="w">              </span><span class="c1">// リスト容量</span>
+<a id="__codelineno-82-13" name="__codelineno-82-13" href="#__codelineno-82-13"></a><span class="w">        </span><span class="nx">arr</span><span class="p">:</span><span class="w">         </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">),</span><span class="w"> </span><span class="c1">// 配列（リスト要素を格納）</span>
+<a id="__codelineno-82-14" name="__codelineno-82-14" href="#__codelineno-82-14"></a><span class="w">        </span><span class="nx">arrSize</span><span class="p">:</span><span class="w">     </span><span class="mi">0</span><span class="p">,</span><span class="w">               </span><span class="c1">// リストの長さ（現在の要素数）</span>
+<a id="__codelineno-82-15" name="__codelineno-82-15" href="#__codelineno-82-15"></a><span class="w">        </span><span class="nx">extendRatio</span><span class="p">:</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w">               </span><span class="c1">// リスト拡張時の増加倍率</span>
+<a id="__codelineno-82-16" name="__codelineno-82-16" href="#__codelineno-82-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-82-17" name="__codelineno-82-17" href="#__codelineno-82-17"></a><span class="p">}</span>
+<a id="__codelineno-82-18" name="__codelineno-82-18" href="#__codelineno-82-18"></a>
+<a id="__codelineno-82-19" name="__codelineno-82-19" href="#__codelineno-82-19"></a><span class="cm">/* リストの長さを取得（現在の要素数） */</span>
+<a id="__codelineno-82-20" name="__codelineno-82-20" href="#__codelineno-82-20"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">l</span><span class="w"> </span><span class="o">*</span><span class="nx">myList</span><span class="p">)</span><span class="w"> </span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-21" name="__codelineno-82-21" href="#__codelineno-82-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">l</span><span class="p">.</span><span class="nx">arrSize</span>
+<a id="__codelineno-82-22" name="__codelineno-82-22" href="#__codelineno-82-22"></a><span class="p">}</span>
+<a id="__codelineno-82-23" name="__codelineno-82-23" href="#__codelineno-82-23"></a>
+<a id="__codelineno-82-24" name="__codelineno-82-24" href="#__codelineno-82-24"></a><span class="cm">/* リスト容量を取得する */</span>
+<a id="__codelineno-82-25" name="__codelineno-82-25" href="#__codelineno-82-25"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">l</span><span class="w"> </span><span class="o">*</span><span class="nx">myList</span><span class="p">)</span><span class="w"> </span><span class="nx">capacity</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-26" name="__codelineno-82-26" href="#__codelineno-82-26"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">l</span><span class="p">.</span><span class="nx">arrCapacity</span>
+<a id="__codelineno-82-27" name="__codelineno-82-27" href="#__codelineno-82-27"></a><span class="p">}</span>
+<a id="__codelineno-82-28" name="__codelineno-82-28" href="#__codelineno-82-28"></a>
+<a id="__codelineno-82-29" name="__codelineno-82-29" href="#__codelineno-82-29"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-82-30" name="__codelineno-82-30" href="#__codelineno-82-30"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">l</span><span class="w"> </span><span class="o">*</span><span class="nx">myList</span><span class="p">)</span><span class="w"> </span><span class="nx">get</span><span class="p">(</span><span class="nx">index</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-31" name="__codelineno-82-31" href="#__codelineno-82-31"></a><span class="w">    </span><span class="c1">// インデックスが範囲外なら例外を送出する。以下同様</span>
+<a id="__codelineno-82-32" name="__codelineno-82-32" href="#__codelineno-82-32"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">l</span><span class="p">.</span><span class="nx">arrSize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-33" name="__codelineno-82-33" href="#__codelineno-82-33"></a><span class="w">        </span><span class="nb">panic</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外です&quot;</span><span class="p">)</span>
+<a id="__codelineno-82-34" name="__codelineno-82-34" href="#__codelineno-82-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-82-35" name="__codelineno-82-35" href="#__codelineno-82-35"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">l</span><span class="p">.</span><span class="nx">arr</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span>
+<a id="__codelineno-82-36" name="__codelineno-82-36" href="#__codelineno-82-36"></a><span class="p">}</span>
+<a id="__codelineno-82-37" name="__codelineno-82-37" href="#__codelineno-82-37"></a>
+<a id="__codelineno-82-38" name="__codelineno-82-38" href="#__codelineno-82-38"></a><span class="cm">/* 要素を更新 */</span>
+<a id="__codelineno-82-39" name="__codelineno-82-39" href="#__codelineno-82-39"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">l</span><span class="w"> </span><span class="o">*</span><span class="nx">myList</span><span class="p">)</span><span class="w"> </span><span class="nx">set</span><span class="p">(</span><span class="nx">num</span><span class="p">,</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-40" name="__codelineno-82-40" href="#__codelineno-82-40"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">l</span><span class="p">.</span><span class="nx">arrSize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-41" name="__codelineno-82-41" href="#__codelineno-82-41"></a><span class="w">        </span><span class="nb">panic</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外です&quot;</span><span class="p">)</span>
+<a id="__codelineno-82-42" name="__codelineno-82-42" href="#__codelineno-82-42"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-82-43" name="__codelineno-82-43" href="#__codelineno-82-43"></a><span class="w">    </span><span class="nx">l</span><span class="p">.</span><span class="nx">arr</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">num</span>
+<a id="__codelineno-82-44" name="__codelineno-82-44" href="#__codelineno-82-44"></a><span class="p">}</span>
+<a id="__codelineno-82-45" name="__codelineno-82-45" href="#__codelineno-82-45"></a>
+<a id="__codelineno-82-46" name="__codelineno-82-46" href="#__codelineno-82-46"></a><span class="cm">/* 末尾に要素を追加 */</span>
+<a id="__codelineno-82-47" name="__codelineno-82-47" href="#__codelineno-82-47"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">l</span><span class="w"> </span><span class="o">*</span><span class="nx">myList</span><span class="p">)</span><span class="w"> </span><span class="nx">add</span><span class="p">(</span><span class="nx">num</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-48" name="__codelineno-82-48" href="#__codelineno-82-48"></a><span class="w">    </span><span class="c1">// 要素数が容量を超えると、拡張機構が発動する</span>
+<a id="__codelineno-82-49" name="__codelineno-82-49" href="#__codelineno-82-49"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">l</span><span class="p">.</span><span class="nx">arrSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">l</span><span class="p">.</span><span class="nx">arrCapacity</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-50" name="__codelineno-82-50" href="#__codelineno-82-50"></a><span class="w">        </span><span class="nx">l</span><span class="p">.</span><span class="nx">extendCapacity</span><span class="p">()</span>
+<a id="__codelineno-82-51" name="__codelineno-82-51" href="#__codelineno-82-51"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-82-52" name="__codelineno-82-52" href="#__codelineno-82-52"></a><span class="w">    </span><span class="nx">l</span><span class="p">.</span><span class="nx">arr</span><span class="p">[</span><span class="nx">l</span><span class="p">.</span><span class="nx">arrSize</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">num</span>
+<a id="__codelineno-82-53" name="__codelineno-82-53" href="#__codelineno-82-53"></a><span class="w">    </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-82-54" name="__codelineno-82-54" href="#__codelineno-82-54"></a><span class="w">    </span><span class="nx">l</span><span class="p">.</span><span class="nx">arrSize</span><span class="o">++</span>
+<a id="__codelineno-82-55" name="__codelineno-82-55" href="#__codelineno-82-55"></a><span class="p">}</span>
+<a id="__codelineno-82-56" name="__codelineno-82-56" href="#__codelineno-82-56"></a>
+<a id="__codelineno-82-57" name="__codelineno-82-57" href="#__codelineno-82-57"></a><span class="cm">/* 中間に要素を挿入 */</span>
+<a id="__codelineno-82-58" name="__codelineno-82-58" href="#__codelineno-82-58"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">l</span><span class="w"> </span><span class="o">*</span><span class="nx">myList</span><span class="p">)</span><span class="w"> </span><span class="nx">insert</span><span class="p">(</span><span class="nx">num</span><span class="p">,</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-59" name="__codelineno-82-59" href="#__codelineno-82-59"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">l</span><span class="p">.</span><span class="nx">arrSize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-60" name="__codelineno-82-60" href="#__codelineno-82-60"></a><span class="w">        </span><span class="nb">panic</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外です&quot;</span><span class="p">)</span>
+<a id="__codelineno-82-61" name="__codelineno-82-61" href="#__codelineno-82-61"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-82-62" name="__codelineno-82-62" href="#__codelineno-82-62"></a><span class="w">    </span><span class="c1">// 要素数が容量を超えると、拡張機構が発動する</span>
+<a id="__codelineno-82-63" name="__codelineno-82-63" href="#__codelineno-82-63"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">l</span><span class="p">.</span><span class="nx">arrSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">l</span><span class="p">.</span><span class="nx">arrCapacity</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-64" name="__codelineno-82-64" href="#__codelineno-82-64"></a><span class="w">        </span><span class="nx">l</span><span class="p">.</span><span class="nx">extendCapacity</span><span class="p">()</span>
+<a id="__codelineno-82-65" name="__codelineno-82-65" href="#__codelineno-82-65"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-82-66" name="__codelineno-82-66" href="#__codelineno-82-66"></a><span class="w">    </span><span class="c1">// index 以降の要素をすべて 1 つ後ろへずらす</span>
+<a id="__codelineno-82-67" name="__codelineno-82-67" href="#__codelineno-82-67"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">l</span><span class="p">.</span><span class="nx">arrSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">index</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">--</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-68" name="__codelineno-82-68" href="#__codelineno-82-68"></a><span class="w">        </span><span class="nx">l</span><span class="p">.</span><span class="nx">arr</span><span class="p">[</span><span class="nx">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">l</span><span class="p">.</span><span class="nx">arr</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span>
+<a id="__codelineno-82-69" name="__codelineno-82-69" href="#__codelineno-82-69"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-82-70" name="__codelineno-82-70" href="#__codelineno-82-70"></a><span class="w">    </span><span class="nx">l</span><span class="p">.</span><span class="nx">arr</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">num</span>
+<a id="__codelineno-82-71" name="__codelineno-82-71" href="#__codelineno-82-71"></a><span class="w">    </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-82-72" name="__codelineno-82-72" href="#__codelineno-82-72"></a><span class="w">    </span><span class="nx">l</span><span class="p">.</span><span class="nx">arrSize</span><span class="o">++</span>
+<a id="__codelineno-82-73" name="__codelineno-82-73" href="#__codelineno-82-73"></a><span class="p">}</span>
+<a id="__codelineno-82-74" name="__codelineno-82-74" href="#__codelineno-82-74"></a>
+<a id="__codelineno-82-75" name="__codelineno-82-75" href="#__codelineno-82-75"></a><span class="cm">/* 要素を削除 */</span>
+<a id="__codelineno-82-76" name="__codelineno-82-76" href="#__codelineno-82-76"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">l</span><span class="w"> </span><span class="o">*</span><span class="nx">myList</span><span class="p">)</span><span class="w"> </span><span class="nx">remove</span><span class="p">(</span><span class="nx">index</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-77" name="__codelineno-82-77" href="#__codelineno-82-77"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">l</span><span class="p">.</span><span class="nx">arrSize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-78" name="__codelineno-82-78" href="#__codelineno-82-78"></a><span class="w">        </span><span class="nb">panic</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外です&quot;</span><span class="p">)</span>
+<a id="__codelineno-82-79" name="__codelineno-82-79" href="#__codelineno-82-79"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-82-80" name="__codelineno-82-80" href="#__codelineno-82-80"></a><span class="w">    </span><span class="nx">num</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">l</span><span class="p">.</span><span class="nx">arr</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span>
+<a id="__codelineno-82-81" name="__codelineno-82-81" href="#__codelineno-82-81"></a><span class="w">    </span><span class="c1">// インデックス index より後の要素をすべて 1 つ前に移動する</span>
+<a id="__codelineno-82-82" name="__codelineno-82-82" href="#__codelineno-82-82"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">index</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">l</span><span class="p">.</span><span class="nx">arrSize</span><span class="o">-</span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-83" name="__codelineno-82-83" href="#__codelineno-82-83"></a><span class="w">        </span><span class="nx">l</span><span class="p">.</span><span class="nx">arr</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">l</span><span class="p">.</span><span class="nx">arr</span><span class="p">[</span><span class="nx">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-82-84" name="__codelineno-82-84" href="#__codelineno-82-84"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-82-85" name="__codelineno-82-85" href="#__codelineno-82-85"></a><span class="w">    </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-82-86" name="__codelineno-82-86" href="#__codelineno-82-86"></a><span class="w">    </span><span class="nx">l</span><span class="p">.</span><span class="nx">arrSize</span><span class="o">--</span>
+<a id="__codelineno-82-87" name="__codelineno-82-87" href="#__codelineno-82-87"></a><span class="w">    </span><span class="c1">// 削除された要素を返す</span>
+<a id="__codelineno-82-88" name="__codelineno-82-88" href="#__codelineno-82-88"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">num</span>
+<a id="__codelineno-82-89" name="__codelineno-82-89" href="#__codelineno-82-89"></a><span class="p">}</span>
+<a id="__codelineno-82-90" name="__codelineno-82-90" href="#__codelineno-82-90"></a>
+<a id="__codelineno-82-91" name="__codelineno-82-91" href="#__codelineno-82-91"></a><span class="cm">/* リストの拡張 */</span>
+<a id="__codelineno-82-92" name="__codelineno-82-92" href="#__codelineno-82-92"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">l</span><span class="w"> </span><span class="o">*</span><span class="nx">myList</span><span class="p">)</span><span class="w"> </span><span class="nx">extendCapacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-93" name="__codelineno-82-93" href="#__codelineno-82-93"></a><span class="w">    </span><span class="c1">// 元の配列の extendRatio 倍の長さを持つ新しい配列を作成し、元の配列をコピーする</span>
+<a id="__codelineno-82-94" name="__codelineno-82-94" href="#__codelineno-82-94"></a><span class="w">    </span><span class="nx">l</span><span class="p">.</span><span class="nx">arr</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">l</span><span class="p">.</span><span class="nx">arr</span><span class="p">,</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">l</span><span class="p">.</span><span class="nx">arrCapacity</span><span class="o">*</span><span class="p">(</span><span class="nx">l</span><span class="p">.</span><span class="nx">extendRatio</span><span class="o">-</span><span class="mi">1</span><span class="p">))</span><span class="o">...</span><span class="p">)</span>
+<a id="__codelineno-82-95" name="__codelineno-82-95" href="#__codelineno-82-95"></a><span class="w">    </span><span class="c1">// リストの容量を更新</span>
+<a id="__codelineno-82-96" name="__codelineno-82-96" href="#__codelineno-82-96"></a><span class="w">    </span><span class="nx">l</span><span class="p">.</span><span class="nx">arrCapacity</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">l</span><span class="p">.</span><span class="nx">arr</span><span class="p">)</span>
+<a id="__codelineno-82-97" name="__codelineno-82-97" href="#__codelineno-82-97"></a><span class="p">}</span>
+<a id="__codelineno-82-98" name="__codelineno-82-98" href="#__codelineno-82-98"></a>
+<a id="__codelineno-82-99" name="__codelineno-82-99" href="#__codelineno-82-99"></a><span class="cm">/* 有効長のリストを返す */</span>
+<a id="__codelineno-82-100" name="__codelineno-82-100" href="#__codelineno-82-100"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">l</span><span class="w"> </span><span class="o">*</span><span class="nx">myList</span><span class="p">)</span><span class="w"> </span><span class="nx">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-101" name="__codelineno-82-101" href="#__codelineno-82-101"></a><span class="w">    </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-82-102" name="__codelineno-82-102" href="#__codelineno-82-102"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">l</span><span class="p">.</span><span class="nx">arr</span><span class="p">[:</span><span class="nx">l</span><span class="p">.</span><span class="nx">arrSize</span><span class="p">]</span>
+<a id="__codelineno-82-103" name="__codelineno-82-103" href="#__codelineno-82-103"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_list.swift</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">MyList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">my_list.swift</span><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="cm">/* リストクラス */</span>
+<a id="__codelineno-83-2" name="__codelineno-83-2" href="#__codelineno-83-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">MyList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-3" name="__codelineno-83-3" href="#__codelineno-83-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">arr</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="c1">// 配列（リスト要素を格納）</span>
+<a id="__codelineno-83-4" name="__codelineno-83-4" href="#__codelineno-83-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">_capacity</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// リスト容量</span>
+<a id="__codelineno-83-5" name="__codelineno-83-5" href="#__codelineno-83-5"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">_size</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// リストの長さ（現在の要素数）</span>
+<a id="__codelineno-83-6" name="__codelineno-83-6" href="#__codelineno-83-6"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">extendRatio</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// リスト拡張時の増加倍率</span>
+<a id="__codelineno-83-7" name="__codelineno-83-7" href="#__codelineno-83-7"></a>
+<a id="__codelineno-83-8" name="__codelineno-83-8" href="#__codelineno-83-8"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-83-9" name="__codelineno-83-9" href="#__codelineno-83-9"></a><span class="w">    </span><span class="kd">init</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-10" name="__codelineno-83-10" href="#__codelineno-83-10"></a><span class="w">        </span><span class="n">_capacity</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">10</span>
+<a id="__codelineno-83-11" name="__codelineno-83-11" href="#__codelineno-83-11"></a><span class="w">        </span><span class="n">_size</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-83-12" name="__codelineno-83-12" href="#__codelineno-83-12"></a><span class="w">        </span><span class="n">extendRatio</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-83-13" name="__codelineno-83-13" href="#__codelineno-83-13"></a><span class="w">        </span><span class="n">arr</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">_capacity</span><span class="p">)</span>
+<a id="__codelineno-83-14" name="__codelineno-83-14" href="#__codelineno-83-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-83-15" name="__codelineno-83-15" href="#__codelineno-83-15"></a>
+<a id="__codelineno-83-16" name="__codelineno-83-16" href="#__codelineno-83-16"></a><span class="w">    </span><span class="cm">/* リストの長さを取得（現在の要素数） */</span>
+<a id="__codelineno-83-17" name="__codelineno-83-17" href="#__codelineno-83-17"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-18" name="__codelineno-83-18" href="#__codelineno-83-18"></a><span class="w">        </span><span class="n">_size</span>
+<a id="__codelineno-83-19" name="__codelineno-83-19" href="#__codelineno-83-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-83-20" name="__codelineno-83-20" href="#__codelineno-83-20"></a>
+<a id="__codelineno-83-21" name="__codelineno-83-21" href="#__codelineno-83-21"></a><span class="w">    </span><span class="cm">/* リスト容量を取得する */</span>
+<a id="__codelineno-83-22" name="__codelineno-83-22" href="#__codelineno-83-22"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-23" name="__codelineno-83-23" href="#__codelineno-83-23"></a><span class="w">        </span><span class="n">_capacity</span>
+<a id="__codelineno-83-24" name="__codelineno-83-24" href="#__codelineno-83-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-83-25" name="__codelineno-83-25" href="#__codelineno-83-25"></a>
+<a id="__codelineno-83-26" name="__codelineno-83-26" href="#__codelineno-83-26"></a><span class="w">    </span><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-83-27" name="__codelineno-83-27" href="#__codelineno-83-27"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="n">index</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-28" name="__codelineno-83-28" href="#__codelineno-83-28"></a><span class="w">        </span><span class="c1">// インデックスが範囲外ならエラーを投げる。以下同様</span>
+<a id="__codelineno-83-29" name="__codelineno-83-29" href="#__codelineno-83-29"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-30" name="__codelineno-83-30" href="#__codelineno-83-30"></a><span class="w">            </span><span class="bp">fatalError</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外&quot;</span><span class="p">)</span>
+<a id="__codelineno-83-31" name="__codelineno-83-31" href="#__codelineno-83-31"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-83-32" name="__codelineno-83-32" href="#__codelineno-83-32"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
+<a id="__codelineno-83-33" name="__codelineno-83-33" href="#__codelineno-83-33"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-83-34" name="__codelineno-83-34" href="#__codelineno-83-34"></a>
+<a id="__codelineno-83-35" name="__codelineno-83-35" href="#__codelineno-83-35"></a><span class="w">    </span><span class="cm">/* 要素を更新 */</span>
+<a id="__codelineno-83-36" name="__codelineno-83-36" href="#__codelineno-83-36"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">set</span><span class="p">(</span><span class="n">index</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-37" name="__codelineno-83-37" href="#__codelineno-83-37"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-38" name="__codelineno-83-38" href="#__codelineno-83-38"></a><span class="w">            </span><span class="bp">fatalError</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外&quot;</span><span class="p">)</span>
+<a id="__codelineno-83-39" name="__codelineno-83-39" href="#__codelineno-83-39"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-83-40" name="__codelineno-83-40" href="#__codelineno-83-40"></a><span class="w">        </span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-83-41" name="__codelineno-83-41" href="#__codelineno-83-41"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-83-42" name="__codelineno-83-42" href="#__codelineno-83-42"></a>
+<a id="__codelineno-83-43" name="__codelineno-83-43" href="#__codelineno-83-43"></a><span class="w">    </span><span class="cm">/* 末尾に要素を追加 */</span>
+<a id="__codelineno-83-44" name="__codelineno-83-44" href="#__codelineno-83-44"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">add</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-45" name="__codelineno-83-45" href="#__codelineno-83-45"></a><span class="w">        </span><span class="c1">// 要素数が容量を超えると、拡張機構が発動する</span>
+<a id="__codelineno-83-46" name="__codelineno-83-46" href="#__codelineno-83-46"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-47" name="__codelineno-83-47" href="#__codelineno-83-47"></a><span class="w">            </span><span class="n">extendCapacity</span><span class="p">()</span>
+<a id="__codelineno-83-48" name="__codelineno-83-48" href="#__codelineno-83-48"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-83-49" name="__codelineno-83-49" href="#__codelineno-83-49"></a><span class="w">        </span><span class="n">arr</span><span class="p">[</span><span class="n">size</span><span class="p">()]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-83-50" name="__codelineno-83-50" href="#__codelineno-83-50"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-83-51" name="__codelineno-83-51" href="#__codelineno-83-51"></a><span class="w">        </span><span class="n">_size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-83-52" name="__codelineno-83-52" href="#__codelineno-83-52"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-83-53" name="__codelineno-83-53" href="#__codelineno-83-53"></a>
+<a id="__codelineno-83-54" name="__codelineno-83-54" href="#__codelineno-83-54"></a><span class="w">    </span><span class="cm">/* 中間に要素を挿入 */</span>
+<a id="__codelineno-83-55" name="__codelineno-83-55" href="#__codelineno-83-55"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">index</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-56" name="__codelineno-83-56" href="#__codelineno-83-56"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-57" name="__codelineno-83-57" href="#__codelineno-83-57"></a><span class="w">            </span><span class="bp">fatalError</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外&quot;</span><span class="p">)</span>
+<a id="__codelineno-83-58" name="__codelineno-83-58" href="#__codelineno-83-58"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-83-59" name="__codelineno-83-59" href="#__codelineno-83-59"></a><span class="w">        </span><span class="c1">// 要素数が容量を超えると、拡張機構が発動する</span>
+<a id="__codelineno-83-60" name="__codelineno-83-60" href="#__codelineno-83-60"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-61" name="__codelineno-83-61" href="#__codelineno-83-61"></a><span class="w">            </span><span class="n">extendCapacity</span><span class="p">()</span>
+<a id="__codelineno-83-62" name="__codelineno-83-62" href="#__codelineno-83-62"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-83-63" name="__codelineno-83-63" href="#__codelineno-83-63"></a><span class="w">        </span><span class="c1">// index 以降の要素をすべて 1 つ後ろへずらす</span>
+<a id="__codelineno-83-64" name="__codelineno-83-64" href="#__codelineno-83-64"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()).</span><span class="n">reversed</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-65" name="__codelineno-83-65" href="#__codelineno-83-65"></a><span class="w">            </span><span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-83-66" name="__codelineno-83-66" href="#__codelineno-83-66"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-83-67" name="__codelineno-83-67" href="#__codelineno-83-67"></a><span class="w">        </span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-83-68" name="__codelineno-83-68" href="#__codelineno-83-68"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-83-69" name="__codelineno-83-69" href="#__codelineno-83-69"></a><span class="w">        </span><span class="n">_size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-83-70" name="__codelineno-83-70" href="#__codelineno-83-70"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-83-71" name="__codelineno-83-71" href="#__codelineno-83-71"></a>
+<a id="__codelineno-83-72" name="__codelineno-83-72" href="#__codelineno-83-72"></a><span class="w">    </span><span class="cm">/* 要素を削除 */</span>
+<a id="__codelineno-83-73" name="__codelineno-83-73" href="#__codelineno-83-73"></a><span class="w">    </span><span class="p">@</span><span class="n">discardableResult</span>
+<a id="__codelineno-83-74" name="__codelineno-83-74" href="#__codelineno-83-74"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">index</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-75" name="__codelineno-83-75" href="#__codelineno-83-75"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-76" name="__codelineno-83-76" href="#__codelineno-83-76"></a><span class="w">            </span><span class="bp">fatalError</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外&quot;</span><span class="p">)</span>
+<a id="__codelineno-83-77" name="__codelineno-83-77" href="#__codelineno-83-77"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-83-78" name="__codelineno-83-78" href="#__codelineno-83-78"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">num</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
+<a id="__codelineno-83-79" name="__codelineno-83-79" href="#__codelineno-83-79"></a><span class="w">        </span><span class="c1">// インデックス index より後の要素をすべて 1 つ前に移動する</span>
+<a id="__codelineno-83-80" name="__codelineno-83-80" href="#__codelineno-83-80"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-81" name="__codelineno-83-81" href="#__codelineno-83-81"></a><span class="w">            </span><span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-83-82" name="__codelineno-83-82" href="#__codelineno-83-82"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-83-83" name="__codelineno-83-83" href="#__codelineno-83-83"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-83-84" name="__codelineno-83-84" href="#__codelineno-83-84"></a><span class="w">        </span><span class="n">_size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-83-85" name="__codelineno-83-85" href="#__codelineno-83-85"></a><span class="w">        </span><span class="c1">// 削除された要素を返す</span>
+<a id="__codelineno-83-86" name="__codelineno-83-86" href="#__codelineno-83-86"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-83-87" name="__codelineno-83-87" href="#__codelineno-83-87"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-83-88" name="__codelineno-83-88" href="#__codelineno-83-88"></a>
+<a id="__codelineno-83-89" name="__codelineno-83-89" href="#__codelineno-83-89"></a><span class="w">    </span><span class="cm">/* リストの拡張 */</span>
+<a id="__codelineno-83-90" name="__codelineno-83-90" href="#__codelineno-83-90"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">extendCapacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-91" name="__codelineno-83-91" href="#__codelineno-83-91"></a><span class="w">        </span><span class="c1">// 元の配列の extendRatio 倍の長さを持つ新しい配列を作成し、元の配列をコピーする</span>
+<a id="__codelineno-83-92" name="__codelineno-83-92" href="#__codelineno-83-92"></a><span class="w">        </span><span class="n">arr</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">extendRatio</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span>
+<a id="__codelineno-83-93" name="__codelineno-83-93" href="#__codelineno-83-93"></a><span class="w">        </span><span class="c1">// リストの容量を更新</span>
+<a id="__codelineno-83-94" name="__codelineno-83-94" href="#__codelineno-83-94"></a><span class="w">        </span><span class="n">_capacity</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">arr</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-83-95" name="__codelineno-83-95" href="#__codelineno-83-95"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-83-96" name="__codelineno-83-96" href="#__codelineno-83-96"></a>
+<a id="__codelineno-83-97" name="__codelineno-83-97" href="#__codelineno-83-97"></a><span class="w">    </span><span class="cm">/* リストを配列に変換する */</span>
+<a id="__codelineno-83-98" name="__codelineno-83-98" href="#__codelineno-83-98"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-99" name="__codelineno-83-99" href="#__codelineno-83-99"></a><span class="w">        </span><span class="nb">Array</span><span class="p">(</span><span class="n">arr</span><span class="p">.</span><span class="kr">prefix</span><span class="p">(</span><span class="n">size</span><span class="p">()))</span>
+<a id="__codelineno-83-100" name="__codelineno-83-100" href="#__codelineno-83-100"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-83-101" name="__codelineno-83-101" href="#__codelineno-83-101"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_list.js</span><pre><span></span><code><a id="__codelineno-78-1" name="__codelineno-78-1" href="#__codelineno-78-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MyList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">my_list.js</span><pre><span></span><code><a id="__codelineno-84-1" name="__codelineno-84-1" href="#__codelineno-84-1"></a><span class="cm">/* リストクラス */</span>
+<a id="__codelineno-84-2" name="__codelineno-84-2" href="#__codelineno-84-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">MyList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-3" name="__codelineno-84-3" href="#__codelineno-84-3"></a><span class="w">    </span><span class="n">#arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">();</span><span class="w"> </span><span class="c1">// 配列（リスト要素を格納）</span>
+<a id="__codelineno-84-4" name="__codelineno-84-4" href="#__codelineno-84-4"></a><span class="w">    </span><span class="n">#capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">10</span><span class="p">;</span><span class="w"> </span><span class="c1">// リスト容量</span>
+<a id="__codelineno-84-5" name="__codelineno-84-5" href="#__codelineno-84-5"></a><span class="w">    </span><span class="n">#size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// リストの長さ（現在の要素数）</span>
+<a id="__codelineno-84-6" name="__codelineno-84-6" href="#__codelineno-84-6"></a><span class="w">    </span><span class="n">#extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// リスト拡張時の増加倍率</span>
+<a id="__codelineno-84-7" name="__codelineno-84-7" href="#__codelineno-84-7"></a>
+<a id="__codelineno-84-8" name="__codelineno-84-8" href="#__codelineno-84-8"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-84-9" name="__codelineno-84-9" href="#__codelineno-84-9"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-10" name="__codelineno-84-10" href="#__codelineno-84-10"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#capacity</span><span class="p">);</span>
+<a id="__codelineno-84-11" name="__codelineno-84-11" href="#__codelineno-84-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-84-12" name="__codelineno-84-12" href="#__codelineno-84-12"></a>
+<a id="__codelineno-84-13" name="__codelineno-84-13" href="#__codelineno-84-13"></a><span class="w">    </span><span class="cm">/* リストの長さを取得（現在の要素数） */</span>
+<a id="__codelineno-84-14" name="__codelineno-84-14" href="#__codelineno-84-14"></a><span class="w">    </span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-15" name="__codelineno-84-15" href="#__codelineno-84-15"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="p">;</span>
+<a id="__codelineno-84-16" name="__codelineno-84-16" href="#__codelineno-84-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-84-17" name="__codelineno-84-17" href="#__codelineno-84-17"></a>
+<a id="__codelineno-84-18" name="__codelineno-84-18" href="#__codelineno-84-18"></a><span class="w">    </span><span class="cm">/* リスト容量を取得する */</span>
+<a id="__codelineno-84-19" name="__codelineno-84-19" href="#__codelineno-84-19"></a><span class="w">    </span><span class="nx">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-20" name="__codelineno-84-20" href="#__codelineno-84-20"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#capacity</span><span class="p">;</span>
+<a id="__codelineno-84-21" name="__codelineno-84-21" href="#__codelineno-84-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-84-22" name="__codelineno-84-22" href="#__codelineno-84-22"></a>
+<a id="__codelineno-84-23" name="__codelineno-84-23" href="#__codelineno-84-23"></a><span class="w">    </span><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-84-24" name="__codelineno-84-24" href="#__codelineno-84-24"></a><span class="w">    </span><span class="nx">get</span><span class="p">(</span><span class="nx">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-25" name="__codelineno-84-25" href="#__codelineno-84-25"></a><span class="w">        </span><span class="c1">// インデックスが範囲外なら例外を送出する。以下同様</span>
+<a id="__codelineno-84-26" name="__codelineno-84-26" href="#__codelineno-84-26"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="p">)</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;インデックスが範囲外です&#39;</span><span class="p">);</span>
+<a id="__codelineno-84-27" name="__codelineno-84-27" href="#__codelineno-84-27"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#arr</span><span class="p">[</span><span class="nx">index</span><span class="p">];</span>
+<a id="__codelineno-84-28" name="__codelineno-84-28" href="#__codelineno-84-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-84-29" name="__codelineno-84-29" href="#__codelineno-84-29"></a>
+<a id="__codelineno-84-30" name="__codelineno-84-30" href="#__codelineno-84-30"></a><span class="w">    </span><span class="cm">/* 要素を更新 */</span>
+<a id="__codelineno-84-31" name="__codelineno-84-31" href="#__codelineno-84-31"></a><span class="w">    </span><span class="nx">set</span><span class="p">(</span><span class="nx">index</span><span class="p">,</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-32" name="__codelineno-84-32" href="#__codelineno-84-32"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="p">)</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;インデックスが範囲外です&#39;</span><span class="p">);</span>
+<a id="__codelineno-84-33" name="__codelineno-84-33" href="#__codelineno-84-33"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#arr</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-84-34" name="__codelineno-84-34" href="#__codelineno-84-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-84-35" name="__codelineno-84-35" href="#__codelineno-84-35"></a>
+<a id="__codelineno-84-36" name="__codelineno-84-36" href="#__codelineno-84-36"></a><span class="w">    </span><span class="cm">/* 末尾に要素を追加 */</span>
+<a id="__codelineno-84-37" name="__codelineno-84-37" href="#__codelineno-84-37"></a><span class="w">    </span><span class="nx">add</span><span class="p">(</span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-38" name="__codelineno-84-38" href="#__codelineno-84-38"></a><span class="w">        </span><span class="c1">// 長さが容量に等しい場合は拡張が必要</span>
+<a id="__codelineno-84-39" name="__codelineno-84-39" href="#__codelineno-84-39"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-40" name="__codelineno-84-40" href="#__codelineno-84-40"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">extendCapacity</span><span class="p">();</span>
+<a id="__codelineno-84-41" name="__codelineno-84-41" href="#__codelineno-84-41"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-84-42" name="__codelineno-84-42" href="#__codelineno-84-42"></a><span class="w">        </span><span class="c1">// 新しい要素をリストの末尾に追加する</span>
+<a id="__codelineno-84-43" name="__codelineno-84-43" href="#__codelineno-84-43"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#arr</span><span class="p">[</span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-84-44" name="__codelineno-84-44" href="#__codelineno-84-44"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-84-45" name="__codelineno-84-45" href="#__codelineno-84-45"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-84-46" name="__codelineno-84-46" href="#__codelineno-84-46"></a>
+<a id="__codelineno-84-47" name="__codelineno-84-47" href="#__codelineno-84-47"></a><span class="w">    </span><span class="cm">/* 中間に要素を挿入 */</span>
+<a id="__codelineno-84-48" name="__codelineno-84-48" href="#__codelineno-84-48"></a><span class="w">    </span><span class="nx">insert</span><span class="p">(</span><span class="nx">index</span><span class="p">,</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-49" name="__codelineno-84-49" href="#__codelineno-84-49"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="p">)</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;インデックスが範囲外です&#39;</span><span class="p">);</span>
+<a id="__codelineno-84-50" name="__codelineno-84-50" href="#__codelineno-84-50"></a><span class="w">        </span><span class="c1">// 要素数が容量を超えると、拡張機構が発動する</span>
+<a id="__codelineno-84-51" name="__codelineno-84-51" href="#__codelineno-84-51"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-52" name="__codelineno-84-52" href="#__codelineno-84-52"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">extendCapacity</span><span class="p">();</span>
+<a id="__codelineno-84-53" name="__codelineno-84-53" href="#__codelineno-84-53"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-84-54" name="__codelineno-84-54" href="#__codelineno-84-54"></a><span class="w">        </span><span class="c1">// index 以降の要素をすべて 1 つ後ろへずらす</span>
+<a id="__codelineno-84-55" name="__codelineno-84-55" href="#__codelineno-84-55"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">index</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-56" name="__codelineno-84-56" href="#__codelineno-84-56"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#arr</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#arr</span><span class="p">[</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-84-57" name="__codelineno-84-57" href="#__codelineno-84-57"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-84-58" name="__codelineno-84-58" href="#__codelineno-84-58"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-84-59" name="__codelineno-84-59" href="#__codelineno-84-59"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#arr</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-84-60" name="__codelineno-84-60" href="#__codelineno-84-60"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-84-61" name="__codelineno-84-61" href="#__codelineno-84-61"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-84-62" name="__codelineno-84-62" href="#__codelineno-84-62"></a>
+<a id="__codelineno-84-63" name="__codelineno-84-63" href="#__codelineno-84-63"></a><span class="w">    </span><span class="cm">/* 要素を削除 */</span>
+<a id="__codelineno-84-64" name="__codelineno-84-64" href="#__codelineno-84-64"></a><span class="w">    </span><span class="nx">remove</span><span class="p">(</span><span class="nx">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-65" name="__codelineno-84-65" href="#__codelineno-84-65"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="p">)</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;インデックスが範囲外です&#39;</span><span class="p">);</span>
+<a id="__codelineno-84-66" name="__codelineno-84-66" href="#__codelineno-84-66"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#arr</span><span class="p">[</span><span class="nx">index</span><span class="p">];</span>
+<a id="__codelineno-84-67" name="__codelineno-84-67" href="#__codelineno-84-67"></a><span class="w">        </span><span class="c1">// インデックス index より後の要素をすべて 1 つ前に移動する</span>
+<a id="__codelineno-84-68" name="__codelineno-84-68" href="#__codelineno-84-68"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">index</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-69" name="__codelineno-84-69" href="#__codelineno-84-69"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#arr</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#arr</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-84-70" name="__codelineno-84-70" href="#__codelineno-84-70"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-84-71" name="__codelineno-84-71" href="#__codelineno-84-71"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-84-72" name="__codelineno-84-72" href="#__codelineno-84-72"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-84-73" name="__codelineno-84-73" href="#__codelineno-84-73"></a><span class="w">        </span><span class="c1">// 削除された要素を返す</span>
+<a id="__codelineno-84-74" name="__codelineno-84-74" href="#__codelineno-84-74"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-84-75" name="__codelineno-84-75" href="#__codelineno-84-75"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-84-76" name="__codelineno-84-76" href="#__codelineno-84-76"></a>
+<a id="__codelineno-84-77" name="__codelineno-84-77" href="#__codelineno-84-77"></a><span class="w">    </span><span class="cm">/* リストの拡張 */</span>
+<a id="__codelineno-84-78" name="__codelineno-84-78" href="#__codelineno-84-78"></a><span class="w">    </span><span class="nx">extendCapacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-79" name="__codelineno-84-79" href="#__codelineno-84-79"></a><span class="w">        </span><span class="c1">// 元の配列の extendRatio 倍の長さを持つ新しい配列を作成し、元の配列をコピーする</span>
+<a id="__codelineno-84-80" name="__codelineno-84-80" href="#__codelineno-84-80"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#arr</span><span class="p">.</span><span class="nx">concat</span><span class="p">(</span>
+<a id="__codelineno-84-81" name="__codelineno-84-81" href="#__codelineno-84-81"></a><span class="w">            </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#extendRatio</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">))</span>
+<a id="__codelineno-84-82" name="__codelineno-84-82" href="#__codelineno-84-82"></a><span class="w">        </span><span class="p">);</span>
+<a id="__codelineno-84-83" name="__codelineno-84-83" href="#__codelineno-84-83"></a><span class="w">        </span><span class="c1">// リストの容量を更新</span>
+<a id="__codelineno-84-84" name="__codelineno-84-84" href="#__codelineno-84-84"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#arr</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-84-85" name="__codelineno-84-85" href="#__codelineno-84-85"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-84-86" name="__codelineno-84-86" href="#__codelineno-84-86"></a>
+<a id="__codelineno-84-87" name="__codelineno-84-87" href="#__codelineno-84-87"></a><span class="w">    </span><span class="cm">/* リストを配列に変換する */</span>
+<a id="__codelineno-84-88" name="__codelineno-84-88" href="#__codelineno-84-88"></a><span class="w">    </span><span class="nx">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-89" name="__codelineno-84-89" href="#__codelineno-84-89"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">();</span>
+<a id="__codelineno-84-90" name="__codelineno-84-90" href="#__codelineno-84-90"></a><span class="w">        </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-84-91" name="__codelineno-84-91" href="#__codelineno-84-91"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">size</span><span class="p">);</span>
+<a id="__codelineno-84-92" name="__codelineno-84-92" href="#__codelineno-84-92"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">size</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-93" name="__codelineno-84-93" href="#__codelineno-84-93"></a><span class="w">            </span><span class="nx">arr</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
+<a id="__codelineno-84-94" name="__codelineno-84-94" href="#__codelineno-84-94"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-84-95" name="__codelineno-84-95" href="#__codelineno-84-95"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">arr</span><span class="p">;</span>
+<a id="__codelineno-84-96" name="__codelineno-84-96" href="#__codelineno-84-96"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-84-97" name="__codelineno-84-97" href="#__codelineno-84-97"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_list.ts</span><pre><span></span><code><a id="__codelineno-79-1" name="__codelineno-79-1" href="#__codelineno-79-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MyList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">my_list.ts</span><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="cm">/* リストクラス */</span>
+<a id="__codelineno-85-2" name="__codelineno-85-2" href="#__codelineno-85-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">MyList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-3" name="__codelineno-85-3" href="#__codelineno-85-3"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">arr</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">;</span><span class="w"> </span><span class="c1">// 配列（リスト要素を格納）</span>
+<a id="__codelineno-85-4" name="__codelineno-85-4" href="#__codelineno-85-4"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">_capacity</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">10</span><span class="p">;</span><span class="w"> </span><span class="c1">// リスト容量</span>
+<a id="__codelineno-85-5" name="__codelineno-85-5" href="#__codelineno-85-5"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">_size</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// リストの長さ（現在の要素数）</span>
+<a id="__codelineno-85-6" name="__codelineno-85-6" href="#__codelineno-85-6"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">extendRatio</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// リスト拡張時の増加倍率</span>
+<a id="__codelineno-85-7" name="__codelineno-85-7" href="#__codelineno-85-7"></a>
+<a id="__codelineno-85-8" name="__codelineno-85-8" href="#__codelineno-85-8"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-85-9" name="__codelineno-85-9" href="#__codelineno-85-9"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-10" name="__codelineno-85-10" href="#__codelineno-85-10"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">_capacity</span><span class="p">);</span>
+<a id="__codelineno-85-11" name="__codelineno-85-11" href="#__codelineno-85-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-85-12" name="__codelineno-85-12" href="#__codelineno-85-12"></a>
+<a id="__codelineno-85-13" name="__codelineno-85-13" href="#__codelineno-85-13"></a><span class="w">    </span><span class="cm">/* リストの長さを取得（現在の要素数） */</span>
+<a id="__codelineno-85-14" name="__codelineno-85-14" href="#__codelineno-85-14"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nx">size</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-15" name="__codelineno-85-15" href="#__codelineno-85-15"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">_size</span><span class="p">;</span>
+<a id="__codelineno-85-16" name="__codelineno-85-16" href="#__codelineno-85-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-85-17" name="__codelineno-85-17" href="#__codelineno-85-17"></a>
+<a id="__codelineno-85-18" name="__codelineno-85-18" href="#__codelineno-85-18"></a><span class="w">    </span><span class="cm">/* リスト容量を取得する */</span>
+<a id="__codelineno-85-19" name="__codelineno-85-19" href="#__codelineno-85-19"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nx">capacity</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-20" name="__codelineno-85-20" href="#__codelineno-85-20"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">_capacity</span><span class="p">;</span>
+<a id="__codelineno-85-21" name="__codelineno-85-21" href="#__codelineno-85-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-85-22" name="__codelineno-85-22" href="#__codelineno-85-22"></a>
+<a id="__codelineno-85-23" name="__codelineno-85-23" href="#__codelineno-85-23"></a><span class="w">    </span><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-85-24" name="__codelineno-85-24" href="#__codelineno-85-24"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nx">get</span><span class="p">(</span><span class="nx">index</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-25" name="__codelineno-85-25" href="#__codelineno-85-25"></a><span class="w">        </span><span class="c1">// インデックスが範囲外なら例外を送出する。以下同様</span>
+<a id="__codelineno-85-26" name="__codelineno-85-26" href="#__codelineno-85-26"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">_size</span><span class="p">)</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;インデックスが範囲外です&#39;</span><span class="p">);</span>
+<a id="__codelineno-85-27" name="__codelineno-85-27" href="#__codelineno-85-27"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">arr</span><span class="p">[</span><span class="nx">index</span><span class="p">];</span>
+<a id="__codelineno-85-28" name="__codelineno-85-28" href="#__codelineno-85-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-85-29" name="__codelineno-85-29" href="#__codelineno-85-29"></a>
+<a id="__codelineno-85-30" name="__codelineno-85-30" href="#__codelineno-85-30"></a><span class="w">    </span><span class="cm">/* 要素を更新 */</span>
+<a id="__codelineno-85-31" name="__codelineno-85-31" href="#__codelineno-85-31"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nx">set</span><span class="p">(</span><span class="nx">index</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">num</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-32" name="__codelineno-85-32" href="#__codelineno-85-32"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">_size</span><span class="p">)</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;インデックスが範囲外です&#39;</span><span class="p">);</span>
+<a id="__codelineno-85-33" name="__codelineno-85-33" href="#__codelineno-85-33"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">arr</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-85-34" name="__codelineno-85-34" href="#__codelineno-85-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-85-35" name="__codelineno-85-35" href="#__codelineno-85-35"></a>
+<a id="__codelineno-85-36" name="__codelineno-85-36" href="#__codelineno-85-36"></a><span class="w">    </span><span class="cm">/* 末尾に要素を追加 */</span>
+<a id="__codelineno-85-37" name="__codelineno-85-37" href="#__codelineno-85-37"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nx">add</span><span class="p">(</span><span class="nx">num</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-38" name="__codelineno-85-38" href="#__codelineno-85-38"></a><span class="w">        </span><span class="c1">// 長さが容量に等しい場合は拡張が必要</span>
+<a id="__codelineno-85-39" name="__codelineno-85-39" href="#__codelineno-85-39"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">_size</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">_capacity</span><span class="p">)</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">extendCapacity</span><span class="p">();</span>
+<a id="__codelineno-85-40" name="__codelineno-85-40" href="#__codelineno-85-40"></a><span class="w">        </span><span class="c1">// 新しい要素をリストの末尾に追加する</span>
+<a id="__codelineno-85-41" name="__codelineno-85-41" href="#__codelineno-85-41"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">arr</span><span class="p">[</span><span class="k">this</span><span class="p">.</span><span class="nx">_size</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-85-42" name="__codelineno-85-42" href="#__codelineno-85-42"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">_size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-85-43" name="__codelineno-85-43" href="#__codelineno-85-43"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-85-44" name="__codelineno-85-44" href="#__codelineno-85-44"></a>
+<a id="__codelineno-85-45" name="__codelineno-85-45" href="#__codelineno-85-45"></a><span class="w">    </span><span class="cm">/* 中間に要素を挿入 */</span>
+<a id="__codelineno-85-46" name="__codelineno-85-46" href="#__codelineno-85-46"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nx">insert</span><span class="p">(</span><span class="nx">index</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">num</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-47" name="__codelineno-85-47" href="#__codelineno-85-47"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">_size</span><span class="p">)</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;インデックスが範囲外です&#39;</span><span class="p">);</span>
+<a id="__codelineno-85-48" name="__codelineno-85-48" href="#__codelineno-85-48"></a><span class="w">        </span><span class="c1">// 要素数が容量を超えると、拡張機構が発動する</span>
+<a id="__codelineno-85-49" name="__codelineno-85-49" href="#__codelineno-85-49"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">_size</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">_capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-50" name="__codelineno-85-50" href="#__codelineno-85-50"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">extendCapacity</span><span class="p">();</span>
+<a id="__codelineno-85-51" name="__codelineno-85-51" href="#__codelineno-85-51"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-85-52" name="__codelineno-85-52" href="#__codelineno-85-52"></a><span class="w">        </span><span class="c1">// index 以降の要素をすべて 1 つ後ろへずらす</span>
+<a id="__codelineno-85-53" name="__codelineno-85-53" href="#__codelineno-85-53"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">_size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">index</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-54" name="__codelineno-85-54" href="#__codelineno-85-54"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">arr</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">arr</span><span class="p">[</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-85-55" name="__codelineno-85-55" href="#__codelineno-85-55"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-85-56" name="__codelineno-85-56" href="#__codelineno-85-56"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-85-57" name="__codelineno-85-57" href="#__codelineno-85-57"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">arr</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-85-58" name="__codelineno-85-58" href="#__codelineno-85-58"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">_size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-85-59" name="__codelineno-85-59" href="#__codelineno-85-59"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-85-60" name="__codelineno-85-60" href="#__codelineno-85-60"></a>
+<a id="__codelineno-85-61" name="__codelineno-85-61" href="#__codelineno-85-61"></a><span class="w">    </span><span class="cm">/* 要素を削除 */</span>
+<a id="__codelineno-85-62" name="__codelineno-85-62" href="#__codelineno-85-62"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nx">remove</span><span class="p">(</span><span class="nx">index</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-63" name="__codelineno-85-63" href="#__codelineno-85-63"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">_size</span><span class="p">)</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;インデックスが範囲外です&#39;</span><span class="p">);</span>
+<a id="__codelineno-85-64" name="__codelineno-85-64" href="#__codelineno-85-64"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">arr</span><span class="p">[</span><span class="nx">index</span><span class="p">];</span>
+<a id="__codelineno-85-65" name="__codelineno-85-65" href="#__codelineno-85-65"></a><span class="w">        </span><span class="c1">// インデックス index より後の要素をすべて 1 つ前に移動する</span>
+<a id="__codelineno-85-66" name="__codelineno-85-66" href="#__codelineno-85-66"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">index</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">_size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-67" name="__codelineno-85-67" href="#__codelineno-85-67"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">arr</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">arr</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-85-68" name="__codelineno-85-68" href="#__codelineno-85-68"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-85-69" name="__codelineno-85-69" href="#__codelineno-85-69"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-85-70" name="__codelineno-85-70" href="#__codelineno-85-70"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">_size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-85-71" name="__codelineno-85-71" href="#__codelineno-85-71"></a><span class="w">        </span><span class="c1">// 削除された要素を返す</span>
+<a id="__codelineno-85-72" name="__codelineno-85-72" href="#__codelineno-85-72"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-85-73" name="__codelineno-85-73" href="#__codelineno-85-73"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-85-74" name="__codelineno-85-74" href="#__codelineno-85-74"></a>
+<a id="__codelineno-85-75" name="__codelineno-85-75" href="#__codelineno-85-75"></a><span class="w">    </span><span class="cm">/* リストの拡張 */</span>
+<a id="__codelineno-85-76" name="__codelineno-85-76" href="#__codelineno-85-76"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nx">extendCapacity</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-77" name="__codelineno-85-77" href="#__codelineno-85-77"></a><span class="w">        </span><span class="c1">// `size` の長さを持つ配列を新規作成し、元の配列を新しい配列にコピーする</span>
+<a id="__codelineno-85-78" name="__codelineno-85-78" href="#__codelineno-85-78"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">arr</span><span class="p">.</span><span class="nx">concat</span><span class="p">(</span>
+<a id="__codelineno-85-79" name="__codelineno-85-79" href="#__codelineno-85-79"></a><span class="w">            </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">extendRatio</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">))</span>
+<a id="__codelineno-85-80" name="__codelineno-85-80" href="#__codelineno-85-80"></a><span class="w">        </span><span class="p">);</span>
+<a id="__codelineno-85-81" name="__codelineno-85-81" href="#__codelineno-85-81"></a><span class="w">        </span><span class="c1">// リストの容量を更新</span>
+<a id="__codelineno-85-82" name="__codelineno-85-82" href="#__codelineno-85-82"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">_capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">arr</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-85-83" name="__codelineno-85-83" href="#__codelineno-85-83"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-85-84" name="__codelineno-85-84" href="#__codelineno-85-84"></a>
+<a id="__codelineno-85-85" name="__codelineno-85-85" href="#__codelineno-85-85"></a><span class="w">    </span><span class="cm">/* リストを配列に変換する */</span>
+<a id="__codelineno-85-86" name="__codelineno-85-86" href="#__codelineno-85-86"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nx">toArray</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-87" name="__codelineno-85-87" href="#__codelineno-85-87"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">();</span>
+<a id="__codelineno-85-88" name="__codelineno-85-88" href="#__codelineno-85-88"></a><span class="w">        </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-85-89" name="__codelineno-85-89" href="#__codelineno-85-89"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">size</span><span class="p">);</span>
+<a id="__codelineno-85-90" name="__codelineno-85-90" href="#__codelineno-85-90"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">size</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-91" name="__codelineno-85-91" href="#__codelineno-85-91"></a><span class="w">            </span><span class="nx">arr</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
+<a id="__codelineno-85-92" name="__codelineno-85-92" href="#__codelineno-85-92"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-85-93" name="__codelineno-85-93" href="#__codelineno-85-93"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">arr</span><span class="p">;</span>
+<a id="__codelineno-85-94" name="__codelineno-85-94" href="#__codelineno-85-94"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-85-95" name="__codelineno-85-95" href="#__codelineno-85-95"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_list.dart</span><pre><span></span><code><a id="__codelineno-80-1" name="__codelineno-80-1" href="#__codelineno-80-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MyList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">my_list.dart</span><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="cm">/* リストクラス */</span>
+<a id="__codelineno-86-2" name="__codelineno-86-2" href="#__codelineno-86-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">MyList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-3" name="__codelineno-86-3" href="#__codelineno-86-3"></a><span class="w">  </span><span class="kd">late</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">_arr</span><span class="p">;</span><span class="w"> </span><span class="c1">// 配列（リスト要素を格納）</span>
+<a id="__codelineno-86-4" name="__codelineno-86-4" href="#__codelineno-86-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">_capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">10</span><span class="p">;</span><span class="w"> </span><span class="c1">// リスト容量</span>
+<a id="__codelineno-86-5" name="__codelineno-86-5" href="#__codelineno-86-5"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">_size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// リストの長さ（現在の要素数）</span>
+<a id="__codelineno-86-6" name="__codelineno-86-6" href="#__codelineno-86-6"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">_extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// リスト拡張時の増加倍率</span>
+<a id="__codelineno-86-7" name="__codelineno-86-7" href="#__codelineno-86-7"></a>
+<a id="__codelineno-86-8" name="__codelineno-86-8" href="#__codelineno-86-8"></a><span class="w">  </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-86-9" name="__codelineno-86-9" href="#__codelineno-86-9"></a><span class="w">  </span><span class="n">MyList</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-10" name="__codelineno-86-10" href="#__codelineno-86-10"></a><span class="w">    </span><span class="n">_arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">_capacity</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-86-11" name="__codelineno-86-11" href="#__codelineno-86-11"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-86-12" name="__codelineno-86-12" href="#__codelineno-86-12"></a>
+<a id="__codelineno-86-13" name="__codelineno-86-13" href="#__codelineno-86-13"></a><span class="w">  </span><span class="cm">/* リストの長さを取得（現在の要素数） */</span>
+<a id="__codelineno-86-14" name="__codelineno-86-14" href="#__codelineno-86-14"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">_size</span><span class="p">;</span>
+<a id="__codelineno-86-15" name="__codelineno-86-15" href="#__codelineno-86-15"></a>
+<a id="__codelineno-86-16" name="__codelineno-86-16" href="#__codelineno-86-16"></a><span class="w">  </span><span class="cm">/* リスト容量を取得する */</span>
+<a id="__codelineno-86-17" name="__codelineno-86-17" href="#__codelineno-86-17"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">_capacity</span><span class="p">;</span>
+<a id="__codelineno-86-18" name="__codelineno-86-18" href="#__codelineno-86-18"></a>
+<a id="__codelineno-86-19" name="__codelineno-86-19" href="#__codelineno-86-19"></a><span class="w">  </span><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-86-20" name="__codelineno-86-20" href="#__codelineno-86-20"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="kd">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-21" name="__codelineno-86-21" href="#__codelineno-86-21"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">_size</span><span class="p">)</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">RangeError</span><span class="p">(</span><span class="s1">&#39;インデックスが範囲外です&#39;</span><span class="p">);</span>
+<a id="__codelineno-86-22" name="__codelineno-86-22" href="#__codelineno-86-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_arr</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-86-23" name="__codelineno-86-23" href="#__codelineno-86-23"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-86-24" name="__codelineno-86-24" href="#__codelineno-86-24"></a>
+<a id="__codelineno-86-25" name="__codelineno-86-25" href="#__codelineno-86-25"></a><span class="w">  </span><span class="cm">/* 要素を更新 */</span>
+<a id="__codelineno-86-26" name="__codelineno-86-26" href="#__codelineno-86-26"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="kd">set</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-27" name="__codelineno-86-27" href="#__codelineno-86-27"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">_size</span><span class="p">)</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">RangeError</span><span class="p">(</span><span class="s1">&#39;インデックスが範囲外です&#39;</span><span class="p">);</span>
+<a id="__codelineno-86-28" name="__codelineno-86-28" href="#__codelineno-86-28"></a><span class="w">    </span><span class="n">_arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_num</span><span class="p">;</span>
+<a id="__codelineno-86-29" name="__codelineno-86-29" href="#__codelineno-86-29"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-86-30" name="__codelineno-86-30" href="#__codelineno-86-30"></a>
+<a id="__codelineno-86-31" name="__codelineno-86-31" href="#__codelineno-86-31"></a><span class="w">  </span><span class="cm">/* 末尾に要素を追加 */</span>
+<a id="__codelineno-86-32" name="__codelineno-86-32" href="#__codelineno-86-32"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">add</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-33" name="__codelineno-86-33" href="#__codelineno-86-33"></a><span class="w">    </span><span class="c1">// 要素数が容量を超えると、拡張機構が発動する</span>
+<a id="__codelineno-86-34" name="__codelineno-86-34" href="#__codelineno-86-34"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">_capacity</span><span class="p">)</span><span class="w"> </span><span class="n">extendCapacity</span><span class="p">();</span>
+<a id="__codelineno-86-35" name="__codelineno-86-35" href="#__codelineno-86-35"></a><span class="w">    </span><span class="n">_arr</span><span class="p">[</span><span class="n">_size</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_num</span><span class="p">;</span>
+<a id="__codelineno-86-36" name="__codelineno-86-36" href="#__codelineno-86-36"></a><span class="w">    </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-86-37" name="__codelineno-86-37" href="#__codelineno-86-37"></a><span class="w">    </span><span class="n">_size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-86-38" name="__codelineno-86-38" href="#__codelineno-86-38"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-86-39" name="__codelineno-86-39" href="#__codelineno-86-39"></a>
+<a id="__codelineno-86-40" name="__codelineno-86-40" href="#__codelineno-86-40"></a><span class="w">  </span><span class="cm">/* 中間に要素を挿入 */</span>
+<a id="__codelineno-86-41" name="__codelineno-86-41" href="#__codelineno-86-41"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">insert</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-42" name="__codelineno-86-42" href="#__codelineno-86-42"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">_size</span><span class="p">)</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">RangeError</span><span class="p">(</span><span class="s1">&#39;インデックスが範囲外です&#39;</span><span class="p">);</span>
+<a id="__codelineno-86-43" name="__codelineno-86-43" href="#__codelineno-86-43"></a><span class="w">    </span><span class="c1">// 要素数が容量を超えると、拡張機構が発動する</span>
+<a id="__codelineno-86-44" name="__codelineno-86-44" href="#__codelineno-86-44"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">_capacity</span><span class="p">)</span><span class="w"> </span><span class="n">extendCapacity</span><span class="p">();</span>
+<a id="__codelineno-86-45" name="__codelineno-86-45" href="#__codelineno-86-45"></a><span class="w">    </span><span class="c1">// index 以降の要素をすべて 1 つ後ろへずらす</span>
+<a id="__codelineno-86-46" name="__codelineno-86-46" href="#__codelineno-86-46"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-47" name="__codelineno-86-47" href="#__codelineno-86-47"></a><span class="w">      </span><span class="n">_arr</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_arr</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-86-48" name="__codelineno-86-48" href="#__codelineno-86-48"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-86-49" name="__codelineno-86-49" href="#__codelineno-86-49"></a><span class="w">    </span><span class="n">_arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_num</span><span class="p">;</span>
+<a id="__codelineno-86-50" name="__codelineno-86-50" href="#__codelineno-86-50"></a><span class="w">    </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-86-51" name="__codelineno-86-51" href="#__codelineno-86-51"></a><span class="w">    </span><span class="n">_size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-86-52" name="__codelineno-86-52" href="#__codelineno-86-52"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-86-53" name="__codelineno-86-53" href="#__codelineno-86-53"></a>
+<a id="__codelineno-86-54" name="__codelineno-86-54" href="#__codelineno-86-54"></a><span class="w">  </span><span class="cm">/* 要素を削除 */</span>
+<a id="__codelineno-86-55" name="__codelineno-86-55" href="#__codelineno-86-55"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-56" name="__codelineno-86-56" href="#__codelineno-86-56"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">_size</span><span class="p">)</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">RangeError</span><span class="p">(</span><span class="s1">&#39;インデックスが範囲外です&#39;</span><span class="p">);</span>
+<a id="__codelineno-86-57" name="__codelineno-86-57" href="#__codelineno-86-57"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_arr</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-86-58" name="__codelineno-86-58" href="#__codelineno-86-58"></a><span class="w">    </span><span class="c1">// インデックス index より後の要素をすべて 1 つ前に移動する</span>
+<a id="__codelineno-86-59" name="__codelineno-86-59" href="#__codelineno-86-59"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">_size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-60" name="__codelineno-86-60" href="#__codelineno-86-60"></a><span class="w">      </span><span class="n">_arr</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_arr</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">];</span>
+<a id="__codelineno-86-61" name="__codelineno-86-61" href="#__codelineno-86-61"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-86-62" name="__codelineno-86-62" href="#__codelineno-86-62"></a><span class="w">    </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-86-63" name="__codelineno-86-63" href="#__codelineno-86-63"></a><span class="w">    </span><span class="n">_size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-86-64" name="__codelineno-86-64" href="#__codelineno-86-64"></a><span class="w">    </span><span class="c1">// 削除された要素を返す</span>
+<a id="__codelineno-86-65" name="__codelineno-86-65" href="#__codelineno-86-65"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_num</span><span class="p">;</span>
+<a id="__codelineno-86-66" name="__codelineno-86-66" href="#__codelineno-86-66"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-86-67" name="__codelineno-86-67" href="#__codelineno-86-67"></a>
+<a id="__codelineno-86-68" name="__codelineno-86-68" href="#__codelineno-86-68"></a><span class="w">  </span><span class="cm">/* リストの拡張 */</span>
+<a id="__codelineno-86-69" name="__codelineno-86-69" href="#__codelineno-86-69"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">extendCapacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-70" name="__codelineno-86-70" href="#__codelineno-86-70"></a><span class="w">    </span><span class="c1">// 元の配列の `_extendRatio` 倍の長さを持つ新しい配列を作成する</span>
+<a id="__codelineno-86-71" name="__codelineno-86-71" href="#__codelineno-86-71"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="n">_newNums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">_capacity</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">_extendRatio</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-86-72" name="__codelineno-86-72" href="#__codelineno-86-72"></a><span class="w">    </span><span class="c1">// 元の配列を新しい配列にコピー</span>
+<a id="__codelineno-86-73" name="__codelineno-86-73" href="#__codelineno-86-73"></a><span class="w">    </span><span class="n">List</span><span class="p">.</span><span class="n">copyRange</span><span class="p">(</span><span class="n">_newNums</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">_arr</span><span class="p">);</span>
+<a id="__codelineno-86-74" name="__codelineno-86-74" href="#__codelineno-86-74"></a><span class="w">    </span><span class="c1">// `_arr` の参照を更新</span>
+<a id="__codelineno-86-75" name="__codelineno-86-75" href="#__codelineno-86-75"></a><span class="w">    </span><span class="n">_arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_newNums</span><span class="p">;</span>
+<a id="__codelineno-86-76" name="__codelineno-86-76" href="#__codelineno-86-76"></a><span class="w">    </span><span class="c1">// リストの容量を更新</span>
+<a id="__codelineno-86-77" name="__codelineno-86-77" href="#__codelineno-86-77"></a><span class="w">    </span><span class="n">_capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_arr</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-86-78" name="__codelineno-86-78" href="#__codelineno-86-78"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-86-79" name="__codelineno-86-79" href="#__codelineno-86-79"></a>
+<a id="__codelineno-86-80" name="__codelineno-86-80" href="#__codelineno-86-80"></a><span class="w">  </span><span class="cm">/* リストを配列に変換する */</span>
+<a id="__codelineno-86-81" name="__codelineno-86-81" href="#__codelineno-86-81"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-82" name="__codelineno-86-82" href="#__codelineno-86-82"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-86-83" name="__codelineno-86-83" href="#__codelineno-86-83"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">_size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-84" name="__codelineno-86-84" href="#__codelineno-86-84"></a><span class="w">      </span><span class="n">arr</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="kd">get</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-86-85" name="__codelineno-86-85" href="#__codelineno-86-85"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-86-86" name="__codelineno-86-86" href="#__codelineno-86-86"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">arr</span><span class="p">;</span>
+<a id="__codelineno-86-87" name="__codelineno-86-87" href="#__codelineno-86-87"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-86-88" name="__codelineno-86-88" href="#__codelineno-86-88"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_list.rs</span><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MyList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">my_list.rs</span><pre><span></span><code><a id="__codelineno-87-1" name="__codelineno-87-1" href="#__codelineno-87-1"></a><span class="cm">/* リストクラス */</span>
+<a id="__codelineno-87-2" name="__codelineno-87-2" href="#__codelineno-87-2"></a><span class="cp">#[allow(dead_code)]</span>
+<a id="__codelineno-87-3" name="__codelineno-87-3" href="#__codelineno-87-3"></a><span class="k">struct</span><span class="w"> </span><span class="nc">MyList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-4" name="__codelineno-87-4" href="#__codelineno-87-4"></a><span class="w">    </span><span class="n">arr</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">,</span><span class="w">       </span><span class="c1">// 配列（リスト要素を格納）</span>
+<a id="__codelineno-87-5" name="__codelineno-87-5" href="#__codelineno-87-5"></a><span class="w">    </span><span class="n">capacity</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w">     </span><span class="c1">// リスト容量</span>
+<a id="__codelineno-87-6" name="__codelineno-87-6" href="#__codelineno-87-6"></a><span class="w">    </span><span class="n">size</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w">         </span><span class="c1">// リストの長さ（現在の要素数）</span>
+<a id="__codelineno-87-7" name="__codelineno-87-7" href="#__codelineno-87-7"></a><span class="w">    </span><span class="n">extend_ratio</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="c1">// リスト拡張時の増加倍率</span>
+<a id="__codelineno-87-8" name="__codelineno-87-8" href="#__codelineno-87-8"></a><span class="p">}</span>
+<a id="__codelineno-87-9" name="__codelineno-87-9" href="#__codelineno-87-9"></a>
+<a id="__codelineno-87-10" name="__codelineno-87-10" href="#__codelineno-87-10"></a><span class="cp">#[allow(unused, unused_comparisons)]</span>
+<a id="__codelineno-87-11" name="__codelineno-87-11" href="#__codelineno-87-11"></a><span class="k">impl</span><span class="w"> </span><span class="n">MyList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-12" name="__codelineno-87-12" href="#__codelineno-87-12"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-87-13" name="__codelineno-87-13" href="#__codelineno-87-13"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">new</span><span class="p">(</span><span class="n">capacity</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-14" name="__codelineno-87-14" href="#__codelineno-87-14"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">vec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">capacity</span><span class="p">];</span>
+<a id="__codelineno-87-15" name="__codelineno-87-15" href="#__codelineno-87-15"></a><span class="w">        </span><span class="bp">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-16" name="__codelineno-87-16" href="#__codelineno-87-16"></a><span class="w">            </span><span class="n">arr</span><span class="p">:</span><span class="w"> </span><span class="nc">vec</span><span class="p">,</span>
+<a id="__codelineno-87-17" name="__codelineno-87-17" href="#__codelineno-87-17"></a><span class="w">            </span><span class="n">capacity</span><span class="p">,</span>
+<a id="__codelineno-87-18" name="__codelineno-87-18" href="#__codelineno-87-18"></a><span class="w">            </span><span class="n">size</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span>
+<a id="__codelineno-87-19" name="__codelineno-87-19" href="#__codelineno-87-19"></a><span class="w">            </span><span class="n">extend_ratio</span><span class="p">:</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span>
+<a id="__codelineno-87-20" name="__codelineno-87-20" href="#__codelineno-87-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-87-21" name="__codelineno-87-21" href="#__codelineno-87-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-87-22" name="__codelineno-87-22" href="#__codelineno-87-22"></a>
+<a id="__codelineno-87-23" name="__codelineno-87-23" href="#__codelineno-87-23"></a><span class="w">    </span><span class="cm">/* リストの長さを取得（現在の要素数） */</span>
+<a id="__codelineno-87-24" name="__codelineno-87-24" href="#__codelineno-87-24"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-25" name="__codelineno-87-25" href="#__codelineno-87-25"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">;</span>
+<a id="__codelineno-87-26" name="__codelineno-87-26" href="#__codelineno-87-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-87-27" name="__codelineno-87-27" href="#__codelineno-87-27"></a>
+<a id="__codelineno-87-28" name="__codelineno-87-28" href="#__codelineno-87-28"></a><span class="w">    </span><span class="cm">/* リスト容量を取得する */</span>
+<a id="__codelineno-87-29" name="__codelineno-87-29" href="#__codelineno-87-29"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">capacity</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-30" name="__codelineno-87-30" href="#__codelineno-87-30"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-87-31" name="__codelineno-87-31" href="#__codelineno-87-31"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-87-32" name="__codelineno-87-32" href="#__codelineno-87-32"></a>
+<a id="__codelineno-87-33" name="__codelineno-87-33" href="#__codelineno-87-33"></a><span class="w">    </span><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-87-34" name="__codelineno-87-34" href="#__codelineno-87-34"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">index</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-35" name="__codelineno-87-35" href="#__codelineno-87-35"></a><span class="w">        </span><span class="c1">// インデックスが範囲外なら例外を送出する。以下同様</span>
+<a id="__codelineno-87-36" name="__codelineno-87-36" href="#__codelineno-87-36"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-37" name="__codelineno-87-37" href="#__codelineno-87-37"></a><span class="w">            </span><span class="fm">panic!</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外です&quot;</span><span class="p">)</span>
+<a id="__codelineno-87-38" name="__codelineno-87-38" href="#__codelineno-87-38"></a><span class="w">        </span><span class="p">};</span>
+<a id="__codelineno-87-39" name="__codelineno-87-39" href="#__codelineno-87-39"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-87-40" name="__codelineno-87-40" href="#__codelineno-87-40"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-87-41" name="__codelineno-87-41" href="#__codelineno-87-41"></a>
+<a id="__codelineno-87-42" name="__codelineno-87-42" href="#__codelineno-87-42"></a><span class="w">    </span><span class="cm">/* 要素を更新 */</span>
+<a id="__codelineno-87-43" name="__codelineno-87-43" href="#__codelineno-87-43"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">set</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">index</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-44" name="__codelineno-87-44" href="#__codelineno-87-44"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-45" name="__codelineno-87-45" href="#__codelineno-87-45"></a><span class="w">            </span><span class="fm">panic!</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外です&quot;</span><span class="p">)</span>
+<a id="__codelineno-87-46" name="__codelineno-87-46" href="#__codelineno-87-46"></a><span class="w">        </span><span class="p">};</span>
+<a id="__codelineno-87-47" name="__codelineno-87-47" href="#__codelineno-87-47"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-87-48" name="__codelineno-87-48" href="#__codelineno-87-48"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-87-49" name="__codelineno-87-49" href="#__codelineno-87-49"></a>
+<a id="__codelineno-87-50" name="__codelineno-87-50" href="#__codelineno-87-50"></a><span class="w">    </span><span class="cm">/* 末尾に要素を追加 */</span>
+<a id="__codelineno-87-51" name="__codelineno-87-51" href="#__codelineno-87-51"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">add</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-52" name="__codelineno-87-52" href="#__codelineno-87-52"></a><span class="w">        </span><span class="c1">// 要素数が容量を超えると、拡張機構が発動する</span>
+<a id="__codelineno-87-53" name="__codelineno-87-53" href="#__codelineno-87-53"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-54" name="__codelineno-87-54" href="#__codelineno-87-54"></a><span class="w">            </span><span class="bp">self</span><span class="p">.</span><span class="n">extend_capacity</span><span class="p">();</span>
+<a id="__codelineno-87-55" name="__codelineno-87-55" href="#__codelineno-87-55"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-87-56" name="__codelineno-87-56" href="#__codelineno-87-56"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">arr</span><span class="p">[</span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-87-57" name="__codelineno-87-57" href="#__codelineno-87-57"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-87-58" name="__codelineno-87-58" href="#__codelineno-87-58"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-87-59" name="__codelineno-87-59" href="#__codelineno-87-59"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-87-60" name="__codelineno-87-60" href="#__codelineno-87-60"></a>
+<a id="__codelineno-87-61" name="__codelineno-87-61" href="#__codelineno-87-61"></a><span class="w">    </span><span class="cm">/* 中間に要素を挿入 */</span>
+<a id="__codelineno-87-62" name="__codelineno-87-62" href="#__codelineno-87-62"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">index</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-63" name="__codelineno-87-63" href="#__codelineno-87-63"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-64" name="__codelineno-87-64" href="#__codelineno-87-64"></a><span class="w">            </span><span class="fm">panic!</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外です&quot;</span><span class="p">)</span>
+<a id="__codelineno-87-65" name="__codelineno-87-65" href="#__codelineno-87-65"></a><span class="w">        </span><span class="p">};</span>
+<a id="__codelineno-87-66" name="__codelineno-87-66" href="#__codelineno-87-66"></a><span class="w">        </span><span class="c1">// 要素数が容量を超えると、拡張機構が発動する</span>
+<a id="__codelineno-87-67" name="__codelineno-87-67" href="#__codelineno-87-67"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-68" name="__codelineno-87-68" href="#__codelineno-87-68"></a><span class="w">            </span><span class="bp">self</span><span class="p">.</span><span class="n">extend_capacity</span><span class="p">();</span>
+<a id="__codelineno-87-69" name="__codelineno-87-69" href="#__codelineno-87-69"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-87-70" name="__codelineno-87-70" href="#__codelineno-87-70"></a><span class="w">        </span><span class="c1">// index 以降の要素をすべて 1 つ後ろへずらす</span>
+<a id="__codelineno-87-71" name="__codelineno-87-71" href="#__codelineno-87-71"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="o">..</span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">).</span><span class="n">rev</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-72" name="__codelineno-87-72" href="#__codelineno-87-72"></a><span class="w">            </span><span class="bp">self</span><span class="p">.</span><span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-87-73" name="__codelineno-87-73" href="#__codelineno-87-73"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-87-74" name="__codelineno-87-74" href="#__codelineno-87-74"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-87-75" name="__codelineno-87-75" href="#__codelineno-87-75"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-87-76" name="__codelineno-87-76" href="#__codelineno-87-76"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-87-77" name="__codelineno-87-77" href="#__codelineno-87-77"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-87-78" name="__codelineno-87-78" href="#__codelineno-87-78"></a>
+<a id="__codelineno-87-79" name="__codelineno-87-79" href="#__codelineno-87-79"></a><span class="w">    </span><span class="cm">/* 要素を削除 */</span>
+<a id="__codelineno-87-80" name="__codelineno-87-80" href="#__codelineno-87-80"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">index</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-81" name="__codelineno-87-81" href="#__codelineno-87-81"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-82" name="__codelineno-87-82" href="#__codelineno-87-82"></a><span class="w">            </span><span class="fm">panic!</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外です&quot;</span><span class="p">)</span>
+<a id="__codelineno-87-83" name="__codelineno-87-83" href="#__codelineno-87-83"></a><span class="w">        </span><span class="p">};</span>
+<a id="__codelineno-87-84" name="__codelineno-87-84" href="#__codelineno-87-84"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-87-85" name="__codelineno-87-85" href="#__codelineno-87-85"></a><span class="w">        </span><span class="c1">// インデックス index より後の要素をすべて 1 つ前に移動する</span>
+<a id="__codelineno-87-86" name="__codelineno-87-86" href="#__codelineno-87-86"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">index</span><span class="o">..</span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-87" name="__codelineno-87-87" href="#__codelineno-87-87"></a><span class="w">            </span><span class="bp">self</span><span class="p">.</span><span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-87-88" name="__codelineno-87-88" href="#__codelineno-87-88"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-87-89" name="__codelineno-87-89" href="#__codelineno-87-89"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-87-90" name="__codelineno-87-90" href="#__codelineno-87-90"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-87-91" name="__codelineno-87-91" href="#__codelineno-87-91"></a><span class="w">        </span><span class="c1">// 削除された要素を返す</span>
+<a id="__codelineno-87-92" name="__codelineno-87-92" href="#__codelineno-87-92"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-87-93" name="__codelineno-87-93" href="#__codelineno-87-93"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-87-94" name="__codelineno-87-94" href="#__codelineno-87-94"></a>
+<a id="__codelineno-87-95" name="__codelineno-87-95" href="#__codelineno-87-95"></a><span class="w">    </span><span class="cm">/* リストの拡張 */</span>
+<a id="__codelineno-87-96" name="__codelineno-87-96" href="#__codelineno-87-96"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">extend_capacity</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-97" name="__codelineno-87-97" href="#__codelineno-87-97"></a><span class="w">        </span><span class="c1">// 元の配列の extend_ratio 倍の長さを持つ新しい配列を作成し、元の配列をコピーする</span>
+<a id="__codelineno-87-98" name="__codelineno-87-98" href="#__codelineno-87-98"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">new_capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">capacity</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">extend_ratio</span><span class="p">;</span>
+<a id="__codelineno-87-99" name="__codelineno-87-99" href="#__codelineno-87-99"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">arr</span><span class="p">.</span><span class="n">resize</span><span class="p">(</span><span class="n">new_capacity</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-87-100" name="__codelineno-87-100" href="#__codelineno-87-100"></a><span class="w">        </span><span class="c1">// リストの容量を更新</span>
+<a id="__codelineno-87-101" name="__codelineno-87-101" href="#__codelineno-87-101"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">new_capacity</span><span class="p">;</span>
+<a id="__codelineno-87-102" name="__codelineno-87-102" href="#__codelineno-87-102"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-87-103" name="__codelineno-87-103" href="#__codelineno-87-103"></a>
+<a id="__codelineno-87-104" name="__codelineno-87-104" href="#__codelineno-87-104"></a><span class="w">    </span><span class="cm">/* リストを配列に変換する */</span>
+<a id="__codelineno-87-105" name="__codelineno-87-105" href="#__codelineno-87-105"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">to_array</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-106" name="__codelineno-87-106" href="#__codelineno-87-106"></a><span class="w">        </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-87-107" name="__codelineno-87-107" href="#__codelineno-87-107"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-87-108" name="__codelineno-87-108" href="#__codelineno-87-108"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-109" name="__codelineno-87-109" href="#__codelineno-87-109"></a><span class="w">            </span><span class="n">arr</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">get</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-87-110" name="__codelineno-87-110" href="#__codelineno-87-110"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-87-111" name="__codelineno-87-111" href="#__codelineno-87-111"></a><span class="w">        </span><span class="n">arr</span>
+<a id="__codelineno-87-112" name="__codelineno-87-112" href="#__codelineno-87-112"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-87-113" name="__codelineno-87-113" href="#__codelineno-87-113"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_list.c</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MyList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">my_list.c</span><pre><span></span><code><a id="__codelineno-88-1" name="__codelineno-88-1" href="#__codelineno-88-1"></a><span class="cm">/* リストクラス */</span>
+<a id="__codelineno-88-2" name="__codelineno-88-2" href="#__codelineno-88-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-3" name="__codelineno-88-3" href="#__codelineno-88-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">arr</span><span class="p">;</span><span class="w">        </span><span class="c1">// 配列（リスト要素を格納）</span>
+<a id="__codelineno-88-4" name="__codelineno-88-4" href="#__codelineno-88-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span><span class="w">    </span><span class="c1">// リスト容量</span>
+<a id="__codelineno-88-5" name="__codelineno-88-5" href="#__codelineno-88-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w">        </span><span class="c1">// リストのサイズ</span>
+<a id="__codelineno-88-6" name="__codelineno-88-6" href="#__codelineno-88-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span><span class="w"> </span><span class="c1">// リストが拡張されるたびの倍率</span>
+<a id="__codelineno-88-7" name="__codelineno-88-7" href="#__codelineno-88-7"></a><span class="p">}</span><span class="w"> </span><span class="n">MyList</span><span class="p">;</span>
+<a id="__codelineno-88-8" name="__codelineno-88-8" href="#__codelineno-88-8"></a>
+<a id="__codelineno-88-9" name="__codelineno-88-9" href="#__codelineno-88-9"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-88-10" name="__codelineno-88-10" href="#__codelineno-88-10"></a><span class="n">MyList</span><span class="w"> </span><span class="o">*</span><span class="nf">newMyList</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-11" name="__codelineno-88-11" href="#__codelineno-88-11"></a><span class="w">    </span><span class="n">MyList</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">MyList</span><span class="p">));</span>
+<a id="__codelineno-88-12" name="__codelineno-88-12" href="#__codelineno-88-12"></a><span class="w">    </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">10</span><span class="p">;</span>
+<a id="__codelineno-88-13" name="__codelineno-88-13" href="#__codelineno-88-13"></a><span class="w">    </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="p">);</span>
+<a id="__codelineno-88-14" name="__codelineno-88-14" href="#__codelineno-88-14"></a><span class="w">    </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-88-15" name="__codelineno-88-15" href="#__codelineno-88-15"></a><span class="w">    </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-88-16" name="__codelineno-88-16" href="#__codelineno-88-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
+<a id="__codelineno-88-17" name="__codelineno-88-17" href="#__codelineno-88-17"></a><span class="p">}</span>
+<a id="__codelineno-88-18" name="__codelineno-88-18" href="#__codelineno-88-18"></a>
+<a id="__codelineno-88-19" name="__codelineno-88-19" href="#__codelineno-88-19"></a><span class="cm">/* デストラクタ */</span>
+<a id="__codelineno-88-20" name="__codelineno-88-20" href="#__codelineno-88-20"></a><span class="kt">void</span><span class="w"> </span><span class="nf">delMyList</span><span class="p">(</span><span class="n">MyList</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-21" name="__codelineno-88-21" href="#__codelineno-88-21"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">arr</span><span class="p">);</span>
+<a id="__codelineno-88-22" name="__codelineno-88-22" href="#__codelineno-88-22"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">nums</span><span class="p">);</span>
+<a id="__codelineno-88-23" name="__codelineno-88-23" href="#__codelineno-88-23"></a><span class="p">}</span>
+<a id="__codelineno-88-24" name="__codelineno-88-24" href="#__codelineno-88-24"></a>
+<a id="__codelineno-88-25" name="__codelineno-88-25" href="#__codelineno-88-25"></a><span class="cm">/* リストの長さを取得 */</span>
+<a id="__codelineno-88-26" name="__codelineno-88-26" href="#__codelineno-88-26"></a><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="n">MyList</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-27" name="__codelineno-88-27" href="#__codelineno-88-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">;</span>
+<a id="__codelineno-88-28" name="__codelineno-88-28" href="#__codelineno-88-28"></a><span class="p">}</span>
+<a id="__codelineno-88-29" name="__codelineno-88-29" href="#__codelineno-88-29"></a>
+<a id="__codelineno-88-30" name="__codelineno-88-30" href="#__codelineno-88-30"></a><span class="cm">/* リスト容量を取得する */</span>
+<a id="__codelineno-88-31" name="__codelineno-88-31" href="#__codelineno-88-31"></a><span class="kt">int</span><span class="w"> </span><span class="nf">capacity</span><span class="p">(</span><span class="n">MyList</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-32" name="__codelineno-88-32" href="#__codelineno-88-32"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-88-33" name="__codelineno-88-33" href="#__codelineno-88-33"></a><span class="p">}</span>
+<a id="__codelineno-88-34" name="__codelineno-88-34" href="#__codelineno-88-34"></a>
+<a id="__codelineno-88-35" name="__codelineno-88-35" href="#__codelineno-88-35"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-88-36" name="__codelineno-88-36" href="#__codelineno-88-36"></a><span class="kt">int</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="n">MyList</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-37" name="__codelineno-88-37" href="#__codelineno-88-37"></a><span class="w">    </span><span class="n">assert</span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">);</span>
+<a id="__codelineno-88-38" name="__codelineno-88-38" href="#__codelineno-88-38"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-88-39" name="__codelineno-88-39" href="#__codelineno-88-39"></a><span class="p">}</span>
+<a id="__codelineno-88-40" name="__codelineno-88-40" href="#__codelineno-88-40"></a>
+<a id="__codelineno-88-41" name="__codelineno-88-41" href="#__codelineno-88-41"></a><span class="cm">/* 要素を更新 */</span>
+<a id="__codelineno-88-42" name="__codelineno-88-42" href="#__codelineno-88-42"></a><span class="kt">void</span><span class="w"> </span><span class="nf">set</span><span class="p">(</span><span class="n">MyList</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-43" name="__codelineno-88-43" href="#__codelineno-88-43"></a><span class="w">    </span><span class="n">assert</span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">);</span>
+<a id="__codelineno-88-44" name="__codelineno-88-44" href="#__codelineno-88-44"></a><span class="w">    </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-88-45" name="__codelineno-88-45" href="#__codelineno-88-45"></a><span class="p">}</span>
+<a id="__codelineno-88-46" name="__codelineno-88-46" href="#__codelineno-88-46"></a>
+<a id="__codelineno-88-47" name="__codelineno-88-47" href="#__codelineno-88-47"></a><span class="cm">/* 末尾に要素を追加 */</span>
+<a id="__codelineno-88-48" name="__codelineno-88-48" href="#__codelineno-88-48"></a><span class="kt">void</span><span class="w"> </span><span class="nf">add</span><span class="p">(</span><span class="n">MyList</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-49" name="__codelineno-88-49" href="#__codelineno-88-49"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">(</span><span class="n">nums</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-50" name="__codelineno-88-50" href="#__codelineno-88-50"></a><span class="w">        </span><span class="n">extendCapacity</span><span class="p">(</span><span class="n">nums</span><span class="p">);</span><span class="w"> </span><span class="c1">// 容量を拡張</span>
+<a id="__codelineno-88-51" name="__codelineno-88-51" href="#__codelineno-88-51"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-88-52" name="__codelineno-88-52" href="#__codelineno-88-52"></a><span class="w">    </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">arr</span><span class="p">[</span><span class="n">size</span><span class="p">(</span><span class="n">nums</span><span class="p">)]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-88-53" name="__codelineno-88-53" href="#__codelineno-88-53"></a><span class="w">    </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-88-54" name="__codelineno-88-54" href="#__codelineno-88-54"></a><span class="p">}</span>
+<a id="__codelineno-88-55" name="__codelineno-88-55" href="#__codelineno-88-55"></a>
+<a id="__codelineno-88-56" name="__codelineno-88-56" href="#__codelineno-88-56"></a><span class="cm">/* 中間に要素を挿入 */</span>
+<a id="__codelineno-88-57" name="__codelineno-88-57" href="#__codelineno-88-57"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">MyList</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-58" name="__codelineno-88-58" href="#__codelineno-88-58"></a><span class="w">    </span><span class="n">assert</span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">nums</span><span class="p">));</span>
+<a id="__codelineno-88-59" name="__codelineno-88-59" href="#__codelineno-88-59"></a><span class="w">    </span><span class="c1">// 要素数が容量を超えると、拡張機構が発動する</span>
+<a id="__codelineno-88-60" name="__codelineno-88-60" href="#__codelineno-88-60"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">(</span><span class="n">nums</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-61" name="__codelineno-88-61" href="#__codelineno-88-61"></a><span class="w">        </span><span class="n">extendCapacity</span><span class="p">(</span><span class="n">nums</span><span class="p">);</span><span class="w"> </span><span class="c1">// 容量を拡張</span>
+<a id="__codelineno-88-62" name="__codelineno-88-62" href="#__codelineno-88-62"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-88-63" name="__codelineno-88-63" href="#__codelineno-88-63"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">nums</span><span class="p">);</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="o">--</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-64" name="__codelineno-88-64" href="#__codelineno-88-64"></a><span class="w">        </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-88-65" name="__codelineno-88-65" href="#__codelineno-88-65"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-88-66" name="__codelineno-88-66" href="#__codelineno-88-66"></a><span class="w">    </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-88-67" name="__codelineno-88-67" href="#__codelineno-88-67"></a><span class="w">    </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-88-68" name="__codelineno-88-68" href="#__codelineno-88-68"></a><span class="p">}</span>
+<a id="__codelineno-88-69" name="__codelineno-88-69" href="#__codelineno-88-69"></a>
+<a id="__codelineno-88-70" name="__codelineno-88-70" href="#__codelineno-88-70"></a><span class="cm">/* 要素を削除 */</span>
+<a id="__codelineno-88-71" name="__codelineno-88-71" href="#__codelineno-88-71"></a><span class="c1">// 注意: stdio.h が remove 識別子を使用している</span>
+<a id="__codelineno-88-72" name="__codelineno-88-72" href="#__codelineno-88-72"></a><span class="kt">int</span><span class="w"> </span><span class="nf">removeItem</span><span class="p">(</span><span class="n">MyList</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-73" name="__codelineno-88-73" href="#__codelineno-88-73"></a><span class="w">    </span><span class="n">assert</span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">nums</span><span class="p">));</span>
+<a id="__codelineno-88-74" name="__codelineno-88-74" href="#__codelineno-88-74"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-88-75" name="__codelineno-88-75" href="#__codelineno-88-75"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-76" name="__codelineno-88-76" href="#__codelineno-88-76"></a><span class="w">        </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-88-77" name="__codelineno-88-77" href="#__codelineno-88-77"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-88-78" name="__codelineno-88-78" href="#__codelineno-88-78"></a><span class="w">    </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-88-79" name="__codelineno-88-79" href="#__codelineno-88-79"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-88-80" name="__codelineno-88-80" href="#__codelineno-88-80"></a><span class="p">}</span>
+<a id="__codelineno-88-81" name="__codelineno-88-81" href="#__codelineno-88-81"></a>
+<a id="__codelineno-88-82" name="__codelineno-88-82" href="#__codelineno-88-82"></a><span class="cm">/* リストの拡張 */</span>
+<a id="__codelineno-88-83" name="__codelineno-88-83" href="#__codelineno-88-83"></a><span class="kt">void</span><span class="w"> </span><span class="nf">extendCapacity</span><span class="p">(</span><span class="n">MyList</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-84" name="__codelineno-88-84" href="#__codelineno-88-84"></a><span class="w">    </span><span class="c1">// 先に領域を確保する</span>
+<a id="__codelineno-88-85" name="__codelineno-88-85" href="#__codelineno-88-85"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">newCapacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">capacity</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">extendRatio</span><span class="p">;</span>
+<a id="__codelineno-88-86" name="__codelineno-88-86" href="#__codelineno-88-86"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">extend</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">newCapacity</span><span class="p">);</span>
+<a id="__codelineno-88-87" name="__codelineno-88-87" href="#__codelineno-88-87"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">arr</span><span class="p">;</span>
+<a id="__codelineno-88-88" name="__codelineno-88-88" href="#__codelineno-88-88"></a>
+<a id="__codelineno-88-89" name="__codelineno-88-89" href="#__codelineno-88-89"></a><span class="w">    </span><span class="c1">// 古いデータを新しいデータにコピー</span>
+<a id="__codelineno-88-90" name="__codelineno-88-90" href="#__codelineno-88-90"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">nums</span><span class="p">);</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
+<a id="__codelineno-88-91" name="__codelineno-88-91" href="#__codelineno-88-91"></a><span class="w">        </span><span class="n">extend</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-88-92" name="__codelineno-88-92" href="#__codelineno-88-92"></a>
+<a id="__codelineno-88-93" name="__codelineno-88-93" href="#__codelineno-88-93"></a><span class="w">    </span><span class="c1">// 古いデータを解放する</span>
+<a id="__codelineno-88-94" name="__codelineno-88-94" href="#__codelineno-88-94"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">temp</span><span class="p">);</span>
+<a id="__codelineno-88-95" name="__codelineno-88-95" href="#__codelineno-88-95"></a>
+<a id="__codelineno-88-96" name="__codelineno-88-96" href="#__codelineno-88-96"></a><span class="w">    </span><span class="c1">// 新しいデータに更新</span>
+<a id="__codelineno-88-97" name="__codelineno-88-97" href="#__codelineno-88-97"></a><span class="w">    </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">extend</span><span class="p">;</span>
+<a id="__codelineno-88-98" name="__codelineno-88-98" href="#__codelineno-88-98"></a><span class="w">    </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newCapacity</span><span class="p">;</span>
+<a id="__codelineno-88-99" name="__codelineno-88-99" href="#__codelineno-88-99"></a><span class="p">}</span>
+<a id="__codelineno-88-100" name="__codelineno-88-100" href="#__codelineno-88-100"></a>
+<a id="__codelineno-88-101" name="__codelineno-88-101" href="#__codelineno-88-101"></a><span class="cm">/* 出力用にリストを Array に変換 */</span>
+<a id="__codelineno-88-102" name="__codelineno-88-102" href="#__codelineno-88-102"></a><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="nf">toArray</span><span class="p">(</span><span class="n">MyList</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-103" name="__codelineno-88-103" href="#__codelineno-88-103"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">arr</span><span class="p">;</span>
+<a id="__codelineno-88-104" name="__codelineno-88-104" href="#__codelineno-88-104"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_list.kt</span><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">MyList</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">my_list.kt</span><pre><span></span><code><a id="__codelineno-89-1" name="__codelineno-89-1" href="#__codelineno-89-1"></a><span class="cm">/* リストクラス */</span>
+<a id="__codelineno-89-2" name="__codelineno-89-2" href="#__codelineno-89-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">MyList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-89-3" name="__codelineno-89-3" href="#__codelineno-89-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">arr</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">intArrayOf</span><span class="p">()</span><span class="w"> </span><span class="c1">// 配列（リスト要素を格納）</span>
+<a id="__codelineno-89-4" name="__codelineno-89-4" href="#__codelineno-89-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">capacity</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">10</span><span class="w"> </span><span class="c1">// リスト容量</span>
+<a id="__codelineno-89-5" name="__codelineno-89-5" href="#__codelineno-89-5"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">size</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="c1">// リストの長さ（現在の要素数）</span>
+<a id="__codelineno-89-6" name="__codelineno-89-6" href="#__codelineno-89-6"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">extendRatio</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="c1">// リスト拡張時の増加倍率</span>
+<a id="__codelineno-89-7" name="__codelineno-89-7" href="#__codelineno-89-7"></a>
+<a id="__codelineno-89-8" name="__codelineno-89-8" href="#__codelineno-89-8"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-89-9" name="__codelineno-89-9" href="#__codelineno-89-9"></a><span class="w">    </span><span class="k">init</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-89-10" name="__codelineno-89-10" href="#__codelineno-89-10"></a><span class="w">        </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">capacity</span><span class="p">)</span>
+<a id="__codelineno-89-11" name="__codelineno-89-11" href="#__codelineno-89-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-89-12" name="__codelineno-89-12" href="#__codelineno-89-12"></a>
+<a id="__codelineno-89-13" name="__codelineno-89-13" href="#__codelineno-89-13"></a><span class="w">    </span><span class="cm">/* リストの長さを取得（現在の要素数） */</span>
+<a id="__codelineno-89-14" name="__codelineno-89-14" href="#__codelineno-89-14"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">size</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-89-15" name="__codelineno-89-15" href="#__codelineno-89-15"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span>
+<a id="__codelineno-89-16" name="__codelineno-89-16" href="#__codelineno-89-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-89-17" name="__codelineno-89-17" href="#__codelineno-89-17"></a>
+<a id="__codelineno-89-18" name="__codelineno-89-18" href="#__codelineno-89-18"></a><span class="w">    </span><span class="cm">/* リスト容量を取得する */</span>
+<a id="__codelineno-89-19" name="__codelineno-89-19" href="#__codelineno-89-19"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">capacity</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-89-20" name="__codelineno-89-20" href="#__codelineno-89-20"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">capacity</span>
+<a id="__codelineno-89-21" name="__codelineno-89-21" href="#__codelineno-89-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-89-22" name="__codelineno-89-22" href="#__codelineno-89-22"></a>
+<a id="__codelineno-89-23" name="__codelineno-89-23" href="#__codelineno-89-23"></a><span class="w">    </span><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-89-24" name="__codelineno-89-24" href="#__codelineno-89-24"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="n">index</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-89-25" name="__codelineno-89-25" href="#__codelineno-89-25"></a><span class="w">        </span><span class="c1">// インデックスが範囲外なら例外を送出する。以下同様</span>
+<a id="__codelineno-89-26" name="__codelineno-89-26" href="#__codelineno-89-26"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">)</span>
+<a id="__codelineno-89-27" name="__codelineno-89-27" href="#__codelineno-89-27"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外&quot;</span><span class="p">)</span>
+<a id="__codelineno-89-28" name="__codelineno-89-28" href="#__codelineno-89-28"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">arr</span><span class="o">[</span><span class="n">index</span><span class="o">]</span>
+<a id="__codelineno-89-29" name="__codelineno-89-29" href="#__codelineno-89-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-89-30" name="__codelineno-89-30" href="#__codelineno-89-30"></a>
+<a id="__codelineno-89-31" name="__codelineno-89-31" href="#__codelineno-89-31"></a><span class="w">    </span><span class="cm">/* 要素を更新 */</span>
+<a id="__codelineno-89-32" name="__codelineno-89-32" href="#__codelineno-89-32"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">set</span><span class="p">(</span><span class="n">index</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-89-33" name="__codelineno-89-33" href="#__codelineno-89-33"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">)</span>
+<a id="__codelineno-89-34" name="__codelineno-89-34" href="#__codelineno-89-34"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外&quot;</span><span class="p">)</span>
+<a id="__codelineno-89-35" name="__codelineno-89-35" href="#__codelineno-89-35"></a><span class="w">        </span><span class="n">arr</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-89-36" name="__codelineno-89-36" href="#__codelineno-89-36"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-89-37" name="__codelineno-89-37" href="#__codelineno-89-37"></a>
+<a id="__codelineno-89-38" name="__codelineno-89-38" href="#__codelineno-89-38"></a><span class="w">    </span><span class="cm">/* 末尾に要素を追加 */</span>
+<a id="__codelineno-89-39" name="__codelineno-89-39" href="#__codelineno-89-39"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">add</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-89-40" name="__codelineno-89-40" href="#__codelineno-89-40"></a><span class="w">        </span><span class="c1">// 要素数が容量を超えると、拡張機構が発動する</span>
+<a id="__codelineno-89-41" name="__codelineno-89-41" href="#__codelineno-89-41"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span>
+<a id="__codelineno-89-42" name="__codelineno-89-42" href="#__codelineno-89-42"></a><span class="w">            </span><span class="n">extendCapacity</span><span class="p">()</span>
+<a id="__codelineno-89-43" name="__codelineno-89-43" href="#__codelineno-89-43"></a><span class="w">        </span><span class="n">arr</span><span class="o">[</span><span class="n">size</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-89-44" name="__codelineno-89-44" href="#__codelineno-89-44"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-89-45" name="__codelineno-89-45" href="#__codelineno-89-45"></a><span class="w">        </span><span class="n">size</span><span class="o">++</span>
+<a id="__codelineno-89-46" name="__codelineno-89-46" href="#__codelineno-89-46"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-89-47" name="__codelineno-89-47" href="#__codelineno-89-47"></a>
+<a id="__codelineno-89-48" name="__codelineno-89-48" href="#__codelineno-89-48"></a><span class="w">    </span><span class="cm">/* 中間に要素を挿入 */</span>
+<a id="__codelineno-89-49" name="__codelineno-89-49" href="#__codelineno-89-49"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">index</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-89-50" name="__codelineno-89-50" href="#__codelineno-89-50"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">)</span>
+<a id="__codelineno-89-51" name="__codelineno-89-51" href="#__codelineno-89-51"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外&quot;</span><span class="p">)</span>
+<a id="__codelineno-89-52" name="__codelineno-89-52" href="#__codelineno-89-52"></a><span class="w">        </span><span class="c1">// 要素数が容量を超えると、拡張機構が発動する</span>
+<a id="__codelineno-89-53" name="__codelineno-89-53" href="#__codelineno-89-53"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span>
+<a id="__codelineno-89-54" name="__codelineno-89-54" href="#__codelineno-89-54"></a><span class="w">            </span><span class="n">extendCapacity</span><span class="p">()</span>
+<a id="__codelineno-89-55" name="__codelineno-89-55" href="#__codelineno-89-55"></a><span class="w">        </span><span class="c1">// index 以降の要素をすべて 1 つ後ろへずらす</span>
+<a id="__codelineno-89-56" name="__codelineno-89-56" href="#__codelineno-89-56"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="n">downTo</span><span class="w"> </span><span class="n">index</span><span class="p">)</span>
+<a id="__codelineno-89-57" name="__codelineno-89-57" href="#__codelineno-89-57"></a><span class="w">            </span><span class="n">arr</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-89-58" name="__codelineno-89-58" href="#__codelineno-89-58"></a><span class="w">        </span><span class="n">arr</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-89-59" name="__codelineno-89-59" href="#__codelineno-89-59"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-89-60" name="__codelineno-89-60" href="#__codelineno-89-60"></a><span class="w">        </span><span class="n">size</span><span class="o">++</span>
+<a id="__codelineno-89-61" name="__codelineno-89-61" href="#__codelineno-89-61"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-89-62" name="__codelineno-89-62" href="#__codelineno-89-62"></a>
+<a id="__codelineno-89-63" name="__codelineno-89-63" href="#__codelineno-89-63"></a><span class="w">    </span><span class="cm">/* 要素を削除 */</span>
+<a id="__codelineno-89-64" name="__codelineno-89-64" href="#__codelineno-89-64"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">index</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-89-65" name="__codelineno-89-65" href="#__codelineno-89-65"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">)</span>
+<a id="__codelineno-89-66" name="__codelineno-89-66" href="#__codelineno-89-66"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外&quot;</span><span class="p">)</span>
+<a id="__codelineno-89-67" name="__codelineno-89-67" href="#__codelineno-89-67"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="o">[</span><span class="n">index</span><span class="o">]</span>
+<a id="__codelineno-89-68" name="__codelineno-89-68" href="#__codelineno-89-68"></a><span class="w">        </span><span class="c1">// インデックス index より後の要素をすべて 1 つ前に移動する</span>
+<a id="__codelineno-89-69" name="__codelineno-89-69" href="#__codelineno-89-69"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">index</span><span class="p">..</span><span class="o">&lt;</span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-89-70" name="__codelineno-89-70" href="#__codelineno-89-70"></a><span class="w">            </span><span class="n">arr</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="o">]</span>
+<a id="__codelineno-89-71" name="__codelineno-89-71" href="#__codelineno-89-71"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-89-72" name="__codelineno-89-72" href="#__codelineno-89-72"></a><span class="w">        </span><span class="n">size</span><span class="o">--</span>
+<a id="__codelineno-89-73" name="__codelineno-89-73" href="#__codelineno-89-73"></a><span class="w">        </span><span class="c1">// 削除された要素を返す</span>
+<a id="__codelineno-89-74" name="__codelineno-89-74" href="#__codelineno-89-74"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-89-75" name="__codelineno-89-75" href="#__codelineno-89-75"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-89-76" name="__codelineno-89-76" href="#__codelineno-89-76"></a>
+<a id="__codelineno-89-77" name="__codelineno-89-77" href="#__codelineno-89-77"></a><span class="w">    </span><span class="cm">/* リストの拡張 */</span>
+<a id="__codelineno-89-78" name="__codelineno-89-78" href="#__codelineno-89-78"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">extendCapacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-89-79" name="__codelineno-89-79" href="#__codelineno-89-79"></a><span class="w">        </span><span class="c1">// 元の配列の extendRatio 倍の長さを持つ新しい配列を作成し、元の配列をコピーする</span>
+<a id="__codelineno-89-80" name="__codelineno-89-80" href="#__codelineno-89-80"></a><span class="w">        </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">.</span><span class="na">copyOf</span><span class="p">(</span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">)</span>
+<a id="__codelineno-89-81" name="__codelineno-89-81" href="#__codelineno-89-81"></a><span class="w">        </span><span class="c1">// リストの容量を更新</span>
+<a id="__codelineno-89-82" name="__codelineno-89-82" href="#__codelineno-89-82"></a><span class="w">        </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-89-83" name="__codelineno-89-83" href="#__codelineno-89-83"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-89-84" name="__codelineno-89-84" href="#__codelineno-89-84"></a>
+<a id="__codelineno-89-85" name="__codelineno-89-85" href="#__codelineno-89-85"></a><span class="w">    </span><span class="cm">/* リストを配列に変換する */</span>
+<a id="__codelineno-89-86" name="__codelineno-89-86" href="#__codelineno-89-86"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">toArray</span><span class="p">():</span><span class="w"> </span><span class="n">IntArray</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-89-87" name="__codelineno-89-87" href="#__codelineno-89-87"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span>
+<a id="__codelineno-89-88" name="__codelineno-89-88" href="#__codelineno-89-88"></a><span class="w">        </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-89-89" name="__codelineno-89-89" href="#__codelineno-89-89"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">size</span><span class="p">)</span>
+<a id="__codelineno-89-90" name="__codelineno-89-90" href="#__codelineno-89-90"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-89-91" name="__codelineno-89-91" href="#__codelineno-89-91"></a><span class="w">            </span><span class="n">arr</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">get</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-89-92" name="__codelineno-89-92" href="#__codelineno-89-92"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-89-93" name="__codelineno-89-93" href="#__codelineno-89-93"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">arr</span>
+<a id="__codelineno-89-94" name="__codelineno-89-94" href="#__codelineno-89-94"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-89-95" name="__codelineno-89-95" href="#__codelineno-89-95"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_list.rb</span><pre><span></span><code><a id="__codelineno-84-1" name="__codelineno-84-1" href="#__codelineno-84-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MyList</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">my_list.rb</span><pre><span></span><code><a id="__codelineno-90-1" name="__codelineno-90-1" href="#__codelineno-90-1"></a><span class="c1">### リストクラス ###</span>
+<a id="__codelineno-90-2" name="__codelineno-90-2" href="#__codelineno-90-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">MyList</span>
+<a id="__codelineno-90-3" name="__codelineno-90-3" href="#__codelineno-90-3"></a><span class="w">  </span><span class="kp">attr_reader</span><span class="w"> </span><span class="ss">:size</span><span class="w">       </span><span class="c1"># リストの長さを取得（現在の要素数）</span>
+<a id="__codelineno-90-4" name="__codelineno-90-4" href="#__codelineno-90-4"></a><span class="w">  </span><span class="kp">attr_reader</span><span class="w"> </span><span class="ss">:capacity</span><span class="w">   </span><span class="c1"># リスト容量を取得する</span>
+<a id="__codelineno-90-5" name="__codelineno-90-5" href="#__codelineno-90-5"></a>
+<a id="__codelineno-90-6" name="__codelineno-90-6" href="#__codelineno-90-6"></a><span class="w">  </span><span class="c1">### コンストラクタ ###</span>
+<a id="__codelineno-90-7" name="__codelineno-90-7" href="#__codelineno-90-7"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span>
+<a id="__codelineno-90-8" name="__codelineno-90-8" href="#__codelineno-90-8"></a><span class="w">    </span><span class="vi">@capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">10</span>
+<a id="__codelineno-90-9" name="__codelineno-90-9" href="#__codelineno-90-9"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-90-10" name="__codelineno-90-10" href="#__codelineno-90-10"></a><span class="w">    </span><span class="vi">@extend_ratio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-90-11" name="__codelineno-90-11" href="#__codelineno-90-11"></a><span class="w">    </span><span class="vi">@arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">capacity</span><span class="p">)</span>
+<a id="__codelineno-90-12" name="__codelineno-90-12" href="#__codelineno-90-12"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-90-13" name="__codelineno-90-13" href="#__codelineno-90-13"></a>
+<a id="__codelineno-90-14" name="__codelineno-90-14" href="#__codelineno-90-14"></a><span class="w">  </span><span class="c1">### 要素にアクセス ###</span>
+<a id="__codelineno-90-15" name="__codelineno-90-15" href="#__codelineno-90-15"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
+<a id="__codelineno-90-16" name="__codelineno-90-16" href="#__codelineno-90-16"></a><span class="w">    </span><span class="c1"># インデックスが範囲外なら例外を送出する。以下同様</span>
+<a id="__codelineno-90-17" name="__codelineno-90-17" href="#__codelineno-90-17"></a><span class="w">    </span><span class="k">raise</span><span class="w"> </span><span class="no">IndexError</span><span class="p">,</span><span class="w"> </span><span class="s2">&quot;インデックスが範囲外です&quot;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span>
+<a id="__codelineno-90-18" name="__codelineno-90-18" href="#__codelineno-90-18"></a><span class="w">    </span><span class="vi">@arr</span><span class="o">[</span><span class="n">index</span><span class="o">]</span>
+<a id="__codelineno-90-19" name="__codelineno-90-19" href="#__codelineno-90-19"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-90-20" name="__codelineno-90-20" href="#__codelineno-90-20"></a>
+<a id="__codelineno-90-21" name="__codelineno-90-21" href="#__codelineno-90-21"></a><span class="w">  </span><span class="c1">### 要素にアクセス ###</span>
+<a id="__codelineno-90-22" name="__codelineno-90-22" href="#__codelineno-90-22"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">set</span><span class="p">(</span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-90-23" name="__codelineno-90-23" href="#__codelineno-90-23"></a><span class="w">    </span><span class="k">raise</span><span class="w"> </span><span class="no">IndexError</span><span class="p">,</span><span class="w"> </span><span class="s2">&quot;インデックスが範囲外です&quot;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span>
+<a id="__codelineno-90-24" name="__codelineno-90-24" href="#__codelineno-90-24"></a><span class="w">    </span><span class="vi">@arr</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-90-25" name="__codelineno-90-25" href="#__codelineno-90-25"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-90-26" name="__codelineno-90-26" href="#__codelineno-90-26"></a>
+<a id="__codelineno-90-27" name="__codelineno-90-27" href="#__codelineno-90-27"></a><span class="w">  </span><span class="c1">### 末尾に要素を追加 ###</span>
+<a id="__codelineno-90-28" name="__codelineno-90-28" href="#__codelineno-90-28"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">add</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-90-29" name="__codelineno-90-29" href="#__codelineno-90-29"></a><span class="w">    </span><span class="c1"># 要素数が容量を超えると、拡張機構が発動する</span>
+<a id="__codelineno-90-30" name="__codelineno-90-30" href="#__codelineno-90-30"></a><span class="w">    </span><span class="n">extend_capacity</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span>
+<a id="__codelineno-90-31" name="__codelineno-90-31" href="#__codelineno-90-31"></a><span class="w">    </span><span class="vi">@arr</span><span class="o">[</span><span class="n">size</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-90-32" name="__codelineno-90-32" href="#__codelineno-90-32"></a>
+<a id="__codelineno-90-33" name="__codelineno-90-33" href="#__codelineno-90-33"></a><span class="w">    </span><span class="c1"># 要素数を更新</span>
+<a id="__codelineno-90-34" name="__codelineno-90-34" href="#__codelineno-90-34"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-90-35" name="__codelineno-90-35" href="#__codelineno-90-35"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-90-36" name="__codelineno-90-36" href="#__codelineno-90-36"></a>
+<a id="__codelineno-90-37" name="__codelineno-90-37" href="#__codelineno-90-37"></a><span class="w">  </span><span class="c1">### 途中に要素を挿入 ###</span>
+<a id="__codelineno-90-38" name="__codelineno-90-38" href="#__codelineno-90-38"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-90-39" name="__codelineno-90-39" href="#__codelineno-90-39"></a><span class="w">    </span><span class="k">raise</span><span class="w"> </span><span class="no">IndexError</span><span class="p">,</span><span class="w"> </span><span class="s2">&quot;インデックスが範囲外です&quot;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span>
+<a id="__codelineno-90-40" name="__codelineno-90-40" href="#__codelineno-90-40"></a>
+<a id="__codelineno-90-41" name="__codelineno-90-41" href="#__codelineno-90-41"></a><span class="w">    </span><span class="c1"># 要素数が容量を超えると、拡張機構が発動する</span>
+<a id="__codelineno-90-42" name="__codelineno-90-42" href="#__codelineno-90-42"></a><span class="w">    </span><span class="n">extend_capacity</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span>
+<a id="__codelineno-90-43" name="__codelineno-90-43" href="#__codelineno-90-43"></a>
+<a id="__codelineno-90-44" name="__codelineno-90-44" href="#__codelineno-90-44"></a><span class="w">    </span><span class="c1"># index 以降の要素をすべて 1 つ後ろへずらす</span>
+<a id="__codelineno-90-45" name="__codelineno-90-45" href="#__codelineno-90-45"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
+<a id="__codelineno-90-46" name="__codelineno-90-46" href="#__codelineno-90-46"></a><span class="w">      </span><span class="vi">@arr</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@arr</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-90-47" name="__codelineno-90-47" href="#__codelineno-90-47"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-90-48" name="__codelineno-90-48" href="#__codelineno-90-48"></a><span class="w">    </span><span class="vi">@arr</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-90-49" name="__codelineno-90-49" href="#__codelineno-90-49"></a>
+<a id="__codelineno-90-50" name="__codelineno-90-50" href="#__codelineno-90-50"></a><span class="w">    </span><span class="c1"># 要素数を更新</span>
+<a id="__codelineno-90-51" name="__codelineno-90-51" href="#__codelineno-90-51"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-90-52" name="__codelineno-90-52" href="#__codelineno-90-52"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-90-53" name="__codelineno-90-53" href="#__codelineno-90-53"></a>
+<a id="__codelineno-90-54" name="__codelineno-90-54" href="#__codelineno-90-54"></a><span class="w">  </span><span class="c1">### 要素の削除 ###</span>
+<a id="__codelineno-90-55" name="__codelineno-90-55" href="#__codelineno-90-55"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
+<a id="__codelineno-90-56" name="__codelineno-90-56" href="#__codelineno-90-56"></a><span class="w">    </span><span class="k">raise</span><span class="w"> </span><span class="no">IndexError</span><span class="p">,</span><span class="w"> </span><span class="s2">&quot;インデックスが範囲外です&quot;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span>
+<a id="__codelineno-90-57" name="__codelineno-90-57" href="#__codelineno-90-57"></a><span class="w">    </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@arr</span><span class="o">[</span><span class="n">index</span><span class="o">]</span>
+<a id="__codelineno-90-58" name="__codelineno-90-58" href="#__codelineno-90-58"></a>
+<a id="__codelineno-90-59" name="__codelineno-90-59" href="#__codelineno-90-59"></a><span class="w">    </span><span class="c1"># インデックス index より後の要素をすべて 1 つ前に移動する</span>
+<a id="__codelineno-90-60" name="__codelineno-90-60" href="#__codelineno-90-60"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">index</span><span class="o">...</span><span class="n">size</span>
+<a id="__codelineno-90-61" name="__codelineno-90-61" href="#__codelineno-90-61"></a><span class="w">      </span><span class="vi">@arr</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@arr</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
+<a id="__codelineno-90-62" name="__codelineno-90-62" href="#__codelineno-90-62"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-90-63" name="__codelineno-90-63" href="#__codelineno-90-63"></a>
+<a id="__codelineno-90-64" name="__codelineno-90-64" href="#__codelineno-90-64"></a><span class="w">    </span><span class="c1"># 要素数を更新</span>
+<a id="__codelineno-90-65" name="__codelineno-90-65" href="#__codelineno-90-65"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-90-66" name="__codelineno-90-66" href="#__codelineno-90-66"></a>
+<a id="__codelineno-90-67" name="__codelineno-90-67" href="#__codelineno-90-67"></a><span class="w">    </span><span class="c1"># 削除された要素を返す</span>
+<a id="__codelineno-90-68" name="__codelineno-90-68" href="#__codelineno-90-68"></a><span class="w">    </span><span class="n">num</span>
+<a id="__codelineno-90-69" name="__codelineno-90-69" href="#__codelineno-90-69"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-90-70" name="__codelineno-90-70" href="#__codelineno-90-70"></a>
+<a id="__codelineno-90-71" name="__codelineno-90-71" href="#__codelineno-90-71"></a><span class="w">  </span><span class="c1">### リストの容量拡張 ###</span>
+<a id="__codelineno-90-72" name="__codelineno-90-72" href="#__codelineno-90-72"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">extend_capacity</span>
+<a id="__codelineno-90-73" name="__codelineno-90-73" href="#__codelineno-90-73"></a><span class="w">    </span><span class="c1"># 元の配列の extend_ratio 倍の長さを持つ新しい配列を作成し、元の配列をコピーする</span>
+<a id="__codelineno-90-74" name="__codelineno-90-74" href="#__codelineno-90-74"></a><span class="w">    </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@arr</span><span class="o">.</span><span class="n">dup</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">capacity</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="vi">@extend_ratio</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span>
+<a id="__codelineno-90-75" name="__codelineno-90-75" href="#__codelineno-90-75"></a><span class="w">    </span><span class="c1"># リストの容量を更新</span>
+<a id="__codelineno-90-76" name="__codelineno-90-76" href="#__codelineno-90-76"></a><span class="w">    </span><span class="vi">@capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-90-77" name="__codelineno-90-77" href="#__codelineno-90-77"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-90-78" name="__codelineno-90-78" href="#__codelineno-90-78"></a>
+<a id="__codelineno-90-79" name="__codelineno-90-79" href="#__codelineno-90-79"></a><span class="w">  </span><span class="c1">### リストを配列に変換 ###</span>
+<a id="__codelineno-90-80" name="__codelineno-90-80" href="#__codelineno-90-80"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">to_array</span>
+<a id="__codelineno-90-81" name="__codelineno-90-81" href="#__codelineno-90-81"></a><span class="w">    </span><span class="n">sz</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span>
+<a id="__codelineno-90-82" name="__codelineno-90-82" href="#__codelineno-90-82"></a><span class="w">    </span><span class="c1"># 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-90-83" name="__codelineno-90-83" href="#__codelineno-90-83"></a><span class="w">    </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">sz</span><span class="p">)</span>
+<a id="__codelineno-90-84" name="__codelineno-90-84" href="#__codelineno-90-84"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">sz</span>
+<a id="__codelineno-90-85" name="__codelineno-90-85" href="#__codelineno-90-85"></a><span class="w">      </span><span class="n">arr</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">get</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-90-86" name="__codelineno-90-86" href="#__codelineno-90-86"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-90-87" name="__codelineno-90-87" href="#__codelineno-90-87"></a><span class="w">    </span><span class="n">arr</span>
+<a id="__codelineno-90-88" name="__codelineno-90-88" href="#__codelineno-90-88"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-90-89" name="__codelineno-90-89" href="#__codelineno-90-89"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20MyList%3A%0A%0A%20%20%20%20def%20__init__%28self%29%3A%0A%20%20%20%20%20%20%20%20self._capacity%3A%20int%20%3D%2010%0A%20%20%20%20%20%20%20%20self._arr%3A%20list%5Bint%5D%20%3D%20%5B0%5D%20%2A%20self._capacity%0A%20%20%20%20%20%20%20%20self._size%3A%20int%20%3D%200%0A%20%20%20%20%20%20%20%20self._extend_ratio%3A%20int%20%3D%202%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%20self._size%0A%0A%20%20%20%20def%20capacity%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%20self._capacity%0A%0A%20%20%20%20def%20get%28self%2C%20index%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20if%20index%20%3C%200%20or%20index%20%3E%3D%20self._size%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%27%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%8C%E7%AF%84%E5%9B%B2%E5%A4%96%E3%81%A7%E3%81%99%27%29%0A%20%20%20%20%20%20%20%20return%20self._arr%5Bindex%5D%0A%0A%20%20%20%20def%20set%28self%2C%20num%3A%20int%2C%20index%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20if%20index%20%3C%200%20or%20index%20%3E%3D%20self._size%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%27%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%8C%E7%AF%84%E5%9B%B2%E5%A4%96%E3%81%A7%E3%81%99%27%29%0A%20%20%20%20%20%20%20%20self._arr%5Bindex%5D%20%3D%20num%0A%0A%20%20%20%20def%20add%28self%2C%20num%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20if%20self.size%28%29%20%3D%3D%20self.capacity%28%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.extend_capacity%28%29%0A%20%20%20%20%20%20%20%20self._arr%5Bself._size%5D%20%3D%20num%0A%20%20%20%20%20%20%20%20self._size%20%2B%3D%201%0A%0A%20%20%20%20def%20insert%28self%2C%20num%3A%20int%2C%20index%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20if%20index%20%3C%200%20or%20index%20%3E%3D%20self._size%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%27%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%8C%E7%AF%84%E5%9B%B2%E5%A4%96%E3%81%A7%E3%81%99%27%29%0A%20%20%20%20%20%20%20%20%20%20%20%20self.extend_capacity%28%29%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28self._size%20-%201%2C%20index%20-%201%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self._arr%5Bj%20%2B%201%5D%20%3D%20self._arr%5Bj%5D%0A%20%20%20%20%20%20%20%20self._arr%5Bindex%5D%20%3D%20num%0A%20%20%20%20%20%20%20%20self._size%20%2B%3D%201%0A%0A%20%20%20%20def%20remove%28self%2C%20index%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20if%20index%20%3C%200%20or%20index%20%3E%3D%20self._size%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%27%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%8C%E7%AF%84%E5%9B%B2%E5%A4%96%E3%81%A7%E3%81%99%27%29%0A%20%20%20%20%20%20%20%20num%20%3D%20self._arr%5Bindex%5D%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28index%2C%20self._size%20-%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self._arr%5Bj%5D%20%3D%20self._arr%5Bj%20%2B%201%5D%0A%20%20%20%20%20%20%20%20self._size%20-%3D%201%0A%20%20%20%20%20%20%20%20return%20num%0A%0A%20%20%20%20def%20extend_capacity%28self%29%3A%0A%20%20%20%20%20%20%20%20self._arr%20%3D%20self._arr%20%2B%20%5B0%5D%20%2A%20self.capacity%28%29%20%2A%20%28self._extend_ratio%20-%201%29%0A%20%20%20%20%20%20%20%20self._capacity%20%3D%20len%28self._arr%29%0Aif%20__name__%20%3D%3D%20%27__main__%27%3A%0A%20%20%20%20nums%20%3D%20MyList%28%29%0A%20%20%20%20nums.add%281%29%0A%20%20%20%20nums.add%283%29%0A%20%20%20%20nums.add%282%29%0A%20%20%20%20nums.add%285%29%0A%20%20%20%20nums.add%284%29%0A%20%20%20%20nums.insert%286%2C%20index%3D3%29%0A%20%20%20%20nums.remove%283%29%0A%20%20%20%20num%20%3D%20nums.get%281%29%0A%20%20%20%20nums.set%280%2C%201%29%0A%20%20%20%20for%20i%20in%20range%2810%29%3A%0A%20%20%20%20%20%20%20%20nums.add%28i%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20MyList%3A%0A%0A%20%20%20%20def%20__init__%28self%29%3A%0A%20%20%20%20%20%20%20%20self._capacity%3A%20int%20%3D%2010%0A%20%20%20%20%20%20%20%20self._arr%3A%20list%5Bint%5D%20%3D%20%5B0%5D%20%2A%20self._capacity%0A%20%20%20%20%20%20%20%20self._size%3A%20int%20%3D%200%0A%20%20%20%20%20%20%20%20self._extend_ratio%3A%20int%20%3D%202%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%20self._size%0A%0A%20%20%20%20def%20capacity%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%20self._capacity%0A%0A%20%20%20%20def%20get%28self%2C%20index%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20if%20index%20%3C%200%20or%20index%20%3E%3D%20self._size%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%27%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%8C%E7%AF%84%E5%9B%B2%E5%A4%96%E3%81%A7%E3%81%99%27%29%0A%20%20%20%20%20%20%20%20return%20self._arr%5Bindex%5D%0A%0A%20%20%20%20def%20set%28self%2C%20num%3A%20int%2C%20index%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20if%20index%20%3C%200%20or%20index%20%3E%3D%20self._size%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%27%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%8C%E7%AF%84%E5%9B%B2%E5%A4%96%E3%81%A7%E3%81%99%27%29%0A%20%20%20%20%20%20%20%20self._arr%5Bindex%5D%20%3D%20num%0A%0A%20%20%20%20def%20add%28self%2C%20num%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20if%20self.size%28%29%20%3D%3D%20self.capacity%28%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.extend_capacity%28%29%0A%20%20%20%20%20%20%20%20self._arr%5Bself._size%5D%20%3D%20num%0A%20%20%20%20%20%20%20%20self._size%20%2B%3D%201%0A%0A%20%20%20%20def%20insert%28self%2C%20num%3A%20int%2C%20index%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20if%20index%20%3C%200%20or%20index%20%3E%3D%20self._size%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%27%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%8C%E7%AF%84%E5%9B%B2%E5%A4%96%E3%81%A7%E3%81%99%27%29%0A%20%20%20%20%20%20%20%20%20%20%20%20self.extend_capacity%28%29%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28self._size%20-%201%2C%20index%20-%201%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self._arr%5Bj%20%2B%201%5D%20%3D%20self._arr%5Bj%5D%0A%20%20%20%20%20%20%20%20self._arr%5Bindex%5D%20%3D%20num%0A%20%20%20%20%20%20%20%20self._size%20%2B%3D%201%0A%0A%20%20%20%20def%20remove%28self%2C%20index%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20if%20index%20%3C%200%20or%20index%20%3E%3D%20self._size%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%27%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%8C%E7%AF%84%E5%9B%B2%E5%A4%96%E3%81%A7%E3%81%99%27%29%0A%20%20%20%20%20%20%20%20num%20%3D%20self._arr%5Bindex%5D%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28index%2C%20self._size%20-%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self._arr%5Bj%5D%20%3D%20self._arr%5Bj%20%2B%201%5D%0A%20%20%20%20%20%20%20%20self._size%20-%3D%201%0A%20%20%20%20%20%20%20%20return%20num%0A%0A%20%20%20%20def%20extend_capacity%28self%29%3A%0A%20%20%20%20%20%20%20%20self._arr%20%3D%20self._arr%20%2B%20%5B0%5D%20%2A%20self.capacity%28%29%20%2A%20%28self._extend_ratio%20-%201%29%0A%20%20%20%20%20%20%20%20self._capacity%20%3D%20len%28self._arr%29%0Aif%20__name__%20%3D%3D%20%27__main__%27%3A%0A%20%20%20%20nums%20%3D%20MyList%28%29%0A%20%20%20%20nums.add%281%29%0A%20%20%20%20nums.add%283%29%0A%20%20%20%20nums.add%282%29%0A%20%20%20%20nums.add%285%29%0A%20%20%20%20nums.add%284%29%0A%20%20%20%20nums.insert%286%2C%20index%3D3%29%0A%20%20%20%20nums.remove%283%29%0A%20%20%20%20num%20%3D%20nums.get%281%29%0A%20%20%20%20nums.set%280%2C%201%29%0A%20%20%20%20for%20i%20in%20range%2810%29%3A%0A%20%20%20%20%20%20%20%20nums.add%28i%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 
 <!-- Source file information -->
 
diff --git a/ja/chapter_array_and_linkedlist/ram_and_cache/index.html b/ja/chapter_array_and_linkedlist/ram_and_cache/index.html
index d77cdc5fb..7d690ed32 100644
--- a/ja/chapter_array_and_linkedlist/ram_and_cache/index.html
+++ b/ja/chapter_array_and_linkedlist/ram_and_cache/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1368,7 +1368,7 @@
   <a href="#441" class="md-nav__link">
     <span class="md-ellipsis">
       
-        4.4.1 &nbsp; コンピュータ記憶装置
+        4.4.1 &nbsp; コンピュータの記憶装置
       
     </span>
   </a>
@@ -1674,7 +1674,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
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             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
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   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2188,7 +2188,7 @@
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-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2574,7 +2574,7 @@
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-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2658,7 +2658,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3196,7 +3196,7 @@
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3473,7 +3473,7 @@
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-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
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-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
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-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
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-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3698,7 +3698,7 @@
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-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
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-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3919,7 +3919,7 @@
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4164,7 +4164,7 @@
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4310,7 +4310,7 @@
   <a href="#441" class="md-nav__link">
     <span class="md-ellipsis">
       
-        4.4.1 &nbsp; コンピュータ記憶装置
+        4.4.1 &nbsp; コンピュータの記憶装置
       
     </span>
   </a>
@@ -4377,11 +4377,11 @@
 
 <!-- Page content -->
 <h1 id="44">4.4 &nbsp; メモリとキャッシュ *<a class="headerlink" href="#44" title="Permanent link">&para;</a></h1>
-<p>この章の最初の2つのセクションでは、「連続格納」と「分散格納」をそれぞれ表現する2つの基本的なデータ構造である配列と連結リストを探究しました。</p>
-<p>実際、<strong>物理構造はプログラムがメモリとキャッシュをどの程度効率的に利用するかを大きく決定し</strong>、これがアルゴリズムの全体的なパフォーマンスに影響を与えます。</p>
-<h2 id="441">4.4.1 &nbsp; コンピュータ記憶装置<a class="headerlink" href="#441" title="Permanent link">&para;</a></h2>
-<p>コンピュータには3種類の記憶装置があります：<u>ハードディスク</u>、<u>ランダムアクセスメモリ（RAM）</u>、および<u>キャッシュメモリ</u>です。以下の表は、コンピュータシステムにおけるそれぞれの役割とパフォーマンス特性を示しています。</p>
-<p align="center"> 表 4-2 &nbsp; コンピュータ記憶装置 </p>
+<p>本章の前二節では、配列と連結リストという二つの基礎的かつ重要なデータ構造を扱いました。これらはそれぞれ「連続格納」と「分散格納」という二つの物理構造を表しています。</p>
+<p>実際には、<strong>物理構造はプログラムにおけるメモリとキャッシュの利用効率を大きく左右し</strong>、ひいてはアルゴリズムプログラム全体の性能に影響します。</p>
+<h2 id="441">4.4.1 &nbsp; コンピュータの記憶装置<a class="headerlink" href="#441" title="Permanent link">&para;</a></h2>
+<p>コンピュータには三種類の記憶装置があります。<u>ハードディスク（hard disk）</u>、<u>メモリ（random-access memory, RAM）</u>、<u>キャッシュ（cache memory）</u>です。以下の表は、これらがコンピュータシステムで担う役割と性能上の特徴を示しています。</p>
+<p align="center"> 表 4-2 &nbsp; コンピュータの記憶装置 </p>
 
 <div class="center-table">
 <table>
@@ -4396,80 +4396,80 @@
 <tbody>
 <tr>
 <td>用途</td>
-<td>OS、プログラム、ファイルなどのデータの長期保存</td>
-<td>現在実行中のプログラムと処理中のデータの一時保存</td>
-<td>頻繁にアクセスされるデータと命令を保存し、CPUのメモリへのアクセス数を削減</td>
+<td>OS、プログラム、ファイルなどを長期保存</td>
+<td>実行中のプログラムや処理中のデータを一時保存</td>
+<td>頻繁にアクセスされるデータや命令を保存し、CPU のメモリアクセス回数を減らす</td>
 </tr>
 <tr>
 <td>揮発性</td>
-<td>電源オフ後もデータは失われない</td>
-<td>電源オフ後にデータは失われる</td>
-<td>電源オフ後にデータは失われる</td>
+<td>電源断後もデータは失われない</td>
+<td>電源断後にデータは失われる</td>
+<td>電源断後にデータは失われる</td>
 </tr>
 <tr>
 <td>容量</td>
-<td>より大きい、TBレベル</td>
-<td>より小さい、GBレベル</td>
-<td>非常に小さい、MBレベル</td>
+<td>大きい、TB 級</td>
+<td>小さい、GB 級</td>
+<td>非常に小さい、MB 級</td>
 </tr>
 <tr>
 <td>速度</td>
-<td>より遅い、数百から数千MB/s</td>
-<td>より高速、数十GB/s</td>
-<td>非常に高速、数十から数百GB/s</td>
+<td>遅い、数百〜数千 MB/s</td>
+<td>速い、数十 GB/s</td>
+<td>非常に速い、数十〜数百 GB/s</td>
 </tr>
 <tr>
-<td>価格（USD）</td>
-<td>より安価、数セント/GB</td>
-<td>より高価、数ドル/GB</td>
-<td>非常に高価、CPUと一緒に価格設定</td>
+<td>価格（人民元）</td>
+<td>比較的安価、数角〜数元 / GB</td>
+<td>比較的高価、数十〜数百元 / GB</td>
+<td>非常に高価、CPU と一体で価格設定される</td>
 </tr>
 </tbody>
 </table>
 </div>
-<p>コンピュータ記憶システムは、下図に示すようにピラミッドとして視覚化できます。ピラミッドの上部にある記憶装置ほど高速で、容量が小さく、より高価です。このマルチレベル設計は偶然ではなく、コンピュータ科学者とエンジニアによる慎重な検討の結果です。</p>
+<p>コンピュータの記憶システムは、下図のようなピラミッド構造として捉えられます。ピラミッドの頂点に近い記憶装置ほど速度は速く、容量は小さく、コストは高くなります。この多層構造は偶然ではなく、コンピュータ科学者やエンジニアによる熟慮の末の設計です。</p>
 <ul>
-<li><strong>ハードディスクをメモリに置き換えるのは困難です</strong>。第一に、メモリ内のデータは電源オフ後に失われるため、長期データ保存には適していません。第二に、メモリはハードディスクよりも大幅に高価で、消費者市場での広範囲な使用の実現可能性を制限しています。</li>
-<li><strong>キャッシュは大容量と高速のトレードオフに直面しています</strong>。L1、L2、L3キャッシュの容量が増加するにつれて、その物理サイズが大きくなり、CPUコアからの距離が増加します。これによりデータ転送時間が長くなり、アクセス遅延が高くなります。現在の技術では、マルチレベルキャッシュ構造が容量、速度、コストの間の最適なバランスを提供します。</li>
+<li><strong>ハードディスクはメモリで置き換えにくい</strong>。まず、メモリ内のデータは電源断後に失われるため、長期保存には向きません。次に、メモリのコストはハードディスクの数十倍であり、消費者市場で広く普及しにくいという問題があります。</li>
+<li><strong>キャッシュは大容量と高速性を両立しにくい</strong>。L1、L2、L3 キャッシュの容量が段階的に増えるにつれて、物理サイズは大きくなり、CPU コアとの物理的距離も遠くなります。その結果、データ転送時間が増え、要素アクセスの遅延も大きくなります。現在の技術では、多層キャッシュ構造が容量、速度、コストの最適なバランスです。</li>
 </ul>
-<p><img alt="コンピュータ記憶システム" class="animation-figure" src="../ram_and_cache.assets/storage_pyramid.png" /></p>
-<p align="center"> 図 4-9 &nbsp; コンピュータ記憶システム </p>
+<p><img alt="コンピュータの記憶システム" class="animation-figure" src="../ram_and_cache.assets/storage_pyramid.png" /></p>
+<p align="center"> 図 4-9 &nbsp; コンピュータの記憶システム </p>
 
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>コンピュータの記憶階層は、速度、容量、コストの間の慎重なバランスを反映しています。このタイプのトレードオフは様々な業界で一般的であり、利益と制限の間の最適なバランスを見つけることが重要です。</p>
+<p>コンピュータの記憶階層は、速度、容量、コストの三者間にある巧妙なバランスを体現しています。実際、このようなトレードオフはあらゆる工業分野に広く存在しており、異なる利点と制約のあいだで最適な均衡点を見つけることが求められます。</p>
 </div>
-<p>全体的に、<strong>ハードディスクは大量のデータの長期保存を提供し、メモリはプログラム実行中に処理されるデータの一時保存として機能し、キャッシュは頻繁にアクセスされるデータと命令を保存して実行効率を向上させます</strong>。それらは一緒になってコンピュータシステムの効率的な動作を保証します。</p>
-<p>下図に示すように、プログラム実行中、データはハードディスクからメモリに読み込まれ、CPU計算が行われます。CPUの拡張として機能するキャッシュは、**メモリからインテリジェントにデータを先読み**し、CPUのより高速なデータアクセスを可能にします。これによりプログラム実行効率が大幅に向上し、低速なメモリへの依存が減少します。</p>
-<p><img alt="ハードディスク、メモリ、キャッシュ間のデータフロー" class="animation-figure" src="../ram_and_cache.assets/computer_storage_devices.png" /></p>
-<p align="center"> 図 4-10 &nbsp; ハードディスク、メモリ、キャッシュ間のデータフロー </p>
+<p>要するに、<strong>ハードディスクは大量データの長期保存に、メモリはプログラム実行中に処理しているデータの一時保存に、キャッシュは頻繁にアクセスされるデータや命令の保存に用いられ</strong>、プログラム実行効率を高めます。三者は協調して動作し、コンピュータシステムの高効率な運用を支えています。</p>
+<p>次の図に示すように、プログラム実行時にはデータがハードディスクからメモリへ読み込まれ、CPU の計算に使われます。キャッシュは CPU の一部と見なせ、<strong>メモリからデータを賢く読み込むことで</strong>、CPU に高速なデータ読み出しを提供し、プログラムの実行効率を大きく高め、低速なメモリへの依存を減らします。</p>
+<p><img alt="ハードディスク、メモリ、キャッシュ間のデータの流れ" class="animation-figure" src="../ram_and_cache.assets/computer_storage_devices.png" /></p>
+<p align="center"> 図 4-10 &nbsp; ハードディスク、メモリ、キャッシュ間のデータの流れ </p>
 
 <h2 id="442">4.4.2 &nbsp; データ構造のメモリ効率<a class="headerlink" href="#442" title="Permanent link">&para;</a></h2>
-<p>メモリ空間利用の観点から、配列と連結リストにはそれぞれ利点と制限があります。</p>
-<p>一方で、**メモリは限られており、複数のプログラム間で共有できない**ため、データ構造での空間使用の最適化は重要です。配列は要素が密接にパックされており、連結リストのように参照（ポインタ）のための追加メモリを必要としないため、空間効率的です。しかし、配列は連続したメモリブロックを事前に割り当てる必要があり、割り当てられた空間が実際の必要量を超える場合、無駄につながる可能性があります。配列の拡張も追加の時間と空間のオーバーヘッドを伴います。対照的に、連結リストは各ノードに対してメモリを動的に割り当て・解放し、ポインタのための追加メモリのコストでより大きな柔軟性を提供します。</p>
-<p>一方で、プログラム実行中、<strong>繰り返されるメモリの割り当てと解放はメモリの断片化を増加させ</strong>、メモリ利用効率を低下させます。配列は連続記憶方式により、メモリ断片化を引き起こす可能性が比較的低いです。対照的に、連結リストは要素を非連続の場所に保存し、頻繁な挿入と削除はメモリ断片化を悪化させる可能性があります。</p>
+<p>メモリ空間の利用という観点では、配列と連結リストにはそれぞれ利点と制約があります。</p>
+<p>一方で、<strong>メモリは有限であり、同じメモリ領域を複数のプログラムで共有することはできません</strong>。そのため、データ構造にはできるだけ効率よく空間を使うことが求められます。配列の要素は密に並んでおり、連結リストのノード間参照（ポインタ）を保持する追加領域が不要なため、空間効率は高くなります。しかし、配列は十分な連続メモリを一度に確保する必要があり、メモリ浪費を招くことがありますし、拡張時にも追加の時間と空間コストがかかります。これに対して連結リストは「ノード」単位で動的にメモリを割り当て・解放でき、より高い柔軟性を備えています。</p>
+<p>他方で、プログラムの実行中には、<strong>メモリの確保と解放を繰り返すにつれて、空きメモリの断片化はますます進み</strong>、メモリ利用効率の低下を招きます。配列は連続した格納方式を取るため、比較的メモリ断片化を起こしにくい構造です。反対に、連結リストの要素は分散して格納されるため、頻繁な挿入や削除を行うと、より断片化を招きやすくなります。</p>
 <h2 id="443">4.4.3 &nbsp; データ構造のキャッシュ効率<a class="headerlink" href="#443" title="Permanent link">&para;</a></h2>
-<p>キャッシュはメモリよりも空間容量がはるかに小さいですが、はるかに高速で、プログラム実行速度において重要な役割を果たします。限られた容量のため、キャッシュは頻繁にアクセスされるデータのサブセットのみを保存できます。CPUがキャッシュに存在しないデータにアクセスしようとすると、<u>キャッシュミス</u>が発生し、CPUは低速なメモリから必要なデータを取得する必要があり、パフォーマンスに影響を与える可能性があります。</p>
-<p>明らかに、<strong>キャッシュミスが少ないほど、CPUのデータ読み書き効率が高く</strong>、プログラムパフォーマンスが向上します。CPUがキャッシュからデータを正常に取得する割合は<u>キャッシュヒット率</u>と呼ばれ、キャッシュ効率を測定するためによく使用される指標です。</p>
-<p>より高い効率を達成するために、キャッシュは以下のデータロードメカニズムを採用します。</p>
+<p>キャッシュは容量こそメモリよりはるかに小さいものの、速度はメモリよりずっと速く、プログラム実行速度において極めて重要な役割を果たします。キャッシュ容量には限りがあり、頻繁にアクセスされる一部のデータしか保持できません。そのため、CPU がアクセスしようとするデータがキャッシュ内に存在しない場合、<u>キャッシュミス（cache miss）</u>が発生し、CPU は低速なメモリから必要なデータを読み込まなければなりません。</p>
+<p>当然ながら、<strong>「キャッシュミス」が少ないほど、CPU のデータ読み書き効率は高くなり</strong>、プログラム性能も向上します。CPU がキャッシュからデータを正常に取得できた割合を<u>キャッシュヒット率（cache hit rate）</u>と呼び、この指標は通常、キャッシュ効率の評価に用いられます。</p>
+<p>できるだけ高い効率を実現するため、キャッシュは次のようなデータ読み込みの仕組みを採用しています。</p>
 <ul>
-<li><strong>キャッシュライン</strong>：キャッシュは個々のバイトではなく、キャッシュラインと呼ばれる単位でデータを保存・ロードして動作します。このアプローチは、一度により大きなデータブロックを転送することで効率を向上させます。</li>
-<li><strong>先読みメカニズム</strong>：プロセッサはデータアクセスパターン（例：連続または固定ストライドアクセス）を予測し、これらのパターンに基づいてデータをキャッシュに先読みして、キャッシュヒット率を向上させます。</li>
-<li><strong>空間的局所性</strong>：特定のデータがアクセスされると、近くのデータもまもなくアクセスされる可能性があります。これを活用するために、キャッシュは要求されたデータと一緒に隣接するデータをロードし、ヒット率を向上させます。</li>
-<li><strong>時間的局所性</strong>：データがアクセスされた場合、近い将来に再びアクセスされる可能性があります。キャッシュはこの原理を使用して、最近アクセスされたデータを保持してヒット率を向上させます。</li>
+<li><strong>キャッシュライン</strong>：キャッシュはデータを 1 バイト単位で保存・読み込みするのではなく、キャッシュライン単位で扱います。1 バイト単位の転送と比べて、キャッシュライン単位のほうが効率的です。</li>
+<li><strong>プリフェッチ機構</strong>：プロセッサはデータアクセスのパターン（たとえば順次アクセス、一定ステップ幅のスキップアクセスなど）を予測し、そのパターンに応じてデータをキャッシュへ読み込むことで、ヒット率を高めます。</li>
+<li><strong>空間的局所性</strong>：あるデータがアクセスされた場合、その近傍のデータも近いうちにアクセスされる可能性があります。そのため、キャッシュはあるデータを読み込む際に、その周辺のデータもあわせて読み込み、ヒット率を高めます。</li>
+<li><strong>時間的局所性</strong>：あるデータがアクセスされた場合、そのデータは近い将来に再びアクセスされる可能性が高いです。キャッシュはこの性質を利用し、最近アクセスしたデータを保持することでヒット率を高めます。</li>
 </ul>
-<p>実際、<strong>配列と連結リストは異なるキャッシュ利用効率を持ち</strong>、これは主に以下の側面に反映されます。</p>
+<p>実際には、<strong>配列と連結リストではキャッシュの利用効率が異なり</strong>、主に次の点に表れます。</p>
 <ul>
-<li><strong>占有空間</strong>：連結リスト要素は配列要素よりも多くの空間を占有するため、キャッシュに保持される有効データが少なくなります。</li>
-<li><strong>キャッシュライン</strong>：連結リストデータはメモリ全体に散在し、キャッシュは「行単位でロード」されるため、ロードされる無効データの割合が高くなります。</li>
-<li><strong>先読みメカニズム</strong>：配列のデータアクセスパターンは連結リストよりも「予測可能」で、つまりシステムがこれからロードされるデータを推測しやすいです。</li>
-<li><strong>空間的局所性</strong>：配列は連続したメモリ空間に保存されるため、ロードされているデータの近くのデータがまもなくアクセスされる可能性が高くなります。</li>
+<li><strong>使用空間</strong>：連結リストの要素は配列要素より多くの空間を占めるため、キャッシュに収まる有効データ量は少なくなります。</li>
+<li><strong>キャッシュライン</strong>：連結リストのデータはメモリの各所に分散しており、キャッシュは「ライン単位で読み込む」ため、無効データまで読み込む割合が高くなります。</li>
+<li><strong>プリフェッチ機構</strong>：配列のほうが連結リストよりもデータアクセスのパターンを「予測しやすく」、システムが次に読み込まれるデータを推測しやすくなります。</li>
+<li><strong>空間的局所性</strong>：配列はまとまったメモリ空間に格納されるため、読み込まれたデータの近くにあるデータも、まもなくアクセスされる可能性が高くなります。</li>
 </ul>
-<p>全体的に、<strong>配列はより高いキャッシュヒット率を持ち、一般的に連結リストよりも操作効率が高いです</strong>。これにより、配列に基づくデータ構造はアルゴリズム問題の解決において人気があります。</p>
-<p>**高いキャッシュ効率が配列が常に連結リストより優れているという意味ではない**ことに注意すべきです。データ構造の選択は特定のアプリケーション要件に依存すべきです。例えば、配列と連結リストの両方が「スタック」データ構造を実装できますが（次章で詳細説明）、それらは異なるシナリオに適しています。</p>
+<p>全体として、<strong>配列はより高いキャッシュヒット率を持つため、操作効率では通常、連結リストより優れています</strong>。このため、アルゴリズム問題を解く際には、配列ベースで実装されたデータ構造のほうが好まれることが多くなります。</p>
+<p>注意すべきなのは、**キャッシュ効率が高いからといって、配列があらゆる状況で連結リストより優れているとは限らない**という点です。実際にどのデータ構造を選ぶかは、具体的な要件に応じて決めるべきです。たとえば、配列と連結リストはいずれも「スタック」データ構造を実装できますが（次章で詳しく説明します）、適した場面は異なります。</p>
 <ul>
-<li>アルゴリズム問題では、より高い操作効率とランダムアクセス機能を提供するため、配列に基づくスタックを選択する傾向があります。唯一のコストは配列に対して一定量のメモリ空間を事前に割り当てる必要があることです。</li>
-<li>データ量が非常に大きく、高度に動的で、スタックの予想サイズを推定するのが困難な場合、連結リストに基づくスタックがより良い選択です。連結リストは大量のデータをメモリの異なる部分に分散でき、配列拡張の追加オーバーヘッドを回避できます。</li>
+<li>アルゴリズム問題に取り組むときは、一般に配列ベースのスタックを選ぶ傾向があります。より高い操作効率とランダムアクセス能力を備えており、その代償は配列用に一定量のメモリを事前確保することだけです。</li>
+<li>データ量が非常に大きく、動的性が高く、スタックの想定サイズを見積もりにくい場合は、連結リストベースのスタックのほうが適しています。連結リストなら大量のデータをメモリの異なる場所に分散して保存でき、配列拡張による追加コストも回避できます。</li>
 </ul>
 
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-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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 <!-- Page content -->
 <h1 id="45">4.5 &nbsp; まとめ<a class="headerlink" href="#45" title="Permanent link">&para;</a></h1>
-<h3 id="1">1. &nbsp; 重要な復習<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<h3 id="1">1. &nbsp; 要点の振り返り<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
-<li>配列と連結リストは2つの基本的なデータ構造であり、コンピュータメモリにおける2つの格納方法を表しています：連続空間格納と非連続空間格納です。それらの特性は互いに補完し合います。</li>
-<li>配列はランダムアクセスをサポートし、使用するメモリが少ない一方で、要素の挿入と削除は非効率的で、初期化後の長さが固定されています。</li>
-<li>連結リストは参照（ポインタ）の変更によって効率的なノードの挿入と削除を実装し、長さを柔軟に調整できますが、ノードアクセス効率が低く、より多くのメモリを消費します。</li>
-<li>連結リストの一般的な種類には、単方向連結リスト、循環連結リスト、双方向連結リストがあり、それぞれに独自の応用シナリオがあります。</li>
-<li>リストは要素の順序付けられたコレクションで、追加、削除、変更をサポートし、通常は動的配列に基づいて実装され、配列の利点を保持しながら柔軟な長さ調整を可能にします。</li>
-<li>リストの出現により配列の実用性が大幅に向上しましたが、一部のメモリ空間の無駄につながる可能性があります。</li>
-<li>プログラム実行中、データは主にメモリに格納されます。配列はより高いメモリ空間効率を提供し、連結リストはメモリ使用においてより柔軟です。</li>
-<li>キャッシュは、キャッシュライン、先読み、空間的局所性、時間的局所性などのメカニズムを通じてCPUに高速データアクセスを提供し、プログラム実行効率を大幅に向上させます。</li>
-<li>より高いキャッシュヒット率により、配列は一般的に連結リストよりも効率的です。データ構造を選択する際は、特定のニーズとシナリオに基づいて適切な選択をすべきです。</li>
+<li>配列と連結リストは 2 種類の基本的なデータ構造であり、それぞれコンピュータメモリにおけるデータの 2 つの格納方式、すなわち連続領域への格納と分散領域への格納を表す。両者の特徴は相互補完的である。</li>
+<li>配列はランダムアクセスをサポートし、使用メモリも少ない。一方で、要素の挿入と削除の効率は低く、初期化後に長さを変更できない。</li>
+<li>連結リストは参照（ポインタ）を変更することでノードの挿入と削除を効率的に行え、長さも柔軟に調整できる。一方で、ノードへのアクセス効率は低く、メモリ使用量も多い。一般的な連結リストには単方向連結リスト、循環連結リスト、双方向連結リストがある。</li>
+<li>リストは、追加・削除・検索・更新をサポートする順序付き要素集合であり、通常は動的配列に基づいて実装される。配列の利点を保ちながら、長さを柔軟に調整できる。</li>
+<li>リストの登場により配列の実用性は大幅に高まったが、一部のメモリ領域が無駄になる可能性がある。</li>
+<li>プログラムの実行時、データは主にメモリに格納される。配列はより高いメモリ空間効率を提供でき、連結リストはメモリ利用の面でより柔軟である。</li>
+<li>キャッシュは、キャッシュライン、プリフェッチ機構、空間局所性と時間局所性といったデータ読み込み機構を通じて CPU に高速なデータアクセスを提供し、プログラムの実行効率を大きく向上させる。</li>
+<li>配列はキャッシュヒット率が高いため、通常は連結リストよりも高効率である。データ構造を選択する際は、具体的な要件や場面に応じて適切に選ぶべきである。</li>
 </ul>
 <h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
-<p><strong>Q</strong>：配列をスタックに格納するかヒープに格納するかは、時間と空間効率に影響しますか？</p>
-<p>スタックとヒープの両方に格納される配列は連続したメモリ空間に格納され、データ操作効率は本質的に同じです。しかし、スタックとヒープには独自の特性があり、以下の違いが生じます。</p>
+<p><strong>Q</strong>：配列をスタックに格納する場合とヒープに格納する場合では、時間効率と空間効率に影響がありますか？</p>
+<p>スタック上とヒープ上の配列はいずれも連続したメモリ領域に格納されるため、データ操作の効率は基本的に同じである。ただし、スタックとヒープにはそれぞれ特徴があり、以下の違いが生じる。</p>
 <ol>
-<li>割り当てと解放効率：スタックはより小さなメモリブロックで、コンパイラによって自動的に割り当てられます。ヒープメモリは比較的大きく、コードで動的に割り当てることができ、断片化しやすいです。したがって、ヒープでの割り当てと解放操作は一般的にスタックよりも遅くなります。</li>
-<li>サイズ制限：スタックメモリは比較的小さく、ヒープサイズは一般的に利用可能なメモリによって制限されます。したがって、ヒープは大きな配列の格納により適しています。</li>
-<li>柔軟性：スタック上の配列のサイズはコンパイル時に決定される必要がありますが、ヒープ上の配列のサイズは実行時に動的に決定できます。</li>
+<li>確保と解放の効率：スタックは比較的小さなメモリ領域で、確保はコンパイラによって自動的に行われる。一方、ヒープメモリは相対的に大きく、コード内で動的に確保できる反面、断片化しやすい。そのため、ヒープ上での確保と解放は通常スタック上より遅い。</li>
+<li>サイズ制限：スタックメモリは比較的小さく、ヒープのサイズは一般に利用可能メモリに制限される。そのため、ヒープは大きな配列の格納により適している。</li>
+<li>柔軟性：スタック上の配列サイズはコンパイル時に確定している必要があるが、ヒープ上の配列サイズは実行時に動的に決定できる。</li>
 </ol>
-<p><strong>Q</strong>：なぜ配列は同じ型の要素を必要とし、連結リストは同じ型の要素を強調しないのですか？</p>
-<p>連結リストは参照（ポインタ）によって接続されたノードで構成され、各ノードはint、double、string、objectなど、異なる型のデータを格納できます。</p>
-<p>対照的に、配列要素は同じ型である必要があり、これにより対応する要素位置にアクセスするためのオフセットを計算できます。例えば、intとlong型の両方を含む配列で、単一要素がそれぞれ4バイトと8バイトを占有する場合、配列に2つの異なる長さの要素が含まれているため、以下の式を使用してオフセットを計算できません。</p>
-<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 要素メモリアドレス = 配列メモリアドレス + 要素長 * 要素インデックス</span>
+<p><strong>Q</strong>：なぜ配列では同じ型の要素が求められるのに、連結リストでは同じ型であることが強調されないのですか？</p>
+<p>連結リストはノードで構成され、ノード同士は参照（ポインタ）で接続されている。各ノードには <code>int</code>、<code>double</code>、<code>string</code>、<code>object</code> など、異なる型のデータを格納できる。</p>
+<p>これに対して、配列要素は同じ型でなければならない。そうでなければ、オフセットを計算して対応する要素位置を取得できないからである。たとえば、配列に <code>int</code> と <code>long</code> の 2 種類が同時に含まれていて、各要素がそれぞれ 4 バイトと 8 バイトを占める場合、配列内に 2 種類の「要素長」が存在するため、次の式ではオフセットを計算できない。</p>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 要素のメモリアドレス = 配列のメモリアドレス（先頭要素のメモリアドレス） + 要素長 * 要素インデックス</span>
 </code></pre></div>
-<p><strong>Q</strong>：ノードを削除した後、<code>P.next</code>を<code>None</code>に設定する必要がありますか？</p>
-<p><code>P.next</code>を変更しなくても問題ありません。連結リストの観点から、ヘッドノードからテールノードまでの巡回で<code>P</code>に遭遇することはもうありません。これは、ノード<code>P</code>がリストから効果的に削除されたことを意味し、<code>P</code>が指す場所はもはやリストに影響しません。</p>
-<p>ガベージコレクションの観点から、Java、Python、Goなどの自動ガベージコレクションメカニズムを持つ言語では、ノード<code>P</code>が収集されるかどうかは、それを指す参照がまだあるかどうかに依存し、<code>P.next</code>の値には依存しません。CやC++などの言語では、ノードのメモリを手動で解放する必要があります。</p>
-<p><strong>Q</strong>：連結リストでは、挿入と削除操作の時間計算量は<code>O(1)</code>です。しかし、挿入や削除前の要素検索には<code>O(n)</code>時間がかかるので、なぜ時間計算量は<code>O(n)</code>ではないのですか？</p>
-<p>要素を最初に検索してから削除する場合、時間計算量は確かに<code>O(n)</code>です。しかし、連結リストの挿入と削除における<code>O(1)</code>の利点は他のアプリケーションで実現できます。例えば、連結リストを使用した両端キューの実装では、常にヘッドとテールノードを指すポインタを維持し、各挿入と削除操作を<code>O(1)</code>にします。</p>
-<p><strong>Q</strong>：「連結リストの定義と格納方法」の図で、薄青色の格納ノードは単一のメモリアドレスを占有しますか、それともノード値と半分を共有しますか？</p>
-<p>図は単なる定性的な表現であり、定量的分析は特定の状況に依存します。</p>
+<p><strong>Q</strong>：ノード <code>P</code> を削除した後、<code>P.next</code> を <code>None</code> に設定する必要はありますか？</p>
+<p><code>P.next</code> を変更しなくてもよい。この連結リストの観点では、先頭ノードから末尾ノードまでたどっても、もはや <code>P</code> に出会うことはない。つまり、ノード <code>P</code> はすでに連結リストから削除されており、この時点で <code>P</code> がどこを指していても、この連結リストには影響しない。</p>
+<p>データ構造とアルゴリズム（問題を解くとき）の観点では、切り離さなくても問題はなく、プログラムのロジックが正しいことを保証すればよい。標準ライブラリの観点では、切り離したほうがより安全で、ロジックも明確である。切り離さない場合、削除されたノードが適切に回収されなかったとすると、後続ノードのメモリ回収に影響する可能性がある。</p>
+<p><strong>Q</strong>：連結リストでの挿入と削除の時間計算量は <span class="arithmatex">\(O(1)\)</span> です。しかし、追加や削除の前には要素を探すのに <span class="arithmatex">\(O(n)\)</span> の時間が必要です。では、なぜ時間計算量は <span class="arithmatex">\(O(n)\)</span> ではないのですか？</p>
+<p>要素を先に探してから削除するのであれば、時間計算量が <span class="arithmatex">\(O(n)\)</span> であるのは確かである。しかし、連結リストの <span class="arithmatex">\(O(1)\)</span> での追加・削除という利点は、ほかの用途で生かせる。たとえば、両端キューは連結リストで実装するのに適しており、先頭ノードと末尾ノードを常に指すポインタ変数を維持すれば、各挿入・削除操作はどれも <span class="arithmatex">\(O(1)\)</span> になる。</p>
+<p><strong>Q</strong>：図「連結リストの定義と格納方式」で、薄青色のノードポインタ部分は 1 つのメモリアドレスを占めているのですか？ それともノード値と半分ずつなのでしょうか？</p>
+<p>この模式図は定性的な表現にすぎず、定量的な表現は具体的な状況に応じて分析する必要がある。</p>
 <ul>
-<li>異なる型のノード値は異なる量の空間を占有します。例えば、int、long、double、オブジェクトインスタンスです。</li>
-<li>ポインタ変数によって占有されるメモリ空間は、使用されるオペレーティングシステムとコンパイル環境に依存し、通常8バイトまたは4バイトです。</li>
+<li>ノード値が占める領域は型によって異なり、たとえば <code>int</code>、<code>long</code>、<code>double</code>、インスタンスオブジェクトなどがある。</li>
+<li>ポインタ変数が占めるメモリ空間の大きさは、使用する OS やコンパイル環境によって異なり、多くは 8 バイトまたは 4 バイトである。</li>
 </ul>
-<p><strong>Q</strong>：リストの末尾への要素追加は常に<code>O(1)</code>ですか？</p>
-<p>要素を追加することでリスト長を超える場合、リストは最初に拡張される必要があります。システムは新しいメモリブロックを要求し、元のリストのすべての要素を移動するため、この場合の時間計算量は<code>O(n)</code>になります。</p>
-<p><strong>Q</strong>：「リストの出現により配列の実用性が大幅に向上しましたが、一部のメモリ空間の無駄につながる可能性があります」という文は、容量、長さ、拡張係数などの追加変数によって占有されるメモリを指していますか？</p>
-<p>ここでの空間の無駄は主に2つの側面を指します：一方で、リストは初期長で設定されますが、常に必要とは限りません。他方で、頻繁な拡張を防ぐため、拡張は通常<span class="arithmatex">\(\times 1.5\)</span>などの係数で乗算されます。これにより多くの空きスロットが生まれ、通常は完全に埋めることができません。</p>
-<p><strong>Q</strong>：Pythonで<code>n = [1, 2, 3]</code>を初期化した後、これら3つの要素のアドレスは連続していますが、<code>m = [2, 1, 3]</code>を初期化すると、各要素の<code>id</code>は連続していないが<code>n</code>のものと同一です。これらの要素のアドレスが連続していない場合、<code>m</code>はまだ配列ですか？</p>
-<p>リスト要素を連結リストノード<code>n = [n1, n2, n3, n4, n5]</code>に置き換える場合、これら5つのノードオブジェクトも通常メモリ全体に分散しています。しかし、リストインデックスが与えられれば、<code>O(1)</code>時間でノードのメモリアドレスにアクセスでき、対応するノードにアクセスできます。これは、配列がノード自体ではなく、ノードへの参照を格納するためです。</p>
-<p>多くの言語とは異なり、Pythonでは数値もオブジェクトとしてラップされ、リストは数値自体ではなく、これらの数値への参照を格納します。したがって、2つの配列の同じ数値が同じ<code>id</code>を持ち、これらの数値のメモリアドレスは連続である必要がないことがわかります。</p>
-<p><strong>Q</strong>：C++ STLの<code>std::list</code>はすでに双方向連結リストを実装していますが、一部のアルゴリズム書籍では直接使用していないようです。何か制限がありますか？</p>
-<p>一方で、アルゴリズムを実装する際は配列を使用することを好み、必要な場合のみ連結リストを使用します。主に2つの理由があります。</p>
+<p><strong>Q</strong>：リストの末尾への要素追加は常に <span class="arithmatex">\(O(1)\)</span> ですか？</p>
+<p>要素を追加する際にリスト長を超える場合は、先にリストを拡張してから追加する必要がある。システムは新しいメモリ領域を確保し、元のリストの全要素をそこへ移動するため、このとき時間計算量は <span class="arithmatex">\(O(n)\)</span> になる。</p>
+<p><strong>Q</strong>：「リストの登場により配列の実用性は大きく向上したが、一部のメモリ空間が無駄になる可能性がある」というのは、容量、長さ、拡張倍率のような追加変数が占めるメモリのことですか？</p>
+<p>ここでいう空間の無駄には主に 2 つの意味がある。一方では、リストには初期長が設定されるが、必ずしもそれだけ必要とは限らない。もう一方では、頻繁な拡張を防ぐため、拡張時には通常ある係数、たとえば <span class="arithmatex">\(\times 1.5\)</span> を掛ける。このため、多くの空きスロットが生じ、通常それらを完全に埋めることはできない。</p>
+<p><strong>Q</strong>：Python で <code>n = [1, 2, 3]</code> を初期化した後、この 3 つの要素のアドレスは連続しています。しかし <code>m = [2, 1, 3]</code> を初期化すると、各要素の id は連続しておらず、それぞれ <code>n</code> 内の同じ値と一致していることがわかります。これらの要素のアドレスが連続していないなら、<code>m</code> も配列なのですか？</p>
+<p>仮にリスト要素を連結リストのノード <code>n = [n1, n2, n3, n4, n5]</code> に置き換えたとしても、通常この 5 つのノードオブジェクトもメモリ上の各所に分散して格納される。それでも、与えられたリストインデックスに対して、私たちは依然として <span class="arithmatex">\(O(1)\)</span> 時間でノードのメモリアドレスを取得し、対応するノードにアクセスできる。これは、配列に格納されているのがノードそのものではなく、ノードへの参照だからである。</p>
+<p>多くの言語と異なり、Python では数値もオブジェクトとしてラップされており、リストに格納されているのは数値そのものではなく、数値への参照である。そのため、2 つの配列内の同じ数値が同一の id を持つことがあり、しかもそれらの数値のメモリアドレスは連続している必要がない。</p>
+<p><strong>Q</strong>：C++ STL の <code>std::list</code> はすでに双方向連結リストを実装していますが、アルゴリズム本ではあまり直接使われないようです。何か制約があるのでしょうか？</p>
+<p>一方では、私たちは多くの場合、アルゴリズムの実装に配列を好み、必要なときにだけ連結リストを使う。その主な理由は 2 つある。</p>
 <ul>
-<li>空間オーバーヘッド：各要素に2つの追加ポインタ（前の要素用と次の要素用）が必要なため、<code>std::list</code>は通常<code>std::vector</code>よりも多くの空間を占有します。</li>
-<li>キャッシュ非友好的：データが連続して格納されていないため、<code>std::list</code>はキャッシュ利用率が低くなります。一般的に、<code>std::vector</code>の方がパフォーマンスが優れています。</li>
+<li>空間オーバーヘッド：各要素には 2 つの追加ポインタ（前の要素用と次の要素用）が必要なため、<code>std::list</code> は通常 <code>std::vector</code> より多くの空間を消費する。</li>
+<li>キャッシュ非効率：データが連続して格納されていないため、<code>std::list</code> はキャッシュの利用効率が低い。一般には、<code>std::vector</code> のほうが性能がよい。</li>
 </ul>
-<p>他方で、連結リストは主に二分木とグラフに必要です。スタックとキューは、連結リストではなく、プログラミング言語の<code>stack</code>と<code>queue</code>クラスを使用して実装されることが多いです。</p>
-<p><strong>Q</strong>：リスト<code>res = [0] * self.size()</code>を初期化すると、<code>res</code>の各要素は同じアドレスを参照しますか？</p>
-<p>いいえ。しかし、この問題は二次元配列で発生します。例えば、二次元リスト<code>res = [[0]] * self.size()</code>を初期化すると、同じリスト<code>[0]</code>を複数回参照することになります。</p>
-<p><strong>Q</strong>：ノードを削除する際、その後続ノードへの参照を断つ必要がありますか？</p>
-<p>データ構造とアルゴリズム（問題解決）の観点から、プログラムのロジックが正しい限り、リンクを断たなくても問題ありません。標準ライブラリの観点から、リンクを断つ方が安全で論理的に明確です。リンクを断たず、削除されたノードが適切にリサイクルされない場合、後続ノードのメモリのリサイクルに影響を与える可能性があります。</p>
+<p>もう一方では、連結リストを使う必要がある代表的な場面は主に二分木とグラフである。スタックやキューについては、連結リストではなく、たいてい言語が提供する <code>stack</code> と <code>queue</code> を使う。</p>
+<p><strong>Q</strong>：<code>res = [[0]] * n</code> という操作で 2 次元リストを生成した場合、それぞれの <code>[0]</code> は独立していますか？</p>
+<p>独立していない。この 2 次元リストでは、すべての <code>[0]</code> は実際には同一オブジェクトへの参照である。そのうちの 1 つを変更すると、対応するすべての要素が一緒に変化することがわかる。</p>
+<p>2 次元リスト内の各 <code>[0]</code> を独立させたい場合は、<code>res = [[0] for _ in range(n)]</code> を使って実現できる。この方式の原理は、独立した <code>[0]</code> リストオブジェクトを <span class="arithmatex">\(n\)</span> 個初期化していることにある。</p>
+<p><strong>Q</strong>：<code>res = [0] * n</code> という操作で生成されたリストでは、それぞれの整数 0 は独立していますか？</p>
+<p>このリストでは、すべての整数 0 が同一オブジェクトへの参照である。これは、Python が小さな整数（通常は -5 から 256）に対してキャッシュプール機構を採用し、オブジェクトの再利用を最大化して性能を向上させているためである。</p>
+<p>それらは同じオブジェクトを指しているが、それでもリスト内の各要素は独立して変更できる。これは、Python の整数が「イミュータブルオブジェクト」だからである。ある要素を変更するとき、実際には別のオブジェクトへの参照に切り替わるのであって、元のオブジェクトそのものを変更しているわけではない。</p>
+<p>しかし、リスト要素が「ミュータブルオブジェクト」（たとえばリスト、辞書、クラスインスタンスなど）である場合は、ある要素を変更するとそのオブジェクト自体が直接変更され、そのオブジェクトを参照しているすべての要素に同じ変化が生じる。</p>
 
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+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
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+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4197,7 +4197,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4343,7 +4343,7 @@
   <a href="#1311" class="md-nav__link">
     <span class="md-ellipsis">
       
-        13.1.1 &nbsp; 試行と後退
+        13.1.1 &nbsp; 試行と戻る
       
     </span>
   </a>
@@ -4354,7 +4354,7 @@
   <a href="#1312" class="md-nav__link">
     <span class="md-ellipsis">
       
-        13.1.2 &nbsp; 剪定
+        13.1.2 &nbsp; 枝刈り
       
     </span>
   </a>
@@ -4387,7 +4387,7 @@
   <a href="#1315" class="md-nav__link">
     <span class="md-ellipsis">
       
-        13.1.5 &nbsp; 長所と限界
+        13.1.5 &nbsp; 利点と限界
       
     </span>
   </a>
@@ -4398,7 +4398,7 @@
   <a href="#1316" class="md-nav__link">
     <span class="md-ellipsis">
       
-        13.1.6 &nbsp; バックトラッキングの典型的な例題
+        13.1.6 &nbsp; バックトラッキングの典型例題
       
     </span>
   </a>
@@ -4443,18 +4443,18 @@
 
 <!-- Page content -->
 <h1 id="131">13.1 &nbsp; バックトラッキングアルゴリズム<a class="headerlink" href="#131" title="Permanent link">&para;</a></h1>
-<p><u>バックトラッキングアルゴリズム</u>は全数探索によって問題を解決する方法です。その核心概念は、初期状態から開始してすべての可能な解を総当たりで探索することです。アルゴリズムは正しいものを記録し、解が見つかるか、すべての可能な解が試されたが解が見つからないまで続けます。</p>
-<p>バックトラッキングは通常「深さ優先探索」を使用して解空間を走査します。「二分木」の章で、前順、中順、後順走査はすべて深さ優先探索であることを述べました。次に、前順走査を使用してバックトラッキング問題を解決し、アルゴリズムの動作を段階的に理解していきます。</p>
+<p><u>バックトラッキングアルゴリズム（backtracking algorithm）</u>は、総当たりによって問題を解く手法です。その中核となる考え方は、初期状態から出発し、あり得るすべての解を力任せに探索し、正しい解に到達したらそれを記録し、解を見つけるか、考えられるすべての選択を試しても解が見つからなくなるまで続ける、というものです。</p>
+<p>バックトラッキングアルゴリズムでは、通常「深さ優先探索」を用いて解空間をたどります。「二分木」の章で述べたように、前順・中順・後順走査はいずれも深さ優先探索に属します。ここでは前順走査を使ってバックトラッキング問題を構成し、その仕組みを段階的に理解していきます。</p>
 <div class="admonition question">
-<p class="admonition-title">例1</p>
-<p>二分木が与えられた場合、値が <span class="arithmatex">\(7\)</span> のすべてのノードを検索して記録し、リストで返してください。</p>
+<p class="admonition-title">例題1</p>
+<p>1 本の二分木が与えられたとき、値が <span class="arithmatex">\(7\)</span> のノードをすべて探索して記録し、そのノードのリストを返してください。</p>
 </div>
-<p>この問題を解決するために、この木を前順で走査し、現在のノードの値が <span class="arithmatex">\(7\)</span> かどうかを確認します。そうであれば、ノードの値を結果リスト <code>res</code> に追加します。プロセスは以下の図に示されています：</p>
+<p>この問題では、この木を前順走査し、現在のノードの値が <span class="arithmatex">\(7\)</span> かどうかを判定します。該当する場合は、そのノードの値を結果リスト <code>res</code> に追加します。関連する処理は下図と次のコードのとおりです。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">preorder_traversal_i_compact.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">):</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;前順走査：例一&quot;&quot;&quot;</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;前順走査：例題 1&quot;&quot;&quot;</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="k">if</span> <span class="n">root</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>        <span class="k">return</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="k">if</span> <span class="n">root</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="mi">7</span><span class="p">:</span>
@@ -4465,7 +4465,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_i_compact.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 前順走査：例１ */</span>
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 前順走査：例題 1 */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
@@ -4480,7 +4480,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_i_compact.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 前順走査：例１ */</span>
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 前順走査：例題 1 */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
@@ -4495,84 +4495,199 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_i_compact.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">preorder_traversal_i_compact</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">PreOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 前順走査：例題 1 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">PreOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">    </span><span class="n">PreOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">left</span><span class="p">);</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">    </span><span class="n">PreOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_i_compact.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">preOrderI</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 前順走査：例題 1 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">preOrderI</span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">Val</span><span class="p">).(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">        </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">root</span><span class="p">)</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">    </span><span class="nx">preOrderI</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">Left</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">    </span><span class="nx">preOrderI</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">Right</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_i_compact.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 前順走査：例題 1 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="k">guard</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">root</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">7</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="kr">left</span><span class="p">)</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="kr">right</span><span class="p">)</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_i_compact.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">preOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 前順走査：例題 1 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">        </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">root</span><span class="p">);</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">    </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">    </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">right</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_i_compact.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">preOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 前順走査：例題 1 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">        </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">root</span><span class="p">);</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">    </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">    </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">right</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_i_compact.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 前順走査：例題 1 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">    </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">    </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">  </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">  </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_i_compact.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">pre_order</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 前順走査：例題 1 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">            </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">        </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">());</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">        </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">());</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_i_compact.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 前順走査：例題 1 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">resSize</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">);</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_i_compact.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">preOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 前順走査：例題 1 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">_val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">        </span><span class="n">res</span><span class="o">!!</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">)</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">)</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_i_compact.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">pre_order</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 前順走査：例題1 ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">root</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="c1"># 解を記録</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="vg">$res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">  </span><span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">  </span><span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p><img alt="前順走査でのノード検索" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_nodes.png" /></p>
-<p align="center"> 図 13-1 &nbsp; 前順走査でのノード検索 </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%20%3D%200%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E5%80%A4%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%8F%B3%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%0Adef%20list_to_tree_dfs%28arr%3A%20list%5Bint%5D%2C%20i%3A%20int%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E4%BA%8C%E5%88%86%E6%9C%A8%E3%81%AB%E3%83%87%E3%82%B7%E3%83%AA%E3%82%A2%E3%83%A9%E3%82%A4%E3%82%BA%E3%81%99%E3%82%8B%3A%20%E5%86%8D%E5%B8%B0%22%22%22%0A%20%20%20%20%23%20%E6%B7%BB%E5%AD%97%E3%81%8C%E9%85%8D%E5%88%97%E9%95%B7%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%8B%E3%80%81%E5%AF%BE%E5%BF%9C%E3%81%99%E3%82%8B%E8%A6%81%E7%B4%A0%E3%81%8C%20None%20%E3%81%AA%E3%82%89%E3%80%81None%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20if%20i%20%3C%200%20or%20i%20%3E%3D%20len%28arr%29%20or%20arr%5Bi%5D%20is%20None%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%23%20%E7%8F%BE%E5%9C%A8%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20root%20%3D%20TreeNode%28arr%5Bi%5D%29%0A%20%20%20%20%23%20%E5%B7%A6%E5%8F%B3%E3%81%AE%E9%83%A8%E5%88%86%E6%9C%A8%E3%82%92%E5%86%8D%E5%B8%B0%E7%9A%84%E3%81%AB%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20root.left%20%3D%20list_to_tree_dfs%28arr%2C%202%20%2A%20i%20%2B%201%29%0A%20%20%20%20root.right%20%3D%20list_to_tree_dfs%28arr%2C%202%20%2A%20i%20%2B%202%29%0A%20%20%20%20return%20root%0A%0Adef%20list_to_tree%28arr%3A%20list%5Bint%5D%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E4%BA%8C%E5%88%86%E6%9C%A8%E3%81%AB%E3%83%87%E3%82%B7%E3%83%AA%E3%82%A2%E3%83%A9%E3%82%A4%E3%82%BA%E3%81%99%E3%82%8B%22%22%22%0A%20%20%20%20return%20list_to_tree_dfs%28arr%2C%200%29%0A%0A%0Adef%20pre_order%28root%3A%20TreeNode%29%3A%0A%20%20%20%20%22%22%22%E5%89%8D%E9%A0%86%E8%B5%B0%E6%9F%BB%EF%BC%9A%E4%BE%8B%E9%A1%8C%201%22%22%22%0A%20%20%20%20if%20root%20is%20None%3A%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20if%20root.val%20%3D%3D%207%3A%0A%20%20%20%20%20%20%20%20%23%20%E8%A7%A3%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20%20%20%20%20res.append%28root%29%0A%20%20%20%20pre_order%28root.left%29%0A%20%20%20%20pre_order%28root.right%29%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20root%20%3D%20list_to_tree%28%5B1%2C%207%2C%203%2C%204%2C%205%2C%206%2C%207%5D%29%0A%0A%20%20%20%20%23%20%E5%85%88%E8%A1%8C%E9%A0%86%E8%B5%B0%E6%9F%BB%0A%20%20%20%20res%20%3D%20list%5BTreeNode%5D%28%29%0A%20%20%20%20pre_order%28root%29%0A%0A%20%20%20%20print%28%22%5Cn%E5%80%A4%E3%81%8C%207%20%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E3%81%99%E3%81%B9%E3%81%A6%E5%87%BA%E5%8A%9B%22%29%0A%20%20%20%20print%28%5Bnode.val%20for%20node%20in%20res%5D%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=126&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%20%3D%200%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E5%80%A4%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%8F%B3%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%0Adef%20list_to_tree_dfs%28arr%3A%20list%5Bint%5D%2C%20i%3A%20int%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E4%BA%8C%E5%88%86%E6%9C%A8%E3%81%AB%E3%83%87%E3%82%B7%E3%83%AA%E3%82%A2%E3%83%A9%E3%82%A4%E3%82%BA%E3%81%99%E3%82%8B%3A%20%E5%86%8D%E5%B8%B0%22%22%22%0A%20%20%20%20%23%20%E6%B7%BB%E5%AD%97%E3%81%8C%E9%85%8D%E5%88%97%E9%95%B7%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%8B%E3%80%81%E5%AF%BE%E5%BF%9C%E3%81%99%E3%82%8B%E8%A6%81%E7%B4%A0%E3%81%8C%20None%20%E3%81%AA%E3%82%89%E3%80%81None%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20if%20i%20%3C%200%20or%20i%20%3E%3D%20len%28arr%29%20or%20arr%5Bi%5D%20is%20None%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%23%20%E7%8F%BE%E5%9C%A8%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20root%20%3D%20TreeNode%28arr%5Bi%5D%29%0A%20%20%20%20%23%20%E5%B7%A6%E5%8F%B3%E3%81%AE%E9%83%A8%E5%88%86%E6%9C%A8%E3%82%92%E5%86%8D%E5%B8%B0%E7%9A%84%E3%81%AB%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20root.left%20%3D%20list_to_tree_dfs%28arr%2C%202%20%2A%20i%20%2B%201%29%0A%20%20%20%20root.right%20%3D%20list_to_tree_dfs%28arr%2C%202%20%2A%20i%20%2B%202%29%0A%20%20%20%20return%20root%0A%0Adef%20list_to_tree%28arr%3A%20list%5Bint%5D%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E4%BA%8C%E5%88%86%E6%9C%A8%E3%81%AB%E3%83%87%E3%82%B7%E3%83%AA%E3%82%A2%E3%83%A9%E3%82%A4%E3%82%BA%E3%81%99%E3%82%8B%22%22%22%0A%20%20%20%20return%20list_to_tree_dfs%28arr%2C%200%29%0A%0A%0Adef%20pre_order%28root%3A%20TreeNode%29%3A%0A%20%20%20%20%22%22%22%E5%89%8D%E9%A0%86%E8%B5%B0%E6%9F%BB%EF%BC%9A%E4%BE%8B%E9%A1%8C%201%22%22%22%0A%20%20%20%20if%20root%20is%20None%3A%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20if%20root.val%20%3D%3D%207%3A%0A%20%20%20%20%20%20%20%20%23%20%E8%A7%A3%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20%20%20%20%20res.append%28root%29%0A%20%20%20%20pre_order%28root.left%29%0A%20%20%20%20pre_order%28root.right%29%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20root%20%3D%20list_to_tree%28%5B1%2C%207%2C%203%2C%204%2C%205%2C%206%2C%207%5D%29%0A%0A%20%20%20%20%23%20%E5%85%88%E8%A1%8C%E9%A0%86%E8%B5%B0%E6%9F%BB%0A%20%20%20%20res%20%3D%20list%5BTreeNode%5D%28%29%0A%20%20%20%20pre_order%28root%29%0A%0A%20%20%20%20print%28%22%5Cn%E5%80%A4%E3%81%8C%207%20%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E3%81%99%E3%81%B9%E3%81%A6%E5%87%BA%E5%8A%9B%22%29%0A%20%20%20%20print%28%5Bnode.val%20for%20node%20in%20res%5D%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=126&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p><img alt="前順走査でノードを探索する" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_nodes.png" /></p>
+<p align="center"> 図 13-1 &nbsp; 前順走査でノードを探索する </p>
 
-<h2 id="1311">13.1.1 &nbsp; 試行と後退<a class="headerlink" href="#1311" title="Permanent link">&para;</a></h2>
-<p><strong>解空間を探索する際に「試行」と「後退」戦略を使用するため、バックトラッキングアルゴリズムと呼ばれます</strong>。探索中、満足のいく解を得るためにもはや進めない状態に遭遇するたびに、前の選択を取り消して前の状態に戻り、次の試行のために他の可能な選択を選択できるようにします。</p>
-<p>例1では、各ノードの訪問が「試行」を開始します。そして葉ノードを通過するか、<code>return</code> 文で親ノードに戻ることが「後退」を示唆します。</p>
-<p><strong>後退は単に関数の戻り値ではないことに注意してください</strong>。例1の問題を少し拡張して、それが何を意味するかを説明します。</p>
+<h2 id="1311">13.1.1 &nbsp; 試行と戻る<a class="headerlink" href="#1311" title="Permanent link">&para;</a></h2>
+<p><strong>バックトラッキングアルゴリズムと呼ばれるのは、解空間を探索する際に「試行」と「戻る」という戦略を取るためです</strong>。探索中に、ある状態から先へ進めない、または条件を満たす解を得られないと分かった場合、アルゴリズムは直前の選択を取り消して前の状態へ戻り、別の選択肢を試します。</p>
+<p>例題1では、各ノードへの訪問が 1 回の「試行」に対応し、葉ノードを越えるか親ノードへ戻る <code>return</code> は「戻る」を表します。</p>
+<p>ここで強調しておきたいのは、**戻るとは関数の return だけを指すわけではない**という点です。これを説明するために、例題1を少し拡張します。</p>
 <div class="admonition question">
-<p class="admonition-title">例2</p>
-<p>二分木で、値が <span class="arithmatex">\(7\)</span> のすべてのノードを検索し、すべてのマッチングノードについて、<strong>ルートノードからそのノードまでのパスを返してください</strong>。</p>
+<p class="admonition-title">例題2</p>
+<p>二分木の中で値が <span class="arithmatex">\(7\)</span> のノードをすべて探索し、<strong>根ノードからそれらのノードまでの経路を返してください</strong>。</p>
 </div>
-<p>例1のコードに基づいて、訪問したノードパスを記録するために <code>path</code> というリストを使用する必要があります。値が <span class="arithmatex">\(7\)</span> のノードに到達すると、<code>path</code> をコピーして結果リスト <code>res</code> に追加します。走査後、<code>res</code> にはすべての解が保持されます。コードは以下の通りです：</p>
+<p>例題1のコードを土台に、訪問済みノードの経路を記録するためのリスト <code>path</code> を導入します。値が <span class="arithmatex">\(7\)</span> のノードに到達したら、<code>path</code> をコピーして結果リスト <code>res</code> に追加します。走査が完了すると、<code>res</code> にはすべての解が保存されています。コードは次のとおりです。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">preorder_traversal_ii_compact.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">):</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;前順走査：例二&quot;&quot;&quot;</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;前順走査：例題 2&quot;&quot;&quot;</span>
 <a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="k">if</span> <span class="n">root</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>        <span class="k">return</span>
-<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># 試行</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># 試す</span>
 <a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>    <span class="n">path</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
 <a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>    <span class="k">if</span> <span class="n">root</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="mi">7</span><span class="p">:</span>
 <a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>        <span class="c1"># 解を記録</span>
 <a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>        <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">path</span><span class="p">))</span>
 <a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>    <span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
 <a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>    <span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
-<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>    <span class="c1"># 撤回</span>
+<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>    <span class="c1"># バックトラック</span>
 <a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a>    <span class="n">path</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_ii_compact.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 前順走査：例２ */</span>
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 前順走査：例題 2 */</span>
 <a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="c1">// 試行</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="c1">// 試す</span>
 <a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">    </span><span class="n">path</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
 <a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">        </span><span class="c1">// 解を記録</span>
@@ -4580,18 +4695,18 @@
 <a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">);</span>
 <a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
-<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">    </span><span class="c1">// 回退</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">    </span><span class="c1">// バックトラック</span>
 <a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">    </span><span class="n">path</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
 <a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_ii_compact.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 前順走査：例２ */</span>
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 前順走査：例題 2 */</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="c1">// 試行</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="c1">// 試す</span>
 <a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="n">path</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
 <a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">        </span><span class="c1">// 解を記録</span>
@@ -4599,59 +4714,232 @@
 <a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">);</span>
 <a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">);</span>
-<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">    </span><span class="c1">// 回退</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">    </span><span class="c1">// バックトラック</span>
 <a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="n">path</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">path</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_ii_compact.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">preorder_traversal_ii_compact</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">PreOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 前順走査：例題 2 */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">PreOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="c1">// 試す</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="n">path</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="p">(</span><span class="n">path</span><span class="p">));</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">    </span><span class="n">PreOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">left</span><span class="p">);</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">    </span><span class="n">PreOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">    </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">    </span><span class="n">path</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="n">path</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_ii_compact.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">preOrderII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 前順走査：例題 2 */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">preOrderII</span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">*</span><span class="p">[][]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">    </span><span class="c1">// 試す</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">    </span><span class="o">*</span><span class="nx">path</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">path</span><span class="p">,</span><span class="w"> </span><span class="nx">root</span><span class="p">)</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">root</span><span class="p">.</span><span class="nx">Val</span><span class="p">.(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">        </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nb">append</span><span class="p">([]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">{},</span><span class="w"> </span><span class="o">*</span><span class="nx">path</span><span class="o">...</span><span class="p">))</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">    </span><span class="nx">preOrderII</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">Left</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">)</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w">    </span><span class="nx">preOrderII</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">Right</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">)</span>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w">    </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">    </span><span class="o">*</span><span class="nx">path</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">path</span><span class="p">)[:</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">path</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_ii_compact.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 前順走査：例題 2 */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="k">guard</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">root</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">    </span><span class="c1">// 試す</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">    </span><span class="n">path</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">7</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">path</span><span class="p">)</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="kr">left</span><span class="p">)</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="kr">right</span><span class="p">)</span>
+<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="w">    </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w">    </span><span class="n">path</span><span class="p">.</span><span class="bp">removeLast</span><span class="p">()</span>
+<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_ii_compact.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">preOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 前順走査：例題 2 */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">    </span><span class="c1">// 試す</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">    </span><span class="nx">path</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">root</span><span class="p">);</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w">        </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">([...</span><span class="nx">path</span><span class="p">]);</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">    </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w">    </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">right</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w">    </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w">    </span><span class="nx">path</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_ii_compact.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">preOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 前順走査：例題 2 */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="nx">root</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="nx">path</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[],</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">    </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[][]</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">    </span><span class="c1">// 試す</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w">    </span><span class="nx">path</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">root</span><span class="p">);</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w">        </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">([...</span><span class="nx">path</span><span class="p">]);</span>
+<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a><span class="w">    </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-20-17" name="__codelineno-20-17" href="#__codelineno-20-17"></a><span class="w">    </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">right</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-20-18" name="__codelineno-20-18" href="#__codelineno-20-18"></a><span class="w">    </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-20-19" name="__codelineno-20-19" href="#__codelineno-20-19"></a><span class="w">    </span><span class="nx">path</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-20-20" name="__codelineno-20-20" href="#__codelineno-20-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_ii_compact.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 前順走査：例題 2 */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="p">,</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">path</span><span class="p">,</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">,</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">    </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="w">  </span><span class="c1">// 試す</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w">  </span><span class="n">path</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w">    </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">List</span><span class="p">.</span><span class="n">from</span><span class="p">(</span><span class="n">path</span><span class="p">));</span>
+<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-17" name="__codelineno-21-17" href="#__codelineno-21-17"></a><span class="w">  </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-21-18" name="__codelineno-21-18" href="#__codelineno-21-18"></a><span class="w">  </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-21-19" name="__codelineno-21-19" href="#__codelineno-21-19"></a><span class="w">  </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-21-20" name="__codelineno-21-20" href="#__codelineno-21-20"></a><span class="w">  </span><span class="n">path</span><span class="p">.</span><span class="n">removeLast</span><span class="p">();</span>
+<a id="__codelineno-21-21" name="__codelineno-21-21" href="#__codelineno-21-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_ii_compact.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">pre_order</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 前順走査：例題 2 */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="n">path</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">    </span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w">        </span><span class="c1">// 試す</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">        </span><span class="n">path</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">            </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">path</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="w">        </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">());</span>
+<a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="w">        </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">());</span>
+<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="w">        </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a><span class="w">        </span><span class="n">path</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
+<a id="__codelineno-22-21" name="__codelineno-22-21" href="#__codelineno-22-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-22" name="__codelineno-22-22" href="#__codelineno-22-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_ii_compact.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 前順走査：例題 2 */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w">    </span><span class="c1">// 試す</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w">    </span><span class="n">path</span><span class="p">[</span><span class="n">pathSize</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">pathSize</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">resSize</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">path</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w">        </span><span class="n">resSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">);</span>
+<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="w">    </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="w">    </span><span class="n">pathSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_ii_compact.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">preOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 前順走査：例題 2 */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">    </span><span class="c1">// 試す</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w">    </span><span class="n">path</span><span class="o">!!</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">_val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w">        </span><span class="n">res</span><span class="o">!!</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">path</span><span class="o">!!</span><span class="p">.</span><span class="na">toMutableList</span><span class="p">())</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">)</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">)</span>
+<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w">    </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="w">    </span><span class="n">path</span><span class="o">!!</span><span class="p">.</span><span class="na">removeAt</span><span class="p">(</span><span class="n">path</span><span class="o">!!</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_ii_compact.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">pre_order</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### 前順走査：例題2 ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">root</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">  </span><span class="c1"># 試す</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">  </span><span class="vg">$path</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">root</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w">  </span><span class="c1"># 解を記録</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">  </span><span class="vg">$res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="vg">$path</span><span class="o">.</span><span class="n">dup</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w">  </span><span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w">  </span><span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a>
+<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w">  </span><span class="c1"># バックトラック</span>
+<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w">  </span><span class="vg">$path</span><span class="o">.</span><span class="n">pop</span>
+<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>各「試行」で、現在のノードを <code>path</code> に追加することでパスを記録します。「後退」が必要なときはいつでも、<code>path</code> からノードをポップして**この失敗した試行前の状態を復元します**。</p>
-<p>以下の図に示すプロセスを観察することで、<strong>試行は「前進」のようで、後退は「元に戻す」のようです</strong>。後者のペアは、対応するものに対する逆操作と見なすことができます。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%20%3D%200%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E5%80%A4%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%8F%B3%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%0Adef%20list_to_tree_dfs%28arr%3A%20list%5Bint%5D%2C%20i%3A%20int%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E4%BA%8C%E5%88%86%E6%9C%A8%E3%81%AB%E3%83%87%E3%82%B7%E3%83%AA%E3%82%A2%E3%83%A9%E3%82%A4%E3%82%BA%E3%81%99%E3%82%8B%3A%20%E5%86%8D%E5%B8%B0%22%22%22%0A%20%20%20%20%23%20%E6%B7%BB%E5%AD%97%E3%81%8C%E9%85%8D%E5%88%97%E9%95%B7%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%8B%E3%80%81%E5%AF%BE%E5%BF%9C%E3%81%99%E3%82%8B%E8%A6%81%E7%B4%A0%E3%81%8C%20None%20%E3%81%AA%E3%82%89%E3%80%81None%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20if%20i%20%3C%200%20or%20i%20%3E%3D%20len%28arr%29%20or%20arr%5Bi%5D%20is%20None%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%23%20%E7%8F%BE%E5%9C%A8%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20root%20%3D%20TreeNode%28arr%5Bi%5D%29%0A%20%20%20%20%23%20%E5%B7%A6%E5%8F%B3%E3%81%AE%E9%83%A8%E5%88%86%E6%9C%A8%E3%82%92%E5%86%8D%E5%B8%B0%E7%9A%84%E3%81%AB%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20root.left%20%3D%20list_to_tree_dfs%28arr%2C%202%20%2A%20i%20%2B%201%29%0A%20%20%20%20root.right%20%3D%20list_to_tree_dfs%28arr%2C%202%20%2A%20i%20%2B%202%29%0A%20%20%20%20return%20root%0A%0Adef%20list_to_tree%28arr%3A%20list%5Bint%5D%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E4%BA%8C%E5%88%86%E6%9C%A8%E3%81%AB%E3%83%87%E3%82%B7%E3%83%AA%E3%82%A2%E3%83%A9%E3%82%A4%E3%82%BA%E3%81%99%E3%82%8B%22%22%22%0A%20%20%20%20return%20list_to_tree_dfs%28arr%2C%200%29%0A%0A%0Adef%20pre_order%28root%3A%20TreeNode%29%3A%0A%20%20%20%20%22%22%22%E5%89%8D%E9%A0%86%E8%B5%B0%E6%9F%BB%EF%BC%9A%E4%BE%8B%E9%A1%8C%202%22%22%22%0A%20%20%20%20if%20root%20is%20None%3A%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20%23%20%E8%A9%A6%E3%81%99%0A%20%20%20%20path.append%28root%29%0A%20%20%20%20if%20root.val%20%3D%3D%207%3A%0A%20%20%20%20%20%20%20%20%23%20%E8%A7%A3%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20%20%20%20%20res.append%28list%28path%29%29%0A%20%20%20%20pre_order%28root.left%29%0A%20%20%20%20pre_order%28root.right%29%0A%20%20%20%20%23%20%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AF%0A%20%20%20%20path.pop%28%29%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20root%20%3D%20list_to_tree%28%5B1%2C%207%2C%203%2C%204%2C%205%2C%206%2C%207%5D%29%0A%0A%20%20%20%20%23%20%E5%85%88%E8%A1%8C%E9%A0%86%E8%B5%B0%E6%9F%BB%0A%20%20%20%20path%20%3D%20list%5BTreeNode%5D%28%29%0A%20%20%20%20res%20%3D%20list%5Blist%5BTreeNode%5D%5D%28%29%0A%20%20%20%20pre_order%28root%29%0A%0A%20%20%20%20print%28%22%5Cn%E6%A0%B9%E3%83%8E%E3%83%BC%E3%83%89%E3%81%8B%E3%82%89%E3%83%8E%E3%83%BC%E3%83%89%207%20%E3%81%BE%E3%81%A7%E3%81%AE%E7%B5%8C%E8%B7%AF%E3%82%92%E3%81%99%E3%81%B9%E3%81%A6%E5%87%BA%E5%8A%9B%22%29%0A%20%20%20%20for%20path%20in%20res%3A%0A%20%20%20%20%20%20%20%20print%28%5Bnode.val%20for%20node%20in%20path%5D%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=126&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%20%3D%200%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E5%80%A4%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%8F%B3%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%0Adef%20list_to_tree_dfs%28arr%3A%20list%5Bint%5D%2C%20i%3A%20int%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E4%BA%8C%E5%88%86%E6%9C%A8%E3%81%AB%E3%83%87%E3%82%B7%E3%83%AA%E3%82%A2%E3%83%A9%E3%82%A4%E3%82%BA%E3%81%99%E3%82%8B%3A%20%E5%86%8D%E5%B8%B0%22%22%22%0A%20%20%20%20%23%20%E6%B7%BB%E5%AD%97%E3%81%8C%E9%85%8D%E5%88%97%E9%95%B7%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%8B%E3%80%81%E5%AF%BE%E5%BF%9C%E3%81%99%E3%82%8B%E8%A6%81%E7%B4%A0%E3%81%8C%20None%20%E3%81%AA%E3%82%89%E3%80%81None%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20if%20i%20%3C%200%20or%20i%20%3E%3D%20len%28arr%29%20or%20arr%5Bi%5D%20is%20None%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%23%20%E7%8F%BE%E5%9C%A8%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20root%20%3D%20TreeNode%28arr%5Bi%5D%29%0A%20%20%20%20%23%20%E5%B7%A6%E5%8F%B3%E3%81%AE%E9%83%A8%E5%88%86%E6%9C%A8%E3%82%92%E5%86%8D%E5%B8%B0%E7%9A%84%E3%81%AB%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20root.left%20%3D%20list_to_tree_dfs%28arr%2C%202%20%2A%20i%20%2B%201%29%0A%20%20%20%20root.right%20%3D%20list_to_tree_dfs%28arr%2C%202%20%2A%20i%20%2B%202%29%0A%20%20%20%20return%20root%0A%0Adef%20list_to_tree%28arr%3A%20list%5Bint%5D%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E4%BA%8C%E5%88%86%E6%9C%A8%E3%81%AB%E3%83%87%E3%82%B7%E3%83%AA%E3%82%A2%E3%83%A9%E3%82%A4%E3%82%BA%E3%81%99%E3%82%8B%22%22%22%0A%20%20%20%20return%20list_to_tree_dfs%28arr%2C%200%29%0A%0A%0Adef%20pre_order%28root%3A%20TreeNode%29%3A%0A%20%20%20%20%22%22%22%E5%89%8D%E9%A0%86%E8%B5%B0%E6%9F%BB%EF%BC%9A%E4%BE%8B%E9%A1%8C%202%22%22%22%0A%20%20%20%20if%20root%20is%20None%3A%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20%23%20%E8%A9%A6%E3%81%99%0A%20%20%20%20path.append%28root%29%0A%20%20%20%20if%20root.val%20%3D%3D%207%3A%0A%20%20%20%20%20%20%20%20%23%20%E8%A7%A3%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20%20%20%20%20res.append%28list%28path%29%29%0A%20%20%20%20pre_order%28root.left%29%0A%20%20%20%20pre_order%28root.right%29%0A%20%20%20%20%23%20%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AF%0A%20%20%20%20path.pop%28%29%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20root%20%3D%20list_to_tree%28%5B1%2C%207%2C%203%2C%204%2C%205%2C%206%2C%207%5D%29%0A%0A%20%20%20%20%23%20%E5%85%88%E8%A1%8C%E9%A0%86%E8%B5%B0%E6%9F%BB%0A%20%20%20%20path%20%3D%20list%5BTreeNode%5D%28%29%0A%20%20%20%20res%20%3D%20list%5Blist%5BTreeNode%5D%5D%28%29%0A%20%20%20%20pre_order%28root%29%0A%0A%20%20%20%20print%28%22%5Cn%E6%A0%B9%E3%83%8E%E3%83%BC%E3%83%89%E3%81%8B%E3%82%89%E3%83%8E%E3%83%BC%E3%83%89%207%20%E3%81%BE%E3%81%A7%E3%81%AE%E7%B5%8C%E8%B7%AF%E3%82%92%E3%81%99%E3%81%B9%E3%81%A6%E5%87%BA%E5%8A%9B%22%29%0A%20%20%20%20for%20path%20in%20res%3A%0A%20%20%20%20%20%20%20%20print%28%5Bnode.val%20for%20node%20in%20path%5D%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=126&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>各「試行」で現在のノードを <code>path</code> に追加して経路を記録し、「戻る」前にはそのノードを <code>path</code> から取り除き、**今回の試行前の状態を復元する**必要があります。</p>
+<p>次の図に示す過程を見ると、<strong>試行と戻るは「前進」と「取り消し」として理解できます</strong>。この 2 つの操作は互いに逆向きです。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="3:11"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">&lt;1&gt;</label><label for="__tabbed_3_2">&lt;2&gt;</label><label for="__tabbed_3_3">&lt;3&gt;</label><label for="__tabbed_3_4">&lt;4&gt;</label><label for="__tabbed_3_5">&lt;5&gt;</label><label for="__tabbed_3_6">&lt;6&gt;</label><label for="__tabbed_3_7">&lt;7&gt;</label><label for="__tabbed_3_8">&lt;8&gt;</label><label for="__tabbed_3_9">&lt;9&gt;</label><label for="__tabbed_3_10">&lt;10&gt;</label><label for="__tabbed_3_11">&lt;11&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="試行と後退" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_paths_step1.png" /></p>
+<p><img alt="試行と戻る" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_paths_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="preorder_find_paths_step2" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_paths_step2.png" /></p>
@@ -4685,42 +4973,42 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 13-2 &nbsp; 試行と後退 </p>
+<p align="center"> 図 13-2 &nbsp; 試行と戻る </p>
 
-<h2 id="1312">13.1.2 &nbsp; 剪定<a class="headerlink" href="#1312" title="Permanent link">&para;</a></h2>
-<p>複雑なバックトラッキング問題は通常1つ以上の制約を含み、<strong>これらは「剪定」によく使用されます</strong>。</p>
+<h2 id="1312">13.1.2 &nbsp; 枝刈り<a class="headerlink" href="#1312" title="Permanent link">&para;</a></h2>
+<p>複雑なバックトラッキング問題には、通常 1 つ以上の制約条件が含まれます。<strong>制約条件は多くの場合「枝刈り」に利用できます</strong>。</p>
 <div class="admonition question">
-<p class="admonition-title">例3</p>
-<p>二分木で、値が <span class="arithmatex">\(7\)</span> のすべてのノードを検索し、ルートからこれらのノードまでのパスを返してください。<strong>ただし、パスには値が <span class="arithmatex">\(3\)</span> のノードを含まないという制限があります</strong>。</p>
+<p class="admonition-title">例題3</p>
+<p>二分木の中で値が <span class="arithmatex">\(7\)</span> のノードをすべて探索し、根ノードからそれらのノードまでの経路を返してください。<strong>ただし、経路には値が <span class="arithmatex">\(3\)</span> のノードを含めてはいけません</strong>。</p>
 </div>
-<p>上記の制約を満たすために、<strong>剪定操作を追加する必要があります</strong>：検索プロセス中に、値が <span class="arithmatex">\(3\)</span> のノードに遭遇した場合、そのパスを通じてさらに検索することを即座に中止します。コードは以下の通りです：</p>
+<p>上の制約条件を満たすために、<strong>枝刈り操作を追加する必要があります</strong>。探索中に値が <span class="arithmatex">\(3\)</span> のノードに出会った場合は、そこで早めに return し、それ以上探索を続けません。コードは次のとおりです。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="4:13"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">preorder_traversal_iii_compact.py</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">):</span>
-<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;前順走査：例三&quot;&quot;&quot;</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;前順走査：例題 3&quot;&quot;&quot;</span>
 <a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>    <span class="c1"># 枝刈り</span>
 <a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>    <span class="k">if</span> <span class="n">root</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">root</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="mi">3</span><span class="p">:</span>
 <a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a>        <span class="k">return</span>
-<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a>    <span class="c1"># 試行</span>
+<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a>    <span class="c1"># 試す</span>
 <a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a>    <span class="n">path</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
 <a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>    <span class="k">if</span> <span class="n">root</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="mi">7</span><span class="p">:</span>
 <a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a>        <span class="c1"># 解を記録</span>
 <a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a>        <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">path</span><span class="p">))</span>
 <a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a>    <span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
 <a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a>    <span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
-<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a>    <span class="c1"># 撤回</span>
+<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a>    <span class="c1"># バックトラック</span>
 <a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a>    <span class="n">path</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_iii_compact.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* 前順走査：例３ */</span>
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* 前順走査：例題 3 */</span>
 <a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="c1">// 剪定</span>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="c1">// 枝刈り</span>
 <a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">root</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">    </span><span class="c1">// 試行</span>
+<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">    </span><span class="c1">// 試す</span>
 <a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w">    </span><span class="n">path</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
 <a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a><span class="w">        </span><span class="c1">// 解を記録</span>
@@ -4728,19 +5016,19 @@
 <a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">);</span>
 <a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
-<a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="w">    </span><span class="c1">// 回退</span>
+<a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="w">    </span><span class="c1">// バックトラック</span>
 <a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></a><span class="w">    </span><span class="n">path</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
 <a id="__codelineno-27-17" name="__codelineno-27-17" href="#__codelineno-27-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_iii_compact.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 前順走査：例３ */</span>
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 前順走査：例題 3 */</span>
 <a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="c1">// 剪定</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="c1">// 枝刈り</span>
 <a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">    </span><span class="c1">// 試行</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">    </span><span class="c1">// 試す</span>
 <a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">    </span><span class="n">path</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
 <a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="w">        </span><span class="c1">// 解を記録</span>
@@ -4748,100 +5036,282 @@
 <a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">);</span>
 <a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">);</span>
-<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="w">    </span><span class="c1">// 回退</span>
+<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="w">    </span><span class="c1">// バックトラック</span>
 <a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a><span class="w">    </span><span class="n">path</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">path</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_iii_compact.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">preorder_traversal_iii_compact</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">PreOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 前順走査：例題 3 */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">PreOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="c1">// 枝刈り</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="c1">// 試す</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">    </span><span class="n">path</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="p">(</span><span class="n">path</span><span class="p">));</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w">    </span><span class="n">PreOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">left</span><span class="p">);</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w">    </span><span class="n">PreOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="w">    </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w">    </span><span class="n">path</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="n">path</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_iii_compact.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">preOrderIII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 前順走査：例題 3 */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">preOrderIII</span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">*</span><span class="p">[][]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="c1">// 枝刈り</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">root</span><span class="p">.</span><span class="nx">Val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">    </span><span class="c1">// 試す</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">    </span><span class="o">*</span><span class="nx">path</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">path</span><span class="p">,</span><span class="w"> </span><span class="nx">root</span><span class="p">)</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">root</span><span class="p">.</span><span class="nx">Val</span><span class="p">.(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w">        </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nb">append</span><span class="p">([]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">{},</span><span class="w"> </span><span class="o">*</span><span class="nx">path</span><span class="o">...</span><span class="p">))</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w">    </span><span class="nx">preOrderIII</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">Left</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">)</span>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w">    </span><span class="nx">preOrderIII</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">Right</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">)</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w">    </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w">    </span><span class="o">*</span><span class="nx">path</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">path</span><span class="p">)[:</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">path</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_iii_compact.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* 前順走査：例題 3 */</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w">    </span><span class="c1">// 枝刈り</span>
+<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w">    </span><span class="k">guard</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">root</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w">    </span><span class="c1">// 試す</span>
+<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w">    </span><span class="n">path</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
+<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">7</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">path</span><span class="p">)</span>
+<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="kr">left</span><span class="p">)</span>
+<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="kr">right</span><span class="p">)</span>
+<a id="__codelineno-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></a><span class="w">    </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-31-16" name="__codelineno-31-16" href="#__codelineno-31-16"></a><span class="w">    </span><span class="n">path</span><span class="p">.</span><span class="bp">removeLast</span><span class="p">()</span>
+<a id="__codelineno-31-17" name="__codelineno-31-17" href="#__codelineno-31-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_iii_compact.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">preOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* 前順走査：例題 3 */</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w">    </span><span class="c1">// 枝刈り</span>
+<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">root</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="w">    </span><span class="c1">// 試す</span>
+<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w">    </span><span class="nx">path</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">root</span><span class="p">);</span>
+<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-10" name="__codelineno-32-10" href="#__codelineno-32-10"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a><span class="w">        </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">([...</span><span class="nx">path</span><span class="p">]);</span>
+<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a><span class="w">    </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-32-14" name="__codelineno-32-14" href="#__codelineno-32-14"></a><span class="w">    </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">right</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-32-15" name="__codelineno-32-15" href="#__codelineno-32-15"></a><span class="w">    </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-32-16" name="__codelineno-32-16" href="#__codelineno-32-16"></a><span class="w">    </span><span class="nx">path</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-32-17" name="__codelineno-32-17" href="#__codelineno-32-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_iii_compact.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">preOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* 前順走査：例題 3 */</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w">    </span><span class="nx">root</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span>
+<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w">    </span><span class="nx">path</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[],</span>
+<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w">    </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[][]</span>
+<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w">    </span><span class="c1">// 枝刈り</span>
+<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">root</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="w">    </span><span class="c1">// 試す</span>
+<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="w">    </span><span class="nx">path</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">root</span><span class="p">);</span>
+<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a><span class="w">        </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">([...</span><span class="nx">path</span><span class="p">]);</span>
+<a id="__codelineno-33-16" name="__codelineno-33-16" href="#__codelineno-33-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-17" name="__codelineno-33-17" href="#__codelineno-33-17"></a><span class="w">    </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-33-18" name="__codelineno-33-18" href="#__codelineno-33-18"></a><span class="w">    </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">right</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-33-19" name="__codelineno-33-19" href="#__codelineno-33-19"></a><span class="w">    </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-33-20" name="__codelineno-33-20" href="#__codelineno-33-20"></a><span class="w">    </span><span class="nx">path</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-33-21" name="__codelineno-33-21" href="#__codelineno-33-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_iii_compact.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* 前順走査：例題 3 */</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="p">,</span>
+<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">path</span><span class="p">,</span>
+<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">,</span>
+<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w">    </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-10" name="__codelineno-34-10" href="#__codelineno-34-10"></a>
+<a id="__codelineno-34-11" name="__codelineno-34-11" href="#__codelineno-34-11"></a><span class="w">  </span><span class="c1">// 試す</span>
+<a id="__codelineno-34-12" name="__codelineno-34-12" href="#__codelineno-34-12"></a><span class="w">  </span><span class="n">path</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
+<a id="__codelineno-34-13" name="__codelineno-34-13" href="#__codelineno-34-13"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-14" name="__codelineno-34-14" href="#__codelineno-34-14"></a><span class="w">    </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-34-15" name="__codelineno-34-15" href="#__codelineno-34-15"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">List</span><span class="p">.</span><span class="n">from</span><span class="p">(</span><span class="n">path</span><span class="p">));</span>
+<a id="__codelineno-34-16" name="__codelineno-34-16" href="#__codelineno-34-16"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-17" name="__codelineno-34-17" href="#__codelineno-34-17"></a><span class="w">  </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-34-18" name="__codelineno-34-18" href="#__codelineno-34-18"></a><span class="w">  </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-34-19" name="__codelineno-34-19" href="#__codelineno-34-19"></a><span class="w">  </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-34-20" name="__codelineno-34-20" href="#__codelineno-34-20"></a><span class="w">  </span><span class="n">path</span><span class="p">.</span><span class="n">removeLast</span><span class="p">();</span>
+<a id="__codelineno-34-21" name="__codelineno-34-21" href="#__codelineno-34-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_iii_compact.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">pre_order</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* 前順走査：例題 3 */</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w">    </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="w">    </span><span class="n">path</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="w">    </span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="w">    </span><span class="c1">// 枝刈り</span>
+<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">as_ref</span><span class="p">().</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-12" name="__codelineno-35-12" href="#__codelineno-35-12"></a><span class="w">        </span><span class="c1">// 試す</span>
+<a id="__codelineno-35-13" name="__codelineno-35-13" href="#__codelineno-35-13"></a><span class="w">        </span><span class="n">path</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-35-14" name="__codelineno-35-14" href="#__codelineno-35-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-15" name="__codelineno-35-15" href="#__codelineno-35-15"></a><span class="w">            </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-35-16" name="__codelineno-35-16" href="#__codelineno-35-16"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">path</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-35-17" name="__codelineno-35-17" href="#__codelineno-35-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-35-18" name="__codelineno-35-18" href="#__codelineno-35-18"></a><span class="w">        </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">());</span>
+<a id="__codelineno-35-19" name="__codelineno-35-19" href="#__codelineno-35-19"></a><span class="w">        </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">());</span>
+<a id="__codelineno-35-20" name="__codelineno-35-20" href="#__codelineno-35-20"></a><span class="w">        </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-35-21" name="__codelineno-35-21" href="#__codelineno-35-21"></a><span class="w">        </span><span class="n">path</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
+<a id="__codelineno-35-22" name="__codelineno-35-22" href="#__codelineno-35-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-23" name="__codelineno-35-23" href="#__codelineno-35-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_iii_compact.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* 前順走査：例題 3 */</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w">    </span><span class="c1">// 枝刈り</span>
+<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">root</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="w">    </span><span class="c1">// 試す</span>
+<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="w">    </span><span class="n">path</span><span class="p">[</span><span class="n">pathSize</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
+<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">pathSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">resSize</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">path</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-36-14" name="__codelineno-36-14" href="#__codelineno-36-14"></a><span class="w">        </span><span class="n">resSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-36-15" name="__codelineno-36-15" href="#__codelineno-36-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-16" name="__codelineno-36-16" href="#__codelineno-36-16"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">);</span>
+<a id="__codelineno-36-17" name="__codelineno-36-17" href="#__codelineno-36-17"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-36-18" name="__codelineno-36-18" href="#__codelineno-36-18"></a><span class="w">    </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-36-19" name="__codelineno-36-19" href="#__codelineno-36-19"></a><span class="w">    </span><span class="n">pathSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-36-20" name="__codelineno-36-20" href="#__codelineno-36-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_iii_compact.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">preOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* 前順走査：例題 3 */</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w">    </span><span class="c1">// 枝刈り</span>
+<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="na">_val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w">    </span><span class="c1">// 試す</span>
+<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="w">    </span><span class="n">path</span><span class="o">!!</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
+<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">_val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a><span class="w">        </span><span class="n">res</span><span class="o">!!</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">path</span><span class="o">!!</span><span class="p">.</span><span class="na">toMutableList</span><span class="p">())</span>
+<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">)</span>
+<a id="__codelineno-37-14" name="__codelineno-37-14" href="#__codelineno-37-14"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">)</span>
+<a id="__codelineno-37-15" name="__codelineno-37-15" href="#__codelineno-37-15"></a><span class="w">    </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-37-16" name="__codelineno-37-16" href="#__codelineno-37-16"></a><span class="w">    </span><span class="n">path</span><span class="o">!!</span><span class="p">.</span><span class="na">removeAt</span><span class="p">(</span><span class="n">path</span><span class="o">!!</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-37-17" name="__codelineno-37-17" href="#__codelineno-37-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_iii_compact.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">pre_order</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="c1">### 前順走査：例題3 ###</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w">  </span><span class="c1"># 枝刈り</span>
+<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="o">!</span><span class="n">root</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">3</span>
+<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a>
+<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w">  </span><span class="c1"># 試す</span>
+<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="w">  </span><span class="vg">$path</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
+<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a>
+<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="w">  </span><span class="c1"># 解を記録</span>
+<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a><span class="w">  </span><span class="vg">$res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="vg">$path</span><span class="o">.</span><span class="n">dup</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span>
+<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a>
+<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a><span class="w">  </span><span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
+<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a><span class="w">  </span><span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a>
+<a id="__codelineno-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a><span class="w">  </span><span class="c1"># バックトラック</span>
+<a id="__codelineno-38-16" name="__codelineno-38-16" href="#__codelineno-38-16"></a><span class="w">  </span><span class="vg">$path</span><span class="o">.</span><span class="n">pop</span>
+<a id="__codelineno-38-17" name="__codelineno-38-17" href="#__codelineno-38-17"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>「剪定」は非常に生き生きとした名詞です。以下の図に示すように、検索プロセスで、<strong>制約を満たさない検索分岐を「切り取り」ます</strong>。さらなる不要な試行を避け、検索効率を向上させます。</p>
-<p><img alt="制約に基づく剪定" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_constrained_paths.png" /></p>
-<p align="center"> 図 13-3 &nbsp; 制約に基づく剪定 </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%20%3D%200%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E5%80%A4%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%8F%B3%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%0Adef%20list_to_tree_dfs%28arr%3A%20list%5Bint%5D%2C%20i%3A%20int%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E4%BA%8C%E5%88%86%E6%9C%A8%E3%81%AB%E3%83%87%E3%82%B7%E3%83%AA%E3%82%A2%E3%83%A9%E3%82%A4%E3%82%BA%E3%81%99%E3%82%8B%3A%20%E5%86%8D%E5%B8%B0%22%22%22%0A%20%20%20%20%23%20%E6%B7%BB%E5%AD%97%E3%81%8C%E9%85%8D%E5%88%97%E9%95%B7%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%8B%E3%80%81%E5%AF%BE%E5%BF%9C%E3%81%99%E3%82%8B%E8%A6%81%E7%B4%A0%E3%81%8C%20None%20%E3%81%AA%E3%82%89%E3%80%81None%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20if%20i%20%3C%200%20or%20i%20%3E%3D%20len%28arr%29%20or%20arr%5Bi%5D%20is%20None%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%23%20%E7%8F%BE%E5%9C%A8%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20root%20%3D%20TreeNode%28arr%5Bi%5D%29%0A%20%20%20%20%23%20%E5%B7%A6%E5%8F%B3%E3%81%AE%E9%83%A8%E5%88%86%E6%9C%A8%E3%82%92%E5%86%8D%E5%B8%B0%E7%9A%84%E3%81%AB%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20root.left%20%3D%20list_to_tree_dfs%28arr%2C%202%20%2A%20i%20%2B%201%29%0A%20%20%20%20root.right%20%3D%20list_to_tree_dfs%28arr%2C%202%20%2A%20i%20%2B%202%29%0A%20%20%20%20return%20root%0A%0Adef%20list_to_tree%28arr%3A%20list%5Bint%5D%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E4%BA%8C%E5%88%86%E6%9C%A8%E3%81%AB%E3%83%87%E3%82%B7%E3%83%AA%E3%82%A2%E3%83%A9%E3%82%A4%E3%82%BA%E3%81%99%E3%82%8B%22%22%22%0A%20%20%20%20return%20list_to_tree_dfs%28arr%2C%200%29%0A%0A%0Adef%20pre_order%28root%3A%20TreeNode%29%3A%0A%20%20%20%20%22%22%22%E5%89%8D%E9%A0%86%E8%B5%B0%E6%9F%BB%EF%BC%9A%E4%BE%8B%E9%A1%8C%203%22%22%22%0A%20%20%20%20%23%20%E6%9E%9D%E5%88%88%E3%82%8A%0A%20%20%20%20if%20root%20is%20None%20or%20root.val%20%3D%3D%203%3A%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20%23%20%E8%A9%A6%E3%81%99%0A%20%20%20%20path.append%28root%29%0A%20%20%20%20if%20root.val%20%3D%3D%207%3A%0A%20%20%20%20%20%20%20%20%23%20%E8%A7%A3%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20%20%20%20%20res.append%28list%28path%29%29%0A%20%20%20%20pre_order%28root.left%29%0A%20%20%20%20pre_order%28root.right%29%0A%20%20%20%20%23%20%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AF%0A%20%20%20%20path.pop%28%29%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20root%20%3D%20list_to_tree%28%5B1%2C%207%2C%203%2C%204%2C%205%2C%206%2C%207%5D%29%0A%0A%20%20%20%20%23%20%E5%85%88%E8%A1%8C%E9%A0%86%E8%B5%B0%E6%9F%BB%0A%20%20%20%20path%20%3D%20list%5BTreeNode%5D%28%29%0A%20%20%20%20res%20%3D%20list%5Blist%5BTreeNode%5D%5D%28%29%0A%20%20%20%20pre_order%28root%29%0A%0A%20%20%20%20print%28%22%5Cn%E6%A0%B9%E3%83%8E%E3%83%BC%E3%83%89%E3%81%8B%E3%82%89%E3%83%8E%E3%83%BC%E3%83%89%207%20%E3%81%BE%E3%81%A7%E3%81%AE%E7%B5%8C%E8%B7%AF%E3%82%92%E3%81%99%E3%81%B9%E3%81%A6%E5%87%BA%E5%8A%9B%E3%81%97%E3%80%81%E7%B5%8C%E8%B7%AF%E3%81%AB%E3%81%AF%E5%80%A4%E3%81%8C%203%20%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E5%90%AB%E3%82%81%E3%81%AA%E3%81%84%22%29%0A%20%20%20%20for%20path%20in%20res%3A%0A%20%20%20%20%20%20%20%20print%28%5Bnode.val%20for%20node%20in%20path%5D%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=126&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%20%3D%200%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E5%80%A4%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%8F%B3%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%0Adef%20list_to_tree_dfs%28arr%3A%20list%5Bint%5D%2C%20i%3A%20int%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E4%BA%8C%E5%88%86%E6%9C%A8%E3%81%AB%E3%83%87%E3%82%B7%E3%83%AA%E3%82%A2%E3%83%A9%E3%82%A4%E3%82%BA%E3%81%99%E3%82%8B%3A%20%E5%86%8D%E5%B8%B0%22%22%22%0A%20%20%20%20%23%20%E6%B7%BB%E5%AD%97%E3%81%8C%E9%85%8D%E5%88%97%E9%95%B7%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%8B%E3%80%81%E5%AF%BE%E5%BF%9C%E3%81%99%E3%82%8B%E8%A6%81%E7%B4%A0%E3%81%8C%20None%20%E3%81%AA%E3%82%89%E3%80%81None%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20if%20i%20%3C%200%20or%20i%20%3E%3D%20len%28arr%29%20or%20arr%5Bi%5D%20is%20None%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%23%20%E7%8F%BE%E5%9C%A8%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20root%20%3D%20TreeNode%28arr%5Bi%5D%29%0A%20%20%20%20%23%20%E5%B7%A6%E5%8F%B3%E3%81%AE%E9%83%A8%E5%88%86%E6%9C%A8%E3%82%92%E5%86%8D%E5%B8%B0%E7%9A%84%E3%81%AB%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20root.left%20%3D%20list_to_tree_dfs%28arr%2C%202%20%2A%20i%20%2B%201%29%0A%20%20%20%20root.right%20%3D%20list_to_tree_dfs%28arr%2C%202%20%2A%20i%20%2B%202%29%0A%20%20%20%20return%20root%0A%0Adef%20list_to_tree%28arr%3A%20list%5Bint%5D%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E4%BA%8C%E5%88%86%E6%9C%A8%E3%81%AB%E3%83%87%E3%82%B7%E3%83%AA%E3%82%A2%E3%83%A9%E3%82%A4%E3%82%BA%E3%81%99%E3%82%8B%22%22%22%0A%20%20%20%20return%20list_to_tree_dfs%28arr%2C%200%29%0A%0A%0Adef%20pre_order%28root%3A%20TreeNode%29%3A%0A%20%20%20%20%22%22%22%E5%89%8D%E9%A0%86%E8%B5%B0%E6%9F%BB%EF%BC%9A%E4%BE%8B%E9%A1%8C%203%22%22%22%0A%20%20%20%20%23%20%E6%9E%9D%E5%88%88%E3%82%8A%0A%20%20%20%20if%20root%20is%20None%20or%20root.val%20%3D%3D%203%3A%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20%23%20%E8%A9%A6%E3%81%99%0A%20%20%20%20path.append%28root%29%0A%20%20%20%20if%20root.val%20%3D%3D%207%3A%0A%20%20%20%20%20%20%20%20%23%20%E8%A7%A3%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20%20%20%20%20res.append%28list%28path%29%29%0A%20%20%20%20pre_order%28root.left%29%0A%20%20%20%20pre_order%28root.right%29%0A%20%20%20%20%23%20%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AF%0A%20%20%20%20path.pop%28%29%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20root%20%3D%20list_to_tree%28%5B1%2C%207%2C%203%2C%204%2C%205%2C%206%2C%207%5D%29%0A%0A%20%20%20%20%23%20%E5%85%88%E8%A1%8C%E9%A0%86%E8%B5%B0%E6%9F%BB%0A%20%20%20%20path%20%3D%20list%5BTreeNode%5D%28%29%0A%20%20%20%20res%20%3D%20list%5Blist%5BTreeNode%5D%5D%28%29%0A%20%20%20%20pre_order%28root%29%0A%0A%20%20%20%20print%28%22%5Cn%E6%A0%B9%E3%83%8E%E3%83%BC%E3%83%89%E3%81%8B%E3%82%89%E3%83%8E%E3%83%BC%E3%83%89%207%20%E3%81%BE%E3%81%A7%E3%81%AE%E7%B5%8C%E8%B7%AF%E3%82%92%E3%81%99%E3%81%B9%E3%81%A6%E5%87%BA%E5%8A%9B%E3%81%97%E3%80%81%E7%B5%8C%E8%B7%AF%E3%81%AB%E3%81%AF%E5%80%A4%E3%81%8C%203%20%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E5%90%AB%E3%82%81%E3%81%AA%E3%81%84%22%29%0A%20%20%20%20for%20path%20in%20res%3A%0A%20%20%20%20%20%20%20%20print%28%5Bnode.val%20for%20node%20in%20path%5D%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=126&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>「枝刈り」は非常にイメージしやすい名称です。次の図のように、探索中に**制約条件を満たさない探索分岐を切り落とす**ことで、多くの無意味な試行を避け、探索効率を高められます。</p>
+<p><img alt="制約条件にもとづく枝刈り" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_constrained_paths.png" /></p>
+<p align="center"> 図 13-3 &nbsp; 制約条件にもとづく枝刈り </p>
 
 <h2 id="1313">13.1.3 &nbsp; フレームワークコード<a class="headerlink" href="#1313" title="Permanent link">&para;</a></h2>
-<p>今度は、バックトラッキングから「試行、後退、剪定」の主要なフレームワークを抽出して、コードの汎用性を向上させてみましょう。</p>
-<p>以下のフレームワークコードでは、<code>state</code> は問題の現在の状態を表し、<code>choices</code> は現在の状態で利用可能な選択肢を表します：</p>
+<p>次に、バックトラッキングにおける「試行・戻る・枝刈り」の本体部分を抽出し、汎用性の高いコードフレームワークへまとめてみます。</p>
+<p>以下のフレームワークコードでは、<code>state</code> は問題の現在状態、<code>choices</code> はその状態で取り得る選択肢を表します。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="5:13"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="n">State</span><span class="p">,</span> <span class="n">choices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">choice</span><span class="p">],</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">state</span><span class="p">]):</span>
-<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキングアルゴリズムフレームワーク&quot;&quot;&quot;</span>
-<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a>    <span class="c1"># 解かどうかを確認</span>
+<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキングアルゴリズムのフレームワーク&quot;&quot;&quot;</span>
+<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a>    <span class="c1"># 解かどうかを判定</span>
 <a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a>    <span class="k">if</span> <span class="n">is_solution</span><span class="p">(</span><span class="n">state</span><span class="p">):</span>
 <a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a>        <span class="c1"># 解を記録</span>
 <a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a>        <span class="n">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
-<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a>        <span class="c1"># 検索を停止</span>
+<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a>        <span class="c1"># これ以上探索しない</span>
 <a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a>        <span class="k">return</span>
-<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a>    <span class="c1"># すべての選択肢を反復</span>
+<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a>    <span class="c1"># すべての選択肢を走査</span>
 <a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a>    <span class="k">for</span> <span class="n">choice</span> <span class="ow">in</span> <span class="n">choices</span><span class="p">:</span>
-<a id="__codelineno-39-11" name="__codelineno-39-11" href="#__codelineno-39-11"></a>        <span class="c1"># 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-39-11" name="__codelineno-39-11" href="#__codelineno-39-11"></a>        <span class="c1"># 枝刈り: 選択が妥当かを判定</span>
 <a id="__codelineno-39-12" name="__codelineno-39-12" href="#__codelineno-39-12"></a>        <span class="k">if</span> <span class="n">is_valid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">):</span>
-<a id="__codelineno-39-13" name="__codelineno-39-13" href="#__codelineno-39-13"></a>            <span class="c1"># 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-39-13" name="__codelineno-39-13" href="#__codelineno-39-13"></a>            <span class="c1"># 試行: 選択を行い、状態を更新</span>
 <a id="__codelineno-39-14" name="__codelineno-39-14" href="#__codelineno-39-14"></a>            <span class="n">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">)</span>
 <a id="__codelineno-39-15" name="__codelineno-39-15" href="#__codelineno-39-15"></a>            <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choices</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
-<a id="__codelineno-39-16" name="__codelineno-39-16" href="#__codelineno-39-16"></a>            <span class="c1"># 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-39-16" name="__codelineno-39-16" href="#__codelineno-39-16"></a>            <span class="c1"># 戻る: 選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-39-17" name="__codelineno-39-17" href="#__codelineno-39-17"></a>            <span class="n">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">)</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* バックトラッキングアルゴリズムフレームワーク */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* バックトラッキングアルゴリズムのフレームワーク */</span>
 <a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">State</span><span class="w"> </span><span class="o">*</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Choice</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">State</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w">    </span><span class="c1">// 解かどうかを判定</span>
 <a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w">        </span><span class="c1">// 解を記録</span>
 <a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w">        </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
-<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w">        </span><span class="c1">// 検索を停止</span>
+<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w">        </span><span class="c1">// これ以上探索しない</span>
 <a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を反復</span>
+<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
 <a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Choice</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w">        </span><span class="c1">// 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w">        </span><span class="c1">// 枝刈り: 選択が妥当かを判定</span>
 <a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
 <a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a><span class="w">            </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
 <a id="__codelineno-40-16" name="__codelineno-40-16" href="#__codelineno-40-16"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
-<a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="w">            </span><span class="c1">// 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="w">            </span><span class="c1">// 戻る: 選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-40-18" name="__codelineno-40-18" href="#__codelineno-40-18"></a><span class="w">            </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
 <a id="__codelineno-40-19" name="__codelineno-40-19" href="#__codelineno-40-19"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-40-20" name="__codelineno-40-20" href="#__codelineno-40-20"></a><span class="w">    </span><span class="p">}</span>
@@ -4849,23 +5319,23 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* バックトラッキングアルゴリズムフレームワーク */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* バックトラッキングアルゴリズムのフレームワーク */</span>
 <a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">State</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Choice</span><span class="o">&gt;</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">State</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w">    </span><span class="c1">// 解かどうかを判定</span>
 <a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="w">        </span><span class="c1">// 解を記録</span>
 <a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a><span class="w">        </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
-<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="w">        </span><span class="c1">// 検索を停止</span>
+<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="w">        </span><span class="c1">// これ以上探索しない</span>
 <a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を反復</span>
+<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
 <a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Choice</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a><span class="w">        </span><span class="c1">// 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a><span class="w">        </span><span class="c1">// 枝刈り: 選択が妥当かを判定</span>
 <a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-41-14" name="__codelineno-41-14" href="#__codelineno-41-14"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-41-14" name="__codelineno-41-14" href="#__codelineno-41-14"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
 <a id="__codelineno-41-15" name="__codelineno-41-15" href="#__codelineno-41-15"></a><span class="w">            </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
 <a id="__codelineno-41-16" name="__codelineno-41-16" href="#__codelineno-41-16"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
-<a id="__codelineno-41-17" name="__codelineno-41-17" href="#__codelineno-41-17"></a><span class="w">            </span><span class="c1">// 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-41-17" name="__codelineno-41-17" href="#__codelineno-41-17"></a><span class="w">            </span><span class="c1">// 戻る: 選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-41-18" name="__codelineno-41-18" href="#__codelineno-41-18"></a><span class="w">            </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
 <a id="__codelineno-41-19" name="__codelineno-41-19" href="#__codelineno-41-19"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-41-20" name="__codelineno-41-20" href="#__codelineno-41-20"></a><span class="w">    </span><span class="p">}</span>
@@ -4873,23 +5343,23 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="cm">/* バックトラッキングアルゴリズムフレームワーク */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="cm">/* バックトラッキングアルゴリズムのフレームワーク */</span>
 <a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Backtrack</span><span class="p">(</span><span class="n">State</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Choice</span><span class="o">&gt;</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">State</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="w">    </span><span class="c1">// 解かどうかを判定</span>
 <a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="w">        </span><span class="c1">// 解を記録</span>
 <a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a><span class="w">        </span><span class="n">RecordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
-<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="w">        </span><span class="c1">// 検索を停止</span>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="w">        </span><span class="c1">// これ以上探索しない</span>
 <a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を反復</span>
+<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
 <a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Choice</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a><span class="w">        </span><span class="c1">// 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a><span class="w">        </span><span class="c1">// 枝刈り: 選択が妥当かを判定</span>
 <a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-42-14" name="__codelineno-42-14" href="#__codelineno-42-14"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-42-14" name="__codelineno-42-14" href="#__codelineno-42-14"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
 <a id="__codelineno-42-15" name="__codelineno-42-15" href="#__codelineno-42-15"></a><span class="w">            </span><span class="n">MakeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
 <a id="__codelineno-42-16" name="__codelineno-42-16" href="#__codelineno-42-16"></a><span class="w">            </span><span class="n">Backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
-<a id="__codelineno-42-17" name="__codelineno-42-17" href="#__codelineno-42-17"></a><span class="w">            </span><span class="c1">// 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-42-17" name="__codelineno-42-17" href="#__codelineno-42-17"></a><span class="w">            </span><span class="c1">// 戻る: 選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-42-18" name="__codelineno-42-18" href="#__codelineno-42-18"></a><span class="w">            </span><span class="n">UndoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
 <a id="__codelineno-42-19" name="__codelineno-42-19" href="#__codelineno-42-19"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-42-20" name="__codelineno-42-20" href="#__codelineno-42-20"></a><span class="w">    </span><span class="p">}</span>
@@ -4897,23 +5367,23 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* バックトラッキングアルゴリズムフレームワーク */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* バックトラッキングアルゴリズムのフレームワーク */</span>
 <a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">*</span><span class="nx">State</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="w"> </span><span class="p">[]</span><span class="nx">Choice</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="nx">State</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w">    </span><span class="c1">// 解かどうかを判定</span>
 <a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">isSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w">        </span><span class="c1">// 解を記録</span>
 <a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w">        </span><span class="nx">recordSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
-<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="w">        </span><span class="c1">// 検索を停止</span>
+<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="w">        </span><span class="c1">// これ以上探索しない</span>
 <a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w">        </span><span class="k">return</span>
 <a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を反復</span>
+<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
 <a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">choices</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w">        </span><span class="c1">// 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w">        </span><span class="c1">// 枝刈り: 選択が妥当かを判定</span>
 <a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">isValid</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-43-14" name="__codelineno-43-14" href="#__codelineno-43-14"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-43-14" name="__codelineno-43-14" href="#__codelineno-43-14"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
 <a id="__codelineno-43-15" name="__codelineno-43-15" href="#__codelineno-43-15"></a><span class="w">            </span><span class="nx">makeChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span>
 <a id="__codelineno-43-16" name="__codelineno-43-16" href="#__codelineno-43-16"></a><span class="w">            </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
-<a id="__codelineno-43-17" name="__codelineno-43-17" href="#__codelineno-43-17"></a><span class="w">            </span><span class="c1">// 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-43-17" name="__codelineno-43-17" href="#__codelineno-43-17"></a><span class="w">            </span><span class="c1">// 戻る: 選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-43-18" name="__codelineno-43-18" href="#__codelineno-43-18"></a><span class="w">            </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span>
 <a id="__codelineno-43-19" name="__codelineno-43-19" href="#__codelineno-43-19"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-43-20" name="__codelineno-43-20" href="#__codelineno-43-20"></a><span class="w">    </span><span class="p">}</span>
@@ -4921,23 +5391,23 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* バックトラッキングアルゴリズムフレームワーク */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* バックトラッキングアルゴリズムのフレームワーク */</span>
 <a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="n">State</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="n">Choice</span><span class="p">],</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="n">State</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w">    </span><span class="c1">// 解かどうかを判定</span>
 <a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w">        </span><span class="c1">// 解を記録</span>
 <a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w">        </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
-<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w">        </span><span class="c1">// 検索を停止</span>
+<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w">        </span><span class="c1">// これ以上探索しない</span>
 <a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w">        </span><span class="k">return</span>
 <a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を反復</span>
+<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
 <a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w">        </span><span class="c1">// 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w">        </span><span class="c1">// 枝刈り: 選択が妥当かを判定</span>
 <a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
 <a id="__codelineno-44-15" name="__codelineno-44-15" href="#__codelineno-44-15"></a><span class="w">            </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
 <a id="__codelineno-44-16" name="__codelineno-44-16" href="#__codelineno-44-16"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
-<a id="__codelineno-44-17" name="__codelineno-44-17" href="#__codelineno-44-17"></a><span class="w">            </span><span class="c1">// 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-44-17" name="__codelineno-44-17" href="#__codelineno-44-17"></a><span class="w">            </span><span class="c1">// 戻る: 選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-44-18" name="__codelineno-44-18" href="#__codelineno-44-18"></a><span class="w">            </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
 <a id="__codelineno-44-19" name="__codelineno-44-19" href="#__codelineno-44-19"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-44-20" name="__codelineno-44-20" href="#__codelineno-44-20"></a><span class="w">    </span><span class="p">}</span>
@@ -4945,23 +5415,23 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="cm">/* バックトラッキングアルゴリズムフレームワーク */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="cm">/* バックトラッキングアルゴリズムのフレームワーク */</span>
 <a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w">    </span><span class="c1">// 解かどうかを判定</span>
 <a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">isSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w">        </span><span class="c1">// 解を記録</span>
 <a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w">        </span><span class="nx">recordSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
-<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="w">        </span><span class="c1">// 検索を停止</span>
+<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="w">        </span><span class="c1">// これ以上探索しない</span>
 <a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を反復</span>
+<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
 <a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w">        </span><span class="c1">// 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w">        </span><span class="c1">// 枝刈り: 選択が妥当かを判定</span>
 <a id="__codelineno-45-13" name="__codelineno-45-13" href="#__codelineno-45-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">isValid</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-45-14" name="__codelineno-45-14" href="#__codelineno-45-14"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-45-14" name="__codelineno-45-14" href="#__codelineno-45-14"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
 <a id="__codelineno-45-15" name="__codelineno-45-15" href="#__codelineno-45-15"></a><span class="w">            </span><span class="nx">makeChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">);</span>
 <a id="__codelineno-45-16" name="__codelineno-45-16" href="#__codelineno-45-16"></a><span class="w">            </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
-<a id="__codelineno-45-17" name="__codelineno-45-17" href="#__codelineno-45-17"></a><span class="w">            </span><span class="c1">// 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-45-17" name="__codelineno-45-17" href="#__codelineno-45-17"></a><span class="w">            </span><span class="c1">// 戻る: 選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-45-18" name="__codelineno-45-18" href="#__codelineno-45-18"></a><span class="w">            </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">);</span>
 <a id="__codelineno-45-19" name="__codelineno-45-19" href="#__codelineno-45-19"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-45-20" name="__codelineno-45-20" href="#__codelineno-45-20"></a><span class="w">    </span><span class="p">}</span>
@@ -4969,23 +5439,23 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="cm">/* バックトラッキングアルゴリズムフレームワーク */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="cm">/* バックトラッキングアルゴリズムのフレームワーク */</span>
 <a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="o">:</span><span class="w"> </span><span class="kt">State</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="o">:</span><span class="w"> </span><span class="kt">Choice</span><span class="p">[],</span><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">State</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w">    </span><span class="c1">// 解かどうかを判定</span>
 <a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">isSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="w">        </span><span class="c1">// 解を記録</span>
 <a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a><span class="w">        </span><span class="nx">recordSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
-<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></a><span class="w">        </span><span class="c1">// 検索を停止</span>
+<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></a><span class="w">        </span><span class="c1">// これ以上探索しない</span>
 <a id="__codelineno-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を反復</span>
+<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
 <a id="__codelineno-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-46-12" name="__codelineno-46-12" href="#__codelineno-46-12"></a><span class="w">        </span><span class="c1">// 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-46-12" name="__codelineno-46-12" href="#__codelineno-46-12"></a><span class="w">        </span><span class="c1">// 枝刈り: 選択が妥当かを判定</span>
 <a id="__codelineno-46-13" name="__codelineno-46-13" href="#__codelineno-46-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">isValid</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-46-14" name="__codelineno-46-14" href="#__codelineno-46-14"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-46-14" name="__codelineno-46-14" href="#__codelineno-46-14"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
 <a id="__codelineno-46-15" name="__codelineno-46-15" href="#__codelineno-46-15"></a><span class="w">            </span><span class="nx">makeChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">);</span>
 <a id="__codelineno-46-16" name="__codelineno-46-16" href="#__codelineno-46-16"></a><span class="w">            </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
-<a id="__codelineno-46-17" name="__codelineno-46-17" href="#__codelineno-46-17"></a><span class="w">            </span><span class="c1">// 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-46-17" name="__codelineno-46-17" href="#__codelineno-46-17"></a><span class="w">            </span><span class="c1">// 戻る: 選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-46-18" name="__codelineno-46-18" href="#__codelineno-46-18"></a><span class="w">            </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">);</span>
 <a id="__codelineno-46-19" name="__codelineno-46-19" href="#__codelineno-46-19"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-46-20" name="__codelineno-46-20" href="#__codelineno-46-20"></a><span class="w">    </span><span class="p">}</span>
@@ -4993,23 +5463,23 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* バックトラッキングアルゴリズムフレームワーク */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* バックトラッキングアルゴリズムのフレームワーク */</span>
 <a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">State</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Choice</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">State</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w">  </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w">  </span><span class="c1">// 解かどうかを判定</span>
 <a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="w">    </span><span class="c1">// 解を記録</span>
 <a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a><span class="w">    </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
-<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="w">    </span><span class="c1">// 検索を停止</span>
+<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="w">    </span><span class="c1">// これ以上探索しない</span>
 <a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a><span class="w">    </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="w">  </span><span class="p">}</span>
-<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="w">  </span><span class="c1">// すべての選択肢を反復</span>
+<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="w">  </span><span class="c1">// すべての選択肢を走査</span>
 <a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Choice</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a><span class="w">    </span><span class="c1">// 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a><span class="w">    </span><span class="c1">// 枝刈り: 選択が妥当かを判定</span>
 <a id="__codelineno-47-13" name="__codelineno-47-13" href="#__codelineno-47-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-47-14" name="__codelineno-47-14" href="#__codelineno-47-14"></a><span class="w">      </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-47-14" name="__codelineno-47-14" href="#__codelineno-47-14"></a><span class="w">      </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
 <a id="__codelineno-47-15" name="__codelineno-47-15" href="#__codelineno-47-15"></a><span class="w">      </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
 <a id="__codelineno-47-16" name="__codelineno-47-16" href="#__codelineno-47-16"></a><span class="w">      </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
-<a id="__codelineno-47-17" name="__codelineno-47-17" href="#__codelineno-47-17"></a><span class="w">      </span><span class="c1">// 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-47-17" name="__codelineno-47-17" href="#__codelineno-47-17"></a><span class="w">      </span><span class="c1">// 戻る: 選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-47-18" name="__codelineno-47-18" href="#__codelineno-47-18"></a><span class="w">      </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
 <a id="__codelineno-47-19" name="__codelineno-47-19" href="#__codelineno-47-19"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-47-20" name="__codelineno-47-20" href="#__codelineno-47-20"></a><span class="w">  </span><span class="p">}</span>
@@ -5017,23 +5487,23 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="cm">/* バックトラッキングアルゴリズムフレームワーク */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="cm">/* バックトラッキングアルゴリズムのフレームワーク */</span>
 <a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="n">State</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">Choice</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">State</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="w">    </span><span class="c1">// 解かどうかを判定</span>
 <a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">is_solution</span><span class="p">(</span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a><span class="w">        </span><span class="c1">// 解を記録</span>
 <a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a><span class="w">        </span><span class="n">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
-<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a><span class="w">        </span><span class="c1">// 検索を停止</span>
+<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a><span class="w">        </span><span class="c1">// これ以上探索しない</span>
 <a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を反復</span>
+<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
 <a id="__codelineno-48-11" name="__codelineno-48-11" href="#__codelineno-48-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-48-12" name="__codelineno-48-12" href="#__codelineno-48-12"></a><span class="w">        </span><span class="c1">// 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-48-12" name="__codelineno-48-12" href="#__codelineno-48-12"></a><span class="w">        </span><span class="c1">// 枝刈り: 選択が妥当かを判定</span>
 <a id="__codelineno-48-13" name="__codelineno-48-13" href="#__codelineno-48-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">is_valid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-48-14" name="__codelineno-48-14" href="#__codelineno-48-14"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-48-14" name="__codelineno-48-14" href="#__codelineno-48-14"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
 <a id="__codelineno-48-15" name="__codelineno-48-15" href="#__codelineno-48-15"></a><span class="w">            </span><span class="n">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
 <a id="__codelineno-48-16" name="__codelineno-48-16" href="#__codelineno-48-16"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
-<a id="__codelineno-48-17" name="__codelineno-48-17" href="#__codelineno-48-17"></a><span class="w">            </span><span class="c1">// 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-48-17" name="__codelineno-48-17" href="#__codelineno-48-17"></a><span class="w">            </span><span class="c1">// 戻る: 選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-48-18" name="__codelineno-48-18" href="#__codelineno-48-18"></a><span class="w">            </span><span class="n">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
 <a id="__codelineno-48-19" name="__codelineno-48-19" href="#__codelineno-48-19"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-48-20" name="__codelineno-48-20" href="#__codelineno-48-20"></a><span class="w">    </span><span class="p">}</span>
@@ -5041,23 +5511,23 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* バックトラッキングアルゴリズムフレームワーク */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* バックトラッキングアルゴリズムのフレームワーク */</span>
 <a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">State</span><span class="w"> </span><span class="o">*</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">Choice</span><span class="w"> </span><span class="o">*</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">numChoices</span><span class="p">,</span><span class="w"> </span><span class="n">State</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">numRes</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="w">    </span><span class="c1">// 解かどうかを判定</span>
 <a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="w">        </span><span class="c1">// 解を記録</span>
 <a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a><span class="w">        </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">numRes</span><span class="p">);</span>
-<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="w">        </span><span class="c1">// 検索を停止</span>
+<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="w">        </span><span class="c1">// これ以上探索しない</span>
 <a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-49-9" name="__codelineno-49-9" href="#__codelineno-49-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-49-10" name="__codelineno-49-10" href="#__codelineno-49-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を反復</span>
+<a id="__codelineno-49-10" name="__codelineno-49-10" href="#__codelineno-49-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
 <a id="__codelineno-49-11" name="__codelineno-49-11" href="#__codelineno-49-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">numChoices</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-49-12" name="__codelineno-49-12" href="#__codelineno-49-12"></a><span class="w">        </span><span class="c1">// 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-49-12" name="__codelineno-49-12" href="#__codelineno-49-12"></a><span class="w">        </span><span class="c1">// 枝刈り: 選択が妥当かを判定</span>
 <a id="__codelineno-49-13" name="__codelineno-49-13" href="#__codelineno-49-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]))</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-49-14" name="__codelineno-49-14" href="#__codelineno-49-14"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-49-14" name="__codelineno-49-14" href="#__codelineno-49-14"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
 <a id="__codelineno-49-15" name="__codelineno-49-15" href="#__codelineno-49-15"></a><span class="w">            </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
 <a id="__codelineno-49-16" name="__codelineno-49-16" href="#__codelineno-49-16"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">numChoices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">numRes</span><span class="p">);</span>
-<a id="__codelineno-49-17" name="__codelineno-49-17" href="#__codelineno-49-17"></a><span class="w">            </span><span class="c1">// 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-49-17" name="__codelineno-49-17" href="#__codelineno-49-17"></a><span class="w">            </span><span class="c1">// 戻る: 選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-49-18" name="__codelineno-49-18" href="#__codelineno-49-18"></a><span class="w">            </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
 <a id="__codelineno-49-19" name="__codelineno-49-19" href="#__codelineno-49-19"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-49-20" name="__codelineno-49-20" href="#__codelineno-49-20"></a><span class="w">    </span><span class="p">}</span>
@@ -5065,23 +5535,23 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* バックトラッキングアルゴリズムフレームワーク */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* バックトラッキングアルゴリズムのフレームワーク */</span>
 <a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">State?,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Choice?&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">State?&gt;</span><span class="o">?</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w">    </span><span class="c1">// 解かどうかを判定</span>
 <a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="w">        </span><span class="c1">// 解を記録</span>
 <a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a><span class="w">        </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
-<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="w">        </span><span class="c1">// 検索を停止</span>
+<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="w">        </span><span class="c1">// これ以上探索しない</span>
 <a id="__codelineno-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a><span class="w">        </span><span class="k">return</span>
 <a id="__codelineno-50-9" name="__codelineno-50-9" href="#__codelineno-50-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-50-10" name="__codelineno-50-10" href="#__codelineno-50-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を反復</span>
+<a id="__codelineno-50-10" name="__codelineno-50-10" href="#__codelineno-50-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
 <a id="__codelineno-50-11" name="__codelineno-50-11" href="#__codelineno-50-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-50-12" name="__codelineno-50-12" href="#__codelineno-50-12"></a><span class="w">        </span><span class="c1">// 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-50-12" name="__codelineno-50-12" href="#__codelineno-50-12"></a><span class="w">        </span><span class="c1">// 枝刈り: 選択が妥当かを判定</span>
 <a id="__codelineno-50-13" name="__codelineno-50-13" href="#__codelineno-50-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-50-14" name="__codelineno-50-14" href="#__codelineno-50-14"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-50-14" name="__codelineno-50-14" href="#__codelineno-50-14"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
 <a id="__codelineno-50-15" name="__codelineno-50-15" href="#__codelineno-50-15"></a><span class="w">            </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
 <a id="__codelineno-50-16" name="__codelineno-50-16" href="#__codelineno-50-16"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
-<a id="__codelineno-50-17" name="__codelineno-50-17" href="#__codelineno-50-17"></a><span class="w">            </span><span class="c1">// 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-50-17" name="__codelineno-50-17" href="#__codelineno-50-17"></a><span class="w">            </span><span class="c1">// 戻る: 選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-50-18" name="__codelineno-50-18" href="#__codelineno-50-18"></a><span class="w">            </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
 <a id="__codelineno-50-19" name="__codelineno-50-19" href="#__codelineno-50-19"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-50-20" name="__codelineno-50-20" href="#__codelineno-50-20"></a><span class="w">    </span><span class="p">}</span>
@@ -5089,23 +5559,23 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="c1">### バックトラッキングアルゴリズムフレームワーク ###</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="c1">### バックトラッキングアルゴリズムのフレームワーク ###</span>
 <a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
-<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w">    </span><span class="c1"># 解かどうかを確認</span>
+<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w">    </span><span class="c1"># 解かどうかを判定</span>
 <a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">is_solution?</span><span class="p">(</span><span class="n">state</span><span class="p">)</span>
 <a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w">        </span><span class="c1"># 解を記録</span>
 <a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a><span class="w">        </span><span class="n">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
 <a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="w">        </span><span class="k">return</span>
 <a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="w">    </span><span class="k">end</span>
 <a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a>
-<a id="__codelineno-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></a><span class="w">    </span><span class="c1"># すべての選択肢を反復</span>
+<a id="__codelineno-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></a><span class="w">    </span><span class="c1"># すべての選択肢を走査</span>
 <a id="__codelineno-51-11" name="__codelineno-51-11" href="#__codelineno-51-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span>
-<a id="__codelineno-51-12" name="__codelineno-51-12" href="#__codelineno-51-12"></a><span class="w">        </span><span class="c1"># 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-51-12" name="__codelineno-51-12" href="#__codelineno-51-12"></a><span class="w">        </span><span class="c1"># 枝刈り: 選択が妥当かを判定</span>
 <a id="__codelineno-51-13" name="__codelineno-51-13" href="#__codelineno-51-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">is_valid?</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
-<a id="__codelineno-51-14" name="__codelineno-51-14" href="#__codelineno-51-14"></a><span class="w">            </span><span class="c1"># 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-51-14" name="__codelineno-51-14" href="#__codelineno-51-14"></a><span class="w">            </span><span class="c1"># 試行: 選択を行い、状態を更新</span>
 <a id="__codelineno-51-15" name="__codelineno-51-15" href="#__codelineno-51-15"></a><span class="w">            </span><span class="n">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
 <a id="__codelineno-51-16" name="__codelineno-51-16" href="#__codelineno-51-16"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
-<a id="__codelineno-51-17" name="__codelineno-51-17" href="#__codelineno-51-17"></a><span class="w">            </span><span class="c1"># 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-51-17" name="__codelineno-51-17" href="#__codelineno-51-17"></a><span class="w">            </span><span class="c1"># 戻る: 選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-51-18" name="__codelineno-51-18" href="#__codelineno-51-18"></a><span class="w">            </span><span class="n">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
 <a id="__codelineno-51-19" name="__codelineno-51-19" href="#__codelineno-51-19"></a><span class="w">        </span><span class="k">end</span>
 <a id="__codelineno-51-20" name="__codelineno-51-20" href="#__codelineno-51-20"></a><span class="w">    </span><span class="k">end</span>
@@ -5114,7 +5584,7 @@
 </div>
 </div>
 </div>
-<p>次に、フレームワークコードに基づいて例題 3 を解きます。状態 <code>state</code> はノードの走査経路を表し、選択肢 <code>choices</code> は現在ノードの左子ノードと右子ノード、結果 <code>res</code> は経路リストです：</p>
+<p>次に、このフレームワークコードを用いて例題3を解きます。状態 <code>state</code> はノードの走査経路、選択肢 <code>choices</code> は現在のノードの左子ノードと右子ノード、結果 <code>res</code> は経路のリストです。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="6:13"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><input id="__tabbed_6_13" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Kotlin</label><label for="__tabbed_6_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
@@ -5127,7 +5597,7 @@
 <a id="__codelineno-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></a>    <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">state</span><span class="p">))</span>
 <a id="__codelineno-52-8" name="__codelineno-52-8" href="#__codelineno-52-8"></a>
 <a id="__codelineno-52-9" name="__codelineno-52-9" href="#__codelineno-52-9"></a><span class="k">def</span><span class="w"> </span><span class="nf">is_valid</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choice</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
-<a id="__codelineno-52-10" name="__codelineno-52-10" href="#__codelineno-52-10"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;現在の状態下で選択が合法かどうかを判定&quot;&quot;&quot;</span>
+<a id="__codelineno-52-10" name="__codelineno-52-10" href="#__codelineno-52-10"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;現在の状態で、この選択が有効かどうかを判定&quot;&quot;&quot;</span>
 <a id="__codelineno-52-11" name="__codelineno-52-11" href="#__codelineno-52-11"></a>    <span class="k">return</span> <span class="n">choice</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span> <span class="ow">and</span> <span class="n">choice</span><span class="o">.</span><span class="n">val</span> <span class="o">!=</span> <span class="mi">3</span>
 <a id="__codelineno-52-12" name="__codelineno-52-12" href="#__codelineno-52-12"></a>
 <a id="__codelineno-52-13" name="__codelineno-52-13" href="#__codelineno-52-13"></a><span class="k">def</span><span class="w"> </span><span class="nf">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choice</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">):</span>
@@ -5135,26 +5605,26 @@
 <a id="__codelineno-52-15" name="__codelineno-52-15" href="#__codelineno-52-15"></a>    <span class="n">state</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>
 <a id="__codelineno-52-16" name="__codelineno-52-16" href="#__codelineno-52-16"></a>
 <a id="__codelineno-52-17" name="__codelineno-52-17" href="#__codelineno-52-17"></a><span class="k">def</span><span class="w"> </span><span class="nf">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choice</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">):</span>
-<a id="__codelineno-52-18" name="__codelineno-52-18" href="#__codelineno-52-18"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;状態を復元&quot;&quot;&quot;</span>
+<a id="__codelineno-52-18" name="__codelineno-52-18" href="#__codelineno-52-18"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;状態を元に戻す&quot;&quot;&quot;</span>
 <a id="__codelineno-52-19" name="__codelineno-52-19" href="#__codelineno-52-19"></a>    <span class="n">state</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
 <a id="__codelineno-52-20" name="__codelineno-52-20" href="#__codelineno-52-20"></a>
 <a id="__codelineno-52-21" name="__codelineno-52-21" href="#__codelineno-52-21"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
 <a id="__codelineno-52-22" name="__codelineno-52-22" href="#__codelineno-52-22"></a>    <span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]]</span>
 <a id="__codelineno-52-23" name="__codelineno-52-23" href="#__codelineno-52-23"></a><span class="p">):</span>
-<a id="__codelineno-52-24" name="__codelineno-52-24" href="#__codelineno-52-24"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキングアルゴリズム：例三&quot;&quot;&quot;</span>
-<a id="__codelineno-52-25" name="__codelineno-52-25" href="#__codelineno-52-25"></a>    <span class="c1"># 解かどうかをチェック</span>
+<a id="__codelineno-52-24" name="__codelineno-52-24" href="#__codelineno-52-24"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキング：例題 3&quot;&quot;&quot;</span>
+<a id="__codelineno-52-25" name="__codelineno-52-25" href="#__codelineno-52-25"></a>    <span class="c1"># 解かどうかを確認</span>
 <a id="__codelineno-52-26" name="__codelineno-52-26" href="#__codelineno-52-26"></a>    <span class="k">if</span> <span class="n">is_solution</span><span class="p">(</span><span class="n">state</span><span class="p">):</span>
 <a id="__codelineno-52-27" name="__codelineno-52-27" href="#__codelineno-52-27"></a>        <span class="c1"># 解を記録</span>
 <a id="__codelineno-52-28" name="__codelineno-52-28" href="#__codelineno-52-28"></a>        <span class="n">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
 <a id="__codelineno-52-29" name="__codelineno-52-29" href="#__codelineno-52-29"></a>    <span class="c1"># すべての選択肢を走査</span>
 <a id="__codelineno-52-30" name="__codelineno-52-30" href="#__codelineno-52-30"></a>    <span class="k">for</span> <span class="n">choice</span> <span class="ow">in</span> <span class="n">choices</span><span class="p">:</span>
-<a id="__codelineno-52-31" name="__codelineno-52-31" href="#__codelineno-52-31"></a>        <span class="c1"># 枝刈り：選択が合法かどうかをチェック</span>
+<a id="__codelineno-52-31" name="__codelineno-52-31" href="#__codelineno-52-31"></a>        <span class="c1"># 枝刈り：選択が妥当かを確認する</span>
 <a id="__codelineno-52-32" name="__codelineno-52-32" href="#__codelineno-52-32"></a>        <span class="k">if</span> <span class="n">is_valid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">):</span>
-<a id="__codelineno-52-33" name="__codelineno-52-33" href="#__codelineno-52-33"></a>            <span class="c1"># 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-52-33" name="__codelineno-52-33" href="#__codelineno-52-33"></a>            <span class="c1"># 試行: 選択を行い、状態を更新</span>
 <a id="__codelineno-52-34" name="__codelineno-52-34" href="#__codelineno-52-34"></a>            <span class="n">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">)</span>
-<a id="__codelineno-52-35" name="__codelineno-52-35" href="#__codelineno-52-35"></a>            <span class="c1"># 次の選択ラウンドに進む</span>
+<a id="__codelineno-52-35" name="__codelineno-52-35" href="#__codelineno-52-35"></a>            <span class="c1"># 次の選択へ進む</span>
 <a id="__codelineno-52-36" name="__codelineno-52-36" href="#__codelineno-52-36"></a>            <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="p">[</span><span class="n">choice</span><span class="o">.</span><span class="n">left</span><span class="p">,</span> <span class="n">choice</span><span class="o">.</span><span class="n">right</span><span class="p">],</span> <span class="n">res</span><span class="p">)</span>
-<a id="__codelineno-52-37" name="__codelineno-52-37" href="#__codelineno-52-37"></a>            <span class="c1"># 撤回：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-52-37" name="__codelineno-52-37" href="#__codelineno-52-37"></a>            <span class="c1"># バックトラック：選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-52-38" name="__codelineno-52-38" href="#__codelineno-52-38"></a>            <span class="n">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">)</span>
 </code></pre></div>
 </div>
@@ -5169,7 +5639,7 @@
 <a id="__codelineno-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">state</span><span class="p">);</span>
 <a id="__codelineno-53-9" name="__codelineno-53-9" href="#__codelineno-53-9"></a><span class="p">}</span>
 <a id="__codelineno-53-10" name="__codelineno-53-10" href="#__codelineno-53-10"></a>
-<a id="__codelineno-53-11" name="__codelineno-53-11" href="#__codelineno-53-11"></a><span class="cm">/* 現在の状態下で選択が合法かどうかを判定 */</span>
+<a id="__codelineno-53-11" name="__codelineno-53-11" href="#__codelineno-53-11"></a><span class="cm">/* 現在の状態で、この選択が有効かどうかを判定 */</span>
 <a id="__codelineno-53-12" name="__codelineno-53-12" href="#__codelineno-53-12"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">isValid</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-53-13" name="__codelineno-53-13" href="#__codelineno-53-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">choice</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
 <a id="__codelineno-53-14" name="__codelineno-53-14" href="#__codelineno-53-14"></a><span class="p">}</span>
@@ -5179,28 +5649,28 @@
 <a id="__codelineno-53-18" name="__codelineno-53-18" href="#__codelineno-53-18"></a><span class="w">    </span><span class="n">state</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
 <a id="__codelineno-53-19" name="__codelineno-53-19" href="#__codelineno-53-19"></a><span class="p">}</span>
 <a id="__codelineno-53-20" name="__codelineno-53-20" href="#__codelineno-53-20"></a>
-<a id="__codelineno-53-21" name="__codelineno-53-21" href="#__codelineno-53-21"></a><span class="cm">/* 状態を復元 */</span>
+<a id="__codelineno-53-21" name="__codelineno-53-21" href="#__codelineno-53-21"></a><span class="cm">/* 状態を元に戻す */</span>
 <a id="__codelineno-53-22" name="__codelineno-53-22" href="#__codelineno-53-22"></a><span class="kt">void</span><span class="w"> </span><span class="nf">undoChoice</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-53-23" name="__codelineno-53-23" href="#__codelineno-53-23"></a><span class="w">    </span><span class="n">state</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
 <a id="__codelineno-53-24" name="__codelineno-53-24" href="#__codelineno-53-24"></a><span class="p">}</span>
 <a id="__codelineno-53-25" name="__codelineno-53-25" href="#__codelineno-53-25"></a>
-<a id="__codelineno-53-26" name="__codelineno-53-26" href="#__codelineno-53-26"></a><span class="cm">/* バックトラッキングアルゴリズム：例３ */</span>
+<a id="__codelineno-53-26" name="__codelineno-53-26" href="#__codelineno-53-26"></a><span class="cm">/* バックトラッキング：例題 3 */</span>
 <a id="__codelineno-53-27" name="__codelineno-53-27" href="#__codelineno-53-27"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-53-28" name="__codelineno-53-28" href="#__codelineno-53-28"></a><span class="w">    </span><span class="c1">// 解かどうかをチェック</span>
+<a id="__codelineno-53-28" name="__codelineno-53-28" href="#__codelineno-53-28"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
 <a id="__codelineno-53-29" name="__codelineno-53-29" href="#__codelineno-53-29"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-53-30" name="__codelineno-53-30" href="#__codelineno-53-30"></a><span class="w">        </span><span class="c1">// 解を記録</span>
 <a id="__codelineno-53-31" name="__codelineno-53-31" href="#__codelineno-53-31"></a><span class="w">        </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
 <a id="__codelineno-53-32" name="__codelineno-53-32" href="#__codelineno-53-32"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-53-33" name="__codelineno-53-33" href="#__codelineno-53-33"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
 <a id="__codelineno-53-34" name="__codelineno-53-34" href="#__codelineno-53-34"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choice</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-53-35" name="__codelineno-53-35" href="#__codelineno-53-35"></a><span class="w">        </span><span class="c1">// 剪定：選択が合法かどうかをチェック</span>
+<a id="__codelineno-53-35" name="__codelineno-53-35" href="#__codelineno-53-35"></a><span class="w">        </span><span class="c1">// 枝刈り：選択が妥当かを確認する</span>
 <a id="__codelineno-53-36" name="__codelineno-53-36" href="#__codelineno-53-36"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-53-37" name="__codelineno-53-37" href="#__codelineno-53-37"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-53-37" name="__codelineno-53-37" href="#__codelineno-53-37"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
 <a id="__codelineno-53-38" name="__codelineno-53-38" href="#__codelineno-53-38"></a><span class="w">            </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
-<a id="__codelineno-53-39" name="__codelineno-53-39" href="#__codelineno-53-39"></a><span class="w">            </span><span class="c1">// 次のラウンドの選択に進む</span>
+<a id="__codelineno-53-39" name="__codelineno-53-39" href="#__codelineno-53-39"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
 <a id="__codelineno-53-40" name="__codelineno-53-40" href="#__codelineno-53-40"></a><span class="w">            </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">nextChoices</span><span class="p">{</span><span class="n">choice</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">};</span>
 <a id="__codelineno-53-41" name="__codelineno-53-41" href="#__codelineno-53-41"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">nextChoices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
-<a id="__codelineno-53-42" name="__codelineno-53-42" href="#__codelineno-53-42"></a><span class="w">            </span><span class="c1">// 回退：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-53-42" name="__codelineno-53-42" href="#__codelineno-53-42"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-53-43" name="__codelineno-53-43" href="#__codelineno-53-43"></a><span class="w">            </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
 <a id="__codelineno-53-44" name="__codelineno-53-44" href="#__codelineno-53-44"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-53-45" name="__codelineno-53-45" href="#__codelineno-53-45"></a><span class="w">    </span><span class="p">}</span>
@@ -5218,7 +5688,7 @@
 <a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
 <a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a><span class="p">}</span>
 <a id="__codelineno-54-10" name="__codelineno-54-10" href="#__codelineno-54-10"></a>
-<a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a><span class="cm">/* 現在の状態下で選択が合法かどうかを判定 */</span>
+<a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a><span class="cm">/* 現在の状態で、この選択が有効かどうかを判定 */</span>
 <a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="kt">boolean</span><span class="w"> </span><span class="nf">isValid</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-54-13" name="__codelineno-54-13" href="#__codelineno-54-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
 <a id="__codelineno-54-14" name="__codelineno-54-14" href="#__codelineno-54-14"></a><span class="p">}</span>
@@ -5228,27 +5698,27 @@
 <a id="__codelineno-54-18" name="__codelineno-54-18" href="#__codelineno-54-18"></a><span class="w">    </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
 <a id="__codelineno-54-19" name="__codelineno-54-19" href="#__codelineno-54-19"></a><span class="p">}</span>
 <a id="__codelineno-54-20" name="__codelineno-54-20" href="#__codelineno-54-20"></a>
-<a id="__codelineno-54-21" name="__codelineno-54-21" href="#__codelineno-54-21"></a><span class="cm">/* 状態を復元 */</span>
+<a id="__codelineno-54-21" name="__codelineno-54-21" href="#__codelineno-54-21"></a><span class="cm">/* 状態を元に戻す */</span>
 <a id="__codelineno-54-22" name="__codelineno-54-22" href="#__codelineno-54-22"></a><span class="kt">void</span><span class="w"> </span><span class="nf">undoChoice</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-54-23" name="__codelineno-54-23" href="#__codelineno-54-23"></a><span class="w">    </span><span class="n">state</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-54-24" name="__codelineno-54-24" href="#__codelineno-54-24"></a><span class="p">}</span>
 <a id="__codelineno-54-25" name="__codelineno-54-25" href="#__codelineno-54-25"></a>
-<a id="__codelineno-54-26" name="__codelineno-54-26" href="#__codelineno-54-26"></a><span class="cm">/* バックトラッキングアルゴリズム：例３ */</span>
+<a id="__codelineno-54-26" name="__codelineno-54-26" href="#__codelineno-54-26"></a><span class="cm">/* バックトラッキング：例題 3 */</span>
 <a id="__codelineno-54-27" name="__codelineno-54-27" href="#__codelineno-54-27"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-54-28" name="__codelineno-54-28" href="#__codelineno-54-28"></a><span class="w">    </span><span class="c1">// 解かどうかをチェック</span>
+<a id="__codelineno-54-28" name="__codelineno-54-28" href="#__codelineno-54-28"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
 <a id="__codelineno-54-29" name="__codelineno-54-29" href="#__codelineno-54-29"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-54-30" name="__codelineno-54-30" href="#__codelineno-54-30"></a><span class="w">        </span><span class="c1">// 解を記録</span>
 <a id="__codelineno-54-31" name="__codelineno-54-31" href="#__codelineno-54-31"></a><span class="w">        </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
 <a id="__codelineno-54-32" name="__codelineno-54-32" href="#__codelineno-54-32"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-54-33" name="__codelineno-54-33" href="#__codelineno-54-33"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
 <a id="__codelineno-54-34" name="__codelineno-54-34" href="#__codelineno-54-34"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-54-35" name="__codelineno-54-35" href="#__codelineno-54-35"></a><span class="w">        </span><span class="c1">// 剪定：選択が合法かどうかをチェック</span>
+<a id="__codelineno-54-35" name="__codelineno-54-35" href="#__codelineno-54-35"></a><span class="w">        </span><span class="c1">// 枝刈り：選択が妥当かを確認する</span>
 <a id="__codelineno-54-36" name="__codelineno-54-36" href="#__codelineno-54-36"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-54-37" name="__codelineno-54-37" href="#__codelineno-54-37"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-54-37" name="__codelineno-54-37" href="#__codelineno-54-37"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
 <a id="__codelineno-54-38" name="__codelineno-54-38" href="#__codelineno-54-38"></a><span class="w">            </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
-<a id="__codelineno-54-39" name="__codelineno-54-39" href="#__codelineno-54-39"></a><span class="w">            </span><span class="c1">// 次のラウンドの選択に進む</span>
+<a id="__codelineno-54-39" name="__codelineno-54-39" href="#__codelineno-54-39"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
 <a id="__codelineno-54-40" name="__codelineno-54-40" href="#__codelineno-54-40"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">Arrays</span><span class="p">.</span><span class="na">asList</span><span class="p">(</span><span class="n">choice</span><span class="p">.</span><span class="na">left</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="na">right</span><span class="p">),</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
-<a id="__codelineno-54-41" name="__codelineno-54-41" href="#__codelineno-54-41"></a><span class="w">            </span><span class="c1">// 回退：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-54-41" name="__codelineno-54-41" href="#__codelineno-54-41"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-54-42" name="__codelineno-54-42" href="#__codelineno-54-42"></a><span class="w">            </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
 <a id="__codelineno-54-43" name="__codelineno-54-43" href="#__codelineno-54-43"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-54-44" name="__codelineno-54-44" href="#__codelineno-54-44"></a><span class="w">    </span><span class="p">}</span>
@@ -5256,240 +5726,615 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_iii_template.cs</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">preorder_traversal_iii_template</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">IsSolution</span><span class="p">}</span>
-<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a>
-<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">preorder_traversal_iii_template</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">RecordSolution</span><span class="p">}</span>
-<a id="__codelineno-55-4" name="__codelineno-55-4" href="#__codelineno-55-4"></a>
-<a id="__codelineno-55-5" name="__codelineno-55-5" href="#__codelineno-55-5"></a><span class="na">[class]</span><span class="p">{</span><span class="n">preorder_traversal_iii_template</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">IsValid</span><span class="p">}</span>
-<a id="__codelineno-55-6" name="__codelineno-55-6" href="#__codelineno-55-6"></a>
-<a id="__codelineno-55-7" name="__codelineno-55-7" href="#__codelineno-55-7"></a><span class="na">[class]</span><span class="p">{</span><span class="n">preorder_traversal_iii_template</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MakeChoice</span><span class="p">}</span>
-<a id="__codelineno-55-8" name="__codelineno-55-8" href="#__codelineno-55-8"></a>
-<a id="__codelineno-55-9" name="__codelineno-55-9" href="#__codelineno-55-9"></a><span class="na">[class]</span><span class="p">{</span><span class="n">preorder_traversal_iii_template</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">UndoChoice</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_iii_template.cs</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="cm">/* 現在の状態が解かどうかを判定 */</span>
+<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">IsSolution</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">state</span><span class="p">[</span><span class="o">^</span><span class="mi">1</span><span class="p">].</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">;</span>
+<a id="__codelineno-55-4" name="__codelineno-55-4" href="#__codelineno-55-4"></a><span class="p">}</span>
+<a id="__codelineno-55-5" name="__codelineno-55-5" href="#__codelineno-55-5"></a>
+<a id="__codelineno-55-6" name="__codelineno-55-6" href="#__codelineno-55-6"></a><span class="cm">/* 解を記録 */</span>
+<a id="__codelineno-55-7" name="__codelineno-55-7" href="#__codelineno-55-7"></a><span class="k">void</span><span class="w"> </span><span class="nf">RecordSolution</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-8" name="__codelineno-55-8" href="#__codelineno-55-8"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
+<a id="__codelineno-55-9" name="__codelineno-55-9" href="#__codelineno-55-9"></a><span class="p">}</span>
 <a id="__codelineno-55-10" name="__codelineno-55-10" href="#__codelineno-55-10"></a>
-<a id="__codelineno-55-11" name="__codelineno-55-11" href="#__codelineno-55-11"></a><span class="na">[class]</span><span class="p">{</span><span class="n">preorder_traversal_iii_template</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Backtrack</span><span class="p">}</span>
+<a id="__codelineno-55-11" name="__codelineno-55-11" href="#__codelineno-55-11"></a><span class="cm">/* 現在の状態で、この選択が有効かどうかを判定 */</span>
+<a id="__codelineno-55-12" name="__codelineno-55-12" href="#__codelineno-55-12"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">IsValid</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-13" name="__codelineno-55-13" href="#__codelineno-55-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
+<a id="__codelineno-55-14" name="__codelineno-55-14" href="#__codelineno-55-14"></a><span class="p">}</span>
+<a id="__codelineno-55-15" name="__codelineno-55-15" href="#__codelineno-55-15"></a>
+<a id="__codelineno-55-16" name="__codelineno-55-16" href="#__codelineno-55-16"></a><span class="cm">/* 状態を更新 */</span>
+<a id="__codelineno-55-17" name="__codelineno-55-17" href="#__codelineno-55-17"></a><span class="k">void</span><span class="w"> </span><span class="nf">MakeChoice</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-18" name="__codelineno-55-18" href="#__codelineno-55-18"></a><span class="w">    </span><span class="n">state</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-55-19" name="__codelineno-55-19" href="#__codelineno-55-19"></a><span class="p">}</span>
+<a id="__codelineno-55-20" name="__codelineno-55-20" href="#__codelineno-55-20"></a>
+<a id="__codelineno-55-21" name="__codelineno-55-21" href="#__codelineno-55-21"></a><span class="cm">/* 状態を元に戻す */</span>
+<a id="__codelineno-55-22" name="__codelineno-55-22" href="#__codelineno-55-22"></a><span class="k">void</span><span class="w"> </span><span class="nf">UndoChoice</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-23" name="__codelineno-55-23" href="#__codelineno-55-23"></a><span class="w">    </span><span class="n">state</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-55-24" name="__codelineno-55-24" href="#__codelineno-55-24"></a><span class="p">}</span>
+<a id="__codelineno-55-25" name="__codelineno-55-25" href="#__codelineno-55-25"></a>
+<a id="__codelineno-55-26" name="__codelineno-55-26" href="#__codelineno-55-26"></a><span class="cm">/* バックトラッキング：例題 3 */</span>
+<a id="__codelineno-55-27" name="__codelineno-55-27" href="#__codelineno-55-27"></a><span class="k">void</span><span class="w"> </span><span class="nf">Backtrack</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-28" name="__codelineno-55-28" href="#__codelineno-55-28"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-55-29" name="__codelineno-55-29" href="#__codelineno-55-29"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-30" name="__codelineno-55-30" href="#__codelineno-55-30"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-55-31" name="__codelineno-55-31" href="#__codelineno-55-31"></a><span class="w">        </span><span class="n">RecordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-55-32" name="__codelineno-55-32" href="#__codelineno-55-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-55-33" name="__codelineno-55-33" href="#__codelineno-55-33"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-55-34" name="__codelineno-55-34" href="#__codelineno-55-34"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-35" name="__codelineno-55-35" href="#__codelineno-55-35"></a><span class="w">        </span><span class="c1">// 枝刈り：選択が妥当かを確認する</span>
+<a id="__codelineno-55-36" name="__codelineno-55-36" href="#__codelineno-55-36"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-37" name="__codelineno-55-37" href="#__codelineno-55-37"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-55-38" name="__codelineno-55-38" href="#__codelineno-55-38"></a><span class="w">            </span><span class="n">MakeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-55-39" name="__codelineno-55-39" href="#__codelineno-55-39"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-55-40" name="__codelineno-55-40" href="#__codelineno-55-40"></a><span class="w">            </span><span class="n">Backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="n">choice</span><span class="p">.</span><span class="n">left</span><span class="o">!</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">right</span><span class="o">!</span><span class="p">],</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-55-41" name="__codelineno-55-41" href="#__codelineno-55-41"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-55-42" name="__codelineno-55-42" href="#__codelineno-55-42"></a><span class="w">            </span><span class="n">UndoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-55-43" name="__codelineno-55-43" href="#__codelineno-55-43"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-55-44" name="__codelineno-55-44" href="#__codelineno-55-44"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-55-45" name="__codelineno-55-45" href="#__codelineno-55-45"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_iii_template.go</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">isSolution</span><span class="p">}</span>
-<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a>
-<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">recordSolution</span><span class="p">}</span>
-<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a>
-<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">isValid</span><span class="p">}</span>
-<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a>
-<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">makeChoice</span><span class="p">}</span>
-<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a>
-<a id="__codelineno-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">undoChoice</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_iii_template.go</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="cm">/* 現在の状態が解かどうかを判定 */</span>
+<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">isSolution</span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)[</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">].</span><span class="nx">Val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span>
+<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a><span class="p">}</span>
+<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a>
+<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a><span class="cm">/* 解を記録 */</span>
+<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a><span class="kd">func</span><span class="w"> </span><span class="nx">recordSolution</span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">*</span><span class="p">[][]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a><span class="w">    </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nb">append</span><span class="p">([]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">{},</span><span class="w"> </span><span class="o">*</span><span class="nx">state</span><span class="o">...</span><span class="p">))</span>
+<a id="__codelineno-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></a><span class="p">}</span>
 <a id="__codelineno-56-10" name="__codelineno-56-10" href="#__codelineno-56-10"></a>
-<a id="__codelineno-56-11" name="__codelineno-56-11" href="#__codelineno-56-11"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">backtrackIII</span><span class="p">}</span>
+<a id="__codelineno-56-11" name="__codelineno-56-11" href="#__codelineno-56-11"></a><span class="cm">/* 現在の状態で、この選択が有効かどうかを判定 */</span>
+<a id="__codelineno-56-12" name="__codelineno-56-12" href="#__codelineno-56-12"></a><span class="kd">func</span><span class="w"> </span><span class="nx">isValid</span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-13" name="__codelineno-56-13" href="#__codelineno-56-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">choice</span><span class="p">.</span><span class="nx">Val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span>
+<a id="__codelineno-56-14" name="__codelineno-56-14" href="#__codelineno-56-14"></a><span class="p">}</span>
+<a id="__codelineno-56-15" name="__codelineno-56-15" href="#__codelineno-56-15"></a>
+<a id="__codelineno-56-16" name="__codelineno-56-16" href="#__codelineno-56-16"></a><span class="cm">/* 状態を更新 */</span>
+<a id="__codelineno-56-17" name="__codelineno-56-17" href="#__codelineno-56-17"></a><span class="kd">func</span><span class="w"> </span><span class="nx">makeChoice</span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-18" name="__codelineno-56-18" href="#__codelineno-56-18"></a><span class="w">    </span><span class="o">*</span><span class="nx">state</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span>
+<a id="__codelineno-56-19" name="__codelineno-56-19" href="#__codelineno-56-19"></a><span class="p">}</span>
+<a id="__codelineno-56-20" name="__codelineno-56-20" href="#__codelineno-56-20"></a>
+<a id="__codelineno-56-21" name="__codelineno-56-21" href="#__codelineno-56-21"></a><span class="cm">/* 状態を元に戻す */</span>
+<a id="__codelineno-56-22" name="__codelineno-56-22" href="#__codelineno-56-22"></a><span class="kd">func</span><span class="w"> </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-23" name="__codelineno-56-23" href="#__codelineno-56-23"></a><span class="w">    </span><span class="o">*</span><span class="nx">state</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)[:</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-56-24" name="__codelineno-56-24" href="#__codelineno-56-24"></a><span class="p">}</span>
+<a id="__codelineno-56-25" name="__codelineno-56-25" href="#__codelineno-56-25"></a>
+<a id="__codelineno-56-26" name="__codelineno-56-26" href="#__codelineno-56-26"></a><span class="cm">/* バックトラッキング：例題 3 */</span>
+<a id="__codelineno-56-27" name="__codelineno-56-27" href="#__codelineno-56-27"></a><span class="kd">func</span><span class="w"> </span><span class="nx">backtrackIII</span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">*</span><span class="p">[][]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-28" name="__codelineno-56-28" href="#__codelineno-56-28"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-56-29" name="__codelineno-56-29" href="#__codelineno-56-29"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">isSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-30" name="__codelineno-56-30" href="#__codelineno-56-30"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-56-31" name="__codelineno-56-31" href="#__codelineno-56-31"></a><span class="w">        </span><span class="nx">recordSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
+<a id="__codelineno-56-32" name="__codelineno-56-32" href="#__codelineno-56-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-56-33" name="__codelineno-56-33" href="#__codelineno-56-33"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-56-34" name="__codelineno-56-34" href="#__codelineno-56-34"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="o">*</span><span class="nx">choices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-35" name="__codelineno-56-35" href="#__codelineno-56-35"></a><span class="w">        </span><span class="c1">// 枝刈り：選択が妥当かを確認する</span>
+<a id="__codelineno-56-36" name="__codelineno-56-36" href="#__codelineno-56-36"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">isValid</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-37" name="__codelineno-56-37" href="#__codelineno-56-37"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-56-38" name="__codelineno-56-38" href="#__codelineno-56-38"></a><span class="w">            </span><span class="nx">makeChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span>
+<a id="__codelineno-56-39" name="__codelineno-56-39" href="#__codelineno-56-39"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-56-40" name="__codelineno-56-40" href="#__codelineno-56-40"></a><span class="w">            </span><span class="nx">temp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-56-41" name="__codelineno-56-41" href="#__codelineno-56-41"></a><span class="w">            </span><span class="nx">temp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">temp</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">.</span><span class="nx">Left</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">.</span><span class="nx">Right</span><span class="p">)</span>
+<a id="__codelineno-56-42" name="__codelineno-56-42" href="#__codelineno-56-42"></a><span class="w">            </span><span class="nx">backtrackIII</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">temp</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
+<a id="__codelineno-56-43" name="__codelineno-56-43" href="#__codelineno-56-43"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-56-44" name="__codelineno-56-44" href="#__codelineno-56-44"></a><span class="w">            </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span>
+<a id="__codelineno-56-45" name="__codelineno-56-45" href="#__codelineno-56-45"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-56-46" name="__codelineno-56-46" href="#__codelineno-56-46"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-56-47" name="__codelineno-56-47" href="#__codelineno-56-47"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_iii_template.swift</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">isSolution</span><span class="p">}</span>
-<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a>
-<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">recordSolution</span><span class="p">}</span>
-<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a>
-<a id="__codelineno-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">isValid</span><span class="p">}</span>
-<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a>
-<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">makeChoice</span><span class="p">}</span>
-<a id="__codelineno-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a>
-<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">undoChoice</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_iii_template.swift</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 現在の状態が解かどうかを判定 */</span>
+<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="n">TreeNode</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="w">    </span><span class="o">!</span><span class="n">state</span><span class="p">.</span><span class="bp">isEmpty</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="bp">last</span><span class="p">!.</span><span class="n">val</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">7</span>
+<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="p">}</span>
+<a id="__codelineno-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a>
+<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a><span class="cm">/* 解を記録 */</span>
+<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></a><span class="kd">func</span><span class="w"> </span><span class="nf">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[[</span><span class="n">TreeNode</span><span class="p">]])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">state</span><span class="p">)</span>
+<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="p">}</span>
 <a id="__codelineno-57-10" name="__codelineno-57-10" href="#__codelineno-57-10"></a>
-<a id="__codelineno-57-11" name="__codelineno-57-11" href="#__codelineno-57-11"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-57-11" name="__codelineno-57-11" href="#__codelineno-57-11"></a><span class="cm">/* 現在の状態で、この選択が有効かどうかを判定 */</span>
+<a id="__codelineno-57-12" name="__codelineno-57-12" href="#__codelineno-57-12"></a><span class="kd">func</span><span class="w"> </span><span class="nf">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-13" name="__codelineno-57-13" href="#__codelineno-57-13"></a><span class="w">    </span><span class="n">choice</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">choice</span><span class="p">!.</span><span class="n">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span>
+<a id="__codelineno-57-14" name="__codelineno-57-14" href="#__codelineno-57-14"></a><span class="p">}</span>
+<a id="__codelineno-57-15" name="__codelineno-57-15" href="#__codelineno-57-15"></a>
+<a id="__codelineno-57-16" name="__codelineno-57-16" href="#__codelineno-57-16"></a><span class="cm">/* 状態を更新 */</span>
+<a id="__codelineno-57-17" name="__codelineno-57-17" href="#__codelineno-57-17"></a><span class="kd">func</span><span class="w"> </span><span class="nf">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-18" name="__codelineno-57-18" href="#__codelineno-57-18"></a><span class="w">    </span><span class="n">state</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-57-19" name="__codelineno-57-19" href="#__codelineno-57-19"></a><span class="p">}</span>
+<a id="__codelineno-57-20" name="__codelineno-57-20" href="#__codelineno-57-20"></a>
+<a id="__codelineno-57-21" name="__codelineno-57-21" href="#__codelineno-57-21"></a><span class="cm">/* 状態を元に戻す */</span>
+<a id="__codelineno-57-22" name="__codelineno-57-22" href="#__codelineno-57-22"></a><span class="kd">func</span><span class="w"> </span><span class="nf">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-23" name="__codelineno-57-23" href="#__codelineno-57-23"></a><span class="w">    </span><span class="n">state</span><span class="p">.</span><span class="bp">removeLast</span><span class="p">()</span>
+<a id="__codelineno-57-24" name="__codelineno-57-24" href="#__codelineno-57-24"></a><span class="p">}</span>
+<a id="__codelineno-57-25" name="__codelineno-57-25" href="#__codelineno-57-25"></a>
+<a id="__codelineno-57-26" name="__codelineno-57-26" href="#__codelineno-57-26"></a><span class="cm">/* バックトラッキング：例題 3 */</span>
+<a id="__codelineno-57-27" name="__codelineno-57-27" href="#__codelineno-57-27"></a><span class="kd">func</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[[</span><span class="n">TreeNode</span><span class="p">]])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-28" name="__codelineno-57-28" href="#__codelineno-57-28"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-57-29" name="__codelineno-57-29" href="#__codelineno-57-29"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-30" name="__codelineno-57-30" href="#__codelineno-57-30"></a><span class="w">        </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-57-31" name="__codelineno-57-31" href="#__codelineno-57-31"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-57-32" name="__codelineno-57-32" href="#__codelineno-57-32"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-57-33" name="__codelineno-57-33" href="#__codelineno-57-33"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-34" name="__codelineno-57-34" href="#__codelineno-57-34"></a><span class="w">        </span><span class="c1">// 枝刈り：選択が妥当かを確認する</span>
+<a id="__codelineno-57-35" name="__codelineno-57-35" href="#__codelineno-57-35"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-36" name="__codelineno-57-36" href="#__codelineno-57-36"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-57-37" name="__codelineno-57-37" href="#__codelineno-57-37"></a><span class="w">            </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-57-38" name="__codelineno-57-38" href="#__codelineno-57-38"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-57-39" name="__codelineno-57-39" href="#__codelineno-57-39"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="n">choice</span><span class="p">.</span><span class="kr">left</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="kr">right</span><span class="p">].</span><span class="n">compactMap</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nv">$0</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-57-40" name="__codelineno-57-40" href="#__codelineno-57-40"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-57-41" name="__codelineno-57-41" href="#__codelineno-57-41"></a><span class="w">            </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-57-42" name="__codelineno-57-42" href="#__codelineno-57-42"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-57-43" name="__codelineno-57-43" href="#__codelineno-57-43"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-57-44" name="__codelineno-57-44" href="#__codelineno-57-44"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_iii_template.js</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">isSolution</span><span class="p">}</span>
-<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a>
-<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">recordSolution</span><span class="p">}</span>
-<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a>
-<a id="__codelineno-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">isValid</span><span class="p">}</span>
-<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a>
-<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">makeChoice</span><span class="p">}</span>
-<a id="__codelineno-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></a>
-<a id="__codelineno-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">undoChoice</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_iii_template.js</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 現在の状態が解かどうかを判定 */</span>
+<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">isSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">state</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">state</span><span class="p">[</span><span class="nx">state</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="o">?</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">7</span><span class="p">;</span>
+<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><span class="p">}</span>
+<a id="__codelineno-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a>
+<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a><span class="cm">/* 解を記録 */</span>
+<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></a><span class="kd">function</span><span class="w"> </span><span class="nx">recordSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></a><span class="w">    </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">([...</span><span class="nx">state</span><span class="p">]);</span>
+<a id="__codelineno-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></a><span class="p">}</span>
 <a id="__codelineno-58-10" name="__codelineno-58-10" href="#__codelineno-58-10"></a>
-<a id="__codelineno-58-11" name="__codelineno-58-11" href="#__codelineno-58-11"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
+<a id="__codelineno-58-11" name="__codelineno-58-11" href="#__codelineno-58-11"></a><span class="cm">/* 現在の状態で、この選択が有効かどうかを判定 */</span>
+<a id="__codelineno-58-12" name="__codelineno-58-12" href="#__codelineno-58-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">isValid</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-13" name="__codelineno-58-13" href="#__codelineno-58-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">choice</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="mf">3</span><span class="p">;</span>
+<a id="__codelineno-58-14" name="__codelineno-58-14" href="#__codelineno-58-14"></a><span class="p">}</span>
+<a id="__codelineno-58-15" name="__codelineno-58-15" href="#__codelineno-58-15"></a>
+<a id="__codelineno-58-16" name="__codelineno-58-16" href="#__codelineno-58-16"></a><span class="cm">/* 状態を更新 */</span>
+<a id="__codelineno-58-17" name="__codelineno-58-17" href="#__codelineno-58-17"></a><span class="kd">function</span><span class="w"> </span><span class="nx">makeChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-18" name="__codelineno-58-18" href="#__codelineno-58-18"></a><span class="w">    </span><span class="nx">state</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">choice</span><span class="p">);</span>
+<a id="__codelineno-58-19" name="__codelineno-58-19" href="#__codelineno-58-19"></a><span class="p">}</span>
+<a id="__codelineno-58-20" name="__codelineno-58-20" href="#__codelineno-58-20"></a>
+<a id="__codelineno-58-21" name="__codelineno-58-21" href="#__codelineno-58-21"></a><span class="cm">/* 状態を元に戻す */</span>
+<a id="__codelineno-58-22" name="__codelineno-58-22" href="#__codelineno-58-22"></a><span class="kd">function</span><span class="w"> </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-23" name="__codelineno-58-23" href="#__codelineno-58-23"></a><span class="w">    </span><span class="nx">state</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-58-24" name="__codelineno-58-24" href="#__codelineno-58-24"></a><span class="p">}</span>
+<a id="__codelineno-58-25" name="__codelineno-58-25" href="#__codelineno-58-25"></a>
+<a id="__codelineno-58-26" name="__codelineno-58-26" href="#__codelineno-58-26"></a><span class="cm">/* バックトラッキング：例題 3 */</span>
+<a id="__codelineno-58-27" name="__codelineno-58-27" href="#__codelineno-58-27"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-28" name="__codelineno-58-28" href="#__codelineno-58-28"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-58-29" name="__codelineno-58-29" href="#__codelineno-58-29"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">isSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-30" name="__codelineno-58-30" href="#__codelineno-58-30"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-58-31" name="__codelineno-58-31" href="#__codelineno-58-31"></a><span class="w">        </span><span class="nx">recordSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-58-32" name="__codelineno-58-32" href="#__codelineno-58-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-58-33" name="__codelineno-58-33" href="#__codelineno-58-33"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-58-34" name="__codelineno-58-34" href="#__codelineno-58-34"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-35" name="__codelineno-58-35" href="#__codelineno-58-35"></a><span class="w">        </span><span class="c1">// 枝刈り：選択が妥当かを確認する</span>
+<a id="__codelineno-58-36" name="__codelineno-58-36" href="#__codelineno-58-36"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">isValid</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-37" name="__codelineno-58-37" href="#__codelineno-58-37"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-58-38" name="__codelineno-58-38" href="#__codelineno-58-38"></a><span class="w">            </span><span class="nx">makeChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">);</span>
+<a id="__codelineno-58-39" name="__codelineno-58-39" href="#__codelineno-58-39"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-58-40" name="__codelineno-58-40" href="#__codelineno-58-40"></a><span class="w">            </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="nx">choice</span><span class="p">.</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">.</span><span class="nx">right</span><span class="p">],</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-58-41" name="__codelineno-58-41" href="#__codelineno-58-41"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-58-42" name="__codelineno-58-42" href="#__codelineno-58-42"></a><span class="w">            </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">);</span>
+<a id="__codelineno-58-43" name="__codelineno-58-43" href="#__codelineno-58-43"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-58-44" name="__codelineno-58-44" href="#__codelineno-58-44"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-58-45" name="__codelineno-58-45" href="#__codelineno-58-45"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_iii_template.ts</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">isSolution</span><span class="p">}</span>
-<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a>
-<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">recordSolution</span><span class="p">}</span>
-<a id="__codelineno-59-4" name="__codelineno-59-4" href="#__codelineno-59-4"></a>
-<a id="__codelineno-59-5" name="__codelineno-59-5" href="#__codelineno-59-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">isValid</span><span class="p">}</span>
-<a id="__codelineno-59-6" name="__codelineno-59-6" href="#__codelineno-59-6"></a>
-<a id="__codelineno-59-7" name="__codelineno-59-7" href="#__codelineno-59-7"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">makeChoice</span><span class="p">}</span>
-<a id="__codelineno-59-8" name="__codelineno-59-8" href="#__codelineno-59-8"></a>
-<a id="__codelineno-59-9" name="__codelineno-59-9" href="#__codelineno-59-9"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">undoChoice</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_iii_template.ts</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="cm">/* 現在の状態が解かどうかを判定 */</span>
+<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">isSolution</span><span class="p">(</span><span class="nx">state</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">state</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">state</span><span class="p">[</span><span class="nx">state</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="o">?</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">7</span><span class="p">;</span>
+<a id="__codelineno-59-4" name="__codelineno-59-4" href="#__codelineno-59-4"></a><span class="p">}</span>
+<a id="__codelineno-59-5" name="__codelineno-59-5" href="#__codelineno-59-5"></a>
+<a id="__codelineno-59-6" name="__codelineno-59-6" href="#__codelineno-59-6"></a><span class="cm">/* 解を記録 */</span>
+<a id="__codelineno-59-7" name="__codelineno-59-7" href="#__codelineno-59-7"></a><span class="kd">function</span><span class="w"> </span><span class="nx">recordSolution</span><span class="p">(</span><span class="nx">state</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[],</span><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[][])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-8" name="__codelineno-59-8" href="#__codelineno-59-8"></a><span class="w">    </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">([...</span><span class="nx">state</span><span class="p">]);</span>
+<a id="__codelineno-59-9" name="__codelineno-59-9" href="#__codelineno-59-9"></a><span class="p">}</span>
 <a id="__codelineno-59-10" name="__codelineno-59-10" href="#__codelineno-59-10"></a>
-<a id="__codelineno-59-11" name="__codelineno-59-11" href="#__codelineno-59-11"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
+<a id="__codelineno-59-11" name="__codelineno-59-11" href="#__codelineno-59-11"></a><span class="cm">/* 現在の状態で、この選択が有効かどうかを判定 */</span>
+<a id="__codelineno-59-12" name="__codelineno-59-12" href="#__codelineno-59-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">isValid</span><span class="p">(</span><span class="nx">state</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[],</span><span class="w"> </span><span class="nx">choice</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-13" name="__codelineno-59-13" href="#__codelineno-59-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">choice</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="mf">3</span><span class="p">;</span>
+<a id="__codelineno-59-14" name="__codelineno-59-14" href="#__codelineno-59-14"></a><span class="p">}</span>
+<a id="__codelineno-59-15" name="__codelineno-59-15" href="#__codelineno-59-15"></a>
+<a id="__codelineno-59-16" name="__codelineno-59-16" href="#__codelineno-59-16"></a><span class="cm">/* 状態を更新 */</span>
+<a id="__codelineno-59-17" name="__codelineno-59-17" href="#__codelineno-59-17"></a><span class="kd">function</span><span class="w"> </span><span class="nx">makeChoice</span><span class="p">(</span><span class="nx">state</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[],</span><span class="w"> </span><span class="nx">choice</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-18" name="__codelineno-59-18" href="#__codelineno-59-18"></a><span class="w">    </span><span class="nx">state</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">choice</span><span class="p">);</span>
+<a id="__codelineno-59-19" name="__codelineno-59-19" href="#__codelineno-59-19"></a><span class="p">}</span>
+<a id="__codelineno-59-20" name="__codelineno-59-20" href="#__codelineno-59-20"></a>
+<a id="__codelineno-59-21" name="__codelineno-59-21" href="#__codelineno-59-21"></a><span class="cm">/* 状態を元に戻す */</span>
+<a id="__codelineno-59-22" name="__codelineno-59-22" href="#__codelineno-59-22"></a><span class="kd">function</span><span class="w"> </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-23" name="__codelineno-59-23" href="#__codelineno-59-23"></a><span class="w">    </span><span class="nx">state</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-59-24" name="__codelineno-59-24" href="#__codelineno-59-24"></a><span class="p">}</span>
+<a id="__codelineno-59-25" name="__codelineno-59-25" href="#__codelineno-59-25"></a>
+<a id="__codelineno-59-26" name="__codelineno-59-26" href="#__codelineno-59-26"></a><span class="cm">/* バックトラッキング：例題 3 */</span>
+<a id="__codelineno-59-27" name="__codelineno-59-27" href="#__codelineno-59-27"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span>
+<a id="__codelineno-59-28" name="__codelineno-59-28" href="#__codelineno-59-28"></a><span class="w">    </span><span class="nx">state</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[],</span>
+<a id="__codelineno-59-29" name="__codelineno-59-29" href="#__codelineno-59-29"></a><span class="w">    </span><span class="nx">choices</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[],</span>
+<a id="__codelineno-59-30" name="__codelineno-59-30" href="#__codelineno-59-30"></a><span class="w">    </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[][]</span>
+<a id="__codelineno-59-31" name="__codelineno-59-31" href="#__codelineno-59-31"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-32" name="__codelineno-59-32" href="#__codelineno-59-32"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-59-33" name="__codelineno-59-33" href="#__codelineno-59-33"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">isSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-34" name="__codelineno-59-34" href="#__codelineno-59-34"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-59-35" name="__codelineno-59-35" href="#__codelineno-59-35"></a><span class="w">        </span><span class="nx">recordSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-59-36" name="__codelineno-59-36" href="#__codelineno-59-36"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-59-37" name="__codelineno-59-37" href="#__codelineno-59-37"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-59-38" name="__codelineno-59-38" href="#__codelineno-59-38"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-39" name="__codelineno-59-39" href="#__codelineno-59-39"></a><span class="w">        </span><span class="c1">// 枝刈り：選択が妥当かを確認する</span>
+<a id="__codelineno-59-40" name="__codelineno-59-40" href="#__codelineno-59-40"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">isValid</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-41" name="__codelineno-59-41" href="#__codelineno-59-41"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-59-42" name="__codelineno-59-42" href="#__codelineno-59-42"></a><span class="w">            </span><span class="nx">makeChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">);</span>
+<a id="__codelineno-59-43" name="__codelineno-59-43" href="#__codelineno-59-43"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-59-44" name="__codelineno-59-44" href="#__codelineno-59-44"></a><span class="w">            </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="nx">choice</span><span class="p">.</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">.</span><span class="nx">right</span><span class="p">],</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-59-45" name="__codelineno-59-45" href="#__codelineno-59-45"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-59-46" name="__codelineno-59-46" href="#__codelineno-59-46"></a><span class="w">            </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">);</span>
+<a id="__codelineno-59-47" name="__codelineno-59-47" href="#__codelineno-59-47"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-59-48" name="__codelineno-59-48" href="#__codelineno-59-48"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-59-49" name="__codelineno-59-49" href="#__codelineno-59-49"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_iii_template.dart</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">isSolution</span><span class="p">}</span>
-<a id="__codelineno-60-2" name="__codelineno-60-2" href="#__codelineno-60-2"></a>
-<a id="__codelineno-60-3" name="__codelineno-60-3" href="#__codelineno-60-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">recordSolution</span><span class="p">}</span>
-<a id="__codelineno-60-4" name="__codelineno-60-4" href="#__codelineno-60-4"></a>
-<a id="__codelineno-60-5" name="__codelineno-60-5" href="#__codelineno-60-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">isValid</span><span class="p">}</span>
-<a id="__codelineno-60-6" name="__codelineno-60-6" href="#__codelineno-60-6"></a>
-<a id="__codelineno-60-7" name="__codelineno-60-7" href="#__codelineno-60-7"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">makeChoice</span><span class="p">}</span>
-<a id="__codelineno-60-8" name="__codelineno-60-8" href="#__codelineno-60-8"></a>
-<a id="__codelineno-60-9" name="__codelineno-60-9" href="#__codelineno-60-9"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">undoChoice</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_iii_template.dart</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="cm">/* 現在の状態が解かどうかを判定 */</span>
+<a id="__codelineno-60-2" name="__codelineno-60-2" href="#__codelineno-60-2"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isSolution</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-3" name="__codelineno-60-3" href="#__codelineno-60-3"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">isNotEmpty</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">last</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">7</span><span class="p">;</span>
+<a id="__codelineno-60-4" name="__codelineno-60-4" href="#__codelineno-60-4"></a><span class="p">}</span>
+<a id="__codelineno-60-5" name="__codelineno-60-5" href="#__codelineno-60-5"></a>
+<a id="__codelineno-60-6" name="__codelineno-60-6" href="#__codelineno-60-6"></a><span class="cm">/* 解を記録 */</span>
+<a id="__codelineno-60-7" name="__codelineno-60-7" href="#__codelineno-60-7"></a><span class="kt">void</span><span class="w"> </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-8" name="__codelineno-60-8" href="#__codelineno-60-8"></a><span class="w">  </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">List</span><span class="p">.</span><span class="n">from</span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
+<a id="__codelineno-60-9" name="__codelineno-60-9" href="#__codelineno-60-9"></a><span class="p">}</span>
 <a id="__codelineno-60-10" name="__codelineno-60-10" href="#__codelineno-60-10"></a>
-<a id="__codelineno-60-11" name="__codelineno-60-11" href="#__codelineno-60-11"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-60-11" name="__codelineno-60-11" href="#__codelineno-60-11"></a><span class="cm">/* 現在の状態で、この選択が有効かどうかを判定 */</span>
+<a id="__codelineno-60-12" name="__codelineno-60-12" href="#__codelineno-60-12"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isValid</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-13" name="__codelineno-60-13" href="#__codelineno-60-13"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="m">3</span><span class="p">;</span>
+<a id="__codelineno-60-14" name="__codelineno-60-14" href="#__codelineno-60-14"></a><span class="p">}</span>
+<a id="__codelineno-60-15" name="__codelineno-60-15" href="#__codelineno-60-15"></a>
+<a id="__codelineno-60-16" name="__codelineno-60-16" href="#__codelineno-60-16"></a><span class="cm">/* 状態を更新 */</span>
+<a id="__codelineno-60-17" name="__codelineno-60-17" href="#__codelineno-60-17"></a><span class="kt">void</span><span class="w"> </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-18" name="__codelineno-60-18" href="#__codelineno-60-18"></a><span class="w">  </span><span class="n">state</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">choice</span><span class="o">!</span><span class="p">);</span>
+<a id="__codelineno-60-19" name="__codelineno-60-19" href="#__codelineno-60-19"></a><span class="p">}</span>
+<a id="__codelineno-60-20" name="__codelineno-60-20" href="#__codelineno-60-20"></a>
+<a id="__codelineno-60-21" name="__codelineno-60-21" href="#__codelineno-60-21"></a><span class="cm">/* 状態を元に戻す */</span>
+<a id="__codelineno-60-22" name="__codelineno-60-22" href="#__codelineno-60-22"></a><span class="kt">void</span><span class="w"> </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-23" name="__codelineno-60-23" href="#__codelineno-60-23"></a><span class="w">  </span><span class="n">state</span><span class="p">.</span><span class="n">removeLast</span><span class="p">();</span>
+<a id="__codelineno-60-24" name="__codelineno-60-24" href="#__codelineno-60-24"></a><span class="p">}</span>
+<a id="__codelineno-60-25" name="__codelineno-60-25" href="#__codelineno-60-25"></a>
+<a id="__codelineno-60-26" name="__codelineno-60-26" href="#__codelineno-60-26"></a><span class="cm">/* バックトラッキング：例題 3 */</span>
+<a id="__codelineno-60-27" name="__codelineno-60-27" href="#__codelineno-60-27"></a><span class="kt">void</span><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span>
+<a id="__codelineno-60-28" name="__codelineno-60-28" href="#__codelineno-60-28"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span>
+<a id="__codelineno-60-29" name="__codelineno-60-29" href="#__codelineno-60-29"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">?&gt;</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span>
+<a id="__codelineno-60-30" name="__codelineno-60-30" href="#__codelineno-60-30"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">,</span>
+<a id="__codelineno-60-31" name="__codelineno-60-31" href="#__codelineno-60-31"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-32" name="__codelineno-60-32" href="#__codelineno-60-32"></a><span class="w">  </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-60-33" name="__codelineno-60-33" href="#__codelineno-60-33"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-34" name="__codelineno-60-34" href="#__codelineno-60-34"></a><span class="w">    </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-60-35" name="__codelineno-60-35" href="#__codelineno-60-35"></a><span class="w">    </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-60-36" name="__codelineno-60-36" href="#__codelineno-60-36"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-60-37" name="__codelineno-60-37" href="#__codelineno-60-37"></a><span class="w">  </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-60-38" name="__codelineno-60-38" href="#__codelineno-60-38"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-39" name="__codelineno-60-39" href="#__codelineno-60-39"></a><span class="w">    </span><span class="c1">// 枝刈り：選択が妥当かを確認する</span>
+<a id="__codelineno-60-40" name="__codelineno-60-40" href="#__codelineno-60-40"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-41" name="__codelineno-60-41" href="#__codelineno-60-41"></a><span class="w">      </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-60-42" name="__codelineno-60-42" href="#__codelineno-60-42"></a><span class="w">      </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-60-43" name="__codelineno-60-43" href="#__codelineno-60-43"></a><span class="w">      </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-60-44" name="__codelineno-60-44" href="#__codelineno-60-44"></a><span class="w">      </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="n">choice</span><span class="o">!</span><span class="p">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">right</span><span class="p">],</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-60-45" name="__codelineno-60-45" href="#__codelineno-60-45"></a><span class="w">      </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-60-46" name="__codelineno-60-46" href="#__codelineno-60-46"></a><span class="w">      </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-60-47" name="__codelineno-60-47" href="#__codelineno-60-47"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-60-48" name="__codelineno-60-48" href="#__codelineno-60-48"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-60-49" name="__codelineno-60-49" href="#__codelineno-60-49"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_iii_template.rs</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">is_solution</span><span class="p">}</span>
-<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a>
-<a id="__codelineno-61-3" name="__codelineno-61-3" href="#__codelineno-61-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">record_solution</span><span class="p">}</span>
-<a id="__codelineno-61-4" name="__codelineno-61-4" href="#__codelineno-61-4"></a>
-<a id="__codelineno-61-5" name="__codelineno-61-5" href="#__codelineno-61-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">is_valid</span><span class="p">}</span>
-<a id="__codelineno-61-6" name="__codelineno-61-6" href="#__codelineno-61-6"></a>
-<a id="__codelineno-61-7" name="__codelineno-61-7" href="#__codelineno-61-7"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">make_choice</span><span class="p">}</span>
-<a id="__codelineno-61-8" name="__codelineno-61-8" href="#__codelineno-61-8"></a>
-<a id="__codelineno-61-9" name="__codelineno-61-9" href="#__codelineno-61-9"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">undo_choice</span><span class="p">}</span>
-<a id="__codelineno-61-10" name="__codelineno-61-10" href="#__codelineno-61-10"></a>
-<a id="__codelineno-61-11" name="__codelineno-61-11" href="#__codelineno-61-11"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_iii_template.rs</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="cm">/* 現在の状態が解かどうかを判定 */</span>
+<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">is_solution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-3" name="__codelineno-61-3" href="#__codelineno-61-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">!</span><span class="n">state</span><span class="p">.</span><span class="n">is_empty</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">last</span><span class="p">().</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">;</span>
+<a id="__codelineno-61-4" name="__codelineno-61-4" href="#__codelineno-61-4"></a><span class="p">}</span>
+<a id="__codelineno-61-5" name="__codelineno-61-5" href="#__codelineno-61-5"></a>
+<a id="__codelineno-61-6" name="__codelineno-61-6" href="#__codelineno-61-6"></a><span class="cm">/* 解を記録 */</span>
+<a id="__codelineno-61-7" name="__codelineno-61-7" href="#__codelineno-61-7"></a><span class="k">fn</span><span class="w"> </span><span class="nf">record_solution</span><span class="p">(</span>
+<a id="__codelineno-61-8" name="__codelineno-61-8" href="#__codelineno-61-8"></a><span class="w">    </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-61-9" name="__codelineno-61-9" href="#__codelineno-61-9"></a><span class="w">    </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-61-10" name="__codelineno-61-10" href="#__codelineno-61-10"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-11" name="__codelineno-61-11" href="#__codelineno-61-11"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-61-12" name="__codelineno-61-12" href="#__codelineno-61-12"></a><span class="p">}</span>
+<a id="__codelineno-61-13" name="__codelineno-61-13" href="#__codelineno-61-13"></a>
+<a id="__codelineno-61-14" name="__codelineno-61-14" href="#__codelineno-61-14"></a><span class="cm">/* 現在の状態で、この選択が有効かどうかを判定 */</span>
+<a id="__codelineno-61-15" name="__codelineno-61-15" href="#__codelineno-61-15"></a><span class="k">fn</span><span class="w"> </span><span class="nf">is_valid</span><span class="p">(</span><span class="n">_</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-16" name="__codelineno-61-16" href="#__codelineno-61-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">is_some</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
+<a id="__codelineno-61-17" name="__codelineno-61-17" href="#__codelineno-61-17"></a><span class="p">}</span>
+<a id="__codelineno-61-18" name="__codelineno-61-18" href="#__codelineno-61-18"></a>
+<a id="__codelineno-61-19" name="__codelineno-61-19" href="#__codelineno-61-19"></a><span class="cm">/* 状態を更新 */</span>
+<a id="__codelineno-61-20" name="__codelineno-61-20" href="#__codelineno-61-20"></a><span class="k">fn</span><span class="w"> </span><span class="nf">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="nc">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-21" name="__codelineno-61-21" href="#__codelineno-61-21"></a><span class="w">    </span><span class="n">state</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-61-22" name="__codelineno-61-22" href="#__codelineno-61-22"></a><span class="p">}</span>
+<a id="__codelineno-61-23" name="__codelineno-61-23" href="#__codelineno-61-23"></a>
+<a id="__codelineno-61-24" name="__codelineno-61-24" href="#__codelineno-61-24"></a><span class="cm">/* 状態を元に戻す */</span>
+<a id="__codelineno-61-25" name="__codelineno-61-25" href="#__codelineno-61-25"></a><span class="k">fn</span><span class="w"> </span><span class="nf">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">_</span><span class="p">:</span><span class="w"> </span><span class="nc">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-26" name="__codelineno-61-26" href="#__codelineno-61-26"></a><span class="w">    </span><span class="n">state</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
+<a id="__codelineno-61-27" name="__codelineno-61-27" href="#__codelineno-61-27"></a><span class="p">}</span>
+<a id="__codelineno-61-28" name="__codelineno-61-28" href="#__codelineno-61-28"></a>
+<a id="__codelineno-61-29" name="__codelineno-61-29" href="#__codelineno-61-29"></a><span class="cm">/* バックトラッキング：例題 3 */</span>
+<a id="__codelineno-61-30" name="__codelineno-61-30" href="#__codelineno-61-30"></a><span class="k">fn</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
+<a id="__codelineno-61-31" name="__codelineno-61-31" href="#__codelineno-61-31"></a><span class="w">    </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-61-32" name="__codelineno-61-32" href="#__codelineno-61-32"></a><span class="w">    </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-61-33" name="__codelineno-61-33" href="#__codelineno-61-33"></a><span class="w">    </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-61-34" name="__codelineno-61-34" href="#__codelineno-61-34"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-35" name="__codelineno-61-35" href="#__codelineno-61-35"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-61-36" name="__codelineno-61-36" href="#__codelineno-61-36"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">is_solution</span><span class="p">(</span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-37" name="__codelineno-61-37" href="#__codelineno-61-37"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-61-38" name="__codelineno-61-38" href="#__codelineno-61-38"></a><span class="w">        </span><span class="n">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-61-39" name="__codelineno-61-39" href="#__codelineno-61-39"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-61-40" name="__codelineno-61-40" href="#__codelineno-61-40"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-61-41" name="__codelineno-61-41" href="#__codelineno-61-41"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">iter</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-42" name="__codelineno-61-42" href="#__codelineno-61-42"></a><span class="w">        </span><span class="c1">// 枝刈り：選択が妥当かを確認する</span>
+<a id="__codelineno-61-43" name="__codelineno-61-43" href="#__codelineno-61-43"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">is_valid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-44" name="__codelineno-61-44" href="#__codelineno-61-44"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-61-45" name="__codelineno-61-45" href="#__codelineno-61-45"></a><span class="w">            </span><span class="n">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">unwrap</span><span class="p">().</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-61-46" name="__codelineno-61-46" href="#__codelineno-61-46"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-61-47" name="__codelineno-61-47" href="#__codelineno-61-47"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span>
+<a id="__codelineno-61-48" name="__codelineno-61-48" href="#__codelineno-61-48"></a><span class="w">                </span><span class="n">state</span><span class="p">,</span>
+<a id="__codelineno-61-49" name="__codelineno-61-49" href="#__codelineno-61-49"></a><span class="w">                </span><span class="o">&amp;</span><span class="fm">vec!</span><span class="p">[</span>
+<a id="__codelineno-61-50" name="__codelineno-61-50" href="#__codelineno-61-50"></a><span class="w">                    </span><span class="n">choice</span><span class="p">.</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">(),</span>
+<a id="__codelineno-61-51" name="__codelineno-61-51" href="#__codelineno-61-51"></a><span class="w">                    </span><span class="n">choice</span><span class="p">.</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">(),</span>
+<a id="__codelineno-61-52" name="__codelineno-61-52" href="#__codelineno-61-52"></a><span class="w">                </span><span class="p">],</span>
+<a id="__codelineno-61-53" name="__codelineno-61-53" href="#__codelineno-61-53"></a><span class="w">                </span><span class="n">res</span><span class="p">,</span>
+<a id="__codelineno-61-54" name="__codelineno-61-54" href="#__codelineno-61-54"></a><span class="w">            </span><span class="p">);</span>
+<a id="__codelineno-61-55" name="__codelineno-61-55" href="#__codelineno-61-55"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-61-56" name="__codelineno-61-56" href="#__codelineno-61-56"></a><span class="w">            </span><span class="n">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">unwrap</span><span class="p">().</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-61-57" name="__codelineno-61-57" href="#__codelineno-61-57"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-61-58" name="__codelineno-61-58" href="#__codelineno-61-58"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-61-59" name="__codelineno-61-59" href="#__codelineno-61-59"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_iii_template.c</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">isSolution</span><span class="p">}</span>
-<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a>
-<a id="__codelineno-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">recordSolution</span><span class="p">}</span>
-<a id="__codelineno-62-4" name="__codelineno-62-4" href="#__codelineno-62-4"></a>
-<a id="__codelineno-62-5" name="__codelineno-62-5" href="#__codelineno-62-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">isValid</span><span class="p">}</span>
-<a id="__codelineno-62-6" name="__codelineno-62-6" href="#__codelineno-62-6"></a>
-<a id="__codelineno-62-7" name="__codelineno-62-7" href="#__codelineno-62-7"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">makeChoice</span><span class="p">}</span>
-<a id="__codelineno-62-8" name="__codelineno-62-8" href="#__codelineno-62-8"></a>
-<a id="__codelineno-62-9" name="__codelineno-62-9" href="#__codelineno-62-9"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">undoChoice</span><span class="p">}</span>
-<a id="__codelineno-62-10" name="__codelineno-62-10" href="#__codelineno-62-10"></a>
-<a id="__codelineno-62-11" name="__codelineno-62-11" href="#__codelineno-62-11"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_iii_template.c</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="cm">/* 現在の状態が解かどうかを判定 */</span>
+<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">isSolution</span><span class="p">(</span><span class="kt">void</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">pathSize</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">path</span><span class="p">[</span><span class="n">pathSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">;</span>
+<a id="__codelineno-62-4" name="__codelineno-62-4" href="#__codelineno-62-4"></a><span class="p">}</span>
+<a id="__codelineno-62-5" name="__codelineno-62-5" href="#__codelineno-62-5"></a>
+<a id="__codelineno-62-6" name="__codelineno-62-6" href="#__codelineno-62-6"></a><span class="cm">/* 解を記録 */</span>
+<a id="__codelineno-62-7" name="__codelineno-62-7" href="#__codelineno-62-7"></a><span class="kt">void</span><span class="w"> </span><span class="nf">recordSolution</span><span class="p">(</span><span class="kt">void</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-8" name="__codelineno-62-8" href="#__codelineno-62-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">pathSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-9" name="__codelineno-62-9" href="#__codelineno-62-9"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">resSize</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">path</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-62-10" name="__codelineno-62-10" href="#__codelineno-62-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-62-11" name="__codelineno-62-11" href="#__codelineno-62-11"></a><span class="w">    </span><span class="n">resSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-62-12" name="__codelineno-62-12" href="#__codelineno-62-12"></a><span class="p">}</span>
+<a id="__codelineno-62-13" name="__codelineno-62-13" href="#__codelineno-62-13"></a>
+<a id="__codelineno-62-14" name="__codelineno-62-14" href="#__codelineno-62-14"></a><span class="cm">/* 現在の状態で、この選択が有効かどうかを判定 */</span>
+<a id="__codelineno-62-15" name="__codelineno-62-15" href="#__codelineno-62-15"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">isValid</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-16" name="__codelineno-62-16" href="#__codelineno-62-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">choice</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
+<a id="__codelineno-62-17" name="__codelineno-62-17" href="#__codelineno-62-17"></a><span class="p">}</span>
+<a id="__codelineno-62-18" name="__codelineno-62-18" href="#__codelineno-62-18"></a>
+<a id="__codelineno-62-19" name="__codelineno-62-19" href="#__codelineno-62-19"></a><span class="cm">/* 状態を更新 */</span>
+<a id="__codelineno-62-20" name="__codelineno-62-20" href="#__codelineno-62-20"></a><span class="kt">void</span><span class="w"> </span><span class="nf">makeChoice</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-21" name="__codelineno-62-21" href="#__codelineno-62-21"></a><span class="w">    </span><span class="n">path</span><span class="p">[</span><span class="n">pathSize</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choice</span><span class="p">;</span>
+<a id="__codelineno-62-22" name="__codelineno-62-22" href="#__codelineno-62-22"></a><span class="p">}</span>
+<a id="__codelineno-62-23" name="__codelineno-62-23" href="#__codelineno-62-23"></a>
+<a id="__codelineno-62-24" name="__codelineno-62-24" href="#__codelineno-62-24"></a><span class="cm">/* 状態を元に戻す */</span>
+<a id="__codelineno-62-25" name="__codelineno-62-25" href="#__codelineno-62-25"></a><span class="kt">void</span><span class="w"> </span><span class="nf">undoChoice</span><span class="p">(</span><span class="kt">void</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-26" name="__codelineno-62-26" href="#__codelineno-62-26"></a><span class="w">    </span><span class="n">pathSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-62-27" name="__codelineno-62-27" href="#__codelineno-62-27"></a><span class="p">}</span>
+<a id="__codelineno-62-28" name="__codelineno-62-28" href="#__codelineno-62-28"></a>
+<a id="__codelineno-62-29" name="__codelineno-62-29" href="#__codelineno-62-29"></a><span class="cm">/* バックトラッキング：例題 3 */</span>
+<a id="__codelineno-62-30" name="__codelineno-62-30" href="#__codelineno-62-30"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choices</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-31" name="__codelineno-62-31" href="#__codelineno-62-31"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-62-32" name="__codelineno-62-32" href="#__codelineno-62-32"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-33" name="__codelineno-62-33" href="#__codelineno-62-33"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-62-34" name="__codelineno-62-34" href="#__codelineno-62-34"></a><span class="w">        </span><span class="n">recordSolution</span><span class="p">();</span>
+<a id="__codelineno-62-35" name="__codelineno-62-35" href="#__codelineno-62-35"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-62-36" name="__codelineno-62-36" href="#__codelineno-62-36"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-62-37" name="__codelineno-62-37" href="#__codelineno-62-37"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-38" name="__codelineno-62-38" href="#__codelineno-62-38"></a><span class="w">        </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choice</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-62-39" name="__codelineno-62-39" href="#__codelineno-62-39"></a><span class="w">        </span><span class="c1">// 枝刈り：選択が妥当かを確認する</span>
+<a id="__codelineno-62-40" name="__codelineno-62-40" href="#__codelineno-62-40"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-41" name="__codelineno-62-41" href="#__codelineno-62-41"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-62-42" name="__codelineno-62-42" href="#__codelineno-62-42"></a><span class="w">            </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-62-43" name="__codelineno-62-43" href="#__codelineno-62-43"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-62-44" name="__codelineno-62-44" href="#__codelineno-62-44"></a><span class="w">            </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">nextChoices</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="n">choice</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">};</span>
+<a id="__codelineno-62-45" name="__codelineno-62-45" href="#__codelineno-62-45"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">nextChoices</span><span class="p">);</span>
+<a id="__codelineno-62-46" name="__codelineno-62-46" href="#__codelineno-62-46"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-62-47" name="__codelineno-62-47" href="#__codelineno-62-47"></a><span class="w">            </span><span class="n">undoChoice</span><span class="p">();</span>
+<a id="__codelineno-62-48" name="__codelineno-62-48" href="#__codelineno-62-48"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-62-49" name="__codelineno-62-49" href="#__codelineno-62-49"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-62-50" name="__codelineno-62-50" href="#__codelineno-62-50"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_iii_template.kt</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">isSolution</span><span class="p">}</span>
-<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a>
-<a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">recordSolution</span><span class="p">}</span>
-<a id="__codelineno-63-4" name="__codelineno-63-4" href="#__codelineno-63-4"></a>
-<a id="__codelineno-63-5" name="__codelineno-63-5" href="#__codelineno-63-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">isValid</span><span class="p">}</span>
-<a id="__codelineno-63-6" name="__codelineno-63-6" href="#__codelineno-63-6"></a>
-<a id="__codelineno-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">makeChoice</span><span class="p">}</span>
-<a id="__codelineno-63-8" name="__codelineno-63-8" href="#__codelineno-63-8"></a>
-<a id="__codelineno-63-9" name="__codelineno-63-9" href="#__codelineno-63-9"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">undoChoice</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_iii_template.kt</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="cm">/* 現在の状態が解かどうかを判定 */</span>
+<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?&gt;</span><span class="p">):</span><span class="w"> </span><span class="kt">Boolean</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="na">isNotEmpty</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">state</span><span class="o">[</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]?.</span><span class="na">_val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">7</span>
+<a id="__codelineno-63-4" name="__codelineno-63-4" href="#__codelineno-63-4"></a><span class="p">}</span>
+<a id="__codelineno-63-5" name="__codelineno-63-5" href="#__codelineno-63-5"></a>
+<a id="__codelineno-63-6" name="__codelineno-63-6" href="#__codelineno-63-6"></a><span class="cm">/* 解を記録 */</span>
+<a id="__codelineno-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?&gt;</span><span class="o">?</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?&gt;</span><span class="o">?&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-8" name="__codelineno-63-8" href="#__codelineno-63-8"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">state</span><span class="o">!!</span><span class="p">.</span><span class="na">toMutableList</span><span class="p">())</span>
+<a id="__codelineno-63-9" name="__codelineno-63-9" href="#__codelineno-63-9"></a><span class="p">}</span>
 <a id="__codelineno-63-10" name="__codelineno-63-10" href="#__codelineno-63-10"></a>
-<a id="__codelineno-63-11" name="__codelineno-63-11" href="#__codelineno-63-11"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-63-11" name="__codelineno-63-11" href="#__codelineno-63-11"></a><span class="cm">/* 現在の状態で、この選択が有効かどうかを判定 */</span>
+<a id="__codelineno-63-12" name="__codelineno-63-12" href="#__codelineno-63-12"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?&gt;</span><span class="o">?</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="p">:</span><span class="w"> </span><span class="kt">Boolean</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-13" name="__codelineno-63-13" href="#__codelineno-63-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="na">_val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="m">3</span>
+<a id="__codelineno-63-14" name="__codelineno-63-14" href="#__codelineno-63-14"></a><span class="p">}</span>
+<a id="__codelineno-63-15" name="__codelineno-63-15" href="#__codelineno-63-15"></a>
+<a id="__codelineno-63-16" name="__codelineno-63-16" href="#__codelineno-63-16"></a><span class="cm">/* 状態を更新 */</span>
+<a id="__codelineno-63-17" name="__codelineno-63-17" href="#__codelineno-63-17"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-18" name="__codelineno-63-18" href="#__codelineno-63-18"></a><span class="w">    </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-63-19" name="__codelineno-63-19" href="#__codelineno-63-19"></a><span class="p">}</span>
+<a id="__codelineno-63-20" name="__codelineno-63-20" href="#__codelineno-63-20"></a>
+<a id="__codelineno-63-21" name="__codelineno-63-21" href="#__codelineno-63-21"></a><span class="cm">/* 状態を元に戻す */</span>
+<a id="__codelineno-63-22" name="__codelineno-63-22" href="#__codelineno-63-22"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-23" name="__codelineno-63-23" href="#__codelineno-63-23"></a><span class="w">    </span><span class="n">state</span><span class="p">.</span><span class="na">removeLast</span><span class="p">()</span>
+<a id="__codelineno-63-24" name="__codelineno-63-24" href="#__codelineno-63-24"></a><span class="p">}</span>
+<a id="__codelineno-63-25" name="__codelineno-63-25" href="#__codelineno-63-25"></a>
+<a id="__codelineno-63-26" name="__codelineno-63-26" href="#__codelineno-63-26"></a><span class="cm">/* バックトラッキング：例題 3 */</span>
+<a id="__codelineno-63-27" name="__codelineno-63-27" href="#__codelineno-63-27"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
+<a id="__codelineno-63-28" name="__codelineno-63-28" href="#__codelineno-63-28"></a><span class="w">    </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?&gt;</span><span class="p">,</span>
+<a id="__codelineno-63-29" name="__codelineno-63-29" href="#__codelineno-63-29"></a><span class="w">    </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?&gt;</span><span class="p">,</span>
+<a id="__codelineno-63-30" name="__codelineno-63-30" href="#__codelineno-63-30"></a><span class="w">    </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?&gt;</span><span class="o">?&gt;</span>
+<a id="__codelineno-63-31" name="__codelineno-63-31" href="#__codelineno-63-31"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-32" name="__codelineno-63-32" href="#__codelineno-63-32"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-63-33" name="__codelineno-63-33" href="#__codelineno-63-33"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-34" name="__codelineno-63-34" href="#__codelineno-63-34"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-63-35" name="__codelineno-63-35" href="#__codelineno-63-35"></a><span class="w">        </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-63-36" name="__codelineno-63-36" href="#__codelineno-63-36"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-63-37" name="__codelineno-63-37" href="#__codelineno-63-37"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-63-38" name="__codelineno-63-38" href="#__codelineno-63-38"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-39" name="__codelineno-63-39" href="#__codelineno-63-39"></a><span class="w">        </span><span class="c1">// 枝刈り：選択が妥当かを確認する</span>
+<a id="__codelineno-63-40" name="__codelineno-63-40" href="#__codelineno-63-40"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-41" name="__codelineno-63-41" href="#__codelineno-63-41"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-63-42" name="__codelineno-63-42" href="#__codelineno-63-42"></a><span class="w">            </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-63-43" name="__codelineno-63-43" href="#__codelineno-63-43"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-63-44" name="__codelineno-63-44" href="#__codelineno-63-44"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">mutableListOf</span><span class="p">(</span><span class="n">choice</span><span class="o">!!</span><span class="p">.</span><span class="na">left</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="na">right</span><span class="p">),</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-63-45" name="__codelineno-63-45" href="#__codelineno-63-45"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-63-46" name="__codelineno-63-46" href="#__codelineno-63-46"></a><span class="w">            </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-63-47" name="__codelineno-63-47" href="#__codelineno-63-47"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-63-48" name="__codelineno-63-48" href="#__codelineno-63-48"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-63-49" name="__codelineno-63-49" href="#__codelineno-63-49"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">preorder_traversal_iii_template.rb</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">is_solution</span><span class="p">}</span>
-<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a>
-<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">record_solution</span><span class="p">}</span>
-<a id="__codelineno-64-4" name="__codelineno-64-4" href="#__codelineno-64-4"></a>
-<a id="__codelineno-64-5" name="__codelineno-64-5" href="#__codelineno-64-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">is_valid</span><span class="p">}</span>
-<a id="__codelineno-64-6" name="__codelineno-64-6" href="#__codelineno-64-6"></a>
-<a id="__codelineno-64-7" name="__codelineno-64-7" href="#__codelineno-64-7"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">make_choice</span><span class="p">}</span>
-<a id="__codelineno-64-8" name="__codelineno-64-8" href="#__codelineno-64-8"></a>
-<a id="__codelineno-64-9" name="__codelineno-64-9" href="#__codelineno-64-9"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">undo_choice</span><span class="p">}</span>
+<div class="highlight"><span class="filename">preorder_traversal_iii_template.rb</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="c1">### 現在の状態が解かどうかを判定 ###</span>
+<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">is_solution?</span><span class="p">(</span><span class="n">state</span><span class="p">)</span>
+<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a><span class="w">  </span><span class="o">!</span><span class="n">state</span><span class="o">.</span><span class="n">empty?</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">state</span><span class="o">.</span><span class="n">last</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span>
+<a id="__codelineno-64-4" name="__codelineno-64-4" href="#__codelineno-64-4"></a><span class="k">end</span>
+<a id="__codelineno-64-5" name="__codelineno-64-5" href="#__codelineno-64-5"></a>
+<a id="__codelineno-64-6" name="__codelineno-64-6" href="#__codelineno-64-6"></a><span class="c1">### 解を記録 ###</span>
+<a id="__codelineno-64-7" name="__codelineno-64-7" href="#__codelineno-64-7"></a><span class="k">def</span><span class="w"> </span><span class="nf">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-64-8" name="__codelineno-64-8" href="#__codelineno-64-8"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">state</span><span class="o">.</span><span class="n">dup</span>
+<a id="__codelineno-64-9" name="__codelineno-64-9" href="#__codelineno-64-9"></a><span class="k">end</span>
 <a id="__codelineno-64-10" name="__codelineno-64-10" href="#__codelineno-64-10"></a>
-<a id="__codelineno-64-11" name="__codelineno-64-11" href="#__codelineno-64-11"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-64-11" name="__codelineno-64-11" href="#__codelineno-64-11"></a><span class="c1">### 現在の状態で、この選択が妥当かを判定 ###</span>
+<a id="__codelineno-64-12" name="__codelineno-64-12" href="#__codelineno-64-12"></a><span class="k">def</span><span class="w"> </span><span class="nf">is_valid?</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-64-13" name="__codelineno-64-13" href="#__codelineno-64-13"></a><span class="w">  </span><span class="n">choice</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">choice</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span>
+<a id="__codelineno-64-14" name="__codelineno-64-14" href="#__codelineno-64-14"></a><span class="k">end</span>
+<a id="__codelineno-64-15" name="__codelineno-64-15" href="#__codelineno-64-15"></a>
+<a id="__codelineno-64-16" name="__codelineno-64-16" href="#__codelineno-64-16"></a><span class="c1">### 状態を更新 ###</span>
+<a id="__codelineno-64-17" name="__codelineno-64-17" href="#__codelineno-64-17"></a><span class="k">def</span><span class="w"> </span><span class="nf">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-64-18" name="__codelineno-64-18" href="#__codelineno-64-18"></a><span class="w">  </span><span class="n">state</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">choice</span>
+<a id="__codelineno-64-19" name="__codelineno-64-19" href="#__codelineno-64-19"></a><span class="k">end</span>
+<a id="__codelineno-64-20" name="__codelineno-64-20" href="#__codelineno-64-20"></a>
+<a id="__codelineno-64-21" name="__codelineno-64-21" href="#__codelineno-64-21"></a><span class="c1">### 状態を復元 ###</span>
+<a id="__codelineno-64-22" name="__codelineno-64-22" href="#__codelineno-64-22"></a><span class="k">def</span><span class="w"> </span><span class="nf">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-64-23" name="__codelineno-64-23" href="#__codelineno-64-23"></a><span class="w">  </span><span class="n">state</span><span class="o">.</span><span class="n">pop</span>
+<a id="__codelineno-64-24" name="__codelineno-64-24" href="#__codelineno-64-24"></a><span class="k">end</span>
+<a id="__codelineno-64-25" name="__codelineno-64-25" href="#__codelineno-64-25"></a>
+<a id="__codelineno-64-26" name="__codelineno-64-26" href="#__codelineno-64-26"></a><span class="c1">### バックトラッキング法：例題3 ###</span>
+<a id="__codelineno-64-27" name="__codelineno-64-27" href="#__codelineno-64-27"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-64-28" name="__codelineno-64-28" href="#__codelineno-64-28"></a><span class="w">  </span><span class="c1"># 解かどうかを確認</span>
+<a id="__codelineno-64-29" name="__codelineno-64-29" href="#__codelineno-64-29"></a><span class="w">  </span><span class="n">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_solution?</span><span class="p">(</span><span class="n">state</span><span class="p">)</span>
+<a id="__codelineno-64-30" name="__codelineno-64-30" href="#__codelineno-64-30"></a>
+<a id="__codelineno-64-31" name="__codelineno-64-31" href="#__codelineno-64-31"></a><span class="w">  </span><span class="c1"># すべての選択肢を走査</span>
+<a id="__codelineno-64-32" name="__codelineno-64-32" href="#__codelineno-64-32"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span>
+<a id="__codelineno-64-33" name="__codelineno-64-33" href="#__codelineno-64-33"></a><span class="w">    </span><span class="c1"># 枝刈り：選択が妥当かを確認する</span>
+<a id="__codelineno-64-34" name="__codelineno-64-34" href="#__codelineno-64-34"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">is_valid?</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-64-35" name="__codelineno-64-35" href="#__codelineno-64-35"></a><span class="w">      </span><span class="c1"># 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-64-36" name="__codelineno-64-36" href="#__codelineno-64-36"></a><span class="w">      </span><span class="n">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-64-37" name="__codelineno-64-37" href="#__codelineno-64-37"></a><span class="w">      </span><span class="c1"># 次の選択へ進む</span>
+<a id="__codelineno-64-38" name="__codelineno-64-38" href="#__codelineno-64-38"></a><span class="w">      </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="o">[</span><span class="n">choice</span><span class="o">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="o">.</span><span class="n">right</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-64-39" name="__codelineno-64-39" href="#__codelineno-64-39"></a><span class="w">      </span><span class="c1"># バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-64-40" name="__codelineno-64-40" href="#__codelineno-64-40"></a><span class="w">      </span><span class="n">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-64-41" name="__codelineno-64-41" href="#__codelineno-64-41"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-64-42" name="__codelineno-64-42" href="#__codelineno-64-42"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-64-43" name="__codelineno-64-43" href="#__codelineno-64-43"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>問題文の意味に従い、値が <span class="arithmatex">\(7\)</span> のノードを見つけた後も探索を続ける必要があります。<strong>したがって、解を記録した後の <code>return</code> 文を削除する必要があります</strong>。次の図は、<code>return</code> 文を保持する場合と削除する場合の探索過程の比較です。</p>
-<p><img alt="returnを保持する場合と削除する場合の探索過程の比較" class="animation-figure" src="../backtracking_algorithm.assets/backtrack_remove_return_or_not.png" /></p>
-<p align="center"> 図 13-4 &nbsp; returnを保持する場合と削除する場合の探索過程の比較 </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%3D0%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%0A%0Adef%20list_to_tree_dfs%28arr%3A%20list%5Bint%5D%2C%20i%3A%20int%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20if%20i%20%3C%200%20or%20i%20%3E%3D%20len%28arr%29%20or%20arr%5Bi%5D%20is%20None%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20root%20%3D%20TreeNode%28arr%5Bi%5D%29%0A%20%20%20%20root.left%20%3D%20list_to_tree_dfs%28arr%2C%202%20%2A%20i%20%2B%201%29%0A%20%20%20%20root.right%20%3D%20list_to_tree_dfs%28arr%2C%202%20%2A%20i%20%2B%202%29%0A%20%20%20%20return%20root%0A%0Adef%20list_to_tree%28arr%3A%20list%5Bint%5D%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20return%20list_to_tree_dfs%28arr%2C%200%29%0A%0Adef%20is_solution%28state%3A%20list%5BTreeNode%5D%29%20-%3E%20bool%3A%0A%20%20%20%20return%20state%20and%20state%5B-1%5D.val%20%3D%3D%207%0A%0Adef%20record_solution%28state%3A%20list%5BTreeNode%5D%2C%20res%3A%20list%5Blist%5BTreeNode%5D%5D%29%3A%0A%20%20%20%20res.append%28list%28state%29%29%0A%0Adef%20is_valid%28state%3A%20list%5BTreeNode%5D%2C%20choice%3A%20TreeNode%29%20-%3E%20bool%3A%0A%20%20%20%20return%20choice%20is%20not%20None%20and%20choice.val%20%21%3D%203%0A%0Adef%20make_choice%28state%3A%20list%5BTreeNode%5D%2C%20choice%3A%20TreeNode%29%3A%0A%20%20%20%20state.append%28choice%29%0A%0Adef%20undo_choice%28state%3A%20list%5BTreeNode%5D%2C%20choice%3A%20TreeNode%29%3A%0A%20%20%20%20state.pop%28%29%0A%0Adef%20backtrack%28state%3A%20list%5BTreeNode%5D%2C%20choices%3A%20list%5BTreeNode%5D%2C%20res%3A%20list%5Blist%5BTreeNode%5D%5D%29%3A%0A%20%20%20%20if%20is_solution%28state%29%3A%0A%20%20%20%20%20%20%20%20record_solution%28state%2C%20res%29%0A%20%20%20%20for%20choice%20in%20choices%3A%0A%20%20%20%20%20%20%20%20if%20is_valid%28state%2C%20choice%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20make_choice%28state%2C%20choice%29%0A%20%20%20%20%20%20%20%20%20%20%20%20backtrack%28state%2C%20%5Bchoice.left%2C%20choice.right%5D%2C%20res%29%0A%20%20%20%20%20%20%20%20%20%20%20%20undo_choice%28state%2C%20choice%29%0Aif%20__name__%20%3D%3D%20%27__main__%27%3A%0A%20%20%20%20root%20%3D%20list_to_tree%28%5B1%2C%207%2C%203%2C%204%2C%205%2C%206%2C%207%5D%29%0A%20%20%20%20res%20%3D%20%5B%5D%0A%20%20%20%20backtrack%28state%3D%5B%5D%2C%20choices%3D%5Broot%5D%2C%20res%3Dres%29%0A%20%20%20%20print%28%27%5Cn%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E7%B5%8C%E8%B7%AF%E3%82%92%E5%87%BA%E5%8A%9B%27%29%0A%20%20%20%20for%20path%20in%20res%3A%0A%20%20%20%20%20%20%20%20print%28%5Bnode.val%20for%20node%20in%20path%5D%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=138&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%3D0%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%0A%0Adef%20list_to_tree_dfs%28arr%3A%20list%5Bint%5D%2C%20i%3A%20int%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20if%20i%20%3C%200%20or%20i%20%3E%3D%20len%28arr%29%20or%20arr%5Bi%5D%20is%20None%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20root%20%3D%20TreeNode%28arr%5Bi%5D%29%0A%20%20%20%20root.left%20%3D%20list_to_tree_dfs%28arr%2C%202%20%2A%20i%20%2B%201%29%0A%20%20%20%20root.right%20%3D%20list_to_tree_dfs%28arr%2C%202%20%2A%20i%20%2B%202%29%0A%20%20%20%20return%20root%0A%0Adef%20list_to_tree%28arr%3A%20list%5Bint%5D%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20return%20list_to_tree_dfs%28arr%2C%200%29%0A%0Adef%20is_solution%28state%3A%20list%5BTreeNode%5D%29%20-%3E%20bool%3A%0A%20%20%20%20return%20state%20and%20state%5B-1%5D.val%20%3D%3D%207%0A%0Adef%20record_solution%28state%3A%20list%5BTreeNode%5D%2C%20res%3A%20list%5Blist%5BTreeNode%5D%5D%29%3A%0A%20%20%20%20res.append%28list%28state%29%29%0A%0Adef%20is_valid%28state%3A%20list%5BTreeNode%5D%2C%20choice%3A%20TreeNode%29%20-%3E%20bool%3A%0A%20%20%20%20return%20choice%20is%20not%20None%20and%20choice.val%20%21%3D%203%0A%0Adef%20make_choice%28state%3A%20list%5BTreeNode%5D%2C%20choice%3A%20TreeNode%29%3A%0A%20%20%20%20state.append%28choice%29%0A%0Adef%20undo_choice%28state%3A%20list%5BTreeNode%5D%2C%20choice%3A%20TreeNode%29%3A%0A%20%20%20%20state.pop%28%29%0A%0Adef%20backtrack%28state%3A%20list%5BTreeNode%5D%2C%20choices%3A%20list%5BTreeNode%5D%2C%20res%3A%20list%5Blist%5BTreeNode%5D%5D%29%3A%0A%20%20%20%20if%20is_solution%28state%29%3A%0A%20%20%20%20%20%20%20%20record_solution%28state%2C%20res%29%0A%20%20%20%20for%20choice%20in%20choices%3A%0A%20%20%20%20%20%20%20%20if%20is_valid%28state%2C%20choice%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20make_choice%28state%2C%20choice%29%0A%20%20%20%20%20%20%20%20%20%20%20%20backtrack%28state%2C%20%5Bchoice.left%2C%20choice.right%5D%2C%20res%29%0A%20%20%20%20%20%20%20%20%20%20%20%20undo_choice%28state%2C%20choice%29%0Aif%20__name__%20%3D%3D%20%27__main__%27%3A%0A%20%20%20%20root%20%3D%20list_to_tree%28%5B1%2C%207%2C%203%2C%204%2C%205%2C%206%2C%207%5D%29%0A%20%20%20%20res%20%3D%20%5B%5D%0A%20%20%20%20backtrack%28state%3D%5B%5D%2C%20choices%3D%5Broot%5D%2C%20res%3Dres%29%0A%20%20%20%20print%28%27%5Cn%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E7%B5%8C%E8%B7%AF%E3%82%92%E5%87%BA%E5%8A%9B%27%29%0A%20%20%20%20for%20path%20in%20res%3A%0A%20%20%20%20%20%20%20%20print%28%5Bnode.val%20for%20node%20in%20path%5D%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=138&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>問題の条件より、値が <span class="arithmatex">\(7\)</span> のノードを見つけた後も探索を続ける必要があります。<strong>そのため、解を記録した後の <code>return</code> 文は削除しなければなりません</strong>。次の図は、<code>return</code> 文を残す場合と削除する場合の探索過程を比較したものです。</p>
+<p><img alt="return を残す場合と削除する場合の探索過程の比較" class="animation-figure" src="../backtracking_algorithm.assets/backtrack_remove_return_or_not.png" /></p>
+<p align="center"> 図 13-4 &nbsp; return を残す場合と削除する場合の探索過程の比較 </p>
 
-<p>前順走査に基づくコード実装と比べると、バックトラッキングアルゴリズムのフレームワークに基づく実装はやや冗長に見えますが、汎用性はより高いです。実際、<strong>多くのバックトラッキング問題はこのフレームワークの下で解くことができます</strong>。具体的な問題に応じて <code>state</code> と <code>choices</code> を定義し、フレームワーク内の各メソッドを実装すればよいのです。</p>
+<p>前順走査にもとづく実装と比べると、バックトラッキングアルゴリズムのフレームワークにもとづく実装はやや冗長に見えますが、汎用性に優れています。実際、<strong>多くのバックトラッキング問題はこのフレームワークで解けます</strong>。具体的な問題に応じて <code>state</code> と <code>choices</code> を定義し、各メソッドを実装すれば十分です。</p>
 <h2 id="1314">13.1.4 &nbsp; よく使われる用語<a class="headerlink" href="#1314" title="Permanent link">&para;</a></h2>
-<p>アルゴリズム問題をより明確に分析するために、バックトラッキングアルゴリズムでよく使われる用語の意味をまとめ、例題 3 の対応例を以下の表に示します。</p>
-<p align="center"> 表 13-1 &nbsp; バックトラッキングアルゴリズムでよく使われる用語 </p>
+<p>アルゴリズム問題をより明確に分析するために、バックトラッキングでよく使われる用語の意味を整理し、例題3に対応する例を次の表にまとめます。</p>
+<p align="center"> 表 13-1 &nbsp; よく使われるバックトラッキング用語 </p>
 
 <div class="center-table">
 <table>
 <thead>
 <tr>
-<th>名称</th>
+<th>用語</th>
 <th>定義</th>
-<th>例題 3</th>
+<th>例題3</th>
 </tr>
 </thead>
 <tbody>
 <tr>
 <td>解（solution）</td>
-<td>解は問題の特定条件を満たす答えであり、1 つまたは複数存在する可能性がある</td>
-<td>根ノードからノード <span class="arithmatex">\(7\)</span> までの制約条件を満たすすべての経路</td>
+<td>問題の特定の条件を満たす答えであり、1 つまたは複数存在し得る</td>
+<td>根ノードからノード <span class="arithmatex">\(7\)</span> までの、制約条件を満たすすべての経路</td>
 </tr>
 <tr>
 <td>制約条件（constraint）</td>
-<td>制約条件は、解の実現可能性を制限する条件であり、通常は枝刈りに使用される</td>
-<td>経路にノード <span class="arithmatex">\(3\)</span> を含まない</td>
+<td>解の実現可能性を制限する条件であり、通常は枝刈りに用いられる</td>
+<td>経路にノード <span class="arithmatex">\(3\)</span> を含まないこと</td>
 </tr>
 <tr>
 <td>状態（state）</td>
-<td>状態は、ある時点での問題の状況を表し、これまでに行った選択を含む</td>
-<td>現在訪問したノード経路、すなわち <code>path</code> ノードリスト</td>
+<td>ある時点における問題の状況を表し、すでに行った選択を含む</td>
+<td>現在までに訪問したノードの経路、すなわち <code>path</code> ノードリスト</td>
 </tr>
 <tr>
 <td>試行（attempt）</td>
-<td>試行は、利用可能な選択肢に基づいて解空間を探索する過程であり、選択を行い、状態を更新し、解かどうかを確認する</td>
-<td>左（右）子ノードを再帰的に訪問し、ノードを <code>path</code> に追加し、ノードの値が <span class="arithmatex">\(7\)</span> かを確認する</td>
+<td>利用可能な選択肢にもとづいて解空間を探索する過程であり、選択、状態更新、解判定を含む</td>
+<td>左右の子ノードを再帰的に訪問し、ノードを <code>path</code> に追加し、値が <span class="arithmatex">\(7\)</span> か判定する</td>
 </tr>
 <tr>
-<td>バックトラック（backtracking）</td>
-<td>制約条件を満たさない状態に遭遇した場合、以前の選択を取り消して前の状態に戻ること</td>
-<td>葉ノードを越えたとき、探索終了、値が <span class="arithmatex">\(3\)</span> のノードに遭遇したとき探索を終了し、関数が戻る</td>
+<td>戻る（backtracking）</td>
+<td>制約条件を満たさない状態に出会ったとき、それまでの選択を取り消して前の状態へ戻ること</td>
+<td>葉ノードを越えたとき、ノード訪問を終えたとき、値が <span class="arithmatex">\(3\)</span> のノードに出会ったときに探索を終了し、関数から戻る</td>
 </tr>
 <tr>
 <td>枝刈り（pruning）</td>
-<td>問題の特性や制約条件に基づき、無意味な探索経路を避ける方法であり、探索効率を向上させる</td>
-<td>値が <span class="arithmatex">\(3\)</span> のノードに遭遇した場合、それ以上探索しない</td>
+<td>問題の性質や制約条件にもとづき、無意味な探索経路を避ける方法であり、探索効率を高める</td>
+<td>値が <span class="arithmatex">\(3\)</span> のノードに出会ったら、それ以上探索しない</td>
 </tr>
 </tbody>
 </table>
 </div>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>問題、解、状態などの概念は一般的なものであり、分割統治、バックトラッキング、動的計画法、貪欲法などのアルゴリズムにも関係します。</p>
+<p>問題、解、状態などの概念は汎用的であり、分割統治、バックトラッキング、動的計画法、貪欲法などのアルゴリズムにも共通して現れます。</p>
 </div>
-<h2 id="1315">13.1.5 &nbsp; 長所と限界<a class="headerlink" href="#1315" title="Permanent link">&para;</a></h2>
-<p>バックトラッキングアルゴリズムは本質的に深さ優先探索（DFS）アルゴリズムの一種であり、条件を満たす解を見つけるまであらゆる可能な解を試みます。この方法の利点は、すべての可能な解を見つけられる点であり、適切な枝刈りを行えば効率が高いことです。</p>
-<p>しかし、大規模または複雑な問題を扱う場合、<strong>バックトラッキングアルゴリズムの実行効率は許容できないほど低下する可能性があります</strong>。</p>
+<h2 id="1315">13.1.5 &nbsp; 利点と限界<a class="headerlink" href="#1315" title="Permanent link">&para;</a></h2>
+<p>バックトラッキングアルゴリズムの本質は深さ優先探索です。条件を満たす解を見つけるまで、あり得るすべての解を試します。この方法の利点は、考えられるすべての解を見つけられることであり、適切な枝刈りを行えば高い効率を発揮します。</p>
+<p>しかし、大規模または複雑な問題を扱う場合、<strong>バックトラッキングアルゴリズムの実行効率は受け入れがたいことがあります</strong>。</p>
 <ul>
-<li><strong>時間</strong>：バックトラッキングアルゴリズムは通常、状態空間のすべての可能性を探索する必要があり、時間計算量は指数オーダーまたは階乗オーダーに達する可能性があります。</li>
-<li><strong>空間</strong>：再帰呼び出し中に現在の状態（例：経路、枝刈り用の補助変数など）を保存する必要があり、深さが大きい場合、空間の使用量が増加します。</li>
+<li><strong>時間</strong>：バックトラッキングアルゴリズムでは通常、状態空間のすべての可能性をたどる必要があり、時間計算量は指数時間や階乗時間に達することがあります。</li>
+<li><strong>空間</strong>：再帰呼び出しの過程では現在の状態（たとえば経路や枝刈り用の補助変数など）を保持する必要があり、深さが大きいと空間使用量も大きくなります。</li>
 </ul>
-<p>それでもなお、<strong>バックトラッキングアルゴリズムは特定の探索問題や制約満足問題の最良の解法であることが多いです</strong>。これらの問題では、どの選択が有効な解を生成するかを予測できないため、すべての可能な選択を試す必要があります。このような場合、**効率の最適化が鍵**となります。一般的な最適化手法は次の 2 つです。</p>
+<p>それでもなお、<strong>バックトラッキングアルゴリズムは一部の探索問題や制約充足問題に対する最良の解法です</strong>。この種の問題では、どの選択が有効な解を生むかを事前に予測できないため、可能な選択肢をすべてたどる必要があります。このときの鍵は**いかに効率を最適化するか**であり、代表的な方法は 2 つあります。</p>
 <ul>
-<li><strong>枝刈り</strong>：解を生成しないことが確実な経路を避けることで、時間と空間を節約します。</li>
-<li><strong>ヒューリスティック探索</strong>：探索中に戦略や評価値を導入し、有効な解を生成する可能性が高い経路を優先的に探索します。</li>
+<li><strong>枝刈り</strong>：解が生じないことが確実な経路を探索しないことで、時間と空間を節約する。</li>
+<li><strong>ヒューリスティック探索</strong>：探索中に何らかの戦略や推定値を導入し、有効な解を生みやすい経路を優先的に探索する。</li>
 </ul>
-<h2 id="1316">13.1.6 &nbsp; バックトラッキングの典型的な例題<a class="headerlink" href="#1316" title="Permanent link">&para;</a></h2>
-<p>バックトラッキングアルゴリズムは、多くの探索問題、制約満足問題、組合せ最適化問題を解くのに使用できます。</p>
+<h2 id="1316">13.1.6 &nbsp; バックトラッキングの典型例題<a class="headerlink" href="#1316" title="Permanent link">&para;</a></h2>
+<p>バックトラッキングアルゴリズムは、多くの探索問題、制約充足問題、組合せ最適化問題の解決に利用できます。</p>
 <p><strong>探索問題</strong>：この種の問題の目標は、特定の条件を満たす解を見つけることです。</p>
 <ul>
-<li>全順列問題：与えられた集合のすべての可能な順列を求める。</li>
-<li>部分和問題：与えられた集合と目標和に対して、和が目標値になるすべての部分集合を求める。</li>
-<li>ハノイの塔：3 本の柱と異なるサイズの円盤があり、すべての円盤を 1 本の柱から別の柱に移す。1 回に 1 枚しか動かせず、大きな円盤を小さい円盤の上に置くことはできない。</li>
+<li>全順列問題：ある集合が与えられたとき、考えられるすべての順列を求める。</li>
+<li>部分和問題：ある集合と目標和が与えられたとき、和が目標値となるすべての部分集合を見つける。</li>
+<li>ハノイの塔問題：3 本の柱と大きさの異なる複数の円盤が与えられたとき、すべての円盤を 1 本の柱から別の柱へ移動する。ただし 1 回に 1 枚しか動かせず、大きい円盤を小さい円盤の上に置いてはならない。</li>
 </ul>
-<p><strong>制約満足問題</strong>：この種の問題の目標は、すべての制約条件を満たす解を見つけることです。</p>
+<p><strong>制約充足問題</strong>：この種の問題の目標は、すべての制約条件を満たす解を見つけることです。</p>
 <ul>
-<li><span class="arithmatex">\(n\)</span> クイーン問題：<span class="arithmatex">\(n imes n\)</span> のチェス盤に <span class="arithmatex">\(n\)</span> 個のクイーンを配置し、互いに攻撃しないようにする。</li>
-<li>数独：<span class="arithmatex">\(9 imes 9\)</span> のグリッドに数字 <span class="arithmatex">\(1\)</span> ~ <span class="arithmatex">\(9\)</span> を入力し、各行、列、<span class="arithmatex">\(3 imes 3\)</span> のサブグリッドに重複がないようにする。</li>
-<li>グラフ彩色問題：与えられた無向グラフに対し、隣接頂点が異なる色になるように最小限の色で彩色する。</li>
+<li><span class="arithmatex">\(n\)</span> クイーン問題：<span class="arithmatex">\(n \times n\)</span> の盤面に <span class="arithmatex">\(n\)</span> 個のクイーンを配置し、互いに攻撃し合わないようにする。</li>
+<li>数独：<span class="arithmatex">\(9 \times 9\)</span> のグリッドに数字 <span class="arithmatex">\(1\)</span> ~ <span class="arithmatex">\(9\)</span> を入れ、各行・各列・各 <span class="arithmatex">\(3 \times 3\)</span> の小区画で数字が重複しないようにする。</li>
+<li>グラフ彩色問題：無向グラフが与えられたとき、隣接する頂点が同じ色にならないように、できるだけ少ない色で各頂点を彩色する。</li>
 </ul>
-<p><strong>組合せ最適化問題</strong>：この種の問題の目標は、組合せ空間内で特定の条件を満たす最適解を見つけることです。</p>
+<p><strong>組合せ最適化問題</strong>：この種の問題の目標は、組合せ空間の中で条件を満たす最適解を見つけることです。</p>
 <ul>
-<li>0-1 ナップサック問題：与えられた物品群とバックパックがあり、各物品には価値と重さが設定されている。バックパックの容量制限内で、総価値を最大化する物品の選択を求める。</li>
-<li>旅行セールスマン問題：グラフ上で、1 つの点から出発し、すべての他の点を 1 回ずつ訪問して出発点に戻る最短経路を求める。</li>
-<li>最大クリーク問題：与えられた無向グラフの中で、任意の 2 頂点間に辺が存在する最大の完全部分グラフを見つける。</li>
+<li>0-1 ナップサック問題：複数の品物とナップサックが与えられ、各品物には価値と重さがある。ナップサック容量の範囲内で総価値が最大になるように品物を選ぶ。</li>
+<li>巡回セールスマン問題：グラフ内のある頂点から出発し、他のすべての頂点をちょうど 1 回ずつ訪れて出発点へ戻るときの最短経路を求める。</li>
+<li>最大クリーク問題：無向グラフが与えられたとき、任意の 2 頂点間に辺が存在する最大の完全部分グラフを見つける。</li>
 </ul>
-<p>注意すべきは、多くの組合せ最適化問題に対して、バックトラッキングが最適解法ではないということです。</p>
+<p>多くの組合せ最適化問題では、バックトラッキングは最適な解法ではない点に注意してください。</p>
 <ul>
-<li>0-1 ナップサック問題は、時間効率を高めるために動的計画法がよく使用されます。</li>
-<li>旅行セールスマン問題は有名な NP-Hard 問題であり、遺伝的アルゴリズムやアントコロニーアルゴリズムなどの手法がよく使われます。</li>
-<li>最大クリーク問題はグラフ理論の古典的な問題であり、貪欲法などのヒューリスティックアルゴリズムで解くことができます。</li>
+<li>0-1 ナップサック問題は通常、より高い時間効率を得るために動的計画法で解く。</li>
+<li>巡回セールスマン問題は著名な NP-Hard 問題であり、よく用いられる解法には遺伝的アルゴリズムや蟻コロニー最適化などがある。</li>
+<li>最大クリーク問題はグラフ理論における古典的問題であり、貪欲法などのヒューリスティックで解ける。</li>
 </ul>
 
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-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
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+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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 <p><img alt="バックトラッキング" class="cover-image" src="../assets/covers/chapter_backtracking.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>迷路の探検家のように、私たちは前進する道で障害に遭遇することがあります。</p>
-<p>バックトラッキングの力は、私たちに新しく始めること、試し続けること、そして最終的に光への出口を見つけることを可能にします。</p>
+<p>私たちは迷宮の探検者のように、前へ進む道で困難に出会うことがあります。</p>
+<p>バックトラッキングの力によってやり直しができ、試行を重ね、最後には光へ通じる出口を見つけられます。</p>
 </div>
 <h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
 <li><a href="backtracking_algorithm/">13.1 &nbsp; バックトラッキングアルゴリズム</a></li>
 <li><a href="permutations_problem/">13.2 &nbsp; 全順列問題</a></li>
-<li><a href="subset_sum_problem/">13.3 &nbsp; 部分集合和問題</a></li>
-<li><a href="n_queens_problem/">13.4 &nbsp; Nクイーン問題</a></li>
+<li><a href="subset_sum_problem/">13.3 &nbsp; 部分和問題</a></li>
+<li><a href="n_queens_problem/">13.4 &nbsp; n クイーン問題</a></li>
 <li><a href="summary/">13.5 &nbsp; まとめ</a></li>
 </ul>
 
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-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
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-        <title>13.4 Nクイーン問題 - Hello アルゴリズム</title>
+        <title>13.4 n クイーン問題 - Hello アルゴリズム</title>
       
     
     
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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 <!-- Page content -->
-<h1 id="134-n">13.4 &nbsp; Nクイーン問題<a class="headerlink" href="#134-n" title="Permanent link">&para;</a></h1>
+<h1 id="134-n">13.4 &nbsp; n クイーン問題<a class="headerlink" href="#134-n" title="Permanent link">&para;</a></h1>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
-<p>チェスのルールによると、クイーンは同じ行、列、または対角線上の駒を攻撃できます。<span class="arithmatex">\(n\)</span> 個のクイーンと <span class="arithmatex">\(n \times n\)</span> のチェスボードが与えられた場合、2つのクイーンが互いに攻撃できない配置を見つけてください。</p>
+<p>チェスのルールによれば、クイーンは同じ行、同じ列、または同じ斜線上にある駒を攻撃できます。<span class="arithmatex">\(n\)</span> 個のクイーンと <span class="arithmatex">\(n \times n\)</span> サイズの盤面が与えられたとき、すべてのクイーンが互いに攻撃し合わない配置を求めます。</p>
 </div>
-<p>以下の図に示すように、<span class="arithmatex">\(n = 4\)</span> の場合、2つの解があります。バックトラッキングアルゴリズムの観点から、<span class="arithmatex">\(n \times n\)</span> のチェスボードには <span class="arithmatex">\(n^2\)</span> 個のマスがあり、すべての可能な選択肢 <code>choices</code> を示しています。チェスボードの状態 <code>state</code> は、各クイーンが配置されるにつれて継続的に変化します。</p>
-<p><img alt="4クイーン問題の解" class="animation-figure" src="../n_queens_problem.assets/solution_4_queens.png" /></p>
-<p align="center"> 図 13-15 &nbsp; 4クイーン問題の解 </p>
+<p>下図に示すように、<span class="arithmatex">\(n = 4\)</span> のとき、2 つの解を見つけることができます。バックトラッキングの観点から見ると、<span class="arithmatex">\(n \times n\)</span> サイズの盤面には合計 <span class="arithmatex">\(n^2\)</span> 個のマスがあり、これがすべての選択肢 <code>choices</code> を与えます。クイーンを 1 つずつ配置していく過程で、盤面の状態は絶えず変化し、その各時点の盤面が状態 <code>state</code> です。</p>
+<p><img alt="4 クイーン問題の解" class="animation-figure" src="../n_queens_problem.assets/solution_4_queens.png" /></p>
+<p align="center"> 図 13-15 &nbsp; 4 クイーン問題の解 </p>
 
-<p>以下の図は、この問題の3つの制約を示しています：<strong>複数のクイーンは同じ行、列、または対角線を占有できません</strong>。対角線は主対角線 <code>\</code> と副対角線 <code>/</code> に分かれることに注意することが重要です。</p>
-<p><img alt="Nクイーン問題の制約" class="animation-figure" src="../n_queens_problem.assets/n_queens_constraints.png" /></p>
-<p align="center"> 図 13-16 &nbsp; Nクイーン問題の制約 </p>
+<p>下図は本問題の 3 つの制約条件を示しています。<strong>複数のクイーンは同じ行、同じ列、同じ対角線上に置けません</strong>。なお、対角線には主対角線 <code>\</code> と副対角線 <code>/</code> の 2 種類があります。</p>
+<p><img alt="n クイーン問題の制約条件" class="animation-figure" src="../n_queens_problem.assets/n_queens_constraints.png" /></p>
+<p align="center"> 図 13-16 &nbsp; n クイーン問題の制約条件 </p>
 
 <h3 id="1">1. &nbsp; 行ごとの配置戦略<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>クイーンの数がチェスボードの行数と等しく、どちらも <span class="arithmatex">\(n\)</span> であるため、**チェスボードの各行には1つのクイーンのみが配置できることが**容易に結論付けられます。</p>
-<p>これは、行ごとの配置戦略を採用できることを意味します：最初の行から開始して、最後の行に到達するまで行ごとに1つのクイーンを配置します。</p>
-<p>以下の図は、4クイーン問題の行ごとの配置プロセスを示しています。スペースの制限により、図は最初の行の1つの検索分岐のみを展開し、列と対角線の制約を満たさない配置を剪定します。</p>
+<p>クイーンの数と盤面の行数はいずれも <span class="arithmatex">\(n\)</span> なので、次の推論を容易に得られます：<strong>盤面の各行にはクイーンを 1 つだけ配置できます</strong>。</p>
+<p>つまり、行ごとの配置戦略を採用できます：最初の行から始めて、各行に 1 つのクイーンを配置し、最後の行まで進みます。</p>
+<p>下図は 4 クイーン問題における行ごとの配置過程を示しています。図の大きさの都合上、下図では 1 行目における検索分岐の 1 つだけを展開し、列制約と対角線制約を満たさない案はすべて枝刈りしています。</p>
 <p><img alt="行ごとの配置戦略" class="animation-figure" src="../n_queens_problem.assets/n_queens_placing.png" /></p>
 <p align="center"> 図 13-17 &nbsp; 行ごとの配置戦略 </p>
 
-<p>本質的に、<strong>行ごとの配置戦略は剪定関数として機能し</strong>、同じ行に複数のクイーンを配置するすべての検索分岐を除去します。</p>
-<h3 id="2">2. &nbsp; 列と対角線の剪定<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>列の制約を満たすために、長さ <span class="arithmatex">\(n\)</span> のブール配列 <code>cols</code> を使用して、各列にクイーンが占有されているかどうかを追跡できます。各配置決定の前に、<code>cols</code> を使用してすでにクイーンがある列を剪定し、バックトラッキング中に動的に更新されます。</p>
+<p>本質的には、<strong>行ごとの配置戦略は枝刈りとして機能します</strong>。これにより、同じ行に複数のクイーンが現れるすべての探索分岐を回避できます。</p>
+<h3 id="2">2. &nbsp; 列と対角線の枝刈り<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>列制約を満たすために、長さ <span class="arithmatex">\(n\)</span> のブール配列 <code>cols</code> を用いて、各列にクイーンがあるかどうかを記録できます。配置を決めるたびに、<code>cols</code> を使って既存のクイーンがある列を枝刈りし、バックトラッキングの中で <code>cols</code> の状態を動的に更新します。</p>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>行列の原点は左上隅にあり、行インデックスは上から下に増加し、列インデックスは左から右に増加することに注意してください。</p>
+<p>注意として、行列の原点は左上にあり、行インデックスは上から下へ、列インデックスは左から右へ増加します。</p>
 </div>
-<p>対角線の制約はどうでしょうか？チェスボード上の特定のセルの行と列のインデックスを <span class="arithmatex">\((row, col)\)</span> とします。特定の主対角線を選択することで、その対角線上のすべてのセルで差 <span class="arithmatex">\(row - col\)</span> が同じであることに気付きます。<strong>つまり、<span class="arithmatex">\(row - col\)</span> は主対角線上で定数値です</strong>。</p>
-<p>言い換えると、2つのセルが <span class="arithmatex">\(row_1 - col_1 = row_2 - col_2\)</span> を満たす場合、それらは確実に同じ主対角線上にあります。このパターンを使用して、以下の図に示す配列 <code>diags1</code> を利用して、クイーンが主対角線上にあるかどうかを追跡できます。</p>
-<p>同様に、<strong><span class="arithmatex">\(row + col\)</span> の和は副対角線上のすべてのセルで定数値です</strong>。配列 <code>diags2</code> を使用して副対角線の制約も処理できます。</p>
-<p><img alt="列と対角線の制約の処理" class="animation-figure" src="../n_queens_problem.assets/n_queens_cols_diagonals.png" /></p>
-<p align="center"> 図 13-18 &nbsp; 列と対角線の制約の処理 </p>
+<p>では、対角線制約はどのように扱えばよいのでしょうか。盤面上のあるマスの行列インデックスを <span class="arithmatex">\((row, col)\)</span> とし、行列内のある主対角線を選ぶと、その対角線上のすべてのマスで行インデックスから列インデックスを引いた値が等しいことが分かります。<strong>つまり、主対角線上のすべてのマスでは <span class="arithmatex">\(row - col\)</span> が一定値になります</strong>。</p>
+<p>つまり、2 つのマスが <span class="arithmatex">\(row_1 - col_1 = row_2 - col_2\)</span> を満たすなら、それらは必ず同じ主対角線上にあります。この性質を利用して、下図の配列 <code>diags1</code> により、各主対角線にクイーンがあるかどうかを記録できます。</p>
+<p>同様に、<strong>副対角線上のすべてのマスでは <span class="arithmatex">\(row + col\)</span> が一定値です</strong>。副対角線制約も配列 <code>diags2</code> を使って処理できます。</p>
+<p><img alt="列制約と対角線制約の処理" class="animation-figure" src="../n_queens_problem.assets/n_queens_cols_diagonals.png" /></p>
+<p align="center"> 図 13-18 &nbsp; 列制約と対角線制約の処理 </p>
 
 <h3 id="3">3. &nbsp; コード実装<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
-<p><span class="arithmatex">\(n\)</span> 次元の正方行列では、<span class="arithmatex">\(row - col\)</span> の範囲は <span class="arithmatex">\([-n + 1, n - 1]\)</span> で、<span class="arithmatex">\(row + col\)</span> の範囲は <span class="arithmatex">\([0, 2n - 2]\)</span> であることに注意してください。したがって、主対角線と副対角線の数はどちらも <span class="arithmatex">\(2n - 1\)</span> で、配列 <code>diags1</code> と <code>diags2</code> の長さは <span class="arithmatex">\(2n - 1\)</span> です。</p>
+<p>注意として、<span class="arithmatex">\(n\)</span> 次正方行列では <span class="arithmatex">\(row - col\)</span> の範囲は <span class="arithmatex">\([-n + 1, n - 1]\)</span> 、<span class="arithmatex">\(row + col\)</span> の範囲は <span class="arithmatex">\([0, 2n - 2]\)</span> です。したがって、主対角線と副対角線の本数はいずれも <span class="arithmatex">\(2n - 1\)</span> であり、配列 <code>diags1</code> と <code>diags2</code> の長さもともに <span class="arithmatex">\(2n - 1\)</span> です。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
@@ -4423,34 +4423,34 @@
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="n">diags1</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">bool</span><span class="p">],</span>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="n">diags2</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">bool</span><span class="p">],</span>
 <a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="p">):</span>
-<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキングアルゴリズム：n クイーン&quot;&quot;&quot;</span>
-<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="c1"># すべての行が配置されたら、解を記録</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキング：N クイーン&quot;&quot;&quot;</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="c1"># すべての行への配置が完了したら、解を記録する</span>
 <a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="k">if</span> <span class="n">row</span> <span class="o">==</span> <span class="n">n</span><span class="p">:</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="nb">list</span><span class="p">(</span><span class="n">row</span><span class="p">)</span> <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="n">state</span><span class="p">])</span>
 <a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>        <span class="k">return</span>
 <a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="c1"># すべての列を走査</span>
 <a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>    <span class="k">for</span> <span class="n">col</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
-<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>        <span class="c1"># セルに対応する主対角線と副対角線を計算</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>        <span class="c1"># このマスに対応する主対角線と副対角線を計算</span>
 <a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>        <span class="n">diag1</span> <span class="o">=</span> <span class="n">row</span> <span class="o">-</span> <span class="n">col</span> <span class="o">+</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span>
 <a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>        <span class="n">diag2</span> <span class="o">=</span> <span class="n">row</span> <span class="o">+</span> <span class="n">col</span>
-<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>        <span class="c1"># 枝刈り：セルの列、主対角線、副対角線にクイーンを配置しない</span>
+<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>        <span class="c1"># 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない</span>
 <a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>        <span class="k">if</span> <span class="ow">not</span> <span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">]</span> <span class="ow">and</span> <span class="ow">not</span> <span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">]</span> <span class="ow">and</span> <span class="ow">not</span> <span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">]:</span>
-<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>            <span class="c1"># 試行：セルにクイーンを配置</span>
+<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>            <span class="c1"># 試行：そのマスにクイーンを置く</span>
 <a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a>            <span class="n">state</span><span class="p">[</span><span class="n">row</span><span class="p">][</span><span class="n">col</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;Q&quot;</span>
 <a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>            <span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">]</span> <span class="o">=</span> <span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">]</span> <span class="o">=</span> <span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">]</span> <span class="o">=</span> <span class="kc">True</span>
-<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>            <span class="c1"># 次の行を配置</span>
+<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>            <span class="c1"># 次の行に配置する</span>
 <a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a>            <span class="n">backtrack</span><span class="p">(</span><span class="n">row</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">state</span><span class="p">,</span> <span class="n">res</span><span class="p">,</span> <span class="n">cols</span><span class="p">,</span> <span class="n">diags1</span><span class="p">,</span> <span class="n">diags2</span><span class="p">)</span>
-<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>            <span class="c1"># 撤回：セルを空のスポットに復元</span>
+<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>            <span class="c1"># 戻す：そのマスを空きマスに戻す</span>
 <a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a>            <span class="n">state</span><span class="p">[</span><span class="n">row</span><span class="p">][</span><span class="n">col</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;#&quot;</span>
 <a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a>            <span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">]</span> <span class="o">=</span> <span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">]</span> <span class="o">=</span> <span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">]</span> <span class="o">=</span> <span class="kc">False</span>
 <a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a>
 <a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a><span class="k">def</span><span class="w"> </span><span class="nf">n_queens</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">str</span><span class="p">]]]:</span>
-<a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;n クイーンを解く&quot;&quot;&quot;</span>
-<a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a>    <span class="c1"># n*n サイズのチェスボードを初期化、&#39;Q&#39; はクイーンを表し、&#39;#&#39; は空のスポットを表す</span>
+<a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;N クイーンを解く&quot;&quot;&quot;</span>
+<a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a>    <span class="c1"># n*n の盤面を初期化する。&#39;Q&#39; はクイーン、&#39;#&#39; は空きマスを表す</span>
 <a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a>    <span class="n">state</span> <span class="o">=</span> <span class="p">[[</span><span class="s2">&quot;#&quot;</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">)]</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">)]</span>
-<a id="__codelineno-0-35" name="__codelineno-0-35" href="#__codelineno-0-35"></a>    <span class="n">cols</span> <span class="o">=</span> <span class="p">[</span><span class="kc">False</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span>  <span class="c1"># クイーンがある列を記録</span>
-<a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a>    <span class="n">diags1</span> <span class="o">=</span> <span class="p">[</span><span class="kc">False</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>  <span class="c1"># クイーンがある主対角線を記録</span>
-<a id="__codelineno-0-37" name="__codelineno-0-37" href="#__codelineno-0-37"></a>    <span class="n">diags2</span> <span class="o">=</span> <span class="p">[</span><span class="kc">False</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>  <span class="c1"># クイーンがある副対角線を記録</span>
+<a id="__codelineno-0-35" name="__codelineno-0-35" href="#__codelineno-0-35"></a>    <span class="n">cols</span> <span class="o">=</span> <span class="p">[</span><span class="kc">False</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span>  <span class="c1"># 列にクイーンがあるか記録</span>
+<a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a>    <span class="n">diags1</span> <span class="o">=</span> <span class="p">[</span><span class="kc">False</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>  <span class="c1"># 主対角線にクイーンがあるかを記録</span>
+<a id="__codelineno-0-37" name="__codelineno-0-37" href="#__codelineno-0-37"></a>    <span class="n">diags2</span> <span class="o">=</span> <span class="p">[</span><span class="kc">False</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>  <span class="c1"># 副対角線にクイーンがあるかを記録</span>
 <a id="__codelineno-0-38" name="__codelineno-0-38" href="#__codelineno-0-38"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
 <a id="__codelineno-0-39" name="__codelineno-0-39" href="#__codelineno-0-39"></a>    <span class="n">backtrack</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">state</span><span class="p">,</span> <span class="n">res</span><span class="p">,</span> <span class="n">cols</span><span class="p">,</span> <span class="n">diags1</span><span class="p">,</span> <span class="n">diags2</span><span class="p">)</span>
 <a id="__codelineno-0-40" name="__codelineno-0-40" href="#__codelineno-0-40"></a>
@@ -4458,40 +4458,40 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">n_queens.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* バックトラッキングアルゴリズム：n クイーン */</span>
+<div class="highlight"><span class="filename">n_queens.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* バックトラッキング：N クイーン */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">row</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">string</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">string</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">cols</span><span class="p">,</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">               </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">diags2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// すべての行が配置されたら、解を記録</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// すべての行への配置が完了したら、解を記録する</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">row</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">state</span><span class="p">);</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="c1">// すべての列を走査</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">col</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="c1">// セルに対応する主対角線と副対角線を計算</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="c1">// このマスに対応する主対角線と副対角線を計算</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">diag1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">diag2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">col</span><span class="p">;</span>
-<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">        </span><span class="c1">// 剪定：セルの列、主対角線、副対角線にクイーンを配置することを許可しない</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">        </span><span class="c1">// 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない</span>
 <a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">            </span><span class="c1">// 試行：セルにクイーンを配置</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">            </span><span class="c1">// 試行：そのマスにクイーンを置く</span>
 <a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">            </span><span class="n">state</span><span class="p">[</span><span class="n">row</span><span class="p">][</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Q&quot;</span><span class="p">;</span>
 <a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">            </span><span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">true</span><span class="p">;</span>
-<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">            </span><span class="c1">// 次の行を配置</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">            </span><span class="c1">// 次の行に配置する</span>
 <a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cols</span><span class="p">,</span><span class="w"> </span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="n">diags2</span><span class="p">);</span>
-<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">            </span><span class="c1">// 回退：セルを空のスポットに復元</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">            </span><span class="c1">// 戻す：そのマスを空きマスに戻す</span>
 <a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w">            </span><span class="n">state</span><span class="p">[</span><span class="n">row</span><span class="p">][</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;#&quot;</span><span class="p">;</span>
 <a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w">            </span><span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">false</span><span class="p">;</span>
 <a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="p">}</span>
 <a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a>
-<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="cm">/* n クイーンを解く */</span>
+<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="cm">/* N クイーンを解く */</span>
 <a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">string</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="n">nQueens</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="w">    </span><span class="c1">// n*n サイズのチェスボードを初期化、&#39;Q&#39; はクイーンを表し、&#39;#&#39; は空のスポットを表す</span>
+<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="w">    </span><span class="c1">// n*n の盤面を初期化する。&#39;Q&#39; はクイーン、&#39;#&#39; は空きマスを表す</span>
 <a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">string</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">string</span><span class="o">&gt;</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;#&quot;</span><span class="p">));</span>
-<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="n">cols</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="nb">false</span><span class="p">);</span><span class="w">           </span><span class="c1">// クイーンのある列を記録</span>
-<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="n">diags1</span><span class="p">(</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nb">false</span><span class="p">);</span><span class="w"> </span><span class="c1">// クイーンのある主対角線を記録</span>
-<a id="__codelineno-1-34" name="__codelineno-1-34" href="#__codelineno-1-34"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="n">diags2</span><span class="p">(</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nb">false</span><span class="p">);</span><span class="w"> </span><span class="c1">// クイーンのある副対角線を記録</span>
+<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="n">cols</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="nb">false</span><span class="p">);</span><span class="w">           </span><span class="c1">// 列にクイーンがあるか記録</span>
+<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="n">diags1</span><span class="p">(</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nb">false</span><span class="p">);</span><span class="w"> </span><span class="c1">// 主対角線にクイーンがあるかを記録</span>
+<a id="__codelineno-1-34" name="__codelineno-1-34" href="#__codelineno-1-34"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="n">diags2</span><span class="p">(</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nb">false</span><span class="p">);</span><span class="w"> </span><span class="c1">// 副対角線にクイーンがあるかを記録</span>
 <a id="__codelineno-1-35" name="__codelineno-1-35" href="#__codelineno-1-35"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">string</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
 <a id="__codelineno-1-36" name="__codelineno-1-36" href="#__codelineno-1-36"></a>
 <a id="__codelineno-1-37" name="__codelineno-1-37" href="#__codelineno-1-37"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cols</span><span class="p">,</span><span class="w"> </span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="n">diags2</span><span class="p">);</span>
@@ -4501,10 +4501,10 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">n_queens.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* バックトラッキングアルゴリズム：n クイーン */</span>
+<div class="highlight"><span class="filename">n_queens.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* バックトラッキング：N クイーン */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">row</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">,</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">        </span><span class="kt">boolean</span><span class="o">[]</span><span class="w"> </span><span class="n">cols</span><span class="p">,</span><span class="w"> </span><span class="kt">boolean</span><span class="o">[]</span><span class="w"> </span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="kt">boolean</span><span class="o">[]</span><span class="w"> </span><span class="n">diags2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// すべての行が配置されたら、解を記録</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// すべての行への配置が完了したら、解を記録する</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">row</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">copyState</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">sRow</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
@@ -4515,26 +4515,26 @@
 <a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">    </span><span class="c1">// すべての列を走査</span>
 <a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">col</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="c1">// セルに対応する主対角線と副対角線を計算</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="c1">// このマスに対応する主対角線と副対角線を計算</span>
 <a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">diag1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">diag2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">col</span><span class="p">;</span>
-<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">        </span><span class="c1">// 剪定：セルの列、主対角線、副対角線にクイーンを配置することを許可しない</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">        </span><span class="c1">// 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない</span>
 <a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">cols</span><span class="o">[</span><span class="n">col</span><span class="o">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">diags1</span><span class="o">[</span><span class="n">diag1</span><span class="o">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">diags2</span><span class="o">[</span><span class="n">diag2</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">            </span><span class="c1">// 試行：セルにクイーンを配置</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">            </span><span class="c1">// 試行：そのマスにクイーンを置く</span>
 <a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">row</span><span class="p">).</span><span class="na">set</span><span class="p">(</span><span class="n">col</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;Q&quot;</span><span class="p">);</span>
 <a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w">            </span><span class="n">cols</span><span class="o">[</span><span class="n">col</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags1</span><span class="o">[</span><span class="n">diag1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags2</span><span class="o">[</span><span class="n">diag2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
-<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">            </span><span class="c1">// 次の行を配置</span>
+<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">            </span><span class="c1">// 次の行に配置する</span>
 <a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cols</span><span class="p">,</span><span class="w"> </span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="n">diags2</span><span class="p">);</span>
-<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="w">            </span><span class="c1">// 回退：セルを空のスポットに復元</span>
+<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="w">            </span><span class="c1">// 戻す：そのマスを空きマスに戻す</span>
 <a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">row</span><span class="p">).</span><span class="na">set</span><span class="p">(</span><span class="n">col</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;#&quot;</span><span class="p">);</span>
 <a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w">            </span><span class="n">cols</span><span class="o">[</span><span class="n">col</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags1</span><span class="o">[</span><span class="n">diag1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags2</span><span class="o">[</span><span class="n">diag2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span>
 <a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a><span class="p">}</span>
 <a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a>
-<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="cm">/* n クイーンを解く */</span>
+<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="cm">/* N クイーンを解く */</span>
 <a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="nf">nQueens</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a><span class="w">    </span><span class="c1">// n*n サイズのチェスボードを初期化、&#39;Q&#39; はクイーンを表し、&#39;#&#39; は空のスポットを表す</span>
+<a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a><span class="w">    </span><span class="c1">// n*n の盤面を初期化する。&#39;Q&#39; はクイーン、&#39;#&#39; は空きマスを表す</span>
 <a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
 <a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-37" name="__codelineno-2-37" href="#__codelineno-2-37"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
@@ -4543,9 +4543,9 @@
 <a id="__codelineno-2-40" name="__codelineno-2-40" href="#__codelineno-2-40"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-2-41" name="__codelineno-2-41" href="#__codelineno-2-41"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">row</span><span class="p">);</span>
 <a id="__codelineno-2-42" name="__codelineno-2-42" href="#__codelineno-2-42"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-43" name="__codelineno-2-43" href="#__codelineno-2-43"></a><span class="w">    </span><span class="kt">boolean</span><span class="o">[]</span><span class="w"> </span><span class="n">cols</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">boolean</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="c1">// クイーンのある列を記録</span>
-<a id="__codelineno-2-44" name="__codelineno-2-44" href="#__codelineno-2-44"></a><span class="w">    </span><span class="kt">boolean</span><span class="o">[]</span><span class="w"> </span><span class="n">diags1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">boolean</span><span class="o">[</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="c1">// クイーンのある主対角線を記録</span>
-<a id="__codelineno-2-45" name="__codelineno-2-45" href="#__codelineno-2-45"></a><span class="w">    </span><span class="kt">boolean</span><span class="o">[]</span><span class="w"> </span><span class="n">diags2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">boolean</span><span class="o">[</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="c1">// クイーンのある副対角線を記録</span>
+<a id="__codelineno-2-43" name="__codelineno-2-43" href="#__codelineno-2-43"></a><span class="w">    </span><span class="kt">boolean</span><span class="o">[]</span><span class="w"> </span><span class="n">cols</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">boolean</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="c1">// 列にクイーンがあるか記録</span>
+<a id="__codelineno-2-44" name="__codelineno-2-44" href="#__codelineno-2-44"></a><span class="w">    </span><span class="kt">boolean</span><span class="o">[]</span><span class="w"> </span><span class="n">diags1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">boolean</span><span class="o">[</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="c1">// 主対角線にクイーンがあるかを記録</span>
+<a id="__codelineno-2-45" name="__codelineno-2-45" href="#__codelineno-2-45"></a><span class="w">    </span><span class="kt">boolean</span><span class="o">[]</span><span class="w"> </span><span class="n">diags2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">boolean</span><span class="o">[</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="c1">// 副対角線にクイーンがあるかを記録</span>
 <a id="__codelineno-2-46" name="__codelineno-2-46" href="#__codelineno-2-46"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
 <a id="__codelineno-2-47" name="__codelineno-2-47" href="#__codelineno-2-47"></a>
 <a id="__codelineno-2-48" name="__codelineno-2-48" href="#__codelineno-2-48"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cols</span><span class="p">,</span><span class="w"> </span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="n">diags2</span><span class="p">);</span>
@@ -4555,69 +4555,535 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">n_queens.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">n_queens</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Backtrack</span><span class="p">}</span>
-<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
-<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">n_queens</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">NQueens</span><span class="p">}</span>
+<div class="highlight"><span class="filename">n_queens.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* バックトラッキング：N クイーン */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Backtrack</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">row</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">string</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">string</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">,</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">        </span><span class="kt">bool</span><span class="p">[]</span><span class="w"> </span><span class="n">cols</span><span class="p">,</span><span class="w"> </span><span class="kt">bool</span><span class="p">[]</span><span class="w"> </span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="kt">bool</span><span class="p">[]</span><span class="w"> </span><span class="n">diags2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="c1">// すべての行への配置が完了したら、解を記録する</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">row</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">string</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">copyState</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">        </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">string</span><span class="o">&gt;</span><span class="w"> </span><span class="n">sRow</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">            </span><span class="n">copyState</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">string</span><span class="o">&gt;</span><span class="p">(</span><span class="n">sRow</span><span class="p">));</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">copyState</span><span class="p">);</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">    </span><span class="c1">// すべての列を走査</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">col</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">        </span><span class="c1">// このマスに対応する主対角線と副対角線を計算</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">diag1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">diag2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">col</span><span class="p">;</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">        </span><span class="c1">// 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w">            </span><span class="c1">// 試行：そのマスにクイーンを置く</span>
+<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w">            </span><span class="n">state</span><span class="p">[</span><span class="n">row</span><span class="p">][</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Q&quot;</span><span class="p">;</span>
+<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="w">            </span><span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">true</span><span class="p">;</span>
+<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="w">            </span><span class="c1">// 次の行に配置する</span>
+<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="w">            </span><span class="n">Backtrack</span><span class="p">(</span><span class="n">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cols</span><span class="p">,</span><span class="w"> </span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="n">diags2</span><span class="p">);</span>
+<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="w">            </span><span class="c1">// 戻す：そのマスを空きマスに戻す</span>
+<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="w">            </span><span class="n">state</span><span class="p">[</span><span class="n">row</span><span class="p">][</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;#&quot;</span><span class="p">;</span>
+<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a><span class="w">            </span><span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">false</span><span class="p">;</span>
+<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a><span class="p">}</span>
+<a id="__codelineno-3-31" name="__codelineno-3-31" href="#__codelineno-3-31"></a>
+<a id="__codelineno-3-32" name="__codelineno-3-32" href="#__codelineno-3-32"></a><span class="cm">/* N クイーンを解く */</span>
+<a id="__codelineno-3-33" name="__codelineno-3-33" href="#__codelineno-3-33"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">string</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="n">NQueens</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-34" name="__codelineno-3-34" href="#__codelineno-3-34"></a><span class="w">    </span><span class="c1">// n*n の盤面を初期化する。&#39;Q&#39; はクイーン、&#39;#&#39; は空きマスを表す</span>
+<a id="__codelineno-3-35" name="__codelineno-3-35" href="#__codelineno-3-35"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">string</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-3-36" name="__codelineno-3-36" href="#__codelineno-3-36"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-37" name="__codelineno-3-37" href="#__codelineno-3-37"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">string</span><span class="o">&gt;</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-3-38" name="__codelineno-3-38" href="#__codelineno-3-38"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-39" name="__codelineno-3-39" href="#__codelineno-3-39"></a><span class="w">            </span><span class="n">row</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="s">&quot;#&quot;</span><span class="p">);</span>
+<a id="__codelineno-3-40" name="__codelineno-3-40" href="#__codelineno-3-40"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-41" name="__codelineno-3-41" href="#__codelineno-3-41"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">row</span><span class="p">);</span>
+<a id="__codelineno-3-42" name="__codelineno-3-42" href="#__codelineno-3-42"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-43" name="__codelineno-3-43" href="#__codelineno-3-43"></a><span class="w">    </span><span class="kt">bool</span><span class="p">[]</span><span class="w"> </span><span class="n">cols</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">bool</span><span class="p">[</span><span class="n">n</span><span class="p">];</span><span class="w"> </span><span class="c1">// 列にクイーンがあるか記録</span>
+<a id="__codelineno-3-44" name="__codelineno-3-44" href="#__codelineno-3-44"></a><span class="w">    </span><span class="kt">bool</span><span class="p">[]</span><span class="w"> </span><span class="n">diags1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">bool</span><span class="p">[</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span><span class="w"> </span><span class="c1">// 主対角線にクイーンがあるかを記録</span>
+<a id="__codelineno-3-45" name="__codelineno-3-45" href="#__codelineno-3-45"></a><span class="w">    </span><span class="kt">bool</span><span class="p">[]</span><span class="w"> </span><span class="n">diags2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">bool</span><span class="p">[</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span><span class="w"> </span><span class="c1">// 副対角線にクイーンがあるかを記録</span>
+<a id="__codelineno-3-46" name="__codelineno-3-46" href="#__codelineno-3-46"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">string</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-3-47" name="__codelineno-3-47" href="#__codelineno-3-47"></a>
+<a id="__codelineno-3-48" name="__codelineno-3-48" href="#__codelineno-3-48"></a><span class="w">    </span><span class="n">Backtrack</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cols</span><span class="p">,</span><span class="w"> </span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="n">diags2</span><span class="p">);</span>
+<a id="__codelineno-3-49" name="__codelineno-3-49" href="#__codelineno-3-49"></a>
+<a id="__codelineno-3-50" name="__codelineno-3-50" href="#__codelineno-3-50"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-3-51" name="__codelineno-3-51" href="#__codelineno-3-51"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">n_queens.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
-<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
-<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">nQueens</span><span class="p">}</span>
+<div class="highlight"><span class="filename">n_queens.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* バックトラッキング：N クイーン */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">row</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">state</span><span class="w"> </span><span class="o">*</span><span class="p">[][]</span><span class="kt">string</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">*</span><span class="p">[][][]</span><span class="kt">string</span><span class="p">,</span><span class="w"> </span><span class="nx">cols</span><span class="p">,</span><span class="w"> </span><span class="nx">diags1</span><span class="p">,</span><span class="w"> </span><span class="nx">diags2</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="kt">bool</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// すべての行への配置が完了したら、解を記録する</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">row</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">        </span><span class="nx">newState</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="kt">string</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">))</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">_</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">newState</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">            </span><span class="nx">newState</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">string</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">((</span><span class="o">*</span><span class="nx">state</span><span class="p">)[</span><span class="mi">0</span><span class="p">]))</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">            </span><span class="nb">copy</span><span class="p">(</span><span class="nx">newState</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)[</span><span class="nx">i</span><span class="p">])</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">        </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">newState</span><span class="p">)</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">    </span><span class="c1">// すべての列を走査</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">col</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">col</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">col</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">        </span><span class="c1">// このマスに対応する主対角線と副対角線を計算</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">        </span><span class="nx">diag1</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">row</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">col</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w">        </span><span class="nx">diag2</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">col</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w">        </span><span class="c1">// 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">!(</span><span class="o">*</span><span class="nx">cols</span><span class="p">)[</span><span class="nx">col</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="p">!(</span><span class="o">*</span><span class="nx">diags1</span><span class="p">)[</span><span class="nx">diag1</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="p">!(</span><span class="o">*</span><span class="nx">diags2</span><span class="p">)[</span><span class="nx">diag2</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w">            </span><span class="c1">// 試行：そのマスにクイーンを置く</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w">            </span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)[</span><span class="nx">row</span><span class="p">][</span><span class="nx">col</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;Q&quot;</span>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="w">            </span><span class="p">(</span><span class="o">*</span><span class="nx">cols</span><span class="p">)[</span><span class="nx">col</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">diags1</span><span class="p">)[</span><span class="nx">diag1</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">diags2</span><span class="p">)[</span><span class="nx">diag2</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">true</span><span class="p">,</span><span class="w"> </span><span class="kc">true</span><span class="p">,</span><span class="w"> </span><span class="kc">true</span>
+<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="w">            </span><span class="c1">// 次の行に配置する</span>
+<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="w">            </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">row</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">cols</span><span class="p">,</span><span class="w"> </span><span class="nx">diags1</span><span class="p">,</span><span class="w"> </span><span class="nx">diags2</span><span class="p">)</span>
+<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="w">            </span><span class="c1">// 戻す：そのマスを空きマスに戻す</span>
+<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w">            </span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)[</span><span class="nx">row</span><span class="p">][</span><span class="nx">col</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;#&quot;</span>
+<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="w">            </span><span class="p">(</span><span class="o">*</span><span class="nx">cols</span><span class="p">)[</span><span class="nx">col</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">diags1</span><span class="p">)[</span><span class="nx">diag1</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">diags2</span><span class="p">)[</span><span class="nx">diag2</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">false</span><span class="p">,</span><span class="w"> </span><span class="kc">false</span><span class="p">,</span><span class="w"> </span><span class="kc">false</span>
+<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-30" name="__codelineno-4-30" href="#__codelineno-4-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-31" name="__codelineno-4-31" href="#__codelineno-4-31"></a><span class="p">}</span>
+<a id="__codelineno-4-32" name="__codelineno-4-32" href="#__codelineno-4-32"></a>
+<a id="__codelineno-4-33" name="__codelineno-4-33" href="#__codelineno-4-33"></a><span class="cm">/* N クイーンを解く */</span>
+<a id="__codelineno-4-34" name="__codelineno-4-34" href="#__codelineno-4-34"></a><span class="kd">func</span><span class="w"> </span><span class="nx">nQueens</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">[][][]</span><span class="kt">string</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-35" name="__codelineno-4-35" href="#__codelineno-4-35"></a><span class="w">    </span><span class="c1">// n*n の盤面を初期化する。&#39;Q&#39; はクイーン、&#39;#&#39; は空きマスを表す</span>
+<a id="__codelineno-4-36" name="__codelineno-4-36" href="#__codelineno-4-36"></a><span class="w">    </span><span class="nx">state</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="kt">string</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
+<a id="__codelineno-4-37" name="__codelineno-4-37" href="#__codelineno-4-37"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-38" name="__codelineno-4-38" href="#__codelineno-4-38"></a><span class="w">        </span><span class="nx">row</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">string</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
+<a id="__codelineno-4-39" name="__codelineno-4-39" href="#__codelineno-4-39"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-40" name="__codelineno-4-40" href="#__codelineno-4-40"></a><span class="w">            </span><span class="nx">row</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;#&quot;</span>
+<a id="__codelineno-4-41" name="__codelineno-4-41" href="#__codelineno-4-41"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-42" name="__codelineno-4-42" href="#__codelineno-4-42"></a><span class="w">        </span><span class="nx">state</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">row</span>
+<a id="__codelineno-4-43" name="__codelineno-4-43" href="#__codelineno-4-43"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-44" name="__codelineno-4-44" href="#__codelineno-4-44"></a><span class="w">    </span><span class="c1">// 列にクイーンがあるか記録</span>
+<a id="__codelineno-4-45" name="__codelineno-4-45" href="#__codelineno-4-45"></a><span class="w">    </span><span class="nx">cols</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">bool</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
+<a id="__codelineno-4-46" name="__codelineno-4-46" href="#__codelineno-4-46"></a><span class="w">    </span><span class="nx">diags1</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">bool</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="o">*</span><span class="nx">n</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-4-47" name="__codelineno-4-47" href="#__codelineno-4-47"></a><span class="w">    </span><span class="nx">diags2</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">bool</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="o">*</span><span class="nx">n</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-4-48" name="__codelineno-4-48" href="#__codelineno-4-48"></a><span class="w">    </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][][]</span><span class="kt">string</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-4-49" name="__codelineno-4-49" href="#__codelineno-4-49"></a><span class="w">    </span><span class="nx">backtrack</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">cols</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">diags1</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">diags2</span><span class="p">)</span>
+<a id="__codelineno-4-50" name="__codelineno-4-50" href="#__codelineno-4-50"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
+<a id="__codelineno-4-51" name="__codelineno-4-51" href="#__codelineno-4-51"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">n_queens.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
-<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">nQueens</span><span class="p">}</span>
+<div class="highlight"><span class="filename">n_queens.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* バックトラッキング：N クイーン */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">row</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[[</span><span class="nb">String</span><span class="p">]],</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[[[</span><span class="nb">String</span><span class="p">]]],</span><span class="w"> </span><span class="n">cols</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Bool</span><span class="p">],</span><span class="w"> </span><span class="n">diags1</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Bool</span><span class="p">],</span><span class="w"> </span><span class="n">diags2</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Bool</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// すべての行への配置が完了したら、解を記録する</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">state</span><span class="p">)</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">    </span><span class="c1">// すべての列を走査</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">        </span><span class="c1">// このマスに対応する主対角線と副対角線を計算</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">diag1</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">diag2</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">col</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">        </span><span class="c1">// 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="o">!</span><span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">            </span><span class="c1">// 試行：そのマスにクイーンを置く</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">            </span><span class="n">state</span><span class="p">[</span><span class="n">row</span><span class="p">][</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;Q&quot;</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">            </span><span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">true</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">            </span><span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">true</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w">            </span><span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">true</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="w">            </span><span class="c1">// 次の行に配置する</span>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">row</span><span class="p">:</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cols</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">cols</span><span class="p">,</span><span class="w"> </span><span class="n">diags1</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="n">diags2</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">diags2</span><span class="p">)</span>
+<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="w">            </span><span class="c1">// 戻す：そのマスを空きマスに戻す</span>
+<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="w">            </span><span class="n">state</span><span class="p">[</span><span class="n">row</span><span class="p">][</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;#&quot;</span>
+<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="w">            </span><span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">false</span>
+<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="w">            </span><span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">false</span>
+<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a><span class="w">            </span><span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">false</span>
+<a id="__codelineno-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-29" name="__codelineno-5-29" href="#__codelineno-5-29"></a><span class="p">}</span>
+<a id="__codelineno-5-30" name="__codelineno-5-30" href="#__codelineno-5-30"></a>
+<a id="__codelineno-5-31" name="__codelineno-5-31" href="#__codelineno-5-31"></a><span class="cm">/* N クイーンを解く */</span>
+<a id="__codelineno-5-32" name="__codelineno-5-32" href="#__codelineno-5-32"></a><span class="kd">func</span><span class="w"> </span><span class="nf">nQueens</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[[[</span><span class="nb">String</span><span class="p">]]]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-33" name="__codelineno-5-33" href="#__codelineno-5-33"></a><span class="w">    </span><span class="c1">// n*n の盤面を初期化する。&#39;Q&#39; はクイーン、&#39;#&#39; は空きマスを表す</span>
+<a id="__codelineno-5-34" name="__codelineno-5-34" href="#__codelineno-5-34"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">state</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="s">&quot;#&quot;</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="p">),</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-5-35" name="__codelineno-5-35" href="#__codelineno-5-35"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">cols</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="kc">false</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="c1">// 列にクイーンがあるか記録</span>
+<a id="__codelineno-5-36" name="__codelineno-5-36" href="#__codelineno-5-36"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">diags1</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="kc">false</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="c1">// 主対角線にクイーンがあるかを記録</span>
+<a id="__codelineno-5-37" name="__codelineno-5-37" href="#__codelineno-5-37"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">diags2</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="kc">false</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="c1">// 副対角線にクイーンがあるかを記録</span>
+<a id="__codelineno-5-38" name="__codelineno-5-38" href="#__codelineno-5-38"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="p">:</span><span class="w"> </span><span class="p">[[[</span><span class="nb">String</span><span class="p">]]]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
+<a id="__codelineno-5-39" name="__codelineno-5-39" href="#__codelineno-5-39"></a>
+<a id="__codelineno-5-40" name="__codelineno-5-40" href="#__codelineno-5-40"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">row</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cols</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">cols</span><span class="p">,</span><span class="w"> </span><span class="n">diags1</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="n">diags2</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">diags2</span><span class="p">)</span>
+<a id="__codelineno-5-41" name="__codelineno-5-41" href="#__codelineno-5-41"></a>
+<a id="__codelineno-5-42" name="__codelineno-5-42" href="#__codelineno-5-42"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-5-43" name="__codelineno-5-43" href="#__codelineno-5-43"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">n_queens.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
-<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
-<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">nQueens</span><span class="p">}</span>
+<div class="highlight"><span class="filename">n_queens.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* バックトラッキング：N クイーン */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">row</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">cols</span><span class="p">,</span><span class="w"> </span><span class="nx">diags1</span><span class="p">,</span><span class="w"> </span><span class="nx">diags2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="c1">// すべての行への配置が完了したら、解を記録する</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">row</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">        </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">state</span><span class="p">.</span><span class="nx">map</span><span class="p">((</span><span class="nx">row</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="nx">row</span><span class="p">.</span><span class="nx">slice</span><span class="p">()));</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">    </span><span class="c1">// すべての列を走査</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">col</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">col</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">col</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">        </span><span class="c1">// このマスに対応する主対角線と副対角線を計算</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">diag1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">row</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">col</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">diag2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">col</span><span class="p">;</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">        </span><span class="c1">// 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="nx">cols</span><span class="p">[</span><span class="nx">col</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="nx">diags1</span><span class="p">[</span><span class="nx">diag1</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="nx">diags2</span><span class="p">[</span><span class="nx">diag2</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">            </span><span class="c1">// 試行：そのマスにクイーンを置く</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w">            </span><span class="nx">state</span><span class="p">[</span><span class="nx">row</span><span class="p">][</span><span class="nx">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s1">&#39;Q&#39;</span><span class="p">;</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w">            </span><span class="nx">cols</span><span class="p">[</span><span class="nx">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">diags1</span><span class="p">[</span><span class="nx">diag1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">diags2</span><span class="p">[</span><span class="nx">diag2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w">            </span><span class="c1">// 次の行に配置する</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">            </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">cols</span><span class="p">,</span><span class="w"> </span><span class="nx">diags1</span><span class="p">,</span><span class="w"> </span><span class="nx">diags2</span><span class="p">);</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w">            </span><span class="c1">// 戻す：そのマスを空きマスに戻す</span>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w">            </span><span class="nx">state</span><span class="p">[</span><span class="nx">row</span><span class="p">][</span><span class="nx">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s1">&#39;#&#39;</span><span class="p">;</span>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w">            </span><span class="nx">cols</span><span class="p">[</span><span class="nx">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">diags1</span><span class="p">[</span><span class="nx">diag1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">diags2</span><span class="p">[</span><span class="nx">diag2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span>
+<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="p">}</span>
+<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a>
+<a id="__codelineno-6-27" name="__codelineno-6-27" href="#__codelineno-6-27"></a><span class="cm">/* N クイーンを解く */</span>
+<a id="__codelineno-6-28" name="__codelineno-6-28" href="#__codelineno-6-28"></a><span class="kd">function</span><span class="w"> </span><span class="nx">nQueens</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-29" name="__codelineno-6-29" href="#__codelineno-6-29"></a><span class="w">    </span><span class="c1">// n*n の盤面を初期化する。&#39;Q&#39; はクイーン、&#39;#&#39; は空きマスを表す</span>
+<a id="__codelineno-6-30" name="__codelineno-6-30" href="#__codelineno-6-30"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="s1">&#39;#&#39;</span><span class="p">));</span>
+<a id="__codelineno-6-31" name="__codelineno-6-31" href="#__codelineno-6-31"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">cols</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="kc">false</span><span class="p">);</span><span class="w"> </span><span class="c1">// 列にクイーンがあるか記録</span>
+<a id="__codelineno-6-32" name="__codelineno-6-32" href="#__codelineno-6-32"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">diags1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="kc">false</span><span class="p">);</span><span class="w"> </span><span class="c1">// 主対角線にクイーンがあるかを記録</span>
+<a id="__codelineno-6-33" name="__codelineno-6-33" href="#__codelineno-6-33"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">diags2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="kc">false</span><span class="p">);</span><span class="w"> </span><span class="c1">// 副対角線にクイーンがあるかを記録</span>
+<a id="__codelineno-6-34" name="__codelineno-6-34" href="#__codelineno-6-34"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-6-35" name="__codelineno-6-35" href="#__codelineno-6-35"></a>
+<a id="__codelineno-6-36" name="__codelineno-6-36" href="#__codelineno-6-36"></a><span class="w">    </span><span class="nx">backtrack</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">cols</span><span class="p">,</span><span class="w"> </span><span class="nx">diags1</span><span class="p">,</span><span class="w"> </span><span class="nx">diags2</span><span class="p">);</span>
+<a id="__codelineno-6-37" name="__codelineno-6-37" href="#__codelineno-6-37"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-6-38" name="__codelineno-6-38" href="#__codelineno-6-38"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">n_queens.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
-<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
-<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">nQueens</span><span class="p">}</span>
+<div class="highlight"><span class="filename">n_queens.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* バックトラッキング：N クイーン */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="nx">row</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="nx">state</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">[][],</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">[][][],</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="nx">cols</span><span class="o">:</span><span class="w"> </span><span class="kt">boolean</span><span class="p">[],</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="nx">diags1</span><span class="o">:</span><span class="w"> </span><span class="kt">boolean</span><span class="p">[],</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="nx">diags2</span><span class="o">:</span><span class="w"> </span><span class="kt">boolean</span><span class="p">[]</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">    </span><span class="c1">// すべての行への配置が完了したら、解を記録する</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">row</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">        </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">state</span><span class="p">.</span><span class="nx">map</span><span class="p">((</span><span class="nx">row</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="nx">row</span><span class="p">.</span><span class="nx">slice</span><span class="p">()));</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">    </span><span class="c1">// すべての列を走査</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">col</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">col</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">col</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">        </span><span class="c1">// このマスに対応する主対角線と副対角線を計算</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">diag1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">row</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">col</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">diag2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">col</span><span class="p">;</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="w">        </span><span class="c1">// 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="nx">cols</span><span class="p">[</span><span class="nx">col</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="nx">diags1</span><span class="p">[</span><span class="nx">diag1</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="nx">diags2</span><span class="p">[</span><span class="nx">diag2</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="w">            </span><span class="c1">// 試行：そのマスにクイーンを置く</span>
+<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="w">            </span><span class="nx">state</span><span class="p">[</span><span class="nx">row</span><span class="p">][</span><span class="nx">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s1">&#39;Q&#39;</span><span class="p">;</span>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="w">            </span><span class="nx">cols</span><span class="p">[</span><span class="nx">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">diags1</span><span class="p">[</span><span class="nx">diag1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">diags2</span><span class="p">[</span><span class="nx">diag2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
+<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="w">            </span><span class="c1">// 次の行に配置する</span>
+<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a><span class="w">            </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">cols</span><span class="p">,</span><span class="w"> </span><span class="nx">diags1</span><span class="p">,</span><span class="w"> </span><span class="nx">diags2</span><span class="p">);</span>
+<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a><span class="w">            </span><span class="c1">// 戻す：そのマスを空きマスに戻す</span>
+<a id="__codelineno-7-29" name="__codelineno-7-29" href="#__codelineno-7-29"></a><span class="w">            </span><span class="nx">state</span><span class="p">[</span><span class="nx">row</span><span class="p">][</span><span class="nx">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s1">&#39;#&#39;</span><span class="p">;</span>
+<a id="__codelineno-7-30" name="__codelineno-7-30" href="#__codelineno-7-30"></a><span class="w">            </span><span class="nx">cols</span><span class="p">[</span><span class="nx">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">diags1</span><span class="p">[</span><span class="nx">diag1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">diags2</span><span class="p">[</span><span class="nx">diag2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span>
+<a id="__codelineno-7-31" name="__codelineno-7-31" href="#__codelineno-7-31"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-32" name="__codelineno-7-32" href="#__codelineno-7-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-33" name="__codelineno-7-33" href="#__codelineno-7-33"></a><span class="p">}</span>
+<a id="__codelineno-7-34" name="__codelineno-7-34" href="#__codelineno-7-34"></a>
+<a id="__codelineno-7-35" name="__codelineno-7-35" href="#__codelineno-7-35"></a><span class="cm">/* N クイーンを解く */</span>
+<a id="__codelineno-7-36" name="__codelineno-7-36" href="#__codelineno-7-36"></a><span class="kd">function</span><span class="w"> </span><span class="nx">nQueens</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">[][][]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-37" name="__codelineno-7-37" href="#__codelineno-7-37"></a><span class="w">    </span><span class="c1">// n*n の盤面を初期化する。&#39;Q&#39; はクイーン、&#39;#&#39; は空きマスを表す</span>
+<a id="__codelineno-7-38" name="__codelineno-7-38" href="#__codelineno-7-38"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="kt">n</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="s1">&#39;#&#39;</span><span class="p">));</span>
+<a id="__codelineno-7-39" name="__codelineno-7-39" href="#__codelineno-7-39"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">cols</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="kc">false</span><span class="p">);</span><span class="w"> </span><span class="c1">// 列にクイーンがあるか記録</span>
+<a id="__codelineno-7-40" name="__codelineno-7-40" href="#__codelineno-7-40"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">diags1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="kc">false</span><span class="p">);</span><span class="w"> </span><span class="c1">// 主対角線にクイーンがあるかを記録</span>
+<a id="__codelineno-7-41" name="__codelineno-7-41" href="#__codelineno-7-41"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">diags2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="kc">false</span><span class="p">);</span><span class="w"> </span><span class="c1">// 副対角線にクイーンがあるかを記録</span>
+<a id="__codelineno-7-42" name="__codelineno-7-42" href="#__codelineno-7-42"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">[][][]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-7-43" name="__codelineno-7-43" href="#__codelineno-7-43"></a>
+<a id="__codelineno-7-44" name="__codelineno-7-44" href="#__codelineno-7-44"></a><span class="w">    </span><span class="nx">backtrack</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">cols</span><span class="p">,</span><span class="w"> </span><span class="nx">diags1</span><span class="p">,</span><span class="w"> </span><span class="nx">diags2</span><span class="p">);</span>
+<a id="__codelineno-7-45" name="__codelineno-7-45" href="#__codelineno-7-45"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-7-46" name="__codelineno-7-46" href="#__codelineno-7-46"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">n_queens.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
-<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">nQueens</span><span class="p">}</span>
+<div class="highlight"><span class="filename">n_queens.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* バックトラッキング：N クイーン */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">row</span><span class="p">,</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">String</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">String</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">,</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="n">cols</span><span class="p">,</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="n">diags1</span><span class="p">,</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="n">diags2</span><span class="p">,</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">  </span><span class="c1">// すべての行への配置が完了したら、解を記録する</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">row</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">String</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">copyState</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">sRow</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">      </span><span class="n">copyState</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">List</span><span class="p">.</span><span class="n">from</span><span class="p">(</span><span class="n">sRow</span><span class="p">));</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">copyState</span><span class="p">);</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w">    </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="w">  </span><span class="c1">// すべての列を走査</span>
+<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">col</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="w">    </span><span class="c1">// このマスに対応する主対角線と副対角線を計算</span>
+<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">diag1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">diag2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">col</span><span class="p">;</span>
+<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a><span class="w">    </span><span class="c1">// 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない</span>
+<a id="__codelineno-8-26" name="__codelineno-8-26" href="#__codelineno-8-26"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-27" name="__codelineno-8-27" href="#__codelineno-8-27"></a><span class="w">      </span><span class="c1">// 試行：そのマスにクイーンを置く</span>
+<a id="__codelineno-8-28" name="__codelineno-8-28" href="#__codelineno-8-28"></a><span class="w">      </span><span class="n">state</span><span class="p">[</span><span class="n">row</span><span class="p">][</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;Q&quot;</span><span class="p">;</span>
+<a id="__codelineno-8-29" name="__codelineno-8-29" href="#__codelineno-8-29"></a><span class="w">      </span><span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
+<a id="__codelineno-8-30" name="__codelineno-8-30" href="#__codelineno-8-30"></a><span class="w">      </span><span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
+<a id="__codelineno-8-31" name="__codelineno-8-31" href="#__codelineno-8-31"></a><span class="w">      </span><span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
+<a id="__codelineno-8-32" name="__codelineno-8-32" href="#__codelineno-8-32"></a><span class="w">      </span><span class="c1">// 次の行に配置する</span>
+<a id="__codelineno-8-33" name="__codelineno-8-33" href="#__codelineno-8-33"></a><span class="w">      </span><span class="n">backtrack</span><span class="p">(</span><span class="n">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cols</span><span class="p">,</span><span class="w"> </span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="n">diags2</span><span class="p">);</span>
+<a id="__codelineno-8-34" name="__codelineno-8-34" href="#__codelineno-8-34"></a><span class="w">      </span><span class="c1">// 戻す：そのマスを空きマスに戻す</span>
+<a id="__codelineno-8-35" name="__codelineno-8-35" href="#__codelineno-8-35"></a><span class="w">      </span><span class="n">state</span><span class="p">[</span><span class="n">row</span><span class="p">][</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;#&quot;</span><span class="p">;</span>
+<a id="__codelineno-8-36" name="__codelineno-8-36" href="#__codelineno-8-36"></a><span class="w">      </span><span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span>
+<a id="__codelineno-8-37" name="__codelineno-8-37" href="#__codelineno-8-37"></a><span class="w">      </span><span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span>
+<a id="__codelineno-8-38" name="__codelineno-8-38" href="#__codelineno-8-38"></a><span class="w">      </span><span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span>
+<a id="__codelineno-8-39" name="__codelineno-8-39" href="#__codelineno-8-39"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-40" name="__codelineno-8-40" href="#__codelineno-8-40"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-41" name="__codelineno-8-41" href="#__codelineno-8-41"></a><span class="p">}</span>
+<a id="__codelineno-8-42" name="__codelineno-8-42" href="#__codelineno-8-42"></a>
+<a id="__codelineno-8-43" name="__codelineno-8-43" href="#__codelineno-8-43"></a><span class="cm">/* N クイーンを解く */</span>
+<a id="__codelineno-8-44" name="__codelineno-8-44" href="#__codelineno-8-44"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">String</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="n">nQueens</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-45" name="__codelineno-8-45" href="#__codelineno-8-45"></a><span class="w">  </span><span class="c1">// n*n の盤面を初期化する。&#39;Q&#39; はクイーン、&#39;#&#39; は空きマスを表す</span>
+<a id="__codelineno-8-46" name="__codelineno-8-46" href="#__codelineno-8-46"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">String</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">generate</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="s2">&quot;#&quot;</span><span class="p">));</span>
+<a id="__codelineno-8-47" name="__codelineno-8-47" href="#__codelineno-8-47"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="n">cols</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="kc">false</span><span class="p">);</span><span class="w"> </span><span class="c1">// 列にクイーンがあるか記録</span>
+<a id="__codelineno-8-48" name="__codelineno-8-48" href="#__codelineno-8-48"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="n">diags1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="kc">false</span><span class="p">);</span><span class="w"> </span><span class="c1">// 主対角線にクイーンがあるかを記録</span>
+<a id="__codelineno-8-49" name="__codelineno-8-49" href="#__codelineno-8-49"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="n">diags2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="kc">false</span><span class="p">);</span><span class="w"> </span><span class="c1">// 副対角線にクイーンがあるかを記録</span>
+<a id="__codelineno-8-50" name="__codelineno-8-50" href="#__codelineno-8-50"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">String</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-8-51" name="__codelineno-8-51" href="#__codelineno-8-51"></a>
+<a id="__codelineno-8-52" name="__codelineno-8-52" href="#__codelineno-8-52"></a><span class="w">  </span><span class="n">backtrack</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cols</span><span class="p">,</span><span class="w"> </span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="n">diags2</span><span class="p">);</span>
+<a id="__codelineno-8-53" name="__codelineno-8-53" href="#__codelineno-8-53"></a>
+<a id="__codelineno-8-54" name="__codelineno-8-54" href="#__codelineno-8-54"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-8-55" name="__codelineno-8-55" href="#__codelineno-8-55"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">n_queens.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
-<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">n_queens</span><span class="p">}</span>
+<div class="highlight"><span class="filename">n_queens.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* バックトラッキング：N クイーン */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="n">row</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">String</span><span class="o">&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">String</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="n">cols</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">bool</span><span class="p">],</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="n">diags1</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">bool</span><span class="p">],</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">    </span><span class="n">diags2</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">bool</span><span class="p">],</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">    </span><span class="c1">// すべての行への配置が完了したら、解を記録する</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">    </span><span class="c1">// すべての列を走査</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">        </span><span class="c1">// このマスに対応する主対角線と副対角線を計算</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">diag1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">col</span><span class="p">;</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">diag2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">col</span><span class="p">;</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w">        </span><span class="c1">// 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない</span>
+<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="o">!</span><span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="w">            </span><span class="c1">// 試行：そのマスにクイーンを置く</span>
+<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="w">            </span><span class="n">state</span><span class="p">[</span><span class="n">row</span><span class="p">][</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Q&quot;</span><span class="p">.</span><span class="n">into</span><span class="p">();</span>
+<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="w">            </span><span class="p">(</span><span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">],</span><span class="w"> </span><span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">],</span><span class="w"> </span><span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">])</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">,</span><span class="w"> </span><span class="kc">true</span><span class="p">,</span><span class="w"> </span><span class="kc">true</span><span class="p">);</span>
+<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="w">            </span><span class="c1">// 次の行に配置する</span>
+<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cols</span><span class="p">,</span><span class="w"> </span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="n">diags2</span><span class="p">);</span>
+<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a><span class="w">            </span><span class="c1">// 戻す：そのマスを空きマスに戻す</span>
+<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="w">            </span><span class="n">state</span><span class="p">[</span><span class="n">row</span><span class="p">][</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;#&quot;</span><span class="p">.</span><span class="n">into</span><span class="p">();</span>
+<a id="__codelineno-9-30" name="__codelineno-9-30" href="#__codelineno-9-30"></a><span class="w">            </span><span class="p">(</span><span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">],</span><span class="w"> </span><span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">],</span><span class="w"> </span><span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">])</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kc">false</span><span class="p">,</span><span class="w"> </span><span class="kc">false</span><span class="p">,</span><span class="w"> </span><span class="kc">false</span><span class="p">);</span>
+<a id="__codelineno-9-31" name="__codelineno-9-31" href="#__codelineno-9-31"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-32" name="__codelineno-9-32" href="#__codelineno-9-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-33" name="__codelineno-9-33" href="#__codelineno-9-33"></a><span class="p">}</span>
+<a id="__codelineno-9-34" name="__codelineno-9-34" href="#__codelineno-9-34"></a>
+<a id="__codelineno-9-35" name="__codelineno-9-35" href="#__codelineno-9-35"></a><span class="cm">/* N クイーンを解く */</span>
+<a id="__codelineno-9-36" name="__codelineno-9-36" href="#__codelineno-9-36"></a><span class="k">fn</span><span class="w"> </span><span class="nf">n_queens</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">String</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-37" name="__codelineno-9-37" href="#__codelineno-9-37"></a><span class="w">    </span><span class="c1">// n*n の盤面を初期化する。&#39;Q&#39; はクイーン、&#39;#&#39; は空きマスを表す</span>
+<a id="__codelineno-9-38" name="__codelineno-9-38" href="#__codelineno-9-38"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">String</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="fm">vec!</span><span class="p">[</span><span class="s">&quot;#&quot;</span><span class="p">.</span><span class="n">to_string</span><span class="p">();</span><span class="w"> </span><span class="n">n</span><span class="p">];</span><span class="w"> </span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-9-39" name="__codelineno-9-39" href="#__codelineno-9-39"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">cols</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="kc">false</span><span class="p">;</span><span class="w"> </span><span class="n">n</span><span class="p">];</span><span class="w"> </span><span class="c1">// 列にクイーンがあるか記録</span>
+<a id="__codelineno-9-40" name="__codelineno-9-40" href="#__codelineno-9-40"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">diags1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="kc">false</span><span class="p">;</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span><span class="w"> </span><span class="c1">// 主対角線にクイーンがあるかを記録</span>
+<a id="__codelineno-9-41" name="__codelineno-9-41" href="#__codelineno-9-41"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">diags2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="kc">false</span><span class="p">;</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span><span class="w"> </span><span class="c1">// 副対角線にクイーンがあるかを記録</span>
+<a id="__codelineno-9-42" name="__codelineno-9-42" href="#__codelineno-9-42"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">String</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-9-43" name="__codelineno-9-43" href="#__codelineno-9-43"></a>
+<a id="__codelineno-9-44" name="__codelineno-9-44" href="#__codelineno-9-44"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span>
+<a id="__codelineno-9-45" name="__codelineno-9-45" href="#__codelineno-9-45"></a><span class="w">        </span><span class="mi">0</span><span class="p">,</span>
+<a id="__codelineno-9-46" name="__codelineno-9-46" href="#__codelineno-9-46"></a><span class="w">        </span><span class="n">n</span><span class="p">,</span>
+<a id="__codelineno-9-47" name="__codelineno-9-47" href="#__codelineno-9-47"></a><span class="w">        </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">state</span><span class="p">,</span>
+<a id="__codelineno-9-48" name="__codelineno-9-48" href="#__codelineno-9-48"></a><span class="w">        </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">,</span>
+<a id="__codelineno-9-49" name="__codelineno-9-49" href="#__codelineno-9-49"></a><span class="w">        </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">cols</span><span class="p">,</span>
+<a id="__codelineno-9-50" name="__codelineno-9-50" href="#__codelineno-9-50"></a><span class="w">        </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">diags1</span><span class="p">,</span>
+<a id="__codelineno-9-51" name="__codelineno-9-51" href="#__codelineno-9-51"></a><span class="w">        </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">diags2</span><span class="p">,</span>
+<a id="__codelineno-9-52" name="__codelineno-9-52" href="#__codelineno-9-52"></a><span class="w">    </span><span class="p">);</span>
+<a id="__codelineno-9-53" name="__codelineno-9-53" href="#__codelineno-9-53"></a>
+<a id="__codelineno-9-54" name="__codelineno-9-54" href="#__codelineno-9-54"></a><span class="w">    </span><span class="n">res</span>
+<a id="__codelineno-9-55" name="__codelineno-9-55" href="#__codelineno-9-55"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">n_queens.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
-<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">nQueens</span><span class="p">}</span>
+<div class="highlight"><span class="filename">n_queens.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* バックトラッキング：N クイーン */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">row</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="kt">char</span><span class="w"> </span><span class="n">state</span><span class="p">[</span><span class="n">MAX_SIZE</span><span class="p">][</span><span class="n">MAX_SIZE</span><span class="p">],</span><span class="w"> </span><span class="kt">char</span><span class="w"> </span><span class="o">***</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">resSize</span><span class="p">,</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="n">cols</span><span class="p">[</span><span class="n">MAX_SIZE</span><span class="p">],</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">               </span><span class="kt">bool</span><span class="w"> </span><span class="n">diags1</span><span class="p">[</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="n">diags2</span><span class="p">[</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="c1">// すべての行への配置が完了したら、解を記録する</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">row</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="o">*</span><span class="n">resSize</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="o">**</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="o">*</span><span class="n">resSize</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">char</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">));</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">            </span><span class="n">strcpy</span><span class="p">(</span><span class="n">res</span><span class="p">[</span><span class="o">*</span><span class="n">resSize</span><span class="p">][</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">state</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">        </span><span class="p">(</span><span class="o">*</span><span class="n">resSize</span><span class="p">)</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">    </span><span class="c1">// すべての列を走査</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">col</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">        </span><span class="c1">// このマスに対応する主対角線と副対角線を計算</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">diag1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">diag2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">col</span><span class="p">;</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w">        </span><span class="c1">// 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない</span>
+<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="w">            </span><span class="c1">// 試行：そのマスにクイーンを置く</span>
+<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w">            </span><span class="n">state</span><span class="p">[</span><span class="n">row</span><span class="p">][</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="sc">&#39;Q&#39;</span><span class="p">;</span>
+<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w">            </span><span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">true</span><span class="p">;</span>
+<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="w">            </span><span class="c1">// 次の行に配置する</span>
+<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">resSize</span><span class="p">,</span><span class="w"> </span><span class="n">cols</span><span class="p">,</span><span class="w"> </span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="n">diags2</span><span class="p">);</span>
+<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="w">            </span><span class="c1">// 戻す：そのマスを空きマスに戻す</span>
+<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="w">            </span><span class="n">state</span><span class="p">[</span><span class="n">row</span><span class="p">][</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="sc">&#39;#&#39;</span><span class="p">;</span>
+<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="w">            </span><span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">false</span><span class="p">;</span>
+<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></a><span class="p">}</span>
+<a id="__codelineno-10-32" name="__codelineno-10-32" href="#__codelineno-10-32"></a>
+<a id="__codelineno-10-33" name="__codelineno-10-33" href="#__codelineno-10-33"></a><span class="cm">/* N クイーンを解く */</span>
+<a id="__codelineno-10-34" name="__codelineno-10-34" href="#__codelineno-10-34"></a><span class="kt">char</span><span class="w"> </span><span class="o">***</span><span class="nf">nQueens</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">returnSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-35" name="__codelineno-10-35" href="#__codelineno-10-35"></a><span class="w">    </span><span class="kt">char</span><span class="w"> </span><span class="n">state</span><span class="p">[</span><span class="n">MAX_SIZE</span><span class="p">][</span><span class="n">MAX_SIZE</span><span class="p">];</span>
+<a id="__codelineno-10-36" name="__codelineno-10-36" href="#__codelineno-10-36"></a><span class="w">    </span><span class="c1">// n*n の盤面を初期化する。&#39;Q&#39; はクイーン、&#39;#&#39; は空きマスを表す</span>
+<a id="__codelineno-10-37" name="__codelineno-10-37" href="#__codelineno-10-37"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-38" name="__codelineno-10-38" href="#__codelineno-10-38"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-39" name="__codelineno-10-39" href="#__codelineno-10-39"></a><span class="w">            </span><span class="n">state</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="sc">&#39;#&#39;</span><span class="p">;</span>
+<a id="__codelineno-10-40" name="__codelineno-10-40" href="#__codelineno-10-40"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-41" name="__codelineno-10-41" href="#__codelineno-10-41"></a><span class="w">        </span><span class="n">state</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">n</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="sc">&#39;\0&#39;</span><span class="p">;</span>
+<a id="__codelineno-10-42" name="__codelineno-10-42" href="#__codelineno-10-42"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-43" name="__codelineno-10-43" href="#__codelineno-10-43"></a><span class="w">    </span><span class="kt">bool</span><span class="w"> </span><span class="n">cols</span><span class="p">[</span><span class="n">MAX_SIZE</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="nb">false</span><span class="p">};</span><span class="w">           </span><span class="c1">// 列にクイーンがあるか記録</span>
+<a id="__codelineno-10-44" name="__codelineno-10-44" href="#__codelineno-10-44"></a><span class="w">    </span><span class="kt">bool</span><span class="w"> </span><span class="n">diags1</span><span class="p">[</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="nb">false</span><span class="p">};</span><span class="w"> </span><span class="c1">// 主対角線にクイーンがあるかを記録</span>
+<a id="__codelineno-10-45" name="__codelineno-10-45" href="#__codelineno-10-45"></a><span class="w">    </span><span class="kt">bool</span><span class="w"> </span><span class="n">diags2</span><span class="p">[</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="nb">false</span><span class="p">};</span><span class="w"> </span><span class="c1">// 副対角線にクイーンがあるかを記録</span>
+<a id="__codelineno-10-46" name="__codelineno-10-46" href="#__codelineno-10-46"></a>
+<a id="__codelineno-10-47" name="__codelineno-10-47" href="#__codelineno-10-47"></a><span class="w">    </span><span class="kt">char</span><span class="w"> </span><span class="o">***</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="o">***</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="o">**</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">);</span>
+<a id="__codelineno-10-48" name="__codelineno-10-48" href="#__codelineno-10-48"></a><span class="w">    </span><span class="o">*</span><span class="n">returnSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-49" name="__codelineno-10-49" href="#__codelineno-10-49"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">returnSize</span><span class="p">,</span><span class="w"> </span><span class="n">cols</span><span class="p">,</span><span class="w"> </span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="n">diags2</span><span class="p">);</span>
+<a id="__codelineno-10-50" name="__codelineno-10-50" href="#__codelineno-10-50"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-10-51" name="__codelineno-10-51" href="#__codelineno-10-51"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">n_queens.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
-<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">nQueens</span><span class="p">}</span>
+<div class="highlight"><span class="filename">n_queens.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* バックトラッキング：N クイーン */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="n">row</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">String</span><span class="o">&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">String</span><span class="o">&gt;&gt;?&gt;</span><span class="p">,</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">    </span><span class="n">cols</span><span class="p">:</span><span class="w"> </span><span class="n">BooleanArray</span><span class="p">,</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">    </span><span class="n">diags1</span><span class="p">:</span><span class="w"> </span><span class="n">BooleanArray</span><span class="p">,</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">    </span><span class="n">diags2</span><span class="p">:</span><span class="w"> </span><span class="n">BooleanArray</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">    </span><span class="c1">// すべての行への配置が完了したら、解を記録する</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">row</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">copyState</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">String</span><span class="o">&gt;&gt;</span><span class="p">()</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">sRow</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">            </span><span class="n">copyState</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">sRow</span><span class="p">.</span><span class="na">toMutableList</span><span class="p">())</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">copyState</span><span class="p">)</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w">    </span><span class="c1">// すべての列を走査</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">col</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="w">        </span><span class="c1">// このマスに対応する主対角線と副対角線を計算</span>
+<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">diag1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">diag2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">col</span>
+<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="w">        </span><span class="c1">// 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない</span>
+<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">cols</span><span class="o">[</span><span class="n">col</span><span class="o">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">diags1</span><span class="o">[</span><span class="n">diag1</span><span class="o">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">diags2</span><span class="o">[</span><span class="n">diag2</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a><span class="w">            </span><span class="c1">// 試行：そのマスにクイーンを置く</span>
+<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="w">            </span><span class="n">state</span><span class="o">[</span><span class="n">row</span><span class="o">][</span><span class="n">col</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Q&quot;</span>
+<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a><span class="w">            </span><span class="n">diags2</span><span class="o">[</span><span class="n">diag2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span>
+<a id="__codelineno-11-30" name="__codelineno-11-30" href="#__codelineno-11-30"></a><span class="w">            </span><span class="n">diags1</span><span class="o">[</span><span class="n">diag1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags2</span><span class="o">[</span><span class="n">diag2</span><span class="o">]</span>
+<a id="__codelineno-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></a><span class="w">            </span><span class="n">cols</span><span class="o">[</span><span class="n">col</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags1</span><span class="o">[</span><span class="n">diag1</span><span class="o">]</span>
+<a id="__codelineno-11-32" name="__codelineno-11-32" href="#__codelineno-11-32"></a><span class="w">            </span><span class="c1">// 次の行に配置する</span>
+<a id="__codelineno-11-33" name="__codelineno-11-33" href="#__codelineno-11-33"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cols</span><span class="p">,</span><span class="w"> </span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="n">diags2</span><span class="p">)</span>
+<a id="__codelineno-11-34" name="__codelineno-11-34" href="#__codelineno-11-34"></a><span class="w">            </span><span class="c1">// 戻す：そのマスを空きマスに戻す</span>
+<a id="__codelineno-11-35" name="__codelineno-11-35" href="#__codelineno-11-35"></a><span class="w">            </span><span class="n">state</span><span class="o">[</span><span class="n">row</span><span class="o">][</span><span class="n">col</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;#&quot;</span>
+<a id="__codelineno-11-36" name="__codelineno-11-36" href="#__codelineno-11-36"></a><span class="w">            </span><span class="n">diags2</span><span class="o">[</span><span class="n">diag2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span>
+<a id="__codelineno-11-37" name="__codelineno-11-37" href="#__codelineno-11-37"></a><span class="w">            </span><span class="n">diags1</span><span class="o">[</span><span class="n">diag1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags2</span><span class="o">[</span><span class="n">diag2</span><span class="o">]</span>
+<a id="__codelineno-11-38" name="__codelineno-11-38" href="#__codelineno-11-38"></a><span class="w">            </span><span class="n">cols</span><span class="o">[</span><span class="n">col</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags1</span><span class="o">[</span><span class="n">diag1</span><span class="o">]</span>
+<a id="__codelineno-11-39" name="__codelineno-11-39" href="#__codelineno-11-39"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-40" name="__codelineno-11-40" href="#__codelineno-11-40"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-41" name="__codelineno-11-41" href="#__codelineno-11-41"></a><span class="p">}</span>
+<a id="__codelineno-11-42" name="__codelineno-11-42" href="#__codelineno-11-42"></a>
+<a id="__codelineno-11-43" name="__codelineno-11-43" href="#__codelineno-11-43"></a><span class="cm">/* N クイーンを解く */</span>
+<a id="__codelineno-11-44" name="__codelineno-11-44" href="#__codelineno-11-44"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">nQueens</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">String</span><span class="o">&gt;&gt;?&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-45" name="__codelineno-11-45" href="#__codelineno-11-45"></a><span class="w">    </span><span class="c1">// n*n の盤面を初期化する。&#39;Q&#39; はクイーン、&#39;#&#39; は空きマスを表す</span>
+<a id="__codelineno-11-46" name="__codelineno-11-46" href="#__codelineno-11-46"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">String</span><span class="o">&gt;&gt;</span><span class="p">()</span>
+<a id="__codelineno-11-47" name="__codelineno-11-47" href="#__codelineno-11-47"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-48" name="__codelineno-11-48" href="#__codelineno-11-48"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">row</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="kt">String</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-11-49" name="__codelineno-11-49" href="#__codelineno-11-49"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-50" name="__codelineno-11-50" href="#__codelineno-11-50"></a><span class="w">            </span><span class="n">row</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="s">&quot;#&quot;</span><span class="p">)</span>
+<a id="__codelineno-11-51" name="__codelineno-11-51" href="#__codelineno-11-51"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-52" name="__codelineno-11-52" href="#__codelineno-11-52"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">row</span><span class="p">)</span>
+<a id="__codelineno-11-53" name="__codelineno-11-53" href="#__codelineno-11-53"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-54" name="__codelineno-11-54" href="#__codelineno-11-54"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">cols</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BooleanArray</span><span class="p">(</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="c1">// 列にクイーンがあるか記録</span>
+<a id="__codelineno-11-55" name="__codelineno-11-55" href="#__codelineno-11-55"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">diags1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BooleanArray</span><span class="p">(</span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="c1">// 主対角線にクイーンがあるかを記録</span>
+<a id="__codelineno-11-56" name="__codelineno-11-56" href="#__codelineno-11-56"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">diags2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BooleanArray</span><span class="p">(</span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="c1">// 副対角線にクイーンがあるかを記録</span>
+<a id="__codelineno-11-57" name="__codelineno-11-57" href="#__codelineno-11-57"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">String</span><span class="o">&gt;&gt;?&gt;</span><span class="p">()</span>
+<a id="__codelineno-11-58" name="__codelineno-11-58" href="#__codelineno-11-58"></a>
+<a id="__codelineno-11-59" name="__codelineno-11-59" href="#__codelineno-11-59"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cols</span><span class="p">,</span><span class="w"> </span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="n">diags2</span><span class="p">)</span>
+<a id="__codelineno-11-60" name="__codelineno-11-60" href="#__codelineno-11-60"></a>
+<a id="__codelineno-11-61" name="__codelineno-11-61" href="#__codelineno-11-61"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-11-62" name="__codelineno-11-62" href="#__codelineno-11-62"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">n_queens.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
-<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">n_queens</span><span class="p">}</span>
+<div class="highlight"><span class="filename">n_queens.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### バックトラッキング法：Nクイーン ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">row</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cols</span><span class="p">,</span><span class="w"> </span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="n">diags2</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># すべての行への配置が完了したら、解を記録する</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">n</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">    </span><span class="n">res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">state</span><span class="o">.</span><span class="n">map</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">row</span><span class="o">|</span><span class="w"> </span><span class="n">row</span><span class="o">.</span><span class="n">dup</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">    </span><span class="k">return</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">  </span><span class="c1"># すべての列を走査</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">    </span><span class="c1"># このマスに対応する主対角線と副対角線を計算</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">    </span><span class="n">diag1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">    </span><span class="n">diag2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">col</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">    </span><span class="c1"># 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="o">!</span><span class="n">cols</span><span class="o">[</span><span class="n">col</span><span class="o">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">diags1</span><span class="o">[</span><span class="n">diag1</span><span class="o">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">diags2</span><span class="o">[</span><span class="n">diag2</span><span class="o">]</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">      </span><span class="c1"># 試行：そのマスにクイーンを置く</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">      </span><span class="n">state</span><span class="o">[</span><span class="n">row</span><span class="o">][</span><span class="n">col</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;Q&quot;</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w">      </span><span class="n">cols</span><span class="o">[</span><span class="n">col</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags1</span><span class="o">[</span><span class="n">diag1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags2</span><span class="o">[</span><span class="n">diag2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kp">true</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w">      </span><span class="c1"># 次の行に配置する</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="w">      </span><span class="n">backtrack</span><span class="p">(</span><span class="n">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cols</span><span class="p">,</span><span class="w"> </span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="n">diags2</span><span class="p">)</span>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w">      </span><span class="c1"># 戻す：そのマスを空きマスに戻す</span>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w">      </span><span class="n">state</span><span class="o">[</span><span class="n">row</span><span class="o">][</span><span class="n">col</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;#&quot;</span>
+<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="w">      </span><span class="n">cols</span><span class="o">[</span><span class="n">col</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags1</span><span class="o">[</span><span class="n">diag1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags2</span><span class="o">[</span><span class="n">diag2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kp">false</span>
+<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a><span class="k">end</span>
+<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a>
+<a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a><span class="c1">### Nクイーンを解く ###</span>
+<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a><span class="k">def</span><span class="w"> </span><span class="nf">n_queens</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a><span class="w">  </span><span class="c1"># n*n の盤面を初期化する。&#39;Q&#39; はクイーン、&#39;#&#39; は空きマスを表す</span>
+<a id="__codelineno-12-31" name="__codelineno-12-31" href="#__codelineno-12-31"></a><span class="w">  </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="s2">&quot;#&quot;</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-12-32" name="__codelineno-12-32" href="#__codelineno-12-32"></a><span class="w">  </span><span class="n">cols</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="kp">false</span><span class="p">)</span><span class="w"> </span><span class="c1"># 列にクイーンがあるか記録</span>
+<a id="__codelineno-12-33" name="__codelineno-12-33" href="#__codelineno-12-33"></a><span class="w">  </span><span class="n">diags1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="kp">false</span><span class="p">)</span><span class="w"> </span><span class="c1"># 主対角線にクイーンがあるかを記録</span>
+<a id="__codelineno-12-34" name="__codelineno-12-34" href="#__codelineno-12-34"></a><span class="w">  </span><span class="n">diags2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="kp">false</span><span class="p">)</span><span class="w"> </span><span class="c1"># 副対角線にクイーンがあるかを記録</span>
+<a id="__codelineno-12-35" name="__codelineno-12-35" href="#__codelineno-12-35"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-12-36" name="__codelineno-12-36" href="#__codelineno-12-36"></a><span class="w">  </span><span class="n">backtrack</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cols</span><span class="p">,</span><span class="w"> </span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="n">diags2</span><span class="p">)</span>
+<a id="__codelineno-12-37" name="__codelineno-12-37" href="#__codelineno-12-37"></a>
+<a id="__codelineno-12-38" name="__codelineno-12-38" href="#__codelineno-12-38"></a><span class="w">  </span><span class="n">res</span>
+<a id="__codelineno-12-39" name="__codelineno-12-39" href="#__codelineno-12-39"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p><span class="arithmatex">\(n\)</span> 個のクイーンを行ごとに配置し、列の制約を考慮して、最初の行から最後の行まで、<span class="arithmatex">\(n\)</span>、<span class="arithmatex">\(n-1\)</span>、<span class="arithmatex">\(\dots\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(1\)</span> の選択肢があり、<span class="arithmatex">\(O(n!)\)</span> 時間を使用します。解を記録する際、行列 <code>state</code> をコピーして <code>res</code> に追加する必要があり、コピー操作は <span class="arithmatex">\(O(n^2)\)</span> 時間を使用します。したがって、<strong>全体の時間計算量は <span class="arithmatex">\(O(n! \cdot n^2)\)</span> です</strong>。実際には、対角線制約に基づく剪定により検索空間を大幅に削減できるため、多くの場合、検索効率は上記の時間計算量よりも優れています。</p>
-<p>配列 <code>state</code> は <span class="arithmatex">\(O(n^2)\)</span> 空間を使用し、配列 <code>cols</code>、<code>diags1</code>、<code>diags2</code> はそれぞれ <span class="arithmatex">\(O(n)\)</span> 空間を使用します。最大再帰深度は <span class="arithmatex">\(n\)</span> で、<span class="arithmatex">\(O(n)\)</span> のスタックフレーム空間を使用します。したがって、<strong>空間計算量は <span class="arithmatex">\(O(n^2)\)</span> です</strong>。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20backtrack%28%0A%20%20%20%20row%3A%20int%2C%0A%20%20%20%20n%3A%20int%2C%0A%20%20%20%20state%3A%20list%5Blist%5Bstr%5D%5D%2C%0A%20%20%20%20res%3A%20list%5Blist%5Blist%5Bstr%5D%5D%5D%2C%0A%20%20%20%20cols%3A%20list%5Bbool%5D%2C%0A%20%20%20%20diags1%3A%20list%5Bbool%5D%2C%0A%20%20%20%20diags2%3A%20list%5Bbool%5D%2C%0A%29%3A%0A%20%20%20%20%22%22%22%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AD%E3%83%B3%E3%82%B0%EF%BC%9AN%20%E3%82%AF%E3%82%A4%E3%83%BC%E3%83%B3%22%22%22%0A%20%20%20%20%23%20%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E8%A1%8C%E3%81%B8%E3%81%AE%E9%85%8D%E7%BD%AE%E3%81%8C%E5%AE%8C%E4%BA%86%E3%81%97%E3%81%9F%E3%82%89%E3%80%81%E8%A7%A3%E3%82%92%E8%A8%98%E9%8C%B2%E3%81%99%E3%82%8B%0A%20%20%20%20if%20row%20%3D%3D%20n%3A%0A%20%20%20%20%20%20%20%20res.append%28%5Blist%28row%29%20for%20row%20in%20state%5D%29%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20%23%20%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E5%88%97%E3%82%92%E8%B5%B0%E6%9F%BB%0A%20%20%20%20for%20col%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E3%81%93%E3%81%AE%E3%83%9E%E3%82%B9%E3%81%AB%E5%AF%BE%E5%BF%9C%E3%81%99%E3%82%8B%E4%B8%BB%E5%AF%BE%E8%A7%92%E7%B7%9A%E3%81%A8%E5%89%AF%E5%AF%BE%E8%A7%92%E7%B7%9A%E3%82%92%E8%A8%88%E7%AE%97%0A%20%20%20%20%20%20%20%20diag1%20%3D%20row%20-%20col%20%2B%20n%20-%201%0A%20%20%20%20%20%20%20%20diag2%20%3D%20row%20%2B%20col%0A%20%20%20%20%20%20%20%20%23%20%E6%9E%9D%E5%88%88%E3%82%8A%EF%BC%9A%E3%81%9D%E3%81%AE%E3%83%9E%E3%82%B9%E3%81%AE%E5%88%97%E3%80%81%E4%B8%BB%E5%AF%BE%E8%A7%92%E7%B7%9A%E3%80%81%E5%89%AF%E5%AF%BE%E8%A7%92%E7%B7%9A%E3%81%AB%E3%82%AF%E3%82%A4%E3%83%BC%E3%83%B3%E3%81%8C%E3%81%82%E3%81%A3%E3%81%A6%E3%81%AF%E3%81%AA%E3%82%89%E3%81%AA%E3%81%84%0A%20%20%20%20%20%20%20%20if%20not%20cols%5Bcol%5D%20and%20not%20diags1%5Bdiag1%5D%20and%20not%20diags2%5Bdiag2%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E8%A9%A6%E8%A1%8C%EF%BC%9A%E3%81%9D%E3%81%AE%E3%83%9E%E3%82%B9%E3%81%AB%E3%82%AF%E3%82%A4%E3%83%BC%E3%83%B3%E3%82%92%E7%BD%AE%E3%81%8F%0A%20%20%20%20%20%20%20%20%20%20%20%20state%5Brow%5D%5Bcol%5D%20%3D%20%22Q%22%0A%20%20%20%20%20%20%20%20%20%20%20%20cols%5Bcol%5D%20%3D%20diags1%5Bdiag1%5D%20%3D%20diags2%5Bdiag2%5D%20%3D%20True%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%AC%A1%E3%81%AE%E8%A1%8C%E3%81%AB%E9%85%8D%E7%BD%AE%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20backtrack%28row%20%2B%201%2C%20n%2C%20state%2C%20res%2C%20cols%2C%20diags1%2C%20diags2%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%88%BB%E3%81%99%EF%BC%9A%E3%81%9D%E3%81%AE%E3%83%9E%E3%82%B9%E3%82%92%E7%A9%BA%E3%81%8D%E3%83%9E%E3%82%B9%E3%81%AB%E6%88%BB%E3%81%99%0A%20%20%20%20%20%20%20%20%20%20%20%20state%5Brow%5D%5Bcol%5D%20%3D%20%22%23%22%0A%20%20%20%20%20%20%20%20%20%20%20%20cols%5Bcol%5D%20%3D%20diags1%5Bdiag1%5D%20%3D%20diags2%5Bdiag2%5D%20%3D%20False%0A%0A%0Adef%20n_queens%28n%3A%20int%29%20-%3E%20list%5Blist%5Blist%5Bstr%5D%5D%5D%3A%0A%20%20%20%20%22%22%22N%20%E3%82%AF%E3%82%A4%E3%83%BC%E3%83%B3%E3%82%92%E8%A7%A3%E3%81%8F%22%22%22%0A%20%20%20%20%23%20n%2An%20%E3%81%AE%E7%9B%A4%E9%9D%A2%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%E3%80%82%27Q%27%20%E3%81%AF%E3%82%AF%E3%82%A4%E3%83%BC%E3%83%B3%E3%80%81%27%23%27%20%E3%81%AF%E7%A9%BA%E3%81%8D%E3%83%9E%E3%82%B9%E3%82%92%E8%A1%A8%E3%81%99%0A%20%20%20%20state%20%3D%20%5B%5B%22%23%22%20for%20_%20in%20range%28n%29%5D%20for%20_%20in%20range%28n%29%5D%0A%20%20%20%20cols%20%3D%20%5BFalse%5D%20%2A%20n%20%20%23%20%E5%88%97%E3%81%AB%E3%82%AF%E3%82%A4%E3%83%BC%E3%83%B3%E3%81%8C%E3%81%82%E3%82%8B%E3%81%8B%E8%A8%98%E9%8C%B2%0A%20%20%20%20diags1%20%3D%20%5BFalse%5D%20%2A%20%282%20%2A%20n%20-%201%29%20%20%23%20%E4%B8%BB%E5%AF%BE%E8%A7%92%E7%B7%9A%E3%81%AB%E3%82%AF%E3%82%A4%E3%83%BC%E3%83%B3%E3%81%8C%E3%81%82%E3%82%8B%E3%81%8B%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20diags2%20%3D%20%5BFalse%5D%20%2A%20%282%20%2A%20n%20-%201%29%20%20%23%20%E5%89%AF%E5%AF%BE%E8%A7%92%E7%B7%9A%E3%81%AB%E3%82%AF%E3%82%A4%E3%83%BC%E3%83%B3%E3%81%8C%E3%81%82%E3%82%8B%E3%81%8B%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20res%20%3D%20%5B%5D%0A%20%20%20%20backtrack%280%2C%20n%2C%20state%2C%20res%2C%20cols%2C%20diags1%2C%20diags2%29%0A%0A%20%20%20%20return%20res%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%204%0A%20%20%20%20res%20%3D%20n_queens%28n%29%0A%0A%20%20%20%20print%28f%22%E5%85%A5%E5%8A%9B%E3%81%95%E3%82%8C%E3%81%9F%E7%9B%A4%E9%9D%A2%E3%81%AE%E7%B8%A6%E6%A8%AA%E3%81%AE%E9%95%B7%E3%81%95%E3%81%AF%20%7Bn%7D%20%E3%81%A7%E3%81%99%22%29%0A%20%20%20%20print%28f%22%E3%82%AF%E3%82%A4%E3%83%BC%E3%83%B3%E3%81%AE%E9%85%8D%E7%BD%AE%E3%83%91%E3%82%BF%E3%83%BC%E3%83%B3%E3%81%AF%E5%85%A8%E9%83%A8%E3%81%A7%20%7Blen%28res%29%7D%20%E9%80%9A%E3%82%8A%E3%81%A7%E3%81%99%22%29%0A%20%20%20%20for%20state%20in%20res%3A%0A%20%20%20%20%20%20%20%20print%28%22--------------------%22%29%0A%20%20%20%20%20%20%20%20for%20row%20in%20state%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20print%28row%29&codeDivHeight=472&codeDivWidth=350&cu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</iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20backtrack%28%0A%20%20%20%20row%3A%20int%2C%0A%20%20%20%20n%3A%20int%2C%0A%20%20%20%20state%3A%20list%5Blist%5Bstr%5D%5D%2C%0A%20%20%20%20res%3A%20list%5Blist%5Blist%5Bstr%5D%5D%5D%2C%0A%20%20%20%20cols%3A%20list%5Bbool%5D%2C%0A%20%20%20%20diags1%3A%20list%5Bbool%5D%2C%0A%20%20%20%20diags2%3A%20list%5Bbool%5D%2C%0A%29%3A%0A%20%20%20%20%22%22%22%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AD%E3%83%B3%E3%82%B0%EF%BC%9AN%20%E3%82%AF%E3%82%A4%E3%83%BC%E3%83%B3%22%22%22%0A%20%20%20%20%23%20%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E8%A1%8C%E3%81%B8%E3%81%AE%E9%85%8D%E7%BD%AE%E3%81%8C%E5%AE%8C%E4%BA%86%E3%81%97%E3%81%9F%E3%82%89%E3%80%81%E8%A7%A3%E3%82%92%E8%A8%98%E9%8C%B2%E3%81%99%E3%82%8B%0A%20%20%20%20if%20row%20%3D%3D%20n%3A%0A%20%20%20%20%20%20%20%20res.append%28%5Blist%28row%29%20for%20row%20in%20state%5D%29%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20%23%20%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E5%88%97%E3%82%92%E8%B5%B0%E6%9F%BB%0A%20%20%20%20for%20col%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E3%81%93%E3%81%AE%E3%83%9E%E3%82%B9%E3%81%AB%E5%AF%BE%E5%BF%9C%E3%81%99%E3%82%8B%E4%B8%BB%E5%AF%BE%E8%A7%92%E7%B7%9A%E3%81%A8%E5%89%AF%E5%AF%BE%E8%A7%92%E7%B7%9A%E3%82%92%E8%A8%88%E7%AE%97%0A%20%20%20%20%20%20%20%20diag1%20%3D%20row%20-%20col%20%2B%20n%20-%201%0A%20%20%20%20%20%20%20%20diag2%20%3D%20row%20%2B%20col%0A%20%20%20%20%20%20%20%20%23%20%E6%9E%9D%E5%88%88%E3%82%8A%EF%BC%9A%E3%81%9D%E3%81%AE%E3%83%9E%E3%82%B9%E3%81%AE%E5%88%97%E3%80%81%E4%B8%BB%E5%AF%BE%E8%A7%92%E7%B7%9A%E3%80%81%E5%89%AF%E5%AF%BE%E8%A7%92%E7%B7%9A%E3%81%AB%E3%82%AF%E3%82%A4%E3%83%BC%E3%83%B3%E3%81%8C%E3%81%82%E3%81%A3%E3%81%A6%E3%81%AF%E3%81%AA%E3%82%89%E3%81%AA%E3%81%84%0A%20%20%20%20%20%20%20%20if%20not%20cols%5Bcol%5D%20and%20not%20diags1%5Bdiag1%5D%20and%20not%20diags2%5Bdiag2%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E8%A9%A6%E8%A1%8C%EF%BC%9A%E3%81%9D%E3%81%AE%E3%83%9E%E3%82%B9%E3%81%AB%E3%82%AF%E3%82%A4%E3%83%BC%E3%83%B3%E3%82%92%E7%BD%AE%E3%81%8F%0A%20%20%20%20%20%20%20%20%20%20%20%20state%5Brow%5D%5Bcol%5D%20%3D%20%22Q%22%0A%20%20%20%20%20%20%20%20%20%20%20%20cols%5Bcol%5D%20%3D%20diags1%5Bdiag1%5D%20%3D%20diags2%5Bdiag2%5D%20%3D%20True%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%AC%A1%E3%81%AE%E8%A1%8C%E3%81%AB%E9%85%8D%E7%BD%AE%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20backtrack%28row%20%2B%201%2C%20n%2C%20state%2C%20res%2C%20cols%2C%20diags1%2C%20diags2%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%88%BB%E3%81%99%EF%BC%9A%E3%81%9D%E3%81%AE%E3%83%9E%E3%82%B9%E3%82%92%E7%A9%BA%E3%81%8D%E3%83%9E%E3%82%B9%E3%81%AB%E6%88%BB%E3%81%99%0A%20%20%20%20%20%20%20%20%20%20%20%20state%5Brow%5D%5Bcol%5D%20%3D%20%22%23%22%0A%20%20%20%20%20%20%20%20%20%20%20%20cols%5Bcol%5D%20%3D%20diags1%5Bdiag1%5D%20%3D%20diags2%5Bdiag2%5D%20%3D%20False%0A%0A%0Adef%20n_queens%28n%3A%20int%29%20-%3E%20list%5Blist%5Blist%5Bstr%5D%5D%5D%3A%0A%20%20%20%20%22%22%22N%20%E3%82%AF%E3%82%A4%E3%83%BC%E3%83%B3%E3%82%92%E8%A7%A3%E3%81%8F%22%22%22%0A%20%20%20%20%23%20n%2An%20%E3%81%AE%E7%9B%A4%E9%9D%A2%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%E3%80%82%27Q%27%20%E3%81%AF%E3%82%AF%E3%82%A4%E3%83%BC%E3%83%B3%E3%80%81%27%23%27%20%E3%81%AF%E7%A9%BA%E3%81%8D%E3%83%9E%E3%82%B9%E3%82%92%E8%A1%A8%E3%81%99%0A%20%20%20%20state%20%3D%20%5B%5B%22%23%22%20for%20_%20in%20range%28n%29%5D%20for%20_%20in%20range%28n%29%5D%0A%20%20%20%20cols%20%3D%20%5BFalse%5D%20%2A%20n%20%20%23%20%E5%88%97%E3%81%AB%E3%82%AF%E3%82%A4%E3%83%BC%E3%83%B3%E3%81%8C%E3%81%82%E3%82%8B%E3%81%8B%E8%A8%98%E9%8C%B2%0A%20%20%20%20diags1%20%3D%20%5BFalse%5D%20%2A%20%282%20%2A%20n%20-%201%29%20%20%23%20%E4%B8%BB%E5%AF%BE%E8%A7%92%E7%B7%9A%E3%81%AB%E3%82%AF%E3%82%A4%E3%83%BC%E3%83%B3%E3%81%8C%E3%81%82%E3%82%8B%E3%81%8B%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20diags2%20%3D%20%5BFalse%5D%20%2A%20%282%20%2A%20n%20-%201%29%20%20%23%20%E5%89%AF%E5%AF%BE%E8%A7%92%E7%B7%9A%E3%81%AB%E3%82%AF%E3%82%A4%E3%83%BC%E3%83%B3%E3%81%8C%E3%81%82%E3%82%8B%E3%81%8B%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20res%20%3D%20%5B%5D%0A%20%20%20%20backtrack%280%2C%20n%2C%20state%2C%20res%2C%20cols%2C%20diags1%2C%20diags2%29%0A%0A%20%20%20%20return%20res%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%204%0A%20%20%20%20res%20%3D%20n_queens%28n%29%0A%0A%20%20%20%20print%28f%22%E5%85%A5%E5%8A%9B%E3%81%95%E3%82%8C%E3%81%9F%E7%9B%A4%E9%9D%A2%E3%81%AE%E7%B8%A6%E6%A8%AA%E3%81%AE%E9%95%B7%E3%81%95%E3%81%AF%20%7Bn%7D%20%E3%81%A7%E3%81%99%22%29%0A%20%20%20%20print%28f%22%E3%82%AF%E3%82%A4%E3%83%BC%E3%83%B3%E3%81%AE%E9%85%8D%E7%BD%AE%E3%83%91%E3%82%BF%E3%83%BC%E3%83%B3%E3%81%AF%E5%85%A8%E9%83%A8%E3%81%A7%20%7Blen%28res%29%7D%20%E9%80%9A%E3%82%8A%E3%81%A7%E3%81%99%22%29%0A%20%20%20%20for%20state%20in%20res%3A%0A%20%20%20%20%20%20%20%20print%28%22--------------------%22%29%0A%20%20%20%20%20%20%20%20for%20row%20in%20state%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20print%28row%29&codeDivHeight=800&codeDivWidth=600&c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target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>行ごとに <span class="arithmatex">\(n\)</span> 回配置し、列制約を考慮すると、1 行目から最終行までの選択肢はそれぞれ <span class="arithmatex">\(n\)</span>、<span class="arithmatex">\(n-1\)</span>、<span class="arithmatex">\(\dots\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(1\)</span> 個となるため、時間計算量は <span class="arithmatex">\(O(n!)\)</span> です。解を記録する際には、行列 <code>state</code> をコピーして <code>res</code> に追加する必要があり、このコピー操作には <span class="arithmatex">\(O(n^2)\)</span> 時間を要します。したがって、<strong>全体の時間計算量は <span class="arithmatex">\(O(n! \cdot n^2)\)</span></strong> です。実際には、対角線制約による枝刈りも探索空間を大きく縮小できるため、探索効率はしばしば上記の時間計算量より良くなります。</p>
+<p>配列 <code>state</code> は <span class="arithmatex">\(O(n^2)\)</span> の空間を使用し、配列 <code>cols</code>、<code>diags1</code>、<code>diags2</code> はいずれも <span class="arithmatex">\(O(n)\)</span> の空間を使用します。最大再帰深さは <span class="arithmatex">\(n\)</span> で、スタックフレーム空間として <span class="arithmatex">\(O(n)\)</span> を使用します。したがって、<strong>空間計算量は <span class="arithmatex">\(O(n^2)\)</span></strong> です。</p>
 
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-    aria-label="前: 13.3 &amp;nbsp; 部分集合和問題"
+    aria-label="前: 13.3 &amp;nbsp; 部分和問題"
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-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
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-        <title>13.2 順列問題 - Hello アルゴリズム</title>
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     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
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-              13.2 &nbsp; 順列問題
+              13.2 &nbsp; 全順列問題
             
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-    3.3 &nbsp; 数値の符号化 *
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4366,19 +4366,19 @@
   <a href="#1321" class="md-nav__link">
     <span class="md-ellipsis">
       
-        13.2.1 &nbsp; 重複要素がない場合
+        13.2.1 &nbsp; 等しい要素がない場合
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="13.2.1 重複要素がない場合">
+    <nav class="md-nav" aria-label="13.2.1 等しい要素がない場合">
       <ul class="md-nav__list">
         
           <li class="md-nav__item">
   <a href="#1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; 重複選択の剪定
+        1. &nbsp; 重複選択の枝刈り
       
     </span>
   </a>
@@ -4405,19 +4405,19 @@
   <a href="#1322" class="md-nav__link">
     <span class="md-ellipsis">
       
-        13.2.2 &nbsp; 重複要素を考慮する場合
+        13.2.2 &nbsp; 等しい要素を考慮する場合
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="13.2.2 重複要素を考慮する場合">
+    <nav class="md-nav" aria-label="13.2.2 等しい要素を考慮する場合">
       <ul class="md-nav__list">
         
           <li class="md-nav__item">
   <a href="#1_1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; 等値要素の剪定
+        1. &nbsp; 等しい要素の枝刈り
       
     </span>
   </a>
@@ -4439,7 +4439,7 @@
   <a href="#3-2" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3. &nbsp; 2つの剪定方法の比較
+        3. &nbsp; 2 種類の枝刈りの比較
       
     </span>
   </a>
@@ -4488,17 +4488,17 @@
 
 
 <!-- Page content -->
-<h1 id="132">13.2 &nbsp; 順列問題<a class="headerlink" href="#132" title="Permanent link">&para;</a></h1>
-<p>順列問題は、バックトラッキングアルゴリズムの典型的な応用です。これは、配列や文字列などの与えられた集合から要素のすべての可能な配置（順列）を見つけることを含みます。</p>
-<p>以下の表は、入力配列とその対応する順列を含むいくつかの例を示しています。</p>
-<p align="center"> 表 13-2 &nbsp; 順列の例 </p>
+<h1 id="132">13.2 &nbsp; 全順列問題<a class="headerlink" href="#132" title="Permanent link">&para;</a></h1>
+<p>全順列問題はバックトラッキングアルゴリズムの典型的な応用例です。これは、ある集合（配列や文字列など）が与えられたとき、その要素のあり得るすべての順列を求める問題です。</p>
+<p>下表に、入力配列とそれに対応するすべての順列から成る例をいくつか示します。</p>
+<p align="center"> 表 13-2 &nbsp; 全順列の例 </p>
 
 <div class="center-table">
 <table>
 <thead>
 <tr>
 <th style="text-align: left;">入力配列</th>
-<th style="text-align: left;">順列</th>
+<th style="text-align: left;">すべての順列</th>
 </tr>
 </thead>
 <tbody>
@@ -4517,38 +4517,38 @@
 </tbody>
 </table>
 </div>
-<h2 id="1321">13.2.1 &nbsp; 重複要素がない場合<a class="headerlink" href="#1321" title="Permanent link">&para;</a></h2>
+<h2 id="1321">13.2.1 &nbsp; 等しい要素がない場合<a class="headerlink" href="#1321" title="Permanent link">&para;</a></h2>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
-<p>重複要素のない整数配列が与えられた場合、すべての可能な順列を返してください。</p>
+<p>重複要素を含まない整数配列を入力として受け取り、あり得るすべての順列を返します。</p>
 </div>
-<p>バックトラッキングの観点から、<strong>順列を生成するプロセスを一連の選択として見ることができます。</strong> 入力配列が <span class="arithmatex">\([1, 2, 3]\)</span> だとします。最初に <span class="arithmatex">\(1\)</span> を選択し、次に <span class="arithmatex">\(3\)</span>、最後に <span class="arithmatex">\(2\)</span> を選択すると、順列 <span class="arithmatex">\([1, 3, 2]\)</span> が得られます。「バックトラッキング」は前の選択を取り消して、代替オプションを探索することを意味します。</p>
-<p>コーディングの観点から、候補集合 <code>choices</code> は入力配列のすべての要素で構成され、<code>state</code> はこれまでに選択された要素を保持します。各要素は一度だけ選択できるため、<strong><code>state</code> のすべての要素は一意である必要があります</strong>。</p>
-<p>以下の図に示すように、検索プロセスを再帰木に展開できます。各ノードは現在の <code>state</code> を表します。ルートノードから開始して、3回の選択の後、葉ノードに到達します—それぞれが順列に対応します。</p>
-<p><img alt="順列の再帰木" class="animation-figure" src="../permutations_problem.assets/permutations_i.png" /></p>
-<p align="center"> 図 13-5 &nbsp; 順列の再帰木 </p>
+<p>バックトラッキングアルゴリズムの観点から見ると、<strong>順列生成の過程は一連の選択の結果として捉えられます</strong>。入力配列が <span class="arithmatex">\([1, 2, 3]\)</span> だとすると、最初に <span class="arithmatex">\(1\)</span> を選び、次に <span class="arithmatex">\(3\)</span> を選び、最後に <span class="arithmatex">\(2\)</span> を選べば、順列 <span class="arithmatex">\([1, 3, 2]\)</span> が得られます。戻る操作は 1 つの選択を取り消し、その後で別の選択を試し続けることを表します。</p>
+<p>バックトラッキングコードの観点では、候補集合 <code>choices</code> は入力配列中のすべての要素であり、状態 <code>state</code> は現時点までに選ばれた要素です。各要素は 1 回しか選べないことに注意してください。<strong>したがって <code>state</code> 内の要素はすべて一意でなければなりません</strong>。</p>
+<p>下図のように、探索過程は再帰木として展開できます。木の各ノードは現在の状態 <code>state</code> を表します。根ノードから始めて 3 ラウンドの選択を経て葉ノードに到達し、各葉ノードが 1 つの順列に対応します。</p>
+<p><img alt="全順列の再帰木" class="animation-figure" src="../permutations_problem.assets/permutations_i.png" /></p>
+<p align="center"> 図 13-5 &nbsp; 全順列の再帰木 </p>
 
-<h3 id="1">1. &nbsp; 重複選択の剪定<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>各要素が一度だけ選択されることを保証するために、ブール配列 <code>selected</code> を導入します。ここで <code>selected[i]</code> は <code>choices[i]</code> が選択されたかどうかを示します。次に、この配列に基づいて剪定ステップを実行します：</p>
+<h3 id="1">1. &nbsp; 重複選択の枝刈り<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>各要素が 1 回しか選ばれないようにするため、ブール配列 <code>selected</code> の導入を考えます。ここで <code>selected[i]</code> は <code>choices[i]</code> がすでに選ばれているかどうかを表し、これに基づいて次の枝刈りを行います。</p>
 <ul>
-<li><code>choice[i]</code> を選択した後、<code>selected[i]</code> を <span class="arithmatex">\(\text{True}\)</span> に設定して選択されたとマークします。</li>
-<li><code>choices</code> を反復処理する際、選択されたとマークされたすべての要素をスキップします（つまり、それらの分岐を剪定します）。</li>
+<li>選択 <code>choice[i]</code> を行った後、<code>selected[i]</code> を <span class="arithmatex">\(\text{True}\)</span> に設定し、その要素が選択済みであることを表します。</li>
+<li>選択肢リスト <code>choices</code> を走査するとき、すでに選ばれたノードはすべてスキップします。これが枝刈りです。</li>
 </ul>
-<p>以下の図に示すように、最初のラウンドで1を選択し、2番目のラウンドで3を選択し、最後のラウンドで2を選択するとします。2番目のラウンドで要素1の分岐と、3番目のラウンドで要素1と3の分岐を剪定する必要があります。</p>
-<p><img alt="順列の剪定例" class="animation-figure" src="../permutations_problem.assets/permutations_i_pruning.png" /></p>
-<p align="center"> 図 13-6 &nbsp; 順列の剪定例 </p>
+<p>下図のように、1 回目に 1、2 回目に 3、3 回目に 2 を選ぶとします。このとき 2 回目では要素 1 の分岐を、3 回目では要素 1 と要素 3 の分岐を刈り取る必要があります。</p>
+<p><img alt="全順列の枝刈り例" class="animation-figure" src="../permutations_problem.assets/permutations_i_pruning.png" /></p>
+<p align="center"> 図 13-6 &nbsp; 全順列の枝刈り例 </p>
 
-<p>図から、この剪定プロセスが検索空間を <span class="arithmatex">\(O(n^n)\)</span> から <span class="arithmatex">\(O(n!)\)</span> に削減することがわかります。</p>
+<p>上図から、この枝刈りにより探索空間の大きさは <span class="arithmatex">\(O(n^n)\)</span> から <span class="arithmatex">\(O(n!)\)</span> へ削減されることがわかります。</p>
 <h3 id="2">2. &nbsp; コード実装<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>この理解により、フレームワークコードの「空欄を埋める」ことができます。全体のコードを簡潔に保つため、フレームワークの各部分を個別に実装せず、代わりに <code>backtrack()</code> 関数ですべてを展開します：</p>
+<p>以上を整理できれば、フレームワークコードの「穴埋め」を行えます。全体のコードを短くするため、フレームワークコード中の各関数を個別には実装せず、これらを <code>backtrack()</code> 関数内に展開します。</p>
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 <div class="highlight"><span class="filename">permutations_i.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
 <a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a>    <span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">choices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">selected</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">bool</span><span class="p">],</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="p">):</span>
-<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキングアルゴリズム：順列 I&quot;&quot;&quot;</span>
-<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="c1"># 状態の長さが要素数と等しいとき、解を記録</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキング：順列 I&quot;&quot;&quot;</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="c1"># 状態の長さが要素数に等しければ、解を記録</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">state</span><span class="p">)</span> <span class="o">==</span> <span class="nb">len</span><span class="p">(</span><span class="n">choices</span><span class="p">):</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">state</span><span class="p">))</span>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="k">return</span>
@@ -4556,26 +4556,26 @@
 <a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">choice</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">choices</span><span class="p">):</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="c1"># 枝刈り：要素の重複選択を許可しない</span>
 <a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="k">if</span> <span class="ow">not</span> <span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]:</span>
-<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>            <span class="c1"># 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>            <span class="c1"># 試行: 選択を行い、状態を更新</span>
 <a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>            <span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="kc">True</span>
 <a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>            <span class="n">state</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>
-<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>            <span class="c1"># 次の選択ラウンドに進む</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>            <span class="c1"># 次の選択へ進む</span>
 <a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>            <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choices</span><span class="p">,</span> <span class="n">selected</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
-<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>            <span class="c1"># 撤回：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>            <span class="c1"># バックトラック：選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>            <span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="kc">False</span>
 <a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>            <span class="n">state</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
 <a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>
 <a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="k">def</span><span class="w"> </span><span class="nf">permutations_i</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]:</span>
-<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;順列 I&quot;&quot;&quot;</span>
+<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;全順列 I&quot;&quot;&quot;</span>
 <a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
 <a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>    <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="o">=</span><span class="p">[],</span> <span class="n">choices</span><span class="o">=</span><span class="n">nums</span><span class="p">,</span> <span class="n">selected</span><span class="o">=</span><span class="p">[</span><span class="kc">False</span><span class="p">]</span> <span class="o">*</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">),</span> <span class="n">res</span><span class="o">=</span><span class="n">res</span><span class="p">)</span>
 <a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a>    <span class="k">return</span> <span class="n">res</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">permutations_i.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* バックトラッキングアルゴリズム：順列 I */</span>
+<div class="highlight"><span class="filename">permutations_i.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* バックトラッキング：順列 I */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数と等しくなったら、解を記録</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数に等しければ、解を記録</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">size</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">state</span><span class="p">);</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
@@ -4583,21 +4583,21 @@
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
-<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="c1">// 剪定：要素の重複選択を許可しない</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="c1">// 枝刈り：要素の重複選択を許可しない</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
 <a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">            </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">true</span><span class="p">;</span>
 <a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
-<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">            </span><span class="c1">// 次のラウンドの選択に進む</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
 <a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
-<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">            </span><span class="c1">// 回退：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">            </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">false</span><span class="p">;</span>
 <a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
 <a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="p">}</span>
 <a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a>
-<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="cm">/* 順列 I */</span>
+<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="cm">/* 全順列 I */</span>
 <a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">permutationsI</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">;</span>
 <a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="n">selected</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">(),</span><span class="w"> </span><span class="nb">false</span><span class="p">);</span>
@@ -4608,9 +4608,9 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">permutations_i.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* バックトラッキングアルゴリズム：順列 I */</span>
+<div class="highlight"><span class="filename">permutations_i.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* バックトラッキング：順列 I */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">boolean</span><span class="o">[]</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数と等しくなったら、解を記録</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数に等しければ、解を記録</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="na">length</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
@@ -4618,21 +4618,21 @@
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="c1">// 剪定：要素の重複選択を許可しない</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="c1">// 枝刈り：要素の重複選択を許可しない</span>
 <a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">selected</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
 <a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">            </span><span class="n">selected</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
 <a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
-<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">            </span><span class="c1">// 次のラウンドの選択に進む</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
 <a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
-<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">            </span><span class="c1">// 回退：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">            </span><span class="n">selected</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span>
 <a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="p">}</span>
 <a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a>
-<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="cm">/* 順列 I */</span>
+<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="cm">/* 全順列 I */</span>
 <a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="nf">permutationsI</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="p">();</span>
 <a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="p">(),</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">boolean</span><span class="o">[</span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
@@ -4641,124 +4641,429 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">permutations_i.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">permutations_i</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Backtrack</span><span class="p">}</span>
-<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
-<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">permutations_i</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">PermutationsI</span><span class="p">}</span>
+<div class="highlight"><span class="filename">permutations_i.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* バックトラッキング：順列 I */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Backtrack</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">bool</span><span class="p">[]</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数に等しければ、解を記録</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">Length</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">        </span><span class="c1">// 枝刈り：要素の重複選択を許可しない</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">            </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">true</span><span class="p">;</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">            </span><span class="n">Backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w">            </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">false</span><span class="p">;</span>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="p">}</span>
+<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a>
+<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="cm">/* 全順列 I */</span>
+<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">PermutationsI</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a><span class="w">    </span><span class="n">Backtrack</span><span class="p">([],</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">bool</span><span class="p">[</span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">],</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">permutations_i.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">backtrackI</span><span class="p">}</span>
-<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
-<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">permutationsI</span><span class="p">}</span>
+<div class="highlight"><span class="filename">permutations_i.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* バックトラッキング：順列 I */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">backtrackI</span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">selected</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="kt">bool</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">*</span><span class="p">[][]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数に等しければ、解を記録</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">        </span><span class="nx">newState</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">append</span><span class="p">([]</span><span class="kt">int</span><span class="p">{},</span><span class="w"> </span><span class="o">*</span><span class="nx">state</span><span class="o">...</span><span class="p">)</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">        </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">newState</span><span class="p">)</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">        </span><span class="nx">choice</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">        </span><span class="c1">// 枝刈り：要素の重複選択を許可しない</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">!(</span><span class="o">*</span><span class="nx">selected</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">            </span><span class="p">(</span><span class="o">*</span><span class="nx">selected</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">true</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">            </span><span class="o">*</span><span class="nx">state</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">            </span><span class="nx">backtrackI</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">selected</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w">            </span><span class="p">(</span><span class="o">*</span><span class="nx">selected</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">false</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w">            </span><span class="o">*</span><span class="nx">state</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)[:</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="p">}</span>
+<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a>
+<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="cm">/* 全順列 I */</span>
+<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="kd">func</span><span class="w"> </span><span class="nx">permutationsI</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">[][]</span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w">    </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="w">    </span><span class="nx">state</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="w">    </span><span class="nx">selected</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">bool</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">))</span>
+<a id="__codelineno-4-30" name="__codelineno-4-30" href="#__codelineno-4-30"></a><span class="w">    </span><span class="nx">backtrackI</span><span class="p">(</span><span class="o">&amp;</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">selected</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">res</span><span class="p">)</span>
+<a id="__codelineno-4-31" name="__codelineno-4-31" href="#__codelineno-4-31"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
+<a id="__codelineno-4-32" name="__codelineno-4-32" href="#__codelineno-4-32"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">permutations_i.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
-<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">permutationsI</span><span class="p">}</span>
+<div class="highlight"><span class="filename">permutations_i.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* バックトラッキング：順列 I */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">selected</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Bool</span><span class="p">],</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[[</span><span class="nb">Int</span><span class="p">]])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数に等しければ、解を記録</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="bp">count</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="bp">count</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">state</span><span class="p">)</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">enumerated</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">        </span><span class="c1">// 枝刈り：要素の重複選択を許可しない</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="o">!</span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">            </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">true</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">            </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">false</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="bp">removeLast</span><span class="p">()</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="p">}</span>
+<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a>
+<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="cm">/* 全順列 I */</span>
+<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="kd">func</span><span class="w"> </span><span class="nf">permutationsI</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[[</span><span class="nb">Int</span><span class="p">]]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">state</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
+<a id="__codelineno-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">selected</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="kc">false</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">count</span><span class="p">)</span>
+<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="p">:</span><span class="w"> </span><span class="p">[[</span><span class="nb">Int</span><span class="p">]]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
+<a id="__codelineno-5-29" name="__codelineno-5-29" href="#__codelineno-5-29"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-5-30" name="__codelineno-5-30" href="#__codelineno-5-30"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-5-31" name="__codelineno-5-31" href="#__codelineno-5-31"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">permutations_i.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
-<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
-<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">permutationsI</span><span class="p">}</span>
+<div class="highlight"><span class="filename">permutations_i.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* バックトラッキング：順列 I */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">selected</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数に等しければ、解を記録</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">state</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">choices</span><span class="p">.</span><span class="nx">length</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">        </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">([...</span><span class="nx">state</span><span class="p">]);</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">    </span><span class="nx">choices</span><span class="p">.</span><span class="nx">forEach</span><span class="p">((</span><span class="nx">choice</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">        </span><span class="c1">// 枝刈り：要素の重複選択を許可しない</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="nx">selected</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">            </span><span class="nx">selected</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">            </span><span class="nx">state</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">choice</span><span class="p">);</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w">            </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">selected</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w">            </span><span class="nx">selected</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">            </span><span class="nx">state</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w">    </span><span class="p">});</span>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="p">}</span>
+<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a>
+<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a><span class="cm">/* 全順列 I */</span>
+<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="kd">function</span><span class="w"> </span><span class="nx">permutationsI</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-6-27" name="__codelineno-6-27" href="#__codelineno-6-27"></a><span class="w">    </span><span class="nx">backtrack</span><span class="p">([],</span><span class="w"> </span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="kc">false</span><span class="p">),</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-6-28" name="__codelineno-6-28" href="#__codelineno-6-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-6-29" name="__codelineno-6-29" href="#__codelineno-6-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">permutations_i.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
-<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
-<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">permutationsI</span><span class="p">}</span>
+<div class="highlight"><span class="filename">permutations_i.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* バックトラッキング：順列 I */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="nx">state</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="nx">choices</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="nx">selected</span><span class="o">:</span><span class="w"> </span><span class="kt">boolean</span><span class="p">[],</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[][]</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数に等しければ、解を記録</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">state</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">choices</span><span class="p">.</span><span class="nx">length</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">        </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">([...</span><span class="nx">state</span><span class="p">]);</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">    </span><span class="nx">choices</span><span class="p">.</span><span class="nx">forEach</span><span class="p">((</span><span class="nx">choice</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">        </span><span class="c1">// 枝刈り：要素の重複選択を許可しない</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="nx">selected</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">            </span><span class="nx">selected</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">            </span><span class="nx">state</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">choice</span><span class="p">);</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="w">            </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">selected</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="w">            </span><span class="nx">selected</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span>
+<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="w">            </span><span class="nx">state</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="w">    </span><span class="p">});</span>
+<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a><span class="p">}</span>
+<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a>
+<a id="__codelineno-7-29" name="__codelineno-7-29" href="#__codelineno-7-29"></a><span class="cm">/* 全順列 I */</span>
+<a id="__codelineno-7-30" name="__codelineno-7-30" href="#__codelineno-7-30"></a><span class="kd">function</span><span class="w"> </span><span class="nx">permutationsI</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[][]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-31" name="__codelineno-7-31" href="#__codelineno-7-31"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[][]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-7-32" name="__codelineno-7-32" href="#__codelineno-7-32"></a><span class="w">    </span><span class="nx">backtrack</span><span class="p">([],</span><span class="w"> </span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="kc">false</span><span class="p">),</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-7-33" name="__codelineno-7-33" href="#__codelineno-7-33"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-7-34" name="__codelineno-7-34" href="#__codelineno-7-34"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">permutations_i.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
-<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">permutationsI</span><span class="p">}</span>
+<div class="highlight"><span class="filename">permutations_i.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* バックトラッキング：順列 I */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">,</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">  </span><span class="c1">// 状態の長さが要素数に等しければ、解を記録</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">length</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">List</span><span class="p">.</span><span class="n">from</span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">    </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">  </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">    </span><span class="c1">// 枝刈り：要素の重複選択を許可しない</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w">      </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w">      </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="w">      </span><span class="n">state</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="w">      </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="w">      </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a><span class="w">      </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a><span class="w">      </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span>
+<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a><span class="w">      </span><span class="n">state</span><span class="p">.</span><span class="n">removeLast</span><span class="p">();</span>
+<a id="__codelineno-8-26" name="__codelineno-8-26" href="#__codelineno-8-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-27" name="__codelineno-8-27" href="#__codelineno-8-27"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-28" name="__codelineno-8-28" href="#__codelineno-8-28"></a><span class="p">}</span>
+<a id="__codelineno-8-29" name="__codelineno-8-29" href="#__codelineno-8-29"></a>
+<a id="__codelineno-8-30" name="__codelineno-8-30" href="#__codelineno-8-30"></a><span class="cm">/* 全順列 I */</span>
+<a id="__codelineno-8-31" name="__codelineno-8-31" href="#__codelineno-8-31"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">permutationsI</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-32" name="__codelineno-8-32" href="#__codelineno-8-32"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-8-33" name="__codelineno-8-33" href="#__codelineno-8-33"></a><span class="w">  </span><span class="n">backtrack</span><span class="p">([],</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="kc">false</span><span class="p">),</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-8-34" name="__codelineno-8-34" href="#__codelineno-8-34"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-8-35" name="__codelineno-8-35" href="#__codelineno-8-35"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">permutations_i.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
-<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">permutations_i</span><span class="p">}</span>
+<div class="highlight"><span class="filename">permutations_i.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* バックトラッキング：順列 I */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="k">mut</span><span class="w"> </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">selected</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">bool</span><span class="p">],</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数に等しければ、解を記録</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">state</span><span class="p">);</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">choices</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">        </span><span class="c1">// 枝刈り：要素の重複選択を許可しない</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="o">!</span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">            </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">clone</span><span class="p">(),</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">            </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="p">}</span>
+<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a>
+<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="cm">/* 全順列 I */</span>
+<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="k">fn</span><span class="w"> </span><span class="nf">permutations_i</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">();</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">(),</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="kc">false</span><span class="p">;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()],</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="w">    </span><span class="n">res</span>
+<a id="__codelineno-9-30" name="__codelineno-9-30" href="#__codelineno-9-30"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">permutations_i.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
-<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">permutationsI</span><span class="p">}</span>
+<div class="highlight"><span class="filename">permutations_i.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* バックトラッキング：順列 I */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">stateSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">choicesSize</span><span class="p">,</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="o">*</span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">**</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">resSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数に等しければ、解を記録</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">stateSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choicesSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="o">*</span><span class="n">resSize</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="n">choicesSize</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choicesSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="o">*</span><span class="n">resSize</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">state</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">        </span><span class="p">(</span><span class="o">*</span><span class="n">resSize</span><span class="p">)</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choicesSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">        </span><span class="c1">// 枝刈り：要素の重複選択を許可しない</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">            </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">true</span><span class="p">;</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w">            </span><span class="n">state</span><span class="p">[</span><span class="n">stateSize</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choice</span><span class="p">;</span>
+<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">stateSize</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">choicesSize</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">resSize</span><span class="p">);</span>
+<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w">            </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">false</span><span class="p">;</span>
+<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="p">}</span>
+<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a>
+<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="cm">/* 全順列 I */</span>
+<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a><span class="kt">int</span><span class="w"> </span><span class="o">**</span><span class="nf">permutationsI</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">numsSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">returnSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="n">numsSize</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></a><span class="w">    </span><span class="kt">bool</span><span class="w"> </span><span class="o">*</span><span class="n">selected</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">bool</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="n">numsSize</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">bool</span><span class="p">));</span>
+<a id="__codelineno-10-32" name="__codelineno-10-32" href="#__codelineno-10-32"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">numsSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-33" name="__codelineno-10-33" href="#__codelineno-10-33"></a><span class="w">        </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">false</span><span class="p">;</span>
+<a id="__codelineno-10-34" name="__codelineno-10-34" href="#__codelineno-10-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-35" name="__codelineno-10-35" href="#__codelineno-10-35"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">**</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">**</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="n">MAX_SIZE</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">));</span>
+<a id="__codelineno-10-36" name="__codelineno-10-36" href="#__codelineno-10-36"></a><span class="w">    </span><span class="o">*</span><span class="n">returnSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-37" name="__codelineno-10-37" href="#__codelineno-10-37"></a>
+<a id="__codelineno-10-38" name="__codelineno-10-38" href="#__codelineno-10-38"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">numsSize</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">returnSize</span><span class="p">);</span>
+<a id="__codelineno-10-39" name="__codelineno-10-39" href="#__codelineno-10-39"></a>
+<a id="__codelineno-10-40" name="__codelineno-10-40" href="#__codelineno-10-40"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">state</span><span class="p">);</span>
+<a id="__codelineno-10-41" name="__codelineno-10-41" href="#__codelineno-10-41"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">selected</span><span class="p">);</span>
+<a id="__codelineno-10-42" name="__codelineno-10-42" href="#__codelineno-10-42"></a>
+<a id="__codelineno-10-43" name="__codelineno-10-43" href="#__codelineno-10-43"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-10-44" name="__codelineno-10-44" href="#__codelineno-10-44"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">permutations_i.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
-<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">permutationsI</span><span class="p">}</span>
+<div class="highlight"><span class="filename">permutations_i.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* バックトラッキング：順列 I */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="n">selected</span><span class="p">:</span><span class="w"> </span><span class="n">BooleanArray</span><span class="p">,</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;?&gt;</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数に等しければ、解を記録</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="na">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">toMutableList</span><span class="p">())</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="na">indices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">choice</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">        </span><span class="c1">// 枝刈り：要素の重複選択を許可しない</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">selected</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w">            </span><span class="n">selected</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="w">            </span><span class="n">selected</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span>
+<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="na">removeAt</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="p">}</span>
+<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a>
+<a id="__codelineno-11-30" name="__codelineno-11-30" href="#__codelineno-11-30"></a><span class="cm">/* 全順列 I */</span>
+<a id="__codelineno-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">permutationsI</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">):</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;?&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-32" name="__codelineno-11-32" href="#__codelineno-11-32"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;?&gt;</span><span class="p">()</span>
+<a id="__codelineno-11-33" name="__codelineno-11-33" href="#__codelineno-11-33"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">mutableListOf</span><span class="p">(),</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">BooleanArray</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="na">size</span><span class="p">),</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-11-34" name="__codelineno-11-34" href="#__codelineno-11-34"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-11-35" name="__codelineno-11-35" href="#__codelineno-11-35"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">permutations_i.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
-<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">permutations_i</span><span class="p">}</span>
+<div class="highlight"><span class="filename">permutations_i.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### バックトラッキング法：全順列 I ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># 状態の長さが要素数に等しければ、解を記録</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="n">state</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">    </span><span class="n">res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">state</span><span class="o">.</span><span class="n">dup</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">    </span><span class="k">return</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">  </span><span class="c1"># すべての選択肢を走査</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">  </span><span class="n">choices</span><span class="o">.</span><span class="n">each_with_index</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="o">|</span><span class="n">choice</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="o">|</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">    </span><span class="c1"># 枝刈り：要素の重複選択を許可しない</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">    </span><span class="k">unless</span><span class="w"> </span><span class="n">selected</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">      </span><span class="c1"># 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">      </span><span class="n">selected</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kp">true</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">      </span><span class="n">state</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">choice</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">      </span><span class="c1"># 次の選択へ進む</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">      </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w">      </span><span class="c1"># バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w">      </span><span class="n">selected</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kp">false</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="w">      </span><span class="n">state</span><span class="o">.</span><span class="n">pop</span>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="k">end</span>
+<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a>
+<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="c1">### 全順列 I ###</span>
+<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a><span class="k">def</span><span class="w"> </span><span class="nf">permutations_i</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a><span class="w">  </span><span class="n">backtrack</span><span class="p">(</span><span class="o">[]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="kp">false</span><span class="p">),</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a><span class="w">  </span><span class="n">res</span>
+<a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h2 id="1322">13.2.2 &nbsp; 重複要素を考慮する場合<a class="headerlink" href="#1322" title="Permanent link">&para;</a></h2>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20backtrack%28%0A%20%20%20%20state%3A%20list%5Bint%5D%2C%20choices%3A%20list%5Bint%5D%2C%20selected%3A%20list%5Bbool%5D%2C%20res%3A%20list%5Blist%5Bint%5D%5D%0A%29%3A%0A%20%20%20%20%22%22%22%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AD%E3%83%B3%E3%82%B0%EF%BC%9A%E9%A0%86%E5%88%97%20I%22%22%22%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E3%81%AE%E9%95%B7%E3%81%95%E3%81%8C%E8%A6%81%E7%B4%A0%E6%95%B0%E3%81%AB%E7%AD%89%E3%81%97%E3%81%91%E3%82%8C%E3%81%B0%E3%80%81%E8%A7%A3%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20if%20len%28state%29%20%3D%3D%20len%28choices%29%3A%0A%20%20%20%20%20%20%20%20res.append%28list%28state%29%29%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20%23%20%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E9%81%B8%E6%8A%9E%E8%82%A2%E3%82%92%E8%B5%B0%E6%9F%BB%0A%20%20%20%20for%20i%2C%20choice%20in%20enumerate%28choices%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E6%9E%9D%E5%88%88%E3%82%8A%EF%BC%9A%E8%A6%81%E7%B4%A0%E3%81%AE%E9%87%8D%E8%A4%87%E9%81%B8%E6%8A%9E%E3%82%92%E8%A8%B1%E5%8F%AF%E3%81%97%E3%81%AA%E3%81%84%0A%20%20%20%20%20%20%20%20if%20not%20selected%5Bi%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E8%A9%A6%E8%A1%8C%3A%20%E9%81%B8%E6%8A%9E%E3%82%92%E8%A1%8C%E3%81%84%E3%80%81%E7%8A%B6%E6%85%8B%E3%82%92%E6%9B%B4%E6%96%B0%0A%20%20%20%20%20%20%20%20%20%20%20%20selected%5Bi%5D%20%3D%20True%0A%20%20%20%20%20%20%20%20%20%20%20%20state.append%28choice%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%AC%A1%E3%81%AE%E9%81%B8%E6%8A%9E%E3%81%B8%E9%80%B2%E3%82%80%0A%20%20%20%20%20%20%20%20%20%20%20%20backtrack%28state%2C%20choices%2C%20selected%2C%20res%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AF%EF%BC%9A%E9%81%B8%E6%8A%9E%E3%82%92%E5%8F%96%E3%82%8A%E6%B6%88%E3%81%97%E3%80%81%E5%89%8D%E3%81%AE%E7%8A%B6%E6%85%8B%E3%81%AB%E6%88%BB%E3%81%99%0A%20%20%20%20%20%20%20%20%20%20%20%20selected%5Bi%5D%20%3D%20False%0A%20%20%20%20%20%20%20%20%20%20%20%20state.pop%28%29%0A%0A%0Adef%20permutations_i%28nums%3A%20list%5Bint%5D%29%20-%3E%20list%5Blist%5Bint%5D%5D%3A%0A%20%20%20%20%22%22%22%E5%85%A8%E9%A0%86%E5%88%97%20I%22%22%22%0A%20%20%20%20res%20%3D%20%5B%5D%0A%20%20%20%20backtrack%28state%3D%5B%5D%2C%20choices%3Dnums%2C%20selected%3D%5BFalse%5D%20%2A%20len%28nums%29%2C%20res%3Dres%29%0A%20%20%20%20return%20res%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B1%2C%202%2C%203%5D%0A%0A%20%20%20%20res%20%3D%20permutations_i%28nums%29%0A%0A%20%20%20%20print%28f%22%E5%85%A5%E5%8A%9B%E9%85%8D%E5%88%97%20nums%20%3D%20%7Bnums%7D%22%29%0A%20%20%20%20print%28f%22%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E9%A0%86%E5%88%97%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=13&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20backtrack%28%0A%20%20%20%20state%3A%20list%5Bint%5D%2C%20choices%3A%20list%5Bint%5D%2C%20selected%3A%20list%5Bbool%5D%2C%20res%3A%20list%5Blist%5Bint%5D%5D%0A%29%3A%0A%20%20%20%20%22%22%22%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AD%E3%83%B3%E3%82%B0%EF%BC%9A%E9%A0%86%E5%88%97%20I%22%22%22%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E3%81%AE%E9%95%B7%E3%81%95%E3%81%8C%E8%A6%81%E7%B4%A0%E6%95%B0%E3%81%AB%E7%AD%89%E3%81%97%E3%81%91%E3%82%8C%E3%81%B0%E3%80%81%E8%A7%A3%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20if%20len%28state%29%20%3D%3D%20len%28choices%29%3A%0A%20%20%20%20%20%20%20%20res.append%28list%28state%29%29%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20%23%20%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E9%81%B8%E6%8A%9E%E8%82%A2%E3%82%92%E8%B5%B0%E6%9F%BB%0A%20%20%20%20for%20i%2C%20choice%20in%20enumerate%28choices%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E6%9E%9D%E5%88%88%E3%82%8A%EF%BC%9A%E8%A6%81%E7%B4%A0%E3%81%AE%E9%87%8D%E8%A4%87%E9%81%B8%E6%8A%9E%E3%82%92%E8%A8%B1%E5%8F%AF%E3%81%97%E3%81%AA%E3%81%84%0A%20%20%20%20%20%20%20%20if%20not%20selected%5Bi%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E8%A9%A6%E8%A1%8C%3A%20%E9%81%B8%E6%8A%9E%E3%82%92%E8%A1%8C%E3%81%84%E3%80%81%E7%8A%B6%E6%85%8B%E3%82%92%E6%9B%B4%E6%96%B0%0A%20%20%20%20%20%20%20%20%20%20%20%20selected%5Bi%5D%20%3D%20True%0A%20%20%20%20%20%20%20%20%20%20%20%20state.append%28choice%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%AC%A1%E3%81%AE%E9%81%B8%E6%8A%9E%E3%81%B8%E9%80%B2%E3%82%80%0A%20%20%20%20%20%20%20%20%20%20%20%20backtrack%28state%2C%20choices%2C%20selected%2C%20res%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AF%EF%BC%9A%E9%81%B8%E6%8A%9E%E3%82%92%E5%8F%96%E3%82%8A%E6%B6%88%E3%81%97%E3%80%81%E5%89%8D%E3%81%AE%E7%8A%B6%E6%85%8B%E3%81%AB%E6%88%BB%E3%81%99%0A%20%20%20%20%20%20%20%20%20%20%20%20selected%5Bi%5D%20%3D%20False%0A%20%20%20%20%20%20%20%20%20%20%20%20state.pop%28%29%0A%0A%0Adef%20permutations_i%28nums%3A%20list%5Bint%5D%29%20-%3E%20list%5Blist%5Bint%5D%5D%3A%0A%20%20%20%20%22%22%22%E5%85%A8%E9%A0%86%E5%88%97%20I%22%22%22%0A%20%20%20%20res%20%3D%20%5B%5D%0A%20%20%20%20backtrack%28state%3D%5B%5D%2C%20choices%3Dnums%2C%20selected%3D%5BFalse%5D%20%2A%20len%28nums%29%2C%20res%3Dres%29%0A%20%20%20%20return%20res%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B1%2C%202%2C%203%5D%0A%0A%20%20%20%20res%20%3D%20permutations_i%28nums%29%0A%0A%20%20%20%20print%28f%22%E5%85%A5%E5%8A%9B%E9%85%8D%E5%88%97%20nums%20%3D%20%7Bnums%7D%22%29%0A%20%20%20%20print%28f%22%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E9%A0%86%E5%88%97%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=13&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h2 id="1322">13.2.2 &nbsp; 等しい要素を考慮する場合<a class="headerlink" href="#1322" title="Permanent link">&para;</a></h2>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
-<p>**重複要素を含む可能性のある**整数配列が与えられた場合、すべての一意の順列を返してください。</p>
+<p>整数配列を入力として受け取り、<strong>配列には重複要素が含まれる場合があります</strong>。重複しない順列をすべて返します。</p>
 </div>
-<p>入力配列が <span class="arithmatex">\([1, 1, 2]\)</span> だとします。2つの同一要素 <span class="arithmatex">\(1\)</span> を区別するために、2番目を <span class="arithmatex">\(\hat{1}\)</span> とラベル付けします。</p>
-<p>以下の図に示すように、この方法で生成される順列の半分は重複です：</p>
-<p><img alt="重複順列" class="animation-figure" src="../permutations_problem.assets/permutations_ii.png" /></p>
-<p align="center"> 図 13-7 &nbsp; 重複順列 </p>
+<p>入力配列が <span class="arithmatex">\([1, 1, 2]\)</span> だと仮定します。2 つの重複する要素 <span class="arithmatex">\(1\)</span> を区別しやすくするため、2 つ目の <span class="arithmatex">\(1\)</span> を <span class="arithmatex">\(\hat{1}\)</span> と記します。</p>
+<p>下図のように、上述の方法で生成される順列の半分は重複しています。</p>
+<p><img alt="重複した順列" class="animation-figure" src="../permutations_problem.assets/permutations_ii.png" /></p>
+<p align="center"> 図 13-7 &nbsp; 重複した順列 </p>
 
-<p>では、これらの重複順列をどのように除去できるでしょうか？一つの直接的なアプローチは、すべての順列を生成した後にハッシュセットを使用して重複を除去することです。しかし、これはあまり優雅ではありません。<strong>重複を生成する分岐は本来不要であり、事前に剪定されるべきだからです</strong>、これによりアルゴリズムの効率が向上します。</p>
-<h3 id="1_1">1. &nbsp; 等値要素の剪定<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
-<p>以下の図を見ると、最初のラウンドで <span class="arithmatex">\(1\)</span> または <span class="arithmatex">\(\hat{1}\)</span> を選択すると同じ順列につながるため、<span class="arithmatex">\(\hat{1}\)</span> を剪定します。</p>
-<p>同様に、最初のラウンドで <span class="arithmatex">\(2\)</span> を選択した後、2番目のラウンドで <span class="arithmatex">\(1\)</span> または <span class="arithmatex">\(\hat{1}\)</span> を選択しても重複分岐につながるため、その時も <span class="arithmatex">\(\hat{1}\)</span> を剪定します。</p>
-<p>本質的に、<strong>私たちの目標は、複数の同一要素が選択の各ラウンドで一度だけ選択されることを保証することです。</strong></p>
-<p><img alt="重複順列の剪定" class="animation-figure" src="../permutations_problem.assets/permutations_ii_pruning.png" /></p>
-<p align="center"> 図 13-8 &nbsp; 重複順列の剪定 </p>
+<p>では、重複した順列をどのように取り除けばよいのでしょうか。最も直接的なのは、ハッシュ集合を用いて順列結果をそのまま重複排除する方法です。しかしこのやり方は十分に洗練されていません。<strong>なぜなら、重複順列を生成する探索分岐はそもそも不要であり、事前に見つけて枝刈りすべきだからです</strong>。そうすることで、アルゴリズム効率をさらに高められます。</p>
+<h3 id="1_1">1. &nbsp; 等しい要素の枝刈り<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
+<p>下図を見ると、1 回目のラウンドでは <span class="arithmatex">\(1\)</span> を選ぶことと <span class="arithmatex">\(\hat{1}\)</span> を選ぶことは等価であり、これら 2 つの選択の下で生成される順列はすべて重複します。したがって <span class="arithmatex">\(\hat{1}\)</span> を枝刈りすべきです。</p>
+<p>同様に、1 回目で <span class="arithmatex">\(2\)</span> を選んだ後では、2 回目のラウンドにおける <span class="arithmatex">\(1\)</span> と <span class="arithmatex">\(\hat{1}\)</span> も重複分岐を生むため、2 回目の <span class="arithmatex">\(\hat{1}\)</span> も枝刈りすべきです。</p>
+<p>本質的には、<strong>各ラウンドの選択において、等しい複数の要素が 1 回しか選ばれないようにすることが目標です</strong>。</p>
+<p><img alt="重複順列の枝刈り" class="animation-figure" src="../permutations_problem.assets/permutations_ii_pruning.png" /></p>
+<p align="center"> 図 13-8 &nbsp; 重複順列の枝刈り </p>
 
 <h3 id="2_1">2. &nbsp; コード実装<a class="headerlink" href="#2_1" title="Permanent link">&para;</a></h3>
-<p>前の問題のコードに基づいて、各ラウンドでハッシュセット <code>duplicated</code> を導入します。このセットは、すでに試行した要素を追跡し、重複を剪定できるようにします：</p>
+<p>前問のコードを土台として、各ラウンドの選択でハッシュ集合 <code>duplicated</code> を 1 つ用意し、そのラウンドですでに試した要素を記録して、重複要素を枝刈りすることを考えます。</p>
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 <div class="highlight"><span class="filename">permutations_ii.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
 <a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a>    <span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">choices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">selected</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">bool</span><span class="p">],</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]</span>
 <a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="p">):</span>
-<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキングアルゴリズム：順列 II&quot;&quot;&quot;</span>
-<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># 状態の長さが要素数と等しいとき、解を記録</span>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキング：順列 II&quot;&quot;&quot;</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># 状態の長さが要素数に等しければ、解を記録</span>
 <a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>    <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">state</span><span class="p">)</span> <span class="o">==</span> <span class="nb">len</span><span class="p">(</span><span class="n">choices</span><span class="p">):</span>
 <a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>        <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">state</span><span class="p">))</span>
 <a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>        <span class="k">return</span>
 <a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>    <span class="c1"># すべての選択肢を走査</span>
 <a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>    <span class="n">duplicated</span> <span class="o">=</span> <span class="nb">set</span><span class="p">[</span><span class="nb">int</span><span class="p">]()</span>
 <a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>    <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">choice</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">choices</span><span class="p">):</span>
-<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>        <span class="c1"># 枝刈り：要素の重複選択を許可せず、等しい要素の重複選択も許可しない</span>
+<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>        <span class="c1"># 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない</span>
 <a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a>        <span class="k">if</span> <span class="ow">not</span> <span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="ow">and</span> <span class="n">choice</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">duplicated</span><span class="p">:</span>
-<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>            <span class="c1"># 試行：選択を行い、状態を更新</span>
-<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a>            <span class="n">duplicated</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>  <span class="c1"># 選択された要素値を記録</span>
+<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>            <span class="c1"># 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a>            <span class="n">duplicated</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>  <span class="c1"># 選択済みの要素値を記録</span>
 <a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a>            <span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="kc">True</span>
 <a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>            <span class="n">state</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>
-<a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a>            <span class="c1"># 次の選択ラウンドに進む</span>
+<a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a>            <span class="c1"># 次の選択へ進む</span>
 <a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a>            <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choices</span><span class="p">,</span> <span class="n">selected</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
-<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a>            <span class="c1"># 撤回：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a>            <span class="c1"># バックトラック：選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a>            <span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="kc">False</span>
 <a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a>            <span class="n">state</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
 <a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a>
 <a id="__codelineno-13-24" name="__codelineno-13-24" href="#__codelineno-13-24"></a><span class="k">def</span><span class="w"> </span><span class="nf">permutations_ii</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]:</span>
-<a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;順列 II&quot;&quot;&quot;</span>
+<a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;全順列 II&quot;&quot;&quot;</span>
 <a id="__codelineno-13-26" name="__codelineno-13-26" href="#__codelineno-13-26"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
 <a id="__codelineno-13-27" name="__codelineno-13-27" href="#__codelineno-13-27"></a>    <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="o">=</span><span class="p">[],</span> <span class="n">choices</span><span class="o">=</span><span class="n">nums</span><span class="p">,</span> <span class="n">selected</span><span class="o">=</span><span class="p">[</span><span class="kc">False</span><span class="p">]</span> <span class="o">*</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">),</span> <span class="n">res</span><span class="o">=</span><span class="n">res</span><span class="p">)</span>
 <a id="__codelineno-13-28" name="__codelineno-13-28" href="#__codelineno-13-28"></a>    <span class="k">return</span> <span class="n">res</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">permutations_ii.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* バックトラッキングアルゴリズム：順列 II */</span>
+<div class="highlight"><span class="filename">permutations_ii.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* バックトラッキング：順列 II */</span>
 <a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数と等しくなったら、解を記録</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数に等しければ、解を記録</span>
 <a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">size</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">state</span><span class="p">);</span>
 <a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
@@ -4767,22 +5072,22 @@
 <a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">    </span><span class="n">unordered_set</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">duplicated</span><span class="p">;</span>
 <a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
-<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">        </span><span class="c1">// 剪定：要素の重複選択を許可せず、等しい要素の重複選択も許可しない</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">        </span><span class="c1">// 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない</span>
 <a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">duplicated</span><span class="p">.</span><span class="n">find</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">duplicated</span><span class="p">.</span><span class="n">end</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
-<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">            </span><span class="n">duplicated</span><span class="p">.</span><span class="n">emplace</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span><span class="w"> </span><span class="c1">// 選択された要素値を記録</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">            </span><span class="n">duplicated</span><span class="p">.</span><span class="n">emplace</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span><span class="w"> </span><span class="c1">// 選択済みの要素値を記録</span>
 <a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">            </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">true</span><span class="p">;</span>
 <a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
-<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w">            </span><span class="c1">// 次のラウンドの選択に進む</span>
+<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
 <a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
-<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w">            </span><span class="c1">// 回退：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a><span class="w">            </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">false</span><span class="p">;</span>
 <a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
 <a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a><span class="p">}</span>
 <a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a>
-<a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a><span class="cm">/* 順列 II */</span>
+<a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a><span class="cm">/* 全順列 II */</span>
 <a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">permutationsII</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">;</span>
 <a id="__codelineno-14-30" name="__codelineno-14-30" href="#__codelineno-14-30"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="n">selected</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">(),</span><span class="w"> </span><span class="nb">false</span><span class="p">);</span>
@@ -4793,9 +5098,9 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">permutations_ii.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* バックトラッキングアルゴリズム：順列 II */</span>
+<div class="highlight"><span class="filename">permutations_ii.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* バックトラッキング：順列 II */</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">boolean</span><span class="o">[]</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数と等しくなったら、解を記録</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数に等しければ、解を記録</span>
 <a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="na">length</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
 <a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
@@ -4804,22 +5109,22 @@
 <a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">    </span><span class="n">Set</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">duplicated</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashSet</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="p">();</span>
 <a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">        </span><span class="c1">// 剪定：要素の重複選択を許可せず、等しい要素の重複選択も許可しない</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">        </span><span class="c1">// 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない</span>
 <a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">selected</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">duplicated</span><span class="p">.</span><span class="na">contains</span><span class="p">(</span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
-<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">            </span><span class="n">duplicated</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span><span class="w"> </span><span class="c1">// 選択された要素値を記録</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">            </span><span class="n">duplicated</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span><span class="w"> </span><span class="c1">// 選択済みの要素値を記録</span>
 <a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">            </span><span class="n">selected</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
 <a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
-<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">            </span><span class="c1">// 次のラウンドの選択に進む</span>
+<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
 <a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
-<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w">            </span><span class="c1">// 回退：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="w">            </span><span class="n">selected</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span>
 <a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-15-24" name="__codelineno-15-24" href="#__codelineno-15-24"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></a><span class="p">}</span>
 <a id="__codelineno-15-26" name="__codelineno-15-26" href="#__codelineno-15-26"></a>
-<a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></a><span class="cm">/* 順列 II */</span>
+<a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></a><span class="cm">/* 全順列 II */</span>
 <a id="__codelineno-15-28" name="__codelineno-15-28" href="#__codelineno-15-28"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="nf">permutationsII</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-29" name="__codelineno-15-29" href="#__codelineno-15-29"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="p">();</span>
 <a id="__codelineno-15-30" name="__codelineno-15-30" href="#__codelineno-15-30"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="p">(),</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">boolean</span><span class="o">[</span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
@@ -4828,78 +5133,404 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">permutations_ii.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">permutations_ii</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Backtrack</span><span class="p">}</span>
-<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a>
-<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">permutations_ii</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">PermutationsII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">permutations_ii.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* バックトラッキング：順列 II */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Backtrack</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">bool</span><span class="p">[]</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数に等しければ、解を記録</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">Length</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">    </span><span class="n">HashSet</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">duplicated</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">        </span><span class="c1">// 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">duplicated</span><span class="p">.</span><span class="n">Contains</span><span class="p">(</span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">            </span><span class="n">duplicated</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span><span class="w"> </span><span class="c1">// 選択済みの要素値を記録</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">            </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">true</span><span class="p">;</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w">            </span><span class="n">Backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="w">            </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">false</span><span class="p">;</span>
+<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-24" name="__codelineno-16-24" href="#__codelineno-16-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-25" name="__codelineno-16-25" href="#__codelineno-16-25"></a><span class="p">}</span>
+<a id="__codelineno-16-26" name="__codelineno-16-26" href="#__codelineno-16-26"></a>
+<a id="__codelineno-16-27" name="__codelineno-16-27" href="#__codelineno-16-27"></a><span class="cm">/* 全順列 II */</span>
+<a id="__codelineno-16-28" name="__codelineno-16-28" href="#__codelineno-16-28"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">PermutationsII</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-29" name="__codelineno-16-29" href="#__codelineno-16-29"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-16-30" name="__codelineno-16-30" href="#__codelineno-16-30"></a><span class="w">    </span><span class="n">Backtrack</span><span class="p">([],</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">bool</span><span class="p">[</span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">],</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-16-31" name="__codelineno-16-31" href="#__codelineno-16-31"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-16-32" name="__codelineno-16-32" href="#__codelineno-16-32"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">permutations_ii.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">backtrackII</span><span class="p">}</span>
-<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a>
-<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">permutationsII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">permutations_ii.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* バックトラッキング：順列 II */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">backtrackII</span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">selected</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="kt">bool</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">*</span><span class="p">[][]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数に等しければ、解を記録</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">        </span><span class="nx">newState</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">append</span><span class="p">([]</span><span class="kt">int</span><span class="p">{},</span><span class="w"> </span><span class="o">*</span><span class="nx">state</span><span class="o">...</span><span class="p">)</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">        </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">newState</span><span class="p">)</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">    </span><span class="nx">duplicated</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">(</span><span class="kd">map</span><span class="p">[</span><span class="kt">int</span><span class="p">]</span><span class="kd">struct</span><span class="p">{},</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w">        </span><span class="nx">choice</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">        </span><span class="c1">// 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">ok</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">duplicated</span><span class="p">[</span><span class="nx">choice</span><span class="p">];</span><span class="w"> </span><span class="p">!</span><span class="nx">ok</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="p">!(</span><span class="o">*</span><span class="nx">selected</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w">            </span><span class="c1">// 試す: 選択を行って状態を更新</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">            </span><span class="c1">// 選択済みの要素値を記録</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w">            </span><span class="nx">duplicated</span><span class="p">[</span><span class="nx">choice</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kd">struct</span><span class="p">{}{}</span>
+<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="w">            </span><span class="p">(</span><span class="o">*</span><span class="nx">selected</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">true</span>
+<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="w">            </span><span class="o">*</span><span class="nx">state</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span>
+<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a><span class="w">            </span><span class="nx">backtrackII</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">selected</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
+<a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-17-22" name="__codelineno-17-22" href="#__codelineno-17-22"></a><span class="w">            </span><span class="p">(</span><span class="o">*</span><span class="nx">selected</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">false</span>
+<a id="__codelineno-17-23" name="__codelineno-17-23" href="#__codelineno-17-23"></a><span class="w">            </span><span class="o">*</span><span class="nx">state</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)[:</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-17-24" name="__codelineno-17-24" href="#__codelineno-17-24"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-17-25" name="__codelineno-17-25" href="#__codelineno-17-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-26" name="__codelineno-17-26" href="#__codelineno-17-26"></a><span class="p">}</span>
+<a id="__codelineno-17-27" name="__codelineno-17-27" href="#__codelineno-17-27"></a>
+<a id="__codelineno-17-28" name="__codelineno-17-28" href="#__codelineno-17-28"></a><span class="cm">/* 全順列 II */</span>
+<a id="__codelineno-17-29" name="__codelineno-17-29" href="#__codelineno-17-29"></a><span class="kd">func</span><span class="w"> </span><span class="nx">permutationsII</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">[][]</span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-30" name="__codelineno-17-30" href="#__codelineno-17-30"></a><span class="w">    </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-17-31" name="__codelineno-17-31" href="#__codelineno-17-31"></a><span class="w">    </span><span class="nx">state</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-17-32" name="__codelineno-17-32" href="#__codelineno-17-32"></a><span class="w">    </span><span class="nx">selected</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">bool</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">))</span>
+<a id="__codelineno-17-33" name="__codelineno-17-33" href="#__codelineno-17-33"></a><span class="w">    </span><span class="nx">backtrackII</span><span class="p">(</span><span class="o">&amp;</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">selected</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">res</span><span class="p">)</span>
+<a id="__codelineno-17-34" name="__codelineno-17-34" href="#__codelineno-17-34"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
+<a id="__codelineno-17-35" name="__codelineno-17-35" href="#__codelineno-17-35"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">permutations_ii.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a>
-<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">permutationsII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">permutations_ii.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* バックトラッキング：順列 II */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">selected</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Bool</span><span class="p">],</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[[</span><span class="nb">Int</span><span class="p">]])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数に等しければ、解を記録</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="bp">count</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="bp">count</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">state</span><span class="p">)</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">duplicated</span><span class="p">:</span><span class="w"> </span><span class="n">Set</span><span class="p">&lt;</span><span class="nb">Int</span><span class="p">&gt;</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">enumerated</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w">        </span><span class="c1">// 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="o">!</span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="o">!</span><span class="n">duplicated</span><span class="p">.</span><span class="bp">contains</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="w">            </span><span class="n">duplicated</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="c1">// 選択済みの要素値を記録</span>
+<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w">            </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">true</span>
+<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a><span class="w">            </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">false</span>
+<a id="__codelineno-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="bp">removeLast</span><span class="p">()</span>
+<a id="__codelineno-18-22" name="__codelineno-18-22" href="#__codelineno-18-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-23" name="__codelineno-18-23" href="#__codelineno-18-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-24" name="__codelineno-18-24" href="#__codelineno-18-24"></a><span class="p">}</span>
+<a id="__codelineno-18-25" name="__codelineno-18-25" href="#__codelineno-18-25"></a>
+<a id="__codelineno-18-26" name="__codelineno-18-26" href="#__codelineno-18-26"></a><span class="cm">/* 全順列 II */</span>
+<a id="__codelineno-18-27" name="__codelineno-18-27" href="#__codelineno-18-27"></a><span class="kd">func</span><span class="w"> </span><span class="nf">permutationsII</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[[</span><span class="nb">Int</span><span class="p">]]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-28" name="__codelineno-18-28" href="#__codelineno-18-28"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">state</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
+<a id="__codelineno-18-29" name="__codelineno-18-29" href="#__codelineno-18-29"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">selected</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="kc">false</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">count</span><span class="p">)</span>
+<a id="__codelineno-18-30" name="__codelineno-18-30" href="#__codelineno-18-30"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="p">:</span><span class="w"> </span><span class="p">[[</span><span class="nb">Int</span><span class="p">]]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
+<a id="__codelineno-18-31" name="__codelineno-18-31" href="#__codelineno-18-31"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-18-32" name="__codelineno-18-32" href="#__codelineno-18-32"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-18-33" name="__codelineno-18-33" href="#__codelineno-18-33"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">permutations_ii.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
-<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a>
-<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">permutationsII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">permutations_ii.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* バックトラッキング：順列 II */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">selected</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数に等しければ、解を記録</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">state</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">choices</span><span class="p">.</span><span class="nx">length</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">        </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">([...</span><span class="nx">state</span><span class="p">]);</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">duplicated</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Set</span><span class="p">();</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w">    </span><span class="nx">choices</span><span class="p">.</span><span class="nx">forEach</span><span class="p">((</span><span class="nx">choice</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w">        </span><span class="c1">// 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="nx">selected</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="nx">duplicated</span><span class="p">.</span><span class="nx">has</span><span class="p">(</span><span class="nx">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w">            </span><span class="nx">duplicated</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">choice</span><span class="p">);</span><span class="w"> </span><span class="c1">// 選択済みの要素値を記録</span>
+<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w">            </span><span class="nx">selected</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
+<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a><span class="w">            </span><span class="nx">state</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">choice</span><span class="p">);</span>
+<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a><span class="w">            </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">selected</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a><span class="w">            </span><span class="nx">selected</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span>
+<a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a><span class="w">            </span><span class="nx">state</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-19-22" name="__codelineno-19-22" href="#__codelineno-19-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-23" name="__codelineno-19-23" href="#__codelineno-19-23"></a><span class="w">    </span><span class="p">});</span>
+<a id="__codelineno-19-24" name="__codelineno-19-24" href="#__codelineno-19-24"></a><span class="p">}</span>
+<a id="__codelineno-19-25" name="__codelineno-19-25" href="#__codelineno-19-25"></a>
+<a id="__codelineno-19-26" name="__codelineno-19-26" href="#__codelineno-19-26"></a><span class="cm">/* 全順列 II */</span>
+<a id="__codelineno-19-27" name="__codelineno-19-27" href="#__codelineno-19-27"></a><span class="kd">function</span><span class="w"> </span><span class="nx">permutationsII</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-28" name="__codelineno-19-28" href="#__codelineno-19-28"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-19-29" name="__codelineno-19-29" href="#__codelineno-19-29"></a><span class="w">    </span><span class="nx">backtrack</span><span class="p">([],</span><span class="w"> </span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="kc">false</span><span class="p">),</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-19-30" name="__codelineno-19-30" href="#__codelineno-19-30"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-19-31" name="__codelineno-19-31" href="#__codelineno-19-31"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">permutations_ii.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
-<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a>
-<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">permutationsII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">permutations_ii.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* バックトラッキング：順列 II */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="nx">state</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="nx">choices</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">    </span><span class="nx">selected</span><span class="o">:</span><span class="w"> </span><span class="kt">boolean</span><span class="p">[],</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">    </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[][]</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数に等しければ、解を記録</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">state</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">choices</span><span class="p">.</span><span class="nx">length</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">        </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">([...</span><span class="nx">state</span><span class="p">]);</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">duplicated</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Set</span><span class="p">();</span>
+<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w">    </span><span class="nx">choices</span><span class="p">.</span><span class="nx">forEach</span><span class="p">((</span><span class="nx">choice</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a><span class="w">        </span><span class="c1">// 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない</span>
+<a id="__codelineno-20-17" name="__codelineno-20-17" href="#__codelineno-20-17"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="nx">selected</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="nx">duplicated</span><span class="p">.</span><span class="nx">has</span><span class="p">(</span><span class="nx">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-18" name="__codelineno-20-18" href="#__codelineno-20-18"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-20-19" name="__codelineno-20-19" href="#__codelineno-20-19"></a><span class="w">            </span><span class="nx">duplicated</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">choice</span><span class="p">);</span><span class="w"> </span><span class="c1">// 選択済みの要素値を記録</span>
+<a id="__codelineno-20-20" name="__codelineno-20-20" href="#__codelineno-20-20"></a><span class="w">            </span><span class="nx">selected</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
+<a id="__codelineno-20-21" name="__codelineno-20-21" href="#__codelineno-20-21"></a><span class="w">            </span><span class="nx">state</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">choice</span><span class="p">);</span>
+<a id="__codelineno-20-22" name="__codelineno-20-22" href="#__codelineno-20-22"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-20-23" name="__codelineno-20-23" href="#__codelineno-20-23"></a><span class="w">            </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">selected</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-20-24" name="__codelineno-20-24" href="#__codelineno-20-24"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-20-25" name="__codelineno-20-25" href="#__codelineno-20-25"></a><span class="w">            </span><span class="nx">selected</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span>
+<a id="__codelineno-20-26" name="__codelineno-20-26" href="#__codelineno-20-26"></a><span class="w">            </span><span class="nx">state</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-20-27" name="__codelineno-20-27" href="#__codelineno-20-27"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-28" name="__codelineno-20-28" href="#__codelineno-20-28"></a><span class="w">    </span><span class="p">});</span>
+<a id="__codelineno-20-29" name="__codelineno-20-29" href="#__codelineno-20-29"></a><span class="p">}</span>
+<a id="__codelineno-20-30" name="__codelineno-20-30" href="#__codelineno-20-30"></a>
+<a id="__codelineno-20-31" name="__codelineno-20-31" href="#__codelineno-20-31"></a><span class="cm">/* 全順列 II */</span>
+<a id="__codelineno-20-32" name="__codelineno-20-32" href="#__codelineno-20-32"></a><span class="kd">function</span><span class="w"> </span><span class="nx">permutationsII</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[][]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-33" name="__codelineno-20-33" href="#__codelineno-20-33"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[][]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-20-34" name="__codelineno-20-34" href="#__codelineno-20-34"></a><span class="w">    </span><span class="nx">backtrack</span><span class="p">([],</span><span class="w"> </span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="kc">false</span><span class="p">),</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-20-35" name="__codelineno-20-35" href="#__codelineno-20-35"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-20-36" name="__codelineno-20-36" href="#__codelineno-20-36"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">permutations_ii.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a>
-<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">permutationsII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">permutations_ii.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* バックトラッキング：順列 II */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">,</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">  </span><span class="c1">// 状態の長さが要素数に等しければ、解を記録</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">length</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">List</span><span class="p">.</span><span class="n">from</span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="w">    </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">  </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w">  </span><span class="n">Set</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">duplicated</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{};</span>
+<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-21-17" name="__codelineno-21-17" href="#__codelineno-21-17"></a><span class="w">    </span><span class="c1">// 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない</span>
+<a id="__codelineno-21-18" name="__codelineno-21-18" href="#__codelineno-21-18"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">duplicated</span><span class="p">.</span><span class="n">contains</span><span class="p">(</span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-19" name="__codelineno-21-19" href="#__codelineno-21-19"></a><span class="w">      </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-21-20" name="__codelineno-21-20" href="#__codelineno-21-20"></a><span class="w">      </span><span class="n">duplicated</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span><span class="w"> </span><span class="c1">// 選択済みの要素値を記録</span>
+<a id="__codelineno-21-21" name="__codelineno-21-21" href="#__codelineno-21-21"></a><span class="w">      </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
+<a id="__codelineno-21-22" name="__codelineno-21-22" href="#__codelineno-21-22"></a><span class="w">      </span><span class="n">state</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-21-23" name="__codelineno-21-23" href="#__codelineno-21-23"></a><span class="w">      </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-21-24" name="__codelineno-21-24" href="#__codelineno-21-24"></a><span class="w">      </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-21-25" name="__codelineno-21-25" href="#__codelineno-21-25"></a><span class="w">      </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-21-26" name="__codelineno-21-26" href="#__codelineno-21-26"></a><span class="w">      </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span>
+<a id="__codelineno-21-27" name="__codelineno-21-27" href="#__codelineno-21-27"></a><span class="w">      </span><span class="n">state</span><span class="p">.</span><span class="n">removeLast</span><span class="p">();</span>
+<a id="__codelineno-21-28" name="__codelineno-21-28" href="#__codelineno-21-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-29" name="__codelineno-21-29" href="#__codelineno-21-29"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-30" name="__codelineno-21-30" href="#__codelineno-21-30"></a><span class="p">}</span>
+<a id="__codelineno-21-31" name="__codelineno-21-31" href="#__codelineno-21-31"></a>
+<a id="__codelineno-21-32" name="__codelineno-21-32" href="#__codelineno-21-32"></a><span class="cm">/* 全順列 II */</span>
+<a id="__codelineno-21-33" name="__codelineno-21-33" href="#__codelineno-21-33"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">permutationsII</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-34" name="__codelineno-21-34" href="#__codelineno-21-34"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-21-35" name="__codelineno-21-35" href="#__codelineno-21-35"></a><span class="w">  </span><span class="n">backtrack</span><span class="p">([],</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="kc">false</span><span class="p">),</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-21-36" name="__codelineno-21-36" href="#__codelineno-21-36"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-21-37" name="__codelineno-21-37" href="#__codelineno-21-37"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">permutations_ii.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a>
-<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">permutations_ii</span><span class="p">}</span>
+<div class="highlight"><span class="filename">permutations_ii.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* バックトラッキング：順列 II */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="k">mut</span><span class="w"> </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">selected</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">bool</span><span class="p">],</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数に等しければ、解を記録</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">state</span><span class="p">);</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">duplicated</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashSet</span><span class="p">::</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">choices</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">        </span><span class="c1">// 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="o">!</span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">duplicated</span><span class="p">.</span><span class="n">contains</span><span class="p">(</span><span class="o">&amp;</span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="w">            </span><span class="n">duplicated</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span><span class="w"> </span><span class="c1">// 選択済みの要素値を記録</span>
+<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="w">            </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
+<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">clone</span><span class="p">(),</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-22-21" name="__codelineno-22-21" href="#__codelineno-22-21"></a><span class="w">            </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span>
+<a id="__codelineno-22-22" name="__codelineno-22-22" href="#__codelineno-22-22"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
+<a id="__codelineno-22-23" name="__codelineno-22-23" href="#__codelineno-22-23"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-24" name="__codelineno-22-24" href="#__codelineno-22-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-25" name="__codelineno-22-25" href="#__codelineno-22-25"></a><span class="p">}</span>
+<a id="__codelineno-22-26" name="__codelineno-22-26" href="#__codelineno-22-26"></a>
+<a id="__codelineno-22-27" name="__codelineno-22-27" href="#__codelineno-22-27"></a><span class="cm">/* 全順列 II */</span>
+<a id="__codelineno-22-28" name="__codelineno-22-28" href="#__codelineno-22-28"></a><span class="k">fn</span><span class="w"> </span><span class="nf">permutations_ii</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-29" name="__codelineno-22-29" href="#__codelineno-22-29"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-22-30" name="__codelineno-22-30" href="#__codelineno-22-30"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">(),</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="kc">false</span><span class="p">;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()],</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-22-31" name="__codelineno-22-31" href="#__codelineno-22-31"></a><span class="w">    </span><span class="n">res</span>
+<a id="__codelineno-22-32" name="__codelineno-22-32" href="#__codelineno-22-32"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">permutations_ii.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a>
-<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">permutationsII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">permutations_ii.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* バックトラッキング：順列 II */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">stateSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">choicesSize</span><span class="p">,</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="o">*</span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">**</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">resSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数に等しければ、解を記録</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">stateSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choicesSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="o">*</span><span class="n">resSize</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="n">choicesSize</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choicesSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="o">*</span><span class="n">resSize</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">state</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w">        </span><span class="p">(</span><span class="o">*</span><span class="n">resSize</span><span class="p">)</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w">    </span><span class="kt">bool</span><span class="w"> </span><span class="n">duplicated</span><span class="p">[</span><span class="n">MAX_SIZE</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="nb">false</span><span class="p">};</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choicesSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="w">        </span><span class="c1">// 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない</span>
+<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">duplicated</span><span class="p">[</span><span class="n">choice</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="w">            </span><span class="n">duplicated</span><span class="p">[</span><span class="n">choice</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">true</span><span class="p">;</span><span class="w"> </span><span class="c1">// 選択済みの要素値を記録</span>
+<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="w">            </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">true</span><span class="p">;</span>
+<a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a><span class="w">            </span><span class="n">state</span><span class="p">[</span><span class="n">stateSize</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choice</span><span class="p">;</span>
+<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-23-23" name="__codelineno-23-23" href="#__codelineno-23-23"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">stateSize</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">choicesSize</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">resSize</span><span class="p">);</span>
+<a id="__codelineno-23-24" name="__codelineno-23-24" href="#__codelineno-23-24"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-23-25" name="__codelineno-23-25" href="#__codelineno-23-25"></a><span class="w">            </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">false</span><span class="p">;</span>
+<a id="__codelineno-23-26" name="__codelineno-23-26" href="#__codelineno-23-26"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-27" name="__codelineno-23-27" href="#__codelineno-23-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-28" name="__codelineno-23-28" href="#__codelineno-23-28"></a><span class="p">}</span>
+<a id="__codelineno-23-29" name="__codelineno-23-29" href="#__codelineno-23-29"></a>
+<a id="__codelineno-23-30" name="__codelineno-23-30" href="#__codelineno-23-30"></a><span class="cm">/* 全順列 II */</span>
+<a id="__codelineno-23-31" name="__codelineno-23-31" href="#__codelineno-23-31"></a><span class="kt">int</span><span class="w"> </span><span class="o">**</span><span class="nf">permutationsII</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">numsSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">returnSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-32" name="__codelineno-23-32" href="#__codelineno-23-32"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="n">numsSize</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-23-33" name="__codelineno-23-33" href="#__codelineno-23-33"></a><span class="w">    </span><span class="kt">bool</span><span class="w"> </span><span class="o">*</span><span class="n">selected</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">bool</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="n">numsSize</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">bool</span><span class="p">));</span>
+<a id="__codelineno-23-34" name="__codelineno-23-34" href="#__codelineno-23-34"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">numsSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-35" name="__codelineno-23-35" href="#__codelineno-23-35"></a><span class="w">        </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">false</span><span class="p">;</span>
+<a id="__codelineno-23-36" name="__codelineno-23-36" href="#__codelineno-23-36"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-37" name="__codelineno-23-37" href="#__codelineno-23-37"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">**</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">**</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="n">MAX_SIZE</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">));</span>
+<a id="__codelineno-23-38" name="__codelineno-23-38" href="#__codelineno-23-38"></a><span class="w">    </span><span class="o">*</span><span class="n">returnSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-23-39" name="__codelineno-23-39" href="#__codelineno-23-39"></a>
+<a id="__codelineno-23-40" name="__codelineno-23-40" href="#__codelineno-23-40"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">numsSize</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">returnSize</span><span class="p">);</span>
+<a id="__codelineno-23-41" name="__codelineno-23-41" href="#__codelineno-23-41"></a>
+<a id="__codelineno-23-42" name="__codelineno-23-42" href="#__codelineno-23-42"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">state</span><span class="p">);</span>
+<a id="__codelineno-23-43" name="__codelineno-23-43" href="#__codelineno-23-43"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">selected</span><span class="p">);</span>
+<a id="__codelineno-23-44" name="__codelineno-23-44" href="#__codelineno-23-44"></a>
+<a id="__codelineno-23-45" name="__codelineno-23-45" href="#__codelineno-23-45"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-23-46" name="__codelineno-23-46" href="#__codelineno-23-46"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">permutations_ii.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a>
-<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">permutationsII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">permutations_ii.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* バックトラッキング：順列 II */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">    </span><span class="n">selected</span><span class="p">:</span><span class="w"> </span><span class="n">BooleanArray</span><span class="p">,</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">    </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;?&gt;</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数に等しければ、解を記録</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="na">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">toMutableList</span><span class="p">())</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">duplicated</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashSet</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="na">indices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">choice</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-24-17" name="__codelineno-24-17" href="#__codelineno-24-17"></a><span class="w">        </span><span class="c1">// 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない</span>
+<a id="__codelineno-24-18" name="__codelineno-24-18" href="#__codelineno-24-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">selected</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">duplicated</span><span class="p">.</span><span class="na">contains</span><span class="p">(</span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-19" name="__codelineno-24-19" href="#__codelineno-24-19"></a><span class="w">            </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-24-20" name="__codelineno-24-20" href="#__codelineno-24-20"></a><span class="w">            </span><span class="n">duplicated</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="c1">// 選択済みの要素値を記録</span>
+<a id="__codelineno-24-21" name="__codelineno-24-21" href="#__codelineno-24-21"></a><span class="w">            </span><span class="n">selected</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span>
+<a id="__codelineno-24-22" name="__codelineno-24-22" href="#__codelineno-24-22"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-24-23" name="__codelineno-24-23" href="#__codelineno-24-23"></a><span class="w">            </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-24-24" name="__codelineno-24-24" href="#__codelineno-24-24"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-24-25" name="__codelineno-24-25" href="#__codelineno-24-25"></a><span class="w">            </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-24-26" name="__codelineno-24-26" href="#__codelineno-24-26"></a><span class="w">            </span><span class="n">selected</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span>
+<a id="__codelineno-24-27" name="__codelineno-24-27" href="#__codelineno-24-27"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="na">removeAt</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-24-28" name="__codelineno-24-28" href="#__codelineno-24-28"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-24-29" name="__codelineno-24-29" href="#__codelineno-24-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-30" name="__codelineno-24-30" href="#__codelineno-24-30"></a><span class="p">}</span>
+<a id="__codelineno-24-31" name="__codelineno-24-31" href="#__codelineno-24-31"></a>
+<a id="__codelineno-24-32" name="__codelineno-24-32" href="#__codelineno-24-32"></a><span class="cm">/* 全順列 II */</span>
+<a id="__codelineno-24-33" name="__codelineno-24-33" href="#__codelineno-24-33"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">permutationsII</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">):</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;?&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-34" name="__codelineno-24-34" href="#__codelineno-24-34"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;?&gt;</span><span class="p">()</span>
+<a id="__codelineno-24-35" name="__codelineno-24-35" href="#__codelineno-24-35"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">mutableListOf</span><span class="p">(),</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">BooleanArray</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="na">size</span><span class="p">),</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-24-36" name="__codelineno-24-36" href="#__codelineno-24-36"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-24-37" name="__codelineno-24-37" href="#__codelineno-24-37"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">permutations_ii.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a>
-<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">permutations_ii</span><span class="p">}</span>
+<div class="highlight"><span class="filename">permutations_ii.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### バックトラッキング法：全順列 II ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="c1"># 状態の長さが要素数に等しければ、解を記録</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="n">state</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">    </span><span class="n">res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">state</span><span class="o">.</span><span class="n">dup</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">    </span><span class="k">return</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">  </span><span class="c1"># すべての選択肢を走査</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w">  </span><span class="n">duplicated</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">Set</span><span class="o">.</span><span class="n">new</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w">  </span><span class="n">choices</span><span class="o">.</span><span class="n">each_with_index</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="o">|</span><span class="n">choice</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="o">|</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w">    </span><span class="c1"># 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない</span>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="o">!</span><span class="n">selected</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">duplicated</span><span class="o">.</span><span class="n">include?</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w">      </span><span class="c1"># 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w">      </span><span class="n">duplicated</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w">      </span><span class="n">selected</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kp">true</span>
+<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="w">      </span><span class="n">state</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">choice</span>
+<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a><span class="w">      </span><span class="c1"># 次の選択へ進む</span>
+<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="w">      </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a><span class="w">      </span><span class="c1"># バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="w">      </span><span class="n">selected</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kp">false</span>
+<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a><span class="w">      </span><span class="n">state</span><span class="o">.</span><span class="n">pop</span>
+<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a><span class="k">end</span>
+<a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></a>
+<a id="__codelineno-25-27" name="__codelineno-25-27" href="#__codelineno-25-27"></a><span class="c1">### 全順列 II ###</span>
+<a id="__codelineno-25-28" name="__codelineno-25-28" href="#__codelineno-25-28"></a><span class="k">def</span><span class="w"> </span><span class="nf">permutations_ii</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-25-29" name="__codelineno-25-29" href="#__codelineno-25-29"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-25-30" name="__codelineno-25-30" href="#__codelineno-25-30"></a><span class="w">  </span><span class="n">backtrack</span><span class="p">(</span><span class="o">[]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="kp">false</span><span class="p">),</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-25-31" name="__codelineno-25-31" href="#__codelineno-25-31"></a><span class="w">  </span><span class="n">res</span>
+<a id="__codelineno-25-32" name="__codelineno-25-32" href="#__codelineno-25-32"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>すべての要素が異なると仮定すると、<span class="arithmatex">\(n\)</span> 個の要素の順列は <span class="arithmatex">\(n!\)</span> （階乗）個あります。各結果を記録するには長さ <span class="arithmatex">\(n\)</span> のリストをコピーする必要があり、これには <span class="arithmatex">\(O(n)\)</span> 時間がかかります。<strong>したがって、総時間計算量は <span class="arithmatex">\(O(n!n)\)</span> です。</strong></p>
-<p>最大再帰深度は <span class="arithmatex">\(n\)</span> で、<span class="arithmatex">\(O(n)\)</span> のスタック空間を使用します。<code>selected</code> 配列も <span class="arithmatex">\(O(n)\)</span> 空間が必要です。一度に最大 <span class="arithmatex">\(n\)</span> 個の個別の <code>duplicated</code> セットが存在する可能性があるため、それらは集合的に <span class="arithmatex">\(O(n^2)\)</span> 空間を占有します。<strong>したがって、空間計算量は <span class="arithmatex">\(O(n^2)\)</span> です。</strong></p>
-<h3 id="3-2">3. &nbsp; 2つの剪定方法の比較<a class="headerlink" href="#3-2" title="Permanent link">&para;</a></h3>
-<p><code>selected</code> と <code>duplicated</code> はどちらも剪定メカニズムとして機能しますが、異なる問題をターゲットにしています：</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20backtrack%28%0A%20%20%20%20state%3A%20list%5Bint%5D%2C%20choices%3A%20list%5Bint%5D%2C%20selected%3A%20list%5Bbool%5D%2C%20res%3A%20list%5Blist%5Bint%5D%5D%0A%29%3A%0A%20%20%20%20%22%22%22%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AD%E3%83%B3%E3%82%B0%EF%BC%9A%E9%A0%86%E5%88%97%20II%22%22%22%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E3%81%AE%E9%95%B7%E3%81%95%E3%81%8C%E8%A6%81%E7%B4%A0%E6%95%B0%E3%81%AB%E7%AD%89%E3%81%97%E3%81%91%E3%82%8C%E3%81%B0%E3%80%81%E8%A7%A3%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20if%20len%28state%29%20%3D%3D%20len%28choices%29%3A%0A%20%20%20%20%20%20%20%20res.append%28list%28state%29%29%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20%23%20%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E9%81%B8%E6%8A%9E%E8%82%A2%E3%82%92%E8%B5%B0%E6%9F%BB%0A%20%20%20%20duplicated%20%3D%20set%5Bint%5D%28%29%0A%20%20%20%20for%20i%2C%20choice%20in%20enumerate%28choices%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E6%9E%9D%E5%88%88%E3%82%8A%EF%BC%9A%E8%A6%81%E7%B4%A0%E3%81%AE%E9%87%8D%E8%A4%87%E9%81%B8%E6%8A%9E%E3%82%92%E8%A8%B1%E5%8F%AF%E3%81%9B%E3%81%9A%E3%80%81%E5%90%8C%E5%80%A4%E8%A6%81%E7%B4%A0%E3%81%AE%E9%87%8D%E8%A4%87%E9%81%B8%E6%8A%9E%E3%82%82%E8%A8%B1%E5%8F%AF%E3%81%97%E3%81%AA%E3%81%84%0A%20%20%20%20%20%20%20%20if%20not%20selected%5Bi%5D%20and%20choice%20not%20in%20duplicated%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E8%A9%A6%E8%A1%8C%3A%20%E9%81%B8%E6%8A%9E%E3%82%92%E8%A1%8C%E3%81%84%E3%80%81%E7%8A%B6%E6%85%8B%E3%82%92%E6%9B%B4%E6%96%B0%0A%20%20%20%20%20%20%20%20%20%20%20%20duplicated.add%28choice%29%20%20%23%20%E9%81%B8%E6%8A%9E%E6%B8%88%E3%81%BF%E3%81%AE%E8%A6%81%E7%B4%A0%E5%80%A4%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20%20%20%20%20%20%20%20%20selected%5Bi%5D%20%3D%20True%0A%20%20%20%20%20%20%20%20%20%20%20%20state.append%28choice%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%AC%A1%E3%81%AE%E9%81%B8%E6%8A%9E%E3%81%B8%E9%80%B2%E3%82%80%0A%20%20%20%20%20%20%20%20%20%20%20%20backtrack%28state%2C%20choices%2C%20selected%2C%20res%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AF%EF%BC%9A%E9%81%B8%E6%8A%9E%E3%82%92%E5%8F%96%E3%82%8A%E6%B6%88%E3%81%97%E3%80%81%E5%89%8D%E3%81%AE%E7%8A%B6%E6%85%8B%E3%81%AB%E6%88%BB%E3%81%99%0A%20%20%20%20%20%20%20%20%20%20%20%20selected%5Bi%5D%20%3D%20False%0A%20%20%20%20%20%20%20%20%20%20%20%20state.pop%28%29%0A%0A%0Adef%20permutations_ii%28nums%3A%20list%5Bint%5D%29%20-%3E%20list%5Blist%5Bint%5D%5D%3A%0A%20%20%20%20%22%22%22%E5%85%A8%E9%A0%86%E5%88%97%20II%22%22%22%0A%20%20%20%20res%20%3D%20%5B%5D%0A%20%20%20%20backtrack%28state%3D%5B%5D%2C%20choices%3Dnums%2C%20selected%3D%5BFalse%5D%20%2A%20len%28nums%29%2C%20res%3Dres%29%0A%20%20%20%20return%20res%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B1%2C%202%2C%202%5D%0A%0A%20%20%20%20res%20%3D%20permutations_ii%28nums%29%0A%0A%20%20%20%20print%28f%22%E5%85%A5%E5%8A%9B%E9%85%8D%E5%88%97%20nums%20%3D%20%7Bnums%7D%22%29%0A%20%20%20%20print%28f%22%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E9%A0%86%E5%88%97%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=13&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20backtrack%28%0A%20%20%20%20state%3A%20list%5Bint%5D%2C%20choices%3A%20list%5Bint%5D%2C%20selected%3A%20list%5Bbool%5D%2C%20res%3A%20list%5Blist%5Bint%5D%5D%0A%29%3A%0A%20%20%20%20%22%22%22%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AD%E3%83%B3%E3%82%B0%EF%BC%9A%E9%A0%86%E5%88%97%20II%22%22%22%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E3%81%AE%E9%95%B7%E3%81%95%E3%81%8C%E8%A6%81%E7%B4%A0%E6%95%B0%E3%81%AB%E7%AD%89%E3%81%97%E3%81%91%E3%82%8C%E3%81%B0%E3%80%81%E8%A7%A3%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20if%20len%28state%29%20%3D%3D%20len%28choices%29%3A%0A%20%20%20%20%20%20%20%20res.append%28list%28state%29%29%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20%23%20%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E9%81%B8%E6%8A%9E%E8%82%A2%E3%82%92%E8%B5%B0%E6%9F%BB%0A%20%20%20%20duplicated%20%3D%20set%5Bint%5D%28%29%0A%20%20%20%20for%20i%2C%20choice%20in%20enumerate%28choices%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E6%9E%9D%E5%88%88%E3%82%8A%EF%BC%9A%E8%A6%81%E7%B4%A0%E3%81%AE%E9%87%8D%E8%A4%87%E9%81%B8%E6%8A%9E%E3%82%92%E8%A8%B1%E5%8F%AF%E3%81%9B%E3%81%9A%E3%80%81%E5%90%8C%E5%80%A4%E8%A6%81%E7%B4%A0%E3%81%AE%E9%87%8D%E8%A4%87%E9%81%B8%E6%8A%9E%E3%82%82%E8%A8%B1%E5%8F%AF%E3%81%97%E3%81%AA%E3%81%84%0A%20%20%20%20%20%20%20%20if%20not%20selected%5Bi%5D%20and%20choice%20not%20in%20duplicated%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E8%A9%A6%E8%A1%8C%3A%20%E9%81%B8%E6%8A%9E%E3%82%92%E8%A1%8C%E3%81%84%E3%80%81%E7%8A%B6%E6%85%8B%E3%82%92%E6%9B%B4%E6%96%B0%0A%20%20%20%20%20%20%20%20%20%20%20%20duplicated.add%28choice%29%20%20%23%20%E9%81%B8%E6%8A%9E%E6%B8%88%E3%81%BF%E3%81%AE%E8%A6%81%E7%B4%A0%E5%80%A4%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20%20%20%20%20%20%20%20%20selected%5Bi%5D%20%3D%20True%0A%20%20%20%20%20%20%20%20%20%20%20%20state.append%28choice%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%AC%A1%E3%81%AE%E9%81%B8%E6%8A%9E%E3%81%B8%E9%80%B2%E3%82%80%0A%20%20%20%20%20%20%20%20%20%20%20%20backtrack%28state%2C%20choices%2C%20selected%2C%20res%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AF%EF%BC%9A%E9%81%B8%E6%8A%9E%E3%82%92%E5%8F%96%E3%82%8A%E6%B6%88%E3%81%97%E3%80%81%E5%89%8D%E3%81%AE%E7%8A%B6%E6%85%8B%E3%81%AB%E6%88%BB%E3%81%99%0A%20%20%20%20%20%20%20%20%20%20%20%20selected%5Bi%5D%20%3D%20False%0A%20%20%20%20%20%20%20%20%20%20%20%20state.pop%28%29%0A%0A%0Adef%20permutations_ii%28nums%3A%20list%5Bint%5D%29%20-%3E%20list%5Blist%5Bint%5D%5D%3A%0A%20%20%20%20%22%22%22%E5%85%A8%E9%A0%86%E5%88%97%20II%22%22%22%0A%20%20%20%20res%20%3D%20%5B%5D%0A%20%20%20%20backtrack%28state%3D%5B%5D%2C%20choices%3Dnums%2C%20selected%3D%5BFalse%5D%20%2A%20len%28nums%29%2C%20res%3Dres%29%0A%20%20%20%20return%20res%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B1%2C%202%2C%202%5D%0A%0A%20%20%20%20res%20%3D%20permutations_ii%28nums%29%0A%0A%20%20%20%20print%28f%22%E5%85%A5%E5%8A%9B%E9%85%8D%E5%88%97%20nums%20%3D%20%7Bnums%7D%22%29%0A%20%20%20%20print%28f%22%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E9%A0%86%E5%88%97%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=13&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>要素どうしがすべて互いに異なると仮定すると、<span class="arithmatex">\(n\)</span> 個の要素には全部で <span class="arithmatex">\(n!\)</span>  通りの順列（階乗）があります。結果を記録する際には、長さ <span class="arithmatex">\(n\)</span> のリストをコピーする必要があり、これに <span class="arithmatex">\(O(n)\)</span> 時間を要します。<strong>したがって時間計算量は <span class="arithmatex">\(O(n!n)\)</span></strong> です。</p>
+<p>再帰の最大深さは <span class="arithmatex">\(n\)</span> であり、<span class="arithmatex">\(O(n)\)</span> のスタックフレーム空間を使います。<code>selected</code> は <span class="arithmatex">\(O(n)\)</span> 空間を使用します。同時刻に存在する <code>duplicated</code> は最大で <span class="arithmatex">\(n\)</span> 個であり、<span class="arithmatex">\(O(n^2)\)</span> 空間を要します。<strong>したがって空間計算量は <span class="arithmatex">\(O(n^2)\)</span></strong> です。</p>
+<h3 id="3-2">3. &nbsp; 2 種類の枝刈りの比較<a class="headerlink" href="#3-2" title="Permanent link">&para;</a></h3>
+<p><code>selected</code> と <code>duplicated</code> はどちらも枝刈りに用いられますが、目的は異なる点に注意してください。</p>
 <ul>
-<li><strong>重複選択の剪定</strong>（<code>selected</code> 経由）：検索全体に単一の <code>selected</code> 配列があり、現在の状態にすでにある要素を示します。これにより、同じ要素が <code>state</code> に複数回現れることを防ぎます。</li>
-<li><strong>等値要素の剪定</strong>（<code>duplicated</code> 経由）：<code>backtrack</code> 関数の各呼び出しは独自の <code>duplicated</code> セットを使用し、その特定の反復（<code>for</code> ループ）ですでに選択された要素を記録します。これにより、等しい要素が選択の各ラウンドで一度だけ選択されることを保証します。</li>
+<li><strong>重複選択の枝刈り</strong>：探索全体を通して <code>selected</code> は 1 つだけです。これは現在の状態にどの要素が含まれているかを記録し、ある要素が <code>state</code> に重複して現れるのを防ぎます。</li>
+<li><strong>等しい要素の枝刈り</strong>：各ラウンドの選択、すなわち各回の <code>backtrack</code> 呼び出しには <code>duplicated</code> が含まれます。これはそのラウンドの走査（<code>for</code> ループ）でどの要素がすでに選ばれたかを記録し、等しい要素が 1 回しか選ばれないことを保証します。</li>
 </ul>
-<p>以下の図は、これら2つの剪定戦略の範囲を示しています。木の各ノードは選択を表します。ルートから任意の葉への経路は、1つの完全な順列に対応します。</p>
-<p><img alt="2つの剪定条件の範囲" class="animation-figure" src="../permutations_problem.assets/permutations_ii_pruning_summary.png" /></p>
-<p align="center"> 図 13-9 &nbsp; 2つの剪定条件の範囲 </p>
+<p>下図は、2 つの枝刈り条件が有効になる範囲を示しています。木の各ノードは 1 つの選択を表し、根ノードから葉ノードまでの経路上の各ノードが 1 つの順列を構成することに注意してください。</p>
+<p><img alt="2 種類の枝刈り条件の作用範囲" class="animation-figure" src="../permutations_problem.assets/permutations_ii_pruning_summary.png" /></p>
+<p align="center"> 図 13-9 &nbsp; 2 種類の枝刈り条件の作用範囲 </p>
 
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-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
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-        <title>13.3 部分集合和問題 - Hello アルゴリズム</title>
+        <title>13.3 部分和問題 - Hello アルゴリズム</title>
       
     
     
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         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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-    3.3 &nbsp; 数値の符号化 *
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
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   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2491,7 +2491,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2547,7 +2547,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2575,7 +2575,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3113,7 +3113,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3169,7 +3169,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3197,7 +3197,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3401,7 +3401,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3419,7 +3419,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3449,19 +3449,19 @@
   <a href="#1331" class="md-nav__link">
     <span class="md-ellipsis">
       
-        13.3.1 &nbsp; 重複要素がない場合
+        13.3.1 &nbsp; 重複しない要素の場合
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="13.3.1 重複要素がない場合">
+    <nav class="md-nav" aria-label="13.3.1 重複しない要素の場合">
       <ul class="md-nav__list">
         
           <li class="md-nav__item">
   <a href="#1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; 順列解法の参考
+        1. &nbsp; 全順列の解法を参考にする
       
     </span>
   </a>
@@ -3472,7 +3472,7 @@
   <a href="#2" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2. &nbsp; 重複部分集合の剪定
+        2. &nbsp; 重複部分集合の枝刈り
       
     </span>
   </a>
@@ -3499,19 +3499,19 @@
   <a href="#1332" class="md-nav__link">
     <span class="md-ellipsis">
       
-        13.3.2 &nbsp; 重複要素がある場合を考慮
+        13.3.2 &nbsp; 重複要素を考慮する場合
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="13.3.2 重複要素がある場合を考慮">
+    <nav class="md-nav" aria-label="13.3.2 重複要素を考慮する場合">
       <ul class="md-nav__list">
         
           <li class="md-nav__item">
   <a href="#1_1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; 等値要素の剪定
+        1. &nbsp; 等しい要素の枝刈り
       
     </span>
   </a>
@@ -3557,7 +3557,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3698,7 +3698,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3726,7 +3726,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3754,7 +3754,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3782,7 +3782,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3975,7 +3975,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4220,7 +4220,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4366,19 +4366,19 @@
   <a href="#1331" class="md-nav__link">
     <span class="md-ellipsis">
       
-        13.3.1 &nbsp; 重複要素がない場合
+        13.3.1 &nbsp; 重複しない要素の場合
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="13.3.1 重複要素がない場合">
+    <nav class="md-nav" aria-label="13.3.1 重複しない要素の場合">
       <ul class="md-nav__list">
         
           <li class="md-nav__item">
   <a href="#1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; 順列解法の参考
+        1. &nbsp; 全順列の解法を参考にする
       
     </span>
   </a>
@@ -4389,7 +4389,7 @@
   <a href="#2" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2. &nbsp; 重複部分集合の剪定
+        2. &nbsp; 重複部分集合の枝刈り
       
     </span>
   </a>
@@ -4416,19 +4416,19 @@
   <a href="#1332" class="md-nav__link">
     <span class="md-ellipsis">
       
-        13.3.2 &nbsp; 重複要素がある場合を考慮
+        13.3.2 &nbsp; 重複要素を考慮する場合
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="13.3.2 重複要素がある場合を考慮">
+    <nav class="md-nav" aria-label="13.3.2 重複要素を考慮する場合">
       <ul class="md-nav__list">
         
           <li class="md-nav__item">
   <a href="#1_1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; 等値要素の剪定
+        1. &nbsp; 等しい要素の枝刈り
       
     </span>
   </a>
@@ -4488,20 +4488,20 @@
 
 
 <!-- Page content -->
-<h1 id="133">13.3 &nbsp; 部分集合和問題<a class="headerlink" href="#133" title="Permanent link">&para;</a></h1>
-<h2 id="1331">13.3.1 &nbsp; 重複要素がない場合<a class="headerlink" href="#1331" title="Permanent link">&para;</a></h2>
+<h1 id="133">13.3 &nbsp; 部分和問題<a class="headerlink" href="#133" title="Permanent link">&para;</a></h1>
+<h2 id="1331">13.3.1 &nbsp; 重複しない要素の場合<a class="headerlink" href="#1331" title="Permanent link">&para;</a></h2>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
-<p>正の整数の配列 <code>nums</code> とターゲット正整数 <code>target</code> が与えられた場合、組み合わせ内の要素の和が <code>target</code> に等しくなるようなすべての可能な組み合わせを見つけてください。与えられた配列には重複要素がなく、各要素は複数回選択できます。これらの組み合わせを重複する組み合わせを含まないリストとして返してください。</p>
+<p>正整数配列 <code>nums</code> と目標の正整数 <code>target</code> が与えられたとき、要素の和が <code>target</code> に等しくなるすべての組合せを見つけてください。配列に重複要素はなく、各要素は複数回選択できます。これらの組合せをリスト形式で返してください。リストに重複する組合せを含めてはなりません。</p>
 </div>
-<p>例えば、入力集合 <span class="arithmatex">\(\{3, 4, 5\}\)</span> とターゲット整数 <span class="arithmatex">\(9\)</span> の場合、解は <span class="arithmatex">\(\{3, 3, 3\}, \{4, 5\}\)</span> です。以下の2点に注意してください。</p>
+<p>例えば、入力集合 <span class="arithmatex">\(\{3, 4, 5\}\)</span> と目標整数 <span class="arithmatex">\(9\)</span> に対する解は <span class="arithmatex">\(\{3, 3, 3\}, \{4, 5\}\)</span> です。次の 2 点に注意してください。</p>
 <ul>
-<li>入力集合の要素は無制限に選択できます。</li>
-<li>部分集合は要素の順序を区別しません。例えば <span class="arithmatex">\(\{4, 5\}\)</span> と <span class="arithmatex">\(\{5, 4\}\)</span> は同じ部分集合です。</li>
+<li>入力集合内の要素は何度でも繰り返し選択できます。</li>
+<li>部分集合では要素の順序を区別しません。例えば <span class="arithmatex">\(\{4, 5\}\)</span> と <span class="arithmatex">\(\{5, 4\}\)</span> は同じ部分集合です。</li>
 </ul>
-<h3 id="1">1. &nbsp; 順列解法の参考<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>順列問題と同様に、部分集合の生成を一連の選択として想像でき、選択プロセス中に「要素和」をリアルタイムで更新できます。要素和が <code>target</code> に等しくなったとき、部分集合を結果リストに記録します。</p>
-<p>順列問題とは異なり、<strong>この問題では要素は無制限に選択できるため</strong>、要素が選択されたかどうかを記録するための <code>selected</code> ブール配列を使用する必要がありません。順列コードに軽微な修正を加えて、最初に問題を解決できます：</p>
+<h3 id="1">1. &nbsp; 全順列の解法を参考にする<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>全順列問題と同様に、部分集合の生成過程を一連の選択結果として捉え、選択の過程で「要素の和」を逐次更新できます。そして要素の和が <code>target</code> に等しくなった時点で、その部分集合を結果リストに記録します。</p>
+<p>ただし全順列問題と異なるのは、**この問題では集合内の要素を無制限に選択できる**点です。そのため、要素がすでに選択されたかどうかを記録する <code>selected</code> ブール配列は不要です。全順列のコードに少し修正を加えると、まず次の解法コードが得られます。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
@@ -4512,192 +4512,512 @@
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="n">choices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]],</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="p">):</span>
-<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキングアルゴリズム：部分集合の和 I&quot;&quot;&quot;</span>
-<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="c1"># 部分集合の和が target と等しいとき、解を記録</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキング：部分和 I&quot;&quot;&quot;</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="c1"># 部分集合の和が target に等しければ、解を記録</span>
 <a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="k">if</span> <span class="n">total</span> <span class="o">==</span> <span class="n">target</span><span class="p">:</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">state</span><span class="p">))</span>
 <a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="k">return</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="c1"># すべての選択肢を走査</span>
 <a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">choices</span><span class="p">)):</span>
-<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>        <span class="c1"># 枝刈り：部分集合の和が target を超える場合、その選択をスキップ</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>        <span class="c1"># 枝刈り：部分和が target を超える場合はその選択をスキップする</span>
 <a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>        <span class="k">if</span> <span class="n">total</span> <span class="o">+</span> <span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">target</span><span class="p">:</span>
 <a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>            <span class="k">continue</span>
-<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>        <span class="c1"># 試行：選択を行い、要素と total を更新</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>        <span class="c1"># 試行：選択を行い、要素と total を更新する</span>
 <a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>        <span class="n">state</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
-<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>        <span class="c1"># 次の選択ラウンドに進む</span>
+<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>        <span class="c1"># 次の選択へ進む</span>
 <a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>        <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">target</span><span class="p">,</span> <span class="n">total</span> <span class="o">+</span> <span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">choices</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
-<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>        <span class="c1"># 撤回：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>        <span class="c1"># バックトラック：選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a>        <span class="n">state</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
 <a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>
 <a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a><span class="k">def</span><span class="w"> </span><span class="nf">subset_sum_i_naive</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]:</span>
-<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;部分集合の和 I を解く（重複する部分集合を含む）&quot;&quot;&quot;</span>
+<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;部分和 I を解く（重複部分集合を含む）&quot;&quot;&quot;</span>
 <a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>    <span class="n">state</span> <span class="o">=</span> <span class="p">[]</span>  <span class="c1"># 状態（部分集合）</span>
-<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a>    <span class="n">total</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># 部分集合の和</span>
-<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>  <span class="c1"># 結果リスト（部分集合リスト）</span>
+<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a>    <span class="n">total</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># 部分和</span>
+<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>  <span class="c1"># 結果リスト（部分集合のリスト）</span>
 <a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a>    <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">target</span><span class="p">,</span> <span class="n">total</span><span class="p">,</span> <span class="n">nums</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
 <a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a>    <span class="k">return</span> <span class="n">res</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i_naive.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* バックトラッキングアルゴリズム：部分集合和 I */</span>
+<div class="highlight"><span class="filename">subset_sum_i_naive.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* バックトラッキング：部分和 I */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">total</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 部分集合の和がtargetと等しいとき、解を記録</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">total</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">state</span><span class="p">);</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
-<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="c1">// 剪定：部分集合の和がtargetを超えた場合、その選択をスキップ</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">size_t</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="c1">// 枝刈り：部分和が target を超える場合はその選択をスキップする</span>
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、要素とtotalを更新</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、要素と total を更新する</span>
 <a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
-<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">        </span><span class="c1">// 次のラウンドの選択に進む</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
 <a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
-<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">        </span><span class="c1">// 回退：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
 <a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="p">}</span>
 <a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a>
-<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="cm">/* 部分集合和 I を解く（重複する部分集合を含む） */</span>
-<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">subsetSumINaive</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="cm">/* 部分和 I を解く（重複部分集合を含む） */</span>
+<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">subsetSumINaive</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">;</span><span class="w">       </span><span class="c1">// 状態（部分集合）</span>
-<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">           </span><span class="c1">// 部分集合の和</span>
-<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合リスト）</span>
+<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">           </span><span class="c1">// 部分和</span>
+<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
 <a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">total</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
 <a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
 <a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i_naive.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* バックトラッキングアルゴリズム：部分集合和 I */</span>
+<div class="highlight"><span class="filename">subset_sum_i_naive.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* バックトラッキング：部分和 I */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">total</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 部分集合の和がtargetと等しいとき、解を記録</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">total</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="c1">// 剪定：部分集合の和がtargetを超えた場合、その選択をスキップ</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="c1">// 枝刈り：部分和が target を超える場合はその選択をスキップする</span>
 <a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、要素とtotalを更新</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、要素と total を更新する</span>
 <a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">);</span>
-<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">        </span><span class="c1">// 次のラウンドの選択に進む</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
 <a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
-<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">        </span><span class="c1">// 回退：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="p">}</span>
 <a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a>
-<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="cm">/* 部分集合和 I を解く（重複する部分集合を含む） */</span>
+<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="cm">/* 部分和 I を解く（重複部分集合を含む） */</span>
 <a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="nf">subsetSumINaive</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
-<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 部分集合の和</span>
-<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合リスト）</span>
+<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 部分和</span>
+<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
 <a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">total</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
 <a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
 <a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i_naive.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">subset_sum_i_naive</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Backtrack</span><span class="p">}</span>
-<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
-<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">subset_sum_i_naive</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">SubsetSumINaive</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_i_naive.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* バックトラッキング：部分和 I */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Backtrack</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">total</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">total</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">        </span><span class="c1">// 枝刈り：部分和が target を超える場合はその選択をスキップする</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、要素と total を更新する</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">        </span><span class="n">Backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="p">}</span>
+<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a>
+<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="cm">/* 部分和 I を解く（重複部分集合を含む） */</span>
+<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">SubsetSumINaive</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 部分和</span>
+<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a><span class="w">    </span><span class="n">Backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">total</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i_naive.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">backtrackSubsetSumINaive</span><span class="p">}</span>
-<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
-<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">subsetSumINaive</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_i_naive.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* バックトラッキング：部分和 I */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">backtrackSubsetSumINaive</span><span class="p">(</span><span class="nx">total</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">*</span><span class="p">[][]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">total</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">        </span><span class="nx">newState</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">append</span><span class="p">([]</span><span class="kt">int</span><span class="p">{},</span><span class="w"> </span><span class="o">*</span><span class="nx">state</span><span class="o">...</span><span class="p">)</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">        </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">newState</span><span class="p">)</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">        </span><span class="c1">// 枝刈り：部分和が target を超える場合はその選択をスキップする</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">total</span><span class="o">+</span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">            </span><span class="k">continue</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、要素と total を更新する</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">        </span><span class="o">*</span><span class="nx">state</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">)[</span><span class="nx">i</span><span class="p">])</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w">        </span><span class="nx">backtrackSubsetSumINaive</span><span class="p">(</span><span class="nx">total</span><span class="o">+</span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">)[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w">        </span><span class="o">*</span><span class="nx">state</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)[:</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="p">}</span>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a>
+<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="cm">/* 部分和 I を解く（重複部分集合を含む） */</span>
+<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="kd">func</span><span class="w"> </span><span class="nx">subsetSumINaive</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">[][]</span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="w">    </span><span class="nx">state</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w">    </span><span class="nx">total</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="w">              </span><span class="c1">// 部分和</span>
+<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="w">    </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="w">    </span><span class="nx">backtrackSubsetSumINaive</span><span class="p">(</span><span class="nx">total</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">res</span><span class="p">)</span>
+<a id="__codelineno-4-30" name="__codelineno-4-30" href="#__codelineno-4-30"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
+<a id="__codelineno-4-31" name="__codelineno-4-31" href="#__codelineno-4-31"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i_naive.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
-<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">subsetSumINaive</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_i_naive.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* バックトラッキング：部分和 I */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">total</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[[</span><span class="nb">Int</span><span class="p">]])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">state</span><span class="p">)</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="bp">indices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">        </span><span class="c1">// 枝刈り：部分和が target を超える場合はその選択をスキップする</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">            </span><span class="k">continue</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、要素と total を更新する</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">total</span><span class="p">:</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="bp">removeLast</span><span class="p">()</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="p">}</span>
+<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a>
+<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="cm">/* 部分和 I を解く（重複部分集合を含む） */</span>
+<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="kd">func</span><span class="w"> </span><span class="nf">subsetSumINaive</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[[</span><span class="nb">Int</span><span class="p">]]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">state</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">total</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1">// 部分和</span>
+<a id="__codelineno-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="p">:</span><span class="w"> </span><span class="p">[[</span><span class="nb">Int</span><span class="p">]]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">total</span><span class="p">:</span><span class="w"> </span><span class="n">total</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-5-29" name="__codelineno-5-29" href="#__codelineno-5-29"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-5-30" name="__codelineno-5-30" href="#__codelineno-5-30"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i_naive.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
-<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
-<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">subsetSumINaive</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_i_naive.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* バックトラッキング：部分和 I */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="nx">total</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">total</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">        </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">([...</span><span class="nx">state</span><span class="p">]);</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">choices</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">        </span><span class="c1">// 枝刈り：部分和が target を超える場合はその選択をスキップする</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">choices</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、要素と total を更新する</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">        </span><span class="nx">state</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">choices</span><span class="p">[</span><span class="nx">i</span><span class="p">]);</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w">        </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="nx">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">choices</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">        </span><span class="nx">state</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="p">}</span>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a>
+<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="cm">/* 部分和 I を解く（重複部分集合を含む） */</span>
+<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a><span class="kd">function</span><span class="w"> </span><span class="nx">subsetSumINaive</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">total</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 部分和</span>
+<a id="__codelineno-6-27" name="__codelineno-6-27" href="#__codelineno-6-27"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-6-28" name="__codelineno-6-28" href="#__codelineno-6-28"></a><span class="w">    </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="nx">total</span><span class="p">,</span><span class="w"> </span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-6-29" name="__codelineno-6-29" href="#__codelineno-6-29"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-6-30" name="__codelineno-6-30" href="#__codelineno-6-30"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i_naive.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
-<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
-<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">subsetSumINaive</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_i_naive.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* バックトラッキング：部分和 I */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="nx">state</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="nx">target</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="nx">total</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="nx">choices</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[][]</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">total</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">        </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">([...</span><span class="nx">state</span><span class="p">]);</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">choices</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">        </span><span class="c1">// 枝刈り：部分和が target を超える場合はその選択をスキップする</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">choices</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、要素と total を更新する</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="w">        </span><span class="nx">state</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">choices</span><span class="p">[</span><span class="nx">i</span><span class="p">]);</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="w">        </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="nx">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">choices</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="w">        </span><span class="nx">state</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a><span class="p">}</span>
+<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a>
+<a id="__codelineno-7-29" name="__codelineno-7-29" href="#__codelineno-7-29"></a><span class="cm">/* 部分和 I を解く（重複部分集合を含む） */</span>
+<a id="__codelineno-7-30" name="__codelineno-7-30" href="#__codelineno-7-30"></a><span class="kd">function</span><span class="w"> </span><span class="nx">subsetSumINaive</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">target</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[][]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-31" name="__codelineno-7-31" href="#__codelineno-7-31"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-7-32" name="__codelineno-7-32" href="#__codelineno-7-32"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">total</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 部分和</span>
+<a id="__codelineno-7-33" name="__codelineno-7-33" href="#__codelineno-7-33"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-7-34" name="__codelineno-7-34" href="#__codelineno-7-34"></a><span class="w">    </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="nx">total</span><span class="p">,</span><span class="w"> </span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-7-35" name="__codelineno-7-35" href="#__codelineno-7-35"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-7-36" name="__codelineno-7-36" href="#__codelineno-7-36"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i_naive.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
-<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">subsetSumINaive</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_i_naive.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* バックトラッキング：部分和 I */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">total</span><span class="p">,</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">,</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">  </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">total</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">List</span><span class="p">.</span><span class="n">from</span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">    </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">  </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">    </span><span class="c1">// 枝刈り：部分和が target を超える場合はその選択をスキップする</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w">      </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="w">    </span><span class="c1">// 試行：選択を行い、要素と total を更新する</span>
+<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="w">    </span><span class="n">state</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="w">    </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a><span class="w">    </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a><span class="w">    </span><span class="n">state</span><span class="p">.</span><span class="n">removeLast</span><span class="p">();</span>
+<a id="__codelineno-8-26" name="__codelineno-8-26" href="#__codelineno-8-26"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-27" name="__codelineno-8-27" href="#__codelineno-8-27"></a><span class="p">}</span>
+<a id="__codelineno-8-28" name="__codelineno-8-28" href="#__codelineno-8-28"></a>
+<a id="__codelineno-8-29" name="__codelineno-8-29" href="#__codelineno-8-29"></a><span class="cm">/* 部分和 I を解く（重複部分集合を含む） */</span>
+<a id="__codelineno-8-30" name="__codelineno-8-30" href="#__codelineno-8-30"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">subsetSumINaive</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-31" name="__codelineno-8-31" href="#__codelineno-8-31"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-8-32" name="__codelineno-8-32" href="#__codelineno-8-32"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 要素の合計</span>
+<a id="__codelineno-8-33" name="__codelineno-8-33" href="#__codelineno-8-33"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-8-34" name="__codelineno-8-34" href="#__codelineno-8-34"></a><span class="w">  </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">total</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-8-35" name="__codelineno-8-35" href="#__codelineno-8-35"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-8-36" name="__codelineno-8-36" href="#__codelineno-8-36"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i_naive.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
-<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">subset_sum_i_naive</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_i_naive.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* バックトラッキング：部分和 I */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="n">total</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">choices</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">        </span><span class="c1">// 枝刈り：部分和が target を超える場合はその選択をスキップする</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、要素と total を更新する</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
+<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="p">}</span>
+<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a>
+<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="cm">/* 部分和 I を解く（重複部分集合を含む） */</span>
+<a id="__codelineno-9-30" name="__codelineno-9-30" href="#__codelineno-9-30"></a><span class="k">fn</span><span class="w"> </span><span class="nf">subset_sum_i_naive</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-31" name="__codelineno-9-31" href="#__codelineno-9-31"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">();</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-9-32" name="__codelineno-9-32" href="#__codelineno-9-32"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 部分和</span>
+<a id="__codelineno-9-33" name="__codelineno-9-33" href="#__codelineno-9-33"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">();</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-9-34" name="__codelineno-9-34" href="#__codelineno-9-34"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">total</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-9-35" name="__codelineno-9-35" href="#__codelineno-9-35"></a><span class="w">    </span><span class="n">res</span>
+<a id="__codelineno-9-36" name="__codelineno-9-36" href="#__codelineno-9-36"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i_naive.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
-<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">subsetSumINaive</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_i_naive.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* バックトラッキング：部分和 I */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">total</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">choicesSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">total</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">stateSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">resSize</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">state</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">        </span><span class="n">resColSizes</span><span class="p">[</span><span class="n">resSize</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stateSize</span><span class="p">;</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choicesSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">        </span><span class="c1">// 枝刈り：部分和が target を超える場合はその選択をスキップする</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、要素と total を更新する</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">        </span><span class="n">state</span><span class="p">[</span><span class="n">stateSize</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">choicesSize</span><span class="p">);</span>
+<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w">        </span><span class="n">stateSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="p">}</span>
+<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a>
+<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="cm">/* 部分和 I を解く（重複部分集合を含む） */</span>
+<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="kt">void</span><span class="w"> </span><span class="nf">subsetSumINaive</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">numsSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="w">    </span><span class="n">resSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 解の個数を 0 に初期化する</span>
+<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">numsSize</span><span class="p">);</span>
+<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i_naive.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
-<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">subsetSumINaive</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_i_naive.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* バックトラッキング：部分和 I */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="n">total</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">    </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;?&gt;</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">total</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">toMutableList</span><span class="p">())</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="na">indices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">        </span><span class="c1">// 枝刈り：部分和が target を超える場合はその選択をスキップする</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">            </span><span class="k">continue</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、要素と total を更新する</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="na">removeAt</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a><span class="p">}</span>
+<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a>
+<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a><span class="cm">/* 部分和 I を解く（重複部分集合を含む） */</span>
+<a id="__codelineno-11-30" name="__codelineno-11-30" href="#__codelineno-11-30"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">subsetSumINaive</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;?&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">()</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-11-32" name="__codelineno-11-32" href="#__codelineno-11-32"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">total</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="c1">// 部分和</span>
+<a id="__codelineno-11-33" name="__codelineno-11-33" href="#__codelineno-11-33"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;?&gt;</span><span class="p">()</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-11-34" name="__codelineno-11-34" href="#__codelineno-11-34"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">total</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-11-35" name="__codelineno-11-35" href="#__codelineno-11-35"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-11-36" name="__codelineno-11-36" href="#__codelineno-11-36"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i_naive.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
-<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">subset_sum_i_naive</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_i_naive.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### バックトラッキング: 部分和 I ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">total</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">    </span><span class="n">res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">state</span><span class="o">.</span><span class="n">dup</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">    </span><span class="k">return</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">  </span><span class="c1"># すべての選択肢を走査</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">choices</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">    </span><span class="c1"># 枝刈り：部分和が target を超える場合はその選択をスキップする</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">    </span><span class="k">next</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">    </span><span class="c1"># 試行：選択を行い、要素と total を更新する</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">    </span><span class="n">state</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">    </span><span class="c1"># 次の選択へ進む</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">    </span><span class="c1"># バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w">    </span><span class="n">state</span><span class="o">.</span><span class="n">pop</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="k">end</span>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="c1">### バックトラッキング: 部分和 I ###</span>
+<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">total</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a><span class="w">  </span><span class="c1"># 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span>
+<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a><span class="w">    </span><span class="n">res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">state</span><span class="o">.</span><span class="n">dup</span>
+<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a><span class="w">    </span><span class="k">return</span>
+<a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a>
+<a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a><span class="w">  </span><span class="c1"># すべての選択肢を走査</span>
+<a id="__codelineno-12-31" name="__codelineno-12-31" href="#__codelineno-12-31"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">choices</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-12-32" name="__codelineno-12-32" href="#__codelineno-12-32"></a><span class="w">    </span><span class="c1"># 枝刈り：部分和が target を超える場合はその選択をスキップする</span>
+<a id="__codelineno-12-33" name="__codelineno-12-33" href="#__codelineno-12-33"></a><span class="w">    </span><span class="k">next</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span>
+<a id="__codelineno-12-34" name="__codelineno-12-34" href="#__codelineno-12-34"></a><span class="w">    </span><span class="c1"># 試行：選択を行い、要素と total を更新する</span>
+<a id="__codelineno-12-35" name="__codelineno-12-35" href="#__codelineno-12-35"></a><span class="w">    </span><span class="n">state</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-12-36" name="__codelineno-12-36" href="#__codelineno-12-36"></a><span class="w">    </span><span class="c1"># 次の選択へ進む</span>
+<a id="__codelineno-12-37" name="__codelineno-12-37" href="#__codelineno-12-37"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-12-38" name="__codelineno-12-38" href="#__codelineno-12-38"></a><span class="w">    </span><span class="c1"># バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-12-39" name="__codelineno-12-39" href="#__codelineno-12-39"></a><span class="w">    </span><span class="n">state</span><span class="o">.</span><span class="n">pop</span>
+<a id="__codelineno-12-40" name="__codelineno-12-40" href="#__codelineno-12-40"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-41" name="__codelineno-12-41" href="#__codelineno-12-41"></a><span class="k">end</span>
+<a id="__codelineno-12-42" name="__codelineno-12-42" href="#__codelineno-12-42"></a>
+<a id="__codelineno-12-43" name="__codelineno-12-43" href="#__codelineno-12-43"></a><span class="c1"># ## 部分和 I を解く（重複する部分集合を含む）###</span>
+<a id="__codelineno-12-44" name="__codelineno-12-44" href="#__codelineno-12-44"></a><span class="k">def</span><span class="w"> </span><span class="nf">subset_sum_i_naive</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-12-45" name="__codelineno-12-45" href="#__codelineno-12-45"></a><span class="w">  </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span><span class="w"> </span><span class="c1"># 状態（部分集合）</span>
+<a id="__codelineno-12-46" name="__codelineno-12-46" href="#__codelineno-12-46"></a><span class="w">  </span><span class="n">total</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1"># 部分和</span>
+<a id="__codelineno-12-47" name="__codelineno-12-47" href="#__codelineno-12-47"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span><span class="w"> </span><span class="c1"># 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-12-48" name="__codelineno-12-48" href="#__codelineno-12-48"></a><span class="w">  </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">total</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-12-49" name="__codelineno-12-49" href="#__codelineno-12-49"></a><span class="w">  </span><span class="n">res</span>
+<a id="__codelineno-12-50" name="__codelineno-12-50" href="#__codelineno-12-50"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>配列 <span class="arithmatex">\([3, 4, 5]\)</span> とターゲット要素 <span class="arithmatex">\(9\)</span> を上記のコードに入力すると、結果 <span class="arithmatex">\([3, 3, 3], [4, 5], [5, 4]\)</span> が得られます。<strong>和が <span class="arithmatex">\(9\)</span> のすべての部分集合を正常に見つけましたが、重複する部分集合 <span class="arithmatex">\([4, 5]\)</span> と <span class="arithmatex">\([5, 4]\)</span> が含まれています</strong>。</p>
-<p>これは、検索プロセスが選択の順序を区別するためですが、部分集合は選択順序を区別しません。以下の図に示すように、<span class="arithmatex">\(5\)</span> の前に <span class="arithmatex">\(4\)</span> を選択することと <span class="arithmatex">\(4\)</span> の前に <span class="arithmatex">\(5\)</span> を選択することは異なる分岐ですが、同じ部分集合に対応します。</p>
-<p><img alt="部分集合の検索と境界外の剪定" class="animation-figure" src="../subset_sum_problem.assets/subset_sum_i_naive.png" /></p>
-<p align="center"> 図 13-10 &nbsp; 部分集合の検索と境界外の剪定 </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20backtrack%28%0A%20%20%20%20state%3A%20list%5Bint%5D%2C%0A%20%20%20%20target%3A%20int%2C%0A%20%20%20%20total%3A%20int%2C%0A%20%20%20%20choices%3A%20list%5Bint%5D%2C%0A%20%20%20%20res%3A%20list%5Blist%5Bint%5D%5D%2C%0A%29%3A%0A%20%20%20%20%22%22%22%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AD%E3%83%B3%E3%82%B0%EF%BC%9A%E9%83%A8%E5%88%86%E5%92%8C%20I%22%22%22%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E9%9B%86%E5%90%88%E3%81%AE%E5%92%8C%E3%81%8C%20target%20%E3%81%AB%E7%AD%89%E3%81%97%E3%81%91%E3%82%8C%E3%81%B0%E3%80%81%E8%A7%A3%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20if%20total%20%3D%3D%20target%3A%0A%20%20%20%20%20%20%20%20res.append%28list%28state%29%29%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20%23%20%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E9%81%B8%E6%8A%9E%E8%82%A2%E3%82%92%E8%B5%B0%E6%9F%BB%0A%20%20%20%20for%20i%20in%20range%28len%28choices%29%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E6%9E%9D%E5%88%88%E3%82%8A%EF%BC%9A%E9%83%A8%E5%88%86%E5%92%8C%E3%81%8C%20target%20%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E5%A0%B4%E5%90%88%E3%81%AF%E3%81%9D%E3%81%AE%E9%81%B8%E6%8A%9E%E3%82%92%E3%82%B9%E3%82%AD%E3%83%83%E3%83%97%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20if%20total%20%2B%20choices%5Bi%5D%20%3E%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20continue%0A%20%20%20%20%20%20%20%20%23%20%E8%A9%A6%E8%A1%8C%EF%BC%9A%E9%81%B8%E6%8A%9E%E3%82%92%E8%A1%8C%E3%81%84%E3%80%81%E8%A6%81%E7%B4%A0%E3%81%A8%20total%20%E3%82%92%E6%9B%B4%E6%96%B0%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20state.append%28choices%5Bi%5D%29%0A%20%20%20%20%20%20%20%20%23%20%E6%AC%A1%E3%81%AE%E9%81%B8%E6%8A%9E%E3%81%B8%E9%80%B2%E3%82%80%0A%20%20%20%20%20%20%20%20backtrack%28state%2C%20target%2C%20total%20%2B%20choices%5Bi%5D%2C%20choices%2C%20res%29%0A%20%20%20%20%20%20%20%20%23%20%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AF%EF%BC%9A%E9%81%B8%E6%8A%9E%E3%82%92%E5%8F%96%E3%82%8A%E6%B6%88%E3%81%97%E3%80%81%E5%89%8D%E3%81%AE%E7%8A%B6%E6%85%8B%E3%81%AB%E6%88%BB%E3%81%99%0A%20%20%20%20%20%20%20%20state.pop%28%29%0A%0A%0Adef%20subset_sum_i_naive%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20list%5Blist%5Bint%5D%5D%3A%0A%20%20%20%20%22%22%22%E9%83%A8%E5%88%86%E5%92%8C%20I%20%E3%82%92%E8%A7%A3%E3%81%8F%EF%BC%88%E9%87%8D%E8%A4%87%E9%83%A8%E5%88%86%E9%9B%86%E5%90%88%E3%82%92%E5%90%AB%E3%82%80%EF%BC%89%22%22%22%0A%20%20%20%20state%20%3D%20%5B%5D%20%20%23%20%E7%8A%B6%E6%85%8B%EF%BC%88%E9%83%A8%E5%88%86%E9%9B%86%E5%90%88%EF%BC%89%0A%20%20%20%20total%20%3D%200%20%20%23%20%E9%83%A8%E5%88%86%E5%92%8C%0A%20%20%20%20res%20%3D%20%5B%5D%20%20%23%20%E7%B5%90%E6%9E%9C%E3%83%AA%E3%82%B9%E3%83%88%EF%BC%88%E9%83%A8%E5%88%86%E9%9B%86%E5%90%88%E3%81%AE%E3%83%AA%E3%82%B9%E3%83%88%EF%BC%89%0A%20%20%20%20backtrack%28state%2C%20target%2C%20total%2C%20nums%2C%20res%29%0A%20%20%20%20return%20res%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B3%2C%204%2C%205%5D%0A%20%20%20%20target%20%3D%209%0A%20%20%20%20res%20%3D%20subset_sum_i_naive%28nums%2C%20target%29%0A%0A%20%20%20%20print%28f%22%E5%85%A5%E5%8A%9B%E9%85%8D%E5%88%97%20nums%20%3D%20%7Bnums%7D%2C%20target%20%3D%20%7Btarget%7D%22%29%0A%20%20%20%20print%28f%22%E5%92%8C%E3%81%8C%20%7Btarget%7D%20%E3%81%AB%E7%AD%89%E3%81%97%E3%81%84%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E9%83%A8%E5%88%86%E9%9B%86%E5%90%88%20res%20%3D%20%7Bres%7D%22%29%0A%20%20%20%20print%28f%22%E6%B3%A8%E6%84%8F%3A%20%E3%81%93%E3%81%AE%E6%96%B9%E6%B3%95%E3%81%AE%E5%87%BA%E5%8A%9B%E7%B5%90%E6%9E%9C%E3%81%AB%E3%81%AF%E9%87%8D%E8%A4%87%E3%81%99%E3%82%8B%E9%9B%86%E5%90%88%E3%81%8C%E5%90%AB%E3%81%BE%E3%82%8C%E3%81%BE%E3%81%99%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=16&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20backtrack%28%0A%20%20%20%20state%3A%20list%5Bint%5D%2C%0A%20%20%20%20target%3A%20int%2C%0A%20%20%20%20total%3A%20int%2C%0A%20%20%20%20choices%3A%20list%5Bint%5D%2C%0A%20%20%20%20res%3A%20list%5Blist%5Bint%5D%5D%2C%0A%29%3A%0A%20%20%20%20%22%22%22%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AD%E3%83%B3%E3%82%B0%EF%BC%9A%E9%83%A8%E5%88%86%E5%92%8C%20I%22%22%22%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E9%9B%86%E5%90%88%E3%81%AE%E5%92%8C%E3%81%8C%20target%20%E3%81%AB%E7%AD%89%E3%81%97%E3%81%91%E3%82%8C%E3%81%B0%E3%80%81%E8%A7%A3%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20if%20total%20%3D%3D%20target%3A%0A%20%20%20%20%20%20%20%20res.append%28list%28state%29%29%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20%23%20%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E9%81%B8%E6%8A%9E%E8%82%A2%E3%82%92%E8%B5%B0%E6%9F%BB%0A%20%20%20%20for%20i%20in%20range%28len%28choices%29%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E6%9E%9D%E5%88%88%E3%82%8A%EF%BC%9A%E9%83%A8%E5%88%86%E5%92%8C%E3%81%8C%20target%20%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E5%A0%B4%E5%90%88%E3%81%AF%E3%81%9D%E3%81%AE%E9%81%B8%E6%8A%9E%E3%82%92%E3%82%B9%E3%82%AD%E3%83%83%E3%83%97%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20if%20total%20%2B%20choices%5Bi%5D%20%3E%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20continue%0A%20%20%20%20%20%20%20%20%23%20%E8%A9%A6%E8%A1%8C%EF%BC%9A%E9%81%B8%E6%8A%9E%E3%82%92%E8%A1%8C%E3%81%84%E3%80%81%E8%A6%81%E7%B4%A0%E3%81%A8%20total%20%E3%82%92%E6%9B%B4%E6%96%B0%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20state.append%28choices%5Bi%5D%29%0A%20%20%20%20%20%20%20%20%23%20%E6%AC%A1%E3%81%AE%E9%81%B8%E6%8A%9E%E3%81%B8%E9%80%B2%E3%82%80%0A%20%20%20%20%20%20%20%20backtrack%28state%2C%20target%2C%20total%20%2B%20choices%5Bi%5D%2C%20choices%2C%20res%29%0A%20%20%20%20%20%20%20%20%23%20%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AF%EF%BC%9A%E9%81%B8%E6%8A%9E%E3%82%92%E5%8F%96%E3%82%8A%E6%B6%88%E3%81%97%E3%80%81%E5%89%8D%E3%81%AE%E7%8A%B6%E6%85%8B%E3%81%AB%E6%88%BB%E3%81%99%0A%20%20%20%20%20%20%20%20state.pop%28%29%0A%0A%0Adef%20subset_sum_i_naive%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20list%5Blist%5Bint%5D%5D%3A%0A%20%20%20%20%22%22%22%E9%83%A8%E5%88%86%E5%92%8C%20I%20%E3%82%92%E8%A7%A3%E3%81%8F%EF%BC%88%E9%87%8D%E8%A4%87%E9%83%A8%E5%88%86%E9%9B%86%E5%90%88%E3%82%92%E5%90%AB%E3%82%80%EF%BC%89%22%22%22%0A%20%20%20%20state%20%3D%20%5B%5D%20%20%23%20%E7%8A%B6%E6%85%8B%EF%BC%88%E9%83%A8%E5%88%86%E9%9B%86%E5%90%88%EF%BC%89%0A%20%20%20%20total%20%3D%200%20%20%23%20%E9%83%A8%E5%88%86%E5%92%8C%0A%20%20%20%20res%20%3D%20%5B%5D%20%20%23%20%E7%B5%90%E6%9E%9C%E3%83%AA%E3%82%B9%E3%83%88%EF%BC%88%E9%83%A8%E5%88%86%E9%9B%86%E5%90%88%E3%81%AE%E3%83%AA%E3%82%B9%E3%83%88%EF%BC%89%0A%20%20%20%20backtrack%28state%2C%20target%2C%20total%2C%20nums%2C%20res%29%0A%20%20%20%20return%20res%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B3%2C%204%2C%205%5D%0A%20%20%20%20target%20%3D%209%0A%20%20%20%20res%20%3D%20subset_sum_i_naive%28nums%2C%20target%29%0A%0A%20%20%20%20print%28f%22%E5%85%A5%E5%8A%9B%E9%85%8D%E5%88%97%20nums%20%3D%20%7Bnums%7D%2C%20target%20%3D%20%7Btarget%7D%22%29%0A%20%20%20%20print%28f%22%E5%92%8C%E3%81%8C%20%7Btarget%7D%20%E3%81%AB%E7%AD%89%E3%81%97%E3%81%84%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E9%83%A8%E5%88%86%E9%9B%86%E5%90%88%20res%20%3D%20%7Bres%7D%22%29%0A%20%20%20%20print%28f%22%E6%B3%A8%E6%84%8F%3A%20%E3%81%93%E3%81%AE%E6%96%B9%E6%B3%95%E3%81%AE%E5%87%BA%E5%8A%9B%E7%B5%90%E6%9E%9C%E3%81%AB%E3%81%AF%E9%87%8D%E8%A4%87%E3%81%99%E3%82%8B%E9%9B%86%E5%90%88%E3%81%8C%E5%90%AB%E3%81%BE%E3%82%8C%E3%81%BE%E3%81%99%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=16&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>上のコードに配列 <span class="arithmatex">\([3, 4, 5]\)</span> と目標値 <span class="arithmatex">\(9\)</span> を入力すると、出力は <span class="arithmatex">\([3, 3, 3], [4, 5], [5, 4]\)</span> となります。<strong>和が <span class="arithmatex">\(9\)</span> となる部分集合はすべて見つかっていますが、重複する部分集合 <span class="arithmatex">\([4, 5]\)</span> と <span class="arithmatex">\([5, 4]\)</span> が含まれています</strong>。</p>
+<p>これは、探索過程では選択順を区別する一方で、部分集合では選択順を区別しないためです。次の図のように、先に <span class="arithmatex">\(4\)</span> を選んでから <span class="arithmatex">\(5\)</span> を選ぶ場合と、先に <span class="arithmatex">\(5\)</span> を選んでから <span class="arithmatex">\(4\)</span> を選ぶ場合は別の分岐ですが、対応する部分集合は同じです。</p>
+<p><img alt="部分集合探索と境界超過の枝刈り" class="animation-figure" src="../subset_sum_problem.assets/subset_sum_i_naive.png" /></p>
+<p align="center"> 図 13-10 &nbsp; 部分集合探索と境界超過の枝刈り </p>
 
-<p>重複する部分集合を除去するために、<strong>直接的なアイデアは結果リストを重複除去することです</strong>。しかし、この方法は2つの理由で非常に非効率的です。</p>
+<p>重複する部分集合を取り除くために、**直接的な方法として結果リストの重複を除去する**ことが考えられます。しかし、この方法は効率が低く、その理由は次の 2 点です。</p>
 <ul>
-<li>配列要素が多い場合、特に <code>target</code> が大きい場合、検索プロセスで大量の重複する部分集合が生成されます。</li>
-<li>部分集合（配列）の差異を比較することは非常に時間がかかり、まず配列をソートし、次に配列の各要素の差異を比較する必要があります。</li>
+<li>配列要素が多い場合、特に <code>target</code> が大きい場合には、探索過程で大量の重複部分集合が生成されます。</li>
+<li>部分集合（配列）同士の違いを比較するのは非常に時間がかかり、まず配列をソートし、その後に各要素を比較する必要があります。</li>
 </ul>
-<h3 id="2">2. &nbsp; 重複部分集合の剪定<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p><strong>剪定を通じて検索プロセス中に重複除去を検討します</strong>。以下の図を観察すると、異なる順序で配列要素を選択するときに重複する部分集合が生成されます。例えば、以下の状況です。</p>
+<h3 id="2">2. &nbsp; 重複部分集合の枝刈り<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>**探索過程で枝刈りを行って重複を除去する**ことを考えます。次の図を観察すると、重複部分集合は配列要素を異なる順序で選択したときに生じます。例えば次のような状況です。</p>
 <ol>
-<li>最初のラウンドで <span class="arithmatex">\(3\)</span> を選択し、2番目のラウンドで <span class="arithmatex">\(4\)</span> を選択すると、これら2つの要素を含むすべての部分集合が生成され、<span class="arithmatex">\([3, 4, \dots]\)</span> と表記されます。</li>
-<li>後で、最初のラウンドで <span class="arithmatex">\(4\)</span> が選択されたとき、<strong>2番目のラウンドは <span class="arithmatex">\(3\)</span> をスキップすべきです</strong>。この選択によって生成される部分集合 <span class="arithmatex">\([4, 3, \dots]\)</span> はステップ <code>1.</code> の部分集合と完全に重複するからです。</li>
+<li>1 回目と 2 回目でそれぞれ <span class="arithmatex">\(3\)</span> と <span class="arithmatex">\(4\)</span> を選ぶと、これら 2 要素を含むすべての部分集合、すなわち <span class="arithmatex">\([3, 4, \dots]\)</span> が生成されます。</li>
+<li>その後、1 回目で <span class="arithmatex">\(4\)</span> を選んだ場合、**2 回目では <span class="arithmatex">\(3\)</span> をスキップすべき**です。というのも、この選択で生成される部分集合 <span class="arithmatex">\([4, 3, \dots]\)</span> は、手順 <code>1.</code> で生成された部分集合と完全に重複するからです。</li>
 </ol>
-<p>検索プロセスでは、各層の選択が左から右に一つずつ試行されるため、右側の分岐ほどより多く剪定されます。</p>
+<p>探索過程では、各階層の選択は左から右へ順に試されるため、右側にある分岐ほど多く枝刈りされます。</p>
 <ol>
-<li>最初の2ラウンドで <span class="arithmatex">\(3\)</span> と <span class="arithmatex">\(5\)</span> を選択し、部分集合 <span class="arithmatex">\([3, 5, \dots]\)</span> を生成します。</li>
-<li>最初の2ラウンドで <span class="arithmatex">\(4\)</span> と <span class="arithmatex">\(5\)</span> を選択し、部分集合 <span class="arithmatex">\([4, 5, \dots]\)</span> を生成します。</li>
-<li>最初のラウンドで <span class="arithmatex">\(5\)</span> が選択された場合、<strong>2番目のラウンドは <span class="arithmatex">\(3\)</span> と <span class="arithmatex">\(4\)</span> をスキップすべきです</strong>。部分集合 <span class="arithmatex">\([5, 3, \dots]\)</span> と <span class="arithmatex">\([5, 4, \dots]\)</span> はステップ <code>1.</code> と <code>2.</code> で記述された部分集合と完全に重複するからです。</li>
+<li>最初の 2 回で <span class="arithmatex">\(3\)</span> と <span class="arithmatex">\(5\)</span> を選ぶと、部分集合 <span class="arithmatex">\([3, 5, \dots]\)</span> が生成されます。</li>
+<li>最初の 2 回で <span class="arithmatex">\(4\)</span> と <span class="arithmatex">\(5\)</span> を選ぶと、部分集合 <span class="arithmatex">\([4, 5, \dots]\)</span> が生成されます。</li>
+<li>もし 1 回目で <span class="arithmatex">\(5\)</span> を選ぶなら、**2 回目では <span class="arithmatex">\(3\)</span> と <span class="arithmatex">\(4\)</span> をスキップすべき**です。なぜなら、部分集合 <span class="arithmatex">\([5, 3, \dots]\)</span> と <span class="arithmatex">\([5, 4, \dots]\)</span> は、手順 <code>1.</code> と手順 <code>2.</code> で述べた部分集合と完全に重複するからです。</li>
 </ol>
-<p><img alt="異なる選択順序による重複部分集合" class="animation-figure" src="../subset_sum_problem.assets/subset_sum_i_pruning.png" /></p>
-<p align="center"> 図 13-11 &nbsp; 異なる選択順序による重複部分集合 </p>
+<p><img alt="異なる選択順によって生じる重複部分集合" class="animation-figure" src="../subset_sum_problem.assets/subset_sum_i_pruning.png" /></p>
+<p align="center"> 図 13-11 &nbsp; 異なる選択順によって生じる重複部分集合 </p>
 
-<p>要約すると、入力配列 <span class="arithmatex">\([x_1, x_2, \dots, x_n]\)</span> が与えられた場合、検索プロセスでの選択シーケンスは <span class="arithmatex">\([x_{i_1}, x_{i_2}, \dots, x_{i_m}]\)</span> であるべきで、<span class="arithmatex">\(i_1 \leq i_2 \leq \dots \leq i_m\)</span> を満たす必要があります。<strong>この条件を満たさない選択シーケンスは重複を引き起こし、剪定されるべきです</strong>。</p>
+<p>まとめると、入力配列 <span class="arithmatex">\([x_1, x_2, \dots, x_n]\)</span> が与えられ、探索過程における選択列を <span class="arithmatex">\([x_{i_1}, x_{i_2}, \dots, x_{i_m}]\)</span> とすると、この選択列は <span class="arithmatex">\(i_1 \leq i_2 \leq \dots \leq i_m\)</span> を満たす必要があります。<strong>この条件を満たさない選択列は重複を生むため、枝刈りすべきです</strong>。</p>
 <h3 id="3">3. &nbsp; コード実装<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
-<p>この剪定を実装するために、変数 <code>start</code> を初期化し、これは走査の開始点を示します。<strong>選択 <span class="arithmatex">\(x_{i}\)</span> を行った後、次のラウンドをインデックス <span class="arithmatex">\(i\)</span> から開始するように設定します</strong>。これにより、選択シーケンスが <span class="arithmatex">\(i_1 \leq i_2 \leq \dots \leq i_m\)</span> を満たすことが保証され、部分集合の一意性が保証されます。</p>
-<p>さらに、コードに以下の2つの最適化を行いました。</p>
+<p>この枝刈りを実現するために、走査の開始位置を示す変数 <code>start</code> を初期化します。**選択 <span class="arithmatex">\(x_{i}\)</span> を行った後、次のラウンドはインデックス <span class="arithmatex">\(i\)</span> から走査を開始する**ように設定します。これにより、選択列が <span class="arithmatex">\(i_1 \leq i_2 \leq \dots \leq i_m\)</span> を満たし、部分集合の一意性が保証されます。</p>
+<p>これに加えて、コードには次の 2 つの最適化も施しています。</p>
 <ul>
-<li>検索を開始する前に、配列 <code>nums</code> をソートします。すべての選択の走査で、<strong>部分集合和が <code>target</code> を超えたときにループを直接終了します</strong>。後続の要素はより大きく、それらの部分集合和は確実に <code>target</code> を超えるからです。</li>
-<li>要素和変数 <code>total</code> を除去し、<strong><code>target</code> に対して減算を実行して要素和をカウントします</strong>。<code>target</code> が <span class="arithmatex">\(0\)</span> に等しくなったとき、解を記録します。</li>
+<li>探索を始める前に、まず配列 <code>nums</code> をソートします。すべての選択肢を走査するとき、**部分集合の和が <code>target</code> を超えたら直ちにループを終了**します。後続の要素はさらに大きいため、その和も必ず <code>target</code> を超えるからです。</li>
+<li>要素和を保持する変数 <code>total</code> は省略し、**<code>target</code> から減算することで要素和を管理**します。<code>target</code> が <span class="arithmatex">\(0\)</span> になったときに解を記録します。</li>
 </ul>
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@@ -4705,186 +5025,515 @@
 <div class="highlight"><span class="filename">subset_sum_i.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
 <a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a>    <span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">choices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">start</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]</span>
 <a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="p">):</span>
-<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキングアルゴリズム：部分集合の和 I&quot;&quot;&quot;</span>
-<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># 部分集合の和が target と等しいとき、解を記録</span>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキング：部分和 I&quot;&quot;&quot;</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># 部分集合の和が target に等しければ、解を記録</span>
 <a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>    <span class="k">if</span> <span class="n">target</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
 <a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>        <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">state</span><span class="p">))</span>
 <a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>        <span class="k">return</span>
 <a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>    <span class="c1"># すべての選択肢を走査</span>
-<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>    <span class="c1"># 枝刈り二：start から走査を開始して重複する部分集合の生成を避ける</span>
+<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>    <span class="c1"># 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
 <a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">start</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">choices</span><span class="p">)):</span>
-<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>        <span class="c1"># 枝刈り一：部分集合の和が target を超える場合、直ちにループを終了</span>
-<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a>        <span class="c1"># これは配列がソートされており、後の要素がより大きいため、部分集合の和は必ず target を超えるため</span>
+<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>        <span class="c1"># 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する</span>
+<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a>        <span class="c1"># 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため</span>
 <a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>        <span class="k">if</span> <span class="n">target</span> <span class="o">-</span> <span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">:</span>
 <a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a>            <span class="k">break</span>
-<a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a>        <span class="c1"># 試行：選択を行い、target、start を更新</span>
+<a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a>        <span class="c1"># 試す：選択を行い、target と start を更新</span>
 <a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>        <span class="n">state</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
-<a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a>        <span class="c1"># 次の選択ラウンドに進む</span>
+<a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a>        <span class="c1"># 次の選択へ進む</span>
 <a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a>        <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">target</span> <span class="o">-</span> <span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">choices</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
-<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a>        <span class="c1"># 撤回：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a>        <span class="c1"># バックトラック：選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a>        <span class="n">state</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
 <a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a>
 <a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a><span class="k">def</span><span class="w"> </span><span class="nf">subset_sum_i</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]:</span>
-<a id="__codelineno-13-24" name="__codelineno-13-24" href="#__codelineno-13-24"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;部分集合の和 I を解く&quot;&quot;&quot;</span>
+<a id="__codelineno-13-24" name="__codelineno-13-24" href="#__codelineno-13-24"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;部分和 I を解く&quot;&quot;&quot;</span>
 <a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a>    <span class="n">state</span> <span class="o">=</span> <span class="p">[]</span>  <span class="c1"># 状態（部分集合）</span>
 <a id="__codelineno-13-26" name="__codelineno-13-26" href="#__codelineno-13-26"></a>    <span class="n">nums</span><span class="o">.</span><span class="n">sort</span><span class="p">()</span>  <span class="c1"># nums をソート</span>
-<a id="__codelineno-13-27" name="__codelineno-13-27" href="#__codelineno-13-27"></a>    <span class="n">start</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># 走査の開始点</span>
-<a id="__codelineno-13-28" name="__codelineno-13-28" href="#__codelineno-13-28"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>  <span class="c1"># 結果リスト（部分集合リスト）</span>
+<a id="__codelineno-13-27" name="__codelineno-13-27" href="#__codelineno-13-27"></a>    <span class="n">start</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># 開始点を走査</span>
+<a id="__codelineno-13-28" name="__codelineno-13-28" href="#__codelineno-13-28"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>  <span class="c1"># 結果リスト（部分集合のリスト）</span>
 <a id="__codelineno-13-29" name="__codelineno-13-29" href="#__codelineno-13-29"></a>    <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">target</span><span class="p">,</span> <span class="n">nums</span><span class="p">,</span> <span class="n">start</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
 <a id="__codelineno-13-30" name="__codelineno-13-30" href="#__codelineno-13-30"></a>    <span class="k">return</span> <span class="n">res</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* バックトラッキングアルゴリズム：部分集合和 I */</span>
+<div class="highlight"><span class="filename">subset_sum_i.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* バックトラッキング：部分和 I */</span>
 <a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="c1">// 部分集合の和がtargetと等しいとき、解を記録</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
 <a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">state</span><span class="p">);</span>
 <a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
-<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">    </span><span class="c1">// 剪定二：startから走査を開始し、重複する部分集合の生成を回避</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">    </span><span class="c1">// 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
 <a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">start</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">        </span><span class="c1">// 剪定一：部分集合の和がtargetを超えた場合、即座にループを終了</span>
-<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">        </span><span class="c1">// 配列がソートされているため、後の要素はさらに大きく、部分集合の和は必ずtargetを超える</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">        </span><span class="c1">// 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">        </span><span class="c1">// 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため</span>
 <a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
 <a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、target、startを更新</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">        </span><span class="c1">// 試す：選択を行い、target と start を更新</span>
 <a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
-<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w">        </span><span class="c1">// 次のラウンドの選択に進む</span>
+<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
 <a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
-<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w">        </span><span class="c1">// 回退：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
 <a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a><span class="p">}</span>
 <a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a>
-<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a><span class="cm">/* 部分集合和 I を解く */</span>
-<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">subsetSumI</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a><span class="cm">/* 部分和 I を解く */</span>
+<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">subsetSumI</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">;</span><span class="w">              </span><span class="c1">// 状態（部分集合）</span>
 <a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a><span class="w">    </span><span class="n">sort</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">end</span><span class="p">());</span><span class="w"> </span><span class="c1">// nums をソート</span>
-<a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                  </span><span class="c1">// 走査の開始点</span>
-<a id="__codelineno-14-30" name="__codelineno-14-30" href="#__codelineno-14-30"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span><span class="w">        </span><span class="c1">// 結果リスト（部分集合リスト）</span>
+<a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                  </span><span class="c1">// 開始点を走査</span>
+<a id="__codelineno-14-30" name="__codelineno-14-30" href="#__codelineno-14-30"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span><span class="w">        </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
 <a id="__codelineno-14-31" name="__codelineno-14-31" href="#__codelineno-14-31"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
 <a id="__codelineno-14-32" name="__codelineno-14-32" href="#__codelineno-14-32"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
 <a id="__codelineno-14-33" name="__codelineno-14-33" href="#__codelineno-14-33"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* バックトラッキングアルゴリズム：部分集合和 I */</span>
+<div class="highlight"><span class="filename">subset_sum_i.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* バックトラッキング：部分和 I */</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 部分集合の和がtargetと等しいとき、解を記録</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
 <a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
 <a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
-<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">    </span><span class="c1">// 剪定二：startから走査を開始し、重複する部分集合の生成を回避</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">    </span><span class="c1">// 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
 <a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">start</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">        </span><span class="c1">// 剪定一：部分集合の和がtargetを超えた場合、即座にループを終了</span>
-<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">        </span><span class="c1">// 配列がソートされているため、後の要素はさらに大きく、部分集合の和は必ずtargetを超える</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">        </span><span class="c1">// 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">        </span><span class="c1">// 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため</span>
 <a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
 <a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、target、startを更新</span>
+<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">        </span><span class="c1">// 試す：選択を行い、target と start を更新</span>
 <a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">);</span>
-<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">        </span><span class="c1">// 次のラウンドの選択に進む</span>
+<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
 <a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
-<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w">        </span><span class="c1">// 回退：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="p">}</span>
 <a id="__codelineno-15-24" name="__codelineno-15-24" href="#__codelineno-15-24"></a>
-<a id="__codelineno-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></a><span class="cm">/* 部分集合和 I を解く */</span>
+<a id="__codelineno-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></a><span class="cm">/* 部分和 I を解く */</span>
 <a id="__codelineno-15-26" name="__codelineno-15-26" href="#__codelineno-15-26"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="nf">subsetSumI</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
 <a id="__codelineno-15-28" name="__codelineno-15-28" href="#__codelineno-15-28"></a><span class="w">    </span><span class="n">Arrays</span><span class="p">.</span><span class="na">sort</span><span class="p">(</span><span class="n">nums</span><span class="p">);</span><span class="w"> </span><span class="c1">// nums をソート</span>
-<a id="__codelineno-15-29" name="__codelineno-15-29" href="#__codelineno-15-29"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 走査の開始点</span>
-<a id="__codelineno-15-30" name="__codelineno-15-30" href="#__codelineno-15-30"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合リスト）</span>
+<a id="__codelineno-15-29" name="__codelineno-15-29" href="#__codelineno-15-29"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 開始点を走査</span>
+<a id="__codelineno-15-30" name="__codelineno-15-30" href="#__codelineno-15-30"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
 <a id="__codelineno-15-31" name="__codelineno-15-31" href="#__codelineno-15-31"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
 <a id="__codelineno-15-32" name="__codelineno-15-32" href="#__codelineno-15-32"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
 <a id="__codelineno-15-33" name="__codelineno-15-33" href="#__codelineno-15-33"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">subset_sum_i</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Backtrack</span><span class="p">}</span>
-<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a>
-<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">subset_sum_i</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">SubsetSumI</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_i.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* バックトラッキング：部分和 I */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Backtrack</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">    </span><span class="c1">// 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">start</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">        </span><span class="c1">// 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">        </span><span class="c1">// 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">        </span><span class="c1">// 試す：選択を行い、target と start を更新</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w">        </span><span class="n">Backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="p">}</span>
+<a id="__codelineno-16-24" name="__codelineno-16-24" href="#__codelineno-16-24"></a>
+<a id="__codelineno-16-25" name="__codelineno-16-25" href="#__codelineno-16-25"></a><span class="cm">/* 部分和 I を解く */</span>
+<a id="__codelineno-16-26" name="__codelineno-16-26" href="#__codelineno-16-26"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">SubsetSumI</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-27" name="__codelineno-16-27" href="#__codelineno-16-27"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-16-28" name="__codelineno-16-28" href="#__codelineno-16-28"></a><span class="w">    </span><span class="n">Array</span><span class="p">.</span><span class="n">Sort</span><span class="p">(</span><span class="n">nums</span><span class="p">);</span><span class="w"> </span><span class="c1">// nums をソート</span>
+<a id="__codelineno-16-29" name="__codelineno-16-29" href="#__codelineno-16-29"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 開始点を走査</span>
+<a id="__codelineno-16-30" name="__codelineno-16-30" href="#__codelineno-16-30"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-16-31" name="__codelineno-16-31" href="#__codelineno-16-31"></a><span class="w">    </span><span class="n">Backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-16-32" name="__codelineno-16-32" href="#__codelineno-16-32"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-16-33" name="__codelineno-16-33" href="#__codelineno-16-33"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">backtrackSubsetSumI</span><span class="p">}</span>
-<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a>
-<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">subsetSumI</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_i.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* バックトラッキング：部分和 I */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">backtrackSubsetSumI</span><span class="p">(</span><span class="nx">start</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">*</span><span class="p">[][]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">        </span><span class="nx">newState</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">append</span><span class="p">([]</span><span class="kt">int</span><span class="p">{},</span><span class="w"> </span><span class="o">*</span><span class="nx">state</span><span class="o">...</span><span class="p">)</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">        </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">newState</span><span class="p">)</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">    </span><span class="c1">// 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">start</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">        </span><span class="c1">// 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w">        </span><span class="c1">// 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため</span>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">target</span><span class="o">-</span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="w">        </span><span class="c1">// 試す：選択を行い、target と start を更新</span>
+<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="w">        </span><span class="o">*</span><span class="nx">state</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">)[</span><span class="nx">i</span><span class="p">])</span>
+<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a><span class="w">        </span><span class="nx">backtrackSubsetSumI</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="o">-</span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">)[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
+<a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-17-22" name="__codelineno-17-22" href="#__codelineno-17-22"></a><span class="w">        </span><span class="o">*</span><span class="nx">state</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)[:</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-17-23" name="__codelineno-17-23" href="#__codelineno-17-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-24" name="__codelineno-17-24" href="#__codelineno-17-24"></a><span class="p">}</span>
+<a id="__codelineno-17-25" name="__codelineno-17-25" href="#__codelineno-17-25"></a>
+<a id="__codelineno-17-26" name="__codelineno-17-26" href="#__codelineno-17-26"></a><span class="cm">/* 部分和 I を解く */</span>
+<a id="__codelineno-17-27" name="__codelineno-17-27" href="#__codelineno-17-27"></a><span class="kd">func</span><span class="w"> </span><span class="nx">subsetSumI</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">[][]</span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-28" name="__codelineno-17-28" href="#__codelineno-17-28"></a><span class="w">    </span><span class="nx">state</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-17-29" name="__codelineno-17-29" href="#__codelineno-17-29"></a><span class="w">    </span><span class="nx">sort</span><span class="p">.</span><span class="nx">Ints</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w">         </span><span class="c1">// nums をソート</span>
+<a id="__codelineno-17-30" name="__codelineno-17-30" href="#__codelineno-17-30"></a><span class="w">    </span><span class="nx">start</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="w">              </span><span class="c1">// 開始点を走査</span>
+<a id="__codelineno-17-31" name="__codelineno-17-31" href="#__codelineno-17-31"></a><span class="w">    </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-17-32" name="__codelineno-17-32" href="#__codelineno-17-32"></a><span class="w">    </span><span class="nx">backtrackSubsetSumI</span><span class="p">(</span><span class="nx">start</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">res</span><span class="p">)</span>
+<a id="__codelineno-17-33" name="__codelineno-17-33" href="#__codelineno-17-33"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
+<a id="__codelineno-17-34" name="__codelineno-17-34" href="#__codelineno-17-34"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a>
-<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">subsetSumI</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_i.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* バックトラッキング：部分和 I */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">start</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[[</span><span class="nb">Int</span><span class="p">]])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">state</span><span class="p">)</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">    </span><span class="c1">// 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="bp">indices</span><span class="p">.</span><span class="bp">dropFirst</span><span class="p">(</span><span class="n">start</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w">        </span><span class="c1">// 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w">        </span><span class="c1">// 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="w">        </span><span class="c1">// 試す：選択を行い、target と start を更新</span>
+<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">start</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="bp">removeLast</span><span class="p">()</span>
+<a id="__codelineno-18-22" name="__codelineno-18-22" href="#__codelineno-18-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-23" name="__codelineno-18-23" href="#__codelineno-18-23"></a><span class="p">}</span>
+<a id="__codelineno-18-24" name="__codelineno-18-24" href="#__codelineno-18-24"></a>
+<a id="__codelineno-18-25" name="__codelineno-18-25" href="#__codelineno-18-25"></a><span class="cm">/* 部分和 I を解く */</span>
+<a id="__codelineno-18-26" name="__codelineno-18-26" href="#__codelineno-18-26"></a><span class="kd">func</span><span class="w"> </span><span class="nf">subsetSumI</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[[</span><span class="nb">Int</span><span class="p">]]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-27" name="__codelineno-18-27" href="#__codelineno-18-27"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">state</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-18-28" name="__codelineno-18-28" href="#__codelineno-18-28"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">sorted</span><span class="p">()</span><span class="w"> </span><span class="c1">// nums をソート</span>
+<a id="__codelineno-18-29" name="__codelineno-18-29" href="#__codelineno-18-29"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">start</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1">// 開始点を走査</span>
+<a id="__codelineno-18-30" name="__codelineno-18-30" href="#__codelineno-18-30"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="p">:</span><span class="w"> </span><span class="p">[[</span><span class="nb">Int</span><span class="p">]]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-18-31" name="__codelineno-18-31" href="#__codelineno-18-31"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">start</span><span class="p">:</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-18-32" name="__codelineno-18-32" href="#__codelineno-18-32"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-18-33" name="__codelineno-18-33" href="#__codelineno-18-33"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
-<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a>
-<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">subsetSumI</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_i.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* バックトラッキング：部分和 I */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">start</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">target</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">        </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">([...</span><span class="nx">state</span><span class="p">]);</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w">    </span><span class="c1">// 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">start</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">choices</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w">        </span><span class="c1">// 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">        </span><span class="c1">// 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">choices</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a><span class="w">        </span><span class="c1">// 試す：選択を行い、target と start を更新</span>
+<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="w">        </span><span class="nx">state</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">choices</span><span class="p">[</span><span class="nx">i</span><span class="p">]);</span>
+<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a><span class="w">        </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">choices</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a><span class="w">        </span><span class="nx">state</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-19-22" name="__codelineno-19-22" href="#__codelineno-19-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-23" name="__codelineno-19-23" href="#__codelineno-19-23"></a><span class="p">}</span>
+<a id="__codelineno-19-24" name="__codelineno-19-24" href="#__codelineno-19-24"></a>
+<a id="__codelineno-19-25" name="__codelineno-19-25" href="#__codelineno-19-25"></a><span class="cm">/* 部分和 I を解く */</span>
+<a id="__codelineno-19-26" name="__codelineno-19-26" href="#__codelineno-19-26"></a><span class="kd">function</span><span class="w"> </span><span class="nx">subsetSumI</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-27" name="__codelineno-19-27" href="#__codelineno-19-27"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-19-28" name="__codelineno-19-28" href="#__codelineno-19-28"></a><span class="w">    </span><span class="nx">nums</span><span class="p">.</span><span class="nx">sort</span><span class="p">((</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">b</span><span class="p">);</span><span class="w"> </span><span class="c1">// nums をソート</span>
+<a id="__codelineno-19-29" name="__codelineno-19-29" href="#__codelineno-19-29"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 開始点を走査</span>
+<a id="__codelineno-19-30" name="__codelineno-19-30" href="#__codelineno-19-30"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-19-31" name="__codelineno-19-31" href="#__codelineno-19-31"></a><span class="w">    </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">start</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-19-32" name="__codelineno-19-32" href="#__codelineno-19-32"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-19-33" name="__codelineno-19-33" href="#__codelineno-19-33"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
-<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a>
-<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">subsetSumI</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_i.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* バックトラッキング：部分和 I */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="nx">state</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="nx">target</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">    </span><span class="nx">choices</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">    </span><span class="nx">start</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">    </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[][]</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">target</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w">        </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">([...</span><span class="nx">state</span><span class="p">]);</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w">    </span><span class="c1">// 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
+<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">start</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">choices</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-17" name="__codelineno-20-17" href="#__codelineno-20-17"></a><span class="w">        </span><span class="c1">// 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する</span>
+<a id="__codelineno-20-18" name="__codelineno-20-18" href="#__codelineno-20-18"></a><span class="w">        </span><span class="c1">// 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため</span>
+<a id="__codelineno-20-19" name="__codelineno-20-19" href="#__codelineno-20-19"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">choices</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-20" name="__codelineno-20-20" href="#__codelineno-20-20"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-20-21" name="__codelineno-20-21" href="#__codelineno-20-21"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-22" name="__codelineno-20-22" href="#__codelineno-20-22"></a><span class="w">        </span><span class="c1">// 試す：選択を行い、target と start を更新</span>
+<a id="__codelineno-20-23" name="__codelineno-20-23" href="#__codelineno-20-23"></a><span class="w">        </span><span class="nx">state</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">choices</span><span class="p">[</span><span class="nx">i</span><span class="p">]);</span>
+<a id="__codelineno-20-24" name="__codelineno-20-24" href="#__codelineno-20-24"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-20-25" name="__codelineno-20-25" href="#__codelineno-20-25"></a><span class="w">        </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">choices</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-20-26" name="__codelineno-20-26" href="#__codelineno-20-26"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-20-27" name="__codelineno-20-27" href="#__codelineno-20-27"></a><span class="w">        </span><span class="nx">state</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-20-28" name="__codelineno-20-28" href="#__codelineno-20-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-29" name="__codelineno-20-29" href="#__codelineno-20-29"></a><span class="p">}</span>
+<a id="__codelineno-20-30" name="__codelineno-20-30" href="#__codelineno-20-30"></a>
+<a id="__codelineno-20-31" name="__codelineno-20-31" href="#__codelineno-20-31"></a><span class="cm">/* 部分和 I を解く */</span>
+<a id="__codelineno-20-32" name="__codelineno-20-32" href="#__codelineno-20-32"></a><span class="kd">function</span><span class="w"> </span><span class="nx">subsetSumI</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">target</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[][]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-33" name="__codelineno-20-33" href="#__codelineno-20-33"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-20-34" name="__codelineno-20-34" href="#__codelineno-20-34"></a><span class="w">    </span><span class="nx">nums</span><span class="p">.</span><span class="nx">sort</span><span class="p">((</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">b</span><span class="p">);</span><span class="w"> </span><span class="c1">// nums をソート</span>
+<a id="__codelineno-20-35" name="__codelineno-20-35" href="#__codelineno-20-35"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 開始点を走査</span>
+<a id="__codelineno-20-36" name="__codelineno-20-36" href="#__codelineno-20-36"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-20-37" name="__codelineno-20-37" href="#__codelineno-20-37"></a><span class="w">    </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">start</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-20-38" name="__codelineno-20-38" href="#__codelineno-20-38"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-20-39" name="__codelineno-20-39" href="#__codelineno-20-39"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a>
-<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">subsetSumI</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_i.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* バックトラッキング：部分和 I */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="p">,</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">,</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">  </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">List</span><span class="p">.</span><span class="n">from</span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w">    </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w">  </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w">  </span><span class="c1">// 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
+<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">start</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-17" name="__codelineno-21-17" href="#__codelineno-21-17"></a><span class="w">    </span><span class="c1">// 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する</span>
+<a id="__codelineno-21-18" name="__codelineno-21-18" href="#__codelineno-21-18"></a><span class="w">    </span><span class="c1">// 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため</span>
+<a id="__codelineno-21-19" name="__codelineno-21-19" href="#__codelineno-21-19"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-20" name="__codelineno-21-20" href="#__codelineno-21-20"></a><span class="w">      </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-21-21" name="__codelineno-21-21" href="#__codelineno-21-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-22" name="__codelineno-21-22" href="#__codelineno-21-22"></a><span class="w">    </span><span class="c1">// 試す：選択を行い、target と start を更新</span>
+<a id="__codelineno-21-23" name="__codelineno-21-23" href="#__codelineno-21-23"></a><span class="w">    </span><span class="n">state</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-21-24" name="__codelineno-21-24" href="#__codelineno-21-24"></a><span class="w">    </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-21-25" name="__codelineno-21-25" href="#__codelineno-21-25"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-21-26" name="__codelineno-21-26" href="#__codelineno-21-26"></a><span class="w">    </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-21-27" name="__codelineno-21-27" href="#__codelineno-21-27"></a><span class="w">    </span><span class="n">state</span><span class="p">.</span><span class="n">removeLast</span><span class="p">();</span>
+<a id="__codelineno-21-28" name="__codelineno-21-28" href="#__codelineno-21-28"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-29" name="__codelineno-21-29" href="#__codelineno-21-29"></a><span class="p">}</span>
+<a id="__codelineno-21-30" name="__codelineno-21-30" href="#__codelineno-21-30"></a>
+<a id="__codelineno-21-31" name="__codelineno-21-31" href="#__codelineno-21-31"></a><span class="cm">/* 部分和 I を解く */</span>
+<a id="__codelineno-21-32" name="__codelineno-21-32" href="#__codelineno-21-32"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">subsetSumI</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-33" name="__codelineno-21-33" href="#__codelineno-21-33"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-21-34" name="__codelineno-21-34" href="#__codelineno-21-34"></a><span class="w">  </span><span class="n">nums</span><span class="p">.</span><span class="n">sort</span><span class="p">();</span><span class="w"> </span><span class="c1">// nums をソート</span>
+<a id="__codelineno-21-35" name="__codelineno-21-35" href="#__codelineno-21-35"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 開始点を走査</span>
+<a id="__codelineno-21-36" name="__codelineno-21-36" href="#__codelineno-21-36"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-21-37" name="__codelineno-21-37" href="#__codelineno-21-37"></a><span class="w">  </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-21-38" name="__codelineno-21-38" href="#__codelineno-21-38"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-21-39" name="__codelineno-21-39" href="#__codelineno-21-39"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a>
-<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">subset_sum_i</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_i.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* バックトラッキング：部分和 I */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">    </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w">    </span><span class="n">start</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">    </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="w">    </span><span class="c1">// 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
+<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">start</span><span class="o">..</span><span class="n">choices</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="w">        </span><span class="c1">// 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する</span>
+<a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="w">        </span><span class="c1">// 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため</span>
+<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-22-21" name="__codelineno-22-21" href="#__codelineno-22-21"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-22" name="__codelineno-22-22" href="#__codelineno-22-22"></a><span class="w">        </span><span class="c1">// 試す：選択を行い、target と start を更新</span>
+<a id="__codelineno-22-23" name="__codelineno-22-23" href="#__codelineno-22-23"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-22-24" name="__codelineno-22-24" href="#__codelineno-22-24"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-22-25" name="__codelineno-22-25" href="#__codelineno-22-25"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-22-26" name="__codelineno-22-26" href="#__codelineno-22-26"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-22-27" name="__codelineno-22-27" href="#__codelineno-22-27"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
+<a id="__codelineno-22-28" name="__codelineno-22-28" href="#__codelineno-22-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-29" name="__codelineno-22-29" href="#__codelineno-22-29"></a><span class="p">}</span>
+<a id="__codelineno-22-30" name="__codelineno-22-30" href="#__codelineno-22-30"></a>
+<a id="__codelineno-22-31" name="__codelineno-22-31" href="#__codelineno-22-31"></a><span class="cm">/* 部分和 I を解く */</span>
+<a id="__codelineno-22-32" name="__codelineno-22-32" href="#__codelineno-22-32"></a><span class="k">fn</span><span class="w"> </span><span class="nf">subset_sum_i</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-33" name="__codelineno-22-33" href="#__codelineno-22-33"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">();</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-22-34" name="__codelineno-22-34" href="#__codelineno-22-34"></a><span class="w">    </span><span class="n">nums</span><span class="p">.</span><span class="n">sort</span><span class="p">();</span><span class="w"> </span><span class="c1">// nums をソート</span>
+<a id="__codelineno-22-35" name="__codelineno-22-35" href="#__codelineno-22-35"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 開始点を走査</span>
+<a id="__codelineno-22-36" name="__codelineno-22-36" href="#__codelineno-22-36"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">();</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-22-37" name="__codelineno-22-37" href="#__codelineno-22-37"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-22-38" name="__codelineno-22-38" href="#__codelineno-22-38"></a><span class="w">    </span><span class="n">res</span>
+<a id="__codelineno-22-39" name="__codelineno-22-39" href="#__codelineno-22-39"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a>
-<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">subsetSumI</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_i.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* バックトラッキング：部分和 I */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">choicesSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">stateSize</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">resSize</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">state</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w">        </span><span class="n">resColSizes</span><span class="p">[</span><span class="n">resSize</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stateSize</span><span class="p">;</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w">    </span><span class="c1">// 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">start</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choicesSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w">        </span><span class="c1">// 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する</span>
+<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="w">        </span><span class="c1">// 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため</span>
+<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="w">        </span><span class="c1">// 試す：選択を行い、target と start を更新</span>
+<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="w">        </span><span class="n">state</span><span class="p">[</span><span class="n">stateSize</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a><span class="w">        </span><span class="n">stateSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-23-23" name="__codelineno-23-23" href="#__codelineno-23-23"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">choicesSize</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-23-24" name="__codelineno-23-24" href="#__codelineno-23-24"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-23-25" name="__codelineno-23-25" href="#__codelineno-23-25"></a><span class="w">        </span><span class="n">stateSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-23-26" name="__codelineno-23-26" href="#__codelineno-23-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-27" name="__codelineno-23-27" href="#__codelineno-23-27"></a><span class="p">}</span>
+<a id="__codelineno-23-28" name="__codelineno-23-28" href="#__codelineno-23-28"></a>
+<a id="__codelineno-23-29" name="__codelineno-23-29" href="#__codelineno-23-29"></a><span class="cm">/* 部分和 I を解く */</span>
+<a id="__codelineno-23-30" name="__codelineno-23-30" href="#__codelineno-23-30"></a><span class="kt">void</span><span class="w"> </span><span class="nf">subsetSumI</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">numsSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-31" name="__codelineno-23-31" href="#__codelineno-23-31"></a><span class="w">    </span><span class="n">qsort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">numsSize</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">),</span><span class="w"> </span><span class="n">cmp</span><span class="p">);</span><span class="w"> </span><span class="c1">// nums をソート</span>
+<a id="__codelineno-23-32" name="__codelineno-23-32" href="#__codelineno-23-32"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                           </span><span class="c1">// 開始点を走査</span>
+<a id="__codelineno-23-33" name="__codelineno-23-33" href="#__codelineno-23-33"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">numsSize</span><span class="p">,</span><span class="w"> </span><span class="n">start</span><span class="p">);</span>
+<a id="__codelineno-23-34" name="__codelineno-23-34" href="#__codelineno-23-34"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a>
-<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">subsetSumI</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_i.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* バックトラッキング：部分和 I */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">    </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">    </span><span class="n">start</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w">    </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;?&gt;</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">toMutableList</span><span class="p">())</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="w">    </span><span class="c1">// 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
+<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">start</span><span class="p">..</span><span class="o">&lt;</span><span class="n">choices</span><span class="p">.</span><span class="na">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-17" name="__codelineno-24-17" href="#__codelineno-24-17"></a><span class="w">        </span><span class="c1">// 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する</span>
+<a id="__codelineno-24-18" name="__codelineno-24-18" href="#__codelineno-24-18"></a><span class="w">        </span><span class="c1">// 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため</span>
+<a id="__codelineno-24-19" name="__codelineno-24-19" href="#__codelineno-24-19"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-20" name="__codelineno-24-20" href="#__codelineno-24-20"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-24-21" name="__codelineno-24-21" href="#__codelineno-24-21"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-24-22" name="__codelineno-24-22" href="#__codelineno-24-22"></a><span class="w">        </span><span class="c1">// 試す：選択を行い、target と start を更新</span>
+<a id="__codelineno-24-23" name="__codelineno-24-23" href="#__codelineno-24-23"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-24-24" name="__codelineno-24-24" href="#__codelineno-24-24"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-24-25" name="__codelineno-24-25" href="#__codelineno-24-25"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-24-26" name="__codelineno-24-26" href="#__codelineno-24-26"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-24-27" name="__codelineno-24-27" href="#__codelineno-24-27"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="na">removeAt</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-24-28" name="__codelineno-24-28" href="#__codelineno-24-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-29" name="__codelineno-24-29" href="#__codelineno-24-29"></a><span class="p">}</span>
+<a id="__codelineno-24-30" name="__codelineno-24-30" href="#__codelineno-24-30"></a>
+<a id="__codelineno-24-31" name="__codelineno-24-31" href="#__codelineno-24-31"></a><span class="cm">/* 部分和 I を解く */</span>
+<a id="__codelineno-24-32" name="__codelineno-24-32" href="#__codelineno-24-32"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">subsetSumI</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;?&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-33" name="__codelineno-24-33" href="#__codelineno-24-33"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">()</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-24-34" name="__codelineno-24-34" href="#__codelineno-24-34"></a><span class="w">    </span><span class="n">nums</span><span class="p">.</span><span class="na">sort</span><span class="p">()</span><span class="w"> </span><span class="c1">// nums をソート</span>
+<a id="__codelineno-24-35" name="__codelineno-24-35" href="#__codelineno-24-35"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="c1">// 開始点を走査</span>
+<a id="__codelineno-24-36" name="__codelineno-24-36" href="#__codelineno-24-36"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;?&gt;</span><span class="p">()</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-24-37" name="__codelineno-24-37" href="#__codelineno-24-37"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-24-38" name="__codelineno-24-38" href="#__codelineno-24-38"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-24-39" name="__codelineno-24-39" href="#__codelineno-24-39"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a>
-<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">subset_sum_i</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_i.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### バックトラッキング: 部分和 I ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="c1"># 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="n">target</span><span class="o">.</span><span class="n">zero?</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">    </span><span class="n">res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">state</span><span class="o">.</span><span class="n">dup</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">    </span><span class="k">return</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w">  </span><span class="c1"># すべての選択肢を走査</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">  </span><span class="c1"># 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">start</span><span class="o">...</span><span class="n">choices</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w">    </span><span class="c1"># 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w">    </span><span class="c1"># 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため</span>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w">    </span><span class="k">break</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w">    </span><span class="c1"># 試す：選択を行い、target と start を更新</span>
+<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w">    </span><span class="n">state</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w">    </span><span class="c1"># 次の選択へ進む</span>
+<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a><span class="w">    </span><span class="c1"># バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="w">    </span><span class="n">state</span><span class="o">.</span><span class="n">pop</span>
+<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="k">end</span>
+<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a>
+<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="c1">### 部分和 I を解く ###</span>
+<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a><span class="k">def</span><span class="w"> </span><span class="nf">subset_sum_i</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a><span class="w">  </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span><span class="w"> </span><span class="c1"># 状態（部分集合）</span>
+<a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></a><span class="w">  </span><span class="n">nums</span><span class="o">.</span><span class="n">sort!</span><span class="w"> </span><span class="c1"># nums をソート</span>
+<a id="__codelineno-25-27" name="__codelineno-25-27" href="#__codelineno-25-27"></a><span class="w">  </span><span class="n">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1"># 開始点を走査</span>
+<a id="__codelineno-25-28" name="__codelineno-25-28" href="#__codelineno-25-28"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span><span class="w"> </span><span class="c1"># 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-25-29" name="__codelineno-25-29" href="#__codelineno-25-29"></a><span class="w">  </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-25-30" name="__codelineno-25-30" href="#__codelineno-25-30"></a><span class="w">  </span><span class="n">res</span>
+<a id="__codelineno-25-31" name="__codelineno-25-31" href="#__codelineno-25-31"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>以下の図は、配列 <span class="arithmatex">\([3, 4, 5]\)</span> とターゲット要素 <span class="arithmatex">\(9\)</span> を上記のコードに入力した後の全体的なバックトラッキングプロセスを示しています。</p>
-<p><img alt="部分集合和 I のバックトラッキングプロセス" class="animation-figure" src="../subset_sum_problem.assets/subset_sum_i.png" /></p>
-<p align="center"> 図 13-12 &nbsp; 部分集合和 I のバックトラッキングプロセス </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20backtrack%28%0A%20%20%20%20state%3A%20list%5Bint%5D%2C%20target%3A%20int%2C%20choices%3A%20list%5Bint%5D%2C%20start%3A%20int%2C%20res%3A%20list%5Blist%5Bint%5D%5D%0A%29%3A%0A%20%20%20%20%22%22%22%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AD%E3%83%B3%E3%82%B0%EF%BC%9A%E9%83%A8%E5%88%86%E5%92%8C%20I%22%22%22%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E9%9B%86%E5%90%88%E3%81%AE%E5%92%8C%E3%81%8C%20target%20%E3%81%AB%E7%AD%89%E3%81%97%E3%81%91%E3%82%8C%E3%81%B0%E3%80%81%E8%A7%A3%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20if%20target%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20res.append%28list%28state%29%29%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20%23%20%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E9%81%B8%E6%8A%9E%E8%82%A2%E3%82%92%E8%B5%B0%E6%9F%BB%0A%20%20%20%20%23%20%E6%9E%9D%E5%88%88%E3%82%8A%202%3A%20start%20%E3%81%8B%E3%82%89%E8%B5%B0%E6%9F%BB%E3%81%97%E3%80%81%E9%87%8D%E8%A4%87%E3%81%99%E3%82%8B%E9%83%A8%E5%88%86%E9%9B%86%E5%90%88%E3%81%AE%E7%94%9F%E6%88%90%E3%82%92%E9%81%BF%E3%81%91%E3%82%8B%0A%20%20%20%20for%20i%20in%20range%28start%2C%20len%28choices%29%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E6%9E%9D%E5%88%88%E3%82%8A1%EF%BC%9A%E9%83%A8%E5%88%86%E9%9B%86%E5%90%88%E3%81%AE%E5%92%8C%E3%81%8C%20target%20%E3%82%92%E8%B6%85%E3%81%88%E3%81%9F%E3%82%89%E3%80%81%E7%9B%B4%E3%81%A1%E3%81%AB%E3%83%AB%E3%83%BC%E3%83%97%E3%82%92%E7%B5%82%E4%BA%86%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20%23%20%E9%85%8D%E5%88%97%E3%81%AF%E3%82%BD%E3%83%BC%E3%83%88%E6%B8%88%E3%81%BF%E3%81%A7%E5%BE%8C%E7%B6%9A%E8%A6%81%E7%B4%A0%E3%81%AE%E3%81%BB%E3%81%86%E3%81%8C%E5%A4%A7%E3%81%8D%E3%81%8F%E3%80%81%E9%83%A8%E5%88%86%E9%9B%86%E5%90%88%E3%81%AE%E5%92%8C%E3%81%AF%E5%BF%85%E3%81%9A%20target%20%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%9F%E3%82%81%0A%20%20%20%20%20%20%20%20if%20target%20-%20choices%5Bi%5D%20%3C%200%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20%23%20%E8%A9%A6%E3%81%99%EF%BC%9A%E9%81%B8%E6%8A%9E%E3%82%92%E8%A1%8C%E3%81%84%E3%80%81target%20%E3%81%A8%20start%20%E3%82%92%E6%9B%B4%E6%96%B0%0A%20%20%20%20%20%20%20%20state.append%28choices%5Bi%5D%29%0A%20%20%20%20%20%20%20%20%23%20%E6%AC%A1%E3%81%AE%E9%81%B8%E6%8A%9E%E3%81%B8%E9%80%B2%E3%82%80%0A%20%20%20%20%20%20%20%20backtrack%28state%2C%20target%20-%20choices%5Bi%5D%2C%20choices%2C%20i%2C%20res%29%0A%20%20%20%20%20%20%20%20%23%20%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AF%EF%BC%9A%E9%81%B8%E6%8A%9E%E3%82%92%E5%8F%96%E3%82%8A%E6%B6%88%E3%81%97%E3%80%81%E5%89%8D%E3%81%AE%E7%8A%B6%E6%85%8B%E3%81%AB%E6%88%BB%E3%81%99%0A%20%20%20%20%20%20%20%20state.pop%28%29%0A%0A%0Adef%20subset_sum_i%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20list%5Blist%5Bint%5D%5D%3A%0A%20%20%20%20%22%22%22%E9%83%A8%E5%88%86%E5%92%8C%20I%20%E3%82%92%E8%A7%A3%E3%81%8F%22%22%22%0A%20%20%20%20state%20%3D%20%5B%5D%20%20%23%20%E7%8A%B6%E6%85%8B%EF%BC%88%E9%83%A8%E5%88%86%E9%9B%86%E5%90%88%EF%BC%89%0A%20%20%20%20nums.sort%28%29%20%20%23%20nums%20%E3%82%92%E3%82%BD%E3%83%BC%E3%83%88%0A%20%20%20%20start%20%3D%200%20%20%23%20%E9%96%8B%E5%A7%8B%E7%82%B9%E3%82%92%E8%B5%B0%E6%9F%BB%0A%20%20%20%20res%20%3D%20%5B%5D%20%20%23%20%E7%B5%90%E6%9E%9C%E3%83%AA%E3%82%B9%E3%83%88%EF%BC%88%E9%83%A8%E5%88%86%E9%9B%86%E5%90%88%E3%81%AE%E3%83%AA%E3%82%B9%E3%83%88%EF%BC%89%0A%20%20%20%20backtrack%28state%2C%20target%2C%20nums%2C%20start%2C%20res%29%0A%20%20%20%20return%20res%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B3%2C%204%2C%205%5D%0A%20%20%20%20target%20%3D%209%0A%20%20%20%20res%20%3D%20subset_sum_i%28nums%2C%20target%29%0A%0A%20%20%20%20print%28f%22%E5%85%A5%E5%8A%9B%E9%85%8D%E5%88%97%20nums%20%3D%20%7Bnums%7D%2C%20target%20%3D%20%7Btarget%7D%22%29%0A%20%20%20%20print%28f%22%E5%92%8C%E3%81%8C%20%7Btarget%7D%20%E3%81%AB%E7%AD%89%E3%81%97%E3%81%84%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E9%83%A8%E5%88%86%E9%9B%86%E5%90%88%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=16&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20backtrack%28%0A%20%20%20%20state%3A%20list%5Bint%5D%2C%20target%3A%20int%2C%20choices%3A%20list%5Bint%5D%2C%20start%3A%20int%2C%20res%3A%20list%5Blist%5Bint%5D%5D%0A%29%3A%0A%20%20%20%20%22%22%22%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AD%E3%83%B3%E3%82%B0%EF%BC%9A%E9%83%A8%E5%88%86%E5%92%8C%20I%22%22%22%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E9%9B%86%E5%90%88%E3%81%AE%E5%92%8C%E3%81%8C%20target%20%E3%81%AB%E7%AD%89%E3%81%97%E3%81%91%E3%82%8C%E3%81%B0%E3%80%81%E8%A7%A3%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20if%20target%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20res.append%28list%28state%29%29%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20%23%20%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E9%81%B8%E6%8A%9E%E8%82%A2%E3%82%92%E8%B5%B0%E6%9F%BB%0A%20%20%20%20%23%20%E6%9E%9D%E5%88%88%E3%82%8A%202%3A%20start%20%E3%81%8B%E3%82%89%E8%B5%B0%E6%9F%BB%E3%81%97%E3%80%81%E9%87%8D%E8%A4%87%E3%81%99%E3%82%8B%E9%83%A8%E5%88%86%E9%9B%86%E5%90%88%E3%81%AE%E7%94%9F%E6%88%90%E3%82%92%E9%81%BF%E3%81%91%E3%82%8B%0A%20%20%20%20for%20i%20in%20range%28start%2C%20len%28choices%29%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E6%9E%9D%E5%88%88%E3%82%8A1%EF%BC%9A%E9%83%A8%E5%88%86%E9%9B%86%E5%90%88%E3%81%AE%E5%92%8C%E3%81%8C%20target%20%E3%82%92%E8%B6%85%E3%81%88%E3%81%9F%E3%82%89%E3%80%81%E7%9B%B4%E3%81%A1%E3%81%AB%E3%83%AB%E3%83%BC%E3%83%97%E3%82%92%E7%B5%82%E4%BA%86%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20%23%20%E9%85%8D%E5%88%97%E3%81%AF%E3%82%BD%E3%83%BC%E3%83%88%E6%B8%88%E3%81%BF%E3%81%A7%E5%BE%8C%E7%B6%9A%E8%A6%81%E7%B4%A0%E3%81%AE%E3%81%BB%E3%81%86%E3%81%8C%E5%A4%A7%E3%81%8D%E3%81%8F%E3%80%81%E9%83%A8%E5%88%86%E9%9B%86%E5%90%88%E3%81%AE%E5%92%8C%E3%81%AF%E5%BF%85%E3%81%9A%20target%20%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%9F%E3%82%81%0A%20%20%20%20%20%20%20%20if%20target%20-%20choices%5Bi%5D%20%3C%200%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20%23%20%E8%A9%A6%E3%81%99%EF%BC%9A%E9%81%B8%E6%8A%9E%E3%82%92%E8%A1%8C%E3%81%84%E3%80%81target%20%E3%81%A8%20start%20%E3%82%92%E6%9B%B4%E6%96%B0%0A%20%20%20%20%20%20%20%20state.append%28choices%5Bi%5D%29%0A%20%20%20%20%20%20%20%20%23%20%E6%AC%A1%E3%81%AE%E9%81%B8%E6%8A%9E%E3%81%B8%E9%80%B2%E3%82%80%0A%20%20%20%20%20%20%20%20backtrack%28state%2C%20target%20-%20choices%5Bi%5D%2C%20choices%2C%20i%2C%20res%29%0A%20%20%20%20%20%20%20%20%23%20%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AF%EF%BC%9A%E9%81%B8%E6%8A%9E%E3%82%92%E5%8F%96%E3%82%8A%E6%B6%88%E3%81%97%E3%80%81%E5%89%8D%E3%81%AE%E7%8A%B6%E6%85%8B%E3%81%AB%E6%88%BB%E3%81%99%0A%20%20%20%20%20%20%20%20state.pop%28%29%0A%0A%0Adef%20subset_sum_i%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20list%5Blist%5Bint%5D%5D%3A%0A%20%20%20%20%22%22%22%E9%83%A8%E5%88%86%E5%92%8C%20I%20%E3%82%92%E8%A7%A3%E3%81%8F%22%22%22%0A%20%20%20%20state%20%3D%20%5B%5D%20%20%23%20%E7%8A%B6%E6%85%8B%EF%BC%88%E9%83%A8%E5%88%86%E9%9B%86%E5%90%88%EF%BC%89%0A%20%20%20%20nums.sort%28%29%20%20%23%20nums%20%E3%82%92%E3%82%BD%E3%83%BC%E3%83%88%0A%20%20%20%20start%20%3D%200%20%20%23%20%E9%96%8B%E5%A7%8B%E7%82%B9%E3%82%92%E8%B5%B0%E6%9F%BB%0A%20%20%20%20res%20%3D%20%5B%5D%20%20%23%20%E7%B5%90%E6%9E%9C%E3%83%AA%E3%82%B9%E3%83%88%EF%BC%88%E9%83%A8%E5%88%86%E9%9B%86%E5%90%88%E3%81%AE%E3%83%AA%E3%82%B9%E3%83%88%EF%BC%89%0A%20%20%20%20backtrack%28state%2C%20target%2C%20nums%2C%20start%2C%20res%29%0A%20%20%20%20return%20res%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B3%2C%204%2C%205%5D%0A%20%20%20%20target%20%3D%209%0A%20%20%20%20res%20%3D%20subset_sum_i%28nums%2C%20target%29%0A%0A%20%20%20%20print%28f%22%E5%85%A5%E5%8A%9B%E9%85%8D%E5%88%97%20nums%20%3D%20%7Bnums%7D%2C%20target%20%3D%20%7Btarget%7D%22%29%0A%20%20%20%20print%28f%22%E5%92%8C%E3%81%8C%20%7Btarget%7D%20%E3%81%AB%E7%AD%89%E3%81%97%E3%81%84%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E9%83%A8%E5%88%86%E9%9B%86%E5%90%88%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=16&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>次の図は、配列 <span class="arithmatex">\([3, 4, 5]\)</span> と目標値 <span class="arithmatex">\(9\)</span> を上のコードに入力したときの、全体のバックトラッキング過程を示しています。</p>
+<p><img alt="部分和 I のバックトラッキング過程" class="animation-figure" src="../subset_sum_problem.assets/subset_sum_i.png" /></p>
+<p align="center"> 図 13-12 &nbsp; 部分和 I のバックトラッキング過程 </p>
 
-<h2 id="1332">13.3.2 &nbsp; 重複要素がある場合を考慮<a class="headerlink" href="#1332" title="Permanent link">&para;</a></h2>
+<h2 id="1332">13.3.2 &nbsp; 重複要素を考慮する場合<a class="headerlink" href="#1332" title="Permanent link">&para;</a></h2>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
-<p>正の整数の配列 <code>nums</code> とターゲット正整数 <code>target</code> が与えられた場合、組み合わせ内の要素の和が <code>target</code> に等しくなるようなすべての可能な組み合わせを見つけてください。<strong>与えられた配列には重複要素が含まれる可能性があり、各要素は一度だけ選択できます</strong>。これらの組み合わせを重複する組み合わせを含まないリストとして返してください。</p>
+<p>正整数配列 <code>nums</code> と目標の正整数 <code>target</code> が与えられたとき、要素の和が <code>target</code> に等しくなるすべての組合せを見つけてください。<strong>与えられた配列には重複要素が含まれる可能性があり、各要素は 1 回しか選択できません</strong>。これらの組合せをリスト形式で返してください。リストに重複する組合せを含めてはなりません。</p>
 </div>
-<p>前の問題と比較して、<strong>この問題の入力配列には重複要素が含まれる可能性があり</strong>、新しい問題が導入されます。例えば、配列 <span class="arithmatex">\([4, \hat{4}, 5]\)</span> とターゲット要素 <span class="arithmatex">\(9\)</span> が与えられた場合、既存のコードの出力結果は <span class="arithmatex">\([4, 5], [\hat{4}, 5]\)</span> となり、重複する部分集合が生成されます。</p>
-<p><strong>この重複の理由は、特定のラウンドで等しい要素が複数回選択されることです</strong>。以下の図では、最初のラウンドに3つの選択肢があり、そのうち2つが <span class="arithmatex">\(4\)</span> であり、2つの重複する検索分岐を生成し、重複する部分集合を出力します。同様に、2番目のラウンドの2つの <span class="arithmatex">\(4\)</span> も重複する部分集合を生成します。</p>
-<p><img alt="等しい要素による重複部分集合" class="animation-figure" src="../subset_sum_problem.assets/subset_sum_ii_repeat.png" /></p>
-<p align="center"> 図 13-13 &nbsp; 等しい要素による重複部分集合 </p>
+<p>前問と比べると、<strong>この問題の入力配列には重複要素が含まれる可能性があります</strong>。そのため、新たな問題が生じます。例えば、配列 <span class="arithmatex">\([4, \hat{4}, 5]\)</span> と目標値 <span class="arithmatex">\(9\)</span> が与えられると、既存コードの出力は <span class="arithmatex">\([4, 5], [\hat{4}, 5]\)</span> となり、重複部分集合が現れます。</p>
+<p><strong>この重複が生じる原因は、同じ値の要素があるラウンドで複数回選ばれてしまうことにあります</strong>。次の図では、1 回目には 3 つの選択肢があり、そのうち 2 つはどちらも <span class="arithmatex">\(4\)</span> です。これにより 2 本の重複した探索分岐が生じ、重複部分集合が出力されます。同様に、2 回目の 2 つの <span class="arithmatex">\(4\)</span> も重複部分集合を生みます。</p>
+<p><img alt="等しい要素によって生じる重複部分集合" class="animation-figure" src="../subset_sum_problem.assets/subset_sum_ii_repeat.png" /></p>
+<p align="center"> 図 13-13 &nbsp; 等しい要素によって生じる重複部分集合 </p>
 
-<h3 id="1_1">1. &nbsp; 等値要素の剪定<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
-<p>この問題を解決するために、<strong>等しい要素がラウンドごとに一度だけ選択されるように制限する必要があります</strong>。実装は非常に巧妙です：配列がソートされているため、等しい要素は隣接しています。これは、特定のラウンドの選択で、現在の要素がその左側の要素と等しい場合、それはすでに選択されていることを意味するため、現在の要素を直接スキップします。</p>
-<p>同時に、<strong>この問題では各配列要素は一度だけ選択できると規定されています</strong>。幸い、変数 <code>start</code> を使用してこの制約も満たすことができます：選択 <span class="arithmatex">\(x_{i}\)</span> を行った後、次のラウンドをインデックス <span class="arithmatex">\(i + 1\)</span> から前方に開始するように設定します。これにより、重複する部分集合が除去されるだけでなく、要素の重複選択も回避されます。</p>
+<h3 id="1_1">1. &nbsp; 等しい要素の枝刈り<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
+<p>この問題を解決するには、<strong>各ラウンドで等しい要素が 1 回しか選ばれないように制限する必要があります</strong>。実装方法は巧妙です。配列はすでにソートされているため、等しい要素は必ず隣り合っています。したがって、あるラウンドの選択で現在の要素が左隣の要素と等しいなら、それはすでに選ばれたことを意味するので、その要素を直接スキップします。</p>
+<p>同時に、**この問題では各配列要素を 1 回しか選択できない**という制約もあります。幸い、この制約も変数 <code>start</code> を使って満たせます。すなわち、選択 <span class="arithmatex">\(x_{i}\)</span> を行った後、次のラウンドはインデックス <span class="arithmatex">\(i + 1\)</span> から後ろへ走査するよう設定します。これにより、重複部分集合を除去できるだけでなく、同じ要素を繰り返し選ぶことも防げます。</p>
 <h3 id="2_1">2. &nbsp; コード実装<a class="headerlink" href="#2_1" title="Permanent link">&para;</a></h3>
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@@ -4892,186 +5541,564 @@
 <div class="highlight"><span class="filename">subset_sum_ii.py</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
 <a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>    <span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">choices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">start</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]</span>
 <a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="p">):</span>
-<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキングアルゴリズム：部分集合の和 II&quot;&quot;&quot;</span>
-<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a>    <span class="c1"># 部分集合の和が target と等しいとき、解を記録</span>
+<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキング：部分和 II&quot;&quot;&quot;</span>
+<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a>    <span class="c1"># 部分集合の和が target に等しければ、解を記録</span>
 <a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a>    <span class="k">if</span> <span class="n">target</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
 <a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a>        <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">state</span><span class="p">))</span>
 <a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>        <span class="k">return</span>
 <a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a>    <span class="c1"># すべての選択肢を走査</span>
-<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a>    <span class="c1"># 枝刈り二：start から走査を開始して重複する部分集合の生成を避ける</span>
-<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a>    <span class="c1"># 枝刈り三：start から走査を開始して同じ要素の重複選択を避ける</span>
+<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a>    <span class="c1"># 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
+<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a>    <span class="c1"># 枝刈り 3: start から走査し、同じ要素の重複選択を避ける</span>
 <a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">start</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">choices</span><span class="p">)):</span>
-<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a>        <span class="c1"># 枝刈り一：部分集合の和が target を超える場合、直ちにループを終了</span>
-<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a>        <span class="c1"># これは配列がソートされており、後の要素がより大きいため、部分集合の和は必ず target を超えるため</span>
+<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a>        <span class="c1"># 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する</span>
+<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a>        <span class="c1"># 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため</span>
 <a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a>        <span class="k">if</span> <span class="n">target</span> <span class="o">-</span> <span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">:</span>
 <a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a>            <span class="k">break</span>
-<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a>        <span class="c1"># 枝刈り四：要素が左の要素と等しい場合、検索分岐が重複していることを示すため、スキップ</span>
+<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a>        <span class="c1"># 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする</span>
 <a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a>        <span class="k">if</span> <span class="n">i</span> <span class="o">&gt;</span> <span class="n">start</span> <span class="ow">and</span> <span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">==</span> <span class="n">choices</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]:</span>
 <a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a>            <span class="k">continue</span>
-<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a>        <span class="c1"># 試行：選択を行い、target、start を更新</span>
+<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a>        <span class="c1"># 試す：選択を行い、target と start を更新</span>
 <a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a>        <span class="n">state</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
-<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a>        <span class="c1"># 次の選択ラウンドに進む</span>
+<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a>        <span class="c1"># 次の選択へ進む</span>
 <a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a>        <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">target</span> <span class="o">-</span> <span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">choices</span><span class="p">,</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
-<a id="__codelineno-26-24" name="__codelineno-26-24" href="#__codelineno-26-24"></a>        <span class="c1"># 撤回：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-26-24" name="__codelineno-26-24" href="#__codelineno-26-24"></a>        <span class="c1"># バックトラック：選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-26-25" name="__codelineno-26-25" href="#__codelineno-26-25"></a>        <span class="n">state</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
 <a id="__codelineno-26-26" name="__codelineno-26-26" href="#__codelineno-26-26"></a>
 <a id="__codelineno-26-27" name="__codelineno-26-27" href="#__codelineno-26-27"></a><span class="k">def</span><span class="w"> </span><span class="nf">subset_sum_ii</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]:</span>
-<a id="__codelineno-26-28" name="__codelineno-26-28" href="#__codelineno-26-28"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;部分集合の和 II を解く&quot;&quot;&quot;</span>
+<a id="__codelineno-26-28" name="__codelineno-26-28" href="#__codelineno-26-28"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;部分和 II を解く&quot;&quot;&quot;</span>
 <a id="__codelineno-26-29" name="__codelineno-26-29" href="#__codelineno-26-29"></a>    <span class="n">state</span> <span class="o">=</span> <span class="p">[]</span>  <span class="c1"># 状態（部分集合）</span>
 <a id="__codelineno-26-30" name="__codelineno-26-30" href="#__codelineno-26-30"></a>    <span class="n">nums</span><span class="o">.</span><span class="n">sort</span><span class="p">()</span>  <span class="c1"># nums をソート</span>
-<a id="__codelineno-26-31" name="__codelineno-26-31" href="#__codelineno-26-31"></a>    <span class="n">start</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># 走査の開始点</span>
-<a id="__codelineno-26-32" name="__codelineno-26-32" href="#__codelineno-26-32"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>  <span class="c1"># 結果リスト（部分集合リスト）</span>
+<a id="__codelineno-26-31" name="__codelineno-26-31" href="#__codelineno-26-31"></a>    <span class="n">start</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># 開始点を走査</span>
+<a id="__codelineno-26-32" name="__codelineno-26-32" href="#__codelineno-26-32"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>  <span class="c1"># 結果リスト（部分集合のリスト）</span>
 <a id="__codelineno-26-33" name="__codelineno-26-33" href="#__codelineno-26-33"></a>    <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">target</span><span class="p">,</span> <span class="n">nums</span><span class="p">,</span> <span class="n">start</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
 <a id="__codelineno-26-34" name="__codelineno-26-34" href="#__codelineno-26-34"></a>    <span class="k">return</span> <span class="n">res</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_ii.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* バックトラッキングアルゴリズム：部分集合和 II */</span>
+<div class="highlight"><span class="filename">subset_sum_ii.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* バックトラッキング：部分和 II */</span>
 <a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="c1">// 部分集合の和がtargetと等しいとき、解を記録</span>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
 <a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">state</span><span class="p">);</span>
 <a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
-<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="w">    </span><span class="c1">// 剪定二：startから走査を開始し、重複する部分集合の生成を回避</span>
-<a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a><span class="w">    </span><span class="c1">// 剪定三：startから走査を開始し、同じ要素の繰り返し選択を回避</span>
+<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="w">    </span><span class="c1">// 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
+<a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a><span class="w">    </span><span class="c1">// 枝刈り 3: start から走査し、同じ要素の重複選択を避ける</span>
 <a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">start</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="w">        </span><span class="c1">// 剪定一：部分集合の和がtargetを超えた場合、即座にループを終了</span>
-<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w">        </span><span class="c1">// 配列がソートされているため、後の要素はさらに大きく、部分集合の和は必ずtargetを超える</span>
+<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="w">        </span><span class="c1">// 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する</span>
+<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w">        </span><span class="c1">// 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため</span>
 <a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
 <a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-27-17" name="__codelineno-27-17" href="#__codelineno-27-17"></a><span class="w">        </span><span class="c1">// 剪定四：要素が左の要素と等しい場合、検索ブランチの重複を示すのでスキップ</span>
+<a id="__codelineno-27-17" name="__codelineno-27-17" href="#__codelineno-27-17"></a><span class="w">        </span><span class="c1">// 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする</span>
 <a id="__codelineno-27-18" name="__codelineno-27-18" href="#__codelineno-27-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-19" name="__codelineno-27-19" href="#__codelineno-27-19"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
 <a id="__codelineno-27-20" name="__codelineno-27-20" href="#__codelineno-27-20"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-27-21" name="__codelineno-27-21" href="#__codelineno-27-21"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、target、startを更新</span>
+<a id="__codelineno-27-21" name="__codelineno-27-21" href="#__codelineno-27-21"></a><span class="w">        </span><span class="c1">// 試す：選択を行い、target と start を更新</span>
 <a id="__codelineno-27-22" name="__codelineno-27-22" href="#__codelineno-27-22"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
-<a id="__codelineno-27-23" name="__codelineno-27-23" href="#__codelineno-27-23"></a><span class="w">        </span><span class="c1">// 次のラウンドの選択に進む</span>
+<a id="__codelineno-27-23" name="__codelineno-27-23" href="#__codelineno-27-23"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
 <a id="__codelineno-27-24" name="__codelineno-27-24" href="#__codelineno-27-24"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
-<a id="__codelineno-27-25" name="__codelineno-27-25" href="#__codelineno-27-25"></a><span class="w">        </span><span class="c1">// 回退：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-27-25" name="__codelineno-27-25" href="#__codelineno-27-25"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-27-26" name="__codelineno-27-26" href="#__codelineno-27-26"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
 <a id="__codelineno-27-27" name="__codelineno-27-27" href="#__codelineno-27-27"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-27-28" name="__codelineno-27-28" href="#__codelineno-27-28"></a><span class="p">}</span>
 <a id="__codelineno-27-29" name="__codelineno-27-29" href="#__codelineno-27-29"></a>
-<a id="__codelineno-27-30" name="__codelineno-27-30" href="#__codelineno-27-30"></a><span class="cm">/* 部分集合和 II を解く */</span>
-<a id="__codelineno-27-31" name="__codelineno-27-31" href="#__codelineno-27-31"></a><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">subsetSumII</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-30" name="__codelineno-27-30" href="#__codelineno-27-30"></a><span class="cm">/* 部分和 II を解く */</span>
+<a id="__codelineno-27-31" name="__codelineno-27-31" href="#__codelineno-27-31"></a><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">subsetSumII</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-32" name="__codelineno-27-32" href="#__codelineno-27-32"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">;</span><span class="w">              </span><span class="c1">// 状態（部分集合）</span>
 <a id="__codelineno-27-33" name="__codelineno-27-33" href="#__codelineno-27-33"></a><span class="w">    </span><span class="n">sort</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">end</span><span class="p">());</span><span class="w"> </span><span class="c1">// nums をソート</span>
-<a id="__codelineno-27-34" name="__codelineno-27-34" href="#__codelineno-27-34"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                  </span><span class="c1">// 走査の開始点</span>
-<a id="__codelineno-27-35" name="__codelineno-27-35" href="#__codelineno-27-35"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span><span class="w">        </span><span class="c1">// 結果リスト（部分集合リスト）</span>
+<a id="__codelineno-27-34" name="__codelineno-27-34" href="#__codelineno-27-34"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                  </span><span class="c1">// 開始点を走査</span>
+<a id="__codelineno-27-35" name="__codelineno-27-35" href="#__codelineno-27-35"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span><span class="w">        </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
 <a id="__codelineno-27-36" name="__codelineno-27-36" href="#__codelineno-27-36"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
 <a id="__codelineno-27-37" name="__codelineno-27-37" href="#__codelineno-27-37"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
 <a id="__codelineno-27-38" name="__codelineno-27-38" href="#__codelineno-27-38"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_ii.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* バックトラッキングアルゴリズム：部分集合和 II */</span>
+<div class="highlight"><span class="filename">subset_sum_ii.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* バックトラッキング：部分和 II */</span>
 <a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="c1">// 部分集合の和がtargetと等しいとき、解を記録</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
 <a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
 <a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
-<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="w">    </span><span class="c1">// 剪定二：startから走査を開始し、重複する部分集合の生成を回避</span>
-<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="w">    </span><span class="c1">// 剪定三：startから走査を開始し、同じ要素の繰り返し選択を回避</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="w">    </span><span class="c1">// 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
+<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="w">    </span><span class="c1">// 枝刈り 3: start から走査し、同じ要素の重複選択を避ける</span>
 <a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">start</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a><span class="w">        </span><span class="c1">// 剪定一：部分集合の和がtargetを超えた場合、即座にループを終了</span>
-<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w">        </span><span class="c1">// 配列がソートされているため、後の要素はさらに大きく、部分集合の和は必ずtargetを超える</span>
+<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a><span class="w">        </span><span class="c1">// 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する</span>
+<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w">        </span><span class="c1">// 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため</span>
 <a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
 <a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a><span class="w">        </span><span class="c1">// 剪定四：要素が左の要素と等しい場合、検索ブランチの重複を示すのでスキップ</span>
+<a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a><span class="w">        </span><span class="c1">// 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする</span>
 <a id="__codelineno-28-18" name="__codelineno-28-18" href="#__codelineno-28-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-19" name="__codelineno-28-19" href="#__codelineno-28-19"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
 <a id="__codelineno-28-20" name="__codelineno-28-20" href="#__codelineno-28-20"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-28-21" name="__codelineno-28-21" href="#__codelineno-28-21"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、target、startを更新</span>
+<a id="__codelineno-28-21" name="__codelineno-28-21" href="#__codelineno-28-21"></a><span class="w">        </span><span class="c1">// 試す：選択を行い、target と start を更新</span>
 <a id="__codelineno-28-22" name="__codelineno-28-22" href="#__codelineno-28-22"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">);</span>
-<a id="__codelineno-28-23" name="__codelineno-28-23" href="#__codelineno-28-23"></a><span class="w">        </span><span class="c1">// 次のラウンドの選択に進む</span>
+<a id="__codelineno-28-23" name="__codelineno-28-23" href="#__codelineno-28-23"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
 <a id="__codelineno-28-24" name="__codelineno-28-24" href="#__codelineno-28-24"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
-<a id="__codelineno-28-25" name="__codelineno-28-25" href="#__codelineno-28-25"></a><span class="w">        </span><span class="c1">// 回退：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-28-25" name="__codelineno-28-25" href="#__codelineno-28-25"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
 <a id="__codelineno-28-26" name="__codelineno-28-26" href="#__codelineno-28-26"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-28-27" name="__codelineno-28-27" href="#__codelineno-28-27"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-28-28" name="__codelineno-28-28" href="#__codelineno-28-28"></a><span class="p">}</span>
 <a id="__codelineno-28-29" name="__codelineno-28-29" href="#__codelineno-28-29"></a>
-<a id="__codelineno-28-30" name="__codelineno-28-30" href="#__codelineno-28-30"></a><span class="cm">/* 部分集合和 II を解く */</span>
+<a id="__codelineno-28-30" name="__codelineno-28-30" href="#__codelineno-28-30"></a><span class="cm">/* 部分和 II を解く */</span>
 <a id="__codelineno-28-31" name="__codelineno-28-31" href="#__codelineno-28-31"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="nf">subsetSumII</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-32" name="__codelineno-28-32" href="#__codelineno-28-32"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
 <a id="__codelineno-28-33" name="__codelineno-28-33" href="#__codelineno-28-33"></a><span class="w">    </span><span class="n">Arrays</span><span class="p">.</span><span class="na">sort</span><span class="p">(</span><span class="n">nums</span><span class="p">);</span><span class="w"> </span><span class="c1">// nums をソート</span>
-<a id="__codelineno-28-34" name="__codelineno-28-34" href="#__codelineno-28-34"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 走査の開始点</span>
-<a id="__codelineno-28-35" name="__codelineno-28-35" href="#__codelineno-28-35"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合リスト）</span>
+<a id="__codelineno-28-34" name="__codelineno-28-34" href="#__codelineno-28-34"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 開始点を走査</span>
+<a id="__codelineno-28-35" name="__codelineno-28-35" href="#__codelineno-28-35"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
 <a id="__codelineno-28-36" name="__codelineno-28-36" href="#__codelineno-28-36"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
 <a id="__codelineno-28-37" name="__codelineno-28-37" href="#__codelineno-28-37"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
 <a id="__codelineno-28-38" name="__codelineno-28-38" href="#__codelineno-28-38"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_ii.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">subset_sum_ii</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Backtrack</span><span class="p">}</span>
-<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a>
-<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">subset_sum_ii</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">SubsetSumII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_ii.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* バックトラッキング：部分和 II */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Backtrack</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">    </span><span class="c1">// 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w">    </span><span class="c1">// 枝刈り 3: start から走査し、同じ要素の重複選択を避ける</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">start</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="w">        </span><span class="c1">// 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w">        </span><span class="c1">// 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="w">        </span><span class="c1">// 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする</span>
+<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-29-20" name="__codelineno-29-20" href="#__codelineno-29-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-21" name="__codelineno-29-21" href="#__codelineno-29-21"></a><span class="w">        </span><span class="c1">// 試す：選択を行い、target と start を更新</span>
+<a id="__codelineno-29-22" name="__codelineno-29-22" href="#__codelineno-29-22"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-29-23" name="__codelineno-29-23" href="#__codelineno-29-23"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-29-24" name="__codelineno-29-24" href="#__codelineno-29-24"></a><span class="w">        </span><span class="n">Backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-29-25" name="__codelineno-29-25" href="#__codelineno-29-25"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-29-26" name="__codelineno-29-26" href="#__codelineno-29-26"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-29-27" name="__codelineno-29-27" href="#__codelineno-29-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-28" name="__codelineno-29-28" href="#__codelineno-29-28"></a><span class="p">}</span>
+<a id="__codelineno-29-29" name="__codelineno-29-29" href="#__codelineno-29-29"></a>
+<a id="__codelineno-29-30" name="__codelineno-29-30" href="#__codelineno-29-30"></a><span class="cm">/* 部分和 II を解く */</span>
+<a id="__codelineno-29-31" name="__codelineno-29-31" href="#__codelineno-29-31"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">SubsetSumII</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-32" name="__codelineno-29-32" href="#__codelineno-29-32"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-29-33" name="__codelineno-29-33" href="#__codelineno-29-33"></a><span class="w">    </span><span class="n">Array</span><span class="p">.</span><span class="n">Sort</span><span class="p">(</span><span class="n">nums</span><span class="p">);</span><span class="w"> </span><span class="c1">// nums をソート</span>
+<a id="__codelineno-29-34" name="__codelineno-29-34" href="#__codelineno-29-34"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 開始点を走査</span>
+<a id="__codelineno-29-35" name="__codelineno-29-35" href="#__codelineno-29-35"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-29-36" name="__codelineno-29-36" href="#__codelineno-29-36"></a><span class="w">    </span><span class="n">Backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-29-37" name="__codelineno-29-37" href="#__codelineno-29-37"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-29-38" name="__codelineno-29-38" href="#__codelineno-29-38"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_ii.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">backtrackSubsetSumII</span><span class="p">}</span>
-<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a>
-<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">subsetSumII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_ii.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* バックトラッキング：部分和 II */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">backtrackSubsetSumII</span><span class="p">(</span><span class="nx">start</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">*</span><span class="p">[][]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">        </span><span class="nx">newState</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">append</span><span class="p">([]</span><span class="kt">int</span><span class="p">{},</span><span class="w"> </span><span class="o">*</span><span class="nx">state</span><span class="o">...</span><span class="p">)</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">        </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">newState</span><span class="p">)</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w">    </span><span class="c1">// 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w">    </span><span class="c1">// 枝刈り 3: start から走査し、同じ要素の重複選択を避ける</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">start</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w">        </span><span class="c1">// 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する</span>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w">        </span><span class="c1">// 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">target</span><span class="o">-</span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a><span class="w">        </span><span class="c1">// 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする</span>
+<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">start</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">)[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></a><span class="w">            </span><span class="k">continue</span>
+<a id="__codelineno-30-21" name="__codelineno-30-21" href="#__codelineno-30-21"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-30-22" name="__codelineno-30-22" href="#__codelineno-30-22"></a><span class="w">        </span><span class="c1">// 試す：選択を行い、target と start を更新</span>
+<a id="__codelineno-30-23" name="__codelineno-30-23" href="#__codelineno-30-23"></a><span class="w">        </span><span class="o">*</span><span class="nx">state</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">)[</span><span class="nx">i</span><span class="p">])</span>
+<a id="__codelineno-30-24" name="__codelineno-30-24" href="#__codelineno-30-24"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-30-25" name="__codelineno-30-25" href="#__codelineno-30-25"></a><span class="w">        </span><span class="nx">backtrackSubsetSumII</span><span class="p">(</span><span class="nx">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="o">-</span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">)[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
+<a id="__codelineno-30-26" name="__codelineno-30-26" href="#__codelineno-30-26"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-30-27" name="__codelineno-30-27" href="#__codelineno-30-27"></a><span class="w">        </span><span class="o">*</span><span class="nx">state</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)[:</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-30-28" name="__codelineno-30-28" href="#__codelineno-30-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-29" name="__codelineno-30-29" href="#__codelineno-30-29"></a><span class="p">}</span>
+<a id="__codelineno-30-30" name="__codelineno-30-30" href="#__codelineno-30-30"></a>
+<a id="__codelineno-30-31" name="__codelineno-30-31" href="#__codelineno-30-31"></a><span class="cm">/* 部分和 II を解く */</span>
+<a id="__codelineno-30-32" name="__codelineno-30-32" href="#__codelineno-30-32"></a><span class="kd">func</span><span class="w"> </span><span class="nx">subsetSumII</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">[][]</span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-33" name="__codelineno-30-33" href="#__codelineno-30-33"></a><span class="w">    </span><span class="nx">state</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-30-34" name="__codelineno-30-34" href="#__codelineno-30-34"></a><span class="w">    </span><span class="nx">sort</span><span class="p">.</span><span class="nx">Ints</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w">         </span><span class="c1">// nums をソート</span>
+<a id="__codelineno-30-35" name="__codelineno-30-35" href="#__codelineno-30-35"></a><span class="w">    </span><span class="nx">start</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="w">              </span><span class="c1">// 開始点を走査</span>
+<a id="__codelineno-30-36" name="__codelineno-30-36" href="#__codelineno-30-36"></a><span class="w">    </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-30-37" name="__codelineno-30-37" href="#__codelineno-30-37"></a><span class="w">    </span><span class="nx">backtrackSubsetSumII</span><span class="p">(</span><span class="nx">start</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">res</span><span class="p">)</span>
+<a id="__codelineno-30-38" name="__codelineno-30-38" href="#__codelineno-30-38"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
+<a id="__codelineno-30-39" name="__codelineno-30-39" href="#__codelineno-30-39"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_ii.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a>
-<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">subsetSumII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_ii.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* バックトラッキング：部分和 II */</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">start</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[[</span><span class="nb">Int</span><span class="p">]])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">state</span><span class="p">)</span>
+<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="w">    </span><span class="c1">// 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
+<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a><span class="w">    </span><span class="c1">// 枝刈り 3: start から走査し、同じ要素の重複選択を避ける</span>
+<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="bp">indices</span><span class="p">.</span><span class="bp">dropFirst</span><span class="p">(</span><span class="n">start</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="w">        </span><span class="c1">// 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する</span>
+<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a><span class="w">        </span><span class="c1">// 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため</span>
+<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-31-16" name="__codelineno-31-16" href="#__codelineno-31-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-31-17" name="__codelineno-31-17" href="#__codelineno-31-17"></a><span class="w">        </span><span class="c1">// 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする</span>
+<a id="__codelineno-31-18" name="__codelineno-31-18" href="#__codelineno-31-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-19" name="__codelineno-31-19" href="#__codelineno-31-19"></a><span class="w">            </span><span class="k">continue</span>
+<a id="__codelineno-31-20" name="__codelineno-31-20" href="#__codelineno-31-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-31-21" name="__codelineno-31-21" href="#__codelineno-31-21"></a><span class="w">        </span><span class="c1">// 試す：選択を行い、target と start を更新</span>
+<a id="__codelineno-31-22" name="__codelineno-31-22" href="#__codelineno-31-22"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+<a id="__codelineno-31-23" name="__codelineno-31-23" href="#__codelineno-31-23"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-31-24" name="__codelineno-31-24" href="#__codelineno-31-24"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">start</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-31-25" name="__codelineno-31-25" href="#__codelineno-31-25"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-31-26" name="__codelineno-31-26" href="#__codelineno-31-26"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="bp">removeLast</span><span class="p">()</span>
+<a id="__codelineno-31-27" name="__codelineno-31-27" href="#__codelineno-31-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-28" name="__codelineno-31-28" href="#__codelineno-31-28"></a><span class="p">}</span>
+<a id="__codelineno-31-29" name="__codelineno-31-29" href="#__codelineno-31-29"></a>
+<a id="__codelineno-31-30" name="__codelineno-31-30" href="#__codelineno-31-30"></a><span class="cm">/* 部分和 II を解く */</span>
+<a id="__codelineno-31-31" name="__codelineno-31-31" href="#__codelineno-31-31"></a><span class="kd">func</span><span class="w"> </span><span class="nf">subsetSumII</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[[</span><span class="nb">Int</span><span class="p">]]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-32" name="__codelineno-31-32" href="#__codelineno-31-32"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">state</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-31-33" name="__codelineno-31-33" href="#__codelineno-31-33"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">sorted</span><span class="p">()</span><span class="w"> </span><span class="c1">// nums をソート</span>
+<a id="__codelineno-31-34" name="__codelineno-31-34" href="#__codelineno-31-34"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">start</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1">// 開始点を走査</span>
+<a id="__codelineno-31-35" name="__codelineno-31-35" href="#__codelineno-31-35"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="p">:</span><span class="w"> </span><span class="p">[[</span><span class="nb">Int</span><span class="p">]]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-31-36" name="__codelineno-31-36" href="#__codelineno-31-36"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">start</span><span class="p">:</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-31-37" name="__codelineno-31-37" href="#__codelineno-31-37"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-31-38" name="__codelineno-31-38" href="#__codelineno-31-38"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_ii.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
-<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a>
-<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">subsetSumII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_ii.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* バックトラッキング：部分和 II */</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">start</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">target</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="w">        </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">([...</span><span class="nx">state</span><span class="p">]);</span>
+<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="w">    </span><span class="c1">// 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
+<a id="__codelineno-32-10" name="__codelineno-32-10" href="#__codelineno-32-10"></a><span class="w">    </span><span class="c1">// 枝刈り 3: start から走査し、同じ要素の重複選択を避ける</span>
+<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">start</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">choices</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a><span class="w">        </span><span class="c1">// 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する</span>
+<a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a><span class="w">        </span><span class="c1">// 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため</span>
+<a id="__codelineno-32-14" name="__codelineno-32-14" href="#__codelineno-32-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">choices</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-15" name="__codelineno-32-15" href="#__codelineno-32-15"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-32-16" name="__codelineno-32-16" href="#__codelineno-32-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-32-17" name="__codelineno-32-17" href="#__codelineno-32-17"></a><span class="w">        </span><span class="c1">// 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする</span>
+<a id="__codelineno-32-18" name="__codelineno-32-18" href="#__codelineno-32-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">start</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">choices</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">choices</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-19" name="__codelineno-32-19" href="#__codelineno-32-19"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-32-20" name="__codelineno-32-20" href="#__codelineno-32-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-32-21" name="__codelineno-32-21" href="#__codelineno-32-21"></a><span class="w">        </span><span class="c1">// 試す：選択を行い、target と start を更新</span>
+<a id="__codelineno-32-22" name="__codelineno-32-22" href="#__codelineno-32-22"></a><span class="w">        </span><span class="nx">state</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">choices</span><span class="p">[</span><span class="nx">i</span><span class="p">]);</span>
+<a id="__codelineno-32-23" name="__codelineno-32-23" href="#__codelineno-32-23"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-32-24" name="__codelineno-32-24" href="#__codelineno-32-24"></a><span class="w">        </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">choices</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-32-25" name="__codelineno-32-25" href="#__codelineno-32-25"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-32-26" name="__codelineno-32-26" href="#__codelineno-32-26"></a><span class="w">        </span><span class="nx">state</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-32-27" name="__codelineno-32-27" href="#__codelineno-32-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-28" name="__codelineno-32-28" href="#__codelineno-32-28"></a><span class="p">}</span>
+<a id="__codelineno-32-29" name="__codelineno-32-29" href="#__codelineno-32-29"></a>
+<a id="__codelineno-32-30" name="__codelineno-32-30" href="#__codelineno-32-30"></a><span class="cm">/* 部分和 II を解く */</span>
+<a id="__codelineno-32-31" name="__codelineno-32-31" href="#__codelineno-32-31"></a><span class="kd">function</span><span class="w"> </span><span class="nx">subsetSumII</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-32" name="__codelineno-32-32" href="#__codelineno-32-32"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-32-33" name="__codelineno-32-33" href="#__codelineno-32-33"></a><span class="w">    </span><span class="nx">nums</span><span class="p">.</span><span class="nx">sort</span><span class="p">((</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">b</span><span class="p">);</span><span class="w"> </span><span class="c1">// nums をソート</span>
+<a id="__codelineno-32-34" name="__codelineno-32-34" href="#__codelineno-32-34"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 開始点を走査</span>
+<a id="__codelineno-32-35" name="__codelineno-32-35" href="#__codelineno-32-35"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-32-36" name="__codelineno-32-36" href="#__codelineno-32-36"></a><span class="w">    </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">start</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-32-37" name="__codelineno-32-37" href="#__codelineno-32-37"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-32-38" name="__codelineno-32-38" href="#__codelineno-32-38"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_ii.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
-<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a>
-<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">subsetSumII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_ii.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* バックトラッキング：部分和 II */</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w">    </span><span class="nx">state</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span>
+<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w">    </span><span class="nx">target</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span>
+<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w">    </span><span class="nx">choices</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span>
+<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="w">    </span><span class="nx">start</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span>
+<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w">    </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[][]</span>
+<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">target</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="w">        </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">([...</span><span class="nx">state</span><span class="p">]);</span>
+<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a><span class="w">    </span><span class="c1">// 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
+<a id="__codelineno-33-16" name="__codelineno-33-16" href="#__codelineno-33-16"></a><span class="w">    </span><span class="c1">// 枝刈り 3: start から走査し、同じ要素の重複選択を避ける</span>
+<a id="__codelineno-33-17" name="__codelineno-33-17" href="#__codelineno-33-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">start</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">choices</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-18" name="__codelineno-33-18" href="#__codelineno-33-18"></a><span class="w">        </span><span class="c1">// 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する</span>
+<a id="__codelineno-33-19" name="__codelineno-33-19" href="#__codelineno-33-19"></a><span class="w">        </span><span class="c1">// 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため</span>
+<a id="__codelineno-33-20" name="__codelineno-33-20" href="#__codelineno-33-20"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">choices</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-21" name="__codelineno-33-21" href="#__codelineno-33-21"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-33-22" name="__codelineno-33-22" href="#__codelineno-33-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-33-23" name="__codelineno-33-23" href="#__codelineno-33-23"></a><span class="w">        </span><span class="c1">// 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする</span>
+<a id="__codelineno-33-24" name="__codelineno-33-24" href="#__codelineno-33-24"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">start</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">choices</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">choices</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-25" name="__codelineno-33-25" href="#__codelineno-33-25"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-33-26" name="__codelineno-33-26" href="#__codelineno-33-26"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-33-27" name="__codelineno-33-27" href="#__codelineno-33-27"></a><span class="w">        </span><span class="c1">// 試す：選択を行い、target と start を更新</span>
+<a id="__codelineno-33-28" name="__codelineno-33-28" href="#__codelineno-33-28"></a><span class="w">        </span><span class="nx">state</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">choices</span><span class="p">[</span><span class="nx">i</span><span class="p">]);</span>
+<a id="__codelineno-33-29" name="__codelineno-33-29" href="#__codelineno-33-29"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-33-30" name="__codelineno-33-30" href="#__codelineno-33-30"></a><span class="w">        </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">choices</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-33-31" name="__codelineno-33-31" href="#__codelineno-33-31"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-33-32" name="__codelineno-33-32" href="#__codelineno-33-32"></a><span class="w">        </span><span class="nx">state</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-33-33" name="__codelineno-33-33" href="#__codelineno-33-33"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-34" name="__codelineno-33-34" href="#__codelineno-33-34"></a><span class="p">}</span>
+<a id="__codelineno-33-35" name="__codelineno-33-35" href="#__codelineno-33-35"></a>
+<a id="__codelineno-33-36" name="__codelineno-33-36" href="#__codelineno-33-36"></a><span class="cm">/* 部分和 II を解く */</span>
+<a id="__codelineno-33-37" name="__codelineno-33-37" href="#__codelineno-33-37"></a><span class="kd">function</span><span class="w"> </span><span class="nx">subsetSumII</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">target</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[][]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-38" name="__codelineno-33-38" href="#__codelineno-33-38"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-33-39" name="__codelineno-33-39" href="#__codelineno-33-39"></a><span class="w">    </span><span class="nx">nums</span><span class="p">.</span><span class="nx">sort</span><span class="p">((</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">b</span><span class="p">);</span><span class="w"> </span><span class="c1">// nums をソート</span>
+<a id="__codelineno-33-40" name="__codelineno-33-40" href="#__codelineno-33-40"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 開始点を走査</span>
+<a id="__codelineno-33-41" name="__codelineno-33-41" href="#__codelineno-33-41"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-33-42" name="__codelineno-33-42" href="#__codelineno-33-42"></a><span class="w">    </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">start</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-33-43" name="__codelineno-33-43" href="#__codelineno-33-43"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-33-44" name="__codelineno-33-44" href="#__codelineno-33-44"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_ii.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a>
-<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">subsetSumII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_ii.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* バックトラッキング：部分和 II */</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span>
+<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span>
+<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span>
+<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="p">,</span>
+<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">,</span>
+<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="w">  </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-34-10" name="__codelineno-34-10" href="#__codelineno-34-10"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-11" name="__codelineno-34-11" href="#__codelineno-34-11"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">List</span><span class="p">.</span><span class="n">from</span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
+<a id="__codelineno-34-12" name="__codelineno-34-12" href="#__codelineno-34-12"></a><span class="w">    </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-34-13" name="__codelineno-34-13" href="#__codelineno-34-13"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-14" name="__codelineno-34-14" href="#__codelineno-34-14"></a><span class="w">  </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-34-15" name="__codelineno-34-15" href="#__codelineno-34-15"></a><span class="w">  </span><span class="c1">// 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
+<a id="__codelineno-34-16" name="__codelineno-34-16" href="#__codelineno-34-16"></a><span class="w">  </span><span class="c1">// 枝刈り 3: start から走査し、同じ要素の重複選択を避ける</span>
+<a id="__codelineno-34-17" name="__codelineno-34-17" href="#__codelineno-34-17"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">start</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-18" name="__codelineno-34-18" href="#__codelineno-34-18"></a><span class="w">    </span><span class="c1">// 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する</span>
+<a id="__codelineno-34-19" name="__codelineno-34-19" href="#__codelineno-34-19"></a><span class="w">    </span><span class="c1">// 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため</span>
+<a id="__codelineno-34-20" name="__codelineno-34-20" href="#__codelineno-34-20"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-21" name="__codelineno-34-21" href="#__codelineno-34-21"></a><span class="w">      </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-34-22" name="__codelineno-34-22" href="#__codelineno-34-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-23" name="__codelineno-34-23" href="#__codelineno-34-23"></a><span class="w">    </span><span class="c1">// 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする</span>
+<a id="__codelineno-34-24" name="__codelineno-34-24" href="#__codelineno-34-24"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-25" name="__codelineno-34-25" href="#__codelineno-34-25"></a><span class="w">      </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-34-26" name="__codelineno-34-26" href="#__codelineno-34-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-27" name="__codelineno-34-27" href="#__codelineno-34-27"></a><span class="w">    </span><span class="c1">// 試す：選択を行い、target と start を更新</span>
+<a id="__codelineno-34-28" name="__codelineno-34-28" href="#__codelineno-34-28"></a><span class="w">    </span><span class="n">state</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-34-29" name="__codelineno-34-29" href="#__codelineno-34-29"></a><span class="w">    </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-34-30" name="__codelineno-34-30" href="#__codelineno-34-30"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-34-31" name="__codelineno-34-31" href="#__codelineno-34-31"></a><span class="w">    </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-34-32" name="__codelineno-34-32" href="#__codelineno-34-32"></a><span class="w">    </span><span class="n">state</span><span class="p">.</span><span class="n">removeLast</span><span class="p">();</span>
+<a id="__codelineno-34-33" name="__codelineno-34-33" href="#__codelineno-34-33"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-34" name="__codelineno-34-34" href="#__codelineno-34-34"></a><span class="p">}</span>
+<a id="__codelineno-34-35" name="__codelineno-34-35" href="#__codelineno-34-35"></a>
+<a id="__codelineno-34-36" name="__codelineno-34-36" href="#__codelineno-34-36"></a><span class="cm">/* 部分和 II を解く */</span>
+<a id="__codelineno-34-37" name="__codelineno-34-37" href="#__codelineno-34-37"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">subsetSumII</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-38" name="__codelineno-34-38" href="#__codelineno-34-38"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-34-39" name="__codelineno-34-39" href="#__codelineno-34-39"></a><span class="w">  </span><span class="n">nums</span><span class="p">.</span><span class="n">sort</span><span class="p">();</span><span class="w"> </span><span class="c1">// nums をソート</span>
+<a id="__codelineno-34-40" name="__codelineno-34-40" href="#__codelineno-34-40"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 開始点を走査</span>
+<a id="__codelineno-34-41" name="__codelineno-34-41" href="#__codelineno-34-41"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-34-42" name="__codelineno-34-42" href="#__codelineno-34-42"></a><span class="w">  </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-34-43" name="__codelineno-34-43" href="#__codelineno-34-43"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-34-44" name="__codelineno-34-44" href="#__codelineno-34-44"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_ii.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a>
-<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">subset_sum_ii</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_ii.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* バックトラッキング：部分和 II */</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w">    </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="w">    </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span>
+<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="w">    </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span>
+<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="w">    </span><span class="n">start</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span>
+<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="w">    </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-35-12" name="__codelineno-35-12" href="#__codelineno-35-12"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-35-13" name="__codelineno-35-13" href="#__codelineno-35-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-14" name="__codelineno-35-14" href="#__codelineno-35-14"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-35-15" name="__codelineno-35-15" href="#__codelineno-35-15"></a><span class="w">    </span><span class="c1">// 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
+<a id="__codelineno-35-16" name="__codelineno-35-16" href="#__codelineno-35-16"></a><span class="w">    </span><span class="c1">// 枝刈り 3: start から走査し、同じ要素の重複選択を避ける</span>
+<a id="__codelineno-35-17" name="__codelineno-35-17" href="#__codelineno-35-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">start</span><span class="o">..</span><span class="n">choices</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-18" name="__codelineno-35-18" href="#__codelineno-35-18"></a><span class="w">        </span><span class="c1">// 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する</span>
+<a id="__codelineno-35-19" name="__codelineno-35-19" href="#__codelineno-35-19"></a><span class="w">        </span><span class="c1">// 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため</span>
+<a id="__codelineno-35-20" name="__codelineno-35-20" href="#__codelineno-35-20"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-21" name="__codelineno-35-21" href="#__codelineno-35-21"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-35-22" name="__codelineno-35-22" href="#__codelineno-35-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-35-23" name="__codelineno-35-23" href="#__codelineno-35-23"></a><span class="w">        </span><span class="c1">// 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする</span>
+<a id="__codelineno-35-24" name="__codelineno-35-24" href="#__codelineno-35-24"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-25" name="__codelineno-35-25" href="#__codelineno-35-25"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-35-26" name="__codelineno-35-26" href="#__codelineno-35-26"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-35-27" name="__codelineno-35-27" href="#__codelineno-35-27"></a><span class="w">        </span><span class="c1">// 試す：選択を行い、target と start を更新</span>
+<a id="__codelineno-35-28" name="__codelineno-35-28" href="#__codelineno-35-28"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-35-29" name="__codelineno-35-29" href="#__codelineno-35-29"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-35-30" name="__codelineno-35-30" href="#__codelineno-35-30"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-35-31" name="__codelineno-35-31" href="#__codelineno-35-31"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-35-32" name="__codelineno-35-32" href="#__codelineno-35-32"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
+<a id="__codelineno-35-33" name="__codelineno-35-33" href="#__codelineno-35-33"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-34" name="__codelineno-35-34" href="#__codelineno-35-34"></a><span class="p">}</span>
+<a id="__codelineno-35-35" name="__codelineno-35-35" href="#__codelineno-35-35"></a>
+<a id="__codelineno-35-36" name="__codelineno-35-36" href="#__codelineno-35-36"></a><span class="cm">/* 部分和 II を解く */</span>
+<a id="__codelineno-35-37" name="__codelineno-35-37" href="#__codelineno-35-37"></a><span class="k">fn</span><span class="w"> </span><span class="nf">subset_sum_ii</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-38" name="__codelineno-35-38" href="#__codelineno-35-38"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">();</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-35-39" name="__codelineno-35-39" href="#__codelineno-35-39"></a><span class="w">    </span><span class="n">nums</span><span class="p">.</span><span class="n">sort</span><span class="p">();</span><span class="w"> </span><span class="c1">// nums をソート</span>
+<a id="__codelineno-35-40" name="__codelineno-35-40" href="#__codelineno-35-40"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 開始点を走査</span>
+<a id="__codelineno-35-41" name="__codelineno-35-41" href="#__codelineno-35-41"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">();</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-35-42" name="__codelineno-35-42" href="#__codelineno-35-42"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-35-43" name="__codelineno-35-43" href="#__codelineno-35-43"></a><span class="w">    </span><span class="n">res</span>
+<a id="__codelineno-35-44" name="__codelineno-35-44" href="#__codelineno-35-44"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_ii.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a>
-<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">subsetSumII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_ii.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* バックトラッキング：部分和 II */</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">choicesSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">stateSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">resSize</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">state</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="w">        </span><span class="n">resColSizes</span><span class="p">[</span><span class="n">resSize</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stateSize</span><span class="p">;</span>
+<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a><span class="w">    </span><span class="c1">// 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
+<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></a><span class="w">    </span><span class="c1">// 枝刈り 3: start から走査し、同じ要素の重複選択を避ける</span>
+<a id="__codelineno-36-14" name="__codelineno-36-14" href="#__codelineno-36-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">start</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choicesSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-15" name="__codelineno-36-15" href="#__codelineno-36-15"></a><span class="w">        </span><span class="c1">// 枝刈り 1: 部分集合の和が target を超えたら、そのままスキップする</span>
+<a id="__codelineno-36-16" name="__codelineno-36-16" href="#__codelineno-36-16"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-17" name="__codelineno-36-17" href="#__codelineno-36-17"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-36-18" name="__codelineno-36-18" href="#__codelineno-36-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-36-19" name="__codelineno-36-19" href="#__codelineno-36-19"></a><span class="w">        </span><span class="c1">// 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする</span>
+<a id="__codelineno-36-20" name="__codelineno-36-20" href="#__codelineno-36-20"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-21" name="__codelineno-36-21" href="#__codelineno-36-21"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-36-22" name="__codelineno-36-22" href="#__codelineno-36-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-36-23" name="__codelineno-36-23" href="#__codelineno-36-23"></a><span class="w">        </span><span class="c1">// 試す：選択を行い、target と start を更新</span>
+<a id="__codelineno-36-24" name="__codelineno-36-24" href="#__codelineno-36-24"></a><span class="w">        </span><span class="n">state</span><span class="p">[</span><span class="n">stateSize</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-36-25" name="__codelineno-36-25" href="#__codelineno-36-25"></a><span class="w">        </span><span class="n">stateSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-36-26" name="__codelineno-36-26" href="#__codelineno-36-26"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-36-27" name="__codelineno-36-27" href="#__codelineno-36-27"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">choicesSize</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-36-28" name="__codelineno-36-28" href="#__codelineno-36-28"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-36-29" name="__codelineno-36-29" href="#__codelineno-36-29"></a><span class="w">        </span><span class="n">stateSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-36-30" name="__codelineno-36-30" href="#__codelineno-36-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-31" name="__codelineno-36-31" href="#__codelineno-36-31"></a><span class="p">}</span>
+<a id="__codelineno-36-32" name="__codelineno-36-32" href="#__codelineno-36-32"></a>
+<a id="__codelineno-36-33" name="__codelineno-36-33" href="#__codelineno-36-33"></a><span class="cm">/* 部分和 II を解く */</span>
+<a id="__codelineno-36-34" name="__codelineno-36-34" href="#__codelineno-36-34"></a><span class="kt">void</span><span class="w"> </span><span class="nf">subsetSumII</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">numsSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-35" name="__codelineno-36-35" href="#__codelineno-36-35"></a><span class="w">    </span><span class="c1">// nums をソート</span>
+<a id="__codelineno-36-36" name="__codelineno-36-36" href="#__codelineno-36-36"></a><span class="w">    </span><span class="n">qsort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">numsSize</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">),</span><span class="w"> </span><span class="n">cmp</span><span class="p">);</span>
+<a id="__codelineno-36-37" name="__codelineno-36-37" href="#__codelineno-36-37"></a><span class="w">    </span><span class="c1">// バックトラッキングを開始</span>
+<a id="__codelineno-36-38" name="__codelineno-36-38" href="#__codelineno-36-38"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">numsSize</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-36-39" name="__codelineno-36-39" href="#__codelineno-36-39"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_ii.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a>
-<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">subsetSumII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_ii.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* バックトラッキング：部分和 II */</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w">    </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w">    </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span>
+<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w">    </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
+<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="w">    </span><span class="n">start</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span>
+<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w">    </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;?&gt;</span>
+<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="w">    </span><span class="c1">// 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">toMutableList</span><span class="p">())</span>
+<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-14" name="__codelineno-37-14" href="#__codelineno-37-14"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-37-15" name="__codelineno-37-15" href="#__codelineno-37-15"></a><span class="w">    </span><span class="c1">// 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
+<a id="__codelineno-37-16" name="__codelineno-37-16" href="#__codelineno-37-16"></a><span class="w">    </span><span class="c1">// 枝刈り 3: start から走査し、同じ要素の重複選択を避ける</span>
+<a id="__codelineno-37-17" name="__codelineno-37-17" href="#__codelineno-37-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">start</span><span class="p">..</span><span class="o">&lt;</span><span class="n">choices</span><span class="p">.</span><span class="na">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-18" name="__codelineno-37-18" href="#__codelineno-37-18"></a><span class="w">        </span><span class="c1">// 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する</span>
+<a id="__codelineno-37-19" name="__codelineno-37-19" href="#__codelineno-37-19"></a><span class="w">        </span><span class="c1">// 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため</span>
+<a id="__codelineno-37-20" name="__codelineno-37-20" href="#__codelineno-37-20"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-21" name="__codelineno-37-21" href="#__codelineno-37-21"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-37-22" name="__codelineno-37-22" href="#__codelineno-37-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-37-23" name="__codelineno-37-23" href="#__codelineno-37-23"></a><span class="w">        </span><span class="c1">// 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする</span>
+<a id="__codelineno-37-24" name="__codelineno-37-24" href="#__codelineno-37-24"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-25" name="__codelineno-37-25" href="#__codelineno-37-25"></a><span class="w">            </span><span class="k">continue</span>
+<a id="__codelineno-37-26" name="__codelineno-37-26" href="#__codelineno-37-26"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-37-27" name="__codelineno-37-27" href="#__codelineno-37-27"></a><span class="w">        </span><span class="c1">// 試す：選択を行い、target と start を更新</span>
+<a id="__codelineno-37-28" name="__codelineno-37-28" href="#__codelineno-37-28"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-37-29" name="__codelineno-37-29" href="#__codelineno-37-29"></a><span class="w">        </span><span class="c1">// 次の選択へ進む</span>
+<a id="__codelineno-37-30" name="__codelineno-37-30" href="#__codelineno-37-30"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-37-31" name="__codelineno-37-31" href="#__codelineno-37-31"></a><span class="w">        </span><span class="c1">// バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-37-32" name="__codelineno-37-32" href="#__codelineno-37-32"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="na">removeAt</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-37-33" name="__codelineno-37-33" href="#__codelineno-37-33"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-34" name="__codelineno-37-34" href="#__codelineno-37-34"></a><span class="p">}</span>
+<a id="__codelineno-37-35" name="__codelineno-37-35" href="#__codelineno-37-35"></a>
+<a id="__codelineno-37-36" name="__codelineno-37-36" href="#__codelineno-37-36"></a><span class="cm">/* 部分和 II を解く */</span>
+<a id="__codelineno-37-37" name="__codelineno-37-37" href="#__codelineno-37-37"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">subsetSumII</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;?&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-38" name="__codelineno-37-38" href="#__codelineno-37-38"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">()</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-37-39" name="__codelineno-37-39" href="#__codelineno-37-39"></a><span class="w">    </span><span class="n">nums</span><span class="p">.</span><span class="na">sort</span><span class="p">()</span><span class="w"> </span><span class="c1">// nums をソート</span>
+<a id="__codelineno-37-40" name="__codelineno-37-40" href="#__codelineno-37-40"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="c1">// 開始点を走査</span>
+<a id="__codelineno-37-41" name="__codelineno-37-41" href="#__codelineno-37-41"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;?&gt;</span><span class="p">()</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-37-42" name="__codelineno-37-42" href="#__codelineno-37-42"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-37-43" name="__codelineno-37-43" href="#__codelineno-37-43"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-37-44" name="__codelineno-37-44" href="#__codelineno-37-44"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_ii.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a>
-<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">subset_sum_ii</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_ii.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="c1">### バックトラッキング法：部分和 II ###</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w">  </span><span class="c1"># 部分集合の和が target に等しければ、解を記録</span>
+<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="n">target</span><span class="o">.</span><span class="n">zero?</span>
+<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="w">    </span><span class="n">res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">state</span><span class="o">.</span><span class="n">dup</span>
+<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w">    </span><span class="k">return</span>
+<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a>
+<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="w">  </span><span class="c1"># すべての選択肢を走査</span>
+<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a><span class="w">  </span><span class="c1"># 枝刈り 2: start から走査し、重複する部分集合の生成を避ける</span>
+<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a><span class="w">  </span><span class="c1"># 枝刈り 3: start から走査し、同じ要素の重複選択を避ける</span>
+<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">start</span><span class="o">...</span><span class="n">choices</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a><span class="w">    </span><span class="c1"># 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する</span>
+<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a><span class="w">    </span><span class="c1"># 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため</span>
+<a id="__codelineno-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a><span class="w">    </span><span class="k">break</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-38-16" name="__codelineno-38-16" href="#__codelineno-38-16"></a><span class="w">    </span><span class="c1"># 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする</span>
+<a id="__codelineno-38-17" name="__codelineno-38-17" href="#__codelineno-38-17"></a><span class="w">    </span><span class="k">next</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
+<a id="__codelineno-38-18" name="__codelineno-38-18" href="#__codelineno-38-18"></a><span class="w">    </span><span class="c1"># 試す：選択を行い、target と start を更新</span>
+<a id="__codelineno-38-19" name="__codelineno-38-19" href="#__codelineno-38-19"></a><span class="w">    </span><span class="n">state</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-38-20" name="__codelineno-38-20" href="#__codelineno-38-20"></a><span class="w">    </span><span class="c1"># 次の選択へ進む</span>
+<a id="__codelineno-38-21" name="__codelineno-38-21" href="#__codelineno-38-21"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-38-22" name="__codelineno-38-22" href="#__codelineno-38-22"></a><span class="w">    </span><span class="c1"># バックトラック：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-38-23" name="__codelineno-38-23" href="#__codelineno-38-23"></a><span class="w">    </span><span class="n">state</span><span class="o">.</span><span class="n">pop</span>
+<a id="__codelineno-38-24" name="__codelineno-38-24" href="#__codelineno-38-24"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-25" name="__codelineno-38-25" href="#__codelineno-38-25"></a><span class="k">end</span>
+<a id="__codelineno-38-26" name="__codelineno-38-26" href="#__codelineno-38-26"></a>
+<a id="__codelineno-38-27" name="__codelineno-38-27" href="#__codelineno-38-27"></a><span class="c1">### 部分和 II を解く ###</span>
+<a id="__codelineno-38-28" name="__codelineno-38-28" href="#__codelineno-38-28"></a><span class="k">def</span><span class="w"> </span><span class="nf">subset_sum_ii</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-38-29" name="__codelineno-38-29" href="#__codelineno-38-29"></a><span class="w">  </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span><span class="w"> </span><span class="c1"># 状態（部分集合）</span>
+<a id="__codelineno-38-30" name="__codelineno-38-30" href="#__codelineno-38-30"></a><span class="w">  </span><span class="n">nums</span><span class="o">.</span><span class="n">sort!</span><span class="w"> </span><span class="c1"># nums をソート</span>
+<a id="__codelineno-38-31" name="__codelineno-38-31" href="#__codelineno-38-31"></a><span class="w">  </span><span class="n">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1"># 開始点を走査</span>
+<a id="__codelineno-38-32" name="__codelineno-38-32" href="#__codelineno-38-32"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span><span class="w"> </span><span class="c1"># 結果リスト（部分集合のリスト）</span>
+<a id="__codelineno-38-33" name="__codelineno-38-33" href="#__codelineno-38-33"></a><span class="w">  </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-38-34" name="__codelineno-38-34" href="#__codelineno-38-34"></a><span class="w">  </span><span class="n">res</span>
+<a id="__codelineno-38-35" name="__codelineno-38-35" href="#__codelineno-38-35"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>以下の図は、配列 <span class="arithmatex">\([4, 4, 5]\)</span> とターゲット要素 <span class="arithmatex">\(9\)</span> のバックトラッキングプロセスを示し、4種類の剪定操作が含まれています。図とコードのコメントを組み合わせて、検索プロセス全体と各種類の剪定操作の動作を理解してください。</p>
-<p><img alt="部分集合和 II のバックトラッキングプロセス" class="animation-figure" src="../subset_sum_problem.assets/subset_sum_ii.png" /></p>
-<p align="center"> 図 13-14 &nbsp; 部分集合和 II のバックトラッキングプロセス </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" 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</iframe></div>
+<div style="margin-top: 5px;"><a 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target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>次の図は、配列 <span class="arithmatex">\([4, 4, 5]\)</span> と目標値 <span class="arithmatex">\(9\)</span> に対するバックトラッキング過程を示しており、全部で 4 種類の枝刈り操作が含まれています。図とコードコメントを対応させながら、探索全体の流れと、各枝刈り操作がどのように機能するかを理解してください。</p>
+<p><img alt="部分和 II のバックトラッキング過程" class="animation-figure" src="../subset_sum_problem.assets/subset_sum_ii.png" /></p>
+<p align="center"> 図 13-14 &nbsp; 部分和 II のバックトラッキング過程 </p>
 
 <!-- Source file information -->
 
@@ -5118,7 +6145,7 @@ aria-label="フッター"
   <a
     href="../n_queens_problem/"
     class="md-footer__link md-footer__link--next"
-    aria-label="次: 13.4 &amp;nbsp; Nクイーン問題"
+    aria-label="次: 13.4 &amp;nbsp; n クイーン問題"
     rel="next"
   >
     <div class="md-footer__title">
@@ -5126,7 +6153,7 @@ aria-label="フッター"
         次
       </span>
       <div class="md-ellipsis">
-        13.4 &nbsp; Nクイーン問題
+        13.4 &nbsp; n クイーン問題
       </div>
     </div>
     <div class="md-footer__button md-icon">
diff --git a/ja/chapter_backtracking/summary/index.html b/ja/chapter_backtracking/summary/index.html
index b2203be1a..e4bfd2c1c 100644
--- a/ja/chapter_backtracking/summary/index.html
+++ b/ja/chapter_backtracking/summary/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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 <!-- Page content -->
 <h1 id="135">13.5 &nbsp; まとめ<a class="headerlink" href="#135" title="Permanent link">&para;</a></h1>
-<h3 id="1">1. &nbsp; 重要な復習<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<h3 id="1">1. &nbsp; 重要なポイントの振り返り<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
-<li>バックトラッキングアルゴリズムの本質は全数探索です。解空間の深さ優先走査を実行することで条件を満たす解を求めます。検索中に満足のいく解が見つかった場合、それを記録し、すべての解が見つかるか走査が完了するまで続けます。</li>
-<li>バックトラッキングアルゴリズムの検索プロセスには試行と後退が含まれます。深さ優先探索を使用して様々な選択を探索し、選択が制約を満たさない場合、前の選択を取り消します。そして前の状態に戻って他のオプションを試し続けます。試行と後退は反対方向の操作です。</li>
-<li>バックトラッキング問題には通常複数の制約が含まれます。これらの制約は剪定操作を実行するために使用できます。剪定は不要な検索分岐を事前に終了し、検索効率を大幅に向上させることができます。</li>
-<li>バックトラッキングアルゴリズムは主に検索問題と制約満足問題を解決するために使用されます。組み合わせ最適化問題はバックトラッキングを使用して解決できますが、多くの場合、より効率的または効果的な解決方法が利用可能です。</li>
-<li>順列問題は、与えられた集合の要素のすべての可能な順列を検索することを目的とします。各要素が選択されたかどうかを記録するために配列を使用し、同じ要素の重複選択を避けます。これにより、各要素が一度だけ選択されることが保証されます。</li>
-<li>順列問題では、集合に重複要素が含まれている場合、最終結果に重複順列が含まれます。同一要素が各ラウンドで一度だけ選択できるように制限する必要があり、これは通常ハッシュセットを使用して実装されます。</li>
-<li>部分集合和問題は、与えられた集合でターゲット値に合計する全ての部分集合を見つけることを目的とします。集合は要素の順序を区別しませんが、検索プロセスでは重複する部分集合が生成される可能性があります。これは、アルゴリズムが異なる要素順序を独特のパスとして探索するために発生します。バックトラッキングの前に、データをソートし、各ラウンドの走査の開始点を示す変数を設定します。これにより、重複する部分集合を生成する検索分岐を剪定できます。</li>
-<li>部分集合和問題では、配列内の等しい要素は重複集合を生成する可能性があります。配列がすでにソートされているという前提条件を使用して、隣接する要素が等しいかどうかを判定することで剪定を行います。これにより、等しい要素がラウンドごとに一度だけ選択されることが保証されます。</li>
-<li><span class="arithmatex">\(n\)</span> クイーン問題は、2つのクイーンが互いに攻撃できないように <span class="arithmatex">\(n \times n\)</span> のチェスボードに <span class="arithmatex">\(n\)</span> 個のクイーンを配置する方案を見つけることを目的とします。問題の制約には行制約、列制約、および主対角線と副対角線の制約が含まれます。行制約を満たすために、行ごとに1つのクイーンを配置する戦略を採用し、各行に1つのクイーンが配置されることを保証します。</li>
-<li>列制約と対角線制約の処理は似ています。列制約については、各列にクイーンがあるかどうかを記録する配列を使用し、選択されたセルが合法かどうかを示します。対角線制約については、2つの配列を使用して主対角線と副対角線にそれぞれクイーンの存在を記録します。課題は、同じ主対角線または副対角線上のセルの行と列のインデックス間の関係を決定することです。</li>
+<li>バックトラッキングアルゴリズムの本質は全探索法であり、解空間を深さ優先で走査することで条件を満たす解を探索します。探索の過程で条件を満たす解に出会ったら記録し、すべての解を見つけるか探索が完了するまで続けます。</li>
+<li>バックトラッキングアルゴリズムの探索過程は、試行と戻るという 2 つの部分から成ります。深さ優先探索によってさまざまな選択を試し、制約条件を満たさない状況に遭遇した場合は直前の選択を取り消して前の状態に戻り、ほかの選択を引き続き試します。試行と戻るは互いに逆方向の操作です。</li>
+<li>バックトラッキング問題には通常複数の制約条件が含まれており、それらを枝刈りに利用できます。枝刈りによって不要な探索分岐を早期に打ち切り、探索効率を大幅に高められます。</li>
+<li>バックトラッキングアルゴリズムは主に探索問題と制約充足問題の解決に用いられます。組合せ最適化問題もバックトラッキングで解けますが、より高効率またはより適した解法が存在することが少なくありません。</li>
+<li>全順列問題の目的は、与えられた集合要素のすべての可能な並べ方を探索することです。各要素が選択済みかどうかを配列で記録し、同じ要素を重複して選ぶ探索分岐を刈り取ることで、各要素が 1 度だけ選ばれるようにします。</li>
+<li>全順列問題では、集合内に重複要素があると最終結果にも重複した順列が現れます。各ラウンドで等しい要素は 1 回しか選べないように制約する必要があり、通常はハッシュ集合を用いて実現します。</li>
+<li>部分和問題の目標は、与えられた集合の中から和が目標値となるすべての部分集合を見つけることです。集合では要素順序を区別しませんが、探索過程では順序違いの結果も出力されるため、重複部分集合が生じます。そこで、バックトラッキング前にデータをソートし、各ラウンドの走査開始位置を示す変数を設定することで、重複部分集合を生成する探索分岐を枝刈りします。</li>
+<li>部分和問題では、配列中の等しい要素が重複集合を生みます。配列がソート済みであるという前提を利用し、隣接要素が等しいかどうかを判定して枝刈りすることで、等しい要素が各ラウンドで 1 回しか選ばれないようにします。</li>
+<li><span class="arithmatex">\(n\)</span> クイーン問題の目的は、<span class="arithmatex">\(n \times n\)</span> の盤面に <span class="arithmatex">\(n\)</span> 個のクイーンを配置する方法を見つけることであり、どの 2 つのクイーンも互いに攻撃できないことが条件です。この問題の制約には行制約、列制約、主対角線制約、副対角線制約があります。行制約を満たすため、行ごとに配置する戦略を採用し、各行に 1 個のクイーンを置くことを保証します。</li>
+<li>列制約と対角線制約の扱い方は似ています。列制約については、各列にクイーンが存在するかどうかを配列で記録し、選択したマスが有効かどうかを判定します。対角線制約については、主対角線と副対角線それぞれにクイーンが存在するかを 2 つの配列で記録します。難点は、同じ主対角線または副対角線上にあるマスが満たす行列インデックスの規則を見つけることにあります。</li>
 </ul>
 <h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
-<p><strong>Q</strong>: バックトラッキングと再帰の関係をどのように理解すればよいですか？</p>
-<p>全体的に、バックトラッキングは「アルゴリズム戦略」であり、再帰はより「ツール」です。</p>
+<p><strong>Q</strong>：バックトラッキングと再帰の関係はどのように理解すればよいですか？</p>
+<p>全体として見ると、バックトラッキングは「アルゴリズム戦略」の一種であり、再帰はむしろ「道具」に近いものです。</p>
 <ul>
-<li>バックトラッキングアルゴリズムは通常再帰に基づいています。しかし、バックトラッキングは再帰の応用シナリオの一つであり、特に検索問題においてです。</li>
-<li>再帰の構造は「部分問題分解」の問題解決パラダイムを反映します。分割統治、バックトラッキング、動的プログラミング（メモ化再帰）を含む問題の解決でよく使用されます。</li>
+<li>バックトラッキングアルゴリズムは通常、再帰に基づいて実装されます。ただし、バックトラッキングは再帰の応用場面の 1 つであり、探索問題における再帰の応用です。</li>
+<li>再帰の構造は「部分問題への分解」という問題解決パラダイムを表しており、分割統治、バックトラッキング、動的計画法（メモ化再帰）などの問題によく用いられます。</li>
 </ul>
 
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     href="../n_queens_problem/"
     class="md-footer__link md-footer__link--prev"
-    aria-label="前: 13.4 &amp;nbsp; Nクイーン問題"
+    aria-label="前: 13.4 &amp;nbsp; n クイーン問題"
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     </div>
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@@ -4421,7 +4421,7 @@ aria-label="フッター"
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     href="../../chapter_dynamic_programming/"
     class="md-footer__link md-footer__link--next"
-    aria-label="次: 第 14 章 &amp;nbsp; 動的プログラミング"
+    aria-label="次: 第 14 章 &amp;nbsp; 動的計画法"
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+        第 14 章 &nbsp; 動的計画法
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@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -39,7 +39,7 @@
     
     
       
-        <title>第 2 章 複雑度解析 - Hello アルゴリズム</title>
+        <title>第 2 章 計算量解析 - Hello アルゴリズム</title>
       
     
     
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
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         <div class="md-header__topic" data-md-component="header-topic">
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-              第 2 章 &nbsp; 複雑度解析
+              第 2 章 &nbsp; 計算量解析
             
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-    序
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+    8.2 &nbsp; ヒープ構築
   
 
     
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+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
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-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3171,7 +3171,7 @@
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3199,7 +3199,7 @@
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-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3392,7 +3392,7 @@
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-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
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-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
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-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
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-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
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   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
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+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4273,16 +4273,16 @@
 
 
 <!-- Page content -->
-<h1 id="2">第 2 章 &nbsp; 複雑度解析<a class="headerlink" href="#2" title="Permanent link">&para;</a></h1>
-<p><img alt="Complexity analysis" class="cover-image" src="../assets/covers/chapter_complexity_analysis.jpg" /></p>
+<h1 id="2">第 2 章 &nbsp; 計算量解析<a class="headerlink" href="#2" title="Permanent link">&para;</a></h1>
+<p><img alt="計算量解析" class="cover-image" src="../assets/covers/chapter_complexity_analysis.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>複雑度解析は、アルゴリズムの広大な宇宙における時空のナビゲーターのようなものです。</p>
-<p>時間と空間の次元をより深く探求し、より優雅な解決策を求めるためのガイドとなります。</p>
+<p>計算量解析は、広大なアルゴリズム宇宙における時空の案内人のようなものです。</p>
+<p>それは、時間と空間という二つの次元で私たちをより深く探求へ導き、より洗練された解決策を見つけ出します。</p>
 </div>
 <h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
-<li><a href="performance_evaluation/">2.1 &nbsp; アルゴリズムの効率評価</a></li>
+<li><a href="performance_evaluation/">2.1 &nbsp; アルゴリズム効率の評価</a></li>
 <li><a href="iteration_and_recursion/">2.2 &nbsp; 反復と再帰</a></li>
 <li><a href="time_complexity/">2.3 &nbsp; 時間計算量</a></li>
 <li><a href="space_complexity/">2.4 &nbsp; 空間計算量</a></li>
@@ -4334,7 +4334,7 @@ aria-label="フッター"
   <a
     href="./performance_evaluation/"
     class="md-footer__link md-footer__link--next"
-    aria-label="次: 2.1 &amp;nbsp; アルゴリズムの効率評価"
+    aria-label="次: 2.1 &amp;nbsp; アルゴリズム効率の評価"
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         次
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-        2.1 &nbsp; アルゴリズムの効率評価
+        2.1 &nbsp; アルゴリズム効率の評価
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@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
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     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
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-    序
+    はじめに
   
 
     
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+    はじめに
   
 
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-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
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-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
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   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
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-        1. &nbsp; forループ
+        1. &nbsp; for ループ
       
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-        2. &nbsp; whileループ
+        2. &nbsp; while ループ
       
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@@ -970,7 +970,7 @@
   <a href="#223" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2.2.3 &nbsp; 比較
+        2.2.3 &nbsp; 両者の比較
       
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   </a>
@@ -1221,7 +1221,7 @@
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-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
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-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
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-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
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-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
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+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
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   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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+    13.3 &nbsp; 部分和問題
   
 
     
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-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
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-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
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-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
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-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
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-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3997,7 +3997,7 @@
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4242,7 +4242,7 @@
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
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   <a href="#1-for" class="md-nav__link">
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+        1. &nbsp; for ループ
       
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-        2.2.3 &nbsp; 比較
+        2.2.3 &nbsp; 両者の比較
       
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@@ -4533,19 +4533,19 @@
 
 <!-- Page content -->
 <h1 id="22">2.2 &nbsp; 反復と再帰<a class="headerlink" href="#22" title="Permanent link">&para;</a></h1>
-<p>アルゴリズムにおいて、タスクの繰り返し実行は非常に一般的であり、複雑度の分析と密接に関係しています。したがって、時間計算量と空間計算量の概念を詳しく学ぶ前に、まずプログラミングで繰り返しタスクを実装する方法を探究しましょう。これには、2つの基本的なプログラミング制御構造である反復と再帰の理解が含まれます。</p>
+<p>アルゴリズムでは、ある処理を繰り返し実行することがよくあり、これは複雑度解析と密接に関係しています。そのため、時間計算量と空間計算量を紹介する前に、まずプログラム内で反復実行を実現する方法、つまり 2 つの基本的な制御構造である反復と再帰について見ていきます。</p>
 <h2 id="221">2.2.1 &nbsp; 反復<a class="headerlink" href="#221" title="Permanent link">&para;</a></h2>
-<p><u>反復</u>は、タスクを繰り返し実行するための制御構造です。反復では、プログラムは特定の条件が満たされている限りコードブロックを繰り返し実行し、この条件が満たされなくなるまで続けます。</p>
-<h3 id="1-for">1. &nbsp; forループ<a class="headerlink" href="#1-for" title="Permanent link">&para;</a></h3>
-<p><code>for</code>ループは反復の最も一般的な形式の1つであり、<strong>反復回数が事前に分かっている場合に特に適しています</strong>。</p>
-<p>以下の関数は<code>for</code>ループを使用して<span class="arithmatex">\(1 + 2 + \dots + n\)</span>の合計を実行し、合計を変数<code>res</code>に格納します。Pythonでは、<code>range(a, b)</code>は<code>a</code>を含み<code>b</code>を除く区間を作成することに注意してください。つまり、<span class="arithmatex">\(a\)</span>から<span class="arithmatex">\(b−1\)</span>までの範囲で反復します。</p>
+<p><u>反復（iteration）</u>は、ある処理を繰り返し実行するための制御構造です。反復では、プログラムは一定の条件を満たす間、あるコード片を繰り返し実行し、その条件を満たさなくなるまで続けます。</p>
+<h3 id="1-for">1. &nbsp; for ループ<a class="headerlink" href="#1-for" title="Permanent link">&para;</a></h3>
+<p><code>for</code> ループは最も一般的な反復形式の 1 つで、<strong>反復回数があらかじめ分かっている場合に適しています</strong>。</p>
+<p>次の関数は <code>for</code> ループを用いて <span class="arithmatex">\(1 + 2 + \dots + n\)</span> の総和を計算しており、その結果は変数 <code>res</code> に記録されます。なお、Python の <code>range(a, b)</code> に対応する区間は「左閉右開」であり、走査範囲は <span class="arithmatex">\(a, a + 1, \dots, b-1\)</span> です。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
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 <div class="highlight"><span class="filename">iteration.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">for_loop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;forループ&quot;&quot;&quot;</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;for ループ&quot;&quot;&quot;</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="n">res</span> <span class="o">=</span> <span class="mi">0</span>
-<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="c1"># 1, 2, ..., n-1, n の合計をループ</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="c1"># 1, 2, ..., n-1, n を順に加算する</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="n">res</span> <span class="o">+=</span> <span class="n">i</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="k">return</span> <span class="n">res</span>
@@ -4555,7 +4555,7 @@
 <div class="highlight"><span class="filename">iteration.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* for ループ */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">forLoop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n の合計をループ計算</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n を順に加算する</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="p">}</span>
@@ -4567,7 +4567,7 @@
 <div class="highlight"><span class="filename">iteration.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* for ループ */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">forLoop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n の合計をループ計算</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n を順に加算する</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="p">}</span>
@@ -4576,66 +4576,153 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">iteration</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">ForLoop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* for ループ */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">ForLoop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n を順に加算する</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">forLoop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* for ループ */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">forLoop</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n を順に加算する</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">        </span><span class="nx">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">i</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">forLoop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* for ループ */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">forLoop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n を順に加算する</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">forLoop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* for ループ */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">forLoop</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n を順に加算する</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">        </span><span class="nx">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">forLoop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* for ループ */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">forLoop</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n を順に加算する</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">        </span><span class="nx">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">forLoop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* for ループ */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">forLoop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="c1">// 1, 2, ..., n-1, n を順に加算する</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">    </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">for_loop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* for ループ */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">for_loop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n を順に加算する</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="n">res</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">forLoop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* for ループ */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">forLoop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n を順に加算する</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">forLoop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* for ループ */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">forLoop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n を順に加算する</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">for_loop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### for ループ ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">for_loop</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="c1"># 1, 2, ..., n-1, n を順に加算する</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..</span><span class="n">n</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">    </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">  </span><span class="n">res</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>以下の図はこの合計関数を表しています。</p>
-<p><img alt="Flowchart of the sum function" class="animation-figure" src="../iteration_and_recursion.assets/iteration.png" /></p>
-<p align="center"> 図 2-1 &nbsp; Flowchart of the sum function </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 405px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20for_loop%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22for%20%E3%83%AB%E3%83%BC%E3%83%97%22%22%22%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20%23%201%2C%202%2C%20...%2C%20n-1%2C%20n%20%E3%82%92%E9%A0%86%E3%81%AB%E5%8A%A0%E7%AE%97%E3%81%99%E3%82%8B%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20res%20%2B%3D%20i%0A%20%20%20%20return%20res%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20for_loop%28n%29%0A%20%20%20%20print%28f%22%5Cnfor%20%E3%83%AB%E3%83%BC%E3%83%97%E3%81%AE%E5%90%88%E8%A8%88%E7%B5%90%E6%9E%9C%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20for_loop%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22for%20%E3%83%AB%E3%83%BC%E3%83%97%22%22%22%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20%23%201%2C%202%2C%20...%2C%20n-1%2C%20n%20%E3%82%92%E9%A0%86%E3%81%AB%E5%8A%A0%E7%AE%97%E3%81%99%E3%82%8B%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20res%20%2B%3D%20i%0A%20%20%20%20return%20res%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20for_loop%28n%29%0A%20%20%20%20print%28f%22%5Cnfor%20%E3%83%AB%E3%83%BC%E3%83%97%E3%81%AE%E5%90%88%E8%A8%88%E7%B5%90%E6%9E%9C%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>次の図は、この総和関数のフローチャートです。</p>
+<p><img alt="総和関数のフローチャート" class="animation-figure" src="../iteration_and_recursion.assets/iteration.png" /></p>
+<p align="center"> 図 2-1 &nbsp; 総和関数のフローチャート </p>
 
-<p>この合計関数での操作数は入力データのサイズ<span class="arithmatex">\(n\)</span>に比例する、つまり線形関係があります。<strong>この「線形関係」こそが時間計算量が記述するものです</strong>。このトピックについては次のセクションで詳しく説明します。</p>
-<h3 id="2-while">2. &nbsp; whileループ<a class="headerlink" href="#2-while" title="Permanent link">&para;</a></h3>
-<p><code>for</code>ループと同様に、<code>while</code>ループは反復を実装するためのもう1つのアプローチです。<code>while</code>ループでは、プログラムは各反復の開始時に条件をチェックし、条件が真の場合は実行を継続し、そうでなければループを終了します。</p>
-<p>以下では<code>while</code>ループを使用して合計<span class="arithmatex">\(1 + 2 + \dots + n\)</span>を実装します。</p>
+<p>この総和関数の操作回数は入力データサイズ <span class="arithmatex">\(n\)</span> に比例し、言い換えれば「線形関係」にあります。実際、<strong>時間計算量が記述するのはこの「線形関係」そのものです</strong>。関連内容は次節で詳しく説明します。</p>
+<h3 id="2-while">2. &nbsp; while ループ<a class="headerlink" href="#2-while" title="Permanent link">&para;</a></h3>
+<p><code>for</code> ループと同様に、<code>while</code> ループも反復を実現する方法の 1 つです。<code>while</code> ループでは、各反復のたびにまず条件を確認し、条件が真であれば実行を続け、そうでなければループを終了します。</p>
+<p>次に、<code>while</code> ループを使って <span class="arithmatex">\(1 + 2 + \dots + n\)</span> の総和を求めてみましょう。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">iteration.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">while_loop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;whileループ&quot;&quot;&quot;</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;while ループ&quot;&quot;&quot;</span>
 <a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="n">res</span> <span class="o">=</span> <span class="mi">0</span>
-<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="n">i</span> <span class="o">=</span> <span class="mi">1</span>  <span class="c1"># 条件変数を初期化</span>
-<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># 1, 2, ..., n-1, n の合計をループ</span>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="n">i</span> <span class="o">=</span> <span class="mi">1</span>  <span class="c1"># 条件変数を初期化する</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># 1, 2, ..., n-1, n を順に加算する</span>
 <a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>    <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;=</span> <span class="n">n</span><span class="p">:</span>
 <a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>        <span class="n">res</span> <span class="o">+=</span> <span class="n">i</span>
-<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>        <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>  <span class="c1"># 条件変数を更新</span>
+<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>        <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>  <span class="c1"># 条件変数を更新する</span>
 <a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>    <span class="k">return</span> <span class="n">res</span>
 </code></pre></div>
 </div>
@@ -4643,11 +4730,11 @@
 <div class="highlight"><span class="filename">iteration.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* while ループ */</span>
 <a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">whileLoop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を初期化</span>
-<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n の合計をループ計算</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を初期化する</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n を順に加算する</span>
 <a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
-<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">        </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を更新</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">        </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を更新する</span>
 <a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
 <a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="p">}</span>
@@ -4657,85 +4744,195 @@
 <div class="highlight"><span class="filename">iteration.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* while ループ */</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">whileLoop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を初期化</span>
-<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n の合計をループ計算</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を初期化する</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n を順に加算する</span>
 <a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
-<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">        </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を更新</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">        </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を更新する</span>
 <a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
 <a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">iteration</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">WhileLoop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* while ループ */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">WhileLoop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を初期化する</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n を順に加算する</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を更新する</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">whileLoop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* while ループ */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">whileLoop</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="c1">// 条件変数を初期化する</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">    </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n を順に加算する</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">        </span><span class="nx">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">i</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">        </span><span class="c1">// 条件変数を更新する</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">        </span><span class="nx">i</span><span class="o">++</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">whileLoop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* while ループ */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">whileLoop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// 条件変数を初期化する</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n を順に加算する</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// 条件変数を更新する</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">whileLoop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* while ループ */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">whileLoop</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を初期化する</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n を順に加算する</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">        </span><span class="nx">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">        </span><span class="nx">i</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を更新する</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">whileLoop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* while ループ */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">whileLoop</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を初期化する</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n を順に加算する</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">        </span><span class="nx">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">        </span><span class="nx">i</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を更新する</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">whileLoop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* while ループ */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">whileLoop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を初期化する</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">  </span><span class="c1">// 1, 2, ..., n-1, n を順に加算する</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">    </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">    </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を更新する</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">while_loop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* while ループ */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">while_loop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を初期化する</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n を順に加算する</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を更新する</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w">    </span><span class="n">res</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">whileLoop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* while ループ */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">whileLoop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を初期化する</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n を順に加算する</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w">        </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を更新する</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">whileLoop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* while ループ */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">whileLoop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="c1">// 条件変数を初期化する</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n を順に加算する</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w">        </span><span class="n">i</span><span class="o">++</span><span class="w"> </span><span class="c1">// 条件変数を更新する</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">while_loop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### while ループ ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">while_loop</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">  </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># 条件変数を初期化する</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">  </span><span class="c1"># 1, 2, ..., n-1, n を順に加算する</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w">    </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">    </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># 条件変数を更新する</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w">  </span><span class="n">res</span>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p><strong><code>while</code>ループは<code>for</code>ループよりも柔軟性を提供します</strong>。特に、条件変数のカスタム初期化と各ステップでの変更が可能です。</p>
-<p>例えば、以下のコードでは、条件変数<span class="arithmatex">\(i\)</span>が各ラウンドで2回更新されますが、これは<code>for</code>ループでは実装が不便です。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 441px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20while_loop%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22while%20%E3%83%AB%E3%83%BC%E3%83%97%22%22%22%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20i%20%3D%201%20%20%23%20%E6%9D%A1%E4%BB%B6%E5%A4%89%E6%95%B0%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20%23%201%2C%202%2C%20...%2C%20n-1%2C%20n%20%E3%82%92%E9%A0%86%E3%81%AB%E5%8A%A0%E7%AE%97%E3%81%99%E3%82%8B%0A%20%20%20%20while%20i%20%3C%3D%20n%3A%0A%20%20%20%20%20%20%20%20res%20%2B%3D%20i%0A%20%20%20%20%20%20%20%20i%20%2B%3D%201%20%20%23%20%E6%9D%A1%E4%BB%B6%E5%A4%89%E6%95%B0%E3%82%92%E6%9B%B4%E6%96%B0%E3%81%99%E3%82%8B%0A%20%20%20%20return%20res%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20while_loop%28n%29%0A%20%20%20%20print%28f%22%5Cnwhile%20%E3%83%AB%E3%83%BC%E3%83%97%E3%81%AE%E5%90%88%E8%A8%88%E7%B5%90%E6%9E%9C%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20while_loop%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22while%20%E3%83%AB%E3%83%BC%E3%83%97%22%22%22%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20i%20%3D%201%20%20%23%20%E6%9D%A1%E4%BB%B6%E5%A4%89%E6%95%B0%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20%23%201%2C%202%2C%20...%2C%20n-1%2C%20n%20%E3%82%92%E9%A0%86%E3%81%AB%E5%8A%A0%E7%AE%97%E3%81%99%E3%82%8B%0A%20%20%20%20while%20i%20%3C%3D%20n%3A%0A%20%20%20%20%20%20%20%20res%20%2B%3D%20i%0A%20%20%20%20%20%20%20%20i%20%2B%3D%201%20%20%23%20%E6%9D%A1%E4%BB%B6%E5%A4%89%E6%95%B0%E3%82%92%E6%9B%B4%E6%96%B0%E3%81%99%E3%82%8B%0A%20%20%20%20return%20res%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20while_loop%28n%29%0A%20%20%20%20print%28f%22%5Cnwhile%20%E3%83%AB%E3%83%BC%E3%83%97%E3%81%AE%E5%90%88%E8%A8%88%E7%B5%90%E6%9E%9C%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>**<code>while</code> ループは <code>for</code> ループより自由度が高い**です。<code>while</code> ループでは、条件変数の初期化や更新手順を柔軟に設計できます。</p>
+<p>たとえば次のコードでは、条件変数 <span class="arithmatex">\(i\)</span> が各反復で 2 回更新されており、このようなケースは <code>for</code> ループではあまり扱いやすくありません。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">iteration.py</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">while_loop_ii</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;whileループ（2つの更新）&quot;&quot;&quot;</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;while ループ（2回更新）&quot;&quot;&quot;</span>
 <a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>    <span class="n">res</span> <span class="o">=</span> <span class="mi">0</span>
-<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>    <span class="n">i</span> <span class="o">=</span> <span class="mi">1</span>  <span class="c1"># 条件変数を初期化</span>
-<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a>    <span class="c1"># 1, 4, 10, ... の合計をループ</span>
+<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>    <span class="n">i</span> <span class="o">=</span> <span class="mi">1</span>  <span class="c1"># 条件変数を初期化する</span>
+<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a>    <span class="c1"># 1, 4, 10, ... を順に加算する</span>
 <a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a>    <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;=</span> <span class="n">n</span><span class="p">:</span>
 <a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a>        <span class="n">res</span> <span class="o">+=</span> <span class="n">i</span>
-<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>        <span class="c1"># 条件変数を更新</span>
+<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>        <span class="c1"># 条件変数を更新する</span>
 <a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a>        <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
 <a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a>        <span class="n">i</span> <span class="o">*=</span> <span class="mi">2</span>
 <a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a>    <span class="k">return</span> <span class="n">res</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* while ループ（2つの更新） */</span>
+<div class="highlight"><span class="filename">iteration.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* while ループ（2回更新） */</span>
 <a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">whileLoopII</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を初期化</span>
-<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">    </span><span class="c1">// 1, 4, 10, ... の合計をループ計算</span>
+<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を初期化する</span>
+<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">    </span><span class="c1">// 1, 4, 10, ... を順に加算する</span>
 <a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
-<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w">        </span><span class="c1">// 条件変数を更新</span>
+<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w">        </span><span class="c1">// 条件変数を更新する</span>
 <a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="w">        </span><span class="n">i</span><span class="o">++</span><span class="p">;</span>
 <a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
 <a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="w">    </span><span class="p">}</span>
@@ -4744,14 +4941,14 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* while ループ（2つの更新） */</span>
+<div class="highlight"><span class="filename">iteration.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* while ループ（2回更新） */</span>
 <a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">whileLoopII</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を初期化</span>
-<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">    </span><span class="c1">// 1, 4, 10, ... の合計をループ計算</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を初期化する</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">    </span><span class="c1">// 1, 4, 10, ... を順に加算する</span>
 <a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
-<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">        </span><span class="c1">// 条件変数を更新</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">        </span><span class="c1">// 条件変数を更新する</span>
 <a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="w">        </span><span class="n">i</span><span class="o">++</span><span class="p">;</span>
 <a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
 <a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="w">    </span><span class="p">}</span>
@@ -4760,71 +4957,214 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">iteration</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">WhileLoopII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* while ループ（2回更新） */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">WhileLoopII</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を初期化する</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">    </span><span class="c1">// 1, 4, 10, ... を順に加算する</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">        </span><span class="c1">// 条件変数を更新する</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">whileLoopII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* while ループ（2回更新） */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">whileLoopII</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="c1">// 条件変数を初期化する</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">    </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="c1">// 1, 4, 10, ... を順に加算する</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">        </span><span class="nx">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">i</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w">        </span><span class="c1">// 条件変数を更新する</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w">        </span><span class="nx">i</span><span class="o">++</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w">        </span><span class="nx">i</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">whileLoopII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* while ループ（2回更新） */</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">whileLoopII</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// 条件変数を初期化する</span>
+<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w">    </span><span class="c1">// 1, 4, 10, ... を順に加算する</span>
+<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w">        </span><span class="c1">// 条件変数を更新する</span>
+<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">whileLoopII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* while ループ（2回更新） */</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">whileLoopII</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を初期化する</span>
+<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="w">    </span><span class="c1">// 1, 4, 10, ... を順に加算する</span>
+<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="w">        </span><span class="nx">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w">        </span><span class="c1">// 条件変数を更新する</span>
+<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="w">        </span><span class="nx">i</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-32-10" name="__codelineno-32-10" href="#__codelineno-32-10"></a><span class="w">        </span><span class="nx">i</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
+<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">whileLoopII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* while ループ（2回更新） */</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">whileLoopII</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を初期化する</span>
+<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w">    </span><span class="c1">// 1, 4, 10, ... を順に加算する</span>
+<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w">        </span><span class="nx">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w">        </span><span class="c1">// 条件変数を更新する</span>
+<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="w">        </span><span class="nx">i</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a><span class="w">        </span><span class="nx">i</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
+<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">whileLoopII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* while ループ（2回更新） */</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">whileLoopII</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を初期化する</span>
+<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w">  </span><span class="c1">// 1, 4, 10, ... を順に加算する</span>
+<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w">    </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w">    </span><span class="c1">// 条件変数を更新する</span>
+<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="w">    </span><span class="n">i</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-34-10" name="__codelineno-34-10" href="#__codelineno-34-10"></a><span class="w">    </span><span class="n">i</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
+<a id="__codelineno-34-11" name="__codelineno-34-11" href="#__codelineno-34-11"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-12" name="__codelineno-34-12" href="#__codelineno-34-12"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-34-13" name="__codelineno-34-13" href="#__codelineno-34-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">while_loop_ii</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* while ループ（2回更新） */</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">while_loop_ii</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を初期化する</span>
+<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a>
+<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="w">    </span><span class="c1">// 1, 4, 10, ... を順に加算する</span>
+<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="w">        </span><span class="c1">// 条件変数を更新する</span>
+<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-35-12" name="__codelineno-35-12" href="#__codelineno-35-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-13" name="__codelineno-35-13" href="#__codelineno-35-13"></a><span class="w">    </span><span class="n">res</span>
+<a id="__codelineno-35-14" name="__codelineno-35-14" href="#__codelineno-35-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">whileLoopII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* while ループ（2回更新） */</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">whileLoopII</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を初期化する</span>
+<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w">    </span><span class="c1">// 1, 4, 10, ... を順に加算する</span>
+<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="w">        </span><span class="c1">// 条件変数を更新する</span>
+<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="w">        </span><span class="n">i</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">whileLoopII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* while ループ（2回更新） */</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">whileLoopII</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="c1">// 条件変数を初期化する</span>
+<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w">    </span><span class="c1">// 1, 4, 10, ... を順に加算する</span>
+<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="w">        </span><span class="c1">// 条件変数を更新する</span>
+<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="w">        </span><span class="n">i</span><span class="o">++</span>
+<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="m">2</span>
+<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">while_loop_ii</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="c1">### while ループ ###</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">while_loop</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w">  </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># 条件変数を初期化する</span>
+<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a>
+<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w">  </span><span class="c1"># 1, 2, ..., n-1, n を順に加算する</span>
+<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span>
+<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="w">    </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="w">    </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># 条件変数を更新する</span>
+<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a>
+<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a><span class="w">  </span><span class="n">res</span>
+<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a><span class="k">end</span>
+<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a>
+<a id="__codelineno-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a><span class="c1"># ## while ループ（2 回更新）###</span>
+<a id="__codelineno-38-16" name="__codelineno-38-16" href="#__codelineno-38-16"></a><span class="k">def</span><span class="w"> </span><span class="nf">while_loop_ii</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-38-17" name="__codelineno-38-17" href="#__codelineno-38-17"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-38-18" name="__codelineno-38-18" href="#__codelineno-38-18"></a><span class="w">  </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># 条件変数を初期化する</span>
+<a id="__codelineno-38-19" name="__codelineno-38-19" href="#__codelineno-38-19"></a>
+<a id="__codelineno-38-20" name="__codelineno-38-20" href="#__codelineno-38-20"></a><span class="w">  </span><span class="c1"># 1, 4, 10, ... を順に加算する</span>
+<a id="__codelineno-38-21" name="__codelineno-38-21" href="#__codelineno-38-21"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span>
+<a id="__codelineno-38-22" name="__codelineno-38-22" href="#__codelineno-38-22"></a><span class="w">    </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-38-23" name="__codelineno-38-23" href="#__codelineno-38-23"></a><span class="w">    </span><span class="c1"># 条件変数を更新する</span>
+<a id="__codelineno-38-24" name="__codelineno-38-24" href="#__codelineno-38-24"></a><span class="w">    </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-38-25" name="__codelineno-38-25" href="#__codelineno-38-25"></a><span class="w">    </span><span class="n">i</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-38-26" name="__codelineno-38-26" href="#__codelineno-38-26"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-27" name="__codelineno-38-27" href="#__codelineno-38-27"></a>
+<a id="__codelineno-38-28" name="__codelineno-38-28" href="#__codelineno-38-28"></a><span class="w">  </span><span class="n">res</span>
+<a id="__codelineno-38-29" name="__codelineno-38-29" href="#__codelineno-38-29"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>全体的に、<strong><code>for</code>ループはより簡潔で、<code>while</code>ループはより柔軟です</strong>。どちらも反復構造を実装できます。どちらを使用するかは、問題の具体的な要件に基づいて決定する必要があります。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 477px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20while_loop_ii%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22while%20%E3%83%AB%E3%83%BC%E3%83%97%EF%BC%882%E5%9B%9E%E6%9B%B4%E6%96%B0%EF%BC%89%22%22%22%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20i%20%3D%201%20%20%23%20%E6%9D%A1%E4%BB%B6%E5%A4%89%E6%95%B0%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20%23%201%2C%204%2C%2010%2C%20...%20%E3%82%92%E9%A0%86%E3%81%AB%E5%8A%A0%E7%AE%97%E3%81%99%E3%82%8B%0A%20%20%20%20while%20i%20%3C%3D%20n%3A%0A%20%20%20%20%20%20%20%20res%20%2B%3D%20i%0A%20%20%20%20%20%20%20%20%23%20%E6%9D%A1%E4%BB%B6%E5%A4%89%E6%95%B0%E3%82%92%E6%9B%B4%E6%96%B0%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20i%20%2B%3D%201%0A%20%20%20%20%20%20%20%20i%20%2A%3D%202%0A%20%20%20%20return%20res%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20while_loop_ii%28n%29%0A%20%20%20%20print%28f%22%5Cnwhile%20%E3%83%AB%E3%83%BC%E3%83%97%EF%BC%882%20%E5%9B%9E%E6%9B%B4%E6%96%B0%EF%BC%89%E3%81%AE%E5%90%88%E8%A8%88%E7%B5%90%E6%9E%9C%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20while_loop_ii%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22while%20%E3%83%AB%E3%83%BC%E3%83%97%EF%BC%882%E5%9B%9E%E6%9B%B4%E6%96%B0%EF%BC%89%22%22%22%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20i%20%3D%201%20%20%23%20%E6%9D%A1%E4%BB%B6%E5%A4%89%E6%95%B0%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20%23%201%2C%204%2C%2010%2C%20...%20%E3%82%92%E9%A0%86%E3%81%AB%E5%8A%A0%E7%AE%97%E3%81%99%E3%82%8B%0A%20%20%20%20while%20i%20%3C%3D%20n%3A%0A%20%20%20%20%20%20%20%20res%20%2B%3D%20i%0A%20%20%20%20%20%20%20%20%23%20%E6%9D%A1%E4%BB%B6%E5%A4%89%E6%95%B0%E3%82%92%E6%9B%B4%E6%96%B0%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20i%20%2B%3D%201%0A%20%20%20%20%20%20%20%20i%20%2A%3D%202%0A%20%20%20%20return%20res%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20while_loop_ii%28n%29%0A%20%20%20%20print%28f%22%5Cnwhile%20%E3%83%AB%E3%83%BC%E3%83%97%EF%BC%882%20%E5%9B%9E%E6%9B%B4%E6%96%B0%EF%BC%89%E3%81%AE%E5%90%88%E8%A8%88%E7%B5%90%E6%9E%9C%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>総じて、**<code>for</code> ループのコードはより簡潔で、<code>while</code> ループはより柔軟**です。どちらも反復構造を実現できますが、どちらを使うかは問題ごとの要件に応じて決めるべきです。</p>
 <h3 id="3">3. &nbsp; ネストしたループ<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
-<p>1つのループ構造を別のループ構造内にネストできます。以下は<code>for</code>ループを使用した例です：</p>
+<p>1 つのループ構造の中に別のループ構造を入れ子にできます。以下では <code>for</code> ループを例にします。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="4:13"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">iteration.py</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">nested_for_loop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">str</span><span class="p">:</span>
-<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二重forループ&quot;&quot;&quot;</span>
+<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二重 for ループ&quot;&quot;&quot;</span>
 <a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a>    <span class="n">res</span> <span class="o">=</span> <span class="s2">&quot;&quot;</span>
-<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a>    <span class="c1"># i = 1, 2, ..., n-1, n をループ</span>
+<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a>    <span class="c1"># i = 1, 2, ..., n-1, n とループする</span>
 <a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
-<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a>        <span class="c1"># j = 1, 2, ..., n-1, n をループ</span>
+<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a>        <span class="c1"># j = 1, 2, ..., n-1, n とループする</span>
 <a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a>            <span class="n">res</span> <span class="o">+=</span> <span class="sa">f</span><span class="s2">&quot;(</span><span class="si">{</span><span class="n">i</span><span class="si">}</span><span class="s2">, </span><span class="si">{</span><span class="n">j</span><span class="si">}</span><span class="s2">), &quot;</span>
 <a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a>    <span class="k">return</span> <span class="n">res</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.cpp</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* 2重 for ループ */</span>
+<div class="highlight"><span class="filename">iteration.cpp</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* 二重 for ループ */</span>
 <a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="n">string</span><span class="w"> </span><span class="nf">nestedForLoop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w">    </span><span class="n">ostringstream</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
-<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w">    </span><span class="c1">// ループ i = 1, 2, ..., n-1, n</span>
+<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w">    </span><span class="c1">// i = 1, 2, ..., n-1, n とループする</span>
 <a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w">        </span><span class="c1">// ループ j = 1, 2, ..., n-1, n</span>
+<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w">        </span><span class="c1">// j = 1, 2, ..., n-1, n とループする</span>
 <a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w">            </span><span class="n">res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;(&quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;, &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;), &quot;</span><span class="p">;</span>
 <a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w">        </span><span class="p">}</span>
@@ -4834,12 +5174,12 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.java</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 2重 for ループ */</span>
+<div class="highlight"><span class="filename">iteration.java</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 二重 for ループ */</span>
 <a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="n">String</span><span class="w"> </span><span class="nf">nestedForLoop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w">    </span><span class="n">StringBuilder</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">StringBuilder</span><span class="p">();</span>
-<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w">    </span><span class="c1">// ループ i = 1, 2, ..., n-1, n</span>
+<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w">    </span><span class="c1">// i = 1, 2, ..., n-1, n とループする</span>
 <a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a><span class="w">        </span><span class="c1">// ループ j = 1, 2, ..., n-1, n</span>
+<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a><span class="w">        </span><span class="c1">// j = 1, 2, ..., n-1, n とループする</span>
 <a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="na">append</span><span class="p">(</span><span class="s">&quot;(&quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot;, &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot;), &quot;</span><span class="p">);</span>
 <a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="w">        </span><span class="p">}</span>
@@ -4849,66 +5189,187 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.cs</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">iteration</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">NestedForLoop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.cs</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="cm">/* 二重 for ループ */</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="kt">string</span><span class="w"> </span><span class="nf">NestedForLoop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="w">    </span><span class="n">StringBuilder</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">();</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w">    </span><span class="c1">// i = 1, 2, ..., n-1, n とループする</span>
+<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a><span class="w">        </span><span class="c1">// j = 1, 2, ..., n-1, n とループする</span>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="n">Append</span><span class="p">(</span><span class="s">$&quot;({i}, {j}), &quot;</span><span class="p">);</span>
+<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">ToString</span><span class="p">();</span>
+<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.go</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">nestedForLoop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.go</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* 二重 for ループ */</span>
+<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">nestedForLoop</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">string</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w">    </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="s">&quot;&quot;</span>
+<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">    </span><span class="c1">// i = 1, 2, ..., n-1, n とループする</span>
+<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="w">            </span><span class="c1">// j = 1, 2, ..., n-1, n とループする</span>
+<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w">            </span><span class="nx">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Sprintf</span><span class="p">(</span><span class="s">&quot;(%d, %d), &quot;</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span>
+<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
+<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.swift</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">nestedForLoop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.swift</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* 二重 for ループ */</span>
+<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">nestedForLoop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">String</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;&quot;</span>
+<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">    </span><span class="c1">// i = 1, 2, ..., n-1, n とループする</span>
+<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w">        </span><span class="c1">// j = 1, 2, ..., n-1, n とループする</span>
+<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="s">&quot;(</span><span class="si">\(</span><span class="n">i</span><span class="si">)</span><span class="s">, </span><span class="si">\(</span><span class="n">j</span><span class="si">)</span><span class="s">), &quot;</span><span class="p">)</span>
+<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.js</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">nestedForLoop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.js</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="cm">/* 二重 for ループ */</span>
+<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">nestedForLoop</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s1">&#39;&#39;</span><span class="p">;</span>
+<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w">    </span><span class="c1">// i = 1, 2, ..., n-1, n とループする</span>
+<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w">        </span><span class="c1">// j = 1, 2, ..., n-1, n とループする</span>
+<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="w">            </span><span class="nx">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="sb">`(</span><span class="si">${</span><span class="nx">i</span><span class="si">}</span><span class="sb">, </span><span class="si">${</span><span class="nx">j</span><span class="si">}</span><span class="sb">), `</span><span class="p">;</span>
+<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.ts</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">nestedForLoop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.ts</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="cm">/* 二重 for ループ */</span>
+<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">nestedForLoop</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s1">&#39;&#39;</span><span class="p">;</span>
+<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w">    </span><span class="c1">// i = 1, 2, ..., n-1, n とループする</span>
+<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a><span class="w">        </span><span class="c1">// j = 1, 2, ..., n-1, n とループする</span>
+<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a><span class="w">            </span><span class="nx">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="sb">`(</span><span class="si">${</span><span class="nx">i</span><span class="si">}</span><span class="sb">, </span><span class="si">${</span><span class="nx">j</span><span class="si">}</span><span class="sb">), `</span><span class="p">;</span>
+<a id="__codelineno-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-46-12" name="__codelineno-46-12" href="#__codelineno-46-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.dart</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">nestedForLoop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.dart</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* 二重 for ループ */</span>
+<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="kt">String</span><span class="w"> </span><span class="n">nestedForLoop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w">  </span><span class="kt">String</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;&quot;</span><span class="p">;</span>
+<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w">  </span><span class="c1">// i = 1, 2, ..., n-1, n とループする</span>
+<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a><span class="w">    </span><span class="c1">// j = 1, 2, ..., n-1, n とループする</span>
+<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a><span class="w">      </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="s2">&quot;(</span><span class="si">$</span><span class="n">i</span><span class="s2">, </span><span class="si">$</span><span class="n">j</span><span class="s2">), &quot;</span><span class="p">;</span>
+<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.rs</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">nested_for_loop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.rs</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="cm">/* 二重 for ループ */</span>
+<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">nested_for_loop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">String</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span>
+<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a><span class="w">    </span><span class="c1">// i = 1, 2, ..., n-1, n とループする</span>
+<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a><span class="w">        </span><span class="c1">// j = 1, 2, ..., n-1, n とループする</span>
+<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="fm">format!</span><span class="p">(</span><span class="s">&quot;({}, {}), &quot;</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">));</span>
+<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-48-11" name="__codelineno-48-11" href="#__codelineno-48-11"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">join</span><span class="p">(</span><span class="s">&quot;&quot;</span><span class="p">)</span>
+<a id="__codelineno-48-12" name="__codelineno-48-12" href="#__codelineno-48-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.c</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">nestedForLoop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.c</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* 二重 for ループ */</span>
+<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="nf">nestedForLoop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="w">    </span><span class="c1">// n * n は対応する点の個数であり、&quot;(i, j), &quot; に対応する文字列長の最大は 6+10*2 で、さらに末尾の空文字 \0 のための追加領域が必要</span>
+<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">26</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="w">    </span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="n">size</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">char</span><span class="p">));</span>
+<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a><span class="w">    </span><span class="c1">// i = 1, 2, ..., n-1, n とループする</span>
+<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="w">        </span><span class="c1">// j = 1, 2, ..., n-1, n とループする</span>
+<a id="__codelineno-49-9" name="__codelineno-49-9" href="#__codelineno-49-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-10" name="__codelineno-49-10" href="#__codelineno-49-10"></a><span class="w">            </span><span class="kt">char</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="mi">26</span><span class="p">];</span>
+<a id="__codelineno-49-11" name="__codelineno-49-11" href="#__codelineno-49-11"></a><span class="w">            </span><span class="n">snprintf</span><span class="p">(</span><span class="n">tmp</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="n">tmp</span><span class="p">),</span><span class="w"> </span><span class="s">&quot;(%d, %d), &quot;</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span>
+<a id="__codelineno-49-12" name="__codelineno-49-12" href="#__codelineno-49-12"></a><span class="w">            </span><span class="n">strncat</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">tmp</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">strlen</span><span class="p">(</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-49-13" name="__codelineno-49-13" href="#__codelineno-49-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-49-14" name="__codelineno-49-14" href="#__codelineno-49-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-49-15" name="__codelineno-49-15" href="#__codelineno-49-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-49-16" name="__codelineno-49-16" href="#__codelineno-49-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.kt</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">nestedForLoop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.kt</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* 二重 for ループ */</span>
+<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">nestedForLoop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">String</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">StringBuilder</span><span class="p">()</span>
+<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w">    </span><span class="c1">// i = 1, 2, ..., n-1, n とループする</span>
+<a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a><span class="w">        </span><span class="c1">// j = 1, 2, ..., n-1, n とループする</span>
+<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="na">append</span><span class="p">(</span><span class="s">&quot; (</span><span class="si">$</span><span class="n">i</span><span class="s">, </span><span class="si">$</span><span class="n">j</span><span class="s">), &quot;</span><span class="p">)</span>
+<a id="__codelineno-50-9" name="__codelineno-50-9" href="#__codelineno-50-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-50-10" name="__codelineno-50-10" href="#__codelineno-50-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-50-11" name="__codelineno-50-11" href="#__codelineno-50-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">toString</span><span class="p">()</span>
+<a id="__codelineno-50-12" name="__codelineno-50-12" href="#__codelineno-50-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">iteration.rb</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">nested_for_loop</span><span class="p">}</span>
+<div class="highlight"><span class="filename">iteration.rb</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="c1">### 二重 for ループ ###</span>
+<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">nested_for_loop</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;&quot;</span>
+<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a>
+<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w">  </span><span class="c1"># i = 1, 2, ..., n-1, n とループする</span>
+<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..</span><span class="n">n</span>
+<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="w">    </span><span class="c1"># j = 1, 2, ..., n-1, n とループする</span>
+<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..</span><span class="n">n</span>
+<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a><span class="w">      </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="s2">&quot;(</span><span class="si">#{</span><span class="n">i</span><span class="si">}</span><span class="s2">, </span><span class="si">#{</span><span class="n">j</span><span class="si">}</span><span class="s2">), &quot;</span>
+<a id="__codelineno-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-51-11" name="__codelineno-51-11" href="#__codelineno-51-11"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-51-12" name="__codelineno-51-12" href="#__codelineno-51-12"></a>
+<a id="__codelineno-51-13" name="__codelineno-51-13" href="#__codelineno-51-13"></a><span class="w">  </span><span class="n">res</span>
+<a id="__codelineno-51-14" name="__codelineno-51-14" href="#__codelineno-51-14"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>以下の図はこのネストしたループを表しています。</p>
-<p><img alt="Flowchart of the nested loop" class="animation-figure" src="../iteration_and_recursion.assets/nested_iteration.png" /></p>
-<p align="center"> 図 2-2 &nbsp; Flowchart of the nested loop </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 441px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20nested_for_loop%28n%3A%20int%29%20-%3E%20str%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E9%87%8D%20for%20%E3%83%AB%E3%83%BC%E3%83%97%22%22%22%0A%20%20%20%20res%20%3D%20%22%22%0A%20%20%20%20%23%20i%20%3D%201%2C%202%2C%20...%2C%20n-1%2C%20n%20%E3%81%A8%E3%83%AB%E3%83%BC%E3%83%97%E3%81%99%E3%82%8B%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%23%20j%20%3D%201%2C%202%2C%20...%2C%20n-1%2C%20n%20%E3%81%A8%E3%83%AB%E3%83%BC%E3%83%97%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20res%20%2B%3D%20f%22%28%7Bi%7D%2C%20%7Bj%7D%29%2C%20%22%0A%20%20%20%20return%20res%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20nested_for_loop%28n%29%0A%20%20%20%20print%28f%22%5Cn%E4%BA%8C%E9%87%8D%20for%20%E3%83%AB%E3%83%BC%E3%83%97%E3%81%AE%E8%B5%B0%E6%9F%BB%E7%B5%90%E6%9E%9C%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20nested_for_loop%28n%3A%20int%29%20-%3E%20str%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E9%87%8D%20for%20%E3%83%AB%E3%83%BC%E3%83%97%22%22%22%0A%20%20%20%20res%20%3D%20%22%22%0A%20%20%20%20%23%20i%20%3D%201%2C%202%2C%20...%2C%20n-1%2C%20n%20%E3%81%A8%E3%83%AB%E3%83%BC%E3%83%97%E3%81%99%E3%82%8B%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%23%20j%20%3D%201%2C%202%2C%20...%2C%20n-1%2C%20n%20%E3%81%A8%E3%83%AB%E3%83%BC%E3%83%97%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20res%20%2B%3D%20f%22%28%7Bi%7D%2C%20%7Bj%7D%29%2C%20%22%0A%20%20%20%20return%20res%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20nested_for_loop%28n%29%0A%20%20%20%20print%28f%22%5Cn%E4%BA%8C%E9%87%8D%20for%20%E3%83%AB%E3%83%BC%E3%83%97%E3%81%AE%E8%B5%B0%E6%9F%BB%E7%B5%90%E6%9E%9C%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>次の図は、このネストしたループのフローチャートです。</p>
+<p><img alt="ネストしたループのフローチャート" class="animation-figure" src="../iteration_and_recursion.assets/nested_iteration.png" /></p>
+<p align="center"> 図 2-2 &nbsp; ネストしたループのフローチャート </p>
 
-<p>このような場合、関数の操作数は<span class="arithmatex">\(n^2\)</span>に比例します。つまり、アルゴリズムの実行時間と入力データのサイズ<span class="arithmatex">\(n\)</span>には「二次関係」があります。</p>
-<p>さらにネストしたループを追加することで複雑度を高めることができ、各レベルのネストは事実上「次元を増加」させ、時間計算量を「三次」、「四次」などに引き上げます。</p>
+<p>この場合、関数の操作回数は <span class="arithmatex">\(n^2\)</span> に比例し、言い換えればアルゴリズムの実行時間は入力データサイズ <span class="arithmatex">\(n\)</span> と「二次関係」にあります。</p>
+<p>さらにネストしたループを追加することもできます。ネストが 1 段増えるたびに「次元が 1 つ上がる」ことになり、時間計算量は「三次関係」「四次関係」へと高くなっていきます。</p>
 <h2 id="222">2.2.2 &nbsp; 再帰<a class="headerlink" href="#222" title="Permanent link">&para;</a></h2>
-<p><u>再帰</u>は、関数が自分自身を呼び出すことで問題を解決するアルゴリズム戦略です。主に2つのフェーズが含まれます：</p>
+<p><u>再帰（recursion）</u>は、関数が自分自身を呼び出すことで問題を解決するアルゴリズム戦略です。主に 2 つの段階から成ります。</p>
 <ol>
-<li><strong>呼び出し</strong>: プログラムが自分自身を繰り返し呼び出し、しばしばより小さいまたはより単純な引数で、「終了条件」に向かって進みます。</li>
-<li><strong>返却</strong>: 「終了条件」がトリガーされると、プログラムは最も深い再帰関数から返り始め、各レイヤーの結果を集約します。</li>
+<li><strong>再帰呼び出し</strong>：プログラムは自分自身をより深く呼び出し続け、通常はより小さい、またはより単純化された引数を渡し、「終了条件」に達するまで進みます。</li>
+<li><strong>復帰</strong>： 「終了条件」が満たされると、プログラムは最も深い再帰関数から 1 層ずつ戻り、各層の結果をまとめていきます。</li>
 </ol>
-<p>実装の観点から、再帰コードは主に3つの要素を含みます。</p>
+<p>実装の観点から見ると、再帰コードは主に 3 つの要素から成ります。</p>
 <ol>
-<li><strong>終了条件</strong>: 「呼び出し」から「返却」にいつ切り替えるかを決定します。</li>
-<li><strong>再帰呼び出し</strong>: 「呼び出し」に対応し、関数が自分自身を呼び出し、通常はより小さいまたはより単純化されたパラメータで行います。</li>
-<li><strong>結果の返却</strong>: 「返却」に対応し、現在の再帰レベルの結果が前のレイヤーに返されます。</li>
+<li><strong>終了条件</strong>：いつ再帰呼び出しから復帰へ切り替わるかを決めます。</li>
+<li><strong>再帰呼び出し</strong>：再帰呼び出しに対応し、関数が自分自身を呼び出します。通常はより小さい、またはより単純化された引数を入力します。</li>
+<li><strong>結果の返却</strong>：復帰に対応し、現在の再帰レベルの結果を 1 つ上の層へ返します。</li>
 </ol>
-<p>以下のコードを観察してください。単純に関数<code>recur(n)</code>を呼び出すだけで<span class="arithmatex">\(1 + 2 + \dots + n\)</span>の合計を計算できます：</p>
+<p>次のコードを見ると、関数 <code>recur(n)</code> を呼び出すだけで <span class="arithmatex">\(1 + 2 + \dots + n\)</span> を計算できます。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="5:13"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
@@ -4919,7 +5380,7 @@
 <a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a>        <span class="k">return</span> <span class="mi">1</span>
 <a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a>    <span class="c1"># 再帰：再帰呼び出し</span>
 <a id="__codelineno-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></a>    <span class="n">res</span> <span class="o">=</span> <span class="n">recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-52-8" name="__codelineno-52-8" href="#__codelineno-52-8"></a>    <span class="c1"># 復帰：結果を返す</span>
+<a id="__codelineno-52-8" name="__codelineno-52-8" href="#__codelineno-52-8"></a>    <span class="c1"># 帰りがけ：結果を返す</span>
 <a id="__codelineno-52-9" name="__codelineno-52-9" href="#__codelineno-52-9"></a>    <span class="k">return</span> <span class="n">n</span> <span class="o">+</span> <span class="n">res</span>
 </code></pre></div>
 </div>
@@ -4931,7 +5392,7 @@
 <a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></a><span class="w">    </span><span class="c1">// 再帰：再帰呼び出し</span>
 <a id="__codelineno-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a><span class="w">    </span><span class="c1">// 戻り値：結果を返す</span>
+<a id="__codelineno-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a><span class="w">    </span><span class="c1">// 帰りがけ：結果を返す</span>
 <a id="__codelineno-53-9" name="__codelineno-53-9" href="#__codelineno-53-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
 <a id="__codelineno-53-10" name="__codelineno-53-10" href="#__codelineno-53-10"></a><span class="p">}</span>
 </code></pre></div>
@@ -4944,85 +5405,179 @@
 <a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w">    </span><span class="c1">// 再帰：再帰呼び出し</span>
 <a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w">    </span><span class="c1">// 戻り値：結果を返す</span>
+<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w">    </span><span class="c1">// 帰りがけ：結果を返す</span>
 <a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
 <a id="__codelineno-54-10" name="__codelineno-54-10" href="#__codelineno-54-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.cs</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">recursion</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Recur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.cs</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="cm">/* 再帰 */</span>
+<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Recur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-55-4" name="__codelineno-55-4" href="#__codelineno-55-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-55-5" name="__codelineno-55-5" href="#__codelineno-55-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-55-6" name="__codelineno-55-6" href="#__codelineno-55-6"></a><span class="w">    </span><span class="c1">// 再帰：再帰呼び出し</span>
+<a id="__codelineno-55-7" name="__codelineno-55-7" href="#__codelineno-55-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-55-8" name="__codelineno-55-8" href="#__codelineno-55-8"></a><span class="w">    </span><span class="c1">// 帰りがけ：結果を返す</span>
+<a id="__codelineno-55-9" name="__codelineno-55-9" href="#__codelineno-55-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-55-10" name="__codelineno-55-10" href="#__codelineno-55-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.go</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">recur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.go</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="cm">/* 再帰 */</span>
+<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a><span class="w">    </span><span class="c1">// 再帰：再帰呼び出し</span>
+<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a><span class="w">    </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></a><span class="w">    </span><span class="c1">// 帰りがけ：結果を返す</span>
+<a id="__codelineno-56-10" name="__codelineno-56-10" href="#__codelineno-56-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">res</span>
+<a id="__codelineno-56-11" name="__codelineno-56-11" href="#__codelineno-56-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.swift</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">recur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.swift</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 再帰 */</span>
+<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></a><span class="w">    </span><span class="c1">// 再帰：再帰呼び出し</span>
+<a id="__codelineno-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="w">    </span><span class="c1">// 帰りがけ：結果を返す</span>
+<a id="__codelineno-57-10" name="__codelineno-57-10" href="#__codelineno-57-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-57-11" name="__codelineno-57-11" href="#__codelineno-57-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.js</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">recur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.js</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 再帰 */</span>
+<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a><span class="w">    </span><span class="c1">// 再帰：再帰呼び出し</span>
+<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></a><span class="w">    </span><span class="c1">// 帰りがけ：結果を返す</span>
+<a id="__codelineno-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.ts</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">recur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.ts</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="cm">/* 再帰 */</span>
+<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-59-4" name="__codelineno-59-4" href="#__codelineno-59-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-59-5" name="__codelineno-59-5" href="#__codelineno-59-5"></a><span class="w">    </span><span class="c1">// 再帰：再帰呼び出し</span>
+<a id="__codelineno-59-6" name="__codelineno-59-6" href="#__codelineno-59-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-59-7" name="__codelineno-59-7" href="#__codelineno-59-7"></a><span class="w">    </span><span class="c1">// 帰りがけ：結果を返す</span>
+<a id="__codelineno-59-8" name="__codelineno-59-8" href="#__codelineno-59-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-59-9" name="__codelineno-59-9" href="#__codelineno-59-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.dart</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">recur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.dart</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="cm">/* 再帰 */</span>
+<a id="__codelineno-60-2" name="__codelineno-60-2" href="#__codelineno-60-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">recur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-3" name="__codelineno-60-3" href="#__codelineno-60-3"></a><span class="w">  </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-60-4" name="__codelineno-60-4" href="#__codelineno-60-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-60-5" name="__codelineno-60-5" href="#__codelineno-60-5"></a><span class="w">  </span><span class="c1">// 再帰：再帰呼び出し</span>
+<a id="__codelineno-60-6" name="__codelineno-60-6" href="#__codelineno-60-6"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-60-7" name="__codelineno-60-7" href="#__codelineno-60-7"></a><span class="w">  </span><span class="c1">// 帰りがけ：結果を返す</span>
+<a id="__codelineno-60-8" name="__codelineno-60-8" href="#__codelineno-60-8"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-60-9" name="__codelineno-60-9" href="#__codelineno-60-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.rs</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">recur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.rs</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="cm">/* 再帰 */</span>
+<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-3" name="__codelineno-61-3" href="#__codelineno-61-3"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-61-4" name="__codelineno-61-4" href="#__codelineno-61-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-5" name="__codelineno-61-5" href="#__codelineno-61-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-61-6" name="__codelineno-61-6" href="#__codelineno-61-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-61-7" name="__codelineno-61-7" href="#__codelineno-61-7"></a><span class="w">    </span><span class="c1">// 再帰：再帰呼び出し</span>
+<a id="__codelineno-61-8" name="__codelineno-61-8" href="#__codelineno-61-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-61-9" name="__codelineno-61-9" href="#__codelineno-61-9"></a><span class="w">    </span><span class="c1">// 帰りがけ：結果を返す</span>
+<a id="__codelineno-61-10" name="__codelineno-61-10" href="#__codelineno-61-10"></a><span class="w">    </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-61-11" name="__codelineno-61-11" href="#__codelineno-61-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.c</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">recur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.c</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="cm">/* 再帰 */</span>
+<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-62-4" name="__codelineno-62-4" href="#__codelineno-62-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-62-5" name="__codelineno-62-5" href="#__codelineno-62-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-62-6" name="__codelineno-62-6" href="#__codelineno-62-6"></a><span class="w">    </span><span class="c1">// 再帰：再帰呼び出し</span>
+<a id="__codelineno-62-7" name="__codelineno-62-7" href="#__codelineno-62-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-62-8" name="__codelineno-62-8" href="#__codelineno-62-8"></a><span class="w">    </span><span class="c1">// 帰りがけ：結果を返す</span>
+<a id="__codelineno-62-9" name="__codelineno-62-9" href="#__codelineno-62-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-62-10" name="__codelineno-62-10" href="#__codelineno-62-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.kt</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">recur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.kt</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="cm">/* 再帰 */</span>
+<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-63-4" name="__codelineno-63-4" href="#__codelineno-63-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-63-5" name="__codelineno-63-5" href="#__codelineno-63-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-63-6" name="__codelineno-63-6" href="#__codelineno-63-6"></a><span class="w">    </span><span class="c1">// 再帰: 再帰呼び出し</span>
+<a id="__codelineno-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-63-8" name="__codelineno-63-8" href="#__codelineno-63-8"></a><span class="w">    </span><span class="c1">// 戻る: 結果を返す</span>
+<a id="__codelineno-63-9" name="__codelineno-63-9" href="#__codelineno-63-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-63-10" name="__codelineno-63-10" href="#__codelineno-63-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.rb</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">recur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.rb</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="c1">### 再帰 ###</span>
+<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a><span class="w">  </span><span class="c1"># 終了条件</span>
+<a id="__codelineno-64-4" name="__codelineno-64-4" href="#__codelineno-64-4"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-64-5" name="__codelineno-64-5" href="#__codelineno-64-5"></a><span class="w">  </span><span class="c1"># 再帰：再帰呼び出し</span>
+<a id="__codelineno-64-6" name="__codelineno-64-6" href="#__codelineno-64-6"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-64-7" name="__codelineno-64-7" href="#__codelineno-64-7"></a><span class="w">  </span><span class="c1"># 帰りがけ：結果を返す</span>
+<a id="__codelineno-64-8" name="__codelineno-64-8" href="#__codelineno-64-8"></a><span class="w">  </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-64-9" name="__codelineno-64-9" href="#__codelineno-64-9"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>以下の図はこの関数の再帰プロセスを示しています。</p>
-<p><img alt="Recursive process of the sum function" class="animation-figure" src="../iteration_and_recursion.assets/recursion_sum.png" /></p>
-<p align="center"> 図 2-3 &nbsp; Recursive process of the sum function </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 441px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%86%8D%E5%B8%B0%22%22%22%0A%20%20%20%20%23%20%E7%B5%82%E4%BA%86%E6%9D%A1%E4%BB%B6%0A%20%20%20%20if%20n%20%3D%3D%201%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20%23%20%E5%86%8D%E5%B8%B0%EF%BC%9A%E5%86%8D%E5%B8%B0%E5%91%BC%E3%81%B3%E5%87%BA%E3%81%97%0A%20%20%20%20res%20%3D%20recur%28n%20-%201%29%0A%20%20%20%20%23%20%E5%B8%B0%E3%82%8A%E3%81%8C%E3%81%91%EF%BC%9A%E7%B5%90%E6%9E%9C%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20n%20%2B%20res%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20recur%28n%29%0A%20%20%20%20print%28f%22%5Cn%E5%86%8D%E5%B8%B0%E9%96%A2%E6%95%B0%E3%81%AE%E5%90%88%E8%A8%88%E7%B5%90%E6%9E%9C%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%86%8D%E5%B8%B0%22%22%22%0A%20%20%20%20%23%20%E7%B5%82%E4%BA%86%E6%9D%A1%E4%BB%B6%0A%20%20%20%20if%20n%20%3D%3D%201%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20%23%20%E5%86%8D%E5%B8%B0%EF%BC%9A%E5%86%8D%E5%B8%B0%E5%91%BC%E3%81%B3%E5%87%BA%E3%81%97%0A%20%20%20%20res%20%3D%20recur%28n%20-%201%29%0A%20%20%20%20%23%20%E5%B8%B0%E3%82%8A%E3%81%8C%E3%81%91%EF%BC%9A%E7%B5%90%E6%9E%9C%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20n%20%2B%20res%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20recur%28n%29%0A%20%20%20%20print%28f%22%5Cn%E5%86%8D%E5%B8%B0%E9%96%A2%E6%95%B0%E3%81%AE%E5%90%88%E8%A8%88%E7%B5%90%E6%9E%9C%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>次の図は、この関数の再帰過程を示しています。</p>
+<p><img alt="総和関数の再帰過程" class="animation-figure" src="../iteration_and_recursion.assets/recursion_sum.png" /></p>
+<p align="center"> 図 2-3 &nbsp; 総和関数の再帰過程 </p>
 
-<p>反復と再帰は計算の観点から同じ結果を達成できますが、<strong>それらは思考と問題解決の全く異なるパラダイムを表します</strong>。</p>
+<p>計算の観点では、反復と再帰は同じ結果を得られますが、<strong>それらは問題を考え解決するためのまったく異なる 2 つのパラダイムを表しています</strong>。</p>
 <ul>
-<li><strong>反復</strong>: 「ボトムアップ」で問題を解決します。最も基本的なステップから始まり、タスクが完了するまでこれらのステップを繰り返し追加または累積します。</li>
-<li><strong>再帰</strong>: 「トップダウン」で問題を解決します。元の問題をより小さなサブ問題に分解し、各サブ問題は元の問題と同じ形式を持ちます。これらのサブ問題は、解が分かっているベースケースで停止するまで、さらに小さなサブ問題に分解されます。</li>
+<li><strong>反復</strong>：「ボトムアップ」で問題を解決します。最も基本的な手順から始め、それらを繰り返したり積み上げたりして、処理が完了するまで進めます。</li>
+<li><strong>再帰</strong>：「トップダウン」で問題を解決します。元の問題をより小さな部分問題に分解し、それらの部分問題は元の問題と同じ形を持ちます。さらに部分問題をより小さな部分問題へと分解し、基本ケースに達したところで停止します（基本ケースの解は既知です）。</li>
 </ul>
-<p>先ほどの合計関数の例を取ってみましょう。<span class="arithmatex">\(f(n) = 1 + 2 + \dots + n\)</span>として定義されます。</p>
+<p>前述の総和関数を例に、問題を <span class="arithmatex">\(f(n) = 1 + 2 + \dots + n\)</span> とします。</p>
 <ul>
-<li><strong>反復</strong>: このアプローチでは、ループ内で合計プロセスをシミュレートします。<span class="arithmatex">\(1\)</span>から始まり<span class="arithmatex">\(n\)</span>まで横断し、各反復で合計操作を実行して最終的に<span class="arithmatex">\(f(n)\)</span>を計算します。</li>
-<li><strong>再帰</strong>: ここでは、問題はサブ問題に分解されます：<span class="arithmatex">\(f(n) = n + f(n-1)\)</span>。この分解は、ベースケースの<span class="arithmatex">\(f(1) = 1\)</span>に到達するまで再帰的に続き、そこで再帰が終了します。</li>
+<li><strong>反復</strong>：ループ内で総和の過程を模擬し、<span class="arithmatex">\(1\)</span> から <span class="arithmatex">\(n\)</span> まで走査して、各反復で加算を行えば <span class="arithmatex">\(f(n)\)</span> を求められます。</li>
+<li><strong>再帰</strong>：問題を部分問題 <span class="arithmatex">\(f(n) = n + f(n-1)\)</span> に分解し、これを再帰的に分解し続け、基本ケース <span class="arithmatex">\(f(1) = 1\)</span> に達したところで終了します。</li>
 </ul>
 <h3 id="1">1. &nbsp; 呼び出しスタック<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>再帰関数が自分自身を呼び出すたびに、システムは新しく開始された関数にメモリを割り当てて、ローカル変数、戻りアドレス、その他の関連情報を格納します。これは2つの主要な結果をもたらします。</p>
+<p>再帰関数が自分自身を呼び出すたびに、システムは新たに開始された関数のためにメモリを割り当て、局所変数、呼び出し先アドレス、その他の情報を保存します。これにより 2 つの結果が生じます。</p>
 <ul>
-<li>関数のコンテキストデータは「スタックフレーム空間」と呼ばれるメモリ領域に格納され、関数が返された後にのみ解放されます。したがって、<strong>再帰は一般的に反復よりも多くのメモリ空間を消費します</strong>。</li>
-<li>再帰呼び出しは追加のオーバーヘッドを導入します。<strong>したがって、再帰は通常ループよりも時間効率が劣ります。</strong></li>
+<li>関数のコンテキストデータは「スタックフレーム領域」と呼ばれるメモリ領域に保存され、関数が戻るまで解放されません。したがって、<strong>再帰は通常、反復より多くのメモリ空間を消費します</strong>。</li>
+<li>再帰による関数呼び出しには追加のオーバーヘッドが発生します。<strong>そのため再帰は通常、ループより時間効率が低くなります</strong>。</li>
 </ul>
-<p>以下の図に示されているように、終了条件がトリガーされる前に<span class="arithmatex">\(n\)</span>個の未返却の再帰関数があり、<strong>再帰の深さが<span class="arithmatex">\(n\)</span>であることを示しています</strong>。</p>
-<p><img alt="Recursion call depth" class="animation-figure" src="../iteration_and_recursion.assets/recursion_sum_depth.png" /></p>
-<p align="center"> 図 2-4 &nbsp; Recursion call depth </p>
+<p>次の図のように、終了条件が発動する前には、まだ戻っていない再帰関数が同時に <span class="arithmatex">\(n\)</span> 個存在し、<strong>再帰の深さは <span class="arithmatex">\(n\)</span></strong> になります。</p>
+<p><img alt="再帰呼び出しの深さ" class="animation-figure" src="../iteration_and_recursion.assets/recursion_sum_depth.png" /></p>
+<p align="center"> 図 2-4 &nbsp; 再帰呼び出しの深さ </p>
 
-<p>実際には、プログラミング言語で許可される再帰の深さは通常制限されており、過度に深い再帰はスタックオーバーフローエラーを引き起こす可能性があります。</p>
+<p>実際には、プログラミング言語が許容する再帰の深さには通常上限があり、深すぎる再帰はスタックオーバーフローを引き起こす可能性があります。</p>
 <h3 id="2">2. &nbsp; 末尾再帰<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>興味深いことに、<strong>関数が返す直前の最後のステップとして再帰呼び出しを実行する場合</strong>、コンパイラまたはインタープリターによって反復と同じ空間効率になるように最適化できます。このシナリオは<u>末尾再帰</u>として知られています。</p>
+<p>興味深いことに、<strong>関数が返る直前の最後の処理で再帰呼び出しを行う場合</strong>、その関数はコンパイラやインタプリタによって最適化され、空間効率が反復と同程度になることがあります。これを<u>末尾再帰（tail recursion）</u>と呼びます。</p>
 <ul>
-<li><strong>通常の再帰</strong>: 標準的な再帰では、関数が前のレベルに戻ったとき、さらにコードを実行し続けるため、システムは前の呼び出しのコンテキストを保存する必要があります。</li>
-<li><strong>末尾再帰</strong>: ここでは、再帰呼び出しは関数が返す前の最終操作です。これは、前のレベルに戻った際に、さらなるアクションが必要ないことを意味するため、システムは前のレベルのコンテキストを保存する必要がありません。</li>
+<li><strong>通常の再帰</strong>：関数が 1 つ上の階層の関数へ戻った後も、引き続きコードを実行する必要があるため、システムは 1 つ上の呼び出しのコンテキストを保存しておく必要があります。</li>
+<li><strong>末尾再帰</strong>：再帰呼び出しが関数の返却前の最後の操作であるため、1 つ上の階層へ戻った後に他の処理を続ける必要がなく、システムは 1 つ上の関数のコンテキストを保存する必要がありません。</li>
 </ul>
-<p>例えば、<span class="arithmatex">\(1 + 2 + \dots + n\)</span>の計算では、結果変数<code>res</code>を関数のパラメータにすることで、末尾再帰を実現できます：</p>
+<p><span class="arithmatex">\(1 + 2 + \dots + n\)</span> の計算を例にすると、結果変数 <code>res</code> を関数の引数にすることで、末尾再帰を実現できます。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="6:13"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><input id="__tabbed_6_13" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Kotlin</label><label for="__tabbed_6_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
@@ -5058,71 +5613,146 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.cs</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">recursion</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">TailRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.cs</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="cm">/* 末尾再帰 */</span>
+<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">TailRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-68-3" name="__codelineno-68-3" href="#__codelineno-68-3"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-68-4" name="__codelineno-68-4" href="#__codelineno-68-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-68-5" name="__codelineno-68-5" href="#__codelineno-68-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-68-6" name="__codelineno-68-6" href="#__codelineno-68-6"></a><span class="w">    </span><span class="c1">// 末尾再帰呼び出し</span>
+<a id="__codelineno-68-7" name="__codelineno-68-7" href="#__codelineno-68-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nf">TailRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-68-8" name="__codelineno-68-8" href="#__codelineno-68-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.go</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">tailRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.go</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="cm">/* 末尾再帰 */</span>
+<a id="__codelineno-69-2" name="__codelineno-69-2" href="#__codelineno-69-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">tailRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-3" name="__codelineno-69-3" href="#__codelineno-69-3"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-69-4" name="__codelineno-69-4" href="#__codelineno-69-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-5" name="__codelineno-69-5" href="#__codelineno-69-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
+<a id="__codelineno-69-6" name="__codelineno-69-6" href="#__codelineno-69-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-69-7" name="__codelineno-69-7" href="#__codelineno-69-7"></a><span class="w">    </span><span class="c1">// 末尾再帰呼び出し</span>
+<a id="__codelineno-69-8" name="__codelineno-69-8" href="#__codelineno-69-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">tailRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="o">+</span><span class="nx">n</span><span class="p">)</span>
+<a id="__codelineno-69-9" name="__codelineno-69-9" href="#__codelineno-69-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.swift</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">tailRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.swift</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="cm">/* 末尾再帰 */</span>
+<a id="__codelineno-70-2" name="__codelineno-70-2" href="#__codelineno-70-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">tailRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-3" name="__codelineno-70-3" href="#__codelineno-70-3"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-70-4" name="__codelineno-70-4" href="#__codelineno-70-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-5" name="__codelineno-70-5" href="#__codelineno-70-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-70-6" name="__codelineno-70-6" href="#__codelineno-70-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-70-7" name="__codelineno-70-7" href="#__codelineno-70-7"></a><span class="w">    </span><span class="c1">// 末尾再帰呼び出し</span>
+<a id="__codelineno-70-8" name="__codelineno-70-8" href="#__codelineno-70-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">tailRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-70-9" name="__codelineno-70-9" href="#__codelineno-70-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.js</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">tailRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.js</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="cm">/* 末尾再帰 */</span>
+<a id="__codelineno-71-2" name="__codelineno-71-2" href="#__codelineno-71-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">tailRecur</span><span class="p">(</span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-3" name="__codelineno-71-3" href="#__codelineno-71-3"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-71-4" name="__codelineno-71-4" href="#__codelineno-71-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-71-5" name="__codelineno-71-5" href="#__codelineno-71-5"></a><span class="w">    </span><span class="c1">// 末尾再帰呼び出し</span>
+<a id="__codelineno-71-6" name="__codelineno-71-6" href="#__codelineno-71-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">tailRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">n</span><span class="p">);</span>
+<a id="__codelineno-71-7" name="__codelineno-71-7" href="#__codelineno-71-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.ts</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">tailRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.ts</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="cm">/* 末尾再帰 */</span>
+<a id="__codelineno-72-2" name="__codelineno-72-2" href="#__codelineno-72-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">tailRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-3" name="__codelineno-72-3" href="#__codelineno-72-3"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-72-4" name="__codelineno-72-4" href="#__codelineno-72-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-72-5" name="__codelineno-72-5" href="#__codelineno-72-5"></a><span class="w">    </span><span class="c1">// 末尾再帰呼び出し</span>
+<a id="__codelineno-72-6" name="__codelineno-72-6" href="#__codelineno-72-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">tailRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">n</span><span class="p">);</span>
+<a id="__codelineno-72-7" name="__codelineno-72-7" href="#__codelineno-72-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.dart</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">tailRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.dart</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="cm">/* 末尾再帰 */</span>
+<a id="__codelineno-73-2" name="__codelineno-73-2" href="#__codelineno-73-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">tailRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-73-3" name="__codelineno-73-3" href="#__codelineno-73-3"></a><span class="w">  </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-73-4" name="__codelineno-73-4" href="#__codelineno-73-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-73-5" name="__codelineno-73-5" href="#__codelineno-73-5"></a><span class="w">  </span><span class="c1">// 末尾再帰呼び出し</span>
+<a id="__codelineno-73-6" name="__codelineno-73-6" href="#__codelineno-73-6"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">tailRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-73-7" name="__codelineno-73-7" href="#__codelineno-73-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.rs</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">tail_recur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.rs</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="cm">/* 末尾再帰 */</span>
+<a id="__codelineno-74-2" name="__codelineno-74-2" href="#__codelineno-74-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">tail_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-3" name="__codelineno-74-3" href="#__codelineno-74-3"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-74-4" name="__codelineno-74-4" href="#__codelineno-74-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-5" name="__codelineno-74-5" href="#__codelineno-74-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-74-6" name="__codelineno-74-6" href="#__codelineno-74-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-74-7" name="__codelineno-74-7" href="#__codelineno-74-7"></a><span class="w">    </span><span class="c1">// 末尾再帰呼び出し</span>
+<a id="__codelineno-74-8" name="__codelineno-74-8" href="#__codelineno-74-8"></a><span class="w">    </span><span class="n">tail_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-74-9" name="__codelineno-74-9" href="#__codelineno-74-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.c</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">tailRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.c</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="cm">/* 末尾再帰 */</span>
+<a id="__codelineno-75-2" name="__codelineno-75-2" href="#__codelineno-75-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">tailRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-75-3" name="__codelineno-75-3" href="#__codelineno-75-3"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-75-4" name="__codelineno-75-4" href="#__codelineno-75-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-75-5" name="__codelineno-75-5" href="#__codelineno-75-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-75-6" name="__codelineno-75-6" href="#__codelineno-75-6"></a><span class="w">    </span><span class="c1">// 末尾再帰呼び出し</span>
+<a id="__codelineno-75-7" name="__codelineno-75-7" href="#__codelineno-75-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">tailRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-75-8" name="__codelineno-75-8" href="#__codelineno-75-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.kt</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">tailRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.kt</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="cm">/* 末尾再帰 */</span>
+<a id="__codelineno-76-2" name="__codelineno-76-2" href="#__codelineno-76-2"></a><span class="kd">tailrec</span><span class="w"> </span><span class="kd">fun</span><span class="w"> </span><span class="nf">tailRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-76-3" name="__codelineno-76-3" href="#__codelineno-76-3"></a><span class="w">    </span><span class="c1">// `tailrec` キーワードを追加して末尾再帰最適化を有効にする</span>
+<a id="__codelineno-76-4" name="__codelineno-76-4" href="#__codelineno-76-4"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-76-5" name="__codelineno-76-5" href="#__codelineno-76-5"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">)</span>
+<a id="__codelineno-76-6" name="__codelineno-76-6" href="#__codelineno-76-6"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-76-7" name="__codelineno-76-7" href="#__codelineno-76-7"></a><span class="w">    </span><span class="c1">// 末尾再帰呼び出し</span>
+<a id="__codelineno-76-8" name="__codelineno-76-8" href="#__codelineno-76-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">tailRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-76-9" name="__codelineno-76-9" href="#__codelineno-76-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.rb</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">tail_recur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.rb</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="c1">### 末尾再帰 ###</span>
+<a id="__codelineno-77-2" name="__codelineno-77-2" href="#__codelineno-77-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">tail_recur</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-77-3" name="__codelineno-77-3" href="#__codelineno-77-3"></a><span class="w">  </span><span class="c1"># 終了条件</span>
+<a id="__codelineno-77-4" name="__codelineno-77-4" href="#__codelineno-77-4"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-77-5" name="__codelineno-77-5" href="#__codelineno-77-5"></a><span class="w">  </span><span class="c1"># 末尾再帰呼び出し</span>
+<a id="__codelineno-77-6" name="__codelineno-77-6" href="#__codelineno-77-6"></a><span class="w">  </span><span class="n">tail_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-77-7" name="__codelineno-77-7" href="#__codelineno-77-7"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>末尾再帰の実行プロセスは以下の図に示されています。通常の再帰と末尾再帰を比較すると、合計操作のポイントが異なります。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 405px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20tail_recur%28n%2C%20res%29%3A%0A%20%20%20%20%22%22%22%E6%9C%AB%E5%B0%BE%E5%86%8D%E5%B8%B0%22%22%22%0A%20%20%20%20%23%20%E7%B5%82%E4%BA%86%E6%9D%A1%E4%BB%B6%0A%20%20%20%20if%20n%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20return%20res%0A%20%20%20%20%23%20%E6%9C%AB%E5%B0%BE%E5%86%8D%E5%B8%B0%E5%91%BC%E3%81%B3%E5%87%BA%E3%81%97%0A%20%20%20%20return%20tail_recur%28n%20-%201%2C%20res%20%2B%20n%29%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20tail_recur%28n%2C%200%29%0A%20%20%20%20print%28f%22%5Cn%E6%9C%AB%E5%B0%BE%E5%86%8D%E5%B8%B0%E9%96%A2%E6%95%B0%E3%81%AE%E5%90%88%E8%A8%88%E7%B5%90%E6%9E%9C%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20tail_recur%28n%2C%20res%29%3A%0A%20%20%20%20%22%22%22%E6%9C%AB%E5%B0%BE%E5%86%8D%E5%B8%B0%22%22%22%0A%20%20%20%20%23%20%E7%B5%82%E4%BA%86%E6%9D%A1%E4%BB%B6%0A%20%20%20%20if%20n%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20return%20res%0A%20%20%20%20%23%20%E6%9C%AB%E5%B0%BE%E5%86%8D%E5%B8%B0%E5%91%BC%E3%81%B3%E5%87%BA%E3%81%97%0A%20%20%20%20return%20tail_recur%28n%20-%201%2C%20res%20%2B%20n%29%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20tail_recur%28n%2C%200%29%0A%20%20%20%20print%28f%22%5Cn%E6%9C%AB%E5%B0%BE%E5%86%8D%E5%B8%B0%E9%96%A2%E6%95%B0%E3%81%AE%E5%90%88%E8%A8%88%E7%B5%90%E6%9E%9C%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>末尾再帰の実行過程を次の図に示します。通常の再帰と末尾再帰を比べると、加算処理が実行されるタイミングが異なります。</p>
 <ul>
-<li><strong>通常の再帰</strong>: 合計操作は「返却」フェーズで発生し、各レイヤーが返った後にもう一度合計が必要です。</li>
-<li><strong>末尾再帰</strong>: 合計操作は「呼び出し」フェーズで発生し、「返却」フェーズは各レイヤーを通じて返すだけです。</li>
+<li><strong>通常の再帰</strong>：加算処理は復帰の過程で実行され、各層が戻るたびにもう一度加算を行います。</li>
+<li><strong>末尾再帰</strong>：加算処理は再帰呼び出しの過程で実行され、復帰の過程では各層が戻るだけで済みます。</li>
 </ul>
-<p><img alt="Tail recursion process" class="animation-figure" src="../iteration_and_recursion.assets/tail_recursion_sum.png" /></p>
-<p align="center"> 図 2-5 &nbsp; Tail recursion process </p>
+<p><img alt="末尾再帰の過程" class="animation-figure" src="../iteration_and_recursion.assets/tail_recursion_sum.png" /></p>
+<p align="center"> 図 2-5 &nbsp; 末尾再帰の過程 </p>
 
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>多くのコンパイラやインタープリターは末尾再帰最適化をサポートしていないことに注意してください。例えば、Pythonはデフォルトで末尾再帰最適化をサポートしていないため、関数が末尾再帰の形式であっても、スタックオーバーフローの問題に遭遇する可能性があります。</p>
+<p>多くのコンパイラやインタプリタは末尾再帰最適化をサポートしていない点に注意してください。たとえば、Python はデフォルトで末尾再帰最適化をサポートしていないため、関数が末尾再帰の形であっても、スタックオーバーフローが発生する可能性があります。</p>
 </div>
 <h3 id="3_1">3. &nbsp; 再帰木<a class="headerlink" href="#3_1" title="Permanent link">&para;</a></h3>
-<p>「分割統治」に関連するアルゴリズムを扱う際、再帰は反復よりもしばしばより直感的なアプローチとより読みやすいコードを提供します。「フィボナッチ数列」を例に取ってみましょう。</p>
+<p>「分割統治」に関連するアルゴリズム問題を扱う際、再帰は反復よりも発想が直感的で、コードも読みやすいことがよくあります。「フィボナッチ数列」を例に見てみましょう。</p>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
-<p>フィボナッチ数列<span class="arithmatex">\(0, 1, 1, 2, 3, 5, 8, 13, \dots\)</span>が与えられた場合、数列の<span class="arithmatex">\(n\)</span>番目の数を求めなさい。</p>
+<p>フィボナッチ数列 <span class="arithmatex">\(0, 1, 1, 2, 3, 5, 8, 13, \dots\)</span> が与えられたとき、この数列の第 <span class="arithmatex">\(n\)</span> 項を求めてください。</p>
 </div>
-<p>フィボナッチ数列の<span class="arithmatex">\(n\)</span>番目の数を<span class="arithmatex">\(f(n)\)</span>とすると、2つの結論を簡単に導き出せます：</p>
+<p>フィボナッチ数列の第 <span class="arithmatex">\(n\)</span> 項を <span class="arithmatex">\(f(n)\)</span> とすると、次の 2 つが容易に分かります。</p>
 <ul>
-<li>数列の最初の2つの数は<span class="arithmatex">\(f(1) = 0\)</span>と<span class="arithmatex">\(f(2) = 1\)</span>です。</li>
-<li>数列の各数は前の2つの数の合計です。つまり、<span class="arithmatex">\(f(n) = f(n - 1) + f(n - 2)\)</span>です。</li>
+<li>数列の最初の 2 項は <span class="arithmatex">\(f(1) = 0\)</span> と <span class="arithmatex">\(f(2) = 1\)</span> です。</li>
+<li>数列中の各項は直前の 2 項の和であり、すなわち <span class="arithmatex">\(f(n) = f(n - 1) + f(n - 2)\)</span> です。</li>
 </ul>
-<p>再帰関係を使用し、最初の2つの数を終了条件として考慮すると、再帰コードを書けます。<code>fib(n)</code>を呼び出すとフィボナッチ数列の<span class="arithmatex">\(n\)</span>番目の数が得られます：</p>
+<p>漸化式に従って再帰呼び出しを行い、最初の 2 項を終了条件とすれば、再帰コードを書けます。<code>fib(n)</code> を呼び出すことでフィボナッチ数列の第 <span class="arithmatex">\(n\)</span> 項を得られます。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="7:13"><input checked="checked" id="__tabbed_7_1" name="__tabbed_7" type="radio" /><input id="__tabbed_7_2" name="__tabbed_7" type="radio" /><input id="__tabbed_7_3" name="__tabbed_7" type="radio" /><input id="__tabbed_7_4" name="__tabbed_7" type="radio" /><input id="__tabbed_7_5" name="__tabbed_7" type="radio" /><input id="__tabbed_7_6" name="__tabbed_7" type="radio" /><input id="__tabbed_7_7" name="__tabbed_7" type="radio" /><input id="__tabbed_7_8" name="__tabbed_7" type="radio" /><input id="__tabbed_7_9" name="__tabbed_7" type="radio" /><input id="__tabbed_7_10" name="__tabbed_7" type="radio" /><input id="__tabbed_7_11" name="__tabbed_7" type="radio" /><input id="__tabbed_7_12" name="__tabbed_7" type="radio" /><input id="__tabbed_7_13" name="__tabbed_7" type="radio" /><div class="tabbed-labels"><label for="__tabbed_7_1">Python</label><label for="__tabbed_7_2">C++</label><label for="__tabbed_7_3">Java</label><label for="__tabbed_7_4">C#</label><label for="__tabbed_7_5">Go</label><label for="__tabbed_7_6">Swift</label><label for="__tabbed_7_7">JS</label><label for="__tabbed_7_8">TS</label><label for="__tabbed_7_9">Dart</label><label for="__tabbed_7_10">Rust</label><label for="__tabbed_7_11">C</label><label for="__tabbed_7_12">Kotlin</label><label for="__tabbed_7_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
@@ -5131,7 +5761,7 @@
 <a id="__codelineno-78-3" name="__codelineno-78-3" href="#__codelineno-78-3"></a>    <span class="c1"># 終了条件 f(1) = 0, f(2) = 1</span>
 <a id="__codelineno-78-4" name="__codelineno-78-4" href="#__codelineno-78-4"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
 <a id="__codelineno-78-5" name="__codelineno-78-5" href="#__codelineno-78-5"></a>        <span class="k">return</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span>
-<a id="__codelineno-78-6" name="__codelineno-78-6" href="#__codelineno-78-6"></a>    <span class="c1"># 再帰呼び出し f(n) = f(n-1) + f(n-2)</span>
+<a id="__codelineno-78-6" name="__codelineno-78-6" href="#__codelineno-78-6"></a>    <span class="c1"># f(n) = f(n-1) + f(n-2) を再帰的に呼び出す</span>
 <a id="__codelineno-78-7" name="__codelineno-78-7" href="#__codelineno-78-7"></a>    <span class="n">res</span> <span class="o">=</span> <span class="n">fib</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">+</span> <span class="n">fib</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">2</span><span class="p">)</span>
 <a id="__codelineno-78-8" name="__codelineno-78-8" href="#__codelineno-78-8"></a>    <span class="c1"># 結果 f(n) を返す</span>
 <a id="__codelineno-78-9" name="__codelineno-78-9" href="#__codelineno-78-9"></a>    <span class="k">return</span> <span class="n">res</span>
@@ -5143,7 +5773,7 @@
 <a id="__codelineno-79-3" name="__codelineno-79-3" href="#__codelineno-79-3"></a><span class="w">    </span><span class="c1">// 終了条件 f(1) = 0, f(2) = 1</span>
 <a id="__codelineno-79-4" name="__codelineno-79-4" href="#__codelineno-79-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
 <a id="__codelineno-79-5" name="__codelineno-79-5" href="#__codelineno-79-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-79-6" name="__codelineno-79-6" href="#__codelineno-79-6"></a><span class="w">    </span><span class="c1">// 再帰呼び出し f(n) = f(n-1) + f(n-2)</span>
+<a id="__codelineno-79-6" name="__codelineno-79-6" href="#__codelineno-79-6"></a><span class="w">    </span><span class="c1">// f(n) = f(n-1) + f(n-2) を再帰的に呼び出す</span>
 <a id="__codelineno-79-7" name="__codelineno-79-7" href="#__codelineno-79-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fib</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">fib</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
 <a id="__codelineno-79-8" name="__codelineno-79-8" href="#__codelineno-79-8"></a><span class="w">    </span><span class="c1">// 結果 f(n) を返す</span>
 <a id="__codelineno-79-9" name="__codelineno-79-9" href="#__codelineno-79-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
@@ -5156,7 +5786,7 @@
 <a id="__codelineno-80-3" name="__codelineno-80-3" href="#__codelineno-80-3"></a><span class="w">    </span><span class="c1">// 終了条件 f(1) = 0, f(2) = 1</span>
 <a id="__codelineno-80-4" name="__codelineno-80-4" href="#__codelineno-80-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
 <a id="__codelineno-80-5" name="__codelineno-80-5" href="#__codelineno-80-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-80-6" name="__codelineno-80-6" href="#__codelineno-80-6"></a><span class="w">    </span><span class="c1">// 再帰呼び出し f(n) = f(n-1) + f(n-2)</span>
+<a id="__codelineno-80-6" name="__codelineno-80-6" href="#__codelineno-80-6"></a><span class="w">    </span><span class="c1">// f(n) = f(n-1) + f(n-2) を再帰的に呼び出す</span>
 <a id="__codelineno-80-7" name="__codelineno-80-7" href="#__codelineno-80-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fib</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">fib</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
 <a id="__codelineno-80-8" name="__codelineno-80-8" href="#__codelineno-80-8"></a><span class="w">    </span><span class="c1">// 結果 f(n) を返す</span>
 <a id="__codelineno-80-9" name="__codelineno-80-9" href="#__codelineno-80-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
@@ -5164,59 +5794,153 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.cs</span><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">recursion</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Fib</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.cs</span><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="cm">/* フィボナッチ数列：再帰 */</span>
+<a id="__codelineno-81-2" name="__codelineno-81-2" href="#__codelineno-81-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Fib</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-3" name="__codelineno-81-3" href="#__codelineno-81-3"></a><span class="w">    </span><span class="c1">// 終了条件 f(1) = 0, f(2) = 1</span>
+<a id="__codelineno-81-4" name="__codelineno-81-4" href="#__codelineno-81-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-81-5" name="__codelineno-81-5" href="#__codelineno-81-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-81-6" name="__codelineno-81-6" href="#__codelineno-81-6"></a><span class="w">    </span><span class="c1">// f(n) = f(n-1) + f(n-2) を再帰的に呼び出す</span>
+<a id="__codelineno-81-7" name="__codelineno-81-7" href="#__codelineno-81-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Fib</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">Fib</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-81-8" name="__codelineno-81-8" href="#__codelineno-81-8"></a><span class="w">    </span><span class="c1">// 結果 f(n) を返す</span>
+<a id="__codelineno-81-9" name="__codelineno-81-9" href="#__codelineno-81-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-81-10" name="__codelineno-81-10" href="#__codelineno-81-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.go</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">fib</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.go</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="cm">/* フィボナッチ数列：再帰 */</span>
+<a id="__codelineno-82-2" name="__codelineno-82-2" href="#__codelineno-82-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">fib</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-3" name="__codelineno-82-3" href="#__codelineno-82-3"></a><span class="w">    </span><span class="c1">// 終了条件 f(1) = 0, f(2) = 1</span>
+<a id="__codelineno-82-4" name="__codelineno-82-4" href="#__codelineno-82-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-5" name="__codelineno-82-5" href="#__codelineno-82-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-82-6" name="__codelineno-82-6" href="#__codelineno-82-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-82-7" name="__codelineno-82-7" href="#__codelineno-82-7"></a><span class="w">    </span><span class="c1">// f(n) = f(n-1) + f(n-2) を再帰的に呼び出す</span>
+<a id="__codelineno-82-8" name="__codelineno-82-8" href="#__codelineno-82-8"></a><span class="w">    </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">fib</span><span class="p">(</span><span class="nx">n</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">fib</span><span class="p">(</span><span class="nx">n</span><span class="o">-</span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-82-9" name="__codelineno-82-9" href="#__codelineno-82-9"></a><span class="w">    </span><span class="c1">// 結果 f(n) を返す</span>
+<a id="__codelineno-82-10" name="__codelineno-82-10" href="#__codelineno-82-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
+<a id="__codelineno-82-11" name="__codelineno-82-11" href="#__codelineno-82-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.swift</span><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">fib</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.swift</span><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="cm">/* フィボナッチ数列：再帰 */</span>
+<a id="__codelineno-83-2" name="__codelineno-83-2" href="#__codelineno-83-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">fib</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-3" name="__codelineno-83-3" href="#__codelineno-83-3"></a><span class="w">    </span><span class="c1">// 終了条件 f(1) = 0, f(2) = 1</span>
+<a id="__codelineno-83-4" name="__codelineno-83-4" href="#__codelineno-83-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-5" name="__codelineno-83-5" href="#__codelineno-83-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-83-6" name="__codelineno-83-6" href="#__codelineno-83-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-83-7" name="__codelineno-83-7" href="#__codelineno-83-7"></a><span class="w">    </span><span class="c1">// f(n) = f(n-1) + f(n-2) を再帰的に呼び出す</span>
+<a id="__codelineno-83-8" name="__codelineno-83-8" href="#__codelineno-83-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">fib</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">fib</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-83-9" name="__codelineno-83-9" href="#__codelineno-83-9"></a><span class="w">    </span><span class="c1">// 結果 f(n) を返す</span>
+<a id="__codelineno-83-10" name="__codelineno-83-10" href="#__codelineno-83-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-83-11" name="__codelineno-83-11" href="#__codelineno-83-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.js</span><pre><span></span><code><a id="__codelineno-84-1" name="__codelineno-84-1" href="#__codelineno-84-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">fib</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.js</span><pre><span></span><code><a id="__codelineno-84-1" name="__codelineno-84-1" href="#__codelineno-84-1"></a><span class="cm">/* フィボナッチ数列：再帰 */</span>
+<a id="__codelineno-84-2" name="__codelineno-84-2" href="#__codelineno-84-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">fib</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-3" name="__codelineno-84-3" href="#__codelineno-84-3"></a><span class="w">    </span><span class="c1">// 終了条件 f(1) = 0, f(2) = 1</span>
+<a id="__codelineno-84-4" name="__codelineno-84-4" href="#__codelineno-84-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-84-5" name="__codelineno-84-5" href="#__codelineno-84-5"></a><span class="w">    </span><span class="c1">// f(n) = f(n-1) + f(n-2) を再帰的に呼び出す</span>
+<a id="__codelineno-84-6" name="__codelineno-84-6" href="#__codelineno-84-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">fib</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">fib</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span>
+<a id="__codelineno-84-7" name="__codelineno-84-7" href="#__codelineno-84-7"></a><span class="w">    </span><span class="c1">// 結果 f(n) を返す</span>
+<a id="__codelineno-84-8" name="__codelineno-84-8" href="#__codelineno-84-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-84-9" name="__codelineno-84-9" href="#__codelineno-84-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.ts</span><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">fib</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.ts</span><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="cm">/* フィボナッチ数列：再帰 */</span>
+<a id="__codelineno-85-2" name="__codelineno-85-2" href="#__codelineno-85-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">fib</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-3" name="__codelineno-85-3" href="#__codelineno-85-3"></a><span class="w">    </span><span class="c1">// 終了条件 f(1) = 0, f(2) = 1</span>
+<a id="__codelineno-85-4" name="__codelineno-85-4" href="#__codelineno-85-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-85-5" name="__codelineno-85-5" href="#__codelineno-85-5"></a><span class="w">    </span><span class="c1">// f(n) = f(n-1) + f(n-2) を再帰的に呼び出す</span>
+<a id="__codelineno-85-6" name="__codelineno-85-6" href="#__codelineno-85-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">fib</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">fib</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span>
+<a id="__codelineno-85-7" name="__codelineno-85-7" href="#__codelineno-85-7"></a><span class="w">    </span><span class="c1">// 結果 f(n) を返す</span>
+<a id="__codelineno-85-8" name="__codelineno-85-8" href="#__codelineno-85-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-85-9" name="__codelineno-85-9" href="#__codelineno-85-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.dart</span><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">fib</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.dart</span><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="cm">/* フィボナッチ数列：再帰 */</span>
+<a id="__codelineno-86-2" name="__codelineno-86-2" href="#__codelineno-86-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">fib</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-3" name="__codelineno-86-3" href="#__codelineno-86-3"></a><span class="w">  </span><span class="c1">// 終了条件 f(1) = 0, f(2) = 1</span>
+<a id="__codelineno-86-4" name="__codelineno-86-4" href="#__codelineno-86-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-86-5" name="__codelineno-86-5" href="#__codelineno-86-5"></a><span class="w">  </span><span class="c1">// f(n) = f(n-1) + f(n-2) を再帰的に呼び出す</span>
+<a id="__codelineno-86-6" name="__codelineno-86-6" href="#__codelineno-86-6"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fib</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">fib</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">2</span><span class="p">);</span>
+<a id="__codelineno-86-7" name="__codelineno-86-7" href="#__codelineno-86-7"></a><span class="w">  </span><span class="c1">// 結果 f(n) を返す</span>
+<a id="__codelineno-86-8" name="__codelineno-86-8" href="#__codelineno-86-8"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-86-9" name="__codelineno-86-9" href="#__codelineno-86-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.rs</span><pre><span></span><code><a id="__codelineno-87-1" name="__codelineno-87-1" href="#__codelineno-87-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">fib</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.rs</span><pre><span></span><code><a id="__codelineno-87-1" name="__codelineno-87-1" href="#__codelineno-87-1"></a><span class="cm">/* フィボナッチ数列：再帰 */</span>
+<a id="__codelineno-87-2" name="__codelineno-87-2" href="#__codelineno-87-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">fib</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-3" name="__codelineno-87-3" href="#__codelineno-87-3"></a><span class="w">    </span><span class="c1">// 終了条件 f(1) = 0, f(2) = 1</span>
+<a id="__codelineno-87-4" name="__codelineno-87-4" href="#__codelineno-87-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-5" name="__codelineno-87-5" href="#__codelineno-87-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-87-6" name="__codelineno-87-6" href="#__codelineno-87-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-87-7" name="__codelineno-87-7" href="#__codelineno-87-7"></a><span class="w">    </span><span class="c1">// f(n) = f(n-1) + f(n-2) を再帰的に呼び出す</span>
+<a id="__codelineno-87-8" name="__codelineno-87-8" href="#__codelineno-87-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fib</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">fib</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-87-9" name="__codelineno-87-9" href="#__codelineno-87-9"></a><span class="w">    </span><span class="c1">// 結果を返す</span>
+<a id="__codelineno-87-10" name="__codelineno-87-10" href="#__codelineno-87-10"></a><span class="w">    </span><span class="n">res</span>
+<a id="__codelineno-87-11" name="__codelineno-87-11" href="#__codelineno-87-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.c</span><pre><span></span><code><a id="__codelineno-88-1" name="__codelineno-88-1" href="#__codelineno-88-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">fib</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.c</span><pre><span></span><code><a id="__codelineno-88-1" name="__codelineno-88-1" href="#__codelineno-88-1"></a><span class="cm">/* フィボナッチ数列：再帰 */</span>
+<a id="__codelineno-88-2" name="__codelineno-88-2" href="#__codelineno-88-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">fib</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-3" name="__codelineno-88-3" href="#__codelineno-88-3"></a><span class="w">    </span><span class="c1">// 終了条件 f(1) = 0, f(2) = 1</span>
+<a id="__codelineno-88-4" name="__codelineno-88-4" href="#__codelineno-88-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-88-5" name="__codelineno-88-5" href="#__codelineno-88-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-88-6" name="__codelineno-88-6" href="#__codelineno-88-6"></a><span class="w">    </span><span class="c1">// f(n) = f(n-1) + f(n-2) を再帰的に呼び出す</span>
+<a id="__codelineno-88-7" name="__codelineno-88-7" href="#__codelineno-88-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fib</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">fib</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-88-8" name="__codelineno-88-8" href="#__codelineno-88-8"></a><span class="w">    </span><span class="c1">// 結果 f(n) を返す</span>
+<a id="__codelineno-88-9" name="__codelineno-88-9" href="#__codelineno-88-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-88-10" name="__codelineno-88-10" href="#__codelineno-88-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.kt</span><pre><span></span><code><a id="__codelineno-89-1" name="__codelineno-89-1" href="#__codelineno-89-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">fib</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.kt</span><pre><span></span><code><a id="__codelineno-89-1" name="__codelineno-89-1" href="#__codelineno-89-1"></a><span class="cm">/* フィボナッチ数列：再帰 */</span>
+<a id="__codelineno-89-2" name="__codelineno-89-2" href="#__codelineno-89-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">fib</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-89-3" name="__codelineno-89-3" href="#__codelineno-89-3"></a><span class="w">    </span><span class="c1">// 終了条件 f(1) = 0, f(2) = 1</span>
+<a id="__codelineno-89-4" name="__codelineno-89-4" href="#__codelineno-89-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">2</span><span class="p">)</span>
+<a id="__codelineno-89-5" name="__codelineno-89-5" href="#__codelineno-89-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-89-6" name="__codelineno-89-6" href="#__codelineno-89-6"></a><span class="w">    </span><span class="c1">// f(n) = f(n-1) + f(n-2) を再帰的に呼び出す</span>
+<a id="__codelineno-89-7" name="__codelineno-89-7" href="#__codelineno-89-7"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fib</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">fib</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">2</span><span class="p">)</span>
+<a id="__codelineno-89-8" name="__codelineno-89-8" href="#__codelineno-89-8"></a><span class="w">    </span><span class="c1">// 結果 f(n) を返す</span>
+<a id="__codelineno-89-9" name="__codelineno-89-9" href="#__codelineno-89-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-89-10" name="__codelineno-89-10" href="#__codelineno-89-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.rb</span><pre><span></span><code><a id="__codelineno-90-1" name="__codelineno-90-1" href="#__codelineno-90-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">fib</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.rb</span><pre><span></span><code><a id="__codelineno-90-1" name="__codelineno-90-1" href="#__codelineno-90-1"></a><span class="c1">### フィボナッチ数列：再帰 ###</span>
+<a id="__codelineno-90-2" name="__codelineno-90-2" href="#__codelineno-90-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">fib</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-90-3" name="__codelineno-90-3" href="#__codelineno-90-3"></a><span class="w">  </span><span class="c1"># 終了条件 f(1) = 0, f(2) = 1</span>
+<a id="__codelineno-90-4" name="__codelineno-90-4" href="#__codelineno-90-4"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-90-5" name="__codelineno-90-5" href="#__codelineno-90-5"></a><span class="w">  </span><span class="c1"># f(n) = f(n-1) + f(n-2) を再帰的に呼び出す</span>
+<a id="__codelineno-90-6" name="__codelineno-90-6" href="#__codelineno-90-6"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fib</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">fib</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-90-7" name="__codelineno-90-7" href="#__codelineno-90-7"></a><span class="w">  </span><span class="c1"># 結果 f(n) を返す</span>
+<a id="__codelineno-90-8" name="__codelineno-90-8" href="#__codelineno-90-8"></a><span class="w">  </span><span class="n">res</span>
+<a id="__codelineno-90-9" name="__codelineno-90-9" href="#__codelineno-90-9"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>上記のコードを観察すると、それ自体の中で2つの関数を再帰的に呼び出していることがわかります。<strong>つまり、1回の呼び出しで2つの分岐呼び出しが生成されます</strong>。以下の図に示されているように、この継続的な再帰呼び出しは最終的に深さ<span class="arithmatex">\(n\)</span>の<u>再帰木</u>を作成します。</p>
-<p><img alt="Fibonacci sequence recursion tree" class="animation-figure" src="../iteration_and_recursion.assets/recursion_tree.png" /></p>
-<p align="center"> 図 2-6 &nbsp; Fibonacci sequence recursion tree </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 441px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20fib%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E3%83%95%E3%82%A3%E3%83%9C%E3%83%8A%E3%83%83%E3%83%81%E6%95%B0%E5%88%97%EF%BC%9A%E5%86%8D%E5%B8%B0%22%22%22%0A%20%20%20%20%23%20%E7%B5%82%E4%BA%86%E6%9D%A1%E4%BB%B6%20f%281%29%20%3D%200%2C%20f%282%29%20%3D%201%0A%20%20%20%20if%20n%20%3D%3D%201%20or%20n%20%3D%3D%202%3A%0A%20%20%20%20%20%20%20%20return%20n%20-%201%0A%20%20%20%20%23%20f%28n%29%20%3D%20f%28n-1%29%20%2B%20f%28n-2%29%20%E3%82%92%E5%86%8D%E5%B8%B0%E7%9A%84%E3%81%AB%E5%91%BC%E3%81%B3%E5%87%BA%E3%81%99%0A%20%20%20%20res%20%3D%20fib%28n%20-%201%29%20%2B%20fib%28n%20-%202%29%0A%20%20%20%20%23%20%E7%B5%90%E6%9E%9C%20f%28n%29%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20res%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20fib%28n%29%0A%20%20%20%20print%28f%22%5Cn%E3%83%95%E3%82%A3%E3%83%9C%E3%83%8A%E3%83%83%E3%83%81%E6%95%B0%E5%88%97%E3%81%AE%E7%AC%AC%20%7Bn%7D%20%E9%A0%85%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20fib%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E3%83%95%E3%82%A3%E3%83%9C%E3%83%8A%E3%83%83%E3%83%81%E6%95%B0%E5%88%97%EF%BC%9A%E5%86%8D%E5%B8%B0%22%22%22%0A%20%20%20%20%23%20%E7%B5%82%E4%BA%86%E6%9D%A1%E4%BB%B6%20f%281%29%20%3D%200%2C%20f%282%29%20%3D%201%0A%20%20%20%20if%20n%20%3D%3D%201%20or%20n%20%3D%3D%202%3A%0A%20%20%20%20%20%20%20%20return%20n%20-%201%0A%20%20%20%20%23%20f%28n%29%20%3D%20f%28n-1%29%20%2B%20f%28n-2%29%20%E3%82%92%E5%86%8D%E5%B8%B0%E7%9A%84%E3%81%AB%E5%91%BC%E3%81%B3%E5%87%BA%E3%81%99%0A%20%20%20%20res%20%3D%20fib%28n%20-%201%29%20%2B%20fib%28n%20-%202%29%0A%20%20%20%20%23%20%E7%B5%90%E6%9E%9C%20f%28n%29%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20res%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20fib%28n%29%0A%20%20%20%20print%28f%22%5Cn%E3%83%95%E3%82%A3%E3%83%9C%E3%83%8A%E3%83%83%E3%83%81%E6%95%B0%E5%88%97%E3%81%AE%E7%AC%AC%20%7Bn%7D%20%E9%A0%85%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>上のコードを見ると、関数内で 2 回の再帰呼び出しを行っています。<strong>これは 1 回の呼び出しから 2 つの呼び出し分岐が生じることを意味します</strong>。次の図のように、この再帰呼び出しを繰り返していくと、最終的に深さ <span class="arithmatex">\(n\)</span> の<u>再帰木（recursion tree）</u>が生成されます。</p>
+<p><img alt="フィボナッチ数列の再帰木" class="animation-figure" src="../iteration_and_recursion.assets/recursion_tree.png" /></p>
+<p align="center"> 図 2-6 &nbsp; フィボナッチ数列の再帰木 </p>
 
-<p>基本的に、再帰は「問題をより小さなサブ問題に分解する」パラダイムを体現しています。この分割統治戦略は重要です。</p>
+<p>本質的に見ると、再帰は「問題をより小さな部分問題へ分解する」という思考パラダイムを体現しており、この分割統治の戦略は非常に重要です。</p>
 <ul>
-<li>アルゴリズムの観点から、探索、ソート、バックトラッキング、分割統治、動的プログラミングなどの多くの重要な戦略は、直接的または間接的にこの思考方法を使用しています。</li>
-<li>データ構造の観点から、再帰は連結リスト、木、グラフを扱うのに自然に適しており、これらは分割統治アプローチを使用した分析に適しているためです。</li>
+<li>アルゴリズムの観点では、探索、ソート、バックトラッキング、分割統治、動的計画法など、多くの重要な戦略が直接または間接にこの考え方を用いています。</li>
+<li>データ構造の観点では、再帰は連結リスト、木、グラフに関する問題の処理に本質的に適しており、これらは分割統治の考え方で分析しやすいからです。</li>
 </ul>
-<h2 id="223">2.2.3 &nbsp; 比較<a class="headerlink" href="#223" title="Permanent link">&para;</a></h2>
-<p>上記の内容をまとめると、以下の表は実装、性能、適用性の観点から反復と再帰の違いを示しています。</p>
-<p align="center"> 表: 反復と再帰の特性の比較 </p>
+<h2 id="223">2.2.3 &nbsp; 両者の比較<a class="headerlink" href="#223" title="Permanent link">&para;</a></h2>
+<p>以上をまとめると、次の表のように、反復と再帰は実装、性能、適用性の面で違いがあります。</p>
+<p align="center"> 表 2-1 &nbsp; 反復と再帰の特徴の比較 </p>
 
 <div class="center-table">
 <table>
@@ -5229,73 +5953,73 @@
 </thead>
 <tbody>
 <tr>
-<td>アプローチ</td>
+<td>実装方法</td>
 <td>ループ構造</td>
 <td>関数が自分自身を呼び出す</td>
 </tr>
 <tr>
 <td>時間効率</td>
-<td>一般的により高い効率、関数呼び出しのオーバーヘッドなし</td>
-<td>各関数呼び出しがオーバーヘッドを生成</td>
+<td>通常は効率が高く、関数呼び出しの負荷がない</td>
+<td>関数呼び出しのたびにオーバーヘッドが発生する</td>
 </tr>
 <tr>
-<td>メモリ使用量</td>
-<td>通常は固定サイズのメモリ空間を使用</td>
-<td>累積的な関数呼び出しが大量のスタックフレーム空間を使用する可能性</td>
+<td>メモリ使用</td>
+<td>通常は固定サイズのメモリ空間を使う</td>
+<td>関数呼び出しの蓄積により大量のスタックフレーム領域を使う可能性がある</td>
 </tr>
 <tr>
-<td>適用可能な問題</td>
-<td>単純なループタスクに適している、直感的で読みやすいコード</td>
-<td>問題の分解に適している（木、グラフ、分割統治、バックトラッキングなど）、簡潔で明確なコード構造</td>
+<td>適用対象</td>
+<td>単純な反復処理に適し、コードが直感的で読みやすい</td>
+<td>木、グラフ、分割統治、バックトラッキングなどの部分問題分解に適し、コード構造が簡潔で明快</td>
 </tr>
 </tbody>
 </table>
 </div>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>以下の内容が理解しにくい場合は、「スタック」の章を読んだ後に再び訪れることを検討してください。</p>
+<p>以下の内容が難しいと感じる場合は、「スタック」の章を読み終えた後に改めて復習してください。</p>
 </div>
-<p>それでは、反復と再帰の本質的な関連は何でしょうか？上記の再帰関数を例に取ると、合計操作は再帰の「返却」フェーズで発生します。これは、最初に呼び出された関数が最後に合計操作を完了することを意味し、<strong>スタックの「後入れ先出し」原理を反映しています</strong>。</p>
-<p>「呼び出しスタック」や「スタックフレーム空間」などの再帰用語は、再帰とスタックの密接な関係を示しています。</p>
+<p>では、反復と再帰にはどのような内在的な関係があるのでしょうか。前述の再帰関数を例にすると、加算処理は再帰の復帰段階で行われます。これは、最初に呼び出された関数が実際には最後に加算を完了することを意味しており、<strong>この動作の仕組みはスタックの「後入れ先出し」の原則とよく似ています</strong>。</p>
+<p>実際、「呼び出しスタック」や「スタックフレーム領域」といった再帰の用語自体が、再帰とスタックの密接な関係を示唆しています。</p>
 <ol>
-<li><strong>呼び出し</strong>: 関数が呼び出されると、システムは「呼び出しスタック」上にその関数用の新しいスタックフレームを割り当て、ローカル変数、パラメータ、戻りアドレス、その他のデータを格納します。</li>
-<li><strong>返却</strong>: 関数が実行を完了して返ると、対応するスタックフレームが「呼び出しスタック」から削除され、前の関数の実行環境が復元されます。</li>
+<li><strong>再帰呼び出し</strong>：関数が呼び出されると、システムは「呼び出しスタック」上にその関数のための新しいスタックフレームを割り当て、局所変数、引数、返却先アドレスなどのデータを保存します。</li>
+<li><strong>復帰</strong>：関数の実行が完了して戻ると、対応するスタックフレームは「呼び出しスタック」から取り除かれ、前の関数の実行環境が復元されます。</li>
 </ol>
-<p>したがって、<strong>明示的なスタックを使用して呼び出しスタックの動作をシミュレートできます</strong>。これにより再帰を反復形式に変換できます：</p>
+<p>したがって、<strong>明示的なスタックを使って呼び出しスタックの振る舞いを模擬することができ</strong>、その結果として再帰を反復形式へ変換できます。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="8:13"><input checked="checked" id="__tabbed_8_1" name="__tabbed_8" type="radio" /><input id="__tabbed_8_2" name="__tabbed_8" type="radio" /><input id="__tabbed_8_3" name="__tabbed_8" type="radio" /><input id="__tabbed_8_4" name="__tabbed_8" type="radio" /><input id="__tabbed_8_5" name="__tabbed_8" type="radio" /><input id="__tabbed_8_6" name="__tabbed_8" type="radio" /><input id="__tabbed_8_7" name="__tabbed_8" type="radio" /><input id="__tabbed_8_8" name="__tabbed_8" type="radio" /><input id="__tabbed_8_9" name="__tabbed_8" type="radio" /><input id="__tabbed_8_10" name="__tabbed_8" type="radio" /><input id="__tabbed_8_11" name="__tabbed_8" type="radio" /><input id="__tabbed_8_12" name="__tabbed_8" type="radio" /><input id="__tabbed_8_13" name="__tabbed_8" type="radio" /><div class="tabbed-labels"><label for="__tabbed_8_1">Python</label><label for="__tabbed_8_2">C++</label><label for="__tabbed_8_3">Java</label><label for="__tabbed_8_4">C#</label><label for="__tabbed_8_5">Go</label><label for="__tabbed_8_6">Swift</label><label for="__tabbed_8_7">JS</label><label for="__tabbed_8_8">TS</label><label for="__tabbed_8_9">Dart</label><label for="__tabbed_8_10">Rust</label><label for="__tabbed_8_11">C</label><label for="__tabbed_8_12">Kotlin</label><label for="__tabbed_8_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">recursion.py</span><pre><span></span><code><a id="__codelineno-91-1" name="__codelineno-91-1" href="#__codelineno-91-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">for_loop_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-91-2" name="__codelineno-91-2" href="#__codelineno-91-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;反復で再帰をシミュレート&quot;&quot;&quot;</span>
-<a id="__codelineno-91-3" name="__codelineno-91-3" href="#__codelineno-91-3"></a>    <span class="c1"># 明示的なスタックを使用してシステムコールスタックをシミュレート</span>
+<a id="__codelineno-91-2" name="__codelineno-91-2" href="#__codelineno-91-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;反復で再帰を模擬する&quot;&quot;&quot;</span>
+<a id="__codelineno-91-3" name="__codelineno-91-3" href="#__codelineno-91-3"></a>    <span class="c1"># 明示的なスタックを使ってシステムコールスタックを模擬する</span>
 <a id="__codelineno-91-4" name="__codelineno-91-4" href="#__codelineno-91-4"></a>    <span class="n">stack</span> <span class="o">=</span> <span class="p">[]</span>
 <a id="__codelineno-91-5" name="__codelineno-91-5" href="#__codelineno-91-5"></a>    <span class="n">res</span> <span class="o">=</span> <span class="mi">0</span>
 <a id="__codelineno-91-6" name="__codelineno-91-6" href="#__codelineno-91-6"></a>    <span class="c1"># 再帰：再帰呼び出し</span>
 <a id="__codelineno-91-7" name="__codelineno-91-7" href="#__codelineno-91-7"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
-<a id="__codelineno-91-8" name="__codelineno-91-8" href="#__codelineno-91-8"></a>        <span class="c1"># 「スタックへのプッシュ」で「再帰」をシミュレート</span>
+<a id="__codelineno-91-8" name="__codelineno-91-8" href="#__codelineno-91-8"></a>        <span class="c1"># 「スタックへのプッシュ」で「再帰」を模擬する</span>
 <a id="__codelineno-91-9" name="__codelineno-91-9" href="#__codelineno-91-9"></a>        <span class="n">stack</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
-<a id="__codelineno-91-10" name="__codelineno-91-10" href="#__codelineno-91-10"></a>    <span class="c1"># 復帰：結果を返す</span>
+<a id="__codelineno-91-10" name="__codelineno-91-10" href="#__codelineno-91-10"></a>    <span class="c1"># 帰りがけ：結果を返す</span>
 <a id="__codelineno-91-11" name="__codelineno-91-11" href="#__codelineno-91-11"></a>    <span class="k">while</span> <span class="n">stack</span><span class="p">:</span>
-<a id="__codelineno-91-12" name="__codelineno-91-12" href="#__codelineno-91-12"></a>        <span class="c1"># 「スタックからのポップ」で「復帰」をシミュレート</span>
+<a id="__codelineno-91-12" name="__codelineno-91-12" href="#__codelineno-91-12"></a>        <span class="c1"># 「スタックから取り出す操作」で「帰り」をシミュレート</span>
 <a id="__codelineno-91-13" name="__codelineno-91-13" href="#__codelineno-91-13"></a>        <span class="n">res</span> <span class="o">+=</span> <span class="n">stack</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
 <a id="__codelineno-91-14" name="__codelineno-91-14" href="#__codelineno-91-14"></a>    <span class="c1"># res = 1+2+3+...+n</span>
 <a id="__codelineno-91-15" name="__codelineno-91-15" href="#__codelineno-91-15"></a>    <span class="k">return</span> <span class="n">res</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.cpp</span><pre><span></span><code><a id="__codelineno-92-1" name="__codelineno-92-1" href="#__codelineno-92-1"></a><span class="cm">/* 反復で再帰をシミュレート */</span>
+<div class="highlight"><span class="filename">recursion.cpp</span><pre><span></span><code><a id="__codelineno-92-1" name="__codelineno-92-1" href="#__codelineno-92-1"></a><span class="cm">/* 反復で再帰を模擬する */</span>
 <a id="__codelineno-92-2" name="__codelineno-92-2" href="#__codelineno-92-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">forLoopRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-92-3" name="__codelineno-92-3" href="#__codelineno-92-3"></a><span class="w">    </span><span class="c1">// 明示的なスタックを使用してシステムコールスタックをシミュレート</span>
+<a id="__codelineno-92-3" name="__codelineno-92-3" href="#__codelineno-92-3"></a><span class="w">    </span><span class="c1">// 明示的なスタックを使ってシステムコールスタックを模擬する</span>
 <a id="__codelineno-92-4" name="__codelineno-92-4" href="#__codelineno-92-4"></a><span class="w">    </span><span class="n">stack</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">stack</span><span class="p">;</span>
 <a id="__codelineno-92-5" name="__codelineno-92-5" href="#__codelineno-92-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-92-6" name="__codelineno-92-6" href="#__codelineno-92-6"></a><span class="w">    </span><span class="c1">// 再帰：再帰呼び出し</span>
 <a id="__codelineno-92-7" name="__codelineno-92-7" href="#__codelineno-92-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-92-8" name="__codelineno-92-8" href="#__codelineno-92-8"></a><span class="w">        </span><span class="c1">// 「スタックへのプッシュ」で「再帰」をシミュレート</span>
+<a id="__codelineno-92-8" name="__codelineno-92-8" href="#__codelineno-92-8"></a><span class="w">        </span><span class="c1">// 「スタックへのプッシュ」で「再帰」を模擬する</span>
 <a id="__codelineno-92-9" name="__codelineno-92-9" href="#__codelineno-92-9"></a><span class="w">        </span><span class="n">stack</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
 <a id="__codelineno-92-10" name="__codelineno-92-10" href="#__codelineno-92-10"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-92-11" name="__codelineno-92-11" href="#__codelineno-92-11"></a><span class="w">    </span><span class="c1">// 戻り値：結果を返す</span>
+<a id="__codelineno-92-11" name="__codelineno-92-11" href="#__codelineno-92-11"></a><span class="w">    </span><span class="c1">// 帰りがけ：結果を返す</span>
 <a id="__codelineno-92-12" name="__codelineno-92-12" href="#__codelineno-92-12"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">stack</span><span class="p">.</span><span class="n">empty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-92-13" name="__codelineno-92-13" href="#__codelineno-92-13"></a><span class="w">        </span><span class="c1">// 「スタックからのポップ」で「戻り値」をシミュレート</span>
+<a id="__codelineno-92-13" name="__codelineno-92-13" href="#__codelineno-92-13"></a><span class="w">        </span><span class="c1">// 「スタックから取り出す操作」で「帰り」をシミュレート</span>
 <a id="__codelineno-92-14" name="__codelineno-92-14" href="#__codelineno-92-14"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">top</span><span class="p">();</span>
 <a id="__codelineno-92-15" name="__codelineno-92-15" href="#__codelineno-92-15"></a><span class="w">        </span><span class="n">stack</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
 <a id="__codelineno-92-16" name="__codelineno-92-16" href="#__codelineno-92-16"></a><span class="w">    </span><span class="p">}</span>
@@ -5305,19 +6029,19 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.java</span><pre><span></span><code><a id="__codelineno-93-1" name="__codelineno-93-1" href="#__codelineno-93-1"></a><span class="cm">/* 反復で再帰をシミュレート */</span>
+<div class="highlight"><span class="filename">recursion.java</span><pre><span></span><code><a id="__codelineno-93-1" name="__codelineno-93-1" href="#__codelineno-93-1"></a><span class="cm">/* 反復で再帰を模擬する */</span>
 <a id="__codelineno-93-2" name="__codelineno-93-2" href="#__codelineno-93-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">forLoopRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-93-3" name="__codelineno-93-3" href="#__codelineno-93-3"></a><span class="w">    </span><span class="c1">// 明示的なスタックを使用してシステムコールスタックをシミュレート</span>
+<a id="__codelineno-93-3" name="__codelineno-93-3" href="#__codelineno-93-3"></a><span class="w">    </span><span class="c1">// 明示的なスタックを使ってシステムコールスタックを模擬する</span>
 <a id="__codelineno-93-4" name="__codelineno-93-4" href="#__codelineno-93-4"></a><span class="w">    </span><span class="n">Stack</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Stack</span><span class="o">&lt;&gt;</span><span class="p">();</span>
 <a id="__codelineno-93-5" name="__codelineno-93-5" href="#__codelineno-93-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-93-6" name="__codelineno-93-6" href="#__codelineno-93-6"></a><span class="w">    </span><span class="c1">// 再帰：再帰呼び出し</span>
 <a id="__codelineno-93-7" name="__codelineno-93-7" href="#__codelineno-93-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-93-8" name="__codelineno-93-8" href="#__codelineno-93-8"></a><span class="w">        </span><span class="c1">// 「スタックへのプッシュ」で「再帰」をシミュレート</span>
+<a id="__codelineno-93-8" name="__codelineno-93-8" href="#__codelineno-93-8"></a><span class="w">        </span><span class="c1">// 「スタックへのプッシュ」で「再帰」を模擬する</span>
 <a id="__codelineno-93-9" name="__codelineno-93-9" href="#__codelineno-93-9"></a><span class="w">        </span><span class="n">stack</span><span class="p">.</span><span class="na">push</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
 <a id="__codelineno-93-10" name="__codelineno-93-10" href="#__codelineno-93-10"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-93-11" name="__codelineno-93-11" href="#__codelineno-93-11"></a><span class="w">    </span><span class="c1">// 戻り値：結果を返す</span>
+<a id="__codelineno-93-11" name="__codelineno-93-11" href="#__codelineno-93-11"></a><span class="w">    </span><span class="c1">// 帰りがけ：結果を返す</span>
 <a id="__codelineno-93-12" name="__codelineno-93-12" href="#__codelineno-93-12"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">stack</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-93-13" name="__codelineno-93-13" href="#__codelineno-93-13"></a><span class="w">        </span><span class="c1">// 「スタックからのポップ」で「戻り値」をシミュレート</span>
+<a id="__codelineno-93-13" name="__codelineno-93-13" href="#__codelineno-93-13"></a><span class="w">        </span><span class="c1">// 「スタックから取り出す操作」で「帰り」をシミュレート</span>
 <a id="__codelineno-93-14" name="__codelineno-93-14" href="#__codelineno-93-14"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">pop</span><span class="p">();</span>
 <a id="__codelineno-93-15" name="__codelineno-93-15" href="#__codelineno-93-15"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-93-16" name="__codelineno-93-16" href="#__codelineno-93-16"></a><span class="w">    </span><span class="c1">// res = 1+2+3+...+n</span>
@@ -5326,53 +6050,230 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.cs</span><pre><span></span><code><a id="__codelineno-94-1" name="__codelineno-94-1" href="#__codelineno-94-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">recursion</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">ForLoopRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.cs</span><pre><span></span><code><a id="__codelineno-94-1" name="__codelineno-94-1" href="#__codelineno-94-1"></a><span class="cm">/* 反復で再帰を模擬する */</span>
+<a id="__codelineno-94-2" name="__codelineno-94-2" href="#__codelineno-94-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">ForLoopRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-94-3" name="__codelineno-94-3" href="#__codelineno-94-3"></a><span class="w">    </span><span class="c1">// 明示的なスタックを使ってシステムコールスタックを模擬する</span>
+<a id="__codelineno-94-4" name="__codelineno-94-4" href="#__codelineno-94-4"></a><span class="w">    </span><span class="n">Stack</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">();</span>
+<a id="__codelineno-94-5" name="__codelineno-94-5" href="#__codelineno-94-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-94-6" name="__codelineno-94-6" href="#__codelineno-94-6"></a><span class="w">    </span><span class="c1">// 再帰：再帰呼び出し</span>
+<a id="__codelineno-94-7" name="__codelineno-94-7" href="#__codelineno-94-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-94-8" name="__codelineno-94-8" href="#__codelineno-94-8"></a><span class="w">        </span><span class="c1">// 「スタックへのプッシュ」で「再帰」を模擬する</span>
+<a id="__codelineno-94-9" name="__codelineno-94-9" href="#__codelineno-94-9"></a><span class="w">        </span><span class="n">stack</span><span class="p">.</span><span class="n">Push</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-94-10" name="__codelineno-94-10" href="#__codelineno-94-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-94-11" name="__codelineno-94-11" href="#__codelineno-94-11"></a><span class="w">    </span><span class="c1">// 帰りがけ：結果を返す</span>
+<a id="__codelineno-94-12" name="__codelineno-94-12" href="#__codelineno-94-12"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">stack</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-94-13" name="__codelineno-94-13" href="#__codelineno-94-13"></a><span class="w">        </span><span class="c1">// 「スタックから取り出す操作」で「帰り」をシミュレート</span>
+<a id="__codelineno-94-14" name="__codelineno-94-14" href="#__codelineno-94-14"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">Pop</span><span class="p">();</span>
+<a id="__codelineno-94-15" name="__codelineno-94-15" href="#__codelineno-94-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-94-16" name="__codelineno-94-16" href="#__codelineno-94-16"></a><span class="w">    </span><span class="c1">// res = 1+2+3+...+n</span>
+<a id="__codelineno-94-17" name="__codelineno-94-17" href="#__codelineno-94-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-94-18" name="__codelineno-94-18" href="#__codelineno-94-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.go</span><pre><span></span><code><a id="__codelineno-95-1" name="__codelineno-95-1" href="#__codelineno-95-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">forLoopRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.go</span><pre><span></span><code><a id="__codelineno-95-1" name="__codelineno-95-1" href="#__codelineno-95-1"></a><span class="cm">/* 反復で再帰を模擬する */</span>
+<a id="__codelineno-95-2" name="__codelineno-95-2" href="#__codelineno-95-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">forLoopRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-95-3" name="__codelineno-95-3" href="#__codelineno-95-3"></a><span class="w">    </span><span class="c1">// 明示的なスタックを使ってシステムコールスタックを模擬する</span>
+<a id="__codelineno-95-4" name="__codelineno-95-4" href="#__codelineno-95-4"></a><span class="w">    </span><span class="nx">stack</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">list</span><span class="p">.</span><span class="nx">New</span><span class="p">()</span>
+<a id="__codelineno-95-5" name="__codelineno-95-5" href="#__codelineno-95-5"></a><span class="w">    </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-95-6" name="__codelineno-95-6" href="#__codelineno-95-6"></a><span class="w">    </span><span class="c1">// 再帰：再帰呼び出し</span>
+<a id="__codelineno-95-7" name="__codelineno-95-7" href="#__codelineno-95-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-95-8" name="__codelineno-95-8" href="#__codelineno-95-8"></a><span class="w">        </span><span class="c1">// 「スタックへのプッシュ」で「再帰」を模擬する</span>
+<a id="__codelineno-95-9" name="__codelineno-95-9" href="#__codelineno-95-9"></a><span class="w">        </span><span class="nx">stack</span><span class="p">.</span><span class="nx">PushBack</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span>
+<a id="__codelineno-95-10" name="__codelineno-95-10" href="#__codelineno-95-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-95-11" name="__codelineno-95-11" href="#__codelineno-95-11"></a><span class="w">    </span><span class="c1">// 帰りがけ：結果を返す</span>
+<a id="__codelineno-95-12" name="__codelineno-95-12" href="#__codelineno-95-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">stack</span><span class="p">.</span><span class="nx">Len</span><span class="p">()</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-95-13" name="__codelineno-95-13" href="#__codelineno-95-13"></a><span class="w">        </span><span class="c1">// 「スタックから取り出す操作」で「帰り」をシミュレート</span>
+<a id="__codelineno-95-14" name="__codelineno-95-14" href="#__codelineno-95-14"></a><span class="w">        </span><span class="nx">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">stack</span><span class="p">.</span><span class="nx">Back</span><span class="p">().</span><span class="nx">Value</span><span class="p">.(</span><span class="kt">int</span><span class="p">)</span>
+<a id="__codelineno-95-15" name="__codelineno-95-15" href="#__codelineno-95-15"></a><span class="w">        </span><span class="nx">stack</span><span class="p">.</span><span class="nx">Remove</span><span class="p">(</span><span class="nx">stack</span><span class="p">.</span><span class="nx">Back</span><span class="p">())</span>
+<a id="__codelineno-95-16" name="__codelineno-95-16" href="#__codelineno-95-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-95-17" name="__codelineno-95-17" href="#__codelineno-95-17"></a><span class="w">    </span><span class="c1">// res = 1+2+3+...+n</span>
+<a id="__codelineno-95-18" name="__codelineno-95-18" href="#__codelineno-95-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
+<a id="__codelineno-95-19" name="__codelineno-95-19" href="#__codelineno-95-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.swift</span><pre><span></span><code><a id="__codelineno-96-1" name="__codelineno-96-1" href="#__codelineno-96-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">forLoopRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.swift</span><pre><span></span><code><a id="__codelineno-96-1" name="__codelineno-96-1" href="#__codelineno-96-1"></a><span class="cm">/* 反復で再帰を模擬する */</span>
+<a id="__codelineno-96-2" name="__codelineno-96-2" href="#__codelineno-96-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">forLoopRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-96-3" name="__codelineno-96-3" href="#__codelineno-96-3"></a><span class="w">    </span><span class="c1">// 明示的なスタックを使ってシステムコールスタックを模擬する</span>
+<a id="__codelineno-96-4" name="__codelineno-96-4" href="#__codelineno-96-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">stack</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
+<a id="__codelineno-96-5" name="__codelineno-96-5" href="#__codelineno-96-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-96-6" name="__codelineno-96-6" href="#__codelineno-96-6"></a><span class="w">    </span><span class="c1">// 再帰：再帰呼び出し</span>
+<a id="__codelineno-96-7" name="__codelineno-96-7" href="#__codelineno-96-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="p">).</span><span class="n">reversed</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-96-8" name="__codelineno-96-8" href="#__codelineno-96-8"></a><span class="w">        </span><span class="c1">// 「スタックへのプッシュ」で「再帰」を模擬する</span>
+<a id="__codelineno-96-9" name="__codelineno-96-9" href="#__codelineno-96-9"></a><span class="w">        </span><span class="n">stack</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-96-10" name="__codelineno-96-10" href="#__codelineno-96-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-96-11" name="__codelineno-96-11" href="#__codelineno-96-11"></a><span class="w">    </span><span class="c1">// 帰りがけ：結果を返す</span>
+<a id="__codelineno-96-12" name="__codelineno-96-12" href="#__codelineno-96-12"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">stack</span><span class="p">.</span><span class="bp">isEmpty</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-96-13" name="__codelineno-96-13" href="#__codelineno-96-13"></a><span class="w">        </span><span class="c1">// 「スタックから取り出す操作」で「帰り」をシミュレート</span>
+<a id="__codelineno-96-14" name="__codelineno-96-14" href="#__codelineno-96-14"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="bp">removeLast</span><span class="p">()</span>
+<a id="__codelineno-96-15" name="__codelineno-96-15" href="#__codelineno-96-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-96-16" name="__codelineno-96-16" href="#__codelineno-96-16"></a><span class="w">    </span><span class="c1">// res = 1+2+3+...+n</span>
+<a id="__codelineno-96-17" name="__codelineno-96-17" href="#__codelineno-96-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-96-18" name="__codelineno-96-18" href="#__codelineno-96-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.js</span><pre><span></span><code><a id="__codelineno-97-1" name="__codelineno-97-1" href="#__codelineno-97-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">forLoopRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.js</span><pre><span></span><code><a id="__codelineno-97-1" name="__codelineno-97-1" href="#__codelineno-97-1"></a><span class="cm">/* 反復で再帰を模擬する */</span>
+<a id="__codelineno-97-2" name="__codelineno-97-2" href="#__codelineno-97-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">forLoopRecur</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-97-3" name="__codelineno-97-3" href="#__codelineno-97-3"></a><span class="w">    </span><span class="c1">// 明示的なスタックを使ってシステムコールスタックを模擬する</span>
+<a id="__codelineno-97-4" name="__codelineno-97-4" href="#__codelineno-97-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-97-5" name="__codelineno-97-5" href="#__codelineno-97-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-97-6" name="__codelineno-97-6" href="#__codelineno-97-6"></a><span class="w">    </span><span class="c1">// 再帰：再帰呼び出し</span>
+<a id="__codelineno-97-7" name="__codelineno-97-7" href="#__codelineno-97-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-97-8" name="__codelineno-97-8" href="#__codelineno-97-8"></a><span class="w">        </span><span class="c1">// 「スタックへのプッシュ」で「再帰」を模擬する</span>
+<a id="__codelineno-97-9" name="__codelineno-97-9" href="#__codelineno-97-9"></a><span class="w">        </span><span class="nx">stack</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
+<a id="__codelineno-97-10" name="__codelineno-97-10" href="#__codelineno-97-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-97-11" name="__codelineno-97-11" href="#__codelineno-97-11"></a><span class="w">    </span><span class="c1">// 帰りがけ：結果を返す</span>
+<a id="__codelineno-97-12" name="__codelineno-97-12" href="#__codelineno-97-12"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">stack</span><span class="p">.</span><span class="nx">length</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-97-13" name="__codelineno-97-13" href="#__codelineno-97-13"></a><span class="w">        </span><span class="c1">// 「スタックから取り出す操作」で「帰り」をシミュレート</span>
+<a id="__codelineno-97-14" name="__codelineno-97-14" href="#__codelineno-97-14"></a><span class="w">        </span><span class="nx">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">stack</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-97-15" name="__codelineno-97-15" href="#__codelineno-97-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-97-16" name="__codelineno-97-16" href="#__codelineno-97-16"></a><span class="w">    </span><span class="c1">// res = 1+2+3+...+n</span>
+<a id="__codelineno-97-17" name="__codelineno-97-17" href="#__codelineno-97-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-97-18" name="__codelineno-97-18" href="#__codelineno-97-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.ts</span><pre><span></span><code><a id="__codelineno-98-1" name="__codelineno-98-1" href="#__codelineno-98-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">forLoopRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.ts</span><pre><span></span><code><a id="__codelineno-98-1" name="__codelineno-98-1" href="#__codelineno-98-1"></a><span class="cm">/* 反復で再帰を模擬する */</span>
+<a id="__codelineno-98-2" name="__codelineno-98-2" href="#__codelineno-98-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">forLoopRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-98-3" name="__codelineno-98-3" href="#__codelineno-98-3"></a><span class="w">    </span><span class="c1">// 明示的なスタックを使ってシステムコールスタックを模擬する</span>
+<a id="__codelineno-98-4" name="__codelineno-98-4" href="#__codelineno-98-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">stack</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-98-5" name="__codelineno-98-5" href="#__codelineno-98-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-98-6" name="__codelineno-98-6" href="#__codelineno-98-6"></a><span class="w">    </span><span class="c1">// 再帰：再帰呼び出し</span>
+<a id="__codelineno-98-7" name="__codelineno-98-7" href="#__codelineno-98-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-98-8" name="__codelineno-98-8" href="#__codelineno-98-8"></a><span class="w">        </span><span class="c1">// 「スタックへのプッシュ」で「再帰」を模擬する</span>
+<a id="__codelineno-98-9" name="__codelineno-98-9" href="#__codelineno-98-9"></a><span class="w">        </span><span class="nx">stack</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
+<a id="__codelineno-98-10" name="__codelineno-98-10" href="#__codelineno-98-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-98-11" name="__codelineno-98-11" href="#__codelineno-98-11"></a><span class="w">    </span><span class="c1">// 帰りがけ：結果を返す</span>
+<a id="__codelineno-98-12" name="__codelineno-98-12" href="#__codelineno-98-12"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">stack</span><span class="p">.</span><span class="nx">length</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-98-13" name="__codelineno-98-13" href="#__codelineno-98-13"></a><span class="w">        </span><span class="c1">// 「スタックから取り出す操作」で「帰り」をシミュレート</span>
+<a id="__codelineno-98-14" name="__codelineno-98-14" href="#__codelineno-98-14"></a><span class="w">        </span><span class="nx">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">stack</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-98-15" name="__codelineno-98-15" href="#__codelineno-98-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-98-16" name="__codelineno-98-16" href="#__codelineno-98-16"></a><span class="w">    </span><span class="c1">// res = 1+2+3+...+n</span>
+<a id="__codelineno-98-17" name="__codelineno-98-17" href="#__codelineno-98-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-98-18" name="__codelineno-98-18" href="#__codelineno-98-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.dart</span><pre><span></span><code><a id="__codelineno-99-1" name="__codelineno-99-1" href="#__codelineno-99-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">forLoopRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.dart</span><pre><span></span><code><a id="__codelineno-99-1" name="__codelineno-99-1" href="#__codelineno-99-1"></a><span class="cm">/* 反復で再帰を模擬する */</span>
+<a id="__codelineno-99-2" name="__codelineno-99-2" href="#__codelineno-99-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">forLoopRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-99-3" name="__codelineno-99-3" href="#__codelineno-99-3"></a><span class="w">  </span><span class="c1">// 明示的なスタックを使ってシステムコールスタックを模擬する</span>
+<a id="__codelineno-99-4" name="__codelineno-99-4" href="#__codelineno-99-4"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-99-5" name="__codelineno-99-5" href="#__codelineno-99-5"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-99-6" name="__codelineno-99-6" href="#__codelineno-99-6"></a><span class="w">  </span><span class="c1">// 再帰：再帰呼び出し</span>
+<a id="__codelineno-99-7" name="__codelineno-99-7" href="#__codelineno-99-7"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-99-8" name="__codelineno-99-8" href="#__codelineno-99-8"></a><span class="w">    </span><span class="c1">// 「スタックへのプッシュ」で「再帰」を模擬する</span>
+<a id="__codelineno-99-9" name="__codelineno-99-9" href="#__codelineno-99-9"></a><span class="w">    </span><span class="n">stack</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-99-10" name="__codelineno-99-10" href="#__codelineno-99-10"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-99-11" name="__codelineno-99-11" href="#__codelineno-99-11"></a><span class="w">  </span><span class="c1">// 帰りがけ：結果を返す</span>
+<a id="__codelineno-99-12" name="__codelineno-99-12" href="#__codelineno-99-12"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">stack</span><span class="p">.</span><span class="n">isEmpty</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-99-13" name="__codelineno-99-13" href="#__codelineno-99-13"></a><span class="w">    </span><span class="c1">// 「スタックから取り出す操作」で「帰り」をシミュレート</span>
+<a id="__codelineno-99-14" name="__codelineno-99-14" href="#__codelineno-99-14"></a><span class="w">    </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">removeLast</span><span class="p">();</span>
+<a id="__codelineno-99-15" name="__codelineno-99-15" href="#__codelineno-99-15"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-99-16" name="__codelineno-99-16" href="#__codelineno-99-16"></a><span class="w">  </span><span class="c1">// res = 1+2+3+...+n</span>
+<a id="__codelineno-99-17" name="__codelineno-99-17" href="#__codelineno-99-17"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-99-18" name="__codelineno-99-18" href="#__codelineno-99-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.rs</span><pre><span></span><code><a id="__codelineno-100-1" name="__codelineno-100-1" href="#__codelineno-100-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">for_loop_recur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.rs</span><pre><span></span><code><a id="__codelineno-100-1" name="__codelineno-100-1" href="#__codelineno-100-1"></a><span class="cm">/* 反復で再帰を模擬する */</span>
+<a id="__codelineno-100-2" name="__codelineno-100-2" href="#__codelineno-100-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">for_loop_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-3" name="__codelineno-100-3" href="#__codelineno-100-3"></a><span class="w">    </span><span class="c1">// 明示的なスタックを使ってシステムコールスタックを模擬する</span>
+<a id="__codelineno-100-4" name="__codelineno-100-4" href="#__codelineno-100-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-100-5" name="__codelineno-100-5" href="#__codelineno-100-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-100-6" name="__codelineno-100-6" href="#__codelineno-100-6"></a><span class="w">    </span><span class="c1">// 再帰：再帰呼び出し</span>
+<a id="__codelineno-100-7" name="__codelineno-100-7" href="#__codelineno-100-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">..=</span><span class="n">n</span><span class="p">).</span><span class="n">rev</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-8" name="__codelineno-100-8" href="#__codelineno-100-8"></a><span class="w">        </span><span class="c1">// 「スタックへのプッシュ」で「再帰」を模擬する</span>
+<a id="__codelineno-100-9" name="__codelineno-100-9" href="#__codelineno-100-9"></a><span class="w">        </span><span class="n">stack</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-100-10" name="__codelineno-100-10" href="#__codelineno-100-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-100-11" name="__codelineno-100-11" href="#__codelineno-100-11"></a><span class="w">    </span><span class="c1">// 帰りがけ：結果を返す</span>
+<a id="__codelineno-100-12" name="__codelineno-100-12" href="#__codelineno-100-12"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">stack</span><span class="p">.</span><span class="n">is_empty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-13" name="__codelineno-100-13" href="#__codelineno-100-13"></a><span class="w">        </span><span class="c1">// 「スタックから取り出す操作」で「帰り」をシミュレート</span>
+<a id="__codelineno-100-14" name="__codelineno-100-14" href="#__codelineno-100-14"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span>
+<a id="__codelineno-100-15" name="__codelineno-100-15" href="#__codelineno-100-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-100-16" name="__codelineno-100-16" href="#__codelineno-100-16"></a><span class="w">    </span><span class="c1">// res = 1+2+3+...+n</span>
+<a id="__codelineno-100-17" name="__codelineno-100-17" href="#__codelineno-100-17"></a><span class="w">    </span><span class="n">res</span>
+<a id="__codelineno-100-18" name="__codelineno-100-18" href="#__codelineno-100-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.c</span><pre><span></span><code><a id="__codelineno-101-1" name="__codelineno-101-1" href="#__codelineno-101-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">forLoopRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.c</span><pre><span></span><code><a id="__codelineno-101-1" name="__codelineno-101-1" href="#__codelineno-101-1"></a><span class="cm">/* 反復で再帰を模擬する */</span>
+<a id="__codelineno-101-2" name="__codelineno-101-2" href="#__codelineno-101-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">forLoopRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-101-3" name="__codelineno-101-3" href="#__codelineno-101-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">stack</span><span class="p">[</span><span class="mi">1000</span><span class="p">];</span><span class="w"> </span><span class="c1">// 大きな配列を使ってスタックを実装する</span>
+<a id="__codelineno-101-4" name="__codelineno-101-4" href="#__codelineno-101-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">top</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span><span class="w">    </span><span class="c1">// スタックトップのインデックス</span>
+<a id="__codelineno-101-5" name="__codelineno-101-5" href="#__codelineno-101-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-101-6" name="__codelineno-101-6" href="#__codelineno-101-6"></a><span class="w">    </span><span class="c1">// 再帰：再帰呼び出し</span>
+<a id="__codelineno-101-7" name="__codelineno-101-7" href="#__codelineno-101-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-101-8" name="__codelineno-101-8" href="#__codelineno-101-8"></a><span class="w">        </span><span class="c1">// 「スタックへのプッシュ」で「再帰」を模擬する</span>
+<a id="__codelineno-101-9" name="__codelineno-101-9" href="#__codelineno-101-9"></a><span class="w">        </span><span class="n">stack</span><span class="p">[</span><span class="mi">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">top</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-101-10" name="__codelineno-101-10" href="#__codelineno-101-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-101-11" name="__codelineno-101-11" href="#__codelineno-101-11"></a><span class="w">    </span><span class="c1">// 帰りがけ：結果を返す</span>
+<a id="__codelineno-101-12" name="__codelineno-101-12" href="#__codelineno-101-12"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">top</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-101-13" name="__codelineno-101-13" href="#__codelineno-101-13"></a><span class="w">        </span><span class="c1">// 「スタックから取り出す操作」で「帰り」をシミュレート</span>
+<a id="__codelineno-101-14" name="__codelineno-101-14" href="#__codelineno-101-14"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">stack</span><span class="p">[</span><span class="n">top</span><span class="o">--</span><span class="p">];</span>
+<a id="__codelineno-101-15" name="__codelineno-101-15" href="#__codelineno-101-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-101-16" name="__codelineno-101-16" href="#__codelineno-101-16"></a><span class="w">    </span><span class="c1">// res = 1+2+3+...+n</span>
+<a id="__codelineno-101-17" name="__codelineno-101-17" href="#__codelineno-101-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-101-18" name="__codelineno-101-18" href="#__codelineno-101-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.kt</span><pre><span></span><code><a id="__codelineno-102-1" name="__codelineno-102-1" href="#__codelineno-102-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">forLoopRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.kt</span><pre><span></span><code><a id="__codelineno-102-1" name="__codelineno-102-1" href="#__codelineno-102-1"></a><span class="cm">/* 反復で再帰を模擬する */</span>
+<a id="__codelineno-102-2" name="__codelineno-102-2" href="#__codelineno-102-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">forLoopRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-102-3" name="__codelineno-102-3" href="#__codelineno-102-3"></a><span class="w">    </span><span class="c1">// 明示的なスタックを使ってシステムコールスタックを模擬する</span>
+<a id="__codelineno-102-4" name="__codelineno-102-4" href="#__codelineno-102-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Stack</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-102-5" name="__codelineno-102-5" href="#__codelineno-102-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-102-6" name="__codelineno-102-6" href="#__codelineno-102-6"></a><span class="w">    </span><span class="c1">// 再帰: 再帰呼び出し</span>
+<a id="__codelineno-102-7" name="__codelineno-102-7" href="#__codelineno-102-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="n">downTo</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-102-8" name="__codelineno-102-8" href="#__codelineno-102-8"></a><span class="w">        </span><span class="c1">// 「スタックへのプッシュ」で「再帰」を模擬する</span>
+<a id="__codelineno-102-9" name="__codelineno-102-9" href="#__codelineno-102-9"></a><span class="w">        </span><span class="n">stack</span><span class="p">.</span><span class="na">push</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-102-10" name="__codelineno-102-10" href="#__codelineno-102-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-102-11" name="__codelineno-102-11" href="#__codelineno-102-11"></a><span class="w">    </span><span class="c1">// 戻る: 結果を返す</span>
+<a id="__codelineno-102-12" name="__codelineno-102-12" href="#__codelineno-102-12"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">stack</span><span class="p">.</span><span class="na">isNotEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-102-13" name="__codelineno-102-13" href="#__codelineno-102-13"></a><span class="w">        </span><span class="c1">// 「スタックから取り出す操作」で「帰り」をシミュレート</span>
+<a id="__codelineno-102-14" name="__codelineno-102-14" href="#__codelineno-102-14"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">pop</span><span class="p">()</span>
+<a id="__codelineno-102-15" name="__codelineno-102-15" href="#__codelineno-102-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-102-16" name="__codelineno-102-16" href="#__codelineno-102-16"></a><span class="w">    </span><span class="c1">// res = 1+2+3+...+n</span>
+<a id="__codelineno-102-17" name="__codelineno-102-17" href="#__codelineno-102-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-102-18" name="__codelineno-102-18" href="#__codelineno-102-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">recursion.rb</span><pre><span></span><code><a id="__codelineno-103-1" name="__codelineno-103-1" href="#__codelineno-103-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">for_loop_recur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">recursion.rb</span><pre><span></span><code><a id="__codelineno-103-1" name="__codelineno-103-1" href="#__codelineno-103-1"></a><span class="c1">### 反復で再帰をシミュレート ###</span>
+<a id="__codelineno-103-2" name="__codelineno-103-2" href="#__codelineno-103-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">for_loop_recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-103-3" name="__codelineno-103-3" href="#__codelineno-103-3"></a><span class="w">  </span><span class="c1"># 明示的なスタックを使ってシステムコールスタックを模擬する</span>
+<a id="__codelineno-103-4" name="__codelineno-103-4" href="#__codelineno-103-4"></a><span class="w">  </span><span class="n">stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-103-5" name="__codelineno-103-5" href="#__codelineno-103-5"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-103-6" name="__codelineno-103-6" href="#__codelineno-103-6"></a>
+<a id="__codelineno-103-7" name="__codelineno-103-7" href="#__codelineno-103-7"></a><span class="w">  </span><span class="c1"># 再帰：再帰呼び出し</span>
+<a id="__codelineno-103-8" name="__codelineno-103-8" href="#__codelineno-103-8"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">n</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-103-9" name="__codelineno-103-9" href="#__codelineno-103-9"></a><span class="w">    </span><span class="c1"># 「スタックへのプッシュ」で「再帰」を模擬する</span>
+<a id="__codelineno-103-10" name="__codelineno-103-10" href="#__codelineno-103-10"></a><span class="w">    </span><span class="n">stack</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-103-11" name="__codelineno-103-11" href="#__codelineno-103-11"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-103-12" name="__codelineno-103-12" href="#__codelineno-103-12"></a><span class="w">  </span><span class="c1"># 帰りがけ：結果を返す</span>
+<a id="__codelineno-103-13" name="__codelineno-103-13" href="#__codelineno-103-13"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">stack</span><span class="o">.</span><span class="n">empty?</span>
+<a id="__codelineno-103-14" name="__codelineno-103-14" href="#__codelineno-103-14"></a><span class="w">    </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">stack</span><span class="o">.</span><span class="n">pop</span>
+<a id="__codelineno-103-15" name="__codelineno-103-15" href="#__codelineno-103-15"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-103-16" name="__codelineno-103-16" href="#__codelineno-103-16"></a>
+<a id="__codelineno-103-17" name="__codelineno-103-17" href="#__codelineno-103-17"></a><span class="w">  </span><span class="c1"># res = 1+2+3+...+n</span>
+<a id="__codelineno-103-18" name="__codelineno-103-18" href="#__codelineno-103-18"></a><span class="w">  </span><span class="n">res</span>
+<a id="__codelineno-103-19" name="__codelineno-103-19" href="#__codelineno-103-19"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>上記のコードを観察すると、再帰が反復に変換されたとき、コードはより複雑になります。反復と再帰はしばしば相互に変換できますが、2つの理由でそうすることが常に推奨されるわけではありません：</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20for_loop_recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%8F%8D%E5%BE%A9%E3%81%A7%E5%86%8D%E5%B8%B0%E3%82%92%E6%A8%A1%E6%93%AC%E3%81%99%E3%82%8B%22%22%22%0A%20%20%20%20%23%20%E6%98%8E%E7%A4%BA%E7%9A%84%E3%81%AA%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%82%92%E4%BD%BF%E3%81%A3%E3%81%A6%E3%82%B7%E3%82%B9%E3%83%86%E3%83%A0%E3%82%B3%E3%83%BC%E3%83%AB%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%82%92%E6%A8%A1%E6%93%AC%E3%81%99%E3%82%8B%0A%20%20%20%20stack%20%3D%20%5B%5D%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20%23%20%E5%86%8D%E5%B8%B0%EF%BC%9A%E5%86%8D%E5%B8%B0%E5%91%BC%E3%81%B3%E5%87%BA%E3%81%97%0A%20%20%20%20for%20i%20in%20range%28n%2C%200%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E3%80%8C%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%81%B8%E3%81%AE%E3%83%97%E3%83%83%E3%82%B7%E3%83%A5%E3%80%8D%E3%81%A7%E3%80%8C%E5%86%8D%E5%B8%B0%E3%80%8D%E3%82%92%E6%A8%A1%E6%93%AC%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20stack.append%28i%29%0A%20%20%20%20%23%20%E5%B8%B0%E3%82%8A%E3%81%8C%E3%81%91%EF%BC%9A%E7%B5%90%E6%9E%9C%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20while%20stack%3A%0A%20%20%20%20%20%20%20%20%23%20%E3%80%8C%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%81%8B%E3%82%89%E5%8F%96%E3%82%8A%E5%87%BA%E3%81%99%E6%93%8D%E4%BD%9C%E3%80%8D%E3%81%A7%E3%80%8C%E5%B8%B0%E3%82%8A%E3%80%8D%E3%82%92%E3%82%B7%E3%83%9F%E3%83%A5%E3%83%AC%E3%83%BC%E3%83%88%0A%20%20%20%20%20%20%20%20res%20%2B%3D%20stack.pop%28%29%0A%20%20%20%20%23%20res%20%3D%201%2B2%2B3%2B...%2Bn%0A%20%20%20%20return%20res%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20for_loop_recur%28n%29%0A%20%20%20%20print%28f%22%5Cn%E5%8F%8D%E5%BE%A9%E3%81%A7%E5%86%8D%E5%B8%B0%E3%82%92%E3%82%B7%E3%83%9F%E3%83%A5%E3%83%AC%E3%83%BC%E3%83%88%E3%81%97%E3%81%9F%E5%90%88%E8%A8%88%E7%B5%90%E6%9E%9C%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20for_loop_recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%8F%8D%E5%BE%A9%E3%81%A7%E5%86%8D%E5%B8%B0%E3%82%92%E6%A8%A1%E6%93%AC%E3%81%99%E3%82%8B%22%22%22%0A%20%20%20%20%23%20%E6%98%8E%E7%A4%BA%E7%9A%84%E3%81%AA%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%82%92%E4%BD%BF%E3%81%A3%E3%81%A6%E3%82%B7%E3%82%B9%E3%83%86%E3%83%A0%E3%82%B3%E3%83%BC%E3%83%AB%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%82%92%E6%A8%A1%E6%93%AC%E3%81%99%E3%82%8B%0A%20%20%20%20stack%20%3D%20%5B%5D%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20%23%20%E5%86%8D%E5%B8%B0%EF%BC%9A%E5%86%8D%E5%B8%B0%E5%91%BC%E3%81%B3%E5%87%BA%E3%81%97%0A%20%20%20%20for%20i%20in%20range%28n%2C%200%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E3%80%8C%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%81%B8%E3%81%AE%E3%83%97%E3%83%83%E3%82%B7%E3%83%A5%E3%80%8D%E3%81%A7%E3%80%8C%E5%86%8D%E5%B8%B0%E3%80%8D%E3%82%92%E6%A8%A1%E6%93%AC%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20stack.append%28i%29%0A%20%20%20%20%23%20%E5%B8%B0%E3%82%8A%E3%81%8C%E3%81%91%EF%BC%9A%E7%B5%90%E6%9E%9C%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20while%20stack%3A%0A%20%20%20%20%20%20%20%20%23%20%E3%80%8C%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%81%8B%E3%82%89%E5%8F%96%E3%82%8A%E5%87%BA%E3%81%99%E6%93%8D%E4%BD%9C%E3%80%8D%E3%81%A7%E3%80%8C%E5%B8%B0%E3%82%8A%E3%80%8D%E3%82%92%E3%82%B7%E3%83%9F%E3%83%A5%E3%83%AC%E3%83%BC%E3%83%88%0A%20%20%20%20%20%20%20%20res%20%2B%3D%20stack.pop%28%29%0A%20%20%20%20%23%20res%20%3D%201%2B2%2B3%2B...%2Bn%0A%20%20%20%20return%20res%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20for_loop_recur%28n%29%0A%20%20%20%20print%28f%22%5Cn%E5%8F%8D%E5%BE%A9%E3%81%A7%E5%86%8D%E5%B8%B0%E3%82%92%E3%82%B7%E3%83%9F%E3%83%A5%E3%83%AC%E3%83%BC%E3%83%88%E3%81%97%E3%81%9F%E5%90%88%E8%A8%88%E7%B5%90%E6%9E%9C%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>上のコードを見ると、再帰を反復へ変換すると、コードはより複雑になります。反復と再帰は多くの場合に相互変換できますが、常にそうする価値があるとは限りません。理由は次の 2 点です。</p>
 <ul>
-<li>変換されたコードは理解がより困難になり、読みにくくなる可能性があります。</li>
-<li>一部の複雑な問題では、システムの呼び出しスタックの動作をシミュレートすることは非常に困難です。</li>
+<li>変換後のコードは理解しにくくなり、可読性が下がる可能性があります。</li>
+<li>複雑な問題によっては、システムの呼び出しスタックの振る舞いを模擬すること自体が非常に難しい場合があります。</li>
 </ul>
-<p>結論として、<strong>反復または再帰を選択するかは問題の具体的な性質によります</strong>。プログラミングの実践では、両方の長所と短所を比較検討し、手元の状況に最も適したアプローチを選択することが重要です。</p>
+<p>要するに、<strong>反復を選ぶか再帰を選ぶかは、対象となる問題の性質によって決まります</strong>。実際のプログラミングでは、両者の長所と短所を見極め、状況に応じて適切な方法を選ぶことが重要です。</p>
 
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     class="md-footer__link md-footer__link--prev"
-    aria-label="前: 2.1 &amp;nbsp; アルゴリズムの効率評価"
+    aria-label="前: 2.1 &amp;nbsp; アルゴリズム効率の評価"
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       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
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-        <title>2.1 アルゴリズムの効率評価 - Hello アルゴリズム</title>
+        <title>2.1 アルゴリズム効率の評価 - Hello アルゴリズム</title>
       
     
     
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         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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-    8.2 &nbsp; ヒープ構築操作
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 <!-- Page content -->
-<h1 id="21">2.1 &nbsp; アルゴリズムの効率評価<a class="headerlink" href="#21" title="Permanent link">&para;</a></h1>
-<p>アルゴリズム設計において、私たちは順序に従って以下の2つの目標を追求します。</p>
+<h1 id="21">2.1 &nbsp; アルゴリズム効率の評価<a class="headerlink" href="#21" title="Permanent link">&para;</a></h1>
+<p>アルゴリズム設計では、次の 2 つのレベルの目標を順に追求します。</p>
 <ol>
-<li><strong>問題の解決策を見つける</strong>: アルゴリズムは、指定された入力範囲内で確実に正しい解を見つけることができるべきです。</li>
-<li><strong>最適解を求める</strong>: 同じ問題に対して複数の解決策が存在する場合があり、私たちは可能な限り最も効率的なアルゴリズムを見つけることを目指します。</li>
+<li><strong>問題の解法を見つける</strong>：アルゴリズムは、定められた入力範囲内で問題の正しい解を確実に求められる必要があります。</li>
+<li><strong>最適な解法を追求する</strong>：同じ問題に対して複数の解法が存在する場合があり、私たちはできるだけ効率的なアルゴリズムを見つけたいと考えます。</li>
 </ol>
-<p>つまり、問題を解決できることを前提として、アルゴリズムの効率がアルゴリズムを評価する主要な基準となっており、これには以下の2つの次元が含まれます。</p>
+<p>つまり、問題を解けることを前提として、アルゴリズム効率はその良し悪しを測る主要な評価指標となっており、次の 2 つの観点を含みます。</p>
 <ul>
-<li><strong>時間効率</strong>: アルゴリズムが実行される速度。</li>
-<li><strong>空間効率</strong>: アルゴリズムが占有するメモリ空間のサイズ。</li>
+<li><strong>時間効率</strong>：アルゴリズムの実行時間の長さ。</li>
+<li><strong>空間効率</strong>：アルゴリズムが使用するメモリ空間の大きさ。</li>
 </ul>
-<p>要するに、<strong>私たちの目標は、高速でメモリ効率の良いデータ構造とアルゴリズムを設計することです</strong>。アルゴリズムの効率を効果的に評価することは重要です。なぜなら、そうすることで初めて様々なアルゴリズムを比較し、アルゴリズムの設計と最適化プロセスを導くことができるからです。</p>
-<p>効率評価には主に2つの方法があります：実際のテストと理論的推定です。</p>
-<h2 id="211">2.1.1 &nbsp; 実際のテスト<a class="headerlink" href="#211" title="Permanent link">&para;</a></h2>
-<p>アルゴリズム<code>A</code>と<code>B</code>があり、どちらも同じ問題を解決でき、それらの効率を比較する必要があるとします。最も直接的な方法は、コンピュータを使用してこれら2つのアルゴリズムを実行し、実行時間とメモリ使用量を監視・記録することです。この評価方法は実際の状況を反映しますが、大きな制限があります。</p>
-<p>一方で、<strong>テスト環境からの干渉を排除することは困難です</strong>。ハードウェア構成はアルゴリズムの性能に影響を与える可能性があります。例えば、並列度の高いアルゴリズムはマルチコアCPUでの実行により適していますし、集約的なメモリ操作を含むアルゴリズムは高性能メモリでより良い性能を発揮します。アルゴリズムのテスト結果は、異なるマシン間で変わる可能性があります。これは、平均効率を計算するために複数のマシンでテストすることが実用的でないことを意味します。</p>
-<p>一方で、<strong>完全なテストを実施することは非常にリソース集約的です</strong>。アルゴリズムの効率は入力データサイズによって変わります。例えば、データ量が少ない場合はアルゴリズム<code>A</code>が<code>B</code>より速く実行される可能性がありますが、データ量が多い場合はテスト結果が逆になる可能性があります。したがって、説得力のある結論を導くためには、幅広い入力データサイズをテストする必要があり、これには過度な計算リソースが必要になります。</p>
-<h2 id="212">2.1.2 &nbsp; 理論的推定<a class="headerlink" href="#212" title="Permanent link">&para;</a></h2>
-<p>実際のテストの大きな制限により、計算のみでアルゴリズムの効率を評価することを検討できます。この推定方法は<u>漸近的複雑度解析</u>、または単に<u>複雑度解析</u>として知られています。</p>
-<p>複雑度解析は、アルゴリズムの実行に必要な時間と空間リソースと入力データのサイズとの関係を反映します。<strong>これは、入力データのサイズが増加するにつれて、アルゴリズムに必要な時間と空間の増加傾向を記述します</strong>。この定義は複雑に聞こえるかもしれませんが、より良く理解するために3つの重要なポイントに分解できます。</p>
+<p>簡単に言えば、**私たちの目標は「高速で省メモリ」なデータ構造とアルゴリズムを設計すること**です。そして、アルゴリズム効率を効果的に評価することは非常に重要です。そうすることで初めて、さまざまなアルゴリズムを比較し、さらにアルゴリズム設計と最適化の過程を導けるからです。</p>
+<p>効率の評価方法は主に 2 種類に分けられます。実測と理論的な見積もりです。</p>
+<h2 id="211">2.1.1 &nbsp; 実測<a class="headerlink" href="#211" title="Permanent link">&para;</a></h2>
+<p>いまアルゴリズム <code>A</code> とアルゴリズム <code>B</code> があり、どちらも同じ問題を解けるとします。この 2 つのアルゴリズムの効率を比較する必要がある場合、最も直接的な方法は 1 台のコンピュータで両者を実行し、その実行時間とメモリ使用量を監視して記録することです。この評価方法は実際の状況を反映できますが、大きな制約もあります。</p>
+<p>一方では、**テスト環境による干渉要因を排除しにくい**という問題があります。ハードウェア構成はアルゴリズムの性能に影響します。たとえば、並列度の高いアルゴリズムはマルチコア CPU での実行により適しており、メモリアクセスが集中的なアルゴリズムは高性能メモリ上でより良い性能を示します。つまり、異なるマシンでのテスト結果は一致しない可能性があります。これは、さまざまなマシンでテストして平均効率を統計的に求める必要があることを意味しますが、それは現実的ではありません。</p>
+<p>他方では、**完全なテストを実施するには非常に多くの資源が必要**です。入力データ量が変化すると、アルゴリズムは異なる効率を示します。たとえば、入力データ量が小さいときはアルゴリズム <code>A</code> の実行時間がアルゴリズム <code>B</code> より短くても、入力データ量が大きいときには結果がちょうど逆になるかもしれません。そのため、説得力のある結論を得るには、さまざまな規模の入力データでテストする必要があり、それには大量の計算資源を要します。</p>
+<h2 id="212">2.1.2 &nbsp; 理論的な見積もり<a class="headerlink" href="#212" title="Permanent link">&para;</a></h2>
+<p>実測には大きな制約があるため、いくつかの計算だけによってアルゴリズムの効率を評価することを考えられます。この見積もり方法は<u>漸近計算量解析（asymptotic complexity analysis）</u>と呼ばれ、略して<u>計算量解析</u>といいます。</p>
+<p>計算量解析は、アルゴリズムの実行に必要な時間資源と空間資源が入力データ規模とどのような関係にあるかを表します。<strong>これは、入力データ規模が増加するにつれて、アルゴリズムの実行に必要な時間と空間がどのように増加するかという傾向を記述するものです</strong>。この定義はややわかりにくいので、次の 3 つのポイントに分けて理解できます。</p>
 <ul>
-<li>「時間と空間リソース」は、それぞれ<u>時間計算量</u>と<u>空間計算量</u>に対応します。</li>
-<li>「入力データのサイズが増加するにつれて」は、複雑度がアルゴリズムの効率と入力データ量との関係を反映することを意味します。</li>
-<li>「時間と空間の増加傾向」は、複雑度解析が実行時間や占有空間の具体的な値ではなく、時間や空間が増加する「率」に焦点を当てることを示します。</li>
+<li>「時間資源と空間資源」は、それぞれ<u>時間計算量（time complexity）</u>と<u>空間計算量（space complexity）</u>に対応します。</li>
+<li>「入力データ規模が増加するにつれて」とは、計算量がアルゴリズムの実行効率と入力データ規模との関係を反映していることを意味します。</li>
+<li>「時間と空間の増加傾向」とは、計算量解析が注目するのは実行時間や使用空間の具体的な値ではなく、時間や空間の増加の「速さ」であることを示します。</li>
 </ul>
-<p><strong>複雑度解析は実際のテスト方法の欠点を克服します</strong>。これは以下の側面で反映されます：</p>
+<p><strong>計算量解析は実測という方法の欠点を克服しています</strong>。その点は次のように表れます。</p>
 <ul>
-<li>実際にコードを実行する必要がないため、より環境に優しく、エネルギー効率が良いです。</li>
-<li>テスト環境に依存せず、すべての動作プラットフォームに適用できます。</li>
-<li>異なるデータ量でのアルゴリズムの効率を反映でき、特に大量データでのアルゴリズムの性能を示します。</li>
+<li>実際にコードを動かす必要がなく、より環境にやさしく省エネルギーです。</li>
+<li>テスト環境から独立しており、解析結果はすべての実行プラットフォームに適用できます。</li>
+<li>異なるデータ量におけるアルゴリズム効率を表せ、とくに大規模データ量での性能を反映できます。</li>
 </ul>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>複雑度の概念についてまだ混乱している場合でも、心配しないでください。以降の章で詳しく取り上げます。</p>
+<p>それでも計算量の概念がまだわかりにくくても、心配はいりません。後続の章で詳しく説明します。</p>
 </div>
-<p>複雑度解析は、アルゴリズムの効率を評価する「ものさし」を提供し、実行に必要な時間と空間リソースを測定し、異なるアルゴリズムの効率を比較することを可能にします。</p>
-<p>複雑度は数学的概念であり、初心者には抽象的で困難かもしれません。この観点から、複雑度解析は最初に紹介するのに最も適したトピックではないかもしれません。しかし、特定のデータ構造やアルゴリズムの特性について議論するとき、その速度と空間使用量を分析することを避けるのは困難です。</p>
-<p>要約すると、データ構造とアルゴリズムに深く入る前に複雑度解析の基本的な理解を身につけることをお勧めします。<strong>これにより、簡単なアルゴリズムで複雑度解析を実行できるようになります</strong>。</p>
+<p>計算量解析は、アルゴリズム効率を評価するための「物差し」を私たちに与えてくれます。これにより、あるアルゴリズムの実行に必要な時間資源と空間資源を測り、異なるアルゴリズム同士の効率を比較できます。</p>
+<p>計算量は数学的な概念であり、初学者にとってはやや抽象的で、学習の難度も比較的高いかもしれません。この観点から見ると、計算量解析は最初に紹介する内容としてはあまり適していない可能性があります。しかし、あるデータ構造やアルゴリズムの特徴を議論する際には、その実行速度や空間使用状況の分析を避けることはできません。</p>
+<p>以上を踏まえると、データ構造とアルゴリズムを深く学ぶ前に、**まず計算量解析について初歩的な理解を持ち、簡単なアルゴリズムの計算量解析ができるようにしておくこと**を勧めます。</p>
 
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+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4393,7 +4393,7 @@
   <a href="#242" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2.4.2 &nbsp; 計算方法
+        2.4.2 &nbsp; 推定方法
       
     </span>
   </a>
@@ -4404,19 +4404,19 @@
   <a href="#243" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2.4.3 &nbsp; 一般的な種類
+        2.4.3 &nbsp; よくある型
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="2.4.3 一般的な種類">
+    <nav class="md-nav" aria-label="2.4.3 よくある型">
       <ul class="md-nav__list">
         
           <li class="md-nav__item">
   <a href="#1-o1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; 定数オーダー
+        1. &nbsp; 定数階
       
     </span>
   </a>
@@ -4427,7 +4427,7 @@
   <a href="#2-on" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2. &nbsp; 線形オーダー
+        2. &nbsp; 線形階
       
     </span>
   </a>
@@ -4438,7 +4438,7 @@
   <a href="#3-on2" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3. &nbsp; 二次オーダー
+        3. &nbsp; 平方階
       
     </span>
   </a>
@@ -4449,7 +4449,7 @@
   <a href="#4-o2n" class="md-nav__link">
     <span class="md-ellipsis">
       
-        4. &nbsp; 指数オーダー
+        4. &nbsp; 指数階
       
     </span>
   </a>
@@ -4460,7 +4460,7 @@
   <a href="#5-olog-n" class="md-nav__link">
     <span class="md-ellipsis">
       
-        5. &nbsp; 対数オーダー
+        5. &nbsp; 対数階
       
     </span>
   </a>
@@ -4476,7 +4476,7 @@
   <a href="#244" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2.4.4 &nbsp; 時間と空間のバランス
+        2.4.4 &nbsp; 時間と空間のトレードオフ
       
     </span>
   </a>
@@ -4521,46 +4521,46 @@
 
 <!-- Page content -->
 <h1 id="24">2.4 &nbsp; 空間計算量<a class="headerlink" href="#24" title="Permanent link">&para;</a></h1>
-<p><u>空間計算量</u>は、データ量が増加するにつれてアルゴリズムが占有するメモリ空間の増加傾向を測定するために使用されます。この概念は時間計算量と非常に似ていますが、「実行時間」が「占有メモリ空間」に置き換えられています。</p>
+<p><u>空間計算量（space complexity）</u>は、アルゴリズムが占有するメモリ空間がデータ量の増加に伴ってどのように増えるかを測る指標です。この概念は時間計算量と非常によく似ており、「実行時間」を「占有メモリ空間」に置き換えるだけです。</p>
 <h2 id="241">2.4.1 &nbsp; アルゴリズムに関連する空間<a class="headerlink" href="#241" title="Permanent link">&para;</a></h2>
-<p>アルゴリズムが実行中に使用するメモリ空間には、主に以下の種類があります。</p>
+<p>アルゴリズムが実行中に使用するメモリ空間には、主に次の種類があります。</p>
 <ul>
-<li><strong>入力空間</strong>: アルゴリズムの入力データを格納するために使用されます。</li>
-<li><strong>一時空間</strong>: アルゴリズムの実行中に変数、オブジェクト、関数コンテキスト、その他のデータを格納するために使用されます。</li>
-<li><strong>出力空間</strong>: アルゴリズムの出力データを格納するために使用されます。</li>
+<li><strong>入力空間</strong>：アルゴリズムの入力データを格納するための空間。</li>
+<li><strong>一時空間</strong>：アルゴリズムの実行中に使用する変数、オブジェクト、関数コンテキストなどのデータを格納するための空間。</li>
+<li><strong>出力空間</strong>：アルゴリズムの出力データを格納するための空間。</li>
 </ul>
-<p>一般的に、空間計算量の統計範囲には「一時空間」と「出力空間」の両方が含まれます。</p>
-<p>一時空間はさらに3つの部分に分けることができます。</p>
+<p>一般に、空間計算量の集計範囲は「一時空間」と「出力空間」を合わせたものです。</p>
+<p>一時空間はさらに三つに分けられます。</p>
 <ul>
-<li><strong>一時データ</strong>: アルゴリズムの実行中に様々な定数、変数、オブジェクトなどを保存するために使用されます。</li>
-<li><strong>スタックフレーム空間</strong>: 呼び出された関数のコンテキストデータを保存するために使用されます。システムは関数が呼び出されるたびにスタックの頂上にスタックフレームを作成し、関数が返された後にスタックフレーム空間を解放します。</li>
-<li><strong>命令空間</strong>: コンパイル済みプログラム命令を格納するために使用され、実際の統計では通常無視できます。</li>
+<li><strong>一時データ</strong>：アルゴリズム実行中の各種定数、変数、オブジェクトなどを保存するための空間。</li>
+<li><strong>スタックフレーム空間</strong>：呼び出された関数のコンテキストデータを保存するための空間。システムは関数を呼び出すたびにスタックの先頭にスタックフレームを作成し、関数が戻るとその空間を解放します。</li>
+<li><strong>命令空間</strong>：コンパイル後のプログラム命令を保存するための空間で、実際の集計では通常無視されます。</li>
 </ul>
-<p>プログラムの空間計算量を分析する際、<strong>通常は一時データ、スタックフレーム空間、出力データをカウントします</strong>。以下の図に示されています。</p>
-<p><img alt="Space types used in algorithms" class="animation-figure" src="../space_complexity.assets/space_types.png" /></p>
-<p align="center"> 図 2-15 &nbsp; Space types used in algorithms </p>
+<p>プログラムの空間計算量を分析する際には、<strong>通常、一時データ、スタックフレーム空間、出力データの三つを数えます</strong>。以下の図に示すとおりです。</p>
+<p><img alt="アルゴリズムで使用される関連空間" class="animation-figure" src="../space_complexity.assets/space_types.png" /></p>
+<p align="center"> 図 2-15 &nbsp; アルゴリズムで使用される関連空間 </p>
 
-<p>関連するコードは以下の通りです：</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="1:12"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label></div>
+<p>関連するコードを以下に示します。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">Node</span><span class="p">:</span>
 <a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;クラス&quot;&quot;&quot;</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">x</span>               <span class="c1"># ノード値</span>
-<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">next</span><span class="p">:</span> <span class="n">Node</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>   <span class="c1"># 次のノードへの参照</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">x</span>              <span class="c1"># ノードの値</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">next</span><span class="p">:</span> <span class="n">Node</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># 次のノードへの参照</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="k">def</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;関数&quot;&quot;&quot;</span>
-<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="c1"># 特定の操作を実行...</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="c1"># いくつかの処理を実行...</span>
 <a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="k">return</span> <span class="mi">0</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>
-<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>    <span class="c1"># 入力データ</span>
-<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="n">A</span> <span class="o">=</span> <span class="mi">0</span>                   <span class="c1"># 一時データ（定数、通常大文字）</span>
-<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="n">b</span> <span class="o">=</span> <span class="mi">0</span>                   <span class="c1"># 一時データ（変数）</span>
-<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="n">node</span> <span class="o">=</span> <span class="n">Node</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>          <span class="c1"># 一時データ（オブジェクト）</span>
-<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>    <span class="n">c</span> <span class="o">=</span> <span class="n">function</span><span class="p">()</span>          <span class="c1"># スタックフレーム空間（関数呼び出し）</span>
-<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>    <span class="k">return</span> <span class="n">A</span> <span class="o">+</span> <span class="n">b</span> <span class="o">+</span> <span class="n">c</span>        <span class="c1"># 出力データ</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>  <span class="c1"># 入力データ</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="n">A</span> <span class="o">=</span> <span class="mi">0</span>                 <span class="c1"># 一時データ（定数。一般に大文字で表す）</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="n">b</span> <span class="o">=</span> <span class="mi">0</span>                 <span class="c1"># 一時データ（変数）</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="n">node</span> <span class="o">=</span> <span class="n">Node</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>        <span class="c1"># 一時データ（オブジェクト）</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>    <span class="n">c</span> <span class="o">=</span> <span class="n">function</span><span class="p">()</span>        <span class="c1"># スタックフレーム空間（関数呼び出し）</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>    <span class="k">return</span> <span class="n">A</span> <span class="o">+</span> <span class="n">b</span> <span class="o">+</span> <span class="n">c</span>      <span class="c1"># 出力データ</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
@@ -4573,16 +4573,16 @@
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="cm">/* 関数 */</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="c1">// 特定の操作を実行...</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="c1">// いくつかの処理を実行...</span>
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="p">}</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a>
-<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="kt">int</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">          </span><span class="c1">// 入力データ</span>
-<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">            </span><span class="c1">// 一時データ（定数）</span>
-<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                  </span><span class="c1">// 一時データ（変数）</span>
-<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="n">Node</span><span class="o">*</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Node</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w">   </span><span class="c1">// 一時データ（オブジェクト）</span>
-<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">func</span><span class="p">();</span><span class="w">             </span><span class="c1">// スタックフレーム空間（関数呼び出し）</span>
-<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">;</span><span class="w">           </span><span class="c1">// 出力データ</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="kt">int</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">        </span><span class="c1">// 入力データ</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">          </span><span class="c1">// 一時データ（定数）</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                </span><span class="c1">// 一時データ（変数）</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="n">Node</span><span class="o">*</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Node</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 一時データ（オブジェクト）</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">func</span><span class="p">();</span><span class="w">           </span><span class="c1">// スタックフレーム空間（関数呼び出し）</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">;</span><span class="w">         </span><span class="c1">// 出力データ</span>
 <a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
@@ -4596,40 +4596,39 @@
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="cm">/* 関数 */</span>
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="kt">int</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="c1">// 特定の操作を実行...</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="c1">// いくつかの処理を実行...</span>
 <a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="p">}</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a>
-<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="kt">int</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">          </span><span class="c1">// 入力データ</span>
-<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">            </span><span class="c1">// 一時データ（定数）</span>
-<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                  </span><span class="c1">// 一時データ（変数）</span>
-<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">    </span><span class="n">Node</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Node</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w">    </span><span class="c1">// 一時データ（オブジェクト）</span>
-<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">function</span><span class="p">();</span><span class="w">         </span><span class="c1">// スタックフレーム空間（関数呼び出し）</span>
-<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">;</span><span class="w">           </span><span class="c1">// 出力データ</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="kt">int</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">        </span><span class="c1">// 入力データ</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">          </span><span class="c1">// 一時データ（定数）</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                </span><span class="c1">// 一時データ（変数）</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">    </span><span class="n">Node</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Node</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w">  </span><span class="c1">// 一時データ（オブジェクト）</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">function</span><span class="p">();</span><span class="w">       </span><span class="c1">// スタックフレーム空間（関数呼び出し）</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">;</span><span class="w">         </span><span class="c1">// 出力データ</span>
 <a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* クラス */</span>
-<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">Node</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">class</span><span class="w"> </span><span class="nf">Node</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span>
 <a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="n">Node</span><span class="w"> </span><span class="n">next</span><span class="p">;</span>
-<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="n">Node</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w"> </span><span class="p">}</span>
-<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="p">}</span>
-<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a>
-<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="cm">/* 関数 */</span>
-<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">    </span><span class="c1">// 特定の操作を実行...</span>
-<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="p">}</span>
-<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a>
-<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// 入力データ</span>
-<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">    </span><span class="c1">// 一時データ（定数）</span>
-<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">          </span><span class="c1">// 一時データ（変数）</span>
-<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">    </span><span class="n">Node</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 一時データ（オブジェクト）</span>
-<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Function</span><span class="p">();</span><span class="w"> </span><span class="c1">// スタックフレーム空間（関数呼び出し）</span>
-<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">;</span><span class="w">   </span><span class="c1">// 出力データ</span>
-<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="p">}</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="p">}</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="cm">/* 関数 */</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="c1">// いくつかの処理を実行...</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="p">}</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">        </span><span class="c1">// 入力データ</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">          </span><span class="c1">// 一時データ（定数）</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                </span><span class="c1">// 一時データ（変数）</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">    </span><span class="n">Node</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w">       </span><span class="c1">// 一時データ（オブジェクト）</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Function</span><span class="p">();</span><span class="w">       </span><span class="c1">// スタックフレーム空間（関数呼び出し）</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">;</span><span class="w">         </span><span class="c1">// 出力データ</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
@@ -4639,14 +4638,14 @@
 <a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">next</span><span class="w"> </span><span class="o">*</span><span class="nx">node</span>
 <a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="p">}</span>
 <a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a>
-<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="cm">/* ノード構造体を作成 */</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="cm">/* node 構造体を作成 */</span>
 <a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="kd">func</span><span class="w"> </span><span class="nx">newNode</span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">node</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">node</span><span class="p">{</span><span class="nx">val</span><span class="p">:</span><span class="w"> </span><span class="nx">val</span><span class="p">}</span>
 <a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="p">}</span>
 <a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a>
 <a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="cm">/* 関数 */</span>
 <a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="kd">func</span><span class="w"> </span><span class="nx">function</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">    </span><span class="c1">// 特定の操作を実行...</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">    </span><span class="c1">// いくつかの処理を実行...</span>
 <a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
 <a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="p">}</span>
 <a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a>
@@ -4672,16 +4671,16 @@
 <a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a>
 <a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="cm">/* 関数 */</span>
 <a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="kd">func</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">    </span><span class="c1">// 特定の操作を実行...</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">    </span><span class="c1">// いくつかの処理を実行...</span>
 <a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
 <a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="p">}</span>
 <a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a>
 <a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 入力データ</span>
-<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span><span class="w">                   </span><span class="c1">// 一時データ（定数）</span>
-<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">b</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span><span class="w">                   </span><span class="c1">// 一時データ（変数）</span>
-<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Node</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w">       </span><span class="c1">// 一時データ（オブジェクト）</span>
-<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">c</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">function</span><span class="p">()</span><span class="w">          </span><span class="c1">// スタックフレーム空間（関数呼び出し）</span>
-<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="w">            </span><span class="c1">// 出力データ</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span><span class="w">             </span><span class="c1">// 一時データ（定数）</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">b</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span><span class="w">             </span><span class="c1">// 一時データ（変数）</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Node</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="c1">// 一時データ（オブジェクト）</span>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">c</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">function</span><span class="p">()</span><span class="w">    </span><span class="c1">// スタックフレーム空間（関数呼び出し）</span>
+<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="w">      </span><span class="c1">// 出力データ</span>
 <a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
@@ -4691,23 +4690,23 @@
 <a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="nx">val</span><span class="p">;</span>
 <a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="nx">next</span><span class="p">;</span>
 <a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// ノード値</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// ノードの値</span>
 <a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span><span class="w">                       </span><span class="c1">// 次のノードへの参照</span>
 <a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="p">}</span>
 <a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a>
 <a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="cm">/* 関数 */</span>
 <a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">    </span><span class="c1">// 特定の操作を実行</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">    </span><span class="c1">// いくつかの処理を実行</span>
 <a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
 <a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="p">}</span>
 <a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a>
-<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">         </span><span class="c1">// 入力データ</span>
-<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w">                </span><span class="c1">// 一時データ（定数）</span>
-<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w">                  </span><span class="c1">// 一時データ（変数）</span>
-<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">Node</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span><span class="w">   </span><span class="c1">// 一時データ（オブジェクト）</span>
-<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">();</span><span class="w">      </span><span class="c1">// スタックフレーム空間（関数呼び出し）</span>
-<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">c</span><span class="p">;</span><span class="w">           </span><span class="c1">// 出力データ</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">       </span><span class="c1">// 入力データ</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w">              </span><span class="c1">// 一時データ（定数）</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w">                </span><span class="c1">// 一時データ（変数）</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">Node</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 一時データ（オブジェクト）</span>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">();</span><span class="w">    </span><span class="c1">// スタックフレーム空間（関数呼び出し）</span>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">c</span><span class="p">;</span><span class="w">         </span><span class="c1">// 出力データ</span>
 <a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
@@ -4717,14 +4716,14 @@
 <a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span>
 <a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="nx">next</span><span class="o">:</span><span class="w"> </span><span class="kt">Node</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
 <a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val?</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// ノード値</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// ノードの値</span>
 <a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span><span class="w">                       </span><span class="c1">// 次のノードへの参照</span>
 <a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="p">}</span>
 <a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a>
 <a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="cm">/* 関数 */</span>
 <a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">    </span><span class="c1">// 特定の操作を実行</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">    </span><span class="c1">// いくつかの処理を実行</span>
 <a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
 <a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="p">}</span>
 <a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a>
@@ -4747,7 +4746,7 @@
 <a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a>
 <a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="cm">/* 関数 */</span>
 <a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="kt">int</span><span class="w"> </span><span class="n">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">  </span><span class="c1">// 特定の操作を実行...</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">  </span><span class="c1">// いくつかの処理を実行...</span>
 <a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
 <a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="p">}</span>
 <a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a>
@@ -4770,7 +4769,7 @@
 <a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">Node</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span>
 <a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="p">}</span>
 <a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a>
-<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="cm">/* Node 構造体を作成 */</span>
 <a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="k">impl</span><span class="w"> </span><span class="n">Node</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">new</span><span class="p">(</span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">Self</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">        </span><span class="bp">Self</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="nc">val</span><span class="p">,</span><span class="w"> </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="p">}</span>
@@ -4778,121 +4777,155 @@
 <a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="p">}</span>
 <a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a>
 <a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="cm">/* 関数 */</span>
-<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="k">fn</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">    </span><span class="c1">// 特定の操作を実行...</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="k">fn</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span><span class="w">      </span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">    </span><span class="c1">// いくつかの処理を実行...</span>
 <a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="p">}</span>
 <a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a>
-<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span><span class="w">   </span><span class="c1">// 入力データ</span>
-<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="n">a</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">           </span><span class="c1">// 一時データ（定数）</span>
-<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">              </span><span class="c1">// 一時データ（変数）</span>
-<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Node</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w">    </span><span class="c1">// 一時データ（オブジェクト）</span>
-<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">function</span><span class="p">();</span><span class="w">         </span><span class="c1">// スタックフレーム空間（関数呼び出し）</span>
-<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">;</span><span class="w">           </span><span class="c1">// 出力データ</span>
+<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span><span class="w">       </span><span class="c1">// 入力データ</span>
+<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="n">a</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">               </span><span class="c1">// 一時データ（定数）</span>
+<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                  </span><span class="c1">// 一時データ（変数）</span>
+<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Node</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w">        </span><span class="c1">// 一時データ（オブジェクト）</span>
+<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">function</span><span class="p">();</span><span class="w">             </span><span class="c1">// スタックフレーム空間（関数呼び出し）</span>
+<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">;</span><span class="w">               </span><span class="c1">// 出力データ</span>
 <a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 関数 */</span>
 <a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="c1">// 特定の操作を実行...</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="c1">// いくつかの処理を実行...</span>
 <a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="p">}</span>
 <a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a>
-<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="kt">int</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// 入力データ</span>
-<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">    </span><span class="c1">// 一時データ（定数）</span>
-<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">          </span><span class="c1">// 一時データ（変数）</span>
-<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">func</span><span class="p">();</span><span class="w">     </span><span class="c1">// スタックフレーム空間（関数呼び出し）</span>
-<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">;</span><span class="w">   </span><span class="c1">// 出力データ</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="kt">int</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 入力データ</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">   </span><span class="c1">// 一時データ（定数）</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">         </span><span class="c1">// 一時データ（変数）</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">func</span><span class="p">();</span><span class="w">    </span><span class="c1">// スタックフレーム空間（関数呼び出し）</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">;</span><span class="w">  </span><span class="c1">// 出力データ</span>
 <a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* クラス */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">Node</span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="nv">_val</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">next</span><span class="p">:</span><span class="w"> </span><span class="n">Node? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="p">}</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="cm">/* 関数 */</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">function</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">    </span><span class="c1">// いくつかの処理を実行...</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="p">}</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 入力データ</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="w">                </span><span class="c1">// 一時データ（定数）</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="w">                </span><span class="c1">// 一時データ（変数）</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Node</span><span class="p">(</span><span class="m">0</span><span class="p">)</span><span class="w">       </span><span class="c1">// 一時データ（オブジェクト）</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">function</span><span class="p">()</span><span class="w">       </span><span class="c1">// スタックフレーム空間（関数呼び出し）</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="w">         </span><span class="c1">// 出力データ</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### クラス ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">Node</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">    </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:val</span><span class="w">      </span><span class="c1"># ノードの値</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">    </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:next</span><span class="w">     </span><span class="c1"># 次のノードへの参照</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">    </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">        </span><span class="vi">@val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="k">end</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="c1">### 関数 ###</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="k">def</span><span class="w"> </span><span class="nf">function</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">    </span><span class="c1"># いくつかの処理を実行...</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">    </span><span class="mi">0</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="k">end</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="c1">### アルゴリズム ###</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">)</span><span class="w">        </span><span class="c1"># 入力データ</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w">               </span><span class="c1"># 一時データ（定数）</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="w">    </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w">               </span><span class="c1"># 一時データ（変数）</span>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">Node</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="w">  </span><span class="c1"># 一時データ（オブジェクト）</span>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w">    </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">function</span><span class="w">        </span><span class="c1"># スタックフレーム空間（関数呼び出し）</span>
+<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="w">           </span><span class="c1"># 出力データ</span>
+<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h2 id="242">2.4.2 &nbsp; 計算方法<a class="headerlink" href="#242" title="Permanent link">&para;</a></h2>
-<p>空間計算量を計算する方法は時間計算量とほぼ同様で、統計対象を「操作数」から「使用空間のサイズ」に変更するだけです。</p>
-<p>しかし、時間計算量とは異なり、<strong>通常は最悪ケース空間計算量のみに焦点を当てます</strong>。これは、メモリ空間がハード要件であり、すべての入力データの下で十分なメモリ空間が確保されていることを保証する必要があるためです。</p>
-<p>以下のコードを考えてみましょう。最悪ケース空間計算量の「最悪ケース」という用語には2つの意味があります。</p>
+<h2 id="242">2.4.2 &nbsp; 推定方法<a class="headerlink" href="#242" title="Permanent link">&para;</a></h2>
+<p>空間計算量の推定方法は時間計算量とおおむね同じで、数える対象を「操作回数」から「使用空間の大きさ」に変えるだけです。</p>
+<p>ただし時間計算量と異なり、<strong>通常は最悪空間計算量だけに注目します</strong>。メモリ空間は厳格な要件であり、どの入力データに対しても十分なメモリを確保できることを保証しなければならないからです。</p>
+<p>以下のコードを見ると、最悪空間計算量における「最悪」には二つの意味があります。</p>
 <ol>
-<li><strong>最悪の入力データに基づく</strong>: <span class="arithmatex">\(n &lt; 10\)</span>の場合、空間計算量は<span class="arithmatex">\(O(1)\)</span>ですが、<span class="arithmatex">\(n &gt; 10\)</span>の場合、初期化された配列<code>nums</code>が<span class="arithmatex">\(O(n)\)</span>の空間を占有するため、最悪ケース空間計算量は<span class="arithmatex">\(O(n)\)</span>です。</li>
-<li><strong>アルゴリズムの実行中に使用されるピークメモリに基づく</strong>: 例えば、最後の行を実行する前、プログラムは<span class="arithmatex">\(O(1)\)</span>の空間を占有します。配列<code>nums</code>を初期化する際、プログラムは<span class="arithmatex">\(O(n)\)</span>の空間を占有するため、最悪ケース空間計算量は<span class="arithmatex">\(O(n)\)</span>です。</li>
+<li><strong>最悪の入力データを基準にする</strong>：<span class="arithmatex">\(n &lt; 10\)</span> のとき空間計算量は <span class="arithmatex">\(O(1)\)</span> ですが、<span class="arithmatex">\(n &gt; 10\)</span> のとき初期化される配列 <code>nums</code> が <span class="arithmatex">\(O(n)\)</span> の空間を占有するため、最悪空間計算量は <span class="arithmatex">\(O(n)\)</span> です。</li>
+<li><strong>アルゴリズム実行中のメモリ使用量のピークを基準にする</strong>：例えば、プログラムは最後の行を実行する前までは <span class="arithmatex">\(O(1)\)</span> の空間しか使いませんが、配列 <code>nums</code> を初期化するときには <span class="arithmatex">\(O(n)\)</span> の空間を占有するため、最悪空間計算量は <span class="arithmatex">\(O(n)\)</span> です。</li>
 </ol>
-<div class="tabbed-set tabbed-alternate" data-tabs="2:12"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label></div>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>    <span class="n">a</span> <span class="o">=</span> <span class="mi">0</span>               <span class="c1"># O(1)</span>
-<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a>    <span class="n">b</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">10000</span>     <span class="c1"># O(1)</span>
-<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">&gt;</span> <span class="mi">10</span><span class="p">:</span>
-<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a>        <span class="n">nums</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span>  <span class="c1"># O(n)</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">               </span><span class="c1">// O(1)</span>
-<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">b</span><span class="p">(</span><span class="mi">10000</span><span class="p">);</span><span class="w">    </span><span class="c1">// O(1)</span>
-<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span>
-<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">(</span><span class="n">n</span><span class="p">);</span><span class="w"> </span><span class="c1">// O(n)</span>
-<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="p">}</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a>    <span class="n">a</span> <span class="o">=</span> <span class="mi">0</span>               <span class="c1"># O(1)</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="n">b</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">10000</span>     <span class="c1"># O(1)</span>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">&gt;</span> <span class="mi">10</span><span class="p">:</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>        <span class="n">nums</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span>  <span class="c1"># O(n)</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                   </span><span class="c1">// O(1)</span>
-<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="mi">10000</span><span class="o">]</span><span class="p">;</span><span class="w">    </span><span class="c1">// O(1)</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">               </span><span class="c1">// O(1)</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">b</span><span class="p">(</span><span class="mi">10000</span><span class="p">);</span><span class="w">    </span><span class="c1">// O(1)</span>
 <a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span>
-<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">        </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="c1">// O(n)</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">(</span><span class="n">n</span><span class="p">);</span><span class="w"> </span><span class="c1">// O(n)</span>
 <a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="k">void</span><span class="w"> </span><span class="nf">Algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                   </span><span class="c1">// O(1)</span>
-<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="mi">10000</span><span class="p">];</span><span class="w">    </span><span class="c1">// O(1)</span>
-<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">        </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="p">];</span><span class="w"> </span><span class="c1">// O(n)</span>
-<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="p">}</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="mi">10000</span><span class="o">]</span><span class="p">;</span><span class="w">    </span><span class="c1">// O(1)</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">        </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="c1">// O(n)</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="w">                      </span><span class="c1">// O(1)</span>
-<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="nx">b</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="mi">10000</span><span class="p">)</span><span class="w">     </span><span class="c1">// O(1)</span>
-<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span>
-<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="mi">10</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">        </span><span class="nx">nums</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span><span class="w">  </span><span class="c1">// O(n)</span>
-<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="p">,</span><span class="w"> </span><span class="nx">nums</span><span class="p">)</span>
-<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="p">}</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="k">void</span><span class="w"> </span><span class="nf">Algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                   </span><span class="c1">// O(1)</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="mi">10000</span><span class="p">];</span><span class="w">    </span><span class="c1">// O(1)</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">        </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="p">];</span><span class="w"> </span><span class="c1">// O(n)</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1">// O(1)</span>
-<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">b</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="mi">10000</span><span class="p">)</span><span class="w"> </span><span class="c1">// O(1)</span>
-<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">10</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="c1">// O(n)</span>
-<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="p">}</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="w">                      </span><span class="c1">// O(1)</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="nx">b</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="mi">10000</span><span class="p">)</span><span class="w">     </span><span class="c1">// O(1)</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="mi">10</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">        </span><span class="nx">nums</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span><span class="w">  </span><span class="c1">// O(n)</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="p">,</span><span class="w"> </span><span class="nx">nums</span><span class="p">)</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w">                   </span><span class="c1">// O(1)</span>
-<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mf">10000</span><span class="p">);</span><span class="w">    </span><span class="c1">// O(1)</span>
-<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">10</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">);</span><span class="w"> </span><span class="c1">// O(n)</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1">// O(1)</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">b</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="mi">10000</span><span class="p">)</span><span class="w"> </span><span class="c1">// O(1)</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">10</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="c1">// O(n)</span>
 <a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w">                   </span><span class="c1">// O(1)</span>
 <a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mf">10000</span><span class="p">);</span><span class="w">    </span><span class="c1">// O(1)</span>
 <a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">10</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
@@ -4902,839 +4935,1634 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w">                            </span><span class="c1">// O(1)</span>
-<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="m">10000</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span><span class="w">  </span><span class="c1">// O(1)</span>
-<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">10</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// O(n)</span>
-<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">  </span><span class="p">}</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w">                   </span><span class="c1">// O(1)</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mf">10000</span><span class="p">);</span><span class="w">    </span><span class="c1">// O(1)</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">10</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">);</span><span class="w"> </span><span class="c1">// O(n)</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                           </span><span class="c1">// O(1)</span>
-<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="mi">10000</span><span class="p">];</span><span class="w">                  </span><span class="c1">// O(1)</span>
-<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">10</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">];</span><span class="w">  </span><span class="c1">// O(n)</span>
-<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">    </span><span class="p">}</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w">                            </span><span class="c1">// O(1)</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="m">10000</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span><span class="w">  </span><span class="c1">// O(1)</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">10</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// O(n)</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">  </span><span class="p">}</span>
 <a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">               </span><span class="c1">// O(1)</span>
-<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="p">[</span><span class="mi">10000</span><span class="p">];</span><span class="w">            </span><span class="c1">// O(1)</span>
-<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span>
-<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">n</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mi">0</span><span class="p">};</span><span class="w">   </span><span class="c1">// O(n)</span>
-<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="p">}</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                              </span><span class="c1">// O(1)</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="mi">10000</span><span class="p">];</span><span class="w">                     </span><span class="c1">// O(1)</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">10</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">];</span><span class="w">     </span><span class="c1">// O(n)</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">               </span><span class="c1">// O(1)</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="p">[</span><span class="mi">10000</span><span class="p">];</span><span class="w">            </span><span class="c1">// O(1)</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">n</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mi">0</span><span class="p">};</span><span class="w">   </span><span class="c1">// O(n)</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="w">                    </span><span class="c1">// O(1)</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="m">10000</span><span class="p">)</span><span class="w">      </span><span class="c1">// O(1)</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">10</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">n</span><span class="p">)</span><span class="w">   </span><span class="c1">// O(n)</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w">                           </span><span class="c1"># O(1)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">    </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">10000</span><span class="p">)</span><span class="w">            </span><span class="c1"># O(1)</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">    </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">10</span><span class="w">   </span><span class="c1"># O(n)</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p><strong>再帰関数では、スタックフレーム空間を考慮に入れる必要があります</strong>。以下のコードを考えてみましょう：</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="3:12"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label></div>
+<p><strong>再帰関数では、スタックフレーム空間の集計に注意が必要です</strong>。以下のコードを見てみましょう。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a>    <span class="c1"># 特定の操作を実行</span>
-<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a>    <span class="k">return</span> <span class="mi">0</span>
-<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a>
-<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="k">def</span><span class="w"> </span><span class="nf">loop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ループ O(1)&quot;&quot;&quot;</span>
-<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
-<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a>        <span class="n">function</span><span class="p">()</span>
-<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a>
-<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="k">def</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;再帰 O(n)&quot;&quot;&quot;</span>
-<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
-<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a>        <span class="k">return</span>
-<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a>    <span class="k">return</span> <span class="n">recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>    <span class="c1"># いくつかの処理を実行</span>
+<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>    <span class="k">return</span> <span class="mi">0</span>
+<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>
+<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="k">def</span><span class="w"> </span><span class="nf">loop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ループの空間計算量は O(1)&quot;&quot;&quot;</span>
+<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>        <span class="n">function</span><span class="p">()</span>
+<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a>
+<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="k">def</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;再帰の空間計算量は O(n)&quot;&quot;&quot;</span>
+<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a>        <span class="k">return</span>
+<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a>    <span class="k">return</span> <span class="n">recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="w">    </span><span class="c1">// 特定の操作を実行</span>
-<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="p">}</span>
-<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="cm">/* サイクル O(1) */</span>
-<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">loop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w">        </span><span class="n">func</span><span class="p">();</span>
-<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="p">}</span>
-<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="cm">/* 再帰 O(n) */</span>
-<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w">    </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="kt">int</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="c1">// 特定の操作を実行</span>
-<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="p">}</span>
-<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="cm">/* サイクル O(1) */</span>
-<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">loop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="w">        </span><span class="n">function</span><span class="p">();</span>
-<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="p">}</span>
-<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="cm">/* 再帰 O(n) */</span>
-<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a><span class="w">    </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="w">    </span><span class="c1">// 特定の操作を実行</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="w">    </span><span class="c1">// いくつかの処理を実行</span>
 <a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="p">}</span>
-<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="cm">/* サイクル O(1) */</span>
-<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="k">void</span><span class="w"> </span><span class="nf">Loop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="cm">/* ループの空間計算量は O(1) */</span>
+<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">loop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w">        </span><span class="n">Function</span><span class="p">();</span>
+<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w">        </span><span class="n">func</span><span class="p">();</span>
 <a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a><span class="p">}</span>
-<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="cm">/* 再帰 O(n) */</span>
-<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Recur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nf">Recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="cm">/* 再帰の空間計算量は O(n) */</span>
+<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a><span class="w">    </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="kd">func</span><span class="w"> </span><span class="nx">function</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="w">    </span><span class="c1">// 特定の操作を実行</span>
-<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="kt">int</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="w">    </span><span class="c1">// いくつかの処理を実行</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="p">}</span>
-<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a>
-<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="cm">/* サイクル O(1) */</span>
-<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="kd">func</span><span class="w"> </span><span class="nx">loop</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="w">        </span><span class="nx">function</span><span class="p">()</span>
-<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="p">}</span>
-<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a>
-<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="cm">/* 再帰 O(n) */</span>
-<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a><span class="kd">func</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a><span class="w">        </span><span class="k">return</span>
-<a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-28-18" name="__codelineno-28-18" href="#__codelineno-28-18"></a><span class="w">    </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-28-19" name="__codelineno-28-19" href="#__codelineno-28-19"></a><span class="p">}</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="cm">/* ループの空間計算量は O(1) */</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">loop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">        </span><span class="n">function</span><span class="p">();</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="p">}</span>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="cm">/* 再帰の空間計算量は O(n) */</span>
+<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a><span class="w">    </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="p">@</span><span class="n">discardableResult</span>
-<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="c1">// 特定の操作を実行</span>
-<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
-<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="p">}</span>
-<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a>
-<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="cm">/* サイクル O(1) */</span>
-<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="kd">func</span><span class="w"> </span><span class="nf">loop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w">        </span><span class="n">function</span><span class="p">()</span>
-<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="p">}</span>
-<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a>
-<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="cm">/* 再帰 O(n) */</span>
-<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="kd">func</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="w">        </span><span class="k">return</span>
-<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="w">    </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-29-20" name="__codelineno-29-20" href="#__codelineno-29-20"></a><span class="p">}</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="w">    </span><span class="c1">// いくつかの処理を実行</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="p">}</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="cm">/* ループの空間計算量は O(1) */</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="k">void</span><span class="w"> </span><span class="nf">Loop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">        </span><span class="n">Function</span><span class="p">();</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="p">}</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="cm">/* 再帰の空間計算量は O(n) */</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Recur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nf">Recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="w">    </span><span class="c1">// 特定の操作を実行</span>
-<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="kd">func</span><span class="w"> </span><span class="nx">function</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="w">    </span><span class="c1">// いくつかの処理を実行</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
 <a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="p">}</span>
-<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="cm">/* サイクル O(1) */</span>
-<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="kd">function</span><span class="w"> </span><span class="nx">loop</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">        </span><span class="nx">constFunc</span><span class="p">();</span>
-<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="p">}</span>
-<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="cm">/* 再帰 O(n) */</span>
-<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
-<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="p">}</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="cm">/* ループの空間計算量は O(1) */</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="kd">func</span><span class="w"> </span><span class="nx">loop</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w">        </span><span class="nx">function</span><span class="p">()</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="p">}</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="cm">/* 再帰の空間計算量は O(n) */</span>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="kd">func</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a><span class="w">    </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="w">    </span><span class="c1">// 特定の操作を実行</span>
-<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
-<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="p">}</span>
-<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="cm">/* サイクル O(1) */</span>
-<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="kd">function</span><span class="w"> </span><span class="nx">loop</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w">        </span><span class="nx">constFunc</span><span class="p">();</span>
-<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a><span class="p">}</span>
-<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="cm">/* 再帰 O(n) */</span>
-<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
-<a id="__codelineno-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></a><span class="p">}</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">@</span><span class="n">discardableResult</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w">    </span><span class="c1">// いくつかの処理を実行</span>
+<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="p">}</span>
+<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a>
+<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="cm">/* ループの空間計算量は O(1) */</span>
+<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="kd">func</span><span class="w"> </span><span class="nf">loop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a><span class="w">        </span><span class="n">function</span><span class="p">()</span>
+<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="p">}</span>
+<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a>
+<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a><span class="cm">/* 再帰の空間計算量は O(n) */</span>
+<a id="__codelineno-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></a><span class="kd">func</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-16" name="__codelineno-31-16" href="#__codelineno-31-16"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-17" name="__codelineno-31-17" href="#__codelineno-31-17"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-31-18" name="__codelineno-31-18" href="#__codelineno-31-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-19" name="__codelineno-31-19" href="#__codelineno-31-19"></a><span class="w">    </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-31-20" name="__codelineno-31-20" href="#__codelineno-31-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="kt">int</span><span class="w"> </span><span class="n">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="w">  </span><span class="c1">// 特定の操作を実行</span>
-<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="w">    </span><span class="c1">// いくつかの処理を実行</span>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
 <a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="p">}</span>
-<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="cm">/* サイクル O(1) */</span>
-<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="kt">void</span><span class="w"> </span><span class="n">loop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w">    </span><span class="n">function</span><span class="p">();</span>
-<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="cm">/* ループの空間計算量は O(1) */</span>
+<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="kd">function</span><span class="w"> </span><span class="nx">loop</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w">        </span><span class="nx">constFunc</span><span class="p">();</span>
+<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-32-10" name="__codelineno-32-10" href="#__codelineno-32-10"></a><span class="p">}</span>
-<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a><span class="cm">/* 再帰 O(n) */</span>
-<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a><span class="kt">void</span><span class="w"> </span><span class="n">recur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-32-14" name="__codelineno-32-14" href="#__codelineno-32-14"></a><span class="w">  </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a><span class="cm">/* 再帰の空間計算量は O(n) */</span>
+<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-32-14" name="__codelineno-32-14" href="#__codelineno-32-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
 <a id="__codelineno-32-15" name="__codelineno-32-15" href="#__codelineno-32-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="k">fn</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="w">    </span><span class="c1">// 特定の操作を実行</span>
-<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="w">    </span><span class="c1">// いくつかの処理を実行</span>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
 <a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="p">}</span>
-<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="cm">/* サイクル O(1) */</span>
-<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="k">fn</span><span class="w"> </span><span class="nf">loop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w">        </span><span class="n">function</span><span class="p">();</span>
+<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="cm">/* ループの空間計算量は O(1) */</span>
+<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="kd">function</span><span class="w"> </span><span class="nx">loop</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w">        </span><span class="nx">constFunc</span><span class="p">();</span>
 <a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a><span class="p">}</span>
-<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="cm">/* 再帰 O(n) */</span>
-<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="n">void</span><span class="w"> </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-33-16" name="__codelineno-33-16" href="#__codelineno-33-16"></a><span class="w">    </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-33-17" name="__codelineno-33-17" href="#__codelineno-33-17"></a><span class="p">}</span>
+<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="cm">/* 再帰の空間計算量は O(n) */</span>
+<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="w">    </span><span class="c1">// 特定の操作を実行</span>
-<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="kt">int</span><span class="w"> </span><span class="n">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="w">  </span><span class="c1">// いくつかの処理を実行</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
 <a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="p">}</span>
-<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="cm">/* サイクル O(1) */</span>
-<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">loop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w">        </span><span class="n">func</span><span class="p">();</span>
-<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="cm">/* ループの空間計算量は O(1) */</span>
+<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="kt">void</span><span class="w"> </span><span class="n">loop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w">    </span><span class="n">function</span><span class="p">();</span>
+<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="w">  </span><span class="p">}</span>
 <a id="__codelineno-34-10" name="__codelineno-34-10" href="#__codelineno-34-10"></a><span class="p">}</span>
-<a id="__codelineno-34-11" name="__codelineno-34-11" href="#__codelineno-34-11"></a><span class="cm">/* 再帰 O(n) */</span>
-<a id="__codelineno-34-12" name="__codelineno-34-12" href="#__codelineno-34-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-34-13" name="__codelineno-34-13" href="#__codelineno-34-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-34-14" name="__codelineno-34-14" href="#__codelineno-34-14"></a><span class="w">    </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-34-11" name="__codelineno-34-11" href="#__codelineno-34-11"></a><span class="cm">/* 再帰の空間計算量は O(n) */</span>
+<a id="__codelineno-34-12" name="__codelineno-34-12" href="#__codelineno-34-12"></a><span class="kt">void</span><span class="w"> </span><span class="n">recur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-13" name="__codelineno-34-13" href="#__codelineno-34-13"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-34-14" name="__codelineno-34-14" href="#__codelineno-34-14"></a><span class="w">  </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
 <a id="__codelineno-34-15" name="__codelineno-34-15" href="#__codelineno-34-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="k">fn</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="w">    </span><span class="c1">// いくつかの処理を実行</span>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="p">}</span>
+<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="cm">/* ループの空間計算量は O(1) */</span>
+<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="k">fn</span><span class="w"> </span><span class="nf">loop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="w">        </span><span class="n">function</span><span class="p">();</span>
+<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="p">}</span>
+<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a><span class="cm">/* 再帰の空間計算量は O(n) */</span>
+<a id="__codelineno-35-12" name="__codelineno-35-12" href="#__codelineno-35-12"></a><span class="k">fn</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-13" name="__codelineno-35-13" href="#__codelineno-35-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-14" name="__codelineno-35-14" href="#__codelineno-35-14"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-35-15" name="__codelineno-35-15" href="#__codelineno-35-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-16" name="__codelineno-35-16" href="#__codelineno-35-16"></a><span class="w">    </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-35-17" name="__codelineno-35-17" href="#__codelineno-35-17"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="w">    </span><span class="c1">// いくつかの処理を実行</span>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="p">}</span>
+<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="cm">/* ループの空間計算量は O(1) */</span>
+<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">loop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="w">        </span><span class="n">func</span><span class="p">();</span>
+<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a><span class="p">}</span>
+<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a><span class="cm">/* 再帰の空間計算量は O(n) */</span>
+<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-36-14" name="__codelineno-36-14" href="#__codelineno-36-14"></a><span class="w">    </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-36-15" name="__codelineno-36-15" href="#__codelineno-36-15"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">function</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="w">    </span><span class="c1">// いくつかの処理を実行</span>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="p">}</span>
+<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="cm">/* ループの空間計算量は O(1) */</span>
+<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">loop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="w">        </span><span class="n">function</span><span class="p">()</span>
+<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="p">}</span>
+<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a><span class="cm">/* 再帰の空間計算量は O(n) */</span>
+<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span>
+<a id="__codelineno-37-14" name="__codelineno-37-14" href="#__codelineno-37-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-37-15" name="__codelineno-37-15" href="#__codelineno-37-15"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">function</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="w">    </span><span class="c1"># いくつかの処理を実行</span>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w">    </span><span class="mi">0</span>
+<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="k">end</span>
+<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a>
+<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="c1">### ループの空間計算量は O(1) ###</span>
+<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="k">def</span><span class="w"> </span><span class="nf">loop</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="w">    </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">function</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="k">end</span>
+<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a>
+<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a><span class="c1">### 再帰の空間計算量は O(n) ###</span>
+<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a><span class="k">def</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a><span class="w">    </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p><code>loop()</code>関数と<code>recur()</code>関数の時間計算量は両方とも<span class="arithmatex">\(O(n)\)</span>ですが、それらの空間計算量は異なります。</p>
+<p>関数 <code>loop()</code> と <code>recur()</code> はどちらも時間計算量は <span class="arithmatex">\(O(n)\)</span> ですが、空間計算量は異なります。</p>
 <ul>
-<li><code>loop()</code>関数はループ内で<code>function()</code>を<span class="arithmatex">\(n\)</span>回呼び出し、各反復の<code>function()</code>は返ってそのスタックフレーム空間を解放するため、空間計算量は<span class="arithmatex">\(O(1)\)</span>のままです。</li>
-<li>再帰関数<code>recur()</code>は実行中に<span class="arithmatex">\(n\)</span>個の未返却の<code>recur()</code>インスタンスが同時に存在するため、<span class="arithmatex">\(O(n)\)</span>のスタックフレーム空間を占有します。</li>
+<li>関数 <code>loop()</code> はループの中で <code>function()</code> を <span class="arithmatex">\(n\)</span> 回呼び出しますが、各反復での <code>function()</code> は戻るたびにスタックフレーム空間が解放されるため、空間計算量は依然として <span class="arithmatex">\(O(1)\)</span> です。</li>
+<li>再帰関数 <code>recur()</code> は実行中に未返却の <code>recur()</code> が同時に <span class="arithmatex">\(n\)</span> 個存在するため、<span class="arithmatex">\(O(n)\)</span> のスタックフレーム空間を占有します。</li>
 </ul>
-<h2 id="243">2.4.3 &nbsp; 一般的な種類<a class="headerlink" href="#243" title="Permanent link">&para;</a></h2>
-<p>入力データのサイズを<span class="arithmatex">\(n\)</span>とすると、下図は一般的な空間計算量の種類を示しています（低いものから高いものへと並べられています）。</p>
+<h2 id="243">2.4.3 &nbsp; よくある型<a class="headerlink" href="#243" title="Permanent link">&para;</a></h2>
+<p>入力データサイズを <span class="arithmatex">\(n\)</span> とすると、以下の図はよくある空間計算量の型を低い順から高い順に示しています。</p>
 <div class="arithmatex">\[
 \begin{aligned}
-&amp; O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
-&amp; \text{定数} &lt; \text{対数} &lt; \text{線形} &lt; \text{二次} &lt; \text{指数}
+O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
+\text{定数階} &lt; \text{対数階} &lt; \text{線形階} &lt; \text{平方階} &lt; \text{指数階}
 \end{aligned}
 \]</div>
-<p><img alt="Common types of space complexity" class="animation-figure" src="../space_complexity.assets/space_complexity_common_types.png" /></p>
-<p align="center"> 図 2-16 &nbsp; Common types of space complexity </p>
+<p><img alt="よくある空間計算量の型" class="animation-figure" src="../space_complexity.assets/space_complexity_common_types.png" /></p>
+<p align="center"> 図 2-16 &nbsp; よくある空間計算量の型 </p>
 
-<h3 id="1-o1">1. &nbsp; 定数オーダー <span class="arithmatex">\(O(1)\)</span><a class="headerlink" href="#1-o1" title="Permanent link">&para;</a></h3>
-<p>定数オーダーは、入力データサイズ<span class="arithmatex">\(n\)</span>とは無関係な定数、変数、オブジェクトで一般的です。</p>
-<p>ループで変数を初期化したり関数を呼び出したりするために占有されるメモリは、次のサイクルに入る際に解放され、空間上で累積されないため、空間計算量は<span class="arithmatex">\(O(1)\)</span>のままです：</p>
+<h3 id="1-o1">1. &nbsp; 定数階 <span class="arithmatex">\(O(1)\)</span><a class="headerlink" href="#1-o1" title="Permanent link">&para;</a></h3>
+<p>定数階は、個数が入力データサイズ <span class="arithmatex">\(n\)</span> に依存しない定数、変数、オブジェクトなどによく現れます。</p>
+<p>注意すべき点として、ループ内で変数を初期化したり関数を呼び出したりして使用されたメモリは、次の反復に入ると解放されるため、空間の占有は累積せず、空間計算量は依然として <span class="arithmatex">\(O(1)\)</span> です。</p>
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-<div class="highlight"><span class="filename">space_complexity.py</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;関数&quot;&quot;&quot;</span>
-<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a>    <span class="c1"># 何らかの操作を実行</span>
-<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a>    <span class="k">return</span> <span class="mi">0</span>
-<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a>
-<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="k">def</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;定数複雑度&quot;&quot;&quot;</span>
-<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a>    <span class="c1"># 定数、変数、オブジェクトは O(1) のスペースを占有</span>
-<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a>    <span class="n">a</span> <span class="o">=</span> <span class="mi">0</span>
-<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a>    <span class="n">nums</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">10000</span>
-<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a>    <span class="n">node</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
-<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a>    <span class="c1"># ループ内の変数は O(1) のスペースを占有</span>
-<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
-<a id="__codelineno-36-14" name="__codelineno-36-14" href="#__codelineno-36-14"></a>        <span class="n">c</span> <span class="o">=</span> <span class="mi">0</span>
-<a id="__codelineno-36-15" name="__codelineno-36-15" href="#__codelineno-36-15"></a>    <span class="c1"># ループ内の関数は O(1) のスペースを占有</span>
-<a id="__codelineno-36-16" name="__codelineno-36-16" href="#__codelineno-36-16"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
-<a id="__codelineno-36-17" name="__codelineno-36-17" href="#__codelineno-36-17"></a>        <span class="n">function</span><span class="p">()</span>
+<div class="highlight"><span class="filename">space_complexity.py</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;関数&quot;&quot;&quot;</span>
+<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a>    <span class="c1"># 何らかの処理を行う</span>
+<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a>    <span class="k">return</span> <span class="mi">0</span>
+<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a>
+<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a><span class="k">def</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;定数階&quot;&quot;&quot;</span>
+<a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a>    <span class="c1"># 定数、変数、オブジェクトは O(1) の空間を占める</span>
+<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a>    <span class="n">a</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a>    <span class="n">nums</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">10000</span>
+<a id="__codelineno-39-11" name="__codelineno-39-11" href="#__codelineno-39-11"></a>    <span class="n">node</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-39-12" name="__codelineno-39-12" href="#__codelineno-39-12"></a>    <span class="c1"># ループ内の変数は O(1) の空間を占める</span>
+<a id="__codelineno-39-13" name="__codelineno-39-13" href="#__codelineno-39-13"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-39-14" name="__codelineno-39-14" href="#__codelineno-39-14"></a>        <span class="n">c</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-39-15" name="__codelineno-39-15" href="#__codelineno-39-15"></a>    <span class="c1"># ループ内の関数は O(1) の空間を占める</span>
+<a id="__codelineno-39-16" name="__codelineno-39-16" href="#__codelineno-39-16"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-39-17" name="__codelineno-39-17" href="#__codelineno-39-17"></a>        <span class="n">function</span><span class="p">()</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.cpp</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* 関数 */</span>
-<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w">    </span><span class="c1">// 何らかの操作を実行</span>
-<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="p">}</span>
-<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a>
-<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="cm">/* 定数計算量 */</span>
-<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="kt">void</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="w">    </span><span class="c1">// 定数、変数、オブジェクトは O(1) 空間を占める</span>
-<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">(</span><span class="mi">10000</span><span class="p">);</span>
-<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
-<a id="__codelineno-37-14" name="__codelineno-37-14" href="#__codelineno-37-14"></a><span class="w">    </span><span class="c1">// ループ内の変数は O(1) 空間を占める</span>
-<a id="__codelineno-37-15" name="__codelineno-37-15" href="#__codelineno-37-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-37-16" name="__codelineno-37-16" href="#__codelineno-37-16"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-37-17" name="__codelineno-37-17" href="#__codelineno-37-17"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-37-18" name="__codelineno-37-18" href="#__codelineno-37-18"></a><span class="w">    </span><span class="c1">// ループ内の関数は O(1) 空間を占める</span>
-<a id="__codelineno-37-19" name="__codelineno-37-19" href="#__codelineno-37-19"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-37-20" name="__codelineno-37-20" href="#__codelineno-37-20"></a><span class="w">        </span><span class="n">func</span><span class="p">();</span>
-<a id="__codelineno-37-21" name="__codelineno-37-21" href="#__codelineno-37-21"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-37-22" name="__codelineno-37-22" href="#__codelineno-37-22"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.cpp</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* 関数 */</span>
+<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w">    </span><span class="c1">// 何らかの処理を行う</span>
+<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="p">}</span>
+<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a>
+<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="cm">/* 定数階 */</span>
+<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="kt">void</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w">    </span><span class="c1">// 定数、変数、オブジェクトは O(1) の空間を占める</span>
+<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">(</span><span class="mi">10000</span><span class="p">);</span>
+<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="w">    </span><span class="c1">// ループ内の変数は O(1) の空間を占める</span>
+<a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-16" name="__codelineno-40-16" href="#__codelineno-40-16"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-40-18" name="__codelineno-40-18" href="#__codelineno-40-18"></a><span class="w">    </span><span class="c1">// ループ内の関数は O(1) の空間を占める</span>
+<a id="__codelineno-40-19" name="__codelineno-40-19" href="#__codelineno-40-19"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-20" name="__codelineno-40-20" href="#__codelineno-40-20"></a><span class="w">        </span><span class="n">func</span><span class="p">();</span>
+<a id="__codelineno-40-21" name="__codelineno-40-21" href="#__codelineno-40-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-40-22" name="__codelineno-40-22" href="#__codelineno-40-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.java</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="cm">/* 関数 */</span>
-<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w">    </span><span class="c1">// 何らかの操作を実行</span>
-<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="p">}</span>
-<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a>
-<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="cm">/* 定数計算量 */</span>
-<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="kt">void</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="w">    </span><span class="c1">// 定数、変数、オブジェクトは O(1) 空間を占める</span>
-<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="mi">10000</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
-<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a><span class="w">    </span><span class="c1">// ループ内の変数は O(1) 空間を占める</span>
-<a id="__codelineno-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-38-16" name="__codelineno-38-16" href="#__codelineno-38-16"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-38-17" name="__codelineno-38-17" href="#__codelineno-38-17"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-38-18" name="__codelineno-38-18" href="#__codelineno-38-18"></a><span class="w">    </span><span class="c1">// ループ内の関数は O(1) 空間を占める</span>
-<a id="__codelineno-38-19" name="__codelineno-38-19" href="#__codelineno-38-19"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-38-20" name="__codelineno-38-20" href="#__codelineno-38-20"></a><span class="w">        </span><span class="n">function</span><span class="p">();</span>
-<a id="__codelineno-38-21" name="__codelineno-38-21" href="#__codelineno-38-21"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-38-22" name="__codelineno-38-22" href="#__codelineno-38-22"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.java</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 関数 */</span>
+<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w">    </span><span class="c1">// 何らかの処理を行う</span>
+<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="p">}</span>
+<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a>
+<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="cm">/* 定数階 */</span>
+<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a><span class="kt">void</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="w">    </span><span class="c1">// 定数、変数、オブジェクトは O(1) の空間を占める</span>
+<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="mi">10000</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-41-14" name="__codelineno-41-14" href="#__codelineno-41-14"></a><span class="w">    </span><span class="c1">// ループ内の変数は O(1) の空間を占める</span>
+<a id="__codelineno-41-15" name="__codelineno-41-15" href="#__codelineno-41-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-41-16" name="__codelineno-41-16" href="#__codelineno-41-16"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-41-17" name="__codelineno-41-17" href="#__codelineno-41-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-41-18" name="__codelineno-41-18" href="#__codelineno-41-18"></a><span class="w">    </span><span class="c1">// ループ内の関数は O(1) の空間を占める</span>
+<a id="__codelineno-41-19" name="__codelineno-41-19" href="#__codelineno-41-19"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-41-20" name="__codelineno-41-20" href="#__codelineno-41-20"></a><span class="w">        </span><span class="n">function</span><span class="p">();</span>
+<a id="__codelineno-41-21" name="__codelineno-41-21" href="#__codelineno-41-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-41-22" name="__codelineno-41-22" href="#__codelineno-41-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.cs</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">space_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Function</span><span class="p">}</span>
-<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a>
-<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">space_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Constant</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.cs</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="cm">/* 関数 */</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="w">    </span><span class="c1">// 何らかの処理を行う</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="p">}</span>
+<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="cm">/* 定数階 */</span>
+<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a><span class="k">void</span><span class="w"> </span><span class="nf">Constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="w">    </span><span class="c1">// 定数、変数、オブジェクトは O(1) の空間を占める</span>
+<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a><span class="w">    </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="mi">10000</span><span class="p">];</span>
+<a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-42-14" name="__codelineno-42-14" href="#__codelineno-42-14"></a><span class="w">    </span><span class="c1">// ループ内の変数は O(1) の空間を占める</span>
+<a id="__codelineno-42-15" name="__codelineno-42-15" href="#__codelineno-42-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-16" name="__codelineno-42-16" href="#__codelineno-42-16"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-42-17" name="__codelineno-42-17" href="#__codelineno-42-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-42-18" name="__codelineno-42-18" href="#__codelineno-42-18"></a><span class="w">    </span><span class="c1">// ループ内の関数は O(1) の空間を占める</span>
+<a id="__codelineno-42-19" name="__codelineno-42-19" href="#__codelineno-42-19"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-20" name="__codelineno-42-20" href="#__codelineno-42-20"></a><span class="w">        </span><span class="n">Function</span><span class="p">();</span>
+<a id="__codelineno-42-21" name="__codelineno-42-21" href="#__codelineno-42-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-42-22" name="__codelineno-42-22" href="#__codelineno-42-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.go</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">function</span><span class="p">}</span>
-<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a>
-<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">spaceConstant</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.go</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* 関数 */</span>
+<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">function</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w">    </span><span class="c1">// いくつかの操作を実行...</span>
+<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="p">}</span>
+<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a>
+<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="cm">/* 定数階 */</span>
+<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="kd">func</span><span class="w"> </span><span class="nx">spaceConstant</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w">    </span><span class="c1">// 定数、変数、オブジェクトは O(1) の空間を占める</span>
+<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w">    </span><span class="nx">b</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w">    </span><span class="nx">nums</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="mi">10000</span><span class="p">)</span>
+<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="w">    </span><span class="nx">node</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">newNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-43-14" name="__codelineno-43-14" href="#__codelineno-43-14"></a><span class="w">    </span><span class="c1">// ループ内の変数は O(1) の空間を占める</span>
+<a id="__codelineno-43-15" name="__codelineno-43-15" href="#__codelineno-43-15"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="kt">int</span>
+<a id="__codelineno-43-16" name="__codelineno-43-16" href="#__codelineno-43-16"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-17" name="__codelineno-43-17" href="#__codelineno-43-17"></a><span class="w">        </span><span class="nx">c</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-43-18" name="__codelineno-43-18" href="#__codelineno-43-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-19" name="__codelineno-43-19" href="#__codelineno-43-19"></a><span class="w">    </span><span class="c1">// ループ内の関数は O(1) の空間を占める</span>
+<a id="__codelineno-43-20" name="__codelineno-43-20" href="#__codelineno-43-20"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-21" name="__codelineno-43-21" href="#__codelineno-43-21"></a><span class="w">        </span><span class="nx">function</span><span class="p">()</span>
+<a id="__codelineno-43-22" name="__codelineno-43-22" href="#__codelineno-43-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-23" name="__codelineno-43-23" href="#__codelineno-43-23"></a><span class="w">    </span><span class="nx">b</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-43-24" name="__codelineno-43-24" href="#__codelineno-43-24"></a><span class="w">    </span><span class="nx">c</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-43-25" name="__codelineno-43-25" href="#__codelineno-43-25"></a><span class="w">    </span><span class="nx">nums</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-43-26" name="__codelineno-43-26" href="#__codelineno-43-26"></a><span class="w">    </span><span class="nx">node</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-43-27" name="__codelineno-43-27" href="#__codelineno-43-27"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.swift</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">function</span><span class="p">}</span>
-<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a>
-<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">constant</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.swift</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* 関数 */</span>
+<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="p">@</span><span class="n">discardableResult</span>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="kd">func</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">    </span><span class="c1">// 何らかの処理を行う</span>
+<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="p">}</span>
+<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a>
+<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="cm">/* 定数階 */</span>
+<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="kd">func</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w">    </span><span class="c1">// 定数、変数、オブジェクトは O(1) の空間を占める</span>
+<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">b</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="mi">10000</span><span class="p">)</span>
+<a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-44-15" name="__codelineno-44-15" href="#__codelineno-44-15"></a><span class="w">    </span><span class="c1">// ループ内の変数は O(1) の空間を占める</span>
+<a id="__codelineno-44-16" name="__codelineno-44-16" href="#__codelineno-44-16"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-17" name="__codelineno-44-17" href="#__codelineno-44-17"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">c</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-44-18" name="__codelineno-44-18" href="#__codelineno-44-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-19" name="__codelineno-44-19" href="#__codelineno-44-19"></a><span class="w">    </span><span class="c1">// ループ内の関数は O(1) の空間を占める</span>
+<a id="__codelineno-44-20" name="__codelineno-44-20" href="#__codelineno-44-20"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-21" name="__codelineno-44-21" href="#__codelineno-44-21"></a><span class="w">        </span><span class="n">function</span><span class="p">()</span>
+<a id="__codelineno-44-22" name="__codelineno-44-22" href="#__codelineno-44-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-23" name="__codelineno-44-23" href="#__codelineno-44-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.js</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">constFunc</span><span class="p">}</span>
-<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a>
-<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">constant</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.js</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="cm">/* 関数 */</span>
+<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w">    </span><span class="c1">// 何らかの処理を行う</span>
+<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="p">}</span>
+<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a>
+<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="cm">/* 定数階 */</span>
+<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constant</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="w">    </span><span class="c1">// 定数、変数、オブジェクトは O(1) の空間を占める</span>
+<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mf">10000</span><span class="p">);</span>
+<a id="__codelineno-45-13" name="__codelineno-45-13" href="#__codelineno-45-13"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-45-14" name="__codelineno-45-14" href="#__codelineno-45-14"></a><span class="w">    </span><span class="c1">// ループ内の変数は O(1) の空間を占める</span>
+<a id="__codelineno-45-15" name="__codelineno-45-15" href="#__codelineno-45-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-16" name="__codelineno-45-16" href="#__codelineno-45-16"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-45-17" name="__codelineno-45-17" href="#__codelineno-45-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-45-18" name="__codelineno-45-18" href="#__codelineno-45-18"></a><span class="w">    </span><span class="c1">// ループ内の関数は O(1) の空間を占める</span>
+<a id="__codelineno-45-19" name="__codelineno-45-19" href="#__codelineno-45-19"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-20" name="__codelineno-45-20" href="#__codelineno-45-20"></a><span class="w">        </span><span class="nx">constFunc</span><span class="p">();</span>
+<a id="__codelineno-45-21" name="__codelineno-45-21" href="#__codelineno-45-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-45-22" name="__codelineno-45-22" href="#__codelineno-45-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.ts</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">constFunc</span><span class="p">}</span>
-<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a>
-<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">constant</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.ts</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="cm">/* 関数 */</span>
+<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w">    </span><span class="c1">// 何らかの処理を行う</span>
+<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="p">}</span>
+<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a>
+<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></a><span class="cm">/* 定数階 */</span>
+<a id="__codelineno-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constant</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></a><span class="w">    </span><span class="c1">// 定数、変数、オブジェクトは O(1) の空間を占める</span>
+<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-46-12" name="__codelineno-46-12" href="#__codelineno-46-12"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mf">10000</span><span class="p">);</span>
+<a id="__codelineno-46-13" name="__codelineno-46-13" href="#__codelineno-46-13"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-46-14" name="__codelineno-46-14" href="#__codelineno-46-14"></a><span class="w">    </span><span class="c1">// ループ内の変数は O(1) の空間を占める</span>
+<a id="__codelineno-46-15" name="__codelineno-46-15" href="#__codelineno-46-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-16" name="__codelineno-46-16" href="#__codelineno-46-16"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-46-17" name="__codelineno-46-17" href="#__codelineno-46-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-46-18" name="__codelineno-46-18" href="#__codelineno-46-18"></a><span class="w">    </span><span class="c1">// ループ内の関数は O(1) の空間を占める</span>
+<a id="__codelineno-46-19" name="__codelineno-46-19" href="#__codelineno-46-19"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-20" name="__codelineno-46-20" href="#__codelineno-46-20"></a><span class="w">        </span><span class="nx">constFunc</span><span class="p">();</span>
+<a id="__codelineno-46-21" name="__codelineno-46-21" href="#__codelineno-46-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-46-22" name="__codelineno-46-22" href="#__codelineno-46-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.dart</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">function</span><span class="p">}</span>
-<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a>
-<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">constant</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.dart</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* 関数 */</span>
+<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w">  </span><span class="c1">// 何らかの処理を行う</span>
+<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="p">}</span>
+<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a>
+<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="cm">/* 定数階 */</span>
+<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a><span class="kt">void</span><span class="w"> </span><span class="n">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="w">  </span><span class="c1">// 定数、変数、オブジェクトは O(1) の空間を占める</span>
+<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="w">  </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="m">10000</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-47-13" name="__codelineno-47-13" href="#__codelineno-47-13"></a><span class="w">  </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-47-14" name="__codelineno-47-14" href="#__codelineno-47-14"></a><span class="w">  </span><span class="c1">// ループ内の変数は O(1) の空間を占める</span>
+<a id="__codelineno-47-15" name="__codelineno-47-15" href="#__codelineno-47-15"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-16" name="__codelineno-47-16" href="#__codelineno-47-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-47-17" name="__codelineno-47-17" href="#__codelineno-47-17"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-47-18" name="__codelineno-47-18" href="#__codelineno-47-18"></a><span class="w">  </span><span class="c1">// ループ内の関数は O(1) の空間を占める</span>
+<a id="__codelineno-47-19" name="__codelineno-47-19" href="#__codelineno-47-19"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-20" name="__codelineno-47-20" href="#__codelineno-47-20"></a><span class="w">    </span><span class="n">function</span><span class="p">();</span>
+<a id="__codelineno-47-21" name="__codelineno-47-21" href="#__codelineno-47-21"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-47-22" name="__codelineno-47-22" href="#__codelineno-47-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.rs</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">function</span><span class="p">}</span>
-<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a>
-<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">constant</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.rs</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="cm">/* 関数 */</span>
+<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="w">    </span><span class="c1">// 何らかの処理を行う</span>
+<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a><span class="p">}</span>
+<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a>
+<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a><span class="cm">/* 定数階 */</span>
+<a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a><span class="cp">#[allow(unused)]</span>
+<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a><span class="k">fn</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a><span class="w">    </span><span class="c1">// 定数、変数、オブジェクトは O(1) の空間を占める</span>
+<a id="__codelineno-48-11" name="__codelineno-48-11" href="#__codelineno-48-11"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="n">A</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-48-12" name="__codelineno-48-12" href="#__codelineno-48-12"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-48-13" name="__codelineno-48-13" href="#__codelineno-48-13"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="mi">10000</span><span class="p">];</span>
+<a id="__codelineno-48-14" name="__codelineno-48-14" href="#__codelineno-48-14"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-48-15" name="__codelineno-48-15" href="#__codelineno-48-15"></a><span class="w">    </span><span class="c1">// ループ内の変数は O(1) の空間を占める</span>
+<a id="__codelineno-48-16" name="__codelineno-48-16" href="#__codelineno-48-16"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-17" name="__codelineno-48-17" href="#__codelineno-48-17"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-48-18" name="__codelineno-48-18" href="#__codelineno-48-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-48-19" name="__codelineno-48-19" href="#__codelineno-48-19"></a><span class="w">    </span><span class="c1">// ループ内の関数は O(1) の空間を占める</span>
+<a id="__codelineno-48-20" name="__codelineno-48-20" href="#__codelineno-48-20"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-21" name="__codelineno-48-21" href="#__codelineno-48-21"></a><span class="w">        </span><span class="n">function</span><span class="p">();</span>
+<a id="__codelineno-48-22" name="__codelineno-48-22" href="#__codelineno-48-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-48-23" name="__codelineno-48-23" href="#__codelineno-48-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.c</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">func</span><span class="p">}</span>
-<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a>
-<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">constant</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.c</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* 関数 */</span>
+<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="w">    </span><span class="c1">// 何らかの処理を行う</span>
+<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="p">}</span>
+<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a>
+<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="cm">/* 定数階 */</span>
+<a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="kt">void</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-9" name="__codelineno-49-9" href="#__codelineno-49-9"></a><span class="w">    </span><span class="c1">// 定数、変数、オブジェクトは O(1) の空間を占める</span>
+<a id="__codelineno-49-10" name="__codelineno-49-10" href="#__codelineno-49-10"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-49-11" name="__codelineno-49-11" href="#__codelineno-49-11"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-49-12" name="__codelineno-49-12" href="#__codelineno-49-12"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="mi">1000</span><span class="p">];</span>
+<a id="__codelineno-49-13" name="__codelineno-49-13" href="#__codelineno-49-13"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newListNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-49-14" name="__codelineno-49-14" href="#__codelineno-49-14"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-49-15" name="__codelineno-49-15" href="#__codelineno-49-15"></a><span class="w">    </span><span class="c1">// ループ内の変数は O(1) の空間を占める</span>
+<a id="__codelineno-49-16" name="__codelineno-49-16" href="#__codelineno-49-16"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-17" name="__codelineno-49-17" href="#__codelineno-49-17"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-49-18" name="__codelineno-49-18" href="#__codelineno-49-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-49-19" name="__codelineno-49-19" href="#__codelineno-49-19"></a><span class="w">    </span><span class="c1">// ループ内の関数は O(1) の空間を占める</span>
+<a id="__codelineno-49-20" name="__codelineno-49-20" href="#__codelineno-49-20"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-21" name="__codelineno-49-21" href="#__codelineno-49-21"></a><span class="w">        </span><span class="n">func</span><span class="p">();</span>
+<a id="__codelineno-49-22" name="__codelineno-49-22" href="#__codelineno-49-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-49-23" name="__codelineno-49-23" href="#__codelineno-49-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.kt</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">function</span><span class="p">}</span>
-<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a>
-<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">constant</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.kt</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* 関数 */</span>
+<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">function</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w">    </span><span class="c1">// 何らかの処理を行う</span>
+<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="p">}</span>
+<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a>
+<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="cm">/* 定数階 */</span>
+<a id="__codelineno-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-9" name="__codelineno-50-9" href="#__codelineno-50-9"></a><span class="w">    </span><span class="c1">// 定数、変数、オブジェクトは O(1) の空間を占める</span>
+<a id="__codelineno-50-10" name="__codelineno-50-10" href="#__codelineno-50-10"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-50-11" name="__codelineno-50-11" href="#__codelineno-50-11"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-50-12" name="__codelineno-50-12" href="#__codelineno-50-12"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Array</span><span class="p">(</span><span class="m">10000</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-50-13" name="__codelineno-50-13" href="#__codelineno-50-13"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
+<a id="__codelineno-50-14" name="__codelineno-50-14" href="#__codelineno-50-14"></a><span class="w">    </span><span class="c1">// ループ内の変数は O(1) の空間を占める</span>
+<a id="__codelineno-50-15" name="__codelineno-50-15" href="#__codelineno-50-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-16" name="__codelineno-50-16" href="#__codelineno-50-16"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-50-17" name="__codelineno-50-17" href="#__codelineno-50-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-50-18" name="__codelineno-50-18" href="#__codelineno-50-18"></a><span class="w">    </span><span class="c1">// ループ内の関数は O(1) の空間を占める</span>
+<a id="__codelineno-50-19" name="__codelineno-50-19" href="#__codelineno-50-19"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-20" name="__codelineno-50-20" href="#__codelineno-50-20"></a><span class="w">        </span><span class="n">function</span><span class="p">()</span>
+<a id="__codelineno-50-21" name="__codelineno-50-21" href="#__codelineno-50-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-50-22" name="__codelineno-50-22" href="#__codelineno-50-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.rb</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">function</span><span class="p">}</span>
-<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a>
-<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">constant</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.rb</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="c1">### 関数 ###</span>
+<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">function</span>
+<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w">  </span><span class="c1"># 何らかの処理を行う</span>
+<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a><span class="w">  </span><span class="mi">0</span>
+<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="k">end</span>
+<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a>
+<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="c1">### 定数階 ###</span>
+<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a><span class="w">  </span><span class="c1"># 定数、変数、オブジェクトは O(1) の空間を占める</span>
+<a id="__codelineno-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></a><span class="w">  </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-51-11" name="__codelineno-51-11" href="#__codelineno-51-11"></a><span class="w">  </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">10000</span>
+<a id="__codelineno-51-12" name="__codelineno-51-12" href="#__codelineno-51-12"></a><span class="w">  </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">ListNode</span><span class="o">.</span><span class="n">new</span>
+<a id="__codelineno-51-13" name="__codelineno-51-13" href="#__codelineno-51-13"></a>
+<a id="__codelineno-51-14" name="__codelineno-51-14" href="#__codelineno-51-14"></a><span class="w">  </span><span class="c1"># ループ内の変数は O(1) の空間を占める</span>
+<a id="__codelineno-51-15" name="__codelineno-51-15" href="#__codelineno-51-15"></a><span class="w">  </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-51-16" name="__codelineno-51-16" href="#__codelineno-51-16"></a><span class="w">  </span><span class="c1"># ループ内の関数は O(1) の空間を占める</span>
+<a id="__codelineno-51-17" name="__codelineno-51-17" href="#__codelineno-51-17"></a><span class="w">  </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">function</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-51-18" name="__codelineno-51-18" href="#__codelineno-51-18"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h3 id="2-on">2. &nbsp; 線形オーダー <span class="arithmatex">\(O(n)\)</span><a class="headerlink" href="#2-on" title="Permanent link">&para;</a></h3>
-<p>線形オーダーは配列、連結リスト、スタック、キューなどで一般的で、要素数は<span class="arithmatex">\(n\)</span>に比例します：</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E5%80%A4%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%BE%8C%E7%B6%9A%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%0Adef%20function%28%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%96%A2%E6%95%B0%22%22%22%0A%20%20%20%20%23%20%E4%BD%95%E3%82%89%E3%81%8B%E3%81%AE%E5%87%A6%E7%90%86%E3%82%92%E8%A1%8C%E3%81%86%0A%20%20%20%20return%200%0A%0Adef%20constant%28n%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E5%AE%9A%E6%95%B0%E9%9A%8E%22%22%22%0A%20%20%20%20%23%20%E5%AE%9A%E6%95%B0%E3%80%81%E5%A4%89%E6%95%B0%E3%80%81%E3%82%AA%E3%83%96%E3%82%B8%E3%82%A7%E3%82%AF%E3%83%88%E3%81%AF%20O%281%29%20%E3%81%AE%E7%A9%BA%E9%96%93%E3%82%92%E5%8D%A0%E3%82%81%E3%82%8B%0A%20%20%20%20a%20%3D%200%0A%20%20%20%20nums%20%3D%20%5B0%5D%20%2A%2010%0A%20%20%20%20node%20%3D%20ListNode%280%29%0A%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%97%E5%86%85%E3%81%AE%E5%A4%89%E6%95%B0%E3%81%AF%20O%281%29%20%E3%81%AE%E7%A9%BA%E9%96%93%E3%82%92%E5%8D%A0%E3%82%81%E3%82%8B%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20c%20%3D%200%0A%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%97%E5%86%85%E3%81%AE%E9%96%A2%E6%95%B0%E3%81%AF%20O%281%29%20%E3%81%AE%E7%A9%BA%E9%96%93%E3%82%92%E5%8D%A0%E3%82%81%E3%82%8B%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20function%28%29%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20%23%20%E5%AE%9A%E6%95%B0%E9%9A%8E%0A%20%20%20%20constant%28n%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%E9%80%A3%E7%B5%90%E3%83%AA%E3%82%B9%E3%83%88%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E5%80%A4%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%BE%8C%E7%B6%9A%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%0Adef%20function%28%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%96%A2%E6%95%B0%22%22%22%0A%20%20%20%20%23%20%E4%BD%95%E3%82%89%E3%81%8B%E3%81%AE%E5%87%A6%E7%90%86%E3%82%92%E8%A1%8C%E3%81%86%0A%20%20%20%20return%200%0A%0Adef%20constant%28n%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E5%AE%9A%E6%95%B0%E9%9A%8E%22%22%22%0A%20%20%20%20%23%20%E5%AE%9A%E6%95%B0%E3%80%81%E5%A4%89%E6%95%B0%E3%80%81%E3%82%AA%E3%83%96%E3%82%B8%E3%82%A7%E3%82%AF%E3%83%88%E3%81%AF%20O%281%29%20%E3%81%AE%E7%A9%BA%E9%96%93%E3%82%92%E5%8D%A0%E3%82%81%E3%82%8B%0A%20%20%20%20a%20%3D%200%0A%20%20%20%20nums%20%3D%20%5B0%5D%20%2A%2010%0A%20%20%20%20node%20%3D%20ListNode%280%29%0A%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%97%E5%86%85%E3%81%AE%E5%A4%89%E6%95%B0%E3%81%AF%20O%281%29%20%E3%81%AE%E7%A9%BA%E9%96%93%E3%82%92%E5%8D%A0%E3%82%81%E3%82%8B%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20c%20%3D%200%0A%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%97%E5%86%85%E3%81%AE%E9%96%A2%E6%95%B0%E3%81%AF%20O%281%29%20%E3%81%AE%E7%A9%BA%E9%96%93%E3%82%92%E5%8D%A0%E3%82%81%E3%82%8B%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20function%28%29%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20%23%20%E5%AE%9A%E6%95%B0%E9%9A%8E%0A%20%20%20%20constant%28n%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h3 id="2-on">2. &nbsp; 線形階 <span class="arithmatex">\(O(n)\)</span><a class="headerlink" href="#2-on" title="Permanent link">&para;</a></h3>
+<p>線形階は、要素数が <span class="arithmatex">\(n\)</span> に比例する配列、連結リスト、スタック、キューなどによく現れます。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="5:13"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.py</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;線形複雑度&quot;&quot;&quot;</span>
-<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a>    <span class="c1"># 長さ n のリストは O(n) のスペースを占有</span>
-<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a>    <span class="n">nums</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span>
-<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a>    <span class="c1"># 長さ n のハッシュマップは O(n) のスペースを占有</span>
-<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a>    <span class="n">hmap</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="nb">str</span><span class="p">]()</span>
-<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
-<a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a>        <span class="n">hmap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="nb">str</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<div class="highlight"><span class="filename">space_complexity.py</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;線形階&quot;&quot;&quot;</span>
+<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a>    <span class="c1"># 長さ n のリストは O(n) の空間を使用</span>
+<a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a>    <span class="n">nums</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span>
+<a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a>    <span class="c1"># 長さ n のハッシュテーブルは O(n) の空間を使用</span>
+<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a>    <span class="n">hmap</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="nb">str</span><span class="p">]()</span>
+<a id="__codelineno-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-52-8" name="__codelineno-52-8" href="#__codelineno-52-8"></a>        <span class="n">hmap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="nb">str</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.cpp</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* 線形計算量 */</span>
-<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w">    </span><span class="c1">// 長さ n の配列は O(n) 空間を占める</span>
-<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
-<a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="w">    </span><span class="c1">// 長さ n のリストは O(n) 空間を占める</span>
-<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nodes</span><span class="p">;</span>
-<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a><span class="w">        </span><span class="n">nodes</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">ListNode</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
-<a id="__codelineno-50-9" name="__codelineno-50-9" href="#__codelineno-50-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-50-10" name="__codelineno-50-10" href="#__codelineno-50-10"></a><span class="w">    </span><span class="c1">// 長さ n のハッシュテーブルは O(n) 空間を占める</span>
-<a id="__codelineno-50-11" name="__codelineno-50-11" href="#__codelineno-50-11"></a><span class="w">    </span><span class="n">unordered_map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="o">&gt;</span><span class="w"> </span><span class="n">map</span><span class="p">;</span>
-<a id="__codelineno-50-12" name="__codelineno-50-12" href="#__codelineno-50-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-50-13" name="__codelineno-50-13" href="#__codelineno-50-13"></a><span class="w">        </span><span class="n">map</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">to_string</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
-<a id="__codelineno-50-14" name="__codelineno-50-14" href="#__codelineno-50-14"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-50-15" name="__codelineno-50-15" href="#__codelineno-50-15"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.cpp</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 線形階 */</span>
+<a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a><span class="w">    </span><span class="c1">// 長さ n の配列は O(n) の空間を使用</span>
+<a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a><span class="w">    </span><span class="c1">// 長さ n のリストは O(n) の空間を使用</span>
+<a id="__codelineno-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nodes</span><span class="p">;</span>
+<a id="__codelineno-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a><span class="w">        </span><span class="n">nodes</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">ListNode</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-53-9" name="__codelineno-53-9" href="#__codelineno-53-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-53-10" name="__codelineno-53-10" href="#__codelineno-53-10"></a><span class="w">    </span><span class="c1">// 長さ n のハッシュテーブルは O(n) の空間を使用</span>
+<a id="__codelineno-53-11" name="__codelineno-53-11" href="#__codelineno-53-11"></a><span class="w">    </span><span class="n">unordered_map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="o">&gt;</span><span class="w"> </span><span class="n">map</span><span class="p">;</span>
+<a id="__codelineno-53-12" name="__codelineno-53-12" href="#__codelineno-53-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-53-13" name="__codelineno-53-13" href="#__codelineno-53-13"></a><span class="w">        </span><span class="n">map</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">to_string</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-53-14" name="__codelineno-53-14" href="#__codelineno-53-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-53-15" name="__codelineno-53-15" href="#__codelineno-53-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.java</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="cm">/* 線形計算量 */</span>
-<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w">    </span><span class="c1">// 長さ n の配列は O(n) 空間を占める</span>
-<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w">    </span><span class="c1">// 長さ n のリストは O(n) 空間を占める</span>
-<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nodes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
-<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="w">        </span><span class="n">nodes</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
-<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></a><span class="w">    </span><span class="c1">// 長さ n のハッシュテーブルは O(n) 空間を占める</span>
-<a id="__codelineno-51-11" name="__codelineno-51-11" href="#__codelineno-51-11"></a><span class="w">    </span><span class="n">Map</span><span class="o">&lt;</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashMap</span><span class="o">&lt;&gt;</span><span class="p">();</span>
-<a id="__codelineno-51-12" name="__codelineno-51-12" href="#__codelineno-51-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-51-13" name="__codelineno-51-13" href="#__codelineno-51-13"></a><span class="w">        </span><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="p">.</span><span class="na">valueOf</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
-<a id="__codelineno-51-14" name="__codelineno-51-14" href="#__codelineno-51-14"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-51-15" name="__codelineno-51-15" href="#__codelineno-51-15"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.java</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="cm">/* 線形階 */</span>
+<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w">    </span><span class="c1">// 長さ n の配列は O(n) の空間を使用</span>
+<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w">    </span><span class="c1">// 長さ n のリストは O(n) の空間を使用</span>
+<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nodes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w">        </span><span class="n">nodes</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-54-10" name="__codelineno-54-10" href="#__codelineno-54-10"></a><span class="w">    </span><span class="c1">// 長さ n のハッシュテーブルは O(n) の空間を使用</span>
+<a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a><span class="w">    </span><span class="n">Map</span><span class="o">&lt;</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashMap</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-54-13" name="__codelineno-54-13" href="#__codelineno-54-13"></a><span class="w">        </span><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="p">.</span><span class="na">valueOf</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-54-14" name="__codelineno-54-14" href="#__codelineno-54-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-54-15" name="__codelineno-54-15" href="#__codelineno-54-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.cs</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">space_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Linear</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.cs</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="cm">/* 線形階 */</span>
+<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="w">    </span><span class="c1">// 長さ n の配列は O(n) の空間を使用</span>
+<a id="__codelineno-55-4" name="__codelineno-55-4" href="#__codelineno-55-4"></a><span class="w">    </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-55-5" name="__codelineno-55-5" href="#__codelineno-55-5"></a><span class="w">    </span><span class="c1">// 長さ n のリストは O(n) の空間を使用</span>
+<a id="__codelineno-55-6" name="__codelineno-55-6" href="#__codelineno-55-6"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nodes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-55-7" name="__codelineno-55-7" href="#__codelineno-55-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-8" name="__codelineno-55-8" href="#__codelineno-55-8"></a><span class="w">        </span><span class="n">nodes</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-55-9" name="__codelineno-55-9" href="#__codelineno-55-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-55-10" name="__codelineno-55-10" href="#__codelineno-55-10"></a><span class="w">    </span><span class="c1">// 長さ n のハッシュテーブルは O(n) の空間を使用</span>
+<a id="__codelineno-55-11" name="__codelineno-55-11" href="#__codelineno-55-11"></a><span class="w">    </span><span class="n">Dictionary</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">string</span><span class="o">&gt;</span><span class="w"> </span><span class="n">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-55-12" name="__codelineno-55-12" href="#__codelineno-55-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-13" name="__codelineno-55-13" href="#__codelineno-55-13"></a><span class="w">        </span><span class="n">map</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">.</span><span class="n">ToString</span><span class="p">());</span>
+<a id="__codelineno-55-14" name="__codelineno-55-14" href="#__codelineno-55-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-55-15" name="__codelineno-55-15" href="#__codelineno-55-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.go</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">spaceLinear</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.go</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="cm">/* 線形階 */</span>
+<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">spaceLinear</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a><span class="w">    </span><span class="c1">// 長さ n の配列は O(n) の空間を使用</span>
+<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a><span class="w">    </span><span class="nx">_</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
+<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a><span class="w">    </span><span class="c1">// 長さ n のリストは O(n) の空間を使用</span>
+<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">nodes</span><span class="w"> </span><span class="p">[]</span><span class="o">*</span><span class="nx">node</span>
+<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a><span class="w">        </span><span class="nx">nodes</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nodes</span><span class="p">,</span><span class="w"> </span><span class="nx">newNode</span><span class="p">(</span><span class="nx">i</span><span class="p">))</span>
+<a id="__codelineno-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-56-10" name="__codelineno-56-10" href="#__codelineno-56-10"></a><span class="w">    </span><span class="c1">// 長さ n のハッシュテーブルは O(n) の空間を使用</span>
+<a id="__codelineno-56-11" name="__codelineno-56-11" href="#__codelineno-56-11"></a><span class="w">    </span><span class="nx">m</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">(</span><span class="kd">map</span><span class="p">[</span><span class="kt">int</span><span class="p">]</span><span class="kt">string</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
+<a id="__codelineno-56-12" name="__codelineno-56-12" href="#__codelineno-56-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-13" name="__codelineno-56-13" href="#__codelineno-56-13"></a><span class="w">        </span><span class="nx">m</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">strconv</span><span class="p">.</span><span class="nx">Itoa</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span>
+<a id="__codelineno-56-14" name="__codelineno-56-14" href="#__codelineno-56-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-56-15" name="__codelineno-56-15" href="#__codelineno-56-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.swift</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">linear</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.swift</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 線形階 */</span>
+<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="w">    </span><span class="c1">// 長さ n の配列は O(n) の空間を使用</span>
+<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a><span class="w">    </span><span class="c1">// 長さ n のリストは O(n) の空間を使用</span>
+<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">nodes</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">).</span><span class="bp">map</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="nv">$0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></a><span class="w">    </span><span class="c1">// 長さ n のハッシュテーブルは O(n) の空間を使用</span>
+<a id="__codelineno-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">map</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Dictionary</span><span class="p">(</span><span class="n">uniqueKeysWithValues</span><span class="p">:</span><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">).</span><span class="bp">map</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="p">(</span><span class="nv">$0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;</span><span class="si">\(</span><span class="nv">$0</span><span class="si">)</span><span class="s">&quot;</span><span class="p">)</span><span class="w"> </span><span class="p">})</span>
+<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.js</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">linear</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.js</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 線形階 */</span>
+<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">linear</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w">    </span><span class="c1">// 長さ n の配列は O(n) の空間を使用</span>
+<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">);</span>
+<a id="__codelineno-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a><span class="w">    </span><span class="c1">// 長さ n のリストは O(n) の空間を使用</span>
+<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">nodes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></a><span class="w">        </span><span class="nx">nodes</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="nx">i</span><span class="p">));</span>
+<a id="__codelineno-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-58-10" name="__codelineno-58-10" href="#__codelineno-58-10"></a><span class="w">    </span><span class="c1">// 長さ n のハッシュテーブルは O(n) の空間を使用</span>
+<a id="__codelineno-58-11" name="__codelineno-58-11" href="#__codelineno-58-11"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Map</span><span class="p">();</span>
+<a id="__codelineno-58-12" name="__codelineno-58-12" href="#__codelineno-58-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-13" name="__codelineno-58-13" href="#__codelineno-58-13"></a><span class="w">        </span><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">.</span><span class="nx">toString</span><span class="p">());</span>
+<a id="__codelineno-58-14" name="__codelineno-58-14" href="#__codelineno-58-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-58-15" name="__codelineno-58-15" href="#__codelineno-58-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.ts</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">linear</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.ts</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="cm">/* 線形階 */</span>
+<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">linear</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="w">    </span><span class="c1">// 長さ n の配列は O(n) の空間を使用</span>
+<a id="__codelineno-59-4" name="__codelineno-59-4" href="#__codelineno-59-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">);</span>
+<a id="__codelineno-59-5" name="__codelineno-59-5" href="#__codelineno-59-5"></a><span class="w">    </span><span class="c1">// 長さ n のリストは O(n) の空間を使用</span>
+<a id="__codelineno-59-6" name="__codelineno-59-6" href="#__codelineno-59-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">nodes</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-59-7" name="__codelineno-59-7" href="#__codelineno-59-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-8" name="__codelineno-59-8" href="#__codelineno-59-8"></a><span class="w">        </span><span class="nx">nodes</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="nx">i</span><span class="p">));</span>
+<a id="__codelineno-59-9" name="__codelineno-59-9" href="#__codelineno-59-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-59-10" name="__codelineno-59-10" href="#__codelineno-59-10"></a><span class="w">    </span><span class="c1">// 長さ n のハッシュテーブルは O(n) の空間を使用</span>
+<a id="__codelineno-59-11" name="__codelineno-59-11" href="#__codelineno-59-11"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Map</span><span class="p">();</span>
+<a id="__codelineno-59-12" name="__codelineno-59-12" href="#__codelineno-59-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-13" name="__codelineno-59-13" href="#__codelineno-59-13"></a><span class="w">        </span><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">.</span><span class="nx">toString</span><span class="p">());</span>
+<a id="__codelineno-59-14" name="__codelineno-59-14" href="#__codelineno-59-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-59-15" name="__codelineno-59-15" href="#__codelineno-59-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.dart</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linear</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.dart</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="cm">/* 線形階 */</span>
+<a id="__codelineno-60-2" name="__codelineno-60-2" href="#__codelineno-60-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-3" name="__codelineno-60-3" href="#__codelineno-60-3"></a><span class="w">  </span><span class="c1">// 長さ n の配列は O(n) の空間を使用</span>
+<a id="__codelineno-60-4" name="__codelineno-60-4" href="#__codelineno-60-4"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-60-5" name="__codelineno-60-5" href="#__codelineno-60-5"></a><span class="w">  </span><span class="c1">// 長さ n のリストは O(n) の空間を使用</span>
+<a id="__codelineno-60-6" name="__codelineno-60-6" href="#__codelineno-60-6"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nodes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-60-7" name="__codelineno-60-7" href="#__codelineno-60-7"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-8" name="__codelineno-60-8" href="#__codelineno-60-8"></a><span class="w">    </span><span class="n">nodes</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">ListNode</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-60-9" name="__codelineno-60-9" href="#__codelineno-60-9"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-60-10" name="__codelineno-60-10" href="#__codelineno-60-10"></a><span class="w">  </span><span class="c1">// 長さ n のハッシュテーブルは O(n) の空間を使用</span>
+<a id="__codelineno-60-11" name="__codelineno-60-11" href="#__codelineno-60-11"></a><span class="w">  </span><span class="n">Map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashMap</span><span class="p">();</span>
+<a id="__codelineno-60-12" name="__codelineno-60-12" href="#__codelineno-60-12"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-13" name="__codelineno-60-13" href="#__codelineno-60-13"></a><span class="w">    </span><span class="n">map</span><span class="p">.</span><span class="n">putIfAbsent</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">i</span><span class="p">.</span><span class="n">toString</span><span class="p">());</span>
+<a id="__codelineno-60-14" name="__codelineno-60-14" href="#__codelineno-60-14"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-60-15" name="__codelineno-60-15" href="#__codelineno-60-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.rs</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linear</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.rs</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="cm">/* 線形階 */</span>
+<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a><span class="cp">#[allow(unused)]</span>
+<a id="__codelineno-61-3" name="__codelineno-61-3" href="#__codelineno-61-3"></a><span class="k">fn</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-4" name="__codelineno-61-4" href="#__codelineno-61-4"></a><span class="w">    </span><span class="c1">// 長さ n の配列は O(n) の空間を使用</span>
+<a id="__codelineno-61-5" name="__codelineno-61-5" href="#__codelineno-61-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">];</span>
+<a id="__codelineno-61-6" name="__codelineno-61-6" href="#__codelineno-61-6"></a><span class="w">    </span><span class="c1">// 長さ n のリストは O(n) の空間を使用</span>
+<a id="__codelineno-61-7" name="__codelineno-61-7" href="#__codelineno-61-7"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">nodes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-61-8" name="__codelineno-61-8" href="#__codelineno-61-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-9" name="__codelineno-61-9" href="#__codelineno-61-9"></a><span class="w">        </span><span class="n">nodes</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">ListNode</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
+<a id="__codelineno-61-10" name="__codelineno-61-10" href="#__codelineno-61-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-61-11" name="__codelineno-61-11" href="#__codelineno-61-11"></a><span class="w">    </span><span class="c1">// 長さ n のハッシュテーブルは O(n) の空間を使用</span>
+<a id="__codelineno-61-12" name="__codelineno-61-12" href="#__codelineno-61-12"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashMap</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-61-13" name="__codelineno-61-13" href="#__codelineno-61-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-14" name="__codelineno-61-14" href="#__codelineno-61-14"></a><span class="w">        </span><span class="n">map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">.</span><span class="n">to_string</span><span class="p">());</span>
+<a id="__codelineno-61-15" name="__codelineno-61-15" href="#__codelineno-61-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-61-16" name="__codelineno-61-16" href="#__codelineno-61-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.c</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">HashTable</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
-<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a>
-<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linear</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.c</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="cm">/* ハッシュテーブル */</span>
+<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">;</span>
+<a id="__codelineno-62-4" name="__codelineno-62-4" href="#__codelineno-62-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-62-5" name="__codelineno-62-5" href="#__codelineno-62-5"></a><span class="w">    </span><span class="n">UT_hash_handle</span><span class="w"> </span><span class="n">hh</span><span class="p">;</span><span class="w"> </span><span class="c1">// uthash.h を用いて実装</span>
+<a id="__codelineno-62-6" name="__codelineno-62-6" href="#__codelineno-62-6"></a><span class="p">}</span><span class="w"> </span><span class="n">HashTable</span><span class="p">;</span>
+<a id="__codelineno-62-7" name="__codelineno-62-7" href="#__codelineno-62-7"></a>
+<a id="__codelineno-62-8" name="__codelineno-62-8" href="#__codelineno-62-8"></a><span class="cm">/* 線形階 */</span>
+<a id="__codelineno-62-9" name="__codelineno-62-9" href="#__codelineno-62-9"></a><span class="kt">void</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-10" name="__codelineno-62-10" href="#__codelineno-62-10"></a><span class="w">    </span><span class="c1">// 長さ n の配列は O(n) の空間を使用</span>
+<a id="__codelineno-62-11" name="__codelineno-62-11" href="#__codelineno-62-11"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-62-12" name="__codelineno-62-12" href="#__codelineno-62-12"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">nums</span><span class="p">);</span>
+<a id="__codelineno-62-13" name="__codelineno-62-13" href="#__codelineno-62-13"></a>
+<a id="__codelineno-62-14" name="__codelineno-62-14" href="#__codelineno-62-14"></a><span class="w">    </span><span class="c1">// 長さ n のリストは O(n) の空間を使用</span>
+<a id="__codelineno-62-15" name="__codelineno-62-15" href="#__codelineno-62-15"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">**</span><span class="n">nodes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-62-16" name="__codelineno-62-16" href="#__codelineno-62-16"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-17" name="__codelineno-62-17" href="#__codelineno-62-17"></a><span class="w">        </span><span class="n">nodes</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newListNode</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-62-18" name="__codelineno-62-18" href="#__codelineno-62-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-62-19" name="__codelineno-62-19" href="#__codelineno-62-19"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-62-20" name="__codelineno-62-20" href="#__codelineno-62-20"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-21" name="__codelineno-62-21" href="#__codelineno-62-21"></a><span class="w">        </span><span class="n">free</span><span class="p">(</span><span class="n">nodes</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-62-22" name="__codelineno-62-22" href="#__codelineno-62-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-62-23" name="__codelineno-62-23" href="#__codelineno-62-23"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">nodes</span><span class="p">);</span>
+<a id="__codelineno-62-24" name="__codelineno-62-24" href="#__codelineno-62-24"></a>
+<a id="__codelineno-62-25" name="__codelineno-62-25" href="#__codelineno-62-25"></a><span class="w">    </span><span class="c1">// 長さ n のハッシュテーブルは O(n) の空間を使用</span>
+<a id="__codelineno-62-26" name="__codelineno-62-26" href="#__codelineno-62-26"></a><span class="w">    </span><span class="n">HashTable</span><span class="w"> </span><span class="o">*</span><span class="n">h</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-62-27" name="__codelineno-62-27" href="#__codelineno-62-27"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-28" name="__codelineno-62-28" href="#__codelineno-62-28"></a><span class="w">        </span><span class="n">HashTable</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">HashTable</span><span class="p">));</span>
+<a id="__codelineno-62-29" name="__codelineno-62-29" href="#__codelineno-62-29"></a><span class="w">        </span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-62-30" name="__codelineno-62-30" href="#__codelineno-62-30"></a><span class="w">        </span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-62-31" name="__codelineno-62-31" href="#__codelineno-62-31"></a><span class="w">        </span><span class="n">HASH_ADD_INT</span><span class="p">(</span><span class="n">h</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">tmp</span><span class="p">);</span>
+<a id="__codelineno-62-32" name="__codelineno-62-32" href="#__codelineno-62-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-62-33" name="__codelineno-62-33" href="#__codelineno-62-33"></a>
+<a id="__codelineno-62-34" name="__codelineno-62-34" href="#__codelineno-62-34"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-62-35" name="__codelineno-62-35" href="#__codelineno-62-35"></a><span class="w">    </span><span class="n">HashTable</span><span class="w"> </span><span class="o">*</span><span class="n">curr</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-62-36" name="__codelineno-62-36" href="#__codelineno-62-36"></a><span class="w">    </span><span class="n">HASH_ITER</span><span class="p">(</span><span class="n">hh</span><span class="p">,</span><span class="w"> </span><span class="n">h</span><span class="p">,</span><span class="w"> </span><span class="n">curr</span><span class="p">,</span><span class="w"> </span><span class="n">tmp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-37" name="__codelineno-62-37" href="#__codelineno-62-37"></a><span class="w">        </span><span class="n">HASH_DEL</span><span class="p">(</span><span class="n">h</span><span class="p">,</span><span class="w"> </span><span class="n">curr</span><span class="p">);</span>
+<a id="__codelineno-62-38" name="__codelineno-62-38" href="#__codelineno-62-38"></a><span class="w">        </span><span class="n">free</span><span class="p">(</span><span class="n">curr</span><span class="p">);</span>
+<a id="__codelineno-62-39" name="__codelineno-62-39" href="#__codelineno-62-39"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-62-40" name="__codelineno-62-40" href="#__codelineno-62-40"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.kt</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">linear</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.kt</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="cm">/* 線形階 */</span>
+<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a><span class="w">    </span><span class="c1">// 長さ n の配列は O(n) の空間を使用</span>
+<a id="__codelineno-63-4" name="__codelineno-63-4" href="#__codelineno-63-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Array</span><span class="p">(</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-63-5" name="__codelineno-63-5" href="#__codelineno-63-5"></a><span class="w">    </span><span class="c1">// 長さ n のリストは O(n) の空間を使用</span>
+<a id="__codelineno-63-6" name="__codelineno-63-6" href="#__codelineno-63-6"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">nodes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-8" name="__codelineno-63-8" href="#__codelineno-63-8"></a><span class="w">        </span><span class="n">nodes</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">ListNode</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
+<a id="__codelineno-63-9" name="__codelineno-63-9" href="#__codelineno-63-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-63-10" name="__codelineno-63-10" href="#__codelineno-63-10"></a><span class="w">    </span><span class="c1">// 長さ n のハッシュテーブルは O(n) の空間を使用</span>
+<a id="__codelineno-63-11" name="__codelineno-63-11" href="#__codelineno-63-11"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableMapOf</span><span class="o">&lt;</span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="kt">String</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-63-12" name="__codelineno-63-12" href="#__codelineno-63-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-13" name="__codelineno-63-13" href="#__codelineno-63-13"></a><span class="w">        </span><span class="n">map</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">.</span><span class="na">toString</span><span class="p">()</span>
+<a id="__codelineno-63-14" name="__codelineno-63-14" href="#__codelineno-63-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-63-15" name="__codelineno-63-15" href="#__codelineno-63-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.rb</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">linear</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.rb</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="c1">### 線形階 ###</span>
+<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a><span class="w">  </span><span class="c1"># 長さ n のリストは O(n) の空間を使用</span>
+<a id="__codelineno-64-4" name="__codelineno-64-4" href="#__codelineno-64-4"></a><span class="w">  </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-64-5" name="__codelineno-64-5" href="#__codelineno-64-5"></a>
+<a id="__codelineno-64-6" name="__codelineno-64-6" href="#__codelineno-64-6"></a><span class="w">  </span><span class="c1"># 長さ n のハッシュテーブルは O(n) の空間を使用</span>
+<a id="__codelineno-64-7" name="__codelineno-64-7" href="#__codelineno-64-7"></a><span class="w">  </span><span class="n">hmap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{}</span>
+<a id="__codelineno-64-8" name="__codelineno-64-8" href="#__codelineno-64-8"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
+<a id="__codelineno-64-9" name="__codelineno-64-9" href="#__codelineno-64-9"></a><span class="w">    </span><span class="n">hmap</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="o">.</span><span class="n">to_s</span>
+<a id="__codelineno-64-10" name="__codelineno-64-10" href="#__codelineno-64-10"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-64-11" name="__codelineno-64-11" href="#__codelineno-64-11"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>下図に示されているように、この関数の再帰深度は<span class="arithmatex">\(n\)</span>で、<span class="arithmatex">\(n\)</span>個の未返却の<code>linear_recur()</code>関数インスタンスがあり、<span class="arithmatex">\(O(n)\)</span>サイズのスタックフレーム空間を使用します：</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 459px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20linear%28n%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E7%B7%9A%E5%BD%A2%E9%9A%8E%22%22%22%0A%20%20%20%20%23%20%E9%95%B7%E3%81%95%20n%20%E3%81%AE%E3%83%AA%E3%82%B9%E3%83%88%E3%81%AF%20O%28n%29%20%E3%81%AE%E7%A9%BA%E9%96%93%E3%82%92%E4%BD%BF%E7%94%A8%0A%20%20%20%20nums%20%3D%20%5B0%5D%20%2A%20n%0A%20%20%20%20%23%20%E9%95%B7%E3%81%95%20n%20%E3%81%AE%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%81%AF%20O%28n%29%20%E3%81%AE%E7%A9%BA%E9%96%93%E3%82%92%E4%BD%BF%E7%94%A8%0A%20%20%20%20hmap%20%3D%20dict%5Bint%2C%20str%5D%28%29%0A%20%20%20%20for%20i%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20hmap%5Bi%5D%20%3D%20str%28i%29%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20%23%20%E7%B7%9A%E5%BD%A2%E9%9A%8E%0A%20%20%20%20linear%28n%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=20&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20linear%28n%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E7%B7%9A%E5%BD%A2%E9%9A%8E%22%22%22%0A%20%20%20%20%23%20%E9%95%B7%E3%81%95%20n%20%E3%81%AE%E3%83%AA%E3%82%B9%E3%83%88%E3%81%AF%20O%28n%29%20%E3%81%AE%E7%A9%BA%E9%96%93%E3%82%92%E4%BD%BF%E7%94%A8%0A%20%20%20%20nums%20%3D%20%5B0%5D%20%2A%20n%0A%20%20%20%20%23%20%E9%95%B7%E3%81%95%20n%20%E3%81%AE%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%81%AF%20O%28n%29%20%E3%81%AE%E7%A9%BA%E9%96%93%E3%82%92%E4%BD%BF%E7%94%A8%0A%20%20%20%20hmap%20%3D%20dict%5Bint%2C%20str%5D%28%29%0A%20%20%20%20for%20i%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20hmap%5Bi%5D%20%3D%20str%28i%29%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20%23%20%E7%B7%9A%E5%BD%A2%E9%9A%8E%0A%20%20%20%20linear%28n%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=20&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>以下の図に示すように、この関数の再帰の深さは <span class="arithmatex">\(n\)</span> であり、同時に <span class="arithmatex">\(n\)</span> 個の未返却 <code>linear_recur()</code> 関数が存在するため、<span class="arithmatex">\(O(n)\)</span> のスタックフレーム空間を使用します。</p>
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 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.py</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;線形複雑度（再帰実装）&quot;&quot;&quot;</span>
-<a id="__codelineno-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></a>    <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;再帰 n =&quot;</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
-<a id="__codelineno-62-4" name="__codelineno-62-4" href="#__codelineno-62-4"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
-<a id="__codelineno-62-5" name="__codelineno-62-5" href="#__codelineno-62-5"></a>        <span class="k">return</span>
-<a id="__codelineno-62-6" name="__codelineno-62-6" href="#__codelineno-62-6"></a>    <span class="n">linear_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<div class="highlight"><span class="filename">space_complexity.py</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;線形時間（再帰実装）&quot;&quot;&quot;</span>
+<a id="__codelineno-65-3" name="__codelineno-65-3" href="#__codelineno-65-3"></a>    <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;再帰 n =&quot;</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-65-4" name="__codelineno-65-4" href="#__codelineno-65-4"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+<a id="__codelineno-65-5" name="__codelineno-65-5" href="#__codelineno-65-5"></a>        <span class="k">return</span>
+<a id="__codelineno-65-6" name="__codelineno-65-6" href="#__codelineno-65-6"></a>    <span class="n">linear_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.cpp</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="cm">/* 線形計算量（再帰実装） */</span>
-<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">linearRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a><span class="w">    </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;再帰 n = &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
-<a id="__codelineno-63-4" name="__codelineno-63-4" href="#__codelineno-63-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-63-5" name="__codelineno-63-5" href="#__codelineno-63-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-63-6" name="__codelineno-63-6" href="#__codelineno-63-6"></a><span class="w">    </span><span class="n">linearRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.cpp</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="cm">/* 線形時間（再帰実装） */</span>
+<a id="__codelineno-66-2" name="__codelineno-66-2" href="#__codelineno-66-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">linearRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-66-3" name="__codelineno-66-3" href="#__codelineno-66-3"></a><span class="w">    </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;再帰 n = &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
+<a id="__codelineno-66-4" name="__codelineno-66-4" href="#__codelineno-66-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-66-5" name="__codelineno-66-5" href="#__codelineno-66-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-66-6" name="__codelineno-66-6" href="#__codelineno-66-6"></a><span class="w">    </span><span class="n">linearRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-66-7" name="__codelineno-66-7" href="#__codelineno-66-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.java</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="cm">/* 線形計算量（再帰実装） */</span>
-<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">linearRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a><span class="w">    </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">&quot;再帰 n = &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
-<a id="__codelineno-64-4" name="__codelineno-64-4" href="#__codelineno-64-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-64-5" name="__codelineno-64-5" href="#__codelineno-64-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-64-6" name="__codelineno-64-6" href="#__codelineno-64-6"></a><span class="w">    </span><span class="n">linearRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-64-7" name="__codelineno-64-7" href="#__codelineno-64-7"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.java</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="cm">/* 線形時間（再帰実装） */</span>
+<a id="__codelineno-67-2" name="__codelineno-67-2" href="#__codelineno-67-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">linearRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-67-3" name="__codelineno-67-3" href="#__codelineno-67-3"></a><span class="w">    </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">&quot;再帰 n = &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-67-4" name="__codelineno-67-4" href="#__codelineno-67-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-67-5" name="__codelineno-67-5" href="#__codelineno-67-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-67-6" name="__codelineno-67-6" href="#__codelineno-67-6"></a><span class="w">    </span><span class="n">linearRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-67-7" name="__codelineno-67-7" href="#__codelineno-67-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.cs</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">space_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">LinearRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.cs</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="cm">/* 線形時間（再帰実装） */</span>
+<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">LinearRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-68-3" name="__codelineno-68-3" href="#__codelineno-68-3"></a><span class="w">    </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="s">&quot;再帰 n = &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-68-4" name="__codelineno-68-4" href="#__codelineno-68-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-68-5" name="__codelineno-68-5" href="#__codelineno-68-5"></a><span class="w">    </span><span class="n">LinearRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-68-6" name="__codelineno-68-6" href="#__codelineno-68-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.go</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">spaceLinearRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.go</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="cm">/* 線形時間（再帰実装） */</span>
+<a id="__codelineno-69-2" name="__codelineno-69-2" href="#__codelineno-69-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">spaceLinearRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-3" name="__codelineno-69-3" href="#__codelineno-69-3"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="s">&quot;再帰 n =&quot;</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
+<a id="__codelineno-69-4" name="__codelineno-69-4" href="#__codelineno-69-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-5" name="__codelineno-69-5" href="#__codelineno-69-5"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-69-6" name="__codelineno-69-6" href="#__codelineno-69-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-69-7" name="__codelineno-69-7" href="#__codelineno-69-7"></a><span class="w">    </span><span class="nx">spaceLinearRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-69-8" name="__codelineno-69-8" href="#__codelineno-69-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.swift</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">linearRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.swift</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="cm">/* 線形時間（再帰実装） */</span>
+<a id="__codelineno-70-2" name="__codelineno-70-2" href="#__codelineno-70-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">linearRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-3" name="__codelineno-70-3" href="#__codelineno-70-3"></a><span class="w">    </span><span class="bp">print</span><span class="p">(</span><span class="s">&quot;再帰 n = </span><span class="si">\(</span><span class="n">n</span><span class="si">)</span><span class="s">&quot;</span><span class="p">)</span>
+<a id="__codelineno-70-4" name="__codelineno-70-4" href="#__codelineno-70-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-5" name="__codelineno-70-5" href="#__codelineno-70-5"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-70-6" name="__codelineno-70-6" href="#__codelineno-70-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-70-7" name="__codelineno-70-7" href="#__codelineno-70-7"></a><span class="w">    </span><span class="n">linearRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-70-8" name="__codelineno-70-8" href="#__codelineno-70-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.js</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">linearRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.js</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="cm">/* 線形時間（再帰実装） */</span>
+<a id="__codelineno-71-2" name="__codelineno-71-2" href="#__codelineno-71-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">linearRecur</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-3" name="__codelineno-71-3" href="#__codelineno-71-3"></a><span class="w">    </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="sb">`再帰 n = </span><span class="si">${</span><span class="nx">n</span><span class="si">}</span><span class="sb">`</span><span class="p">);</span>
+<a id="__codelineno-71-4" name="__codelineno-71-4" href="#__codelineno-71-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-71-5" name="__codelineno-71-5" href="#__codelineno-71-5"></a><span class="w">    </span><span class="nx">linearRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-71-6" name="__codelineno-71-6" href="#__codelineno-71-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.ts</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">linearRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.ts</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="cm">/* 線形時間（再帰実装） */</span>
+<a id="__codelineno-72-2" name="__codelineno-72-2" href="#__codelineno-72-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">linearRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-3" name="__codelineno-72-3" href="#__codelineno-72-3"></a><span class="w">    </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="sb">`再帰 n = </span><span class="si">${</span><span class="nx">n</span><span class="si">}</span><span class="sb">`</span><span class="p">);</span>
+<a id="__codelineno-72-4" name="__codelineno-72-4" href="#__codelineno-72-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-72-5" name="__codelineno-72-5" href="#__codelineno-72-5"></a><span class="w">    </span><span class="nx">linearRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-72-6" name="__codelineno-72-6" href="#__codelineno-72-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.dart</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linearRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.dart</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="cm">/* 線形時間（再帰実装） */</span>
+<a id="__codelineno-73-2" name="__codelineno-73-2" href="#__codelineno-73-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">linearRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-73-3" name="__codelineno-73-3" href="#__codelineno-73-3"></a><span class="w">  </span><span class="n">print</span><span class="p">(</span><span class="s1">&#39;再帰 n = </span><span class="si">$</span><span class="n">n</span><span class="s1">&#39;</span><span class="p">);</span>
+<a id="__codelineno-73-4" name="__codelineno-73-4" href="#__codelineno-73-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-73-5" name="__codelineno-73-5" href="#__codelineno-73-5"></a><span class="w">  </span><span class="n">linearRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-73-6" name="__codelineno-73-6" href="#__codelineno-73-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.rs</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linear_recur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.rs</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="cm">/* 線形時間（再帰実装） */</span>
+<a id="__codelineno-74-2" name="__codelineno-74-2" href="#__codelineno-74-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">linear_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-3" name="__codelineno-74-3" href="#__codelineno-74-3"></a><span class="w">    </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;再帰 n = {}&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-74-4" name="__codelineno-74-4" href="#__codelineno-74-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-5" name="__codelineno-74-5" href="#__codelineno-74-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-74-6" name="__codelineno-74-6" href="#__codelineno-74-6"></a><span class="w">    </span><span class="p">};</span>
+<a id="__codelineno-74-7" name="__codelineno-74-7" href="#__codelineno-74-7"></a><span class="w">    </span><span class="n">linear_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-74-8" name="__codelineno-74-8" href="#__codelineno-74-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.c</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linearRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.c</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="cm">/* 線形時間（再帰実装） */</span>
+<a id="__codelineno-75-2" name="__codelineno-75-2" href="#__codelineno-75-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">linearRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-75-3" name="__codelineno-75-3" href="#__codelineno-75-3"></a><span class="w">    </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;再帰 n = %d</span><span class="se">\r\n</span><span class="s">&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-75-4" name="__codelineno-75-4" href="#__codelineno-75-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-75-5" name="__codelineno-75-5" href="#__codelineno-75-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-75-6" name="__codelineno-75-6" href="#__codelineno-75-6"></a><span class="w">    </span><span class="n">linearRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-75-7" name="__codelineno-75-7" href="#__codelineno-75-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.kt</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">linearRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.kt</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="cm">/* 線形時間（再帰実装） */</span>
+<a id="__codelineno-76-2" name="__codelineno-76-2" href="#__codelineno-76-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">linearRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-76-3" name="__codelineno-76-3" href="#__codelineno-76-3"></a><span class="w">    </span><span class="n">println</span><span class="p">(</span><span class="s">&quot;再帰 n = </span><span class="si">$</span><span class="n">n</span><span class="s">&quot;</span><span class="p">)</span>
+<a id="__codelineno-76-4" name="__codelineno-76-4" href="#__codelineno-76-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-76-5" name="__codelineno-76-5" href="#__codelineno-76-5"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-76-6" name="__codelineno-76-6" href="#__codelineno-76-6"></a><span class="w">    </span><span class="n">linearRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-76-7" name="__codelineno-76-7" href="#__codelineno-76-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.rb</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">linear_recur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.rb</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="c1">### 線形階 ###</span>
+<a id="__codelineno-77-2" name="__codelineno-77-2" href="#__codelineno-77-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-77-3" name="__codelineno-77-3" href="#__codelineno-77-3"></a><span class="w">  </span><span class="c1"># 長さ n のリストは O(n) の空間を使用</span>
+<a id="__codelineno-77-4" name="__codelineno-77-4" href="#__codelineno-77-4"></a><span class="w">  </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-77-5" name="__codelineno-77-5" href="#__codelineno-77-5"></a>
+<a id="__codelineno-77-6" name="__codelineno-77-6" href="#__codelineno-77-6"></a><span class="w">  </span><span class="c1"># 長さ n のハッシュテーブルは O(n) の空間を使用</span>
+<a id="__codelineno-77-7" name="__codelineno-77-7" href="#__codelineno-77-7"></a><span class="w">  </span><span class="n">hmap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{}</span>
+<a id="__codelineno-77-8" name="__codelineno-77-8" href="#__codelineno-77-8"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
+<a id="__codelineno-77-9" name="__codelineno-77-9" href="#__codelineno-77-9"></a><span class="w">    </span><span class="n">hmap</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="o">.</span><span class="n">to_s</span>
+<a id="__codelineno-77-10" name="__codelineno-77-10" href="#__codelineno-77-10"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-77-11" name="__codelineno-77-11" href="#__codelineno-77-11"></a><span class="k">end</span>
+<a id="__codelineno-77-12" name="__codelineno-77-12" href="#__codelineno-77-12"></a>
+<a id="__codelineno-77-13" name="__codelineno-77-13" href="#__codelineno-77-13"></a><span class="c1"># ## 線形階（再帰実装）###</span>
+<a id="__codelineno-77-14" name="__codelineno-77-14" href="#__codelineno-77-14"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear_recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-77-15" name="__codelineno-77-15" href="#__codelineno-77-15"></a><span class="w">  </span><span class="nb">puts</span><span class="w"> </span><span class="s2">&quot;再帰 n = </span><span class="si">#{</span><span class="n">n</span><span class="si">}</span><span class="s2">&quot;</span>
+<a id="__codelineno-77-16" name="__codelineno-77-16" href="#__codelineno-77-16"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-77-17" name="__codelineno-77-17" href="#__codelineno-77-17"></a><span class="w">  </span><span class="n">linear_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-77-18" name="__codelineno-77-18" href="#__codelineno-77-18"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p><img alt="Recursive function generating linear order space complexity" class="animation-figure" src="../space_complexity.assets/space_complexity_recursive_linear.png" /></p>
-<p align="center"> 図 2-17 &nbsp; Recursive function generating linear order space complexity </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 423px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20linear_recur%28n%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E7%B7%9A%E5%BD%A2%E6%99%82%E9%96%93%EF%BC%88%E5%86%8D%E5%B8%B0%E5%AE%9F%E8%A3%85%EF%BC%89%22%22%22%0A%20%20%20%20print%28%22%E5%86%8D%E5%B8%B0%20n%20%3D%22%2C%20n%29%0A%20%20%20%20if%20n%20%3D%3D%201%3A%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20linear_recur%28n%20-%201%29%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20%23%20%E7%B7%9A%E5%BD%A2%E9%9A%8E%0A%20%20%20%20linear_recur%28n%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=25&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20linear_recur%28n%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E7%B7%9A%E5%BD%A2%E6%99%82%E9%96%93%EF%BC%88%E5%86%8D%E5%B8%B0%E5%AE%9F%E8%A3%85%EF%BC%89%22%22%22%0A%20%20%20%20print%28%22%E5%86%8D%E5%B8%B0%20n%20%3D%22%2C%20n%29%0A%20%20%20%20if%20n%20%3D%3D%201%3A%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20linear_recur%28n%20-%201%29%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20%23%20%E7%B7%9A%E5%BD%A2%E9%9A%8E%0A%20%20%20%20linear_recur%28n%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=25&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p><img alt="再帰関数が生み出す線形階の空間計算量" class="animation-figure" src="../space_complexity.assets/space_complexity_recursive_linear.png" /></p>
+<p align="center"> 図 2-17 &nbsp; 再帰関数が生み出す線形階の空間計算量 </p>
 
-<h3 id="3-on2">3. &nbsp; 二次オーダー <span class="arithmatex">\(O(n^2)\)</span><a class="headerlink" href="#3-on2" title="Permanent link">&para;</a></h3>
-<p>二次オーダーは行列やグラフで一般的で、要素数は<span class="arithmatex">\(n\)</span>の二乗に比例します：</p>
+<h3 id="3-on2">3. &nbsp; 平方階 <span class="arithmatex">\(O(n^2)\)</span><a class="headerlink" href="#3-on2" title="Permanent link">&para;</a></h3>
+<p>平方階は、要素数が <span class="arithmatex">\(n\)</span> の二乗に比例する行列やグラフによく現れます。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="7:13"><input checked="checked" id="__tabbed_7_1" name="__tabbed_7" type="radio" /><input id="__tabbed_7_2" name="__tabbed_7" type="radio" /><input id="__tabbed_7_3" name="__tabbed_7" type="radio" /><input id="__tabbed_7_4" name="__tabbed_7" type="radio" /><input id="__tabbed_7_5" name="__tabbed_7" type="radio" /><input id="__tabbed_7_6" name="__tabbed_7" type="radio" /><input id="__tabbed_7_7" name="__tabbed_7" type="radio" /><input id="__tabbed_7_8" name="__tabbed_7" type="radio" /><input id="__tabbed_7_9" name="__tabbed_7" type="radio" /><input id="__tabbed_7_10" name="__tabbed_7" type="radio" /><input id="__tabbed_7_11" name="__tabbed_7" type="radio" /><input id="__tabbed_7_12" name="__tabbed_7" type="radio" /><input id="__tabbed_7_13" name="__tabbed_7" type="radio" /><div class="tabbed-labels"><label for="__tabbed_7_1">Python</label><label for="__tabbed_7_2">C++</label><label for="__tabbed_7_3">Java</label><label for="__tabbed_7_4">C#</label><label for="__tabbed_7_5">Go</label><label for="__tabbed_7_6">Swift</label><label for="__tabbed_7_7">JS</label><label for="__tabbed_7_8">TS</label><label for="__tabbed_7_9">Dart</label><label for="__tabbed_7_10">Rust</label><label for="__tabbed_7_11">C</label><label for="__tabbed_7_12">Kotlin</label><label for="__tabbed_7_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.py</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-75-2" name="__codelineno-75-2" href="#__codelineno-75-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;平方複雑度&quot;&quot;&quot;</span>
-<a id="__codelineno-75-3" name="__codelineno-75-3" href="#__codelineno-75-3"></a>    <span class="c1"># 二次元リストは O(n^2) のスペースを占有</span>
-<a id="__codelineno-75-4" name="__codelineno-75-4" href="#__codelineno-75-4"></a>    <span class="n">num_matrix</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">)]</span>
+<div class="highlight"><span class="filename">space_complexity.py</span><pre><span></span><code><a id="__codelineno-78-1" name="__codelineno-78-1" href="#__codelineno-78-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-78-2" name="__codelineno-78-2" href="#__codelineno-78-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二乗階&quot;&quot;&quot;</span>
+<a id="__codelineno-78-3" name="__codelineno-78-3" href="#__codelineno-78-3"></a>    <span class="c1"># 二次元リストは O(n^2) の空間を使用</span>
+<a id="__codelineno-78-4" name="__codelineno-78-4" href="#__codelineno-78-4"></a>    <span class="n">num_matrix</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">)]</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.cpp</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="cm">/* 二次計算量 */</span>
-<a id="__codelineno-76-2" name="__codelineno-76-2" href="#__codelineno-76-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-76-3" name="__codelineno-76-3" href="#__codelineno-76-3"></a><span class="w">    </span><span class="c1">// 二次元リストは O(n^2) 空間を占める</span>
-<a id="__codelineno-76-4" name="__codelineno-76-4" href="#__codelineno-76-4"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">numMatrix</span><span class="p">;</span>
-<a id="__codelineno-76-5" name="__codelineno-76-5" href="#__codelineno-76-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-76-6" name="__codelineno-76-6" href="#__codelineno-76-6"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
-<a id="__codelineno-76-7" name="__codelineno-76-7" href="#__codelineno-76-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-76-8" name="__codelineno-76-8" href="#__codelineno-76-8"></a><span class="w">            </span><span class="n">tmp</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
-<a id="__codelineno-76-9" name="__codelineno-76-9" href="#__codelineno-76-9"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-76-10" name="__codelineno-76-10" href="#__codelineno-76-10"></a><span class="w">        </span><span class="n">numMatrix</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">tmp</span><span class="p">);</span>
-<a id="__codelineno-76-11" name="__codelineno-76-11" href="#__codelineno-76-11"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-76-12" name="__codelineno-76-12" href="#__codelineno-76-12"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.cpp</span><pre><span></span><code><a id="__codelineno-79-1" name="__codelineno-79-1" href="#__codelineno-79-1"></a><span class="cm">/* 二乗階 */</span>
+<a id="__codelineno-79-2" name="__codelineno-79-2" href="#__codelineno-79-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-3" name="__codelineno-79-3" href="#__codelineno-79-3"></a><span class="w">    </span><span class="c1">// 二次元リストは O(n^2) の空間を使用</span>
+<a id="__codelineno-79-4" name="__codelineno-79-4" href="#__codelineno-79-4"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">numMatrix</span><span class="p">;</span>
+<a id="__codelineno-79-5" name="__codelineno-79-5" href="#__codelineno-79-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-6" name="__codelineno-79-6" href="#__codelineno-79-6"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-79-7" name="__codelineno-79-7" href="#__codelineno-79-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-8" name="__codelineno-79-8" href="#__codelineno-79-8"></a><span class="w">            </span><span class="n">tmp</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-79-9" name="__codelineno-79-9" href="#__codelineno-79-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-79-10" name="__codelineno-79-10" href="#__codelineno-79-10"></a><span class="w">        </span><span class="n">numMatrix</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">tmp</span><span class="p">);</span>
+<a id="__codelineno-79-11" name="__codelineno-79-11" href="#__codelineno-79-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-79-12" name="__codelineno-79-12" href="#__codelineno-79-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.java</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="cm">/* 二次計算量 */</span>
-<a id="__codelineno-77-2" name="__codelineno-77-2" href="#__codelineno-77-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-77-3" name="__codelineno-77-3" href="#__codelineno-77-3"></a><span class="w">    </span><span class="c1">// 行列は O(n^2) 空間を占める</span>
-<a id="__codelineno-77-4" name="__codelineno-77-4" href="#__codelineno-77-4"></a><span class="w">    </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">numMatrix</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-77-5" name="__codelineno-77-5" href="#__codelineno-77-5"></a><span class="w">    </span><span class="c1">// 二次元リストは O(n^2) 空間を占める</span>
-<a id="__codelineno-77-6" name="__codelineno-77-6" href="#__codelineno-77-6"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">numList</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
-<a id="__codelineno-77-7" name="__codelineno-77-7" href="#__codelineno-77-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-77-8" name="__codelineno-77-8" href="#__codelineno-77-8"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
-<a id="__codelineno-77-9" name="__codelineno-77-9" href="#__codelineno-77-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-77-10" name="__codelineno-77-10" href="#__codelineno-77-10"></a><span class="w">            </span><span class="n">tmp</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
-<a id="__codelineno-77-11" name="__codelineno-77-11" href="#__codelineno-77-11"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-77-12" name="__codelineno-77-12" href="#__codelineno-77-12"></a><span class="w">        </span><span class="n">numList</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">tmp</span><span class="p">);</span>
-<a id="__codelineno-77-13" name="__codelineno-77-13" href="#__codelineno-77-13"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-77-14" name="__codelineno-77-14" href="#__codelineno-77-14"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.java</span><pre><span></span><code><a id="__codelineno-80-1" name="__codelineno-80-1" href="#__codelineno-80-1"></a><span class="cm">/* 二乗階 */</span>
+<a id="__codelineno-80-2" name="__codelineno-80-2" href="#__codelineno-80-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-3" name="__codelineno-80-3" href="#__codelineno-80-3"></a><span class="w">    </span><span class="c1">// 行列は O(n^2) の空間を使用する</span>
+<a id="__codelineno-80-4" name="__codelineno-80-4" href="#__codelineno-80-4"></a><span class="w">    </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">numMatrix</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-80-5" name="__codelineno-80-5" href="#__codelineno-80-5"></a><span class="w">    </span><span class="c1">// 二次元リストは O(n^2) の空間を使用</span>
+<a id="__codelineno-80-6" name="__codelineno-80-6" href="#__codelineno-80-6"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">numList</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-80-7" name="__codelineno-80-7" href="#__codelineno-80-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-8" name="__codelineno-80-8" href="#__codelineno-80-8"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-80-9" name="__codelineno-80-9" href="#__codelineno-80-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-10" name="__codelineno-80-10" href="#__codelineno-80-10"></a><span class="w">            </span><span class="n">tmp</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-80-11" name="__codelineno-80-11" href="#__codelineno-80-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-80-12" name="__codelineno-80-12" href="#__codelineno-80-12"></a><span class="w">        </span><span class="n">numList</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">tmp</span><span class="p">);</span>
+<a id="__codelineno-80-13" name="__codelineno-80-13" href="#__codelineno-80-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-80-14" name="__codelineno-80-14" href="#__codelineno-80-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.cs</span><pre><span></span><code><a id="__codelineno-78-1" name="__codelineno-78-1" href="#__codelineno-78-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">space_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Quadratic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.cs</span><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="cm">/* 二乗階 */</span>
+<a id="__codelineno-81-2" name="__codelineno-81-2" href="#__codelineno-81-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-3" name="__codelineno-81-3" href="#__codelineno-81-3"></a><span class="w">    </span><span class="c1">// 行列は O(n^2) の空間を使用する</span>
+<a id="__codelineno-81-4" name="__codelineno-81-4" href="#__codelineno-81-4"></a><span class="w">    </span><span class="kt">int</span><span class="p">[,]</span><span class="w"> </span><span class="n">numMatrix</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-81-5" name="__codelineno-81-5" href="#__codelineno-81-5"></a><span class="w">    </span><span class="c1">// 二次元リストは O(n^2) の空間を使用</span>
+<a id="__codelineno-81-6" name="__codelineno-81-6" href="#__codelineno-81-6"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">numList</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-81-7" name="__codelineno-81-7" href="#__codelineno-81-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-8" name="__codelineno-81-8" href="#__codelineno-81-8"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-81-9" name="__codelineno-81-9" href="#__codelineno-81-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-10" name="__codelineno-81-10" href="#__codelineno-81-10"></a><span class="w">            </span><span class="n">tmp</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-81-11" name="__codelineno-81-11" href="#__codelineno-81-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-81-12" name="__codelineno-81-12" href="#__codelineno-81-12"></a><span class="w">        </span><span class="n">numList</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">tmp</span><span class="p">);</span>
+<a id="__codelineno-81-13" name="__codelineno-81-13" href="#__codelineno-81-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-81-14" name="__codelineno-81-14" href="#__codelineno-81-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.go</span><pre><span></span><code><a id="__codelineno-79-1" name="__codelineno-79-1" href="#__codelineno-79-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">spaceQuadratic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.go</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="cm">/* 二乗階 */</span>
+<a id="__codelineno-82-2" name="__codelineno-82-2" href="#__codelineno-82-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">spaceQuadratic</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-3" name="__codelineno-82-3" href="#__codelineno-82-3"></a><span class="w">    </span><span class="c1">// 行列は O(n^2) の空間を使用する</span>
+<a id="__codelineno-82-4" name="__codelineno-82-4" href="#__codelineno-82-4"></a><span class="w">    </span><span class="nx">numMatrix</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
+<a id="__codelineno-82-5" name="__codelineno-82-5" href="#__codelineno-82-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-6" name="__codelineno-82-6" href="#__codelineno-82-6"></a><span class="w">        </span><span class="nx">numMatrix</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
+<a id="__codelineno-82-7" name="__codelineno-82-7" href="#__codelineno-82-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-82-8" name="__codelineno-82-8" href="#__codelineno-82-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.swift</span><pre><span></span><code><a id="__codelineno-80-1" name="__codelineno-80-1" href="#__codelineno-80-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">quadratic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.swift</span><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="cm">/* 二乗階 */</span>
+<a id="__codelineno-83-2" name="__codelineno-83-2" href="#__codelineno-83-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-3" name="__codelineno-83-3" href="#__codelineno-83-3"></a><span class="w">    </span><span class="c1">// 二次元リストは O(n^2) の空間を使用</span>
+<a id="__codelineno-83-4" name="__codelineno-83-4" href="#__codelineno-83-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">numList</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="p">),</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-83-5" name="__codelineno-83-5" href="#__codelineno-83-5"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.js</span><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">quadratic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.js</span><pre><span></span><code><a id="__codelineno-84-1" name="__codelineno-84-1" href="#__codelineno-84-1"></a><span class="cm">/* 二乗階 */</span>
+<a id="__codelineno-84-2" name="__codelineno-84-2" href="#__codelineno-84-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">quadratic</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-3" name="__codelineno-84-3" href="#__codelineno-84-3"></a><span class="w">    </span><span class="c1">// 行列は O(n^2) の空間を使用する</span>
+<a id="__codelineno-84-4" name="__codelineno-84-4" href="#__codelineno-84-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">numMatrix</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span>
+<a id="__codelineno-84-5" name="__codelineno-84-5" href="#__codelineno-84-5"></a><span class="w">        </span><span class="p">.</span><span class="nx">fill</span><span class="p">(</span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-84-6" name="__codelineno-84-6" href="#__codelineno-84-6"></a><span class="w">        </span><span class="p">.</span><span class="nx">map</span><span class="p">(()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="kc">null</span><span class="p">));</span>
+<a id="__codelineno-84-7" name="__codelineno-84-7" href="#__codelineno-84-7"></a><span class="w">    </span><span class="c1">// 二次元リストは O(n^2) の空間を使用</span>
+<a id="__codelineno-84-8" name="__codelineno-84-8" href="#__codelineno-84-8"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">numList</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-84-9" name="__codelineno-84-9" href="#__codelineno-84-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-10" name="__codelineno-84-10" href="#__codelineno-84-10"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-84-11" name="__codelineno-84-11" href="#__codelineno-84-11"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-12" name="__codelineno-84-12" href="#__codelineno-84-12"></a><span class="w">            </span><span class="nx">tmp</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-84-13" name="__codelineno-84-13" href="#__codelineno-84-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-84-14" name="__codelineno-84-14" href="#__codelineno-84-14"></a><span class="w">        </span><span class="nx">numList</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">tmp</span><span class="p">);</span>
+<a id="__codelineno-84-15" name="__codelineno-84-15" href="#__codelineno-84-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-84-16" name="__codelineno-84-16" href="#__codelineno-84-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.ts</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">quadratic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.ts</span><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="cm">/* 二乗階 */</span>
+<a id="__codelineno-85-2" name="__codelineno-85-2" href="#__codelineno-85-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">quadratic</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-3" name="__codelineno-85-3" href="#__codelineno-85-3"></a><span class="w">    </span><span class="c1">// 行列は O(n^2) の空間を使用する</span>
+<a id="__codelineno-85-4" name="__codelineno-85-4" href="#__codelineno-85-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">numMatrix</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span>
+<a id="__codelineno-85-5" name="__codelineno-85-5" href="#__codelineno-85-5"></a><span class="w">        </span><span class="p">.</span><span class="nx">fill</span><span class="p">(</span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-85-6" name="__codelineno-85-6" href="#__codelineno-85-6"></a><span class="w">        </span><span class="p">.</span><span class="nx">map</span><span class="p">(()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="kc">null</span><span class="p">));</span>
+<a id="__codelineno-85-7" name="__codelineno-85-7" href="#__codelineno-85-7"></a><span class="w">    </span><span class="c1">// 二次元リストは O(n^2) の空間を使用</span>
+<a id="__codelineno-85-8" name="__codelineno-85-8" href="#__codelineno-85-8"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">numList</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-85-9" name="__codelineno-85-9" href="#__codelineno-85-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-10" name="__codelineno-85-10" href="#__codelineno-85-10"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-85-11" name="__codelineno-85-11" href="#__codelineno-85-11"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-12" name="__codelineno-85-12" href="#__codelineno-85-12"></a><span class="w">            </span><span class="nx">tmp</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-85-13" name="__codelineno-85-13" href="#__codelineno-85-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-85-14" name="__codelineno-85-14" href="#__codelineno-85-14"></a><span class="w">        </span><span class="nx">numList</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">tmp</span><span class="p">);</span>
+<a id="__codelineno-85-15" name="__codelineno-85-15" href="#__codelineno-85-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-85-16" name="__codelineno-85-16" href="#__codelineno-85-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.dart</span><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quadratic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.dart</span><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="cm">/* 二乗階 */</span>
+<a id="__codelineno-86-2" name="__codelineno-86-2" href="#__codelineno-86-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-3" name="__codelineno-86-3" href="#__codelineno-86-3"></a><span class="w">  </span><span class="c1">// 行列は O(n^2) の空間を使用する</span>
+<a id="__codelineno-86-4" name="__codelineno-86-4" href="#__codelineno-86-4"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">numMatrix</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">generate</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">_</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">));</span>
+<a id="__codelineno-86-5" name="__codelineno-86-5" href="#__codelineno-86-5"></a><span class="w">  </span><span class="c1">// 二次元リストは O(n^2) の空間を使用</span>
+<a id="__codelineno-86-6" name="__codelineno-86-6" href="#__codelineno-86-6"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">numList</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-86-7" name="__codelineno-86-7" href="#__codelineno-86-7"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-8" name="__codelineno-86-8" href="#__codelineno-86-8"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-86-9" name="__codelineno-86-9" href="#__codelineno-86-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-10" name="__codelineno-86-10" href="#__codelineno-86-10"></a><span class="w">      </span><span class="n">tmp</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-86-11" name="__codelineno-86-11" href="#__codelineno-86-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-86-12" name="__codelineno-86-12" href="#__codelineno-86-12"></a><span class="w">    </span><span class="n">numList</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">tmp</span><span class="p">);</span>
+<a id="__codelineno-86-13" name="__codelineno-86-13" href="#__codelineno-86-13"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-86-14" name="__codelineno-86-14" href="#__codelineno-86-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.rs</span><pre><span></span><code><a id="__codelineno-84-1" name="__codelineno-84-1" href="#__codelineno-84-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quadratic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.rs</span><pre><span></span><code><a id="__codelineno-87-1" name="__codelineno-87-1" href="#__codelineno-87-1"></a><span class="cm">/* 二乗階 */</span>
+<a id="__codelineno-87-2" name="__codelineno-87-2" href="#__codelineno-87-2"></a><span class="cp">#[allow(unused)]</span>
+<a id="__codelineno-87-3" name="__codelineno-87-3" href="#__codelineno-87-3"></a><span class="k">fn</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-4" name="__codelineno-87-4" href="#__codelineno-87-4"></a><span class="w">    </span><span class="c1">// 行列は O(n^2) の空間を使用する</span>
+<a id="__codelineno-87-5" name="__codelineno-87-5" href="#__codelineno-87-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">num_matrix</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">];</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">];</span>
+<a id="__codelineno-87-6" name="__codelineno-87-6" href="#__codelineno-87-6"></a><span class="w">    </span><span class="c1">// 二次元リストは O(n^2) の空間を使用</span>
+<a id="__codelineno-87-7" name="__codelineno-87-7" href="#__codelineno-87-7"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">num_list</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-87-8" name="__codelineno-87-8" href="#__codelineno-87-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-9" name="__codelineno-87-9" href="#__codelineno-87-9"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-87-10" name="__codelineno-87-10" href="#__codelineno-87-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-11" name="__codelineno-87-11" href="#__codelineno-87-11"></a><span class="w">            </span><span class="n">tmp</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-87-12" name="__codelineno-87-12" href="#__codelineno-87-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-87-13" name="__codelineno-87-13" href="#__codelineno-87-13"></a><span class="w">        </span><span class="n">num_list</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">tmp</span><span class="p">);</span>
+<a id="__codelineno-87-14" name="__codelineno-87-14" href="#__codelineno-87-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-87-15" name="__codelineno-87-15" href="#__codelineno-87-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.c</span><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quadratic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.c</span><pre><span></span><code><a id="__codelineno-88-1" name="__codelineno-88-1" href="#__codelineno-88-1"></a><span class="cm">/* 二乗階 */</span>
+<a id="__codelineno-88-2" name="__codelineno-88-2" href="#__codelineno-88-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-3" name="__codelineno-88-3" href="#__codelineno-88-3"></a><span class="w">    </span><span class="c1">// 二次元リストは O(n^2) の空間を使用</span>
+<a id="__codelineno-88-4" name="__codelineno-88-4" href="#__codelineno-88-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">**</span><span class="n">numMatrix</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-88-5" name="__codelineno-88-5" href="#__codelineno-88-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-6" name="__codelineno-88-6" href="#__codelineno-88-6"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-88-7" name="__codelineno-88-7" href="#__codelineno-88-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-8" name="__codelineno-88-8" href="#__codelineno-88-8"></a><span class="w">            </span><span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-88-9" name="__codelineno-88-9" href="#__codelineno-88-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-88-10" name="__codelineno-88-10" href="#__codelineno-88-10"></a><span class="w">        </span><span class="n">numMatrix</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-88-11" name="__codelineno-88-11" href="#__codelineno-88-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-88-12" name="__codelineno-88-12" href="#__codelineno-88-12"></a>
+<a id="__codelineno-88-13" name="__codelineno-88-13" href="#__codelineno-88-13"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-88-14" name="__codelineno-88-14" href="#__codelineno-88-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-15" name="__codelineno-88-15" href="#__codelineno-88-15"></a><span class="w">        </span><span class="n">free</span><span class="p">(</span><span class="n">numMatrix</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-88-16" name="__codelineno-88-16" href="#__codelineno-88-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-88-17" name="__codelineno-88-17" href="#__codelineno-88-17"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">numMatrix</span><span class="p">);</span>
+<a id="__codelineno-88-18" name="__codelineno-88-18" href="#__codelineno-88-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.kt</span><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">quadratic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.kt</span><pre><span></span><code><a id="__codelineno-89-1" name="__codelineno-89-1" href="#__codelineno-89-1"></a><span class="cm">/* 二乗階 */</span>
+<a id="__codelineno-89-2" name="__codelineno-89-2" href="#__codelineno-89-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-89-3" name="__codelineno-89-3" href="#__codelineno-89-3"></a><span class="w">    </span><span class="c1">// 行列は O(n^2) の空間を使用する</span>
+<a id="__codelineno-89-4" name="__codelineno-89-4" href="#__codelineno-89-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">numMatrix</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arrayOfNulls</span><span class="o">&lt;</span><span class="n">Array</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;?&gt;</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-89-5" name="__codelineno-89-5" href="#__codelineno-89-5"></a><span class="w">    </span><span class="c1">// 二次元リストは O(n^2) の空間を使用</span>
+<a id="__codelineno-89-6" name="__codelineno-89-6" href="#__codelineno-89-6"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">numList</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;&gt;</span><span class="p">()</span>
+<a id="__codelineno-89-7" name="__codelineno-89-7" href="#__codelineno-89-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-89-8" name="__codelineno-89-8" href="#__codelineno-89-8"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-89-9" name="__codelineno-89-9" href="#__codelineno-89-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-89-10" name="__codelineno-89-10" href="#__codelineno-89-10"></a><span class="w">            </span><span class="n">tmp</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
+<a id="__codelineno-89-11" name="__codelineno-89-11" href="#__codelineno-89-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-89-12" name="__codelineno-89-12" href="#__codelineno-89-12"></a><span class="w">        </span><span class="n">numList</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">tmp</span><span class="p">)</span>
+<a id="__codelineno-89-13" name="__codelineno-89-13" href="#__codelineno-89-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-89-14" name="__codelineno-89-14" href="#__codelineno-89-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.rb</span><pre><span></span><code><a id="__codelineno-87-1" name="__codelineno-87-1" href="#__codelineno-87-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">quadratic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.rb</span><pre><span></span><code><a id="__codelineno-90-1" name="__codelineno-90-1" href="#__codelineno-90-1"></a><span class="c1">### 平方階 ###</span>
+<a id="__codelineno-90-2" name="__codelineno-90-2" href="#__codelineno-90-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-90-3" name="__codelineno-90-3" href="#__codelineno-90-3"></a><span class="w">  </span><span class="c1"># 二次元リストは O(n^2) の空間を使用</span>
+<a id="__codelineno-90-4" name="__codelineno-90-4" href="#__codelineno-90-4"></a><span class="w">  </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-90-5" name="__codelineno-90-5" href="#__codelineno-90-5"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>下図に示されているように、この関数の再帰深度は<span class="arithmatex">\(n\)</span>で、各再帰呼び出しで長さ<span class="arithmatex">\(n\)</span>、<span class="arithmatex">\(n-1\)</span>、<span class="arithmatex">\(\dots\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(1\)</span>の配列が初期化され、平均<span class="arithmatex">\(n/2\)</span>となり、全体として<span class="arithmatex">\(O(n^2)\)</span>の空間を占有します：</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 387px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20quadratic%28n%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E4%B9%97%E9%9A%8E%22%22%22%0A%20%20%20%20%23%20%E4%BA%8C%E6%AC%A1%E5%85%83%E3%83%AA%E3%82%B9%E3%83%88%E3%81%AF%20O%28n%5E2%29%20%E3%81%AE%E7%A9%BA%E9%96%93%E3%82%92%E4%BD%BF%E7%94%A8%0A%20%20%20%20num_matrix%20%3D%20%5B%5B0%5D%20%2A%20n%20for%20_%20in%20range%28n%29%5D%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20%23%20%E4%BA%8C%E4%B9%97%E9%9A%8E%0A%20%20%20%20quadratic%28n%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=16&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20quadratic%28n%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E4%B9%97%E9%9A%8E%22%22%22%0A%20%20%20%20%23%20%E4%BA%8C%E6%AC%A1%E5%85%83%E3%83%AA%E3%82%B9%E3%83%88%E3%81%AF%20O%28n%5E2%29%20%E3%81%AE%E7%A9%BA%E9%96%93%E3%82%92%E4%BD%BF%E7%94%A8%0A%20%20%20%20num_matrix%20%3D%20%5B%5B0%5D%20%2A%20n%20for%20_%20in%20range%28n%29%5D%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20%23%20%E4%BA%8C%E4%B9%97%E9%9A%8E%0A%20%20%20%20quadratic%28n%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=16&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>以下の図に示すように、この関数の再帰の深さは <span class="arithmatex">\(n\)</span> であり、各再帰関数の中で長さがそれぞれ <span class="arithmatex">\(n\)</span>、<span class="arithmatex">\(n-1\)</span>、<span class="arithmatex">\(\dots\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(1\)</span> の配列を初期化しています。平均長は <span class="arithmatex">\(n / 2\)</span> なので、全体では <span class="arithmatex">\(O(n^2)\)</span> の空間を占有します。</p>
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 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.py</span><pre><span></span><code><a id="__codelineno-88-1" name="__codelineno-88-1" href="#__codelineno-88-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-88-2" name="__codelineno-88-2" href="#__codelineno-88-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;平方複雑度（再帰実装）&quot;&quot;&quot;</span>
-<a id="__codelineno-88-3" name="__codelineno-88-3" href="#__codelineno-88-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">&lt;=</span> <span class="mi">0</span><span class="p">:</span>
-<a id="__codelineno-88-4" name="__codelineno-88-4" href="#__codelineno-88-4"></a>        <span class="k">return</span> <span class="mi">0</span>
-<a id="__codelineno-88-5" name="__codelineno-88-5" href="#__codelineno-88-5"></a>    <span class="n">nums</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span>
-<a id="__codelineno-88-6" name="__codelineno-88-6" href="#__codelineno-88-6"></a>    <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;再帰 n = </span><span class="si">{</span><span class="n">n</span><span class="si">}</span><span class="s2"> の中で配列の長さ = </span><span class="si">{</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
-<a id="__codelineno-88-7" name="__codelineno-88-7" href="#__codelineno-88-7"></a>    <span class="k">return</span> <span class="n">quadratic_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<div class="highlight"><span class="filename">space_complexity.py</span><pre><span></span><code><a id="__codelineno-91-1" name="__codelineno-91-1" href="#__codelineno-91-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-91-2" name="__codelineno-91-2" href="#__codelineno-91-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二次時間（再帰実装）&quot;&quot;&quot;</span>
+<a id="__codelineno-91-3" name="__codelineno-91-3" href="#__codelineno-91-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">&lt;=</span> <span class="mi">0</span><span class="p">:</span>
+<a id="__codelineno-91-4" name="__codelineno-91-4" href="#__codelineno-91-4"></a>        <span class="k">return</span> <span class="mi">0</span>
+<a id="__codelineno-91-5" name="__codelineno-91-5" href="#__codelineno-91-5"></a>    <span class="c1"># 配列 nums の長さは n, n-1, ..., 2, 1</span>
+<a id="__codelineno-91-6" name="__codelineno-91-6" href="#__codelineno-91-6"></a>    <span class="n">nums</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span>
+<a id="__codelineno-91-7" name="__codelineno-91-7" href="#__codelineno-91-7"></a>    <span class="k">return</span> <span class="n">quadratic_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.cpp</span><pre><span></span><code><a id="__codelineno-89-1" name="__codelineno-89-1" href="#__codelineno-89-1"></a><span class="cm">/* 二次計算量（再帰実装） */</span>
-<a id="__codelineno-89-2" name="__codelineno-89-2" href="#__codelineno-89-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">quadraticRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-89-3" name="__codelineno-89-3" href="#__codelineno-89-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
-<a id="__codelineno-89-4" name="__codelineno-89-4" href="#__codelineno-89-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-89-5" name="__codelineno-89-5" href="#__codelineno-89-5"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
-<a id="__codelineno-89-6" name="__codelineno-89-6" href="#__codelineno-89-6"></a><span class="w">    </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;再帰 n = &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;, nums の長さ = &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
-<a id="__codelineno-89-7" name="__codelineno-89-7" href="#__codelineno-89-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">quadraticRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-89-8" name="__codelineno-89-8" href="#__codelineno-89-8"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.cpp</span><pre><span></span><code><a id="__codelineno-92-1" name="__codelineno-92-1" href="#__codelineno-92-1"></a><span class="cm">/* 二次時間（再帰実装） */</span>
+<a id="__codelineno-92-2" name="__codelineno-92-2" href="#__codelineno-92-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">quadraticRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-92-3" name="__codelineno-92-3" href="#__codelineno-92-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-92-4" name="__codelineno-92-4" href="#__codelineno-92-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-92-5" name="__codelineno-92-5" href="#__codelineno-92-5"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-92-6" name="__codelineno-92-6" href="#__codelineno-92-6"></a><span class="w">    </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;再帰 n = &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot; における nums の長さ = &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
+<a id="__codelineno-92-7" name="__codelineno-92-7" href="#__codelineno-92-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">quadraticRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-92-8" name="__codelineno-92-8" href="#__codelineno-92-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.java</span><pre><span></span><code><a id="__codelineno-90-1" name="__codelineno-90-1" href="#__codelineno-90-1"></a><span class="cm">/* 二次計算量（再帰実装） */</span>
-<a id="__codelineno-90-2" name="__codelineno-90-2" href="#__codelineno-90-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">quadraticRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-90-3" name="__codelineno-90-3" href="#__codelineno-90-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
-<a id="__codelineno-90-4" name="__codelineno-90-4" href="#__codelineno-90-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-90-5" name="__codelineno-90-5" href="#__codelineno-90-5"></a><span class="w">    </span><span class="c1">// 配列 nums の長さ = n, n-1, ..., 2, 1</span>
-<a id="__codelineno-90-6" name="__codelineno-90-6" href="#__codelineno-90-6"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-90-7" name="__codelineno-90-7" href="#__codelineno-90-7"></a><span class="w">    </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">&quot;再帰 n = &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot; の nums の長さ = &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">);</span>
-<a id="__codelineno-90-8" name="__codelineno-90-8" href="#__codelineno-90-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">quadraticRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-90-9" name="__codelineno-90-9" href="#__codelineno-90-9"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.java</span><pre><span></span><code><a id="__codelineno-93-1" name="__codelineno-93-1" href="#__codelineno-93-1"></a><span class="cm">/* 二次時間（再帰実装） */</span>
+<a id="__codelineno-93-2" name="__codelineno-93-2" href="#__codelineno-93-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">quadraticRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-93-3" name="__codelineno-93-3" href="#__codelineno-93-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-93-4" name="__codelineno-93-4" href="#__codelineno-93-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-93-5" name="__codelineno-93-5" href="#__codelineno-93-5"></a><span class="w">    </span><span class="c1">// 配列 nums の長さは n, n-1, ..., 2, 1</span>
+<a id="__codelineno-93-6" name="__codelineno-93-6" href="#__codelineno-93-6"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-93-7" name="__codelineno-93-7" href="#__codelineno-93-7"></a><span class="w">    </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">&quot;再帰 n = &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot; における nums の長さ = &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">);</span>
+<a id="__codelineno-93-8" name="__codelineno-93-8" href="#__codelineno-93-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">quadraticRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-93-9" name="__codelineno-93-9" href="#__codelineno-93-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.cs</span><pre><span></span><code><a id="__codelineno-91-1" name="__codelineno-91-1" href="#__codelineno-91-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">space_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">QuadraticRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.cs</span><pre><span></span><code><a id="__codelineno-94-1" name="__codelineno-94-1" href="#__codelineno-94-1"></a><span class="cm">/* 二次時間（再帰実装） */</span>
+<a id="__codelineno-94-2" name="__codelineno-94-2" href="#__codelineno-94-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">QuadraticRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-94-3" name="__codelineno-94-3" href="#__codelineno-94-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-94-4" name="__codelineno-94-4" href="#__codelineno-94-4"></a><span class="w">    </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-94-5" name="__codelineno-94-5" href="#__codelineno-94-5"></a><span class="w">    </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="s">&quot;再帰 n = &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot; における nums の長さ = &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">);</span>
+<a id="__codelineno-94-6" name="__codelineno-94-6" href="#__codelineno-94-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nf">QuadraticRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-94-7" name="__codelineno-94-7" href="#__codelineno-94-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.go</span><pre><span></span><code><a id="__codelineno-92-1" name="__codelineno-92-1" href="#__codelineno-92-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">spaceQuadraticRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.go</span><pre><span></span><code><a id="__codelineno-95-1" name="__codelineno-95-1" href="#__codelineno-95-1"></a><span class="cm">/* 二次時間（再帰実装） */</span>
+<a id="__codelineno-95-2" name="__codelineno-95-2" href="#__codelineno-95-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">spaceQuadraticRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-95-3" name="__codelineno-95-3" href="#__codelineno-95-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-95-4" name="__codelineno-95-4" href="#__codelineno-95-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-95-5" name="__codelineno-95-5" href="#__codelineno-95-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-95-6" name="__codelineno-95-6" href="#__codelineno-95-6"></a><span class="w">    </span><span class="nx">nums</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
+<a id="__codelineno-95-7" name="__codelineno-95-7" href="#__codelineno-95-7"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Printf</span><span class="p">(</span><span class="s">&quot;再帰 n = %d における nums の長さ = %d \n&quot;</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">))</span>
+<a id="__codelineno-95-8" name="__codelineno-95-8" href="#__codelineno-95-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">spaceQuadraticRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-95-9" name="__codelineno-95-9" href="#__codelineno-95-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.swift</span><pre><span></span><code><a id="__codelineno-93-1" name="__codelineno-93-1" href="#__codelineno-93-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">quadraticRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.swift</span><pre><span></span><code><a id="__codelineno-96-1" name="__codelineno-96-1" href="#__codelineno-96-1"></a><span class="cm">/* 二次時間（再帰実装） */</span>
+<a id="__codelineno-96-2" name="__codelineno-96-2" href="#__codelineno-96-2"></a><span class="p">@</span><span class="n">discardableResult</span>
+<a id="__codelineno-96-3" name="__codelineno-96-3" href="#__codelineno-96-3"></a><span class="kd">func</span><span class="w"> </span><span class="nf">quadraticRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-96-4" name="__codelineno-96-4" href="#__codelineno-96-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-96-5" name="__codelineno-96-5" href="#__codelineno-96-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-96-6" name="__codelineno-96-6" href="#__codelineno-96-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-96-7" name="__codelineno-96-7" href="#__codelineno-96-7"></a><span class="w">    </span><span class="c1">// 配列 nums の長さは n, n-1, ..., 2, 1</span>
+<a id="__codelineno-96-8" name="__codelineno-96-8" href="#__codelineno-96-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-96-9" name="__codelineno-96-9" href="#__codelineno-96-9"></a><span class="w">    </span><span class="bp">print</span><span class="p">(</span><span class="s">&quot;再帰 n = </span><span class="si">\(</span><span class="n">n</span><span class="si">)</span><span class="s"> における nums の長さ = </span><span class="si">\(</span><span class="n">nums</span><span class="p">.</span><span class="bp">count</span><span class="si">)</span><span class="s">&quot;</span><span class="p">)</span>
+<a id="__codelineno-96-10" name="__codelineno-96-10" href="#__codelineno-96-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">quadraticRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-96-11" name="__codelineno-96-11" href="#__codelineno-96-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.js</span><pre><span></span><code><a id="__codelineno-94-1" name="__codelineno-94-1" href="#__codelineno-94-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">quadraticRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.js</span><pre><span></span><code><a id="__codelineno-97-1" name="__codelineno-97-1" href="#__codelineno-97-1"></a><span class="cm">/* 二次時間（再帰実装） */</span>
+<a id="__codelineno-97-2" name="__codelineno-97-2" href="#__codelineno-97-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">quadraticRecur</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-97-3" name="__codelineno-97-3" href="#__codelineno-97-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-97-4" name="__codelineno-97-4" href="#__codelineno-97-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">);</span>
+<a id="__codelineno-97-5" name="__codelineno-97-5" href="#__codelineno-97-5"></a><span class="w">    </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="sb">`再帰 n = </span><span class="si">${</span><span class="nx">n</span><span class="si">}</span><span class="sb"> における nums の長さ = </span><span class="si">${</span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="si">}</span><span class="sb">`</span><span class="p">);</span>
+<a id="__codelineno-97-6" name="__codelineno-97-6" href="#__codelineno-97-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">quadraticRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-97-7" name="__codelineno-97-7" href="#__codelineno-97-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.ts</span><pre><span></span><code><a id="__codelineno-95-1" name="__codelineno-95-1" href="#__codelineno-95-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">quadraticRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.ts</span><pre><span></span><code><a id="__codelineno-98-1" name="__codelineno-98-1" href="#__codelineno-98-1"></a><span class="cm">/* 二次時間（再帰実装） */</span>
+<a id="__codelineno-98-2" name="__codelineno-98-2" href="#__codelineno-98-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">quadraticRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-98-3" name="__codelineno-98-3" href="#__codelineno-98-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-98-4" name="__codelineno-98-4" href="#__codelineno-98-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">);</span>
+<a id="__codelineno-98-5" name="__codelineno-98-5" href="#__codelineno-98-5"></a><span class="w">    </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="sb">`再帰 n = </span><span class="si">${</span><span class="nx">n</span><span class="si">}</span><span class="sb"> における nums の長さ = </span><span class="si">${</span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="si">}</span><span class="sb">`</span><span class="p">);</span>
+<a id="__codelineno-98-6" name="__codelineno-98-6" href="#__codelineno-98-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">quadraticRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-98-7" name="__codelineno-98-7" href="#__codelineno-98-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.dart</span><pre><span></span><code><a id="__codelineno-96-1" name="__codelineno-96-1" href="#__codelineno-96-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quadraticRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.dart</span><pre><span></span><code><a id="__codelineno-99-1" name="__codelineno-99-1" href="#__codelineno-99-1"></a><span class="cm">/* 二次時間（再帰実装） */</span>
+<a id="__codelineno-99-2" name="__codelineno-99-2" href="#__codelineno-99-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">quadraticRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-99-3" name="__codelineno-99-3" href="#__codelineno-99-3"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-99-4" name="__codelineno-99-4" href="#__codelineno-99-4"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-99-5" name="__codelineno-99-5" href="#__codelineno-99-5"></a><span class="w">  </span><span class="n">print</span><span class="p">(</span><span class="s1">&#39;再帰 n = </span><span class="si">$</span><span class="n">n</span><span class="s1"> における nums の長さ = </span><span class="si">${</span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">);</span>
+<a id="__codelineno-99-6" name="__codelineno-99-6" href="#__codelineno-99-6"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">quadraticRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-99-7" name="__codelineno-99-7" href="#__codelineno-99-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.rs</span><pre><span></span><code><a id="__codelineno-97-1" name="__codelineno-97-1" href="#__codelineno-97-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quadratic_recur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.rs</span><pre><span></span><code><a id="__codelineno-100-1" name="__codelineno-100-1" href="#__codelineno-100-1"></a><span class="cm">/* 二次時間（再帰実装） */</span>
+<a id="__codelineno-100-2" name="__codelineno-100-2" href="#__codelineno-100-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">quadratic_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-3" name="__codelineno-100-3" href="#__codelineno-100-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-4" name="__codelineno-100-4" href="#__codelineno-100-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-100-5" name="__codelineno-100-5" href="#__codelineno-100-5"></a><span class="w">    </span><span class="p">};</span>
+<a id="__codelineno-100-6" name="__codelineno-100-6" href="#__codelineno-100-6"></a><span class="w">    </span><span class="c1">// 配列 nums の長さは n, n-1, ..., 2, 1</span>
+<a id="__codelineno-100-7" name="__codelineno-100-7" href="#__codelineno-100-7"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">];</span>
+<a id="__codelineno-100-8" name="__codelineno-100-8" href="#__codelineno-100-8"></a><span class="w">    </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;再帰 n = {} における nums の長さ = {}&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">());</span>
+<a id="__codelineno-100-9" name="__codelineno-100-9" href="#__codelineno-100-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">quadratic_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-100-10" name="__codelineno-100-10" href="#__codelineno-100-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.c</span><pre><span></span><code><a id="__codelineno-98-1" name="__codelineno-98-1" href="#__codelineno-98-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quadraticRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.c</span><pre><span></span><code><a id="__codelineno-101-1" name="__codelineno-101-1" href="#__codelineno-101-1"></a><span class="cm">/* 二次時間（再帰実装） */</span>
+<a id="__codelineno-101-2" name="__codelineno-101-2" href="#__codelineno-101-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">quadraticRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-101-3" name="__codelineno-101-3" href="#__codelineno-101-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-101-4" name="__codelineno-101-4" href="#__codelineno-101-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-101-5" name="__codelineno-101-5" href="#__codelineno-101-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-101-6" name="__codelineno-101-6" href="#__codelineno-101-6"></a><span class="w">    </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;再帰 n = %d における nums の長さ = %d</span><span class="se">\r\n</span><span class="s">&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-101-7" name="__codelineno-101-7" href="#__codelineno-101-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">quadraticRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-101-8" name="__codelineno-101-8" href="#__codelineno-101-8"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">nums</span><span class="p">);</span>
+<a id="__codelineno-101-9" name="__codelineno-101-9" href="#__codelineno-101-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-101-10" name="__codelineno-101-10" href="#__codelineno-101-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.kt</span><pre><span></span><code><a id="__codelineno-99-1" name="__codelineno-99-1" href="#__codelineno-99-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">quadraticRecur</span><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.rb</span><pre><span></span><code><a id="__codelineno-100-1" name="__codelineno-100-1" href="#__codelineno-100-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">quadratic_recur</span><span class="p">}</span>
-</code></pre></div>
-</div>
-</div>
-</div>
-<p><img alt="Recursive function generating quadratic order space complexity" class="animation-figure" src="../space_complexity.assets/space_complexity_recursive_quadratic.png" /></p>
-<p align="center"> 図 2-18 &nbsp; Recursive function generating quadratic order space complexity </p>
-
-<h3 id="4-o2n">4. &nbsp; 指数オーダー <span class="arithmatex">\(O(2^n)\)</span><a class="headerlink" href="#4-o2n" title="Permanent link">&para;</a></h3>
-<p>指数オーダーは二分木で一般的です。下図を観察すると、<span class="arithmatex">\(n\)</span>レベルの「完全二分木」は<span class="arithmatex">\(2^n - 1\)</span>個のノードを持ち、<span class="arithmatex">\(O(2^n)\)</span>の空間を占有します：</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="9:13"><input checked="checked" id="__tabbed_9_1" name="__tabbed_9" type="radio" /><input id="__tabbed_9_2" name="__tabbed_9" type="radio" /><input id="__tabbed_9_3" name="__tabbed_9" type="radio" /><input id="__tabbed_9_4" name="__tabbed_9" type="radio" /><input id="__tabbed_9_5" name="__tabbed_9" type="radio" /><input id="__tabbed_9_6" name="__tabbed_9" type="radio" /><input id="__tabbed_9_7" name="__tabbed_9" type="radio" /><input id="__tabbed_9_8" name="__tabbed_9" type="radio" /><input id="__tabbed_9_9" name="__tabbed_9" type="radio" /><input id="__tabbed_9_10" name="__tabbed_9" type="radio" /><input id="__tabbed_9_11" name="__tabbed_9" type="radio" /><input id="__tabbed_9_12" name="__tabbed_9" type="radio" /><input id="__tabbed_9_13" name="__tabbed_9" type="radio" /><div class="tabbed-labels"><label for="__tabbed_9_1">Python</label><label for="__tabbed_9_2">C++</label><label for="__tabbed_9_3">Java</label><label for="__tabbed_9_4">C#</label><label for="__tabbed_9_5">Go</label><label for="__tabbed_9_6">Swift</label><label for="__tabbed_9_7">JS</label><label for="__tabbed_9_8">TS</label><label for="__tabbed_9_9">Dart</label><label for="__tabbed_9_10">Rust</label><label for="__tabbed_9_11">C</label><label for="__tabbed_9_12">Kotlin</label><label for="__tabbed_9_13">Ruby</label></div>
-<div class="tabbed-content">
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.py</span><pre><span></span><code><a id="__codelineno-101-1" name="__codelineno-101-1" href="#__codelineno-101-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">build_tree</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-101-2" name="__codelineno-101-2" href="#__codelineno-101-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;指数複雑度（完全二分木の構築）&quot;&quot;&quot;</span>
-<a id="__codelineno-101-3" name="__codelineno-101-3" href="#__codelineno-101-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
-<a id="__codelineno-101-4" name="__codelineno-101-4" href="#__codelineno-101-4"></a>        <span class="k">return</span> <span class="kc">None</span>
-<a id="__codelineno-101-5" name="__codelineno-101-5" href="#__codelineno-101-5"></a>    <span class="n">root</span> <span class="o">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
-<a id="__codelineno-101-6" name="__codelineno-101-6" href="#__codelineno-101-6"></a>    <span class="n">root</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">build_tree</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-101-7" name="__codelineno-101-7" href="#__codelineno-101-7"></a>    <span class="n">root</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="n">build_tree</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-101-8" name="__codelineno-101-8" href="#__codelineno-101-8"></a>    <span class="k">return</span> <span class="n">root</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.cpp</span><pre><span></span><code><a id="__codelineno-102-1" name="__codelineno-102-1" href="#__codelineno-102-1"></a><span class="cm">/* 指数計算量（完全二分木の構築） */</span>
-<a id="__codelineno-102-2" name="__codelineno-102-2" href="#__codelineno-102-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">buildTree</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-102-3" name="__codelineno-102-3" href="#__codelineno-102-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
-<a id="__codelineno-102-4" name="__codelineno-102-4" href="#__codelineno-102-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
-<a id="__codelineno-102-5" name="__codelineno-102-5" href="#__codelineno-102-5"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
-<a id="__codelineno-102-6" name="__codelineno-102-6" href="#__codelineno-102-6"></a><span class="w">    </span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-102-7" name="__codelineno-102-7" href="#__codelineno-102-7"></a><span class="w">    </span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-102-8" name="__codelineno-102-8" href="#__codelineno-102-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
+<div class="highlight"><span class="filename">space_complexity.kt</span><pre><span></span><code><a id="__codelineno-102-1" name="__codelineno-102-1" href="#__codelineno-102-1"></a><span class="cm">/* 二次時間（再帰実装） */</span>
+<a id="__codelineno-102-2" name="__codelineno-102-2" href="#__codelineno-102-2"></a><span class="kd">tailrec</span><span class="w"> </span><span class="kd">fun</span><span class="w"> </span><span class="nf">quadraticRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-102-3" name="__codelineno-102-3" href="#__codelineno-102-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="m">0</span><span class="p">)</span>
+<a id="__codelineno-102-4" name="__codelineno-102-4" href="#__codelineno-102-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-102-5" name="__codelineno-102-5" href="#__codelineno-102-5"></a><span class="w">    </span><span class="c1">// 配列 nums の長さは n, n-1, ..., 2, 1</span>
+<a id="__codelineno-102-6" name="__codelineno-102-6" href="#__codelineno-102-6"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Array</span><span class="p">(</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-102-7" name="__codelineno-102-7" href="#__codelineno-102-7"></a><span class="w">    </span><span class="n">println</span><span class="p">(</span><span class="s">&quot;再帰 n = </span><span class="si">$</span><span class="n">n</span><span class="s"> における nums の長さ = </span><span class="si">${</span><span class="n">nums</span><span class="p">.</span><span class="na">size</span><span class="si">}</span><span class="s">&quot;</span><span class="p">)</span>
+<a id="__codelineno-102-8" name="__codelineno-102-8" href="#__codelineno-102-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">quadraticRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
 <a id="__codelineno-102-9" name="__codelineno-102-9" href="#__codelineno-102-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.java</span><pre><span></span><code><a id="__codelineno-103-1" name="__codelineno-103-1" href="#__codelineno-103-1"></a><span class="cm">/* 指数計算量（完全二分木の構築） */</span>
-<a id="__codelineno-103-2" name="__codelineno-103-2" href="#__codelineno-103-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">buildTree</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-103-3" name="__codelineno-103-3" href="#__codelineno-103-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
-<a id="__codelineno-103-4" name="__codelineno-103-4" href="#__codelineno-103-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
-<a id="__codelineno-103-5" name="__codelineno-103-5" href="#__codelineno-103-5"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
-<a id="__codelineno-103-6" name="__codelineno-103-6" href="#__codelineno-103-6"></a><span class="w">    </span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-103-7" name="__codelineno-103-7" href="#__codelineno-103-7"></a><span class="w">    </span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-103-8" name="__codelineno-103-8" href="#__codelineno-103-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
-<a id="__codelineno-103-9" name="__codelineno-103-9" href="#__codelineno-103-9"></a><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.cs</span><pre><span></span><code><a id="__codelineno-104-1" name="__codelineno-104-1" href="#__codelineno-104-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">space_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BuildTree</span><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.go</span><pre><span></span><code><a id="__codelineno-105-1" name="__codelineno-105-1" href="#__codelineno-105-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">buildTree</span><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.swift</span><pre><span></span><code><a id="__codelineno-106-1" name="__codelineno-106-1" href="#__codelineno-106-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">buildTree</span><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.js</span><pre><span></span><code><a id="__codelineno-107-1" name="__codelineno-107-1" href="#__codelineno-107-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">buildTree</span><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.ts</span><pre><span></span><code><a id="__codelineno-108-1" name="__codelineno-108-1" href="#__codelineno-108-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">buildTree</span><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.dart</span><pre><span></span><code><a id="__codelineno-109-1" name="__codelineno-109-1" href="#__codelineno-109-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">buildTree</span><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.rs</span><pre><span></span><code><a id="__codelineno-110-1" name="__codelineno-110-1" href="#__codelineno-110-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">build_tree</span><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.c</span><pre><span></span><code><a id="__codelineno-111-1" name="__codelineno-111-1" href="#__codelineno-111-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">buildTree</span><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.kt</span><pre><span></span><code><a id="__codelineno-112-1" name="__codelineno-112-1" href="#__codelineno-112-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">buildTree</span><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">space_complexity.rb</span><pre><span></span><code><a id="__codelineno-113-1" name="__codelineno-113-1" href="#__codelineno-113-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">build_tree</span><span class="p">}</span>
+<div class="highlight"><span class="filename">space_complexity.rb</span><pre><span></span><code><a id="__codelineno-103-1" name="__codelineno-103-1" href="#__codelineno-103-1"></a><span class="c1">### 平方階 ###</span>
+<a id="__codelineno-103-2" name="__codelineno-103-2" href="#__codelineno-103-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-103-3" name="__codelineno-103-3" href="#__codelineno-103-3"></a><span class="w">  </span><span class="c1"># 二次元リストは O(n^2) の空間を使用</span>
+<a id="__codelineno-103-4" name="__codelineno-103-4" href="#__codelineno-103-4"></a><span class="w">  </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-103-5" name="__codelineno-103-5" href="#__codelineno-103-5"></a><span class="k">end</span>
+<a id="__codelineno-103-6" name="__codelineno-103-6" href="#__codelineno-103-6"></a>
+<a id="__codelineno-103-7" name="__codelineno-103-7" href="#__codelineno-103-7"></a><span class="c1"># ## 平方階（再帰実装）###</span>
+<a id="__codelineno-103-8" name="__codelineno-103-8" href="#__codelineno-103-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic_recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-103-9" name="__codelineno-103-9" href="#__codelineno-103-9"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-103-10" name="__codelineno-103-10" href="#__codelineno-103-10"></a>
+<a id="__codelineno-103-11" name="__codelineno-103-11" href="#__codelineno-103-11"></a><span class="w">  </span><span class="c1"># 配列 nums の長さは n, n-1, ..., 2, 1</span>
+<a id="__codelineno-103-12" name="__codelineno-103-12" href="#__codelineno-103-12"></a><span class="w">  </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-103-13" name="__codelineno-103-13" href="#__codelineno-103-13"></a><span class="w">  </span><span class="n">quadratic_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-103-14" name="__codelineno-103-14" href="#__codelineno-103-14"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p><img alt="Full binary tree generating exponential order space complexity" class="animation-figure" src="../space_complexity.assets/space_complexity_exponential.png" /></p>
-<p align="center"> 図 2-19 &nbsp; Full binary tree generating exponential order space complexity </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 441px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20quadratic_recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E6%AC%A1%E6%99%82%E9%96%93%EF%BC%88%E5%86%8D%E5%B8%B0%E5%AE%9F%E8%A3%85%EF%BC%89%22%22%22%0A%20%20%20%20if%20n%20%3C%3D%200%3A%0A%20%20%20%20%20%20%20%20return%200%0A%20%20%20%20%23%20%E9%85%8D%E5%88%97%20nums%20%E3%81%AE%E9%95%B7%E3%81%95%E3%81%AF%20n%2C%20n-1%2C%20...%2C%202%2C%201%0A%20%20%20%20nums%20%3D%20%5B0%5D%20%2A%20n%0A%20%20%20%20return%20quadratic_recur%28n%20-%201%29%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20%23%20%E4%BA%8C%E4%B9%97%E9%9A%8E%0A%20%20%20%20quadratic_recur%28n%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=28&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20quadratic_recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E6%AC%A1%E6%99%82%E9%96%93%EF%BC%88%E5%86%8D%E5%B8%B0%E5%AE%9F%E8%A3%85%EF%BC%89%22%22%22%0A%20%20%20%20if%20n%20%3C%3D%200%3A%0A%20%20%20%20%20%20%20%20return%200%0A%20%20%20%20%23%20%E9%85%8D%E5%88%97%20nums%20%E3%81%AE%E9%95%B7%E3%81%95%E3%81%AF%20n%2C%20n-1%2C%20...%2C%202%2C%201%0A%20%20%20%20nums%20%3D%20%5B0%5D%20%2A%20n%0A%20%20%20%20return%20quadratic_recur%28n%20-%201%29%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20%23%20%E4%BA%8C%E4%B9%97%E9%9A%8E%0A%20%20%20%20quadratic_recur%28n%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=28&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p><img alt="再帰関数が生み出す平方階の空間計算量" class="animation-figure" src="../space_complexity.assets/space_complexity_recursive_quadratic.png" /></p>
+<p align="center"> 図 2-18 &nbsp; 再帰関数が生み出す平方階の空間計算量 </p>
 
-<h3 id="5-olog-n">5. &nbsp; 対数オーダー <span class="arithmatex">\(O(\log n)\)</span><a class="headerlink" href="#5-olog-n" title="Permanent link">&para;</a></h3>
-<p>対数オーダーは分割統治アルゴリズムで一般的です。例えば、マージソートでは、長さ<span class="arithmatex">\(n\)</span>の配列が各ラウンドで再帰的に半分に分割され、高さ<span class="arithmatex">\(\log n\)</span>の再帰木を形成し、<span class="arithmatex">\(O(\log n)\)</span>のスタックフレーム空間を使用します。</p>
-<p>別の例は、数値を文字列に変換することです。正の整数<span class="arithmatex">\(n\)</span>が与えられた場合、その桁数は<span class="arithmatex">\(\log_{10} n + 1\)</span>で、文字列の長さに対応するため、空間計算量は<span class="arithmatex">\(O(\log_{10} n + 1) = O(\log n)\)</span>です。</p>
-<h2 id="244">2.4.4 &nbsp; 時間と空間のバランス<a class="headerlink" href="#244" title="Permanent link">&para;</a></h2>
-<p>理想的には、時間計算量と空間計算量の両方が最適であることを目指します。しかし、実際には両方を同時に最適化することはしばしば困難です。</p>
-<p><strong>時間計算量を下げることは通常、空間計算量の増加を代償とし、その逆も同様です</strong>。アルゴリズムの速度を向上させるためにメモリ空間を犠牲にするアプローチは「時空トレードオフ」として知られ、その逆は「空時トレードオフ」として知られています。</p>
-<p>選択は、どちらの側面をより重視するかに依存します。ほとんどの場合、時間は空間よりも貴重であるため、「時空トレードオフ」がより一般的な戦略です。もちろん、大量のデータを扱う際は空間計算量を制御することも非常に重要です。</p>
+<h3 id="4-o2n">4. &nbsp; 指数階 <span class="arithmatex">\(O(2^n)\)</span><a class="headerlink" href="#4-o2n" title="Permanent link">&para;</a></h3>
+<p>指数階は二分木によく現れます。以下の図を見ると、高さが <span class="arithmatex">\(n\)</span> の「満二分木」のノード数は <span class="arithmatex">\(2^n - 1\)</span> であり、<span class="arithmatex">\(O(2^n)\)</span> の空間を占有します。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="9:13"><input checked="checked" id="__tabbed_9_1" name="__tabbed_9" type="radio" /><input id="__tabbed_9_2" name="__tabbed_9" type="radio" /><input id="__tabbed_9_3" name="__tabbed_9" type="radio" /><input id="__tabbed_9_4" name="__tabbed_9" type="radio" /><input id="__tabbed_9_5" name="__tabbed_9" type="radio" /><input id="__tabbed_9_6" name="__tabbed_9" type="radio" /><input id="__tabbed_9_7" name="__tabbed_9" type="radio" /><input id="__tabbed_9_8" name="__tabbed_9" type="radio" /><input id="__tabbed_9_9" name="__tabbed_9" type="radio" /><input id="__tabbed_9_10" name="__tabbed_9" type="radio" /><input id="__tabbed_9_11" name="__tabbed_9" type="radio" /><input id="__tabbed_9_12" name="__tabbed_9" type="radio" /><input id="__tabbed_9_13" name="__tabbed_9" type="radio" /><div class="tabbed-labels"><label for="__tabbed_9_1">Python</label><label for="__tabbed_9_2">C++</label><label for="__tabbed_9_3">Java</label><label for="__tabbed_9_4">C#</label><label for="__tabbed_9_5">Go</label><label for="__tabbed_9_6">Swift</label><label for="__tabbed_9_7">JS</label><label for="__tabbed_9_8">TS</label><label for="__tabbed_9_9">Dart</label><label for="__tabbed_9_10">Rust</label><label for="__tabbed_9_11">C</label><label for="__tabbed_9_12">Kotlin</label><label for="__tabbed_9_13">Ruby</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.py</span><pre><span></span><code><a id="__codelineno-104-1" name="__codelineno-104-1" href="#__codelineno-104-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">build_tree</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-104-2" name="__codelineno-104-2" href="#__codelineno-104-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;指数時間（完全二分木の構築）&quot;&quot;&quot;</span>
+<a id="__codelineno-104-3" name="__codelineno-104-3" href="#__codelineno-104-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+<a id="__codelineno-104-4" name="__codelineno-104-4" href="#__codelineno-104-4"></a>        <span class="k">return</span> <span class="kc">None</span>
+<a id="__codelineno-104-5" name="__codelineno-104-5" href="#__codelineno-104-5"></a>    <span class="n">root</span> <span class="o">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-104-6" name="__codelineno-104-6" href="#__codelineno-104-6"></a>    <span class="n">root</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">build_tree</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-104-7" name="__codelineno-104-7" href="#__codelineno-104-7"></a>    <span class="n">root</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="n">build_tree</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-104-8" name="__codelineno-104-8" href="#__codelineno-104-8"></a>    <span class="k">return</span> <span class="n">root</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.cpp</span><pre><span></span><code><a id="__codelineno-105-1" name="__codelineno-105-1" href="#__codelineno-105-1"></a><span class="cm">/* 指数時間（完全二分木の構築） */</span>
+<a id="__codelineno-105-2" name="__codelineno-105-2" href="#__codelineno-105-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">buildTree</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-105-3" name="__codelineno-105-3" href="#__codelineno-105-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-105-4" name="__codelineno-105-4" href="#__codelineno-105-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
+<a id="__codelineno-105-5" name="__codelineno-105-5" href="#__codelineno-105-5"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-105-6" name="__codelineno-105-6" href="#__codelineno-105-6"></a><span class="w">    </span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-105-7" name="__codelineno-105-7" href="#__codelineno-105-7"></a><span class="w">    </span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-105-8" name="__codelineno-105-8" href="#__codelineno-105-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
+<a id="__codelineno-105-9" name="__codelineno-105-9" href="#__codelineno-105-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.java</span><pre><span></span><code><a id="__codelineno-106-1" name="__codelineno-106-1" href="#__codelineno-106-1"></a><span class="cm">/* 指数時間（完全二分木の構築） */</span>
+<a id="__codelineno-106-2" name="__codelineno-106-2" href="#__codelineno-106-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">buildTree</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-106-3" name="__codelineno-106-3" href="#__codelineno-106-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-106-4" name="__codelineno-106-4" href="#__codelineno-106-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-106-5" name="__codelineno-106-5" href="#__codelineno-106-5"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-106-6" name="__codelineno-106-6" href="#__codelineno-106-6"></a><span class="w">    </span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-106-7" name="__codelineno-106-7" href="#__codelineno-106-7"></a><span class="w">    </span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-106-8" name="__codelineno-106-8" href="#__codelineno-106-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
+<a id="__codelineno-106-9" name="__codelineno-106-9" href="#__codelineno-106-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.cs</span><pre><span></span><code><a id="__codelineno-107-1" name="__codelineno-107-1" href="#__codelineno-107-1"></a><span class="cm">/* 指数時間（完全二分木の構築） */</span>
+<a id="__codelineno-107-2" name="__codelineno-107-2" href="#__codelineno-107-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">BuildTree</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-107-3" name="__codelineno-107-3" href="#__codelineno-107-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
+<a id="__codelineno-107-4" name="__codelineno-107-4" href="#__codelineno-107-4"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-107-5" name="__codelineno-107-5" href="#__codelineno-107-5"></a><span class="w">        </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BuildTree</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">),</span>
+<a id="__codelineno-107-6" name="__codelineno-107-6" href="#__codelineno-107-6"></a><span class="w">        </span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BuildTree</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-107-7" name="__codelineno-107-7" href="#__codelineno-107-7"></a><span class="w">    </span><span class="p">};</span>
+<a id="__codelineno-107-8" name="__codelineno-107-8" href="#__codelineno-107-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
+<a id="__codelineno-107-9" name="__codelineno-107-9" href="#__codelineno-107-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.go</span><pre><span></span><code><a id="__codelineno-108-1" name="__codelineno-108-1" href="#__codelineno-108-1"></a><span class="cm">/* 指数時間（完全二分木の構築） */</span>
+<a id="__codelineno-108-2" name="__codelineno-108-2" href="#__codelineno-108-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">buildTree</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-108-3" name="__codelineno-108-3" href="#__codelineno-108-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-108-4" name="__codelineno-108-4" href="#__codelineno-108-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-108-5" name="__codelineno-108-5" href="#__codelineno-108-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-108-6" name="__codelineno-108-6" href="#__codelineno-108-6"></a><span class="w">    </span><span class="nx">root</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewTreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-108-7" name="__codelineno-108-7" href="#__codelineno-108-7"></a><span class="w">    </span><span class="nx">root</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">buildTree</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-108-8" name="__codelineno-108-8" href="#__codelineno-108-8"></a><span class="w">    </span><span class="nx">root</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">buildTree</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-108-9" name="__codelineno-108-9" href="#__codelineno-108-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span>
+<a id="__codelineno-108-10" name="__codelineno-108-10" href="#__codelineno-108-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.swift</span><pre><span></span><code><a id="__codelineno-109-1" name="__codelineno-109-1" href="#__codelineno-109-1"></a><span class="cm">/* 指数時間（完全二分木の構築） */</span>
+<a id="__codelineno-109-2" name="__codelineno-109-2" href="#__codelineno-109-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">buildTree</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-109-3" name="__codelineno-109-3" href="#__codelineno-109-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-109-4" name="__codelineno-109-4" href="#__codelineno-109-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-109-5" name="__codelineno-109-5" href="#__codelineno-109-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-109-6" name="__codelineno-109-6" href="#__codelineno-109-6"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">root</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-109-7" name="__codelineno-109-7" href="#__codelineno-109-7"></a><span class="w">    </span><span class="n">root</span><span class="p">.</span><span class="kr">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-109-8" name="__codelineno-109-8" href="#__codelineno-109-8"></a><span class="w">    </span><span class="n">root</span><span class="p">.</span><span class="kr">right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-109-9" name="__codelineno-109-9" href="#__codelineno-109-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span>
+<a id="__codelineno-109-10" name="__codelineno-109-10" href="#__codelineno-109-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.js</span><pre><span></span><code><a id="__codelineno-110-1" name="__codelineno-110-1" href="#__codelineno-110-1"></a><span class="cm">/* 指数時間（完全二分木の構築） */</span>
+<a id="__codelineno-110-2" name="__codelineno-110-2" href="#__codelineno-110-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">buildTree</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-110-3" name="__codelineno-110-3" href="#__codelineno-110-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-110-4" name="__codelineno-110-4" href="#__codelineno-110-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-110-5" name="__codelineno-110-5" href="#__codelineno-110-5"></a><span class="w">    </span><span class="nx">root</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">buildTree</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-110-6" name="__codelineno-110-6" href="#__codelineno-110-6"></a><span class="w">    </span><span class="nx">root</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">buildTree</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-110-7" name="__codelineno-110-7" href="#__codelineno-110-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span><span class="p">;</span>
+<a id="__codelineno-110-8" name="__codelineno-110-8" href="#__codelineno-110-8"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.ts</span><pre><span></span><code><a id="__codelineno-111-1" name="__codelineno-111-1" href="#__codelineno-111-1"></a><span class="cm">/* 指数時間（完全二分木の構築） */</span>
+<a id="__codelineno-111-2" name="__codelineno-111-2" href="#__codelineno-111-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">buildTree</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-111-3" name="__codelineno-111-3" href="#__codelineno-111-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-111-4" name="__codelineno-111-4" href="#__codelineno-111-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-111-5" name="__codelineno-111-5" href="#__codelineno-111-5"></a><span class="w">    </span><span class="nx">root</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">buildTree</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-111-6" name="__codelineno-111-6" href="#__codelineno-111-6"></a><span class="w">    </span><span class="nx">root</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">buildTree</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-111-7" name="__codelineno-111-7" href="#__codelineno-111-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span><span class="p">;</span>
+<a id="__codelineno-111-8" name="__codelineno-111-8" href="#__codelineno-111-8"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.dart</span><pre><span></span><code><a id="__codelineno-112-1" name="__codelineno-112-1" href="#__codelineno-112-1"></a><span class="cm">/* 指数時間（完全二分木の構築） */</span>
+<a id="__codelineno-112-2" name="__codelineno-112-2" href="#__codelineno-112-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-112-3" name="__codelineno-112-3" href="#__codelineno-112-3"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-112-4" name="__codelineno-112-4" href="#__codelineno-112-4"></a><span class="w">  </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-112-5" name="__codelineno-112-5" href="#__codelineno-112-5"></a><span class="w">  </span><span class="n">root</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-112-6" name="__codelineno-112-6" href="#__codelineno-112-6"></a><span class="w">  </span><span class="n">root</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-112-7" name="__codelineno-112-7" href="#__codelineno-112-7"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
+<a id="__codelineno-112-8" name="__codelineno-112-8" href="#__codelineno-112-8"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.rs</span><pre><span></span><code><a id="__codelineno-113-1" name="__codelineno-113-1" href="#__codelineno-113-1"></a><span class="cm">/* 指数時間（完全二分木の構築） */</span>
+<a id="__codelineno-113-2" name="__codelineno-113-2" href="#__codelineno-113-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">build_tree</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-113-3" name="__codelineno-113-3" href="#__codelineno-113-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-113-4" name="__codelineno-113-4" href="#__codelineno-113-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nb">None</span><span class="p">;</span>
+<a id="__codelineno-113-5" name="__codelineno-113-5" href="#__codelineno-113-5"></a><span class="w">    </span><span class="p">};</span>
+<a id="__codelineno-113-6" name="__codelineno-113-6" href="#__codelineno-113-6"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-113-7" name="__codelineno-113-7" href="#__codelineno-113-7"></a><span class="w">    </span><span class="n">root</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">build_tree</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-113-8" name="__codelineno-113-8" href="#__codelineno-113-8"></a><span class="w">    </span><span class="n">root</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">build_tree</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-113-9" name="__codelineno-113-9" href="#__codelineno-113-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
+<a id="__codelineno-113-10" name="__codelineno-113-10" href="#__codelineno-113-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.c</span><pre><span></span><code><a id="__codelineno-114-1" name="__codelineno-114-1" href="#__codelineno-114-1"></a><span class="cm">/* 指数時間（完全二分木の構築） */</span>
+<a id="__codelineno-114-2" name="__codelineno-114-2" href="#__codelineno-114-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">buildTree</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-114-3" name="__codelineno-114-3" href="#__codelineno-114-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-114-4" name="__codelineno-114-4" href="#__codelineno-114-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-114-5" name="__codelineno-114-5" href="#__codelineno-114-5"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newTreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-114-6" name="__codelineno-114-6" href="#__codelineno-114-6"></a><span class="w">    </span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-114-7" name="__codelineno-114-7" href="#__codelineno-114-7"></a><span class="w">    </span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-114-8" name="__codelineno-114-8" href="#__codelineno-114-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
+<a id="__codelineno-114-9" name="__codelineno-114-9" href="#__codelineno-114-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.kt</span><pre><span></span><code><a id="__codelineno-115-1" name="__codelineno-115-1" href="#__codelineno-115-1"></a><span class="cm">/* 指数時間（完全二分木の構築） */</span>
+<a id="__codelineno-115-2" name="__codelineno-115-2" href="#__codelineno-115-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">buildTree</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="n">TreeNode? </span><span class="p">{</span>
+<a id="__codelineno-115-3" name="__codelineno-115-3" href="#__codelineno-115-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">)</span>
+<a id="__codelineno-115-4" name="__codelineno-115-4" href="#__codelineno-115-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span>
+<a id="__codelineno-115-5" name="__codelineno-115-5" href="#__codelineno-115-5"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
+<a id="__codelineno-115-6" name="__codelineno-115-6" href="#__codelineno-115-6"></a><span class="w">    </span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-115-7" name="__codelineno-115-7" href="#__codelineno-115-7"></a><span class="w">    </span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-115-8" name="__codelineno-115-8" href="#__codelineno-115-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span>
+<a id="__codelineno-115-9" name="__codelineno-115-9" href="#__codelineno-115-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.rb</span><pre><span></span><code><a id="__codelineno-116-1" name="__codelineno-116-1" href="#__codelineno-116-1"></a><span class="c1">### 平方階 ###</span>
+<a id="__codelineno-116-2" name="__codelineno-116-2" href="#__codelineno-116-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-116-3" name="__codelineno-116-3" href="#__codelineno-116-3"></a><span class="w">  </span><span class="c1"># 二次元リストは O(n^2) の空間を使用</span>
+<a id="__codelineno-116-4" name="__codelineno-116-4" href="#__codelineno-116-4"></a><span class="w">  </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-116-5" name="__codelineno-116-5" href="#__codelineno-116-5"></a><span class="k">end</span>
+<a id="__codelineno-116-6" name="__codelineno-116-6" href="#__codelineno-116-6"></a>
+<a id="__codelineno-116-7" name="__codelineno-116-7" href="#__codelineno-116-7"></a><span class="c1"># ## 平方階（再帰実装）###</span>
+<a id="__codelineno-116-8" name="__codelineno-116-8" href="#__codelineno-116-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic_recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-116-9" name="__codelineno-116-9" href="#__codelineno-116-9"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-116-10" name="__codelineno-116-10" href="#__codelineno-116-10"></a>
+<a id="__codelineno-116-11" name="__codelineno-116-11" href="#__codelineno-116-11"></a><span class="w">  </span><span class="c1"># 配列 nums の長さは n, n-1, ..., 2, 1</span>
+<a id="__codelineno-116-12" name="__codelineno-116-12" href="#__codelineno-116-12"></a><span class="w">  </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-116-13" name="__codelineno-116-13" href="#__codelineno-116-13"></a><span class="w">  </span><span class="n">quadratic_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-116-14" name="__codelineno-116-14" href="#__codelineno-116-14"></a><span class="k">end</span>
+<a id="__codelineno-116-15" name="__codelineno-116-15" href="#__codelineno-116-15"></a>
+<a id="__codelineno-116-16" name="__codelineno-116-16" href="#__codelineno-116-16"></a><span class="c1"># ## 指数階（満二分木を構築）###</span>
+<a id="__codelineno-116-17" name="__codelineno-116-17" href="#__codelineno-116-17"></a><span class="k">def</span><span class="w"> </span><span class="nf">build_tree</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-116-18" name="__codelineno-116-18" href="#__codelineno-116-18"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-116-19" name="__codelineno-116-19" href="#__codelineno-116-19"></a>
+<a id="__codelineno-116-20" name="__codelineno-116-20" href="#__codelineno-116-20"></a><span class="w">  </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="o">.</span><span class="n">tap</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="o">|</span><span class="n">root</span><span class="o">|</span>
+<a id="__codelineno-116-21" name="__codelineno-116-21" href="#__codelineno-116-21"></a><span class="w">    </span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">build_tree</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-116-22" name="__codelineno-116-22" href="#__codelineno-116-22"></a><span class="w">    </span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">build_tree</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-116-23" name="__codelineno-116-23" href="#__codelineno-116-23"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-116-24" name="__codelineno-116-24" href="#__codelineno-116-24"></a><span class="k">end</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%20%3D%200%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E5%80%A4%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%8F%B3%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%0Adef%20build_tree%28n%3A%20int%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E6%8C%87%E6%95%B0%E6%99%82%E9%96%93%EF%BC%88%E5%AE%8C%E5%85%A8%E4%BA%8C%E5%88%86%E6%9C%A8%E3%81%AE%E6%A7%8B%E7%AF%89%EF%BC%89%22%22%22%0A%20%20%20%20if%20n%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20root%20%3D%20TreeNode%280%29%0A%20%20%20%20root.left%20%3D%20build_tree%28n%20-%201%29%0A%20%20%20%20root.right%20%3D%20build_tree%28n%20-%201%29%0A%20%20%20%20return%20root%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20%23%20%E6%8C%87%E6%95%B0%E3%82%AA%E3%83%BC%E3%83%80%E3%83%BC%0A%20%20%20%20root%20%3D%20build_tree%28n%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=507&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%20%3D%200%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E5%80%A4%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%8F%B3%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%0Adef%20build_tree%28n%3A%20int%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E6%8C%87%E6%95%B0%E6%99%82%E9%96%93%EF%BC%88%E5%AE%8C%E5%85%A8%E4%BA%8C%E5%88%86%E6%9C%A8%E3%81%AE%E6%A7%8B%E7%AF%89%EF%BC%89%22%22%22%0A%20%20%20%20if%20n%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20root%20%3D%20TreeNode%280%29%0A%20%20%20%20root.left%20%3D%20build_tree%28n%20-%201%29%0A%20%20%20%20root.right%20%3D%20build_tree%28n%20-%201%29%0A%20%20%20%20return%20root%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20%23%20%E6%8C%87%E6%95%B0%E3%82%AA%E3%83%BC%E3%83%80%E3%83%BC%0A%20%20%20%20root%20%3D%20build_tree%28n%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=507&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p><img alt="満二分木が生み出す指数階の空間計算量" class="animation-figure" src="../space_complexity.assets/space_complexity_exponential.png" /></p>
+<p align="center"> 図 2-19 &nbsp; 満二分木が生み出す指数階の空間計算量 </p>
+
+<h3 id="5-olog-n">5. &nbsp; 対数階 <span class="arithmatex">\(O(\log n)\)</span><a class="headerlink" href="#5-olog-n" title="Permanent link">&para;</a></h3>
+<p>対数階は分割統治アルゴリズムによく現れます。例えばマージソートでは、長さ <span class="arithmatex">\(n\)</span> の配列を入力として、各再帰で配列を中央から二つに分割するため、高さ <span class="arithmatex">\(\log n\)</span> の再帰木が形成され、<span class="arithmatex">\(O(\log n)\)</span> のスタックフレーム空間を使用します。</p>
+<p>また、数値を文字列に変換する場合を考えると、正の整数 <span class="arithmatex">\(n\)</span> の桁数は <span class="arithmatex">\(\lfloor \log_{10} n \rfloor + 1\)</span> であり、対応する文字列長も <span class="arithmatex">\(\lfloor \log_{10} n \rfloor + 1\)</span> です。したがって空間計算量は <span class="arithmatex">\(O(\log_{10} n + 1) = O(\log n)\)</span> となります。</p>
+<h2 id="244">2.4.4 &nbsp; 時間と空間のトレードオフ<a class="headerlink" href="#244" title="Permanent link">&para;</a></h2>
+<p>理想的には、アルゴリズムの時間計算量と空間計算量の両方を最適にしたいところです。しかし実際には、この二つを同時に最適化するのは通常きわめて困難です。</p>
+<p><strong>時間計算量を下げるには、通常、空間計算量を増やす代償が必要であり、その逆も同様です</strong>。メモリ空間を犠牲にして実行速度を上げる考え方を「空間を時間と引き換えにする」と呼び、その逆を「時間を空間と引き換えにする」と呼びます。</p>
+<p>どちらの考え方を選ぶかは、何をより重視するかによって決まります。多くの場合、空間より時間のほうが貴重なので、「空間を時間と引き換えにする」戦略のほうが一般的です。もちろん、データ量が非常に大きい場合には、空間計算量を抑えることも同じくらい重要です。</p>
 
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-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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 <!-- Page content -->
 <h1 id="25">2.5 &nbsp; まとめ<a class="headerlink" href="#25" title="Permanent link">&para;</a></h1>
-<h3 id="1">1. &nbsp; 重要なレビュー<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p><strong>アルゴリズム効率評価</strong></p>
+<h3 id="1">1. &nbsp; 要点の振り返り<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p><strong>アルゴリズム効率の評価</strong></p>
 <ul>
-<li>時間効率と空間効率は、アルゴリズムの優劣を評価する2つの主要な基準です。</li>
-<li>実際のテストによってアルゴリズムの効率を評価できますが、テスト環境の影響を排除することは困難で、大量の計算リソースを消費します。</li>
-<li>複雑度分析は実際のテストの欠点を克服できます。その結果はすべての動作プラットフォームに適用でき、異なるデータスケールでのアルゴリズムの効率を明らかにできます。</li>
+<li>時間効率と空間効率は、アルゴリズムの良し悪しを測る二つの主要な評価指標です。</li>
+<li>実測によってアルゴリズム効率を評価できますが、テスト環境の影響を排除しにくく、多くの計算資源も消費します。</li>
+<li>複雑度分析は実測の欠点を補い、分析結果はすべての実行プラットフォームに適用でき、データ規模ごとの効率も明らかにできます。</li>
 </ul>
 <p><strong>時間計算量</strong></p>
 <ul>
-<li>時間計算量は、データ量の増加に伴うアルゴリズムの実行時間の傾向を測定し、アルゴリズムの効率を効果的に評価します。しかし、入力データ量が少ない場合や時間計算量が同じ場合など、特定のケースでは失敗することがあり、アルゴリズムの効率を正確に比較することが困難になります。</li>
-<li>最悪ケース時間計算量はビッグ<span class="arithmatex">\(O\)</span>記法を使用して表記され、漸近上限を表し、<span class="arithmatex">\(n\)</span>が無限大に近づくにつれての操作数<span class="arithmatex">\(T(n)\)</span>の増加レベルを反映します。</li>
-<li>時間計算量の計算には2つのステップが含まれます：まず操作数をカウントし、次に漸近上限を決定します。</li>
-<li>一般的な時間計算量は、低いものから高いものへと並べると、<span class="arithmatex">\(O(1)\)</span>、<span class="arithmatex">\(O(\log n)\)</span>、<span class="arithmatex">\(O(n)\)</span>、<span class="arithmatex">\(O(n \log n)\)</span>、<span class="arithmatex">\(O(n^2)\)</span>、<span class="arithmatex">\(O(2^n)\)</span>、<span class="arithmatex">\(O(n!)\)</span>などが含まれます。</li>
-<li>一部のアルゴリズムの時間計算量は固定されておらず、入力データの分布に依存します。時間計算量は最悪、最良、平均のケースに分けられます。最良ケースは、入力データが最良ケースを達成するために厳格な条件を満たす必要があるため、ほとんど使用されません。</li>
-<li>平均時間計算量は、ランダムデータ入力下でのアルゴリズムの効率を反映し、実際のアプリケーションでのアルゴリズムの性能に密接に類似しています。平均時間計算量の計算には、入力データの分布とその後の数学的期待値を考慮する必要があります。</li>
+<li>時間計算量は、アルゴリズムの実行時間がデータ量の増加に伴ってどう変化するかを測るためのものであり、効率評価に有効です。ただし、入力データ量が小さい場合や時間計算量が同じ場合などには、効率の優劣を正確に比較できないことがあります。</li>
+<li>最悪時間計算量はビッグオー記法 <span class="arithmatex">\(O\)</span> で表され、関数の漸近上界に対応し、<span class="arithmatex">\(n\)</span> が正の無限大に近づくときの操作回数 <span class="arithmatex">\(T(n)\)</span> の増加の度合いを表します。</li>
+<li>時間計算量の推定は二段階に分かれ、まず操作回数を数え、次に漸近上界を判断します。</li>
+<li>一般的な時間計算量を低い順から並べると、<span class="arithmatex">\(O(1)\)</span>、<span class="arithmatex">\(O(\log n)\)</span>、<span class="arithmatex">\(O(n)\)</span>、<span class="arithmatex">\(O(n \log n)\)</span>、<span class="arithmatex">\(O(n^2)\)</span>、<span class="arithmatex">\(O(2^n)\)</span>、<span class="arithmatex">\(O(n!)\)</span> などがあります。</li>
+<li>一部のアルゴリズムの時間計算量は固定ではなく、入力データの分布に関係します。時間計算量には最悪、最良、平均時間計算量がありますが、最良時間計算量は入力データが厳しい条件を満たす必要があるため、ほとんど使われません。</li>
+<li>平均時間計算量は、ランダムな入力データに対するアルゴリズムの実行効率を表し、実運用時の性能に最も近い指標です。平均時間計算量を求めるには、入力データの分布と、それを踏まえた数学的期待値を統計する必要があります。</li>
 </ul>
 <p><strong>空間計算量</strong></p>
 <ul>
-<li>空間計算量は、時間計算量と同様に、データ量の増加に伴うアルゴリズムが占有するメモリ空間の傾向を測定します。</li>
-<li>アルゴリズムの実行中に使用される関連メモリ空間は、入力空間、一時空間、出力空間に分けることができます。一般的に、入力空間は空間計算量の計算に含まれません。一時空間は一時データ、スタックフレーム空間、命令空間に分けることができ、スタックフレーム空間は通常、再帰関数でのみ空間計算量に影響します。</li>
-<li>通常は最悪ケース空間計算量のみに焦点を当てます。これは、最悪の入力データと操作の最悪の瞬間でのアルゴリズムの空間計算量を計算することを意味します。</li>
-<li>一般的な空間計算量は、低いものから高いものへと並べると、<span class="arithmatex">\(O(1)\)</span>、<span class="arithmatex">\(O(\log n)\)</span>、<span class="arithmatex">\(O(n)\)</span>、<span class="arithmatex">\(O(n^2)\)</span>、<span class="arithmatex">\(O(2^n)\)</span>などが含まれます。</li>
+<li>空間計算量の役割は時間計算量に似ており、アルゴリズムが使用するメモリ空間がデータ量の増加に伴ってどう変化するかを測ります。</li>
+<li>アルゴリズム実行中に関係するメモリ空間は、入力空間、一時空間、出力空間に分けられます。通常、入力空間は空間計算量の計算に含めません。一時空間は一時データ、スタックフレーム空間、命令空間に分けられ、このうちスタックフレーム空間は通常、再帰関数でのみ空間計算量に影響します。</li>
+<li>私たちは通常、最悪空間計算量のみに注目し、最悪の入力データと最悪の実行時点における空間計算量を数えます。</li>
+<li>一般的な空間計算量を低い順から並べると、<span class="arithmatex">\(O(1)\)</span>、<span class="arithmatex">\(O(\log n)\)</span>、<span class="arithmatex">\(O(n)\)</span>、<span class="arithmatex">\(O(n^2)\)</span>、<span class="arithmatex">\(O(2^n)\)</span> などがあります。</li>
 </ul>
 <h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
-<p><strong>Q</strong>: 末尾再帰の空間計算量は<span class="arithmatex">\(O(1)\)</span>ですか？</p>
-<p>理論的には、末尾再帰関数の空間計算量は<span class="arithmatex">\(O(1)\)</span>に最適化できます。しかし、ほとんどのプログラミング言語（Java、Python、C++、Go、C#など）は末尾再帰の自動最適化をサポートしていないため、一般的に空間計算量は<span class="arithmatex">\(O(n)\)</span>と考えられています。</p>
-<p><strong>Q</strong>: 「関数」と「メソッド」という用語の違いは何ですか？</p>
-<p><u>関数</u>は独立して実行でき、すべてのパラメータが明示的に渡されます。<u>メソッド</u>はオブジェクトに関連付けられ、それを呼び出すオブジェクトに暗黙的に渡され、クラスのインスタンス内に含まれるデータを操作できます。</p>
-<p>一般的なプログラミング言語からの例をいくつか示します：</p>
+<p><strong>Q</strong>：尾再帰の空間計算量は <span class="arithmatex">\(O(1)\)</span> ですか？</p>
+<p>理論上、尾再帰関数の空間計算量は <span class="arithmatex">\(O(1)\)</span> まで最適化できます。ただし、ほとんどのプログラミング言語（Java、Python、C++、Go、C# など）は尾再帰の自動最適化をサポートしていないため、通常は空間計算量を <span class="arithmatex">\(O(n)\)</span> と見なします。</p>
+<p><strong>Q</strong>：関数とメソッドという二つの用語の違いは何ですか？</p>
+<p><u>関数（function）</u>は独立して実行でき、すべての引数は明示的に渡されます。<u>メソッド（method）</u>はオブジェクトに関連付けられ、それを呼び出すオブジェクトが暗黙的に渡され、クラスのインスタンスに含まれるデータを操作できます。</p>
+<p>以下では、いくつかの一般的なプログラミング言語を例に説明します。</p>
 <ul>
-<li>Cは手続き型プログラミング言語で、オブジェクト指向の概念がないため、関数のみがあります。しかし、構造体（struct）を作成することでオブジェクト指向プログラミングをシミュレートでき、これらの構造体に関連付けられた関数は他のプログラミング言語のメソッドと同等です。</li>
-<li>JavaとC#はオブジェクト指向プログラミング言語で、コードブロック（メソッド）は通常クラスの一部です。静的メソッドはクラスにバインドされ、特定のインスタンス変数にアクセスできないため、関数のように動作します。</li>
-<li>C++とPythonは手続き型プログラミング（関数）とオブジェクト指向プログラミング（メソッド）の両方をサポートしています。</li>
+<li>C 言語は手続き型プログラミング言語であり、オブジェクト指向の概念がないため、関数しかありません。ただし、構造体（struct）を作成してオブジェクト指向プログラミングを模倣でき、構造体に関連付けられた関数は、他のプログラミング言語におけるメソッドに相当します。</li>
+<li>Java と C# はオブジェクト指向のプログラミング言語であり、コードブロック（メソッド）は通常あるクラスの一部です。静的メソッドの振る舞いは関数に似ており、クラスに束縛され、特定のインスタンス変数にはアクセスできません。</li>
+<li>C++ と Python は、手続き型プログラミング（関数）にもオブジェクト指向プログラミング（メソッド）にも対応しています。</li>
 </ul>
-<p><strong>Q</strong>: 「空間計算量の一般的な種類」の図は、占有空間の絶対サイズを反映していますか？</p>
-<p>いいえ、図は空間計算量を示しており、これは増加傾向を反映するものであり、占有空間の絶対サイズではありません。</p>
-<p><span class="arithmatex">\(n = 8\)</span>を取ると、各曲線の値がその関数に対応していないことに気づくかもしれません。これは、各曲線に定数項が含まれているためで、値の範囲を視覚的に快適な範囲に圧縮することを意図しています。</p>
-<p>実際には、通常は各メソッドの「定数項」複雑度を知らないため、複雑度のみに基づいて<span class="arithmatex">\(n = 8\)</span>の最良ソリューションを選択することは一般的に不可能です。しかし、<span class="arithmatex">\(n = 8^5\)</span>の場合、増加傾向が支配的になるため、選択がはるかに容易になります。</p>
+<p><strong>Q</strong>：「一般的な空間計算量の種類」の図が表しているのは、使用空間の絶対量ですか？</p>
+<p>いいえ。この図が示しているのは空間計算量であり、表しているのは増加傾向であって、使用空間の絶対量ではありません。</p>
+<p><span class="arithmatex">\(n = 8\)</span> と仮定すると、各曲線の値が対応する関数と一致していないように見えるかもしれません。これは、各曲線に定数項が含まれており、値の範囲を視覚的に見やすい範囲へ圧縮しているためです。</p>
+<p>実際には、各手法の「定数項」の複雑度がどれほどか通常は分からないため、一般に複雑度だけを根拠に <span class="arithmatex">\(n = 8\)</span> 以下で最適解を選ぶことはできません。ただし、<span class="arithmatex">\(n = 8^5\)</span> であれば選びやすく、このときは増加傾向がすでに支配的になっています。</p>
+<p><strong>Q</strong> 実際の利用場面に応じて、時間（または空間）を犠牲にしてアルゴリズムを設計することはありますか？</p>
+<p>実際の応用では、多くの場合、空間を犠牲にして時間を得る選択をします。たとえばデータベースのインデックスでは、通常 B+ 木やハッシュインデックスを構築し、大量のメモリ空間を使う代わりに、<span class="arithmatex">\(O(\log n)\)</span> あるいは <span class="arithmatex">\(O(1)\)</span> の高速な検索を実現します。</p>
+<p>空間資源が貴重な場面では、時間を犠牲にして空間を得ることもあります。たとえば組み込み開発では、デバイスのメモリが非常に貴重なため、エンジニアはハッシュテーブルの使用をやめ、配列による順次探索を選んでメモリ使用量を節約することがあります。その代償として探索は遅くなります。</p>
 
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-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
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+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4297,7 +4297,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4443,7 +4443,7 @@
   <a href="#231" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2.3.1 &nbsp; 時間増加傾向の評価
+        2.3.1 &nbsp; 実行時間の増加傾向を捉える
       
     </span>
   </a>
@@ -4454,7 +4454,7 @@
   <a href="#232" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2.3.2 &nbsp; 漸近上限
+        2.3.2 &nbsp; 関数の漸近上界
       
     </span>
   </a>
@@ -4465,19 +4465,19 @@
   <a href="#233" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2.3.3 &nbsp; 計算方法
+        2.3.3 &nbsp; 求め方
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="2.3.3 計算方法">
+    <nav class="md-nav" aria-label="2.3.3 求め方">
       <ul class="md-nav__list">
         
           <li class="md-nav__item">
   <a href="#1-1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; ステップ1: 操作数のカウント
+        1. &nbsp; 第 1 ステップ：操作回数を数える
       
     </span>
   </a>
@@ -4488,7 +4488,7 @@
   <a href="#2-2" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2. &nbsp; ステップ2: 漸近上限の決定
+        2. &nbsp; 第 2 ステップ：漸近上界を判断する
       
     </span>
   </a>
@@ -4504,19 +4504,19 @@
   <a href="#234" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2.3.4 &nbsp; 一般的な時間計算量の種類
+        2.3.4 &nbsp; よくある種類
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="2.3.4 一般的な時間計算量の種類">
+    <nav class="md-nav" aria-label="2.3.4 よくある種類">
       <ul class="md-nav__list">
         
           <li class="md-nav__item">
   <a href="#1-o1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; 定数オーダー
+        1. &nbsp; 定数階
       
     </span>
   </a>
@@ -4527,7 +4527,7 @@
   <a href="#2-on" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2. &nbsp; 線形オーダー
+        2. &nbsp; 線形階
       
     </span>
   </a>
@@ -4538,7 +4538,7 @@
   <a href="#3-on2" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3. &nbsp; 二次オーダー
+        3. &nbsp; 平方階
       
     </span>
   </a>
@@ -4549,7 +4549,7 @@
   <a href="#4-o2n" class="md-nav__link">
     <span class="md-ellipsis">
       
-        4. &nbsp; 指数オーダー
+        4. &nbsp; 指数階
       
     </span>
   </a>
@@ -4560,7 +4560,7 @@
   <a href="#5-olog-n" class="md-nav__link">
     <span class="md-ellipsis">
       
-        5. &nbsp; 対数オーダー
+        5. &nbsp; 対数階
       
     </span>
   </a>
@@ -4571,7 +4571,7 @@
   <a href="#6-on-log-n" class="md-nav__link">
     <span class="md-ellipsis">
       
-        6. &nbsp; 線形対数オーダー
+        6. &nbsp; 線形対数階
       
     </span>
   </a>
@@ -4582,7 +4582,7 @@
   <a href="#7-on" class="md-nav__link">
     <span class="md-ellipsis">
       
-        7. &nbsp; 階乗オーダー
+        7. &nbsp; 階乗階
       
     </span>
   </a>
@@ -4598,7 +4598,7 @@
   <a href="#235" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2.3.5 &nbsp; 最悪、最良、平均時間計算量
+        2.3.5 &nbsp; 最悪・最良・平均時間計算量
       
     </span>
   </a>
@@ -4643,72 +4643,72 @@
 
 <!-- Page content -->
 <h1 id="23">2.3 &nbsp; 時間計算量<a class="headerlink" href="#23" title="Permanent link">&para;</a></h1>
-<p>実行時間は、アルゴリズムの効率を直感的に評価できます。アルゴリズムの実行時間を正確に推定するにはどうすればよいでしょうか？</p>
+<p>実行時間はアルゴリズムの効率を直感的かつ正確に反映します。あるコードの実行時間を正確に見積もりたい場合、どのようにすればよいでしょうか？</p>
 <ol>
-<li><strong>実行プラットフォームの決定</strong>: これには、ハードウェア構成、プログラミング言語、システム環境などが含まれ、これらすべてがコードの実行効率に影響する可能性があります。</li>
-<li><strong>様々な計算操作の実行時間の評価</strong>: 例えば、加算操作<code>+</code>は1 ns、乗算操作<code>*</code>は10 ns、印刷操作<code>print()</code>は5 nsなどかかる可能性があります。</li>
-<li><strong>コード内のすべての計算操作をカウント</strong>: これらすべての操作の実行時間を合計すると、総実行時間が得られます。</li>
+<li><strong>実行プラットフォームを特定する</strong>。ハードウェア構成、プログラミング言語、システム環境などが含まれ、これらの要因はいずれもコードの実行効率に影響します。</li>
+<li><strong>各種計算操作に必要な実行時間を評価する</strong>。例えば加算 <code>+</code> には 1 ns 、乗算 <code>*</code> には 10 ns 、出力 <code>print()</code> には 5 ns などが必要です。</li>
+<li><strong>コード中のすべての計算操作を数える</strong>。そして各操作の実行時間を合計することで、実行時間を得ます。</li>
 </ol>
-<p>例えば、入力サイズが<span class="arithmatex">\(n\)</span>の以下のコードを考えてみましょう：</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="1:12"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label></div>
+<p>例えば次のコードでは、入力データサイズを <span class="arithmatex">\(n\)</span> とします：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 特定の操作プラットフォーム下で</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># ある実行プラットフォーム上で</span>
 <a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="n">a</span> <span class="o">=</span> <span class="mi">2</span>      <span class="c1"># 1 ns</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">+</span> <span class="mi">1</span>  <span class="c1"># 1 ns</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">*</span> <span class="mi">2</span>  <span class="c1"># 10 ns</span>
-<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># n回ループ</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># n 回ループ</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>  <span class="c1"># 1 ns</span>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>        <span class="c1"># 5 ns</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="c1">// 特定の操作プラットフォーム下で</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="c1">// ある実行プラットフォーム上で</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// 10 ns</span>
-<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// n回ループ</span>
-<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// 1 ns, 毎回i++が実行される</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// n 回ループ</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">        </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span><span class="w">         </span><span class="c1">// 5 ns</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="c1">// 特定の操作プラットフォーム下で</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="c1">// ある実行プラットフォーム上で</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// 10 ns</span>
-<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// n回ループ</span>
-<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// 1 ns, 毎回i++が実行される</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// n 回ループ</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">        </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w">     </span><span class="c1">// 5 ns</span>
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="c1">// 特定の操作プラットフォーム下で</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="c1">// ある実行プラットフォーム上で</span>
 <a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// 10 ns</span>
-<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="c1">// n回ループ</span>
-<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// 1 ns, 毎回i++が実行される</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="c1">// n 回ループ</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">        </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w">      </span><span class="c1">// 5 ns</span>
 <a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="c1">// 特定の操作プラットフォーム下で</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="c1">// ある実行プラットフォーム上で</span>
 <a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">2</span><span class="w">     </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w">  </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w">  </span><span class="c1">// 10 ns</span>
-<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="c1">// n回ループ</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="c1">// n 回ループ</span>
 <a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">        </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">a</span><span class="p">)</span><span class="w">        </span><span class="c1">// 5 ns</span>
 <a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="p">}</span>
@@ -4716,12 +4716,12 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="c1">// 特定の操作プラットフォーム下で</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="c1">// ある実行プラットフォーム上で</span>
 <a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1">// 10 ns</span>
-<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="c1">// n回ループ</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="c1">// n 回ループ</span>
 <a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">        </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="c1">// 5 ns</span>
 <a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">    </span><span class="p">}</span>
@@ -4729,229 +4729,232 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="c1">// 特定の操作プラットフォーム下で</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="c1">// ある実行プラットフォーム上で</span>
 <a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 10 ns</span>
-<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="c1">// n回ループ</span>
-<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="k">for</span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 ns, 毎回i++が実行される</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="c1">// n 回ループ</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="k">for</span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 5 ns</span>
 <a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="c1">// 特定の操作プラットフォーム下で</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="c1">// ある実行プラットフォーム上で</span>
 <a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">a</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 10 ns</span>
-<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="c1">// n回ループ</span>
-<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="k">for</span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 ns, 毎回i++が実行される</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="c1">// n 回ループ</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="k">for</span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 5 ns</span>
 <a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="c1">// 特定の操作プラットフォーム下で</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="c1">// ある実行プラットフォーム上で</span>
 <a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 10 ns</span>
-<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="c1">// n回ループ</span>
-<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 ns, 毎回i++が実行される</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="c1">// n 回ループ</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">    </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 5 ns</span>
 <a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">  </span><span class="p">}</span>
 <a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="c1">// 特定の操作プラットフォーム下で</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="c1">// ある実行プラットフォーム上で</span>
 <a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">      </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">          </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">          </span><span class="c1">// 10 ns</span>
-<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="c1">// n回ループ</span>
-<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span><span class="w">     </span><span class="c1">// 毎回i++で1 ns</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="c1">// n 回ループ</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span><span class="w">     </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">        </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span><span class="w">  </span><span class="c1">// 5 ns</span>
 <a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// 特定の操作プラットフォーム下で</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// ある実行プラットフォーム上で</span>
 <a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// 10 ns</span>
-<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="c1">// n回ループ</span>
-<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">   </span><span class="c1">// 1 ns, 毎回i++が実行される</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="c1">// n 回ループ</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">   </span><span class="c1">// 1 ns</span>
 <a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">        </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span><span class="w">            </span><span class="c1">// 5 ns</span>
 <a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="c1">// ある実行プラットフォーム上で</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="c1">// 10 ns</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="c1">// n 回ループ</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">        </span><span class="n">println</span><span class="p">(</span><span class="m">0</span><span class="p">)</span><span class="w">      </span><span class="c1">// 5 ns</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1"># ある実行プラットフォーム上で</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="w">       </span><span class="c1"># 1 ns</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w">   </span><span class="c1"># 1 ns</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w">   </span><span class="c1"># 10 ns</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">    </span><span class="c1"># n 回ループ</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">    </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="c1"># 1 ns</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">        </span><span class="nb">puts</span><span class="w"> </span><span class="mi">0</span><span class="w">      </span><span class="c1"># 5 ns</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>上記の方法を使用すると、アルゴリズムの実行時間は<span class="arithmatex">\((6n + 12)\)</span> nsとして計算できます：</p>
+<p>上記の方法に基づくと、アルゴリズムの実行時間は <span class="arithmatex">\((6n + 12)\)</span> ns になります：</p>
 <div class="arithmatex">\[
 1 + 1 + 10 + (1 + 5) \times n = 6n + 12
 \]</div>
-<p>しかし、実際には、<strong>アルゴリズムの実行時間をカウントすることは実用的でも合理的でもありません</strong>。第一に、推定時間を実行プラットフォームに結び付けたくありません。アルゴリズムは様々なプラットフォームで実行される必要があるからです。第二に、各種操作の実行時間を知ることは困難であり、推定プロセスを難しくします。</p>
-<h2 id="231">2.3.1 &nbsp; 時間増加傾向の評価<a class="headerlink" href="#231" title="Permanent link">&para;</a></h2>
-<p>時間計算量分析は、アルゴリズムの実行時間をカウントするのではなく、**データ量が増加するにつれての実行時間の増加傾向**を分析します。</p>
-<p>この「時間増加傾向」の概念を例で理解しましょう。入力データサイズを<span class="arithmatex">\(n\)</span>とし、3つのアルゴリズム<code>A</code>、<code>B</code>、<code>C</code>を考えてみます：</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="2:12"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label></div>
+<p>しかし実際には、<strong>アルゴリズムの実行時間を統計的に求めることは合理的でも現実的でもありません</strong>。まず、見積もり時間を実行プラットフォームに縛りたくありません。アルゴリズムはさまざまな異なるプラットフォームで動作する必要があるからです。次に、各種操作の実行時間を知ること自体が難しく、見積もりの難易度を大きく引き上げます。</p>
+<h2 id="231">2.3.1 &nbsp; 実行時間の増加傾向を捉える<a class="headerlink" href="#231" title="Permanent link">&para;</a></h2>
+<p>時間計算量の分析で扱うのはアルゴリズムの実行時間そのものではなく、**データ量が増えたときに実行時間がどう増加するかという傾向**です。</p>
+<p>「実行時間の増加傾向」という概念はやや抽象的なので、例を通して理解してみましょう。入力データサイズを <span class="arithmatex">\(n\)</span> とし、3 つのアルゴリズム <code>A</code>、<code>B</code>、<code>C</code> を考えます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1"># アルゴリズムAの時間計算量：定数オーダー</span>
-<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm_A</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a>    <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
-<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="c1"># アルゴリズムBの時間計算量：線形オーダー</span>
-<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
-<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a>        <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
-<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="c1"># アルゴリズムCの時間計算量：定数オーダー</span>
-<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1000000</span><span class="p">):</span>
-<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a>        <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="c1"># アルゴリズム A の時間計算量：定数階</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm_A</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="c1"># アルゴリズム B の時間計算量：線形階</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>        <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="c1"># アルゴリズム C の時間計算量：定数階</span>
+<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1000000</span><span class="p">):</span>
+<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>        <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="c1">// アルゴリズムAの時間計算量：定数オーダー</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_A</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="w">    </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
-<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="p">}</span>
-<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="c1">// アルゴリズムBの時間計算量：線形オーダー</span>
-<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="w">        </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
-<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a><span class="p">}</span>
-<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="c1">// アルゴリズムCの時間計算量：定数オーダー</span>
-<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">1000000</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a><span class="w">        </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
-<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="c1">// アルゴリズムAの時間計算量：定数オーダー</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="c1">// アルゴリズム A の時間計算量：定数階</span>
 <a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_A</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
 <a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="p">}</span>
-<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="c1">// アルゴリズムBの時間計算量：線形オーダー</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="c1">// アルゴリズム B の時間計算量：線形階</span>
 <a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">        </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">        </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
 <a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="p">}</span>
-<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="c1">// アルゴリズムCの時間計算量：定数オーダー</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="c1">// アルゴリズム C の時間計算量：定数階</span>
 <a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">1000000</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">        </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">        </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
 <a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="c1">// アルゴリズムAの時間計算量：定数オーダー</span>
-<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">AlgorithmA</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="c1">// アルゴリズム A の時間計算量：定数階</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_A</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="p">}</span>
-<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="c1">// アルゴリズムBの時間計算量：線形オーダー</span>
-<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="k">void</span><span class="w"> </span><span class="nf">AlgorithmB</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="c1">// アルゴリズム B の時間計算量：線形階</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">        </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">        </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="p">}</span>
-<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="c1">// アルゴリズムCの時間計算量：定数オーダー</span>
-<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="k">void</span><span class="w"> </span><span class="nf">AlgorithmC</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="c1">// アルゴリズム C の時間計算量：定数階</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">1000000</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">        </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">        </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="c1">// アルゴリズムAの時間計算量：定数オーダー</span>
-<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm_A</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="c1">// アルゴリズム A の時間計算量：定数階</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">AlgorithmA</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="p">}</span>
-<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="c1">// アルゴリズムBの時間計算量：線形オーダー</span>
-<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm_B</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">        </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="c1">// アルゴリズム B の時間計算量：線形階</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="k">void</span><span class="w"> </span><span class="nf">AlgorithmB</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">        </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="p">}</span>
-<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="c1">// アルゴリズムCの時間計算量：定数オーダー</span>
-<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm_C</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">1000000</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">        </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="c1">// アルゴリズム C の時間計算量：定数階</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="k">void</span><span class="w"> </span><span class="nf">AlgorithmC</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">1000000</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">        </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="c1">// アルゴリズムAの時間計算量：定数オーダー</span>
-<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithmA</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="c1">// アルゴリズム A の時間計算量：定数階</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm_A</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
 <a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="p">}</span>
-<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a>
-<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="c1">// アルゴリズムBの時間計算量：線形オーダー</span>
-<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithmB</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">        </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
-<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="p">}</span>
-<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a>
-<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="c1">// アルゴリズムCの時間計算量：定数オーダー</span>
-<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithmC</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="mi">1_000_000</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w">        </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
-<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="p">}</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="c1">// アルゴリズム B の時間計算量：線形階</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm_B</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">        </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="p">}</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="c1">// アルゴリズム C の時間計算量：定数階</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm_C</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">1000000</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w">        </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="c1">// アルゴリズムAの時間計算量：定数オーダー</span>
-<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_A</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="c1">// アルゴリズム A の時間計算量：定数階</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithmA</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
 <a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="p">}</span>
-<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="c1">// アルゴリズムBの時間計算量：線形オーダー</span>
-<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_B</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
-<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="p">}</span>
-<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="c1">// アルゴリズムCの時間計算量：定数オーダー</span>
-<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_C</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">1000000</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
-<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="p">}</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="c1">// アルゴリズム B の時間計算量：線形階</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithmB</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">        </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="p">}</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="c1">// アルゴリズム C の時間計算量：定数階</span>
+<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithmC</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="mi">1_000_000</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="w">        </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="c1">// アルゴリズムAの時間計算量：定数オーダー</span>
-<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_A</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="c1">// アルゴリズム A の時間計算量：定数階</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_A</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
 <a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="p">}</span>
-<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="c1">// アルゴリズムBの時間計算量：線形オーダー</span>
-<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_B</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="c1">// アルゴリズム B の時間計算量：線形階</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_B</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
 <a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="p">}</span>
-<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="c1">// アルゴリズムCの時間計算量：定数オーダー</span>
-<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_C</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="c1">// アルゴリズム C の時間計算量：定数階</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_C</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">1000000</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
 <a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w">    </span><span class="p">}</span>
@@ -4959,460 +4962,558 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="c1">// アルゴリズムAの時間計算量：定数オーダー</span>
-<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithmA</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">  </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="c1">// アルゴリズム A の時間計算量：定数階</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_A</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
 <a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="p">}</span>
-<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="c1">// アルゴリズムBの時間計算量：線形オーダー</span>
-<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithmB</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">    </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
-<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="c1">// アルゴリズム B の時間計算量：線形階</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_B</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="p">}</span>
-<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="c1">// アルゴリズムCの時間計算量：定数オーダー</span>
-<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithmC</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">1000000</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w">    </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
-<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="c1">// アルゴリズム C の時間計算量：定数階</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_C</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">1000000</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="c1">// アルゴリズムAの時間計算量：定数オーダー</span>
-<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm_A</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">    </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="c1">// アルゴリズム A の時間計算量：定数階</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithmA</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
 <a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="p">}</span>
-<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="c1">// アルゴリズムBの時間計算量：線形オーダー</span>
-<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">        </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
-<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="c1">// アルゴリズム B の時間計算量：線形階</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithmB</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">    </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">  </span><span class="p">}</span>
 <a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="p">}</span>
-<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="c1">// アルゴリズムCの時間計算量：定数オーダー</span>
-<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="mi">1000000</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w">        </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
-<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="c1">// アルゴリズム C の時間計算量：定数階</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithmC</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">1000000</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w">    </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w">  </span><span class="p">}</span>
 <a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="c1">// アルゴリズムAの時間計算量：定数オーダー</span>
-<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_A</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="c1">// アルゴリズム A の時間計算量：定数階</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm_A</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="p">}</span>
-<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="c1">// アルゴリズムBの時間計算量：線形オーダー</span>
-<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">        </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="c1">// アルゴリズム B の時間計算量：線形階</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">        </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="p">}</span>
-<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="c1">// アルゴリズムCの時間計算量：定数オーダー</span>
-<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">1000000</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">        </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="c1">// アルゴリズム C の時間計算量：定数階</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="mi">1000000</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">        </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="c1">// アルゴリズム A の時間計算量：定数階</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_A</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="p">}</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="c1">// アルゴリズム B の時間計算量：線形階</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w">        </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="p">}</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="c1">// アルゴリズム C の時間計算量：定数階</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">1000000</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w">        </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="c1">// アルゴリズム A の時間計算量：定数階</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">algoritm_A</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="n">println</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="p">}</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="c1">// アルゴリズム B の時間計算量：線形階</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">){</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w">        </span><span class="n">println</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="p">}</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="c1">// アルゴリズム C の時間計算量：定数階</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="m">1000000</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w">        </span><span class="n">println</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
+<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1"># アルゴリズム A の時間計算量：定数階</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm_A</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">    </span><span class="nb">puts</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="k">end</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="c1"># アルゴリズム B の時間計算量：線形階</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w">    </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">puts</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="k">end</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="c1"># アルゴリズム C の時間計算量：定数階</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w">    </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="mi">1_000_000</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">puts</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>下図はこれら3つのアルゴリズムの時間計算量を示しています。</p>
+<p>以下の図は、上記 3 つのアルゴリズム関数の時間計算量を示しています。</p>
 <ul>
-<li>アルゴリズム<code>A</code>には1つの印刷操作のみがあり、その実行時間は<span class="arithmatex">\(n\)</span>とともに増加しません。その時間計算量は「定数オーダー」と考えられます。</li>
-<li>アルゴリズム<code>B</code>には<span class="arithmatex">\(n\)</span>回ループする印刷操作があり、その実行時間は<span class="arithmatex">\(n\)</span>と線形に増加します。その時間計算量は「線形オーダー」です。</li>
-<li>アルゴリズム<code>C</code>には1,000,000回ループする印刷操作があります。時間はかかりますが、入力データサイズ<span class="arithmatex">\(n\)</span>とは無関係です。したがって、<code>C</code>の時間計算量は<code>A</code>と同じ「定数オーダー」です。</li>
+<li>アルゴリズム <code>A</code> には出力操作が <span class="arithmatex">\(1\)</span> 回しかなく、実行時間は <span class="arithmatex">\(n\)</span> が大きくなっても増加しません。このアルゴリズムの時間計算量を「定数階」と呼びます。</li>
+<li>アルゴリズム <code>B</code> の出力操作は <span class="arithmatex">\(n\)</span> 回ループする必要があり、実行時間は <span class="arithmatex">\(n\)</span> の増加に対して線形に増加します。このアルゴリズムの時間計算量は「線形階」と呼ばれます。</li>
+<li>アルゴリズム <code>C</code> の出力操作は <span class="arithmatex">\(1000000\)</span> 回ループする必要があり、実行時間は長いものの、入力データサイズ <span class="arithmatex">\(n\)</span> とは無関係です。したがって <code>C</code> の時間計算量は <code>A</code> と同じく、依然として「定数階」です。</li>
 </ul>
-<p><img alt="Time growth trend of algorithms a, b, and c" class="animation-figure" src="../time_complexity.assets/time_complexity_simple_example.png" /></p>
-<p align="center"> 図 2-7 &nbsp; Time growth trend of algorithms a, b, and c </p>
+<p><img alt="アルゴリズム A、B、C の時間増加傾向" class="animation-figure" src="../time_complexity.assets/time_complexity_simple_example.png" /></p>
+<p align="center"> 図 2-7 &nbsp; アルゴリズム A、B、C の時間増加傾向 </p>
 
-<p>アルゴリズムの実行時間を直接カウントすることと比較して、時間計算量分析の特徴は何でしょうか？</p>
+<p>アルゴリズムの実行時間を直接数える方法と比べて、時間計算量分析にはどのような特徴があるでしょうか？</p>
 <ul>
-<li><strong>時間計算量はアルゴリズムの効率を効果的に評価します</strong>。例えば、アルゴリズム<code>B</code>は線形に増加する実行時間を持ち、<span class="arithmatex">\(n &gt; 1\)</span>の時はアルゴリズム<code>A</code>より遅く、<span class="arithmatex">\(n &gt; 1,000,000\)</span>の時は<code>C</code>より遅くなります。実際、入力データサイズ<span class="arithmatex">\(n\)</span>が十分に大きい限り、「定数オーダー」複雑度アルゴリズムは常に「線形オーダー」よりも優れており、時間増加傾向の本質を示しています。</li>
-<li><strong>時間計算量分析はより直感的です</strong>。明らかに、実行プラットフォームと計算操作の種類は実行時間増加の傾向とは無関係です。したがって、時間計算量分析では、すべての計算操作の実行時間を同じ「単位時間」として扱うことができ、「計算操作実行時間カウント」を「計算操作カウント」に単純化できます。これにより推定の複雑さが大幅に軽減されます。</li>
-<li><strong>時間計算量には制限があります</strong>。例えば、アルゴリズム<code>A</code>と<code>C</code>は同じ時間計算量を持ちますが、実際の実行時間は大きく異なる場合があります。同様に、アルゴリズム<code>B</code>は<code>C</code>よりも高い時間計算量を持ちますが、入力データサイズ<span class="arithmatex">\(n\)</span>が小さい場合は明らかに優れています。これらの場合、時間計算量のみに基づいてアルゴリズムの効率を判断することは困難です。しかし、これらの問題にもかかわらず、複雑度分析はアルゴリズムの効率を評価するための最も効果的で一般的に使用される方法です。</li>
+<li><strong>時間計算量はアルゴリズム効率を有効に評価できます</strong>。例えばアルゴリズム <code>B</code> の実行時間は線形に増加するため、<span class="arithmatex">\(n &gt; 1\)</span> ではアルゴリズム <code>A</code> より遅く、<span class="arithmatex">\(n &gt; 1000000\)</span> ではアルゴリズム <code>C</code> より遅くなります。実際、入力データサイズ <span class="arithmatex">\(n\)</span> が十分に大きければ、「定数階」のアルゴリズムは必ず「線形階」のアルゴリズムより優れます。これが実行時間の増加傾向の意味です。</li>
+<li><strong>時間計算量の見積もり方法はより簡潔です</strong>。実行プラットフォームや計算操作の種類は、アルゴリズム実行時間の増加傾向とは無関係です。そのため時間計算量分析では、すべての計算操作の実行時間を同じ「単位時間」とみなしてよく、「計算操作の実行時間を数える」作業を「計算操作の個数を数える」作業へ簡略化できます。これにより見積もりの難易度は大きく下がります。</li>
+<li><strong>時間計算量には一定の限界もあります</strong>。例えばアルゴリズム <code>A</code> と <code>C</code> の時間計算量は同じでも、実際の実行時間には大きな差があります。同様に、アルゴリズム <code>B</code> の時間計算量は <code>C</code> より高いものの、入力データサイズ <span class="arithmatex">\(n\)</span> が小さい場合にはアルゴリズム <code>B</code> のほうが明らかに優れます。このような場合、時間計算量だけでアルゴリズム効率の高低を判断するのは難しいことがあります。もっとも、こうした問題があっても、複雑度分析は依然としてアルゴリズム効率を評価する最も有効で一般的な方法です。</li>
 </ul>
-<h2 id="232">2.3.2 &nbsp; 漸近上限<a class="headerlink" href="#232" title="Permanent link">&para;</a></h2>
-<p>入力サイズが<span class="arithmatex">\(n\)</span>の関数を考えてみましょう：</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="3:12"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label></div>
+<h2 id="232">2.3.2 &nbsp; 関数の漸近上界<a class="headerlink" href="#232" title="Permanent link">&para;</a></h2>
+<p>入力サイズが <span class="arithmatex">\(n\)</span> の次の関数を考えます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a>    <span class="n">a</span> <span class="o">=</span> <span class="mi">1</span>      <span class="c1"># +1</span>
-<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">+</span> <span class="mi">1</span>  <span class="c1"># +1</span>
-<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">*</span> <span class="mi">2</span>  <span class="c1"># +1</span>
-<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a>    <span class="c1"># n回ループ</span>
-<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>  <span class="c1"># +1</span>
-<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a>        <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>        <span class="c1"># +1</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>    <span class="n">a</span> <span class="o">=</span> <span class="mi">1</span>      <span class="c1"># +1</span>
+<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">+</span> <span class="mi">1</span>  <span class="c1"># +1</span>
+<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">*</span> <span class="mi">2</span>  <span class="c1"># +1</span>
+<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a>    <span class="c1"># n 回ループ</span>
+<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>  <span class="c1"># +1</span>
+<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a>        <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>        <span class="c1"># +1</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
-<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
-<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
-<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">    </span><span class="c1">// n回ループ</span>
-<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1 (毎回i++が実行される)</span>
-<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">        </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span><span class="w">    </span><span class="c1">// +1</span>
-<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
-<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
-<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
-<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w">    </span><span class="c1">// n回ループ</span>
-<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1 (毎回i++が実行される)</span>
-<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="w">        </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w">    </span><span class="c1">// +1</span>
-<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="k">void</span><span class="w"> </span><span class="nf">Algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
 <a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
 <a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
-<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">    </span><span class="c1">// n回ループ</span>
-<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">   </span><span class="c1">// +1 (毎回i++が実行される)</span>
-<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">        </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w">   </span><span class="c1">// +1</span>
+<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">    </span><span class="c1">// n 回ループ</span>
+<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1（各反復で i ++ を実行）</span>
+<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">        </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span><span class="w">    </span><span class="c1">// +1</span>
 <a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="w">      </span><span class="c1">// +1</span>
-<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w">   </span><span class="c1">// +1</span>
-<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w">   </span><span class="c1">// +1</span>
-<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">    </span><span class="c1">// n回ループ</span>
-<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span><span class="w">   </span><span class="c1">// +1</span>
-<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">        </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">a</span><span class="p">)</span><span class="w">         </span><span class="c1">// +1</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">    </span><span class="c1">// n 回ループ</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1（各反復で i ++ を実行）</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">        </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w">    </span><span class="c1">// +1</span>
 <a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// +1</span>
-<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// +1</span>
-<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1">// +1</span>
-<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">    </span><span class="c1">// n回ループ</span>
-<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1</span>
-<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">        </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="c1">// +1</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="k">void</span><span class="w"> </span><span class="nf">Algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">    </span><span class="c1">// n 回ループ</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">   </span><span class="c1">// +1（各反復で i ++ を実行）</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">        </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w">   </span><span class="c1">// +1</span>
 <a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
-<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
-<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
-<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">    </span><span class="c1">// n回ループ</span>
-<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="k">for</span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">){</span><span class="w"> </span><span class="c1">// +1 (毎回i++が実行される)</span>
-<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="w">      </span><span class="c1">// +1</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w">   </span><span class="c1">// +1</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w">   </span><span class="c1">// +1</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">    </span><span class="c1">// n 回ループ</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span><span class="w">   </span><span class="c1">// +1</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">        </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">a</span><span class="p">)</span><span class="w">         </span><span class="c1">// +1</span>
 <a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="p">{</span>
-<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">a</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
-<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
-<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
-<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w">    </span><span class="c1">// n回ループ</span>
-<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w">    </span><span class="k">for</span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">){</span><span class="w"> </span><span class="c1">// +1 (毎回i++が実行される)</span>
-<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w">    </span><span class="c1">// n 回ループ</span>
+<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w">        </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="c1">// +1</span>
 <a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
-<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w">  </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
-<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="w">  </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
-<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="w">  </span><span class="c1">// n回ループ</span>
-<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1 (毎回i++が実行される)</span>
-<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="w">    </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
-<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w">  </span><span class="p">}</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="w">    </span><span class="c1">// n 回ループ</span>
+<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="w">    </span><span class="k">for</span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">){</span><span class="w"> </span><span class="c1">// +1（各反復で i ++ を実行）</span>
+<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">   </span><span class="c1">// +1</span>
-<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">      </span><span class="c1">// +1</span>
-<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">      </span><span class="c1">// +1</span>
-<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a>
-<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="w">    </span><span class="c1">// n回ループ</span>
-<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1 (毎回i++が実行される)</span>
-<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w">        </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
-<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a><span class="p">}</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="p">{</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">a</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w">    </span><span class="c1">// n 回ループ</span>
+<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="w">    </span><span class="k">for</span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">){</span><span class="w"> </span><span class="c1">// +1（各反復で i ++ を実行）</span>
+<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
-<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
-<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
-<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w">    </span><span class="c1">// n回ループ</span>
-<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">   </span><span class="c1">// +1 (毎回i++が実行される)</span>
-<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w">        </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span><span class="w">            </span><span class="c1">// +1</span>
-<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w">    </span><span class="p">}</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w">  </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w">  </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w">  </span><span class="c1">// n 回ループ</span>
+<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1（各反復で i ++ を実行）</span>
+<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w">    </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w">  </span><span class="p">}</span>
 <a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">   </span><span class="c1">// +1</span>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">      </span><span class="c1">// +1</span>
+<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">      </span><span class="c1">// +1</span>
+<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a>
+<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="w">    </span><span class="c1">// n 回ループ</span>
+<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1（各反復で i ++ を実行）</span>
+<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="w">        </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
+<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
+<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w">    </span><span class="c1">// n 回ループ</span>
+<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">   </span><span class="c1">// +1（各反復で i ++ を実行）</span>
+<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="w">        </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span><span class="w">            </span><span class="c1">// +1</span>
+<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w">    </span><span class="c1">// n 回ループ</span>
+<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1（各反復で i ++ を実行）</span>
+<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w">        </span><span class="n">println</span><span class="p">(</span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="w">       </span><span class="c1"># +1</span>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w">   </span><span class="c1"># +1</span>
+<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w">   </span><span class="c1"># +1</span>
+<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="w">    </span><span class="c1"># n 回ループ</span>
+<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w">    </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="c1"># +1</span>
+<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="w">        </span><span class="nb">puts</span><span class="w"> </span><span class="mi">0</span><span class="w">      </span><span class="c1"># +1</span>
+<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>アルゴリズムの操作数を入力サイズ<span class="arithmatex">\(n\)</span>の関数として表す関数を<span class="arithmatex">\(T(n)\)</span>とすると、以下の例を考えてみましょう：</p>
+<p>アルゴリズムの操作回数を入力データサイズ <span class="arithmatex">\(n\)</span> の関数とし、<span class="arithmatex">\(T(n)\)</span> と表すと、上の関数の操作回数は次のようになります：</p>
 <div class="arithmatex">\[
 T(n) = 3 + 2n
 \]</div>
-<p><span class="arithmatex">\(T(n)\)</span>は線形関数であるため、その増加傾向は線形であり、したがって、その時間計算量は線形オーダーで、<span class="arithmatex">\(O(n)\)</span>と表記されます。この数学記法は<u>ビッグO記法</u>として知られ、関数<span class="arithmatex">\(T(n)\)</span>の<u>漸近上限</u>を表します。</p>
-<p>本質的に、時間計算量分析は「操作数<span class="arithmatex">\(T(n)\)</span>」の漸近上限を見つけることです。それには正確な数学的定義があります。</p>
+<p><span class="arithmatex">\(T(n)\)</span> は一次関数であり、実行時間の増加傾向が線形であることを示しています。したがってその時間計算量は線形階です。</p>
+<p>線形階の時間計算量を <span class="arithmatex">\(O(n)\)</span> と表します。この数学記号は<u>ビッグ <span class="arithmatex">\(O\)</span> 記法（big-<span class="arithmatex">\(O\)</span> notation）</u>と呼ばれ、関数 <span class="arithmatex">\(T(n)\)</span> の<u>漸近上界（asymptotic upper bound）</u>を表します。</p>
+<p>時間計算量の分析は本質的に「操作回数 <span class="arithmatex">\(T(n)\)</span>」の漸近上界を求めることであり、明確な数学的定義があります。</p>
 <div class="admonition note">
-<p class="admonition-title">漸近上限</p>
-<p>すべての<span class="arithmatex">\(n &gt; n_0\)</span>に対して<span class="arithmatex">\(T(n) \leq c \cdot f(n)\)</span>となるような正の実数<span class="arithmatex">\(c\)</span>と<span class="arithmatex">\(n_0\)</span>が存在する場合、<span class="arithmatex">\(f(n)\)</span>は<span class="arithmatex">\(T(n)\)</span>の漸近上限とみなされ、<span class="arithmatex">\(T(n) = O(f(n))\)</span>と表記されます。</p>
+<p class="admonition-title">関数の漸近上界</p>
+<p>正の実数 <span class="arithmatex">\(c\)</span> と実数 <span class="arithmatex">\(n_0\)</span> が存在し、すべての <span class="arithmatex">\(n &gt; n_0\)</span> について <span class="arithmatex">\(T(n) \leq c \cdot f(n)\)</span> が成り立つならば、<span class="arithmatex">\(f(n)\)</span> は <span class="arithmatex">\(T(n)\)</span> の漸近上界の 1 つであるとみなせます。これを <span class="arithmatex">\(T(n) = O(f(n))\)</span> と記します。</p>
 </div>
-<p>下図に示されているように、漸近上限の計算では、<span class="arithmatex">\(n\)</span>が無限大に近づくにつれて、<span class="arithmatex">\(T(n)\)</span>と<span class="arithmatex">\(f(n)\)</span>が同じ増加オーダーを持ち、定数因子<span class="arithmatex">\(c\)</span>のみが異なるような関数<span class="arithmatex">\(f(n)\)</span>を見つけることが含まれます。</p>
-<p><img alt="Asymptotic upper bound of a function" class="animation-figure" src="../time_complexity.assets/asymptotic_upper_bound.png" /></p>
-<p align="center"> 図 2-8 &nbsp; Asymptotic upper bound of a function </p>
+<p>下図のように、漸近上界を求めるとは関数 <span class="arithmatex">\(f(n)\)</span> を探すことであり、<span class="arithmatex">\(n\)</span> が無限大へ近づくときに <span class="arithmatex">\(T(n)\)</span> と <span class="arithmatex">\(f(n)\)</span> が同じ増加オーダーにあり、定数係数 <span class="arithmatex">\(c\)</span> だけが異なる状態を表します。</p>
+<p><img alt="関数の漸近上界" class="animation-figure" src="../time_complexity.assets/asymptotic_upper_bound.png" /></p>
+<p align="center"> 図 2-8 &nbsp; 関数の漸近上界 </p>
 
-<h2 id="233">2.3.3 &nbsp; 計算方法<a class="headerlink" href="#233" title="Permanent link">&para;</a></h2>
-<p>漸近上限の概念は数学的に濃密に見えるかもしれませんが、今すぐ完全に理解する必要はありません。まず計算方法を理解し、時間をかけて練習し理解しましょう。</p>
-<p><span class="arithmatex">\(f(n)\)</span>が決まれば、時間計算量<span class="arithmatex">\(O(f(n))\)</span>が得られます。しかし、漸近上限<span class="arithmatex">\(f(n)\)</span>をどのように決定するのでしょうか？このプロセスには一般的に2つのステップが含まれます：操作数のカウントと漸近上限の決定です。</p>
-<h3 id="1-1">1. &nbsp; ステップ1: 操作数のカウント<a class="headerlink" href="#1-1" title="Permanent link">&para;</a></h3>
-<p>このステップでは、コードを行ごとに確認します。しかし、<span class="arithmatex">\(c \cdot f(n)\)</span>の定数<span class="arithmatex">\(c\)</span>の存在により、<strong><span class="arithmatex">\(T(n)\)</span>のすべての係数と定数項は無視できます</strong>。この原理により、操作をカウントする際の簡略化技法が可能になります。</p>
+<h2 id="233">2.3.3 &nbsp; 求め方<a class="headerlink" href="#233" title="Permanent link">&para;</a></h2>
+<p>漸近上界はやや数学色が強い概念ですが、完全に理解できていなくても心配はいりません。まずは求め方を押さえ、実践を重ねる中で徐々にその数学的意味をつかめば十分です。</p>
+<p>定義より、<span class="arithmatex">\(f(n)\)</span> が定まれば時間計算量 <span class="arithmatex">\(O(f(n))\)</span> が得られます。では、漸近上界 <span class="arithmatex">\(f(n)\)</span> をどのように決めればよいのでしょうか。大きく 2 段階あります。まず操作回数を数え、その後で漸近上界を判断します。</p>
+<h3 id="1-1">1. &nbsp; 第 1 ステップ：操作回数を数える<a class="headerlink" href="#1-1" title="Permanent link">&para;</a></h3>
+<p>コードについては、上から下へ 1 行ずつ数えれば十分です。しかし、前述の <span class="arithmatex">\(c \cdot f(n)\)</span> における定数係数 <span class="arithmatex">\(c\)</span> は任意に大きく取れるため、<strong>操作回数 <span class="arithmatex">\(T(n)\)</span> に含まれるさまざまな係数や定数項は無視できます</strong>。この原則から、次のような簡略化のコツが得られます。</p>
 <ol>
-<li><strong><span class="arithmatex">\(T(n)\)</span>の定数項を無視します</strong>。これらは<span class="arithmatex">\(n\)</span>とは無関係であるため、時間計算量に影響しません。</li>
-<li><strong>すべての係数を省略します</strong>。例えば、<span class="arithmatex">\(2n\)</span>、<span class="arithmatex">\(5n + 1\)</span>回などのループは、<span class="arithmatex">\(n\)</span>の前の係数が時間計算量に影響しないため、<span class="arithmatex">\(n\)</span>回に簡略化できます。</li>
-<li><strong>ネストしたループには乗算を使用します</strong>。総操作数は各ループの操作数の積であり、ポイント1と2の簡略化技法を各ループレベルに適用します。</li>
+<li><strong><span class="arithmatex">\(T(n)\)</span> 中の定数を無視する</strong>。それらはすべて <span class="arithmatex">\(n\)</span> と無関係なので、時間計算量には影響しません。</li>
+<li><strong>すべての係数を省略する</strong>。例えば <span class="arithmatex">\(2n\)</span> 回や <span class="arithmatex">\(5n + 1\)</span> 回のループは、いずれも <span class="arithmatex">\(n\)</span> 回と簡略化できます。<span class="arithmatex">\(n\)</span> の前の係数は時間計算量に影響しないからです。</li>
+<li><strong>ループが入れ子のときは乗算を使う</strong>。総操作回数は外側のループと内側のループの操作回数の積に等しく、各ループ層には引き続き <code>1.</code> と <code>2.</code> のコツをそれぞれ適用できます。</li>
 </ol>
-<p>関数が与えられた場合、これらの技法を使用して操作をカウントできます：</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="4:12"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label></div>
+<p>次の関数では、上記のコツを使って操作回数を数えられます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="4:13"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a>    <span class="n">a</span> <span class="o">=</span> <span class="mi">1</span>      <span class="c1"># +0 (技法1)</span>
-<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">+</span> <span class="n">n</span>  <span class="c1"># +0 (技法1)</span>
-<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a>    <span class="c1"># +n (技法2)</span>
-<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">5</span> <span class="o">*</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
-<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a>        <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
-<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a>    <span class="c1"># +n*n (技法3)</span>
-<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">n</span><span class="p">):</span>
-<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
-<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a>            <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a>    <span class="n">a</span> <span class="o">=</span> <span class="mi">1</span>      <span class="c1"># +0（コツ 1）</span>
+<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">+</span> <span class="n">n</span>  <span class="c1"># +0（コツ 1）</span>
+<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a>    <span class="c1"># +n（コツ 2）</span>
+<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">5</span> <span class="o">*</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a>        <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a>    <span class="c1"># +n*n（コツ 3）</span>
+<a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a>            <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
-<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
-<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w">    </span><span class="c1">// +n (技法2)</span>
-<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="w">        </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
-<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="w">    </span><span class="c1">// +n*n (技法3)</span>
-<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a><span class="w">            </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
-<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-37-14" name="__codelineno-37-14" href="#__codelineno-37-14"></a><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
-<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
-<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w">    </span><span class="c1">// +n (技法2)</span>
-<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w">        </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
-<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="w">    </span><span class="c1">// +n*n (技法3)</span>
-<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a><span class="w">            </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
-<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="k">void</span><span class="w"> </span><span class="nf">Algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
-<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
-<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a><span class="w">    </span><span class="c1">// +n (技法2)</span>
-<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a><span class="w">        </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
-<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a><span class="w">    </span><span class="c1">// +n*n (技法3)</span>
-<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-39-11" name="__codelineno-39-11" href="#__codelineno-39-11"></a><span class="w">            </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
-<a id="__codelineno-39-12" name="__codelineno-39-12" href="#__codelineno-39-12"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-39-13" name="__codelineno-39-13" href="#__codelineno-39-13"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-39-14" name="__codelineno-39-14" href="#__codelineno-39-14"></a><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="w">     </span><span class="c1">// +0 (技法1)</span>
-<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">n</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
-<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w">    </span><span class="c1">// +n (技法2)</span>
-<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w">        </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0（コツ 1）</span>
+<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0（コツ 1）</span>
+<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w">    </span><span class="c1">// +n（コツ 2）</span>
+<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w">        </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
 <a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w">    </span><span class="c1">// +n*n (技法3)</span>
-<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w">            </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w">    </span><span class="c1">// +n*n（コツ 3）</span>
+<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w">            </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
 <a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// +0 (技法1)</span>
-<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="c1">// +0 (技法1)</span>
-<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w">    </span><span class="c1">// +n (技法2)</span>
-<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="p">(</span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a><span class="w">        </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0（コツ 1）</span>
+<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0（コツ 1）</span>
+<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w">    </span><span class="c1">// +n（コツ 2）</span>
+<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a><span class="w">        </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a><span class="w">    </span><span class="c1">// +n*n (技法3)</span>
-<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="p">(</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a><span class="w">            </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a><span class="w">    </span><span class="c1">// +n*n（コツ 3）</span>
+<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a><span class="w">            </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-41-14" name="__codelineno-41-14" href="#__codelineno-41-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
-<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
-<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w">    </span><span class="c1">// +n (技法2)</span>
-<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="k">void</span><span class="w"> </span><span class="nf">Algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0（コツ 1）</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0（コツ 1）</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w">    </span><span class="c1">// +n（コツ 2）</span>
+<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a><span class="w">        </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a><span class="w">    </span><span class="c1">// +n*n (技法3)</span>
-<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a><span class="w">            </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a><span class="w">    </span><span class="c1">// +n*n（コツ 3）</span>
+<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a><span class="w">            </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-42-14" name="__codelineno-42-14" href="#__codelineno-42-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
-<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
-<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">    </span><span class="c1">// +n (技法2)</span>
-<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="w">     </span><span class="c1">// +0（コツ 1）</span>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">n</span><span class="w">  </span><span class="c1">// +0（コツ 1）</span>
+<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">    </span><span class="c1">// +n（コツ 2）</span>
+<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w">        </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
 <a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w">    </span><span class="c1">// +n*n (技法3)</span>
-<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w">            </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w">    </span><span class="c1">// +n*n（コツ 3）</span>
+<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w">            </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
 <a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-43-14" name="__codelineno-43-14" href="#__codelineno-43-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0 (技法1)</span>
-<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w">  </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0 (技法1)</span>
-<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">  </span><span class="c1">// +n (技法2)</span>
-<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w">    </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
-<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w">  </span><span class="p">}</span>
-<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w">  </span><span class="c1">// +n*n (技法3)</span>
-<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w">      </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
-<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="w">  </span><span class="p">}</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// +0（コツ 1）</span>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="c1">// +0（コツ 1）</span>
+<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">    </span><span class="c1">// +n（コツ 2）</span>
+<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="p">(</span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w">        </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w">    </span><span class="c1">// +n*n（コツ 3）</span>
+<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="p">(</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w">            </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">     </span><span class="c1">// +0 (技法1)</span>
-<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w">        </span><span class="c1">// +0 (技法1)</span>
-<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a>
-<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w">    </span><span class="c1">// +n (技法2)</span>
-<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="p">(</span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="w">        </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
-<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a>
-<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="w">    </span><span class="c1">// +n*n (技法3)</span>
-<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="p">(</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-45-13" name="__codelineno-45-13" href="#__codelineno-45-13"></a><span class="w">            </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
-<a id="__codelineno-45-14" name="__codelineno-45-14" href="#__codelineno-45-14"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-45-15" name="__codelineno-45-15" href="#__codelineno-45-15"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-45-16" name="__codelineno-45-16" href="#__codelineno-45-16"></a><span class="p">}</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0（コツ 1）</span>
+<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0（コツ 1）</span>
+<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w">    </span><span class="c1">// +n（コツ 2）</span>
+<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="w">    </span><span class="c1">// +n*n（コツ 3）</span>
+<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w">            </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-45-13" name="__codelineno-45-13" href="#__codelineno-45-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-45-14" name="__codelineno-45-14" href="#__codelineno-45-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
-<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
-<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w">    </span><span class="c1">// +n (技法2)</span>
-<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a><span class="w">        </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0（コツ 1）</span>
+<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0（コツ 1）</span>
+<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w">    </span><span class="c1">// +n（コツ 2）</span>
+<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
 <a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a><span class="w">    </span><span class="c1">// +n*n (技法3)</span>
-<a id="__codelineno-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></a><span class="w">            </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a><span class="w">    </span><span class="c1">// +n*n（コツ 3）</span>
+<a id="__codelineno-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></a><span class="w">            </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
 <a id="__codelineno-46-12" name="__codelineno-46-12" href="#__codelineno-46-12"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-46-13" name="__codelineno-46-13" href="#__codelineno-46-13"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-46-14" name="__codelineno-46-14" href="#__codelineno-46-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0（コツ 1）</span>
+<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w">  </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0（コツ 1）</span>
+<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w">  </span><span class="c1">// +n（コツ 2）</span>
+<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a><span class="w">    </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a><span class="w">  </span><span class="c1">// +n*n（コツ 3）</span>
+<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="w">      </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-47-13" name="__codelineno-47-13" href="#__codelineno-47-13"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-47-14" name="__codelineno-47-14" href="#__codelineno-47-14"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">     </span><span class="c1">// +0（コツ 1）</span>
+<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w">        </span><span class="c1">// +0（コツ 1）</span>
+<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a>
+<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a><span class="w">    </span><span class="c1">// +n（コツ 2）</span>
+<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="p">(</span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a><span class="w">        </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a>
+<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a><span class="w">    </span><span class="c1">// +n*n（コツ 3）</span>
+<a id="__codelineno-48-11" name="__codelineno-48-11" href="#__codelineno-48-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="p">(</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-12" name="__codelineno-48-12" href="#__codelineno-48-12"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-13" name="__codelineno-48-13" href="#__codelineno-48-13"></a><span class="w">            </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-48-14" name="__codelineno-48-14" href="#__codelineno-48-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-48-15" name="__codelineno-48-15" href="#__codelineno-48-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-48-16" name="__codelineno-48-16" href="#__codelineno-48-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0（コツ 1）</span>
+<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0（コツ 1）</span>
+<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w">    </span><span class="c1">// +n（コツ 2）</span>
+<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a><span class="w">        </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="w">    </span><span class="c1">// +n*n（コツ 3）</span>
+<a id="__codelineno-49-9" name="__codelineno-49-9" href="#__codelineno-49-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-10" name="__codelineno-49-10" href="#__codelineno-49-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-11" name="__codelineno-49-11" href="#__codelineno-49-11"></a><span class="w">            </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-49-12" name="__codelineno-49-12" href="#__codelineno-49-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-49-13" name="__codelineno-49-13" href="#__codelineno-49-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-49-14" name="__codelineno-49-14" href="#__codelineno-49-14"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="w">   </span><span class="c1">// +0（コツ 1）</span>
+<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="w">   </span><span class="c1">// +0（コツ 1）</span>
+<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w">    </span><span class="c1">// +n（コツ 2）</span>
+<a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="m">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a><span class="w">        </span><span class="n">println</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
+<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a><span class="w">    </span><span class="c1">// +n*n（コツ 3）</span>
+<a id="__codelineno-50-9" name="__codelineno-50-9" href="#__codelineno-50-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-10" name="__codelineno-50-10" href="#__codelineno-50-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-11" name="__codelineno-50-11" href="#__codelineno-50-11"></a><span class="w">            </span><span class="n">println</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
+<a id="__codelineno-50-12" name="__codelineno-50-12" href="#__codelineno-50-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-50-13" name="__codelineno-50-13" href="#__codelineno-50-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-50-14" name="__codelineno-50-14" href="#__codelineno-50-14"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="w">       </span><span class="c1"># +0（コツ 1）</span>
+<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="w">   </span><span class="c1"># +0（コツ 1）</span>
+<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a><span class="w">    </span><span class="c1"># +n（コツ 2）</span>
+<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w">    </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="p">(</span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">puts</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a><span class="w">    </span><span class="c1"># +n*n（コツ 3）</span>
+<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="w">    </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="p">(</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span>
+<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="w">        </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">puts</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>以下の式は、簡略化前後のカウント結果を示しており、どちらも<span class="arithmatex">\(O(n^2)\)</span>の時間計算量に導きます：</p>
+<p>次の式は、上記のコツを使う前後の集計結果を示したもので、どちらから求めても時間計算量は <span class="arithmatex">\(O(n^2)\)</span> です。</p>
 <div class="arithmatex">\[
 \begin{aligned}
-T(n) &amp; = 2n(n + 1) + (5n + 1) + 2 &amp; \text{完全カウント (-.-|||)} \newline
+T(n) &amp; = 2n(n + 1) + (5n + 1) + 2 &amp; \text{厳密集計 (-.-|||)} \newline
 &amp; = 2n^2 + 7n + 3 \newline
-T(n) &amp; = n^2 + n &amp; \text{簡略化カウント (o.O)}
+T(n) &amp; = n^2 + n &amp; \text{手抜き集計 (o.O)}
 \end{aligned}
 \]</div>
-<h3 id="2-2">2. &nbsp; ステップ2: 漸近上限の決定<a class="headerlink" href="#2-2" title="Permanent link">&para;</a></h3>
-<p><strong>時間計算量は<span class="arithmatex">\(T(n)\)</span>の最高次項によって決定されます</strong>。これは、<span class="arithmatex">\(n\)</span>が無限大に近づくにつれて、最高次項が支配的になり、他の項の影響は無視できるようになるためです。</p>
-<p>以下の表は、異なる操作カウントとそれに対応する時間計算量の例を示しています。係数が増加オーダーを変更できないことを強調するために、誇張された値が使用されています。<span class="arithmatex">\(n\)</span>が非常に大きくなると、これらの定数は重要でなくなります。</p>
-<p align="center"> 表: 異なる操作カウントに対する時間計算量 </p>
+<h3 id="2-2">2. &nbsp; 第 2 ステップ：漸近上界を判断する<a class="headerlink" href="#2-2" title="Permanent link">&para;</a></h3>
+<p><strong>時間計算量は <span class="arithmatex">\(T(n)\)</span> の最高次の項によって決まります</strong>。これは、<span class="arithmatex">\(n\)</span> が無限大に近づくとき、最高次の項が支配的となり、他の項の影響は無視できるからです。</p>
+<p>以下の表はその例です。いくつか極端な値を入れているのは、「係数では次数は変わらない」という結論を強調するためです。<span class="arithmatex">\(n\)</span> が無限大に近づくと、これらの定数は重要でなくなります。</p>
+<p align="center"> 表 2-2 &nbsp; 異なる操作回数に対応する時間計算量 </p>
 
 <div class="center-table">
 <table>
 <thead>
 <tr>
-<th>操作カウント <span class="arithmatex">\(T(n)\)</span></th>
+<th>操作回数 <span class="arithmatex">\(T(n)\)</span></th>
 <th>時間計算量 <span class="arithmatex">\(O(f(n))\)</span></th>
 </tr>
 </thead>
@@ -5440,1111 +5541,2608 @@ T(n) &amp; = n^2 + n &amp; \text{簡略化カウント (o.O)}
 </tbody>
 </table>
 </div>
-<h2 id="234">2.3.4 &nbsp; 一般的な時間計算量の種類<a class="headerlink" href="#234" title="Permanent link">&para;</a></h2>
-<p>入力データサイズを<span class="arithmatex">\(n\)</span>としましょう。一般的な時間計算量の種類を下図に示し、低いものから高いものへと並べています：</p>
+<h2 id="234">2.3.4 &nbsp; よくある種類<a class="headerlink" href="#234" title="Permanent link">&para;</a></h2>
+<p>入力データサイズを <span class="arithmatex">\(n\)</span> とすると、よくある時間計算量の種類は次図のとおりです（小さい順に並べています）。</p>
 <div class="arithmatex">\[
 \begin{aligned}
-&amp; O(1) &lt; O(\log n) &lt; O(n) &lt; O(n \log n) &lt; O(n^2) &lt; O(2^n) &lt; O(n!) \newline
-&amp; \text{定数} &lt; \text{対数} &lt; \text{線形} &lt; \text{線形対数} &lt; \text{二次} &lt; \text{指数} &lt; \text{階乗}
+O(1) &lt; O(\log n) &lt; O(n) &lt; O(n \log n) &lt; O(n^2) &lt; O(2^n) &lt; O(n!) \newline
+\text{定数階} &lt; \text{対数階} &lt; \text{線形階} &lt; \text{線形対数階} &lt; \text{平方階} &lt; \text{指数階} &lt; \text{階乗階}
 \end{aligned}
 \]</div>
-<p><img alt="Common types of time complexity" class="animation-figure" src="../time_complexity.assets/time_complexity_common_types.png" /></p>
-<p align="center"> 図 2-9 &nbsp; Common types of time complexity </p>
+<p><img alt="よくある時間計算量の種類" class="animation-figure" src="../time_complexity.assets/time_complexity_common_types.png" /></p>
+<p align="center"> 図 2-9 &nbsp; よくある時間計算量の種類 </p>
 
-<h3 id="1-o1">1. &nbsp; 定数オーダー <span class="arithmatex">\(O(1)\)</span><a class="headerlink" href="#1-o1" title="Permanent link">&para;</a></h3>
-<p>定数オーダーは、操作数が入力データサイズ<span class="arithmatex">\(n\)</span>とは無関係であることを意味します。以下の関数では、操作数<code>size</code>が大きい場合でも、<span class="arithmatex">\(n\)</span>とは無関係であるため、時間計算量は<span class="arithmatex">\(O(1)\)</span>のままです：</p>
+<h3 id="1-o1">1. &nbsp; 定数階 <span class="arithmatex">\(O(1)\)</span><a class="headerlink" href="#1-o1" title="Permanent link">&para;</a></h3>
+<p>定数階の操作回数は入力データサイズ <span class="arithmatex">\(n\)</span> と無関係であり、<span class="arithmatex">\(n\)</span> が変化しても増減しません。</p>
+<p>次の関数では、操作回数 <code>size</code> が大きい可能性はありますが、入力データサイズ <span class="arithmatex">\(n\)</span> とは無関係なので、時間計算量は依然として <span class="arithmatex">\(O(1)\)</span> です：</p>
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 <div class="tabbed-content">
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-<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;定数複雑度&quot;&quot;&quot;</span>
-<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
-<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a>    <span class="n">size</span> <span class="o">=</span> <span class="mi">100000</span>
-<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">size</span><span class="p">):</span>
-<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
-<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a>    <span class="k">return</span> <span class="n">count</span>
+<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;定数階&quot;&quot;&quot;</span>
+<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a>    <span class="n">size</span> <span class="o">=</span> <span class="mi">100000</span>
+<a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">size</span><span class="p">):</span>
+<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></a>    <span class="k">return</span> <span class="n">count</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* 定数計算量 */</span>
-<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span><span class="p">;</span>
-<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
-<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
-<a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 定数階 */</span>
+<a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span><span class="p">;</span>
+<a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
+<a id="__codelineno-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* 定数計算量 */</span>
-<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span><span class="p">;</span>
-<a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
-<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
-<a id="__codelineno-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="cm">/* 定数階 */</span>
+<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span><span class="p">;</span>
+<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
+<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Constant</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="cm">/* 定数階 */</span>
+<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-55-4" name="__codelineno-55-4" href="#__codelineno-55-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span><span class="p">;</span>
+<a id="__codelineno-55-5" name="__codelineno-55-5" href="#__codelineno-55-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
+<a id="__codelineno-55-6" name="__codelineno-55-6" href="#__codelineno-55-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-55-7" name="__codelineno-55-7" href="#__codelineno-55-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-55-8" name="__codelineno-55-8" href="#__codelineno-55-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">constant</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="cm">/* 定数階 */</span>
+<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">constant</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a><span class="w">    </span><span class="nx">size</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">100000</span>
+<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">size</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a><span class="w">        </span><span class="nx">count</span><span class="o">++</span>
+<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
+<a id="__codelineno-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">constant</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 定数階 */</span>
+<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">size</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">100_000</span>
+<a id="__codelineno-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a><span class="w">        </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="bp">count</span>
+<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">constant</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 定数階 */</span>
+<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constant</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">100000</span><span class="p">;</span>
+<a id="__codelineno-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">size</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
+<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">constant</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="cm">/* 定数階 */</span>
+<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constant</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-59-4" name="__codelineno-59-4" href="#__codelineno-59-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">100000</span><span class="p">;</span>
+<a id="__codelineno-59-5" name="__codelineno-59-5" href="#__codelineno-59-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">size</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-59-6" name="__codelineno-59-6" href="#__codelineno-59-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
+<a id="__codelineno-59-7" name="__codelineno-59-7" href="#__codelineno-59-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">constant</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="cm">/* 定数階 */</span>
+<a id="__codelineno-60-2" name="__codelineno-60-2" href="#__codelineno-60-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-3" name="__codelineno-60-3" href="#__codelineno-60-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-60-4" name="__codelineno-60-4" href="#__codelineno-60-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">100000</span><span class="p">;</span>
+<a id="__codelineno-60-5" name="__codelineno-60-5" href="#__codelineno-60-5"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-6" name="__codelineno-60-6" href="#__codelineno-60-6"></a><span class="w">    </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-60-7" name="__codelineno-60-7" href="#__codelineno-60-7"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-60-8" name="__codelineno-60-8" href="#__codelineno-60-8"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-60-9" name="__codelineno-60-9" href="#__codelineno-60-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">constant</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="cm">/* 定数階 */</span>
+<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-3" name="__codelineno-61-3" href="#__codelineno-61-3"></a><span class="w">    </span><span class="n">_</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
+<a id="__codelineno-61-4" name="__codelineno-61-4" href="#__codelineno-61-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-61-5" name="__codelineno-61-5" href="#__codelineno-61-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100_000</span><span class="p">;</span>
+<a id="__codelineno-61-6" name="__codelineno-61-6" href="#__codelineno-61-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">size</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-7" name="__codelineno-61-7" href="#__codelineno-61-7"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-61-8" name="__codelineno-61-8" href="#__codelineno-61-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-61-9" name="__codelineno-61-9" href="#__codelineno-61-9"></a><span class="w">    </span><span class="n">count</span>
+<a id="__codelineno-61-10" name="__codelineno-61-10" href="#__codelineno-61-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">constant</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="cm">/* 定数階 */</span>
+<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-62-4" name="__codelineno-62-4" href="#__codelineno-62-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span><span class="p">;</span>
+<a id="__codelineno-62-5" name="__codelineno-62-5" href="#__codelineno-62-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-62-6" name="__codelineno-62-6" href="#__codelineno-62-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-7" name="__codelineno-62-7" href="#__codelineno-62-7"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-62-8" name="__codelineno-62-8" href="#__codelineno-62-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-62-9" name="__codelineno-62-9" href="#__codelineno-62-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-62-10" name="__codelineno-62-10" href="#__codelineno-62-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">constant</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="cm">/* 定数階 */</span>
+<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-63-4" name="__codelineno-63-4" href="#__codelineno-63-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">100000</span>
+<a id="__codelineno-63-5" name="__codelineno-63-5" href="#__codelineno-63-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">size</span><span class="p">)</span>
+<a id="__codelineno-63-6" name="__codelineno-63-6" href="#__codelineno-63-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span>
+<a id="__codelineno-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
+<a id="__codelineno-63-8" name="__codelineno-63-8" href="#__codelineno-63-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">constant</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="c1">### 定数階 ###</span>
+<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a><span class="w">  </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-64-4" name="__codelineno-64-4" href="#__codelineno-64-4"></a><span class="w">  </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span>
+<a id="__codelineno-64-5" name="__codelineno-64-5" href="#__codelineno-64-5"></a>
+<a id="__codelineno-64-6" name="__codelineno-64-6" href="#__codelineno-64-6"></a><span class="w">  </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">size</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-64-7" name="__codelineno-64-7" href="#__codelineno-64-7"></a>
+<a id="__codelineno-64-8" name="__codelineno-64-8" href="#__codelineno-64-8"></a><span class="w">  </span><span class="n">count</span>
+<a id="__codelineno-64-9" name="__codelineno-64-9" href="#__codelineno-64-9"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h3 id="2-on">2. &nbsp; 線形オーダー <span class="arithmatex">\(O(n)\)</span><a class="headerlink" href="#2-on" title="Permanent link">&para;</a></h3>
-<p>線形オーダーは、操作数が入力データサイズ<span class="arithmatex">\(n\)</span>と線形に増加することを示します。線形オーダーは一般的に単一ループ構造で現れます：</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 441px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20constant%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%AE%9A%E6%95%B0%E9%9A%8E%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20size%20%3D%2010%0A%20%20%20%20for%20_%20in%20range%28size%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20constant%28n%29%0A%20%20%20%20print%28%22%E5%AE%9A%E6%95%B0%E6%99%82%E9%96%93%E3%81%AE%E6%93%8D%E4%BD%9C%E5%9B%9E%E6%95%B0%20%3D%22%2C%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20constant%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%AE%9A%E6%95%B0%E9%9A%8E%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20size%20%3D%2010%0A%20%20%20%20for%20_%20in%20range%28size%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20constant%28n%29%0A%20%20%20%20print%28%22%E5%AE%9A%E6%95%B0%E6%99%82%E9%96%93%E3%81%AE%E6%93%8D%E4%BD%9C%E5%9B%9E%E6%95%B0%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h3 id="2-on">2. &nbsp; 線形階 <span class="arithmatex">\(O(n)\)</span><a class="headerlink" href="#2-on" title="Permanent link">&para;</a></h3>
+<p>線形階の操作回数は入力データサイズ <span class="arithmatex">\(n\)</span> に対して線形に増加します。線形階は通常、単一ループに現れます：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="6:13"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><input id="__tabbed_6_13" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Kotlin</label><label for="__tabbed_6_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;線形複雑度&quot;&quot;&quot;</span>
-<a id="__codelineno-61-3" name="__codelineno-61-3" href="#__codelineno-61-3"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
-<a id="__codelineno-61-4" name="__codelineno-61-4" href="#__codelineno-61-4"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
-<a id="__codelineno-61-5" name="__codelineno-61-5" href="#__codelineno-61-5"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
-<a id="__codelineno-61-6" name="__codelineno-61-6" href="#__codelineno-61-6"></a>    <span class="k">return</span> <span class="n">count</span>
+<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;線形階&quot;&quot;&quot;</span>
+<a id="__codelineno-65-3" name="__codelineno-65-3" href="#__codelineno-65-3"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-65-4" name="__codelineno-65-4" href="#__codelineno-65-4"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-65-5" name="__codelineno-65-5" href="#__codelineno-65-5"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-65-6" name="__codelineno-65-6" href="#__codelineno-65-6"></a>    <span class="k">return</span> <span class="n">count</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="cm">/* 線形計算量 */</span>
-<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-62-4" name="__codelineno-62-4" href="#__codelineno-62-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
-<a id="__codelineno-62-5" name="__codelineno-62-5" href="#__codelineno-62-5"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-62-6" name="__codelineno-62-6" href="#__codelineno-62-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
-<a id="__codelineno-62-7" name="__codelineno-62-7" href="#__codelineno-62-7"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="cm">/* 線形階 */</span>
+<a id="__codelineno-66-2" name="__codelineno-66-2" href="#__codelineno-66-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-66-3" name="__codelineno-66-3" href="#__codelineno-66-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-66-4" name="__codelineno-66-4" href="#__codelineno-66-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
+<a id="__codelineno-66-5" name="__codelineno-66-5" href="#__codelineno-66-5"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-66-6" name="__codelineno-66-6" href="#__codelineno-66-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-66-7" name="__codelineno-66-7" href="#__codelineno-66-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="cm">/* 線形計算量 */</span>
-<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-63-4" name="__codelineno-63-4" href="#__codelineno-63-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
-<a id="__codelineno-63-5" name="__codelineno-63-5" href="#__codelineno-63-5"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-63-6" name="__codelineno-63-6" href="#__codelineno-63-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
-<a id="__codelineno-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="cm">/* 線形階 */</span>
+<a id="__codelineno-67-2" name="__codelineno-67-2" href="#__codelineno-67-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-67-3" name="__codelineno-67-3" href="#__codelineno-67-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-67-4" name="__codelineno-67-4" href="#__codelineno-67-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
+<a id="__codelineno-67-5" name="__codelineno-67-5" href="#__codelineno-67-5"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-67-6" name="__codelineno-67-6" href="#__codelineno-67-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-67-7" name="__codelineno-67-7" href="#__codelineno-67-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Linear</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="cm">/* 線形階 */</span>
+<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-68-3" name="__codelineno-68-3" href="#__codelineno-68-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-68-4" name="__codelineno-68-4" href="#__codelineno-68-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
+<a id="__codelineno-68-5" name="__codelineno-68-5" href="#__codelineno-68-5"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-68-6" name="__codelineno-68-6" href="#__codelineno-68-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-68-7" name="__codelineno-68-7" href="#__codelineno-68-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">linear</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="cm">/* 線形階 */</span>
+<a id="__codelineno-69-2" name="__codelineno-69-2" href="#__codelineno-69-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">linear</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-3" name="__codelineno-69-3" href="#__codelineno-69-3"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-69-4" name="__codelineno-69-4" href="#__codelineno-69-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-5" name="__codelineno-69-5" href="#__codelineno-69-5"></a><span class="w">        </span><span class="nx">count</span><span class="o">++</span>
+<a id="__codelineno-69-6" name="__codelineno-69-6" href="#__codelineno-69-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-69-7" name="__codelineno-69-7" href="#__codelineno-69-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
+<a id="__codelineno-69-8" name="__codelineno-69-8" href="#__codelineno-69-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">linear</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="cm">/* 線形階 */</span>
+<a id="__codelineno-70-2" name="__codelineno-70-2" href="#__codelineno-70-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-3" name="__codelineno-70-3" href="#__codelineno-70-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-70-4" name="__codelineno-70-4" href="#__codelineno-70-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-5" name="__codelineno-70-5" href="#__codelineno-70-5"></a><span class="w">        </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-70-6" name="__codelineno-70-6" href="#__codelineno-70-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-70-7" name="__codelineno-70-7" href="#__codelineno-70-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="bp">count</span>
+<a id="__codelineno-70-8" name="__codelineno-70-8" href="#__codelineno-70-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">linear</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="cm">/* 線形階 */</span>
+<a id="__codelineno-71-2" name="__codelineno-71-2" href="#__codelineno-71-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">linear</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-3" name="__codelineno-71-3" href="#__codelineno-71-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-71-4" name="__codelineno-71-4" href="#__codelineno-71-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-71-5" name="__codelineno-71-5" href="#__codelineno-71-5"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
+<a id="__codelineno-71-6" name="__codelineno-71-6" href="#__codelineno-71-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">linear</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="cm">/* 線形階 */</span>
+<a id="__codelineno-72-2" name="__codelineno-72-2" href="#__codelineno-72-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">linear</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-3" name="__codelineno-72-3" href="#__codelineno-72-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-72-4" name="__codelineno-72-4" href="#__codelineno-72-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-72-5" name="__codelineno-72-5" href="#__codelineno-72-5"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
+<a id="__codelineno-72-6" name="__codelineno-72-6" href="#__codelineno-72-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linear</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="cm">/* 線形階 */</span>
+<a id="__codelineno-73-2" name="__codelineno-73-2" href="#__codelineno-73-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-73-3" name="__codelineno-73-3" href="#__codelineno-73-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-73-4" name="__codelineno-73-4" href="#__codelineno-73-4"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-73-5" name="__codelineno-73-5" href="#__codelineno-73-5"></a><span class="w">    </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-73-6" name="__codelineno-73-6" href="#__codelineno-73-6"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-73-7" name="__codelineno-73-7" href="#__codelineno-73-7"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-73-8" name="__codelineno-73-8" href="#__codelineno-73-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linear</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="cm">/* 線形階 */</span>
+<a id="__codelineno-74-2" name="__codelineno-74-2" href="#__codelineno-74-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-3" name="__codelineno-74-3" href="#__codelineno-74-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-74-4" name="__codelineno-74-4" href="#__codelineno-74-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-5" name="__codelineno-74-5" href="#__codelineno-74-5"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-74-6" name="__codelineno-74-6" href="#__codelineno-74-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-74-7" name="__codelineno-74-7" href="#__codelineno-74-7"></a><span class="w">    </span><span class="n">count</span>
+<a id="__codelineno-74-8" name="__codelineno-74-8" href="#__codelineno-74-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linear</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="cm">/* 線形階 */</span>
+<a id="__codelineno-75-2" name="__codelineno-75-2" href="#__codelineno-75-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-75-3" name="__codelineno-75-3" href="#__codelineno-75-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-75-4" name="__codelineno-75-4" href="#__codelineno-75-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-75-5" name="__codelineno-75-5" href="#__codelineno-75-5"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-75-6" name="__codelineno-75-6" href="#__codelineno-75-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-75-7" name="__codelineno-75-7" href="#__codelineno-75-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-75-8" name="__codelineno-75-8" href="#__codelineno-75-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">linear</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="cm">/* 線形階 */</span>
+<a id="__codelineno-76-2" name="__codelineno-76-2" href="#__codelineno-76-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-76-3" name="__codelineno-76-3" href="#__codelineno-76-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-76-4" name="__codelineno-76-4" href="#__codelineno-76-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-76-5" name="__codelineno-76-5" href="#__codelineno-76-5"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span>
+<a id="__codelineno-76-6" name="__codelineno-76-6" href="#__codelineno-76-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
+<a id="__codelineno-76-7" name="__codelineno-76-7" href="#__codelineno-76-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">linear</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="c1">### 線形階 ###</span>
+<a id="__codelineno-77-2" name="__codelineno-77-2" href="#__codelineno-77-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-77-3" name="__codelineno-77-3" href="#__codelineno-77-3"></a><span class="w">  </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-77-4" name="__codelineno-77-4" href="#__codelineno-77-4"></a><span class="w">  </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-77-5" name="__codelineno-77-5" href="#__codelineno-77-5"></a><span class="w">  </span><span class="n">count</span>
+<a id="__codelineno-77-6" name="__codelineno-77-6" href="#__codelineno-77-6"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>配列の走査や連結リストの走査などの操作は時間計算量が<span class="arithmatex">\(O(n)\)</span>で、<span class="arithmatex">\(n\)</span>は配列またはリストの長さです：</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 423px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20linear%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%B7%9A%E5%BD%A2%E9%9A%8E%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20linear%28n%29%0A%20%20%20%20print%28%22%E7%B7%9A%E5%BD%A2%E6%99%82%E9%96%93%E3%81%AE%E6%93%8D%E4%BD%9C%E5%9B%9E%E6%95%B0%20%3D%22%2C%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20linear%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%B7%9A%E5%BD%A2%E9%9A%8E%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20linear%28n%29%0A%20%20%20%20print%28%22%E7%B7%9A%E5%BD%A2%E6%99%82%E9%96%93%E3%81%AE%E6%93%8D%E4%BD%9C%E5%9B%9E%E6%95%B0%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>配列走査や連結リスト走査などの操作の時間計算量はいずれも <span class="arithmatex">\(O(n)\)</span> であり、ここでの <span class="arithmatex">\(n\)</span> は配列または連結リストの長さです：</p>
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 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">array_traversal</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-74-2" name="__codelineno-74-2" href="#__codelineno-74-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;線形複雑度（配列の走査）&quot;&quot;&quot;</span>
-<a id="__codelineno-74-3" name="__codelineno-74-3" href="#__codelineno-74-3"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
-<a id="__codelineno-74-4" name="__codelineno-74-4" href="#__codelineno-74-4"></a>    <span class="c1"># ループ回数は配列の長さに比例する</span>
-<a id="__codelineno-74-5" name="__codelineno-74-5" href="#__codelineno-74-5"></a>    <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">nums</span><span class="p">:</span>
-<a id="__codelineno-74-6" name="__codelineno-74-6" href="#__codelineno-74-6"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
-<a id="__codelineno-74-7" name="__codelineno-74-7" href="#__codelineno-74-7"></a>    <span class="k">return</span> <span class="n">count</span>
+<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-78-1" name="__codelineno-78-1" href="#__codelineno-78-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">array_traversal</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-78-2" name="__codelineno-78-2" href="#__codelineno-78-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;線形時間（配列を走査）&quot;&quot;&quot;</span>
+<a id="__codelineno-78-3" name="__codelineno-78-3" href="#__codelineno-78-3"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-78-4" name="__codelineno-78-4" href="#__codelineno-78-4"></a>    <span class="c1"># ループ回数は配列長に比例する</span>
+<a id="__codelineno-78-5" name="__codelineno-78-5" href="#__codelineno-78-5"></a>    <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">nums</span><span class="p">:</span>
+<a id="__codelineno-78-6" name="__codelineno-78-6" href="#__codelineno-78-6"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-78-7" name="__codelineno-78-7" href="#__codelineno-78-7"></a>    <span class="k">return</span> <span class="n">count</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="cm">/* 線形計算量（配列の走査） */</span>
-<a id="__codelineno-75-2" name="__codelineno-75-2" href="#__codelineno-75-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">arrayTraversal</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-75-3" name="__codelineno-75-3" href="#__codelineno-75-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-75-4" name="__codelineno-75-4" href="#__codelineno-75-4"></a><span class="w">    </span><span class="c1">// ループ回数は配列の長さに比例</span>
-<a id="__codelineno-75-5" name="__codelineno-75-5" href="#__codelineno-75-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-75-6" name="__codelineno-75-6" href="#__codelineno-75-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-75-7" name="__codelineno-75-7" href="#__codelineno-75-7"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-75-8" name="__codelineno-75-8" href="#__codelineno-75-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
-<a id="__codelineno-75-9" name="__codelineno-75-9" href="#__codelineno-75-9"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-79-1" name="__codelineno-79-1" href="#__codelineno-79-1"></a><span class="cm">/* 線形時間（配列を走査） */</span>
+<a id="__codelineno-79-2" name="__codelineno-79-2" href="#__codelineno-79-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">arrayTraversal</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-3" name="__codelineno-79-3" href="#__codelineno-79-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-79-4" name="__codelineno-79-4" href="#__codelineno-79-4"></a><span class="w">    </span><span class="c1">// ループ回数は配列長に比例する</span>
+<a id="__codelineno-79-5" name="__codelineno-79-5" href="#__codelineno-79-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-6" name="__codelineno-79-6" href="#__codelineno-79-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-79-7" name="__codelineno-79-7" href="#__codelineno-79-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-79-8" name="__codelineno-79-8" href="#__codelineno-79-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-79-9" name="__codelineno-79-9" href="#__codelineno-79-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="cm">/* 線形計算量（配列の走査） */</span>
-<a id="__codelineno-76-2" name="__codelineno-76-2" href="#__codelineno-76-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">arrayTraversal</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-76-3" name="__codelineno-76-3" href="#__codelineno-76-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-76-4" name="__codelineno-76-4" href="#__codelineno-76-4"></a><span class="w">    </span><span class="c1">// ループ回数は配列の長さに比例</span>
-<a id="__codelineno-76-5" name="__codelineno-76-5" href="#__codelineno-76-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-76-6" name="__codelineno-76-6" href="#__codelineno-76-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-76-7" name="__codelineno-76-7" href="#__codelineno-76-7"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-76-8" name="__codelineno-76-8" href="#__codelineno-76-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
-<a id="__codelineno-76-9" name="__codelineno-76-9" href="#__codelineno-76-9"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-80-1" name="__codelineno-80-1" href="#__codelineno-80-1"></a><span class="cm">/* 線形時間（配列を走査） */</span>
+<a id="__codelineno-80-2" name="__codelineno-80-2" href="#__codelineno-80-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">arrayTraversal</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-3" name="__codelineno-80-3" href="#__codelineno-80-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-80-4" name="__codelineno-80-4" href="#__codelineno-80-4"></a><span class="w">    </span><span class="c1">// ループ回数は配列長に比例する</span>
+<a id="__codelineno-80-5" name="__codelineno-80-5" href="#__codelineno-80-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-6" name="__codelineno-80-6" href="#__codelineno-80-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-80-7" name="__codelineno-80-7" href="#__codelineno-80-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-80-8" name="__codelineno-80-8" href="#__codelineno-80-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-80-9" name="__codelineno-80-9" href="#__codelineno-80-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">ArrayTraversal</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="cm">/* 線形時間（配列を走査） */</span>
+<a id="__codelineno-81-2" name="__codelineno-81-2" href="#__codelineno-81-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">ArrayTraversal</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-3" name="__codelineno-81-3" href="#__codelineno-81-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-81-4" name="__codelineno-81-4" href="#__codelineno-81-4"></a><span class="w">    </span><span class="c1">// ループ回数は配列長に比例する</span>
+<a id="__codelineno-81-5" name="__codelineno-81-5" href="#__codelineno-81-5"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-6" name="__codelineno-81-6" href="#__codelineno-81-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-81-7" name="__codelineno-81-7" href="#__codelineno-81-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-81-8" name="__codelineno-81-8" href="#__codelineno-81-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-81-9" name="__codelineno-81-9" href="#__codelineno-81-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-78-1" name="__codelineno-78-1" href="#__codelineno-78-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">arrayTraversal</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="cm">/* 線形時間（配列を走査） */</span>
+<a id="__codelineno-82-2" name="__codelineno-82-2" href="#__codelineno-82-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">arrayTraversal</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-3" name="__codelineno-82-3" href="#__codelineno-82-3"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-82-4" name="__codelineno-82-4" href="#__codelineno-82-4"></a><span class="w">    </span><span class="c1">// ループ回数は配列長に比例する</span>
+<a id="__codelineno-82-5" name="__codelineno-82-5" href="#__codelineno-82-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-6" name="__codelineno-82-6" href="#__codelineno-82-6"></a><span class="w">        </span><span class="nx">count</span><span class="o">++</span>
+<a id="__codelineno-82-7" name="__codelineno-82-7" href="#__codelineno-82-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-82-8" name="__codelineno-82-8" href="#__codelineno-82-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
+<a id="__codelineno-82-9" name="__codelineno-82-9" href="#__codelineno-82-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-79-1" name="__codelineno-79-1" href="#__codelineno-79-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">arrayTraversal</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="cm">/* 線形時間（配列を走査） */</span>
+<a id="__codelineno-83-2" name="__codelineno-83-2" href="#__codelineno-83-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">arrayTraversal</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-3" name="__codelineno-83-3" href="#__codelineno-83-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-83-4" name="__codelineno-83-4" href="#__codelineno-83-4"></a><span class="w">    </span><span class="c1">// ループ回数は配列長に比例する</span>
+<a id="__codelineno-83-5" name="__codelineno-83-5" href="#__codelineno-83-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-6" name="__codelineno-83-6" href="#__codelineno-83-6"></a><span class="w">        </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-83-7" name="__codelineno-83-7" href="#__codelineno-83-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-83-8" name="__codelineno-83-8" href="#__codelineno-83-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="bp">count</span>
+<a id="__codelineno-83-9" name="__codelineno-83-9" href="#__codelineno-83-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-80-1" name="__codelineno-80-1" href="#__codelineno-80-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">arrayTraversal</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-84-1" name="__codelineno-84-1" href="#__codelineno-84-1"></a><span class="cm">/* 線形時間（配列を走査） */</span>
+<a id="__codelineno-84-2" name="__codelineno-84-2" href="#__codelineno-84-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">arrayTraversal</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-3" name="__codelineno-84-3" href="#__codelineno-84-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-84-4" name="__codelineno-84-4" href="#__codelineno-84-4"></a><span class="w">    </span><span class="c1">// ループ回数は配列長に比例する</span>
+<a id="__codelineno-84-5" name="__codelineno-84-5" href="#__codelineno-84-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-6" name="__codelineno-84-6" href="#__codelineno-84-6"></a><span class="w">        </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-84-7" name="__codelineno-84-7" href="#__codelineno-84-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-84-8" name="__codelineno-84-8" href="#__codelineno-84-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
+<a id="__codelineno-84-9" name="__codelineno-84-9" href="#__codelineno-84-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">arrayTraversal</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="cm">/* 線形時間（配列を走査） */</span>
+<a id="__codelineno-85-2" name="__codelineno-85-2" href="#__codelineno-85-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">arrayTraversal</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-3" name="__codelineno-85-3" href="#__codelineno-85-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-85-4" name="__codelineno-85-4" href="#__codelineno-85-4"></a><span class="w">    </span><span class="c1">// ループ回数は配列長に比例する</span>
+<a id="__codelineno-85-5" name="__codelineno-85-5" href="#__codelineno-85-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-6" name="__codelineno-85-6" href="#__codelineno-85-6"></a><span class="w">        </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-85-7" name="__codelineno-85-7" href="#__codelineno-85-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-85-8" name="__codelineno-85-8" href="#__codelineno-85-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
+<a id="__codelineno-85-9" name="__codelineno-85-9" href="#__codelineno-85-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">arrayTraversal</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="cm">/* 線形時間（配列を走査） */</span>
+<a id="__codelineno-86-2" name="__codelineno-86-2" href="#__codelineno-86-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">arrayTraversal</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-3" name="__codelineno-86-3" href="#__codelineno-86-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-86-4" name="__codelineno-86-4" href="#__codelineno-86-4"></a><span class="w">  </span><span class="c1">// ループ回数は配列長に比例する</span>
+<a id="__codelineno-86-5" name="__codelineno-86-5" href="#__codelineno-86-5"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">_num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-6" name="__codelineno-86-6" href="#__codelineno-86-6"></a><span class="w">    </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-86-7" name="__codelineno-86-7" href="#__codelineno-86-7"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-86-8" name="__codelineno-86-8" href="#__codelineno-86-8"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-86-9" name="__codelineno-86-9" href="#__codelineno-86-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">array_traversal</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-87-1" name="__codelineno-87-1" href="#__codelineno-87-1"></a><span class="cm">/* 線形時間（配列を走査） */</span>
+<a id="__codelineno-87-2" name="__codelineno-87-2" href="#__codelineno-87-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">array_traversal</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-3" name="__codelineno-87-3" href="#__codelineno-87-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-87-4" name="__codelineno-87-4" href="#__codelineno-87-4"></a><span class="w">    </span><span class="c1">// ループ回数は配列長に比例する</span>
+<a id="__codelineno-87-5" name="__codelineno-87-5" href="#__codelineno-87-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-6" name="__codelineno-87-6" href="#__codelineno-87-6"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-87-7" name="__codelineno-87-7" href="#__codelineno-87-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-87-8" name="__codelineno-87-8" href="#__codelineno-87-8"></a><span class="w">    </span><span class="n">count</span>
+<a id="__codelineno-87-9" name="__codelineno-87-9" href="#__codelineno-87-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-84-1" name="__codelineno-84-1" href="#__codelineno-84-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">arrayTraversal</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-88-1" name="__codelineno-88-1" href="#__codelineno-88-1"></a><span class="cm">/* 線形時間（配列を走査） */</span>
+<a id="__codelineno-88-2" name="__codelineno-88-2" href="#__codelineno-88-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">arrayTraversal</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-3" name="__codelineno-88-3" href="#__codelineno-88-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-88-4" name="__codelineno-88-4" href="#__codelineno-88-4"></a><span class="w">    </span><span class="c1">// ループ回数は配列長に比例する</span>
+<a id="__codelineno-88-5" name="__codelineno-88-5" href="#__codelineno-88-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-6" name="__codelineno-88-6" href="#__codelineno-88-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-88-7" name="__codelineno-88-7" href="#__codelineno-88-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-88-8" name="__codelineno-88-8" href="#__codelineno-88-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-88-9" name="__codelineno-88-9" href="#__codelineno-88-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">arrayTraversal</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-89-1" name="__codelineno-89-1" href="#__codelineno-89-1"></a><span class="cm">/* 線形時間（配列を走査） */</span>
+<a id="__codelineno-89-2" name="__codelineno-89-2" href="#__codelineno-89-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">arrayTraversal</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-89-3" name="__codelineno-89-3" href="#__codelineno-89-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-89-4" name="__codelineno-89-4" href="#__codelineno-89-4"></a><span class="w">    </span><span class="c1">// ループ回数は配列長に比例する</span>
+<a id="__codelineno-89-5" name="__codelineno-89-5" href="#__codelineno-89-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-89-6" name="__codelineno-89-6" href="#__codelineno-89-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span>
+<a id="__codelineno-89-7" name="__codelineno-89-7" href="#__codelineno-89-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-89-8" name="__codelineno-89-8" href="#__codelineno-89-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
+<a id="__codelineno-89-9" name="__codelineno-89-9" href="#__codelineno-89-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">array_traversal</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-90-1" name="__codelineno-90-1" href="#__codelineno-90-1"></a><span class="c1">### 線形階 ###</span>
+<a id="__codelineno-90-2" name="__codelineno-90-2" href="#__codelineno-90-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-90-3" name="__codelineno-90-3" href="#__codelineno-90-3"></a><span class="w">  </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-90-4" name="__codelineno-90-4" href="#__codelineno-90-4"></a><span class="w">  </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-90-5" name="__codelineno-90-5" href="#__codelineno-90-5"></a><span class="w">  </span><span class="n">count</span>
+<a id="__codelineno-90-6" name="__codelineno-90-6" href="#__codelineno-90-6"></a><span class="k">end</span>
+<a id="__codelineno-90-7" name="__codelineno-90-7" href="#__codelineno-90-7"></a>
+<a id="__codelineno-90-8" name="__codelineno-90-8" href="#__codelineno-90-8"></a><span class="c1"># ## 線形階（配列を走査）###</span>
+<a id="__codelineno-90-9" name="__codelineno-90-9" href="#__codelineno-90-9"></a><span class="k">def</span><span class="w"> </span><span class="nf">array_traversal</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-90-10" name="__codelineno-90-10" href="#__codelineno-90-10"></a><span class="w">  </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-90-11" name="__codelineno-90-11" href="#__codelineno-90-11"></a>
+<a id="__codelineno-90-12" name="__codelineno-90-12" href="#__codelineno-90-12"></a><span class="w">  </span><span class="c1"># ループ回数は配列長に比例する</span>
+<a id="__codelineno-90-13" name="__codelineno-90-13" href="#__codelineno-90-13"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span>
+<a id="__codelineno-90-14" name="__codelineno-90-14" href="#__codelineno-90-14"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-90-15" name="__codelineno-90-15" href="#__codelineno-90-15"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-90-16" name="__codelineno-90-16" href="#__codelineno-90-16"></a>
+<a id="__codelineno-90-17" name="__codelineno-90-17" href="#__codelineno-90-17"></a><span class="w">  </span><span class="n">count</span>
+<a id="__codelineno-90-18" name="__codelineno-90-18" href="#__codelineno-90-18"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p><strong>入力データサイズ<span class="arithmatex">\(n\)</span>は入力データの種類に基づいて決定する必要があります</strong>。例えば、最初の例では、<span class="arithmatex">\(n\)</span>は入力データサイズを表し、2番目の例では、配列の長さ<span class="arithmatex">\(n\)</span>がデータサイズです。</p>
-<h3 id="3-on2">3. &nbsp; 二次オーダー <span class="arithmatex">\(O(n^2)\)</span><a class="headerlink" href="#3-on2" title="Permanent link">&para;</a></h3>
-<p>二次オーダーは、操作数が入力データサイズ<span class="arithmatex">\(n\)</span>の二乗に比例して増加することを意味します。二次オーダーは通常ネストしたループで現れ、外側と内側のループの両方が時間計算量<span class="arithmatex">\(O(n)\)</span>を持ち、全体の複雑度は<span class="arithmatex">\(O(n^2)\)</span>になります：</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 441px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20array_traversal%28nums%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%B7%9A%E5%BD%A2%E6%99%82%E9%96%93%EF%BC%88%E9%85%8D%E5%88%97%E3%82%92%E8%B5%B0%E6%9F%BB%EF%BC%89%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%97%E5%9B%9E%E6%95%B0%E3%81%AF%E9%85%8D%E5%88%97%E9%95%B7%E3%81%AB%E6%AF%94%E4%BE%8B%E3%81%99%E3%82%8B%0A%20%20%20%20for%20num%20in%20nums%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20array_traversal%28%5B0%5D%20%2A%20n%29%0A%20%20%20%20print%28%22%E7%B7%9A%E5%BD%A2%E6%99%82%E9%96%93%EF%BC%88%E9%85%8D%E5%88%97%E8%B5%B0%E6%9F%BB%EF%BC%89%E3%81%AE%E6%93%8D%E4%BD%9C%E5%9B%9E%E6%95%B0%20%3D%22%2C%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20array_traversal%28nums%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%B7%9A%E5%BD%A2%E6%99%82%E9%96%93%EF%BC%88%E9%85%8D%E5%88%97%E3%82%92%E8%B5%B0%E6%9F%BB%EF%BC%89%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%97%E5%9B%9E%E6%95%B0%E3%81%AF%E9%85%8D%E5%88%97%E9%95%B7%E3%81%AB%E6%AF%94%E4%BE%8B%E3%81%99%E3%82%8B%0A%20%20%20%20for%20num%20in%20nums%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20array_traversal%28%5B0%5D%20%2A%20n%29%0A%20%20%20%20print%28%22%E7%B7%9A%E5%BD%A2%E6%99%82%E9%96%93%EF%BC%88%E9%85%8D%E5%88%97%E8%B5%B0%E6%9F%BB%EF%BC%89%E3%81%AE%E6%93%8D%E4%BD%9C%E5%9B%9E%E6%95%B0%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>注意すべきなのは、**入力データサイズ <span class="arithmatex">\(n\)</span> は入力データの型に応じて具体的に定める必要がある**ということです。例えば 1 つ目の例では変数 <span class="arithmatex">\(n\)</span> が入力データサイズであり、2 つ目の例では配列長 <span class="arithmatex">\(n\)</span> がデータサイズです。</p>
+<h3 id="3-on2">3. &nbsp; 平方階 <span class="arithmatex">\(O(n^2)\)</span><a class="headerlink" href="#3-on2" title="Permanent link">&para;</a></h3>
+<p>平方階の操作回数は入力データサイズ <span class="arithmatex">\(n\)</span> に対して二乗のオーダーで増加します。平方階は通常、入れ子ループに現れ、外側のループと内側のループの時間計算量がともに <span class="arithmatex">\(O(n)\)</span> であるため、全体の時間計算量は <span class="arithmatex">\(O(n^2)\)</span> になります：</p>
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 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-87-1" name="__codelineno-87-1" href="#__codelineno-87-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-87-2" name="__codelineno-87-2" href="#__codelineno-87-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二次複雑度&quot;&quot;&quot;</span>
-<a id="__codelineno-87-3" name="__codelineno-87-3" href="#__codelineno-87-3"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
-<a id="__codelineno-87-4" name="__codelineno-87-4" href="#__codelineno-87-4"></a>    <span class="c1"># ループ回数はデータサイズnの二乗に比例する</span>
-<a id="__codelineno-87-5" name="__codelineno-87-5" href="#__codelineno-87-5"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
-<a id="__codelineno-87-6" name="__codelineno-87-6" href="#__codelineno-87-6"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
-<a id="__codelineno-87-7" name="__codelineno-87-7" href="#__codelineno-87-7"></a>            <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
-<a id="__codelineno-87-8" name="__codelineno-87-8" href="#__codelineno-87-8"></a>    <span class="k">return</span> <span class="n">count</span>
+<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-91-1" name="__codelineno-91-1" href="#__codelineno-91-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-91-2" name="__codelineno-91-2" href="#__codelineno-91-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二乗階&quot;&quot;&quot;</span>
+<a id="__codelineno-91-3" name="__codelineno-91-3" href="#__codelineno-91-3"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-91-4" name="__codelineno-91-4" href="#__codelineno-91-4"></a>    <span class="c1"># ループ回数はデータサイズ n の二乗に比例する</span>
+<a id="__codelineno-91-5" name="__codelineno-91-5" href="#__codelineno-91-5"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-91-6" name="__codelineno-91-6" href="#__codelineno-91-6"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-91-7" name="__codelineno-91-7" href="#__codelineno-91-7"></a>            <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-91-8" name="__codelineno-91-8" href="#__codelineno-91-8"></a>    <span class="k">return</span> <span class="n">count</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-88-1" name="__codelineno-88-1" href="#__codelineno-88-1"></a><span class="cm">/* 二次計算量 */</span>
-<a id="__codelineno-88-2" name="__codelineno-88-2" href="#__codelineno-88-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-88-3" name="__codelineno-88-3" href="#__codelineno-88-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-88-4" name="__codelineno-88-4" href="#__codelineno-88-4"></a><span class="w">    </span><span class="c1">// ループ回数はデータサイズ n の二乗に比例</span>
-<a id="__codelineno-88-5" name="__codelineno-88-5" href="#__codelineno-88-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-88-6" name="__codelineno-88-6" href="#__codelineno-88-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-88-7" name="__codelineno-88-7" href="#__codelineno-88-7"></a><span class="w">            </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-88-8" name="__codelineno-88-8" href="#__codelineno-88-8"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-88-9" name="__codelineno-88-9" href="#__codelineno-88-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-88-10" name="__codelineno-88-10" href="#__codelineno-88-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
-<a id="__codelineno-88-11" name="__codelineno-88-11" href="#__codelineno-88-11"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-92-1" name="__codelineno-92-1" href="#__codelineno-92-1"></a><span class="cm">/* 二乗階 */</span>
+<a id="__codelineno-92-2" name="__codelineno-92-2" href="#__codelineno-92-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-92-3" name="__codelineno-92-3" href="#__codelineno-92-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-92-4" name="__codelineno-92-4" href="#__codelineno-92-4"></a><span class="w">    </span><span class="c1">// ループ回数はデータサイズ n の二乗に比例する</span>
+<a id="__codelineno-92-5" name="__codelineno-92-5" href="#__codelineno-92-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-92-6" name="__codelineno-92-6" href="#__codelineno-92-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-92-7" name="__codelineno-92-7" href="#__codelineno-92-7"></a><span class="w">            </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-92-8" name="__codelineno-92-8" href="#__codelineno-92-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-92-9" name="__codelineno-92-9" href="#__codelineno-92-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-92-10" name="__codelineno-92-10" href="#__codelineno-92-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-92-11" name="__codelineno-92-11" href="#__codelineno-92-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-89-1" name="__codelineno-89-1" href="#__codelineno-89-1"></a><span class="cm">/* 二次計算量 */</span>
-<a id="__codelineno-89-2" name="__codelineno-89-2" href="#__codelineno-89-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-89-3" name="__codelineno-89-3" href="#__codelineno-89-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-89-4" name="__codelineno-89-4" href="#__codelineno-89-4"></a><span class="w">    </span><span class="c1">// ループ回数はデータサイズ n の二乗に比例</span>
-<a id="__codelineno-89-5" name="__codelineno-89-5" href="#__codelineno-89-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-89-6" name="__codelineno-89-6" href="#__codelineno-89-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-89-7" name="__codelineno-89-7" href="#__codelineno-89-7"></a><span class="w">            </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-89-8" name="__codelineno-89-8" href="#__codelineno-89-8"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-89-9" name="__codelineno-89-9" href="#__codelineno-89-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-89-10" name="__codelineno-89-10" href="#__codelineno-89-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
-<a id="__codelineno-89-11" name="__codelineno-89-11" href="#__codelineno-89-11"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-93-1" name="__codelineno-93-1" href="#__codelineno-93-1"></a><span class="cm">/* 二乗階 */</span>
+<a id="__codelineno-93-2" name="__codelineno-93-2" href="#__codelineno-93-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-93-3" name="__codelineno-93-3" href="#__codelineno-93-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-93-4" name="__codelineno-93-4" href="#__codelineno-93-4"></a><span class="w">    </span><span class="c1">// ループ回数はデータサイズ n の二乗に比例する</span>
+<a id="__codelineno-93-5" name="__codelineno-93-5" href="#__codelineno-93-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-93-6" name="__codelineno-93-6" href="#__codelineno-93-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-93-7" name="__codelineno-93-7" href="#__codelineno-93-7"></a><span class="w">            </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-93-8" name="__codelineno-93-8" href="#__codelineno-93-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-93-9" name="__codelineno-93-9" href="#__codelineno-93-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-93-10" name="__codelineno-93-10" href="#__codelineno-93-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-93-11" name="__codelineno-93-11" href="#__codelineno-93-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-90-1" name="__codelineno-90-1" href="#__codelineno-90-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Quadratic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-94-1" name="__codelineno-94-1" href="#__codelineno-94-1"></a><span class="cm">/* 二乗階 */</span>
+<a id="__codelineno-94-2" name="__codelineno-94-2" href="#__codelineno-94-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-94-3" name="__codelineno-94-3" href="#__codelineno-94-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-94-4" name="__codelineno-94-4" href="#__codelineno-94-4"></a><span class="w">    </span><span class="c1">// ループ回数はデータサイズ n の二乗に比例する</span>
+<a id="__codelineno-94-5" name="__codelineno-94-5" href="#__codelineno-94-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-94-6" name="__codelineno-94-6" href="#__codelineno-94-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-94-7" name="__codelineno-94-7" href="#__codelineno-94-7"></a><span class="w">            </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-94-8" name="__codelineno-94-8" href="#__codelineno-94-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-94-9" name="__codelineno-94-9" href="#__codelineno-94-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-94-10" name="__codelineno-94-10" href="#__codelineno-94-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-94-11" name="__codelineno-94-11" href="#__codelineno-94-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-91-1" name="__codelineno-91-1" href="#__codelineno-91-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">quadratic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-95-1" name="__codelineno-95-1" href="#__codelineno-95-1"></a><span class="cm">/* 二乗階 */</span>
+<a id="__codelineno-95-2" name="__codelineno-95-2" href="#__codelineno-95-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">quadratic</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-95-3" name="__codelineno-95-3" href="#__codelineno-95-3"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-95-4" name="__codelineno-95-4" href="#__codelineno-95-4"></a><span class="w">    </span><span class="c1">// ループ回数はデータサイズ n の二乗に比例する</span>
+<a id="__codelineno-95-5" name="__codelineno-95-5" href="#__codelineno-95-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-95-6" name="__codelineno-95-6" href="#__codelineno-95-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-95-7" name="__codelineno-95-7" href="#__codelineno-95-7"></a><span class="w">            </span><span class="nx">count</span><span class="o">++</span>
+<a id="__codelineno-95-8" name="__codelineno-95-8" href="#__codelineno-95-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-95-9" name="__codelineno-95-9" href="#__codelineno-95-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-95-10" name="__codelineno-95-10" href="#__codelineno-95-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
+<a id="__codelineno-95-11" name="__codelineno-95-11" href="#__codelineno-95-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-92-1" name="__codelineno-92-1" href="#__codelineno-92-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">quadratic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-96-1" name="__codelineno-96-1" href="#__codelineno-96-1"></a><span class="cm">/* 二乗階 */</span>
+<a id="__codelineno-96-2" name="__codelineno-96-2" href="#__codelineno-96-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-96-3" name="__codelineno-96-3" href="#__codelineno-96-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-96-4" name="__codelineno-96-4" href="#__codelineno-96-4"></a><span class="w">    </span><span class="c1">// ループ回数はデータサイズ n の二乗に比例する</span>
+<a id="__codelineno-96-5" name="__codelineno-96-5" href="#__codelineno-96-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-96-6" name="__codelineno-96-6" href="#__codelineno-96-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-96-7" name="__codelineno-96-7" href="#__codelineno-96-7"></a><span class="w">            </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-96-8" name="__codelineno-96-8" href="#__codelineno-96-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-96-9" name="__codelineno-96-9" href="#__codelineno-96-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-96-10" name="__codelineno-96-10" href="#__codelineno-96-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="bp">count</span>
+<a id="__codelineno-96-11" name="__codelineno-96-11" href="#__codelineno-96-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-93-1" name="__codelineno-93-1" href="#__codelineno-93-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">quadratic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-97-1" name="__codelineno-97-1" href="#__codelineno-97-1"></a><span class="cm">/* 二乗階 */</span>
+<a id="__codelineno-97-2" name="__codelineno-97-2" href="#__codelineno-97-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">quadratic</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-97-3" name="__codelineno-97-3" href="#__codelineno-97-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-97-4" name="__codelineno-97-4" href="#__codelineno-97-4"></a><span class="w">    </span><span class="c1">// ループ回数はデータサイズ n の二乗に比例する</span>
+<a id="__codelineno-97-5" name="__codelineno-97-5" href="#__codelineno-97-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-97-6" name="__codelineno-97-6" href="#__codelineno-97-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-97-7" name="__codelineno-97-7" href="#__codelineno-97-7"></a><span class="w">            </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-97-8" name="__codelineno-97-8" href="#__codelineno-97-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-97-9" name="__codelineno-97-9" href="#__codelineno-97-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-97-10" name="__codelineno-97-10" href="#__codelineno-97-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
+<a id="__codelineno-97-11" name="__codelineno-97-11" href="#__codelineno-97-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-94-1" name="__codelineno-94-1" href="#__codelineno-94-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">quadratic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-98-1" name="__codelineno-98-1" href="#__codelineno-98-1"></a><span class="cm">/* 二乗階 */</span>
+<a id="__codelineno-98-2" name="__codelineno-98-2" href="#__codelineno-98-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">quadratic</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-98-3" name="__codelineno-98-3" href="#__codelineno-98-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-98-4" name="__codelineno-98-4" href="#__codelineno-98-4"></a><span class="w">    </span><span class="c1">// ループ回数はデータサイズ n の二乗に比例する</span>
+<a id="__codelineno-98-5" name="__codelineno-98-5" href="#__codelineno-98-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-98-6" name="__codelineno-98-6" href="#__codelineno-98-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-98-7" name="__codelineno-98-7" href="#__codelineno-98-7"></a><span class="w">            </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-98-8" name="__codelineno-98-8" href="#__codelineno-98-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-98-9" name="__codelineno-98-9" href="#__codelineno-98-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-98-10" name="__codelineno-98-10" href="#__codelineno-98-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
+<a id="__codelineno-98-11" name="__codelineno-98-11" href="#__codelineno-98-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-95-1" name="__codelineno-95-1" href="#__codelineno-95-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quadratic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-99-1" name="__codelineno-99-1" href="#__codelineno-99-1"></a><span class="cm">/* 二乗階 */</span>
+<a id="__codelineno-99-2" name="__codelineno-99-2" href="#__codelineno-99-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-99-3" name="__codelineno-99-3" href="#__codelineno-99-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-99-4" name="__codelineno-99-4" href="#__codelineno-99-4"></a><span class="w">  </span><span class="c1">// ループ回数はデータサイズ n の二乗に比例する</span>
+<a id="__codelineno-99-5" name="__codelineno-99-5" href="#__codelineno-99-5"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-99-6" name="__codelineno-99-6" href="#__codelineno-99-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-99-7" name="__codelineno-99-7" href="#__codelineno-99-7"></a><span class="w">      </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-99-8" name="__codelineno-99-8" href="#__codelineno-99-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-99-9" name="__codelineno-99-9" href="#__codelineno-99-9"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-99-10" name="__codelineno-99-10" href="#__codelineno-99-10"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-99-11" name="__codelineno-99-11" href="#__codelineno-99-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-96-1" name="__codelineno-96-1" href="#__codelineno-96-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quadratic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-100-1" name="__codelineno-100-1" href="#__codelineno-100-1"></a><span class="cm">/* 二乗階 */</span>
+<a id="__codelineno-100-2" name="__codelineno-100-2" href="#__codelineno-100-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-3" name="__codelineno-100-3" href="#__codelineno-100-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-100-4" name="__codelineno-100-4" href="#__codelineno-100-4"></a><span class="w">    </span><span class="c1">// ループ回数はデータサイズ n の二乗に比例する</span>
+<a id="__codelineno-100-5" name="__codelineno-100-5" href="#__codelineno-100-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-6" name="__codelineno-100-6" href="#__codelineno-100-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-7" name="__codelineno-100-7" href="#__codelineno-100-7"></a><span class="w">            </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-100-8" name="__codelineno-100-8" href="#__codelineno-100-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-100-9" name="__codelineno-100-9" href="#__codelineno-100-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-100-10" name="__codelineno-100-10" href="#__codelineno-100-10"></a><span class="w">    </span><span class="n">count</span>
+<a id="__codelineno-100-11" name="__codelineno-100-11" href="#__codelineno-100-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-97-1" name="__codelineno-97-1" href="#__codelineno-97-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quadratic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-101-1" name="__codelineno-101-1" href="#__codelineno-101-1"></a><span class="cm">/* 二乗階 */</span>
+<a id="__codelineno-101-2" name="__codelineno-101-2" href="#__codelineno-101-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-101-3" name="__codelineno-101-3" href="#__codelineno-101-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-101-4" name="__codelineno-101-4" href="#__codelineno-101-4"></a><span class="w">    </span><span class="c1">// ループ回数はデータサイズ n の二乗に比例する</span>
+<a id="__codelineno-101-5" name="__codelineno-101-5" href="#__codelineno-101-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-101-6" name="__codelineno-101-6" href="#__codelineno-101-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-101-7" name="__codelineno-101-7" href="#__codelineno-101-7"></a><span class="w">            </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-101-8" name="__codelineno-101-8" href="#__codelineno-101-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-101-9" name="__codelineno-101-9" href="#__codelineno-101-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-101-10" name="__codelineno-101-10" href="#__codelineno-101-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-101-11" name="__codelineno-101-11" href="#__codelineno-101-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-98-1" name="__codelineno-98-1" href="#__codelineno-98-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">quadratic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-102-1" name="__codelineno-102-1" href="#__codelineno-102-1"></a><span class="cm">/* 二乗階 */</span>
+<a id="__codelineno-102-2" name="__codelineno-102-2" href="#__codelineno-102-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-102-3" name="__codelineno-102-3" href="#__codelineno-102-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-102-4" name="__codelineno-102-4" href="#__codelineno-102-4"></a><span class="w">    </span><span class="c1">// ループ回数はデータサイズ n の二乗に比例する</span>
+<a id="__codelineno-102-5" name="__codelineno-102-5" href="#__codelineno-102-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-102-6" name="__codelineno-102-6" href="#__codelineno-102-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-102-7" name="__codelineno-102-7" href="#__codelineno-102-7"></a><span class="w">            </span><span class="n">count</span><span class="o">++</span>
+<a id="__codelineno-102-8" name="__codelineno-102-8" href="#__codelineno-102-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-102-9" name="__codelineno-102-9" href="#__codelineno-102-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-102-10" name="__codelineno-102-10" href="#__codelineno-102-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
+<a id="__codelineno-102-11" name="__codelineno-102-11" href="#__codelineno-102-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-99-1" name="__codelineno-99-1" href="#__codelineno-99-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">quadratic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-103-1" name="__codelineno-103-1" href="#__codelineno-103-1"></a><span class="c1">### 平方階 ###</span>
+<a id="__codelineno-103-2" name="__codelineno-103-2" href="#__codelineno-103-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-103-3" name="__codelineno-103-3" href="#__codelineno-103-3"></a><span class="w">  </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-103-4" name="__codelineno-103-4" href="#__codelineno-103-4"></a>
+<a id="__codelineno-103-5" name="__codelineno-103-5" href="#__codelineno-103-5"></a><span class="w">  </span><span class="c1"># ループ回数はデータサイズ n の二乗に比例する</span>
+<a id="__codelineno-103-6" name="__codelineno-103-6" href="#__codelineno-103-6"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
+<a id="__codelineno-103-7" name="__codelineno-103-7" href="#__codelineno-103-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
+<a id="__codelineno-103-8" name="__codelineno-103-8" href="#__codelineno-103-8"></a><span class="w">      </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-103-9" name="__codelineno-103-9" href="#__codelineno-103-9"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-103-10" name="__codelineno-103-10" href="#__codelineno-103-10"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-103-11" name="__codelineno-103-11" href="#__codelineno-103-11"></a>
+<a id="__codelineno-103-12" name="__codelineno-103-12" href="#__codelineno-103-12"></a><span class="w">  </span><span class="n">count</span>
+<a id="__codelineno-103-13" name="__codelineno-103-13" href="#__codelineno-103-13"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>下図は定数オーダー、線形オーダー、二次オーダーの時間計算量を比較しています。</p>
-<p><img alt="Constant, linear, and quadratic order time complexities" class="animation-figure" src="../time_complexity.assets/time_complexity_constant_linear_quadratic.png" /></p>
-<p align="center"> 図 2-10 &nbsp; Constant, linear, and quadratic order time complexities </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 459px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20quadratic%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E4%B9%97%E9%9A%8E%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%97%E5%9B%9E%E6%95%B0%E3%81%AF%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%E3%81%AE%E4%BA%8C%E4%B9%97%E3%81%AB%E6%AF%94%E4%BE%8B%E3%81%99%E3%82%8B%0A%20%20%20%20for%20i%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20quadratic%28n%29%0A%20%20%20%20print%28%22%E4%BA%8C%E4%B9%97%E6%99%82%E9%96%93%E3%81%AE%E6%93%8D%E4%BD%9C%E5%9B%9E%E6%95%B0%20%3D%22%2C%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20quadratic%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E4%B9%97%E9%9A%8E%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%97%E5%9B%9E%E6%95%B0%E3%81%AF%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%E3%81%AE%E4%BA%8C%E4%B9%97%E3%81%AB%E6%AF%94%E4%BE%8B%E3%81%99%E3%82%8B%0A%20%20%20%20for%20i%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20quadratic%28n%29%0A%20%20%20%20print%28%22%E4%BA%8C%E4%B9%97%E6%99%82%E9%96%93%E3%81%AE%E6%93%8D%E4%BD%9C%E5%9B%9E%E6%95%B0%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>以下の図は、定数階・線形階・平方階の 3 種類の時間計算量を比較したものです。</p>
+<p><img alt="定数階、線形階、平方階の時間計算量" class="animation-figure" src="../time_complexity.assets/time_complexity_constant_linear_quadratic.png" /></p>
+<p align="center"> 図 2-10 &nbsp; 定数階、線形階、平方階の時間計算量 </p>
 
-<p>例えば、バブルソートでは、外側のループが<span class="arithmatex">\(n - 1\)</span>回実行され、内側のループが<span class="arithmatex">\(n-1\)</span>、<span class="arithmatex">\(n-2\)</span>、...、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(1\)</span>回実行され、平均<span class="arithmatex">\(n / 2\)</span>回となり、時間計算量は<span class="arithmatex">\(O((n - 1) n / 2) = O(n^2)\)</span>になります：</p>
+<p>バブルソートを例にとると、外側のループは <span class="arithmatex">\(n - 1\)</span> 回実行され、内側のループは <span class="arithmatex">\(n-1\)</span>、<span class="arithmatex">\(n-2\)</span>、<span class="arithmatex">\(\dots\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(1\)</span> 回実行され、平均すると <span class="arithmatex">\(n / 2\)</span> 回です。したがって時間計算量は <span class="arithmatex">\(O((n - 1) n / 2) = O(n^2)\)</span> となります：</p>
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-<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-100-1" name="__codelineno-100-1" href="#__codelineno-100-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-100-2" name="__codelineno-100-2" href="#__codelineno-100-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二次複雑度（バブルソート）&quot;&quot;&quot;</span>
-<a id="__codelineno-100-3" name="__codelineno-100-3" href="#__codelineno-100-3"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># カウンタ</span>
-<a id="__codelineno-100-4" name="__codelineno-100-4" href="#__codelineno-100-4"></a>    <span class="c1"># 外側のループ: 未ソート範囲は [0, i]</span>
-<a id="__codelineno-100-5" name="__codelineno-100-5" href="#__codelineno-100-5"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
-<a id="__codelineno-100-6" name="__codelineno-100-6" href="#__codelineno-100-6"></a>        <span class="c1"># 内側のループ: 未ソート範囲 [0, i] の最大要素を右端にスワップ</span>
-<a id="__codelineno-100-7" name="__codelineno-100-7" href="#__codelineno-100-7"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">i</span><span class="p">):</span>
-<a id="__codelineno-100-8" name="__codelineno-100-8" href="#__codelineno-100-8"></a>            <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]:</span>
-<a id="__codelineno-100-9" name="__codelineno-100-9" href="#__codelineno-100-9"></a>                <span class="c1"># nums[j] と nums[j + 1] をスワップ</span>
-<a id="__codelineno-100-10" name="__codelineno-100-10" href="#__codelineno-100-10"></a>                <span class="n">tmp</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
-<a id="__codelineno-100-11" name="__codelineno-100-11" href="#__codelineno-100-11"></a>                <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span>
-<a id="__codelineno-100-12" name="__codelineno-100-12" href="#__codelineno-100-12"></a>                <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">tmp</span>
-<a id="__codelineno-100-13" name="__codelineno-100-13" href="#__codelineno-100-13"></a>                <span class="n">count</span> <span class="o">+=</span> <span class="mi">3</span>  <span class="c1"># 要素のスワップは3つの個別操作を含む</span>
-<a id="__codelineno-100-14" name="__codelineno-100-14" href="#__codelineno-100-14"></a>    <span class="k">return</span> <span class="n">count</span>
+<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-104-1" name="__codelineno-104-1" href="#__codelineno-104-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-104-2" name="__codelineno-104-2" href="#__codelineno-104-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二次時間（バブルソート）&quot;&quot;&quot;</span>
+<a id="__codelineno-104-3" name="__codelineno-104-3" href="#__codelineno-104-3"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># カウンタ</span>
+<a id="__codelineno-104-4" name="__codelineno-104-4" href="#__codelineno-104-4"></a>    <span class="c1"># 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-104-5" name="__codelineno-104-5" href="#__codelineno-104-5"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-104-6" name="__codelineno-104-6" href="#__codelineno-104-6"></a>        <span class="c1"># 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-104-7" name="__codelineno-104-7" href="#__codelineno-104-7"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">i</span><span class="p">):</span>
+<a id="__codelineno-104-8" name="__codelineno-104-8" href="#__codelineno-104-8"></a>            <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]:</span>
+<a id="__codelineno-104-9" name="__codelineno-104-9" href="#__codelineno-104-9"></a>                <span class="c1"># nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-104-10" name="__codelineno-104-10" href="#__codelineno-104-10"></a>                <span class="n">tmp</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-104-11" name="__codelineno-104-11" href="#__codelineno-104-11"></a>                <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-104-12" name="__codelineno-104-12" href="#__codelineno-104-12"></a>                <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">tmp</span>
+<a id="__codelineno-104-13" name="__codelineno-104-13" href="#__codelineno-104-13"></a>                <span class="n">count</span> <span class="o">+=</span> <span class="mi">3</span>  <span class="c1"># 要素交換には 3 回の単位操作が含まれる</span>
+<a id="__codelineno-104-14" name="__codelineno-104-14" href="#__codelineno-104-14"></a>    <span class="k">return</span> <span class="n">count</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-101-1" name="__codelineno-101-1" href="#__codelineno-101-1"></a><span class="cm">/* 二次計算量（バブルソート） */</span>
-<a id="__codelineno-101-2" name="__codelineno-101-2" href="#__codelineno-101-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">bubbleSort</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-101-3" name="__codelineno-101-3" href="#__codelineno-101-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// カウンター</span>
-<a id="__codelineno-101-4" name="__codelineno-101-4" href="#__codelineno-101-4"></a><span class="w">    </span><span class="c1">// 外側ループ：未ソート範囲は [0, i]</span>
-<a id="__codelineno-101-5" name="__codelineno-101-5" href="#__codelineno-101-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-101-6" name="__codelineno-101-6" href="#__codelineno-101-6"></a><span class="w">        </span><span class="c1">// 内側ループ：未ソート範囲 [0, i] の最大要素を範囲の右端にスワップ</span>
-<a id="__codelineno-101-7" name="__codelineno-101-7" href="#__codelineno-101-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-101-8" name="__codelineno-101-8" href="#__codelineno-101-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-101-9" name="__codelineno-101-9" href="#__codelineno-101-9"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] をスワップ</span>
-<a id="__codelineno-101-10" name="__codelineno-101-10" href="#__codelineno-101-10"></a><span class="w">                </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
-<a id="__codelineno-101-11" name="__codelineno-101-11" href="#__codelineno-101-11"></a><span class="w">                </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
-<a id="__codelineno-101-12" name="__codelineno-101-12" href="#__codelineno-101-12"></a><span class="w">                </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
-<a id="__codelineno-101-13" name="__codelineno-101-13" href="#__codelineno-101-13"></a><span class="w">                </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// 要素のスワップには3つの個別操作が含まれる</span>
-<a id="__codelineno-101-14" name="__codelineno-101-14" href="#__codelineno-101-14"></a><span class="w">            </span><span class="p">}</span>
-<a id="__codelineno-101-15" name="__codelineno-101-15" href="#__codelineno-101-15"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-101-16" name="__codelineno-101-16" href="#__codelineno-101-16"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-101-17" name="__codelineno-101-17" href="#__codelineno-101-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
-<a id="__codelineno-101-18" name="__codelineno-101-18" href="#__codelineno-101-18"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-105-1" name="__codelineno-105-1" href="#__codelineno-105-1"></a><span class="cm">/* 二次時間（バブルソート） */</span>
+<a id="__codelineno-105-2" name="__codelineno-105-2" href="#__codelineno-105-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">bubbleSort</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-105-3" name="__codelineno-105-3" href="#__codelineno-105-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// カウンタ</span>
+<a id="__codelineno-105-4" name="__codelineno-105-4" href="#__codelineno-105-4"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-105-5" name="__codelineno-105-5" href="#__codelineno-105-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-105-6" name="__codelineno-105-6" href="#__codelineno-105-6"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-105-7" name="__codelineno-105-7" href="#__codelineno-105-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-105-8" name="__codelineno-105-8" href="#__codelineno-105-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-105-9" name="__codelineno-105-9" href="#__codelineno-105-9"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-105-10" name="__codelineno-105-10" href="#__codelineno-105-10"></a><span class="w">                </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-105-11" name="__codelineno-105-11" href="#__codelineno-105-11"></a><span class="w">                </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-105-12" name="__codelineno-105-12" href="#__codelineno-105-12"></a><span class="w">                </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-105-13" name="__codelineno-105-13" href="#__codelineno-105-13"></a><span class="w">                </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// 要素交換には 3 回の単位操作が含まれる</span>
+<a id="__codelineno-105-14" name="__codelineno-105-14" href="#__codelineno-105-14"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-105-15" name="__codelineno-105-15" href="#__codelineno-105-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-105-16" name="__codelineno-105-16" href="#__codelineno-105-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-105-17" name="__codelineno-105-17" href="#__codelineno-105-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-105-18" name="__codelineno-105-18" href="#__codelineno-105-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-102-1" name="__codelineno-102-1" href="#__codelineno-102-1"></a><span class="cm">/* 二次計算量（バブルソート） */</span>
-<a id="__codelineno-102-2" name="__codelineno-102-2" href="#__codelineno-102-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">bubbleSort</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-102-3" name="__codelineno-102-3" href="#__codelineno-102-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// カウンター</span>
-<a id="__codelineno-102-4" name="__codelineno-102-4" href="#__codelineno-102-4"></a><span class="w">    </span><span class="c1">// 外側ループ：未ソート範囲は [0, i]</span>
-<a id="__codelineno-102-5" name="__codelineno-102-5" href="#__codelineno-102-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-102-6" name="__codelineno-102-6" href="#__codelineno-102-6"></a><span class="w">        </span><span class="c1">// 内側ループ：未ソート範囲 [0, i] の最大要素を範囲の右端にスワップ</span>
-<a id="__codelineno-102-7" name="__codelineno-102-7" href="#__codelineno-102-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-102-8" name="__codelineno-102-8" href="#__codelineno-102-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-102-9" name="__codelineno-102-9" href="#__codelineno-102-9"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] をスワップ</span>
-<a id="__codelineno-102-10" name="__codelineno-102-10" href="#__codelineno-102-10"></a><span class="w">                </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-102-11" name="__codelineno-102-11" href="#__codelineno-102-11"></a><span class="w">                </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-102-12" name="__codelineno-102-12" href="#__codelineno-102-12"></a><span class="w">                </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
-<a id="__codelineno-102-13" name="__codelineno-102-13" href="#__codelineno-102-13"></a><span class="w">                </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// 要素のスワップには3つの個別操作が含まれる</span>
-<a id="__codelineno-102-14" name="__codelineno-102-14" href="#__codelineno-102-14"></a><span class="w">            </span><span class="p">}</span>
-<a id="__codelineno-102-15" name="__codelineno-102-15" href="#__codelineno-102-15"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-102-16" name="__codelineno-102-16" href="#__codelineno-102-16"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-102-17" name="__codelineno-102-17" href="#__codelineno-102-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
-<a id="__codelineno-102-18" name="__codelineno-102-18" href="#__codelineno-102-18"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-106-1" name="__codelineno-106-1" href="#__codelineno-106-1"></a><span class="cm">/* 二次時間（バブルソート） */</span>
+<a id="__codelineno-106-2" name="__codelineno-106-2" href="#__codelineno-106-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">bubbleSort</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-106-3" name="__codelineno-106-3" href="#__codelineno-106-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// カウンタ</span>
+<a id="__codelineno-106-4" name="__codelineno-106-4" href="#__codelineno-106-4"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-106-5" name="__codelineno-106-5" href="#__codelineno-106-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-106-6" name="__codelineno-106-6" href="#__codelineno-106-6"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-106-7" name="__codelineno-106-7" href="#__codelineno-106-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-106-8" name="__codelineno-106-8" href="#__codelineno-106-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-106-9" name="__codelineno-106-9" href="#__codelineno-106-9"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-106-10" name="__codelineno-106-10" href="#__codelineno-106-10"></a><span class="w">                </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-106-11" name="__codelineno-106-11" href="#__codelineno-106-11"></a><span class="w">                </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-106-12" name="__codelineno-106-12" href="#__codelineno-106-12"></a><span class="w">                </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-106-13" name="__codelineno-106-13" href="#__codelineno-106-13"></a><span class="w">                </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// 要素交換には 3 回の単位操作が含まれる</span>
+<a id="__codelineno-106-14" name="__codelineno-106-14" href="#__codelineno-106-14"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-106-15" name="__codelineno-106-15" href="#__codelineno-106-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-106-16" name="__codelineno-106-16" href="#__codelineno-106-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-106-17" name="__codelineno-106-17" href="#__codelineno-106-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-106-18" name="__codelineno-106-18" href="#__codelineno-106-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-103-1" name="__codelineno-103-1" href="#__codelineno-103-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BubbleSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-107-1" name="__codelineno-107-1" href="#__codelineno-107-1"></a><span class="cm">/* 二次時間（バブルソート） */</span>
+<a id="__codelineno-107-2" name="__codelineno-107-2" href="#__codelineno-107-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">BubbleSort</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-107-3" name="__codelineno-107-3" href="#__codelineno-107-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">  </span><span class="c1">// カウンタ</span>
+<a id="__codelineno-107-4" name="__codelineno-107-4" href="#__codelineno-107-4"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-107-5" name="__codelineno-107-5" href="#__codelineno-107-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-107-6" name="__codelineno-107-6" href="#__codelineno-107-6"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-107-7" name="__codelineno-107-7" href="#__codelineno-107-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-107-8" name="__codelineno-107-8" href="#__codelineno-107-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-107-9" name="__codelineno-107-9" href="#__codelineno-107-9"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-107-10" name="__codelineno-107-10" href="#__codelineno-107-10"></a><span class="w">                </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-107-11" name="__codelineno-107-11" href="#__codelineno-107-11"></a><span class="w">                </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w">  </span><span class="c1">// 要素交換には 3 回の単位操作が含まれる</span>
+<a id="__codelineno-107-12" name="__codelineno-107-12" href="#__codelineno-107-12"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-107-13" name="__codelineno-107-13" href="#__codelineno-107-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-107-14" name="__codelineno-107-14" href="#__codelineno-107-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-107-15" name="__codelineno-107-15" href="#__codelineno-107-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-107-16" name="__codelineno-107-16" href="#__codelineno-107-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-104-1" name="__codelineno-104-1" href="#__codelineno-104-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">bubbleSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-108-1" name="__codelineno-108-1" href="#__codelineno-108-1"></a><span class="cm">/* 二次時間（バブルソート） */</span>
+<a id="__codelineno-108-2" name="__codelineno-108-2" href="#__codelineno-108-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">bubbleSort</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-108-3" name="__codelineno-108-3" href="#__codelineno-108-3"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1">// カウンタ</span>
+<a id="__codelineno-108-4" name="__codelineno-108-4" href="#__codelineno-108-4"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-108-5" name="__codelineno-108-5" href="#__codelineno-108-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-108-6" name="__codelineno-108-6" href="#__codelineno-108-6"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-108-7" name="__codelineno-108-7" href="#__codelineno-108-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-108-8" name="__codelineno-108-8" href="#__codelineno-108-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-108-9" name="__codelineno-108-9" href="#__codelineno-108-9"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-108-10" name="__codelineno-108-10" href="#__codelineno-108-10"></a><span class="w">                </span><span class="nx">tmp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span>
+<a id="__codelineno-108-11" name="__codelineno-108-11" href="#__codelineno-108-11"></a><span class="w">                </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-108-12" name="__codelineno-108-12" href="#__codelineno-108-12"></a><span class="w">                </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">tmp</span>
+<a id="__codelineno-108-13" name="__codelineno-108-13" href="#__codelineno-108-13"></a><span class="w">                </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="c1">// 要素交換には 3 回の単位操作が含まれる</span>
+<a id="__codelineno-108-14" name="__codelineno-108-14" href="#__codelineno-108-14"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-108-15" name="__codelineno-108-15" href="#__codelineno-108-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-108-16" name="__codelineno-108-16" href="#__codelineno-108-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-108-17" name="__codelineno-108-17" href="#__codelineno-108-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
+<a id="__codelineno-108-18" name="__codelineno-108-18" href="#__codelineno-108-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-105-1" name="__codelineno-105-1" href="#__codelineno-105-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">bubbleSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-109-1" name="__codelineno-109-1" href="#__codelineno-109-1"></a><span class="cm">/* 二次時間（バブルソート） */</span>
+<a id="__codelineno-109-2" name="__codelineno-109-2" href="#__codelineno-109-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">bubbleSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-109-3" name="__codelineno-109-3" href="#__codelineno-109-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1">// カウンタ</span>
+<a id="__codelineno-109-4" name="__codelineno-109-4" href="#__codelineno-109-4"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-109-5" name="__codelineno-109-5" href="#__codelineno-109-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="p">.</span><span class="bp">dropFirst</span><span class="p">().</span><span class="n">reversed</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-109-6" name="__codelineno-109-6" href="#__codelineno-109-6"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-109-7" name="__codelineno-109-7" href="#__codelineno-109-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-109-8" name="__codelineno-109-8" href="#__codelineno-109-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-109-9" name="__codelineno-109-9" href="#__codelineno-109-9"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-109-10" name="__codelineno-109-10" href="#__codelineno-109-10"></a><span class="w">                </span><span class="kd">let</span><span class="w"> </span><span class="nv">tmp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-109-11" name="__codelineno-109-11" href="#__codelineno-109-11"></a><span class="w">                </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-109-12" name="__codelineno-109-12" href="#__codelineno-109-12"></a><span class="w">                </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">tmp</span>
+<a id="__codelineno-109-13" name="__codelineno-109-13" href="#__codelineno-109-13"></a><span class="w">                </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="c1">// 要素交換には 3 回の単位操作が含まれる</span>
+<a id="__codelineno-109-14" name="__codelineno-109-14" href="#__codelineno-109-14"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-109-15" name="__codelineno-109-15" href="#__codelineno-109-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-109-16" name="__codelineno-109-16" href="#__codelineno-109-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-109-17" name="__codelineno-109-17" href="#__codelineno-109-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="bp">count</span>
+<a id="__codelineno-109-18" name="__codelineno-109-18" href="#__codelineno-109-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-106-1" name="__codelineno-106-1" href="#__codelineno-106-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">bubbleSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-110-1" name="__codelineno-110-1" href="#__codelineno-110-1"></a><span class="cm">/* 二次時間（バブルソート） */</span>
+<a id="__codelineno-110-2" name="__codelineno-110-2" href="#__codelineno-110-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">bubbleSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-110-3" name="__codelineno-110-3" href="#__codelineno-110-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// カウンタ</span>
+<a id="__codelineno-110-4" name="__codelineno-110-4" href="#__codelineno-110-4"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-110-5" name="__codelineno-110-5" href="#__codelineno-110-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-110-6" name="__codelineno-110-6" href="#__codelineno-110-6"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-110-7" name="__codelineno-110-7" href="#__codelineno-110-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-110-8" name="__codelineno-110-8" href="#__codelineno-110-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-110-9" name="__codelineno-110-9" href="#__codelineno-110-9"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-110-10" name="__codelineno-110-10" href="#__codelineno-110-10"></a><span class="w">                </span><span class="kd">let</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-110-11" name="__codelineno-110-11" href="#__codelineno-110-11"></a><span class="w">                </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-110-12" name="__codelineno-110-12" href="#__codelineno-110-12"></a><span class="w">                </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">;</span>
+<a id="__codelineno-110-13" name="__codelineno-110-13" href="#__codelineno-110-13"></a><span class="w">                </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mf">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// 要素交換には 3 回の単位操作が含まれる</span>
+<a id="__codelineno-110-14" name="__codelineno-110-14" href="#__codelineno-110-14"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-110-15" name="__codelineno-110-15" href="#__codelineno-110-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-110-16" name="__codelineno-110-16" href="#__codelineno-110-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-110-17" name="__codelineno-110-17" href="#__codelineno-110-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
+<a id="__codelineno-110-18" name="__codelineno-110-18" href="#__codelineno-110-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-107-1" name="__codelineno-107-1" href="#__codelineno-107-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">bubbleSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-111-1" name="__codelineno-111-1" href="#__codelineno-111-1"></a><span class="cm">/* 二次時間（バブルソート） */</span>
+<a id="__codelineno-111-2" name="__codelineno-111-2" href="#__codelineno-111-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">bubbleSort</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-111-3" name="__codelineno-111-3" href="#__codelineno-111-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// カウンタ</span>
+<a id="__codelineno-111-4" name="__codelineno-111-4" href="#__codelineno-111-4"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-111-5" name="__codelineno-111-5" href="#__codelineno-111-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-111-6" name="__codelineno-111-6" href="#__codelineno-111-6"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-111-7" name="__codelineno-111-7" href="#__codelineno-111-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-111-8" name="__codelineno-111-8" href="#__codelineno-111-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-111-9" name="__codelineno-111-9" href="#__codelineno-111-9"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-111-10" name="__codelineno-111-10" href="#__codelineno-111-10"></a><span class="w">                </span><span class="kd">let</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-111-11" name="__codelineno-111-11" href="#__codelineno-111-11"></a><span class="w">                </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-111-12" name="__codelineno-111-12" href="#__codelineno-111-12"></a><span class="w">                </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">;</span>
+<a id="__codelineno-111-13" name="__codelineno-111-13" href="#__codelineno-111-13"></a><span class="w">                </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mf">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// 要素交換には 3 回の単位操作が含まれる</span>
+<a id="__codelineno-111-14" name="__codelineno-111-14" href="#__codelineno-111-14"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-111-15" name="__codelineno-111-15" href="#__codelineno-111-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-111-16" name="__codelineno-111-16" href="#__codelineno-111-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-111-17" name="__codelineno-111-17" href="#__codelineno-111-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
+<a id="__codelineno-111-18" name="__codelineno-111-18" href="#__codelineno-111-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-108-1" name="__codelineno-108-1" href="#__codelineno-108-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bubbleSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-112-1" name="__codelineno-112-1" href="#__codelineno-112-1"></a><span class="cm">/* 二次時間（バブルソート） */</span>
+<a id="__codelineno-112-2" name="__codelineno-112-2" href="#__codelineno-112-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">bubbleSort</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-112-3" name="__codelineno-112-3" href="#__codelineno-112-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// カウンタ</span>
+<a id="__codelineno-112-4" name="__codelineno-112-4" href="#__codelineno-112-4"></a><span class="w">  </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-112-5" name="__codelineno-112-5" href="#__codelineno-112-5"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-112-6" name="__codelineno-112-6" href="#__codelineno-112-6"></a><span class="w">    </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-112-7" name="__codelineno-112-7" href="#__codelineno-112-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-112-8" name="__codelineno-112-8" href="#__codelineno-112-8"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-112-9" name="__codelineno-112-9" href="#__codelineno-112-9"></a><span class="w">        </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-112-10" name="__codelineno-112-10" href="#__codelineno-112-10"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-112-11" name="__codelineno-112-11" href="#__codelineno-112-11"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">];</span>
+<a id="__codelineno-112-12" name="__codelineno-112-12" href="#__codelineno-112-12"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-112-13" name="__codelineno-112-13" href="#__codelineno-112-13"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="m">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// 要素交換には 3 回の単位操作が含まれる</span>
+<a id="__codelineno-112-14" name="__codelineno-112-14" href="#__codelineno-112-14"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-112-15" name="__codelineno-112-15" href="#__codelineno-112-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-112-16" name="__codelineno-112-16" href="#__codelineno-112-16"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-112-17" name="__codelineno-112-17" href="#__codelineno-112-17"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-112-18" name="__codelineno-112-18" href="#__codelineno-112-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-109-1" name="__codelineno-109-1" href="#__codelineno-109-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bubble_sort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-113-1" name="__codelineno-113-1" href="#__codelineno-113-1"></a><span class="cm">/* 二次時間（バブルソート） */</span>
+<a id="__codelineno-113-2" name="__codelineno-113-2" href="#__codelineno-113-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-113-3" name="__codelineno-113-3" href="#__codelineno-113-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// カウンタ</span>
+<a id="__codelineno-113-4" name="__codelineno-113-4" href="#__codelineno-113-4"></a>
+<a id="__codelineno-113-5" name="__codelineno-113-5" href="#__codelineno-113-5"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-113-6" name="__codelineno-113-6" href="#__codelineno-113-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">..</span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()).</span><span class="n">rev</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-113-7" name="__codelineno-113-7" href="#__codelineno-113-7"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-113-8" name="__codelineno-113-8" href="#__codelineno-113-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">i</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-113-9" name="__codelineno-113-9" href="#__codelineno-113-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-113-10" name="__codelineno-113-10" href="#__codelineno-113-10"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-113-11" name="__codelineno-113-11" href="#__codelineno-113-11"></a><span class="w">                </span><span class="kd">let</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-113-12" name="__codelineno-113-12" href="#__codelineno-113-12"></a><span class="w">                </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-113-13" name="__codelineno-113-13" href="#__codelineno-113-13"></a><span class="w">                </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-113-14" name="__codelineno-113-14" href="#__codelineno-113-14"></a><span class="w">                </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// 要素交換には 3 回の単位操作が含まれる</span>
+<a id="__codelineno-113-15" name="__codelineno-113-15" href="#__codelineno-113-15"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-113-16" name="__codelineno-113-16" href="#__codelineno-113-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-113-17" name="__codelineno-113-17" href="#__codelineno-113-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-113-18" name="__codelineno-113-18" href="#__codelineno-113-18"></a><span class="w">    </span><span class="n">count</span>
+<a id="__codelineno-113-19" name="__codelineno-113-19" href="#__codelineno-113-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-110-1" name="__codelineno-110-1" href="#__codelineno-110-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bubbleSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-114-1" name="__codelineno-114-1" href="#__codelineno-114-1"></a><span class="cm">/* 二次時間（バブルソート） */</span>
+<a id="__codelineno-114-2" name="__codelineno-114-2" href="#__codelineno-114-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">bubbleSort</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-114-3" name="__codelineno-114-3" href="#__codelineno-114-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// カウンタ</span>
+<a id="__codelineno-114-4" name="__codelineno-114-4" href="#__codelineno-114-4"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-114-5" name="__codelineno-114-5" href="#__codelineno-114-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-114-6" name="__codelineno-114-6" href="#__codelineno-114-6"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-114-7" name="__codelineno-114-7" href="#__codelineno-114-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-114-8" name="__codelineno-114-8" href="#__codelineno-114-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-114-9" name="__codelineno-114-9" href="#__codelineno-114-9"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-114-10" name="__codelineno-114-10" href="#__codelineno-114-10"></a><span class="w">                </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-114-11" name="__codelineno-114-11" href="#__codelineno-114-11"></a><span class="w">                </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-114-12" name="__codelineno-114-12" href="#__codelineno-114-12"></a><span class="w">                </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-114-13" name="__codelineno-114-13" href="#__codelineno-114-13"></a><span class="w">                </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// 要素交換には 3 回の単位操作が含まれる</span>
+<a id="__codelineno-114-14" name="__codelineno-114-14" href="#__codelineno-114-14"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-114-15" name="__codelineno-114-15" href="#__codelineno-114-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-114-16" name="__codelineno-114-16" href="#__codelineno-114-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-114-17" name="__codelineno-114-17" href="#__codelineno-114-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-114-18" name="__codelineno-114-18" href="#__codelineno-114-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-111-1" name="__codelineno-111-1" href="#__codelineno-111-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">bubbleSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-115-1" name="__codelineno-115-1" href="#__codelineno-115-1"></a><span class="cm">/* 二次時間（バブルソート） */</span>
+<a id="__codelineno-115-2" name="__codelineno-115-2" href="#__codelineno-115-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">bubbleSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-115-3" name="__codelineno-115-3" href="#__codelineno-115-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="c1">// カウンタ</span>
+<a id="__codelineno-115-4" name="__codelineno-115-4" href="#__codelineno-115-4"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-115-5" name="__codelineno-115-5" href="#__codelineno-115-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="n">downTo</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-115-6" name="__codelineno-115-6" href="#__codelineno-115-6"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-115-7" name="__codelineno-115-7" href="#__codelineno-115-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-115-8" name="__codelineno-115-8" href="#__codelineno-115-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-115-9" name="__codelineno-115-9" href="#__codelineno-115-9"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-115-10" name="__codelineno-115-10" href="#__codelineno-115-10"></a><span class="w">                </span><span class="kd">val</span><span class="w"> </span><span class="nv">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-115-11" name="__codelineno-115-11" href="#__codelineno-115-11"></a><span class="w">                </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="o">]</span>
+<a id="__codelineno-115-12" name="__codelineno-115-12" href="#__codelineno-115-12"></a><span class="w">                </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span>
+<a id="__codelineno-115-13" name="__codelineno-115-13" href="#__codelineno-115-13"></a><span class="w">                </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="m">3</span><span class="w"> </span><span class="c1">// 要素交換には 3 回の単位操作が含まれる</span>
+<a id="__codelineno-115-14" name="__codelineno-115-14" href="#__codelineno-115-14"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-115-15" name="__codelineno-115-15" href="#__codelineno-115-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-115-16" name="__codelineno-115-16" href="#__codelineno-115-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-115-17" name="__codelineno-115-17" href="#__codelineno-115-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
+<a id="__codelineno-115-18" name="__codelineno-115-18" href="#__codelineno-115-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-112-1" name="__codelineno-112-1" href="#__codelineno-112-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">bubble_sort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-116-1" name="__codelineno-116-1" href="#__codelineno-116-1"></a><span class="c1">### 平方階 ###</span>
+<a id="__codelineno-116-2" name="__codelineno-116-2" href="#__codelineno-116-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-116-3" name="__codelineno-116-3" href="#__codelineno-116-3"></a><span class="w">  </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-116-4" name="__codelineno-116-4" href="#__codelineno-116-4"></a>
+<a id="__codelineno-116-5" name="__codelineno-116-5" href="#__codelineno-116-5"></a><span class="w">  </span><span class="c1"># ループ回数はデータサイズ n の二乗に比例する</span>
+<a id="__codelineno-116-6" name="__codelineno-116-6" href="#__codelineno-116-6"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
+<a id="__codelineno-116-7" name="__codelineno-116-7" href="#__codelineno-116-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
+<a id="__codelineno-116-8" name="__codelineno-116-8" href="#__codelineno-116-8"></a><span class="w">      </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-116-9" name="__codelineno-116-9" href="#__codelineno-116-9"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-116-10" name="__codelineno-116-10" href="#__codelineno-116-10"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-116-11" name="__codelineno-116-11" href="#__codelineno-116-11"></a>
+<a id="__codelineno-116-12" name="__codelineno-116-12" href="#__codelineno-116-12"></a><span class="w">  </span><span class="n">count</span>
+<a id="__codelineno-116-13" name="__codelineno-116-13" href="#__codelineno-116-13"></a><span class="k">end</span>
+<a id="__codelineno-116-14" name="__codelineno-116-14" href="#__codelineno-116-14"></a>
+<a id="__codelineno-116-15" name="__codelineno-116-15" href="#__codelineno-116-15"></a><span class="c1"># ## 平方階（バブルソート）###</span>
+<a id="__codelineno-116-16" name="__codelineno-116-16" href="#__codelineno-116-16"></a><span class="k">def</span><span class="w"> </span><span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-116-17" name="__codelineno-116-17" href="#__codelineno-116-17"></a><span class="w">  </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w">  </span><span class="c1"># カウンタ</span>
+<a id="__codelineno-116-18" name="__codelineno-116-18" href="#__codelineno-116-18"></a>
+<a id="__codelineno-116-19" name="__codelineno-116-19" href="#__codelineno-116-19"></a><span class="w">  </span><span class="c1"># 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-116-20" name="__codelineno-116-20" href="#__codelineno-116-20"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-116-21" name="__codelineno-116-21" href="#__codelineno-116-21"></a><span class="w">    </span><span class="c1"># 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-116-22" name="__codelineno-116-22" href="#__codelineno-116-22"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">i</span>
+<a id="__codelineno-116-23" name="__codelineno-116-23" href="#__codelineno-116-23"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
+<a id="__codelineno-116-24" name="__codelineno-116-24" href="#__codelineno-116-24"></a><span class="w">        </span><span class="c1"># nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-116-25" name="__codelineno-116-25" href="#__codelineno-116-25"></a><span class="w">        </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-116-26" name="__codelineno-116-26" href="#__codelineno-116-26"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
+<a id="__codelineno-116-27" name="__codelineno-116-27" href="#__codelineno-116-27"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span>
+<a id="__codelineno-116-28" name="__codelineno-116-28" href="#__codelineno-116-28"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="c1"># 要素交換には 3 回の単位操作が含まれる</span>
+<a id="__codelineno-116-29" name="__codelineno-116-29" href="#__codelineno-116-29"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-116-30" name="__codelineno-116-30" href="#__codelineno-116-30"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-116-31" name="__codelineno-116-31" href="#__codelineno-116-31"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-116-32" name="__codelineno-116-32" href="#__codelineno-116-32"></a>
+<a id="__codelineno-116-33" name="__codelineno-116-33" href="#__codelineno-116-33"></a><span class="w">  </span><span class="n">count</span>
+<a id="__codelineno-116-34" name="__codelineno-116-34" href="#__codelineno-116-34"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h3 id="4-o2n">4. &nbsp; 指数オーダー <span class="arithmatex">\(O(2^n)\)</span><a class="headerlink" href="#4-o2n" title="Permanent link">&para;</a></h3>
-<p>生物学的「細胞分裂」は指数オーダー増加の典型例です：1つの細胞から始まり、1回の分裂後に2つ、2回の分裂後に4つとなり、<span class="arithmatex">\(n\)</span>回の分裂後に<span class="arithmatex">\(2^n\)</span>個の細胞になります。</p>
-<p>下図とコードは細胞分裂プロセスをシミュレートし、時間計算量は<span class="arithmatex">\(O(2^n)\)</span>です：</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20bubble_sort%28nums%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E6%AC%A1%E6%99%82%E9%96%93%EF%BC%88%E3%83%90%E3%83%96%E3%83%AB%E3%82%BD%E3%83%BC%E3%83%88%EF%BC%89%22%22%22%0A%20%20%20%20count%20%3D%200%20%20%23%20%E3%82%AB%E3%82%A6%E3%83%B3%E3%82%BF%0A%20%20%20%20%23%20%E5%A4%96%E5%81%B4%E3%81%AE%E3%83%AB%E3%83%BC%E3%83%97%EF%BC%9A%E6%9C%AA%E3%82%BD%E3%83%BC%E3%83%88%E5%8C%BA%E9%96%93%E3%81%AF%20%5B0%2C%20i%5D%0A%20%20%20%20for%20i%20in%20range%28len%28nums%29%20-%201%2C%200%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E5%86%85%E5%81%B4%E3%81%AE%E3%83%AB%E3%83%BC%E3%83%97%EF%BC%9A%E6%9C%AA%E3%82%BD%E3%83%BC%E3%83%88%E5%8C%BA%E9%96%93%20%5B0%2C%20i%5D%20%E3%81%AE%E6%9C%80%E5%A4%A7%E8%A6%81%E7%B4%A0%E3%82%92%E3%81%9D%E3%81%AE%E5%8C%BA%E9%96%93%E3%81%AE%E6%9C%80%E5%8F%B3%E7%AB%AF%E3%81%B8%E4%BA%A4%E6%8F%9B%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28i%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20nums%5Bj%5D%20%3E%20nums%5Bj%20%2B%201%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20nums%5Bj%5D%20%E3%81%A8%20nums%5Bj%20%2B%201%5D%20%E3%82%92%E4%BA%A4%E6%8F%9B%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20tmp%20%3D%20nums%5Bj%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20nums%5Bj%5D%20%3D%20nums%5Bj%20%2B%201%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20nums%5Bj%20%2B%201%5D%20%3D%20tmp%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20count%20%2B%3D%203%20%20%23%20%E8%A6%81%E7%B4%A0%E4%BA%A4%E6%8F%9B%E3%81%AB%E3%81%AF%203%20%E5%9B%9E%E3%81%AE%E5%8D%98%E4%BD%8D%E6%93%8D%E4%BD%9C%E3%81%8C%E5%90%AB%E3%81%BE%E3%82%8C%E3%82%8B%0A%20%20%20%20return%20count%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20nums%20%3D%20%5Bi%20for%20i%20in%20range%28n%2C%200%2C%20-1%29%5D%20%20%23%20%5Bn%2C%20n-1%2C%20...%2C%202%2C%201%5D%0A%20%20%20%20count%20%3D%20bubble_sort%28nums%29%0A%20%20%20%20print%28%22%E4%BA%8C%E4%B9%97%E6%99%82%E9%96%93%EF%BC%88%E3%83%90%E3%83%96%E3%83%AB%E3%82%BD%E3%83%BC%E3%83%88%EF%BC%89%E3%81%AE%E6%93%8D%E4%BD%9C%E5%9B%9E%E6%95%B0%20%3D%22%2C%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20bubble_sort%28nums%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E6%AC%A1%E6%99%82%E9%96%93%EF%BC%88%E3%83%90%E3%83%96%E3%83%AB%E3%82%BD%E3%83%BC%E3%83%88%EF%BC%89%22%22%22%0A%20%20%20%20count%20%3D%200%20%20%23%20%E3%82%AB%E3%82%A6%E3%83%B3%E3%82%BF%0A%20%20%20%20%23%20%E5%A4%96%E5%81%B4%E3%81%AE%E3%83%AB%E3%83%BC%E3%83%97%EF%BC%9A%E6%9C%AA%E3%82%BD%E3%83%BC%E3%83%88%E5%8C%BA%E9%96%93%E3%81%AF%20%5B0%2C%20i%5D%0A%20%20%20%20for%20i%20in%20range%28len%28nums%29%20-%201%2C%200%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E5%86%85%E5%81%B4%E3%81%AE%E3%83%AB%E3%83%BC%E3%83%97%EF%BC%9A%E6%9C%AA%E3%82%BD%E3%83%BC%E3%83%88%E5%8C%BA%E9%96%93%20%5B0%2C%20i%5D%20%E3%81%AE%E6%9C%80%E5%A4%A7%E8%A6%81%E7%B4%A0%E3%82%92%E3%81%9D%E3%81%AE%E5%8C%BA%E9%96%93%E3%81%AE%E6%9C%80%E5%8F%B3%E7%AB%AF%E3%81%B8%E4%BA%A4%E6%8F%9B%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28i%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20nums%5Bj%5D%20%3E%20nums%5Bj%20%2B%201%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20nums%5Bj%5D%20%E3%81%A8%20nums%5Bj%20%2B%201%5D%20%E3%82%92%E4%BA%A4%E6%8F%9B%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20tmp%20%3D%20nums%5Bj%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20nums%5Bj%5D%20%3D%20nums%5Bj%20%2B%201%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20nums%5Bj%20%2B%201%5D%20%3D%20tmp%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20count%20%2B%3D%203%20%20%23%20%E8%A6%81%E7%B4%A0%E4%BA%A4%E6%8F%9B%E3%81%AB%E3%81%AF%203%20%E5%9B%9E%E3%81%AE%E5%8D%98%E4%BD%8D%E6%93%8D%E4%BD%9C%E3%81%8C%E5%90%AB%E3%81%BE%E3%82%8C%E3%82%8B%0A%20%20%20%20return%20count%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20nums%20%3D%20%5Bi%20for%20i%20in%20range%28n%2C%200%2C%20-1%29%5D%20%20%23%20%5Bn%2C%20n-1%2C%20...%2C%202%2C%201%5D%0A%20%20%20%20count%20%3D%20bubble_sort%28nums%29%0A%20%20%20%20print%28%22%E4%BA%8C%E4%B9%97%E6%99%82%E9%96%93%EF%BC%88%E3%83%90%E3%83%96%E3%83%AB%E3%82%BD%E3%83%BC%E3%83%88%EF%BC%89%E3%81%AE%E6%93%8D%E4%BD%9C%E5%9B%9E%E6%95%B0%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h3 id="4-o2n">4. &nbsp; 指数階 <span class="arithmatex">\(O(2^n)\)</span><a class="headerlink" href="#4-o2n" title="Permanent link">&para;</a></h3>
+<p>生物学における「細胞分裂」は指数階増加の典型例です。初期状態では細胞が <span class="arithmatex">\(1\)</span> 個あり、1 回分裂すると <span class="arithmatex">\(2\)</span> 個、2 回分裂すると <span class="arithmatex">\(4\)</span> 個となり、以下同様に、<span class="arithmatex">\(n\)</span> 回分裂すると <span class="arithmatex">\(2^n\)</span> 個の細胞になります。</p>
+<p>以下の図とコードは細胞分裂の過程を模擬したもので、時間計算量は <span class="arithmatex">\(O(2^n)\)</span> です。なお、入力の <span class="arithmatex">\(n\)</span> は分裂回数を表し、戻り値 <code>count</code> は総分裂回数を表します。</p>
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 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-113-1" name="__codelineno-113-1" href="#__codelineno-113-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-113-2" name="__codelineno-113-2" href="#__codelineno-113-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;指数複雑度（ループ実装）&quot;&quot;&quot;</span>
-<a id="__codelineno-113-3" name="__codelineno-113-3" href="#__codelineno-113-3"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
-<a id="__codelineno-113-4" name="__codelineno-113-4" href="#__codelineno-113-4"></a>    <span class="n">base</span> <span class="o">=</span> <span class="mi">1</span>
-<a id="__codelineno-113-5" name="__codelineno-113-5" href="#__codelineno-113-5"></a>    <span class="c1"># セルは毎回2つに分裂し、1, 2, 4, 8, ..., 2^(n-1) の数列を形成する</span>
-<a id="__codelineno-113-6" name="__codelineno-113-6" href="#__codelineno-113-6"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
-<a id="__codelineno-113-7" name="__codelineno-113-7" href="#__codelineno-113-7"></a>        <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">base</span><span class="p">):</span>
-<a id="__codelineno-113-8" name="__codelineno-113-8" href="#__codelineno-113-8"></a>            <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
-<a id="__codelineno-113-9" name="__codelineno-113-9" href="#__codelineno-113-9"></a>        <span class="n">base</span> <span class="o">*=</span> <span class="mi">2</span>
-<a id="__codelineno-113-10" name="__codelineno-113-10" href="#__codelineno-113-10"></a>    <span class="c1"># count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
-<a id="__codelineno-113-11" name="__codelineno-113-11" href="#__codelineno-113-11"></a>    <span class="k">return</span> <span class="n">count</span>
+<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-117-1" name="__codelineno-117-1" href="#__codelineno-117-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-117-2" name="__codelineno-117-2" href="#__codelineno-117-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;指数時間（ループ実装）&quot;&quot;&quot;</span>
+<a id="__codelineno-117-3" name="__codelineno-117-3" href="#__codelineno-117-3"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-117-4" name="__codelineno-117-4" href="#__codelineno-117-4"></a>    <span class="n">base</span> <span class="o">=</span> <span class="mi">1</span>
+<a id="__codelineno-117-5" name="__codelineno-117-5" href="#__codelineno-117-5"></a>    <span class="c1"># 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する</span>
+<a id="__codelineno-117-6" name="__codelineno-117-6" href="#__codelineno-117-6"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-117-7" name="__codelineno-117-7" href="#__codelineno-117-7"></a>        <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">base</span><span class="p">):</span>
+<a id="__codelineno-117-8" name="__codelineno-117-8" href="#__codelineno-117-8"></a>            <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-117-9" name="__codelineno-117-9" href="#__codelineno-117-9"></a>        <span class="n">base</span> <span class="o">*=</span> <span class="mi">2</span>
+<a id="__codelineno-117-10" name="__codelineno-117-10" href="#__codelineno-117-10"></a>    <span class="c1"># count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
+<a id="__codelineno-117-11" name="__codelineno-117-11" href="#__codelineno-117-11"></a>    <span class="k">return</span> <span class="n">count</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-114-1" name="__codelineno-114-1" href="#__codelineno-114-1"></a><span class="cm">/* 指数計算量（ループ実装） */</span>
-<a id="__codelineno-114-2" name="__codelineno-114-2" href="#__codelineno-114-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-114-3" name="__codelineno-114-3" href="#__codelineno-114-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-114-4" name="__codelineno-114-4" href="#__codelineno-114-4"></a><span class="w">    </span><span class="c1">// セルは毎ラウンド2つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成</span>
-<a id="__codelineno-114-5" name="__codelineno-114-5" href="#__codelineno-114-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-114-6" name="__codelineno-114-6" href="#__codelineno-114-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-114-7" name="__codelineno-114-7" href="#__codelineno-114-7"></a><span class="w">            </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-114-8" name="__codelineno-114-8" href="#__codelineno-114-8"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-114-9" name="__codelineno-114-9" href="#__codelineno-114-9"></a><span class="w">        </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
-<a id="__codelineno-114-10" name="__codelineno-114-10" href="#__codelineno-114-10"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-114-11" name="__codelineno-114-11" href="#__codelineno-114-11"></a><span class="w">    </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
-<a id="__codelineno-114-12" name="__codelineno-114-12" href="#__codelineno-114-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
-<a id="__codelineno-114-13" name="__codelineno-114-13" href="#__codelineno-114-13"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-118-1" name="__codelineno-118-1" href="#__codelineno-118-1"></a><span class="cm">/* 指数時間（ループ実装） */</span>
+<a id="__codelineno-118-2" name="__codelineno-118-2" href="#__codelineno-118-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-118-3" name="__codelineno-118-3" href="#__codelineno-118-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-118-4" name="__codelineno-118-4" href="#__codelineno-118-4"></a><span class="w">    </span><span class="c1">// 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する</span>
+<a id="__codelineno-118-5" name="__codelineno-118-5" href="#__codelineno-118-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-118-6" name="__codelineno-118-6" href="#__codelineno-118-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-118-7" name="__codelineno-118-7" href="#__codelineno-118-7"></a><span class="w">            </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-118-8" name="__codelineno-118-8" href="#__codelineno-118-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-118-9" name="__codelineno-118-9" href="#__codelineno-118-9"></a><span class="w">        </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-118-10" name="__codelineno-118-10" href="#__codelineno-118-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-118-11" name="__codelineno-118-11" href="#__codelineno-118-11"></a><span class="w">    </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
+<a id="__codelineno-118-12" name="__codelineno-118-12" href="#__codelineno-118-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-118-13" name="__codelineno-118-13" href="#__codelineno-118-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-115-1" name="__codelineno-115-1" href="#__codelineno-115-1"></a><span class="cm">/* 指数計算量（ループ実装） */</span>
-<a id="__codelineno-115-2" name="__codelineno-115-2" href="#__codelineno-115-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-115-3" name="__codelineno-115-3" href="#__codelineno-115-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-115-4" name="__codelineno-115-4" href="#__codelineno-115-4"></a><span class="w">    </span><span class="c1">// セルは毎ラウンド2つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成</span>
-<a id="__codelineno-115-5" name="__codelineno-115-5" href="#__codelineno-115-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-115-6" name="__codelineno-115-6" href="#__codelineno-115-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-115-7" name="__codelineno-115-7" href="#__codelineno-115-7"></a><span class="w">            </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-115-8" name="__codelineno-115-8" href="#__codelineno-115-8"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-115-9" name="__codelineno-115-9" href="#__codelineno-115-9"></a><span class="w">        </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
-<a id="__codelineno-115-10" name="__codelineno-115-10" href="#__codelineno-115-10"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-115-11" name="__codelineno-115-11" href="#__codelineno-115-11"></a><span class="w">    </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
-<a id="__codelineno-115-12" name="__codelineno-115-12" href="#__codelineno-115-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
-<a id="__codelineno-115-13" name="__codelineno-115-13" href="#__codelineno-115-13"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-119-1" name="__codelineno-119-1" href="#__codelineno-119-1"></a><span class="cm">/* 指数時間（ループ実装） */</span>
+<a id="__codelineno-119-2" name="__codelineno-119-2" href="#__codelineno-119-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-119-3" name="__codelineno-119-3" href="#__codelineno-119-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-119-4" name="__codelineno-119-4" href="#__codelineno-119-4"></a><span class="w">    </span><span class="c1">// 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する</span>
+<a id="__codelineno-119-5" name="__codelineno-119-5" href="#__codelineno-119-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-119-6" name="__codelineno-119-6" href="#__codelineno-119-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-119-7" name="__codelineno-119-7" href="#__codelineno-119-7"></a><span class="w">            </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-119-8" name="__codelineno-119-8" href="#__codelineno-119-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-119-9" name="__codelineno-119-9" href="#__codelineno-119-9"></a><span class="w">        </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-119-10" name="__codelineno-119-10" href="#__codelineno-119-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-119-11" name="__codelineno-119-11" href="#__codelineno-119-11"></a><span class="w">    </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
+<a id="__codelineno-119-12" name="__codelineno-119-12" href="#__codelineno-119-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-119-13" name="__codelineno-119-13" href="#__codelineno-119-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-116-1" name="__codelineno-116-1" href="#__codelineno-116-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Exponential</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-120-1" name="__codelineno-120-1" href="#__codelineno-120-1"></a><span class="cm">/* 指数時間（ループ実装） */</span>
+<a id="__codelineno-120-2" name="__codelineno-120-2" href="#__codelineno-120-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Exponential</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-120-3" name="__codelineno-120-3" href="#__codelineno-120-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">bas</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-120-4" name="__codelineno-120-4" href="#__codelineno-120-4"></a><span class="w">    </span><span class="c1">// 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する</span>
+<a id="__codelineno-120-5" name="__codelineno-120-5" href="#__codelineno-120-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-120-6" name="__codelineno-120-6" href="#__codelineno-120-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">bas</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-120-7" name="__codelineno-120-7" href="#__codelineno-120-7"></a><span class="w">            </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-120-8" name="__codelineno-120-8" href="#__codelineno-120-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-120-9" name="__codelineno-120-9" href="#__codelineno-120-9"></a><span class="w">        </span><span class="n">bas</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-120-10" name="__codelineno-120-10" href="#__codelineno-120-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-120-11" name="__codelineno-120-11" href="#__codelineno-120-11"></a><span class="w">    </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
+<a id="__codelineno-120-12" name="__codelineno-120-12" href="#__codelineno-120-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-120-13" name="__codelineno-120-13" href="#__codelineno-120-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-117-1" name="__codelineno-117-1" href="#__codelineno-117-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">exponential</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-121-1" name="__codelineno-121-1" href="#__codelineno-121-1"></a><span class="cm">/* 指数時間（ループ実装） */</span>
+<a id="__codelineno-121-2" name="__codelineno-121-2" href="#__codelineno-121-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">exponential</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-121-3" name="__codelineno-121-3" href="#__codelineno-121-3"></a><span class="w">    </span><span class="nx">count</span><span class="p">,</span><span class="w"> </span><span class="nx">base</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-121-4" name="__codelineno-121-4" href="#__codelineno-121-4"></a><span class="w">    </span><span class="c1">// 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する</span>
+<a id="__codelineno-121-5" name="__codelineno-121-5" href="#__codelineno-121-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-121-6" name="__codelineno-121-6" href="#__codelineno-121-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">base</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-121-7" name="__codelineno-121-7" href="#__codelineno-121-7"></a><span class="w">            </span><span class="nx">count</span><span class="o">++</span>
+<a id="__codelineno-121-8" name="__codelineno-121-8" href="#__codelineno-121-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-121-9" name="__codelineno-121-9" href="#__codelineno-121-9"></a><span class="w">        </span><span class="nx">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-121-10" name="__codelineno-121-10" href="#__codelineno-121-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-121-11" name="__codelineno-121-11" href="#__codelineno-121-11"></a><span class="w">    </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
+<a id="__codelineno-121-12" name="__codelineno-121-12" href="#__codelineno-121-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
+<a id="__codelineno-121-13" name="__codelineno-121-13" href="#__codelineno-121-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-118-1" name="__codelineno-118-1" href="#__codelineno-118-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">exponential</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-122-1" name="__codelineno-122-1" href="#__codelineno-122-1"></a><span class="cm">/* 指数時間（ループ実装） */</span>
+<a id="__codelineno-122-2" name="__codelineno-122-2" href="#__codelineno-122-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-122-3" name="__codelineno-122-3" href="#__codelineno-122-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-122-4" name="__codelineno-122-4" href="#__codelineno-122-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">base</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-122-5" name="__codelineno-122-5" href="#__codelineno-122-5"></a><span class="w">    </span><span class="c1">// 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する</span>
+<a id="__codelineno-122-6" name="__codelineno-122-6" href="#__codelineno-122-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-122-7" name="__codelineno-122-7" href="#__codelineno-122-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-122-8" name="__codelineno-122-8" href="#__codelineno-122-8"></a><span class="w">            </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-122-9" name="__codelineno-122-9" href="#__codelineno-122-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-122-10" name="__codelineno-122-10" href="#__codelineno-122-10"></a><span class="w">        </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-122-11" name="__codelineno-122-11" href="#__codelineno-122-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-122-12" name="__codelineno-122-12" href="#__codelineno-122-12"></a><span class="w">    </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
+<a id="__codelineno-122-13" name="__codelineno-122-13" href="#__codelineno-122-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="bp">count</span>
+<a id="__codelineno-122-14" name="__codelineno-122-14" href="#__codelineno-122-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-119-1" name="__codelineno-119-1" href="#__codelineno-119-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">exponential</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-123-1" name="__codelineno-123-1" href="#__codelineno-123-1"></a><span class="cm">/* 指数時間（ループ実装） */</span>
+<a id="__codelineno-123-2" name="__codelineno-123-2" href="#__codelineno-123-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">exponential</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-123-3" name="__codelineno-123-3" href="#__codelineno-123-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span>
+<a id="__codelineno-123-4" name="__codelineno-123-4" href="#__codelineno-123-4"></a><span class="w">        </span><span class="nx">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-123-5" name="__codelineno-123-5" href="#__codelineno-123-5"></a><span class="w">    </span><span class="c1">// 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する</span>
+<a id="__codelineno-123-6" name="__codelineno-123-6" href="#__codelineno-123-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-123-7" name="__codelineno-123-7" href="#__codelineno-123-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">base</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-123-8" name="__codelineno-123-8" href="#__codelineno-123-8"></a><span class="w">            </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-123-9" name="__codelineno-123-9" href="#__codelineno-123-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-123-10" name="__codelineno-123-10" href="#__codelineno-123-10"></a><span class="w">        </span><span class="nx">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
+<a id="__codelineno-123-11" name="__codelineno-123-11" href="#__codelineno-123-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-123-12" name="__codelineno-123-12" href="#__codelineno-123-12"></a><span class="w">    </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
+<a id="__codelineno-123-13" name="__codelineno-123-13" href="#__codelineno-123-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
+<a id="__codelineno-123-14" name="__codelineno-123-14" href="#__codelineno-123-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-120-1" name="__codelineno-120-1" href="#__codelineno-120-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">exponential</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-124-1" name="__codelineno-124-1" href="#__codelineno-124-1"></a><span class="cm">/* 指数時間（ループ実装） */</span>
+<a id="__codelineno-124-2" name="__codelineno-124-2" href="#__codelineno-124-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">exponential</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-124-3" name="__codelineno-124-3" href="#__codelineno-124-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span>
+<a id="__codelineno-124-4" name="__codelineno-124-4" href="#__codelineno-124-4"></a><span class="w">        </span><span class="nx">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-124-5" name="__codelineno-124-5" href="#__codelineno-124-5"></a><span class="w">    </span><span class="c1">// 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する</span>
+<a id="__codelineno-124-6" name="__codelineno-124-6" href="#__codelineno-124-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-124-7" name="__codelineno-124-7" href="#__codelineno-124-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">base</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-124-8" name="__codelineno-124-8" href="#__codelineno-124-8"></a><span class="w">            </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-124-9" name="__codelineno-124-9" href="#__codelineno-124-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-124-10" name="__codelineno-124-10" href="#__codelineno-124-10"></a><span class="w">        </span><span class="nx">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
+<a id="__codelineno-124-11" name="__codelineno-124-11" href="#__codelineno-124-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-124-12" name="__codelineno-124-12" href="#__codelineno-124-12"></a><span class="w">    </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
+<a id="__codelineno-124-13" name="__codelineno-124-13" href="#__codelineno-124-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
+<a id="__codelineno-124-14" name="__codelineno-124-14" href="#__codelineno-124-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-121-1" name="__codelineno-121-1" href="#__codelineno-121-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">exponential</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-125-1" name="__codelineno-125-1" href="#__codelineno-125-1"></a><span class="cm">/* 指数時間（ループ実装） */</span>
+<a id="__codelineno-125-2" name="__codelineno-125-2" href="#__codelineno-125-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">exponential</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-125-3" name="__codelineno-125-3" href="#__codelineno-125-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-125-4" name="__codelineno-125-4" href="#__codelineno-125-4"></a><span class="w">  </span><span class="c1">// 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する</span>
+<a id="__codelineno-125-5" name="__codelineno-125-5" href="#__codelineno-125-5"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-125-6" name="__codelineno-125-6" href="#__codelineno-125-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-125-7" name="__codelineno-125-7" href="#__codelineno-125-7"></a><span class="w">      </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-125-8" name="__codelineno-125-8" href="#__codelineno-125-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-125-9" name="__codelineno-125-9" href="#__codelineno-125-9"></a><span class="w">    </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
+<a id="__codelineno-125-10" name="__codelineno-125-10" href="#__codelineno-125-10"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-125-11" name="__codelineno-125-11" href="#__codelineno-125-11"></a><span class="w">  </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
+<a id="__codelineno-125-12" name="__codelineno-125-12" href="#__codelineno-125-12"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-125-13" name="__codelineno-125-13" href="#__codelineno-125-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-122-1" name="__codelineno-122-1" href="#__codelineno-122-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">exponential</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-126-1" name="__codelineno-126-1" href="#__codelineno-126-1"></a><span class="cm">/* 指数時間（ループ実装） */</span>
+<a id="__codelineno-126-2" name="__codelineno-126-2" href="#__codelineno-126-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-126-3" name="__codelineno-126-3" href="#__codelineno-126-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-126-4" name="__codelineno-126-4" href="#__codelineno-126-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-126-5" name="__codelineno-126-5" href="#__codelineno-126-5"></a><span class="w">    </span><span class="c1">// 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する</span>
+<a id="__codelineno-126-6" name="__codelineno-126-6" href="#__codelineno-126-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-126-7" name="__codelineno-126-7" href="#__codelineno-126-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">base</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-126-8" name="__codelineno-126-8" href="#__codelineno-126-8"></a><span class="w">            </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-126-9" name="__codelineno-126-9" href="#__codelineno-126-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-126-10" name="__codelineno-126-10" href="#__codelineno-126-10"></a><span class="w">        </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-126-11" name="__codelineno-126-11" href="#__codelineno-126-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-126-12" name="__codelineno-126-12" href="#__codelineno-126-12"></a><span class="w">    </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
+<a id="__codelineno-126-13" name="__codelineno-126-13" href="#__codelineno-126-13"></a><span class="w">    </span><span class="n">count</span>
+<a id="__codelineno-126-14" name="__codelineno-126-14" href="#__codelineno-126-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-123-1" name="__codelineno-123-1" href="#__codelineno-123-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">exponential</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-127-1" name="__codelineno-127-1" href="#__codelineno-127-1"></a><span class="cm">/* 指数時間（ループ実装） */</span>
+<a id="__codelineno-127-2" name="__codelineno-127-2" href="#__codelineno-127-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-127-3" name="__codelineno-127-3" href="#__codelineno-127-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-127-4" name="__codelineno-127-4" href="#__codelineno-127-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">bas</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-127-5" name="__codelineno-127-5" href="#__codelineno-127-5"></a><span class="w">    </span><span class="c1">// 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する</span>
+<a id="__codelineno-127-6" name="__codelineno-127-6" href="#__codelineno-127-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-127-7" name="__codelineno-127-7" href="#__codelineno-127-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">bas</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-127-8" name="__codelineno-127-8" href="#__codelineno-127-8"></a><span class="w">            </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-127-9" name="__codelineno-127-9" href="#__codelineno-127-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-127-10" name="__codelineno-127-10" href="#__codelineno-127-10"></a><span class="w">        </span><span class="n">bas</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-127-11" name="__codelineno-127-11" href="#__codelineno-127-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-127-12" name="__codelineno-127-12" href="#__codelineno-127-12"></a><span class="w">    </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
+<a id="__codelineno-127-13" name="__codelineno-127-13" href="#__codelineno-127-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-127-14" name="__codelineno-127-14" href="#__codelineno-127-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-124-1" name="__codelineno-124-1" href="#__codelineno-124-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">exponential</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-128-1" name="__codelineno-128-1" href="#__codelineno-128-1"></a><span class="cm">/* 指数時間（ループ実装） */</span>
+<a id="__codelineno-128-2" name="__codelineno-128-2" href="#__codelineno-128-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-128-3" name="__codelineno-128-3" href="#__codelineno-128-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-128-4" name="__codelineno-128-4" href="#__codelineno-128-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-128-5" name="__codelineno-128-5" href="#__codelineno-128-5"></a><span class="w">    </span><span class="c1">// 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する</span>
+<a id="__codelineno-128-6" name="__codelineno-128-6" href="#__codelineno-128-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-128-7" name="__codelineno-128-7" href="#__codelineno-128-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">base</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-128-8" name="__codelineno-128-8" href="#__codelineno-128-8"></a><span class="w">            </span><span class="n">count</span><span class="o">++</span>
+<a id="__codelineno-128-9" name="__codelineno-128-9" href="#__codelineno-128-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-128-10" name="__codelineno-128-10" href="#__codelineno-128-10"></a><span class="w">        </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="m">2</span>
+<a id="__codelineno-128-11" name="__codelineno-128-11" href="#__codelineno-128-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-128-12" name="__codelineno-128-12" href="#__codelineno-128-12"></a><span class="w">    </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
+<a id="__codelineno-128-13" name="__codelineno-128-13" href="#__codelineno-128-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
+<a id="__codelineno-128-14" name="__codelineno-128-14" href="#__codelineno-128-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-125-1" name="__codelineno-125-1" href="#__codelineno-125-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">exponential</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-129-1" name="__codelineno-129-1" href="#__codelineno-129-1"></a><span class="c1">### 平方階 ###</span>
+<a id="__codelineno-129-2" name="__codelineno-129-2" href="#__codelineno-129-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-129-3" name="__codelineno-129-3" href="#__codelineno-129-3"></a><span class="w">  </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-129-4" name="__codelineno-129-4" href="#__codelineno-129-4"></a>
+<a id="__codelineno-129-5" name="__codelineno-129-5" href="#__codelineno-129-5"></a><span class="w">  </span><span class="c1"># ループ回数はデータサイズ n の二乗に比例する</span>
+<a id="__codelineno-129-6" name="__codelineno-129-6" href="#__codelineno-129-6"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
+<a id="__codelineno-129-7" name="__codelineno-129-7" href="#__codelineno-129-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
+<a id="__codelineno-129-8" name="__codelineno-129-8" href="#__codelineno-129-8"></a><span class="w">      </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-129-9" name="__codelineno-129-9" href="#__codelineno-129-9"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-129-10" name="__codelineno-129-10" href="#__codelineno-129-10"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-129-11" name="__codelineno-129-11" href="#__codelineno-129-11"></a>
+<a id="__codelineno-129-12" name="__codelineno-129-12" href="#__codelineno-129-12"></a><span class="w">  </span><span class="n">count</span>
+<a id="__codelineno-129-13" name="__codelineno-129-13" href="#__codelineno-129-13"></a><span class="k">end</span>
+<a id="__codelineno-129-14" name="__codelineno-129-14" href="#__codelineno-129-14"></a>
+<a id="__codelineno-129-15" name="__codelineno-129-15" href="#__codelineno-129-15"></a><span class="c1"># ## 平方階（バブルソート）###</span>
+<a id="__codelineno-129-16" name="__codelineno-129-16" href="#__codelineno-129-16"></a><span class="k">def</span><span class="w"> </span><span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-129-17" name="__codelineno-129-17" href="#__codelineno-129-17"></a><span class="w">  </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w">  </span><span class="c1"># カウンタ</span>
+<a id="__codelineno-129-18" name="__codelineno-129-18" href="#__codelineno-129-18"></a>
+<a id="__codelineno-129-19" name="__codelineno-129-19" href="#__codelineno-129-19"></a><span class="w">  </span><span class="c1"># 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-129-20" name="__codelineno-129-20" href="#__codelineno-129-20"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-129-21" name="__codelineno-129-21" href="#__codelineno-129-21"></a><span class="w">    </span><span class="c1"># 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-129-22" name="__codelineno-129-22" href="#__codelineno-129-22"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">i</span>
+<a id="__codelineno-129-23" name="__codelineno-129-23" href="#__codelineno-129-23"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
+<a id="__codelineno-129-24" name="__codelineno-129-24" href="#__codelineno-129-24"></a><span class="w">        </span><span class="c1"># nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-129-25" name="__codelineno-129-25" href="#__codelineno-129-25"></a><span class="w">        </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-129-26" name="__codelineno-129-26" href="#__codelineno-129-26"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
+<a id="__codelineno-129-27" name="__codelineno-129-27" href="#__codelineno-129-27"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span>
+<a id="__codelineno-129-28" name="__codelineno-129-28" href="#__codelineno-129-28"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="c1"># 要素交換には 3 回の単位操作が含まれる</span>
+<a id="__codelineno-129-29" name="__codelineno-129-29" href="#__codelineno-129-29"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-129-30" name="__codelineno-129-30" href="#__codelineno-129-30"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-129-31" name="__codelineno-129-31" href="#__codelineno-129-31"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-129-32" name="__codelineno-129-32" href="#__codelineno-129-32"></a>
+<a id="__codelineno-129-33" name="__codelineno-129-33" href="#__codelineno-129-33"></a><span class="w">  </span><span class="n">count</span>
+<a id="__codelineno-129-34" name="__codelineno-129-34" href="#__codelineno-129-34"></a><span class="k">end</span>
+<a id="__codelineno-129-35" name="__codelineno-129-35" href="#__codelineno-129-35"></a>
+<a id="__codelineno-129-36" name="__codelineno-129-36" href="#__codelineno-129-36"></a><span class="c1"># ## 指数階（ループ実装）###</span>
+<a id="__codelineno-129-37" name="__codelineno-129-37" href="#__codelineno-129-37"></a><span class="k">def</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-129-38" name="__codelineno-129-38" href="#__codelineno-129-38"></a><span class="w">  </span><span class="n">count</span><span class="p">,</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-129-39" name="__codelineno-129-39" href="#__codelineno-129-39"></a>
+<a id="__codelineno-129-40" name="__codelineno-129-40" href="#__codelineno-129-40"></a><span class="w">  </span><span class="c1"># 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する</span>
+<a id="__codelineno-129-41" name="__codelineno-129-41" href="#__codelineno-129-41"></a><span class="w">  </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span>
+<a id="__codelineno-129-42" name="__codelineno-129-42" href="#__codelineno-129-42"></a><span class="w">    </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">base</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-129-43" name="__codelineno-129-43" href="#__codelineno-129-43"></a><span class="w">    </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-129-44" name="__codelineno-129-44" href="#__codelineno-129-44"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-129-45" name="__codelineno-129-45" href="#__codelineno-129-45"></a>
+<a id="__codelineno-129-46" name="__codelineno-129-46" href="#__codelineno-129-46"></a><span class="w">  </span><span class="c1"># count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
+<a id="__codelineno-129-47" name="__codelineno-129-47" href="#__codelineno-129-47"></a><span class="w">  </span><span class="n">count</span>
+<a id="__codelineno-129-48" name="__codelineno-129-48" href="#__codelineno-129-48"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p><img alt="Exponential order time complexity" class="animation-figure" src="../time_complexity.assets/time_complexity_exponential.png" /></p>
-<p align="center"> 図 2-11 &nbsp; Exponential order time complexity </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 513px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20exponential%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E6%8C%87%E6%95%B0%E6%99%82%E9%96%93%EF%BC%88%E3%83%AB%E3%83%BC%E3%83%97%E5%AE%9F%E8%A3%85%EF%BC%89%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20base%20%3D%201%0A%20%20%20%20%23%20%E7%B4%B0%E8%83%9E%E3%81%AF%E5%90%84%E3%83%A9%E3%82%A6%E3%83%B3%E3%83%89%E3%81%A7%202%20%E3%81%A4%E3%81%AB%E5%88%86%E8%A3%82%E3%81%97%E3%80%81%E6%95%B0%E5%88%97%201%2C%202%2C%204%2C%208%2C%20...%2C%202%5E%28n-1%29%20%E3%82%92%E5%BD%A2%E6%88%90%E3%81%99%E3%82%8B%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20for%20_%20in%20range%28base%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20%20%20%20%20base%20%2A%3D%202%0A%20%20%20%20%23%20count%20%3D%201%20%2B%202%20%2B%204%20%2B%208%20%2B%20..%20%2B%202%5E%28n-1%29%20%3D%202%5En%20-%201%0A%20%20%20%20return%20count%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20exponential%28n%29%0A%20%20%20%20print%28%22%E6%8C%87%E6%95%B0%E6%99%82%E9%96%93%EF%BC%88%E3%83%AB%E3%83%BC%E3%83%97%E5%AE%9F%E8%A3%85%EF%BC%89%E3%81%AE%E6%93%8D%E4%BD%9C%E5%9B%9E%E6%95%B0%20%3D%22%2C%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20exponential%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E6%8C%87%E6%95%B0%E6%99%82%E9%96%93%EF%BC%88%E3%83%AB%E3%83%BC%E3%83%97%E5%AE%9F%E8%A3%85%EF%BC%89%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20base%20%3D%201%0A%20%20%20%20%23%20%E7%B4%B0%E8%83%9E%E3%81%AF%E5%90%84%E3%83%A9%E3%82%A6%E3%83%B3%E3%83%89%E3%81%A7%202%20%E3%81%A4%E3%81%AB%E5%88%86%E8%A3%82%E3%81%97%E3%80%81%E6%95%B0%E5%88%97%201%2C%202%2C%204%2C%208%2C%20...%2C%202%5E%28n-1%29%20%E3%82%92%E5%BD%A2%E6%88%90%E3%81%99%E3%82%8B%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20for%20_%20in%20range%28base%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20%20%20%20%20base%20%2A%3D%202%0A%20%20%20%20%23%20count%20%3D%201%20%2B%202%20%2B%204%20%2B%208%20%2B%20..%20%2B%202%5E%28n-1%29%20%3D%202%5En%20-%201%0A%20%20%20%20return%20count%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20exponential%28n%29%0A%20%20%20%20print%28%22%E6%8C%87%E6%95%B0%E6%99%82%E9%96%93%EF%BC%88%E3%83%AB%E3%83%BC%E3%83%97%E5%AE%9F%E8%A3%85%EF%BC%89%E3%81%AE%E6%93%8D%E4%BD%9C%E5%9B%9E%E6%95%B0%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p><img alt="指数階の時間計算量" class="animation-figure" src="../time_complexity.assets/time_complexity_exponential.png" /></p>
+<p align="center"> 図 2-11 &nbsp; 指数階の時間計算量 </p>
 
-<p>実際には、指数オーダーは再帰関数でよく現れます。例えば、以下のコードでは、再帰的に2つの半分に分割し、<span class="arithmatex">\(n\)</span>回の分割後に停止します：</p>
+<p>実際のアルゴリズムでも、指数階は再帰関数によく現れます。例えば次のコードでは、再帰的に 2 つへ分岐し、<span class="arithmatex">\(n\)</span> 回分裂した後に停止します：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="11:13"><input checked="checked" id="__tabbed_11_1" name="__tabbed_11" type="radio" /><input id="__tabbed_11_2" name="__tabbed_11" type="radio" /><input id="__tabbed_11_3" name="__tabbed_11" type="radio" /><input id="__tabbed_11_4" name="__tabbed_11" type="radio" /><input id="__tabbed_11_5" name="__tabbed_11" type="radio" /><input id="__tabbed_11_6" name="__tabbed_11" type="radio" /><input id="__tabbed_11_7" name="__tabbed_11" type="radio" /><input id="__tabbed_11_8" name="__tabbed_11" type="radio" /><input id="__tabbed_11_9" name="__tabbed_11" type="radio" /><input id="__tabbed_11_10" name="__tabbed_11" type="radio" /><input id="__tabbed_11_11" name="__tabbed_11" type="radio" /><input id="__tabbed_11_12" name="__tabbed_11" type="radio" /><input id="__tabbed_11_13" name="__tabbed_11" type="radio" /><div class="tabbed-labels"><label for="__tabbed_11_1">Python</label><label for="__tabbed_11_2">C++</label><label for="__tabbed_11_3">Java</label><label for="__tabbed_11_4">C#</label><label for="__tabbed_11_5">Go</label><label for="__tabbed_11_6">Swift</label><label for="__tabbed_11_7">JS</label><label for="__tabbed_11_8">TS</label><label for="__tabbed_11_9">Dart</label><label for="__tabbed_11_10">Rust</label><label for="__tabbed_11_11">C</label><label for="__tabbed_11_12">Kotlin</label><label for="__tabbed_11_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-126-1" name="__codelineno-126-1" href="#__codelineno-126-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-126-2" name="__codelineno-126-2" href="#__codelineno-126-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;指数複雑度（再帰実装）&quot;&quot;&quot;</span>
-<a id="__codelineno-126-3" name="__codelineno-126-3" href="#__codelineno-126-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
-<a id="__codelineno-126-4" name="__codelineno-126-4" href="#__codelineno-126-4"></a>        <span class="k">return</span> <span class="mi">1</span>
-<a id="__codelineno-126-5" name="__codelineno-126-5" href="#__codelineno-126-5"></a>    <span class="k">return</span> <span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">+</span> <span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
+<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-130-1" name="__codelineno-130-1" href="#__codelineno-130-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-130-2" name="__codelineno-130-2" href="#__codelineno-130-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;指数時間（再帰実装）&quot;&quot;&quot;</span>
+<a id="__codelineno-130-3" name="__codelineno-130-3" href="#__codelineno-130-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+<a id="__codelineno-130-4" name="__codelineno-130-4" href="#__codelineno-130-4"></a>        <span class="k">return</span> <span class="mi">1</span>
+<a id="__codelineno-130-5" name="__codelineno-130-5" href="#__codelineno-130-5"></a>    <span class="k">return</span> <span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">+</span> <span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-127-1" name="__codelineno-127-1" href="#__codelineno-127-1"></a><span class="cm">/* 指数計算量（再帰実装） */</span>
-<a id="__codelineno-127-2" name="__codelineno-127-2" href="#__codelineno-127-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">expRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-127-3" name="__codelineno-127-3" href="#__codelineno-127-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-127-4" name="__codelineno-127-4" href="#__codelineno-127-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-127-5" name="__codelineno-127-5" href="#__codelineno-127-5"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-127-6" name="__codelineno-127-6" href="#__codelineno-127-6"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-131-1" name="__codelineno-131-1" href="#__codelineno-131-1"></a><span class="cm">/* 指数時間（再帰実装） */</span>
+<a id="__codelineno-131-2" name="__codelineno-131-2" href="#__codelineno-131-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">expRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-131-3" name="__codelineno-131-3" href="#__codelineno-131-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-131-4" name="__codelineno-131-4" href="#__codelineno-131-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-131-5" name="__codelineno-131-5" href="#__codelineno-131-5"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-131-6" name="__codelineno-131-6" href="#__codelineno-131-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-128-1" name="__codelineno-128-1" href="#__codelineno-128-1"></a><span class="cm">/* 指数計算量（再帰実装） */</span>
-<a id="__codelineno-128-2" name="__codelineno-128-2" href="#__codelineno-128-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">expRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-128-3" name="__codelineno-128-3" href="#__codelineno-128-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-128-4" name="__codelineno-128-4" href="#__codelineno-128-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-128-5" name="__codelineno-128-5" href="#__codelineno-128-5"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-128-6" name="__codelineno-128-6" href="#__codelineno-128-6"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-132-1" name="__codelineno-132-1" href="#__codelineno-132-1"></a><span class="cm">/* 指数時間（再帰実装） */</span>
+<a id="__codelineno-132-2" name="__codelineno-132-2" href="#__codelineno-132-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">expRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-132-3" name="__codelineno-132-3" href="#__codelineno-132-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-132-4" name="__codelineno-132-4" href="#__codelineno-132-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-132-5" name="__codelineno-132-5" href="#__codelineno-132-5"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-132-6" name="__codelineno-132-6" href="#__codelineno-132-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-129-1" name="__codelineno-129-1" href="#__codelineno-129-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">ExpRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-133-1" name="__codelineno-133-1" href="#__codelineno-133-1"></a><span class="cm">/* 指数時間（再帰実装） */</span>
+<a id="__codelineno-133-2" name="__codelineno-133-2" href="#__codelineno-133-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">ExpRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-133-3" name="__codelineno-133-3" href="#__codelineno-133-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-133-4" name="__codelineno-133-4" href="#__codelineno-133-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nf">ExpRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">ExpRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-133-5" name="__codelineno-133-5" href="#__codelineno-133-5"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-130-1" name="__codelineno-130-1" href="#__codelineno-130-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">expRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-134-1" name="__codelineno-134-1" href="#__codelineno-134-1"></a><span class="cm">/* 指数時間（再帰実装） */</span>
+<a id="__codelineno-134-2" name="__codelineno-134-2" href="#__codelineno-134-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-134-3" name="__codelineno-134-3" href="#__codelineno-134-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-134-4" name="__codelineno-134-4" href="#__codelineno-134-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-134-5" name="__codelineno-134-5" href="#__codelineno-134-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-134-6" name="__codelineno-134-6" href="#__codelineno-134-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-134-7" name="__codelineno-134-7" href="#__codelineno-134-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-131-1" name="__codelineno-131-1" href="#__codelineno-131-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">expRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-135-1" name="__codelineno-135-1" href="#__codelineno-135-1"></a><span class="cm">/* 指数時間（再帰実装） */</span>
+<a id="__codelineno-135-2" name="__codelineno-135-2" href="#__codelineno-135-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">expRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-135-3" name="__codelineno-135-3" href="#__codelineno-135-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-135-4" name="__codelineno-135-4" href="#__codelineno-135-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-135-5" name="__codelineno-135-5" href="#__codelineno-135-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-135-6" name="__codelineno-135-6" href="#__codelineno-135-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-135-7" name="__codelineno-135-7" href="#__codelineno-135-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-132-1" name="__codelineno-132-1" href="#__codelineno-132-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">expRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-136-1" name="__codelineno-136-1" href="#__codelineno-136-1"></a><span class="cm">/* 指数時間（再帰実装） */</span>
+<a id="__codelineno-136-2" name="__codelineno-136-2" href="#__codelineno-136-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-136-3" name="__codelineno-136-3" href="#__codelineno-136-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-136-4" name="__codelineno-136-4" href="#__codelineno-136-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-136-5" name="__codelineno-136-5" href="#__codelineno-136-5"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-133-1" name="__codelineno-133-1" href="#__codelineno-133-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">expRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-137-1" name="__codelineno-137-1" href="#__codelineno-137-1"></a><span class="cm">/* 指数時間（再帰実装） */</span>
+<a id="__codelineno-137-2" name="__codelineno-137-2" href="#__codelineno-137-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-137-3" name="__codelineno-137-3" href="#__codelineno-137-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-137-4" name="__codelineno-137-4" href="#__codelineno-137-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-137-5" name="__codelineno-137-5" href="#__codelineno-137-5"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-134-1" name="__codelineno-134-1" href="#__codelineno-134-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">expRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-138-1" name="__codelineno-138-1" href="#__codelineno-138-1"></a><span class="cm">/* 指数時間（再帰実装） */</span>
+<a id="__codelineno-138-2" name="__codelineno-138-2" href="#__codelineno-138-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-138-3" name="__codelineno-138-3" href="#__codelineno-138-3"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-138-4" name="__codelineno-138-4" href="#__codelineno-138-4"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-138-5" name="__codelineno-138-5" href="#__codelineno-138-5"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-135-1" name="__codelineno-135-1" href="#__codelineno-135-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">exp_recur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-139-1" name="__codelineno-139-1" href="#__codelineno-139-1"></a><span class="cm">/* 指数時間（再帰実装） */</span>
+<a id="__codelineno-139-2" name="__codelineno-139-2" href="#__codelineno-139-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-139-3" name="__codelineno-139-3" href="#__codelineno-139-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-139-4" name="__codelineno-139-4" href="#__codelineno-139-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-139-5" name="__codelineno-139-5" href="#__codelineno-139-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-139-6" name="__codelineno-139-6" href="#__codelineno-139-6"></a><span class="w">    </span><span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-139-7" name="__codelineno-139-7" href="#__codelineno-139-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-136-1" name="__codelineno-136-1" href="#__codelineno-136-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">expRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-140-1" name="__codelineno-140-1" href="#__codelineno-140-1"></a><span class="cm">/* 指数時間（再帰実装） */</span>
+<a id="__codelineno-140-2" name="__codelineno-140-2" href="#__codelineno-140-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">expRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-140-3" name="__codelineno-140-3" href="#__codelineno-140-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-140-4" name="__codelineno-140-4" href="#__codelineno-140-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-140-5" name="__codelineno-140-5" href="#__codelineno-140-5"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-140-6" name="__codelineno-140-6" href="#__codelineno-140-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-137-1" name="__codelineno-137-1" href="#__codelineno-137-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">expRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-141-1" name="__codelineno-141-1" href="#__codelineno-141-1"></a><span class="cm">/* 指数時間（再帰実装） */</span>
+<a id="__codelineno-141-2" name="__codelineno-141-2" href="#__codelineno-141-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">expRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-141-3" name="__codelineno-141-3" href="#__codelineno-141-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-141-4" name="__codelineno-141-4" href="#__codelineno-141-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-141-5" name="__codelineno-141-5" href="#__codelineno-141-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-141-6" name="__codelineno-141-6" href="#__codelineno-141-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-141-7" name="__codelineno-141-7" href="#__codelineno-141-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-138-1" name="__codelineno-138-1" href="#__codelineno-138-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">exp_recur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-142-1" name="__codelineno-142-1" href="#__codelineno-142-1"></a><span class="c1">### 平方階 ###</span>
+<a id="__codelineno-142-2" name="__codelineno-142-2" href="#__codelineno-142-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-142-3" name="__codelineno-142-3" href="#__codelineno-142-3"></a><span class="w">  </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-142-4" name="__codelineno-142-4" href="#__codelineno-142-4"></a>
+<a id="__codelineno-142-5" name="__codelineno-142-5" href="#__codelineno-142-5"></a><span class="w">  </span><span class="c1"># ループ回数はデータサイズ n の二乗に比例する</span>
+<a id="__codelineno-142-6" name="__codelineno-142-6" href="#__codelineno-142-6"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
+<a id="__codelineno-142-7" name="__codelineno-142-7" href="#__codelineno-142-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
+<a id="__codelineno-142-8" name="__codelineno-142-8" href="#__codelineno-142-8"></a><span class="w">      </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-142-9" name="__codelineno-142-9" href="#__codelineno-142-9"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-142-10" name="__codelineno-142-10" href="#__codelineno-142-10"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-142-11" name="__codelineno-142-11" href="#__codelineno-142-11"></a>
+<a id="__codelineno-142-12" name="__codelineno-142-12" href="#__codelineno-142-12"></a><span class="w">  </span><span class="n">count</span>
+<a id="__codelineno-142-13" name="__codelineno-142-13" href="#__codelineno-142-13"></a><span class="k">end</span>
+<a id="__codelineno-142-14" name="__codelineno-142-14" href="#__codelineno-142-14"></a>
+<a id="__codelineno-142-15" name="__codelineno-142-15" href="#__codelineno-142-15"></a><span class="c1"># ## 平方階（バブルソート）###</span>
+<a id="__codelineno-142-16" name="__codelineno-142-16" href="#__codelineno-142-16"></a><span class="k">def</span><span class="w"> </span><span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-142-17" name="__codelineno-142-17" href="#__codelineno-142-17"></a><span class="w">  </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w">  </span><span class="c1"># カウンタ</span>
+<a id="__codelineno-142-18" name="__codelineno-142-18" href="#__codelineno-142-18"></a>
+<a id="__codelineno-142-19" name="__codelineno-142-19" href="#__codelineno-142-19"></a><span class="w">  </span><span class="c1"># 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-142-20" name="__codelineno-142-20" href="#__codelineno-142-20"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-142-21" name="__codelineno-142-21" href="#__codelineno-142-21"></a><span class="w">    </span><span class="c1"># 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-142-22" name="__codelineno-142-22" href="#__codelineno-142-22"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">i</span>
+<a id="__codelineno-142-23" name="__codelineno-142-23" href="#__codelineno-142-23"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
+<a id="__codelineno-142-24" name="__codelineno-142-24" href="#__codelineno-142-24"></a><span class="w">        </span><span class="c1"># nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-142-25" name="__codelineno-142-25" href="#__codelineno-142-25"></a><span class="w">        </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-142-26" name="__codelineno-142-26" href="#__codelineno-142-26"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
+<a id="__codelineno-142-27" name="__codelineno-142-27" href="#__codelineno-142-27"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span>
+<a id="__codelineno-142-28" name="__codelineno-142-28" href="#__codelineno-142-28"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="c1"># 要素交換には 3 回の単位操作が含まれる</span>
+<a id="__codelineno-142-29" name="__codelineno-142-29" href="#__codelineno-142-29"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-142-30" name="__codelineno-142-30" href="#__codelineno-142-30"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-142-31" name="__codelineno-142-31" href="#__codelineno-142-31"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-142-32" name="__codelineno-142-32" href="#__codelineno-142-32"></a>
+<a id="__codelineno-142-33" name="__codelineno-142-33" href="#__codelineno-142-33"></a><span class="w">  </span><span class="n">count</span>
+<a id="__codelineno-142-34" name="__codelineno-142-34" href="#__codelineno-142-34"></a><span class="k">end</span>
+<a id="__codelineno-142-35" name="__codelineno-142-35" href="#__codelineno-142-35"></a>
+<a id="__codelineno-142-36" name="__codelineno-142-36" href="#__codelineno-142-36"></a><span class="c1"># ## 指数階（ループ実装）###</span>
+<a id="__codelineno-142-37" name="__codelineno-142-37" href="#__codelineno-142-37"></a><span class="k">def</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-142-38" name="__codelineno-142-38" href="#__codelineno-142-38"></a><span class="w">  </span><span class="n">count</span><span class="p">,</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-142-39" name="__codelineno-142-39" href="#__codelineno-142-39"></a>
+<a id="__codelineno-142-40" name="__codelineno-142-40" href="#__codelineno-142-40"></a><span class="w">  </span><span class="c1"># 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する</span>
+<a id="__codelineno-142-41" name="__codelineno-142-41" href="#__codelineno-142-41"></a><span class="w">  </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span>
+<a id="__codelineno-142-42" name="__codelineno-142-42" href="#__codelineno-142-42"></a><span class="w">    </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">base</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-142-43" name="__codelineno-142-43" href="#__codelineno-142-43"></a><span class="w">    </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-142-44" name="__codelineno-142-44" href="#__codelineno-142-44"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-142-45" name="__codelineno-142-45" href="#__codelineno-142-45"></a>
+<a id="__codelineno-142-46" name="__codelineno-142-46" href="#__codelineno-142-46"></a><span class="w">  </span><span class="c1"># count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
+<a id="__codelineno-142-47" name="__codelineno-142-47" href="#__codelineno-142-47"></a><span class="w">  </span><span class="n">count</span>
+<a id="__codelineno-142-48" name="__codelineno-142-48" href="#__codelineno-142-48"></a><span class="k">end</span>
+<a id="__codelineno-142-49" name="__codelineno-142-49" href="#__codelineno-142-49"></a>
+<a id="__codelineno-142-50" name="__codelineno-142-50" href="#__codelineno-142-50"></a><span class="c1"># ## 指数階（再帰実装）###</span>
+<a id="__codelineno-142-51" name="__codelineno-142-51" href="#__codelineno-142-51"></a><span class="k">def</span><span class="w"> </span><span class="nf">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-142-52" name="__codelineno-142-52" href="#__codelineno-142-52"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-142-53" name="__codelineno-142-53" href="#__codelineno-142-53"></a><span class="w">  </span><span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-142-54" name="__codelineno-142-54" href="#__codelineno-142-54"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>指数オーダーの増加は極めて急速で、全数探索法（ブルートフォース、バックトラッキングなど）でよく見られます。大規模問題では、指数オーダーは受け入れられず、しばしば動的プログラミングや貪欲アルゴリズムが解決策として必要になります。</p>
-<h3 id="5-olog-n">5. &nbsp; 対数オーダー <span class="arithmatex">\(O(\log n)\)</span><a class="headerlink" href="#5-olog-n" title="Permanent link">&para;</a></h3>
-<p>指数オーダーとは対照的に、対数オーダーは「各ラウンドでサイズが半分になる」状況を反映します。入力データサイズが<span class="arithmatex">\(n\)</span>の場合、各ラウンドでサイズが半分になるため、反復回数は<span class="arithmatex">\(\log_2 n\)</span>で、これは<span class="arithmatex">\(2^n\)</span>の逆関数です。</p>
-<p>下図とコードは「各ラウンドで半分にする」プロセスをシミュレートし、時間計算量は<span class="arithmatex">\(O(\log_2 n)\)</span>で、一般的に<span class="arithmatex">\(O(\log n)\)</span>と省略されます：</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 405px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20exp_recur%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E6%8C%87%E6%95%B0%E6%99%82%E9%96%93%EF%BC%88%E5%86%8D%E5%B8%B0%E5%AE%9F%E8%A3%85%EF%BC%89%22%22%22%0A%20%20%20%20if%20n%20%3D%3D%201%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20return%20exp_recur%28n%20-%201%29%20%2B%20exp_recur%28n%20-%201%29%20%2B%201%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%207%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20exp_recur%28n%29%0A%20%20%20%20print%28%22%E6%8C%87%E6%95%B0%E6%99%82%E9%96%93%EF%BC%88%E5%86%8D%E5%B8%B0%E5%AE%9F%E8%A3%85%EF%BC%89%E3%81%AE%E6%93%8D%E4%BD%9C%E5%9B%9E%E6%95%B0%20%3D%22%2C%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20exp_recur%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E6%8C%87%E6%95%B0%E6%99%82%E9%96%93%EF%BC%88%E5%86%8D%E5%B8%B0%E5%AE%9F%E8%A3%85%EF%BC%89%22%22%22%0A%20%20%20%20if%20n%20%3D%3D%201%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20return%20exp_recur%28n%20-%201%29%20%2B%20exp_recur%28n%20-%201%29%20%2B%201%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%207%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20exp_recur%28n%29%0A%20%20%20%20print%28%22%E6%8C%87%E6%95%B0%E6%99%82%E9%96%93%EF%BC%88%E5%86%8D%E5%B8%B0%E5%AE%9F%E8%A3%85%EF%BC%89%E3%81%AE%E6%93%8D%E4%BD%9C%E5%9B%9E%E6%95%B0%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>指数階の増加は非常に速く、全探索法（ブルートフォース、バックトラッキングなど）によく見られます。データ規模が大きい問題では、指数階は受け入れられず、通常は動的計画法や貪欲法などを使って解く必要があります。</p>
+<h3 id="5-olog-n">5. &nbsp; 対数階 <span class="arithmatex">\(O(\log n)\)</span><a class="headerlink" href="#5-olog-n" title="Permanent link">&para;</a></h3>
+<p>指数階とは逆に、対数階は「各ラウンドで半分になる」状況を表します。入力データサイズを <span class="arithmatex">\(n\)</span> とすると、各ラウンドで半減するため、ループ回数は <span class="arithmatex">\(\log_2 n\)</span>、すなわち <span class="arithmatex">\(2^n\)</span> の逆関数になります。</p>
+<p>以下の図とコードは、「各ラウンドで半分になる」過程を模擬したもので、時間計算量は <span class="arithmatex">\(O(\log_2 n)\)</span>、簡潔には <span class="arithmatex">\(O(\log n)\)</span> と書きます：</p>
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 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-139-1" name="__codelineno-139-1" href="#__codelineno-139-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-139-2" name="__codelineno-139-2" href="#__codelineno-139-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;対数複雑度（ループ実装）&quot;&quot;&quot;</span>
-<a id="__codelineno-139-3" name="__codelineno-139-3" href="#__codelineno-139-3"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
-<a id="__codelineno-139-4" name="__codelineno-139-4" href="#__codelineno-139-4"></a>    <span class="k">while</span> <span class="n">n</span> <span class="o">&gt;</span> <span class="mi">1</span><span class="p">:</span>
-<a id="__codelineno-139-5" name="__codelineno-139-5" href="#__codelineno-139-5"></a>        <span class="n">n</span> <span class="o">=</span> <span class="n">n</span> <span class="o">/</span> <span class="mi">2</span>
-<a id="__codelineno-139-6" name="__codelineno-139-6" href="#__codelineno-139-6"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
-<a id="__codelineno-139-7" name="__codelineno-139-7" href="#__codelineno-139-7"></a>    <span class="k">return</span> <span class="n">count</span>
+<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-143-1" name="__codelineno-143-1" href="#__codelineno-143-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-143-2" name="__codelineno-143-2" href="#__codelineno-143-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;対数時間（ループ実装）&quot;&quot;&quot;</span>
+<a id="__codelineno-143-3" name="__codelineno-143-3" href="#__codelineno-143-3"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-143-4" name="__codelineno-143-4" href="#__codelineno-143-4"></a>    <span class="k">while</span> <span class="n">n</span> <span class="o">&gt;</span> <span class="mi">1</span><span class="p">:</span>
+<a id="__codelineno-143-5" name="__codelineno-143-5" href="#__codelineno-143-5"></a>        <span class="n">n</span> <span class="o">=</span> <span class="n">n</span> <span class="o">/</span> <span class="mi">2</span>
+<a id="__codelineno-143-6" name="__codelineno-143-6" href="#__codelineno-143-6"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-143-7" name="__codelineno-143-7" href="#__codelineno-143-7"></a>    <span class="k">return</span> <span class="n">count</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-140-1" name="__codelineno-140-1" href="#__codelineno-140-1"></a><span class="cm">/* 対数計算量（ループ実装） */</span>
-<a id="__codelineno-140-2" name="__codelineno-140-2" href="#__codelineno-140-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-140-3" name="__codelineno-140-3" href="#__codelineno-140-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-140-4" name="__codelineno-140-4" href="#__codelineno-140-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-140-5" name="__codelineno-140-5" href="#__codelineno-140-5"></a><span class="w">        </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
-<a id="__codelineno-140-6" name="__codelineno-140-6" href="#__codelineno-140-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-140-7" name="__codelineno-140-7" href="#__codelineno-140-7"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-140-8" name="__codelineno-140-8" href="#__codelineno-140-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
-<a id="__codelineno-140-9" name="__codelineno-140-9" href="#__codelineno-140-9"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-144-1" name="__codelineno-144-1" href="#__codelineno-144-1"></a><span class="cm">/* 対数時間（ループ実装） */</span>
+<a id="__codelineno-144-2" name="__codelineno-144-2" href="#__codelineno-144-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-144-3" name="__codelineno-144-3" href="#__codelineno-144-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-144-4" name="__codelineno-144-4" href="#__codelineno-144-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-144-5" name="__codelineno-144-5" href="#__codelineno-144-5"></a><span class="w">        </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-144-6" name="__codelineno-144-6" href="#__codelineno-144-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-144-7" name="__codelineno-144-7" href="#__codelineno-144-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-144-8" name="__codelineno-144-8" href="#__codelineno-144-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-144-9" name="__codelineno-144-9" href="#__codelineno-144-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-141-1" name="__codelineno-141-1" href="#__codelineno-141-1"></a><span class="cm">/* 対数計算量（ループ実装） */</span>
-<a id="__codelineno-141-2" name="__codelineno-141-2" href="#__codelineno-141-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-141-3" name="__codelineno-141-3" href="#__codelineno-141-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-141-4" name="__codelineno-141-4" href="#__codelineno-141-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-141-5" name="__codelineno-141-5" href="#__codelineno-141-5"></a><span class="w">        </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
-<a id="__codelineno-141-6" name="__codelineno-141-6" href="#__codelineno-141-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-141-7" name="__codelineno-141-7" href="#__codelineno-141-7"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-141-8" name="__codelineno-141-8" href="#__codelineno-141-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
-<a id="__codelineno-141-9" name="__codelineno-141-9" href="#__codelineno-141-9"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-145-1" name="__codelineno-145-1" href="#__codelineno-145-1"></a><span class="cm">/* 対数時間（ループ実装） */</span>
+<a id="__codelineno-145-2" name="__codelineno-145-2" href="#__codelineno-145-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-145-3" name="__codelineno-145-3" href="#__codelineno-145-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-145-4" name="__codelineno-145-4" href="#__codelineno-145-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-145-5" name="__codelineno-145-5" href="#__codelineno-145-5"></a><span class="w">        </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-145-6" name="__codelineno-145-6" href="#__codelineno-145-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-145-7" name="__codelineno-145-7" href="#__codelineno-145-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-145-8" name="__codelineno-145-8" href="#__codelineno-145-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-145-9" name="__codelineno-145-9" href="#__codelineno-145-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-142-1" name="__codelineno-142-1" href="#__codelineno-142-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Logarithmic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-146-1" name="__codelineno-146-1" href="#__codelineno-146-1"></a><span class="cm">/* 対数時間（ループ実装） */</span>
+<a id="__codelineno-146-2" name="__codelineno-146-2" href="#__codelineno-146-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Logarithmic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-146-3" name="__codelineno-146-3" href="#__codelineno-146-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-146-4" name="__codelineno-146-4" href="#__codelineno-146-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-146-5" name="__codelineno-146-5" href="#__codelineno-146-5"></a><span class="w">        </span><span class="n">n</span><span class="w"> </span><span class="o">/=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-146-6" name="__codelineno-146-6" href="#__codelineno-146-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-146-7" name="__codelineno-146-7" href="#__codelineno-146-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-146-8" name="__codelineno-146-8" href="#__codelineno-146-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-146-9" name="__codelineno-146-9" href="#__codelineno-146-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-143-1" name="__codelineno-143-1" href="#__codelineno-143-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">logarithmic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-147-1" name="__codelineno-147-1" href="#__codelineno-147-1"></a><span class="cm">/* 対数時間（ループ実装） */</span>
+<a id="__codelineno-147-2" name="__codelineno-147-2" href="#__codelineno-147-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">logarithmic</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-147-3" name="__codelineno-147-3" href="#__codelineno-147-3"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-147-4" name="__codelineno-147-4" href="#__codelineno-147-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-147-5" name="__codelineno-147-5" href="#__codelineno-147-5"></a><span class="w">        </span><span class="nx">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-147-6" name="__codelineno-147-6" href="#__codelineno-147-6"></a><span class="w">        </span><span class="nx">count</span><span class="o">++</span>
+<a id="__codelineno-147-7" name="__codelineno-147-7" href="#__codelineno-147-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-147-8" name="__codelineno-147-8" href="#__codelineno-147-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
+<a id="__codelineno-147-9" name="__codelineno-147-9" href="#__codelineno-147-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-144-1" name="__codelineno-144-1" href="#__codelineno-144-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">logarithmic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-148-1" name="__codelineno-148-1" href="#__codelineno-148-1"></a><span class="cm">/* 対数時間（ループ実装） */</span>
+<a id="__codelineno-148-2" name="__codelineno-148-2" href="#__codelineno-148-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-148-3" name="__codelineno-148-3" href="#__codelineno-148-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-148-4" name="__codelineno-148-4" href="#__codelineno-148-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n</span>
+<a id="__codelineno-148-5" name="__codelineno-148-5" href="#__codelineno-148-5"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-148-6" name="__codelineno-148-6" href="#__codelineno-148-6"></a><span class="w">        </span><span class="n">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-148-7" name="__codelineno-148-7" href="#__codelineno-148-7"></a><span class="w">        </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-148-8" name="__codelineno-148-8" href="#__codelineno-148-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-148-9" name="__codelineno-148-9" href="#__codelineno-148-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="bp">count</span>
+<a id="__codelineno-148-10" name="__codelineno-148-10" href="#__codelineno-148-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-145-1" name="__codelineno-145-1" href="#__codelineno-145-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">logarithmic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-149-1" name="__codelineno-149-1" href="#__codelineno-149-1"></a><span class="cm">/* 対数時間（ループ実装） */</span>
+<a id="__codelineno-149-2" name="__codelineno-149-2" href="#__codelineno-149-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">logarithmic</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-149-3" name="__codelineno-149-3" href="#__codelineno-149-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-149-4" name="__codelineno-149-4" href="#__codelineno-149-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-149-5" name="__codelineno-149-5" href="#__codelineno-149-5"></a><span class="w">        </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
+<a id="__codelineno-149-6" name="__codelineno-149-6" href="#__codelineno-149-6"></a><span class="w">        </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-149-7" name="__codelineno-149-7" href="#__codelineno-149-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-149-8" name="__codelineno-149-8" href="#__codelineno-149-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
+<a id="__codelineno-149-9" name="__codelineno-149-9" href="#__codelineno-149-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-146-1" name="__codelineno-146-1" href="#__codelineno-146-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">logarithmic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-150-1" name="__codelineno-150-1" href="#__codelineno-150-1"></a><span class="cm">/* 対数時間（ループ実装） */</span>
+<a id="__codelineno-150-2" name="__codelineno-150-2" href="#__codelineno-150-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">logarithmic</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-150-3" name="__codelineno-150-3" href="#__codelineno-150-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-150-4" name="__codelineno-150-4" href="#__codelineno-150-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-150-5" name="__codelineno-150-5" href="#__codelineno-150-5"></a><span class="w">        </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
+<a id="__codelineno-150-6" name="__codelineno-150-6" href="#__codelineno-150-6"></a><span class="w">        </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-150-7" name="__codelineno-150-7" href="#__codelineno-150-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-150-8" name="__codelineno-150-8" href="#__codelineno-150-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
+<a id="__codelineno-150-9" name="__codelineno-150-9" href="#__codelineno-150-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-147-1" name="__codelineno-147-1" href="#__codelineno-147-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">logarithmic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-151-1" name="__codelineno-151-1" href="#__codelineno-151-1"></a><span class="cm">/* 対数時間（ループ実装） */</span>
+<a id="__codelineno-151-2" name="__codelineno-151-2" href="#__codelineno-151-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">logarithmic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-151-3" name="__codelineno-151-3" href="#__codelineno-151-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-151-4" name="__codelineno-151-4" href="#__codelineno-151-4"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-151-5" name="__codelineno-151-5" href="#__codelineno-151-5"></a><span class="w">    </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
+<a id="__codelineno-151-6" name="__codelineno-151-6" href="#__codelineno-151-6"></a><span class="w">    </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-151-7" name="__codelineno-151-7" href="#__codelineno-151-7"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-151-8" name="__codelineno-151-8" href="#__codelineno-151-8"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-151-9" name="__codelineno-151-9" href="#__codelineno-151-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-148-1" name="__codelineno-148-1" href="#__codelineno-148-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">logarithmic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-152-1" name="__codelineno-152-1" href="#__codelineno-152-1"></a><span class="cm">/* 対数時間（ループ実装） */</span>
+<a id="__codelineno-152-2" name="__codelineno-152-2" href="#__codelineno-152-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="k">mut</span><span class="w"> </span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-152-3" name="__codelineno-152-3" href="#__codelineno-152-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-152-4" name="__codelineno-152-4" href="#__codelineno-152-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-152-5" name="__codelineno-152-5" href="#__codelineno-152-5"></a><span class="w">        </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-152-6" name="__codelineno-152-6" href="#__codelineno-152-6"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-152-7" name="__codelineno-152-7" href="#__codelineno-152-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-152-8" name="__codelineno-152-8" href="#__codelineno-152-8"></a><span class="w">    </span><span class="n">count</span>
+<a id="__codelineno-152-9" name="__codelineno-152-9" href="#__codelineno-152-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-149-1" name="__codelineno-149-1" href="#__codelineno-149-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">logarithmic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-153-1" name="__codelineno-153-1" href="#__codelineno-153-1"></a><span class="cm">/* 対数時間（ループ実装） */</span>
+<a id="__codelineno-153-2" name="__codelineno-153-2" href="#__codelineno-153-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-153-3" name="__codelineno-153-3" href="#__codelineno-153-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-153-4" name="__codelineno-153-4" href="#__codelineno-153-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-153-5" name="__codelineno-153-5" href="#__codelineno-153-5"></a><span class="w">        </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-153-6" name="__codelineno-153-6" href="#__codelineno-153-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-153-7" name="__codelineno-153-7" href="#__codelineno-153-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-153-8" name="__codelineno-153-8" href="#__codelineno-153-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-153-9" name="__codelineno-153-9" href="#__codelineno-153-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-150-1" name="__codelineno-150-1" href="#__codelineno-150-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">logarithmic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-154-1" name="__codelineno-154-1" href="#__codelineno-154-1"></a><span class="cm">/* 対数時間（ループ実装） */</span>
+<a id="__codelineno-154-2" name="__codelineno-154-2" href="#__codelineno-154-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-154-3" name="__codelineno-154-3" href="#__codelineno-154-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span>
+<a id="__codelineno-154-4" name="__codelineno-154-4" href="#__codelineno-154-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-154-5" name="__codelineno-154-5" href="#__codelineno-154-5"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n1</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-154-6" name="__codelineno-154-6" href="#__codelineno-154-6"></a><span class="w">        </span><span class="n">n1</span><span class="w"> </span><span class="o">/=</span><span class="w"> </span><span class="m">2</span>
+<a id="__codelineno-154-7" name="__codelineno-154-7" href="#__codelineno-154-7"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span>
+<a id="__codelineno-154-8" name="__codelineno-154-8" href="#__codelineno-154-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-154-9" name="__codelineno-154-9" href="#__codelineno-154-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
+<a id="__codelineno-154-10" name="__codelineno-154-10" href="#__codelineno-154-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-151-1" name="__codelineno-151-1" href="#__codelineno-151-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">logarithmic</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-155-1" name="__codelineno-155-1" href="#__codelineno-155-1"></a><span class="c1">### 平方階 ###</span>
+<a id="__codelineno-155-2" name="__codelineno-155-2" href="#__codelineno-155-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-155-3" name="__codelineno-155-3" href="#__codelineno-155-3"></a><span class="w">  </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-155-4" name="__codelineno-155-4" href="#__codelineno-155-4"></a>
+<a id="__codelineno-155-5" name="__codelineno-155-5" href="#__codelineno-155-5"></a><span class="w">  </span><span class="c1"># ループ回数はデータサイズ n の二乗に比例する</span>
+<a id="__codelineno-155-6" name="__codelineno-155-6" href="#__codelineno-155-6"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
+<a id="__codelineno-155-7" name="__codelineno-155-7" href="#__codelineno-155-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
+<a id="__codelineno-155-8" name="__codelineno-155-8" href="#__codelineno-155-8"></a><span class="w">      </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-155-9" name="__codelineno-155-9" href="#__codelineno-155-9"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-155-10" name="__codelineno-155-10" href="#__codelineno-155-10"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-155-11" name="__codelineno-155-11" href="#__codelineno-155-11"></a>
+<a id="__codelineno-155-12" name="__codelineno-155-12" href="#__codelineno-155-12"></a><span class="w">  </span><span class="n">count</span>
+<a id="__codelineno-155-13" name="__codelineno-155-13" href="#__codelineno-155-13"></a><span class="k">end</span>
+<a id="__codelineno-155-14" name="__codelineno-155-14" href="#__codelineno-155-14"></a>
+<a id="__codelineno-155-15" name="__codelineno-155-15" href="#__codelineno-155-15"></a><span class="c1"># ## 平方階（バブルソート）###</span>
+<a id="__codelineno-155-16" name="__codelineno-155-16" href="#__codelineno-155-16"></a><span class="k">def</span><span class="w"> </span><span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-155-17" name="__codelineno-155-17" href="#__codelineno-155-17"></a><span class="w">  </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w">  </span><span class="c1"># カウンタ</span>
+<a id="__codelineno-155-18" name="__codelineno-155-18" href="#__codelineno-155-18"></a>
+<a id="__codelineno-155-19" name="__codelineno-155-19" href="#__codelineno-155-19"></a><span class="w">  </span><span class="c1"># 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-155-20" name="__codelineno-155-20" href="#__codelineno-155-20"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-155-21" name="__codelineno-155-21" href="#__codelineno-155-21"></a><span class="w">    </span><span class="c1"># 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-155-22" name="__codelineno-155-22" href="#__codelineno-155-22"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">i</span>
+<a id="__codelineno-155-23" name="__codelineno-155-23" href="#__codelineno-155-23"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
+<a id="__codelineno-155-24" name="__codelineno-155-24" href="#__codelineno-155-24"></a><span class="w">        </span><span class="c1"># nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-155-25" name="__codelineno-155-25" href="#__codelineno-155-25"></a><span class="w">        </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-155-26" name="__codelineno-155-26" href="#__codelineno-155-26"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
+<a id="__codelineno-155-27" name="__codelineno-155-27" href="#__codelineno-155-27"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span>
+<a id="__codelineno-155-28" name="__codelineno-155-28" href="#__codelineno-155-28"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="c1"># 要素交換には 3 回の単位操作が含まれる</span>
+<a id="__codelineno-155-29" name="__codelineno-155-29" href="#__codelineno-155-29"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-155-30" name="__codelineno-155-30" href="#__codelineno-155-30"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-155-31" name="__codelineno-155-31" href="#__codelineno-155-31"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-155-32" name="__codelineno-155-32" href="#__codelineno-155-32"></a>
+<a id="__codelineno-155-33" name="__codelineno-155-33" href="#__codelineno-155-33"></a><span class="w">  </span><span class="n">count</span>
+<a id="__codelineno-155-34" name="__codelineno-155-34" href="#__codelineno-155-34"></a><span class="k">end</span>
+<a id="__codelineno-155-35" name="__codelineno-155-35" href="#__codelineno-155-35"></a>
+<a id="__codelineno-155-36" name="__codelineno-155-36" href="#__codelineno-155-36"></a><span class="c1"># ## 指数階（ループ実装）###</span>
+<a id="__codelineno-155-37" name="__codelineno-155-37" href="#__codelineno-155-37"></a><span class="k">def</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-155-38" name="__codelineno-155-38" href="#__codelineno-155-38"></a><span class="w">  </span><span class="n">count</span><span class="p">,</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-155-39" name="__codelineno-155-39" href="#__codelineno-155-39"></a>
+<a id="__codelineno-155-40" name="__codelineno-155-40" href="#__codelineno-155-40"></a><span class="w">  </span><span class="c1"># 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する</span>
+<a id="__codelineno-155-41" name="__codelineno-155-41" href="#__codelineno-155-41"></a><span class="w">  </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span>
+<a id="__codelineno-155-42" name="__codelineno-155-42" href="#__codelineno-155-42"></a><span class="w">    </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">base</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-155-43" name="__codelineno-155-43" href="#__codelineno-155-43"></a><span class="w">    </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-155-44" name="__codelineno-155-44" href="#__codelineno-155-44"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-155-45" name="__codelineno-155-45" href="#__codelineno-155-45"></a>
+<a id="__codelineno-155-46" name="__codelineno-155-46" href="#__codelineno-155-46"></a><span class="w">  </span><span class="c1"># count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
+<a id="__codelineno-155-47" name="__codelineno-155-47" href="#__codelineno-155-47"></a><span class="w">  </span><span class="n">count</span>
+<a id="__codelineno-155-48" name="__codelineno-155-48" href="#__codelineno-155-48"></a><span class="k">end</span>
+<a id="__codelineno-155-49" name="__codelineno-155-49" href="#__codelineno-155-49"></a>
+<a id="__codelineno-155-50" name="__codelineno-155-50" href="#__codelineno-155-50"></a><span class="c1"># ## 指数階（再帰実装）###</span>
+<a id="__codelineno-155-51" name="__codelineno-155-51" href="#__codelineno-155-51"></a><span class="k">def</span><span class="w"> </span><span class="nf">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-155-52" name="__codelineno-155-52" href="#__codelineno-155-52"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-155-53" name="__codelineno-155-53" href="#__codelineno-155-53"></a><span class="w">  </span><span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-155-54" name="__codelineno-155-54" href="#__codelineno-155-54"></a><span class="k">end</span>
+<a id="__codelineno-155-55" name="__codelineno-155-55" href="#__codelineno-155-55"></a>
+<a id="__codelineno-155-56" name="__codelineno-155-56" href="#__codelineno-155-56"></a><span class="c1"># ## 対数階（ループ実装）###</span>
+<a id="__codelineno-155-57" name="__codelineno-155-57" href="#__codelineno-155-57"></a><span class="k">def</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-155-58" name="__codelineno-155-58" href="#__codelineno-155-58"></a><span class="w">  </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-155-59" name="__codelineno-155-59" href="#__codelineno-155-59"></a>
+<a id="__codelineno-155-60" name="__codelineno-155-60" href="#__codelineno-155-60"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-155-61" name="__codelineno-155-61" href="#__codelineno-155-61"></a><span class="w">    </span><span class="n">n</span><span class="w"> </span><span class="o">/=</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-155-62" name="__codelineno-155-62" href="#__codelineno-155-62"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-155-63" name="__codelineno-155-63" href="#__codelineno-155-63"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-155-64" name="__codelineno-155-64" href="#__codelineno-155-64"></a>
+<a id="__codelineno-155-65" name="__codelineno-155-65" href="#__codelineno-155-65"></a><span class="w">  </span><span class="n">count</span>
+<a id="__codelineno-155-66" name="__codelineno-155-66" href="#__codelineno-155-66"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p><img alt="Logarithmic order time complexity" class="animation-figure" src="../time_complexity.assets/time_complexity_logarithmic.png" /></p>
-<p align="center"> 図 2-12 &nbsp; Logarithmic order time complexity </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 441px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20logarithmic%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%AF%BE%E6%95%B0%E6%99%82%E9%96%93%EF%BC%88%E3%83%AB%E3%83%BC%E3%83%97%E5%AE%9F%E8%A3%85%EF%BC%89%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20while%20n%20%3E%201%3A%0A%20%20%20%20%20%20%20%20n%20%3D%20n%20%2F%202%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20logarithmic%28n%29%0A%20%20%20%20print%28%22%E5%AF%BE%E6%95%B0%E6%99%82%E9%96%93%EF%BC%88%E3%83%AB%E3%83%BC%E3%83%97%E5%AE%9F%E8%A3%85%EF%BC%89%E3%81%AE%E6%93%8D%E4%BD%9C%E5%9B%9E%E6%95%B0%20%3D%22%2C%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20logarithmic%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%AF%BE%E6%95%B0%E6%99%82%E9%96%93%EF%BC%88%E3%83%AB%E3%83%BC%E3%83%97%E5%AE%9F%E8%A3%85%EF%BC%89%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20while%20n%20%3E%201%3A%0A%20%20%20%20%20%20%20%20n%20%3D%20n%20%2F%202%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20logarithmic%28n%29%0A%20%20%20%20print%28%22%E5%AF%BE%E6%95%B0%E6%99%82%E9%96%93%EF%BC%88%E3%83%AB%E3%83%BC%E3%83%97%E5%AE%9F%E8%A3%85%EF%BC%89%E3%81%AE%E6%93%8D%E4%BD%9C%E5%9B%9E%E6%95%B0%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p><img alt="対数階の時間計算量" class="animation-figure" src="../time_complexity.assets/time_complexity_logarithmic.png" /></p>
+<p align="center"> 図 2-12 &nbsp; 対数階の時間計算量 </p>
 
-<p>指数オーダーと同様に、対数オーダーも再帰関数で頻繁に現れます。以下のコードは高さ<span class="arithmatex">\(\log_2 n\)</span>の再帰木を形成します：</p>
+<p>指数階と同様に、対数階も再帰関数によく現れます。次のコードは高さ <span class="arithmatex">\(\log_2 n\)</span> の再帰木を形成します：</p>
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 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-152-1" name="__codelineno-152-1" href="#__codelineno-152-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">log_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-152-2" name="__codelineno-152-2" href="#__codelineno-152-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;対数複雑度（再帰実装）&quot;&quot;&quot;</span>
-<a id="__codelineno-152-3" name="__codelineno-152-3" href="#__codelineno-152-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">&lt;=</span> <span class="mi">1</span><span class="p">:</span>
-<a id="__codelineno-152-4" name="__codelineno-152-4" href="#__codelineno-152-4"></a>        <span class="k">return</span> <span class="mi">0</span>
-<a id="__codelineno-152-5" name="__codelineno-152-5" href="#__codelineno-152-5"></a>    <span class="k">return</span> <span class="n">log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
+<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-156-1" name="__codelineno-156-1" href="#__codelineno-156-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">log_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-156-2" name="__codelineno-156-2" href="#__codelineno-156-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;対数時間（再帰実装）&quot;&quot;&quot;</span>
+<a id="__codelineno-156-3" name="__codelineno-156-3" href="#__codelineno-156-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">&lt;=</span> <span class="mi">1</span><span class="p">:</span>
+<a id="__codelineno-156-4" name="__codelineno-156-4" href="#__codelineno-156-4"></a>        <span class="k">return</span> <span class="mi">0</span>
+<a id="__codelineno-156-5" name="__codelineno-156-5" href="#__codelineno-156-5"></a>    <span class="k">return</span> <span class="n">log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-153-1" name="__codelineno-153-1" href="#__codelineno-153-1"></a><span class="cm">/* 対数計算量（再帰実装） */</span>
-<a id="__codelineno-153-2" name="__codelineno-153-2" href="#__codelineno-153-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-153-3" name="__codelineno-153-3" href="#__codelineno-153-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-153-4" name="__codelineno-153-4" href="#__codelineno-153-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-153-5" name="__codelineno-153-5" href="#__codelineno-153-5"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-153-6" name="__codelineno-153-6" href="#__codelineno-153-6"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-157-1" name="__codelineno-157-1" href="#__codelineno-157-1"></a><span class="cm">/* 対数時間（再帰実装） */</span>
+<a id="__codelineno-157-2" name="__codelineno-157-2" href="#__codelineno-157-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-157-3" name="__codelineno-157-3" href="#__codelineno-157-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-157-4" name="__codelineno-157-4" href="#__codelineno-157-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-157-5" name="__codelineno-157-5" href="#__codelineno-157-5"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-157-6" name="__codelineno-157-6" href="#__codelineno-157-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-154-1" name="__codelineno-154-1" href="#__codelineno-154-1"></a><span class="cm">/* 対数計算量（再帰実装） */</span>
-<a id="__codelineno-154-2" name="__codelineno-154-2" href="#__codelineno-154-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-154-3" name="__codelineno-154-3" href="#__codelineno-154-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-154-4" name="__codelineno-154-4" href="#__codelineno-154-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-154-5" name="__codelineno-154-5" href="#__codelineno-154-5"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-154-6" name="__codelineno-154-6" href="#__codelineno-154-6"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-158-1" name="__codelineno-158-1" href="#__codelineno-158-1"></a><span class="cm">/* 対数時間（再帰実装） */</span>
+<a id="__codelineno-158-2" name="__codelineno-158-2" href="#__codelineno-158-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-158-3" name="__codelineno-158-3" href="#__codelineno-158-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-158-4" name="__codelineno-158-4" href="#__codelineno-158-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-158-5" name="__codelineno-158-5" href="#__codelineno-158-5"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-158-6" name="__codelineno-158-6" href="#__codelineno-158-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-155-1" name="__codelineno-155-1" href="#__codelineno-155-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">LogRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-159-1" name="__codelineno-159-1" href="#__codelineno-159-1"></a><span class="cm">/* 対数時間（再帰実装） */</span>
+<a id="__codelineno-159-2" name="__codelineno-159-2" href="#__codelineno-159-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">LogRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-159-3" name="__codelineno-159-3" href="#__codelineno-159-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-159-4" name="__codelineno-159-4" href="#__codelineno-159-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nf">LogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-159-5" name="__codelineno-159-5" href="#__codelineno-159-5"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-156-1" name="__codelineno-156-1" href="#__codelineno-156-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">logRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-160-1" name="__codelineno-160-1" href="#__codelineno-160-1"></a><span class="cm">/* 対数時間（再帰実装） */</span>
+<a id="__codelineno-160-2" name="__codelineno-160-2" href="#__codelineno-160-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">logRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-160-3" name="__codelineno-160-3" href="#__codelineno-160-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-160-4" name="__codelineno-160-4" href="#__codelineno-160-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-160-5" name="__codelineno-160-5" href="#__codelineno-160-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-160-6" name="__codelineno-160-6" href="#__codelineno-160-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">logRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-160-7" name="__codelineno-160-7" href="#__codelineno-160-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-157-1" name="__codelineno-157-1" href="#__codelineno-157-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">logRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-161-1" name="__codelineno-161-1" href="#__codelineno-161-1"></a><span class="cm">/* 対数時間（再帰実装） */</span>
+<a id="__codelineno-161-2" name="__codelineno-161-2" href="#__codelineno-161-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">logRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-161-3" name="__codelineno-161-3" href="#__codelineno-161-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-161-4" name="__codelineno-161-4" href="#__codelineno-161-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-161-5" name="__codelineno-161-5" href="#__codelineno-161-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-161-6" name="__codelineno-161-6" href="#__codelineno-161-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-161-7" name="__codelineno-161-7" href="#__codelineno-161-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-158-1" name="__codelineno-158-1" href="#__codelineno-158-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">logRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-162-1" name="__codelineno-162-1" href="#__codelineno-162-1"></a><span class="cm">/* 対数時間（再帰実装） */</span>
+<a id="__codelineno-162-2" name="__codelineno-162-2" href="#__codelineno-162-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">logRecur</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-162-3" name="__codelineno-162-3" href="#__codelineno-162-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-162-4" name="__codelineno-162-4" href="#__codelineno-162-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">logRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-162-5" name="__codelineno-162-5" href="#__codelineno-162-5"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-159-1" name="__codelineno-159-1" href="#__codelineno-159-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">logRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-163-1" name="__codelineno-163-1" href="#__codelineno-163-1"></a><span class="cm">/* 対数時間（再帰実装） */</span>
+<a id="__codelineno-163-2" name="__codelineno-163-2" href="#__codelineno-163-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">logRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-163-3" name="__codelineno-163-3" href="#__codelineno-163-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-163-4" name="__codelineno-163-4" href="#__codelineno-163-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">logRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-163-5" name="__codelineno-163-5" href="#__codelineno-163-5"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-160-1" name="__codelineno-160-1" href="#__codelineno-160-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">logRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-164-1" name="__codelineno-164-1" href="#__codelineno-164-1"></a><span class="cm">/* 対数時間（再帰実装） */</span>
+<a id="__codelineno-164-2" name="__codelineno-164-2" href="#__codelineno-164-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-164-3" name="__codelineno-164-3" href="#__codelineno-164-3"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-164-4" name="__codelineno-164-4" href="#__codelineno-164-4"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-164-5" name="__codelineno-164-5" href="#__codelineno-164-5"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-161-1" name="__codelineno-161-1" href="#__codelineno-161-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">log_recur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-165-1" name="__codelineno-165-1" href="#__codelineno-165-1"></a><span class="cm">/* 対数時間（再帰実装） */</span>
+<a id="__codelineno-165-2" name="__codelineno-165-2" href="#__codelineno-165-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">log_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-165-3" name="__codelineno-165-3" href="#__codelineno-165-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-165-4" name="__codelineno-165-4" href="#__codelineno-165-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-165-5" name="__codelineno-165-5" href="#__codelineno-165-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-165-6" name="__codelineno-165-6" href="#__codelineno-165-6"></a><span class="w">    </span><span class="n">log_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-165-7" name="__codelineno-165-7" href="#__codelineno-165-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-162-1" name="__codelineno-162-1" href="#__codelineno-162-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">logRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-166-1" name="__codelineno-166-1" href="#__codelineno-166-1"></a><span class="cm">/* 対数時間（再帰実装） */</span>
+<a id="__codelineno-166-2" name="__codelineno-166-2" href="#__codelineno-166-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-166-3" name="__codelineno-166-3" href="#__codelineno-166-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-166-4" name="__codelineno-166-4" href="#__codelineno-166-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-166-5" name="__codelineno-166-5" href="#__codelineno-166-5"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-166-6" name="__codelineno-166-6" href="#__codelineno-166-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-163-1" name="__codelineno-163-1" href="#__codelineno-163-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">logRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-167-1" name="__codelineno-167-1" href="#__codelineno-167-1"></a><span class="cm">/* 対数時間（再帰実装） */</span>
+<a id="__codelineno-167-2" name="__codelineno-167-2" href="#__codelineno-167-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">logRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-167-3" name="__codelineno-167-3" href="#__codelineno-167-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-167-4" name="__codelineno-167-4" href="#__codelineno-167-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-167-5" name="__codelineno-167-5" href="#__codelineno-167-5"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-167-6" name="__codelineno-167-6" href="#__codelineno-167-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-164-1" name="__codelineno-164-1" href="#__codelineno-164-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">log_recur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-168-1" name="__codelineno-168-1" href="#__codelineno-168-1"></a><span class="c1">### 平方階 ###</span>
+<a id="__codelineno-168-2" name="__codelineno-168-2" href="#__codelineno-168-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-168-3" name="__codelineno-168-3" href="#__codelineno-168-3"></a><span class="w">  </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-168-4" name="__codelineno-168-4" href="#__codelineno-168-4"></a>
+<a id="__codelineno-168-5" name="__codelineno-168-5" href="#__codelineno-168-5"></a><span class="w">  </span><span class="c1"># ループ回数はデータサイズ n の二乗に比例する</span>
+<a id="__codelineno-168-6" name="__codelineno-168-6" href="#__codelineno-168-6"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
+<a id="__codelineno-168-7" name="__codelineno-168-7" href="#__codelineno-168-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
+<a id="__codelineno-168-8" name="__codelineno-168-8" href="#__codelineno-168-8"></a><span class="w">      </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-168-9" name="__codelineno-168-9" href="#__codelineno-168-9"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-168-10" name="__codelineno-168-10" href="#__codelineno-168-10"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-168-11" name="__codelineno-168-11" href="#__codelineno-168-11"></a>
+<a id="__codelineno-168-12" name="__codelineno-168-12" href="#__codelineno-168-12"></a><span class="w">  </span><span class="n">count</span>
+<a id="__codelineno-168-13" name="__codelineno-168-13" href="#__codelineno-168-13"></a><span class="k">end</span>
+<a id="__codelineno-168-14" name="__codelineno-168-14" href="#__codelineno-168-14"></a>
+<a id="__codelineno-168-15" name="__codelineno-168-15" href="#__codelineno-168-15"></a><span class="c1"># ## 平方階（バブルソート）###</span>
+<a id="__codelineno-168-16" name="__codelineno-168-16" href="#__codelineno-168-16"></a><span class="k">def</span><span class="w"> </span><span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-168-17" name="__codelineno-168-17" href="#__codelineno-168-17"></a><span class="w">  </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w">  </span><span class="c1"># カウンタ</span>
+<a id="__codelineno-168-18" name="__codelineno-168-18" href="#__codelineno-168-18"></a>
+<a id="__codelineno-168-19" name="__codelineno-168-19" href="#__codelineno-168-19"></a><span class="w">  </span><span class="c1"># 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-168-20" name="__codelineno-168-20" href="#__codelineno-168-20"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-168-21" name="__codelineno-168-21" href="#__codelineno-168-21"></a><span class="w">    </span><span class="c1"># 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-168-22" name="__codelineno-168-22" href="#__codelineno-168-22"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">i</span>
+<a id="__codelineno-168-23" name="__codelineno-168-23" href="#__codelineno-168-23"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
+<a id="__codelineno-168-24" name="__codelineno-168-24" href="#__codelineno-168-24"></a><span class="w">        </span><span class="c1"># nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-168-25" name="__codelineno-168-25" href="#__codelineno-168-25"></a><span class="w">        </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-168-26" name="__codelineno-168-26" href="#__codelineno-168-26"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
+<a id="__codelineno-168-27" name="__codelineno-168-27" href="#__codelineno-168-27"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span>
+<a id="__codelineno-168-28" name="__codelineno-168-28" href="#__codelineno-168-28"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="c1"># 要素交換には 3 回の単位操作が含まれる</span>
+<a id="__codelineno-168-29" name="__codelineno-168-29" href="#__codelineno-168-29"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-168-30" name="__codelineno-168-30" href="#__codelineno-168-30"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-168-31" name="__codelineno-168-31" href="#__codelineno-168-31"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-168-32" name="__codelineno-168-32" href="#__codelineno-168-32"></a>
+<a id="__codelineno-168-33" name="__codelineno-168-33" href="#__codelineno-168-33"></a><span class="w">  </span><span class="n">count</span>
+<a id="__codelineno-168-34" name="__codelineno-168-34" href="#__codelineno-168-34"></a><span class="k">end</span>
+<a id="__codelineno-168-35" name="__codelineno-168-35" href="#__codelineno-168-35"></a>
+<a id="__codelineno-168-36" name="__codelineno-168-36" href="#__codelineno-168-36"></a><span class="c1"># ## 指数階（ループ実装）###</span>
+<a id="__codelineno-168-37" name="__codelineno-168-37" href="#__codelineno-168-37"></a><span class="k">def</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-168-38" name="__codelineno-168-38" href="#__codelineno-168-38"></a><span class="w">  </span><span class="n">count</span><span class="p">,</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-168-39" name="__codelineno-168-39" href="#__codelineno-168-39"></a>
+<a id="__codelineno-168-40" name="__codelineno-168-40" href="#__codelineno-168-40"></a><span class="w">  </span><span class="c1"># 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する</span>
+<a id="__codelineno-168-41" name="__codelineno-168-41" href="#__codelineno-168-41"></a><span class="w">  </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span>
+<a id="__codelineno-168-42" name="__codelineno-168-42" href="#__codelineno-168-42"></a><span class="w">    </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">base</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-168-43" name="__codelineno-168-43" href="#__codelineno-168-43"></a><span class="w">    </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-168-44" name="__codelineno-168-44" href="#__codelineno-168-44"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-168-45" name="__codelineno-168-45" href="#__codelineno-168-45"></a>
+<a id="__codelineno-168-46" name="__codelineno-168-46" href="#__codelineno-168-46"></a><span class="w">  </span><span class="c1"># count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
+<a id="__codelineno-168-47" name="__codelineno-168-47" href="#__codelineno-168-47"></a><span class="w">  </span><span class="n">count</span>
+<a id="__codelineno-168-48" name="__codelineno-168-48" href="#__codelineno-168-48"></a><span class="k">end</span>
+<a id="__codelineno-168-49" name="__codelineno-168-49" href="#__codelineno-168-49"></a>
+<a id="__codelineno-168-50" name="__codelineno-168-50" href="#__codelineno-168-50"></a><span class="c1"># ## 指数階（再帰実装）###</span>
+<a id="__codelineno-168-51" name="__codelineno-168-51" href="#__codelineno-168-51"></a><span class="k">def</span><span class="w"> </span><span class="nf">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-168-52" name="__codelineno-168-52" href="#__codelineno-168-52"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-168-53" name="__codelineno-168-53" href="#__codelineno-168-53"></a><span class="w">  </span><span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-168-54" name="__codelineno-168-54" href="#__codelineno-168-54"></a><span class="k">end</span>
+<a id="__codelineno-168-55" name="__codelineno-168-55" href="#__codelineno-168-55"></a>
+<a id="__codelineno-168-56" name="__codelineno-168-56" href="#__codelineno-168-56"></a><span class="c1"># ## 対数階（ループ実装）###</span>
+<a id="__codelineno-168-57" name="__codelineno-168-57" href="#__codelineno-168-57"></a><span class="k">def</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-168-58" name="__codelineno-168-58" href="#__codelineno-168-58"></a><span class="w">  </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-168-59" name="__codelineno-168-59" href="#__codelineno-168-59"></a>
+<a id="__codelineno-168-60" name="__codelineno-168-60" href="#__codelineno-168-60"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-168-61" name="__codelineno-168-61" href="#__codelineno-168-61"></a><span class="w">    </span><span class="n">n</span><span class="w"> </span><span class="o">/=</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-168-62" name="__codelineno-168-62" href="#__codelineno-168-62"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-168-63" name="__codelineno-168-63" href="#__codelineno-168-63"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-168-64" name="__codelineno-168-64" href="#__codelineno-168-64"></a>
+<a id="__codelineno-168-65" name="__codelineno-168-65" href="#__codelineno-168-65"></a><span class="w">  </span><span class="n">count</span>
+<a id="__codelineno-168-66" name="__codelineno-168-66" href="#__codelineno-168-66"></a><span class="k">end</span>
+<a id="__codelineno-168-67" name="__codelineno-168-67" href="#__codelineno-168-67"></a>
+<a id="__codelineno-168-68" name="__codelineno-168-68" href="#__codelineno-168-68"></a><span class="c1"># ## 対数階（再帰実装）###</span>
+<a id="__codelineno-168-69" name="__codelineno-168-69" href="#__codelineno-168-69"></a><span class="k">def</span><span class="w"> </span><span class="nf">log_recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-168-70" name="__codelineno-168-70" href="#__codelineno-168-70"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-168-71" name="__codelineno-168-71" href="#__codelineno-168-71"></a><span class="w">  </span><span class="n">log_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-168-72" name="__codelineno-168-72" href="#__codelineno-168-72"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>対数オーダーは分割統治戦略に基づくアルゴリズムの典型で、「多くに分割」と「複雑な問題を単純化」するアプローチを体現しています。増加が遅く、定数オーダーの次に最も理想的な時間計算量です。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 405px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20log_recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%AF%BE%E6%95%B0%E6%99%82%E9%96%93%EF%BC%88%E5%86%8D%E5%B8%B0%E5%AE%9F%E8%A3%85%EF%BC%89%22%22%22%0A%20%20%20%20if%20n%20%3C%3D%201%3A%0A%20%20%20%20%20%20%20%20return%200%0A%20%20%20%20return%20log_recur%28n%20%2F%202%29%20%2B%201%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20log_recur%28n%29%0A%20%20%20%20print%28%22%E5%AF%BE%E6%95%B0%E6%99%82%E9%96%93%EF%BC%88%E5%86%8D%E5%B8%B0%E5%AE%9F%E8%A3%85%EF%BC%89%E3%81%AE%E6%93%8D%E4%BD%9C%E5%9B%9E%E6%95%B0%20%3D%22%2C%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20log_recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%AF%BE%E6%95%B0%E6%99%82%E9%96%93%EF%BC%88%E5%86%8D%E5%B8%B0%E5%AE%9F%E8%A3%85%EF%BC%89%22%22%22%0A%20%20%20%20if%20n%20%3C%3D%201%3A%0A%20%20%20%20%20%20%20%20return%200%0A%20%20%20%20return%20log_recur%28n%20%2F%202%29%20%2B%201%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20log_recur%28n%29%0A%20%20%20%20print%28%22%E5%AF%BE%E6%95%B0%E6%99%82%E9%96%93%EF%BC%88%E5%86%8D%E5%B8%B0%E5%AE%9F%E8%A3%85%EF%BC%89%E3%81%AE%E6%93%8D%E4%BD%9C%E5%9B%9E%E6%95%B0%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>対数階は分割統治に基づくアルゴリズムによく現れ、「1 つを複数に分ける」「複雑なものを単純化する」という考え方を体現しています。増加は緩やかで、定数階に次いで理想的な時間計算量です。</p>
 <div class="admonition tip">
-<p class="admonition-title"><span class="arithmatex">\(O(\log n)\)</span>の底は何ですか？</p>
-<p>技術的には、「<span class="arithmatex">\(m\)</span>に分割」は時間計算量<span class="arithmatex">\(O(\log_m n)\)</span>に対応します。対数の底変更公式を使用すると、異なる対数複雑度を等価にできます：</p>
+<p class="admonition-title"><span class="arithmatex">\(O(\log n)\)</span> の底は何か？</p>
+<p>正確には、「<span class="arithmatex">\(m\)</span> 個に分ける」場合に対応する時間計算量は <span class="arithmatex">\(O(\log_m n)\)</span> です。そして対数の底の変換公式により、底が異なっても同値な時間計算量が得られます：</p>
 <div class="arithmatex">\[
 O(\log_m n) = O(\log_k n / \log_k m) = O(\log_k n)
 \]</div>
-<p>これは、底<span class="arithmatex">\(m\)</span>を複雑度に影響を与えることなく変更できることを意味します。したがって、しばしば底<span class="arithmatex">\(m\)</span>を省略し、単に対数オーダーを<span class="arithmatex">\(O(\log n)\)</span>と表記します。</p>
+<p>つまり、底 <span class="arithmatex">\(m\)</span> は複雑度に影響を与えずに変換できます。そのため通常は底 <span class="arithmatex">\(m\)</span> を省略し、対数階を単に <span class="arithmatex">\(O(\log n)\)</span> と記します。</p>
 </div>
-<h3 id="6-on-log-n">6. &nbsp; 線形対数オーダー <span class="arithmatex">\(O(n \log n)\)</span><a class="headerlink" href="#6-on-log-n" title="Permanent link">&para;</a></h3>
-<p>線形対数オーダーはネストしたループでよく現れ、2つのループの複雑度がそれぞれ<span class="arithmatex">\(O(\log n)\)</span>と<span class="arithmatex">\(O(n)\)</span>です。関連するコードは以下の通りです：</p>
+<h3 id="6-on-log-n">6. &nbsp; 線形対数階 <span class="arithmatex">\(O(n \log n)\)</span><a class="headerlink" href="#6-on-log-n" title="Permanent link">&para;</a></h3>
+<p>線形対数階は入れ子ループによく現れ、2 層のループの時間計算量はそれぞれ <span class="arithmatex">\(O(\log n)\)</span> と <span class="arithmatex">\(O(n)\)</span> です。関連するコードは次のとおりです：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="14:13"><input checked="checked" id="__tabbed_14_1" name="__tabbed_14" type="radio" /><input id="__tabbed_14_2" name="__tabbed_14" type="radio" /><input id="__tabbed_14_3" name="__tabbed_14" type="radio" /><input id="__tabbed_14_4" name="__tabbed_14" type="radio" /><input id="__tabbed_14_5" name="__tabbed_14" type="radio" /><input id="__tabbed_14_6" name="__tabbed_14" type="radio" /><input id="__tabbed_14_7" name="__tabbed_14" type="radio" /><input id="__tabbed_14_8" name="__tabbed_14" type="radio" /><input id="__tabbed_14_9" name="__tabbed_14" type="radio" /><input id="__tabbed_14_10" name="__tabbed_14" type="radio" /><input id="__tabbed_14_11" name="__tabbed_14" type="radio" /><input id="__tabbed_14_12" name="__tabbed_14" type="radio" /><input id="__tabbed_14_13" name="__tabbed_14" type="radio" /><div class="tabbed-labels"><label for="__tabbed_14_1">Python</label><label for="__tabbed_14_2">C++</label><label for="__tabbed_14_3">Java</label><label for="__tabbed_14_4">C#</label><label for="__tabbed_14_5">Go</label><label for="__tabbed_14_6">Swift</label><label for="__tabbed_14_7">JS</label><label for="__tabbed_14_8">TS</label><label for="__tabbed_14_9">Dart</label><label for="__tabbed_14_10">Rust</label><label for="__tabbed_14_11">C</label><label for="__tabbed_14_12">Kotlin</label><label for="__tabbed_14_13">Ruby</label></div>
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-<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-165-1" name="__codelineno-165-1" href="#__codelineno-165-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-165-2" name="__codelineno-165-2" href="#__codelineno-165-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;線形対数複雑度&quot;&quot;&quot;</span>
-<a id="__codelineno-165-3" name="__codelineno-165-3" href="#__codelineno-165-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">&lt;=</span> <span class="mi">1</span><span class="p">:</span>
-<a id="__codelineno-165-4" name="__codelineno-165-4" href="#__codelineno-165-4"></a>        <span class="k">return</span> <span class="mi">1</span>
-<a id="__codelineno-165-5" name="__codelineno-165-5" href="#__codelineno-165-5"></a>    <span class="n">count</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span>
-<a id="__codelineno-165-6" name="__codelineno-165-6" href="#__codelineno-165-6"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
-<a id="__codelineno-165-7" name="__codelineno-165-7" href="#__codelineno-165-7"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
-<a id="__codelineno-165-8" name="__codelineno-165-8" href="#__codelineno-165-8"></a>    <span class="k">return</span> <span class="n">count</span>
+<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-169-1" name="__codelineno-169-1" href="#__codelineno-169-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-169-2" name="__codelineno-169-2" href="#__codelineno-169-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;線形対数時間&quot;&quot;&quot;</span>
+<a id="__codelineno-169-3" name="__codelineno-169-3" href="#__codelineno-169-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">&lt;=</span> <span class="mi">1</span><span class="p">:</span>
+<a id="__codelineno-169-4" name="__codelineno-169-4" href="#__codelineno-169-4"></a>        <span class="k">return</span> <span class="mi">1</span>
+<a id="__codelineno-169-5" name="__codelineno-169-5" href="#__codelineno-169-5"></a>    <span class="c1"># 二つに分割すると、部分問題の規模は半分になる</span>
+<a id="__codelineno-169-6" name="__codelineno-169-6" href="#__codelineno-169-6"></a>    <span class="n">count</span> <span class="o">=</span> <span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-169-7" name="__codelineno-169-7" href="#__codelineno-169-7"></a>    <span class="c1"># 現在の部分問題には n 個の操作が含まれる</span>
+<a id="__codelineno-169-8" name="__codelineno-169-8" href="#__codelineno-169-8"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-169-9" name="__codelineno-169-9" href="#__codelineno-169-9"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-169-10" name="__codelineno-169-10" href="#__codelineno-169-10"></a>    <span class="k">return</span> <span class="n">count</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-166-1" name="__codelineno-166-1" href="#__codelineno-166-1"></a><span class="cm">/* 線形対数計算量 */</span>
-<a id="__codelineno-166-2" name="__codelineno-166-2" href="#__codelineno-166-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linearLogRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-166-3" name="__codelineno-166-3" href="#__codelineno-166-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-166-4" name="__codelineno-166-4" href="#__codelineno-166-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-166-5" name="__codelineno-166-5" href="#__codelineno-166-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
-<a id="__codelineno-166-6" name="__codelineno-166-6" href="#__codelineno-166-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-166-7" name="__codelineno-166-7" href="#__codelineno-166-7"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-166-8" name="__codelineno-166-8" href="#__codelineno-166-8"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-166-9" name="__codelineno-166-9" href="#__codelineno-166-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
-<a id="__codelineno-166-10" name="__codelineno-166-10" href="#__codelineno-166-10"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-170-1" name="__codelineno-170-1" href="#__codelineno-170-1"></a><span class="cm">/* 線形対数時間 */</span>
+<a id="__codelineno-170-2" name="__codelineno-170-2" href="#__codelineno-170-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linearLogRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-170-3" name="__codelineno-170-3" href="#__codelineno-170-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-170-4" name="__codelineno-170-4" href="#__codelineno-170-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-170-5" name="__codelineno-170-5" href="#__codelineno-170-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-170-6" name="__codelineno-170-6" href="#__codelineno-170-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-170-7" name="__codelineno-170-7" href="#__codelineno-170-7"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-170-8" name="__codelineno-170-8" href="#__codelineno-170-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-170-9" name="__codelineno-170-9" href="#__codelineno-170-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-170-10" name="__codelineno-170-10" href="#__codelineno-170-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-167-1" name="__codelineno-167-1" href="#__codelineno-167-1"></a><span class="cm">/* 線形対数計算量 */</span>
-<a id="__codelineno-167-2" name="__codelineno-167-2" href="#__codelineno-167-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linearLogRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-167-3" name="__codelineno-167-3" href="#__codelineno-167-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-167-4" name="__codelineno-167-4" href="#__codelineno-167-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-167-5" name="__codelineno-167-5" href="#__codelineno-167-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
-<a id="__codelineno-167-6" name="__codelineno-167-6" href="#__codelineno-167-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-167-7" name="__codelineno-167-7" href="#__codelineno-167-7"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-167-8" name="__codelineno-167-8" href="#__codelineno-167-8"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-167-9" name="__codelineno-167-9" href="#__codelineno-167-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
-<a id="__codelineno-167-10" name="__codelineno-167-10" href="#__codelineno-167-10"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-171-1" name="__codelineno-171-1" href="#__codelineno-171-1"></a><span class="cm">/* 線形対数時間 */</span>
+<a id="__codelineno-171-2" name="__codelineno-171-2" href="#__codelineno-171-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linearLogRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-171-3" name="__codelineno-171-3" href="#__codelineno-171-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-171-4" name="__codelineno-171-4" href="#__codelineno-171-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-171-5" name="__codelineno-171-5" href="#__codelineno-171-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-171-6" name="__codelineno-171-6" href="#__codelineno-171-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-171-7" name="__codelineno-171-7" href="#__codelineno-171-7"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-171-8" name="__codelineno-171-8" href="#__codelineno-171-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-171-9" name="__codelineno-171-9" href="#__codelineno-171-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-171-10" name="__codelineno-171-10" href="#__codelineno-171-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-168-1" name="__codelineno-168-1" href="#__codelineno-168-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">LinearLogRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-172-1" name="__codelineno-172-1" href="#__codelineno-172-1"></a><span class="cm">/* 線形対数時間 */</span>
+<a id="__codelineno-172-2" name="__codelineno-172-2" href="#__codelineno-172-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">LinearLogRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-172-3" name="__codelineno-172-3" href="#__codelineno-172-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-172-4" name="__codelineno-172-4" href="#__codelineno-172-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">LinearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">LinearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-172-5" name="__codelineno-172-5" href="#__codelineno-172-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-172-6" name="__codelineno-172-6" href="#__codelineno-172-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-172-7" name="__codelineno-172-7" href="#__codelineno-172-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-172-8" name="__codelineno-172-8" href="#__codelineno-172-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-172-9" name="__codelineno-172-9" href="#__codelineno-172-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-169-1" name="__codelineno-169-1" href="#__codelineno-169-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">linearLogRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-173-1" name="__codelineno-173-1" href="#__codelineno-173-1"></a><span class="cm">/* 線形対数時間 */</span>
+<a id="__codelineno-173-2" name="__codelineno-173-2" href="#__codelineno-173-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-173-3" name="__codelineno-173-3" href="#__codelineno-173-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-173-4" name="__codelineno-173-4" href="#__codelineno-173-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-173-5" name="__codelineno-173-5" href="#__codelineno-173-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-173-6" name="__codelineno-173-6" href="#__codelineno-173-6"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-173-7" name="__codelineno-173-7" href="#__codelineno-173-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-173-8" name="__codelineno-173-8" href="#__codelineno-173-8"></a><span class="w">        </span><span class="nx">count</span><span class="o">++</span>
+<a id="__codelineno-173-9" name="__codelineno-173-9" href="#__codelineno-173-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-173-10" name="__codelineno-173-10" href="#__codelineno-173-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
+<a id="__codelineno-173-11" name="__codelineno-173-11" href="#__codelineno-173-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-170-1" name="__codelineno-170-1" href="#__codelineno-170-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">linearLogRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-174-1" name="__codelineno-174-1" href="#__codelineno-174-1"></a><span class="cm">/* 線形対数時間 */</span>
+<a id="__codelineno-174-2" name="__codelineno-174-2" href="#__codelineno-174-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-174-3" name="__codelineno-174-3" href="#__codelineno-174-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-174-4" name="__codelineno-174-4" href="#__codelineno-174-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-174-5" name="__codelineno-174-5" href="#__codelineno-174-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-174-6" name="__codelineno-174-6" href="#__codelineno-174-6"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-174-7" name="__codelineno-174-7" href="#__codelineno-174-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">to</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">by</span><span class="p">:</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-174-8" name="__codelineno-174-8" href="#__codelineno-174-8"></a><span class="w">        </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-174-9" name="__codelineno-174-9" href="#__codelineno-174-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-174-10" name="__codelineno-174-10" href="#__codelineno-174-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="bp">count</span>
+<a id="__codelineno-174-11" name="__codelineno-174-11" href="#__codelineno-174-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-171-1" name="__codelineno-171-1" href="#__codelineno-171-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">linearLogRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-175-1" name="__codelineno-175-1" href="#__codelineno-175-1"></a><span class="cm">/* 線形対数時間 */</span>
+<a id="__codelineno-175-2" name="__codelineno-175-2" href="#__codelineno-175-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-175-3" name="__codelineno-175-3" href="#__codelineno-175-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-175-4" name="__codelineno-175-4" href="#__codelineno-175-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span>
+<a id="__codelineno-175-5" name="__codelineno-175-5" href="#__codelineno-175-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-175-6" name="__codelineno-175-6" href="#__codelineno-175-6"></a><span class="w">        </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-175-7" name="__codelineno-175-7" href="#__codelineno-175-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-175-8" name="__codelineno-175-8" href="#__codelineno-175-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
+<a id="__codelineno-175-9" name="__codelineno-175-9" href="#__codelineno-175-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-172-1" name="__codelineno-172-1" href="#__codelineno-172-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">linearLogRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-176-1" name="__codelineno-176-1" href="#__codelineno-176-1"></a><span class="cm">/* 線形対数時間 */</span>
+<a id="__codelineno-176-2" name="__codelineno-176-2" href="#__codelineno-176-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-176-3" name="__codelineno-176-3" href="#__codelineno-176-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-176-4" name="__codelineno-176-4" href="#__codelineno-176-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span>
+<a id="__codelineno-176-5" name="__codelineno-176-5" href="#__codelineno-176-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-176-6" name="__codelineno-176-6" href="#__codelineno-176-6"></a><span class="w">        </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-176-7" name="__codelineno-176-7" href="#__codelineno-176-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-176-8" name="__codelineno-176-8" href="#__codelineno-176-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
+<a id="__codelineno-176-9" name="__codelineno-176-9" href="#__codelineno-176-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-173-1" name="__codelineno-173-1" href="#__codelineno-173-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linearLogRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-177-1" name="__codelineno-177-1" href="#__codelineno-177-1"></a><span class="cm">/* 線形対数時間 */</span>
+<a id="__codelineno-177-2" name="__codelineno-177-2" href="#__codelineno-177-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-177-3" name="__codelineno-177-3" href="#__codelineno-177-3"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-177-4" name="__codelineno-177-4" href="#__codelineno-177-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="m">2</span><span class="p">);</span>
+<a id="__codelineno-177-5" name="__codelineno-177-5" href="#__codelineno-177-5"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-177-6" name="__codelineno-177-6" href="#__codelineno-177-6"></a><span class="w">    </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-177-7" name="__codelineno-177-7" href="#__codelineno-177-7"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-177-8" name="__codelineno-177-8" href="#__codelineno-177-8"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-177-9" name="__codelineno-177-9" href="#__codelineno-177-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-174-1" name="__codelineno-174-1" href="#__codelineno-174-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linear_log_recur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-178-1" name="__codelineno-178-1" href="#__codelineno-178-1"></a><span class="cm">/* 線形対数時間 */</span>
+<a id="__codelineno-178-2" name="__codelineno-178-2" href="#__codelineno-178-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-178-3" name="__codelineno-178-3" href="#__codelineno-178-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-178-4" name="__codelineno-178-4" href="#__codelineno-178-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-178-5" name="__codelineno-178-5" href="#__codelineno-178-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-178-6" name="__codelineno-178-6" href="#__codelineno-178-6"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-178-7" name="__codelineno-178-7" href="#__codelineno-178-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-178-8" name="__codelineno-178-8" href="#__codelineno-178-8"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-178-9" name="__codelineno-178-9" href="#__codelineno-178-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-178-10" name="__codelineno-178-10" href="#__codelineno-178-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-178-11" name="__codelineno-178-11" href="#__codelineno-178-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-175-1" name="__codelineno-175-1" href="#__codelineno-175-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linearLogRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-179-1" name="__codelineno-179-1" href="#__codelineno-179-1"></a><span class="cm">/* 線形対数時間 */</span>
+<a id="__codelineno-179-2" name="__codelineno-179-2" href="#__codelineno-179-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linearLogRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-179-3" name="__codelineno-179-3" href="#__codelineno-179-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-179-4" name="__codelineno-179-4" href="#__codelineno-179-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-179-5" name="__codelineno-179-5" href="#__codelineno-179-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-179-6" name="__codelineno-179-6" href="#__codelineno-179-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-179-7" name="__codelineno-179-7" href="#__codelineno-179-7"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-179-8" name="__codelineno-179-8" href="#__codelineno-179-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-179-9" name="__codelineno-179-9" href="#__codelineno-179-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-179-10" name="__codelineno-179-10" href="#__codelineno-179-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-176-1" name="__codelineno-176-1" href="#__codelineno-176-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">linearLogRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-180-1" name="__codelineno-180-1" href="#__codelineno-180-1"></a><span class="cm">/* 線形対数時間 */</span>
+<a id="__codelineno-180-2" name="__codelineno-180-2" href="#__codelineno-180-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-180-3" name="__codelineno-180-3" href="#__codelineno-180-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-180-4" name="__codelineno-180-4" href="#__codelineno-180-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-180-5" name="__codelineno-180-5" href="#__codelineno-180-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="p">)</span>
+<a id="__codelineno-180-6" name="__codelineno-180-6" href="#__codelineno-180-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-180-7" name="__codelineno-180-7" href="#__codelineno-180-7"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span>
+<a id="__codelineno-180-8" name="__codelineno-180-8" href="#__codelineno-180-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-180-9" name="__codelineno-180-9" href="#__codelineno-180-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
+<a id="__codelineno-180-10" name="__codelineno-180-10" href="#__codelineno-180-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-177-1" name="__codelineno-177-1" href="#__codelineno-177-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">linear_log_recur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-181-1" name="__codelineno-181-1" href="#__codelineno-181-1"></a><span class="c1">### 線形対数時間 ###</span>
+<a id="__codelineno-181-2" name="__codelineno-181-2" href="#__codelineno-181-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-181-3" name="__codelineno-181-3" href="#__codelineno-181-3"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-181-4" name="__codelineno-181-4" href="#__codelineno-181-4"></a>
+<a id="__codelineno-181-5" name="__codelineno-181-5" href="#__codelineno-181-5"></a><span class="w">  </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-181-6" name="__codelineno-181-6" href="#__codelineno-181-6"></a><span class="w">  </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-181-7" name="__codelineno-181-7" href="#__codelineno-181-7"></a>
+<a id="__codelineno-181-8" name="__codelineno-181-8" href="#__codelineno-181-8"></a><span class="w">  </span><span class="n">count</span>
+<a id="__codelineno-181-9" name="__codelineno-181-9" href="#__codelineno-181-9"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>下図は線形対数オーダーがどのように生成されるかを示しています。二分木の各レベルには<span class="arithmatex">\(n\)</span>個の操作があり、木には<span class="arithmatex">\(\log_2 n + 1\)</span>レベルがあり、時間計算量は<span class="arithmatex">\(O(n \log n)\)</span>になります。</p>
-<p><img alt="Linear-logarithmic order time complexity" class="animation-figure" src="../time_complexity.assets/time_complexity_logarithmic_linear.png" /></p>
-<p align="center"> 図 2-13 &nbsp; Linear-logarithmic order time complexity </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 459px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20linear_log_recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%B7%9A%E5%BD%A2%E5%AF%BE%E6%95%B0%E6%99%82%E9%96%93%22%22%22%0A%20%20%20%20if%20n%20%3C%3D%201%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20count%20%3D%20linear_log_recur%28n%20%2F%2F%202%29%20%2B%20linear_log_recur%28n%20%2F%2F%202%29%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20linear_log_recur%28n%29%0A%20%20%20%20print%28%22%E7%B7%9A%E5%BD%A2%E5%AF%BE%E6%95%B0%E6%99%82%E9%96%93%EF%BC%88%E5%86%8D%E5%B8%B0%E5%AE%9F%E8%A3%85%EF%BC%89%E3%81%AE%E6%93%8D%E4%BD%9C%E5%9B%9E%E6%95%B0%20%3D%22%2C%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20linear_log_recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%B7%9A%E5%BD%A2%E5%AF%BE%E6%95%B0%E6%99%82%E9%96%93%22%22%22%0A%20%20%20%20if%20n%20%3C%3D%201%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20count%20%3D%20linear_log_recur%28n%20%2F%2F%202%29%20%2B%20linear_log_recur%28n%20%2F%2F%202%29%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20linear_log_recur%28n%29%0A%20%20%20%20print%28%22%E7%B7%9A%E5%BD%A2%E5%AF%BE%E6%95%B0%E6%99%82%E9%96%93%EF%BC%88%E5%86%8D%E5%B8%B0%E5%AE%9F%E8%A3%85%EF%BC%89%E3%81%AE%E6%93%8D%E4%BD%9C%E5%9B%9E%E6%95%B0%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>下図は線形対数階がどのように生じるかを示しています。二分木の各層の操作総数はすべて <span class="arithmatex">\(n\)</span> であり、木全体は <span class="arithmatex">\(\log_2 n + 1\)</span> 層あるため、時間計算量は <span class="arithmatex">\(O(n \log n)\)</span> です。</p>
+<p><img alt="線形対数階の時間計算量" class="animation-figure" src="../time_complexity.assets/time_complexity_logarithmic_linear.png" /></p>
+<p align="center"> 図 2-13 &nbsp; 線形対数階の時間計算量 </p>
 
-<p>主流のソートアルゴリズムは通常<span class="arithmatex">\(O(n \log n)\)</span>の時間計算量を持ち、クイックソート、マージソート、ヒープソートなどがあります。</p>
-<h3 id="7-on">7. &nbsp; 階乗オーダー <span class="arithmatex">\(O(n!)\)</span><a class="headerlink" href="#7-on" title="Permanent link">&para;</a></h3>
-<p>階乗オーダーは「全順列」の数学問題に対応します。<span class="arithmatex">\(n\)</span>個の異なる要素が与えられた場合、可能な順列の総数は：</p>
+<p>主なソートアルゴリズムの時間計算量は通常 <span class="arithmatex">\(O(n \log n)\)</span> であり、例えばクイックソート、マージソート、ヒープソートなどがあります。</p>
+<h3 id="7-on">7. &nbsp; 階乗階 <span class="arithmatex">\(O(n!)\)</span><a class="headerlink" href="#7-on" title="Permanent link">&para;</a></h3>
+<p>階乗階は、数学における「全順列」の問題に対応します。互いに重複しない <span class="arithmatex">\(n\)</span> 個の要素が与えられたとき、そのすべての並べ方を求めると、通り数は次のようになります：</p>
 <div class="arithmatex">\[
 n! = n \times (n - 1) \times (n - 2) \times \dots \times 2 \times 1
 \]</div>
-<p>階乗は通常再帰を使用して実装されます。以下のコードと図に示されているように、第1レベルは<span class="arithmatex">\(n\)</span>個の分岐に分割され、第2レベルは<span class="arithmatex">\(n - 1\)</span>個の分岐に分割され、第<span class="arithmatex">\(n\)</span>レベル後に停止します：</p>
+<p>階乗は通常、再帰で実装されます。以下の図とコードのように、第 1 層では <span class="arithmatex">\(n\)</span> 個に分岐し、第 2 層では <span class="arithmatex">\(n - 1\)</span> 個に分岐し、以下同様に、第 <span class="arithmatex">\(n\)</span> 層で分岐が停止します：</p>
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 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-178-1" name="__codelineno-178-1" href="#__codelineno-178-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">factorial_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-178-2" name="__codelineno-178-2" href="#__codelineno-178-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;階乗複雑度（再帰実装）&quot;&quot;&quot;</span>
-<a id="__codelineno-178-3" name="__codelineno-178-3" href="#__codelineno-178-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
-<a id="__codelineno-178-4" name="__codelineno-178-4" href="#__codelineno-178-4"></a>        <span class="k">return</span> <span class="mi">1</span>
-<a id="__codelineno-178-5" name="__codelineno-178-5" href="#__codelineno-178-5"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
-<a id="__codelineno-178-6" name="__codelineno-178-6" href="#__codelineno-178-6"></a>    <span class="c1"># 1つからnに分岐</span>
-<a id="__codelineno-178-7" name="__codelineno-178-7" href="#__codelineno-178-7"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
-<a id="__codelineno-178-8" name="__codelineno-178-8" href="#__codelineno-178-8"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="n">factorial_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-178-9" name="__codelineno-178-9" href="#__codelineno-178-9"></a>    <span class="k">return</span> <span class="n">count</span>
+<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-182-1" name="__codelineno-182-1" href="#__codelineno-182-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">factorial_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-182-2" name="__codelineno-182-2" href="#__codelineno-182-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;階乗時間（再帰実装）&quot;&quot;&quot;</span>
+<a id="__codelineno-182-3" name="__codelineno-182-3" href="#__codelineno-182-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+<a id="__codelineno-182-4" name="__codelineno-182-4" href="#__codelineno-182-4"></a>        <span class="k">return</span> <span class="mi">1</span>
+<a id="__codelineno-182-5" name="__codelineno-182-5" href="#__codelineno-182-5"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-182-6" name="__codelineno-182-6" href="#__codelineno-182-6"></a>    <span class="c1"># 1個から n 個に分裂</span>
+<a id="__codelineno-182-7" name="__codelineno-182-7" href="#__codelineno-182-7"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-182-8" name="__codelineno-182-8" href="#__codelineno-182-8"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="n">factorial_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-182-9" name="__codelineno-182-9" href="#__codelineno-182-9"></a>    <span class="k">return</span> <span class="n">count</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-179-1" name="__codelineno-179-1" href="#__codelineno-179-1"></a><span class="cm">/* 階乗計算量（再帰実装） */</span>
-<a id="__codelineno-179-2" name="__codelineno-179-2" href="#__codelineno-179-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">factorialRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-179-3" name="__codelineno-179-3" href="#__codelineno-179-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
-<a id="__codelineno-179-4" name="__codelineno-179-4" href="#__codelineno-179-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-179-5" name="__codelineno-179-5" href="#__codelineno-179-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-179-6" name="__codelineno-179-6" href="#__codelineno-179-6"></a><span class="w">    </span><span class="c1">// 1から n に分裂</span>
-<a id="__codelineno-179-7" name="__codelineno-179-7" href="#__codelineno-179-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-179-8" name="__codelineno-179-8" href="#__codelineno-179-8"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-179-9" name="__codelineno-179-9" href="#__codelineno-179-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-179-10" name="__codelineno-179-10" href="#__codelineno-179-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
-<a id="__codelineno-179-11" name="__codelineno-179-11" href="#__codelineno-179-11"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-183-1" name="__codelineno-183-1" href="#__codelineno-183-1"></a><span class="cm">/* 階乗時間（再帰実装） */</span>
+<a id="__codelineno-183-2" name="__codelineno-183-2" href="#__codelineno-183-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">factorialRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-183-3" name="__codelineno-183-3" href="#__codelineno-183-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-183-4" name="__codelineno-183-4" href="#__codelineno-183-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-183-5" name="__codelineno-183-5" href="#__codelineno-183-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-183-6" name="__codelineno-183-6" href="#__codelineno-183-6"></a><span class="w">    </span><span class="c1">// 1個から n 個に分裂</span>
+<a id="__codelineno-183-7" name="__codelineno-183-7" href="#__codelineno-183-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-183-8" name="__codelineno-183-8" href="#__codelineno-183-8"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-183-9" name="__codelineno-183-9" href="#__codelineno-183-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-183-10" name="__codelineno-183-10" href="#__codelineno-183-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-183-11" name="__codelineno-183-11" href="#__codelineno-183-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-180-1" name="__codelineno-180-1" href="#__codelineno-180-1"></a><span class="cm">/* 階乗計算量（再帰実装） */</span>
-<a id="__codelineno-180-2" name="__codelineno-180-2" href="#__codelineno-180-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">factorialRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-180-3" name="__codelineno-180-3" href="#__codelineno-180-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
-<a id="__codelineno-180-4" name="__codelineno-180-4" href="#__codelineno-180-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-180-5" name="__codelineno-180-5" href="#__codelineno-180-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-180-6" name="__codelineno-180-6" href="#__codelineno-180-6"></a><span class="w">    </span><span class="c1">// 1から n に分裂</span>
-<a id="__codelineno-180-7" name="__codelineno-180-7" href="#__codelineno-180-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-180-8" name="__codelineno-180-8" href="#__codelineno-180-8"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-180-9" name="__codelineno-180-9" href="#__codelineno-180-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-180-10" name="__codelineno-180-10" href="#__codelineno-180-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
-<a id="__codelineno-180-11" name="__codelineno-180-11" href="#__codelineno-180-11"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-184-1" name="__codelineno-184-1" href="#__codelineno-184-1"></a><span class="cm">/* 階乗時間（再帰実装） */</span>
+<a id="__codelineno-184-2" name="__codelineno-184-2" href="#__codelineno-184-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">factorialRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-184-3" name="__codelineno-184-3" href="#__codelineno-184-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-184-4" name="__codelineno-184-4" href="#__codelineno-184-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-184-5" name="__codelineno-184-5" href="#__codelineno-184-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-184-6" name="__codelineno-184-6" href="#__codelineno-184-6"></a><span class="w">    </span><span class="c1">// 1個から n 個に分裂</span>
+<a id="__codelineno-184-7" name="__codelineno-184-7" href="#__codelineno-184-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-184-8" name="__codelineno-184-8" href="#__codelineno-184-8"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-184-9" name="__codelineno-184-9" href="#__codelineno-184-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-184-10" name="__codelineno-184-10" href="#__codelineno-184-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-184-11" name="__codelineno-184-11" href="#__codelineno-184-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-181-1" name="__codelineno-181-1" href="#__codelineno-181-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">FactorialRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-185-1" name="__codelineno-185-1" href="#__codelineno-185-1"></a><span class="cm">/* 階乗時間（再帰実装） */</span>
+<a id="__codelineno-185-2" name="__codelineno-185-2" href="#__codelineno-185-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">FactorialRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-185-3" name="__codelineno-185-3" href="#__codelineno-185-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-185-4" name="__codelineno-185-4" href="#__codelineno-185-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-185-5" name="__codelineno-185-5" href="#__codelineno-185-5"></a><span class="w">    </span><span class="c1">// 1個から n 個に分裂</span>
+<a id="__codelineno-185-6" name="__codelineno-185-6" href="#__codelineno-185-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-185-7" name="__codelineno-185-7" href="#__codelineno-185-7"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">FactorialRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-185-8" name="__codelineno-185-8" href="#__codelineno-185-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-185-9" name="__codelineno-185-9" href="#__codelineno-185-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-185-10" name="__codelineno-185-10" href="#__codelineno-185-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-182-1" name="__codelineno-182-1" href="#__codelineno-182-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">factorialRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-186-1" name="__codelineno-186-1" href="#__codelineno-186-1"></a><span class="cm">/* 階乗時間（再帰実装） */</span>
+<a id="__codelineno-186-2" name="__codelineno-186-2" href="#__codelineno-186-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">factorialRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-186-3" name="__codelineno-186-3" href="#__codelineno-186-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-186-4" name="__codelineno-186-4" href="#__codelineno-186-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-186-5" name="__codelineno-186-5" href="#__codelineno-186-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-186-6" name="__codelineno-186-6" href="#__codelineno-186-6"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-186-7" name="__codelineno-186-7" href="#__codelineno-186-7"></a><span class="w">    </span><span class="c1">// 1個から n 個に分裂</span>
+<a id="__codelineno-186-8" name="__codelineno-186-8" href="#__codelineno-186-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-186-9" name="__codelineno-186-9" href="#__codelineno-186-9"></a><span class="w">        </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">factorialRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-186-10" name="__codelineno-186-10" href="#__codelineno-186-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-186-11" name="__codelineno-186-11" href="#__codelineno-186-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
+<a id="__codelineno-186-12" name="__codelineno-186-12" href="#__codelineno-186-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-183-1" name="__codelineno-183-1" href="#__codelineno-183-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">factorialRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-187-1" name="__codelineno-187-1" href="#__codelineno-187-1"></a><span class="cm">/* 階乗時間（再帰実装） */</span>
+<a id="__codelineno-187-2" name="__codelineno-187-2" href="#__codelineno-187-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-187-3" name="__codelineno-187-3" href="#__codelineno-187-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-187-4" name="__codelineno-187-4" href="#__codelineno-187-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-187-5" name="__codelineno-187-5" href="#__codelineno-187-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-187-6" name="__codelineno-187-6" href="#__codelineno-187-6"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-187-7" name="__codelineno-187-7" href="#__codelineno-187-7"></a><span class="w">    </span><span class="c1">// 1個から n 個に分裂</span>
+<a id="__codelineno-187-8" name="__codelineno-187-8" href="#__codelineno-187-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-187-9" name="__codelineno-187-9" href="#__codelineno-187-9"></a><span class="w">        </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-187-10" name="__codelineno-187-10" href="#__codelineno-187-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-187-11" name="__codelineno-187-11" href="#__codelineno-187-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="bp">count</span>
+<a id="__codelineno-187-12" name="__codelineno-187-12" href="#__codelineno-187-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-184-1" name="__codelineno-184-1" href="#__codelineno-184-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">factorialRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-188-1" name="__codelineno-188-1" href="#__codelineno-188-1"></a><span class="cm">/* 階乗時間（再帰実装） */</span>
+<a id="__codelineno-188-2" name="__codelineno-188-2" href="#__codelineno-188-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">factorialRecur</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-188-3" name="__codelineno-188-3" href="#__codelineno-188-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-188-4" name="__codelineno-188-4" href="#__codelineno-188-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-188-5" name="__codelineno-188-5" href="#__codelineno-188-5"></a><span class="w">    </span><span class="c1">// 1個から n 個に分裂</span>
+<a id="__codelineno-188-6" name="__codelineno-188-6" href="#__codelineno-188-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-188-7" name="__codelineno-188-7" href="#__codelineno-188-7"></a><span class="w">        </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">factorialRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-188-8" name="__codelineno-188-8" href="#__codelineno-188-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-188-9" name="__codelineno-188-9" href="#__codelineno-188-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
+<a id="__codelineno-188-10" name="__codelineno-188-10" href="#__codelineno-188-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-185-1" name="__codelineno-185-1" href="#__codelineno-185-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">factorialRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-189-1" name="__codelineno-189-1" href="#__codelineno-189-1"></a><span class="cm">/* 階乗時間（再帰実装） */</span>
+<a id="__codelineno-189-2" name="__codelineno-189-2" href="#__codelineno-189-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">factorialRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-189-3" name="__codelineno-189-3" href="#__codelineno-189-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-189-4" name="__codelineno-189-4" href="#__codelineno-189-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-189-5" name="__codelineno-189-5" href="#__codelineno-189-5"></a><span class="w">    </span><span class="c1">// 1個から n 個に分裂</span>
+<a id="__codelineno-189-6" name="__codelineno-189-6" href="#__codelineno-189-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-189-7" name="__codelineno-189-7" href="#__codelineno-189-7"></a><span class="w">        </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">factorialRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-189-8" name="__codelineno-189-8" href="#__codelineno-189-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-189-9" name="__codelineno-189-9" href="#__codelineno-189-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
+<a id="__codelineno-189-10" name="__codelineno-189-10" href="#__codelineno-189-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-186-1" name="__codelineno-186-1" href="#__codelineno-186-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">factorialRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-190-1" name="__codelineno-190-1" href="#__codelineno-190-1"></a><span class="cm">/* 階乗時間（再帰実装） */</span>
+<a id="__codelineno-190-2" name="__codelineno-190-2" href="#__codelineno-190-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-190-3" name="__codelineno-190-3" href="#__codelineno-190-3"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-190-4" name="__codelineno-190-4" href="#__codelineno-190-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-190-5" name="__codelineno-190-5" href="#__codelineno-190-5"></a><span class="w">  </span><span class="c1">// 1個から n 個に分裂</span>
+<a id="__codelineno-190-6" name="__codelineno-190-6" href="#__codelineno-190-6"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-190-7" name="__codelineno-190-7" href="#__codelineno-190-7"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-190-8" name="__codelineno-190-8" href="#__codelineno-190-8"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-190-9" name="__codelineno-190-9" href="#__codelineno-190-9"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-190-10" name="__codelineno-190-10" href="#__codelineno-190-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-187-1" name="__codelineno-187-1" href="#__codelineno-187-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">factorial_recur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-191-1" name="__codelineno-191-1" href="#__codelineno-191-1"></a><span class="cm">/* 階乗時間（再帰実装） */</span>
+<a id="__codelineno-191-2" name="__codelineno-191-2" href="#__codelineno-191-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">factorial_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-191-3" name="__codelineno-191-3" href="#__codelineno-191-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-191-4" name="__codelineno-191-4" href="#__codelineno-191-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-191-5" name="__codelineno-191-5" href="#__codelineno-191-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-191-6" name="__codelineno-191-6" href="#__codelineno-191-6"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-191-7" name="__codelineno-191-7" href="#__codelineno-191-7"></a><span class="w">    </span><span class="c1">// 1個から n 個に分裂</span>
+<a id="__codelineno-191-8" name="__codelineno-191-8" href="#__codelineno-191-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-191-9" name="__codelineno-191-9" href="#__codelineno-191-9"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorial_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-191-10" name="__codelineno-191-10" href="#__codelineno-191-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-191-11" name="__codelineno-191-11" href="#__codelineno-191-11"></a><span class="w">    </span><span class="n">count</span>
+<a id="__codelineno-191-12" name="__codelineno-191-12" href="#__codelineno-191-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-188-1" name="__codelineno-188-1" href="#__codelineno-188-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">factorialRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-192-1" name="__codelineno-192-1" href="#__codelineno-192-1"></a><span class="cm">/* 階乗時間（再帰実装） */</span>
+<a id="__codelineno-192-2" name="__codelineno-192-2" href="#__codelineno-192-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">factorialRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-192-3" name="__codelineno-192-3" href="#__codelineno-192-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-192-4" name="__codelineno-192-4" href="#__codelineno-192-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-192-5" name="__codelineno-192-5" href="#__codelineno-192-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-192-6" name="__codelineno-192-6" href="#__codelineno-192-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-192-7" name="__codelineno-192-7" href="#__codelineno-192-7"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-192-8" name="__codelineno-192-8" href="#__codelineno-192-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-192-9" name="__codelineno-192-9" href="#__codelineno-192-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-192-10" name="__codelineno-192-10" href="#__codelineno-192-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-189-1" name="__codelineno-189-1" href="#__codelineno-189-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">factorialRecur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-193-1" name="__codelineno-193-1" href="#__codelineno-193-1"></a><span class="cm">/* 階乗時間（再帰実装） */</span>
+<a id="__codelineno-193-2" name="__codelineno-193-2" href="#__codelineno-193-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-193-3" name="__codelineno-193-3" href="#__codelineno-193-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">)</span>
+<a id="__codelineno-193-4" name="__codelineno-193-4" href="#__codelineno-193-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-193-5" name="__codelineno-193-5" href="#__codelineno-193-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-193-6" name="__codelineno-193-6" href="#__codelineno-193-6"></a><span class="w">    </span><span class="c1">// 1個から n 個に分裂</span>
+<a id="__codelineno-193-7" name="__codelineno-193-7" href="#__codelineno-193-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-193-8" name="__codelineno-193-8" href="#__codelineno-193-8"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-193-9" name="__codelineno-193-9" href="#__codelineno-193-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-193-10" name="__codelineno-193-10" href="#__codelineno-193-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
+<a id="__codelineno-193-11" name="__codelineno-193-11" href="#__codelineno-193-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-190-1" name="__codelineno-190-1" href="#__codelineno-190-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">factorial_recur</span><span class="p">}</span>
+<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-194-1" name="__codelineno-194-1" href="#__codelineno-194-1"></a><span class="c1">### 線形対数時間 ###</span>
+<a id="__codelineno-194-2" name="__codelineno-194-2" href="#__codelineno-194-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-194-3" name="__codelineno-194-3" href="#__codelineno-194-3"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-194-4" name="__codelineno-194-4" href="#__codelineno-194-4"></a>
+<a id="__codelineno-194-5" name="__codelineno-194-5" href="#__codelineno-194-5"></a><span class="w">  </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-194-6" name="__codelineno-194-6" href="#__codelineno-194-6"></a><span class="w">  </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-194-7" name="__codelineno-194-7" href="#__codelineno-194-7"></a>
+<a id="__codelineno-194-8" name="__codelineno-194-8" href="#__codelineno-194-8"></a><span class="w">  </span><span class="n">count</span>
+<a id="__codelineno-194-9" name="__codelineno-194-9" href="#__codelineno-194-9"></a><span class="k">end</span>
+<a id="__codelineno-194-10" name="__codelineno-194-10" href="#__codelineno-194-10"></a>
+<a id="__codelineno-194-11" name="__codelineno-194-11" href="#__codelineno-194-11"></a><span class="c1"># ## 階乗階（再帰実装）###</span>
+<a id="__codelineno-194-12" name="__codelineno-194-12" href="#__codelineno-194-12"></a><span class="k">def</span><span class="w"> </span><span class="nf">factorial_recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-194-13" name="__codelineno-194-13" href="#__codelineno-194-13"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-194-14" name="__codelineno-194-14" href="#__codelineno-194-14"></a>
+<a id="__codelineno-194-15" name="__codelineno-194-15" href="#__codelineno-194-15"></a><span class="w">  </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-194-16" name="__codelineno-194-16" href="#__codelineno-194-16"></a><span class="w">  </span><span class="c1"># 1個から n 個に分裂</span>
+<a id="__codelineno-194-17" name="__codelineno-194-17" href="#__codelineno-194-17"></a><span class="w">  </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorial_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-194-18" name="__codelineno-194-18" href="#__codelineno-194-18"></a>
+<a id="__codelineno-194-19" name="__codelineno-194-19" href="#__codelineno-194-19"></a><span class="w">  </span><span class="n">count</span>
+<a id="__codelineno-194-20" name="__codelineno-194-20" href="#__codelineno-194-20"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p><img alt="Factorial order time complexity" class="animation-figure" src="../time_complexity.assets/time_complexity_factorial.png" /></p>
-<p align="center"> 図 2-14 &nbsp; Factorial order time complexity </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 477px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20factorial_recur%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%9A%8E%E4%B9%97%E6%99%82%E9%96%93%EF%BC%88%E5%86%8D%E5%B8%B0%E5%AE%9F%E8%A3%85%EF%BC%89%22%22%22%0A%20%20%20%20if%20n%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%201%E5%80%8B%E3%81%8B%E3%82%89%20n%20%E5%80%8B%E3%81%AB%E5%88%86%E8%A3%82%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%20factorial_recur%28n%20-%201%29%0A%20%20%20%20return%20count%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%204%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20factorial_recur%28n%29%0A%20%20%20%20print%28%22%E9%9A%8E%E4%B9%97%E6%99%82%E9%96%93%EF%BC%88%E5%86%8D%E5%B8%B0%E5%AE%9F%E8%A3%85%EF%BC%89%E3%81%AE%E6%93%8D%E4%BD%9C%E5%9B%9E%E6%95%B0%20%3D%22%2C%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20factorial_recur%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%9A%8E%E4%B9%97%E6%99%82%E9%96%93%EF%BC%88%E5%86%8D%E5%B8%B0%E5%AE%9F%E8%A3%85%EF%BC%89%22%22%22%0A%20%20%20%20if%20n%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%201%E5%80%8B%E3%81%8B%E3%82%89%20n%20%E5%80%8B%E3%81%AB%E5%88%86%E8%A3%82%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%20factorial_recur%28n%20-%201%29%0A%20%20%20%20return%20count%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%204%0A%20%20%20%20print%28%22%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%BA%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20factorial_recur%28n%29%0A%20%20%20%20print%28%22%E9%9A%8E%E4%B9%97%E6%99%82%E9%96%93%EF%BC%88%E5%86%8D%E5%B8%B0%E5%AE%9F%E8%A3%85%EF%BC%89%E3%81%AE%E6%93%8D%E4%BD%9C%E5%9B%9E%E6%95%B0%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p><img alt="階乗階の時間計算量" class="animation-figure" src="../time_complexity.assets/time_complexity_factorial.png" /></p>
+<p align="center"> 図 2-14 &nbsp; 階乗階の時間計算量 </p>
 
-<p>階乗オーダーは指数オーダーよりもさらに速く増加することに注意してください。より大きな<span class="arithmatex">\(n\)</span>値では受け入れられません。</p>
-<h2 id="235">2.3.5 &nbsp; 最悪、最良、平均時間計算量<a class="headerlink" href="#235" title="Permanent link">&para;</a></h2>
-<p><strong>アルゴリズムの時間効率は固定されていないことが多く、入力データの分布に依存します</strong>。長さ<span class="arithmatex">\(n\)</span>の配列<code>nums</code>があり、<span class="arithmatex">\(1\)</span>から<span class="arithmatex">\(n\)</span>までの数で構成され、それぞれが一度だけ現れますが、ランダムにシャッフルされた順序であるとします。タスクは要素<span class="arithmatex">\(1\)</span>のインデックスを返すことです。以下の結論を導けます：</p>
+<p>注意すべき点として、<span class="arithmatex">\(n \geq 4\)</span> なら常に <span class="arithmatex">\(n! &gt; 2^n\)</span> なので、階乗階は指数階よりもさらに速く増加し、<span class="arithmatex">\(n\)</span> が大きい場合にはやはり受け入れられません。</p>
+<h2 id="235">2.3.5 &nbsp; 最悪・最良・平均時間計算量<a class="headerlink" href="#235" title="Permanent link">&para;</a></h2>
+<p><strong>アルゴリズムの時間効率は固定ではなく、入力データの分布に左右されることが多いです</strong>。長さ <span class="arithmatex">\(n\)</span> の配列 <code>nums</code> を考えます。<code>nums</code> は <span class="arithmatex">\(1\)</span> から <span class="arithmatex">\(n\)</span> までの数字で構成され、各数字は 1 回だけ現れます。ただし要素の順序はランダムにシャッフルされており、目標は要素 <span class="arithmatex">\(1\)</span> のインデックスを返すことです。ここから次の結論が得られます。</p>
 <ul>
-<li><code>nums = [?, ?, ..., 1]</code>の場合、つまり最後の要素が<span class="arithmatex">\(1\)</span>の場合、配列の完全な走査が必要で、<strong>最悪ケース時間計算量<span class="arithmatex">\(O(n)\)</span>を達成します</strong>。</li>
-<li><code>nums = [1, ?, ?, ...]</code>の場合、つまり最初の要素が<span class="arithmatex">\(1\)</span>の場合、配列の長さに関係なく、さらなる走査は不要で、<strong>最良ケース時間計算量<span class="arithmatex">\(\Omega(1)\)</span>を達成します</strong>。</li>
+<li><code>nums = [?, ?, ..., 1]</code>、つまり末尾の要素が <span class="arithmatex">\(1\)</span> の場合は、配列全体を最後まで走査する必要があり、<strong>最悪時間計算量 <span class="arithmatex">\(O(n)\)</span></strong> になります。</li>
+<li><code>nums = [1, ?, ?, ...]</code>、つまり先頭要素が <span class="arithmatex">\(1\)</span> の場合は、配列がどれだけ長くてもそれ以上走査する必要がなく、<strong>最良時間計算量 <span class="arithmatex">\(\Omega(1)\)</span></strong> になります。</li>
 </ul>
-<p>「最悪ケース時間計算量」は漸近上限に対応し、大きな<span class="arithmatex">\(O\)</span>記法で表されます。対応して、「最良ケース時間計算量」は漸近下限に対応し、<span class="arithmatex">\(\Omega\)</span>で表されます：</p>
+<p>「最悪時間計算量」は関数の漸近上界に対応し、ビッグ <span class="arithmatex">\(O\)</span> 記法で表します。同様に、「最良時間計算量」は関数の漸近下界に対応し、<span class="arithmatex">\(\Omega\)</span> 記法で表します：</p>
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-<div class="highlight"><span class="filename">worst_best_time_complexity.py</span><pre><span></span><code><a id="__codelineno-191-1" name="__codelineno-191-1" href="#__codelineno-191-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">random_numbers</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
-<a id="__codelineno-191-2" name="__codelineno-191-2" href="#__codelineno-191-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;要素 1, 2, ..., n を含む配列を生成、順序はシャッフル&quot;&quot;&quot;</span>
-<a id="__codelineno-191-3" name="__codelineno-191-3" href="#__codelineno-191-3"></a>    <span class="c1"># 配列 nums = 1, 2, 3, ..., n を生成</span>
-<a id="__codelineno-191-4" name="__codelineno-191-4" href="#__codelineno-191-4"></a>    <span class="n">nums</span> <span class="o">=</span> <span class="p">[</span><span class="n">i</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span>
-<a id="__codelineno-191-5" name="__codelineno-191-5" href="#__codelineno-191-5"></a>    <span class="c1"># 配列要素をランダムにシャッフル</span>
-<a id="__codelineno-191-6" name="__codelineno-191-6" href="#__codelineno-191-6"></a>    <span class="n">random</span><span class="o">.</span><span class="n">shuffle</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
-<a id="__codelineno-191-7" name="__codelineno-191-7" href="#__codelineno-191-7"></a>    <span class="k">return</span> <span class="n">nums</span>
-<a id="__codelineno-191-8" name="__codelineno-191-8" href="#__codelineno-191-8"></a>
-<a id="__codelineno-191-9" name="__codelineno-191-9" href="#__codelineno-191-9"></a><span class="k">def</span><span class="w"> </span><span class="nf">find_one</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-191-10" name="__codelineno-191-10" href="#__codelineno-191-10"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;配列 nums で数値 1 のインデックスを検索&quot;&quot;&quot;</span>
-<a id="__codelineno-191-11" name="__codelineno-191-11" href="#__codelineno-191-11"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
-<a id="__codelineno-191-12" name="__codelineno-191-12" href="#__codelineno-191-12"></a>        <span class="c1"># 要素 1 が配列の最初にある場合、最良時間計算量 O(1) を達成</span>
-<a id="__codelineno-191-13" name="__codelineno-191-13" href="#__codelineno-191-13"></a>        <span class="c1"># 要素 1 が配列の最後にある場合、最悪時間計算量 O(n) を達成</span>
-<a id="__codelineno-191-14" name="__codelineno-191-14" href="#__codelineno-191-14"></a>        <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
-<a id="__codelineno-191-15" name="__codelineno-191-15" href="#__codelineno-191-15"></a>            <span class="k">return</span> <span class="n">i</span>
-<a id="__codelineno-191-16" name="__codelineno-191-16" href="#__codelineno-191-16"></a>    <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>
+<div class="highlight"><span class="filename">worst_best_time_complexity.py</span><pre><span></span><code><a id="__codelineno-195-1" name="__codelineno-195-1" href="#__codelineno-195-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">random_numbers</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-195-2" name="__codelineno-195-2" href="#__codelineno-195-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;要素が 1, 2, ..., n で順序がシャッフルされた配列を生成する&quot;&quot;&quot;</span>
+<a id="__codelineno-195-3" name="__codelineno-195-3" href="#__codelineno-195-3"></a>    <span class="c1"># 配列 nums =: 1, 2, 3, ..., n を生成する</span>
+<a id="__codelineno-195-4" name="__codelineno-195-4" href="#__codelineno-195-4"></a>    <span class="n">nums</span> <span class="o">=</span> <span class="p">[</span><span class="n">i</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span>
+<a id="__codelineno-195-5" name="__codelineno-195-5" href="#__codelineno-195-5"></a>    <span class="c1"># 配列要素をランダムにシャッフル</span>
+<a id="__codelineno-195-6" name="__codelineno-195-6" href="#__codelineno-195-6"></a>    <span class="n">random</span><span class="o">.</span><span class="n">shuffle</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-195-7" name="__codelineno-195-7" href="#__codelineno-195-7"></a>    <span class="k">return</span> <span class="n">nums</span>
+<a id="__codelineno-195-8" name="__codelineno-195-8" href="#__codelineno-195-8"></a>
+<a id="__codelineno-195-9" name="__codelineno-195-9" href="#__codelineno-195-9"></a><span class="k">def</span><span class="w"> </span><span class="nf">find_one</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-195-10" name="__codelineno-195-10" href="#__codelineno-195-10"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;配列 nums 内で数値 1 のインデックスを探す&quot;&quot;&quot;</span>
+<a id="__codelineno-195-11" name="__codelineno-195-11" href="#__codelineno-195-11"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
+<a id="__codelineno-195-12" name="__codelineno-195-12" href="#__codelineno-195-12"></a>        <span class="c1"># 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる</span>
+<a id="__codelineno-195-13" name="__codelineno-195-13" href="#__codelineno-195-13"></a>        <span class="c1"># 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる</span>
+<a id="__codelineno-195-14" name="__codelineno-195-14" href="#__codelineno-195-14"></a>        <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+<a id="__codelineno-195-15" name="__codelineno-195-15" href="#__codelineno-195-15"></a>            <span class="k">return</span> <span class="n">i</span>
+<a id="__codelineno-195-16" name="__codelineno-195-16" href="#__codelineno-195-16"></a>    <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">worst_best_time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-192-1" name="__codelineno-192-1" href="#__codelineno-192-1"></a><span class="cm">/* 要素 {1, 2, ..., n} をランダムにシャッフルした配列を生成 */</span>
-<a id="__codelineno-192-2" name="__codelineno-192-2" href="#__codelineno-192-2"></a><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">randomNumbers</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-192-3" name="__codelineno-192-3" href="#__codelineno-192-3"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
-<a id="__codelineno-192-4" name="__codelineno-192-4" href="#__codelineno-192-4"></a><span class="w">    </span><span class="c1">// 配列 nums = { 1, 2, 3, ..., n } を生成</span>
-<a id="__codelineno-192-5" name="__codelineno-192-5" href="#__codelineno-192-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-192-6" name="__codelineno-192-6" href="#__codelineno-192-6"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-192-7" name="__codelineno-192-7" href="#__codelineno-192-7"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-192-8" name="__codelineno-192-8" href="#__codelineno-192-8"></a><span class="w">    </span><span class="c1">// システム時刻を使用してランダムシードを生成</span>
-<a id="__codelineno-192-9" name="__codelineno-192-9" href="#__codelineno-192-9"></a><span class="w">    </span><span class="kt">unsigned</span><span class="w"> </span><span class="n">seed</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">chrono</span><span class="o">::</span><span class="n">system_clock</span><span class="o">::</span><span class="n">now</span><span class="p">().</span><span class="n">time_since_epoch</span><span class="p">().</span><span class="n">count</span><span class="p">();</span>
-<a id="__codelineno-192-10" name="__codelineno-192-10" href="#__codelineno-192-10"></a><span class="w">    </span><span class="c1">// 配列要素をランダムにシャッフル</span>
-<a id="__codelineno-192-11" name="__codelineno-192-11" href="#__codelineno-192-11"></a><span class="w">    </span><span class="n">shuffle</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">end</span><span class="p">(),</span><span class="w"> </span><span class="n">default_random_engine</span><span class="p">(</span><span class="n">seed</span><span class="p">));</span>
-<a id="__codelineno-192-12" name="__codelineno-192-12" href="#__codelineno-192-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
-<a id="__codelineno-192-13" name="__codelineno-192-13" href="#__codelineno-192-13"></a><span class="p">}</span>
-<a id="__codelineno-192-14" name="__codelineno-192-14" href="#__codelineno-192-14"></a>
-<a id="__codelineno-192-15" name="__codelineno-192-15" href="#__codelineno-192-15"></a><span class="cm">/* 配列 nums で数値1のインデックスを見つける */</span>
-<a id="__codelineno-192-16" name="__codelineno-192-16" href="#__codelineno-192-16"></a><span class="kt">int</span><span class="w"> </span><span class="n">findOne</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-192-17" name="__codelineno-192-17" href="#__codelineno-192-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-192-18" name="__codelineno-192-18" href="#__codelineno-192-18"></a><span class="w">        </span><span class="c1">// 要素1が配列の先頭にある場合、最良時間計算量 O(1) を達成</span>
-<a id="__codelineno-192-19" name="__codelineno-192-19" href="#__codelineno-192-19"></a><span class="w">        </span><span class="c1">// 要素1が配列の末尾にある場合、最悪時間計算量 O(n) を達成</span>
-<a id="__codelineno-192-20" name="__codelineno-192-20" href="#__codelineno-192-20"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-192-21" name="__codelineno-192-21" href="#__codelineno-192-21"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
-<a id="__codelineno-192-22" name="__codelineno-192-22" href="#__codelineno-192-22"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-192-23" name="__codelineno-192-23" href="#__codelineno-192-23"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
-<a id="__codelineno-192-24" name="__codelineno-192-24" href="#__codelineno-192-24"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">worst_best_time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-196-1" name="__codelineno-196-1" href="#__codelineno-196-1"></a><span class="cm">/* 要素が { 1, 2, ..., n } で、順序がシャッフルされた配列を生成 */</span>
+<a id="__codelineno-196-2" name="__codelineno-196-2" href="#__codelineno-196-2"></a><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">randomNumbers</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-196-3" name="__codelineno-196-3" href="#__codelineno-196-3"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-196-4" name="__codelineno-196-4" href="#__codelineno-196-4"></a><span class="w">    </span><span class="c1">// 配列 nums = { 1, 2, 3, ..., n } を生成</span>
+<a id="__codelineno-196-5" name="__codelineno-196-5" href="#__codelineno-196-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-196-6" name="__codelineno-196-6" href="#__codelineno-196-6"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-196-7" name="__codelineno-196-7" href="#__codelineno-196-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-196-8" name="__codelineno-196-8" href="#__codelineno-196-8"></a><span class="w">    </span><span class="c1">// システム時刻を使って乱数シードを生成する</span>
+<a id="__codelineno-196-9" name="__codelineno-196-9" href="#__codelineno-196-9"></a><span class="w">    </span><span class="kt">unsigned</span><span class="w"> </span><span class="n">seed</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">chrono</span><span class="o">::</span><span class="n">system_clock</span><span class="o">::</span><span class="n">now</span><span class="p">().</span><span class="n">time_since_epoch</span><span class="p">().</span><span class="n">count</span><span class="p">();</span>
+<a id="__codelineno-196-10" name="__codelineno-196-10" href="#__codelineno-196-10"></a><span class="w">    </span><span class="c1">// 配列要素をランダムにシャッフル</span>
+<a id="__codelineno-196-11" name="__codelineno-196-11" href="#__codelineno-196-11"></a><span class="w">    </span><span class="n">shuffle</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">end</span><span class="p">(),</span><span class="w"> </span><span class="n">default_random_engine</span><span class="p">(</span><span class="n">seed</span><span class="p">));</span>
+<a id="__codelineno-196-12" name="__codelineno-196-12" href="#__codelineno-196-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
+<a id="__codelineno-196-13" name="__codelineno-196-13" href="#__codelineno-196-13"></a><span class="p">}</span>
+<a id="__codelineno-196-14" name="__codelineno-196-14" href="#__codelineno-196-14"></a>
+<a id="__codelineno-196-15" name="__codelineno-196-15" href="#__codelineno-196-15"></a><span class="cm">/* 配列 nums 内で数値 1 のインデックスを探す */</span>
+<a id="__codelineno-196-16" name="__codelineno-196-16" href="#__codelineno-196-16"></a><span class="kt">int</span><span class="w"> </span><span class="n">findOne</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-196-17" name="__codelineno-196-17" href="#__codelineno-196-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-196-18" name="__codelineno-196-18" href="#__codelineno-196-18"></a><span class="w">        </span><span class="c1">// 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる</span>
+<a id="__codelineno-196-19" name="__codelineno-196-19" href="#__codelineno-196-19"></a><span class="w">        </span><span class="c1">// 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる</span>
+<a id="__codelineno-196-20" name="__codelineno-196-20" href="#__codelineno-196-20"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-196-21" name="__codelineno-196-21" href="#__codelineno-196-21"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-196-22" name="__codelineno-196-22" href="#__codelineno-196-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-196-23" name="__codelineno-196-23" href="#__codelineno-196-23"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-196-24" name="__codelineno-196-24" href="#__codelineno-196-24"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">worst_best_time_complexity.java</span><pre><span></span><code><a id="__codelineno-193-1" name="__codelineno-193-1" href="#__codelineno-193-1"></a><span class="cm">/* 要素 {1, 2, ..., n} をランダムにシャッフルした配列を生成 */</span>
-<a id="__codelineno-193-2" name="__codelineno-193-2" href="#__codelineno-193-2"></a><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">randomNumbers</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-193-3" name="__codelineno-193-3" href="#__codelineno-193-3"></a><span class="w">    </span><span class="n">Integer</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Integer</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-193-4" name="__codelineno-193-4" href="#__codelineno-193-4"></a><span class="w">    </span><span class="c1">// 配列 nums = { 1, 2, 3, ..., n } を生成</span>
-<a id="__codelineno-193-5" name="__codelineno-193-5" href="#__codelineno-193-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-193-6" name="__codelineno-193-6" href="#__codelineno-193-6"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-193-7" name="__codelineno-193-7" href="#__codelineno-193-7"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-193-8" name="__codelineno-193-8" href="#__codelineno-193-8"></a><span class="w">    </span><span class="c1">// 配列要素をランダムにシャッフル</span>
-<a id="__codelineno-193-9" name="__codelineno-193-9" href="#__codelineno-193-9"></a><span class="w">    </span><span class="n">Collections</span><span class="p">.</span><span class="na">shuffle</span><span class="p">(</span><span class="n">Arrays</span><span class="p">.</span><span class="na">asList</span><span class="p">(</span><span class="n">nums</span><span class="p">));</span>
-<a id="__codelineno-193-10" name="__codelineno-193-10" href="#__codelineno-193-10"></a><span class="w">    </span><span class="c1">// Integer[] -&gt; int[]</span>
-<a id="__codelineno-193-11" name="__codelineno-193-11" href="#__codelineno-193-11"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-193-12" name="__codelineno-193-12" href="#__codelineno-193-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-193-13" name="__codelineno-193-13" href="#__codelineno-193-13"></a><span class="w">        </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-193-14" name="__codelineno-193-14" href="#__codelineno-193-14"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-193-15" name="__codelineno-193-15" href="#__codelineno-193-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
-<a id="__codelineno-193-16" name="__codelineno-193-16" href="#__codelineno-193-16"></a><span class="p">}</span>
-<a id="__codelineno-193-17" name="__codelineno-193-17" href="#__codelineno-193-17"></a>
-<a id="__codelineno-193-18" name="__codelineno-193-18" href="#__codelineno-193-18"></a><span class="cm">/* 配列 nums で数値1のインデックスを見つける */</span>
-<a id="__codelineno-193-19" name="__codelineno-193-19" href="#__codelineno-193-19"></a><span class="kt">int</span><span class="w"> </span><span class="nf">findOne</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-193-20" name="__codelineno-193-20" href="#__codelineno-193-20"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-193-21" name="__codelineno-193-21" href="#__codelineno-193-21"></a><span class="w">        </span><span class="c1">// 要素1が配列の先頭にある場合、最良時間計算量 O(1) を達成</span>
-<a id="__codelineno-193-22" name="__codelineno-193-22" href="#__codelineno-193-22"></a><span class="w">        </span><span class="c1">// 要素1が配列の末尾にある場合、最悪時間計算量 O(n) を達成</span>
-<a id="__codelineno-193-23" name="__codelineno-193-23" href="#__codelineno-193-23"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-193-24" name="__codelineno-193-24" href="#__codelineno-193-24"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
-<a id="__codelineno-193-25" name="__codelineno-193-25" href="#__codelineno-193-25"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-193-26" name="__codelineno-193-26" href="#__codelineno-193-26"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-193-27" name="__codelineno-193-27" href="#__codelineno-193-27"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">worst_best_time_complexity.java</span><pre><span></span><code><a id="__codelineno-197-1" name="__codelineno-197-1" href="#__codelineno-197-1"></a><span class="cm">/* 要素が { 1, 2, ..., n } で、順序がシャッフルされた配列を生成 */</span>
+<a id="__codelineno-197-2" name="__codelineno-197-2" href="#__codelineno-197-2"></a><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">randomNumbers</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-197-3" name="__codelineno-197-3" href="#__codelineno-197-3"></a><span class="w">    </span><span class="n">Integer</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Integer</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-197-4" name="__codelineno-197-4" href="#__codelineno-197-4"></a><span class="w">    </span><span class="c1">// 配列 nums = { 1, 2, 3, ..., n } を生成</span>
+<a id="__codelineno-197-5" name="__codelineno-197-5" href="#__codelineno-197-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-197-6" name="__codelineno-197-6" href="#__codelineno-197-6"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-197-7" name="__codelineno-197-7" href="#__codelineno-197-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-197-8" name="__codelineno-197-8" href="#__codelineno-197-8"></a><span class="w">    </span><span class="c1">// 配列要素をランダムにシャッフル</span>
+<a id="__codelineno-197-9" name="__codelineno-197-9" href="#__codelineno-197-9"></a><span class="w">    </span><span class="n">Collections</span><span class="p">.</span><span class="na">shuffle</span><span class="p">(</span><span class="n">Arrays</span><span class="p">.</span><span class="na">asList</span><span class="p">(</span><span class="n">nums</span><span class="p">));</span>
+<a id="__codelineno-197-10" name="__codelineno-197-10" href="#__codelineno-197-10"></a><span class="w">    </span><span class="c1">// Integer[] -&gt; int[]</span>
+<a id="__codelineno-197-11" name="__codelineno-197-11" href="#__codelineno-197-11"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-197-12" name="__codelineno-197-12" href="#__codelineno-197-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-197-13" name="__codelineno-197-13" href="#__codelineno-197-13"></a><span class="w">        </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-197-14" name="__codelineno-197-14" href="#__codelineno-197-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-197-15" name="__codelineno-197-15" href="#__codelineno-197-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-197-16" name="__codelineno-197-16" href="#__codelineno-197-16"></a><span class="p">}</span>
+<a id="__codelineno-197-17" name="__codelineno-197-17" href="#__codelineno-197-17"></a>
+<a id="__codelineno-197-18" name="__codelineno-197-18" href="#__codelineno-197-18"></a><span class="cm">/* 配列 nums 内で数値 1 のインデックスを探す */</span>
+<a id="__codelineno-197-19" name="__codelineno-197-19" href="#__codelineno-197-19"></a><span class="kt">int</span><span class="w"> </span><span class="nf">findOne</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-197-20" name="__codelineno-197-20" href="#__codelineno-197-20"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-197-21" name="__codelineno-197-21" href="#__codelineno-197-21"></a><span class="w">        </span><span class="c1">// 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる</span>
+<a id="__codelineno-197-22" name="__codelineno-197-22" href="#__codelineno-197-22"></a><span class="w">        </span><span class="c1">// 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる</span>
+<a id="__codelineno-197-23" name="__codelineno-197-23" href="#__codelineno-197-23"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-197-24" name="__codelineno-197-24" href="#__codelineno-197-24"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-197-25" name="__codelineno-197-25" href="#__codelineno-197-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-197-26" name="__codelineno-197-26" href="#__codelineno-197-26"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-197-27" name="__codelineno-197-27" href="#__codelineno-197-27"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">worst_best_time_complexity.cs</span><pre><span></span><code><a id="__codelineno-194-1" name="__codelineno-194-1" href="#__codelineno-194-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">worst_best_time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">RandomNumbers</span><span class="p">}</span>
-<a id="__codelineno-194-2" name="__codelineno-194-2" href="#__codelineno-194-2"></a>
-<a id="__codelineno-194-3" name="__codelineno-194-3" href="#__codelineno-194-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">worst_best_time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">FindOne</span><span class="p">}</span>
+<div class="highlight"><span class="filename">worst_best_time_complexity.cs</span><pre><span></span><code><a id="__codelineno-198-1" name="__codelineno-198-1" href="#__codelineno-198-1"></a><span class="cm">/* 要素が { 1, 2, ..., n } で、順序がシャッフルされた配列を生成 */</span>
+<a id="__codelineno-198-2" name="__codelineno-198-2" href="#__codelineno-198-2"></a><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="nf">RandomNumbers</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-198-3" name="__codelineno-198-3" href="#__codelineno-198-3"></a><span class="w">    </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-198-4" name="__codelineno-198-4" href="#__codelineno-198-4"></a><span class="w">    </span><span class="c1">// 配列 nums = { 1, 2, 3, ..., n } を生成</span>
+<a id="__codelineno-198-5" name="__codelineno-198-5" href="#__codelineno-198-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-198-6" name="__codelineno-198-6" href="#__codelineno-198-6"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-198-7" name="__codelineno-198-7" href="#__codelineno-198-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-198-8" name="__codelineno-198-8" href="#__codelineno-198-8"></a>
+<a id="__codelineno-198-9" name="__codelineno-198-9" href="#__codelineno-198-9"></a><span class="w">    </span><span class="c1">// 配列要素をランダムにシャッフル</span>
+<a id="__codelineno-198-10" name="__codelineno-198-10" href="#__codelineno-198-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-198-11" name="__codelineno-198-11" href="#__codelineno-198-11"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Random</span><span class="p">().</span><span class="n">Next</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">);</span>
+<a id="__codelineno-198-12" name="__codelineno-198-12" href="#__codelineno-198-12"></a><span class="w">        </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">index</span><span class="p">])</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">index</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-198-13" name="__codelineno-198-13" href="#__codelineno-198-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-198-14" name="__codelineno-198-14" href="#__codelineno-198-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
+<a id="__codelineno-198-15" name="__codelineno-198-15" href="#__codelineno-198-15"></a><span class="p">}</span>
+<a id="__codelineno-198-16" name="__codelineno-198-16" href="#__codelineno-198-16"></a>
+<a id="__codelineno-198-17" name="__codelineno-198-17" href="#__codelineno-198-17"></a><span class="cm">/* 配列 nums 内で数値 1 のインデックスを探す */</span>
+<a id="__codelineno-198-18" name="__codelineno-198-18" href="#__codelineno-198-18"></a><span class="kt">int</span><span class="w"> </span><span class="nf">FindOne</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-198-19" name="__codelineno-198-19" href="#__codelineno-198-19"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-198-20" name="__codelineno-198-20" href="#__codelineno-198-20"></a><span class="w">        </span><span class="c1">// 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる</span>
+<a id="__codelineno-198-21" name="__codelineno-198-21" href="#__codelineno-198-21"></a><span class="w">        </span><span class="c1">// 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる</span>
+<a id="__codelineno-198-22" name="__codelineno-198-22" href="#__codelineno-198-22"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-198-23" name="__codelineno-198-23" href="#__codelineno-198-23"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-198-24" name="__codelineno-198-24" href="#__codelineno-198-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-198-25" name="__codelineno-198-25" href="#__codelineno-198-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-198-26" name="__codelineno-198-26" href="#__codelineno-198-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">worst_best_time_complexity.go</span><pre><span></span><code><a id="__codelineno-195-1" name="__codelineno-195-1" href="#__codelineno-195-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">randomNumbers</span><span class="p">}</span>
-<a id="__codelineno-195-2" name="__codelineno-195-2" href="#__codelineno-195-2"></a>
-<a id="__codelineno-195-3" name="__codelineno-195-3" href="#__codelineno-195-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">findOne</span><span class="p">}</span>
+<div class="highlight"><span class="filename">worst_best_time_complexity.go</span><pre><span></span><code><a id="__codelineno-199-1" name="__codelineno-199-1" href="#__codelineno-199-1"></a><span class="cm">/* 要素が { 1, 2, ..., n } で、順序がシャッフルされた配列を生成 */</span>
+<a id="__codelineno-199-2" name="__codelineno-199-2" href="#__codelineno-199-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">randomNumbers</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-199-3" name="__codelineno-199-3" href="#__codelineno-199-3"></a><span class="w">    </span><span class="nx">nums</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
+<a id="__codelineno-199-4" name="__codelineno-199-4" href="#__codelineno-199-4"></a><span class="w">    </span><span class="c1">// 配列 nums = { 1, 2, 3, ..., n } を生成</span>
+<a id="__codelineno-199-5" name="__codelineno-199-5" href="#__codelineno-199-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-199-6" name="__codelineno-199-6" href="#__codelineno-199-6"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-199-7" name="__codelineno-199-7" href="#__codelineno-199-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-199-8" name="__codelineno-199-8" href="#__codelineno-199-8"></a><span class="w">    </span><span class="c1">// 配列要素をランダムにシャッフル</span>
+<a id="__codelineno-199-9" name="__codelineno-199-9" href="#__codelineno-199-9"></a><span class="w">    </span><span class="nx">rand</span><span class="p">.</span><span class="nx">Shuffle</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">),</span><span class="w"> </span><span class="kd">func</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-199-10" name="__codelineno-199-10" href="#__codelineno-199-10"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
+<a id="__codelineno-199-11" name="__codelineno-199-11" href="#__codelineno-199-11"></a><span class="w">    </span><span class="p">})</span>
+<a id="__codelineno-199-12" name="__codelineno-199-12" href="#__codelineno-199-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">nums</span>
+<a id="__codelineno-199-13" name="__codelineno-199-13" href="#__codelineno-199-13"></a><span class="p">}</span>
+<a id="__codelineno-199-14" name="__codelineno-199-14" href="#__codelineno-199-14"></a>
+<a id="__codelineno-199-15" name="__codelineno-199-15" href="#__codelineno-199-15"></a><span class="cm">/* 配列 nums 内で数値 1 のインデックスを探す */</span>
+<a id="__codelineno-199-16" name="__codelineno-199-16" href="#__codelineno-199-16"></a><span class="kd">func</span><span class="w"> </span><span class="nx">findOne</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-199-17" name="__codelineno-199-17" href="#__codelineno-199-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-199-18" name="__codelineno-199-18" href="#__codelineno-199-18"></a><span class="w">        </span><span class="c1">// 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる</span>
+<a id="__codelineno-199-19" name="__codelineno-199-19" href="#__codelineno-199-19"></a><span class="w">        </span><span class="c1">// 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる</span>
+<a id="__codelineno-199-20" name="__codelineno-199-20" href="#__codelineno-199-20"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-199-21" name="__codelineno-199-21" href="#__codelineno-199-21"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span>
+<a id="__codelineno-199-22" name="__codelineno-199-22" href="#__codelineno-199-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-199-23" name="__codelineno-199-23" href="#__codelineno-199-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-199-24" name="__codelineno-199-24" href="#__codelineno-199-24"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-199-25" name="__codelineno-199-25" href="#__codelineno-199-25"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">worst_best_time_complexity.swift</span><pre><span></span><code><a id="__codelineno-196-1" name="__codelineno-196-1" href="#__codelineno-196-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">randomNumbers</span><span class="p">}</span>
-<a id="__codelineno-196-2" name="__codelineno-196-2" href="#__codelineno-196-2"></a>
-<a id="__codelineno-196-3" name="__codelineno-196-3" href="#__codelineno-196-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">findOne</span><span class="p">}</span>
+<div class="highlight"><span class="filename">worst_best_time_complexity.swift</span><pre><span></span><code><a id="__codelineno-200-1" name="__codelineno-200-1" href="#__codelineno-200-1"></a><span class="cm">/* 要素が { 1, 2, ..., n } で、順序がシャッフルされた配列を生成 */</span>
+<a id="__codelineno-200-2" name="__codelineno-200-2" href="#__codelineno-200-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">randomNumbers</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-200-3" name="__codelineno-200-3" href="#__codelineno-200-3"></a><span class="w">    </span><span class="c1">// 配列 nums = { 1, 2, 3, ..., n } を生成</span>
+<a id="__codelineno-200-4" name="__codelineno-200-4" href="#__codelineno-200-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-200-5" name="__codelineno-200-5" href="#__codelineno-200-5"></a><span class="w">    </span><span class="c1">// 配列要素をランダムにシャッフル</span>
+<a id="__codelineno-200-6" name="__codelineno-200-6" href="#__codelineno-200-6"></a><span class="w">    </span><span class="n">nums</span><span class="p">.</span><span class="n">shuffle</span><span class="p">()</span>
+<a id="__codelineno-200-7" name="__codelineno-200-7" href="#__codelineno-200-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span>
+<a id="__codelineno-200-8" name="__codelineno-200-8" href="#__codelineno-200-8"></a><span class="p">}</span>
+<a id="__codelineno-200-9" name="__codelineno-200-9" href="#__codelineno-200-9"></a>
+<a id="__codelineno-200-10" name="__codelineno-200-10" href="#__codelineno-200-10"></a><span class="cm">/* 配列 nums 内で数値 1 のインデックスを探す */</span>
+<a id="__codelineno-200-11" name="__codelineno-200-11" href="#__codelineno-200-11"></a><span class="kd">func</span><span class="w"> </span><span class="nf">findOne</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-200-12" name="__codelineno-200-12" href="#__codelineno-200-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-200-13" name="__codelineno-200-13" href="#__codelineno-200-13"></a><span class="w">        </span><span class="c1">// 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる</span>
+<a id="__codelineno-200-14" name="__codelineno-200-14" href="#__codelineno-200-14"></a><span class="w">        </span><span class="c1">// 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる</span>
+<a id="__codelineno-200-15" name="__codelineno-200-15" href="#__codelineno-200-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-200-16" name="__codelineno-200-16" href="#__codelineno-200-16"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-200-17" name="__codelineno-200-17" href="#__codelineno-200-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-200-18" name="__codelineno-200-18" href="#__codelineno-200-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-200-19" name="__codelineno-200-19" href="#__codelineno-200-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-200-20" name="__codelineno-200-20" href="#__codelineno-200-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">worst_best_time_complexity.js</span><pre><span></span><code><a id="__codelineno-197-1" name="__codelineno-197-1" href="#__codelineno-197-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">randomNumbers</span><span class="p">}</span>
-<a id="__codelineno-197-2" name="__codelineno-197-2" href="#__codelineno-197-2"></a>
-<a id="__codelineno-197-3" name="__codelineno-197-3" href="#__codelineno-197-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">findOne</span><span class="p">}</span>
+<div class="highlight"><span class="filename">worst_best_time_complexity.js</span><pre><span></span><code><a id="__codelineno-201-1" name="__codelineno-201-1" href="#__codelineno-201-1"></a><span class="cm">/* 要素が { 1, 2, ..., n } で、順序がシャッフルされた配列を生成 */</span>
+<a id="__codelineno-201-2" name="__codelineno-201-2" href="#__codelineno-201-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">randomNumbers</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-201-3" name="__codelineno-201-3" href="#__codelineno-201-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">);</span>
+<a id="__codelineno-201-4" name="__codelineno-201-4" href="#__codelineno-201-4"></a><span class="w">    </span><span class="c1">// 配列 nums = { 1, 2, 3, ..., n } を生成</span>
+<a id="__codelineno-201-5" name="__codelineno-201-5" href="#__codelineno-201-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-201-6" name="__codelineno-201-6" href="#__codelineno-201-6"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-201-7" name="__codelineno-201-7" href="#__codelineno-201-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-201-8" name="__codelineno-201-8" href="#__codelineno-201-8"></a><span class="w">    </span><span class="c1">// 配列要素をランダムにシャッフル</span>
+<a id="__codelineno-201-9" name="__codelineno-201-9" href="#__codelineno-201-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-201-10" name="__codelineno-201-10" href="#__codelineno-201-10"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nb">Math</span><span class="p">.</span><span class="nx">random</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">));</span>
+<a id="__codelineno-201-11" name="__codelineno-201-11" href="#__codelineno-201-11"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-201-12" name="__codelineno-201-12" href="#__codelineno-201-12"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">r</span><span class="p">];</span>
+<a id="__codelineno-201-13" name="__codelineno-201-13" href="#__codelineno-201-13"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">r</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">temp</span><span class="p">;</span>
+<a id="__codelineno-201-14" name="__codelineno-201-14" href="#__codelineno-201-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-201-15" name="__codelineno-201-15" href="#__codelineno-201-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">nums</span><span class="p">;</span>
+<a id="__codelineno-201-16" name="__codelineno-201-16" href="#__codelineno-201-16"></a><span class="p">}</span>
+<a id="__codelineno-201-17" name="__codelineno-201-17" href="#__codelineno-201-17"></a>
+<a id="__codelineno-201-18" name="__codelineno-201-18" href="#__codelineno-201-18"></a><span class="cm">/* 配列 nums 内で数値 1 のインデックスを探す */</span>
+<a id="__codelineno-201-19" name="__codelineno-201-19" href="#__codelineno-201-19"></a><span class="kd">function</span><span class="w"> </span><span class="nx">findOne</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-201-20" name="__codelineno-201-20" href="#__codelineno-201-20"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-201-21" name="__codelineno-201-21" href="#__codelineno-201-21"></a><span class="w">        </span><span class="c1">// 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる</span>
+<a id="__codelineno-201-22" name="__codelineno-201-22" href="#__codelineno-201-22"></a><span class="w">        </span><span class="c1">// 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる</span>
+<a id="__codelineno-201-23" name="__codelineno-201-23" href="#__codelineno-201-23"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-201-24" name="__codelineno-201-24" href="#__codelineno-201-24"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-201-25" name="__codelineno-201-25" href="#__codelineno-201-25"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-201-26" name="__codelineno-201-26" href="#__codelineno-201-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-201-27" name="__codelineno-201-27" href="#__codelineno-201-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-201-28" name="__codelineno-201-28" href="#__codelineno-201-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">worst_best_time_complexity.ts</span><pre><span></span><code><a id="__codelineno-198-1" name="__codelineno-198-1" href="#__codelineno-198-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">randomNumbers</span><span class="p">}</span>
-<a id="__codelineno-198-2" name="__codelineno-198-2" href="#__codelineno-198-2"></a>
-<a id="__codelineno-198-3" name="__codelineno-198-3" href="#__codelineno-198-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">findOne</span><span class="p">}</span>
+<div class="highlight"><span class="filename">worst_best_time_complexity.ts</span><pre><span></span><code><a id="__codelineno-202-1" name="__codelineno-202-1" href="#__codelineno-202-1"></a><span class="cm">/* 要素が { 1, 2, ..., n } で、順序がシャッフルされた配列を生成 */</span>
+<a id="__codelineno-202-2" name="__codelineno-202-2" href="#__codelineno-202-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">randomNumbers</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-202-3" name="__codelineno-202-3" href="#__codelineno-202-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">);</span>
+<a id="__codelineno-202-4" name="__codelineno-202-4" href="#__codelineno-202-4"></a><span class="w">    </span><span class="c1">// 配列 nums = { 1, 2, 3, ..., n } を生成</span>
+<a id="__codelineno-202-5" name="__codelineno-202-5" href="#__codelineno-202-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-202-6" name="__codelineno-202-6" href="#__codelineno-202-6"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-202-7" name="__codelineno-202-7" href="#__codelineno-202-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-202-8" name="__codelineno-202-8" href="#__codelineno-202-8"></a><span class="w">    </span><span class="c1">// 配列要素をランダムにシャッフル</span>
+<a id="__codelineno-202-9" name="__codelineno-202-9" href="#__codelineno-202-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-202-10" name="__codelineno-202-10" href="#__codelineno-202-10"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nb">Math</span><span class="p">.</span><span class="nx">random</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">));</span>
+<a id="__codelineno-202-11" name="__codelineno-202-11" href="#__codelineno-202-11"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-202-12" name="__codelineno-202-12" href="#__codelineno-202-12"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">r</span><span class="p">];</span>
+<a id="__codelineno-202-13" name="__codelineno-202-13" href="#__codelineno-202-13"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">r</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">temp</span><span class="p">;</span>
+<a id="__codelineno-202-14" name="__codelineno-202-14" href="#__codelineno-202-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-202-15" name="__codelineno-202-15" href="#__codelineno-202-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">nums</span><span class="p">;</span>
+<a id="__codelineno-202-16" name="__codelineno-202-16" href="#__codelineno-202-16"></a><span class="p">}</span>
+<a id="__codelineno-202-17" name="__codelineno-202-17" href="#__codelineno-202-17"></a>
+<a id="__codelineno-202-18" name="__codelineno-202-18" href="#__codelineno-202-18"></a><span class="cm">/* 配列 nums 内で数値 1 のインデックスを探す */</span>
+<a id="__codelineno-202-19" name="__codelineno-202-19" href="#__codelineno-202-19"></a><span class="kd">function</span><span class="w"> </span><span class="nx">findOne</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-202-20" name="__codelineno-202-20" href="#__codelineno-202-20"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-202-21" name="__codelineno-202-21" href="#__codelineno-202-21"></a><span class="w">        </span><span class="c1">// 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる</span>
+<a id="__codelineno-202-22" name="__codelineno-202-22" href="#__codelineno-202-22"></a><span class="w">        </span><span class="c1">// 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる</span>
+<a id="__codelineno-202-23" name="__codelineno-202-23" href="#__codelineno-202-23"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-202-24" name="__codelineno-202-24" href="#__codelineno-202-24"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-202-25" name="__codelineno-202-25" href="#__codelineno-202-25"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-202-26" name="__codelineno-202-26" href="#__codelineno-202-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-202-27" name="__codelineno-202-27" href="#__codelineno-202-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-202-28" name="__codelineno-202-28" href="#__codelineno-202-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">worst_best_time_complexity.dart</span><pre><span></span><code><a id="__codelineno-199-1" name="__codelineno-199-1" href="#__codelineno-199-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">randomNumbers</span><span class="p">}</span>
-<a id="__codelineno-199-2" name="__codelineno-199-2" href="#__codelineno-199-2"></a>
-<a id="__codelineno-199-3" name="__codelineno-199-3" href="#__codelineno-199-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">findOne</span><span class="p">}</span>
+<div class="highlight"><span class="filename">worst_best_time_complexity.dart</span><pre><span></span><code><a id="__codelineno-203-1" name="__codelineno-203-1" href="#__codelineno-203-1"></a><span class="cm">/* 要素が { 1, 2, ..., n } で、順序がシャッフルされた配列を生成 */</span>
+<a id="__codelineno-203-2" name="__codelineno-203-2" href="#__codelineno-203-2"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">randomNumbers</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-203-3" name="__codelineno-203-3" href="#__codelineno-203-3"></a><span class="w">  </span><span class="kd">final</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-203-4" name="__codelineno-203-4" href="#__codelineno-203-4"></a><span class="w">  </span><span class="c1">// 配列 nums = { 1, 2, 3, ..., n } を生成</span>
+<a id="__codelineno-203-5" name="__codelineno-203-5" href="#__codelineno-203-5"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-203-6" name="__codelineno-203-6" href="#__codelineno-203-6"></a><span class="w">    </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-203-7" name="__codelineno-203-7" href="#__codelineno-203-7"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-203-8" name="__codelineno-203-8" href="#__codelineno-203-8"></a><span class="w">  </span><span class="c1">// 配列要素をランダムにシャッフル</span>
+<a id="__codelineno-203-9" name="__codelineno-203-9" href="#__codelineno-203-9"></a><span class="w">  </span><span class="n">nums</span><span class="p">.</span><span class="n">shuffle</span><span class="p">();</span>
+<a id="__codelineno-203-10" name="__codelineno-203-10" href="#__codelineno-203-10"></a>
+<a id="__codelineno-203-11" name="__codelineno-203-11" href="#__codelineno-203-11"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
+<a id="__codelineno-203-12" name="__codelineno-203-12" href="#__codelineno-203-12"></a><span class="p">}</span>
+<a id="__codelineno-203-13" name="__codelineno-203-13" href="#__codelineno-203-13"></a>
+<a id="__codelineno-203-14" name="__codelineno-203-14" href="#__codelineno-203-14"></a><span class="cm">/* 配列 nums 内で数値 1 のインデックスを探す */</span>
+<a id="__codelineno-203-15" name="__codelineno-203-15" href="#__codelineno-203-15"></a><span class="kt">int</span><span class="w"> </span><span class="n">findOne</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-203-16" name="__codelineno-203-16" href="#__codelineno-203-16"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-203-17" name="__codelineno-203-17" href="#__codelineno-203-17"></a><span class="w">    </span><span class="c1">// 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる</span>
+<a id="__codelineno-203-18" name="__codelineno-203-18" href="#__codelineno-203-18"></a><span class="w">    </span><span class="c1">// 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる</span>
+<a id="__codelineno-203-19" name="__codelineno-203-19" href="#__codelineno-203-19"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-203-20" name="__codelineno-203-20" href="#__codelineno-203-20"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-203-21" name="__codelineno-203-21" href="#__codelineno-203-21"></a>
+<a id="__codelineno-203-22" name="__codelineno-203-22" href="#__codelineno-203-22"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-203-23" name="__codelineno-203-23" href="#__codelineno-203-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">worst_best_time_complexity.rs</span><pre><span></span><code><a id="__codelineno-200-1" name="__codelineno-200-1" href="#__codelineno-200-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">random_numbers</span><span class="p">}</span>
-<a id="__codelineno-200-2" name="__codelineno-200-2" href="#__codelineno-200-2"></a>
-<a id="__codelineno-200-3" name="__codelineno-200-3" href="#__codelineno-200-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">find_one</span><span class="p">}</span>
+<div class="highlight"><span class="filename">worst_best_time_complexity.rs</span><pre><span></span><code><a id="__codelineno-204-1" name="__codelineno-204-1" href="#__codelineno-204-1"></a><span class="cm">/* 要素が { 1, 2, ..., n } で、順序がシャッフルされた配列を生成 */</span>
+<a id="__codelineno-204-2" name="__codelineno-204-2" href="#__codelineno-204-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">random_numbers</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-204-3" name="__codelineno-204-3" href="#__codelineno-204-3"></a><span class="w">    </span><span class="c1">// 配列 nums = { 1, 2, 3, ..., n } を生成</span>
+<a id="__codelineno-204-4" name="__codelineno-204-4" href="#__codelineno-204-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">..=</span><span class="n">n</span><span class="p">).</span><span class="n">collect</span><span class="p">::</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-204-5" name="__codelineno-204-5" href="#__codelineno-204-5"></a><span class="w">    </span><span class="c1">// 配列要素をランダムにシャッフル</span>
+<a id="__codelineno-204-6" name="__codelineno-204-6" href="#__codelineno-204-6"></a><span class="w">    </span><span class="n">nums</span><span class="p">.</span><span class="n">shuffle</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">thread_rng</span><span class="p">());</span>
+<a id="__codelineno-204-7" name="__codelineno-204-7" href="#__codelineno-204-7"></a><span class="w">    </span><span class="n">nums</span>
+<a id="__codelineno-204-8" name="__codelineno-204-8" href="#__codelineno-204-8"></a><span class="p">}</span>
+<a id="__codelineno-204-9" name="__codelineno-204-9" href="#__codelineno-204-9"></a>
+<a id="__codelineno-204-10" name="__codelineno-204-10" href="#__codelineno-204-10"></a><span class="cm">/* 配列 nums 内で数値 1 のインデックスを探す */</span>
+<a id="__codelineno-204-11" name="__codelineno-204-11" href="#__codelineno-204-11"></a><span class="k">fn</span><span class="w"> </span><span class="nf">find_one</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="kt">usize</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-204-12" name="__codelineno-204-12" href="#__codelineno-204-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-204-13" name="__codelineno-204-13" href="#__codelineno-204-13"></a><span class="w">        </span><span class="c1">// 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる</span>
+<a id="__codelineno-204-14" name="__codelineno-204-14" href="#__codelineno-204-14"></a><span class="w">        </span><span class="c1">// 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる</span>
+<a id="__codelineno-204-15" name="__codelineno-204-15" href="#__codelineno-204-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-204-16" name="__codelineno-204-16" href="#__codelineno-204-16"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-204-17" name="__codelineno-204-17" href="#__codelineno-204-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-204-18" name="__codelineno-204-18" href="#__codelineno-204-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-204-19" name="__codelineno-204-19" href="#__codelineno-204-19"></a><span class="w">    </span><span class="nb">None</span>
+<a id="__codelineno-204-20" name="__codelineno-204-20" href="#__codelineno-204-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">worst_best_time_complexity.c</span><pre><span></span><code><a id="__codelineno-201-1" name="__codelineno-201-1" href="#__codelineno-201-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">randomNumbers</span><span class="p">}</span>
-<a id="__codelineno-201-2" name="__codelineno-201-2" href="#__codelineno-201-2"></a>
-<a id="__codelineno-201-3" name="__codelineno-201-3" href="#__codelineno-201-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">findOne</span><span class="p">}</span>
+<div class="highlight"><span class="filename">worst_best_time_complexity.c</span><pre><span></span><code><a id="__codelineno-205-1" name="__codelineno-205-1" href="#__codelineno-205-1"></a><span class="cm">/* 要素が { 1, 2, ..., n } で、順序がシャッフルされた配列を生成 */</span>
+<a id="__codelineno-205-2" name="__codelineno-205-2" href="#__codelineno-205-2"></a><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="nf">randomNumbers</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-205-3" name="__codelineno-205-3" href="#__codelineno-205-3"></a><span class="w">    </span><span class="c1">// ヒープ領域にメモリを確保する（要素数 n、要素型 int の一次元可変長配列を作成）</span>
+<a id="__codelineno-205-4" name="__codelineno-205-4" href="#__codelineno-205-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-205-5" name="__codelineno-205-5" href="#__codelineno-205-5"></a><span class="w">    </span><span class="c1">// 配列 nums = { 1, 2, 3, ..., n } を生成</span>
+<a id="__codelineno-205-6" name="__codelineno-205-6" href="#__codelineno-205-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-205-7" name="__codelineno-205-7" href="#__codelineno-205-7"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-205-8" name="__codelineno-205-8" href="#__codelineno-205-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-205-9" name="__codelineno-205-9" href="#__codelineno-205-9"></a><span class="w">    </span><span class="c1">// 配列要素をランダムにシャッフル</span>
+<a id="__codelineno-205-10" name="__codelineno-205-10" href="#__codelineno-205-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-205-11" name="__codelineno-205-11" href="#__codelineno-205-11"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rand</span><span class="p">()</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-205-12" name="__codelineno-205-12" href="#__codelineno-205-12"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-205-13" name="__codelineno-205-13" href="#__codelineno-205-13"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-205-14" name="__codelineno-205-14" href="#__codelineno-205-14"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span>
+<a id="__codelineno-205-15" name="__codelineno-205-15" href="#__codelineno-205-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-205-16" name="__codelineno-205-16" href="#__codelineno-205-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
+<a id="__codelineno-205-17" name="__codelineno-205-17" href="#__codelineno-205-17"></a><span class="p">}</span>
+<a id="__codelineno-205-18" name="__codelineno-205-18" href="#__codelineno-205-18"></a>
+<a id="__codelineno-205-19" name="__codelineno-205-19" href="#__codelineno-205-19"></a><span class="cm">/* 配列 nums 内で数値 1 のインデックスを探す */</span>
+<a id="__codelineno-205-20" name="__codelineno-205-20" href="#__codelineno-205-20"></a><span class="kt">int</span><span class="w"> </span><span class="nf">findOne</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-205-21" name="__codelineno-205-21" href="#__codelineno-205-21"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-205-22" name="__codelineno-205-22" href="#__codelineno-205-22"></a><span class="w">        </span><span class="c1">// 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる</span>
+<a id="__codelineno-205-23" name="__codelineno-205-23" href="#__codelineno-205-23"></a><span class="w">        </span><span class="c1">// 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる</span>
+<a id="__codelineno-205-24" name="__codelineno-205-24" href="#__codelineno-205-24"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-205-25" name="__codelineno-205-25" href="#__codelineno-205-25"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-205-26" name="__codelineno-205-26" href="#__codelineno-205-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-205-27" name="__codelineno-205-27" href="#__codelineno-205-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-205-28" name="__codelineno-205-28" href="#__codelineno-205-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">worst_best_time_complexity.kt</span><pre><span></span><code><a id="__codelineno-202-1" name="__codelineno-202-1" href="#__codelineno-202-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">randomNumbers</span><span class="p">}</span>
-<a id="__codelineno-202-2" name="__codelineno-202-2" href="#__codelineno-202-2"></a>
-<a id="__codelineno-202-3" name="__codelineno-202-3" href="#__codelineno-202-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">findOne</span><span class="p">}</span>
+<div class="highlight"><span class="filename">worst_best_time_complexity.kt</span><pre><span></span><code><a id="__codelineno-206-1" name="__codelineno-206-1" href="#__codelineno-206-1"></a><span class="cm">/* 要素が { 1, 2, ..., n } で、順序がシャッフルされた配列を生成 */</span>
+<a id="__codelineno-206-2" name="__codelineno-206-2" href="#__codelineno-206-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">randomNumbers</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="n">Array</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-206-3" name="__codelineno-206-3" href="#__codelineno-206-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-206-4" name="__codelineno-206-4" href="#__codelineno-206-4"></a><span class="w">    </span><span class="c1">// 配列 nums = { 1, 2, 3, ..., n } を生成</span>
+<a id="__codelineno-206-5" name="__codelineno-206-5" href="#__codelineno-206-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-206-6" name="__codelineno-206-6" href="#__codelineno-206-6"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-206-7" name="__codelineno-206-7" href="#__codelineno-206-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-206-8" name="__codelineno-206-8" href="#__codelineno-206-8"></a><span class="w">    </span><span class="c1">// 配列要素をランダムにシャッフル</span>
+<a id="__codelineno-206-9" name="__codelineno-206-9" href="#__codelineno-206-9"></a><span class="w">    </span><span class="n">nums</span><span class="p">.</span><span class="na">shuffle</span><span class="p">()</span>
+<a id="__codelineno-206-10" name="__codelineno-206-10" href="#__codelineno-206-10"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arrayOfNulls</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-206-11" name="__codelineno-206-11" href="#__codelineno-206-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-206-12" name="__codelineno-206-12" href="#__codelineno-206-12"></a><span class="w">        </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-206-13" name="__codelineno-206-13" href="#__codelineno-206-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-206-14" name="__codelineno-206-14" href="#__codelineno-206-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-206-15" name="__codelineno-206-15" href="#__codelineno-206-15"></a><span class="p">}</span>
+<a id="__codelineno-206-16" name="__codelineno-206-16" href="#__codelineno-206-16"></a>
+<a id="__codelineno-206-17" name="__codelineno-206-17" href="#__codelineno-206-17"></a><span class="cm">/* 配列 nums 内で数値 1 のインデックスを探す */</span>
+<a id="__codelineno-206-18" name="__codelineno-206-18" href="#__codelineno-206-18"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">findOne</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">Array</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="o">&gt;</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-206-19" name="__codelineno-206-19" href="#__codelineno-206-19"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">indices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-206-20" name="__codelineno-206-20" href="#__codelineno-206-20"></a><span class="w">        </span><span class="c1">// 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる</span>
+<a id="__codelineno-206-21" name="__codelineno-206-21" href="#__codelineno-206-21"></a><span class="w">        </span><span class="c1">// 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる</span>
+<a id="__codelineno-206-22" name="__codelineno-206-22" href="#__codelineno-206-22"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-206-23" name="__codelineno-206-23" href="#__codelineno-206-23"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-206-24" name="__codelineno-206-24" href="#__codelineno-206-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-206-25" name="__codelineno-206-25" href="#__codelineno-206-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="m">1</span>
+<a id="__codelineno-206-26" name="__codelineno-206-26" href="#__codelineno-206-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">worst_best_time_complexity.rb</span><pre><span></span><code><a id="__codelineno-203-1" name="__codelineno-203-1" href="#__codelineno-203-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">random_numbers</span><span class="p">}</span>
-<a id="__codelineno-203-2" name="__codelineno-203-2" href="#__codelineno-203-2"></a>
-<a id="__codelineno-203-3" name="__codelineno-203-3" href="#__codelineno-203-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">find_one</span><span class="p">}</span>
+<div class="highlight"><span class="filename">worst_best_time_complexity.rb</span><pre><span></span><code><a id="__codelineno-207-1" name="__codelineno-207-1" href="#__codelineno-207-1"></a><span class="c1">### 1, 2, ..., n を要素とする配列を生成し、順序をシャッフルする ###</span>
+<a id="__codelineno-207-2" name="__codelineno-207-2" href="#__codelineno-207-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">random_numbers</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-207-3" name="__codelineno-207-3" href="#__codelineno-207-3"></a><span class="w">  </span><span class="c1"># 配列 nums =: 1, 2, 3, ..., n を生成する</span>
+<a id="__codelineno-207-4" name="__codelineno-207-4" href="#__codelineno-207-4"></a><span class="w">  </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-207-5" name="__codelineno-207-5" href="#__codelineno-207-5"></a><span class="w">  </span><span class="c1"># 配列要素をランダムにシャッフル</span>
+<a id="__codelineno-207-6" name="__codelineno-207-6" href="#__codelineno-207-6"></a><span class="w">  </span><span class="n">nums</span><span class="o">.</span><span class="n">shuffle!</span>
+<a id="__codelineno-207-7" name="__codelineno-207-7" href="#__codelineno-207-7"></a><span class="k">end</span>
+<a id="__codelineno-207-8" name="__codelineno-207-8" href="#__codelineno-207-8"></a>
+<a id="__codelineno-207-9" name="__codelineno-207-9" href="#__codelineno-207-9"></a><span class="c1">### 配列 nums 内の数値 1 のインデックスを探す ###</span>
+<a id="__codelineno-207-10" name="__codelineno-207-10" href="#__codelineno-207-10"></a><span class="k">def</span><span class="w"> </span><span class="nf">find_one</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-207-11" name="__codelineno-207-11" href="#__codelineno-207-11"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-207-12" name="__codelineno-207-12" href="#__codelineno-207-12"></a><span class="w">    </span><span class="c1"># 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる</span>
+<a id="__codelineno-207-13" name="__codelineno-207-13" href="#__codelineno-207-13"></a><span class="w">    </span><span class="c1"># 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる</span>
+<a id="__codelineno-207-14" name="__codelineno-207-14" href="#__codelineno-207-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-207-15" name="__codelineno-207-15" href="#__codelineno-207-15"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-207-16" name="__codelineno-207-16" href="#__codelineno-207-16"></a>
+<a id="__codelineno-207-17" name="__codelineno-207-17" href="#__codelineno-207-17"></a><span class="w">  </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-207-18" name="__codelineno-207-18" href="#__codelineno-207-18"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>最良ケース時間計算量は実際にはほとんど使用されないことに注意してください。通常は非常に低い確率でのみ達成可能で、誤解を招く可能性があるからです。<strong>最悪ケース時間計算量はより実用的で、効率の安全値を提供し</strong>、アルゴリズムを自信を持って使用できるようにします。</p>
-<p>上記の例から、最悪ケースと最良ケースの時間計算量は両方とも「特殊なデータ分布」下でのみ発生し、発生確率が小さく、アルゴリズムの実行効率を正確に反映しない可能性があることが明らかです。対照的に、<strong>平均時間計算量はランダム入力データ下でのアルゴリズムの効率を反映でき</strong>、<span class="arithmatex">\(\Theta\)</span>記法で表されます。</p>
-<p>一部のアルゴリズムでは、ランダムデータ分布下での平均ケースを簡単に推定できます。例えば、前述の例では、入力配列がシャッフルされているため、要素<span class="arithmatex">\(1\)</span>が任意のインデックスに現れる確率は等しいです。したがって、アルゴリズムの平均ループ数は配列長さの半分<span class="arithmatex">\(n / 2\)</span>で、平均時間計算量は<span class="arithmatex">\(\Theta(n / 2) = \Theta(n)\)</span>です。</p>
-<p>しかし、より複雑なアルゴリズムの平均時間計算量を計算することは非常に困難です。データ分布下での全体的な数学的期待値を分析することが困難だからです。そのような場合、通常はアルゴリズムの効率を判断する基準として最悪ケース時間計算量を使用します。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=import%20random%0A%0Adef%20random_numbers%28n%3A%20int%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%22%22%22%E8%A6%81%E7%B4%A0%E3%81%8C%201%2C%202%2C%20...%2C%20n%20%E3%81%A7%E9%A0%86%E5%BA%8F%E3%81%8C%E3%82%B7%E3%83%A3%E3%83%83%E3%83%95%E3%83%AB%E3%81%95%E3%82%8C%E3%81%9F%E9%85%8D%E5%88%97%E3%82%92%E7%94%9F%E6%88%90%E3%81%99%E3%82%8B%22%22%22%0A%20%20%20%20%23%20%E9%85%8D%E5%88%97%20nums%20%3D%3A%201%2C%202%2C%203%2C%20...%2C%20n%20%E3%82%92%E7%94%9F%E6%88%90%E3%81%99%E3%82%8B%0A%20%20%20%20nums%20%3D%20%5Bi%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%5D%0A%20%20%20%20%23%20%E9%85%8D%E5%88%97%E8%A6%81%E7%B4%A0%E3%82%92%E3%83%A9%E3%83%B3%E3%83%80%E3%83%A0%E3%81%AB%E3%82%B7%E3%83%A3%E3%83%83%E3%83%95%E3%83%AB%0A%20%20%20%20random.shuffle%28nums%29%0A%20%20%20%20return%20nums%0A%0Adef%20find_one%28nums%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%85%8D%E5%88%97%20nums%20%E5%86%85%E3%81%A7%E6%95%B0%E5%80%A4%201%20%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E6%8E%A2%E3%81%99%22%22%22%0A%20%20%20%20for%20i%20in%20range%28len%28nums%29%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E8%A6%81%E7%B4%A0%201%20%E3%81%8C%E9%85%8D%E5%88%97%E3%81%AE%E5%85%88%E9%A0%AD%E3%81%AB%E3%81%82%E3%82%8B%E3%81%A8%E3%81%8D%E3%80%81%E6%9C%80%E8%89%AF%E6%99%82%E9%96%93%E8%A8%88%E7%AE%97%E9%87%8F%20O%281%29%20%E3%81%A8%E3%81%AA%E3%82%8B%0A%20%20%20%20%20%20%20%20%23%20%E8%A6%81%E7%B4%A0%201%20%E3%81%8C%E9%85%8D%E5%88%97%E3%81%AE%E6%9C%AB%E5%B0%BE%E3%81%AB%E3%81%82%E3%82%8B%E3%81%A8%E3%81%8D%E3%80%81%E6%9C%80%E6%82%AA%E6%99%82%E9%96%93%E8%A8%88%E7%AE%97%E9%87%8F%20O%28n%29%20%E3%81%A8%E3%81%AA%E3%82%8B%0A%20%20%20%20%20%20%20%20if%20nums%5Bi%5D%20%3D%3D%201%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20i%0A%20%20%20%20return%20-1%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%2010%0A%20%20%20%20nums%20%3D%20random_numbers%28n%29%0A%20%20%20%20index%20%3D%20find_one%28nums%29%0A%20%20%20%20print%28%22%5Cn%E9%85%8D%E5%88%97%20%5B%201%2C%202%2C%20...%2C%20n%20%5D%20%E3%82%92%E3%82%B7%E3%83%A3%E3%83%83%E3%83%95%E3%83%AB%E3%81%99%E3%82%8B%E3%81%A8%20%3D%22%2C%20nums%29%0A%20%20%20%20print%28%22%E6%95%B0%E5%80%A4%201%20%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%AF%22%2C%20index%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=25&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=import%20random%0A%0Adef%20random_numbers%28n%3A%20int%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%22%22%22%E8%A6%81%E7%B4%A0%E3%81%8C%201%2C%202%2C%20...%2C%20n%20%E3%81%A7%E9%A0%86%E5%BA%8F%E3%81%8C%E3%82%B7%E3%83%A3%E3%83%83%E3%83%95%E3%83%AB%E3%81%95%E3%82%8C%E3%81%9F%E9%85%8D%E5%88%97%E3%82%92%E7%94%9F%E6%88%90%E3%81%99%E3%82%8B%22%22%22%0A%20%20%20%20%23%20%E9%85%8D%E5%88%97%20nums%20%3D%3A%201%2C%202%2C%203%2C%20...%2C%20n%20%E3%82%92%E7%94%9F%E6%88%90%E3%81%99%E3%82%8B%0A%20%20%20%20nums%20%3D%20%5Bi%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%5D%0A%20%20%20%20%23%20%E9%85%8D%E5%88%97%E8%A6%81%E7%B4%A0%E3%82%92%E3%83%A9%E3%83%B3%E3%83%80%E3%83%A0%E3%81%AB%E3%82%B7%E3%83%A3%E3%83%83%E3%83%95%E3%83%AB%0A%20%20%20%20random.shuffle%28nums%29%0A%20%20%20%20return%20nums%0A%0Adef%20find_one%28nums%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%85%8D%E5%88%97%20nums%20%E5%86%85%E3%81%A7%E6%95%B0%E5%80%A4%201%20%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E6%8E%A2%E3%81%99%22%22%22%0A%20%20%20%20for%20i%20in%20range%28len%28nums%29%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E8%A6%81%E7%B4%A0%201%20%E3%81%8C%E9%85%8D%E5%88%97%E3%81%AE%E5%85%88%E9%A0%AD%E3%81%AB%E3%81%82%E3%82%8B%E3%81%A8%E3%81%8D%E3%80%81%E6%9C%80%E8%89%AF%E6%99%82%E9%96%93%E8%A8%88%E7%AE%97%E9%87%8F%20O%281%29%20%E3%81%A8%E3%81%AA%E3%82%8B%0A%20%20%20%20%20%20%20%20%23%20%E8%A6%81%E7%B4%A0%201%20%E3%81%8C%E9%85%8D%E5%88%97%E3%81%AE%E6%9C%AB%E5%B0%BE%E3%81%AB%E3%81%82%E3%82%8B%E3%81%A8%E3%81%8D%E3%80%81%E6%9C%80%E6%82%AA%E6%99%82%E9%96%93%E8%A8%88%E7%AE%97%E9%87%8F%20O%28n%29%20%E3%81%A8%E3%81%AA%E3%82%8B%0A%20%20%20%20%20%20%20%20if%20nums%5Bi%5D%20%3D%3D%201%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20i%0A%20%20%20%20return%20-1%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%2010%0A%20%20%20%20nums%20%3D%20random_numbers%28n%29%0A%20%20%20%20index%20%3D%20find_one%28nums%29%0A%20%20%20%20print%28%22%5Cn%E9%85%8D%E5%88%97%20%5B%201%2C%202%2C%20...%2C%20n%20%5D%20%E3%82%92%E3%82%B7%E3%83%A3%E3%83%83%E3%83%95%E3%83%AB%E3%81%99%E3%82%8B%E3%81%A8%20%3D%22%2C%20nums%29%0A%20%20%20%20print%28%22%E6%95%B0%E5%80%A4%201%20%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%AF%22%2C%20index%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=25&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>実際には、最良時間計算量を使うことはあまりありません。通常それが実現する確率はごく低く、誤解を招く可能性があるからです。**一方で最悪時間計算量はより実用的で、効率の安全側の目安を与えてくれる**ため、安心してアルゴリズムを使えます。</p>
+<p>上の例から分かるように、最悪時間計算量と最良時間計算量は「特殊なデータ分布」でのみ現れ、その発生確率は低いことが多く、アルゴリズムの実行効率をそのまま正確に反映するわけではありません。それに対して、**平均時間計算量はランダム入力におけるアルゴリズムの実行効率を表せる**ため、<span class="arithmatex">\(\Theta\)</span> 記法で表します。</p>
+<p>一部のアルゴリズムでは、ランダムなデータ分布における平均的な状況を比較的簡単に求められます。例えば上の例では、入力配列はシャッフルされているため、要素 <span class="arithmatex">\(1\)</span> が任意のインデックスに現れる確率は等しいです。したがってアルゴリズムの平均ループ回数は配列長の半分 <span class="arithmatex">\(n / 2\)</span> となり、平均時間計算量は <span class="arithmatex">\(\Theta(n / 2) = \Theta(n)\)</span> です。</p>
+<p>しかし、より複雑なアルゴリズムでは、平均時間計算量を計算するのはしばしば困難です。データ分布に対する全体の数学的期待値を分析するのが難しいからです。そのような場合、通常は最悪時間計算量をアルゴリズム効率の評価基準として用います。</p>
 <div class="admonition question">
-<p class="admonition-title"><span class="arithmatex">\(\Theta\)</span>記号はなぜほとんど見られないのですか？</p>
-<p>おそらく<span class="arithmatex">\(O\)</span>記法がより一般的に話されるため、平均時間計算量を表すためによく使用されます。しかし、厳密に言えば、この実践は正確ではありません。この本や他の資料で「平均時間計算量<span class="arithmatex">\(O(n)\)</span>」のような表現に遭遇した場合は、直接<span class="arithmatex">\(\Theta(n)\)</span>として理解してください。</p>
+<p class="admonition-title">なぜ <span class="arithmatex">\(\Theta\)</span> 記号をあまり見かけないのか？</p>
+<p>おそらく <span class="arithmatex">\(O\)</span> 記号のほうが口にしやすいため、平均時間計算量を表すのにもよく使われます。ただし厳密には、この用法は正確ではありません。本書や他の資料で「平均時間計算量 <span class="arithmatex">\(O(n)\)</span>」のような表現を見かけた場合は、そのまま <span class="arithmatex">\(\Theta(n)\)</span> と理解してください。</p>
 </div>
 
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diff --git a/ja/chapter_data_structure/basic_data_types/index.html b/ja/chapter_data_structure/basic_data_types/index.html
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+++ b/ja/chapter_data_structure/basic_data_types/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1072,7 +1072,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1100,7 +1100,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1603,7 +1603,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1625,7 +1625,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1647,7 +1647,7 @@
   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1954,7 +1954,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2117,7 +2117,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2503,7 +2503,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2559,7 +2559,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2587,7 +2587,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3125,7 +3125,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3181,7 +3181,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3209,7 +3209,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3402,7 +3402,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3430,7 +3430,7 @@
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-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3571,7 +3571,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3599,7 +3599,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3627,7 +3627,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3655,7 +3655,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3848,7 +3848,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4093,7 +4093,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4265,30 +4265,30 @@
 
 <!-- Page content -->
 <h1 id="32">3.2 &nbsp; 基本データ型<a class="headerlink" href="#32" title="Permanent link">&para;</a></h1>
-<p>コンピュータ内のデータについて考える際、テキスト、画像、動画、音声、3Dモデルなど、様々な形式が思い浮かびます。これらの組織的な形式は異なりますが、すべて様々な基本データ型から構成されています。</p>
-<p>**基本データ型とは、CPUが直接操作できるもの**であり、アルゴリズムで直接使用されます。主に以下が含まれます。</p>
+<p>コンピュータ内のデータについて考えるとき、テキスト、画像、動画、音声、3D モデルなど、さまざまな形態を思い浮かべます。これらのデータの構成形式はそれぞれ異なりますが、いずれも各種の基本データ型によって成り立っています。</p>
+<p>**基本データ型は CPU が直接演算できる型**であり、アルゴリズムの中で直接使われます。主なものは次のとおりです。</p>
 <ul>
-<li>整数型：<code>byte</code>、<code>short</code>、<code>int</code>、<code>long</code></li>
-<li>浮動小数点型：<code>float</code>、<code>double</code>、小数を表現するために使用</li>
-<li>文字型：<code>char</code>、様々な言語の文字、句読点、さらには絵文字を表現するために使用</li>
-<li>ブール型：<code>bool</code>、「はい」または「いいえ」の判断を表現するために使用</li>
+<li>整数型 <code>byte</code>、<code>short</code>、<code>int</code>、<code>long</code> 。</li>
+<li>浮動小数点数型 <code>float</code>、<code>double</code> ，小数を表すために使います。</li>
+<li>文字型 <code>char</code> ，各言語の文字、句読点、さらには絵文字などを表すために使います。</li>
+<li>真偽値型 <code>bool</code> ，真か偽かの判定を表すために使います。</li>
 </ul>
-<p><strong>基本データ型は、コンピュータ内で二進形式で格納されます</strong>。1つの二進桁は1ビットです。ほとんどの現代的なオペレーティングシステムでは、1バイトは8ビットで構成されています。</p>
-<p>基本データ型の値の範囲は、それらが占める空間のサイズに依存します。以下では、Javaを例に説明します。</p>
+<p><strong>基本データ型はコンピュータ内で 2 進数の形で格納されます</strong>。1 つの二進桁は <span class="arithmatex">\(1\)</span> ビットです。現代のほとんどのオペレーティングシステムでは、<span class="arithmatex">\(1\)</span> バイト（byte）は <span class="arithmatex">\(8\)</span> ビット（bit）で構成されます。</p>
+<p>基本データ型の値域は、その型が占める領域の大きさによって決まります。以下では Java を例に取ります。</p>
 <ul>
-<li>整数型<code>byte</code>は1バイト = 8ビットを占め、<span class="arithmatex">\(2^8\)</span>個の数値を表現できます。</li>
-<li>整数型<code>int</code>は4バイト = 32ビットを占め、<span class="arithmatex">\(2^{32}\)</span>個の数値を表現できます。</li>
+<li>整数型 <code>byte</code> は <span class="arithmatex">\(1\)</span> バイト = <span class="arithmatex">\(8\)</span> ビットを占め、<span class="arithmatex">\(2^{8}\)</span> 個の数を表せます。</li>
+<li>整数型 <code>int</code> は <span class="arithmatex">\(4\)</span> バイト = <span class="arithmatex">\(32\)</span> ビットを占め、<span class="arithmatex">\(2^{32}\)</span> 個の数を表せます。</li>
 </ul>
-<p>以下の表は、Javaにおける様々な基本データ型が占める空間、値の範囲、デフォルト値を示しています。この表を暗記する必要はありませんが、一般的な理解を持ち、必要時に参照することをお勧めします。</p>
-<p align="center"> 表 3-1 &nbsp; 基本データ型が占める空間と値の範囲 </p>
+<p>下表は、Java における各種基本データ型の使用領域、値域、デフォルト値を示したものです。この表を丸暗記する必要はなく、大まかに理解しておけば十分であり、必要になったときに参照すればかまいません。</p>
+<p align="center"> 表 3-1 &nbsp; 基本データ型の使用領域と値域 </p>
 
 <div class="center-table">
 <table>
 <thead>
 <tr>
 <th>型</th>
-<th>シンボル</th>
-<th>占有空間</th>
+<th>記号</th>
+<th>使用領域</th>
 <th>最小値</th>
 <th>最大値</th>
 <th>デフォルト値</th>
@@ -4298,39 +4298,39 @@
 <tr>
 <td>整数</td>
 <td><code>byte</code></td>
-<td>1バイト</td>
+<td>1 バイト</td>
 <td><span class="arithmatex">\(-2^7\)</span> (<span class="arithmatex">\(-128\)</span>)</td>
 <td><span class="arithmatex">\(2^7 - 1\)</span> (<span class="arithmatex">\(127\)</span>)</td>
-<td>0</td>
+<td><span class="arithmatex">\(0\)</span></td>
 </tr>
 <tr>
 <td></td>
 <td><code>short</code></td>
-<td>2バイト</td>
+<td>2 バイト</td>
 <td><span class="arithmatex">\(-2^{15}\)</span></td>
 <td><span class="arithmatex">\(2^{15} - 1\)</span></td>
-<td>0</td>
+<td><span class="arithmatex">\(0\)</span></td>
 </tr>
 <tr>
 <td></td>
 <td><code>int</code></td>
-<td>4バイト</td>
+<td>4 バイト</td>
 <td><span class="arithmatex">\(-2^{31}\)</span></td>
 <td><span class="arithmatex">\(2^{31} - 1\)</span></td>
-<td>0</td>
+<td><span class="arithmatex">\(0\)</span></td>
 </tr>
 <tr>
 <td></td>
 <td><code>long</code></td>
-<td>8バイト</td>
+<td>8 バイト</td>
 <td><span class="arithmatex">\(-2^{63}\)</span></td>
 <td><span class="arithmatex">\(2^{63} - 1\)</span></td>
-<td>0</td>
+<td><span class="arithmatex">\(0\)</span></td>
 </tr>
 <tr>
-<td>浮動小数点</td>
+<td>浮動小数点数</td>
 <td><code>float</code></td>
-<td>4バイト</td>
+<td>4 バイト</td>
 <td><span class="arithmatex">\(1.175 \times 10^{-38}\)</span></td>
 <td><span class="arithmatex">\(3.403 \times 10^{38}\)</span></td>
 <td><span class="arithmatex">\(0.0\text{f}\)</span></td>
@@ -4338,23 +4338,23 @@
 <tr>
 <td></td>
 <td><code>double</code></td>
-<td>8バイト</td>
+<td>8 バイト</td>
 <td><span class="arithmatex">\(2.225 \times 10^{-308}\)</span></td>
 <td><span class="arithmatex">\(1.798 \times 10^{308}\)</span></td>
-<td>0.0</td>
+<td><span class="arithmatex">\(0.0\)</span></td>
 </tr>
 <tr>
 <td>文字</td>
 <td><code>char</code></td>
-<td>2バイト</td>
-<td>0</td>
+<td>2 バイト</td>
+<td><span class="arithmatex">\(0\)</span></td>
 <td><span class="arithmatex">\(2^{16} - 1\)</span></td>
-<td>0</td>
+<td><span class="arithmatex">\(0\)</span></td>
 </tr>
 <tr>
-<td>ブール</td>
+<td>真偽値</td>
 <td><code>bool</code></td>
-<td>1バイト</td>
+<td>1 バイト</td>
 <td><span class="arithmatex">\(\text{false}\)</span></td>
 <td><span class="arithmatex">\(\text{true}\)</span></td>
 <td><span class="arithmatex">\(\text{false}\)</span></td>
@@ -4362,31 +4362,31 @@
 </tbody>
 </table>
 </div>
-<p>上記の表はJavaの基本データ型に特有であることにご注意ください。すべてのプログラミング言語には独自のデータ型定義があり、占有空間、値の範囲、デフォルト値が異なる場合があります。</p>
+<p>注意してください。上表は Java の基本データ型に対するものです。各プログラミング言語にはそれぞれ独自のデータ型定義があり、使用領域、値域、デフォルト値は異なる場合があります。</p>
 <ul>
-<li>Pythonでは、整数型<code>int</code>は任意のサイズになることができ、利用可能なメモリによってのみ制限されます。浮動小数点<code>float</code>は倍精度64ビットです。<code>char</code>型は存在せず、単一文字は実際には長さ1の文字列<code>str</code>です。</li>
-<li>CおよびC++では基本データ型のサイズが指定されておらず、実装とプラットフォームによって異なります。上記の表はLP64<a href="https://en.cppreference.com/w/cpp/language/types#Properties">データモデル</a>に従っており、LinuxやmacOSを含むUnix 64ビットオペレーティングシステムで使用されています。</li>
-<li>CおよびC++における<code>char</code>のサイズは1バイトですが、ほとんどのプログラミング言語では、特定の文字エンコーディング方法に依存し、詳細は「文字エンコーディング」の章で説明されています。</li>
-<li>ブール値の表現には1ビット（0または1）のみが必要ですが、通常はメモリ内に1バイトとして格納されます。これは、現代のコンピュータCPUが通常1バイトを最小のアドレス可能なメモリ単位として使用するためです。</li>
+<li>Python では、整数型 <code>int</code> は利用可能なメモリに制限されるだけで任意の大きさを取れます。浮動小数点数 <code>float</code> は倍精度 64 ビットです。<code>char</code> 型はなく、1 文字は実際には長さ 1 の文字列 <code>str</code> です。</li>
+<li>C と C++ では基本データ型の大きさは明確に規定されておらず、実装やプラットフォームによって異なります。上表は LP64 <a href="https://en.cppreference.com/w/cpp/language/types#Properties">データモデル</a> に従っており、Linux や macOS を含む Unix 系 64 ビット OS で用いられています。</li>
+<li><code>char</code> の大きさは C と C++ では 1 バイトですが、多くのプログラミング言語では採用する文字エンコーディング方式によって決まります。詳しくは「文字エンコーディング」の章を参照してください。</li>
+<li>真偽値を表すのに必要なのは 1 ビット（<span class="arithmatex">\(0\)</span> または <span class="arithmatex">\(1\)</span>）だけですが、メモリ上では通常 1 バイトとして格納されます。これは、現代のコンピュータ CPU が通常 1 バイトを最小のアドレス指定可能なメモリ単位としているためです。</li>
 </ul>
-<p>では、基本データ型とデータ構造の関係は何でしょうか？データ構造とは、コンピュータ内でデータを組織化し格納する方法であることを知っています。ここでの焦点は「データ」ではなく「構造」です。</p>
-<p>「数値の列」を表現したい場合、自然に配列の使用を考えます。これは、配列の線形構造が数値の隣接性と順序性を表現できるためですが、格納される内容が整数<code>int</code>、小数<code>float</code>、文字<code>char</code>のいずれであっても、「データ構造」とは無関係です。</p>
-<p>言い換えると、<strong>基本データ型はデータの「内容型」を提供し、データ構造はデータの「組織化方法」を提供します</strong>。例えば、以下のコードでは、同じデータ構造（配列）を使用して、<code>int</code>、<code>float</code>、<code>char</code>、<code>bool</code>などの異なる基本データ型を格納し表現しています。</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="1:12"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label></div>
+<p>では、基本データ型とデータ構造の間にはどのような関係があるのでしょうか。データ構造とは、コンピュータ内でデータを組織し格納する方法のことです。この言葉で主役なのは「データ」ではなく「構造」です。</p>
+<p>「数字の並び」を表したいなら、自然に配列の使用を思い浮かべるでしょう。これは、配列の線形構造が数字どうしの隣接関係や順序関係を表せるからです。しかし、格納する内容が整数 <code>int</code> なのか、小数 <code>float</code> なのか、文字 <code>char</code> なのかは、「データ構造」とは関係ありません。</p>
+<p>言い換えると、<strong>基本データ型はデータの「内容の型」を提供し、データ構造はデータの「組織方法」を提供します</strong>。たとえば次のコードでは、同じデータ構造（配列）を使って <code>int</code>、<code>float</code>、<code>char</code>、<code>bool</code> など異なる基本データ型を格納・表現しています。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 様々な基本データ型を使用して配列を初期化</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># さまざまな基本データ型で配列を初期化する</span>
 <a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="n">numbers</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">5</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="n">decimals</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">float</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">5</span>
-<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="c1"># Pythonの文字は実際には長さ1の文字列</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="c1"># Python の文字は実際には長さ 1 の文字列</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="n">characters</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">str</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;0&#39;</span><span class="p">]</span> <span class="o">*</span> <span class="mi">5</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="n">bools</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">bool</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="kc">False</span><span class="p">]</span> <span class="o">*</span> <span class="mi">5</span>
-<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="c1"># Pythonのリストは様々な基本データ型とオブジェクト参照を自由に格納可能</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="c1"># Python のリストはさまざまな基本データ型とオブジェクト参照を自由に格納できる</span>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="n">data</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="s1">&#39;a&#39;</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="n">ListNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)]</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="c1">// 様々な基本データ型を使用して配列を初期化</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="c1">// さまざまな基本データ型で配列を初期化する</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">numbers</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="kt">float</span><span class="w"> </span><span class="n">decimals</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="kt">char</span><span class="w"> </span><span class="n">characters</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
@@ -4394,7 +4394,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="c1">// 様々な基本データ型を使用して配列を初期化</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="c1">// さまざまな基本データ型で配列を初期化する</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">numbers</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="mi">5</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="kt">float</span><span class="o">[]</span><span class="w"> </span><span class="n">decimals</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">float</span><span class="o">[</span><span class="mi">5</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="kt">char</span><span class="o">[]</span><span class="w"> </span><span class="n">characters</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">char</span><span class="o">[</span><span class="mi">5</span><span class="o">]</span><span class="p">;</span>
@@ -4402,7 +4402,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="c1">// 様々な基本データ型を使用して配列を初期化</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="c1">// さまざまな基本データ型で配列を初期化する</span>
 <a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">numbers</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
 <a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="kt">float</span><span class="p">[]</span><span class="w"> </span><span class="n">decimals</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">float</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
 <a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="kt">char</span><span class="p">[]</span><span class="w"> </span><span class="n">characters</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">char</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
@@ -4410,7 +4410,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="c1">// 様々な基本データ型を使用して配列を初期化</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="c1">// さまざまな基本データ型で配列を初期化する</span>
 <a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">var</span><span class="w"> </span><span class="nx">numbers</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="kt">int</span><span class="p">{}</span>
 <a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="kd">var</span><span class="w"> </span><span class="nx">decimals</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="kt">float64</span><span class="p">{}</span>
 <a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="kd">var</span><span class="w"> </span><span class="nx">characters</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="kt">byte</span><span class="p">{}</span>
@@ -4418,7 +4418,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="c1">// 様々な基本データ型を使用して配列を初期化</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="c1">// さまざまな基本データ型で配列を初期化する</span>
 <a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">let</span><span class="w"> </span><span class="nv">numbers</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span>
 <a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">let</span><span class="w"> </span><span class="nv">decimals</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mf">0.0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span>
 <a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="kd">let</span><span class="w"> </span><span class="nv">characters</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Character</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="s">&quot;a&quot;</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span>
@@ -4426,19 +4426,19 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="c1">// JavaScriptの配列は様々な基本データ型とオブジェクトを自由に格納可能</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="c1">// JavaScript の配列はさまざまな基本データ型とオブジェクトを自由に格納できる</span>
 <a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">array</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="mf">0.0</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;a&#39;</span><span class="p">,</span><span class="w"> </span><span class="kc">false</span><span class="p">];</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="c1">// 様々な基本データ型を使用して配列を初期化</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="c1">// さまざまな基本データ型で配列を初期化する</span>
 <a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">numbers</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
 <a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="kd">const</span><span class="w"> </span><span class="nx">characters</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
 <a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="kd">const</span><span class="w"> </span><span class="nx">bools</span><span class="o">:</span><span class="w"> </span><span class="kt">boolean</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="c1">// 様々な基本データ型を使用して配列を初期化</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="c1">// さまざまな基本データ型で配列を初期化する</span>
 <a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">numbers</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
 <a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">double</span><span class="o">&gt;</span><span class="w"> </span><span class="n">decimals</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="m">0.0</span><span class="p">);</span>
 <a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">characters</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;a&#39;</span><span class="p">);</span>
@@ -4446,15 +4446,15 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="c1">// 様々な基本データ型を使用して配列を初期化</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="c1">// さまざまな基本データ型で配列を初期化する</span>
 <a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="kd">let</span><span class="w"> </span><span class="n">numbers</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="mi">5</span><span class="p">];</span>
-<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="kd">let</span><span class="w"> </span><span class="n">decimals</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">f32</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mf">0.0</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">];</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="kd">let</span><span class="w"> </span><span class="n">decimals</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">f32</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mf">0.0</span><span class="p">;</span><span class="w"> </span><span class="mi">5</span><span class="p">];</span>
 <a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="kd">let</span><span class="w"> </span><span class="n">characters</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">char</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="sc">&#39;0&#39;</span><span class="p">;</span><span class="w"> </span><span class="mi">5</span><span class="p">];</span>
 <a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="kd">let</span><span class="w"> </span><span class="n">bools</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="kc">false</span><span class="p">;</span><span class="w"> </span><span class="mi">5</span><span class="p">];</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// 様々な基本データ型を使用して配列を初期化</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// さまざまな基本データ型で配列を初期化する</span>
 <a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">numbers</span><span class="p">[</span><span class="mi">10</span><span class="p">];</span>
 <a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="kt">float</span><span class="w"> </span><span class="n">decimals</span><span class="p">[</span><span class="mi">10</span><span class="p">];</span>
 <a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="kt">char</span><span class="w"> </span><span class="n">characters</span><span class="p">[</span><span class="mi">10</span><span class="p">];</span>
@@ -4462,11 +4462,24 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="c1">// さまざまな基本データ型で配列を初期化する</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">val</span><span class="w"> </span><span class="nv">numbers</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="m">5</span><span class="p">)</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="kd">val</span><span class="w"> </span><span class="nv">decinals</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">FloatArray</span><span class="p">(</span><span class="m">5</span><span class="p">)</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="kd">val</span><span class="w"> </span><span class="nv">characters</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">CharArray</span><span class="p">(</span><span class="m">5</span><span class="p">)</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="kd">val</span><span class="w"> </span><span class="nv">bools</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BooleanArray</span><span class="p">(</span><span class="m">5</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1"># Ruby のリストはさまざまな基本データ型とオブジェクト参照を自由に格納できる</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="n">data</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="o">.</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;a&#39;</span><span class="p">,</span><span class="w"> </span><span class="kp">false</span><span class="p">,</span><span class="w"> </span><span class="no">ListNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="o">]</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>実行の可視化</summary>
+<p>https://pythontutor.com/render.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%E9%93%BE%E8%A1%A8%E8%8A%82%E7%82%B9%E7%B1%BB%22%22%22%0A%20%20%20%20def%20__init__%28self,%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E8%8A%82%E7%82%B9%E5%80%BC%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%90%8E%E7%BB%A7%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E4%BD%BF%E7%94%A8%E5%A4%9A%E7%A7%8D%E5%9F%BA%E6%9C%AC%E6%95%B0%E6%8D%AE%E7%B1%BB%E5%9E%8B%E6%9D%A5%E5%88%9D%E5%A7%8B%E5%8C%96%E6%95%B0%E7%BB%84%0A%20%20%20%20numbers%20%3D%20%5B0%5D%20*%205%0A%20%20%20%20decimals%20%3D%20%5B0.0%5D%20*%205%0A%20%20%20%20%23%20Python%20%E7%9A%84%E5%AD%97%E7%AC%A6%E5%AE%9E%E9%99%85%E4%B8%8A%E6%98%AF%E9%95%BF%E5%BA%A6%E4%B8%BA%201%20%E7%9A%84%E5%AD%97%E7%AC%A6%E4%B8%B2%0A%20%20%20%20characters%20%3D%20%5B'0'%5D%20*%205%0A%20%20%20%20bools%20%3D%20%5BFalse%5D%20*%205%0A%20%20%20%20%23%20Python%20%E7%9A%84%E5%88%97%E8%A1%A8%E5%8F%AF%E4%BB%A5%E8%87%AA%E7%94%B1%E5%AD%98%E5%82%A8%E5%90%84%E7%A7%8D%E5%9F%BA%E6%9C%AC%E6%95%B0%E6%8D%AE%E7%B1%BB%E5%9E%8B%E5%92%8C%E5%AF%B9%E8%B1%A1%E5%BC%95%E7%94%A8%0A%20%20%20%20data%20%3D%20%5B0,%200.0,%20'a',%20False,%20ListNode%280%29%5D&amp;cumulative=false&amp;curInstr=12&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>
+</details>
 
 <!-- Source file information -->
 
@@ -4513,7 +4526,7 @@ aria-label="フッター"
   <a
     href="../number_encoding/"
     class="md-footer__link md-footer__link--next"
-    aria-label="次: 3.3 &amp;nbsp; 数値の符号化 *"
+    aria-label="次: 3.3 &amp;nbsp; 数値エンコーディング *"
     rel="next"
   >
     <div class="md-footer__title">
@@ -4521,7 +4534,7 @@ aria-label="フッター"
         次
       </span>
       <div class="md-ellipsis">
-        3.3 &nbsp; 数値の符号化 *
+        3.3 &nbsp; 数値エンコーディング *
       </div>
     </div>
     <div class="md-footer__button md-icon">
diff --git a/ja/chapter_data_structure/character_encoding/index.html b/ja/chapter_data_structure/character_encoding/index.html
index 3c6c3de3b..088acc4de 100644
--- a/ja/chapter_data_structure/character_encoding/index.html
+++ b/ja/chapter_data_structure/character_encoding/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1062,7 +1062,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1099,7 +1099,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1117,7 +1117,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1147,7 +1147,7 @@
   <a href="#341-ascii" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3.4.1 &nbsp; ASCII文字セット
+        3.4.1 &nbsp; ASCII 文字セット
       
     </span>
   </a>
@@ -1158,7 +1158,7 @@
   <a href="#342-gbk" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3.4.2 &nbsp; GBK文字セット
+        3.4.2 &nbsp; GBK 文字セット
       
     </span>
   </a>
@@ -1169,7 +1169,7 @@
   <a href="#343-unicode" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3.4.3 &nbsp; Unicode文字セット
+        3.4.3 &nbsp; Unicode 文字セット
       
     </span>
   </a>
@@ -1180,7 +1180,7 @@
   <a href="#344-utf-8" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3.4.4 &nbsp; UTF-8エンコーディング
+        3.4.4 &nbsp; UTF-8 エンコーディング
       
     </span>
   </a>
@@ -1191,7 +1191,7 @@
   <a href="#345" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3.4.5 &nbsp; プログラミング言語における文字エンコーディング
+        3.4.5 &nbsp; プログラミング言語の文字エンコーディング
       
     </span>
   </a>
@@ -1696,7 +1696,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1718,7 +1718,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1740,7 +1740,7 @@
   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -2047,7 +2047,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2210,7 +2210,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2596,7 +2596,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2652,7 +2652,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2680,7 +2680,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3218,7 +3218,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3274,7 +3274,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3302,7 +3302,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3495,7 +3495,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3523,7 +3523,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3664,7 +3664,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3692,7 +3692,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3720,7 +3720,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3748,7 +3748,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3941,7 +3941,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4186,7 +4186,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4332,7 +4332,7 @@
   <a href="#341-ascii" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3.4.1 &nbsp; ASCII文字セット
+        3.4.1 &nbsp; ASCII 文字セット
       
     </span>
   </a>
@@ -4343,7 +4343,7 @@
   <a href="#342-gbk" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3.4.2 &nbsp; GBK文字セット
+        3.4.2 &nbsp; GBK 文字セット
       
     </span>
   </a>
@@ -4354,7 +4354,7 @@
   <a href="#343-unicode" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3.4.3 &nbsp; Unicode文字セット
+        3.4.3 &nbsp; Unicode 文字セット
       
     </span>
   </a>
@@ -4365,7 +4365,7 @@
   <a href="#344-utf-8" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3.4.4 &nbsp; UTF-8エンコーディング
+        3.4.4 &nbsp; UTF-8 エンコーディング
       
     </span>
   </a>
@@ -4376,7 +4376,7 @@
   <a href="#345" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3.4.5 &nbsp; プログラミング言語における文字エンコーディング
+        3.4.5 &nbsp; プログラミング言語の文字エンコーディング
       
     </span>
   </a>
@@ -4421,69 +4421,69 @@
 
 <!-- Page content -->
 <h1 id="34">3.4 &nbsp; 文字エンコーディング *<a class="headerlink" href="#34" title="Permanent link">&para;</a></h1>
-<p>コンピュータシステムでは、すべてのデータが二進形式で格納され、<code>char</code>も例外ではありません。文字を表現するために、各文字と二進数の一対一のマッピングを定義する「文字セット」を開発する必要があります。文字セットがあれば、コンピュータは表を参照して二進数を文字に変換できます。</p>
-<h2 id="341-ascii">3.4.1 &nbsp; ASCII文字セット<a class="headerlink" href="#341-ascii" title="Permanent link">&para;</a></h2>
-<p><u>ASCIIコード</u>は最も初期の文字セットの一つで、正式にはAmerican Standard Code for Information Interchangeとして知られています。7つの二進桁（1バイトの下位7ビット）を使用して文字を表現し、最大128種類の異なる文字を表現できます。以下の図に示すように、ASCIIには英語の大文字と小文字、0〜9の数字、様々な句読点、特定の制御文字（改行やタブなど）が含まれています。</p>
-<p><img alt="ASCIIコード" class="animation-figure" src="../character_encoding.assets/ascii_table.png" /></p>
-<p align="center"> 図 3-6 &nbsp; ASCIIコード </p>
+<p>コンピュータでは、すべてのデータは二進数の形で保存されており、文字 <code>char</code> も例外ではありません。文字を表すためには、「文字セット」を定義し、各文字と二進数の間の一対一の対応関係を定める必要があります。文字セットがあれば、コンピュータは対応表を参照して二進数から文字への変換を行えます。</p>
+<h2 id="341-ascii">3.4.1 &nbsp; ASCII 文字セット<a class="headerlink" href="#341-ascii" title="Permanent link">&para;</a></h2>
+<p><u>ASCII コード</u>は最も早く登場した文字セットで、その正式名称は American Standard Code for Information Interchange（米国標準情報交換コード）です。これは 7 ビットの二進数（1 バイトの下位 7 ビット）で 1 文字を表し、最大で 128 種類の異なる文字を表現できます。下図のように、ASCII コードには英字の大文字と小文字、数字 0 ~ 9、いくつかの句読点、そしていくつかの制御文字（改行やタブなど）が含まれます。</p>
+<p><img alt="ASCII コード" class="animation-figure" src="../character_encoding.assets/ascii_table.png" /></p>
+<p align="center"> 図 3-6 &nbsp; ASCII コード </p>
 
-<p>しかし、<strong>ASCIIは英語の文字のみを表現できます</strong>。コンピュータのグローバル化に伴い、より多くの言語を表現するために<u>EASCII</u>と呼ばれる文字セットが開発されました。ASCIIの7ビット構造から8ビットに拡張し、256文字の表現を可能にしました。</p>
-<p>世界的に、様々な地域固有のEASCII文字セットが導入されました。これらのセットの最初の128文字はASCIIと一致していますが、残りの128文字は異なる言語の要件に対応するために異なって定義されています。</p>
-<h2 id="342-gbk">3.4.2 &nbsp; GBK文字セット<a class="headerlink" href="#342-gbk" title="Permanent link">&para;</a></h2>
-<p>後に、**EASCIIでも多くの言語の文字要件を満たすことができない**ことが判明しました。例えば、中国語には約10万の漢字があり、そのうち数千が定期的に使用されています。1980年、中国標準化委員会は6763の中国語文字を含む<u>GB2312</u>文字セットを発表し、中国語のコンピュータ処理ニーズを本質的に満たしました。</p>
-<p>しかし、GB2312は一部の稀少文字や繁体字を処理できませんでした。<u>GBK</u>文字セットはGB2312を拡張し、21886の中国語文字を含んでいます。GBKエンコーディングスキームでは、ASCII文字は1バイトで表現され、中国語文字は2バイトを使用します。</p>
-<h2 id="343-unicode">3.4.3 &nbsp; Unicode文字セット<a class="headerlink" href="#343-unicode" title="Permanent link">&para;</a></h2>
-<p>コンピュータ技術の急速な発展と多数の文字セットおよびエンコーディング標準により、数多くの問題が発生しました。一方では、これらの文字セットは一般的に特定の言語の文字のみを定義し、多言語環境では適切に機能できませんでした。他方では、同じ言語に対する複数の文字セット標準の存在により、異なるエンコーディング標準を使用するコンピュータ間で情報交換を行う際に文字化けが発生しました。</p>
-<p>当時の研究者たちは考えました：<strong>世界のすべての言語と記号を含む包括的な文字セットが開発されれば、言語横断環境と文字化けに関連する問題を解決できるのではないでしょうか？</strong> このアイデアにインスパイアされて、広範囲な文字セットであるUnicodeが誕生しました。</p>
-<p><u>Unicode</u>は中国語で「统一码」（統一コード）と呼ばれ、理論的に100万文字以上を収容できます。世界中のすべての文字を単一のセットに組み込み、様々な言語の処理と表示のための汎用文字セットを提供し、異なるエンコーディング標準による文字化けの問題を減らすことを目指しています。</p>
-<p>1991年のリリース以来、Unicodeは新しい言語と文字を含むよう継続的に拡張されています。2022年9月現在、Unicodeには149,186文字が含まれており、様々な言語の文字、記号、さらには絵文字も含まれています。広大なUnicode文字セットでは、一般的に使用される文字は2バイトを占有し、一部の稀少な文字は3バイトまたは4バイトを占有する場合があります。</p>
-<p>Unicodeは各文字に数値（「コードポイント」と呼ばれる）を割り当てる汎用文字セットですが、<strong>これらの文字コードポイントがコンピュータシステムにどのように格納されるべきかは指定していません</strong>。疑問が生じるかもしれません：システムはテキスト内の異なる長さのUnicodeコードポイントをどのように解釈するのでしょうか？例えば、2バイトのコードが与えられた場合、システムはそれが単一の2バイト文字を表すのか、2つの1バイト文字を表すのかをどのように判断するのでしょうか？</p>
-<p><strong>この問題に対する簡単な解決策は、すべての文字を等長エンコーディングとして格納することです</strong>。以下の図に示すように、「Hello」の各文字は1バイトを占有し、「算法」（アルゴリズム）の各文字は2バイトを占有します。上位ビットをゼロで埋めることで、「Hello 算法」のすべての文字を2バイトとしてエンコードできます。この方法により、システムは2バイトごとに文字を解釈し、フレーズの内容を復元できます。</p>
-<p><img alt="Unicodeエンコーディング例" class="animation-figure" src="../character_encoding.assets/unicode_hello_algo.png" /></p>
-<p align="center"> 図 3-7 &nbsp; Unicodeエンコーディング例 </p>
+<p>しかし、<strong>ASCII コードで表現できるのは英語だけです</strong>。コンピュータのグローバル化に伴い、より多くの言語を表せる <u>EASCII</u> 文字セットが生まれました。これは ASCII の 7 ビットを 8 ビットへ拡張したもので、256 種類の異なる文字を表現できます。</p>
+<p>世界では、さまざまな地域に適した EASCII 文字セットが次々に登場しました。これらの文字セットでは、前半の 128 文字は ASCII コードで統一され、後半の 128 文字は各言語の要件に合わせて個別に定義されています。</p>
+<h2 id="342-gbk">3.4.2 &nbsp; GBK 文字セット<a class="headerlink" href="#342-gbk" title="Permanent link">&para;</a></h2>
+<p>その後、人々は**EASCII コードでも多くの言語に必要な文字数を満たせない**ことに気づきました。たとえば漢字は 10 万字近くあり、日常的に使うものだけでも数千字あります。中国国家標準総局は 1980 年に <u>GB2312</u> 文字セットを公開し、6763 字の漢字を収録して、漢字のコンピュータ処理の基本的な需要を満たしました。</p>
+<p>しかし、GB2312 では一部の珍しい字や繁体字を扱えません。<u>GBK</u> 文字セットは GB2312 を基に拡張されたもので、合計 21886 字の漢字を収録しています。GBK のエンコーディング方式では、ASCII 文字は 1 バイト、漢字は 2 バイトで表されます。</p>
+<h2 id="343-unicode">3.4.3 &nbsp; Unicode 文字セット<a class="headerlink" href="#343-unicode" title="Permanent link">&para;</a></h2>
+<p>コンピュータ技術が急速に発展するにつれて、文字セットと符号化規格は百花繚乱の状態となり、それに伴って多くの問題も生じました。一方では、これらの文字セットは通常、特定の言語の文字しか定義しておらず、多言語環境では正常に動作できませんでした。もう一方では、同じ言語にも複数の文字セット規格が存在し、2 台のコンピュータが異なる符号化規格を使っていると、情報伝達の際に文字化けが発生しました。</p>
+<p>当時の研究者たちはこう考えました。<strong>十分に完全な文字セットを打ち出して、世界中のあらゆる言語と記号をそこに収録すれば、多言語環境や文字化けの問題を解決できるのではないか</strong>。この発想に後押しされて、大規模で包括的な文字セット Unicode が誕生しました。</p>
+<p><u>Unicode</u> の中国語名は「統一コード」であり、理論上は 100 万を超える文字を収容できます。Unicode は世界中の文字を 1 つの文字セットに統合することを目指し、さまざまな言語の文字を処理・表示できる汎用文字セットを提供することで、符号化規格の違いによる文字化けを減らそうとしています。</p>
+<p>1991 年の公開以来、Unicode は新しい言語と文字を継続的に拡充してきました。2022 年 9 月時点で、Unicode にはすでに 149186 文字が含まれており、各種言語の文字、記号、さらには絵文字まで収録されています。巨大な Unicode 文字セットでは、よく使われる文字は 2 バイトを占め、一部の珍しい文字は 3 バイト、さらには 4 バイトを占めます。</p>
+<p>Unicode は汎用文字セットであり、本質的には各文字に番号（「コードポイント」）を割り当てるものですが、<strong>それらのコードポイントをコンピュータ内でどのように保存するかまでは規定していません</strong>。ここで疑問が生じます。長さの異なる Unicode コードポイントが同じテキストに現れたとき、システムはどのように文字を解析するのでしょうか。たとえば長さ 2 バイトの符号が与えられたとき、それが 2 バイトの 1 文字なのか、1 バイトの 2 文字なのかをどう判定するのでしょうか。</p>
+<p>この問題に対して、**すべての文字を固定長の符号として保存する**という直接的な解決策があります。下図のように、「Hello」の各文字は 1 バイト、「アルゴリズム」の各文字は 2 バイトを占めます。上位ビットを 0 で埋めることで、「Hello アルゴリズム」のすべての文字を 2 バイト長にエンコードできます。こうすれば、システムは 2 バイトごとに 1 文字を解析して、この語句の内容を復元できます。</p>
+<p><img alt="Unicode エンコーディングの例" class="animation-figure" src="../character_encoding.assets/unicode_hello_algo.png" /></p>
+<p align="center"> 図 3-7 &nbsp; Unicode エンコーディングの例 </p>
 
-<p>しかし、ASCIIが示したように、英語のエンコーディングには1バイトのみが必要です。上記のアプローチを使用すると、英語テキストが占有する空間がASCIIエンコーディングと比較して2倍になり、メモリ空間の無駄になります。したがって、より効率的なUnicodeエンコーディング方法が必要です。</p>
-<h2 id="344-utf-8">3.4.4 &nbsp; UTF-8エンコーディング<a class="headerlink" href="#344-utf-8" title="Permanent link">&para;</a></h2>
-<p>現在、UTF-8は国際的に最も広く使用されているUnicodeエンコーディング方法になっています。**これは可変長エンコーディング**で、文字の複雑さに応じて1〜4バイトを使用して文字を表現します。ASCII文字は1バイトのみが必要で、ラテン文字とギリシャ文字は2バイト、一般的に使用される中国語文字は3バイト、その他の稀少な文字は4バイトが必要です。</p>
-<p>UTF-8のエンコーディング規則は複雑ではなく、2つのケースに分けることができます：</p>
+<p>しかし ASCII コードはすでに、英語の符号化には 1 バイトで十分であることを示しています。上記の方式を採用すると、英語のテキストが占める空間は ASCII エンコーディング時の 2 倍になり、メモリ空間の浪費が大きくなります。そのため、より効率的な Unicode エンコーディング方式が必要です。</p>
+<h2 id="344-utf-8">3.4.4 &nbsp; UTF-8 エンコーディング<a class="headerlink" href="#344-utf-8" title="Permanent link">&para;</a></h2>
+<p>現在、UTF-8 は国際的に最も広く使われている Unicode エンコーディング方式になっています。**これは可変長のエンコーディング**であり、1 文字を 1 〜 4 バイトで表し、文字の複雑さに応じて長さが変わります。ASCII 文字は 1 バイト、ラテン文字とギリシャ文字は 2 バイト、一般的な漢字は 3 バイト、そのほかの一部の珍しい文字は 4 バイト必要です。</p>
+<p>UTF-8 の符号化規則はそれほど複雑ではなく、次の 2 つのケースに分けられます。</p>
 <ul>
-<li>1バイト文字の場合、最上位ビットを<span class="arithmatex">\(0\)</span>に設定し、残りの7ビットをUnicodeコードポイントに設定します。注目すべきは、ASCII文字がUnicodeセットの最初の128コードポイントを占有することです。これは**UTF-8エンコーディングがASCIIと後方互換性がある**ことを意味します。これは、UTF-8を使用して古いASCIIテキストを解析できることを意味します。</li>
-<li>長さ<span class="arithmatex">\(n\)</span>バイトの文字（<span class="arithmatex">\(n &gt; 1\)</span>）の場合、最初のバイトの最上位<span class="arithmatex">\(n\)</span>ビットを<span class="arithmatex">\(1\)</span>に設定し、<span class="arithmatex">\((n + 1)^{\text{th}}\)</span>ビットを<span class="arithmatex">\(0\)</span>に設定します。2番目のバイトから、各バイトの最上位2ビットを<span class="arithmatex">\(10\)</span>に設定します。残りのビットはUnicodeコードポイントを埋めるために使用されます。</li>
+<li>長さ 1 バイトの文字では、最上位ビットを <span class="arithmatex">\(0\)</span> にし、残りの 7 ビットを Unicode コードポイントに設定します。ここで注意すべきなのは、ASCII 文字が Unicode 文字セットの先頭 128 個のコードポイントを占めていることです。つまり、<strong>UTF-8 エンコーディングは ASCII コードと下位互換性があります</strong>。このため、UTF-8 を使って古い ASCII コードのテキストを解析できます。</li>
+<li>長さ <span class="arithmatex">\(n\)</span> バイトの文字（ただし <span class="arithmatex">\(n &gt; 1\)</span>）では、先頭バイトの上位 <span class="arithmatex">\(n\)</span> ビットをすべて <span class="arithmatex">\(1\)</span> にし、第 <span class="arithmatex">\(n + 1\)</span> ビットを <span class="arithmatex">\(0\)</span> に設定します。2 バイト目以降では、各バイトの上位 2 ビットをいずれも <span class="arithmatex">\(10\)</span> にし、残りのすべてのビットで文字の Unicode コードポイントを埋めます。</li>
 </ul>
-<p>以下の図は「Hello算法」のUTF-8エンコーディングを示しています。最上位<span class="arithmatex">\(n\)</span>ビットが<span class="arithmatex">\(1\)</span>に設定されているため、システムは最上位ビットで<span class="arithmatex">\(1\)</span>に設定されたビット数を数えることで文字の長さを<span class="arithmatex">\(n\)</span>として決定できることが観察できます。</p>
-<p>しかし、なぜ残りのバイトの最上位2ビットを<span class="arithmatex">\(10\)</span>に設定するのでしょうか？実際、この<span class="arithmatex">\(10\)</span>は一種のチェックサムとして機能します。システムが間違ったバイトからテキストの解析を開始した場合、バイトの先頭の<span class="arithmatex">\(10\)</span>によりシステムは異常を迅速に検出できます。</p>
-<p><span class="arithmatex">\(10\)</span>をチェックサムとして使用する理由は、UTF-8エンコーディング規則の下では、文字の最上位2ビットが<span class="arithmatex">\(10\)</span>になることは不可能だからです。これは矛盾により証明できます：文字の最上位2ビットが<span class="arithmatex">\(10\)</span>の場合、文字の長さが<span class="arithmatex">\(1\)</span>であることを示し、これはASCIIに対応します。しかし、ASCII文字の最上位ビットは<span class="arithmatex">\(0\)</span>であるべきで、これは仮定と矛盾します。</p>
-<p><img alt="UTF-8エンコーディング例" class="animation-figure" src="../character_encoding.assets/utf-8_hello_algo.png" /></p>
-<p align="center"> 図 3-8 &nbsp; UTF-8エンコーディング例 </p>
+<p>下図は「Helloアルゴリズム」に対応する UTF-8 エンコーディングを示しています。観察すると、上位 <span class="arithmatex">\(n\)</span> ビットがすべて <span class="arithmatex">\(1\)</span> に設定されているため、システムは先頭から連続する <span class="arithmatex">\(1\)</span> の個数を読むことで、その文字の長さが <span class="arithmatex">\(n\)</span> であると解析できます。</p>
+<p>では、なぜ残りのすべてのバイトの上位 2 ビットを <span class="arithmatex">\(10\)</span> にするのでしょうか。実は、この <span class="arithmatex">\(10\)</span> は検査用の印として機能します。システムが誤ったバイト位置からテキストを解析し始めたとしても、バイト先頭の <span class="arithmatex">\(10\)</span> によって異常を素早く判定できます。</p>
+<p>この <span class="arithmatex">\(10\)</span> を検査用の印とする理由は、UTF-8 の符号化規則では上位 2 ビットが <span class="arithmatex">\(10\)</span> になる文字は存在しないからです。この結論は背理法で証明できます。ある文字の上位 2 ビットが <span class="arithmatex">\(10\)</span> だと仮定すると、その文字の長さは <span class="arithmatex">\(1\)</span> であり、ASCII コードに対応することになります。しかし ASCII コードの最上位ビットは <span class="arithmatex">\(0\)</span> であるはずなので、仮定と矛盾します。</p>
+<p><img alt="UTF-8 エンコーディングの例" class="animation-figure" src="../character_encoding.assets/utf-8_hello_algo.png" /></p>
+<p align="center"> 図 3-8 &nbsp; UTF-8 エンコーディングの例 </p>
 
-<p>UTF-8以外にも、他の一般的なエンコーディング方法には以下があります：</p>
+<p>UTF-8 以外にも、一般的なエンコーディング方式として次の 2 つがあります。</p>
 <ul>
-<li><strong>UTF-16エンコーディング</strong>：2または4バイトを使用して文字を表現します。すべてのASCII文字と一般的に使用される非英語文字は2バイトで表現され、少数の文字は4バイトが必要です。2バイト文字の場合、UTF-16エンコーディングはUnicodeコードポイントと等しくなります。</li>
-<li><strong>UTF-32エンコーディング</strong>：すべての文字が4バイトを使用します。これは、UTF-32がUTF-8やUTF-16よりも多くの空間を占有することを意味し、特にASCII文字の割合が高いテキストでは顕著です。</li>
+<li><strong>UTF-16 エンコーディング</strong>：1 文字を 2 バイトまたは 4 バイトで表します。すべての ASCII 文字と一般的な非英語文字は 2 バイトで表し、一部の文字だけが 4 バイトを必要とします。2 バイトの文字については、UTF-16 エンコーディングは Unicode コードポイントと等しくなります。</li>
+<li><strong>UTF-32 エンコーディング</strong>：各文字を必ず 4 バイトで表します。つまり UTF-32 は UTF-8 や UTF-16 よりも多くの領域を消費し、とくに ASCII 文字の比率が高いテキストでその傾向が顕著です。</li>
 </ul>
-<p>ストレージ空間の観点から、UTF-8を使用して英語文字を表現することは1バイトのみが必要なため非常に効率的です。UTF-16を使用して一部の非英語文字（中国語など）をエンコードすることは、2バイトのみが必要なためより効率的になる場合があります。一方、UTF-8では3バイトが必要になる場合があります。</p>
-<p>互換性の観点から、UTF-8は最も汎用性があり、多くのツールとライブラリがUTF-8を優先的にサポートしています。</p>
-<h2 id="345">3.4.5 &nbsp; プログラミング言語における文字エンコーディング<a class="headerlink" href="#345" title="Permanent link">&para;</a></h2>
-<p>歴史的に、多くのプログラミング言語はプログラム実行中の文字列処理にUTF-16やUTF-32などの固定長エンコーディングを利用していました。これにより文字列を配列として処理でき、いくつかの利点があります：</p>
+<p>記憶領域の使用量という観点では、UTF-8 は英語文字の表現に非常に効率的で、必要なのは 1 バイトだけです。一方、UTF-16 は一部の非英語文字（たとえば中国語の文字）の符号化でより効率的になることがあり、必要なのは 2 バイトだけで、UTF-8 では 3 バイト必要になる場合があります。</p>
+<p>互換性という観点では、UTF-8 の汎用性が最も高く、多くのツールやライブラリが UTF-8 を優先的にサポートしています。</p>
+<h2 id="345">3.4.5 &nbsp; プログラミング言語の文字エンコーディング<a class="headerlink" href="#345" title="Permanent link">&para;</a></h2>
+<p>従来の多くのプログラミング言語では、実行中の文字列に UTF-16 や UTF-32 のような固定長エンコーディングが使われています。固定長エンコーディングでは、文字列を配列のように扱えるため、次のような利点があります。</p>
 <ul>
-<li><strong>ランダムアクセス</strong>：UTF-16でエンコードされた文字列は簡単にランダムアクセスできます。可変長エンコーディングであるUTF-8の場合、<span class="arithmatex">\(i^{th}\)</span>文字の位置を特定するには文字列の開始から<span class="arithmatex">\(i^{th}\)</span>位置まで走査する必要があり、<span class="arithmatex">\(O(n)\)</span>時間がかかります。</li>
-<li><strong>文字数カウント</strong>：ランダムアクセスと同様に、UTF-16でエンコードされた文字列の文字数をカウントすることは<span class="arithmatex">\(O(1)\)</span>操作です。しかし、UTF-8でエンコードされた文字列の文字数をカウントするには文字列全体を走査する必要があります。</li>
-<li><strong>文字列操作</strong>：分割、連結、挿入、削除などの多くの文字列操作は、UTF-16でエンコードされた文字列で簡単です。これらの操作は一般的に、UTF-8エンコーディングの有効性を確保するためにUTF-8でエンコードされた文字列で追加の計算が必要です。</li>
+<li><strong>ランダムアクセス</strong>：UTF-16 で符号化された文字列はランダムアクセスが容易です。UTF-8 は可変長エンコーディングなので、第 <span class="arithmatex">\(i\)</span> 文字を見つけるには文字列の先頭から第 <span class="arithmatex">\(i\)</span> 文字まで走査する必要があり、<span class="arithmatex">\(O(n)\)</span> の時間がかかります。</li>
+<li><strong>文字数の計算</strong>：ランダムアクセスと同様に、UTF-16 で符号化された文字列の長さを計算するのも <span class="arithmatex">\(O(1)\)</span> の操作です。しかし、UTF-8 で符号化された文字列の長さを計算するには、文字列全体を走査する必要があります。</li>
+<li><strong>文字列操作</strong>：UTF-16 で符号化された文字列では、多くの文字列操作（分割、連結、挿入、削除など）をより簡単に行えます。UTF-8 で符号化された文字列では、これらの操作を行う際に、無効な UTF-8 エンコーディングを生じさせないための追加計算が通常必要になります。</li>
 </ul>
-<p>プログラミング言語における文字エンコーディングスキームの設計は、様々な要因を含む興味深いトピックです：</p>
+<p>実際、プログラミング言語における文字エンコーディング方式の設計は、とても興味深い話題であり、多くの要因が関わっています。</p>
 <ul>
-<li>Javaの<code>String</code>型はUTF-16エンコーディングを使用し、各文字が2バイトを占有します。これは、16ビットがすべての可能な文字を表現するのに十分であるという初期の信念に基づいており、後に間違いであることが証明されました。Unicode標準が16ビットを超えて拡張されると、Javaの文字は「サロゲートペア」として知られる16ビット値のペアで表現される場合があります。</li>
-<li>JavaScriptとTypeScriptは、Javaと同様の理由でUTF-16エンコーディングを使用します。JavaScriptが1995年にNetscapeによって最初に導入されたとき、Unicodeはまだ初期段階にあり、16ビットエンコーディングはすべてのUnicode文字を表現するのに十分でした。</li>
-<li>C#はUTF-16エンコーディングを使用し、これは主にMicrosoftによって設計された.NETプラットフォーム、および多くのMicrosoft技術（Windowsオペレーティングシステムを含む）がUTF-16エンコーディングを広範囲に使用しているためです。</li>
+<li>Java の <code>String</code> 型は UTF-16 エンコーディングを使用し、各文字は 2 バイトを占めます。これは Java 言語の設計当初、人々が 16 ビットあればあらゆる文字を表現するのに十分だと考えていたためです。しかし、これは誤った判断でした。その後 Unicode 規格は 16 ビットを超える範囲へ拡張されたため、現在の Java では 1 文字が 16 ビット値の組（「サロゲートペア」）で表されることがあります。</li>
+<li>JavaScript と TypeScript の文字列が UTF-16 エンコーディングを使う理由も Java と似ています。1995 年に Netscape 社が初めて JavaScript 言語を公開した当時、Unicode はまだ発展初期にあり、16 ビットの符号化で十分すべての Unicode 文字を表せると考えられていました。</li>
+<li>C# が UTF-16 エンコーディングを使う主な理由は、.NET プラットフォームが Microsoft によって設計され、Microsoft の多くの技術（Windows オペレーティングシステムを含む）で UTF-16 エンコーディングが広く使われているためです。</li>
 </ul>
-<p>文字数の過小評価により、これらの言語は16ビットを超えるUnicode文字を表現するために「サロゲートペア」を使用する必要がありました。このアプローチには欠点があります：サロゲートペアを含む文字列は2バイトまたは4バイトを占有する文字を持つ場合があり、固定長エンコーディングの利点を失います。さらに、サロゲートペアの処理はプログラミングに複雑さとデバッグの困難さを追加します。</p>
-<p>これらの課題に対処するため、一部の言語は代替エンコーディング戦略を採用しています：</p>
+<p>以上のプログラミング言語は文字数を過小評価していたため、16 ビットを超える長さの Unicode 文字を表すために「サロゲートペア」を採用せざるを得ませんでした。これはやむを得ない妥協策です。一方では、サロゲートペアを含む文字列では、1 文字が 2 バイトまたは 4 バイトを占める可能性があり、固定長エンコーディングの利点が失われます。もう一方では、サロゲートペアの処理には追加のコードが必要となり、プログラミングの複雑さとデバッグの難しさが増します。</p>
+<p>こうした理由から、一部のプログラミング言語では別のエンコーディング方式が採用されました。</p>
 <ul>
-<li>Pythonの<code>str</code>型は、文字のストレージ長が文字列内の最大のUnicodeコードポイントに依存する柔軟な表現でUnicodeエンコーディングを使用します。すべての文字がASCIIの場合、各文字は1バイトを占有し、基本多言語面（BMP）内の文字は2バイト、BMPを超える文字は4バイトを占有します。</li>
-<li>Goの<code>string</code>型は内部的にUTF-8エンコーディングを使用します。Goは個別のUnicodeコードポイントを表現するための<code>rune</code>型も提供します。</li>
-<li>Rustの<code>str</code>と<code>String</code>型は内部的にUTF-8エンコーディングを使用します。Rustは個別のUnicodeコードポイント用の<code>char</code>型も提供します。</li>
+<li>Python の <code>str</code> は Unicode エンコーディングを使用し、柔軟な文字列表現を採用しています。保存される文字の長さは、その文字列中で最大の Unicode コードポイントに依存します。文字列がすべて ASCII 文字であれば各文字は 1 バイト、ASCII の範囲を超える文字があってもすべてが基本多言語面（BMP）内であれば各文字は 2 バイト、BMP を超える文字があれば各文字は 4 バイトを占めます。</li>
+<li>Go 言語の <code>string</code> 型は内部で UTF-8 エンコーディングを使用します。Go 言語には単一の Unicode コードポイントを表す <code>rune</code> 型も用意されています。</li>
+<li>Rust 言語の <code>str</code> と <code>String</code> 型は内部で UTF-8 エンコーディングを使用します。Rust にも単一の Unicode コードポイントを表す <code>char</code> 型があります。</li>
 </ul>
-<p>上記の議論は、プログラミング言語での文字列の格納方法に関するものであり、**ファイルでの文字列の格納方法やネットワーク上での送信方法とは異なる**ことに注意することが重要です。ファイルストレージやネットワーク送信では、文字列は通常、最適な互換性と空間効率のためにUTF-8形式でエンコードされます。</p>
+<p>注意すべきなのは、ここまでの議論はすべて、プログラミング言語内での文字列の保存方法についてであり、**文字列をファイルに保存したりネットワークで転送したりする方法とは別の問題である**ということです。ファイル保存やネットワーク転送では、通常、互換性と空間効率を最適化するために文字列を UTF-8 形式にエンコードします。</p>
 
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-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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 <!-- Page content -->
 <h1 id="31">3.1 &nbsp; データ構造の分類<a class="headerlink" href="#31" title="Permanent link">&para;</a></h1>
-<p>一般的なデータ構造には、配列、連結リスト、スタック、キュー、ハッシュ表、木、ヒープ、グラフがあります。これらは「論理構造」と「物理構造」に分類できます。</p>
+<p>代表的なデータ構造には、配列、連結リスト、スタック、キュー、ハッシュテーブル、木、ヒープ、グラフがあり、これらは「論理構造」と「物理構造」の 2 つの観点から分類できます。</p>
 <h2 id="311">3.1.1 &nbsp; 論理構造：線形と非線形<a class="headerlink" href="#311" title="Permanent link">&para;</a></h2>
-<p><strong>論理構造はデータ要素間の論理的関係を明らかにします</strong>。配列と連結リストでは、データは特定の順序で配置され、データ間の線形関係を示しています。一方、木では、データは上から下へ階層的に配置され、「祖先」と「子孫」間の派生関係を示しています。そして、グラフはノードとエッジから構成され、複雑なネットワーク関係を反映しています。</p>
-<p>下図に示されているように、論理構造は「線形」と「非線形」の2つの主要カテゴリに分けることができます。線形構造はより直感的で、データが論理関係において線形に配置されていることを示しています。非線形構造は、逆に非線形に配置されています。</p>
+<p><strong>論理構造はデータ要素間の論理的な関係を示します</strong>。配列と連結リストでは、データは一定の順序で並び、データ間の線形関係を表します。一方、木ではデータは上から下へ階層的に並び、「祖先」と「子孫」の派生関係を示します。グラフはノードと辺で構成され、複雑なネットワーク関係を反映します。</p>
+<p>以下の図に示すように、論理構造は「線形」と「非線形」の 2 つに大別できます。線形構造は比較的直感的で、データが論理関係において線形に並ぶことを指します。非線形構造はその逆で、非線形に配置されます。</p>
 <ul>
-<li><strong>線形データ構造</strong>：配列、連結リスト、スタック、キュー、ハッシュ表。要素が一対一の順次関係を持ちます。</li>
-<li><strong>非線形データ構造</strong>：木、ヒープ、グラフ、ハッシュ表。</li>
+<li><strong>線形データ構造</strong>：配列、連結リスト、スタック、キュー、ハッシュテーブルであり、要素間は 1 対 1 の順序関係です。</li>
+<li><strong>非線形データ構造</strong>：木、ヒープ、グラフ、ハッシュテーブル。</li>
 </ul>
-<p>非線形データ構造は、さらに木構造とネットワーク構造に分けることができます。</p>
+<p>非線形データ構造は、さらに木構造と網状構造に分けられます。</p>
 <ul>
-<li><strong>木構造</strong>：木、ヒープ、ハッシュ表。要素が一対多の関係を持ちます。</li>
-<li><strong>ネットワーク構造</strong>：グラフ。要素が多対多の関係を持ちます。</li>
+<li><strong>木構造</strong>：木、ヒープ、ハッシュテーブルであり、要素間は 1 対多の関係です。</li>
+<li><strong>網状構造</strong>：グラフであり、要素間は多対多の関係です。</li>
 </ul>
-<p><img alt="Linear and non-linear data structures" class="animation-figure" src="../classification_of_data_structure.assets/classification_logic_structure.png" /></p>
-<p align="center"> 図 3-1 &nbsp; Linear and non-linear data structures </p>
+<p><img alt="線形データ構造と非線形データ構造" class="animation-figure" src="../classification_of_data_structure.assets/classification_logic_structure.png" /></p>
+<p align="center"> 図 3-1 &nbsp; 線形データ構造と非線形データ構造 </p>
 
 <h2 id="312">3.1.2 &nbsp; 物理構造：連続と分散<a class="headerlink" href="#312" title="Permanent link">&para;</a></h2>
-<p><strong>アルゴリズムの実行中、処理されるデータはメモリに格納されます</strong>。下図はコンピュータのメモリスティックを示しており、各黒い正方形は物理メモリ空間です。メモリを巨大なExcelスプレッドシートと考えることができ、各セルは一定量のデータを格納できます。</p>
-<p><strong>システムはメモリアドレスによって目標位置のデータにアクセスします</strong>。下図に示されているように、コンピュータは特定のルールに従って表の各セルに一意の識別子を割り当て、各メモリ空間が一意のメモリアドレスを持つことを保証します。これらのアドレスにより、プログラムはメモリに格納されたデータにアクセスできます。</p>
-<p><img alt="Memory stick, memory spaces, memory addresses" class="animation-figure" src="../classification_of_data_structure.assets/computer_memory_location.png" /></p>
-<p align="center"> 図 3-2 &nbsp; Memory stick, memory spaces, memory addresses </p>
+<p><strong>アルゴリズムのプログラムが実行されるとき、処理中のデータは主にメモリに格納されます</strong>。下図はコンピュータのメモリモジュールを示しており、各黒い四角はそれぞれ 1 つのメモリ空間を表しています。メモリは巨大な Excel の表のようなものだと考えることができ、各セルには一定量のデータを格納できます。</p>
+<p><strong>システムはメモリアドレスを通じて目的の位置にあるデータへアクセスします</strong>。下図に示すように、コンピュータは特定の規則に従って表内の各セルに番号を割り当て、各メモリ空間が一意のメモリアドレスを持つようにします。これらのアドレスがあれば、プログラムはメモリ内のデータにアクセスできます。</p>
+<p><img alt="メモリモジュール、メモリ空間、メモリアドレス" class="animation-figure" src="../classification_of_data_structure.assets/computer_memory_location.png" /></p>
+<p align="center"> 図 3-2 &nbsp; メモリモジュール、メモリ空間、メモリアドレス </p>
 
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>メモリをExcelスプレッドシートに比較することは簡略化された類推であることに注意してください。メモリの実際の動作メカニズムはより複雑で、アドレス空間、メモリ管理、キャッシュメカニズム、仮想メモリ、物理メモリなどの概念が関係しています。</p>
+<p>補足すると、メモリを Excel の表にたとえるのは単純化した比喩であり、実際のメモリの動作機構はより複雑で、アドレス空間、メモリ管理、キャッシュ機構、仮想メモリ、物理メモリなどの概念が関わります。</p>
 </div>
-<p>メモリはすべてのプログラムの共有リソースです。あるメモリブロックが1つのプログラムによって占有されると、他のプログラムが同時に使用することはできません。<strong>したがって、メモリリソースはデータ構造とアルゴリズムの設計における重要な考慮事項です</strong>。例えば、アルゴリズムのピークメモリ使用量は、システムの残り空きメモリを超えてはいけません。連続したメモリブロックが不足している場合は、非連続メモリブロックに格納できるデータ構造を選択する必要があります。</p>
-<p>下図に示されているように、<strong>物理構造はコンピュータメモリにおけるデータの格納方法を反映し</strong>、連続空間格納（配列）と非連続空間格納（連結リスト）に分けることができます。2つのタイプの物理構造は、時間効率と空間効率の観点で補完的な特性を示します。</p>
-<p><img alt="Contiguous space storage and dispersed space storage" class="animation-figure" src="../classification_of_data_structure.assets/classification_phisical_structure.png" /></p>
-<p align="center"> 図 3-3 &nbsp; Contiguous space storage and dispersed space storage </p>
+<p>メモリはすべてのプログラムで共有される資源であり、あるメモリ領域が 1 つのプログラムに占有されると、通常は他のプログラムが同時に利用できません。<strong>したがって、データ構造とアルゴリズムの設計では、メモリ資源は重要な考慮要素です</strong>。たとえば、アルゴリズムが使用するメモリ使用量のピークは、システムに残っている空きメモリを超えてはなりません。大きな連続メモリ領域が不足している場合、選択するデータ構造は分散したメモリ空間に格納できる必要があります。</p>
+<p>下図に示すように、<strong>物理構造はデータがコンピュータメモリ内にどのように格納されるかを表します</strong>。これは連続空間への格納（配列）と分散空間への格納（連結リスト）に分けられます。物理構造は低レベルでデータのアクセス、更新、追加、削除などの操作方法を決定し、2 種類の物理構造は時間効率と空間効率の面で相補的な特徴を持ちます。</p>
+<p><img alt="連続空間格納と分散空間格納" class="animation-figure" src="../classification_of_data_structure.assets/classification_phisical_structure.png" /></p>
+<p align="center"> 図 3-3 &nbsp; 連続空間格納と分散空間格納 </p>
 
-<p><strong>すべてのデータ構造は配列、連結リスト、またはその組み合わせに基づいて実装されていることに注意してください</strong>。例えば、スタックとキューは配列または連結リストのどちらでも実装できます。ハッシュ表の実装には配列と連結リストの両方が関係する場合があります。</p>
+<p>補足すると、<strong>すべてのデータ構造は配列、連結リスト、またはその両者の組み合わせに基づいて実装されます</strong>。たとえば、スタックとキューは配列でも連結リストでも実装できます。一方、ハッシュテーブルの実装には配列と連結リストの両方が含まれる場合があります。</p>
 <ul>
-<li><strong>配列ベースの実装</strong>：スタック、キュー、ハッシュ表、木、ヒープ、グラフ、行列、テンソル（次元<span class="arithmatex">\(\geq 3\)</span>の配列）。</li>
-<li><strong>連結リストベースの実装</strong>：スタック、キュー、ハッシュ表、木、ヒープ、グラフなど。</li>
+<li><strong>配列に基づいて実装可能</strong>：スタック、キュー、ハッシュテーブル、木、ヒープ、グラフ、行列、テンソル（次元 <span class="arithmatex">\(\geq 3\)</span> の配列）など。</li>
+<li><strong>連結リストに基づいて実装可能</strong>：スタック、キュー、ハッシュテーブル、木、ヒープ、グラフなど。</li>
 </ul>
-<p>配列に基づいて実装されたデータ構造は「静的データ構造」とも呼ばれ、初期化後に長さを変更できないことを意味します。逆に、連結リストに基づいたものは「動的データ構造」と呼ばれ、プログラム実行中にサイズを調整できます。</p>
+<p>連結リストは初期化後も、プログラムの実行中に長さを調整できるため、「動的データ構造」とも呼ばれます。配列は初期化後に長さを変更できないため、「静的データ構造」とも呼ばれます。なお、配列もメモリを再割り当てすることで長さを変更でき、ある程度の「動的性」を持たせることができます。</p>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>物理構造を理解するのが困難な場合は、次の章「配列と連結リスト」を読んでから、この節に戻ることをお勧めします。</p>
+<p>物理構造の理解が難しいと感じる場合は、先に次の章を読んでから本節を振り返ることを勧めます。</p>
 </div>
 
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       <meta charset="utf-8">
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-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
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@@ -341,7 +341,7 @@
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+    はじめに
   
 
     
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+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
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-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
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-    12.1 &nbsp; 分割統治アルゴリズム
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+    12.3 &nbsp; 二分木の構築問題
   
 
     
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+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
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+    15.1 &nbsp; 貪欲法
   
 
     
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4274,18 +4274,18 @@
 
 <!-- Page content -->
 <h1 id="3">第 3 章 &nbsp; データ構造<a class="headerlink" href="#3" title="Permanent link">&para;</a></h1>
-<p><img alt="Data structures" class="cover-image" src="../assets/covers/chapter_data_structure.jpg" /></p>
+<p><img alt="データ構造" class="cover-image" src="../assets/covers/chapter_data_structure.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>データ構造は堅牢で多様なフレームワークとして機能します。</p>
-<p>データの整然とした組織化のための設計図を提供し、その上でアルゴリズムが生き生きと動き出します。</p>
+<p>データ構造は、堅固で多様な枠組みのようなものである。</p>
+<p>それはデータを秩序立てて組織するための青写真を示し、アルゴリズムはその上で生き生きと動き出す。</p>
 </div>
 <h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
 <li><a href="classification_of_data_structure/">3.1 &nbsp; データ構造の分類</a></li>
 <li><a href="basic_data_types/">3.2 &nbsp; 基本データ型</a></li>
-<li><a href="number_encoding/">3.3 &nbsp; 数値の符号化 *</a></li>
-<li><a href="character_encoding/">3.4 &nbsp; 文字の符号化 *</a></li>
+<li><a href="number_encoding/">3.3 &nbsp; 数値エンコーディング *</a></li>
+<li><a href="character_encoding/">3.4 &nbsp; 文字エンコーディング *</a></li>
 <li><a href="summary/">3.5 &nbsp; まとめ</a></li>
 </ul>
 
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+++ b/ja/chapter_data_structure/number_encoding/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
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+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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-  <a href="#331" class="md-nav__link">
+  <a href="#331-1-2" class="md-nav__link">
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-        3.3.1 &nbsp; 整数エンコーディング
+        3.3.1 &nbsp; 符号付き絶対値表現、1 の補数、2 の補数
       
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-        3.3.2 &nbsp; 浮動小数点数エンコーディング
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+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2647,7 +2647,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3185,7 +3185,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3241,7 +3241,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3269,7 +3269,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3462,7 +3462,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3490,7 +3490,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3631,7 +3631,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3659,7 +3659,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3687,7 +3687,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3715,7 +3715,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3908,7 +3908,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4153,7 +4153,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4296,10 +4296,10 @@
     <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
       
         <li class="md-nav__item">
-  <a href="#331" class="md-nav__link">
+  <a href="#331-1-2" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3.3.1 &nbsp; 整数エンコーディング
+        3.3.1 &nbsp; 符号付き絶対値表現、1 の補数、2 の補数
       
     </span>
   </a>
@@ -4310,7 +4310,7 @@
   <a href="#332" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3.3.2 &nbsp; 浮動小数点数エンコーディング
+        3.3.2 &nbsp; 浮動小数点数のエンコーディング
       
     </span>
   </a>
@@ -4357,21 +4357,21 @@
 <h1 id="33">3.3 &nbsp; 数値エンコーディング *<a class="headerlink" href="#33" title="Permanent link">&para;</a></h1>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>本書では、アスタリスク「*」が付いた章は任意読書です。時間が不足している場合や難しいと感じる場合は、最初はこれらをスキップして、必須の章を完了した後に戻ることができます。</p>
+<p>本書では、タイトルに * 記号が付いている章は選読です。時間が限られている場合や理解が難しいと感じる場合は、いったん読み飛ばし、必読章を終えてから個別に取り組んでください。</p>
 </div>
-<h2 id="331">3.3.1 &nbsp; 整数エンコーディング<a class="headerlink" href="#331" title="Permanent link">&para;</a></h2>
-<p>前の節の表で、すべての整数型は正の数よりも1つ多い負の数を表現できることを観察しました。例えば、<code>byte</code>の範囲は<span class="arithmatex">\([-128, 127]\)</span>です。この現象は直感に反するように見え、その根本的な理由には符号絶対値、1の補数、2の補数エンコーディングの知識が関与しています。</p>
-<p>まず重要なことは、**数値はコンピュータ内で2の補数形式で格納される**ということです。なぜそうなのかを分析する前に、これら3つのエンコーディング方法を定義しましょう：</p>
+<h2 id="331-1-2">3.3.1 &nbsp; 符号付き絶対値表現、1 の補数、2 の補数<a class="headerlink" href="#331-1-2" title="Permanent link">&para;</a></h2>
+<p>前節の表を見ると、すべての整数型で表せる負数の個数は正数より 1 つ多く、たとえば <code>byte</code> の値域は <span class="arithmatex">\([-128, 127]\)</span> です。この現象は直感に反するように見えますが、その背景には符号付き絶対値表現、1 の補数、2 の補数に関する知識があります。</p>
+<p>まず押さえておくべきなのは、**数値はコンピュータ内で「2 の補数」の形で保存される**ということです。その理由を説明する前に、まずはこの 3 つの定義を示します。</p>
 <ul>
-<li><strong>符号絶対値</strong>：数値の二進表現の最上位ビットを符号ビットとし、<span class="arithmatex">\(0\)</span>は正の数、<span class="arithmatex">\(1\)</span>は負の数を表します。残りのビットは数値の値を表します。</li>
-<li><strong>1の補数</strong>：正の数の1の補数は符号絶対値と同じです。負の数の場合、符号ビット以外のすべてのビットを反転して得られます。</li>
-<li><strong>2の補数</strong>：正の数の2の補数は符号絶対値と同じです。負の数の場合、その1の補数に<span class="arithmatex">\(1\)</span>を加えて得られます。</li>
+<li><strong>符号付き絶対値表現</strong>：数値の二進表現の最上位ビットを符号ビットとみなし、<span class="arithmatex">\(0\)</span> は正数、<span class="arithmatex">\(1\)</span> は負数を表し、残りのビットが数値の値を表します。</li>
+<li><strong>1 の補数</strong>：正数の 1 の補数は符号付き絶対値表現と同じで、負数の 1 の補数は符号ビットを除くすべてのビットを反転したものです。</li>
+<li><strong>2 の補数</strong>：正数の 2 の補数は符号付き絶対値表現と同じで、負数の 2 の補数は 1 の補数に <span class="arithmatex">\(1\)</span> を加えたものです。</li>
 </ul>
-<p>以下の図は、符号絶対値、1の補数、2の補数間の変換を示しています：</p>
-<p><img alt="符号絶対値、1の補数、2の補数間の変換" class="animation-figure" src="../number_encoding.assets/1s_2s_complement.png" /></p>
-<p align="center"> 図 3-4 &nbsp; 符号絶対値、1の補数、2の補数間の変換 </p>
+<p>下図は、符号付き絶対値表現、1 の補数、2 の補数の変換方法を示しています。</p>
+<p><img alt="符号付き絶対値表現、1 の補数、2 の補数の相互変換" class="animation-figure" src="../number_encoding.assets/1s_2s_complement.png" /></p>
+<p align="center"> 図 3-4 &nbsp; 符号付き絶対値表現、1 の補数、2 の補数の相互変換 </p>
 
-<p><u>符号絶対値</u>は最も直感的ですが、制限があります。一つには、<strong>符号絶対値の負の数は計算で直接使用できません</strong>。例えば、符号絶対値で<span class="arithmatex">\(1 + (-2)\)</span>を計算すると<span class="arithmatex">\(-3\)</span>になり、これは正しくありません。</p>
+<p><u>符号付き絶対値表現（sign-magnitude）</u>は最も直感的ですが、いくつかの制約があります。まず、<strong>負数の符号付き絶対値表現はそのまま演算に使えません</strong>。たとえば符号付き絶対値表現で <span class="arithmatex">\(1 + (-2)\)</span> を計算すると、結果は <span class="arithmatex">\(-3\)</span> になってしまい、これは明らかに誤りです。</p>
 <div class="arithmatex">\[
 \begin{aligned}
 &amp; 1 + (-2) \newline
@@ -4380,96 +4380,96 @@
 &amp; \rightarrow -3
 \end{aligned}
 \]</div>
-<p>この問題に対処するため、コンピュータは<u>1の補数</u>を導入しました。1の補数に変換して<span class="arithmatex">\(1 + (-2)\)</span>を計算し、結果を符号絶対値に戻すと、正しい結果<span class="arithmatex">\(-1\)</span>が得られます。</p>
+<p>この問題を解決するために、コンピュータには<u>1 の補数（1's complement）</u>が導入されました。まず符号付き絶対値表現を 1 の補数に変換し、1 の補数で <span class="arithmatex">\(1 + (-2)\)</span> を計算してから、結果を 1 の補数から符号付き絶対値表現へ戻すと、正しい結果 <span class="arithmatex">\(-1\)</span> が得られます。</p>
 <div class="arithmatex">\[
 \begin{aligned}
 &amp; 1 + (-2) \newline
-&amp; \rightarrow 0000 \; 0001 \; \text{(符号絶対値)} + 1000 \; 0010 \; \text{(符号絶対値)} \newline
-&amp; = 0000 \; 0001 \; \text{(1の補数)} + 1111 \; 1101 \; \text{(1の補数)} \newline
-&amp; = 1111 \; 1110 \; \text{(1の補数)} \newline
-&amp; = 1000 \; 0001 \; \text{(符号絶対値)} \newline
+&amp; \rightarrow 0000 \; 0001 \; \text{(符号付き絶対値表現)} + 1000 \; 0010 \; \text{(符号付き絶対値表現)} \newline
+&amp; = 0000 \; 0001 \; \text{(1 の補数)} + 1111  \; 1101 \; \text{(1 の補数)} \newline
+&amp; = 1111 \; 1110 \; \text{(1 の補数)} \newline
+&amp; = 1000 \; 0001 \; \text{(符号付き絶対値表現)} \newline
 &amp; \rightarrow -1
 \end{aligned}
 \]</div>
-<p>また、<strong>符号絶対値では0に2つの表現があります</strong>：<span class="arithmatex">\(+0\)</span>と<span class="arithmatex">\(-0\)</span>です。これは0に対して2つの異なる二進エンコーディングがあることを意味し、曖昧さを引き起こす可能性があります。例えば、条件チェックで正と負の0を区別しないと、正しくない結果になる可能性があります。この曖昧さに対処するには追加のチェックが必要で、計算効率が低下する可能性があります。</p>
+<p>一方、<strong>数値 0 の符号付き絶対値表現には <span class="arithmatex">\(+0\)</span> と <span class="arithmatex">\(-0\)</span> の 2 つの表し方があります</strong>。つまり、数値 0 に対して異なる 2 つの二進コードが対応しており、これは曖昧さの原因になります。たとえば条件判定で正のゼロと負のゼロを区別しないと、誤った判定結果になる可能性があります。また、この曖昧さを解消しようとすると追加の判定処理が必要になり、計算効率が下がるおそれがあります。</p>
 <div class="arithmatex">\[
 \begin{aligned}
 +0 &amp; \rightarrow 0000 \; 0000 \newline
 -0 &amp; \rightarrow 1000 \; 0000
 \end{aligned}
 \]</div>
-<p>符号絶対値と同様に、1の補数も正と負の0の曖昧さに悩まされます。そのため、コンピュータはさらに<u>2の補数</u>を導入しました。符号絶対値、1の補数、2の補数における負の0の変換過程を観察してみましょう：</p>
+<p>符号付き絶対値表現と同様に、1 の補数にも正負のゼロの曖昧さがあります。そこでコンピュータはさらに<u>2 の補数（2's complement）</u>を導入しました。まずは負のゼロについて、符号付き絶対値表現、1 の補数、2 の補数の変換を見てみましょう。</p>
 <div class="arithmatex">\[
 \begin{aligned}
--0 \rightarrow \; &amp; 1000 \; 0000 \; \text{(符号絶対値)} \newline
-= \; &amp; 1111 \; 1111 \; \text{(1の補数)} \newline
-= 1 \; &amp; 0000 \; 0000 \; \text{(2の補数)} \newline
+-0 \rightarrow \; &amp; 1000 \; 0000 \; \text{(符号付き絶対値表現)} \newline
+= \; &amp; 1111 \; 1111 \; \text{(1 の補数)} \newline
+= 1 \; &amp; 0000 \; 0000 \; \text{(2 の補数)} \newline
 \end{aligned}
 \]</div>
-<p>負の0の1の補数に<span class="arithmatex">\(1\)</span>を加えると桁上がりが発生しますが、<code>byte</code>の長さは8ビットのみのため、9番目のビットへの桁上がり<span class="arithmatex">\(1\)</span>は破棄されます。したがって、**負の0の2の補数は<span class="arithmatex">\(0000 \; 0000\)</span>**で、正の0と同じになり、曖昧さが解決されます。</p>
-<p>最後の謎は、<code>byte</code>の<span class="arithmatex">\([-128, 127]\)</span>の範囲で、追加の負の数<span class="arithmatex">\(-128\)</span>があることです。<span class="arithmatex">\([-127, +127]\)</span>の区間では、すべての整数に対応する符号絶対値、1の補数、2の補数があり、相互変換が可能であることを観察します。</p>
-<p>しかし、<strong>2の補数<span class="arithmatex">\(1000 \; 0000\)</span>は対応する符号絶対値を持たない例外です</strong>。変換方法によると、その符号絶対値は<span class="arithmatex">\(0000 \; 0000\)</span>で、0を示します。これは矛盾を示しています。なぜなら、その2の補数は自分自身を表すべきだからです。コンピュータは、この特別な2の補数<span class="arithmatex">\(1000 \; 0000\)</span>を<span class="arithmatex">\(-128\)</span>を表すものとして指定しています。実際、2の補数での<span class="arithmatex">\((-1) + (-127)\)</span>の計算結果は<span class="arithmatex">\(-128\)</span>になります。</p>
+<p>負のゼロの 1 の補数に <span class="arithmatex">\(1\)</span> を加えると桁上がりが発生しますが、<code>byte</code> 型の長さは 8 ビットしかないため、第 9 ビットへあふれた <span class="arithmatex">\(1\)</span> は捨てられます。つまり、<strong>負のゼロの 2 の補数は <span class="arithmatex">\(0000 \; 0000\)</span> であり、正のゼロの 2 の補数と同じです</strong>。そのため、2 の補数表現ではゼロは 1 つしか存在せず、正負のゼロの曖昧さは解消されます。</p>
+<p>最後にもう 1 つ疑問が残ります。<code>byte</code> 型の値域は <span class="arithmatex">\([-128, 127]\)</span> ですが、余分にある負数 <span class="arithmatex">\(-128\)</span> はどのように得られるのでしょうか。区間 <span class="arithmatex">\([-127, +127]\)</span> にあるすべての整数には、それぞれ対応する符号付き絶対値表現、1 の補数、2 の補数があり、符号付き絶対値表現と 2 の補数の間は相互に変換できます。</p>
+<p>しかし、<strong>2 の補数 <span class="arithmatex">\(1000 \; 0000\)</span> だけは例外で、対応する符号付き絶対値表現を持ちません</strong>。変換規則に従うと、この 2 の補数に対応する符号付き絶対値表現は <span class="arithmatex">\(0000 \; 0000\)</span> になります。これは明らかに矛盾しています。なぜなら、この符号付き絶対値表現は数値 <span class="arithmatex">\(0\)</span> を表し、その 2 の補数は自分自身であるはずだからです。コンピュータでは、この特別な 2 の補数 <span class="arithmatex">\(1000 \; 0000\)</span> を <span class="arithmatex">\(-128\)</span> と定めています。実際、2 の補数での <span class="arithmatex">\((-1) + (-127)\)</span> の計算結果はちょうど <span class="arithmatex">\(-128\)</span> になります。</p>
 <div class="arithmatex">\[
 \begin{aligned}
 &amp; (-127) + (-1) \newline
-&amp; \rightarrow 1111 \; 1111 \; \text{(符号絶対値)} + 1000 \; 0001 \; \text{(符号絶対値)} \newline
-&amp; = 1000 \; 0000 \; \text{(1の補数)} + 1111 \; 1110 \; \text{(1の補数)} \newline
-&amp; = 1000 \; 0001 \; \text{(2の補数)} + 1111 \; 1111 \; \text{(2の補数)} \newline
-&amp; = 1000 \; 0000 \; \text{(2の補数)} \newline
+&amp; \rightarrow 1111 \; 1111 \; \text{(符号付き絶対値表現)} + 1000 \; 0001 \; \text{(符号付き絶対値表現)} \newline
+&amp; = 1000 \; 0000 \; \text{(1 の補数)} + 1111  \; 1110 \; \text{(1 の補数)} \newline
+&amp; = 1000 \; 0001 \; \text{(2 の補数)} + 1111  \; 1111 \; \text{(2 の補数)} \newline
+&amp; = 1000 \; 0000 \; \text{(2 の補数)} \newline
 &amp; \rightarrow -128
 \end{aligned}
 \]</div>
-<p>お気づきかもしれませんが、これらの計算はすべて加算であり、重要な事実を示唆しています：<strong>コンピュータの内部ハードウェア回路は主に加算演算を中心に設計されています</strong>。これは、加算が乗算、除算、減算などの他の演算と比較してハードウェアで実装しやすく、並列化が容易で高速計算が可能だからです。</p>
-<p>これはコンピュータが加算のみを実行できることを意味するものではありません。<strong>加算と基本的な論理演算を組み合わせることで、コンピュータは様々な他の数学演算を実行できます</strong>。例えば、減算<span class="arithmatex">\(a - b\)</span>は<span class="arithmatex">\(a + (-b)\)</span>に変換でき、乗算と除算は複数の加算または減算に変換できます。</p>
-<p>コンピュータで2の補数を使用する理由をまとめることができます：2の補数表現により、コンピュータは同じ回路と演算を使用して正と負の数の加算を処理でき、減算用の特別なハードウェア回路の必要性を排除し、正と負の0の曖昧さを回避できます。これによりハードウェア設計が大幅に簡素化され、計算効率が向上します。</p>
-<p>2の補数の設計は非常に巧妙で、スペースの制約により、ここで停止します。興味のある読者はさらに探求することを奨励します。</p>
-<h2 id="332">3.3.2 &nbsp; 浮動小数点数エンコーディング<a class="headerlink" href="#332" title="Permanent link">&para;</a></h2>
-<p>興味深いことに気づいたかもしれません：同じ4バイトの長さにもかかわらず、なぜ<code>float</code>は<code>int</code>と比較してはるかに大きい値の範囲を持つのでしょうか？これは直感に反するように見えます。<code>float</code>は分数を表現する必要があるため、範囲が縮小すると予想されるからです。</p>
-<p>実際、<strong>これは浮動小数点数（<code>float</code>）で使用される異なる表現方法によるものです</strong>。32ビットの二進数を次のように考えてみましょう：</p>
+<p>すでにお気づきかもしれませんが、上の計算はすべて加算です。これは重要な事実を示しています。**コンピュータ内部のハードウェア回路は、主として加算を基準に設計されている**のです。なぜなら、加算はほかの演算（乗算、除算、減算など）に比べてハードウェアで実装しやすく、並列化もしやすく、演算速度も速いからです。</p>
+<p>ただし、これはコンピュータが加算しかできないという意味ではありません。<strong>加算といくつかの基本的な論理演算を組み合わせることで、コンピュータはさまざまな数学演算を実現できます</strong>。たとえば減算 <span class="arithmatex">\(a - b\)</span> は加算 <span class="arithmatex">\(a + (-b)\)</span> に変換できますし、乗算や除算も繰り返しの加算または減算に変換できます。</p>
+<p>これで、コンピュータが 2 の補数を使う理由をまとめられます。2 の補数表現に基づけば、コンピュータは同じ回路と操作で正数と負数の加算を扱うことができ、減算専用の特別なハードウェア回路を設計する必要がなく、正負のゼロの曖昧さも特別に処理しなくて済みます。これにより、ハードウェア設計は大幅に簡略化され、演算効率も向上します。</p>
+<p>2 の補数の設計は非常に巧妙ですが、紙幅の都合上ここまでにします。興味のある読者は、さらに深く調べてみてください。</p>
+<h2 id="332">3.3.2 &nbsp; 浮動小数点数のエンコーディング<a class="headerlink" href="#332" title="Permanent link">&para;</a></h2>
+<p>注意深い人なら気づくかもしれません。<code>int</code> と <code>float</code> はどちらも長さが 4 バイトで同じなのに、なぜ <code>float</code> の値域は <code>int</code> よりはるかに広いのでしょうか。これはかなり直感に反します。というのも、<code>float</code> は小数を表す必要があるので、本来なら値域は狭くなるはずだからです。</p>
+<p>実際には、<strong>これは浮動小数点数 <code>float</code> が異なる表現方法を採用しているためです</strong>。32 ビット長の二進数を次のように表します。</p>
 <div class="arithmatex">\[
 b_{31} b_{30} b_{29} \ldots b_2 b_1 b_0
 \]</div>
-<p>IEEE 754標準によると、32ビットの<code>float</code>は次の3つの部分で構成されます：</p>
+<p>IEEE 754 標準によれば、32-bit 長の <code>float</code> は次の 3 つの部分から構成されます。</p>
 <ul>
-<li>符号ビット<span class="arithmatex">\(\mathrm{S}\)</span>：1ビットを占有し、<span class="arithmatex">\(b_{31}\)</span>に対応します。</li>
-<li>指数ビット<span class="arithmatex">\(\mathrm{E}\)</span>：8ビットを占有し、<span class="arithmatex">\(b_{30} b_{29} \ldots b_{23}\)</span>に対応します。</li>
-<li>仮数ビット<span class="arithmatex">\(\mathrm{N}\)</span>：23ビットを占有し、<span class="arithmatex">\(b_{22} b_{21} \ldots b_0\)</span>に対応します。</li>
+<li>符号部 <span class="arithmatex">\(\mathrm{S}\)</span> ：1 ビットを占め、<span class="arithmatex">\(b_{31}\)</span> に対応します。</li>
+<li>指数部 <span class="arithmatex">\(\mathrm{E}\)</span> ：8 ビットを占め、<span class="arithmatex">\(b_{30} b_{29} \ldots b_{23}\)</span> に対応します。</li>
+<li>仮数部 <span class="arithmatex">\(\mathrm{N}\)</span> ：23 ビットを占め、<span class="arithmatex">\(b_{22} b_{21} \ldots b_0\)</span> に対応します。</li>
 </ul>
-<p>二進<code>float</code>数の値は次のように計算されます：</p>
+<p>二進数 <code>float</code> に対応する値は次式で計算されます。</p>
 <div class="arithmatex">\[
-\text{val} = (-1)^{b_{31}} \times 2^{\left(b_{30} b_{29} \ldots b_{23}\right)_2 - 127} \times \left(1 . b_{22} b_{21} \ldots b_0\right)_2
+\text {val} = (-1)^{b_{31}} \times 2^{\left(b_{30} b_{29} \ldots b_{23}\right)_2-127} \times\left(1 . b_{22} b_{21} \ldots b_0\right)_2
 \]</div>
-<p>十進公式に変換すると、次のようになります：</p>
+<p>十進数に直すと、計算式は次のようになります。</p>
 <div class="arithmatex">\[
-\text{val} = (-1)^{\mathrm{S}} \times 2^{\mathrm{E} - 127} \times (1 + \mathrm{N})
+\text {val}=(-1)^{\mathrm{S}} \times 2^{\mathrm{E} -127} \times (1 + \mathrm{N})
 \]</div>
-<p>各成分の範囲は：</p>
+<p>各項の取り得る範囲は次のとおりです。</p>
 <div class="arithmatex">\[
 \begin{aligned}
 \mathrm{S} \in &amp; \{ 0, 1\}, \quad \mathrm{E} \in \{ 1, 2, \dots, 254 \} \newline
-(1 + \mathrm{N}) = &amp; (1 + \sum_{i=1}^{23} b_{23-i} \times 2^{-i}) \subset [1, 2 - 2^{-23}]
+(1 + \mathrm{N}) = &amp; (1 + \sum_{i=1}^{23} b_{23-i} 2^{-i}) \subset [1, 2 - 2^{-23}]
 \end{aligned}
 \]</div>
-<p><img alt="IEEE 754標準での浮動小数点数の計算例" class="animation-figure" src="../number_encoding.assets/ieee_754_float.png" /></p>
-<p align="center"> 図 3-5 &nbsp; IEEE 754標準での浮動小数点数の計算例 </p>
+<p><img alt="IEEE 754 標準における float の計算例" class="animation-figure" src="../number_encoding.assets/ieee_754_float.png" /></p>
+<p align="center"> 図 3-5 &nbsp; IEEE 754 標準における float の計算例 </p>
 
-<p>上の図を観察すると、例のデータ<span class="arithmatex">\(\mathrm{S} = 0\)</span>、<span class="arithmatex">\(\mathrm{E} = 124\)</span>、<span class="arithmatex">\(\mathrm{N} = 2^{-2} + 2^{-3} = 0.375\)</span>が与えられた場合：</p>
+<p>上図を見ると、例として <span class="arithmatex">\(\mathrm{S} = 0\)</span> 、 <span class="arithmatex">\(\mathrm{E} = 124\)</span> 、<span class="arithmatex">\(\mathrm{N} = 2^{-2} + 2^{-3} = 0.375\)</span> が与えられた場合、次のようになります。</p>
 <div class="arithmatex">\[
-\text{val} = (-1)^0 \times 2^{124 - 127} \times (1 + 0.375) = 0.171875
+\text { val } = (-1)^0 \times 2^{124 - 127} \times (1 + 0.375) = 0.171875
 \]</div>
-<p>これで最初の質問に答えることができます：<strong><code>float</code>の表現には指数ビットが含まれているため、<code>int</code>よりもはるかに大きい範囲を持ちます</strong>。上記の計算に基づくと、<code>float</code>で表現可能な最大正の数は約<span class="arithmatex">\(2^{254 - 127} \times (2 - 2^{-23}) \approx 3.4 \times 10^{38}\)</span>で、最小負の数は符号ビットを切り替えることで得られます。</p>
-<p><strong>しかし、<code>float</code>の拡張された範囲のトレードオフは精度の犠牲です</strong>。整数型<code>int</code>は32ビットすべてを数値表現に使用し、値は均等に分布していますが、指数ビットのため、<code>float</code>の値が大きいほど、隣接する数値間の差が大きくなります。</p>
-<p>以下の表に示すように、指数ビット<span class="arithmatex">\(\mathrm{E} = 0\)</span>と<span class="arithmatex">\(\mathrm{E} = 255\)</span>は特別な意味を持ち、<strong>0、無限大、<span class="arithmatex">\(\mathrm{NaN}\)</span>などを表現するために使用されます</strong>。</p>
-<p align="center"> 表 3-2 &nbsp; 指数ビットの意味 </p>
+<p>これで最初の疑問に答えられます。**<code>float</code> の表現方法には指数部が含まれているため、その値域は <code>int</code> よりはるかに広い**のです。上の計算より、<code>float</code> が表せる最大の正数は <span class="arithmatex">\(2^{254 - 127} \times (2 - 2^{-23}) \approx 3.4 \times 10^{38}\)</span> であり、符号ビットを切り替えれば最小の負数が得られます。</p>
+<p><strong>浮動小数点数 <code>float</code> は値域を広げる一方で、その代償として精度を犠牲にしています</strong>。整数型 <code>int</code> は 32 ビットすべてを数値の表現に使うため、数値は一様に分布します。しかし指数部があるため、浮動小数点数 <code>float</code> は値が大きくなるほど、隣り合う 2 つの数の差も大きくなる傾向があります。</p>
+<p>次の表のとおり、指数部 <span class="arithmatex">\(\mathrm{E} = 0\)</span> と <span class="arithmatex">\(\mathrm{E} = 255\)</span> には特別な意味があり、<strong>ゼロ、無限大、<span class="arithmatex">\(\mathrm{NaN}\)</span> などを表すために使われます</strong>。</p>
+<p align="center"> 表 3-2 &nbsp; 指数部の意味 </p>
 
 <div class="center-table">
 <table>
 <thead>
 <tr>
-<th>指数ビットE</th>
-<th>仮数ビット<span class="arithmatex">\(\mathrm{N} = 0\)</span></th>
-<th>仮数ビット<span class="arithmatex">\(\mathrm{N} \ne 0\)</span></th>
-<th>計算公式</th>
+<th>指数部 E</th>
+<th>仮数部 <span class="arithmatex">\(\mathrm{N} = 0\)</span></th>
+<th>仮数部 <span class="arithmatex">\(\mathrm{N} \ne 0\)</span></th>
+<th>計算式</th>
 </tr>
 </thead>
 <tbody>
@@ -4494,8 +4494,8 @@ b_{31} b_{30} b_{29} \ldots b_2 b_1 b_0
 </tbody>
 </table>
 </div>
-<p>非正規化数は浮動小数点数の精度を大幅に向上させることは注目に値します。最小の正の正規化数は<span class="arithmatex">\(2^{-126}\)</span>で、最小の正の非正規化数は<span class="arithmatex">\(2^{-126} \times 2^{-23}\)</span>です。</p>
-<p>倍精度<code>double</code>も<code>float</code>と同様の表現方法を使用しますが、簡潔さのためここでは詳述しません。</p>
+<p>なお、非正規化数によって浮動小数点数の精度は大きく向上します。最小の正の正規化数は <span class="arithmatex">\(2^{-126}\)</span> であり、最小の正の非正規化数は <span class="arithmatex">\(2^{-126} \times 2^{-23}\)</span> です。</p>
+<p>倍精度 <code>double</code> も <code>float</code> と同様の表現方法を採用しているため、ここでは詳述しません。</p>
 
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     href="../character_encoding/"
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-    aria-label="次: 3.4 &amp;nbsp; 文字の符号化 *"
+    aria-label="次: 3.4 &amp;nbsp; 文字エンコーディング *"
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+        3.4 &nbsp; 文字エンコーディング *
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@@ -6,7 +6,7 @@
       <meta charset="utf-8">
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-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
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             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
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-    1.1 &nbsp; アルゴリズムはどこにでもある
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-    1.2 &nbsp; アルゴリズムとは何か
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 <!-- Page content -->
 <h1 id="35">3.5 &nbsp; まとめ<a class="headerlink" href="#35" title="Permanent link">&para;</a></h1>
-<h3 id="1">1. &nbsp; 重要なポイント<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<h3 id="1">1. &nbsp; 重要ポイントの振り返り<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
-<li>データ構造は論理構造と物理構造の2つの観点から分類できます。論理構造はデータ間の論理的関係を記述し、物理構造はデータがメモリにどのように格納されるかを記述します。</li>
-<li>よく使用される論理構造には、線形構造、木、ネットワークがあります。通常、論理構造に基づいてデータ構造を線形（配列、連結リスト、スタック、キュー）と非線形（木、グラフ、ヒープ）に分けます。ハッシュ表の実装は線形と非線形の両方のデータ構造を含む場合があります。</li>
-<li>プログラムが実行中の際、データはメモリに格納されます。各メモリ空間には対応するアドレスがあり、プログラムはこれらのアドレスを通じてデータにアクセスします。</li>
-<li>物理構造は連続空間格納（配列）と離散空間格納（連結リスト）に分けることができます。すべてのデータ構造は配列、連結リスト、またはその両方の組み合わせを使用して実装されます。</li>
-<li>コンピュータの基本データ型には、整数（<code>byte</code>、<code>short</code>、<code>int</code>、<code>long</code>）、浮動小数点数（<code>float</code>、<code>double</code>）、文字（<code>char</code>）、ブール値（<code>bool</code>）が含まれます。データ型の値の範囲は、そのサイズと表現に依存します。</li>
-<li>符号絶対値、1の補数、2の補数は、コンピュータで整数をエンコードする3つの方法であり、相互に変換することができます。符号絶対値の最上位ビットは符号ビットで、残りのビットは数値の値を表します。</li>
-<li>整数はコンピュータで2の補数によってエンコードされます。この表現の利点には、(i)コンピュータが正と負の整数の加算を統一できる、(ii)減算用の特別なハードウェア回路を設計する必要がない、(iii)正と負の0の曖昧さがない、があります。</li>
-<li>浮動小数点数のエンコーディングは、1つの符号ビット、8つの指数ビット、23の仮数ビットで構成されます。指数ビットのため、浮動小数点数の範囲は整数よりもはるかに大きくなりますが、精度を犠牲にします。</li>
-<li>ASCIIは最初期の英語文字セットで、1バイトの長さで計127文字です。GBKは人気のある中国語文字セットで、2万文字以上の中国語文字を含みます。Unicodeは世界の様々な言語の文字を含む完全な文字セット標準を提供することを目的とし、文字エンコーディング方法の不一致による文字化け問題を解決します。</li>
-<li>UTF-8は最も人気があり一般的なUnicodeエンコーディング方法です。これは可変長エンコーディング方法で、優れた拡張性と空間効率を持ちます。UTF-16とUTF-32は固定長エンコーディング方法です。中国語文字をエンコードする際、UTF-16はUTF-8よりも少ない空間を使用します。JavaやC#などのプログラミング言語はデフォルトでUTF-16エンコーディングを使用します。</li>
+<li>データ構造は、論理構造と物理構造という 2 つの観点から分類できます。論理構造はデータ要素間の論理的関係を記述し、物理構造はデータのコンピュータメモリ上での格納方法を記述します。</li>
+<li>代表的な論理構造には、線形、木構造、網状構造などがあります。通常、論理構造に基づいてデータ構造を線形（配列、連結リスト、スタック、キュー）と非線形（木、グラフ、ヒープ）の 2 種類に分類します。ハッシュテーブルの実装には、線形データ構造と非線形データ構造が同時に含まれる場合があります。</li>
+<li>プログラムの実行時、データはコンピュータメモリに格納されます。各メモリ空間には対応するメモリアドレスがあり、プログラムはそれらのメモリアドレスを通じてデータにアクセスします。</li>
+<li>物理構造は主に連続領域への格納（配列）と分散領域への格納（連結リスト）に分けられます。すべてのデータ構造は、配列、連結リスト、またはその両方の組み合わせによって実装されます。</li>
+<li>コンピュータにおける基本データ型には、整数 <code>byte</code>、<code>short</code>、<code>int</code>、<code>long</code>、浮動小数点数 <code>float</code>、<code>double</code>、文字 <code>char</code>、真偽値 <code>bool</code> があります。これらの値域は、使用する記憶領域の大きさと表現方式によって決まります。</li>
+<li>符号付き絶対値表現、1 の補数、2 の補数は、コンピュータで数値を符号化する 3 つの方法であり、相互に変換できます。整数の符号付き絶対値表現では最上位ビットが符号ビットで、残りのビットが数値の値です。</li>
+<li>整数はコンピュータ内では 2 の補数の形式で格納されます。2 の補数表現では、コンピュータは正数と負数の加算を同じように扱うことができ、減算のために特別なハードウェア回路を別途設計する必要がなく、さらに正負のゼロが重複する問題もありません。</li>
+<li>浮動小数点数の符号化は、1 ビットの符号部、8 ビットの指数部、23 ビットの仮数部で構成されます。指数部があるため、浮動小数点数の値域は整数よりはるかに広くなりますが、その代償として精度が犠牲になります。</li>
+<li>ASCII コードは最も早く登場した英字文字集合で、長さは 1 バイト、収録文字数は 127 です。GBK 文字集合はよく使われる中国語文字集合で、2 万字以上の漢字を収録しています。Unicode は完全な文字集合標準を提供することを目指しており、世界中のさまざまな言語の文字を収録することで、文字コード方式の不一致によって生じる文字化けの問題を解決します。</li>
+<li>UTF-8 は最も広く使われている Unicode の符号化方式で、汎用性が非常に高いです。可変長の符号化方式であり、拡張性に優れ、記憶領域の利用効率を効果的に高めます。UTF-16 と UTF-32 は固定長の符号化方式です。中国語を符号化する場合、UTF-16 は UTF-8 よりも使用領域が小さくなります。Java や C# などのプログラミング言語は、デフォルトで UTF-16 を使用します。</li>
 </ul>
 <h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
-<p><strong>Q</strong>: なぜハッシュ表は線形と非線形の両方のデータ構造を含むのですか？</p>
-<p>ハッシュ表の基礎構造は配列です。ハッシュ衝突を解決するために、「チェイン法」を使用する場合があります（後の節「ハッシュ衝突」で説明）：配列の各バケットは連結リストを指し、その長さが特定の閾値より大きくなると木（通常は赤黒木）に変換される可能性があります。
-格納の観点から、ハッシュ表の基礎構造は配列で、各バケットには値、連結リスト、または木が含まれる場合があります。したがって、ハッシュ表は線形データ構造（配列、連結リスト）と非線形データ構造（木）の両方を含む場合があります。</p>
-<p><strong>Q</strong>: <code>char</code>型の長さは1バイトですか？</p>
-<p><code>char</code>型の長さは、プログラミング言語のエンコーディング方法によって決まります。例えば、Java、JavaScript、TypeScript、C#はすべてUTF-16エンコーディング（Unicodeコードポイントを保存するため）を使用するため、<code>char</code>型の長さは2バイトです。</p>
-<p><strong>Q</strong>: 配列ベースのデータ構造を「静的データ構造」と呼ぶことに曖昧さはありませんか？スタックもプッシュやポップなどの「動的」操作を実行できます。</p>
-<p>スタックは動的なデータ操作を実装できますが、データ構造は依然として「静的」です（長さが固定）。配列ベースのデータ構造は動的に要素を追加または削除できますが、その容量は固定されています。スタックサイズが事前に割り当てられたサイズを超える場合、古い配列は新しく作成されたより大きな配列にコピーされます。</p>
-<p><strong>Q</strong>: スタック（キュー）を構築する際、そのサイズが指定されていないのに、なぜ「静的データ構造」なのですか？</p>
-<p>高級プログラミング言語では、スタック（キュー）の初期容量を手動で指定する必要はありません。このタスクはクラス内で自動的に完了されます。例えば、Javaの<code>ArrayList</code>の初期容量は通常10です。さらに、拡張操作も自動的に完了されます。詳細については、後続の「リスト」の章を参照してください。</p>
-<p><strong>Q</strong>: 符号絶対値を2の補数に変換する方法は「最初に否定してから1を加える」ですので、2の補数を符号絶対値に変換することはその逆操作「最初に1を減算してから否定する」であるべきです。
-しかし、2の補数も「最初に否定してから1を加える」を通じて符号絶対値に変換できます。なぜですか？</p>
-<p><strong>A</strong>: これは、符号絶対値と2の補数間の相互変換が「補数」の計算と等価だからです。まず補数を定義します：<span class="arithmatex">\(a + b = c\)</span>と仮定すると、<span class="arithmatex">\(a\)</span>は<span class="arithmatex">\(b\)</span>の<span class="arithmatex">\(c\)</span>に対する補数と言い、逆に<span class="arithmatex">\(b\)</span>は<span class="arithmatex">\(a\)</span>の<span class="arithmatex">\(c\)</span>に対する補数と言います。</p>
-<p>長さ<span class="arithmatex">\(n = 4\)</span>の二進数<span class="arithmatex">\(0010\)</span>が与えられた場合、この数が符号絶対値（符号ビットを無視）の場合、その2の補数は「最初に否定してから1を加える」ことで得られます：</p>
+<p><strong>Q</strong>：なぜハッシュテーブルには線形データ構造と非線形データ構造が同時に含まれるのですか？</p>
+<p>ハッシュテーブルの基盤は配列であり、ハッシュ衝突を解決するために「チェイン法」（後続の「ハッシュ衝突」の章で説明します）を使うことがあります。配列内の各バケットは 1 つの連結リストを指し、その連結リストの長さがある閾値を超えると、木（通常は赤黒木）に変換されることもあります。</p>
+<p>格納の観点から見ると、ハッシュテーブルの基盤は配列であり、各バケットスロットには値が入ることもあれば、連結リストや木が入ることもあります。したがって、ハッシュテーブルには線形データ構造（配列、連結リスト）と非線形データ構造（木）が同時に含まれる場合があります。</p>
+<p><strong>Q</strong>：<code>char</code> 型の長さは 1 バイトですか？</p>
+<p><code>char</code> 型の長さは、プログラミング言語が採用する符号化方式によって決まります。たとえば、Java、JavaScript、TypeScript、C# はいずれも UTF-16 符号化（Unicode コードポイントを保持）を採用しているため、<code>char</code> 型の長さは 2 バイトです。</p>
+<p><strong>Q</strong>：配列ベースで実装されたデータ構造を「静的データ構造」と呼ぶのは曖昧ではありませんか？ スタックも push や pop などの操作ができ、これらの操作はどれも「動的」です。</p>
+<p>スタックは確かに動的なデータ操作を実現できますが、データ構造自体は依然として「静的」（長さが不変）です。配列ベースのデータ構造でも要素を動的に追加または削除できますが、その容量は固定です。データ量が事前に確保した大きさを超えた場合は、より大きな新しい配列を作成し、古い配列の内容を新しい配列にコピーする必要があります。</p>
+<p><strong>Q</strong>：スタック（キュー）を構築するときにサイズを指定していないのに、なぜそれらは「静的データ構造」なのですか？</p>
+<p>高水準プログラミング言語では、スタック（キュー）の初期容量を人手で指定する必要はなく、この作業はクラス内部で自動的に行われます。たとえば、Java の <code>ArrayList</code> の初期容量は通常 10 です。また、容量拡張も自動的に実装されています。詳しくは後続の「リスト」の章を参照してください。</p>
+<p><strong>Q</strong>：符号付き絶対値表現から 2 の補数への変換方法は「先にビット反転してから 1 を加える」ですが、2 の補数から符号付き絶対値表現への変換は逆演算である「先に 1 を引いてからビット反転する」べきなのに、同じく「先にビット反転してから 1 を加える」でも求められます。これはなぜですか？</p>
+<p>これは、符号付き絶対値表現と 2 の補数の相互変換が、実際には「補数」を計算する過程だからです。まず補数の定義を示します。<span class="arithmatex">\(a + b = c\)</span> とすると、<span class="arithmatex">\(a\)</span> を <span class="arithmatex">\(b\)</span> から <span class="arithmatex">\(c\)</span> への補数と呼び、逆に <span class="arithmatex">\(b\)</span> も <span class="arithmatex">\(a\)</span> から <span class="arithmatex">\(c\)</span> への補数と呼びます。</p>
+<p>長さ <span class="arithmatex">\(n = 4\)</span> ビットの 2 進数 <span class="arithmatex">\(0010\)</span> が与えられたとします。この数を符号付き絶対値表現（符号ビットは考慮しない）とみなすと、その 2 の補数は「先にビット反転してから 1 を加える」ことで得られます。</p>
 <div class="arithmatex">\[
 0010 \rightarrow 1101 \rightarrow 1110
 \]</div>
-<p>符号絶対値と2の補数の和が<span class="arithmatex">\(0010 + 1110 = 10000\)</span>であることを観察します。つまり、2の補数<span class="arithmatex">\(1110\)</span>は符号絶対値<span class="arithmatex">\(0010\)</span>の<span class="arithmatex">\(10000\)</span>に対する「補数」です。<strong>これは、上記の「最初に否定してから1を加える」が<span class="arithmatex">\(10000\)</span>に対する補数の計算と等価であることを意味します</strong>。</p>
-<p>では、<span class="arithmatex">\(1110\)</span>の<span class="arithmatex">\(10000\)</span>に対する「補数」は何でしょうか？「最初に否定してから1を加える」ことで計算できます：</p>
+<p>ここで、符号付き絶対値表現と 2 の補数の和は <span class="arithmatex">\(0010 + 1110 = 10000\)</span> となります。つまり、2 の補数 <span class="arithmatex">\(1110\)</span> は符号付き絶対値表現 <span class="arithmatex">\(0010\)</span> から <span class="arithmatex">\(10000\)</span> への「補数」です。<strong>これは、上記の「先にビット反転してから 1 を加える」が、実際には <span class="arithmatex">\(10000\)</span> への補数を計算する過程であることを意味します。</strong></p>
+<p>では、2 の補数 <span class="arithmatex">\(1110\)</span> から <span class="arithmatex">\(10000\)</span> への「補数」はいくつでしょうか。これもやはり「先にビット反転してから 1 を加える」ことで求められます。</p>
 <div class="arithmatex">\[
 1110 \rightarrow 0001 \rightarrow 0010
 \]</div>
-<p>言い換えると、符号絶対値と2の補数は互いに<span class="arithmatex">\(10000\)</span>に対する「補数」であるため、「符号絶対値から2の補数」と「2の補数から符号絶対値」は同じ操作（最初に否定してから1を加える）で実装できます。</p>
-<p>もちろん、「最初に否定してから1を加える」の逆操作を使用して2の補数<span class="arithmatex">\(1110\)</span>の符号絶対値を求めることもできます。つまり、「最初に1を減算してから否定する」：</p>
+<p>言い換えると、符号付き絶対値表現と 2 の補数は互いに相手から <span class="arithmatex">\(10000\)</span> への「補数」なので、「符号付き絶対値表現から 2 の補数への変換」と「2 の補数から符号付き絶対値表現への変換」は同じ操作（先にビット反転してから 1 を加える）で実現できます。</p>
+<p>もちろん、逆演算を用いて 2 の補数 <span class="arithmatex">\(1110\)</span> の符号付き絶対値表現を求めることもでき、その場合は「先に 1 を引いてからビット反転する」ことになります。</p>
 <div class="arithmatex">\[
 1110 \rightarrow 1101 \rightarrow 0010
 \]</div>
-<p>要約すると、「最初に否定してから1を加える」と「最初に1を減算してから否定する」は両方とも<span class="arithmatex">\(10000\)</span>に対する補数を計算しており、等価です。</p>
-<p>本質的に、「否定」操作は実際には<span class="arithmatex">\(1111\)</span>に対する補数を求めることです（<code>符号絶対値 + 1の補数 = 1111</code>が常に成り立つため）。そして1の補数に1を加えることは<span class="arithmatex">\(10000\)</span>に対する2の補数と等しくなります。</p>
-<p>上記では<span class="arithmatex">\(n = 4\)</span>を例に取りましたが、任意の桁数の任意の二進数に一般化できます。</p>
+<p>まとめると、「先にビット反転してから 1 を加える」と「先に 1 を引いてからビット反転する」の 2 つの演算は、どちらも <span class="arithmatex">\(10000\)</span> への補数を計算しており、等価です。</p>
+<p>本質的には、「ビット反転」という操作は実際には <span class="arithmatex">\(1111\)</span> への補数を求めています（常に <code>符号付き絶対値表現 + 1 の補数 = 1111</code> が成り立つため）。そして、1 の補数にさらに 1 を加えて得られる 2 の補数が、<span class="arithmatex">\(10000\)</span> への補数です。</p>
+<p>上記では <span class="arithmatex">\(n = 4\)</span> を例にしましたが、この考え方は任意のビット長の 2 進数に一般化できます。</p>
 
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@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1635,7 +1635,7 @@
   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1942,7 +1942,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2105,7 +2105,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2491,7 +2491,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2547,7 +2547,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2575,7 +2575,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3115,7 +3115,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3200,7 +3200,7 @@
   <a href="#1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; 分割統治に基づく二分探索の実装
+        1. &nbsp; 分割統治に基づく二分探索
       
     </span>
   </a>
@@ -3230,7 +3230,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3258,7 +3258,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3451,7 +3451,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3479,7 +3479,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3620,7 +3620,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3648,7 +3648,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3676,7 +3676,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3704,7 +3704,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3897,7 +3897,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4142,7 +4142,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4288,7 +4288,7 @@
   <a href="#1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; 分割統治に基づく二分探索の実装
+        1. &nbsp; 分割統治に基づく二分探索
       
     </span>
   </a>
@@ -4332,60 +4332,60 @@
 
 
 <!-- Page content -->
-<h1 id="122">12.2 &nbsp; 分割統治検索戦略<a class="headerlink" href="#122" title="Permanent link">&para;</a></h1>
-<p>私たちは検索アルゴリズムが主に2つのカテゴリに分類されることを学びました。</p>
+<h1 id="122">12.2 &nbsp; 分割統治探索戦略<a class="headerlink" href="#122" title="Permanent link">&para;</a></h1>
+<p>私たちはすでに学んだように、探索アルゴリズムは大きく二つに分けられる。</p>
 <ul>
-<li><strong>総当たり検索</strong>：データ構造を走査することで実装され、時間計算量は <span class="arithmatex">\(O(n)\)</span> です。</li>
-<li><strong>適応検索</strong>：独特なデータ組織形式や事前情報を利用し、時間計算量は <span class="arithmatex">\(O(\log n)\)</span> または <span class="arithmatex">\(O(1)\)</span> に達することができます。</li>
+<li><strong>力ずく探索</strong>：データ構造を走査することで実現され、時間計算量は <span class="arithmatex">\(O(n)\)</span> である。</li>
+<li><strong>適応的探索</strong>：固有のデータ構造や事前情報を利用し、時間計算量は <span class="arithmatex">\(O(\log n)\)</span> 、さらには <span class="arithmatex">\(O(1)\)</span> に達しうる。</li>
 </ul>
-<p>実際、<strong>時間計算量が <span class="arithmatex">\(O(\log n)\)</span> の検索アルゴリズムは通常分割統治戦略に基づいています</strong>。例えば、二分探索や木などです。</p>
+<p>実際、<strong>時間計算量が <span class="arithmatex">\(O(\log n)\)</span> の探索アルゴリズムは通常、分割統治戦略に基づいて実装される</strong>。たとえば二分探索や木構造である。</p>
 <ul>
-<li>二分探索の各ステップは、問題（配列内でターゲット要素を検索する）をより小さな問題（配列の半分でターゲット要素を検索する）に分割し、配列が空になるかターゲット要素が見つかるまで続けます。</li>
-<li>木は分割統治のアイデアを表現し、二分探索木、AVL木、ヒープなどのデータ構造では、様々な操作の時間計算量は <span class="arithmatex">\(O(\log n)\)</span> です。</li>
+<li>二分探索の各ステップでは、問題（配列内で目標要素を探索すること）を小さな問題（配列の半分で目標要素を探索すること）に分解し、この過程は配列が空になるか目標要素が見つかるまで続く。</li>
+<li>木構造は分割統治の考え方を代表するものであり、二分探索木、AVL 木、ヒープなどのデータ構造では、さまざまな操作の時間計算量はいずれも <span class="arithmatex">\(O(\log n)\)</span> である。</li>
 </ul>
-<p>二分探索の分割統治戦略は以下の通りです。</p>
+<p>二分探索の分割統治戦略は以下のとおりである。</p>
 <ul>
-<li><strong>問題を分割できる</strong>：二分探索は元の問題（配列内での検索）を部分問題（配列の半分での検索）に再帰的に分割し、中間要素とターゲット要素を比較することで実現されます。</li>
-<li><strong>部分問題は独立している</strong>：二分探索では、各ラウンドで一つの部分問題を処理し、他の部分問題に影響されません。</li>
-<li><strong>部分問題の解をマージする必要がない</strong>：二分探索は特定の要素を見つけることを目的としているため、部分問題の解をマージする必要がありません。部分問題が解決されると、元の問題も解決されます。</li>
+<li><strong>問題は分解できる</strong>：二分探索は、元の問題（配列内で探索すること）を部分問題（配列の半分で探索すること）へ再帰的に分解する。これは中央要素と目標要素を比較することで実現される。</li>
+<li><strong>部分問題は独立している</strong>：二分探索では、各ラウンドで一つの部分問題だけを処理し、ほかの部分問題の影響を受けない。</li>
+<li><strong>部分問題の解を統合する必要はない</strong>：二分探索は特定の要素を探すことを目的としているため、部分問題の解を統合する必要がない。部分問題が解決されると、元の問題も同時に解決される。</li>
 </ul>
-<p>分割統治は検索効率を向上させることができます。なぜなら、総当たり検索はラウンドごとに1つの選択肢しか除去できませんが、<strong>分割統治は選択肢の半分を除去できるからです</strong>。</p>
-<h3 id="1">1. &nbsp; 分割統治に基づく二分探索の実装<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>前の章では、二分探索は反復に基づいて実装されました。今度は、分割統治（再帰）に基づいて実装します。</p>
+<p>分割統治が探索効率を高められる本質的な理由は、力ずく探索では各ラウンドで一つの候補しか除外できないのに対し、**分割統治による探索では各ラウンドで候補の半分を除外できる**からである。</p>
+<h3 id="1">1. &nbsp; 分割統治に基づく二分探索<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>前の章では、二分探索を漸化式（反復）に基づいて実装した。ここでは分割統治（再帰）に基づいてこれを実装する。</p>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
-<p>長さ <span class="arithmatex">\(n\)</span> の順序付けられた配列 <code>nums</code> が与えられ、すべての要素が一意である場合、要素 <code>target</code> を見つけてください。</p>
+<p>長さ <span class="arithmatex">\(n\)</span> の昇順配列 <code>nums</code> が与えられ、そのすべての要素は一意である。要素 <code>target</code> を探索せよ。</p>
 </div>
-<p>分割統治の観点から、検索区間 <span class="arithmatex">\([i, j]\)</span> に対応する部分問題を <span class="arithmatex">\(f(i, j)\)</span> と表します。</p>
-<p>元の問題 <span class="arithmatex">\(f(0, n-1)\)</span> から開始して、以下のステップで二分探索を実行します。</p>
+<p>分割統治の観点から、探索区間 <span class="arithmatex">\([i, j]\)</span> に対応する部分問題を <span class="arithmatex">\(f(i, j)\)</span> と記す。</p>
+<p>元の問題 <span class="arithmatex">\(f(0, n-1)\)</span> を出発点として、次の手順で二分探索を行う。</p>
 <ol>
-<li>検索区間 <span class="arithmatex">\([i, j]\)</span> の中点 <span class="arithmatex">\(m\)</span> を計算し、それを使用して検索区間の半分を除去します。</li>
-<li>半分のサイズに縮小された部分問題を再帰的に解決します。これは <span class="arithmatex">\(f(i, m-1)\)</span> または <span class="arithmatex">\(f(m+1, j)\)</span> になる可能性があります。</li>
-<li><code>target</code> が見つかるか区間が空になってリターンするまで、ステップ <code>1.</code> と <code>2.</code> を繰り返します。</li>
+<li>探索区間 <span class="arithmatex">\([i, j]\)</span> の中点 <span class="arithmatex">\(m\)</span> を計算し、それに基づいて探索区間の半分を除外する。</li>
+<li>規模が半分に縮小された部分問題を再帰的に解く。候補は <span class="arithmatex">\(f(i, m-1)\)</span> または <span class="arithmatex">\(f(m+1, j)\)</span> である。</li>
+<li><code>1.</code> と <code>2.</code> の手順を繰り返し、<code>target</code> が見つかるか区間が空になったら返す。</li>
 </ol>
-<p>以下の図は、配列内で要素 <span class="arithmatex">\(6\)</span> を探す二分探索の分割統治過程を示しています。</p>
-<p><img alt="二分探索の分割統治過程" class="animation-figure" src="../binary_search_recur.assets/binary_search_recur.png" /></p>
-<p align="center"> 図 12-4 &nbsp; 二分探索の分割統治過程 </p>
+<p>次の図は、配列内で要素 <span class="arithmatex">\(6\)</span> を二分探索する分割統治の過程を示している。</p>
+<p><img alt="二分探索の分割統治の過程" class="animation-figure" src="../binary_search_recur.assets/binary_search_recur.png" /></p>
+<p align="center"> 図 12-4 &nbsp; 二分探索の分割統治の過程 </p>
 
-<p>実装コードでは、問題 <span class="arithmatex">\(f(i, j)\)</span> を解決するために再帰関数 <code>dfs()</code> を宣言します：</p>
+<p>実装コードでは、再帰関数 <code>dfs()</code> を宣言して問題 <span class="arithmatex">\(f(i, j)\)</span> を解く。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
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 <div class="highlight"><span class="filename">binary_search_recur.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
 <a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二分探索：問題 f(i, j)&quot;&quot;&quot;</span>
-<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 区間が空の場合、対象要素がないことを示すため、-1 を返す</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 区間が空なら対象要素は存在しないので -1 を返す</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">if</span> <span class="n">i</span> <span class="o">&gt;</span> <span class="n">j</span><span class="p">:</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 中点インデックス m を計算</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="n">m</span> <span class="o">=</span> <span class="p">(</span><span class="n">i</span> <span class="o">+</span> <span class="n">j</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span> <span class="o">&lt;</span> <span class="n">target</span><span class="p">:</span>
-<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="c1"># 再帰部分問題 f(m+1, j)</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="c1"># 部分問題 f(m+1, j) を再帰的に解く</span>
 <a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="k">return</span> <span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">target</span><span class="p">,</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">j</span><span class="p">)</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="k">elif</span> <span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">target</span><span class="p">:</span>
-<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="c1"># 再帰部分問題 f(i, m-1)</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="c1"># 部分問題 f(i, m-1) を再帰的に解く</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="k">return</span> <span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">target</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">m</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
 <a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="k">else</span><span class="p">:</span>
-<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>        <span class="c1"># 対象要素を発見したため、そのインデックスを返す</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>        <span class="c1"># 目標要素が見つかったらそのインデックスを返す</span>
 <a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>        <span class="k">return</span> <span class="n">m</span>
 <a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>
 <a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a><span class="k">def</span><span class="w"> </span><span class="nf">binary_search</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
@@ -4398,20 +4398,20 @@
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_search_recur.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 二分探索：問題 f(i, j) */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 区間が空の場合、対象要素が存在しないことを示すため、-1 を返す</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 区間が空なら対象要素は存在しないので -1 を返す</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="c1">// 中点インデックス m を計算</span>
-<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="c1">// 再帰的な部分問題 f(m+1, j)</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="c1">// 部分問題 f(m+1, j) を再帰的に解く</span>
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="c1">// 再帰的な部分問題 f(i, m-1)</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="c1">// 部分問題 f(i, m-1) を再帰的に解く</span>
 <a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">        </span><span class="c1">// 対象要素が見つかったため、そのインデックスを返す</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">        </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
 <a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
 <a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="p">}</span>
@@ -4427,20 +4427,20 @@
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_search_recur.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 二分探索：問題 f(i, j) */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 区間が空の場合、対象要素が存在しないことを示すため、-1 を返す</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 区間が空なら対象要素は存在しないので -1 を返す</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="c1">// 中点インデックス m を計算</span>
-<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="c1">// 再帰的な部分問題 f(m+1, j)</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="c1">// 部分問題 f(m+1, j) を再帰的に解く</span>
 <a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span>
 <a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="c1">// 再帰的な部分問題 f(i, m-1)</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="c1">// 部分問題 f(i, m-1) を再帰的に解く</span>
 <a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">        </span><span class="c1">// 対象要素が見つかったため、そのインデックスを返す</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">        </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
 <a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
 <a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="p">}</span>
@@ -4454,67 +4454,307 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_recur.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_search_recur</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">DFS</span><span class="p">}</span>
-<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
-<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_search_recur</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BinarySearch</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_recur.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 二分探索：問題 f(i, j) */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">DFS</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="c1">// 区間が空なら対象要素は存在しないので -1 を返す</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">        </span><span class="c1">// 部分問題 f(m+1, j) を再帰的に解く</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nf">DFS</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">        </span><span class="c1">// 部分問題 f(i, m-1) を再帰的に解く</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nf">DFS</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">        </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="p">}</span>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a>
+<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="cm">/* 二分探索 */</span>
+<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="kt">int</span><span class="w"> </span><span class="nf">BinarySearch</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
+<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="w">    </span><span class="c1">// 問題 f(0, n-1) を解く</span>
+<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nf">DFS</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_recur.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
-<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
-<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">binarySearch</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_recur.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 二分探索：問題 f(i, j) */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// 区間が空なら対象要素は存在しないため、-1 を返す</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="c1">// 中点インデックスを計算する</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">    </span><span class="nx">m</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">((</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="c1">// 中点の要素と目標要素の大小を判定する</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">        </span><span class="c1">// 小さければ右半分の配列を再帰</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">        </span><span class="c1">// 部分問題 f(m+1, j) を解く</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">        </span><span class="c1">// 大きければ左半分の配列を再帰</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">        </span><span class="c1">// 部分問題 f(i, m-1) を解く</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w">        </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">m</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="p">}</span>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a>
+<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="cm">/* 二分探索 */</span>
+<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="kd">func</span><span class="w"> </span><span class="nx">binarySearch</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="w">    </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span>
+<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_recur.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
-<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">binarySearch</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_recur.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 二分探索：問題 f(i, j) */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// 区間が空なら対象要素は存在しないので -1 を返す</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">        </span><span class="c1">// 部分問題 f(m+1, j) を再帰的に解く</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">        </span><span class="c1">// 部分問題 f(i, m-1) を再帰的に解く</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">        </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">m</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="p">}</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="cm">/* 二分探索 */</span>
+<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="kd">func</span><span class="w"> </span><span class="nf">binarySearch</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="w">    </span><span class="c1">// 問題 f(0, n-1) を解く</span>
+<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">startIndex</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">endIndex</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_recur.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
-<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
-<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearch</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_recur.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 二分探索：問題 f(i, j) */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="c1">// 区間が空なら対象要素は存在しないので -1 を返す</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">((</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">        </span><span class="c1">// 部分問題 f(m+1, j) を再帰的に解く</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">);</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">        </span><span class="c1">// 部分問題 f(i, m-1) を再帰的に解く</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w">        </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="p">}</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="cm">/* 二分探索 */</span>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="kd">function</span><span class="w"> </span><span class="nx">binarySearch</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a><span class="w">    </span><span class="c1">// 問題 f(0, n-1) を解く</span>
+<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_recur.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
-<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
-<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearch</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_recur.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 二分探索：問題 f(i, j) */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">target</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="c1">// 区間が空なら対象要素は存在しないので -1 を返す</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">((</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">        </span><span class="c1">// 部分問題 f(m+1, j) を再帰的に解く</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">);</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">        </span><span class="c1">// 部分問題 f(i, m-1) を再帰的に解く</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">        </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="p">}</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="cm">/* 二分探索 */</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="kd">function</span><span class="w"> </span><span class="nx">binarySearch</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">target</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="w">    </span><span class="c1">// 問題 f(0, n-1) を解く</span>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_recur.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
-<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearch</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_recur.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 二分探索：問題 f(i, j) */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="c1">// 区間が空なら対象要素は存在しないので -1 を返す</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">    </span><span class="c1">// 部分問題 f(m+1, j) を再帰的に解く</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">  </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">    </span><span class="c1">// 部分問題 f(i, m-1) を再帰的に解く</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">  </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">    </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="p">}</span>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a>
+<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="cm">/* 二分探索 */</span>
+<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="kt">int</span><span class="w"> </span><span class="n">binarySearch</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a><span class="w">  </span><span class="c1">// 問題 f(0, n-1) を解く</span>
+<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-8-26" name="__codelineno-8-26" href="#__codelineno-8-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_recur.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
-<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binary_search</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_recur.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 二分探索：問題 f(i, j) */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="c1">// 区間が空なら対象要素は存在しないので -1 を返す</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">m</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">        </span><span class="c1">// 部分問題 f(m+1, j) を再帰的に解く</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">        </span><span class="c1">// 部分問題 f(i, m-1) を再帰的に解く</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">        </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="p">}</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="cm">/* 二分探索 */</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="k">fn</span><span class="w"> </span><span class="nf">binary_search</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">;</span>
+<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="w">    </span><span class="c1">// 問題 f(0, n-1) を解く</span>
+<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_recur.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
-<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearch</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_recur.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 二分探索：問題 f(i, j) */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="c1">// 区間が空なら対象要素は存在しないので -1 を返す</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">    </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">        </span><span class="c1">// 部分問題 f(m+1, j) を再帰的に解く</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">        </span><span class="c1">// 部分問題 f(i, m-1) を再帰的に解く</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">        </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="p">}</span>
+<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a>
+<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="cm">/* 二分探索 */</span>
+<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearch</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">numsSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">numsSize</span><span class="p">;</span>
+<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="w">    </span><span class="c1">// 問題 f(0, n-1) を解く</span>
+<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_recur.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
-<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binarySearch</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_recur.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 二分探索：問題 f(i, j) */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">    </span><span class="c1">// 区間が空なら対象要素は存在しないので -1 を返す</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="m">1</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">    </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">        </span><span class="c1">// 部分問題 f(m+1, j) を再帰的に解く</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">        </span><span class="c1">// 部分問題 f(i, m-1) を再帰的に解く</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="w">        </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="w">        </span><span class="n">m</span>
+<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="p">}</span>
+<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a>
+<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="cm">/* 二分探索 */</span>
+<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">binarySearch</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a><span class="w">    </span><span class="c1">// 問題 f(0, n-1) を解く</span>
+<a id="__codelineno-11-30" name="__codelineno-11-30" href="#__codelineno-11-30"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_recur.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
-<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binary_search</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_recur.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 二分探索: 問題 f(i, j) ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># 区間が空なら対象要素は存在しないので -1 を返す</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">j</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="c1"># 中点インデックス m を計算</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">  </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">    </span><span class="c1"># 部分問題 f(m+1, j) を再帰的に解く</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">  </span><span class="k">elsif</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">    </span><span class="c1"># 部分問題 f(i, m-1) を再帰的に解く</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">  </span><span class="k">else</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">    </span><span class="c1"># 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">m</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="k">end</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="c1">### 二分探索 ###</span>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="k">def</span><span class="w"> </span><span class="nf">binary_search</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="w">  </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a><span class="w">  </span><span class="c1"># 問題 f(0, n-1) を解く</span>
+<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="w">  </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20dfs%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%2C%20i%3A%20int%2C%20j%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%EF%BC%9A%E5%95%8F%E9%A1%8C%20f%28i%2C%20j%29%22%22%22%0A%20%20%20%20%23%20%E5%8C%BA%E9%96%93%E3%81%8C%E7%A9%BA%E3%81%AA%E3%82%89%E5%AF%BE%E8%B1%A1%E8%A6%81%E7%B4%A0%E3%81%AF%E5%AD%98%E5%9C%A8%E3%81%97%E3%81%AA%E3%81%84%E3%81%AE%E3%81%A7%20-1%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20if%20i%20%3E%20j%3A%0A%20%20%20%20%20%20%20%20return%20-1%0A%20%20%20%20%23%20%E4%B8%AD%E7%82%B9%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20m%20%E3%82%92%E8%A8%88%E7%AE%97%0A%20%20%20%20m%20%3D%20%28i%20%2B%20j%29%20%2F%2F%202%0A%20%20%20%20if%20nums%5Bm%5D%20%3C%20target%3A%0A%20%20%20%20%20%20%20%20%23%20%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%20f%28m%2B1%2C%20j%29%20%E3%82%92%E5%86%8D%E5%B8%B0%E7%9A%84%E3%81%AB%E8%A7%A3%E3%81%8F%0A%20%20%20%20%20%20%20%20return%20dfs%28nums%2C%20target%2C%20m%20%2B%201%2C%20j%29%0A%20%20%20%20elif%20nums%5Bm%5D%20%3E%20target%3A%0A%20%20%20%20%20%20%20%20%23%20%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%20f%28i%2C%20m-1%29%20%E3%82%92%E5%86%8D%E5%B8%B0%E7%9A%84%E3%81%AB%E8%A7%A3%E3%81%8F%0A%20%20%20%20%20%20%20%20return%20dfs%28nums%2C%20target%2C%20i%2C%20m%20-%201%29%0A%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%23%20%E7%9B%AE%E6%A8%99%E8%A6%81%E7%B4%A0%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%81%A3%E3%81%9F%E3%82%89%E3%81%9D%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20%20%20%20%20return%20m%0A%0Adef%20binary_search%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%22%22%22%0A%20%20%20%20n%20%3D%20len%28nums%29%0A%20%20%20%20%23%20%E5%95%8F%E9%A1%8C%20f%280%2C%20n-1%29%20%E3%82%92%E8%A7%A3%E3%81%8F%0A%20%20%20%20return%20dfs%28nums%2C%20target%2C%200%2C%20n%20-%201%29%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20target%20%3D%206%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%206%2C%208%2C%2012%2C%2015%2C%2023%2C%2026%2C%2031%2C%2035%5D%0A%0A%20%20%20%20%23%20%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%EF%BC%88%E4%B8%A1%E9%96%89%E5%8C%BA%E9%96%93%EF%BC%89%0A%20%20%20%20index%20%3D%20binary_search%28nums%2C%20target%29%0A%20%20%20%20print%28%22%E5%AF%BE%E8%B1%A1%E8%A6%81%E7%B4%A0%206%20%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20%3D%20%22%2C%20index%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20dfs%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%2C%20i%3A%20int%2C%20j%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%EF%BC%9A%E5%95%8F%E9%A1%8C%20f%28i%2C%20j%29%22%22%22%0A%20%20%20%20%23%20%E5%8C%BA%E9%96%93%E3%81%8C%E7%A9%BA%E3%81%AA%E3%82%89%E5%AF%BE%E8%B1%A1%E8%A6%81%E7%B4%A0%E3%81%AF%E5%AD%98%E5%9C%A8%E3%81%97%E3%81%AA%E3%81%84%E3%81%AE%E3%81%A7%20-1%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20if%20i%20%3E%20j%3A%0A%20%20%20%20%20%20%20%20return%20-1%0A%20%20%20%20%23%20%E4%B8%AD%E7%82%B9%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20m%20%E3%82%92%E8%A8%88%E7%AE%97%0A%20%20%20%20m%20%3D%20%28i%20%2B%20j%29%20%2F%2F%202%0A%20%20%20%20if%20nums%5Bm%5D%20%3C%20target%3A%0A%20%20%20%20%20%20%20%20%23%20%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%20f%28m%2B1%2C%20j%29%20%E3%82%92%E5%86%8D%E5%B8%B0%E7%9A%84%E3%81%AB%E8%A7%A3%E3%81%8F%0A%20%20%20%20%20%20%20%20return%20dfs%28nums%2C%20target%2C%20m%20%2B%201%2C%20j%29%0A%20%20%20%20elif%20nums%5Bm%5D%20%3E%20target%3A%0A%20%20%20%20%20%20%20%20%23%20%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%20f%28i%2C%20m-1%29%20%E3%82%92%E5%86%8D%E5%B8%B0%E7%9A%84%E3%81%AB%E8%A7%A3%E3%81%8F%0A%20%20%20%20%20%20%20%20return%20dfs%28nums%2C%20target%2C%20i%2C%20m%20-%201%29%0A%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%23%20%E7%9B%AE%E6%A8%99%E8%A6%81%E7%B4%A0%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%81%A3%E3%81%9F%E3%82%89%E3%81%9D%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20%20%20%20%20return%20m%0A%0Adef%20binary_search%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%22%22%22%0A%20%20%20%20n%20%3D%20len%28nums%29%0A%20%20%20%20%23%20%E5%95%8F%E9%A1%8C%20f%280%2C%20n-1%29%20%E3%82%92%E8%A7%A3%E3%81%8F%0A%20%20%20%20return%20dfs%28nums%2C%20target%2C%200%2C%20n%20-%201%29%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20target%20%3D%206%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%206%2C%208%2C%2012%2C%2015%2C%2023%2C%2026%2C%2031%2C%2035%5D%0A%0A%20%20%20%20%23%20%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%EF%BC%88%E4%B8%A1%E9%96%89%E5%8C%BA%E9%96%93%EF%BC%89%0A%20%20%20%20index%20%3D%20binary_search%28nums%2C%20target%29%0A%20%20%20%20print%28%22%E5%AF%BE%E8%B1%A1%E8%A6%81%E7%B4%A0%206%20%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20%3D%20%22%2C%20index%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 
 <!-- Source file information -->
 
@@ -4537,7 +4777,7 @@ aria-label="フッター"
   <a
     href="../divide_and_conquer/"
     class="md-footer__link md-footer__link--prev"
-    aria-label="前: 12.1 &amp;nbsp; 分割統治アルゴリズム"
+    aria-label="前: 12.1 &amp;nbsp; 分割統治法"
     rel="prev"
   >
     <div class="md-footer__button md-icon">
@@ -4549,7 +4789,7 @@ aria-label="フッター"
         前
       </span>
       <div class="md-ellipsis">
-        12.1 &nbsp; 分割統治アルゴリズム
+        12.1 &nbsp; 分割統治法
       </div>
     </div>
   </a>
@@ -4561,7 +4801,7 @@ aria-label="フッター"
   <a
     href="../build_binary_tree_problem/"
     class="md-footer__link md-footer__link--next"
-    aria-label="次: 12.3 &amp;nbsp; 木の構築問題"
+    aria-label="次: 12.3 &amp;nbsp; 二分木の構築問題"
     rel="next"
   >
     <div class="md-footer__title">
@@ -4569,7 +4809,7 @@ aria-label="フッター"
         次
       </span>
       <div class="md-ellipsis">
-        12.3 &nbsp; 木の構築問題
+        12.3 &nbsp; 二分木の構築問題
       </div>
     </div>
     <div class="md-footer__button md-icon">
diff --git a/ja/chapter_divide_and_conquer/build_binary_tree_problem/index.html b/ja/chapter_divide_and_conquer/build_binary_tree_problem/index.html
index 4d45511db..5cc132bd5 100644
--- a/ja/chapter_divide_and_conquer/build_binary_tree_problem/index.html
+++ b/ja/chapter_divide_and_conquer/build_binary_tree_problem/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -39,7 +39,7 @@
     
     
       
-        <title>12.3 二分木構築問題 - Hello アルゴリズム</title>
+        <title>12.3 二分木の構築問題 - Hello アルゴリズム</title>
       
     
     
@@ -117,7 +117,7 @@
         <path
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
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@@ -152,7 +152,7 @@
         <div class="md-header__topic" data-md-component="header-topic">
           <span class="md-ellipsis">
             
-              12.3 &nbsp; 二分木構築問題
+              12.3 &nbsp; 二分木の構築問題
             
           </span>
         </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
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-    序
+    はじめに
   
 
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-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
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-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
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-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
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   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
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   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
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-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
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-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
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-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
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-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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   <a href="#1" class="md-nav__link">
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-        1. &nbsp; 分割統治問題かどうかの判定
+        1. &nbsp; 分割統治問題かどうかを判断する
       
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   <a href="#2" class="md-nav__link">
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-        2. &nbsp; 部分木の分割方法
+        2. &nbsp; 部分木をどのように分割するか
       
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   <a href="#3" class="md-nav__link">
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-        3. &nbsp; 変数に基づく部分木範囲の記述
+        3. &nbsp; 変数を用いて部分木区間を記述する
       
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-        4. &nbsp; コード実装
+        4. &nbsp; コードの実装
       
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-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
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-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
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-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
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-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
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-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
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-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
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   <a href="#1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; 分割統治問題かどうかの判定
+        1. &nbsp; 分割統治問題かどうかを判断する
       
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   <a href="#2" class="md-nav__link">
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-        2. &nbsp; 部分木の分割方法
+        2. &nbsp; 部分木をどのように分割するか
       
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   <a href="#3" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3. &nbsp; 変数に基づく部分木範囲の記述
+        3. &nbsp; 変数を用いて部分木区間を記述する
       
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   <a href="#4" class="md-nav__link">
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-        4. &nbsp; コード実装
+        4. &nbsp; コードの実装
       
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   </a>
@@ -4398,54 +4398,54 @@
 
 
 <!-- Page content -->
-<h1 id="123">12.3 &nbsp; 二分木構築問題<a class="headerlink" href="#123" title="Permanent link">&para;</a></h1>
+<h1 id="123">12.3 &nbsp; 二分木の構築問題<a class="headerlink" href="#123" title="Permanent link">&para;</a></h1>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
-<p>二分木の前順走査 <code>preorder</code> シーケンスと中順走査 <code>inorder</code> シーケンスが与えられた場合、二分木を構築してそのルートノードを返してください。二分木に重複するノード値がないと仮定します（以下の図に示すように）。</p>
+<p>二分木の前順走査 <code>preorder</code> と中順走査 <code>inorder</code> が与えられたとき、これらから二分木を構築し、その根ノードを返してください。二分木には値が重複するノードが存在しないものとします（下図のとおり）。</p>
 </div>
-<p><img alt="二分木構築のサンプルデータ" class="animation-figure" src="../build_binary_tree_problem.assets/build_tree_example.png" /></p>
-<p align="center"> 図 12-5 &nbsp; 二分木構築のサンプルデータ </p>
+<p><img alt="二分木を構築する例のデータ" class="animation-figure" src="../build_binary_tree_problem.assets/build_tree_example.png" /></p>
+<p align="center"> 図 12-5 &nbsp; 二分木を構築する例のデータ </p>
 
-<h3 id="1">1. &nbsp; 分割統治問題かどうかの判定<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p><code>preorder</code> と <code>inorder</code> シーケンスから二分木を構築する元の問題は、典型的な分割統治問題です。</p>
+<h3 id="1">1. &nbsp; 分割統治問題かどうかを判断する<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>元の問題は <code>preorder</code> と <code>inorder</code> から二分木を構築することであり、典型的な分割統治問題です。</p>
 <ul>
-<li><strong>問題を分解できる</strong>：分割統治の観点から、元の問題を2つの部分問題（左の部分木の構築と右の部分木の構築）とルートノードの初期化という1つの操作に分割できます。各部分木（部分問題）について、同じアプローチを継続的に適用し、より小さな部分木（部分問題）に分割し、最小の部分問題（空の部分木）に到達するまで続けます。</li>
-<li><strong>部分問題は独立している</strong>：左と右の部分木は重複しません。左の部分木を構築する際、左の部分木に対応する中順走査と前順走査のセグメントのみが必要です。右の部分木にも同じアプローチが適用されます。</li>
-<li><strong>部分問題の解を組み合わせることができる</strong>：左と右の部分木（部分問題の解）を構築したら、それらをルートノードに接続して元の問題の解を取得できます。</li>
+<li><strong>問題は分解できる</strong>：分割統治の観点から見ると、元の問題は 2 つの部分問題、すなわち左部分木の構築と右部分木の構築に分けられ、さらに根ノードを初期化する 1 ステップが加わります。各部分木（部分問題）に対しても、同じ分割方法を再利用してより小さな部分木（部分問題）へと分けていき、最小の部分問題（空部分木）に達した時点で終了します。</li>
+<li><strong>部分問題は独立している</strong>：左部分木と右部分木は互いに独立しており、両者の間に重なりはありません。左部分木を構築するときは、中順走査と前順走査のうち左部分木に対応する部分だけを見れば十分です。右部分木も同様です。</li>
+<li><strong>部分問題の解は統合できる</strong>：左部分木と右部分木（部分問題の解）が得られたら、それらを根ノードに接続することで元の問題の解を得られます。</li>
 </ul>
-<h3 id="2">2. &nbsp; 部分木の分割方法<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>上記の分析に基づいて、この問題は分割統治を使用して解決できます。<strong>しかし、前順走査 <code>preorder</code> シーケンスと中順走査 <code>inorder</code> シーケンスを使用して左と右の部分木をどのように分割すればよいでしょうか？</strong></p>
-<p>定義により、<code>preorder</code> と <code>inorder</code> シーケンスの両方を3つの部分に分割できます：</p>
+<h3 id="2">2. &nbsp; 部分木をどのように分割するか<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>以上の分析より、この問題は分割統治で解けます。<strong>では、前順走査 <code>preorder</code> と中順走査 <code>inorder</code> を使って左部分木と右部分木をどのように分割すればよいのでしょうか</strong>？</p>
+<p>定義に従うと、<code>preorder</code> と <code>inorder</code> はいずれも 3 つの部分に分けられます。</p>
 <ul>
-<li>前順走査：<code>[ ルート | 左の部分木 | 右の部分木 ]</code>。例えば、図では、木は <code>[ 3 | 9 | 2 1 7 ]</code> に対応します。</li>
-<li>中順走査：<code>[ 左の部分木 | ルート | 右の部分木 ]</code>。例えば、図では、木は <code>[ 9 | 3 | 1 2 7 ]</code> に対応します。</li>
+<li>前順走査：<code>[ 根ノード | 左部分木 | 右部分木 ]</code> ，例えば上図の木は <code>[ 3 | 9 | 2 1 7 ]</code> に対応します。</li>
+<li>中順走査：<code>[ 左部分木 | 根ノード ｜ 右部分木 ]</code> ，例えば上図の木は <code>[ 9 | 3 | 1 2 7 ]</code> に対応します。</li>
 </ul>
-<p>前の図のデータを使用して、次の図に示すステップに従って分割結果を取得できます：</p>
+<p>上図のデータを例にすると、下図の手順によって分割結果を得られます。</p>
 <ol>
-<li>前順走査の最初の要素3がルートノードの値です。</li>
-<li><code>inorder</code> シーケンス内でルートノード3のインデックスを見つけ、このインデックスを使用して <code>inorder</code> を <code>[ 9 | 3 ｜ 1 2 7 ]</code> に分割します。</li>
-<li><code>inorder</code> シーケンスの分割に従って、左と右の部分木がそれぞれ1個と3個のノードを含むことが簡単に決定できるため、<code>preorder</code> シーケンスを <code>[ 3 | 9 | 2 1 7 ]</code> に対応して分割できます。</li>
+<li>前順走査の先頭要素 3 が根ノードの値です。</li>
+<li>根ノード 3 の <code>inorder</code> におけるインデックスを探すと、そのインデックスを用いて <code>inorder</code> を <code>[ 9 | 3 ｜ 1 2 7 ]</code> に分割できます。</li>
+<li><code>inorder</code> の分割結果から、左部分木と右部分木のノード数はそれぞれ 1 と 3 であることがわかり、したがって <code>preorder</code> を <code>[ 3 | 9 | 2 1 7 ]</code> に分割できます。</li>
 </ol>
-<p><img alt="前順走査と中順走査での部分木の分割" class="animation-figure" src="../build_binary_tree_problem.assets/build_tree_preorder_inorder_division.png" /></p>
-<p align="center"> 図 12-6 &nbsp; 前順走査と中順走査での部分木の分割 </p>
+<p><img alt="前順走査と中順走査で部分木を分割する" class="animation-figure" src="../build_binary_tree_problem.assets/build_tree_preorder_inorder_division.png" /></p>
+<p align="center"> 図 12-6 &nbsp; 前順走査と中順走査で部分木を分割する </p>
 
-<h3 id="3">3. &nbsp; 変数に基づく部分木範囲の記述<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
-<p>上記の分割方法に基づいて、<strong><code>preorder</code> と <code>inorder</code> シーケンスにおけるルート、左の部分木、右の部分木のインデックス範囲を取得しました</strong>。これらのインデックス範囲を記述するために、いくつかのポインタ変数を使用します。</p>
+<h3 id="3">3. &nbsp; 変数を用いて部分木区間を記述する<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
+<p>以上の分割方法により、**根ノード、左部分木、右部分木が <code>preorder</code> と <code>inorder</code> の中で占めるインデックス区間**が得られました。これらのインデックス区間を表すために、いくつかのポインタ変数を導入します。</p>
 <ul>
-<li>現在の木のルートノードの <code>preorder</code> シーケンスでのインデックスを <span class="arithmatex">\(i\)</span> とします。</li>
-<li>現在の木のルートノードの <code>inorder</code> シーケンスでのインデックスを <span class="arithmatex">\(m\)</span> とします。</li>
-<li>現在の木の <code>inorder</code> シーケンスでのインデックス範囲を <span class="arithmatex">\([l, r]\)</span> とします。</li>
+<li>現在の木の根ノードが <code>preorder</code> に現れるインデックスを <span class="arithmatex">\(i\)</span> とします。</li>
+<li>現在の木の根ノードが <code>inorder</code> に現れるインデックスを <span class="arithmatex">\(m\)</span> とします。</li>
+<li>現在の木が <code>inorder</code> において占めるインデックス区間を <span class="arithmatex">\([l, r]\)</span> とします。</li>
 </ul>
-<p>以下の表に示すように、これらの変数は <code>preorder</code> シーケンスでのルートノードのインデックスと <code>inorder</code> シーケンスでの部分木のインデックス範囲を表します。</p>
-<p align="center"> 表 12-1 &nbsp; 前順走査と中順走査でのルートノードと部分木のインデックス </p>
+<p>次の表のように、これらの変数を用いれば根ノードの <code>preorder</code> におけるインデックスと、部分木の <code>inorder</code> におけるインデックス区間を表せます。</p>
+<p align="center"> 表 12-1 &nbsp; 根ノードと部分木の前順走査・中順走査におけるインデックス </p>
 
 <div class="center-table">
 <table>
 <thead>
 <tr>
 <th></th>
-<th><code>preorder</code> でのルートノードインデックス</th>
-<th><code>inorder</code> での部分木インデックス範囲</th>
+<th>根ノードの <code>preorder</code> におけるインデックス</th>
+<th>部分木の <code>inorder</code> におけるインデックス区間</th>
 </tr>
 </thead>
 <tbody>
@@ -4455,24 +4455,24 @@
 <td><span class="arithmatex">\([l, r]\)</span></td>
 </tr>
 <tr>
-<td>左の部分木</td>
+<td>左部分木</td>
 <td><span class="arithmatex">\(i + 1\)</span></td>
 <td><span class="arithmatex">\([l, m-1]\)</span></td>
 </tr>
 <tr>
-<td>右の部分木</td>
+<td>右部分木</td>
 <td><span class="arithmatex">\(i + 1 + (m - l)\)</span></td>
 <td><span class="arithmatex">\([m+1, r]\)</span></td>
 </tr>
 </tbody>
 </table>
 </div>
-<p>右の部分木のルートインデックスの <span class="arithmatex">\((m-l)\)</span> は「左の部分木のノード数」を表すことに注意してください。より明確な理解のために、以下の図を参照することが役立つ場合があります。</p>
-<p><img alt="ルートノードと左右の部分木のインデックス" class="animation-figure" src="../build_binary_tree_problem.assets/build_tree_division_pointers.png" /></p>
-<p align="center"> 図 12-7 &nbsp; ルートノードと左右の部分木のインデックス </p>
+<p>右部分木の根ノードのインデックスにある <span class="arithmatex">\((m-l)\)</span> は「左部分木のノード数」を意味します。下図と合わせて理解することを勧めます。</p>
+<p><img alt="根ノードと左右部分木のインデックス区間の表し方" class="animation-figure" src="../build_binary_tree_problem.assets/build_tree_division_pointers.png" /></p>
+<p align="center"> 図 12-7 &nbsp; 根ノードと左右部分木のインデックス区間の表し方 </p>
 
-<h3 id="4">4. &nbsp; コード実装<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
-<p><span class="arithmatex">\(m\)</span> の問い合わせの効率を向上させるために、ハッシュテーブル <code>hmap</code> を使用して <code>inorder</code> シーケンスの要素からそのインデックスへのマッピングを格納します：</p>
+<h3 id="4">4. &nbsp; コードの実装<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
+<p><span class="arithmatex">\(m\)</span> の検索効率を高めるために、ハッシュテーブル <code>hmap</code> を用いて配列 <code>inorder</code> の要素からインデックスへの対応を保存します。</p>
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 <div class="tabbed-content">
 <div class="tabbed-block">
@@ -4483,50 +4483,50 @@
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="n">l</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="n">r</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二分木の構築：分割統治&quot;&quot;&quot;</span>
-<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="c1"># 部分木の区間が空のとき終了</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二分木を構築：分割統治&quot;&quot;&quot;</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="c1"># 部分木区間が空なら終了する</span>
 <a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="k">if</span> <span class="n">r</span> <span class="o">-</span> <span class="n">l</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">:</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="k">return</span> <span class="kc">None</span>
-<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="c1"># ルートノードを初期化</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="c1"># ルートノードを初期化する</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="n">root</span> <span class="o">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
-<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="c1"># m をクエリして左部分木と右部分木を分割</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="c1"># m を求めて左右部分木を分割する</span>
 <a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="n">m</span> <span class="o">=</span> <span class="n">inorder_map</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span>
-<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>    <span class="c1"># 部分問題：左部分木を構築</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>    <span class="c1"># 部分問題：左部分木を構築する</span>
 <a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>    <span class="n">root</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span> <span class="n">inorder_map</span><span class="p">,</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="n">m</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>    <span class="c1"># 部分問題：右部分木を構築</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>    <span class="c1"># 部分問題：右部分木を構築する</span>
 <a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>    <span class="n">root</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span> <span class="n">inorder_map</span><span class="p">,</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span> <span class="o">+</span> <span class="n">m</span> <span class="o">-</span> <span class="n">l</span><span class="p">,</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">r</span><span class="p">)</span>
-<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>    <span class="c1"># ルートノードを返す</span>
+<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>    <span class="c1"># 根ノードを返す</span>
 <a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>    <span class="k">return</span> <span class="n">root</span>
 <a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>
 <a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a><span class="k">def</span><span class="w"> </span><span class="nf">build_tree</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">inorder</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二分木を構築&quot;&quot;&quot;</span>
-<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>    <span class="c1"># ハッシュテーブルを初期化、中順走査の要素からインデックスへのマッピングを保存</span>
+<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>    <span class="c1"># inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
 <a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a>    <span class="n">inorder_map</span> <span class="o">=</span> <span class="p">{</span><span class="n">val</span><span class="p">:</span> <span class="n">i</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">val</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">inorder</span><span class="p">)}</span>
 <a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>    <span class="n">root</span> <span class="o">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span> <span class="n">inorder_map</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">inorder</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
 <a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a>    <span class="k">return</span> <span class="n">root</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">build_tree.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 二分木の構築：分割統治 */</span>
+<div class="highlight"><span class="filename">build_tree.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 二分木を構築：分割統治 */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">dfs</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">unordered_map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 部分木の区間が空の場合に終了</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 部分木区間が空なら終了する</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
-<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// ルートノードを初期化</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// ルートノードを初期化する</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
-<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="c1">// m を問い合わせて左右の部分木を分割</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="c1">// m を求めて左右部分木を分割する</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]];</span>
-<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="c1">// 部分問題：左の部分木を構築</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="c1">// 部分問題：左部分木を構築する</span>
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="c1">// 部分問題：右の部分木を構築</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="c1">// 部分問題：右部分木を構築する</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">);</span>
-<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="c1">// ルートノードを返す</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="c1">// 根ノードを返す</span>
 <a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
 <a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="p">}</span>
 <a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a>
-<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="cm">/* 二分木の構築 */</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="cm">/* 二分木を構築 */</span>
 <a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">buildTree</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">inorder</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">    </span><span class="c1">// ハッシュテーブルを初期化し、中間順序の要素からインデックスへのマッピングを格納</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">    </span><span class="c1">// inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
 <a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">    </span><span class="n">unordered_map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">;</span>
 <a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w">        </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">inorder</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
@@ -4537,26 +4537,26 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">build_tree.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 二分木の構築：分割統治 */</span>
+<div class="highlight"><span class="filename">build_tree.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 二分木を構築：分割統治 */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">Map</span><span class="o">&lt;</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 部分木の区間が空の場合に終了</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 部分木区間が空なら終了する</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
-<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// ルートノードを初期化</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// ルートノードを初期化する</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">preorder</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">);</span>
-<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="c1">// m を問い合わせて左右の部分木を分割</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="c1">// m を求めて左右部分木を分割する</span>
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">preorder</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">);</span>
-<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="c1">// 部分問題：左の部分木を構築</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="c1">// 部分問題：左部分木を構築する</span>
 <a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="c1">// 部分問題：右の部分木を構築</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="c1">// 部分問題：右部分木を構築する</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">    </span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">);</span>
-<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="c1">// ルートノードを返す</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="c1">// 根ノードを返す</span>
 <a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
 <a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="p">}</span>
 <a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a>
-<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="cm">/* 二分木の構築 */</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="cm">/* 二分木を構築 */</span>
 <a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">buildTree</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">inorder</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">    </span><span class="c1">// ハッシュテーブルを初期化し、中間順序の要素からインデックスへのマッピングを格納</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">    </span><span class="c1">// inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
 <a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">    </span><span class="n">Map</span><span class="o">&lt;</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashMap</span><span class="o">&lt;&gt;</span><span class="p">();</span>
 <a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">        </span><span class="n">inorderMap</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="n">inorder</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
@@ -4567,72 +4567,341 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">build_tree.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">build_tree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">DFS</span><span class="p">}</span>
-<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
-<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">build_tree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BuildTree</span><span class="p">}</span>
+<div class="highlight"><span class="filename">build_tree.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 二分木を構築：分割統治 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">Dictionary</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="c1">// 部分木区間が空なら終了する</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="c1">// ルートノードを初期化する</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="c1">// m を求めて左右部分木を分割する</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]];</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">    </span><span class="c1">// 部分問題：左部分木を構築する</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">    </span><span class="n">root</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">    </span><span class="c1">// 部分問題：右部分木を構築する</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">    </span><span class="n">root</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">);</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">    </span><span class="c1">// 根ノードを返す</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="p">}</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="cm">/* 二分木を構築 */</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">BuildTree</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">inorder</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w">    </span><span class="c1">// inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
+<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w">    </span><span class="n">Dictionary</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="w">        </span><span class="n">inorderMap</span><span class="p">.</span><span class="n">TryAdd</span><span class="p">(</span><span class="n">inorder</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="w">    </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
+<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">build_tree.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">dfsBuildTree</span><span class="p">}</span>
-<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
-<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">buildTree</span><span class="p">}</span>
+<div class="highlight"><span class="filename">build_tree.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 二分木を構築：分割統治 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">dfsBuildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="w"> </span><span class="kd">map</span><span class="p">[</span><span class="kt">int</span><span class="p">]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// 部分木区間が空なら終了する</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">r</span><span class="o">-</span><span class="nx">l</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="c1">// ルートノードを初期化する</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">    </span><span class="nx">root</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewTreeNode</span><span class="p">(</span><span class="nx">preorder</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="c1">// m を求めて左右部分木を分割する</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">    </span><span class="nx">m</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">[</span><span class="nx">preorder</span><span class="p">[</span><span class="nx">i</span><span class="p">]]</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">    </span><span class="c1">// 部分問題：左部分木を構築する</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">    </span><span class="nx">root</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dfsBuildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">    </span><span class="c1">// 部分問題：右部分木を構築する</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">    </span><span class="nx">root</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dfsBuildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">+</span><span class="mi">1</span><span class="o">+</span><span class="nx">m</span><span class="o">-</span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">r</span><span class="p">)</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">    </span><span class="c1">// 根ノードを返す</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="p">}</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="cm">/* 二分木を構築 */</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="kd">func</span><span class="w"> </span><span class="nx">buildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorder</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w">    </span><span class="c1">// inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w">    </span><span class="nx">inorderMap</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">(</span><span class="kd">map</span><span class="p">[</span><span class="kt">int</span><span class="p">]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">inorder</span><span class="p">))</span>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">inorder</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="w">        </span><span class="nx">inorderMap</span><span class="p">[</span><span class="nx">inorder</span><span class="p">[</span><span class="nx">i</span><span class="p">]]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">i</span>
+<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a>
+<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w">    </span><span class="nx">root</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">dfsBuildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">inorder</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span>
+<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">build_tree.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
-<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">buildTree</span><span class="p">}</span>
+<div class="highlight"><span class="filename">build_tree.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 二分木を構築：分割統治 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// 部分木区間が空なら終了する</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="c1">// ルートノードを初期化する</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">root</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">    </span><span class="c1">// m を求めて左右部分木を分割する</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span><span class="o">!</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">    </span><span class="c1">// 部分問題：左部分木を構築する</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">    </span><span class="n">root</span><span class="p">.</span><span class="kr">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">:</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">:</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">:</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">    </span><span class="c1">// 部分問題：右部分木を構築する</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">    </span><span class="n">root</span><span class="p">.</span><span class="kr">right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">:</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">:</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">:</span><span class="w"> </span><span class="n">r</span><span class="p">)</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">    </span><span class="c1">// 根ノードを返す</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="p">}</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="cm">/* 二分木を構築 */</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="kd">func</span><span class="w"> </span><span class="nf">buildTree</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">inorder</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w">    </span><span class="c1">// inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
+<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">inorderMap</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">enumerated</span><span class="p">().</span><span class="bp">reduce</span><span class="p">(</span><span class="n">into</span><span class="p">:</span><span class="w"> </span><span class="p">[:])</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nv">$0</span><span class="p">[</span><span class="nv">$1</span><span class="p">.</span><span class="n">element</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nv">$1</span><span class="p">.</span><span class="n">offset</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">:</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">startIndex</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">:</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">startIndex</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">:</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">endIndex</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">build_tree.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
-<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
-<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">buildTree</span><span class="p">}</span>
+<div class="highlight"><span class="filename">build_tree.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 二分木を構築：分割統治 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">r</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="c1">// 部分木区間が空なら終了する</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="c1">// ルートノードを初期化する</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="nx">preorder</span><span class="p">[</span><span class="nx">i</span><span class="p">]);</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="c1">// m を求めて左右部分木を分割する</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">preorder</span><span class="p">[</span><span class="nx">i</span><span class="p">]);</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">    </span><span class="c1">// 部分問題：左部分木を構築する</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">    </span><span class="nx">root</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">    </span><span class="c1">// 部分問題：右部分木を構築する</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">    </span><span class="nx">root</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">r</span><span class="p">);</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">    </span><span class="c1">// 根ノードを返す</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span><span class="p">;</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="p">}</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="cm">/* 二分木を構築 */</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="kd">function</span><span class="w"> </span><span class="nx">buildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorder</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">    </span><span class="c1">// inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Map</span><span class="p">();</span>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">inorder</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w">        </span><span class="nx">inorderMap</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="nx">inorder</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">i</span><span class="p">);</span>
+<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="nx">inorder</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span><span class="p">;</span>
+<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">build_tree.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
-<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
-<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">buildTree</span><span class="p">}</span>
+<div class="highlight"><span class="filename">build_tree.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 二分木を構築：分割統治 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="nx">preorder</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="nx">inorderMap</span><span class="o">:</span><span class="w"> </span><span class="kt">Map</span><span class="o">&lt;</span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="kt">number</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="nx">l</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="nx">r</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="c1">// 部分木区間が空なら終了する</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">    </span><span class="c1">// ルートノードを初期化する</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">root</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="nx">preorder</span><span class="p">[</span><span class="nx">i</span><span class="p">]);</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">    </span><span class="c1">// m を求めて左右部分木を分割する</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">preorder</span><span class="p">[</span><span class="nx">i</span><span class="p">]);</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">    </span><span class="c1">// 部分問題：左部分木を構築する</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">    </span><span class="nx">root</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">    </span><span class="c1">// 部分問題：右部分木を構築する</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">    </span><span class="nx">root</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">r</span><span class="p">);</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">    </span><span class="c1">// 根ノードを返す</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span><span class="p">;</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="p">}</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="cm">/* 二分木を構築 */</span>
+<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="kd">function</span><span class="w"> </span><span class="nx">buildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">inorder</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="w">    </span><span class="c1">// inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
+<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Map</span><span class="o">&lt;</span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="kt">number</span><span class="o">&gt;</span><span class="p">();</span>
+<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">inorder</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a><span class="w">        </span><span class="nx">inorderMap</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="nx">inorder</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">i</span><span class="p">);</span>
+<a id="__codelineno-7-29" name="__codelineno-7-29" href="#__codelineno-7-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-30" name="__codelineno-7-30" href="#__codelineno-7-30"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="nx">inorder</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-7-31" name="__codelineno-7-31" href="#__codelineno-7-31"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span><span class="p">;</span>
+<a id="__codelineno-7-32" name="__codelineno-7-32" href="#__codelineno-7-32"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">build_tree.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
-<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">buildTree</span><span class="p">}</span>
+<div class="highlight"><span class="filename">build_tree.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 二分木を構築：分割統治 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="n">Map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="p">,</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="p">,</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">  </span><span class="c1">// 部分木区間が空なら終了する</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">  </span><span class="c1">// ルートノードを初期化する</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">  </span><span class="c1">// m を求めて左右部分木を分割する</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span><span class="o">!</span><span class="p">;</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">  </span><span class="c1">// 部分問題：左部分木を構築する</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w">  </span><span class="n">root</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w">  </span><span class="c1">// 部分問題：右部分木を構築する</span>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="w">  </span><span class="n">root</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">);</span>
+<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="w">  </span><span class="c1">// 根ノードを返す</span>
+<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
+<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a><span class="p">}</span>
+<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a>
+<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a><span class="cm">/* 二分木を構築 */</span>
+<a id="__codelineno-8-26" name="__codelineno-8-26" href="#__codelineno-8-26"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inorder</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-27" name="__codelineno-8-27" href="#__codelineno-8-27"></a><span class="w">  </span><span class="c1">// inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
+<a id="__codelineno-8-28" name="__codelineno-8-28" href="#__codelineno-8-28"></a><span class="w">  </span><span class="n">Map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{};</span>
+<a id="__codelineno-8-29" name="__codelineno-8-29" href="#__codelineno-8-29"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-30" name="__codelineno-8-30" href="#__codelineno-8-30"></a><span class="w">    </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">inorder</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-8-31" name="__codelineno-8-31" href="#__codelineno-8-31"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-32" name="__codelineno-8-32" href="#__codelineno-8-32"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-8-33" name="__codelineno-8-33" href="#__codelineno-8-33"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
+<a id="__codelineno-8-34" name="__codelineno-8-34" href="#__codelineno-8-34"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">build_tree.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
-<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">build_tree</span><span class="p">}</span>
+<div class="highlight"><span class="filename">build_tree.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 二分木を構築：分割統治 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="n">preorder</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="n">inorder_map</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">HashMap</span><span class="o">&lt;</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="n">l</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="n">r</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">    </span><span class="c1">// 部分木区間が空なら終了する</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nb">None</span><span class="p">;</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">    </span><span class="c1">// ルートノードを初期化する</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]);</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">    </span><span class="c1">// m を求めて左右部分木を分割する</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorder_map</span><span class="p">.</span><span class="n">get</span><span class="p">(</span><span class="o">&amp;</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]).</span><span class="n">unwrap</span><span class="p">();</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">    </span><span class="c1">// 部分問題：左部分木を構築する</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">    </span><span class="n">root</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorder_map</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">    </span><span class="c1">// 部分問題：右部分木を構築する</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w">    </span><span class="n">root</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorder_map</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">);</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w">    </span><span class="c1">// 根ノードを返す</span>
+<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="w">    </span><span class="nb">Some</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
+<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="p">}</span>
+<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a>
+<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="cm">/* 二分木を構築 */</span>
+<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="k">fn</span><span class="w"> </span><span class="nf">build_tree</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">inorder</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="w">    </span><span class="c1">// inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
+<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">inorder_map</span><span class="p">:</span><span class="w"> </span><span class="nc">HashMap</span><span class="o">&lt;</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashMap</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">inorder</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-30" name="__codelineno-9-30" href="#__codelineno-9-30"></a><span class="w">        </span><span class="n">inorder_map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">inorder</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">);</span>
+<a id="__codelineno-9-31" name="__codelineno-9-31" href="#__codelineno-9-31"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-32" name="__codelineno-9-32" href="#__codelineno-9-32"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="n">inorder_map</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-9-33" name="__codelineno-9-33" href="#__codelineno-9-33"></a><span class="w">    </span><span class="n">root</span>
+<a id="__codelineno-9-34" name="__codelineno-9-34" href="#__codelineno-9-34"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">build_tree.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
-<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">buildTree</span><span class="p">}</span>
+<div class="highlight"><span class="filename">build_tree.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 二分木を構築：分割統治 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="c1">// 部分木区間が空なら終了する</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="c1">// ルートノードを初期化する</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">TreeNode</span><span class="p">));</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">    </span><span class="n">root</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">    </span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="c1">// m を求めて左右部分木を分割する</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]];</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">    </span><span class="c1">// 部分問題：左部分木を構築する</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">    </span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">);</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">    </span><span class="c1">// 部分問題：右部分木を構築する</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">    </span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">);</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">    </span><span class="c1">// 根ノードを返す</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="p">}</span>
+<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a>
+<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="cm">/* 二分木を構築 */</span>
+<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">buildTree</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">preorderSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">inorder</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">inorderSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w">    </span><span class="c1">// inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
+<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">);</span>
+<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">inorderSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="w">        </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">inorder</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorderSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">inorderSize</span><span class="p">);</span>
+<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">inorderMap</span><span class="p">);</span>
+<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
+<a id="__codelineno-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">build_tree.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
-<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">buildTree</span><span class="p">}</span>
+<div class="highlight"><span class="filename">build_tree.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 二分木を構築：分割統治 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="n">preorder</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="n">inorderMap</span><span class="p">:</span><span class="w"> </span><span class="n">Map</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="p">,</span><span class="w"> </span><span class="kt">Int?</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="n">l</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">    </span><span class="n">r</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="p">):</span><span class="w"> </span><span class="n">TreeNode? </span><span class="p">{</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">    </span><span class="c1">// 部分木区間が空なら終了する</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">    </span><span class="c1">// ルートノードを初期化する</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">preorder</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">    </span><span class="c1">// m を求めて左右部分木を分割する</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="o">[</span><span class="n">preorder</span><span class="o">[</span><span class="n">i</span><span class="o">]]!!</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">    </span><span class="c1">// 部分問題：左部分木を構築する</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">    </span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">    </span><span class="c1">// 部分問題：右部分木を構築する</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">    </span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">)</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w">    </span><span class="c1">// 根ノードを返す</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="p">}</span>
+<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a>
+<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="cm">/* 二分木を構築 */</span>
+<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">buildTree</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">):</span><span class="w"> </span><span class="n">TreeNode? </span><span class="p">{</span>
+<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="w">    </span><span class="c1">// inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
+<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashMap</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="p">,</span><span class="w"> </span><span class="kt">Int?</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="na">indices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="w">        </span><span class="n">inorderMap</span><span class="o">[</span><span class="n">inorder</span><span class="o">[</span><span class="n">i</span><span class="o">]]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-30" name="__codelineno-11-30" href="#__codelineno-11-30"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span>
+<a id="__codelineno-11-32" name="__codelineno-11-32" href="#__codelineno-11-32"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">build_tree.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
-<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">build_tree</span><span class="p">}</span>
+<div class="highlight"><span class="filename">build_tree.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 二分木を構築：分割統治 ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorder_map</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># 部分木区間が空なら終了する</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="c1"># ルートノードを初期化する</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">  </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">preorder</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">  </span><span class="c1"># m を求めて左右部分木を分割する</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">  </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorder_map</span><span class="o">[</span><span class="n">preorder</span><span class="o">[</span><span class="n">i</span><span class="o">]]</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">  </span><span class="c1"># 部分問題：左部分木を構築する</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">  </span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorder_map</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">  </span><span class="c1"># 部分問題：右部分木を構築する</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">  </span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorder_map</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">)</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">  </span><span class="c1"># 根ノードを返す</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">  </span><span class="n">root</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="k">end</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="c1">### 二分木を構築 ###</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="k">def</span><span class="w"> </span><span class="nf">build_tree</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="p">)</span>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w">  </span><span class="c1"># inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w">  </span><span class="n">inorder_map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{}</span>
+<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="w">  </span><span class="n">inorder</span><span class="o">.</span><span class="n">each_with_index</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">inorder_map</span><span class="o">[</span><span class="n">val</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a><span class="w">  </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorder_map</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>以下の図は、二分木を構築する再帰過程を示しています。各ノードは再帰の「下降」段階で作成され、各エッジ（参照）は「上昇」段階で形成されます。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%20%3D%200%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E5%80%A4%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%8F%B3%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%0Adef%20dfs%28%0A%20%20%20%20preorder%3A%20list%5Bint%5D%2C%0A%20%20%20%20inorder_map%3A%20dict%5Bint%2C%20int%5D%2C%0A%20%20%20%20i%3A%20int%2C%0A%20%20%20%20l%3A%20int%2C%0A%20%20%20%20r%3A%20int%2C%0A%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%82%92%E6%A7%8B%E7%AF%89%EF%BC%9A%E5%88%86%E5%89%B2%E7%B5%B1%E6%B2%BB%22%22%22%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E6%9C%A8%E5%8C%BA%E9%96%93%E3%81%8C%E7%A9%BA%E3%81%AA%E3%82%89%E7%B5%82%E4%BA%86%E3%81%99%E3%82%8B%0A%20%20%20%20if%20r%20-%20l%20%3C%200%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%88%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20root%20%3D%20TreeNode%28preorder%5Bi%5D%29%0A%20%20%20%20%23%20m%20%E3%82%92%E6%B1%82%E3%82%81%E3%81%A6%E5%B7%A6%E5%8F%B3%E9%83%A8%E5%88%86%E6%9C%A8%E3%82%92%E5%88%86%E5%89%B2%E3%81%99%E3%82%8B%0A%20%20%20%20m%20%3D%20inorder_map%5Bpreorder%5Bi%5D%5D%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%EF%BC%9A%E5%B7%A6%E9%83%A8%E5%88%86%E6%9C%A8%E3%82%92%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20root.left%20%3D%20dfs%28preorder%2C%20inorder_map%2C%20i%20%2B%201%2C%20l%2C%20m%20-%201%29%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%EF%BC%9A%E5%8F%B3%E9%83%A8%E5%88%86%E6%9C%A8%E3%82%92%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20root.right%20%3D%20dfs%28preorder%2C%20inorder_map%2C%20i%20%2B%201%20%2B%20m%20-%20l%2C%20m%20%2B%201%2C%20r%29%0A%20%20%20%20%23%20%E6%A0%B9%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20root%0A%0A%0Adef%20build_tree%28preorder%3A%20list%5Bint%5D%2C%20inorder%3A%20list%5Bint%5D%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%82%92%E6%A7%8B%E7%AF%89%22%22%22%0A%20%20%20%20%23%20inorder%20%E3%81%AE%E8%A6%81%E7%B4%A0%E3%81%8B%E3%82%89%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%B8%E3%81%AE%E5%AF%BE%E5%BF%9C%E3%82%92%E6%A0%BC%E7%B4%8D%E3%81%99%E3%82%8B%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20inorder_map%20%3D%20%7Bval%3A%20i%20for%20i%2C%20val%20in%20enumerate%28inorder%29%7D%0A%20%20%20%20root%20%3D%20dfs%28preorder%2C%20inorder_map%2C%200%2C%200%2C%20len%28inorder%29%20-%201%29%0A%20%20%20%20return%20root%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20preorder%20%3D%20%5B3%2C%209%2C%202%2C%201%2C%207%5D%0A%20%20%20%20inorder%20%3D%20%5B9%2C%203%2C%201%2C%202%2C%207%5D%0A%20%20%20%20print%28f%22%E5%89%8D%E9%A0%86%E8%B5%B0%E6%9F%BB%20%3D%20%7Bpreorder%7D%22%29%0A%20%20%20%20print%28f%22%E4%B8%AD%E9%A0%86%E8%B5%B0%E6%9F%BB%20%3D%20%7Binorder%7D%22%29%0A%20%20%20%20root%20%3D%20build_tree%28preorder%2C%20inorder%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=21&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%20%3D%200%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E5%80%A4%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%8F%B3%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%0Adef%20dfs%28%0A%20%20%20%20preorder%3A%20list%5Bint%5D%2C%0A%20%20%20%20inorder_map%3A%20dict%5Bint%2C%20int%5D%2C%0A%20%20%20%20i%3A%20int%2C%0A%20%20%20%20l%3A%20int%2C%0A%20%20%20%20r%3A%20int%2C%0A%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%82%92%E6%A7%8B%E7%AF%89%EF%BC%9A%E5%88%86%E5%89%B2%E7%B5%B1%E6%B2%BB%22%22%22%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E6%9C%A8%E5%8C%BA%E9%96%93%E3%81%8C%E7%A9%BA%E3%81%AA%E3%82%89%E7%B5%82%E4%BA%86%E3%81%99%E3%82%8B%0A%20%20%20%20if%20r%20-%20l%20%3C%200%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%88%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20root%20%3D%20TreeNode%28preorder%5Bi%5D%29%0A%20%20%20%20%23%20m%20%E3%82%92%E6%B1%82%E3%82%81%E3%81%A6%E5%B7%A6%E5%8F%B3%E9%83%A8%E5%88%86%E6%9C%A8%E3%82%92%E5%88%86%E5%89%B2%E3%81%99%E3%82%8B%0A%20%20%20%20m%20%3D%20inorder_map%5Bpreorder%5Bi%5D%5D%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%EF%BC%9A%E5%B7%A6%E9%83%A8%E5%88%86%E6%9C%A8%E3%82%92%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20root.left%20%3D%20dfs%28preorder%2C%20inorder_map%2C%20i%20%2B%201%2C%20l%2C%20m%20-%201%29%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%EF%BC%9A%E5%8F%B3%E9%83%A8%E5%88%86%E6%9C%A8%E3%82%92%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20root.right%20%3D%20dfs%28preorder%2C%20inorder_map%2C%20i%20%2B%201%20%2B%20m%20-%20l%2C%20m%20%2B%201%2C%20r%29%0A%20%20%20%20%23%20%E6%A0%B9%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20root%0A%0A%0Adef%20build_tree%28preorder%3A%20list%5Bint%5D%2C%20inorder%3A%20list%5Bint%5D%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%82%92%E6%A7%8B%E7%AF%89%22%22%22%0A%20%20%20%20%23%20inorder%20%E3%81%AE%E8%A6%81%E7%B4%A0%E3%81%8B%E3%82%89%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%B8%E3%81%AE%E5%AF%BE%E5%BF%9C%E3%82%92%E6%A0%BC%E7%B4%8D%E3%81%99%E3%82%8B%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20inorder_map%20%3D%20%7Bval%3A%20i%20for%20i%2C%20val%20in%20enumerate%28inorder%29%7D%0A%20%20%20%20root%20%3D%20dfs%28preorder%2C%20inorder_map%2C%200%2C%200%2C%20len%28inorder%29%20-%201%29%0A%20%20%20%20return%20root%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20preorder%20%3D%20%5B3%2C%209%2C%202%2C%201%2C%207%5D%0A%20%20%20%20inorder%20%3D%20%5B9%2C%203%2C%201%2C%202%2C%207%5D%0A%20%20%20%20print%28f%22%E5%89%8D%E9%A0%86%E8%B5%B0%E6%9F%BB%20%3D%20%7Bpreorder%7D%22%29%0A%20%20%20%20print%28f%22%E4%B8%AD%E9%A0%86%E8%B5%B0%E6%9F%BB%20%3D%20%7Binorder%7D%22%29%0A%20%20%20%20root%20%3D%20build_tree%28preorder%2C%20inorder%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=21&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>下図は二分木を構築する再帰過程を示しています。各ノードは下向きに「再帰していく」過程で生成され、各辺（参照）は上向きに「戻る」過程で張られます。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:9"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">&lt;1&gt;</label><label for="__tabbed_2_2">&lt;2&gt;</label><label for="__tabbed_2_3">&lt;3&gt;</label><label for="__tabbed_2_4">&lt;4&gt;</label><label for="__tabbed_2_5">&lt;5&gt;</label><label for="__tabbed_2_6">&lt;6&gt;</label><label for="__tabbed_2_7">&lt;7&gt;</label><label for="__tabbed_2_8">&lt;8&gt;</label><label for="__tabbed_2_9">&lt;9&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="二分木構築の再帰過程" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step1.png" /></p>
+<p><img alt="二分木を構築する再帰過程" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="built_tree_step2" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step2.png" /></p>
@@ -4660,14 +4929,14 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 12-8 &nbsp; 二分木構築の再帰過程 </p>
+<p align="center"> 図 12-8 &nbsp; 二分木を構築する再帰過程 </p>
 
-<p>各再帰関数の <code>preorder</code> と <code>inorder</code> シーケンスの分割は以下の図に示されています。</p>
-<p><img alt="各再帰関数での分割" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_overall.png" /></p>
-<p align="center"> 図 12-9 &nbsp; 各再帰関数での分割 </p>
+<p>各再帰関数における前順走査 <code>preorder</code> と中順走査 <code>inorder</code> の分割結果を下図に示します。</p>
+<p><img alt="各再帰関数での分割結果" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_overall.png" /></p>
+<p align="center"> 図 12-9 &nbsp; 各再帰関数での分割結果 </p>
 
-<p>二分木が <span class="arithmatex">\(n\)</span> 個のノードを持つと仮定すると、各ノードの初期化（再帰関数 <code>dfs()</code> の呼び出し）には <span class="arithmatex">\(O(1)\)</span> 時間がかかります。<strong>したがって、全体の時間計算量は <span class="arithmatex">\(O(n)\)</span> です</strong>。</p>
-<p>ハッシュテーブルは <code>inorder</code> 要素からそのインデックスへのマッピングを格納するため、<span class="arithmatex">\(O(n)\)</span> スペースが必要です。最悪の場合、二分木が連結リストに退化すると、再帰の深さは <span class="arithmatex">\(n\)</span> に達し、<span class="arithmatex">\(O(n)\)</span> のスタックスペースを消費する可能性があります。<strong>したがって、全体の空間計算量は <span class="arithmatex">\(O(n)\)</span> です</strong>。</p>
+<p>木のノード数を <span class="arithmatex">\(n\)</span> とすると、各ノードの初期化（再帰関数 <code>dfs()</code> の 1 回の実行）には <span class="arithmatex">\(O(1)\)</span> 時間かかります。<strong>したがって、全体の時間計算量は <span class="arithmatex">\(O(n)\)</span></strong> です。</p>
+<p>ハッシュテーブルには <code>inorder</code> の要素からインデックスへの対応を保存するため、空間計算量は <span class="arithmatex">\(O(n)\)</span> です。最悪の場合、すなわち二分木が連結リストに退化すると、再帰の深さは <span class="arithmatex">\(n\)</span> に達し、<span class="arithmatex">\(O(n)\)</span> のスタックフレーム空間を使用します。<strong>したがって、全体の空間計算量は <span class="arithmatex">\(O(n)\)</span></strong> です。</p>
 
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     href="../hanota_problem/"
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-    aria-label="次: 12.4 &amp;nbsp; ハノイの塔問題"
+    aria-label="次: 12.4 &amp;nbsp; ハノイの塔の問題"
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-        12.4 &nbsp; ハノイの塔問題
+        12.4 &nbsp; ハノイの塔の問題
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@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
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-        <title>12.1 分割統治アルゴリズム - Hello アルゴリズム</title>
+        <title>12.1 分割統治法 - Hello アルゴリズム</title>
       
     
     
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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         <div class="md-header__topic" data-md-component="header-topic">
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-              12.1 &nbsp; 分割統治アルゴリズム
+              12.1 &nbsp; 分割統治法
             
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-    序
+    はじめに
   
 
     
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+    はじめに
   
 
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-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
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-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
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-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
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-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
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-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
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+    6.1 &nbsp; ハッシュテーブル
   
 
     
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
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-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
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-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
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-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
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-        12.1.1 &nbsp; 分割統治問題を特定する方法
+        12.1.1 &nbsp; 分割統治法の問題を見極めるには
       
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-        12.1.2 &nbsp; 分割統治による効率の向上
+        12.1.2 &nbsp; 分割統治法で効率を高める
       
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-    <nav class="md-nav" aria-label="12.1.2 分割統治による効率の向上">
+    <nav class="md-nav" aria-label="12.1.2 分割統治法で効率を高める">
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+        1. &nbsp; 操作回数の最適化
       
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+        2. &nbsp; 並列計算の最適化
       
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-        12.1.3 &nbsp; 分割統治の一般的な応用
+        12.1.3 &nbsp; 分割統治法の代表的な応用
       
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+    12.3 &nbsp; 二分木の構築問題
   
 
     
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+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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+    13.3 &nbsp; 部分和問題
   
 
     
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+    14.1 &nbsp; 動的計画法入門
   
 
     
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+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
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+    15.1 &nbsp; 貪欲法
   
 
     
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+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
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-        12.1.2 &nbsp; 分割統治による効率の向上
+        12.1.2 &nbsp; 分割統治法で効率を高める
       
     </span>
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-    <nav class="md-nav" aria-label="12.1.2 分割統治による効率の向上">
+    <nav class="md-nav" aria-label="12.1.2 分割統治法で効率を高める">
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+        12.1.3 &nbsp; 分割統治法の代表的な応用
       
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@@ -4432,45 +4432,45 @@
 
 
 <!-- Page content -->
-<h1 id="121">12.1 &nbsp; 分割統治アルゴリズム<a class="headerlink" href="#121" title="Permanent link">&para;</a></h1>
-<p><u>分割統治</u>は重要で人気のあるアルゴリズム戦略です。名前が示すように、アルゴリズムは通常再帰的に実装され、「分割」と「統治」の2つのステップから構成されます。</p>
+<h1 id="121">12.1 &nbsp; 分割統治法<a class="headerlink" href="#121" title="Permanent link">&para;</a></h1>
+<p><u>分割統治法（divide and conquer）</u>は、問題を分けて統べるという意味であり、非常に重要で一般的なアルゴリズム戦略です。分割統治法は通常、再帰に基づいて実装され、「分」と「治」の 2 つのステップから構成されます。</p>
 <ol>
-<li><strong>分割（分割段階）</strong>：元の問題を再帰的に2つ以上の小さな部分問題に分解し、最小の部分問題に到達するまで続けます。</li>
-<li><strong>統治（マージ段階）</strong>：解決方法が既知の最小の部分問題から開始し、部分問題の解をボトムアップ方式でマージして元の問題の解を構築します。</li>
+<li><strong>分（分割段階）</strong>：元の問題を 2 つ以上の部分問題へ再帰的に分解し、最小の部分問題に到達した時点で停止します。</li>
+<li><strong>治（統合段階）</strong>：解が既知である最小の部分問題から始めて、部分問題の解を下から上へ統合し、元の問題の解を構築します。</li>
 </ol>
 <p>以下の図に示すように、「マージソート」は分割統治戦略の典型的な応用の一つです。</p>
 <ol>
-<li><strong>分割</strong>：元の配列（元の問題）を再帰的に2つの副配列（部分問題）に分割し、副配列が1つの要素のみになるまで（最小の部分問題）続けます。</li>
-<li><strong>統治</strong>：順序付けられた副配列（部分問題の解）をボトムアップでマージして、順序付けられた元の配列（元の問題の解）を取得します。</li>
+<li><strong>分</strong>：元の配列（元の問題）を 2 つの部分配列（部分問題）へ再帰的に分割し、部分配列に要素が 1 つだけ残るまで続けます。</li>
+<li><strong>治</strong>：整列済みの部分配列（部分問題の解）を下から上へ統合し、整列済みの元の配列（元の問題の解）を得ます。</li>
 </ol>
 <p><img alt="マージソートの分割統治戦略" class="animation-figure" src="../divide_and_conquer.assets/divide_and_conquer_merge_sort.png" /></p>
 <p align="center"> 図 12-1 &nbsp; マージソートの分割統治戦略 </p>
 
-<h2 id="1211">12.1.1 &nbsp; 分割統治問題を特定する方法<a class="headerlink" href="#1211" title="Permanent link">&para;</a></h2>
-<p>問題が分割統治解決に適しているかどうかは、通常以下の基準に基づいて決定できます。</p>
+<h2 id="1211">12.1.1 &nbsp; 分割統治法の問題を見極めるには<a class="headerlink" href="#1211" title="Permanent link">&para;</a></h2>
+<p>ある問題が分割統治法で解くのに適しているかどうかは、通常、次の判断基準を参考にできます。</p>
 <ol>
-<li><strong>問題をより小さなものに分解できる</strong>：元の問題をより小さく類似した部分問題に分割でき、そのような過程を同じ方法で再帰的に実行できます。</li>
-<li><strong>部分問題は独立している</strong>：部分問題間に重複がなく、独立しており、個別に解決できます。</li>
-<li><strong>部分問題の解をマージできる</strong>：元の問題の解は、部分問題の解を組み合わせることで導出されます。</li>
+<li><strong>問題は分解できる</strong>：元の問題は、より小さく類似した部分問題に分解でき、同じ方法で再帰的に分割できます。</li>
+<li><strong>部分問題は独立している</strong>：部分問題同士に重複がなく、相互依存もないため、独立して解決できます。</li>
+<li><strong>部分問題の解は統合できる</strong>：元の問題の解は、部分問題の解を統合することで得られます。</li>
 </ol>
-<p>明らかに、マージソートはこれら3つの基準を満たしています。</p>
+<p>明らかに、マージソートは以上の 3 つの判断基準を満たしています。</p>
 <ol>
-<li><strong>問題をより小さなものに分解できる</strong>：配列（元の問題）を再帰的に2つの副配列（部分問題）に分割します。</li>
-<li><strong>部分問題は独立している</strong>：各副配列は独立してソートできます（部分問題は独立して解決できます）。</li>
-<li><strong>部分問題の解をマージできる</strong>：2つの順序付けられた副配列（部分問題の解）を1つの順序付けられた配列（元の問題の解）にマージできます。</li>
+<li><strong>問題は分解できる</strong>：配列（元の問題）を 2 つの部分配列（部分問題）へ再帰的に分割します。</li>
+<li><strong>部分問題は独立している</strong>：各部分配列は独立にソートできます（部分問題は独立に解けます）。</li>
+<li><strong>部分問題の解は統合できる</strong>：2 つの整列済み部分配列（部分問題の解）は、1 つの整列済み配列（元の問題の解）に統合できます。</li>
 </ol>
-<h2 id="1212">12.1.2 &nbsp; 分割統治による効率の向上<a class="headerlink" href="#1212" title="Permanent link">&para;</a></h2>
-<p><strong>分割統治戦略はアルゴリズム問題を効果的に解決するだけでなく、しばしば効率を向上させます</strong>。ソートアルゴリズムでは、クイックソート、マージソート、ヒープソートは、分割統治戦略を適用しているため、選択ソート、バブルソート、挿入ソートよりも高速です。</p>
-<p>私たちの心には疑問があるかもしれません：<strong>なぜ分割統治はアルゴリズムの効率を向上させることができ、その根本的な論理は何ですか？</strong> つまり、問題を部分問題に分解し、それらを解決し、それらの解を組み合わせて元の問題に対処することが、元の問題を直接解決するよりも効率的である理由は何ですか？この質問は2つの側面から分析できます：操作数と並列計算。</p>
-<h3 id="1">1. &nbsp; 操作数の最適化<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>「バブルソート」を例にとると、長さ <span class="arithmatex">\(n\)</span> の配列を処理するのに <span class="arithmatex">\(O(n^2)\)</span> 時間が必要です。以下の図に示すように、配列を中点から2つの副配列に分割するとします。そのような分割には <span class="arithmatex">\(O(n)\)</span> 時間が必要です。各副配列のソートには <span class="arithmatex">\(O((n / 2)^2)\)</span> 時間が必要です。そして2つの副配列のマージには <span class="arithmatex">\(O(n)\)</span> 時間が必要です。したがって、全体の時間計算量は：</p>
+<h2 id="1212">12.1.2 &nbsp; 分割統治法で効率を高める<a class="headerlink" href="#1212" title="Permanent link">&para;</a></h2>
+<p><strong>分割統治法はアルゴリズムの問題を効果的に解けるだけでなく、多くの場合アルゴリズムの効率も高められます</strong>。ソートアルゴリズムでは、クイックソート、マージソート、ヒープソートが選択ソート、バブルソート、挿入ソートより高速ですが、これは分割統治戦略を適用しているためです。</p>
+<p>ここで次の疑問が生じます。<strong>なぜ分割統治法はアルゴリズム効率を高められるのでしょうか。その根本的な仕組みは何でしょうか</strong>？言い換えると、大きな問題を複数の部分問題に分解し、部分問題を解き、それらの解を統合して元の問題の解にするという手順は、なぜ元の問題を直接解くより効率的なのでしょうか。この問題は、操作回数と並列計算の 2 つの観点から議論できます。</p>
+<h3 id="1">1. &nbsp; 操作回数の最適化<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>「バブルソート」を例に取ると、長さ <span class="arithmatex">\(n\)</span> の配列を処理するのに <span class="arithmatex">\(O(n^2)\)</span> の時間がかかります。以下の図のように、配列を中央で 2 つの部分配列に分けると仮定すると、分割には <span class="arithmatex">\(O(n)\)</span> の時間、各部分配列のソートには <span class="arithmatex">\(O((n / 2)^2)\)</span> の時間、2 つの部分配列の統合には <span class="arithmatex">\(O(n)\)</span> の時間が必要で、全体の時間計算量は次のようになります：</p>
 <div class="arithmatex">\[
 O(n + (\frac{n}{2})^2 \times 2 + n) = O(\frac{n^2}{2} + 2n)
 \]</div>
 <p><img alt="配列分割前後のバブルソート" class="animation-figure" src="../divide_and_conquer.assets/divide_and_conquer_bubble_sort.png" /></p>
 <p align="center"> 図 12-2 &nbsp; 配列分割前後のバブルソート </p>
 
-<p>以下の不等式を計算してみましょう。左側は分割前の総操作数を表し、右側は分割後の総操作数をそれぞれ表します：</p>
+<p>次に、以下の不等式を計算します。左辺と右辺はそれぞれ、分割前と分割後の操作総数です：</p>
 <div class="arithmatex">\[
 \begin{aligned}
 n^2 &amp; &gt; \frac{n^2}{2} + 2n \newline
@@ -4478,36 +4478,36 @@ n^2 - \frac{n^2}{2} - 2n &amp; &gt; 0 \newline
 n(n - 4) &amp; &gt; 0
 \end{aligned}
 \]</div>
-<p><strong>これは <span class="arithmatex">\(n &gt; 4\)</span> の場合、分割後の操作数が少なく、より良いパフォーマンスにつながることを意味します</strong>。分割後の時間計算量は依然として二次 <span class="arithmatex">\(O(n^2)\)</span> ですが、計算量の定数係数が減少していることに注意してください。</p>
-<p>さらに進むことができます。<strong>副配列をその中点からさらに2つの副配列に分割し続けて、副配列が1つの要素のみになるまで続けたらどうでしょうか？</strong> このアイデアは実際には「マージソート」で、時間計算量は <span class="arithmatex">\(O(n \log n)\)</span> です。</p>
-<p>少し違うことを試してみましょう。<strong>2つではなく、より多くの分割に分割したらどうでしょうか？</strong> 例えば、元の配列を <span class="arithmatex">\(k\)</span> 個の副配列に均等に分割しますか？このアプローチは「バケットソート」と非常に似ており、大量のデータのソートに非常に適しています。理論的には、時間計算量は <span class="arithmatex">\(O(n + k)\)</span> に達することができます。</p>
-<h3 id="2">2. &nbsp; 並列計算による最適化<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>分割統治によって生成される部分問題は互いに独立していることが分かっています。<strong>これは、それらを並列で解決できることを意味します。</strong> その結果、分割統治はアルゴリズムの時間計算量を減らすだけでなく、<strong>現代のオペレーティングシステムによる並列最適化も促進します。</strong></p>
-<p>並列最適化は、複数のコアやプロセッサを持つ環境で特に効果的です。システムが複数の部分問題を同時に処理できるため、計算リソースを完全に活用し、全体的な実行時間が大幅に短縮されます。</p>
-<p>例えば、以下の図に示す「バケットソート」では、大量のデータを様々なバケットに均等に分解します。各バケットのソート作業は、利用可能な計算ユニットに割り当てることができます。すべての作業が完了すると、すべてのソートされたバケットがマージされて最終結果が生成されます。</p>
+<p><strong>これは、<span class="arithmatex">\(n &gt; 4\)</span> のときに分割後の操作回数の方が少なくなり、ソート効率が高くなることを意味します</strong>。ただし、分割後の時間計算量は依然として 2 次の <span class="arithmatex">\(O(n^2)\)</span> であり、計算量の定数項が小さくなっただけです。</p>
+<p>さらに考えると、<strong>部分配列を中央からさらに 2 つの部分配列へと分割し続け</strong>、部分配列に要素が 1 つだけ残るまで分割を止めないとしたらどうでしょうか。この考え方がまさに「マージソート」であり、時間計算量は <span class="arithmatex">\(O(n \log n)\)</span> です。</p>
+<p>さらに、<strong>分割点をいくつか増やして</strong>、元の配列を平均的に <span class="arithmatex">\(k\)</span> 個の部分配列に分けるとしたらどうでしょうか。この状況は「バケットソート」と非常によく似ており、大量データのソートに非常に適しています。理論上の時間計算量は <span class="arithmatex">\(O(n + k)\)</span> に達します。</p>
+<h3 id="2">2. &nbsp; 並列計算の最適化<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>分割統治法で生成される部分問題は互いに独立しているため、<strong>通常は並列に解くことができます</strong>。つまり、分割統治法はアルゴリズムの時間計算量を下げられるだけでなく、<strong>オペレーティングシステムの並列最適化にも有利です</strong>。</p>
+<p>並列最適化は、マルチコアまたはマルチプロセッサ環境で特に有効です。システムが複数の部分問題を同時に処理でき、計算資源をより十分に活用できるため、全体の実行時間を大幅に短縮できます。</p>
+<p>たとえば、以下の図に示す「バケットソート」では、大量のデータを各バケットに均等に割り当てることで、すべてのバケットのソート処理を各計算ユニットに分散し、完了後に結果を統合できます。</p>
 <p><img alt="バケットソートの並列計算" class="animation-figure" src="../divide_and_conquer.assets/divide_and_conquer_parallel_computing.png" /></p>
 <p align="center"> 図 12-3 &nbsp; バケットソートの並列計算 </p>
 
-<h2 id="1213">12.1.3 &nbsp; 分割統治の一般的な応用<a class="headerlink" href="#1213" title="Permanent link">&para;</a></h2>
-<p>分割統治は多くの古典的なアルゴリズム問題を解決するために使用できます。</p>
+<h2 id="1213">12.1.3 &nbsp; 分割統治法の代表的な応用<a class="headerlink" href="#1213" title="Permanent link">&para;</a></h2>
+<p>一方では、分割統治法は多くの古典的なアルゴリズム問題を解くのに使えます。</p>
 <ul>
-<li><strong>最近点対の発見</strong>：このアルゴリズムは点の集合を2つの半分に分割することで動作します。そして各半分で再帰的に最近点対を見つけます。最後に、2つの半分にまたがるペアを考慮して、全体の最近点対を見つけます。</li>
-<li><strong>大整数の乗算</strong>：一つのアルゴリズムはKaratsubaと呼ばれます。大整数の乗算をいくつかの小さな整数の乗算と加算に分解します。</li>
-<li><strong>行列の乗算</strong>：一例はStrassenアルゴリズムです。大きな行列の乗算を複数の小さな行列の乗算と加算に分解します。</li>
-<li><strong>ハノイの塔問題</strong>：ハノイの塔問題は再帰的に解決でき、分割統治戦略の典型的な応用です。</li>
-<li><strong>転倒対の解決</strong>：シーケンスで、前の数が後の数より大きい場合、これら2つの数は転倒対を構成します。転倒対問題の解決は、マージソートの助けを借りて、分割統治のアイデアを利用できます。</li>
+<li><strong>最近点対探索</strong>：このアルゴリズムは、まず点集合を 2 つに分け、それぞれの部分における最近点対を求め、最後に 2 つの部分をまたぐ最近点対を求めます。</li>
+<li><strong>大整数乗算</strong>：たとえば Karatsuba 法では、大整数の乗算を、より小さな整数どうしのいくつかの乗算と加算に分解します。</li>
+<li><strong>行列乗算</strong>：たとえば Strassen 法では、大きな行列の乗算を、複数の小さな行列の乗算と加算に分解します。</li>
+<li><strong>ハノイの塔問題</strong>：ハノイの塔問題は再帰によって解くことができ、これは典型的な分割統治戦略の応用です。</li>
+<li><strong>反転対の計算</strong>：ある数列で前の数が後ろの数より大きい場合、その 2 つの数は反転対を構成します。反転対の問題は、分割統治の考え方を利用し、マージソートを用いて解けます。</li>
 </ul>
-<p>分割統治はアルゴリズムとデータ構造の設計にも広く応用されています。</p>
+<p>他方で、分割統治法はアルゴリズムとデータ構造の設計にも非常に広く応用されています。</p>
 <ul>
-<li><strong>二分探索</strong>：二分探索は、ソート済み配列を中点インデックスから2つの半分に分割します。そして、ターゲット値と中間要素値の比較結果に基づいて、一方の半分が破棄されます。同じプロセスで残りの半分で検索が続行され、ターゲットが見つかるか残りの要素がなくなるまで続きます。</li>
-<li><strong>マージソート</strong>：この節の冒頭ですでに紹介したため、さらなる詳述は不要です。</li>
-<li><strong>クイックソート</strong>：クイックソートはピボット値を選択して配列を2つの副配列に分割し、一方はピボットより小さい要素、もう一方はピボットより大きい要素を持ちます。このプロセスは、これら2つの副配列のそれぞれに対して、1つの要素のみを保持するまで続きます。</li>
-<li><strong>バケットソート</strong>：バケットソートの基本的なアイデアは、データを複数のバケットに分散させることです。各バケット内の要素をソートした後、バケットから順序よく要素を取得して順序付けられた配列を取得します。</li>
-<li><strong>木</strong>：例えば、二分探索木、AVL木、赤黒木、B木、B+木など。その操作（検索、挿入、削除）はすべて分割統治戦略の応用と見なすことができます。</li>
-<li><strong>ヒープ</strong>：ヒープは特別なタイプの完全二分木です。その様々な操作（挿入、削除、ヒープ化）は、実際に分割統治のアイデアを含意しています。</li>
-<li><strong>ハッシュテーブル</strong>：ハッシュテーブルは直接分割統治を適用しませんが、一部のハッシュ衝突解決ソリューションは間接的にこの戦略を適用します。例えば、チェイン法の長いリストは、クエリ効率を向上させるために赤黒木に変換される場合があります。</li>
+<li><strong>二分探索</strong>：二分探索では、整列済み配列を中央のインデックスで 2 つに分け、目標値と中央要素の比較結果に基づいてどちらの半区間を除外するかを決め、残った区間で同じ二分操作を行います。</li>
+<li><strong>マージソート</strong>：本節の冒頭で紹介したため、ここでは繰り返しません。</li>
+<li><strong>クイックソート</strong>：クイックソートは基準値を 1 つ選び、配列を、基準値より小さい要素の部分配列と、基準値より大きい要素の部分配列に分け、その後それぞれに対して同じ分割操作を行い、部分配列に要素が 1 つだけ残るまで続けます。</li>
+<li><strong>バケットソート</strong>：バケットソートの基本的な考え方は、データを複数のバケットに分散し、各バケット内の要素をソートしたうえで、各バケットの要素を順に取り出して整列済み配列を得ることです。</li>
+<li><strong>木構造</strong>：たとえば二分探索木、AVL 木、赤黒木、B 木、B+ 木などでは、探索・挿入・削除などの操作をいずれも分割統治戦略の応用とみなせます。</li>
+<li><strong>ヒープ</strong>：ヒープは特殊な完全二分木であり、挿入、削除、ヒープ化などの各種操作には、実際には分割統治の考え方が含まれています。</li>
+<li><strong>ハッシュテーブル</strong>：ハッシュテーブル自体は分割統治を直接適用しているわけではありませんが、いくつかのハッシュ衝突解決法では間接的に分割統治戦略が使われています。たとえば、連鎖アドレス法における長い連結リストは、検索効率を高めるために赤黒木へ変換されます。</li>
 </ul>
-<p>**分割統治は巧妙に浸透するアルゴリズムアイデア**であり、様々なアルゴリズムとデータ構造に組み込まれていることが分かります。</p>
+<p>このように、**分割統治法は「静かに物を潤す」ようなアルゴリズム思想**であり、さまざまなアルゴリズムやデータ構造の中に潜んでいます。</p>
 
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@@ -6,7 +6,7 @@
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-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
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-        <title>12.4 ハノイの塔問題 - Hello アルゴリズム</title>
+        <title>12.4 ハノイの塔の問題 - Hello アルゴリズム</title>
       
     
     
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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           </label>
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   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1942,7 +1942,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2105,7 +2105,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2491,7 +2491,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2547,7 +2547,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2575,7 +2575,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3115,7 +3115,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3171,7 +3171,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3208,7 +3208,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3226,7 +3226,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3267,7 +3267,7 @@
   <a href="#2" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2. &nbsp; 部分問題の分解
+        2. &nbsp; 部分問題への分解
       
     </span>
   </a>
@@ -3278,7 +3278,7 @@
   <a href="#3" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3. &nbsp; コード実装
+        3. &nbsp; コードの実装
       
     </span>
   </a>
@@ -3473,7 +3473,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3501,7 +3501,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3642,7 +3642,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3670,7 +3670,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3698,7 +3698,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3726,7 +3726,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3919,7 +3919,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4164,7 +4164,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4321,7 +4321,7 @@
   <a href="#2" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2. &nbsp; 部分問題の分解
+        2. &nbsp; 部分問題への分解
       
     </span>
   </a>
@@ -4332,7 +4332,7 @@
   <a href="#3" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3. &nbsp; コード実装
+        3. &nbsp; コードの実装
       
     </span>
   </a>
@@ -4376,45 +4376,45 @@
 
 
 <!-- Page content -->
-<h1 id="124">12.4 &nbsp; ハノイの塔問題<a class="headerlink" href="#124" title="Permanent link">&para;</a></h1>
-<p>マージソートと二分木構築の両方で、元の問題を2つの部分問題に分解し、それぞれが元の問題のサイズの半分でした。しかし、ハノイの塔では、異なる分解戦略を採用します。</p>
+<h1 id="124">12.4 &nbsp; ハノイの塔の問題<a class="headerlink" href="#124" title="Permanent link">&para;</a></h1>
+<p>マージソートや二分木の構築では、いずれも元の問題を元問題の半分の規模をもつ 2 つの部分問題に分解していました。しかし、ハノイの塔の問題では、異なる分解戦略を採用します。</p>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
-<p>3つの柱があり、それぞれ <code>A</code>、<code>B</code>、<code>C</code> と表記されます。最初、柱 <code>A</code> には <span class="arithmatex">\(n\)</span> 枚の円盤があり、上から下に向かって昇順のサイズで配置されています。私たちのタスクは、これらの <span class="arithmatex">\(n\)</span> 枚の円盤を柱 <code>C</code> に移動し、元の順序を維持することです（以下の図に示すように）。移動中には以下のルールが適用されます：</p>
+<p>3 本の柱があり、それぞれを <code>A</code>、<code>B</code>、<code>C</code> とします。初期状態では、柱 <code>A</code> に <span class="arithmatex">\(n\)</span> 枚の円盤が通されており、上から下へ小さい順に並んでいます。私たちの課題は、この <span class="arithmatex">\(n\)</span> 枚の円盤を柱 <code>C</code> に移し、元の順序を保つことです（以下の図のとおり）。円盤を移動する際には、次のルールに従う必要があります。</p>
 <ol>
-<li>円盤は柱の上部からのみ取り除くことができ、別の柱の上部に置く必要があります。</li>
-<li>一度に移動できるのは1枚の円盤のみです。</li>
-<li>小さい円盤は常に大きい円盤の上にある必要があります。</li>
+<li>円盤は 1 本の柱の頂上から取り出し、別の柱の頂上に置くことしかできません。</li>
+<li>1 回に移動できる円盤は 1 枚だけです。</li>
+<li>小さい円盤は常に大きい円盤の上になければなりません。</li>
 </ol>
 </div>
-<p><img alt="ハノイの塔の例" class="animation-figure" src="../hanota_problem.assets/hanota_example.png" /></p>
-<p align="center"> 図 12-10 &nbsp; ハノイの塔の例 </p>
+<p><img alt="ハノイの塔の問題の例" class="animation-figure" src="../hanota_problem.assets/hanota_example.png" /></p>
+<p align="center"> 図 12-10 &nbsp; ハノイの塔の問題の例 </p>
 
-<p><strong>サイズ <span class="arithmatex">\(i\)</span> のハノイの塔問題を <span class="arithmatex">\(f(i)\)</span> と表記します</strong>。例えば、<span class="arithmatex">\(f(3)\)</span> は3枚の円盤を柱 <code>A</code> から柱 <code>C</code> に移動することを表します。</p>
+<p><strong>規模が <span class="arithmatex">\(i\)</span> のハノイの塔の問題を <span class="arithmatex">\(f(i)\)</span> と表します</strong> 。たとえば <span class="arithmatex">\(f(3)\)</span> は、<span class="arithmatex">\(3\)</span> 枚の円盤を <code>A</code> から <code>C</code> へ移動するハノイの塔の問題を表します。</p>
 <h3 id="1">1. &nbsp; 基本ケースを考える<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>以下の図に示すように、問題 <span class="arithmatex">\(f(1)\)</span>（円盤が1枚のみ）については、<code>A</code> から <code>C</code> に直接移動できます。</p>
+<p>以下の図に示すように、問題 <span class="arithmatex">\(f(1)\)</span> 、すなわち円盤が 1 枚だけの場合は、それを <code>A</code> から <code>C</code> へ直接移動すれば済みます。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:2"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="サイズ1の問題の解" class="animation-figure" src="../hanota_problem.assets/hanota_f1_step1.png" /></p>
+<p><img alt="規模 1 の問題の解" class="animation-figure" src="../hanota_problem.assets/hanota_f1_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="hanota_f1_step2" class="animation-figure" src="../hanota_problem.assets/hanota_f1_step2.png" /></p>
 </div>
 </div>
 </div>
-<p align="center"> 図 12-11 &nbsp; サイズ1の問題の解 </p>
+<p align="center"> 図 12-11 &nbsp; 規模 1 の問題の解 </p>
 
-<p><span class="arithmatex">\(f(2)\)</span>（円盤が2枚）については、**柱 <code>B</code> の助けを借りて小さい円盤を大きい円盤の上に保つ**必要があります。以下の図に示すように：</p>
+<p>以下の図に示すように、問題 <span class="arithmatex">\(f(2)\)</span> 、すなわち円盤が 2 枚ある場合は、<strong>小さい円盤が常に大きい円盤の上にある条件を満たすため、<code>B</code> を借りて移動を行う必要があります</strong>。</p>
 <ol>
-<li>まず、小さい円盤を <code>A</code> から <code>B</code> に移動します。</li>
-<li>次に、大きい円盤を <code>A</code> から <code>C</code> に移動します。</li>
-<li>最後に、小さい円盤を <code>B</code> から <code>C</code> に移動します。</li>
+<li>まず上の小さい円盤を <code>A</code> から <code>B</code> へ移します。</li>
+<li>次に大きい円盤を <code>A</code> から <code>C</code> へ移します。</li>
+<li>最後に小さい円盤を <code>B</code> から <code>C</code> へ移します。</li>
 </ol>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:4"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">&lt;1&gt;</label><label for="__tabbed_2_2">&lt;2&gt;</label><label for="__tabbed_2_3">&lt;3&gt;</label><label for="__tabbed_2_4">&lt;4&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="サイズ2の問題の解" class="animation-figure" src="../hanota_problem.assets/hanota_f2_step1.png" /></p>
+<p><img alt="規模 2 の問題の解" class="animation-figure" src="../hanota_problem.assets/hanota_f2_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="hanota_f2_step2" class="animation-figure" src="../hanota_problem.assets/hanota_f2_step2.png" /></p>
@@ -4427,21 +4427,21 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 12-12 &nbsp; サイズ2の問題の解 </p>
+<p align="center"> 図 12-12 &nbsp; 規模 2 の問題の解 </p>
 
-<p><span class="arithmatex">\(f(2)\)</span> を解決する過程は次のように要約できます：<strong><code>B</code> の助けを借りて2枚の円盤を <code>A</code> から <code>C</code> に移動する</strong>。ここで、<code>C</code> をターゲット柱、<code>B</code> をバッファ柱と呼びます。</p>
-<h3 id="2">2. &nbsp; 部分問題の分解<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>問題 <span class="arithmatex">\(f(3)\)</span>（つまり、円盤が3枚の場合）については、状況がやや複雑になります。</p>
-<p>すでに <span class="arithmatex">\(f(1)\)</span> と <span class="arithmatex">\(f(2)\)</span> の解が分かっているので、分割統治の観点を採用し、<strong><code>A</code> の上の2枚の円盤を1つの単位として扱い</strong>、以下の図に示すステップを実行できます。これにより、3枚の円盤を <code>A</code> から <code>C</code> に正常に移動できます。</p>
+<p>問題 <span class="arithmatex">\(f(2)\)</span> を解く過程は、**2 枚の円盤を <code>B</code> を介して <code>A</code> から <code>C</code> へ移す**と要約できます。このとき、<code>C</code> を目標の柱、<code>B</code> を補助の柱と呼びます。</p>
+<h3 id="2">2. &nbsp; 部分問題への分解<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>問題 <span class="arithmatex">\(f(3)\)</span> 、すなわち円盤が 3 枚ある場合になると、状況はやや複雑になります。</p>
+<p><span class="arithmatex">\(f(1)\)</span> と <span class="arithmatex">\(f(2)\)</span> の解が既知なので、分割統治の観点から、<strong><code>A</code> の上部にある 2 枚の円盤をひとまとまりとみなして</strong>、次の図の手順を実行できます。こうして 3 枚の円盤を <code>A</code> から <code>C</code> へ順調に移動できます。</p>
 <ol>
-<li><code>B</code> をターゲット柱、<code>C</code> をバッファ柱として、2枚の円盤を <code>A</code> から <code>B</code> に移動します。</li>
-<li>残りの円盤を <code>A</code> から直接 <code>C</code> に移動します。</li>
-<li><code>C</code> をターゲット柱、<code>A</code> をバッファ柱として、2枚の円盤を <code>B</code> から <code>C</code> に移動します。</li>
+<li><code>B</code> を目標の柱、<code>C</code> を補助の柱として、2 枚の円盤を <code>A</code> から <code>B</code> へ移します。</li>
+<li><code>A</code> に残った 1 枚の円盤を <code>A</code> から <code>C</code> へ直接移動します。</li>
+<li><code>C</code> を目標の柱、<code>A</code> を補助の柱として、2 枚の円盤を <code>B</code> から <code>C</code> へ移します。</li>
 </ol>
 <div class="tabbed-set tabbed-alternate" data-tabs="3:4"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">&lt;1&gt;</label><label for="__tabbed_3_2">&lt;2&gt;</label><label for="__tabbed_3_3">&lt;3&gt;</label><label for="__tabbed_3_4">&lt;4&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="サイズ3の問題の解" class="animation-figure" src="../hanota_problem.assets/hanota_f3_step1.png" /></p>
+<p><img alt="規模 3 の問題の解" class="animation-figure" src="../hanota_problem.assets/hanota_f3_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="hanota_f3_step2" class="animation-figure" src="../hanota_problem.assets/hanota_f3_step2.png" /></p>
@@ -4454,206 +4454,458 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 12-13 &nbsp; サイズ3の問題の解 </p>
+<p align="center"> 図 12-13 &nbsp; 規模 3 の問題の解 </p>
 
-<p>本質的に、<strong><span class="arithmatex">\(f(3)\)</span> を2つの <span class="arithmatex">\(f(2)\)</span> 部分問題と1つの <span class="arithmatex">\(f(1)\)</span> 部分問題に分解します</strong>。これら3つの部分問題を順次解決することで、元の問題が解決され、部分問題が独立しており、それらの解をマージできることを示しています。</p>
-<p>ここから、以下の図に示すハノイの塔の分割統治戦略を要約できます。元の問題 <span class="arithmatex">\(f(n)\)</span> を2つの部分問題 <span class="arithmatex">\(f(n-1)\)</span> と1つの部分問題 <span class="arithmatex">\(f(1)\)</span> に分割し、以下の順序でこれら3つの部分問題を解決します：</p>
+<p>本質的には、<strong>問題 <span class="arithmatex">\(f(3)\)</span> を 2 つの部分問題 <span class="arithmatex">\(f(2)\)</span> と 1 つの部分問題 <span class="arithmatex">\(f(1)\)</span> に分けています</strong> 。この 3 つの部分問題を順に解けば、元の問題も解決されます。これは、部分問題が独立しており、解を組み合わせられることを示しています。</p>
+<p>ここまでで、次の図に示すハノイの塔の問題を解く分割統治戦略をまとめられます。元の問題 <span class="arithmatex">\(f(n)\)</span> を 2 つの部分問題 <span class="arithmatex">\(f(n-1)\)</span> と 1 つの部分問題 <span class="arithmatex">\(f(1)\)</span> に分け、次の順序でこの 3 つの部分問題を解きます。</p>
 <ol>
-<li><code>C</code> をバッファとして使用し、<span class="arithmatex">\(n-1\)</span> 枚の円盤を <code>A</code> から <code>B</code> に移動します。</li>
-<li>残りの円盤を <code>A</code> から直接 <code>C</code> に移動します。</li>
-<li><code>A</code> をバッファとして使用し、<span class="arithmatex">\(n-1\)</span> 枚の円盤を <code>B</code> から <code>C</code> に移動します。</li>
+<li><span class="arithmatex">\(n-1\)</span> 枚の円盤を <code>C</code> を介して <code>A</code> から <code>B</code> へ移します。</li>
+<li>残り <span class="arithmatex">\(1\)</span> 枚の円盤を <code>A</code> から <code>C</code> へ直接移します。</li>
+<li><span class="arithmatex">\(n-1\)</span> 枚の円盤を <code>A</code> を介して <code>B</code> から <code>C</code> へ移します。</li>
 </ol>
-<p>各 <span class="arithmatex">\(f(n-1)\)</span> 部分問題について、<strong>同じ再帰分割を適用でき</strong>、最小の部分問題 <span class="arithmatex">\(f(1)\)</span> に到達するまで続けます。<span class="arithmatex">\(f(1)\)</span> は単一の移動のみが必要であることがすでに分かっているため、解決するのは簡単です。</p>
-<p><img alt="ハノイの塔を解決するための分割統治戦略" class="animation-figure" src="../hanota_problem.assets/hanota_divide_and_conquer.png" /></p>
-<p align="center"> 図 12-14 &nbsp; ハノイの塔を解決するための分割統治戦略 </p>
+<p>この 2 つの部分問題 <span class="arithmatex">\(f(n-1)\)</span> は、<strong>同じ方法で再帰的に分割できます</strong>。最小の部分問題 <span class="arithmatex">\(f(1)\)</span> に到達するまでこれを続けます。一方、<span class="arithmatex">\(f(1)\)</span> の解は既知であり、1 回の移動操作だけで済みます。</p>
+<p><img alt="ハノイの塔の問題を解く分割統治戦略" class="animation-figure" src="../hanota_problem.assets/hanota_divide_and_conquer.png" /></p>
+<p align="center"> 図 12-14 &nbsp; ハノイの塔の問題を解く分割統治戦略 </p>
 
-<h3 id="3">3. &nbsp; コード実装<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
-<p>コードでは、再帰関数 <code>dfs(i, src, buf, tar)</code> を定義します。これは柱 <code>src</code> から上の <span class="arithmatex">\(i\)</span> 枚の円盤を柱 <code>tar</code> に移動し、柱 <code>buf</code> をバッファとして使用します：</p>
+<h3 id="3">3. &nbsp; コードの実装<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
+<p>コードでは、再帰関数 <code>dfs(i, src, buf, tar)</code> を定義します。その役割は、柱 <code>src</code> の上部にある <span class="arithmatex">\(i\)</span> 枚の円盤を、補助の柱 <code>buf</code> を使って目標の柱 <code>tar</code> へ移動することです：</p>
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 <div class="highlight"><span class="filename">hanota.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">move</span><span class="p">(</span><span class="n">src</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">tar</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;円盤を移動&quot;&quot;&quot;</span>
-<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># src の上から円盤を取り出す</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;円盤を 1 枚移動&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># src の上から円盤を1枚取り出す</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">pan</span> <span class="o">=</span> <span class="n">src</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="c1"># 円盤を tar の上に置く</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="n">tar</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">pan</span><span class="p">)</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">src</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">buf</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">tar</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
-<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ハノイの塔問題 f(i) を解く&quot;&quot;&quot;</span>
-<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="c1"># src に円盤が 1 つだけ残っている場合、それを tar に移動</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ハノイの塔の問題 f(i) を解く&quot;&quot;&quot;</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="c1"># src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
 <a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span> <span class="n">tar</span><span class="p">)</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="k">return</span>
-<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="c1"># 部分問題 f(i-1)：tar の助けを借りて src の上の i-1 個の円盤を buf に移動</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="c1"># 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す</span>
 <a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="n">dfs</span><span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">src</span><span class="p">,</span> <span class="n">tar</span><span class="p">,</span> <span class="n">buf</span><span class="p">)</span>
-<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>    <span class="c1"># 部分問題 f(1)：残りの 1 個の円盤を src から tar に移動</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>    <span class="c1"># 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す</span>
 <a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>    <span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span> <span class="n">tar</span><span class="p">)</span>
-<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>    <span class="c1"># 部分問題 f(i-1)：src の助けを借りて buf の上の i-1 個の円盤を tar に移動</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>    <span class="c1"># 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す</span>
 <a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>    <span class="n">dfs</span><span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">buf</span><span class="p">,</span> <span class="n">src</span><span class="p">,</span> <span class="n">tar</span><span class="p">)</span>
 <a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>
 <a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="k">def</span><span class="w"> </span><span class="nf">solve_hanota</span><span class="p">(</span><span class="n">A</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">B</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">C</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
-<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ハノイの塔問題を解く&quot;&quot;&quot;</span>
+<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ハノイの塔を解く&quot;&quot;&quot;</span>
 <a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
-<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>    <span class="c1"># B の助けを借りて A の上の n 個の円盤を C に移動</span>
+<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>    <span class="c1"># A の上から n 枚の円盤を B を介して C へ移す</span>
 <a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>    <span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">C</span><span class="p">)</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hanota.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 円盤を移動 */</span>
+<div class="highlight"><span class="filename">hanota.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 円盤を 1 枚移動 */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">move</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">tar</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// src の最上部から円盤を取り出す</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// src の上から円盤を1枚取り出す</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pan</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">src</span><span class="p">.</span><span class="n">back</span><span class="p">();</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="n">src</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
-<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// 円盤を tar の最上部に配置</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// 円盤を tar の上に置く</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="n">tar</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">pan</span><span class="p">);</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="p">}</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a>
-<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="cm">/* ハノイの塔問題 f(i) を解く */</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="cm">/* ハノイの塔の問題 f(i) を解く */</span>
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">tar</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="c1">// src に円盤が1つだけ残っている場合、それを tar に移動</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="c1">// src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">        </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
 <a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：tar の助けを借りて、上位 i-1 個の円盤を src から buf に移動</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す</span>
 <a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">);</span>
-<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">    </span><span class="c1">// 部分問題 f(1)：残りの1つの円盤を src から tar に移動</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">    </span><span class="c1">// 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す</span>
 <a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">    </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
-<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：src の助けを借りて、上位 i-1 個の円盤を buf から tar に移動</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す</span>
 <a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
 <a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="p">}</span>
 <a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a>
-<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="cm">/* ハノイの塔問題を解く */</span>
+<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="cm">/* ハノイの塔を解く */</span>
 <a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="kt">void</span><span class="w"> </span><span class="nf">solveHanota</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">C</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">A</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
-<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="w">    </span><span class="c1">// B の助けを借りて、上位 n 個の円盤を A から C に移動</span>
+<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="w">    </span><span class="c1">// A の上から n 枚の円盤を B を介して C へ移す</span>
 <a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">C</span><span class="p">);</span>
 <a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hanota.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 円盤を移動 */</span>
+<div class="highlight"><span class="filename">hanota.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 円盤を 1 枚移動 */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">move</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// src の最上部から円盤を取り出す</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// src の上から円盤を1枚取り出す</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="n">Integer</span><span class="w"> </span><span class="n">pan</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">src</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">src</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="c1">// 円盤を tar の最上部に配置</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="c1">// 円盤を tar の上に置く</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="n">tar</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">pan</span><span class="p">);</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="p">}</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a>
-<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="cm">/* ハノイの塔問題 f(i) を解く */</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="cm">/* ハノイの塔の問題 f(i) を解く */</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="c1">// src に円盤が1つだけ残っている場合、それを tar に移動</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="c1">// src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す</span>
 <a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
 <a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：tar の助けを借りて、上位 i-1 個の円盤を src から buf に移動</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す</span>
 <a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">);</span>
-<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">    </span><span class="c1">// 部分問題 f(1)：残りの1つの円盤を src から tar に移動</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">    </span><span class="c1">// 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す</span>
 <a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">    </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
-<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：src の助けを借りて、上位 i-1 個の円盤を buf から tar に移動</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す</span>
 <a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
 <a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="p">}</span>
 <a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a>
-<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="cm">/* ハノイの塔問題を解く */</span>
+<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="cm">/* ハノイの塔を解く */</span>
 <a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="kt">void</span><span class="w"> </span><span class="nf">solveHanota</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">C</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">A</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
-<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w">    </span><span class="c1">// B の助けを借りて、上位 n 個の円盤を A から C に移動</span>
+<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w">    </span><span class="c1">// A の上から n 枚の円盤を B を介して C へ移す</span>
 <a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">C</span><span class="p">);</span>
 <a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hanota.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">hanota</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Move</span><span class="p">}</span>
-<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
-<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">hanota</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">DFS</span><span class="p">}</span>
-<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a>
-<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="na">[class]</span><span class="p">{</span><span class="n">hanota</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">SolveHanota</span><span class="p">}</span>
+<div class="highlight"><span class="filename">hanota.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 円盤を 1 枚移動 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Move</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="c1">// src の上から円盤を1枚取り出す</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pan</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">src</span><span class="p">[</span><span class="o">^</span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="n">src</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="n">src</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="c1">// 円盤を tar の上に置く</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="n">tar</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">pan</span><span class="p">);</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="p">}</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="cm">/* ハノイの塔の問題 f(i) を解く */</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="k">void</span><span class="w"> </span><span class="nf">DFS</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">    </span><span class="c1">// src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">        </span><span class="n">Move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">    </span><span class="n">DFS</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">);</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w">    </span><span class="c1">// 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す</span>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w">    </span><span class="n">Move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
+<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す</span>
+<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="w">    </span><span class="n">DFS</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
+<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="p">}</span>
+<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a>
+<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="cm">/* ハノイの塔を解く */</span>
+<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="k">void</span><span class="w"> </span><span class="nf">SolveHanota</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">C</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">A</span><span class="p">.</span><span class="n">Count</span><span class="p">;</span>
+<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a><span class="w">    </span><span class="c1">// A の上から n 枚の円盤を B を介して C へ移す</span>
+<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a><span class="w">    </span><span class="n">DFS</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">C</span><span class="p">);</span>
+<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hanota.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">move</span><span class="p">}</span>
-<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
-<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">dfsHanota</span><span class="p">}</span>
-<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a>
-<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">solveHanota</span><span class="p">}</span>
+<div class="highlight"><span class="filename">hanota.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 円盤を 1 枚移動 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">move</span><span class="p">(</span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="w"> </span><span class="o">*</span><span class="nx">list</span><span class="p">.</span><span class="nx">List</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// src の上から円盤を1枚取り出す</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">pan</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">src</span><span class="p">.</span><span class="nx">Back</span><span class="p">()</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="c1">// 円盤を tar の上に置く</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="nx">tar</span><span class="p">.</span><span class="nx">PushBack</span><span class="p">(</span><span class="nx">pan</span><span class="p">.</span><span class="nx">Value</span><span class="p">)</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="c1">// `src` の最上部の円盤を取り外す</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">    </span><span class="nx">src</span><span class="p">.</span><span class="nx">Remove</span><span class="p">(</span><span class="nx">pan</span><span class="p">)</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="p">}</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="cm">/* ハノイの塔の問題 f(i) を解く */</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="kd">func</span><span class="w"> </span><span class="nx">dfsHanota</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">buf</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="w"> </span><span class="o">*</span><span class="nx">list</span><span class="p">.</span><span class="nx">List</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">    </span><span class="c1">// src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">        </span><span class="nx">move</span><span class="p">(</span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">)</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w">    </span><span class="nx">dfsHanota</span><span class="p">(</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">,</span><span class="w"> </span><span class="nx">buf</span><span class="p">)</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w">    </span><span class="c1">// 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w">    </span><span class="nx">move</span><span class="p">(</span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">)</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す</span>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="w">    </span><span class="nx">dfsHanota</span><span class="p">(</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">buf</span><span class="p">,</span><span class="w"> </span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">)</span>
+<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="p">}</span>
+<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a>
+<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="cm">/* ハノイの塔を解く */</span>
+<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="kd">func</span><span class="w"> </span><span class="nx">solveHanota</span><span class="p">(</span><span class="nx">A</span><span class="p">,</span><span class="w"> </span><span class="nx">B</span><span class="p">,</span><span class="w"> </span><span class="nx">C</span><span class="w"> </span><span class="o">*</span><span class="nx">list</span><span class="p">.</span><span class="nx">List</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="w">    </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">A</span><span class="p">.</span><span class="nx">Len</span><span class="p">()</span>
+<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="w">    </span><span class="c1">// A の上から n 枚の円盤を B を介して C へ移す</span>
+<a id="__codelineno-4-30" name="__codelineno-4-30" href="#__codelineno-4-30"></a><span class="w">    </span><span class="nx">dfsHanota</span><span class="p">(</span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">A</span><span class="p">,</span><span class="w"> </span><span class="nx">B</span><span class="p">,</span><span class="w"> </span><span class="nx">C</span><span class="p">)</span>
+<a id="__codelineno-4-31" name="__codelineno-4-31" href="#__codelineno-4-31"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hanota.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">move</span><span class="p">}</span>
-<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
-<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>
-<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">solveHanota</span><span class="p">}</span>
+<div class="highlight"><span class="filename">hanota.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 円盤を 1 枚移動 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">move</span><span class="p">(</span><span class="n">src</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">tar</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// src の上から円盤を1枚取り出す</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">pan</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">src</span><span class="p">.</span><span class="n">popLast</span><span class="p">()</span><span class="o">!</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="c1">// 円盤を tar の上に置く</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="n">tar</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">pan</span><span class="p">)</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="p">}</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="cm">/* ハノイの塔の問題 f(i) を解く */</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="kd">func</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">buf</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">tar</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">    </span><span class="c1">// src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">        </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">tar</span><span class="p">)</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">buf</span><span class="p">)</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">    </span><span class="c1">// 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w">    </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">tar</span><span class="p">)</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す</span>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">tar</span><span class="p">)</span>
+<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="p">}</span>
+<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a>
+<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="cm">/* ハノイの塔を解く */</span>
+<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="kd">func</span><span class="w"> </span><span class="nf">solveHanota</span><span class="p">(</span><span class="n">A</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">B</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">C</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">A</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a><span class="w">    </span><span class="c1">// リストの末尾が柱の上端に対応する</span>
+<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a><span class="w">    </span><span class="c1">// src の上から n 個の円盤を、B を介して C に移動する</span>
+<a id="__codelineno-5-29" name="__codelineno-5-29" href="#__codelineno-5-29"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">C</span><span class="p">)</span>
+<a id="__codelineno-5-30" name="__codelineno-5-30" href="#__codelineno-5-30"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hanota.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">move</span><span class="p">}</span>
-<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
-<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
-<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a>
-<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">solveHanota</span><span class="p">}</span>
+<div class="highlight"><span class="filename">hanota.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 円盤を 1 枚移動 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">move</span><span class="p">(</span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="c1">// src の上から円盤を1枚取り出す</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">pan</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">src</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="c1">// 円盤を tar の上に置く</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="nx">tar</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">pan</span><span class="p">);</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="p">}</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="cm">/* ハノイの塔の問題 f(i) を解く */</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="kd">function</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">buf</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">    </span><span class="c1">// src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">        </span><span class="nx">move</span><span class="p">(</span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">);</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w">    </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">,</span><span class="w"> </span><span class="nx">buf</span><span class="p">);</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w">    </span><span class="c1">// 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">    </span><span class="nx">move</span><span class="p">(</span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">);</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す</span>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w">    </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">buf</span><span class="p">,</span><span class="w"> </span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">);</span>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="p">}</span>
+<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a>
+<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a><span class="cm">/* ハノイの塔を解く */</span>
+<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="kd">function</span><span class="w"> </span><span class="nx">solveHanota</span><span class="p">(</span><span class="nx">A</span><span class="p">,</span><span class="w"> </span><span class="nx">B</span><span class="p">,</span><span class="w"> </span><span class="nx">C</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">A</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-6-27" name="__codelineno-6-27" href="#__codelineno-6-27"></a><span class="w">    </span><span class="c1">// A の上から n 枚の円盤を B を介して C へ移す</span>
+<a id="__codelineno-6-28" name="__codelineno-6-28" href="#__codelineno-6-28"></a><span class="w">    </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">A</span><span class="p">,</span><span class="w"> </span><span class="nx">B</span><span class="p">,</span><span class="w"> </span><span class="nx">C</span><span class="p">);</span>
+<a id="__codelineno-6-29" name="__codelineno-6-29" href="#__codelineno-6-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hanota.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">move</span><span class="p">}</span>
-<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
-<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
-<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a>
-<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">solveHanota</span><span class="p">}</span>
+<div class="highlight"><span class="filename">hanota.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 円盤を 1 枚移動 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">move</span><span class="p">(</span><span class="nx">src</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">tar</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="c1">// src の上から円盤を1枚取り出す</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">pan</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">src</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="c1">// 円盤を tar の上に置く</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="nx">tar</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">pan</span><span class="p">);</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="p">}</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="cm">/* ハノイの塔の問題 f(i) を解く */</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="kd">function</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">src</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">buf</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">tar</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">    </span><span class="c1">// src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">        </span><span class="nx">move</span><span class="p">(</span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">);</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">    </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">,</span><span class="w"> </span><span class="nx">buf</span><span class="p">);</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">    </span><span class="c1">// 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">    </span><span class="nx">move</span><span class="p">(</span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">);</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="w">    </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">buf</span><span class="p">,</span><span class="w"> </span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">);</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="p">}</span>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a>
+<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="cm">/* ハノイの塔を解く */</span>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="kd">function</span><span class="w"> </span><span class="nx">solveHanota</span><span class="p">(</span><span class="nx">A</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">B</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">C</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">A</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a><span class="w">    </span><span class="c1">// A の上から n 枚の円盤を B を介して C へ移す</span>
+<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a><span class="w">    </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">A</span><span class="p">,</span><span class="w"> </span><span class="nx">B</span><span class="p">,</span><span class="w"> </span><span class="nx">C</span><span class="p">);</span>
+<a id="__codelineno-7-29" name="__codelineno-7-29" href="#__codelineno-7-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hanota.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">move</span><span class="p">}</span>
-<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
-<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a>
-<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">solveHanota</span><span class="p">}</span>
+<div class="highlight"><span class="filename">hanota.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 円盤を 1 枚移動 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">move</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="c1">// src の上から円盤を1枚取り出す</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">pan</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">src</span><span class="p">.</span><span class="n">removeLast</span><span class="p">();</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="c1">// 円盤を tar の上に置く</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="n">tar</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">pan</span><span class="p">);</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="p">}</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="cm">/* ハノイの塔の問題 f(i) を解く */</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="kt">void</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">  </span><span class="c1">// src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">    </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">    </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">  </span><span class="c1">// 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">  </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">);</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w">  </span><span class="c1">// 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w">  </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="w">  </span><span class="c1">// 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す</span>
+<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="w">  </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
+<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="p">}</span>
+<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a>
+<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a><span class="cm">/* ハノイの塔を解く */</span>
+<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a><span class="kt">void</span><span class="w"> </span><span class="n">solveHanota</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">C</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-26" name="__codelineno-8-26" href="#__codelineno-8-26"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">A</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-8-27" name="__codelineno-8-27" href="#__codelineno-8-27"></a><span class="w">  </span><span class="c1">// A の上から n 枚の円盤を B を介して C へ移す</span>
+<a id="__codelineno-8-28" name="__codelineno-8-28" href="#__codelineno-8-28"></a><span class="w">  </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">C</span><span class="p">);</span>
+<a id="__codelineno-8-29" name="__codelineno-8-29" href="#__codelineno-8-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hanota.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">move_pan</span><span class="p">}</span>
-<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
-<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a>
-<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">solve_hanota</span><span class="p">}</span>
+<div class="highlight"><span class="filename">hanota.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 円盤を 1 枚移動 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">move_pan</span><span class="p">(</span><span class="n">src</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="c1">// src の上から円盤を1枚取り出す</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">pan</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">src</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="c1">// 円盤を tar の上に置く</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="n">tar</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">pan</span><span class="p">);</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="p">}</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="cm">/* ハノイの塔の問題 f(i) を解く */</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="k">fn</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">    </span><span class="c1">// src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">        </span><span class="n">move_pan</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">);</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">    </span><span class="c1">// 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">    </span><span class="n">move_pan</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
+<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="p">}</span>
+<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a>
+<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="cm">/* ハノイの塔を解く */</span>
+<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="k">fn</span><span class="w"> </span><span class="nf">solve_hanota</span><span class="p">(</span><span class="n">A</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">B</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">C</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">A</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">;</span>
+<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="w">    </span><span class="c1">// A の上から n 枚の円盤を B を介して C へ移す</span>
+<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">C</span><span class="p">);</span>
+<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hanota.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">move</span><span class="p">}</span>
-<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
-<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a>
-<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">solveHanota</span><span class="p">}</span>
+<div class="highlight"><span class="filename">hanota.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 円盤を 1 枚移動 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">move</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">srcSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">tarSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="c1">// src の上から円盤を1枚取り出す</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pan</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">src</span><span class="p">[</span><span class="o">*</span><span class="n">srcSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">    </span><span class="n">src</span><span class="p">[</span><span class="o">*</span><span class="n">srcSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="p">(</span><span class="o">*</span><span class="n">srcSize</span><span class="p">)</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">    </span><span class="c1">// 円盤を tar の上に置く</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">    </span><span class="n">tar</span><span class="p">[</span><span class="o">*</span><span class="n">tarSize</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pan</span><span class="p">;</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">    </span><span class="p">(</span><span class="o">*</span><span class="n">tarSize</span><span class="p">)</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="p">}</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="cm">/* ハノイの塔の問題 f(i) を解く */</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">srcSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">bufSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">tarSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">    </span><span class="c1">// src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">        </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">srcSize</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">tarSize</span><span class="p">);</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す</span>
+<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">srcSize</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">tarSize</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">bufSize</span><span class="p">);</span>
+<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="w">    </span><span class="c1">// 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す</span>
+<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w">    </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">srcSize</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">tarSize</span><span class="p">);</span>
+<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す</span>
+<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">bufSize</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">srcSize</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">tarSize</span><span class="p">);</span>
+<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="p">}</span>
+<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a>
+<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="cm">/* ハノイの塔を解く */</span>
+<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="kt">void</span><span class="w"> </span><span class="nf">solveHanota</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">ASize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">BSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">C</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">CSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a><span class="w">    </span><span class="c1">// A の上から n 枚の円盤を B を介して C へ移す</span>
+<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="o">*</span><span class="n">ASize</span><span class="p">,</span><span class="w"> </span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">ASize</span><span class="p">,</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">BSize</span><span class="p">,</span><span class="w"> </span><span class="n">C</span><span class="p">,</span><span class="w"> </span><span class="n">CSize</span><span class="p">);</span>
+<a id="__codelineno-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hanota.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">move</span><span class="p">}</span>
-<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
-<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a>
-<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">solveHanota</span><span class="p">}</span>
+<div class="highlight"><span class="filename">hanota.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 円盤を 1 枚移動 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">move</span><span class="p">(</span><span class="n">src</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="c1">// src の上から円盤を1枚取り出す</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">pan</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">src</span><span class="p">.</span><span class="na">removeAt</span><span class="p">(</span><span class="n">src</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="c1">// 円盤を tar の上に置く</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="n">tar</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">pan</span><span class="p">)</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="p">}</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="cm">/* ハノイの塔の問題 f(i) を解く */</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">    </span><span class="c1">// src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">        </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">)</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">    </span><span class="c1">// 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w">    </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span>
+<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="p">}</span>
+<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a>
+<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="cm">/* ハノイの塔を解く */</span>
+<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">solveHanota</span><span class="p">(</span><span class="n">A</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">B</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">C</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">A</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a><span class="w">    </span><span class="c1">// A の上から n 枚の円盤を B を介して C へ移す</span>
+<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">C</span><span class="p">)</span>
+<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hanota.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">move</span><span class="p">}</span>
-<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
-<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
-<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">solve_hanota</span><span class="p">}</span>
+<div class="highlight"><span class="filename">hanota.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 円盤を1枚移動 ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># src の上から円盤を1枚取り出す</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="n">pan</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">src</span><span class="o">.</span><span class="n">pop</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="c1"># 円盤を tar の上に置く</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="n">tar</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">pan</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="k">end</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="c1">### ハノイの塔 f(i) を解く ###</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">  </span><span class="c1"># src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">    </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">    </span><span class="k">return</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">  </span><span class="c1"># 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w">  </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">)</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w">  </span><span class="c1"># 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="w">  </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w">  </span><span class="c1"># 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す</span>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w">  </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span>
+<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="k">end</span>
+<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a>
+<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="c1">### ハノイの塔を解く ###</span>
+<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a><span class="k">def</span><span class="w"> </span><span class="nf">solve_hanota</span><span class="p">(</span><span class="n">_A</span><span class="p">,</span><span class="w"> </span><span class="n">_B</span><span class="p">,</span><span class="w"> </span><span class="n">_C</span><span class="p">)</span>
+<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a><span class="w">  </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_A</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a><span class="w">  </span><span class="c1"># A の上から n 枚の円盤を B を介して C へ移す</span>
+<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a><span class="w">  </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">_A</span><span class="p">,</span><span class="w"> </span><span class="n">_B</span><span class="p">,</span><span class="w"> </span><span class="n">_C</span><span class="p">)</span>
+<a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>以下の図に示すように、ハノイの塔問題は高さ <span class="arithmatex">\(n\)</span> の再帰木として視覚化できます。各ノードは部分問題を表し、<code>dfs()</code> の呼び出しに対応します。<strong>したがって、時間計算量は <span class="arithmatex">\(O(2^n)\)</span>、空間計算量は <span class="arithmatex">\(O(n)\)</span> です。</strong></p>
-<p><img alt="ハノイの塔の再帰木" class="animation-figure" src="../hanota_problem.assets/hanota_recursive_tree.png" /></p>
-<p align="center"> 図 12-15 &nbsp; ハノイの塔の再帰木 </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20move%28src%3A%20list%5Bint%5D%2C%20tar%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%22%22%22%E5%86%86%E7%9B%A4%E3%82%92%201%20%E6%9E%9A%E7%A7%BB%E5%8B%95%22%22%22%0A%20%20%20%20%23%20src%20%E3%81%AE%E4%B8%8A%E3%81%8B%E3%82%89%E5%86%86%E7%9B%A4%E3%82%921%E6%9E%9A%E5%8F%96%E3%82%8A%E5%87%BA%E3%81%99%0A%20%20%20%20pan%20%3D%20src.pop%28%29%0A%20%20%20%20%23%20%E5%86%86%E7%9B%A4%E3%82%92%20tar%20%E3%81%AE%E4%B8%8A%E3%81%AB%E7%BD%AE%E3%81%8F%0A%20%20%20%20tar.append%28pan%29%0A%0A%0Adef%20dfs%28i%3A%20int%2C%20src%3A%20list%5Bint%5D%2C%20buf%3A%20list%5Bint%5D%2C%20tar%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%22%22%22%E3%83%8F%E3%83%8E%E3%82%A4%E3%81%AE%E5%A1%94%E3%81%AE%E5%95%8F%E9%A1%8C%20f%28i%29%20%E3%82%92%E8%A7%A3%E3%81%8F%22%22%22%0A%20%20%20%20%23%20src%20%E3%81%AB%E5%86%86%E7%9B%A4%E3%81%8C%201%20%E6%9E%9A%E3%81%A0%E3%81%91%E6%AE%8B%E3%81%A3%E3%81%A6%E3%81%84%E3%82%8B%E5%A0%B4%E5%90%88%E3%81%AF%E3%80%81%E3%81%9D%E3%81%AE%E3%81%BE%E3%81%BE%20tar%20%E3%81%B8%E7%A7%BB%E3%81%99%0A%20%20%20%20if%20i%20%3D%3D%201%3A%0A%20%20%20%20%20%20%20%20move%28src%2C%20tar%29%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%20f%28i-1%29%EF%BC%9Asrc%20%E3%81%AE%E4%B8%8A%E9%83%A8%20i-1%20%E6%9E%9A%E3%81%AE%E5%86%86%E7%9B%A4%E3%82%92%20tar%20%E3%82%92%E8%A3%9C%E5%8A%A9%E3%81%AB%E3%81%97%E3%81%A6%20buf%20%E3%81%B8%E7%A7%BB%E3%81%99%0A%20%20%20%20dfs%28i%20-%201%2C%20src%2C%20tar%2C%20buf%29%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%20f%281%29%EF%BC%9Asrc%20%E3%81%AB%E6%AE%8B%E3%82%8B%201%20%E6%9E%9A%E3%81%AE%E5%86%86%E7%9B%A4%E3%82%92%20tar%20%E3%81%AB%E7%A7%BB%E3%81%99%0A%20%20%20%20move%28src%2C%20tar%29%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%20f%28i-1%29%EF%BC%9Abuf%20%E3%81%AE%E4%B8%8A%E9%83%A8%20i-1%20%E6%9E%9A%E3%81%AE%E5%86%86%E7%9B%A4%E3%82%92%20src%20%E3%82%92%E8%A3%9C%E5%8A%A9%E3%81%AB%E3%81%97%E3%81%A6%20tar%20%E3%81%B8%E7%A7%BB%E3%81%99%0A%20%20%20%20dfs%28i%20-%201%2C%20buf%2C%20src%2C%20tar%29%0A%0A%0Adef%20solve_hanota%28A%3A%20list%5Bint%5D%2C%20B%3A%20list%5Bint%5D%2C%20C%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%22%22%22%E3%83%8F%E3%83%8E%E3%82%A4%E3%81%AE%E5%A1%94%E3%82%92%E8%A7%A3%E3%81%8F%22%22%22%0A%20%20%20%20n%20%3D%20len%28A%29%0A%20%20%20%20%23%20A%20%E3%81%AE%E4%B8%8A%E3%81%8B%E3%82%89%20n%20%E6%9E%9A%E3%81%AE%E5%86%86%E7%9B%A4%E3%82%92%20B%20%E3%82%92%E4%BB%8B%E3%81%97%E3%81%A6%20C%20%E3%81%B8%E7%A7%BB%E3%81%99%0A%20%20%20%20dfs%28n%2C%20A%2C%20B%2C%20C%29%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E3%83%AA%E3%82%B9%E3%83%88%E6%9C%AB%E5%B0%BE%E3%81%8C%E6%9F%B1%E3%81%AE%E9%A0%82%E4%B8%8A%0A%20%20%20%20A%20%3D%20%5B5%2C%204%2C%203%2C%202%2C%201%5D%0A%20%20%20%20B%20%3D%20%5B%5D%0A%20%20%20%20C%20%3D%20%5B%5D%0A%20%20%20%20print%28%22%E5%88%9D%E6%9C%9F%E7%8A%B6%E6%85%8B%3A%22%29%0A%20%20%20%20print%28f%22A%20%3D%20%7BA%7D%22%29%0A%20%20%20%20print%28f%22B%20%3D%20%7BB%7D%22%29%0A%20%20%20%20print%28f%22C%20%3D%20%7BC%7D%22%29%0A%0A%20%20%20%20solve_hanota%28A%2C%20B%2C%20C%29%0A%0A%20%20%20%20print%28%22%E5%86%86%E7%9B%A4%E3%81%AE%E7%A7%BB%E5%8B%95%E5%AE%8C%E4%BA%86%E5%BE%8C%3A%22%29%0A%20%20%20%20print%28f%22A%20%3D%20%7BA%7D%22%29%0A%20%20%20%20print%28f%22B%20%3D%20%7BB%7D%22%29%0A%20%20%20%20print%28f%22C%20%3D%20%7BC%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=12&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20move%28src%3A%20list%5Bint%5D%2C%20tar%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%22%22%22%E5%86%86%E7%9B%A4%E3%82%92%201%20%E6%9E%9A%E7%A7%BB%E5%8B%95%22%22%22%0A%20%20%20%20%23%20src%20%E3%81%AE%E4%B8%8A%E3%81%8B%E3%82%89%E5%86%86%E7%9B%A4%E3%82%921%E6%9E%9A%E5%8F%96%E3%82%8A%E5%87%BA%E3%81%99%0A%20%20%20%20pan%20%3D%20src.pop%28%29%0A%20%20%20%20%23%20%E5%86%86%E7%9B%A4%E3%82%92%20tar%20%E3%81%AE%E4%B8%8A%E3%81%AB%E7%BD%AE%E3%81%8F%0A%20%20%20%20tar.append%28pan%29%0A%0A%0Adef%20dfs%28i%3A%20int%2C%20src%3A%20list%5Bint%5D%2C%20buf%3A%20list%5Bint%5D%2C%20tar%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%22%22%22%E3%83%8F%E3%83%8E%E3%82%A4%E3%81%AE%E5%A1%94%E3%81%AE%E5%95%8F%E9%A1%8C%20f%28i%29%20%E3%82%92%E8%A7%A3%E3%81%8F%22%22%22%0A%20%20%20%20%23%20src%20%E3%81%AB%E5%86%86%E7%9B%A4%E3%81%8C%201%20%E6%9E%9A%E3%81%A0%E3%81%91%E6%AE%8B%E3%81%A3%E3%81%A6%E3%81%84%E3%82%8B%E5%A0%B4%E5%90%88%E3%81%AF%E3%80%81%E3%81%9D%E3%81%AE%E3%81%BE%E3%81%BE%20tar%20%E3%81%B8%E7%A7%BB%E3%81%99%0A%20%20%20%20if%20i%20%3D%3D%201%3A%0A%20%20%20%20%20%20%20%20move%28src%2C%20tar%29%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%20f%28i-1%29%EF%BC%9Asrc%20%E3%81%AE%E4%B8%8A%E9%83%A8%20i-1%20%E6%9E%9A%E3%81%AE%E5%86%86%E7%9B%A4%E3%82%92%20tar%20%E3%82%92%E8%A3%9C%E5%8A%A9%E3%81%AB%E3%81%97%E3%81%A6%20buf%20%E3%81%B8%E7%A7%BB%E3%81%99%0A%20%20%20%20dfs%28i%20-%201%2C%20src%2C%20tar%2C%20buf%29%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%20f%281%29%EF%BC%9Asrc%20%E3%81%AB%E6%AE%8B%E3%82%8B%201%20%E6%9E%9A%E3%81%AE%E5%86%86%E7%9B%A4%E3%82%92%20tar%20%E3%81%AB%E7%A7%BB%E3%81%99%0A%20%20%20%20move%28src%2C%20tar%29%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%20f%28i-1%29%EF%BC%9Abuf%20%E3%81%AE%E4%B8%8A%E9%83%A8%20i-1%20%E6%9E%9A%E3%81%AE%E5%86%86%E7%9B%A4%E3%82%92%20src%20%E3%82%92%E8%A3%9C%E5%8A%A9%E3%81%AB%E3%81%97%E3%81%A6%20tar%20%E3%81%B8%E7%A7%BB%E3%81%99%0A%20%20%20%20dfs%28i%20-%201%2C%20buf%2C%20src%2C%20tar%29%0A%0A%0Adef%20solve_hanota%28A%3A%20list%5Bint%5D%2C%20B%3A%20list%5Bint%5D%2C%20C%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%22%22%22%E3%83%8F%E3%83%8E%E3%82%A4%E3%81%AE%E5%A1%94%E3%82%92%E8%A7%A3%E3%81%8F%22%22%22%0A%20%20%20%20n%20%3D%20len%28A%29%0A%20%20%20%20%23%20A%20%E3%81%AE%E4%B8%8A%E3%81%8B%E3%82%89%20n%20%E6%9E%9A%E3%81%AE%E5%86%86%E7%9B%A4%E3%82%92%20B%20%E3%82%92%E4%BB%8B%E3%81%97%E3%81%A6%20C%20%E3%81%B8%E7%A7%BB%E3%81%99%0A%20%20%20%20dfs%28n%2C%20A%2C%20B%2C%20C%29%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E3%83%AA%E3%82%B9%E3%83%88%E6%9C%AB%E5%B0%BE%E3%81%8C%E6%9F%B1%E3%81%AE%E9%A0%82%E4%B8%8A%0A%20%20%20%20A%20%3D%20%5B5%2C%204%2C%203%2C%202%2C%201%5D%0A%20%20%20%20B%20%3D%20%5B%5D%0A%20%20%20%20C%20%3D%20%5B%5D%0A%20%20%20%20print%28%22%E5%88%9D%E6%9C%9F%E7%8A%B6%E6%85%8B%3A%22%29%0A%20%20%20%20print%28f%22A%20%3D%20%7BA%7D%22%29%0A%20%20%20%20print%28f%22B%20%3D%20%7BB%7D%22%29%0A%20%20%20%20print%28f%22C%20%3D%20%7BC%7D%22%29%0A%0A%20%20%20%20solve_hanota%28A%2C%20B%2C%20C%29%0A%0A%20%20%20%20print%28%22%E5%86%86%E7%9B%A4%E3%81%AE%E7%A7%BB%E5%8B%95%E5%AE%8C%E4%BA%86%E5%BE%8C%3A%22%29%0A%20%20%20%20print%28f%22A%20%3D%20%7BA%7D%22%29%0A%20%20%20%20print%28f%22B%20%3D%20%7BB%7D%22%29%0A%20%20%20%20print%28f%22C%20%3D%20%7BC%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=12&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>以下の図に示すように、ハノイの塔の問題は高さ <span class="arithmatex">\(n\)</span> の再帰木を形成し、各ノードは 1 つの部分問題、すなわち 1 つ起動された <code>dfs()</code> 関数に対応します。<strong>したがって時間計算量は <span class="arithmatex">\(O(2^n)\)</span> 、空間計算量は <span class="arithmatex">\(O(n)\)</span></strong> です。</p>
+<p><img alt="ハノイの塔の問題の再帰木" class="animation-figure" src="../hanota_problem.assets/hanota_recursive_tree.png" /></p>
+<p align="center"> 図 12-15 &nbsp; ハノイの塔の問題の再帰木 </p>
 
 <div class="admonition quote">
 <p class="admonition-title">Quote</p>
-<p>ハノイの塔は古代の伝説に由来します。古代インドの寺院で、僧侶たちは3本の高いダイヤモンドの柱と、異なるサイズの <span class="arithmatex">\(64\)</span> 枚の金の円盤を持っていました。彼らは、最後の円盤が正しく置かれたとき、世界が終わると信じていました。</p>
-<p>しかし、僧侶たちが1秒に1枚の円盤を移動したとしても、約 <span class="arithmatex">\(2^{64} \approx 1.84×10^{19}\)</span> —約5850億年—かかり、宇宙の年齢の現在の推定をはるかに超えています。したがって、この伝説が真実であれば、世界の終わりについて心配する必要はおそらくないでしょう。</p>
+<p>ハノイの塔の問題は古い伝説に由来します。古代インドのある寺院で、僧侶たちは 3 本の高いダイヤモンドの柱と、<span class="arithmatex">\(64\)</span> 枚の大きさの異なる金の円盤を持っていました。僧侶たちは絶えず円盤を動かし、最後の 1 枚が正しく置かれた瞬間に世界が終わると信じていました。</p>
+<p>しかし、たとえ僧侶たちが 1 秒に 1 回移動するとしても、合計でおよそ <span class="arithmatex">\(2^{64} \approx 1.84×10^{19}\)</span> 秒、約 <span class="arithmatex">\(5850\)</span> 億年が必要で、現在推定されている宇宙の年齢をはるかに上回ります。したがって、この伝説が本当だったとしても、世界の終わりを心配する必要はなさそうです。</p>
 </div>
 
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     href="../build_binary_tree_problem/"
     class="md-footer__link md-footer__link--prev"
-    aria-label="前: 12.3 &amp;nbsp; 木の構築問題"
+    aria-label="前: 12.3 &amp;nbsp; 二分木の構築問題"
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-        12.3 &nbsp; 木の構築問題
+        12.3 &nbsp; 二分木の構築問題
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diff --git a/ja/chapter_divide_and_conquer/index.html b/ja/chapter_divide_and_conquer/index.html
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       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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+    7.5 &nbsp; AVL 木 *
   
 
     
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-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
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-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2575,7 +2575,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3115,7 +3115,7 @@
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
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-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
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-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
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-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
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-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
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-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4083,7 +4083,7 @@
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4277,15 +4277,15 @@
 <p><img alt="分割統治" class="cover-image" src="../assets/covers/chapter_divide_and_conquer.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>困難な問題は層を重ねて分解され、各分解によってより単純になります。</p>
-<p>分割統治は深い真理を明らかにします：単純さから始めれば、複雑さは解決される。</p>
+<p>難題は段階的に分解され、そのたびにより単純になっていく。</p>
+<p>分割統治は一つの重要な事実を示している。単純なことから始めれば、すべてはもはや複雑ではない。</p>
 </div>
 <h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
-<li><a href="divide_and_conquer/">12.1 &nbsp; 分割統治アルゴリズム</a></li>
+<li><a href="divide_and_conquer/">12.1 &nbsp; 分割統治法</a></li>
 <li><a href="binary_search_recur/">12.2 &nbsp; 分割統治探索戦略</a></li>
-<li><a href="build_binary_tree_problem/">12.3 &nbsp; 木の構築問題</a></li>
-<li><a href="hanota_problem/">12.4 &nbsp; ハノイの塔問題</a></li>
+<li><a href="build_binary_tree_problem/">12.3 &nbsp; 二分木の構築問題</a></li>
+<li><a href="hanota_problem/">12.4 &nbsp; ハノイの塔の問題</a></li>
 <li><a href="summary/">12.5 &nbsp; まとめ</a></li>
 </ul>
 
@@ -4334,7 +4334,7 @@ aria-label="フッター"
   <a
     href="./divide_and_conquer/"
     class="md-footer__link md-footer__link--next"
-    aria-label="次: 12.1 &amp;nbsp; 分割統治アルゴリズム"
+    aria-label="次: 12.1 &amp;nbsp; 分割統治法"
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     <div class="md-footer__title">
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         次
       </span>
       <div class="md-ellipsis">
-        12.1 &nbsp; 分割統治アルゴリズム
+        12.1 &nbsp; 分割統治法
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diff --git a/ja/chapter_divide_and_conquer/summary/index.html b/ja/chapter_divide_and_conquer/summary/index.html
index 14d376e3c..bb8849981 100644
--- a/ja/chapter_divide_and_conquer/summary/index.html
+++ b/ja/chapter_divide_and_conquer/summary/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
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     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
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@@ -341,7 +341,7 @@
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-    序
+    はじめに
   
 
     
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-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
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-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
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-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
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-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
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-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
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-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2105,7 +2105,7 @@
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-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
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-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2547,7 +2547,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
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-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3171,7 +3171,7 @@
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3199,7 +3199,7 @@
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-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3229,6 +3229,24 @@
         
       
       
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    12.5 &nbsp; まとめ
+  
+
+    
+  </span>
+  
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
       <a href="././" class="md-nav__link md-nav__link--active">
         
   
@@ -3246,6 +3264,37 @@
 
       </a>
       
+        
+
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      
+        1. &nbsp; 要点の振り返り
+      
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
     </li>
   
 
@@ -3402,7 +3451,7 @@
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-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
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-    13.4 &nbsp; Nクイーン問題
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-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3599,7 +3648,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3627,7 +3676,7 @@
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-    14.3 &nbsp; DP の解法の考え方
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@@ -3655,7 +3704,7 @@
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-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3848,7 +3897,7 @@
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4093,7 +4142,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4229,6 +4278,25 @@
     
   
   
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      
+        1. &nbsp; 要点の振り返り
+      
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
 </nav>
                   </div>
                 </div>
@@ -4265,16 +4333,17 @@
 
 <!-- Page content -->
 <h1 id="125">12.5 &nbsp; まとめ<a class="headerlink" href="#125" title="Permanent link">&para;</a></h1>
+<h3 id="1">1. &nbsp; 要点の振り返り<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
-<li>分割統治は一般的なアルゴリズム設計戦略で、分割（分割）と統治（マージ）の2つの段階から構成され、一般的に再帰を使用して実装されます。</li>
-<li>問題が分割統治アプローチに適しているかどうかを判断するために、問題が分解可能かどうか、部分問題が独立しているかどうか、部分問題をマージできるかどうかを確認します。</li>
-<li>マージソートは分割統治戦略の典型的な例です。配列を再帰的に2つの等しい長さの副配列に分割し、1つの要素のみが残るまで続け、次にこれらの副配列を層ごとにマージしてソートを完了します。</li>
-<li>分割統治戦略の導入は、しばしばアルゴリズムの効率を向上させます。一方では操作数を減らし、他方では分割後のシステムの並列最適化を促進します。</li>
-<li>分割統治は多数のアルゴリズム問題に適用でき、データ構造とアルゴリズム設計で広く使用され、多くのシナリオに現れます。</li>
-<li>総当たり検索と比較して、適応検索はより効率的です。時間計算量が <span class="arithmatex">\(O(\log n)\)</span> の検索アルゴリズムは、通常分割統治戦略に基づいています。</li>
-<li>二分探索は分割統治戦略のもう一つの古典的な応用です。部分問題の解のマージを含まず、再帰的な分割統治アプローチで実装できます。</li>
-<li>二分木構築問題では、木の構築（元の問題）を左の部分木と右の部分木の構築（部分問題）に分割できます。これは前順走査と中順走査のインデックス範囲を分割することで実現できます。</li>
-<li>ハノイの塔問題では、サイズ <span class="arithmatex">\(n\)</span> の問題をサイズ <span class="arithmatex">\(n-1\)</span> の2つの部分問題とサイズ <span class="arithmatex">\(1\)</span> の1つの部分問題に分解できます。これら3つの部分問題を順次解決することで、元の問題が解決されます。</li>
+<li>分割統治法は一般的なアルゴリズム設計戦略であり、分（分割）と治（統合）の 2 つの段階からなり、通常は再帰に基づいて実装されます。</li>
+<li>それが分割統治法の問題かどうかを判断する基準には、問題を分解できるか、部分問題が独立しているか、部分問題を統合できるかが含まれます。</li>
+<li>マージソートは分割統治法の典型的な応用であり、配列を再帰的に同じ長さの 2 つの部分配列に分割し、要素が 1 つだけになるまで続け、その後で各層を順に統合してソートを完了します。</li>
+<li>分割統治法を導入すると、多くの場合アルゴリズムの効率を高められます。一方では操作回数が減り、他方では分割後にシステムの並列最適化を行いやすくなります。</li>
+<li>分割統治法は多くのアルゴリズム問題を解決できるだけでなく、データ構造やアルゴリズム設計にも広く応用されており、至る所でその姿を見ることができます。</li>
+<li>総当たり探索と比べて、適応的な探索のほうが効率的です。時間計算量が <span class="arithmatex">\(O(\log n)\)</span> の探索アルゴリズムは、通常は分割統治法に基づいて実装されます。</li>
+<li>二分探索は分割統治法のもう 1 つの典型的な応用であり、部分問題の解を統合する手順を含みません。再帰的な分割統治によって二分探索を実現できます。</li>
+<li>二分木を構築する問題では、木の構築（元の問題）を左部分木と右部分木の構築（部分問題）に分けられます。これは、先行順序走査と中間順序走査のインデックス区間を分割することで実現できます。</li>
+<li>ハノイの塔の問題では、規模 <span class="arithmatex">\(n\)</span> の問題を、規模 <span class="arithmatex">\(n-1\)</span> の 2 つの部分問題と規模 <span class="arithmatex">\(1\)</span> の 1 つの部分問題に分けられます。これら 3 つの部分問題を順に解くと、元の問題も解決されます。</li>
 </ul>
 
 <!-- Source file information -->
@@ -4298,7 +4367,7 @@ aria-label="フッター"
   <a
     href="../hanota_problem/"
     class="md-footer__link md-footer__link--prev"
-    aria-label="前: 12.4 &amp;nbsp; ハノイの塔問題"
+    aria-label="前: 12.4 &amp;nbsp; ハノイの塔の問題"
     rel="prev"
   >
     <div class="md-footer__button md-icon">
@@ -4310,7 +4379,7 @@ aria-label="フッター"
         前
       </span>
       <div class="md-ellipsis">
-        12.4 &nbsp; ハノイの塔問題
+        12.4 &nbsp; ハノイの塔の問題
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     </div>
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index 7704fcc69..206eb7d14 100644
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+++ b/ja/chapter_dynamic_programming/dp_problem_features/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -39,7 +39,7 @@
     
     
       
-        <title>14.2 動的プログラミング問題の特徴 - Hello アルゴリズム</title>
+        <title>14.2 動的計画法の問題特性 - Hello アルゴリズム</title>
       
     
     
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -152,7 +152,7 @@
         <div class="md-header__topic" data-md-component="header-topic">
           <span class="md-ellipsis">
             
-              14.2 &nbsp; 動的プログラミング問題の特徴
+              14.2 &nbsp; 動的計画法の問題特性
             
           </span>
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-    序
+    はじめに
   
 
     
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-    序
+    はじめに
   
 
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@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
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-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
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   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
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   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
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-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
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-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
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-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
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-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
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-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
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-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
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-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
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-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
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   <a href="#1422" class="md-nav__link">
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-        14.2.2 &nbsp; 無記憶性
+        14.2.2 &nbsp; 無後効性
       
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-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
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-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
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   <a href="#1422" class="md-nav__link">
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-        14.2.2 &nbsp; 無記憶性
+        14.2.2 &nbsp; 無後効性
       
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   </a>
@@ -4354,62 +4354,62 @@
 
 
 <!-- Page content -->
-<h1 id="142">14.2 &nbsp; 動的プログラミング問題の特徴<a class="headerlink" href="#142" title="Permanent link">&para;</a></h1>
-<p>前のセクションでは、動的プログラミングが問題を部分問題に分解することで元の問題を解決する方法を学びました。実際、部分問題の分解は一般的なアルゴリズムアプローチであり、分割統治法、動的プログラミング、バックトラッキングでは異なる重点があります。</p>
+<h1 id="142">14.2 &nbsp; 動的計画法の問題特性<a class="headerlink" href="#142" title="Permanent link">&para;</a></h1>
+<p>前節では、動的計画法が部分問題への分解によってどのように元の問題を解くのかを学びました。実際、部分問題への分解は汎用的なアルゴリズムの考え方であり、分割統治法、動的計画法、バックトラッキングでは重視点が異なります。</p>
 <ul>
-<li>分割統治法アルゴリズムは元の問題を複数の独立した部分問題に再帰的に分割し、最小の部分問題に到達するまで続け、バックトラッキング時に部分問題の解を組み合わせて最終的に元の問題の解を得ます。</li>
-<li>動的プログラミングも問題を再帰的に分解しますが、分割統治法アルゴリズムとの主な違いは、動的プログラミングの部分問題が相互依存的であり、分解プロセス中に多くの重複する部分問題が現れることです。</li>
-<li>バックトラッキングアルゴリズムは試行錯誤によってすべての可能な解を網羅し、枝刈りによって不必要な探索分岐を避けます。元の問題の解は一連の決定ステップから構成され、各決定ステップ前の各部分シーケンスを部分問題として考えることができます。</li>
+<li>分割統治法は、元の問題を再帰的に複数の互いに独立した部分問題へ分割し、最小の部分問題に至るまで分解したうえで、バックトラック時に部分問題の解を統合し、最終的に元の問題の解を得ます。</li>
+<li>動的計画法も問題を再帰的に分解しますが、分割統治法との主な違いは、動的計画法における部分問題が相互依存しており、分解の過程で多数の重複部分問題が現れることです。</li>
+<li>バックトラッキング法は、試行と巻き戻しの中ですべての可能な解を列挙し、枝刈りによって不要な探索分岐を避けます。元の問題の解は一連の意思決定ステップから構成されるため、各決定ステップ以前の部分系列を一つの部分問題と見なせます。</li>
 </ul>
-<p>実際、動的プログラミングは最適化問題を解決するためによく使用され、これらは重複する部分問題を含むだけでなく、他に2つの主要な特徴があります：最適部分構造と無記憶性です。</p>
+<p>実際、動的計画法は最適化問題を解くためによく用いられます。これらは重複部分問題を含むだけでなく、さらに二つの大きな特性、すなわち最適部分構造と無後効性を備えています。</p>
 <h2 id="1421">14.2.1 &nbsp; 最適部分構造<a class="headerlink" href="#1421" title="Permanent link">&para;</a></h2>
-<p>階段登り問題を少し修正して、最適部分構造の概念を実証するのにより適したものにします。</p>
+<p>階段昇り問題を少し変更し、最適部分構造の概念をより示しやすくします。</p>
 <div class="admonition question">
-<p class="admonition-title">階段登りの最小コスト</p>
-<p>階段があり、一度に1段または2段上ることができ、階段の各段にはその段で支払う必要があるコストを表す非負の整数があります。非負の整数配列 <span class="arithmatex">\(cost\)</span> が与えられ、<span class="arithmatex">\(cost[i]\)</span> は <span class="arithmatex">\(i\)</span> 段目で支払う必要があるコストを表し、<span class="arithmatex">\(cost[0]\)</span> は地面（開始点）です。頂上に到達するために必要な最小コストは何ですか？</p>
+<p class="admonition-title">階段昇りの最小コスト</p>
+<p>階段が与えられ、各ステップで <span class="arithmatex">\(1\)</span> 段または <span class="arithmatex">\(2\)</span> 段上ることができます。各段には非負整数が貼られており、その段に到達するために支払う必要があるコストを表します。非負整数配列 <span class="arithmatex">\(cost\)</span> が与えられ、<span class="arithmatex">\(cost[i]\)</span> は第 <span class="arithmatex">\(i\)</span> 段で支払うコストを表し、<span class="arithmatex">\(cost[0]\)</span> は地面（開始地点）です。頂上に到達するために必要な最小コストを求めてください。</p>
 </div>
-<p>下の図に示すように、1段目、2段目、3段目のコストがそれぞれ <span class="arithmatex">\(1\)</span>、<span class="arithmatex">\(10\)</span>、<span class="arithmatex">\(1\)</span> の場合、地面から3段目に登る最小コストは <span class="arithmatex">\(2\)</span> です。</p>
-<p><img alt="3段目に登る最小コスト" class="animation-figure" src="../dp_problem_features.assets/min_cost_cs_example.png" /></p>
-<p align="center"> 図 14-6 &nbsp; 3段目に登る最小コスト </p>
+<p>下図に示すように、第 <span class="arithmatex">\(1\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(3\)</span> 段のコストがそれぞれ <span class="arithmatex">\(1\)</span>、<span class="arithmatex">\(10\)</span>、<span class="arithmatex">\(1\)</span> である場合、地面から第 <span class="arithmatex">\(3\)</span> 段まで上る最小コストは <span class="arithmatex">\(2\)</span> です。</p>
+<p><img alt="第 3 段まで上る最小コスト" class="animation-figure" src="../dp_problem_features.assets/min_cost_cs_example.png" /></p>
+<p align="center"> 図 14-6 &nbsp; 第 3 段まで上る最小コスト </p>
 
-<p><span class="arithmatex">\(dp[i]\)</span> を <span class="arithmatex">\(i\)</span> 段目に登る累積コストとします。<span class="arithmatex">\(i\)</span> 段目は <span class="arithmatex">\(i-1\)</span> 段目または <span class="arithmatex">\(i-2\)</span> 段目からのみ来ることができるため、<span class="arithmatex">\(dp[i]\)</span> は <span class="arithmatex">\(dp[i-1] + cost[i]\)</span> または <span class="arithmatex">\(dp[i-2] + cost[i]\)</span> のいずれかしかありえません。コストを最小化するために、2つのうち小さい方を選択すべきです：</p>
+<p><span class="arithmatex">\(dp[i]\)</span> を第 <span class="arithmatex">\(i\)</span> 段まで上るのに累積して支払ったコストとします。第 <span class="arithmatex">\(i\)</span> 段には <span class="arithmatex">\(i - 1\)</span> 段または <span class="arithmatex">\(i - 2\)</span> 段からしか到達できないため、<span class="arithmatex">\(dp[i]\)</span> は <span class="arithmatex">\(dp[i - 1] + cost[i]\)</span> または <span class="arithmatex">\(dp[i - 2] + cost[i]\)</span> のいずれかになります。コストをできるだけ小さくするには、この二つのうち小さいほうを選べばよいです。</p>
 <div class="arithmatex">\[
 dp[i] = \min(dp[i-1], dp[i-2]) + cost[i]
 \]</div>
-<p>これにより最適部分構造の意味がわかります：<strong>元の問題の最適解は部分問題の最適解から構築される</strong>。</p>
-<p>この問題は明らかに最適部分構造を持っています：2つの部分問題 <span class="arithmatex">\(dp[i-1]\)</span> と <span class="arithmatex">\(dp[i-2]\)</span> の最適解からより良い方を選択し、それを使用して元の問題 <span class="arithmatex">\(dp[i]\)</span> の最適解を構築します。</p>
-<p>では、前のセクションの階段登り問題は最適部分構造を持っているでしょうか？その目標は解の数を求めることで、これは数え上げ問題のようですが、別の方法で尋ねてみましょう：「解の最大数を求める」。驚くことに、**問題が変わったにもかかわらず、最適部分構造が現れた**ことがわかります：<span class="arithmatex">\(n\)</span> 段目での解の最大数は、<span class="arithmatex">\(n-1\)</span> 段目と <span class="arithmatex">\(n-2\)</span> 段目での解の最大数の和に等しいです。したがって、最適部分構造の解釈は非常に柔軟で、異なる問題では異なる意味を持ちます。</p>
-<p>状態遷移方程式と初期状態 <span class="arithmatex">\(dp[1] = cost[1]\)</span> および <span class="arithmatex">\(dp[2] = cost[2]\)</span> に従って、動的プログラミングコードを得ることができます：</p>
+<p>ここから最適部分構造の意味を導けます。**元の問題の最適解は、部分問題の最適解から構築される**ということです。</p>
+<p>この問題が最適部分構造を持つことは明らかです。二つの部分問題の最適解 <span class="arithmatex">\(dp[i-1]\)</span> と <span class="arithmatex">\(dp[i-2]\)</span> からより良いほうを選び、それを用いて元の問題 <span class="arithmatex">\(dp[i]\)</span> の最適解を構築しています。</p>
+<p>では、前節の階段昇り問題には最適部分構造があるのでしょうか。その目的は方法数を求めることで、一見すると計数問題です。しかし問い方を変えて「最大の方法数を求める」とすると、意外にも、<strong>問題の変更前後は等価であるにもかかわらず、最適部分構造が現れます</strong>。すなわち、第 <span class="arithmatex">\(n\)</span> 段の最大方法数は第 <span class="arithmatex">\(n-1\)</span> 段と第 <span class="arithmatex">\(n-2\)</span> 段の最大方法数の和に等しいのです。このように、最適部分構造の解釈は比較的柔軟であり、問題によって意味合いが異なります。</p>
+<p>状態遷移方程式と初期状態 <span class="arithmatex">\(dp[1] = cost[1]\)</span> および <span class="arithmatex">\(dp[2] = cost[2]\)</span> に基づいて、次の動的計画法コードが得られます。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
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 <div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_cost_climbing_stairs_dp</span><span class="p">(</span><span class="n">cost</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;最小コスト階段登り：動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;階段登りの最小コスト：動的計画法&quot;&quot;&quot;</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">cost</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="k">return</span> <span class="n">cost</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>
-<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># dp テーブルを初期化、部分問題の解を格納するために使用</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 部分問題の解を保存するために dp テーブルを初期化</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="c1"># 初期状態：最小の部分問題の解を事前設定</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="c1"># 初期状態：最小部分問題の解をあらかじめ設定</span>
 <a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">cost</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">cost</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span>
-<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="c1"># 状態遷移：小さい部分問題から大きい部分問題を段階的に解く</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="c1"># 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">2</span><span class="p">])</span> <span class="o">+</span> <span class="n">cost</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 最小コスト階段登り：動的プログラミング */</span>
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 階段登りの最小コスト：動的計画法 */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minCostClimbingStairsDP</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">cost</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
-<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化し、部分問題の解を格納するために使用</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="c1">// 初期状態：最小の部分問題の解を事前設定</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="mi">1</span><span class="p">];</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="mi">2</span><span class="p">];</span>
-<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="c1">// 状態遷移：小さな問題から大きな部分問題を段階的に解く</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
 <a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="p">}</span>
@@ -4418,17 +4418,17 @@ dp[i] = \min(dp[i-1], dp[i-2]) + cost[i]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 最小コスト階段登り：動的プログラミング */</span>
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 階段登りの最小コスト：動的計画法 */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minCostClimbingStairsDP</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">cost</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化し、部分問題の解を格納するために使用</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="c1">// 初期状態：最小の部分問題の解を事前設定</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="mi">2</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="c1">// 状態遷移：小さな問題から大きな部分問題を段階的に解く</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
 <a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="p">}</span>
@@ -4437,57 +4437,220 @@ dp[i] = \min(dp[i-1], dp[i-2]) + cost[i]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">min_cost_climbing_stairs_dp</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MinCostClimbingStairsDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 階段登りの最小コスト：動的計画法 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">MinCostClimbingStairsDP</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">cost</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="mi">2</span><span class="p">];</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">minCostClimbingStairsDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 階段登りの最小コスト：動的計画法 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">minCostClimbingStairsDP</span><span class="p">(</span><span class="nx">cost</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">cost</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="nx">n</span><span class="p">]</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="nx">min</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="kd">func</span><span class="p">(</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nx">a</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">b</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">    </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">min</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">2</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">]</span>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">minCostClimbingStairsDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 階段登りの最小コスト：動的計画法 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">minCostClimbingStairsDP</span><span class="p">(</span><span class="n">cost</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">cost</span><span class="p">.</span><span class="bp">count</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">minCostClimbingStairsDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 階段登りの最小コスト：動的計画法 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">minCostClimbingStairsDP</span><span class="p">(</span><span class="nx">cost</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cost</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="nx">n</span><span class="p">];</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mf">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="mf">2</span><span class="p">];</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">2</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">];</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">minCostClimbingStairsDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 階段登りの最小コスト：動的計画法 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">minCostClimbingStairsDP</span><span class="p">(</span><span class="nx">cost</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cost</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="nx">n</span><span class="p">];</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mf">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="mf">2</span><span class="p">];</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">2</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">];</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minCostClimbingStairsDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 階段登りの最小コスト：動的計画法 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">minCostClimbingStairsDP</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">cost</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">  </span><span class="n">dp</span><span class="p">[</span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="m">1</span><span class="p">];</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">  </span><span class="n">dp</span><span class="p">[</span><span class="m">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="m">2</span><span class="p">];</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">  </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">2</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">min_cost_climbing_stairs_dp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 階段登りの最小コスト：動的計画法 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">min_cost_climbing_stairs_dp</span><span class="p">(</span><span class="n">cost</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="mi">2</span><span class="p">];</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">3</span><span class="o">..=</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cmp</span><span class="p">::</span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minCostClimbingStairsDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 階段登りの最小コスト：動的計画法 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minCostClimbingStairsDP</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">cost</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">costSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">costSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">calloc</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="mi">2</span><span class="p">];</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">myMin</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">dp</span><span class="p">);</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">minCostClimbingStairsDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 階段登りの最小コスト：動的計画法 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">minCostClimbingStairsDP</span><span class="p">(</span><span class="n">cost</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">n</span><span class="o">]</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="m">1</span><span class="o">]</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="m">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="m">2</span><span class="o">]</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">3.</span><span class="p">.</span><span class="na">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">2</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">]</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">min_cost_climbing_stairs_dp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 階段登りの最小コスト：動的計画法 ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_cost_climbing_stairs_dp</span><span class="p">(</span><span class="n">cost</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="c1"># 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">  </span><span class="c1"># 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="mi">2</span><span class="o">]</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">  </span><span class="c1"># 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">  </span><span class="p">(</span><span class="mi">3</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="o">]].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">]</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>下の図は上記コードの動的プログラミングプロセスを示しています。</p>
-<p><img alt="階段登りの最小コストの動的プログラミングプロセス" class="animation-figure" src="../dp_problem_features.assets/min_cost_cs_dp.png" /></p>
-<p align="center"> 図 14-7 &nbsp; 階段登りの最小コストの動的プログラミングプロセス </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20min_cost_climbing_stairs_dp%28cost%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%9A%8E%E6%AE%B5%E7%99%BB%E3%82%8A%E3%81%AE%E6%9C%80%E5%B0%8F%E3%82%B3%E3%82%B9%E3%83%88%EF%BC%9A%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%20%3D%20len%28cost%29%20-%201%0A%20%20%20%20if%20n%20%3D%3D%201%20or%20n%20%3D%3D%202%3A%0A%20%20%20%20%20%20%20%20return%20cost%5Bn%5D%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%E3%81%AE%E8%A7%A3%E3%82%92%E4%BF%9D%E5%AD%98%E3%81%99%E3%82%8B%E3%81%9F%E3%82%81%E3%81%AB%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5B0%5D%20%2A%20%28n%20%2B%201%29%0A%20%20%20%20%23%20%E5%88%9D%E6%9C%9F%E7%8A%B6%E6%85%8B%EF%BC%9A%E6%9C%80%E5%B0%8F%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%E3%81%AE%E8%A7%A3%E3%82%92%E3%81%82%E3%82%89%E3%81%8B%E3%81%98%E3%82%81%E8%A8%AD%E5%AE%9A%0A%20%20%20%20dp%5B1%5D%2C%20dp%5B2%5D%20%3D%20cost%5B1%5D%2C%20cost%5B2%5D%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%B0%8F%E3%81%95%E3%81%84%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%E3%81%8B%E3%82%89%E5%A4%A7%E3%81%8D%E3%81%84%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%E3%81%B8%E9%A0%86%E3%81%AB%E8%A7%A3%E3%81%8F%0A%20%20%20%20for%20i%20in%20range%283%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20dp%5Bi%5D%20%3D%20min%28dp%5Bi%20-%201%5D%2C%20dp%5Bi%20-%202%5D%29%20%2B%20cost%5Bi%5D%0A%20%20%20%20return%20dp%5Bn%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20cost%20%3D%20%5B0%2C%201%2C%2010%2C%201%2C%201%2C%201%2C%2010%2C%201%2C%201%2C%2010%2C%201%5D%0A%20%20%20%20print%28f%22%E5%85%A5%E5%8A%9B%E3%81%95%E3%82%8C%E3%81%9F%E9%9A%8E%E6%AE%B5%E3%82%B3%E3%82%B9%E3%83%88%E3%81%AE%E3%83%AA%E3%82%B9%E3%83%88%E3%81%AF%20%7Bcost%7D%22%29%0A%0A%20%20%20%20res%20%3D%20min_cost_climbing_stairs_dp%28cost%29%0A%20%20%20%20print%28f%22%E9%9A%8E%E6%AE%B5%E3%82%92%E4%B8%8A%E3%82%8A%E5%88%87%E3%82%8B%E6%9C%80%E5%B0%8F%E3%82%B3%E3%82%B9%E3%83%88%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20min_cost_climbing_stairs_dp%28cost%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%9A%8E%E6%AE%B5%E7%99%BB%E3%82%8A%E3%81%AE%E6%9C%80%E5%B0%8F%E3%82%B3%E3%82%B9%E3%83%88%EF%BC%9A%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%20%3D%20len%28cost%29%20-%201%0A%20%20%20%20if%20n%20%3D%3D%201%20or%20n%20%3D%3D%202%3A%0A%20%20%20%20%20%20%20%20return%20cost%5Bn%5D%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%E3%81%AE%E8%A7%A3%E3%82%92%E4%BF%9D%E5%AD%98%E3%81%99%E3%82%8B%E3%81%9F%E3%82%81%E3%81%AB%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5B0%5D%20%2A%20%28n%20%2B%201%29%0A%20%20%20%20%23%20%E5%88%9D%E6%9C%9F%E7%8A%B6%E6%85%8B%EF%BC%9A%E6%9C%80%E5%B0%8F%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%E3%81%AE%E8%A7%A3%E3%82%92%E3%81%82%E3%82%89%E3%81%8B%E3%81%98%E3%82%81%E8%A8%AD%E5%AE%9A%0A%20%20%20%20dp%5B1%5D%2C%20dp%5B2%5D%20%3D%20cost%5B1%5D%2C%20cost%5B2%5D%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%B0%8F%E3%81%95%E3%81%84%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%E3%81%8B%E3%82%89%E5%A4%A7%E3%81%8D%E3%81%84%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%E3%81%B8%E9%A0%86%E3%81%AB%E8%A7%A3%E3%81%8F%0A%20%20%20%20for%20i%20in%20range%283%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20dp%5Bi%5D%20%3D%20min%28dp%5Bi%20-%201%5D%2C%20dp%5Bi%20-%202%5D%29%20%2B%20cost%5Bi%5D%0A%20%20%20%20return%20dp%5Bn%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20cost%20%3D%20%5B0%2C%201%2C%2010%2C%201%2C%201%2C%201%2C%2010%2C%201%2C%201%2C%2010%2C%201%5D%0A%20%20%20%20print%28f%22%E5%85%A5%E5%8A%9B%E3%81%95%E3%82%8C%E3%81%9F%E9%9A%8E%E6%AE%B5%E3%82%B3%E3%82%B9%E3%83%88%E3%81%AE%E3%83%AA%E3%82%B9%E3%83%88%E3%81%AF%20%7Bcost%7D%22%29%0A%0A%20%20%20%20res%20%3D%20min_cost_climbing_stairs_dp%28cost%29%0A%20%20%20%20print%28f%22%E9%9A%8E%E6%AE%B5%E3%82%92%E4%B8%8A%E3%82%8A%E5%88%87%E3%82%8B%E6%9C%80%E5%B0%8F%E3%82%B3%E3%82%B9%E3%83%88%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>下図は上記コードの動的計画法の過程を示しています。</p>
+<p><img alt="階段昇り最小コストの動的計画法の過程" class="animation-figure" src="../dp_problem_features.assets/min_cost_cs_dp.png" /></p>
+<p align="center"> 図 14-7 &nbsp; 階段昇り最小コストの動的計画法の過程 </p>
 
-<p>この問題も空間最適化が可能で、1次元を0に圧縮し、空間計算量を <span class="arithmatex">\(O(n)\)</span> から <span class="arithmatex">\(O(1)\)</span> に削減できます：</p>
+<p>この問題では空間最適化も可能であり、一次元をゼロ次元まで圧縮することで、空間計算量を <span class="arithmatex">\(O(n)\)</span> から <span class="arithmatex">\(O(1)\)</span> に削減できます。</p>
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 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_cost_climbing_stairs_dp_comp</span><span class="p">(</span><span class="n">cost</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;最小コスト階段登り：空間最適化動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;階段昇りの最小コスト：空間最適化後の動的計画法&quot;&quot;&quot;</span>
 <a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">cost</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>
 <a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
 <a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>        <span class="k">return</span> <span class="n">cost</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>
@@ -4498,7 +4661,7 @@ dp[i] = \min(dp[i-1], dp[i-2]) + cost[i]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 最小コスト階段登り：空間最適化動的プログラミング */</span>
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 階段昇りの最小コスト：空間最適化後の動的計画法 */</span>
 <a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minCostClimbingStairsDPComp</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">cost</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
@@ -4514,7 +4677,7 @@ dp[i] = \min(dp[i-1], dp[i-2]) + cost[i]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 最小コスト階段登り：空間最適化動的プログラミング */</span>
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 階段昇りの最小コスト：空間最適化後の動的計画法 */</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minCostClimbingStairsDPComp</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">cost</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
@@ -4530,90 +4693,235 @@ dp[i] = \min(dp[i-1], dp[i-2]) + cost[i]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">min_cost_climbing_stairs_dp</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MinCostClimbingStairsDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 階段昇りの最小コスト：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">MinCostClimbingStairsDPComp</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">cost</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="mi">2</span><span class="p">];</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">        </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Min</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">tmp</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">        </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">minCostClimbingStairsDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 階段昇りの最小コスト：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">minCostClimbingStairsDPComp</span><span class="p">(</span><span class="nx">cost</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">cost</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="nx">n</span><span class="p">]</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">    </span><span class="nx">min</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="kd">func</span><span class="p">(</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nx">a</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">b</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w">    </span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="w">        </span><span class="nx">tmp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">b</span>
+<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="w">        </span><span class="nx">b</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">min</span><span class="p">(</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">tmp</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
+<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="w">        </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">tmp</span>
+<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">b</span>
+<a id="__codelineno-17-22" name="__codelineno-17-22" href="#__codelineno-17-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">minCostClimbingStairsDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 階段昇りの最小コスト：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">minCostClimbingStairsDPComp</span><span class="p">(</span><span class="n">cost</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">cost</span><span class="p">.</span><span class="bp">count</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="n">cost</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">        </span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="p">,</span><span class="w"> </span><span class="bp">min</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">b</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">minCostClimbingStairsDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 階段昇りの最小コスト：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">minCostClimbingStairsDPComp</span><span class="p">(</span><span class="nx">cost</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cost</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="nx">n</span><span class="p">];</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="mf">1</span><span class="p">],</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">        </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="mf">2</span><span class="p">];</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">b</span><span class="p">;</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w">        </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">tmp</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">        </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">;</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">b</span><span class="p">;</span>
+<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">minCostClimbingStairsDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 階段昇りの最小コスト：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">minCostClimbingStairsDPComp</span><span class="p">(</span><span class="nx">cost</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cost</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="nx">n</span><span class="p">];</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="mf">1</span><span class="p">],</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">        </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="mf">2</span><span class="p">];</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">b</span><span class="p">;</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w">        </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">tmp</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">        </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">;</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">b</span><span class="p">;</span>
+<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minCostClimbingStairsDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 階段昇りの最小コスト：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">minCostClimbingStairsDPComp</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">cost</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="m">1</span><span class="p">],</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="m">2</span><span class="p">];</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">    </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">tmp</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">min_cost_climbing_stairs_dp_comp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 階段昇りの最小コスト：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">min_cost_climbing_stairs_dp_comp</span><span class="p">(</span><span class="n">cost</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w">    </span><span class="p">};</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="p">(</span><span class="k">mut</span><span class="w"> </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">b</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">cost</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="mi">2</span><span class="p">]);</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">3</span><span class="o">..=</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w">        </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cmp</span><span class="p">::</span><span class="n">min</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">tmp</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w">        </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">    </span><span class="n">b</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minCostClimbingStairsDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 階段昇りの最小コスト：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minCostClimbingStairsDPComp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">cost</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">costSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">costSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="mi">2</span><span class="p">];</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w">        </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">myMin</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">tmp</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w">        </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">minCostClimbingStairsDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 階段昇りの最小コスト：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">minCostClimbingStairsDPComp</span><span class="p">(</span><span class="n">cost</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">n</span><span class="o">]</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="m">1</span><span class="o">]</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="m">2</span><span class="o">]</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">3.</span><span class="p">.</span><span class="na">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">b</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w">        </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">tmp</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w">        </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">b</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">min_cost_climbing_stairs_dp_comp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### 階段登りの最小コスト：動的計画法 ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_cost_climbing_stairs_dp</span><span class="p">(</span><span class="n">cost</span><span class="p">)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">  </span><span class="c1"># 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">  </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">  </span><span class="c1"># 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="mi">2</span><span class="o">]</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">  </span><span class="c1"># 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w">  </span><span class="p">(</span><span class="mi">3</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="o">]].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">]</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="k">end</span>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a>
+<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="c1"># 階段昇りの最小コスト：空間最適化後の動的計画法</span>
+<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_cost_climbing_stairs_dp_comp</span><span class="p">(</span><span class="n">cost</span><span class="p">)</span>
+<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w">  </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a><span class="w">  </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="mi">2</span><span class="o">]</span>
+<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="w">  </span><span class="p">(</span><span class="mi">3</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">b</span><span class="p">,</span><span class="w"> </span><span class="o">[</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="o">].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a><span class="w">  </span><span class="n">b</span>
+<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h2 id="1422">14.2.2 &nbsp; 無記憶性<a class="headerlink" href="#1422" title="Permanent link">&para;</a></h2>
-<p>無記憶性は動的プログラミングが問題解決に効果的であることを可能にする重要な特徴の1つです。その定義は：<strong>特定の状態が与えられたとき、その将来の発展は現在の状態のみに関連し、過去に経験したすべての状態とは無関係である</strong>。</p>
-<p>階段登り問題を例に取ると、状態 <span class="arithmatex">\(i\)</span> が与えられたとき、それは状態 <span class="arithmatex">\(i+1\)</span> と <span class="arithmatex">\(i+2\)</span> に発展し、それぞれ1段ジャンプと2段ジャンプに対応します。これら2つの選択をするとき、状態 <span class="arithmatex">\(i\)</span> より前の状態を考慮する必要はありません。なぜなら、それらは状態 <span class="arithmatex">\(i\)</span> の将来に影響しないからです。</p>
-<p>しかし、階段登り問題に制約を追加すると、状況が変わります。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 495px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20min_cost_climbing_stairs_dp_comp%28cost%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%9A%8E%E6%AE%B5%E6%98%87%E3%82%8A%E3%81%AE%E6%9C%80%E5%B0%8F%E3%82%B3%E3%82%B9%E3%83%88%EF%BC%9A%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E5%BE%8C%E3%81%AE%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%20%3D%20len%28cost%29%20-%201%0A%20%20%20%20if%20n%20%3D%3D%201%20or%20n%20%3D%3D%202%3A%0A%20%20%20%20%20%20%20%20return%20cost%5Bn%5D%0A%20%20%20%20a%2C%20b%20%3D%20cost%5B1%5D%2C%20cost%5B2%5D%0A%20%20%20%20for%20i%20in%20range%283%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20a%2C%20b%20%3D%20b%2C%20min%28a%2C%20b%29%20%2B%20cost%5Bi%5D%0A%20%20%20%20return%20b%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20cost%20%3D%20%5B0%2C%201%2C%2010%2C%201%2C%201%2C%201%2C%2010%2C%201%2C%201%2C%2010%2C%201%5D%0A%20%20%20%20print%28f%22%E5%85%A5%E5%8A%9B%E3%81%95%E3%82%8C%E3%81%9F%E9%9A%8E%E6%AE%B5%E3%82%B3%E3%82%B9%E3%83%88%E3%81%AE%E3%83%AA%E3%82%B9%E3%83%88%E3%81%AF%20%7Bcost%7D%22%29%0A%0A%20%20%20%20res%20%3D%20min_cost_climbing_stairs_dp_comp%28cost%29%0A%20%20%20%20print%28f%22%E9%9A%8E%E6%AE%B5%E3%82%92%E4%B8%8A%E3%82%8A%E5%88%87%E3%82%8B%E6%9C%80%E5%B0%8F%E3%82%B3%E3%82%B9%E3%83%88%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20min_cost_climbing_stairs_dp_comp%28cost%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%9A%8E%E6%AE%B5%E6%98%87%E3%82%8A%E3%81%AE%E6%9C%80%E5%B0%8F%E3%82%B3%E3%82%B9%E3%83%88%EF%BC%9A%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E5%BE%8C%E3%81%AE%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%20%3D%20len%28cost%29%20-%201%0A%20%20%20%20if%20n%20%3D%3D%201%20or%20n%20%3D%3D%202%3A%0A%20%20%20%20%20%20%20%20return%20cost%5Bn%5D%0A%20%20%20%20a%2C%20b%20%3D%20cost%5B1%5D%2C%20cost%5B2%5D%0A%20%20%20%20for%20i%20in%20range%283%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20a%2C%20b%20%3D%20b%2C%20min%28a%2C%20b%29%20%2B%20cost%5Bi%5D%0A%20%20%20%20return%20b%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20cost%20%3D%20%5B0%2C%201%2C%2010%2C%201%2C%201%2C%201%2C%2010%2C%201%2C%201%2C%2010%2C%201%5D%0A%20%20%20%20print%28f%22%E5%85%A5%E5%8A%9B%E3%81%95%E3%82%8C%E3%81%9F%E9%9A%8E%E6%AE%B5%E3%82%B3%E3%82%B9%E3%83%88%E3%81%AE%E3%83%AA%E3%82%B9%E3%83%88%E3%81%AF%20%7Bcost%7D%22%29%0A%0A%20%20%20%20res%20%3D%20min_cost_climbing_stairs_dp_comp%28cost%29%0A%20%20%20%20print%28f%22%E9%9A%8E%E6%AE%B5%E3%82%92%E4%B8%8A%E3%82%8A%E5%88%87%E3%82%8B%E6%9C%80%E5%B0%8F%E3%82%B3%E3%82%B9%E3%83%88%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h2 id="1422">14.2.2 &nbsp; 無後効性<a class="headerlink" href="#1422" title="Permanent link">&para;</a></h2>
+<p>無後効性は、動的計画法が問題を効率よく解ける重要な特性の一つであり、その定義は次のとおりです。<strong>ある確定した状態が与えられたとき、その後の発展は現在の状態のみに依存し、過去に経たすべての状態には依存しない</strong>。</p>
+<p>階段昇り問題を例にすると、状態 <span class="arithmatex">\(i\)</span> が与えられたとき、そこから状態 <span class="arithmatex">\(i+1\)</span> と状態 <span class="arithmatex">\(i+2\)</span> へ発展し、それぞれ <span class="arithmatex">\(1\)</span> 段進む場合と <span class="arithmatex">\(2\)</span> 段進む場合に対応します。この二つの選択を行う際、状態 <span class="arithmatex">\(i\)</span> より前の状態を考慮する必要はなく、それらは状態 <span class="arithmatex">\(i\)</span> の将来に影響を与えません。</p>
+<p>しかし、階段昇り問題に制約を一つ追加すると、状況は変わります。</p>
 <div class="admonition question">
-<p class="admonition-title">制約付き階段登り</p>
-<p><span class="arithmatex">\(n\)</span> 段の階段があり、毎回1段または2段上ることができますが、<strong>1段を2回連続でジャンプすることはできません</strong>。頂上に登る方法は何通りありますか？</p>
+<p class="admonition-title">制約付き階段昇り</p>
+<p>全部で <span class="arithmatex">\(n\)</span> 段ある階段が与えられ、各ステップで <span class="arithmatex">\(1\)</span> 段または <span class="arithmatex">\(2\)</span> 段上ることができます。<strong>ただし、連続する 2 回で <span class="arithmatex">\(1\)</span> 段ずつ上ることはできません</strong>。頂上まで上る方法は何通りあるでしょうか。</p>
 </div>
-<p>下の図に示すように、3段目に登る実行可能な選択肢は2つだけで、1段を3回連続でジャンプする選択肢は制約条件を満たさないため破棄されます。</p>
-<p><img alt="制約付きで3段目に登る実行可能な選択肢の数" class="animation-figure" src="../dp_problem_features.assets/climbing_stairs_constraint_example.png" /></p>
-<p align="center"> 図 14-8 &nbsp; 制約付きで3段目に登る実行可能な選択肢の数 </p>
+<p>下図に示すように、第 <span class="arithmatex">\(3\)</span> 段まで上る実行可能な方法は <span class="arithmatex">\(2\)</span> 通りしか残りません。そのうち、<span class="arithmatex">\(1\)</span> 段ずつ 3 回連続で上る方法は制約を満たさないため除外されます。</p>
+<p><img alt="制約付きで第 3 段まで上る方法数" class="animation-figure" src="../dp_problem_features.assets/climbing_stairs_constraint_example.png" /></p>
+<p align="center"> 図 14-8 &nbsp; 制約付きで第 3 段まで上る方法数 </p>
 
-<p>この問題では、前回が1段ジャンプだった場合、次回は必ず2段ジャンプでなければなりません。これは**次のステップの選択が現在の状態（現在の階段段数）だけでは独立して決定できず、前の状態（前回の階段段数）にも依存する**ことを意味します。</p>
-<p>この問題がもはや無記憶性を満たさず、状態遷移方程式 <span class="arithmatex">\(dp[i] = dp[i-1] + dp[i-2]\)</span> も失敗することは容易にわかります。なぜなら <span class="arithmatex">\(dp[i-1]\)</span> は今回の1段ジャンプを表しますが、多くの「前回が1段ジャンプだった」選択肢を含んでおり、制約を満たすためにはこれらを直接 <span class="arithmatex">\(dp[i]\)</span> に含めることはできません。</p>
-<p>このため、状態定義を拡張する必要があります：<strong>状態 <span class="arithmatex">\([i, j]\)</span> は <span class="arithmatex">\(i\)</span> 段目にいて、前回が <span class="arithmatex">\(j\)</span> 段ジャンプだったことを表す</strong>。ここで <span class="arithmatex">\(j \in \{1, 2\}\)</span> です。この状態定義は前回が1段ジャンプだったか2段ジャンプだったかを効果的に区別し、現在の状態がどこから来たかを適切に判断できます。</p>
+<p>この問題では、前回が <span class="arithmatex">\(1\)</span> 段上りだった場合、次回は必ず <span class="arithmatex">\(2\)</span> 段上らなければなりません。これは、**次の一手が現在の状態（現在いる階段の段数）だけでは独立に決まらず、一つ前の状態（前回いた段数）にも関係する**ことを意味します。</p>
+<p>容易に分かるように、この問題はもはや無後効性を満たしておらず、状態遷移方程式 <span class="arithmatex">\(dp[i] = dp[i-1] + dp[i-2]\)</span> も成立しません。というのも、<span class="arithmatex">\(dp[i-1]\)</span> は今回 <span class="arithmatex">\(1\)</span> 段上る場合を表しますが、その中には「前回も <span class="arithmatex">\(1\)</span> 段上ってきた」方法が多数含まれており、制約を満たすためには <span class="arithmatex">\(dp[i-1]\)</span> をそのまま <span class="arithmatex">\(dp[i]\)</span> に加えることができないからです。</p>
+<p>このため、状態定義を拡張する必要があります。**状態 <span class="arithmatex">\([i, j]\)</span> は、第 <span class="arithmatex">\(i\)</span> 段にいて前回に <span class="arithmatex">\(j\)</span> 段上ったことを表す**とし、ここで <span class="arithmatex">\(j \in \{1, 2\}\)</span> です。この状態定義により、前回が <span class="arithmatex">\(1\)</span> 段上りか <span class="arithmatex">\(2\)</span> 段上りかを有効に区別でき、現在の状態がどこから来たのかを判断できます。</p>
 <ul>
-<li>前回が1段ジャンプだった場合、前々回は必ず2段ジャンプを選択していたはずです。つまり、<span class="arithmatex">\(dp[i, 1]\)</span> は <span class="arithmatex">\(dp[i-1, 2]\)</span> からのみ遷移できます。</li>
-<li>前回が2段ジャンプだった場合、前々回は1段ジャンプまたは2段ジャンプを選択できました。つまり、<span class="arithmatex">\(dp[i, 2]\)</span> は <span class="arithmatex">\(dp[i-2, 1]\)</span> または <span class="arithmatex">\(dp[i-2, 2]\)</span> から遷移できます。</li>
+<li>前回に <span class="arithmatex">\(1\)</span> 段上った場合、その前の回は <span class="arithmatex">\(2\)</span> 段上りしか選べないため、<span class="arithmatex">\(dp[i, 1]\)</span> は <span class="arithmatex">\(dp[i-1, 2]\)</span> からのみ遷移できます。</li>
+<li>前回に <span class="arithmatex">\(2\)</span> 段上った場合、その前の回は <span class="arithmatex">\(1\)</span> 段上りまたは <span class="arithmatex">\(2\)</span> 段上りを選べるため、<span class="arithmatex">\(dp[i, 2]\)</span> は <span class="arithmatex">\(dp[i-2, 1]\)</span> または <span class="arithmatex">\(dp[i-2, 2]\)</span> から遷移できます。</li>
 </ul>
-<p>下の図に示すように、<span class="arithmatex">\(dp[i, j]\)</span> は状態 <span class="arithmatex">\([i, j]\)</span> の解の数を表します。この時点で、状態遷移方程式は次のようになります：</p>
+<p>下図に示すように、この定義のもとでは <span class="arithmatex">\(dp[i, j]\)</span> は状態 <span class="arithmatex">\([i, j]\)</span> に対応する方法数を表します。このとき状態遷移方程式は次のようになります。</p>
 <div class="arithmatex">\[
 \begin{cases}
 dp[i, 1] = dp[i-1, 2] \\
 dp[i, 2] = dp[i-2, 1] + dp[i-2, 2]
 \end{cases}
 \]</div>
-<p><img alt="制約を考慮した再帰関係" class="animation-figure" src="../dp_problem_features.assets/climbing_stairs_constraint_state_transfer.png" /></p>
-<p align="center"> 図 14-9 &nbsp; 制約を考慮した再帰関係 </p>
+<p><img alt="制約を考慮した漸化関係" class="animation-figure" src="../dp_problem_features.assets/climbing_stairs_constraint_state_transfer.png" /></p>
+<p align="center"> 図 14-9 &nbsp; 制約を考慮した漸化関係 </p>
 
-<p>最終的に、<span class="arithmatex">\(dp[n, 1] + dp[n, 2]\)</span> を返せばよく、この2つの合計が <span class="arithmatex">\(n\)</span> 段目に登る解の総数を表します：</p>
+<p>最終的に、<span class="arithmatex">\(dp[n, 1] + dp[n, 2]\)</span> を返せば十分であり、その和が第 <span class="arithmatex">\(n\)</span> 段まで上る方法の総数を表します。</p>
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 <div class="tabbed-block">
 <div class="highlight"><span class="filename">climbing_stairs_constraint_dp.py</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_constraint_dp</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;制約付き階段登り：動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;制約付き階段登り：動的計画法&quot;&quot;&quot;</span>
 <a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
 <a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>        <span class="k">return</span> <span class="mi">1</span>
-<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a>    <span class="c1"># dp テーブルを初期化、部分問題の解を格納するために使用</span>
+<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a>    <span class="c1"># 部分問題の解を保存するために dp テーブルを初期化</span>
 <a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">3</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span>
-<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a>    <span class="c1"># 初期状態：最小の部分問題の解を事前設定</span>
+<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a>    <span class="c1"># 初期状態：最小部分問題の解をあらかじめ設定</span>
 <a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>    <span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">1</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span>
 <a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a>    <span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">1</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span>
-<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a>    <span class="c1"># 状態遷移：小さい部分問題から大きい部分問題を段階的に解く</span>
+<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a>    <span class="c1"># 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
 <a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a>        <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span>
 <a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a>        <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">2</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">2</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span>
@@ -4621,19 +4929,19 @@ dp[i, 2] = dp[i-2, 1] + dp[i-2, 2]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* 制約付き階段登り：動的プログラミング */</span>
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* 制約付き階段登り：動的計画法 */</span>
 <a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsConstraintDP</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化し、部分問題の解を格納するために使用</span>
+<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
 <a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">));</span>
-<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w">    </span><span class="c1">// 初期状態：最小の部分問題の解を事前設定</span>
+<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
 <a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w">    </span><span class="c1">// 状態遷移：小さな問題から大きな部分問題を段階的に解く</span>
+<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
 <a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="mi">2</span><span class="p">];</span>
 <a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">][</span><span class="mi">2</span><span class="p">];</span>
@@ -4643,19 +4951,19 @@ dp[i, 2] = dp[i-2, 1] + dp[i-2, 2]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 制約付き階段登り：動的プログラミング */</span>
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 制約付き階段登り：動的計画法 */</span>
 <a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsConstraintDP</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化し、部分問題の解を格納するために使用</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
 <a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">    </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="mi">3</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">    </span><span class="c1">// 初期状態：最小の部分問題の解を事前設定</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
 <a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">1</span><span class="o">][</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">1</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">2</span><span class="o">][</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">2</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w">    </span><span class="c1">// 状態遷移：小さな問題から大きな部分問題を段階的に解く</span>
+<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
 <a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="o">][</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span><span class="p">;</span>
@@ -4665,54 +4973,246 @@ dp[i, 2] = dp[i-2, 1] + dp[i-2, 2]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">climbing_stairs_constraint_dp</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">ClimbingStairsConstraintDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 制約付き階段登り：動的計画法 */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">ClimbingStairsConstraintDP</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="kt">int</span><span class="p">[,]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">];</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">];</span>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">];</span>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">];</span>
+<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">climbingStairsConstraintDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 制約付き階段登り：動的計画法 */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">climbingStairsConstraintDP</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">    </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][</span><span class="mi">3</span><span class="p">]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">2</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">2</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span>
+<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span>
+<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">climbingStairsConstraintDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* 制約付き階段登り：動的計画法 */</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">climbingStairsConstraintDP</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="mi">3</span><span class="p">),</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span>
+<a id="__codelineno-31-16" name="__codelineno-31-16" href="#__codelineno-31-16"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span>
+<a id="__codelineno-31-17" name="__codelineno-31-17" href="#__codelineno-31-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-18" name="__codelineno-31-18" href="#__codelineno-31-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span>
+<a id="__codelineno-31-19" name="__codelineno-31-19" href="#__codelineno-31-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">climbingStairsConstraintDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* 制約付き階段登り：動的計画法 */</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">climbingStairsConstraintDP</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">(</span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">),</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mf">3</span><span class="p">));</span>
+<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-32-10" name="__codelineno-32-10" href="#__codelineno-32-10"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="mf">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mf">2</span><span class="p">][</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mf">2</span><span class="p">][</span><span class="mf">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-32-14" name="__codelineno-32-14" href="#__codelineno-32-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-15" name="__codelineno-32-15" href="#__codelineno-32-15"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="mf">2</span><span class="p">];</span>
+<a id="__codelineno-32-16" name="__codelineno-32-16" href="#__codelineno-32-16"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mf">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">2</span><span class="p">][</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">2</span><span class="p">][</span><span class="mf">2</span><span class="p">];</span>
+<a id="__codelineno-32-17" name="__codelineno-32-17" href="#__codelineno-32-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-18" name="__codelineno-32-18" href="#__codelineno-32-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="mf">2</span><span class="p">];</span>
+<a id="__codelineno-32-19" name="__codelineno-32-19" href="#__codelineno-32-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">climbingStairsConstraintDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* 制約付き階段登り：動的計画法 */</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">climbingStairsConstraintDP</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="kt">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mf">3</span><span class="p">));</span>
+<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="mf">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mf">2</span><span class="p">][</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mf">2</span><span class="p">][</span><span class="mf">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="mf">2</span><span class="p">];</span>
+<a id="__codelineno-33-16" name="__codelineno-33-16" href="#__codelineno-33-16"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mf">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">2</span><span class="p">][</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">2</span><span class="p">][</span><span class="mf">2</span><span class="p">];</span>
+<a id="__codelineno-33-17" name="__codelineno-33-17" href="#__codelineno-33-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-18" name="__codelineno-33-18" href="#__codelineno-33-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="mf">2</span><span class="p">];</span>
+<a id="__codelineno-33-19" name="__codelineno-33-19" href="#__codelineno-33-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsConstraintDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* 制約付き階段登り：動的計画法 */</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">climbingStairsConstraintDP</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="w">  </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">generate</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">));</span>
+<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w">  </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="w">  </span><span class="n">dp</span><span class="p">[</span><span class="m">1</span><span class="p">][</span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-34-10" name="__codelineno-34-10" href="#__codelineno-34-10"></a><span class="w">  </span><span class="n">dp</span><span class="p">[</span><span class="m">1</span><span class="p">][</span><span class="m">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-34-11" name="__codelineno-34-11" href="#__codelineno-34-11"></a><span class="w">  </span><span class="n">dp</span><span class="p">[</span><span class="m">2</span><span class="p">][</span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-34-12" name="__codelineno-34-12" href="#__codelineno-34-12"></a><span class="w">  </span><span class="n">dp</span><span class="p">[</span><span class="m">2</span><span class="p">][</span><span class="m">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-34-13" name="__codelineno-34-13" href="#__codelineno-34-13"></a><span class="w">  </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-34-14" name="__codelineno-34-14" href="#__codelineno-34-14"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-15" name="__codelineno-34-15" href="#__codelineno-34-15"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">][</span><span class="m">2</span><span class="p">];</span>
+<a id="__codelineno-34-16" name="__codelineno-34-16" href="#__codelineno-34-16"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="m">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">2</span><span class="p">][</span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">2</span><span class="p">][</span><span class="m">2</span><span class="p">];</span>
+<a id="__codelineno-34-17" name="__codelineno-34-17" href="#__codelineno-34-17"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-18" name="__codelineno-34-18" href="#__codelineno-34-18"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="m">2</span><span class="p">];</span>
+<a id="__codelineno-34-19" name="__codelineno-34-19" href="#__codelineno-34-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbing_stairs_constraint_dp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* 制約付き階段登り：動的計画法 */</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">climbing_stairs_constraint_dp</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="w">    </span><span class="p">};</span>
+<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="fm">vec!</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="mi">3</span><span class="p">];</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-35-12" name="__codelineno-35-12" href="#__codelineno-35-12"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-35-13" name="__codelineno-35-13" href="#__codelineno-35-13"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-35-14" name="__codelineno-35-14" href="#__codelineno-35-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">3</span><span class="o">..=</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-15" name="__codelineno-35-15" href="#__codelineno-35-15"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="mi">2</span><span class="p">];</span>
+<a id="__codelineno-35-16" name="__codelineno-35-16" href="#__codelineno-35-16"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">][</span><span class="mi">2</span><span class="p">];</span>
+<a id="__codelineno-35-17" name="__codelineno-35-17" href="#__codelineno-35-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-18" name="__codelineno-35-18" href="#__codelineno-35-18"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span>
+<a id="__codelineno-35-19" name="__codelineno-35-19" href="#__codelineno-35-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsConstraintDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* 制約付き階段登り：動的計画法 */</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsConstraintDP</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">**</span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">((</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">));</span>
+<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">calloc</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-36-14" name="__codelineno-36-14" href="#__codelineno-36-14"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-36-15" name="__codelineno-36-15" href="#__codelineno-36-15"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-36-16" name="__codelineno-36-16" href="#__codelineno-36-16"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-36-17" name="__codelineno-36-17" href="#__codelineno-36-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-18" name="__codelineno-36-18" href="#__codelineno-36-18"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="mi">2</span><span class="p">];</span>
+<a id="__codelineno-36-19" name="__codelineno-36-19" href="#__codelineno-36-19"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">][</span><span class="mi">2</span><span class="p">];</span>
+<a id="__codelineno-36-20" name="__codelineno-36-20" href="#__codelineno-36-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-21" name="__codelineno-36-21" href="#__codelineno-36-21"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="mi">2</span><span class="p">];</span>
+<a id="__codelineno-36-22" name="__codelineno-36-22" href="#__codelineno-36-22"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-36-23" name="__codelineno-36-23" href="#__codelineno-36-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-24" name="__codelineno-36-24" href="#__codelineno-36-24"></a><span class="w">        </span><span class="n">free</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-36-25" name="__codelineno-36-25" href="#__codelineno-36-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-26" name="__codelineno-36-26" href="#__codelineno-36-26"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">dp</span><span class="p">);</span>
+<a id="__codelineno-36-27" name="__codelineno-36-27" href="#__codelineno-36-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-36-28" name="__codelineno-36-28" href="#__codelineno-36-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbingStairsConstraintDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* 制約付き階段登り：動的計画法 */</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">climbingStairsConstraintDP</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Array</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="m">3</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="m">1</span><span class="o">][</span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="m">1</span><span class="o">][</span><span class="m">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="m">2</span><span class="o">][</span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="m">2</span><span class="o">][</span><span class="m">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-37-14" name="__codelineno-37-14" href="#__codelineno-37-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">3.</span><span class="p">.</span><span class="na">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-15" name="__codelineno-37-15" href="#__codelineno-37-15"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">][</span><span class="m">2</span><span class="o">]</span>
+<a id="__codelineno-37-16" name="__codelineno-37-16" href="#__codelineno-37-16"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="m">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">2</span><span class="o">][</span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">2</span><span class="o">][</span><span class="m">2</span><span class="o">]</span>
+<a id="__codelineno-37-17" name="__codelineno-37-17" href="#__codelineno-37-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-18" name="__codelineno-37-18" href="#__codelineno-37-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="m">2</span><span class="o">]</span>
+<a id="__codelineno-37-19" name="__codelineno-37-19" href="#__codelineno-37-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbing_stairs_constraint_dp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="c1">### 制約付き階段登り：動的計画法 ###</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_constraint_dp</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a>
+<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="w">  </span><span class="c1"># 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w">  </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="w">  </span><span class="c1"># 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="mi">1</span><span class="o">][</span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">1</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="mi">2</span><span class="o">][</span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">2</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a><span class="w">  </span><span class="c1"># 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">3</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span>
+<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="o">][</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span>
+<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a>
+<a id="__codelineno-38-16" name="__codelineno-38-16" href="#__codelineno-38-16"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span>
+<a id="__codelineno-38-17" name="__codelineno-38-17" href="#__codelineno-38-17"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>上記のケースでは、前の状態のみを考慮すればよいため、状態定義を拡張することで依然として無記憶性を満たすことができます。しかし、一部の問題では非常に深刻な「状態効果」があります。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20climbing_stairs_constraint_dp%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%88%B6%E7%B4%84%E4%BB%98%E3%81%8D%E9%9A%8E%E6%AE%B5%E7%99%BB%E3%82%8A%EF%BC%9A%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20if%20n%20%3D%3D%201%20or%20n%20%3D%3D%202%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%E3%81%AE%E8%A7%A3%E3%82%92%E4%BF%9D%E5%AD%98%E3%81%99%E3%82%8B%E3%81%9F%E3%82%81%E3%81%AB%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5B%5B0%5D%20%2A%203%20for%20_%20in%20range%28n%20%2B%201%29%5D%0A%20%20%20%20%23%20%E5%88%9D%E6%9C%9F%E7%8A%B6%E6%85%8B%EF%BC%9A%E6%9C%80%E5%B0%8F%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%E3%81%AE%E8%A7%A3%E3%82%92%E3%81%82%E3%82%89%E3%81%8B%E3%81%98%E3%82%81%E8%A8%AD%E5%AE%9A%0A%20%20%20%20dp%5B1%5D%5B1%5D%2C%20dp%5B1%5D%5B2%5D%20%3D%201%2C%200%0A%20%20%20%20dp%5B2%5D%5B1%5D%2C%20dp%5B2%5D%5B2%5D%20%3D%200%2C%201%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%B0%8F%E3%81%95%E3%81%84%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%E3%81%8B%E3%82%89%E5%A4%A7%E3%81%8D%E3%81%84%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%E3%81%B8%E9%A0%86%E3%81%AB%E8%A7%A3%E3%81%8F%0A%20%20%20%20for%20i%20in%20range%283%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20dp%5Bi%5D%5B1%5D%20%3D%20dp%5Bi%20-%201%5D%5B2%5D%0A%20%20%20%20%20%20%20%20dp%5Bi%5D%5B2%5D%20%3D%20dp%5Bi%20-%202%5D%5B1%5D%20%2B%20dp%5Bi%20-%202%5D%5B2%5D%0A%20%20%20%20return%20dp%5Bn%5D%5B1%5D%20%2B%20dp%5Bn%5D%5B2%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%209%0A%0A%20%20%20%20res%20%3D%20climbing_stairs_constraint_dp%28n%29%0A%20%20%20%20print%28f%22%7Bn%7D%20%E6%AE%B5%E3%81%AE%E9%9A%8E%E6%AE%B5%E3%82%92%E4%B8%8A%E3%82%8B%E6%96%B9%E6%B3%95%E3%81%AF%E5%85%A8%E9%83%A8%E3%81%A7%20%7Bres%7D%20%E9%80%9A%E3%82%8A%E3%81%A7%E3%81%99%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20climbing_stairs_constraint_dp%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%88%B6%E7%B4%84%E4%BB%98%E3%81%8D%E9%9A%8E%E6%AE%B5%E7%99%BB%E3%82%8A%EF%BC%9A%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20if%20n%20%3D%3D%201%20or%20n%20%3D%3D%202%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%E3%81%AE%E8%A7%A3%E3%82%92%E4%BF%9D%E5%AD%98%E3%81%99%E3%82%8B%E3%81%9F%E3%82%81%E3%81%AB%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5B%5B0%5D%20%2A%203%20for%20_%20in%20range%28n%20%2B%201%29%5D%0A%20%20%20%20%23%20%E5%88%9D%E6%9C%9F%E7%8A%B6%E6%85%8B%EF%BC%9A%E6%9C%80%E5%B0%8F%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%E3%81%AE%E8%A7%A3%E3%82%92%E3%81%82%E3%82%89%E3%81%8B%E3%81%98%E3%82%81%E8%A8%AD%E5%AE%9A%0A%20%20%20%20dp%5B1%5D%5B1%5D%2C%20dp%5B1%5D%5B2%5D%20%3D%201%2C%200%0A%20%20%20%20dp%5B2%5D%5B1%5D%2C%20dp%5B2%5D%5B2%5D%20%3D%200%2C%201%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%B0%8F%E3%81%95%E3%81%84%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%E3%81%8B%E3%82%89%E5%A4%A7%E3%81%8D%E3%81%84%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%E3%81%B8%E9%A0%86%E3%81%AB%E8%A7%A3%E3%81%8F%0A%20%20%20%20for%20i%20in%20range%283%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20dp%5Bi%5D%5B1%5D%20%3D%20dp%5Bi%20-%201%5D%5B2%5D%0A%20%20%20%20%20%20%20%20dp%5Bi%5D%5B2%5D%20%3D%20dp%5Bi%20-%202%5D%5B1%5D%20%2B%20dp%5Bi%20-%202%5D%5B2%5D%0A%20%20%20%20return%20dp%5Bn%5D%5B1%5D%20%2B%20dp%5Bn%5D%5B2%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%209%0A%0A%20%20%20%20res%20%3D%20climbing_stairs_constraint_dp%28n%29%0A%20%20%20%20print%28f%22%7Bn%7D%20%E6%AE%B5%E3%81%AE%E9%9A%8E%E6%AE%B5%E3%82%92%E4%B8%8A%E3%82%8B%E6%96%B9%E6%B3%95%E3%81%AF%E5%85%A8%E9%83%A8%E3%81%A7%20%7Bres%7D%20%E9%80%9A%E3%82%8A%E3%81%A7%E3%81%99%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>上の例では、追加で考慮すべきなのは一つ前の状態だけであるため、状態定義を拡張することで問題を再び無後効性に適合させることができます。しかし、問題によっては非常に強い「後効性」があります。</p>
 <div class="admonition question">
-<p class="admonition-title">障害物生成付き階段登り</p>
-<p><span class="arithmatex">\(n\)</span> 段の階段があり、毎回1段または2段上ることができます。**<span class="arithmatex">\(i\)</span> 段目に登ったとき、システムが自動的に <span class="arithmatex">\(2i\)</span> 段目に障害物を置き、その後のすべてのラウンドで <span class="arithmatex">\(2i\)</span> 段目にジャンプすることが禁止される**と規定されています。例えば、最初の2ラウンドで2段目と3段目にジャンプした場合、その後は4段目と6段目にジャンプできません。頂上に登る方法は何通りありますか？</p>
+<p class="admonition-title">階段昇りと障害物生成</p>
+<p>全部で <span class="arithmatex">\(n\)</span> 段ある階段が与えられ、各ステップで <span class="arithmatex">\(1\)</span> 段または <span class="arithmatex">\(2\)</span> 段上ることができます。**第 <span class="arithmatex">\(i\)</span> 段に到達すると、システムは自動的に第 <span class="arithmatex">\(2i\)</span> 段に障害物を置き、それ以降はどの回でも第 <span class="arithmatex">\(2i\)</span> 段へ跳ぶことができない**とします。例えば、最初の 2 回でそれぞれ第 <span class="arithmatex">\(2\)</span> 段、第 <span class="arithmatex">\(3\)</span> 段に到達した場合、その後は第 <span class="arithmatex">\(4\)</span> 段と第 <span class="arithmatex">\(6\)</span> 段に跳ぶことはできません。頂上まで上る方法は何通りあるでしょうか。</p>
 </div>
-<p>この問題では、次のジャンプはすべての過去の状態に依存します。各ジャンプがより高い段に障害物を置き、将来のジャンプに影響するからです。このような問題では、動的プログラミングはしばしば解決に苦労します。</p>
-<p>実際、多くの複雑な組み合わせ最適化問題（巡回セールスマン問題など）は無記憶性を満たしません。このような問題に対しては、通常、ヒューリスティック探索、遺伝的アルゴリズム、強化学習などの他の方法を選択して、限られた時間内に使用可能な局所最適解を得ます。</p>
+<p>この問題では、次の跳躍が過去のすべての状態に依存します。なぜなら、各跳躍がより高い段に障害物を設置し、将来の跳躍に影響するからです。この種の問題は、動的計画法では解きにくいことが多いです。</p>
+<p>実際、多くの複雑な組合せ最適化問題（例えば巡回セールスマン問題）は無後効性を満たしません。このような問題に対しては、通常、ヒューリスティック探索、遺伝的アルゴリズム、強化学習などの他の方法を用いて、限られた時間内に実用的な局所最適解を得ます。</p>
 
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+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
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-        <title>14.3 動的プログラミング問題解決アプローチ - Hello アルゴリズム</title>
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         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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-        2. &nbsp; 方法2：メモ化探索
+        2. &nbsp; 方法 2：メモ化探索
       
     </span>
   </a>
@@ -3719,7 +3719,7 @@
   <a href="#3-3" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3. &nbsp; 方法3：動的プログラミング
+        3. &nbsp; 方法 3：動的計画法
       
     </span>
   </a>
@@ -3765,7 +3765,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3958,7 +3958,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4203,7 +4203,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4360,19 +4360,19 @@
   <a href="#1432" class="md-nav__link">
     <span class="md-ellipsis">
       
-        14.3.2 &nbsp; 問題解決ステップ
+        14.3.2 &nbsp; 問題を解く手順
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="14.3.2 問題解決ステップ">
+    <nav class="md-nav" aria-label="14.3.2 問題を解く手順">
       <ul class="md-nav__list">
         
           <li class="md-nav__item">
   <a href="#1-1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; 方法1：力任せ探索
+        1. &nbsp; 方法 1：力任せ探索
       
     </span>
   </a>
@@ -4383,7 +4383,7 @@
   <a href="#2-2" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2. &nbsp; 方法2：メモ化探索
+        2. &nbsp; 方法 2：メモ化探索
       
     </span>
   </a>
@@ -4394,7 +4394,7 @@
   <a href="#3-3" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3. &nbsp; 方法3：動的プログラミング
+        3. &nbsp; 方法 3：動的計画法
       
     </span>
   </a>
@@ -4454,53 +4454,53 @@
 
 
 <!-- Page content -->
-<h1 id="143">14.3 &nbsp; 動的プログラミング問題解決アプローチ<a class="headerlink" href="#143" title="Permanent link">&para;</a></h1>
-<p>前の2つのセクションでは、動的プログラミング問題の主要な特徴を紹介しました。次に、より実用的な2つの問題を一緒に探索しましょう。</p>
+<h1 id="143">14.3 &nbsp; 動的計画法の問題解決の考え方<a class="headerlink" href="#143" title="Permanent link">&para;</a></h1>
+<p>前の 2 節では動的計画法の問題の主要な特徴を紹介しました。ここからは、さらに実用的な 2 つの問題を一緒に考えていきます。</p>
 <ol>
-<li>問題が動的プログラミング問題かどうかをどのように判断するか？</li>
-<li>動的プログラミング問題を解決する完全なステップは何か？</li>
+<li>ある問題が動的計画法の問題かどうかを、どのように判断すればよいでしょうか？</li>
+<li>動的計画法の問題を解くには、どこから着手し、完全な手順はどのようなものでしょうか？</li>
 </ol>
 <h2 id="1431">14.3.1 &nbsp; 問題の判定<a class="headerlink" href="#1431" title="Permanent link">&para;</a></h2>
-<p>一般的に言えば、問題が重複する部分問題、最適部分構造を含み、無記憶性を示す場合、通常動的プログラミング解法に適しています。しかし、問題の説明から直接これらの特徴を抽出することはしばしば困難です。したがって、通常は条件を緩和し、**まず問題がバックトラッキング（全探索）を使用した解決に適しているかどうかを観察**します。</p>
-<p>**バックトラッキングに適した問題は通常「決定木モデル」に適合**し、これは木構造を使用して記述でき、各ノードは決定を表し、各パスは決定のシーケンスを表します。</p>
-<p>言い換えると、問題が明示的な決定概念を含み、解が一連の決定を通じて生成される場合、それは決定木モデルに適合し、通常バックトラッキングを使用して解決できます。</p>
-<p>この基礎の上で、動的プログラミング問題を判定するための「ボーナスポイント」があります。</p>
+<p>一般に、ある問題が重複部分問題と最適部分構造を含み、さらに無後效性を満たしているなら、通常は動的計画法で解くのに適しています。しかし、問題文からこれらの性質を直接読み取るのは簡単ではありません。そのため通常は条件を少し緩めて、**まずその問題がバックトラッキング（全探索）で解くのに適しているか**を観察します。</p>
+<p><strong>バックトラッキングで解くのに適した問題は、通常「決定木モデル」を満たします</strong>。この種の問題は木構造で表現でき、各ノードは 1 つの決定を表し、各経路は 1 つの決定列を表します。</p>
+<p>言い換えると、問題に明確な決定の概念が含まれており、解が一連の決定によって生成されるなら、その問題は決定木モデルを満たし、通常はバックトラッキングで解くことができます。</p>
+<p>これに加えて、動的計画法の問題には判定のための「加点要素」もあります。</p>
 <ul>
-<li>問題に最大化（最小化）または最も（最も少ない）最適な解を見つけるという記述が含まれている。</li>
-<li>問題の状態がリスト、多次元行列、または木を使用して表現でき、状態がその周囲の状態と再帰関係を持っている。</li>
+<li>問題文に最大（最小）や最多（最少）などの最適化に関する記述がある。</li>
+<li>問題の状態が配列、多次元行列、または木で表現でき、ある状態とその周辺の状態の間に漸化的な関係がある。</li>
 </ul>
-<p>対応して、「ペナルティポイント」もあります。</p>
+<p>反対に、「減点要素」もあります。</p>
 <ul>
-<li>問題の目標は最適解だけでなく、すべての可能な解を見つけることである。</li>
-<li>問題の説明に順列と組み合わせの明らかな特徴があり、特定の複数の解を返す必要がある。</li>
+<li>問題の目的が最適解を求めることではなく、あり得るすべての解を列挙することである。</li>
+<li>問題文に明確な順列・組合せの特徴があり、具体的な複数の解を返す必要がある。</li>
 </ul>
-<p>問題が決定木モデルに適合し、比較的明らかな「ボーナスポイント」を持つ場合、それが動的プログラミング問題であると仮定し、解決プロセス中に検証できます。</p>
-<h2 id="1432">14.3.2 &nbsp; 問題解決ステップ<a class="headerlink" href="#1432" title="Permanent link">&para;</a></h2>
-<p>動的プログラミング問題解決プロセスは問題の性質と難易度によって異なりますが、一般的に次のステップに従います：決定の記述、状態の定義、<span class="arithmatex">\(dp\)</span> テーブルの確立、状態遷移方程式の導出、境界条件の決定など。</p>
-<p>問題解決ステップをより具体的に説明するために、古典的な問題「最小経路和」を例として使用します。</p>
+<p>ある問題が決定木モデルを満たし、さらに比較的明確な「加点要素」を備えているなら、その問題は動的計画法の問題であると仮定し、解く過程でそれを検証できます。</p>
+<h2 id="1432">14.3.2 &nbsp; 問題を解く手順<a class="headerlink" href="#1432" title="Permanent link">&para;</a></h2>
+<p>動的計画法の解法の流れは問題の性質や難易度によって異なりますが、通常は次の手順に従います。すなわち、決定を記述し、状態を定義し、<span class="arithmatex">\(dp\)</span> テーブルを構築し、状態遷移方程式を導出し、境界条件を定めます。</p>
+<p>解法の手順をより具体的に示すために、ここでは古典的な問題である「最小経路和」を例にします。</p>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
-<p><span class="arithmatex">\(n \times m\)</span> の二次元グリッド <code>grid</code> が与えられ、グリッドの各セルには負でない整数が含まれ、そのセルのコストを表します。ロボットは左上のセルから始まり、各ステップで下または右にのみ移動でき、右下のセルに到達するまで続けます。左上から右下への最小経路和を返してください。</p>
+<p><span class="arithmatex">\(n \times m\)</span> の 2 次元グリッド <code>grid</code> が与えられます。グリッドの各セルには非負整数が格納されており、そのセルのコストを表します。ロボットは左上のセルを始点とし、毎回下または右に 1 マスだけ移動して、右下のセルまで進みます。左上から右下までの最小経路和を返してください。</p>
 </div>
-<p>下の図は例を示しており、与えられたグリッドの最小経路和は <span class="arithmatex">\(13\)</span> です。</p>
-<p><img alt="最小経路和の例データ" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_example.png" /></p>
-<p align="center"> 図 14-10 &nbsp; 最小経路和の例データ </p>
+<p>次の図は 1 つの例を示しており、このグリッドの最小経路和は <span class="arithmatex">\(13\)</span> です。</p>
+<p><img alt="最小経路和のサンプルデータ" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_example.png" /></p>
+<p align="center"> 図 14-10 &nbsp; 最小経路和のサンプルデータ </p>
 
-<p><strong>第1ステップ：各ラウンドの決定を考え、状態を定義し、それにより <span class="arithmatex">\(dp\)</span> テーブルを得る</strong></p>
-<p>この問題の各ラウンドの決定は、現在のセルから下または右に1ステップ移動することです。現在のセルの行と列のインデックスが <span class="arithmatex">\([i, j]\)</span> であると仮定すると、下または右に移動した後、インデックスは <span class="arithmatex">\([i+1, j]\)</span> または <span class="arithmatex">\([i, j+1]\)</span> になります。したがって、状態には2つの変数が含まれるべきです：行インデックスと列インデックス、<span class="arithmatex">\([i, j]\)</span> と表記されます。</p>
-<p>状態 <span class="arithmatex">\([i, j]\)</span> は部分問題に対応します：開始点 <span class="arithmatex">\([0, 0]\)</span> から <span class="arithmatex">\([i, j]\)</span> への最小経路和、<span class="arithmatex">\(dp[i, j]\)</span> と表記されます。</p>
-<p>このようにして、下の図に示す二次元 <span class="arithmatex">\(dp\)</span> 行列を得ます。そのサイズは入力グリッド <span class="arithmatex">\(grid\)</span> と同じです。</p>
-<p><img alt="状態定義とDPテーブル" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_solution_state_definition.png" /></p>
-<p align="center"> 図 14-11 &nbsp; 状態定義とDPテーブル </p>
+<p><strong>ステップ 1：各ラウンドの決定を考え、状態を定義して、<span class="arithmatex">\(dp\)</span> テーブルを得る</strong></p>
+<p>この問題における各ラウンドの決定は、現在のマスから下または右へ 1 マス進むことです。現在のマスの行・列インデックスを <span class="arithmatex">\([i, j]\)</span> とすると、下または右へ 1 マス進んだ後のインデックスは <span class="arithmatex">\([i+1, j]\)</span> または <span class="arithmatex">\([i, j+1]\)</span> になります。したがって、状態には行インデックスと列インデックスの 2 つの変数を含め、<span class="arithmatex">\([i, j]\)</span> と表します。</p>
+<p>状態 <span class="arithmatex">\([i, j]\)</span> に対応する部分問題は、始点 <span class="arithmatex">\([0, 0]\)</span> から <span class="arithmatex">\([i, j]\)</span> まで進む最小経路和であり、その解を <span class="arithmatex">\(dp[i, j]\)</span> と記します。</p>
+<p>これで、次の図に示す 2 次元の <span class="arithmatex">\(dp\)</span> 行列が得られます。そのサイズは入力グリッド <span class="arithmatex">\(grid\)</span> と同じです。</p>
+<p><img alt="状態の定義と dp テーブル" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_solution_state_definition.png" /></p>
+<p align="center"> 図 14-11 &nbsp; 状態の定義と dp テーブル </p>
 
 <div class="admonition note">
 <p class="admonition-title">Note</p>
-<p>動的プログラミングとバックトラッキングは決定のシーケンスとして記述でき、状態はすべての決定変数から構成されます。問題解決の進行を記述するすべての変数を含むべきで、次の状態を導出するのに十分な情報を含んでいる必要があります。</p>
-<p>各状態は部分問題に対応し、すべての部分問題の解を保存するための <span class="arithmatex">\(dp\)</span> テーブルを定義します。状態の各独立変数は <span class="arithmatex">\(dp\)</span> テーブルの次元です。本質的に、<span class="arithmatex">\(dp\)</span> テーブルは状態と部分問題の解の間のマッピングです。</p>
+<p>動的計画法とバックトラッキングの過程は、いずれも 1 つの決定列として記述できます。そして状態は、すべての決定変数から構成されます。状態には解法の進行状況を表すすべての変数が含まれているべきであり、次の状態を導くのに十分な情報を持っている必要があります。</p>
+<p>各状態は 1 つの部分問題に対応しており、すべての部分問題の解を保存するために <span class="arithmatex">\(dp\)</span> テーブルを定義します。状態の各独立変数は、<span class="arithmatex">\(dp\)</span> テーブルの 1 つの次元に対応します。本質的に、<span class="arithmatex">\(dp\)</span> テーブルは状態と部分問題の解との対応関係です。</p>
 </div>
-<p><strong>第2ステップ：最適部分構造を特定し、状態遷移方程式を導出する</strong></p>
-<p>状態 <span class="arithmatex">\([i, j]\)</span> について、それは上のセル <span class="arithmatex">\([i-1, j]\)</span> または左のセル <span class="arithmatex">\([i, j-1]\)</span> からのみ導出できます。したがって、最適部分構造は：<span class="arithmatex">\([i, j]\)</span> に到達する最小経路和は、<span class="arithmatex">\([i, j-1]\)</span> と <span class="arithmatex">\([i-1, j]\)</span> の最小経路和の小さい方によって決定されます。</p>
-<p>上記の分析に基づいて、下の図に示す状態遷移方程式を導出できます：</p>
+<p><strong>ステップ 2：最適部分構造を見つけ、状態遷移方程式を導出する</strong></p>
+<p>状態 <span class="arithmatex">\([i, j]\)</span> は、上のマス <span class="arithmatex">\([i-1, j]\)</span> または左のマス <span class="arithmatex">\([i, j-1]\)</span> からしか遷移してきません。したがって最適部分構造は、<span class="arithmatex">\([i, j]\)</span> に到達する最小経路和が、<span class="arithmatex">\([i, j-1]\)</span> の最小経路和と <span class="arithmatex">\([i-1, j]\)</span> の最小経路和のうち小さい方によって決まる、ということです。</p>
+<p>以上の分析から、次の図に示す状態遷移方程式を導くことができます。</p>
 <div class="arithmatex">\[
 dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
 \]</div>
@@ -4509,252 +4509,637 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
 
 <div class="admonition note">
 <p class="admonition-title">Note</p>
-<p>定義された <span class="arithmatex">\(dp\)</span> テーブルに基づいて、元の問題と部分問題の関係を考え、部分問題の最適解から元の問題の最適解をどのように構築するか、つまり最適部分構造を見つけます。</p>
-<p>最適部分構造を特定したら、それを使用して状態遷移方程式を構築できます。</p>
+<p>定義済みの <span class="arithmatex">\(dp\)</span> テーブルに基づいて、元の問題と部分問題の関係を考え、部分問題の最適解から元の問題の最適解を構成する方法、すなわち最適部分構造を見つけます。</p>
+<p>ひとたび最適部分構造が見つかれば、それを使って状態遷移方程式を構築できます。</p>
 </div>
-<p><strong>第3ステップ：境界条件と状態遷移順序を決定する</strong></p>
-<p>この問題では、最初の行の状態は左の状態からのみ来ることができ、最初の列の状態は上の状態からのみ来ることができるため、最初の行 <span class="arithmatex">\(i = 0\)</span> と最初の列 <span class="arithmatex">\(j = 0\)</span> が境界条件です。</p>
-<p>下の図に示すように、各セルは左のセルと上のセルから導出されるため、ループを使用して行列を走査し、外側のループは行を反復し、内側のループは列を反復します。</p>
-<p><img alt="境界条件と状態遷移順序" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_solution_initial_state.png" /></p>
-<p align="center"> 図 14-13 &nbsp; 境界条件と状態遷移順序 </p>
+<p><strong>ステップ 3：境界条件と状態遷移の順序を決める</strong></p>
+<p>この問題では、先頭行にある状態は左の状態からしか得られず、先頭列にある状態は上の状態からしか得られません。したがって、先頭行 <span class="arithmatex">\(i = 0\)</span> と先頭列 <span class="arithmatex">\(j = 0\)</span> が境界条件になります。</p>
+<p>次の図に示すように、各マスは左のマスと上のマスから遷移してくるため、ループを用いて行列を走査します。外側のループで各行を、内側のループで各列を走査します。</p>
+<p><img alt="境界条件と状態遷移の順序" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_solution_initial_state.png" /></p>
+<p align="center"> 図 14-13 &nbsp; 境界条件と状態遷移の順序 </p>
 
 <div class="admonition note">
 <p class="admonition-title">Note</p>
-<p>境界条件は動的プログラミングで <span class="arithmatex">\(dp\)</span> テーブルを初期化するために使用され、探索では枝刈りに使用されます。</p>
-<p>状態遷移順序の核心は、現在の問題の解を計算するとき、それが依存するすべての小さな部分問題が既に正しく計算されていることを確保することです。</p>
+<p>境界条件は、動的計画法では <span class="arithmatex">\(dp\)</span> テーブルの初期化に使われ、探索では枝刈りに使われます。</p>
+<p>状態遷移の順序で重要なのは、現在の問題の解を計算するときに、それが依存するより小さな部分問題の解がすべてすでに正しく計算済みであることを保証する点です。</p>
 </div>
-<p>上記の分析に基づいて、動的プログラミングコードを直接書くことができます。しかし、部分問題の分解はトップダウンアプローチであるため、「力任せ探索 → メモ化探索 → 動的プログラミング」の順序で実装することが習慣的な思考により適合します。</p>
-<h3 id="1-1">1. &nbsp; 方法1：力任せ探索<a class="headerlink" href="#1-1" title="Permanent link">&para;</a></h3>
-<p>状態 <span class="arithmatex">\([i, j]\)</span> から探索を開始し、それを常により小さな状態 <span class="arithmatex">\([i-1, j]\)</span> と <span class="arithmatex">\([i, j-1]\)</span> に分解します。再帰関数には以下の要素が含まれます。</p>
+<p>以上の分析により、すでに動的計画法のコードを直接書くことができます。しかし、部分問題への分解はトップダウンの考え方であるため、「力任せ探索 <span class="arithmatex">\(\rightarrow\)</span> メモ化探索 <span class="arithmatex">\(\rightarrow\)</span> 動的計画法」の順に実装するほうが、思考の流れにはより自然です。</p>
+<h3 id="1-1">1. &nbsp; 方法 1：力任せ探索<a class="headerlink" href="#1-1" title="Permanent link">&para;</a></h3>
+<p>状態 <span class="arithmatex">\([i, j]\)</span> から探索を開始し、より小さな状態 <span class="arithmatex">\([i-1, j]\)</span> と <span class="arithmatex">\([i, j-1]\)</span> へと分解していきます。再帰関数には次の要素が含まれます。</p>
 <ul>
-<li><strong>再帰パラメータ</strong>：状態 <span class="arithmatex">\([i, j]\)</span>。</li>
-<li><strong>戻り値</strong>：<span class="arithmatex">\([0, 0]\)</span> から <span class="arithmatex">\([i, j]\)</span> への最小経路和 <span class="arithmatex">\(dp[i, j]\)</span>。</li>
+<li><strong>再帰引数</strong>：状態 <span class="arithmatex">\([i, j]\)</span> 。</li>
+<li><strong>戻り値</strong>：<span class="arithmatex">\([0, 0]\)</span> から <span class="arithmatex">\([i, j]\)</span> までの最小経路和 <span class="arithmatex">\(dp[i, j]\)</span> 。</li>
 <li><strong>終了条件</strong>：<span class="arithmatex">\(i = 0\)</span> かつ <span class="arithmatex">\(j = 0\)</span> のとき、コスト <span class="arithmatex">\(grid[0, 0]\)</span> を返す。</li>
-<li><strong>枝刈り</strong>：<span class="arithmatex">\(i &lt; 0\)</span> または <span class="arithmatex">\(j &lt; 0\)</span> でインデックスが範囲外のとき、コスト <span class="arithmatex">\(+\infty\)</span> を返し、実行不可能性を表す。</li>
+<li><strong>枝刈り</strong>：<span class="arithmatex">\(i &lt; 0\)</span> または <span class="arithmatex">\(j &lt; 0\)</span> でインデックスが範囲外になった場合、コスト <span class="arithmatex">\(+\infty\)</span> を返し、実行不可能であることを表す。</li>
 </ul>
-<p>実装コードは以下の通りです：</p>
+<p>実装コードは次のとおりです。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">min_path_sum.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_path_sum_dfs</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]],</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;最小パス和：ブルートフォース探索&quot;&quot;&quot;</span>
-<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 左上のセルの場合、探索を終了</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;最小経路和：全探索&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 左上のセルなら探索を終了する</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="mi">0</span> <span class="ow">and</span> <span class="n">j</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="k">return</span> <span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
-<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 行または列のインデックスが範囲外の場合、+∞ コストを返す</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="k">if</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">j</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">:</span>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="k">return</span> <span class="n">inf</span>
-<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="c1"># 左上から (i-1, j) と (i, j-1) への最小パスコストを計算</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="c1"># 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する</span>
 <a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="n">up</span> <span class="o">=</span> <span class="n">min_path_sum_dfs</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">j</span><span class="p">)</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="n">left</span> <span class="o">=</span> <span class="n">min_path_sum_dfs</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="c1"># 左上から (i, j) への最小パスコストを返す</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="c1"># 左上隅から (i, j) までの最小経路コストを返す</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="k">return</span> <span class="nb">min</span><span class="p">(</span><span class="n">left</span><span class="p">,</span> <span class="n">up</span><span class="p">)</span> <span class="o">+</span> <span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 最小パス和：ブルートフォース探索 */</span>
+<div class="highlight"><span class="filename">min_path_sum.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 最小経路和：全探索 */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minPathSumDFS</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 左上のセルの場合、探索を終了</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 左上のセルなら探索を終了する</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外の場合、+∞ のコストを返す</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">;</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="c1">// 左上から (i-1, j) と (i, j-1) への最小パスコストを計算</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="c1">// 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFS</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFS</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="c1">// 左上から (i, j) への最小パスコストを返す</span>
-<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="c1">// 左上隅から (i, j) までの最小経路コストを返す</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="p">)</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">INT_MAX</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">;</span>
 <a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 最小パス和：ブルートフォース探索 */</span>
+<div class="highlight"><span class="filename">min_path_sum.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 最小経路和：全探索 */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minPathSumDFS</span><span class="p">(</span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 左上のセルの場合、探索を終了</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 左上のセルなら探索を終了する</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外の場合、+∞ のコストを返す</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">Integer</span><span class="p">.</span><span class="na">MAX_VALUE</span><span class="p">;</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="c1">// 左上から (i-1, j) と (i, j-1) への最小パスコストを計算</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="c1">// 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する</span>
 <a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFS</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFS</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="c1">// 左上から (i, j) への最小パスコストを返す</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="c1">// 左上隅から (i, j) までの最小経路コストを返す</span>
 <a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">min_path_sum</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MinPathSumDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 最小経路和：全探索 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">MinPathSumDFS</span><span class="p">(</span><span class="kt">int</span><span class="p">[][]</span><span class="w"> </span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="c1">// 左上のセルなら探索を終了する</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kt">int</span><span class="p">.</span><span class="n">MaxValue</span><span class="p">;</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">    </span><span class="c1">// 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MinPathSumDFS</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MinPathSumDFS</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">    </span><span class="c1">// 左上隅から (i, j) までの最小経路コストを返す</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Min</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">minPathSumDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 最小経路和：全探索 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">minPathSumDFS</span><span class="p">(</span><span class="nx">grid</span><span class="w"> </span><span class="p">[][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// 左上のセルなら探索を終了する</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">MaxInt</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">    </span><span class="c1">// 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">    </span><span class="nx">up</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">minPathSumDFS</span><span class="p">(</span><span class="nx">grid</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">    </span><span class="nx">left</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">minPathSumDFS</span><span class="p">(</span><span class="nx">grid</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">    </span><span class="c1">// 左上隅から (i, j) までの最小経路コストを返す</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Min</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">left</span><span class="p">),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">up</span><span class="p">)))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">minPathSumDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 最小経路和：全探索 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">minPathSumDFS</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span><span class="w"> </span><span class="p">[[</span><span class="nb">Int</span><span class="p">]],</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// 左上のセルなら探索を終了する</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">.</span><span class="bp">max</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">    </span><span class="c1">// 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">up</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">minPathSumDFS</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span><span class="w"> </span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">minPathSumDFS</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span><span class="w"> </span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">    </span><span class="c1">// 左上隅から (i, j) までの最小経路コストを返す</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="bp">min</span><span class="p">(</span><span class="kr">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">minPathSumDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 最小経路和：全探索 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">minPathSumDFS</span><span class="p">(</span><span class="nx">grid</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="c1">// 左上のセルなら探索を終了する</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="mf">0</span><span class="p">];</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">Infinity</span><span class="p">;</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">    </span><span class="c1">// 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">minPathSumDFS</span><span class="p">(</span><span class="nx">grid</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">);</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">minPathSumDFS</span><span class="p">(</span><span class="nx">grid</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">    </span><span class="c1">// 左上隅から (i, j) までの最小経路コストを返す</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">up</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">minPathSumDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 最小経路和：全探索 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">minPathSumDFS</span><span class="p">(</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="nx">grid</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="nb">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="nx">j</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="c1">// 左上のセルなら探索を終了する</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="mf">0</span><span class="p">];</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">Infinity</span><span class="p">;</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">    </span><span class="c1">// 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">minPathSumDFS</span><span class="p">(</span><span class="nx">grid</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">);</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">minPathSumDFS</span><span class="p">(</span><span class="nx">grid</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">    </span><span class="c1">// 左上隅から (i, j) までの最小経路コストを返す</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">up</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minPathSumDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 最小経路和：全探索 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">minPathSumDFS</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="c1">// 左上のセルなら探索を終了する</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="m">0</span><span class="p">][</span><span class="m">0</span><span class="p">];</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="c1">// 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">    </span><span class="c1">// Dart では、int 型は固定範囲の整数であり、「無限大」を表す値は存在しない</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">BigInt</span><span class="p">.</span><span class="n">from</span><span class="p">(</span><span class="m">2</span><span class="p">).</span><span class="n">pow</span><span class="p">(</span><span class="m">31</span><span class="p">).</span><span class="n">toInt</span><span class="p">();</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">  </span><span class="c1">// 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFS</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFS</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">  </span><span class="c1">// 左上隅から (i, j) までの最小経路コストを返す</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">min_path_sum_dfs</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 最小経路和：全探索 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">min_path_sum_dfs</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="c1">// 左上のセルなら探索を終了する</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kt">i32</span><span class="p">::</span><span class="n">MAX</span><span class="p">;</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">    </span><span class="c1">// 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min_path_sum_dfs</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min_path_sum_dfs</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">    </span><span class="c1">// 左上隅から (i, j) までの最小経路コストを返す</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">    </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">min</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minPathSumDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 最小経路和：全探索 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minPathSumDFS</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">MAX_SIZE</span><span class="p">][</span><span class="n">MAX_SIZE</span><span class="p">],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="c1">// 左上のセルなら探索を終了する</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">;</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="c1">// 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFS</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFS</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">    </span><span class="c1">// 左上隅から (i, j) までの最小経路コストを返す</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">myMin</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="p">)</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">INT_MAX</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">myMin</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">;</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">minPathSumDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 最小経路和：全探索 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">minPathSumDFS</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span><span class="w"> </span><span class="n">Array</span><span class="o">&lt;</span><span class="n">IntArray</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="c1">// 左上のセルなら探索を終了する</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="m">0</span><span class="o">][</span><span class="m">0</span><span class="o">]</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kt">Int</span><span class="p">.</span><span class="na">MAX_VALUE</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">    </span><span class="c1">// 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFS</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFS</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">    </span><span class="c1">// 左上隅から (i, j) までの最小経路コストを返す</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">min_path_sum_dfs</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 最小経路和：全探索 ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_path_sum_dfs</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># 左上のセルなら探索を終了する</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="c1"># 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="nb">Float</span><span class="o">::</span><span class="no">INFINITY</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">  </span><span class="c1"># 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">  </span><span class="n">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min_path_sum_dfs</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">  </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min_path_sum_dfs</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">  </span><span class="c1"># 左上隅から (i, j) までの最小経路コストを返す</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">  </span><span class="o">[</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="o">].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>下の図は <span class="arithmatex">\(dp[2, 1]\)</span> を根とする再帰木を示しており、いくつかの重複する部分問題を含み、その数はグリッド <code>grid</code> のサイズが増加すると急激に増加します。</p>
-<p>本質的に、重複する部分問題の理由は：**左上隅から特定のセルに到達する複数のパスが存在する**ことです。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=from%20math%20import%20inf%0A%0Adef%20min_path_sum_dfs%28grid%3A%20list%5Blist%5Bint%5D%5D%2C%20i%3A%20int%2C%20j%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E6%9C%80%E5%B0%8F%E7%B5%8C%E8%B7%AF%E5%92%8C%EF%BC%9A%E5%85%A8%E6%8E%A2%E7%B4%A2%22%22%22%0A%20%20%20%20%23%20%E5%B7%A6%E4%B8%8A%E3%81%AE%E3%82%BB%E3%83%AB%E3%81%AA%E3%82%89%E6%8E%A2%E7%B4%A2%E3%82%92%E7%B5%82%E4%BA%86%E3%81%99%E3%82%8B%0A%20%20%20%20if%20i%20%3D%3D%200%20and%20j%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20return%20grid%5B0%5D%5B0%5D%0A%20%20%20%20%23%20%E8%A1%8C%E3%81%BE%E3%81%9F%E3%81%AF%E5%88%97%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%8C%E7%AF%84%E5%9B%B2%E5%A4%96%E3%81%AA%E3%82%89%E3%80%81%E3%82%B3%E3%82%B9%E3%83%88%20%2B%E2%88%9E%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20if%20i%20%3C%200%20or%20j%20%3C%200%3A%0A%20%20%20%20%20%20%20%20return%20inf%0A%20%20%20%20%23%20%E5%B7%A6%E4%B8%8A%E3%81%8B%E3%82%89%20%28i-1%2C%20j%29%20%E3%81%8A%E3%82%88%E3%81%B3%20%28i%2C%20j-1%29%20%E3%81%BE%E3%81%A7%E3%81%AE%E6%9C%80%E5%B0%8F%E7%B5%8C%E8%B7%AF%E3%82%B3%E3%82%B9%E3%83%88%E3%82%92%E8%A8%88%E7%AE%97%E3%81%99%E3%82%8B%0A%20%20%20%20up%20%3D%20min_path_sum_dfs%28grid%2C%20i%20-%201%2C%20j%29%0A%20%20%20%20left%20%3D%20min_path_sum_dfs%28grid%2C%20i%2C%20j%20-%201%29%0A%20%20%20%20%23%20%E5%B7%A6%E4%B8%8A%E9%9A%85%E3%81%8B%E3%82%89%20%28i%2C%20j%29%20%E3%81%BE%E3%81%A7%E3%81%AE%E6%9C%80%E5%B0%8F%E7%B5%8C%E8%B7%AF%E3%82%B3%E3%82%B9%E3%83%88%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20min%28left%2C%20up%29%20%2B%20grid%5Bi%5D%5Bj%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20grid%20%3D%20%5B%5B1%2C%203%2C%201%2C%205%5D%2C%20%5B2%2C%202%2C%204%2C%202%5D%2C%20%5B5%2C%203%2C%202%2C%201%5D%2C%20%5B4%2C%203%2C%205%2C%202%5D%5D%0A%20%20%20%20n%2C%20m%20%3D%20len%28grid%29%2C%20len%28grid%5B0%5D%29%0A%0A%20%20%20%20%23%20%E5%85%A8%E6%8E%A2%E7%B4%A2%0A%20%20%20%20res%20%3D%20min_path_sum_dfs%28grid%2C%20n%20-%201%2C%20m%20-%201%29%0A%20%20%20%20print%28f%22%E5%B7%A6%E4%B8%8A%E3%81%8B%E3%82%89%E5%8F%B3%E4%B8%8B%E3%81%BE%E3%81%A7%E3%81%AE%E6%9C%80%E5%B0%8F%E7%B5%8C%E8%B7%AF%E5%92%8C%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=from%20math%20import%20inf%0A%0Adef%20min_path_sum_dfs%28grid%3A%20list%5Blist%5Bint%5D%5D%2C%20i%3A%20int%2C%20j%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E6%9C%80%E5%B0%8F%E7%B5%8C%E8%B7%AF%E5%92%8C%EF%BC%9A%E5%85%A8%E6%8E%A2%E7%B4%A2%22%22%22%0A%20%20%20%20%23%20%E5%B7%A6%E4%B8%8A%E3%81%AE%E3%82%BB%E3%83%AB%E3%81%AA%E3%82%89%E6%8E%A2%E7%B4%A2%E3%82%92%E7%B5%82%E4%BA%86%E3%81%99%E3%82%8B%0A%20%20%20%20if%20i%20%3D%3D%200%20and%20j%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20return%20grid%5B0%5D%5B0%5D%0A%20%20%20%20%23%20%E8%A1%8C%E3%81%BE%E3%81%9F%E3%81%AF%E5%88%97%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%8C%E7%AF%84%E5%9B%B2%E5%A4%96%E3%81%AA%E3%82%89%E3%80%81%E3%82%B3%E3%82%B9%E3%83%88%20%2B%E2%88%9E%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20if%20i%20%3C%200%20or%20j%20%3C%200%3A%0A%20%20%20%20%20%20%20%20return%20inf%0A%20%20%20%20%23%20%E5%B7%A6%E4%B8%8A%E3%81%8B%E3%82%89%20%28i-1%2C%20j%29%20%E3%81%8A%E3%82%88%E3%81%B3%20%28i%2C%20j-1%29%20%E3%81%BE%E3%81%A7%E3%81%AE%E6%9C%80%E5%B0%8F%E7%B5%8C%E8%B7%AF%E3%82%B3%E3%82%B9%E3%83%88%E3%82%92%E8%A8%88%E7%AE%97%E3%81%99%E3%82%8B%0A%20%20%20%20up%20%3D%20min_path_sum_dfs%28grid%2C%20i%20-%201%2C%20j%29%0A%20%20%20%20left%20%3D%20min_path_sum_dfs%28grid%2C%20i%2C%20j%20-%201%29%0A%20%20%20%20%23%20%E5%B7%A6%E4%B8%8A%E9%9A%85%E3%81%8B%E3%82%89%20%28i%2C%20j%29%20%E3%81%BE%E3%81%A7%E3%81%AE%E6%9C%80%E5%B0%8F%E7%B5%8C%E8%B7%AF%E3%82%B3%E3%82%B9%E3%83%88%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20min%28left%2C%20up%29%20%2B%20grid%5Bi%5D%5Bj%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20grid%20%3D%20%5B%5B1%2C%203%2C%201%2C%205%5D%2C%20%5B2%2C%202%2C%204%2C%202%5D%2C%20%5B5%2C%203%2C%202%2C%201%5D%2C%20%5B4%2C%203%2C%205%2C%202%5D%5D%0A%20%20%20%20n%2C%20m%20%3D%20len%28grid%29%2C%20len%28grid%5B0%5D%29%0A%0A%20%20%20%20%23%20%E5%85%A8%E6%8E%A2%E7%B4%A2%0A%20%20%20%20res%20%3D%20min_path_sum_dfs%28grid%2C%20n%20-%201%2C%20m%20-%201%29%0A%20%20%20%20print%28f%22%E5%B7%A6%E4%B8%8A%E3%81%8B%E3%82%89%E5%8F%B3%E4%B8%8B%E3%81%BE%E3%81%A7%E3%81%AE%E6%9C%80%E5%B0%8F%E7%B5%8C%E8%B7%AF%E5%92%8C%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>次の図は、<span class="arithmatex">\(dp[2, 1]\)</span> を根ノードとする再帰木を示しています。この中にはいくつかの重複部分問題が含まれており、その数はグリッド <code>grid</code> のサイズが大きくなるにつれて急激に増加します。</p>
+<p>本質的に、重複部分問題が生じる理由は、**左上からあるセルへ到達する経路が複数存在すること**にあります。</p>
 <p><img alt="力任せ探索の再帰木" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_dfs.png" /></p>
 <p align="center"> 図 14-14 &nbsp; 力任せ探索の再帰木 </p>
 
-<p>各状態には下と右の2つの選択があるため、左上隅から右下隅までの総ステップ数は <span class="arithmatex">\(m + n - 2\)</span> で、最悪時間計算量は <span class="arithmatex">\(O(2^{m + n})\)</span> です。この計算方法はグリッドエッジ近くの状況を考慮していないことに注意してください。ネットワークエッジに到達したとき、選択肢が1つしか残らないため、実際のパス数はより少なくなります。</p>
-<h3 id="2-2">2. &nbsp; 方法2：メモ化探索<a class="headerlink" href="#2-2" title="Permanent link">&para;</a></h3>
-<p>グリッド <code>grid</code> と同じサイズのメモリスト <code>mem</code> を導入し、様々な部分問題の解を記録し、重複する部分問題を枝刈りします：</p>
+<p>各状態には下と右の 2 通りの選択肢があり、左上から右下まで進むには合計で <span class="arithmatex">\(m + n - 2\)</span> 歩必要です。したがって最悪時間計算量は <span class="arithmatex">\(O(2^{m + n})\)</span> です。ここで、<span class="arithmatex">\(n\)</span> と <span class="arithmatex">\(m\)</span> はそれぞれグリッドの行数と列数を表します。なお、この見積もりではグリッド境界付近の状況を考慮していません。境界に達すると選択肢は 1 つだけになるため、実際の経路数はこれより少なくなります。</p>
+<h3 id="2-2">2. &nbsp; 方法 2：メモ化探索<a class="headerlink" href="#2-2" title="Permanent link">&para;</a></h3>
+<p>グリッド <code>grid</code> と同じサイズのメモ配列 <code>mem</code> を導入し、各部分問題の解を記録して、重複部分問題を枝刈りします。</p>
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 <div class="tabbed-block">
 <div class="highlight"><span class="filename">min_path_sum.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_path_sum_dfs_mem</span><span class="p">(</span>
 <a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a>    <span class="n">grid</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]],</span> <span class="n">mem</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]],</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="nb">int</span>
 <a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;最小パス和：記憶化探索&quot;&quot;&quot;</span>
-<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># 左上のセルの場合、探索を終了</span>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;最小経路和：メモ化探索&quot;&quot;&quot;</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># 左上のセルなら探索を終了する</span>
 <a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>    <span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="mi">0</span> <span class="ow">and</span> <span class="n">j</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
 <a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>        <span class="k">return</span> <span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
-<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>    <span class="c1"># 行または列のインデックスが範囲外の場合、+∞ コストを返す</span>
+<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>    <span class="c1"># 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
 <a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>    <span class="k">if</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">j</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">:</span>
 <a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>        <span class="k">return</span> <span class="n">inf</span>
-<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>    <span class="c1"># 記録がある場合、それを返す</span>
+<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>    <span class="c1"># 既に記録があればそのまま返す</span>
 <a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>    <span class="k">if</span> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">!=</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span>
 <a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a>        <span class="k">return</span> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
-<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>    <span class="c1"># 左と上のセルからの最小パスコスト</span>
+<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>    <span class="c1"># 左と上のセルからの最小経路コスト</span>
 <a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a>    <span class="n">up</span> <span class="o">=</span> <span class="n">min_path_sum_dfs_mem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span> <span class="n">mem</span><span class="p">,</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">j</span><span class="p">)</span>
 <a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a>    <span class="n">left</span> <span class="o">=</span> <span class="n">min_path_sum_dfs_mem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span> <span class="n">mem</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>    <span class="c1"># 左上から (i, j) への最小パスコストを記録して返す</span>
+<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>    <span class="c1"># 左上から (i, j) までの最小経路コストを記録して返す</span>
 <a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a>    <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">left</span><span class="p">,</span> <span class="n">up</span><span class="p">)</span> <span class="o">+</span> <span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
 <a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a>    <span class="k">return</span> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="p">[</span><span class="k">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minPathSumDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 最小経路和：メモ化探索 */</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minPathSumDFSMem</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="c1">// 左上のセルなら探索を終了する</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">;</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">    </span><span class="c1">// 既に記録があればそのまま返す</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">-1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">    </span><span class="c1">// 左と上のセルからの最小経路コスト</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFSMem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span>
+<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFSMem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w">    </span><span class="c1">// 左上から (i, j) までの最小経路コストを記録して返す</span>
+<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w">    </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="p">)</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">INT_MAX</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">;</span>
+<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 最小パス和：メモ化探索 */</span>
+<div class="highlight"><span class="filename">min_path_sum.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 最小経路和：メモ化探索 */</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minPathSumDFSMem</span><span class="p">(</span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 左上のセルの場合、探索を終了</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 左上のセルなら探索を終了する</span>
 <a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外の場合、+∞ のコストを返す</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
 <a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">Integer</span><span class="p">.</span><span class="na">MAX_VALUE</span><span class="p">;</span>
 <a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">    </span><span class="c1">// 記録がある場合、それを返す</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">    </span><span class="c1">// 既に記録があればそのまま返す</span>
 <a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="c1">// 左と上のセルからの最小パスコスト</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="c1">// 左と上のセルからの最小経路コスト</span>
 <a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFSMem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span>
 <a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFSMem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">    </span><span class="c1">// 左上から (i, j) への最小パスコストを記録して返す</span>
+<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">    </span><span class="c1">// 左上から (i, j) までの最小経路コストを記録して返す</span>
 <a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w">    </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">min_path_sum</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MinPathSumDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 最小経路和：メモ化探索 */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">MinPathSumDFSMem</span><span class="p">(</span><span class="kt">int</span><span class="p">[][]</span><span class="w"> </span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="p">[][]</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="c1">// 左上のセルなら探索を終了する</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kt">int</span><span class="p">.</span><span class="n">MaxValue</span><span class="p">;</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">    </span><span class="c1">// 既に記録があればそのまま返す</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">    </span><span class="c1">// 左と上のセルからの最小経路コスト</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MinPathSumDFSMem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MinPathSumDFSMem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">    </span><span class="c1">// 左上から (i, j) までの最小経路コストを記録して返す</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w">    </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Min</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">minPathSumDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 最小経路和：メモ化探索 */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">minPathSumDFSMem</span><span class="p">(</span><span class="nx">grid</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="w"> </span><span class="p">[][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="c1">// 左上のセルなら探索を終了する</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">MaxInt</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w">    </span><span class="c1">// 既に記録があればそのまま返す</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">    </span><span class="c1">// 左と上のセルからの最小経路コスト</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w">    </span><span class="nx">up</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">minPathSumDFSMem</span><span class="p">(</span><span class="nx">grid</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span>
+<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="w">    </span><span class="nx">left</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">minPathSumDFSMem</span><span class="p">(</span><span class="nx">grid</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="w">    </span><span class="c1">// 左上から (i, j) までの最小経路コストを記録して返す</span>
+<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="w">    </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Min</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">left</span><span class="p">),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">up</span><span class="p">)))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span>
+<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span>
+<a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">minPathSumDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 最小経路和：メモ化探索 */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">minPathSumDFSMem</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span><span class="w"> </span><span class="p">[[</span><span class="nb">Int</span><span class="p">]],</span><span class="w"> </span><span class="n">mem</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[[</span><span class="nb">Int</span><span class="p">]],</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="c1">// 左上のセルなら探索を終了する</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">.</span><span class="bp">max</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w">    </span><span class="c1">// 既に記録があればそのまま返す</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w">    </span><span class="c1">// 左と上のセルからの最小経路コスト</span>
+<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">up</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">minPathSumDFSMem</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span><span class="w"> </span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
+<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">minPathSumDFSMem</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span><span class="w"> </span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="w">    </span><span class="c1">// 左上から (i, j) までの最小経路コストを記録して返す</span>
+<a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a><span class="w">    </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">min</span><span class="p">(</span><span class="kr">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">minPathSumDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 最小経路和：メモ化探索 */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">minPathSumDFSMem</span><span class="p">(</span><span class="nx">grid</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="c1">// 左上のセルなら探索を終了する</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="mf">0</span><span class="p">];</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">Infinity</span><span class="p">;</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w">    </span><span class="c1">// 既に記録があればそのまま返す</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w">    </span><span class="c1">// 左と上のセルからの最小経路コスト</span>
+<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">minPathSumDFSMem</span><span class="p">(</span><span class="nx">grid</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">);</span>
+<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">minPathSumDFSMem</span><span class="p">(</span><span class="nx">grid</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a><span class="w">    </span><span class="c1">// 左上から (i, j) までの最小経路コストを記録して返す</span>
+<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a><span class="w">    </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">up</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">minPathSumDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 最小経路和：メモ化探索 */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">minPathSumDFSMem</span><span class="p">(</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="nx">grid</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="nb">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="nx">mem</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="nb">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">    </span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">    </span><span class="nx">j</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">    </span><span class="c1">// 左上のセルなら探索を終了する</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="mf">0</span><span class="p">];</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">Infinity</span><span class="p">;</span>
+<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a><span class="w">    </span><span class="c1">// 既に記録があればそのまま返す</span>
+<a id="__codelineno-20-17" name="__codelineno-20-17" href="#__codelineno-20-17"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-18" name="__codelineno-20-18" href="#__codelineno-20-18"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-20-19" name="__codelineno-20-19" href="#__codelineno-20-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-20" name="__codelineno-20-20" href="#__codelineno-20-20"></a><span class="w">    </span><span class="c1">// 左と上のセルからの最小経路コスト</span>
+<a id="__codelineno-20-21" name="__codelineno-20-21" href="#__codelineno-20-21"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">minPathSumDFSMem</span><span class="p">(</span><span class="nx">grid</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">);</span>
+<a id="__codelineno-20-22" name="__codelineno-20-22" href="#__codelineno-20-22"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">minPathSumDFSMem</span><span class="p">(</span><span class="nx">grid</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-20-23" name="__codelineno-20-23" href="#__codelineno-20-23"></a><span class="w">    </span><span class="c1">// 左上から (i, j) までの最小経路コストを記録して返す</span>
+<a id="__codelineno-20-24" name="__codelineno-20-24" href="#__codelineno-20-24"></a><span class="w">    </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">up</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-20-25" name="__codelineno-20-25" href="#__codelineno-20-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-20-26" name="__codelineno-20-26" href="#__codelineno-20-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minPathSumDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 最小経路和：メモ化探索 */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">minPathSumDFSMem</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="c1">// 左上のセルなら探索を終了する</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="m">0</span><span class="p">][</span><span class="m">0</span><span class="p">];</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">  </span><span class="c1">// 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">    </span><span class="c1">// Dart では、int 型は固定範囲の整数であり、「無限大」を表す値は存在しない</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">BigInt</span><span class="p">.</span><span class="n">from</span><span class="p">(</span><span class="m">2</span><span class="p">).</span><span class="n">pow</span><span class="p">(</span><span class="m">31</span><span class="p">).</span><span class="n">toInt</span><span class="p">();</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w">  </span><span class="c1">// 既に記録があればそのまま返す</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="w">  </span><span class="c1">// 左と上のセルからの最小経路コスト</span>
+<a id="__codelineno-21-17" name="__codelineno-21-17" href="#__codelineno-21-17"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFSMem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span>
+<a id="__codelineno-21-18" name="__codelineno-21-18" href="#__codelineno-21-18"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFSMem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-21-19" name="__codelineno-21-19" href="#__codelineno-21-19"></a><span class="w">  </span><span class="c1">// 左上から (i, j) までの最小経路コストを記録して返す</span>
+<a id="__codelineno-21-20" name="__codelineno-21-20" href="#__codelineno-21-20"></a><span class="w">  </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-21-21" name="__codelineno-21-21" href="#__codelineno-21-21"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-21-22" name="__codelineno-21-22" href="#__codelineno-21-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">min_path_sum_dfs_mem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 最小経路和：メモ化探索 */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">min_path_sum_dfs_mem</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="c1">// 左上のセルなら探索を終了する</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kt">i32</span><span class="p">::</span><span class="n">MAX</span><span class="p">;</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w">    </span><span class="c1">// 既に記録があればそのまま返す</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">];</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="w">    </span><span class="c1">// 左と上のセルからの最小経路コスト</span>
+<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min_path_sum_dfs_mem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span>
+<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min_path_sum_dfs_mem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="w">    </span><span class="c1">// 左上から (i, j) までの最小経路コストを記録して返す</span>
+<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="w">    </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">min</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">];</span>
+<a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a><span class="w">    </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span>
+<a id="__codelineno-22-21" name="__codelineno-22-21" href="#__codelineno-22-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minPathSumDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 最小経路和：メモ化探索 */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minPathSumDFSMem</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">MAX_SIZE</span><span class="p">][</span><span class="n">MAX_SIZE</span><span class="p">],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">MAX_SIZE</span><span class="p">][</span><span class="n">MAX_SIZE</span><span class="p">],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="c1">// 左上のセルなら探索を終了する</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">;</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w">    </span><span class="c1">// 既に記録があればそのまま返す</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">-1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="w">    </span><span class="c1">// 左と上のセルからの最小経路コスト</span>
+<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFSMem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span>
+<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFSMem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="w">    </span><span class="c1">// 左上から (i, j) までの最小経路コストを記録して返す</span>
+<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="w">    </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">myMin</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="p">)</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">INT_MAX</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">myMin</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">;</span>
+<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">minPathSumDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 最小経路和：メモ化探索 */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">minPathSumDFSMem</span><span class="p">(</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="n">grid</span><span class="p">:</span><span class="w"> </span><span class="n">Array</span><span class="o">&lt;</span><span class="n">IntArray</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="n">mem</span><span class="p">:</span><span class="w"> </span><span class="n">Array</span><span class="o">&lt;</span><span class="n">IntArray</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">    </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">    </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w">    </span><span class="c1">// 左上のセルなら探索を終了する</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="m">0</span><span class="o">][</span><span class="m">0</span><span class="o">]</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kt">Int</span><span class="p">.</span><span class="na">MAX_VALUE</span>
+<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="w">    </span><span class="c1">// 既に記録があればそのまま返す</span>
+<a id="__codelineno-24-17" name="__codelineno-24-17" href="#__codelineno-24-17"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-18" name="__codelineno-24-18" href="#__codelineno-24-18"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-24-19" name="__codelineno-24-19" href="#__codelineno-24-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-20" name="__codelineno-24-20" href="#__codelineno-24-20"></a><span class="w">    </span><span class="c1">// 左と上のセルからの最小経路コスト</span>
+<a id="__codelineno-24-21" name="__codelineno-24-21" href="#__codelineno-24-21"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFSMem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
+<a id="__codelineno-24-22" name="__codelineno-24-22" href="#__codelineno-24-22"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFSMem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-24-23" name="__codelineno-24-23" href="#__codelineno-24-23"></a><span class="w">    </span><span class="c1">// 左上から (i, j) までの最小経路コストを記録して返す</span>
+<a id="__codelineno-24-24" name="__codelineno-24-24" href="#__codelineno-24-24"></a><span class="w">    </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-24-25" name="__codelineno-24-25" href="#__codelineno-24-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-24-26" name="__codelineno-24-26" href="#__codelineno-24-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">min_path_sum_dfs_mem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### 最小経路和：メモ化探索 ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_path_sum_dfs_mem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="c1"># 左上のセルなら探索を終了する</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">  </span><span class="c1"># 行または列のインデックスが範囲外なら、コスト +∞ を返す</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="nb">Float</span><span class="o">::</span><span class="no">INFINITY</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">  </span><span class="c1"># 既に記録があればそのまま返す</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">  </span><span class="c1"># 左と上のセルからの最小経路コスト</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w">  </span><span class="n">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min_path_sum_dfs_mem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w">  </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min_path_sum_dfs_mem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w">  </span><span class="c1"># 左上から (i, j) までの最小経路コストを記録して返す</span>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w">  </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="o">].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>下の図に示すように、メモ化を導入した後、すべての部分問題の解は一度だけ計算される必要があるため、時間計算量は状態の総数、つまりグリッドサイズ <span class="arithmatex">\(O(nm)\)</span> に依存します。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=from%20math%20import%20inf%0A%0Adef%20min_path_sum_dfs_mem%28%0A%20%20%20%20grid%3A%20list%5Blist%5Bint%5D%5D%2C%20mem%3A%20list%5Blist%5Bint%5D%5D%2C%20i%3A%20int%2C%20j%3A%20int%0A%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E6%9C%80%E5%B0%8F%E7%B5%8C%E8%B7%AF%E5%92%8C%EF%BC%9A%E3%83%A1%E3%83%A2%E5%8C%96%E6%8E%A2%E7%B4%A2%22%22%22%0A%20%20%20%20%23%20%E5%B7%A6%E4%B8%8A%E3%81%AE%E3%82%BB%E3%83%AB%E3%81%AA%E3%82%89%E6%8E%A2%E7%B4%A2%E3%82%92%E7%B5%82%E4%BA%86%E3%81%99%E3%82%8B%0A%20%20%20%20if%20i%20%3D%3D%200%20and%20j%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20return%20grid%5B0%5D%5B0%5D%0A%20%20%20%20%23%20%E8%A1%8C%E3%81%BE%E3%81%9F%E3%81%AF%E5%88%97%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%8C%E7%AF%84%E5%9B%B2%E5%A4%96%E3%81%AA%E3%82%89%E3%80%81%E3%82%B3%E3%82%B9%E3%83%88%20%2B%E2%88%9E%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20if%20i%20%3C%200%20or%20j%20%3C%200%3A%0A%20%20%20%20%20%20%20%20return%20inf%0A%20%20%20%20%23%20%E6%97%A2%E3%81%AB%E8%A8%98%E9%8C%B2%E3%81%8C%E3%81%82%E3%82%8C%E3%81%B0%E3%81%9D%E3%81%AE%E3%81%BE%E3%81%BE%E8%BF%94%E3%81%99%0A%20%20%20%20if%20mem%5Bi%5D%5Bj%5D%20%21%3D%20-1%3A%0A%20%20%20%20%20%20%20%20return%20mem%5Bi%5D%5Bj%5D%0A%20%20%20%20%23%20%E5%B7%A6%E3%81%A8%E4%B8%8A%E3%81%AE%E3%82%BB%E3%83%AB%E3%81%8B%E3%82%89%E3%81%AE%E6%9C%80%E5%B0%8F%E7%B5%8C%E8%B7%AF%E3%82%B3%E3%82%B9%E3%83%88%0A%20%20%20%20up%20%3D%20min_path_sum_dfs_mem%28grid%2C%20mem%2C%20i%20-%201%2C%20j%29%0A%20%20%20%20left%20%3D%20min_path_sum_dfs_mem%28grid%2C%20mem%2C%20i%2C%20j%20-%201%29%0A%20%20%20%20%23%20%E5%B7%A6%E4%B8%8A%E3%81%8B%E3%82%89%20%28i%2C%20j%29%20%E3%81%BE%E3%81%A7%E3%81%AE%E6%9C%80%E5%B0%8F%E7%B5%8C%E8%B7%AF%E3%82%B3%E3%82%B9%E3%83%88%E3%82%92%E8%A8%98%E9%8C%B2%E3%81%97%E3%81%A6%E8%BF%94%E3%81%99%0A%20%20%20%20mem%5Bi%5D%5Bj%5D%20%3D%20min%28left%2C%20up%29%20%2B%20grid%5Bi%5D%5Bj%5D%0A%20%20%20%20return%20mem%5Bi%5D%5Bj%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20grid%20%3D%20%5B%5B1%2C%203%2C%201%2C%205%5D%2C%20%5B2%2C%202%2C%204%2C%202%5D%2C%20%5B5%2C%203%2C%202%2C%201%5D%2C%20%5B4%2C%203%2C%205%2C%202%5D%5D%0A%20%20%20%20n%2C%20m%20%3D%20len%28grid%29%2C%20len%28grid%5B0%5D%29%0A%0A%20%20%20%23%20%E3%83%A1%E3%83%A2%E5%8C%96%E6%8E%A2%E7%B4%A2%0A%20%20%20%20mem%20%3D%20%5B%5B-1%5D%20%2A%20m%20for%20_%20in%20range%28n%29%5D%0A%20%20%20%20res%20%3D%20min_path_sum_dfs_mem%28grid%2C%20mem%2C%20n%20-%201%2C%20m%20-%201%29%0A%20%20%20%20print%28f%22%E5%B7%A6%E4%B8%8A%E3%81%8B%E3%82%89%E5%8F%B3%E4%B8%8B%E3%81%BE%E3%81%A7%E3%81%AE%E6%9C%80%E5%B0%8F%E7%B5%8C%E8%B7%AF%E5%92%8C%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=16&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=from%20math%20import%20inf%0A%0Adef%20min_path_sum_dfs_mem%28%0A%20%20%20%20grid%3A%20list%5Blist%5Bint%5D%5D%2C%20mem%3A%20list%5Blist%5Bint%5D%5D%2C%20i%3A%20int%2C%20j%3A%20int%0A%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E6%9C%80%E5%B0%8F%E7%B5%8C%E8%B7%AF%E5%92%8C%EF%BC%9A%E3%83%A1%E3%83%A2%E5%8C%96%E6%8E%A2%E7%B4%A2%22%22%22%0A%20%20%20%20%23%20%E5%B7%A6%E4%B8%8A%E3%81%AE%E3%82%BB%E3%83%AB%E3%81%AA%E3%82%89%E6%8E%A2%E7%B4%A2%E3%82%92%E7%B5%82%E4%BA%86%E3%81%99%E3%82%8B%0A%20%20%20%20if%20i%20%3D%3D%200%20and%20j%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20return%20grid%5B0%5D%5B0%5D%0A%20%20%20%20%23%20%E8%A1%8C%E3%81%BE%E3%81%9F%E3%81%AF%E5%88%97%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%8C%E7%AF%84%E5%9B%B2%E5%A4%96%E3%81%AA%E3%82%89%E3%80%81%E3%82%B3%E3%82%B9%E3%83%88%20%2B%E2%88%9E%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20if%20i%20%3C%200%20or%20j%20%3C%200%3A%0A%20%20%20%20%20%20%20%20return%20inf%0A%20%20%20%20%23%20%E6%97%A2%E3%81%AB%E8%A8%98%E9%8C%B2%E3%81%8C%E3%81%82%E3%82%8C%E3%81%B0%E3%81%9D%E3%81%AE%E3%81%BE%E3%81%BE%E8%BF%94%E3%81%99%0A%20%20%20%20if%20mem%5Bi%5D%5Bj%5D%20%21%3D%20-1%3A%0A%20%20%20%20%20%20%20%20return%20mem%5Bi%5D%5Bj%5D%0A%20%20%20%20%23%20%E5%B7%A6%E3%81%A8%E4%B8%8A%E3%81%AE%E3%82%BB%E3%83%AB%E3%81%8B%E3%82%89%E3%81%AE%E6%9C%80%E5%B0%8F%E7%B5%8C%E8%B7%AF%E3%82%B3%E3%82%B9%E3%83%88%0A%20%20%20%20up%20%3D%20min_path_sum_dfs_mem%28grid%2C%20mem%2C%20i%20-%201%2C%20j%29%0A%20%20%20%20left%20%3D%20min_path_sum_dfs_mem%28grid%2C%20mem%2C%20i%2C%20j%20-%201%29%0A%20%20%20%20%23%20%E5%B7%A6%E4%B8%8A%E3%81%8B%E3%82%89%20%28i%2C%20j%29%20%E3%81%BE%E3%81%A7%E3%81%AE%E6%9C%80%E5%B0%8F%E7%B5%8C%E8%B7%AF%E3%82%B3%E3%82%B9%E3%83%88%E3%82%92%E8%A8%98%E9%8C%B2%E3%81%97%E3%81%A6%E8%BF%94%E3%81%99%0A%20%20%20%20mem%5Bi%5D%5Bj%5D%20%3D%20min%28left%2C%20up%29%20%2B%20grid%5Bi%5D%5Bj%5D%0A%20%20%20%20return%20mem%5Bi%5D%5Bj%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20grid%20%3D%20%5B%5B1%2C%203%2C%201%2C%205%5D%2C%20%5B2%2C%202%2C%204%2C%202%5D%2C%20%5B5%2C%203%2C%202%2C%201%5D%2C%20%5B4%2C%203%2C%205%2C%202%5D%5D%0A%20%20%20%20n%2C%20m%20%3D%20len%28grid%29%2C%20len%28grid%5B0%5D%29%0A%0A%20%20%20%23%20%E3%83%A1%E3%83%A2%E5%8C%96%E6%8E%A2%E7%B4%A2%0A%20%20%20%20mem%20%3D%20%5B%5B-1%5D%20%2A%20m%20for%20_%20in%20range%28n%29%5D%0A%20%20%20%20res%20%3D%20min_path_sum_dfs_mem%28grid%2C%20mem%2C%20n%20-%201%2C%20m%20-%201%29%0A%20%20%20%20print%28f%22%E5%B7%A6%E4%B8%8A%E3%81%8B%E3%82%89%E5%8F%B3%E4%B8%8B%E3%81%BE%E3%81%A7%E3%81%AE%E6%9C%80%E5%B0%8F%E7%B5%8C%E8%B7%AF%E5%92%8C%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=16&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>次の図に示すように、メモ化を導入すると、すべての部分問題の解は 1 回だけ計算すればよくなります。したがって時間計算量は状態総数、すなわちグリッドサイズの <span class="arithmatex">\(O(nm)\)</span> に依存します。</p>
 <p><img alt="メモ化探索の再帰木" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_dfs_mem.png" /></p>
 <p align="center"> 図 14-15 &nbsp; メモ化探索の再帰木 </p>
 
-<h3 id="3-3">3. &nbsp; 方法3：動的プログラミング<a class="headerlink" href="#3-3" title="Permanent link">&para;</a></h3>
-<p>動的プログラミング解法を反復的に実装します。コードは以下の通りです：</p>
+<h3 id="3-3">3. &nbsp; 方法 3：動的計画法<a class="headerlink" href="#3-3" title="Permanent link">&para;</a></h3>
+<p>反復に基づいて動的計画法の解法を実装すると、コードは次のようになります。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">min_path_sum.py</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_path_sum_dp</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;最小パス和：動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;最小経路和：動的計画法&quot;&quot;&quot;</span>
 <a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>    <span class="n">n</span><span class="p">,</span> <span class="n">m</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">grid</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
 <a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>    <span class="c1"># dp テーブルを初期化</span>
 <a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">m</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">)]</span>
 <a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a>    <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
-<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a>    <span class="c1"># 状態遷移：最初の行</span>
+<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a>    <span class="c1"># 状態遷移：先頭行</span>
 <a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>    <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">m</span><span class="p">):</span>
 <a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a>        <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
-<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a>    <span class="c1"># 状態遷移：最初の列</span>
+<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a>    <span class="c1"># 状態遷移：先頭列</span>
 <a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
 <a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a>        <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
-<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a>    <span class="c1"># 状態遷移：残りの行と列</span>
+<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a>    <span class="c1"># 状態遷移: 残りの行と列</span>
 <a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
 <a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">m</span><span class="p">):</span>
 <a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a>            <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">])</span> <span class="o">+</span> <span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
@@ -4762,21 +5147,21 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* 最小パス和：動的プログラミング */</span>
+<div class="highlight"><span class="filename">min_path_sum.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* 最小経路和：動的計画法 */</span>
 <a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minPathSumDP</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">grid</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">.</span><span class="n">size</span><span class="p">(),</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">].</span><span class="n">size</span><span class="p">();</span>
-<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
 <a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">(</span><span class="n">m</span><span class="p">));</span>
 <a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
-<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">    </span><span class="c1">// 状態遷移：最初の行</span>
+<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
 <a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
 <a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="w">    </span><span class="c1">// 状態遷移：最初の列</span>
+<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭列</span>
 <a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
 <a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行と列</span>
+<a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
 <a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-17" name="__codelineno-27-17" href="#__codelineno-27-17"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-18" name="__codelineno-27-18" href="#__codelineno-27-18"></a><span class="w">            </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
@@ -4787,21 +5172,21 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 最小パス和：動的プログラミング */</span>
+<div class="highlight"><span class="filename">min_path_sum.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 最小経路和：動的計画法 */</span>
 <a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minPathSumDP</span><span class="p">(</span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">grid</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">.</span><span class="na">length</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
-<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
 <a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">    </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">m</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">    </span><span class="c1">// 状態遷移：最初の行</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
 <a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="w">    </span><span class="c1">// 状態遷移：最初の列</span>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭列</span>
 <a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行と列</span>
+<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
 <a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-18" name="__codelineno-28-18" href="#__codelineno-28-18"></a><span class="w">            </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
@@ -4812,53 +5197,282 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">min_path_sum</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MinPathSumDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 最小経路和：動的計画法 */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">MinPathSumDP</span><span class="p">(</span><span class="kt">int</span><span class="p">[][]</span><span class="w"> </span><span class="n">grid</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">.</span><span class="n">Length</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">].</span><span class="n">Length</span><span class="p">;</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">    </span><span class="kt">int</span><span class="p">[,]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="p">];</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w">            </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-20" name="__codelineno-29-20" href="#__codelineno-29-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-21" name="__codelineno-29-21" href="#__codelineno-29-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-29-22" name="__codelineno-29-22" href="#__codelineno-29-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">minPathSumDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 最小経路和：動的計画法 */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">minPathSumDP</span><span class="p">(</span><span class="nx">grid</span><span class="w"> </span><span class="p">[][]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">grid</span><span class="p">),</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">    </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="p">)</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-21" name="__codelineno-30-21" href="#__codelineno-30-21"></a><span class="w">            </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Min</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">j</span><span class="p">])))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span>
+<a id="__codelineno-30-22" name="__codelineno-30-22" href="#__codelineno-30-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-30-23" name="__codelineno-30-23" href="#__codelineno-30-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-24" name="__codelineno-30-24" href="#__codelineno-30-24"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">m</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-30-25" name="__codelineno-30-25" href="#__codelineno-30-25"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">minPathSumDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* 最小経路和：動的計画法 */</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">minPathSumDP</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span><span class="w"> </span><span class="p">[[</span><span class="nb">Int</span><span class="p">]])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">grid</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">].</span><span class="bp">count</span>
+<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">m</span><span class="p">),</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-16" name="__codelineno-31-16" href="#__codelineno-31-16"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-31-17" name="__codelineno-31-17" href="#__codelineno-31-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-18" name="__codelineno-31-18" href="#__codelineno-31-18"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-19" name="__codelineno-31-19" href="#__codelineno-31-19"></a><span class="w">            </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-31-20" name="__codelineno-31-20" href="#__codelineno-31-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-31-21" name="__codelineno-31-21" href="#__codelineno-31-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-22" name="__codelineno-31-22" href="#__codelineno-31-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-31-23" name="__codelineno-31-23" href="#__codelineno-31-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">minPathSumDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* 最小経路和：動的計画法 */</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">minPathSumDP</span><span class="p">(</span><span class="nx">grid</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">grid</span><span class="p">.</span><span class="nx">length</span><span class="p">,</span>
+<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="w">        </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mf">0</span><span class="p">].</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span>
+<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="w">        </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span>
+<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w">    </span><span class="p">);</span>
+<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="mf">0</span><span class="p">];</span>
+<a id="__codelineno-32-10" name="__codelineno-32-10" href="#__codelineno-32-10"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-14" name="__codelineno-32-14" href="#__codelineno-32-14"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-32-15" name="__codelineno-32-15" href="#__codelineno-32-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-16" name="__codelineno-32-16" href="#__codelineno-32-16"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mf">0</span><span class="p">];</span>
+<a id="__codelineno-32-17" name="__codelineno-32-17" href="#__codelineno-32-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-18" name="__codelineno-32-18" href="#__codelineno-32-18"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-32-19" name="__codelineno-32-19" href="#__codelineno-32-19"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-20" name="__codelineno-32-20" href="#__codelineno-32-20"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-21" name="__codelineno-32-21" href="#__codelineno-32-21"></a><span class="w">            </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">j</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-32-22" name="__codelineno-32-22" href="#__codelineno-32-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-32-23" name="__codelineno-32-23" href="#__codelineno-32-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-24" name="__codelineno-32-24" href="#__codelineno-32-24"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-32-25" name="__codelineno-32-25" href="#__codelineno-32-25"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">minPathSumDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* 最小経路和：動的計画法 */</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">minPathSumDP</span><span class="p">(</span><span class="nx">grid</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="nb">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;&gt;</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">grid</span><span class="p">.</span><span class="nx">length</span><span class="p">,</span>
+<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w">        </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mf">0</span><span class="p">].</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="kt">n</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span>
+<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w">        </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="kt">m</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span>
+<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w">    </span><span class="p">);</span>
+<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="mf">0</span><span class="p">];</span>
+<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-16" name="__codelineno-33-16" href="#__codelineno-33-16"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mf">0</span><span class="p">];</span>
+<a id="__codelineno-33-17" name="__codelineno-33-17" href="#__codelineno-33-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-18" name="__codelineno-33-18" href="#__codelineno-33-18"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-33-19" name="__codelineno-33-19" href="#__codelineno-33-19"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-20" name="__codelineno-33-20" href="#__codelineno-33-20"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-21" name="__codelineno-33-21" href="#__codelineno-33-21"></a><span class="w">            </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">j</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-33-22" name="__codelineno-33-22" href="#__codelineno-33-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-33-23" name="__codelineno-33-23" href="#__codelineno-33-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-24" name="__codelineno-33-24" href="#__codelineno-33-24"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-33-25" name="__codelineno-33-25" href="#__codelineno-33-25"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minPathSumDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* 最小経路和：動的計画法 */</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">minPathSumDP</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">grid</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="m">0</span><span class="p">].</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w">  </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">generate</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">));</span>
+<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="w">  </span><span class="n">dp</span><span class="p">[</span><span class="m">0</span><span class="p">][</span><span class="m">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="m">0</span><span class="p">][</span><span class="m">0</span><span class="p">];</span>
+<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w">  </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="m">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="m">0</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="m">0</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-34-10" name="__codelineno-34-10" href="#__codelineno-34-10"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-11" name="__codelineno-34-11" href="#__codelineno-34-11"></a><span class="w">  </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-34-12" name="__codelineno-34-12" href="#__codelineno-34-12"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-13" name="__codelineno-34-13" href="#__codelineno-34-13"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="m">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">][</span><span class="m">0</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="m">0</span><span class="p">];</span>
+<a id="__codelineno-34-14" name="__codelineno-34-14" href="#__codelineno-34-14"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-15" name="__codelineno-34-15" href="#__codelineno-34-15"></a><span class="w">  </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-34-16" name="__codelineno-34-16" href="#__codelineno-34-16"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-17" name="__codelineno-34-17" href="#__codelineno-34-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-18" name="__codelineno-34-18" href="#__codelineno-34-18"></a><span class="w">      </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">][</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-34-19" name="__codelineno-34-19" href="#__codelineno-34-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-20" name="__codelineno-34-20" href="#__codelineno-34-20"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-21" name="__codelineno-34-21" href="#__codelineno-34-21"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">][</span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">];</span>
+<a id="__codelineno-34-22" name="__codelineno-34-22" href="#__codelineno-34-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">min_path_sum_dp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* 最小経路和：動的計画法 */</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">min_path_sum_dp</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">grid</span><span class="p">.</span><span class="n">len</span><span class="p">(),</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">].</span><span class="n">len</span><span class="p">());</span>
+<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">m</span><span class="p">];</span><span class="w"> </span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..</span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-35-12" name="__codelineno-35-12" href="#__codelineno-35-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-13" name="__codelineno-35-13" href="#__codelineno-35-13"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-35-14" name="__codelineno-35-14" href="#__codelineno-35-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-15" name="__codelineno-35-15" href="#__codelineno-35-15"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-35-16" name="__codelineno-35-16" href="#__codelineno-35-16"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-17" name="__codelineno-35-17" href="#__codelineno-35-17"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..</span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-18" name="__codelineno-35-18" href="#__codelineno-35-18"></a><span class="w">            </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-35-19" name="__codelineno-35-19" href="#__codelineno-35-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-35-20" name="__codelineno-35-20" href="#__codelineno-35-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-21" name="__codelineno-35-21" href="#__codelineno-35-21"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-35-22" name="__codelineno-35-22" href="#__codelineno-35-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minPathSumDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* 最小経路和：動的計画法 */</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minPathSumDP</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">MAX_SIZE</span><span class="p">][</span><span class="n">MAX_SIZE</span><span class="p">],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">**</span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">));</span>
+<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">calloc</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-36-14" name="__codelineno-36-14" href="#__codelineno-36-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-15" name="__codelineno-36-15" href="#__codelineno-36-15"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-36-16" name="__codelineno-36-16" href="#__codelineno-36-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-17" name="__codelineno-36-17" href="#__codelineno-36-17"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-36-18" name="__codelineno-36-18" href="#__codelineno-36-18"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-19" name="__codelineno-36-19" href="#__codelineno-36-19"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-20" name="__codelineno-36-20" href="#__codelineno-36-20"></a><span class="w">            </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">myMin</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-36-21" name="__codelineno-36-21" href="#__codelineno-36-21"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-36-22" name="__codelineno-36-22" href="#__codelineno-36-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-23" name="__codelineno-36-23" href="#__codelineno-36-23"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-36-24" name="__codelineno-36-24" href="#__codelineno-36-24"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-36-25" name="__codelineno-36-25" href="#__codelineno-36-25"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-26" name="__codelineno-36-26" href="#__codelineno-36-26"></a><span class="w">        </span><span class="n">free</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-36-27" name="__codelineno-36-27" href="#__codelineno-36-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-28" name="__codelineno-36-28" href="#__codelineno-36-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-36-29" name="__codelineno-36-29" href="#__codelineno-36-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">minPathSumDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* 最小経路和：動的計画法 */</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">minPathSumDP</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span><span class="w"> </span><span class="n">Array</span><span class="o">&lt;</span><span class="n">IntArray</span><span class="o">&gt;</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="m">0</span><span class="o">]</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Array</span><span class="p">(</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="m">0</span><span class="o">][</span><span class="m">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="m">0</span><span class="o">][</span><span class="m">0</span><span class="o">]</span>
+<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="m">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="m">0</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="m">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-14" name="__codelineno-37-14" href="#__codelineno-37-14"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="m">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">][</span><span class="m">0</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="m">0</span><span class="o">]</span>
+<a id="__codelineno-37-15" name="__codelineno-37-15" href="#__codelineno-37-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-16" name="__codelineno-37-16" href="#__codelineno-37-16"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-37-17" name="__codelineno-37-17" href="#__codelineno-37-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-18" name="__codelineno-37-18" href="#__codelineno-37-18"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-19" name="__codelineno-37-19" href="#__codelineno-37-19"></a><span class="w">            </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-37-20" name="__codelineno-37-20" href="#__codelineno-37-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-37-21" name="__codelineno-37-21" href="#__codelineno-37-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-22" name="__codelineno-37-22" href="#__codelineno-37-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">][</span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span>
+<a id="__codelineno-37-23" name="__codelineno-37-23" href="#__codelineno-37-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">min_path_sum_dp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="c1">### 最小経路和：動的計画法 ###</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_path_sum_dp</span><span class="p">(</span><span class="n">grid</span><span class="p">)</span>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w">  </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="o">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="n">grid</span><span class="o">.</span><span class="n">first</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w">  </span><span class="c1"># dp テーブルを初期化</span>
+<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="w">  </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span>
+<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="w">  </span><span class="c1"># 状態遷移：先頭行</span>
+<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="w">  </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="n">m</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">j</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="w">  </span><span class="c1"># 状態遷移：先頭列</span>
+<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a><span class="w">  </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a><span class="w">  </span><span class="c1"># 状態遷移: 残りの行と列</span>
+<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="n">n</span>
+<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="n">m</span>
+<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a><span class="w">      </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">j</span><span class="o">]].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-38-16" name="__codelineno-38-16" href="#__codelineno-38-16"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-17" name="__codelineno-38-17" href="#__codelineno-38-17"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="o">][</span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="o">]</span>
+<a id="__codelineno-38-18" name="__codelineno-38-18" href="#__codelineno-38-18"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>下の図は最小経路和の状態遷移プロセスを示し、グリッド全体を走査するため、<strong>時間計算量は <span class="arithmatex">\(O(nm)\)</span></strong> です。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=from%20math%20import%20inf%0A%0Adef%20min_path_sum_dp%28grid%3A%20list%5Blist%5Bint%5D%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E6%9C%80%E5%B0%8F%E7%B5%8C%E8%B7%AF%E5%92%8C%EF%BC%9A%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%2C%20m%20%3D%20len%28grid%29%2C%20len%28grid%5B0%5D%29%0A%20%20%20%20%23%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5B%5B0%5D%20%2A%20m%20for%20_%20in%20range%28n%29%5D%0A%20%20%20%20dp%5B0%5D%5B0%5D%20%3D%20grid%5B0%5D%5B0%5D%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%85%88%E9%A0%AD%E8%A1%8C%0A%20%20%20%20for%20j%20in%20range%281%2C%20m%29%3A%0A%20%20%20%20%20%20%20%20dp%5B0%5D%5Bj%5D%20%3D%20dp%5B0%5D%5Bj%20-%201%5D%20%2B%20grid%5B0%5D%5Bj%5D%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%85%88%E9%A0%AD%E5%88%97%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%29%3A%0A%20%20%20%20%20%20%20%20dp%5Bi%5D%5B0%5D%20%3D%20dp%5Bi%20-%201%5D%5B0%5D%20%2B%20grid%5Bi%5D%5B0%5D%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%3A%20%E6%AE%8B%E3%82%8A%E3%81%AE%E8%A1%8C%E3%81%A8%E5%88%97%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%29%3A%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%281%2C%20m%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Bj%5D%20%3D%20min%28dp%5Bi%5D%5Bj%20-%201%5D%2C%20dp%5Bi%20-%201%5D%5Bj%5D%29%20%2B%20grid%5Bi%5D%5Bj%5D%0A%20%20%20%20return%20dp%5Bn%20-%201%5D%5Bm%20-%201%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20grid%20%3D%20%5B%5B1%2C%203%2C%201%2C%205%5D%2C%20%5B2%2C%202%2C%204%2C%202%5D%2C%20%5B5%2C%203%2C%202%2C%201%5D%2C%20%5B4%2C%203%2C%205%2C%202%5D%5D%0A%20%20%20%20n%2C%20m%20%3D%20len%28grid%29%2C%20len%28grid%5B0%5D%29%0A%0A%20%20%20%20%23%20%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20min_path_sum_dp%28grid%29%0A%20%20%20%20print%28f%22%E5%B7%A6%E4%B8%8A%E3%81%8B%E3%82%89%E5%8F%B3%E4%B8%8B%E3%81%BE%E3%81%A7%E3%81%AE%E6%9C%80%E5%B0%8F%E7%B5%8C%E8%B7%AF%E5%92%8C%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=from%20math%20import%20inf%0A%0Adef%20min_path_sum_dp%28grid%3A%20list%5Blist%5Bint%5D%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E6%9C%80%E5%B0%8F%E7%B5%8C%E8%B7%AF%E5%92%8C%EF%BC%9A%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%2C%20m%20%3D%20len%28grid%29%2C%20len%28grid%5B0%5D%29%0A%20%20%20%20%23%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5B%5B0%5D%20%2A%20m%20for%20_%20in%20range%28n%29%5D%0A%20%20%20%20dp%5B0%5D%5B0%5D%20%3D%20grid%5B0%5D%5B0%5D%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%85%88%E9%A0%AD%E8%A1%8C%0A%20%20%20%20for%20j%20in%20range%281%2C%20m%29%3A%0A%20%20%20%20%20%20%20%20dp%5B0%5D%5Bj%5D%20%3D%20dp%5B0%5D%5Bj%20-%201%5D%20%2B%20grid%5B0%5D%5Bj%5D%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%85%88%E9%A0%AD%E5%88%97%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%29%3A%0A%20%20%20%20%20%20%20%20dp%5Bi%5D%5B0%5D%20%3D%20dp%5Bi%20-%201%5D%5B0%5D%20%2B%20grid%5Bi%5D%5B0%5D%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%3A%20%E6%AE%8B%E3%82%8A%E3%81%AE%E8%A1%8C%E3%81%A8%E5%88%97%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%29%3A%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%281%2C%20m%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Bj%5D%20%3D%20min%28dp%5Bi%5D%5Bj%20-%201%5D%2C%20dp%5Bi%20-%201%5D%5Bj%5D%29%20%2B%20grid%5Bi%5D%5Bj%5D%0A%20%20%20%20return%20dp%5Bn%20-%201%5D%5Bm%20-%201%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20grid%20%3D%20%5B%5B1%2C%203%2C%201%2C%205%5D%2C%20%5B2%2C%202%2C%204%2C%202%5D%2C%20%5B5%2C%203%2C%202%2C%201%5D%2C%20%5B4%2C%203%2C%205%2C%202%5D%5D%0A%20%20%20%20n%2C%20m%20%3D%20len%28grid%29%2C%20len%28grid%5B0%5D%29%0A%0A%20%20%20%20%23%20%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20min_path_sum_dp%28grid%29%0A%20%20%20%20print%28f%22%E5%B7%A6%E4%B8%8A%E3%81%8B%E3%82%89%E5%8F%B3%E4%B8%8B%E3%81%BE%E3%81%A7%E3%81%AE%E6%9C%80%E5%B0%8F%E7%B5%8C%E8%B7%AF%E5%92%8C%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>次の図は最小経路和の状態遷移の過程を示しています。グリッド全体を走査するため、<strong>時間計算量は <span class="arithmatex">\(O(nm)\)</span></strong> です。</p>
 <p>配列 <code>dp</code> のサイズは <span class="arithmatex">\(n \times m\)</span> であるため、<strong>空間計算量は <span class="arithmatex">\(O(nm)\)</span></strong> です。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="4:12"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">&lt;1&gt;</label><label for="__tabbed_4_2">&lt;2&gt;</label><label for="__tabbed_4_3">&lt;3&gt;</label><label for="__tabbed_4_4">&lt;4&gt;</label><label for="__tabbed_4_5">&lt;5&gt;</label><label for="__tabbed_4_6">&lt;6&gt;</label><label for="__tabbed_4_7">&lt;7&gt;</label><label for="__tabbed_4_8">&lt;8&gt;</label><label for="__tabbed_4_9">&lt;9&gt;</label><label for="__tabbed_4_10">&lt;10&gt;</label><label for="__tabbed_4_11">&lt;11&gt;</label><label for="__tabbed_4_12">&lt;12&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="最小経路和の動的プログラミングプロセス" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_dp_step1.png" /></p>
+<p><img alt="最小経路和の動的計画法の過程" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_dp_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="min_path_sum_dp_step2" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_dp_step2.png" /></p>
@@ -4895,26 +5509,26 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
 </div>
 </div>
 </div>
-<p align="center"> 図 14-16 &nbsp; 最小経路和の動的プログラミングプロセス </p>
+<p align="center"> 図 14-16 &nbsp; 最小経路和の動的計画法の過程 </p>
 
 <h3 id="4">4. &nbsp; 空間最適化<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
-<p>各セルは左と上のセルのみに関連するため、単一行配列を使用して <span class="arithmatex">\(dp\)</span> テーブルを実装できます。</p>
-<p>配列 <code>dp</code> は1行の状態のみを表現できるため、最初の列の状態を事前に初期化できず、各行を走査するときに更新することに注意してください：</p>
+<p>各マスは左のマスと上のマスにのみ関係するため、1 行の配列だけを使って <span class="arithmatex">\(dp\)</span> テーブルを実装できます。</p>
+<p>ただし、配列 <code>dp</code> は 1 行分の状態しか表せないため、先頭列の状態を事前に初期化することはできず、各行を走査するときに更新する必要があります。</p>
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 <div class="highlight"><span class="filename">min_path_sum.py</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_path_sum_dp_comp</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;最小パス和：空間最適化動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;最小経路和：空間最適化後の動的計画法&quot;&quot;&quot;</span>
 <a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a>    <span class="n">n</span><span class="p">,</span> <span class="n">m</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">grid</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
 <a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a>    <span class="c1"># dp テーブルを初期化</span>
 <a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">m</span>
-<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a>    <span class="c1"># 状態遷移：最初の行</span>
+<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a>    <span class="c1"># 状態遷移：先頭行</span>
 <a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a>    <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
 <a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a>    <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">m</span><span class="p">):</span>
 <a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a>        <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
 <a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a>    <span class="c1"># 状態遷移：残りの行</span>
 <a id="__codelineno-39-11" name="__codelineno-39-11" href="#__codelineno-39-11"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
-<a id="__codelineno-39-12" name="__codelineno-39-12" href="#__codelineno-39-12"></a>        <span class="c1"># 状態遷移：最初の列</span>
+<a id="__codelineno-39-12" name="__codelineno-39-12" href="#__codelineno-39-12"></a>        <span class="c1"># 状態遷移：先頭列</span>
 <a id="__codelineno-39-13" name="__codelineno-39-13" href="#__codelineno-39-13"></a>        <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
 <a id="__codelineno-39-14" name="__codelineno-39-14" href="#__codelineno-39-14"></a>        <span class="c1"># 状態遷移：残りの列</span>
 <a id="__codelineno-39-15" name="__codelineno-39-15" href="#__codelineno-39-15"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">m</span><span class="p">):</span>
@@ -4923,23 +5537,43 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.cpp</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="p">[</span><span class="k">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minPathSumDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.cpp</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* 最小経路和：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minPathSumDPComp</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">grid</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">.</span><span class="n">size</span><span class="p">(),</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">].</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">m</span><span class="p">);</span>
+<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行</span>
+<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w">        </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a><span class="w">        </span><span class="c1">// 状態遷移：残りの列</span>
+<a id="__codelineno-40-16" name="__codelineno-40-16" href="#__codelineno-40-16"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="w">            </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-40-18" name="__codelineno-40-18" href="#__codelineno-40-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-40-19" name="__codelineno-40-19" href="#__codelineno-40-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-40-20" name="__codelineno-40-20" href="#__codelineno-40-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-40-21" name="__codelineno-40-21" href="#__codelineno-40-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.java</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 最小パス和：空間最適化動的プログラミング */</span>
+<div class="highlight"><span class="filename">min_path_sum.java</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 最小経路和：空間最適化後の動的計画法 */</span>
 <a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minPathSumDPComp</span><span class="p">(</span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">grid</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">.</span><span class="na">length</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
-<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
 <a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a><span class="w">    </span><span class="c1">// 状態遷移：最初の行</span>
+<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
 <a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行</span>
 <a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a><span class="w">        </span><span class="c1">// 状態遷移：最初の列</span>
+<a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a><span class="w">        </span><span class="c1">// 状態遷移：先頭列</span>
 <a id="__codelineno-41-14" name="__codelineno-41-14" href="#__codelineno-41-14"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-41-15" name="__codelineno-41-15" href="#__codelineno-41-15"></a><span class="w">        </span><span class="c1">// 状態遷移：残りの列</span>
 <a id="__codelineno-41-16" name="__codelineno-41-16" href="#__codelineno-41-16"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
@@ -4951,47 +5585,253 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.cs</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">min_path_sum</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MinPathSumDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.cs</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="cm">/* 最小経路和：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">MinPathSumDPComp</span><span class="p">(</span><span class="kt">int</span><span class="p">[][]</span><span class="w"> </span><span class="n">grid</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">.</span><span class="n">Length</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">].</span><span class="n">Length</span><span class="p">;</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="w">    </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">m</span><span class="p">];</span>
+<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行</span>
+<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a><span class="w">        </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-42-14" name="__codelineno-42-14" href="#__codelineno-42-14"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-42-15" name="__codelineno-42-15" href="#__codelineno-42-15"></a><span class="w">        </span><span class="c1">// 状態遷移：残りの列</span>
+<a id="__codelineno-42-16" name="__codelineno-42-16" href="#__codelineno-42-16"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-17" name="__codelineno-42-17" href="#__codelineno-42-17"></a><span class="w">            </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-42-18" name="__codelineno-42-18" href="#__codelineno-42-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-42-19" name="__codelineno-42-19" href="#__codelineno-42-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-42-20" name="__codelineno-42-20" href="#__codelineno-42-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-42-21" name="__codelineno-42-21" href="#__codelineno-42-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.go</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">minPathSumDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.go</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* 最小経路和：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">minPathSumDPComp</span><span class="p">(</span><span class="nx">grid</span><span class="w"> </span><span class="p">[][]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w">    </span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">grid</span><span class="p">),</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w">    </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="p">)</span>
+<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span>
+<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="w">        </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-43-14" name="__codelineno-43-14" href="#__codelineno-43-14"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-43-15" name="__codelineno-43-15" href="#__codelineno-43-15"></a><span class="w">        </span><span class="c1">// 状態遷移：残りの列</span>
+<a id="__codelineno-43-16" name="__codelineno-43-16" href="#__codelineno-43-16"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-17" name="__codelineno-43-17" href="#__codelineno-43-17"></a><span class="w">            </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Min</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">])))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span>
+<a id="__codelineno-43-18" name="__codelineno-43-18" href="#__codelineno-43-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-43-19" name="__codelineno-43-19" href="#__codelineno-43-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-20" name="__codelineno-43-20" href="#__codelineno-43-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">m</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-43-21" name="__codelineno-43-21" href="#__codelineno-43-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.swift</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">minPathSumDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.swift</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* 最小経路和：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">minPathSumDPComp</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span><span class="w"> </span><span class="p">[[</span><span class="nb">Int</span><span class="p">]])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">grid</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">].</span><span class="bp">count</span>
+<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">m</span><span class="p">)</span>
+<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行</span>
+<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a><span class="w">        </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-44-15" name="__codelineno-44-15" href="#__codelineno-44-15"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-44-16" name="__codelineno-44-16" href="#__codelineno-44-16"></a><span class="w">        </span><span class="c1">// 状態遷移：残りの列</span>
+<a id="__codelineno-44-17" name="__codelineno-44-17" href="#__codelineno-44-17"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-18" name="__codelineno-44-18" href="#__codelineno-44-18"></a><span class="w">            </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-44-19" name="__codelineno-44-19" href="#__codelineno-44-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-44-20" name="__codelineno-44-20" href="#__codelineno-44-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-21" name="__codelineno-44-21" href="#__codelineno-44-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-44-22" name="__codelineno-44-22" href="#__codelineno-44-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.js</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">minPathSumDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.js</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="cm">/* 最小経路和：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">minPathSumDPComp</span><span class="p">(</span><span class="nx">grid</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">grid</span><span class="p">.</span><span class="nx">length</span><span class="p">,</span>
+<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w">        </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mf">0</span><span class="p">].</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">m</span><span class="p">);</span>
+<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="mf">0</span><span class="p">];</span>
+<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行</span>
+<a id="__codelineno-45-13" name="__codelineno-45-13" href="#__codelineno-45-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-14" name="__codelineno-45-14" href="#__codelineno-45-14"></a><span class="w">        </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-45-15" name="__codelineno-45-15" href="#__codelineno-45-15"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mf">0</span><span class="p">];</span>
+<a id="__codelineno-45-16" name="__codelineno-45-16" href="#__codelineno-45-16"></a><span class="w">        </span><span class="c1">// 状態遷移：残りの列</span>
+<a id="__codelineno-45-17" name="__codelineno-45-17" href="#__codelineno-45-17"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-18" name="__codelineno-45-18" href="#__codelineno-45-18"></a><span class="w">            </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-45-19" name="__codelineno-45-19" href="#__codelineno-45-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-45-20" name="__codelineno-45-20" href="#__codelineno-45-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-45-21" name="__codelineno-45-21" href="#__codelineno-45-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-45-22" name="__codelineno-45-22" href="#__codelineno-45-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.ts</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">minPathSumDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.ts</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="cm">/* 最小経路和：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">minPathSumDPComp</span><span class="p">(</span><span class="nx">grid</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="nb">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;&gt;</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">grid</span><span class="p">.</span><span class="nx">length</span><span class="p">,</span>
+<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w">        </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mf">0</span><span class="p">].</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">m</span><span class="p">);</span>
+<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="mf">0</span><span class="p">];</span>
+<a id="__codelineno-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-46-12" name="__codelineno-46-12" href="#__codelineno-46-12"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行</span>
+<a id="__codelineno-46-13" name="__codelineno-46-13" href="#__codelineno-46-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-14" name="__codelineno-46-14" href="#__codelineno-46-14"></a><span class="w">        </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-46-15" name="__codelineno-46-15" href="#__codelineno-46-15"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mf">0</span><span class="p">];</span>
+<a id="__codelineno-46-16" name="__codelineno-46-16" href="#__codelineno-46-16"></a><span class="w">        </span><span class="c1">// 状態遷移：残りの列</span>
+<a id="__codelineno-46-17" name="__codelineno-46-17" href="#__codelineno-46-17"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-18" name="__codelineno-46-18" href="#__codelineno-46-18"></a><span class="w">            </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-46-19" name="__codelineno-46-19" href="#__codelineno-46-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-46-20" name="__codelineno-46-20" href="#__codelineno-46-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-46-21" name="__codelineno-46-21" href="#__codelineno-46-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-46-22" name="__codelineno-46-22" href="#__codelineno-46-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.dart</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minPathSumDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.dart</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* 最小経路和：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">minPathSumDPComp</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">grid</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="m">0</span><span class="p">].</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w">  </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a><span class="w">  </span><span class="n">dp</span><span class="p">[</span><span class="m">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="m">0</span><span class="p">][</span><span class="m">0</span><span class="p">];</span>
+<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="m">0</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="w">  </span><span class="c1">// 状態遷移：残りの行</span>
+<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-47-13" name="__codelineno-47-13" href="#__codelineno-47-13"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="m">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="m">0</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="m">0</span><span class="p">];</span>
+<a id="__codelineno-47-14" name="__codelineno-47-14" href="#__codelineno-47-14"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの列</span>
+<a id="__codelineno-47-15" name="__codelineno-47-15" href="#__codelineno-47-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-16" name="__codelineno-47-16" href="#__codelineno-47-16"></a><span class="w">      </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-47-17" name="__codelineno-47-17" href="#__codelineno-47-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-47-18" name="__codelineno-47-18" href="#__codelineno-47-18"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-47-19" name="__codelineno-47-19" href="#__codelineno-47-19"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">];</span>
+<a id="__codelineno-47-20" name="__codelineno-47-20" href="#__codelineno-47-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.rs</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">min_path_sum_dp_comp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.rs</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="cm">/* 最小経路和：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">min_path_sum_dp_comp</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">grid</span><span class="p">.</span><span class="n">len</span><span class="p">(),</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">].</span><span class="n">len</span><span class="p">());</span>
+<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">m</span><span class="p">];</span>
+<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..</span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-48-11" name="__codelineno-48-11" href="#__codelineno-48-11"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行</span>
+<a id="__codelineno-48-12" name="__codelineno-48-12" href="#__codelineno-48-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-13" name="__codelineno-48-13" href="#__codelineno-48-13"></a><span class="w">        </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-48-14" name="__codelineno-48-14" href="#__codelineno-48-14"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-48-15" name="__codelineno-48-15" href="#__codelineno-48-15"></a><span class="w">        </span><span class="c1">// 状態遷移：残りの列</span>
+<a id="__codelineno-48-16" name="__codelineno-48-16" href="#__codelineno-48-16"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..</span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-17" name="__codelineno-48-17" href="#__codelineno-48-17"></a><span class="w">            </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-48-18" name="__codelineno-48-18" href="#__codelineno-48-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-48-19" name="__codelineno-48-19" href="#__codelineno-48-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-48-20" name="__codelineno-48-20" href="#__codelineno-48-20"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-48-21" name="__codelineno-48-21" href="#__codelineno-48-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.c</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minPathSumDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.c</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* 最小経路和：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minPathSumDPComp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">MAX_SIZE</span><span class="p">][</span><span class="n">MAX_SIZE</span><span class="p">],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">calloc</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-49-9" name="__codelineno-49-9" href="#__codelineno-49-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-49-10" name="__codelineno-49-10" href="#__codelineno-49-10"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行</span>
+<a id="__codelineno-49-11" name="__codelineno-49-11" href="#__codelineno-49-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-12" name="__codelineno-49-12" href="#__codelineno-49-12"></a><span class="w">        </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-49-13" name="__codelineno-49-13" href="#__codelineno-49-13"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-49-14" name="__codelineno-49-14" href="#__codelineno-49-14"></a><span class="w">        </span><span class="c1">// 状態遷移：残りの列</span>
+<a id="__codelineno-49-15" name="__codelineno-49-15" href="#__codelineno-49-15"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-16" name="__codelineno-49-16" href="#__codelineno-49-16"></a><span class="w">            </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">myMin</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-49-17" name="__codelineno-49-17" href="#__codelineno-49-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-49-18" name="__codelineno-49-18" href="#__codelineno-49-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-49-19" name="__codelineno-49-19" href="#__codelineno-49-19"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-49-20" name="__codelineno-49-20" href="#__codelineno-49-20"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-49-21" name="__codelineno-49-21" href="#__codelineno-49-21"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">dp</span><span class="p">);</span>
+<a id="__codelineno-49-22" name="__codelineno-49-22" href="#__codelineno-49-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-49-23" name="__codelineno-49-23" href="#__codelineno-49-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.kt</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">minPathSumDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.kt</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* 最小経路和：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">minPathSumDPComp</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span><span class="w"> </span><span class="n">Array</span><span class="o">&lt;</span><span class="n">IntArray</span><span class="o">&gt;</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="m">0</span><span class="o">]</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
+<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="m">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="m">0</span><span class="o">][</span><span class="m">0</span><span class="o">]</span>
+<a id="__codelineno-50-9" name="__codelineno-50-9" href="#__codelineno-50-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-10" name="__codelineno-50-10" href="#__codelineno-50-10"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="m">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-50-11" name="__codelineno-50-11" href="#__codelineno-50-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-50-12" name="__codelineno-50-12" href="#__codelineno-50-12"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行</span>
+<a id="__codelineno-50-13" name="__codelineno-50-13" href="#__codelineno-50-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-14" name="__codelineno-50-14" href="#__codelineno-50-14"></a><span class="w">        </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-50-15" name="__codelineno-50-15" href="#__codelineno-50-15"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="m">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="m">0</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="m">0</span><span class="o">]</span>
+<a id="__codelineno-50-16" name="__codelineno-50-16" href="#__codelineno-50-16"></a><span class="w">        </span><span class="c1">// 状態遷移：残りの列</span>
+<a id="__codelineno-50-17" name="__codelineno-50-17" href="#__codelineno-50-17"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-18" name="__codelineno-50-18" href="#__codelineno-50-18"></a><span class="w">            </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-50-19" name="__codelineno-50-19" href="#__codelineno-50-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-50-20" name="__codelineno-50-20" href="#__codelineno-50-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-50-21" name="__codelineno-50-21" href="#__codelineno-50-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span>
+<a id="__codelineno-50-22" name="__codelineno-50-22" href="#__codelineno-50-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">min_path_sum_dp_comp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="c1">### 最小経路和：空間最適化後の動的計画法 ###</span>
+<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_path_sum_dp_comp</span><span class="p">(</span><span class="n">grid</span><span class="p">)</span>
+<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w">  </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="o">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="n">grid</span><span class="o">.</span><span class="n">first</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a><span class="w">  </span><span class="c1"># dp テーブルを初期化</span>
+<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w">  </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a><span class="w">  </span><span class="c1"># 状態遷移：先頭行</span>
+<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span>
+<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="w">  </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="n">m</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">j</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a><span class="w">  </span><span class="c1"># 状態遷移：残りの行</span>
+<a id="__codelineno-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="n">n</span>
+<a id="__codelineno-51-11" name="__codelineno-51-11" href="#__codelineno-51-11"></a><span class="w">    </span><span class="c1"># 状態遷移：先頭列</span>
+<a id="__codelineno-51-12" name="__codelineno-51-12" href="#__codelineno-51-12"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span>
+<a id="__codelineno-51-13" name="__codelineno-51-13" href="#__codelineno-51-13"></a><span class="w">    </span><span class="c1"># 状態遷移：残りの列</span>
+<a id="__codelineno-51-14" name="__codelineno-51-14" href="#__codelineno-51-14"></a><span class="w">    </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="n">m</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">j</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-51-15" name="__codelineno-51-15" href="#__codelineno-51-15"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-51-16" name="__codelineno-51-16" href="#__codelineno-51-16"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
+<a id="__codelineno-51-17" name="__codelineno-51-17" href="#__codelineno-51-17"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=from%20math%20import%20inf%0A%0Adef%20min_path_sum_dp_comp%28grid%3A%20list%5Blist%5Bint%5D%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E6%9C%80%E5%B0%8F%E7%B5%8C%E8%B7%AF%E5%92%8C%EF%BC%9A%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E5%BE%8C%E3%81%AE%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%2C%20m%20%3D%20len%28grid%29%2C%20len%28grid%5B0%5D%29%0A%20%20%20%20%23%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5B0%5D%20%2A%20m%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%85%88%E9%A0%AD%E8%A1%8C%0A%20%20%20%20dp%5B0%5D%20%3D%20grid%5B0%5D%5B0%5D%0A%20%20%20%20for%20j%20in%20range%281%2C%20m%29%3A%0A%20%20%20%20%20%20%20%20dp%5Bj%5D%20%3D%20dp%5Bj%20-%201%5D%20%2B%20grid%5B0%5D%5Bj%5D%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E6%AE%8B%E3%82%8A%E3%81%AE%E8%A1%8C%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%85%88%E9%A0%AD%E5%88%97%0A%20%20%20%20%20%20%20%20dp%5B0%5D%20%3D%20dp%5B0%5D%20%2B%20grid%5Bi%5D%5B0%5D%0A%20%20%20%20%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E6%AE%8B%E3%82%8A%E3%81%AE%E5%88%97%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%281%2C%20m%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bj%5D%20%3D%20min%28dp%5Bj%20-%201%5D%2C%20dp%5Bj%5D%29%20%2B%20grid%5Bi%5D%5Bj%5D%0A%20%20%20%20return%20dp%5Bm%20-%201%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20grid%20%3D%20%5B%5B1%2C%203%2C%201%2C%205%5D%2C%20%5B2%2C%202%2C%204%2C%202%5D%2C%20%5B5%2C%203%2C%202%2C%201%5D%2C%20%5B4%2C%203%2C%205%2C%202%5D%5D%0A%20%20%20%20n%2C%20m%20%3D%20len%28grid%29%2C%20len%28grid%5B0%5D%29%0A%0A%20%20%20%20%23%20%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E5%BE%8C%E3%81%AE%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20min_path_sum_dp_comp%28grid%29%0A%20%20%20%20print%28f%22%E5%B7%A6%E4%B8%8A%E3%81%8B%E3%82%89%E5%8F%B3%E4%B8%8B%E3%81%BE%E3%81%A7%E3%81%AE%E6%9C%80%E5%B0%8F%E7%B5%8C%E8%B7%AF%E5%92%8C%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=from%20math%20import%20inf%0A%0Adef%20min_path_sum_dp_comp%28grid%3A%20list%5Blist%5Bint%5D%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E6%9C%80%E5%B0%8F%E7%B5%8C%E8%B7%AF%E5%92%8C%EF%BC%9A%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E5%BE%8C%E3%81%AE%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%2C%20m%20%3D%20len%28grid%29%2C%20len%28grid%5B0%5D%29%0A%20%20%20%20%23%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5B0%5D%20%2A%20m%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%85%88%E9%A0%AD%E8%A1%8C%0A%20%20%20%20dp%5B0%5D%20%3D%20grid%5B0%5D%5B0%5D%0A%20%20%20%20for%20j%20in%20range%281%2C%20m%29%3A%0A%20%20%20%20%20%20%20%20dp%5Bj%5D%20%3D%20dp%5Bj%20-%201%5D%20%2B%20grid%5B0%5D%5Bj%5D%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E6%AE%8B%E3%82%8A%E3%81%AE%E8%A1%8C%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%85%88%E9%A0%AD%E5%88%97%0A%20%20%20%20%20%20%20%20dp%5B0%5D%20%3D%20dp%5B0%5D%20%2B%20grid%5Bi%5D%5B0%5D%0A%20%20%20%20%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E6%AE%8B%E3%82%8A%E3%81%AE%E5%88%97%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%281%2C%20m%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bj%5D%20%3D%20min%28dp%5Bj%20-%201%5D%2C%20dp%5Bj%5D%29%20%2B%20grid%5Bi%5D%5Bj%5D%0A%20%20%20%20return%20dp%5Bm%20-%201%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20grid%20%3D%20%5B%5B1%2C%203%2C%201%2C%205%5D%2C%20%5B2%2C%202%2C%204%2C%202%5D%2C%20%5B5%2C%203%2C%202%2C%201%5D%2C%20%5B4%2C%203%2C%205%2C%202%5D%5D%0A%20%20%20%20n%2C%20m%20%3D%20len%28grid%29%2C%20len%28grid%5B0%5D%29%0A%0A%20%20%20%20%23%20%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E5%BE%8C%E3%81%AE%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20min_path_sum_dp_comp%28grid%29%0A%20%20%20%20print%28f%22%E5%B7%A6%E4%B8%8A%E3%81%8B%E3%82%89%E5%8F%B3%E4%B8%8B%E3%81%BE%E3%81%A7%E3%81%AE%E6%9C%80%E5%B0%8F%E7%B5%8C%E8%B7%AF%E5%92%8C%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 
 <!-- Source file information -->
 
@@ -5014,7 +5854,7 @@ aria-label="フッター"
   <a
     href="../dp_problem_features/"
     class="md-footer__link md-footer__link--prev"
-    aria-label="前: 14.2 &amp;nbsp; DP 問題の特性"
+    aria-label="前: 14.2 &amp;nbsp; 動的計画法の問題特性"
     rel="prev"
   >
     <div class="md-footer__button md-icon">
@@ -5026,7 +5866,7 @@ aria-label="フッター"
         前
       </span>
       <div class="md-ellipsis">
-        14.2 &nbsp; DP 問題の特性
+        14.2 &nbsp; 動的計画法の問題特性
       </div>
     </div>
   </a>
@@ -5038,7 +5878,7 @@ aria-label="フッター"
   <a
     href="../knapsack_problem/"
     class="md-footer__link md-footer__link--next"
-    aria-label="次: 14.4 &amp;nbsp; 0-1ナップサック問題"
+    aria-label="次: 14.4 &amp;nbsp; 0-1 ナップサック問題"
     rel="next"
   >
     <div class="md-footer__title">
@@ -5046,7 +5886,7 @@ aria-label="フッター"
         次
       </span>
       <div class="md-ellipsis">
-        14.4 &nbsp; 0-1ナップサック問題
+        14.4 &nbsp; 0-1 ナップサック問題
       </div>
     </div>
     <div class="md-footer__button md-icon">
diff --git a/ja/chapter_dynamic_programming/edit_distance_problem/index.html b/ja/chapter_dynamic_programming/edit_distance_problem/index.html
index 385e5f2b6..3883b2dfe 100644
--- a/ja/chapter_dynamic_programming/edit_distance_problem/index.html
+++ b/ja/chapter_dynamic_programming/edit_distance_problem/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1635,7 +1635,7 @@
   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1942,7 +1942,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2105,7 +2105,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
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-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
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-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
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-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
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-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
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-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
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-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
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-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
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   <a href="#1" class="md-nav__link">
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-        1. &nbsp; 動的プログラミングアプローチ
+        1. &nbsp; 動的計画法の考え方
       
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+        2. &nbsp; コードの実装
       
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
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-        1. &nbsp; 動的プログラミングアプローチ
+        1. &nbsp; 動的計画法の考え方
       
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-        2. &nbsp; コード実装
+        2. &nbsp; コードの実装
       
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@@ -4377,99 +4377,99 @@
 
 <!-- Page content -->
 <h1 id="146">14.6 &nbsp; 編集距離問題<a class="headerlink" href="#146" title="Permanent link">&para;</a></h1>
-<p>編集距離は、レーベンシュタイン距離とも呼ばれ、一つの文字列を別の文字列に変換するために必要な最小修正回数を指し、情報検索や自然言語処理で2つのシーケンス間の類似度を測定するためによく使用されます。</p>
+<p>編集距離は、Levenshtein 距離とも呼ばれ、2つの文字列の相互変換に必要な最小の編集回数を指し、通常は情報検索や自然言語処理において2つの系列の類似度を測るために用いられます。</p>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
-<p>2つの文字列 <span class="arithmatex">\(s\)</span> と <span class="arithmatex">\(t\)</span> が与えられたとき、<span class="arithmatex">\(s\)</span> を <span class="arithmatex">\(t\)</span> に変換するために必要な最小編集回数を返してください。</p>
-<p>文字列に対して3種類の編集を実行できます：文字の挿入、文字の削除、または文字を他の任意の文字に置換。</p>
+<p>2つの文字列 <span class="arithmatex">\(s\)</span> と <span class="arithmatex">\(t\)</span> を入力し、<span class="arithmatex">\(s\)</span> を <span class="arithmatex">\(t\)</span> に変換するのに必要な最小編集回数を返してください。</p>
+<p>1つの文字列に対して3種類の編集操作を行えます。1文字の挿入、1文字の削除、任意の文字への置換です。</p>
 </div>
-<p>下の図に示すように、<code>kitten</code> を <code>sitting</code> に変換するには3回の編集が必要で、2回の置換と1回の挿入を含みます。<code>hello</code> を <code>algo</code> に変換するには3ステップが必要で、2回の置換と1回の削除を含みます。</p>
-<p><img alt="編集距離の例データ" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_example.png" /></p>
-<p align="center"> 図 14-27 &nbsp; 編集距離の例データ </p>
+<p>下図に示すように、<code>kitten</code> を <code>sitting</code> に変換するには 3 回の編集が必要で、内訳は 2 回の置換と 1 回の挿入です。<code>hello</code> を <code>algo</code> に変換する場合も 3 回必要で、内訳は 2 回の置換と 1 回の削除です。</p>
+<p><img alt="編集距離のサンプルデータ" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_example.png" /></p>
+<p align="center"> 図 14-27 &nbsp; 編集距離のサンプルデータ </p>
 
-<p><strong>編集距離問題は決定木モデルで自然に説明できます</strong>。文字列は木のノードに対応し、1ラウンドの決定（編集操作）は木のエッジに対応します。</p>
-<p>下の図に示すように、操作に制限がない場合、各ノードは多くのエッジを導出でき、それぞれが1つの操作に対応するため、<code>hello</code> を <code>algo</code> に変換する可能な経路は多数あります。</p>
-<p>決定木の観点から、この問題の目標は、ノード <code>hello</code> とノード <code>algo</code> の間の最短経路を見つけることです。</p>
-<p><img alt="決定木モデルに基づいて表現された編集距離問題" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_decision_tree.png" /></p>
-<p align="center"> 図 14-28 &nbsp; 決定木モデルに基づいて表現された編集距離問題 </p>
+<p><strong>編集距離問題は決定木モデルで自然に説明できます</strong>。文字列が木のノードに対応し、1回の決定（1回の編集操作）が木の1本の辺に対応します。</p>
+<p>下図に示すように、操作に制限がない場合、各ノードからは多くの辺を派生でき、それぞれの辺が1種類の操作に対応します。これは <code>hello</code> から <code>algo</code> への変換に多くの経路があり得ることを意味します。</p>
+<p>決定木の観点から見ると、本問の目標はノード <code>hello</code> とノード <code>algo</code> の間の最短経路を求めることです。</p>
+<p><img alt="決定木モデルに基づく編集距離問題の表現" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_decision_tree.png" /></p>
+<p align="center"> 図 14-28 &nbsp; 決定木モデルに基づく編集距離問題の表現 </p>
 
-<h3 id="1">1. &nbsp; 動的プログラミングアプローチ<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p><strong>ステップ1：各ラウンドの決定を考え、状態を定義し、それにより <span class="arithmatex">\(dp\)</span> テーブルを得る</strong></p>
-<p>各ラウンドの決定は、文字列 <span class="arithmatex">\(s\)</span> に対して1つの編集操作を実行することを含みます。</p>
-<p>編集プロセス中に問題のサイズを段階的に縮小することを目指し、これにより部分問題を構築できます。文字列 <span class="arithmatex">\(s\)</span> と <span class="arithmatex">\(t\)</span> の長さをそれぞれ <span class="arithmatex">\(n\)</span> と <span class="arithmatex">\(m\)</span> とします。まず、両方の文字列の末尾文字 <span class="arithmatex">\(s[n-1]\)</span> と <span class="arithmatex">\(t[m-1]\)</span> を考慮します。</p>
+<h3 id="1">1. &nbsp; 動的計画法の考え方<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p><strong>第1ステップ：各ラウンドの決定を考え、状態を定義して、<span class="arithmatex">\(dp\)</span> テーブルを得る</strong></p>
+<p>各ラウンドの決定は、文字列 <span class="arithmatex">\(s\)</span> に対して1回の編集操作を行うことです。</p>
+<p>編集操作の過程で問題の規模が徐々に小さくなることを期待します。そうして初めて部分問題を構築できます。文字列 <span class="arithmatex">\(s\)</span> と <span class="arithmatex">\(t\)</span> の長さをそれぞれ <span class="arithmatex">\(n\)</span> と <span class="arithmatex">\(m\)</span> とし、まず両文字列の末尾の文字 <span class="arithmatex">\(s[n-1]\)</span> と <span class="arithmatex">\(t[m-1]\)</span> を考えます。</p>
 <ul>
-<li><span class="arithmatex">\(s[n-1]\)</span> と <span class="arithmatex">\(t[m-1]\)</span> が同じ場合、それらをスキップして直接 <span class="arithmatex">\(s[n-2]\)</span> と <span class="arithmatex">\(t[m-2]\)</span> を考慮できます。</li>
-<li><span class="arithmatex">\(s[n-1]\)</span> と <span class="arithmatex">\(t[m-1]\)</span> が異なる場合、<span class="arithmatex">\(s\)</span> に対して1つの編集（挿入、削除、置換）を実行して、2つの文字列の末尾文字を一致させ、それらをスキップしてより小規模な問題を考慮できるようにする必要があります。</li>
+<li><span class="arithmatex">\(s[n-1]\)</span> と <span class="arithmatex">\(t[m-1]\)</span> が同じなら、それらをスキップして、直接 <span class="arithmatex">\(s[n-2]\)</span> と <span class="arithmatex">\(t[m-2]\)</span> を考えます。</li>
+<li><span class="arithmatex">\(s[n-1]\)</span> と <span class="arithmatex">\(t[m-1]\)</span> が異なるなら、<span class="arithmatex">\(s\)</span> に対して1回の編集（挿入、削除、置換）を行い、両文字列の末尾の文字を同じにします。そうすることでそれらをスキップし、より小さい問題を考えられます。</li>
 </ul>
-<p>したがって、文字列 <span class="arithmatex">\(s\)</span> での各ラウンドの決定（編集操作）は、<span class="arithmatex">\(s\)</span> と <span class="arithmatex">\(t\)</span> でマッチされる残りの文字を変更します。したがって、状態は <span class="arithmatex">\(s\)</span> と <span class="arithmatex">\(t\)</span> で現在考慮されている <span class="arithmatex">\(i\)</span> 番目と <span class="arithmatex">\(j\)</span> 番目の文字であり、<span class="arithmatex">\([i, j]\)</span> と表記されます。</p>
-<p>状態 <span class="arithmatex">\([i, j]\)</span> は部分問題に対応します：<strong><span class="arithmatex">\(s\)</span> の最初の <span class="arithmatex">\(i\)</span> 文字を <span class="arithmatex">\(t\)</span> の最初の <span class="arithmatex">\(j\)</span> 文字に変更するために必要な最小編集回数</strong>。</p>
-<p>これから、サイズ <span class="arithmatex">\((i+1) \times (j+1)\)</span> の二次元 <span class="arithmatex">\(dp\)</span> テーブルを得ます。</p>
-<p><strong>ステップ2：最適部分構造を特定し、状態遷移方程式を導出する</strong></p>
-<p>部分問題 <span class="arithmatex">\(dp[i, j]\)</span> を考慮すると、これに対応する2つの文字列の末尾文字は <span class="arithmatex">\(s[i-1]\)</span> と <span class="arithmatex">\(t[j-1]\)</span> であり、下の図に示すように3つのシナリオに分けることができます。</p>
+<p>つまり、文字列 <span class="arithmatex">\(s\)</span> に対する各ラウンドの決定（編集操作）は、<span class="arithmatex">\(s\)</span> と <span class="arithmatex">\(t\)</span> における残りの未一致文字を変化させます。したがって、状態は現在 <span class="arithmatex">\(s\)</span> と <span class="arithmatex">\(t\)</span> で考えている第 <span class="arithmatex">\(i\)</span> と第 <span class="arithmatex">\(j\)</span> 文字とし、<span class="arithmatex">\([i, j]\)</span> と記します。</p>
+<p>状態 <span class="arithmatex">\([i, j]\)</span> に対応する部分問題は、**<span class="arithmatex">\(s\)</span> の先頭 <span class="arithmatex">\(i\)</span> 文字を <span class="arithmatex">\(t\)</span> の先頭 <span class="arithmatex">\(j\)</span> 文字に変換するのに必要な最小編集回数**です。</p>
+<p>これにより、サイズが <span class="arithmatex">\((i+1) \times (j+1)\)</span> の2次元 <span class="arithmatex">\(dp\)</span> テーブルが得られます。</p>
+<p><strong>第2ステップ：最適部分構造を見つけ、状態遷移方程式を導く</strong></p>
+<p>部分問題 <span class="arithmatex">\(dp[i, j]\)</span> を考えます。これに対応する2つの文字列の末尾文字は <span class="arithmatex">\(s[i-1]\)</span> と <span class="arithmatex">\(t[j-1]\)</span> であり、編集操作の違いに応じて下図の3つの場合に分けられます。</p>
 <ol>
-<li><span class="arithmatex">\(s[i-1]\)</span> の後に <span class="arithmatex">\(t[j-1]\)</span> を追加すると、残りの部分問題は <span class="arithmatex">\(dp[i, j-1]\)</span> です。</li>
-<li><span class="arithmatex">\(s[i-1]\)</span> を削除すると、残りの部分問題は <span class="arithmatex">\(dp[i-1, j]\)</span> です。</li>
-<li><span class="arithmatex">\(s[i-1]\)</span> を <span class="arithmatex">\(t[j-1]\)</span> に置換すると、残りの部分問題は <span class="arithmatex">\(dp[i-1, j-1]\)</span> です。</li>
+<li><span class="arithmatex">\(s[i-1]\)</span> の後ろに <span class="arithmatex">\(t[j-1]\)</span> を追加する。このとき残る部分問題は <span class="arithmatex">\(dp[i, j-1]\)</span> です。</li>
+<li><span class="arithmatex">\(s[i-1]\)</span> を削除する。このとき残る部分問題は <span class="arithmatex">\(dp[i-1, j]\)</span> です。</li>
+<li><span class="arithmatex">\(s[i-1]\)</span> を <span class="arithmatex">\(t[j-1]\)</span> に置き換える。このとき残る部分問題は <span class="arithmatex">\(dp[i-1, j-1]\)</span> です。</li>
 </ol>
 <p><img alt="編集距離の状態遷移" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_state_transfer.png" /></p>
 <p align="center"> 図 14-29 &nbsp; 編集距離の状態遷移 </p>
 
-<p>上記の分析に基づいて、最適部分構造を決定できます：<span class="arithmatex">\(dp[i, j]\)</span> の最小編集回数は、<span class="arithmatex">\(dp[i, j-1]\)</span>、<span class="arithmatex">\(dp[i-1, j]\)</span>、<span class="arithmatex">\(dp[i-1, j-1]\)</span> の中の最小値に編集ステップ <span class="arithmatex">\(1\)</span> を加えたものです。対応する状態遷移方程式は：</p>
+<p>以上の分析から、最適部分構造は次のように得られます。<span class="arithmatex">\(dp[i, j]\)</span> の最小編集回数は、<span class="arithmatex">\(dp[i, j-1]\)</span>、<span class="arithmatex">\(dp[i-1, j]\)</span>、<span class="arithmatex">\(dp[i-1, j-1]\)</span> の3つのうち最小の編集回数に、今回の編集回数 <span class="arithmatex">\(1\)</span> を加えたものです。対応する状態遷移方程式は次のとおりです：</p>
 <div class="arithmatex">\[
 dp[i, j] = \min(dp[i, j-1], dp[i-1, j], dp[i-1, j-1]) + 1
 \]</div>
-<p>注意してください。<strong><span class="arithmatex">\(s[i-1]\)</span> と <span class="arithmatex">\(t[j-1]\)</span> が同じ場合、現在の文字に対して編集は必要ありません</strong>。この場合、状態遷移方程式は：</p>
+<p>注意すべき点として、<strong><span class="arithmatex">\(s[i-1]\)</span> と <span class="arithmatex">\(t[j-1]\)</span> が同じ場合、現在の文字を編集する必要はありません</strong>。この場合の状態遷移方程式は次のとおりです：</p>
 <div class="arithmatex">\[
 dp[i, j] = dp[i-1, j-1]
 \]</div>
-<p><strong>ステップ3：境界条件と状態遷移の順序を決定する</strong></p>
-<p>両方の文字列が空の場合、編集回数は <span class="arithmatex">\(0\)</span> です。つまり、<span class="arithmatex">\(dp[0, 0] = 0\)</span> です。<span class="arithmatex">\(s\)</span> が空で <span class="arithmatex">\(t\)</span> が空でない場合、最小編集回数は <span class="arithmatex">\(t\)</span> の長さに等しく、つまり最初の行 <span class="arithmatex">\(dp[0, j] = j\)</span> です。<span class="arithmatex">\(s\)</span> が空でなく <span class="arithmatex">\(t\)</span> が空の場合、最小編集回数は <span class="arithmatex">\(s\)</span> の長さに等しく、つまり最初の列 <span class="arithmatex">\(dp[i, 0] = i\)</span> です。</p>
-<p>状態遷移方程式を観察すると、<span class="arithmatex">\(dp[i, j]\)</span> の解決は左、上、左上の解に依存するため、二重ループを使用して正しい順序で <span class="arithmatex">\(dp\)</span> テーブル全体を走査できます。</p>
-<h3 id="2">2. &nbsp; コード実装<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p><strong>第3ステップ：境界条件と状態遷移の順序を決める</strong></p>
+<p>2つの文字列がともに空のとき、編集回数は <span class="arithmatex">\(0\)</span>、すなわち <span class="arithmatex">\(dp[0, 0] = 0\)</span> です。<span class="arithmatex">\(s\)</span> が空で <span class="arithmatex">\(t\)</span> が空でないとき、最小編集回数は <span class="arithmatex">\(t\)</span> の長さに等しいため、先頭行は <span class="arithmatex">\(dp[0, j] = j\)</span> です。<span class="arithmatex">\(s\)</span> が空でなく <span class="arithmatex">\(t\)</span> が空のとき、最小編集回数は <span class="arithmatex">\(s\)</span> の長さに等しいため、先頭列は <span class="arithmatex">\(dp[i, 0] = i\)</span> です。</p>
+<p>状態遷移方程式を観察すると、<span class="arithmatex">\(dp[i, j]\)</span> の解は左、上、左上の解に依存します。そのため、2重ループで <span class="arithmatex">\(dp\)</span> テーブル全体を順方向に走査すれば十分です。</p>
+<h3 id="2">2. &nbsp; コードの実装<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
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 <div class="highlight"><span class="filename">edit_distance.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">edit_distance_dp</span><span class="p">(</span><span class="n">s</span><span class="p">:</span> <span class="nb">str</span><span class="p">,</span> <span class="n">t</span><span class="p">:</span> <span class="nb">str</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;編集距離：動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;編集距離：動的計画法&quot;&quot;&quot;</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="n">n</span><span class="p">,</span> <span class="n">m</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">s</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span>
-<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="c1"># 状態遷移：最初の行と最初の列</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="c1"># 状態遷移：先頭行と先頭列</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">i</span>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">j</span>
-<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="c1"># 状態遷移：残りの行と列</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="c1"># 状態遷移: 残りの行と列</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>            <span class="k">if</span> <span class="n">s</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">==</span> <span class="n">t</span><span class="p">[</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]:</span>
-<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>                <span class="c1"># 2 つの文字が等しい場合、これら 2 つの文字をスキップ</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>                <span class="c1"># 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
 <a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span>
 <a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>            <span class="k">else</span><span class="p">:</span>
-<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>                <span class="c1"># 最小編集数 = 3 つの操作（挿入、削除、置換）からの最小編集数 + 1</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>                <span class="c1"># 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
 <a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span> <span class="o">+</span> <span class="mi">1</span>
 <a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">m</span><span class="p">]</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">edit_distance.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 編集距離：動的プログラミング */</span>
+<div class="highlight"><span class="filename">edit_distance.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 編集距離：動的計画法 */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">editDistanceDP</span><span class="p">(</span><span class="n">string</span><span class="w"> </span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">length</span><span class="p">(),</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="n">length</span><span class="p">();</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">));</span>
-<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="c1">// 状態遷移：最初の行と最初の列</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行と先頭列</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行と列</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">                </span><span class="c1">// 2つの文字が等しい場合、これら2つの文字をスキップ</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">                </span><span class="c1">// 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
 <a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
 <a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">                </span><span class="c1">// 最小編集数 = 3つの操作（挿入、削除、置換）からの最小編集数 + 1</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">                </span><span class="c1">// 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
 <a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">]),</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w">        </span><span class="p">}</span>
@@ -4479,25 +4479,25 @@ dp[i, j] = dp[i-1, j-1]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">edit_distance.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 編集距離：動的プログラミング */</span>
+<div class="highlight"><span class="filename">edit_distance.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 編集距離：動的計画法 */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">editDistanceDP</span><span class="p">(</span><span class="n">String</span><span class="w"> </span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="na">length</span><span class="p">(),</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="na">length</span><span class="p">();</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="c1">// 状態遷移：最初の行と最初の列</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行と先頭列</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
 <a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行と列</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">.</span><span class="na">charAt</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="na">charAt</span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">                </span><span class="c1">// 2つの文字が等しい場合、これら2つの文字をスキップ</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">                </span><span class="c1">// 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
 <a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">                </span><span class="c1">// 最小編集数 = 3つの操作（挿入、削除、置換）からの最小編集数 + 1</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">                </span><span class="c1">// 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
 <a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">),</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w">        </span><span class="p">}</span>
@@ -4507,52 +4507,313 @@ dp[i, j] = dp[i-1, j-1]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">edit_distance.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">edit_distance</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">EditDistanceDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">edit_distance.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 編集距離：動的計画法 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">EditDistanceDP</span><span class="p">(</span><span class="kt">string</span><span class="w"> </span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="kt">string</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">Length</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="kt">int</span><span class="p">[,]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行と先頭列</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">                </span><span class="c1">// 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w">                </span><span class="c1">// 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Min</span><span class="p">(</span><span class="n">Math</span><span class="p">.</span><span class="n">Min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">]),</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="p">];</span>
+<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">edit_distance.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">editDistanceDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">edit_distance.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 編集距離：動的計画法 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">editDistanceDP</span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="kt">string</span><span class="p">,</span><span class="w"> </span><span class="nx">t</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">s</span><span class="p">)</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">m</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">t</span><span class="p">)</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行と先頭列</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">i</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">j</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="nx">s</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">t</span><span class="p">[</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w">                </span><span class="c1">// 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="w">                </span><span class="c1">// 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
+<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">MinInt</span><span class="p">(</span><span class="nx">MinInt</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">j</span><span class="p">]),</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">m</span><span class="p">]</span>
+<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">edit_distance.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">editDistanceDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">edit_distance.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 編集距離：動的計画法 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">editDistanceDP</span><span class="p">(</span><span class="n">s</span><span class="p">:</span><span class="w"> </span><span class="nb">String</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="p">:</span><span class="w"> </span><span class="nb">String</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">utf8CString</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="n">utf8CString</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">),</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行と先頭列</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">j</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">utf8CString</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="n">utf8CString</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">                </span><span class="c1">// 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="w">                </span><span class="c1">// 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">min</span><span class="p">(</span><span class="bp">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">]),</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">m</span><span class="p">]</span>
+<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">edit_distance.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">editDistanceDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">edit_distance.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 編集距離：動的計画法 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">editDistanceDP</span><span class="p">(</span><span class="nx">s</span><span class="p">,</span><span class="w"> </span><span class="nx">t</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">length</span><span class="p">,</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">        </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">));</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行と先頭列</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">j</span><span class="p">;</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="p">.</span><span class="nx">charAt</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">charAt</span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w">                </span><span class="c1">// 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w">                </span><span class="c1">// 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w">                    </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">j</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">m</span><span class="p">];</span>
+<a id="__codelineno-6-27" name="__codelineno-6-27" href="#__codelineno-6-27"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">edit_distance.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">editDistanceDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">edit_distance.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 編集距離：動的計画法 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">editDistanceDP</span><span class="p">(</span><span class="nx">s</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">,</span><span class="w"> </span><span class="nx">t</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">length</span><span class="p">,</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">        </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="kt">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">        </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="kt">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="p">);</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行と先頭列</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">j</span><span class="p">;</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="p">.</span><span class="nx">charAt</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">charAt</span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">                </span><span class="c1">// 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="w">                </span><span class="c1">// 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span>
+<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="w">                    </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">j</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">m</span><span class="p">];</span>
+<a id="__codelineno-7-29" name="__codelineno-7-29" href="#__codelineno-7-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">edit_distance.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">editDistanceDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">edit_distance.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 編集距離：動的計画法 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">editDistanceDP</span><span class="p">(</span><span class="kt">String</span><span class="w"> </span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="kt">String</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">generate</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">_</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">));</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="c1">// 状態遷移：先頭行と先頭列</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="m">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="m">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">  </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">        </span><span class="c1">// 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">];</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w">      </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w">        </span><span class="c1">// 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">][</span><span class="n">j</span><span class="p">]),</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">m</span><span class="p">];</span>
+<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">edit_distance.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">edit_distance_dp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">edit_distance.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 編集距離：動的計画法 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">edit_distance_dp</span><span class="p">(</span><span class="n">s</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="kt">str</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="kt">str</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">.</span><span class="n">len</span><span class="p">(),</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="n">len</span><span class="p">());</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行と先頭列</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">;</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..</span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">;</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">chars</span><span class="p">().</span><span class="n">nth</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="n">chars</span><span class="p">().</span><span class="n">nth</span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">                </span><span class="c1">// 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">                </span><span class="c1">// 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w">                    </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">min</span><span class="p">(</span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">]),</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">m</span><span class="p">]</span>
+<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">edit_distance.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">editDistanceDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">edit_distance.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 編集距離：動的計画法 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">editDistanceDP</span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="n">t</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">**</span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">((</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">));</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">calloc</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行と先頭列</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">                </span><span class="c1">// 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="w">                </span><span class="c1">// 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
+<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">myMin</span><span class="p">(</span><span class="n">myMin</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">]),</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">m</span><span class="p">];</span>
+<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a><span class="w">        </span><span class="n">free</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-10-32" name="__codelineno-10-32" href="#__codelineno-10-32"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">edit_distance.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">editDistanceDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">edit_distance.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 編集距離：動的計画法 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">editDistanceDP</span><span class="p">(</span><span class="n">s</span><span class="p">:</span><span class="w"> </span><span class="kt">String</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="p">:</span><span class="w"> </span><span class="kt">String</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="na">length</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="na">length</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Array</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行と先頭列</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="m">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="m">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">                </span><span class="c1">// 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w">                </span><span class="c1">// 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">),</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">m</span><span class="o">]</span>
+<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">edit_distance.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">edit_distance_dp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">edit_distance.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 編集距離：動的計画法 ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">edit_distance_dp</span><span class="p">(</span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="o">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="c1"># 状態遷移：先頭行と先頭列</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">  </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">j</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">  </span><span class="c1"># 状態遷移: 残りの行と列</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="n">s</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">        </span><span class="c1"># 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">      </span><span class="k">else</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">        </span><span class="c1"># 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">m</span><span class="o">]</span>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>下の図に示すように、編集距離問題の状態遷移プロセスはナップサック問題と非常に似ており、二次元グリッドを埋めることと見なすことができます。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20edit_distance_dp%28s%3A%20str%2C%20t%3A%20str%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%B7%A8%E9%9B%86%E8%B7%9D%E9%9B%A2%EF%BC%9A%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%2C%20m%20%3D%20len%28s%29%2C%20len%28t%29%0A%20%20%20%20dp%20%3D%20%5B%5B0%5D%20%2A%20%28m%20%2B%201%29%20for%20_%20in%20range%28n%20%2B%201%29%5D%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%85%88%E9%A0%AD%E8%A1%8C%E3%81%A8%E5%85%88%E9%A0%AD%E5%88%97%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20dp%5Bi%5D%5B0%5D%20%3D%20i%0A%20%20%20%20for%20j%20in%20range%281%2C%20m%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20dp%5B0%5D%5Bj%5D%20%3D%20j%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%3A%20%E6%AE%8B%E3%82%8A%E3%81%AE%E8%A1%8C%E3%81%A8%E5%88%97%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%281%2C%20m%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20s%5Bi%20-%201%5D%20%3D%3D%20t%5Bj%20-%201%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%202%20%E3%81%A4%E3%81%AE%E6%96%87%E5%AD%97%E3%81%8C%E7%AD%89%E3%81%97%E3%81%91%E3%82%8C%E3%81%B0%E3%80%81%E3%81%9D%E3%81%AE%202%20%E6%96%87%E5%AD%97%E3%82%92%E3%81%9D%E3%81%AE%E3%81%BE%E3%81%BE%E3%82%B9%E3%82%AD%E3%83%83%E3%83%97%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Bj%5D%20%3D%20dp%5Bi%20-%201%5D%5Bj%20-%201%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%9C%80%E5%B0%8F%E7%B7%A8%E9%9B%86%E5%9B%9E%E6%95%B0%20%3D%20%E6%8C%BF%E5%85%A5%E3%83%BB%E5%89%8A%E9%99%A4%E3%83%BB%E7%BD%AE%E6%8F%9B%E3%81%AE%203%20%E6%93%8D%E4%BD%9C%E3%81%AB%E3%81%8A%E3%81%91%E3%82%8B%E6%9C%80%E5%B0%8F%E7%B7%A8%E9%9B%86%E5%9B%9E%E6%95%B0%20%2B%201%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Bj%5D%20%3D%20min%28dp%5Bi%5D%5Bj%20-%201%5D%2C%20dp%5Bi%20-%201%5D%5Bj%5D%2C%20dp%5Bi%20-%201%5D%5Bj%20-%201%5D%29%20%2B%201%0A%20%20%20%20return%20dp%5Bn%5D%5Bm%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20s%20%3D%20%22bag%22%0A%20%20%20%20t%20%3D%20%22pack%22%0A%20%20%20%20n%2C%20m%20%3D%20len%28s%29%2C%20len%28t%29%0A%0A%20%20%20%20%23%20%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20edit_distance_dp%28s%2C%20t%29%0A%20%20%20%20print%28f%22%7Bs%7D%20%E3%82%92%20%7Bt%7D%20%E3%81%AB%E5%A4%89%E6%9B%B4%E3%81%99%E3%82%8B%E3%81%AB%E3%81%AF%E6%9C%80%E5%B0%8F%E3%81%A7%20%7Bres%7D%20%E5%9B%9E%E3%81%AE%E7%B7%A8%E9%9B%86%E3%81%8C%E5%BF%85%E8%A6%81%E3%81%A7%E3%81%99%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20edit_distance_dp%28s%3A%20str%2C%20t%3A%20str%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%B7%A8%E9%9B%86%E8%B7%9D%E9%9B%A2%EF%BC%9A%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%2C%20m%20%3D%20len%28s%29%2C%20len%28t%29%0A%20%20%20%20dp%20%3D%20%5B%5B0%5D%20%2A%20%28m%20%2B%201%29%20for%20_%20in%20range%28n%20%2B%201%29%5D%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%85%88%E9%A0%AD%E8%A1%8C%E3%81%A8%E5%85%88%E9%A0%AD%E5%88%97%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20dp%5Bi%5D%5B0%5D%20%3D%20i%0A%20%20%20%20for%20j%20in%20range%281%2C%20m%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20dp%5B0%5D%5Bj%5D%20%3D%20j%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%3A%20%E6%AE%8B%E3%82%8A%E3%81%AE%E8%A1%8C%E3%81%A8%E5%88%97%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%281%2C%20m%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20s%5Bi%20-%201%5D%20%3D%3D%20t%5Bj%20-%201%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%202%20%E3%81%A4%E3%81%AE%E6%96%87%E5%AD%97%E3%81%8C%E7%AD%89%E3%81%97%E3%81%91%E3%82%8C%E3%81%B0%E3%80%81%E3%81%9D%E3%81%AE%202%20%E6%96%87%E5%AD%97%E3%82%92%E3%81%9D%E3%81%AE%E3%81%BE%E3%81%BE%E3%82%B9%E3%82%AD%E3%83%83%E3%83%97%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Bj%5D%20%3D%20dp%5Bi%20-%201%5D%5Bj%20-%201%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%9C%80%E5%B0%8F%E7%B7%A8%E9%9B%86%E5%9B%9E%E6%95%B0%20%3D%20%E6%8C%BF%E5%85%A5%E3%83%BB%E5%89%8A%E9%99%A4%E3%83%BB%E7%BD%AE%E6%8F%9B%E3%81%AE%203%20%E6%93%8D%E4%BD%9C%E3%81%AB%E3%81%8A%E3%81%91%E3%82%8B%E6%9C%80%E5%B0%8F%E7%B7%A8%E9%9B%86%E5%9B%9E%E6%95%B0%20%2B%201%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Bj%5D%20%3D%20min%28dp%5Bi%5D%5Bj%20-%201%5D%2C%20dp%5Bi%20-%201%5D%5Bj%5D%2C%20dp%5Bi%20-%201%5D%5Bj%20-%201%5D%29%20%2B%201%0A%20%20%20%20return%20dp%5Bn%5D%5Bm%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20s%20%3D%20%22bag%22%0A%20%20%20%20t%20%3D%20%22pack%22%0A%20%20%20%20n%2C%20m%20%3D%20len%28s%29%2C%20len%28t%29%0A%0A%20%20%20%20%23%20%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20edit_distance_dp%28s%2C%20t%29%0A%20%20%20%20print%28f%22%7Bs%7D%20%E3%82%92%20%7Bt%7D%20%E3%81%AB%E5%A4%89%E6%9B%B4%E3%81%99%E3%82%8B%E3%81%AB%E3%81%AF%E6%9C%80%E5%B0%8F%E3%81%A7%20%7Bres%7D%20%E5%9B%9E%E3%81%AE%E7%B7%A8%E9%9B%86%E3%81%8C%E5%BF%85%E8%A6%81%E3%81%A7%E3%81%99%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>下図に示すように、編集距離問題の状態遷移の過程はナップサック問題と非常によく似ており、どちらも2次元グリッドを埋めていく過程とみなせます。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:15"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><input id="__tabbed_2_15" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">&lt;1&gt;</label><label for="__tabbed_2_2">&lt;2&gt;</label><label for="__tabbed_2_3">&lt;3&gt;</label><label for="__tabbed_2_4">&lt;4&gt;</label><label for="__tabbed_2_5">&lt;5&gt;</label><label for="__tabbed_2_6">&lt;6&gt;</label><label for="__tabbed_2_7">&lt;7&gt;</label><label for="__tabbed_2_8">&lt;8&gt;</label><label for="__tabbed_2_9">&lt;9&gt;</label><label for="__tabbed_2_10">&lt;10&gt;</label><label for="__tabbed_2_11">&lt;11&gt;</label><label for="__tabbed_2_12">&lt;12&gt;</label><label for="__tabbed_2_13">&lt;13&gt;</label><label for="__tabbed_2_14">&lt;14&gt;</label><label for="__tabbed_2_15">&lt;15&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="編集距離の動的プログラミングプロセス" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_dp_step1.png" /></p>
+<p><img alt="編集距離の動的計画法の過程" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_dp_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="edit_distance_dp_step2" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_dp_step2.png" /></p>
@@ -4598,68 +4859,95 @@ dp[i, j] = dp[i-1, j-1]
 </div>
 </div>
 </div>
-<p align="center"> 図 14-30 &nbsp; 編集距離の動的プログラミングプロセス </p>
+<p align="center"> 図 14-30 &nbsp; 編集距離の動的計画法の過程 </p>
 
 <h3 id="3">3. &nbsp; 空間最適化<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
-<p><span class="arithmatex">\(dp[i, j]\)</span> は上の <span class="arithmatex">\(dp[i-1, j]\)</span>、左の <span class="arithmatex">\(dp[i, j-1]\)</span>、左上の <span class="arithmatex">\(dp[i-1, j-1]\)</span> の解から導出され、直接走査では左上の解 <span class="arithmatex">\(dp[i-1, j-1]\)</span> が失われ、逆走査では事前に <span class="arithmatex">\(dp[i, j-1]\)</span> を構築できないため、どちらの走査順序も実行可能ではありません。</p>
-<p>この理由で、変数 <code>leftup</code> を使用して左上の <span class="arithmatex">\(dp[i-1, j-1]\)</span> からの解を一時的に保存し、左と上の解のみを考慮すればよくなります。この状況は無制限ナップサック問題と似ており、直接走査が可能です。コードは以下の通りです：</p>
+<p><span class="arithmatex">\(dp[i,j]\)</span> は上の <span class="arithmatex">\(dp[i-1, j]\)</span>、左の <span class="arithmatex">\(dp[i, j-1]\)</span>、左上の <span class="arithmatex">\(dp[i-1, j-1]\)</span> から遷移されますが、順方向走査では左上の <span class="arithmatex">\(dp[i-1, j-1]\)</span> を失い、逆方向走査では <span class="arithmatex">\(dp[i, j-1]\)</span> を事前に構築できません。そのため、どちらの走査順序も適切ではありません。</p>
+<p>そのため、変数 <code>leftup</code> を用いて左上の解 <span class="arithmatex">\(dp[i-1, j-1]\)</span> を一時保存し、左と上の解だけを考えればよくなります。このときの状況は完全ナップサック問題と同じであり、順方向走査を用いることができます。コードは次のとおりです：</p>
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 <div class="highlight"><span class="filename">edit_distance.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">edit_distance_dp_comp</span><span class="p">(</span><span class="n">s</span><span class="p">:</span> <span class="nb">str</span><span class="p">,</span> <span class="n">t</span><span class="p">:</span> <span class="nb">str</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;編集距離：空間最適化動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;編集距離：空間最適化した動的計画法&quot;&quot;&quot;</span>
 <a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="n">n</span><span class="p">,</span> <span class="n">m</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">s</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
 <a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># 状態遷移：最初の行</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># 状態遷移：先頭行</span>
 <a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>    <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>        <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">j</span>
 <a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>    <span class="c1"># 状態遷移：残りの行</span>
 <a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
-<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>        <span class="c1"># 状態遷移：最初の列</span>
-<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>        <span class="n">leftup</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>  <span class="c1"># dp[i-1, j-1] を一時的に保存</span>
+<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>        <span class="c1"># 状態遷移：先頭列</span>
+<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>        <span class="n">leftup</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>  <span class="c1"># dp[i-1, j-1] を一時保存する</span>
 <a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>        <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
 <a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a>        <span class="c1"># 状態遷移：残りの列</span>
 <a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a>            <span class="n">temp</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
 <a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a>            <span class="k">if</span> <span class="n">s</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">==</span> <span class="n">t</span><span class="p">[</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]:</span>
-<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>                <span class="c1"># 2 つの文字が等しい場合、これら 2 つの文字をスキップ</span>
+<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>                <span class="c1"># 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
 <a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">leftup</span>
 <a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a>            <span class="k">else</span><span class="p">:</span>
-<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a>                <span class="c1"># 最小編集数 = 3 つの操作（挿入、削除、置換）からの最小編集数 + 1</span>
+<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a>                <span class="c1"># 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
 <a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">],</span> <span class="n">leftup</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
-<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a>            <span class="n">leftup</span> <span class="o">=</span> <span class="n">temp</span>  <span class="c1"># 次の dp[i-1, j-1] のために更新</span>
+<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a>            <span class="n">leftup</span> <span class="o">=</span> <span class="n">temp</span>  <span class="c1"># 次の反復の dp[i-1, j-1] に更新する</span>
 <a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">m</span><span class="p">]</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">edit_distance.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="p">[</span><span class="k">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">editDistanceDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">edit_distance.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 編集距離：空間最適化した動的計画法 */</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">editDistanceDPComp</span><span class="p">(</span><span class="n">string</span><span class="w"> </span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">length</span><span class="p">(),</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="n">length</span><span class="p">();</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">        </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span><span class="w"> </span><span class="c1">// dp[i-1, j-1] を一時保存する</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">        </span><span class="c1">// 状態遷移：残りの列</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">            </span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w">                </span><span class="c1">// 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
+<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftup</span><span class="p">;</span>
+<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a><span class="w">                </span><span class="c1">// 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
+<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]),</span><span class="w"> </span><span class="n">leftup</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a><span class="w">            </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span><span class="w"> </span><span class="c1">// 次の反復の dp[i-1, j-1] に更新する</span>
+<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">m</span><span class="p">];</span>
+<a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">edit_distance.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 編集距離：空間最適化動的プログラミング */</span>
+<div class="highlight"><span class="filename">edit_distance.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 編集距離：空間最適化した動的計画法 */</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">editDistanceDPComp</span><span class="p">(</span><span class="n">String</span><span class="w"> </span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="na">length</span><span class="p">(),</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="na">length</span><span class="p">();</span>
 <a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="c1">// 状態遷移：最初の行</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
 <a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
 <a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行</span>
 <a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">        </span><span class="c1">// 状態遷移：最初の列</span>
-<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="c1">// dp[i-1, j-1] を一時的に格納</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">        </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="c1">// dp[i-1, j-1] を一時保存する</span>
 <a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
 <a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">        </span><span class="c1">// 状態遷移：残りの列</span>
 <a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">            </span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">.</span><span class="na">charAt</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="na">charAt</span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">                </span><span class="c1">// 2つの文字が等しい場合、これら2つの文字をスキップ</span>
+<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">                </span><span class="c1">// 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
 <a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftup</span><span class="p">;</span>
 <a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="w">                </span><span class="c1">// 最小編集数 = 3つの操作（挿入、削除、置換）からの最小編集数 + 1</span>
+<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="w">                </span><span class="c1">// 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
 <a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">),</span><span class="w"> </span><span class="n">leftup</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="w">            </span><span class="p">}</span>
-<a id="__codelineno-15-24" name="__codelineno-15-24" href="#__codelineno-15-24"></a><span class="w">            </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span><span class="w"> </span><span class="c1">// 次のラウンドの dp[i-1, j-1] のために更新</span>
+<a id="__codelineno-15-24" name="__codelineno-15-24" href="#__codelineno-15-24"></a><span class="w">            </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span><span class="w"> </span><span class="c1">// 次の反復の dp[i-1, j-1] に更新する</span>
 <a id="__codelineno-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-15-26" name="__codelineno-15-26" href="#__codelineno-15-26"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="p">;</span>
@@ -4667,47 +4955,327 @@ dp[i, j] = dp[i-1, j-1]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">edit_distance.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">edit_distance</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">EditDistanceDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">edit_distance.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 編集距離：空間最適化した動的計画法 */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">EditDistanceDPComp</span><span class="p">(</span><span class="kt">string</span><span class="w"> </span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="kt">string</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">Length</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">        </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span><span class="w"> </span><span class="c1">// dp[i-1, j-1] を一時保存する</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">        </span><span class="c1">// 状態遷移：残りの列</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">            </span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">                </span><span class="c1">// 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftup</span><span class="p">;</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="w">                </span><span class="c1">// 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
+<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Min</span><span class="p">(</span><span class="n">Math</span><span class="p">.</span><span class="n">Min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]),</span><span class="w"> </span><span class="n">leftup</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-16-24" name="__codelineno-16-24" href="#__codelineno-16-24"></a><span class="w">            </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span><span class="w"> </span><span class="c1">// 次の反復の dp[i-1, j-1] に更新する</span>
+<a id="__codelineno-16-25" name="__codelineno-16-25" href="#__codelineno-16-25"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-26" name="__codelineno-16-26" href="#__codelineno-16-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-27" name="__codelineno-16-27" href="#__codelineno-16-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">m</span><span class="p">];</span>
+<a id="__codelineno-16-28" name="__codelineno-16-28" href="#__codelineno-16-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">edit_distance.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">editDistanceDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">edit_distance.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 編集距離：空間最適化した動的計画法 */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">editDistanceDPComp</span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="kt">string</span><span class="p">,</span><span class="w"> </span><span class="nx">t</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">s</span><span class="p">)</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="nx">m</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">t</span><span class="p">)</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">    </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">j</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">        </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w">        </span><span class="nx">leftUp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="c1">// dp[i-1, j-1] を一時保存する</span>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">i</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">        </span><span class="c1">// 状態遷移：残りの列</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="w">            </span><span class="nx">temp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span>
+<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="nx">s</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">t</span><span class="p">[</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="w">                </span><span class="c1">// 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
+<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">leftUp</span>
+<a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-22" name="__codelineno-17-22" href="#__codelineno-17-22"></a><span class="w">                </span><span class="c1">// 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
+<a id="__codelineno-17-23" name="__codelineno-17-23" href="#__codelineno-17-23"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">MinInt</span><span class="p">(</span><span class="nx">MinInt</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]),</span><span class="w"> </span><span class="nx">leftUp</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-17-24" name="__codelineno-17-24" href="#__codelineno-17-24"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-17-25" name="__codelineno-17-25" href="#__codelineno-17-25"></a><span class="w">            </span><span class="nx">leftUp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">temp</span><span class="w"> </span><span class="c1">// 次の反復の dp[i-1, j-1] に更新する</span>
+<a id="__codelineno-17-26" name="__codelineno-17-26" href="#__codelineno-17-26"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-17-27" name="__codelineno-17-27" href="#__codelineno-17-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-28" name="__codelineno-17-28" href="#__codelineno-17-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span>
+<a id="__codelineno-17-29" name="__codelineno-17-29" href="#__codelineno-17-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">edit_distance.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">editDistanceDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">edit_distance.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 編集距離：空間最適化した動的計画法 */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">editDistanceDPComp</span><span class="p">(</span><span class="n">s</span><span class="p">:</span><span class="w"> </span><span class="nb">String</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="p">:</span><span class="w"> </span><span class="nb">String</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">utf8CString</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="n">utf8CString</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">j</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w">        </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">leftup</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="c1">// dp[i-1, j-1] を一時保存する</span>
+<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w">        </span><span class="c1">// 状態遷移：残りの列</span>
+<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="nv">temp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">utf8CString</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="n">utf8CString</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a><span class="w">                </span><span class="c1">// 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
+<a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">leftup</span>
+<a id="__codelineno-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-22" name="__codelineno-18-22" href="#__codelineno-18-22"></a><span class="w">                </span><span class="c1">// 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
+<a id="__codelineno-18-23" name="__codelineno-18-23" href="#__codelineno-18-23"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">min</span><span class="p">(</span><span class="bp">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]),</span><span class="w"> </span><span class="n">leftup</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-18-24" name="__codelineno-18-24" href="#__codelineno-18-24"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-18-25" name="__codelineno-18-25" href="#__codelineno-18-25"></a><span class="w">            </span><span class="n">leftup</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="c1">// 次の反復の dp[i-1, j-1] に更新する</span>
+<a id="__codelineno-18-26" name="__codelineno-18-26" href="#__codelineno-18-26"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-27" name="__codelineno-18-27" href="#__codelineno-18-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-28" name="__codelineno-18-28" href="#__codelineno-18-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">m</span><span class="p">]</span>
+<a id="__codelineno-18-29" name="__codelineno-18-29" href="#__codelineno-18-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">edit_distance.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">editDistanceDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">edit_distance.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 編集距離：空間最適化した動的計画法 */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">editDistanceDPComp</span><span class="p">(</span><span class="nx">s</span><span class="p">,</span><span class="w"> </span><span class="nx">t</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">length</span><span class="p">,</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">        </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">j</span><span class="p">;</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">        </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span><span class="w"> </span><span class="c1">// dp[i-1, j-1] を一時保存する</span>
+<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w">        </span><span class="c1">// 状態遷移：残りの列</span>
+<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="w">            </span><span class="kd">const</span><span class="w"> </span><span class="nx">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="p">.</span><span class="nx">charAt</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">charAt</span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a><span class="w">                </span><span class="c1">// 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
+<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">leftup</span><span class="p">;</span>
+<a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-22" name="__codelineno-19-22" href="#__codelineno-19-22"></a><span class="w">                </span><span class="c1">// 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
+<a id="__codelineno-19-23" name="__codelineno-19-23" href="#__codelineno-19-23"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">],</span><span class="w"> </span><span class="nx">leftup</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-19-24" name="__codelineno-19-24" href="#__codelineno-19-24"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-19-25" name="__codelineno-19-25" href="#__codelineno-19-25"></a><span class="w">            </span><span class="nx">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">temp</span><span class="p">;</span><span class="w"> </span><span class="c1">// 次の反復の dp[i-1, j-1] に更新する</span>
+<a id="__codelineno-19-26" name="__codelineno-19-26" href="#__codelineno-19-26"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-27" name="__codelineno-19-27" href="#__codelineno-19-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-28" name="__codelineno-19-28" href="#__codelineno-19-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">m</span><span class="p">];</span>
+<a id="__codelineno-19-29" name="__codelineno-19-29" href="#__codelineno-19-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">edit_distance.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">editDistanceDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">edit_distance.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 編集距離：空間最適化した動的計画法 */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">editDistanceDPComp</span><span class="p">(</span><span class="nx">s</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">,</span><span class="w"> </span><span class="nx">t</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">length</span><span class="p">,</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">        </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">j</span><span class="p">;</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">        </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span><span class="w"> </span><span class="c1">// dp[i-1, j-1] を一時保存する</span>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w">        </span><span class="c1">// 状態遷移：残りの列</span>
+<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-17" name="__codelineno-20-17" href="#__codelineno-20-17"></a><span class="w">            </span><span class="kd">const</span><span class="w"> </span><span class="nx">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-20-18" name="__codelineno-20-18" href="#__codelineno-20-18"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="p">.</span><span class="nx">charAt</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">charAt</span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-19" name="__codelineno-20-19" href="#__codelineno-20-19"></a><span class="w">                </span><span class="c1">// 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
+<a id="__codelineno-20-20" name="__codelineno-20-20" href="#__codelineno-20-20"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">leftup</span><span class="p">;</span>
+<a id="__codelineno-20-21" name="__codelineno-20-21" href="#__codelineno-20-21"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-22" name="__codelineno-20-22" href="#__codelineno-20-22"></a><span class="w">                </span><span class="c1">// 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
+<a id="__codelineno-20-23" name="__codelineno-20-23" href="#__codelineno-20-23"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">],</span><span class="w"> </span><span class="nx">leftup</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-20-24" name="__codelineno-20-24" href="#__codelineno-20-24"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-20-25" name="__codelineno-20-25" href="#__codelineno-20-25"></a><span class="w">            </span><span class="nx">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">temp</span><span class="p">;</span><span class="w"> </span><span class="c1">// 次の反復の dp[i-1, j-1] に更新する</span>
+<a id="__codelineno-20-26" name="__codelineno-20-26" href="#__codelineno-20-26"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-27" name="__codelineno-20-27" href="#__codelineno-20-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-28" name="__codelineno-20-28" href="#__codelineno-20-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">m</span><span class="p">];</span>
+<a id="__codelineno-20-29" name="__codelineno-20-29" href="#__codelineno-20-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">edit_distance.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">editDistanceDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">edit_distance.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 編集距離：空間最適化した動的計画法 */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">editDistanceDPComp</span><span class="p">(</span><span class="kt">String</span><span class="w"> </span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="kt">String</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">  </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">  </span><span class="c1">// 状態遷移：残りの行</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="m">0</span><span class="p">];</span><span class="w"> </span><span class="c1">// dp[i-1, j-1] を一時保存する</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="m">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの列</span>
+<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="w">      </span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-21-17" name="__codelineno-21-17" href="#__codelineno-21-17"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-18" name="__codelineno-21-18" href="#__codelineno-21-18"></a><span class="w">        </span><span class="c1">// 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
+<a id="__codelineno-21-19" name="__codelineno-21-19" href="#__codelineno-21-19"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftup</span><span class="p">;</span>
+<a id="__codelineno-21-20" name="__codelineno-21-20" href="#__codelineno-21-20"></a><span class="w">      </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-21" name="__codelineno-21-21" href="#__codelineno-21-21"></a><span class="w">        </span><span class="c1">// 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
+<a id="__codelineno-21-22" name="__codelineno-21-22" href="#__codelineno-21-22"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]),</span><span class="w"> </span><span class="n">leftup</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-21-23" name="__codelineno-21-23" href="#__codelineno-21-23"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-21-24" name="__codelineno-21-24" href="#__codelineno-21-24"></a><span class="w">      </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span><span class="w"> </span><span class="c1">// 次の反復の dp[i-1, j-1] に更新する</span>
+<a id="__codelineno-21-25" name="__codelineno-21-25" href="#__codelineno-21-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-26" name="__codelineno-21-26" href="#__codelineno-21-26"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-27" name="__codelineno-21-27" href="#__codelineno-21-27"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">m</span><span class="p">];</span>
+<a id="__codelineno-21-28" name="__codelineno-21-28" href="#__codelineno-21-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">edit_distance.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">edit_distance_dp_comp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">edit_distance.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 編集距離：空間最適化した動的計画法 */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">edit_distance_dp_comp</span><span class="p">(</span><span class="n">s</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="kt">str</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="kt">str</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">.</span><span class="n">len</span><span class="p">(),</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="n">len</span><span class="p">());</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..</span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">;</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w">        </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span><span class="w"> </span><span class="c1">// dp[i-1, j-1] を一時保存する</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">;</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">        </span><span class="c1">// 状態遷移：残りの列</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">chars</span><span class="p">().</span><span class="n">nth</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="n">chars</span><span class="p">().</span><span class="n">nth</span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="w">                </span><span class="c1">// 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
+<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftup</span><span class="p">;</span>
+<a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-21" name="__codelineno-22-21" href="#__codelineno-22-21"></a><span class="w">                </span><span class="c1">// 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
+<a id="__codelineno-22-22" name="__codelineno-22-22" href="#__codelineno-22-22"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">min</span><span class="p">(</span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]),</span><span class="w"> </span><span class="n">leftup</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-22-23" name="__codelineno-22-23" href="#__codelineno-22-23"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-22-24" name="__codelineno-22-24" href="#__codelineno-22-24"></a><span class="w">            </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span><span class="w"> </span><span class="c1">// 次の反復の dp[i-1, j-1] に更新する</span>
+<a id="__codelineno-22-25" name="__codelineno-22-25" href="#__codelineno-22-25"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-26" name="__codelineno-22-26" href="#__codelineno-22-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-27" name="__codelineno-22-27" href="#__codelineno-22-27"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="n">m</span><span class="p">]</span>
+<a id="__codelineno-22-28" name="__codelineno-22-28" href="#__codelineno-22-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">edit_distance.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">editDistanceDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">edit_distance.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 編集距離：空間最適化した動的計画法 */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">editDistanceDPComp</span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="n">t</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">calloc</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w">        </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span><span class="w"> </span><span class="c1">// dp[i-1, j-1] を一時保存する</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w">        </span><span class="c1">// 状態遷移：残りの列</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="w">            </span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="w">                </span><span class="c1">// 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
+<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftup</span><span class="p">;</span>
+<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="w">                </span><span class="c1">// 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
+<a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">myMin</span><span class="p">(</span><span class="n">myMin</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]),</span><span class="w"> </span><span class="n">leftup</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-23-23" name="__codelineno-23-23" href="#__codelineno-23-23"></a><span class="w">            </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span><span class="w"> </span><span class="c1">// 次の反復の dp[i-1, j-1] に更新する</span>
+<a id="__codelineno-23-24" name="__codelineno-23-24" href="#__codelineno-23-24"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-25" name="__codelineno-23-25" href="#__codelineno-23-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-26" name="__codelineno-23-26" href="#__codelineno-23-26"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">m</span><span class="p">];</span>
+<a id="__codelineno-23-27" name="__codelineno-23-27" href="#__codelineno-23-27"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-23-28" name="__codelineno-23-28" href="#__codelineno-23-28"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">dp</span><span class="p">);</span>
+<a id="__codelineno-23-29" name="__codelineno-23-29" href="#__codelineno-23-29"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-23-30" name="__codelineno-23-30" href="#__codelineno-23-30"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">edit_distance.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">editDistanceDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">edit_distance.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 編集距離：空間最適化した動的計画法 */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">editDistanceDPComp</span><span class="p">(</span><span class="n">s</span><span class="p">:</span><span class="w"> </span><span class="kt">String</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="p">:</span><span class="w"> </span><span class="kt">String</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="na">length</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="na">length</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">        </span><span class="c1">// 状態遷移：先頭列</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="m">0</span><span class="o">]</span><span class="w"> </span><span class="c1">// dp[i-1, j-1] を一時保存する</span>
+<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="m">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="w">        </span><span class="c1">// 状態遷移：残りの列</span>
+<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-17" name="__codelineno-24-17" href="#__codelineno-24-17"></a><span class="w">            </span><span class="kd">val</span><span class="w"> </span><span class="nv">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-24-18" name="__codelineno-24-18" href="#__codelineno-24-18"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-19" name="__codelineno-24-19" href="#__codelineno-24-19"></a><span class="w">                </span><span class="c1">// 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
+<a id="__codelineno-24-20" name="__codelineno-24-20" href="#__codelineno-24-20"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftup</span>
+<a id="__codelineno-24-21" name="__codelineno-24-21" href="#__codelineno-24-21"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-22" name="__codelineno-24-22" href="#__codelineno-24-22"></a><span class="w">                </span><span class="c1">// 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
+<a id="__codelineno-24-23" name="__codelineno-24-23" href="#__codelineno-24-23"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">),</span><span class="w"> </span><span class="n">leftup</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-24-24" name="__codelineno-24-24" href="#__codelineno-24-24"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-24-25" name="__codelineno-24-25" href="#__codelineno-24-25"></a><span class="w">            </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="c1">// 次の反復の dp[i-1, j-1] に更新する</span>
+<a id="__codelineno-24-26" name="__codelineno-24-26" href="#__codelineno-24-26"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-24-27" name="__codelineno-24-27" href="#__codelineno-24-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-28" name="__codelineno-24-28" href="#__codelineno-24-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">m</span><span class="o">]</span>
+<a id="__codelineno-24-29" name="__codelineno-24-29" href="#__codelineno-24-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">edit_distance.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">edit_distance_dp_comp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">edit_distance.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### 編集距離：空間最適化した動的計画法 ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">edit_distance_dp_comp</span><span class="p">(</span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="p">)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="o">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">  </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">  </span><span class="c1"># 状態遷移：先頭行</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">  </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">j</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">  </span><span class="c1"># 状態遷移：残りの行</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">    </span><span class="c1"># 状態遷移：先頭列</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w">    </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">.</span><span class="n">first</span><span class="w"> </span><span class="c1"># dp[i-1, j-1] を一時保存する</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w">    </span><span class="c1"># 状態遷移：残りの列</span>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w">      </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="n">s</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
+<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w">        </span><span class="c1"># 2 つの文字が等しければ、その 2 文字をそのままスキップする</span>
+<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftup</span>
+<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a><span class="w">      </span><span class="k">else</span>
+<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="w">        </span><span class="c1"># 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1</span>
+<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">leftup</span><span class="o">].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a><span class="w">      </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="c1"># 次の反復の dp[i-1, j-1] に更新する</span>
+<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="n">m</span><span class="o">]</span>
+<a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20edit_distance_dp_comp%28s%3A%20str%2C%20t%3A%20str%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%B7%A8%E9%9B%86%E8%B7%9D%E9%9B%A2%EF%BC%9A%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E3%81%97%E3%81%9F%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%2C%20m%20%3D%20len%28s%29%2C%20len%28t%29%0A%20%20%20%20dp%20%3D%20%5B0%5D%20%2A%20%28m%20%2B%201%29%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%85%88%E9%A0%AD%E8%A1%8C%0A%20%20%20%20for%20j%20in%20range%281%2C%20m%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20dp%5Bj%5D%20%3D%20j%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E6%AE%8B%E3%82%8A%E3%81%AE%E8%A1%8C%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%85%88%E9%A0%AD%E5%88%97%0A%20%20%20%20%20%20%20%20leftup%20%3D%20dp%5B0%5D%20%20%23%20dp%5Bi-1%2C%20j-1%5D%20%E3%82%92%E4%B8%80%E6%99%82%E4%BF%9D%E5%AD%98%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20dp%5B0%5D%20%2B%3D%201%0A%20%20%20%20%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E6%AE%8B%E3%82%8A%E3%81%AE%E5%88%97%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%281%2C%20m%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20temp%20%3D%20dp%5Bj%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20s%5Bi%20-%201%5D%20%3D%3D%20t%5Bj%20-%201%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%202%20%E3%81%A4%E3%81%AE%E6%96%87%E5%AD%97%E3%81%8C%E7%AD%89%E3%81%97%E3%81%91%E3%82%8C%E3%81%B0%E3%80%81%E3%81%9D%E3%81%AE%202%20%E6%96%87%E5%AD%97%E3%82%92%E3%81%9D%E3%81%AE%E3%81%BE%E3%81%BE%E3%82%B9%E3%82%AD%E3%83%83%E3%83%97%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bj%5D%20%3D%20leftup%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%9C%80%E5%B0%8F%E7%B7%A8%E9%9B%86%E5%9B%9E%E6%95%B0%20%3D%20%E6%8C%BF%E5%85%A5%E3%83%BB%E5%89%8A%E9%99%A4%E3%83%BB%E7%BD%AE%E6%8F%9B%E3%81%AE%203%20%E6%93%8D%E4%BD%9C%E3%81%AB%E3%81%8A%E3%81%91%E3%82%8B%E6%9C%80%E5%B0%8F%E7%B7%A8%E9%9B%86%E5%9B%9E%E6%95%B0%20%2B%201%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bj%5D%20%3D%20min%28dp%5Bj%20-%201%5D%2C%20dp%5Bj%5D%2C%20leftup%29%20%2B%201%0A%20%20%20%20%20%20%20%20%20%20%20%20leftup%20%3D%20temp%20%20%23%20%E6%AC%A1%E3%81%AE%E5%8F%8D%E5%BE%A9%E3%81%AE%20dp%5Bi-1%2C%20j-1%5D%20%E3%81%AB%E6%9B%B4%E6%96%B0%E3%81%99%E3%82%8B%0A%20%20%20%20return%20dp%5Bm%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20s%20%3D%20%22bag%22%0A%20%20%20%20t%20%3D%20%22pack%22%0A%20%20%20%20n%2C%20m%20%3D%20len%28s%29%2C%20len%28t%29%0A%0A%20%20%20%20%23%20%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E5%BE%8C%E3%81%AE%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20edit_distance_dp_comp%28s%2C%20t%29%0A%20%20%20%20print%28f%22%7Bs%7D%20%E3%82%92%20%7Bt%7D%20%E3%81%AB%E5%A4%89%E6%9B%B4%E3%81%99%E3%82%8B%E3%81%AB%E3%81%AF%E6%9C%80%E5%B0%8F%E3%81%A7%20%7Bres%7D%20%E5%9B%9E%E3%81%AE%E7%B7%A8%E9%9B%86%E3%81%8C%E5%BF%85%E8%A6%81%E3%81%A7%E3%81%99%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20edit_distance_dp_comp%28s%3A%20str%2C%20t%3A%20str%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%B7%A8%E9%9B%86%E8%B7%9D%E9%9B%A2%EF%BC%9A%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E3%81%97%E3%81%9F%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%2C%20m%20%3D%20len%28s%29%2C%20len%28t%29%0A%20%20%20%20dp%20%3D%20%5B0%5D%20%2A%20%28m%20%2B%201%29%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%85%88%E9%A0%AD%E8%A1%8C%0A%20%20%20%20for%20j%20in%20range%281%2C%20m%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20dp%5Bj%5D%20%3D%20j%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E6%AE%8B%E3%82%8A%E3%81%AE%E8%A1%8C%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%85%88%E9%A0%AD%E5%88%97%0A%20%20%20%20%20%20%20%20leftup%20%3D%20dp%5B0%5D%20%20%23%20dp%5Bi-1%2C%20j-1%5D%20%E3%82%92%E4%B8%80%E6%99%82%E4%BF%9D%E5%AD%98%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20dp%5B0%5D%20%2B%3D%201%0A%20%20%20%20%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E6%AE%8B%E3%82%8A%E3%81%AE%E5%88%97%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%281%2C%20m%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20temp%20%3D%20dp%5Bj%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20s%5Bi%20-%201%5D%20%3D%3D%20t%5Bj%20-%201%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%202%20%E3%81%A4%E3%81%AE%E6%96%87%E5%AD%97%E3%81%8C%E7%AD%89%E3%81%97%E3%81%91%E3%82%8C%E3%81%B0%E3%80%81%E3%81%9D%E3%81%AE%202%20%E6%96%87%E5%AD%97%E3%82%92%E3%81%9D%E3%81%AE%E3%81%BE%E3%81%BE%E3%82%B9%E3%82%AD%E3%83%83%E3%83%97%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bj%5D%20%3D%20leftup%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%9C%80%E5%B0%8F%E7%B7%A8%E9%9B%86%E5%9B%9E%E6%95%B0%20%3D%20%E6%8C%BF%E5%85%A5%E3%83%BB%E5%89%8A%E9%99%A4%E3%83%BB%E7%BD%AE%E6%8F%9B%E3%81%AE%203%20%E6%93%8D%E4%BD%9C%E3%81%AB%E3%81%8A%E3%81%91%E3%82%8B%E6%9C%80%E5%B0%8F%E7%B7%A8%E9%9B%86%E5%9B%9E%E6%95%B0%20%2B%201%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bj%5D%20%3D%20min%28dp%5Bj%20-%201%5D%2C%20dp%5Bj%5D%2C%20leftup%29%20%2B%201%0A%20%20%20%20%20%20%20%20%20%20%20%20leftup%20%3D%20temp%20%20%23%20%E6%AC%A1%E3%81%AE%E5%8F%8D%E5%BE%A9%E3%81%AE%20dp%5Bi-1%2C%20j-1%5D%20%E3%81%AB%E6%9B%B4%E6%96%B0%E3%81%99%E3%82%8B%0A%20%20%20%20return%20dp%5Bm%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20s%20%3D%20%22bag%22%0A%20%20%20%20t%20%3D%20%22pack%22%0A%20%20%20%20n%2C%20m%20%3D%20len%28s%29%2C%20len%28t%29%0A%0A%20%20%20%20%23%20%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E5%BE%8C%E3%81%AE%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20edit_distance_dp_comp%28s%2C%20t%29%0A%20%20%20%20print%28f%22%7Bs%7D%20%E3%82%92%20%7Bt%7D%20%E3%81%AB%E5%A4%89%E6%9B%B4%E3%81%99%E3%82%8B%E3%81%AB%E3%81%AF%E6%9C%80%E5%B0%8F%E3%81%A7%20%7Bres%7D%20%E5%9B%9E%E3%81%AE%E7%B7%A8%E9%9B%86%E3%81%8C%E5%BF%85%E8%A6%81%E3%81%A7%E3%81%99%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 
 <!-- Source file information -->
 
diff --git a/ja/chapter_dynamic_programming/index.html b/ja/chapter_dynamic_programming/index.html
index ba4625c68..d64569182 100644
--- a/ja/chapter_dynamic_programming/index.html
+++ b/ja/chapter_dynamic_programming/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -39,7 +39,7 @@
     
     
       
-        <title>第 14 章 動的プログラミング - Hello アルゴリズム</title>
+        <title>第 14 章 動的計画法 - Hello アルゴリズム</title>
       
     
     
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -152,7 +152,7 @@
         <div class="md-header__topic" data-md-component="header-topic">
           <span class="md-ellipsis">
             
-              第 14 章 &nbsp; 動的プログラミング
+              第 14 章 &nbsp; 動的計画法
             
           </span>
         </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1635,7 +1635,7 @@
   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1942,7 +1942,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2105,7 +2105,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2491,7 +2491,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2547,7 +2547,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2575,7 +2575,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3113,7 +3113,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3169,7 +3169,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3197,7 +3197,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3390,7 +3390,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3418,7 +3418,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3561,7 +3561,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3589,7 +3589,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3617,7 +3617,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3645,7 +3645,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3838,7 +3838,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4083,7 +4083,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4273,19 +4273,19 @@
 
 
 <!-- Page content -->
-<h1 id="14">第 14 章 &nbsp; 動的プログラミング<a class="headerlink" href="#14" title="Permanent link">&para;</a></h1>
-<p><img alt="動的プログラミング" class="cover-image" src="../assets/covers/chapter_dynamic_programming.jpg" /></p>
+<h1 id="14">第 14 章 &nbsp; 動的計画法<a class="headerlink" href="#14" title="Permanent link">&para;</a></h1>
+<p><img alt="動的計画法" class="cover-image" src="../assets/covers/chapter_dynamic_programming.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>川が流れて海に注ぐように、</p>
-<p>動的プログラミングは小さな問題の解を織り合わせて、より大きな問題の解へと導きます。一歩一歩進んで、最終的な答えが待つ彼岸へと向かいます。</p>
+<p>小川は川へと注ぎ、河川は大海へと注ぐ。</p>
+<p>動的計画法は小さな問題の解を集めて大きな問題の答えとし、一歩ずつ私たちを問題解決の彼岸へと導く。</p>
 </div>
 <h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
-<li><a href="intro_to_dynamic_programming/">14.1 &nbsp; 動的計画法の初歩</a></li>
-<li><a href="dp_problem_features/">14.2 &nbsp; DP 問題の特性</a></li>
-<li><a href="dp_solution_pipeline/">14.3 &nbsp; DP の解法の考え方</a></li>
-<li><a href="knapsack_problem/">14.4 &nbsp; 0-1ナップサック問題</a></li>
+<li><a href="intro_to_dynamic_programming/">14.1 &nbsp; 動的計画法入門</a></li>
+<li><a href="dp_problem_features/">14.2 &nbsp; 動的計画法の問題特性</a></li>
+<li><a href="dp_solution_pipeline/">14.3 &nbsp; 動的計画法の問題解決の考え方</a></li>
+<li><a href="knapsack_problem/">14.4 &nbsp; 0-1 ナップサック問題</a></li>
 <li><a href="unbounded_knapsack_problem/">14.5 &nbsp; 完全ナップサック問題</a></li>
 <li><a href="edit_distance_problem/">14.6 &nbsp; 編集距離問題</a></li>
 <li><a href="summary/">14.7 &nbsp; まとめ</a></li>
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     href="./intro_to_dynamic_programming/"
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-    aria-label="次: 14.1 &amp;nbsp; 動的計画法の初歩"
+    aria-label="次: 14.1 &amp;nbsp; 動的計画法入門"
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-        14.1 &nbsp; 動的計画法の初歩
+        14.1 &nbsp; 動的計画法入門
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@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -39,7 +39,7 @@
     
     
       
-        <title>14.1 動的プログラミングの紹介 - Hello アルゴリズム</title>
+        <title>14.1 動的計画法入門 - Hello アルゴリズム</title>
       
     
     
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
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         <div class="md-header__topic" data-md-component="header-topic">
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-              14.1 &nbsp; 動的プログラミングの紹介
+              14.1 &nbsp; 動的計画法入門
             
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-    序
+    はじめに
   
 
     
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-    序
+    はじめに
   
 
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-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
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-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
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-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
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-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
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-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
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+    6.1 &nbsp; ハッシュテーブル
   
 
     
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
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-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
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-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
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-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
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+    13.4 &nbsp; n クイーン問題
   
 
     
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+    14.1 &nbsp; 動的計画法入門
   
 
     
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+    14.1 &nbsp; 動的計画法入門
   
 
     
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-        14.1.1 &nbsp; 方法1：力任せ探索
+        14.1.1 &nbsp; 方法 1：総当たり探索
       
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-        14.1.2 &nbsp; 方法2：メモ化探索
+        14.1.2 &nbsp; 方法 2：メモ化探索
       
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-        14.1.3 &nbsp; 方法3：動的プログラミング
+        14.1.3 &nbsp; 方法 3：動的計画法
       
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-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
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-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
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+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4175,7 +4175,7 @@
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4321,7 +4321,7 @@
   <a href="#1411-1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        14.1.1 &nbsp; 方法1：力任せ探索
+        14.1.1 &nbsp; 方法 1：総当たり探索
       
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-        14.1.2 &nbsp; 方法2：メモ化探索
+        14.1.2 &nbsp; 方法 2：メモ化探索
       
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-        14.1.3 &nbsp; 方法3：動的プログラミング
+        14.1.3 &nbsp; 方法 3：動的計画法
       
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@@ -4398,40 +4398,40 @@
 
 
 <!-- Page content -->
-<h1 id="141">14.1 &nbsp; 動的プログラミングの紹介<a class="headerlink" href="#141" title="Permanent link">&para;</a></h1>
-<p><u>動的プログラミング</u>は重要なアルゴリズムパラダイムであり、問題を一連の小さな部分問題に分解し、これらの部分問題の解を保存することで冗長な計算を避け、時間効率を大幅に向上させます。</p>
-<p>このセクションでは、古典的な問題から始めて、まず力任せの探索法による解法を提示し、重複する部分問題を特定してから、より効率的な動的プログラミング解法を段階的に導出します。</p>
+<h1 id="141">14.1 &nbsp; 動的計画法入門<a class="headerlink" href="#141" title="Permanent link">&para;</a></h1>
+<p><u>動的計画法（dynamic programming）</u>は重要なアルゴリズムパラダイムであり、問題をより小さな部分問題の列に分解し、それらの解を保存して重複計算を避けることで、時間効率を大幅に向上させます。</p>
+<p>本節では、古典的な例題から始めて、まずその力任せのバックトラッキング解法を示し、そこに含まれる重複部分問題を観察したうえで、より効率的な動的計画法の解法を段階的に導きます。</p>
 <div class="admonition question">
-<p class="admonition-title">階段登り</p>
-<p><span class="arithmatex">\(n\)</span> 段の階段があり、一度に <span class="arithmatex">\(1\)</span> 段または <span class="arithmatex">\(2\)</span> 段上ることができます。頂上に到達する方法は何通りありますか？</p>
+<p class="admonition-title">階段を上る</p>
+<p>全体で <span class="arithmatex">\(n\)</span> 段ある階段が与えられ、各ステップで <span class="arithmatex">\(1\)</span> 段または <span class="arithmatex">\(2\)</span> 段上ることができます。頂上まで到達する方法は何通りあるでしょうか？</p>
 </div>
-<p>下の図に示すように、<span class="arithmatex">\(3\)</span> 段の階段の頂上に到達する方法は <span class="arithmatex">\(3\)</span> 通りあります。</p>
-<p><img alt="3段目に到達する方法の数" class="animation-figure" src="../intro_to_dynamic_programming.assets/climbing_stairs_example.png" /></p>
-<p align="center"> 図 14-1 &nbsp; 3段目に到達する方法の数 </p>
+<p>次の図に示すように、<span class="arithmatex">\(3\)</span> 段の階段では、頂上まで到達する方法は全部で <span class="arithmatex">\(3\)</span> 通りあります。</p>
+<p><img alt="3 段の階段を上る方法の数" class="animation-figure" src="../intro_to_dynamic_programming.assets/climbing_stairs_example.png" /></p>
+<p align="center"> 図 14-1 &nbsp; 3 段の階段を上る方法の数 </p>
 
-<p>この問題は**バックトラッキングを用いてすべての可能性を網羅**することで方法の数を計算することを目的としています。具体的には、階段登りの問題を多段階選択プロセスとして考えます：地面から始めて、毎回 <span class="arithmatex">\(1\)</span> 段または <span class="arithmatex">\(2\)</span> 段上るかを選択し、階段の頂上に到達したら方法の数をカウントし、頂上を超えた場合はプルーニング（枝刈り）を行います。コードは以下の通りです：</p>
+<p>この問題の目的は方法の総数を求めることです。<strong>考えられるすべての可能性をバックトラッキングで総当たりすることができます</strong>。具体的には、階段を上ることを複数ラウンドの選択過程とみなし、地面から出発して各ラウンドで <span class="arithmatex">\(1\)</span> 段または <span class="arithmatex">\(2\)</span> 段上ります。階段の頂上に到達するたびに方法数を <span class="arithmatex">\(1\)</span> 増やし、頂上を越えた場合は枝刈りします。コードは次のとおりです：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
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 <div class="highlight"><span class="filename">climbing_stairs_backtrack.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">state</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
 <a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキング&quot;&quot;&quot;</span>
-<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># n 段目に登ったとき、解の数に 1 を加える</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 第 n 段に到達したら、方法数を 1 増やす</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">if</span> <span class="n">state</span> <span class="o">==</span> <span class="n">n</span><span class="p">:</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="n">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># すべての選択肢を走査</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="k">for</span> <span class="n">choice</span> <span class="ow">in</span> <span class="n">choices</span><span class="p">:</span>
-<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="c1"># 枝刈り：n 段を超えて登ることを許可しない</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="c1"># 枝刈り: 第 n 段を超えないようにする</span>
 <a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="k">if</span> <span class="n">state</span> <span class="o">+</span> <span class="n">choice</span> <span class="o">&gt;</span> <span class="n">n</span><span class="p">:</span>
 <a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>            <span class="k">continue</span>
-<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="c1"># 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="c1"># 試行: 選択を行い、状態を更新</span>
 <a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span> <span class="n">state</span> <span class="o">+</span> <span class="n">choice</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
-<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="c1"># 撤回</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="c1"># バックトラック</span>
 <a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>
 <a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_backtrack</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
 <a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;階段登り：バックトラッキング&quot;&quot;&quot;</span>
-<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>    <span class="n">choices</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">]</span>  <span class="c1"># 1 段または 2 段登ることを選択可能</span>
-<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>    <span class="n">state</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># 0 段目から登り始める</span>
-<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span>  <span class="c1"># res[0] を使用して解の数を記録</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>    <span class="n">choices</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">]</span>  <span class="c1"># 1 段または 2 段上ることを選べる</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>    <span class="n">state</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># 第 0 段から上り始める</span>
+<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span>  <span class="c1"># res[0] を使って方法数を記録する</span>
 <a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>    <span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span> <span class="n">state</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
 <a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>    <span class="k">return</span> <span class="n">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
 </code></pre></div>
@@ -4439,25 +4439,25 @@
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">climbing_stairs_backtrack.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* バックトラッキング */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// n段目に到達したとき、解の数に1を加える</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 第 n 段に到達したら、方法数を 1 増やす</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">++</span><span class="p">;</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choice</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">        </span><span class="c1">// 剪定：n段を超えて登ることを許可しない</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">        </span><span class="c1">// 枝刈り: 第 n 段を超えないようにする</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
-<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
-<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="c1">// 撤回</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="c1">// バックトラック</span>
 <a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="p">}</span>
 <a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a>
 <a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="cm">/* 階段登り：バックトラッキング */</span>
 <a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsBacktrack</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">choices</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">};</span><span class="w"> </span><span class="c1">// 1段または2段登ることを選択可能</span>
-<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                </span><span class="c1">// 0段目から登り始める</span>
-<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mi">0</span><span class="p">};</span><span class="w">        </span><span class="c1">// res[0] を使用して解の数を記録</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">choices</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">};</span><span class="w"> </span><span class="c1">// 1 段または 2 段上ることを選べる</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                </span><span class="c1">// 第 0 段から上り始める</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mi">0</span><span class="p">};</span><span class="w">        </span><span class="c1">// res[0] を使って方法数を記録する</span>
 <a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
 <a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span>
 <a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="p">}</span>
@@ -4466,116 +4466,356 @@
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">climbing_stairs_backtrack.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* バックトラッキング */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// n段目に到達したとき、解の数に1を加える</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 第 n 段に到達したら、方法数を 1 増やす</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="na">set</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Integer</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">        </span><span class="c1">// 剪定：n段を超えて登ることを許可しない</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">        </span><span class="c1">// 枝刈り: 第 n 段を超えないようにする</span>
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
-<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
 <a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
-<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="c1">// 撤回</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="c1">// バックトラック</span>
 <a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="p">}</span>
 <a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a>
 <a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="cm">/* 階段登り：バックトラッキング */</span>
 <a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsBacktrack</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">choices</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Arrays</span><span class="p">.</span><span class="na">asList</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 1段または2段登ることを選択可能</span>
-<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 0段目から登り始める</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">choices</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Arrays</span><span class="p">.</span><span class="na">asList</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 1 段または 2 段上ることを選べる</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 第 0 段から上り始める</span>
 <a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
-<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// res[0] を使用して解の数を記録</span>
+<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// res[0] を使って方法数を記録する</span>
 <a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
 <a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_backtrack.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">climbing_stairs_backtrack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Backtrack</span><span class="p">}</span>
-<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
-<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">climbing_stairs_backtrack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">ClimbingStairsBacktrack</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_backtrack.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* バックトラッキング */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Backtrack</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="c1">// 第 n 段に到達したら、方法数を 1 増やす</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">        </span><span class="c1">// 枝刈り: 第 n 段を超えないようにする</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">        </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">        </span><span class="n">Backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">        </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="p">}</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="cm">/* 階段登り：バックトラッキング */</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="kt">int</span><span class="w"> </span><span class="nf">ClimbingStairsBacktrack</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">choices</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">];</span><span class="w"> </span><span class="c1">// 1 段または 2 段上ることを選べる</span>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 第 0 段から上り始める</span>
+<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mi">0</span><span class="p">];</span><span class="w"> </span><span class="c1">// res[0] を使って方法数を記録する</span>
+<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="w">    </span><span class="n">Backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_backtrack.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
-<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
-<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">climbingStairsBacktrack</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_backtrack.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* バックトラッキング */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">choices</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// 第 n 段に到達したら、方法数を 1 増やす</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">state</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">        </span><span class="nx">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">choices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">        </span><span class="c1">// 枝刈り: 第 n 段を超えないようにする</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">state</span><span class="o">+</span><span class="nx">choice</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">            </span><span class="k">continue</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">        </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">        </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">state</span><span class="o">+</span><span class="nx">choice</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">        </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="p">}</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="cm">/* 階段登り：バックトラッキング */</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="kd">func</span><span class="w"> </span><span class="nx">climbingStairsBacktrack</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w">    </span><span class="c1">// 1 段または 2 段上ることを選べる</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w">    </span><span class="nx">choices</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">}</span>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="w">    </span><span class="c1">// 第 0 段から上り始める</span>
+<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="w">    </span><span class="nx">state</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="w">    </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="w">    </span><span class="c1">// res[0] を使って方法数を記録する</span>
+<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w">    </span><span class="nx">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="w">    </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
+<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-4-30" name="__codelineno-4-30" href="#__codelineno-4-30"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_backtrack.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
-<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">climbingStairsBacktrack</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_backtrack.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* バックトラッキング */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// 第 n 段に到達したら、方法数を 1 増やす</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">        </span><span class="c1">// 枝刈り: 第 n 段を超えないようにする</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">            </span><span class="k">continue</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">        </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">        </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="p">}</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="cm">/* 階段登り：バックトラッキング */</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="kd">func</span><span class="w"> </span><span class="nf">climbingStairsBacktrack</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">choices</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="c1">// 1 段または 2 段上ることを選べる</span>
+<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">state</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1">// 第 0 段から上り始める</span>
+<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
+<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="c1">// res[0] を使って方法数を記録する</span>
+<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_backtrack.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
-<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
-<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">climbingStairsBacktrack</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_backtrack.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* バックトラッキング */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="c1">// 第 n 段に到達したら、方法数を 1 増やす</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">        </span><span class="c1">// 枝刈り: 第 n 段を超えないようにする</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">        </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">        </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">choice</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">        </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="p">}</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="cm">/* 階段登り：バックトラッキング */</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="kd">function</span><span class="w"> </span><span class="nx">climbingStairsBacktrack</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">choices</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">];</span><span class="w"> </span><span class="c1">// 1 段または 2 段上ることを選べる</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 第 0 段から上り始める</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Map</span><span class="p">();</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w">    </span><span class="nx">res</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// res[0] を使って方法数を記録する</span>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w">    </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_backtrack.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
-<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
-<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">climbingStairsBacktrack</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_backtrack.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* バックトラッキング */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="nx">choices</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="nx">state</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">Map</span><span class="o">&lt;</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="nx">any</span><span class="o">&gt;</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="c1">// 第 n 段に到達したら、方法数を 1 増やす</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">        </span><span class="c1">// 枝刈り: 第 n 段を超えないようにする</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">        </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">        </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">choice</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">        </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="p">}</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="cm">/* 階段登り：バックトラッキング */</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="kd">function</span><span class="w"> </span><span class="nx">climbingStairsBacktrack</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">choices</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">];</span><span class="w"> </span><span class="c1">// 1 段または 2 段上ることを選べる</span>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 第 0 段から上り始める</span>
+<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Map</span><span class="p">();</span>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="w">    </span><span class="nx">res</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// res[0] を使って方法数を記録する</span>
+<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="w">    </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_backtrack.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
-<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsBacktrack</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_backtrack.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* バックトラッキング */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="c1">// 第 n 段に到達したら、方法数を 1 増やす</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">    </span><span class="n">res</span><span class="p">[</span><span class="m">0</span><span class="p">]</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">    </span><span class="c1">// 枝刈り: 第 n 段を超えないようにする</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">    </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">    </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="p">}</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="cm">/* 階段登り：バックトラッキング */</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">climbingStairsBacktrack</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">choices</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">2</span><span class="p">];</span><span class="w"> </span><span class="c1">// 1 段または 2 段上ることを選べる</span>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 第 0 段から上り始める</span>
+<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="w">  </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// res[0] を使って方法数を記録する</span>
+<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a><span class="w">  </span><span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="m">0</span><span class="p">];</span>
+<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_backtrack.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
-<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbing_stairs_backtrack</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_backtrack.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* バックトラッキング */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="c1">// 第 n 段に到達したら、方法数を 1 増やす</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">        </span><span class="c1">// 枝刈り: 第 n 段を超えないようにする</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">        </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">        </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="p">}</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="cm">/* 階段登り：バックトラッキング */</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="k">fn</span><span class="w"> </span><span class="nf">climbing_stairs_backtrack</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">choices</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">];</span><span class="w"> </span><span class="c1">// 1 段または 2 段上ることを選べる</span>
+<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 第 0 段から上り始める</span>
+<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// res[0] を使って方法数を記録する</span>
+<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="o">&amp;</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="w">    </span><span class="n">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_backtrack.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
-<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsBacktrack</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_backtrack.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* バックトラッキング */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">len</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="c1">// 第 n 段に到達したら、方法数を 1 増やす</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">len</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">        </span><span class="c1">// 枝刈り: 第 n 段を超えないようにする</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">        </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">len</span><span class="p">);</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">        </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="p">}</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="cm">/* 階段登り：バックトラッキング */</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsBacktrack</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">};</span><span class="w"> </span><span class="c1">// 1 段または 2 段上ることを選べる</span>
+<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">           </span><span class="c1">// 第 0 段から上り始める</span>
+<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w">    </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// res[0] を使って方法数を記録する</span>
+<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">len</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">);</span>
+<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">len</span><span class="p">);</span>
+<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">result</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">result</span><span class="p">;</span>
+<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_backtrack.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
-<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbingStairsBacktrack</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_backtrack.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* バックトラッキング */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">    </span><span class="c1">// 第 n 段に到達したら、方法数を 1 増やす</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">        </span><span class="n">res</span><span class="o">[</span><span class="m">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="o">[</span><span class="m">0</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">        </span><span class="c1">// 枝刈り: 第 n 段を超えないようにする</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="k">continue</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">        </span><span class="c1">// 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">        </span><span class="c1">// バックトラック</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="p">}</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="cm">/* 階段登り：バックトラッキング */</span>
+<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">climbingStairsBacktrack</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">choices</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="p">(</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="c1">// 1 段または 2 段上ることを選べる</span>
+<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="c1">// 第 0 段から上り始める</span>
+<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="c1">// res[0] を使って方法数を記録する</span>
+<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="o">[</span><span class="m">0</span><span class="o">]</span>
+<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_backtrack.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
-<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbing_stairs_backtrack</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_backtrack.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### バックトラッキング ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># 第 n 段に到達したら、方法数を 1 増やす</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="n">res</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">n</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="c1"># すべての選択肢を走査</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">    </span><span class="c1"># 枝刈り: 第 n 段を超えないようにする</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">    </span><span class="k">next</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">n</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">    </span><span class="c1"># 試行: 選択を行い、状態を更新</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">  </span><span class="c1"># バックトラック</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="k">end</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="c1">### 階段登り：バックトラッキング ###</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_backtrack</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w">  </span><span class="n">choices</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="c1"># 1 段または 2 段上ることを選べる</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w">  </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1"># 第 0 段から上り始める</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="c1"># res[0] を使って方法数を記録する</span>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w">  </span><span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w">  </span><span class="n">res</span><span class="o">.</span><span class="n">first</span>
+<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h2 id="1411-1">14.1.1 &nbsp; 方法1：力任せ探索<a class="headerlink" href="#1411-1" title="Permanent link">&para;</a></h2>
-<p>バックトラッキングアルゴリズムは問題を明示的に部分問題に分解しません。代わりに、問題を一連の決定ステップとして扱い、試行と枝刈りを通じてすべての可能性を探索します。</p>
-<p>この問題を分解アプローチを使って分析できます。<span class="arithmatex">\(dp[i]\)</span> を <span class="arithmatex">\(i\)</span> 段目に到達する方法の数とします。この場合、<span class="arithmatex">\(dp[i]\)</span> が元の問題であり、その部分問題は次のようになります：</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20backtrack%28choices%3A%20list%5Bint%5D%2C%20state%3A%20int%2C%20n%3A%20int%2C%20res%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AD%E3%83%B3%E3%82%B0%22%22%22%0A%20%20%20%20%23%20%E7%AC%AC%20n%20%E6%AE%B5%E3%81%AB%E5%88%B0%E9%81%94%E3%81%97%E3%81%9F%E3%82%89%E3%80%81%E6%96%B9%E6%B3%95%E6%95%B0%E3%82%92%201%20%E5%A2%97%E3%82%84%E3%81%99%0A%20%20%20%20if%20state%20%3D%3D%20n%3A%0A%20%20%20%20%20%20%20%20res%5B0%5D%20%2B%3D%201%0A%20%20%20%20%23%20%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E9%81%B8%E6%8A%9E%E8%82%A2%E3%82%92%E8%B5%B0%E6%9F%BB%0A%20%20%20%20for%20choice%20in%20choices%3A%0A%20%20%20%20%20%20%20%20%23%20%E6%9E%9D%E5%88%88%E3%82%8A%3A%20%E7%AC%AC%20n%20%E6%AE%B5%E3%82%92%E8%B6%85%E3%81%88%E3%81%AA%E3%81%84%E3%82%88%E3%81%86%E3%81%AB%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20if%20state%20%2B%20choice%20%3E%20n%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20continue%0A%20%20%20%20%20%20%20%20%23%20%E8%A9%A6%E8%A1%8C%3A%20%E9%81%B8%E6%8A%9E%E3%82%92%E8%A1%8C%E3%81%84%E3%80%81%E7%8A%B6%E6%85%8B%E3%82%92%E6%9B%B4%E6%96%B0%0A%20%20%20%20%20%20%20%20backtrack%28choices%2C%20state%20%2B%20choice%2C%20n%2C%20res%29%0A%20%20%20%20%20%20%20%20%23%20%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AF%0A%0A%0Adef%20climbing_stairs_backtrack%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%9A%8E%E6%AE%B5%E7%99%BB%E3%82%8A%EF%BC%9A%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AD%E3%83%B3%E3%82%B0%22%22%22%0A%20%20%20%20choices%20%3D%20%5B1%2C%202%5D%20%20%23%201%20%E6%AE%B5%E3%81%BE%E3%81%9F%E3%81%AF%202%20%E6%AE%B5%E4%B8%8A%E3%82%8B%E3%81%93%E3%81%A8%E3%82%92%E9%81%B8%E3%81%B9%E3%82%8B%0A%20%20%20%20state%20%3D%200%20%20%23%20%E7%AC%AC%200%20%E6%AE%B5%E3%81%8B%E3%82%89%E4%B8%8A%E3%82%8A%E5%A7%8B%E3%82%81%E3%82%8B%0A%20%20%20%20res%20%3D%20%5B0%5D%20%20%23%20res%5B0%5D%20%E3%82%92%E4%BD%BF%E3%81%A3%E3%81%A6%E6%96%B9%E6%B3%95%E6%95%B0%E3%82%92%E8%A8%98%E9%8C%B2%E3%81%99%E3%82%8B%0A%20%20%20%20backtrack%28choices%2C%20state%2C%20n%2C%20res%29%0A%20%20%20%20return%20res%5B0%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%204%0A%0A%20%20%20%20res%20%3D%20climbing_stairs_backtrack%28n%29%0A%20%20%20%20print%28f%22%7Bn%7D%20%E6%AE%B5%E3%81%AE%E9%9A%8E%E6%AE%B5%E3%82%92%E4%B8%8A%E3%82%8B%E6%96%B9%E6%B3%95%E3%81%AF%E5%85%A8%E9%83%A8%E3%81%A7%20%7Bres%7D%20%E9%80%9A%E3%82%8A%E3%81%A7%E3%81%99%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20backtrack%28choices%3A%20list%5Bint%5D%2C%20state%3A%20int%2C%20n%3A%20int%2C%20res%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AD%E3%83%B3%E3%82%B0%22%22%22%0A%20%20%20%20%23%20%E7%AC%AC%20n%20%E6%AE%B5%E3%81%AB%E5%88%B0%E9%81%94%E3%81%97%E3%81%9F%E3%82%89%E3%80%81%E6%96%B9%E6%B3%95%E6%95%B0%E3%82%92%201%20%E5%A2%97%E3%82%84%E3%81%99%0A%20%20%20%20if%20state%20%3D%3D%20n%3A%0A%20%20%20%20%20%20%20%20res%5B0%5D%20%2B%3D%201%0A%20%20%20%20%23%20%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E9%81%B8%E6%8A%9E%E8%82%A2%E3%82%92%E8%B5%B0%E6%9F%BB%0A%20%20%20%20for%20choice%20in%20choices%3A%0A%20%20%20%20%20%20%20%20%23%20%E6%9E%9D%E5%88%88%E3%82%8A%3A%20%E7%AC%AC%20n%20%E6%AE%B5%E3%82%92%E8%B6%85%E3%81%88%E3%81%AA%E3%81%84%E3%82%88%E3%81%86%E3%81%AB%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20if%20state%20%2B%20choice%20%3E%20n%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20continue%0A%20%20%20%20%20%20%20%20%23%20%E8%A9%A6%E8%A1%8C%3A%20%E9%81%B8%E6%8A%9E%E3%82%92%E8%A1%8C%E3%81%84%E3%80%81%E7%8A%B6%E6%85%8B%E3%82%92%E6%9B%B4%E6%96%B0%0A%20%20%20%20%20%20%20%20backtrack%28choices%2C%20state%20%2B%20choice%2C%20n%2C%20res%29%0A%20%20%20%20%20%20%20%20%23%20%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AF%0A%0A%0Adef%20climbing_stairs_backtrack%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%9A%8E%E6%AE%B5%E7%99%BB%E3%82%8A%EF%BC%9A%E3%83%90%E3%83%83%E3%82%AF%E3%83%88%E3%83%A9%E3%83%83%E3%82%AD%E3%83%B3%E3%82%B0%22%22%22%0A%20%20%20%20choices%20%3D%20%5B1%2C%202%5D%20%20%23%201%20%E6%AE%B5%E3%81%BE%E3%81%9F%E3%81%AF%202%20%E6%AE%B5%E4%B8%8A%E3%82%8B%E3%81%93%E3%81%A8%E3%82%92%E9%81%B8%E3%81%B9%E3%82%8B%0A%20%20%20%20state%20%3D%200%20%20%23%20%E7%AC%AC%200%20%E6%AE%B5%E3%81%8B%E3%82%89%E4%B8%8A%E3%82%8A%E5%A7%8B%E3%82%81%E3%82%8B%0A%20%20%20%20res%20%3D%20%5B0%5D%20%20%23%20res%5B0%5D%20%E3%82%92%E4%BD%BF%E3%81%A3%E3%81%A6%E6%96%B9%E6%B3%95%E6%95%B0%E3%82%92%E8%A8%98%E9%8C%B2%E3%81%99%E3%82%8B%0A%20%20%20%20backtrack%28choices%2C%20state%2C%20n%2C%20res%29%0A%20%20%20%20return%20res%5B0%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%204%0A%0A%20%20%20%20res%20%3D%20climbing_stairs_backtrack%28n%29%0A%20%20%20%20print%28f%22%7Bn%7D%20%E6%AE%B5%E3%81%AE%E9%9A%8E%E6%AE%B5%E3%82%92%E4%B8%8A%E3%82%8B%E6%96%B9%E6%B3%95%E3%81%AF%E5%85%A8%E9%83%A8%E3%81%A7%20%7Bres%7D%20%E9%80%9A%E3%82%8A%E3%81%A7%E3%81%99%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h2 id="1411-1">14.1.1 &nbsp; 方法 1：総当たり探索<a class="headerlink" href="#1411-1" title="Permanent link">&para;</a></h2>
+<p>バックトラッキング法は通常、問題を明示的に分解するのではなく、問題解決を一連の意思決定ステップとみなし、試行と枝刈りによってあらゆる可能な解を探索します。</p>
+<p>この問題を問題分解の観点から分析してみましょう。<span class="arithmatex">\(i\)</span> 段目まで上る方法が全部で <span class="arithmatex">\(dp[i]\)</span> 通りあるとすると、<span class="arithmatex">\(dp[i]\)</span> が元の問題であり、その部分問題には次が含まれます：</p>
 <div class="arithmatex">\[
 dp[i-1], dp[i-2], \dots, dp[2], dp[1]
 \]</div>
-<p>各移動は <span class="arithmatex">\(1\)</span> 段または <span class="arithmatex">\(2\)</span> 段しか進めないため、<span class="arithmatex">\(i\)</span> 段目に立っているとき、前のステップは <span class="arithmatex">\(i-1\)</span> 段目または <span class="arithmatex">\(i-2\)</span> 段目のいずれかにいたはずです。つまり、<span class="arithmatex">\(i\)</span> 段目には <span class="arithmatex">\(i-1\)</span> 段目または <span class="arithmatex">\(i-2\)</span> 段目からしか到達できません。</p>
-<p>これにより重要な結論が得られます：<strong><span class="arithmatex">\(i-1\)</span> 段目に到達する方法の数に <span class="arithmatex">\(i-2\)</span> 段目に到達する方法の数を加えたものが、<span class="arithmatex">\(i\)</span> 段目に到達する方法の数に等しい</strong>。式は以下の通りです：</p>
+<p>各ラウンドでは <span class="arithmatex">\(1\)</span> 段または <span class="arithmatex">\(2\)</span> 段しか上れないため、<span class="arithmatex">\(i\)</span> 段目の階段に立っているとき、直前のラウンドでは <span class="arithmatex">\(i - 1\)</span> 段目または <span class="arithmatex">\(i - 2\)</span> 段目にしか立てません。言い換えると、<span class="arithmatex">\(i -1\)</span> 段目または <span class="arithmatex">\(i - 2\)</span> 段目からしか <span class="arithmatex">\(i\)</span> 段目へ進めません。</p>
+<p>ここから重要な帰結が得られます。**<span class="arithmatex">\(i - 1\)</span> 段目まで上る方法数と <span class="arithmatex">\(i - 2\)</span> 段目まで上る方法数の和が、<span class="arithmatex">\(i\)</span> 段目まで上る方法数に等しい**のです。式は次のとおりです：</p>
 <div class="arithmatex">\[
 dp[i] = dp[i-1] + dp[i-2]
 \]</div>
-<p>これは、階段登り問題において部分問題間に再帰関係があることを意味し、<strong>元の問題の解は部分問題の解から構築できます</strong>。下の図はこの再帰関係を示しています。</p>
-<p><img alt="解の数の再帰関係" class="animation-figure" src="../intro_to_dynamic_programming.assets/climbing_stairs_state_transfer.png" /></p>
-<p align="center"> 図 14-2 &nbsp; 解の数の再帰関係 </p>
+<p>これは、階段を上る問題では各部分問題の間に漸化関係があり、**元の問題の解は部分問題の解から構築できる**ことを意味します。次の図はこの漸化関係を示しています。</p>
+<p><img alt="方法数の漸化関係" class="animation-figure" src="../intro_to_dynamic_programming.assets/climbing_stairs_state_transfer.png" /></p>
+<p align="center"> 図 14-2 &nbsp; 方法数の漸化関係 </p>
 
-<p>再帰式に従って力任せ探索解法を得ることができます。<span class="arithmatex">\(dp[n]\)</span> から始めて、**より大きな問題を再帰的に2つの小さな部分問題の和に分解**し、解が既知の最小の部分問題 <span class="arithmatex">\(dp[1]\)</span> と <span class="arithmatex">\(dp[2]\)</span> に到達するまで続けます。<span class="arithmatex">\(dp[1] = 1\)</span> と <span class="arithmatex">\(dp[2] = 2\)</span> で、それぞれ1段目と2段目に登る方法が <span class="arithmatex">\(1\)</span> 通りと <span class="arithmatex">\(2\)</span> 通りあることを表します。</p>
-<p>以下のコードを観察すると、標準的なバックトラッキングコードと同様に深さ優先探索に属しますが、より簡潔です：</p>
+<p>漸化式に基づいて総当たり探索の解法を得ることができます。<span class="arithmatex">\(dp[n]\)</span> を出発点とし、**より大きな問題を再帰的に 2 つのより小さな問題の和へ分解**していき、最小部分問題 <span class="arithmatex">\(dp[1]\)</span> と <span class="arithmatex">\(dp[2]\)</span> に到達したら返します。ここで最小部分問題の解は既知であり、<span class="arithmatex">\(dp[1] = 1\)</span>、<span class="arithmatex">\(dp[2] = 2\)</span> です。これは、第 <span class="arithmatex">\(1\)</span> 段目と第 <span class="arithmatex">\(2\)</span> 段目まで上る方法がそれぞれ <span class="arithmatex">\(1\)</span> 通り、<span class="arithmatex">\(2\)</span> 通りであることを表します。</p>
+<p>次のコードを見ると、標準的なバックトラッキングコードと同じく深さ優先探索に属しますが、より簡潔です：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">climbing_stairs_dfs.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;探索&quot;&quot;&quot;</span>
-<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="c1"># 既知の dp[1] と dp[2] は、それらを返す</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;検索&quot;&quot;&quot;</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="c1"># dp[1] と dp[2] は既知なので返す</span>
 <a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">i</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
 <a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>        <span class="k">return</span> <span class="n">i</span>
 <a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>    <span class="c1"># dp[i] = dp[i-1] + dp[i-2]</span>
@@ -4588,9 +4828,9 @@ dp[i] = dp[i-1] + dp[i-2]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dfs.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 探索 */</span>
+<div class="highlight"><span class="filename">climbing_stairs_dfs.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 検索 */</span>
 <a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="c1">// 既知の dp[1] と dp[2] を返す</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="c1">// dp[1] と dp[2] は既知なので返す</span>
 <a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
 <a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
 <a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
@@ -4605,9 +4845,9 @@ dp[i] = dp[i-1] + dp[i-2]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dfs.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 探索 */</span>
+<div class="highlight"><span class="filename">climbing_stairs_dfs.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 検索 */</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 既知の dp[1] と dp[2] を返す</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// dp[1] と dp[2] は既知なので返す</span>
 <a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
 <a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
 <a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
@@ -4622,100 +4862,212 @@ dp[i] = dp[i-1] + dp[i-2]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dfs.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">climbing_stairs_dfs</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">DFS</span><span class="p">}</span>
-<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a>
-<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">climbing_stairs_dfs</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">ClimbingStairsDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dfs.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 検索 */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">DFS</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="c1">// dp[1] と dp[2] は既知なので返す</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="p">}</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="cm">/* 階段登り：探索 */</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">ClimbingStairsDFS</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nf">DFS</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dfs.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
-<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a>
-<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">climbingStairsDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dfs.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 検索 */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="c1">// dp[1] と dp[2] は既知なので返す</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">    </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="o">-</span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="p">}</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="cm">/* 階段登り：探索 */</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="kd">func</span><span class="w"> </span><span class="nx">climbingStairsDFS</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dfs.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a>
-<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">climbingStairsDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dfs.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 検索 */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="c1">// dp[1] と dp[2] は既知なので返す</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">    </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="bp">count</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="p">}</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="cm">/* 階段登り：探索 */</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="kd">func</span><span class="w"> </span><span class="nf">climbingStairsDFS</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dfs.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
-<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a>
-<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">climbingStairsDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dfs.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 検索 */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="c1">// dp[1] と dp[2] は既知なので返す</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">    </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="p">}</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="cm">/* 階段登り：探索 */</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="kd">function</span><span class="w"> </span><span class="nx">climbingStairsDFS</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">n</span><span class="p">);</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dfs.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
-<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a>
-<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">climbingStairsDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dfs.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 検索 */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="c1">// dp[1] と dp[2] は既知なので返す</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">    </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="p">}</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="cm">/* 階段登り：探索 */</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="kd">function</span><span class="w"> </span><span class="nx">climbingStairsDFS</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">n</span><span class="p">);</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dfs.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a>
-<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dfs.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 検索 */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="c1">// dp[1] と dp[2] は既知なので返す</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">  </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">2</span><span class="p">);</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="p">}</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="cm">/* 階段登り：探索 */</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="kt">int</span><span class="w"> </span><span class="n">climbingStairsDFS</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dfs.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a>
-<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbing_stairs_dfs</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dfs.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 検索 */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="c1">// dp[1] と dp[2] は既知なので返す</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">;</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">    </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">    </span><span class="n">count</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="p">}</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="cm">/* 階段登り：探索 */</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="k">fn</span><span class="w"> </span><span class="nf">climbing_stairs_dfs</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dfs.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a>
-<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dfs.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 検索 */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="c1">// dp[1] と dp[2] は既知なので返す</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w">    </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="p">}</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="cm">/* 階段登り：探索 */</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsDFS</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dfs.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a>
-<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbingStairsDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dfs.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 検索 */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="c1">// dp[1] と dp[2] は既知なので返す</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">    </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">2</span><span class="p">)</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="p">}</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="cm">/* 階段登り：探索 */</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">climbingStairsDFS</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dfs.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a>
-<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbing_stairs_dfs</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dfs.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### 探索 ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="c1"># dp[1] と dp[2] は既知なので返す</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">  </span><span class="c1"># dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">  </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="k">end</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="c1">### 階段登り：探索 ###</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_dfs</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w">  </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>下の図は力任せ探索によって形成される再帰木を示しています。問題 <span class="arithmatex">\(dp[n]\)</span> について、その再帰木の深さは <span class="arithmatex">\(n\)</span> で、時間計算量は <span class="arithmatex">\(O(2^n)\)</span> です。この指数的増加により、<span class="arithmatex">\(n\)</span> が大きいとプログラムの実行がはるかに遅くなり、長い待機時間が生じます。</p>
-<p><img alt="階段登りの再帰木" class="animation-figure" src="../intro_to_dynamic_programming.assets/climbing_stairs_dfs_tree.png" /></p>
-<p align="center"> 図 14-3 &nbsp; 階段登りの再帰木 </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20dfs%28i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E6%A4%9C%E7%B4%A2%22%22%22%0A%20%20%20%20%23%20dp%5B1%5D%20%E3%81%A8%20dp%5B2%5D%20%E3%81%AF%E6%97%A2%E7%9F%A5%E3%81%AA%E3%81%AE%E3%81%A7%E8%BF%94%E3%81%99%0A%20%20%20%20if%20i%20%3D%3D%201%20or%20i%20%3D%3D%202%3A%0A%20%20%20%20%20%20%20%20return%20i%0A%20%20%20%20%23%20dp%5Bi%5D%20%3D%20dp%5Bi-1%5D%20%2B%20dp%5Bi-2%5D%0A%20%20%20%20count%20%3D%20dfs%28i%20-%201%29%20%2B%20dfs%28i%20-%202%29%0A%20%20%20%20return%20count%0A%0A%0Adef%20climbing_stairs_dfs%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%9A%8E%E6%AE%B5%E7%99%BB%E3%82%8A%EF%BC%9A%E6%8E%A2%E7%B4%A2%22%22%22%0A%20%20%20%20return%20dfs%28n%29%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%209%0A%0A%20%20%20%20res%20%3D%20climbing_stairs_dfs%28n%29%0A%20%20%20%20print%28f%22%7Bn%7D%20%E6%AE%B5%E3%81%AE%E9%9A%8E%E6%AE%B5%E3%82%92%E4%B8%8A%E3%82%8B%E6%96%B9%E6%B3%95%E3%81%AF%E5%85%A8%E9%83%A8%E3%81%A7%20%7Bres%7D%20%E9%80%9A%E3%82%8A%E3%81%A7%E3%81%99%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20dfs%28i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E6%A4%9C%E7%B4%A2%22%22%22%0A%20%20%20%20%23%20dp%5B1%5D%20%E3%81%A8%20dp%5B2%5D%20%E3%81%AF%E6%97%A2%E7%9F%A5%E3%81%AA%E3%81%AE%E3%81%A7%E8%BF%94%E3%81%99%0A%20%20%20%20if%20i%20%3D%3D%201%20or%20i%20%3D%3D%202%3A%0A%20%20%20%20%20%20%20%20return%20i%0A%20%20%20%20%23%20dp%5Bi%5D%20%3D%20dp%5Bi-1%5D%20%2B%20dp%5Bi-2%5D%0A%20%20%20%20count%20%3D%20dfs%28i%20-%201%29%20%2B%20dfs%28i%20-%202%29%0A%20%20%20%20return%20count%0A%0A%0Adef%20climbing_stairs_dfs%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%9A%8E%E6%AE%B5%E7%99%BB%E3%82%8A%EF%BC%9A%E6%8E%A2%E7%B4%A2%22%22%22%0A%20%20%20%20return%20dfs%28n%29%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%209%0A%0A%20%20%20%20res%20%3D%20climbing_stairs_dfs%28n%29%0A%20%20%20%20print%28f%22%7Bn%7D%20%E6%AE%B5%E3%81%AE%E9%9A%8E%E6%AE%B5%E3%82%92%E4%B8%8A%E3%82%8B%E6%96%B9%E6%B3%95%E3%81%AF%E5%85%A8%E9%83%A8%E3%81%A7%20%7Bres%7D%20%E9%80%9A%E3%82%8A%E3%81%A7%E3%81%99%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>次の図は総当たり探索によって形成される再帰木を示しています。問題 <span class="arithmatex">\(dp[n]\)</span> に対して、その再帰木の深さは <span class="arithmatex">\(n\)</span>、時間計算量は <span class="arithmatex">\(O(2^n)\)</span> です。指数オーダーは爆発的に増加するため、比較的大きな <span class="arithmatex">\(n\)</span> を入力すると長時間待たされることになります。</p>
+<p><img alt="階段上りに対応する再帰木" class="animation-figure" src="../intro_to_dynamic_programming.assets/climbing_stairs_dfs_tree.png" /></p>
+<p align="center"> 図 14-3 &nbsp; 階段上りに対応する再帰木 </p>
 
-<p>上の図を観察すると、**指数時間計算量は「重複する部分問題」によって引き起こされる**ことがわかります。例えば、<span class="arithmatex">\(dp[9]\)</span> は <span class="arithmatex">\(dp[8]\)</span> と <span class="arithmatex">\(dp[7]\)</span> に分解され、<span class="arithmatex">\(dp[8]\)</span> はさらに <span class="arithmatex">\(dp[7]\)</span> と <span class="arithmatex">\(dp[6]\)</span> に分解され、両方とも部分問題 <span class="arithmatex">\(dp[7]\)</span> を含んでいます。</p>
-<p>このように、部分問題にはさらに小さな重複する部分問題が含まれ、これは無限に続きます。計算リソースの大部分がこれらの重複する部分問題に浪費されています。</p>
-<h2 id="1412-2">14.1.2 &nbsp; 方法2：メモ化探索<a class="headerlink" href="#1412-2" title="Permanent link">&para;</a></h2>
-<p>アルゴリズムの効率を向上させるため、**すべての重複する部分問題を一度だけ計算したい**と考えます。この目的のため、各部分問題の解を記録する配列 <code>mem</code> を宣言し、探索プロセス中に重複する部分問題を枝刈りします。</p>
+<p>上の図を見ると、<strong>指数オーダーの時間計算量は「重複部分問題」によって生じています</strong>。たとえば <span class="arithmatex">\(dp[9]\)</span> は <span class="arithmatex">\(dp[8]\)</span> と <span class="arithmatex">\(dp[7]\)</span> に分解され、<span class="arithmatex">\(dp[8]\)</span> は <span class="arithmatex">\(dp[7]\)</span> と <span class="arithmatex">\(dp[6]\)</span> に分解されるため、どちらにも部分問題 <span class="arithmatex">\(dp[7]\)</span> が含まれています。</p>
+<p>このように、部分問題の中にはさらに小さな重複部分問題が含まれ、それが際限なく続いていきます。計算資源の大部分は、こうした重複部分問題に浪費されています。</p>
+<h2 id="1412-2">14.1.2 &nbsp; 方法 2：メモ化探索<a class="headerlink" href="#1412-2" title="Permanent link">&para;</a></h2>
+<p>アルゴリズム効率を高めるため、**すべての重複部分問題を 1 回だけ計算したい**と考えます。そのために、各部分問題の解を記録する配列 <code>mem</code> を宣言し、探索の過程で重複部分問題を枝刈りします。</p>
 <ol>
-<li><span class="arithmatex">\(dp[i]\)</span> が初めて計算されるとき、後で使用するために <code>mem[i]</code> に記録します。</li>
-<li><span class="arithmatex">\(dp[i]\)</span> を再度計算する必要があるとき、<code>mem[i]</code> から直接結果を取得でき、その部分問題の冗長な計算を避けられます。</li>
+<li><span class="arithmatex">\(dp[i]\)</span> を初めて計算したとき、その結果を <code>mem[i]</code> に記録して後で使えるようにします。</li>
+<li>再び <span class="arithmatex">\(dp[i]\)</span> を計算する必要が生じたときは、<code>mem[i]</code> から直接結果を取得し、その部分問題の重複計算を避けます。</li>
 </ol>
-<p>コードは以下の通りです：</p>
+<p>コードは次のとおりです：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">climbing_stairs_dfs_mem.py</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">mem</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;記憶化探索&quot;&quot;&quot;</span>
-<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>    <span class="c1"># 既知の dp[1] と dp[2] は、それらを返す</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;メモ化探索&quot;&quot;&quot;</span>
+<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>    <span class="c1"># dp[1] と dp[2] は既知なので返す</span>
 <a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>    <span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">i</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
 <a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a>        <span class="k">return</span> <span class="n">i</span>
-<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a>    <span class="c1"># dp[i] の記録がある場合、それを返す</span>
+<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a>    <span class="c1"># dp[i] の記録があれば、それをそのまま返す</span>
 <a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a>    <span class="k">if</span> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">!=</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span>
 <a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>        <span class="k">return</span> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
 <a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a>    <span class="c1"># dp[i] = dp[i-1] + dp[i-2]</span>
 <a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a>    <span class="n">count</span> <span class="o">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">mem</span><span class="p">)</span> <span class="o">+</span> <span class="n">dfs</span><span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">2</span><span class="p">,</span> <span class="n">mem</span><span class="p">)</span>
-<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a>    <span class="c1"># dp[i] を記録</span>
+<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a>    <span class="c1"># dp[i] を記録する</span>
 <a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a>    <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">count</span>
 <a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a>    <span class="k">return</span> <span class="n">count</span>
 <a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a>
 <a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_dfs_mem</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;階段登り：記憶化探索&quot;&quot;&quot;</span>
-<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a>    <span class="c1"># mem[i] は i 段目に登る解の総数を記録、-1 は記録なしを意味する</span>
+<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;階段登り：メモ化探索&quot;&quot;&quot;</span>
+<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a>    <span class="c1"># mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す</span>
 <a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a>    <span class="n">mem</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
 <a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a>    <span class="k">return</span> <span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">mem</span><span class="p">)</span>
 </code></pre></div>
@@ -4723,22 +5075,22 @@ dp[i] = dp[i-1] + dp[i-2]
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">climbing_stairs_dfs_mem.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* メモ化探索 */</span>
 <a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">mem</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="c1">// 既知の dp[1] と dp[2] を返す</span>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="c1">// dp[1] と dp[2] は既知なので返す</span>
 <a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
 <a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
-<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w">    </span><span class="c1">// dp[i] の記録がある場合、それを返す</span>
+<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w">    </span><span class="c1">// dp[i] の記録があれば、それをそのまま返す</span>
 <a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">-1</span><span class="p">)</span>
 <a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
 <a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="w">    </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
 <a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">);</span>
-<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="w">    </span><span class="c1">// dp[i] を記録</span>
+<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="w">    </span><span class="c1">// dp[i] を記録する</span>
 <a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="w">    </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
 <a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
 <a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a><span class="p">}</span>
 <a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a>
 <a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></a><span class="cm">/* 階段登り：メモ化探索 */</span>
 <a id="__codelineno-27-17" name="__codelineno-27-17" href="#__codelineno-27-17"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsDFSMem</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-18" name="__codelineno-27-18" href="#__codelineno-27-18"></a><span class="w">    </span><span class="c1">// mem[i] は i 段目に登る総解数を記録、-1 は記録なしを意味する</span>
+<a id="__codelineno-27-18" name="__codelineno-27-18" href="#__codelineno-27-18"></a><span class="w">    </span><span class="c1">// mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す</span>
 <a id="__codelineno-27-19" name="__codelineno-27-19" href="#__codelineno-27-19"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">mem</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">-1</span><span class="p">);</span>
 <a id="__codelineno-27-20" name="__codelineno-27-20" href="#__codelineno-27-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">);</span>
 <a id="__codelineno-27-21" name="__codelineno-27-21" href="#__codelineno-27-21"></a><span class="p">}</span>
@@ -4747,22 +5099,22 @@ dp[i] = dp[i-1] + dp[i-2]
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">climbing_stairs_dfs_mem.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* メモ化探索 */</span>
 <a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="c1">// 既知の dp[1] と dp[2] を返す</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="c1">// dp[1] と dp[2] は既知なので返す</span>
 <a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
 <a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
-<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w">    </span><span class="c1">// dp[i] の記録がある場合、それを返す</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w">    </span><span class="c1">// dp[i] の記録があれば、それをそのまま返す</span>
 <a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
 <a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="w">    </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
 <a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">);</span>
-<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="w">    </span><span class="c1">// dp[i] を記録</span>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="w">    </span><span class="c1">// dp[i] を記録する</span>
 <a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a><span class="w">    </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
 <a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
 <a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a><span class="p">}</span>
 <a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a>
 <a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a><span class="cm">/* 階段登り：メモ化探索 */</span>
 <a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsDFSMem</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-28-18" name="__codelineno-28-18" href="#__codelineno-28-18"></a><span class="w">    </span><span class="c1">// mem[i] は i 段目に登る総解数を記録、-1 は記録なしを意味する</span>
+<a id="__codelineno-28-18" name="__codelineno-28-18" href="#__codelineno-28-18"></a><span class="w">    </span><span class="c1">// mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す</span>
 <a id="__codelineno-28-19" name="__codelineno-28-19" href="#__codelineno-28-19"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">mem</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-28-20" name="__codelineno-28-20" href="#__codelineno-28-20"></a><span class="w">    </span><span class="n">Arrays</span><span class="p">.</span><span class="na">fill</span><span class="p">(</span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-28-21" name="__codelineno-28-21" href="#__codelineno-28-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">);</span>
@@ -4770,103 +5122,294 @@ dp[i] = dp[i-1] + dp[i-2]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">climbing_stairs_dfs_mem</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">DFS</span><span class="p">}</span>
-<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a>
-<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">climbing_stairs_dfs_mem</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">ClimbingStairsDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* メモ化探索 */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">DFS</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="c1">// dp[1] と dp[2] は既知なので返す</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="c1">// dp[i] の記録があれば、それをそのまま返す</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">    </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">);</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="w">    </span><span class="c1">// dp[i] を記録する</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="w">    </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="p">}</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="cm">/* 階段登り：メモ化探索 */</span>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="kt">int</span><span class="w"> </span><span class="nf">ClimbingStairsDFSMem</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w">    </span><span class="c1">// mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す</span>
+<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="w">    </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">mem</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-29-20" name="__codelineno-29-20" href="#__codelineno-29-20"></a><span class="w">    </span><span class="n">Array</span><span class="p">.</span><span class="n">Fill</span><span class="p">(</span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-29-21" name="__codelineno-29-21" href="#__codelineno-29-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nf">DFS</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">);</span>
+<a id="__codelineno-29-22" name="__codelineno-29-22" href="#__codelineno-29-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">dfsMem</span><span class="p">}</span>
-<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a>
-<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">climbingStairsDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* メモ化探索 */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">dfsMem</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="c1">// dp[1] と dp[2] は既知なので返す</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">    </span><span class="c1">// dp[i] の記録があれば、それをそのまま返す</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w">    </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">dfsMem</span><span class="p">(</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dfsMem</span><span class="p">(</span><span class="nx">i</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">)</span>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w">    </span><span class="c1">// dp[i] を記録する</span>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w">    </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">count</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="p">}</span>
+<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a>
+<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a><span class="cm">/* 階段登り：メモ化探索 */</span>
+<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="kd">func</span><span class="w"> </span><span class="nx">climbingStairsDFSMem</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></a><span class="w">    </span><span class="c1">// mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す</span>
+<a id="__codelineno-30-21" name="__codelineno-30-21" href="#__codelineno-30-21"></a><span class="w">    </span><span class="nx">mem</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-30-22" name="__codelineno-30-22" href="#__codelineno-30-22"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">mem</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-23" name="__codelineno-30-23" href="#__codelineno-30-23"></a><span class="w">        </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-30-24" name="__codelineno-30-24" href="#__codelineno-30-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-25" name="__codelineno-30-25" href="#__codelineno-30-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dfsMem</span><span class="p">(</span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">)</span>
+<a id="__codelineno-30-26" name="__codelineno-30-26" href="#__codelineno-30-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a>
-<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">climbingStairsDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* メモ化探索 */</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w">    </span><span class="c1">// dp[1] と dp[2] は既知なので返す</span>
+<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w">    </span><span class="c1">// dp[i] の記録があれば、それをそのまま返す</span>
+<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="w">    </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">mem</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">mem</span><span class="p">)</span>
+<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a><span class="w">    </span><span class="c1">// dp[i] を記録する</span>
+<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a><span class="w">    </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">count</span>
+<a id="__codelineno-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="bp">count</span>
+<a id="__codelineno-31-16" name="__codelineno-31-16" href="#__codelineno-31-16"></a><span class="p">}</span>
+<a id="__codelineno-31-17" name="__codelineno-31-17" href="#__codelineno-31-17"></a>
+<a id="__codelineno-31-18" name="__codelineno-31-18" href="#__codelineno-31-18"></a><span class="cm">/* 階段登り：メモ化探索 */</span>
+<a id="__codelineno-31-19" name="__codelineno-31-19" href="#__codelineno-31-19"></a><span class="kd">func</span><span class="w"> </span><span class="nf">climbingStairsDFSMem</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-20" name="__codelineno-31-20" href="#__codelineno-31-20"></a><span class="w">    </span><span class="c1">// mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す</span>
+<a id="__codelineno-31-21" name="__codelineno-31-21" href="#__codelineno-31-21"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">mem</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-31-22" name="__codelineno-31-22" href="#__codelineno-31-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">mem</span><span class="p">)</span>
+<a id="__codelineno-31-23" name="__codelineno-31-23" href="#__codelineno-31-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
-<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a>
-<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">climbingStairsDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* メモ化探索 */</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w">    </span><span class="c1">// dp[1] と dp[2] は既知なので返す</span>
+<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="w">    </span><span class="c1">// dp[i] の記録があれば、それをそのまま返す</span>
+<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="w">    </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">);</span>
+<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="w">    </span><span class="c1">// dp[i] を記録する</span>
+<a id="__codelineno-32-10" name="__codelineno-32-10" href="#__codelineno-32-10"></a><span class="w">    </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
+<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
+<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a><span class="p">}</span>
+<a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a>
+<a id="__codelineno-32-14" name="__codelineno-32-14" href="#__codelineno-32-14"></a><span class="cm">/* 階段登り：メモ化探索 */</span>
+<a id="__codelineno-32-15" name="__codelineno-32-15" href="#__codelineno-32-15"></a><span class="kd">function</span><span class="w"> </span><span class="nx">climbingStairsDFSMem</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-16" name="__codelineno-32-16" href="#__codelineno-32-16"></a><span class="w">    </span><span class="c1">// mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す</span>
+<a id="__codelineno-32-17" name="__codelineno-32-17" href="#__codelineno-32-17"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">mem</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="o">-</span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-32-18" name="__codelineno-32-18" href="#__codelineno-32-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">);</span>
+<a id="__codelineno-32-19" name="__codelineno-32-19" href="#__codelineno-32-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
-<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a>
-<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">climbingStairsDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* メモ化探索 */</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w">    </span><span class="c1">// dp[1] と dp[2] は既知なので返す</span>
+<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w">    </span><span class="c1">// dp[i] の記録があれば、それをそのまま返す</span>
+<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w">    </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">);</span>
+<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="w">    </span><span class="c1">// dp[i] を記録する</span>
+<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a><span class="w">    </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
+<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
+<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="p">}</span>
+<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a>
+<a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a><span class="cm">/* 階段登り：メモ化探索 */</span>
+<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a><span class="kd">function</span><span class="w"> </span><span class="nx">climbingStairsDFSMem</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-16" name="__codelineno-33-16" href="#__codelineno-33-16"></a><span class="w">    </span><span class="c1">// mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す</span>
+<a id="__codelineno-33-17" name="__codelineno-33-17" href="#__codelineno-33-17"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">mem</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="o">-</span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-33-18" name="__codelineno-33-18" href="#__codelineno-33-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">);</span>
+<a id="__codelineno-33-19" name="__codelineno-33-19" href="#__codelineno-33-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a>
-<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* メモ化探索 */</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w">  </span><span class="c1">// dp[1] と dp[2] は既知なので返す</span>
+<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w">  </span><span class="c1">// dp[i] の記録があれば、それをそのまま返す</span>
+<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w">  </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">);</span>
+<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="w">  </span><span class="c1">// dp[i] を記録する</span>
+<a id="__codelineno-34-10" name="__codelineno-34-10" href="#__codelineno-34-10"></a><span class="w">  </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-34-11" name="__codelineno-34-11" href="#__codelineno-34-11"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-34-12" name="__codelineno-34-12" href="#__codelineno-34-12"></a><span class="p">}</span>
+<a id="__codelineno-34-13" name="__codelineno-34-13" href="#__codelineno-34-13"></a>
+<a id="__codelineno-34-14" name="__codelineno-34-14" href="#__codelineno-34-14"></a><span class="cm">/* 階段登り：メモ化探索 */</span>
+<a id="__codelineno-34-15" name="__codelineno-34-15" href="#__codelineno-34-15"></a><span class="kt">int</span><span class="w"> </span><span class="n">climbingStairsDFSMem</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-16" name="__codelineno-34-16" href="#__codelineno-34-16"></a><span class="w">  </span><span class="c1">// mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す</span>
+<a id="__codelineno-34-17" name="__codelineno-34-17" href="#__codelineno-34-17"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">mem</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-34-18" name="__codelineno-34-18" href="#__codelineno-34-18"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">);</span>
+<a id="__codelineno-34-19" name="__codelineno-34-19" href="#__codelineno-34-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a>
-<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbing_stairs_dfs_mem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* メモ化探索 */</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w">    </span><span class="c1">// dp[1] と dp[2] は既知なので返す</span>
+<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">;</span>
+<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="w">    </span><span class="c1">// dp[i] の記録があれば、それをそのまま返す</span>
+<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a><span class="w">    </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-35-12" name="__codelineno-35-12" href="#__codelineno-35-12"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">);</span>
+<a id="__codelineno-35-13" name="__codelineno-35-13" href="#__codelineno-35-13"></a><span class="w">    </span><span class="c1">// dp[i] を記録する</span>
+<a id="__codelineno-35-14" name="__codelineno-35-14" href="#__codelineno-35-14"></a><span class="w">    </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-35-15" name="__codelineno-35-15" href="#__codelineno-35-15"></a><span class="w">    </span><span class="n">count</span>
+<a id="__codelineno-35-16" name="__codelineno-35-16" href="#__codelineno-35-16"></a><span class="p">}</span>
+<a id="__codelineno-35-17" name="__codelineno-35-17" href="#__codelineno-35-17"></a>
+<a id="__codelineno-35-18" name="__codelineno-35-18" href="#__codelineno-35-18"></a><span class="cm">/* 階段登り：メモ化探索 */</span>
+<a id="__codelineno-35-19" name="__codelineno-35-19" href="#__codelineno-35-19"></a><span class="k">fn</span><span class="w"> </span><span class="nf">climbing_stairs_dfs_mem</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-20" name="__codelineno-35-20" href="#__codelineno-35-20"></a><span class="w">    </span><span class="c1">// mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す</span>
+<a id="__codelineno-35-21" name="__codelineno-35-21" href="#__codelineno-35-21"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">mem</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-35-22" name="__codelineno-35-22" href="#__codelineno-35-22"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span>
+<a id="__codelineno-35-23" name="__codelineno-35-23" href="#__codelineno-35-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a>
-<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* メモ化探索 */</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">mem</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w">    </span><span class="c1">// dp[1] と dp[2] は既知なので返す</span>
+<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="w">    </span><span class="c1">// dp[i] の記録があれば、それをそのまま返す</span>
+<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">-1</span><span class="p">)</span>
+<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="w">    </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">);</span>
+<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a><span class="w">    </span><span class="c1">// dp[i] を記録する</span>
+<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a><span class="w">    </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-36-14" name="__codelineno-36-14" href="#__codelineno-36-14"></a><span class="p">}</span>
+<a id="__codelineno-36-15" name="__codelineno-36-15" href="#__codelineno-36-15"></a>
+<a id="__codelineno-36-16" name="__codelineno-36-16" href="#__codelineno-36-16"></a><span class="cm">/* 階段登り：メモ化探索 */</span>
+<a id="__codelineno-36-17" name="__codelineno-36-17" href="#__codelineno-36-17"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsDFSMem</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-18" name="__codelineno-36-18" href="#__codelineno-36-18"></a><span class="w">    </span><span class="c1">// mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す</span>
+<a id="__codelineno-36-19" name="__codelineno-36-19" href="#__codelineno-36-19"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">mem</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">((</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-36-20" name="__codelineno-36-20" href="#__codelineno-36-20"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-21" name="__codelineno-36-21" href="#__codelineno-36-21"></a><span class="w">        </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-36-22" name="__codelineno-36-22" href="#__codelineno-36-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-23" name="__codelineno-36-23" href="#__codelineno-36-23"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">result</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">);</span>
+<a id="__codelineno-36-24" name="__codelineno-36-24" href="#__codelineno-36-24"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">mem</span><span class="p">);</span>
+<a id="__codelineno-36-25" name="__codelineno-36-25" href="#__codelineno-36-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">result</span><span class="p">;</span>
+<a id="__codelineno-36-26" name="__codelineno-36-26" href="#__codelineno-36-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a>
-<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbingStairsDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* メモ化探索 */</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w">    </span><span class="c1">// dp[1] と dp[2] は既知なので返す</span>
+<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w">    </span><span class="c1">// dp[i] の記録があれば、それをそのまま返す</span>
+<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w">    </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span>
+<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="w">    </span><span class="c1">// dp[i] を記録する</span>
+<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="w">    </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">count</span>
+<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
+<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a><span class="p">}</span>
+<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a>
+<a id="__codelineno-37-14" name="__codelineno-37-14" href="#__codelineno-37-14"></a><span class="cm">/* 階段登り：メモ化探索 */</span>
+<a id="__codelineno-37-15" name="__codelineno-37-15" href="#__codelineno-37-15"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">climbingStairsDFSMem</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-16" name="__codelineno-37-16" href="#__codelineno-37-16"></a><span class="w">    </span><span class="c1">// mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す</span>
+<a id="__codelineno-37-17" name="__codelineno-37-17" href="#__codelineno-37-17"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">mem</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-37-18" name="__codelineno-37-18" href="#__codelineno-37-18"></a><span class="w">    </span><span class="n">mem</span><span class="p">.</span><span class="na">fill</span><span class="p">(</span><span class="o">-</span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-37-19" name="__codelineno-37-19" href="#__codelineno-37-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span>
+<a id="__codelineno-37-20" name="__codelineno-37-20" href="#__codelineno-37-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a>
-<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbing_stairs_dfs_mem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="c1">### メモ化探索 ###</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w">  </span><span class="c1"># dp[1] と dp[2] は既知なので返す</span>
+<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="w">  </span><span class="c1"># dp[i] の記録があれば、それをそのまま返す</span>
+<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a>
+<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="w">  </span><span class="c1"># dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="w">  </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span>
+<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a><span class="w">  </span><span class="c1"># dp[i] を記録する</span>
+<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a><span class="w">  </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">count</span>
+<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a><span class="k">end</span>
+<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a>
+<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a><span class="c1">### 階段登り：メモ化探索 ###</span>
+<a id="__codelineno-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_dfs_mem</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-38-16" name="__codelineno-38-16" href="#__codelineno-38-16"></a><span class="w">  </span><span class="c1"># mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す</span>
+<a id="__codelineno-38-17" name="__codelineno-38-17" href="#__codelineno-38-17"></a><span class="w">  </span><span class="n">mem</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-38-18" name="__codelineno-38-18" href="#__codelineno-38-18"></a><span class="w">  </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span>
+<a id="__codelineno-38-19" name="__codelineno-38-19" href="#__codelineno-38-19"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>下の図を観察すると、**メモ化後、すべての重複する部分問題は一度だけ計算される必要があり、時間計算量を <span class="arithmatex">\(O(n)\)</span> に最適化**します。これは大幅な改善です。</p>
-<p><img alt="メモ化探索による再帰木" class="animation-figure" src="../intro_to_dynamic_programming.assets/climbing_stairs_dfs_memo_tree.png" /></p>
-<p align="center"> 図 14-4 &nbsp; メモ化探索による再帰木 </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20dfs%28i%3A%20int%2C%20mem%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E3%83%A1%E3%83%A2%E5%8C%96%E6%8E%A2%E7%B4%A2%22%22%22%0A%20%20%20%20%23%20dp%5B1%5D%20%E3%81%A8%20dp%5B2%5D%20%E3%81%AF%E6%97%A2%E7%9F%A5%E3%81%AA%E3%81%AE%E3%81%A7%E8%BF%94%E3%81%99%0A%20%20%20%20if%20i%20%3D%3D%201%20or%20i%20%3D%3D%202%3A%0A%20%20%20%20%20%20%20%20return%20i%0A%20%20%20%20%23%20dp%5Bi%5D%20%E3%81%AE%E8%A8%98%E9%8C%B2%E3%81%8C%E3%81%82%E3%82%8C%E3%81%B0%E3%80%81%E3%81%9D%E3%82%8C%E3%82%92%E3%81%9D%E3%81%AE%E3%81%BE%E3%81%BE%E8%BF%94%E3%81%99%0A%20%20%20%20if%20mem%5Bi%5D%20%21%3D%20-1%3A%0A%20%20%20%20%20%20%20%20return%20mem%5Bi%5D%0A%20%20%20%20%23%20dp%5Bi%5D%20%3D%20dp%5Bi-1%5D%20%2B%20dp%5Bi-2%5D%0A%20%20%20%20count%20%3D%20dfs%28i%20-%201%2C%20mem%29%20%2B%20dfs%28i%20-%202%2C%20mem%29%0A%20%20%20%20%23%20dp%5Bi%5D%20%E3%82%92%E8%A8%98%E9%8C%B2%E3%81%99%E3%82%8B%0A%20%20%20%20mem%5Bi%5D%20%3D%20count%0A%20%20%20%20return%20count%0A%0A%0Adef%20climbing_stairs_dfs_mem%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%9A%8E%E6%AE%B5%E7%99%BB%E3%82%8A%EF%BC%9A%E3%83%A1%E3%83%A2%E5%8C%96%E6%8E%A2%E7%B4%A2%22%22%22%0A%20%20%20%20%23%20mem%5Bi%5D%20%E3%81%AF%E7%AC%AC%20i%20%E6%AE%B5%E3%81%BE%E3%81%A7%E4%B8%8A%E3%82%8B%E6%96%B9%E6%B3%95%E3%81%AE%E7%B7%8F%E6%95%B0%E3%82%92%E8%A8%98%E9%8C%B2%E3%81%97%E3%80%81-1%20%E3%81%AF%E6%9C%AA%E8%A8%98%E9%8C%B2%E3%82%92%E8%A1%A8%E3%81%99%0A%20%20%20%20mem%20%3D%20%5B-1%5D%20%2A%20%28n%20%2B%201%29%0A%20%20%20%20return%20dfs%28n%2C%20mem%29%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%209%0A%0A%20%20%20%20res%20%3D%20climbing_stairs_dfs_mem%28n%29%0A%20%20%20%20print%28f%22%7Bn%7D%20%E6%AE%B5%E3%81%AE%E9%9A%8E%E6%AE%B5%E3%82%92%E4%B8%8A%E3%82%8B%E6%96%B9%E6%B3%95%E3%81%AF%E5%85%A8%E9%83%A8%E3%81%A7%20%7Bres%7D%20%E9%80%9A%E3%82%8A%E3%81%A7%E3%81%99%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20dfs%28i%3A%20int%2C%20mem%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E3%83%A1%E3%83%A2%E5%8C%96%E6%8E%A2%E7%B4%A2%22%22%22%0A%20%20%20%20%23%20dp%5B1%5D%20%E3%81%A8%20dp%5B2%5D%20%E3%81%AF%E6%97%A2%E7%9F%A5%E3%81%AA%E3%81%AE%E3%81%A7%E8%BF%94%E3%81%99%0A%20%20%20%20if%20i%20%3D%3D%201%20or%20i%20%3D%3D%202%3A%0A%20%20%20%20%20%20%20%20return%20i%0A%20%20%20%20%23%20dp%5Bi%5D%20%E3%81%AE%E8%A8%98%E9%8C%B2%E3%81%8C%E3%81%82%E3%82%8C%E3%81%B0%E3%80%81%E3%81%9D%E3%82%8C%E3%82%92%E3%81%9D%E3%81%AE%E3%81%BE%E3%81%BE%E8%BF%94%E3%81%99%0A%20%20%20%20if%20mem%5Bi%5D%20%21%3D%20-1%3A%0A%20%20%20%20%20%20%20%20return%20mem%5Bi%5D%0A%20%20%20%20%23%20dp%5Bi%5D%20%3D%20dp%5Bi-1%5D%20%2B%20dp%5Bi-2%5D%0A%20%20%20%20count%20%3D%20dfs%28i%20-%201%2C%20mem%29%20%2B%20dfs%28i%20-%202%2C%20mem%29%0A%20%20%20%20%23%20dp%5Bi%5D%20%E3%82%92%E8%A8%98%E9%8C%B2%E3%81%99%E3%82%8B%0A%20%20%20%20mem%5Bi%5D%20%3D%20count%0A%20%20%20%20return%20count%0A%0A%0Adef%20climbing_stairs_dfs_mem%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%9A%8E%E6%AE%B5%E7%99%BB%E3%82%8A%EF%BC%9A%E3%83%A1%E3%83%A2%E5%8C%96%E6%8E%A2%E7%B4%A2%22%22%22%0A%20%20%20%20%23%20mem%5Bi%5D%20%E3%81%AF%E7%AC%AC%20i%20%E6%AE%B5%E3%81%BE%E3%81%A7%E4%B8%8A%E3%82%8B%E6%96%B9%E6%B3%95%E3%81%AE%E7%B7%8F%E6%95%B0%E3%82%92%E8%A8%98%E9%8C%B2%E3%81%97%E3%80%81-1%20%E3%81%AF%E6%9C%AA%E8%A8%98%E9%8C%B2%E3%82%92%E8%A1%A8%E3%81%99%0A%20%20%20%20mem%20%3D%20%5B-1%5D%20%2A%20%28n%20%2B%201%29%0A%20%20%20%20return%20dfs%28n%2C%20mem%29%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%209%0A%0A%20%20%20%20res%20%3D%20climbing_stairs_dfs_mem%28n%29%0A%20%20%20%20print%28f%22%7Bn%7D%20%E6%AE%B5%E3%81%AE%E9%9A%8E%E6%AE%B5%E3%82%92%E4%B8%8A%E3%82%8B%E6%96%B9%E6%B3%95%E3%81%AF%E5%85%A8%E9%83%A8%E3%81%A7%20%7Bres%7D%20%E9%80%9A%E3%82%8A%E3%81%A7%E3%81%99%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>次の図を見ると、<strong>メモ化を行うことで、すべての重複部分問題は 1 回だけ計算すればよくなり、時間計算量は <span class="arithmatex">\(O(n)\)</span> まで改善されます</strong>。これは大きな飛躍です。</p>
+<p><img alt="メモ化探索に対応する再帰木" class="animation-figure" src="../intro_to_dynamic_programming.assets/climbing_stairs_dfs_memo_tree.png" /></p>
+<p align="center"> 図 14-4 &nbsp; メモ化探索に対応する再帰木 </p>
 
-<h2 id="1413-3">14.1.3 &nbsp; 方法3：動的プログラミング<a class="headerlink" href="#1413-3" title="Permanent link">&para;</a></h2>
-<p>**メモ化探索は「トップダウン」方式**です：元の問題（根ノード）から始めて、より大きな部分問題をより小さなものに再帰的に分解し、最小の既知の部分問題（葉ノード）の解に到達するまで続けます。その後、バックトラッキングにより部分問題の解を収集し、元の問題の解を構築します。</p>
-<p>一方、**動的プログラミングは「ボトムアップ」方式**です：最小の部分問題の解から始めて、元の問題が解決されるまで、より大きな部分問題の解を反復的に構築します。</p>
-<p>動的プログラミングはバックトラッキングを必要としないため、ループを使った反復のみが必要で、再帰は不要です。以下のコードでは、配列 <code>dp</code> を初期化して部分問題の解を保存し、メモ化探索の配列 <code>mem</code> と同じ記録機能を果たします：</p>
+<h2 id="1413-3">14.1.3 &nbsp; 方法 3：動的計画法<a class="headerlink" href="#1413-3" title="Permanent link">&para;</a></h2>
+<p>**メモ化探索は「トップダウン」の方法**です。元の問題（根ノード）から始めて、より大きな部分問題を再帰的により小さな部分問題へ分解し、解が既知である最小部分問題（葉ノード）に至ります。その後、バックトラックしながら各層で部分問題の解を集め、元の問題の解を構築します。</p>
+<p>これとは対照的に、**動的計画法は「ボトムアップ」の方法**です。最小部分問題の解から始めて、より大きな部分問題の解を反復的に構築し、最終的に元の問題の解を得ます。</p>
+<p>動的計画法にはバックトラックの過程が含まれないため、再帰を使う必要はなく、ループによる反復だけで実装できます。次のコードでは、部分問題の解を保存する配列 <code>dp</code> を初期化しており、これはメモ化探索における配列 <code>mem</code> と同じ記録の役割を果たします：</p>
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 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">climbing_stairs_dp.py</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_dp</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;階段登り：動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;階段登り：動的計画法&quot;&quot;&quot;</span>
 <a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
 <a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a>        <span class="k">return</span> <span class="n">n</span>
-<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a>    <span class="c1"># dp テーブルを初期化、部分問題の解を格納するため使用</span>
+<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a>    <span class="c1"># 部分問題の解を保存するために dp テーブルを初期化</span>
 <a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a>    <span class="c1"># 初期状態：最小の部分問題の解を事前設定</span>
+<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a>    <span class="c1"># 初期状態：最小部分問題の解をあらかじめ設定</span>
 <a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a>    <span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span>
-<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a>    <span class="c1"># 状態遷移：小さい部分問題から大きい部分問題を段階的に解く</span>
+<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a>    <span class="c1"># 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
 <a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-39-11" name="__codelineno-39-11" href="#__codelineno-39-11"></a>        <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">2</span><span class="p">]</span>
 <a id="__codelineno-39-12" name="__codelineno-39-12" href="#__codelineno-39-12"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.cpp</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* 階段登り：動的プログラミング */</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.cpp</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* 階段登り：動的計画法 */</span>
 <a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsDP</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
 <a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
-<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化し、部分問題の解を格納するために使用</span>
+<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
 <a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w">    </span><span class="c1">// 初期状態：最小の部分問題の解を事前設定</span>
+<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
 <a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
-<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w">    </span><span class="c1">// 状態遷移：小さな問題から大きな部分問題を段階的に解く</span>
+<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
 <a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">];</span>
 <a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w">    </span><span class="p">}</span>
@@ -4875,16 +5418,16 @@ dp[i] = dp[i-1] + dp[i-2]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.java</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 階段登り：動的プログラミング */</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.java</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 階段登り：動的計画法 */</span>
 <a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsDP</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
 <a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
-<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化し、部分問題の解を格納するために使用</span>
+<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
 <a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="w">    </span><span class="c1">// 初期状態：最小の部分問題の解を事前設定</span>
+<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
 <a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
-<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="w">    </span><span class="c1">// 状態遷移：小さな問題から大きな部分問題を段階的に解く</span>
+<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
 <a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a><span class="w">    </span><span class="p">}</span>
@@ -4893,65 +5436,210 @@ dp[i] = dp[i-1] + dp[i-2]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.cs</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">climbing_stairs_dp</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">ClimbingStairsDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.cs</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="cm">/* 階段登り：動的計画法 */</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">ClimbingStairsDP</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
+<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a><span class="w">    </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">];</span>
+<a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-42-14" name="__codelineno-42-14" href="#__codelineno-42-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-42-15" name="__codelineno-42-15" href="#__codelineno-42-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.go</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">climbingStairsDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.go</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* 階段登り：動的計画法 */</span>
+<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">climbingStairsDP</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">n</span>
+<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="w">    </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">2</span><span class="p">]</span>
+<a id="__codelineno-43-14" name="__codelineno-43-14" href="#__codelineno-43-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-15" name="__codelineno-43-15" href="#__codelineno-43-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">]</span>
+<a id="__codelineno-43-16" name="__codelineno-43-16" href="#__codelineno-43-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.swift</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">climbingStairsDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.swift</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* 階段登り：動的計画法 */</span>
+<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">climbingStairsDP</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span>
+<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">]</span>
+<a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-15" name="__codelineno-44-15" href="#__codelineno-44-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>
+<a id="__codelineno-44-16" name="__codelineno-44-16" href="#__codelineno-44-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.js</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">climbingStairsDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.js</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="cm">/* 階段登り：動的計画法 */</span>
+<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">climbingStairsDP</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span>
+<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="o">-</span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mf">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
+<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">2</span><span class="p">];</span>
+<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-45-13" name="__codelineno-45-13" href="#__codelineno-45-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">];</span>
+<a id="__codelineno-45-14" name="__codelineno-45-14" href="#__codelineno-45-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.ts</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">climbingStairsDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.ts</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="cm">/* 階段登り：動的計画法 */</span>
+<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">climbingStairsDP</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span>
+<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="o">-</span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mf">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
+<a id="__codelineno-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">2</span><span class="p">];</span>
+<a id="__codelineno-46-12" name="__codelineno-46-12" href="#__codelineno-46-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-46-13" name="__codelineno-46-13" href="#__codelineno-46-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">];</span>
+<a id="__codelineno-46-14" name="__codelineno-46-14" href="#__codelineno-46-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.dart</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.dart</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* 階段登り：動的計画法 */</span>
+<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">climbingStairsDP</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
+<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w">  </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a><span class="w">  </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="w">  </span><span class="n">dp</span><span class="p">[</span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a><span class="w">  </span><span class="n">dp</span><span class="p">[</span><span class="m">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
+<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="w">  </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">2</span><span class="p">];</span>
+<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-47-13" name="__codelineno-47-13" href="#__codelineno-47-13"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-47-14" name="__codelineno-47-14" href="#__codelineno-47-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.rs</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbing_stairs_dp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.rs</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="cm">/* 階段登り：動的計画法 */</span>
+<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">climbing_stairs_dp</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="w">    </span><span class="c1">// dp[1] と dp[2] は既知なので返す</span>
+<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">;</span>
+<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-48-11" name="__codelineno-48-11" href="#__codelineno-48-11"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-48-12" name="__codelineno-48-12" href="#__codelineno-48-12"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-48-13" name="__codelineno-48-13" href="#__codelineno-48-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">3</span><span class="o">..=</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-14" name="__codelineno-48-14" href="#__codelineno-48-14"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">];</span>
+<a id="__codelineno-48-15" name="__codelineno-48-15" href="#__codelineno-48-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-48-16" name="__codelineno-48-16" href="#__codelineno-48-16"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>
+<a id="__codelineno-48-17" name="__codelineno-48-17" href="#__codelineno-48-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.c</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.c</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* 階段登り：動的計画法 */</span>
+<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsDP</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
+<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">((</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-49-9" name="__codelineno-49-9" href="#__codelineno-49-9"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-49-10" name="__codelineno-49-10" href="#__codelineno-49-10"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-49-11" name="__codelineno-49-11" href="#__codelineno-49-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-12" name="__codelineno-49-12" href="#__codelineno-49-12"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">];</span>
+<a id="__codelineno-49-13" name="__codelineno-49-13" href="#__codelineno-49-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-49-14" name="__codelineno-49-14" href="#__codelineno-49-14"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">result</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-49-15" name="__codelineno-49-15" href="#__codelineno-49-15"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">dp</span><span class="p">);</span>
+<a id="__codelineno-49-16" name="__codelineno-49-16" href="#__codelineno-49-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">result</span><span class="p">;</span>
+<a id="__codelineno-49-17" name="__codelineno-49-17" href="#__codelineno-49-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.kt</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbingStairsDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.kt</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* 階段登り：動的計画法 */</span>
+<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">climbingStairsDP</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">n</span>
+<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w">    </span><span class="c1">// 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a><span class="w">    </span><span class="c1">// 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="m">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2</span>
+<a id="__codelineno-50-9" name="__codelineno-50-9" href="#__codelineno-50-9"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-50-10" name="__codelineno-50-10" href="#__codelineno-50-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">3.</span><span class="p">.</span><span class="na">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-11" name="__codelineno-50-11" href="#__codelineno-50-11"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">2</span><span class="o">]</span>
+<a id="__codelineno-50-12" name="__codelineno-50-12" href="#__codelineno-50-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-50-13" name="__codelineno-50-13" href="#__codelineno-50-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">]</span>
+<a id="__codelineno-50-14" name="__codelineno-50-14" href="#__codelineno-50-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbing_stairs_dp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="c1">### 階段登り：動的計画法 ###</span>
+<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_dp</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a>
+<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w">  </span><span class="c1"># 部分問題の解を保存するために dp テーブルを初期化</span>
+<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a><span class="w">  </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="w">  </span><span class="c1"># 初期状態：最小部分問題の解をあらかじめ設定</span>
+<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a><span class="w">  </span><span class="c1"># 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></a><span class="w">  </span><span class="p">(</span><span class="mi">3</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-51-11" name="__codelineno-51-11" href="#__codelineno-51-11"></a>
+<a id="__codelineno-51-12" name="__codelineno-51-12" href="#__codelineno-51-12"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">]</span>
+<a id="__codelineno-51-13" name="__codelineno-51-13" href="#__codelineno-51-13"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>下の図は上記コードの実行プロセスをシミュレートしています。</p>
-<p><img alt="階段登りの動的プログラミングプロセス" class="animation-figure" src="../intro_to_dynamic_programming.assets/climbing_stairs_dp.png" /></p>
-<p align="center"> 図 14-5 &nbsp; 階段登りの動的プログラミングプロセス </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 531px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20climbing_stairs_dp%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%9A%8E%E6%AE%B5%E7%99%BB%E3%82%8A%EF%BC%9A%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20if%20n%20%3D%3D%201%20or%20n%20%3D%3D%202%3A%0A%20%20%20%20%20%20%20%20return%20n%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%E3%81%AE%E8%A7%A3%E3%82%92%E4%BF%9D%E5%AD%98%E3%81%99%E3%82%8B%E3%81%9F%E3%82%81%E3%81%AB%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5B0%5D%20%2A%20%28n%20%2B%201%29%0A%20%20%20%20%23%20%E5%88%9D%E6%9C%9F%E7%8A%B6%E6%85%8B%EF%BC%9A%E6%9C%80%E5%B0%8F%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%E3%81%AE%E8%A7%A3%E3%82%92%E3%81%82%E3%82%89%E3%81%8B%E3%81%98%E3%82%81%E8%A8%AD%E5%AE%9A%0A%20%20%20%20dp%5B1%5D%2C%20dp%5B2%5D%20%3D%201%2C%202%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%B0%8F%E3%81%95%E3%81%84%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%E3%81%8B%E3%82%89%E5%A4%A7%E3%81%8D%E3%81%84%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%E3%81%B8%E9%A0%86%E3%81%AB%E8%A7%A3%E3%81%8F%0A%20%20%20%20for%20i%20in%20range%283%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20dp%5Bi%5D%20%3D%20dp%5Bi%20-%201%5D%20%2B%20dp%5Bi%20-%202%5D%0A%20%20%20%20return%20dp%5Bn%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%209%0A%0A%20%20%20%20res%20%3D%20climbing_stairs_dp%28n%29%0A%20%20%20%20print%28f%22%7Bn%7D%20%E6%AE%B5%E3%81%AE%E9%9A%8E%E6%AE%B5%E3%82%92%E4%B8%8A%E3%82%8B%E6%96%B9%E6%B3%95%E3%81%AF%E5%85%A8%E9%83%A8%E3%81%A7%20%7Bres%7D%20%E9%80%9A%E3%82%8A%E3%81%A7%E3%81%99%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20climbing_stairs_dp%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%9A%8E%E6%AE%B5%E7%99%BB%E3%82%8A%EF%BC%9A%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20if%20n%20%3D%3D%201%20or%20n%20%3D%3D%202%3A%0A%20%20%20%20%20%20%20%20return%20n%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%E3%81%AE%E8%A7%A3%E3%82%92%E4%BF%9D%E5%AD%98%E3%81%99%E3%82%8B%E3%81%9F%E3%82%81%E3%81%AB%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5B0%5D%20%2A%20%28n%20%2B%201%29%0A%20%20%20%20%23%20%E5%88%9D%E6%9C%9F%E7%8A%B6%E6%85%8B%EF%BC%9A%E6%9C%80%E5%B0%8F%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%E3%81%AE%E8%A7%A3%E3%82%92%E3%81%82%E3%82%89%E3%81%8B%E3%81%98%E3%82%81%E8%A8%AD%E5%AE%9A%0A%20%20%20%20dp%5B1%5D%2C%20dp%5B2%5D%20%3D%201%2C%202%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%B0%8F%E3%81%95%E3%81%84%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%E3%81%8B%E3%82%89%E5%A4%A7%E3%81%8D%E3%81%84%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%E3%81%B8%E9%A0%86%E3%81%AB%E8%A7%A3%E3%81%8F%0A%20%20%20%20for%20i%20in%20range%283%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20dp%5Bi%5D%20%3D%20dp%5Bi%20-%201%5D%20%2B%20dp%5Bi%20-%202%5D%0A%20%20%20%20return%20dp%5Bn%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%209%0A%0A%20%20%20%20res%20%3D%20climbing_stairs_dp%28n%29%0A%20%20%20%20print%28f%22%7Bn%7D%20%E6%AE%B5%E3%81%AE%E9%9A%8E%E6%AE%B5%E3%82%92%E4%B8%8A%E3%82%8B%E6%96%B9%E6%B3%95%E3%81%AF%E5%85%A8%E9%83%A8%E3%81%A7%20%7Bres%7D%20%E9%80%9A%E3%82%8A%E3%81%A7%E3%81%99%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>次の図は、以上のコードの実行過程をシミュレートしたものです。</p>
+<p><img alt="階段上りの動的計画法の過程" class="animation-figure" src="../intro_to_dynamic_programming.assets/climbing_stairs_dp.png" /></p>
+<p align="center"> 図 14-5 &nbsp; 階段上りの動的計画法の過程 </p>
 
-<p>バックトラッキングアルゴリズムと同様に、動的プログラミングも「状態」の概念を使用して問題解決の特定の段階を表現し、各状態は部分問題とその局所最適解に対応します。例えば、階段登り問題の状態は現在のステップ番号 <span class="arithmatex">\(i\)</span> として定義されます。</p>
-<p>上記の内容に基づいて、動的プログラミングでよく使用される用語をまとめることができます。</p>
+<p>バックトラッキング法と同様に、動的計画法でも問題解決の特定段階を表すために「状態」という概念を用います。各状態は 1 つの部分問題と、それに対応する局所最適解に対応します。たとえば、階段を上る問題では、状態は現在いる階段の段数 <span class="arithmatex">\(i\)</span> と定義されます。</p>
+<p>以上を踏まえると、動的計画法のよく使われる用語を次のようにまとめられます。</p>
 <ul>
-<li>配列 <code>dp</code> は<u>DPテーブル</u>と呼ばれ、<span class="arithmatex">\(dp[i]\)</span> は状態 <span class="arithmatex">\(i\)</span> に対応する部分問題の解を表します。</li>
-<li>最小の部分問題（ステップ <span class="arithmatex">\(1\)</span> と <span class="arithmatex">\(2\)</span>）に対応する状態は<u>初期状態</u>と呼ばれます。</li>
-<li>再帰式 <span class="arithmatex">\(dp[i] = dp[i-1] + dp[i-2]\)</span> は<u>状態遷移方程式</u>と呼ばれます。</li>
+<li>配列 <code>dp</code> を <u>dp テーブル</u> と呼び、<span class="arithmatex">\(dp[i]\)</span> は状態 <span class="arithmatex">\(i\)</span> に対応する部分問題の解を表します。</li>
+<li>最小部分問題に対応する状態（第 <span class="arithmatex">\(1\)</span> 段目と第 <span class="arithmatex">\(2\)</span> 段目の階段）を<u>初期状態</u>と呼びます。</li>
+<li>漸化式 <span class="arithmatex">\(dp[i] = dp[i-1] + dp[i-2]\)</span> を<u>状態遷移方程式</u>と呼びます。</li>
 </ul>
 <h2 id="1414">14.1.4 &nbsp; 空間最適化<a class="headerlink" href="#1414" title="Permanent link">&para;</a></h2>
-<p>注意深い読者は**<span class="arithmatex">\(dp[i]\)</span> は <span class="arithmatex">\(dp[i-1]\)</span> と <span class="arithmatex">\(dp[i-2]\)</span> のみに関連するため、すべての部分問題の解を保存するために配列 <code>dp</code> を使用する必要がない**ことに気づくでしょう。単に2つの変数を使って反復的に進めることができます。コードは以下の通りです：</p>
+<p>注意深い読者は気づいたかもしれません。<strong><span class="arithmatex">\(dp[i]\)</span> は <span class="arithmatex">\(dp[i-1]\)</span> と <span class="arithmatex">\(dp[i-2]\)</span> にしか依存しないため、すべての部分問題の解を保存するために配列 <code>dp</code> を使う必要はありません</strong>。2 つの変数を順に更新していくだけで十分です。コードは次のとおりです：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="5:13"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">climbing_stairs_dp.py</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_dp_comp</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;階段登り：空間最適化動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;階段登り：空間最適化した動的計画法&quot;&quot;&quot;</span>
 <a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
 <a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a>        <span class="k">return</span> <span class="n">n</span>
 <a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a>    <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span>
@@ -4961,7 +5649,7 @@ dp[i] = dp[i-1] + dp[i-2]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.cpp</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 階段登り：空間最適化動的プログラミング */</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.cpp</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 階段登り：空間最適化した動的計画法 */</span>
 <a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsDPComp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
 <a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
@@ -4976,7 +5664,7 @@ dp[i] = dp[i-1] + dp[i-2]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.java</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="cm">/* 階段登り：空間最適化動的プログラミング */</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.java</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="cm">/* 階段登り：空間最適化した動的計画法 */</span>
 <a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsDPComp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
 <a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
@@ -4991,49 +5679,161 @@ dp[i] = dp[i-1] + dp[i-2]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.cs</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">climbing_stairs_dp</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">ClimbingStairsDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.cs</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="cm">/* 階段登り：空間最適化した動的計画法 */</span>
+<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">ClimbingStairsDPComp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-55-4" name="__codelineno-55-4" href="#__codelineno-55-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
+<a id="__codelineno-55-5" name="__codelineno-55-5" href="#__codelineno-55-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-55-6" name="__codelineno-55-6" href="#__codelineno-55-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-7" name="__codelineno-55-7" href="#__codelineno-55-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-55-8" name="__codelineno-55-8" href="#__codelineno-55-8"></a><span class="w">        </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-55-9" name="__codelineno-55-9" href="#__codelineno-55-9"></a><span class="w">        </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-55-10" name="__codelineno-55-10" href="#__codelineno-55-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-55-11" name="__codelineno-55-11" href="#__codelineno-55-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-55-12" name="__codelineno-55-12" href="#__codelineno-55-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.go</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">climbingStairsDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.go</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="cm">/* 階段登り：空間最適化した動的計画法 */</span>
+<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">climbingStairsDPComp</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">n</span>
+<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a><span class="w">    </span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a><span class="w">    </span><span class="c1">// 状態遷移：小さい部分問題から大きい部分問題へ順に解く</span>
+<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></a><span class="w">        </span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">b</span><span class="p">,</span><span class="w"> </span><span class="nx">a</span><span class="o">+</span><span class="nx">b</span>
+<a id="__codelineno-56-10" name="__codelineno-56-10" href="#__codelineno-56-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-56-11" name="__codelineno-56-11" href="#__codelineno-56-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">b</span>
+<a id="__codelineno-56-12" name="__codelineno-56-12" href="#__codelineno-56-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.swift</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">climbingStairsDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.swift</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 階段登り：空間最適化した動的計画法 */</span>
+<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">climbingStairsDPComp</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span>
+<a id="__codelineno-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">b</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="w">        </span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="p">)</span>
+<a id="__codelineno-57-10" name="__codelineno-57-10" href="#__codelineno-57-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-57-11" name="__codelineno-57-11" href="#__codelineno-57-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">b</span>
+<a id="__codelineno-57-12" name="__codelineno-57-12" href="#__codelineno-57-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.js</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">climbingStairsDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.js</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 階段登り：空間最適化した動的計画法 */</span>
+<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">climbingStairsDPComp</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span>
+<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span>
+<a id="__codelineno-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a><span class="w">        </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
+<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">b</span><span class="p">;</span>
+<a id="__codelineno-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></a><span class="w">        </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">b</span><span class="p">;</span>
+<a id="__codelineno-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></a><span class="w">        </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">;</span>
+<a id="__codelineno-58-10" name="__codelineno-58-10" href="#__codelineno-58-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-58-11" name="__codelineno-58-11" href="#__codelineno-58-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">b</span><span class="p">;</span>
+<a id="__codelineno-58-12" name="__codelineno-58-12" href="#__codelineno-58-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.ts</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">climbingStairsDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.ts</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="cm">/* 階段登り：空間最適化した動的計画法 */</span>
+<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">climbingStairsDPComp</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span>
+<a id="__codelineno-59-4" name="__codelineno-59-4" href="#__codelineno-59-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span>
+<a id="__codelineno-59-5" name="__codelineno-59-5" href="#__codelineno-59-5"></a><span class="w">        </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
+<a id="__codelineno-59-6" name="__codelineno-59-6" href="#__codelineno-59-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-7" name="__codelineno-59-7" href="#__codelineno-59-7"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">b</span><span class="p">;</span>
+<a id="__codelineno-59-8" name="__codelineno-59-8" href="#__codelineno-59-8"></a><span class="w">        </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">b</span><span class="p">;</span>
+<a id="__codelineno-59-9" name="__codelineno-59-9" href="#__codelineno-59-9"></a><span class="w">        </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">;</span>
+<a id="__codelineno-59-10" name="__codelineno-59-10" href="#__codelineno-59-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-59-11" name="__codelineno-59-11" href="#__codelineno-59-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">b</span><span class="p">;</span>
+<a id="__codelineno-59-12" name="__codelineno-59-12" href="#__codelineno-59-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.dart</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.dart</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="cm">/* 階段登り：空間最適化した動的計画法 */</span>
+<a id="__codelineno-60-2" name="__codelineno-60-2" href="#__codelineno-60-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">climbingStairsDPComp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-3" name="__codelineno-60-3" href="#__codelineno-60-3"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
+<a id="__codelineno-60-4" name="__codelineno-60-4" href="#__codelineno-60-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
+<a id="__codelineno-60-5" name="__codelineno-60-5" href="#__codelineno-60-5"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-6" name="__codelineno-60-6" href="#__codelineno-60-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-60-7" name="__codelineno-60-7" href="#__codelineno-60-7"></a><span class="w">    </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-60-8" name="__codelineno-60-8" href="#__codelineno-60-8"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-60-9" name="__codelineno-60-9" href="#__codelineno-60-9"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-60-10" name="__codelineno-60-10" href="#__codelineno-60-10"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-60-11" name="__codelineno-60-11" href="#__codelineno-60-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.rs</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbing_stairs_dp_comp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.rs</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="cm">/* 階段登り：空間最適化した動的計画法 */</span>
+<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">climbing_stairs_dp_comp</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-3" name="__codelineno-61-3" href="#__codelineno-61-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-4" name="__codelineno-61-4" href="#__codelineno-61-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">;</span>
+<a id="__codelineno-61-5" name="__codelineno-61-5" href="#__codelineno-61-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-61-6" name="__codelineno-61-6" href="#__codelineno-61-6"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="p">(</span><span class="k">mut</span><span class="w"> </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">b</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-61-7" name="__codelineno-61-7" href="#__codelineno-61-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">3</span><span class="o">..=</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-8" name="__codelineno-61-8" href="#__codelineno-61-8"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-61-9" name="__codelineno-61-9" href="#__codelineno-61-9"></a><span class="w">        </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-61-10" name="__codelineno-61-10" href="#__codelineno-61-10"></a><span class="w">        </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-61-11" name="__codelineno-61-11" href="#__codelineno-61-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-61-12" name="__codelineno-61-12" href="#__codelineno-61-12"></a><span class="w">    </span><span class="n">b</span>
+<a id="__codelineno-61-13" name="__codelineno-61-13" href="#__codelineno-61-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.c</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.c</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="cm">/* 階段登り：空間最適化した動的計画法 */</span>
+<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsDPComp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-62-4" name="__codelineno-62-4" href="#__codelineno-62-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
+<a id="__codelineno-62-5" name="__codelineno-62-5" href="#__codelineno-62-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-62-6" name="__codelineno-62-6" href="#__codelineno-62-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-7" name="__codelineno-62-7" href="#__codelineno-62-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-62-8" name="__codelineno-62-8" href="#__codelineno-62-8"></a><span class="w">        </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-62-9" name="__codelineno-62-9" href="#__codelineno-62-9"></a><span class="w">        </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-62-10" name="__codelineno-62-10" href="#__codelineno-62-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-62-11" name="__codelineno-62-11" href="#__codelineno-62-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-62-12" name="__codelineno-62-12" href="#__codelineno-62-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.kt</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbingStairsDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.kt</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="cm">/* 階段登り：空間最適化した動的計画法 */</span>
+<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">climbingStairsDPComp</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">n</span>
+<a id="__codelineno-63-4" name="__codelineno-63-4" href="#__codelineno-63-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-63-5" name="__codelineno-63-5" href="#__codelineno-63-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2</span>
+<a id="__codelineno-63-6" name="__codelineno-63-6" href="#__codelineno-63-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">3.</span><span class="p">.</span><span class="na">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">b</span>
+<a id="__codelineno-63-8" name="__codelineno-63-8" href="#__codelineno-63-8"></a><span class="w">        </span><span class="n">b</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">a</span>
+<a id="__codelineno-63-9" name="__codelineno-63-9" href="#__codelineno-63-9"></a><span class="w">        </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span>
+<a id="__codelineno-63-10" name="__codelineno-63-10" href="#__codelineno-63-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-63-11" name="__codelineno-63-11" href="#__codelineno-63-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">b</span>
+<a id="__codelineno-63-12" name="__codelineno-63-12" href="#__codelineno-63-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbing_stairs_dp_comp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="c1">### 階段登り：空間最適化後の動的計画法 ###</span>
+<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_dp_comp</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-64-4" name="__codelineno-64-4" href="#__codelineno-64-4"></a>
+<a id="__codelineno-64-5" name="__codelineno-64-5" href="#__codelineno-64-5"></a><span class="w">  </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-64-6" name="__codelineno-64-6" href="#__codelineno-64-6"></a><span class="w">  </span><span class="p">(</span><span class="mi">3</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">b</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-64-7" name="__codelineno-64-7" href="#__codelineno-64-7"></a>
+<a id="__codelineno-64-8" name="__codelineno-64-8" href="#__codelineno-64-8"></a><span class="w">  </span><span class="n">b</span>
+<a id="__codelineno-64-9" name="__codelineno-64-9" href="#__codelineno-64-9"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>上記のコードを観察すると、配列 <code>dp</code> が占有していた空間が削除されるため、空間計算量は <span class="arithmatex">\(O(n)\)</span> から <span class="arithmatex">\(O(1)\)</span> に削減されます。</p>
-<p>多くの動的プログラミング問題では、現在の状態は限られた数の前の状態のみに依存するため、必要な状態のみを保持し、「次元削減」によってメモリ空間を節約できます。<strong>この空間最適化技術は「ローリング変数」または「ローリング配列」として知られています</strong>。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 459px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20climbing_stairs_dp_comp%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%9A%8E%E6%AE%B5%E7%99%BB%E3%82%8A%EF%BC%9A%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E3%81%97%E3%81%9F%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20if%20n%20%3D%3D%201%20or%20n%20%3D%3D%202%3A%0A%20%20%20%20%20%20%20%20return%20n%0A%20%20%20%20a%2C%20b%20%3D%201%2C%202%0A%20%20%20%20for%20_%20in%20range%283%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20a%2C%20b%20%3D%20b%2C%20a%20%2B%20b%0A%20%20%20%20return%20b%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%209%0A%0A%20%20%20%20res%20%3D%20climbing_stairs_dp_comp%28n%29%0A%20%20%20%20print%28f%22%7Bn%7D%20%E6%AE%B5%E3%81%AE%E9%9A%8E%E6%AE%B5%E3%82%92%E4%B8%8A%E3%82%8B%E6%96%B9%E6%B3%95%E3%81%AF%E5%85%A8%E9%83%A8%E3%81%A7%20%7Bres%7D%20%E9%80%9A%E3%82%8A%E3%81%A7%E3%81%99%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20climbing_stairs_dp_comp%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%9A%8E%E6%AE%B5%E7%99%BB%E3%82%8A%EF%BC%9A%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E3%81%97%E3%81%9F%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20if%20n%20%3D%3D%201%20or%20n%20%3D%3D%202%3A%0A%20%20%20%20%20%20%20%20return%20n%0A%20%20%20%20a%2C%20b%20%3D%201%2C%202%0A%20%20%20%20for%20_%20in%20range%283%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20a%2C%20b%20%3D%20b%2C%20a%20%2B%20b%0A%20%20%20%20return%20b%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%209%0A%0A%20%20%20%20res%20%3D%20climbing_stairs_dp_comp%28n%29%0A%20%20%20%20print%28f%22%7Bn%7D%20%E6%AE%B5%E3%81%AE%E9%9A%8E%E6%AE%B5%E3%82%92%E4%B8%8A%E3%82%8B%E6%96%B9%E6%B3%95%E3%81%AF%E5%85%A8%E9%83%A8%E3%81%A7%20%7Bres%7D%20%E9%80%9A%E3%82%8A%E3%81%A7%E3%81%99%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>上のコードを見ると、配列 <code>dp</code> が占めていた領域を省けるため、空間計算量は <span class="arithmatex">\(O(n)\)</span> から <span class="arithmatex">\(O(1)\)</span> へと下がります。</p>
+<p>動的計画法の問題では、現在の状態はしばしば直前の限られた個数の状態にしか関係しません。このような場合は、必要な状態だけを保持し、「次元削減」によってメモリ空間を節約できます。<strong>この空間最適化の技巧は「ローリング変数」または「ローリング配列」と呼ばれます</strong>。</p>
 
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-    aria-label="前: 第 14 章 &amp;nbsp; 動的プログラミング"
+    aria-label="前: 第 14 章 &amp;nbsp; 動的計画法"
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-    aria-label="次: 14.2 &amp;nbsp; DP 問題の特性"
+    aria-label="次: 14.2 &amp;nbsp; 動的計画法の問題特性"
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-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
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-        <title>14.4 0-1ナップサック問題 - Hello アルゴリズム</title>
+        <title>14.4 0-1 ナップサック問題 - Hello アルゴリズム</title>
       
     
     
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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 <!-- Page content -->
-<h1 id="144-0-1">14.4 &nbsp; 0-1ナップサック問題<a class="headerlink" href="#144-0-1" title="Permanent link">&para;</a></h1>
-<p>ナップサック問題は動的プログラミングの優れた入門問題であり、動的プログラミングで最も一般的な問題タイプです。0-1ナップサック問題、無制限ナップサック問題、複数ナップサック問題など、多くの変種があります。</p>
-<p>このセクションでは、まず最も一般的な0-1ナップサック問題を解決します。</p>
+<h1 id="144-0-1">14.4 &nbsp; 0-1 ナップサック問題<a class="headerlink" href="#144-0-1" title="Permanent link">&para;</a></h1>
+<p>ナップサック問題は、動的計画法の入門として非常に適した問題であり、動的計画法で最もよく見られる問題形式の1つです。これには 0-1 ナップサック問題、完全ナップサック問題、多重ナップサック問題など、多くの派生があります。</p>
+<p>本節では、まず最も一般的な 0-1 ナップサック問題を解いていきます。</p>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
-<p><span class="arithmatex">\(n\)</span> 個のアイテムが与えられ、<span class="arithmatex">\(i\)</span> 番目のアイテムの重量は <span class="arithmatex">\(wgt[i-1]\)</span> で値は <span class="arithmatex">\(val[i-1]\)</span> です。容量が <span class="arithmatex">\(cap\)</span> のナップサックがあります。各アイテムは1回のみ選択できます。容量制限下でナップサックに入れることができるアイテムの最大値は何ですか？</p>
+<p><span class="arithmatex">\(n\)</span> 個の品物が与えられ、<span class="arithmatex">\(i\)</span> 番目の品物の重さは <span class="arithmatex">\(wgt[i-1]\)</span>、価値は <span class="arithmatex">\(val[i-1]\)</span> であり、容量 <span class="arithmatex">\(cap\)</span> のナップサックがあります。各品物は1回しか選べないとき、ナップサック容量の制約下で入れられる品物の最大価値を求めてください。</p>
 </div>
-<p>下の図を観察すると、アイテム番号 <span class="arithmatex">\(i\)</span> は1から数え始め、配列インデックスは0から始まるため、アイテム <span class="arithmatex">\(i\)</span> の重量は <span class="arithmatex">\(wgt[i-1]\)</span> に対応し、値は <span class="arithmatex">\(val[i-1]\)</span> に対応します。</p>
-<p><img alt="0-1ナップサックの例データ" class="animation-figure" src="../knapsack_problem.assets/knapsack_example.png" /></p>
-<p align="center"> 図 14-17 &nbsp; 0-1ナップサックの例データ </p>
+<p>以下の図を見てみましょう。品物番号 <span class="arithmatex">\(i\)</span> は <span class="arithmatex">\(1\)</span> から始まり、配列のインデックスは <span class="arithmatex">\(0\)</span> から始まるため、品物 <span class="arithmatex">\(i\)</span> は重さ <span class="arithmatex">\(wgt[i-1]\)</span>、価値 <span class="arithmatex">\(val[i-1]\)</span> に対応します。</p>
+<p><img alt="0-1 ナップサックのサンプルデータ" class="animation-figure" src="../knapsack_problem.assets/knapsack_example.png" /></p>
+<p align="center"> 図 14-17 &nbsp; 0-1 ナップサックのサンプルデータ </p>
 
-<p>0-1ナップサック問題を <span class="arithmatex">\(n\)</span> ラウンドの決定から構成されるプロセスとして考えることができます。各アイテムについて入れない、または入れるという2つの決定があり、したがって問題は決定木モデルに適合します。</p>
-<p>この問題の目的は「限られた容量の下でナップサックに入れることができるアイテムの値を最大化する」ことであり、動的プログラミング問題である可能性が高いです。</p>
-<p><strong>第1ステップ：各ラウンドの決定を考え、状態を定義し、それにより <span class="arithmatex">\(dp\)</span> テーブルを得る</strong></p>
-<p>各アイテムについて、ナップサックに入れなければ容量は変わらず、入れれば容量は減少します。これから状態定義を得ることができます：現在のアイテム番号 <span class="arithmatex">\(i\)</span> とナップサック容量 <span class="arithmatex">\(c\)</span>、<span class="arithmatex">\([i, c]\)</span> と表記されます。</p>
-<p>状態 <span class="arithmatex">\([i, c]\)</span> は部分問題に対応します：<strong>容量 <span class="arithmatex">\(c\)</span> のナップサックでの最初の <span class="arithmatex">\(i\)</span> 個のアイテムの最大値</strong>、<span class="arithmatex">\(dp[i, c]\)</span> と表記されます。</p>
-<p>探している解は <span class="arithmatex">\(dp[n, cap]\)</span> であるため、サイズ <span class="arithmatex">\((n+1) \times (cap+1)\)</span> の二次元 <span class="arithmatex">\(dp\)</span> テーブルが必要です。</p>
-<p><strong>第2ステップ：最適部分構造を特定し、状態遷移方程式を導出する</strong></p>
-<p>アイテム <span class="arithmatex">\(i\)</span> の決定を行った後、残るのは最初の <span class="arithmatex">\(i-1\)</span> 個のアイテムの決定の部分問題であり、これは2つのケースに分けることができます。</p>
+<p>0-1 ナップサック問題は、<span class="arithmatex">\(n\)</span> 回の意思決定からなる過程とみなせます。各品物について「入れない」「入れる」という2つの選択肢があるため、この問題は決定木モデルを満たします。</p>
+<p>この問題の目的は「ナップサック容量の制約下で入れられる品物の最大価値」を求めることなので、動的計画法の問題である可能性が高いです。</p>
+<p><strong>ステップ1：各ラウンドの選択を考え、状態を定義して、<span class="arithmatex">\(dp\)</span> テーブルを得る</strong></p>
+<p>各品物について、ナップサックに入れなければ容量は変わらず、入れれば容量は減少します。ここから状態を、現在の品物番号 <span class="arithmatex">\(i\)</span> とナップサック容量 <span class="arithmatex">\(c\)</span> として定義し、<span class="arithmatex">\([i, c]\)</span> と表せます。</p>
+<p>状態 <span class="arithmatex">\([i, c]\)</span> に対応する部分問題は、<strong>先頭 <span class="arithmatex">\(i\)</span> 個の品物を容量 <span class="arithmatex">\(c\)</span> のナップサックに入れるときの最大価値</strong> であり、これを <span class="arithmatex">\(dp[i, c]\)</span> と記します。</p>
+<p>求めるべきものは <span class="arithmatex">\(dp[n, cap]\)</span> なので、サイズ <span class="arithmatex">\((n+1) \times (cap+1)\)</span> の2次元 <span class="arithmatex">\(dp\)</span> テーブルが必要です。</p>
+<p><strong>ステップ2：最適部分構造を見つけ、状態遷移方程式を導く</strong></p>
+<p>品物 <span class="arithmatex">\(i\)</span> に対する選択を行った後に残るのは、先頭 <span class="arithmatex">\(i-1\)</span> 個の品物に対する部分問題であり、次の2つのケースに分けられます。</p>
 <ul>
-<li><strong>アイテム <span class="arithmatex">\(i\)</span> を入れない</strong>：ナップサック容量は変わらず、状態は <span class="arithmatex">\([i-1, c]\)</span> に変わります。</li>
-<li><strong>アイテム <span class="arithmatex">\(i\)</span> を入れる</strong>：ナップサック容量は <span class="arithmatex">\(wgt[i-1]\)</span> だけ減少し、値は <span class="arithmatex">\(val[i-1]\)</span> だけ増加し、状態は <span class="arithmatex">\([i-1, c-wgt[i-1]]\)</span> に変わります。</li>
+<li><strong>品物 <span class="arithmatex">\(i\)</span> を入れない</strong> ：ナップサック容量は変わらず、状態は <span class="arithmatex">\([i-1, c]\)</span> に変化します。</li>
+<li><strong>品物 <span class="arithmatex">\(i\)</span> を入れる</strong> ：ナップサック容量は <span class="arithmatex">\(wgt[i-1]\)</span> だけ減少し、価値は <span class="arithmatex">\(val[i-1]\)</span> だけ増加して、状態は <span class="arithmatex">\([i-1, c-wgt[i-1]]\)</span> に変化します。</li>
 </ul>
-<p>上記の分析により、この問題の最適部分構造が明らかになります：<strong>最大値 <span class="arithmatex">\(dp[i, c]\)</span> は、アイテム <span class="arithmatex">\(i\)</span> を入れない方案とアイテム <span class="arithmatex">\(i\)</span> を入れる方案の2つのうち、より大きな値に等しい</strong>。これから状態遷移方程式を導出できます：</p>
+<p>以上の分析から、この問題の最適部分構造が分かります。すなわち、<strong>最大価値 <span class="arithmatex">\(dp[i, c]\)</span> は、品物 <span class="arithmatex">\(i\)</span> を入れない場合と入れる場合のうち、より価値の大きい方に等しい</strong> ということです。これにより、次の状態遷移方程式を導けます。</p>
 <div class="arithmatex">\[
 dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
 \]</div>
-<p>現在のアイテムの重量 <span class="arithmatex">\(wgt[i - 1]\)</span> が残りのナップサック容量 <span class="arithmatex">\(c\)</span> を超える場合、唯一の選択肢はナップサックに入れないことであることに注意することが重要です。</p>
-<p><strong>第3ステップ：境界条件と状態遷移の順序を決定する</strong></p>
-<p>アイテムがない場合またはナップサック容量が <span class="arithmatex">\(0\)</span> の場合、最大値は <span class="arithmatex">\(0\)</span> です。つまり、最初の列 <span class="arithmatex">\(dp[i, 0]\)</span> と最初の行 <span class="arithmatex">\(dp[0, c]\)</span> はどちらも <span class="arithmatex">\(0\)</span> に等しいです。</p>
-<p>現在の状態 <span class="arithmatex">\([i, c]\)</span> は直接上の状態 <span class="arithmatex">\([i-1, c]\)</span> と左上の状態 <span class="arithmatex">\([i-1, c-wgt[i-1]]\)</span> から遷移するため、2層のループを通じて <span class="arithmatex">\(dp\)</span> テーブル全体を順序通りに走査します。</p>
-<p>上記の分析に従って、次に力任せ探索、メモ化探索、動的プログラミングの順序で解法を実装します。</p>
-<h3 id="1-1">1. &nbsp; 方法1：力任せ探索<a class="headerlink" href="#1-1" title="Permanent link">&para;</a></h3>
-<p>探索コードには以下の要素が含まれます。</p>
+<p>注意すべき点として、現在の品物の重さ <span class="arithmatex">\(wgt[i - 1]\)</span> が残りのナップサック容量 <span class="arithmatex">\(c\)</span> を超える場合は、入れない選択しかできません。</p>
+<p><strong>ステップ3：境界条件と状態遷移の順序を決める</strong></p>
+<p>品物がない場合、またはナップサック容量が <span class="arithmatex">\(0\)</span> の場合、最大価値は <span class="arithmatex">\(0\)</span> です。すなわち、先頭列 <span class="arithmatex">\(dp[i, 0]\)</span> と先頭行 <span class="arithmatex">\(dp[0, c]\)</span> はいずれも <span class="arithmatex">\(0\)</span> になります。</p>
+<p>現在の状態 <span class="arithmatex">\([i, c]\)</span> は、上側の状態 <span class="arithmatex">\([i-1, c]\)</span> と左上の状態 <span class="arithmatex">\([i-1, c-wgt[i-1]]\)</span> から遷移してくるため、2重ループで <span class="arithmatex">\(dp\)</span> テーブル全体を順方向に走査すれば十分です。</p>
+<p>以上の分析に基づき、次に全探索、メモ化探索、動的計画法の順で実装していきます。</p>
+<h3 id="1-1">1. &nbsp; 方法1：全探索<a class="headerlink" href="#1-1" title="Permanent link">&para;</a></h3>
+<p>探索コードには次の要素が含まれます。</p>
 <ul>
-<li><strong>再帰パラメータ</strong>：状態 <span class="arithmatex">\([i, c]\)</span>。</li>
-<li><strong>戻り値</strong>：部分問題 <span class="arithmatex">\(dp[i, c]\)</span> の解。</li>
-<li><strong>終了条件</strong>：アイテム番号が範囲外 <span class="arithmatex">\(i = 0\)</span> またはナップサックの残り容量が <span class="arithmatex">\(0\)</span> のとき、再帰を終了し値 <span class="arithmatex">\(0\)</span> を返す。</li>
-<li><strong>枝刈り</strong>：現在のアイテムの重量がナップサックの残り容量を超える場合、唯一の選択肢はナップサックに入れないことです。</li>
+<li><strong>再帰引数</strong>：状態 <span class="arithmatex">\([i, c]\)</span> です。</li>
+<li><strong>戻り値</strong>：部分問題の解 <span class="arithmatex">\(dp[i, c]\)</span> です。</li>
+<li><strong>終了条件</strong>：品物番号が範囲外である <span class="arithmatex">\(i = 0\)</span>、またはナップサックの残り容量が <span class="arithmatex">\(0\)</span> のとき、再帰を終了して価値 <span class="arithmatex">\(0\)</span> を返します。</li>
+<li><strong>枝刈り</strong>：現在の品物の重さがナップサックの残り容量を超える場合、入れない選択しかできません。</li>
 </ul>
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 <div class="highlight"><span class="filename">knapsack.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">knapsack_dfs</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">val</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">c</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;0-1 ナップサック：ブルートフォース探索&quot;&quot;&quot;</span>
-<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># すべてのアイテムが選択されたかナップサックに残り容量がない場合、値 0 を返す</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;0-1 ナップサック：総当たり探索&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">c</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="k">return</span> <span class="mi">0</span>
-<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># ナップサック容量を超える場合、ナップサックに入れないことしか選択できない</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># ナップサック容量を超える場合は、入れない選択しかできない</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="k">if</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">c</span><span class="p">:</span>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="k">return</span> <span class="n">knapsack_dfs</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span> <span class="n">val</span><span class="p">,</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">c</span><span class="p">)</span>
-<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="c1"># アイテム i を入れないのと入れるのとの最大値を計算</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="c1"># 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
 <a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="n">no</span> <span class="o">=</span> <span class="n">knapsack_dfs</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span> <span class="n">val</span><span class="p">,</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">c</span><span class="p">)</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="n">yes</span> <span class="o">=</span> <span class="n">knapsack_dfs</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span> <span class="n">val</span><span class="p">,</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">c</span> <span class="o">-</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span> <span class="o">+</span> <span class="n">val</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span>
-<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="c1"># 2 つの選択肢のうち大きい値を返す</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="c1"># 2つの案のうち価値が大きいほうを返す</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="k">return</span> <span class="nb">max</span><span class="p">(</span><span class="n">no</span><span class="p">,</span> <span class="n">yes</span><span class="p">)</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 0-1 ナップサック：ブルートフォース探索 */</span>
+<div class="highlight"><span class="filename">knapsack.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 0-1 ナップサック：総当たり探索 */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">knapsackDFS</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// すべてのアイテムが選択されたか、ナップサックに残り容量がない場合、値 0 を返す</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="c1">// ナップサックの容量を超える場合、ナップサックに入れないことしか選択できない</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="c1">// ナップサック容量を超える場合は、入れない選択しかできない</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="c1">// アイテム i を入れない場合と入れる場合の最大値を計算</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="c1">// 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
-<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="c1">// 2つの選択肢のより大きい値を返す</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="c1">// 2つの案のうち価値が大きいほうを返す</span>
 <a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="p">);</span>
 <a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 0-1 ナップサック：ブルートフォース探索 */</span>
+<div class="highlight"><span class="filename">knapsack.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 0-1 ナップサック：総当たり探索 */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">knapsackDFS</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// すべてのアイテムが選択されたか、ナップサックに残り容量がない場合、値 0 を返す</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="c1">// ナップサックの容量を超える場合、ナップサックに入れないことしか選択できない</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="c1">// ナップサック容量を超える場合は、入れない選択しかできない</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="c1">// アイテム i を入れない場合と入れる場合の最大値を計算</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="c1">// 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
 <a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="c1">// 2つの選択肢のより大きい値を返す</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="c1">// 2つの案のうち価値が大きいほうを返す</span>
 <a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">max</span><span class="p">(</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="p">);</span>
 <a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">knapsack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">KnapsackDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 0-1 ナップサック：総当たり探索 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">KnapsackDFS</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">weight</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="c1">// すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="c1">// ナップサック容量を超える場合は、入れない選択しかできない</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">weight</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nf">KnapsackDFS</span><span class="p">(</span><span class="n">weight</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">    </span><span class="c1">// 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">KnapsackDFS</span><span class="p">(</span><span class="n">weight</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">KnapsackDFS</span><span class="p">(</span><span class="n">weight</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">weight</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">    </span><span class="c1">// 2つの案のうち価値が大きいほうを返す</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Max</span><span class="p">(</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="p">);</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">knapsackDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 0-1 ナップサック：総当たり探索 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">knapsackDFS</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="c1">// ナップサック容量を超える場合は、入れない選択しかできない</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">knapsackDFS</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="p">)</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">    </span><span class="c1">// 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">    </span><span class="nx">no</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">knapsackDFS</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="p">)</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">    </span><span class="nx">yes</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">knapsackDFS</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="o">-</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">    </span><span class="c1">// 2つの案のうち価値が大きいほうを返す</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Max</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">no</span><span class="p">),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">yes</span><span class="p">)))</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">knapsackDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 0-1 ナップサック：総当たり探索 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="c1">// ナップサック容量を超える場合は、入れない選択しかできない</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">:</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">    </span><span class="c1">// 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">no</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">:</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">yes</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">:</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">    </span><span class="c1">// 2つの案のうち価値が大きいほうを返す</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="bp">max</span><span class="p">(</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="p">)</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">knapsackDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 0-1 ナップサック：総当たり探索 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">knapsackDFS</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="c1">// すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="c1">// ナップサック容量を超える場合は、入れない選択しかできない</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">knapsackDFS</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="p">);</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">    </span><span class="c1">// 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">knapsackDFS</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="p">);</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">knapsackDFS</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">    </span><span class="c1">// 2つの案のうち価値が大きいほうを返す</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">max</span><span class="p">(</span><span class="nx">no</span><span class="p">,</span><span class="w"> </span><span class="nx">yes</span><span class="p">);</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">knapsackDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 0-1 ナップサック：総当たり探索 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">knapsackDFS</span><span class="p">(</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="nx">wgt</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="nx">c</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="c1">// すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">    </span><span class="c1">// ナップサック容量を超える場合は、入れない選択しかできない</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">knapsackDFS</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="p">);</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">    </span><span class="c1">// 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">knapsackDFS</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="p">);</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">knapsackDFS</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">    </span><span class="c1">// 2つの案のうち価値が大きいほうを返す</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">max</span><span class="p">(</span><span class="nx">no</span><span class="p">,</span><span class="w"> </span><span class="nx">yes</span><span class="p">);</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsackDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 0-1 ナップサック：総当たり探索 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="c1">// すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="c1">// ナップサック容量を超える場合は、入れない選択しかできない</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">  </span><span class="c1">// 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">];</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">  </span><span class="c1">// 2つの案のうち価値が大きいほうを返す</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="p">);</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsack_dfs</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 0-1 ナップサック：総当たり探索 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">knapsack_dfs</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="c1">// すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="c1">// ナップサック容量を超える場合は、入れない選択しかできない</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">knapsack_dfs</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">    </span><span class="c1">// 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsack_dfs</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsack_dfs</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">    </span><span class="c1">// 2つの案のうち価値が大きいほうを返す</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">    </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">max</span><span class="p">(</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="p">)</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsackDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 0-1 ナップサック：総当たり探索 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">knapsackDFS</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">wgt</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="c1">// すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">    </span><span class="c1">// ナップサック容量を超える場合は、入れない選択しかできない</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="c1">// 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">    </span><span class="c1">// 2つの案のうち価値が大きいほうを返す</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">myMax</span><span class="p">(</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="p">);</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">knapsackDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 0-1 ナップサック：総当たり探索 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">knapsackDFS</span><span class="p">(</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="n">_val</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="n">c</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">    </span><span class="c1">// すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">    </span><span class="c1">// ナップサック容量を超える場合は、入れない選択しかできない</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">    </span><span class="c1">// 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">_val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w">    </span><span class="c1">// 2つの案のうち価値が大きいほうを返す</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="p">)</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">knapsack_dfs</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 0-1 ナップサック: 全探索 ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">knapsack_dfs</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="c1"># ナップサック容量を超える場合は、入れない選択しかできない</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">knapsack_dfs</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">  </span><span class="c1"># 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">  </span><span class="n">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsack_dfs</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">  </span><span class="n">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsack_dfs</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">  </span><span class="c1"># 2つの案のうち価値が大きいほうを返す</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">  </span><span class="o">[</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="o">].</span><span class="n">max</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>下の図に示すように、各アイテムは選択しないと選択するという2つの探索分岐を生成するため、時間計算量は <span class="arithmatex">\(O(2^n)\)</span> です。</p>
-<p>再帰木を観察すると、<span class="arithmatex">\(dp[1, 10]\)</span> などの重複する部分問題があることが容易にわかります。アイテムが多く、ナップサック容量が大きい場合、特に同じ重量のアイテムが多い場合、重複する部分問題の数は大幅に増加します。</p>
-<p><img alt="0-1ナップサック問題の力任せ探索再帰木" class="animation-figure" src="../knapsack_problem.assets/knapsack_dfs.png" /></p>
-<p align="center"> 図 14-18 &nbsp; 0-1ナップサック問題の力任せ探索再帰木 </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20knapsack_dfs%28wgt%3A%20list%5Bint%5D%2C%20val%3A%20list%5Bint%5D%2C%20i%3A%20int%2C%20c%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%220-1%20%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%EF%BC%9A%E7%B7%8F%E5%BD%93%E3%81%9F%E3%82%8A%E6%8E%A2%E7%B4%A2%22%22%22%0A%20%20%20%20%23%20%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E5%93%81%E7%89%A9%E3%82%92%E9%81%B8%E3%81%B3%E7%B5%82%E3%81%88%E3%81%9F%E3%81%8B%E3%80%81%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E3%81%AB%E6%AE%8B%E3%82%8A%E5%AE%B9%E9%87%8F%E3%81%8C%E3%81%AA%E3%81%91%E3%82%8C%E3%81%B0%E3%80%81%E4%BE%A1%E5%80%A4%200%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20if%20i%20%3D%3D%200%20or%20c%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20return%200%0A%20%20%20%20%23%20%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E5%A0%B4%E5%90%88%E3%81%AF%E3%80%81%E5%85%A5%E3%82%8C%E3%81%AA%E3%81%84%E9%81%B8%E6%8A%9E%E3%81%97%E3%81%8B%E3%81%A7%E3%81%8D%E3%81%AA%E3%81%84%0A%20%20%20%20if%20wgt%5Bi%20-%201%5D%20%3E%20c%3A%0A%20%20%20%20%20%20%20%20return%20knapsack_dfs%28wgt%2C%20val%2C%20i%20-%201%2C%20c%29%0A%20%20%20%20%23%20%E5%93%81%E7%89%A9%20i%20%E3%82%92%E5%85%A5%E3%82%8C%E3%81%AA%E3%81%84%E5%A0%B4%E5%90%88%E3%81%A8%E5%85%A5%E3%82%8C%E3%82%8B%E5%A0%B4%E5%90%88%E3%81%AE%E6%9C%80%E5%A4%A7%E4%BE%A1%E5%80%A4%E3%82%92%E8%A8%88%E7%AE%97%E3%81%99%E3%82%8B%0A%20%20%20%20no%20%3D%20knapsack_dfs%28wgt%2C%20val%2C%20i%20-%201%2C%20c%29%0A%20%20%20%20yes%20%3D%20knapsack_dfs%28wgt%2C%20val%2C%20i%20-%201%2C%20c%20-%20wgt%5Bi%20-%201%5D%29%20%2B%20val%5Bi%20-%201%5D%0A%20%20%20%20%23%202%E3%81%A4%E3%81%AE%E6%A1%88%E3%81%AE%E3%81%86%E3%81%A1%E4%BE%A1%E5%80%A4%E3%81%8C%E5%A4%A7%E3%81%8D%E3%81%84%E3%81%BB%E3%81%86%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20max%28no%2C%20yes%29%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20wgt%20%3D%20%5B10%2C%2020%2C%2030%2C%2040%2C%2050%5D%0A%20%20%20%20val%20%3D%20%5B50%2C%20120%2C%20150%2C%20210%2C%20240%5D%0A%20%20%20%20cap%20%3D%2050%0A%20%20%20%20n%20%3D%20len%28wgt%29%0A%0A%20%20%20%20%23%20%E5%85%A8%E6%8E%A2%E7%B4%A2%0A%20%20%20%20res%20%3D%20knapsack_dfs%28wgt%2C%20val%2C%20n%2C%20cap%29%0A%20%20%20%20print%28f%22%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%81%AA%E3%81%84%E6%9C%80%E5%A4%A7%E4%BE%A1%E5%80%A4%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=7&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20knapsack_dfs%28wgt%3A%20list%5Bint%5D%2C%20val%3A%20list%5Bint%5D%2C%20i%3A%20int%2C%20c%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%220-1%20%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%EF%BC%9A%E7%B7%8F%E5%BD%93%E3%81%9F%E3%82%8A%E6%8E%A2%E7%B4%A2%22%22%22%0A%20%20%20%20%23%20%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E5%93%81%E7%89%A9%E3%82%92%E9%81%B8%E3%81%B3%E7%B5%82%E3%81%88%E3%81%9F%E3%81%8B%E3%80%81%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E3%81%AB%E6%AE%8B%E3%82%8A%E5%AE%B9%E9%87%8F%E3%81%8C%E3%81%AA%E3%81%91%E3%82%8C%E3%81%B0%E3%80%81%E4%BE%A1%E5%80%A4%200%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20if%20i%20%3D%3D%200%20or%20c%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20return%200%0A%20%20%20%20%23%20%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E5%A0%B4%E5%90%88%E3%81%AF%E3%80%81%E5%85%A5%E3%82%8C%E3%81%AA%E3%81%84%E9%81%B8%E6%8A%9E%E3%81%97%E3%81%8B%E3%81%A7%E3%81%8D%E3%81%AA%E3%81%84%0A%20%20%20%20if%20wgt%5Bi%20-%201%5D%20%3E%20c%3A%0A%20%20%20%20%20%20%20%20return%20knapsack_dfs%28wgt%2C%20val%2C%20i%20-%201%2C%20c%29%0A%20%20%20%20%23%20%E5%93%81%E7%89%A9%20i%20%E3%82%92%E5%85%A5%E3%82%8C%E3%81%AA%E3%81%84%E5%A0%B4%E5%90%88%E3%81%A8%E5%85%A5%E3%82%8C%E3%82%8B%E5%A0%B4%E5%90%88%E3%81%AE%E6%9C%80%E5%A4%A7%E4%BE%A1%E5%80%A4%E3%82%92%E8%A8%88%E7%AE%97%E3%81%99%E3%82%8B%0A%20%20%20%20no%20%3D%20knapsack_dfs%28wgt%2C%20val%2C%20i%20-%201%2C%20c%29%0A%20%20%20%20yes%20%3D%20knapsack_dfs%28wgt%2C%20val%2C%20i%20-%201%2C%20c%20-%20wgt%5Bi%20-%201%5D%29%20%2B%20val%5Bi%20-%201%5D%0A%20%20%20%20%23%202%E3%81%A4%E3%81%AE%E6%A1%88%E3%81%AE%E3%81%86%E3%81%A1%E4%BE%A1%E5%80%A4%E3%81%8C%E5%A4%A7%E3%81%8D%E3%81%84%E3%81%BB%E3%81%86%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20max%28no%2C%20yes%29%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20wgt%20%3D%20%5B10%2C%2020%2C%2030%2C%2040%2C%2050%5D%0A%20%20%20%20val%20%3D%20%5B50%2C%20120%2C%20150%2C%20210%2C%20240%5D%0A%20%20%20%20cap%20%3D%2050%0A%20%20%20%20n%20%3D%20len%28wgt%29%0A%0A%20%20%20%20%23%20%E5%85%A8%E6%8E%A2%E7%B4%A2%0A%20%20%20%20res%20%3D%20knapsack_dfs%28wgt%2C%20val%2C%20n%2C%20cap%29%0A%20%20%20%20print%28f%22%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%81%AA%E3%81%84%E6%9C%80%E5%A4%A7%E4%BE%A1%E5%80%A4%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=7&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>以下の図のように、各品物ごとに「選ばない」「選ぶ」の2つの探索分岐が生じるため、時間計算量は <span class="arithmatex">\(O(2^n)\)</span> です。</p>
+<p>再帰木を観察すると、<span class="arithmatex">\(dp[1, 10]\)</span> などの重複部分問題が存在することが分かります。品物数が多く、ナップサック容量が大きく、特に同じ重さの品物が多い場合には、重複部分問題の数は大幅に増加します。</p>
+<p><img alt="0-1 ナップサック問題の全探索の再帰木" class="animation-figure" src="../knapsack_problem.assets/knapsack_dfs.png" /></p>
+<p align="center"> 図 14-18 &nbsp; 0-1 ナップサック問題の全探索の再帰木 </p>
 
 <h3 id="2-2">2. &nbsp; 方法2：メモ化探索<a class="headerlink" href="#2-2" title="Permanent link">&para;</a></h3>
-<p>重複する部分問題が一度だけ計算されることを確保するために、部分問題の解を記録するメモ化リスト <code>mem</code> を使用します。ここで <code>mem[i][c]</code> は <span class="arithmatex">\(dp[i, c]\)</span> に対応します。</p>
-<p>メモ化を導入した後、**時間計算量は部分問題の数に依存**し、<span class="arithmatex">\(O(n \times cap)\)</span> になります。実装コードは以下の通りです：</p>
+<p>重複部分問題が一度だけ計算されるようにするため、メモ配列 <code>mem</code> を用いて部分問題の解を記録します。ここで <code>mem[i][c]</code> は <span class="arithmatex">\(dp[i, c]\)</span> に対応します。</p>
+<p>メモ化を導入すると、<strong>時間計算量は部分問題の数に依存し</strong>、すなわち <span class="arithmatex">\(O(n \times cap)\)</span> になります。実装コードは次のとおりです。</p>
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 <div class="highlight"><span class="filename">knapsack.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">knapsack_dfs_mem</span><span class="p">(</span>
 <a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a>    <span class="n">wgt</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">val</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">mem</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]],</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">c</span><span class="p">:</span> <span class="nb">int</span>
 <a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;0-1 ナップサック：記憶化探索&quot;&quot;&quot;</span>
-<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># すべてのアイテムが選択されたかナップサックに残り容量がない場合、値 0 を返す</span>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;0-1 ナップサック：メモ化探索&quot;&quot;&quot;</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
 <a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>    <span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">c</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
 <a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>        <span class="k">return</span> <span class="mi">0</span>
-<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>    <span class="c1"># 記録がある場合、それを返す</span>
+<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>    <span class="c1"># 既に記録があればそのまま返す</span>
 <a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>    <span class="k">if</span> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span> <span class="o">!=</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span>
 <a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>        <span class="k">return</span> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span>
-<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>    <span class="c1"># ナップサック容量を超える場合、ナップサックに入れないことしか選択できない</span>
+<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>    <span class="c1"># ナップサック容量を超える場合は、入れない選択しかできない</span>
 <a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>    <span class="k">if</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">c</span><span class="p">:</span>
 <a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a>        <span class="k">return</span> <span class="n">knapsack_dfs_mem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span> <span class="n">val</span><span class="p">,</span> <span class="n">mem</span><span class="p">,</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">c</span><span class="p">)</span>
-<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>    <span class="c1"># アイテム i を入れないのと入れるのとの最大値を計算</span>
+<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>    <span class="c1"># 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
 <a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a>    <span class="n">no</span> <span class="o">=</span> <span class="n">knapsack_dfs_mem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span> <span class="n">val</span><span class="p">,</span> <span class="n">mem</span><span class="p">,</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">c</span><span class="p">)</span>
 <a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a>    <span class="n">yes</span> <span class="o">=</span> <span class="n">knapsack_dfs_mem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span> <span class="n">val</span><span class="p">,</span> <span class="n">mem</span><span class="p">,</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">c</span> <span class="o">-</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span> <span class="o">+</span> <span class="n">val</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span>
-<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>    <span class="c1"># 2 つの選択肢のうち大きい値を記録して返す</span>
+<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>    <span class="c1"># 2 つの案のうち価値が大きい方を記録して返す</span>
 <a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a>    <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">no</span><span class="p">,</span> <span class="n">yes</span><span class="p">)</span>
 <a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a>    <span class="k">return</span> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="p">[</span><span class="k">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsackDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 0-1 ナップサック：メモ化探索 */</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">knapsackDFSMem</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="c1">// すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">    </span><span class="c1">// 既に記録があればそのまま返す</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">-1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">];</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">    </span><span class="c1">// ナップサック容量を超える場合は、入れない選択しかできない</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">    </span><span class="c1">// 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
+<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w">    </span><span class="c1">// 2 つの案のうち価値が大きい方を記録して返す</span>
+<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w">    </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="p">);</span>
+<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">];</span>
+<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">knapsack.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 0-1 ナップサック：メモ化探索 */</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">knapsackDFSMem</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// すべてのアイテムが選択されたか、ナップサックに残り容量がない場合、値 0 を返す</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
 <a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="c1">// 記録がある場合、それを返す</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="c1">// 既に記録があればそのまま返す</span>
 <a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">    </span><span class="c1">// ナップサックの容量を超える場合、ナップサックに入れないことしか選択できない</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">    </span><span class="c1">// ナップサック容量を超える場合は、入れない選択しかできない</span>
 <a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
 <a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="c1">// アイテム i を入れない場合と入れる場合の最大値を計算</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="c1">// 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
 <a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
 <a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">    </span><span class="c1">// 2つの選択肢のより大きい値を記録して返す</span>
+<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">    </span><span class="c1">// 2 つの案のうち価値が大きい方を記録して返す</span>
 <a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w">    </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">max</span><span class="p">(</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="p">);</span>
 <a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">knapsack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">KnapsackDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 0-1 ナップサック：メモ化探索 */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">KnapsackDFSMem</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">weight</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="p">[][]</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="c1">// すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="c1">// 既に記録があればそのまま返す</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">];</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">    </span><span class="c1">// ナップサック容量を超える場合は、入れない選択しかできない</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">weight</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nf">KnapsackDFSMem</span><span class="p">(</span><span class="n">weight</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">    </span><span class="c1">// 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">KnapsackDFSMem</span><span class="p">(</span><span class="n">weight</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">KnapsackDFSMem</span><span class="p">(</span><span class="n">weight</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">weight</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">    </span><span class="c1">// 2 つの案のうち価値が大きい方を記録して返す</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w">    </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Max</span><span class="p">(</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="p">);</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">];</span>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">knapsackDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 0-1 ナップサック：メモ化探索 */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">knapsackDFSMem</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="w"> </span><span class="p">[][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="c1">// すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">    </span><span class="c1">// 既に記録があればそのまま返す</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w">    </span><span class="c1">// ナップサック容量を超える場合は、入れない選択しかできない</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">knapsackDFSMem</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="p">)</span>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">    </span><span class="c1">// 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w">    </span><span class="nx">no</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">knapsackDFSMem</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="p">)</span>
+<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="w">    </span><span class="nx">yes</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">knapsackDFSMem</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="o">-</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="w">    </span><span class="c1">// 2つの案のうち価値が大きいほうを返す</span>
+<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="w">    </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Max</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">no</span><span class="p">),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">yes</span><span class="p">)))</span>
+<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span>
+<a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">knapsackDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 0-1 ナップサック：メモ化探索 */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">mem</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[[</span><span class="nb">Int</span><span class="p">]],</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="c1">// すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">    </span><span class="c1">// 既に記録があればそのまま返す</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w">    </span><span class="c1">// ナップサック容量を超える場合は、入れない選択しかできない</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">:</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
+<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w">    </span><span class="c1">// 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
+<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">no</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">:</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
+<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">yes</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">:</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="w">    </span><span class="c1">// 2 つの案のうち価値が大きい方を記録して返す</span>
+<a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a><span class="w">    </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">max</span><span class="p">(</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="p">)</span>
+<a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span>
+<a id="__codelineno-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">knapsackDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 0-1 ナップサック：メモ化探索 */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">knapsackDFSMem</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="c1">// すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">    </span><span class="c1">// 既に記録があればそのまま返す</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">];</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w">    </span><span class="c1">// ナップサック容量を超える場合は、入れない選択しかできない</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">knapsackDFSMem</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="p">);</span>
+<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w">    </span><span class="c1">// 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
+<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">knapsackDFSMem</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="p">);</span>
+<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">yes</span><span class="w"> </span><span class="o">=</span>
+<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a><span class="w">        </span><span class="nx">knapsackDFSMem</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a><span class="w">    </span><span class="c1">// 2 つの案のうち価値が大きい方を記録して返す</span>
+<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a><span class="w">    </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">max</span><span class="p">(</span><span class="nx">no</span><span class="p">,</span><span class="w"> </span><span class="nx">yes</span><span class="p">);</span>
+<a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">];</span>
+<a id="__codelineno-19-22" name="__codelineno-19-22" href="#__codelineno-19-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">knapsackDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 0-1 ナップサック：メモ化探索 */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">knapsackDFSMem</span><span class="p">(</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="nx">wgt</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">    </span><span class="nx">mem</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="nb">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">    </span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">    </span><span class="nx">c</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">    </span><span class="c1">// すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w">    </span><span class="c1">// 既に記録があればそのまま返す</span>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">];</span>
+<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-17" name="__codelineno-20-17" href="#__codelineno-20-17"></a><span class="w">    </span><span class="c1">// ナップサック容量を超える場合は、入れない選択しかできない</span>
+<a id="__codelineno-20-18" name="__codelineno-20-18" href="#__codelineno-20-18"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-19" name="__codelineno-20-19" href="#__codelineno-20-19"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">knapsackDFSMem</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="p">);</span>
+<a id="__codelineno-20-20" name="__codelineno-20-20" href="#__codelineno-20-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-21" name="__codelineno-20-21" href="#__codelineno-20-21"></a><span class="w">    </span><span class="c1">// 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
+<a id="__codelineno-20-22" name="__codelineno-20-22" href="#__codelineno-20-22"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">knapsackDFSMem</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="p">);</span>
+<a id="__codelineno-20-23" name="__codelineno-20-23" href="#__codelineno-20-23"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">yes</span><span class="w"> </span><span class="o">=</span>
+<a id="__codelineno-20-24" name="__codelineno-20-24" href="#__codelineno-20-24"></a><span class="w">        </span><span class="nx">knapsackDFSMem</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-20-25" name="__codelineno-20-25" href="#__codelineno-20-25"></a><span class="w">    </span><span class="c1">// 2 つの案のうち価値が大きい方を記録して返す</span>
+<a id="__codelineno-20-26" name="__codelineno-20-26" href="#__codelineno-20-26"></a><span class="w">    </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">max</span><span class="p">(</span><span class="nx">no</span><span class="p">,</span><span class="w"> </span><span class="nx">yes</span><span class="p">);</span>
+<a id="__codelineno-20-27" name="__codelineno-20-27" href="#__codelineno-20-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">];</span>
+<a id="__codelineno-20-28" name="__codelineno-20-28" href="#__codelineno-20-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsackDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 0-1 ナップサック：メモ化探索 */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">val</span><span class="p">,</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="p">,</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">  </span><span class="c1">// すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">  </span><span class="c1">// 既に記録があればそのまま返す</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">];</span>
+<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-17" name="__codelineno-21-17" href="#__codelineno-21-17"></a><span class="w">  </span><span class="c1">// ナップサック容量を超える場合は、入れない選択しかできない</span>
+<a id="__codelineno-21-18" name="__codelineno-21-18" href="#__codelineno-21-18"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-19" name="__codelineno-21-19" href="#__codelineno-21-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
+<a id="__codelineno-21-20" name="__codelineno-21-20" href="#__codelineno-21-20"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-21" name="__codelineno-21-21" href="#__codelineno-21-21"></a><span class="w">  </span><span class="c1">// 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
+<a id="__codelineno-21-22" name="__codelineno-21-22" href="#__codelineno-21-22"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
+<a id="__codelineno-21-23" name="__codelineno-21-23" href="#__codelineno-21-23"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">];</span>
+<a id="__codelineno-21-24" name="__codelineno-21-24" href="#__codelineno-21-24"></a><span class="w">  </span><span class="c1">// 2 つの案のうち価値が大きい方を記録して返す</span>
+<a id="__codelineno-21-25" name="__codelineno-21-25" href="#__codelineno-21-25"></a><span class="w">  </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="p">);</span>
+<a id="__codelineno-21-26" name="__codelineno-21-26" href="#__codelineno-21-26"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">];</span>
+<a id="__codelineno-21-27" name="__codelineno-21-27" href="#__codelineno-21-27"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsack_dfs_mem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 0-1 ナップサック：メモ化探索 */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">knapsack_dfs_mem</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">mem</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="c1">// すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">    </span><span class="c1">// 既に記録があればそのまま返す</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">];</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w">    </span><span class="c1">// ナップサック容量を超える場合は、入れない選択しかできない</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">knapsack_dfs_mem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="w">    </span><span class="c1">// 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
+<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsack_dfs_mem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
+<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsack_dfs_mem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="w">    </span><span class="c1">// 2 つの案のうち価値が大きい方を記録して返す</span>
+<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="w">    </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">max</span><span class="p">(</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="p">);</span>
+<a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a><span class="w">    </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span>
+<a id="__codelineno-22-21" name="__codelineno-22-21" href="#__codelineno-22-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsackDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 0-1 ナップサック：メモ化探索 */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">knapsackDFSMem</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">wgt</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">memCols</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">**</span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="c1">// すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w">    </span><span class="c1">// 既に記録があればそのまま返す</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">-1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">];</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w">    </span><span class="c1">// ナップサック容量を超える場合は、入れない選択しかできない</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">memCols</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="w">    </span><span class="c1">// 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
+<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">memCols</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
+<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">memCols</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="w">    </span><span class="c1">// 2 つの案のうち価値が大きい方を記録して返す</span>
+<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="w">    </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">myMax</span><span class="p">(</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="p">);</span>
+<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">];</span>
+<a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">knapsackDFSMem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 0-1 ナップサック：メモ化探索 */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">knapsackDFSMem</span><span class="p">(</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="n">_val</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">    </span><span class="n">mem</span><span class="p">:</span><span class="w"> </span><span class="n">Array</span><span class="o">&lt;</span><span class="n">IntArray</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">    </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w">    </span><span class="n">c</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w">    </span><span class="c1">// すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w">    </span><span class="c1">// 既に記録があればそのまま返す</span>
+<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span>
+<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-17" name="__codelineno-24-17" href="#__codelineno-24-17"></a><span class="w">    </span><span class="c1">// ナップサック容量を超える場合は、入れない選択しかできない</span>
+<a id="__codelineno-24-18" name="__codelineno-24-18" href="#__codelineno-24-18"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-19" name="__codelineno-24-19" href="#__codelineno-24-19"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
+<a id="__codelineno-24-20" name="__codelineno-24-20" href="#__codelineno-24-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-21" name="__codelineno-24-21" href="#__codelineno-24-21"></a><span class="w">    </span><span class="c1">// 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
+<a id="__codelineno-24-22" name="__codelineno-24-22" href="#__codelineno-24-22"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
+<a id="__codelineno-24-23" name="__codelineno-24-23" href="#__codelineno-24-23"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">_val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span>
+<a id="__codelineno-24-24" name="__codelineno-24-24" href="#__codelineno-24-24"></a><span class="w">    </span><span class="c1">// 2 つの案のうち価値が大きい方を記録して返す</span>
+<a id="__codelineno-24-25" name="__codelineno-24-25" href="#__codelineno-24-25"></a><span class="w">    </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="p">)</span>
+<a id="__codelineno-24-26" name="__codelineno-24-26" href="#__codelineno-24-26"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span>
+<a id="__codelineno-24-27" name="__codelineno-24-27" href="#__codelineno-24-27"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">knapsack_dfs_mem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### 0-1 ナップサック: メモ化探索 ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">knapsack_dfs_mem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="c1"># すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">  </span><span class="c1"># 既に記録があればそのまま返す</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">  </span><span class="c1"># ナップサック容量を超える場合は、入れない選択しかできない</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">knapsack_dfs_mem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">  </span><span class="c1"># 品物 i を入れない場合と入れる場合の最大価値を計算する</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w">  </span><span class="n">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsack_dfs_mem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w">  </span><span class="n">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsack_dfs_mem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w">  </span><span class="c1"># 2 つの案のうち価値が大きい方を記録して返す</span>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w">  </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="o">].</span><span class="n">max</span>
+<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>下の図はメモ化探索で枝刈りされる探索分岐を示しています。</p>
-<p><img alt="0-1ナップサック問題のメモ化探索再帰木" class="animation-figure" src="../knapsack_problem.assets/knapsack_dfs_mem.png" /></p>
-<p align="center"> 図 14-19 &nbsp; 0-1ナップサック問題のメモ化探索再帰木 </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20knapsack_dfs_mem%28%0A%20%20%20%20wgt%3A%20list%5Bint%5D%2C%20val%3A%20list%5Bint%5D%2C%20mem%3A%20list%5Blist%5Bint%5D%5D%2C%20i%3A%20int%2C%20c%3A%20int%0A%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%220-1%20%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%EF%BC%9A%E3%83%A1%E3%83%A2%E5%8C%96%E6%8E%A2%E7%B4%A2%22%22%22%0A%20%20%20%20%23%20%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E5%93%81%E7%89%A9%E3%82%92%E9%81%B8%E3%81%B3%E7%B5%82%E3%81%88%E3%81%9F%E3%81%8B%E3%80%81%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E3%81%AB%E6%AE%8B%E3%82%8A%E5%AE%B9%E9%87%8F%E3%81%8C%E3%81%AA%E3%81%91%E3%82%8C%E3%81%B0%E3%80%81%E4%BE%A1%E5%80%A4%200%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20if%20i%20%3D%3D%200%20or%20c%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20return%200%0A%20%20%20%20%23%20%E6%97%A2%E3%81%AB%E8%A8%98%E9%8C%B2%E3%81%8C%E3%81%82%E3%82%8C%E3%81%B0%E3%81%9D%E3%81%AE%E3%81%BE%E3%81%BE%E8%BF%94%E3%81%99%0A%20%20%20%20if%20mem%5Bi%5D%5Bc%5D%20%21%3D%20-1%3A%0A%20%20%20%20%20%20%20%20return%20mem%5Bi%5D%5Bc%5D%0A%20%20%20%20%23%20%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E5%A0%B4%E5%90%88%E3%81%AF%E3%80%81%E5%85%A5%E3%82%8C%E3%81%AA%E3%81%84%E9%81%B8%E6%8A%9E%E3%81%97%E3%81%8B%E3%81%A7%E3%81%8D%E3%81%AA%E3%81%84%0A%20%20%20%20if%20wgt%5Bi%20-%201%5D%20%3E%20c%3A%0A%20%20%20%20%20%20%20%20return%20knapsack_dfs_mem%28wgt%2C%20val%2C%20mem%2C%20i%20-%201%2C%20c%29%0A%20%20%20%20%23%20%E5%93%81%E7%89%A9%20i%20%E3%82%92%E5%85%A5%E3%82%8C%E3%81%AA%E3%81%84%E5%A0%B4%E5%90%88%E3%81%A8%E5%85%A5%E3%82%8C%E3%82%8B%E5%A0%B4%E5%90%88%E3%81%AE%E6%9C%80%E5%A4%A7%E4%BE%A1%E5%80%A4%E3%82%92%E8%A8%88%E7%AE%97%E3%81%99%E3%82%8B%0A%20%20%20%20no%20%3D%20knapsack_dfs_mem%28wgt%2C%20val%2C%20mem%2C%20i%20-%201%2C%20c%29%0A%20%20%20%20yes%20%3D%20knapsack_dfs_mem%28wgt%2C%20val%2C%20mem%2C%20i%20-%201%2C%20c%20-%20wgt%5Bi%20-%201%5D%29%20%2B%20val%5Bi%20-%201%5D%0A%20%20%20%20%23%202%20%E3%81%A4%E3%81%AE%E6%A1%88%E3%81%AE%E3%81%86%E3%81%A1%E4%BE%A1%E5%80%A4%E3%81%8C%E5%A4%A7%E3%81%8D%E3%81%84%E6%96%B9%E3%82%92%E8%A8%98%E9%8C%B2%E3%81%97%E3%81%A6%E8%BF%94%E3%81%99%0A%20%20%20%20mem%5Bi%5D%5Bc%5D%20%3D%20max%28no%2C%20yes%29%0A%20%20%20%20return%20mem%5Bi%5D%5Bc%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20wgt%20%3D%20%5B10%2C%2020%2C%2030%2C%2040%2C%2050%5D%0A%20%20%20%20val%20%3D%20%5B50%2C%20120%2C%20150%2C%20210%2C%20240%5D%0A%20%20%20%20cap%20%3D%2050%0A%20%20%20%20n%20%3D%20len%28wgt%29%0A%0A%20%20%20%20%23%20%E3%83%A1%E3%83%A2%E5%8C%96%E6%8E%A2%E7%B4%A2%0A%20%20%20%20mem%20%3D%20%5B%5B-1%5D%20%2A%20%28cap%20%2B%201%29%20for%20_%20in%20range%28n%20%2B%201%29%5D%0A%20%20%20%20res%20%3D%20knapsack_dfs_mem%28wgt%2C%20val%2C%20mem%2C%20n%2C%20cap%29%0A%20%20%20%20print%28f%22%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%81%AA%E3%81%84%E6%9C%80%E5%A4%A7%E4%BE%A1%E5%80%A4%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=20&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20knapsack_dfs_mem%28%0A%20%20%20%20wgt%3A%20list%5Bint%5D%2C%20val%3A%20list%5Bint%5D%2C%20mem%3A%20list%5Blist%5Bint%5D%5D%2C%20i%3A%20int%2C%20c%3A%20int%0A%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%220-1%20%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%EF%BC%9A%E3%83%A1%E3%83%A2%E5%8C%96%E6%8E%A2%E7%B4%A2%22%22%22%0A%20%20%20%20%23%20%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E5%93%81%E7%89%A9%E3%82%92%E9%81%B8%E3%81%B3%E7%B5%82%E3%81%88%E3%81%9F%E3%81%8B%E3%80%81%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E3%81%AB%E6%AE%8B%E3%82%8A%E5%AE%B9%E9%87%8F%E3%81%8C%E3%81%AA%E3%81%91%E3%82%8C%E3%81%B0%E3%80%81%E4%BE%A1%E5%80%A4%200%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20if%20i%20%3D%3D%200%20or%20c%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20return%200%0A%20%20%20%20%23%20%E6%97%A2%E3%81%AB%E8%A8%98%E9%8C%B2%E3%81%8C%E3%81%82%E3%82%8C%E3%81%B0%E3%81%9D%E3%81%AE%E3%81%BE%E3%81%BE%E8%BF%94%E3%81%99%0A%20%20%20%20if%20mem%5Bi%5D%5Bc%5D%20%21%3D%20-1%3A%0A%20%20%20%20%20%20%20%20return%20mem%5Bi%5D%5Bc%5D%0A%20%20%20%20%23%20%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E5%A0%B4%E5%90%88%E3%81%AF%E3%80%81%E5%85%A5%E3%82%8C%E3%81%AA%E3%81%84%E9%81%B8%E6%8A%9E%E3%81%97%E3%81%8B%E3%81%A7%E3%81%8D%E3%81%AA%E3%81%84%0A%20%20%20%20if%20wgt%5Bi%20-%201%5D%20%3E%20c%3A%0A%20%20%20%20%20%20%20%20return%20knapsack_dfs_mem%28wgt%2C%20val%2C%20mem%2C%20i%20-%201%2C%20c%29%0A%20%20%20%20%23%20%E5%93%81%E7%89%A9%20i%20%E3%82%92%E5%85%A5%E3%82%8C%E3%81%AA%E3%81%84%E5%A0%B4%E5%90%88%E3%81%A8%E5%85%A5%E3%82%8C%E3%82%8B%E5%A0%B4%E5%90%88%E3%81%AE%E6%9C%80%E5%A4%A7%E4%BE%A1%E5%80%A4%E3%82%92%E8%A8%88%E7%AE%97%E3%81%99%E3%82%8B%0A%20%20%20%20no%20%3D%20knapsack_dfs_mem%28wgt%2C%20val%2C%20mem%2C%20i%20-%201%2C%20c%29%0A%20%20%20%20yes%20%3D%20knapsack_dfs_mem%28wgt%2C%20val%2C%20mem%2C%20i%20-%201%2C%20c%20-%20wgt%5Bi%20-%201%5D%29%20%2B%20val%5Bi%20-%201%5D%0A%20%20%20%20%23%202%20%E3%81%A4%E3%81%AE%E6%A1%88%E3%81%AE%E3%81%86%E3%81%A1%E4%BE%A1%E5%80%A4%E3%81%8C%E5%A4%A7%E3%81%8D%E3%81%84%E6%96%B9%E3%82%92%E8%A8%98%E9%8C%B2%E3%81%97%E3%81%A6%E8%BF%94%E3%81%99%0A%20%20%20%20mem%5Bi%5D%5Bc%5D%20%3D%20max%28no%2C%20yes%29%0A%20%20%20%20return%20mem%5Bi%5D%5Bc%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20wgt%20%3D%20%5B10%2C%2020%2C%2030%2C%2040%2C%2050%5D%0A%20%20%20%20val%20%3D%20%5B50%2C%20120%2C%20150%2C%20210%2C%20240%5D%0A%20%20%20%20cap%20%3D%2050%0A%20%20%20%20n%20%3D%20len%28wgt%29%0A%0A%20%20%20%20%23%20%E3%83%A1%E3%83%A2%E5%8C%96%E6%8E%A2%E7%B4%A2%0A%20%20%20%20mem%20%3D%20%5B%5B-1%5D%20%2A%20%28cap%20%2B%201%29%20for%20_%20in%20range%28n%20%2B%201%29%5D%0A%20%20%20%20res%20%3D%20knapsack_dfs_mem%28wgt%2C%20val%2C%20mem%2C%20n%2C%20cap%29%0A%20%20%20%20print%28f%22%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%81%AA%E3%81%84%E6%9C%80%E5%A4%A7%E4%BE%A1%E5%80%A4%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=20&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>次の図は、メモ化探索で剪定された探索分岐を示しています。</p>
+<p><img alt="0-1 ナップサック問題のメモ化探索の再帰木" class="animation-figure" src="../knapsack_problem.assets/knapsack_dfs_mem.png" /></p>
+<p align="center"> 図 14-19 &nbsp; 0-1 ナップサック問題のメモ化探索の再帰木 </p>
 
-<h3 id="3-3">3. &nbsp; 方法3：動的プログラミング<a class="headerlink" href="#3-3" title="Permanent link">&para;</a></h3>
-<p>動的プログラミングは本質的に状態遷移中に <span class="arithmatex">\(dp\)</span> テーブルを埋めることを含みます。コードは下の図に示されています：</p>
+<h3 id="3-3">3. &nbsp; 方法3：動的計画法<a class="headerlink" href="#3-3" title="Permanent link">&para;</a></h3>
+<p>動的計画法の本質は、状態遷移に従って <span class="arithmatex">\(dp\)</span> テーブルを埋めていく過程です。コードは次のようになります。</p>
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 <div class="highlight"><span class="filename">knapsack.py</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">knapsack_dp</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">val</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">cap</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;0-1 ナップサック：動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;0-1 ナップサック：動的計画法&quot;&quot;&quot;</span>
 <a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">wgt</span><span class="p">)</span>
 <a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>    <span class="c1"># dp テーブルを初期化</span>
 <a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">cap</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span>
@@ -4656,28 +5055,28 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
 <a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>        <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">cap</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a>            <span class="k">if</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">c</span><span class="p">:</span>
-<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a>                <span class="c1"># ナップサック容量を超える場合、アイテム i を選択しない</span>
+<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a>                <span class="c1"># ナップサック容量を超えるなら品物 i は選ばない</span>
 <a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">]</span>
 <a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a>            <span class="k">else</span><span class="p">:</span>
-<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a>                <span class="c1"># アイテム i を選択しないのと選択するのとで大きい値</span>
+<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a>                <span class="c1"># 品物 i を選ばない場合と選ぶ場合の大きい方</span>
 <a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">c</span> <span class="o">-</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span> <span class="o">+</span> <span class="n">val</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span>
 <a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">cap</span><span class="p">]</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* 0-1 ナップサック：動的プログラミング */</span>
+<div class="highlight"><span class="filename">knapsack.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* 0-1 ナップサック：動的計画法 */</span>
 <a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">knapsackDP</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
-<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
 <a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">));</span>
 <a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
 <a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a><span class="w">                </span><span class="c1">// ナップサックの容量を超える場合、アイテム i を選択しない</span>
+<a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
 <a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">];</span>
 <a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w">                </span><span class="c1">// 選択しない場合とアイテム i を選択する場合のより大きい値</span>
+<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
 <a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
 <a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></a><span class="w">        </span><span class="p">}</span>
@@ -4687,19 +5086,19 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 0-1 ナップサック：動的プログラミング */</span>
+<div class="highlight"><span class="filename">knapsack.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 0-1 ナップサック：動的計画法 */</span>
 <a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">knapsackDP</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
-<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
 <a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">    </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
 <a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="w">                </span><span class="c1">// ナップサックの容量を超える場合、アイテム i を選択しない</span>
+<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
 <a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w">                </span><span class="c1">// 選択しない場合とアイテム i を選択する場合のより大きい値</span>
+<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
 <a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">max</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">);</span>
 <a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a><span class="w">        </span><span class="p">}</span>
@@ -4709,52 +5108,265 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">knapsack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">KnapsackDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 0-1 ナップサック：動的計画法 */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">KnapsackDP</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">weight</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">weight</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">    </span><span class="kt">int</span><span class="p">[,]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">weight</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">];</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">weight</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">]);</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">];</span>
+<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">knapsackDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 0-1 ナップサック：動的計画法 */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">knapsackDP</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">wgt</span><span class="p">)</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">    </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">cap</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Max</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">c</span><span class="p">]),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">c</span><span class="o">-</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]]</span><span class="o">+</span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">])))</span>
+<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-21" name="__codelineno-30-21" href="#__codelineno-30-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">cap</span><span class="p">]</span>
+<a id="__codelineno-30-22" name="__codelineno-30-22" href="#__codelineno-30-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">knapsackDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* 0-1 ナップサック：動的計画法 */</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">knapsackDP</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">cap</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">),</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">]</span>
+<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span>
+<a id="__codelineno-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-31-16" name="__codelineno-31-16" href="#__codelineno-31-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-31-17" name="__codelineno-31-17" href="#__codelineno-31-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-18" name="__codelineno-31-18" href="#__codelineno-31-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">cap</span><span class="p">]</span>
+<a id="__codelineno-31-19" name="__codelineno-31-19" href="#__codelineno-31-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">knapsackDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* 0-1 ナップサック：動的計画法 */</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">knapsackDP</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">wgt</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span>
+<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="w">        </span><span class="p">.</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">)</span>
+<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="w">        </span><span class="p">.</span><span class="nx">map</span><span class="p">(()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">));</span>
+<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-10" name="__codelineno-32-10" href="#__codelineno-32-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">cap</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">c</span><span class="p">];</span>
+<a id="__codelineno-32-14" name="__codelineno-32-14" href="#__codelineno-32-14"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-15" name="__codelineno-32-15" href="#__codelineno-32-15"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-32-16" name="__codelineno-32-16" href="#__codelineno-32-16"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">max</span><span class="p">(</span>
+<a id="__codelineno-32-17" name="__codelineno-32-17" href="#__codelineno-32-17"></a><span class="w">                    </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">c</span><span class="p">],</span>
+<a id="__codelineno-32-18" name="__codelineno-32-18" href="#__codelineno-32-18"></a><span class="w">                    </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span>
+<a id="__codelineno-32-19" name="__codelineno-32-19" href="#__codelineno-32-19"></a><span class="w">                </span><span class="p">);</span>
+<a id="__codelineno-32-20" name="__codelineno-32-20" href="#__codelineno-32-20"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-32-21" name="__codelineno-32-21" href="#__codelineno-32-21"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-32-22" name="__codelineno-32-22" href="#__codelineno-32-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-23" name="__codelineno-32-23" href="#__codelineno-32-23"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">cap</span><span class="p">];</span>
+<a id="__codelineno-32-24" name="__codelineno-32-24" href="#__codelineno-32-24"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">knapsackDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* 0-1 ナップサック：動的計画法 */</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">knapsackDP</span><span class="p">(</span>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w">    </span><span class="nx">wgt</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w">    </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w">    </span><span class="nx">cap</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span>
+<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">wgt</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="kt">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span>
+<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a><span class="w">        </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="kt">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span>
+<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="w">    </span><span class="p">);</span>
+<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">cap</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-16" name="__codelineno-33-16" href="#__codelineno-33-16"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-33-17" name="__codelineno-33-17" href="#__codelineno-33-17"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">c</span><span class="p">];</span>
+<a id="__codelineno-33-18" name="__codelineno-33-18" href="#__codelineno-33-18"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-19" name="__codelineno-33-19" href="#__codelineno-33-19"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-33-20" name="__codelineno-33-20" href="#__codelineno-33-20"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">max</span><span class="p">(</span>
+<a id="__codelineno-33-21" name="__codelineno-33-21" href="#__codelineno-33-21"></a><span class="w">                    </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">c</span><span class="p">],</span>
+<a id="__codelineno-33-22" name="__codelineno-33-22" href="#__codelineno-33-22"></a><span class="w">                    </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span>
+<a id="__codelineno-33-23" name="__codelineno-33-23" href="#__codelineno-33-23"></a><span class="w">                </span><span class="p">);</span>
+<a id="__codelineno-33-24" name="__codelineno-33-24" href="#__codelineno-33-24"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-33-25" name="__codelineno-33-25" href="#__codelineno-33-25"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-33-26" name="__codelineno-33-26" href="#__codelineno-33-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-27" name="__codelineno-33-27" href="#__codelineno-33-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">cap</span><span class="p">];</span>
+<a id="__codelineno-33-28" name="__codelineno-33-28" href="#__codelineno-33-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsackDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* 0-1 ナップサック：動的計画法 */</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">knapsackDP</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w">  </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">generate</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">));</span>
+<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="w">  </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-10" name="__codelineno-34-10" href="#__codelineno-34-10"></a><span class="w">        </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-34-11" name="__codelineno-34-11" href="#__codelineno-34-11"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">][</span><span class="n">c</span><span class="p">];</span>
+<a id="__codelineno-34-12" name="__codelineno-34-12" href="#__codelineno-34-12"></a><span class="w">      </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-13" name="__codelineno-34-13" href="#__codelineno-34-13"></a><span class="w">        </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-34-14" name="__codelineno-34-14" href="#__codelineno-34-14"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">][</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]);</span>
+<a id="__codelineno-34-15" name="__codelineno-34-15" href="#__codelineno-34-15"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-34-16" name="__codelineno-34-16" href="#__codelineno-34-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-17" name="__codelineno-34-17" href="#__codelineno-34-17"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-18" name="__codelineno-34-18" href="#__codelineno-34-18"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">cap</span><span class="p">];</span>
+<a id="__codelineno-34-19" name="__codelineno-34-19" href="#__codelineno-34-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsack_dp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* 0-1 ナップサック：動的計画法 */</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">knapsack_dp</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">cap</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
+<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">cap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">];</span>
+<a id="__codelineno-35-12" name="__codelineno-35-12" href="#__codelineno-35-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-13" name="__codelineno-35-13" href="#__codelineno-35-13"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-35-14" name="__codelineno-35-14" href="#__codelineno-35-14"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">max</span><span class="p">(</span>
+<a id="__codelineno-35-15" name="__codelineno-35-15" href="#__codelineno-35-15"></a><span class="w">                    </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">],</span>
+<a id="__codelineno-35-16" name="__codelineno-35-16" href="#__codelineno-35-16"></a><span class="w">                    </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span>
+<a id="__codelineno-35-17" name="__codelineno-35-17" href="#__codelineno-35-17"></a><span class="w">                </span><span class="p">);</span>
+<a id="__codelineno-35-18" name="__codelineno-35-18" href="#__codelineno-35-18"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-35-19" name="__codelineno-35-19" href="#__codelineno-35-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-35-20" name="__codelineno-35-20" href="#__codelineno-35-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-21" name="__codelineno-35-21" href="#__codelineno-35-21"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">cap</span><span class="p">]</span>
+<a id="__codelineno-35-22" name="__codelineno-35-22" href="#__codelineno-35-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsackDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* 0-1 ナップサック：動的計画法 */</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">knapsackDP</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">wgt</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">wgtSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgtSize</span><span class="p">;</span>
+<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">**</span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">((</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">));</span>
+<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">calloc</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-36-14" name="__codelineno-36-14" href="#__codelineno-36-14"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">];</span>
+<a id="__codelineno-36-15" name="__codelineno-36-15" href="#__codelineno-36-15"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-16" name="__codelineno-36-16" href="#__codelineno-36-16"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-36-17" name="__codelineno-36-17" href="#__codelineno-36-17"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">myMax</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-36-18" name="__codelineno-36-18" href="#__codelineno-36-18"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-36-19" name="__codelineno-36-19" href="#__codelineno-36-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-36-20" name="__codelineno-36-20" href="#__codelineno-36-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-21" name="__codelineno-36-21" href="#__codelineno-36-21"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">cap</span><span class="p">];</span>
+<a id="__codelineno-36-22" name="__codelineno-36-22" href="#__codelineno-36-22"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-36-23" name="__codelineno-36-23" href="#__codelineno-36-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-24" name="__codelineno-36-24" href="#__codelineno-36-24"></a><span class="w">        </span><span class="n">free</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-36-25" name="__codelineno-36-25" href="#__codelineno-36-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-26" name="__codelineno-36-26" href="#__codelineno-36-26"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-36-27" name="__codelineno-36-27" href="#__codelineno-36-27"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">knapsackDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* 0-1 ナップサック：動的計画法 */</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">knapsackDP</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Array</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span>
+<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-37-14" name="__codelineno-37-14" href="#__codelineno-37-14"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">_val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-37-15" name="__codelineno-37-15" href="#__codelineno-37-15"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-37-16" name="__codelineno-37-16" href="#__codelineno-37-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-37-17" name="__codelineno-37-17" href="#__codelineno-37-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-18" name="__codelineno-37-18" href="#__codelineno-37-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">cap</span><span class="o">]</span>
+<a id="__codelineno-37-19" name="__codelineno-37-19" href="#__codelineno-37-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">knapsack_dp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="c1">### 0-1 ナップサック: 動的計画法 ###</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">knapsack_dp</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w">  </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w">  </span><span class="c1"># dp テーブルを初期化</span>
+<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="w">  </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w">  </span><span class="c1"># 状態遷移</span>
+<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span>
+<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a><span class="w">        </span><span class="c1"># ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span>
+<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a><span class="w">      </span><span class="k">else</span>
+<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a><span class="w">        </span><span class="c1"># 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]].</span><span class="n">max</span>
+<a id="__codelineno-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-38-16" name="__codelineno-38-16" href="#__codelineno-38-16"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-38-17" name="__codelineno-38-17" href="#__codelineno-38-17"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-18" name="__codelineno-38-18" href="#__codelineno-38-18"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">cap</span><span class="o">]</span>
+<a id="__codelineno-38-19" name="__codelineno-38-19" href="#__codelineno-38-19"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>下の図に示すように、時間計算量と空間計算量の両方が配列 <code>dp</code> のサイズ、つまり <span class="arithmatex">\(O(n \times cap)\)</span> によって決定されます。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20knapsack_dp%28wgt%3A%20list%5Bint%5D%2C%20val%3A%20list%5Bint%5D%2C%20cap%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%220-1%20%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%EF%BC%9A%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%20%3D%20len%28wgt%29%0A%20%20%20%20%23%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5B%5B0%5D%20%2A%20%28cap%20%2B%201%29%20for%20_%20in%20range%28n%20%2B%201%29%5D%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20for%20c%20in%20range%281%2C%20cap%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20wgt%5Bi%20-%201%5D%20%3E%20c%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%AA%E3%82%89%E5%93%81%E7%89%A9%20i%20%E3%81%AF%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Bc%5D%20%3D%20dp%5Bi%20-%201%5D%5Bc%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E5%93%81%E7%89%A9%20i%20%E3%82%92%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%E5%A0%B4%E5%90%88%E3%81%A8%E9%81%B8%E3%81%B6%E5%A0%B4%E5%90%88%E3%81%AE%E5%A4%A7%E3%81%8D%E3%81%84%E6%96%B9%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Bc%5D%20%3D%20max%28dp%5Bi%20-%201%5D%5Bc%5D%2C%20dp%5Bi%20-%201%5D%5Bc%20-%20wgt%5Bi%20-%201%5D%5D%20%2B%20val%5Bi%20-%201%5D%29%0A%20%20%20%20return%20dp%5Bn%5D%5Bcap%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20wgt%20%3D%20%5B10%2C%2020%2C%2030%2C%2040%2C%2050%5D%0A%20%20%20%20val%20%3D%20%5B50%2C%20120%2C%20150%2C%20210%2C%20240%5D%0A%20%20%20%20cap%20%3D%2050%0A%20%20%20%20n%20%3D%20len%28wgt%29%0A%0A%20%20%20%20%23%20%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20knapsack_dp%28wgt%2C%20val%2C%20cap%29%0A%20%20%20%20print%28f%22%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%81%AA%E3%81%84%E6%9C%80%E5%A4%A7%E4%BE%A1%E5%80%A4%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=7&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20knapsack_dp%28wgt%3A%20list%5Bint%5D%2C%20val%3A%20list%5Bint%5D%2C%20cap%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%220-1%20%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%EF%BC%9A%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%20%3D%20len%28wgt%29%0A%20%20%20%20%23%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5B%5B0%5D%20%2A%20%28cap%20%2B%201%29%20for%20_%20in%20range%28n%20%2B%201%29%5D%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20for%20c%20in%20range%281%2C%20cap%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20wgt%5Bi%20-%201%5D%20%3E%20c%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%AA%E3%82%89%E5%93%81%E7%89%A9%20i%20%E3%81%AF%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Bc%5D%20%3D%20dp%5Bi%20-%201%5D%5Bc%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E5%93%81%E7%89%A9%20i%20%E3%82%92%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%E5%A0%B4%E5%90%88%E3%81%A8%E9%81%B8%E3%81%B6%E5%A0%B4%E5%90%88%E3%81%AE%E5%A4%A7%E3%81%8D%E3%81%84%E6%96%B9%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Bc%5D%20%3D%20max%28dp%5Bi%20-%201%5D%5Bc%5D%2C%20dp%5Bi%20-%201%5D%5Bc%20-%20wgt%5Bi%20-%201%5D%5D%20%2B%20val%5Bi%20-%201%5D%29%0A%20%20%20%20return%20dp%5Bn%5D%5Bcap%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20wgt%20%3D%20%5B10%2C%2020%2C%2030%2C%2040%2C%2050%5D%0A%20%20%20%20val%20%3D%20%5B50%2C%20120%2C%20150%2C%20210%2C%20240%5D%0A%20%20%20%20cap%20%3D%2050%0A%20%20%20%20n%20%3D%20len%28wgt%29%0A%0A%20%20%20%20%23%20%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20knapsack_dp%28wgt%2C%20val%2C%20cap%29%0A%20%20%20%20print%28f%22%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%81%AA%E3%81%84%E6%9C%80%E5%A4%A7%E4%BE%A1%E5%80%A4%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=7&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>以下の図のように、時間計算量と空間計算量はいずれも配列 <code>dp</code> のサイズによって決まり、<span class="arithmatex">\(O(n \times cap)\)</span> です。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="4:14"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><input id="__tabbed_4_14" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">&lt;1&gt;</label><label for="__tabbed_4_2">&lt;2&gt;</label><label for="__tabbed_4_3">&lt;3&gt;</label><label for="__tabbed_4_4">&lt;4&gt;</label><label for="__tabbed_4_5">&lt;5&gt;</label><label for="__tabbed_4_6">&lt;6&gt;</label><label for="__tabbed_4_7">&lt;7&gt;</label><label for="__tabbed_4_8">&lt;8&gt;</label><label for="__tabbed_4_9">&lt;9&gt;</label><label for="__tabbed_4_10">&lt;10&gt;</label><label for="__tabbed_4_11">&lt;11&gt;</label><label for="__tabbed_4_12">&lt;12&gt;</label><label for="__tabbed_4_13">&lt;13&gt;</label><label for="__tabbed_4_14">&lt;14&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="0-1ナップサック問題の動的プログラミングプロセス" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_step1.png" /></p>
+<p><img alt="0-1 ナップサック問題の動的計画法の過程" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="knapsack_dp_step2" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_step2.png" /></p>
@@ -4797,20 +5409,20 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
 </div>
 </div>
 </div>
-<p align="center"> 図 14-20 &nbsp; 0-1ナップサック問題の動的プログラミングプロセス </p>
+<p align="center"> 図 14-20 &nbsp; 0-1 ナップサック問題の動的計画法の過程 </p>
 
 <h3 id="4">4. &nbsp; 空間最適化<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
-<p>各状態は上の行の状態のみに関連するため、2つの配列を使用してローリング前進させ、空間計算量を <span class="arithmatex">\(O(n^2)\)</span> から <span class="arithmatex">\(O(n)\)</span> に削減できます。</p>
-<p>さらに考えてみると、1つの配列だけで空間最適化を達成できるでしょうか？各状態が直接上のセルまたは左上のセルから遷移することが観察できます。配列が1つしかない場合、<span class="arithmatex">\(i\)</span> 行目の走査を開始するとき、その配列はまだ <span class="arithmatex">\(i-1\)</span> 行目の状態を保存しています。</p>
+<p>各状態は直前の行の状態にしか依存しないため、2つの配列をローテーションして用いることで、空間計算量を <span class="arithmatex">\(O(n^2)\)</span> から <span class="arithmatex">\(O(n)\)</span> に削減できます。</p>
+<p>さらに考えると、1つの配列だけで空間最適化を実現できるでしょうか。観察すると、各状態は真上または左上のマスから遷移してきます。配列が1つしかないと仮定すると、<span class="arithmatex">\(i\)</span> 行目の走査を開始した時点では、その配列にはまだ <span class="arithmatex">\(i-1\)</span> 行目の状態が格納されています。</p>
 <ul>
-<li>通常の順序で走査する場合、<span class="arithmatex">\(dp[i, j]\)</span> に走査したとき、左上の <span class="arithmatex">\(dp[i-1, 1]\)</span> ～ <span class="arithmatex">\(dp[i-1, j-1]\)</span> の値がすでに上書きされている可能性があり、正しい状態遷移結果を得ることができません。</li>
-<li>逆順で走査する場合、上書き問題はなく、状態遷移を正しく実行できます。</li>
+<li>順方向に走査すると、<span class="arithmatex">\(dp[i, j]\)</span> に到達した時点で、左上にある <span class="arithmatex">\(dp[i-1, 1]\)</span> ~ <span class="arithmatex">\(dp[i-1, j-1]\)</span> の値がすでに上書きされている可能性があり、正しい状態遷移結果を得られません。</li>
+<li>逆方向に走査すれば、上書きの問題は発生せず、状態遷移を正しく行えます。</li>
 </ul>
-<p>下の図は単一配列での <span class="arithmatex">\(i = 1\)</span> 行目から <span class="arithmatex">\(i = 2\)</span> 行目への遷移プロセスを示しています。通常順序走査と逆順走査の違いについて考えてみてください。</p>
+<p>次の図は、単一配列のもとで <span class="arithmatex">\(i = 1\)</span> 行目から <span class="arithmatex">\(i = 2\)</span> 行目へ変換する過程を示しています。順方向走査と逆方向走査の違いを考えてみてください。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="5:6"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">&lt;1&gt;</label><label for="__tabbed_5_2">&lt;2&gt;</label><label for="__tabbed_5_3">&lt;3&gt;</label><label for="__tabbed_5_4">&lt;4&gt;</label><label for="__tabbed_5_5">&lt;5&gt;</label><label for="__tabbed_5_6">&lt;6&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="0-1ナップサックの空間最適化動的プログラミングプロセス" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_comp_step1.png" /></p>
+<p><img alt="0-1 ナップサックの空間最適化後の動的計画法の過程" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_comp_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="knapsack_dp_comp_step2" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_comp_step2.png" /></p>
@@ -4829,42 +5441,42 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
 </div>
 </div>
 </div>
-<p align="center"> 図 14-21 &nbsp; 0-1ナップサックの空間最適化動的プログラミングプロセス </p>
+<p align="center"> 図 14-21 &nbsp; 0-1 ナップサックの空間最適化後の動的計画法の過程 </p>
 
-<p>コード実装では、配列 <code>dp</code> の最初の次元 <span class="arithmatex">\(i\)</span> を削除し、内側のループを逆走査に変更するだけです：</p>
+<p>コード実装では、配列 <code>dp</code> の第1次元 <span class="arithmatex">\(i\)</span> をそのまま削除し、内側のループを逆方向走査に変更するだけで済みます。</p>
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 <div class="highlight"><span class="filename">knapsack.py</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">knapsack_dp_comp</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">val</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">cap</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;0-1 ナップサック：空間最適化動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;0-1 ナップサック：空間最適化後の動的計画法&quot;&quot;&quot;</span>
 <a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">wgt</span><span class="p">)</span>
 <a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a>    <span class="c1"># dp テーブルを初期化</span>
 <a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">cap</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
 <a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a>    <span class="c1"># 状態遷移</span>
 <a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
-<a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a>        <span class="c1"># 逆順で走査</span>
+<a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a>        <span class="c1"># 逆順に走査する</span>
 <a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a>        <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">cap</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a>            <span class="k">if</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">c</span><span class="p">:</span>
-<a id="__codelineno-39-11" name="__codelineno-39-11" href="#__codelineno-39-11"></a>                <span class="c1"># ナップサック容量を超える場合、アイテム i を選択しない</span>
+<a id="__codelineno-39-11" name="__codelineno-39-11" href="#__codelineno-39-11"></a>                <span class="c1"># ナップサック容量を超えるなら品物 i は選ばない</span>
 <a id="__codelineno-39-12" name="__codelineno-39-12" href="#__codelineno-39-12"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span>
 <a id="__codelineno-39-13" name="__codelineno-39-13" href="#__codelineno-39-13"></a>            <span class="k">else</span><span class="p">:</span>
-<a id="__codelineno-39-14" name="__codelineno-39-14" href="#__codelineno-39-14"></a>                <span class="c1"># アイテム i を選択しないのと選択するのとで大きい値</span>
+<a id="__codelineno-39-14" name="__codelineno-39-14" href="#__codelineno-39-14"></a>                <span class="c1"># 品物 i を選ばない場合と選ぶ場合の大きい方</span>
 <a id="__codelineno-39-15" name="__codelineno-39-15" href="#__codelineno-39-15"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">c</span> <span class="o">-</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span> <span class="o">+</span> <span class="n">val</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span>
 <a id="__codelineno-39-16" name="__codelineno-39-16" href="#__codelineno-39-16"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">cap</span><span class="p">]</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.cpp</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* 0-1 ナップサック：空間最適化動的プログラミング */</span>
+<div class="highlight"><span class="filename">knapsack.cpp</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* 0-1 ナップサック：空間最適化後の動的計画法 */</span>
 <a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">knapsackDPComp</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
-<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
 <a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
 <a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w">        </span><span class="c1">// 逆順で走査</span>
+<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w">        </span><span class="c1">// 逆順に走査する</span>
 <a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w">                </span><span class="c1">// 選択しない場合とアイテム i を選択する場合のより大きい値</span>
+<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
 <a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
 <a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="w">        </span><span class="p">}</span>
@@ -4874,17 +5486,17 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.java</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 0-1 ナップサック：空間最適化動的プログラミング */</span>
+<div class="highlight"><span class="filename">knapsack.java</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 0-1 ナップサック：空間最適化後の動的計画法 */</span>
 <a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">knapsackDPComp</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
-<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
 <a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
 <a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a><span class="w">        </span><span class="c1">// 逆順で走査</span>
+<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a><span class="w">        </span><span class="c1">// 逆順に走査する</span>
 <a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a><span class="w">                </span><span class="c1">// 選択しない場合とアイテム i を選択する場合のより大きい値</span>
+<a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
 <a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">max</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">);</span>
 <a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-41-14" name="__codelineno-41-14" href="#__codelineno-41-14"></a><span class="w">        </span><span class="p">}</span>
@@ -4894,47 +5506,225 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.cs</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">knapsack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">KnapsackDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.cs</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="cm">/* 0-1 ナップサック：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">KnapsackDPComp</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">weight</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">weight</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="w">    </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a><span class="w">        </span><span class="c1">// 逆順に走査する</span>
+<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">weight</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">];</span>
+<a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-14" name="__codelineno-42-14" href="#__codelineno-42-14"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-42-15" name="__codelineno-42-15" href="#__codelineno-42-15"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">weight</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-42-16" name="__codelineno-42-16" href="#__codelineno-42-16"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-42-17" name="__codelineno-42-17" href="#__codelineno-42-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-42-18" name="__codelineno-42-18" href="#__codelineno-42-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-42-19" name="__codelineno-42-19" href="#__codelineno-42-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">cap</span><span class="p">];</span>
+<a id="__codelineno-42-20" name="__codelineno-42-20" href="#__codelineno-42-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.go</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">knapsackDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.go</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* 0-1 ナップサック：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">knapsackDPComp</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w">    </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">wgt</span><span class="p">)</span>
+<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w">    </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w">        </span><span class="c1">// 逆順に走査する</span>
+<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">cap</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="o">--</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Max</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="p">]),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="o">-</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]]</span><span class="o">+</span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">])))</span>
+<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-43-14" name="__codelineno-43-14" href="#__codelineno-43-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-43-15" name="__codelineno-43-15" href="#__codelineno-43-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-16" name="__codelineno-43-16" href="#__codelineno-43-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">cap</span><span class="p">]</span>
+<a id="__codelineno-43-17" name="__codelineno-43-17" href="#__codelineno-43-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.swift</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">knapsackDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.swift</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* 0-1 ナップサック：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">knapsackDPComp</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">cap</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w">        </span><span class="c1">// 逆順に走査する</span>
+<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">cap</span><span class="p">).</span><span class="n">reversed</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span>
+<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-44-15" name="__codelineno-44-15" href="#__codelineno-44-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-16" name="__codelineno-44-16" href="#__codelineno-44-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">cap</span><span class="p">]</span>
+<a id="__codelineno-44-17" name="__codelineno-44-17" href="#__codelineno-44-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.js</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">knapsackDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.js</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="cm">/* 0-1 ナップサック：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">knapsackDPComp</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">wgt</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="w">        </span><span class="c1">// 逆順に走査する</span>
+<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cap</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">max</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]);</span>
+<a id="__codelineno-45-13" name="__codelineno-45-13" href="#__codelineno-45-13"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-45-14" name="__codelineno-45-14" href="#__codelineno-45-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-45-15" name="__codelineno-45-15" href="#__codelineno-45-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-45-16" name="__codelineno-45-16" href="#__codelineno-45-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">cap</span><span class="p">];</span>
+<a id="__codelineno-45-17" name="__codelineno-45-17" href="#__codelineno-45-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.ts</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">knapsackDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.ts</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="cm">/* 0-1 ナップサック：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">knapsackDPComp</span><span class="p">(</span>
+<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w">    </span><span class="nx">wgt</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w">    </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="w">    </span><span class="nx">cap</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span>
+<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">wgt</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-12" name="__codelineno-46-12" href="#__codelineno-46-12"></a><span class="w">        </span><span class="c1">// 逆順に走査する</span>
+<a id="__codelineno-46-13" name="__codelineno-46-13" href="#__codelineno-46-13"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cap</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-14" name="__codelineno-46-14" href="#__codelineno-46-14"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-15" name="__codelineno-46-15" href="#__codelineno-46-15"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-46-16" name="__codelineno-46-16" href="#__codelineno-46-16"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">max</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]);</span>
+<a id="__codelineno-46-17" name="__codelineno-46-17" href="#__codelineno-46-17"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-46-18" name="__codelineno-46-18" href="#__codelineno-46-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-46-19" name="__codelineno-46-19" href="#__codelineno-46-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-46-20" name="__codelineno-46-20" href="#__codelineno-46-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">cap</span><span class="p">];</span>
+<a id="__codelineno-46-21" name="__codelineno-46-21" href="#__codelineno-46-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.dart</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsackDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.dart</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* 0-1 ナップサック：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">knapsackDPComp</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w">  </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a><span class="w">  </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a><span class="w">    </span><span class="c1">// 逆順に走査する</span>
+<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="w">        </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]);</span>
+<a id="__codelineno-47-13" name="__codelineno-47-13" href="#__codelineno-47-13"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-47-14" name="__codelineno-47-14" href="#__codelineno-47-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-47-15" name="__codelineno-47-15" href="#__codelineno-47-15"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-47-16" name="__codelineno-47-16" href="#__codelineno-47-16"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">cap</span><span class="p">];</span>
+<a id="__codelineno-47-17" name="__codelineno-47-17" href="#__codelineno-47-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.rs</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsack_dp_comp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.rs</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="cm">/* 0-1 ナップサック：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">knapsack_dp_comp</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">cap</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
+<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a><span class="w">        </span><span class="c1">// 逆順に走査する</span>
+<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">..=</span><span class="n">cap</span><span class="p">).</span><span class="n">rev</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-11" name="__codelineno-48-11" href="#__codelineno-48-11"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-48-12" name="__codelineno-48-12" href="#__codelineno-48-12"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-48-13" name="__codelineno-48-13" href="#__codelineno-48-13"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-48-14" name="__codelineno-48-14" href="#__codelineno-48-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-48-15" name="__codelineno-48-15" href="#__codelineno-48-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-48-16" name="__codelineno-48-16" href="#__codelineno-48-16"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="n">cap</span><span class="p">]</span>
+<a id="__codelineno-48-17" name="__codelineno-48-17" href="#__codelineno-48-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.c</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsackDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.c</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* 0-1 ナップサック：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">knapsackDPComp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">wgt</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">wgtSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgtSize</span><span class="p">;</span>
+<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">calloc</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="w">        </span><span class="c1">// 逆順に走査する</span>
+<a id="__codelineno-49-9" name="__codelineno-49-9" href="#__codelineno-49-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-10" name="__codelineno-49-10" href="#__codelineno-49-10"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-11" name="__codelineno-49-11" href="#__codelineno-49-11"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-49-12" name="__codelineno-49-12" href="#__codelineno-49-12"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">myMax</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-49-13" name="__codelineno-49-13" href="#__codelineno-49-13"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-49-14" name="__codelineno-49-14" href="#__codelineno-49-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-49-15" name="__codelineno-49-15" href="#__codelineno-49-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-49-16" name="__codelineno-49-16" href="#__codelineno-49-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">cap</span><span class="p">];</span>
+<a id="__codelineno-49-17" name="__codelineno-49-17" href="#__codelineno-49-17"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-49-18" name="__codelineno-49-18" href="#__codelineno-49-18"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">dp</span><span class="p">);</span>
+<a id="__codelineno-49-19" name="__codelineno-49-19" href="#__codelineno-49-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-49-20" name="__codelineno-49-20" href="#__codelineno-49-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.kt</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">knapsackDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.kt</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* 0-1 ナップサック：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">knapsackDPComp</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a><span class="w">        </span><span class="c1">// 逆順に走査する</span>
+<a id="__codelineno-50-9" name="__codelineno-50-9" href="#__codelineno-50-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="n">downTo</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-10" name="__codelineno-50-10" href="#__codelineno-50-10"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-11" name="__codelineno-50-11" href="#__codelineno-50-11"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-50-12" name="__codelineno-50-12" href="#__codelineno-50-12"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">_val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-50-13" name="__codelineno-50-13" href="#__codelineno-50-13"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-50-14" name="__codelineno-50-14" href="#__codelineno-50-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-50-15" name="__codelineno-50-15" href="#__codelineno-50-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-50-16" name="__codelineno-50-16" href="#__codelineno-50-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">cap</span><span class="o">]</span>
+<a id="__codelineno-50-17" name="__codelineno-50-17" href="#__codelineno-50-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">knapsack_dp_comp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="c1">### 0-1 ナップサック: 空間最適化後の動的計画法 ###</span>
+<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">knapsack_dp_comp</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span>
+<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w">  </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a><span class="w">  </span><span class="c1"># dp テーブルを初期化</span>
+<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w">  </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a><span class="w">  </span><span class="c1"># 状態遷移</span>
+<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="w">    </span><span class="c1"># 逆順に走査する</span>
+<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">cap</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span>
+<a id="__codelineno-51-11" name="__codelineno-51-11" href="#__codelineno-51-11"></a><span class="w">        </span><span class="c1"># ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-51-12" name="__codelineno-51-12" href="#__codelineno-51-12"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span>
+<a id="__codelineno-51-13" name="__codelineno-51-13" href="#__codelineno-51-13"></a><span class="w">      </span><span class="k">else</span>
+<a id="__codelineno-51-14" name="__codelineno-51-14" href="#__codelineno-51-14"></a><span class="w">        </span><span class="c1"># 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-51-15" name="__codelineno-51-15" href="#__codelineno-51-15"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]].</span><span class="n">max</span>
+<a id="__codelineno-51-16" name="__codelineno-51-16" href="#__codelineno-51-16"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-51-17" name="__codelineno-51-17" href="#__codelineno-51-17"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-51-18" name="__codelineno-51-18" href="#__codelineno-51-18"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-51-19" name="__codelineno-51-19" href="#__codelineno-51-19"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="n">cap</span><span class="o">]</span>
+<a id="__codelineno-51-20" name="__codelineno-51-20" href="#__codelineno-51-20"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20knapsack_dp_comp%28wgt%3A%20list%5Bint%5D%2C%20val%3A%20list%5Bint%5D%2C%20cap%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%220-1%20%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%EF%BC%9A%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E5%BE%8C%E3%81%AE%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%20%3D%20len%28wgt%29%0A%20%20%20%20%23%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5B0%5D%20%2A%20%28cap%20%2B%201%29%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E9%80%86%E9%A0%86%E3%81%AB%E8%B5%B0%E6%9F%BB%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20for%20c%20in%20range%28cap%2C%200%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20wgt%5Bi%20-%201%5D%20%3E%20c%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%AA%E3%82%89%E5%93%81%E7%89%A9%20i%20%E3%81%AF%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bc%5D%20%3D%20dp%5Bc%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E5%93%81%E7%89%A9%20i%20%E3%82%92%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%E5%A0%B4%E5%90%88%E3%81%A8%E9%81%B8%E3%81%B6%E5%A0%B4%E5%90%88%E3%81%AE%E5%A4%A7%E3%81%8D%E3%81%84%E6%96%B9%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bc%5D%20%3D%20max%28dp%5Bc%5D%2C%20dp%5Bc%20-%20wgt%5Bi%20-%201%5D%5D%20%2B%20val%5Bi%20-%201%5D%29%0A%20%20%20%20return%20dp%5Bcap%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20wgt%20%3D%20%5B10%2C%2020%2C%2030%2C%2040%2C%2050%5D%0A%20%20%20%20val%20%3D%20%5B50%2C%20120%2C%20150%2C%20210%2C%20240%5D%0A%20%20%20%20cap%20%3D%2050%0A%20%20%20%20n%20%3D%20len%28wgt%29%0A%0A%20%20%20%20%23%20%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E5%BE%8C%E3%81%AE%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20knapsack_dp_comp%28wgt%2C%20val%2C%20cap%29%0A%20%20%20%20print%28f%22%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%81%AA%E3%81%84%E6%9C%80%E5%A4%A7%E4%BE%A1%E5%80%A4%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=7&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20knapsack_dp_comp%28wgt%3A%20list%5Bint%5D%2C%20val%3A%20list%5Bint%5D%2C%20cap%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%220-1%20%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%EF%BC%9A%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E5%BE%8C%E3%81%AE%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%20%3D%20len%28wgt%29%0A%20%20%20%20%23%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5B0%5D%20%2A%20%28cap%20%2B%201%29%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E9%80%86%E9%A0%86%E3%81%AB%E8%B5%B0%E6%9F%BB%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20for%20c%20in%20range%28cap%2C%200%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20wgt%5Bi%20-%201%5D%20%3E%20c%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%AA%E3%82%89%E5%93%81%E7%89%A9%20i%20%E3%81%AF%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bc%5D%20%3D%20dp%5Bc%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E5%93%81%E7%89%A9%20i%20%E3%82%92%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%E5%A0%B4%E5%90%88%E3%81%A8%E9%81%B8%E3%81%B6%E5%A0%B4%E5%90%88%E3%81%AE%E5%A4%A7%E3%81%8D%E3%81%84%E6%96%B9%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bc%5D%20%3D%20max%28dp%5Bc%5D%2C%20dp%5Bc%20-%20wgt%5Bi%20-%201%5D%5D%20%2B%20val%5Bi%20-%201%5D%29%0A%20%20%20%20return%20dp%5Bcap%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20wgt%20%3D%20%5B10%2C%2020%2C%2030%2C%2040%2C%2050%5D%0A%20%20%20%20val%20%3D%20%5B50%2C%20120%2C%20150%2C%20210%2C%20240%5D%0A%20%20%20%20cap%20%3D%2050%0A%20%20%20%20n%20%3D%20len%28wgt%29%0A%0A%20%20%20%20%23%20%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E5%BE%8C%E3%81%AE%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20knapsack_dp_comp%28wgt%2C%20val%2C%20cap%29%0A%20%20%20%20print%28f%22%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%81%AA%E3%81%84%E6%9C%80%E5%A4%A7%E4%BE%A1%E5%80%A4%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=7&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 
 <!-- Source file information -->
 
@@ -4957,7 +5747,7 @@ aria-label="フッター"
   <a
     href="../dp_solution_pipeline/"
     class="md-footer__link md-footer__link--prev"
-    aria-label="前: 14.3 &amp;nbsp; DP の解法の考え方"
+    aria-label="前: 14.3 &amp;nbsp; 動的計画法の問題解決の考え方"
     rel="prev"
   >
     <div class="md-footer__button md-icon">
@@ -4969,7 +5759,7 @@ aria-label="フッター"
         前
       </span>
       <div class="md-ellipsis">
-        14.3 &nbsp; DP の解法の考え方
+        14.3 &nbsp; 動的計画法の問題解決の考え方
       </div>
     </div>
   </a>
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@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
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@@ -341,7 +341,7 @@
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-    序
+    はじめに
   
 
     
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-    序
+    はじめに
   
 
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-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
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-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
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-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
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-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
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-    3.4 &nbsp; 文字の符号化 *
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-    第 6 章 &nbsp; ハッシュ表
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
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-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
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-    10.5 &nbsp; 探索アルゴリズムの再認識
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-    12.1 &nbsp; 分割統治アルゴリズム
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-    12.3 &nbsp; 木の構築問題
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-    13.4 &nbsp; Nクイーン問題
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-    14.2 &nbsp; DP 問題の特性
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-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
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+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    14.7 &nbsp; まとめ
+  
+
+    
+  </span>
+  
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
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+        
+
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      
+        1. &nbsp; 要点の振り返り
+      
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
     </li>
   
 
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
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+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      
+        1. &nbsp; 要点の振り返り
+      
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
 </nav>
                   </div>
                 </div>
@@ -4265,28 +4333,29 @@
 
 <!-- Page content -->
 <h1 id="147">14.7 &nbsp; まとめ<a class="headerlink" href="#147" title="Permanent link">&para;</a></h1>
+<h3 id="1">1. &nbsp; 要点の振り返り<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
-<li>動的プログラミングは問題を分解し、部分問題の解を保存することで冗長な計算を避け、計算効率を向上させます。</li>
-<li>時間を考慮しなければ、すべての動的プログラミング問題はバックトラッキング（力任せ探索）を使用して解決できますが、再帰木には多くの重複する部分問題があり、効率が非常に低くなります。記憶化リストを導入することで、計算されたすべての部分問題の解を保存し、重複する部分問題が一度だけ計算されることを保証できます。</li>
-<li>記憶化探索はトップダウンの再帰解法であり、動的プログラミングはボトムアップの反復アプローチに対応し、「表を埋める」ことに似ています。現在の状態は特定の局所状態のみに依存するため、dpテーブルの1次元を削除して空間計算量を削減できます。</li>
-<li>部分問題の分解は汎用的なアルゴリズムアプローチであり、分割統治法、動的プログラミング、バックトラッキングで特徴が異なります。</li>
-<li>動的プログラミング問題には3つの主要な特徴があります：重複する部分問題、最適部分構造、無記憶性。</li>
-<li>元の問題の最適解がその部分問題の最適解から構築できる場合、最適部分構造を持ちます。</li>
-<li>無記憶性とは、状態の将来の発展が現在の状態のみに依存し、過去に経験したすべての状態に依存しないことを意味します。多くの組み合わせ最適化問題にはこの特性がなく、動的プログラミングを使用して迅速に解決することはできません。</li>
+<li>動的計画法は問題を分解し、部分問題の解を保存することで重複計算を避け、計算効率を高めます。</li>
+<li>時間を考慮しなければ、すべての動的計画法の問題はバックトラッキング（総当たり探索）で解けますが、再帰木には大量の重複部分問題が存在するため、効率はきわめて低くなります。メモ化配列を導入すると、計算済みのすべての部分問題の解を保存でき、重複部分問題が 1 回だけ計算されることを保証できます。</li>
+<li>メモ化探索はトップダウンの再帰的解法であり、それに対応する動的計画法はボトムアップの漸化式による解法で、ちょうど「表を埋める」ようなものです。現在の状態は一部の局所状態にのみ依存するため、<span class="arithmatex">\(dp\)</span> 表の 1 次元を削減して空間計算量を下げることができます。</li>
+<li>部分問題への分解は汎用的なアルゴリズムの考え方であり、分割統治、動的計画法、バックトラッキングではそれぞれ異なる性質を持ちます。</li>
+<li>動的計画法の問題には 3 つの大きな特徴があります。重複部分問題、最適部分構造、無後効性です。</li>
+<li>元の問題の最適解が部分問題の最適解から構築できるなら、その問題は最適部分構造を持ちます。</li>
+<li>無後効性とは、ある状態の将来の発展がその状態のみに関係し、過去に経たすべての状態とは無関係であることを指します。多くの組合せ最適化問題は無後効性を持たず、動的計画法で高速に解くことはできません。</li>
 </ul>
 <p><strong>ナップサック問題</strong></p>
 <ul>
-<li>ナップサック問題は最も典型的な動的プログラミング問題の1つで、0-1ナップサック、無制限ナップサック、複数ナップサックなどの変種があります。</li>
-<li>0-1ナップサックの状態定義は、最初の <span class="arithmatex">\(i\)</span> 個のアイテムを含む容量 <span class="arithmatex">\(c\)</span> のナップサックでの最大値です。アイテムをナップサックに入れないまたは入れるという決定に基づいて、最適部分構造を特定し、状態遷移方程式を構築できます。空間最適化では、各状態が直接上と左上の状態に依存するため、左上の状態の上書きを避けるためにリストを逆順で走査する必要があります。</li>
-<li>無制限ナップサック問題では、各種類のアイテムを選択できる数に制限がないため、アイテムを含める状態遷移は0-1ナップサックと異なります。状態が直接上と左の状態に依存するため、空間最適化では前方走査を含める必要があります。</li>
-<li>コイン交換問題は無制限ナップサック問題の変種で、「最大」値を求めることから「最小」コイン数を求めることに変わり、状態遷移方程式は <span class="arithmatex">\(\max()\)</span> を <span class="arithmatex">\(\min()\)</span> に変更する必要があります。ナップサックの容量を「超えない」ことを追求することから、正確に目標金額を求めることに変わり、「目標金額を構成できない」無効解を表すために <span class="arithmatex">\(amt + 1\)</span> を使用します。</li>
-<li>コイン交換問題IIは「最小コイン数」を求めることから「コインの組み合わせ数」を求めることに変わり、状態遷移方程式を <span class="arithmatex">\(\min()\)</span> から和算演算子に変更します。</li>
+<li>ナップサック問題は最も典型的な動的計画法の問題の 1 つであり、0-1 ナップサック、完全ナップサック、多重ナップサックなどの派生があります。</li>
+<li>0-1 ナップサックの状態は、容量 <span class="arithmatex">\(c\)</span> のナップサックに対して、前 <span class="arithmatex">\(i\)</span> 個の品物で得られる最大価値として定義されます。ナップサックに入れない場合と入れる場合の 2 つの判断から最適部分構造を得て、状態遷移方程式を構築できます。空間最適化では、各状態が真上と左上の状態に依存するため、左上の状態が上書きされるのを避けるために配列を逆順に走査する必要があります。</li>
+<li>完全ナップサック問題では各品物の選択数に制限がないため、品物を入れる場合の状態遷移は 0-1 ナップサック問題とは異なります。状態は真上と真左の状態に依存するので、空間最適化では順方向に走査するべきです。</li>
+<li>コイン両替問題は完全ナップサック問題の変種です。「最大」価値を求める問題から「最小」の硬貨枚数を求める問題へ変わるため、状態遷移方程式の <span class="arithmatex">\(\max()\)</span> は <span class="arithmatex">\(\min()\)</span> に置き換える必要があります。また、ナップサック容量を「超えない」ことを目指すのではなく、目標金額を「ちょうど」作ることを目指すため、<span class="arithmatex">\(amt + 1\)</span> を「目標金額を作れない」無効解の表現として用います。</li>
+<li>コイン両替問題 II では、「最少硬貨枚数」を求める問題から「硬貨の組合せ数」を求める問題へ変わるため、状態遷移方程式も <span class="arithmatex">\(\min()\)</span> から総和演算子へ対応して変わります。</li>
 </ul>
 <p><strong>編集距離問題</strong></p>
 <ul>
-<li>編集距離（レーベンシュタイン距離）は2つの文字列間の類似度を測定し、一つの文字列を別の文字列に変更するために必要な最小編集ステップ数として定義され、編集操作には追加、削除、置換が含まれます。</li>
-<li>編集距離問題の状態定義は、<span class="arithmatex">\(s\)</span> の最初の <span class="arithmatex">\(i\)</span> 文字を <span class="arithmatex">\(t\)</span> の最初の <span class="arithmatex">\(j\)</span> 文字に変更するために必要な最小編集ステップ数です。<span class="arithmatex">\(s[i] \ne t[j]\)</span> の場合、追加、削除、置換の3つの決定があり、それぞれに対応する残余部分問題があります。これから最適部分構造を特定し、状態遷移方程式を構築できます。<span class="arithmatex">\(s[i] = t[j]\)</span> の場合、現在の文字の編集は必要ありません。</li>
-<li>編集距離では、状態が直接上、左、左上の状態に依存します。したがって、空間最適化後、前方走査も逆走査も正しく状態遷移を実行できません。これに対処するため、変数を使用して左上の状態を一時的に保存し、無制限ナップサック問題の状況と同等にし、空間最適化後に前方走査を可能にします。</li>
+<li>編集距離（Levenshtein 距離）は 2 つの文字列間の類似度を測るために用いられ、ある文字列を別の文字列へ変換するための最小編集回数として定義されます。編集操作には追加、削除、置換が含まれます。</li>
+<li>編集距離問題の状態は、<span class="arithmatex">\(s\)</span> の前 <span class="arithmatex">\(i\)</span> 文字を <span class="arithmatex">\(t\)</span> の前 <span class="arithmatex">\(j\)</span> 文字へ変更するのに必要な最小編集回数として定義されます。<span class="arithmatex">\(s[i] \ne t[j]\)</span> のときは、追加、削除、置換の 3 つの判断があり、それぞれに対応する残りの部分問題があります。これにより最適部分構造を見いだし、状態遷移方程式を構築できます。一方、<span class="arithmatex">\(s[i] = t[j]\)</span> のときは現在の文字を編集する必要はありません。</li>
+<li>編集距離では、状態は真上、真左、左上の状態に依存します。そのため、空間最適化後は順方向でも逆方向でも正しく状態遷移できません。そこで、変数を 1 つ用いて左上の状態を一時保存し、完全ナップサック問題と等価な形へ変換することで、空間最適化後に順方向走査を行えるようにします。</li>
 </ul>
 
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index f98bac1fc..db7ab8ebc 100644
--- a/ja/chapter_dynamic_programming/unbounded_knapsack_problem/index.html
+++ b/ja/chapter_dynamic_programming/unbounded_knapsack_problem/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -39,7 +39,7 @@
     
     
       
-        <title>14.5 無制限ナップサック問題 - Hello アルゴリズム</title>
+        <title>14.5 完全ナップサック問題 - Hello アルゴリズム</title>
       
     
     
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -152,7 +152,7 @@
         <div class="md-header__topic" data-md-component="header-topic">
           <span class="md-ellipsis">
             
-              14.5 &nbsp; 無制限ナップサック問題
+              14.5 &nbsp; 完全ナップサック問題
             
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-    序
+    はじめに
   
 
     
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-    序
+    はじめに
   
 
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-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
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   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
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   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
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   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
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-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
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-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
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-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
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-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
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-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
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-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
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-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
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-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
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-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
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   <a href="#1451" class="md-nav__link">
     <span class="md-ellipsis">
       
-        14.5.1 &nbsp; 無制限ナップサック問題
+        14.5.1 &nbsp; 完全ナップサック問題
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="14.5.1 無制限ナップサック問題">
+    <nav class="md-nav" aria-label="14.5.1 完全ナップサック問題">
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           <li class="md-nav__item">
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-        1. &nbsp; 動的プログラミングアプローチ
+        1. &nbsp; 動的計画法の考え方
       
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   <a href="#1452" class="md-nav__link">
     <span class="md-ellipsis">
       
-        14.5.2 &nbsp; コイン交換問題
+        14.5.2 &nbsp; 硬貨交換問題
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="14.5.2 コイン交換問題">
+    <nav class="md-nav" aria-label="14.5.2 硬貨交換問題">
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-        1. &nbsp; 動的プログラミングアプローチ
+        1. &nbsp; 動的計画法の考え方
       
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@@ -3830,19 +3830,19 @@
   <a href="#1453-ii" class="md-nav__link">
     <span class="md-ellipsis">
       
-        14.5.3 &nbsp; コイン交換問題II
+        14.5.3 &nbsp; 硬貨交換問題 II
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="14.5.3 コイン交換問題II">
+    <nav class="md-nav" aria-label="14.5.3 硬貨交換問題 II">
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           <li class="md-nav__item">
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-        1. &nbsp; 動的プログラミングアプローチ
+        1. &nbsp; 動的計画法の考え方
       
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
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   <a href="#1451" class="md-nav__link">
     <span class="md-ellipsis">
       
-        14.5.1 &nbsp; 無制限ナップサック問題
+        14.5.1 &nbsp; 完全ナップサック問題
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="14.5.1 無制限ナップサック問題">
+    <nav class="md-nav" aria-label="14.5.1 完全ナップサック問題">
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           <li class="md-nav__item">
   <a href="#1" class="md-nav__link">
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-        1. &nbsp; 動的プログラミングアプローチ
+        1. &nbsp; 動的計画法の考え方
       
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   <a href="#1452" class="md-nav__link">
     <span class="md-ellipsis">
       
-        14.5.2 &nbsp; コイン交換問題
+        14.5.2 &nbsp; 硬貨交換問題
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="14.5.2 コイン交換問題">
+    <nav class="md-nav" aria-label="14.5.2 硬貨交換問題">
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-        1. &nbsp; 動的プログラミングアプローチ
+        1. &nbsp; 動的計画法の考え方
       
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   <a href="#1453-ii" class="md-nav__link">
     <span class="md-ellipsis">
       
-        14.5.3 &nbsp; コイン交換問題II
+        14.5.3 &nbsp; 硬貨交換問題 II
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="14.5.3 コイン交換問題II">
+    <nav class="md-nav" aria-label="14.5.3 硬貨交換問題 II">
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   <a href="#1_2" class="md-nav__link">
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-        1. &nbsp; 動的プログラミングアプローチ
+        1. &nbsp; 動的計画法の考え方
       
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@@ -4610,38 +4610,38 @@
 
 
 <!-- Page content -->
-<h1 id="145">14.5 &nbsp; 無制限ナップサック問題<a class="headerlink" href="#145" title="Permanent link">&para;</a></h1>
-<p>このセクションでは、まず別の一般的なナップサック問題である無制限ナップサックを解決し、次にその特殊ケースであるコイン交換問題を探索します。</p>
-<h2 id="1451">14.5.1 &nbsp; 無制限ナップサック問題<a class="headerlink" href="#1451" title="Permanent link">&para;</a></h2>
+<h1 id="145">14.5 &nbsp; 完全ナップサック問題<a class="headerlink" href="#145" title="Permanent link">&para;</a></h1>
+<p>本節では、まずもう 1 つの代表的なナップサック問題である完全ナップサック問題を解き、その特殊例である硬貨交換問題について見ていきます。</p>
+<h2 id="1451">14.5.1 &nbsp; 完全ナップサック問題<a class="headerlink" href="#1451" title="Permanent link">&para;</a></h2>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
-<p><span class="arithmatex">\(n\)</span> 個のアイテムが与えられ、<span class="arithmatex">\(i\)</span> 番目のアイテムの重量は <span class="arithmatex">\(wgt[i-1]\)</span> で値は <span class="arithmatex">\(val[i-1]\)</span> です。容量が <span class="arithmatex">\(cap\)</span> のバックパックがあります。<strong>各アイテムは複数回選択できます</strong>。容量を超えることなくバックパックに入れることができるアイテムの最大値は何ですか？以下の例を参照してください。</p>
+<p><span class="arithmatex">\(n\)</span> 個の品物が与えられ、<span class="arithmatex">\(i\)</span> 番目の品物の重さは <span class="arithmatex">\(wgt[i-1]\)</span>、価値は <span class="arithmatex">\(val[i-1]\)</span> であり、容量 <span class="arithmatex">\(cap\)</span> のナップサックがあります。<strong>各品物は繰り返し選択できます</strong>。ナップサック容量の制約下で入れられる品物の最大価値を求めてください。例を以下の図に示します。</p>
 </div>
-<p><img alt="無制限ナップサック問題の例データ" class="animation-figure" src="../unbounded_knapsack_problem.assets/unbounded_knapsack_example.png" /></p>
-<p align="center"> 図 14-22 &nbsp; 無制限ナップサック問題の例データ </p>
+<p><img alt="完全ナップサック問題のサンプルデータ" class="animation-figure" src="../unbounded_knapsack_problem.assets/unbounded_knapsack_example.png" /></p>
+<p align="center"> 図 14-22 &nbsp; 完全ナップサック問題のサンプルデータ </p>
 
-<h3 id="1">1. &nbsp; 動的プログラミングアプローチ<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>無制限ナップサック問題は0-1ナップサック問題と非常に似ており、<strong>唯一の違いはアイテムを選択できる回数に制限がないことです</strong>。</p>
+<h3 id="1">1. &nbsp; 動的計画法の考え方<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>完全ナップサック問題は 0-1 ナップサック問題と非常によく似ています。<strong>違いは、品物の選択回数に制限がない点だけです</strong>。</p>
 <ul>
-<li>0-1ナップサック問題では、各アイテムは1つしかないため、アイテム <span class="arithmatex">\(i\)</span> をバックパックに入れた後は、前の <span class="arithmatex">\(i-1\)</span> 個のアイテムからのみ選択できます。</li>
-<li>無制限ナップサック問題では、各アイテムの数量は無制限であるため、アイテム <span class="arithmatex">\(i\)</span> をバックパックに入れた後も、<strong>前の <span class="arithmatex">\(i\)</span> 個のアイテムから引き続き選択できます</strong>。</li>
+<li>0-1 ナップサック問題では、各品物は 1 つしかないため、品物 <span class="arithmatex">\(i\)</span> をナップサックに入れた後は先頭 <span class="arithmatex">\(i-1\)</span> 個の品物からしか選べません。</li>
+<li>完全ナップサック問題では、各品物の数は無限であるため、品物 <span class="arithmatex">\(i\)</span> をナップサックに入れた後も、<strong>引き続き先頭 <span class="arithmatex">\(i\)</span> 個の品物から選べます</strong>。</li>
 </ul>
-<p>無制限ナップサック問題のルールの下で、状態 <span class="arithmatex">\([i, c]\)</span> は2つの方法で変化できます。</p>
+<p>完全ナップサック問題では、状態 <span class="arithmatex">\([i, c]\)</span> の変化は 2 つの場合に分けられます。</p>
 <ul>
-<li><strong>アイテム <span class="arithmatex">\(i\)</span> を入れない</strong>：0-1ナップサック問題と同様に、<span class="arithmatex">\([i-1, c]\)</span> に遷移します。</li>
-<li><strong>アイテム <span class="arithmatex">\(i\)</span> を入れる</strong>：0-1ナップサック問題とは異なり、<span class="arithmatex">\([i, c-wgt[i-1]]\)</span> に遷移します。</li>
+<li><strong>品物 <span class="arithmatex">\(i\)</span> を入れない</strong> ：0-1 ナップサック問題と同様に、<span class="arithmatex">\([i-1, c]\)</span> へ遷移します。</li>
+<li><strong>品物 <span class="arithmatex">\(i\)</span> を入れる</strong> ：0-1 ナップサック問題とは異なり、<span class="arithmatex">\([i, c-wgt[i-1]]\)</span> へ遷移します。</li>
 </ul>
-<p>したがって、状態遷移方程式は次のようになります：</p>
+<p>したがって、状態遷移方程式は次のようになります。</p>
 <div class="arithmatex">\[
 dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
 \]</div>
 <h3 id="2">2. &nbsp; コード実装<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>2つの問題のコードを比較すると、状態遷移が <span class="arithmatex">\(i-1\)</span> から <span class="arithmatex">\(i\)</span> に変わり、残りは完全に同一です：</p>
+<p>2 つの問題のコードを比較すると、状態遷移の中で 1 か所だけ <span class="arithmatex">\(i-1\)</span> が <span class="arithmatex">\(i\)</span> に変わり、それ以外は完全に同じです。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
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 <div class="highlight"><span class="filename">unbounded_knapsack.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">unbounded_knapsack_dp</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">val</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">cap</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;完全ナップサック：動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;完全ナップサック問題：動的計画法&quot;&quot;&quot;</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">wgt</span><span class="p">)</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="c1"># dp テーブルを初期化</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">cap</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span>
@@ -4649,28 +4649,28 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">cap</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>            <span class="k">if</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">c</span><span class="p">:</span>
-<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>                <span class="c1"># ナップサック容量を超える場合、アイテム i を選択しない</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>                <span class="c1"># ナップサック容量を超えるなら品物 i は選ばない</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">]</span>
 <a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>            <span class="k">else</span><span class="p">:</span>
-<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>                <span class="c1"># アイテム i を選択しないのと選択するのとで大きい値</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>                <span class="c1"># 品物 i を選ばない場合と選ぶ場合の大きい方</span>
 <a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span> <span class="o">-</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span> <span class="o">+</span> <span class="n">val</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span>
 <a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">cap</span><span class="p">]</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">unbounded_knapsack.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 完全ナップサック：動的プログラミング */</span>
+<div class="highlight"><span class="filename">unbounded_knapsack.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 完全ナップサック問題：動的計画法 */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">unboundedKnapsackDP</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
-<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">));</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">                </span><span class="c1">// ナップサックの容量を超える場合、アイテム i を選択しない</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">];</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">                </span><span class="c1">// 選択しない場合とアイテム i を選択する場合のより大きい値</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
 <a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
 <a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">        </span><span class="p">}</span>
@@ -4680,19 +4680,19 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">unbounded_knapsack.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 完全ナップサック：動的プログラミング */</span>
+<div class="highlight"><span class="filename">unbounded_knapsack.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 完全ナップサック問題：動的計画法 */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">unboundedKnapsackDP</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
-<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">                </span><span class="c1">// ナップサックの容量を超える場合、アイテム i を選択しない</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
 <a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">                </span><span class="c1">// 選択しない場合とアイテム i を選択する場合のより大きい値</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
 <a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">max</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">);</span>
 <a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">        </span><span class="p">}</span>
@@ -4702,54 +4702,264 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">unbounded_knapsack.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">unbounded_knapsack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">UnboundedKnapsackDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">unbounded_knapsack.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 完全ナップサック問題：動的計画法 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">UnboundedKnapsackDP</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="kt">int</span><span class="p">[,]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">];</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">];</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">unbounded_knapsack.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">unboundedKnapsackDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">unbounded_knapsack.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 完全ナップサック問題：動的計画法 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">unboundedKnapsackDP</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">wgt</span><span class="p">)</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">cap</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Max</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">c</span><span class="p">]),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="o">-</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]]</span><span class="o">+</span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">])))</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">cap</span><span class="p">]</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">unbounded_knapsack.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">unboundedKnapsackDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">unbounded_knapsack.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 完全ナップサック問題：動的計画法 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">unboundedKnapsackDP</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">cap</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">),</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">]</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">cap</span><span class="p">]</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">unbounded_knapsack.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">unboundedKnapsackDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">unbounded_knapsack.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 完全ナップサック問題：動的計画法 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">unboundedKnapsackDP</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">wgt</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">        </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="nx">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="p">);</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">cap</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">c</span><span class="p">];</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">max</span><span class="p">(</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w">                    </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">c</span><span class="p">],</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w">                    </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">                </span><span class="p">);</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">cap</span><span class="p">];</span>
+<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">unbounded_knapsack.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">unboundedKnapsackDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">unbounded_knapsack.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 完全ナップサック問題：動的計画法 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">unboundedKnapsackDP</span><span class="p">(</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="nx">wgt</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="nx">cap</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">wgt</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="kt">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">        </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="kt">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">    </span><span class="p">);</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">cap</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">c</span><span class="p">];</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">max</span><span class="p">(</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="w">                    </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">c</span><span class="p">],</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="w">                    </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="w">                </span><span class="p">);</span>
+<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">cap</span><span class="p">];</span>
+<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">unbounded_knapsack.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">unboundedKnapsackDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">unbounded_knapsack.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 完全ナップサック問題：動的計画法 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">unboundedKnapsackDP</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">generate</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">));</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">        </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">][</span><span class="n">c</span><span class="p">];</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">      </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">        </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">][</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]);</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">cap</span><span class="p">];</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">unbounded_knapsack.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">unbounded_knapsack_dp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">unbounded_knapsack.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 完全ナップサック問題：動的計画法 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">unbounded_knapsack_dp</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">cap</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">cap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">];</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">cap</span><span class="p">];</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">unbounded_knapsack.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">unboundedKnapsackDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">unbounded_knapsack.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 完全ナップサック問題：動的計画法 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">unboundedKnapsackDP</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">wgt</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">wgtSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgtSize</span><span class="p">;</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">**</span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">((</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">));</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">calloc</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">];</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">myMax</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">cap</span><span class="p">];</span>
+<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="w">        </span><span class="n">free</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">unbounded_knapsack.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">unboundedKnapsackDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">unbounded_knapsack.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 完全ナップサック問題：動的計画法 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">unboundedKnapsackDP</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Array</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">_val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">cap</span><span class="o">]</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">unbounded_knapsack.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">unbounded_knapsack_dp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">unbounded_knapsack.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 完全ナップサック：動的計画法 ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">unbounded_knapsack_dp</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="c1"># dp テーブルを初期化</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="c1"># 状態遷移</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">        </span><span class="c1"># ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">      </span><span class="k">else</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">        </span><span class="c1"># 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]].</span><span class="n">max</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">cap</span><span class="o">]</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20unbounded_knapsack_dp%28wgt%3A%20list%5Bint%5D%2C%20val%3A%20list%5Bint%5D%2C%20cap%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%AE%8C%E5%85%A8%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%95%8F%E9%A1%8C%EF%BC%9A%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%20%3D%20len%28wgt%29%0A%20%20%20%20%23%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5B%5B0%5D%20%2A%20%28cap%20%2B%201%29%20for%20_%20in%20range%28n%20%2B%201%29%5D%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20for%20c%20in%20range%281%2C%20cap%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20wgt%5Bi%20-%201%5D%20%3E%20c%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%AA%E3%82%89%E5%93%81%E7%89%A9%20i%20%E3%81%AF%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Bc%5D%20%3D%20dp%5Bi%20-%201%5D%5Bc%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E5%93%81%E7%89%A9%20i%20%E3%82%92%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%E5%A0%B4%E5%90%88%E3%81%A8%E9%81%B8%E3%81%B6%E5%A0%B4%E5%90%88%E3%81%AE%E5%A4%A7%E3%81%8D%E3%81%84%E6%96%B9%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Bc%5D%20%3D%20max%28dp%5Bi%20-%201%5D%5Bc%5D%2C%20dp%5Bi%5D%5Bc%20-%20wgt%5Bi%20-%201%5D%5D%20%2B%20val%5Bi%20-%201%5D%29%0A%20%20%20%20return%20dp%5Bn%5D%5Bcap%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20wgt%20%3D%20%5B1%2C%202%2C%203%5D%0A%20%20%20%20val%20%3D%20%5B5%2C%2011%2C%2015%5D%0A%20%20%20%20cap%20%3D%204%0A%0A%20%20%20%20%23%20%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20unbounded_knapsack_dp%28wgt%2C%20val%2C%20cap%29%0A%20%20%20%20print%28f%22%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%81%AA%E3%81%84%E6%9C%80%E5%A4%A7%E4%BE%A1%E5%80%A4%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20unbounded_knapsack_dp%28wgt%3A%20list%5Bint%5D%2C%20val%3A%20list%5Bint%5D%2C%20cap%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%AE%8C%E5%85%A8%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%95%8F%E9%A1%8C%EF%BC%9A%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%20%3D%20len%28wgt%29%0A%20%20%20%20%23%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5B%5B0%5D%20%2A%20%28cap%20%2B%201%29%20for%20_%20in%20range%28n%20%2B%201%29%5D%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20for%20c%20in%20range%281%2C%20cap%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20wgt%5Bi%20-%201%5D%20%3E%20c%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%AA%E3%82%89%E5%93%81%E7%89%A9%20i%20%E3%81%AF%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Bc%5D%20%3D%20dp%5Bi%20-%201%5D%5Bc%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E5%93%81%E7%89%A9%20i%20%E3%82%92%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%E5%A0%B4%E5%90%88%E3%81%A8%E9%81%B8%E3%81%B6%E5%A0%B4%E5%90%88%E3%81%AE%E5%A4%A7%E3%81%8D%E3%81%84%E6%96%B9%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Bc%5D%20%3D%20max%28dp%5Bi%20-%201%5D%5Bc%5D%2C%20dp%5Bi%5D%5Bc%20-%20wgt%5Bi%20-%201%5D%5D%20%2B%20val%5Bi%20-%201%5D%29%0A%20%20%20%20return%20dp%5Bn%5D%5Bcap%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20wgt%20%3D%20%5B1%2C%202%2C%203%5D%0A%20%20%20%20val%20%3D%20%5B5%2C%2011%2C%2015%5D%0A%20%20%20%20cap%20%3D%204%0A%0A%20%20%20%20%23%20%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20unbounded_knapsack_dp%28wgt%2C%20val%2C%20cap%29%0A%20%20%20%20print%28f%22%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%81%AA%E3%81%84%E6%9C%80%E5%A4%A7%E4%BE%A1%E5%80%A4%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 <h3 id="3">3. &nbsp; 空間最適化<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
-<p>現在の状態は左と上の状態から来るため、<strong>空間最適化解法は <span class="arithmatex">\(dp\)</span> テーブルの各行に対して前方走査を実行する必要があります</strong>。</p>
-<p>この走査順序は0-1ナップサックの場合とは逆です。違いを理解するために下の図を参照してください。</p>
+<p>現在の状態は左側と上側の状態から遷移してくるため、<strong>空間最適化後は <span class="arithmatex">\(dp\)</span> テーブルの各行を順方向に走査する必要があります</strong>。</p>
+<p>この走査順序は 0-1 ナップサックとはちょうど逆です。両者の違いは次の図を用いて理解してください。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:6"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">&lt;1&gt;</label><label for="__tabbed_2_2">&lt;2&gt;</label><label for="__tabbed_2_3">&lt;3&gt;</label><label for="__tabbed_2_4">&lt;4&gt;</label><label for="__tabbed_2_5">&lt;5&gt;</label><label for="__tabbed_2_6">&lt;6&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="空間最適化後の無制限ナップサック問題の動的プログラミングプロセス" class="animation-figure" src="../unbounded_knapsack_problem.assets/unbounded_knapsack_dp_comp_step1.png" /></p>
+<p><img alt="完全ナップサック問題における空間最適化後の動的計画法の過程" class="animation-figure" src="../unbounded_knapsack_problem.assets/unbounded_knapsack_dp_comp_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="unbounded_knapsack_dp_comp_step2" class="animation-figure" src="../unbounded_knapsack_problem.assets/unbounded_knapsack_dp_comp_step2.png" /></p>
@@ -4768,44 +4978,44 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
 </div>
 </div>
 </div>
-<p align="center"> 図 14-23 &nbsp; 空間最適化後の無制限ナップサック問題の動的プログラミングプロセス </p>
+<p align="center"> 図 14-23 &nbsp; 完全ナップサック問題における空間最適化後の動的計画法の過程 </p>
 
-<p>コード実装は非常に簡単で、配列 <code>dp</code> の最初の次元を削除するだけです：</p>
+<p>コード実装は比較的簡単で、配列 <code>dp</code> の第 1 次元を削除するだけです。</p>
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 <div class="highlight"><span class="filename">unbounded_knapsack.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">unbounded_knapsack_dp_comp</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">val</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">cap</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;完全ナップサック：空間最適化動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;完全ナップサック問題：空間最適化後の動的計画法&quot;&quot;&quot;</span>
 <a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">wgt</span><span class="p">)</span>
 <a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="c1"># dp テーブルを初期化</span>
 <a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">cap</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
 <a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>    <span class="c1"># 状態遷移</span>
 <a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
-<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>        <span class="c1"># 順序で走査</span>
+<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>        <span class="c1"># 順方向に走査する</span>
 <a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>        <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">cap</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>            <span class="k">if</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">c</span><span class="p">:</span>
-<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>                <span class="c1"># ナップサック容量を超える場合、アイテム i を選択しない</span>
+<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>                <span class="c1"># ナップサック容量を超えるなら品物 i は選ばない</span>
 <a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span>
 <a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a>            <span class="k">else</span><span class="p">:</span>
-<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>                <span class="c1"># アイテム i を選択しないのと選択するのとで大きい値</span>
+<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>                <span class="c1"># 品物 i を選ばない場合と選ぶ場合の大きい方</span>
 <a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">c</span> <span class="o">-</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span> <span class="o">+</span> <span class="n">val</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span>
 <a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">cap</span><span class="p">]</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">unbounded_knapsack.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 完全ナップサック：空間最適化動的プログラミング */</span>
+<div class="highlight"><span class="filename">unbounded_knapsack.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 完全ナップサック問題：空間最適化後の動的計画法 */</span>
 <a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">unboundedKnapsackDPComp</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
-<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
 <a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
 <a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">                </span><span class="c1">// ナップサックの容量を超える場合、アイテム i を選択しない</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
 <a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">];</span>
 <a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">                </span><span class="c1">// 選択しない場合とアイテム i を選択する場合のより大きい値</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
 <a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
 <a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">        </span><span class="p">}</span>
@@ -4815,19 +5025,19 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">unbounded_knapsack.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 完全ナップサック：空間最適化動的プログラミング */</span>
+<div class="highlight"><span class="filename">unbounded_knapsack.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 完全ナップサック問題：空間最適化後の動的計画法 */</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">unboundedKnapsackDPComp</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
-<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
 <a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
 <a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">                </span><span class="c1">// ナップサックの容量を超える場合、アイテム i を選択しない</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
 <a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">                </span><span class="c1">// 選択しない場合とアイテム i を選択する場合のより大きい値</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
 <a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">max</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">);</span>
 <a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">        </span><span class="p">}</span>
@@ -4837,124 +5047,341 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">unbounded_knapsack.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">unbounded_knapsack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">UnboundedKnapsackDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">unbounded_knapsack.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 完全ナップサック問題：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">UnboundedKnapsackDPComp</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">];</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">cap</span><span class="p">];</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">unbounded_knapsack.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">unboundedKnapsackDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">unbounded_knapsack.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 完全ナップサック問題：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">unboundedKnapsackDPComp</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">wgt</span><span class="p">)</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">    </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">cap</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="p">]</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Max</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="p">]),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="o">-</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]]</span><span class="o">+</span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">])))</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">cap</span><span class="p">]</span>
+<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">unbounded_knapsack.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">unboundedKnapsackDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">unbounded_knapsack.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 完全ナップサック問題：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">unboundedKnapsackDPComp</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">cap</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span>
+<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">cap</span><span class="p">]</span>
+<a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">unbounded_knapsack.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">unboundedKnapsackDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">unbounded_knapsack.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 完全ナップサック問題：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">unboundedKnapsackDPComp</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">wgt</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="nx">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">cap</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="p">];</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">max</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]);</span>
+<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">cap</span><span class="p">];</span>
+<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">unbounded_knapsack.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">unboundedKnapsackDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">unbounded_knapsack.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 完全ナップサック問題：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">unboundedKnapsackDPComp</span><span class="p">(</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="nx">wgt</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">    </span><span class="nx">cap</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">wgt</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="kt">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">cap</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="p">];</span>
+<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-17" name="__codelineno-20-17" href="#__codelineno-20-17"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-20-18" name="__codelineno-20-18" href="#__codelineno-20-18"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">max</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]);</span>
+<a id="__codelineno-20-19" name="__codelineno-20-19" href="#__codelineno-20-19"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-20-20" name="__codelineno-20-20" href="#__codelineno-20-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-21" name="__codelineno-20-21" href="#__codelineno-20-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-22" name="__codelineno-20-22" href="#__codelineno-20-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">cap</span><span class="p">];</span>
+<a id="__codelineno-20-23" name="__codelineno-20-23" href="#__codelineno-20-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">unbounded_knapsack.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">unboundedKnapsackDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">unbounded_knapsack.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 完全ナップサック問題：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">unboundedKnapsackDPComp</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">  </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="w">        </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">];</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w">      </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">        </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]);</span>
+<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-17" name="__codelineno-21-17" href="#__codelineno-21-17"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-18" name="__codelineno-21-18" href="#__codelineno-21-18"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">cap</span><span class="p">];</span>
+<a id="__codelineno-21-19" name="__codelineno-21-19" href="#__codelineno-21-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">unbounded_knapsack.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">unbounded_knapsack_dp_comp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">unbounded_knapsack.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 完全ナップサック問題：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">unbounded_knapsack_dp_comp</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">cap</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">cap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">];</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="n">cap</span><span class="p">]</span>
+<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">unbounded_knapsack.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">unboundedKnapsackDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">unbounded_knapsack.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 完全ナップサック問題：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">unboundedKnapsackDPComp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">wgt</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">wgtSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgtSize</span><span class="p">;</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">calloc</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">];</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">myMax</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">cap</span><span class="p">];</span>
+<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">dp</span><span class="p">);</span>
+<a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">unbounded_knapsack.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">unboundedKnapsackDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">unbounded_knapsack.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 完全ナップサック問題：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">unboundedKnapsackDPComp</span><span class="p">(</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="n">_val</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">    </span><span class="n">cap</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w">                </span><span class="c1">// ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span>
+<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-17" name="__codelineno-24-17" href="#__codelineno-24-17"></a><span class="w">                </span><span class="c1">// 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-24-18" name="__codelineno-24-18" href="#__codelineno-24-18"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">_val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-24-19" name="__codelineno-24-19" href="#__codelineno-24-19"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-24-20" name="__codelineno-24-20" href="#__codelineno-24-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-24-21" name="__codelineno-24-21" href="#__codelineno-24-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-22" name="__codelineno-24-22" href="#__codelineno-24-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">cap</span><span class="o">]</span>
+<a id="__codelineno-24-23" name="__codelineno-24-23" href="#__codelineno-24-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">unbounded_knapsack.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">unbounded_knapsack_dp_comp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">unbounded_knapsack.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### 完全ナップサック：動的計画法 ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">unbounded_knapsack_dp</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">  </span><span class="c1"># dp テーブルを初期化</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">  </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">  </span><span class="c1"># 状態遷移</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w">        </span><span class="c1"># ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w">      </span><span class="k">else</span>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w">        </span><span class="c1"># 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]].</span><span class="n">max</span>
+<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">cap</span><span class="o">]</span>
+<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="k">end</span>
+<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a>
+<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="c1"># ## 完全ナップサック: 空間最適化後の動的計画法 ##3</span>
+<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a><span class="k">def</span><span class="w"> </span><span class="nf">unbounded_knapsack_dp_comp</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span>
+<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="w">  </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a><span class="w">  </span><span class="c1"># dp テーブルを初期化</span>
+<a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a><span class="w">  </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></a><span class="w">  </span><span class="c1"># 状態遷移</span>
+<a id="__codelineno-25-27" name="__codelineno-25-27" href="#__codelineno-25-27"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-25-28" name="__codelineno-25-28" href="#__codelineno-25-28"></a><span class="w">    </span><span class="c1"># 順方向に走査する</span>
+<a id="__codelineno-25-29" name="__codelineno-25-29" href="#__codelineno-25-29"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-25-30" name="__codelineno-25-30" href="#__codelineno-25-30"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span>
+<a id="__codelineno-25-31" name="__codelineno-25-31" href="#__codelineno-25-31"></a><span class="w">        </span><span class="c1"># ナップサック容量を超えるなら品物 i は選ばない</span>
+<a id="__codelineno-25-32" name="__codelineno-25-32" href="#__codelineno-25-32"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span>
+<a id="__codelineno-25-33" name="__codelineno-25-33" href="#__codelineno-25-33"></a><span class="w">      </span><span class="k">else</span>
+<a id="__codelineno-25-34" name="__codelineno-25-34" href="#__codelineno-25-34"></a><span class="w">        </span><span class="c1"># 品物 i を選ばない場合と選ぶ場合の大きい方</span>
+<a id="__codelineno-25-35" name="__codelineno-25-35" href="#__codelineno-25-35"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]].</span><span class="n">max</span>
+<a id="__codelineno-25-36" name="__codelineno-25-36" href="#__codelineno-25-36"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-25-37" name="__codelineno-25-37" href="#__codelineno-25-37"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-25-38" name="__codelineno-25-38" href="#__codelineno-25-38"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-39" name="__codelineno-25-39" href="#__codelineno-25-39"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="n">cap</span><span class="o">]</span>
+<a id="__codelineno-25-40" name="__codelineno-25-40" href="#__codelineno-25-40"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h2 id="1452">14.5.2 &nbsp; コイン交換問題<a class="headerlink" href="#1452" title="Permanent link">&para;</a></h2>
-<p>ナップサック問題は動的プログラミング問題の大きなクラスの代表であり、コイン交換問題など多くの変種があります。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20unbounded_knapsack_dp_comp%28wgt%3A%20list%5Bint%5D%2C%20val%3A%20list%5Bint%5D%2C%20cap%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%AE%8C%E5%85%A8%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%95%8F%E9%A1%8C%EF%BC%9A%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E5%BE%8C%E3%81%AE%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%20%3D%20len%28wgt%29%0A%20%20%20%20%23%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5B0%5D%20%2A%20%28cap%20%2B%201%29%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E9%A0%86%E6%96%B9%E5%90%91%E3%81%AB%E8%B5%B0%E6%9F%BB%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20for%20c%20in%20range%281%2C%20cap%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20wgt%5Bi%20-%201%5D%20%3E%20c%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%AA%E3%82%89%E5%93%81%E7%89%A9%20i%20%E3%81%AF%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bc%5D%20%3D%20dp%5Bc%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E5%93%81%E7%89%A9%20i%20%E3%82%92%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%E5%A0%B4%E5%90%88%E3%81%A8%E9%81%B8%E3%81%B6%E5%A0%B4%E5%90%88%E3%81%AE%E5%A4%A7%E3%81%8D%E3%81%84%E6%96%B9%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bc%5D%20%3D%20max%28dp%5Bc%5D%2C%20dp%5Bc%20-%20wgt%5Bi%20-%201%5D%5D%20%2B%20val%5Bi%20-%201%5D%29%0A%20%20%20%20return%20dp%5Bcap%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20wgt%20%3D%20%5B1%2C%202%2C%203%5D%0A%20%20%20%20val%20%3D%20%5B5%2C%2011%2C%2015%5D%0A%20%20%20%20cap%20%3D%204%0A%0A%20%20%20%20%23%20%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E5%BE%8C%E3%81%AE%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20unbounded_knapsack_dp_comp%28wgt%2C%20val%2C%20cap%29%0A%20%20%20%20print%28f%22%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%81%AA%E3%81%84%E6%9C%80%E5%A4%A7%E4%BE%A1%E5%80%A4%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20unbounded_knapsack_dp_comp%28wgt%3A%20list%5Bint%5D%2C%20val%3A%20list%5Bint%5D%2C%20cap%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%AE%8C%E5%85%A8%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%95%8F%E9%A1%8C%EF%BC%9A%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E5%BE%8C%E3%81%AE%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%20%3D%20len%28wgt%29%0A%20%20%20%20%23%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5B0%5D%20%2A%20%28cap%20%2B%201%29%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E9%A0%86%E6%96%B9%E5%90%91%E3%81%AB%E8%B5%B0%E6%9F%BB%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20for%20c%20in%20range%281%2C%20cap%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20wgt%5Bi%20-%201%5D%20%3E%20c%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%AA%E3%82%89%E5%93%81%E7%89%A9%20i%20%E3%81%AF%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bc%5D%20%3D%20dp%5Bc%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E5%93%81%E7%89%A9%20i%20%E3%82%92%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%E5%A0%B4%E5%90%88%E3%81%A8%E9%81%B8%E3%81%B6%E5%A0%B4%E5%90%88%E3%81%AE%E5%A4%A7%E3%81%8D%E3%81%84%E6%96%B9%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bc%5D%20%3D%20max%28dp%5Bc%5D%2C%20dp%5Bc%20-%20wgt%5Bi%20-%201%5D%5D%20%2B%20val%5Bi%20-%201%5D%29%0A%20%20%20%20return%20dp%5Bcap%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20wgt%20%3D%20%5B1%2C%202%2C%203%5D%0A%20%20%20%20val%20%3D%20%5B5%2C%2011%2C%2015%5D%0A%20%20%20%20cap%20%3D%204%0A%0A%20%20%20%20%23%20%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E5%BE%8C%E3%81%AE%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20unbounded_knapsack_dp_comp%28wgt%2C%20val%2C%20cap%29%0A%20%20%20%20print%28f%22%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%81%AA%E3%81%84%E6%9C%80%E5%A4%A7%E4%BE%A1%E5%80%A4%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h2 id="1452">14.5.2 &nbsp; 硬貨交換問題<a class="headerlink" href="#1452" title="Permanent link">&para;</a></h2>
+<p>ナップサック問題は動的計画法の代表的な問題群であり、多くの派生問題があります。硬貨交換問題もその 1 つです。</p>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
-<p><span class="arithmatex">\(n\)</span> 種類のコインが与えられ、<span class="arithmatex">\(i\)</span> 番目の種類のコインの額面は <span class="arithmatex">\(coins[i - 1]\)</span> で、目標金額は <span class="arithmatex">\(amt\)</span> です。<strong>各種類のコインは複数回選択できます</strong>。目標金額を構成するのに必要な最小コイン数は何ですか？目標金額を構成できない場合は <span class="arithmatex">\(-1\)</span> を返してください。以下の例を参照してください。</p>
+<p><span class="arithmatex">\(n\)</span> 種類の硬貨が与えられ、<span class="arithmatex">\(i\)</span> 番目の硬貨の額面は <span class="arithmatex">\(coins[i - 1]\)</span> 、目標金額は <span class="arithmatex">\(amt\)</span> です。<strong>各硬貨は繰り返し選択できます</strong>。目標金額を作るために必要な最小の硬貨枚数を求めてください。目標金額を作れない場合は <span class="arithmatex">\(-1\)</span> を返します。例を以下の図に示します。</p>
 </div>
-<p><img alt="コイン交換問題の例データ" class="animation-figure" src="../unbounded_knapsack_problem.assets/coin_change_example.png" /></p>
-<p align="center"> 図 14-24 &nbsp; コイン交換問題の例データ </p>
+<p><img alt="硬貨交換問題のサンプルデータ" class="animation-figure" src="../unbounded_knapsack_problem.assets/coin_change_example.png" /></p>
+<p align="center"> 図 14-24 &nbsp; 硬貨交換問題のサンプルデータ </p>
 
-<h3 id="1_1">1. &nbsp; 動的プログラミングアプローチ<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
-<p><strong>コイン交換は無制限ナップサック問題の特殊ケースと見なすことができ</strong>、以下の類似点と相違点を共有しています。</p>
+<h3 id="1_1">1. &nbsp; 動的計画法の考え方<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
+<p><strong>硬貨交換は完全ナップサック問題の特殊なケースとみなせます</strong>。両者には次の対応関係と相違点があります。</p>
 <ul>
-<li>2つの問題は互いに変換できます：「アイテム」は「コイン」に対応し、「アイテムの重量」は「コインの額面」に対応し、「バックパックの容量」は「目標金額」に対応します。</li>
-<li>最適化目標は逆です：無制限ナップサック問題はアイテムの値を最大化することを目的とし、コイン交換問題はコインの数を最小化することを目的とします。</li>
-<li>無制限ナップサック問題はバックパック容量を「超えない」解を求め、コイン交換は目標金額を「正確に」構成する解を求めます。</li>
+<li>2 つの問題は相互に変換でき、「品物」は「硬貨」、「品物の重さ」は「硬貨の額面」、「ナップサック容量」は「目標金額」に対応します。</li>
+<li>最適化の目標は逆であり、完全ナップサック問題は品物価値の最大化、硬貨交換問題は硬貨枚数の最小化を目指します。</li>
+<li>完全ナップサック問題はナップサック容量を「超えない」解を求めますが、硬貨交換は目標金額に「ちょうど」一致する解を求めます。</li>
 </ul>
-<p><strong>第1ステップ：各ラウンドの意思決定を考え、状態を定義し、それにより <span class="arithmatex">\(dp\)</span> テーブルを導出する</strong></p>
-<p>状態 <span class="arithmatex">\([i, a]\)</span> は部分問題に対応します：<strong>最初の <span class="arithmatex">\(i\)</span> 種類のコインを使用して金額 <span class="arithmatex">\(a\)</span> を構成できる最小コイン数</strong>、<span class="arithmatex">\(dp[i, a]\)</span> と表記されます。</p>
-<p>二次元 <span class="arithmatex">\(dp\)</span> テーブルのサイズは <span class="arithmatex">\((n+1) \times (amt+1)\)</span> です。</p>
-<p><strong>第2ステップ：最適部分構造を特定し、状態遷移方程式を導出する</strong></p>
-<p>この問題は状態遷移方程式の2つの側面で無制限ナップサック問題と異なります。</p>
+<p><strong>ステップ 1：各ラウンドの選択を考え、状態を定義して、<span class="arithmatex">\(dp\)</span> テーブルを得る</strong></p>
+<p>状態 <span class="arithmatex">\([i, a]\)</span> に対応する部分問題は、**先頭 <span class="arithmatex">\(i\)</span> 種類の硬貨で金額 <span class="arithmatex">\(a\)</span> を作るための最小硬貨枚数**であり、これを <span class="arithmatex">\(dp[i, a]\)</span> と表します。</p>
+<p>2 次元 <span class="arithmatex">\(dp\)</span> テーブルのサイズは <span class="arithmatex">\((n+1) \times (amt+1)\)</span> です。</p>
+<p><strong>ステップ 2：最適部分構造を見つけ、状態遷移方程式を導く</strong></p>
+<p>本問の状態遷移方程式は、完全ナップサック問題と比べて次の 2 点が異なります。</p>
 <ul>
-<li>この問題は最小値を求めるため、演算子 <span class="arithmatex">\(\max()\)</span> を <span class="arithmatex">\(\min()\)</span> に変更する必要があります。</li>
-<li>最適化はコインの数に焦点を当てているため、コインが選択されたときに単純に <span class="arithmatex">\(+1\)</span> を追加します。</li>
+<li>本問では最小値を求めるため、演算子 <span class="arithmatex">\(\max()\)</span> を <span class="arithmatex">\(\min()\)</span> に変更する必要があります。</li>
+<li>最適化の対象は品物価値ではなく硬貨枚数であるため、硬貨を選んだときは <span class="arithmatex">\(+1\)</span> すれば十分です。</li>
 </ul>
 <div class="arithmatex">\[
 dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
 \]</div>
-<p><strong>第3ステップ：境界条件と状態遷移順序を定義する</strong></p>
-<p>目標金額が <span class="arithmatex">\(0\)</span> の場合、それを構成するのに必要な最小コイン数は <span class="arithmatex">\(0\)</span> であるため、最初の列のすべての <span class="arithmatex">\(dp[i, 0]\)</span> は <span class="arithmatex">\(0\)</span> です。</p>
-<p>コインがない場合、**任意の金額 &gt;0 を構成することは不可能**であり、これは無効な解です。状態遷移方程式の <span class="arithmatex">\(\min()\)</span> 関数が無効な解を認識してフィルタリングできるように、<span class="arithmatex">\(+\infty\)</span> を使用してそれらを表現することを検討し、つまり最初の行のすべての <span class="arithmatex">\(dp[0, a]\)</span> を <span class="arithmatex">\(+\infty\)</span> に設定します。</p>
+<p><strong>ステップ 3：境界条件と状態遷移順序を決める</strong></p>
+<p>目標金額が <span class="arithmatex">\(0\)</span> のとき、それを作るための最小硬貨枚数は <span class="arithmatex">\(0\)</span> です。つまり、先頭列のすべての <span class="arithmatex">\(dp[i, 0]\)</span> は <span class="arithmatex">\(0\)</span> になります。</p>
+<p>硬貨が 1 枚もない場合、<strong>任意の <span class="arithmatex">\(&gt; 0\)</span> の目標金額を作ることはできません</strong>。これは無効解です。状態遷移方程式内の <span class="arithmatex">\(\min()\)</span> 関数が無効解を識別して除外できるように、それらを <span class="arithmatex">\(+ \infty\)</span> で表すことを考えます。すなわち、先頭行のすべての <span class="arithmatex">\(dp[0, a]\)</span> を <span class="arithmatex">\(+ \infty\)</span> とします。</p>
 <h3 id="2_1">2. &nbsp; コード実装<a class="headerlink" href="#2_1" title="Permanent link">&para;</a></h3>
-<p>ほとんどのプログラミング言語は <span class="arithmatex">\(+\infty\)</span> 変数を提供しておらず、整数 <code>int</code> の最大値のみを代替として使用できます。これによりオーバーフローが発生する可能性があります：状態遷移方程式の <span class="arithmatex">\(+1\)</span> 演算がオーバーフローする可能性があります。</p>
-<p>この理由で、数値 <span class="arithmatex">\(amt + 1\)</span> を使用して無効な解を表します。なぜなら、<span class="arithmatex">\(amt\)</span> を構成するのに必要な最大コイン数は最大でも <span class="arithmatex">\(amt\)</span> だからです。結果を返す前に、<span class="arithmatex">\(dp[n, amt]\)</span> が <span class="arithmatex">\(amt + 1\)</span> に等しいかどうかを確認し、そうであれば <span class="arithmatex">\(-1\)</span> を返し、目標金額を構成できないことを示します。コードは以下の通りです：</p>
+<p>多くのプログラミング言語には <span class="arithmatex">\(+ \infty\)</span> を表す変数が用意されていないため、通常は整数型 <code>int</code> の最大値で代用します。しかし、その場合は大きな数のオーバーフローが起こり得ます。状態遷移方程式中の <span class="arithmatex">\(+ 1\)</span> 操作で桁あふれが発生する可能性があるためです。</p>
+<p>そのため、ここでは数値 <span class="arithmatex">\(amt + 1\)</span> を無効解の表現として用います。金額 <span class="arithmatex">\(amt\)</span> を作るための硬貨枚数は最大でも <span class="arithmatex">\(amt\)</span> 枚だからです。最後に返す前に、<span class="arithmatex">\(dp[n, amt]\)</span> が <span class="arithmatex">\(amt + 1\)</span> に等しいかを判定し、等しければ <span class="arithmatex">\(-1\)</span> を返して目標金額を作れないことを表します。コードは次のとおりです。</p>
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 <div class="highlight"><span class="filename">coin_change.py</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_dp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">amt</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;硬貨交換：動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;コイン両替：動的計画法&quot;&quot;&quot;</span>
 <a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">coins</span><span class="p">)</span>
 <a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>    <span class="n">MAX</span> <span class="o">=</span> <span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span>
 <a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a>    <span class="c1"># dp テーブルを初期化</span>
 <a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span>
-<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a>    <span class="c1"># 状態遷移：最初の行と最初の列</span>
+<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a>    <span class="c1"># 状態遷移：先頭行と先頭列</span>
 <a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>    <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a>        <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="n">MAX</span>
-<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a>    <span class="c1"># 状態遷移：残りの行と列</span>
+<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a>    <span class="c1"># 状態遷移: 残りの行と列</span>
 <a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a>        <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a>            <span class="k">if</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">a</span><span class="p">:</span>
-<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a>                <span class="c1"># 目標金額を超える場合、硬貨 i を選択しない</span>
+<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a>                <span class="c1"># 目標金額を超えるなら硬貨 i は選ばない</span>
 <a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">]</span>
 <a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a>            <span class="k">else</span><span class="p">:</span>
-<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a>                <span class="c1"># 硬貨 i を選択しないのと選択するのとで小さい値</span>
+<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a>                <span class="c1"># 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
 <a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span> <span class="o">-</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
 <a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span> <span class="k">if</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span> <span class="o">!=</span> <span class="n">MAX</span> <span class="k">else</span> <span class="o">-</span><span class="mi">1</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* 硬貨両替：動的プログラミング */</span>
+<div class="highlight"><span class="filename">coin_change.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* コイン両替：動的計画法 */</span>
 <a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeDP</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
 <a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
 <a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">));</span>
-<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">    </span><span class="c1">// 状態遷移：最初の行と最初の列</span>
+<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行と先頭列</span>
 <a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MAX</span><span class="p">;</span>
 <a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行と列</span>
+<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
 <a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="w">                </span><span class="c1">// 目標金額を超える場合、硬貨 i を選択しない</span>
+<a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
 <a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">];</span>
 <a id="__codelineno-27-17" name="__codelineno-27-17" href="#__codelineno-27-17"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-18" name="__codelineno-27-18" href="#__codelineno-27-18"></a><span class="w">                </span><span class="c1">// 選択しない場合と硬貨 i を選択する場合のより小さい値</span>
+<a id="__codelineno-27-18" name="__codelineno-27-18" href="#__codelineno-27-18"></a><span class="w">                </span><span class="c1">// 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
 <a id="__codelineno-27-19" name="__codelineno-27-19" href="#__codelineno-27-19"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-27-20" name="__codelineno-27-20" href="#__codelineno-27-20"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-27-21" name="__codelineno-27-21" href="#__codelineno-27-21"></a><span class="w">        </span><span class="p">}</span>
@@ -4964,24 +5391,24 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 硬貨両替：動的プログラミング */</span>
+<div class="highlight"><span class="filename">coin_change.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* コイン両替：動的計画法 */</span>
 <a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeDP</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
 <a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
 <a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w">    </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">    </span><span class="c1">// 状態遷移：最初の行と最初の列</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行と先頭列</span>
 <a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MAX</span><span class="p">;</span>
 <a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行と列</span>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
 <a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="w">                </span><span class="c1">// 目標金額を超える場合、硬貨 i を選択しない</span>
+<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
 <a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-28-18" name="__codelineno-28-18" href="#__codelineno-28-18"></a><span class="w">                </span><span class="c1">// 選択しない場合と硬貨 i を選択する場合のより小さい値</span>
+<a id="__codelineno-28-18" name="__codelineno-28-18" href="#__codelineno-28-18"></a><span class="w">                </span><span class="c1">// 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
 <a id="__codelineno-28-19" name="__codelineno-28-19" href="#__codelineno-28-19"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-28-20" name="__codelineno-28-20" href="#__codelineno-28-20"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-28-21" name="__codelineno-28-21" href="#__codelineno-28-21"></a><span class="w">        </span><span class="p">}</span>
@@ -4991,52 +5418,308 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">coin_change</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">CoinChangeDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* コイン両替：動的計画法 */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">CoinChangeDP</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="kt">int</span><span class="p">[,]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行と先頭列</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MAX</span><span class="p">;</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">];</span>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w">                </span><span class="c1">// 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
+<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-29-20" name="__codelineno-29-20" href="#__codelineno-29-20"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-29-21" name="__codelineno-29-21" href="#__codelineno-29-21"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-22" name="__codelineno-29-22" href="#__codelineno-29-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-23" name="__codelineno-29-23" href="#__codelineno-29-23"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-29-24" name="__codelineno-29-24" href="#__codelineno-29-24"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">coinChangeDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* コイン両替：動的計画法 */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">coinChangeDP</span><span class="p">(</span><span class="nx">coins</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">coins</span><span class="p">)</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="nx">max</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行と先頭列</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">amt</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">max</span>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">amt</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span>
+<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-21" name="__codelineno-30-21" href="#__codelineno-30-21"></a><span class="w">                </span><span class="c1">// 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
+<a id="__codelineno-30-22" name="__codelineno-30-22" href="#__codelineno-30-22"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Min</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">a</span><span class="p">]),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">a</span><span class="o">-</span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]]</span><span class="o">+</span><span class="mi">1</span><span class="p">)))</span>
+<a id="__codelineno-30-23" name="__codelineno-30-23" href="#__codelineno-30-23"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-30-24" name="__codelineno-30-24" href="#__codelineno-30-24"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-30-25" name="__codelineno-30-25" href="#__codelineno-30-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-26" name="__codelineno-30-26" href="#__codelineno-30-26"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nx">max</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-27" name="__codelineno-30-27" href="#__codelineno-30-27"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">amt</span><span class="p">]</span>
+<a id="__codelineno-30-28" name="__codelineno-30-28" href="#__codelineno-30-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-29" name="__codelineno-30-29" href="#__codelineno-30-29"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-30-30" name="__codelineno-30-30" href="#__codelineno-30-30"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">coinChangeDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* コイン両替：動的計画法 */</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">coinChangeDP</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">MAX</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">),</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行と先頭列</span>
+<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">MAX</span>
+<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-31-16" name="__codelineno-31-16" href="#__codelineno-31-16"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">]</span>
+<a id="__codelineno-31-17" name="__codelineno-31-17" href="#__codelineno-31-17"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-18" name="__codelineno-31-18" href="#__codelineno-31-18"></a><span class="w">                </span><span class="c1">// 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
+<a id="__codelineno-31-19" name="__codelineno-31-19" href="#__codelineno-31-19"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-31-20" name="__codelineno-31-20" href="#__codelineno-31-20"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-31-21" name="__codelineno-31-21" href="#__codelineno-31-21"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-31-22" name="__codelineno-31-22" href="#__codelineno-31-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-23" name="__codelineno-31-23" href="#__codelineno-31-23"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="p">?</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-31-24" name="__codelineno-31-24" href="#__codelineno-31-24"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">coinChangeDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* コイン両替：動的計画法 */</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">coinChangeDP</span><span class="p">(</span><span class="nx">coins</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coins</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span>
+<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="w">        </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span>
+<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w">    </span><span class="p">);</span>
+<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行と先頭列</span>
+<a id="__codelineno-32-10" name="__codelineno-32-10" href="#__codelineno-32-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">amt</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">MAX</span><span class="p">;</span>
+<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-32-14" name="__codelineno-32-14" href="#__codelineno-32-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-15" name="__codelineno-32-15" href="#__codelineno-32-15"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">amt</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-16" name="__codelineno-32-16" href="#__codelineno-32-16"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-17" name="__codelineno-32-17" href="#__codelineno-32-17"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-32-18" name="__codelineno-32-18" href="#__codelineno-32-18"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">a</span><span class="p">];</span>
+<a id="__codelineno-32-19" name="__codelineno-32-19" href="#__codelineno-32-19"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-20" name="__codelineno-32-20" href="#__codelineno-32-20"></a><span class="w">                </span><span class="c1">// 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
+<a id="__codelineno-32-21" name="__codelineno-32-21" href="#__codelineno-32-21"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">a</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-32-22" name="__codelineno-32-22" href="#__codelineno-32-22"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-32-23" name="__codelineno-32-23" href="#__codelineno-32-23"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-32-24" name="__codelineno-32-24" href="#__codelineno-32-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-25" name="__codelineno-32-25" href="#__codelineno-32-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="nx">MAX</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">amt</span><span class="p">]</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-32-26" name="__codelineno-32-26" href="#__codelineno-32-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">coinChangeDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* コイン両替：動的計画法 */</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">coinChangeDP</span><span class="p">(</span><span class="nx">coins</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coins</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="kt">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span>
+<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w">        </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="kt">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span>
+<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w">    </span><span class="p">);</span>
+<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行と先頭列</span>
+<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">amt</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">MAX</span><span class="p">;</span>
+<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">amt</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-16" name="__codelineno-33-16" href="#__codelineno-33-16"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-17" name="__codelineno-33-17" href="#__codelineno-33-17"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-33-18" name="__codelineno-33-18" href="#__codelineno-33-18"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">a</span><span class="p">];</span>
+<a id="__codelineno-33-19" name="__codelineno-33-19" href="#__codelineno-33-19"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-20" name="__codelineno-33-20" href="#__codelineno-33-20"></a><span class="w">                </span><span class="c1">// 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
+<a id="__codelineno-33-21" name="__codelineno-33-21" href="#__codelineno-33-21"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">a</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-33-22" name="__codelineno-33-22" href="#__codelineno-33-22"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-33-23" name="__codelineno-33-23" href="#__codelineno-33-23"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-33-24" name="__codelineno-33-24" href="#__codelineno-33-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-25" name="__codelineno-33-25" href="#__codelineno-33-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="nx">MAX</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">amt</span><span class="p">]</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-33-26" name="__codelineno-33-26" href="#__codelineno-33-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* コイン両替：動的計画法 */</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">coinChangeDP</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w">  </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">generate</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">));</span>
+<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w">  </span><span class="c1">// 状態遷移：先頭行と先頭列</span>
+<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="m">0</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MAX</span><span class="p">;</span>
+<a id="__codelineno-34-10" name="__codelineno-34-10" href="#__codelineno-34-10"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-11" name="__codelineno-34-11" href="#__codelineno-34-11"></a><span class="w">  </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-34-12" name="__codelineno-34-12" href="#__codelineno-34-12"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-13" name="__codelineno-34-13" href="#__codelineno-34-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-14" name="__codelineno-34-14" href="#__codelineno-34-14"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-15" name="__codelineno-34-15" href="#__codelineno-34-15"></a><span class="w">        </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-34-16" name="__codelineno-34-16" href="#__codelineno-34-16"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">][</span><span class="n">a</span><span class="p">];</span>
+<a id="__codelineno-34-17" name="__codelineno-34-17" href="#__codelineno-34-17"></a><span class="w">      </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-18" name="__codelineno-34-18" href="#__codelineno-34-18"></a><span class="w">        </span><span class="c1">// 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
+<a id="__codelineno-34-19" name="__codelineno-34-19" href="#__codelineno-34-19"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">][</span><span class="n">a</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-34-20" name="__codelineno-34-20" href="#__codelineno-34-20"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-34-21" name="__codelineno-34-21" href="#__codelineno-34-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-22" name="__codelineno-34-22" href="#__codelineno-34-22"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-23" name="__codelineno-34-23" href="#__codelineno-34-23"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-34-24" name="__codelineno-34-24" href="#__codelineno-34-24"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coin_change_dp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* コイン両替：動的計画法 */</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">coin_change_dp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
+<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行と先頭列</span>
+<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">amt</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">;</span>
+<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-35-12" name="__codelineno-35-12" href="#__codelineno-35-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-13" name="__codelineno-35-13" href="#__codelineno-35-13"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">amt</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-14" name="__codelineno-35-14" href="#__codelineno-35-14"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-15" name="__codelineno-35-15" href="#__codelineno-35-15"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-35-16" name="__codelineno-35-16" href="#__codelineno-35-16"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">];</span>
+<a id="__codelineno-35-17" name="__codelineno-35-17" href="#__codelineno-35-17"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-18" name="__codelineno-35-18" href="#__codelineno-35-18"></a><span class="w">                </span><span class="c1">// 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
+<a id="__codelineno-35-19" name="__codelineno-35-19" href="#__codelineno-35-19"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-35-20" name="__codelineno-35-20" href="#__codelineno-35-20"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-35-21" name="__codelineno-35-21" href="#__codelineno-35-21"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-35-22" name="__codelineno-35-22" href="#__codelineno-35-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-23" name="__codelineno-35-23" href="#__codelineno-35-23"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-24" name="__codelineno-35-24" href="#__codelineno-35-24"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">;</span>
+<a id="__codelineno-35-25" name="__codelineno-35-25" href="#__codelineno-35-25"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-26" name="__codelineno-35-26" href="#__codelineno-35-26"></a><span class="w">        </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-35-27" name="__codelineno-35-27" href="#__codelineno-35-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-28" name="__codelineno-35-28" href="#__codelineno-35-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* コイン両替：動的計画法 */</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeDP</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">coins</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">coinsSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coinsSize</span><span class="p">;</span>
+<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">**</span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">((</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">));</span>
+<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">calloc</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行と先頭列</span>
+<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MAX</span><span class="p">;</span>
+<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-14" name="__codelineno-36-14" href="#__codelineno-36-14"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-36-15" name="__codelineno-36-15" href="#__codelineno-36-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-16" name="__codelineno-36-16" href="#__codelineno-36-16"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-17" name="__codelineno-36-17" href="#__codelineno-36-17"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-18" name="__codelineno-36-18" href="#__codelineno-36-18"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-36-19" name="__codelineno-36-19" href="#__codelineno-36-19"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">];</span>
+<a id="__codelineno-36-20" name="__codelineno-36-20" href="#__codelineno-36-20"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-21" name="__codelineno-36-21" href="#__codelineno-36-21"></a><span class="w">                </span><span class="c1">// 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
+<a id="__codelineno-36-22" name="__codelineno-36-22" href="#__codelineno-36-22"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">myMin</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-36-23" name="__codelineno-36-23" href="#__codelineno-36-23"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-36-24" name="__codelineno-36-24" href="#__codelineno-36-24"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-36-25" name="__codelineno-36-25" href="#__codelineno-36-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-26" name="__codelineno-36-26" href="#__codelineno-36-26"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-36-27" name="__codelineno-36-27" href="#__codelineno-36-27"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-36-28" name="__codelineno-36-28" href="#__codelineno-36-28"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-29" name="__codelineno-36-29" href="#__codelineno-36-29"></a><span class="w">        </span><span class="n">free</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-36-30" name="__codelineno-36-30" href="#__codelineno-36-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-31" name="__codelineno-36-31" href="#__codelineno-36-31"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">dp</span><span class="p">);</span>
+<a id="__codelineno-36-32" name="__codelineno-36-32" href="#__codelineno-36-32"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-36-33" name="__codelineno-36-33" href="#__codelineno-36-33"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coinChangeDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* コイン両替：動的計画法 */</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">coinChangeDP</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Array</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w">    </span><span class="c1">// 状態遷移：先頭行と先頭列</span>
+<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="m">0</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MAX</span>
+<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-14" name="__codelineno-37-14" href="#__codelineno-37-14"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-15" name="__codelineno-37-15" href="#__codelineno-37-15"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-37-16" name="__codelineno-37-16" href="#__codelineno-37-16"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">][</span><span class="n">a</span><span class="o">]</span>
+<a id="__codelineno-37-17" name="__codelineno-37-17" href="#__codelineno-37-17"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-18" name="__codelineno-37-18" href="#__codelineno-37-18"></a><span class="w">                </span><span class="c1">// 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
+<a id="__codelineno-37-19" name="__codelineno-37-19" href="#__codelineno-37-19"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-37-20" name="__codelineno-37-20" href="#__codelineno-37-20"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-37-21" name="__codelineno-37-21" href="#__codelineno-37-21"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-37-22" name="__codelineno-37-22" href="#__codelineno-37-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-23" name="__codelineno-37-23" href="#__codelineno-37-23"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">amt</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">MAX</span><span class="p">)</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">amt</span><span class="o">]</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="o">-</span><span class="m">1</span>
+<a id="__codelineno-37-24" name="__codelineno-37-24" href="#__codelineno-37-24"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coin_change_dp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="c1">### コイン両替：動的計画法 ###</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_dp</span><span class="p">(</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w">  </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w">  </span><span class="n">_MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="w">  </span><span class="c1"># dp テーブルを初期化</span>
+<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w">  </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="w">  </span><span class="c1"># 状態遷移：先頭行と先頭列</span>
+<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="w">  </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">a</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_MAX</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="w">  </span><span class="c1"># 状態遷移: 残りの行と列</span>
+<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span>
+<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a><span class="w">        </span><span class="c1"># 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">a</span><span class="o">]</span>
+<a id="__codelineno-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a><span class="w">      </span><span class="k">else</span>
+<a id="__codelineno-38-16" name="__codelineno-38-16" href="#__codelineno-38-16"></a><span class="w">        </span><span class="c1"># 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
+<a id="__codelineno-38-17" name="__codelineno-38-17" href="#__codelineno-38-17"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">].</span><span class="n">min</span>
+<a id="__codelineno-38-18" name="__codelineno-38-18" href="#__codelineno-38-18"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-38-19" name="__codelineno-38-19" href="#__codelineno-38-19"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-38-20" name="__codelineno-38-20" href="#__codelineno-38-20"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-21" name="__codelineno-38-21" href="#__codelineno-38-21"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">amt</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">_MAX</span><span class="w"> </span><span class="p">?</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">amt</span><span class="o">]</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-38-22" name="__codelineno-38-22" href="#__codelineno-38-22"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>下の図はコイン交換問題の動的プログラミングプロセスを示しており、無制限ナップサック問題と非常に似ています。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20coin_change_dp%28coins%3A%20list%5Bint%5D%2C%20amt%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E3%82%B3%E3%82%A4%E3%83%B3%E4%B8%A1%E6%9B%BF%EF%BC%9A%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%20%3D%20len%28coins%29%0A%20%20%20%20MAX%20%3D%20amt%20%2B%201%0A%20%20%20%20%23%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5B%5B0%5D%20%2A%20%28amt%20%2B%201%29%20for%20_%20in%20range%28n%20%2B%201%29%5D%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%85%88%E9%A0%AD%E8%A1%8C%E3%81%A8%E5%85%88%E9%A0%AD%E5%88%97%0A%20%20%20%20for%20a%20in%20range%281%2C%20amt%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20dp%5B0%5D%5Ba%5D%20%3D%20MAX%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%3A%20%E6%AE%8B%E3%82%8A%E3%81%AE%E8%A1%8C%E3%81%A8%E5%88%97%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20for%20a%20in%20range%281%2C%20amt%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20coins%5Bi%20-%201%5D%20%3E%20a%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E7%9B%AE%E6%A8%99%E9%87%91%E9%A1%8D%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%AA%E3%82%89%E7%A1%AC%E8%B2%A8%20i%20%E3%81%AF%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Ba%5D%20%3D%20dp%5Bi%20-%201%5D%5Ba%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E7%A1%AC%E8%B2%A8%20i%20%E3%82%92%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%E5%A0%B4%E5%90%88%E3%81%A8%E9%81%B8%E3%81%B6%E5%A0%B4%E5%90%88%E3%81%AE%E5%B0%8F%E3%81%95%E3%81%84%E6%96%B9%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Ba%5D%20%3D%20min%28dp%5Bi%20-%201%5D%5Ba%5D%2C%20dp%5Bi%5D%5Ba%20-%20coins%5Bi%20-%201%5D%5D%20%2B%201%29%0A%20%20%20%20return%20dp%5Bn%5D%5Bamt%5D%20if%20dp%5Bn%5D%5Bamt%5D%20%21%3D%20MAX%20else%20-1%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20coins%20%3D%20%5B1%2C%202%2C%205%5D%0A%20%20%20%20amt%20%3D%204%0A%0A%20%20%20%20%23%20%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20coin_change_dp%28coins%2C%20amt%29%0A%20%20%20%20print%28f%22%E7%9B%AE%E6%A8%99%E9%87%91%E9%A1%8D%E3%82%92%E4%BD%9C%E3%82%8B%E3%81%AE%E3%81%AB%E5%BF%85%E8%A6%81%E3%81%AA%E6%9C%80%E5%B0%8F%E7%A1%AC%E8%B2%A8%E6%9E%9A%E6%95%B0%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20coin_change_dp%28coins%3A%20list%5Bint%5D%2C%20amt%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E3%82%B3%E3%82%A4%E3%83%B3%E4%B8%A1%E6%9B%BF%EF%BC%9A%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%20%3D%20len%28coins%29%0A%20%20%20%20MAX%20%3D%20amt%20%2B%201%0A%20%20%20%20%23%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5B%5B0%5D%20%2A%20%28amt%20%2B%201%29%20for%20_%20in%20range%28n%20%2B%201%29%5D%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%85%88%E9%A0%AD%E8%A1%8C%E3%81%A8%E5%85%88%E9%A0%AD%E5%88%97%0A%20%20%20%20for%20a%20in%20range%281%2C%20amt%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20dp%5B0%5D%5Ba%5D%20%3D%20MAX%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%3A%20%E6%AE%8B%E3%82%8A%E3%81%AE%E8%A1%8C%E3%81%A8%E5%88%97%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20for%20a%20in%20range%281%2C%20amt%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20coins%5Bi%20-%201%5D%20%3E%20a%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E7%9B%AE%E6%A8%99%E9%87%91%E9%A1%8D%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%AA%E3%82%89%E7%A1%AC%E8%B2%A8%20i%20%E3%81%AF%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Ba%5D%20%3D%20dp%5Bi%20-%201%5D%5Ba%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E7%A1%AC%E8%B2%A8%20i%20%E3%82%92%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%E5%A0%B4%E5%90%88%E3%81%A8%E9%81%B8%E3%81%B6%E5%A0%B4%E5%90%88%E3%81%AE%E5%B0%8F%E3%81%95%E3%81%84%E6%96%B9%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Ba%5D%20%3D%20min%28dp%5Bi%20-%201%5D%5Ba%5D%2C%20dp%5Bi%5D%5Ba%20-%20coins%5Bi%20-%201%5D%5D%20%2B%201%29%0A%20%20%20%20return%20dp%5Bn%5D%5Bamt%5D%20if%20dp%5Bn%5D%5Bamt%5D%20%21%3D%20MAX%20else%20-1%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20coins%20%3D%20%5B1%2C%202%2C%205%5D%0A%20%20%20%20amt%20%3D%204%0A%0A%20%20%20%20%23%20%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20coin_change_dp%28coins%2C%20amt%29%0A%20%20%20%20print%28f%22%E7%9B%AE%E6%A8%99%E9%87%91%E9%A1%8D%E3%82%92%E4%BD%9C%E3%82%8B%E3%81%AE%E3%81%AB%E5%BF%85%E8%A6%81%E3%81%AA%E6%9C%80%E5%B0%8F%E7%A1%AC%E8%B2%A8%E6%9E%9A%E6%95%B0%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>次の図は硬貨交換の動的計画法の過程を示しており、完全ナップサック問題と非常によく似ています。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="5:15"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><input id="__tabbed_5_14" name="__tabbed_5" type="radio" /><input id="__tabbed_5_15" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">&lt;1&gt;</label><label for="__tabbed_5_2">&lt;2&gt;</label><label for="__tabbed_5_3">&lt;3&gt;</label><label for="__tabbed_5_4">&lt;4&gt;</label><label for="__tabbed_5_5">&lt;5&gt;</label><label for="__tabbed_5_6">&lt;6&gt;</label><label for="__tabbed_5_7">&lt;7&gt;</label><label for="__tabbed_5_8">&lt;8&gt;</label><label for="__tabbed_5_9">&lt;9&gt;</label><label for="__tabbed_5_10">&lt;10&gt;</label><label for="__tabbed_5_11">&lt;11&gt;</label><label for="__tabbed_5_12">&lt;12&gt;</label><label for="__tabbed_5_13">&lt;13&gt;</label><label for="__tabbed_5_14">&lt;14&gt;</label><label for="__tabbed_5_15">&lt;15&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="コイン交換問題の動的プログラミングプロセス" class="animation-figure" src="../unbounded_knapsack_problem.assets/coin_change_dp_step1.png" /></p>
+<p><img alt="硬貨交換問題の動的計画法の過程" class="animation-figure" src="../unbounded_knapsack_problem.assets/coin_change_dp_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="coin_change_dp_step2" class="animation-figure" src="../unbounded_knapsack_problem.assets/coin_change_dp_step2.png" /></p>
@@ -5082,15 +5765,15 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
 </div>
 </div>
 </div>
-<p align="center"> 図 14-25 &nbsp; コイン交換問題の動的プログラミングプロセス </p>
+<p align="center"> 図 14-25 &nbsp; 硬貨交換問題の動的計画法の過程 </p>
 
 <h3 id="3_1">3. &nbsp; 空間最適化<a class="headerlink" href="#3_1" title="Permanent link">&para;</a></h3>
-<p>コイン交換問題の空間最適化は無制限ナップサック問題と同じ方法で処理されます：</p>
+<p>硬貨交換の空間最適化の方法は、完全ナップサック問題と同じです。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="6:13"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><input id="__tabbed_6_13" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Kotlin</label><label for="__tabbed_6_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">coin_change.py</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_dp_comp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">amt</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;硬貨交換：空間最適化動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;コイン交換：空間最適化後の動的計画法&quot;&quot;&quot;</span>
 <a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">coins</span><span class="p">)</span>
 <a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a>    <span class="n">MAX</span> <span class="o">=</span> <span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span>
 <a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a>    <span class="c1"># dp テーブルを初期化</span>
@@ -5098,33 +5781,33 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
 <a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a>    <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
 <a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a>    <span class="c1"># 状態遷移</span>
 <a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
-<a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a>        <span class="c1"># 順序で走査</span>
+<a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a>        <span class="c1"># 順方向に走査する</span>
 <a id="__codelineno-39-11" name="__codelineno-39-11" href="#__codelineno-39-11"></a>        <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-39-12" name="__codelineno-39-12" href="#__codelineno-39-12"></a>            <span class="k">if</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">a</span><span class="p">:</span>
-<a id="__codelineno-39-13" name="__codelineno-39-13" href="#__codelineno-39-13"></a>                <span class="c1"># 目標金額を超える場合、硬貨 i を選択しない</span>
+<a id="__codelineno-39-13" name="__codelineno-39-13" href="#__codelineno-39-13"></a>                <span class="c1"># 目標金額を超えるなら硬貨 i は選ばない</span>
 <a id="__codelineno-39-14" name="__codelineno-39-14" href="#__codelineno-39-14"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span>
 <a id="__codelineno-39-15" name="__codelineno-39-15" href="#__codelineno-39-15"></a>            <span class="k">else</span><span class="p">:</span>
-<a id="__codelineno-39-16" name="__codelineno-39-16" href="#__codelineno-39-16"></a>                <span class="c1"># 硬貨 i を選択しないのと選択するのとで小さい値</span>
+<a id="__codelineno-39-16" name="__codelineno-39-16" href="#__codelineno-39-16"></a>                <span class="c1"># 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
 <a id="__codelineno-39-17" name="__codelineno-39-17" href="#__codelineno-39-17"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">a</span> <span class="o">-</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
 <a id="__codelineno-39-18" name="__codelineno-39-18" href="#__codelineno-39-18"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span> <span class="k">if</span> <span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span> <span class="o">!=</span> <span class="n">MAX</span> <span class="k">else</span> <span class="o">-</span><span class="mi">1</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change.cpp</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* 硬貨両替：空間最適化動的プログラミング */</span>
+<div class="highlight"><span class="filename">coin_change.cpp</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* コイン交換：空間最適化後の動的計画法 */</span>
 <a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeDPComp</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
 <a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
 <a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">MAX</span><span class="p">);</span>
 <a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
 <a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w">                </span><span class="c1">// 目標金額を超える場合、硬貨 i を選択しない</span>
+<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
 <a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">];</span>
 <a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a><span class="w">                </span><span class="c1">// 選択しない場合と硬貨 i を選択する場合のより小さい値</span>
+<a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a><span class="w">                </span><span class="c1">// 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
 <a id="__codelineno-40-16" name="__codelineno-40-16" href="#__codelineno-40-16"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-40-18" name="__codelineno-40-18" href="#__codelineno-40-18"></a><span class="w">        </span><span class="p">}</span>
@@ -5134,11 +5817,11 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change.java</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 硬貨両替：空間最適化動的プログラミング */</span>
+<div class="highlight"><span class="filename">coin_change.java</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* コイン交換：空間最適化後の動的計画法 */</span>
 <a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeDPComp</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
 <a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
 <a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="w">    </span><span class="n">Arrays</span><span class="p">.</span><span class="na">fill</span><span class="p">(</span><span class="n">dp</span><span class="p">,</span><span class="w"> </span><span class="n">MAX</span><span class="p">);</span>
 <a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
@@ -5146,10 +5829,10 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
 <a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a><span class="w">                </span><span class="c1">// 目標金額を超える場合、硬貨 i を選択しない</span>
+<a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
 <a id="__codelineno-41-14" name="__codelineno-41-14" href="#__codelineno-41-14"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-41-15" name="__codelineno-41-15" href="#__codelineno-41-15"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-41-16" name="__codelineno-41-16" href="#__codelineno-41-16"></a><span class="w">                </span><span class="c1">// 選択しない場合と硬貨 i を選択する場合のより小さい値</span>
+<a id="__codelineno-41-16" name="__codelineno-41-16" href="#__codelineno-41-16"></a><span class="w">                </span><span class="c1">// 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
 <a id="__codelineno-41-17" name="__codelineno-41-17" href="#__codelineno-41-17"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-41-18" name="__codelineno-41-18" href="#__codelineno-41-18"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-41-19" name="__codelineno-41-19" href="#__codelineno-41-19"></a><span class="w">        </span><span class="p">}</span>
@@ -5159,93 +5842,319 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change.cs</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">coin_change</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">CoinChangeDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change.cs</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="cm">/* コイン交換：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">CoinChangeDPComp</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a><span class="w">    </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="w">    </span><span class="n">Array</span><span class="p">.</span><span class="n">Fill</span><span class="p">(</span><span class="n">dp</span><span class="p">,</span><span class="w"> </span><span class="n">MAX</span><span class="p">);</span>
+<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-42-14" name="__codelineno-42-14" href="#__codelineno-42-14"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">];</span>
+<a id="__codelineno-42-15" name="__codelineno-42-15" href="#__codelineno-42-15"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-16" name="__codelineno-42-16" href="#__codelineno-42-16"></a><span class="w">                </span><span class="c1">// 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
+<a id="__codelineno-42-17" name="__codelineno-42-17" href="#__codelineno-42-17"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-42-18" name="__codelineno-42-18" href="#__codelineno-42-18"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-42-19" name="__codelineno-42-19" href="#__codelineno-42-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-42-20" name="__codelineno-42-20" href="#__codelineno-42-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-42-21" name="__codelineno-42-21" href="#__codelineno-42-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-42-22" name="__codelineno-42-22" href="#__codelineno-42-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change.go</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">coinChangeDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change.go</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* コイン両替：動的計画法 */</span>
+<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">coinChangeDPComp</span><span class="p">(</span><span class="nx">coins</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w">    </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">coins</span><span class="p">)</span>
+<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">    </span><span class="nx">max</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w">    </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">amt</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">max</span>
+<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w">        </span><span class="c1">// 順方向に走査する</span>
+<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">amt</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-14" name="__codelineno-43-14" href="#__codelineno-43-14"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-15" name="__codelineno-43-15" href="#__codelineno-43-15"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-43-16" name="__codelineno-43-16" href="#__codelineno-43-16"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]</span>
+<a id="__codelineno-43-17" name="__codelineno-43-17" href="#__codelineno-43-17"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-18" name="__codelineno-43-18" href="#__codelineno-43-18"></a><span class="w">                </span><span class="c1">// 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
+<a id="__codelineno-43-19" name="__codelineno-43-19" href="#__codelineno-43-19"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Min</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="o">-</span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]]</span><span class="o">+</span><span class="mi">1</span><span class="p">)))</span>
+<a id="__codelineno-43-20" name="__codelineno-43-20" href="#__codelineno-43-20"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-43-21" name="__codelineno-43-21" href="#__codelineno-43-21"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-43-22" name="__codelineno-43-22" href="#__codelineno-43-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-23" name="__codelineno-43-23" href="#__codelineno-43-23"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nx">max</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-24" name="__codelineno-43-24" href="#__codelineno-43-24"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">amt</span><span class="p">]</span>
+<a id="__codelineno-43-25" name="__codelineno-43-25" href="#__codelineno-43-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-26" name="__codelineno-43-26" href="#__codelineno-43-26"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-43-27" name="__codelineno-43-27" href="#__codelineno-43-27"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change.swift</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">coinChangeDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change.swift</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* コイン交換：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">coinChangeDPComp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">MAX</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="n">MAX</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span>
+<a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-15" name="__codelineno-44-15" href="#__codelineno-44-15"></a><span class="w">                </span><span class="c1">// 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
+<a id="__codelineno-44-16" name="__codelineno-44-16" href="#__codelineno-44-16"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-44-17" name="__codelineno-44-17" href="#__codelineno-44-17"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-44-18" name="__codelineno-44-18" href="#__codelineno-44-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-44-19" name="__codelineno-44-19" href="#__codelineno-44-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-20" name="__codelineno-44-20" href="#__codelineno-44-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="p">?</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-44-21" name="__codelineno-44-21" href="#__codelineno-44-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change.js</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">coinChangeDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change.js</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="cm">/* コイン交換：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">coinChangeDPComp</span><span class="p">(</span><span class="nx">coins</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coins</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="nx">MAX</span><span class="p">);</span>
+<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">amt</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-45-13" name="__codelineno-45-13" href="#__codelineno-45-13"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">];</span>
+<a id="__codelineno-45-14" name="__codelineno-45-14" href="#__codelineno-45-14"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-15" name="__codelineno-45-15" href="#__codelineno-45-15"></a><span class="w">                </span><span class="c1">// 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
+<a id="__codelineno-45-16" name="__codelineno-45-16" href="#__codelineno-45-16"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-45-17" name="__codelineno-45-17" href="#__codelineno-45-17"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-45-18" name="__codelineno-45-18" href="#__codelineno-45-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-45-19" name="__codelineno-45-19" href="#__codelineno-45-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-45-20" name="__codelineno-45-20" href="#__codelineno-45-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="nx">MAX</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">amt</span><span class="p">]</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-45-21" name="__codelineno-45-21" href="#__codelineno-45-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change.ts</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">coinChangeDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change.ts</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="cm">/* コイン交換：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">coinChangeDPComp</span><span class="p">(</span><span class="nx">coins</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coins</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="kt">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="nx">MAX</span><span class="p">);</span>
+<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">amt</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-12" name="__codelineno-46-12" href="#__codelineno-46-12"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-46-13" name="__codelineno-46-13" href="#__codelineno-46-13"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">];</span>
+<a id="__codelineno-46-14" name="__codelineno-46-14" href="#__codelineno-46-14"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-15" name="__codelineno-46-15" href="#__codelineno-46-15"></a><span class="w">                </span><span class="c1">// 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
+<a id="__codelineno-46-16" name="__codelineno-46-16" href="#__codelineno-46-16"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-46-17" name="__codelineno-46-17" href="#__codelineno-46-17"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-46-18" name="__codelineno-46-18" href="#__codelineno-46-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-46-19" name="__codelineno-46-19" href="#__codelineno-46-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-46-20" name="__codelineno-46-20" href="#__codelineno-46-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="nx">MAX</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">amt</span><span class="p">]</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-46-21" name="__codelineno-46-21" href="#__codelineno-46-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change.dart</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change.dart</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* コイン交換：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">coinChangeDPComp</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="w">  </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">MAX</span><span class="p">);</span>
+<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="w">  </span><span class="n">dp</span><span class="p">[</span><span class="m">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a><span class="w">  </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a><span class="w">        </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-47-13" name="__codelineno-47-13" href="#__codelineno-47-13"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">];</span>
+<a id="__codelineno-47-14" name="__codelineno-47-14" href="#__codelineno-47-14"></a><span class="w">      </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-15" name="__codelineno-47-15" href="#__codelineno-47-15"></a><span class="w">        </span><span class="c1">// 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
+<a id="__codelineno-47-16" name="__codelineno-47-16" href="#__codelineno-47-16"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-47-17" name="__codelineno-47-17" href="#__codelineno-47-17"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-47-18" name="__codelineno-47-18" href="#__codelineno-47-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-47-19" name="__codelineno-47-19" href="#__codelineno-47-19"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-47-20" name="__codelineno-47-20" href="#__codelineno-47-20"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-47-21" name="__codelineno-47-21" href="#__codelineno-47-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change.rs</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coin_change_dp_comp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change.rs</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="cm">/* コイン交換：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">coin_change_dp_comp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
+<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a><span class="w">    </span><span class="n">dp</span><span class="p">.</span><span class="n">fill</span><span class="p">(</span><span class="n">max</span><span class="p">);</span>
+<a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-11" name="__codelineno-48-11" href="#__codelineno-48-11"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">amt</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-12" name="__codelineno-48-12" href="#__codelineno-48-12"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-13" name="__codelineno-48-13" href="#__codelineno-48-13"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-48-14" name="__codelineno-48-14" href="#__codelineno-48-14"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">];</span>
+<a id="__codelineno-48-15" name="__codelineno-48-15" href="#__codelineno-48-15"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-16" name="__codelineno-48-16" href="#__codelineno-48-16"></a><span class="w">                </span><span class="c1">// 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
+<a id="__codelineno-48-17" name="__codelineno-48-17" href="#__codelineno-48-17"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-48-18" name="__codelineno-48-18" href="#__codelineno-48-18"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-48-19" name="__codelineno-48-19" href="#__codelineno-48-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-48-20" name="__codelineno-48-20" href="#__codelineno-48-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-48-21" name="__codelineno-48-21" href="#__codelineno-48-21"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-22" name="__codelineno-48-22" href="#__codelineno-48-22"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">;</span>
+<a id="__codelineno-48-23" name="__codelineno-48-23" href="#__codelineno-48-23"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-24" name="__codelineno-48-24" href="#__codelineno-48-24"></a><span class="w">        </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-48-25" name="__codelineno-48-25" href="#__codelineno-48-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-48-26" name="__codelineno-48-26" href="#__codelineno-48-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change.c</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change.c</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* コイン交換：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeDPComp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">coins</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">coinsSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coinsSize</span><span class="p">;</span>
+<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">((</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MAX</span><span class="p">;</span>
+<a id="__codelineno-49-9" name="__codelineno-49-9" href="#__codelineno-49-9"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span>
+<a id="__codelineno-49-10" name="__codelineno-49-10" href="#__codelineno-49-10"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-49-11" name="__codelineno-49-11" href="#__codelineno-49-11"></a>
+<a id="__codelineno-49-12" name="__codelineno-49-12" href="#__codelineno-49-12"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-49-13" name="__codelineno-49-13" href="#__codelineno-49-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-14" name="__codelineno-49-14" href="#__codelineno-49-14"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-15" name="__codelineno-49-15" href="#__codelineno-49-15"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-16" name="__codelineno-49-16" href="#__codelineno-49-16"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-49-17" name="__codelineno-49-17" href="#__codelineno-49-17"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">];</span>
+<a id="__codelineno-49-18" name="__codelineno-49-18" href="#__codelineno-49-18"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-19" name="__codelineno-49-19" href="#__codelineno-49-19"></a><span class="w">                </span><span class="c1">// 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
+<a id="__codelineno-49-20" name="__codelineno-49-20" href="#__codelineno-49-20"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">myMin</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-49-21" name="__codelineno-49-21" href="#__codelineno-49-21"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-49-22" name="__codelineno-49-22" href="#__codelineno-49-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-49-23" name="__codelineno-49-23" href="#__codelineno-49-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-49-24" name="__codelineno-49-24" href="#__codelineno-49-24"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-49-25" name="__codelineno-49-25" href="#__codelineno-49-25"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-49-26" name="__codelineno-49-26" href="#__codelineno-49-26"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">dp</span><span class="p">);</span>
+<a id="__codelineno-49-27" name="__codelineno-49-27" href="#__codelineno-49-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-49-28" name="__codelineno-49-28" href="#__codelineno-49-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change.kt</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coinChangeDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change.kt</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* コイン交換：空間最適化後の動的計画法 */</span>
+<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">coinChangeDPComp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="w">    </span><span class="n">dp</span><span class="p">.</span><span class="na">fill</span><span class="p">(</span><span class="n">MAX</span><span class="p">)</span>
+<a id="__codelineno-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="m">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-50-9" name="__codelineno-50-9" href="#__codelineno-50-9"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-50-10" name="__codelineno-50-10" href="#__codelineno-50-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-11" name="__codelineno-50-11" href="#__codelineno-50-11"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-12" name="__codelineno-50-12" href="#__codelineno-50-12"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-13" name="__codelineno-50-13" href="#__codelineno-50-13"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-50-14" name="__codelineno-50-14" href="#__codelineno-50-14"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span>
+<a id="__codelineno-50-15" name="__codelineno-50-15" href="#__codelineno-50-15"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-16" name="__codelineno-50-16" href="#__codelineno-50-16"></a><span class="w">                </span><span class="c1">// 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
+<a id="__codelineno-50-17" name="__codelineno-50-17" href="#__codelineno-50-17"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-50-18" name="__codelineno-50-18" href="#__codelineno-50-18"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-50-19" name="__codelineno-50-19" href="#__codelineno-50-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-50-20" name="__codelineno-50-20" href="#__codelineno-50-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-50-21" name="__codelineno-50-21" href="#__codelineno-50-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">amt</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">MAX</span><span class="p">)</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">amt</span><span class="o">]</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="o">-</span><span class="m">1</span>
+<a id="__codelineno-50-22" name="__codelineno-50-22" href="#__codelineno-50-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change.rb</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coin_change_dp_comp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change.rb</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="c1">### コイン両替：空間最適化した動的計画法 ###</span>
+<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_dp_comp</span><span class="p">(</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span>
+<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w">  </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a><span class="w">  </span><span class="n">_MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w">  </span><span class="c1"># dp テーブルを初期化</span>
+<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a><span class="w">  </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">_MAX</span><span class="p">)</span>
+<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="w">  </span><span class="c1"># 状態遷移</span>
+<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></a><span class="w">    </span><span class="c1"># 順方向に走査する</span>
+<a id="__codelineno-51-11" name="__codelineno-51-11" href="#__codelineno-51-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-51-12" name="__codelineno-51-12" href="#__codelineno-51-12"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span>
+<a id="__codelineno-51-13" name="__codelineno-51-13" href="#__codelineno-51-13"></a><span class="w">        </span><span class="c1"># 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-51-14" name="__codelineno-51-14" href="#__codelineno-51-14"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span>
+<a id="__codelineno-51-15" name="__codelineno-51-15" href="#__codelineno-51-15"></a><span class="w">      </span><span class="k">else</span>
+<a id="__codelineno-51-16" name="__codelineno-51-16" href="#__codelineno-51-16"></a><span class="w">        </span><span class="c1"># 硬貨 i を選ばない場合と選ぶ場合の小さい方</span>
+<a id="__codelineno-51-17" name="__codelineno-51-17" href="#__codelineno-51-17"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">].</span><span class="n">min</span>
+<a id="__codelineno-51-18" name="__codelineno-51-18" href="#__codelineno-51-18"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-51-19" name="__codelineno-51-19" href="#__codelineno-51-19"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-51-20" name="__codelineno-51-20" href="#__codelineno-51-20"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-51-21" name="__codelineno-51-21" href="#__codelineno-51-21"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="n">amt</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">_MAX</span><span class="w"> </span><span class="p">?</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">amt</span><span class="o">]</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-51-22" name="__codelineno-51-22" href="#__codelineno-51-22"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h2 id="1453-ii">14.5.3 &nbsp; コイン交換問題II<a class="headerlink" href="#1453-ii" title="Permanent link">&para;</a></h2>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20coin_change_dp_comp%28coins%3A%20list%5Bint%5D%2C%20amt%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E3%82%B3%E3%82%A4%E3%83%B3%E4%BA%A4%E6%8F%9B%EF%BC%9A%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E5%BE%8C%E3%81%AE%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%20%3D%20len%28coins%29%0A%20%20%20%20MAX%20%3D%20amt%20%2B%201%0A%20%20%20%20%23%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5BMAX%5D%20%2A%20%28amt%20%2B%201%29%0A%20%20%20%20dp%5B0%5D%20%3D%200%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E9%A0%86%E6%96%B9%E5%90%91%E3%81%AB%E8%B5%B0%E6%9F%BB%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20for%20a%20in%20range%281%2C%20amt%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20coins%5Bi%20-%201%5D%20%3E%20a%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E7%9B%AE%E6%A8%99%E9%87%91%E9%A1%8D%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%AA%E3%82%89%E7%A1%AC%E8%B2%A8%20i%20%E3%81%AF%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Ba%5D%20%3D%20dp%5Ba%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E7%A1%AC%E8%B2%A8%20i%20%E3%82%92%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%E5%A0%B4%E5%90%88%E3%81%A8%E9%81%B8%E3%81%B6%E5%A0%B4%E5%90%88%E3%81%AE%E5%B0%8F%E3%81%95%E3%81%84%E6%96%B9%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Ba%5D%20%3D%20min%28dp%5Ba%5D%2C%20dp%5Ba%20-%20coins%5Bi%20-%201%5D%5D%20%2B%201%29%0A%20%20%20%20return%20dp%5Bamt%5D%20if%20dp%5Bamt%5D%20%21%3D%20MAX%20else%20-1%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20coins%20%3D%20%5B1%2C%202%2C%205%5D%0A%20%20%20%20amt%20%3D%204%0A%0A%20%20%20%20%23%20%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E5%BE%8C%E3%81%AE%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20coin_change_dp_comp%28coins%2C%20amt%29%0A%20%20%20%20print%28f%22%E7%9B%AE%E6%A8%99%E9%87%91%E9%A1%8D%E3%82%92%E4%BD%9C%E3%82%8B%E3%81%AE%E3%81%AB%E5%BF%85%E8%A6%81%E3%81%AA%E6%9C%80%E5%B0%8F%E7%A1%AC%E8%B2%A8%E6%9E%9A%E6%95%B0%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20coin_change_dp_comp%28coins%3A%20list%5Bint%5D%2C%20amt%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E3%82%B3%E3%82%A4%E3%83%B3%E4%BA%A4%E6%8F%9B%EF%BC%9A%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E5%BE%8C%E3%81%AE%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%20%3D%20len%28coins%29%0A%20%20%20%20MAX%20%3D%20amt%20%2B%201%0A%20%20%20%20%23%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5BMAX%5D%20%2A%20%28amt%20%2B%201%29%0A%20%20%20%20dp%5B0%5D%20%3D%200%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E9%A0%86%E6%96%B9%E5%90%91%E3%81%AB%E8%B5%B0%E6%9F%BB%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20for%20a%20in%20range%281%2C%20amt%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20coins%5Bi%20-%201%5D%20%3E%20a%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E7%9B%AE%E6%A8%99%E9%87%91%E9%A1%8D%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%AA%E3%82%89%E7%A1%AC%E8%B2%A8%20i%20%E3%81%AF%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Ba%5D%20%3D%20dp%5Ba%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E7%A1%AC%E8%B2%A8%20i%20%E3%82%92%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%E5%A0%B4%E5%90%88%E3%81%A8%E9%81%B8%E3%81%B6%E5%A0%B4%E5%90%88%E3%81%AE%E5%B0%8F%E3%81%95%E3%81%84%E6%96%B9%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Ba%5D%20%3D%20min%28dp%5Ba%5D%2C%20dp%5Ba%20-%20coins%5Bi%20-%201%5D%5D%20%2B%201%29%0A%20%20%20%20return%20dp%5Bamt%5D%20if%20dp%5Bamt%5D%20%21%3D%20MAX%20else%20-1%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20coins%20%3D%20%5B1%2C%202%2C%205%5D%0A%20%20%20%20amt%20%3D%204%0A%0A%20%20%20%20%23%20%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E5%BE%8C%E3%81%AE%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20coin_change_dp_comp%28coins%2C%20amt%29%0A%20%20%20%20print%28f%22%E7%9B%AE%E6%A8%99%E9%87%91%E9%A1%8D%E3%82%92%E4%BD%9C%E3%82%8B%E3%81%AE%E3%81%AB%E5%BF%85%E8%A6%81%E3%81%AA%E6%9C%80%E5%B0%8F%E7%A1%AC%E8%B2%A8%E6%9E%9A%E6%95%B0%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h2 id="1453-ii">14.5.3 &nbsp; 硬貨交換問題 II<a class="headerlink" href="#1453-ii" title="Permanent link">&para;</a></h2>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
-<p><span class="arithmatex">\(n\)</span> 種類のコインが与えられ、<span class="arithmatex">\(i\)</span> 番目の種類のコインの額面は <span class="arithmatex">\(coins[i - 1]\)</span> で、目標金額は <span class="arithmatex">\(amt\)</span> です。各種類のコインは複数回選択でき、<strong>目標金額を構成できるコインの組み合わせは何通りありますか</strong>。以下の例を参照してください。</p>
+<p><span class="arithmatex">\(n\)</span> 種類の硬貨が与えられ、<span class="arithmatex">\(i\)</span> 番目の硬貨の額面は <span class="arithmatex">\(coins[i - 1]\)</span> 、目標金額は <span class="arithmatex">\(amt\)</span> です。各硬貨は繰り返し選択できるとして、**目標金額を作る硬貨の組合せ数**を求めてください。例を以下の図に示します。</p>
 </div>
-<p><img alt="コイン交換問題IIの例データ" class="animation-figure" src="../unbounded_knapsack_problem.assets/coin_change_ii_example.png" /></p>
-<p align="center"> 図 14-26 &nbsp; コイン交換問題IIの例データ </p>
+<p><img alt="硬貨交換問題 II のサンプルデータ" class="animation-figure" src="../unbounded_knapsack_problem.assets/coin_change_ii_example.png" /></p>
+<p align="center"> 図 14-26 &nbsp; 硬貨交換問題 II のサンプルデータ </p>
 
-<h3 id="1_2">1. &nbsp; 動的プログラミングアプローチ<a class="headerlink" href="#1_2" title="Permanent link">&para;</a></h3>
-<p>前の問題と比較して、この問題の目標は組み合わせの数を決定することであるため、部分問題は次のようになります：<strong>最初の <span class="arithmatex">\(i\)</span> 種類のコインを使用して金額 <span class="arithmatex">\(a\)</span> を構成できる組み合わせの数</strong>。<span class="arithmatex">\(dp\)</span> テーブルはサイズ <span class="arithmatex">\((n+1) \times (amt + 1)\)</span> の二次元行列のまま残ります。</p>
-<p>現在の状態の組み合わせ数は、現在のコインを選択しない組み合わせと現在のコインを選択する組み合わせの合計です。状態遷移方程式は：</p>
+<h3 id="1_2">1. &nbsp; 動的計画法の考え方<a class="headerlink" href="#1_2" title="Permanent link">&para;</a></h3>
+<p>前問と比べて、本問の目的は組合せ数を求めることです。そのため、部分問題は <strong>先頭 <span class="arithmatex">\(i\)</span> 種類の硬貨で金額 <span class="arithmatex">\(a\)</span> を作れる組合せ数</strong> になります。一方、<span class="arithmatex">\(dp\)</span> テーブルは引き続きサイズ <span class="arithmatex">\((n+1) \times (amt + 1)\)</span> の 2 次元行列です。</p>
+<p>現在の状態における組合せ数は、現在の硬貨を選ばない場合と選ぶ場合の 2 つの選択肢の組合せ数の和に等しくなります。状態遷移方程式は次のとおりです。</p>
 <div class="arithmatex">\[
 dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
 \]</div>
-<p>目標金額が <span class="arithmatex">\(0\)</span> の場合、目標金額を構成するのにコインは必要ないため、最初の列のすべての <span class="arithmatex">\(dp[i, 0]\)</span> は <span class="arithmatex">\(1\)</span> に初期化されるべきです。コインがない場合、任意の金額 &gt;0 を構成することは不可能であるため、最初の行のすべての <span class="arithmatex">\(dp[0, a]\)</span> は <span class="arithmatex">\(0\)</span> に設定されるべきです。</p>
+<p>目標金額が <span class="arithmatex">\(0\)</span> のときは、どの硬貨も選ばなくても目標金額を作れるため、先頭列のすべての <span class="arithmatex">\(dp[i, 0]\)</span> を <span class="arithmatex">\(1\)</span> に初期化します。硬貨がないときは、任意の <span class="arithmatex">\(&gt;0\)</span> の目標金額を作れないため、先頭行のすべての <span class="arithmatex">\(dp[0, a]\)</span> は <span class="arithmatex">\(0\)</span> になります。</p>
 <h3 id="2_2">2. &nbsp; コード実装<a class="headerlink" href="#2_2" title="Permanent link">&para;</a></h3>
 <div class="tabbed-set tabbed-alternate" data-tabs="7:13"><input checked="checked" id="__tabbed_7_1" name="__tabbed_7" type="radio" /><input id="__tabbed_7_2" name="__tabbed_7" type="radio" /><input id="__tabbed_7_3" name="__tabbed_7" type="radio" /><input id="__tabbed_7_4" name="__tabbed_7" type="radio" /><input id="__tabbed_7_5" name="__tabbed_7" type="radio" /><input id="__tabbed_7_6" name="__tabbed_7" type="radio" /><input id="__tabbed_7_7" name="__tabbed_7" type="radio" /><input id="__tabbed_7_8" name="__tabbed_7" type="radio" /><input id="__tabbed_7_9" name="__tabbed_7" type="radio" /><input id="__tabbed_7_10" name="__tabbed_7" type="radio" /><input id="__tabbed_7_11" name="__tabbed_7" type="radio" /><input id="__tabbed_7_12" name="__tabbed_7" type="radio" /><input id="__tabbed_7_13" name="__tabbed_7" type="radio" /><div class="tabbed-labels"><label for="__tabbed_7_1">Python</label><label for="__tabbed_7_2">C++</label><label for="__tabbed_7_3">Java</label><label for="__tabbed_7_4">C#</label><label for="__tabbed_7_5">Go</label><label for="__tabbed_7_6">Swift</label><label for="__tabbed_7_7">JS</label><label for="__tabbed_7_8">TS</label><label for="__tabbed_7_9">Dart</label><label for="__tabbed_7_10">Rust</label><label for="__tabbed_7_11">C</label><label for="__tabbed_7_12">Kotlin</label><label for="__tabbed_7_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">coin_change_ii.py</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_ii_dp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">amt</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;硬貨交換 II：動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;コイン両替 II：動的計画法&quot;&quot;&quot;</span>
 <a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">coins</span><span class="p">)</span>
 <a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a>    <span class="c1"># dp テーブルを初期化</span>
 <a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span>
-<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a>    <span class="c1"># 最初の列を初期化</span>
+<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a>    <span class="c1"># 先頭列を初期化する</span>
 <a id="__codelineno-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-52-8" name="__codelineno-52-8" href="#__codelineno-52-8"></a>        <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
 <a id="__codelineno-52-9" name="__codelineno-52-9" href="#__codelineno-52-9"></a>    <span class="c1"># 状態遷移</span>
 <a id="__codelineno-52-10" name="__codelineno-52-10" href="#__codelineno-52-10"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-52-11" name="__codelineno-52-11" href="#__codelineno-52-11"></a>        <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-52-12" name="__codelineno-52-12" href="#__codelineno-52-12"></a>            <span class="k">if</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">a</span><span class="p">:</span>
-<a id="__codelineno-52-13" name="__codelineno-52-13" href="#__codelineno-52-13"></a>                <span class="c1"># 目標金額を超える場合、硬貨 i を選択しない</span>
+<a id="__codelineno-52-13" name="__codelineno-52-13" href="#__codelineno-52-13"></a>                <span class="c1"># 目標金額を超えるなら硬貨 i は選ばない</span>
 <a id="__codelineno-52-14" name="__codelineno-52-14" href="#__codelineno-52-14"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">]</span>
 <a id="__codelineno-52-15" name="__codelineno-52-15" href="#__codelineno-52-15"></a>            <span class="k">else</span><span class="p">:</span>
-<a id="__codelineno-52-16" name="__codelineno-52-16" href="#__codelineno-52-16"></a>                <span class="c1"># 硬貨 i を選択しないのと選択するのとの両方の選択肢の和</span>
+<a id="__codelineno-52-16" name="__codelineno-52-16" href="#__codelineno-52-16"></a>                <span class="c1"># コイン i を選ばない場合と選ぶ場合の和</span>
 <a id="__codelineno-52-17" name="__codelineno-52-17" href="#__codelineno-52-17"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">]</span> <span class="o">+</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span> <span class="o">-</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span>
 <a id="__codelineno-52-18" name="__codelineno-52-18" href="#__codelineno-52-18"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_ii.cpp</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 硬貨両替 II：動的プログラミング */</span>
+<div class="highlight"><span class="filename">coin_change_ii.cpp</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* コイン両替 II：動的計画法 */</span>
 <a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeIIDP</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
-<a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
 <a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">));</span>
-<a id="__codelineno-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></a><span class="w">    </span><span class="c1">// 最初の列を初期化</span>
+<a id="__codelineno-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></a><span class="w">    </span><span class="c1">// 先頭列を初期化する</span>
 <a id="__codelineno-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-53-9" name="__codelineno-53-9" href="#__codelineno-53-9"></a><span class="w">    </span><span class="p">}</span>
@@ -5253,10 +6162,10 @@ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
 <a id="__codelineno-53-11" name="__codelineno-53-11" href="#__codelineno-53-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-53-12" name="__codelineno-53-12" href="#__codelineno-53-12"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-53-13" name="__codelineno-53-13" href="#__codelineno-53-13"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-53-14" name="__codelineno-53-14" href="#__codelineno-53-14"></a><span class="w">                </span><span class="c1">// 目標金額を超える場合、硬貨 i を選択しない</span>
+<a id="__codelineno-53-14" name="__codelineno-53-14" href="#__codelineno-53-14"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
 <a id="__codelineno-53-15" name="__codelineno-53-15" href="#__codelineno-53-15"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">];</span>
 <a id="__codelineno-53-16" name="__codelineno-53-16" href="#__codelineno-53-16"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-53-17" name="__codelineno-53-17" href="#__codelineno-53-17"></a><span class="w">                </span><span class="c1">// 選択しない場合と硬貨 i を選択する場合の2つの選択肢の合計</span>
+<a id="__codelineno-53-17" name="__codelineno-53-17" href="#__codelineno-53-17"></a><span class="w">                </span><span class="c1">// コイン i を選ばない場合と選ぶ場合の和</span>
 <a id="__codelineno-53-18" name="__codelineno-53-18" href="#__codelineno-53-18"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]];</span>
 <a id="__codelineno-53-19" name="__codelineno-53-19" href="#__codelineno-53-19"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-53-20" name="__codelineno-53-20" href="#__codelineno-53-20"></a><span class="w">        </span><span class="p">}</span>
@@ -5266,12 +6175,12 @@ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_ii.java</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="cm">/* 硬貨両替 II：動的プログラミング */</span>
+<div class="highlight"><span class="filename">coin_change_ii.java</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="cm">/* コイン両替 II：動的計画法 */</span>
 <a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeIIDP</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
-<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
 <a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w">    </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w">    </span><span class="c1">// 最初の列を初期化</span>
+<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w">    </span><span class="c1">// 先頭列を初期化する</span>
 <a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a><span class="w">    </span><span class="p">}</span>
@@ -5279,10 +6188,10 @@ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
 <a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-54-13" name="__codelineno-54-13" href="#__codelineno-54-13"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-54-14" name="__codelineno-54-14" href="#__codelineno-54-14"></a><span class="w">                </span><span class="c1">// 目標金額を超える場合、硬貨 i を選択しない</span>
+<a id="__codelineno-54-14" name="__codelineno-54-14" href="#__codelineno-54-14"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
 <a id="__codelineno-54-15" name="__codelineno-54-15" href="#__codelineno-54-15"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-54-16" name="__codelineno-54-16" href="#__codelineno-54-16"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-54-17" name="__codelineno-54-17" href="#__codelineno-54-17"></a><span class="w">                </span><span class="c1">// 選択しない場合と硬貨 i を選択する場合の2つの選択肢の合計</span>
+<a id="__codelineno-54-17" name="__codelineno-54-17" href="#__codelineno-54-17"></a><span class="w">                </span><span class="c1">// コイン i を選ばない場合と選ぶ場合の和</span>
 <a id="__codelineno-54-18" name="__codelineno-54-18" href="#__codelineno-54-18"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="p">;</span>
 <a id="__codelineno-54-19" name="__codelineno-54-19" href="#__codelineno-54-19"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-54-20" name="__codelineno-54-20" href="#__codelineno-54-20"></a><span class="w">        </span><span class="p">}</span>
@@ -5292,86 +6201,325 @@ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_ii.cs</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">coin_change_ii</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">CoinChangeIIDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_ii.cs</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="cm">/* コイン両替 II：動的計画法 */</span>
+<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">CoinChangeIIDP</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
+<a id="__codelineno-55-4" name="__codelineno-55-4" href="#__codelineno-55-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-55-5" name="__codelineno-55-5" href="#__codelineno-55-5"></a><span class="w">    </span><span class="kt">int</span><span class="p">[,]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-55-6" name="__codelineno-55-6" href="#__codelineno-55-6"></a><span class="w">    </span><span class="c1">// 先頭列を初期化する</span>
+<a id="__codelineno-55-7" name="__codelineno-55-7" href="#__codelineno-55-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-8" name="__codelineno-55-8" href="#__codelineno-55-8"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-55-9" name="__codelineno-55-9" href="#__codelineno-55-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-55-10" name="__codelineno-55-10" href="#__codelineno-55-10"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-55-11" name="__codelineno-55-11" href="#__codelineno-55-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-12" name="__codelineno-55-12" href="#__codelineno-55-12"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-13" name="__codelineno-55-13" href="#__codelineno-55-13"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-14" name="__codelineno-55-14" href="#__codelineno-55-14"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-55-15" name="__codelineno-55-15" href="#__codelineno-55-15"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">];</span>
+<a id="__codelineno-55-16" name="__codelineno-55-16" href="#__codelineno-55-16"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-17" name="__codelineno-55-17" href="#__codelineno-55-17"></a><span class="w">                </span><span class="c1">// コイン i を選ばない場合と選ぶ場合の和</span>
+<a id="__codelineno-55-18" name="__codelineno-55-18" href="#__codelineno-55-18"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]];</span>
+<a id="__codelineno-55-19" name="__codelineno-55-19" href="#__codelineno-55-19"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-55-20" name="__codelineno-55-20" href="#__codelineno-55-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-55-21" name="__codelineno-55-21" href="#__codelineno-55-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-55-22" name="__codelineno-55-22" href="#__codelineno-55-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">];</span>
+<a id="__codelineno-55-23" name="__codelineno-55-23" href="#__codelineno-55-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_ii.go</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">coinChangeIIDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_ii.go</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="cm">/* コイン両替 II：動的計画法 */</span>
+<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">coinChangeIIDP</span><span class="p">(</span><span class="nx">coins</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a><span class="w">    </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">coins</span><span class="p">)</span>
+<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a><span class="w">    </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></a><span class="w">    </span><span class="c1">// 先頭列を初期化する</span>
+<a id="__codelineno-56-10" name="__codelineno-56-10" href="#__codelineno-56-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-11" name="__codelineno-56-11" href="#__codelineno-56-11"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-56-12" name="__codelineno-56-12" href="#__codelineno-56-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-56-13" name="__codelineno-56-13" href="#__codelineno-56-13"></a><span class="w">    </span><span class="c1">// 状態遷移: 残りの行と列</span>
+<a id="__codelineno-56-14" name="__codelineno-56-14" href="#__codelineno-56-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-15" name="__codelineno-56-15" href="#__codelineno-56-15"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">amt</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-16" name="__codelineno-56-16" href="#__codelineno-56-16"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-17" name="__codelineno-56-17" href="#__codelineno-56-17"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-56-18" name="__codelineno-56-18" href="#__codelineno-56-18"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span>
+<a id="__codelineno-56-19" name="__codelineno-56-19" href="#__codelineno-56-19"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-20" name="__codelineno-56-20" href="#__codelineno-56-20"></a><span class="w">                </span><span class="c1">// コイン i を選ばない場合と選ぶ場合の和</span>
+<a id="__codelineno-56-21" name="__codelineno-56-21" href="#__codelineno-56-21"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">a</span><span class="o">-</span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]]</span>
+<a id="__codelineno-56-22" name="__codelineno-56-22" href="#__codelineno-56-22"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-56-23" name="__codelineno-56-23" href="#__codelineno-56-23"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-56-24" name="__codelineno-56-24" href="#__codelineno-56-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-56-25" name="__codelineno-56-25" href="#__codelineno-56-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">amt</span><span class="p">]</span>
+<a id="__codelineno-56-26" name="__codelineno-56-26" href="#__codelineno-56-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_ii.swift</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">coinChangeIIDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_ii.swift</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* コイン両替 II：動的計画法 */</span>
+<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">coinChangeIIDP</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">),</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a><span class="w">    </span><span class="c1">// 先頭列を初期化する</span>
+<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-57-10" name="__codelineno-57-10" href="#__codelineno-57-10"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-57-11" name="__codelineno-57-11" href="#__codelineno-57-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-12" name="__codelineno-57-12" href="#__codelineno-57-12"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-13" name="__codelineno-57-13" href="#__codelineno-57-13"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-14" name="__codelineno-57-14" href="#__codelineno-57-14"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-57-15" name="__codelineno-57-15" href="#__codelineno-57-15"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">]</span>
+<a id="__codelineno-57-16" name="__codelineno-57-16" href="#__codelineno-57-16"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-17" name="__codelineno-57-17" href="#__codelineno-57-17"></a><span class="w">                </span><span class="c1">// コイン i を選ばない場合と選ぶ場合の和</span>
+<a id="__codelineno-57-18" name="__codelineno-57-18" href="#__codelineno-57-18"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span>
+<a id="__codelineno-57-19" name="__codelineno-57-19" href="#__codelineno-57-19"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-57-20" name="__codelineno-57-20" href="#__codelineno-57-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-57-21" name="__codelineno-57-21" href="#__codelineno-57-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-57-22" name="__codelineno-57-22" href="#__codelineno-57-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span>
+<a id="__codelineno-57-23" name="__codelineno-57-23" href="#__codelineno-57-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_ii.js</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">coinChangeIIDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_ii.js</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* コイン両替 II：動的計画法 */</span>
+<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">coinChangeIIDP</span><span class="p">(</span><span class="nx">coins</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coins</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span>
+<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a><span class="w">        </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span>
+<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></a><span class="w">    </span><span class="p">);</span>
+<a id="__codelineno-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></a><span class="w">    </span><span class="c1">// 先頭列を初期化する</span>
+<a id="__codelineno-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-10" name="__codelineno-58-10" href="#__codelineno-58-10"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-58-11" name="__codelineno-58-11" href="#__codelineno-58-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-58-12" name="__codelineno-58-12" href="#__codelineno-58-12"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-58-13" name="__codelineno-58-13" href="#__codelineno-58-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-14" name="__codelineno-58-14" href="#__codelineno-58-14"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">amt</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-15" name="__codelineno-58-15" href="#__codelineno-58-15"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-16" name="__codelineno-58-16" href="#__codelineno-58-16"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-58-17" name="__codelineno-58-17" href="#__codelineno-58-17"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">a</span><span class="p">];</span>
+<a id="__codelineno-58-18" name="__codelineno-58-18" href="#__codelineno-58-18"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-19" name="__codelineno-58-19" href="#__codelineno-58-19"></a><span class="w">                </span><span class="c1">// コイン i を選ばない場合と選ぶ場合の和</span>
+<a id="__codelineno-58-20" name="__codelineno-58-20" href="#__codelineno-58-20"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]];</span>
+<a id="__codelineno-58-21" name="__codelineno-58-21" href="#__codelineno-58-21"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-58-22" name="__codelineno-58-22" href="#__codelineno-58-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-58-23" name="__codelineno-58-23" href="#__codelineno-58-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-58-24" name="__codelineno-58-24" href="#__codelineno-58-24"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">amt</span><span class="p">];</span>
+<a id="__codelineno-58-25" name="__codelineno-58-25" href="#__codelineno-58-25"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_ii.ts</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">coinChangeIIDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_ii.ts</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="cm">/* コイン両替 II：動的計画法 */</span>
+<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">coinChangeIIDP</span><span class="p">(</span><span class="nx">coins</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coins</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-59-4" name="__codelineno-59-4" href="#__codelineno-59-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-59-5" name="__codelineno-59-5" href="#__codelineno-59-5"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="kt">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span>
+<a id="__codelineno-59-6" name="__codelineno-59-6" href="#__codelineno-59-6"></a><span class="w">        </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="kt">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span>
+<a id="__codelineno-59-7" name="__codelineno-59-7" href="#__codelineno-59-7"></a><span class="w">    </span><span class="p">);</span>
+<a id="__codelineno-59-8" name="__codelineno-59-8" href="#__codelineno-59-8"></a><span class="w">    </span><span class="c1">// 先頭列を初期化する</span>
+<a id="__codelineno-59-9" name="__codelineno-59-9" href="#__codelineno-59-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-10" name="__codelineno-59-10" href="#__codelineno-59-10"></a><span class="w">        </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-59-11" name="__codelineno-59-11" href="#__codelineno-59-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-59-12" name="__codelineno-59-12" href="#__codelineno-59-12"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-59-13" name="__codelineno-59-13" href="#__codelineno-59-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-14" name="__codelineno-59-14" href="#__codelineno-59-14"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">amt</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-15" name="__codelineno-59-15" href="#__codelineno-59-15"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-16" name="__codelineno-59-16" href="#__codelineno-59-16"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-59-17" name="__codelineno-59-17" href="#__codelineno-59-17"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">a</span><span class="p">];</span>
+<a id="__codelineno-59-18" name="__codelineno-59-18" href="#__codelineno-59-18"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-19" name="__codelineno-59-19" href="#__codelineno-59-19"></a><span class="w">                </span><span class="c1">// コイン i を選ばない場合と選ぶ場合の和</span>
+<a id="__codelineno-59-20" name="__codelineno-59-20" href="#__codelineno-59-20"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]];</span>
+<a id="__codelineno-59-21" name="__codelineno-59-21" href="#__codelineno-59-21"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-59-22" name="__codelineno-59-22" href="#__codelineno-59-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-59-23" name="__codelineno-59-23" href="#__codelineno-59-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-59-24" name="__codelineno-59-24" href="#__codelineno-59-24"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">amt</span><span class="p">];</span>
+<a id="__codelineno-59-25" name="__codelineno-59-25" href="#__codelineno-59-25"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_ii.dart</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeIIDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_ii.dart</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="cm">/* コイン両替 II：動的計画法 */</span>
+<a id="__codelineno-60-2" name="__codelineno-60-2" href="#__codelineno-60-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">coinChangeIIDP</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-3" name="__codelineno-60-3" href="#__codelineno-60-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-60-4" name="__codelineno-60-4" href="#__codelineno-60-4"></a><span class="w">  </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-60-5" name="__codelineno-60-5" href="#__codelineno-60-5"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">generate</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">));</span>
+<a id="__codelineno-60-6" name="__codelineno-60-6" href="#__codelineno-60-6"></a><span class="w">  </span><span class="c1">// 先頭列を初期化する</span>
+<a id="__codelineno-60-7" name="__codelineno-60-7" href="#__codelineno-60-7"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-8" name="__codelineno-60-8" href="#__codelineno-60-8"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="m">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-60-9" name="__codelineno-60-9" href="#__codelineno-60-9"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-60-10" name="__codelineno-60-10" href="#__codelineno-60-10"></a><span class="w">  </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-60-11" name="__codelineno-60-11" href="#__codelineno-60-11"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-12" name="__codelineno-60-12" href="#__codelineno-60-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-13" name="__codelineno-60-13" href="#__codelineno-60-13"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-14" name="__codelineno-60-14" href="#__codelineno-60-14"></a><span class="w">        </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-60-15" name="__codelineno-60-15" href="#__codelineno-60-15"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">][</span><span class="n">a</span><span class="p">];</span>
+<a id="__codelineno-60-16" name="__codelineno-60-16" href="#__codelineno-60-16"></a><span class="w">      </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-17" name="__codelineno-60-17" href="#__codelineno-60-17"></a><span class="w">        </span><span class="c1">// コイン i を選ばない場合と選ぶ場合の和</span>
+<a id="__codelineno-60-18" name="__codelineno-60-18" href="#__codelineno-60-18"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]];</span>
+<a id="__codelineno-60-19" name="__codelineno-60-19" href="#__codelineno-60-19"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-60-20" name="__codelineno-60-20" href="#__codelineno-60-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-60-21" name="__codelineno-60-21" href="#__codelineno-60-21"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-60-22" name="__codelineno-60-22" href="#__codelineno-60-22"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">];</span>
+<a id="__codelineno-60-23" name="__codelineno-60-23" href="#__codelineno-60-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_ii.rs</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coin_change_ii_dp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_ii.rs</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="cm">/* コイン両替 II：動的計画法 */</span>
+<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">coin_change_ii_dp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-3" name="__codelineno-61-3" href="#__codelineno-61-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
+<a id="__codelineno-61-4" name="__codelineno-61-4" href="#__codelineno-61-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-61-5" name="__codelineno-61-5" href="#__codelineno-61-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-61-6" name="__codelineno-61-6" href="#__codelineno-61-6"></a><span class="w">    </span><span class="c1">// 先頭列を初期化する</span>
+<a id="__codelineno-61-7" name="__codelineno-61-7" href="#__codelineno-61-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..=</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-8" name="__codelineno-61-8" href="#__codelineno-61-8"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-61-9" name="__codelineno-61-9" href="#__codelineno-61-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-61-10" name="__codelineno-61-10" href="#__codelineno-61-10"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-61-11" name="__codelineno-61-11" href="#__codelineno-61-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-12" name="__codelineno-61-12" href="#__codelineno-61-12"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">amt</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-13" name="__codelineno-61-13" href="#__codelineno-61-13"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-14" name="__codelineno-61-14" href="#__codelineno-61-14"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-61-15" name="__codelineno-61-15" href="#__codelineno-61-15"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">];</span>
+<a id="__codelineno-61-16" name="__codelineno-61-16" href="#__codelineno-61-16"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-17" name="__codelineno-61-17" href="#__codelineno-61-17"></a><span class="w">                </span><span class="c1">// コイン i を選ばない場合と選ぶ場合の和</span>
+<a id="__codelineno-61-18" name="__codelineno-61-18" href="#__codelineno-61-18"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">];</span>
+<a id="__codelineno-61-19" name="__codelineno-61-19" href="#__codelineno-61-19"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-61-20" name="__codelineno-61-20" href="#__codelineno-61-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-61-21" name="__codelineno-61-21" href="#__codelineno-61-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-61-22" name="__codelineno-61-22" href="#__codelineno-61-22"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span>
+<a id="__codelineno-61-23" name="__codelineno-61-23" href="#__codelineno-61-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_ii.c</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeIIDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_ii.c</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="cm">/* コイン両替 II：動的計画法 */</span>
+<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeIIDP</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">coins</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">coinsSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coinsSize</span><span class="p">;</span>
+<a id="__codelineno-62-4" name="__codelineno-62-4" href="#__codelineno-62-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-62-5" name="__codelineno-62-5" href="#__codelineno-62-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">**</span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">((</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">));</span>
+<a id="__codelineno-62-6" name="__codelineno-62-6" href="#__codelineno-62-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-7" name="__codelineno-62-7" href="#__codelineno-62-7"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">calloc</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-62-8" name="__codelineno-62-8" href="#__codelineno-62-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-62-9" name="__codelineno-62-9" href="#__codelineno-62-9"></a><span class="w">    </span><span class="c1">// 先頭列を初期化する</span>
+<a id="__codelineno-62-10" name="__codelineno-62-10" href="#__codelineno-62-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-11" name="__codelineno-62-11" href="#__codelineno-62-11"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-62-12" name="__codelineno-62-12" href="#__codelineno-62-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-62-13" name="__codelineno-62-13" href="#__codelineno-62-13"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-62-14" name="__codelineno-62-14" href="#__codelineno-62-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-15" name="__codelineno-62-15" href="#__codelineno-62-15"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-16" name="__codelineno-62-16" href="#__codelineno-62-16"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-17" name="__codelineno-62-17" href="#__codelineno-62-17"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-62-18" name="__codelineno-62-18" href="#__codelineno-62-18"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">];</span>
+<a id="__codelineno-62-19" name="__codelineno-62-19" href="#__codelineno-62-19"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-20" name="__codelineno-62-20" href="#__codelineno-62-20"></a><span class="w">                </span><span class="c1">// コイン i を選ばない場合と選ぶ場合の和</span>
+<a id="__codelineno-62-21" name="__codelineno-62-21" href="#__codelineno-62-21"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]];</span>
+<a id="__codelineno-62-22" name="__codelineno-62-22" href="#__codelineno-62-22"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-62-23" name="__codelineno-62-23" href="#__codelineno-62-23"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-62-24" name="__codelineno-62-24" href="#__codelineno-62-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-62-25" name="__codelineno-62-25" href="#__codelineno-62-25"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">];</span>
+<a id="__codelineno-62-26" name="__codelineno-62-26" href="#__codelineno-62-26"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-62-27" name="__codelineno-62-27" href="#__codelineno-62-27"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-28" name="__codelineno-62-28" href="#__codelineno-62-28"></a><span class="w">        </span><span class="n">free</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-62-29" name="__codelineno-62-29" href="#__codelineno-62-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-62-30" name="__codelineno-62-30" href="#__codelineno-62-30"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">dp</span><span class="p">);</span>
+<a id="__codelineno-62-31" name="__codelineno-62-31" href="#__codelineno-62-31"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-62-32" name="__codelineno-62-32" href="#__codelineno-62-32"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_ii.kt</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coinChangeIIDP</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_ii.kt</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="cm">/* コイン両替 II：動的計画法 */</span>
+<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">coinChangeIIDP</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-63-4" name="__codelineno-63-4" href="#__codelineno-63-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-63-5" name="__codelineno-63-5" href="#__codelineno-63-5"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Array</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-63-6" name="__codelineno-63-6" href="#__codelineno-63-6"></a><span class="w">    </span><span class="c1">// 先頭列を初期化する</span>
+<a id="__codelineno-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="na">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-8" name="__codelineno-63-8" href="#__codelineno-63-8"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="m">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-63-9" name="__codelineno-63-9" href="#__codelineno-63-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-63-10" name="__codelineno-63-10" href="#__codelineno-63-10"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-63-11" name="__codelineno-63-11" href="#__codelineno-63-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-12" name="__codelineno-63-12" href="#__codelineno-63-12"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-13" name="__codelineno-63-13" href="#__codelineno-63-13"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-14" name="__codelineno-63-14" href="#__codelineno-63-14"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-63-15" name="__codelineno-63-15" href="#__codelineno-63-15"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">][</span><span class="n">a</span><span class="o">]</span>
+<a id="__codelineno-63-16" name="__codelineno-63-16" href="#__codelineno-63-16"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-17" name="__codelineno-63-17" href="#__codelineno-63-17"></a><span class="w">                </span><span class="c1">// コイン i を選ばない場合と選ぶ場合の和</span>
+<a id="__codelineno-63-18" name="__codelineno-63-18" href="#__codelineno-63-18"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]]</span>
+<a id="__codelineno-63-19" name="__codelineno-63-19" href="#__codelineno-63-19"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-63-20" name="__codelineno-63-20" href="#__codelineno-63-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-63-21" name="__codelineno-63-21" href="#__codelineno-63-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-63-22" name="__codelineno-63-22" href="#__codelineno-63-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">amt</span><span class="o">]</span>
+<a id="__codelineno-63-23" name="__codelineno-63-23" href="#__codelineno-63-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_ii.rb</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coin_change_ii_dp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_ii.rb</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="c1">### コイン両替 II：動的計画法 ###</span>
+<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_ii_dp</span><span class="p">(</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span>
+<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a><span class="w">  </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-64-4" name="__codelineno-64-4" href="#__codelineno-64-4"></a><span class="w">  </span><span class="c1"># dp テーブルを初期化</span>
+<a id="__codelineno-64-5" name="__codelineno-64-5" href="#__codelineno-64-5"></a><span class="w">  </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-64-6" name="__codelineno-64-6" href="#__codelineno-64-6"></a><span class="w">  </span><span class="c1"># 先頭列を初期化する</span>
+<a id="__codelineno-64-7" name="__codelineno-64-7" href="#__codelineno-64-7"></a><span class="w">  </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-64-8" name="__codelineno-64-8" href="#__codelineno-64-8"></a><span class="w">  </span><span class="c1"># 状態遷移</span>
+<a id="__codelineno-64-9" name="__codelineno-64-9" href="#__codelineno-64-9"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-64-10" name="__codelineno-64-10" href="#__codelineno-64-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-64-11" name="__codelineno-64-11" href="#__codelineno-64-11"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span>
+<a id="__codelineno-64-12" name="__codelineno-64-12" href="#__codelineno-64-12"></a><span class="w">        </span><span class="c1"># 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-64-13" name="__codelineno-64-13" href="#__codelineno-64-13"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">a</span><span class="o">]</span>
+<a id="__codelineno-64-14" name="__codelineno-64-14" href="#__codelineno-64-14"></a><span class="w">      </span><span class="k">else</span>
+<a id="__codelineno-64-15" name="__codelineno-64-15" href="#__codelineno-64-15"></a><span class="w">        </span><span class="c1"># コイン i を選ばない場合と選ぶ場合の和</span>
+<a id="__codelineno-64-16" name="__codelineno-64-16" href="#__codelineno-64-16"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span>
+<a id="__codelineno-64-17" name="__codelineno-64-17" href="#__codelineno-64-17"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-64-18" name="__codelineno-64-18" href="#__codelineno-64-18"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-64-19" name="__codelineno-64-19" href="#__codelineno-64-19"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-64-20" name="__codelineno-64-20" href="#__codelineno-64-20"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">amt</span><span class="o">]</span>
+<a id="__codelineno-64-21" name="__codelineno-64-21" href="#__codelineno-64-21"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20coin_change_ii_dp%28coins%3A%20list%5Bint%5D%2C%20amt%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E3%82%B3%E3%82%A4%E3%83%B3%E4%B8%A1%E6%9B%BF%20II%EF%BC%9A%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%20%3D%20len%28coins%29%0A%20%20%20%20%23%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5B%5B0%5D%20%2A%20%28amt%20%2B%201%29%20for%20_%20in%20range%28n%20%2B%201%29%5D%0A%20%20%20%20%23%20%E5%85%88%E9%A0%AD%E5%88%97%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20for%20i%20in%20range%28n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20dp%5Bi%5D%5B0%5D%20%3D%201%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20for%20a%20in%20range%281%2C%20amt%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20coins%5Bi%20-%201%5D%20%3E%20a%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E7%9B%AE%E6%A8%99%E9%87%91%E9%A1%8D%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%AA%E3%82%89%E7%A1%AC%E8%B2%A8%20i%20%E3%81%AF%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Ba%5D%20%3D%20dp%5Bi%20-%201%5D%5Ba%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E3%82%B3%E3%82%A4%E3%83%B3%20i%20%E3%82%92%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%E5%A0%B4%E5%90%88%E3%81%A8%E9%81%B8%E3%81%B6%E5%A0%B4%E5%90%88%E3%81%AE%E5%92%8C%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Ba%5D%20%3D%20dp%5Bi%20-%201%5D%5Ba%5D%20%2B%20dp%5Bi%5D%5Ba%20-%20coins%5Bi%20-%201%5D%5D%0A%20%20%20%20return%20dp%5Bn%5D%5Bamt%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20coins%20%3D%20%5B1%2C%202%2C%205%5D%0A%20%20%20%20amt%20%3D%205%0A%0A%20%20%20%20%23%20%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20coin_change_ii_dp%28coins%2C%20amt%29%0A%20%20%20%20print%28f%22%E7%9B%AE%E6%A8%99%E9%87%91%E9%A1%8D%E3%82%92%E4%BD%9C%E3%82%8B%E7%A1%AC%E8%B2%A8%E3%81%AE%E7%B5%84%E3%81%BF%E5%90%88%E3%82%8F%E3%81%9B%E6%95%B0%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20coin_change_ii_dp%28coins%3A%20list%5Bint%5D%2C%20amt%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E3%82%B3%E3%82%A4%E3%83%B3%E4%B8%A1%E6%9B%BF%20II%EF%BC%9A%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%20%3D%20len%28coins%29%0A%20%20%20%20%23%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5B%5B0%5D%20%2A%20%28amt%20%2B%201%29%20for%20_%20in%20range%28n%20%2B%201%29%5D%0A%20%20%20%20%23%20%E5%85%88%E9%A0%AD%E5%88%97%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20for%20i%20in%20range%28n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20dp%5Bi%5D%5B0%5D%20%3D%201%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20for%20a%20in%20range%281%2C%20amt%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20coins%5Bi%20-%201%5D%20%3E%20a%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E7%9B%AE%E6%A8%99%E9%87%91%E9%A1%8D%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%AA%E3%82%89%E7%A1%AC%E8%B2%A8%20i%20%E3%81%AF%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Ba%5D%20%3D%20dp%5Bi%20-%201%5D%5Ba%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E3%82%B3%E3%82%A4%E3%83%B3%20i%20%E3%82%92%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%E5%A0%B4%E5%90%88%E3%81%A8%E9%81%B8%E3%81%B6%E5%A0%B4%E5%90%88%E3%81%AE%E5%92%8C%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Ba%5D%20%3D%20dp%5Bi%20-%201%5D%5Ba%5D%20%2B%20dp%5Bi%5D%5Ba%20-%20coins%5Bi%20-%201%5D%5D%0A%20%20%20%20return%20dp%5Bn%5D%5Bamt%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20coins%20%3D%20%5B1%2C%202%2C%205%5D%0A%20%20%20%20amt%20%3D%205%0A%0A%20%20%20%20%23%20%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20coin_change_ii_dp%28coins%2C%20amt%29%0A%20%20%20%20print%28f%22%E7%9B%AE%E6%A8%99%E9%87%91%E9%A1%8D%E3%82%92%E4%BD%9C%E3%82%8B%E7%A1%AC%E8%B2%A8%E3%81%AE%E7%B5%84%E3%81%BF%E5%90%88%E3%82%8F%E3%81%9B%E6%95%B0%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 <h3 id="3_2">3. &nbsp; 空間最適化<a class="headerlink" href="#3_2" title="Permanent link">&para;</a></h3>
-<p>空間最適化アプローチは同じで、コインの次元を削除するだけです：</p>
+<p>空間最適化の方法も同様で、硬貨の次元を削除するだけです。</p>
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 <div class="highlight"><span class="filename">coin_change_ii.py</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_ii_dp_comp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">amt</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;硬貨交換 II：空間最適化動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;コイン両替 II：空間最適化した動的計画法&quot;&quot;&quot;</span>
 <a id="__codelineno-65-3" name="__codelineno-65-3" href="#__codelineno-65-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">coins</span><span class="p">)</span>
 <a id="__codelineno-65-4" name="__codelineno-65-4" href="#__codelineno-65-4"></a>    <span class="c1"># dp テーブルを初期化</span>
 <a id="__codelineno-65-5" name="__codelineno-65-5" href="#__codelineno-65-5"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
 <a id="__codelineno-65-6" name="__codelineno-65-6" href="#__codelineno-65-6"></a>    <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
 <a id="__codelineno-65-7" name="__codelineno-65-7" href="#__codelineno-65-7"></a>    <span class="c1"># 状態遷移</span>
 <a id="__codelineno-65-8" name="__codelineno-65-8" href="#__codelineno-65-8"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
-<a id="__codelineno-65-9" name="__codelineno-65-9" href="#__codelineno-65-9"></a>        <span class="c1"># 順序で走査</span>
+<a id="__codelineno-65-9" name="__codelineno-65-9" href="#__codelineno-65-9"></a>        <span class="c1"># 順方向に走査する</span>
 <a id="__codelineno-65-10" name="__codelineno-65-10" href="#__codelineno-65-10"></a>        <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-65-11" name="__codelineno-65-11" href="#__codelineno-65-11"></a>            <span class="k">if</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">a</span><span class="p">:</span>
-<a id="__codelineno-65-12" name="__codelineno-65-12" href="#__codelineno-65-12"></a>                <span class="c1"># 目標金額を超える場合、硬貨 i を選択しない</span>
+<a id="__codelineno-65-12" name="__codelineno-65-12" href="#__codelineno-65-12"></a>                <span class="c1"># 目標金額を超えるなら硬貨 i は選ばない</span>
 <a id="__codelineno-65-13" name="__codelineno-65-13" href="#__codelineno-65-13"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span>
 <a id="__codelineno-65-14" name="__codelineno-65-14" href="#__codelineno-65-14"></a>            <span class="k">else</span><span class="p">:</span>
-<a id="__codelineno-65-15" name="__codelineno-65-15" href="#__codelineno-65-15"></a>                <span class="c1"># 硬貨 i を選択しないのと選択するのとの両方の選択肢の和</span>
+<a id="__codelineno-65-15" name="__codelineno-65-15" href="#__codelineno-65-15"></a>                <span class="c1"># コイン i を選ばない場合と選ぶ場合の和</span>
 <a id="__codelineno-65-16" name="__codelineno-65-16" href="#__codelineno-65-16"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">+</span> <span class="n">dp</span><span class="p">[</span><span class="n">a</span> <span class="o">-</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span>
 <a id="__codelineno-65-17" name="__codelineno-65-17" href="#__codelineno-65-17"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_ii.cpp</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="cm">/* 硬貨両替 II：空間最適化動的プログラミング */</span>
+<div class="highlight"><span class="filename">coin_change_ii.cpp</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="cm">/* コイン両替 II：空間最適化した動的計画法 */</span>
 <a id="__codelineno-66-2" name="__codelineno-66-2" href="#__codelineno-66-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeIIDPComp</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-66-3" name="__codelineno-66-3" href="#__codelineno-66-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
-<a id="__codelineno-66-4" name="__codelineno-66-4" href="#__codelineno-66-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-66-4" name="__codelineno-66-4" href="#__codelineno-66-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
 <a id="__codelineno-66-5" name="__codelineno-66-5" href="#__codelineno-66-5"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-66-6" name="__codelineno-66-6" href="#__codelineno-66-6"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-66-7" name="__codelineno-66-7" href="#__codelineno-66-7"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
 <a id="__codelineno-66-8" name="__codelineno-66-8" href="#__codelineno-66-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-66-9" name="__codelineno-66-9" href="#__codelineno-66-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-66-10" name="__codelineno-66-10" href="#__codelineno-66-10"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-66-11" name="__codelineno-66-11" href="#__codelineno-66-11"></a><span class="w">                </span><span class="c1">// 目標金額を超える場合、硬貨 i を選択しない</span>
+<a id="__codelineno-66-11" name="__codelineno-66-11" href="#__codelineno-66-11"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
 <a id="__codelineno-66-12" name="__codelineno-66-12" href="#__codelineno-66-12"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">];</span>
 <a id="__codelineno-66-13" name="__codelineno-66-13" href="#__codelineno-66-13"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-66-14" name="__codelineno-66-14" href="#__codelineno-66-14"></a><span class="w">                </span><span class="c1">// 選択しない場合と硬貨 i を選択する場合の2つの選択肢の合計</span>
+<a id="__codelineno-66-14" name="__codelineno-66-14" href="#__codelineno-66-14"></a><span class="w">                </span><span class="c1">// コイン i を選ばない場合と選ぶ場合の和</span>
 <a id="__codelineno-66-15" name="__codelineno-66-15" href="#__codelineno-66-15"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]];</span>
 <a id="__codelineno-66-16" name="__codelineno-66-16" href="#__codelineno-66-16"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-66-17" name="__codelineno-66-17" href="#__codelineno-66-17"></a><span class="w">        </span><span class="p">}</span>
@@ -5381,20 +6529,20 @@ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_ii.java</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="cm">/* 硬貨両替 II：空間最適化動的プログラミング */</span>
+<div class="highlight"><span class="filename">coin_change_ii.java</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="cm">/* コイン両替 II：空間最適化した動的計画法 */</span>
 <a id="__codelineno-67-2" name="__codelineno-67-2" href="#__codelineno-67-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeIIDPComp</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-67-3" name="__codelineno-67-3" href="#__codelineno-67-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
-<a id="__codelineno-67-4" name="__codelineno-67-4" href="#__codelineno-67-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-67-4" name="__codelineno-67-4" href="#__codelineno-67-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
 <a id="__codelineno-67-5" name="__codelineno-67-5" href="#__codelineno-67-5"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-67-6" name="__codelineno-67-6" href="#__codelineno-67-6"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-67-7" name="__codelineno-67-7" href="#__codelineno-67-7"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
 <a id="__codelineno-67-8" name="__codelineno-67-8" href="#__codelineno-67-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-67-9" name="__codelineno-67-9" href="#__codelineno-67-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-67-10" name="__codelineno-67-10" href="#__codelineno-67-10"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-67-11" name="__codelineno-67-11" href="#__codelineno-67-11"></a><span class="w">                </span><span class="c1">// 目標金額を超える場合、硬貨 i を選択しない</span>
+<a id="__codelineno-67-11" name="__codelineno-67-11" href="#__codelineno-67-11"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
 <a id="__codelineno-67-12" name="__codelineno-67-12" href="#__codelineno-67-12"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-67-13" name="__codelineno-67-13" href="#__codelineno-67-13"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-67-14" name="__codelineno-67-14" href="#__codelineno-67-14"></a><span class="w">                </span><span class="c1">// 選択しない場合と硬貨 i を選択する場合の2つの選択肢の合計</span>
+<a id="__codelineno-67-14" name="__codelineno-67-14" href="#__codelineno-67-14"></a><span class="w">                </span><span class="c1">// コイン i を選ばない場合と選ぶ場合の和</span>
 <a id="__codelineno-67-15" name="__codelineno-67-15" href="#__codelineno-67-15"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="p">;</span>
 <a id="__codelineno-67-16" name="__codelineno-67-16" href="#__codelineno-67-16"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-67-17" name="__codelineno-67-17" href="#__codelineno-67-17"></a><span class="w">        </span><span class="p">}</span>
@@ -5404,47 +6552,247 @@ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_ii.cs</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">coin_change_ii</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">CoinChangeIIDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_ii.cs</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="cm">/* コイン両替 II：空間最適化した動的計画法 */</span>
+<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">CoinChangeIIDPComp</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-68-3" name="__codelineno-68-3" href="#__codelineno-68-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
+<a id="__codelineno-68-4" name="__codelineno-68-4" href="#__codelineno-68-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-68-5" name="__codelineno-68-5" href="#__codelineno-68-5"></a><span class="w">    </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-68-6" name="__codelineno-68-6" href="#__codelineno-68-6"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-68-7" name="__codelineno-68-7" href="#__codelineno-68-7"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-68-8" name="__codelineno-68-8" href="#__codelineno-68-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-68-9" name="__codelineno-68-9" href="#__codelineno-68-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-68-10" name="__codelineno-68-10" href="#__codelineno-68-10"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-68-11" name="__codelineno-68-11" href="#__codelineno-68-11"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-68-12" name="__codelineno-68-12" href="#__codelineno-68-12"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">];</span>
+<a id="__codelineno-68-13" name="__codelineno-68-13" href="#__codelineno-68-13"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-68-14" name="__codelineno-68-14" href="#__codelineno-68-14"></a><span class="w">                </span><span class="c1">// コイン i を選ばない場合と選ぶ場合の和</span>
+<a id="__codelineno-68-15" name="__codelineno-68-15" href="#__codelineno-68-15"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]];</span>
+<a id="__codelineno-68-16" name="__codelineno-68-16" href="#__codelineno-68-16"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-68-17" name="__codelineno-68-17" href="#__codelineno-68-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-68-18" name="__codelineno-68-18" href="#__codelineno-68-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-68-19" name="__codelineno-68-19" href="#__codelineno-68-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">];</span>
+<a id="__codelineno-68-20" name="__codelineno-68-20" href="#__codelineno-68-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_ii.go</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">coinChangeIIDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_ii.go</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="cm">/* コイン両替 II：空間最適化した動的計画法 */</span>
+<a id="__codelineno-69-2" name="__codelineno-69-2" href="#__codelineno-69-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">coinChangeIIDPComp</span><span class="p">(</span><span class="nx">coins</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-3" name="__codelineno-69-3" href="#__codelineno-69-3"></a><span class="w">    </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">coins</span><span class="p">)</span>
+<a id="__codelineno-69-4" name="__codelineno-69-4" href="#__codelineno-69-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-69-5" name="__codelineno-69-5" href="#__codelineno-69-5"></a><span class="w">    </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-69-6" name="__codelineno-69-6" href="#__codelineno-69-6"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-69-7" name="__codelineno-69-7" href="#__codelineno-69-7"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-69-8" name="__codelineno-69-8" href="#__codelineno-69-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-9" name="__codelineno-69-9" href="#__codelineno-69-9"></a><span class="w">        </span><span class="c1">// 順方向に走査する</span>
+<a id="__codelineno-69-10" name="__codelineno-69-10" href="#__codelineno-69-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">amt</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-11" name="__codelineno-69-11" href="#__codelineno-69-11"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-12" name="__codelineno-69-12" href="#__codelineno-69-12"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-69-13" name="__codelineno-69-13" href="#__codelineno-69-13"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]</span>
+<a id="__codelineno-69-14" name="__codelineno-69-14" href="#__codelineno-69-14"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-15" name="__codelineno-69-15" href="#__codelineno-69-15"></a><span class="w">                </span><span class="c1">// コイン i を選ばない場合と選ぶ場合の和</span>
+<a id="__codelineno-69-16" name="__codelineno-69-16" href="#__codelineno-69-16"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="o">-</span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]]</span>
+<a id="__codelineno-69-17" name="__codelineno-69-17" href="#__codelineno-69-17"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-69-18" name="__codelineno-69-18" href="#__codelineno-69-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-69-19" name="__codelineno-69-19" href="#__codelineno-69-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-69-20" name="__codelineno-69-20" href="#__codelineno-69-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">amt</span><span class="p">]</span>
+<a id="__codelineno-69-21" name="__codelineno-69-21" href="#__codelineno-69-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_ii.swift</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">coinChangeIIDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_ii.swift</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="cm">/* コイン両替 II：空間最適化した動的計画法 */</span>
+<a id="__codelineno-70-2" name="__codelineno-70-2" href="#__codelineno-70-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">coinChangeIIDPComp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-3" name="__codelineno-70-3" href="#__codelineno-70-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-70-4" name="__codelineno-70-4" href="#__codelineno-70-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-70-5" name="__codelineno-70-5" href="#__codelineno-70-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-70-6" name="__codelineno-70-6" href="#__codelineno-70-6"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-70-7" name="__codelineno-70-7" href="#__codelineno-70-7"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-70-8" name="__codelineno-70-8" href="#__codelineno-70-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-9" name="__codelineno-70-9" href="#__codelineno-70-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-10" name="__codelineno-70-10" href="#__codelineno-70-10"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-11" name="__codelineno-70-11" href="#__codelineno-70-11"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-70-12" name="__codelineno-70-12" href="#__codelineno-70-12"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span>
+<a id="__codelineno-70-13" name="__codelineno-70-13" href="#__codelineno-70-13"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-14" name="__codelineno-70-14" href="#__codelineno-70-14"></a><span class="w">                </span><span class="c1">// コイン i を選ばない場合と選ぶ場合の和</span>
+<a id="__codelineno-70-15" name="__codelineno-70-15" href="#__codelineno-70-15"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span>
+<a id="__codelineno-70-16" name="__codelineno-70-16" href="#__codelineno-70-16"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-70-17" name="__codelineno-70-17" href="#__codelineno-70-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-70-18" name="__codelineno-70-18" href="#__codelineno-70-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-70-19" name="__codelineno-70-19" href="#__codelineno-70-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span>
+<a id="__codelineno-70-20" name="__codelineno-70-20" href="#__codelineno-70-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_ii.js</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">coinChangeIIDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_ii.js</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="cm">/* コイン両替 II：空間最適化した動的計画法 */</span>
+<a id="__codelineno-71-2" name="__codelineno-71-2" href="#__codelineno-71-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">coinChangeIIDPComp</span><span class="p">(</span><span class="nx">coins</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-3" name="__codelineno-71-3" href="#__codelineno-71-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coins</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-71-4" name="__codelineno-71-4" href="#__codelineno-71-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-71-5" name="__codelineno-71-5" href="#__codelineno-71-5"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-71-6" name="__codelineno-71-6" href="#__codelineno-71-6"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-71-7" name="__codelineno-71-7" href="#__codelineno-71-7"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-71-8" name="__codelineno-71-8" href="#__codelineno-71-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-9" name="__codelineno-71-9" href="#__codelineno-71-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">amt</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-10" name="__codelineno-71-10" href="#__codelineno-71-10"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-11" name="__codelineno-71-11" href="#__codelineno-71-11"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-71-12" name="__codelineno-71-12" href="#__codelineno-71-12"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">];</span>
+<a id="__codelineno-71-13" name="__codelineno-71-13" href="#__codelineno-71-13"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-14" name="__codelineno-71-14" href="#__codelineno-71-14"></a><span class="w">                </span><span class="c1">// コイン i を選ばない場合と選ぶ場合の和</span>
+<a id="__codelineno-71-15" name="__codelineno-71-15" href="#__codelineno-71-15"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]];</span>
+<a id="__codelineno-71-16" name="__codelineno-71-16" href="#__codelineno-71-16"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-71-17" name="__codelineno-71-17" href="#__codelineno-71-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-71-18" name="__codelineno-71-18" href="#__codelineno-71-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-71-19" name="__codelineno-71-19" href="#__codelineno-71-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">amt</span><span class="p">];</span>
+<a id="__codelineno-71-20" name="__codelineno-71-20" href="#__codelineno-71-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_ii.ts</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">coinChangeIIDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_ii.ts</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="cm">/* コイン両替 II：空間最適化した動的計画法 */</span>
+<a id="__codelineno-72-2" name="__codelineno-72-2" href="#__codelineno-72-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">coinChangeIIDPComp</span><span class="p">(</span><span class="nx">coins</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-3" name="__codelineno-72-3" href="#__codelineno-72-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coins</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-72-4" name="__codelineno-72-4" href="#__codelineno-72-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-72-5" name="__codelineno-72-5" href="#__codelineno-72-5"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="kt">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-72-6" name="__codelineno-72-6" href="#__codelineno-72-6"></a><span class="w">    </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-72-7" name="__codelineno-72-7" href="#__codelineno-72-7"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-72-8" name="__codelineno-72-8" href="#__codelineno-72-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-9" name="__codelineno-72-9" href="#__codelineno-72-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">amt</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-10" name="__codelineno-72-10" href="#__codelineno-72-10"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-11" name="__codelineno-72-11" href="#__codelineno-72-11"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-72-12" name="__codelineno-72-12" href="#__codelineno-72-12"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">];</span>
+<a id="__codelineno-72-13" name="__codelineno-72-13" href="#__codelineno-72-13"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-14" name="__codelineno-72-14" href="#__codelineno-72-14"></a><span class="w">                </span><span class="c1">// コイン i を選ばない場合と選ぶ場合の和</span>
+<a id="__codelineno-72-15" name="__codelineno-72-15" href="#__codelineno-72-15"></a><span class="w">                </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]];</span>
+<a id="__codelineno-72-16" name="__codelineno-72-16" href="#__codelineno-72-16"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-72-17" name="__codelineno-72-17" href="#__codelineno-72-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-72-18" name="__codelineno-72-18" href="#__codelineno-72-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-72-19" name="__codelineno-72-19" href="#__codelineno-72-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">amt</span><span class="p">];</span>
+<a id="__codelineno-72-20" name="__codelineno-72-20" href="#__codelineno-72-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_ii.dart</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeIIDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_ii.dart</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="cm">/* コイン両替 II：空間最適化した動的計画法 */</span>
+<a id="__codelineno-73-2" name="__codelineno-73-2" href="#__codelineno-73-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">coinChangeIIDPComp</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-73-3" name="__codelineno-73-3" href="#__codelineno-73-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-73-4" name="__codelineno-73-4" href="#__codelineno-73-4"></a><span class="w">  </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-73-5" name="__codelineno-73-5" href="#__codelineno-73-5"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-73-6" name="__codelineno-73-6" href="#__codelineno-73-6"></a><span class="w">  </span><span class="n">dp</span><span class="p">[</span><span class="m">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-73-7" name="__codelineno-73-7" href="#__codelineno-73-7"></a><span class="w">  </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-73-8" name="__codelineno-73-8" href="#__codelineno-73-8"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-73-9" name="__codelineno-73-9" href="#__codelineno-73-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-73-10" name="__codelineno-73-10" href="#__codelineno-73-10"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-73-11" name="__codelineno-73-11" href="#__codelineno-73-11"></a><span class="w">        </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-73-12" name="__codelineno-73-12" href="#__codelineno-73-12"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">];</span>
+<a id="__codelineno-73-13" name="__codelineno-73-13" href="#__codelineno-73-13"></a><span class="w">      </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-73-14" name="__codelineno-73-14" href="#__codelineno-73-14"></a><span class="w">        </span><span class="c1">// コイン i を選ばない場合と選ぶ場合の和</span>
+<a id="__codelineno-73-15" name="__codelineno-73-15" href="#__codelineno-73-15"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]];</span>
+<a id="__codelineno-73-16" name="__codelineno-73-16" href="#__codelineno-73-16"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-73-17" name="__codelineno-73-17" href="#__codelineno-73-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-73-18" name="__codelineno-73-18" href="#__codelineno-73-18"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-73-19" name="__codelineno-73-19" href="#__codelineno-73-19"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">];</span>
+<a id="__codelineno-73-20" name="__codelineno-73-20" href="#__codelineno-73-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_ii.rs</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coin_change_ii_dp_comp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_ii.rs</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="cm">/* コイン両替 II：空間最適化した動的計画法 */</span>
+<a id="__codelineno-74-2" name="__codelineno-74-2" href="#__codelineno-74-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">coin_change_ii_dp_comp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-3" name="__codelineno-74-3" href="#__codelineno-74-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
+<a id="__codelineno-74-4" name="__codelineno-74-4" href="#__codelineno-74-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-74-5" name="__codelineno-74-5" href="#__codelineno-74-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-74-6" name="__codelineno-74-6" href="#__codelineno-74-6"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-74-7" name="__codelineno-74-7" href="#__codelineno-74-7"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-74-8" name="__codelineno-74-8" href="#__codelineno-74-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-9" name="__codelineno-74-9" href="#__codelineno-74-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">amt</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-10" name="__codelineno-74-10" href="#__codelineno-74-10"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-11" name="__codelineno-74-11" href="#__codelineno-74-11"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-74-12" name="__codelineno-74-12" href="#__codelineno-74-12"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">];</span>
+<a id="__codelineno-74-13" name="__codelineno-74-13" href="#__codelineno-74-13"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-14" name="__codelineno-74-14" href="#__codelineno-74-14"></a><span class="w">                </span><span class="c1">// コイン i を選ばない場合と選ぶ場合の和</span>
+<a id="__codelineno-74-15" name="__codelineno-74-15" href="#__codelineno-74-15"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">];</span>
+<a id="__codelineno-74-16" name="__codelineno-74-16" href="#__codelineno-74-16"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-74-17" name="__codelineno-74-17" href="#__codelineno-74-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-74-18" name="__codelineno-74-18" href="#__codelineno-74-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-74-19" name="__codelineno-74-19" href="#__codelineno-74-19"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span>
+<a id="__codelineno-74-20" name="__codelineno-74-20" href="#__codelineno-74-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_ii.c</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeIIDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_ii.c</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="cm">/* コイン両替 II：空間最適化した動的計画法 */</span>
+<a id="__codelineno-75-2" name="__codelineno-75-2" href="#__codelineno-75-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeIIDPComp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">coins</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">coinsSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-75-3" name="__codelineno-75-3" href="#__codelineno-75-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coinsSize</span><span class="p">;</span>
+<a id="__codelineno-75-4" name="__codelineno-75-4" href="#__codelineno-75-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-75-5" name="__codelineno-75-5" href="#__codelineno-75-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">calloc</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-75-6" name="__codelineno-75-6" href="#__codelineno-75-6"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-75-7" name="__codelineno-75-7" href="#__codelineno-75-7"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-75-8" name="__codelineno-75-8" href="#__codelineno-75-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-75-9" name="__codelineno-75-9" href="#__codelineno-75-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-75-10" name="__codelineno-75-10" href="#__codelineno-75-10"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-75-11" name="__codelineno-75-11" href="#__codelineno-75-11"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-75-12" name="__codelineno-75-12" href="#__codelineno-75-12"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">];</span>
+<a id="__codelineno-75-13" name="__codelineno-75-13" href="#__codelineno-75-13"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-75-14" name="__codelineno-75-14" href="#__codelineno-75-14"></a><span class="w">                </span><span class="c1">// コイン i を選ばない場合と選ぶ場合の和</span>
+<a id="__codelineno-75-15" name="__codelineno-75-15" href="#__codelineno-75-15"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]];</span>
+<a id="__codelineno-75-16" name="__codelineno-75-16" href="#__codelineno-75-16"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-75-17" name="__codelineno-75-17" href="#__codelineno-75-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-75-18" name="__codelineno-75-18" href="#__codelineno-75-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-75-19" name="__codelineno-75-19" href="#__codelineno-75-19"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">];</span>
+<a id="__codelineno-75-20" name="__codelineno-75-20" href="#__codelineno-75-20"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-75-21" name="__codelineno-75-21" href="#__codelineno-75-21"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">dp</span><span class="p">);</span>
+<a id="__codelineno-75-22" name="__codelineno-75-22" href="#__codelineno-75-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-75-23" name="__codelineno-75-23" href="#__codelineno-75-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_ii.kt</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coinChangeIIDPComp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_ii.kt</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="cm">/* コイン両替 II：空間最適化した動的計画法 */</span>
+<a id="__codelineno-76-2" name="__codelineno-76-2" href="#__codelineno-76-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">coinChangeIIDPComp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-76-3" name="__codelineno-76-3" href="#__codelineno-76-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-76-4" name="__codelineno-76-4" href="#__codelineno-76-4"></a><span class="w">    </span><span class="c1">// dp テーブルを初期化</span>
+<a id="__codelineno-76-5" name="__codelineno-76-5" href="#__codelineno-76-5"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-76-6" name="__codelineno-76-6" href="#__codelineno-76-6"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="m">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-76-7" name="__codelineno-76-7" href="#__codelineno-76-7"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-76-8" name="__codelineno-76-8" href="#__codelineno-76-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-76-9" name="__codelineno-76-9" href="#__codelineno-76-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-76-10" name="__codelineno-76-10" href="#__codelineno-76-10"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-76-11" name="__codelineno-76-11" href="#__codelineno-76-11"></a><span class="w">                </span><span class="c1">// 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-76-12" name="__codelineno-76-12" href="#__codelineno-76-12"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span>
+<a id="__codelineno-76-13" name="__codelineno-76-13" href="#__codelineno-76-13"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-76-14" name="__codelineno-76-14" href="#__codelineno-76-14"></a><span class="w">                </span><span class="c1">// コイン i を選ばない場合と選ぶ場合の和</span>
+<a id="__codelineno-76-15" name="__codelineno-76-15" href="#__codelineno-76-15"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]]</span>
+<a id="__codelineno-76-16" name="__codelineno-76-16" href="#__codelineno-76-16"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-76-17" name="__codelineno-76-17" href="#__codelineno-76-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-76-18" name="__codelineno-76-18" href="#__codelineno-76-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-76-19" name="__codelineno-76-19" href="#__codelineno-76-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">amt</span><span class="o">]</span>
+<a id="__codelineno-76-20" name="__codelineno-76-20" href="#__codelineno-76-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_ii.rb</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coin_change_ii_dp_comp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_ii.rb</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="c1">### コイン両替 II：空間最適化した動的計画法 ###</span>
+<a id="__codelineno-77-2" name="__codelineno-77-2" href="#__codelineno-77-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_ii_dp_comp</span><span class="p">(</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span>
+<a id="__codelineno-77-3" name="__codelineno-77-3" href="#__codelineno-77-3"></a><span class="w">  </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-77-4" name="__codelineno-77-4" href="#__codelineno-77-4"></a><span class="w">  </span><span class="c1"># dp テーブルを初期化</span>
+<a id="__codelineno-77-5" name="__codelineno-77-5" href="#__codelineno-77-5"></a><span class="w">  </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-77-6" name="__codelineno-77-6" href="#__codelineno-77-6"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-77-7" name="__codelineno-77-7" href="#__codelineno-77-7"></a><span class="w">  </span><span class="c1"># 状態遷移</span>
+<a id="__codelineno-77-8" name="__codelineno-77-8" href="#__codelineno-77-8"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-77-9" name="__codelineno-77-9" href="#__codelineno-77-9"></a><span class="w">    </span><span class="c1"># 順方向に走査する</span>
+<a id="__codelineno-77-10" name="__codelineno-77-10" href="#__codelineno-77-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-77-11" name="__codelineno-77-11" href="#__codelineno-77-11"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span>
+<a id="__codelineno-77-12" name="__codelineno-77-12" href="#__codelineno-77-12"></a><span class="w">        </span><span class="c1"># 目標金額を超えるなら硬貨 i は選ばない</span>
+<a id="__codelineno-77-13" name="__codelineno-77-13" href="#__codelineno-77-13"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span>
+<a id="__codelineno-77-14" name="__codelineno-77-14" href="#__codelineno-77-14"></a><span class="w">      </span><span class="k">else</span>
+<a id="__codelineno-77-15" name="__codelineno-77-15" href="#__codelineno-77-15"></a><span class="w">        </span><span class="c1"># コイン i を選ばない場合と選ぶ場合の和</span>
+<a id="__codelineno-77-16" name="__codelineno-77-16" href="#__codelineno-77-16"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span>
+<a id="__codelineno-77-17" name="__codelineno-77-17" href="#__codelineno-77-17"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-77-18" name="__codelineno-77-18" href="#__codelineno-77-18"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-77-19" name="__codelineno-77-19" href="#__codelineno-77-19"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-77-20" name="__codelineno-77-20" href="#__codelineno-77-20"></a><span class="w">  </span><span class="n">dp</span><span class="o">[</span><span class="n">amt</span><span class="o">]</span>
+<a id="__codelineno-77-21" name="__codelineno-77-21" href="#__codelineno-77-21"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20coin_change_ii_dp_comp%28coins%3A%20list%5Bint%5D%2C%20amt%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E3%82%B3%E3%82%A4%E3%83%B3%E4%B8%A1%E6%9B%BF%20II%EF%BC%9A%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E3%81%97%E3%81%9F%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%20%3D%20len%28coins%29%0A%20%20%20%20%23%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5B0%5D%20%2A%20%28amt%20%2B%201%29%0A%20%20%20%20dp%5B0%5D%20%3D%201%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E9%A0%86%E6%96%B9%E5%90%91%E3%81%AB%E8%B5%B0%E6%9F%BB%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20for%20a%20in%20range%281%2C%20amt%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20coins%5Bi%20-%201%5D%20%3E%20a%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E7%9B%AE%E6%A8%99%E9%87%91%E9%A1%8D%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%AA%E3%82%89%E7%A1%AC%E8%B2%A8%20i%20%E3%81%AF%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Ba%5D%20%3D%20dp%5Ba%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E3%82%B3%E3%82%A4%E3%83%B3%20i%20%E3%82%92%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%E5%A0%B4%E5%90%88%E3%81%A8%E9%81%B8%E3%81%B6%E5%A0%B4%E5%90%88%E3%81%AE%E5%92%8C%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Ba%5D%20%3D%20dp%5Ba%5D%20%2B%20dp%5Ba%20-%20coins%5Bi%20-%201%5D%5D%0A%20%20%20%20return%20dp%5Bamt%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20coins%20%3D%20%5B1%2C%202%2C%205%5D%0A%20%20%20%20amt%20%3D%205%0A%0A%20%20%20%20%23%20%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E5%BE%8C%E3%81%AE%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20coin_change_ii_dp_comp%28coins%2C%20amt%29%0A%20%20%20%20print%28f%22%E7%9B%AE%E6%A8%99%E9%87%91%E9%A1%8D%E3%82%92%E4%BD%9C%E3%82%8B%E7%A1%AC%E8%B2%A8%E3%81%AE%E7%B5%84%E3%81%BF%E5%90%88%E3%82%8F%E3%81%9B%E6%95%B0%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20coin_change_ii_dp_comp%28coins%3A%20list%5Bint%5D%2C%20amt%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E3%82%B3%E3%82%A4%E3%83%B3%E4%B8%A1%E6%9B%BF%20II%EF%BC%9A%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E3%81%97%E3%81%9F%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n%20%3D%20len%28coins%29%0A%20%20%20%20%23%20dp%20%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20dp%20%3D%20%5B0%5D%20%2A%20%28amt%20%2B%201%29%0A%20%20%20%20dp%5B0%5D%20%3D%201%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E9%A0%86%E6%96%B9%E5%90%91%E3%81%AB%E8%B5%B0%E6%9F%BB%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20for%20a%20in%20range%281%2C%20amt%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20coins%5Bi%20-%201%5D%20%3E%20a%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E7%9B%AE%E6%A8%99%E9%87%91%E9%A1%8D%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%AA%E3%82%89%E7%A1%AC%E8%B2%A8%20i%20%E3%81%AF%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Ba%5D%20%3D%20dp%5Ba%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E3%82%B3%E3%82%A4%E3%83%B3%20i%20%E3%82%92%E9%81%B8%E3%81%B0%E3%81%AA%E3%81%84%E5%A0%B4%E5%90%88%E3%81%A8%E9%81%B8%E3%81%B6%E5%A0%B4%E5%90%88%E3%81%AE%E5%92%8C%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Ba%5D%20%3D%20dp%5Ba%5D%20%2B%20dp%5Ba%20-%20coins%5Bi%20-%201%5D%5D%0A%20%20%20%20return%20dp%5Bamt%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20coins%20%3D%20%5B1%2C%202%2C%205%5D%0A%20%20%20%20amt%20%3D%205%0A%0A%20%20%20%20%23%20%E7%A9%BA%E9%96%93%E6%9C%80%E9%81%A9%E5%8C%96%E5%BE%8C%E3%81%AE%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20coin_change_ii_dp_comp%28coins%2C%20amt%29%0A%20%20%20%20print%28f%22%E7%9B%AE%E6%A8%99%E9%87%91%E9%A1%8D%E3%82%92%E4%BD%9C%E3%82%8B%E7%A1%AC%E8%B2%A8%E3%81%AE%E7%B5%84%E3%81%BF%E5%90%88%E3%82%8F%E3%81%9B%E6%95%B0%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 
 <!-- Source file information -->
 
@@ -5467,7 +6815,7 @@ aria-label="フッター"
   <a
     href="../knapsack_problem/"
     class="md-footer__link md-footer__link--prev"
-    aria-label="前: 14.4 &amp;nbsp; 0-1ナップサック問題"
+    aria-label="前: 14.4 &amp;nbsp; 0-1 ナップサック問題"
     rel="prev"
   >
     <div class="md-footer__button md-icon">
@@ -5479,7 +6827,7 @@ aria-label="フッター"
         前
       </span>
       <div class="md-ellipsis">
-        14.4 &nbsp; 0-1ナップサック問題
+        14.4 &nbsp; 0-1 ナップサック問題
       </div>
     </div>
   </a>
diff --git a/ja/chapter_graph/graph/index.html b/ja/chapter_graph/graph/index.html
index d9a4c8d89..dbdb9b6cc 100644
--- a/ja/chapter_graph/graph/index.html
+++ b/ja/chapter_graph/graph/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1635,7 +1635,7 @@
   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1942,7 +1942,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2105,7 +2105,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2602,7 +2602,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2658,7 +2658,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2686,7 +2686,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3224,7 +3224,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3280,7 +3280,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3308,7 +3308,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3501,7 +3501,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3529,7 +3529,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3670,7 +3670,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3698,7 +3698,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3726,7 +3726,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3754,7 +3754,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3947,7 +3947,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4192,7 +4192,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4433,7 +4433,7 @@
 
 <!-- Page content -->
 <h1 id="91">9.1 &nbsp; グラフ<a class="headerlink" href="#91" title="Permanent link">&para;</a></h1>
-<p><u>グラフ</u>は非線形データ構造の一種で、<u>頂点</u>と<u>辺</u>で構成されます。グラフ<span class="arithmatex">\(G\)</span>は、頂点の集合<span class="arithmatex">\(V\)</span>と辺の集合<span class="arithmatex">\(E\)</span>の組み合わせとして抽象的に表現できます。以下の例は、5つの頂点と7つの辺を含むグラフを示しています。</p>
+<p><u>グラフ（graph）</u>は、<u>頂点（vertex）</u>と<u>辺（edge）</u>から構成される非線形データ構造です。グラフ <span class="arithmatex">\(G\)</span> は、頂点集合 <span class="arithmatex">\(V\)</span> と辺集合 <span class="arithmatex">\(E\)</span> からなる集合として抽象的に表せます。以下の例は、5 個の頂点と 7 本の辺を含むグラフを示しています。</p>
 <div class="arithmatex">\[
 \begin{aligned}
 V &amp; = \{ 1, 2, 3, 4, 5 \} \newline
@@ -4441,62 +4441,62 @@ E &amp; = \{ (1,2), (1,3), (1,5), (2,3), (2,4), (2,5), (4,5) \} \newline
 G &amp; = \{ V, E \} \newline
 \end{aligned}
 \]</div>
-<p>頂点をノード、辺をノードを接続する参照（ポインタ）と見なすと、グラフは連結リストから拡張されたデータ構造として見ることができます。下図に示すように、<strong>線形関係（連結リスト）や分割統治関係（木）と比較して、ネットワーク関係（グラフ）は自由度が高いため、より複雑です</strong>。</p>
+<p>頂点をノード、辺を各ノードをつなぐ参照（ポインタ）とみなせば、グラフは連結リストを拡張したデータ構造の一種と捉えられます。次の図に示すように、<strong>線形関係（連結リスト）や分治関係（木）と比べて、ネットワーク関係（グラフ）は自由度が高く</strong>、そのぶん複雑です。</p>
 <p><img alt="連結リスト、木、グラフの関係" class="animation-figure" src="../graph.assets/linkedlist_tree_graph.png" /></p>
 <p align="center"> 図 9-1 &nbsp; 連結リスト、木、グラフの関係 </p>
 
 <h2 id="911">9.1.1 &nbsp; グラフの一般的な種類と用語<a class="headerlink" href="#911" title="Permanent link">&para;</a></h2>
-<p>グラフは、辺に方向があるかどうかによって<u>無向グラフ</u>と<u>有向グラフ</u>に分けることができます（下図参照）。</p>
+<p>辺が方向性を持つかどうかに応じて、<u>無向グラフ（undirected graph）</u>と<u>有向グラフ（directed graph）</u>に分けられます。次の図のとおりです。</p>
 <ul>
-<li>無向グラフでは、辺は2つの頂点間の「双方向」接続を表します。例えば、Facebookの「友達」関係です。</li>
-<li>有向グラフでは、辺に方向性があります。つまり、辺<span class="arithmatex">\(A \rightarrow B\)</span>と<span class="arithmatex">\(A \leftarrow B\)</span>は互いに独立しています。例えば、InstagramやTikTokの「フォロー」と「フォロワー」の関係です。</li>
+<li>無向グラフでは、辺は 2 つの頂点間の「双方向」の接続関係を表します。例えば WeChat や QQ における「友だち関係」です。</li>
+<li>有向グラフでは、辺は方向性を持ち、すなわち <span class="arithmatex">\(A \rightarrow B\)</span> と <span class="arithmatex">\(A \leftarrow B\)</span> の 2 方向の辺は互いに独立です。例えば Weibo や Douyin における「フォロー」と「フォロワー」の関係です。</li>
 </ul>
 <p><img alt="有向グラフと無向グラフ" class="animation-figure" src="../graph.assets/directed_graph.png" /></p>
 <p align="center"> 図 9-2 &nbsp; 有向グラフと無向グラフ </p>
 
-<p>すべての頂点が接続されているかどうかによって、グラフは<u>連結グラフ</u>と<u>非連結グラフ</u>に分けることができます（下図参照）。</p>
+<p>すべての頂点が連結しているかどうかに応じて、<u>連結グラフ（connected graph）</u>と<u>非連結グラフ（disconnected graph）</u>に分けられます。次の図のとおりです。</p>
 <ul>
-<li>連結グラフでは、任意の頂点から開始して他の任意の頂点に到達することが可能です。</li>
-<li>非連結グラフでは、任意の開始頂点から到達できない頂点が少なくとも1つ存在します。</li>
+<li>連結グラフでは、ある頂点から出発すると、ほかの任意の頂点に到達できます。</li>
+<li>非連結グラフでは、ある頂点から出発すると、少なくとも 1 つの頂点には到達できません。</li>
 </ul>
 <p><img alt="連結グラフと非連結グラフ" class="animation-figure" src="../graph.assets/connected_graph.png" /></p>
 <p align="center"> 図 9-3 &nbsp; 連結グラフと非連結グラフ </p>
 
-<p>辺に重み変数を追加することもでき、その結果として<u>重み付きグラフ</u>が生まれます（下図参照）。例えば、Instagramでは、システムがあなたと他のユーザーとの間の相互作用レベル（いいね、閲覧、コメントなど）によってフォロワーとフォロー中のリストをソートします。このような相互作用ネットワークは重み付きグラフで表現できます。</p>
+<p>辺に「重み」の変数を追加すると、次の図に示すような<u>重み付きグラフ（weighted graph）</u>が得られます。例えば『Honor of Kings』のようなモバイルゲームでは、システムが共にプレイした時間に基づいてプレイヤー間の「親密度」を計算します。この親密度ネットワークは重み付きグラフで表せます。</p>
 <p><img alt="重み付きグラフと重みなしグラフ" class="animation-figure" src="../graph.assets/weighted_graph.png" /></p>
 <p align="center"> 図 9-4 &nbsp; 重み付きグラフと重みなしグラフ </p>
 
-<p>グラフデータ構造には、以下のような一般的に使用される用語があります。</p>
+<p>グラフというデータ構造には、次のような基本用語があります。</p>
 <ul>
-<li><u>隣接</u>：2つの頂点を接続する辺がある場合、これら2つの頂点は「隣接」していると言われます。上図では、頂点1の隣接頂点は頂点2、3、5です。</li>
-<li><u>パス</u>：頂点Aから頂点Bまでに通過する辺のシーケンスを、AからBへのパスと呼びます。上図では、辺のシーケンス1-5-2-4は頂点1から頂点4へのパスです。</li>
-<li><u>次数</u>：頂点が持つ辺の数です。有向グラフの場合、<u>入次数</u>はその頂点を指す辺の数、<u>出次数</u>はその頂点から出る辺の数を指します。</li>
+<li><u>隣接（adjacency）</u>：2 つの頂点の間に辺が存在するとき、この 2 つの頂点は「隣接している」といいます。上図では、頂点 1 に隣接する頂点は 2、3、5 です。</li>
+<li><u>経路（path）</u>：頂点 A から頂点 B までに通過する辺で構成された列を、A から B への「経路」と呼びます。上図では、辺の列 1-5-2-4 は頂点 1 から頂点 4 への 1 本の経路です。</li>
+<li><u>次数（degree）</u>：ある頂点が持つ辺の本数です。有向グラフでは、<u>入次数（in-degree）</u>はその頂点に向かう辺の本数を表し、<u>出次数（out-degree）</u>はその頂点から出る辺の本数を表します。</li>
 </ul>
 <h2 id="912">9.1.2 &nbsp; グラフの表現<a class="headerlink" href="#912" title="Permanent link">&para;</a></h2>
-<p>グラフの一般的な表現には「隣接行列」と「隣接リスト」があります。以下の例では無向グラフを使用します。</p>
+<p>グラフの一般的な表現方法には「隣接行列」と「隣接リスト」があります。以下では無向グラフを例に説明します。</p>
 <h3 id="1">1. &nbsp; 隣接行列<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>グラフの頂点数を<span class="arithmatex">\(n\)</span>とすると、<u>隣接行列</u>は<span class="arithmatex">\(n \times n\)</span>の行列を使用してグラフを表現します。各行（列）は頂点を表し、行列要素は辺を表し、2つの頂点間に辺があるかどうかを<span class="arithmatex">\(1\)</span>または<span class="arithmatex">\(0\)</span>で示します。</p>
-<p>下図に示すように、隣接行列を<span class="arithmatex">\(M\)</span>、頂点のリストを<span class="arithmatex">\(V\)</span>とすると、行列要素<span class="arithmatex">\(M[i, j] = 1\)</span>は頂点<span class="arithmatex">\(V[i]\)</span>と頂点<span class="arithmatex">\(V[j]\)</span>の間に辺があることを示し、逆に<span class="arithmatex">\(M[i, j] = 0\)</span>は2つの頂点間に辺がないことを示します。</p>
-<p><img alt="隣接行列によるグラフの表現" class="animation-figure" src="../graph.assets/adjacency_matrix.png" /></p>
-<p align="center"> 図 9-5 &nbsp; 隣接行列によるグラフの表現 </p>
+<p>グラフの頂点数を <span class="arithmatex">\(n\)</span> とすると、<u>隣接行列（adjacency matrix）</u>は <span class="arithmatex">\(n \times n\)</span> の行列を用いてグラフを表します。各行（列）は 1 つの頂点を表し、行列要素は辺を表します。<span class="arithmatex">\(1\)</span> または <span class="arithmatex">\(0\)</span> を用いて、2 つの頂点の間に辺があるかどうかを示します。</p>
+<p>次の図のように、隣接行列を <span class="arithmatex">\(M\)</span>、頂点リストを <span class="arithmatex">\(V\)</span> とすると、行列要素 <span class="arithmatex">\(M[i, j] = 1\)</span> は頂点 <span class="arithmatex">\(V[i]\)</span> から頂点 <span class="arithmatex">\(V[j]\)</span> への辺が存在することを表し、逆に <span class="arithmatex">\(M[i, j] = 0\)</span> は 2 つの頂点の間に辺がないことを表します。</p>
+<p><img alt="グラフの隣接行列による表現" class="animation-figure" src="../graph.assets/adjacency_matrix.png" /></p>
+<p align="center"> 図 9-5 &nbsp; グラフの隣接行列による表現 </p>
 
-<p>隣接行列には以下の特性があります。</p>
+<p>隣接行列には次の特徴があります。</p>
 <ul>
-<li>頂点は自分自身に接続することはできないため、隣接行列の主対角線上の要素は意味がありません。</li>
-<li>無向グラフの場合、両方向の辺は等価であるため、隣接行列は主対角線に関して対称です。</li>
-<li>隣接行列の要素を<span class="arithmatex">\(1\)</span>と<span class="arithmatex">\(0\)</span>から重みに置き換えることで、重み付きグラフを表現できます。</li>
+<li>単純グラフでは、頂点は自分自身とは接続できないため、このとき隣接行列の主対角線上の要素には意味がありません。</li>
+<li>無向グラフでは、2 方向の辺は等価であるため、このとき隣接行列は主対角線に関して対称です。</li>
+<li>隣接行列の要素を <span class="arithmatex">\(1\)</span> と <span class="arithmatex">\(0\)</span> から重みに置き換えると、重み付きグラフを表せます。</li>
 </ul>
-<p>隣接行列でグラフを表現する場合、行列要素に直接アクセスして辺を取得できるため、追加、削除、検索、変更の操作が効率的で、すべて時間計算量<span class="arithmatex">\(O(1)\)</span>です。ただし、行列の空間計算量は<span class="arithmatex">\(O(n^2)\)</span>で、より多くのメモリを消費します。</p>
+<p>隣接行列でグラフを表す場合、行列要素に直接アクセスして辺を取得できるため、追加・削除・検索・更新の操作効率は高く、時間計算量はいずれも <span class="arithmatex">\(O(1)\)</span> です。しかし、行列の空間計算量は <span class="arithmatex">\(O(n^2)\)</span> であり、メモリ使用量は多くなります。</p>
 <h3 id="2">2. &nbsp; 隣接リスト<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p><u>隣接リスト</u>は<span class="arithmatex">\(n\)</span>個の連結リストを使用してグラフを表現し、各連結リストノードは頂点を表します。<span class="arithmatex">\(i\)</span>番目の連結リストは頂点<span class="arithmatex">\(i\)</span>に対応し、すべての隣接頂点（その頂点に接続された頂点）を含みます。下図は隣接リストを使用して格納されたグラフの例を示しています。</p>
-<p><img alt="隣接リストによるグラフの表現" class="animation-figure" src="../graph.assets/adjacency_list.png" /></p>
-<p align="center"> 図 9-6 &nbsp; 隣接リストによるグラフの表現 </p>
+<p><u>隣接リスト（adjacency list）</u>は、<span class="arithmatex">\(n\)</span> 本の連結リストを使ってグラフを表します。連結リストのノードは頂点を表します。第 <span class="arithmatex">\(i\)</span> 本の連結リストは頂点 <span class="arithmatex">\(i\)</span> に対応し、その頂点に隣接するすべての頂点（その頂点と接続された頂点）を格納します。次の図は、隣接リストで保存したグラフの例です。</p>
+<p><img alt="グラフの隣接リストによる表現" class="animation-figure" src="../graph.assets/adjacency_list.png" /></p>
+<p align="center"> 図 9-6 &nbsp; グラフの隣接リストによる表現 </p>
 
-<p>隣接リストは実際の辺のみを格納し、辺の総数は<span class="arithmatex">\(n^2\)</span>よりもはるかに少ないことが多く、より空間効率的です。ただし、隣接リストで辺を見つけるには連結リストを走査する必要があるため、その時間効率は隣接行列ほど良くありません。</p>
-<p>上図を観察すると、<strong>隣接リストの構造はハッシュテーブルの「チェイン法」と非常に似ているため、同様の方法を使用して効率を最適化できます</strong>。例えば、連結リストが長い場合、それをAVL木や赤黒木に変換して、時間効率を<span class="arithmatex">\(O(n)\)</span>から<span class="arithmatex">\(O(\log n)\)</span>に最適化できます。連結リストをハッシュテーブルに変換することで、時間計算量を<span class="arithmatex">\(O(1)\)</span>に削減することもできます。</p>
+<p>隣接リストは実際に存在する辺だけを格納し、辺の総数は通常 <span class="arithmatex">\(n^2\)</span> よりはるかに小さいため、より省スペースです。しかし、隣接リストでは辺を見つけるために連結リストを走査する必要があるため、時間効率は隣接行列に及びません。</p>
+<p>上図を見ると、<strong>隣接リストの構造はハッシュテーブルにおける「連鎖アドレス法」と非常によく似ているため、同様の方法で効率を最適化できます</strong>。例えば、連結リストが長い場合は AVL 木や赤黒木に変換して時間効率を <span class="arithmatex">\(O(n)\)</span> から <span class="arithmatex">\(O(\log n)\)</span> に改善できます。さらに、連結リストをハッシュテーブルに変換すれば、時間計算量を <span class="arithmatex">\(O(1)\)</span> まで下げられます。</p>
 <h2 id="913">9.1.3 &nbsp; グラフの一般的な応用<a class="headerlink" href="#913" title="Permanent link">&para;</a></h2>
-<p>下表に示すように、多くの現実世界のシステムはグラフでモデル化でき、対応する問題はグラフ計算問題に削減できます。</p>
-<p align="center"> 表 9-1 &nbsp; 現実生活の一般的なグラフ </p>
+<p>次の表のように、多くの現実のシステムはグラフでモデル化でき、対応する問題もグラフ計算の問題に帰着できます。</p>
+<p align="center"> 表 9-1 &nbsp; 現実世界でよく見られるグラフ </p>
 
 <div class="center-table">
 <table>
@@ -4512,20 +4512,20 @@ G &amp; = \{ V, E \} \newline
 <tr>
 <td>ソーシャルネットワーク</td>
 <td>ユーザー</td>
-<td>フォロー / フォロワー関係</td>
-<td>潜在的フォロー推薦</td>
+<td>友だち関係</td>
+<td>潜在的な友だちの推薦</td>
 </tr>
 <tr>
 <td>地下鉄路線</td>
 <td>駅</td>
 <td>駅間の接続性</td>
-<td>最短ルート推薦</td>
+<td>最短経路の推薦</td>
 </tr>
 <tr>
 <td>太陽系</td>
 <td>天体</td>
-<td>天体間の重力</td>
-<td>惑星軌道計算</td>
+<td>天体間の万有引力作用</td>
+<td>惑星軌道の計算</td>
 </tr>
 </tbody>
 </table>
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-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
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+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1635,7 +1635,7 @@
   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1942,7 +1942,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2105,7 +2105,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2574,7 +2574,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2630,7 +2630,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2658,7 +2658,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3196,7 +3196,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3252,7 +3252,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3280,7 +3280,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3473,7 +3473,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3501,7 +3501,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3642,7 +3642,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3670,7 +3670,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3698,7 +3698,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3726,7 +3726,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3919,7 +3919,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4164,7 +4164,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4377,19 +4377,19 @@
 
 <!-- Page content -->
 <h1 id="92">9.2 &nbsp; グラフの基本操作<a class="headerlink" href="#92" title="Permanent link">&para;</a></h1>
-<p>グラフの基本操作は「辺」に対する操作と「頂点」に対する操作に分けることができます。「隣接行列」と「隣接リスト」の2つの表現方法の下では、実装が異なります。</p>
+<p>グラフの基本操作は、「辺」に対する操作と「頂点」に対する操作に分けられます。「隣接行列」と「隣接リスト」の 2 つの表現方法では、実装方法が異なります。</p>
 <h2 id="921">9.2.1 &nbsp; 隣接行列に基づく実装<a class="headerlink" href="#921" title="Permanent link">&para;</a></h2>
-<p><span class="arithmatex">\(n\)</span>個の頂点を持つ無向グラフが与えられた場合、さまざまな操作は下図のように実装されます。</p>
+<p>頂点数が <span class="arithmatex">\(n\)</span> の無向グラフを与えると、各種操作の実装方法は次図のとおりです。</p>
 <ul>
-<li><strong>辺の追加または削除</strong>：隣接行列内の指定された辺を直接変更し、<span class="arithmatex">\(O(1)\)</span>時間を使用します。無向グラフであるため、両方向の辺を同時に更新する必要があります。</li>
-<li><strong>頂点の追加</strong>：隣接行列の末尾に行と列を追加し、すべて<span class="arithmatex">\(0\)</span>で埋めます。<span class="arithmatex">\(O(n)\)</span>時間を使用します。</li>
-<li><strong>頂点の削除</strong>：隣接行列内の行と列を削除します。最悪の場合は最初の行と列が削除されるときで、<span class="arithmatex">\((n-1)^2\)</span>個の要素を「上と左に移動」する必要があり、<span class="arithmatex">\(O(n^2)\)</span>時間を使用します。</li>
-<li><strong>初期化</strong>：<span class="arithmatex">\(n\)</span>個の頂点を渡し、長さ<span class="arithmatex">\(n\)</span>の頂点リスト<code>vertices</code>を初期化し、<span class="arithmatex">\(O(n)\)</span>時間を使用します。<span class="arithmatex">\(n \times n\)</span>サイズの隣接行列<code>adjMat</code>を初期化し、<span class="arithmatex">\(O(n^2)\)</span>時間を使用します。</li>
+<li><strong>辺の追加または削除</strong>：隣接行列で指定した辺を直接変更すればよく、<span class="arithmatex">\(O(1)\)</span> 時間です。無向グラフであるため、2 方向の辺を同時に更新する必要があります。</li>
+<li><strong>頂点の追加</strong>：隣接行列の末尾に 1 行 1 列を追加し、すべてを <span class="arithmatex">\(0\)</span> で埋めればよく、<span class="arithmatex">\(O(n)\)</span> 時間です。</li>
+<li><strong>頂点の削除</strong>：隣接行列から 1 行 1 列を削除します。先頭行と先頭列を削除する場合が最悪で、<span class="arithmatex">\((n-1)^2\)</span> 個の要素を「左上へ移動」させる必要があるため、<span class="arithmatex">\(O(n^2)\)</span> 時間です。</li>
+<li><strong>初期化</strong>：<span class="arithmatex">\(n\)</span> 個の頂点を受け取り、長さ <span class="arithmatex">\(n\)</span> の頂点リスト <code>vertices</code> を初期化するのに <span class="arithmatex">\(O(n)\)</span> 時間、サイズ <span class="arithmatex">\(n \times n\)</span> の隣接行列 <code>adjMat</code> を初期化するのに <span class="arithmatex">\(O(n^2)\)</span> 時間かかります。</li>
 </ul>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:5"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">隣接行列の初期化</label><label for="__tabbed_1_2">辺の追加</label><label for="__tabbed_1_3">辺の削除</label><label for="__tabbed_1_4">頂点の追加</label><label for="__tabbed_1_5">頂点の削除</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="隣接行列での初期化、辺の追加と削除、頂点の追加と削除" class="animation-figure" src="../graph_operations.assets/adjacency_matrix_step1_initialization.png" /></p>
+<p><img alt="隣接行列の初期化、辺の追加と削除、頂点の追加と削除" class="animation-figure" src="../graph_operations.assets/adjacency_matrix_step1_initialization.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="adjacency_matrix_add_edge" class="animation-figure" src="../graph_operations.assets/adjacency_matrix_step2_add_edge.png" /></p>
@@ -4405,9 +4405,9 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 9-7 &nbsp; 隣接行列での初期化、辺の追加と削除、頂点の追加と削除 </p>
+<p align="center"> 図 9-7 &nbsp; 隣接行列の初期化、辺の追加と削除、頂点の追加と削除 </p>
 
-<p>以下は隣接行列を使用して表現されたグラフの実装コードです：</p>
+<p>以下は、隣接行列でグラフを表した実装コードです：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
@@ -4416,15 +4416,15 @@
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">vertices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">edges</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]):</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
-<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="c1"># 頂点リスト、要素は「頂点値」を表し、インデックスは「頂点インデックス」を表す</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="c1"># 頂点リスト。要素は「頂点値」、インデックスは「頂点インデックス」を表す</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">vertices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
-<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="c1"># 隣接行列、行と列のインデックスは「頂点インデックス」に対応</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="c1"># 隣接行列。行・列のインデックスは「頂点インデックス」に対応</span>
 <a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]</span> <span class="o">=</span> <span class="p">[]</span>
 <a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="c1"># 頂点を追加</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="k">for</span> <span class="n">val</span> <span class="ow">in</span> <span class="n">vertices</span><span class="p">:</span>
 <a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">add_vertex</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="c1"># 辺を追加</span>
-<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>        <span class="c1"># edges要素は頂点インデックスを表す</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>        <span class="c1"># 注意：edges の各要素は頂点インデックスを表し、vertices の要素インデックスに対応する</span>
 <a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>        <span class="k">for</span> <span class="n">e</span> <span class="ow">in</span> <span class="n">edges</span><span class="p">:</span>
 <a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="n">e</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">e</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
 <a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>
@@ -4435,12 +4435,12 @@
 <a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">add_vertex</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
 <a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;頂点を追加&quot;&quot;&quot;</span>
 <a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>        <span class="n">n</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span>
-<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>        <span class="c1"># 頂点リストに新しい頂点値を追加</span>
+<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>        <span class="c1"># 頂点リストに新しい頂点の値を追加</span>
 <a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">vertices</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
-<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>        <span class="c1"># 隣接行列に行を追加</span>
+<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>        <span class="c1"># 隣接行列に 1 行追加</span>
 <a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a>        <span class="n">new_row</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span>
 <a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">new_row</span><span class="p">)</span>
-<a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a>        <span class="c1"># 隣接行列に列を追加</span>
+<a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a>        <span class="c1"># 隣接行列に 1 列追加</span>
 <a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a>        <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</span><span class="p">:</span>
 <a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a>            <span class="n">row</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
 <a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a>
@@ -4448,28 +4448,28 @@
 <a id="__codelineno-0-35" name="__codelineno-0-35" href="#__codelineno-0-35"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;頂点を削除&quot;&quot;&quot;</span>
 <a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a>        <span class="k">if</span> <span class="n">index</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">():</span>
 <a id="__codelineno-0-37" name="__codelineno-0-37" href="#__codelineno-0-37"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">()</span>
-<a id="__codelineno-0-38" name="__codelineno-0-38" href="#__codelineno-0-38"></a>        <span class="c1"># 頂点リストから`index`の頂点を削除</span>
+<a id="__codelineno-0-38" name="__codelineno-0-38" href="#__codelineno-0-38"></a>        <span class="c1"># 頂点リストから index の頂点を削除する</span>
 <a id="__codelineno-0-39" name="__codelineno-0-39" href="#__codelineno-0-39"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">vertices</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
-<a id="__codelineno-0-40" name="__codelineno-0-40" href="#__codelineno-0-40"></a>        <span class="c1"># 隣接行列から`index`の行を削除</span>
+<a id="__codelineno-0-40" name="__codelineno-0-40" href="#__codelineno-0-40"></a>        <span class="c1"># 隣接行列で index 行を削除する</span>
 <a id="__codelineno-0-41" name="__codelineno-0-41" href="#__codelineno-0-41"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
-<a id="__codelineno-0-42" name="__codelineno-0-42" href="#__codelineno-0-42"></a>        <span class="c1"># 隣接行列から`index`の列を削除</span>
+<a id="__codelineno-0-42" name="__codelineno-0-42" href="#__codelineno-0-42"></a>        <span class="c1"># 隣接行列で index 列を削除する</span>
 <a id="__codelineno-0-43" name="__codelineno-0-43" href="#__codelineno-0-43"></a>        <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</span><span class="p">:</span>
 <a id="__codelineno-0-44" name="__codelineno-0-44" href="#__codelineno-0-44"></a>            <span class="n">row</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
 <a id="__codelineno-0-45" name="__codelineno-0-45" href="#__codelineno-0-45"></a>
 <a id="__codelineno-0-46" name="__codelineno-0-46" href="#__codelineno-0-46"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">add_edge</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
 <a id="__codelineno-0-47" name="__codelineno-0-47" href="#__codelineno-0-47"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;辺を追加&quot;&quot;&quot;</span>
-<a id="__codelineno-0-48" name="__codelineno-0-48" href="#__codelineno-0-48"></a>        <span class="c1"># パラメータi、jは頂点要素のインデックスに対応</span>
-<a id="__codelineno-0-49" name="__codelineno-0-49" href="#__codelineno-0-49"></a>        <span class="c1"># インデックスの範囲外と等価性を処理</span>
+<a id="__codelineno-0-48" name="__codelineno-0-48" href="#__codelineno-0-48"></a>        <span class="c1"># パラメータ i, j は vertices の要素インデックスに対応する</span>
+<a id="__codelineno-0-49" name="__codelineno-0-49" href="#__codelineno-0-49"></a>        <span class="c1"># 範囲外と同値の場合の処理</span>
 <a id="__codelineno-0-50" name="__codelineno-0-50" href="#__codelineno-0-50"></a>        <span class="k">if</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">j</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">i</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="ow">or</span> <span class="n">j</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="ow">or</span> <span class="n">i</span> <span class="o">==</span> <span class="n">j</span><span class="p">:</span>
 <a id="__codelineno-0-51" name="__codelineno-0-51" href="#__codelineno-0-51"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">()</span>
-<a id="__codelineno-0-52" name="__codelineno-0-52" href="#__codelineno-0-52"></a>        <span class="c1"># 無向グラフでは、隣接行列は主対角線について対称、すなわち (i, j) == (j, i) を満たす</span>
+<a id="__codelineno-0-52" name="__codelineno-0-52" href="#__codelineno-0-52"></a>        <span class="c1"># 無向グラフでは、隣接行列は主対角線に関して対称、すなわち (i, j) == (j, i) を満たす</span>
 <a id="__codelineno-0-53" name="__codelineno-0-53" href="#__codelineno-0-53"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
 <a id="__codelineno-0-54" name="__codelineno-0-54" href="#__codelineno-0-54"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</span><span class="p">[</span><span class="n">j</span><span class="p">][</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
 <a id="__codelineno-0-55" name="__codelineno-0-55" href="#__codelineno-0-55"></a>
 <a id="__codelineno-0-56" name="__codelineno-0-56" href="#__codelineno-0-56"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">remove_edge</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
 <a id="__codelineno-0-57" name="__codelineno-0-57" href="#__codelineno-0-57"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;辺を削除&quot;&quot;&quot;</span>
-<a id="__codelineno-0-58" name="__codelineno-0-58" href="#__codelineno-0-58"></a>        <span class="c1"># パラメータi、jは頂点要素のインデックスに対応</span>
-<a id="__codelineno-0-59" name="__codelineno-0-59" href="#__codelineno-0-59"></a>        <span class="c1"># インデックスの範囲外と等価性を処理</span>
+<a id="__codelineno-0-58" name="__codelineno-0-58" href="#__codelineno-0-58"></a>        <span class="c1"># パラメータ i, j は vertices の要素インデックスに対応する</span>
+<a id="__codelineno-0-59" name="__codelineno-0-59" href="#__codelineno-0-59"></a>        <span class="c1"># 範囲外と同値の場合の処理</span>
 <a id="__codelineno-0-60" name="__codelineno-0-60" href="#__codelineno-0-60"></a>        <span class="k">if</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">j</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">i</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="ow">or</span> <span class="n">j</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="ow">or</span> <span class="n">i</span> <span class="o">==</span> <span class="n">j</span><span class="p">:</span>
 <a id="__codelineno-0-61" name="__codelineno-0-61" href="#__codelineno-0-61"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">()</span>
 <a id="__codelineno-0-62" name="__codelineno-0-62" href="#__codelineno-0-62"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
@@ -4485,8 +4485,8 @@
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">graph_adjacency_matrix.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 隣接行列に基づく無向グラフクラス */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">GraphAdjMat</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">vertices</span><span class="p">;</span><span class="w">       </span><span class="c1">// 頂点リスト、要素は「頂点値」を表し、インデックスは「頂点インデックス」を表す</span>
-<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">adjMat</span><span class="p">;</span><span class="w"> </span><span class="c1">// 隣接行列、行と列のインデックスは「頂点インデックス」に対応</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">vertices</span><span class="p">;</span><span class="w">       </span><span class="c1">// 頂点リスト。要素は「頂点値」、インデックスは「頂点インデックス」を表す</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">adjMat</span><span class="p">;</span><span class="w"> </span><span class="c1">// 隣接行列。行・列のインデックスは「頂点インデックス」に対応</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
@@ -4496,7 +4496,7 @@
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">            </span><span class="n">addVertex</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="c1">// 辺を追加</span>
-<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">        </span><span class="c1">// 辺の要素は頂点インデックスを表す</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">        </span><span class="c1">// 注意：edges の各要素は頂点インデックスを表し、vertices の要素インデックスに対応する</span>
 <a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">edge</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">            </span><span class="n">addEdge</span><span class="p">(</span><span class="n">edge</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="n">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">]);</span>
 <a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">        </span><span class="p">}</span>
@@ -4510,11 +4510,11 @@
 <a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w">    </span><span class="cm">/* 頂点を追加 */</span>
 <a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">addVertex</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="p">();</span>
-<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="w">        </span><span class="c1">// 頂点リストに新しい頂点値を追加</span>
+<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="w">        </span><span class="c1">// 頂点リストに新しい頂点の値を追加</span>
 <a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="w">        </span><span class="n">vertices</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
-<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="w">        </span><span class="c1">// 隣接行列に行を追加</span>
+<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="w">        </span><span class="c1">// 隣接行列に 1 行追加</span>
 <a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">.</span><span class="n">emplace_back</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">));</span>
-<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="w">        </span><span class="c1">// 隣接行列に列を追加</span>
+<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="w">        </span><span class="c1">// 隣接行列に 1 列追加</span>
 <a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">row</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">adjMat</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-34" name="__codelineno-1-34" href="#__codelineno-1-34"></a><span class="w">            </span><span class="n">row</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-1-35" name="__codelineno-1-35" href="#__codelineno-1-35"></a><span class="w">        </span><span class="p">}</span>
@@ -4523,42 +4523,42 @@
 <a id="__codelineno-1-38" name="__codelineno-1-38" href="#__codelineno-1-38"></a><span class="w">    </span><span class="cm">/* 頂点を削除 */</span>
 <a id="__codelineno-1-39" name="__codelineno-1-39" href="#__codelineno-1-39"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">removeVertex</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-40" name="__codelineno-1-40" href="#__codelineno-1-40"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-41" name="__codelineno-1-41" href="#__codelineno-1-41"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Vertex does not exist&quot;</span><span class="p">);</span>
+<a id="__codelineno-1-41" name="__codelineno-1-41" href="#__codelineno-1-41"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;頂点が存在しません&quot;</span><span class="p">);</span>
 <a id="__codelineno-1-42" name="__codelineno-1-42" href="#__codelineno-1-42"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-1-43" name="__codelineno-1-43" href="#__codelineno-1-43"></a><span class="w">        </span><span class="c1">// 頂点リストから`index`の頂点を削除</span>
+<a id="__codelineno-1-43" name="__codelineno-1-43" href="#__codelineno-1-43"></a><span class="w">        </span><span class="c1">// 頂点リストから index の頂点を削除する</span>
 <a id="__codelineno-1-44" name="__codelineno-1-44" href="#__codelineno-1-44"></a><span class="w">        </span><span class="n">vertices</span><span class="p">.</span><span class="n">erase</span><span class="p">(</span><span class="n">vertices</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">index</span><span class="p">);</span>
-<a id="__codelineno-1-45" name="__codelineno-1-45" href="#__codelineno-1-45"></a><span class="w">        </span><span class="c1">// 隣接行列から`index`の行を削除</span>
+<a id="__codelineno-1-45" name="__codelineno-1-45" href="#__codelineno-1-45"></a><span class="w">        </span><span class="c1">// 隣接行列で index 行を削除する</span>
 <a id="__codelineno-1-46" name="__codelineno-1-46" href="#__codelineno-1-46"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">.</span><span class="n">erase</span><span class="p">(</span><span class="n">adjMat</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">index</span><span class="p">);</span>
-<a id="__codelineno-1-47" name="__codelineno-1-47" href="#__codelineno-1-47"></a><span class="w">        </span><span class="c1">// 隣接行列から`index`の列を削除</span>
+<a id="__codelineno-1-47" name="__codelineno-1-47" href="#__codelineno-1-47"></a><span class="w">        </span><span class="c1">// 隣接行列で index 列を削除する</span>
 <a id="__codelineno-1-48" name="__codelineno-1-48" href="#__codelineno-1-48"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">row</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">adjMat</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-49" name="__codelineno-1-49" href="#__codelineno-1-49"></a><span class="w">            </span><span class="n">row</span><span class="p">.</span><span class="n">erase</span><span class="p">(</span><span class="n">row</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">index</span><span class="p">);</span>
 <a id="__codelineno-1-50" name="__codelineno-1-50" href="#__codelineno-1-50"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-1-51" name="__codelineno-1-51" href="#__codelineno-1-51"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-1-52" name="__codelineno-1-52" href="#__codelineno-1-52"></a>
 <a id="__codelineno-1-53" name="__codelineno-1-53" href="#__codelineno-1-53"></a><span class="w">    </span><span class="cm">/* 辺を追加 */</span>
-<a id="__codelineno-1-54" name="__codelineno-1-54" href="#__codelineno-1-54"></a><span class="w">    </span><span class="c1">// パラメータi、jは頂点要素のインデックスに対応</span>
+<a id="__codelineno-1-54" name="__codelineno-1-54" href="#__codelineno-1-54"></a><span class="w">    </span><span class="c1">// 引数 i, j は vertices の要素インデックスに対応する</span>
 <a id="__codelineno-1-55" name="__codelineno-1-55" href="#__codelineno-1-55"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">addEdge</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-56" name="__codelineno-1-56" href="#__codelineno-1-56"></a><span class="w">        </span><span class="c1">// インデックス範囲外と等価性を処理</span>
+<a id="__codelineno-1-56" name="__codelineno-1-56" href="#__codelineno-1-56"></a><span class="w">        </span><span class="c1">// インデックスの範囲外と等値の処理</span>
 <a id="__codelineno-1-57" name="__codelineno-1-57" href="#__codelineno-1-57"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-58" name="__codelineno-1-58" href="#__codelineno-1-58"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Vertex does not exist&quot;</span><span class="p">);</span>
+<a id="__codelineno-1-58" name="__codelineno-1-58" href="#__codelineno-1-58"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;頂点が存在しません&quot;</span><span class="p">);</span>
 <a id="__codelineno-1-59" name="__codelineno-1-59" href="#__codelineno-1-59"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-1-60" name="__codelineno-1-60" href="#__codelineno-1-60"></a><span class="w">        </span><span class="c1">// 無向グラフでは、隣接行列は主対角線について対称、即ち(i, j) == (j, i)を満たす</span>
+<a id="__codelineno-1-60" name="__codelineno-1-60" href="#__codelineno-1-60"></a><span class="w">        </span><span class="c1">// 無向グラフでは、隣接行列は主対角線に関して対称、すなわち (i, j) == (j, i) を満たす</span>
 <a id="__codelineno-1-61" name="__codelineno-1-61" href="#__codelineno-1-61"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-1-62" name="__codelineno-1-62" href="#__codelineno-1-62"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">[</span><span class="n">j</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-1-63" name="__codelineno-1-63" href="#__codelineno-1-63"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-1-64" name="__codelineno-1-64" href="#__codelineno-1-64"></a>
 <a id="__codelineno-1-65" name="__codelineno-1-65" href="#__codelineno-1-65"></a><span class="w">    </span><span class="cm">/* 辺を削除 */</span>
-<a id="__codelineno-1-66" name="__codelineno-1-66" href="#__codelineno-1-66"></a><span class="w">    </span><span class="c1">// パラメータi、jは頂点要素のインデックスに対応</span>
+<a id="__codelineno-1-66" name="__codelineno-1-66" href="#__codelineno-1-66"></a><span class="w">    </span><span class="c1">// 引数 i, j は vertices の要素インデックスに対応する</span>
 <a id="__codelineno-1-67" name="__codelineno-1-67" href="#__codelineno-1-67"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">removeEdge</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-68" name="__codelineno-1-68" href="#__codelineno-1-68"></a><span class="w">        </span><span class="c1">// インデックス範囲外と等価性を処理</span>
+<a id="__codelineno-1-68" name="__codelineno-1-68" href="#__codelineno-1-68"></a><span class="w">        </span><span class="c1">// インデックスの範囲外と等値の処理</span>
 <a id="__codelineno-1-69" name="__codelineno-1-69" href="#__codelineno-1-69"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-70" name="__codelineno-1-70" href="#__codelineno-1-70"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Vertex does not exist&quot;</span><span class="p">);</span>
+<a id="__codelineno-1-70" name="__codelineno-1-70" href="#__codelineno-1-70"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;頂点が存在しません&quot;</span><span class="p">);</span>
 <a id="__codelineno-1-71" name="__codelineno-1-71" href="#__codelineno-1-71"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-1-72" name="__codelineno-1-72" href="#__codelineno-1-72"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-1-73" name="__codelineno-1-73" href="#__codelineno-1-73"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">[</span><span class="n">j</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-1-74" name="__codelineno-1-74" href="#__codelineno-1-74"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-1-75" name="__codelineno-1-75" href="#__codelineno-1-75"></a>
-<a id="__codelineno-1-76" name="__codelineno-1-76" href="#__codelineno-1-76"></a><span class="w">    </span><span class="cm">/* 隣接行列を印刷 */</span>
+<a id="__codelineno-1-76" name="__codelineno-1-76" href="#__codelineno-1-76"></a><span class="w">    </span><span class="cm">/* 隣接行列を出力 */</span>
 <a id="__codelineno-1-77" name="__codelineno-1-77" href="#__codelineno-1-77"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-78" name="__codelineno-1-78" href="#__codelineno-1-78"></a><span class="w">        </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;頂点リスト = &quot;</span><span class="p">;</span>
 <a id="__codelineno-1-79" name="__codelineno-1-79" href="#__codelineno-1-79"></a><span class="w">        </span><span class="n">printVector</span><span class="p">(</span><span class="n">vertices</span><span class="p">);</span>
@@ -4571,8 +4571,8 @@
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">graph_adjacency_matrix.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 隣接行列に基づく無向グラフクラス */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kd">class</span> <span class="nc">GraphAdjMat</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">vertices</span><span class="p">;</span><span class="w"> </span><span class="c1">// 頂点リスト、要素は「頂点値」を表し、インデックスは「頂点インデックス」を表す</span>
-<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">adjMat</span><span class="p">;</span><span class="w"> </span><span class="c1">// 隣接行列、行と列のインデックスは「頂点インデックス」に対応</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">vertices</span><span class="p">;</span><span class="w"> </span><span class="c1">// 頂点リスト。要素は「頂点値」、インデックスは「頂点インデックス」を表す</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">adjMat</span><span class="p">;</span><span class="w"> </span><span class="c1">// 隣接行列。行・列のインデックスは「頂点インデックス」に対応</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">GraphAdjMat</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">vertices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
@@ -4583,7 +4583,7 @@
 <a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">            </span><span class="n">addVertex</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">        </span><span class="c1">// 辺を追加</span>
-<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="c1">// 辺の要素は頂点インデックスを表す</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="c1">// 注意：edges の各要素は頂点インデックスを表し、vertices の要素インデックスに対応する</span>
 <a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">e</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">            </span><span class="n">addEdge</span><span class="p">(</span><span class="n">e</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">e</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">);</span>
 <a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">        </span><span class="p">}</span>
@@ -4597,15 +4597,15 @@
 <a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w">    </span><span class="cm">/* 頂点を追加 */</span>
 <a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">addVertex</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="p">();</span>
-<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="w">        </span><span class="c1">// 頂点リストに新しい頂点値を追加</span>
+<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="w">        </span><span class="c1">// 頂点リストに新しい頂点の値を追加</span>
 <a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a><span class="w">        </span><span class="n">vertices</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
-<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="w">        </span><span class="c1">// 隣接行列に行を追加</span>
+<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="w">        </span><span class="c1">// 隣接行列に 1 行追加</span>
 <a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">newRow</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
 <a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a><span class="w">            </span><span class="n">newRow</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">newRow</span><span class="p">);</span>
-<a id="__codelineno-2-37" name="__codelineno-2-37" href="#__codelineno-2-37"></a><span class="w">        </span><span class="c1">// 隣接行列に列を追加</span>
+<a id="__codelineno-2-37" name="__codelineno-2-37" href="#__codelineno-2-37"></a><span class="w">        </span><span class="c1">// 隣接行列に 1 列追加</span>
 <a id="__codelineno-2-38" name="__codelineno-2-38" href="#__codelineno-2-38"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">adjMat</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-39" name="__codelineno-2-39" href="#__codelineno-2-39"></a><span class="w">            </span><span class="n">row</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-2-40" name="__codelineno-2-40" href="#__codelineno-2-40"></a><span class="w">        </span><span class="p">}</span>
@@ -4615,31 +4615,31 @@
 <a id="__codelineno-2-44" name="__codelineno-2-44" href="#__codelineno-2-44"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">removeVertex</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-45" name="__codelineno-2-45" href="#__codelineno-2-45"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
 <a id="__codelineno-2-46" name="__codelineno-2-46" href="#__codelineno-2-46"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
-<a id="__codelineno-2-47" name="__codelineno-2-47" href="#__codelineno-2-47"></a><span class="w">        </span><span class="c1">// 頂点リストから `index` の頂点を削除</span>
+<a id="__codelineno-2-47" name="__codelineno-2-47" href="#__codelineno-2-47"></a><span class="w">        </span><span class="c1">// 頂点リストから index の頂点を削除する</span>
 <a id="__codelineno-2-48" name="__codelineno-2-48" href="#__codelineno-2-48"></a><span class="w">        </span><span class="n">vertices</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
-<a id="__codelineno-2-49" name="__codelineno-2-49" href="#__codelineno-2-49"></a><span class="w">        </span><span class="c1">// 隣接行列から `index` の行を削除</span>
+<a id="__codelineno-2-49" name="__codelineno-2-49" href="#__codelineno-2-49"></a><span class="w">        </span><span class="c1">// 隣接行列で index 行を削除する</span>
 <a id="__codelineno-2-50" name="__codelineno-2-50" href="#__codelineno-2-50"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
-<a id="__codelineno-2-51" name="__codelineno-2-51" href="#__codelineno-2-51"></a><span class="w">        </span><span class="c1">// 隣接行列から `index` の列を削除</span>
+<a id="__codelineno-2-51" name="__codelineno-2-51" href="#__codelineno-2-51"></a><span class="w">        </span><span class="c1">// 隣接行列で index 列を削除する</span>
 <a id="__codelineno-2-52" name="__codelineno-2-52" href="#__codelineno-2-52"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">adjMat</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-53" name="__codelineno-2-53" href="#__codelineno-2-53"></a><span class="w">            </span><span class="n">row</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
 <a id="__codelineno-2-54" name="__codelineno-2-54" href="#__codelineno-2-54"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-2-55" name="__codelineno-2-55" href="#__codelineno-2-55"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-2-56" name="__codelineno-2-56" href="#__codelineno-2-56"></a>
 <a id="__codelineno-2-57" name="__codelineno-2-57" href="#__codelineno-2-57"></a><span class="w">    </span><span class="cm">/* 辺を追加 */</span>
-<a id="__codelineno-2-58" name="__codelineno-2-58" href="#__codelineno-2-58"></a><span class="w">    </span><span class="c1">// パラメータ i、j は頂点要素のインデックスに対応</span>
+<a id="__codelineno-2-58" name="__codelineno-2-58" href="#__codelineno-2-58"></a><span class="w">    </span><span class="c1">// 引数 i, j は vertices の要素インデックスに対応する</span>
 <a id="__codelineno-2-59" name="__codelineno-2-59" href="#__codelineno-2-59"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">addEdge</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-60" name="__codelineno-2-60" href="#__codelineno-2-60"></a><span class="w">        </span><span class="c1">// インデックスの範囲外と等価性を処理</span>
+<a id="__codelineno-2-60" name="__codelineno-2-60" href="#__codelineno-2-60"></a><span class="w">        </span><span class="c1">// インデックスの範囲外と等値の処理</span>
 <a id="__codelineno-2-61" name="__codelineno-2-61" href="#__codelineno-2-61"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
 <a id="__codelineno-2-62" name="__codelineno-2-62" href="#__codelineno-2-62"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
-<a id="__codelineno-2-63" name="__codelineno-2-63" href="#__codelineno-2-63"></a><span class="w">        </span><span class="c1">// 無向グラフでは、隣接行列は主対角線について対称、すなわち (i, j) == (j, i) を満たす</span>
+<a id="__codelineno-2-63" name="__codelineno-2-63" href="#__codelineno-2-63"></a><span class="w">        </span><span class="c1">// 無向グラフでは、隣接行列は主対角線に関して対称、すなわち (i, j) == (j, i) を満たす</span>
 <a id="__codelineno-2-64" name="__codelineno-2-64" href="#__codelineno-2-64"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">i</span><span class="p">).</span><span class="na">set</span><span class="p">(</span><span class="n">j</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-2-65" name="__codelineno-2-65" href="#__codelineno-2-65"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">j</span><span class="p">).</span><span class="na">set</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-2-66" name="__codelineno-2-66" href="#__codelineno-2-66"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-2-67" name="__codelineno-2-67" href="#__codelineno-2-67"></a>
 <a id="__codelineno-2-68" name="__codelineno-2-68" href="#__codelineno-2-68"></a><span class="w">    </span><span class="cm">/* 辺を削除 */</span>
-<a id="__codelineno-2-69" name="__codelineno-2-69" href="#__codelineno-2-69"></a><span class="w">    </span><span class="c1">// パラメータ i、j は頂点要素のインデックスに対応</span>
+<a id="__codelineno-2-69" name="__codelineno-2-69" href="#__codelineno-2-69"></a><span class="w">    </span><span class="c1">// 引数 i, j は vertices の要素インデックスに対応する</span>
 <a id="__codelineno-2-70" name="__codelineno-2-70" href="#__codelineno-2-70"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">removeEdge</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-71" name="__codelineno-2-71" href="#__codelineno-2-71"></a><span class="w">        </span><span class="c1">// インデックスの範囲外と等価性を処理</span>
+<a id="__codelineno-2-71" name="__codelineno-2-71" href="#__codelineno-2-71"></a><span class="w">        </span><span class="c1">// インデックスの範囲外と等値の処理</span>
 <a id="__codelineno-2-72" name="__codelineno-2-72" href="#__codelineno-2-72"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
 <a id="__codelineno-2-73" name="__codelineno-2-73" href="#__codelineno-2-73"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
 <a id="__codelineno-2-74" name="__codelineno-2-74" href="#__codelineno-2-74"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">i</span><span class="p">).</span><span class="na">set</span><span class="p">(</span><span class="n">j</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
@@ -4657,60 +4657,925 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_adjacency_matrix.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">GraphAdjMat</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">graph_adjacency_matrix.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 隣接行列に基づく無向グラフクラス */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">GraphAdjMat</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">vertices</span><span class="p">;</span><span class="w">     </span><span class="c1">// 頂点リスト。要素は「頂点値」、インデックスは「頂点インデックス」を表す</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">adjMat</span><span class="p">;</span><span class="w"> </span><span class="c1">// 隣接行列。行・列のインデックスは「頂点インデックス」に対応</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nf">GraphAdjMat</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">vertices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="p">[][]</span><span class="w"> </span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">vertices</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">adjMat</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">        </span><span class="c1">// 頂点を追加</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">        </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">vertices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">            </span><span class="n">AddVertex</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">        </span><span class="c1">// 辺を追加</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">        </span><span class="c1">// 注意：edges の各要素は頂点インデックスを表し、vertices の要素インデックスに対応する</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">        </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">e</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">            </span><span class="n">AddEdge</span><span class="p">(</span><span class="n">e</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="n">e</span><span class="p">[</span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a>
+<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w">    </span><span class="cm">/* 頂点数を取得 */</span>
+<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="nf">Size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">vertices</span><span class="p">.</span><span class="n">Count</span><span class="p">;</span>
+<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a>
+<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="w">    </span><span class="cm">/* 頂点を追加 */</span>
+<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">AddVertex</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Size</span><span class="p">();</span>
+<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a><span class="w">        </span><span class="c1">// 頂点リストに新しい頂点の値を追加</span>
+<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a><span class="w">        </span><span class="n">vertices</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-3-31" name="__codelineno-3-31" href="#__codelineno-3-31"></a><span class="w">        </span><span class="c1">// 隣接行列に 1 行追加</span>
+<a id="__codelineno-3-32" name="__codelineno-3-32" href="#__codelineno-3-32"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">newRow</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-3-33" name="__codelineno-3-33" href="#__codelineno-3-33"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-34" name="__codelineno-3-34" href="#__codelineno-3-34"></a><span class="w">            </span><span class="n">newRow</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-3-35" name="__codelineno-3-35" href="#__codelineno-3-35"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-36" name="__codelineno-3-36" href="#__codelineno-3-36"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">newRow</span><span class="p">);</span>
+<a id="__codelineno-3-37" name="__codelineno-3-37" href="#__codelineno-3-37"></a><span class="w">        </span><span class="c1">// 隣接行列に 1 列追加</span>
+<a id="__codelineno-3-38" name="__codelineno-3-38" href="#__codelineno-3-38"></a><span class="w">        </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">adjMat</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-39" name="__codelineno-3-39" href="#__codelineno-3-39"></a><span class="w">            </span><span class="n">row</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-3-40" name="__codelineno-3-40" href="#__codelineno-3-40"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-41" name="__codelineno-3-41" href="#__codelineno-3-41"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-42" name="__codelineno-3-42" href="#__codelineno-3-42"></a>
+<a id="__codelineno-3-43" name="__codelineno-3-43" href="#__codelineno-3-43"></a><span class="w">    </span><span class="cm">/* 頂点を削除 */</span>
+<a id="__codelineno-3-44" name="__codelineno-3-44" href="#__codelineno-3-44"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">RemoveVertex</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-45" name="__codelineno-3-45" href="#__codelineno-3-45"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">Size</span><span class="p">())</span>
+<a id="__codelineno-3-46" name="__codelineno-3-46" href="#__codelineno-3-46"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="nf">IndexOutOfRangeException</span><span class="p">();</span>
+<a id="__codelineno-3-47" name="__codelineno-3-47" href="#__codelineno-3-47"></a><span class="w">        </span><span class="c1">// 頂点リストから index の頂点を削除する</span>
+<a id="__codelineno-3-48" name="__codelineno-3-48" href="#__codelineno-3-48"></a><span class="w">        </span><span class="n">vertices</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
+<a id="__codelineno-3-49" name="__codelineno-3-49" href="#__codelineno-3-49"></a><span class="w">        </span><span class="c1">// 隣接行列で index 行を削除する</span>
+<a id="__codelineno-3-50" name="__codelineno-3-50" href="#__codelineno-3-50"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
+<a id="__codelineno-3-51" name="__codelineno-3-51" href="#__codelineno-3-51"></a><span class="w">        </span><span class="c1">// 隣接行列で index 列を削除する</span>
+<a id="__codelineno-3-52" name="__codelineno-3-52" href="#__codelineno-3-52"></a><span class="w">        </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">adjMat</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-53" name="__codelineno-3-53" href="#__codelineno-3-53"></a><span class="w">            </span><span class="n">row</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
+<a id="__codelineno-3-54" name="__codelineno-3-54" href="#__codelineno-3-54"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-55" name="__codelineno-3-55" href="#__codelineno-3-55"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-56" name="__codelineno-3-56" href="#__codelineno-3-56"></a>
+<a id="__codelineno-3-57" name="__codelineno-3-57" href="#__codelineno-3-57"></a><span class="w">    </span><span class="cm">/* 辺を追加 */</span>
+<a id="__codelineno-3-58" name="__codelineno-3-58" href="#__codelineno-3-58"></a><span class="w">    </span><span class="c1">// 引数 i, j は vertices の要素インデックスに対応する</span>
+<a id="__codelineno-3-59" name="__codelineno-3-59" href="#__codelineno-3-59"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">AddEdge</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-60" name="__codelineno-3-60" href="#__codelineno-3-60"></a><span class="w">        </span><span class="c1">// インデックスの範囲外と等値の処理</span>
+<a id="__codelineno-3-61" name="__codelineno-3-61" href="#__codelineno-3-61"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">Size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">Size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
+<a id="__codelineno-3-62" name="__codelineno-3-62" href="#__codelineno-3-62"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="nf">IndexOutOfRangeException</span><span class="p">();</span>
+<a id="__codelineno-3-63" name="__codelineno-3-63" href="#__codelineno-3-63"></a><span class="w">        </span><span class="c1">// 無向グラフでは、隣接行列は主対角線に関して対称、すなわち (i, j) == (j, i) を満たす</span>
+<a id="__codelineno-3-64" name="__codelineno-3-64" href="#__codelineno-3-64"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-3-65" name="__codelineno-3-65" href="#__codelineno-3-65"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">[</span><span class="n">j</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-3-66" name="__codelineno-3-66" href="#__codelineno-3-66"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-67" name="__codelineno-3-67" href="#__codelineno-3-67"></a>
+<a id="__codelineno-3-68" name="__codelineno-3-68" href="#__codelineno-3-68"></a><span class="w">    </span><span class="cm">/* 辺を削除 */</span>
+<a id="__codelineno-3-69" name="__codelineno-3-69" href="#__codelineno-3-69"></a><span class="w">    </span><span class="c1">// 引数 i, j は vertices の要素インデックスに対応する</span>
+<a id="__codelineno-3-70" name="__codelineno-3-70" href="#__codelineno-3-70"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">RemoveEdge</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-71" name="__codelineno-3-71" href="#__codelineno-3-71"></a><span class="w">        </span><span class="c1">// インデックスの範囲外と等値の処理</span>
+<a id="__codelineno-3-72" name="__codelineno-3-72" href="#__codelineno-3-72"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">Size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">Size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
+<a id="__codelineno-3-73" name="__codelineno-3-73" href="#__codelineno-3-73"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="nf">IndexOutOfRangeException</span><span class="p">();</span>
+<a id="__codelineno-3-74" name="__codelineno-3-74" href="#__codelineno-3-74"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-3-75" name="__codelineno-3-75" href="#__codelineno-3-75"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">[</span><span class="n">j</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-3-76" name="__codelineno-3-76" href="#__codelineno-3-76"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-77" name="__codelineno-3-77" href="#__codelineno-3-77"></a>
+<a id="__codelineno-3-78" name="__codelineno-3-78" href="#__codelineno-3-78"></a><span class="w">    </span><span class="cm">/* 隣接行列を出力 */</span>
+<a id="__codelineno-3-79" name="__codelineno-3-79" href="#__codelineno-3-79"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">Print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-80" name="__codelineno-3-80" href="#__codelineno-3-80"></a><span class="w">        </span><span class="n">Console</span><span class="p">.</span><span class="n">Write</span><span class="p">(</span><span class="s">&quot;頂点リスト = &quot;</span><span class="p">);</span>
+<a id="__codelineno-3-81" name="__codelineno-3-81" href="#__codelineno-3-81"></a><span class="w">        </span><span class="n">PrintUtil</span><span class="p">.</span><span class="n">PrintList</span><span class="p">(</span><span class="n">vertices</span><span class="p">);</span>
+<a id="__codelineno-3-82" name="__codelineno-3-82" href="#__codelineno-3-82"></a><span class="w">        </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="s">&quot;隣接行列 =&quot;</span><span class="p">);</span>
+<a id="__codelineno-3-83" name="__codelineno-3-83" href="#__codelineno-3-83"></a><span class="w">        </span><span class="n">PrintUtil</span><span class="p">.</span><span class="n">PrintMatrix</span><span class="p">(</span><span class="n">adjMat</span><span class="p">);</span>
+<a id="__codelineno-3-84" name="__codelineno-3-84" href="#__codelineno-3-84"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-85" name="__codelineno-3-85" href="#__codelineno-3-85"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_adjacency_matrix.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">graphAdjMat</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">graph_adjacency_matrix.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 隣接行列に基づく無向グラフクラス */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">graphAdjMat</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// 頂点リスト。要素は「頂点値」、インデックスは「頂点インデックス」を表す</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">vertices</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="c1">// 隣接行列。行・列のインデックスは「頂点インデックス」に対応</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="nx">adjMat</span><span class="w"> </span><span class="p">[][]</span><span class="kt">int</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="p">}</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="kd">func</span><span class="w"> </span><span class="nx">newGraphAdjMat</span><span class="p">(</span><span class="nx">vertices</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">edges</span><span class="w"> </span><span class="p">[][]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjMat</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">    </span><span class="c1">// 頂点を追加</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">    </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">vertices</span><span class="p">)</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">    </span><span class="nx">adjMat</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">adjMat</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">        </span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">    </span><span class="c1">// グラフを初期化する</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w">    </span><span class="nx">g</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">graphAdjMat</span><span class="p">{</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w">        </span><span class="nx">vertices</span><span class="p">:</span><span class="w"> </span><span class="nx">vertices</span><span class="p">,</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w">        </span><span class="nx">adjMat</span><span class="p">:</span><span class="w">   </span><span class="nx">adjMat</span><span class="p">,</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w">    </span><span class="c1">// 辺を追加</span>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="w">    </span><span class="c1">// 注意：edges の各要素は頂点インデックスを表し、vertices の要素インデックスに対応する</span>
+<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">edges</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="w">        </span><span class="nx">g</span><span class="p">.</span><span class="nx">addEdge</span><span class="p">(</span><span class="nx">edges</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="nx">edges</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mi">1</span><span class="p">])</span>
+<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">g</span>
+<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="p">}</span>
+<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a>
+<a id="__codelineno-4-30" name="__codelineno-4-30" href="#__codelineno-4-30"></a><span class="cm">/* 頂点数を取得 */</span>
+<a id="__codelineno-4-31" name="__codelineno-4-31" href="#__codelineno-4-31"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjMat</span><span class="p">)</span><span class="w"> </span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-32" name="__codelineno-4-32" href="#__codelineno-4-32"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">g</span><span class="p">.</span><span class="nx">vertices</span><span class="p">)</span>
+<a id="__codelineno-4-33" name="__codelineno-4-33" href="#__codelineno-4-33"></a><span class="p">}</span>
+<a id="__codelineno-4-34" name="__codelineno-4-34" href="#__codelineno-4-34"></a>
+<a id="__codelineno-4-35" name="__codelineno-4-35" href="#__codelineno-4-35"></a><span class="cm">/* 頂点を追加 */</span>
+<a id="__codelineno-4-36" name="__codelineno-4-36" href="#__codelineno-4-36"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjMat</span><span class="p">)</span><span class="w"> </span><span class="nx">addVertex</span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-37" name="__codelineno-4-37" href="#__codelineno-4-37"></a><span class="w">    </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span>
+<a id="__codelineno-4-38" name="__codelineno-4-38" href="#__codelineno-4-38"></a><span class="w">    </span><span class="c1">// 頂点リストに新しい頂点の値を追加</span>
+<a id="__codelineno-4-39" name="__codelineno-4-39" href="#__codelineno-4-39"></a><span class="w">    </span><span class="nx">g</span><span class="p">.</span><span class="nx">vertices</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">g</span><span class="p">.</span><span class="nx">vertices</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">)</span>
+<a id="__codelineno-4-40" name="__codelineno-4-40" href="#__codelineno-4-40"></a><span class="w">    </span><span class="c1">// 隣接行列に 1 行追加</span>
+<a id="__codelineno-4-41" name="__codelineno-4-41" href="#__codelineno-4-41"></a><span class="w">    </span><span class="nx">newRow</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
+<a id="__codelineno-4-42" name="__codelineno-4-42" href="#__codelineno-4-42"></a><span class="w">    </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">,</span><span class="w"> </span><span class="nx">newRow</span><span class="p">)</span>
+<a id="__codelineno-4-43" name="__codelineno-4-43" href="#__codelineno-4-43"></a><span class="w">    </span><span class="c1">// 隣接行列に 1 列追加</span>
+<a id="__codelineno-4-44" name="__codelineno-4-44" href="#__codelineno-4-44"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-45" name="__codelineno-4-45" href="#__codelineno-4-45"></a><span class="w">        </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-4-46" name="__codelineno-4-46" href="#__codelineno-4-46"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-47" name="__codelineno-4-47" href="#__codelineno-4-47"></a><span class="p">}</span>
+<a id="__codelineno-4-48" name="__codelineno-4-48" href="#__codelineno-4-48"></a>
+<a id="__codelineno-4-49" name="__codelineno-4-49" href="#__codelineno-4-49"></a><span class="cm">/* 頂点を削除 */</span>
+<a id="__codelineno-4-50" name="__codelineno-4-50" href="#__codelineno-4-50"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjMat</span><span class="p">)</span><span class="w"> </span><span class="nx">removeVertex</span><span class="p">(</span><span class="nx">index</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-51" name="__codelineno-4-51" href="#__codelineno-4-51"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-52" name="__codelineno-4-52" href="#__codelineno-4-52"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-4-53" name="__codelineno-4-53" href="#__codelineno-4-53"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-54" name="__codelineno-4-54" href="#__codelineno-4-54"></a><span class="w">    </span><span class="c1">// 頂点リストから index の頂点を削除する</span>
+<a id="__codelineno-4-55" name="__codelineno-4-55" href="#__codelineno-4-55"></a><span class="w">    </span><span class="nx">g</span><span class="p">.</span><span class="nx">vertices</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">g</span><span class="p">.</span><span class="nx">vertices</span><span class="p">[:</span><span class="nx">index</span><span class="p">],</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">vertices</span><span class="p">[</span><span class="nx">index</span><span class="o">+</span><span class="mi">1</span><span class="p">:]</span><span class="o">...</span><span class="p">)</span>
+<a id="__codelineno-4-56" name="__codelineno-4-56" href="#__codelineno-4-56"></a><span class="w">    </span><span class="c1">// 隣接行列で index 行を削除する</span>
+<a id="__codelineno-4-57" name="__codelineno-4-57" href="#__codelineno-4-57"></a><span class="w">    </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[:</span><span class="nx">index</span><span class="p">],</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">index</span><span class="o">+</span><span class="mi">1</span><span class="p">:]</span><span class="o">...</span><span class="p">)</span>
+<a id="__codelineno-4-58" name="__codelineno-4-58" href="#__codelineno-4-58"></a><span class="w">    </span><span class="c1">// 隣接行列で index 列を削除する</span>
+<a id="__codelineno-4-59" name="__codelineno-4-59" href="#__codelineno-4-59"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-60" name="__codelineno-4-60" href="#__codelineno-4-60"></a><span class="w">        </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">i</span><span class="p">][:</span><span class="nx">index</span><span class="p">],</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">index</span><span class="o">+</span><span class="mi">1</span><span class="p">:]</span><span class="o">...</span><span class="p">)</span>
+<a id="__codelineno-4-61" name="__codelineno-4-61" href="#__codelineno-4-61"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-62" name="__codelineno-4-62" href="#__codelineno-4-62"></a><span class="p">}</span>
+<a id="__codelineno-4-63" name="__codelineno-4-63" href="#__codelineno-4-63"></a>
+<a id="__codelineno-4-64" name="__codelineno-4-64" href="#__codelineno-4-64"></a><span class="cm">/* 辺を追加 */</span>
+<a id="__codelineno-4-65" name="__codelineno-4-65" href="#__codelineno-4-65"></a><span class="c1">// 引数 i, j は vertices の要素インデックスに対応する</span>
+<a id="__codelineno-4-66" name="__codelineno-4-66" href="#__codelineno-4-66"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjMat</span><span class="p">)</span><span class="w"> </span><span class="nx">addEdge</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-67" name="__codelineno-4-67" href="#__codelineno-4-67"></a><span class="w">    </span><span class="c1">// インデックスの範囲外と等値の処理</span>
+<a id="__codelineno-4-68" name="__codelineno-4-68" href="#__codelineno-4-68"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-69" name="__codelineno-4-69" href="#__codelineno-4-69"></a><span class="w">        </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Errorf</span><span class="p">(</span><span class="s">&quot;%s&quot;</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;Index Out Of Bounds Exception&quot;</span><span class="p">)</span>
+<a id="__codelineno-4-70" name="__codelineno-4-70" href="#__codelineno-4-70"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-71" name="__codelineno-4-71" href="#__codelineno-4-71"></a><span class="w">    </span><span class="c1">// 無向グラフでは、隣接行列は主対角線に関して対称、すなわち (i, j) == (j, i) を満たす</span>
+<a id="__codelineno-4-72" name="__codelineno-4-72" href="#__codelineno-4-72"></a><span class="w">    </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-4-73" name="__codelineno-4-73" href="#__codelineno-4-73"></a><span class="w">    </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">j</span><span class="p">][</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-4-74" name="__codelineno-4-74" href="#__codelineno-4-74"></a><span class="p">}</span>
+<a id="__codelineno-4-75" name="__codelineno-4-75" href="#__codelineno-4-75"></a>
+<a id="__codelineno-4-76" name="__codelineno-4-76" href="#__codelineno-4-76"></a><span class="cm">/* 辺を削除 */</span>
+<a id="__codelineno-4-77" name="__codelineno-4-77" href="#__codelineno-4-77"></a><span class="c1">// 引数 i, j は vertices の要素インデックスに対応する</span>
+<a id="__codelineno-4-78" name="__codelineno-4-78" href="#__codelineno-4-78"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjMat</span><span class="p">)</span><span class="w"> </span><span class="nx">removeEdge</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-79" name="__codelineno-4-79" href="#__codelineno-4-79"></a><span class="w">    </span><span class="c1">// インデックスの範囲外と等値の処理</span>
+<a id="__codelineno-4-80" name="__codelineno-4-80" href="#__codelineno-4-80"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-81" name="__codelineno-4-81" href="#__codelineno-4-81"></a><span class="w">        </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Errorf</span><span class="p">(</span><span class="s">&quot;%s&quot;</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;Index Out Of Bounds Exception&quot;</span><span class="p">)</span>
+<a id="__codelineno-4-82" name="__codelineno-4-82" href="#__codelineno-4-82"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-83" name="__codelineno-4-83" href="#__codelineno-4-83"></a><span class="w">    </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-4-84" name="__codelineno-4-84" href="#__codelineno-4-84"></a><span class="w">    </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">j</span><span class="p">][</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-4-85" name="__codelineno-4-85" href="#__codelineno-4-85"></a><span class="p">}</span>
+<a id="__codelineno-4-86" name="__codelineno-4-86" href="#__codelineno-4-86"></a>
+<a id="__codelineno-4-87" name="__codelineno-4-87" href="#__codelineno-4-87"></a><span class="cm">/* 隣接行列を出力 */</span>
+<a id="__codelineno-4-88" name="__codelineno-4-88" href="#__codelineno-4-88"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjMat</span><span class="p">)</span><span class="w"> </span><span class="nb">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-89" name="__codelineno-4-89" href="#__codelineno-4-89"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Printf</span><span class="p">(</span><span class="s">&quot;\t頂点リスト = %v\n&quot;</span><span class="p">,</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">vertices</span><span class="p">)</span>
+<a id="__codelineno-4-90" name="__codelineno-4-90" href="#__codelineno-4-90"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Printf</span><span class="p">(</span><span class="s">&quot;\t隣接行列 = \n&quot;</span><span class="p">)</span>
+<a id="__codelineno-4-91" name="__codelineno-4-91" href="#__codelineno-4-91"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-92" name="__codelineno-4-92" href="#__codelineno-4-92"></a><span class="w">        </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Printf</span><span class="p">(</span><span class="s">&quot;\t\t\t%v\n&quot;</span><span class="p">,</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span>
+<a id="__codelineno-4-93" name="__codelineno-4-93" href="#__codelineno-4-93"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-94" name="__codelineno-4-94" href="#__codelineno-4-94"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_adjacency_matrix.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">GraphAdjMat</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">graph_adjacency_matrix.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 隣接行列に基づく無向グラフクラス */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">GraphAdjMat</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">vertices</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="c1">// 頂点リスト。要素は「頂点値」、インデックスは「頂点インデックス」を表す</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">adjMat</span><span class="p">:</span><span class="w"> </span><span class="p">[[</span><span class="nb">Int</span><span class="p">]]</span><span class="w"> </span><span class="c1">// 隣接行列。行・列のインデックスは「頂点インデックス」に対応</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="kd">init</span><span class="p">(</span><span class="n">vertices</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">edges</span><span class="p">:</span><span class="w"> </span><span class="p">[[</span><span class="nb">Int</span><span class="p">]])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">        </span><span class="kc">self</span><span class="p">.</span><span class="n">vertices</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">        </span><span class="n">adjMat</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">        </span><span class="c1">// 頂点を追加</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">vertices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">            </span><span class="n">addVertex</span><span class="p">(</span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">        </span><span class="c1">// 辺を追加</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">        </span><span class="c1">// 注意：edges の各要素は頂点インデックスを表し、vertices の要素インデックスに対応する</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">e</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">edges</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">            </span><span class="n">addEdge</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">e</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="n">e</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w">    </span><span class="cm">/* 頂点数を取得 */</span>
+<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="w">        </span><span class="n">vertices</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a>
+<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a><span class="w">    </span><span class="cm">/* 頂点を追加 */</span>
+<a id="__codelineno-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">addVertex</span><span class="p">(</span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span>
+<a id="__codelineno-5-29" name="__codelineno-5-29" href="#__codelineno-5-29"></a><span class="w">        </span><span class="c1">// 頂点リストに新しい頂点の値を追加</span>
+<a id="__codelineno-5-30" name="__codelineno-5-30" href="#__codelineno-5-30"></a><span class="w">        </span><span class="n">vertices</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-5-31" name="__codelineno-5-31" href="#__codelineno-5-31"></a><span class="w">        </span><span class="c1">// 隣接行列に 1 行追加</span>
+<a id="__codelineno-5-32" name="__codelineno-5-32" href="#__codelineno-5-32"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">newRow</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-5-33" name="__codelineno-5-33" href="#__codelineno-5-33"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">newRow</span><span class="p">)</span>
+<a id="__codelineno-5-34" name="__codelineno-5-34" href="#__codelineno-5-34"></a><span class="w">        </span><span class="c1">// 隣接行列に 1 列追加</span>
+<a id="__codelineno-5-35" name="__codelineno-5-35" href="#__codelineno-5-35"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">adjMat</span><span class="p">.</span><span class="bp">indices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-36" name="__codelineno-5-36" href="#__codelineno-5-36"></a><span class="w">            </span><span class="n">adjMat</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">append</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-5-37" name="__codelineno-5-37" href="#__codelineno-5-37"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-38" name="__codelineno-5-38" href="#__codelineno-5-38"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-39" name="__codelineno-5-39" href="#__codelineno-5-39"></a>
+<a id="__codelineno-5-40" name="__codelineno-5-40" href="#__codelineno-5-40"></a><span class="w">    </span><span class="cm">/* 頂点を削除 */</span>
+<a id="__codelineno-5-41" name="__codelineno-5-41" href="#__codelineno-5-41"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">removeVertex</span><span class="p">(</span><span class="n">index</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-42" name="__codelineno-5-42" href="#__codelineno-5-42"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-43" name="__codelineno-5-43" href="#__codelineno-5-43"></a><span class="w">            </span><span class="bp">fatalError</span><span class="p">(</span><span class="s">&quot;範囲外&quot;</span><span class="p">)</span>
+<a id="__codelineno-5-44" name="__codelineno-5-44" href="#__codelineno-5-44"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-45" name="__codelineno-5-45" href="#__codelineno-5-45"></a><span class="w">        </span><span class="c1">// 頂点リストから index の頂点を削除する</span>
+<a id="__codelineno-5-46" name="__codelineno-5-46" href="#__codelineno-5-46"></a><span class="w">        </span><span class="n">vertices</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">at</span><span class="p">:</span><span class="w"> </span><span class="n">index</span><span class="p">)</span>
+<a id="__codelineno-5-47" name="__codelineno-5-47" href="#__codelineno-5-47"></a><span class="w">        </span><span class="c1">// 隣接行列で index 行を削除する</span>
+<a id="__codelineno-5-48" name="__codelineno-5-48" href="#__codelineno-5-48"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">at</span><span class="p">:</span><span class="w"> </span><span class="n">index</span><span class="p">)</span>
+<a id="__codelineno-5-49" name="__codelineno-5-49" href="#__codelineno-5-49"></a><span class="w">        </span><span class="c1">// 隣接行列で index 列を削除する</span>
+<a id="__codelineno-5-50" name="__codelineno-5-50" href="#__codelineno-5-50"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">adjMat</span><span class="p">.</span><span class="bp">indices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-51" name="__codelineno-5-51" href="#__codelineno-5-51"></a><span class="w">            </span><span class="n">adjMat</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">remove</span><span class="p">(</span><span class="n">at</span><span class="p">:</span><span class="w"> </span><span class="n">index</span><span class="p">)</span>
+<a id="__codelineno-5-52" name="__codelineno-5-52" href="#__codelineno-5-52"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-53" name="__codelineno-5-53" href="#__codelineno-5-53"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-54" name="__codelineno-5-54" href="#__codelineno-5-54"></a>
+<a id="__codelineno-5-55" name="__codelineno-5-55" href="#__codelineno-5-55"></a><span class="w">    </span><span class="cm">/* 辺を追加 */</span>
+<a id="__codelineno-5-56" name="__codelineno-5-56" href="#__codelineno-5-56"></a><span class="w">    </span><span class="c1">// 引数 i, j は vertices の要素インデックスに対応する</span>
+<a id="__codelineno-5-57" name="__codelineno-5-57" href="#__codelineno-5-57"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">addEdge</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-58" name="__codelineno-5-58" href="#__codelineno-5-58"></a><span class="w">        </span><span class="c1">// インデックスの範囲外と等値の処理</span>
+<a id="__codelineno-5-59" name="__codelineno-5-59" href="#__codelineno-5-59"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-60" name="__codelineno-5-60" href="#__codelineno-5-60"></a><span class="w">            </span><span class="bp">fatalError</span><span class="p">(</span><span class="s">&quot;範囲外&quot;</span><span class="p">)</span>
+<a id="__codelineno-5-61" name="__codelineno-5-61" href="#__codelineno-5-61"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-62" name="__codelineno-5-62" href="#__codelineno-5-62"></a><span class="w">        </span><span class="c1">// 無向グラフでは、隣接行列は主対角線に関して対称、すなわち (i, j) == (j, i) を満たす</span>
+<a id="__codelineno-5-63" name="__codelineno-5-63" href="#__codelineno-5-63"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-64" name="__codelineno-5-64" href="#__codelineno-5-64"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">[</span><span class="n">j</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-65" name="__codelineno-5-65" href="#__codelineno-5-65"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-66" name="__codelineno-5-66" href="#__codelineno-5-66"></a>
+<a id="__codelineno-5-67" name="__codelineno-5-67" href="#__codelineno-5-67"></a><span class="w">    </span><span class="cm">/* 辺を削除 */</span>
+<a id="__codelineno-5-68" name="__codelineno-5-68" href="#__codelineno-5-68"></a><span class="w">    </span><span class="c1">// 引数 i, j は vertices の要素インデックスに対応する</span>
+<a id="__codelineno-5-69" name="__codelineno-5-69" href="#__codelineno-5-69"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">removeEdge</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-70" name="__codelineno-5-70" href="#__codelineno-5-70"></a><span class="w">        </span><span class="c1">// インデックスの範囲外と等値の処理</span>
+<a id="__codelineno-5-71" name="__codelineno-5-71" href="#__codelineno-5-71"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-72" name="__codelineno-5-72" href="#__codelineno-5-72"></a><span class="w">            </span><span class="bp">fatalError</span><span class="p">(</span><span class="s">&quot;範囲外&quot;</span><span class="p">)</span>
+<a id="__codelineno-5-73" name="__codelineno-5-73" href="#__codelineno-5-73"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-74" name="__codelineno-5-74" href="#__codelineno-5-74"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-5-75" name="__codelineno-5-75" href="#__codelineno-5-75"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">[</span><span class="n">j</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-5-76" name="__codelineno-5-76" href="#__codelineno-5-76"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-77" name="__codelineno-5-77" href="#__codelineno-5-77"></a>
+<a id="__codelineno-5-78" name="__codelineno-5-78" href="#__codelineno-5-78"></a><span class="w">    </span><span class="cm">/* 隣接行列を出力 */</span>
+<a id="__codelineno-5-79" name="__codelineno-5-79" href="#__codelineno-5-79"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-80" name="__codelineno-5-80" href="#__codelineno-5-80"></a><span class="w">        </span><span class="n">Swift</span><span class="p">.</span><span class="bp">print</span><span class="p">(</span><span class="s">&quot;頂点リスト = &quot;</span><span class="p">,</span><span class="w"> </span><span class="n">terminator</span><span class="p">:</span><span class="w"> </span><span class="s">&quot;&quot;</span><span class="p">)</span>
+<a id="__codelineno-5-81" name="__codelineno-5-81" href="#__codelineno-5-81"></a><span class="w">        </span><span class="n">Swift</span><span class="p">.</span><span class="bp">print</span><span class="p">(</span><span class="n">vertices</span><span class="p">)</span>
+<a id="__codelineno-5-82" name="__codelineno-5-82" href="#__codelineno-5-82"></a><span class="w">        </span><span class="n">Swift</span><span class="p">.</span><span class="bp">print</span><span class="p">(</span><span class="s">&quot;隣接行列 =&quot;</span><span class="p">)</span>
+<a id="__codelineno-5-83" name="__codelineno-5-83" href="#__codelineno-5-83"></a><span class="w">        </span><span class="n">PrintUtil</span><span class="p">.</span><span class="n">printMatrix</span><span class="p">(</span><span class="n">matrix</span><span class="p">:</span><span class="w"> </span><span class="n">adjMat</span><span class="p">)</span>
+<a id="__codelineno-5-84" name="__codelineno-5-84" href="#__codelineno-5-84"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-85" name="__codelineno-5-85" href="#__codelineno-5-85"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_adjacency_matrix.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">GraphAdjMat</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">graph_adjacency_matrix.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 隣接行列に基づく無向グラフクラス */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">GraphAdjMat</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="nx">vertices</span><span class="p">;</span><span class="w"> </span><span class="c1">// 頂点リスト。要素は「頂点値」、インデックスは「頂点インデックス」を表す</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="nx">adjMat</span><span class="p">;</span><span class="w"> </span><span class="c1">// 隣接行列。行・列のインデックスは「頂点インデックス」に対応</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">vertices</span><span class="p">,</span><span class="w"> </span><span class="nx">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">vertices</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjMat</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">        </span><span class="c1">// 頂点を追加</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">vertices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">addVertex</span><span class="p">(</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">        </span><span class="c1">// 辺を追加</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">        </span><span class="c1">// 注意：edges の各要素は頂点インデックスを表し、vertices の要素インデックスに対応する</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">e</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">addEdge</span><span class="p">(</span><span class="nx">e</span><span class="p">[</span><span class="mf">0</span><span class="p">],</span><span class="w"> </span><span class="nx">e</span><span class="p">[</span><span class="mf">1</span><span class="p">]);</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w">    </span><span class="cm">/* 頂点数を取得 */</span>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w">    </span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">vertices</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a>
+<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="w">    </span><span class="cm">/* 頂点を追加 */</span>
+<a id="__codelineno-6-27" name="__codelineno-6-27" href="#__codelineno-6-27"></a><span class="w">    </span><span class="nx">addVertex</span><span class="p">(</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-28" name="__codelineno-6-28" href="#__codelineno-6-28"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">();</span>
+<a id="__codelineno-6-29" name="__codelineno-6-29" href="#__codelineno-6-29"></a><span class="w">        </span><span class="c1">// 頂点リストに新しい頂点の値を追加</span>
+<a id="__codelineno-6-30" name="__codelineno-6-30" href="#__codelineno-6-30"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">vertices</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-6-31" name="__codelineno-6-31" href="#__codelineno-6-31"></a><span class="w">        </span><span class="c1">// 隣接行列に 1 行追加</span>
+<a id="__codelineno-6-32" name="__codelineno-6-32" href="#__codelineno-6-32"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">newRow</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-6-33" name="__codelineno-6-33" href="#__codelineno-6-33"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-34" name="__codelineno-6-34" href="#__codelineno-6-34"></a><span class="w">            </span><span class="nx">newRow</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-6-35" name="__codelineno-6-35" href="#__codelineno-6-35"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-36" name="__codelineno-6-36" href="#__codelineno-6-36"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">newRow</span><span class="p">);</span>
+<a id="__codelineno-6-37" name="__codelineno-6-37" href="#__codelineno-6-37"></a><span class="w">        </span><span class="c1">// 隣接行列に 1 列追加</span>
+<a id="__codelineno-6-38" name="__codelineno-6-38" href="#__codelineno-6-38"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">row</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-39" name="__codelineno-6-39" href="#__codelineno-6-39"></a><span class="w">            </span><span class="nx">row</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-6-40" name="__codelineno-6-40" href="#__codelineno-6-40"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-41" name="__codelineno-6-41" href="#__codelineno-6-41"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-42" name="__codelineno-6-42" href="#__codelineno-6-42"></a>
+<a id="__codelineno-6-43" name="__codelineno-6-43" href="#__codelineno-6-43"></a><span class="w">    </span><span class="cm">/* 頂点を削除 */</span>
+<a id="__codelineno-6-44" name="__codelineno-6-44" href="#__codelineno-6-44"></a><span class="w">    </span><span class="nx">removeVertex</span><span class="p">(</span><span class="nx">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-45" name="__codelineno-6-45" href="#__codelineno-6-45"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-46" name="__codelineno-6-46" href="#__codelineno-6-46"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">RangeError</span><span class="p">(</span><span class="s1">&#39;Index Out Of Bounds Exception&#39;</span><span class="p">);</span>
+<a id="__codelineno-6-47" name="__codelineno-6-47" href="#__codelineno-6-47"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-48" name="__codelineno-6-48" href="#__codelineno-6-48"></a><span class="w">        </span><span class="c1">// 頂点リストから index の頂点を削除する</span>
+<a id="__codelineno-6-49" name="__codelineno-6-49" href="#__codelineno-6-49"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">vertices</span><span class="p">.</span><span class="nx">splice</span><span class="p">(</span><span class="nx">index</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-6-50" name="__codelineno-6-50" href="#__codelineno-6-50"></a>
+<a id="__codelineno-6-51" name="__codelineno-6-51" href="#__codelineno-6-51"></a><span class="w">        </span><span class="c1">// 隣接行列で index 行を削除する</span>
+<a id="__codelineno-6-52" name="__codelineno-6-52" href="#__codelineno-6-52"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">.</span><span class="nx">splice</span><span class="p">(</span><span class="nx">index</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-6-53" name="__codelineno-6-53" href="#__codelineno-6-53"></a><span class="w">        </span><span class="c1">// 隣接行列で index 列を削除する</span>
+<a id="__codelineno-6-54" name="__codelineno-6-54" href="#__codelineno-6-54"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">row</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-55" name="__codelineno-6-55" href="#__codelineno-6-55"></a><span class="w">            </span><span class="nx">row</span><span class="p">.</span><span class="nx">splice</span><span class="p">(</span><span class="nx">index</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-6-56" name="__codelineno-6-56" href="#__codelineno-6-56"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-57" name="__codelineno-6-57" href="#__codelineno-6-57"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-58" name="__codelineno-6-58" href="#__codelineno-6-58"></a>
+<a id="__codelineno-6-59" name="__codelineno-6-59" href="#__codelineno-6-59"></a><span class="w">    </span><span class="cm">/* 辺を追加 */</span>
+<a id="__codelineno-6-60" name="__codelineno-6-60" href="#__codelineno-6-60"></a><span class="w">    </span><span class="c1">// 引数 i, j は vertices の要素インデックスに対応する</span>
+<a id="__codelineno-6-61" name="__codelineno-6-61" href="#__codelineno-6-61"></a><span class="w">    </span><span class="nx">addEdge</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-62" name="__codelineno-6-62" href="#__codelineno-6-62"></a><span class="w">        </span><span class="c1">// インデックスの範囲外と等値の処理</span>
+<a id="__codelineno-6-63" name="__codelineno-6-63" href="#__codelineno-6-63"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-64" name="__codelineno-6-64" href="#__codelineno-6-64"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">RangeError</span><span class="p">(</span><span class="s1">&#39;Index Out Of Bounds Exception&#39;</span><span class="p">);</span>
+<a id="__codelineno-6-65" name="__codelineno-6-65" href="#__codelineno-6-65"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-66" name="__codelineno-6-66" href="#__codelineno-6-66"></a><span class="w">        </span><span class="c1">// 無向グラフでは、隣接行列は主対角線に関して対称であり、(i, j) === (j, i) を満たす</span>
+<a id="__codelineno-6-67" name="__codelineno-6-67" href="#__codelineno-6-67"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-6-68" name="__codelineno-6-68" href="#__codelineno-6-68"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">j</span><span class="p">][</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-6-69" name="__codelineno-6-69" href="#__codelineno-6-69"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-70" name="__codelineno-6-70" href="#__codelineno-6-70"></a>
+<a id="__codelineno-6-71" name="__codelineno-6-71" href="#__codelineno-6-71"></a><span class="w">    </span><span class="cm">/* 辺を削除 */</span>
+<a id="__codelineno-6-72" name="__codelineno-6-72" href="#__codelineno-6-72"></a><span class="w">    </span><span class="c1">// 引数 i, j は vertices の要素インデックスに対応する</span>
+<a id="__codelineno-6-73" name="__codelineno-6-73" href="#__codelineno-6-73"></a><span class="w">    </span><span class="nx">removeEdge</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-74" name="__codelineno-6-74" href="#__codelineno-6-74"></a><span class="w">        </span><span class="c1">// インデックスの範囲外と等値の処理</span>
+<a id="__codelineno-6-75" name="__codelineno-6-75" href="#__codelineno-6-75"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-76" name="__codelineno-6-76" href="#__codelineno-6-76"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">RangeError</span><span class="p">(</span><span class="s1">&#39;Index Out Of Bounds Exception&#39;</span><span class="p">);</span>
+<a id="__codelineno-6-77" name="__codelineno-6-77" href="#__codelineno-6-77"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-78" name="__codelineno-6-78" href="#__codelineno-6-78"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-6-79" name="__codelineno-6-79" href="#__codelineno-6-79"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">j</span><span class="p">][</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-6-80" name="__codelineno-6-80" href="#__codelineno-6-80"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-81" name="__codelineno-6-81" href="#__codelineno-6-81"></a>
+<a id="__codelineno-6-82" name="__codelineno-6-82" href="#__codelineno-6-82"></a><span class="w">    </span><span class="cm">/* 隣接行列を出力 */</span>
+<a id="__codelineno-6-83" name="__codelineno-6-83" href="#__codelineno-6-83"></a><span class="w">    </span><span class="nx">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-84" name="__codelineno-6-84" href="#__codelineno-6-84"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="s1">&#39;頂点リスト = &#39;</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">vertices</span><span class="p">);</span>
+<a id="__codelineno-6-85" name="__codelineno-6-85" href="#__codelineno-6-85"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="s1">&#39;隣接行列 =&#39;</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">);</span>
+<a id="__codelineno-6-86" name="__codelineno-6-86" href="#__codelineno-6-86"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-87" name="__codelineno-6-87" href="#__codelineno-6-87"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_adjacency_matrix.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">GraphAdjMat</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">graph_adjacency_matrix.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 隣接行列に基づく無向グラフクラス */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">GraphAdjMat</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="nx">vertices</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[];</span><span class="w"> </span><span class="c1">// 頂点リスト。要素は「頂点値」、インデックスは「頂点インデックス」を表す</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="nx">adjMat</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[][];</span><span class="w"> </span><span class="c1">// 隣接行列。行・列のインデックスは「頂点インデックス」に対応</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">vertices</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">edges</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[][])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">vertices</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjMat</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">        </span><span class="c1">// 頂点を追加</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">vertices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">addVertex</span><span class="p">(</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">        </span><span class="c1">// 辺を追加</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">        </span><span class="c1">// 注意：edges の各要素は頂点インデックスを表し、vertices の要素インデックスに対応する</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">e</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">addEdge</span><span class="p">(</span><span class="nx">e</span><span class="p">[</span><span class="mf">0</span><span class="p">],</span><span class="w"> </span><span class="nx">e</span><span class="p">[</span><span class="mf">1</span><span class="p">]);</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="w">    </span><span class="cm">/* 頂点数を取得 */</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="w">    </span><span class="nx">size</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">vertices</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a>
+<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="w">    </span><span class="cm">/* 頂点を追加 */</span>
+<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a><span class="w">    </span><span class="nx">addVertex</span><span class="p">(</span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">();</span>
+<a id="__codelineno-7-29" name="__codelineno-7-29" href="#__codelineno-7-29"></a><span class="w">        </span><span class="c1">// 頂点リストに新しい頂点の値を追加</span>
+<a id="__codelineno-7-30" name="__codelineno-7-30" href="#__codelineno-7-30"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">vertices</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-7-31" name="__codelineno-7-31" href="#__codelineno-7-31"></a><span class="w">        </span><span class="c1">// 隣接行列に 1 行追加</span>
+<a id="__codelineno-7-32" name="__codelineno-7-32" href="#__codelineno-7-32"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">newRow</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-7-33" name="__codelineno-7-33" href="#__codelineno-7-33"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-34" name="__codelineno-7-34" href="#__codelineno-7-34"></a><span class="w">            </span><span class="nx">newRow</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-7-35" name="__codelineno-7-35" href="#__codelineno-7-35"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-36" name="__codelineno-7-36" href="#__codelineno-7-36"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">newRow</span><span class="p">);</span>
+<a id="__codelineno-7-37" name="__codelineno-7-37" href="#__codelineno-7-37"></a><span class="w">        </span><span class="c1">// 隣接行列に 1 列追加</span>
+<a id="__codelineno-7-38" name="__codelineno-7-38" href="#__codelineno-7-38"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">row</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-39" name="__codelineno-7-39" href="#__codelineno-7-39"></a><span class="w">            </span><span class="nx">row</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-7-40" name="__codelineno-7-40" href="#__codelineno-7-40"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-41" name="__codelineno-7-41" href="#__codelineno-7-41"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-42" name="__codelineno-7-42" href="#__codelineno-7-42"></a>
+<a id="__codelineno-7-43" name="__codelineno-7-43" href="#__codelineno-7-43"></a><span class="w">    </span><span class="cm">/* 頂点を削除 */</span>
+<a id="__codelineno-7-44" name="__codelineno-7-44" href="#__codelineno-7-44"></a><span class="w">    </span><span class="nx">removeVertex</span><span class="p">(</span><span class="nx">index</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-45" name="__codelineno-7-45" href="#__codelineno-7-45"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-46" name="__codelineno-7-46" href="#__codelineno-7-46"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">RangeError</span><span class="p">(</span><span class="s1">&#39;Index Out Of Bounds Exception&#39;</span><span class="p">);</span>
+<a id="__codelineno-7-47" name="__codelineno-7-47" href="#__codelineno-7-47"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-48" name="__codelineno-7-48" href="#__codelineno-7-48"></a><span class="w">        </span><span class="c1">// 頂点リストから index の頂点を削除する</span>
+<a id="__codelineno-7-49" name="__codelineno-7-49" href="#__codelineno-7-49"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">vertices</span><span class="p">.</span><span class="nx">splice</span><span class="p">(</span><span class="nx">index</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-7-50" name="__codelineno-7-50" href="#__codelineno-7-50"></a>
+<a id="__codelineno-7-51" name="__codelineno-7-51" href="#__codelineno-7-51"></a><span class="w">        </span><span class="c1">// 隣接行列で index 行を削除する</span>
+<a id="__codelineno-7-52" name="__codelineno-7-52" href="#__codelineno-7-52"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">.</span><span class="nx">splice</span><span class="p">(</span><span class="nx">index</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-7-53" name="__codelineno-7-53" href="#__codelineno-7-53"></a><span class="w">        </span><span class="c1">// 隣接行列で index 列を削除する</span>
+<a id="__codelineno-7-54" name="__codelineno-7-54" href="#__codelineno-7-54"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">row</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-55" name="__codelineno-7-55" href="#__codelineno-7-55"></a><span class="w">            </span><span class="nx">row</span><span class="p">.</span><span class="nx">splice</span><span class="p">(</span><span class="nx">index</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-7-56" name="__codelineno-7-56" href="#__codelineno-7-56"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-57" name="__codelineno-7-57" href="#__codelineno-7-57"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-58" name="__codelineno-7-58" href="#__codelineno-7-58"></a>
+<a id="__codelineno-7-59" name="__codelineno-7-59" href="#__codelineno-7-59"></a><span class="w">    </span><span class="cm">/* 辺を追加 */</span>
+<a id="__codelineno-7-60" name="__codelineno-7-60" href="#__codelineno-7-60"></a><span class="w">    </span><span class="c1">// 引数 i, j は vertices の要素インデックスに対応する</span>
+<a id="__codelineno-7-61" name="__codelineno-7-61" href="#__codelineno-7-61"></a><span class="w">    </span><span class="nx">addEdge</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-62" name="__codelineno-7-62" href="#__codelineno-7-62"></a><span class="w">        </span><span class="c1">// インデックスの範囲外と等値の処理</span>
+<a id="__codelineno-7-63" name="__codelineno-7-63" href="#__codelineno-7-63"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-64" name="__codelineno-7-64" href="#__codelineno-7-64"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">RangeError</span><span class="p">(</span><span class="s1">&#39;Index Out Of Bounds Exception&#39;</span><span class="p">);</span>
+<a id="__codelineno-7-65" name="__codelineno-7-65" href="#__codelineno-7-65"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-66" name="__codelineno-7-66" href="#__codelineno-7-66"></a><span class="w">        </span><span class="c1">// 無向グラフでは、隣接行列は主対角線に関して対称であり、(i, j) === (j, i) を満たす</span>
+<a id="__codelineno-7-67" name="__codelineno-7-67" href="#__codelineno-7-67"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-7-68" name="__codelineno-7-68" href="#__codelineno-7-68"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">j</span><span class="p">][</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-7-69" name="__codelineno-7-69" href="#__codelineno-7-69"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-70" name="__codelineno-7-70" href="#__codelineno-7-70"></a>
+<a id="__codelineno-7-71" name="__codelineno-7-71" href="#__codelineno-7-71"></a><span class="w">    </span><span class="cm">/* 辺を削除 */</span>
+<a id="__codelineno-7-72" name="__codelineno-7-72" href="#__codelineno-7-72"></a><span class="w">    </span><span class="c1">// 引数 i, j は vertices の要素インデックスに対応する</span>
+<a id="__codelineno-7-73" name="__codelineno-7-73" href="#__codelineno-7-73"></a><span class="w">    </span><span class="nx">removeEdge</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-74" name="__codelineno-7-74" href="#__codelineno-7-74"></a><span class="w">        </span><span class="c1">// インデックスの範囲外と等値の処理</span>
+<a id="__codelineno-7-75" name="__codelineno-7-75" href="#__codelineno-7-75"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-76" name="__codelineno-7-76" href="#__codelineno-7-76"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">RangeError</span><span class="p">(</span><span class="s1">&#39;Index Out Of Bounds Exception&#39;</span><span class="p">);</span>
+<a id="__codelineno-7-77" name="__codelineno-7-77" href="#__codelineno-7-77"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-78" name="__codelineno-7-78" href="#__codelineno-7-78"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-7-79" name="__codelineno-7-79" href="#__codelineno-7-79"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">j</span><span class="p">][</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-7-80" name="__codelineno-7-80" href="#__codelineno-7-80"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-81" name="__codelineno-7-81" href="#__codelineno-7-81"></a>
+<a id="__codelineno-7-82" name="__codelineno-7-82" href="#__codelineno-7-82"></a><span class="w">    </span><span class="cm">/* 隣接行列を出力 */</span>
+<a id="__codelineno-7-83" name="__codelineno-7-83" href="#__codelineno-7-83"></a><span class="w">    </span><span class="nx">print</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-84" name="__codelineno-7-84" href="#__codelineno-7-84"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="s1">&#39;頂点リスト = &#39;</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">vertices</span><span class="p">);</span>
+<a id="__codelineno-7-85" name="__codelineno-7-85" href="#__codelineno-7-85"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="s1">&#39;隣接行列 =&#39;</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">);</span>
+<a id="__codelineno-7-86" name="__codelineno-7-86" href="#__codelineno-7-86"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-87" name="__codelineno-7-87" href="#__codelineno-7-87"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_adjacency_matrix.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">GraphAdjMat</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">graph_adjacency_matrix.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 隣接行列に基づく無向グラフクラス */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">GraphAdjMat</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">vertices</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 頂点要素。要素は「頂点値」を表し、インデックスは「頂点インデックス」を表す</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">adjMat</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span><span class="w"> </span><span class="c1">// 隣接行列。行・列のインデックスは「頂点インデックス」に対応</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="n">GraphAdjMat</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">vertices</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="n">vertices</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="n">adjMat</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">    </span><span class="c1">// 頂点を追加</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">vertices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">      </span><span class="n">addVertex</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">    </span><span class="c1">// 辺を追加</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">    </span><span class="c1">// 注意：edges の各要素は頂点インデックスを表し、vertices の要素インデックスに対応する</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">e</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">      </span><span class="n">addEdge</span><span class="p">(</span><span class="n">e</span><span class="p">[</span><span class="m">0</span><span class="p">],</span><span class="w"> </span><span class="n">e</span><span class="p">[</span><span class="m">1</span><span class="p">]);</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a>
+<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="w">  </span><span class="cm">/* 頂点数を取得 */</span>
+<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">vertices</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a>
+<a id="__codelineno-8-26" name="__codelineno-8-26" href="#__codelineno-8-26"></a><span class="w">  </span><span class="cm">/* 頂点を追加 */</span>
+<a id="__codelineno-8-27" name="__codelineno-8-27" href="#__codelineno-8-27"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">addVertex</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-28" name="__codelineno-8-28" href="#__codelineno-8-28"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-8-29" name="__codelineno-8-29" href="#__codelineno-8-29"></a><span class="w">    </span><span class="c1">// 頂点リストに新しい頂点の値を追加</span>
+<a id="__codelineno-8-30" name="__codelineno-8-30" href="#__codelineno-8-30"></a><span class="w">    </span><span class="n">vertices</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-8-31" name="__codelineno-8-31" href="#__codelineno-8-31"></a><span class="w">    </span><span class="c1">// 隣接行列に 1 行追加</span>
+<a id="__codelineno-8-32" name="__codelineno-8-32" href="#__codelineno-8-32"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">newRow</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="nl">growable:</span><span class="w"> </span><span class="kc">true</span><span class="p">);</span>
+<a id="__codelineno-8-33" name="__codelineno-8-33" href="#__codelineno-8-33"></a><span class="w">    </span><span class="n">adjMat</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">newRow</span><span class="p">);</span>
+<a id="__codelineno-8-34" name="__codelineno-8-34" href="#__codelineno-8-34"></a><span class="w">    </span><span class="c1">// 隣接行列に 1 列追加</span>
+<a id="__codelineno-8-35" name="__codelineno-8-35" href="#__codelineno-8-35"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">adjMat</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-36" name="__codelineno-8-36" href="#__codelineno-8-36"></a><span class="w">      </span><span class="n">row</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-8-37" name="__codelineno-8-37" href="#__codelineno-8-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-38" name="__codelineno-8-38" href="#__codelineno-8-38"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-39" name="__codelineno-8-39" href="#__codelineno-8-39"></a>
+<a id="__codelineno-8-40" name="__codelineno-8-40" href="#__codelineno-8-40"></a><span class="w">  </span><span class="cm">/* 頂点を削除 */</span>
+<a id="__codelineno-8-41" name="__codelineno-8-41" href="#__codelineno-8-41"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">removeVertex</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-42" name="__codelineno-8-42" href="#__codelineno-8-42"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-43" name="__codelineno-8-43" href="#__codelineno-8-43"></a><span class="w">      </span><span class="k">throw</span><span class="w"> </span><span class="n">IndexError</span><span class="p">;</span>
+<a id="__codelineno-8-44" name="__codelineno-8-44" href="#__codelineno-8-44"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-45" name="__codelineno-8-45" href="#__codelineno-8-45"></a><span class="w">    </span><span class="c1">// 頂点リストから index の頂点を削除する</span>
+<a id="__codelineno-8-46" name="__codelineno-8-46" href="#__codelineno-8-46"></a><span class="w">    </span><span class="n">vertices</span><span class="p">.</span><span class="n">removeAt</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
+<a id="__codelineno-8-47" name="__codelineno-8-47" href="#__codelineno-8-47"></a><span class="w">    </span><span class="c1">// 隣接行列で index 行を削除する</span>
+<a id="__codelineno-8-48" name="__codelineno-8-48" href="#__codelineno-8-48"></a><span class="w">    </span><span class="n">adjMat</span><span class="p">.</span><span class="n">removeAt</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
+<a id="__codelineno-8-49" name="__codelineno-8-49" href="#__codelineno-8-49"></a><span class="w">    </span><span class="c1">// 隣接行列で index 列を削除する</span>
+<a id="__codelineno-8-50" name="__codelineno-8-50" href="#__codelineno-8-50"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">adjMat</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-51" name="__codelineno-8-51" href="#__codelineno-8-51"></a><span class="w">      </span><span class="n">row</span><span class="p">.</span><span class="n">removeAt</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
+<a id="__codelineno-8-52" name="__codelineno-8-52" href="#__codelineno-8-52"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-53" name="__codelineno-8-53" href="#__codelineno-8-53"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-54" name="__codelineno-8-54" href="#__codelineno-8-54"></a>
+<a id="__codelineno-8-55" name="__codelineno-8-55" href="#__codelineno-8-55"></a><span class="w">  </span><span class="cm">/* 辺を追加 */</span>
+<a id="__codelineno-8-56" name="__codelineno-8-56" href="#__codelineno-8-56"></a><span class="w">  </span><span class="c1">// 引数 i, j は vertices の要素インデックスに対応する</span>
+<a id="__codelineno-8-57" name="__codelineno-8-57" href="#__codelineno-8-57"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">addEdge</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-58" name="__codelineno-8-58" href="#__codelineno-8-58"></a><span class="w">    </span><span class="c1">// インデックスの範囲外と等値の処理</span>
+<a id="__codelineno-8-59" name="__codelineno-8-59" href="#__codelineno-8-59"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-60" name="__codelineno-8-60" href="#__codelineno-8-60"></a><span class="w">      </span><span class="k">throw</span><span class="w"> </span><span class="n">IndexError</span><span class="p">;</span>
+<a id="__codelineno-8-61" name="__codelineno-8-61" href="#__codelineno-8-61"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-62" name="__codelineno-8-62" href="#__codelineno-8-62"></a><span class="w">    </span><span class="c1">// 無向グラフでは、隣接行列は主対角線に関して対称、すなわち (i, j) == (j, i) を満たす</span>
+<a id="__codelineno-8-63" name="__codelineno-8-63" href="#__codelineno-8-63"></a><span class="w">    </span><span class="n">adjMat</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-8-64" name="__codelineno-8-64" href="#__codelineno-8-64"></a><span class="w">    </span><span class="n">adjMat</span><span class="p">[</span><span class="n">j</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-8-65" name="__codelineno-8-65" href="#__codelineno-8-65"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-66" name="__codelineno-8-66" href="#__codelineno-8-66"></a>
+<a id="__codelineno-8-67" name="__codelineno-8-67" href="#__codelineno-8-67"></a><span class="w">  </span><span class="cm">/* 辺を削除 */</span>
+<a id="__codelineno-8-68" name="__codelineno-8-68" href="#__codelineno-8-68"></a><span class="w">  </span><span class="c1">// 引数 i, j は vertices の要素インデックスに対応する</span>
+<a id="__codelineno-8-69" name="__codelineno-8-69" href="#__codelineno-8-69"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">removeEdge</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-70" name="__codelineno-8-70" href="#__codelineno-8-70"></a><span class="w">    </span><span class="c1">// インデックスの範囲外と等値の処理</span>
+<a id="__codelineno-8-71" name="__codelineno-8-71" href="#__codelineno-8-71"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-72" name="__codelineno-8-72" href="#__codelineno-8-72"></a><span class="w">      </span><span class="k">throw</span><span class="w"> </span><span class="n">IndexError</span><span class="p">;</span>
+<a id="__codelineno-8-73" name="__codelineno-8-73" href="#__codelineno-8-73"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-74" name="__codelineno-8-74" href="#__codelineno-8-74"></a><span class="w">    </span><span class="n">adjMat</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-8-75" name="__codelineno-8-75" href="#__codelineno-8-75"></a><span class="w">    </span><span class="n">adjMat</span><span class="p">[</span><span class="n">j</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-8-76" name="__codelineno-8-76" href="#__codelineno-8-76"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-77" name="__codelineno-8-77" href="#__codelineno-8-77"></a>
+<a id="__codelineno-8-78" name="__codelineno-8-78" href="#__codelineno-8-78"></a><span class="w">  </span><span class="cm">/* 隣接行列を出力 */</span>
+<a id="__codelineno-8-79" name="__codelineno-8-79" href="#__codelineno-8-79"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">printAdjMat</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-80" name="__codelineno-8-80" href="#__codelineno-8-80"></a><span class="w">    </span><span class="n">print</span><span class="p">(</span><span class="s2">&quot;頂点リスト = </span><span class="si">$</span><span class="n">vertices</span><span class="s2">&quot;</span><span class="p">);</span>
+<a id="__codelineno-8-81" name="__codelineno-8-81" href="#__codelineno-8-81"></a><span class="w">    </span><span class="n">print</span><span class="p">(</span><span class="s2">&quot;隣接行列 = &quot;</span><span class="p">);</span>
+<a id="__codelineno-8-82" name="__codelineno-8-82" href="#__codelineno-8-82"></a><span class="w">    </span><span class="n">printMatrix</span><span class="p">(</span><span class="n">adjMat</span><span class="p">);</span>
+<a id="__codelineno-8-83" name="__codelineno-8-83" href="#__codelineno-8-83"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-84" name="__codelineno-8-84" href="#__codelineno-8-84"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_adjacency_matrix.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">GraphAdjMat</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">graph_adjacency_matrix.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 隣接行列に基づく無向グラフ型 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">pub</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">GraphAdjMat</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="c1">// 頂点リスト。要素は「頂点値」、インデックスは「頂点インデックス」を表す</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="n">vertices</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="c1">// 隣接行列。行・列のインデックスは「頂点インデックス」に対応</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="n">adj_mat</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="p">}</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="k">impl</span><span class="w"> </span><span class="n">GraphAdjMat</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">new</span><span class="p">(</span><span class="n">vertices</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">edges</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="p">[</span><span class="kt">usize</span><span class="p">;</span><span class="w"> </span><span class="mi">2</span><span class="p">]</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">graph</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">GraphAdjMat</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">            </span><span class="n">vertices</span><span class="p">:</span><span class="w"> </span><span class="nc">vec</span><span class="o">!</span><span class="p">[],</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">            </span><span class="n">adj_mat</span><span class="p">:</span><span class="w"> </span><span class="nc">vec</span><span class="o">!</span><span class="p">[],</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">        </span><span class="p">};</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">        </span><span class="c1">// 頂点を追加</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">vertices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">            </span><span class="n">graph</span><span class="p">.</span><span class="n">add_vertex</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w">        </span><span class="c1">// 辺を追加</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w">        </span><span class="c1">// 注意：edges の各要素は頂点インデックスを表し、vertices の要素インデックスに対応する</span>
+<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">edge</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">edges</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="w">            </span><span class="n">graph</span><span class="p">.</span><span class="n">add_edge</span><span class="p">(</span><span class="n">edge</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="n">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a>
+<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="w">        </span><span class="n">graph</span>
+<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a>
+<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="w">    </span><span class="cm">/* 頂点数を取得 */</span>
+<a id="__codelineno-9-30" name="__codelineno-9-30" href="#__codelineno-9-30"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-31" name="__codelineno-9-31" href="#__codelineno-9-31"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">vertices</span><span class="p">.</span><span class="n">len</span><span class="p">()</span>
+<a id="__codelineno-9-32" name="__codelineno-9-32" href="#__codelineno-9-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-33" name="__codelineno-9-33" href="#__codelineno-9-33"></a>
+<a id="__codelineno-9-34" name="__codelineno-9-34" href="#__codelineno-9-34"></a><span class="w">    </span><span class="cm">/* 頂点を追加 */</span>
+<a id="__codelineno-9-35" name="__codelineno-9-35" href="#__codelineno-9-35"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">add_vertex</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-36" name="__codelineno-9-36" href="#__codelineno-9-36"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-9-37" name="__codelineno-9-37" href="#__codelineno-9-37"></a><span class="w">        </span><span class="c1">// 頂点リストに新しい頂点の値を追加</span>
+<a id="__codelineno-9-38" name="__codelineno-9-38" href="#__codelineno-9-38"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">vertices</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-9-39" name="__codelineno-9-39" href="#__codelineno-9-39"></a><span class="w">        </span><span class="c1">// 隣接行列に 1 行追加</span>
+<a id="__codelineno-9-40" name="__codelineno-9-40" href="#__codelineno-9-40"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">adj_mat</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">n</span><span class="p">]);</span>
+<a id="__codelineno-9-41" name="__codelineno-9-41" href="#__codelineno-9-41"></a><span class="w">        </span><span class="c1">// 隣接行列に 1 列追加</span>
+<a id="__codelineno-9-42" name="__codelineno-9-42" href="#__codelineno-9-42"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">adj_mat</span><span class="p">.</span><span class="n">iter_mut</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-43" name="__codelineno-9-43" href="#__codelineno-9-43"></a><span class="w">            </span><span class="n">row</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-9-44" name="__codelineno-9-44" href="#__codelineno-9-44"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-45" name="__codelineno-9-45" href="#__codelineno-9-45"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-46" name="__codelineno-9-46" href="#__codelineno-9-46"></a>
+<a id="__codelineno-9-47" name="__codelineno-9-47" href="#__codelineno-9-47"></a><span class="w">    </span><span class="cm">/* 頂点を削除 */</span>
+<a id="__codelineno-9-48" name="__codelineno-9-48" href="#__codelineno-9-48"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">remove_vertex</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">index</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-49" name="__codelineno-9-49" href="#__codelineno-9-49"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-50" name="__codelineno-9-50" href="#__codelineno-9-50"></a><span class="w">            </span><span class="fm">panic!</span><span class="p">(</span><span class="s">&quot;index error&quot;</span><span class="p">)</span>
+<a id="__codelineno-9-51" name="__codelineno-9-51" href="#__codelineno-9-51"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-52" name="__codelineno-9-52" href="#__codelineno-9-52"></a><span class="w">        </span><span class="c1">// 頂点リストから index の頂点を削除する</span>
+<a id="__codelineno-9-53" name="__codelineno-9-53" href="#__codelineno-9-53"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">vertices</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
+<a id="__codelineno-9-54" name="__codelineno-9-54" href="#__codelineno-9-54"></a><span class="w">        </span><span class="c1">// 隣接行列で index 行を削除する</span>
+<a id="__codelineno-9-55" name="__codelineno-9-55" href="#__codelineno-9-55"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">adj_mat</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
+<a id="__codelineno-9-56" name="__codelineno-9-56" href="#__codelineno-9-56"></a><span class="w">        </span><span class="c1">// 隣接行列で index 列を削除する</span>
+<a id="__codelineno-9-57" name="__codelineno-9-57" href="#__codelineno-9-57"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">adj_mat</span><span class="p">.</span><span class="n">iter_mut</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-58" name="__codelineno-9-58" href="#__codelineno-9-58"></a><span class="w">            </span><span class="n">row</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
+<a id="__codelineno-9-59" name="__codelineno-9-59" href="#__codelineno-9-59"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-60" name="__codelineno-9-60" href="#__codelineno-9-60"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-61" name="__codelineno-9-61" href="#__codelineno-9-61"></a>
+<a id="__codelineno-9-62" name="__codelineno-9-62" href="#__codelineno-9-62"></a><span class="w">    </span><span class="cm">/* 辺を追加 */</span>
+<a id="__codelineno-9-63" name="__codelineno-9-63" href="#__codelineno-9-63"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">add_edge</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-64" name="__codelineno-9-64" href="#__codelineno-9-64"></a><span class="w">        </span><span class="c1">// パラメータ i, j は vertices の要素インデックスに対応する</span>
+<a id="__codelineno-9-65" name="__codelineno-9-65" href="#__codelineno-9-65"></a><span class="w">        </span><span class="c1">// 範囲外と同値の場合の処理</span>
+<a id="__codelineno-9-66" name="__codelineno-9-66" href="#__codelineno-9-66"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-67" name="__codelineno-9-67" href="#__codelineno-9-67"></a><span class="w">            </span><span class="fm">panic!</span><span class="p">(</span><span class="s">&quot;index error&quot;</span><span class="p">)</span>
+<a id="__codelineno-9-68" name="__codelineno-9-68" href="#__codelineno-9-68"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-69" name="__codelineno-9-69" href="#__codelineno-9-69"></a><span class="w">        </span><span class="c1">// 無向グラフでは、隣接行列は主対角線に関して対称、すなわち (i, j) == (j, i) を満たす</span>
+<a id="__codelineno-9-70" name="__codelineno-9-70" href="#__codelineno-9-70"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">adj_mat</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-71" name="__codelineno-9-71" href="#__codelineno-9-71"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">adj_mat</span><span class="p">[</span><span class="n">j</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-72" name="__codelineno-9-72" href="#__codelineno-9-72"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-73" name="__codelineno-9-73" href="#__codelineno-9-73"></a>
+<a id="__codelineno-9-74" name="__codelineno-9-74" href="#__codelineno-9-74"></a><span class="w">    </span><span class="cm">/* 辺を削除 */</span>
+<a id="__codelineno-9-75" name="__codelineno-9-75" href="#__codelineno-9-75"></a><span class="w">    </span><span class="c1">// 引数 i, j は vertices の要素インデックスに対応する</span>
+<a id="__codelineno-9-76" name="__codelineno-9-76" href="#__codelineno-9-76"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">remove_edge</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-77" name="__codelineno-9-77" href="#__codelineno-9-77"></a><span class="w">        </span><span class="c1">// パラメータ i, j は vertices の要素インデックスに対応する</span>
+<a id="__codelineno-9-78" name="__codelineno-9-78" href="#__codelineno-9-78"></a><span class="w">        </span><span class="c1">// 範囲外と同値の場合の処理</span>
+<a id="__codelineno-9-79" name="__codelineno-9-79" href="#__codelineno-9-79"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-80" name="__codelineno-9-80" href="#__codelineno-9-80"></a><span class="w">            </span><span class="fm">panic!</span><span class="p">(</span><span class="s">&quot;index error&quot;</span><span class="p">)</span>
+<a id="__codelineno-9-81" name="__codelineno-9-81" href="#__codelineno-9-81"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-82" name="__codelineno-9-82" href="#__codelineno-9-82"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">adj_mat</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-9-83" name="__codelineno-9-83" href="#__codelineno-9-83"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">adj_mat</span><span class="p">[</span><span class="n">j</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-9-84" name="__codelineno-9-84" href="#__codelineno-9-84"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-85" name="__codelineno-9-85" href="#__codelineno-9-85"></a>
+<a id="__codelineno-9-86" name="__codelineno-9-86" href="#__codelineno-9-86"></a><span class="w">    </span><span class="cm">/* 隣接行列を出力 */</span>
+<a id="__codelineno-9-87" name="__codelineno-9-87" href="#__codelineno-9-87"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">print</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-88" name="__codelineno-9-88" href="#__codelineno-9-88"></a><span class="w">        </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;頂点リスト = {:?}&quot;</span><span class="p">,</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">vertices</span><span class="p">);</span>
+<a id="__codelineno-9-89" name="__codelineno-9-89" href="#__codelineno-9-89"></a><span class="w">        </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;隣接行列 =&quot;</span><span class="p">);</span>
+<a id="__codelineno-9-90" name="__codelineno-9-90" href="#__codelineno-9-90"></a><span class="w">        </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;[&quot;</span><span class="p">);</span>
+<a id="__codelineno-9-91" name="__codelineno-9-91" href="#__codelineno-9-91"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="o">&amp;</span><span class="bp">self</span><span class="p">.</span><span class="n">adj_mat</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-92" name="__codelineno-9-92" href="#__codelineno-9-92"></a><span class="w">            </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;  {:?},&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">row</span><span class="p">);</span>
+<a id="__codelineno-9-93" name="__codelineno-9-93" href="#__codelineno-9-93"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-94" name="__codelineno-9-94" href="#__codelineno-9-94"></a><span class="w">        </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;]&quot;</span><span class="p">)</span>
+<a id="__codelineno-9-95" name="__codelineno-9-95" href="#__codelineno-9-95"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-96" name="__codelineno-9-96" href="#__codelineno-9-96"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_adjacency_matrix.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">GraphAdjMat</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">graph_adjacency_matrix.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 隣接行列に基づく無向グラフ構造体 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">vertices</span><span class="p">[</span><span class="n">MAX_SIZE</span><span class="p">];</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">adjMat</span><span class="p">[</span><span class="n">MAX_SIZE</span><span class="p">][</span><span class="n">MAX_SIZE</span><span class="p">];</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="p">}</span><span class="w"> </span><span class="n">GraphAdjMat</span><span class="p">;</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="n">GraphAdjMat</span><span class="w"> </span><span class="o">*</span><span class="nf">newGraphAdjMat</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="n">GraphAdjMat</span><span class="w"> </span><span class="o">*</span><span class="n">graph</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">GraphAdjMat</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">GraphAdjMat</span><span class="p">));</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">            </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">adjMat</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">graph</span><span class="p">;</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="p">}</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a>
+<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="cm">/* デストラクタ */</span>
+<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="kt">void</span><span class="w"> </span><span class="nf">delGraphAdjMat</span><span class="p">(</span><span class="n">GraphAdjMat</span><span class="w"> </span><span class="o">*</span><span class="n">graph</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">graph</span><span class="p">);</span>
+<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="p">}</span>
+<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a>
+<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="cm">/* 頂点を追加 */</span>
+<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="kt">void</span><span class="w"> </span><span class="nf">addVertex</span><span class="p">(</span><span class="n">GraphAdjMat</span><span class="w"> </span><span class="o">*</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="w">        </span><span class="n">fprintf</span><span class="p">(</span><span class="n">stderr</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;グラフの頂点数が最大値に達しました</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">);</span>
+<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></a><span class="w">    </span><span class="c1">// n 番目の頂点を追加し、n 行目と n 列目を 0 にする</span>
+<a id="__codelineno-10-32" name="__codelineno-10-32" href="#__codelineno-10-32"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">;</span>
+<a id="__codelineno-10-33" name="__codelineno-10-33" href="#__codelineno-10-33"></a><span class="w">    </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">vertices</span><span class="p">[</span><span class="n">n</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-10-34" name="__codelineno-10-34" href="#__codelineno-10-34"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-35" name="__codelineno-10-35" href="#__codelineno-10-35"></a><span class="w">        </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">adjMat</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">adjMat</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">n</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-36" name="__codelineno-10-36" href="#__codelineno-10-36"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-37" name="__codelineno-10-37" href="#__codelineno-10-37"></a><span class="w">    </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-10-38" name="__codelineno-10-38" href="#__codelineno-10-38"></a><span class="p">}</span>
+<a id="__codelineno-10-39" name="__codelineno-10-39" href="#__codelineno-10-39"></a>
+<a id="__codelineno-10-40" name="__codelineno-10-40" href="#__codelineno-10-40"></a><span class="cm">/* 頂点を削除 */</span>
+<a id="__codelineno-10-41" name="__codelineno-10-41" href="#__codelineno-10-41"></a><span class="kt">void</span><span class="w"> </span><span class="nf">removeVertex</span><span class="p">(</span><span class="n">GraphAdjMat</span><span class="w"> </span><span class="o">*</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-42" name="__codelineno-10-42" href="#__codelineno-10-42"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-43" name="__codelineno-10-43" href="#__codelineno-10-43"></a><span class="w">        </span><span class="n">fprintf</span><span class="p">(</span><span class="n">stderr</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;頂点インデックスが範囲外です</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">);</span>
+<a id="__codelineno-10-44" name="__codelineno-10-44" href="#__codelineno-10-44"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-10-45" name="__codelineno-10-45" href="#__codelineno-10-45"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-46" name="__codelineno-10-46" href="#__codelineno-10-46"></a><span class="w">    </span><span class="c1">// 頂点リストから index の頂点を削除する</span>
+<a id="__codelineno-10-47" name="__codelineno-10-47" href="#__codelineno-10-47"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-48" name="__codelineno-10-48" href="#__codelineno-10-48"></a><span class="w">        </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">vertices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">vertices</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-10-49" name="__codelineno-10-49" href="#__codelineno-10-49"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-50" name="__codelineno-10-50" href="#__codelineno-10-50"></a><span class="w">    </span><span class="c1">// 隣接行列で index 行を削除する</span>
+<a id="__codelineno-10-51" name="__codelineno-10-51" href="#__codelineno-10-51"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-52" name="__codelineno-10-52" href="#__codelineno-10-52"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-53" name="__codelineno-10-53" href="#__codelineno-10-53"></a><span class="w">            </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">adjMat</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">adjMat</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-10-54" name="__codelineno-10-54" href="#__codelineno-10-54"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-55" name="__codelineno-10-55" href="#__codelineno-10-55"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-56" name="__codelineno-10-56" href="#__codelineno-10-56"></a><span class="w">    </span><span class="c1">// 隣接行列で index 列を削除する</span>
+<a id="__codelineno-10-57" name="__codelineno-10-57" href="#__codelineno-10-57"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-58" name="__codelineno-10-58" href="#__codelineno-10-58"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-59" name="__codelineno-10-59" href="#__codelineno-10-59"></a><span class="w">            </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">adjMat</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">adjMat</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-10-60" name="__codelineno-10-60" href="#__codelineno-10-60"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-61" name="__codelineno-10-61" href="#__codelineno-10-61"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-62" name="__codelineno-10-62" href="#__codelineno-10-62"></a><span class="w">    </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-10-63" name="__codelineno-10-63" href="#__codelineno-10-63"></a><span class="p">}</span>
+<a id="__codelineno-10-64" name="__codelineno-10-64" href="#__codelineno-10-64"></a>
+<a id="__codelineno-10-65" name="__codelineno-10-65" href="#__codelineno-10-65"></a><span class="cm">/* 辺を追加 */</span>
+<a id="__codelineno-10-66" name="__codelineno-10-66" href="#__codelineno-10-66"></a><span class="c1">// 引数 i, j は vertices の要素インデックスに対応する</span>
+<a id="__codelineno-10-67" name="__codelineno-10-67" href="#__codelineno-10-67"></a><span class="kt">void</span><span class="w"> </span><span class="nf">addEdge</span><span class="p">(</span><span class="n">GraphAdjMat</span><span class="w"> </span><span class="o">*</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-68" name="__codelineno-10-68" href="#__codelineno-10-68"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-69" name="__codelineno-10-69" href="#__codelineno-10-69"></a><span class="w">        </span><span class="n">fprintf</span><span class="p">(</span><span class="n">stderr</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;辺インデックスが範囲外であるか、同一です</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">);</span>
+<a id="__codelineno-10-70" name="__codelineno-10-70" href="#__codelineno-10-70"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-10-71" name="__codelineno-10-71" href="#__codelineno-10-71"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-72" name="__codelineno-10-72" href="#__codelineno-10-72"></a><span class="w">    </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">adjMat</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-10-73" name="__codelineno-10-73" href="#__codelineno-10-73"></a><span class="w">    </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">adjMat</span><span class="p">[</span><span class="n">j</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-10-74" name="__codelineno-10-74" href="#__codelineno-10-74"></a><span class="p">}</span>
+<a id="__codelineno-10-75" name="__codelineno-10-75" href="#__codelineno-10-75"></a>
+<a id="__codelineno-10-76" name="__codelineno-10-76" href="#__codelineno-10-76"></a><span class="cm">/* 辺を削除 */</span>
+<a id="__codelineno-10-77" name="__codelineno-10-77" href="#__codelineno-10-77"></a><span class="c1">// 引数 i, j は vertices の要素インデックスに対応する</span>
+<a id="__codelineno-10-78" name="__codelineno-10-78" href="#__codelineno-10-78"></a><span class="kt">void</span><span class="w"> </span><span class="nf">removeEdge</span><span class="p">(</span><span class="n">GraphAdjMat</span><span class="w"> </span><span class="o">*</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-79" name="__codelineno-10-79" href="#__codelineno-10-79"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-80" name="__codelineno-10-80" href="#__codelineno-10-80"></a><span class="w">        </span><span class="n">fprintf</span><span class="p">(</span><span class="n">stderr</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;辺インデックスが範囲外であるか、同一です</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">);</span>
+<a id="__codelineno-10-81" name="__codelineno-10-81" href="#__codelineno-10-81"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-10-82" name="__codelineno-10-82" href="#__codelineno-10-82"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-83" name="__codelineno-10-83" href="#__codelineno-10-83"></a><span class="w">    </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">adjMat</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-84" name="__codelineno-10-84" href="#__codelineno-10-84"></a><span class="w">    </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">adjMat</span><span class="p">[</span><span class="n">j</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-85" name="__codelineno-10-85" href="#__codelineno-10-85"></a><span class="p">}</span>
+<a id="__codelineno-10-86" name="__codelineno-10-86" href="#__codelineno-10-86"></a>
+<a id="__codelineno-10-87" name="__codelineno-10-87" href="#__codelineno-10-87"></a><span class="cm">/* 隣接行列を出力 */</span>
+<a id="__codelineno-10-88" name="__codelineno-10-88" href="#__codelineno-10-88"></a><span class="kt">void</span><span class="w"> </span><span class="nf">printGraphAdjMat</span><span class="p">(</span><span class="n">GraphAdjMat</span><span class="w"> </span><span class="o">*</span><span class="n">graph</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-89" name="__codelineno-10-89" href="#__codelineno-10-89"></a><span class="w">    </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;頂点リスト = &quot;</span><span class="p">);</span>
+<a id="__codelineno-10-90" name="__codelineno-10-90" href="#__codelineno-10-90"></a><span class="w">    </span><span class="n">printArray</span><span class="p">(</span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">vertices</span><span class="p">,</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">);</span>
+<a id="__codelineno-10-91" name="__codelineno-10-91" href="#__codelineno-10-91"></a><span class="w">    </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;隣接行列 =</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">);</span>
+<a id="__codelineno-10-92" name="__codelineno-10-92" href="#__codelineno-10-92"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-93" name="__codelineno-10-93" href="#__codelineno-10-93"></a><span class="w">        </span><span class="n">printArray</span><span class="p">(</span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">adjMat</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">);</span>
+<a id="__codelineno-10-94" name="__codelineno-10-94" href="#__codelineno-10-94"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-95" name="__codelineno-10-95" href="#__codelineno-10-95"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_adjacency_matrix.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">GraphAdjMat</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">graph_adjacency_matrix.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 隣接行列に基づく無向グラフクラス */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">GraphAdjMat</span><span class="p">(</span><span class="n">vertices</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">edges</span><span class="p">:</span><span class="w"> </span><span class="n">Array</span><span class="o">&lt;</span><span class="n">IntArray</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">vertices</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">()</span><span class="w"> </span><span class="c1">// 頂点リスト。要素は「頂点値」、インデックスは「頂点インデックス」を表す</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">adjMat</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;&gt;</span><span class="p">()</span><span class="w"> </span><span class="c1">// 隣接行列。行・列のインデックスは「頂点インデックス」に対応</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">    </span><span class="k">init</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">        </span><span class="c1">// 頂点を追加</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">vertex</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">vertices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">            </span><span class="n">addVertex</span><span class="p">(</span><span class="n">vertex</span><span class="p">)</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">        </span><span class="c1">// 辺を追加</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">        </span><span class="c1">// 注意：edges の各要素は頂点インデックスを表し、vertices の要素インデックスに対応する</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">edge</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">            </span><span class="n">addEdge</span><span class="p">(</span><span class="n">edge</span><span class="o">[</span><span class="m">0</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">edge</span><span class="o">[</span><span class="m">1</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w">    </span><span class="cm">/* 頂点数を取得 */</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">size</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">vertices</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a>
+<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="w">    </span><span class="cm">/* 頂点を追加 */</span>
+<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">addVertex</span><span class="p">(</span><span class="n">_val</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span>
+<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a><span class="w">        </span><span class="c1">// 頂点リストに新しい頂点の値を追加</span>
+<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="w">        </span><span class="n">vertices</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">_val</span><span class="p">)</span>
+<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a><span class="w">        </span><span class="c1">// 隣接行列に 1 行追加</span>
+<a id="__codelineno-11-30" name="__codelineno-11-30" href="#__codelineno-11-30"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">newRow</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-32" name="__codelineno-11-32" href="#__codelineno-11-32"></a><span class="w">            </span><span class="n">newRow</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
+<a id="__codelineno-11-33" name="__codelineno-11-33" href="#__codelineno-11-33"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-34" name="__codelineno-11-34" href="#__codelineno-11-34"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">newRow</span><span class="p">)</span>
+<a id="__codelineno-11-35" name="__codelineno-11-35" href="#__codelineno-11-35"></a><span class="w">        </span><span class="c1">// 隣接行列に 1 列追加</span>
+<a id="__codelineno-11-36" name="__codelineno-11-36" href="#__codelineno-11-36"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">row</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">adjMat</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-37" name="__codelineno-11-37" href="#__codelineno-11-37"></a><span class="w">            </span><span class="n">row</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
+<a id="__codelineno-11-38" name="__codelineno-11-38" href="#__codelineno-11-38"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-39" name="__codelineno-11-39" href="#__codelineno-11-39"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-40" name="__codelineno-11-40" href="#__codelineno-11-40"></a>
+<a id="__codelineno-11-41" name="__codelineno-11-41" href="#__codelineno-11-41"></a><span class="w">    </span><span class="cm">/* 頂点を削除 */</span>
+<a id="__codelineno-11-42" name="__codelineno-11-42" href="#__codelineno-11-42"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">removeVertex</span><span class="p">(</span><span class="n">index</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-43" name="__codelineno-11-43" href="#__codelineno-11-43"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
+<a id="__codelineno-11-44" name="__codelineno-11-44" href="#__codelineno-11-44"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">()</span>
+<a id="__codelineno-11-45" name="__codelineno-11-45" href="#__codelineno-11-45"></a><span class="w">        </span><span class="c1">// 頂点リストから index の頂点を削除する</span>
+<a id="__codelineno-11-46" name="__codelineno-11-46" href="#__codelineno-11-46"></a><span class="w">        </span><span class="n">vertices</span><span class="p">.</span><span class="na">removeAt</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
+<a id="__codelineno-11-47" name="__codelineno-11-47" href="#__codelineno-11-47"></a><span class="w">        </span><span class="c1">// 隣接行列で index 行を削除する</span>
+<a id="__codelineno-11-48" name="__codelineno-11-48" href="#__codelineno-11-48"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">.</span><span class="na">removeAt</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
+<a id="__codelineno-11-49" name="__codelineno-11-49" href="#__codelineno-11-49"></a><span class="w">        </span><span class="c1">// 隣接行列で index 列を削除する</span>
+<a id="__codelineno-11-50" name="__codelineno-11-50" href="#__codelineno-11-50"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">row</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">adjMat</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-51" name="__codelineno-11-51" href="#__codelineno-11-51"></a><span class="w">            </span><span class="n">row</span><span class="p">.</span><span class="na">removeAt</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
+<a id="__codelineno-11-52" name="__codelineno-11-52" href="#__codelineno-11-52"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-53" name="__codelineno-11-53" href="#__codelineno-11-53"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-54" name="__codelineno-11-54" href="#__codelineno-11-54"></a>
+<a id="__codelineno-11-55" name="__codelineno-11-55" href="#__codelineno-11-55"></a><span class="w">    </span><span class="cm">/* 辺を追加 */</span>
+<a id="__codelineno-11-56" name="__codelineno-11-56" href="#__codelineno-11-56"></a><span class="w">    </span><span class="c1">// 引数 i, j は vertices の要素インデックスに対応する</span>
+<a id="__codelineno-11-57" name="__codelineno-11-57" href="#__codelineno-11-57"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">addEdge</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-58" name="__codelineno-11-58" href="#__codelineno-11-58"></a><span class="w">        </span><span class="c1">// インデックスの範囲外と等値の処理</span>
+<a id="__codelineno-11-59" name="__codelineno-11-59" href="#__codelineno-11-59"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
+<a id="__codelineno-11-60" name="__codelineno-11-60" href="#__codelineno-11-60"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">()</span>
+<a id="__codelineno-11-61" name="__codelineno-11-61" href="#__codelineno-11-61"></a><span class="w">        </span><span class="c1">// 無向グラフでは、隣接行列は主対角線に関して対称、すなわち (i, j) == (j, i) を満たす</span>
+<a id="__codelineno-11-62" name="__codelineno-11-62" href="#__codelineno-11-62"></a><span class="w">        </span><span class="n">adjMat</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-11-63" name="__codelineno-11-63" href="#__codelineno-11-63"></a><span class="w">        </span><span class="n">adjMat</span><span class="o">[</span><span class="n">j</span><span class="o">][</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-11-64" name="__codelineno-11-64" href="#__codelineno-11-64"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-65" name="__codelineno-11-65" href="#__codelineno-11-65"></a>
+<a id="__codelineno-11-66" name="__codelineno-11-66" href="#__codelineno-11-66"></a><span class="w">    </span><span class="cm">/* 辺を削除 */</span>
+<a id="__codelineno-11-67" name="__codelineno-11-67" href="#__codelineno-11-67"></a><span class="w">    </span><span class="c1">// 引数 i, j は vertices の要素インデックスに対応する</span>
+<a id="__codelineno-11-68" name="__codelineno-11-68" href="#__codelineno-11-68"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">removeEdge</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-69" name="__codelineno-11-69" href="#__codelineno-11-69"></a><span class="w">        </span><span class="c1">// インデックスの範囲外と等値の処理</span>
+<a id="__codelineno-11-70" name="__codelineno-11-70" href="#__codelineno-11-70"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
+<a id="__codelineno-11-71" name="__codelineno-11-71" href="#__codelineno-11-71"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">()</span>
+<a id="__codelineno-11-72" name="__codelineno-11-72" href="#__codelineno-11-72"></a><span class="w">        </span><span class="n">adjMat</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-11-73" name="__codelineno-11-73" href="#__codelineno-11-73"></a><span class="w">        </span><span class="n">adjMat</span><span class="o">[</span><span class="n">j</span><span class="o">][</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-11-74" name="__codelineno-11-74" href="#__codelineno-11-74"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-75" name="__codelineno-11-75" href="#__codelineno-11-75"></a>
+<a id="__codelineno-11-76" name="__codelineno-11-76" href="#__codelineno-11-76"></a><span class="w">    </span><span class="cm">/* 隣接行列を出力 */</span>
+<a id="__codelineno-11-77" name="__codelineno-11-77" href="#__codelineno-11-77"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-78" name="__codelineno-11-78" href="#__codelineno-11-78"></a><span class="w">        </span><span class="n">print</span><span class="p">(</span><span class="s">&quot;頂点リスト = &quot;</span><span class="p">)</span>
+<a id="__codelineno-11-79" name="__codelineno-11-79" href="#__codelineno-11-79"></a><span class="w">        </span><span class="n">println</span><span class="p">(</span><span class="n">vertices</span><span class="p">)</span>
+<a id="__codelineno-11-80" name="__codelineno-11-80" href="#__codelineno-11-80"></a><span class="w">        </span><span class="n">println</span><span class="p">(</span><span class="s">&quot;隣接行列 =&quot;</span><span class="p">)</span>
+<a id="__codelineno-11-81" name="__codelineno-11-81" href="#__codelineno-11-81"></a><span class="w">        </span><span class="n">printMatrix</span><span class="p">(</span><span class="n">adjMat</span><span class="p">)</span>
+<a id="__codelineno-11-82" name="__codelineno-11-82" href="#__codelineno-11-82"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-83" name="__codelineno-11-83" href="#__codelineno-11-83"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_adjacency_matrix.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">GraphAdjMat</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">graph_adjacency_matrix.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 隣接行列で実装した無向グラフクラス ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">GraphAdjMat</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">vertices</span><span class="p">,</span><span class="w"> </span><span class="n">edges</span><span class="p">)</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">    </span><span class="c1">### コンストラクタ ###</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">    </span><span class="c1"># 頂点リスト。要素は「頂点値」、インデックスは「頂点インデックス」を表す</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">    </span><span class="vi">@vertices</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">    </span><span class="c1"># 隣接行列。行・列のインデックスは「頂点インデックス」に対応</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">    </span><span class="vi">@adj_mat</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">    </span><span class="c1"># 頂点を追加</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">    </span><span class="n">vertices</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">val</span><span class="o">|</span><span class="w"> </span><span class="n">add_vertex</span><span class="p">(</span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">    </span><span class="c1"># 辺を追加</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">    </span><span class="c1"># 注意：edges の各要素は頂点インデックスを表し、vertices の要素インデックスに対応する</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">    </span><span class="n">edges</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">e</span><span class="o">|</span><span class="w"> </span><span class="n">add_edge</span><span class="p">(</span><span class="n">e</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">e</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">  </span><span class="c1">### 頂点数を取得 ###</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">size</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w">    </span><span class="vi">@vertices</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w">  </span><span class="c1">### 頂点を追加 ###</span>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">add_vertex</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="w">    </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span>
+<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a><span class="w">    </span><span class="c1"># 頂点リストに新しい頂点の値を追加</span>
+<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="w">    </span><span class="vi">@vertices</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span>
+<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a><span class="w">    </span><span class="c1"># 隣接行列に 1 行追加</span>
+<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a><span class="w">    </span><span class="n">new_row</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a><span class="w">    </span><span class="vi">@adj_mat</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">new_row</span>
+<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a><span class="w">    </span><span class="c1"># 隣接行列に 1 列追加</span>
+<a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a><span class="w">    </span><span class="vi">@adj_mat</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">row</span><span class="o">|</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-12-31" name="__codelineno-12-31" href="#__codelineno-12-31"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-32" name="__codelineno-12-32" href="#__codelineno-12-32"></a>
+<a id="__codelineno-12-33" name="__codelineno-12-33" href="#__codelineno-12-33"></a><span class="w">  </span><span class="c1">### 頂点を削除 ###</span>
+<a id="__codelineno-12-34" name="__codelineno-12-34" href="#__codelineno-12-34"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">remove_vertex</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
+<a id="__codelineno-12-35" name="__codelineno-12-35" href="#__codelineno-12-35"></a><span class="w">    </span><span class="k">raise</span><span class="w"> </span><span class="no">IndexError</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span>
+<a id="__codelineno-12-36" name="__codelineno-12-36" href="#__codelineno-12-36"></a>
+<a id="__codelineno-12-37" name="__codelineno-12-37" href="#__codelineno-12-37"></a><span class="w">    </span><span class="c1"># 頂点リストから index の頂点を削除する</span>
+<a id="__codelineno-12-38" name="__codelineno-12-38" href="#__codelineno-12-38"></a><span class="w">    </span><span class="vi">@vertices</span><span class="o">.</span><span class="n">delete_at</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
+<a id="__codelineno-12-39" name="__codelineno-12-39" href="#__codelineno-12-39"></a><span class="w">    </span><span class="c1"># 隣接行列で index 行を削除する</span>
+<a id="__codelineno-12-40" name="__codelineno-12-40" href="#__codelineno-12-40"></a><span class="w">    </span><span class="vi">@adj_mat</span><span class="o">.</span><span class="n">delete_at</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
+<a id="__codelineno-12-41" name="__codelineno-12-41" href="#__codelineno-12-41"></a><span class="w">    </span><span class="c1"># 隣接行列で index 列を削除する</span>
+<a id="__codelineno-12-42" name="__codelineno-12-42" href="#__codelineno-12-42"></a><span class="w">    </span><span class="vi">@adj_mat</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">row</span><span class="o">|</span><span class="w"> </span><span class="n">row</span><span class="o">.</span><span class="n">delete_at</span><span class="p">(</span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-12-43" name="__codelineno-12-43" href="#__codelineno-12-43"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-44" name="__codelineno-12-44" href="#__codelineno-12-44"></a>
+<a id="__codelineno-12-45" name="__codelineno-12-45" href="#__codelineno-12-45"></a><span class="w">  </span><span class="c1">### 辺を追加 ###</span>
+<a id="__codelineno-12-46" name="__codelineno-12-46" href="#__codelineno-12-46"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">add_edge</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
+<a id="__codelineno-12-47" name="__codelineno-12-47" href="#__codelineno-12-47"></a><span class="w">    </span><span class="c1"># パラメータ i, j は vertices の要素インデックスに対応する</span>
+<a id="__codelineno-12-48" name="__codelineno-12-48" href="#__codelineno-12-48"></a><span class="w">    </span><span class="c1"># 範囲外と同値の場合の処理</span>
+<a id="__codelineno-12-49" name="__codelineno-12-49" href="#__codelineno-12-49"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">j</span>
+<a id="__codelineno-12-50" name="__codelineno-12-50" href="#__codelineno-12-50"></a><span class="w">      </span><span class="k">raise</span><span class="w"> </span><span class="no">IndexError</span>
+<a id="__codelineno-12-51" name="__codelineno-12-51" href="#__codelineno-12-51"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-52" name="__codelineno-12-52" href="#__codelineno-12-52"></a><span class="w">    </span><span class="c1"># 無向グラフでは、隣接行列は主対角線に関して対称、すなわち (i, j) == (j, i) を満たす</span>
+<a id="__codelineno-12-53" name="__codelineno-12-53" href="#__codelineno-12-53"></a><span class="w">    </span><span class="vi">@adj_mat</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-54" name="__codelineno-12-54" href="#__codelineno-12-54"></a><span class="w">    </span><span class="vi">@adj_mat</span><span class="o">[</span><span class="n">j</span><span class="o">][</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-55" name="__codelineno-12-55" href="#__codelineno-12-55"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-56" name="__codelineno-12-56" href="#__codelineno-12-56"></a>
+<a id="__codelineno-12-57" name="__codelineno-12-57" href="#__codelineno-12-57"></a><span class="w">  </span><span class="c1">### 辺を削除 ###</span>
+<a id="__codelineno-12-58" name="__codelineno-12-58" href="#__codelineno-12-58"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">remove_edge</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
+<a id="__codelineno-12-59" name="__codelineno-12-59" href="#__codelineno-12-59"></a><span class="w">    </span><span class="c1"># パラメータ i, j は vertices の要素インデックスに対応する</span>
+<a id="__codelineno-12-60" name="__codelineno-12-60" href="#__codelineno-12-60"></a><span class="w">    </span><span class="c1"># 範囲外と同値の場合の処理</span>
+<a id="__codelineno-12-61" name="__codelineno-12-61" href="#__codelineno-12-61"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">j</span>
+<a id="__codelineno-12-62" name="__codelineno-12-62" href="#__codelineno-12-62"></a><span class="w">      </span><span class="k">raise</span><span class="w"> </span><span class="no">IndexError</span>
+<a id="__codelineno-12-63" name="__codelineno-12-63" href="#__codelineno-12-63"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-64" name="__codelineno-12-64" href="#__codelineno-12-64"></a><span class="w">    </span><span class="vi">@adj_mat</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-12-65" name="__codelineno-12-65" href="#__codelineno-12-65"></a><span class="w">    </span><span class="vi">@adj_mat</span><span class="o">[</span><span class="n">j</span><span class="o">][</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-12-66" name="__codelineno-12-66" href="#__codelineno-12-66"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-67" name="__codelineno-12-67" href="#__codelineno-12-67"></a>
+<a id="__codelineno-12-68" name="__codelineno-12-68" href="#__codelineno-12-68"></a><span class="w">  </span><span class="c1">### 隣接行列を出力 ###</span>
+<a id="__codelineno-12-69" name="__codelineno-12-69" href="#__codelineno-12-69"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="n">__print__</span>
+<a id="__codelineno-12-70" name="__codelineno-12-70" href="#__codelineno-12-70"></a><span class="w">    </span><span class="nb">puts</span><span class="w"> </span><span class="s2">&quot;頂点リスト = </span><span class="si">#{</span><span class="vi">@vertices</span><span class="si">}</span><span class="s2">&quot;</span>
+<a id="__codelineno-12-71" name="__codelineno-12-71" href="#__codelineno-12-71"></a><span class="w">    </span><span class="nb">puts</span><span class="w"> </span><span class="s1">&#39;隣接行列 =&#39;</span>
+<a id="__codelineno-12-72" name="__codelineno-12-72" href="#__codelineno-12-72"></a><span class="w">    </span><span class="n">print_matrix</span><span class="p">(</span><span class="vi">@adj_mat</span><span class="p">)</span>
+<a id="__codelineno-12-73" name="__codelineno-12-73" href="#__codelineno-12-73"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-74" name="__codelineno-12-74" href="#__codelineno-12-74"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20GraphAdjMat%3A%0A%0A%20%20%20%20def%20__init__%28self%2C%20vertices%3A%20list%5Bint%5D%2C%20edges%3A%20list%5Blist%5Bint%5D%5D%29%3A%0A%20%20%20%20%20%20%20%20self.vertices%3A%20list%5Bint%5D%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20self.adj_mat%3A%20list%5Blist%5Bint%5D%5D%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20for%20val%20in%20vertices%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_vertex%28val%29%0A%20%20%20%20%20%20%20%20for%20e%20in%20edges%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_edge%28e%5B0%5D%2C%20e%5B1%5D%29%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%20len%28self.vertices%29%0A%0A%20%20%20%20def%20add_vertex%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20n%20%3D%20self.size%28%29%0A%20%20%20%20%20%20%20%20self.vertices.append%28val%29%0A%20%20%20%20%20%20%20%20new_row%20%3D%20%5B0%5D%20%2A%20n%0A%20%20%20%20%20%20%20%20self.adj_mat.append%28new_row%29%0A%20%20%20%20%20%20%20%20for%20row%20in%20self.adj_mat%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20row.append%280%29%0A%0A%20%20%20%20def%20remove_vertex%28self%2C%20index%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20if%20index%20%3E%3D%20self.size%28%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%29%0A%20%20%20%20%20%20%20%20self.vertices.pop%28index%29%0A%20%20%20%20%20%20%20%20self.adj_mat.pop%28index%29%0A%20%20%20%20%20%20%20%20for%20row%20in%20self.adj_mat%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20row.pop%28index%29%0A%0A%20%20%20%20def%20add_edge%28self%2C%20i%3A%20int%2C%20j%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20if%20i%20%3C%200%20or%20j%20%3C%200%20or%20i%20%3E%3D%20self.size%28%29%20or%20%28j%20%3E%3D%20self.size%28%29%29%20or%20%28i%20%3D%3D%20j%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%29%0A%20%20%20%20%20%20%20%20self.adj_mat%5Bi%5D%5Bj%5D%20%3D%201%0A%20%20%20%20%20%20%20%20self.adj_mat%5Bj%5D%5Bi%5D%20%3D%201%0A%0A%20%20%20%20def%20remove_edge%28self%2C%20i%3A%20int%2C%20j%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20if%20i%20%3C%200%20or%20j%20%3C%200%20or%20i%20%3E%3D%20self.size%28%29%20or%20%28j%20%3E%3D%20self.size%28%29%29%20or%20%28i%20%3D%3D%20j%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%29%0A%20%20%20%20%20%20%20%20self.adj_mat%5Bi%5D%5Bj%5D%20%3D%200%0A%20%20%20%20%20%20%20%20self.adj_mat%5Bj%5D%5Bi%5D%20%3D%200%0Aif%20__name__%20%3D%3D%20%27__main__%27%3A%0A%20%20%20%20vertices%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20edges%20%3D%20%5B%5B0%2C%201%5D%2C%20%5B0%2C%203%5D%2C%20%5B1%2C%202%5D%2C%20%5B2%2C%203%5D%2C%20%5B2%2C%204%5D%2C%20%5B3%2C%204%5D%5D%0A%20%20%20%20graph%20%3D%20GraphAdjMat%28vertices%2C%20edges%29%0A%20%20%20%20graph.add_edge%280%2C%202%29%0A%20%20%20%20graph.remove_edge%280%2C%201%29%0A%20%20%20%20graph.add_vertex%286%29%0A%20%20%20%20graph.remove_vertex%281%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20GraphAdjMat%3A%0A%0A%20%20%20%20def%20__init__%28self%2C%20vertices%3A%20list%5Bint%5D%2C%20edges%3A%20list%5Blist%5Bint%5D%5D%29%3A%0A%20%20%20%20%20%20%20%20self.vertices%3A%20list%5Bint%5D%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20self.adj_mat%3A%20list%5Blist%5Bint%5D%5D%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20for%20val%20in%20vertices%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_vertex%28val%29%0A%20%20%20%20%20%20%20%20for%20e%20in%20edges%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_edge%28e%5B0%5D%2C%20e%5B1%5D%29%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%20len%28self.vertices%29%0A%0A%20%20%20%20def%20add_vertex%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20n%20%3D%20self.size%28%29%0A%20%20%20%20%20%20%20%20self.vertices.append%28val%29%0A%20%20%20%20%20%20%20%20new_row%20%3D%20%5B0%5D%20%2A%20n%0A%20%20%20%20%20%20%20%20self.adj_mat.append%28new_row%29%0A%20%20%20%20%20%20%20%20for%20row%20in%20self.adj_mat%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20row.append%280%29%0A%0A%20%20%20%20def%20remove_vertex%28self%2C%20index%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20if%20index%20%3E%3D%20self.size%28%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%29%0A%20%20%20%20%20%20%20%20self.vertices.pop%28index%29%0A%20%20%20%20%20%20%20%20self.adj_mat.pop%28index%29%0A%20%20%20%20%20%20%20%20for%20row%20in%20self.adj_mat%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20row.pop%28index%29%0A%0A%20%20%20%20def%20add_edge%28self%2C%20i%3A%20int%2C%20j%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20if%20i%20%3C%200%20or%20j%20%3C%200%20or%20i%20%3E%3D%20self.size%28%29%20or%20%28j%20%3E%3D%20self.size%28%29%29%20or%20%28i%20%3D%3D%20j%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%29%0A%20%20%20%20%20%20%20%20self.adj_mat%5Bi%5D%5Bj%5D%20%3D%201%0A%20%20%20%20%20%20%20%20self.adj_mat%5Bj%5D%5Bi%5D%20%3D%201%0A%0A%20%20%20%20def%20remove_edge%28self%2C%20i%3A%20int%2C%20j%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20if%20i%20%3C%200%20or%20j%20%3C%200%20or%20i%20%3E%3D%20self.size%28%29%20or%20%28j%20%3E%3D%20self.size%28%29%29%20or%20%28i%20%3D%3D%20j%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%29%0A%20%20%20%20%20%20%20%20self.adj_mat%5Bi%5D%5Bj%5D%20%3D%200%0A%20%20%20%20%20%20%20%20self.adj_mat%5Bj%5D%5Bi%5D%20%3D%200%0Aif%20__name__%20%3D%3D%20%27__main__%27%3A%0A%20%20%20%20vertices%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20edges%20%3D%20%5B%5B0%2C%201%5D%2C%20%5B0%2C%203%5D%2C%20%5B1%2C%202%5D%2C%20%5B2%2C%203%5D%2C%20%5B2%2C%204%5D%2C%20%5B3%2C%204%5D%5D%0A%20%20%20%20graph%20%3D%20GraphAdjMat%28vertices%2C%20edges%29%0A%20%20%20%20graph.add_edge%280%2C%202%29%0A%20%20%20%20graph.remove_edge%280%2C%201%29%0A%20%20%20%20graph.add_vertex%286%29%0A%20%20%20%20graph.remove_vertex%281%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 <h2 id="922">9.2.2 &nbsp; 隣接リストに基づく実装<a class="headerlink" href="#922" title="Permanent link">&para;</a></h2>
-<p>総計<span class="arithmatex">\(n\)</span>個の頂点と<span class="arithmatex">\(m\)</span>個の辺を持つ無向グラフが与えられた場合、さまざまな操作は下図のように実装できます。</p>
+<p>無向グラフの頂点総数を <span class="arithmatex">\(n\)</span>、辺総数を <span class="arithmatex">\(m\)</span> とすると、各種操作は次図の方法で実装できます。</p>
 <ul>
-<li><strong>辺の追加</strong>：対応する頂点の連結リストの末尾に辺を追加するだけで、<span class="arithmatex">\(O(1)\)</span>時間を使用します。無向グラフであるため、両方向に同時に辺を追加する必要があります。</li>
-<li><strong>辺の削除</strong>：対応する頂点の連結リスト内で指定された辺を見つけて削除し、<span class="arithmatex">\(O(m)\)</span>時間を使用します。無向グラフでは、両方向の辺を同時に削除する必要があります。</li>
-<li><strong>頂点の追加</strong>：隣接リストに連結リストを追加し、新しい頂点をリストのヘッドノードにし、<span class="arithmatex">\(O(1)\)</span>時間を使用します。</li>
-<li><strong>頂点の削除</strong>：隣接リスト全体を走査し、指定された頂点を含むすべての辺を削除する必要があり、<span class="arithmatex">\(O(n + m)\)</span>時間を使用します。</li>
-<li><strong>初期化</strong>：隣接リストに<span class="arithmatex">\(n\)</span>個の頂点と<span class="arithmatex">\(2m\)</span>個の辺を作成し、<span class="arithmatex">\(O(n + m)\)</span>時間を使用します。</li>
+<li><strong>辺の追加</strong>：頂点に対応する連結リストの末尾に辺を追加すればよく、<span class="arithmatex">\(O(1)\)</span> 時間です。無向グラフなので、2 方向の辺を同時に追加する必要があります。</li>
+<li><strong>辺の削除</strong>：頂点に対応する連結リストから指定した辺を探して削除するため、<span class="arithmatex">\(O(m)\)</span> 時間です。無向グラフでは、2 方向の辺を同時に削除する必要があります。</li>
+<li><strong>頂点の追加</strong>：隣接リストに 1 つの連結リストを追加し、新しい頂点をその連結リストの先頭ノードとするため、<span class="arithmatex">\(O(1)\)</span> 時間です。</li>
+<li><strong>頂点の削除</strong>：隣接リスト全体を走査し、指定した頂点を含むすべての辺を削除する必要があるため、<span class="arithmatex">\(O(n + m)\)</span> 時間です。</li>
+<li><strong>初期化</strong>：隣接リストに <span class="arithmatex">\(n\)</span> 個の頂点と <span class="arithmatex">\(2m\)</span> 本の辺を作成するため、<span class="arithmatex">\(O(n + m)\)</span> 時間です。</li>
 </ul>
 <div class="tabbed-set tabbed-alternate" data-tabs="3:5"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">隣接リストの初期化</label><label for="__tabbed_3_2">辺の追加</label><label for="__tabbed_3_3">辺の削除</label><label for="__tabbed_3_4">頂点の追加</label><label for="__tabbed_3_5">頂点の削除</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="隣接リストでの初期化、辺の追加と削除、頂点の追加と削除" class="animation-figure" src="../graph_operations.assets/adjacency_list_step1_initialization.png" /></p>
+<p><img alt="隣接リストの初期化、辺の追加と削除、頂点の追加と削除" class="animation-figure" src="../graph_operations.assets/adjacency_list_step1_initialization.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="adjacency_list_add_edge" class="animation-figure" src="../graph_operations.assets/adjacency_list_step2_add_edge.png" /></p>
@@ -4726,14 +5591,14 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 9-8 &nbsp; 隣接リストでの初期化、辺の追加と削除、頂点の追加と削除 </p>
+<p align="center"> 図 9-8 &nbsp; 隣接リストの初期化、辺の追加と削除、頂点の追加と削除 </p>
 
-<p>以下は隣接リストのコード実装です。上図と比較して、実際のコードには以下の違いがあります。</p>
+<p>以下は隣接リストのコード実装です。上図と比べると、実際のコードには次の違いがあります。</p>
 <ul>
-<li>頂点の追加と削除の便宜、およびコードの簡素化のため、連結リストの代わりにリスト（動的配列）を使用します。</li>
-<li>ハッシュテーブルを使用して隣接リストを格納し、<code>key</code>が頂点インスタンス、<code>value</code>がその頂点の隣接頂点のリスト（連結リスト）です。</li>
+<li>頂点の追加と削除を容易にし、コードを簡潔にするため、連結リストの代わりにリスト（動的配列）を使用しています。</li>
+<li>ハッシュテーブルを用いて隣接リストを格納しており、<code>key</code> は頂点インスタンス、<code>value</code> はその頂点に隣接する頂点のリスト（連結リスト）です。</li>
 </ul>
-<p>さらに、隣接リストで頂点を表現するために<code>Vertex</code>クラスを使用します。その理由は：隣接行列のようにリストインデックスを使用して異なる頂点を区別する場合、インデックス<span class="arithmatex">\(i\)</span>の頂点を削除したい場合、隣接リスト全体を走査し、<span class="arithmatex">\(i\)</span>より大きいすべてのインデックスを1つずつ減少させる必要があり、これは非常に非効率的です。しかし、各頂点が一意の<code>Vertex</code>インスタンスである場合、頂点を削除しても他の頂点に変更を加える必要がありません。</p>
+<p>また、隣接リストでは頂点を表すために <code>Vertex</code> クラスを使用しています。その理由は、もし隣接行列と同様にリストのインデックスで異なる頂点を区別すると、インデックス <span class="arithmatex">\(i\)</span> の頂点を削除する場合、隣接リスト全体を走査して、<span class="arithmatex">\(i\)</span> より大きいすべてのインデックスを <span class="arithmatex">\(1\)</span> 減らす必要があり、効率が非常に低いためです。これに対して、各頂点が一意な <code>Vertex</code> インスタンスであれば、ある頂点を削除しても他の頂点を変更する必要はありません。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="4:13"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
@@ -4742,7 +5607,7 @@
 <a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>
 <a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">edges</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]]):</span>
 <a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
-<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>        <span class="c1"># 隣接リスト、キー: 頂点、値: その頂点の隣接する全頂点</span>
+<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>        <span class="c1"># 隣接リスト。key は頂点、value はその頂点に隣接する全頂点</span>
 <a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">[</span><span class="n">Vertex</span><span class="p">,</span> <span class="nb">list</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]]()</span>
 <a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>        <span class="c1"># すべての頂点と辺を追加</span>
 <a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>        <span class="k">for</span> <span class="n">edge</span> <span class="ow">in</span> <span class="n">edges</span><span class="p">:</span>
@@ -4774,16 +5639,16 @@
 <a id="__codelineno-13-35" name="__codelineno-13-35" href="#__codelineno-13-35"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;頂点を追加&quot;&quot;&quot;</span>
 <a id="__codelineno-13-36" name="__codelineno-13-36" href="#__codelineno-13-36"></a>        <span class="k">if</span> <span class="n">vet</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">:</span>
 <a id="__codelineno-13-37" name="__codelineno-13-37" href="#__codelineno-13-37"></a>            <span class="k">return</span>
-<a id="__codelineno-13-38" name="__codelineno-13-38" href="#__codelineno-13-38"></a>        <span class="c1"># 隣接リストに新しい連結リストを追加</span>
+<a id="__codelineno-13-38" name="__codelineno-13-38" href="#__codelineno-13-38"></a>        <span class="c1"># 隣接リストに新しいリストを追加</span>
 <a id="__codelineno-13-39" name="__codelineno-13-39" href="#__codelineno-13-39"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">[</span><span class="n">vet</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
 <a id="__codelineno-13-40" name="__codelineno-13-40" href="#__codelineno-13-40"></a>
 <a id="__codelineno-13-41" name="__codelineno-13-41" href="#__codelineno-13-41"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">remove_vertex</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">vet</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">):</span>
 <a id="__codelineno-13-42" name="__codelineno-13-42" href="#__codelineno-13-42"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;頂点を削除&quot;&quot;&quot;</span>
 <a id="__codelineno-13-43" name="__codelineno-13-43" href="#__codelineno-13-43"></a>        <span class="k">if</span> <span class="n">vet</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">:</span>
 <a id="__codelineno-13-44" name="__codelineno-13-44" href="#__codelineno-13-44"></a>            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">()</span>
-<a id="__codelineno-13-45" name="__codelineno-13-45" href="#__codelineno-13-45"></a>        <span class="c1"># 隣接リストから頂点vetに対応する連結リストを削除</span>
+<a id="__codelineno-13-45" name="__codelineno-13-45" href="#__codelineno-13-45"></a>        <span class="c1"># 隣接リストから頂点 vet に対応するリストを削除</span>
 <a id="__codelineno-13-46" name="__codelineno-13-46" href="#__codelineno-13-46"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>
-<a id="__codelineno-13-47" name="__codelineno-13-47" href="#__codelineno-13-47"></a>        <span class="c1"># 他の頂点の連結リストを走査し、vetを含むすべての辺を削除</span>
+<a id="__codelineno-13-47" name="__codelineno-13-47" href="#__codelineno-13-47"></a>        <span class="c1"># 他の頂点のリストを走査し、vet を含むすべての辺を削除</span>
 <a id="__codelineno-13-48" name="__codelineno-13-48" href="#__codelineno-13-48"></a>        <span class="k">for</span> <span class="n">vertex</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">:</span>
 <a id="__codelineno-13-49" name="__codelineno-13-49" href="#__codelineno-13-49"></a>            <span class="k">if</span> <span class="n">vet</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">[</span><span class="n">vertex</span><span class="p">]:</span>
 <a id="__codelineno-13-50" name="__codelineno-13-50" href="#__codelineno-13-50"></a>                <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">[</span><span class="n">vertex</span><span class="p">]</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>
@@ -4800,10 +5665,10 @@
 <div class="highlight"><span class="filename">graph_adjacency_list.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 隣接リストに基づく無向グラフクラス */</span>
 <a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">GraphAdjList</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
-<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="c1">// 隣接リスト、キー：頂点、値：その頂点のすべての隣接頂点</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="c1">// 隣接リスト。key は頂点、value はその頂点に隣接する全頂点</span>
 <a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="n">unordered_map</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;&gt;</span><span class="w"> </span><span class="n">adjList</span><span class="p">;</span>
 <a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>
-<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">    </span><span class="cm">/* ベクターから指定されたノードを削除 */</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">    </span><span class="cm">/* vector 内の指定ノードを削除 */</span>
 <a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">vec</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">vec</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">vec</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
@@ -4831,7 +5696,7 @@
 <a id="__codelineno-14-32" name="__codelineno-14-32" href="#__codelineno-14-32"></a><span class="w">    </span><span class="cm">/* 辺を追加 */</span>
 <a id="__codelineno-14-33" name="__codelineno-14-33" href="#__codelineno-14-33"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">addEdge</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet1</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-34" name="__codelineno-14-34" href="#__codelineno-14-34"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="n">count</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="n">count</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">vet1</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span>
-<a id="__codelineno-14-35" name="__codelineno-14-35" href="#__codelineno-14-35"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">invalid_argument</span><span class="p">(</span><span class="s">&quot;Vertex does not exist&quot;</span><span class="p">);</span>
+<a id="__codelineno-14-35" name="__codelineno-14-35" href="#__codelineno-14-35"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">invalid_argument</span><span class="p">(</span><span class="s">&quot;頂点が存在しません&quot;</span><span class="p">);</span>
 <a id="__codelineno-14-36" name="__codelineno-14-36" href="#__codelineno-14-36"></a><span class="w">        </span><span class="c1">// 辺 vet1 - vet2 を追加</span>
 <a id="__codelineno-14-37" name="__codelineno-14-37" href="#__codelineno-14-37"></a><span class="w">        </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet1</span><span class="p">].</span><span class="n">push_back</span><span class="p">(</span><span class="n">vet2</span><span class="p">);</span>
 <a id="__codelineno-14-38" name="__codelineno-14-38" href="#__codelineno-14-38"></a><span class="w">        </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet2</span><span class="p">].</span><span class="n">push_back</span><span class="p">(</span><span class="n">vet1</span><span class="p">);</span>
@@ -4840,7 +5705,7 @@
 <a id="__codelineno-14-41" name="__codelineno-14-41" href="#__codelineno-14-41"></a><span class="w">    </span><span class="cm">/* 辺を削除 */</span>
 <a id="__codelineno-14-42" name="__codelineno-14-42" href="#__codelineno-14-42"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">removeEdge</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet1</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-43" name="__codelineno-14-43" href="#__codelineno-14-43"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="n">count</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="n">count</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">vet1</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span>
-<a id="__codelineno-14-44" name="__codelineno-14-44" href="#__codelineno-14-44"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">invalid_argument</span><span class="p">(</span><span class="s">&quot;Vertex does not exist&quot;</span><span class="p">);</span>
+<a id="__codelineno-14-44" name="__codelineno-14-44" href="#__codelineno-14-44"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">invalid_argument</span><span class="p">(</span><span class="s">&quot;頂点が存在しません&quot;</span><span class="p">);</span>
 <a id="__codelineno-14-45" name="__codelineno-14-45" href="#__codelineno-14-45"></a><span class="w">        </span><span class="c1">// 辺 vet1 - vet2 を削除</span>
 <a id="__codelineno-14-46" name="__codelineno-14-46" href="#__codelineno-14-46"></a><span class="w">        </span><span class="n">remove</span><span class="p">(</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet1</span><span class="p">],</span><span class="w"> </span><span class="n">vet2</span><span class="p">);</span>
 <a id="__codelineno-14-47" name="__codelineno-14-47" href="#__codelineno-14-47"></a><span class="w">        </span><span class="n">remove</span><span class="p">(</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet2</span><span class="p">],</span><span class="w"> </span><span class="n">vet1</span><span class="p">);</span>
@@ -4850,23 +5715,23 @@
 <a id="__codelineno-14-51" name="__codelineno-14-51" href="#__codelineno-14-51"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">addVertex</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-52" name="__codelineno-14-52" href="#__codelineno-14-52"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">adjList</span><span class="p">.</span><span class="n">count</span><span class="p">(</span><span class="n">vet</span><span class="p">))</span>
 <a id="__codelineno-14-53" name="__codelineno-14-53" href="#__codelineno-14-53"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-14-54" name="__codelineno-14-54" href="#__codelineno-14-54"></a><span class="w">        </span><span class="c1">// 隣接リストに新しい連結リストを追加</span>
+<a id="__codelineno-14-54" name="__codelineno-14-54" href="#__codelineno-14-54"></a><span class="w">        </span><span class="c1">// 隣接リストに新しいリストを追加</span>
 <a id="__codelineno-14-55" name="__codelineno-14-55" href="#__codelineno-14-55"></a><span class="w">        </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="p">();</span>
 <a id="__codelineno-14-56" name="__codelineno-14-56" href="#__codelineno-14-56"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-57" name="__codelineno-14-57" href="#__codelineno-14-57"></a>
 <a id="__codelineno-14-58" name="__codelineno-14-58" href="#__codelineno-14-58"></a><span class="w">    </span><span class="cm">/* 頂点を削除 */</span>
 <a id="__codelineno-14-59" name="__codelineno-14-59" href="#__codelineno-14-59"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">removeVertex</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-60" name="__codelineno-14-60" href="#__codelineno-14-60"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="n">count</span><span class="p">(</span><span class="n">vet</span><span class="p">))</span>
-<a id="__codelineno-14-61" name="__codelineno-14-61" href="#__codelineno-14-61"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">invalid_argument</span><span class="p">(</span><span class="s">&quot;Vertex does not exist&quot;</span><span class="p">);</span>
-<a id="__codelineno-14-62" name="__codelineno-14-62" href="#__codelineno-14-62"></a><span class="w">        </span><span class="c1">// 隣接リストから頂点vetに対応する連結リストを削除</span>
+<a id="__codelineno-14-61" name="__codelineno-14-61" href="#__codelineno-14-61"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">invalid_argument</span><span class="p">(</span><span class="s">&quot;頂点が存在しません&quot;</span><span class="p">);</span>
+<a id="__codelineno-14-62" name="__codelineno-14-62" href="#__codelineno-14-62"></a><span class="w">        </span><span class="c1">// 隣接リストから頂点 vet に対応するリストを削除</span>
 <a id="__codelineno-14-63" name="__codelineno-14-63" href="#__codelineno-14-63"></a><span class="w">        </span><span class="n">adjList</span><span class="p">.</span><span class="n">erase</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span>
-<a id="__codelineno-14-64" name="__codelineno-14-64" href="#__codelineno-14-64"></a><span class="w">        </span><span class="c1">// 他の頂点の連結リストを走査し、vetを含むすべての辺を削除</span>
+<a id="__codelineno-14-64" name="__codelineno-14-64" href="#__codelineno-14-64"></a><span class="w">        </span><span class="c1">// 他の頂点のリストを走査し、vet を含むすべての辺を削除</span>
 <a id="__codelineno-14-65" name="__codelineno-14-65" href="#__codelineno-14-65"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="o">&amp;</span><span class="n">adj</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">adjList</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-66" name="__codelineno-14-66" href="#__codelineno-14-66"></a><span class="w">            </span><span class="n">remove</span><span class="p">(</span><span class="n">adj</span><span class="p">.</span><span class="n">second</span><span class="p">,</span><span class="w"> </span><span class="n">vet</span><span class="p">);</span>
 <a id="__codelineno-14-67" name="__codelineno-14-67" href="#__codelineno-14-67"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-14-68" name="__codelineno-14-68" href="#__codelineno-14-68"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-69" name="__codelineno-14-69" href="#__codelineno-14-69"></a>
-<a id="__codelineno-14-70" name="__codelineno-14-70" href="#__codelineno-14-70"></a><span class="w">    </span><span class="cm">/* 隣接リストを印刷 */</span>
+<a id="__codelineno-14-70" name="__codelineno-14-70" href="#__codelineno-14-70"></a><span class="w">    </span><span class="cm">/* 隣接リストを出力 */</span>
 <a id="__codelineno-14-71" name="__codelineno-14-71" href="#__codelineno-14-71"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-72" name="__codelineno-14-72" href="#__codelineno-14-72"></a><span class="w">        </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;隣接リスト =&quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
 <a id="__codelineno-14-73" name="__codelineno-14-73" href="#__codelineno-14-73"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="o">&amp;</span><span class="n">adj</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">adjList</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
@@ -4882,7 +5747,7 @@
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">graph_adjacency_list.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 隣接リストに基づく無向グラフクラス */</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kd">class</span> <span class="nc">GraphAdjList</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 隣接リスト、キー: 頂点、値: その頂点のすべての隣接頂点</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 隣接リスト。key は頂点、value はその頂点に隣接する全頂点</span>
 <a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="n">Map</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">adjList</span><span class="p">;</span>
 <a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a>
 <a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
@@ -4923,7 +5788,7 @@
 <a id="__codelineno-15-41" name="__codelineno-15-41" href="#__codelineno-15-41"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">addVertex</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-42" name="__codelineno-15-42" href="#__codelineno-15-42"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">adjList</span><span class="p">.</span><span class="na">containsKey</span><span class="p">(</span><span class="n">vet</span><span class="p">))</span>
 <a id="__codelineno-15-43" name="__codelineno-15-43" href="#__codelineno-15-43"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-15-44" name="__codelineno-15-44" href="#__codelineno-15-44"></a><span class="w">        </span><span class="c1">// 隣接リストに新しい連結リストを追加</span>
+<a id="__codelineno-15-44" name="__codelineno-15-44" href="#__codelineno-15-44"></a><span class="w">        </span><span class="c1">// 隣接リストに新しいリストを追加</span>
 <a id="__codelineno-15-45" name="__codelineno-15-45" href="#__codelineno-15-45"></a><span class="w">        </span><span class="n">adjList</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="n">vet</span><span class="p">,</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">());</span>
 <a id="__codelineno-15-46" name="__codelineno-15-46" href="#__codelineno-15-46"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-47" name="__codelineno-15-47" href="#__codelineno-15-47"></a>
@@ -4931,9 +5796,9 @@
 <a id="__codelineno-15-49" name="__codelineno-15-49" href="#__codelineno-15-49"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">removeVertex</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-50" name="__codelineno-15-50" href="#__codelineno-15-50"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="na">containsKey</span><span class="p">(</span><span class="n">vet</span><span class="p">))</span>
 <a id="__codelineno-15-51" name="__codelineno-15-51" href="#__codelineno-15-51"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IllegalArgumentException</span><span class="p">();</span>
-<a id="__codelineno-15-52" name="__codelineno-15-52" href="#__codelineno-15-52"></a><span class="w">        </span><span class="c1">// 隣接リストから頂点 vet に対応する連結リストを削除</span>
+<a id="__codelineno-15-52" name="__codelineno-15-52" href="#__codelineno-15-52"></a><span class="w">        </span><span class="c1">// 隣接リストから頂点 vet に対応するリストを削除</span>
 <a id="__codelineno-15-53" name="__codelineno-15-53" href="#__codelineno-15-53"></a><span class="w">        </span><span class="n">adjList</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span>
-<a id="__codelineno-15-54" name="__codelineno-15-54" href="#__codelineno-15-54"></a><span class="w">        </span><span class="c1">// 他の頂点の連結リストを走査し、vet を含むすべての辺を削除</span>
+<a id="__codelineno-15-54" name="__codelineno-15-54" href="#__codelineno-15-54"></a><span class="w">        </span><span class="c1">// 他の頂点のリストを走査し、vet を含むすべての辺を削除</span>
 <a id="__codelineno-15-55" name="__codelineno-15-55" href="#__codelineno-15-55"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">list</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">adjList</span><span class="p">.</span><span class="na">values</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-56" name="__codelineno-15-56" href="#__codelineno-15-56"></a><span class="w">            </span><span class="n">list</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span>
 <a id="__codelineno-15-57" name="__codelineno-15-57" href="#__codelineno-15-57"></a><span class="w">        </span><span class="p">}</span>
@@ -4953,51 +5818,891 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_adjacency_list.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">GraphAdjList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">graph_adjacency_list.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 隣接リストに基づく無向グラフクラス */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">GraphAdjList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="c1">// 隣接リスト。key は頂点、value はその頂点に隣接する全頂点</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="n">Dictionary</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">adjList</span><span class="p">;</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nf">GraphAdjList</span><span class="p">(</span><span class="n">Vertex</span><span class="p">[][]</span><span class="w"> </span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">        </span><span class="n">adjList</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">        </span><span class="c1">// すべての頂点と辺を追加</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">        </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="p">[]</span><span class="w"> </span><span class="n">edge</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">            </span><span class="n">AddVertex</span><span class="p">(</span><span class="n">edge</span><span class="p">[</span><span class="mi">0</span><span class="p">]);</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">            </span><span class="n">AddVertex</span><span class="p">(</span><span class="n">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">            </span><span class="n">AddEdge</span><span class="p">(</span><span class="n">edge</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="n">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">    </span><span class="cm">/* 頂点数を取得 */</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="nf">Size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">adjList</span><span class="p">.</span><span class="n">Count</span><span class="p">;</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a>
+<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="w">    </span><span class="cm">/* 辺を追加 */</span>
+<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">AddEdge</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet1</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-24" name="__codelineno-16-24" href="#__codelineno-16-24"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="n">ContainsKey</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="n">ContainsKey</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">vet1</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span>
+<a id="__codelineno-16-25" name="__codelineno-16-25" href="#__codelineno-16-25"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="nf">InvalidOperationException</span><span class="p">();</span>
+<a id="__codelineno-16-26" name="__codelineno-16-26" href="#__codelineno-16-26"></a><span class="w">        </span><span class="c1">// 辺 vet1 - vet2 を追加</span>
+<a id="__codelineno-16-27" name="__codelineno-16-27" href="#__codelineno-16-27"></a><span class="w">        </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet1</span><span class="p">].</span><span class="n">Add</span><span class="p">(</span><span class="n">vet2</span><span class="p">);</span>
+<a id="__codelineno-16-28" name="__codelineno-16-28" href="#__codelineno-16-28"></a><span class="w">        </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet2</span><span class="p">].</span><span class="n">Add</span><span class="p">(</span><span class="n">vet1</span><span class="p">);</span>
+<a id="__codelineno-16-29" name="__codelineno-16-29" href="#__codelineno-16-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-30" name="__codelineno-16-30" href="#__codelineno-16-30"></a>
+<a id="__codelineno-16-31" name="__codelineno-16-31" href="#__codelineno-16-31"></a><span class="w">    </span><span class="cm">/* 辺を削除 */</span>
+<a id="__codelineno-16-32" name="__codelineno-16-32" href="#__codelineno-16-32"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">RemoveEdge</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet1</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-33" name="__codelineno-16-33" href="#__codelineno-16-33"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="n">ContainsKey</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="n">ContainsKey</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">vet1</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span>
+<a id="__codelineno-16-34" name="__codelineno-16-34" href="#__codelineno-16-34"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="nf">InvalidOperationException</span><span class="p">();</span>
+<a id="__codelineno-16-35" name="__codelineno-16-35" href="#__codelineno-16-35"></a><span class="w">        </span><span class="c1">// 辺 vet1 - vet2 を削除</span>
+<a id="__codelineno-16-36" name="__codelineno-16-36" href="#__codelineno-16-36"></a><span class="w">        </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet1</span><span class="p">].</span><span class="n">Remove</span><span class="p">(</span><span class="n">vet2</span><span class="p">);</span>
+<a id="__codelineno-16-37" name="__codelineno-16-37" href="#__codelineno-16-37"></a><span class="w">        </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet2</span><span class="p">].</span><span class="n">Remove</span><span class="p">(</span><span class="n">vet1</span><span class="p">);</span>
+<a id="__codelineno-16-38" name="__codelineno-16-38" href="#__codelineno-16-38"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-39" name="__codelineno-16-39" href="#__codelineno-16-39"></a>
+<a id="__codelineno-16-40" name="__codelineno-16-40" href="#__codelineno-16-40"></a><span class="w">    </span><span class="cm">/* 頂点を追加 */</span>
+<a id="__codelineno-16-41" name="__codelineno-16-41" href="#__codelineno-16-41"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">AddVertex</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-42" name="__codelineno-16-42" href="#__codelineno-16-42"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">adjList</span><span class="p">.</span><span class="n">ContainsKey</span><span class="p">(</span><span class="n">vet</span><span class="p">))</span>
+<a id="__codelineno-16-43" name="__codelineno-16-43" href="#__codelineno-16-43"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-16-44" name="__codelineno-16-44" href="#__codelineno-16-44"></a><span class="w">        </span><span class="c1">// 隣接リストに新しいリストを追加</span>
+<a id="__codelineno-16-45" name="__codelineno-16-45" href="#__codelineno-16-45"></a><span class="w">        </span><span class="n">adjList</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">vet</span><span class="p">,</span><span class="w"> </span><span class="p">[]);</span>
+<a id="__codelineno-16-46" name="__codelineno-16-46" href="#__codelineno-16-46"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-47" name="__codelineno-16-47" href="#__codelineno-16-47"></a>
+<a id="__codelineno-16-48" name="__codelineno-16-48" href="#__codelineno-16-48"></a><span class="w">    </span><span class="cm">/* 頂点を削除 */</span>
+<a id="__codelineno-16-49" name="__codelineno-16-49" href="#__codelineno-16-49"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">RemoveVertex</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-50" name="__codelineno-16-50" href="#__codelineno-16-50"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="n">ContainsKey</span><span class="p">(</span><span class="n">vet</span><span class="p">))</span>
+<a id="__codelineno-16-51" name="__codelineno-16-51" href="#__codelineno-16-51"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="nf">InvalidOperationException</span><span class="p">();</span>
+<a id="__codelineno-16-52" name="__codelineno-16-52" href="#__codelineno-16-52"></a><span class="w">        </span><span class="c1">// 隣接リストから頂点 vet に対応するリストを削除</span>
+<a id="__codelineno-16-53" name="__codelineno-16-53" href="#__codelineno-16-53"></a><span class="w">        </span><span class="n">adjList</span><span class="p">.</span><span class="n">Remove</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span>
+<a id="__codelineno-16-54" name="__codelineno-16-54" href="#__codelineno-16-54"></a><span class="w">        </span><span class="c1">// 他の頂点のリストを走査し、vet を含むすべての辺を削除</span>
+<a id="__codelineno-16-55" name="__codelineno-16-55" href="#__codelineno-16-55"></a><span class="w">        </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">list</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">adjList</span><span class="p">.</span><span class="n">Values</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-56" name="__codelineno-16-56" href="#__codelineno-16-56"></a><span class="w">            </span><span class="n">list</span><span class="p">.</span><span class="n">Remove</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span>
+<a id="__codelineno-16-57" name="__codelineno-16-57" href="#__codelineno-16-57"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-58" name="__codelineno-16-58" href="#__codelineno-16-58"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-59" name="__codelineno-16-59" href="#__codelineno-16-59"></a>
+<a id="__codelineno-16-60" name="__codelineno-16-60" href="#__codelineno-16-60"></a><span class="w">    </span><span class="cm">/* 隣接リストを出力 */</span>
+<a id="__codelineno-16-61" name="__codelineno-16-61" href="#__codelineno-16-61"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">Print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-62" name="__codelineno-16-62" href="#__codelineno-16-62"></a><span class="w">        </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="s">&quot;隣接リスト =&quot;</span><span class="p">);</span>
+<a id="__codelineno-16-63" name="__codelineno-16-63" href="#__codelineno-16-63"></a><span class="w">        </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">KeyValuePair</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">adjList</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-64" name="__codelineno-16-64" href="#__codelineno-16-64"></a><span class="w">            </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-16-65" name="__codelineno-16-65" href="#__codelineno-16-65"></a><span class="w">            </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">vertex</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">Value</span><span class="p">)</span>
+<a id="__codelineno-16-66" name="__codelineno-16-66" href="#__codelineno-16-66"></a><span class="w">                </span><span class="n">tmp</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">vertex</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-16-67" name="__codelineno-16-67" href="#__codelineno-16-67"></a><span class="w">            </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="n">Key</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot;: [&quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="kt">string</span><span class="p">.</span><span class="n">Join</span><span class="p">(</span><span class="s">&quot;, &quot;</span><span class="p">,</span><span class="w"> </span><span class="n">tmp</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot;],&quot;</span><span class="p">);</span>
+<a id="__codelineno-16-68" name="__codelineno-16-68" href="#__codelineno-16-68"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-69" name="__codelineno-16-69" href="#__codelineno-16-69"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-70" name="__codelineno-16-70" href="#__codelineno-16-70"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_adjacency_list.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">graphAdjList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">graph_adjacency_list.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 隣接リストに基づく無向グラフクラス */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">graphAdjList</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="c1">// 隣接リスト。key は頂点、value はその頂点に隣接する全頂点</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="nx">adjList</span><span class="w"> </span><span class="kd">map</span><span class="p">[</span><span class="nx">Vertex</span><span class="p">][]</span><span class="nx">Vertex</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="p">}</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="kd">func</span><span class="w"> </span><span class="nx">newGraphAdjList</span><span class="p">(</span><span class="nx">edges</span><span class="w"> </span><span class="p">[][]</span><span class="nx">Vertex</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">    </span><span class="nx">g</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">graphAdjList</span><span class="p">{</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">        </span><span class="nx">adjList</span><span class="p">:</span><span class="w"> </span><span class="nb">make</span><span class="p">(</span><span class="kd">map</span><span class="p">[</span><span class="nx">Vertex</span><span class="p">][]</span><span class="nx">Vertex</span><span class="p">),</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">    </span><span class="c1">// すべての頂点と辺を追加</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">edge</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">edges</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w">        </span><span class="nx">g</span><span class="p">.</span><span class="nx">addVertex</span><span class="p">(</span><span class="nx">edge</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">        </span><span class="nx">g</span><span class="p">.</span><span class="nx">addVertex</span><span class="p">(</span><span class="nx">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w">        </span><span class="nx">g</span><span class="p">.</span><span class="nx">addEdge</span><span class="p">(</span><span class="nx">edge</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="nx">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">g</span>
+<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="p">}</span>
+<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a>
+<a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></a><span class="cm">/* 頂点数を取得 */</span>
+<a id="__codelineno-17-22" name="__codelineno-17-22" href="#__codelineno-17-22"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjList</span><span class="p">)</span><span class="w"> </span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-23" name="__codelineno-17-23" href="#__codelineno-17-23"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">)</span>
+<a id="__codelineno-17-24" name="__codelineno-17-24" href="#__codelineno-17-24"></a><span class="p">}</span>
+<a id="__codelineno-17-25" name="__codelineno-17-25" href="#__codelineno-17-25"></a>
+<a id="__codelineno-17-26" name="__codelineno-17-26" href="#__codelineno-17-26"></a><span class="cm">/* 辺を追加 */</span>
+<a id="__codelineno-17-27" name="__codelineno-17-27" href="#__codelineno-17-27"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjList</span><span class="p">)</span><span class="w"> </span><span class="nx">addEdge</span><span class="p">(</span><span class="nx">vet1</span><span class="w"> </span><span class="nx">Vertex</span><span class="p">,</span><span class="w"> </span><span class="nx">vet2</span><span class="w"> </span><span class="nx">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-28" name="__codelineno-17-28" href="#__codelineno-17-28"></a><span class="w">    </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">ok1</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet1</span><span class="p">]</span>
+<a id="__codelineno-17-29" name="__codelineno-17-29" href="#__codelineno-17-29"></a><span class="w">    </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">ok2</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet2</span><span class="p">]</span>
+<a id="__codelineno-17-30" name="__codelineno-17-30" href="#__codelineno-17-30"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">!</span><span class="nx">ok1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">!</span><span class="nx">ok2</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">vet1</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">vet2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-31" name="__codelineno-17-31" href="#__codelineno-17-31"></a><span class="w">        </span><span class="nb">panic</span><span class="p">(</span><span class="s">&quot;error&quot;</span><span class="p">)</span>
+<a id="__codelineno-17-32" name="__codelineno-17-32" href="#__codelineno-17-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-33" name="__codelineno-17-33" href="#__codelineno-17-33"></a><span class="w">    </span><span class="c1">// 辺 `vet1 - vet2` を追加し、無名 `struct{}` を追加する</span>
+<a id="__codelineno-17-34" name="__codelineno-17-34" href="#__codelineno-17-34"></a><span class="w">    </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet1</span><span class="p">],</span><span class="w"> </span><span class="nx">vet2</span><span class="p">)</span>
+<a id="__codelineno-17-35" name="__codelineno-17-35" href="#__codelineno-17-35"></a><span class="w">    </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet2</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet2</span><span class="p">],</span><span class="w"> </span><span class="nx">vet1</span><span class="p">)</span>
+<a id="__codelineno-17-36" name="__codelineno-17-36" href="#__codelineno-17-36"></a><span class="p">}</span>
+<a id="__codelineno-17-37" name="__codelineno-17-37" href="#__codelineno-17-37"></a>
+<a id="__codelineno-17-38" name="__codelineno-17-38" href="#__codelineno-17-38"></a><span class="cm">/* 辺を削除 */</span>
+<a id="__codelineno-17-39" name="__codelineno-17-39" href="#__codelineno-17-39"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjList</span><span class="p">)</span><span class="w"> </span><span class="nx">removeEdge</span><span class="p">(</span><span class="nx">vet1</span><span class="w"> </span><span class="nx">Vertex</span><span class="p">,</span><span class="w"> </span><span class="nx">vet2</span><span class="w"> </span><span class="nx">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-40" name="__codelineno-17-40" href="#__codelineno-17-40"></a><span class="w">    </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">ok1</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet1</span><span class="p">]</span>
+<a id="__codelineno-17-41" name="__codelineno-17-41" href="#__codelineno-17-41"></a><span class="w">    </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">ok2</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet2</span><span class="p">]</span>
+<a id="__codelineno-17-42" name="__codelineno-17-42" href="#__codelineno-17-42"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">!</span><span class="nx">ok1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">!</span><span class="nx">ok2</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">vet1</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">vet2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-43" name="__codelineno-17-43" href="#__codelineno-17-43"></a><span class="w">        </span><span class="nb">panic</span><span class="p">(</span><span class="s">&quot;error&quot;</span><span class="p">)</span>
+<a id="__codelineno-17-44" name="__codelineno-17-44" href="#__codelineno-17-44"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-45" name="__codelineno-17-45" href="#__codelineno-17-45"></a><span class="w">    </span><span class="c1">// 辺 vet1 - vet2 を削除</span>
+<a id="__codelineno-17-46" name="__codelineno-17-46" href="#__codelineno-17-46"></a><span class="w">    </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">DeleteSliceElms</span><span class="p">(</span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet1</span><span class="p">],</span><span class="w"> </span><span class="nx">vet2</span><span class="p">)</span>
+<a id="__codelineno-17-47" name="__codelineno-17-47" href="#__codelineno-17-47"></a><span class="w">    </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet2</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">DeleteSliceElms</span><span class="p">(</span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet2</span><span class="p">],</span><span class="w"> </span><span class="nx">vet1</span><span class="p">)</span>
+<a id="__codelineno-17-48" name="__codelineno-17-48" href="#__codelineno-17-48"></a><span class="p">}</span>
+<a id="__codelineno-17-49" name="__codelineno-17-49" href="#__codelineno-17-49"></a>
+<a id="__codelineno-17-50" name="__codelineno-17-50" href="#__codelineno-17-50"></a><span class="cm">/* 頂点を追加 */</span>
+<a id="__codelineno-17-51" name="__codelineno-17-51" href="#__codelineno-17-51"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjList</span><span class="p">)</span><span class="w"> </span><span class="nx">addVertex</span><span class="p">(</span><span class="nx">vet</span><span class="w"> </span><span class="nx">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-52" name="__codelineno-17-52" href="#__codelineno-17-52"></a><span class="w">    </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">ok</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet</span><span class="p">]</span>
+<a id="__codelineno-17-53" name="__codelineno-17-53" href="#__codelineno-17-53"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">ok</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-54" name="__codelineno-17-54" href="#__codelineno-17-54"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-17-55" name="__codelineno-17-55" href="#__codelineno-17-55"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-56" name="__codelineno-17-56" href="#__codelineno-17-56"></a><span class="w">    </span><span class="c1">// 隣接リストに新しいリストを追加</span>
+<a id="__codelineno-17-57" name="__codelineno-17-57" href="#__codelineno-17-57"></a><span class="w">    </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="nx">Vertex</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-17-58" name="__codelineno-17-58" href="#__codelineno-17-58"></a><span class="p">}</span>
+<a id="__codelineno-17-59" name="__codelineno-17-59" href="#__codelineno-17-59"></a>
+<a id="__codelineno-17-60" name="__codelineno-17-60" href="#__codelineno-17-60"></a><span class="cm">/* 頂点を削除 */</span>
+<a id="__codelineno-17-61" name="__codelineno-17-61" href="#__codelineno-17-61"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjList</span><span class="p">)</span><span class="w"> </span><span class="nx">removeVertex</span><span class="p">(</span><span class="nx">vet</span><span class="w"> </span><span class="nx">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-62" name="__codelineno-17-62" href="#__codelineno-17-62"></a><span class="w">    </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">ok</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet</span><span class="p">]</span>
+<a id="__codelineno-17-63" name="__codelineno-17-63" href="#__codelineno-17-63"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">!</span><span class="nx">ok</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-64" name="__codelineno-17-64" href="#__codelineno-17-64"></a><span class="w">        </span><span class="nb">panic</span><span class="p">(</span><span class="s">&quot;error&quot;</span><span class="p">)</span>
+<a id="__codelineno-17-65" name="__codelineno-17-65" href="#__codelineno-17-65"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-66" name="__codelineno-17-66" href="#__codelineno-17-66"></a><span class="w">    </span><span class="c1">// 隣接リストから頂点 vet に対応するリストを削除</span>
+<a id="__codelineno-17-67" name="__codelineno-17-67" href="#__codelineno-17-67"></a><span class="w">    </span><span class="nb">delete</span><span class="p">(</span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">,</span><span class="w"> </span><span class="nx">vet</span><span class="p">)</span>
+<a id="__codelineno-17-68" name="__codelineno-17-68" href="#__codelineno-17-68"></a><span class="w">    </span><span class="c1">// 他の頂点のリストを走査し、vet を含むすべての辺を削除</span>
+<a id="__codelineno-17-69" name="__codelineno-17-69" href="#__codelineno-17-69"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">v</span><span class="p">,</span><span class="w"> </span><span class="nx">list</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-70" name="__codelineno-17-70" href="#__codelineno-17-70"></a><span class="w">        </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">v</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">DeleteSliceElms</span><span class="p">(</span><span class="nx">list</span><span class="p">,</span><span class="w"> </span><span class="nx">vet</span><span class="p">)</span>
+<a id="__codelineno-17-71" name="__codelineno-17-71" href="#__codelineno-17-71"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-72" name="__codelineno-17-72" href="#__codelineno-17-72"></a><span class="p">}</span>
+<a id="__codelineno-17-73" name="__codelineno-17-73" href="#__codelineno-17-73"></a>
+<a id="__codelineno-17-74" name="__codelineno-17-74" href="#__codelineno-17-74"></a><span class="cm">/* 隣接リストを出力 */</span>
+<a id="__codelineno-17-75" name="__codelineno-17-75" href="#__codelineno-17-75"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjList</span><span class="p">)</span><span class="w"> </span><span class="nb">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-76" name="__codelineno-17-76" href="#__codelineno-17-76"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">builder</span><span class="w"> </span><span class="nx">strings</span><span class="p">.</span><span class="nx">Builder</span>
+<a id="__codelineno-17-77" name="__codelineno-17-77" href="#__codelineno-17-77"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Printf</span><span class="p">(</span><span class="s">&quot;隣接リスト = \n&quot;</span><span class="p">)</span>
+<a id="__codelineno-17-78" name="__codelineno-17-78" href="#__codelineno-17-78"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">k</span><span class="p">,</span><span class="w"> </span><span class="nx">v</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-79" name="__codelineno-17-79" href="#__codelineno-17-79"></a><span class="w">        </span><span class="nx">builder</span><span class="p">.</span><span class="nx">WriteString</span><span class="p">(</span><span class="s">&quot;\t\t&quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">strconv</span><span class="p">.</span><span class="nx">Itoa</span><span class="p">(</span><span class="nx">k</span><span class="p">.</span><span class="nx">Val</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot;: &quot;</span><span class="p">)</span>
+<a id="__codelineno-17-80" name="__codelineno-17-80" href="#__codelineno-17-80"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">vet</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">v</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-81" name="__codelineno-17-81" href="#__codelineno-17-81"></a><span class="w">            </span><span class="nx">builder</span><span class="p">.</span><span class="nx">WriteString</span><span class="p">(</span><span class="nx">strconv</span><span class="p">.</span><span class="nx">Itoa</span><span class="p">(</span><span class="nx">vet</span><span class="p">.</span><span class="nx">Val</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot; &quot;</span><span class="p">)</span>
+<a id="__codelineno-17-82" name="__codelineno-17-82" href="#__codelineno-17-82"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-17-83" name="__codelineno-17-83" href="#__codelineno-17-83"></a><span class="w">        </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">builder</span><span class="p">.</span><span class="nx">String</span><span class="p">())</span>
+<a id="__codelineno-17-84" name="__codelineno-17-84" href="#__codelineno-17-84"></a><span class="w">        </span><span class="nx">builder</span><span class="p">.</span><span class="nx">Reset</span><span class="p">()</span>
+<a id="__codelineno-17-85" name="__codelineno-17-85" href="#__codelineno-17-85"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-86" name="__codelineno-17-86" href="#__codelineno-17-86"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_adjacency_list.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">GraphAdjList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">graph_adjacency_list.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 隣接リストに基づく無向グラフクラス */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">GraphAdjList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="c1">// 隣接リスト。key は頂点、value はその頂点に隣接する全頂点</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kd">private</span><span class="p">(</span><span class="kr">set</span><span class="p">)</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">adjList</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="n">Vertex</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="n">Vertex</span><span class="p">]]</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kd">init</span><span class="p">(</span><span class="n">edges</span><span class="p">:</span><span class="w"> </span><span class="p">[[</span><span class="n">Vertex</span><span class="p">]])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">        </span><span class="n">adjList</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[:]</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">        </span><span class="c1">// すべての頂点と辺を追加</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">edge</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">edges</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w">            </span><span class="n">addVertex</span><span class="p">(</span><span class="n">vet</span><span class="p">:</span><span class="w"> </span><span class="n">edge</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w">            </span><span class="n">addVertex</span><span class="p">(</span><span class="n">vet</span><span class="p">:</span><span class="w"> </span><span class="n">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w">            </span><span class="n">addEdge</span><span class="p">(</span><span class="n">vet1</span><span class="p">:</span><span class="w"> </span><span class="n">edge</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="n">vet2</span><span class="p">:</span><span class="w"> </span><span class="n">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a>
+<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="w">    </span><span class="cm">/* 頂点数を取得 */</span>
+<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kd">func</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a><span class="w">        </span><span class="n">adjList</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></a>
+<a id="__codelineno-18-22" name="__codelineno-18-22" href="#__codelineno-18-22"></a><span class="w">    </span><span class="cm">/* 辺を追加 */</span>
+<a id="__codelineno-18-23" name="__codelineno-18-23" href="#__codelineno-18-23"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kd">func</span><span class="w"> </span><span class="nf">addEdge</span><span class="p">(</span><span class="n">vet1</span><span class="p">:</span><span class="w"> </span><span class="n">Vertex</span><span class="p">,</span><span class="w"> </span><span class="n">vet2</span><span class="p">:</span><span class="w"> </span><span class="n">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-24" name="__codelineno-18-24" href="#__codelineno-18-24"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet1</span><span class="p">]</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet2</span><span class="p">]</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">vet1</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">vet2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-25" name="__codelineno-18-25" href="#__codelineno-18-25"></a><span class="w">            </span><span class="bp">fatalError</span><span class="p">(</span><span class="s">&quot;引数エラー&quot;</span><span class="p">)</span>
+<a id="__codelineno-18-26" name="__codelineno-18-26" href="#__codelineno-18-26"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-27" name="__codelineno-18-27" href="#__codelineno-18-27"></a><span class="w">        </span><span class="c1">// 辺 vet1 - vet2 を追加</span>
+<a id="__codelineno-18-28" name="__codelineno-18-28" href="#__codelineno-18-28"></a><span class="w">        </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet1</span><span class="p">]?.</span><span class="n">append</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span>
+<a id="__codelineno-18-29" name="__codelineno-18-29" href="#__codelineno-18-29"></a><span class="w">        </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet2</span><span class="p">]?.</span><span class="n">append</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span>
+<a id="__codelineno-18-30" name="__codelineno-18-30" href="#__codelineno-18-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-31" name="__codelineno-18-31" href="#__codelineno-18-31"></a>
+<a id="__codelineno-18-32" name="__codelineno-18-32" href="#__codelineno-18-32"></a><span class="w">    </span><span class="cm">/* 辺を削除 */</span>
+<a id="__codelineno-18-33" name="__codelineno-18-33" href="#__codelineno-18-33"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kd">func</span><span class="w"> </span><span class="nf">removeEdge</span><span class="p">(</span><span class="n">vet1</span><span class="p">:</span><span class="w"> </span><span class="n">Vertex</span><span class="p">,</span><span class="w"> </span><span class="n">vet2</span><span class="p">:</span><span class="w"> </span><span class="n">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-34" name="__codelineno-18-34" href="#__codelineno-18-34"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet1</span><span class="p">]</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet2</span><span class="p">]</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">vet1</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">vet2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-35" name="__codelineno-18-35" href="#__codelineno-18-35"></a><span class="w">            </span><span class="bp">fatalError</span><span class="p">(</span><span class="s">&quot;引数エラー&quot;</span><span class="p">)</span>
+<a id="__codelineno-18-36" name="__codelineno-18-36" href="#__codelineno-18-36"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-37" name="__codelineno-18-37" href="#__codelineno-18-37"></a><span class="w">        </span><span class="c1">// 辺 vet1 - vet2 を削除</span>
+<a id="__codelineno-18-38" name="__codelineno-18-38" href="#__codelineno-18-38"></a><span class="w">        </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet1</span><span class="p">]?.</span><span class="bp">removeAll</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nv">$0</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">vet2</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-18-39" name="__codelineno-18-39" href="#__codelineno-18-39"></a><span class="w">        </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet2</span><span class="p">]?.</span><span class="bp">removeAll</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nv">$0</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">vet1</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-18-40" name="__codelineno-18-40" href="#__codelineno-18-40"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-41" name="__codelineno-18-41" href="#__codelineno-18-41"></a>
+<a id="__codelineno-18-42" name="__codelineno-18-42" href="#__codelineno-18-42"></a><span class="w">    </span><span class="cm">/* 頂点を追加 */</span>
+<a id="__codelineno-18-43" name="__codelineno-18-43" href="#__codelineno-18-43"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kd">func</span><span class="w"> </span><span class="nf">addVertex</span><span class="p">(</span><span class="n">vet</span><span class="p">:</span><span class="w"> </span><span class="n">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-44" name="__codelineno-18-44" href="#__codelineno-18-44"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-45" name="__codelineno-18-45" href="#__codelineno-18-45"></a><span class="w">            </span><span class="k">return</span>
+<a id="__codelineno-18-46" name="__codelineno-18-46" href="#__codelineno-18-46"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-47" name="__codelineno-18-47" href="#__codelineno-18-47"></a><span class="w">        </span><span class="c1">// 隣接リストに新しいリストを追加</span>
+<a id="__codelineno-18-48" name="__codelineno-18-48" href="#__codelineno-18-48"></a><span class="w">        </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
+<a id="__codelineno-18-49" name="__codelineno-18-49" href="#__codelineno-18-49"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-50" name="__codelineno-18-50" href="#__codelineno-18-50"></a>
+<a id="__codelineno-18-51" name="__codelineno-18-51" href="#__codelineno-18-51"></a><span class="w">    </span><span class="cm">/* 頂点を削除 */</span>
+<a id="__codelineno-18-52" name="__codelineno-18-52" href="#__codelineno-18-52"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kd">func</span><span class="w"> </span><span class="nf">removeVertex</span><span class="p">(</span><span class="n">vet</span><span class="p">:</span><span class="w"> </span><span class="n">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-53" name="__codelineno-18-53" href="#__codelineno-18-53"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">]</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-54" name="__codelineno-18-54" href="#__codelineno-18-54"></a><span class="w">            </span><span class="bp">fatalError</span><span class="p">(</span><span class="s">&quot;引数エラー&quot;</span><span class="p">)</span>
+<a id="__codelineno-18-55" name="__codelineno-18-55" href="#__codelineno-18-55"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-56" name="__codelineno-18-56" href="#__codelineno-18-56"></a><span class="w">        </span><span class="c1">// 隣接リストから頂点 vet に対応するリストを削除</span>
+<a id="__codelineno-18-57" name="__codelineno-18-57" href="#__codelineno-18-57"></a><span class="w">        </span><span class="n">adjList</span><span class="p">.</span><span class="n">removeValue</span><span class="p">(</span><span class="n">forKey</span><span class="p">:</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span>
+<a id="__codelineno-18-58" name="__codelineno-18-58" href="#__codelineno-18-58"></a><span class="w">        </span><span class="c1">// 他の頂点のリストを走査し、vet を含むすべての辺を削除</span>
+<a id="__codelineno-18-59" name="__codelineno-18-59" href="#__codelineno-18-59"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">adjList</span><span class="p">.</span><span class="n">keys</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-60" name="__codelineno-18-60" href="#__codelineno-18-60"></a><span class="w">            </span><span class="n">adjList</span><span class="p">[</span><span class="n">key</span><span class="p">]?.</span><span class="bp">removeAll</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nv">$0</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">vet</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-18-61" name="__codelineno-18-61" href="#__codelineno-18-61"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-62" name="__codelineno-18-62" href="#__codelineno-18-62"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-63" name="__codelineno-18-63" href="#__codelineno-18-63"></a>
+<a id="__codelineno-18-64" name="__codelineno-18-64" href="#__codelineno-18-64"></a><span class="w">    </span><span class="cm">/* 隣接リストを出力 */</span>
+<a id="__codelineno-18-65" name="__codelineno-18-65" href="#__codelineno-18-65"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kd">func</span><span class="w"> </span><span class="nf">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-66" name="__codelineno-18-66" href="#__codelineno-18-66"></a><span class="w">        </span><span class="n">Swift</span><span class="p">.</span><span class="bp">print</span><span class="p">(</span><span class="s">&quot;隣接リスト =&quot;</span><span class="p">)</span>
+<a id="__codelineno-18-67" name="__codelineno-18-67" href="#__codelineno-18-67"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">vertex</span><span class="p">,</span><span class="w"> </span><span class="n">list</span><span class="p">)</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">adjList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-68" name="__codelineno-18-68" href="#__codelineno-18-68"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="nv">list</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">list</span><span class="p">.</span><span class="bp">map</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nv">$0</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-18-69" name="__codelineno-18-69" href="#__codelineno-18-69"></a><span class="w">            </span><span class="n">Swift</span><span class="p">.</span><span class="bp">print</span><span class="p">(</span><span class="s">&quot;</span><span class="si">\(</span><span class="n">vertex</span><span class="p">.</span><span class="n">val</span><span class="si">)</span><span class="s">: </span><span class="si">\(</span><span class="n">list</span><span class="si">)</span><span class="s">,&quot;</span><span class="p">)</span>
+<a id="__codelineno-18-70" name="__codelineno-18-70" href="#__codelineno-18-70"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-71" name="__codelineno-18-71" href="#__codelineno-18-71"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-72" name="__codelineno-18-72" href="#__codelineno-18-72"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_adjacency_list.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">GraphAdjList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">graph_adjacency_list.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 隣接リストに基づく無向グラフクラス */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">GraphAdjList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="c1">// 隣接リスト。key は頂点、value はその頂点に隣接する全頂点</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="nx">adjList</span><span class="p">;</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Map</span><span class="p">();</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w">        </span><span class="c1">// すべての頂点と辺を追加</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">edge</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">addVertex</span><span class="p">(</span><span class="nx">edge</span><span class="p">[</span><span class="mf">0</span><span class="p">]);</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">addVertex</span><span class="p">(</span><span class="nx">edge</span><span class="p">[</span><span class="mf">1</span><span class="p">]);</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">addEdge</span><span class="p">(</span><span class="nx">edge</span><span class="p">[</span><span class="mf">0</span><span class="p">],</span><span class="w"> </span><span class="nx">edge</span><span class="p">[</span><span class="mf">1</span><span class="p">]);</span>
+<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a>
+<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="w">    </span><span class="cm">/* 頂点数を取得 */</span>
+<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a><span class="w">    </span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">size</span><span class="p">;</span>
+<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a>
+<a id="__codelineno-19-22" name="__codelineno-19-22" href="#__codelineno-19-22"></a><span class="w">    </span><span class="cm">/* 辺を追加 */</span>
+<a id="__codelineno-19-23" name="__codelineno-19-23" href="#__codelineno-19-23"></a><span class="w">    </span><span class="nx">addEdge</span><span class="p">(</span><span class="nx">vet1</span><span class="p">,</span><span class="w"> </span><span class="nx">vet2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-24" name="__codelineno-19-24" href="#__codelineno-19-24"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span>
+<a id="__codelineno-19-25" name="__codelineno-19-25" href="#__codelineno-19-25"></a><span class="w">            </span><span class="o">!</span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">has</span><span class="p">(</span><span class="nx">vet1</span><span class="p">)</span><span class="w"> </span><span class="o">||</span>
+<a id="__codelineno-19-26" name="__codelineno-19-26" href="#__codelineno-19-26"></a><span class="w">            </span><span class="o">!</span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">has</span><span class="p">(</span><span class="nx">vet2</span><span class="p">)</span><span class="w"> </span><span class="o">||</span>
+<a id="__codelineno-19-27" name="__codelineno-19-27" href="#__codelineno-19-27"></a><span class="w">            </span><span class="nx">vet1</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">vet2</span>
+<a id="__codelineno-19-28" name="__codelineno-19-28" href="#__codelineno-19-28"></a><span class="w">        </span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-29" name="__codelineno-19-29" href="#__codelineno-19-29"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;Illegal Argument Exception&#39;</span><span class="p">);</span>
+<a id="__codelineno-19-30" name="__codelineno-19-30" href="#__codelineno-19-30"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-31" name="__codelineno-19-31" href="#__codelineno-19-31"></a><span class="w">        </span><span class="c1">// 辺 vet1 - vet2 を追加</span>
+<a id="__codelineno-19-32" name="__codelineno-19-32" href="#__codelineno-19-32"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">vet1</span><span class="p">).</span><span class="nx">push</span><span class="p">(</span><span class="nx">vet2</span><span class="p">);</span>
+<a id="__codelineno-19-33" name="__codelineno-19-33" href="#__codelineno-19-33"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">vet2</span><span class="p">).</span><span class="nx">push</span><span class="p">(</span><span class="nx">vet1</span><span class="p">);</span>
+<a id="__codelineno-19-34" name="__codelineno-19-34" href="#__codelineno-19-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-35" name="__codelineno-19-35" href="#__codelineno-19-35"></a>
+<a id="__codelineno-19-36" name="__codelineno-19-36" href="#__codelineno-19-36"></a><span class="w">    </span><span class="cm">/* 辺を削除 */</span>
+<a id="__codelineno-19-37" name="__codelineno-19-37" href="#__codelineno-19-37"></a><span class="w">    </span><span class="nx">removeEdge</span><span class="p">(</span><span class="nx">vet1</span><span class="p">,</span><span class="w"> </span><span class="nx">vet2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-38" name="__codelineno-19-38" href="#__codelineno-19-38"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span>
+<a id="__codelineno-19-39" name="__codelineno-19-39" href="#__codelineno-19-39"></a><span class="w">            </span><span class="o">!</span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">has</span><span class="p">(</span><span class="nx">vet1</span><span class="p">)</span><span class="w"> </span><span class="o">||</span>
+<a id="__codelineno-19-40" name="__codelineno-19-40" href="#__codelineno-19-40"></a><span class="w">            </span><span class="o">!</span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">has</span><span class="p">(</span><span class="nx">vet2</span><span class="p">)</span><span class="w"> </span><span class="o">||</span>
+<a id="__codelineno-19-41" name="__codelineno-19-41" href="#__codelineno-19-41"></a><span class="w">            </span><span class="nx">vet1</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">vet2</span><span class="w"> </span><span class="o">||</span>
+<a id="__codelineno-19-42" name="__codelineno-19-42" href="#__codelineno-19-42"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">vet1</span><span class="p">).</span><span class="nx">indexOf</span><span class="p">(</span><span class="nx">vet2</span><span class="p">)</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span>
+<a id="__codelineno-19-43" name="__codelineno-19-43" href="#__codelineno-19-43"></a><span class="w">        </span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-44" name="__codelineno-19-44" href="#__codelineno-19-44"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;Illegal Argument Exception&#39;</span><span class="p">);</span>
+<a id="__codelineno-19-45" name="__codelineno-19-45" href="#__codelineno-19-45"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-46" name="__codelineno-19-46" href="#__codelineno-19-46"></a><span class="w">        </span><span class="c1">// 辺 vet1 - vet2 を削除</span>
+<a id="__codelineno-19-47" name="__codelineno-19-47" href="#__codelineno-19-47"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">vet1</span><span class="p">).</span><span class="nx">splice</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">vet1</span><span class="p">).</span><span class="nx">indexOf</span><span class="p">(</span><span class="nx">vet2</span><span class="p">),</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-19-48" name="__codelineno-19-48" href="#__codelineno-19-48"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">vet2</span><span class="p">).</span><span class="nx">splice</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">vet2</span><span class="p">).</span><span class="nx">indexOf</span><span class="p">(</span><span class="nx">vet1</span><span class="p">),</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-19-49" name="__codelineno-19-49" href="#__codelineno-19-49"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-50" name="__codelineno-19-50" href="#__codelineno-19-50"></a>
+<a id="__codelineno-19-51" name="__codelineno-19-51" href="#__codelineno-19-51"></a><span class="w">    </span><span class="cm">/* 頂点を追加 */</span>
+<a id="__codelineno-19-52" name="__codelineno-19-52" href="#__codelineno-19-52"></a><span class="w">    </span><span class="nx">addVertex</span><span class="p">(</span><span class="nx">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-53" name="__codelineno-19-53" href="#__codelineno-19-53"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">has</span><span class="p">(</span><span class="nx">vet</span><span class="p">))</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-19-54" name="__codelineno-19-54" href="#__codelineno-19-54"></a><span class="w">        </span><span class="c1">// 隣接リストに新しいリストを追加</span>
+<a id="__codelineno-19-55" name="__codelineno-19-55" href="#__codelineno-19-55"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="nx">vet</span><span class="p">,</span><span class="w"> </span><span class="p">[]);</span>
+<a id="__codelineno-19-56" name="__codelineno-19-56" href="#__codelineno-19-56"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-57" name="__codelineno-19-57" href="#__codelineno-19-57"></a>
+<a id="__codelineno-19-58" name="__codelineno-19-58" href="#__codelineno-19-58"></a><span class="w">    </span><span class="cm">/* 頂点を削除 */</span>
+<a id="__codelineno-19-59" name="__codelineno-19-59" href="#__codelineno-19-59"></a><span class="w">    </span><span class="nx">removeVertex</span><span class="p">(</span><span class="nx">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-60" name="__codelineno-19-60" href="#__codelineno-19-60"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">has</span><span class="p">(</span><span class="nx">vet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-61" name="__codelineno-19-61" href="#__codelineno-19-61"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;Illegal Argument Exception&#39;</span><span class="p">);</span>
+<a id="__codelineno-19-62" name="__codelineno-19-62" href="#__codelineno-19-62"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-63" name="__codelineno-19-63" href="#__codelineno-19-63"></a><span class="w">        </span><span class="c1">// 隣接リストから頂点 vet に対応するリストを削除</span>
+<a id="__codelineno-19-64" name="__codelineno-19-64" href="#__codelineno-19-64"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="ow">delete</span><span class="p">(</span><span class="nx">vet</span><span class="p">);</span>
+<a id="__codelineno-19-65" name="__codelineno-19-65" href="#__codelineno-19-65"></a><span class="w">        </span><span class="c1">// 他の頂点のリストを走査し、vet を含むすべての辺を削除</span>
+<a id="__codelineno-19-66" name="__codelineno-19-66" href="#__codelineno-19-66"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">set</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">values</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-67" name="__codelineno-19-67" href="#__codelineno-19-67"></a><span class="w">            </span><span class="kd">const</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">set</span><span class="p">.</span><span class="nx">indexOf</span><span class="p">(</span><span class="nx">vet</span><span class="p">);</span>
+<a id="__codelineno-19-68" name="__codelineno-19-68" href="#__codelineno-19-68"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">index</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-69" name="__codelineno-19-69" href="#__codelineno-19-69"></a><span class="w">                </span><span class="nx">set</span><span class="p">.</span><span class="nx">splice</span><span class="p">(</span><span class="nx">index</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-19-70" name="__codelineno-19-70" href="#__codelineno-19-70"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-19-71" name="__codelineno-19-71" href="#__codelineno-19-71"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-72" name="__codelineno-19-72" href="#__codelineno-19-72"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-73" name="__codelineno-19-73" href="#__codelineno-19-73"></a>
+<a id="__codelineno-19-74" name="__codelineno-19-74" href="#__codelineno-19-74"></a><span class="w">    </span><span class="cm">/* 隣接リストを出力 */</span>
+<a id="__codelineno-19-75" name="__codelineno-19-75" href="#__codelineno-19-75"></a><span class="w">    </span><span class="nx">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-76" name="__codelineno-19-76" href="#__codelineno-19-76"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="s1">&#39;隣接リスト =&#39;</span><span class="p">);</span>
+<a id="__codelineno-19-77" name="__codelineno-19-77" href="#__codelineno-19-77"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="p">[</span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="nx">value</span><span class="p">]</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-78" name="__codelineno-19-78" href="#__codelineno-19-78"></a><span class="w">            </span><span class="kd">const</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-19-79" name="__codelineno-19-79" href="#__codelineno-19-79"></a><span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">vertex</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">value</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-80" name="__codelineno-19-80" href="#__codelineno-19-80"></a><span class="w">                </span><span class="nx">tmp</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">vertex</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-19-81" name="__codelineno-19-81" href="#__codelineno-19-81"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-19-82" name="__codelineno-19-82" href="#__codelineno-19-82"></a><span class="w">            </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="nx">key</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s1">&#39;: &#39;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">tmp</span><span class="p">.</span><span class="nx">join</span><span class="p">());</span>
+<a id="__codelineno-19-83" name="__codelineno-19-83" href="#__codelineno-19-83"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-84" name="__codelineno-19-84" href="#__codelineno-19-84"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-85" name="__codelineno-19-85" href="#__codelineno-19-85"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_adjacency_list.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">GraphAdjList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">graph_adjacency_list.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 隣接リストに基づく無向グラフクラス */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">GraphAdjList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="c1">// 隣接リスト。key は頂点、value はその頂点に隣接する全頂点</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="nx">adjList</span><span class="o">:</span><span class="w"> </span><span class="kt">Map</span><span class="o">&lt;</span><span class="nx">Vertex</span><span class="p">,</span><span class="w"> </span><span class="nx">Vertex</span><span class="p">[]</span><span class="o">&gt;</span><span class="p">;</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">edges</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span><span class="p">[][])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Map</span><span class="p">();</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">        </span><span class="c1">// すべての頂点と辺を追加</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">edge</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">addVertex</span><span class="p">(</span><span class="nx">edge</span><span class="p">[</span><span class="mf">0</span><span class="p">]);</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">addVertex</span><span class="p">(</span><span class="nx">edge</span><span class="p">[</span><span class="mf">1</span><span class="p">]);</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">addEdge</span><span class="p">(</span><span class="nx">edge</span><span class="p">[</span><span class="mf">0</span><span class="p">],</span><span class="w"> </span><span class="nx">edge</span><span class="p">[</span><span class="mf">1</span><span class="p">]);</span>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a>
+<a id="__codelineno-20-17" name="__codelineno-20-17" href="#__codelineno-20-17"></a><span class="w">    </span><span class="cm">/* 頂点数を取得 */</span>
+<a id="__codelineno-20-18" name="__codelineno-20-18" href="#__codelineno-20-18"></a><span class="w">    </span><span class="nx">size</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-19" name="__codelineno-20-19" href="#__codelineno-20-19"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">size</span><span class="p">;</span>
+<a id="__codelineno-20-20" name="__codelineno-20-20" href="#__codelineno-20-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-21" name="__codelineno-20-21" href="#__codelineno-20-21"></a>
+<a id="__codelineno-20-22" name="__codelineno-20-22" href="#__codelineno-20-22"></a><span class="w">    </span><span class="cm">/* 辺を追加 */</span>
+<a id="__codelineno-20-23" name="__codelineno-20-23" href="#__codelineno-20-23"></a><span class="w">    </span><span class="nx">addEdge</span><span class="p">(</span><span class="nx">vet1</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span><span class="p">,</span><span class="w"> </span><span class="nx">vet2</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-24" name="__codelineno-20-24" href="#__codelineno-20-24"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span>
+<a id="__codelineno-20-25" name="__codelineno-20-25" href="#__codelineno-20-25"></a><span class="w">            </span><span class="o">!</span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">has</span><span class="p">(</span><span class="nx">vet1</span><span class="p">)</span><span class="w"> </span><span class="o">||</span>
+<a id="__codelineno-20-26" name="__codelineno-20-26" href="#__codelineno-20-26"></a><span class="w">            </span><span class="o">!</span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">has</span><span class="p">(</span><span class="nx">vet2</span><span class="p">)</span><span class="w"> </span><span class="o">||</span>
+<a id="__codelineno-20-27" name="__codelineno-20-27" href="#__codelineno-20-27"></a><span class="w">            </span><span class="nx">vet1</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">vet2</span>
+<a id="__codelineno-20-28" name="__codelineno-20-28" href="#__codelineno-20-28"></a><span class="w">        </span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-29" name="__codelineno-20-29" href="#__codelineno-20-29"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;Illegal Argument Exception&#39;</span><span class="p">);</span>
+<a id="__codelineno-20-30" name="__codelineno-20-30" href="#__codelineno-20-30"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-31" name="__codelineno-20-31" href="#__codelineno-20-31"></a><span class="w">        </span><span class="c1">// 辺 vet1 - vet2 を追加</span>
+<a id="__codelineno-20-32" name="__codelineno-20-32" href="#__codelineno-20-32"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">vet1</span><span class="p">).</span><span class="nx">push</span><span class="p">(</span><span class="nx">vet2</span><span class="p">);</span>
+<a id="__codelineno-20-33" name="__codelineno-20-33" href="#__codelineno-20-33"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">vet2</span><span class="p">).</span><span class="nx">push</span><span class="p">(</span><span class="nx">vet1</span><span class="p">);</span>
+<a id="__codelineno-20-34" name="__codelineno-20-34" href="#__codelineno-20-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-35" name="__codelineno-20-35" href="#__codelineno-20-35"></a>
+<a id="__codelineno-20-36" name="__codelineno-20-36" href="#__codelineno-20-36"></a><span class="w">    </span><span class="cm">/* 辺を削除 */</span>
+<a id="__codelineno-20-37" name="__codelineno-20-37" href="#__codelineno-20-37"></a><span class="w">    </span><span class="nx">removeEdge</span><span class="p">(</span><span class="nx">vet1</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span><span class="p">,</span><span class="w"> </span><span class="nx">vet2</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-38" name="__codelineno-20-38" href="#__codelineno-20-38"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span>
+<a id="__codelineno-20-39" name="__codelineno-20-39" href="#__codelineno-20-39"></a><span class="w">            </span><span class="o">!</span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">has</span><span class="p">(</span><span class="nx">vet1</span><span class="p">)</span><span class="w"> </span><span class="o">||</span>
+<a id="__codelineno-20-40" name="__codelineno-20-40" href="#__codelineno-20-40"></a><span class="w">            </span><span class="o">!</span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">has</span><span class="p">(</span><span class="nx">vet2</span><span class="p">)</span><span class="w"> </span><span class="o">||</span>
+<a id="__codelineno-20-41" name="__codelineno-20-41" href="#__codelineno-20-41"></a><span class="w">            </span><span class="nx">vet1</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">vet2</span><span class="w"> </span><span class="o">||</span>
+<a id="__codelineno-20-42" name="__codelineno-20-42" href="#__codelineno-20-42"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">vet1</span><span class="p">).</span><span class="nx">indexOf</span><span class="p">(</span><span class="nx">vet2</span><span class="p">)</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span>
+<a id="__codelineno-20-43" name="__codelineno-20-43" href="#__codelineno-20-43"></a><span class="w">        </span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-44" name="__codelineno-20-44" href="#__codelineno-20-44"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;Illegal Argument Exception&#39;</span><span class="p">);</span>
+<a id="__codelineno-20-45" name="__codelineno-20-45" href="#__codelineno-20-45"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-46" name="__codelineno-20-46" href="#__codelineno-20-46"></a><span class="w">        </span><span class="c1">// 辺 vet1 - vet2 を削除</span>
+<a id="__codelineno-20-47" name="__codelineno-20-47" href="#__codelineno-20-47"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">vet1</span><span class="p">).</span><span class="nx">splice</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">vet1</span><span class="p">).</span><span class="nx">indexOf</span><span class="p">(</span><span class="nx">vet2</span><span class="p">),</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-20-48" name="__codelineno-20-48" href="#__codelineno-20-48"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">vet2</span><span class="p">).</span><span class="nx">splice</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">vet2</span><span class="p">).</span><span class="nx">indexOf</span><span class="p">(</span><span class="nx">vet1</span><span class="p">),</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-20-49" name="__codelineno-20-49" href="#__codelineno-20-49"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-50" name="__codelineno-20-50" href="#__codelineno-20-50"></a>
+<a id="__codelineno-20-51" name="__codelineno-20-51" href="#__codelineno-20-51"></a><span class="w">    </span><span class="cm">/* 頂点を追加 */</span>
+<a id="__codelineno-20-52" name="__codelineno-20-52" href="#__codelineno-20-52"></a><span class="w">    </span><span class="nx">addVertex</span><span class="p">(</span><span class="nx">vet</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-53" name="__codelineno-20-53" href="#__codelineno-20-53"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">has</span><span class="p">(</span><span class="nx">vet</span><span class="p">))</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-20-54" name="__codelineno-20-54" href="#__codelineno-20-54"></a><span class="w">        </span><span class="c1">// 隣接リストに新しいリストを追加</span>
+<a id="__codelineno-20-55" name="__codelineno-20-55" href="#__codelineno-20-55"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="nx">vet</span><span class="p">,</span><span class="w"> </span><span class="p">[]);</span>
+<a id="__codelineno-20-56" name="__codelineno-20-56" href="#__codelineno-20-56"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-57" name="__codelineno-20-57" href="#__codelineno-20-57"></a>
+<a id="__codelineno-20-58" name="__codelineno-20-58" href="#__codelineno-20-58"></a><span class="w">    </span><span class="cm">/* 頂点を削除 */</span>
+<a id="__codelineno-20-59" name="__codelineno-20-59" href="#__codelineno-20-59"></a><span class="w">    </span><span class="nx">removeVertex</span><span class="p">(</span><span class="nx">vet</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-60" name="__codelineno-20-60" href="#__codelineno-20-60"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">has</span><span class="p">(</span><span class="nx">vet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-61" name="__codelineno-20-61" href="#__codelineno-20-61"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;Illegal Argument Exception&#39;</span><span class="p">);</span>
+<a id="__codelineno-20-62" name="__codelineno-20-62" href="#__codelineno-20-62"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-63" name="__codelineno-20-63" href="#__codelineno-20-63"></a><span class="w">        </span><span class="c1">// 隣接リストから頂点 vet に対応するリストを削除</span>
+<a id="__codelineno-20-64" name="__codelineno-20-64" href="#__codelineno-20-64"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="ow">delete</span><span class="p">(</span><span class="nx">vet</span><span class="p">);</span>
+<a id="__codelineno-20-65" name="__codelineno-20-65" href="#__codelineno-20-65"></a><span class="w">        </span><span class="c1">// 他の頂点のリストを走査し、vet を含むすべての辺を削除</span>
+<a id="__codelineno-20-66" name="__codelineno-20-66" href="#__codelineno-20-66"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">set</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">values</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-67" name="__codelineno-20-67" href="#__codelineno-20-67"></a><span class="w">            </span><span class="kd">const</span><span class="w"> </span><span class="nx">index</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">set</span><span class="p">.</span><span class="nx">indexOf</span><span class="p">(</span><span class="nx">vet</span><span class="p">);</span>
+<a id="__codelineno-20-68" name="__codelineno-20-68" href="#__codelineno-20-68"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">index</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-69" name="__codelineno-20-69" href="#__codelineno-20-69"></a><span class="w">                </span><span class="nx">set</span><span class="p">.</span><span class="nx">splice</span><span class="p">(</span><span class="nx">index</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-20-70" name="__codelineno-20-70" href="#__codelineno-20-70"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-20-71" name="__codelineno-20-71" href="#__codelineno-20-71"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-72" name="__codelineno-20-72" href="#__codelineno-20-72"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-73" name="__codelineno-20-73" href="#__codelineno-20-73"></a>
+<a id="__codelineno-20-74" name="__codelineno-20-74" href="#__codelineno-20-74"></a><span class="w">    </span><span class="cm">/* 隣接リストを出力 */</span>
+<a id="__codelineno-20-75" name="__codelineno-20-75" href="#__codelineno-20-75"></a><span class="w">    </span><span class="nx">print</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-76" name="__codelineno-20-76" href="#__codelineno-20-76"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="s1">&#39;隣接リスト =&#39;</span><span class="p">);</span>
+<a id="__codelineno-20-77" name="__codelineno-20-77" href="#__codelineno-20-77"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="p">[</span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="nx">value</span><span class="p">]</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">entries</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-78" name="__codelineno-20-78" href="#__codelineno-20-78"></a><span class="w">            </span><span class="kd">const</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-20-79" name="__codelineno-20-79" href="#__codelineno-20-79"></a><span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">vertex</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">value</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-80" name="__codelineno-20-80" href="#__codelineno-20-80"></a><span class="w">                </span><span class="nx">tmp</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">vertex</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-20-81" name="__codelineno-20-81" href="#__codelineno-20-81"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-20-82" name="__codelineno-20-82" href="#__codelineno-20-82"></a><span class="w">            </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="nx">key</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s1">&#39;: &#39;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">tmp</span><span class="p">.</span><span class="nx">join</span><span class="p">());</span>
+<a id="__codelineno-20-83" name="__codelineno-20-83" href="#__codelineno-20-83"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-84" name="__codelineno-20-84" href="#__codelineno-20-84"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-85" name="__codelineno-20-85" href="#__codelineno-20-85"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_adjacency_list.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">GraphAdjList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">graph_adjacency_list.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 隣接リストに基づく無向グラフクラス */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">GraphAdjList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="c1">// 隣接リスト。key は頂点、value はその頂点に隣接する全頂点</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="n">Map</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">adjList</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{};</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">  </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">  </span><span class="n">GraphAdjList</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">edge</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">      </span><span class="n">addVertex</span><span class="p">(</span><span class="n">edge</span><span class="p">[</span><span class="m">0</span><span class="p">]);</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="w">      </span><span class="n">addVertex</span><span class="p">(</span><span class="n">edge</span><span class="p">[</span><span class="m">1</span><span class="p">]);</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="w">      </span><span class="n">addEdge</span><span class="p">(</span><span class="n">edge</span><span class="p">[</span><span class="m">0</span><span class="p">],</span><span class="w"> </span><span class="n">edge</span><span class="p">[</span><span class="m">1</span><span class="p">]);</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a>
+<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w">  </span><span class="cm">/* 頂点数を取得 */</span>
+<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-17" name="__codelineno-21-17" href="#__codelineno-21-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">adjList</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-21-18" name="__codelineno-21-18" href="#__codelineno-21-18"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-19" name="__codelineno-21-19" href="#__codelineno-21-19"></a>
+<a id="__codelineno-21-20" name="__codelineno-21-20" href="#__codelineno-21-20"></a><span class="w">  </span><span class="cm">/* 辺を追加 */</span>
+<a id="__codelineno-21-21" name="__codelineno-21-21" href="#__codelineno-21-21"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">addEdge</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet1</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-22" name="__codelineno-21-22" href="#__codelineno-21-22"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="n">containsKey</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span><span class="w"> </span><span class="o">||</span>
+<a id="__codelineno-21-23" name="__codelineno-21-23" href="#__codelineno-21-23"></a><span class="w">        </span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="n">containsKey</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="o">||</span>
+<a id="__codelineno-21-24" name="__codelineno-21-24" href="#__codelineno-21-24"></a><span class="w">        </span><span class="n">vet1</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-25" name="__codelineno-21-25" href="#__codelineno-21-25"></a><span class="w">      </span><span class="k">throw</span><span class="w"> </span><span class="n">ArgumentError</span><span class="p">;</span>
+<a id="__codelineno-21-26" name="__codelineno-21-26" href="#__codelineno-21-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-27" name="__codelineno-21-27" href="#__codelineno-21-27"></a><span class="w">    </span><span class="c1">// 辺 vet1 - vet2 を追加</span>
+<a id="__codelineno-21-28" name="__codelineno-21-28" href="#__codelineno-21-28"></a><span class="w">    </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet1</span><span class="p">]</span><span class="o">!</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">vet2</span><span class="p">);</span>
+<a id="__codelineno-21-29" name="__codelineno-21-29" href="#__codelineno-21-29"></a><span class="w">    </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet2</span><span class="p">]</span><span class="o">!</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">vet1</span><span class="p">);</span>
+<a id="__codelineno-21-30" name="__codelineno-21-30" href="#__codelineno-21-30"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-31" name="__codelineno-21-31" href="#__codelineno-21-31"></a>
+<a id="__codelineno-21-32" name="__codelineno-21-32" href="#__codelineno-21-32"></a><span class="w">  </span><span class="cm">/* 辺を削除 */</span>
+<a id="__codelineno-21-33" name="__codelineno-21-33" href="#__codelineno-21-33"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">removeEdge</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet1</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-34" name="__codelineno-21-34" href="#__codelineno-21-34"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="n">containsKey</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span><span class="w"> </span><span class="o">||</span>
+<a id="__codelineno-21-35" name="__codelineno-21-35" href="#__codelineno-21-35"></a><span class="w">        </span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="n">containsKey</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="o">||</span>
+<a id="__codelineno-21-36" name="__codelineno-21-36" href="#__codelineno-21-36"></a><span class="w">        </span><span class="n">vet1</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-37" name="__codelineno-21-37" href="#__codelineno-21-37"></a><span class="w">      </span><span class="k">throw</span><span class="w"> </span><span class="n">ArgumentError</span><span class="p">;</span>
+<a id="__codelineno-21-38" name="__codelineno-21-38" href="#__codelineno-21-38"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-39" name="__codelineno-21-39" href="#__codelineno-21-39"></a><span class="w">    </span><span class="c1">// 辺 vet1 - vet2 を削除</span>
+<a id="__codelineno-21-40" name="__codelineno-21-40" href="#__codelineno-21-40"></a><span class="w">    </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet1</span><span class="p">]</span><span class="o">!</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">vet2</span><span class="p">);</span>
+<a id="__codelineno-21-41" name="__codelineno-21-41" href="#__codelineno-21-41"></a><span class="w">    </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet2</span><span class="p">]</span><span class="o">!</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">vet1</span><span class="p">);</span>
+<a id="__codelineno-21-42" name="__codelineno-21-42" href="#__codelineno-21-42"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-43" name="__codelineno-21-43" href="#__codelineno-21-43"></a>
+<a id="__codelineno-21-44" name="__codelineno-21-44" href="#__codelineno-21-44"></a><span class="w">  </span><span class="cm">/* 頂点を追加 */</span>
+<a id="__codelineno-21-45" name="__codelineno-21-45" href="#__codelineno-21-45"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">addVertex</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-46" name="__codelineno-21-46" href="#__codelineno-21-46"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">adjList</span><span class="p">.</span><span class="n">containsKey</span><span class="p">(</span><span class="n">vet</span><span class="p">))</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-21-47" name="__codelineno-21-47" href="#__codelineno-21-47"></a><span class="w">    </span><span class="c1">// 隣接リストに新しいリストを追加</span>
+<a id="__codelineno-21-48" name="__codelineno-21-48" href="#__codelineno-21-48"></a><span class="w">    </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-21-49" name="__codelineno-21-49" href="#__codelineno-21-49"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-50" name="__codelineno-21-50" href="#__codelineno-21-50"></a>
+<a id="__codelineno-21-51" name="__codelineno-21-51" href="#__codelineno-21-51"></a><span class="w">  </span><span class="cm">/* 頂点を削除 */</span>
+<a id="__codelineno-21-52" name="__codelineno-21-52" href="#__codelineno-21-52"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">removeVertex</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-53" name="__codelineno-21-53" href="#__codelineno-21-53"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="n">containsKey</span><span class="p">(</span><span class="n">vet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-54" name="__codelineno-21-54" href="#__codelineno-21-54"></a><span class="w">      </span><span class="k">throw</span><span class="w"> </span><span class="n">ArgumentError</span><span class="p">;</span>
+<a id="__codelineno-21-55" name="__codelineno-21-55" href="#__codelineno-21-55"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-56" name="__codelineno-21-56" href="#__codelineno-21-56"></a><span class="w">    </span><span class="c1">// 隣接リストから頂点 vet に対応するリストを削除</span>
+<a id="__codelineno-21-57" name="__codelineno-21-57" href="#__codelineno-21-57"></a><span class="w">    </span><span class="n">adjList</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span>
+<a id="__codelineno-21-58" name="__codelineno-21-58" href="#__codelineno-21-58"></a><span class="w">    </span><span class="c1">// 他の頂点のリストを走査し、vet を含むすべての辺を削除</span>
+<a id="__codelineno-21-59" name="__codelineno-21-59" href="#__codelineno-21-59"></a><span class="w">    </span><span class="n">adjList</span><span class="p">.</span><span class="n">forEach</span><span class="p">((</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">value</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-60" name="__codelineno-21-60" href="#__codelineno-21-60"></a><span class="w">      </span><span class="n">value</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span>
+<a id="__codelineno-21-61" name="__codelineno-21-61" href="#__codelineno-21-61"></a><span class="w">    </span><span class="p">});</span>
+<a id="__codelineno-21-62" name="__codelineno-21-62" href="#__codelineno-21-62"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-63" name="__codelineno-21-63" href="#__codelineno-21-63"></a>
+<a id="__codelineno-21-64" name="__codelineno-21-64" href="#__codelineno-21-64"></a><span class="w">  </span><span class="cm">/* 隣接リストを出力 */</span>
+<a id="__codelineno-21-65" name="__codelineno-21-65" href="#__codelineno-21-65"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">printAdjList</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-66" name="__codelineno-21-66" href="#__codelineno-21-66"></a><span class="w">    </span><span class="n">print</span><span class="p">(</span><span class="s2">&quot;隣接リスト =&quot;</span><span class="p">);</span>
+<a id="__codelineno-21-67" name="__codelineno-21-67" href="#__codelineno-21-67"></a><span class="w">    </span><span class="n">adjList</span><span class="p">.</span><span class="n">forEach</span><span class="p">((</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">value</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-68" name="__codelineno-21-68" href="#__codelineno-21-68"></a><span class="w">      </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-21-69" name="__codelineno-21-69" href="#__codelineno-21-69"></a><span class="w">      </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">vertex</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">value</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-70" name="__codelineno-21-70" href="#__codelineno-21-70"></a><span class="w">        </span><span class="n">tmp</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">vertex</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-21-71" name="__codelineno-21-71" href="#__codelineno-21-71"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-21-72" name="__codelineno-21-72" href="#__codelineno-21-72"></a><span class="w">      </span><span class="n">print</span><span class="p">(</span><span class="s2">&quot;</span><span class="si">${</span><span class="n">key</span><span class="p">.</span><span class="n">val</span><span class="si">}</span><span class="s2">: </span><span class="si">$</span><span class="n">tmp</span><span class="s2">,&quot;</span><span class="p">);</span>
+<a id="__codelineno-21-73" name="__codelineno-21-73" href="#__codelineno-21-73"></a><span class="w">    </span><span class="p">});</span>
+<a id="__codelineno-21-74" name="__codelineno-21-74" href="#__codelineno-21-74"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-75" name="__codelineno-21-75" href="#__codelineno-21-75"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_adjacency_list.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">GraphAdjList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">graph_adjacency_list.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 隣接リストに基づく無向グラフ型 */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">pub</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">GraphAdjList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="c1">// 隣接リスト。key は頂点、value はその頂点に隣接する全頂点</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="n">adj_list</span><span class="p">:</span><span class="w"> </span><span class="nc">HashMap</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="p">,</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="c1">// maybe HashSet&lt;Vertex&gt; for value part is better?</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="p">}</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="k">impl</span><span class="w"> </span><span class="n">GraphAdjList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">new</span><span class="p">(</span><span class="n">edges</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="p">[</span><span class="n">Vertex</span><span class="p">;</span><span class="w"> </span><span class="mi">2</span><span class="p">]</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">graph</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">GraphAdjList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w">            </span><span class="n">adj_list</span><span class="p">:</span><span class="w"> </span><span class="nc">HashMap</span><span class="p">::</span><span class="n">new</span><span class="p">(),</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">        </span><span class="p">};</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">        </span><span class="c1">// すべての頂点と辺を追加</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">edge</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">edges</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="w">            </span><span class="n">graph</span><span class="p">.</span><span class="n">add_vertex</span><span class="p">(</span><span class="n">edge</span><span class="p">[</span><span class="mi">0</span><span class="p">]);</span>
+<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="w">            </span><span class="n">graph</span><span class="p">.</span><span class="n">add_vertex</span><span class="p">(</span><span class="n">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="w">            </span><span class="n">graph</span><span class="p">.</span><span class="n">add_edge</span><span class="p">(</span><span class="n">edge</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="n">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a>
+<a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a><span class="w">        </span><span class="n">graph</span>
+<a id="__codelineno-22-21" name="__codelineno-22-21" href="#__codelineno-22-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-22" name="__codelineno-22-22" href="#__codelineno-22-22"></a>
+<a id="__codelineno-22-23" name="__codelineno-22-23" href="#__codelineno-22-23"></a><span class="w">    </span><span class="cm">/* 頂点数を取得 */</span>
+<a id="__codelineno-22-24" name="__codelineno-22-24" href="#__codelineno-22-24"></a><span class="w">    </span><span class="cp">#[allow(unused)]</span>
+<a id="__codelineno-22-25" name="__codelineno-22-25" href="#__codelineno-22-25"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-26" name="__codelineno-22-26" href="#__codelineno-22-26"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">adj_list</span><span class="p">.</span><span class="n">len</span><span class="p">()</span>
+<a id="__codelineno-22-27" name="__codelineno-22-27" href="#__codelineno-22-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-28" name="__codelineno-22-28" href="#__codelineno-22-28"></a>
+<a id="__codelineno-22-29" name="__codelineno-22-29" href="#__codelineno-22-29"></a><span class="w">    </span><span class="cm">/* 辺を追加 */</span>
+<a id="__codelineno-22-30" name="__codelineno-22-30" href="#__codelineno-22-30"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">add_edge</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">vet1</span><span class="p">:</span><span class="w"> </span><span class="nc">Vertex</span><span class="p">,</span><span class="w"> </span><span class="n">vet2</span><span class="p">:</span><span class="w"> </span><span class="nc">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-31" name="__codelineno-22-31" href="#__codelineno-22-31"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">vet1</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-32" name="__codelineno-22-32" href="#__codelineno-22-32"></a><span class="w">            </span><span class="fm">panic!</span><span class="p">(</span><span class="s">&quot;value error&quot;</span><span class="p">);</span>
+<a id="__codelineno-22-33" name="__codelineno-22-33" href="#__codelineno-22-33"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-34" name="__codelineno-22-34" href="#__codelineno-22-34"></a><span class="w">        </span><span class="c1">// 辺 vet1 - vet2 を追加</span>
+<a id="__codelineno-22-35" name="__codelineno-22-35" href="#__codelineno-22-35"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">adj_list</span><span class="p">.</span><span class="n">entry</span><span class="p">(</span><span class="n">vet1</span><span class="p">).</span><span class="n">or_default</span><span class="p">().</span><span class="n">push</span><span class="p">(</span><span class="n">vet2</span><span class="p">);</span>
+<a id="__codelineno-22-36" name="__codelineno-22-36" href="#__codelineno-22-36"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">adj_list</span><span class="p">.</span><span class="n">entry</span><span class="p">(</span><span class="n">vet2</span><span class="p">).</span><span class="n">or_default</span><span class="p">().</span><span class="n">push</span><span class="p">(</span><span class="n">vet1</span><span class="p">);</span>
+<a id="__codelineno-22-37" name="__codelineno-22-37" href="#__codelineno-22-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-38" name="__codelineno-22-38" href="#__codelineno-22-38"></a>
+<a id="__codelineno-22-39" name="__codelineno-22-39" href="#__codelineno-22-39"></a><span class="w">    </span><span class="cm">/* 辺を削除 */</span>
+<a id="__codelineno-22-40" name="__codelineno-22-40" href="#__codelineno-22-40"></a><span class="w">    </span><span class="cp">#[allow(unused)]</span>
+<a id="__codelineno-22-41" name="__codelineno-22-41" href="#__codelineno-22-41"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">remove_edge</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">vet1</span><span class="p">:</span><span class="w"> </span><span class="nc">Vertex</span><span class="p">,</span><span class="w"> </span><span class="n">vet2</span><span class="p">:</span><span class="w"> </span><span class="nc">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-42" name="__codelineno-22-42" href="#__codelineno-22-42"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">vet1</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-43" name="__codelineno-22-43" href="#__codelineno-22-43"></a><span class="w">            </span><span class="fm">panic!</span><span class="p">(</span><span class="s">&quot;value error&quot;</span><span class="p">);</span>
+<a id="__codelineno-22-44" name="__codelineno-22-44" href="#__codelineno-22-44"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-45" name="__codelineno-22-45" href="#__codelineno-22-45"></a><span class="w">        </span><span class="c1">// 辺 vet1 - vet2 を削除</span>
+<a id="__codelineno-22-46" name="__codelineno-22-46" href="#__codelineno-22-46"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">adj_list</span>
+<a id="__codelineno-22-47" name="__codelineno-22-47" href="#__codelineno-22-47"></a><span class="w">            </span><span class="p">.</span><span class="n">entry</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span>
+<a id="__codelineno-22-48" name="__codelineno-22-48" href="#__codelineno-22-48"></a><span class="w">            </span><span class="p">.</span><span class="n">and_modify</span><span class="p">(</span><span class="o">|</span><span class="n">v</span><span class="o">|</span><span class="w"> </span><span class="n">v</span><span class="p">.</span><span class="n">retain</span><span class="p">(</span><span class="o">|&amp;</span><span class="n">e</span><span class="o">|</span><span class="w"> </span><span class="n">e</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">vet2</span><span class="p">));</span>
+<a id="__codelineno-22-49" name="__codelineno-22-49" href="#__codelineno-22-49"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">adj_list</span>
+<a id="__codelineno-22-50" name="__codelineno-22-50" href="#__codelineno-22-50"></a><span class="w">            </span><span class="p">.</span><span class="n">entry</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span>
+<a id="__codelineno-22-51" name="__codelineno-22-51" href="#__codelineno-22-51"></a><span class="w">            </span><span class="p">.</span><span class="n">and_modify</span><span class="p">(</span><span class="o">|</span><span class="n">v</span><span class="o">|</span><span class="w"> </span><span class="n">v</span><span class="p">.</span><span class="n">retain</span><span class="p">(</span><span class="o">|&amp;</span><span class="n">e</span><span class="o">|</span><span class="w"> </span><span class="n">e</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">vet1</span><span class="p">));</span>
+<a id="__codelineno-22-52" name="__codelineno-22-52" href="#__codelineno-22-52"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-53" name="__codelineno-22-53" href="#__codelineno-22-53"></a>
+<a id="__codelineno-22-54" name="__codelineno-22-54" href="#__codelineno-22-54"></a><span class="w">    </span><span class="cm">/* 頂点を追加 */</span>
+<a id="__codelineno-22-55" name="__codelineno-22-55" href="#__codelineno-22-55"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">add_vertex</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">vet</span><span class="p">:</span><span class="w"> </span><span class="nc">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-56" name="__codelineno-22-56" href="#__codelineno-22-56"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">adj_list</span><span class="p">.</span><span class="n">contains_key</span><span class="p">(</span><span class="o">&amp;</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-57" name="__codelineno-22-57" href="#__codelineno-22-57"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-22-58" name="__codelineno-22-58" href="#__codelineno-22-58"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-59" name="__codelineno-22-59" href="#__codelineno-22-59"></a><span class="w">        </span><span class="c1">// 隣接リストに新しいリストを追加</span>
+<a id="__codelineno-22-60" name="__codelineno-22-60" href="#__codelineno-22-60"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">adj_list</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">vet</span><span class="p">,</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[]);</span>
+<a id="__codelineno-22-61" name="__codelineno-22-61" href="#__codelineno-22-61"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-62" name="__codelineno-22-62" href="#__codelineno-22-62"></a>
+<a id="__codelineno-22-63" name="__codelineno-22-63" href="#__codelineno-22-63"></a><span class="w">    </span><span class="cm">/* 頂点を削除 */</span>
+<a id="__codelineno-22-64" name="__codelineno-22-64" href="#__codelineno-22-64"></a><span class="w">    </span><span class="cp">#[allow(unused)]</span>
+<a id="__codelineno-22-65" name="__codelineno-22-65" href="#__codelineno-22-65"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">remove_vertex</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">vet</span><span class="p">:</span><span class="w"> </span><span class="nc">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-66" name="__codelineno-22-66" href="#__codelineno-22-66"></a><span class="w">        </span><span class="c1">// 隣接リストから頂点 vet に対応するリストを削除</span>
+<a id="__codelineno-22-67" name="__codelineno-22-67" href="#__codelineno-22-67"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">adj_list</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="o">&amp;</span><span class="n">vet</span><span class="p">);</span>
+<a id="__codelineno-22-68" name="__codelineno-22-68" href="#__codelineno-22-68"></a><span class="w">        </span><span class="c1">// 他の頂点のリストを走査し、vet を含むすべての辺を削除</span>
+<a id="__codelineno-22-69" name="__codelineno-22-69" href="#__codelineno-22-69"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">list</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">adj_list</span><span class="p">.</span><span class="n">values_mut</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-70" name="__codelineno-22-70" href="#__codelineno-22-70"></a><span class="w">            </span><span class="n">list</span><span class="p">.</span><span class="n">retain</span><span class="p">(</span><span class="o">|&amp;</span><span class="n">v</span><span class="o">|</span><span class="w"> </span><span class="n">v</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">vet</span><span class="p">);</span>
+<a id="__codelineno-22-71" name="__codelineno-22-71" href="#__codelineno-22-71"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-72" name="__codelineno-22-72" href="#__codelineno-22-72"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-73" name="__codelineno-22-73" href="#__codelineno-22-73"></a>
+<a id="__codelineno-22-74" name="__codelineno-22-74" href="#__codelineno-22-74"></a><span class="w">    </span><span class="cm">/* 隣接リストを出力 */</span>
+<a id="__codelineno-22-75" name="__codelineno-22-75" href="#__codelineno-22-75"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">print</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-76" name="__codelineno-22-76" href="#__codelineno-22-76"></a><span class="w">        </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;隣接リスト =&quot;</span><span class="p">);</span>
+<a id="__codelineno-22-77" name="__codelineno-22-77" href="#__codelineno-22-77"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">vertex</span><span class="p">,</span><span class="w"> </span><span class="n">list</span><span class="p">)</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="o">&amp;</span><span class="bp">self</span><span class="p">.</span><span class="n">adj_list</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-78" name="__codelineno-22-78" href="#__codelineno-22-78"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="n">list</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">list</span><span class="p">.</span><span class="n">iter</span><span class="p">().</span><span class="n">map</span><span class="p">(</span><span class="o">|</span><span class="n">vertex</span><span class="o">|</span><span class="w"> </span><span class="n">vertex</span><span class="p">.</span><span class="n">val</span><span class="p">).</span><span class="n">collect</span><span class="p">::</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-22-79" name="__codelineno-22-79" href="#__codelineno-22-79"></a><span class="w">            </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}: {:?},&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">vertex</span><span class="p">.</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">list</span><span class="p">);</span>
+<a id="__codelineno-22-80" name="__codelineno-22-80" href="#__codelineno-22-80"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-81" name="__codelineno-22-81" href="#__codelineno-22-81"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-82" name="__codelineno-22-82" href="#__codelineno-22-82"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_adjacency_list.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AdjListNode</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
-<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a>
-<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">GraphAdjList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">graph_adjacency_list.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* ノード構造体 */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">AdjListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vertex</span><span class="p">;</span><span class="w">           </span><span class="c1">// 頂点</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="k">struct</span><span class="w"> </span><span class="nc">AdjListNode</span><span class="w"> </span><span class="o">*</span><span class="n">next</span><span class="p">;</span><span class="w"> </span><span class="c1">// 後続ノード</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="p">}</span><span class="w"> </span><span class="n">AdjListNode</span><span class="p">;</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="cm">/* 頂点に対応するノードを検索 */</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="n">AdjListNode</span><span class="w"> </span><span class="o">*</span><span class="nf">findNode</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">*</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">heads</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">vertex</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">heads</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="p">}</span>
+<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a>
+<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="cm">/* 辺を追加する補助関数 */</span>
+<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="kt">void</span><span class="w"> </span><span class="nf">addEdgeHelper</span><span class="p">(</span><span class="n">AdjListNode</span><span class="w"> </span><span class="o">*</span><span class="n">head</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="w">    </span><span class="n">AdjListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">AdjListNode</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">AdjListNode</span><span class="p">));</span>
+<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">vertex</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vet</span><span class="p">;</span>
+<a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a><span class="w">    </span><span class="c1">// 先頭挿入法</span>
+<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-23-23" name="__codelineno-23-23" href="#__codelineno-23-23"></a><span class="w">    </span><span class="n">head</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-23-24" name="__codelineno-23-24" href="#__codelineno-23-24"></a><span class="p">}</span>
+<a id="__codelineno-23-25" name="__codelineno-23-25" href="#__codelineno-23-25"></a>
+<a id="__codelineno-23-26" name="__codelineno-23-26" href="#__codelineno-23-26"></a><span class="cm">/* 辺削除の補助関数 */</span>
+<a id="__codelineno-23-27" name="__codelineno-23-27" href="#__codelineno-23-27"></a><span class="kt">void</span><span class="w"> </span><span class="nf">removeEdgeHelper</span><span class="p">(</span><span class="n">AdjListNode</span><span class="w"> </span><span class="o">*</span><span class="n">head</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-28" name="__codelineno-23-28" href="#__codelineno-23-28"></a><span class="w">    </span><span class="n">AdjListNode</span><span class="w"> </span><span class="o">*</span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="p">;</span>
+<a id="__codelineno-23-29" name="__codelineno-23-29" href="#__codelineno-23-29"></a><span class="w">    </span><span class="n">AdjListNode</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-23-30" name="__codelineno-23-30" href="#__codelineno-23-30"></a><span class="w">    </span><span class="c1">// 連結リスト内で vet に対応するノードを探索</span>
+<a id="__codelineno-23-31" name="__codelineno-23-31" href="#__codelineno-23-31"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">vertex</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-32" name="__codelineno-23-32" href="#__codelineno-23-32"></a><span class="w">        </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
+<a id="__codelineno-23-33" name="__codelineno-23-33" href="#__codelineno-23-33"></a><span class="w">        </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-23-34" name="__codelineno-23-34" href="#__codelineno-23-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-35" name="__codelineno-23-35" href="#__codelineno-23-35"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span>
+<a id="__codelineno-23-36" name="__codelineno-23-36" href="#__codelineno-23-36"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-23-37" name="__codelineno-23-37" href="#__codelineno-23-37"></a><span class="w">    </span><span class="c1">// vet に対応するノードを連結リストから削除</span>
+<a id="__codelineno-23-38" name="__codelineno-23-38" href="#__codelineno-23-38"></a><span class="w">    </span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-23-39" name="__codelineno-23-39" href="#__codelineno-23-39"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-23-40" name="__codelineno-23-40" href="#__codelineno-23-40"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">cur</span><span class="p">);</span>
+<a id="__codelineno-23-41" name="__codelineno-23-41" href="#__codelineno-23-41"></a><span class="p">}</span>
+<a id="__codelineno-23-42" name="__codelineno-23-42" href="#__codelineno-23-42"></a>
+<a id="__codelineno-23-43" name="__codelineno-23-43" href="#__codelineno-23-43"></a><span class="cm">/* 隣接リストに基づく無向グラフクラス */</span>
+<a id="__codelineno-23-44" name="__codelineno-23-44" href="#__codelineno-23-44"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-45" name="__codelineno-23-45" href="#__codelineno-23-45"></a><span class="w">    </span><span class="n">AdjListNode</span><span class="w"> </span><span class="o">*</span><span class="n">heads</span><span class="p">[</span><span class="n">MAX_SIZE</span><span class="p">];</span><span class="w"> </span><span class="c1">// ノード配列</span>
+<a id="__codelineno-23-46" name="__codelineno-23-46" href="#__codelineno-23-46"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w">                     </span><span class="c1">// ノード数</span>
+<a id="__codelineno-23-47" name="__codelineno-23-47" href="#__codelineno-23-47"></a><span class="p">}</span><span class="w"> </span><span class="n">GraphAdjList</span><span class="p">;</span>
+<a id="__codelineno-23-48" name="__codelineno-23-48" href="#__codelineno-23-48"></a>
+<a id="__codelineno-23-49" name="__codelineno-23-49" href="#__codelineno-23-49"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-23-50" name="__codelineno-23-50" href="#__codelineno-23-50"></a><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">*</span><span class="nf">newGraphAdjList</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-51" name="__codelineno-23-51" href="#__codelineno-23-51"></a><span class="w">    </span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">*</span><span class="n">graph</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="p">));</span>
+<a id="__codelineno-23-52" name="__codelineno-23-52" href="#__codelineno-23-52"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">graph</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-53" name="__codelineno-23-53" href="#__codelineno-23-53"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-23-54" name="__codelineno-23-54" href="#__codelineno-23-54"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-55" name="__codelineno-23-55" href="#__codelineno-23-55"></a><span class="w">    </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-23-56" name="__codelineno-23-56" href="#__codelineno-23-56"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-57" name="__codelineno-23-57" href="#__codelineno-23-57"></a><span class="w">        </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">heads</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-23-58" name="__codelineno-23-58" href="#__codelineno-23-58"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-59" name="__codelineno-23-59" href="#__codelineno-23-59"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">graph</span><span class="p">;</span>
+<a id="__codelineno-23-60" name="__codelineno-23-60" href="#__codelineno-23-60"></a><span class="p">}</span>
+<a id="__codelineno-23-61" name="__codelineno-23-61" href="#__codelineno-23-61"></a>
+<a id="__codelineno-23-62" name="__codelineno-23-62" href="#__codelineno-23-62"></a><span class="cm">/* デストラクタ */</span>
+<a id="__codelineno-23-63" name="__codelineno-23-63" href="#__codelineno-23-63"></a><span class="kt">void</span><span class="w"> </span><span class="nf">delGraphAdjList</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">*</span><span class="n">graph</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-64" name="__codelineno-23-64" href="#__codelineno-23-64"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-65" name="__codelineno-23-65" href="#__codelineno-23-65"></a><span class="w">        </span><span class="n">AdjListNode</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">heads</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-23-66" name="__codelineno-23-66" href="#__codelineno-23-66"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-67" name="__codelineno-23-67" href="#__codelineno-23-67"></a><span class="w">            </span><span class="n">AdjListNode</span><span class="w"> </span><span class="o">*</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-23-68" name="__codelineno-23-68" href="#__codelineno-23-68"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">heads</span><span class="p">[</span><span class="n">i</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-69" name="__codelineno-23-69" href="#__codelineno-23-69"></a><span class="w">                </span><span class="n">free</span><span class="p">(</span><span class="n">cur</span><span class="p">);</span>
+<a id="__codelineno-23-70" name="__codelineno-23-70" href="#__codelineno-23-70"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-23-71" name="__codelineno-23-71" href="#__codelineno-23-71"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-23-72" name="__codelineno-23-72" href="#__codelineno-23-72"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-73" name="__codelineno-23-73" href="#__codelineno-23-73"></a><span class="w">        </span><span class="n">free</span><span class="p">(</span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">heads</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">vertex</span><span class="p">);</span>
+<a id="__codelineno-23-74" name="__codelineno-23-74" href="#__codelineno-23-74"></a><span class="w">        </span><span class="n">free</span><span class="p">(</span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">heads</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-23-75" name="__codelineno-23-75" href="#__codelineno-23-75"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-76" name="__codelineno-23-76" href="#__codelineno-23-76"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">graph</span><span class="p">);</span>
+<a id="__codelineno-23-77" name="__codelineno-23-77" href="#__codelineno-23-77"></a><span class="p">}</span>
+<a id="__codelineno-23-78" name="__codelineno-23-78" href="#__codelineno-23-78"></a>
+<a id="__codelineno-23-79" name="__codelineno-23-79" href="#__codelineno-23-79"></a><span class="cm">/* 頂点に対応するノードを検索 */</span>
+<a id="__codelineno-23-80" name="__codelineno-23-80" href="#__codelineno-23-80"></a><span class="n">AdjListNode</span><span class="w"> </span><span class="o">*</span><span class="nf">findNode</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">*</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-81" name="__codelineno-23-81" href="#__codelineno-23-81"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-82" name="__codelineno-23-82" href="#__codelineno-23-82"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">heads</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">vertex</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-83" name="__codelineno-23-83" href="#__codelineno-23-83"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">heads</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-23-84" name="__codelineno-23-84" href="#__codelineno-23-84"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-85" name="__codelineno-23-85" href="#__codelineno-23-85"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-86" name="__codelineno-23-86" href="#__codelineno-23-86"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-23-87" name="__codelineno-23-87" href="#__codelineno-23-87"></a><span class="p">}</span>
+<a id="__codelineno-23-88" name="__codelineno-23-88" href="#__codelineno-23-88"></a>
+<a id="__codelineno-23-89" name="__codelineno-23-89" href="#__codelineno-23-89"></a><span class="cm">/* 辺を追加 */</span>
+<a id="__codelineno-23-90" name="__codelineno-23-90" href="#__codelineno-23-90"></a><span class="kt">void</span><span class="w"> </span><span class="nf">addEdge</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">*</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet1</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-91" name="__codelineno-23-91" href="#__codelineno-23-91"></a><span class="w">    </span><span class="n">AdjListNode</span><span class="w"> </span><span class="o">*</span><span class="n">head1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findNode</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">vet1</span><span class="p">);</span>
+<a id="__codelineno-23-92" name="__codelineno-23-92" href="#__codelineno-23-92"></a><span class="w">    </span><span class="n">AdjListNode</span><span class="w"> </span><span class="o">*</span><span class="n">head2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findNode</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">vet2</span><span class="p">);</span>
+<a id="__codelineno-23-93" name="__codelineno-23-93" href="#__codelineno-23-93"></a><span class="w">    </span><span class="n">assert</span><span class="p">(</span><span class="n">head1</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">head2</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">head1</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">head2</span><span class="p">);</span>
+<a id="__codelineno-23-94" name="__codelineno-23-94" href="#__codelineno-23-94"></a><span class="w">    </span><span class="c1">// 辺 vet1 - vet2 を追加</span>
+<a id="__codelineno-23-95" name="__codelineno-23-95" href="#__codelineno-23-95"></a><span class="w">    </span><span class="n">addEdgeHelper</span><span class="p">(</span><span class="n">head1</span><span class="p">,</span><span class="w"> </span><span class="n">vet2</span><span class="p">);</span>
+<a id="__codelineno-23-96" name="__codelineno-23-96" href="#__codelineno-23-96"></a><span class="w">    </span><span class="n">addEdgeHelper</span><span class="p">(</span><span class="n">head2</span><span class="p">,</span><span class="w"> </span><span class="n">vet1</span><span class="p">);</span>
+<a id="__codelineno-23-97" name="__codelineno-23-97" href="#__codelineno-23-97"></a><span class="p">}</span>
+<a id="__codelineno-23-98" name="__codelineno-23-98" href="#__codelineno-23-98"></a>
+<a id="__codelineno-23-99" name="__codelineno-23-99" href="#__codelineno-23-99"></a><span class="cm">/* 辺を削除 */</span>
+<a id="__codelineno-23-100" name="__codelineno-23-100" href="#__codelineno-23-100"></a><span class="kt">void</span><span class="w"> </span><span class="nf">removeEdge</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">*</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet1</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-101" name="__codelineno-23-101" href="#__codelineno-23-101"></a><span class="w">    </span><span class="n">AdjListNode</span><span class="w"> </span><span class="o">*</span><span class="n">head1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findNode</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">vet1</span><span class="p">);</span>
+<a id="__codelineno-23-102" name="__codelineno-23-102" href="#__codelineno-23-102"></a><span class="w">    </span><span class="n">AdjListNode</span><span class="w"> </span><span class="o">*</span><span class="n">head2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findNode</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">vet2</span><span class="p">);</span>
+<a id="__codelineno-23-103" name="__codelineno-23-103" href="#__codelineno-23-103"></a><span class="w">    </span><span class="n">assert</span><span class="p">(</span><span class="n">head1</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">head2</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">);</span>
+<a id="__codelineno-23-104" name="__codelineno-23-104" href="#__codelineno-23-104"></a><span class="w">    </span><span class="c1">// 辺 vet1 - vet2 を削除</span>
+<a id="__codelineno-23-105" name="__codelineno-23-105" href="#__codelineno-23-105"></a><span class="w">    </span><span class="n">removeEdgeHelper</span><span class="p">(</span><span class="n">head1</span><span class="p">,</span><span class="w"> </span><span class="n">head2</span><span class="o">-&gt;</span><span class="n">vertex</span><span class="p">);</span>
+<a id="__codelineno-23-106" name="__codelineno-23-106" href="#__codelineno-23-106"></a><span class="w">    </span><span class="n">removeEdgeHelper</span><span class="p">(</span><span class="n">head2</span><span class="p">,</span><span class="w"> </span><span class="n">head1</span><span class="o">-&gt;</span><span class="n">vertex</span><span class="p">);</span>
+<a id="__codelineno-23-107" name="__codelineno-23-107" href="#__codelineno-23-107"></a><span class="p">}</span>
+<a id="__codelineno-23-108" name="__codelineno-23-108" href="#__codelineno-23-108"></a>
+<a id="__codelineno-23-109" name="__codelineno-23-109" href="#__codelineno-23-109"></a><span class="cm">/* 頂点を追加 */</span>
+<a id="__codelineno-23-110" name="__codelineno-23-110" href="#__codelineno-23-110"></a><span class="kt">void</span><span class="w"> </span><span class="nf">addVertex</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">*</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-111" name="__codelineno-23-111" href="#__codelineno-23-111"></a><span class="w">    </span><span class="n">assert</span><span class="p">(</span><span class="n">graph</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">);</span>
+<a id="__codelineno-23-112" name="__codelineno-23-112" href="#__codelineno-23-112"></a><span class="w">    </span><span class="n">AdjListNode</span><span class="w"> </span><span class="o">*</span><span class="n">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">AdjListNode</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">AdjListNode</span><span class="p">));</span>
+<a id="__codelineno-23-113" name="__codelineno-23-113" href="#__codelineno-23-113"></a><span class="w">    </span><span class="n">head</span><span class="o">-&gt;</span><span class="n">vertex</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vet</span><span class="p">;</span>
+<a id="__codelineno-23-114" name="__codelineno-23-114" href="#__codelineno-23-114"></a><span class="w">    </span><span class="n">head</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-23-115" name="__codelineno-23-115" href="#__codelineno-23-115"></a><span class="w">    </span><span class="c1">// 隣接リストに新しいリストを追加</span>
+<a id="__codelineno-23-116" name="__codelineno-23-116" href="#__codelineno-23-116"></a><span class="w">    </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">heads</span><span class="p">[</span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="p">;</span>
+<a id="__codelineno-23-117" name="__codelineno-23-117" href="#__codelineno-23-117"></a><span class="p">}</span>
+<a id="__codelineno-23-118" name="__codelineno-23-118" href="#__codelineno-23-118"></a>
+<a id="__codelineno-23-119" name="__codelineno-23-119" href="#__codelineno-23-119"></a><span class="cm">/* 頂点を削除 */</span>
+<a id="__codelineno-23-120" name="__codelineno-23-120" href="#__codelineno-23-120"></a><span class="kt">void</span><span class="w"> </span><span class="nf">removeVertex</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">*</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-121" name="__codelineno-23-121" href="#__codelineno-23-121"></a><span class="w">    </span><span class="n">AdjListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findNode</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">vet</span><span class="p">);</span>
+<a id="__codelineno-23-122" name="__codelineno-23-122" href="#__codelineno-23-122"></a><span class="w">    </span><span class="n">assert</span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">);</span>
+<a id="__codelineno-23-123" name="__codelineno-23-123" href="#__codelineno-23-123"></a><span class="w">    </span><span class="c1">// 隣接リストから頂点 vet に対応するリストを削除</span>
+<a id="__codelineno-23-124" name="__codelineno-23-124" href="#__codelineno-23-124"></a><span class="w">    </span><span class="n">AdjListNode</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-23-125" name="__codelineno-23-125" href="#__codelineno-23-125"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-126" name="__codelineno-23-126" href="#__codelineno-23-126"></a><span class="w">        </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
+<a id="__codelineno-23-127" name="__codelineno-23-127" href="#__codelineno-23-127"></a><span class="w">        </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-23-128" name="__codelineno-23-128" href="#__codelineno-23-128"></a><span class="w">        </span><span class="n">free</span><span class="p">(</span><span class="n">pre</span><span class="p">);</span>
+<a id="__codelineno-23-129" name="__codelineno-23-129" href="#__codelineno-23-129"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-130" name="__codelineno-23-130" href="#__codelineno-23-130"></a><span class="w">    </span><span class="c1">// 他の頂点のリストを走査し、vet を含むすべての辺を削除</span>
+<a id="__codelineno-23-131" name="__codelineno-23-131" href="#__codelineno-23-131"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-132" name="__codelineno-23-132" href="#__codelineno-23-132"></a><span class="w">        </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">heads</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-23-133" name="__codelineno-23-133" href="#__codelineno-23-133"></a><span class="w">        </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-23-134" name="__codelineno-23-134" href="#__codelineno-23-134"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-135" name="__codelineno-23-135" href="#__codelineno-23-135"></a><span class="w">            </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
+<a id="__codelineno-23-136" name="__codelineno-23-136" href="#__codelineno-23-136"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-23-137" name="__codelineno-23-137" href="#__codelineno-23-137"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">vertex</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-138" name="__codelineno-23-138" href="#__codelineno-23-138"></a><span class="w">                </span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-23-139" name="__codelineno-23-139" href="#__codelineno-23-139"></a><span class="w">                </span><span class="n">free</span><span class="p">(</span><span class="n">cur</span><span class="p">);</span>
+<a id="__codelineno-23-140" name="__codelineno-23-140" href="#__codelineno-23-140"></a><span class="w">                </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-23-141" name="__codelineno-23-141" href="#__codelineno-23-141"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-23-142" name="__codelineno-23-142" href="#__codelineno-23-142"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-143" name="__codelineno-23-143" href="#__codelineno-23-143"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-144" name="__codelineno-23-144" href="#__codelineno-23-144"></a><span class="w">    </span><span class="c1">// この頂点より後ろの頂点を前に詰めて欠損を埋める</span>
+<a id="__codelineno-23-145" name="__codelineno-23-145" href="#__codelineno-23-145"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-23-146" name="__codelineno-23-146" href="#__codelineno-23-146"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-147" name="__codelineno-23-147" href="#__codelineno-23-147"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">heads</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-23-148" name="__codelineno-23-148" href="#__codelineno-23-148"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-23-149" name="__codelineno-23-149" href="#__codelineno-23-149"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-150" name="__codelineno-23-150" href="#__codelineno-23-150"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-151" name="__codelineno-23-151" href="#__codelineno-23-151"></a><span class="w">        </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">heads</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">heads</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-23-152" name="__codelineno-23-152" href="#__codelineno-23-152"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-153" name="__codelineno-23-153" href="#__codelineno-23-153"></a><span class="w">    </span><span class="n">graph</span><span class="o">-&gt;</span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-23-154" name="__codelineno-23-154" href="#__codelineno-23-154"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span>
+<a id="__codelineno-23-155" name="__codelineno-23-155" href="#__codelineno-23-155"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_adjacency_list.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">GraphAdjList</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">graph_adjacency_list.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 隣接リストに基づく無向グラフクラス */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">GraphAdjList</span><span class="p">(</span><span class="n">edges</span><span class="p">:</span><span class="w"> </span><span class="n">Array</span><span class="o">&lt;</span><span class="n">Array</span><span class="o">&lt;</span><span class="n">Vertex?&gt;</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="c1">// 隣接リスト。key は頂点、value はその頂点に隣接する全頂点</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">adjList</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashMap</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="p">,</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;&gt;</span><span class="p">()</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w">    </span><span class="k">init</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w">        </span><span class="c1">// すべての頂点と辺を追加</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">edge</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w">            </span><span class="n">addVertex</span><span class="p">(</span><span class="n">edge</span><span class="o">[</span><span class="m">0</span><span class="o">]!!</span><span class="p">)</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="w">            </span><span class="n">addVertex</span><span class="p">(</span><span class="n">edge</span><span class="o">[</span><span class="m">1</span><span class="o">]!!</span><span class="p">)</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">            </span><span class="n">addEdge</span><span class="p">(</span><span class="n">edge</span><span class="o">[</span><span class="m">0</span><span class="o">]!!</span><span class="p">,</span><span class="w"> </span><span class="n">edge</span><span class="o">[</span><span class="m">1</span><span class="o">]!!</span><span class="p">)</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a>
+<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="w">    </span><span class="cm">/* 頂点数を取得 */</span>
+<a id="__codelineno-24-17" name="__codelineno-24-17" href="#__codelineno-24-17"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">size</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-18" name="__codelineno-24-18" href="#__codelineno-24-18"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">adjList</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-24-19" name="__codelineno-24-19" href="#__codelineno-24-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-20" name="__codelineno-24-20" href="#__codelineno-24-20"></a>
+<a id="__codelineno-24-21" name="__codelineno-24-21" href="#__codelineno-24-21"></a><span class="w">    </span><span class="cm">/* 辺を追加 */</span>
+<a id="__codelineno-24-22" name="__codelineno-24-22" href="#__codelineno-24-22"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">addEdge</span><span class="p">(</span><span class="n">vet1</span><span class="p">:</span><span class="w"> </span><span class="n">Vertex</span><span class="p">,</span><span class="w"> </span><span class="n">vet2</span><span class="p">:</span><span class="w"> </span><span class="n">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-23" name="__codelineno-24-23" href="#__codelineno-24-23"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="na">containsKey</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="na">containsKey</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">vet1</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span>
+<a id="__codelineno-24-24" name="__codelineno-24-24" href="#__codelineno-24-24"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">IllegalArgumentException</span><span class="p">()</span>
+<a id="__codelineno-24-25" name="__codelineno-24-25" href="#__codelineno-24-25"></a><span class="w">        </span><span class="c1">// 辺 vet1 - vet2 を追加</span>
+<a id="__codelineno-24-26" name="__codelineno-24-26" href="#__codelineno-24-26"></a><span class="w">        </span><span class="n">adjList</span><span class="o">[</span><span class="n">vet1</span><span class="o">]?.</span><span class="na">add</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span>
+<a id="__codelineno-24-27" name="__codelineno-24-27" href="#__codelineno-24-27"></a><span class="w">        </span><span class="n">adjList</span><span class="o">[</span><span class="n">vet2</span><span class="o">]?.</span><span class="na">add</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span>
+<a id="__codelineno-24-28" name="__codelineno-24-28" href="#__codelineno-24-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-29" name="__codelineno-24-29" href="#__codelineno-24-29"></a>
+<a id="__codelineno-24-30" name="__codelineno-24-30" href="#__codelineno-24-30"></a><span class="w">    </span><span class="cm">/* 辺を削除 */</span>
+<a id="__codelineno-24-31" name="__codelineno-24-31" href="#__codelineno-24-31"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">removeEdge</span><span class="p">(</span><span class="n">vet1</span><span class="p">:</span><span class="w"> </span><span class="n">Vertex</span><span class="p">,</span><span class="w"> </span><span class="n">vet2</span><span class="p">:</span><span class="w"> </span><span class="n">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-32" name="__codelineno-24-32" href="#__codelineno-24-32"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="na">containsKey</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="na">containsKey</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">vet1</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span>
+<a id="__codelineno-24-33" name="__codelineno-24-33" href="#__codelineno-24-33"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">IllegalArgumentException</span><span class="p">()</span>
+<a id="__codelineno-24-34" name="__codelineno-24-34" href="#__codelineno-24-34"></a><span class="w">        </span><span class="c1">// 辺 vet1 - vet2 を削除</span>
+<a id="__codelineno-24-35" name="__codelineno-24-35" href="#__codelineno-24-35"></a><span class="w">        </span><span class="n">adjList</span><span class="o">[</span><span class="n">vet1</span><span class="o">]?.</span><span class="na">remove</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span>
+<a id="__codelineno-24-36" name="__codelineno-24-36" href="#__codelineno-24-36"></a><span class="w">        </span><span class="n">adjList</span><span class="o">[</span><span class="n">vet2</span><span class="o">]?.</span><span class="na">remove</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span>
+<a id="__codelineno-24-37" name="__codelineno-24-37" href="#__codelineno-24-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-38" name="__codelineno-24-38" href="#__codelineno-24-38"></a>
+<a id="__codelineno-24-39" name="__codelineno-24-39" href="#__codelineno-24-39"></a><span class="w">    </span><span class="cm">/* 頂点を追加 */</span>
+<a id="__codelineno-24-40" name="__codelineno-24-40" href="#__codelineno-24-40"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">addVertex</span><span class="p">(</span><span class="n">vet</span><span class="p">:</span><span class="w"> </span><span class="n">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-41" name="__codelineno-24-41" href="#__codelineno-24-41"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">adjList</span><span class="p">.</span><span class="na">containsKey</span><span class="p">(</span><span class="n">vet</span><span class="p">))</span>
+<a id="__codelineno-24-42" name="__codelineno-24-42" href="#__codelineno-24-42"></a><span class="w">            </span><span class="k">return</span>
+<a id="__codelineno-24-43" name="__codelineno-24-43" href="#__codelineno-24-43"></a><span class="w">        </span><span class="c1">// 隣接リストに新しいリストを追加</span>
+<a id="__codelineno-24-44" name="__codelineno-24-44" href="#__codelineno-24-44"></a><span class="w">        </span><span class="n">adjList</span><span class="o">[</span><span class="n">vet</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="p">()</span>
+<a id="__codelineno-24-45" name="__codelineno-24-45" href="#__codelineno-24-45"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-46" name="__codelineno-24-46" href="#__codelineno-24-46"></a>
+<a id="__codelineno-24-47" name="__codelineno-24-47" href="#__codelineno-24-47"></a><span class="w">    </span><span class="cm">/* 頂点を削除 */</span>
+<a id="__codelineno-24-48" name="__codelineno-24-48" href="#__codelineno-24-48"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">removeVertex</span><span class="p">(</span><span class="n">vet</span><span class="p">:</span><span class="w"> </span><span class="n">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-49" name="__codelineno-24-49" href="#__codelineno-24-49"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="na">containsKey</span><span class="p">(</span><span class="n">vet</span><span class="p">))</span>
+<a id="__codelineno-24-50" name="__codelineno-24-50" href="#__codelineno-24-50"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">IllegalArgumentException</span><span class="p">()</span>
+<a id="__codelineno-24-51" name="__codelineno-24-51" href="#__codelineno-24-51"></a><span class="w">        </span><span class="c1">// 隣接リストから頂点 vet に対応するリストを削除</span>
+<a id="__codelineno-24-52" name="__codelineno-24-52" href="#__codelineno-24-52"></a><span class="w">        </span><span class="n">adjList</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>
+<a id="__codelineno-24-53" name="__codelineno-24-53" href="#__codelineno-24-53"></a><span class="w">        </span><span class="c1">// 他の頂点のリストを走査し、vet を含むすべての辺を削除</span>
+<a id="__codelineno-24-54" name="__codelineno-24-54" href="#__codelineno-24-54"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">list</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">adjList</span><span class="p">.</span><span class="na">values</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-55" name="__codelineno-24-55" href="#__codelineno-24-55"></a><span class="w">            </span><span class="n">list</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>
+<a id="__codelineno-24-56" name="__codelineno-24-56" href="#__codelineno-24-56"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-24-57" name="__codelineno-24-57" href="#__codelineno-24-57"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-58" name="__codelineno-24-58" href="#__codelineno-24-58"></a>
+<a id="__codelineno-24-59" name="__codelineno-24-59" href="#__codelineno-24-59"></a><span class="w">    </span><span class="cm">/* 隣接リストを出力 */</span>
+<a id="__codelineno-24-60" name="__codelineno-24-60" href="#__codelineno-24-60"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-61" name="__codelineno-24-61" href="#__codelineno-24-61"></a><span class="w">        </span><span class="n">println</span><span class="p">(</span><span class="s">&quot;隣接リスト =&quot;</span><span class="p">)</span>
+<a id="__codelineno-24-62" name="__codelineno-24-62" href="#__codelineno-24-62"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">adjList</span><span class="p">.</span><span class="na">entries</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-63" name="__codelineno-24-63" href="#__codelineno-24-63"></a><span class="w">            </span><span class="kd">val</span><span class="w"> </span><span class="nv">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-24-64" name="__codelineno-24-64" href="#__codelineno-24-64"></a><span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">vertex</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">value</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-65" name="__codelineno-24-65" href="#__codelineno-24-65"></a><span class="w">                </span><span class="n">tmp</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">vertex</span><span class="p">.</span><span class="na">_val</span><span class="p">)</span>
+<a id="__codelineno-24-66" name="__codelineno-24-66" href="#__codelineno-24-66"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-24-67" name="__codelineno-24-67" href="#__codelineno-24-67"></a><span class="w">            </span><span class="n">println</span><span class="p">(</span><span class="s">&quot;</span><span class="si">${</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="p">.</span><span class="na">_val</span><span class="si">}</span><span class="s">: </span><span class="si">$</span><span class="n">tmp</span><span class="s">,&quot;</span><span class="p">)</span>
+<a id="__codelineno-24-68" name="__codelineno-24-68" href="#__codelineno-24-68"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-24-69" name="__codelineno-24-69" href="#__codelineno-24-69"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-70" name="__codelineno-24-70" href="#__codelineno-24-70"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_adjacency_list.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">GraphAdjList</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">graph_adjacency_list.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### 隣接リストで実装した無向グラフクラス ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">GraphAdjList</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="kp">attr_reader</span><span class="w"> </span><span class="ss">:adj_list</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">  </span><span class="c1">### コンストラクタ ###</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">edges</span><span class="p">)</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">    </span><span class="c1"># 隣接リスト。key は頂点、value はその頂点に隣接する全頂点</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w">    </span><span class="vi">@adj_list</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{}</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">    </span><span class="c1"># すべての頂点と辺を追加</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">edge</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">edges</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w">      </span><span class="n">add_vertex</span><span class="p">(</span><span class="n">edge</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w">      </span><span class="n">add_vertex</span><span class="p">(</span><span class="n">edge</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w">      </span><span class="n">add_edge</span><span class="p">(</span><span class="n">edge</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">edge</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a>
+<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="w">  </span><span class="c1">### 頂点数を取得 ###</span>
+<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">size</span>
+<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="w">    </span><span class="vi">@adj_list</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a>
+<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a><span class="w">  </span><span class="c1">### 辺を追加 ###</span>
+<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">add_edge</span><span class="p">(</span><span class="n">vet1</span><span class="p">,</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span>
+<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a><span class="w">    </span><span class="k">raise</span><span class="w"> </span><span class="no">ArgumentError</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="o">!</span><span class="vi">@adj_list</span><span class="o">.</span><span class="n">include?</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="o">!</span><span class="vi">@adj_list</span><span class="o">.</span><span class="n">include?</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span>
+<a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a>
+<a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></a><span class="w">    </span><span class="vi">@adj_list</span><span class="o">[</span><span class="n">vet1</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">vet2</span>
+<a id="__codelineno-25-27" name="__codelineno-25-27" href="#__codelineno-25-27"></a><span class="w">    </span><span class="vi">@adj_list</span><span class="o">[</span><span class="n">vet2</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">vet1</span>
+<a id="__codelineno-25-28" name="__codelineno-25-28" href="#__codelineno-25-28"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-29" name="__codelineno-25-29" href="#__codelineno-25-29"></a>
+<a id="__codelineno-25-30" name="__codelineno-25-30" href="#__codelineno-25-30"></a><span class="w">  </span><span class="c1">### 辺を削除 ###</span>
+<a id="__codelineno-25-31" name="__codelineno-25-31" href="#__codelineno-25-31"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">remove_edge</span><span class="p">(</span><span class="n">vet1</span><span class="p">,</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span>
+<a id="__codelineno-25-32" name="__codelineno-25-32" href="#__codelineno-25-32"></a><span class="w">    </span><span class="k">raise</span><span class="w"> </span><span class="no">ArgumentError</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="o">!</span><span class="vi">@adj_list</span><span class="o">.</span><span class="n">include?</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="o">!</span><span class="vi">@adj_list</span><span class="o">.</span><span class="n">include?</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span>
+<a id="__codelineno-25-33" name="__codelineno-25-33" href="#__codelineno-25-33"></a>
+<a id="__codelineno-25-34" name="__codelineno-25-34" href="#__codelineno-25-34"></a><span class="w">    </span><span class="c1"># 辺 vet1 - vet2 を削除</span>
+<a id="__codelineno-25-35" name="__codelineno-25-35" href="#__codelineno-25-35"></a><span class="w">    </span><span class="vi">@adj_list</span><span class="o">[</span><span class="n">vet1</span><span class="o">].</span><span class="n">delete</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span>
+<a id="__codelineno-25-36" name="__codelineno-25-36" href="#__codelineno-25-36"></a><span class="w">    </span><span class="vi">@adj_list</span><span class="o">[</span><span class="n">vet2</span><span class="o">].</span><span class="n">delete</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span>
+<a id="__codelineno-25-37" name="__codelineno-25-37" href="#__codelineno-25-37"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-38" name="__codelineno-25-38" href="#__codelineno-25-38"></a>
+<a id="__codelineno-25-39" name="__codelineno-25-39" href="#__codelineno-25-39"></a><span class="w">  </span><span class="c1">### 頂点を追加 ###</span>
+<a id="__codelineno-25-40" name="__codelineno-25-40" href="#__codelineno-25-40"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">add_vertex</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>
+<a id="__codelineno-25-41" name="__codelineno-25-41" href="#__codelineno-25-41"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="vi">@adj_list</span><span class="o">.</span><span class="n">include?</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>
+<a id="__codelineno-25-42" name="__codelineno-25-42" href="#__codelineno-25-42"></a>
+<a id="__codelineno-25-43" name="__codelineno-25-43" href="#__codelineno-25-43"></a><span class="w">    </span><span class="c1"># 隣接リストに新しいリストを追加</span>
+<a id="__codelineno-25-44" name="__codelineno-25-44" href="#__codelineno-25-44"></a><span class="w">    </span><span class="vi">@adj_list</span><span class="o">[</span><span class="n">vet</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-25-45" name="__codelineno-25-45" href="#__codelineno-25-45"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-46" name="__codelineno-25-46" href="#__codelineno-25-46"></a>
+<a id="__codelineno-25-47" name="__codelineno-25-47" href="#__codelineno-25-47"></a><span class="w">  </span><span class="c1">### 頂点を削除 ###</span>
+<a id="__codelineno-25-48" name="__codelineno-25-48" href="#__codelineno-25-48"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">remove_vertex</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>
+<a id="__codelineno-25-49" name="__codelineno-25-49" href="#__codelineno-25-49"></a><span class="w">    </span><span class="k">raise</span><span class="w"> </span><span class="no">ArgumentError</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="vi">@adj_list</span><span class="o">.</span><span class="n">include?</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>
+<a id="__codelineno-25-50" name="__codelineno-25-50" href="#__codelineno-25-50"></a>
+<a id="__codelineno-25-51" name="__codelineno-25-51" href="#__codelineno-25-51"></a><span class="w">    </span><span class="c1"># 隣接リストから頂点 vet に対応するリストを削除</span>
+<a id="__codelineno-25-52" name="__codelineno-25-52" href="#__codelineno-25-52"></a><span class="w">    </span><span class="vi">@adj_list</span><span class="o">.</span><span class="n">delete</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>
+<a id="__codelineno-25-53" name="__codelineno-25-53" href="#__codelineno-25-53"></a><span class="w">    </span><span class="c1"># 他の頂点のリストを走査し、vet を含むすべての辺を削除</span>
+<a id="__codelineno-25-54" name="__codelineno-25-54" href="#__codelineno-25-54"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">vertex</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="vi">@adj_list</span>
+<a id="__codelineno-25-55" name="__codelineno-25-55" href="#__codelineno-25-55"></a><span class="w">      </span><span class="vi">@adj_list</span><span class="o">[</span><span class="n">vertex</span><span class="o">.</span><span class="n">first</span><span class="o">].</span><span class="n">delete</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="vi">@adj_list</span><span class="o">[</span><span class="n">vertex</span><span class="o">.</span><span class="n">first</span><span class="o">].</span><span class="n">include?</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>
+<a id="__codelineno-25-56" name="__codelineno-25-56" href="#__codelineno-25-56"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-25-57" name="__codelineno-25-57" href="#__codelineno-25-57"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-58" name="__codelineno-25-58" href="#__codelineno-25-58"></a>
+<a id="__codelineno-25-59" name="__codelineno-25-59" href="#__codelineno-25-59"></a><span class="w">  </span><span class="c1">### 隣接リストを出力 ###</span>
+<a id="__codelineno-25-60" name="__codelineno-25-60" href="#__codelineno-25-60"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="n">__print__</span>
+<a id="__codelineno-25-61" name="__codelineno-25-61" href="#__codelineno-25-61"></a><span class="w">    </span><span class="nb">puts</span><span class="w"> </span><span class="s1">&#39;隣接リスト =&#39;</span>
+<a id="__codelineno-25-62" name="__codelineno-25-62" href="#__codelineno-25-62"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">vertex</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="vi">@adj_list</span>
+<a id="__codelineno-25-63" name="__codelineno-25-63" href="#__codelineno-25-63"></a><span class="w">      </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@adj_list</span><span class="o">[</span><span class="n">vertex</span><span class="o">.</span><span class="n">first</span><span class="o">].</span><span class="n">map</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">v</span><span class="o">|</span><span class="w"> </span><span class="n">v</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-25-64" name="__codelineno-25-64" href="#__codelineno-25-64"></a><span class="w">      </span><span class="nb">puts</span><span class="w"> </span><span class="s2">&quot;</span><span class="si">#{</span><span class="n">vertex</span><span class="o">.</span><span class="n">first</span><span class="o">.</span><span class="n">val</span><span class="si">}</span><span class="s2">: </span><span class="si">#{</span><span class="n">tmp</span><span class="si">}</span><span class="s2">,&quot;</span>
+<a id="__codelineno-25-65" name="__codelineno-25-65" href="#__codelineno-25-65"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-25-66" name="__codelineno-25-66" href="#__codelineno-25-66"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-67" name="__codelineno-25-67" href="#__codelineno-25-67"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20Vertex%3A%0A%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%20%3D%20val%0A%0Adef%20vals_to_vets%28vals%3A%20list%5Bint%5D%29%20-%3E%20list%5B%27Vertex%27%5D%3A%0A%20%20%20%20return%20%5BVertex%28val%29%20for%20val%20in%20vals%5D%0A%0Aclass%20GraphAdjList%3A%0A%0A%20%20%20%20def%20__init__%28self%2C%20edges%3A%20list%5Blist%5BVertex%5D%5D%29%3A%0A%20%20%20%20%20%20%20%20self.adj_list%20%3D%20dict%5BVertex%2C%20list%5BVertex%5D%5D%28%29%0A%20%20%20%20%20%20%20%20for%20edge%20in%20edges%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_vertex%28edge%5B0%5D%29%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_vertex%28edge%5B1%5D%29%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_edge%28edge%5B0%5D%2C%20edge%5B1%5D%29%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%20len%28self.adj_list%29%0A%0A%20%20%20%20def%20add_edge%28self%2C%20vet1%3A%20Vertex%2C%20vet2%3A%20Vertex%29%3A%0A%20%20%20%20%20%20%20%20if%20vet1%20not%20in%20self.adj_list%20or%20vet2%20not%20in%20self.adj_list%20or%20vet1%20%3D%3D%20vet2%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20ValueError%28%29%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet1%5D.append%28vet2%29%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet2%5D.append%28vet1%29%0A%0A%20%20%20%20def%20remove_edge%28self%2C%20vet1%3A%20Vertex%2C%20vet2%3A%20Vertex%29%3A%0A%20%20%20%20%20%20%20%20if%20vet1%20not%20in%20self.adj_list%20or%20vet2%20not%20in%20self.adj_list%20or%20vet1%20%3D%3D%20vet2%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20ValueError%28%29%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet1%5D.remove%28vet2%29%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet2%5D.remove%28vet1%29%0A%0A%20%20%20%20def%20add_vertex%28self%2C%20vet%3A%20Vertex%29%3A%0A%20%20%20%20%20%20%20%20if%20vet%20in%20self.adj_list%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet%5D%20%3D%20%5B%5D%0A%0A%20%20%20%20def%20remove_vertex%28self%2C%20vet%3A%20Vertex%29%3A%0A%20%20%20%20%20%20%20%20if%20vet%20not%20in%20self.adj_list%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20ValueError%28%29%0A%20%20%20%20%20%20%20%20self.adj_list.pop%28vet%29%0A%20%20%20%20%20%20%20%20for%20vertex%20in%20self.adj_list%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20vet%20in%20self.adj_list%5Bvertex%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20self.adj_list%5Bvertex%5D.remove%28vet%29%0Aif%20__name__%20%3D%3D%20%27__main__%27%3A%0A%20%20%20%20v%20%3D%20vals_to_vets%28%5B1%2C%203%2C%202%2C%205%2C%204%5D%29%0A%20%20%20%20edges%20%3D%20%5B%5Bv%5B0%5D%2C%20v%5B1%5D%5D%2C%20%5Bv%5B0%5D%2C%20v%5B3%5D%5D%2C%20%5Bv%5B1%5D%2C%20v%5B2%5D%5D%2C%20%5Bv%5B2%5D%2C%20v%5B3%5D%5D%2C%20%5Bv%5B2%5D%2C%20v%5B4%5D%5D%2C%20%5Bv%5B3%5D%2C%20v%5B4%5D%5D%5D%0A%20%20%20%20graph%20%3D%20GraphAdjList%28edges%29%0A%20%20%20%20del%20edges%0A%20%20%20%20graph.add_edge%28v%5B0%5D%2C%20v%5B2%5D%29%0A%20%20%20%20graph.remove_edge%28v%5B0%5D%2C%20v%5B1%5D%29%0A%20%20%20%20v5%20%3D%20Vertex%286%29%0A%20%20%20%20graph.add_vertex%28v5%29%0A%20%20%20%20graph.remove_vertex%28v%5B1%5D%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=39&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20Vertex%3A%0A%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%20%3D%20val%0A%0Adef%20vals_to_vets%28vals%3A%20list%5Bint%5D%29%20-%3E%20list%5B%27Vertex%27%5D%3A%0A%20%20%20%20return%20%5BVertex%28val%29%20for%20val%20in%20vals%5D%0A%0Aclass%20GraphAdjList%3A%0A%0A%20%20%20%20def%20__init__%28self%2C%20edges%3A%20list%5Blist%5BVertex%5D%5D%29%3A%0A%20%20%20%20%20%20%20%20self.adj_list%20%3D%20dict%5BVertex%2C%20list%5BVertex%5D%5D%28%29%0A%20%20%20%20%20%20%20%20for%20edge%20in%20edges%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_vertex%28edge%5B0%5D%29%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_vertex%28edge%5B1%5D%29%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_edge%28edge%5B0%5D%2C%20edge%5B1%5D%29%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%20len%28self.adj_list%29%0A%0A%20%20%20%20def%20add_edge%28self%2C%20vet1%3A%20Vertex%2C%20vet2%3A%20Vertex%29%3A%0A%20%20%20%20%20%20%20%20if%20vet1%20not%20in%20self.adj_list%20or%20vet2%20not%20in%20self.adj_list%20or%20vet1%20%3D%3D%20vet2%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20ValueError%28%29%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet1%5D.append%28vet2%29%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet2%5D.append%28vet1%29%0A%0A%20%20%20%20def%20remove_edge%28self%2C%20vet1%3A%20Vertex%2C%20vet2%3A%20Vertex%29%3A%0A%20%20%20%20%20%20%20%20if%20vet1%20not%20in%20self.adj_list%20or%20vet2%20not%20in%20self.adj_list%20or%20vet1%20%3D%3D%20vet2%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20ValueError%28%29%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet1%5D.remove%28vet2%29%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet2%5D.remove%28vet1%29%0A%0A%20%20%20%20def%20add_vertex%28self%2C%20vet%3A%20Vertex%29%3A%0A%20%20%20%20%20%20%20%20if%20vet%20in%20self.adj_list%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet%5D%20%3D%20%5B%5D%0A%0A%20%20%20%20def%20remove_vertex%28self%2C%20vet%3A%20Vertex%29%3A%0A%20%20%20%20%20%20%20%20if%20vet%20not%20in%20self.adj_list%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20ValueError%28%29%0A%20%20%20%20%20%20%20%20self.adj_list.pop%28vet%29%0A%20%20%20%20%20%20%20%20for%20vertex%20in%20self.adj_list%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20vet%20in%20self.adj_list%5Bvertex%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20self.adj_list%5Bvertex%5D.remove%28vet%29%0Aif%20__name__%20%3D%3D%20%27__main__%27%3A%0A%20%20%20%20v%20%3D%20vals_to_vets%28%5B1%2C%203%2C%202%2C%205%2C%204%5D%29%0A%20%20%20%20edges%20%3D%20%5B%5Bv%5B0%5D%2C%20v%5B1%5D%5D%2C%20%5Bv%5B0%5D%2C%20v%5B3%5D%5D%2C%20%5Bv%5B1%5D%2C%20v%5B2%5D%5D%2C%20%5Bv%5B2%5D%2C%20v%5B3%5D%5D%2C%20%5Bv%5B2%5D%2C%20v%5B4%5D%5D%2C%20%5Bv%5B3%5D%2C%20v%5B4%5D%5D%5D%0A%20%20%20%20graph%20%3D%20GraphAdjList%28edges%29%0A%20%20%20%20del%20edges%0A%20%20%20%20graph.add_edge%28v%5B0%5D%2C%20v%5B2%5D%29%0A%20%20%20%20graph.remove_edge%28v%5B0%5D%2C%20v%5B1%5D%29%0A%20%20%20%20v5%20%3D%20Vertex%286%29%0A%20%20%20%20graph.add_vertex%28v5%29%0A%20%20%20%20graph.remove_vertex%28v%5B1%5D%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=39&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 <h2 id="923">9.2.3 &nbsp; 効率の比較<a class="headerlink" href="#923" title="Permanent link">&para;</a></h2>
-<p>グラフに<span class="arithmatex">\(n\)</span>個の頂点と<span class="arithmatex">\(m\)</span>個の辺があると仮定すると、下表は隣接行列と隣接リストの時間効率と空間効率を比較しています。</p>
+<p>グラフに <span class="arithmatex">\(n\)</span> 個の頂点と <span class="arithmatex">\(m\)</span> 本の辺があるとすると、次の表は隣接行列と隣接リストの時間効率および空間効率を比較したものです。なお、隣接リスト（連結リスト）は本記事の実装に対応し、隣接リスト（ハッシュテーブル）はすべての連結リストをハッシュテーブルに置き換えた実装を指します。</p>
 <p align="center"> 表 9-2 &nbsp; 隣接行列と隣接リストの比較 </p>
 
 <div class="center-table">
@@ -5012,9 +6717,9 @@
 </thead>
 <tbody>
 <tr>
-<td>隣接性の判定</td>
+<td>隣接判定</td>
 <td><span class="arithmatex">\(O(1)\)</span></td>
-<td><span class="arithmatex">\(O(m)\)</span></td>
+<td><span class="arithmatex">\(O(n)\)</span></td>
 <td><span class="arithmatex">\(O(1)\)</span></td>
 </tr>
 <tr>
@@ -5026,7 +6731,7 @@
 <tr>
 <td>辺の削除</td>
 <td><span class="arithmatex">\(O(1)\)</span></td>
-<td><span class="arithmatex">\(O(m)\)</span></td>
+<td><span class="arithmatex">\(O(n)\)</span></td>
 <td><span class="arithmatex">\(O(1)\)</span></td>
 </tr>
 <tr>
@@ -5042,7 +6747,7 @@
 <td><span class="arithmatex">\(O(n)\)</span></td>
 </tr>
 <tr>
-<td>メモリ空間使用量</td>
+<td>メモリ使用量</td>
 <td><span class="arithmatex">\(O(n^2)\)</span></td>
 <td><span class="arithmatex">\(O(n + m)\)</span></td>
 <td><span class="arithmatex">\(O(n + m)\)</span></td>
@@ -5050,7 +6755,7 @@
 </tbody>
 </table>
 </div>
-<p>上表を観察すると、隣接リスト（ハッシュテーブル）が最高の時間効率と空間効率を持っているように見えます。しかし、実際には、隣接行列での辺に対する操作がより効率的で、単一の配列アクセスまたは代入操作のみが必要です。全体的に、隣接行列は「空間と時間のトレードオフ」の原則を例示し、隣接リストは「時間と空間のトレードオフ」を例示しています。</p>
+<p>上表を見ると、隣接リスト（ハッシュテーブル）の時間効率と空間効率が最も優れているように見えます。しかし実際には、隣接行列のほうが辺の操作効率は高く、必要なのは 1 回の配列アクセスまたは代入だけです。総合的に見ると、隣接行列は「空間を時間と引き換えにする」原則を体現し、隣接リストは「時間を空間と引き換えにする」原則を体現しています。</p>
 
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diff --git a/ja/chapter_graph/graph_traversal/index.html b/ja/chapter_graph/graph_traversal/index.html
index 234a11387..43050a6a3 100644
--- a/ja/chapter_graph/graph_traversal/index.html
+++ b/ja/chapter_graph/graph_traversal/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -39,7 +39,7 @@
     
     
       
-        <title>9.3 グラフ走査 - Hello アルゴリズム</title>
+        <title>9.3 グラフの走査 - Hello アルゴリズム</title>
       
     
     
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -152,7 +152,7 @@
         <div class="md-header__topic" data-md-component="header-topic">
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-              9.3 &nbsp; グラフ走査
+              9.3 &nbsp; グラフの走査
             
           </span>
         </div>
@@ -341,7 +341,7 @@
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-    序
+    はじめに
   
 
     
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-    序
+    はじめに
   
 
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-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
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-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
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-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
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-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
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-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2105,7 +2105,7 @@
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-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
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   <a href="#931" class="md-nav__link">
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-        9.3.1 &nbsp; 幅優先探索
+        9.3.1 &nbsp; 幅優先走査
       
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-    <nav class="md-nav" aria-label="9.3.1 幅優先探索">
+    <nav class="md-nav" aria-label="9.3.1 幅優先走査">
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-        2. &nbsp; 計算量分析
+        2. &nbsp; 計算量の分析
       
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   <a href="#932" class="md-nav__link">
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-        9.3.2 &nbsp; 深さ優先探索
+        9.3.2 &nbsp; 深さ優先走査
       
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-    <nav class="md-nav" aria-label="9.3.2 深さ優先探索">
+    <nav class="md-nav" aria-label="9.3.2 深さ優先走査">
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   <a href="#2_1" class="md-nav__link">
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-        2. &nbsp; 計算量分析
+        2. &nbsp; 計算量の分析
       
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@@ -2619,7 +2619,7 @@
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-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
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-    10.5 &nbsp; 探索アルゴリズムの再認識
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
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+    13.4 &nbsp; n クイーン問題
   
 
     
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-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
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-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
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   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
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-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3964,7 +3964,7 @@
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
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   <a href="#931" class="md-nav__link">
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-        9.3.1 &nbsp; 幅優先探索
+        9.3.1 &nbsp; 幅優先走査
       
     </span>
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-    <nav class="md-nav" aria-label="9.3.1 幅優先探索">
+    <nav class="md-nav" aria-label="9.3.1 幅優先走査">
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-        2. &nbsp; 計算量分析
+        2. &nbsp; 計算量の分析
       
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@@ -4394,12 +4394,12 @@
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-        9.3.2 &nbsp; 深さ優先探索
+        9.3.2 &nbsp; 深さ優先走査
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="9.3.2 深さ優先探索">
+    <nav class="md-nav" aria-label="9.3.2 深さ優先走査">
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@@ -4417,7 +4417,7 @@
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+        2. &nbsp; 計算量の分析
       
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@@ -4466,157 +4466,459 @@
 
 
 <!-- Page content -->
-<h1 id="93">9.3 &nbsp; グラフ走査<a class="headerlink" href="#93" title="Permanent link">&para;</a></h1>
-<p>木は「一対多」の関係を表現し、グラフはより高い自由度を持ち、任意の「多対多」の関係を表現できます。したがって、木をグラフの特別なケースと見なすことができます。明らかに、<strong>木の走査操作もグラフ走査操作の特別なケースです</strong>。</p>
-<p>グラフと木の両方で、走査操作を実装するために探索アルゴリズムの応用が必要です。グラフ走査は2つのタイプに分けることができます：<u>幅優先探索（BFS）</u>と<u>深さ優先探索（DFS）</u>です。</p>
-<h2 id="931">9.3.1 &nbsp; 幅優先探索<a class="headerlink" href="#931" title="Permanent link">&para;</a></h2>
-<p><strong>幅優先探索は近くから遠くへの走査方法で、ある頂点から開始し、常に最も近い頂点を優先的に訪問し、層ごとに外側に展開していきます</strong>。下図に示すように、左上の頂点から開始し、まずその頂点のすべての隣接頂点を走査し、次に次の頂点のすべての隣接頂点を走査し、以下同様に、すべての頂点が訪問されるまで続けます。</p>
+<h1 id="93">9.3 &nbsp; グラフの走査<a class="headerlink" href="#93" title="Permanent link">&para;</a></h1>
+<p>木は「一対多」の関係を表すのに対し、グラフはより高い自由度を持ち、任意の「多対多」の関係を表現できます。したがって、木はグラフの一種の特殊な場合とみなせます。明らかに、<strong>木の走査操作もグラフの走査操作の一種の特殊な場合です</strong>。</p>
+<p>グラフと木はいずれも、走査操作を実現するために探索アルゴリズムを用いる必要があります。グラフの走査方法も、<u>幅優先走査</u>と<u>深さ優先走査</u>の 2 種類に分けられます。</p>
+<h2 id="931">9.3.1 &nbsp; 幅優先走査<a class="headerlink" href="#931" title="Permanent link">&para;</a></h2>
+<p><strong>幅優先走査は、近いところから遠いところへ向かう走査方法であり、ある頂点から出発して、常に最も近い頂点を優先して訪問し、層ごとに外側へ広がっていきます</strong>。以下の図に示すように、左上の頂点から出発し、まずその頂点のすべての隣接頂点を走査し、次に次の頂点のすべての隣接頂点を走査し、これを繰り返して、すべての頂点を訪問するまで続けます。</p>
 <p><img alt="グラフの幅優先走査" class="animation-figure" src="../graph_traversal.assets/graph_bfs.png" /></p>
 <p align="center"> 図 9-9 &nbsp; グラフの幅優先走査 </p>
 
 <h3 id="1">1. &nbsp; アルゴリズムの実装<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>BFSは通常キューの助けを借りて実装されます（下記のコード参照）。キューは「先入先出」で、これは「近くから遠くへ」走査するBFSの考え方と一致します。</p>
+<p>BFS は通常キューを用いて実装され、コードは以下のとおりです。キューは「先入れ先出し」という性質を持ち、これは BFS の「近いところから遠いところへ」という考え方と本質的に一致しています。</p>
 <ol>
-<li>開始頂点<code>startVet</code>をキューに追加し、ループを開始します。</li>
-<li>ループの各反復で、キューの先頭の頂点をポップし、それを訪問済みとして記録し、次にその頂点のすべての隣接頂点をキューの末尾に追加します。</li>
-<li>すべての頂点が訪問されるまで手順<code>2.</code>を繰り返します。</li>
+<li>走査の開始頂点 <code>startVet</code> をキューに追加し、ループを開始します。</li>
+<li>ループの各反復で、キュー先頭の頂点を取り出して訪問を記録し、その後その頂点のすべての隣接頂点をキューの末尾に追加します。</li>
+<li>手順 <code>2.</code> を繰り返し、すべての頂点が訪問されると終了します。</li>
 </ol>
-<p>頂点の再訪問を防ぐために、ハッシュセット<code>visited</code>を使用してどのノードが訪問されたかを記録します。</p>
+<p>頂点の重複走査を防ぐために、どの頂点が訪問済みかを記録するハッシュ集合 <code>visited</code> を用います。</p>
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>ハッシュ集合は、<code>value</code> を持たず <code>key</code> だけを格納するハッシュテーブルとみなせます。これは <span class="arithmatex">\(O(1)\)</span> の時間計算量で <code>key</code> の追加・削除・検索・更新を行えます。<code>key</code> の一意性にもとづき、ハッシュ集合は通常、データの重複排除などの場面で用いられます。</p>
+</div>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">graph_bfs.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">graph_bfs</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span> <span class="n">GraphAdjList</span><span class="p">,</span> <span class="n">start_vet</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]:</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;幅優先走査&quot;&quot;&quot;</span>
-<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 隣接リストを使用してグラフを表現し、指定された頂点のすべての隣接頂点を取得</span>
-<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="c1"># 頂点走査シーケンス</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;幅優先探索&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 指定した頂点の隣接頂点をすべて取得できるよう、隣接リストでグラフを表現する</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="c1"># 頂点の走査順序</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
-<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># ハッシュセット、訪問済み頂点を記録するために使用</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 訪問済み頂点を記録するためのハッシュ集合</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="n">visited</span> <span class="o">=</span> <span class="nb">set</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]([</span><span class="n">start_vet</span><span class="p">])</span>
-<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="c1"># BFSを実装するために使用されるキュー</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="c1"># BFS の実装にキューを用いる</span>
 <a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="n">que</span> <span class="o">=</span> <span class="n">deque</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]([</span><span class="n">start_vet</span><span class="p">])</span>
-<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="c1"># 頂点vetから開始し、すべての頂点が訪問されるまでループ</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="c1"># 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="k">while</span> <span class="nb">len</span><span class="p">(</span><span class="n">que</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
-<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="n">vet</span> <span class="o">=</span> <span class="n">que</span><span class="o">.</span><span class="n">popleft</span><span class="p">()</span>  <span class="c1"># キューの先頭の頂点をデキュー</span>
-<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>  <span class="c1"># 訪問済み頂点を記録</span>
-<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>        <span class="c1"># その頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="n">vet</span> <span class="o">=</span> <span class="n">que</span><span class="o">.</span><span class="n">popleft</span><span class="p">()</span>  <span class="c1"># 先頭の頂点をデキュー</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>  <span class="c1"># 訪問した頂点を記録</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>        <span class="c1"># この頂点のすべての隣接頂点を走査</span>
 <a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>        <span class="k">for</span> <span class="n">adj_vet</span> <span class="ow">in</span> <span class="n">graph</span><span class="o">.</span><span class="n">adj_list</span><span class="p">[</span><span class="n">vet</span><span class="p">]:</span>
 <a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>            <span class="k">if</span> <span class="n">adj_vet</span> <span class="ow">in</span> <span class="n">visited</span><span class="p">:</span>
-<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>                <span class="k">continue</span>  <span class="c1"># 既に訪問済みの頂点をスキップ</span>
-<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>            <span class="n">que</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">adj_vet</span><span class="p">)</span>  <span class="c1"># 未訪問の頂点のみをエンキュー</span>
-<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>            <span class="n">visited</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">adj_vet</span><span class="p">)</span>  <span class="c1"># 頂点を訪問済みとしてマーク</span>
-<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>    <span class="c1"># 頂点走査シーケンスを返す</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>                <span class="k">continue</span>  <span class="c1"># 訪問済みの頂点をスキップ</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>            <span class="n">que</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">adj_vet</span><span class="p">)</span>  <span class="c1"># 未訪問の頂点のみをキューに追加</span>
+<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>            <span class="n">visited</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">adj_vet</span><span class="p">)</span>  <span class="c1"># この頂点を訪問済みにする</span>
+<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>    <span class="c1"># 頂点の走査順を返す</span>
 <a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>    <span class="k">return</span> <span class="n">res</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_bfs.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 幅優先走査 */</span>
-<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// 隣接リストを使用してグラフを表現し、指定された頂点のすべての隣接頂点を取得</span>
+<div class="highlight"><span class="filename">graph_bfs.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 幅優先探索 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="n">vector</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">graphBFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">&amp;</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// 頂点走査順序</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// 頂点の走査順序</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
-<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// ハッシュセット、訪問済み頂点を記録するために使用</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// 訪問済み頂点を記録するためのハッシュ集合</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="n">unordered_set</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="n">startVet</span><span class="p">};</span>
-<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="c1">// BFSを実装するために使用されるキュー</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="c1">// BFS の実装にキューを用いる</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="n">queue</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">que</span><span class="p">;</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="n">que</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">startVet</span><span class="p">);</span>
-<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="c1">// 頂点vetから開始し、すべての頂点が訪問されるまでループ</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="c1">// 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">que</span><span class="p">.</span><span class="n">empty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="n">front</span><span class="p">();</span>
-<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">        </span><span class="n">que</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w">          </span><span class="c1">// キューの先頭の頂点をデキュー</span>
-<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 訪問済み頂点を記録</span>
-<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">        </span><span class="c1">// その頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">        </span><span class="n">que</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w">          </span><span class="c1">// 先頭の頂点をデキュー</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 訪問した頂点を記録</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">        </span><span class="c1">// この頂点のすべての隣接頂点を走査</span>
 <a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="n">adjVet</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="n">count</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span>
-<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">                </span><span class="k">continue</span><span class="p">;</span><span class="w">            </span><span class="c1">// すでに訪問済みの頂点をスキップ</span>
-<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">            </span><span class="n">que</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w">        </span><span class="c1">// 未訪問の頂点のみをエンキュー</span>
-<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">            </span><span class="n">visited</span><span class="p">.</span><span class="n">emplace</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 頂点を訪問済みとしてマーク</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">                </span><span class="k">continue</span><span class="p">;</span><span class="w">            </span><span class="c1">// 訪問済みの頂点をスキップ</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">            </span><span class="n">que</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w">        </span><span class="c1">// 未訪問の頂点のみをキューに追加</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">            </span><span class="n">visited</span><span class="p">.</span><span class="n">emplace</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w"> </span><span class="c1">// この頂点を訪問済みにする</span>
 <a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="w">    </span><span class="c1">// 頂点走査順序を返す</span>
+<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="w">    </span><span class="c1">// 頂点の走査順を返す</span>
 <a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
 <a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_bfs.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 幅優先走査 */</span>
-<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="c1">// 隣接リストを使用してグラフを表現し、指定した頂点のすべての隣接頂点を取得</span>
+<div class="highlight"><span class="filename">graph_bfs.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 幅優先探索 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="c1">// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">graphBFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// 頂点走査順序</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// 頂点の走査順序</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
-<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// ハッシュセット、訪問済みの頂点を記録するために使用</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// 訪問済み頂点を記録するためのハッシュ集合</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="n">Set</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashSet</span><span class="o">&lt;&gt;</span><span class="p">();</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="n">visited</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">startVet</span><span class="p">);</span>
-<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="c1">// BFS を実装するために使用するキュー</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="c1">// BFS の実装にキューを用いる</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="n">Queue</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">que</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">LinkedList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
 <a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="n">que</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">startVet</span><span class="p">);</span>
-<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="c1">// 頂点 vet から開始し、すべての頂点が訪問されるまでループ</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="c1">// 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">que</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">        </span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// キューの先頭の頂点をデキュー</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">        </span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// 先頭の頂点をデキュー</span>
 <a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w">            </span><span class="c1">// 訪問した頂点を記録</span>
-<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">        </span><span class="c1">// その頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">        </span><span class="c1">// この頂点のすべての隣接頂点を走査</span>
 <a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">adjVet</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="na">adjList</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">vet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="na">contains</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span>
-<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">                </span><span class="k">continue</span><span class="p">;</span><span class="w">        </span><span class="c1">// すでに訪問済みの頂点をスキップ</span>
-<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">            </span><span class="n">que</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w">   </span><span class="c1">// 未訪問の頂点のみをエンキュー</span>
-<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">            </span><span class="n">visited</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 頂点を訪問済みとしてマーク</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">                </span><span class="k">continue</span><span class="p">;</span><span class="w">        </span><span class="c1">// 訪問済みの頂点をスキップ</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">            </span><span class="n">que</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w">   </span><span class="c1">// 未訪問の頂点のみをキューに追加</span>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">            </span><span class="n">visited</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w"> </span><span class="c1">// この頂点を訪問済みにする</span>
 <a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w">    </span><span class="c1">// 頂点走査順序を返す</span>
+<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w">    </span><span class="c1">// 頂点の走査順を返す</span>
 <a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
 <a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_bfs.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">graph_bfs</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">GraphBFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">graph_bfs.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 幅優先探索 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="c1">// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">GraphBFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="c1">// 頂点の走査順序</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="c1">// 訪問済み頂点を記録するためのハッシュ集合</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="n">HashSet</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="n">startVet</span><span class="p">];</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="c1">// BFS の実装にキューを用いる</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="n">Queue</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">que</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">();</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">    </span><span class="n">que</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="n">startVet</span><span class="p">);</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">    </span><span class="c1">// 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">que</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">        </span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w"> </span><span class="c1">// 先頭の頂点をデキュー</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w">               </span><span class="c1">// 訪問した頂点を記録</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">        </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">adjVet</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="n">Contains</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">                </span><span class="k">continue</span><span class="p">;</span><span class="w">          </span><span class="c1">// 訪問済みの頂点をスキップ</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w">            </span><span class="n">que</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w">   </span><span class="c1">// 未訪問の頂点のみをキューに追加</span>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w">            </span><span class="n">visited</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w">   </span><span class="c1">// この頂点を訪問済みにする</span>
+<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a>
+<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="w">    </span><span class="c1">// 頂点の走査順を返す</span>
+<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_bfs.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">graphBFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">graph_bfs.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 幅優先探索 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="c1">// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="kd">func</span><span class="w"> </span><span class="nx">graphBFS</span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjList</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="w"> </span><span class="nx">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">[]</span><span class="nx">Vertex</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="c1">// 頂点の走査順序</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="nx">Vertex</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="c1">// 訪問済み頂点を記録するためのハッシュ集合</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="nx">visited</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">(</span><span class="kd">map</span><span class="p">[</span><span class="nx">Vertex</span><span class="p">]</span><span class="kd">struct</span><span class="p">{})</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">    </span><span class="nx">visited</span><span class="p">[</span><span class="nx">startVet</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kd">struct</span><span class="p">{}{}</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="c1">// キューは BFS の実装に用い、スライスでキューをシミュレートする</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">    </span><span class="nx">queue</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="nx">Vertex</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">    </span><span class="nx">queue</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">queue</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="p">)</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">    </span><span class="c1">// 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">queue</span><span class="p">)</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">        </span><span class="c1">// 先頭の頂点をデキュー</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">        </span><span class="nx">vet</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">queue</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">        </span><span class="nx">queue</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">queue</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">        </span><span class="c1">// 訪問した頂点を記録</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w">        </span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">vet</span><span class="p">)</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w">        </span><span class="c1">// この頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">adjVet</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w">            </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">isExist</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">visited</span><span class="p">[</span><span class="nx">adjVet</span><span class="p">]</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w">            </span><span class="c1">// 未訪問の頂点のみをキューに追加</span>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">!</span><span class="nx">isExist</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="w">                </span><span class="nx">queue</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">queue</span><span class="p">,</span><span class="w"> </span><span class="nx">adjVet</span><span class="p">)</span>
+<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="w">                </span><span class="nx">visited</span><span class="p">[</span><span class="nx">adjVet</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kd">struct</span><span class="p">{}{}</span>
+<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="w">    </span><span class="c1">// 頂点の走査順を返す</span>
+<a id="__codelineno-4-30" name="__codelineno-4-30" href="#__codelineno-4-30"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
+<a id="__codelineno-4-31" name="__codelineno-4-31" href="#__codelineno-4-31"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_bfs.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">graphBFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">graph_bfs.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 幅優先探索 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="c1">// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">func</span><span class="w"> </span><span class="nf">graphBFS</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span><span class="w"> </span><span class="n">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">:</span><span class="w"> </span><span class="n">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="n">Vertex</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="c1">// 頂点の走査順序</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="n">Vertex</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="c1">// 訪問済み頂点を記録するためのハッシュ集合</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">visited</span><span class="p">:</span><span class="w"> </span><span class="n">Set</span><span class="p">&lt;</span><span class="n">Vertex</span><span class="p">&gt;</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="n">startVet</span><span class="p">]</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">    </span><span class="c1">// BFS の実装にキューを用いる</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">que</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="n">Vertex</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="n">startVet</span><span class="p">]</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">    </span><span class="c1">// 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">que</span><span class="p">.</span><span class="bp">isEmpty</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">vet</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="n">removeFirst</span><span class="p">()</span><span class="w"> </span><span class="c1">// 先頭の頂点をデキュー</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="c1">// 訪問した頂点を記録</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">        </span><span class="c1">// この頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">adjVet</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">]</span><span class="w"> </span><span class="p">??</span><span class="w"> </span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="bp">contains</span><span class="p">(</span><span class="n">adjVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">                </span><span class="k">continue</span><span class="w"> </span><span class="c1">// 訪問済みの頂点をスキップ</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w">            </span><span class="n">que</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">adjVet</span><span class="p">)</span><span class="w"> </span><span class="c1">// 未訪問の頂点のみをキューに追加</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="w">            </span><span class="n">visited</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="n">adjVet</span><span class="p">)</span><span class="w"> </span><span class="c1">// この頂点を訪問済みにする</span>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="w">    </span><span class="c1">// 頂点の走査順を返す</span>
+<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_bfs.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">graphBFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">graph_bfs.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 幅優先探索 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="c1">// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="kd">function</span><span class="w"> </span><span class="nx">graphBFS</span><span class="p">(</span><span class="nx">graph</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="c1">// 頂点の走査順序</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="c1">// 訪問済み頂点を記録するためのハッシュ集合</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Set</span><span class="p">();</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">    </span><span class="nx">visited</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">startVet</span><span class="p">);</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">    </span><span class="c1">// BFS の実装にキューを用いる</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">que</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">startVet</span><span class="p">];</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">    </span><span class="c1">// 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">que</span><span class="p">.</span><span class="nx">length</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">vet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">que</span><span class="p">.</span><span class="nx">shift</span><span class="p">();</span><span class="w"> </span><span class="c1">// 先頭の頂点をデキュー</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">        </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 訪問した頂点を記録</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">        </span><span class="c1">// この頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">adjVet</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">graph</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">vet</span><span class="p">)</span><span class="w"> </span><span class="o">??</span><span class="w"> </span><span class="p">[])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">visited</span><span class="p">.</span><span class="nx">has</span><span class="p">(</span><span class="nx">adjVet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w">                </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 訪問済みの頂点をスキップ</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w">            </span><span class="nx">que</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">adjVet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 未訪問の頂点のみをキューに追加</span>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w">            </span><span class="nx">visited</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">adjVet</span><span class="p">);</span><span class="w"> </span><span class="c1">// この頂点を訪問済みにする</span>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a><span class="w">    </span><span class="c1">// 頂点の走査順を返す</span>
+<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_bfs.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">graphBFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">graph_bfs.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 幅優先探索 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="c1">// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="kd">function</span><span class="w"> </span><span class="nx">graphBFS</span><span class="p">(</span><span class="nx">graph</span><span class="o">:</span><span class="w"> </span><span class="kt">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="nx">Vertex</span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="c1">// 頂点の走査順序</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="c1">// 訪問済み頂点を記録するためのハッシュ集合</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">visited</span><span class="o">:</span><span class="w"> </span><span class="kt">Set</span><span class="o">&lt;</span><span class="nx">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Set</span><span class="p">();</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="nx">visited</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">startVet</span><span class="p">);</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="c1">// BFS の実装にキューを用いる</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">que</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">startVet</span><span class="p">];</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">    </span><span class="c1">// 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">que</span><span class="p">.</span><span class="nx">length</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">vet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">que</span><span class="p">.</span><span class="nx">shift</span><span class="p">();</span><span class="w"> </span><span class="c1">// 先頭の頂点をデキュー</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">        </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 訪問した頂点を記録</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">        </span><span class="c1">// この頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">adjVet</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">graph</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">vet</span><span class="p">)</span><span class="w"> </span><span class="o">??</span><span class="w"> </span><span class="p">[])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">visited</span><span class="p">.</span><span class="nx">has</span><span class="p">(</span><span class="nx">adjVet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">                </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 訪問済みの頂点をスキップ</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w">            </span><span class="nx">que</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">adjVet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 未訪問のものだけをキューに入れる</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="w">            </span><span class="nx">visited</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">adjVet</span><span class="p">);</span><span class="w"> </span><span class="c1">// この頂点を訪問済みにする</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="w">    </span><span class="c1">// 頂点の走査順を返す</span>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_bfs.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">graphBFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">graph_bfs.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 幅優先探索 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">graphBFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="c1">// 指定した頂点の隣接頂点をすべて取得できるよう、隣接リストでグラフを表現する</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="c1">// 頂点の走査順序</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="c1">// 訪問済み頂点を記録するためのハッシュ集合</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="n">Set</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{};</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">  </span><span class="n">visited</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">startVet</span><span class="p">);</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">  </span><span class="c1">// BFS の実装にキューを用いる</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">  </span><span class="n">Queue</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">que</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Queue</span><span class="p">();</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">  </span><span class="n">que</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">startVet</span><span class="p">);</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">  </span><span class="c1">// 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">que</span><span class="p">.</span><span class="n">isNotEmpty</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">    </span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="n">removeFirst</span><span class="p">();</span><span class="w"> </span><span class="c1">// 先頭の頂点をデキュー</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 訪問した頂点を記録</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">    </span><span class="c1">// この頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">adjVet</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">]</span><span class="o">!</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="n">contains</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w">        </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 訪問済みの頂点をスキップ</span>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="w">      </span><span class="n">que</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 未訪問の頂点のみをキューに追加</span>
+<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="w">      </span><span class="n">visited</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w"> </span><span class="c1">// この頂点を訪問済みにする</span>
+<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a><span class="w">  </span><span class="c1">// 頂点の走査順を返す</span>
+<a id="__codelineno-8-26" name="__codelineno-8-26" href="#__codelineno-8-26"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-8-27" name="__codelineno-8-27" href="#__codelineno-8-27"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_bfs.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">graph_bfs</span><span class="p">}</span>
+<div class="highlight"><span class="filename">graph_bfs.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 幅優先探索 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="c1">// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="k">fn</span><span class="w"> </span><span class="nf">graph_bfs</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span><span class="w"> </span><span class="nc">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="n">start_vet</span><span class="p">:</span><span class="w"> </span><span class="nc">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="c1">// 頂点の走査順序</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="c1">// 訪問済み頂点を記録するためのハッシュ集合</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashSet</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="n">visited</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">start_vet</span><span class="p">);</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">    </span><span class="c1">// BFS の実装にキューを用いる</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">que</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">VecDeque</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">    </span><span class="n">que</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">start_vet</span><span class="p">);</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">    </span><span class="c1">// 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="n">pop_front</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 訪問した頂点を記録</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">        </span><span class="c1">// この頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">adj_vets</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="n">adj_list</span><span class="p">.</span><span class="n">get</span><span class="p">(</span><span class="o">&amp;</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="o">&amp;</span><span class="n">adj_vet</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">adj_vets</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">                </span><span class="k">if</span><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="n">contains</span><span class="p">(</span><span class="o">&amp;</span><span class="n">adj_vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w">                    </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 訪問済みの頂点をスキップ</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w">                </span><span class="p">}</span>
+<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="w">                </span><span class="n">que</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">adj_vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 未訪問の頂点のみをキューに追加</span>
+<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="w">                </span><span class="n">visited</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">adj_vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// この頂点を訪問済みにする</span>
+<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="w">    </span><span class="c1">// 頂点の走査順を返す</span>
+<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a><span class="w">    </span><span class="n">res</span>
+<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_bfs.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">Queue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
-<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
-<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">isVisited</span><span class="p">}</span>
-<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a>
-<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">graphBFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">graph_bfs.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* ノードキュー構造体 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vertices</span><span class="p">[</span><span class="n">MAX_SIZE</span><span class="p">];</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">front</span><span class="p">,</span><span class="w"> </span><span class="n">rear</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">;</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="p">}</span><span class="w"> </span><span class="n">Queue</span><span class="p">;</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="n">Queue</span><span class="w"> </span><span class="o">*</span><span class="nf">newQueue</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">    </span><span class="n">Queue</span><span class="w"> </span><span class="o">*</span><span class="n">q</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">Queue</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">Queue</span><span class="p">));</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="n">q</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">q</span><span class="o">-&gt;</span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">q</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">q</span><span class="p">;</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="p">}</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="kt">int</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">(</span><span class="n">Queue</span><span class="w"> </span><span class="o">*</span><span class="n">q</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">q</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="p">}</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="cm">/* エンキュー操作 */</span>
+<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="kt">void</span><span class="w"> </span><span class="nf">enqueue</span><span class="p">(</span><span class="n">Queue</span><span class="w"> </span><span class="o">*</span><span class="n">q</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="w">    </span><span class="n">q</span><span class="o">-&gt;</span><span class="n">vertices</span><span class="p">[</span><span class="n">q</span><span class="o">-&gt;</span><span class="n">rear</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vet</span><span class="p">;</span>
+<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w">    </span><span class="n">q</span><span class="o">-&gt;</span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">q</span><span class="o">-&gt;</span><span class="n">rear</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">;</span>
+<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w">    </span><span class="n">q</span><span class="o">-&gt;</span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="p">}</span>
+<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a>
+<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="cm">/* デキュー操作 */</span>
+<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="nf">dequeue</span><span class="p">(</span><span class="n">Queue</span><span class="w"> </span><span class="o">*</span><span class="n">q</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="w">    </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">q</span><span class="o">-&gt;</span><span class="n">vertices</span><span class="p">[</span><span class="n">q</span><span class="o">-&gt;</span><span class="n">front</span><span class="p">];</span>
+<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a><span class="w">    </span><span class="n">q</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">q</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">;</span>
+<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="w">    </span><span class="n">q</span><span class="o">-&gt;</span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">vet</span><span class="p">;</span>
+<a id="__codelineno-10-32" name="__codelineno-10-32" href="#__codelineno-10-32"></a><span class="p">}</span>
+<a id="__codelineno-10-33" name="__codelineno-10-33" href="#__codelineno-10-33"></a>
+<a id="__codelineno-10-34" name="__codelineno-10-34" href="#__codelineno-10-34"></a><span class="cm">/* 頂点が訪問済みかを確認 */</span>
+<a id="__codelineno-10-35" name="__codelineno-10-35" href="#__codelineno-10-35"></a><span class="kt">int</span><span class="w"> </span><span class="nf">isVisited</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="o">**</span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-36" name="__codelineno-10-36" href="#__codelineno-10-36"></a><span class="w">    </span><span class="c1">// 走査してノードを探すため、O(n) 時間を要する</span>
+<a id="__codelineno-10-37" name="__codelineno-10-37" href="#__codelineno-10-37"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-38" name="__codelineno-10-38" href="#__codelineno-10-38"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span>
+<a id="__codelineno-10-39" name="__codelineno-10-39" href="#__codelineno-10-39"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-10-40" name="__codelineno-10-40" href="#__codelineno-10-40"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-41" name="__codelineno-10-41" href="#__codelineno-10-41"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-42" name="__codelineno-10-42" href="#__codelineno-10-42"></a><span class="p">}</span>
+<a id="__codelineno-10-43" name="__codelineno-10-43" href="#__codelineno-10-43"></a>
+<a id="__codelineno-10-44" name="__codelineno-10-44" href="#__codelineno-10-44"></a><span class="cm">/* 幅優先探索 */</span>
+<a id="__codelineno-10-45" name="__codelineno-10-45" href="#__codelineno-10-45"></a><span class="c1">// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする</span>
+<a id="__codelineno-10-46" name="__codelineno-10-46" href="#__codelineno-10-46"></a><span class="kt">void</span><span class="w"> </span><span class="nf">graphBFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">*</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">startVet</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">**</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">resSize</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">**</span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">visitedSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-47" name="__codelineno-10-47" href="#__codelineno-10-47"></a><span class="w">    </span><span class="c1">// BFS の実装にキューを用いる</span>
+<a id="__codelineno-10-48" name="__codelineno-10-48" href="#__codelineno-10-48"></a><span class="w">    </span><span class="n">Queue</span><span class="w"> </span><span class="o">*</span><span class="n">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newQueue</span><span class="p">();</span>
+<a id="__codelineno-10-49" name="__codelineno-10-49" href="#__codelineno-10-49"></a><span class="w">    </span><span class="n">enqueue</span><span class="p">(</span><span class="n">queue</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">);</span>
+<a id="__codelineno-10-50" name="__codelineno-10-50" href="#__codelineno-10-50"></a><span class="w">    </span><span class="n">visited</span><span class="p">[(</span><span class="o">*</span><span class="n">visitedSize</span><span class="p">)</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">startVet</span><span class="p">;</span>
+<a id="__codelineno-10-51" name="__codelineno-10-51" href="#__codelineno-10-51"></a><span class="w">    </span><span class="c1">// 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す</span>
+<a id="__codelineno-10-52" name="__codelineno-10-52" href="#__codelineno-10-52"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">isEmpty</span><span class="p">(</span><span class="n">queue</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-53" name="__codelineno-10-53" href="#__codelineno-10-53"></a><span class="w">        </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dequeue</span><span class="p">(</span><span class="n">queue</span><span class="p">);</span><span class="w"> </span><span class="c1">// 先頭の頂点をデキュー</span>
+<a id="__codelineno-10-54" name="__codelineno-10-54" href="#__codelineno-10-54"></a><span class="w">        </span><span class="n">res</span><span class="p">[(</span><span class="o">*</span><span class="n">resSize</span><span class="p">)</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vet</span><span class="p">;</span><span class="w">      </span><span class="c1">// 訪問した頂点を記録</span>
+<a id="__codelineno-10-55" name="__codelineno-10-55" href="#__codelineno-10-55"></a><span class="w">        </span><span class="c1">// この頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-10-56" name="__codelineno-10-56" href="#__codelineno-10-56"></a><span class="w">        </span><span class="n">AdjListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findNode</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">vet</span><span class="p">);</span>
+<a id="__codelineno-10-57" name="__codelineno-10-57" href="#__codelineno-10-57"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-58" name="__codelineno-10-58" href="#__codelineno-10-58"></a><span class="w">            </span><span class="c1">// 訪問済みの頂点をスキップ</span>
+<a id="__codelineno-10-59" name="__codelineno-10-59" href="#__codelineno-10-59"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">isVisited</span><span class="p">(</span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">visitedSize</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">vertex</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-60" name="__codelineno-10-60" href="#__codelineno-10-60"></a><span class="w">                </span><span class="n">enqueue</span><span class="p">(</span><span class="n">queue</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">vertex</span><span class="p">);</span><span class="w">             </span><span class="c1">// 未訪問の頂点のみをキューに追加</span>
+<a id="__codelineno-10-61" name="__codelineno-10-61" href="#__codelineno-10-61"></a><span class="w">                </span><span class="n">visited</span><span class="p">[(</span><span class="o">*</span><span class="n">visitedSize</span><span class="p">)</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">vertex</span><span class="p">;</span><span class="w"> </span><span class="c1">// この頂点を訪問済みにする</span>
+<a id="__codelineno-10-62" name="__codelineno-10-62" href="#__codelineno-10-62"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-10-63" name="__codelineno-10-63" href="#__codelineno-10-63"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-10-64" name="__codelineno-10-64" href="#__codelineno-10-64"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-65" name="__codelineno-10-65" href="#__codelineno-10-65"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-66" name="__codelineno-10-66" href="#__codelineno-10-66"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-10-67" name="__codelineno-10-67" href="#__codelineno-10-67"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">queue</span><span class="p">);</span>
+<a id="__codelineno-10-68" name="__codelineno-10-68" href="#__codelineno-10-68"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_bfs.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">graphBFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">graph_bfs.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 幅優先探索 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="c1">// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">graphBFS</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span><span class="w"> </span><span class="n">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">:</span><span class="w"> </span><span class="n">Vertex</span><span class="p">):</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">Vertex?&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="c1">// 頂点の走査順序</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="n">Vertex?&gt;</span><span class="p">()</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="c1">// 訪問済み頂点を記録するためのハッシュ集合</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashSet</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">    </span><span class="n">visited</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">startVet</span><span class="p">)</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">    </span><span class="c1">// BFS の実装にキューを用いる</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">que</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">LinkedList</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">    </span><span class="n">que</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">startVet</span><span class="p">)</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">    </span><span class="c1">// 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">que</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">vet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="na">poll</span><span class="p">()</span><span class="w"> </span><span class="c1">// 先頭の頂点をデキュー</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span><span class="w">         </span><span class="c1">// 訪問した頂点を記録</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">        </span><span class="c1">// この頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">adjVet</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="na">adjList</span><span class="o">[</span><span class="n">vet</span><span class="o">]!!</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="na">contains</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w">                </span><span class="k">continue</span><span class="w">        </span><span class="c1">// 訪問済みの頂点をスキップ</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w">            </span><span class="n">que</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">adjVet</span><span class="p">)</span><span class="w">   </span><span class="c1">// 未訪問の頂点のみをキューに追加</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="w">            </span><span class="n">visited</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">adjVet</span><span class="p">)</span><span class="w"> </span><span class="c1">// この頂点を訪問済みにする</span>
+<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="w">    </span><span class="c1">// 頂点の走査順を返す</span>
+<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_bfs.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">graph_bfs</span><span class="p">}</span>
+<div class="highlight"><span class="filename">graph_bfs.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 幅優先探索 ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">graph_bfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">start_vet</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># 指定した頂点の隣接頂点をすべて取得できるよう、隣接リストでグラフを表現する</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="c1"># 頂点の走査順序</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="c1"># 訪問済み頂点を記録するためのハッシュ集合</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">  </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">Set</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="o">[</span><span class="n">start_vet</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">  </span><span class="c1"># BFS の実装にキューを用いる</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">  </span><span class="n">que</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">start_vet</span><span class="o">]</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">  </span><span class="c1"># 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="n">que</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">    </span><span class="n">vet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">que</span><span class="o">.</span><span class="n">shift</span><span class="w"> </span><span class="c1"># 先頭の頂点をデキュー</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">    </span><span class="n">res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">vet</span><span class="w"> </span><span class="c1"># 訪問した頂点を記録</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">    </span><span class="c1"># この頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">adj_vet</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">graph</span><span class="o">.</span><span class="n">adj_list</span><span class="o">[</span><span class="n">vet</span><span class="o">]</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">      </span><span class="k">next</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">visited</span><span class="o">.</span><span class="n">include?</span><span class="p">(</span><span class="n">adj_vet</span><span class="p">)</span><span class="w"> </span><span class="c1"># 訪問済みの頂点をスキップ</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">      </span><span class="n">que</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">adj_vet</span><span class="w"> </span><span class="c1"># 未訪問の頂点のみをキューに追加</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w">      </span><span class="n">visited</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">adj_vet</span><span class="p">)</span><span class="w"> </span><span class="c1"># この頂点を訪問済みにする</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w">  </span><span class="c1"># 頂点の走査順を返す</span>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w">  </span><span class="n">res</span>
+<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>コードは比較的抽象的ですが、下図と比較することでより良く理解できます。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" 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</iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=from%20collections%20import%20deque%0A%0Aclass%20Vertex%3A%0A%20%20%20%20%22%22%22%E9%A0%82%E7%82%B9%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%20%3D%20val%0A%0Adef%20vals_to_vets%28vals%3A%20list%5Bint%5D%29%20-%3E%20list%5B%22Vertex%22%5D%3A%0A%20%20%20%20%22%22%22%E5%80%A4%E3%83%AA%E3%82%B9%E3%83%88%20vals%20%E3%82%92%E5%85%A5%E5%8A%9B%E3%81%97%E3%80%81%E9%A0%82%E7%82%B9%E3%83%AA%E3%82%B9%E3%83%88%20vets%20%E3%82%92%E8%BF%94%E3%81%99%22%22%22%0A%20%20%20%20return%20%5BVertex%28val%29%20for%20val%20in%20vals%5D%0A%0Aclass%20GraphAdjList%3A%0A%20%20%20%20%22%22%22%E9%9A%A3%E6%8E%A5%E3%83%AA%E3%82%B9%E3%83%88%E3%81%AB%E5%9F%BA%E3%81%A5%E3%81%8F%E7%84%A1%E5%90%91%E3%82%B0%E3%83%A9%E3%83%95%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%0A%20%20%20%20def%20__init__%28self%2C%20edges%3A%20list%5Blist%5BVertex%5D%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%82%B3%E3%83%B3%E3%82%B9%E3%83%88%E3%83%A9%E3%82%AF%E3%82%BF%22%22%22%0A%20%20%20%20%20%20%20%20self.adj_list%20%3D%20dict%5BVertex%2C%20list%5BVertex%5D%5D%28%29%0A%20%20%20%20%20%20%20%20for%20edge%20in%20edges%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_vertex%28edge%5B0%5D%29%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_vertex%28edge%5B1%5D%29%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_edge%28edge%5B0%5D%2C%20edge%5B1%5D%29%0A%0A%20%20%20%20def%20add_edge%28self%2C%20vet1%3A%20Vertex%2C%20vet2%3A%20Vertex%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%BE%BA%E3%82%92%E8%BF%BD%E5%8A%A0%22%22%22%0A%20%20%20%20%20%20%20%20if%20vet1%20not%20in%20self.adj_list%20or%20vet2%20not%20in%20self.adj_list%20or%20vet1%20%3D%3D%20vet2%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20ValueError%28%29%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet1%5D.append%28vet2%29%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet2%5D.append%28vet1%29%0A%0A%20%20%20%20def%20add_vertex%28self%2C%20vet%3A%20Vertex%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E9%A0%82%E7%82%B9%E3%82%92%E8%BF%BD%E5%8A%A0%22%22%22%0A%20%20%20%20%20%20%20%20if%20vet%20in%20self.adj_list%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet%5D%20%3D%20%5B%5D%0A%0A%0Adef%20graph_bfs%28graph%3A%20GraphAdjList%2C%20start_vet%3A%20Vertex%29%20-%3E%20list%5BVertex%5D%3A%0A%20%20%20%20%22%22%22%E5%B9%85%E5%84%AA%E5%85%88%E6%8E%A2%E7%B4%A2%22%22%22%0A%20%20%20%20%23%20%E9%A0%82%E7%82%B9%E3%81%AE%E8%B5%B0%E6%9F%BB%E9%A0%86%E5%BA%8F%0A%20%20%20%20res%20%3D%20%5B%5D%0A%20%20%20%20%23%20%E8%A8%AA%E5%95%8F%E6%B8%88%E3%81%BF%E3%81%AE%E9%A0%82%E7%82%B9%E3%82%92%E8%A8%98%E9%8C%B2%E3%81%99%E3%82%8B%E3%81%9F%E3%82%81%E3%81%AE%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%0A%20%20%20%20visited%20%3D%20set%5BVertex%5D%28%5Bstart_vet%5D%29%0A%20%20%20%20%23%20BFS%20%E3%81%AE%E5%AE%9F%E8%A3%85%E3%81%AB%E3%82%AD%E3%83%A5%E3%83%BC%E3%82%92%E7%94%A8%E3%81%84%E3%82%8B%0A%20%20%20%20que%20%3D%20deque%5BVertex%5D%28%5Bstart_vet%5D%29%0A%20%20%20%20%23%20%E9%A0%82%E7%82%B9%20vet%20%E3%82%92%E8%B5%B7%E7%82%B9%E3%81%AB%E3%80%81%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E9%A0%82%E7%82%B9%E3%82%92%E8%A8%AA%E5%95%8F%E3%81%97%E7%B5%82%E3%81%88%E3%82%8B%E3%81%BE%E3%81%A7%E7%B9%B0%E3%82%8A%E8%BF%94%E3%81%99%0A%20%20%20%20while%20len%28que%29%20%3E%200%3A%0A%20%20%20%20%20%20%20%20vet%20%3D%20que.popleft%28%29%20%20%23%20%E5%85%88%E9%A0%AD%E3%81%AE%E9%A0%82%E7%82%B9%E3%82%92%E3%83%87%E3%82%AD%E3%83%A5%E3%83%BC%0A%20%20%20%20%20%20%20%20res.append%28vet%29%20%20%23%20%E8%A8%AA%E5%95%8F%E3%81%97%E3%81%9F%E9%A0%82%E7%82%B9%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20%20%20%20%20%23%20%E3%81%93%E3%81%AE%E9%A0%82%E7%82%B9%E3%81%AE%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E9%9A%A3%E6%8E%A5%E9%A0%82%E7%82%B9%E3%82%92%E8%B5%B0%E6%9F%BB%0A%20%20%20%20%20%20%20%20for%20adj_vet%20in%20graph.adj_list%5Bvet%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20adj_vet%20in%20visited%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20continue%20%20%23%20%E8%A8%AA%E5%95%8F%E6%B8%88%E3%81%BF%E3%81%AE%E9%A0%82%E7%82%B9%E3%82%92%E3%82%B9%E3%82%AD%E3%83%83%E3%83%97%0A%20%20%20%20%20%20%20%20%20%20%20%20que.append%28adj_vet%29%20%20%23%20%E6%9C%AA%E8%A8%AA%E5%95%8F%E3%81%AE%E9%A0%82%E7%82%B9%E3%81%AE%E3%81%BF%E3%82%92%E3%82%AD%E3%83%A5%E3%83%BC%E3%81%AB%E8%BF%BD%E5%8A%A0%0A%20%20%20%20%20%20%20%20%20%20%20%20visited.add%28adj_vet%29%20%20%23%20%E3%81%93%E3%81%AE%E9%A0%82%E7%82%B9%E3%82%92%E8%A8%AA%E5%95%8F%E6%B8%88%E3%81%BF%E3%81%AB%E3%81%99%E3%82%8B%0A%20%20%20%20%23%20%E9%A0%82%E7%82%B9%E3%81%AE%E8%B5%B0%E6%9F%BB%E9%A0%86%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20res%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E7%84%A1%E5%90%91%E3%82%B0%E3%83%A9%E3%83%95%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20v%20%3D%20vals_to_vets%28%5B0%2C%201%2C%202%2C%203%2C%204%5D%29%0A%20%20%20%20edges%20%3D%20%5B%0A%20%20%20%20%20%20%20%20%5Bv%5B0%5D%2C%20v%5B1%5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target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>コードはやや抽象的なので、以下の図と照らし合わせて理解を深めることを勧めます。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:11"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">&lt;1&gt;</label><label for="__tabbed_2_2">&lt;2&gt;</label><label for="__tabbed_2_3">&lt;3&gt;</label><label for="__tabbed_2_4">&lt;4&gt;</label><label for="__tabbed_2_5">&lt;5&gt;</label><label for="__tabbed_2_6">&lt;6&gt;</label><label for="__tabbed_2_7">&lt;7&gt;</label><label for="__tabbed_2_8">&lt;8&gt;</label><label for="__tabbed_2_9">&lt;9&gt;</label><label for="__tabbed_2_10">&lt;10&gt;</label><label for="__tabbed_2_11">&lt;11&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="グラフの幅優先探索の手順" class="animation-figure" src="../graph_traversal.assets/graph_bfs_step1.png" /></p>
+<p><img alt="グラフの幅優先走査の手順" class="animation-figure" src="../graph_traversal.assets/graph_bfs_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="graph_bfs_step2" class="animation-figure" src="../graph_traversal.assets/graph_bfs_step2.png" /></p>
@@ -4650,67 +4952,67 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 9-10 &nbsp; グラフの幅優先探索の手順 </p>
+<p align="center"> 図 9-10 &nbsp; グラフの幅優先走査の手順 </p>
 
 <div class="admonition question">
-<p class="admonition-title">幅優先走査のシーケンスは一意ですか？</p>
-<p>一意ではありません。幅優先走査は「近くから遠く」の順序で走査することのみを要求し、<strong>同じ距離の頂点の走査順序は任意にできます</strong>。例えば、上図では、頂点<span class="arithmatex">\(1\)</span>と<span class="arithmatex">\(3\)</span>の訪問順序を交換できますし、頂点<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(4\)</span>、<span class="arithmatex">\(6\)</span>の順序も同様です。</p>
+<p class="admonition-title">幅優先走査の順序列は一意ですか？</p>
+<p>一意ではありません。幅優先走査は「近いところから遠いところへ」の順で走査することだけを要求し、<strong>同じ距離にある複数の頂点の走査順は任意に入れ替えて構いません</strong>。上図を例にすると、頂点 <span class="arithmatex">\(1\)</span> と <span class="arithmatex">\(3\)</span> の訪問順は交換でき、頂点 <span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(4\)</span>、<span class="arithmatex">\(6\)</span> の訪問順も任意に入れ替えられます。</p>
 </div>
-<h3 id="2">2. &nbsp; 計算量分析<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p><strong>時間計算量</strong>：すべての頂点が一度ずつエンキューおよびデキューされ、<span class="arithmatex">\(O(|V|)\)</span>時間を使用します。隣接頂点を走査する過程で、無向グラフであるため、すべての辺が<span class="arithmatex">\(2\)</span>回訪問され、<span class="arithmatex">\(O(2|E|)\)</span>時間を使用します。全体で<span class="arithmatex">\(O(|V| + |E|)\)</span>時間を使用します。</p>
-<p><strong>空間計算量</strong>：リスト<code>res</code>、ハッシュセット<code>visited</code>、キュー<code>que</code>の最大頂点数は<span class="arithmatex">\(|V|\)</span>で、<span class="arithmatex">\(O(|V|)\)</span>空間を使用します。</p>
-<h2 id="932">9.3.2 &nbsp; 深さ優先探索<a class="headerlink" href="#932" title="Permanent link">&para;</a></h2>
-<p><strong>深さ優先探索は可能な限り遠くまで行き、それ以上のパスがない場合にバックトラックする走査方法です</strong>。下図に示すように、左上の頂点から開始し、それ以上のパスがなくなるまで現在の頂点のいずれかの隣接頂点を訪問し、次に戻って続行し、すべての頂点が走査されるまで続けます。</p>
+<h3 id="2">2. &nbsp; 計算量の分析<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p><strong>時間計算量</strong>：すべての頂点は 1 回ずつキューに入り、1 回ずつキューから出るため、<span class="arithmatex">\(O(|V|)\)</span> 時間です。隣接頂点を走査する過程では、無向グラフであるため、すべての辺が <span class="arithmatex">\(2\)</span> 回訪問され、<span class="arithmatex">\(O(2|E|)\)</span> 時間です。したがって全体では <span class="arithmatex">\(O(|V| + |E|)\)</span> 時間です。</p>
+<p><strong>空間計算量</strong>：リスト <code>res</code>、ハッシュ集合 <code>visited</code>、キュー <code>que</code> に含まれる頂点数は最大で <span class="arithmatex">\(|V|\)</span> であるため、<span class="arithmatex">\(O(|V|)\)</span> 空間です。</p>
+<h2 id="932">9.3.2 &nbsp; 深さ優先走査<a class="headerlink" href="#932" title="Permanent link">&para;</a></h2>
+<p><strong>深さ優先走査は、まず行けるところまで進み、進めなくなったら戻る走査方法です</strong>。以下の図に示すように、左上の頂点から出発し、現在の頂点のある隣接頂点を訪問して、行き止まりに達するまで進んだら戻り、再び別の方向へ進んで行き止まりまで進んで戻る、ということを繰り返し、すべての頂点の走査が完了するまで続けます。</p>
 <p><img alt="グラフの深さ優先走査" class="animation-figure" src="../graph_traversal.assets/graph_dfs.png" /></p>
 <p align="center"> 図 9-11 &nbsp; グラフの深さ優先走査 </p>
 
 <h3 id="1_1">1. &nbsp; アルゴリズムの実装<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
-<p>この「可能な限り遠くまで行ってから戻る」アルゴリズムパラダイムは通常再帰に基づいて実装されます。幅優先探索と同様に、深さ優先探索でも、再訪問を避けるために訪問済み頂点を記録するハッシュセット<code>visited</code>の助けが必要です。</p>
+<p>この「行き止まりまで進んでから戻る」アルゴリズムのパターンは、通常再帰にもとづいて実装されます。幅優先走査と同様に、深さ優先走査でも、頂点の重複訪問を避けるために、訪問済みの頂点を記録するハッシュ集合 <code>visited</code> を用います。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">graph_dfs.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span> <span class="n">GraphAdjList</span><span class="p">,</span> <span class="n">visited</span><span class="p">:</span> <span class="nb">set</span><span class="p">[</span><span class="n">Vertex</span><span class="p">],</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">Vertex</span><span class="p">],</span> <span class="n">vet</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">):</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;深さ優先走査のヘルパー関数&quot;&quot;&quot;</span>
-<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>  <span class="c1"># 訪問済み頂点を記録</span>
-<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="n">visited</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>  <span class="c1"># 頂点を訪問済みとしてマーク</span>
-<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># その頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;深さ優先走査の補助関数&quot;&quot;&quot;</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>  <span class="c1"># 訪問した頂点を記録</span>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="n">visited</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>  <span class="c1"># この頂点を訪問済みにする</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># この頂点のすべての隣接頂点を走査</span>
 <a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>    <span class="k">for</span> <span class="n">adjVet</span> <span class="ow">in</span> <span class="n">graph</span><span class="o">.</span><span class="n">adj_list</span><span class="p">[</span><span class="n">vet</span><span class="p">]:</span>
 <a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>        <span class="k">if</span> <span class="n">adjVet</span> <span class="ow">in</span> <span class="n">visited</span><span class="p">:</span>
-<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>            <span class="k">continue</span>  <span class="c1"># 既に訪問済みの頂点をスキップ</span>
+<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>            <span class="k">continue</span>  <span class="c1"># 訪問済みの頂点をスキップ</span>
 <a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>        <span class="c1"># 隣接頂点を再帰的に訪問</span>
 <a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>        <span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span> <span class="n">visited</span><span class="p">,</span> <span class="n">res</span><span class="p">,</span> <span class="n">adjVet</span><span class="p">)</span>
 <a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>
 <a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a><span class="k">def</span><span class="w"> </span><span class="nf">graph_dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span> <span class="n">GraphAdjList</span><span class="p">,</span> <span class="n">start_vet</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]:</span>
-<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;深さ優先走査&quot;&quot;&quot;</span>
-<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>    <span class="c1"># 隣接リストを使用してグラフを表現し、指定された頂点のすべての隣接頂点を取得</span>
-<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a>    <span class="c1"># 頂点走査シーケンス</span>
+<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;深さ優先探索&quot;&quot;&quot;</span>
+<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>    <span class="c1"># 指定した頂点の隣接頂点をすべて取得できるよう、隣接リストでグラフを表現する</span>
+<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a>    <span class="c1"># 頂点の走査順序</span>
 <a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
-<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>    <span class="c1"># ハッシュセット、訪問済み頂点を記録するために使用</span>
+<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>    <span class="c1"># 訪問済み頂点を記録するためのハッシュ集合</span>
 <a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a>    <span class="n">visited</span> <span class="o">=</span> <span class="nb">set</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]()</span>
 <a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a>    <span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span> <span class="n">visited</span><span class="p">,</span> <span class="n">res</span><span class="p">,</span> <span class="n">start_vet</span><span class="p">)</span>
 <a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a>    <span class="k">return</span> <span class="n">res</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_dfs.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 深さ優先走査ヘルパー関数 */</span>
+<div class="highlight"><span class="filename">graph_dfs.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 深さ優先走査の補助関数 */</span>
 <a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">&amp;</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">unordered_set</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w">   </span><span class="c1">// 訪問済み頂点を記録</span>
-<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="n">visited</span><span class="p">.</span><span class="n">emplace</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 頂点を訪問済みとしてマーク</span>
-<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="c1">// その頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w">   </span><span class="c1">// 訪問した頂点を記録</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="n">visited</span><span class="p">.</span><span class="n">emplace</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// この頂点を訪問済みにする</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="c1">// この頂点のすべての隣接頂点を走査</span>
 <a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">adjVet</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="n">count</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span>
-<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// すでに訪問済みの頂点をスキップ</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 訪問済みの頂点をスキップ</span>
 <a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">        </span><span class="c1">// 隣接頂点を再帰的に訪問</span>
 <a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">adjVet</span><span class="p">);</span>
 <a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="p">}</span>
 <a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a>
-<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="cm">/* 深さ優先走査 */</span>
-<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="c1">// 隣接リストを使用してグラフを表現し、指定された頂点のすべての隣接頂点を取得</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="cm">/* 深さ優先探索 */</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="c1">// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする</span>
 <a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="n">vector</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">graphDFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">&amp;</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w">    </span><span class="c1">// 頂点走査順序</span>
+<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w">    </span><span class="c1">// 頂点の走査順序</span>
 <a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
-<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w">    </span><span class="c1">// ハッシュセット、訪問済み頂点を記録するために使用</span>
+<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w">    </span><span class="c1">// 訪問済み頂点を記録するためのハッシュ集合</span>
 <a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w">    </span><span class="n">unordered_set</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">visited</span><span class="p">;</span>
 <a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">);</span>
 <a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
@@ -4721,22 +5023,22 @@
 <div class="highlight"><span class="filename">graph_dfs.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 深さ優先走査の補助関数 */</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Set</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w">     </span><span class="c1">// 訪問した頂点を記録</span>
-<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="n">visited</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 頂点を訪問済みとしてマーク</span>
-<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="c1">// その頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="n">visited</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// この頂点を訪問済みにする</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="c1">// この頂点のすべての隣接頂点を走査</span>
 <a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">adjVet</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="na">adjList</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">vet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="na">contains</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span>
-<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// すでに訪問済みの頂点をスキップ</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 訪問済みの頂点をスキップ</span>
 <a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">        </span><span class="c1">// 隣接頂点を再帰的に訪問</span>
 <a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">adjVet</span><span class="p">);</span>
 <a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="p">}</span>
 <a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a>
-<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="cm">/* 深さ優先走査 */</span>
-<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="c1">// 隣接リストを使用してグラフを表現し、指定した頂点のすべての隣接頂点を取得</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="cm">/* 深さ優先探索 */</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="c1">// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする</span>
 <a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">graphDFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">    </span><span class="c1">// 頂点走査順序</span>
+<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">    </span><span class="c1">// 頂点の走査順序</span>
 <a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
-<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w">    </span><span class="c1">// ハッシュセット、訪問済みの頂点を記録するために使用</span>
+<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w">    </span><span class="c1">// 訪問済み頂点を記録するためのハッシュ集合</span>
 <a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w">    </span><span class="n">Set</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashSet</span><span class="o">&lt;&gt;</span><span class="p">();</span>
 <a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">);</span>
 <a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
@@ -4744,79 +5046,317 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_dfs.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">graph_dfs</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">DFS</span><span class="p">}</span>
-<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a>
-<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">graph_dfs</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">GraphDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">graph_dfs.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 深さ優先走査の補助関数 */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">DFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">HashSet</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w">     </span><span class="c1">// 訪問した頂点を記録</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="n">visited</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// この頂点を訪問済みにする</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="c1">// この頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">adjVet</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="n">Contains</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 訪問済みの頂点をスキップ</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">        </span><span class="c1">// 隣接頂点を再帰的に訪問</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">        </span><span class="n">DFS</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">adjVet</span><span class="p">);</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="p">}</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="cm">/* 深さ優先探索 */</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="c1">// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">GraphDFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">    </span><span class="c1">// 頂点の走査順序</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w">    </span><span class="c1">// 訪問済み頂点を記録するためのハッシュ集合</span>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="w">    </span><span class="n">HashSet</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="w">    </span><span class="n">DFS</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">);</span>
+<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-16-24" name="__codelineno-16-24" href="#__codelineno-16-24"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_dfs.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
-<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a>
-<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">graphDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">graph_dfs.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 深さ優先走査の補助関数 */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjList</span><span class="p">,</span><span class="w"> </span><span class="nx">visited</span><span class="w"> </span><span class="kd">map</span><span class="p">[</span><span class="nx">Vertex</span><span class="p">]</span><span class="kd">struct</span><span class="p">{},</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="nx">Vertex</span><span class="p">,</span><span class="w"> </span><span class="nx">vet</span><span class="w"> </span><span class="nx">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="c1">// append 操作は新しい参照を返すため、元の参照を新しい slice の参照で再代入する必要がある</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">vet</span><span class="p">)</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">    </span><span class="nx">visited</span><span class="p">[</span><span class="nx">vet</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kd">struct</span><span class="p">{}{}</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">    </span><span class="c1">// この頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">adjVet</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">        </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">isExist</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">visited</span><span class="p">[</span><span class="nx">adjVet</span><span class="p">]</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">        </span><span class="c1">// 隣接頂点を再帰的に訪問</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">!</span><span class="nx">isExist</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w">            </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">g</span><span class="p">,</span><span class="w"> </span><span class="nx">visited</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">adjVet</span><span class="p">)</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="p">}</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="cm">/* 深さ優先探索 */</span>
+<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="c1">// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする</span>
+<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="kd">func</span><span class="w"> </span><span class="nx">graphDFS</span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjList</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="w"> </span><span class="nx">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">[]</span><span class="nx">Vertex</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="w">    </span><span class="c1">// 頂点の走査順序</span>
+<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a><span class="w">    </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="nx">Vertex</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></a><span class="w">    </span><span class="c1">// 訪問済み頂点を記録するためのハッシュ集合</span>
+<a id="__codelineno-17-22" name="__codelineno-17-22" href="#__codelineno-17-22"></a><span class="w">    </span><span class="nx">visited</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">(</span><span class="kd">map</span><span class="p">[</span><span class="nx">Vertex</span><span class="p">]</span><span class="kd">struct</span><span class="p">{})</span>
+<a id="__codelineno-17-23" name="__codelineno-17-23" href="#__codelineno-17-23"></a><span class="w">    </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">g</span><span class="p">,</span><span class="w"> </span><span class="nx">visited</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="p">)</span>
+<a id="__codelineno-17-24" name="__codelineno-17-24" href="#__codelineno-17-24"></a><span class="w">    </span><span class="c1">// 頂点の走査順を返す</span>
+<a id="__codelineno-17-25" name="__codelineno-17-25" href="#__codelineno-17-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
+<a id="__codelineno-17-26" name="__codelineno-17-26" href="#__codelineno-17-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_dfs.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a>
-<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">graphDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">graph_dfs.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 深さ優先走査の補助関数 */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span><span class="w"> </span><span class="n">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="n">Set</span><span class="p">&lt;</span><span class="n">Vertex</span><span class="p">&gt;,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="n">Vertex</span><span class="p">],</span><span class="w"> </span><span class="n">vet</span><span class="p">:</span><span class="w"> </span><span class="n">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="c1">// 訪問した頂点を記録</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="n">visited</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="c1">// この頂点を訪問済みにする</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">    </span><span class="c1">// この頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">adjVet</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">]</span><span class="w"> </span><span class="p">??</span><span class="w"> </span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="bp">contains</span><span class="p">(</span><span class="n">adjVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">            </span><span class="k">continue</span><span class="w"> </span><span class="c1">// 訪問済みの頂点をスキップ</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">        </span><span class="c1">// 隣接頂点を再帰的に訪問</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">vet</span><span class="p">:</span><span class="w"> </span><span class="n">adjVet</span><span class="p">)</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="p">}</span>
+<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a>
+<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="cm">/* 深さ優先探索 */</span>
+<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="c1">// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする</span>
+<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="kd">func</span><span class="w"> </span><span class="nf">graphDFS</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span><span class="w"> </span><span class="n">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">:</span><span class="w"> </span><span class="n">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="n">Vertex</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="w">    </span><span class="c1">// 頂点の走査順序</span>
+<a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="n">Vertex</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
+<a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a><span class="w">    </span><span class="c1">// 訪問済み頂点を記録するためのハッシュ集合</span>
+<a id="__codelineno-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">visited</span><span class="p">:</span><span class="w"> </span><span class="n">Set</span><span class="p">&lt;</span><span class="n">Vertex</span><span class="p">&gt;</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
+<a id="__codelineno-18-22" name="__codelineno-18-22" href="#__codelineno-18-22"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">vet</span><span class="p">:</span><span class="w"> </span><span class="n">startVet</span><span class="p">)</span>
+<a id="__codelineno-18-23" name="__codelineno-18-23" href="#__codelineno-18-23"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-18-24" name="__codelineno-18-24" href="#__codelineno-18-24"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_dfs.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
-<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a>
-<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">graphDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">graph_dfs.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 深さ優先探索 */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="c1">// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="kd">function</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">graph</span><span class="p">,</span><span class="w"> </span><span class="nx">visited</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 訪問した頂点を記録</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">    </span><span class="nx">visited</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// この頂点を訪問済みにする</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">    </span><span class="c1">// この頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">adjVet</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">graph</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">vet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">visited</span><span class="p">.</span><span class="nx">has</span><span class="p">(</span><span class="nx">adjVet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 訪問済みの頂点をスキップ</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w">        </span><span class="c1">// 隣接頂点を再帰的に訪問</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">        </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">graph</span><span class="p">,</span><span class="w"> </span><span class="nx">visited</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">adjVet</span><span class="p">);</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="p">}</span>
+<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a>
+<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a><span class="cm">/* 深さ優先探索 */</span>
+<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="c1">// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする</span>
+<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a><span class="kd">function</span><span class="w"> </span><span class="nx">graphDFS</span><span class="p">(</span><span class="nx">graph</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a><span class="w">    </span><span class="c1">// 頂点の走査順序</span>
+<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a><span class="w">    </span><span class="c1">// 訪問済み頂点を記録するためのハッシュ集合</span>
+<a id="__codelineno-19-22" name="__codelineno-19-22" href="#__codelineno-19-22"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Set</span><span class="p">();</span>
+<a id="__codelineno-19-23" name="__codelineno-19-23" href="#__codelineno-19-23"></a><span class="w">    </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">graph</span><span class="p">,</span><span class="w"> </span><span class="nx">visited</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="p">);</span>
+<a id="__codelineno-19-24" name="__codelineno-19-24" href="#__codelineno-19-24"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-19-25" name="__codelineno-19-25" href="#__codelineno-19-25"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_dfs.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
-<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a>
-<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">graphDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">graph_dfs.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 深さ優先走査の補助関数 */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="nx">graph</span><span class="o">:</span><span class="w"> </span><span class="kt">GraphAdjList</span><span class="p">,</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="nx">visited</span><span class="o">:</span><span class="w"> </span><span class="kt">Set</span><span class="o">&lt;</span><span class="nx">Vertex</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">    </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span><span class="p">[],</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">    </span><span class="nx">vet</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">    </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 訪問した頂点を記録</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">    </span><span class="nx">visited</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// この頂点を訪問済みにする</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">    </span><span class="c1">// この頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">adjVet</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">graph</span><span class="p">.</span><span class="nx">adjList</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">vet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">visited</span><span class="p">.</span><span class="nx">has</span><span class="p">(</span><span class="nx">adjVet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 訪問済みの頂点をスキップ</span>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w">        </span><span class="c1">// 隣接頂点を再帰的に訪問</span>
+<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a><span class="w">        </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">graph</span><span class="p">,</span><span class="w"> </span><span class="nx">visited</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">adjVet</span><span class="p">);</span>
+<a id="__codelineno-20-17" name="__codelineno-20-17" href="#__codelineno-20-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-18" name="__codelineno-20-18" href="#__codelineno-20-18"></a><span class="p">}</span>
+<a id="__codelineno-20-19" name="__codelineno-20-19" href="#__codelineno-20-19"></a>
+<a id="__codelineno-20-20" name="__codelineno-20-20" href="#__codelineno-20-20"></a><span class="cm">/* 深さ優先探索 */</span>
+<a id="__codelineno-20-21" name="__codelineno-20-21" href="#__codelineno-20-21"></a><span class="c1">// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする</span>
+<a id="__codelineno-20-22" name="__codelineno-20-22" href="#__codelineno-20-22"></a><span class="kd">function</span><span class="w"> </span><span class="nx">graphDFS</span><span class="p">(</span><span class="nx">graph</span><span class="o">:</span><span class="w"> </span><span class="kt">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="nx">Vertex</span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-23" name="__codelineno-20-23" href="#__codelineno-20-23"></a><span class="w">    </span><span class="c1">// 頂点の走査順序</span>
+<a id="__codelineno-20-24" name="__codelineno-20-24" href="#__codelineno-20-24"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-20-25" name="__codelineno-20-25" href="#__codelineno-20-25"></a><span class="w">    </span><span class="c1">// 訪問済み頂点を記録するためのハッシュ集合</span>
+<a id="__codelineno-20-26" name="__codelineno-20-26" href="#__codelineno-20-26"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">visited</span><span class="o">:</span><span class="w"> </span><span class="kt">Set</span><span class="o">&lt;</span><span class="nx">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Set</span><span class="p">();</span>
+<a id="__codelineno-20-27" name="__codelineno-20-27" href="#__codelineno-20-27"></a><span class="w">    </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">graph</span><span class="p">,</span><span class="w"> </span><span class="nx">visited</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="p">);</span>
+<a id="__codelineno-20-28" name="__codelineno-20-28" href="#__codelineno-20-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-20-29" name="__codelineno-20-29" href="#__codelineno-20-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_dfs.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a>
-<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">graphDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">graph_dfs.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 深さ優先走査の補助関数 */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="n">Set</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">,</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">  </span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="p">,</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">  </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 訪問した頂点を記録</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">  </span><span class="n">visited</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// この頂点を訪問済みにする</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="w">  </span><span class="c1">// この頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">adjVet</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">]</span><span class="o">!</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="n">contains</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">      </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 訪問済みの頂点をスキップ</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w">    </span><span class="c1">// 隣接頂点を再帰的に訪問</span>
+<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">adjVet</span><span class="p">);</span>
+<a id="__codelineno-21-17" name="__codelineno-21-17" href="#__codelineno-21-17"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-18" name="__codelineno-21-18" href="#__codelineno-21-18"></a><span class="p">}</span>
+<a id="__codelineno-21-19" name="__codelineno-21-19" href="#__codelineno-21-19"></a>
+<a id="__codelineno-21-20" name="__codelineno-21-20" href="#__codelineno-21-20"></a><span class="cm">/* 深さ優先探索 */</span>
+<a id="__codelineno-21-21" name="__codelineno-21-21" href="#__codelineno-21-21"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">graphDFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-22" name="__codelineno-21-22" href="#__codelineno-21-22"></a><span class="w">  </span><span class="c1">// 頂点の走査順序</span>
+<a id="__codelineno-21-23" name="__codelineno-21-23" href="#__codelineno-21-23"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-21-24" name="__codelineno-21-24" href="#__codelineno-21-24"></a><span class="w">  </span><span class="c1">// 訪問済み頂点を記録するためのハッシュ集合</span>
+<a id="__codelineno-21-25" name="__codelineno-21-25" href="#__codelineno-21-25"></a><span class="w">  </span><span class="n">Set</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{};</span>
+<a id="__codelineno-21-26" name="__codelineno-21-26" href="#__codelineno-21-26"></a><span class="w">  </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">);</span>
+<a id="__codelineno-21-27" name="__codelineno-21-27" href="#__codelineno-21-27"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-21-28" name="__codelineno-21-28" href="#__codelineno-21-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_dfs.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a>
-<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">graph_dfs</span><span class="p">}</span>
+<div class="highlight"><span class="filename">graph_dfs.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 深さ優先走査の補助関数 */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="n">HashSet</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">vet</span><span class="p">:</span><span class="w"> </span><span class="nc">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 訪問した頂点を記録</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="n">visited</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// この頂点を訪問済みにする</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">                         </span><span class="c1">// この頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">adj_vets</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="n">adj_list</span><span class="p">.</span><span class="n">get</span><span class="p">(</span><span class="o">&amp;</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="o">&amp;</span><span class="n">adj_vet</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">adj_vets</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="n">contains</span><span class="p">(</span><span class="o">&amp;</span><span class="n">adj_vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">                </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// 訪問済みの頂点をスキップ</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w">            </span><span class="c1">// 隣接頂点を再帰的に訪問</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">            </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">adj_vet</span><span class="p">);</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="p">}</span>
+<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a>
+<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="cm">/* 深さ優先探索 */</span>
+<a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="c1">// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする</span>
+<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="k">fn</span><span class="w"> </span><span class="nf">graph_dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span><span class="w"> </span><span class="nc">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="n">start_vet</span><span class="p">:</span><span class="w"> </span><span class="nc">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a><span class="w">    </span><span class="c1">// 頂点の走査順序</span>
+<a id="__codelineno-22-21" name="__codelineno-22-21" href="#__codelineno-22-21"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span>
+<a id="__codelineno-22-22" name="__codelineno-22-22" href="#__codelineno-22-22"></a><span class="w">    </span><span class="c1">// 訪問済み頂点を記録するためのハッシュ集合</span>
+<a id="__codelineno-22-23" name="__codelineno-22-23" href="#__codelineno-22-23"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashSet</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-22-24" name="__codelineno-22-24" href="#__codelineno-22-24"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="o">&amp;</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">start_vet</span><span class="p">);</span>
+<a id="__codelineno-22-25" name="__codelineno-22-25" href="#__codelineno-22-25"></a>
+<a id="__codelineno-22-26" name="__codelineno-22-26" href="#__codelineno-22-26"></a><span class="w">    </span><span class="n">res</span>
+<a id="__codelineno-22-27" name="__codelineno-22-27" href="#__codelineno-22-27"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_dfs.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">isVisited</span><span class="p">}</span>
-<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a>
-<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a>
-<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">graphDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">graph_dfs.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 頂点が訪問済みかを確認 */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">isVisited</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="o">**</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="c1">// 走査してノードを探すため、O(n) 時間を要する</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="p">}</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="cm">/* 深さ優先走査の補助関数 */</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">*</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">**</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">resSize</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w">    </span><span class="c1">// 訪問した頂点を記録</span>
+<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="w">    </span><span class="n">res</span><span class="p">[(</span><span class="o">*</span><span class="n">resSize</span><span class="p">)</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vet</span><span class="p">;</span>
+<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="w">    </span><span class="c1">// この頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="w">    </span><span class="n">AdjListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findNode</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">vet</span><span class="p">);</span>
+<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="w">        </span><span class="c1">// 訪問済みの頂点をスキップ</span>
+<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">isVisited</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">resSize</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">vertex</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a><span class="w">            </span><span class="c1">// 隣接頂点を再帰的に訪問</span>
+<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a><span class="w">            </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">resSize</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">vertex</span><span class="p">);</span>
+<a id="__codelineno-23-23" name="__codelineno-23-23" href="#__codelineno-23-23"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-24" name="__codelineno-23-24" href="#__codelineno-23-24"></a><span class="w">        </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-23-25" name="__codelineno-23-25" href="#__codelineno-23-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-26" name="__codelineno-23-26" href="#__codelineno-23-26"></a><span class="p">}</span>
+<a id="__codelineno-23-27" name="__codelineno-23-27" href="#__codelineno-23-27"></a>
+<a id="__codelineno-23-28" name="__codelineno-23-28" href="#__codelineno-23-28"></a><span class="cm">/* 深さ優先探索 */</span>
+<a id="__codelineno-23-29" name="__codelineno-23-29" href="#__codelineno-23-29"></a><span class="c1">// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする</span>
+<a id="__codelineno-23-30" name="__codelineno-23-30" href="#__codelineno-23-30"></a><span class="kt">void</span><span class="w"> </span><span class="nf">graphDFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">*</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">startVet</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">**</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">resSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-31" name="__codelineno-23-31" href="#__codelineno-23-31"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">resSize</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">);</span>
+<a id="__codelineno-23-32" name="__codelineno-23-32" href="#__codelineno-23-32"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_dfs.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a>
-<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">graphDFS</span><span class="p">}</span>
+<div class="highlight"><span class="filename">graph_dfs.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 深さ優先走査の補助関数 */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="n">graph</span><span class="p">:</span><span class="w"> </span><span class="n">GraphAdjList</span><span class="p">,</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="n">visited</span><span class="p">:</span><span class="w"> </span><span class="n">MutableSet</span><span class="o">&lt;</span><span class="n">Vertex?&gt;</span><span class="p">,</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">    </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">Vertex?&gt;</span><span class="p">,</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">    </span><span class="n">vet</span><span class="p">:</span><span class="w"> </span><span class="n">Vertex?</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span><span class="w">     </span><span class="c1">// 訪問した頂点を記録</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w">    </span><span class="n">visited</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="c1">// この頂点を訪問済みにする</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w">    </span><span class="c1">// この頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">adjVet</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="na">adjList</span><span class="o">[</span><span class="n">vet</span><span class="o">]!!</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="na">contains</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w">            </span><span class="k">continue</span><span class="w">  </span><span class="c1">// 訪問済みの頂点をスキップ</span>
+<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w">        </span><span class="c1">// 隣接頂点を再帰的に訪問</span>
+<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">adjVet</span><span class="p">)</span>
+<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-17" name="__codelineno-24-17" href="#__codelineno-24-17"></a><span class="p">}</span>
+<a id="__codelineno-24-18" name="__codelineno-24-18" href="#__codelineno-24-18"></a>
+<a id="__codelineno-24-19" name="__codelineno-24-19" href="#__codelineno-24-19"></a><span class="cm">/* 深さ優先探索 */</span>
+<a id="__codelineno-24-20" name="__codelineno-24-20" href="#__codelineno-24-20"></a><span class="c1">// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする</span>
+<a id="__codelineno-24-21" name="__codelineno-24-21" href="#__codelineno-24-21"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">graphDFS</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span><span class="w"> </span><span class="n">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">:</span><span class="w"> </span><span class="n">Vertex?)</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">Vertex?&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-22" name="__codelineno-24-22" href="#__codelineno-24-22"></a><span class="w">    </span><span class="c1">// 頂点の走査順序</span>
+<a id="__codelineno-24-23" name="__codelineno-24-23" href="#__codelineno-24-23"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="n">Vertex?&gt;</span><span class="p">()</span>
+<a id="__codelineno-24-24" name="__codelineno-24-24" href="#__codelineno-24-24"></a><span class="w">    </span><span class="c1">// 訪問済み頂点を記録するためのハッシュ集合</span>
+<a id="__codelineno-24-25" name="__codelineno-24-25" href="#__codelineno-24-25"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashSet</span><span class="o">&lt;</span><span class="n">Vertex?&gt;</span><span class="p">()</span>
+<a id="__codelineno-24-26" name="__codelineno-24-26" href="#__codelineno-24-26"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">)</span>
+<a id="__codelineno-24-27" name="__codelineno-24-27" href="#__codelineno-24-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-24-28" name="__codelineno-24-28" href="#__codelineno-24-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">graph_dfs.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
-<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a>
-<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">graph_dfs</span><span class="p">}</span>
+<div class="highlight"><span class="filename">graph_dfs.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### 深さ優先探索の補助関数 ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">vet</span><span class="w"> </span><span class="c1"># 訪問した頂点を記録</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">  </span><span class="n">visited</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="c1"># この頂点を訪問済みにする</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">  </span><span class="c1"># この頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">adj_vet</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">graph</span><span class="o">.</span><span class="n">adj_list</span><span class="o">[</span><span class="n">vet</span><span class="o">]</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">    </span><span class="k">next</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">visited</span><span class="o">.</span><span class="n">include?</span><span class="p">(</span><span class="n">adj_vet</span><span class="p">)</span><span class="w"> </span><span class="c1"># 訪問済みの頂点をスキップ</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w">    </span><span class="c1"># 隣接頂点を再帰的に訪問</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">adj_vet</span><span class="p">)</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="k">end</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="c1">### 深さ優先探索 ###</span>
+<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="k">def</span><span class="w"> </span><span class="nf">graph_dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">start_vet</span><span class="p">)</span>
+<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w">  </span><span class="c1"># 指定した頂点の隣接頂点をすべて取得できるよう、隣接リストでグラフを表現する</span>
+<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w">  </span><span class="c1"># 頂点の走査順序</span>
+<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a><span class="w">  </span><span class="c1"># 訪問済み頂点を記録するためのハッシュ集合</span>
+<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="w">  </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">Set</span><span class="o">.</span><span class="n">new</span>
+<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a><span class="w">  </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">start_vet</span><span class="p">)</span>
+<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="w">  </span><span class="n">res</span>
+<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>深さ優先探索のアルゴリズムプロセスを下図に示します。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20Vertex%3A%0A%20%20%20%20%22%22%22%E9%A0%82%E7%82%B9%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%20%3D%20val%0A%0Adef%20vals_to_vets%28vals%3A%20list%5Bint%5D%29%20-%3E%20list%5B%22Vertex%22%5D%3A%0A%20%20%20%20%22%22%22%E5%80%A4%E3%83%AA%E3%82%B9%E3%83%88%20vals%20%E3%82%92%E5%85%A5%E5%8A%9B%E3%81%97%E3%80%81%E9%A0%82%E7%82%B9%E3%83%AA%E3%82%B9%E3%83%88%20vets%20%E3%82%92%E8%BF%94%E3%81%99%22%22%22%0A%20%20%20%20return%20%5BVertex%28val%29%20for%20val%20in%20vals%5D%0A%0Aclass%20GraphAdjList%3A%0A%20%20%20%20%22%22%22%E9%9A%A3%E6%8E%A5%E3%83%AA%E3%82%B9%E3%83%88%E3%81%AB%E5%9F%BA%E3%81%A5%E3%81%8F%E7%84%A1%E5%90%91%E3%82%B0%E3%83%A9%E3%83%95%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%0A%20%20%20%20def%20__init__%28self%2C%20edges%3A%20list%5Blist%5BVertex%5D%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%82%B3%E3%83%B3%E3%82%B9%E3%83%88%E3%83%A9%E3%82%AF%E3%82%BF%22%22%22%0A%20%20%20%20%20%20%20%20self.adj_list%20%3D%20dict%5BVertex%2C%20list%5BVertex%5D%5D%28%29%0A%20%20%20%20%20%20%20%20for%20edge%20in%20edges%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_vertex%28edge%5B0%5D%29%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_vertex%28edge%5B1%5D%29%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_edge%28edge%5B0%5D%2C%20edge%5B1%5D%29%0A%0A%20%20%20%20def%20add_edge%28self%2C%20vet1%3A%20Vertex%2C%20vet2%3A%20Vertex%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%BE%BA%E3%82%92%E8%BF%BD%E5%8A%A0%22%22%22%0A%20%20%20%20%20%20%20%20if%20vet1%20not%20in%20self.adj_list%20or%20vet2%20not%20in%20self.adj_list%20or%20vet1%20%3D%3D%20vet2%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20ValueError%28%29%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet1%5D.append%28vet2%29%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet2%5D.append%28vet1%29%0A%0A%20%20%20%20def%20add_vertex%28self%2C%20vet%3A%20Vertex%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E9%A0%82%E7%82%B9%E3%82%92%E8%BF%BD%E5%8A%A0%22%22%22%0A%20%20%20%20%20%20%20%20if%20vet%20in%20self.adj_list%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet%5D%20%3D%20%5B%5D%0A%0A%0Adef%20dfs%28graph%3A%20GraphAdjList%2C%20visited%3A%20set%5BVertex%5D%2C%20res%3A%20list%5BVertex%5D%2C%20vet%3A%20Vertex%29%3A%0A%20%20%20%20%22%22%22%E6%B7%B1%E3%81%95%E5%84%AA%E5%85%88%E8%B5%B0%E6%9F%BB%E3%81%AE%E8%A3%9C%E5%8A%A9%E9%96%A2%E6%95%B0%22%22%22%0A%20%20%20%20res.append%28vet%29%20%20%23%20%E8%A8%AA%E5%95%8F%E3%81%97%E3%81%9F%E9%A0%82%E7%82%B9%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20visited.add%28vet%29%20%20%23%20%E3%81%93%E3%81%AE%E9%A0%82%E7%82%B9%E3%82%92%E8%A8%AA%E5%95%8F%E6%B8%88%E3%81%BF%E3%81%AB%E3%81%99%E3%82%8B%0A%20%20%20%20%23%20%E3%81%93%E3%81%AE%E9%A0%82%E7%82%B9%E3%81%AE%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E9%9A%A3%E6%8E%A5%E9%A0%82%E7%82%B9%E3%82%92%E8%B5%B0%E6%9F%BB%0A%20%20%20%20for%20adjVet%20in%20graph.adj_list%5Bvet%5D%3A%0A%20%20%20%20%20%20%20%20if%20adjVet%20in%20visited%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20continue%20%20%23%20%E8%A8%AA%E5%95%8F%E6%B8%88%E3%81%BF%E3%81%AE%E9%A0%82%E7%82%B9%E3%82%92%E3%82%B9%E3%82%AD%E3%83%83%E3%83%97%0A%20%20%20%20%20%20%20%20%23%20%E9%9A%A3%E6%8E%A5%E9%A0%82%E7%82%B9%E3%82%92%E5%86%8D%E5%B8%B0%E7%9A%84%E3%81%AB%E8%A8%AA%E5%95%8F%0A%20%20%20%20%20%20%20%20dfs%28graph%2C%20visited%2C%20res%2C%20adjVet%29%0A%0A%0Adef%20graph_dfs%28graph%3A%20GraphAdjList%2C%20start_vet%3A%20Vertex%29%20-%3E%20list%5BVertex%5D%3A%0A%20%20%20%20%22%22%22%E6%B7%B1%E3%81%95%E5%84%AA%E5%85%88%E6%8E%A2%E7%B4%A2%22%22%22%0A%20%20%20%20%23%20%E6%8C%87%E5%AE%9A%E3%81%97%E3%81%9F%E9%A0%82%E7%82%B9%E3%81%AE%E9%9A%A3%E6%8E%A5%E9%A0%82%E7%82%B9%E3%82%92%E3%81%99%E3%81%B9%E3%81%A6%E5%8F%96%E5%BE%97%E3%81%A7%E3%81%8D%E3%82%8B%E3%82%88%E3%81%86%E3%80%81%E9%9A%A3%E6%8E%A5%E3%83%AA%E3%82%B9%E3%83%88%E3%81%A7%E3%82%B0%E3%83%A9%E3%83%95%E3%82%92%E8%A1%A8%E7%8F%BE%E3%81%99%E3%82%8B%0A%20%20%20%20%23%20%E9%A0%82%E7%82%B9%E3%81%AE%E8%B5%B0%E6%9F%BB%E9%A0%86%E5%BA%8F%0A%20%20%20%20res%20%3D%20%5B%5D%0A%20%20%20%20%23%20%E8%A8%AA%E5%95%8F%E6%B8%88%E3%81%BF%E3%81%AE%E9%A0%82%E7%82%B9%E3%82%92%E8%A8%98%E9%8C%B2%E3%81%99%E3%82%8B%E3%81%9F%E3%82%81%E3%81%AE%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%0A%20%20%20%20visited%20%3D%20set%5BVertex%5D%28%29%0A%20%20%20%20dfs%28graph%2C%20visited%2C%20res%2C%20start_vet%29%0A%20%20%20%20return%20res%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E7%84%A1%E5%90%91%E3%82%B0%E3%83%A9%E3%83%95%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20v%20%3D%20vals_to_vets%28%5B0%2C%201%2C%202%2C%203%2C%204%5D%29%0A%20%20%20%20edges%20%3D%20%5B%0A%20%20%20%20%20%20%20%20%5Bv%5B0%5D%2C%20v%5B1%5D%5D%2C%0A%20%20%20%20%20%20%20%20%5Bv%5B0%5D%2C%20v%5B3%5D%5D%2C%0A%20%20%20%20%20%20%20%20%5Bv%5B1%5D%2C%20v%5B2%5D%5D%2C%0A%20%20%20%20%20%20%20%20%5Bv%5B1%5D%2C%20v%5B4%5D%5D%2C%0A%20%20%20%20%20%20%20%20%5Bv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</iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20Vertex%3A%0A%20%20%20%20%22%22%22%E9%A0%82%E7%82%B9%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%20%3D%20val%0A%0Adef%20vals_to_vets%28vals%3A%20list%5Bint%5D%29%20-%3E%20list%5B%22Vertex%22%5D%3A%0A%20%20%20%20%22%22%22%E5%80%A4%E3%83%AA%E3%82%B9%E3%83%88%20vals%20%E3%82%92%E5%85%A5%E5%8A%9B%E3%81%97%E3%80%81%E9%A0%82%E7%82%B9%E3%83%AA%E3%82%B9%E3%83%88%20vets%20%E3%82%92%E8%BF%94%E3%81%99%22%22%22%0A%20%20%20%20return%20%5BVertex%28val%29%20for%20val%20in%20vals%5D%0A%0Aclass%20GraphAdjList%3A%0A%20%20%20%20%22%22%22%E9%9A%A3%E6%8E%A5%E3%83%AA%E3%82%B9%E3%83%88%E3%81%AB%E5%9F%BA%E3%81%A5%E3%81%8F%E7%84%A1%E5%90%91%E3%82%B0%E3%83%A9%E3%83%95%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%0A%20%20%20%20def%20__init__%28self%2C%20edges%3A%20list%5Blist%5BVertex%5D%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%82%B3%E3%83%B3%E3%82%B9%E3%83%88%E3%83%A9%E3%82%AF%E3%82%BF%22%22%22%0A%20%20%20%20%20%20%20%20self.adj_list%20%3D%20dict%5BVertex%2C%20list%5BVertex%5D%5D%28%29%0A%20%20%20%20%20%20%20%20for%20edge%20in%20edges%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_vertex%28edge%5B0%5D%29%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_vertex%28edge%5B1%5D%29%0A%20%20%20%20%20%20%20%20%20%20%20%20self.add_edge%28edge%5B0%5D%2C%20edge%5B1%5D%29%0A%0A%20%20%20%20def%20add_edge%28self%2C%20vet1%3A%20Vertex%2C%20vet2%3A%20Vertex%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%BE%BA%E3%82%92%E8%BF%BD%E5%8A%A0%22%22%22%0A%20%20%20%20%20%20%20%20if%20vet1%20not%20in%20self.adj_list%20or%20vet2%20not%20in%20self.adj_list%20or%20vet1%20%3D%3D%20vet2%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20ValueError%28%29%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet1%5D.append%28vet2%29%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet2%5D.append%28vet1%29%0A%0A%20%20%20%20def%20add_vertex%28self%2C%20vet%3A%20Vertex%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E9%A0%82%E7%82%B9%E3%82%92%E8%BF%BD%E5%8A%A0%22%22%22%0A%20%20%20%20%20%20%20%20if%20vet%20in%20self.adj_list%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%0A%20%20%20%20%20%20%20%20self.adj_list%5Bvet%5D%20%3D%20%5B%5D%0A%0A%0Adef%20dfs%28graph%3A%20GraphAdjList%2C%20visited%3A%20set%5BVertex%5D%2C%20res%3A%20list%5BVertex%5D%2C%20vet%3A%20Vertex%29%3A%0A%20%20%20%20%22%22%22%E6%B7%B1%E3%81%95%E5%84%AA%E5%85%88%E8%B5%B0%E6%9F%BB%E3%81%AE%E8%A3%9C%E5%8A%A9%E9%96%A2%E6%95%B0%22%22%22%0A%20%20%20%20res.append%28vet%29%20%20%23%20%E8%A8%AA%E5%95%8F%E3%81%97%E3%81%9F%E9%A0%82%E7%82%B9%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20visited.add%28vet%29%20%20%23%20%E3%81%93%E3%81%AE%E9%A0%82%E7%82%B9%E3%82%92%E8%A8%AA%E5%95%8F%E6%B8%88%E3%81%BF%E3%81%AB%E3%81%99%E3%82%8B%0A%20%20%20%20%23%20%E3%81%93%E3%81%AE%E9%A0%82%E7%82%B9%E3%81%AE%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E9%9A%A3%E6%8E%A5%E9%A0%82%E7%82%B9%E3%82%92%E8%B5%B0%E6%9F%BB%0A%20%20%20%20for%20adjVet%20in%20graph.adj_list%5Bvet%5D%3A%0A%20%20%20%20%20%20%20%20if%20adjVet%20in%20visited%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20continue%20%20%23%20%E8%A8%AA%E5%95%8F%E6%B8%88%E3%81%BF%E3%81%AE%E9%A0%82%E7%82%B9%E3%82%92%E3%82%B9%E3%82%AD%E3%83%83%E3%83%97%0A%20%20%20%20%20%20%20%20%23%20%E9%9A%A3%E6%8E%A5%E9%A0%82%E7%82%B9%E3%82%92%E5%86%8D%E5%B8%B0%E7%9A%84%E3%81%AB%E8%A8%AA%E5%95%8F%0A%20%20%20%20%20%20%20%20dfs%28graph%2C%20visited%2C%20res%2C%20adjVet%29%0A%0A%0Adef%20graph_dfs%28graph%3A%20GraphAdjList%2C%20start_vet%3A%20Vertex%29%20-%3E%20list%5BVertex%5D%3A%0A%20%20%20%20%22%22%22%E6%B7%B1%E3%81%95%E5%84%AA%E5%85%88%E6%8E%A2%E7%B4%A2%22%22%22%0A%20%20%20%20%23%20%E6%8C%87%E5%AE%9A%E3%81%97%E3%81%9F%E9%A0%82%E7%82%B9%E3%81%AE%E9%9A%A3%E6%8E%A5%E9%A0%82%E7%82%B9%E3%82%92%E3%81%99%E3%81%B9%E3%81%A6%E5%8F%96%E5%BE%97%E3%81%A7%E3%81%8D%E3%82%8B%E3%82%88%E3%81%86%E3%80%81%E9%9A%A3%E6%8E%A5%E3%83%AA%E3%82%B9%E3%83%88%E3%81%A7%E3%82%B0%E3%83%A9%E3%83%95%E3%82%92%E8%A1%A8%E7%8F%BE%E3%81%99%E3%82%8B%0A%20%20%20%20%23%20%E9%A0%82%E7%82%B9%E3%81%AE%E8%B5%B0%E6%9F%BB%E9%A0%86%E5%BA%8F%0A%20%20%20%20res%20%3D%20%5B%5D%0A%20%20%20%20%23%20%E8%A8%AA%E5%95%8F%E6%B8%88%E3%81%BF%E3%81%AE%E9%A0%82%E7%82%B9%E3%82%92%E8%A8%98%E9%8C%B2%E3%81%99%E3%82%8B%E3%81%9F%E3%82%81%E3%81%AE%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%0A%20%20%20%20visited%20%3D%20set%5BVertex%5D%28%29%0A%20%20%20%20dfs%28graph%2C%20visited%2C%20res%2C%20start_vet%29%0A%20%20%20%20return%20res%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E7%84%A1%E5%90%91%E3%82%B0%E3%83%A9%E3%83%95%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20v%20%3D%20vals_to_vets%28%5B0%2C%201%2C%202%2C%203%2C%204%5D%29%0A%20%20%20%20edges%20%3D%20%5B%0A%20%20%20%20%20%20%20%20%5Bv%5B0%5D%2C%20v%5B1%5D%5D%2C%0A%20%20%20%20%20%20%20%20%5Bv%5B0%5D%2C%20v%5B3%5D%5D%2C%0A%20%20%20%20%20%20%20%20%5Bv%5B1%5D%2C%20v%5B2%5D%5D%2C%0A%20%20%20%20%20%20%20%20%5Bv%5B1%5D%2C%20v%5B4%5D%5D%2C%0A%20%20%20%20%20%20%20%20%5B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target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>深さ優先走査のアルゴリズムの流れは以下の図のとおりです。</p>
 <ul>
-<li><strong>破線は下向きの再帰を表し</strong>、新しい頂点を訪問するために新しい再帰メソッドが開始されたことを示します。</li>
-<li><strong>曲線の破線は上向きのバックトラックを表し</strong>、この再帰メソッドがこのメソッドが開始された位置に戻ったことを示します。</li>
+<li>**直線の破線は下向きの再帰呼び出し**を表し、新しい頂点を訪問するために新たな再帰メソッドが開始されたことを意味します。</li>
+<li>**曲線の破線は上向きのバックトラック**を表し、この再帰メソッドがすでに戻って、呼び出し元の位置までたどり着いたことを意味します。</li>
 </ul>
-<p>理解を深めるため、下図とコードを組み合わせて、DFSプロセス全体を頭の中でシミュレート（または描画）することをお勧めします。各再帰メソッドがいつ開始され、いつ戻るかを含めてです。</p>
+<p>理解を深めるために、以下の図とコードを結びつけて、DFS 全体の過程を頭の中でシミュレーションする（あるいは紙に書き出す）ことを勧めます。各再帰メソッドがいつ開始し、いつ戻るかも含めて追ってみてください。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="4:11"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">&lt;1&gt;</label><label for="__tabbed_4_2">&lt;2&gt;</label><label for="__tabbed_4_3">&lt;3&gt;</label><label for="__tabbed_4_4">&lt;4&gt;</label><label for="__tabbed_4_5">&lt;5&gt;</label><label for="__tabbed_4_6">&lt;6&gt;</label><label for="__tabbed_4_7">&lt;7&gt;</label><label for="__tabbed_4_8">&lt;8&gt;</label><label for="__tabbed_4_9">&lt;9&gt;</label><label for="__tabbed_4_10">&lt;10&gt;</label><label for="__tabbed_4_11">&lt;11&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="グラフの深さ優先探索の手順" class="animation-figure" src="../graph_traversal.assets/graph_dfs_step1.png" /></p>
+<p><img alt="グラフの深さ優先走査の手順" class="animation-figure" src="../graph_traversal.assets/graph_dfs_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="graph_dfs_step2" class="animation-figure" src="../graph_traversal.assets/graph_dfs_step2.png" /></p>
@@ -4850,16 +5390,16 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 9-12 &nbsp; グラフの深さ優先探索の手順 </p>
+<p align="center"> 図 9-12 &nbsp; グラフの深さ優先走査の手順 </p>
 
 <div class="admonition question">
-<p class="admonition-title">深さ優先走査のシーケンスは一意ですか？</p>
-<p>幅優先走査と同様に、深さ優先走査シーケンスの順序も一意ではありません。ある頂点が与えられた場合、どの方向を最初に探索することも可能です。つまり、隣接頂点の順序は任意にシャッフルできますが、すべて深さ優先走査の一部です。</p>
-<p>木の走査を例に取ると、「根 <span class="arithmatex">\(\rightarrow\)</span> 左 <span class="arithmatex">\(\rightarrow\)</span> 右」、「左 <span class="arithmatex">\(\rightarrow\)</span> 根 <span class="arithmatex">\(\rightarrow\)</span> 右」、「左 <span class="arithmatex">\(\rightarrow\)</span> 右 <span class="arithmatex">\(\rightarrow\)</span> 根」は、それぞれ前順、中順、後順走査に対応します。これらは3つの異なる走査優先度を示していますが、3つすべてが深さ優先走査と見なされます。</p>
+<p class="admonition-title">深さ優先走査の順序列は一意ですか？</p>
+<p>幅優先走査と同様に、深さ優先走査の順序列も一意ではありません。ある頂点が与えられたとき、どの方向を先に探索してもよく、つまり隣接頂点の順序は任意に入れ替えられ、それでも深さ優先走査になります。</p>
+<p>木の走査を例にすると、「根 <span class="arithmatex">\(\rightarrow\)</span> 左 <span class="arithmatex">\(\rightarrow\)</span> 右」「左 <span class="arithmatex">\(\rightarrow\)</span> 根 <span class="arithmatex">\(\rightarrow\)</span> 右」「左 <span class="arithmatex">\(\rightarrow\)</span> 右 <span class="arithmatex">\(\rightarrow\)</span> 根」は、それぞれ先行順、中間順、後行順走査に対応します。これらは 3 種類の走査優先順位を示していますが、いずれも深さ優先走査に属します。</p>
 </div>
-<h3 id="2_1">2. &nbsp; 計算量分析<a class="headerlink" href="#2_1" title="Permanent link">&para;</a></h3>
-<p><strong>時間計算量</strong>：すべての頂点が一度訪問され、<span class="arithmatex">\(O(|V|)\)</span>時間を使用します。すべての辺が2回訪問され、<span class="arithmatex">\(O(2|E|)\)</span>時間を使用します。全体で<span class="arithmatex">\(O(|V| + |E|)\)</span>時間を使用します。</p>
-<p><strong>空間計算量</strong>：リスト<code>res</code>、ハッシュセット<code>visited</code>の最大頂点数は<span class="arithmatex">\(|V|\)</span>で、最大再帰深度は<span class="arithmatex">\(|V|\)</span>です。したがって、<span class="arithmatex">\(O(|V|)\)</span>空間を使用します。</p>
+<h3 id="2_1">2. &nbsp; 計算量の分析<a class="headerlink" href="#2_1" title="Permanent link">&para;</a></h3>
+<p><strong>時間計算量</strong>：すべての頂点は <span class="arithmatex">\(1\)</span> 回ずつ訪問されるため、<span class="arithmatex">\(O(|V|)\)</span> 時間です。すべての辺は <span class="arithmatex">\(2\)</span> 回ずつ訪問されるため、<span class="arithmatex">\(O(2|E|)\)</span> 時間です。したがって全体では <span class="arithmatex">\(O(|V| + |E|)\)</span> 時間です。</p>
+<p><strong>空間計算量</strong>：リスト <code>res</code> とハッシュ集合 <code>visited</code> に含まれる頂点数は最大で <span class="arithmatex">\(|V|\)</span> であり、再帰の深さも最大で <span class="arithmatex">\(|V|\)</span> であるため、<span class="arithmatex">\(O(|V|)\)</span> 空間です。</p>
 
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diff --git a/ja/chapter_graph/index.html b/ja/chapter_graph/index.html
index c7e33cba3..6b02b3279 100644
--- a/ja/chapter_graph/index.html
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@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
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-    序
+    はじめに
   
 
     
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-    序
+    はじめに
   
 
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-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
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-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
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-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
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-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
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-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
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 <p><img alt="グラフ" class="cover-image" src="../assets/covers/chapter_graph.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>人生の旅路において、私たちの一人一人はノードであり、無数の見えない辺で結ばれています。</p>
-<p>一つ一つの出会いと別れが、この広大な人生のグラフに独特の印を残していきます。</p>
+<p>人生の旅路において、私たちはそれぞれ一つひとつのノードのようなものであり、無数の見えない辺によって結ばれています。</p>
+<p>出会いと別れのたびに、この巨大なネットワークグラフの中に固有の足跡が刻まれます。</p>
 </div>
 <h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
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-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
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+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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 <!-- Page content -->
 <h1 id="94">9.4 &nbsp; まとめ<a class="headerlink" href="#94" title="Permanent link">&para;</a></h1>
-<h3 id="1">1. &nbsp; 重要な復習<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<h3 id="1">1. &nbsp; 重要なポイントの振り返り<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
-<li>グラフは頂点と辺で構成されます。頂点の集合と辺の集合として記述できます。</li>
-<li>線形関係（連結リストなど）や階層関係（木など）と比較して、ネットワーク関係（グラフ）はより大きな柔軟性を提供し、より複雑になります。</li>
-<li>有向グラフでは、辺に方向があります。連結グラフでは、任意の頂点から他の任意の頂点に到達できます。重み付きグラフでは、各辺に関連する重み変数があります。</li>
-<li>隣接行列は、行列（2次元配列）を使用してグラフを表現する方法です。行と列は頂点を表します。行列要素の値は、2つの頂点間に辺があるかどうかを示し、辺がある場合は<span class="arithmatex">\(1\)</span>、ない場合は<span class="arithmatex">\(0\)</span>を使用します。隣接行列は辺の追加、削除、チェックなどの操作に非常に効率的ですが、より多くのスペースが必要です。</li>
-<li>隣接リストは、連結リストの集合を使用してグラフを表現するもう一つの一般的な方法です。グラフ内の各頂点には、その隣接するすべての頂点を含むリストがあります。<span class="arithmatex">\(i\)</span>番目のリストは頂点<span class="arithmatex">\(i\)</span>を表します。隣接リストは隣接行列と比較してより少ないスペースを使用します。ただし、辺を見つけるためにリストを走査する必要があるため、時間効率は低くなります。</li>
-<li>隣接リストの連結リストが十分に長くなったとき、ルックアップ効率を向上させるために赤黒木やハッシュテーブルに変換できます。</li>
-<li>アルゴリズム設計の観点から、隣接行列は「空間と時間のトレードオフ」の概念を反映し、隣接リストは「時間と空間のトレードオフ」を反映します。</li>
-<li>グラフは、ソーシャルネットワークや地下鉄路線など、さまざまな現実世界のシステムをモデル化するために使用できます。</li>
-<li>木はグラフの特別なケースであり、木の走査もグラフ走査の特別なケースです。</li>
-<li>グラフの幅優先走査は、近くから遠くへと層ごとに拡張する探索方法で、通常キューを使用します。</li>
-<li>グラフの深さ優先走査は、それ以上のパスがない場合にバックトラックする前に、まず終端に到達することを優先する探索方法です。しばしば再帰を使用して実装されます。</li>
+<li>グラフは頂点と辺から構成され、一組の頂点と一組の辺からなる集合として表せます。</li>
+<li>線形関係（連結リスト）や分治関係（木）と比べて、ネットワーク関係（グラフ）は自由度が高く、そのぶん複雑です。</li>
+<li>有向グラフの辺は方向性を持ち、連結グラフでは任意の頂点に到達でき、重み付きグラフの各辺は重み変数を含みます。</li>
+<li>隣接行列は行列を用いてグラフを表し、各行（列）が 1 つの頂点を表し、行列要素が辺を表します。<span class="arithmatex">\(1\)</span> または <span class="arithmatex">\(0\)</span> を用いて、2 つの頂点の間に辺があるかないかを示します。隣接行列は追加・削除・検索・更新の操作効率が高い一方で、より多くの空間を消費します。</li>
+<li>隣接リストは複数の連結リストを使ってグラフを表し、第 <span class="arithmatex">\(i\)</span> 個の連結リストが頂点 <span class="arithmatex">\(i\)</span> に対応し、その頂点に隣接するすべての頂点を格納します。隣接リストは隣接行列よりも省スペースですが、辺を探すために連結リストを走査する必要があるため、時間効率は低くなります。</li>
+<li>隣接リスト内の連結リストが長くなりすぎた場合は、赤黒木やハッシュテーブルに変換することで、検索効率を高められます。</li>
+<li>アルゴリズムの考え方という観点では、隣接行列は「空間を時間と引き換えにする」ことを体現し、隣接リストは「時間を空間と引き換えにする」ことを体現します。</li>
+<li>グラフは、ソーシャルネットワークや地下鉄路線など、さまざまな現実のシステムをモデル化するために使えます。</li>
+<li>木はグラフの特殊な一例であり、木の走査もグラフ走査の特殊な一例です。</li>
+<li>グラフの幅優先探索は、近いところから遠いところへ、層ごとに広がっていく探索方法であり、通常はキューを使って実装します。</li>
+<li>グラフの深さ優先探索は、まず行けるところまで進み、進めなくなったらバックトラックする探索方法であり、通常は再帰に基づいて実装します。</li>
 </ul>
 <h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
-<p><strong>Q</strong>: パスは頂点のシーケンスとして定義されますか、それとも辺のシーケンスとして定義されますか？</p>
-<p>グラフ理論では、グラフ内のパスは頂点のシーケンスを結ぶ有限または無限の辺のシーケンスです。</p>
-<p>この文書では、パスは頂点のシーケンスではなく、辺のシーケンスと考えられます。これは、2つの頂点を結ぶ複数の辺がある可能性があり、その場合各辺がパスに対応するためです。</p>
-<p><strong>Q</strong>: 非連結グラフでは、走査できない点がありますか？</p>
-<p>非連結グラフでは、特定の点から到達できない頂点が少なくとも1つあります。非連結グラフを走査するには、グラフのすべての連結成分を走査するために複数の開始点を設定する必要があります。</p>
-<p><strong>Q</strong>: 隣接リストで、「その頂点に接続されたすべての頂点」の順序は重要ですか？</p>
-<p>任意の順序で構いません。ただし、実際のアプリケーションでは、頂点が追加された順序や頂点値の順序など、特定のルールに従ってそれらをソートする必要がある場合があります。これにより、特定の極値を持つ頂点を素早く見つけることができます。</p>
+<p><strong>Q</strong>：経路の定義は頂点列ですか、それとも辺列ですか？</p>
+<p>Wikipedia では言語版ごとに定義が一致していません。英語版では「経路は辺の列」であり、中国語版では「経路は頂点の列」です。以下は英語版の原文です：In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices.</p>
+<p>本書では、経路を頂点列ではなく辺列とみなします。これは、2 つの頂点の間に複数の辺が存在する可能性があり、その場合は各辺がそれぞれ 1 本の経路に対応するためです。</p>
+<p><strong>Q</strong>：非連結グラフには到達できない頂点がありますか？</p>
+<p>非連結グラフでは、ある頂点から出発すると、少なくとも 1 つの頂点には到達できません。非連結グラフ全体を走査するには、グラフ内のすべての連結成分をたどれるように複数の始点を設定する必要があります。</p>
+<p><strong>Q</strong>：隣接リストにおいて、「その頂点に接続されたすべての頂点」の順序に決まりはありますか？</p>
+<p>順序は任意でかまいません。ただし実際の応用では、頂点を追加した順序や頂点値の大小順など、特定の規則に従って並べ替える必要がある場合があります。そうすることで、「ある種の極値を持つ」頂点をすばやく見つけやすくなります。</p>
 
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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-    序
+    はじめに
   
 
     
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+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
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-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
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-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
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-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
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+    3.4 &nbsp; 文字エンコーディング *
   
 
     
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+    12.3 &nbsp; 二分木の構築問題
   
 
     
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 <h1 id="152">15.2 &nbsp; 分数ナップサック問題<a class="headerlink" href="#152" title="Permanent link">&para;</a></h1>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
-<p><span class="arithmatex">\(n\)</span> 個のアイテムが与えられ、<span class="arithmatex">\(i\)</span> 番目のアイテムの重量は <span class="arithmatex">\(wgt[i-1]\)</span> で値は <span class="arithmatex">\(val[i-1]\)</span> です。容量が <span class="arithmatex">\(cap\)</span> のナップサックがあります。各アイテムは1回のみ選択できますが、<strong>アイテムの一部を選択することができ、その値は選択された重量の割合に基づいて計算されます</strong>。限られた容量の下でナップサック内のアイテムの最大値は何ですか？例を下の図に示します。</p>
+<p><span class="arithmatex">\(n\)</span> 個の品物が与えられ、第 <span class="arithmatex">\(i\)</span> 個の品物の重さは <span class="arithmatex">\(wgt[i-1]\)</span>、価値は <span class="arithmatex">\(val[i-1]\)</span> であり、容量が <span class="arithmatex">\(cap\)</span> のナップサックがある。各品物は 1 回だけ選択できるが、<strong>品物の一部を選ぶこともでき、価値は選択した重量の割合に応じて計算される</strong>。容量制限の下でナップサック内の品物の最大価値を求めよ。例を以下に示す。</p>
 </div>
 <p><img alt="分数ナップサック問題の例データ" class="animation-figure" src="../fractional_knapsack_problem.assets/fractional_knapsack_example.png" /></p>
 <p align="center"> 図 15-3 &nbsp; 分数ナップサック問題の例データ </p>
 
-<p>分数ナップサック問題は全体的に0-1ナップサック問題と非常に似ており、現在のアイテム <span class="arithmatex">\(i\)</span> と容量 <span class="arithmatex">\(c\)</span> を含み、ナップサックの限られた容量内で値を最大化することを目的としています。</p>
-<p>違いは、この問題ではアイテムの一部のみを選択できることです。下の図に示すように、<strong>アイテムを任意に分割し、重量の割合に基づいて対応する値を計算できます</strong>。</p>
+<p>分数ナップサック問題は 0-1 ナップサック問題と全体として非常によく似ており、状態には現在の品物 <span class="arithmatex">\(i\)</span> と容量 <span class="arithmatex">\(c\)</span> が含まれ、目標は容量制限下での最大価値を求めることである。</p>
+<p>異なる点は、本問では品物の一部だけを選べることである。以下に示すように、<strong>品物は任意に分割でき、対応する価値は重量の割合に応じて計算される</strong>。</p>
 <ol>
-<li>アイテム <span class="arithmatex">\(i\)</span> について、その単位重量あたりの値は <span class="arithmatex">\(val[i-1] / wgt[i-1]\)</span> で、単位値と呼ばれます。</li>
-<li>重量 <span class="arithmatex">\(w\)</span> のアイテム <span class="arithmatex">\(i\)</span> の一部をナップサックに入れるとすると、ナップサックに追加される値は <span class="arithmatex">\(w \times val[i-1] / wgt[i-1]\)</span> です。</li>
+<li>品物 <span class="arithmatex">\(i\)</span> について、単位重量あたりの価値は <span class="arithmatex">\(val[i-1] / wgt[i-1]\)</span> であり、これを単位価値と呼ぶ。</li>
+<li>品物 <span class="arithmatex">\(i\)</span> の一部を重さ <span class="arithmatex">\(w\)</span> だけ入れると、ナップサックに増える価値は <span class="arithmatex">\(w \times val[i-1] / wgt[i-1]\)</span> となる。</li>
 </ol>
-<p><img alt="アイテムの単位重量あたりの値" class="animation-figure" src="../fractional_knapsack_problem.assets/fractional_knapsack_unit_value.png" /></p>
-<p align="center"> 図 15-4 &nbsp; アイテムの単位重量あたりの値 </p>
+<p><img alt="品物の単位重量あたりの価値" class="animation-figure" src="../fractional_knapsack_problem.assets/fractional_knapsack_unit_value.png" /></p>
+<p align="center"> 図 15-4 &nbsp; 品物の単位重量あたりの価値 </p>
 
 <h3 id="1">1. &nbsp; 貪欲戦略の決定<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>ナップサック内のアイテムの総値を最大化することは、<strong>本質的に単位重量あたりの値を最大化することを意味します</strong>。これから、下の図に示す貪欲戦略を導出できます。</p>
+<p>ナップサック内の品物の総価値を最大化することは、**本質的には単位重量あたりの品物価値を最大化すること**である。そこから、以下に示す貪欲戦略を導ける。</p>
 <ol>
-<li>アイテムを単位値の高い順から低い順にソートします。</li>
-<li>すべてのアイテムを反復し、**各ラウンドで最も高い単位値を持つアイテムを貪欲に選択**します。</li>
-<li>ナップサックの残り容量が不十分な場合、現在のアイテムの一部を使用してナップサックを満たします。</li>
+<li>品物を単位価値の高い順にソートする。</li>
+<li>すべての品物を走査し、<strong>各回で単位価値が最も高い品物を貪欲に選択する</strong>。</li>
+<li>残りのナップサック容量が足りない場合は、現在の品物の一部を使ってナップサックを満たす。</li>
 </ol>
 <p><img alt="分数ナップサック問題の貪欲戦略" class="animation-figure" src="../fractional_knapsack_problem.assets/fractional_knapsack_greedy_strategy.png" /></p>
 <p align="center"> 図 15-5 &nbsp; 分数ナップサック問題の貪欲戦略 </p>
 
 <h3 id="2">2. &nbsp; コード実装<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>アイテムを単位値でソートするために <code>Item</code> クラスを作成しました。ナップサックが満たされるまでループして貪欲な選択を行い、その後終了して解を返します：</p>
+<p>品物を単位価値でソートできるように、<code>Item</code> クラスを定義する。貪欲選択を繰り返し、ナップサックが満杯になったら終了して解を返す。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">fractional_knapsack.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">Item</span><span class="p">:</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;アイテム&quot;&quot;&quot;</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;品物&quot;&quot;&quot;</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">w</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">v</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">w</span> <span class="o">=</span> <span class="n">w</span>  <span class="c1"># アイテムの重量</span>
-<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">v</span> <span class="o">=</span> <span class="n">v</span>  <span class="c1"># アイテムの価値</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">w</span> <span class="o">=</span> <span class="n">w</span>  <span class="c1"># 品物の重さ</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">v</span> <span class="o">=</span> <span class="n">v</span>  <span class="c1"># 品物の価値</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">fractional_knapsack</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">val</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">cap</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
 <a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;分数ナップサック：貪欲法&quot;&quot;&quot;</span>
-<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="c1"># アイテムリストを作成、2 つの属性を含む：重量、価値</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="c1"># 重さと価値の 2 属性を持つ品物リストを作成</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="n">items</span> <span class="o">=</span> <span class="p">[</span><span class="n">Item</span><span class="p">(</span><span class="n">w</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span> <span class="k">for</span> <span class="n">w</span><span class="p">,</span> <span class="n">v</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span> <span class="n">val</span><span class="p">)]</span>
-<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="c1"># 単位価値 item.v / item.w で高い順にソート</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="c1"># 単位価値 item.v / item.w の高い順にソートする</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="n">items</span><span class="o">.</span><span class="n">sort</span><span class="p">(</span><span class="n">key</span><span class="o">=</span><span class="k">lambda</span> <span class="n">item</span><span class="p">:</span> <span class="n">item</span><span class="o">.</span><span class="n">v</span> <span class="o">/</span> <span class="n">item</span><span class="o">.</span><span class="n">w</span><span class="p">,</span> <span class="n">reverse</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
-<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="c1"># 貪欲選択をループ</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="c1"># 貪欲選択を繰り返す</span>
 <a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="n">res</span> <span class="o">=</span> <span class="mi">0</span>
 <a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>    <span class="k">for</span> <span class="n">item</span> <span class="ow">in</span> <span class="n">items</span><span class="p">:</span>
 <a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>        <span class="k">if</span> <span class="n">item</span><span class="o">.</span><span class="n">w</span> <span class="o">&lt;=</span> <span class="n">cap</span><span class="p">:</span>
-<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>            <span class="c1"># 残り容量が十分な場合、アイテム全体をナップサックに入れる</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>            <span class="c1"># 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる</span>
 <a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>            <span class="n">res</span> <span class="o">+=</span> <span class="n">item</span><span class="o">.</span><span class="n">v</span>
 <a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>            <span class="n">cap</span> <span class="o">-=</span> <span class="n">item</span><span class="o">.</span><span class="n">w</span>
 <a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>        <span class="k">else</span><span class="p">:</span>
-<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>            <span class="c1"># 残り容量が不十分な場合、アイテムの一部をナップサックに入れる</span>
+<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>            <span class="c1"># 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる</span>
 <a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a>            <span class="n">res</span> <span class="o">+=</span> <span class="p">(</span><span class="n">item</span><span class="o">.</span><span class="n">v</span> <span class="o">/</span> <span class="n">item</span><span class="o">.</span><span class="n">w</span><span class="p">)</span> <span class="o">*</span> <span class="n">cap</span>
-<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>            <span class="c1"># 残り容量がなくなったため、ループを中断</span>
+<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>            <span class="c1"># 残り容量がないため、ループを抜ける</span>
 <a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>            <span class="k">break</span>
 <a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a>    <span class="k">return</span> <span class="n">res</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">fractional_knapsack.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* アイテム */</span>
+<div class="highlight"><span class="filename">fractional_knapsack.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 品物 */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">Item</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
-<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">w</span><span class="p">;</span><span class="w"> </span><span class="c1">// アイテムの重量</span>
-<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">v</span><span class="p">;</span><span class="w"> </span><span class="c1">// アイテムの価値</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">w</span><span class="p">;</span><span class="w"> </span><span class="c1">// 品物の重さ</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">v</span><span class="p">;</span><span class="w"> </span><span class="c1">// 品物の価値</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="n">Item</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">w</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">v</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">w</span><span class="p">(</span><span class="n">w</span><span class="p">),</span><span class="w"> </span><span class="n">v</span><span class="p">(</span><span class="n">v</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="p">}</span>
@@ -4449,24 +4449,24 @@
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a>
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="cm">/* 分数ナップサック：貪欲法 */</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="kt">double</span><span class="w"> </span><span class="nf">fractionalKnapsack</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="c1">// アイテムリストを作成、2つの属性を含む：重量、価値</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="c1">// 重さと価値の 2 属性を持つ品物リストを作成</span>
 <a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Item</span><span class="o">&gt;</span><span class="w"> </span><span class="n">items</span><span class="p">;</span>
 <a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">        </span><span class="n">items</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">Item</span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="p">]));</span>
 <a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="c1">// 単位価値 item.v / item.w で高い順にソート</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="c1">// 単位価値 item.v / item.w の高い順にソートする</span>
 <a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">    </span><span class="n">sort</span><span class="p">(</span><span class="n">items</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">items</span><span class="p">.</span><span class="n">end</span><span class="p">(),</span><span class="w"> </span><span class="p">[](</span><span class="n">Item</span><span class="w"> </span><span class="o">&amp;</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">Item</span><span class="w"> </span><span class="o">&amp;</span><span class="n">b</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="n">a</span><span class="p">.</span><span class="n">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">a</span><span class="p">.</span><span class="n">w</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="n">b</span><span class="p">.</span><span class="n">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">b</span><span class="p">.</span><span class="n">w</span><span class="p">;</span><span class="w"> </span><span class="p">});</span>
-<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">    </span><span class="c1">// 貪欲選択をループ</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">    </span><span class="c1">// 貪欲選択を繰り返す</span>
 <a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">    </span><span class="kt">double</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="o">&amp;</span><span class="n">item</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">items</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">item</span><span class="p">.</span><span class="n">w</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="w">            </span><span class="c1">// 残り容量が十分な場合、アイテム全体をナップサックに入れる</span>
+<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="w">            </span><span class="c1">// 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる</span>
 <a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w">            </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="n">v</span><span class="p">;</span>
 <a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="w">            </span><span class="n">cap</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="n">w</span><span class="p">;</span>
 <a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="w">            </span><span class="c1">// 残り容量が不十分な場合、アイテムの一部をナップサックに入れる</span>
+<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="w">            </span><span class="c1">// 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる</span>
 <a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="w">            </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="n">item</span><span class="p">.</span><span class="n">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="n">w</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span>
-<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="w">            </span><span class="c1">// 残り容量がなくなったため、ループを中断</span>
+<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="w">            </span><span class="c1">// 残り容量がないため、ループを抜ける</span>
 <a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
 <a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="w">    </span><span class="p">}</span>
@@ -4475,10 +4475,10 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">fractional_knapsack.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* アイテム */</span>
+<div class="highlight"><span class="filename">fractional_knapsack.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 品物 */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kd">class</span> <span class="nc">Item</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">w</span><span class="p">;</span><span class="w"> </span><span class="c1">// アイテムの重量</span>
-<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">v</span><span class="p">;</span><span class="w"> </span><span class="c1">// アイテムの価値</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">w</span><span class="p">;</span><span class="w"> </span><span class="c1">// 品物の重さ</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">v</span><span class="p">;</span><span class="w"> </span><span class="c1">// 品物の価値</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">Item</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">w</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">v</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="na">w</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">w</span><span class="p">;</span>
@@ -4488,24 +4488,24 @@
 <a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a>
 <a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="cm">/* 分数ナップサック：貪欲法 */</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="kt">double</span><span class="w"> </span><span class="nf">fractionalKnapsack</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="c1">// アイテムリストを作成、2つの属性を含む：重量、価値</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="c1">// 重さと価値の 2 属性を持つ品物リストを作成</span>
 <a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="n">Item</span><span class="o">[]</span><span class="w"> </span><span class="n">items</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Item</span><span class="o">[</span><span class="n">wgt</span><span class="p">.</span><span class="na">length</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">        </span><span class="n">items</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Item</span><span class="p">(</span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">);</span>
 <a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">    </span><span class="c1">// 単位価値 item.v / item.w で高い順にソート</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">    </span><span class="c1">// 単位価値 item.v / item.w の高い順にソートする</span>
 <a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">    </span><span class="n">Arrays</span><span class="p">.</span><span class="na">sort</span><span class="p">(</span><span class="n">items</span><span class="p">,</span><span class="w"> </span><span class="n">Comparator</span><span class="p">.</span><span class="na">comparingDouble</span><span class="p">(</span><span class="n">item</span><span class="w"> </span><span class="o">-&gt;</span><span class="w"> </span><span class="o">-</span><span class="p">((</span><span class="kt">double</span><span class="p">)</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="na">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="na">w</span><span class="p">)));</span>
-<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">    </span><span class="c1">// 貪欲選択をループ</span>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">    </span><span class="c1">// 貪欲選択を繰り返す</span>
 <a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w">    </span><span class="kt">double</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Item</span><span class="w"> </span><span class="n">item</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">items</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">item</span><span class="p">.</span><span class="na">w</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="w">            </span><span class="c1">// 残り容量が十分な場合、アイテム全体をナップサックに入れる</span>
+<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="w">            </span><span class="c1">// 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる</span>
 <a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w">            </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="na">v</span><span class="p">;</span>
 <a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w">            </span><span class="n">cap</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="na">w</span><span class="p">;</span>
 <a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="w">            </span><span class="c1">// 残り容量が不十分な場合、アイテムの一部をナップサックに入れる</span>
+<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="w">            </span><span class="c1">// 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる</span>
 <a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a><span class="w">            </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="na">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="na">w</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span>
-<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="w">            </span><span class="c1">// 残り容量がなくなったため、ループを中断</span>
+<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="w">            </span><span class="c1">// 残り容量がないため、ループを抜ける</span>
 <a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
 <a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a><span class="w">    </span><span class="p">}</span>
@@ -4514,74 +4514,380 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">fractional_knapsack.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">Item</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
-<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
-<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">fractional_knapsack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">FractionalKnapsack</span><span class="p">}</span>
+<div class="highlight"><span class="filename">fractional_knapsack.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 品物 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">class</span><span class="w"> </span><span class="nf">Item</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">w</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">v</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">w</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">w</span><span class="p">;</span><span class="w"> </span><span class="c1">// 品物の重さ</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">v</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">v</span><span class="p">;</span><span class="w"> </span><span class="c1">// 品物の価値</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="p">}</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="cm">/* 分数ナップサック：貪欲法 */</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="kt">double</span><span class="w"> </span><span class="nf">FractionalKnapsack</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="c1">// 重さと価値の 2 属性を持つ品物リストを作成</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">    </span><span class="n">Item</span><span class="p">[]</span><span class="w"> </span><span class="n">items</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Item</span><span class="p">[</span><span class="n">wgt</span><span class="p">.</span><span class="n">Length</span><span class="p">];</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">        </span><span class="n">items</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Item</span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">    </span><span class="c1">// 単位価値 item.v / item.w の高い順にソートする</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">    </span><span class="n">Array</span><span class="p">.</span><span class="n">Sort</span><span class="p">(</span><span class="n">items</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">y</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">y</span><span class="p">.</span><span class="n">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">y</span><span class="p">.</span><span class="n">w</span><span class="p">).</span><span class="n">CompareTo</span><span class="p">(</span><span class="n">x</span><span class="p">.</span><span class="n">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">x</span><span class="p">.</span><span class="n">w</span><span class="p">));</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">    </span><span class="c1">// 貪欲選択を繰り返す</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">    </span><span class="kt">double</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Item</span><span class="w"> </span><span class="n">item</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">items</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">item</span><span class="p">.</span><span class="n">w</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w">            </span><span class="c1">// 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる</span>
+<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w">            </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="n">v</span><span class="p">;</span>
+<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="w">            </span><span class="n">cap</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="n">w</span><span class="p">;</span>
+<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="w">            </span><span class="c1">// 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる</span>
+<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="w">            </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="n">item</span><span class="p">.</span><span class="n">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="n">w</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span>
+<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="w">            </span><span class="c1">// 残り容量がないため、ループを抜ける</span>
+<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-3-31" name="__codelineno-3-31" href="#__codelineno-3-31"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">fractional_knapsack.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">Item</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
-<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
-<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">fractionalKnapsack</span><span class="p">}</span>
+<div class="highlight"><span class="filename">fractional_knapsack.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 品物 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">Item</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="nx">w</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="c1">// 品物の重さ</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">v</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="c1">// 品物の価値</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="p">}</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="cm">/* 分数ナップサック：貪欲法 */</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="kd">func</span><span class="w"> </span><span class="nx">fractionalKnapsack</span><span class="p">(</span><span class="nx">wgt</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">float64</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="c1">// 重さと価値の 2 属性を持つ品物リストを作成</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">    </span><span class="nx">items</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="nx">Item</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">wgt</span><span class="p">))</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">wgt</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">        </span><span class="nx">items</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">Item</span><span class="p">{</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="p">]}</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">    </span><span class="c1">// 単位価値 item.v / item.w の高い順にソートする</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">    </span><span class="nx">sort</span><span class="p">.</span><span class="nx">Slice</span><span class="p">(</span><span class="nx">items</span><span class="p">,</span><span class="w"> </span><span class="kd">func</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">items</span><span class="p">[</span><span class="nx">i</span><span class="p">].</span><span class="nx">v</span><span class="p">)</span><span class="o">/</span><span class="nb">float64</span><span class="p">(</span><span class="nx">items</span><span class="p">[</span><span class="nx">i</span><span class="p">].</span><span class="nx">w</span><span class="p">)</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">items</span><span class="p">[</span><span class="nx">j</span><span class="p">].</span><span class="nx">v</span><span class="p">)</span><span class="o">/</span><span class="nb">float64</span><span class="p">(</span><span class="nx">items</span><span class="p">[</span><span class="nx">j</span><span class="p">].</span><span class="nx">w</span><span class="p">)</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">    </span><span class="p">})</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w">    </span><span class="c1">// 貪欲選択を繰り返す</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w">    </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mf">0.0</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">item</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">items</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">item</span><span class="p">.</span><span class="nx">w</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">cap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w">            </span><span class="c1">// 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる</span>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="w">            </span><span class="nx">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">item</span><span class="p">.</span><span class="nx">v</span><span class="p">)</span>
+<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="w">            </span><span class="nx">cap</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="nx">item</span><span class="p">.</span><span class="nx">w</span>
+<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="w">            </span><span class="c1">// 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる</span>
+<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w">            </span><span class="nx">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">item</span><span class="p">.</span><span class="nx">v</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">item</span><span class="p">.</span><span class="nx">w</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">cap</span><span class="p">)</span>
+<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="w">            </span><span class="c1">// 残り容量がないため、ループを抜ける</span>
+<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-4-30" name="__codelineno-4-30" href="#__codelineno-4-30"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-31" name="__codelineno-4-31" href="#__codelineno-4-31"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-32" name="__codelineno-4-32" href="#__codelineno-4-32"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
+<a id="__codelineno-4-33" name="__codelineno-4-33" href="#__codelineno-4-33"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">fractional_knapsack.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">Item</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
-<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
-<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">fractionalKnapsack</span><span class="p">}</span>
+<div class="highlight"><span class="filename">fractional_knapsack.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 品物 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">Item</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">w</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// 品物の重さ</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">v</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// 品物の価値</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="kd">init</span><span class="p">(</span><span class="n">w</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">v</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">        </span><span class="kc">self</span><span class="p">.</span><span class="n">w</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">w</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">        </span><span class="kc">self</span><span class="p">.</span><span class="n">v</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">v</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="p">}</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="cm">/* 分数ナップサック：貪欲法 */</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="kd">func</span><span class="w"> </span><span class="nf">fractionalKnapsack</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">cap</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Double</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">    </span><span class="c1">// 重さと価値の 2 属性を持つ品物リストを作成</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">items</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">zip</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">).</span><span class="bp">map</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">Item</span><span class="p">(</span><span class="n">w</span><span class="p">:</span><span class="w"> </span><span class="nv">$0</span><span class="p">,</span><span class="w"> </span><span class="n">v</span><span class="p">:</span><span class="w"> </span><span class="nv">$1</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">    </span><span class="c1">// 単位価値 item.v / item.w の高い順にソートする</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">    </span><span class="n">items</span><span class="p">.</span><span class="bp">sort</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">-</span><span class="p">(</span><span class="nb">Double</span><span class="p">(</span><span class="nv">$0</span><span class="p">.</span><span class="n">v</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nb">Double</span><span class="p">(</span><span class="nv">$0</span><span class="p">.</span><span class="n">w</span><span class="p">))</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="o">-</span><span class="p">(</span><span class="nb">Double</span><span class="p">(</span><span class="nv">$1</span><span class="p">.</span><span class="n">v</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nb">Double</span><span class="p">(</span><span class="nv">$1</span><span class="p">.</span><span class="n">w</span><span class="p">))</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">    </span><span class="c1">// 貪欲選択を繰り返す</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mf">0.0</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">cap</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">cap</span>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">item</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">items</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="n">w</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="w">            </span><span class="c1">// 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる</span>
+<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="w">            </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nb">Double</span><span class="p">(</span><span class="n">item</span><span class="p">.</span><span class="n">v</span><span class="p">)</span>
+<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="w">            </span><span class="n">cap</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="n">w</span>
+<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a><span class="w">            </span><span class="c1">// 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる</span>
+<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a><span class="w">            </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nb">Double</span><span class="p">(</span><span class="n">item</span><span class="p">.</span><span class="n">v</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nb">Double</span><span class="p">(</span><span class="n">item</span><span class="p">.</span><span class="n">w</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">Double</span><span class="p">(</span><span class="n">cap</span><span class="p">)</span>
+<a id="__codelineno-5-29" name="__codelineno-5-29" href="#__codelineno-5-29"></a><span class="w">            </span><span class="c1">// 残り容量がないため、ループを抜ける</span>
+<a id="__codelineno-5-30" name="__codelineno-5-30" href="#__codelineno-5-30"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-5-31" name="__codelineno-5-31" href="#__codelineno-5-31"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-32" name="__codelineno-5-32" href="#__codelineno-5-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-33" name="__codelineno-5-33" href="#__codelineno-5-33"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-5-34" name="__codelineno-5-34" href="#__codelineno-5-34"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">fractional_knapsack.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">Item</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
-<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
-<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">fractionalKnapsack</span><span class="p">}</span>
+<div class="highlight"><span class="filename">fractional_knapsack.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 品物 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">Item</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">w</span><span class="p">,</span><span class="w"> </span><span class="nx">v</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">w</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">w</span><span class="p">;</span><span class="w"> </span><span class="c1">// 品物の重さ</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">v</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">v</span><span class="p">;</span><span class="w"> </span><span class="c1">// 品物の価値</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="p">}</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="cm">/* 分数ナップサック：貪欲法 */</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="kd">function</span><span class="w"> </span><span class="nx">fractionalKnapsack</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">    </span><span class="c1">// 重さと価値の 2 属性を持つ品物リストを作成</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">items</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">wgt</span><span class="p">.</span><span class="nx">map</span><span class="p">((</span><span class="nx">w</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">Item</span><span class="p">(</span><span class="nx">w</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="p">]));</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">    </span><span class="c1">// 単位価値 item.v / item.w の高い順にソートする</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">    </span><span class="nx">items</span><span class="p">.</span><span class="nx">sort</span><span class="p">((</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="nx">b</span><span class="p">.</span><span class="nx">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nx">b</span><span class="p">.</span><span class="nx">w</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">a</span><span class="p">.</span><span class="nx">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nx">a</span><span class="p">.</span><span class="nx">w</span><span class="p">);</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">    </span><span class="c1">// 貪欲選択を繰り返す</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">item</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">items</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">item</span><span class="p">.</span><span class="nx">w</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">            </span><span class="c1">// 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w">            </span><span class="nx">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">item</span><span class="p">.</span><span class="nx">v</span><span class="p">;</span>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w">            </span><span class="nx">cap</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="nx">item</span><span class="p">.</span><span class="nx">w</span><span class="p">;</span>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="w">            </span><span class="c1">// 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる</span>
+<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a><span class="w">            </span><span class="nx">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="p">(</span><span class="nx">item</span><span class="p">.</span><span class="nx">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nx">item</span><span class="p">.</span><span class="nx">w</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">cap</span><span class="p">;</span>
+<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="w">            </span><span class="c1">// 残り容量がないため、ループを抜ける</span>
+<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-6-27" name="__codelineno-6-27" href="#__codelineno-6-27"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-28" name="__codelineno-6-28" href="#__codelineno-6-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-29" name="__codelineno-6-29" href="#__codelineno-6-29"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-6-30" name="__codelineno-6-30" href="#__codelineno-6-30"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">fractional_knapsack.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">Item</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
-<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
-<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">fractionalKnapsack</span><span class="p">}</span>
+<div class="highlight"><span class="filename">fractional_knapsack.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 品物 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">Item</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="nx">w</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// 品物の重さ</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="nx">v</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// 品物の価値</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">w</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">v</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">w</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">w</span><span class="p">;</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">v</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">v</span><span class="p">;</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="p">}</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="cm">/* 分数ナップサック：貪欲法 */</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="kd">function</span><span class="w"> </span><span class="nx">fractionalKnapsack</span><span class="p">(</span><span class="nx">wgt</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">cap</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">    </span><span class="c1">// 重さと価値の 2 属性を持つ品物リストを作成</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">items</span><span class="o">:</span><span class="w"> </span><span class="kt">Item</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">wgt</span><span class="p">.</span><span class="nx">map</span><span class="p">((</span><span class="nx">w</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">Item</span><span class="p">(</span><span class="nx">w</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="p">]));</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">    </span><span class="c1">// 単位価値 item.v / item.w の高い順にソートする</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">    </span><span class="nx">items</span><span class="p">.</span><span class="nx">sort</span><span class="p">((</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="nx">b</span><span class="p">.</span><span class="nx">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nx">b</span><span class="p">.</span><span class="nx">w</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">a</span><span class="p">.</span><span class="nx">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nx">a</span><span class="p">.</span><span class="nx">w</span><span class="p">);</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">    </span><span class="c1">// 貪欲選択を繰り返す</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">item</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">items</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">item</span><span class="p">.</span><span class="nx">w</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="w">            </span><span class="c1">// 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる</span>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="w">            </span><span class="nx">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">item</span><span class="p">.</span><span class="nx">v</span><span class="p">;</span>
+<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="w">            </span><span class="nx">cap</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="nx">item</span><span class="p">.</span><span class="nx">w</span><span class="p">;</span>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="w">            </span><span class="c1">// 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる</span>
+<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a><span class="w">            </span><span class="nx">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="p">(</span><span class="nx">item</span><span class="p">.</span><span class="nx">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nx">item</span><span class="p">.</span><span class="nx">w</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">cap</span><span class="p">;</span>
+<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a><span class="w">            </span><span class="c1">// 残り容量がないため、ループを抜ける</span>
+<a id="__codelineno-7-29" name="__codelineno-7-29" href="#__codelineno-7-29"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-7-30" name="__codelineno-7-30" href="#__codelineno-7-30"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-31" name="__codelineno-7-31" href="#__codelineno-7-31"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-32" name="__codelineno-7-32" href="#__codelineno-7-32"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-7-33" name="__codelineno-7-33" href="#__codelineno-7-33"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">fractional_knapsack.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">Item</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
-<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
-<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">fractionalKnapsack</span><span class="p">}</span>
+<div class="highlight"><span class="filename">fractional_knapsack.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 品物 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">Item</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">w</span><span class="p">;</span><span class="w"> </span><span class="c1">// 品物の重さ</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">v</span><span class="p">;</span><span class="w"> </span><span class="c1">// 品物の価値</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="n">Item</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">w</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">v</span><span class="p">);</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="p">}</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="cm">/* 分数ナップサック：貪欲法 */</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="kt">double</span><span class="w"> </span><span class="n">fractionalKnapsack</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">  </span><span class="c1">// 重さと価値の 2 属性を持つ品物リストを作成</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Item</span><span class="o">&gt;</span><span class="w"> </span><span class="n">items</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">generate</span><span class="p">(</span><span class="n">wgt</span><span class="p">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">Item</span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="p">]));</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">  </span><span class="c1">// 単位価値 item.v / item.w の高い順にソートする</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">  </span><span class="n">items</span><span class="p">.</span><span class="n">sort</span><span class="p">((</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="p">.</span><span class="n">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">b</span><span class="p">.</span><span class="n">w</span><span class="p">).</span><span class="n">compareTo</span><span class="p">(</span><span class="n">a</span><span class="p">.</span><span class="n">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">a</span><span class="p">.</span><span class="n">w</span><span class="p">));</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">  </span><span class="c1">// 貪欲選択を繰り返す</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">  </span><span class="kt">double</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Item</span><span class="w"> </span><span class="n">item</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">items</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">item</span><span class="p">.</span><span class="n">w</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w">      </span><span class="c1">// 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる</span>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="w">      </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="n">v</span><span class="p">;</span>
+<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="w">      </span><span class="n">cap</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="n">w</span><span class="p">;</span>
+<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a><span class="w">      </span><span class="c1">// 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる</span>
+<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a><span class="w">      </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="n">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="n">w</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span>
+<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a><span class="w">      </span><span class="c1">// 残り容量がないため、ループを抜ける</span>
+<a id="__codelineno-8-26" name="__codelineno-8-26" href="#__codelineno-8-26"></a><span class="w">      </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-8-27" name="__codelineno-8-27" href="#__codelineno-8-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-28" name="__codelineno-8-28" href="#__codelineno-8-28"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-29" name="__codelineno-8-29" href="#__codelineno-8-29"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-8-30" name="__codelineno-8-30" href="#__codelineno-8-30"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">fractional_knapsack.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">Item</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
-<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
-<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">fractional_knapsack</span><span class="p">}</span>
+<div class="highlight"><span class="filename">fractional_knapsack.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 品物 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">Item</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="n">w</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="c1">// 品物の重さ</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="n">v</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="c1">// 品物の価値</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="p">}</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="k">impl</span><span class="w"> </span><span class="n">Item</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">new</span><span class="p">(</span><span class="n">w</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">v</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">        </span><span class="bp">Self</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">w</span><span class="p">,</span><span class="w"> </span><span class="n">v</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="p">}</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="cm">/* 分数ナップサック：貪欲法 */</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="k">fn</span><span class="w"> </span><span class="nf">fractional_knapsack</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">cap</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">f64</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">    </span><span class="c1">// 重さと価値の 2 属性を持つ品物リストを作成</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">items</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">        </span><span class="p">.</span><span class="n">iter</span><span class="p">()</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">        </span><span class="p">.</span><span class="n">zip</span><span class="p">(</span><span class="n">val</span><span class="p">.</span><span class="n">iter</span><span class="p">())</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">        </span><span class="p">.</span><span class="n">map</span><span class="p">(</span><span class="o">|</span><span class="p">(</span><span class="o">&amp;</span><span class="n">w</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="n">v</span><span class="p">)</span><span class="o">|</span><span class="w"> </span><span class="n">Item</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">w</span><span class="p">,</span><span class="w"> </span><span class="n">v</span><span class="p">))</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w">        </span><span class="p">.</span><span class="n">collect</span><span class="p">::</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">Item</span><span class="o">&gt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w">    </span><span class="c1">// 単位価値 item.v / item.w の高い順にソートする</span>
+<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="w">    </span><span class="n">items</span><span class="p">.</span><span class="n">sort_by</span><span class="p">(</span><span class="o">|</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="o">|</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="w">        </span><span class="p">(</span><span class="n">b</span><span class="p">.</span><span class="n">v</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">f64</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">b</span><span class="p">.</span><span class="n">w</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">f64</span><span class="p">)</span>
+<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="w">            </span><span class="p">.</span><span class="n">partial_cmp</span><span class="p">(</span><span class="o">&amp;</span><span class="p">(</span><span class="n">a</span><span class="p">.</span><span class="n">v</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">f64</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">a</span><span class="p">.</span><span class="n">w</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">f64</span><span class="p">))</span>
+<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="w">            </span><span class="p">.</span><span class="n">unwrap</span><span class="p">()</span>
+<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="w">    </span><span class="p">});</span>
+<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="w">    </span><span class="c1">// 貪欲選択を繰り返す</span>
+<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0.0</span><span class="p">;</span>
+<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">item</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="o">&amp;</span><span class="n">items</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-30" name="__codelineno-9-30" href="#__codelineno-9-30"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="n">w</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-31" name="__codelineno-9-31" href="#__codelineno-9-31"></a><span class="w">            </span><span class="c1">// 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる</span>
+<a id="__codelineno-9-32" name="__codelineno-9-32" href="#__codelineno-9-32"></a><span class="w">            </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="n">v</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">f64</span><span class="p">;</span>
+<a id="__codelineno-9-33" name="__codelineno-9-33" href="#__codelineno-9-33"></a><span class="w">            </span><span class="n">cap</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="n">w</span><span class="p">;</span>
+<a id="__codelineno-9-34" name="__codelineno-9-34" href="#__codelineno-9-34"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-35" name="__codelineno-9-35" href="#__codelineno-9-35"></a><span class="w">            </span><span class="c1">// 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる</span>
+<a id="__codelineno-9-36" name="__codelineno-9-36" href="#__codelineno-9-36"></a><span class="w">            </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="n">v</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">f64</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="n">w</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">f64</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">f64</span><span class="p">;</span>
+<a id="__codelineno-9-37" name="__codelineno-9-37" href="#__codelineno-9-37"></a><span class="w">            </span><span class="c1">// 残り容量がないため、ループを抜ける</span>
+<a id="__codelineno-9-38" name="__codelineno-9-38" href="#__codelineno-9-38"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-9-39" name="__codelineno-9-39" href="#__codelineno-9-39"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-40" name="__codelineno-9-40" href="#__codelineno-9-40"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-41" name="__codelineno-9-41" href="#__codelineno-9-41"></a><span class="w">    </span><span class="n">res</span>
+<a id="__codelineno-9-42" name="__codelineno-9-42" href="#__codelineno-9-42"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">fractional_knapsack.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">Item</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
-<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
-<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">fractionalKnapsack</span><span class="p">}</span>
+<div class="highlight"><span class="filename">fractional_knapsack.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 品物 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">w</span><span class="p">;</span><span class="w"> </span><span class="c1">// 品物の重さ</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">v</span><span class="p">;</span><span class="w"> </span><span class="c1">// 品物の価値</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="p">}</span><span class="w"> </span><span class="n">Item</span><span class="p">;</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="cm">/* 分数ナップサック：貪欲法 */</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="kt">float</span><span class="w"> </span><span class="nf">fractionalKnapsack</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">wgt</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">itemCount</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">    </span><span class="c1">// 重さと価値の 2 属性を持つ品物リストを作成</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="n">Item</span><span class="w"> </span><span class="o">*</span><span class="n">items</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">Item</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">itemCount</span><span class="p">);</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">itemCount</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">        </span><span class="n">items</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">Item</span><span class="p">){.</span><span class="n">w</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="p">.</span><span class="n">v</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="p">]};</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">    </span><span class="c1">// 単位価値 item.v / item.w の高い順にソートする</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">    </span><span class="n">qsort</span><span class="p">(</span><span class="n">items</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="kt">size_t</span><span class="p">)</span><span class="n">itemCount</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="n">Item</span><span class="p">),</span><span class="w"> </span><span class="n">sortByValueDensity</span><span class="p">);</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">    </span><span class="c1">// 貪欲選択を繰り返す</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">    </span><span class="kt">float</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0.0</span><span class="p">;</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">itemCount</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">items</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">w</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="w">            </span><span class="c1">// 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる</span>
+<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="w">            </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">items</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">v</span><span class="p">;</span>
+<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w">            </span><span class="n">cap</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">items</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">w</span><span class="p">;</span>
+<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="w">            </span><span class="c1">// 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる</span>
+<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="w">            </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="p">(</span><span class="kt">float</span><span class="p">)</span><span class="n">cap</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">items</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">w</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">items</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">v</span><span class="p">;</span>
+<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="w">            </span><span class="n">cap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">items</span><span class="p">);</span>
+<a id="__codelineno-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-10-32" name="__codelineno-10-32" href="#__codelineno-10-32"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">fractional_knapsack.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">Item</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
-<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
-<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">fractionalKnapsack</span><span class="p">}</span>
+<div class="highlight"><span class="filename">fractional_knapsack.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 品物 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">Item</span><span class="p">(</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">w</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="c1">// 品物</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">v</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w">  </span><span class="c1">// 品物の価値</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="p">)</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="cm">/* 分数ナップサック：貪欲法 */</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">fractionalKnapsack</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Double</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">    </span><span class="c1">// 重さと価値の 2 属性を持つ品物リストを作成</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">cap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">c</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">items</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arrayOfNulls</span><span class="o">&lt;</span><span class="n">Item</span><span class="o">&gt;</span><span class="p">(</span><span class="n">wgt</span><span class="p">.</span><span class="na">size</span><span class="p">)</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="na">indices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">        </span><span class="n">items</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Item</span><span class="p">(</span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">    </span><span class="c1">// 単位価値 item.v / item.w の高い順にソートする</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">    </span><span class="n">items</span><span class="p">.</span><span class="na">sortBy</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">item</span><span class="p">:</span><span class="w"> </span><span class="n">Item? </span><span class="o">-&gt;</span><span class="w"> </span><span class="o">-</span><span class="p">(</span><span class="n">item</span><span class="o">!!</span><span class="p">.</span><span class="na">v</span><span class="p">.</span><span class="na">toDouble</span><span class="p">()</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="na">w</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">    </span><span class="c1">// 貪欲選択を繰り返す</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0.0</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">item</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">items</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">item</span><span class="o">!!</span><span class="p">.</span><span class="na">w</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="w">            </span><span class="c1">// 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる</span>
+<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="w">            </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="na">v</span>
+<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="w">            </span><span class="n">cap</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="na">w</span>
+<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="w">            </span><span class="c1">// 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる</span>
+<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="w">            </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="na">v</span><span class="p">.</span><span class="na">toDouble</span><span class="p">()</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="na">w</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">cap</span>
+<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a><span class="w">            </span><span class="c1">// 残り容量がないため、ループを抜ける</span>
+<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-30" name="__codelineno-11-30" href="#__codelineno-11-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-11-32" name="__codelineno-11-32" href="#__codelineno-11-32"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">fractional_knapsack.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">Item</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
-<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
-<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">fractional_knapsack</span><span class="p">}</span>
+<div class="highlight"><span class="filename">fractional_knapsack.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### アイテム ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">Item</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:w</span><span class="w"> </span><span class="c1"># 品物の重さ</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:v</span><span class="w"> </span><span class="c1"># 品物の価値</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">w</span><span class="p">,</span><span class="w"> </span><span class="n">v</span><span class="p">)</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">    </span><span class="vi">@w</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">w</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">    </span><span class="vi">@v</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">v</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="k">end</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="c1">### 分数ナップサック：貪欲法 ###</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="k">def</span><span class="w"> </span><span class="nf">fractional_knapsack</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">  </span><span class="c1"># 重さと価値の 2 属性を持つ品物リストを作成する</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">  </span><span class="n">items</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="o">.</span><span class="n">each_with_index</span><span class="o">.</span><span class="n">map</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">w</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="no">Item</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">w</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">  </span><span class="c1"># 単位価値 item.v / item.w の高い順にソートする</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">  </span><span class="n">items</span><span class="o">.</span><span class="n">sort!</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="o">|</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="o">.</span><span class="n">v</span><span class="o">.</span><span class="n">to_f</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">b</span><span class="o">.</span><span class="n">w</span><span class="p">)</span><span class="w"> </span><span class="o">&lt;=&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">a</span><span class="o">.</span><span class="n">v</span><span class="o">.</span><span class="n">to_f</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">a</span><span class="o">.</span><span class="n">w</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w">  </span><span class="c1"># 貪欲選択を繰り返す</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">item</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">items</span>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">item</span><span class="o">.</span><span class="n">w</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w">      </span><span class="c1"># 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる</span>
+<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="w">      </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">item</span><span class="o">.</span><span class="n">v</span>
+<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a><span class="w">      </span><span class="n">cap</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">item</span><span class="o">.</span><span class="n">w</span>
+<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a><span class="w">      </span><span class="c1"># 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる</span>
+<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a><span class="w">      </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="p">(</span><span class="n">item</span><span class="o">.</span><span class="n">v</span><span class="o">.</span><span class="n">to_f</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">item</span><span class="o">.</span><span class="n">w</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">cap</span>
+<a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a><span class="w">      </span><span class="c1"># 残り容量がないため、ループを抜ける</span>
+<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a><span class="w">      </span><span class="k">break</span>
+<a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-31" name="__codelineno-12-31" href="#__codelineno-12-31"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-32" name="__codelineno-12-32" href="#__codelineno-12-32"></a><span class="w">  </span><span class="n">res</span>
+<a id="__codelineno-12-33" name="__codelineno-12-33" href="#__codelineno-12-33"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>ソート以外に、最悪の場合、アイテムのリスト全体を走査する必要があるため、<strong>時間計算量は <span class="arithmatex">\(O(n)\)</span></strong> です。ここで <span class="arithmatex">\(n\)</span> はアイテムの数です。</p>
-<p><code>Item</code> オブジェクトリストが初期化されるため、<strong>空間計算量は <span class="arithmatex">\(O(n)\)</span></strong> です。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20Item%3A%0A%20%20%20%20%22%22%22%E5%93%81%E7%89%A9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20w%3A%20int%2C%20v%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.w%20%3D%20w%20%20%23%20%E5%93%81%E7%89%A9%E3%81%AE%E9%87%8D%E3%81%95%0A%20%20%20%20%20%20%20%20self.v%20%3D%20v%20%20%23%20%E5%93%81%E7%89%A9%E3%81%AE%E4%BE%A1%E5%80%A4%0A%0Adef%20fractional_knapsack%28wgt%3A%20list%5Bint%5D%2C%20val%3A%20list%5Bint%5D%2C%20cap%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%88%86%E6%95%B0%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%EF%BC%9A%E8%B2%AA%E6%AC%B2%E6%B3%95%22%22%22%0A%20%20%20%20%23%20%E9%87%8D%E3%81%95%E3%81%A8%E4%BE%A1%E5%80%A4%E3%81%AE%202%20%E5%B1%9E%E6%80%A7%E3%82%92%E6%8C%81%E3%81%A4%E5%93%81%E7%89%A9%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E4%BD%9C%E6%88%90%0A%20%20%20%20items%20%3D%20%5BItem%28w%2C%20v%29%20for%20w%2C%20v%20in%20zip%28wgt%2C%20val%29%5D%0A%20%20%20%20%23%20%E5%8D%98%E4%BD%8D%E4%BE%A1%E5%80%A4%20item.v%20%2F%20item.w%20%E3%81%AE%E9%AB%98%E3%81%84%E9%A0%86%E3%81%AB%E3%82%BD%E3%83%BC%E3%83%88%E3%81%99%E3%82%8B%0A%20%20%20%20items.sort%28key%3Dlambda%20item%3A%20item.v%20%2F%20item.w%2C%20reverse%3DTrue%29%0A%20%20%20%20%23%20%E8%B2%AA%E6%AC%B2%E9%81%B8%E6%8A%9E%E3%82%92%E7%B9%B0%E3%82%8A%E8%BF%94%E3%81%99%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20for%20item%20in%20items%3A%0A%20%20%20%20%20%20%20%20if%20item.w%20%3C%3D%20cap%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%AE%8B%E3%82%8A%E5%AE%B9%E9%87%8F%E3%81%8C%E5%8D%81%E5%88%86%E3%81%AA%E3%82%89%E3%80%81%E7%8F%BE%E5%9C%A8%E3%81%AE%E5%93%81%E7%89%A9%E3%82%92%E4%B8%B8%E3%81%94%E3%81%A8%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E3%81%AB%E5%85%A5%E3%82%8C%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20res%20%2B%3D%20item.v%0A%20%20%20%20%20%20%20%20%20%20%20%20cap%20-%3D%20item.w%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%AE%8B%E3%82%8A%E5%AE%B9%E9%87%8F%E3%81%8C%E8%B6%B3%E3%82%8A%E3%81%AA%E3%81%84%E5%A0%B4%E5%90%88%E3%81%AF%E3%80%81%E7%8F%BE%E5%9C%A8%E3%81%AE%E5%93%81%E7%89%A9%E3%81%AE%E4%B8%80%E9%83%A8%E3%81%A0%E3%81%91%E3%82%92%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E3%81%AB%E5%85%A5%E3%82%8C%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20res%20%2B%3D%20%28item.v%20%2F%20item.w%29%20%2A%20cap%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%AE%8B%E3%82%8A%E5%AE%B9%E9%87%8F%E3%81%8C%E3%81%AA%E3%81%84%E3%81%9F%E3%82%81%E3%80%81%E3%83%AB%E3%83%BC%E3%83%97%E3%82%92%E6%8A%9C%E3%81%91%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20return%20res%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20wgt%20%3D%20%5B10%2C%2020%2C%2030%2C%2040%2C%2050%5D%0A%20%20%20%20val%20%3D%20%5B50%2C%20120%2C%20150%2C%20210%2C%20240%5D%0A%20%20%20%20cap%20%3D%2050%0A%20%20%20%20n%20%3D%20len%28wgt%29%0A%0A%20%20%20%20%23%20%E8%B2%AA%E6%AC%B2%E6%B3%95%0A%20%20%20%20res%20%3D%20fractional_knapsack%28wgt%2C%20val%2C%20cap%29%0A%20%20%20%20print%28f%22%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%81%AA%E3%81%84%E6%9C%80%E5%A4%A7%E4%BE%A1%E5%80%A4%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=8&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20Item%3A%0A%20%20%20%20%22%22%22%E5%93%81%E7%89%A9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20w%3A%20int%2C%20v%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.w%20%3D%20w%20%20%23%20%E5%93%81%E7%89%A9%E3%81%AE%E9%87%8D%E3%81%95%0A%20%20%20%20%20%20%20%20self.v%20%3D%20v%20%20%23%20%E5%93%81%E7%89%A9%E3%81%AE%E4%BE%A1%E5%80%A4%0A%0Adef%20fractional_knapsack%28wgt%3A%20list%5Bint%5D%2C%20val%3A%20list%5Bint%5D%2C%20cap%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%88%86%E6%95%B0%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%EF%BC%9A%E8%B2%AA%E6%AC%B2%E6%B3%95%22%22%22%0A%20%20%20%20%23%20%E9%87%8D%E3%81%95%E3%81%A8%E4%BE%A1%E5%80%A4%E3%81%AE%202%20%E5%B1%9E%E6%80%A7%E3%82%92%E6%8C%81%E3%81%A4%E5%93%81%E7%89%A9%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E4%BD%9C%E6%88%90%0A%20%20%20%20items%20%3D%20%5BItem%28w%2C%20v%29%20for%20w%2C%20v%20in%20zip%28wgt%2C%20val%29%5D%0A%20%20%20%20%23%20%E5%8D%98%E4%BD%8D%E4%BE%A1%E5%80%A4%20item.v%20%2F%20item.w%20%E3%81%AE%E9%AB%98%E3%81%84%E9%A0%86%E3%81%AB%E3%82%BD%E3%83%BC%E3%83%88%E3%81%99%E3%82%8B%0A%20%20%20%20items.sort%28key%3Dlambda%20item%3A%20item.v%20%2F%20item.w%2C%20reverse%3DTrue%29%0A%20%20%20%20%23%20%E8%B2%AA%E6%AC%B2%E9%81%B8%E6%8A%9E%E3%82%92%E7%B9%B0%E3%82%8A%E8%BF%94%E3%81%99%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20for%20item%20in%20items%3A%0A%20%20%20%20%20%20%20%20if%20item.w%20%3C%3D%20cap%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%AE%8B%E3%82%8A%E5%AE%B9%E9%87%8F%E3%81%8C%E5%8D%81%E5%88%86%E3%81%AA%E3%82%89%E3%80%81%E7%8F%BE%E5%9C%A8%E3%81%AE%E5%93%81%E7%89%A9%E3%82%92%E4%B8%B8%E3%81%94%E3%81%A8%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E3%81%AB%E5%85%A5%E3%82%8C%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20res%20%2B%3D%20item.v%0A%20%20%20%20%20%20%20%20%20%20%20%20cap%20-%3D%20item.w%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%AE%8B%E3%82%8A%E5%AE%B9%E9%87%8F%E3%81%8C%E8%B6%B3%E3%82%8A%E3%81%AA%E3%81%84%E5%A0%B4%E5%90%88%E3%81%AF%E3%80%81%E7%8F%BE%E5%9C%A8%E3%81%AE%E5%93%81%E7%89%A9%E3%81%AE%E4%B8%80%E9%83%A8%E3%81%A0%E3%81%91%E3%82%92%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E3%81%AB%E5%85%A5%E3%82%8C%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20res%20%2B%3D%20%28item.v%20%2F%20item.w%29%20%2A%20cap%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%AE%8B%E3%82%8A%E5%AE%B9%E9%87%8F%E3%81%8C%E3%81%AA%E3%81%84%E3%81%9F%E3%82%81%E3%80%81%E3%83%AB%E3%83%BC%E3%83%97%E3%82%92%E6%8A%9C%E3%81%91%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20return%20res%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20wgt%20%3D%20%5B10%2C%2020%2C%2030%2C%2040%2C%2050%5D%0A%20%20%20%20val%20%3D%20%5B50%2C%20120%2C%20150%2C%20210%2C%20240%5D%0A%20%20%20%20cap%20%3D%2050%0A%20%20%20%20n%20%3D%20len%28wgt%29%0A%0A%20%20%20%20%23%20%E8%B2%AA%E6%AC%B2%E6%B3%95%0A%20%20%20%20res%20%3D%20fractional_knapsack%28wgt%2C%20val%2C%20cap%29%0A%20%20%20%20print%28f%22%E3%83%8A%E3%83%83%E3%83%97%E3%82%B5%E3%83%83%E3%82%AF%E5%AE%B9%E9%87%8F%E3%82%92%E8%B6%85%E3%81%88%E3%81%AA%E3%81%84%E6%9C%80%E5%A4%A7%E4%BE%A1%E5%80%A4%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=8&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>組み込みのソートアルゴリズムの時間計算量は通常 <span class="arithmatex">\(O(\log n)\)</span>、空間計算量は通常 <span class="arithmatex">\(O(\log n)\)</span> または <span class="arithmatex">\(O(n)\)</span> であり、具体的な値はプログラミング言語の実装に依存する。</p>
+<p>ソートを除けば、最悪の場合は品物リスト全体を走査する必要があるため、<strong>時間計算量は <span class="arithmatex">\(O(n)\)</span></strong> であり、ここで <span class="arithmatex">\(n\)</span> は品物数である。</p>
+<p><code>Item</code> オブジェクトのリストを初期化しているため、<strong>空間計算量は <span class="arithmatex">\(O(n)\)</span></strong> である。</p>
 <h3 id="3">3. &nbsp; 正しさの証明<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
-<p>背理法を使用します。アイテム <span class="arithmatex">\(x\)</span> が最高の単位値を持ち、あるアルゴリズムが最大値 <code>res</code> を生成するが、解にアイテム <span class="arithmatex">\(x\)</span> が含まれていないと仮定します。</p>
-<p>今、ナップサックから任意のアイテムの単位重量を取り除き、アイテム <span class="arithmatex">\(x\)</span> の単位重量で置き換えます。アイテム <span class="arithmatex">\(x\)</span> の単位値が最高であるため、置き換え後の総値は確実に <code>res</code> より大きくなります。<strong>これは <code>res</code> が最適解であるという仮定と矛盾し、最適解には必ずアイテム <span class="arithmatex">\(x\)</span> が含まれることを証明します</strong>。</p>
-<p>この解の他のアイテムについても、上記の矛盾を構築できます。全体的に、**単位値がより大きいアイテムは常により良い選択**であり、貪欲戦略が効果的であることを証明します。</p>
-<p>下の図に示すように、アイテムの重量と単位値をそれぞれ二次元チャートの横軸と縦軸と見なすと、分数ナップサック問題は「限られた横軸範囲内で囲まれる最大面積を求める」ことに変換できます。この類推は、幾何学的観点から貪欲戦略の効果を理解するのに役立ちます。</p>
+<p>背理法を用いる。品物 <span class="arithmatex">\(x\)</span> が単位価値最大の品物であり、あるアルゴリズムで得られた最大価値を <code>res</code> とするが、その解には品物 <span class="arithmatex">\(x\)</span> が含まれていないと仮定する。</p>
+<p>ここでナップサックから単位重量の任意の品物を取り出し、単位重量の品物 <span class="arithmatex">\(x\)</span> に置き換える。品物 <span class="arithmatex">\(x\)</span> の単位価値が最大であるため、置き換え後の総価値は必ず <code>res</code> より大きくなる。<strong>これは <code>res</code> が最適解であることに矛盾し、最適解には必ず品物 <span class="arithmatex">\(x\)</span> が含まれなければならないことを示す</strong>。</p>
+<p>この解に含まれる他の品物についても、同様の矛盾を構成できる。要するに、<strong>単位価値がより大きい品物は常により良い選択である</strong>。これは貪欲戦略が有効であることを示している。</p>
+<p>以下に示すように、品物の重さと品物の単位価値をそれぞれ二次元グラフの横軸と縦軸とみなすと、分数ナップサック問題は「有限な横軸区間で囲まれる最大面積を求める問題」に変換できる。この類比は、幾何学的な観点から貪欲戦略の有効性を理解する助けになる。</p>
 <p><img alt="分数ナップサック問題の幾何学的表現" class="animation-figure" src="../fractional_knapsack_problem.assets/fractional_knapsack_area_chart.png" /></p>
 <p align="center"> 図 15-6 &nbsp; 分数ナップサック問題の幾何学的表現 </p>
 
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-    aria-label="前: 15.1 &amp;nbsp; 貪欲アルゴリズム"
+    aria-label="前: 15.1 &amp;nbsp; 貪欲法"
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-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
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-        <title>15.1 貪欲アルゴリズム - Hello アルゴリズム</title>
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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-    1.2 &nbsp; アルゴリズムとは何か
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-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
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   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1635,7 +1635,7 @@
   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1942,7 +1942,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2105,7 +2105,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2491,7 +2491,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2547,7 +2547,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2575,7 +2575,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3113,7 +3113,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3169,7 +3169,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3197,7 +3197,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3390,7 +3390,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3418,7 +3418,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3559,7 +3559,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3587,7 +3587,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3615,7 +3615,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
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   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3847,7 +3847,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
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   <a href="#1511" class="md-nav__link">
     <span class="md-ellipsis">
       
-        15.1.1 &nbsp; 貪欲アルゴリズムの利点と制限
+        15.1.1 &nbsp; 貪欲法の利点と限界
       
     </span>
   </a>
@@ -3906,7 +3906,7 @@
   <a href="#1512" class="md-nav__link">
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-        15.1.2 &nbsp; 貪欲アルゴリズムの特徴
+        15.1.2 &nbsp; 貪欲法の特性
       
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@@ -3917,7 +3917,7 @@
   <a href="#1513" class="md-nav__link">
     <span class="md-ellipsis">
       
-        15.1.3 &nbsp; 貪欲アルゴリズムによる問題解決のステップ
+        15.1.3 &nbsp; 貪欲法の問題解決手順
       
     </span>
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-        15.1.4 &nbsp; 貪欲アルゴリズムで解決される典型的な問題
+        15.1.4 &nbsp; 貪欲法の典型問題
       
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@@ -4175,7 +4175,7 @@
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
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   <a href="#1511" class="md-nav__link">
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-        15.1.1 &nbsp; 貪欲アルゴリズムの利点と制限
+        15.1.1 &nbsp; 貪欲法の利点と限界
       
     </span>
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@@ -4332,7 +4332,7 @@
   <a href="#1512" class="md-nav__link">
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-        15.1.2 &nbsp; 貪欲アルゴリズムの特徴
+        15.1.2 &nbsp; 貪欲法の特性
       
     </span>
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@@ -4343,7 +4343,7 @@
   <a href="#1513" class="md-nav__link">
     <span class="md-ellipsis">
       
-        15.1.3 &nbsp; 貪欲アルゴリズムによる問題解決のステップ
+        15.1.3 &nbsp; 貪欲法の問題解決手順
       
     </span>
   </a>
@@ -4354,7 +4354,7 @@
   <a href="#1514" class="md-nav__link">
     <span class="md-ellipsis">
       
-        15.1.4 &nbsp; 貪欲アルゴリズムで解決される典型的な問題
+        15.1.4 &nbsp; 貪欲法の典型問題
       
     </span>
   </a>
@@ -4398,183 +4398,367 @@
 
 
 <!-- Page content -->
-<h1 id="151">15.1 &nbsp; 貪欲アルゴリズム<a class="headerlink" href="#151" title="Permanent link">&para;</a></h1>
-<p><u>貪欲アルゴリズム</u>は最適化問題を解決するための一般的なアルゴリズムで、基本的に問題の各意思決定段階で最も良い選択をすること、つまり局所的に最適な決定を貪欲に行い、グローバルに最適な解を見つけることを望みます。貪欲アルゴリズムは簡潔で効率的であり、多くの実用的な問題で広く使用されています。</p>
-<p>貪欲アルゴリズムと動的プログラミングは、どちらも最適化問題を解決するためによく使用されます。両者は最適部分構造の性質に依存するなど、いくつかの類似点を共有していますが、動作方法が異なります。</p>
+<h1 id="151">15.1 &nbsp; 貪欲法<a class="headerlink" href="#151" title="Permanent link">&para;</a></h1>
+<p><u>貪欲法（greedy algorithm）</u>は、最適化問題を解くための一般的なアルゴリズムです。その基本的な考え方は、問題の各意思決定段階において、その時点で最善に見える選択を行い、すなわち貪欲に局所最適な決定を下すことで、大域最適解を得ようとするものです。貪欲法は簡潔で効率的であり、多くの実際の問題で広く用いられています。</p>
+<p>貪欲法と動的計画法は、どちらも最適化問題を解く際によく用いられます。両者には、最適部分構造に依存するなどの共通点がありますが、その動作原理は異なります。</p>
 <ul>
-<li>動的プログラミングは現在の決定段階ですべての以前の決定を考慮し、過去の部分問題の解を使用して現在の部分問題の解を構築します。</li>
-<li>貪欲アルゴリズムは過去の決定を考慮せず、代わりに貪欲な選択を続け、問題が解決されるまで問題の範囲を継続的に狭めます。</li>
+<li>動的計画法は、前の段階までのすべての決定に基づいて現在の決定を考え、過去の部分問題の解を用いて現在の部分問題の解を構築します。</li>
+<li>貪欲法は過去の決定を考慮せず、ひたすら前に進みながら貪欲な選択を行い、問題の範囲を縮小し続けて、最終的に問題を解決します。</li>
 </ul>
-<p>まず、「完全ナップサック問題」の章で紹介された「コイン交換」の例を通じて貪欲アルゴリズムの動作原理を理解しましょう。すでによく知っていると思います。</p>
+<p>まずは例題「コイン両替」を通して、貪欲法の仕組みを理解しましょう。この問題はすでに「完全ナップサック問題」の節で紹介しているので、見覚えがあるはずです。</p>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
-<p><span class="arithmatex">\(n\)</span> 種類のコインが与えられ、<span class="arithmatex">\(i\)</span> 番目の種類のコインの額面は <span class="arithmatex">\(coins[i - 1]\)</span> で、目標金額は <span class="arithmatex">\(amt\)</span> です。各種類のコインは無制限に利用可能で、目標金額を構成するのに必要な最小コイン数は何ですか？目標金額を構成できない場合は <span class="arithmatex">\(-1\)</span> を返してください。</p>
+<p><span class="arithmatex">\(n\)</span> 種類の硬貨が与えられ、<span class="arithmatex">\(i\)</span> 番目の硬貨の額面は <span class="arithmatex">\(coins[i - 1]\)</span> 、目標金額は <span class="arithmatex">\(amt\)</span> です。各硬貨は何度でも選べるとき、目標金額を作るために必要な最小の硬貨枚数を求めてください。目標金額を作れない場合は <span class="arithmatex">\(-1\)</span> を返します。</p>
 </div>
-<p>この問題で採用される貪欲戦略を下の図に示します。目標金額が与えられたとき、**それに最も近く、それを超えないコインを貪欲に選択**し、目標金額が満たされるまでこのステップを繰り返します。</p>
-<p><img alt="コイン交換の貪欲戦略" class="animation-figure" src="../greedy_algorithm.assets/coin_change_greedy_strategy.png" /></p>
-<p align="center"> 図 15-1 &nbsp; コイン交換の貪欲戦略 </p>
+<p>この問題で採用する貪欲戦略は下図のとおりです。目標金額が与えられたら、<strong>それを超えず、かつ最も近い硬貨を貪欲に選択し</strong>、この手順を目標金額を作り切るまで繰り返します。</p>
+<p><img alt="コイン両替の貪欲戦略" class="animation-figure" src="../greedy_algorithm.assets/coin_change_greedy_strategy.png" /></p>
+<p align="center"> 図 15-1 &nbsp; コイン両替の貪欲戦略 </p>
 
-<p>実装コードは以下の通りです：</p>
+<p>実装コードは次のとおりです。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">coin_change_greedy.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_greedy</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">amt</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;硬貨交換：貪欲法&quot;&quot;&quot;</span>
-<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># coins リストがソートされていると仮定</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;コイン交換：貪欲法&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># coins リストはソート済みと仮定する</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">i</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">coins</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
-<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 残り金額がなくなるまで貪欲選択をループ</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 残額がなくなるまで貪欲選択を繰り返す</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="k">while</span> <span class="n">amt</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
-<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="c1"># 残り金額に最も近く、それより小さい硬貨を見つける</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="c1"># 残額以下で最も近い硬貨を見つける</span>
 <a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="k">while</span> <span class="n">i</span> <span class="o">&gt;</span> <span class="mi">0</span> <span class="ow">and</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">amt</span><span class="p">:</span>
 <a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>            <span class="n">i</span> <span class="o">-=</span> <span class="mi">1</span>
-<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="c1"># coins[i] を選択</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="c1"># coins[i] を選択する</span>
 <a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="n">amt</span> <span class="o">-=</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
-<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="c1"># 実行可能な解が見つからない場合、-1 を返す</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="c1"># 実行可能な解が見つからなければ -1 を返す</span>
 <a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="k">return</span> <span class="n">count</span> <span class="k">if</span> <span class="n">amt</span> <span class="o">==</span> <span class="mi">0</span> <span class="k">else</span> <span class="o">-</span><span class="mi">1</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_greedy.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 硬貨両替：貪欲法 */</span>
+<div class="highlight"><span class="filename">coin_change_greedy.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* コイン交換：貪欲法 */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeGreedy</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 硬貨リストが順序付けされていると仮定</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// coins リストはソート済みと仮定する</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// 残り金額がなくなるまで貪欲選択をループ</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// 残額がなくなるまで貪欲選択を繰り返す</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">        </span><span class="c1">// 残り金額に近く、それ以下の最小硬貨を見つける</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">        </span><span class="c1">// 残額以下で最も近い硬貨を見つける</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">            </span><span class="n">i</span><span class="o">--</span><span class="p">;</span>
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="c1">// coins[i] を選択</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="c1">// coins[i] を選択する</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="n">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
 <a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
 <a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">    </span><span class="c1">// 実行可能な解が見つからない場合、-1 を返す</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">    </span><span class="c1">// 実行可能な解が見つからなければ -1 を返す</span>
 <a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
 <a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_greedy.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 硬貨両替：貪欲法 */</span>
+<div class="highlight"><span class="filename">coin_change_greedy.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* コイン交換：貪欲法 */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeGreedy</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 硬貨リストが順序付けされていると仮定</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// coins リストはソート済みと仮定する</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// 残り金額がなくなるまで貪欲選択をループ</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// 残額がなくなるまで貪欲選択を繰り返す</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">        </span><span class="c1">// 残り金額に近く、それ以下の最小硬貨を見つける</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">        </span><span class="c1">// 残額以下で最も近い硬貨を見つける</span>
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">            </span><span class="n">i</span><span class="o">--</span><span class="p">;</span>
 <a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="c1">// coins[i] を選択</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="c1">// coins[i] を選択する</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="n">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
 <a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="c1">// 実行可能な解が見つからない場合、-1 を返す</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="c1">// 実行可能な解が見つからなければ -1 を返す</span>
 <a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_greedy.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">coin_change_greedy</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">CoinChangeGreedy</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_greedy.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* コイン交換：貪欲法 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">CoinChangeGreedy</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="c1">// coins リストはソート済みと仮定する</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="c1">// 残額がなくなるまで貪欲選択を繰り返す</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">        </span><span class="c1">// 残額以下で最も近い硬貨を見つける</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">            </span><span class="n">i</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">        </span><span class="c1">// coins[i] を選択する</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">        </span><span class="n">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">    </span><span class="c1">// 実行可能な解が見つからなければ -1 を返す</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_greedy.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">coinChangeGreedy</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_greedy.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* コイン交換：貪欲法 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">coinChangeGreedy</span><span class="p">(</span><span class="nx">coins</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// coins リストはソート済みと仮定する</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">coins</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="c1">// 残額がなくなるまで貪欲選択を繰り返す</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">        </span><span class="c1">// 残額以下で最も近い硬貨を見つける</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">            </span><span class="nx">i</span><span class="o">--</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">        </span><span class="c1">// coins[i] を選択する</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">        </span><span class="nx">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">        </span><span class="nx">count</span><span class="o">++</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">    </span><span class="c1">// 実行可能な解が見つからなければ -1 を返す</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_greedy.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">coinChangeGreedy</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_greedy.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* コイン交換：貪欲法 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">coinChangeGreedy</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// coins リストはソート済みと仮定する</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="bp">count</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">amt</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">amt</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="c1">// 残額がなくなるまで貪欲選択を繰り返す</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">        </span><span class="c1">// 残額以下で最も近い硬貨を見つける</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">        </span><span class="c1">// coins[i] を選択する</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">        </span><span class="n">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">        </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">    </span><span class="c1">// 実行可能な解が見つからなければ -1 を返す</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">?</span><span class="w"> </span><span class="bp">count</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_greedy.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">coinChangeGreedy</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_greedy.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* コイン交換：貪欲法 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">coinChangeGreedy</span><span class="p">(</span><span class="nx">coins</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="c1">// coins 配列はソート済みと仮定する</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coins</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="c1">// 残額がなくなるまで貪欲選択を繰り返す</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">        </span><span class="c1">// 残額以下で最も近い硬貨を見つける</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">            </span><span class="nx">i</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">        </span><span class="c1">// coins[i] を選択する</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">        </span><span class="nx">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">        </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w">    </span><span class="c1">// 実行可能な解が見つからなければ -1 を返す</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_greedy.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">coinChangeGreedy</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_greedy.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* コイン交換：貪欲法 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">coinChangeGreedy</span><span class="p">(</span><span class="nx">coins</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">amt</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="c1">// coins 配列はソート済みと仮定する</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coins</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="c1">// 残額がなくなるまで貪欲選択を繰り返す</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">        </span><span class="c1">// 残額以下で最も近い硬貨を見つける</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">            </span><span class="nx">i</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">        </span><span class="c1">// coins[i] を選択する</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">        </span><span class="nx">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">        </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">    </span><span class="c1">// 実行可能な解が見つからなければ -1 を返す</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_greedy.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeGreedy</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_greedy.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* コイン交換：貪欲法 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">coinChangeGreedy</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="c1">// coins リストはソート済みと仮定する</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="c1">// 残額がなくなるまで貪欲選択を繰り返す</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">    </span><span class="c1">// 残額以下で最も近い硬貨を見つける</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">      </span><span class="n">i</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">    </span><span class="c1">// coins[i] を選択する</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">    </span><span class="n">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">    </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">  </span><span class="c1">// 実行可能な解が見つからなければ -1 を返す</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_greedy.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coin_change_greedy</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_greedy.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* コイン交換：貪欲法 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">coin_change_greedy</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="c1">// coins リストはソート済みと仮定する</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="c1">// 残額がなくなるまで貪欲選択を繰り返す</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">        </span><span class="c1">// 残額以下で最も近い硬貨を見つける</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">        </span><span class="c1">// coins[i] を選択する</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">        </span><span class="n">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">    </span><span class="c1">// 実行可能な解が見つからなければ -1 を返す</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">        </span><span class="n">count</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w">        </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_greedy.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeGreedy</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_greedy.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* コイン交換：貪欲法 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeGreedy</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="c1">// coins リストはソート済みと仮定する</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="c1">// 残額がなくなるまで貪欲選択を繰り返す</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">        </span><span class="c1">// 残額以下で最も近い硬貨を見つける</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">            </span><span class="n">i</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">        </span><span class="c1">// coins[i] を選択する</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">        </span><span class="n">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">    </span><span class="c1">// 実行可能な解が見つからなければ -1 を返す</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_greedy.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coinChangeGreedy</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_greedy.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* コイン交換：貪欲法 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">coinChangeGreedy</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="c1">// coins リストはソート済みと仮定する</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">am</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">    </span><span class="c1">// 残額がなくなるまで貪欲選択を繰り返す</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">am</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">        </span><span class="c1">// 残額以下で最も近い硬貨を見つける</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">am</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">            </span><span class="n">i</span><span class="o">--</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">        </span><span class="c1">// coins[i] を選択する</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">        </span><span class="n">am</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">    </span><span class="c1">// 実行可能な解が見つからなければ -1 を返す</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">am</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="o">-</span><span class="m">1</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_greedy.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coin_change_greedy</span><span class="p">}</span>
+<div class="highlight"><span class="filename">coin_change_greedy.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### コイン両替：貪欲法 ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_greedy</span><span class="p">(</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># coins リストはソート済みと仮定する</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="c1"># 残額がなくなるまで貪欲選択を繰り返す</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">    </span><span class="c1"># 残額以下で最も近い硬貨を見つける</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">amt</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">      </span><span class="n">i</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">    </span><span class="c1"># coins[i] を選択する</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">    </span><span class="n">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">  </span><span class="c1"># 実行可能な解が見つからなければ `-1` を返す</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">  </span><span class="n">amt</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>感嘆するかもしれません：なんて簡潔なんだ！貪欲アルゴリズムは約10行のコードでコイン交換問題を解決します。</p>
-<h2 id="1511">15.1.1 &nbsp; 貪欲アルゴリズムの利点と制限<a class="headerlink" href="#1511" title="Permanent link">&para;</a></h2>
-<p><strong>貪欲アルゴリズムは直接的で実装が簡単であるだけでなく、通常非常に効率的でもあります</strong>。上記のコードで、最小のコイン額面を <span class="arithmatex">\(\min(coins)\)</span> とすると、貪欲な選択ループは最大 <span class="arithmatex">\(amt / \min(coins)\)</span> 回実行され、時間計算量は <span class="arithmatex">\(O(amt / \min(coins))\)</span> になります。これは動的プログラミング解法の時間計算量 <span class="arithmatex">\(O(n \times amt)\)</span> よりも一桁小さいです。</p>
-<p>しかし、<strong>一部のコイン額面の組み合わせでは、貪欲アルゴリズムは最適解を見つけることができません</strong>。下の図は2つの例を示しています。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20coin_change_greedy%28coins%3A%20list%5Bint%5D%2C%20amt%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E3%82%B3%E3%82%A4%E3%83%B3%E4%BA%A4%E6%8F%9B%EF%BC%9A%E8%B2%AA%E6%AC%B2%E6%B3%95%22%22%22%0A%20%20%20%20%23%20coins%20%E3%83%AA%E3%82%B9%E3%83%88%E3%81%AF%E3%82%BD%E3%83%BC%E3%83%88%E6%B8%88%E3%81%BF%E3%81%A8%E4%BB%AE%E5%AE%9A%E3%81%99%E3%82%8B%0A%20%20%20%20i%20%3D%20len%28coins%29%20-%201%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%E6%AE%8B%E9%A1%8D%E3%81%8C%E3%81%AA%E3%81%8F%E3%81%AA%E3%82%8B%E3%81%BE%E3%81%A7%E8%B2%AA%E6%AC%B2%E9%81%B8%E6%8A%9E%E3%82%92%E7%B9%B0%E3%82%8A%E8%BF%94%E3%81%99%0A%20%20%20%20while%20amt%20%3E%200%3A%0A%20%20%20%20%20%20%20%20%23%20%E6%AE%8B%E9%A1%8D%E4%BB%A5%E4%B8%8B%E3%81%A7%E6%9C%80%E3%82%82%E8%BF%91%E3%81%84%E7%A1%AC%E8%B2%A8%E3%82%92%E8%A6%8B%E3%81%A4%E3%81%91%E3%82%8B%0A%20%20%20%20%20%20%20%20while%20i%20%3E%200%20and%20coins%5Bi%5D%20%3E%20amt%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20-%3D%201%0A%20%20%20%20%20%20%20%20%23%20coins%5Bi%5D%20%E3%82%92%E9%81%B8%E6%8A%9E%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20amt%20-%3D%20coins%5Bi%5D%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20%23%20%E5%AE%9F%E8%A1%8C%E5%8F%AF%E8%83%BD%E3%81%AA%E8%A7%A3%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%82%89%E3%81%AA%E3%81%91%E3%82%8C%E3%81%B0%20-1%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20count%20if%20amt%20%3D%3D%200%20else%20-1%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E8%B2%AA%E6%AC%B2%E6%B3%95%EF%BC%9A%E5%A4%A7%E5%9F%9F%E6%9C%80%E9%81%A9%E8%A7%A3%E3%82%92%E4%BF%9D%E8%A8%BC%E3%81%A7%E3%81%8D%E3%82%8B%0A%20%20%20%20coins%20%3D%20%5B1%2C%205%2C%2010%2C%2020%2C%2050%2C%20100%5D%0A%20%20%20%20amt%20%3D%20186%0A%20%20%20%20res%20%3D%20coin_change_greedy%28coins%2C%20amt%29%0A%20%20%20%20print%28f%22%5Cncoins%20%3D%20%7Bcoins%7D%2C%20amt%20%3D%20%7Bamt%7D%22%29%0A%20%20%20%20print%28f%22%7Bamt%7D%20%E3%82%92%E4%BD%9C%E3%82%8B%E3%81%AE%E3%81%AB%E5%BF%85%E8%A6%81%E3%81%AA%E6%9C%80%E5%B0%8F%E3%81%AE%E7%A1%AC%E8%B2%A8%E6%9E%9A%E6%95%B0%E3%81%AF%20%7Bres%7D%22%29%0A%0A%20%20%20%20%23%20%E8%B2%AA%E6%AC%B2%E6%B3%95%EF%BC%9A%E5%A4%A7%E5%9F%9F%E6%9C%80%E9%81%A9%E8%A7%A3%E3%82%92%E4%BF%9D%E8%A8%BC%E3%81%A7%E3%81%8D%E3%81%AA%E3%81%84%0A%20%20%20%20coins%20%3D%20%5B1%2C%2020%2C%2050%5D%0A%20%20%20%20amt%20%3D%2060%0A%20%20%20%20res%20%3D%20coin_change_greedy%28coins%2C%20amt%29%0A%20%20%20%20print%28f%22%5Cncoins%20%3D%20%7Bcoins%7D%2C%20amt%20%3D%20%7Bamt%7D%22%29%0A%20%20%20%20print%28f%22%7Bamt%7D%20%E3%82%92%E4%BD%9C%E3%82%8B%E3%81%AE%E3%81%AB%E5%BF%85%E8%A6%81%E3%81%AA%E6%9C%80%E5%B0%8F%E3%81%AE%E7%A1%AC%E8%B2%A8%E6%9E%9A%E6%95%B0%E3%81%AF%20%7Bres%7D%22%29%0A%20%20%20%20print%28f%22%E5%AE%9F%E9%9A%9B%E3%81%AB%E5%BF%85%E8%A6%81%E3%81%AA%E6%9C%80%E5%B0%8F%E6%9E%9A%E6%95%B0%E3%81%AF%203%20%EF%BC%8C%E3%81%A4%E3%81%BE%E3%82%8A%2020%20%2B%2020%20%2B%2020%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20coin_change_greedy%28coins%3A%20list%5Bint%5D%2C%20amt%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E3%82%B3%E3%82%A4%E3%83%B3%E4%BA%A4%E6%8F%9B%EF%BC%9A%E8%B2%AA%E6%AC%B2%E6%B3%95%22%22%22%0A%20%20%20%20%23%20coins%20%E3%83%AA%E3%82%B9%E3%83%88%E3%81%AF%E3%82%BD%E3%83%BC%E3%83%88%E6%B8%88%E3%81%BF%E3%81%A8%E4%BB%AE%E5%AE%9A%E3%81%99%E3%82%8B%0A%20%20%20%20i%20%3D%20len%28coins%29%20-%201%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%E6%AE%8B%E9%A1%8D%E3%81%8C%E3%81%AA%E3%81%8F%E3%81%AA%E3%82%8B%E3%81%BE%E3%81%A7%E8%B2%AA%E6%AC%B2%E9%81%B8%E6%8A%9E%E3%82%92%E7%B9%B0%E3%82%8A%E8%BF%94%E3%81%99%0A%20%20%20%20while%20amt%20%3E%200%3A%0A%20%20%20%20%20%20%20%20%23%20%E6%AE%8B%E9%A1%8D%E4%BB%A5%E4%B8%8B%E3%81%A7%E6%9C%80%E3%82%82%E8%BF%91%E3%81%84%E7%A1%AC%E8%B2%A8%E3%82%92%E8%A6%8B%E3%81%A4%E3%81%91%E3%82%8B%0A%20%20%20%20%20%20%20%20while%20i%20%3E%200%20and%20coins%5Bi%5D%20%3E%20amt%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20-%3D%201%0A%20%20%20%20%20%20%20%20%23%20coins%5Bi%5D%20%E3%82%92%E9%81%B8%E6%8A%9E%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20amt%20-%3D%20coins%5Bi%5D%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20%23%20%E5%AE%9F%E8%A1%8C%E5%8F%AF%E8%83%BD%E3%81%AA%E8%A7%A3%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%82%89%E3%81%AA%E3%81%91%E3%82%8C%E3%81%B0%20-1%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20count%20if%20amt%20%3D%3D%200%20else%20-1%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E8%B2%AA%E6%AC%B2%E6%B3%95%EF%BC%9A%E5%A4%A7%E5%9F%9F%E6%9C%80%E9%81%A9%E8%A7%A3%E3%82%92%E4%BF%9D%E8%A8%BC%E3%81%A7%E3%81%8D%E3%82%8B%0A%20%20%20%20coins%20%3D%20%5B1%2C%205%2C%2010%2C%2020%2C%2050%2C%20100%5D%0A%20%20%20%20amt%20%3D%20186%0A%20%20%20%20res%20%3D%20coin_change_greedy%28coins%2C%20amt%29%0A%20%20%20%20print%28f%22%5Cncoins%20%3D%20%7Bcoins%7D%2C%20amt%20%3D%20%7Bamt%7D%22%29%0A%20%20%20%20print%28f%22%7Bamt%7D%20%E3%82%92%E4%BD%9C%E3%82%8B%E3%81%AE%E3%81%AB%E5%BF%85%E8%A6%81%E3%81%AA%E6%9C%80%E5%B0%8F%E3%81%AE%E7%A1%AC%E8%B2%A8%E6%9E%9A%E6%95%B0%E3%81%AF%20%7Bres%7D%22%29%0A%0A%20%20%20%20%23%20%E8%B2%AA%E6%AC%B2%E6%B3%95%EF%BC%9A%E5%A4%A7%E5%9F%9F%E6%9C%80%E9%81%A9%E8%A7%A3%E3%82%92%E4%BF%9D%E8%A8%BC%E3%81%A7%E3%81%8D%E3%81%AA%E3%81%84%0A%20%20%20%20coins%20%3D%20%5B1%2C%2020%2C%2050%5D%0A%20%20%20%20amt%20%3D%2060%0A%20%20%20%20res%20%3D%20coin_change_greedy%28coins%2C%20amt%29%0A%20%20%20%20print%28f%22%5Cncoins%20%3D%20%7Bcoins%7D%2C%20amt%20%3D%20%7Bamt%7D%22%29%0A%20%20%20%20print%28f%22%7Bamt%7D%20%E3%82%92%E4%BD%9C%E3%82%8B%E3%81%AE%E3%81%AB%E5%BF%85%E8%A6%81%E3%81%AA%E6%9C%80%E5%B0%8F%E3%81%AE%E7%A1%AC%E8%B2%A8%E6%9E%9A%E6%95%B0%E3%81%AF%20%7Bres%7D%22%29%0A%20%20%20%20print%28f%22%E5%AE%9F%E9%9A%9B%E3%81%AB%E5%BF%85%E8%A6%81%E3%81%AA%E6%9C%80%E5%B0%8F%E6%9E%9A%E6%95%B0%E3%81%AF%203%20%EF%BC%8C%E3%81%A4%E3%81%BE%E3%82%8A%2020%20%2B%2020%20%2B%2020%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>思わずこう言いたくなるかもしれません。So clean！貪欲法はわずか十行ほどのコードでコイン両替問題を解いてしまいます。</p>
+<h2 id="1511">15.1.1 &nbsp; 貪欲法の利点と限界<a class="headerlink" href="#1511" title="Permanent link">&para;</a></h2>
+<p>**貪欲法は操作が直接的で実装が簡単なだけでなく、通常は効率も高い**です。上のコードでは、硬貨の最小額面を <span class="arithmatex">\(\min(coins)\)</span> とすると、貪欲選択のループ回数は高々 <span class="arithmatex">\(amt / \min(coins)\)</span> 回であり、時間計算量は <span class="arithmatex">\(O(amt / \min(coins))\)</span> です。これは動的計画法による解法の時間計算量 <span class="arithmatex">\(O(n \times amt)\)</span> より 1 桁小さいオーダーです。</p>
+<p>しかし、<strong>硬貨の額面の組み合わせによっては、貪欲法では最適解を見つけられません</strong>。下図に 2 つの例を示します。</p>
 <ul>
-<li><strong>正の例 <span class="arithmatex">\(coins = [1, 5, 10, 20, 50, 100]\)</span></strong>：このコインの組み合わせでは、任意の <span class="arithmatex">\(amt\)</span> に対して、貪欲アルゴリズムは最適解を見つけることができます。</li>
-<li><strong>負の例 <span class="arithmatex">\(coins = [1, 20, 50]\)</span></strong>：<span class="arithmatex">\(amt = 60\)</span> とすると、貪欲アルゴリズムは組み合わせ <span class="arithmatex">\(50 + 1 \times 10\)</span> しか見つけられず、合計11枚のコインですが、動的プログラミングは最適解 <span class="arithmatex">\(20 + 20 + 20\)</span> を見つけることができ、3枚のコインのみが必要です。</li>
-<li><strong>負の例 <span class="arithmatex">\(coins = [1, 49, 50]\)</span></strong>：<span class="arithmatex">\(amt = 98\)</span> とすると、貪欲アルゴリズムは組み合わせ <span class="arithmatex">\(50 + 1 \times 48\)</span> しか見つけられず、合計49枚のコインですが、動的プログラミングは最適解 <span class="arithmatex">\(49 + 49\)</span> を見つけることができ、2枚のコインのみが必要です。</li>
+<li><strong>正例 <span class="arithmatex">\(coins = [1, 5, 10, 20, 50, 100]\)</span></strong>：この硬貨の組み合わせでは、任意の <span class="arithmatex">\(amt\)</span> に対して貪欲法で最適解を見つけられます。</li>
+<li><strong>反例 <span class="arithmatex">\(coins = [1, 20, 50]\)</span></strong>：<span class="arithmatex">\(amt = 60\)</span> とすると、貪欲法では <span class="arithmatex">\(50 + 1 \times 10\)</span> という両替しか見つからず、硬貨は合計 <span class="arithmatex">\(11\)</span> 枚になります。しかし動的計画法なら最適解 <span class="arithmatex">\(20 + 20 + 20\)</span> を見つけられ、必要なのはわずか <span class="arithmatex">\(3\)</span> 枚です。</li>
+<li><strong>反例 <span class="arithmatex">\(coins = [1, 49, 50]\)</span></strong>：<span class="arithmatex">\(amt = 98\)</span> とすると、貪欲法では <span class="arithmatex">\(50 + 1 \times 48\)</span> という両替しか見つからず、硬貨は合計 <span class="arithmatex">\(49\)</span> 枚になります。しかし動的計画法なら最適解 <span class="arithmatex">\(49 + 49\)</span> を見つけられ、必要なのはわずか <span class="arithmatex">\(2\)</span> 枚です。</li>
 </ul>
-<p><img alt="貪欲アルゴリズムが最適解を見つけられない例" class="animation-figure" src="../greedy_algorithm.assets/coin_change_greedy_vs_dp.png" /></p>
-<p align="center"> 図 15-2 &nbsp; 貪欲アルゴリズムが最適解を見つけられない例 </p>
+<p><img alt="貪欲法では最適解を見つけられない例" class="animation-figure" src="../greedy_algorithm.assets/coin_change_greedy_vs_dp.png" /></p>
+<p align="center"> 図 15-2 &nbsp; 貪欲法では最適解を見つけられない例 </p>
 
-<p>これは、コイン交換問題において、貪欲アルゴリズムがグローバルに最適な解を見つけることを保証できず、非常に悪い解を見つける可能性があることを意味します。動的プログラミングの方が適しています。</p>
-<p>一般的に、貪欲アルゴリズムの適用性は2つのカテゴリに分類されます。</p>
+<p>つまり、コイン両替問題に対して、貪欲法は大域最適解を保証できず、非常に悪い解を見つけてしまうこともあります。この問題は動的計画法で解くほうが適しています。</p>
+<p>一般に、貪欲法が適用できる状況は次の 2 つに分けられます。</p>
 <ol>
-<li><strong>最適解を見つけることが保証される</strong>：これらの場合、貪欲アルゴリズムはしばしば最良の選択で、バックトラッキングや動的プログラミングよりも効率的である傾向があります。</li>
-<li><strong>準最適解を見つけることができる</strong>：貪欲アルゴリズムはここでも適用可能です。多くの複雑な問題では、グローバル最適解を見つけることは非常に困難であり、高効率の準最適解を見つけることも非常に価値があります。</li>
+<li><strong>最適解を保証できる場合</strong>：この場合、貪欲法はしばしば最良の選択です。多くの場合、バックトラッキングや動的計画法より効率的だからです。</li>
+<li><strong>近似最適解を見つけられる場合</strong>：この場合も貪欲法は有効です。多くの複雑な問題では、大域最適解を求めること自体が非常に難しく、より高い効率で準最適解を得られるだけでも十分価値があります。</li>
 </ol>
-<h2 id="1512">15.1.2 &nbsp; 貪欲アルゴリズムの特徴<a class="headerlink" href="#1512" title="Permanent link">&para;</a></h2>
-<p>それでは、どのような問題が貪欲アルゴリズムで解決するのに適しているのでしょうか？言い換えれば、どのような条件下で貪欲アルゴリズムは最適解を見つけることを保証できるのでしょうか？</p>
-<p>動的プログラミングと比較して、貪欲アルゴリズムはより厳しい使用条件を持ち、主に問題の2つの性質に焦点を当てています。</p>
+<h2 id="1512">15.1.2 &nbsp; 貪欲法の特性<a class="headerlink" href="#1512" title="Permanent link">&para;</a></h2>
+<p>では、どのような問題が貪欲法に適しているのでしょうか。言い換えると、貪欲法はどのような場合に最適解を保証できるのでしょうか。</p>
+<p>動的計画法と比べると、貪欲法の適用条件はより厳しく、主に次の 2 つの性質に注目します。</p>
 <ul>
-<li><strong>貪欲選択性</strong>：局所的に最適な選択が常にグローバルに最適な解に導くことができる場合のみ、貪欲アルゴリズムは最適解を得ることを保証できます。</li>
-<li><strong>最適部分構造</strong>：元の問題の最適解はその部分問題の最適解を含みます。</li>
+<li><strong>貪欲選択性</strong>：局所最適な選択が常に大域最適解につながる場合にのみ、貪欲法は最適解を保証できます。</li>
+<li><strong>最適部分構造</strong>：元の問題の最適解が、部分問題の最適解を含むことです。</li>
 </ul>
-<p>最適部分構造は「動的プログラミング」の章ですでに紹介されているため、ここではこれ以上議論しません。一部の問題には明らかな最適部分構造がありませんが、それでも貪欲アルゴリズムを使用して解決できることに注意することが重要です。</p>
-<p>主に貪欲選択性を決定する方法を探索します。その記述は単純に見えますが、<strong>実際には、多くの問題の貪欲選択性を証明することは容易ではありません</strong>。</p>
-<p>例えば、コイン交換問題では、貪欲選択性を反証するために反例を簡単に挙げることができますが、それを証明することははるかに困難です。**コインの組み合わせが貪欲アルゴリズムを使用して解決できるためには、どのような条件を満たす必要があるか**と尋ねられた場合、厳密な数学的証明を提供することが困難であるため、しばしば直感や例に頼って曖昧な答えを提供しなければなりません。</p>
+<p>最適部分構造については「動的計画法」の節ですでに紹介したので、ここでは繰り返しません。なお、問題によっては最適部分構造が明確でなくても、貪欲法で解ける場合があります。</p>
+<p>ここでは主に、貪欲選択性をどのように判定するかを考えます。説明だけを見ると単純そうですが、<strong>実際には多くの問題で、貪欲選択性を証明するのは容易ではありません</strong>。</p>
+<p>たとえばコイン両替問題では、反例を挙げて貪欲選択性が成り立たないことを示すのは簡単ですが、成り立つことを証明するのは難しいです。もし、**どのような条件を満たす硬貨の組み合わせなら貪欲法で解けるのか**と問われると、直感や例示に頼った曖昧な答えしか出せず、厳密な数学的証明を与えるのは困難です。</p>
 <div class="admonition quote">
 <p class="admonition-title">Quote</p>
-<p>ある論文では、コインの組み合わせが任意の金額に対して貪欲アルゴリズムを使用して最適解を見つけることができるかどうかを判定するための時間計算量 <span class="arithmatex">\(O(n^3)\)</span> のアルゴリズムが提示されています。</p>
+<p>ある論文では、ある硬貨の組み合わせについて、任意の金額に対する最適解を貪欲法で求められるかどうかを判定する、時間計算量 <span class="arithmatex">\(O(n^3)\)</span> のアルゴリズムが示されています。</p>
 <p>Pearson, D. A polynomial-time algorithm for the change-making problem[J]. Operations Research Letters, 2005, 33(3): 231-234.</p>
 </div>
-<h2 id="1513">15.1.3 &nbsp; 貪欲アルゴリズムによる問題解決のステップ<a class="headerlink" href="#1513" title="Permanent link">&para;</a></h2>
-<p>貪欲問題の問題解決プロセスは、一般的に以下の3つのステップに分けることができます。</p>
+<h2 id="1513">15.1.3 &nbsp; 貪欲法の問題解決手順<a class="headerlink" href="#1513" title="Permanent link">&para;</a></h2>
+<p>貪欲法による問題解決の流れは、おおむね次の 3 段階に分けられます。</p>
 <ol>
-<li><strong>問題分析</strong>：問題の特徴を整理し理解する。状態定義、最適化目標、制約などを含みます。このステップはバックトラッキングや動的プログラミングでも関与します。</li>
-<li><strong>貪欲戦略の決定</strong>：各ステップで貪欲な選択をする方法を決定する。この戦略は各ステップで問題の規模を縮小し、最終的に問題全体を解決できます。</li>
-<li><strong>正確性の証明</strong>：通常、問題が貪欲選択性と最適部分構造の両方を持つことを証明する必要があります。このステップには、帰納法や背理法などの数学的証明が必要な場合があります。</li>
+<li><strong>問題分析</strong>：状態の定義、最適化目標、制約条件などを整理し、問題の性質を理解します。この段階はバックトラッキングや動的計画法でも共通して現れます。</li>
+<li><strong>貪欲戦略の決定</strong>：各ステップでどのように貪欲選択を行うかを定めます。この戦略により各ステップで問題規模を縮小し、最終的に問題全体を解決します。</li>
+<li><strong>正しさの証明</strong>：通常は、その問題が貪欲選択性と最適部分構造を持つことを示す必要があります。この段階では、帰納法や背理法などの数学的証明が必要になることがあります。</li>
 </ol>
-<p>貪欲戦略の決定は問題解決の核心ステップですが、実装は容易ではない場合があります。主な理由は以下の通りです。</p>
+<p>貪欲戦略を定めることは問題解決の核心ですが、実際には簡単ではないことも多く、主な理由は次のとおりです。</p>
 <ul>
-<li><strong>異なる問題間で貪欲戦略は大きく異なる</strong>。多くの問題では、貪欲戦略はかなり直接的で、一般的な思考と試行を通じて思いつくことができます。しかし、一部の複雑な問題では、貪欲戦略は非常に見つけにくく、これは個人の問題解決経験とアルゴリズム能力の真のテストです。</li>
-<li><strong>一部の貪欲戦略は非常に誤解を招く</strong>。自信を持って貪欲戦略を設計し、コードを書いてテストに提出したとき、一部のテストケースが通らない可能性が高いです。これは設計された貪欲戦略が「部分的に正しい」だけであるためで、上記のコイン交換の例で説明した通りです。</li>
+<li><strong>問題ごとに貪欲戦略の差が大きい</strong>。多くの問題では貪欲戦略は比較的わかりやすく、おおまかな考察や試行だけで見つけられます。しかし複雑な問題では、貪欲戦略が非常に見えにくいことがあり、その場合は解法経験やアルゴリズム力が大きく問われます。</li>
+<li><strong>一見もっともらしい貪欲戦略もある</strong>。自信を持って貪欲戦略を設計し、コードを書いて提出しても、一部のテストケースを通過できないことがあります。これは、その貪欲戦略が「部分的にしか正しくない」ためであり、先ほどのコイン両替は典型例です。</li>
 </ul>
-<p>正確性を確保するために、貪欲戦略に対して厳密な数学的証明を提供すべきで、<strong>通常は背理法や数学的帰納法を含みます</strong>。</p>
-<p>しかし、正確性を証明することは容易な作業ではない場合があります。途方に暮れた場合、通常はテストケースに基づいてコードをデバッグし、貪欲戦略を段階的に修正し検証することを選択します。</p>
-<h2 id="1514">15.1.4 &nbsp; 貪欲アルゴリズムで解決される典型的な問題<a class="headerlink" href="#1514" title="Permanent link">&para;</a></h2>
-<p>貪欲アルゴリズムは、貪欲選択と最適部分構造の性質を満たす最適化問題によく適用されます。以下は典型的な貪欲アルゴリズム問題のいくつかです。</p>
+<p>正しさを保証するためには、貪欲戦略に対して厳密な数学的証明を行うべきであり、<strong>通常は背理法や数学的帰納法が必要になります</strong>。</p>
+<p>しかし、正しさの証明もまた簡単とは限りません。手がかりがない場合には、テストケースを使ってコードをデバッグしながら、貪欲戦略を少しずつ修正して検証していくことがよくあります。</p>
+<h2 id="1514">15.1.4 &nbsp; 貪欲法の典型問題<a class="headerlink" href="#1514" title="Permanent link">&para;</a></h2>
+<p>貪欲法は、貪欲選択性と最適部分構造を満たす最適化問題によく用いられます。以下に典型的な貪欲法の問題をいくつか挙げます。</p>
 <ul>
-<li><strong>コイン交換問題</strong>：一部のコインの組み合わせでは、貪欲アルゴリズムは常に最適解を提供します。</li>
-<li><strong>区間スケジューリング問題</strong>：いくつかのタスクがあり、それぞれが一定期間にわたって行われるとします。目標はできるだけ多くのタスクを完了することです。常に最も早く終了するタスクを選択すると、貪欲アルゴリズムは最適解を達成できます。</li>
-<li><strong>分数ナップサック問題</strong>：アイテムのセットと運搬容量が与えられ、目標は総重量が運搬容量を超えず、総価値が最大化されるようなアイテムのセットを選択することです。常に最高の価値対重量比（価値/重量）のアイテムを選択すると、貪欲アルゴリズムは一部のケースで最適解を達成できます。</li>
-<li><strong>株式取引問題</strong>：株価の履歴のセットが与えられ、複数回の取引を行うことができますが、すでに株式を所有している場合は売却後でないと再度購入できません。目標は最大利益を達成することです。</li>
-<li><strong>ハフマン符号化</strong>：ハフマン符号化は無損失データ圧縮に使用される貪欲アルゴリズムです。ハフマン木を構築することにより、常に最低頻度の2つのノードを統合し、最小重み付きパス長（符号化長）のハフマン木を生成します。</li>
-<li><strong>ダイクストラのアルゴリズム</strong>：これは与えられたソース頂点から他のすべての頂点への最短経路問題を解決するための貪欲アルゴリズムです。</li>
+<li><strong>硬貨のお釣り問題</strong>：ある種の硬貨の組み合わせでは、貪欲法で常に最適解が得られます。</li>
+<li><strong>区間スケジューリング問題</strong>：いくつかのタスクがあり、それぞれがある時間区間で実行されるとします。できるだけ多くのタスクを完了することが目標で、毎回終了時刻が最も早いタスクを選ぶなら、貪欲法で最適解を得られます。</li>
+<li><strong>分数ナップサック問題</strong>：一群の品物と積載容量が与えられたとき、総重量が容量を超えず、かつ総価値が最大になるように品物を選ぶ問題です。毎回、価値対重量比（価値 / 重量）が最も高い品物を選ぶなら、ある条件下で貪欲法は最適解を得られます。</li>
+<li><strong>株式売買問題</strong>：株価の履歴が与えられ、複数回の売買が可能ですが、すでに株を保有している場合は売却前に再度購入することはできません。目標は最大利益を得ることです。</li>
+<li><strong>ハフマン符号化</strong>：ハフマン符号化は、可逆データ圧縮に用いられる貪欲法です。ハフマン木を構築する際、毎回出現頻度が最も低い 2 つのノードを選んで併合すると、最終的に得られるハフマン木の重み付きパス長（符号長）は最小になります。</li>
+<li><strong>Dijkstra アルゴリズム</strong>：与えられた始点から他の各頂点への最短経路問題を解く貪欲法です。</li>
 </ul>
 
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-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
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+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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 <p><img alt="貪欲法" class="cover-image" src="../assets/covers/chapter_greedy.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>ひまわりは太陽の方を向き、常に自分にとって最大の成長を求めます。</p>
-<p>貪欲な戦略は、一連の単純な選択を通じて、段階的に最良の答えへと導きます。</p>
+<p>ヒマワリは太陽に向かって回り、自らが最も大きく成長できる可能性を常に追い求める。</p>
+<p>貪欲戦略は、一回ごとの単純な選択を通じて、徐々に最適な答えへと導く。</p>
 </div>
 <h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
-<li><a href="greedy_algorithm/">15.1 &nbsp; 貪欲アルゴリズム</a></li>
+<li><a href="greedy_algorithm/">15.1 &nbsp; 貪欲法</a></li>
 <li><a href="fractional_knapsack_problem/">15.2 &nbsp; 分数ナップサック問題</a></li>
 <li><a href="max_capacity_problem/">15.3 &nbsp; 最大容量問題</a></li>
 <li><a href="max_product_cutting_problem/">15.4 &nbsp; 最大積分割問題</a></li>
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
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-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
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-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
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-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
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 <h1 id="153">15.3 &nbsp; 最大容量問題<a class="headerlink" href="#153" title="Permanent link">&para;</a></h1>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
-<p>配列 <span class="arithmatex">\(ht\)</span> を入力します。各要素は垂直仕切りの高さを表します。配列内の任意の2つの仕切りと、それらの間のスペースによってコンテナを形成できます。</p>
-<p>コンテナの容量は高さと幅の積（面積）で、高さは短い方の仕切りによって決定され、幅は2つの仕切りの配列インデックスの差です。</p>
-<p>コンテナの容量を最大化する2つの仕切りを配列から選択し、この最大容量を返してください。例を下の図に示します。</p>
+<p>配列 <span class="arithmatex">\(ht\)</span> が与えられ、各要素は垂直な仕切り板の高さを表します。配列内の任意の 2 枚の仕切り板と、その間の空間で容器を構成できます。</p>
+<p>容器の容量は高さと幅の積（面積）に等しく、高さは短い方の仕切り板で決まり、幅は 2 枚の仕切り板の配列インデックスの差です。</p>
+<p>配列から 2 枚の仕切り板を選び、構成される容器の容量が最大となるようにしてください。最大容量を返します。例を以下の図に示します。</p>
 </div>
-<p><img alt="最大容量問題の例データ" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_example.png" /></p>
-<p align="center"> 図 15-7 &nbsp; 最大容量問題の例データ </p>
+<p><img alt="最大容量問題のサンプルデータ" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_example.png" /></p>
+<p align="center"> 図 15-7 &nbsp; 最大容量問題のサンプルデータ </p>
 
-<p>コンテナは任意の2つの仕切りによって形成されるため、<strong>この問題の状態は2つの仕切りのインデックスで表現され、<span class="arithmatex">\([i, j]\)</span> と表記されます</strong>。</p>
-<p>問題の記述によれば、容量は高さと幅の積に等しく、高さは短い方の仕切りによって決定され、幅は2つの仕切りの配列インデックスの差です。容量 <span class="arithmatex">\(cap[i, j]\)</span> の式は：</p>
+<p>容器は任意の 2 枚の仕切り板で囲まれるため、<strong>本問の状態は 2 枚の仕切り板のインデックスで表され、<span class="arithmatex">\([i, j]\)</span> と記します</strong>。</p>
+<p>問題の条件より、容量は高さと幅の積に等しく、高さは短い板で決まり、幅は 2 枚の仕切り板の配列インデックスの差です。容量を <span class="arithmatex">\(cap[i, j]\)</span> とすると、計算式は次のようになります。</p>
 <div class="arithmatex">\[
 cap[i, j] = \min(ht[i], ht[j]) \times (j - i)
 \]</div>
-<p>配列の長さを <span class="arithmatex">\(n\)</span> と仮定すると、2つの仕切りの組み合わせ数（状態の総数）は <span class="arithmatex">\(C_n^2 = \frac{n(n - 1)}{2}\)</span> です。最も直接的なアプローチは**すべての可能な状態を列挙する**ことで、時間計算量は <span class="arithmatex">\(O(n^2)\)</span> になります。</p>
+<p>配列の長さを <span class="arithmatex">\(n\)</span> とすると、2 枚の仕切り板の組合せ数（状態総数）は <span class="arithmatex">\(C_n^2 = \frac{n(n - 1)}{2}\)</span> 個です。最も直接的には、<strong>すべての状態を総当たりできます</strong>。これにより最大容量を求められ、時間計算量は <span class="arithmatex">\(O(n^2)\)</span> です。</p>
 <h3 id="1">1. &nbsp; 貪欲戦略の決定<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>この問題にはより効率的な解法があります。下の図に示すように、インデックス <span class="arithmatex">\(i &lt; j\)</span> かつ高さ <span class="arithmatex">\(ht[i] &lt; ht[j]\)</span> の状態 <span class="arithmatex">\([i, j]\)</span> を選択します。つまり、<span class="arithmatex">\(i\)</span> は短い仕切り、<span class="arithmatex">\(j\)</span> は高い仕切りです。</p>
+<p>この問題にはさらに効率的な解法があります。以下の図のように、状態 <span class="arithmatex">\([i, j]\)</span> を 1 つ選び、インデックスが <span class="arithmatex">\(i &lt; j\)</span> かつ高さが <span class="arithmatex">\(ht[i] &lt; ht[j]\)</span> を満たすとします。つまり、<span class="arithmatex">\(i\)</span> が短い板、<span class="arithmatex">\(j\)</span> が長い板です。</p>
 <p><img alt="初期状態" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_initial_state.png" /></p>
 <p align="center"> 図 15-8 &nbsp; 初期状態 </p>
 
-<p>下の図に示すように、<strong>高い仕切り <span class="arithmatex">\(j\)</span> を短い仕切り <span class="arithmatex">\(i\)</span> に近づけて移動すると、容量は確実に減少します</strong>。</p>
-<p>これは、高い仕切り <span class="arithmatex">\(j\)</span> を移動すると、幅 <span class="arithmatex">\(j-i\)</span> が確実に減少するためです。高さは短い仕切りによって決定されるため、高さは同じまま（<span class="arithmatex">\(i\)</span> が短い仕切りのまま）か減少（移動した <span class="arithmatex">\(j\)</span> が短い仕切りになる）しかありません。</p>
-<p><img alt="高い仕切りを内側に移動した後の状態" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_moving_long_board.png" /></p>
-<p align="center"> 図 15-9 &nbsp; 高い仕切りを内側に移動した後の状態 </p>
+<p>以下の図のように、<strong>このとき長い板 <span class="arithmatex">\(j\)</span> を短い板 <span class="arithmatex">\(i\)</span> に近づけると、容量は必ず小さくなります</strong>。</p>
+<p>これは、長い板 <span class="arithmatex">\(j\)</span> を動かした後は幅 <span class="arithmatex">\(j-i\)</span> が必ず小さくなるためです。また、高さは短い板で決まるので、高さは変わらない（ <span class="arithmatex">\(i\)</span> が依然として短い板）か、小さくなる（移動後の <span class="arithmatex">\(j\)</span> が短い板になる）ことしかありません。</p>
+<p><img alt="長い板を内側へ動かした後の状態" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_moving_long_board.png" /></p>
+<p align="center"> 図 15-9 &nbsp; 長い板を内側へ動かした後の状態 </p>
 
-<p>逆に、<strong>短い仕切り <span class="arithmatex">\(i\)</span> を内側に移動することによってのみ容量を増加させることが可能です</strong>。幅は確実に減少しますが、<strong>高さが増加する可能性があります</strong>（移動した短い仕切り <span class="arithmatex">\(i\)</span> が高くなる場合）。例えば、下の図では、短い仕切りを移動した後に面積が増加しています。</p>
-<p><img alt="短い仕切りを内側に移動した後の状態" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_moving_short_board.png" /></p>
-<p align="center"> 図 15-10 &nbsp; 短い仕切りを内側に移動した後の状態 </p>
+<p>逆に考えると、<strong>短い板 <span class="arithmatex">\(i\)</span> を内側へ縮めた場合にのみ、容量が大きくなる可能性があります</strong>。幅は必ず小さくなりますが、**高さは大きくなる可能性がある**からです（移動後の短い板 <span class="arithmatex">\(i\)</span> がより長くなる可能性があります）。たとえば次の図では、短い板を動かした後に面積が大きくなっています。</p>
+<p><img alt="短い板を内側へ動かした後の状態" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_moving_short_board.png" /></p>
+<p align="center"> 図 15-10 &nbsp; 短い板を内側へ動かした後の状態 </p>
 
-<p>これにより、この問題の貪欲戦略が導かれます：コンテナの両端に2つのポインタを初期化し、各ラウンドで短い仕切りに対応するポインタを内側に移動し、2つのポインタが出会うまで続けます。</p>
-<p>下の図は貪欲戦略の実行を示しています。</p>
+<p>以上から、本問の貪欲戦略を導けます。2 本のポインタを初期化して容器の両端に置き、各ラウンドで短い板に対応するポインタを内側へ縮め、2 本のポインタが出会うまで続けます。</p>
+<p>以下の図は、貪欲戦略の実行過程を示しています。</p>
 <ol>
-<li>最初に、ポインタ <span class="arithmatex">\(i\)</span> と <span class="arithmatex">\(j\)</span> が配列の両端に配置されます。</li>
+<li>初期状態では、ポインタ <span class="arithmatex">\(i\)</span> と <span class="arithmatex">\(j\)</span> は配列の両端にあります。</li>
 <li>現在の状態の容量 <span class="arithmatex">\(cap[i, j]\)</span> を計算し、最大容量を更新します。</li>
-<li>仕切り <span class="arithmatex">\(i\)</span> と <span class="arithmatex">\(j\)</span> の高さを比較し、短い仕切りを1ステップ内側に移動します。</li>
-<li><span class="arithmatex">\(i\)</span> と <span class="arithmatex">\(j\)</span> が出会うまでステップ <code>2.</code> と <code>3.</code> を繰り返します。</li>
+<li>板 <span class="arithmatex">\(i\)</span> と板 <span class="arithmatex">\(j\)</span> の高さを比較し、短い板を内側へ 1 マス移動します。</li>
+<li><code>2.</code> と <code>3.</code> を繰り返し実行し、<span class="arithmatex">\(i\)</span> と <span class="arithmatex">\(j\)</span> が出会ったら終了します。</li>
 </ol>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:9"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label><label for="__tabbed_1_5">&lt;5&gt;</label><label for="__tabbed_1_6">&lt;6&gt;</label><label for="__tabbed_1_7">&lt;7&gt;</label><label for="__tabbed_1_8">&lt;8&gt;</label><label for="__tabbed_1_9">&lt;9&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="最大容量問題の貪欲プロセス" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_greedy_step1.png" /></p>
+<p><img alt="最大容量問題の貪欲な過程" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_greedy_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="max_capacity_greedy_step2" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_greedy_step2.png" /></p>
@@ -4445,26 +4445,26 @@ cap[i, j] = \min(ht[i], ht[j]) \times (j - i)
 </div>
 </div>
 </div>
-<p align="center"> 図 15-11 &nbsp; 最大容量問題の貪欲プロセス </p>
+<p align="center"> 図 15-11 &nbsp; 最大容量問題の貪欲な過程 </p>
 
-<h3 id="2">2. &nbsp; 実装<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>コードは最大 <span class="arithmatex">\(n\)</span> 回ループするため、<strong>時間計算量は <span class="arithmatex">\(O(n)\)</span></strong> です。</p>
-<p>変数 <span class="arithmatex">\(i\)</span>、<span class="arithmatex">\(j\)</span>、<span class="arithmatex">\(res\)</span> は一定量の追加スペースを使用するため、<strong>空間計算量は <span class="arithmatex">\(O(1)\)</span></strong> です。</p>
+<h3 id="2">2. &nbsp; コード実装<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>コードのループ回数は最大でも <span class="arithmatex">\(n\)</span> 回であるため、<strong>時間計算量は <span class="arithmatex">\(O(n)\)</span></strong> です。</p>
+<p>変数 <span class="arithmatex">\(i\)</span>、<span class="arithmatex">\(j\)</span>、<span class="arithmatex">\(res\)</span> が使う追加領域は定数サイズなので、<strong>空間計算量は <span class="arithmatex">\(O(1)\)</span></strong> です。</p>
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 <div class="highlight"><span class="filename">max_capacity.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">max_capacity</span><span class="p">(</span><span class="n">ht</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
 <a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;最大容量：貪欲法&quot;&quot;&quot;</span>
-<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># i、j を初期化、配列の両端で分割させる</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># i, j を初期化し、それぞれ配列の両端に置く</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">ht</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>
-<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="c1"># 初期最大容量は 0</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="c1"># 初期の最大容量は 0</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="n">res</span> <span class="o">=</span> <span class="mi">0</span>
-<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="c1"># 2 つの板が出会うまで貪欲選択をループ</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="c1"># 2 枚の板が出会うまで貪欲選択を繰り返す</span>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="n">j</span><span class="p">:</span>
-<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="c1"># 最大容量を更新</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="c1"># 最大容量を更新する</span>
 <a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="n">cap</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span> <span class="o">*</span> <span class="p">(</span><span class="n">j</span> <span class="o">-</span> <span class="n">i</span><span class="p">)</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="n">res</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">res</span><span class="p">,</span> <span class="n">cap</span><span class="p">)</span>
-<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="c1"># 短い板を内側に移動</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="c1"># 短い方を内側へ動かす</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="k">if</span> <span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&lt;</span> <span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">]:</span>
 <a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>            <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
 <a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>        <span class="k">else</span><span class="p">:</span>
@@ -4475,16 +4475,16 @@ cap[i, j] = \min(ht[i], ht[j]) \times (j - i)
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">max_capacity.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 最大容量：貪欲法 */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">maxCapacity</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">ht</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// i、j を初期化し、配列の両端で分割させる</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// i, j を初期化し、それぞれ配列の両端に置く</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ht</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="c1">// 初期最大容量は 0</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="c1">// 初期の最大容量は 0</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="c1">// 2つの板が出会うまで貪欲選択をループ</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="c1">// 2 枚の板が出会うまで貪欲選択を繰り返す</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">        </span><span class="c1">// 最大容量を更新</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">        </span><span class="c1">// 最大容量を更新する</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">);</span>
-<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="c1">// より短い板を内側に移動</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="c1">// 短い方を内側へ動かす</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span><span class="p">;</span>
 <a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
@@ -4498,16 +4498,16 @@ cap[i, j] = \min(ht[i], ht[j]) \times (j - i)
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">max_capacity.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 最大容量：貪欲法 */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">maxCapacity</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">ht</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// i、j を初期化し、配列の両端で分割させる</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// i, j を初期化し、それぞれ配列の両端に置く</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ht</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="c1">// 初期最大容量は 0</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="c1">// 初期の最大容量は 0</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="c1">// 2つの板が出会うまで貪欲選択をループ</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="c1">// 2 枚の板が出会うまで貪欲選択を繰り返す</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">        </span><span class="c1">// 最大容量を更新</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">        </span><span class="c1">// 最大容量を更新する</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">ht</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">ht</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
 <a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">max</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">);</span>
-<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="c1">// より短い板を内側に移動</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="c1">// 短い方を内側へ動かす</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ht</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">ht</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span><span class="p">;</span>
 <a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
@@ -4519,58 +4519,260 @@ cap[i, j] = \min(ht[i], ht[j]) \times (j - i)
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">max_capacity.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">max_capacity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MaxCapacity</span><span class="p">}</span>
+<div class="highlight"><span class="filename">max_capacity.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 最大容量：貪欲法 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">MaxCapacity</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">ht</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="c1">// i, j を初期化し、それぞれ配列の両端に置く</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ht</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="c1">// 初期の最大容量は 0</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="c1">// 2 枚の板が出会うまで貪欲選択を繰り返す</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">        </span><span class="c1">// 最大容量を更新する</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Min</span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Max</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">);</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">        </span><span class="c1">// 短い方を内側へ動かす</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">max_capacity.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">maxCapacity</span><span class="p">}</span>
+<div class="highlight"><span class="filename">max_capacity.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 最大容量：貪欲法 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">maxCapacity</span><span class="p">(</span><span class="nx">ht</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// i, j を初期化し、それぞれ配列の両端に置く</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">ht</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="c1">// 初期の最大容量は 0</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="c1">// 2 枚の板が出会うまで貪欲選択を繰り返す</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">        </span><span class="c1">// 最大容量を更新する</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">        </span><span class="nx">capacity</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Min</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">ht</span><span class="p">[</span><span class="nx">i</span><span class="p">]),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">ht</span><span class="p">[</span><span class="nx">j</span><span class="p">])))</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">        </span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Max</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">res</span><span class="p">),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">capacity</span><span class="p">)))</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">        </span><span class="c1">// 短い方を内側へ動かす</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">ht</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">ht</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">            </span><span class="nx">i</span><span class="o">++</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">            </span><span class="nx">j</span><span class="o">--</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">max_capacity.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">maxCapacity</span><span class="p">}</span>
+<div class="highlight"><span class="filename">max_capacity.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 最大容量：貪欲法 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">maxCapacity</span><span class="p">(</span><span class="n">ht</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// i, j を初期化し、それぞれ配列の両端に置く</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ht</span><span class="p">.</span><span class="n">startIndex</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ht</span><span class="p">.</span><span class="n">endIndex</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="c1">// 初期の最大容量は 0</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="c1">// 2 枚の板が出会うまで貪欲選択を繰り返す</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">        </span><span class="c1">// 最大容量を更新する</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">cap</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">min</span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">max</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">        </span><span class="c1">// 短い方を内側へ動かす</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">max_capacity.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">maxCapacity</span><span class="p">}</span>
+<div class="highlight"><span class="filename">max_capacity.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 最大容量：貪欲法 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">maxCapacity</span><span class="p">(</span><span class="nx">ht</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="c1">// i, j を初期化し、それぞれ配列の両端に置く</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">        </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">ht</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="c1">// 初期の最大容量は 0</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">    </span><span class="c1">// 2 枚の板が出会うまで貪欲選択を繰り返す</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">        </span><span class="c1">// 最大容量を更新する</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">cap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">ht</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">ht</span><span class="p">[</span><span class="nx">j</span><span class="p">])</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">i</span><span class="p">);</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">        </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">max</span><span class="p">(</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="p">);</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">        </span><span class="c1">// 短い方を内側へ動かす</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">ht</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">ht</span><span class="p">[</span><span class="nx">j</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">            </span><span class="nx">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">max_capacity.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">maxCapacity</span><span class="p">}</span>
+<div class="highlight"><span class="filename">max_capacity.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 最大容量：貪欲法 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">maxCapacity</span><span class="p">(</span><span class="nx">ht</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="c1">// i, j を初期化し、それぞれ配列の両端に置く</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">        </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">ht</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="c1">// 初期の最大容量は 0</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="c1">// 2 枚の板が出会うまで貪欲選択を繰り返す</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">        </span><span class="c1">// 最大容量を更新する</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">cap</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">ht</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">ht</span><span class="p">[</span><span class="nx">j</span><span class="p">])</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">i</span><span class="p">);</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">        </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">max</span><span class="p">(</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="p">);</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">        </span><span class="c1">// 短い方を内側へ動かす</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">ht</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">ht</span><span class="p">[</span><span class="nx">j</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">            </span><span class="nx">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">max_capacity.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">maxCapacity</span><span class="p">}</span>
+<div class="highlight"><span class="filename">max_capacity.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 最大容量：貪欲法 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">maxCapacity</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">ht</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="c1">// i, j を初期化し、それぞれ配列の両端に置く</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ht</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="c1">// 初期の最大容量は 0</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="c1">// 2 枚の板が出会うまで貪欲選択を繰り返す</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">    </span><span class="c1">// 最大容量を更新する</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">    </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">);</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">    </span><span class="c1">// 短い方を内側へ動かす</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">      </span><span class="n">i</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">      </span><span class="n">j</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">max_capacity.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">max_capacity</span><span class="p">}</span>
+<div class="highlight"><span class="filename">max_capacity.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 最大容量：貪欲法 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">max_capacity</span><span class="p">(</span><span class="n">ht</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="c1">// i, j を初期化し、それぞれ配列の両端に置く</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ht</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="c1">// 初期の最大容量は 0</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="c1">// 2 枚の板が出会うまで貪欲選択を繰り返す</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">        </span><span class="c1">// 最大容量を更新する</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">min</span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">;</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">max</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">);</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">        </span><span class="c1">// 短い方を内側へ動かす</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w">    </span><span class="n">res</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">max_capacity.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">maxCapacity</span><span class="p">}</span>
+<div class="highlight"><span class="filename">max_capacity.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 最大容量：貪欲法 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">maxCapacity</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">ht</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">htLength</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="c1">// i, j を初期化し、それぞれ配列の両端に置く</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">htLength</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="c1">// 初期の最大容量は 0</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">    </span><span class="c1">// 2 枚の板が出会うまで貪欲選択を繰り返す</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">        </span><span class="c1">// 最大容量を更新する</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">myMin</span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">myMax</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">capacity</span><span class="p">);</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">        </span><span class="c1">// 短い方を内側へ動かす</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">max_capacity.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">maxCapacity</span><span class="p">}</span>
+<div class="highlight"><span class="filename">max_capacity.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 最大容量：貪欲法 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">maxCapacity</span><span class="p">(</span><span class="n">ht</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="c1">// i, j を初期化し、それぞれ配列の両端に置く</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ht</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="c1">// 初期の最大容量は 0</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">    </span><span class="c1">// 2 枚の板が出会うまで貪欲選択を繰り返す</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">        </span><span class="c1">// 最大容量を更新する</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">cap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">ht</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">ht</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">        </span><span class="c1">// 短い方を内側へ動かす</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ht</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">ht</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">max_capacity.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">max_capacity</span><span class="p">}</span>
+<div class="highlight"><span class="filename">max_capacity.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 最大容量：貪欲法 ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">max_capacity</span><span class="p">(</span><span class="n">ht</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># i, j を初期化し、それぞれ配列の両端に置く</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">ht</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="c1"># 初期の最大容量は 0</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">  </span><span class="c1"># 2 枚の板が出会うまで貪欲選択を繰り返す</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">    </span><span class="c1"># 最大容量を更新する</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">    </span><span class="n">cap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">ht</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">ht</span><span class="o">[</span><span class="n">j</span><span class="o">]].</span><span class="n">min</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">    </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="o">].</span><span class="n">max</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">    </span><span class="c1"># 短い方を内側へ動かす</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">ht</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">ht</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">      </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">      </span><span class="n">j</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w">  </span><span class="n">res</span>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20max_capacity%28ht%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E6%9C%80%E5%A4%A7%E5%AE%B9%E9%87%8F%EF%BC%9A%E8%B2%AA%E6%AC%B2%E6%B3%95%22%22%22%0A%20%20%20%20%23%20i%2C%20j%20%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%97%E3%80%81%E3%81%9D%E3%82%8C%E3%81%9E%E3%82%8C%E9%85%8D%E5%88%97%E3%81%AE%E4%B8%A1%E7%AB%AF%E3%81%AB%E7%BD%AE%E3%81%8F%0A%20%20%20%20i%2C%20j%20%3D%200%2C%20len%28ht%29%20-%201%0A%20%20%20%20%23%20%E5%88%9D%E6%9C%9F%E3%81%AE%E6%9C%80%E5%A4%A7%E5%AE%B9%E9%87%8F%E3%81%AF%200%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20%23%202%20%E6%9E%9A%E3%81%AE%E6%9D%BF%E3%81%8C%E5%87%BA%E4%BC%9A%E3%81%86%E3%81%BE%E3%81%A7%E8%B2%AA%E6%AC%B2%E9%81%B8%E6%8A%9E%E3%82%92%E7%B9%B0%E3%82%8A%E8%BF%94%E3%81%99%0A%20%20%20%20while%20i%20%3C%20j%3A%0A%20%20%20%20%20%20%20%20%23%20%E6%9C%80%E5%A4%A7%E5%AE%B9%E9%87%8F%E3%82%92%E6%9B%B4%E6%96%B0%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20cap%20%3D%20min%28ht%5Bi%5D%2C%20ht%5Bj%5D%29%20%2A%20%28j%20-%20i%29%0A%20%20%20%20%20%20%20%20res%20%3D%20max%28res%2C%20cap%29%0A%20%20%20%20%20%20%20%20%23%20%E7%9F%AD%E3%81%84%E6%96%B9%E3%82%92%E5%86%85%E5%81%B4%E3%81%B8%E5%8B%95%E3%81%8B%E3%81%99%0A%20%20%20%20%20%20%20%20if%20ht%5Bi%5D%20%3C%20ht%5Bj%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%2B%3D%201%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20-%3D%201%0A%20%20%20%20return%20res%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20ht%20%3D%20%5B3%2C%208%2C%205%2C%202%2C%207%2C%207%2C%203%2C%204%5D%0A%0A%20%20%20%20%23%20%E8%B2%AA%E6%AC%B2%E6%B3%95%0A%20%20%20%20res%20%3D%20max_capacity%28ht%29%0A%20%20%20%20print%28f%22%E6%9C%80%E5%A4%A7%E5%AE%B9%E9%87%8F%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20max_capacity%28ht%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E6%9C%80%E5%A4%A7%E5%AE%B9%E9%87%8F%EF%BC%9A%E8%B2%AA%E6%AC%B2%E6%B3%95%22%22%22%0A%20%20%20%20%23%20i%2C%20j%20%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%97%E3%80%81%E3%81%9D%E3%82%8C%E3%81%9E%E3%82%8C%E9%85%8D%E5%88%97%E3%81%AE%E4%B8%A1%E7%AB%AF%E3%81%AB%E7%BD%AE%E3%81%8F%0A%20%20%20%20i%2C%20j%20%3D%200%2C%20len%28ht%29%20-%201%0A%20%20%20%20%23%20%E5%88%9D%E6%9C%9F%E3%81%AE%E6%9C%80%E5%A4%A7%E5%AE%B9%E9%87%8F%E3%81%AF%200%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20%23%202%20%E6%9E%9A%E3%81%AE%E6%9D%BF%E3%81%8C%E5%87%BA%E4%BC%9A%E3%81%86%E3%81%BE%E3%81%A7%E8%B2%AA%E6%AC%B2%E9%81%B8%E6%8A%9E%E3%82%92%E7%B9%B0%E3%82%8A%E8%BF%94%E3%81%99%0A%20%20%20%20while%20i%20%3C%20j%3A%0A%20%20%20%20%20%20%20%20%23%20%E6%9C%80%E5%A4%A7%E5%AE%B9%E9%87%8F%E3%82%92%E6%9B%B4%E6%96%B0%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20cap%20%3D%20min%28ht%5Bi%5D%2C%20ht%5Bj%5D%29%20%2A%20%28j%20-%20i%29%0A%20%20%20%20%20%20%20%20res%20%3D%20max%28res%2C%20cap%29%0A%20%20%20%20%20%20%20%20%23%20%E7%9F%AD%E3%81%84%E6%96%B9%E3%82%92%E5%86%85%E5%81%B4%E3%81%B8%E5%8B%95%E3%81%8B%E3%81%99%0A%20%20%20%20%20%20%20%20if%20ht%5Bi%5D%20%3C%20ht%5Bj%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%2B%3D%201%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20-%3D%201%0A%20%20%20%20return%20res%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20ht%20%3D%20%5B3%2C%208%2C%205%2C%202%2C%207%2C%207%2C%203%2C%204%5D%0A%0A%20%20%20%20%23%20%E8%B2%AA%E6%AC%B2%E6%B3%95%0A%20%20%20%20res%20%3D%20max_capacity%28ht%29%0A%20%20%20%20print%28f%22%E6%9C%80%E5%A4%A7%E5%AE%B9%E9%87%8F%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 <h3 id="3">3. &nbsp; 正しさの証明<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
-<p>貪欲法が列挙よりも高速である理由は、各ラウンドの貪欲選択が一部の状態を「スキップ」するからです。</p>
-<p>例えば、<span class="arithmatex">\(i\)</span> が短い仕切りで <span class="arithmatex">\(j\)</span> が高い仕切りである状態 <span class="arithmatex">\(cap[i, j]\)</span> の下で、短い仕切り <span class="arithmatex">\(i\)</span> を貪欲に1ステップ内側に移動すると、下の図に示す「スキップされた」状態につながります。<strong>これは、これらの状態の容量を後で検証できないことを意味します</strong>。</p>
+<p>貪欲法が総当たりより速いのは、各ラウンドの貪欲な選択がいくつかの状態を「スキップ」するためです。</p>
+<p>たとえば状態 <span class="arithmatex">\(cap[i, j]\)</span> において、<span class="arithmatex">\(i\)</span> が短い板、<span class="arithmatex">\(j\)</span> が長い板だとします。貪欲に短い板 <span class="arithmatex">\(i\)</span> を内側へ 1 マス動かすと、次の図に示す状態が「スキップ」されます。<strong>これは、その後それらの状態の容量を検証できないことを意味します</strong>。</p>
 <div class="arithmatex">\[
 cap[i, i+1], cap[i, i+2], \dots, cap[i, j-2], cap[i, j-1]
 \]</div>
-<p><img alt="短い仕切りの移動によってスキップされる状態" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_skipped_states.png" /></p>
-<p align="center"> 図 15-12 &nbsp; 短い仕切りの移動によってスキップされる状態 </p>
+<p><img alt="短い板の移動によってスキップされる状態" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_skipped_states.png" /></p>
+<p align="center"> 図 15-12 &nbsp; 短い板の移動によってスキップされる状態 </p>
 
-<p>観察すると、<strong>これらのスキップされた状態は実際には高い仕切り <span class="arithmatex">\(j\)</span> が内側に移動したすべての状態**です。高い仕切りを内側に移動すると容量が確実に減少することをすでに証明しました。したがって、スキップされた状態は最適解である可能性がなく、**それらをスキップしても最適解を見逃すことはありません</strong>。</p>
-<p>分析により、短い仕切りを移動する操作は「安全」であり、貪欲戦略が効果的であることが示されます。</p>
+<p>観察すると、<strong>これらのスキップされた状態は、実際には長い板 <span class="arithmatex">\(j\)</span> を内側へ動かしたすべての状態そのものです</strong>。前述のとおり、長い板を内側へ動かすと容量は必ず小さくなります。つまり、スキップされた状態はいずれも最適解にはなりえず、<strong>それらを飛ばしても最適解を逃すことはありません</strong>。</p>
+<p>以上の分析から、短い板を動かす操作は「安全」であり、貪欲戦略は有効であると分かります。</p>
 
 <!-- Source file information -->
 
diff --git a/ja/chapter_greedy/max_product_cutting_problem/index.html b/ja/chapter_greedy/max_product_cutting_problem/index.html
index 1c8e5a334..7b9abf08f 100644
--- a/ja/chapter_greedy/max_product_cutting_problem/index.html
+++ b/ja/chapter_greedy/max_product_cutting_problem/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -39,7 +39,7 @@
     
     
       
-        <title>15.4 最大積切断問題 - Hello アルゴリズム</title>
+        <title>15.4 最大積分割問題 - Hello アルゴリズム</title>
       
     
     
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -152,7 +152,7 @@
         <div class="md-header__topic" data-md-component="header-topic">
           <span class="md-ellipsis">
             
-              15.4 &nbsp; 最大積切断問題
+              15.4 &nbsp; 最大積分割問題
             
           </span>
         </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
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             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
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   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
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   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2105,7 +2105,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2491,7 +2491,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2547,7 +2547,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2575,7 +2575,7 @@
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-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3113,7 +3113,7 @@
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3169,7 +3169,7 @@
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
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-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
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-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
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-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
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-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
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-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3838,7 +3838,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4164,7 +4164,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4376,25 +4376,25 @@
 
 
 <!-- Page content -->
-<h1 id="154">15.4 &nbsp; 最大積切断問題<a class="headerlink" href="#154" title="Permanent link">&para;</a></h1>
+<h1 id="154">15.4 &nbsp; 最大積分割問題<a class="headerlink" href="#154" title="Permanent link">&para;</a></h1>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
-<p>正の整数 <span class="arithmatex">\(n\)</span> が与えられたとき、それを合計が <span class="arithmatex">\(n\)</span> になる少なくとも2つの正の整数に分割し、これらの整数の最大積を求めてください。下の図に示すとおりです。</p>
+<p>正整数 <span class="arithmatex">\(n\)</span> が与えられたとき、それを少なくとも 2 つの正整数の和に分割し、分割後のすべての整数の積の最大値を求めよ。下図に示す。</p>
 </div>
-<p><img alt="最大積切断問題の定義" class="animation-figure" src="../max_product_cutting_problem.assets/max_product_cutting_definition.png" /></p>
-<p align="center"> 図 15-13 &nbsp; 最大積切断問題の定義 </p>
+<p><img alt="最大積分割問題の定義" class="animation-figure" src="../max_product_cutting_problem.assets/max_product_cutting_definition.png" /></p>
+<p align="center"> 図 15-13 &nbsp; 最大積分割問題の定義 </p>
 
-<p><span class="arithmatex">\(n\)</span> を <span class="arithmatex">\(m\)</span> 個の整数因子に分割すると仮定し、<span class="arithmatex">\(i\)</span> 番目の因子を <span class="arithmatex">\(n_i\)</span> と表記すると、</p>
+<p>仮に <span class="arithmatex">\(n\)</span> を <span class="arithmatex">\(m\)</span> 個の整数因子に分割し、そのうち第 <span class="arithmatex">\(i\)</span> 個の因子を <span class="arithmatex">\(n_i\)</span> と記すと、</p>
 <div class="arithmatex">\[
 n = \sum_{i=1}^{m}n_i
 \]</div>
-<p>この問題の目標は、すべての整数因子の最大積を見つけることです。すなわち、</p>
+<p>本問題の目的は、すべての整数因子の積の最大値を求めることであり、すなわち</p>
 <div class="arithmatex">\[
 \max(\prod_{i=1}^{m}n_i)
 \]</div>
-<p>考慮すべき点：分割数 <span class="arithmatex">\(m\)</span> はどの程度大きくすべきか、各 <span class="arithmatex">\(n_i\)</span> は何であるべきか？</p>
+<p>考えるべきことは、分割数 <span class="arithmatex">\(m\)</span> をいくつにすべきか、各 <span class="arithmatex">\(n_i\)</span> をいくつにすべきかである。</p>
 <h3 id="1">1. &nbsp; 貪欲戦略の決定<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>経験的に、2つの整数の積は多くの場合その和よりも大きくなります。<span class="arithmatex">\(n\)</span> から因子 <span class="arithmatex">\(2\)</span> を分割すると仮定すると、その積は <span class="arithmatex">\(2(n-2)\)</span> です。この積を <span class="arithmatex">\(n\)</span> と比較します：</p>
+<p>経験的に、2 つの整数の積はその和より大きくなることが多い。<span class="arithmatex">\(n\)</span> から因子 <span class="arithmatex">\(2\)</span> を 1 つ切り出すと、それらの積は <span class="arithmatex">\(2(n-2)\)</span> となる。この積を <span class="arithmatex">\(n\)</span> と比較すると、</p>
 <div class="arithmatex">\[
 \begin{aligned}
 2(n-2) &amp; \geq n \newline
@@ -4402,153 +4402,341 @@ n = \sum_{i=1}^{m}n_i
 n &amp; \geq 4
 \end{aligned}
 \]</div>
-<p>下の図に示すように、<span class="arithmatex">\(n \geq 4\)</span> のとき、<span class="arithmatex">\(2\)</span> を分割すると積が増加します。<strong>これは4以上の整数を分割すべきであることを示しています</strong>。</p>
-<p><strong>貪欲戦略1</strong>：分割スキームが <span class="arithmatex">\(\geq 4\)</span> の因子を含む場合、それらはさらに分割されるべきです。最終的な分割は因子 <span class="arithmatex">\(1\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(3\)</span> のみを含むべきです。</p>
-<p><img alt="分割による積の増加" class="animation-figure" src="../max_product_cutting_problem.assets/max_product_cutting_greedy_infer1.png" /></p>
-<p align="center"> 図 15-14 &nbsp; 分割による積の増加 </p>
+<p>下図のように、<span class="arithmatex">\(n \geq 4\)</span> のとき、<span class="arithmatex">\(2\)</span> を 1 つ切り出すと積は大きくなる。<strong>これは、<span class="arithmatex">\(4\)</span> 以上の整数はすべて分割すべきことを意味する</strong>。</p>
+<p><strong>貪欲戦略一</strong>：分割方法に <span class="arithmatex">\(\geq 4\)</span> の因子が含まれるなら、それはさらに分割すべきである。最終的な分割方法に現れる因子は <span class="arithmatex">\(1\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(3\)</span> の 3 種類だけである。</p>
+<p><img alt="分割により積が大きくなる" class="animation-figure" src="../max_product_cutting_problem.assets/max_product_cutting_greedy_infer1.png" /></p>
+<p align="center"> 図 15-14 &nbsp; 分割により積が大きくなる </p>
 
-<p>次に、どの因子が最適かを考慮します。因子 <span class="arithmatex">\(1\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(3\)</span> の中で、明らかに <span class="arithmatex">\(1\)</span> が最悪です。<span class="arithmatex">\(1 \times (n-1) &lt; n\)</span> が常に成り立つため、<span class="arithmatex">\(1\)</span> を分割すると実際に積が減少します。</p>
-<p>下の図に示すように、<span class="arithmatex">\(n = 6\)</span> のとき、<span class="arithmatex">\(3 \times 3 &gt; 2 \times 2 \times 2\)</span> です。<strong>これは <span class="arithmatex">\(3\)</span> を分割する方が <span class="arithmatex">\(2\)</span> を分割するよりも良いことを意味します</strong>。</p>
-<p><strong>貪欲戦略2</strong>：分割スキームには最大で2つの <span class="arithmatex">\(2\)</span> があるべきです。3つの <span class="arithmatex">\(2\)</span> は常に2つの <span class="arithmatex">\(3\)</span> に置き換えてより高い積を得ることができるからです。</p>
+<p>次に、どの因子が最適かを考える。<span class="arithmatex">\(1\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(3\)</span> の 3 つの因子のうち、明らかに <span class="arithmatex">\(1\)</span> が最も悪い。なぜなら <span class="arithmatex">\(1 \times (n-1) &lt; n\)</span> は常に成り立ち、<span class="arithmatex">\(1\)</span> を切り出すとかえって積が小さくなるからである。</p>
+<p>下図のように、<span class="arithmatex">\(n = 6\)</span> のとき、<span class="arithmatex">\(3 \times 3 &gt; 2 \times 2 \times 2\)</span> が成り立つ。<strong>これは、<span class="arithmatex">\(2\)</span> を切り出すより <span class="arithmatex">\(3\)</span> を切り出すほうが有利であることを意味する</strong>。</p>
+<p><strong>貪欲戦略二</strong>：分割方法の中に存在してよい <span class="arithmatex">\(2\)</span> は高々 2 つである。なぜなら、3 つの <span class="arithmatex">\(2\)</span> は常に 2 つの <span class="arithmatex">\(3\)</span> に置き換えられ、より大きな積を得られるからである。</p>
 <p><img alt="最適な分割因子" class="animation-figure" src="../max_product_cutting_problem.assets/max_product_cutting_greedy_infer2.png" /></p>
 <p align="center"> 図 15-15 &nbsp; 最適な分割因子 </p>
 
-<p>上記から、以下の貪欲戦略を導出できます。</p>
+<p>以上より、次の貪欲戦略が導かれる。</p>
 <ol>
-<li>入力整数 <span class="arithmatex">\(n\)</span> について、余りが <span class="arithmatex">\(0\)</span>、<span class="arithmatex">\(1\)</span>、または <span class="arithmatex">\(2\)</span> になるまで因子 <span class="arithmatex">\(3\)</span> を継続的に分割します。</li>
-<li>余りが <span class="arithmatex">\(0\)</span> の場合、<span class="arithmatex">\(n\)</span> が <span class="arithmatex">\(3\)</span> の倍数であることを意味するため、それ以上の行動は取りません。</li>
-<li>余りが <span class="arithmatex">\(2\)</span> の場合、さらに分割を続けず、そのまま保持します。</li>
-<li>余りが <span class="arithmatex">\(1\)</span> の場合、<span class="arithmatex">\(2 \times 2 &gt; 1 \times 3\)</span> であるため、最後の <span class="arithmatex">\(3\)</span> を <span class="arithmatex">\(2\)</span> に置き換えるべきです。</li>
+<li>整数 <span class="arithmatex">\(n\)</span> を入力し、余りが <span class="arithmatex">\(0\)</span>、<span class="arithmatex">\(1\)</span>、<span class="arithmatex">\(2\)</span> になるまで、そこから因子 <span class="arithmatex">\(3\)</span> を繰り返し切り出す。</li>
+<li>余りが <span class="arithmatex">\(0\)</span> のとき、<span class="arithmatex">\(n\)</span> は <span class="arithmatex">\(3\)</span> の倍数であることを表すため、何も処理しない。</li>
+<li>余りが <span class="arithmatex">\(2\)</span> のときは、それ以上分割せず、そのまま残す。</li>
+<li>余りが <span class="arithmatex">\(1\)</span> のとき、<span class="arithmatex">\(2 \times 2 &gt; 1 \times 3\)</span> であるため、最後の <span class="arithmatex">\(3\)</span> を <span class="arithmatex">\(2\)</span> に置き換えるべきである。</li>
 </ol>
 <h3 id="2">2. &nbsp; コード実装<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>下の図に示すように、整数を分割するためにループを使用する必要はなく、床除算演算を使用して <span class="arithmatex">\(3\)</span> の数 <span class="arithmatex">\(a\)</span> を取得し、剰余演算を使用して余り <span class="arithmatex">\(b\)</span> を取得できます。したがって：</p>
+<p>下図のように、ループで整数を分割する必要はなく、切り捨て除算によって <span class="arithmatex">\(3\)</span> の個数 <span class="arithmatex">\(a\)</span> を、剰余演算によって余り <span class="arithmatex">\(b\)</span> を得られる。このとき、</p>
 <div class="arithmatex">\[
-n = 3a + b
+n = 3 a + b
 \]</div>
-<p><span class="arithmatex">\(n \leq 3\)</span> の境界ケースでは、<span class="arithmatex">\(1\)</span> を分割する必要があり、積は <span class="arithmatex">\(1 \times (n - 1)\)</span> であることに注意してください。</p>
+<p>なお、<span class="arithmatex">\(n \leq 3\)</span> の境界ケースでは、必ず <span class="arithmatex">\(1\)</span> を 1 つ分割する必要があり、積は <span class="arithmatex">\(1 \times (n - 1)\)</span> となる。</p>
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 <div class="tabbed-block">
 <div class="highlight"><span class="filename">max_product_cutting.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">max_product_cutting</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;切断の最大積：貪欲法&quot;&quot;&quot;</span>
-<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># n &lt;= 3 の場合、1 を切り出す必要がある</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;最大切断積：貪欲法&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># n &lt;= 3 のときは、必ず 1 を切り出す</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">&lt;=</span> <span class="mi">3</span><span class="p">:</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="k">return</span> <span class="mi">1</span> <span class="o">*</span> <span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 貪欲的に 3 を切り出す、a は 3 の個数、b は余り</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="o">=</span> <span class="n">n</span> <span class="o">//</span> <span class="mi">3</span><span class="p">,</span> <span class="n">n</span> <span class="o">%</span> <span class="mi">3</span>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="k">if</span> <span class="n">b</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
-<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="c1"># 余りが 1 の場合、1 * 3 のペアを 2 * 2 に変換</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="c1"># 余りが 1 のときは、1 * 3 を 2 * 2 に変える</span>
 <a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="k">return</span> <span class="nb">int</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">a</span> <span class="o">-</span> <span class="mi">1</span><span class="p">))</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="mi">2</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="k">if</span> <span class="n">b</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
-<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="c1"># 余りが 2 の場合、何もしない</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="c1"># 余りが 2 のときは、そのままにする</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="k">return</span> <span class="nb">int</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">a</span><span class="p">))</span> <span class="o">*</span> <span class="mi">2</span>
-<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="c1"># 余りが 0 の場合、何もしない</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="c1"># 余りが 0 のときは、そのままにする</span>
 <a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="k">return</span> <span class="nb">int</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">a</span><span class="p">))</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">max_product_cutting.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 最大積切断：貪欲法 */</span>
+<div class="highlight"><span class="filename">max_product_cutting.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 最大切断積：貪欲法 */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">maxProductCutting</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// n &lt;= 3 の場合、1 を切り出す必要がある</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// n &lt;= 3 のときは、必ず 1 を切り出す</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="c1">// 貪欲に 3 を切り出す。a は 3 の個数、b は余り</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="c1">// 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="c1">// 余りが 1 の場合、1 * 3 のペアを 2 * 2 に変換</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="c1">// 余りが 1 のときは、1 * 3 を 2 * 2 に変える</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="c1">// 余りが 2 の場合、何もしない</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="c1">// 余りが 2 のときは、そのままにする</span>
 <a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
 <a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="c1">// 余りが 0 の場合、何もしない</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="c1">// 余りが 0 のときは、そのままにする</span>
 <a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">);</span>
 <a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">max_product_cutting.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 最大積切断：貪欲法 */</span>
+<div class="highlight"><span class="filename">max_product_cutting.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 最大切断積：貪欲法 */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">maxProductCutting</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// n &lt;= 3 の場合、1 を切り出す必要がある</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// n &lt;= 3 のときは、必ず 1 を切り出す</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="c1">// 貪欲に 3 を切り出す。a は 3 の個数、b は余り</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="c1">// 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="c1">// 余りが 1 の場合、1 * 3 のペアを 2 * 2 に変換</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="c1">// 余りが 1 のときは、1 * 3 を 2 * 2 に変える</span>
 <a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="c1">// 余りが 2 の場合、何もしない</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="c1">// 余りが 2 のときは、そのままにする</span>
 <a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
 <a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">    </span><span class="c1">// 余りが 0 の場合、何もしない</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">    </span><span class="c1">// 余りが 0 のときは、そのままにする</span>
 <a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">);</span>
 <a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">max_product_cutting.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">max_product_cutting</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MaxProductCutting</span><span class="p">}</span>
+<div class="highlight"><span class="filename">max_product_cutting.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 最大切断積：貪欲法 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">MaxProductCutting</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="c1">// n &lt;= 3 のときは、必ず 1 を切り出す</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="c1">// 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">        </span><span class="c1">// 余りが 1 のときは、1 * 3 を 2 * 2 に変える</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">Math</span><span class="p">.</span><span class="n">Pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">        </span><span class="c1">// 余りが 2 のときは、そのままにする</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">Math</span><span class="p">.</span><span class="n">Pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">    </span><span class="c1">// 余りが 0 のときは、そのままにする</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">Math</span><span class="p">.</span><span class="n">Pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">);</span>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">max_product_cutting.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">maxProductCutting</span><span class="p">}</span>
+<div class="highlight"><span class="filename">max_product_cutting.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 最大切断積：貪欲法 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">maxProductCutting</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// n &lt;= 3 のときは、必ず 1 を切り出す</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="c1">// 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">3</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="nx">b</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">3</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">        </span><span class="c1">// 余りが 1 のときは、1 * 3 を 2 * 2 に変える</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">a</span><span class="o">-</span><span class="mi">1</span><span class="p">)))</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">        </span><span class="c1">// 余りが 2 のときは、そのままにする</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">a</span><span class="p">)))</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w">    </span><span class="c1">// 余りが 0 のときは、そのままにする</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">a</span><span class="p">)))</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">max_product_cutting.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">maxProductCutting</span><span class="p">}</span>
+<div class="highlight"><span class="filename">max_product_cutting.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 最大切断積：貪欲法 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">maxProductCutting</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// n &lt;= 3 のときは、必ず 1 を切り出す</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="c1">// 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">3</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">b</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">3</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">        </span><span class="c1">// 余りが 1 のときは、1 * 3 を 2 * 2 に変える</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">        </span><span class="c1">// 余りが 2 のときは、そのままにする</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">    </span><span class="c1">// 余りが 0 のときは、そのままにする</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">)</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">max_product_cutting.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">maxProductCutting</span><span class="p">}</span>
+<div class="highlight"><span class="filename">max_product_cutting.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 最大切断積：貪欲法 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">maxProductCutting</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="c1">// n &lt;= 3 のときは、必ず 1 を切り出す</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mf">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="c1">// 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3</span><span class="p">);</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mf">3</span><span class="p">;</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">b</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">        </span><span class="c1">// 余りが 1 のときは、1 * 3 を 2 * 2 に変える</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">b</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">        </span><span class="c1">// 余りが 2 のときは、そのままにする</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="nx">a</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w">    </span><span class="c1">// 余りが 0 のときは、そのままにする</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="nx">a</span><span class="p">);</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">max_product_cutting.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">maxProductCutting</span><span class="p">}</span>
+<div class="highlight"><span class="filename">max_product_cutting.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 最大切断積：貪欲法 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">maxProductCutting</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="c1">// n &lt;= 3 のときは、必ず 1 を切り出す</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mf">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="c1">// 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3</span><span class="p">);</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">b</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mf">3</span><span class="p">;</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">b</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">        </span><span class="c1">// 余りが 1 のときは、1 * 3 を 2 * 2 に変える</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">b</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">        </span><span class="c1">// 余りが 2 のときは、そのままにする</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="nx">a</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">    </span><span class="c1">// 余りが 0 のときは、そのままにする</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="nx">a</span><span class="p">);</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">max_product_cutting.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">maxProductCutting</span><span class="p">}</span>
+<div class="highlight"><span class="filename">max_product_cutting.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 最大切断積：貪欲法 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">maxProductCutting</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="c1">// n &lt;= 3 のときは、必ず 1 を切り出す</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="m">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="c1">// 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="m">3</span><span class="p">;</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="m">3</span><span class="p">;</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">    </span><span class="c1">// 余りが 1 のときは、1 * 3 を 2 * 2 に変える</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">pow</span><span class="p">(</span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span><span class="p">).</span><span class="n">toInt</span><span class="p">();</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">    </span><span class="c1">// 余りが 2 のときは、そのままにする</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">pow</span><span class="p">(</span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span><span class="p">).</span><span class="n">toInt</span><span class="p">();</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w">  </span><span class="c1">// 余りが 0 のときは、そのままにする</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">pow</span><span class="p">(</span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">).</span><span class="n">toInt</span><span class="p">();</span>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">max_product_cutting.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">max_product_cutting</span><span class="p">}</span>
+<div class="highlight"><span class="filename">max_product_cutting.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 最大切断積：貪欲法 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">max_product_cutting</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="c1">// n &lt;= 3 のときは、必ず 1 を切り出す</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="c1">// 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">        </span><span class="c1">// 余りが 1 のときは、1 * 3 を 2 * 2 に変える</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">        </span><span class="mi">3_</span><span class="k">i32</span><span class="p">.</span><span class="n">pow</span><span class="p">(</span><span class="n">a</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">u32</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">        </span><span class="c1">// 余りが 2 のときは、そのままにする</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">        </span><span class="mi">3_</span><span class="k">i32</span><span class="p">.</span><span class="n">pow</span><span class="p">(</span><span class="n">a</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">u32</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">        </span><span class="c1">// 余りが 0 のときは、そのままにする</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">        </span><span class="mi">3_</span><span class="k">i32</span><span class="p">.</span><span class="n">pow</span><span class="p">(</span><span class="n">a</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">u32</span><span class="p">)</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">max_product_cutting.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">maxProductCutting</span><span class="p">}</span>
+<div class="highlight"><span class="filename">max_product_cutting.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 最大切断積：貪欲法 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">maxProductCutting</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="c1">// n &lt;= 3 のときは、必ず 1 を切り出す</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">    </span><span class="c1">// 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">        </span><span class="c1">// 余りが 1 のときは、1 * 3 を 2 * 2 に変える</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">        </span><span class="c1">// 余りが 2 のときは、そのままにする</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">    </span><span class="c1">// 余りが 0 のときは、そのままにする</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">);</span>
+<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">max_product_cutting.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">maxProductCutting</span><span class="p">}</span>
+<div class="highlight"><span class="filename">max_product_cutting.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 最大切断積：貪欲法 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">maxProductCutting</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="c1">// n &lt;= 3 のときは、必ず 1 を切り出す</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="m">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">    </span><span class="c1">// 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">3</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="m">3</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">        </span><span class="c1">// 余りが 1 のときは、1 * 3 を 2 * 2 に変える</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="m">3.0</span><span class="p">.</span><span class="na">pow</span><span class="p">((</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)).</span><span class="na">toInt</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">        </span><span class="c1">// 余りが 2 のときは、そのままにする</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="m">3.0</span><span class="p">.</span><span class="na">pow</span><span class="p">(</span><span class="n">a</span><span class="p">).</span><span class="na">toInt</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">    </span><span class="c1">// 余りが 0 のときは、そのままにする</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="m">3.0</span><span class="p">.</span><span class="na">pow</span><span class="p">(</span><span class="n">a</span><span class="p">).</span><span class="na">toInt</span><span class="p">()</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">max_product_cutting.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">max_product_cutting</span><span class="p">}</span>
+<div class="highlight"><span class="filename">max_product_cutting.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 最大分割積：貪欲法 ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">max_product_cutting</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># n &lt;= 3 のときは、必ず 1 を切り出す</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">3</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="c1"># 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">3</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">  </span><span class="c1"># 余りが 1 のときは、1 * 3 を 2 * 2 に変える</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="mi">3</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">to_i</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">  </span><span class="c1"># 余りが 2 のときは、そのままにする</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="mi">3</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">to_i</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">  </span><span class="c1"># 余りが 0 のときは、そのままにする</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">  </span><span class="mi">3</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="n">a</span><span class="p">)</span><span class="o">.</span><span class="n">to_i</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p><img alt="切断後の最大積の計算方法" class="animation-figure" src="../max_product_cutting_problem.assets/max_product_cutting_greedy_calculation.png" /></p>
-<p align="center"> 図 15-16 &nbsp; 切断後の最大積の計算方法 </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=import%20math%0A%0Adef%20max_product_cutting%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E6%9C%80%E5%A4%A7%E5%88%87%E6%96%AD%E7%A9%8D%EF%BC%9A%E8%B2%AA%E6%AC%B2%E6%B3%95%22%22%22%0A%20%20%20%20%23%20n%20%3C%3D%203%20%E3%81%AE%E3%81%A8%E3%81%8D%E3%81%AF%E3%80%81%E5%BF%85%E3%81%9A%201%20%E3%82%92%E5%88%87%E3%82%8A%E5%87%BA%E3%81%99%0A%20%20%20%20if%20n%20%3C%3D%203%3A%0A%20%20%20%20%20%20%20%20return%201%20%2A%20%28n%20-%201%29%0A%20%20%20%20%23%20%E8%B2%AA%E6%AC%B2%E3%81%AB%203%20%E3%82%92%E5%88%87%E3%82%8A%E5%87%BA%E3%81%97%E3%80%81a%20%E3%82%92%203%20%E3%81%AE%E5%80%8B%E6%95%B0%E3%80%81b%20%E3%82%92%E4%BD%99%E3%82%8A%E3%81%A8%E3%81%99%E3%82%8B%0A%20%20%20%20a%2C%20b%20%3D%20n%20%2F%2F%203%2C%20n%20%25%203%0A%20%20%20%20if%20b%20%3D%3D%201%3A%0A%20%20%20%20%20%20%20%20%23%20%E4%BD%99%E3%82%8A%E3%81%8C%201%20%E3%81%AE%E3%81%A8%E3%81%8D%E3%81%AF%E3%80%811%20%2A%203%20%E3%82%92%202%20%2A%202%20%E3%81%AB%E5%A4%89%E3%81%88%E3%82%8B%0A%20%20%20%20%20%20%20%20return%20int%28math.pow%283%2C%20a%20-%201%29%29%20%2A%202%20%2A%202%0A%20%20%20%20if%20b%20%3D%3D%202%3A%0A%20%20%20%20%20%20%20%20%23%20%E4%BD%99%E3%82%8A%E3%81%8C%202%20%E3%81%AE%E3%81%A8%E3%81%8D%E3%81%AF%E3%80%81%E3%81%9D%E3%81%AE%E3%81%BE%E3%81%BE%E3%81%AB%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20return%20int%28math.pow%283%2C%20a%29%29%20%2A%202%0A%20%20%20%20%23%20%E4%BD%99%E3%82%8A%E3%81%8C%200%20%E3%81%AE%E3%81%A8%E3%81%8D%E3%81%AF%E3%80%81%E3%81%9D%E3%81%AE%E3%81%BE%E3%81%BE%E3%81%AB%E3%81%99%E3%82%8B%0A%20%20%20%20return%20int%28math.pow%283%2C%20a%29%29%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%2058%0A%0A%20%20%20%20%23%20%E8%B2%AA%E6%AC%B2%E6%B3%95%0A%20%20%20%20res%20%3D%20max_product_cutting%28n%29%0A%20%20%20%20print%28f%22%E6%9C%80%E5%A4%A7%E5%88%86%E5%89%B2%E7%A9%8D%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=import%20math%0A%0Adef%20max_product_cutting%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E6%9C%80%E5%A4%A7%E5%88%87%E6%96%AD%E7%A9%8D%EF%BC%9A%E8%B2%AA%E6%AC%B2%E6%B3%95%22%22%22%0A%20%20%20%20%23%20n%20%3C%3D%203%20%E3%81%AE%E3%81%A8%E3%81%8D%E3%81%AF%E3%80%81%E5%BF%85%E3%81%9A%201%20%E3%82%92%E5%88%87%E3%82%8A%E5%87%BA%E3%81%99%0A%20%20%20%20if%20n%20%3C%3D%203%3A%0A%20%20%20%20%20%20%20%20return%201%20%2A%20%28n%20-%201%29%0A%20%20%20%20%23%20%E8%B2%AA%E6%AC%B2%E3%81%AB%203%20%E3%82%92%E5%88%87%E3%82%8A%E5%87%BA%E3%81%97%E3%80%81a%20%E3%82%92%203%20%E3%81%AE%E5%80%8B%E6%95%B0%E3%80%81b%20%E3%82%92%E4%BD%99%E3%82%8A%E3%81%A8%E3%81%99%E3%82%8B%0A%20%20%20%20a%2C%20b%20%3D%20n%20%2F%2F%203%2C%20n%20%25%203%0A%20%20%20%20if%20b%20%3D%3D%201%3A%0A%20%20%20%20%20%20%20%20%23%20%E4%BD%99%E3%82%8A%E3%81%8C%201%20%E3%81%AE%E3%81%A8%E3%81%8D%E3%81%AF%E3%80%811%20%2A%203%20%E3%82%92%202%20%2A%202%20%E3%81%AB%E5%A4%89%E3%81%88%E3%82%8B%0A%20%20%20%20%20%20%20%20return%20int%28math.pow%283%2C%20a%20-%201%29%29%20%2A%202%20%2A%202%0A%20%20%20%20if%20b%20%3D%3D%202%3A%0A%20%20%20%20%20%20%20%20%23%20%E4%BD%99%E3%82%8A%E3%81%8C%202%20%E3%81%AE%E3%81%A8%E3%81%8D%E3%81%AF%E3%80%81%E3%81%9D%E3%81%AE%E3%81%BE%E3%81%BE%E3%81%AB%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20return%20int%28math.pow%283%2C%20a%29%29%20%2A%202%0A%20%20%20%20%23%20%E4%BD%99%E3%82%8A%E3%81%8C%200%20%E3%81%AE%E3%81%A8%E3%81%8D%E3%81%AF%E3%80%81%E3%81%9D%E3%81%AE%E3%81%BE%E3%81%BE%E3%81%AB%E3%81%99%E3%82%8B%0A%20%20%20%20return%20int%28math.pow%283%2C%20a%29%29%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%2058%0A%0A%20%20%20%20%23%20%E8%B2%AA%E6%AC%B2%E6%B3%95%0A%20%20%20%20res%20%3D%20max_product_cutting%28n%29%0A%20%20%20%20print%28f%22%E6%9C%80%E5%A4%A7%E5%88%86%E5%89%B2%E7%A9%8D%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p><img alt="最大積分割の計算方法" class="animation-figure" src="../max_product_cutting_problem.assets/max_product_cutting_greedy_calculation.png" /></p>
+<p align="center"> 図 15-16 &nbsp; 最大積分割の計算方法 </p>
 
-<p><strong>時間計算量はプログラミング言語のべき乗演算の実装に依存します</strong>。Pythonでは、よく使用されるべき乗計算関数は3種類あります：</p>
+<p><strong>時間計算量は、プログラミング言語におけるべき乗演算の実装方法に依存する</strong>。Python を例に取ると、よく使われるべき乗計算関数は 3 種類ある。</p>
 <ul>
-<li>演算子 <code>**</code> と関数 <code>pow()</code> の両方の時間計算量は <span class="arithmatex">\(O(\log⁡ a)\)</span> です。</li>
-<li><code>math.pow()</code> 関数は内部でC言語ライブラリの <code>pow()</code> 関数を呼び出し、浮動小数点べき乗を実行し、時間計算量は <span class="arithmatex">\(O(1)\)</span> です。</li>
+<li>演算子 <code>**</code> と関数 <code>pow()</code> の時間計算量はいずれも <span class="arithmatex">\(O(\log⁡ a)\)</span> である。</li>
+<li>関数 <code>math.pow()</code> は内部で C 言語ライブラリの <code>pow()</code> 関数を呼び出し、浮動小数点のべき乗を実行するため、時間計算量は <span class="arithmatex">\(O(1)\)</span> である。</li>
 </ul>
-<p>変数 <span class="arithmatex">\(a\)</span> と <span class="arithmatex">\(b\)</span> は一定サイズの追加スペースを使用するため、<strong>空間計算量は <span class="arithmatex">\(O(1)\)</span></strong> です。</p>
+<p>変数 <span class="arithmatex">\(a\)</span> と <span class="arithmatex">\(b\)</span> が使う追加領域は定数サイズであり、<strong>したがって空間計算量は <span class="arithmatex">\(O(1)\)</span> である</strong>。</p>
 <h3 id="3">3. &nbsp; 正しさの証明<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
-<p>背理法を使用し、<span class="arithmatex">\(n \geq 3\)</span> のケースのみを分析します。</p>
+<p>背理法を用い、<span class="arithmatex">\(n \geq 4\)</span> の場合のみを考える。</p>
 <ol>
-<li><strong>すべての因子 <span class="arithmatex">\(\leq 3\)</span></strong>：最適分割スキームが因子 <span class="arithmatex">\(x \geq 4\)</span> を含むと仮定すると、それを確実に <span class="arithmatex">\(2(x-2)\)</span> にさらに分割でき、より大きな積を得られます。これは仮定と矛盾します。</li>
-<li><strong>分割スキームに <span class="arithmatex">\(1\)</span> が含まれない</strong>：最適分割スキームが因子 <span class="arithmatex">\(1\)</span> を含むと仮定すると、それを確実に別の因子と結合してより大きな積を得られます。これは仮定と矛盾します。</li>
-<li><strong>分割スキームには最大で2つの <span class="arithmatex">\(2\)</span> が含まれる</strong>：最適分割スキームが3つの <span class="arithmatex">\(2\)</span> を含むと仮定すると、それらを確実に2つの <span class="arithmatex">\(3\)</span> に置き換えて、より高い積を達成できます。これは仮定と矛盾します。</li>
+<li><strong>すべての因子は <span class="arithmatex">\(\leq 3\)</span></strong> ：最適な分割方法に <span class="arithmatex">\(\geq 4\)</span> の因子 <span class="arithmatex">\(x\)</span> が存在すると仮定すると、それは必ずさらに <span class="arithmatex">\(2(x-2)\)</span> に分割でき、より大きい（または等しい）積が得られる。これは仮定に矛盾する。</li>
+<li><strong>分割方法に <span class="arithmatex">\(1\)</span> は含まれない</strong> ：最適な分割方法に因子 <span class="arithmatex">\(1\)</span> が 1 つ存在すると仮定すると、それは必ず別の因子に併合でき、より大きい積を得られる。これは仮定に矛盾する。</li>
+<li><strong>分割方法に含まれる <span class="arithmatex">\(2\)</span> は高々 2 つ</strong> ：最適な分割方法に 3 つの <span class="arithmatex">\(2\)</span> が含まれると仮定すると、それは必ず 2 つの <span class="arithmatex">\(3\)</span> に置き換えられ、積はより大きくなる。これは仮定に矛盾する。</li>
 </ol>
 
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diff --git a/ja/chapter_greedy/summary/index.html b/ja/chapter_greedy/summary/index.html
index ed4b2b836..9ae66757e 100644
--- a/ja/chapter_greedy/summary/index.html
+++ b/ja/chapter_greedy/summary/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
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             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
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   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
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-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
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-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
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-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
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-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
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-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
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-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
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-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
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-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
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-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -3952,6 +3952,24 @@
         
       
       
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    15.5 &nbsp; まとめ
+  
+
+    
+  </span>
+  
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
       <a href="././" class="md-nav__link md-nav__link--active">
         
   
@@ -3969,6 +3987,37 @@
 
       </a>
       
+        
+
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      
+        1. &nbsp; 重要な振り返り
+      
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
     </li>
   
 
@@ -4093,7 +4142,7 @@
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4229,6 +4278,25 @@
     
   
   
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      
+        1. &nbsp; 重要な振り返り
+      
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
 </nav>
                   </div>
                 </div>
@@ -4265,17 +4333,18 @@
 
 <!-- Page content -->
 <h1 id="155">15.5 &nbsp; まとめ<a class="headerlink" href="#155" title="Permanent link">&para;</a></h1>
+<h3 id="1">1. &nbsp; 重要な振り返り<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
-<li>貪欲アルゴリズムは最適化問題を解決するためによく使用され、原理は各決定段階で局所的に最適な決定を行い、グローバルに最適な解を達成することです。</li>
-<li>貪欲アルゴリズムは貪欲な選択を次々と反復的に行い、各ラウンドで問題をより小さな部分問題に変換し、問題が解決されるまで続けます。</li>
-<li>貪欲アルゴリズムは実装が簡単なだけでなく、問題解決効率も高いです。動的プログラミングと比較して、貪欲アルゴリズムは一般的により低い時間計算量を持ちます。</li>
-<li>コイン交換問題において、貪欲アルゴリズムは特定のコインの組み合わせに対して最適解を保証できますが、他の組み合わせでは貪欲アルゴリズムが非常に悪い解を見つける可能性があります。</li>
-<li>貪欲アルゴリズム解法に適した問題は2つの主要な性質を持ちます：貪欲選択性と最適部分構造。貪欲選択性は貪欲戦略の効果を表します。</li>
-<li>一部の複雑な問題では、貪欲選択性を証明することは簡単ではありません。逆に、無効性を証明することはしばしばより容易で、コイン交換問題などがその例です。</li>
-<li>貪欲問題の解決は主に3つのステップから構成されます：問題分析、貪欲戦略の決定、正しさの証明。このうち、貪欲戦略の決定が重要なステップであり、正しさの証明がしばしば挑戦となります。</li>
-<li>分数ナップサック問題は0-1ナップサック問題に基づいてアイテムの一部の選択を可能にし、したがって貪欲アルゴリズムを使用して解決できます。貪欲戦略の正しさは背理法によって証明できます。</li>
-<li>最大容量問題は全探索法で解決でき、時間計算量は <span class="arithmatex">\(O(n^2)\)</span> です。貪欲戦略を設計することで、各ラウンドで短い板を内側に移動し、時間計算量を <span class="arithmatex">\(O(n)\)</span> に最適化します。</li>
-<li>切断後の最大積問題において、2つの貪欲戦略を導出します：<span class="arithmatex">\(\geq 4\)</span> の整数は継続的に切断されるべきで、最適な切断因子は <span class="arithmatex">\(3\)</span> です。コードにはべき乗演算が含まれ、時間計算量はべき乗演算の実装方法に依存し、一般的に <span class="arithmatex">\(O(1)\)</span> または <span class="arithmatex">\(O(\log n)\)</span> です。</li>
+<li>貪欲法は通常、最適化問題を解くために用いられ、その原理は各意思決定段階で局所最適な決定を行い、全体最適解を得ることを目指すというものである。</li>
+<li>貪欲法は反復的に次々と貪欲な選択を行い、各ラウンドで問題をより小さな部分問題へと変換し、最終的に問題を解決する。</li>
+<li>貪欲法は実装が簡単であるだけでなく、問題を解く効率も高い。動的計画法と比べると、貪欲法の時間計算量は通常より低い。</li>
+<li>硬貨両替問題では、ある種の硬貨の組み合わせに対しては貪欲法で最適解を保証できるが、別の組み合わせではそうではなく、非常に悪い解を見つけてしまう可能性がある。</li>
+<li>貪欲法による解法に適した問題は、貪欲選択性と最適部分構造という 2 つの性質を備えている。貪欲選択性は、貪欲戦略の有効性を表している。</li>
+<li>一部の複雑な問題では、貪欲選択性を証明するのは容易ではない。相対的には、反例による否定のほうが簡単であり、硬貨両替問題がその一例である。</li>
+<li>貪欲法の問題を解く流れは主に 3 段階に分かれる。すなわち、問題分析、貪欲戦略の決定、正しさの証明である。このうち、貪欲戦略の決定が中核であり、正しさの証明はしばしば難所となる。</li>
+<li>分数ナップサック問題は 0-1 ナップサックを基に、品物の一部を選ぶことを許しているため、貪欲法で解くことができる。貪欲戦略の正しさは背理法で証明できる。</li>
+<li>最大容量問題は全探索で解くことができ、時間計算量は <span class="arithmatex">\(O(n^2)\)</span> である。貪欲戦略を設計し、各ラウンドで短い板を内側へ動かすことで、時間計算量を <span class="arithmatex">\(O(n)\)</span> に最適化できる。</li>
+<li>最大分割積問題では、2 つの貪欲戦略を順に導いた。すなわち、<span class="arithmatex">\(\geq 4\)</span> の整数はすべてさらに分割すべきであり、最適な分割因子は <span class="arithmatex">\(3\)</span> である。コードにはべき乗演算が含まれており、時間計算量はその実装方法に依存し、通常は <span class="arithmatex">\(O(1)\)</span> または <span class="arithmatex">\(O(\log n)\)</span> である。</li>
 </ul>
 
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@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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-    序
+    はじめに
   
 
     
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-    序
+    はじめに
   
 
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-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
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-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
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-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
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-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
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-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
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-    第 6 章 &nbsp; ハッシュ表
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-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
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     </span>
   </a>
   
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#634" class="md-nav__link">
+    <span class="md-ellipsis">
+      
+        6.3.4 &nbsp; データ構造のハッシュ値
+      
+    </span>
+  </a>
+  
 </li>
       
     </ul>
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
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-    8.2 &nbsp; ヒープ構築操作
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-    10.2 &nbsp; 二分探索の挿入点
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-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
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-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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+</li>
+      
+        <li class="md-nav__item">
+  <a href="#634" class="md-nav__link">
+    <span class="md-ellipsis">
+      
+        6.3.4 &nbsp; データ構造のハッシュ値
+      
+    </span>
+  </a>
+  
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 <!-- Page content -->
 <h1 id="63">6.3 &nbsp; ハッシュアルゴリズム<a class="headerlink" href="#63" title="Permanent link">&para;</a></h1>
-<p>前の2つの節では、ハッシュ表の動作原理とハッシュ衝突を処理する方法を紹介しました。しかし、オープンアドレス法と連鎖法はどちらも**衝突が発生した際にハッシュ表が正常に機能することのみを保証でき、ハッシュ衝突の発生頻度を減らすことはできません**。</p>
-<p>ハッシュ衝突があまりにも頻繁に発生すると、ハッシュ表の性能は劇的に悪化します。下図に示すように、連鎖法ハッシュ表では、理想的なケースではキー値ペアがバケット間に均等に分散され、最適なクエリ効率を実現します。最悪のケースでは、すべてのキー値ペアが同じバケットに格納され、時間計算量が<span class="arithmatex">\(O(n)\)</span>に悪化します。</p>
-<p><img alt="ハッシュ衝突の理想的および最悪のケース" class="animation-figure" src="../hash_algorithm.assets/hash_collision_best_worst_condition.png" /></p>
-<p align="center"> 図 6-8 &nbsp; ハッシュ衝突の理想的および最悪のケース </p>
+<p>前の 2 節では、ハッシュテーブルの動作原理とハッシュ衝突の処理方法を紹介しました。しかし、オープンアドレス法であれ連鎖方式であれ、<strong>それらが保証できるのは衝突発生時でもハッシュテーブルが正常に動作することだけであり、ハッシュ衝突そのものを減らすことはできません</strong>。</p>
+<p>ハッシュ衝突があまりにも頻繁に発生すると、ハッシュテーブルの性能は急激に劣化します。下図のように、連鎖方式のハッシュテーブルでは、理想的な場合にはキーと値のペアが各バケットに均等に分布し、最良の検索効率を達成します。最悪の場合には、すべてのキーと値のペアが同じバケットに格納され、時間計算量は <span class="arithmatex">\(O(n)\)</span> に劣化します。</p>
+<p><img alt="ハッシュ衝突の最良ケースと最悪ケース" class="animation-figure" src="../hash_algorithm.assets/hash_collision_best_worst_condition.png" /></p>
+<p align="center"> 図 6-8 &nbsp; ハッシュ衝突の最良ケースと最悪ケース </p>
 
-<p><strong>キー値ペアの分布はハッシュ関数によって決定されます</strong>。ハッシュ関数の計算ステップを思い出すと、まずハッシュ値を計算し、次に配列長で剰余を取ります：</p>
+<p><strong>キーと値のペアの分布はハッシュ関数によって決まります</strong>。ハッシュ関数の計算手順を思い出すと、まずハッシュ値を計算し、その後で配列長に対して剰余を取ります。</p>
 <div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nv">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span>hash<span class="o">(</span>key<span class="o">)</span><span class="w"> </span>%<span class="w"> </span>capacity
 </code></pre></div>
-<p>上記の式を観察すると、ハッシュ表の容量<code>capacity</code>が固定されている場合、<strong>ハッシュアルゴリズム<code>hash()</code>が出力値を決定し</strong>、それによってハッシュ表におけるキー値ペアの分布を決定します。</p>
-<p>これは、ハッシュ衝突の確率を減らすために、ハッシュアルゴリズム<code>hash()</code>の設計に焦点を当てるべきであることを意味します。</p>
+<p>上の式から分かるように、ハッシュテーブルの容量 <code>capacity</code> が固定されているとき、<strong>出力値を決めるのはハッシュアルゴリズム <code>hash()</code> です</strong>。したがって、それがキーと値のペアのハッシュテーブル内での分布も決定します。</p>
+<p>これは、ハッシュ衝突の発生確率を下げるには、ハッシュアルゴリズム <code>hash()</code> の設計に注目すべきだということを意味します。</p>
 <h2 id="631">6.3.1 &nbsp; ハッシュアルゴリズムの目標<a class="headerlink" href="#631" title="Permanent link">&para;</a></h2>
-<p>「高速で安定した」ハッシュ表データ構造を実現するために、ハッシュアルゴリズムは以下の特性を持つべきです：</p>
+<p>「高速かつ安定した」ハッシュテーブルというデータ構造を実現するために、ハッシュアルゴリズムは次の特徴を備える必要があります。</p>
 <ul>
-<li><strong>決定性</strong>: 同じ入力に対して、ハッシュアルゴリズムは常に同じ出力を生成するべきです。そうでなければハッシュ表は信頼できません。</li>
-<li><strong>高効率</strong>: ハッシュ値を計算するプロセスは十分に高速である必要があります。計算オーバーヘッドが小さいほど、ハッシュ表はより実用的になります。</li>
-<li><strong>均等分散</strong>: ハッシュアルゴリズムはキー値ペアがハッシュ表に均等に分散されることを保証するべきです。分散が均等であるほど、ハッシュ衝突の確率は低くなります。</li>
+<li><strong>決定性</strong>：同じ入力に対して、ハッシュアルゴリズムは常に同じ出力を生成しなければなりません。そうして初めて、ハッシュテーブルの信頼性が保たれます。</li>
+<li><strong>高効率</strong>：ハッシュ値の計算過程は十分に高速であるべきです。計算コストが小さいほど、ハッシュテーブルの実用性は高くなります。</li>
+<li><strong>均一分布</strong>：ハッシュアルゴリズムは、キーと値のペアがハッシュテーブル内に均等に分布するようにすべきです。分布が均一であるほど、ハッシュ衝突の確率は低くなります。</li>
 </ul>
-<p>実際、ハッシュアルゴリズムはハッシュ表の実装だけでなく、他の分野でも広く応用されています。</p>
+<p>実際には、ハッシュアルゴリズムはハッシュテーブルの実装だけでなく、ほかの多くの分野でも広く利用されています。</p>
 <ul>
-<li><strong>パスワード保存</strong>: ユーザーパスワードのセキュリティを保護するために、システムは通常平文パスワードを保存せず、パスワードのハッシュ値を保存します。ユーザーがパスワードを入力すると、システムは入力のハッシュ値を計算し、保存されているハッシュ値と比較します。一致すれば、パスワードは正しいと見なされます。</li>
-<li><strong>データ整合性チェック</strong>: データ送信者はデータのハッシュ値を計算して一緒に送信できます。受信者は受信したデータのハッシュ値を再計算し、受信したハッシュ値と比較できます。一致すれば、データは完全であると見なされます。</li>
+<li><strong>パスワード保存</strong>：ユーザーのパスワードを保護するために、システムは通常、平文パスワードを直接保存せず、そのハッシュ値を保存します。ユーザーがパスワードを入力すると、システムは入力内容のハッシュ値を計算し、保存済みのハッシュ値と比較します。一致すれば、そのパスワードは正しいと見なされます。</li>
+<li><strong>データ完全性検査</strong>：送信側はデータのハッシュ値を計算してデータと一緒に送信できます。受信側は受け取ったデータのハッシュ値を再計算し、受信したハッシュ値と比較できます。両者が一致すれば、そのデータは完全だと見なされます。</li>
 </ul>
-<p>暗号化アプリケーションでは、ハッシュ値から元のパスワードを推測するなどの逆行分析を防ぐために、ハッシュアルゴリズムはより高いレベルのセキュリティ機能が必要です。</p>
+<p>暗号分野の応用では、ハッシュ値から元のパスワードを推測するといった逆解析を防ぐために、ハッシュアルゴリズムにはさらに高いレベルの安全性が求められます。</p>
 <ul>
-<li><strong>一方向性</strong>: ハッシュ値から入力データに関する情報を推測することは不可能であるべきです。</li>
-<li><strong>衝突耐性</strong>: 同じハッシュ値を生成する2つの異なる入力を見つけることは極めて困難であるべきです。</li>
-<li><strong>雪崩効果</strong>: 入力の小さな変更は、出力に大きく予測不可能な変化をもたらすべきです。</li>
+<li><strong>一方向性</strong>：ハッシュ値から入力データに関するいかなる情報も逆算できないこと。</li>
+<li><strong>耐衝突性</strong>：異なる 2 つの入力で同じハッシュ値になるものを見つけることが、極めて困難であること。</li>
+<li><strong>アバランシェ効果</strong>：入力のわずかな変化が、出力の大きく予測不能な変化を引き起こすこと。</li>
 </ul>
-<p>**「均等分散」と「衝突耐性」は2つの別々の概念**であることに注意してください。均等分散を満たしても、必ずしも衝突耐性があるとは限りません。例えば、ランダムな入力<code>key</code>の下で、ハッシュ関数<code>key % 100</code>は均等に分散された出力を生成できます。しかし、このハッシュアルゴリズムは過度にシンプルで、下二桁が同じすべての<code>key</code>は同じ出力を持つため、ハッシュ値から使用可能な<code>key</code>を簡単に推測でき、パスワードを破ることができます。</p>
+<p>注意してほしいのは、**「均一分布」と「耐衝突性」は独立した 2 つの概念である**という点です。均一分布を満たしていても、耐衝突性を満たすとは限りません。たとえば、入力 <code>key</code> がランダムである場合、ハッシュ関数 <code>key % 100</code> は均一に分布した出力を生成できます。しかし、このハッシュアルゴリズムはあまりにも単純で、下 2 桁が同じ <code>key</code> はすべて同じ出力になります。そのため、ハッシュ値から利用可能な <code>key</code> を容易に逆算でき、結果としてパスワードが破られてしまいます。</p>
 <h2 id="632">6.3.2 &nbsp; ハッシュアルゴリズムの設計<a class="headerlink" href="#632" title="Permanent link">&para;</a></h2>
-<p>ハッシュアルゴリズムの設計は多くの要因を考慮する必要がある複雑な問題です。しかし、要求が少ない一部のシナリオでは、いくつかの簡単なハッシュアルゴリズムを設計することもできます。</p>
+<p>ハッシュアルゴリズムの設計は、多くの要素を考慮しなければならない複雑な問題です。しかし、要求の高くない場面であれば、いくつかの単純なハッシュアルゴリズムを設計することもできます。</p>
 <ul>
-<li><strong>加算ハッシュ</strong>: 入力の各文字のASCIIコードを合計し、合計をハッシュ値として使用します。</li>
-<li><strong>乗算ハッシュ</strong>: 乗算の非相関性を利用し、各ラウンドで定数を乗算し、各文字のASCIIコードをハッシュ値に累積します。</li>
-<li><strong>XORハッシュ</strong>: 入力データの各要素をXORすることでハッシュ値を累積します。</li>
-<li><strong>回転ハッシュ</strong>: 各文字のASCIIコードをハッシュ値に累積し、各累積前にハッシュ値に回転操作を実行します。</li>
+<li><strong>加算ハッシュ</strong>：入力の各文字の ASCII コードを足し合わせ、その合計をハッシュ値とします。</li>
+<li><strong>乗算ハッシュ</strong>：乗算の非相関性を利用し、各ラウンドで定数を掛けながら、各文字の ASCII コードをハッシュ値に累積します。</li>
+<li><strong>XOR ハッシュ</strong>：入力データの各要素を XOR 演算で 1 つのハッシュ値に累積します。</li>
+<li><strong>回転ハッシュ</strong>：各文字の ASCII コードを 1 つのハッシュ値に累積し、各回の累積前にハッシュ値を回転させます。</li>
 </ul>
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 <div class="highlight"><span class="filename">simple_hash.py</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">add_hash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span> <span class="nb">str</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;加法ハッシュ&quot;&quot;&quot;</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;加算ハッシュ&quot;&quot;&quot;</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a>    <span class="nb">hash</span> <span class="o">=</span> <span class="mi">0</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a>    <span class="n">modulus</span> <span class="o">=</span> <span class="mi">1000000007</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a>    <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">key</span><span class="p">:</span>
@@ -4426,7 +4448,7 @@
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a>    <span class="k">return</span> <span class="nb">hash</span> <span class="o">%</span> <span class="n">modulus</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="k">def</span><span class="w"> </span><span class="nf">mul_hash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span> <span class="nb">str</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;乗法ハッシュ&quot;&quot;&quot;</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;乗算ハッシュ&quot;&quot;&quot;</span>
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a>    <span class="nb">hash</span> <span class="o">=</span> <span class="mi">0</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a>    <span class="n">modulus</span> <span class="o">=</span> <span class="mi">1000000007</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a>    <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">key</span><span class="p">:</span>
@@ -4434,7 +4456,7 @@
 <a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a>    <span class="k">return</span> <span class="nb">hash</span> <span class="o">%</span> <span class="n">modulus</span>
 <a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a>
 <a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="k">def</span><span class="w"> </span><span class="nf">xor_hash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span> <span class="nb">str</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;XORハッシュ&quot;&quot;&quot;</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;XOR ハッシュ&quot;&quot;&quot;</span>
 <a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a>    <span class="nb">hash</span> <span class="o">=</span> <span class="mi">0</span>
 <a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a>    <span class="n">modulus</span> <span class="o">=</span> <span class="mi">1000000007</span>
 <a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a>    <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">key</span><span class="p">:</span>
@@ -4471,7 +4493,7 @@
 <a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">hash</span><span class="p">;</span>
 <a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="p">}</span>
 <a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a>
-<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="cm">/* XORハッシュ */</span>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="cm">/* XOR ハッシュ */</span>
 <a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="kt">int</span><span class="w"> </span><span class="nf">xorHash</span><span class="p">(</span><span class="n">string</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
@@ -4513,7 +4535,7 @@
 <a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">hash</span><span class="p">;</span>
 <a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="p">}</span>
 <a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a>
-<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="cm">/* XORハッシュ */</span>
+<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="cm">/* XOR ハッシュ */</span>
 <a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="kt">int</span><span class="w"> </span><span class="nf">xorHash</span><span class="p">(</span><span class="n">String</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
@@ -4535,110 +4557,461 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">simple_hash.cs</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">simple_hash</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">AddHash</span><span class="p">}</span>
-<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
-<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">simple_hash</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MulHash</span><span class="p">}</span>
-<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a>
-<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="na">[class]</span><span class="p">{</span><span class="n">simple_hash</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">XorHash</span><span class="p">}</span>
-<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a>
-<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="na">[class]</span><span class="p">{</span><span class="n">simple_hash</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">RotHash</span><span class="p">}</span>
+<div class="highlight"><span class="filename">simple_hash.cs</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 加算ハッシュ */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">AddHash</span><span class="p">(</span><span class="kt">string</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">hash</span><span class="p">;</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="p">}</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="cm">/* 乗算ハッシュ */</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">MulHash</span><span class="p">(</span><span class="kt">string</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">    </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="mi">31</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">hash</span><span class="p">;</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="p">}</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="cm">/* XOR ハッシュ */</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="kt">int</span><span class="w"> </span><span class="nf">XorHash</span><span class="p">(</span><span class="kt">string</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">^=</span><span class="w"> </span><span class="n">c</span><span class="p">;</span>
+<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="p">}</span>
+<a id="__codelineno-4-30" name="__codelineno-4-30" href="#__codelineno-4-30"></a>
+<a id="__codelineno-4-31" name="__codelineno-4-31" href="#__codelineno-4-31"></a><span class="cm">/* 回転ハッシュ */</span>
+<a id="__codelineno-4-32" name="__codelineno-4-32" href="#__codelineno-4-32"></a><span class="kt">int</span><span class="w"> </span><span class="nf">RotHash</span><span class="p">(</span><span class="kt">string</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-33" name="__codelineno-4-33" href="#__codelineno-4-33"></a><span class="w">    </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-4-34" name="__codelineno-4-34" href="#__codelineno-4-34"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-4-35" name="__codelineno-4-35" href="#__codelineno-4-35"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-36" name="__codelineno-4-36" href="#__codelineno-4-36"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">((</span><span class="n">hash</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="mi">28</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-4-37" name="__codelineno-4-37" href="#__codelineno-4-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-38" name="__codelineno-4-38" href="#__codelineno-4-38"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">hash</span><span class="p">;</span>
+<a id="__codelineno-4-39" name="__codelineno-4-39" href="#__codelineno-4-39"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">simple_hash.go</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">addHash</span><span class="p">}</span>
-<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
-<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">mulHash</span><span class="p">}</span>
-<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>
-<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">xorHash</span><span class="p">}</span>
-<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a>
-<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">rotHash</span><span class="p">}</span>
+<div class="highlight"><span class="filename">simple_hash.go</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 加算ハッシュ */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">addHash</span><span class="p">(</span><span class="nx">key</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="kt">int64</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">modulus</span><span class="w"> </span><span class="kt">int64</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="nx">modulus</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1000000007</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="p">[]</span><span class="nb">byte</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">        </span><span class="nx">hash</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="nx">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nb">int64</span><span class="p">(</span><span class="nx">b</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">modulus</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">hash</span><span class="p">)</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="p">}</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="cm">/* 乗算ハッシュ */</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="kd">func</span><span class="w"> </span><span class="nx">mulHash</span><span class="p">(</span><span class="nx">key</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="kt">int64</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">modulus</span><span class="w"> </span><span class="kt">int64</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">    </span><span class="nx">modulus</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1000000007</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="p">[]</span><span class="nb">byte</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="w">        </span><span class="nx">hash</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="mi">31</span><span class="o">*</span><span class="nx">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nb">int64</span><span class="p">(</span><span class="nx">b</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">modulus</span>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">hash</span><span class="p">)</span>
+<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="p">}</span>
+<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a>
+<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="cm">/* XOR ハッシュ */</span>
+<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a><span class="kd">func</span><span class="w"> </span><span class="nx">xorHash</span><span class="p">(</span><span class="nx">key</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a><span class="w">    </span><span class="nx">hash</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a><span class="w">    </span><span class="nx">modulus</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1000000007</span>
+<a id="__codelineno-5-29" name="__codelineno-5-29" href="#__codelineno-5-29"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="p">[]</span><span class="nb">byte</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-30" name="__codelineno-5-30" href="#__codelineno-5-30"></a><span class="w">        </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="nx">b</span><span class="p">))</span>
+<a id="__codelineno-5-31" name="__codelineno-5-31" href="#__codelineno-5-31"></a><span class="w">        </span><span class="nx">hash</span><span class="w"> </span><span class="p">^=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">b</span><span class="p">)</span>
+<a id="__codelineno-5-32" name="__codelineno-5-32" href="#__codelineno-5-32"></a><span class="w">        </span><span class="nx">hash</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="mi">31</span><span class="o">*</span><span class="nx">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">b</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">modulus</span>
+<a id="__codelineno-5-33" name="__codelineno-5-33" href="#__codelineno-5-33"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-34" name="__codelineno-5-34" href="#__codelineno-5-34"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="nx">modulus</span>
+<a id="__codelineno-5-35" name="__codelineno-5-35" href="#__codelineno-5-35"></a><span class="p">}</span>
+<a id="__codelineno-5-36" name="__codelineno-5-36" href="#__codelineno-5-36"></a>
+<a id="__codelineno-5-37" name="__codelineno-5-37" href="#__codelineno-5-37"></a><span class="cm">/* 回転ハッシュ */</span>
+<a id="__codelineno-5-38" name="__codelineno-5-38" href="#__codelineno-5-38"></a><span class="kd">func</span><span class="w"> </span><span class="nx">rotHash</span><span class="p">(</span><span class="nx">key</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-39" name="__codelineno-5-39" href="#__codelineno-5-39"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="kt">int64</span>
+<a id="__codelineno-5-40" name="__codelineno-5-40" href="#__codelineno-5-40"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">modulus</span><span class="w"> </span><span class="kt">int64</span>
+<a id="__codelineno-5-41" name="__codelineno-5-41" href="#__codelineno-5-41"></a>
+<a id="__codelineno-5-42" name="__codelineno-5-42" href="#__codelineno-5-42"></a><span class="w">    </span><span class="nx">modulus</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1000000007</span>
+<a id="__codelineno-5-43" name="__codelineno-5-43" href="#__codelineno-5-43"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="p">[]</span><span class="nb">byte</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-44" name="__codelineno-5-44" href="#__codelineno-5-44"></a><span class="w">        </span><span class="nx">hash</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">((</span><span class="nx">hash</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span><span class="w"> </span><span class="p">^</span><span class="w"> </span><span class="p">(</span><span class="nx">hash</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="mi">28</span><span class="p">)</span><span class="w"> </span><span class="p">^</span><span class="w"> </span><span class="nb">int64</span><span class="p">(</span><span class="nx">b</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">modulus</span>
+<a id="__codelineno-5-45" name="__codelineno-5-45" href="#__codelineno-5-45"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-46" name="__codelineno-5-46" href="#__codelineno-5-46"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">hash</span><span class="p">)</span>
+<a id="__codelineno-5-47" name="__codelineno-5-47" href="#__codelineno-5-47"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">simple_hash.swift</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">addHash</span><span class="p">}</span>
-<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
-<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">mulHash</span><span class="p">}</span>
-<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a>
-<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">xorHash</span><span class="p">}</span>
-<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a>
-<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">rotHash</span><span class="p">}</span>
+<div class="highlight"><span class="filename">simple_hash.swift</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 加算ハッシュ */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">addHash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="nb">String</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">hash</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">MODULUS</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1_000_000_007</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">scalar</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">c</span><span class="p">.</span><span class="n">unicodeScalars</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">            </span><span class="n">hash</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nb">Int</span><span class="p">(</span><span class="n">scalar</span><span class="p">.</span><span class="n">value</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">hash</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="p">}</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="cm">/* 乗算ハッシュ */</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="kd">func</span><span class="w"> </span><span class="nf">mulHash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="nb">String</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">hash</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">MODULUS</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1_000_000_007</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">scalar</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">c</span><span class="p">.</span><span class="n">unicodeScalars</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">            </span><span class="n">hash</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="mi">31</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nb">Int</span><span class="p">(</span><span class="n">scalar</span><span class="p">.</span><span class="n">value</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">hash</span>
+<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="p">}</span>
+<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a>
+<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="cm">/* XOR ハッシュ */</span>
+<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="kd">func</span><span class="w"> </span><span class="nf">xorHash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="nb">String</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-27" name="__codelineno-6-27" href="#__codelineno-6-27"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">hash</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-6-28" name="__codelineno-6-28" href="#__codelineno-6-28"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">MODULUS</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1_000_000_007</span>
+<a id="__codelineno-6-29" name="__codelineno-6-29" href="#__codelineno-6-29"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-30" name="__codelineno-6-30" href="#__codelineno-6-30"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">scalar</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">c</span><span class="p">.</span><span class="n">unicodeScalars</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-31" name="__codelineno-6-31" href="#__codelineno-6-31"></a><span class="w">            </span><span class="n">hash</span><span class="w"> </span><span class="o">^=</span><span class="w"> </span><span class="nb">Int</span><span class="p">(</span><span class="n">scalar</span><span class="p">.</span><span class="n">value</span><span class="p">)</span>
+<a id="__codelineno-6-32" name="__codelineno-6-32" href="#__codelineno-6-32"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-33" name="__codelineno-6-33" href="#__codelineno-6-33"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-34" name="__codelineno-6-34" href="#__codelineno-6-34"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="n">MODULUS</span>
+<a id="__codelineno-6-35" name="__codelineno-6-35" href="#__codelineno-6-35"></a><span class="p">}</span>
+<a id="__codelineno-6-36" name="__codelineno-6-36" href="#__codelineno-6-36"></a>
+<a id="__codelineno-6-37" name="__codelineno-6-37" href="#__codelineno-6-37"></a><span class="cm">/* 回転ハッシュ */</span>
+<a id="__codelineno-6-38" name="__codelineno-6-38" href="#__codelineno-6-38"></a><span class="kd">func</span><span class="w"> </span><span class="nf">rotHash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="nb">String</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-39" name="__codelineno-6-39" href="#__codelineno-6-39"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">hash</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-6-40" name="__codelineno-6-40" href="#__codelineno-6-40"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">MODULUS</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1_000_000_007</span>
+<a id="__codelineno-6-41" name="__codelineno-6-41" href="#__codelineno-6-41"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-42" name="__codelineno-6-42" href="#__codelineno-6-42"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">scalar</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">c</span><span class="p">.</span><span class="n">unicodeScalars</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-43" name="__codelineno-6-43" href="#__codelineno-6-43"></a><span class="w">            </span><span class="n">hash</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">((</span><span class="n">hash</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="mi">28</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="nb">Int</span><span class="p">(</span><span class="n">scalar</span><span class="p">.</span><span class="n">value</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span>
+<a id="__codelineno-6-44" name="__codelineno-6-44" href="#__codelineno-6-44"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-45" name="__codelineno-6-45" href="#__codelineno-6-45"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-46" name="__codelineno-6-46" href="#__codelineno-6-46"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">hash</span>
+<a id="__codelineno-6-47" name="__codelineno-6-47" href="#__codelineno-6-47"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">simple_hash.js</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">addHash</span><span class="p">}</span>
-<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
-<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">mulHash</span><span class="p">}</span>
-<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a>
-<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">xorHash</span><span class="p">}</span>
-<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a>
-<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">rotHash</span><span class="p">}</span>
+<div class="highlight"><span class="filename">simple_hash.js</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 加算ハッシュ */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">addHash</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1000000007</span><span class="p">;</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">        </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="nx">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">c</span><span class="p">.</span><span class="nx">charCodeAt</span><span class="p">(</span><span class="mf">0</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">hash</span><span class="p">;</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="p">}</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="cm">/* 乗算ハッシュ */</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">mulHash</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1000000007</span><span class="p">;</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">        </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="mf">31</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">c</span><span class="p">.</span><span class="nx">charCodeAt</span><span class="p">(</span><span class="mf">0</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">hash</span><span class="p">;</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="p">}</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="cm">/* XOR ハッシュ */</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="kd">function</span><span class="w"> </span><span class="nx">xorHash</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1000000007</span><span class="p">;</span>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="w">        </span><span class="nx">hash</span><span class="w"> </span><span class="o">^=</span><span class="w"> </span><span class="nx">c</span><span class="p">.</span><span class="nx">charCodeAt</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-7-29" name="__codelineno-7-29" href="#__codelineno-7-29"></a><span class="p">}</span>
+<a id="__codelineno-7-30" name="__codelineno-7-30" href="#__codelineno-7-30"></a>
+<a id="__codelineno-7-31" name="__codelineno-7-31" href="#__codelineno-7-31"></a><span class="cm">/* 回転ハッシュ */</span>
+<a id="__codelineno-7-32" name="__codelineno-7-32" href="#__codelineno-7-32"></a><span class="kd">function</span><span class="w"> </span><span class="nx">rotHash</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-33" name="__codelineno-7-33" href="#__codelineno-7-33"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-7-34" name="__codelineno-7-34" href="#__codelineno-7-34"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1000000007</span><span class="p">;</span>
+<a id="__codelineno-7-35" name="__codelineno-7-35" href="#__codelineno-7-35"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-36" name="__codelineno-7-36" href="#__codelineno-7-36"></a><span class="w">        </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">((</span><span class="nx">hash</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mf">4</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="nx">hash</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="mf">28</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="nx">c</span><span class="p">.</span><span class="nx">charCodeAt</span><span class="p">(</span><span class="mf">0</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-7-37" name="__codelineno-7-37" href="#__codelineno-7-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-38" name="__codelineno-7-38" href="#__codelineno-7-38"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">hash</span><span class="p">;</span>
+<a id="__codelineno-7-39" name="__codelineno-7-39" href="#__codelineno-7-39"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">simple_hash.ts</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">addHash</span><span class="p">}</span>
-<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
-<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">mulHash</span><span class="p">}</span>
-<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a>
-<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">xorHash</span><span class="p">}</span>
-<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a>
-<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">rotHash</span><span class="p">}</span>
+<div class="highlight"><span class="filename">simple_hash.ts</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 加算ハッシュ */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">addHash</span><span class="p">(</span><span class="nx">key</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1000000007</span><span class="p">;</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">        </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="nx">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">c</span><span class="p">.</span><span class="nx">charCodeAt</span><span class="p">(</span><span class="mf">0</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">hash</span><span class="p">;</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="p">}</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="cm">/* 乗算ハッシュ */</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">mulHash</span><span class="p">(</span><span class="nx">key</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1000000007</span><span class="p">;</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">        </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="mf">31</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">c</span><span class="p">.</span><span class="nx">charCodeAt</span><span class="p">(</span><span class="mf">0</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">hash</span><span class="p">;</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="p">}</span>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a>
+<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="cm">/* XOR ハッシュ */</span>
+<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="kd">function</span><span class="w"> </span><span class="nx">xorHash</span><span class="p">(</span><span class="nx">key</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1000000007</span><span class="p">;</span>
+<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-26" name="__codelineno-8-26" href="#__codelineno-8-26"></a><span class="w">        </span><span class="nx">hash</span><span class="w"> </span><span class="o">^=</span><span class="w"> </span><span class="nx">c</span><span class="p">.</span><span class="nx">charCodeAt</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-8-27" name="__codelineno-8-27" href="#__codelineno-8-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-28" name="__codelineno-8-28" href="#__codelineno-8-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-8-29" name="__codelineno-8-29" href="#__codelineno-8-29"></a><span class="p">}</span>
+<a id="__codelineno-8-30" name="__codelineno-8-30" href="#__codelineno-8-30"></a>
+<a id="__codelineno-8-31" name="__codelineno-8-31" href="#__codelineno-8-31"></a><span class="cm">/* 回転ハッシュ */</span>
+<a id="__codelineno-8-32" name="__codelineno-8-32" href="#__codelineno-8-32"></a><span class="kd">function</span><span class="w"> </span><span class="nx">rotHash</span><span class="p">(</span><span class="nx">key</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-33" name="__codelineno-8-33" href="#__codelineno-8-33"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-8-34" name="__codelineno-8-34" href="#__codelineno-8-34"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1000000007</span><span class="p">;</span>
+<a id="__codelineno-8-35" name="__codelineno-8-35" href="#__codelineno-8-35"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-36" name="__codelineno-8-36" href="#__codelineno-8-36"></a><span class="w">        </span><span class="nx">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">((</span><span class="nx">hash</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mf">4</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="nx">hash</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="mf">28</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="nx">c</span><span class="p">.</span><span class="nx">charCodeAt</span><span class="p">(</span><span class="mf">0</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-8-37" name="__codelineno-8-37" href="#__codelineno-8-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-38" name="__codelineno-8-38" href="#__codelineno-8-38"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">hash</span><span class="p">;</span>
+<a id="__codelineno-8-39" name="__codelineno-8-39" href="#__codelineno-8-39"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">simple_hash.dart</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">addHash</span><span class="p">}</span>
-<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
-<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">mulHash</span><span class="p">}</span>
-<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a>
-<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">xorHash</span><span class="p">}</span>
-<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a>
-<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">rotHash</span><span class="p">}</span>
+<div class="highlight"><span class="filename">simple_hash.dart</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 加算ハッシュ */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">addHash</span><span class="p">(</span><span class="kt">String</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">  </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1000000007</span><span class="p">;</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="n">codeUnitAt</span><span class="p">(</span><span class="n">i</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">hash</span><span class="p">;</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="p">}</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="cm">/* 乗算ハッシュ */</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="kt">int</span><span class="w"> </span><span class="n">mulHash</span><span class="p">(</span><span class="kt">String</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">  </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1000000007</span><span class="p">;</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">    </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="m">31</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="n">codeUnitAt</span><span class="p">(</span><span class="n">i</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">hash</span><span class="p">;</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="p">}</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="cm">/* XOR ハッシュ */</span>
+<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="kt">int</span><span class="w"> </span><span class="n">xorHash</span><span class="p">(</span><span class="kt">String</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="w">  </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1000000007</span><span class="p">;</span>
+<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="w">    </span><span class="n">hash</span><span class="w"> </span><span class="o">^=</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="n">codeUnitAt</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="p">}</span>
+<a id="__codelineno-9-30" name="__codelineno-9-30" href="#__codelineno-9-30"></a>
+<a id="__codelineno-9-31" name="__codelineno-9-31" href="#__codelineno-9-31"></a><span class="cm">/* 回転ハッシュ */</span>
+<a id="__codelineno-9-32" name="__codelineno-9-32" href="#__codelineno-9-32"></a><span class="kt">int</span><span class="w"> </span><span class="n">rotHash</span><span class="p">(</span><span class="kt">String</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-33" name="__codelineno-9-33" href="#__codelineno-9-33"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-9-34" name="__codelineno-9-34" href="#__codelineno-9-34"></a><span class="w">  </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1000000007</span><span class="p">;</span>
+<a id="__codelineno-9-35" name="__codelineno-9-35" href="#__codelineno-9-35"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-36" name="__codelineno-9-36" href="#__codelineno-9-36"></a><span class="w">    </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">((</span><span class="n">hash</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="m">4</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="m">28</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="n">codeUnitAt</span><span class="p">(</span><span class="n">i</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-9-37" name="__codelineno-9-37" href="#__codelineno-9-37"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-9-38" name="__codelineno-9-38" href="#__codelineno-9-38"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">hash</span><span class="p">;</span>
+<a id="__codelineno-9-39" name="__codelineno-9-39" href="#__codelineno-9-39"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">simple_hash.rs</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">add_hash</span><span class="p">}</span>
-<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
-<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">mul_hash</span><span class="p">}</span>
-<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a>
-<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">xor_hash</span><span class="p">}</span>
-<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a>
-<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">rot_hash</span><span class="p">}</span>
+<div class="highlight"><span class="filename">simple_hash.rs</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 加算ハッシュ */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">add_hash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="kt">str</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0_</span><span class="k">i64</span><span class="p">;</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">:</span><span class="w"> </span><span class="kt">i64</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="n">chars</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i64</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="n">hash</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="p">}</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="cm">/* 乗算ハッシュ */</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="k">fn</span><span class="w"> </span><span class="nf">mul_hash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="kt">str</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0_</span><span class="k">i64</span><span class="p">;</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">:</span><span class="w"> </span><span class="kt">i64</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="n">chars</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="mi">31</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i64</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a>
+<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w">    </span><span class="n">hash</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span>
+<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="p">}</span>
+<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a>
+<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="cm">/* XOR ハッシュ */</span>
+<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="k">fn</span><span class="w"> </span><span class="nf">xor_hash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="kt">str</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0_</span><span class="k">i64</span><span class="p">;</span>
+<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">:</span><span class="w"> </span><span class="kt">i64</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a>
+<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="n">chars</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">^=</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i64</span><span class="p">;</span>
+<a id="__codelineno-10-32" name="__codelineno-10-32" href="#__codelineno-10-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-33" name="__codelineno-10-33" href="#__codelineno-10-33"></a>
+<a id="__codelineno-10-34" name="__codelineno-10-34" href="#__codelineno-10-34"></a><span class="w">    </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">)</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span>
+<a id="__codelineno-10-35" name="__codelineno-10-35" href="#__codelineno-10-35"></a><span class="p">}</span>
+<a id="__codelineno-10-36" name="__codelineno-10-36" href="#__codelineno-10-36"></a>
+<a id="__codelineno-10-37" name="__codelineno-10-37" href="#__codelineno-10-37"></a><span class="cm">/* 回転ハッシュ */</span>
+<a id="__codelineno-10-38" name="__codelineno-10-38" href="#__codelineno-10-38"></a><span class="k">fn</span><span class="w"> </span><span class="nf">rot_hash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="kt">str</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-39" name="__codelineno-10-39" href="#__codelineno-10-39"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0_</span><span class="k">i64</span><span class="p">;</span>
+<a id="__codelineno-10-40" name="__codelineno-10-40" href="#__codelineno-10-40"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">:</span><span class="w"> </span><span class="kt">i64</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-10-41" name="__codelineno-10-41" href="#__codelineno-10-41"></a>
+<a id="__codelineno-10-42" name="__codelineno-10-42" href="#__codelineno-10-42"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="n">chars</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-43" name="__codelineno-10-43" href="#__codelineno-10-43"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">((</span><span class="n">hash</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="mi">28</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i64</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-10-44" name="__codelineno-10-44" href="#__codelineno-10-44"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-45" name="__codelineno-10-45" href="#__codelineno-10-45"></a>
+<a id="__codelineno-10-46" name="__codelineno-10-46" href="#__codelineno-10-46"></a><span class="w">    </span><span class="n">hash</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span>
+<a id="__codelineno-10-47" name="__codelineno-10-47" href="#__codelineno-10-47"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">simple_hash.c</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">addHash</span><span class="p">}</span>
-<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
-<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">mulHash</span><span class="p">}</span>
-<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a>
-<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">xorHash</span><span class="p">}</span>
-<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a>
-<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">rotHash</span><span class="p">}</span>
+<div class="highlight"><span class="filename">simple_hash.c</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 加算ハッシュ */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">addHash</span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="kt">long</span><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">strlen</span><span class="p">(</span><span class="n">key</span><span class="p">);</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="kt">unsigned</span><span class="w"> </span><span class="kt">char</span><span class="p">)</span><span class="n">key</span><span class="p">[</span><span class="n">i</span><span class="p">])</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">hash</span><span class="p">;</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="p">}</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="cm">/* 乗算ハッシュ */</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">mulHash</span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">    </span><span class="kt">long</span><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">strlen</span><span class="p">(</span><span class="n">key</span><span class="p">);</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="mi">31</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="kt">unsigned</span><span class="w"> </span><span class="kt">char</span><span class="p">)</span><span class="n">key</span><span class="p">[</span><span class="n">i</span><span class="p">])</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">hash</span><span class="p">;</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="p">}</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="cm">/* XOR ハッシュ */</span>
+<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="kt">int</span><span class="w"> </span><span class="nf">xorHash</span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a>
+<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">strlen</span><span class="p">(</span><span class="n">key</span><span class="p">);</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">^=</span><span class="w"> </span><span class="p">(</span><span class="kt">unsigned</span><span class="w"> </span><span class="kt">char</span><span class="p">)</span><span class="n">key</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-11-30" name="__codelineno-11-30" href="#__codelineno-11-30"></a><span class="p">}</span>
+<a id="__codelineno-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></a>
+<a id="__codelineno-11-32" name="__codelineno-11-32" href="#__codelineno-11-32"></a><span class="cm">/* 回転ハッシュ */</span>
+<a id="__codelineno-11-33" name="__codelineno-11-33" href="#__codelineno-11-33"></a><span class="kt">int</span><span class="w"> </span><span class="nf">rotHash</span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-34" name="__codelineno-11-34" href="#__codelineno-11-34"></a><span class="w">    </span><span class="kt">long</span><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-11-35" name="__codelineno-11-35" href="#__codelineno-11-35"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-11-36" name="__codelineno-11-36" href="#__codelineno-11-36"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">strlen</span><span class="p">(</span><span class="n">key</span><span class="p">);</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-37" name="__codelineno-11-37" href="#__codelineno-11-37"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">((</span><span class="n">hash</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="mi">28</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="kt">unsigned</span><span class="w"> </span><span class="kt">char</span><span class="p">)</span><span class="n">key</span><span class="p">[</span><span class="n">i</span><span class="p">])</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-11-38" name="__codelineno-11-38" href="#__codelineno-11-38"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-39" name="__codelineno-11-39" href="#__codelineno-11-39"></a>
+<a id="__codelineno-11-40" name="__codelineno-11-40" href="#__codelineno-11-40"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">hash</span><span class="p">;</span>
+<a id="__codelineno-11-41" name="__codelineno-11-41" href="#__codelineno-11-41"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">simple_hash.kt</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">addHash</span><span class="p">}</span>
-<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
-<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">mulHash</span><span class="p">}</span>
-<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
-<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">xorHash</span><span class="p">}</span>
-<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a>
-<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">rotHash</span><span class="p">}</span>
+<div class="highlight"><span class="filename">simple_hash.kt</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="cm">/* 加算ハッシュ */</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">addHash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">String</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0L</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1000000007</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="na">toCharArray</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">.</span><span class="na">code</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">hash</span><span class="p">.</span><span class="na">toInt</span><span class="p">()</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="p">}</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="cm">/* 乗算ハッシュ */</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">mulHash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">String</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0L</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1000000007</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="na">toCharArray</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="m">31</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">.</span><span class="na">code</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">hash</span><span class="p">.</span><span class="na">toInt</span><span class="p">()</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="p">}</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="cm">/* XOR ハッシュ */</span>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">xorHash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">String</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1000000007</span>
+<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="na">toCharArray</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="n">xor</span><span class="w"> </span><span class="n">c</span><span class="p">.</span><span class="na">code</span>
+<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="n">and</span><span class="w"> </span><span class="n">MODULUS</span>
+<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a><span class="p">}</span>
+<a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a>
+<a id="__codelineno-12-31" name="__codelineno-12-31" href="#__codelineno-12-31"></a><span class="cm">/* 回転ハッシュ */</span>
+<a id="__codelineno-12-32" name="__codelineno-12-32" href="#__codelineno-12-32"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">rotHash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">String</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-12-33" name="__codelineno-12-33" href="#__codelineno-12-33"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0L</span>
+<a id="__codelineno-12-34" name="__codelineno-12-34" href="#__codelineno-12-34"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1000000007</span>
+<a id="__codelineno-12-35" name="__codelineno-12-35" href="#__codelineno-12-35"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="na">toCharArray</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-12-36" name="__codelineno-12-36" href="#__codelineno-12-36"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">((</span><span class="n">hash</span><span class="w"> </span><span class="n">shl</span><span class="w"> </span><span class="m">4</span><span class="p">)</span><span class="w"> </span><span class="n">xor</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="n">shr</span><span class="w"> </span><span class="m">28</span><span class="p">)</span><span class="w"> </span><span class="n">xor</span><span class="w"> </span><span class="n">c</span><span class="p">.</span><span class="na">code</span><span class="p">.</span><span class="na">toLong</span><span class="p">())</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span>
+<a id="__codelineno-12-37" name="__codelineno-12-37" href="#__codelineno-12-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-12-38" name="__codelineno-12-38" href="#__codelineno-12-38"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">hash</span><span class="p">.</span><span class="na">toInt</span><span class="p">()</span>
+<a id="__codelineno-12-39" name="__codelineno-12-39" href="#__codelineno-12-39"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">simple_hash.rb</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">add_hash</span><span class="p">}</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a>
-<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">mul_hash</span><span class="p">}</span>
-<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>
-<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">xor_hash</span><span class="p">}</span>
-<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>
-<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">rot_hash</span><span class="p">}</span>
+<div class="highlight"><span class="filename">simple_hash.rb</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="c1">### 加算ハッシュ ###</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">add_hash</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="w">  </span><span class="nb">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="w">  </span><span class="n">modulus</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1_000_000_007</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>
+<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="w">  </span><span class="n">key</span><span class="o">.</span><span class="n">each_char</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">c</span><span class="o">|</span><span class="w"> </span><span class="nb">hash</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">c</span><span class="o">.</span><span class="n">ord</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>
+<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="w">  </span><span class="nb">hash</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">modulus</span>
+<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="k">end</span>
+<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>
+<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="c1">### 乗算ハッシュ ###</span>
+<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a><span class="k">def</span><span class="w"> </span><span class="nf">mul_hash</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a><span class="w">  </span><span class="nb">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a><span class="w">  </span><span class="n">modulus</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1_000_000_007</span>
+<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a>
+<a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a><span class="w">  </span><span class="n">key</span><span class="o">.</span><span class="n">each_char</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">c</span><span class="o">|</span><span class="w"> </span><span class="nb">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">31</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="o">.</span><span class="n">ord</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>
+<a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a><span class="w">  </span><span class="nb">hash</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">modulus</span>
+<a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a><span class="k">end</span>
+<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a>
+<a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a><span class="c1">### XOR ハッシュ ###</span>
+<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a><span class="k">def</span><span class="w"> </span><span class="nf">xor_hash</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a><span class="w">  </span><span class="nb">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-13-24" name="__codelineno-13-24" href="#__codelineno-13-24"></a><span class="w">  </span><span class="n">modulus</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1_000_000_007</span>
+<a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a>
+<a id="__codelineno-13-26" name="__codelineno-13-26" href="#__codelineno-13-26"></a><span class="w">  </span><span class="n">key</span><span class="o">.</span><span class="n">each_char</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">c</span><span class="o">|</span><span class="w"> </span><span class="nb">hash</span><span class="w"> </span><span class="o">^=</span><span class="w"> </span><span class="n">c</span><span class="o">.</span><span class="n">ord</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-13-27" name="__codelineno-13-27" href="#__codelineno-13-27"></a>
+<a id="__codelineno-13-28" name="__codelineno-13-28" href="#__codelineno-13-28"></a><span class="w">  </span><span class="nb">hash</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">modulus</span>
+<a id="__codelineno-13-29" name="__codelineno-13-29" href="#__codelineno-13-29"></a><span class="k">end</span>
+<a id="__codelineno-13-30" name="__codelineno-13-30" href="#__codelineno-13-30"></a>
+<a id="__codelineno-13-31" name="__codelineno-13-31" href="#__codelineno-13-31"></a><span class="c1">### 回転ハッシュ ###</span>
+<a id="__codelineno-13-32" name="__codelineno-13-32" href="#__codelineno-13-32"></a><span class="k">def</span><span class="w"> </span><span class="nf">rot_hash</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-13-33" name="__codelineno-13-33" href="#__codelineno-13-33"></a><span class="w">  </span><span class="nb">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-13-34" name="__codelineno-13-34" href="#__codelineno-13-34"></a><span class="w">  </span><span class="n">modulus</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1_000_000_007</span>
+<a id="__codelineno-13-35" name="__codelineno-13-35" href="#__codelineno-13-35"></a>
+<a id="__codelineno-13-36" name="__codelineno-13-36" href="#__codelineno-13-36"></a><span class="w">  </span><span class="n">key</span><span class="o">.</span><span class="n">each_char</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">c</span><span class="o">|</span><span class="w"> </span><span class="nb">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="nb">hash</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="nb">hash</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="mi">28</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="n">c</span><span class="o">.</span><span class="n">ord</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-13-37" name="__codelineno-13-37" href="#__codelineno-13-37"></a>
+<a id="__codelineno-13-38" name="__codelineno-13-38" href="#__codelineno-13-38"></a><span class="w">  </span><span class="nb">hash</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">modulus</span>
+<a id="__codelineno-13-39" name="__codelineno-13-39" href="#__codelineno-13-39"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>各ハッシュアルゴリズムの最後のステップが大きな素数<span class="arithmatex">\(1000000007\)</span>の剰余を取ることで、ハッシュ値が適切な範囲内にあることを保証していることが観察されます。なぜ素数の剰余を取ることが強調されるのか、または合成数の剰余を取ることの欠点は何かを考える価値があります。これは興味深い質問です。</p>
-<p>結論として：<strong>大きな素数を剰余として使用することで、ハッシュ値の均等分散を最大化できます</strong>。素数は他の数と共通因子を持たないため、剰余演算によって引き起こされる周期的パターンを減らし、ハッシュ衝突を回避できます。</p>
-<p>例えば、合成数<span class="arithmatex">\(9\)</span>を剰余として選択するとします。これは<span class="arithmatex">\(3\)</span>で割り切れるため、<span class="arithmatex">\(3\)</span>で割り切れるすべての<code>key</code>はハッシュ値<span class="arithmatex">\(0\)</span>、<span class="arithmatex">\(3\)</span>、<span class="arithmatex">\(6\)</span>にマッピングされます。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20add_hash%28key%3A%20str%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%8A%A0%E7%AE%97%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%22%22%22%0A%20%20%20%20hash%20%3D%200%0A%20%20%20%20modulus%20%3D%201000000007%0A%20%20%20%20for%20c%20in%20key%3A%0A%20%20%20%20%20%20%20%20hash%20%2B%3D%20ord%28c%29%0A%20%20%20%20return%20hash%20%25%20modulus%0A%0A%0Adef%20mul_hash%28key%3A%20str%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%B9%97%E7%AE%97%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%22%22%22%0A%20%20%20%20hash%20%3D%200%0A%20%20%20%20modulus%20%3D%201000000007%0A%20%20%20%20for%20c%20in%20key%3A%0A%20%20%20%20%20%20%20%20hash%20%3D%2031%20%2A%20hash%20%2B%20ord%28c%29%0A%20%20%20%20return%20hash%20%25%20modulus%0A%0A%0Adef%20xor_hash%28key%3A%20str%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22XOR%20%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%22%22%22%0A%20%20%20%20hash%20%3D%200%0A%20%20%20%20modulus%20%3D%201000000007%0A%20%20%20%20for%20c%20in%20key%3A%0A%20%20%20%20%20%20%20%20hash%20%5E%3D%20ord%28c%29%0A%20%20%20%20return%20hash%20%25%20modulus%0A%0A%0Adef%20rot_hash%28key%3A%20str%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%9B%9E%E8%BB%A2%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%22%22%22%0A%20%20%20%20hash%20%3D%200%0A%20%20%20%20modulus%20%3D%201000000007%0A%20%20%20%20for%20c%20in%20key%3A%0A%20%20%20%20%20%20%20%20hash%20%3D%20%28hash%20%3C%3C%204%29%20%5E%20%28hash%20%3E%3E%2028%29%20%5E%20ord%28c%29%0A%20%20%20%20return%20hash%20%25%20modulus%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20key%20%3D%20%22Hello%20%E3%82%A2%E3%83%AB%E3%82%B4%E3%83%AA%E3%82%BA%E3%83%A0%22%0A%0A%20%20%20%20hash%20%3D%20add_hash%28key%29%0A%20%20%20%20print%28f%22%E5%8A%A0%E7%AE%97%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%E5%80%A4%E3%81%AF%20%7Bhash%7D%22%29%0A%0A%20%20%20%20hash%20%3D%20mul_hash%28key%29%0A%20%20%20%20print%28f%22%E4%B9%97%E7%AE%97%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%E5%80%A4%E3%81%AF%20%7Bhash%7D%22%29%0A%0A%20%20%20%20hash%20%3D%20xor_hash%28key%29%0A%20%20%20%20print%28f%22XOR%20%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%E5%80%A4%E3%81%AF%20%7Bhash%7D%22%29%0A%0A%20%20%20%20hash%20%3D%20rot_hash%28key%29%0A%20%20%20%20print%28f%22%E5%9B%9E%E8%BB%A2%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%E5%80%A4%E3%81%AF%20%7Bhash%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20add_hash%28key%3A%20str%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%8A%A0%E7%AE%97%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%22%22%22%0A%20%20%20%20hash%20%3D%200%0A%20%20%20%20modulus%20%3D%201000000007%0A%20%20%20%20for%20c%20in%20key%3A%0A%20%20%20%20%20%20%20%20hash%20%2B%3D%20ord%28c%29%0A%20%20%20%20return%20hash%20%25%20modulus%0A%0A%0Adef%20mul_hash%28key%3A%20str%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%B9%97%E7%AE%97%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%22%22%22%0A%20%20%20%20hash%20%3D%200%0A%20%20%20%20modulus%20%3D%201000000007%0A%20%20%20%20for%20c%20in%20key%3A%0A%20%20%20%20%20%20%20%20hash%20%3D%2031%20%2A%20hash%20%2B%20ord%28c%29%0A%20%20%20%20return%20hash%20%25%20modulus%0A%0A%0Adef%20xor_hash%28key%3A%20str%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22XOR%20%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%22%22%22%0A%20%20%20%20hash%20%3D%200%0A%20%20%20%20modulus%20%3D%201000000007%0A%20%20%20%20for%20c%20in%20key%3A%0A%20%20%20%20%20%20%20%20hash%20%5E%3D%20ord%28c%29%0A%20%20%20%20return%20hash%20%25%20modulus%0A%0A%0Adef%20rot_hash%28key%3A%20str%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%9B%9E%E8%BB%A2%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%22%22%22%0A%20%20%20%20hash%20%3D%200%0A%20%20%20%20modulus%20%3D%201000000007%0A%20%20%20%20for%20c%20in%20key%3A%0A%20%20%20%20%20%20%20%20hash%20%3D%20%28hash%20%3C%3C%204%29%20%5E%20%28hash%20%3E%3E%2028%29%20%5E%20ord%28c%29%0A%20%20%20%20return%20hash%20%25%20modulus%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20key%20%3D%20%22Hello%20%E3%82%A2%E3%83%AB%E3%82%B4%E3%83%AA%E3%82%BA%E3%83%A0%22%0A%0A%20%20%20%20hash%20%3D%20add_hash%28key%29%0A%20%20%20%20print%28f%22%E5%8A%A0%E7%AE%97%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%E5%80%A4%E3%81%AF%20%7Bhash%7D%22%29%0A%0A%20%20%20%20hash%20%3D%20mul_hash%28key%29%0A%20%20%20%20print%28f%22%E4%B9%97%E7%AE%97%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%E5%80%A4%E3%81%AF%20%7Bhash%7D%22%29%0A%0A%20%20%20%20hash%20%3D%20xor_hash%28key%29%0A%20%20%20%20print%28f%22XOR%20%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%E5%80%A4%E3%81%AF%20%7Bhash%7D%22%29%0A%0A%20%20%20%20hash%20%3D%20rot_hash%28key%29%0A%20%20%20%20print%28f%22%E5%9B%9E%E8%BB%A2%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%E5%80%A4%E3%81%AF%20%7Bhash%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>見て分かるように、各ハッシュアルゴリズムの最後のステップでは、大きな素数 <span class="arithmatex">\(1000000007\)</span> で剰余を取り、ハッシュ値が適切な範囲に収まるようにしています。ここで考えてみる価値があるのは、なぜ素数での剰余を強調するのか、あるいは合成数で剰余を取ることにどんな欠点があるのか、という点です。これは興味深い問題です。</p>
+<p>先に結論を述べると、<strong>法として大きな素数を使うと、ハッシュ値が均一に分布することを最大限に保証できます</strong>。素数はほかの数と公約数を持たないため、剰余演算によって生じる周期的なパターンを減らし、ハッシュ衝突を避けやすくなります。</p>
+<p>たとえば、法として合成数 <span class="arithmatex">\(9\)</span> を選ぶとします。これは <span class="arithmatex">\(3\)</span> で割り切れるため、<span class="arithmatex">\(3\)</span> で割り切れるすべての <code>key</code> は、<span class="arithmatex">\(0\)</span>、<span class="arithmatex">\(3\)</span>、<span class="arithmatex">\(6\)</span> の 3 つのハッシュ値に写像されます。</p>
 <div class="arithmatex">\[
 \begin{aligned}
 \text{modulus} &amp; = 9 \newline
@@ -4646,7 +5019,7 @@
 \text{hash} &amp; = \{ 0, 3, 6, 0, 3, 6, 0, 3, 6, 0, 3, 6,\dots \}
 \end{aligned}
 \]</div>
-<p>入力<code>key</code>がたまたまこの種の等差数列分布を持つ場合、ハッシュ値がクラスターし、ハッシュ衝突を悪化させます。今度は<code>modulus</code>を素数<span class="arithmatex">\(13\)</span>に置き換えるとします。<code>key</code>と<code>modulus</code>の間に共通因子がないため、出力ハッシュ値の均等性が大幅に改善されます。</p>
+<p>入力 <code>key</code> がたまたまこのような等差数列の分布をしていると、ハッシュ値に偏りが生じ、ハッシュ衝突がさらに深刻になります。そこで <code>modulus</code> を素数 <span class="arithmatex">\(13\)</span> に置き換えると仮定すると、<code>key</code> と <code>modulus</code> の間に公約数が存在しないため、出力されるハッシュ値の均一性は明らかに向上します。</p>
 <div class="arithmatex">\[
 \begin{aligned}
 \text{modulus} &amp; = 13 \newline
@@ -4654,16 +5027,16 @@
 \text{hash} &amp; = \{ 0, 3, 6, 9, 12, 2, 5, 8, 11, 1, 4, 7, \dots \}
 \end{aligned}
 \]</div>
-<p><code>key</code>がランダムで均等に分散されることが保証されている場合、剰余として素数または合成数を選択しても、両方とも均等に分散されたハッシュ値を生成できることは注目に値します。しかし、<code>key</code>の分布にある種の周期性がある場合、合成数の剰余はクラスタリングを引き起こしやすくなります。</p>
-<p>要約すると、通常は素数を剰余として選択し、この素数は周期的パターンを可能な限り排除し、ハッシュアルゴリズムの堅牢性を向上させるために十分大きくある必要があります。</p>
+<p>補足すると、<code>key</code> がランダムかつ均一に分布していると保証できるなら、法に素数を選んでも合成数を選んでも構いません。どちらでも均一に分布したハッシュ値を出力できます。しかし、<code>key</code> の分布に何らかの周期性がある場合、合成数で剰余を取るほうが偏りが生じやすくなります。</p>
+<p>要するに、通常は法として素数を選び、その素数はできるだけ大きいほうが望ましいです。そうすることで周期的なパターンをできる限り取り除き、ハッシュアルゴリズムの堅牢性を高められます。</p>
 <h2 id="633">6.3.3 &nbsp; 一般的なハッシュアルゴリズム<a class="headerlink" href="#633" title="Permanent link">&para;</a></h2>
-<p>上記で言及した簡単なハッシュアルゴリズムはかなり「脆弱」で、ハッシュアルゴリズムの設計目標から程遠いことは難しくありません。例えば、加算とXORは交換法則に従うため、加算ハッシュとXORハッシュは同じ内容だが順序が異なる文字列を区別できず、ハッシュ衝突を悪化させ、セキュリティ問題を引き起こす可能性があります。</p>
-<p>実際には、通常MD5、SHA-1、SHA-2、SHA-3などの標準ハッシュアルゴリズムを使用します。これらは任意の長さの入力データを固定長のハッシュ値にマッピングできます。</p>
-<p>過去1世紀にわたって、ハッシュアルゴリズムは継続的なアップグレードと最適化のプロセスにありました。一部の研究者はハッシュアルゴリズムの性能向上に努め、ハッカーを含む他の人々はハッシュアルゴリズムのセキュリティ問題を見つけることに専念しています。以下の表は、実用的なアプリケーションで一般的に使用されるハッシュアルゴリズムを示しています。</p>
+<p>上で紹介した単純なハッシュアルゴリズムは、どれも比較的「脆弱」であり、ハッシュアルゴリズムの設計目標にはほど遠いことが分かります。たとえば、加算と XOR は交換法則を満たすため、加算ハッシュと XOR ハッシュでは、内容が同じで順序だけ異なる文字列を区別できません。これはハッシュ衝突を悪化させ、一部の安全上の問題を引き起こす可能性があります。</p>
+<p>実際には、MD5、SHA-1、SHA-2、SHA-3 などの標準的なハッシュアルゴリズムを用いることが一般的です。これらは任意長の入力データを、固定長のハッシュ値へ写像できます。</p>
+<p>ここ 1 世紀近くの間、ハッシュアルゴリズムは継続的に改良と最適化が進められてきました。ある研究者たちは性能向上に取り組み、別の研究者やハッカーたちは安全性の弱点を探し続けてきました。次の表は、実際の応用でよく使われるハッシュアルゴリズムを示したものです。</p>
 <ul>
-<li>MD5とSHA-1は複数回攻撃に成功しており、さまざまなセキュリティアプリケーションで放棄されています。</li>
-<li>SHA-2シリーズ、特にSHA-256は、現在最も安全なハッシュアルゴリズムの1つで、成功した攻撃は報告されておらず、さまざまなセキュリティアプリケーションとプロトコルで一般的に使用されています。</li>
-<li>SHA-3はSHA-2と比較して実装コストが低く、計算効率が高いですが、現在の使用範囲はSHA-2シリーズほど広範囲ではありません。</li>
+<li>MD5 と SHA-1 は何度も攻撃に成功されているため、各種のセキュリティ用途では廃止されています。</li>
+<li>SHA-2 系列の SHA-256 は最も安全なハッシュアルゴリズムの 1 つであり、いまだに成功した攻撃例がないため、多くのセキュリティ用途やプロトコルで広く使われています。</li>
+<li>SHA-3 は SHA-2 と比べて実装コストが低く、計算効率も高い一方で、現時点での普及度は SHA-2 系列に及びません。</li>
 </ul>
 <p align="center"> 表 6-2 &nbsp; 一般的なハッシュアルゴリズム </p>
 
@@ -4680,7 +5053,7 @@
 </thead>
 <tbody>
 <tr>
-<td>リリース年</td>
+<td>発表年</td>
 <td>1992</td>
 <td>1995</td>
 <td>2002</td>
@@ -4695,203 +5068,203 @@
 </tr>
 <tr>
 <td>ハッシュ衝突</td>
-<td>頻繁</td>
-<td>頻繁</td>
-<td>まれ</td>
-<td>まれ</td>
+<td>多い</td>
+<td>多い</td>
+<td>非常に少ない</td>
+<td>非常に少ない</td>
 </tr>
 <tr>
 <td>セキュリティレベル</td>
-<td>低、攻撃に成功している</td>
-<td>低、攻撃に成功している</td>
-<td>高</td>
-<td>高</td>
+<td>低く、攻撃に成功されている</td>
+<td>低く、攻撃に成功されている</td>
+<td>高い</td>
+<td>高い</td>
 </tr>
 <tr>
-<td>アプリケーション</td>
-<td>放棄、データ整合性チェックにまだ使用</td>
-<td>放棄</td>
-<td>暗号通貨取引検証、デジタル署名など</td>
-<td>SHA-2の代替として使用可能</td>
+<td>用途</td>
+<td>廃止済みだが、データ完全性検査には使われる</td>
+<td>廃止済み</td>
+<td>暗号資産の取引検証、デジタル署名など</td>
+<td>SHA-2 の代替に使える</td>
 </tr>
 </tbody>
 </table>
 </div>
-<h1 id="_1">データ構造におけるハッシュ値<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h1>
-<p>ハッシュ表のキーは整数、小数、文字列などのさまざまなデータ型にできることを知っています。プログラミング言語は通常、これらのデータ型に対して組み込みのハッシュアルゴリズムを提供し、ハッシュ表のバケットインデックスを計算します。Pythonを例に取ると、<code>hash()</code>関数を使用してさまざまなデータ型のハッシュ値を計算できます。</p>
+<h2 id="634">6.3.4 &nbsp; データ構造のハッシュ値<a class="headerlink" href="#634" title="Permanent link">&para;</a></h2>
+<p>ご存じのように、ハッシュテーブルの <code>key</code> には整数、小数、文字列などのデータ型を使えます。プログラミング言語は通常、これらのデータ型に対して組み込みのハッシュアルゴリズムを提供し、ハッシュテーブル内のバケットインデックス計算に利用します。Python を例にすると、<code>hash()</code> 関数を呼び出して各種データ型のハッシュ値を計算できます。</p>
 <ul>
-<li>整数とブール値のハッシュ値は、それら自身の値です。</li>
-<li>浮動小数点数と文字列のハッシュ値の計算はより複雑で、興味のある読者は自分で研究することをお勧めします。</li>
-<li>タプルのハッシュ値は、その各要素のハッシュ値の組み合わせで、単一のハッシュ値になります。</li>
-<li>オブジェクトのハッシュ値は、そのメモリアドレスに基づいて生成されます。オブジェクトのハッシュメソッドをオーバーライドすることで、内容に基づいてハッシュ値を生成できます。</li>
+<li>整数と真理値のハッシュ値は、その値自身です。</li>
+<li>浮動小数点数と文字列のハッシュ値の計算はやや複雑なので、興味がある読者は自分で調べてみてください。</li>
+<li>タプルのハッシュ値は、各要素のハッシュ値を求めてから、それらを組み合わせて 1 つのハッシュ値にしたものです。</li>
+<li>オブジェクトのハッシュ値は、そのメモリアドレスに基づいて生成されます。オブジェクトのハッシュメソッドをオーバーライドすれば、内容に基づくハッシュ値を実装できます。</li>
 </ul>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>異なるプログラミング言語における組み込みハッシュ値計算関数の定義と方法は異なることに注意してください。</p>
+<p>注意してください。組み込みのハッシュ値計算関数の定義や方法は、プログラミング言語ごとに異なります。</p>
 </div>
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 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">built_in_hash.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="n">num</span> <span class="o">=</span> <span class="mi">3</span>
 <a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="n">hash_num</span> <span class="o">=</span> <span class="nb">hash</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
-<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="c1"># 整数3のハッシュ値は3</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="c1"># 整数 3 のハッシュ値は 3</span>
 <a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a>
 <a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="n">bol</span> <span class="o">=</span> <span class="kc">True</span>
 <a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="n">hash_bol</span> <span class="o">=</span> <span class="nb">hash</span><span class="p">(</span><span class="n">bol</span><span class="p">)</span>
-<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="c1"># ブール値Trueのハッシュ値は1</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="c1"># 真理値 True のハッシュ値は 1</span>
 <a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>
 <a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="n">dec</span> <span class="o">=</span> <span class="mf">3.14159</span>
 <a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="n">hash_dec</span> <span class="o">=</span> <span class="nb">hash</span><span class="p">(</span><span class="n">dec</span><span class="p">)</span>
-<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="c1"># 小数3.14159のハッシュ値は326484311674566659</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="c1"># 小数 3.14159 のハッシュ値は 326484311674566659</span>
 <a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a>
-<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="nb">str</span> <span class="o">=</span> <span class="s2">&quot;Hello 算法&quot;</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="nb">str</span> <span class="o">=</span> <span class="s2">&quot;Hello アルゴリズム&quot;</span>
 <a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="n">hash_str</span> <span class="o">=</span> <span class="nb">hash</span><span class="p">(</span><span class="nb">str</span><span class="p">)</span>
-<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="c1"># 文字列&quot;Hello 算法&quot;のハッシュ値は4617003410720528961</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="c1"># 文字列「Hello アルゴリズム」のハッシュ値は 4617003410720528961</span>
 <a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a>
-<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="n">tup</span> <span class="o">=</span> <span class="p">(</span><span class="mi">12836</span><span class="p">,</span> <span class="s2">&quot;小哈&quot;</span><span class="p">)</span>
+<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="n">tup</span> <span class="o">=</span> <span class="p">(</span><span class="mi">12836</span><span class="p">,</span> <span class="s2">&quot;シャオハ&quot;</span><span class="p">)</span>
 <a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="n">hash_tup</span> <span class="o">=</span> <span class="nb">hash</span><span class="p">(</span><span class="n">tup</span><span class="p">)</span>
-<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="c1"># タプル(12836, &#39;小哈&#39;)のハッシュ値は1029005403108185979</span>
+<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="c1"># タプル (12836, &#39;シャオハ&#39;) のハッシュ値は 1029005403108185979</span>
 <a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a>
 <a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a><span class="n">obj</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
 <a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a><span class="n">hash_obj</span> <span class="o">=</span> <span class="nb">hash</span><span class="p">(</span><span class="n">obj</span><span class="p">)</span>
-<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a><span class="c1"># ListNodeオブジェクト0x1058fd810のハッシュ値は274267521</span>
+<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a><span class="c1"># ノードオブジェクト &lt;ListNode object at 0x1058fd810&gt; のハッシュ値は 274267521</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">built_in_hash.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">size_t</span><span class="w"> </span><span class="n">hashNum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hash</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">()(</span><span class="n">num</span><span class="p">);</span>
-<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="c1">// 整数3のハッシュ値は3</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="c1">// 整数 3 のハッシュ値は 3</span>
 <a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a>
 <a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="kt">bool</span><span class="w"> </span><span class="n">bol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">true</span><span class="p">;</span>
 <a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="kt">size_t</span><span class="w"> </span><span class="n">hashBol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hash</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="p">()(</span><span class="n">bol</span><span class="p">);</span>
-<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="c1">// ブール値1のハッシュ値は1</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="c1">// 真理値 1 のハッシュ値は 1</span>
 <a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a>
 <a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="kt">double</span><span class="w"> </span><span class="n">dec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3.14159</span><span class="p">;</span>
 <a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="kt">size_t</span><span class="w"> </span><span class="n">hashDec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hash</span><span class="o">&lt;</span><span class="kt">double</span><span class="o">&gt;</span><span class="p">()(</span><span class="n">dec</span><span class="p">);</span>
-<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="c1">// 小数3.14159のハッシュ値は4614256650576692846</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="c1">// 小数 3.14159 のハッシュ値は 4614256650576692846</span>
 <a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a>
-<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="n">string</span><span class="w"> </span><span class="n">str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Hello 算法&quot;</span><span class="p">;</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="n">string</span><span class="w"> </span><span class="n">str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Hello アルゴリズム&quot;</span><span class="p">;</span>
 <a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="kt">size_t</span><span class="w"> </span><span class="n">hashStr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hash</span><span class="o">&lt;</span><span class="n">string</span><span class="o">&gt;</span><span class="p">()(</span><span class="n">str</span><span class="p">);</span>
-<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="c1">// 文字列&quot;Hello 算法&quot;のハッシュ値は15466937326284535026</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="c1">// 文字列「Hello アルゴリズム」のハッシュ値は 15466937326284535026</span>
 <a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a>
-<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="c1">// C++では、組み込みstd::hash()は基本データ型のハッシュ値のみを提供</span>
-<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="c1">// 配列とオブジェクトのハッシュ値は別途実装が必要</span>
+<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="c1">// C++ では、組み込みの std:hash() は基本データ型のハッシュ値計算のみを提供する</span>
+<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="c1">// 配列やオブジェクトのハッシュ値計算は自分で実装する必要がある</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">built_in_hash.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
 <a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashNum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Integer</span><span class="p">.</span><span class="na">hashCode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
-<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="c1">// 整数3のハッシュ値は3</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="c1">// 整数 3 のハッシュ値は 3</span>
 <a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a>
 <a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="kt">boolean</span><span class="w"> </span><span class="n">bol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
 <a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashBol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Boolean</span><span class="p">.</span><span class="na">hashCode</span><span class="p">(</span><span class="n">bol</span><span class="p">);</span>
-<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="c1">// ブール値trueのハッシュ値は1231</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="c1">// 真理値 true のハッシュ値は 1231</span>
 <a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a>
 <a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="kt">double</span><span class="w"> </span><span class="n">dec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3.14159</span><span class="p">;</span>
 <a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashDec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Double</span><span class="p">.</span><span class="na">hashCode</span><span class="p">(</span><span class="n">dec</span><span class="p">);</span>
-<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="c1">// 小数3.14159のハッシュ値は-1340954729</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="c1">// 小数 3.14159 のハッシュ値は -1340954729</span>
 <a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a>
-<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="n">String</span><span class="w"> </span><span class="n">str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Hello 算法&quot;</span><span class="p">;</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="n">String</span><span class="w"> </span><span class="n">str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Hello アルゴリズム&quot;</span><span class="p">;</span>
 <a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashStr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">str</span><span class="p">.</span><span class="na">hashCode</span><span class="p">();</span>
-<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="c1">// 文字列&quot;Hello 算法&quot;のハッシュ値は-727081396</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="c1">// 文字列「Hello アルゴリズム」のハッシュ値は -727081396</span>
 <a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a>
-<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="n">Object</span><span class="o">[]</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">12836</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小哈&quot;</span><span class="w"> </span><span class="p">};</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="n">Object</span><span class="o">[]</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">12836</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;シャオハ&quot;</span><span class="w"> </span><span class="p">};</span>
 <a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashTup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Arrays</span><span class="p">.</span><span class="na">hashCode</span><span class="p">(</span><span class="n">arr</span><span class="p">);</span>
-<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="c1">// 配列[12836, 小哈]のハッシュ値は1151158</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="c1">// 配列 [12836, シャオハ] のハッシュ値は 1151158</span>
 <a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a>
 <a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">obj</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashObj</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">obj</span><span class="p">.</span><span class="na">hashCode</span><span class="p">();</span>
-<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="c1">// ListNodeオブジェクトutils.ListNode@7dc5e7b4のハッシュ値は2110121908</span>
+<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="c1">// ノードオブジェクト utils.ListNode@7dc5e7b4 のハッシュ値は 2110121908</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">built_in_hash.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
 <a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashNum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">.</span><span class="n">GetHashCode</span><span class="p">();</span>
-<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="c1">// 整数3のハッシュ値は3;</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="c1">// 整数 3 のハッシュ値は 3;</span>
 <a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a>
 <a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="kt">bool</span><span class="w"> </span><span class="n">bol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">true</span><span class="p">;</span>
 <a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashBol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bol</span><span class="p">.</span><span class="n">GetHashCode</span><span class="p">();</span>
-<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="c1">// ブール値trueのハッシュ値は1;</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="c1">// 真理値 true のハッシュ値は 1;</span>
 <a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a>
 <a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="kt">double</span><span class="w"> </span><span class="n">dec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3.14159</span><span class="p">;</span>
 <a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashDec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dec</span><span class="p">.</span><span class="n">GetHashCode</span><span class="p">();</span>
-<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="c1">// 小数3.14159のハッシュ値は-1340954729;</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="c1">// 小数 3.14159 のハッシュ値は -1340954729;</span>
 <a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a>
-<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="kt">string</span><span class="w"> </span><span class="n">str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Hello 算法&quot;</span><span class="p">;</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="kt">string</span><span class="w"> </span><span class="n">str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Hello アルゴリズム&quot;</span><span class="p">;</span>
 <a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashStr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">str</span><span class="p">.</span><span class="n">GetHashCode</span><span class="p">();</span>
-<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="c1">// 文字列&quot;Hello 算法&quot;のハッシュ値は-586107568;</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="c1">// 文字列「Hello アルゴリズム」のハッシュ値は -586107568;</span>
 <a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a>
-<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="kt">object</span><span class="p">[]</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mi">12836</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小哈&quot;</span><span class="p">];</span>
+<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="kt">object</span><span class="p">[]</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mi">12836</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;シャオハ&quot;</span><span class="p">];</span>
 <a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashTup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">.</span><span class="n">GetHashCode</span><span class="p">();</span>
-<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="c1">// 配列[12836, 小哈]のハッシュ値は42931033;</span>
+<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="c1">// 配列 [12836, シャオハ] のハッシュ値は 42931033;</span>
 <a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a>
 <a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">obj</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-17-22" name="__codelineno-17-22" href="#__codelineno-17-22"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashObj</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">obj</span><span class="p">.</span><span class="n">GetHashCode</span><span class="p">();</span>
-<a id="__codelineno-17-23" name="__codelineno-17-23" href="#__codelineno-17-23"></a><span class="c1">// ListNodeオブジェクト0のハッシュ値は39053774;</span>
+<a id="__codelineno-17-23" name="__codelineno-17-23" href="#__codelineno-17-23"></a><span class="c1">// ノードオブジェクト 0 のハッシュ値は 39053774;</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">built_in_hash.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="c1">// Goには組み込みのハッシュコード関数が提供されていません</span>
+<div class="highlight"><span class="filename">built_in_hash.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="c1">// Go は組み込みの hash code 関数を提供していない</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">built_in_hash.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="kd">let</span><span class="w"> </span><span class="nv">num</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">3</span>
 <a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">let</span><span class="w"> </span><span class="nv">hashNum</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">num</span><span class="p">.</span><span class="n">hashValue</span>
-<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="c1">// 整数3のハッシュ値は9047044699613009734</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="c1">// 整数 3 のハッシュ値は 9047044699613009734</span>
 <a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a>
 <a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="kd">let</span><span class="w"> </span><span class="nv">bol</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">true</span>
 <a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="kd">let</span><span class="w"> </span><span class="nv">hashBol</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">bol</span><span class="p">.</span><span class="n">hashValue</span>
-<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="c1">// ブール値trueのハッシュ値は-4431640247352757451</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="c1">// 真理値 true のハッシュ値は -4431640247352757451</span>
 <a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a>
 <a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="kd">let</span><span class="w"> </span><span class="nv">dec</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mf">3.14159</span>
 <a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="kd">let</span><span class="w"> </span><span class="nv">hashDec</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dec</span><span class="p">.</span><span class="n">hashValue</span>
-<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="c1">// 小数3.14159のハッシュ値は-2465384235396674631</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="c1">// 小数 3.14159 のハッシュ値は -2465384235396674631</span>
 <a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a>
-<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="kd">let</span><span class="w"> </span><span class="nv">str</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;Hello 算法&quot;</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="kd">let</span><span class="w"> </span><span class="nv">str</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;Hello アルゴリズム&quot;</span>
 <a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="kd">let</span><span class="w"> </span><span class="nv">hashStr</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">str</span><span class="p">.</span><span class="n">hashValue</span>
-<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="c1">// 文字列&quot;Hello 算法&quot;のハッシュ値は-7850626797806988787</span>
+<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="c1">// 文字列「Hello アルゴリズム」のハッシュ値は -7850626797806988787</span>
 <a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a>
-<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="kd">let</span><span class="w"> </span><span class="nv">arr</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="n">AnyHashable</span><span class="p">(</span><span class="mi">12836</span><span class="p">),</span><span class="w"> </span><span class="n">AnyHashable</span><span class="p">(</span><span class="s">&quot;小哈&quot;</span><span class="p">)]</span>
+<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="kd">let</span><span class="w"> </span><span class="nv">arr</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="n">AnyHashable</span><span class="p">(</span><span class="mi">12836</span><span class="p">),</span><span class="w"> </span><span class="n">AnyHashable</span><span class="p">(</span><span class="s">&quot;シャオハ&quot;</span><span class="p">)]</span>
 <a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a><span class="kd">let</span><span class="w"> </span><span class="nv">hashTup</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">arr</span><span class="p">.</span><span class="n">hashValue</span>
-<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a><span class="c1">// 配列[AnyHashable(12836), AnyHashable(&quot;小哈&quot;)]のハッシュ値は-2308633508154532996</span>
+<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a><span class="c1">// 配列 [AnyHashable(12836), AnyHashable(&quot;シャオハ&quot;)] のハッシュ値は -2308633508154532996</span>
 <a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a>
 <a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a><span class="kd">let</span><span class="w"> </span><span class="nv">obj</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
 <a id="__codelineno-19-22" name="__codelineno-19-22" href="#__codelineno-19-22"></a><span class="kd">let</span><span class="w"> </span><span class="nv">hashObj</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">obj</span><span class="p">.</span><span class="n">hashValue</span>
-<a id="__codelineno-19-23" name="__codelineno-19-23" href="#__codelineno-19-23"></a><span class="c1">// ListNodeオブジェクトutils.ListNodeのハッシュ値は-2434780518035996159</span>
+<a id="__codelineno-19-23" name="__codelineno-19-23" href="#__codelineno-19-23"></a><span class="c1">// ノードオブジェクト utils.ListNode のハッシュ値は -2434780518035996159</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">built_in_hash.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="c1">// JavaScriptには組み込みのハッシュコード関数が提供されていません</span>
+<div class="highlight"><span class="filename">built_in_hash.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="c1">// JavaScript は組み込みの hash code 関数を提供していない</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">built_in_hash.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="c1">// TypeScriptには組み込みのハッシュコード関数が提供されていません</span>
+<div class="highlight"><span class="filename">built_in_hash.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="c1">// TypeScript は組み込みの hash code 関数を提供していない</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">built_in_hash.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="kt">int</span><span class="w"> </span><span class="kt">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">3</span><span class="p">;</span>
 <a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashNum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kt">num</span><span class="p">.</span><span class="n">hashCode</span><span class="p">;</span>
-<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="c1">// 整数3のハッシュ値は34803</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="c1">// 整数 3 のハッシュ値は 34803</span>
 <a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a>
 <a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="kt">bool</span><span class="w"> </span><span class="n">bol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
 <a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashBol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bol</span><span class="p">.</span><span class="n">hashCode</span><span class="p">;</span>
-<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="c1">// ブール値trueのハッシュ値は1231</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="c1">// 真理値 true のハッシュ値は 1231</span>
 <a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a>
 <a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="kt">double</span><span class="w"> </span><span class="n">dec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">3.14159</span><span class="p">;</span>
 <a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashDec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dec</span><span class="p">.</span><span class="n">hashCode</span><span class="p">;</span>
-<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="c1">// 小数3.14159のハッシュ値は2570631074981783</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="c1">// 小数 3.14159 のハッシュ値は 2570631074981783</span>
 <a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a>
-<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="kt">String</span><span class="w"> </span><span class="n">str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;Hello 算法&quot;</span><span class="p">;</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="kt">String</span><span class="w"> </span><span class="n">str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;Hello アルゴリズム&quot;</span><span class="p">;</span>
 <a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashStr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">str</span><span class="p">.</span><span class="n">hashCode</span><span class="p">;</span>
-<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="c1">// 文字列&quot;Hello 算法&quot;のハッシュ値は468167534</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="c1">// 文字列「Hello アルゴリズム」のハッシュ値は 468167534</span>
 <a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a>
-<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="n">List</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="m">12836</span><span class="p">,</span><span class="w"> </span><span class="s2">&quot;小哈&quot;</span><span class="p">];</span>
+<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="n">List</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="m">12836</span><span class="p">,</span><span class="w"> </span><span class="s2">&quot;シャオハ&quot;</span><span class="p">];</span>
 <a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashArr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">.</span><span class="n">hashCode</span><span class="p">;</span>
-<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="c1">// 配列[12836, 小哈]のハッシュ値は976512528</span>
+<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="c1">// 配列 [12836, シャオハ] のハッシュ値は 976512528</span>
 <a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a>
 <a id="__codelineno-22-21" name="__codelineno-22-21" href="#__codelineno-22-21"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">obj</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
 <a id="__codelineno-22-22" name="__codelineno-22-22" href="#__codelineno-22-22"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashObj</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">obj</span><span class="p">.</span><span class="n">hashCode</span><span class="p">;</span>
-<a id="__codelineno-22-23" name="__codelineno-22-23" href="#__codelineno-22-23"></a><span class="c1">// ListNodeオブジェクトInstance of &#39;ListNode&#39;のハッシュ値は1033450432</span>
+<a id="__codelineno-22-23" name="__codelineno-22-23" href="#__codelineno-22-23"></a><span class="c1">// ノードオブジェクト Instance of &#39;ListNode&#39; のハッシュ値は 1033450432</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
@@ -4902,52 +5275,104 @@
 <a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">num_hasher</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DefaultHasher</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
 <a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="n">num</span><span class="p">.</span><span class="n">hash</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">num_hasher</span><span class="p">);</span>
 <a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="kd">let</span><span class="w"> </span><span class="n">hash_num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num_hasher</span><span class="p">.</span><span class="n">finish</span><span class="p">();</span>
-<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="c1">// 整数3のハッシュ値は568126464209439262</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="c1">// 整数 3 のハッシュ値は 568126464209439262</span>
 <a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a>
 <a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="kd">let</span><span class="w"> </span><span class="n">bol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
 <a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">bol_hasher</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DefaultHasher</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
 <a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="n">bol</span><span class="p">.</span><span class="n">hash</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">bol_hasher</span><span class="p">);</span>
 <a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="kd">let</span><span class="w"> </span><span class="n">hash_bol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bol_hasher</span><span class="p">.</span><span class="n">finish</span><span class="p">();</span>
-<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="c1">// ブール値trueのハッシュ値は4952851536318644461</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="c1">// 真理値 true のハッシュ値は 4952851536318644461</span>
 <a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a>
 <a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="kd">let</span><span class="w"> </span><span class="n">dec</span><span class="p">:</span><span class="w"> </span><span class="kt">f32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3.14159</span><span class="p">;</span>
 <a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">dec_hasher</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DefaultHasher</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
 <a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="n">dec</span><span class="p">.</span><span class="n">to_bits</span><span class="p">().</span><span class="n">hash</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">dec_hasher</span><span class="p">);</span>
 <a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="kd">let</span><span class="w"> </span><span class="n">hash_dec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dec_hasher</span><span class="p">.</span><span class="n">finish</span><span class="p">();</span>
-<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="c1">// 小数3.14159のハッシュ値は2566941990314602357</span>
+<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="c1">// 小数 3.14159 のハッシュ値は 2566941990314602357</span>
 <a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a>
-<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a><span class="kd">let</span><span class="w"> </span><span class="kt">str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Hello 算法&quot;</span><span class="p">;</span>
+<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a><span class="kd">let</span><span class="w"> </span><span class="kt">str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Hello アルゴリズム&quot;</span><span class="p">;</span>
 <a id="__codelineno-23-23" name="__codelineno-23-23" href="#__codelineno-23-23"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">str_hasher</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DefaultHasher</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
 <a id="__codelineno-23-24" name="__codelineno-23-24" href="#__codelineno-23-24"></a><span class="kt">str</span><span class="p">.</span><span class="n">hash</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">str_hasher</span><span class="p">);</span>
 <a id="__codelineno-23-25" name="__codelineno-23-25" href="#__codelineno-23-25"></a><span class="kd">let</span><span class="w"> </span><span class="n">hash_str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">str_hasher</span><span class="p">.</span><span class="n">finish</span><span class="p">();</span>
-<a id="__codelineno-23-26" name="__codelineno-23-26" href="#__codelineno-23-26"></a><span class="c1">// 文字列&quot;Hello 算法&quot;のハッシュ値は16092673739211250988</span>
+<a id="__codelineno-23-26" name="__codelineno-23-26" href="#__codelineno-23-26"></a><span class="c1">// 文字列「Hello アルゴリズム」のハッシュ値は 16092673739211250988</span>
 <a id="__codelineno-23-27" name="__codelineno-23-27" href="#__codelineno-23-27"></a>
-<a id="__codelineno-23-28" name="__codelineno-23-28" href="#__codelineno-23-28"></a><span class="kd">let</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="o">&amp;</span><span class="mi">12836</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="s">&quot;小哈&quot;</span><span class="p">);</span>
+<a id="__codelineno-23-28" name="__codelineno-23-28" href="#__codelineno-23-28"></a><span class="kd">let</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="o">&amp;</span><span class="mi">12836</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="s">&quot;シャオハ&quot;</span><span class="p">);</span>
 <a id="__codelineno-23-29" name="__codelineno-23-29" href="#__codelineno-23-29"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">tup_hasher</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DefaultHasher</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
 <a id="__codelineno-23-30" name="__codelineno-23-30" href="#__codelineno-23-30"></a><span class="n">arr</span><span class="p">.</span><span class="n">hash</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">tup_hasher</span><span class="p">);</span>
 <a id="__codelineno-23-31" name="__codelineno-23-31" href="#__codelineno-23-31"></a><span class="kd">let</span><span class="w"> </span><span class="n">hash_tup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tup_hasher</span><span class="p">.</span><span class="n">finish</span><span class="p">();</span>
-<a id="__codelineno-23-32" name="__codelineno-23-32" href="#__codelineno-23-32"></a><span class="c1">// タプル(12836, &quot;小哈&quot;)のハッシュ値は1885128010422702749</span>
+<a id="__codelineno-23-32" name="__codelineno-23-32" href="#__codelineno-23-32"></a><span class="c1">// タプル (12836, &quot;シャオハ&quot;) のハッシュ値は 1885128010422702749</span>
 <a id="__codelineno-23-33" name="__codelineno-23-33" href="#__codelineno-23-33"></a>
 <a id="__codelineno-23-34" name="__codelineno-23-34" href="#__codelineno-23-34"></a><span class="kd">let</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="mi">42</span><span class="p">);</span>
 <a id="__codelineno-23-35" name="__codelineno-23-35" href="#__codelineno-23-35"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">hasher</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DefaultHasher</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
 <a id="__codelineno-23-36" name="__codelineno-23-36" href="#__codelineno-23-36"></a><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">.</span><span class="n">hash</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">hasher</span><span class="p">);</span>
 <a id="__codelineno-23-37" name="__codelineno-23-37" href="#__codelineno-23-37"></a><span class="kd">let</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hasher</span><span class="p">.</span><span class="n">finish</span><span class="p">();</span>
-<a id="__codelineno-23-38" name="__codelineno-23-38" href="#__codelineno-23-38"></a><span class="c1">// ListNodeオブジェクトRefCell { value: ListNode { val: 42, next: None } }のハッシュ値は15387811073369036852</span>
+<a id="__codelineno-23-38" name="__codelineno-23-38" href="#__codelineno-23-38"></a><span class="c1">// ノードオブジェクト RefCell { value: ListNode { val: 42, next: None } } のハッシュ値は15387811073369036852</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">built_in_hash.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="c1">// Cには組み込みのハッシュコード関数が提供されていません</span>
+<div class="highlight"><span class="filename">built_in_hash.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="c1">// C は組み込みの hash code 関数を提供していない</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">built_in_hash.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a>
+<div class="highlight"><span class="filename">built_in_hash.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="kd">val</span><span class="w"> </span><span class="nv">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">3</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="kd">val</span><span class="w"> </span><span class="nv">hashNum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">.</span><span class="na">hashCode</span><span class="p">()</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="c1">// 整数 3 のハッシュ値は 3</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="kd">val</span><span class="w"> </span><span class="nv">bol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="kd">val</span><span class="w"> </span><span class="nv">hashBol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bol</span><span class="p">.</span><span class="na">hashCode</span><span class="p">()</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="c1">// 真理値 true のハッシュ値は 1231</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="kd">val</span><span class="w"> </span><span class="nv">dec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">3.14159</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="kd">val</span><span class="w"> </span><span class="nv">hashDec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dec</span><span class="p">.</span><span class="na">hashCode</span><span class="p">()</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="c1">// 小数 3.14159 のハッシュ値は -1340954729</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="kd">val</span><span class="w"> </span><span class="nv">str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Hello アルゴリズム&quot;</span>
+<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="kd">val</span><span class="w"> </span><span class="nv">hashStr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">str</span><span class="p">.</span><span class="na">hashCode</span><span class="p">()</span>
+<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="c1">// 文字列「Hello アルゴリズム」のハッシュ値は -727081396</span>
+<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a>
+<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="kd">val</span><span class="w"> </span><span class="nv">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arrayOf</span><span class="o">&lt;</span><span class="kt">Any</span><span class="o">&gt;</span><span class="p">(</span><span class="m">12836</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;シャオハ&quot;</span><span class="p">)</span>
+<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a><span class="kd">val</span><span class="w"> </span><span class="nv">hashTup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">.</span><span class="na">hashCode</span><span class="p">()</span>
+<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="c1">// 配列 [12836, シャオハ] のハッシュ値は 189568618</span>
+<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a>
+<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="kd">val</span><span class="w"> </span><span class="nv">obj</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
+<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a><span class="kd">val</span><span class="w"> </span><span class="nv">hashObj</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">obj</span><span class="p">.</span><span class="na">hashCode</span><span class="p">()</span>
+<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="c1">// ノードオブジェクト utils.ListNode@1d81eb93 のハッシュ値は 495053715</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">built_in_hash.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="n">hash_num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="o">.</span><span class="n">hash</span>
+<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="c1"># 整数 3 のハッシュ値は -4385856518450339636</span>
+<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>
+<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="n">bol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kp">true</span>
+<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="n">hash_bol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bol</span><span class="o">.</span><span class="n">hash</span>
+<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="c1"># 真理値 true のハッシュ値は -1617938112149317027</span>
+<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>
+<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="n">dec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="o">.</span><span class="mi">14159</span>
+<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="n">hash_dec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dec</span><span class="o">.</span><span class="n">hash</span>
+<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="c1"># 小数 3.14159 のハッシュ値は -1479186995943067893</span>
+<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a>
+<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="n">str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;Hello アルゴリズム&quot;</span>
+<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a><span class="n">hash_str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">str</span><span class="o">.</span><span class="n">hash</span>
+<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="c1"># 文字列「Hello アルゴリズム」のハッシュ値は -4075943250025831763</span>
+<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a>
+<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a><span class="n">tup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="mi">12836</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;シャオハ&#39;</span><span class="o">]</span>
+<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a><span class="n">hash_tup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tup</span><span class="o">.</span><span class="n">hash</span>
+<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a><span class="c1"># タプル (12836, &#39;シャオハ&#39;) のハッシュ値は 1999544809202288822</span>
+<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a>
+<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a><span class="n">obj</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">ListNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a><span class="n">hash_obj</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">obj</span><span class="o">.</span><span class="n">hash</span>
+<a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a><span class="c1"># ノードオブジェクト #&lt;ListNode:0x000078133140ab70&gt; のハッシュ値は 4302940560806366381</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>多くのプログラミング言語では、<strong>不変オブジェクトのみがハッシュ表の<code>key</code>として機能できます</strong>。リスト（動的配列）を<code>key</code>として使用する場合、リストの内容が変更されると、そのハッシュ値も変更され、ハッシュ表で元の<code>value</code>を見つけることができなくなります。</p>
-<p>カスタムオブジェクト（連結リストノードなど）のメンバー変数は可変ですが、ハッシュ可能です。<strong>これは、オブジェクトのハッシュ値が通常そのメモリアドレスに基づいて生成されるためです</strong>。オブジェクトの内容が変更されても、メモリアドレスは同じままなので、ハッシュ値は変更されません。</p>
-<p>異なるコンソールで出力されるハッシュ値が異なることに気づいたかもしれません。<strong>これは、Pythonインタープリターが起動するたびに文字列ハッシュ関数にランダムソルトを追加するためです</strong>。このアプローチはHashDoS攻撃を効果的に防ぎ、ハッシュアルゴリズムのセキュリティを向上させます。</p>
+<details class="pythontutor">
+<summary>可視化実行</summary>
+<p>https://pythontutor.com/render.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%E9%93%BE%E8%A1%A8%E8%8A%82%E7%82%B9%E7%B1%BB%22%22%22%0A%20%20%20%20def%20__init__%28self,%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E8%8A%82%E7%82%B9%E5%80%BC%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%90%8E%E7%BB%A7%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20num%20%3D%203%0A%20%20%20%20hash_num%20%3D%20hash%28num%29%0A%20%20%20%20%23%20%E6%95%B4%E6%95%B0%203%20%E7%9A%84%E5%93%88%E5%B8%8C%E5%80%BC%E4%B8%BA%203%0A%0A%20%20%20%20bol%20%3D%20True%0A%20%20%20%20hash_bol%20%3D%20hash%28bol%29%0A%20%20%20%20%23%20%E5%B8%83%E5%B0%94%E9%87%8F%20True%20%E7%9A%84%E5%93%88%E5%B8%8C%E5%80%BC%E4%B8%BA%201%0A%0A%20%20%20%20dec%20%3D%203.14159%0A%20%20%20%20hash_dec%20%3D%20hash%28dec%29%0A%20%20%20%20%23%20%E5%B0%8F%E6%95%B0%203.14159%20%E7%9A%84%E5%93%88%E5%B8%8C%E5%80%BC%E4%B8%BA%20326484311674566659%0A%0A%20%20%20%20str%20%3D%20%22Hello%20%E7%AE%97%E6%B3%95%22%0A%20%20%20%20hash_str%20%3D%20hash%28str%29%0A%20%20%20%20%23%20%E5%AD%97%E7%AC%A6%E4%B8%B2%E2%80%9CHello%20%E7%AE%97%E6%B3%95%E2%80%9D%E7%9A%84%E5%93%88%E5%B8%8C%E5%80%BC%E4%B8%BA%204617003410720528961%0A%0A%20%20%20%20tup%20%3D%20%2812836,%20%22%E5%B0%8F%E5%93%88%22%29%0A%20%20%20%20hash_tup%20%3D%20hash%28tup%29%0A%20%20%20%20%23%20%E5%85%83%E7%BB%84%20%2812836,%20'%E5%B0%8F%E5%93%88'%29%20%E7%9A%84%E5%93%88%E5%B8%8C%E5%80%BC%E4%B8%BA%201029005403108185979%0A%0A%20%20%20%20obj%20%3D%20ListNode%280%29%0A%20%20%20%20hash_obj%20%3D%20hash%28obj%29%0A%20%20%20%20%23%20%E8%8A%82%E7%82%B9%E5%AF%B9%E8%B1%A1%20%3CListNode%20object%20at%200x1058fd810%3E%20%E7%9A%84%E5%93%88%E5%B8%8C%E5%80%BC%E4%B8%BA%20274267521&amp;cumulative=false&amp;curInstr=19&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>
+</details>
+<p>多くのプログラミング言語では、<strong>不変オブジェクトだけがハッシュテーブルの <code>key</code> として使えます</strong>。仮にリスト（動的配列）を <code>key</code> とすると、その内容が変化したときにハッシュ値も変わってしまうため、もとの <code>value</code> をハッシュテーブルから検索できなくなります。</p>
+<p>カスタムオブジェクト（たとえば連結リストのノード）のメンバ変数は可変ですが、それでもハッシュ可能です。<strong>これは、オブジェクトのハッシュ値が通常はメモリアドレスに基づいて生成されるためです</strong>。オブジェクトの内容が変化しても、メモリアドレスが変わらなければ、ハッシュ値も変わりません。</p>
+<p>注意深い人なら、異なるコンソールでプログラムを実行したときに、出力されるハッシュ値が異なることに気づくかもしれません。<strong>これは、Python インタプリタが起動のたびに文字列ハッシュ関数へランダムな salt 値を追加しているためです</strong>。この方法によって HashDoS 攻撃を効果的に防ぎ、ハッシュアルゴリズムの安全性を高めています。</p>
 
 <!-- Source file information -->
 
diff --git a/ja/chapter_hashing/hash_collision/index.html b/ja/chapter_hashing/hash_collision/index.html
index 328a825b8..6a8a11afd 100644
--- a/ja/chapter_hashing/hash_collision/index.html
+++ b/ja/chapter_hashing/hash_collision/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1593,7 +1593,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1615,7 +1615,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1637,7 +1637,7 @@
   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1722,7 +1722,7 @@
   <a href="#621" class="md-nav__link">
     <span class="md-ellipsis">
       
-        6.2.1 &nbsp; 連鎖法
+        6.2.1 &nbsp; チェイン法
       
     </span>
   </a>
@@ -1733,19 +1733,19 @@
   <a href="#622" class="md-nav__link">
     <span class="md-ellipsis">
       
-        6.2.2 &nbsp; オープンアドレス法
+        6.2.2 &nbsp; オープンアドレッシング
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="6.2.2 オープンアドレス法">
+    <nav class="md-nav" aria-label="6.2.2 オープンアドレッシング">
       <ul class="md-nav__list">
         
           <li class="md-nav__item">
   <a href="#1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; 線形プローブ
+        1. &nbsp; 線形探索
       
     </span>
   </a>
@@ -1756,7 +1756,7 @@
   <a href="#2" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2. &nbsp; 二次プローブ
+        2. &nbsp; 二次探索
       
     </span>
   </a>
@@ -1767,7 +1767,7 @@
   <a href="#3" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3. &nbsp; 二重ハッシュ
+        3. &nbsp; 多重ハッシュ
       
     </span>
   </a>
@@ -2064,7 +2064,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2227,7 +2227,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2613,7 +2613,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2669,7 +2669,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2697,7 +2697,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3235,7 +3235,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3291,7 +3291,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3319,7 +3319,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3512,7 +3512,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3540,7 +3540,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3681,7 +3681,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3709,7 +3709,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3737,7 +3737,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3765,7 +3765,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3958,7 +3958,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4203,7 +4203,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4349,7 +4349,7 @@
   <a href="#621" class="md-nav__link">
     <span class="md-ellipsis">
       
-        6.2.1 &nbsp; 連鎖法
+        6.2.1 &nbsp; チェイン法
       
     </span>
   </a>
@@ -4360,19 +4360,19 @@
   <a href="#622" class="md-nav__link">
     <span class="md-ellipsis">
       
-        6.2.2 &nbsp; オープンアドレス法
+        6.2.2 &nbsp; オープンアドレッシング
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="6.2.2 オープンアドレス法">
+    <nav class="md-nav" aria-label="6.2.2 オープンアドレッシング">
       <ul class="md-nav__list">
         
           <li class="md-nav__item">
   <a href="#1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; 線形プローブ
+        1. &nbsp; 線形探索
       
     </span>
   </a>
@@ -4383,7 +4383,7 @@
   <a href="#2" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2. &nbsp; 二次プローブ
+        2. &nbsp; 二次探索
       
     </span>
   </a>
@@ -4394,7 +4394,7 @@
   <a href="#3" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3. &nbsp; 二重ハッシュ
+        3. &nbsp; 多重ハッシュ
       
     </span>
   </a>
@@ -4455,46 +4455,46 @@
 
 <!-- Page content -->
 <h1 id="62">6.2 &nbsp; ハッシュ衝突<a class="headerlink" href="#62" title="Permanent link">&para;</a></h1>
-<p>前節で述べたように、**ほとんどの場合、ハッシュ関数の入力空間は出力空間よりもはるかに大きい**ため、理論的にはハッシュ衝突は避けられません。例えば、入力空間がすべての整数で、出力空間が配列容量のサイズの場合、複数の整数が必然的に同じバケットインデックスにマッピングされます。</p>
-<p>ハッシュ衝突は誤ったクエリ結果につながり、ハッシュ表の使いやすさに深刻な影響を与える可能性があります。この問題に対処するために、ハッシュ衝突が発生するたびに、衝突が消えるまでハッシュ表のリサイズを実行します。このアプローチは非常にシンプルで直接的であり、うまく機能します。しかし、テーブルの拡張には大量のデータ移行とハッシュコードの再計算が含まれ、これらは高コストであるため、非常に非効率的に見えます。効率を向上させるために、以下の戦略を採用できます：</p>
+<p>前節で述べたように、**通常、ハッシュ関数の入力空間は出力空間よりもはるかに大きい**ため、理論上ハッシュ衝突は避けられません。例えば、入力空間がすべての整数で、出力空間が配列の容量サイズである場合、必然的に複数の整数が同じバケットインデックスに写像されます。</p>
+<p>ハッシュ衝突は検索結果の誤りを招き、ハッシュテーブルの利用可能性に深刻な影響を与えます。この問題を解決するために、ハッシュ衝突が発生するたびにハッシュテーブルを拡張し、衝突が消えるまで続けることが考えられます。この方法は単純で効果的ですが、効率が低すぎます。なぜなら、ハッシュテーブルの拡張には大量のデータ移動とハッシュ値の計算が必要だからです。効率を高めるために、次の戦略を採用できます。</p>
 <ol>
-<li>**ハッシュ衝突が発生した場合でも、ターゲット要素の検索が適切に機能する**ようにハッシュ表のデータ構造を改善する。</li>
-<li>深刻な衝突が観察され、必要になる前に、拡張は最後の手段とする。</li>
+<li>ハッシュテーブルのデータ構造を改良し、<strong>ハッシュ衝突が発生してもハッシュテーブルが正常に動作できるようにする</strong>。</li>
+<li>必要な場合、すなわちハッシュ衝突が比較的深刻なときにのみ、拡張操作を実行する。</li>
 </ol>
-<p>ハッシュ表の構造を改善する主な方法は2つあります：「連鎖法」と「オープンアドレス法」です。</p>
-<h2 id="621">6.2.1 &nbsp; 連鎖法<a class="headerlink" href="#621" title="Permanent link">&para;</a></h2>
-<p>元のハッシュ表では、各バケットは1つのキー値ペアのみを格納できます。<u>連鎖法</u>は単一の要素を連結リストに変換し、キー値ペアをリストノードとして扱い、衝突するすべてのキー値ペアを同じ連結リストに格納します。下図は連鎖法を使用したハッシュ表の例を示しています。</p>
-<p><img alt="連鎖法ハッシュ表" class="animation-figure" src="../hash_collision.assets/hash_table_chaining.png" /></p>
-<p align="center"> 図 6-5 &nbsp; 連鎖法ハッシュ表 </p>
+<p>ハッシュテーブルの構造改善方法には、主に「チェイン法」と「オープンアドレッシング」があります。</p>
+<h2 id="621">6.2.1 &nbsp; チェイン法<a class="headerlink" href="#621" title="Permanent link">&para;</a></h2>
+<p>元のハッシュテーブルでは、各バケットには 1 つのキーと値のペアしか格納できません。<u>チェイン法（separate chaining）</u>では、単一要素を連結リストに置き換え、キーと値のペアを連結リストのノードとして扱い、衝突したすべてのキーと値のペアを同じ連結リストに格納します。下図はチェイン法によるハッシュテーブルの例を示しています。</p>
+<p><img alt="チェイン法ハッシュテーブル" class="animation-figure" src="../hash_collision.assets/hash_table_chaining.png" /></p>
+<p align="center"> 図 6-5 &nbsp; チェイン法ハッシュテーブル </p>
 
-<p>連鎖法で実装されたハッシュ表の操作は以下のように変更されます：</p>
+<p>チェイン法で実装されたハッシュテーブルでは、操作方法が次のように変わります。</p>
 <ul>
-<li><strong>要素のクエリ</strong>: <code>key</code>を入力し、ハッシュ関数を通してバケットインデックスを取得し、連結リストのヘッドノードにアクセスします。連結リストを走査してキーを比較し、ターゲットキー値ペアを見つけます。</li>
-<li><strong>要素の追加</strong>: ハッシュ関数を通して連結リストのヘッドノードにアクセスし、ノード（キー値ペア）をリストに追加します。</li>
-<li><strong>要素の削除</strong>: ハッシュ関数の結果に基づいて連結リストのヘッドにアクセスし、連結リストを走査してターゲットノードを見つけて削除します。</li>
+<li><strong>要素の検索</strong>：入力 <code>key</code> をハッシュ関数に通してバケットインデックスを得ると、連結リストの先頭ノードにアクセスできます。その後、連結リストを走査して <code>key</code> を比較し、目的のキーと値のペアを探します。</li>
+<li><strong>要素の追加</strong>：まずハッシュ関数で連結リストの先頭ノードにアクセスし、その後ノード（キーと値のペア）を連結リストに追加します。</li>
+<li><strong>要素の削除</strong>：ハッシュ関数の結果に基づいて連結リストの先頭にアクセスし、続いて連結リストを走査して対象ノードを探し、削除します。</li>
 </ul>
-<p>連鎖法には以下の制限があります：</p>
+<p>チェイン法には次の制約があります。</p>
 <ul>
-<li><strong>空間使用量の増加</strong>: 連結リストにはノードポインタが含まれており、配列よりも多くのメモリ空間を消費します。</li>
-<li><strong>クエリ効率の低下</strong>: 対応する要素を見つけるために連結リストの線形走査が必要になるためです。</li>
+<li><strong>使用メモリの増加</strong>：連結リストにはノードポインタが含まれるため、配列よりも多くのメモリを消費します。</li>
+<li><strong>検索効率の低下</strong>：対応する要素を見つけるために連結リストを線形走査する必要があるためです。</li>
 </ul>
-<p>以下のコードは連鎖法ハッシュ表の簡単な実装を提供し、注意すべき2つの点があります：</p>
+<p>以下のコードはチェイン法ハッシュテーブルの簡単な実装を示しています。注意すべき点は 2 つあります。</p>
 <ul>
-<li>簡単にするために、連結リストの代わりにリスト（動的配列）を使用します。この設定では、ハッシュ表（配列）は複数のバケットを含み、各バケットはリストです。</li>
-<li>この実装にはハッシュ表のリサイズメソッドが含まれています。負荷率が<span class="arithmatex">\(\frac{2}{3}\)</span>を超えると、ハッシュ表を元のサイズの2倍に拡張します。</li>
+<li>連結リストの代わりにリスト（動的配列）を使って、コードを簡潔にしています。この設定では、ハッシュテーブル（配列）は複数のバケットを含み、各バケットは 1 つのリストです。</li>
+<li>以下の実装にはハッシュテーブルの拡張メソッドが含まれています。負荷率が <span class="arithmatex">\(\frac{2}{3}\)</span> を超えたとき、ハッシュテーブルを元の <span class="arithmatex">\(2\)</span> 倍に拡張します。</li>
 </ul>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">hash_map_chaining.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">HashMapChaining</span><span class="p">:</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;チェーンアドレス法ハッシュテーブル&quot;&quot;&quot;</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;チェイン法ハッシュテーブル&quot;&quot;&quot;</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
-<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># キー値ペアの数</span>
-<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span> <span class="o">=</span> <span class="mi">4</span>  <span class="c1"># ハッシュテーブルの容量</span>
-<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">load_thres</span> <span class="o">=</span> <span class="mf">2.0</span> <span class="o">/</span> <span class="mf">3.0</span>  <span class="c1"># 拡張をトリガーする負荷率の閾値</span>
-<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">extend_ratio</span> <span class="o">=</span> <span class="mi">2</span>  <span class="c1"># 拡張の倍数</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># キーと値のペア数</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span> <span class="o">=</span> <span class="mi">4</span>  <span class="c1"># ハッシュテーブル容量</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">load_thres</span> <span class="o">=</span> <span class="mf">2.0</span> <span class="o">/</span> <span class="mf">3.0</span>  <span class="c1"># リサイズを発動する負荷率のしきい値</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">extend_ratio</span> <span class="o">=</span> <span class="mi">2</span>  <span class="c1"># 拡張倍率</span>
 <a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span> <span class="o">=</span> <span class="p">[[]</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">)]</span>  <span class="c1"># バケット配列</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>
 <a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">hash_func</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
@@ -4506,29 +4506,29 @@
 <a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span>
 <a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>
 <a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">str</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;照会操作&quot;&quot;&quot;</span>
+<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;検索操作&quot;&quot;&quot;</span>
 <a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>        <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
 <a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a>        <span class="n">bucket</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
-<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>        <span class="c1"># バケットを走査し、キーが見つかれば対応する val を返す</span>
+<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>        <span class="c1"># バケットを走査し、key が見つかれば対応する val を返す</span>
 <a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>        <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="n">bucket</span><span class="p">:</span>
 <a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a>            <span class="k">if</span> <span class="n">pair</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="n">key</span><span class="p">:</span>
 <a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>                <span class="k">return</span> <span class="n">pair</span><span class="o">.</span><span class="n">val</span>
-<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a>        <span class="c1"># キーが見つからない場合、None を返す</span>
+<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a>        <span class="c1"># key が見つからない場合は None を返す</span>
 <a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a>        <span class="k">return</span> <span class="kc">None</span>
 <a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a>
 <a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">str</span><span class="p">):</span>
 <a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;追加操作&quot;&quot;&quot;</span>
-<a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a>        <span class="c1"># 負荷率が閾値を超えた場合、拡張を実行</span>
+<a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a>        <span class="c1"># 負荷率がしきい値を超えたら、リサイズを実行</span>
 <a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">load_factor</span><span class="p">()</span> <span class="o">&gt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">load_thres</span><span class="p">:</span>
 <a id="__codelineno-0-35" name="__codelineno-0-35" href="#__codelineno-0-35"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">extend</span><span class="p">()</span>
 <a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a>        <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
 <a id="__codelineno-0-37" name="__codelineno-0-37" href="#__codelineno-0-37"></a>        <span class="n">bucket</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
-<a id="__codelineno-0-38" name="__codelineno-0-38" href="#__codelineno-0-38"></a>        <span class="c1"># バケットを走査し、指定されたキーに遭遇した場合、対応する val を更新して返す</span>
+<a id="__codelineno-0-38" name="__codelineno-0-38" href="#__codelineno-0-38"></a>        <span class="c1"># バケットを走査し、指定した key が見つかれば対応する val を更新して返す</span>
 <a id="__codelineno-0-39" name="__codelineno-0-39" href="#__codelineno-0-39"></a>        <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="n">bucket</span><span class="p">:</span>
 <a id="__codelineno-0-40" name="__codelineno-0-40" href="#__codelineno-0-40"></a>            <span class="k">if</span> <span class="n">pair</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="n">key</span><span class="p">:</span>
 <a id="__codelineno-0-41" name="__codelineno-0-41" href="#__codelineno-0-41"></a>                <span class="n">pair</span><span class="o">.</span><span class="n">val</span> <span class="o">=</span> <span class="n">val</span>
 <a id="__codelineno-0-42" name="__codelineno-0-42" href="#__codelineno-0-42"></a>                <span class="k">return</span>
-<a id="__codelineno-0-43" name="__codelineno-0-43" href="#__codelineno-0-43"></a>        <span class="c1"># キーが見つからない場合、キー値ペアを末尾に追加</span>
+<a id="__codelineno-0-43" name="__codelineno-0-43" href="#__codelineno-0-43"></a>        <span class="c1"># その key が存在しなければ、キーと値のペアを末尾に追加</span>
 <a id="__codelineno-0-44" name="__codelineno-0-44" href="#__codelineno-0-44"></a>        <span class="n">pair</span> <span class="o">=</span> <span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
 <a id="__codelineno-0-45" name="__codelineno-0-45" href="#__codelineno-0-45"></a>        <span class="n">bucket</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">pair</span><span class="p">)</span>
 <a id="__codelineno-0-46" name="__codelineno-0-46" href="#__codelineno-0-46"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">+=</span> <span class="mi">1</span>
@@ -4537,7 +4537,7 @@
 <a id="__codelineno-0-49" name="__codelineno-0-49" href="#__codelineno-0-49"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;削除操作&quot;&quot;&quot;</span>
 <a id="__codelineno-0-50" name="__codelineno-0-50" href="#__codelineno-0-50"></a>        <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
 <a id="__codelineno-0-51" name="__codelineno-0-51" href="#__codelineno-0-51"></a>        <span class="n">bucket</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
-<a id="__codelineno-0-52" name="__codelineno-0-52" href="#__codelineno-0-52"></a>        <span class="c1"># バケットを走査し、その中からキー値ペアを削除</span>
+<a id="__codelineno-0-52" name="__codelineno-0-52" href="#__codelineno-0-52"></a>        <span class="c1"># バケットを走査してキーと値のペアを削除</span>
 <a id="__codelineno-0-53" name="__codelineno-0-53" href="#__codelineno-0-53"></a>        <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="n">bucket</span><span class="p">:</span>
 <a id="__codelineno-0-54" name="__codelineno-0-54" href="#__codelineno-0-54"></a>            <span class="k">if</span> <span class="n">pair</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="n">key</span><span class="p">:</span>
 <a id="__codelineno-0-55" name="__codelineno-0-55" href="#__codelineno-0-55"></a>                <span class="n">bucket</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">pair</span><span class="p">)</span>
@@ -4546,13 +4546,13 @@
 <a id="__codelineno-0-58" name="__codelineno-0-58" href="#__codelineno-0-58"></a>
 <a id="__codelineno-0-59" name="__codelineno-0-59" href="#__codelineno-0-59"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">extend</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
 <a id="__codelineno-0-60" name="__codelineno-0-60" href="#__codelineno-0-60"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;ハッシュテーブルを拡張&quot;&quot;&quot;</span>
-<a id="__codelineno-0-61" name="__codelineno-0-61" href="#__codelineno-0-61"></a>        <span class="c1"># 元のハッシュテーブルを一時的に保存</span>
+<a id="__codelineno-0-61" name="__codelineno-0-61" href="#__codelineno-0-61"></a>        <span class="c1"># 元のハッシュテーブルを一時保存</span>
 <a id="__codelineno-0-62" name="__codelineno-0-62" href="#__codelineno-0-62"></a>        <span class="n">buckets</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span>
-<a id="__codelineno-0-63" name="__codelineno-0-63" href="#__codelineno-0-63"></a>        <span class="c1"># 拡張された新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-0-63" name="__codelineno-0-63" href="#__codelineno-0-63"></a>        <span class="c1"># リサイズ後の新しいハッシュテーブルを初期化</span>
 <a id="__codelineno-0-64" name="__codelineno-0-64" href="#__codelineno-0-64"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span> <span class="o">*=</span> <span class="bp">self</span><span class="o">.</span><span class="n">extend_ratio</span>
 <a id="__codelineno-0-65" name="__codelineno-0-65" href="#__codelineno-0-65"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span> <span class="o">=</span> <span class="p">[[]</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">)]</span>
 <a id="__codelineno-0-66" name="__codelineno-0-66" href="#__codelineno-0-66"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">=</span> <span class="mi">0</span>
-<a id="__codelineno-0-67" name="__codelineno-0-67" href="#__codelineno-0-67"></a>        <span class="c1"># 元のハッシュテーブルから新しいハッシュテーブルにキー値ペアを移動</span>
+<a id="__codelineno-0-67" name="__codelineno-0-67" href="#__codelineno-0-67"></a>        <span class="c1"># キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
 <a id="__codelineno-0-68" name="__codelineno-0-68" href="#__codelineno-0-68"></a>        <span class="k">for</span> <span class="n">bucket</span> <span class="ow">in</span> <span class="n">buckets</span><span class="p">:</span>
 <a id="__codelineno-0-69" name="__codelineno-0-69" href="#__codelineno-0-69"></a>            <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="n">bucket</span><span class="p">:</span>
 <a id="__codelineno-0-70" name="__codelineno-0-70" href="#__codelineno-0-70"></a>                <span class="bp">self</span><span class="o">.</span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="p">,</span> <span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
@@ -4570,9 +4570,9 @@
 <div class="highlight"><span class="filename">hash_map_chaining.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* チェイン法ハッシュテーブル */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">HashMapChaining</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
-<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w">                       </span><span class="c1">// キー値ペアの数</span>
-<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span><span class="w">                   </span><span class="c1">// ハッシュテーブルの容量</span>
-<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="kt">double</span><span class="w"> </span><span class="n">loadThres</span><span class="p">;</span><span class="w">               </span><span class="c1">// 拡張をトリガーする負荷率の閾値</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w">                       </span><span class="c1">// キーと値のペア数</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span><span class="w">                   </span><span class="c1">// ハッシュテーブル容量</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="kt">double</span><span class="w"> </span><span class="n">loadThres</span><span class="p">;</span><span class="w">               </span><span class="c1">// リサイズを発動する負荷率のしきい値</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span><span class="w">                </span><span class="c1">// 拡張倍率</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Pair</span><span class="w"> </span><span class="o">*&gt;&gt;</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span><span class="w"> </span><span class="c1">// バケット配列</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a>
@@ -4582,11 +4582,11 @@
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="n">buckets</span><span class="p">.</span><span class="n">resize</span><span class="p">(</span><span class="n">capacity</span><span class="p">);</span>
 <a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a>
-<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">    </span><span class="cm">/* デストラクタ */</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">    </span><span class="cm">/* デストラクタメソッド */</span>
 <a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="o">~</span><span class="n">HashMapChaining</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="o">&amp;</span><span class="n">bucket</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">                </span><span class="c1">// メモリを解放</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">                </span><span class="c1">// メモリを解放する</span>
 <a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">                </span><span class="k">delete</span><span class="w"> </span><span class="n">pair</span><span class="p">;</span>
 <a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w">        </span><span class="p">}</span>
@@ -4602,34 +4602,34 @@
 <a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="n">size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="n">capacity</span><span class="p">;</span>
 <a id="__codelineno-1-34" name="__codelineno-1-34" href="#__codelineno-1-34"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-1-35" name="__codelineno-1-35" href="#__codelineno-1-35"></a>
-<a id="__codelineno-1-36" name="__codelineno-1-36" href="#__codelineno-1-36"></a><span class="w">    </span><span class="cm">/* クエリ操作 */</span>
+<a id="__codelineno-1-36" name="__codelineno-1-36" href="#__codelineno-1-36"></a><span class="w">    </span><span class="cm">/* 検索操作 */</span>
 <a id="__codelineno-1-37" name="__codelineno-1-37" href="#__codelineno-1-37"></a><span class="w">    </span><span class="n">string</span><span class="w"> </span><span class="n">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-38" name="__codelineno-1-38" href="#__codelineno-1-38"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
-<a id="__codelineno-1-39" name="__codelineno-1-39" href="#__codelineno-1-39"></a><span class="w">        </span><span class="c1">// バケットを走査、キーが見つかった場合、対応するvalを返却</span>
+<a id="__codelineno-1-39" name="__codelineno-1-39" href="#__codelineno-1-39"></a><span class="w">        </span><span class="c1">// バケットを走査し、key が見つかれば対応する val を返す</span>
 <a id="__codelineno-1-40" name="__codelineno-1-40" href="#__codelineno-1-40"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-41" name="__codelineno-1-41" href="#__codelineno-1-41"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-42" name="__codelineno-1-42" href="#__codelineno-1-42"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
 <a id="__codelineno-1-43" name="__codelineno-1-43" href="#__codelineno-1-43"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-1-44" name="__codelineno-1-44" href="#__codelineno-1-44"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-1-45" name="__codelineno-1-45" href="#__codelineno-1-45"></a><span class="w">        </span><span class="c1">// キーが見つからない場合、空文字列を返却</span>
+<a id="__codelineno-1-45" name="__codelineno-1-45" href="#__codelineno-1-45"></a><span class="w">        </span><span class="c1">// key が見つからない場合は空文字列を返す</span>
 <a id="__codelineno-1-46" name="__codelineno-1-46" href="#__codelineno-1-46"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="s">&quot;&quot;</span><span class="p">;</span>
 <a id="__codelineno-1-47" name="__codelineno-1-47" href="#__codelineno-1-47"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-1-48" name="__codelineno-1-48" href="#__codelineno-1-48"></a>
 <a id="__codelineno-1-49" name="__codelineno-1-49" href="#__codelineno-1-49"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
 <a id="__codelineno-1-50" name="__codelineno-1-50" href="#__codelineno-1-50"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-51" name="__codelineno-1-51" href="#__codelineno-1-51"></a><span class="w">        </span><span class="c1">// 負荷率が閾値を超えた場合、拡張を実行</span>
+<a id="__codelineno-1-51" name="__codelineno-1-51" href="#__codelineno-1-51"></a><span class="w">        </span><span class="c1">// 負荷率がしきい値を超えたら、リサイズを実行</span>
 <a id="__codelineno-1-52" name="__codelineno-1-52" href="#__codelineno-1-52"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">loadThres</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-53" name="__codelineno-1-53" href="#__codelineno-1-53"></a><span class="w">            </span><span class="n">extend</span><span class="p">();</span>
 <a id="__codelineno-1-54" name="__codelineno-1-54" href="#__codelineno-1-54"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-1-55" name="__codelineno-1-55" href="#__codelineno-1-55"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
-<a id="__codelineno-1-56" name="__codelineno-1-56" href="#__codelineno-1-56"></a><span class="w">        </span><span class="c1">// バケットを走査、指定キーに遭遇した場合、対応するvalを更新して返却</span>
+<a id="__codelineno-1-56" name="__codelineno-1-56" href="#__codelineno-1-56"></a><span class="w">        </span><span class="c1">// バケットを走査し、指定した key が見つかれば対応する val を更新して返す</span>
 <a id="__codelineno-1-57" name="__codelineno-1-57" href="#__codelineno-1-57"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-58" name="__codelineno-1-58" href="#__codelineno-1-58"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-59" name="__codelineno-1-59" href="#__codelineno-1-59"></a><span class="w">                </span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
 <a id="__codelineno-1-60" name="__codelineno-1-60" href="#__codelineno-1-60"></a><span class="w">                </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-1-61" name="__codelineno-1-61" href="#__codelineno-1-61"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-1-62" name="__codelineno-1-62" href="#__codelineno-1-62"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-1-63" name="__codelineno-1-63" href="#__codelineno-1-63"></a><span class="w">        </span><span class="c1">// キーが見つからない場合、キー値ペアを末尾に追加</span>
+<a id="__codelineno-1-63" name="__codelineno-1-63" href="#__codelineno-1-63"></a><span class="w">        </span><span class="c1">// その key が存在しなければ、キーと値のペアを末尾に追加</span>
 <a id="__codelineno-1-64" name="__codelineno-1-64" href="#__codelineno-1-64"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">push_back</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">));</span>
 <a id="__codelineno-1-65" name="__codelineno-1-65" href="#__codelineno-1-65"></a><span class="w">        </span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
 <a id="__codelineno-1-66" name="__codelineno-1-66" href="#__codelineno-1-66"></a><span class="w">    </span><span class="p">}</span>
@@ -4638,12 +4638,12 @@
 <a id="__codelineno-1-69" name="__codelineno-1-69" href="#__codelineno-1-69"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-70" name="__codelineno-1-70" href="#__codelineno-1-70"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
 <a id="__codelineno-1-71" name="__codelineno-1-71" href="#__codelineno-1-71"></a><span class="w">        </span><span class="k">auto</span><span class="w"> </span><span class="o">&amp;</span><span class="n">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
-<a id="__codelineno-1-72" name="__codelineno-1-72" href="#__codelineno-1-72"></a><span class="w">        </span><span class="c1">// バケットを走査、キー値ペアを削除</span>
+<a id="__codelineno-1-72" name="__codelineno-1-72" href="#__codelineno-1-72"></a><span class="w">        </span><span class="c1">// バケットを走査してキーと値のペアを削除</span>
 <a id="__codelineno-1-73" name="__codelineno-1-73" href="#__codelineno-1-73"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">bucket</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-74" name="__codelineno-1-74" href="#__codelineno-1-74"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">bucket</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-75" name="__codelineno-1-75" href="#__codelineno-1-75"></a><span class="w">                </span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bucket</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
-<a id="__codelineno-1-76" name="__codelineno-1-76" href="#__codelineno-1-76"></a><span class="w">                </span><span class="n">bucket</span><span class="p">.</span><span class="n">erase</span><span class="p">(</span><span class="n">bucket</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="p">);</span><span class="w"> </span><span class="c1">// キー値ペアを削除</span>
-<a id="__codelineno-1-77" name="__codelineno-1-77" href="#__codelineno-1-77"></a><span class="w">                </span><span class="k">delete</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span><span class="w">                       </span><span class="c1">// メモリを解放</span>
+<a id="__codelineno-1-76" name="__codelineno-1-76" href="#__codelineno-1-76"></a><span class="w">                </span><span class="n">bucket</span><span class="p">.</span><span class="n">erase</span><span class="p">(</span><span class="n">bucket</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="p">);</span><span class="w"> </span><span class="c1">// そこからキーと値の組を削除する</span>
+<a id="__codelineno-1-77" name="__codelineno-1-77" href="#__codelineno-1-77"></a><span class="w">                </span><span class="k">delete</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span><span class="w">                       </span><span class="c1">// メモリを解放する</span>
 <a id="__codelineno-1-78" name="__codelineno-1-78" href="#__codelineno-1-78"></a><span class="w">                </span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
 <a id="__codelineno-1-79" name="__codelineno-1-79" href="#__codelineno-1-79"></a><span class="w">                </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-1-80" name="__codelineno-1-80" href="#__codelineno-1-80"></a><span class="w">            </span><span class="p">}</span>
@@ -4654,22 +4654,22 @@
 <a id="__codelineno-1-85" name="__codelineno-1-85" href="#__codelineno-1-85"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">extend</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-86" name="__codelineno-1-86" href="#__codelineno-1-86"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルを一時保存</span>
 <a id="__codelineno-1-87" name="__codelineno-1-87" href="#__codelineno-1-87"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Pair</span><span class="w"> </span><span class="o">*&gt;&gt;</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span>
-<a id="__codelineno-1-88" name="__codelineno-1-88" href="#__codelineno-1-88"></a><span class="w">        </span><span class="c1">// 拡張された新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-1-88" name="__codelineno-1-88" href="#__codelineno-1-88"></a><span class="w">        </span><span class="c1">// リサイズ後の新しいハッシュテーブルを初期化</span>
 <a id="__codelineno-1-89" name="__codelineno-1-89" href="#__codelineno-1-89"></a><span class="w">        </span><span class="n">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span>
 <a id="__codelineno-1-90" name="__codelineno-1-90" href="#__codelineno-1-90"></a><span class="w">        </span><span class="n">buckets</span><span class="p">.</span><span class="n">clear</span><span class="p">();</span>
 <a id="__codelineno-1-91" name="__codelineno-1-91" href="#__codelineno-1-91"></a><span class="w">        </span><span class="n">buckets</span><span class="p">.</span><span class="n">resize</span><span class="p">(</span><span class="n">capacity</span><span class="p">);</span>
 <a id="__codelineno-1-92" name="__codelineno-1-92" href="#__codelineno-1-92"></a><span class="w">        </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-1-93" name="__codelineno-1-93" href="#__codelineno-1-93"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルから新しいハッシュテーブルにキー値ペアを移動</span>
+<a id="__codelineno-1-93" name="__codelineno-1-93" href="#__codelineno-1-93"></a><span class="w">        </span><span class="c1">// キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
 <a id="__codelineno-1-94" name="__codelineno-1-94" href="#__codelineno-1-94"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="o">&amp;</span><span class="n">bucket</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-95" name="__codelineno-1-95" href="#__codelineno-1-95"></a><span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-96" name="__codelineno-1-96" href="#__codelineno-1-96"></a><span class="w">                </span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
-<a id="__codelineno-1-97" name="__codelineno-1-97" href="#__codelineno-1-97"></a><span class="w">                </span><span class="c1">// メモリを解放</span>
+<a id="__codelineno-1-97" name="__codelineno-1-97" href="#__codelineno-1-97"></a><span class="w">                </span><span class="c1">// メモリを解放する</span>
 <a id="__codelineno-1-98" name="__codelineno-1-98" href="#__codelineno-1-98"></a><span class="w">                </span><span class="k">delete</span><span class="w"> </span><span class="n">pair</span><span class="p">;</span>
 <a id="__codelineno-1-99" name="__codelineno-1-99" href="#__codelineno-1-99"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-1-100" name="__codelineno-1-100" href="#__codelineno-1-100"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-1-101" name="__codelineno-1-101" href="#__codelineno-1-101"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-1-102" name="__codelineno-1-102" href="#__codelineno-1-102"></a>
-<a id="__codelineno-1-103" name="__codelineno-1-103" href="#__codelineno-1-103"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを印刷 */</span>
+<a id="__codelineno-1-103" name="__codelineno-1-103" href="#__codelineno-1-103"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを出力 */</span>
 <a id="__codelineno-1-104" name="__codelineno-1-104" href="#__codelineno-1-104"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-105" name="__codelineno-1-105" href="#__codelineno-1-105"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="o">&amp;</span><span class="n">bucket</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-106" name="__codelineno-1-106" href="#__codelineno-1-106"></a><span class="w">            </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;[&quot;</span><span class="p">;</span>
@@ -4685,9 +4685,9 @@
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">hash_map_chaining.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* チェイン法ハッシュテーブル */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kd">class</span> <span class="nc">HashMapChaining</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="c1">// キー値ペアの数</span>
-<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span><span class="w"> </span><span class="c1">// ハッシュテーブルの容量</span>
-<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="kt">double</span><span class="w"> </span><span class="n">loadThres</span><span class="p">;</span><span class="w"> </span><span class="c1">// 拡張をトリガーする負荷率の閾値</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="c1">// キーと値のペア数</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span><span class="w"> </span><span class="c1">// ハッシュテーブル容量</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="kt">double</span><span class="w"> </span><span class="n">loadThres</span><span class="p">;</span><span class="w"> </span><span class="c1">// リサイズを発動する負荷率のしきい値</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span><span class="w"> </span><span class="c1">// 拡張倍率</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span><span class="w"> </span><span class="c1">// バケット配列</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a>
@@ -4713,36 +4713,36 @@
 <a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
 <a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a>
-<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="w">    </span><span class="cm">/* クエリ操作 */</span>
+<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="w">    </span><span class="cm">/* 検索操作 */</span>
 <a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="w">    </span><span class="n">String</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
 <a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
-<a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a><span class="w">        </span><span class="c1">// バケットを走査、キーが見つかった場合対応するvalを返す</span>
+<a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a><span class="w">        </span><span class="c1">// バケットを走査し、key が見つかれば対応する val を返す</span>
 <a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-37" name="__codelineno-2-37" href="#__codelineno-2-37"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-38" name="__codelineno-2-38" href="#__codelineno-2-38"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
 <a id="__codelineno-2-39" name="__codelineno-2-39" href="#__codelineno-2-39"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-2-40" name="__codelineno-2-40" href="#__codelineno-2-40"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-2-41" name="__codelineno-2-41" href="#__codelineno-2-41"></a><span class="w">        </span><span class="c1">// キーが見つからない場合、nullを返す</span>
+<a id="__codelineno-2-41" name="__codelineno-2-41" href="#__codelineno-2-41"></a><span class="w">        </span><span class="c1">// key が見つからない場合は null を返す</span>
 <a id="__codelineno-2-42" name="__codelineno-2-42" href="#__codelineno-2-42"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
 <a id="__codelineno-2-43" name="__codelineno-2-43" href="#__codelineno-2-43"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-2-44" name="__codelineno-2-44" href="#__codelineno-2-44"></a>
 <a id="__codelineno-2-45" name="__codelineno-2-45" href="#__codelineno-2-45"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
 <a id="__codelineno-2-46" name="__codelineno-2-46" href="#__codelineno-2-46"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-47" name="__codelineno-2-47" href="#__codelineno-2-47"></a><span class="w">        </span><span class="c1">// 負荷率が閾値を超えた場合、拡張を実行</span>
+<a id="__codelineno-2-47" name="__codelineno-2-47" href="#__codelineno-2-47"></a><span class="w">        </span><span class="c1">// 負荷率がしきい値を超えたら、リサイズを実行</span>
 <a id="__codelineno-2-48" name="__codelineno-2-48" href="#__codelineno-2-48"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">loadThres</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-49" name="__codelineno-2-49" href="#__codelineno-2-49"></a><span class="w">            </span><span class="n">extend</span><span class="p">();</span>
 <a id="__codelineno-2-50" name="__codelineno-2-50" href="#__codelineno-2-50"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-2-51" name="__codelineno-2-51" href="#__codelineno-2-51"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
 <a id="__codelineno-2-52" name="__codelineno-2-52" href="#__codelineno-2-52"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
-<a id="__codelineno-2-53" name="__codelineno-2-53" href="#__codelineno-2-53"></a><span class="w">        </span><span class="c1">// バケットを走査、指定したキーに遭遇した場合、対応するvalを更新して戻る</span>
+<a id="__codelineno-2-53" name="__codelineno-2-53" href="#__codelineno-2-53"></a><span class="w">        </span><span class="c1">// バケットを走査し、指定した key が見つかれば対応する val を更新して返す</span>
 <a id="__codelineno-2-54" name="__codelineno-2-54" href="#__codelineno-2-54"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-55" name="__codelineno-2-55" href="#__codelineno-2-55"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-56" name="__codelineno-2-56" href="#__codelineno-2-56"></a><span class="w">                </span><span class="n">pair</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
 <a id="__codelineno-2-57" name="__codelineno-2-57" href="#__codelineno-2-57"></a><span class="w">                </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-2-58" name="__codelineno-2-58" href="#__codelineno-2-58"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-2-59" name="__codelineno-2-59" href="#__codelineno-2-59"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-2-60" name="__codelineno-2-60" href="#__codelineno-2-60"></a><span class="w">        </span><span class="c1">// キーが見つからない場合、キー値ペアを末尾に追加</span>
+<a id="__codelineno-2-60" name="__codelineno-2-60" href="#__codelineno-2-60"></a><span class="w">        </span><span class="c1">// その key が存在しなければ、キーと値のペアを末尾に追加</span>
 <a id="__codelineno-2-61" name="__codelineno-2-61" href="#__codelineno-2-61"></a><span class="w">        </span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
 <a id="__codelineno-2-62" name="__codelineno-2-62" href="#__codelineno-2-62"></a><span class="w">        </span><span class="n">bucket</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">pair</span><span class="p">);</span>
 <a id="__codelineno-2-63" name="__codelineno-2-63" href="#__codelineno-2-63"></a><span class="w">        </span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
@@ -4752,7 +4752,7 @@
 <a id="__codelineno-2-67" name="__codelineno-2-67" href="#__codelineno-2-67"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-68" name="__codelineno-2-68" href="#__codelineno-2-68"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
 <a id="__codelineno-2-69" name="__codelineno-2-69" href="#__codelineno-2-69"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
-<a id="__codelineno-2-70" name="__codelineno-2-70" href="#__codelineno-2-70"></a><span class="w">        </span><span class="c1">// バケットを走査、その中からキー値ペアを削除</span>
+<a id="__codelineno-2-70" name="__codelineno-2-70" href="#__codelineno-2-70"></a><span class="w">        </span><span class="c1">// バケットを走査してキーと値のペアを削除</span>
 <a id="__codelineno-2-71" name="__codelineno-2-71" href="#__codelineno-2-71"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-72" name="__codelineno-2-72" href="#__codelineno-2-72"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-73" name="__codelineno-2-73" href="#__codelineno-2-73"></a><span class="w">                </span><span class="n">bucket</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">pair</span><span class="p">);</span>
@@ -4764,16 +4764,16 @@
 <a id="__codelineno-2-79" name="__codelineno-2-79" href="#__codelineno-2-79"></a>
 <a id="__codelineno-2-80" name="__codelineno-2-80" href="#__codelineno-2-80"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを拡張 */</span>
 <a id="__codelineno-2-81" name="__codelineno-2-81" href="#__codelineno-2-81"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="nf">extend</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-82" name="__codelineno-2-82" href="#__codelineno-2-82"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルを一時的に保存</span>
+<a id="__codelineno-2-82" name="__codelineno-2-82" href="#__codelineno-2-82"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルを一時保存</span>
 <a id="__codelineno-2-83" name="__codelineno-2-83" href="#__codelineno-2-83"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span>
-<a id="__codelineno-2-84" name="__codelineno-2-84" href="#__codelineno-2-84"></a><span class="w">        </span><span class="c1">// 拡張された新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-2-84" name="__codelineno-2-84" href="#__codelineno-2-84"></a><span class="w">        </span><span class="c1">// リサイズ後の新しいハッシュテーブルを初期化</span>
 <a id="__codelineno-2-85" name="__codelineno-2-85" href="#__codelineno-2-85"></a><span class="w">        </span><span class="n">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span>
 <a id="__codelineno-2-86" name="__codelineno-2-86" href="#__codelineno-2-86"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">capacity</span><span class="p">);</span>
 <a id="__codelineno-2-87" name="__codelineno-2-87" href="#__codelineno-2-87"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-88" name="__codelineno-2-88" href="#__codelineno-2-88"></a><span class="w">            </span><span class="n">buckets</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">());</span>
 <a id="__codelineno-2-89" name="__codelineno-2-89" href="#__codelineno-2-89"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-2-90" name="__codelineno-2-90" href="#__codelineno-2-90"></a><span class="w">        </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-2-91" name="__codelineno-2-91" href="#__codelineno-2-91"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルから新しいハッシュテーブルにキー値ペアを移動</span>
+<a id="__codelineno-2-91" name="__codelineno-2-91" href="#__codelineno-2-91"></a><span class="w">        </span><span class="c1">// キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
 <a id="__codelineno-2-92" name="__codelineno-2-92" href="#__codelineno-2-92"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-93" name="__codelineno-2-93" href="#__codelineno-2-93"></a><span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-94" name="__codelineno-2-94" href="#__codelineno-2-94"></a><span class="w">                </span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
@@ -4781,7 +4781,7 @@
 <a id="__codelineno-2-96" name="__codelineno-2-96" href="#__codelineno-2-96"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-2-97" name="__codelineno-2-97" href="#__codelineno-2-97"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-2-98" name="__codelineno-2-98" href="#__codelineno-2-98"></a>
-<a id="__codelineno-2-99" name="__codelineno-2-99" href="#__codelineno-2-99"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを印刷 */</span>
+<a id="__codelineno-2-99" name="__codelineno-2-99" href="#__codelineno-2-99"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを出力 */</span>
 <a id="__codelineno-2-100" name="__codelineno-2-100" href="#__codelineno-2-100"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="nf">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-101" name="__codelineno-2-101" href="#__codelineno-2-101"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-102" name="__codelineno-2-102" href="#__codelineno-2-102"></a><span class="w">            </span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
@@ -4795,72 +4795,1180 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map_chaining.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">HashMapChaining</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">hash_map_chaining.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* チェイン法ハッシュテーブル */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">HashMapChaining</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="c1">// キーと値のペア数</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span><span class="w"> </span><span class="c1">// ハッシュテーブル容量</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="kt">double</span><span class="w"> </span><span class="n">loadThres</span><span class="p">;</span><span class="w"> </span><span class="c1">// リサイズを発動する負荷率のしきい値</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span><span class="w"> </span><span class="c1">// 拡張倍率</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span><span class="w"> </span><span class="c1">// バケット配列</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nf">HashMapChaining</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">        </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">        </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">4</span><span class="p">;</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">        </span><span class="n">loadThres</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3.0</span><span class="p">;</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">        </span><span class="n">extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;&gt;</span><span class="p">(</span><span class="n">capacity</span><span class="p">);</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">            </span><span class="n">buckets</span><span class="p">.</span><span class="n">Add</span><span class="p">([]);</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a>
+<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="nf">HashFunc</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a>
+<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="w">    </span><span class="cm">/* 負荷率 */</span>
+<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a><span class="w">    </span><span class="kt">double</span><span class="w"> </span><span class="nf">LoadFactor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="n">size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a>
+<a id="__codelineno-3-31" name="__codelineno-3-31" href="#__codelineno-3-31"></a><span class="w">    </span><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-3-32" name="__codelineno-3-32" href="#__codelineno-3-32"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">string?</span><span class="w"> </span><span class="n">Get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-33" name="__codelineno-3-33" href="#__codelineno-3-33"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-3-34" name="__codelineno-3-34" href="#__codelineno-3-34"></a><span class="w">        </span><span class="c1">// バケットを走査し、key が見つかれば対応する val を返す</span>
+<a id="__codelineno-3-35" name="__codelineno-3-35" href="#__codelineno-3-35"></a><span class="w">        </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-36" name="__codelineno-3-36" href="#__codelineno-3-36"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-37" name="__codelineno-3-37" href="#__codelineno-3-37"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-3-38" name="__codelineno-3-38" href="#__codelineno-3-38"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-3-39" name="__codelineno-3-39" href="#__codelineno-3-39"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-40" name="__codelineno-3-40" href="#__codelineno-3-40"></a><span class="w">        </span><span class="c1">// key が見つからない場合は null を返す</span>
+<a id="__codelineno-3-41" name="__codelineno-3-41" href="#__codelineno-3-41"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
+<a id="__codelineno-3-42" name="__codelineno-3-42" href="#__codelineno-3-42"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-43" name="__codelineno-3-43" href="#__codelineno-3-43"></a>
+<a id="__codelineno-3-44" name="__codelineno-3-44" href="#__codelineno-3-44"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-3-45" name="__codelineno-3-45" href="#__codelineno-3-45"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">Put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="kt">string</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-46" name="__codelineno-3-46" href="#__codelineno-3-46"></a><span class="w">        </span><span class="c1">// 負荷率がしきい値を超えたら、リサイズを実行</span>
+<a id="__codelineno-3-47" name="__codelineno-3-47" href="#__codelineno-3-47"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">LoadFactor</span><span class="p">()</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">loadThres</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-48" name="__codelineno-3-48" href="#__codelineno-3-48"></a><span class="w">            </span><span class="n">Extend</span><span class="p">();</span>
+<a id="__codelineno-3-49" name="__codelineno-3-49" href="#__codelineno-3-49"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-50" name="__codelineno-3-50" href="#__codelineno-3-50"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-3-51" name="__codelineno-3-51" href="#__codelineno-3-51"></a><span class="w">        </span><span class="c1">// バケットを走査し、指定した key が見つかれば対応する val を更新して返す</span>
+<a id="__codelineno-3-52" name="__codelineno-3-52" href="#__codelineno-3-52"></a><span class="w">        </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-53" name="__codelineno-3-53" href="#__codelineno-3-53"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-54" name="__codelineno-3-54" href="#__codelineno-3-54"></a><span class="w">                </span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-3-55" name="__codelineno-3-55" href="#__codelineno-3-55"></a><span class="w">                </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-3-56" name="__codelineno-3-56" href="#__codelineno-3-56"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-3-57" name="__codelineno-3-57" href="#__codelineno-3-57"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-58" name="__codelineno-3-58" href="#__codelineno-3-58"></a><span class="w">        </span><span class="c1">// その key が存在しなければ、キーと値のペアを末尾に追加</span>
+<a id="__codelineno-3-59" name="__codelineno-3-59" href="#__codelineno-3-59"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">Add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">));</span>
+<a id="__codelineno-3-60" name="__codelineno-3-60" href="#__codelineno-3-60"></a><span class="w">        </span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-3-61" name="__codelineno-3-61" href="#__codelineno-3-61"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-62" name="__codelineno-3-62" href="#__codelineno-3-62"></a>
+<a id="__codelineno-3-63" name="__codelineno-3-63" href="#__codelineno-3-63"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-3-64" name="__codelineno-3-64" href="#__codelineno-3-64"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">Remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-65" name="__codelineno-3-65" href="#__codelineno-3-65"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-3-66" name="__codelineno-3-66" href="#__codelineno-3-66"></a><span class="w">        </span><span class="c1">// バケットを走査してキーと値のペアを削除</span>
+<a id="__codelineno-3-67" name="__codelineno-3-67" href="#__codelineno-3-67"></a><span class="w">        </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">ToList</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-68" name="__codelineno-3-68" href="#__codelineno-3-68"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-69" name="__codelineno-3-69" href="#__codelineno-3-69"></a><span class="w">                </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">Remove</span><span class="p">(</span><span class="n">pair</span><span class="p">);</span>
+<a id="__codelineno-3-70" name="__codelineno-3-70" href="#__codelineno-3-70"></a><span class="w">                </span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-3-71" name="__codelineno-3-71" href="#__codelineno-3-71"></a><span class="w">                </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-3-72" name="__codelineno-3-72" href="#__codelineno-3-72"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-3-73" name="__codelineno-3-73" href="#__codelineno-3-73"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-74" name="__codelineno-3-74" href="#__codelineno-3-74"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-75" name="__codelineno-3-75" href="#__codelineno-3-75"></a>
+<a id="__codelineno-3-76" name="__codelineno-3-76" href="#__codelineno-3-76"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを拡張 */</span>
+<a id="__codelineno-3-77" name="__codelineno-3-77" href="#__codelineno-3-77"></a><span class="w">    </span><span class="k">void</span><span class="w"> </span><span class="nf">Extend</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-78" name="__codelineno-3-78" href="#__codelineno-3-78"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルを一時保存</span>
+<a id="__codelineno-3-79" name="__codelineno-3-79" href="#__codelineno-3-79"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span>
+<a id="__codelineno-3-80" name="__codelineno-3-80" href="#__codelineno-3-80"></a><span class="w">        </span><span class="c1">// リサイズ後の新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-3-81" name="__codelineno-3-81" href="#__codelineno-3-81"></a><span class="w">        </span><span class="n">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span>
+<a id="__codelineno-3-82" name="__codelineno-3-82" href="#__codelineno-3-82"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;&gt;</span><span class="p">(</span><span class="n">capacity</span><span class="p">);</span>
+<a id="__codelineno-3-83" name="__codelineno-3-83" href="#__codelineno-3-83"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-84" name="__codelineno-3-84" href="#__codelineno-3-84"></a><span class="w">            </span><span class="n">buckets</span><span class="p">.</span><span class="n">Add</span><span class="p">([]);</span>
+<a id="__codelineno-3-85" name="__codelineno-3-85" href="#__codelineno-3-85"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-86" name="__codelineno-3-86" href="#__codelineno-3-86"></a><span class="w">        </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-3-87" name="__codelineno-3-87" href="#__codelineno-3-87"></a><span class="w">        </span><span class="c1">// キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
+<a id="__codelineno-3-88" name="__codelineno-3-88" href="#__codelineno-3-88"></a><span class="w">        </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-89" name="__codelineno-3-89" href="#__codelineno-3-89"></a><span class="w">            </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-90" name="__codelineno-3-90" href="#__codelineno-3-90"></a><span class="w">                </span><span class="n">Put</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-3-91" name="__codelineno-3-91" href="#__codelineno-3-91"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-3-92" name="__codelineno-3-92" href="#__codelineno-3-92"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-93" name="__codelineno-3-93" href="#__codelineno-3-93"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-94" name="__codelineno-3-94" href="#__codelineno-3-94"></a>
+<a id="__codelineno-3-95" name="__codelineno-3-95" href="#__codelineno-3-95"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-3-96" name="__codelineno-3-96" href="#__codelineno-3-96"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">Print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-97" name="__codelineno-3-97" href="#__codelineno-3-97"></a><span class="w">        </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-98" name="__codelineno-3-98" href="#__codelineno-3-98"></a><span class="w">            </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">string</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-3-99" name="__codelineno-3-99" href="#__codelineno-3-99"></a><span class="w">            </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-100" name="__codelineno-3-100" href="#__codelineno-3-100"></a><span class="w">                </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-3-101" name="__codelineno-3-101" href="#__codelineno-3-101"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-3-102" name="__codelineno-3-102" href="#__codelineno-3-102"></a><span class="w">            </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">string</span><span class="w"> </span><span class="n">kv</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-103" name="__codelineno-3-103" href="#__codelineno-3-103"></a><span class="w">                </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="n">kv</span><span class="p">);</span>
+<a id="__codelineno-3-104" name="__codelineno-3-104" href="#__codelineno-3-104"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-3-105" name="__codelineno-3-105" href="#__codelineno-3-105"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-106" name="__codelineno-3-106" href="#__codelineno-3-106"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-107" name="__codelineno-3-107" href="#__codelineno-3-107"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map_chaining.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">hashMapChaining</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">hash_map_chaining.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* チェイン法ハッシュテーブル */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">hashMapChaining</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="nx">size</span><span class="w">        </span><span class="kt">int</span><span class="w">      </span><span class="c1">// キーと値のペア数</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">capacity</span><span class="w">    </span><span class="kt">int</span><span class="w">      </span><span class="c1">// ハッシュテーブル容量</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="nx">loadThres</span><span class="w">   </span><span class="kt">float64</span><span class="w">  </span><span class="c1">// リサイズを発動する負荷率のしきい値</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="nx">extendRatio</span><span class="w"> </span><span class="kt">int</span><span class="w">      </span><span class="c1">// 拡張倍率</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="nx">buckets</span><span class="w">     </span><span class="p">[][]</span><span class="nx">pair</span><span class="w"> </span><span class="c1">// バケット配列</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="p">}</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="kd">func</span><span class="w"> </span><span class="nx">newHashMapChaining</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="nx">hashMapChaining</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">    </span><span class="nx">buckets</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="nx">pair</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">4</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">        </span><span class="nx">buckets</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="nx">pair</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">hashMapChaining</span><span class="p">{</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">        </span><span class="nx">size</span><span class="p">:</span><span class="w">        </span><span class="mi">0</span><span class="p">,</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w">        </span><span class="nx">capacity</span><span class="p">:</span><span class="w">    </span><span class="mi">4</span><span class="p">,</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w">        </span><span class="nx">loadThres</span><span class="p">:</span><span class="w">   </span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3.0</span><span class="p">,</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w">        </span><span class="nx">extendRatio</span><span class="p">:</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w">        </span><span class="nx">buckets</span><span class="p">:</span><span class="w">     </span><span class="nx">buckets</span><span class="p">,</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="p">}</span>
+<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a>
+<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">m</span><span class="w"> </span><span class="o">*</span><span class="nx">hashMapChaining</span><span class="p">)</span><span class="w"> </span><span class="nx">hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">capacity</span>
+<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="p">}</span>
+<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a>
+<a id="__codelineno-4-30" name="__codelineno-4-30" href="#__codelineno-4-30"></a><span class="cm">/* 負荷率 */</span>
+<a id="__codelineno-4-31" name="__codelineno-4-31" href="#__codelineno-4-31"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">m</span><span class="w"> </span><span class="o">*</span><span class="nx">hashMapChaining</span><span class="p">)</span><span class="w"> </span><span class="nx">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="kt">float64</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-32" name="__codelineno-4-32" href="#__codelineno-4-32"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">m</span><span class="p">.</span><span class="nx">size</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">m</span><span class="p">.</span><span class="nx">capacity</span><span class="p">)</span>
+<a id="__codelineno-4-33" name="__codelineno-4-33" href="#__codelineno-4-33"></a><span class="p">}</span>
+<a id="__codelineno-4-34" name="__codelineno-4-34" href="#__codelineno-4-34"></a>
+<a id="__codelineno-4-35" name="__codelineno-4-35" href="#__codelineno-4-35"></a><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-4-36" name="__codelineno-4-36" href="#__codelineno-4-36"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">m</span><span class="w"> </span><span class="o">*</span><span class="nx">hashMapChaining</span><span class="p">)</span><span class="w"> </span><span class="nx">get</span><span class="p">(</span><span class="nx">key</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">string</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-37" name="__codelineno-4-37" href="#__codelineno-4-37"></a><span class="w">    </span><span class="nx">idx</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span>
+<a id="__codelineno-4-38" name="__codelineno-4-38" href="#__codelineno-4-38"></a><span class="w">    </span><span class="nx">bucket</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">idx</span><span class="p">]</span>
+<a id="__codelineno-4-39" name="__codelineno-4-39" href="#__codelineno-4-39"></a><span class="w">    </span><span class="c1">// バケットを走査し、key が見つかれば対応する val を返す</span>
+<a id="__codelineno-4-40" name="__codelineno-4-40" href="#__codelineno-4-40"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">p</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-41" name="__codelineno-4-41" href="#__codelineno-4-41"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">p</span><span class="p">.</span><span class="nx">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">key</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-42" name="__codelineno-4-42" href="#__codelineno-4-42"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nx">p</span><span class="p">.</span><span class="nx">val</span>
+<a id="__codelineno-4-43" name="__codelineno-4-43" href="#__codelineno-4-43"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-44" name="__codelineno-4-44" href="#__codelineno-4-44"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-45" name="__codelineno-4-45" href="#__codelineno-4-45"></a><span class="w">    </span><span class="c1">// key が見つからない場合は空文字列を返す</span>
+<a id="__codelineno-4-46" name="__codelineno-4-46" href="#__codelineno-4-46"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="s">&quot;&quot;</span>
+<a id="__codelineno-4-47" name="__codelineno-4-47" href="#__codelineno-4-47"></a><span class="p">}</span>
+<a id="__codelineno-4-48" name="__codelineno-4-48" href="#__codelineno-4-48"></a>
+<a id="__codelineno-4-49" name="__codelineno-4-49" href="#__codelineno-4-49"></a><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-4-50" name="__codelineno-4-50" href="#__codelineno-4-50"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">m</span><span class="w"> </span><span class="o">*</span><span class="nx">hashMapChaining</span><span class="p">)</span><span class="w"> </span><span class="nx">put</span><span class="p">(</span><span class="nx">key</span><span class="w"> </span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-51" name="__codelineno-4-51" href="#__codelineno-4-51"></a><span class="w">    </span><span class="c1">// 負荷率がしきい値を超えたら、リサイズを実行</span>
+<a id="__codelineno-4-52" name="__codelineno-4-52" href="#__codelineno-4-52"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">loadThres</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-53" name="__codelineno-4-53" href="#__codelineno-4-53"></a><span class="w">        </span><span class="nx">m</span><span class="p">.</span><span class="nx">extend</span><span class="p">()</span>
+<a id="__codelineno-4-54" name="__codelineno-4-54" href="#__codelineno-4-54"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-55" name="__codelineno-4-55" href="#__codelineno-4-55"></a><span class="w">    </span><span class="nx">idx</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span>
+<a id="__codelineno-4-56" name="__codelineno-4-56" href="#__codelineno-4-56"></a><span class="w">    </span><span class="c1">// バケットを走査し、指定した key が見つかれば対応する val を更新して返す</span>
+<a id="__codelineno-4-57" name="__codelineno-4-57" href="#__codelineno-4-57"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">idx</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-58" name="__codelineno-4-58" href="#__codelineno-4-58"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">idx</span><span class="p">][</span><span class="nx">i</span><span class="p">].</span><span class="nx">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">key</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-59" name="__codelineno-4-59" href="#__codelineno-4-59"></a><span class="w">            </span><span class="nx">m</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">idx</span><span class="p">][</span><span class="nx">i</span><span class="p">].</span><span class="nx">val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">val</span>
+<a id="__codelineno-4-60" name="__codelineno-4-60" href="#__codelineno-4-60"></a><span class="w">            </span><span class="k">return</span>
+<a id="__codelineno-4-61" name="__codelineno-4-61" href="#__codelineno-4-61"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-62" name="__codelineno-4-62" href="#__codelineno-4-62"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-63" name="__codelineno-4-63" href="#__codelineno-4-63"></a><span class="w">    </span><span class="c1">// その key が存在しなければ、キーと値のペアを末尾に追加</span>
+<a id="__codelineno-4-64" name="__codelineno-4-64" href="#__codelineno-4-64"></a><span class="w">    </span><span class="nx">p</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">pair</span><span class="p">{</span>
+<a id="__codelineno-4-65" name="__codelineno-4-65" href="#__codelineno-4-65"></a><span class="w">        </span><span class="nx">key</span><span class="p">:</span><span class="w"> </span><span class="nx">key</span><span class="p">,</span>
+<a id="__codelineno-4-66" name="__codelineno-4-66" href="#__codelineno-4-66"></a><span class="w">        </span><span class="nx">val</span><span class="p">:</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span>
+<a id="__codelineno-4-67" name="__codelineno-4-67" href="#__codelineno-4-67"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-68" name="__codelineno-4-68" href="#__codelineno-4-68"></a><span class="w">    </span><span class="nx">m</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">idx</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">m</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">idx</span><span class="p">],</span><span class="w"> </span><span class="nx">p</span><span class="p">)</span>
+<a id="__codelineno-4-69" name="__codelineno-4-69" href="#__codelineno-4-69"></a><span class="w">    </span><span class="nx">m</span><span class="p">.</span><span class="nx">size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-4-70" name="__codelineno-4-70" href="#__codelineno-4-70"></a><span class="p">}</span>
+<a id="__codelineno-4-71" name="__codelineno-4-71" href="#__codelineno-4-71"></a>
+<a id="__codelineno-4-72" name="__codelineno-4-72" href="#__codelineno-4-72"></a><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-4-73" name="__codelineno-4-73" href="#__codelineno-4-73"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">m</span><span class="w"> </span><span class="o">*</span><span class="nx">hashMapChaining</span><span class="p">)</span><span class="w"> </span><span class="nx">remove</span><span class="p">(</span><span class="nx">key</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-74" name="__codelineno-4-74" href="#__codelineno-4-74"></a><span class="w">    </span><span class="nx">idx</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span>
+<a id="__codelineno-4-75" name="__codelineno-4-75" href="#__codelineno-4-75"></a><span class="w">    </span><span class="c1">// バケットを走査してキーと値のペアを削除</span>
+<a id="__codelineno-4-76" name="__codelineno-4-76" href="#__codelineno-4-76"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">p</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">idx</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-77" name="__codelineno-4-77" href="#__codelineno-4-77"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">p</span><span class="p">.</span><span class="nx">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">key</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-78" name="__codelineno-4-78" href="#__codelineno-4-78"></a><span class="w">            </span><span class="c1">// スライスから削除する</span>
+<a id="__codelineno-4-79" name="__codelineno-4-79" href="#__codelineno-4-79"></a><span class="w">            </span><span class="nx">m</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">idx</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">m</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">idx</span><span class="p">][:</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">idx</span><span class="p">][</span><span class="nx">i</span><span class="o">+</span><span class="mi">1</span><span class="p">:]</span><span class="o">...</span><span class="p">)</span>
+<a id="__codelineno-4-80" name="__codelineno-4-80" href="#__codelineno-4-80"></a><span class="w">            </span><span class="nx">m</span><span class="p">.</span><span class="nx">size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-4-81" name="__codelineno-4-81" href="#__codelineno-4-81"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-4-82" name="__codelineno-4-82" href="#__codelineno-4-82"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-83" name="__codelineno-4-83" href="#__codelineno-4-83"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-84" name="__codelineno-4-84" href="#__codelineno-4-84"></a><span class="p">}</span>
+<a id="__codelineno-4-85" name="__codelineno-4-85" href="#__codelineno-4-85"></a>
+<a id="__codelineno-4-86" name="__codelineno-4-86" href="#__codelineno-4-86"></a><span class="cm">/* ハッシュテーブルを拡張 */</span>
+<a id="__codelineno-4-87" name="__codelineno-4-87" href="#__codelineno-4-87"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">m</span><span class="w"> </span><span class="o">*</span><span class="nx">hashMapChaining</span><span class="p">)</span><span class="w"> </span><span class="nx">extend</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-88" name="__codelineno-4-88" href="#__codelineno-4-88"></a><span class="w">    </span><span class="c1">// 元のハッシュテーブルを一時保存</span>
+<a id="__codelineno-4-89" name="__codelineno-4-89" href="#__codelineno-4-89"></a><span class="w">    </span><span class="nx">tmpBuckets</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="nx">pair</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">m</span><span class="p">.</span><span class="nx">buckets</span><span class="p">))</span>
+<a id="__codelineno-4-90" name="__codelineno-4-90" href="#__codelineno-4-90"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">m</span><span class="p">.</span><span class="nx">buckets</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-91" name="__codelineno-4-91" href="#__codelineno-4-91"></a><span class="w">        </span><span class="nx">tmpBuckets</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="nx">pair</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">m</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">i</span><span class="p">]))</span>
+<a id="__codelineno-4-92" name="__codelineno-4-92" href="#__codelineno-4-92"></a><span class="w">        </span><span class="nb">copy</span><span class="p">(</span><span class="nx">tmpBuckets</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span>
+<a id="__codelineno-4-93" name="__codelineno-4-93" href="#__codelineno-4-93"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-94" name="__codelineno-4-94" href="#__codelineno-4-94"></a><span class="w">    </span><span class="c1">// リサイズ後の新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-4-95" name="__codelineno-4-95" href="#__codelineno-4-95"></a><span class="w">    </span><span class="nx">m</span><span class="p">.</span><span class="nx">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">extendRatio</span>
+<a id="__codelineno-4-96" name="__codelineno-4-96" href="#__codelineno-4-96"></a><span class="w">    </span><span class="nx">m</span><span class="p">.</span><span class="nx">buckets</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="nx">pair</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">capacity</span><span class="p">)</span>
+<a id="__codelineno-4-97" name="__codelineno-4-97" href="#__codelineno-4-97"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">capacity</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-98" name="__codelineno-4-98" href="#__codelineno-4-98"></a><span class="w">        </span><span class="nx">m</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="nx">pair</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-4-99" name="__codelineno-4-99" href="#__codelineno-4-99"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-100" name="__codelineno-4-100" href="#__codelineno-4-100"></a><span class="w">    </span><span class="nx">m</span><span class="p">.</span><span class="nx">size</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-4-101" name="__codelineno-4-101" href="#__codelineno-4-101"></a><span class="w">    </span><span class="c1">// キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
+<a id="__codelineno-4-102" name="__codelineno-4-102" href="#__codelineno-4-102"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">tmpBuckets</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-103" name="__codelineno-4-103" href="#__codelineno-4-103"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">p</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-104" name="__codelineno-4-104" href="#__codelineno-4-104"></a><span class="w">            </span><span class="nx">m</span><span class="p">.</span><span class="nx">put</span><span class="p">(</span><span class="nx">p</span><span class="p">.</span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="nx">p</span><span class="p">.</span><span class="nx">val</span><span class="p">)</span>
+<a id="__codelineno-4-105" name="__codelineno-4-105" href="#__codelineno-4-105"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-106" name="__codelineno-4-106" href="#__codelineno-4-106"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-107" name="__codelineno-4-107" href="#__codelineno-4-107"></a><span class="p">}</span>
+<a id="__codelineno-4-108" name="__codelineno-4-108" href="#__codelineno-4-108"></a>
+<a id="__codelineno-4-109" name="__codelineno-4-109" href="#__codelineno-4-109"></a><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-4-110" name="__codelineno-4-110" href="#__codelineno-4-110"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">m</span><span class="w"> </span><span class="o">*</span><span class="nx">hashMapChaining</span><span class="p">)</span><span class="w"> </span><span class="nb">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-111" name="__codelineno-4-111" href="#__codelineno-4-111"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">builder</span><span class="w"> </span><span class="nx">strings</span><span class="p">.</span><span class="nx">Builder</span>
+<a id="__codelineno-4-112" name="__codelineno-4-112" href="#__codelineno-4-112"></a>
+<a id="__codelineno-4-113" name="__codelineno-4-113" href="#__codelineno-4-113"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">buckets</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-114" name="__codelineno-4-114" href="#__codelineno-4-114"></a><span class="w">        </span><span class="nx">builder</span><span class="p">.</span><span class="nx">WriteString</span><span class="p">(</span><span class="s">&quot;[&quot;</span><span class="p">)</span>
+<a id="__codelineno-4-115" name="__codelineno-4-115" href="#__codelineno-4-115"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">p</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-116" name="__codelineno-4-116" href="#__codelineno-4-116"></a><span class="w">            </span><span class="nx">builder</span><span class="p">.</span><span class="nx">WriteString</span><span class="p">(</span><span class="nx">strconv</span><span class="p">.</span><span class="nx">Itoa</span><span class="p">(</span><span class="nx">p</span><span class="p">.</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">p</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot; &quot;</span><span class="p">)</span>
+<a id="__codelineno-4-117" name="__codelineno-4-117" href="#__codelineno-4-117"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-118" name="__codelineno-4-118" href="#__codelineno-4-118"></a><span class="w">        </span><span class="nx">builder</span><span class="p">.</span><span class="nx">WriteString</span><span class="p">(</span><span class="s">&quot;]&quot;</span><span class="p">)</span>
+<a id="__codelineno-4-119" name="__codelineno-4-119" href="#__codelineno-4-119"></a><span class="w">        </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">builder</span><span class="p">.</span><span class="nx">String</span><span class="p">())</span>
+<a id="__codelineno-4-120" name="__codelineno-4-120" href="#__codelineno-4-120"></a><span class="w">        </span><span class="nx">builder</span><span class="p">.</span><span class="nx">Reset</span><span class="p">()</span>
+<a id="__codelineno-4-121" name="__codelineno-4-121" href="#__codelineno-4-121"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-122" name="__codelineno-4-122" href="#__codelineno-4-122"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map_chaining.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">HashMapChaining</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">hash_map_chaining.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* チェイン法ハッシュテーブル */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">HashMapChaining</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">size</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// キーと値のペア数</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">capacity</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// ハッシュテーブル容量</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">loadThres</span><span class="p">:</span><span class="w"> </span><span class="nb">Double</span><span class="w"> </span><span class="c1">// リサイズを発動する負荷率のしきい値</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">extendRatio</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// 拡張倍率</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">buckets</span><span class="p">:</span><span class="w"> </span><span class="p">[[</span><span class="n">Pair</span><span class="p">]]</span><span class="w"> </span><span class="c1">// バケット配列</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">    </span><span class="kd">init</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">        </span><span class="n">size</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">        </span><span class="n">capacity</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">4</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">        </span><span class="n">loadThres</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3.0</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">        </span><span class="n">extendRatio</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="p">[],</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="w">        </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a>
+<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="w">    </span><span class="cm">/* 負荷率 */</span>
+<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Double</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="w">        </span><span class="nb">Double</span><span class="p">(</span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nb">Double</span><span class="p">(</span><span class="n">capacity</span><span class="p">)</span>
+<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a>
+<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a><span class="w">    </span><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-5-29" name="__codelineno-5-29" href="#__codelineno-5-29"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">String</span><span class="p">?</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-30" name="__codelineno-5-30" href="#__codelineno-5-30"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">index</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-5-31" name="__codelineno-5-31" href="#__codelineno-5-31"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">bucket</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
+<a id="__codelineno-5-32" name="__codelineno-5-32" href="#__codelineno-5-32"></a><span class="w">        </span><span class="c1">// バケットを走査し、key が見つかれば対応する val を返す</span>
+<a id="__codelineno-5-33" name="__codelineno-5-33" href="#__codelineno-5-33"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-34" name="__codelineno-5-34" href="#__codelineno-5-34"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-35" name="__codelineno-5-35" href="#__codelineno-5-35"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">val</span>
+<a id="__codelineno-5-36" name="__codelineno-5-36" href="#__codelineno-5-36"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-5-37" name="__codelineno-5-37" href="#__codelineno-5-37"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-38" name="__codelineno-5-38" href="#__codelineno-5-38"></a><span class="w">        </span><span class="c1">// `key` が見つからなければ `nil` を返す</span>
+<a id="__codelineno-5-39" name="__codelineno-5-39" href="#__codelineno-5-39"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-5-40" name="__codelineno-5-40" href="#__codelineno-5-40"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-41" name="__codelineno-5-41" href="#__codelineno-5-41"></a>
+<a id="__codelineno-5-42" name="__codelineno-5-42" href="#__codelineno-5-42"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-5-43" name="__codelineno-5-43" href="#__codelineno-5-43"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="nb">String</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-44" name="__codelineno-5-44" href="#__codelineno-5-44"></a><span class="w">        </span><span class="c1">// 負荷率がしきい値を超えたら、リサイズを実行</span>
+<a id="__codelineno-5-45" name="__codelineno-5-45" href="#__codelineno-5-45"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">loadThres</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-46" name="__codelineno-5-46" href="#__codelineno-5-46"></a><span class="w">            </span><span class="bp">extend</span><span class="p">()</span>
+<a id="__codelineno-5-47" name="__codelineno-5-47" href="#__codelineno-5-47"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-48" name="__codelineno-5-48" href="#__codelineno-5-48"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">index</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-5-49" name="__codelineno-5-49" href="#__codelineno-5-49"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">bucket</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
+<a id="__codelineno-5-50" name="__codelineno-5-50" href="#__codelineno-5-50"></a><span class="w">        </span><span class="c1">// バケットを走査し、指定した key が見つかれば対応する val を更新して返す</span>
+<a id="__codelineno-5-51" name="__codelineno-5-51" href="#__codelineno-5-51"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-52" name="__codelineno-5-52" href="#__codelineno-5-52"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-53" name="__codelineno-5-53" href="#__codelineno-5-53"></a><span class="w">                </span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">val</span>
+<a id="__codelineno-5-54" name="__codelineno-5-54" href="#__codelineno-5-54"></a><span class="w">                </span><span class="k">return</span>
+<a id="__codelineno-5-55" name="__codelineno-5-55" href="#__codelineno-5-55"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-5-56" name="__codelineno-5-56" href="#__codelineno-5-56"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-57" name="__codelineno-5-57" href="#__codelineno-5-57"></a><span class="w">        </span><span class="c1">// その key が存在しなければ、キーと値のペアを末尾に追加</span>
+<a id="__codelineno-5-58" name="__codelineno-5-58" href="#__codelineno-5-58"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">pair</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-5-59" name="__codelineno-5-59" href="#__codelineno-5-59"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">append</span><span class="p">(</span><span class="n">pair</span><span class="p">)</span>
+<a id="__codelineno-5-60" name="__codelineno-5-60" href="#__codelineno-5-60"></a><span class="w">        </span><span class="n">size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-61" name="__codelineno-5-61" href="#__codelineno-5-61"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-62" name="__codelineno-5-62" href="#__codelineno-5-62"></a>
+<a id="__codelineno-5-63" name="__codelineno-5-63" href="#__codelineno-5-63"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-5-64" name="__codelineno-5-64" href="#__codelineno-5-64"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-65" name="__codelineno-5-65" href="#__codelineno-5-65"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">index</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-5-66" name="__codelineno-5-66" href="#__codelineno-5-66"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">bucket</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
+<a id="__codelineno-5-67" name="__codelineno-5-67" href="#__codelineno-5-67"></a><span class="w">        </span><span class="c1">// バケットを走査してキーと値のペアを削除</span>
+<a id="__codelineno-5-68" name="__codelineno-5-68" href="#__codelineno-5-68"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">pairIndex</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">)</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span><span class="p">.</span><span class="n">enumerated</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-69" name="__codelineno-5-69" href="#__codelineno-5-69"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-70" name="__codelineno-5-70" href="#__codelineno-5-70"></a><span class="w">                </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">remove</span><span class="p">(</span><span class="n">at</span><span class="p">:</span><span class="w"> </span><span class="n">pairIndex</span><span class="p">)</span>
+<a id="__codelineno-5-71" name="__codelineno-5-71" href="#__codelineno-5-71"></a><span class="w">                </span><span class="n">size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-72" name="__codelineno-5-72" href="#__codelineno-5-72"></a><span class="w">                </span><span class="k">break</span>
+<a id="__codelineno-5-73" name="__codelineno-5-73" href="#__codelineno-5-73"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-5-74" name="__codelineno-5-74" href="#__codelineno-5-74"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-75" name="__codelineno-5-75" href="#__codelineno-5-75"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-76" name="__codelineno-5-76" href="#__codelineno-5-76"></a>
+<a id="__codelineno-5-77" name="__codelineno-5-77" href="#__codelineno-5-77"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを拡張 */</span>
+<a id="__codelineno-5-78" name="__codelineno-5-78" href="#__codelineno-5-78"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">extend</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-79" name="__codelineno-5-79" href="#__codelineno-5-79"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルを一時保存</span>
+<a id="__codelineno-5-80" name="__codelineno-5-80" href="#__codelineno-5-80"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">bucketsTmp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">buckets</span>
+<a id="__codelineno-5-81" name="__codelineno-5-81" href="#__codelineno-5-81"></a><span class="w">        </span><span class="c1">// リサイズ後の新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-5-82" name="__codelineno-5-82" href="#__codelineno-5-82"></a><span class="w">        </span><span class="n">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="n">extendRatio</span>
+<a id="__codelineno-5-83" name="__codelineno-5-83" href="#__codelineno-5-83"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="p">[],</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span>
+<a id="__codelineno-5-84" name="__codelineno-5-84" href="#__codelineno-5-84"></a><span class="w">        </span><span class="n">size</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-5-85" name="__codelineno-5-85" href="#__codelineno-5-85"></a><span class="w">        </span><span class="c1">// キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
+<a id="__codelineno-5-86" name="__codelineno-5-86" href="#__codelineno-5-86"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-87" name="__codelineno-5-87" href="#__codelineno-5-87"></a><span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-88" name="__codelineno-5-88" href="#__codelineno-5-88"></a><span class="w">                </span><span class="n">put</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-5-89" name="__codelineno-5-89" href="#__codelineno-5-89"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-5-90" name="__codelineno-5-90" href="#__codelineno-5-90"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-91" name="__codelineno-5-91" href="#__codelineno-5-91"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-92" name="__codelineno-5-92" href="#__codelineno-5-92"></a>
+<a id="__codelineno-5-93" name="__codelineno-5-93" href="#__codelineno-5-93"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-5-94" name="__codelineno-5-94" href="#__codelineno-5-94"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-95" name="__codelineno-5-95" href="#__codelineno-5-95"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-96" name="__codelineno-5-96" href="#__codelineno-5-96"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">bucket</span><span class="p">.</span><span class="bp">map</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="s">&quot;</span><span class="si">\(</span><span class="nv">$0</span><span class="p">.</span><span class="n">key</span><span class="si">)</span><span class="s"> -&gt; </span><span class="si">\(</span><span class="nv">$0</span><span class="p">.</span><span class="n">val</span><span class="si">)</span><span class="s">&quot;</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-5-97" name="__codelineno-5-97" href="#__codelineno-5-97"></a><span class="w">            </span><span class="n">Swift</span><span class="p">.</span><span class="bp">print</span><span class="p">(</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-5-98" name="__codelineno-5-98" href="#__codelineno-5-98"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-99" name="__codelineno-5-99" href="#__codelineno-5-99"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-100" name="__codelineno-5-100" href="#__codelineno-5-100"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map_chaining.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">HashMapChaining</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">hash_map_chaining.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* チェイン法ハッシュテーブル */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">HashMapChaining</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="n">#size</span><span class="p">;</span><span class="w"> </span><span class="c1">// キーと値のペア数</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="n">#capacity</span><span class="p">;</span><span class="w"> </span><span class="c1">// ハッシュテーブル容量</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="n">#loadThres</span><span class="p">;</span><span class="w"> </span><span class="c1">// リサイズを発動する負荷率のしきい値</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="n">#extendRatio</span><span class="p">;</span><span class="w"> </span><span class="c1">// 拡張倍率</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="n">#buckets</span><span class="p">;</span><span class="w"> </span><span class="c1">// バケット配列</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">4</span><span class="p">;</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#loadThres</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3.0</span><span class="p">;</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#capacity</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="kc">null</span><span class="p">).</span><span class="nx">map</span><span class="p">((</span><span class="nx">x</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="p">[]);</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">    </span><span class="n">#hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#capacity</span><span class="p">;</span>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a>
+<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="w">    </span><span class="cm">/* 負荷率 */</span>
+<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a><span class="w">    </span><span class="n">#loadFactor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#capacity</span><span class="p">;</span>
+<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-27" name="__codelineno-6-27" href="#__codelineno-6-27"></a>
+<a id="__codelineno-6-28" name="__codelineno-6-28" href="#__codelineno-6-28"></a><span class="w">    </span><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-6-29" name="__codelineno-6-29" href="#__codelineno-6-29"></a><span class="w">    </span><span class="nx">get</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-30" name="__codelineno-6-30" href="#__codelineno-6-30"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">);</span>
+<a id="__codelineno-6-31" name="__codelineno-6-31" href="#__codelineno-6-31"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">];</span>
+<a id="__codelineno-6-32" name="__codelineno-6-32" href="#__codelineno-6-32"></a><span class="w">        </span><span class="c1">// バケットを走査し、key が見つかれば対応する val を返す</span>
+<a id="__codelineno-6-33" name="__codelineno-6-33" href="#__codelineno-6-33"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-34" name="__codelineno-6-34" href="#__codelineno-6-34"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">pair</span><span class="p">.</span><span class="nx">key</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-35" name="__codelineno-6-35" href="#__codelineno-6-35"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-6-36" name="__codelineno-6-36" href="#__codelineno-6-36"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-6-37" name="__codelineno-6-37" href="#__codelineno-6-37"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-38" name="__codelineno-6-38" href="#__codelineno-6-38"></a><span class="w">        </span><span class="c1">// key が見つからない場合は null を返す</span>
+<a id="__codelineno-6-39" name="__codelineno-6-39" href="#__codelineno-6-39"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-6-40" name="__codelineno-6-40" href="#__codelineno-6-40"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-41" name="__codelineno-6-41" href="#__codelineno-6-41"></a>
+<a id="__codelineno-6-42" name="__codelineno-6-42" href="#__codelineno-6-42"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-6-43" name="__codelineno-6-43" href="#__codelineno-6-43"></a><span class="w">    </span><span class="nx">put</span><span class="p">(</span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-44" name="__codelineno-6-44" href="#__codelineno-6-44"></a><span class="w">        </span><span class="c1">// 負荷率がしきい値を超えたら、リサイズを実行</span>
+<a id="__codelineno-6-45" name="__codelineno-6-45" href="#__codelineno-6-45"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#loadFactor</span><span class="p">()</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#loadThres</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-46" name="__codelineno-6-46" href="#__codelineno-6-46"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#extend</span><span class="p">();</span>
+<a id="__codelineno-6-47" name="__codelineno-6-47" href="#__codelineno-6-47"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-48" name="__codelineno-6-48" href="#__codelineno-6-48"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">);</span>
+<a id="__codelineno-6-49" name="__codelineno-6-49" href="#__codelineno-6-49"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">];</span>
+<a id="__codelineno-6-50" name="__codelineno-6-50" href="#__codelineno-6-50"></a><span class="w">        </span><span class="c1">// バケットを走査し、指定した key が見つかれば対応する val を更新して返す</span>
+<a id="__codelineno-6-51" name="__codelineno-6-51" href="#__codelineno-6-51"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-52" name="__codelineno-6-52" href="#__codelineno-6-52"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">pair</span><span class="p">.</span><span class="nx">key</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-53" name="__codelineno-6-53" href="#__codelineno-6-53"></a><span class="w">                </span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-6-54" name="__codelineno-6-54" href="#__codelineno-6-54"></a><span class="w">                </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-6-55" name="__codelineno-6-55" href="#__codelineno-6-55"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-6-56" name="__codelineno-6-56" href="#__codelineno-6-56"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-57" name="__codelineno-6-57" href="#__codelineno-6-57"></a><span class="w">        </span><span class="c1">// その key が存在しなければ、キーと値のペアを末尾に追加</span>
+<a id="__codelineno-6-58" name="__codelineno-6-58" href="#__codelineno-6-58"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">Pair</span><span class="p">(</span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-6-59" name="__codelineno-6-59" href="#__codelineno-6-59"></a><span class="w">        </span><span class="nx">bucket</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">pair</span><span class="p">);</span>
+<a id="__codelineno-6-60" name="__codelineno-6-60" href="#__codelineno-6-60"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-6-61" name="__codelineno-6-61" href="#__codelineno-6-61"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-62" name="__codelineno-6-62" href="#__codelineno-6-62"></a>
+<a id="__codelineno-6-63" name="__codelineno-6-63" href="#__codelineno-6-63"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-6-64" name="__codelineno-6-64" href="#__codelineno-6-64"></a><span class="w">    </span><span class="nx">remove</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-65" name="__codelineno-6-65" href="#__codelineno-6-65"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">);</span>
+<a id="__codelineno-6-66" name="__codelineno-6-66" href="#__codelineno-6-66"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">];</span>
+<a id="__codelineno-6-67" name="__codelineno-6-67" href="#__codelineno-6-67"></a><span class="w">        </span><span class="c1">// バケットを走査してキーと値のペアを削除</span>
+<a id="__codelineno-6-68" name="__codelineno-6-68" href="#__codelineno-6-68"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">bucket</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-69" name="__codelineno-6-69" href="#__codelineno-6-69"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">bucket</span><span class="p">[</span><span class="nx">i</span><span class="p">].</span><span class="nx">key</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-70" name="__codelineno-6-70" href="#__codelineno-6-70"></a><span class="w">                </span><span class="nx">bucket</span><span class="p">.</span><span class="nx">splice</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-6-71" name="__codelineno-6-71" href="#__codelineno-6-71"></a><span class="w">                </span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-6-72" name="__codelineno-6-72" href="#__codelineno-6-72"></a><span class="w">                </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-6-73" name="__codelineno-6-73" href="#__codelineno-6-73"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-6-74" name="__codelineno-6-74" href="#__codelineno-6-74"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-75" name="__codelineno-6-75" href="#__codelineno-6-75"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-76" name="__codelineno-6-76" href="#__codelineno-6-76"></a>
+<a id="__codelineno-6-77" name="__codelineno-6-77" href="#__codelineno-6-77"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを拡張 */</span>
+<a id="__codelineno-6-78" name="__codelineno-6-78" href="#__codelineno-6-78"></a><span class="w">    </span><span class="n">#extend</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-79" name="__codelineno-6-79" href="#__codelineno-6-79"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルを一時保存</span>
+<a id="__codelineno-6-80" name="__codelineno-6-80" href="#__codelineno-6-80"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">bucketsTmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">;</span>
+<a id="__codelineno-6-81" name="__codelineno-6-81" href="#__codelineno-6-81"></a><span class="w">        </span><span class="c1">// リサイズ後の新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-6-82" name="__codelineno-6-82" href="#__codelineno-6-82"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#extendRatio</span><span class="p">;</span>
+<a id="__codelineno-6-83" name="__codelineno-6-83" href="#__codelineno-6-83"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#capacity</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="kc">null</span><span class="p">).</span><span class="nx">map</span><span class="p">((</span><span class="nx">x</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="p">[]);</span>
+<a id="__codelineno-6-84" name="__codelineno-6-84" href="#__codelineno-6-84"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-6-85" name="__codelineno-6-85" href="#__codelineno-6-85"></a><span class="w">        </span><span class="c1">// キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
+<a id="__codelineno-6-86" name="__codelineno-6-86" href="#__codelineno-6-86"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">bucketsTmp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-87" name="__codelineno-6-87" href="#__codelineno-6-87"></a><span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-88" name="__codelineno-6-88" href="#__codelineno-6-88"></a><span class="w">                </span><span class="k">this</span><span class="p">.</span><span class="nx">put</span><span class="p">(</span><span class="nx">pair</span><span class="p">.</span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-6-89" name="__codelineno-6-89" href="#__codelineno-6-89"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-6-90" name="__codelineno-6-90" href="#__codelineno-6-90"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-91" name="__codelineno-6-91" href="#__codelineno-6-91"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-92" name="__codelineno-6-92" href="#__codelineno-6-92"></a>
+<a id="__codelineno-6-93" name="__codelineno-6-93" href="#__codelineno-6-93"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-6-94" name="__codelineno-6-94" href="#__codelineno-6-94"></a><span class="w">    </span><span class="nx">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-95" name="__codelineno-6-95" href="#__codelineno-6-95"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-96" name="__codelineno-6-96" href="#__codelineno-6-96"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-6-97" name="__codelineno-6-97" href="#__codelineno-6-97"></a><span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-98" name="__codelineno-6-98" href="#__codelineno-6-98"></a><span class="w">                </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">pair</span><span class="p">.</span><span class="nx">key</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s1">&#39; -&gt; &#39;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-6-99" name="__codelineno-6-99" href="#__codelineno-6-99"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-6-100" name="__codelineno-6-100" href="#__codelineno-6-100"></a><span class="w">            </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-6-101" name="__codelineno-6-101" href="#__codelineno-6-101"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-102" name="__codelineno-6-102" href="#__codelineno-6-102"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-103" name="__codelineno-6-103" href="#__codelineno-6-103"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map_chaining.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">HashMapChaining</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">hash_map_chaining.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* チェイン法ハッシュテーブル */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">HashMapChaining</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="n">#size</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// キーと値のペア数</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="n">#capacity</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// ハッシュテーブル容量</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="n">#loadThres</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// リサイズを発動する負荷率のしきい値</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="n">#extendRatio</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// 拡張倍率</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="n">#buckets</span><span class="o">:</span><span class="w"> </span><span class="nx">Pair</span><span class="p">[][];</span><span class="w"> </span><span class="c1">// バケット配列</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">4</span><span class="p">;</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#loadThres</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3.0</span><span class="p">;</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#capacity</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="kc">null</span><span class="p">).</span><span class="nx">map</span><span class="p">((</span><span class="nx">x</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="p">[]);</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">    </span><span class="n">#hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#capacity</span><span class="p">;</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="w">    </span><span class="cm">/* 負荷率 */</span>
+<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="w">    </span><span class="n">#loadFactor</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#capacity</span><span class="p">;</span>
+<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a>
+<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a><span class="w">    </span><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-7-29" name="__codelineno-7-29" href="#__codelineno-7-29"></a><span class="w">    </span><span class="nx">get</span><span class="p">(</span><span class="nx">key</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-30" name="__codelineno-7-30" href="#__codelineno-7-30"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">);</span>
+<a id="__codelineno-7-31" name="__codelineno-7-31" href="#__codelineno-7-31"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">];</span>
+<a id="__codelineno-7-32" name="__codelineno-7-32" href="#__codelineno-7-32"></a><span class="w">        </span><span class="c1">// バケットを走査し、key が見つかれば対応する val を返す</span>
+<a id="__codelineno-7-33" name="__codelineno-7-33" href="#__codelineno-7-33"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-34" name="__codelineno-7-34" href="#__codelineno-7-34"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">pair</span><span class="p">.</span><span class="nx">key</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-35" name="__codelineno-7-35" href="#__codelineno-7-35"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-7-36" name="__codelineno-7-36" href="#__codelineno-7-36"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-7-37" name="__codelineno-7-37" href="#__codelineno-7-37"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-38" name="__codelineno-7-38" href="#__codelineno-7-38"></a><span class="w">        </span><span class="c1">// key が見つからない場合は null を返す</span>
+<a id="__codelineno-7-39" name="__codelineno-7-39" href="#__codelineno-7-39"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-7-40" name="__codelineno-7-40" href="#__codelineno-7-40"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-41" name="__codelineno-7-41" href="#__codelineno-7-41"></a>
+<a id="__codelineno-7-42" name="__codelineno-7-42" href="#__codelineno-7-42"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-7-43" name="__codelineno-7-43" href="#__codelineno-7-43"></a><span class="w">    </span><span class="nx">put</span><span class="p">(</span><span class="nx">key</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-44" name="__codelineno-7-44" href="#__codelineno-7-44"></a><span class="w">        </span><span class="c1">// 負荷率がしきい値を超えたら、リサイズを実行</span>
+<a id="__codelineno-7-45" name="__codelineno-7-45" href="#__codelineno-7-45"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#loadFactor</span><span class="p">()</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#loadThres</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-46" name="__codelineno-7-46" href="#__codelineno-7-46"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#extend</span><span class="p">();</span>
+<a id="__codelineno-7-47" name="__codelineno-7-47" href="#__codelineno-7-47"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-48" name="__codelineno-7-48" href="#__codelineno-7-48"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">);</span>
+<a id="__codelineno-7-49" name="__codelineno-7-49" href="#__codelineno-7-49"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">];</span>
+<a id="__codelineno-7-50" name="__codelineno-7-50" href="#__codelineno-7-50"></a><span class="w">        </span><span class="c1">// バケットを走査し、指定した key が見つかれば対応する val を更新して返す</span>
+<a id="__codelineno-7-51" name="__codelineno-7-51" href="#__codelineno-7-51"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-52" name="__codelineno-7-52" href="#__codelineno-7-52"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">pair</span><span class="p">.</span><span class="nx">key</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-53" name="__codelineno-7-53" href="#__codelineno-7-53"></a><span class="w">                </span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-7-54" name="__codelineno-7-54" href="#__codelineno-7-54"></a><span class="w">                </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-7-55" name="__codelineno-7-55" href="#__codelineno-7-55"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-7-56" name="__codelineno-7-56" href="#__codelineno-7-56"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-57" name="__codelineno-7-57" href="#__codelineno-7-57"></a><span class="w">        </span><span class="c1">// その key が存在しなければ、キーと値のペアを末尾に追加</span>
+<a id="__codelineno-7-58" name="__codelineno-7-58" href="#__codelineno-7-58"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">Pair</span><span class="p">(</span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-7-59" name="__codelineno-7-59" href="#__codelineno-7-59"></a><span class="w">        </span><span class="nx">bucket</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">pair</span><span class="p">);</span>
+<a id="__codelineno-7-60" name="__codelineno-7-60" href="#__codelineno-7-60"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-7-61" name="__codelineno-7-61" href="#__codelineno-7-61"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-62" name="__codelineno-7-62" href="#__codelineno-7-62"></a>
+<a id="__codelineno-7-63" name="__codelineno-7-63" href="#__codelineno-7-63"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-7-64" name="__codelineno-7-64" href="#__codelineno-7-64"></a><span class="w">    </span><span class="nx">remove</span><span class="p">(</span><span class="nx">key</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-65" name="__codelineno-7-65" href="#__codelineno-7-65"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">);</span>
+<a id="__codelineno-7-66" name="__codelineno-7-66" href="#__codelineno-7-66"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">];</span>
+<a id="__codelineno-7-67" name="__codelineno-7-67" href="#__codelineno-7-67"></a><span class="w">        </span><span class="c1">// バケットを走査してキーと値のペアを削除</span>
+<a id="__codelineno-7-68" name="__codelineno-7-68" href="#__codelineno-7-68"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">bucket</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-69" name="__codelineno-7-69" href="#__codelineno-7-69"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">bucket</span><span class="p">[</span><span class="nx">i</span><span class="p">].</span><span class="nx">key</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-70" name="__codelineno-7-70" href="#__codelineno-7-70"></a><span class="w">                </span><span class="nx">bucket</span><span class="p">.</span><span class="nx">splice</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-7-71" name="__codelineno-7-71" href="#__codelineno-7-71"></a><span class="w">                </span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-7-72" name="__codelineno-7-72" href="#__codelineno-7-72"></a><span class="w">                </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-7-73" name="__codelineno-7-73" href="#__codelineno-7-73"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-7-74" name="__codelineno-7-74" href="#__codelineno-7-74"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-75" name="__codelineno-7-75" href="#__codelineno-7-75"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-76" name="__codelineno-7-76" href="#__codelineno-7-76"></a>
+<a id="__codelineno-7-77" name="__codelineno-7-77" href="#__codelineno-7-77"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを拡張 */</span>
+<a id="__codelineno-7-78" name="__codelineno-7-78" href="#__codelineno-7-78"></a><span class="w">    </span><span class="n">#extend</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-79" name="__codelineno-7-79" href="#__codelineno-7-79"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルを一時保存</span>
+<a id="__codelineno-7-80" name="__codelineno-7-80" href="#__codelineno-7-80"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">bucketsTmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">;</span>
+<a id="__codelineno-7-81" name="__codelineno-7-81" href="#__codelineno-7-81"></a><span class="w">        </span><span class="c1">// リサイズ後の新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-7-82" name="__codelineno-7-82" href="#__codelineno-7-82"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#extendRatio</span><span class="p">;</span>
+<a id="__codelineno-7-83" name="__codelineno-7-83" href="#__codelineno-7-83"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#capacity</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="kc">null</span><span class="p">).</span><span class="nx">map</span><span class="p">((</span><span class="nx">x</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="p">[]);</span>
+<a id="__codelineno-7-84" name="__codelineno-7-84" href="#__codelineno-7-84"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-7-85" name="__codelineno-7-85" href="#__codelineno-7-85"></a><span class="w">        </span><span class="c1">// キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
+<a id="__codelineno-7-86" name="__codelineno-7-86" href="#__codelineno-7-86"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">bucketsTmp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-87" name="__codelineno-7-87" href="#__codelineno-7-87"></a><span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-88" name="__codelineno-7-88" href="#__codelineno-7-88"></a><span class="w">                </span><span class="k">this</span><span class="p">.</span><span class="nx">put</span><span class="p">(</span><span class="nx">pair</span><span class="p">.</span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-7-89" name="__codelineno-7-89" href="#__codelineno-7-89"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-7-90" name="__codelineno-7-90" href="#__codelineno-7-90"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-91" name="__codelineno-7-91" href="#__codelineno-7-91"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-92" name="__codelineno-7-92" href="#__codelineno-7-92"></a>
+<a id="__codelineno-7-93" name="__codelineno-7-93" href="#__codelineno-7-93"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-7-94" name="__codelineno-7-94" href="#__codelineno-7-94"></a><span class="w">    </span><span class="nx">print</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-95" name="__codelineno-7-95" href="#__codelineno-7-95"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-96" name="__codelineno-7-96" href="#__codelineno-7-96"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-7-97" name="__codelineno-7-97" href="#__codelineno-7-97"></a><span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-98" name="__codelineno-7-98" href="#__codelineno-7-98"></a><span class="w">                </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">pair</span><span class="p">.</span><span class="nx">key</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s1">&#39; -&gt; &#39;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-7-99" name="__codelineno-7-99" href="#__codelineno-7-99"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-7-100" name="__codelineno-7-100" href="#__codelineno-7-100"></a><span class="w">            </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-7-101" name="__codelineno-7-101" href="#__codelineno-7-101"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-102" name="__codelineno-7-102" href="#__codelineno-7-102"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-103" name="__codelineno-7-103" href="#__codelineno-7-103"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map_chaining.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">HashMapChaining</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">hash_map_chaining.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* チェイン法ハッシュテーブル */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">HashMapChaining</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="kd">late</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="c1">// キーと値のペア数</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="kd">late</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span><span class="w"> </span><span class="c1">// ハッシュテーブル容量</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="kd">late</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">loadThres</span><span class="p">;</span><span class="w"> </span><span class="c1">// リサイズを発動する負荷率のしきい値</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="kd">late</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span><span class="w"> </span><span class="c1">// 拡張倍率</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="kd">late</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span><span class="w"> </span><span class="c1">// バケット配列</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">  </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">  </span><span class="n">HashMapChaining</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">    </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">    </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">4</span><span class="p">;</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">    </span><span class="n">loadThres</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">3.0</span><span class="p">;</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">    </span><span class="n">extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">    </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">generate</span><span class="p">(</span><span class="n">capacity</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">_</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">[]);</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w">  </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a>
+<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a><span class="w">  </span><span class="cm">/* 負荷率 */</span>
+<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a><span class="w">  </span><span class="kt">double</span><span class="w"> </span><span class="n">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-8-26" name="__codelineno-8-26" href="#__codelineno-8-26"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-27" name="__codelineno-8-27" href="#__codelineno-8-27"></a>
+<a id="__codelineno-8-28" name="__codelineno-8-28" href="#__codelineno-8-28"></a><span class="w">  </span><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-8-29" name="__codelineno-8-29" href="#__codelineno-8-29"></a><span class="w">  </span><span class="kt">String</span><span class="o">?</span><span class="w"> </span><span class="kd">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-30" name="__codelineno-8-30" href="#__codelineno-8-30"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-8-31" name="__codelineno-8-31" href="#__codelineno-8-31"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-8-32" name="__codelineno-8-32" href="#__codelineno-8-32"></a><span class="w">    </span><span class="c1">// バケットを走査し、key が見つかれば対応する val を返す</span>
+<a id="__codelineno-8-33" name="__codelineno-8-33" href="#__codelineno-8-33"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-34" name="__codelineno-8-34" href="#__codelineno-8-34"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-35" name="__codelineno-8-35" href="#__codelineno-8-35"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-8-36" name="__codelineno-8-36" href="#__codelineno-8-36"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-8-37" name="__codelineno-8-37" href="#__codelineno-8-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-38" name="__codelineno-8-38" href="#__codelineno-8-38"></a><span class="w">    </span><span class="c1">// key が見つからない場合は null を返す</span>
+<a id="__codelineno-8-39" name="__codelineno-8-39" href="#__codelineno-8-39"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-8-40" name="__codelineno-8-40" href="#__codelineno-8-40"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-41" name="__codelineno-8-41" href="#__codelineno-8-41"></a>
+<a id="__codelineno-8-42" name="__codelineno-8-42" href="#__codelineno-8-42"></a><span class="w">  </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-8-43" name="__codelineno-8-43" href="#__codelineno-8-43"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="kt">String</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-44" name="__codelineno-8-44" href="#__codelineno-8-44"></a><span class="w">    </span><span class="c1">// 負荷率がしきい値を超えたら、リサイズを実行</span>
+<a id="__codelineno-8-45" name="__codelineno-8-45" href="#__codelineno-8-45"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">loadThres</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-46" name="__codelineno-8-46" href="#__codelineno-8-46"></a><span class="w">      </span><span class="n">extend</span><span class="p">();</span>
+<a id="__codelineno-8-47" name="__codelineno-8-47" href="#__codelineno-8-47"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-48" name="__codelineno-8-48" href="#__codelineno-8-48"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-8-49" name="__codelineno-8-49" href="#__codelineno-8-49"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-8-50" name="__codelineno-8-50" href="#__codelineno-8-50"></a><span class="w">    </span><span class="c1">// バケットを走査し、指定した key が見つかれば対応する val を更新して返す</span>
+<a id="__codelineno-8-51" name="__codelineno-8-51" href="#__codelineno-8-51"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-52" name="__codelineno-8-52" href="#__codelineno-8-52"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-53" name="__codelineno-8-53" href="#__codelineno-8-53"></a><span class="w">        </span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-8-54" name="__codelineno-8-54" href="#__codelineno-8-54"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-8-55" name="__codelineno-8-55" href="#__codelineno-8-55"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-8-56" name="__codelineno-8-56" href="#__codelineno-8-56"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-57" name="__codelineno-8-57" href="#__codelineno-8-57"></a><span class="w">    </span><span class="c1">// その key が存在しなければ、キーと値のペアを末尾に追加</span>
+<a id="__codelineno-8-58" name="__codelineno-8-58" href="#__codelineno-8-58"></a><span class="w">    </span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-8-59" name="__codelineno-8-59" href="#__codelineno-8-59"></a><span class="w">    </span><span class="n">bucket</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">pair</span><span class="p">);</span>
+<a id="__codelineno-8-60" name="__codelineno-8-60" href="#__codelineno-8-60"></a><span class="w">    </span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-8-61" name="__codelineno-8-61" href="#__codelineno-8-61"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-62" name="__codelineno-8-62" href="#__codelineno-8-62"></a>
+<a id="__codelineno-8-63" name="__codelineno-8-63" href="#__codelineno-8-63"></a><span class="w">  </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-8-64" name="__codelineno-8-64" href="#__codelineno-8-64"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-65" name="__codelineno-8-65" href="#__codelineno-8-65"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-8-66" name="__codelineno-8-66" href="#__codelineno-8-66"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-8-67" name="__codelineno-8-67" href="#__codelineno-8-67"></a><span class="w">    </span><span class="c1">// バケットを走査してキーと値のペアを削除</span>
+<a id="__codelineno-8-68" name="__codelineno-8-68" href="#__codelineno-8-68"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-69" name="__codelineno-8-69" href="#__codelineno-8-69"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-70" name="__codelineno-8-70" href="#__codelineno-8-70"></a><span class="w">        </span><span class="n">bucket</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">pair</span><span class="p">);</span>
+<a id="__codelineno-8-71" name="__codelineno-8-71" href="#__codelineno-8-71"></a><span class="w">        </span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-8-72" name="__codelineno-8-72" href="#__codelineno-8-72"></a><span class="w">        </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-8-73" name="__codelineno-8-73" href="#__codelineno-8-73"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-8-74" name="__codelineno-8-74" href="#__codelineno-8-74"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-75" name="__codelineno-8-75" href="#__codelineno-8-75"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-76" name="__codelineno-8-76" href="#__codelineno-8-76"></a>
+<a id="__codelineno-8-77" name="__codelineno-8-77" href="#__codelineno-8-77"></a><span class="w">  </span><span class="cm">/* ハッシュテーブルを拡張 */</span>
+<a id="__codelineno-8-78" name="__codelineno-8-78" href="#__codelineno-8-78"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">extend</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-79" name="__codelineno-8-79" href="#__codelineno-8-79"></a><span class="w">    </span><span class="c1">// 元のハッシュテーブルを一時保存</span>
+<a id="__codelineno-8-80" name="__codelineno-8-80" href="#__codelineno-8-80"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span>
+<a id="__codelineno-8-81" name="__codelineno-8-81" href="#__codelineno-8-81"></a><span class="w">    </span><span class="c1">// リサイズ後の新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-8-82" name="__codelineno-8-82" href="#__codelineno-8-82"></a><span class="w">    </span><span class="n">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span>
+<a id="__codelineno-8-83" name="__codelineno-8-83" href="#__codelineno-8-83"></a><span class="w">    </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">generate</span><span class="p">(</span><span class="n">capacity</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">_</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">[]);</span>
+<a id="__codelineno-8-84" name="__codelineno-8-84" href="#__codelineno-8-84"></a><span class="w">    </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-8-85" name="__codelineno-8-85" href="#__codelineno-8-85"></a><span class="w">    </span><span class="c1">// キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
+<a id="__codelineno-8-86" name="__codelineno-8-86" href="#__codelineno-8-86"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-87" name="__codelineno-8-87" href="#__codelineno-8-87"></a><span class="w">      </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-88" name="__codelineno-8-88" href="#__codelineno-8-88"></a><span class="w">        </span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-8-89" name="__codelineno-8-89" href="#__codelineno-8-89"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-8-90" name="__codelineno-8-90" href="#__codelineno-8-90"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-91" name="__codelineno-8-91" href="#__codelineno-8-91"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-92" name="__codelineno-8-92" href="#__codelineno-8-92"></a>
+<a id="__codelineno-8-93" name="__codelineno-8-93" href="#__codelineno-8-93"></a><span class="w">  </span><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-8-94" name="__codelineno-8-94" href="#__codelineno-8-94"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">printHashMap</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-95" name="__codelineno-8-95" href="#__codelineno-8-95"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-96" name="__codelineno-8-96" href="#__codelineno-8-96"></a><span class="w">      </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-8-97" name="__codelineno-8-97" href="#__codelineno-8-97"></a><span class="w">      </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-98" name="__codelineno-8-98" href="#__codelineno-8-98"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="s2">&quot;</span><span class="si">${</span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="si">}</span><span class="s2"> -&gt; </span><span class="si">${</span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">);</span>
+<a id="__codelineno-8-99" name="__codelineno-8-99" href="#__codelineno-8-99"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-8-100" name="__codelineno-8-100" href="#__codelineno-8-100"></a><span class="w">      </span><span class="n">print</span><span class="p">(</span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-8-101" name="__codelineno-8-101" href="#__codelineno-8-101"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-102" name="__codelineno-8-102" href="#__codelineno-8-102"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-103" name="__codelineno-8-103" href="#__codelineno-8-103"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map_chaining.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">HashMapChaining</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">hash_map_chaining.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* チェイン法ハッシュテーブル */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">HashMapChaining</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="n">size</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="n">capacity</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="n">load_thres</span><span class="p">:</span><span class="w"> </span><span class="kt">f32</span><span class="p">,</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="n">extend_ratio</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="n">buckets</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="p">}</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="k">impl</span><span class="w"> </span><span class="n">HashMapChaining</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">new</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">        </span><span class="bp">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">            </span><span class="n">size</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">            </span><span class="n">capacity</span><span class="p">:</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">            </span><span class="n">load_thres</span><span class="p">:</span><span class="w"> </span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3.0</span><span class="p">,</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">            </span><span class="n">extend_ratio</span><span class="p">:</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">            </span><span class="n">buckets</span><span class="p">:</span><span class="w"> </span><span class="nc">vec</span><span class="o">!</span><span class="p">[</span><span class="fm">vec!</span><span class="p">[];</span><span class="w"> </span><span class="mi">4</span><span class="p">],</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a>
+<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">hash_func</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="w">        </span><span class="n">key</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">capacity</span>
+<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a>
+<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="w">    </span><span class="cm">/* 負荷率 */</span>
+<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">load_factor</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">f32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">f32</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">capacity</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">f32</span>
+<a id="__codelineno-9-30" name="__codelineno-9-30" href="#__codelineno-9-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-31" name="__codelineno-9-31" href="#__codelineno-9-31"></a>
+<a id="__codelineno-9-32" name="__codelineno-9-32" href="#__codelineno-9-32"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-9-33" name="__codelineno-9-33" href="#__codelineno-9-33"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="nb">String</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-34" name="__codelineno-9-34" href="#__codelineno-9-34"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-9-35" name="__codelineno-9-35" href="#__codelineno-9-35"></a>
+<a id="__codelineno-9-36" name="__codelineno-9-36" href="#__codelineno-9-36"></a><span class="w">        </span><span class="c1">// バケットを走査してキーと値のペアを削除</span>
+<a id="__codelineno-9-37" name="__codelineno-9-37" href="#__codelineno-9-37"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">)</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">iter_mut</span><span class="p">().</span><span class="n">enumerate</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-38" name="__codelineno-9-38" href="#__codelineno-9-38"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">p</span><span class="p">.</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-39" name="__codelineno-9-39" href="#__codelineno-9-39"></a><span class="w">                </span><span class="kd">let</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">remove</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-9-40" name="__codelineno-9-40" href="#__codelineno-9-40"></a><span class="w">                </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-41" name="__codelineno-9-41" href="#__codelineno-9-41"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-9-42" name="__codelineno-9-42" href="#__codelineno-9-42"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-9-43" name="__codelineno-9-43" href="#__codelineno-9-43"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-44" name="__codelineno-9-44" href="#__codelineno-9-44"></a>
+<a id="__codelineno-9-45" name="__codelineno-9-45" href="#__codelineno-9-45"></a><span class="w">        </span><span class="c1">// key が見つからない場合は None を返す</span>
+<a id="__codelineno-9-46" name="__codelineno-9-46" href="#__codelineno-9-46"></a><span class="w">        </span><span class="nb">None</span>
+<a id="__codelineno-9-47" name="__codelineno-9-47" href="#__codelineno-9-47"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-48" name="__codelineno-9-48" href="#__codelineno-9-48"></a>
+<a id="__codelineno-9-49" name="__codelineno-9-49" href="#__codelineno-9-49"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを拡張 */</span>
+<a id="__codelineno-9-50" name="__codelineno-9-50" href="#__codelineno-9-50"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">extend</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-51" name="__codelineno-9-51" href="#__codelineno-9-51"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルを一時保存</span>
+<a id="__codelineno-9-52" name="__codelineno-9-52" href="#__codelineno-9-52"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">buckets_tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">mem</span><span class="p">::</span><span class="n">take</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">);</span>
+<a id="__codelineno-9-53" name="__codelineno-9-53" href="#__codelineno-9-53"></a>
+<a id="__codelineno-9-54" name="__codelineno-9-54" href="#__codelineno-9-54"></a><span class="w">        </span><span class="c1">// リサイズ後の新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-9-55" name="__codelineno-9-55" href="#__codelineno-9-55"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">extend_ratio</span><span class="p">;</span>
+<a id="__codelineno-9-56" name="__codelineno-9-56" href="#__codelineno-9-56"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">();</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">capacity</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">];</span>
+<a id="__codelineno-9-57" name="__codelineno-9-57" href="#__codelineno-9-57"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-9-58" name="__codelineno-9-58" href="#__codelineno-9-58"></a>
+<a id="__codelineno-9-59" name="__codelineno-9-59" href="#__codelineno-9-59"></a><span class="w">        </span><span class="c1">// キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
+<a id="__codelineno-9-60" name="__codelineno-9-60" href="#__codelineno-9-60"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets_tmp</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-61" name="__codelineno-9-61" href="#__codelineno-9-61"></a><span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-62" name="__codelineno-9-62" href="#__codelineno-9-62"></a><span class="w">                </span><span class="bp">self</span><span class="p">.</span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-9-63" name="__codelineno-9-63" href="#__codelineno-9-63"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-9-64" name="__codelineno-9-64" href="#__codelineno-9-64"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-65" name="__codelineno-9-65" href="#__codelineno-9-65"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-66" name="__codelineno-9-66" href="#__codelineno-9-66"></a>
+<a id="__codelineno-9-67" name="__codelineno-9-67" href="#__codelineno-9-67"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-9-68" name="__codelineno-9-68" href="#__codelineno-9-68"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">print</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-69" name="__codelineno-9-69" href="#__codelineno-9-69"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="o">&amp;</span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-70" name="__codelineno-9-70" href="#__codelineno-9-70"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-9-71" name="__codelineno-9-71" href="#__codelineno-9-71"></a><span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-72" name="__codelineno-9-72" href="#__codelineno-9-72"></a><span class="w">                </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="fm">format!</span><span class="p">(</span><span class="s">&quot;{} -&gt; {}&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">));</span>
+<a id="__codelineno-9-73" name="__codelineno-9-73" href="#__codelineno-9-73"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-9-74" name="__codelineno-9-74" href="#__codelineno-9-74"></a><span class="w">            </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{:?}&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-9-75" name="__codelineno-9-75" href="#__codelineno-9-75"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-76" name="__codelineno-9-76" href="#__codelineno-9-76"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-77" name="__codelineno-9-77" href="#__codelineno-9-77"></a>
+<a id="__codelineno-9-78" name="__codelineno-9-78" href="#__codelineno-9-78"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-9-79" name="__codelineno-9-79" href="#__codelineno-9-79"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="nb">String</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-80" name="__codelineno-9-80" href="#__codelineno-9-80"></a><span class="w">        </span><span class="c1">// 負荷率がしきい値を超えたら、リサイズを実行</span>
+<a id="__codelineno-9-81" name="__codelineno-9-81" href="#__codelineno-9-81"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">load_factor</span><span class="p">()</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">load_thres</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-82" name="__codelineno-9-82" href="#__codelineno-9-82"></a><span class="w">            </span><span class="bp">self</span><span class="p">.</span><span class="n">extend</span><span class="p">();</span>
+<a id="__codelineno-9-83" name="__codelineno-9-83" href="#__codelineno-9-83"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-84" name="__codelineno-9-84" href="#__codelineno-9-84"></a>
+<a id="__codelineno-9-85" name="__codelineno-9-85" href="#__codelineno-9-85"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-9-86" name="__codelineno-9-86" href="#__codelineno-9-86"></a>
+<a id="__codelineno-9-87" name="__codelineno-9-87" href="#__codelineno-9-87"></a><span class="w">        </span><span class="c1">// バケットを走査し、指定した key が見つかれば対応する val を更新して返す</span>
+<a id="__codelineno-9-88" name="__codelineno-9-88" href="#__codelineno-9-88"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">iter_mut</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-89" name="__codelineno-9-89" href="#__codelineno-9-89"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-90" name="__codelineno-9-90" href="#__codelineno-9-90"></a><span class="w">                </span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-9-91" name="__codelineno-9-91" href="#__codelineno-9-91"></a><span class="w">                </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-9-92" name="__codelineno-9-92" href="#__codelineno-9-92"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-9-93" name="__codelineno-9-93" href="#__codelineno-9-93"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-94" name="__codelineno-9-94" href="#__codelineno-9-94"></a>
+<a id="__codelineno-9-95" name="__codelineno-9-95" href="#__codelineno-9-95"></a><span class="w">        </span><span class="c1">// その key が存在しなければ、キーと値のペアを末尾に追加</span>
+<a id="__codelineno-9-96" name="__codelineno-9-96" href="#__codelineno-9-96"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Pair</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="p">};</span>
+<a id="__codelineno-9-97" name="__codelineno-9-97" href="#__codelineno-9-97"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">push</span><span class="p">(</span><span class="n">pair</span><span class="p">);</span>
+<a id="__codelineno-9-98" name="__codelineno-9-98" href="#__codelineno-9-98"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-99" name="__codelineno-9-99" href="#__codelineno-9-99"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-100" name="__codelineno-9-100" href="#__codelineno-9-100"></a>
+<a id="__codelineno-9-101" name="__codelineno-9-101" href="#__codelineno-9-101"></a><span class="w">    </span><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-9-102" name="__codelineno-9-102" href="#__codelineno-9-102"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="kt">str</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-103" name="__codelineno-9-103" href="#__codelineno-9-103"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-9-104" name="__codelineno-9-104" href="#__codelineno-9-104"></a>
+<a id="__codelineno-9-105" name="__codelineno-9-105" href="#__codelineno-9-105"></a><span class="w">        </span><span class="c1">// バケットを走査し、key が見つかれば対応する val を返す</span>
+<a id="__codelineno-9-106" name="__codelineno-9-106" href="#__codelineno-9-106"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">iter</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-107" name="__codelineno-9-107" href="#__codelineno-9-107"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-108" name="__codelineno-9-108" href="#__codelineno-9-108"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="o">&amp;</span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-9-109" name="__codelineno-9-109" href="#__codelineno-9-109"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-9-110" name="__codelineno-9-110" href="#__codelineno-9-110"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-111" name="__codelineno-9-111" href="#__codelineno-9-111"></a>
+<a id="__codelineno-9-112" name="__codelineno-9-112" href="#__codelineno-9-112"></a><span class="w">        </span><span class="c1">// key が見つからない場合は None を返す</span>
+<a id="__codelineno-9-113" name="__codelineno-9-113" href="#__codelineno-9-113"></a><span class="w">        </span><span class="nb">None</span>
+<a id="__codelineno-9-114" name="__codelineno-9-114" href="#__codelineno-9-114"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-115" name="__codelineno-9-115" href="#__codelineno-9-115"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map_chaining.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">Node</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
-<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
-<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">HashMapChaining</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">hash_map_chaining.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 連結リストノード */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">Node</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="p">;</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="k">struct</span><span class="w"> </span><span class="nc">Node</span><span class="w"> </span><span class="o">*</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="p">}</span><span class="w"> </span><span class="n">Node</span><span class="p">;</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="cm">/* チェイン法ハッシュテーブル */</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w">         </span><span class="c1">// キーと値のペア数</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span><span class="w">     </span><span class="c1">// ハッシュテーブル容量</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="kt">double</span><span class="w"> </span><span class="n">loadThres</span><span class="p">;</span><span class="w"> </span><span class="c1">// リサイズを発動する負荷率のしきい値</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span><span class="w">  </span><span class="c1">// 拡張倍率</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">    </span><span class="n">Node</span><span class="w"> </span><span class="o">**</span><span class="n">buckets</span><span class="p">;</span><span class="w">   </span><span class="c1">// バケット配列</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="p">}</span><span class="w"> </span><span class="n">HashMapChaining</span><span class="p">;</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="n">HashMapChaining</span><span class="w"> </span><span class="o">*</span><span class="nf">newHashMapChaining</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">    </span><span class="n">HashMapChaining</span><span class="w"> </span><span class="o">*</span><span class="n">hashMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">HashMapChaining</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">HashMapChaining</span><span class="p">));</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w">    </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="w">    </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">4</span><span class="p">;</span>
+<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="w">    </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">loadThres</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3.0</span><span class="p">;</span>
+<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w">    </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w">    </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">Node</span><span class="w"> </span><span class="o">**</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="n">Node</span><span class="w"> </span><span class="o">*</span><span class="p">));</span>
+<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="w">        </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">hashMap</span><span class="p">;</span>
+<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="p">}</span>
+<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a>
+<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="cm">/* デストラクタ */</span>
+<a id="__codelineno-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></a><span class="kt">void</span><span class="w"> </span><span class="nf">delHashMapChaining</span><span class="p">(</span><span class="n">HashMapChaining</span><span class="w"> </span><span class="o">*</span><span class="n">hashMap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-32" name="__codelineno-10-32" href="#__codelineno-10-32"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-33" name="__codelineno-10-33" href="#__codelineno-10-33"></a><span class="w">        </span><span class="n">Node</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-10-34" name="__codelineno-10-34" href="#__codelineno-10-34"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-35" name="__codelineno-10-35" href="#__codelineno-10-35"></a><span class="w">            </span><span class="n">Node</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
+<a id="__codelineno-10-36" name="__codelineno-10-36" href="#__codelineno-10-36"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-10-37" name="__codelineno-10-37" href="#__codelineno-10-37"></a><span class="w">            </span><span class="n">free</span><span class="p">(</span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">pair</span><span class="p">);</span>
+<a id="__codelineno-10-38" name="__codelineno-10-38" href="#__codelineno-10-38"></a><span class="w">            </span><span class="n">free</span><span class="p">(</span><span class="n">tmp</span><span class="p">);</span>
+<a id="__codelineno-10-39" name="__codelineno-10-39" href="#__codelineno-10-39"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-40" name="__codelineno-10-40" href="#__codelineno-10-40"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-41" name="__codelineno-10-41" href="#__codelineno-10-41"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">);</span>
+<a id="__codelineno-10-42" name="__codelineno-10-42" href="#__codelineno-10-42"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">hashMap</span><span class="p">);</span>
+<a id="__codelineno-10-43" name="__codelineno-10-43" href="#__codelineno-10-43"></a><span class="p">}</span>
+<a id="__codelineno-10-44" name="__codelineno-10-44" href="#__codelineno-10-44"></a>
+<a id="__codelineno-10-45" name="__codelineno-10-45" href="#__codelineno-10-45"></a><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-10-46" name="__codelineno-10-46" href="#__codelineno-10-46"></a><span class="kt">int</span><span class="w"> </span><span class="nf">hashFunc</span><span class="p">(</span><span class="n">HashMapChaining</span><span class="w"> </span><span class="o">*</span><span class="n">hashMap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-47" name="__codelineno-10-47" href="#__codelineno-10-47"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-10-48" name="__codelineno-10-48" href="#__codelineno-10-48"></a><span class="p">}</span>
+<a id="__codelineno-10-49" name="__codelineno-10-49" href="#__codelineno-10-49"></a>
+<a id="__codelineno-10-50" name="__codelineno-10-50" href="#__codelineno-10-50"></a><span class="cm">/* 負荷率 */</span>
+<a id="__codelineno-10-51" name="__codelineno-10-51" href="#__codelineno-10-51"></a><span class="kt">double</span><span class="w"> </span><span class="nf">loadFactor</span><span class="p">(</span><span class="n">HashMapChaining</span><span class="w"> </span><span class="o">*</span><span class="n">hashMap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-52" name="__codelineno-10-52" href="#__codelineno-10-52"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-10-53" name="__codelineno-10-53" href="#__codelineno-10-53"></a><span class="p">}</span>
+<a id="__codelineno-10-54" name="__codelineno-10-54" href="#__codelineno-10-54"></a>
+<a id="__codelineno-10-55" name="__codelineno-10-55" href="#__codelineno-10-55"></a><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-10-56" name="__codelineno-10-56" href="#__codelineno-10-56"></a><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="nf">get</span><span class="p">(</span><span class="n">HashMapChaining</span><span class="w"> </span><span class="o">*</span><span class="n">hashMap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-57" name="__codelineno-10-57" href="#__codelineno-10-57"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">hashMap</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-10-58" name="__codelineno-10-58" href="#__codelineno-10-58"></a><span class="w">    </span><span class="c1">// バケットを走査し、key が見つかれば対応する val を返す</span>
+<a id="__codelineno-10-59" name="__codelineno-10-59" href="#__codelineno-10-59"></a><span class="w">    </span><span class="n">Node</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-10-60" name="__codelineno-10-60" href="#__codelineno-10-60"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-61" name="__codelineno-10-61" href="#__codelineno-10-61"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-62" name="__codelineno-10-62" href="#__codelineno-10-62"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-10-63" name="__codelineno-10-63" href="#__codelineno-10-63"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-64" name="__codelineno-10-64" href="#__codelineno-10-64"></a><span class="w">        </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-10-65" name="__codelineno-10-65" href="#__codelineno-10-65"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-66" name="__codelineno-10-66" href="#__codelineno-10-66"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="s">&quot;&quot;</span><span class="p">;</span><span class="w"> </span><span class="c1">// key が見つからない場合は空文字列を返す</span>
+<a id="__codelineno-10-67" name="__codelineno-10-67" href="#__codelineno-10-67"></a><span class="p">}</span>
+<a id="__codelineno-10-68" name="__codelineno-10-68" href="#__codelineno-10-68"></a>
+<a id="__codelineno-10-69" name="__codelineno-10-69" href="#__codelineno-10-69"></a><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-10-70" name="__codelineno-10-70" href="#__codelineno-10-70"></a><span class="kt">void</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="n">HashMapChaining</span><span class="w"> </span><span class="o">*</span><span class="n">hashMap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-71" name="__codelineno-10-71" href="#__codelineno-10-71"></a><span class="w">    </span><span class="c1">// 負荷率がしきい値を超えたら、リサイズを実行</span>
+<a id="__codelineno-10-72" name="__codelineno-10-72" href="#__codelineno-10-72"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">loadFactor</span><span class="p">(</span><span class="n">hashMap</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">loadThres</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-73" name="__codelineno-10-73" href="#__codelineno-10-73"></a><span class="w">        </span><span class="n">extend</span><span class="p">(</span><span class="n">hashMap</span><span class="p">);</span>
+<a id="__codelineno-10-74" name="__codelineno-10-74" href="#__codelineno-10-74"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-75" name="__codelineno-10-75" href="#__codelineno-10-75"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">hashMap</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-10-76" name="__codelineno-10-76" href="#__codelineno-10-76"></a><span class="w">    </span><span class="c1">// バケットを走査し、指定した key が見つかれば対応する val を更新して返す</span>
+<a id="__codelineno-10-77" name="__codelineno-10-77" href="#__codelineno-10-77"></a><span class="w">    </span><span class="n">Node</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-10-78" name="__codelineno-10-78" href="#__codelineno-10-78"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-79" name="__codelineno-10-79" href="#__codelineno-10-79"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-80" name="__codelineno-10-80" href="#__codelineno-10-80"></a><span class="w">            </span><span class="n">strcpy</span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span><span class="w"> </span><span class="c1">// 指定した `key` に遭遇したら、対応する `val` を更新して返す</span>
+<a id="__codelineno-10-81" name="__codelineno-10-81" href="#__codelineno-10-81"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-10-82" name="__codelineno-10-82" href="#__codelineno-10-82"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-83" name="__codelineno-10-83" href="#__codelineno-10-83"></a><span class="w">        </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-10-84" name="__codelineno-10-84" href="#__codelineno-10-84"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-85" name="__codelineno-10-85" href="#__codelineno-10-85"></a><span class="w">    </span><span class="c1">// 該当する `key` がなければ、キーと値のペアを連結リストの先頭に追加する</span>
+<a id="__codelineno-10-86" name="__codelineno-10-86" href="#__codelineno-10-86"></a><span class="w">    </span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">newPair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">Pair</span><span class="p">));</span>
+<a id="__codelineno-10-87" name="__codelineno-10-87" href="#__codelineno-10-87"></a><span class="w">    </span><span class="n">newPair</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="p">;</span>
+<a id="__codelineno-10-88" name="__codelineno-10-88" href="#__codelineno-10-88"></a><span class="w">    </span><span class="n">strcpy</span><span class="p">(</span><span class="n">newPair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-10-89" name="__codelineno-10-89" href="#__codelineno-10-89"></a><span class="w">    </span><span class="n">Node</span><span class="w"> </span><span class="o">*</span><span class="n">newNode</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">Node</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">Node</span><span class="p">));</span>
+<a id="__codelineno-10-90" name="__codelineno-10-90" href="#__codelineno-10-90"></a><span class="w">    </span><span class="n">newNode</span><span class="o">-&gt;</span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newPair</span><span class="p">;</span>
+<a id="__codelineno-10-91" name="__codelineno-10-91" href="#__codelineno-10-91"></a><span class="w">    </span><span class="n">newNode</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-10-92" name="__codelineno-10-92" href="#__codelineno-10-92"></a><span class="w">    </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newNode</span><span class="p">;</span>
+<a id="__codelineno-10-93" name="__codelineno-10-93" href="#__codelineno-10-93"></a><span class="w">    </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-10-94" name="__codelineno-10-94" href="#__codelineno-10-94"></a><span class="p">}</span>
+<a id="__codelineno-10-95" name="__codelineno-10-95" href="#__codelineno-10-95"></a>
+<a id="__codelineno-10-96" name="__codelineno-10-96" href="#__codelineno-10-96"></a><span class="cm">/* ハッシュテーブルを拡張 */</span>
+<a id="__codelineno-10-97" name="__codelineno-10-97" href="#__codelineno-10-97"></a><span class="kt">void</span><span class="w"> </span><span class="nf">extend</span><span class="p">(</span><span class="n">HashMapChaining</span><span class="w"> </span><span class="o">*</span><span class="n">hashMap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-98" name="__codelineno-10-98" href="#__codelineno-10-98"></a><span class="w">    </span><span class="c1">// 元のハッシュテーブルを一時保存</span>
+<a id="__codelineno-10-99" name="__codelineno-10-99" href="#__codelineno-10-99"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">oldCapacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-10-100" name="__codelineno-10-100" href="#__codelineno-10-100"></a><span class="w">    </span><span class="n">Node</span><span class="w"> </span><span class="o">**</span><span class="n">oldBuckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">;</span>
+<a id="__codelineno-10-101" name="__codelineno-10-101" href="#__codelineno-10-101"></a><span class="w">    </span><span class="c1">// リサイズ後の新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-10-102" name="__codelineno-10-102" href="#__codelineno-10-102"></a><span class="w">    </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">extendRatio</span><span class="p">;</span>
+<a id="__codelineno-10-103" name="__codelineno-10-103" href="#__codelineno-10-103"></a><span class="w">    </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">Node</span><span class="w"> </span><span class="o">**</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="n">Node</span><span class="w"> </span><span class="o">*</span><span class="p">));</span>
+<a id="__codelineno-10-104" name="__codelineno-10-104" href="#__codelineno-10-104"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-105" name="__codelineno-10-105" href="#__codelineno-10-105"></a><span class="w">        </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-10-106" name="__codelineno-10-106" href="#__codelineno-10-106"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-107" name="__codelineno-10-107" href="#__codelineno-10-107"></a><span class="w">    </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-108" name="__codelineno-10-108" href="#__codelineno-10-108"></a><span class="w">    </span><span class="c1">// キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
+<a id="__codelineno-10-109" name="__codelineno-10-109" href="#__codelineno-10-109"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">oldCapacity</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-110" name="__codelineno-10-110" href="#__codelineno-10-110"></a><span class="w">        </span><span class="n">Node</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">oldBuckets</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-10-111" name="__codelineno-10-111" href="#__codelineno-10-111"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-112" name="__codelineno-10-112" href="#__codelineno-10-112"></a><span class="w">            </span><span class="n">put</span><span class="p">(</span><span class="n">hashMap</span><span class="p">,</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-10-113" name="__codelineno-10-113" href="#__codelineno-10-113"></a><span class="w">            </span><span class="n">Node</span><span class="w"> </span><span class="o">*</span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
+<a id="__codelineno-10-114" name="__codelineno-10-114" href="#__codelineno-10-114"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-10-115" name="__codelineno-10-115" href="#__codelineno-10-115"></a><span class="w">            </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-10-116" name="__codelineno-10-116" href="#__codelineno-10-116"></a><span class="w">            </span><span class="n">free</span><span class="p">(</span><span class="n">temp</span><span class="o">-&gt;</span><span class="n">pair</span><span class="p">);</span>
+<a id="__codelineno-10-117" name="__codelineno-10-117" href="#__codelineno-10-117"></a><span class="w">            </span><span class="n">free</span><span class="p">(</span><span class="n">temp</span><span class="p">);</span>
+<a id="__codelineno-10-118" name="__codelineno-10-118" href="#__codelineno-10-118"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-119" name="__codelineno-10-119" href="#__codelineno-10-119"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-120" name="__codelineno-10-120" href="#__codelineno-10-120"></a>
+<a id="__codelineno-10-121" name="__codelineno-10-121" href="#__codelineno-10-121"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">oldBuckets</span><span class="p">);</span>
+<a id="__codelineno-10-122" name="__codelineno-10-122" href="#__codelineno-10-122"></a><span class="p">}</span>
+<a id="__codelineno-10-123" name="__codelineno-10-123" href="#__codelineno-10-123"></a>
+<a id="__codelineno-10-124" name="__codelineno-10-124" href="#__codelineno-10-124"></a><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-10-125" name="__codelineno-10-125" href="#__codelineno-10-125"></a><span class="kt">void</span><span class="w"> </span><span class="nf">removeItem</span><span class="p">(</span><span class="n">HashMapChaining</span><span class="w"> </span><span class="o">*</span><span class="n">hashMap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-126" name="__codelineno-10-126" href="#__codelineno-10-126"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">hashMap</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-10-127" name="__codelineno-10-127" href="#__codelineno-10-127"></a><span class="w">    </span><span class="n">Node</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-10-128" name="__codelineno-10-128" href="#__codelineno-10-128"></a><span class="w">    </span><span class="n">Node</span><span class="w"> </span><span class="o">*</span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-10-129" name="__codelineno-10-129" href="#__codelineno-10-129"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-130" name="__codelineno-10-130" href="#__codelineno-10-130"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-131" name="__codelineno-10-131" href="#__codelineno-10-131"></a><span class="w">            </span><span class="c1">// そこからキーと値の組を削除する</span>
+<a id="__codelineno-10-132" name="__codelineno-10-132" href="#__codelineno-10-132"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-133" name="__codelineno-10-133" href="#__codelineno-10-133"></a><span class="w">                </span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-10-134" name="__codelineno-10-134" href="#__codelineno-10-134"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-135" name="__codelineno-10-135" href="#__codelineno-10-135"></a><span class="w">                </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-10-136" name="__codelineno-10-136" href="#__codelineno-10-136"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-10-137" name="__codelineno-10-137" href="#__codelineno-10-137"></a><span class="w">            </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-10-138" name="__codelineno-10-138" href="#__codelineno-10-138"></a><span class="w">            </span><span class="n">free</span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">pair</span><span class="p">);</span>
+<a id="__codelineno-10-139" name="__codelineno-10-139" href="#__codelineno-10-139"></a><span class="w">            </span><span class="n">free</span><span class="p">(</span><span class="n">cur</span><span class="p">);</span>
+<a id="__codelineno-10-140" name="__codelineno-10-140" href="#__codelineno-10-140"></a><span class="w">            </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-10-141" name="__codelineno-10-141" href="#__codelineno-10-141"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-10-142" name="__codelineno-10-142" href="#__codelineno-10-142"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-143" name="__codelineno-10-143" href="#__codelineno-10-143"></a><span class="w">        </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
+<a id="__codelineno-10-144" name="__codelineno-10-144" href="#__codelineno-10-144"></a><span class="w">        </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-10-145" name="__codelineno-10-145" href="#__codelineno-10-145"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-146" name="__codelineno-10-146" href="#__codelineno-10-146"></a><span class="p">}</span>
+<a id="__codelineno-10-147" name="__codelineno-10-147" href="#__codelineno-10-147"></a>
+<a id="__codelineno-10-148" name="__codelineno-10-148" href="#__codelineno-10-148"></a><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-10-149" name="__codelineno-10-149" href="#__codelineno-10-149"></a><span class="kt">void</span><span class="w"> </span><span class="nf">print</span><span class="p">(</span><span class="n">HashMapChaining</span><span class="w"> </span><span class="o">*</span><span class="n">hashMap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-150" name="__codelineno-10-150" href="#__codelineno-10-150"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-151" name="__codelineno-10-151" href="#__codelineno-10-151"></a><span class="w">        </span><span class="n">Node</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-10-152" name="__codelineno-10-152" href="#__codelineno-10-152"></a><span class="w">        </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;[&quot;</span><span class="p">);</span>
+<a id="__codelineno-10-153" name="__codelineno-10-153" href="#__codelineno-10-153"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-154" name="__codelineno-10-154" href="#__codelineno-10-154"></a><span class="w">            </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d -&gt; %s, &quot;</span><span class="p">,</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-10-155" name="__codelineno-10-155" href="#__codelineno-10-155"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-10-156" name="__codelineno-10-156" href="#__codelineno-10-156"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-157" name="__codelineno-10-157" href="#__codelineno-10-157"></a><span class="w">        </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;]</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">);</span>
+<a id="__codelineno-10-158" name="__codelineno-10-158" href="#__codelineno-10-158"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-159" name="__codelineno-10-159" href="#__codelineno-10-159"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map_chaining.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">HashMapChaining</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">hash_map_chaining.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* チェイン法ハッシュテーブル */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">HashMapChaining</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">size</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="c1">// キーと値のペア数</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">capacity</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="c1">// ハッシュテーブル容量</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">loadThres</span><span class="p">:</span><span class="w"> </span><span class="kt">Double</span><span class="w"> </span><span class="c1">// リサイズを発動する負荷率のしきい値</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">extendRatio</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="c1">// 拡張倍率</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">buckets</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="c1">// バケット配列</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">    </span><span class="k">init</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">        </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">        </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">4</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">        </span><span class="n">loadThres</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">3.0</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">        </span><span class="n">extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="p">()</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">            </span><span class="n">buckets</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">mutableListOf</span><span class="p">())</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span>
+<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a>
+<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="w">    </span><span class="cm">/* 負荷率 */</span>
+<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">loadFactor</span><span class="p">():</span><span class="w"> </span><span class="kt">Double</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">capacity</span><span class="p">).</span><span class="na">toDouble</span><span class="p">()</span>
+<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-30" name="__codelineno-11-30" href="#__codelineno-11-30"></a>
+<a id="__codelineno-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></a><span class="w">    </span><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-11-32" name="__codelineno-11-32" href="#__codelineno-11-32"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">String?</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-33" name="__codelineno-11-33" href="#__codelineno-11-33"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-11-34" name="__codelineno-11-34" href="#__codelineno-11-34"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span>
+<a id="__codelineno-11-35" name="__codelineno-11-35" href="#__codelineno-11-35"></a><span class="w">        </span><span class="c1">// バケットを走査し、key が見つかれば対応する val を返す</span>
+<a id="__codelineno-11-36" name="__codelineno-11-36" href="#__codelineno-11-36"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-37" name="__codelineno-11-37" href="#__codelineno-11-37"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">_val</span>
+<a id="__codelineno-11-38" name="__codelineno-11-38" href="#__codelineno-11-38"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-39" name="__codelineno-11-39" href="#__codelineno-11-39"></a><span class="w">        </span><span class="c1">// key が見つからない場合は null を返す</span>
+<a id="__codelineno-11-40" name="__codelineno-11-40" href="#__codelineno-11-40"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span>
+<a id="__codelineno-11-41" name="__codelineno-11-41" href="#__codelineno-11-41"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-42" name="__codelineno-11-42" href="#__codelineno-11-42"></a>
+<a id="__codelineno-11-43" name="__codelineno-11-43" href="#__codelineno-11-43"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-11-44" name="__codelineno-11-44" href="#__codelineno-11-44"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">:</span><span class="w"> </span><span class="kt">String</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-45" name="__codelineno-11-45" href="#__codelineno-11-45"></a><span class="w">        </span><span class="c1">// 負荷率がしきい値を超えたら、リサイズを実行</span>
+<a id="__codelineno-11-46" name="__codelineno-11-46" href="#__codelineno-11-46"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">loadThres</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-47" name="__codelineno-11-47" href="#__codelineno-11-47"></a><span class="w">            </span><span class="n">extend</span><span class="p">()</span>
+<a id="__codelineno-11-48" name="__codelineno-11-48" href="#__codelineno-11-48"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-49" name="__codelineno-11-49" href="#__codelineno-11-49"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-11-50" name="__codelineno-11-50" href="#__codelineno-11-50"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span>
+<a id="__codelineno-11-51" name="__codelineno-11-51" href="#__codelineno-11-51"></a><span class="w">        </span><span class="c1">// バケットを走査し、指定した key が見つかれば対応する val を更新して返す</span>
+<a id="__codelineno-11-52" name="__codelineno-11-52" href="#__codelineno-11-52"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-53" name="__codelineno-11-53" href="#__codelineno-11-53"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-54" name="__codelineno-11-54" href="#__codelineno-11-54"></a><span class="w">                </span><span class="n">pair</span><span class="p">.</span><span class="na">_val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_val</span>
+<a id="__codelineno-11-55" name="__codelineno-11-55" href="#__codelineno-11-55"></a><span class="w">                </span><span class="k">return</span>
+<a id="__codelineno-11-56" name="__codelineno-11-56" href="#__codelineno-11-56"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-11-57" name="__codelineno-11-57" href="#__codelineno-11-57"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-58" name="__codelineno-11-58" href="#__codelineno-11-58"></a><span class="w">        </span><span class="c1">// その key が存在しなければ、キーと値のペアを末尾に追加</span>
+<a id="__codelineno-11-59" name="__codelineno-11-59" href="#__codelineno-11-59"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">)</span>
+<a id="__codelineno-11-60" name="__codelineno-11-60" href="#__codelineno-11-60"></a><span class="w">        </span><span class="n">bucket</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">pair</span><span class="p">)</span>
+<a id="__codelineno-11-61" name="__codelineno-11-61" href="#__codelineno-11-61"></a><span class="w">        </span><span class="n">size</span><span class="o">++</span>
+<a id="__codelineno-11-62" name="__codelineno-11-62" href="#__codelineno-11-62"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-63" name="__codelineno-11-63" href="#__codelineno-11-63"></a>
+<a id="__codelineno-11-64" name="__codelineno-11-64" href="#__codelineno-11-64"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-11-65" name="__codelineno-11-65" href="#__codelineno-11-65"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-66" name="__codelineno-11-66" href="#__codelineno-11-66"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-11-67" name="__codelineno-11-67" href="#__codelineno-11-67"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span>
+<a id="__codelineno-11-68" name="__codelineno-11-68" href="#__codelineno-11-68"></a><span class="w">        </span><span class="c1">// バケットを走査してキーと値のペアを削除</span>
+<a id="__codelineno-11-69" name="__codelineno-11-69" href="#__codelineno-11-69"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-70" name="__codelineno-11-70" href="#__codelineno-11-70"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-71" name="__codelineno-11-71" href="#__codelineno-11-71"></a><span class="w">                </span><span class="n">bucket</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">pair</span><span class="p">)</span>
+<a id="__codelineno-11-72" name="__codelineno-11-72" href="#__codelineno-11-72"></a><span class="w">                </span><span class="n">size</span><span class="o">--</span>
+<a id="__codelineno-11-73" name="__codelineno-11-73" href="#__codelineno-11-73"></a><span class="w">                </span><span class="k">break</span>
+<a id="__codelineno-11-74" name="__codelineno-11-74" href="#__codelineno-11-74"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-11-75" name="__codelineno-11-75" href="#__codelineno-11-75"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-76" name="__codelineno-11-76" href="#__codelineno-11-76"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-77" name="__codelineno-11-77" href="#__codelineno-11-77"></a>
+<a id="__codelineno-11-78" name="__codelineno-11-78" href="#__codelineno-11-78"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを拡張 */</span>
+<a id="__codelineno-11-79" name="__codelineno-11-79" href="#__codelineno-11-79"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">extend</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-80" name="__codelineno-11-80" href="#__codelineno-11-80"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルを一時保存</span>
+<a id="__codelineno-11-81" name="__codelineno-11-81" href="#__codelineno-11-81"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">bucketsTmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span>
+<a id="__codelineno-11-82" name="__codelineno-11-82" href="#__codelineno-11-82"></a><span class="w">        </span><span class="c1">// リサイズ後の新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-11-83" name="__codelineno-11-83" href="#__codelineno-11-83"></a><span class="w">        </span><span class="n">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="n">extendRatio</span>
+<a id="__codelineno-11-84" name="__codelineno-11-84" href="#__codelineno-11-84"></a><span class="w">        </span><span class="c1">// mutablelist には固定サイズがない</span>
+<a id="__codelineno-11-85" name="__codelineno-11-85" href="#__codelineno-11-85"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="p">()</span>
+<a id="__codelineno-11-86" name="__codelineno-11-86" href="#__codelineno-11-86"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-87" name="__codelineno-11-87" href="#__codelineno-11-87"></a><span class="w">            </span><span class="n">buckets</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">mutableListOf</span><span class="p">())</span>
+<a id="__codelineno-11-88" name="__codelineno-11-88" href="#__codelineno-11-88"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-89" name="__codelineno-11-89" href="#__codelineno-11-89"></a><span class="w">        </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-11-90" name="__codelineno-11-90" href="#__codelineno-11-90"></a><span class="w">        </span><span class="c1">// キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
+<a id="__codelineno-11-91" name="__codelineno-11-91" href="#__codelineno-11-91"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">bucket</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-92" name="__codelineno-11-92" href="#__codelineno-11-92"></a><span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-93" name="__codelineno-11-93" href="#__codelineno-11-93"></a><span class="w">                </span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">_val</span><span class="p">)</span>
+<a id="__codelineno-11-94" name="__codelineno-11-94" href="#__codelineno-11-94"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-11-95" name="__codelineno-11-95" href="#__codelineno-11-95"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-96" name="__codelineno-11-96" href="#__codelineno-11-96"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-97" name="__codelineno-11-97" href="#__codelineno-11-97"></a>
+<a id="__codelineno-11-98" name="__codelineno-11-98" href="#__codelineno-11-98"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-11-99" name="__codelineno-11-99" href="#__codelineno-11-99"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-100" name="__codelineno-11-100" href="#__codelineno-11-100"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">bucket</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-101" name="__codelineno-11-101" href="#__codelineno-11-101"></a><span class="w">            </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="kt">String</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-11-102" name="__codelineno-11-102" href="#__codelineno-11-102"></a><span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-103" name="__codelineno-11-103" href="#__codelineno-11-103"></a><span class="w">                </span><span class="kd">val</span><span class="w"> </span><span class="nv">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">key</span>
+<a id="__codelineno-11-104" name="__codelineno-11-104" href="#__codelineno-11-104"></a><span class="w">                </span><span class="kd">val</span><span class="w"> </span><span class="nv">v</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">_val</span>
+<a id="__codelineno-11-105" name="__codelineno-11-105" href="#__codelineno-11-105"></a><span class="w">                </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="s">&quot;</span><span class="si">$</span><span class="n">k</span><span class="s"> -&gt; </span><span class="si">$</span><span class="n">v</span><span class="s">&quot;</span><span class="p">)</span>
+<a id="__codelineno-11-106" name="__codelineno-11-106" href="#__codelineno-11-106"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-11-107" name="__codelineno-11-107" href="#__codelineno-11-107"></a><span class="w">            </span><span class="n">println</span><span class="p">(</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-11-108" name="__codelineno-11-108" href="#__codelineno-11-108"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-109" name="__codelineno-11-109" href="#__codelineno-11-109"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-110" name="__codelineno-11-110" href="#__codelineno-11-110"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map_chaining.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">HashMapChaining</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">hash_map_chaining.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### キーアドレス法ハッシュテーブル ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">HashMapChaining</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1">### コンストラクタ ###</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1"># キーと値のペア数</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">    </span><span class="vi">@capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">4</span><span class="w"> </span><span class="c1"># ハッシュテーブル容量</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">    </span><span class="vi">@load_thres</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="o">.</span><span class="mi">0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">3</span><span class="o">.</span><span class="mi">0</span><span class="w"> </span><span class="c1"># リサイズを発動する負荷率のしきい値</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">    </span><span class="vi">@extend_ratio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1"># 拡張倍率</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">    </span><span class="vi">@buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="vi">@capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">[]</span><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="c1"># バケット配列</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">  </span><span class="c1">### ハッシュ関数 ###</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">    </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="vi">@capacity</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">  </span><span class="c1">### 負荷率 ###</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">load_factor</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="vi">@capacity</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w">  </span><span class="c1">### 検索操作 ###</span>
+<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a><span class="w">    </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="w">    </span><span class="n">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span>
+<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a><span class="w">    </span><span class="c1"># バケットを走査し、key が見つかれば対応する val を返す</span>
+<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span>
+<a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a><span class="w">      </span><span class="k">return</span><span class="w"> </span><span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span>
+<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a><span class="w">    </span><span class="c1"># `key` が見つからなければ `nil` を返す</span>
+<a id="__codelineno-12-31" name="__codelineno-12-31" href="#__codelineno-12-31"></a><span class="w">    </span><span class="kp">nil</span>
+<a id="__codelineno-12-32" name="__codelineno-12-32" href="#__codelineno-12-32"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-33" name="__codelineno-12-33" href="#__codelineno-12-33"></a>
+<a id="__codelineno-12-34" name="__codelineno-12-34" href="#__codelineno-12-34"></a><span class="w">  </span><span class="c1">### 追加操作 ###</span>
+<a id="__codelineno-12-35" name="__codelineno-12-35" href="#__codelineno-12-35"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-12-36" name="__codelineno-12-36" href="#__codelineno-12-36"></a><span class="w">    </span><span class="c1"># 負荷率がしきい値を超えたら、リサイズを実行</span>
+<a id="__codelineno-12-37" name="__codelineno-12-37" href="#__codelineno-12-37"></a><span class="w">    </span><span class="kp">extend</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">load_factor</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="vi">@load_thres</span>
+<a id="__codelineno-12-38" name="__codelineno-12-38" href="#__codelineno-12-38"></a><span class="w">    </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-12-39" name="__codelineno-12-39" href="#__codelineno-12-39"></a><span class="w">    </span><span class="n">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span>
+<a id="__codelineno-12-40" name="__codelineno-12-40" href="#__codelineno-12-40"></a><span class="w">    </span><span class="c1"># バケットを走査し、指定した key が見つかれば対応する val を更新して返す</span>
+<a id="__codelineno-12-41" name="__codelineno-12-41" href="#__codelineno-12-41"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span>
+<a id="__codelineno-12-42" name="__codelineno-12-42" href="#__codelineno-12-42"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span>
+<a id="__codelineno-12-43" name="__codelineno-12-43" href="#__codelineno-12-43"></a><span class="w">        </span><span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span>
+<a id="__codelineno-12-44" name="__codelineno-12-44" href="#__codelineno-12-44"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-12-45" name="__codelineno-12-45" href="#__codelineno-12-45"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-12-46" name="__codelineno-12-46" href="#__codelineno-12-46"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-47" name="__codelineno-12-47" href="#__codelineno-12-47"></a><span class="w">    </span><span class="c1"># その key が存在しなければ、キーと値のペアを末尾に追加</span>
+<a id="__codelineno-12-48" name="__codelineno-12-48" href="#__codelineno-12-48"></a><span class="w">    </span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">Pair</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-12-49" name="__codelineno-12-49" href="#__codelineno-12-49"></a><span class="w">    </span><span class="n">bucket</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">pair</span>
+<a id="__codelineno-12-50" name="__codelineno-12-50" href="#__codelineno-12-50"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-51" name="__codelineno-12-51" href="#__codelineno-12-51"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-52" name="__codelineno-12-52" href="#__codelineno-12-52"></a>
+<a id="__codelineno-12-53" name="__codelineno-12-53" href="#__codelineno-12-53"></a><span class="w">  </span><span class="c1">### 削除操作 ###</span>
+<a id="__codelineno-12-54" name="__codelineno-12-54" href="#__codelineno-12-54"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-12-55" name="__codelineno-12-55" href="#__codelineno-12-55"></a><span class="w">    </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-12-56" name="__codelineno-12-56" href="#__codelineno-12-56"></a><span class="w">    </span><span class="n">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span>
+<a id="__codelineno-12-57" name="__codelineno-12-57" href="#__codelineno-12-57"></a><span class="w">    </span><span class="c1"># バケットを走査してキーと値のペアを削除</span>
+<a id="__codelineno-12-58" name="__codelineno-12-58" href="#__codelineno-12-58"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span>
+<a id="__codelineno-12-59" name="__codelineno-12-59" href="#__codelineno-12-59"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span>
+<a id="__codelineno-12-60" name="__codelineno-12-60" href="#__codelineno-12-60"></a><span class="w">        </span><span class="n">bucket</span><span class="o">.</span><span class="n">delete</span><span class="p">(</span><span class="n">pair</span><span class="p">)</span>
+<a id="__codelineno-12-61" name="__codelineno-12-61" href="#__codelineno-12-61"></a><span class="w">        </span><span class="vi">@size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-62" name="__codelineno-12-62" href="#__codelineno-12-62"></a><span class="w">        </span><span class="k">break</span>
+<a id="__codelineno-12-63" name="__codelineno-12-63" href="#__codelineno-12-63"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-12-64" name="__codelineno-12-64" href="#__codelineno-12-64"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-65" name="__codelineno-12-65" href="#__codelineno-12-65"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-66" name="__codelineno-12-66" href="#__codelineno-12-66"></a>
+<a id="__codelineno-12-67" name="__codelineno-12-67" href="#__codelineno-12-67"></a><span class="w">  </span><span class="c1">### ハッシュテーブルを拡張 ###</span>
+<a id="__codelineno-12-68" name="__codelineno-12-68" href="#__codelineno-12-68"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">extend</span>
+<a id="__codelineno-12-69" name="__codelineno-12-69" href="#__codelineno-12-69"></a><span class="w">    </span><span class="c1"># 元のハッシュテーブルを一時保存</span>
+<a id="__codelineno-12-70" name="__codelineno-12-70" href="#__codelineno-12-70"></a><span class="w">    </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@buckets</span>
+<a id="__codelineno-12-71" name="__codelineno-12-71" href="#__codelineno-12-71"></a><span class="w">    </span><span class="c1"># リサイズ後の新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-12-72" name="__codelineno-12-72" href="#__codelineno-12-72"></a><span class="w">    </span><span class="vi">@capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="vi">@extend_ratio</span>
+<a id="__codelineno-12-73" name="__codelineno-12-73" href="#__codelineno-12-73"></a><span class="w">    </span><span class="vi">@buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="vi">@capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">[]</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-12-74" name="__codelineno-12-74" href="#__codelineno-12-74"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-12-75" name="__codelineno-12-75" href="#__codelineno-12-75"></a><span class="w">    </span><span class="c1"># キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
+<a id="__codelineno-12-76" name="__codelineno-12-76" href="#__codelineno-12-76"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span>
+<a id="__codelineno-12-77" name="__codelineno-12-77" href="#__codelineno-12-77"></a><span class="w">      </span><span class="k">for</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span>
+<a id="__codelineno-12-78" name="__codelineno-12-78" href="#__codelineno-12-78"></a><span class="w">        </span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-12-79" name="__codelineno-12-79" href="#__codelineno-12-79"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-12-80" name="__codelineno-12-80" href="#__codelineno-12-80"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-81" name="__codelineno-12-81" href="#__codelineno-12-81"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-82" name="__codelineno-12-82" href="#__codelineno-12-82"></a>
+<a id="__codelineno-12-83" name="__codelineno-12-83" href="#__codelineno-12-83"></a><span class="w">  </span><span class="c1">### ハッシュテーブルを出力 ###</span>
+<a id="__codelineno-12-84" name="__codelineno-12-84" href="#__codelineno-12-84"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">print</span>
+<a id="__codelineno-12-85" name="__codelineno-12-85" href="#__codelineno-12-85"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="vi">@buckets</span>
+<a id="__codelineno-12-86" name="__codelineno-12-86" href="#__codelineno-12-86"></a><span class="w">      </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-12-87" name="__codelineno-12-87" href="#__codelineno-12-87"></a><span class="w">      </span><span class="k">for</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span>
+<a id="__codelineno-12-88" name="__codelineno-12-88" href="#__codelineno-12-88"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s2">&quot;</span><span class="si">#{</span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="si">}</span><span class="s2"> -&gt; </span><span class="si">#{</span><span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="si">}</span><span class="s2">&quot;</span>
+<a id="__codelineno-12-89" name="__codelineno-12-89" href="#__codelineno-12-89"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-12-90" name="__codelineno-12-90" href="#__codelineno-12-90"></a><span class="w">      </span><span class="n">pp</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-12-91" name="__codelineno-12-91" href="#__codelineno-12-91"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-92" name="__codelineno-12-92" href="#__codelineno-12-92"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-93" name="__codelineno-12-93" href="#__codelineno-12-93"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>連結リストが非常に長い場合、クエリ効率<span class="arithmatex">\(O(n)\)</span>が悪いことは注目に値します。<strong>この場合、リストを「AVL木」または「赤黒木」に変換して</strong>、クエリ操作の時間計算量を<span class="arithmatex">\(O(\log n)\)</span>に最適化できます。</p>
-<h2 id="622">6.2.2 &nbsp; オープンアドレス法<a class="headerlink" href="#622" title="Permanent link">&para;</a></h2>
-<p><u>オープンアドレス法</u>は追加のデータ構造を導入せず、代わりに「複数回プローブ」を通してハッシュ衝突を処理します。プローブ方法には主に線形プローブ、二次プローブ、二重ハッシュがあります。</p>
-<p>線形プローブを例にして、オープンアドレス法ハッシュ表のメカニズムを紹介しましょう。</p>
-<h3 id="1">1. &nbsp; 線形プローブ<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>線形プローブは固定ステップの線形検索をプローブに使用し、通常のハッシュ表とは異なります。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" 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target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>注意すべきなのは、連結リストが長い場合、検索効率 <span class="arithmatex">\(O(n)\)</span> は非常に低いことです。<strong>このとき、連結リストを「AVL 木」または「赤黒木」に変換することで</strong>、検索操作の時間計算量を <span class="arithmatex">\(O(\log n)\)</span> に最適化できます。</p>
+<h2 id="622">6.2.2 &nbsp; オープンアドレッシング<a class="headerlink" href="#622" title="Permanent link">&para;</a></h2>
+<p><u>オープンアドレッシング（open addressing）</u>では追加のデータ構造を導入せず、「複数回の探索」によってハッシュ衝突を処理します。探索方法には主に線形探索、二次探索、多重ハッシュなどがあります。</p>
+<p>以下では線形探索を例に、オープンアドレッシングハッシュテーブルの動作の仕組みを説明します。</p>
+<h3 id="1">1. &nbsp; 線形探索<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>線形探索では、固定ステップ長の線形探索によって探索を行います。その操作方法は通常のハッシュテーブルとは異なります。</p>
 <ul>
-<li><strong>要素の挿入</strong>: ハッシュ関数を使用してバケットインデックスを計算します。バケットに既に要素が含まれている場合、衝突位置から線形に前方に走査し（通常ステップサイズは<span class="arithmatex">\(1\)</span>）、空のバケットが見つかるまで進み、要素を挿入します。</li>
-<li><strong>要素の検索</strong>: ハッシュ衝突に遭遇した場合、同じステップサイズを使用して線形に前方に走査し、対応する要素が見つかったら<code>value</code>を返します。空のバケットに遭遇した場合、ターゲット要素がハッシュ表にないことを意味するため、<code>None</code>を返します。</li>
+<li><strong>要素の挿入</strong>：ハッシュ関数によってバケットインデックスを計算し、バケット内にすでに要素がある場合は、衝突位置から後方へ線形に走査し（ステップ長は通常 <span class="arithmatex">\(1\)</span> ）、空のバケットが見つかるまで進み、その中に要素を挿入します。</li>
+<li><strong>要素の検索</strong>：ハッシュ衝突が見つかった場合は、同じステップ長で後方へ線形走査を行い、対応する要素が見つかるまで続け、 <code>value</code> を返します。空のバケットに遭遇した場合は、対象要素がハッシュテーブル内に存在しないことを意味するため、 <code>None</code> を返します。</li>
 </ul>
-<p>下図はオープンアドレス法（線形プローブ）ハッシュ表におけるキー値ペアの分布を示しています。このハッシュ関数によると、下二桁が同じキーは同じバケットにマッピングされます。線形プローブを通して、それらはそのバケットとその下のバケットに順次格納されます。</p>
-<p><img alt="オープンアドレス法（線形プローブ）ハッシュ表におけるキー値ペアの分布" class="animation-figure" src="../hash_collision.assets/hash_table_linear_probing.png" /></p>
-<p align="center"> 図 6-6 &nbsp; オープンアドレス法（線形プローブ）ハッシュ表におけるキー値ペアの分布 </p>
+<p>下図はオープンアドレッシング（線形探索）ハッシュテーブルにおけるキーと値のペアの分布を示しています。このハッシュ関数では、末尾 2 桁が同じ <code>key</code> はすべて同じバケットに写像されます。線形探索によって、それらはそのバケットとその後続のバケットに順に格納されます。</p>
+<p><img alt="オープンアドレッシング（線形探索）ハッシュテーブルにおけるキーと値のペアの分布" class="animation-figure" src="../hash_collision.assets/hash_table_linear_probing.png" /></p>
+<p align="center"> 図 6-6 &nbsp; オープンアドレッシング（線形探索）ハッシュテーブルにおけるキーと値のペアの分布 </p>
 
-<p>しかし、<strong>線形プローブは「クラスタリング」を作りやすい傾向があります</strong>。具体的には、配列内の連続的に占有された位置が長いほど、これらの連続した位置でハッシュ衝突が発生する確率が高くなり、その位置でのクラスタリングの成長をさらに促進し、悪循環を形成し、最終的に挿入、削除、クエリ、更新操作の効率低下につながります。</p>
-<p>**オープンアドレス法ハッシュ表では要素を直接削除できない**ことに注意することが重要です。要素を削除すると、配列に空のバケット<code>None</code>が作成されます。要素を検索する際、線形プローブがこの空のバケットに遭遇すると戻ってしまい、このバケットの下の要素にアクセスできなくなります。プログラムはこれらの要素が存在しないと誤って仮定する可能性があります。下図に示すとおりです。</p>
-<p><img alt="オープンアドレス法での削除によるクエリ問題" class="animation-figure" src="../hash_collision.assets/hash_table_open_addressing_deletion.png" /></p>
-<p align="center"> 図 6-7 &nbsp; オープンアドレス法での削除によるクエリ問題 </p>
+<p>しかし、**線形探索では「クラスタリング現象」が起こりやすい**です。具体的には、配列内で連続して占有された位置が長いほど、それらの連続位置でハッシュ衝突が発生する可能性が高くなり、さらにその位置の集積成長を促して悪循環を生み、最終的には追加・削除・検索・更新操作の効率低下を招きます。</p>
+<p>注意すべきなのは、**オープンアドレッシングハッシュテーブルでは要素を直接削除できない**ことです。これは、要素を削除すると配列内に空バケット <code>None</code> が生じ、要素を検索するときに線形探索がその空バケットに到達した時点で返ってしまうため、その空バケットより後ろの要素には二度とアクセスできなくなるからです。結果として、プログラムがそれらの要素を存在しないと誤判定する可能性があります。下図のとおりです。</p>
+<p><img alt="オープンアドレッシングで要素を削除したことによる検索問題" class="animation-figure" src="../hash_collision.assets/hash_table_open_addressing_deletion.png" /></p>
+<p align="center"> 図 6-7 &nbsp; オープンアドレッシングで要素を削除したことによる検索問題 </p>
 
-<p>この問題を解決するために、<u>遅延削除</u>メカニズムを採用できます：ハッシュ表から要素を直接削除する代わりに、<strong>定数<code>TOMBSTONE</code>を使用してバケットをマークします</strong>。このメカニズムでは、<code>None</code>と<code>TOMBSTONE</code>の両方が空のバケットを表し、キー値ペアを保持できます。ただし、線形プローブが<code>TOMBSTONE</code>に遭遇した場合、その下にまだキー値ペアがある可能性があるため、走査を続ける必要があります。</p>
-<p>しかし、<strong>遅延削除はハッシュ表の性能劣化を加速する可能性があります</strong>。削除操作のたびに削除マークが生成され、<code>TOMBSTONE</code>が増加すると、線形プローブがターゲット要素を見つけるために複数の<code>TOMBSTONE</code>をスキップする必要がある可能性があるため、検索時間も増加します。</p>
-<p>これに対処するために、線形プローブ中に最初に遭遇した<code>TOMBSTONE</code>のインデックスを記録し、検索されたターゲット要素とその<code>TOMBSTONE</code>の位置を交換することを検討してください。これを行う利点は、要素がクエリまたは追加されるたびに、要素がその理想的な位置（プローブの開始点）により近いバケットに移動され、クエリ効率が最適化されることです。</p>
-<p>以下のコードは、遅延削除を使用したオープンアドレス法（線形プローブ）ハッシュ表を実装しています。ハッシュ表の空間をより有効に活用するために、ハッシュ表を「循環配列」として扱います。配列の終わりを超えると、最初に戻って走査を続けます。</p>
+<p>この問題を解決するために、<u>遅延削除（lazy deletion）</u>の仕組みを採用できます。これは要素をハッシュテーブルから直接取り除かず、<strong>代わりに定数 <code>TOMBSTONE</code> を使ってこのバケットをマークします</strong>。この仕組みでは、<code>None</code> と <code>TOMBSTONE</code> はどちらも空バケットを表し、どちらにもキーと値のペアを配置できます。ただし異なるのは、線形探索が <code>TOMBSTONE</code> に到達した場合は、その先にキーと値のペアが存在する可能性があるため、探索を続けるべきだという点です。</p>
+<p>しかし、<strong>遅延削除はハッシュテーブルの性能劣化を加速させる可能性があります</strong>。これは、削除操作のたびに削除マークが 1 つ生成され、<code>TOMBSTONE</code> が増えるにつれて探索時間も増加するためです。線形探索では、対象要素を見つけるまでに複数の <code>TOMBSTONE</code> を飛び越える必要があるかもしれません。</p>
+<p>そのため、線形探索では、遭遇した最初の <code>TOMBSTONE</code> のインデックスを記録し、見つかった対象要素とその <code>TOMBSTONE</code> を交換することを考えます。こうする利点は、要素を検索または追加するたびに、要素が理想位置（探索開始点）により近いバケットへ移動し、検索効率が向上することです。</p>
+<p>以下のコードは、遅延削除を含むオープンアドレッシング（線形探索）ハッシュテーブルを実装したものです。ハッシュテーブルの空間をより十分に活用するために、ハッシュテーブルを「環状配列」とみなし、配列末尾を越えたら先頭に戻って探索を続けます。</p>
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 <div class="tabbed-block">
@@ -4869,12 +5977,12 @@
 <a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>
 <a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
 <a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
-<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># キー値ペアの数</span>
-<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span> <span class="o">=</span> <span class="mi">4</span>  <span class="c1"># ハッシュテーブルの容量</span>
-<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">load_thres</span> <span class="o">=</span> <span class="mf">2.0</span> <span class="o">/</span> <span class="mf">3.0</span>  <span class="c1"># 拡張をトリガーする負荷率の閾値</span>
-<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">extend_ratio</span> <span class="o">=</span> <span class="mi">2</span>  <span class="c1"># 拡張の倍数</span>
+<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># キーと値のペア数</span>
+<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span> <span class="o">=</span> <span class="mi">4</span>  <span class="c1"># ハッシュテーブル容量</span>
+<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">load_thres</span> <span class="o">=</span> <span class="mf">2.0</span> <span class="o">/</span> <span class="mf">3.0</span>  <span class="c1"># リサイズを発動する負荷率のしきい値</span>
+<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">extend_ratio</span> <span class="o">=</span> <span class="mi">2</span>  <span class="c1"># 拡張倍率</span>
 <a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">Pair</span> <span class="o">|</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="kc">None</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span>  <span class="c1"># バケット配列</span>
-<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span> <span class="o">=</span> <span class="n">Pair</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="s2">&quot;-1&quot;</span><span class="p">)</span>  <span class="c1"># 削除マーク</span>
+<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span> <span class="o">=</span> <span class="n">Pair</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="s2">&quot;-1&quot;</span><span class="p">)</span>  <span class="c1"># 削除済みマーク</span>
 <a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>
 <a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">hash_func</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
 <a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;ハッシュ関数&quot;&quot;&quot;</span>
@@ -4885,70 +5993,70 @@
 <a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span>
 <a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a>
 <a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">find_bucket</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;key に対応するバケットインデックスを検索&quot;&quot;&quot;</span>
+<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;key に対応するバケットインデックスを探す&quot;&quot;&quot;</span>
 <a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a>        <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
 <a id="__codelineno-13-24" name="__codelineno-13-24" href="#__codelineno-13-24"></a>        <span class="n">first_tombstone</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span>
-<a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a>        <span class="c1"># 線形探査、空のバケットに遭遇したらブレーク</span>
+<a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a>        <span class="c1"># 線形プロービングを行い、空バケットに達したら終了</span>
 <a id="__codelineno-13-26" name="__codelineno-13-26" href="#__codelineno-13-26"></a>        <span class="k">while</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-13-27" name="__codelineno-13-27" href="#__codelineno-13-27"></a>            <span class="c1"># キーに遭遇した場合、対応するバケットインデックスを返す</span>
+<a id="__codelineno-13-27" name="__codelineno-13-27" href="#__codelineno-13-27"></a>            <span class="c1"># key が見つかったら、対応するバケットのインデックスを返す</span>
 <a id="__codelineno-13-28" name="__codelineno-13-28" href="#__codelineno-13-28"></a>            <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="n">key</span><span class="p">:</span>
-<a id="__codelineno-13-29" name="__codelineno-13-29" href="#__codelineno-13-29"></a>                <span class="c1"># 削除マークが以前に遭遇していた場合、キー値ペアをそのインデックスに移動</span>
+<a id="__codelineno-13-29" name="__codelineno-13-29" href="#__codelineno-13-29"></a>                <span class="c1"># 以前に削除マークが見つかっていれば、そのインデックスへキーと値のペアを移動</span>
 <a id="__codelineno-13-30" name="__codelineno-13-30" href="#__codelineno-13-30"></a>                <span class="k">if</span> <span class="n">first_tombstone</span> <span class="o">!=</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span>
 <a id="__codelineno-13-31" name="__codelineno-13-31" href="#__codelineno-13-31"></a>                    <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">first_tombstone</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
 <a id="__codelineno-13-32" name="__codelineno-13-32" href="#__codelineno-13-32"></a>                    <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span>
-<a id="__codelineno-13-33" name="__codelineno-13-33" href="#__codelineno-13-33"></a>                    <span class="k">return</span> <span class="n">first_tombstone</span>  <span class="c1"># 移動されたバケットインデックスを返す</span>
-<a id="__codelineno-13-34" name="__codelineno-13-34" href="#__codelineno-13-34"></a>                <span class="k">return</span> <span class="n">index</span>  <span class="c1"># バケットインデックスを返す</span>
-<a id="__codelineno-13-35" name="__codelineno-13-35" href="#__codelineno-13-35"></a>            <span class="c1"># 最初に遭遇した削除マークを記録</span>
+<a id="__codelineno-13-33" name="__codelineno-13-33" href="#__codelineno-13-33"></a>                    <span class="k">return</span> <span class="n">first_tombstone</span>  <span class="c1"># 移動後のバケットインデックスを返す</span>
+<a id="__codelineno-13-34" name="__codelineno-13-34" href="#__codelineno-13-34"></a>                <span class="k">return</span> <span class="n">index</span>  <span class="c1"># バケットのインデックスを返す</span>
+<a id="__codelineno-13-35" name="__codelineno-13-35" href="#__codelineno-13-35"></a>            <span class="c1"># 最初に見つかった削除マークを記録</span>
 <a id="__codelineno-13-36" name="__codelineno-13-36" href="#__codelineno-13-36"></a>            <span class="k">if</span> <span class="n">first_tombstone</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="ow">is</span> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span><span class="p">:</span>
 <a id="__codelineno-13-37" name="__codelineno-13-37" href="#__codelineno-13-37"></a>                <span class="n">first_tombstone</span> <span class="o">=</span> <span class="n">index</span>
-<a id="__codelineno-13-38" name="__codelineno-13-38" href="#__codelineno-13-38"></a>            <span class="c1"># バケットインデックスを計算、末尾を超えた場合は先頭に戻る</span>
+<a id="__codelineno-13-38" name="__codelineno-13-38" href="#__codelineno-13-38"></a>            <span class="c1"># バケットのインデックスを計算し、末尾を越えたら先頭に戻る</span>
 <a id="__codelineno-13-39" name="__codelineno-13-39" href="#__codelineno-13-39"></a>            <span class="n">index</span> <span class="o">=</span> <span class="p">(</span><span class="n">index</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span>
-<a id="__codelineno-13-40" name="__codelineno-13-40" href="#__codelineno-13-40"></a>        <span class="c1"># キーが存在しない場合、挿入ポイントのインデックスを返す</span>
+<a id="__codelineno-13-40" name="__codelineno-13-40" href="#__codelineno-13-40"></a>        <span class="c1"># key が存在しない場合は追加位置のインデックスを返す</span>
 <a id="__codelineno-13-41" name="__codelineno-13-41" href="#__codelineno-13-41"></a>        <span class="k">return</span> <span class="n">index</span> <span class="k">if</span> <span class="n">first_tombstone</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span> <span class="k">else</span> <span class="n">first_tombstone</span>
 <a id="__codelineno-13-42" name="__codelineno-13-42" href="#__codelineno-13-42"></a>
 <a id="__codelineno-13-43" name="__codelineno-13-43" href="#__codelineno-13-43"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">str</span><span class="p">:</span>
-<a id="__codelineno-13-44" name="__codelineno-13-44" href="#__codelineno-13-44"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;照会操作&quot;&quot;&quot;</span>
-<a id="__codelineno-13-45" name="__codelineno-13-45" href="#__codelineno-13-45"></a>        <span class="c1"># key に対応するバケットインデックスを検索</span>
+<a id="__codelineno-13-44" name="__codelineno-13-44" href="#__codelineno-13-44"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;検索操作&quot;&quot;&quot;</span>
+<a id="__codelineno-13-45" name="__codelineno-13-45" href="#__codelineno-13-45"></a>        <span class="c1"># key に対応するバケットインデックスを探す</span>
 <a id="__codelineno-13-46" name="__codelineno-13-46" href="#__codelineno-13-46"></a>        <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">find_bucket</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
-<a id="__codelineno-13-47" name="__codelineno-13-47" href="#__codelineno-13-47"></a>        <span class="c1"># キー値ペアが見つかれば、対応する val を返す</span>
+<a id="__codelineno-13-47" name="__codelineno-13-47" href="#__codelineno-13-47"></a>        <span class="c1"># キーと値の組が見つかったら、対応する val を返す</span>
 <a id="__codelineno-13-48" name="__codelineno-13-48" href="#__codelineno-13-48"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span><span class="p">]:</span>
 <a id="__codelineno-13-49" name="__codelineno-13-49" href="#__codelineno-13-49"></a>            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">.</span><span class="n">val</span>
-<a id="__codelineno-13-50" name="__codelineno-13-50" href="#__codelineno-13-50"></a>        <span class="c1"># キー値ペアが存在しない場合、None を返す</span>
+<a id="__codelineno-13-50" name="__codelineno-13-50" href="#__codelineno-13-50"></a>        <span class="c1"># キーと値のペアが存在しない場合は `None` を返す</span>
 <a id="__codelineno-13-51" name="__codelineno-13-51" href="#__codelineno-13-51"></a>        <span class="k">return</span> <span class="kc">None</span>
 <a id="__codelineno-13-52" name="__codelineno-13-52" href="#__codelineno-13-52"></a>
 <a id="__codelineno-13-53" name="__codelineno-13-53" href="#__codelineno-13-53"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">str</span><span class="p">):</span>
 <a id="__codelineno-13-54" name="__codelineno-13-54" href="#__codelineno-13-54"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;追加操作&quot;&quot;&quot;</span>
-<a id="__codelineno-13-55" name="__codelineno-13-55" href="#__codelineno-13-55"></a>        <span class="c1"># 負荷率が閾値を超えた場合、拡張を実行</span>
+<a id="__codelineno-13-55" name="__codelineno-13-55" href="#__codelineno-13-55"></a>        <span class="c1"># 負荷率がしきい値を超えたら、リサイズを実行</span>
 <a id="__codelineno-13-56" name="__codelineno-13-56" href="#__codelineno-13-56"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">load_factor</span><span class="p">()</span> <span class="o">&gt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">load_thres</span><span class="p">:</span>
 <a id="__codelineno-13-57" name="__codelineno-13-57" href="#__codelineno-13-57"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">extend</span><span class="p">()</span>
-<a id="__codelineno-13-58" name="__codelineno-13-58" href="#__codelineno-13-58"></a>        <span class="c1"># key に対応するバケットインデックスを検索</span>
+<a id="__codelineno-13-58" name="__codelineno-13-58" href="#__codelineno-13-58"></a>        <span class="c1"># key に対応するバケットインデックスを探す</span>
 <a id="__codelineno-13-59" name="__codelineno-13-59" href="#__codelineno-13-59"></a>        <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">find_bucket</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
-<a id="__codelineno-13-60" name="__codelineno-13-60" href="#__codelineno-13-60"></a>        <span class="c1"># キー値ペアが見つかれば、val を上書きして返す</span>
+<a id="__codelineno-13-60" name="__codelineno-13-60" href="#__codelineno-13-60"></a>        <span class="c1"># キーと値の組が見つかったら、val を上書きして返す</span>
 <a id="__codelineno-13-61" name="__codelineno-13-61" href="#__codelineno-13-61"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span><span class="p">]:</span>
 <a id="__codelineno-13-62" name="__codelineno-13-62" href="#__codelineno-13-62"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">.</span><span class="n">val</span> <span class="o">=</span> <span class="n">val</span>
 <a id="__codelineno-13-63" name="__codelineno-13-63" href="#__codelineno-13-63"></a>            <span class="k">return</span>
-<a id="__codelineno-13-64" name="__codelineno-13-64" href="#__codelineno-13-64"></a>        <span class="c1"># キー値ペアが存在しない場合、キー値ペアを追加</span>
+<a id="__codelineno-13-64" name="__codelineno-13-64" href="#__codelineno-13-64"></a>        <span class="c1"># キーと値の組が存在しない場合は、その組を追加する</span>
 <a id="__codelineno-13-65" name="__codelineno-13-65" href="#__codelineno-13-65"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
 <a id="__codelineno-13-66" name="__codelineno-13-66" href="#__codelineno-13-66"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">+=</span> <span class="mi">1</span>
 <a id="__codelineno-13-67" name="__codelineno-13-67" href="#__codelineno-13-67"></a>
 <a id="__codelineno-13-68" name="__codelineno-13-68" href="#__codelineno-13-68"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
 <a id="__codelineno-13-69" name="__codelineno-13-69" href="#__codelineno-13-69"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;削除操作&quot;&quot;&quot;</span>
-<a id="__codelineno-13-70" name="__codelineno-13-70" href="#__codelineno-13-70"></a>        <span class="c1"># key に対応するバケットインデックスを検索</span>
+<a id="__codelineno-13-70" name="__codelineno-13-70" href="#__codelineno-13-70"></a>        <span class="c1"># key に対応するバケットインデックスを探す</span>
 <a id="__codelineno-13-71" name="__codelineno-13-71" href="#__codelineno-13-71"></a>        <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">find_bucket</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
-<a id="__codelineno-13-72" name="__codelineno-13-72" href="#__codelineno-13-72"></a>        <span class="c1"># キー値ペアが見つかれば、削除マークで覆う</span>
+<a id="__codelineno-13-72" name="__codelineno-13-72" href="#__codelineno-13-72"></a>        <span class="c1"># キーと値の組が見つかったら、削除マーカーで上書きする</span>
 <a id="__codelineno-13-73" name="__codelineno-13-73" href="#__codelineno-13-73"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span><span class="p">]:</span>
 <a id="__codelineno-13-74" name="__codelineno-13-74" href="#__codelineno-13-74"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span>
 <a id="__codelineno-13-75" name="__codelineno-13-75" href="#__codelineno-13-75"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">-=</span> <span class="mi">1</span>
 <a id="__codelineno-13-76" name="__codelineno-13-76" href="#__codelineno-13-76"></a>
 <a id="__codelineno-13-77" name="__codelineno-13-77" href="#__codelineno-13-77"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">extend</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
 <a id="__codelineno-13-78" name="__codelineno-13-78" href="#__codelineno-13-78"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;ハッシュテーブルを拡張&quot;&quot;&quot;</span>
-<a id="__codelineno-13-79" name="__codelineno-13-79" href="#__codelineno-13-79"></a>        <span class="c1"># 元のハッシュテーブルを一時的に保存</span>
+<a id="__codelineno-13-79" name="__codelineno-13-79" href="#__codelineno-13-79"></a>        <span class="c1"># 元のハッシュテーブルを一時保存</span>
 <a id="__codelineno-13-80" name="__codelineno-13-80" href="#__codelineno-13-80"></a>        <span class="n">buckets_tmp</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span>
-<a id="__codelineno-13-81" name="__codelineno-13-81" href="#__codelineno-13-81"></a>        <span class="c1"># 拡張された新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-13-81" name="__codelineno-13-81" href="#__codelineno-13-81"></a>        <span class="c1"># リサイズ後の新しいハッシュテーブルを初期化</span>
 <a id="__codelineno-13-82" name="__codelineno-13-82" href="#__codelineno-13-82"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span> <span class="o">*=</span> <span class="bp">self</span><span class="o">.</span><span class="n">extend_ratio</span>
 <a id="__codelineno-13-83" name="__codelineno-13-83" href="#__codelineno-13-83"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span> <span class="o">=</span> <span class="p">[</span><span class="kc">None</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span>
 <a id="__codelineno-13-84" name="__codelineno-13-84" href="#__codelineno-13-84"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">=</span> <span class="mi">0</span>
-<a id="__codelineno-13-85" name="__codelineno-13-85" href="#__codelineno-13-85"></a>        <span class="c1"># 元のハッシュテーブルから新しいハッシュテーブルにキー値ペアを移動</span>
+<a id="__codelineno-13-85" name="__codelineno-13-85" href="#__codelineno-13-85"></a>        <span class="c1"># キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
 <a id="__codelineno-13-86" name="__codelineno-13-86" href="#__codelineno-13-86"></a>        <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="n">buckets_tmp</span><span class="p">:</span>
 <a id="__codelineno-13-87" name="__codelineno-13-87" href="#__codelineno-13-87"></a>            <span class="k">if</span> <span class="n">pair</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span><span class="p">]:</span>
 <a id="__codelineno-13-88" name="__codelineno-13-88" href="#__codelineno-13-88"></a>                <span class="bp">self</span><span class="o">.</span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="p">,</span> <span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
@@ -4968,19 +6076,19 @@
 <div class="highlight"><span class="filename">hash_map_open_addressing.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* オープンアドレス法ハッシュテーブル */</span>
 <a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">HashMapOpenAddressing</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
-<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w">                             </span><span class="c1">// キー値ペアの数</span>
-<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">4</span><span class="p">;</span><span class="w">                     </span><span class="c1">// ハッシュテーブルの容量</span>
-<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">loadThres</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3.0</span><span class="p">;</span><span class="w">     </span><span class="c1">// 拡張をトリガーする負荷率の閾値</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w">                             </span><span class="c1">// キーと値のペア数</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">4</span><span class="p">;</span><span class="w">                     </span><span class="c1">// ハッシュテーブル容量</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">loadThres</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3.0</span><span class="p">;</span><span class="w">     </span><span class="c1">// リサイズを発動する負荷率のしきい値</span>
 <a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">            </span><span class="c1">// 拡張倍率</span>
 <a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Pair</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span><span class="w">               </span><span class="c1">// バケット配列</span>
-<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">    </span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">TOMBSTONE</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="mi">-1</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;-1&quot;</span><span class="p">);</span><span class="w"> </span><span class="c1">// 削除マーク</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">    </span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">TOMBSTONE</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="mi">-1</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;-1&quot;</span><span class="p">);</span><span class="w"> </span><span class="c1">// 削除済みマーク</span>
 <a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>
 <a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
 <a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
 <a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">    </span><span class="n">HashMapOpenAddressing</span><span class="p">()</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="mi">0</span><span class="p">),</span><span class="w"> </span><span class="n">buckets</span><span class="p">(</span><span class="n">capacity</span><span class="p">,</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a>
-<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">    </span><span class="cm">/* デストラクタ */</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">    </span><span class="cm">/* デストラクタメソッド */</span>
 <a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w">    </span><span class="o">~</span><span class="n">HashMapOpenAddressing</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
@@ -5000,68 +6108,68 @@
 <a id="__codelineno-14-33" name="__codelineno-14-33" href="#__codelineno-14-33"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="n">size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
 <a id="__codelineno-14-34" name="__codelineno-14-34" href="#__codelineno-14-34"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-35" name="__codelineno-14-35" href="#__codelineno-14-35"></a>
-<a id="__codelineno-14-36" name="__codelineno-14-36" href="#__codelineno-14-36"></a><span class="w">    </span><span class="cm">/* keyに対応するバケットインデックスを検索 */</span>
+<a id="__codelineno-14-36" name="__codelineno-14-36" href="#__codelineno-14-36"></a><span class="w">    </span><span class="cm">/* key に対応するバケットインデックスを探す */</span>
 <a id="__codelineno-14-37" name="__codelineno-14-37" href="#__codelineno-14-37"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-38" name="__codelineno-14-38" href="#__codelineno-14-38"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
 <a id="__codelineno-14-39" name="__codelineno-14-39" href="#__codelineno-14-39"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
-<a id="__codelineno-14-40" name="__codelineno-14-40" href="#__codelineno-14-40"></a><span class="w">        </span><span class="c1">// 線形探査、空のバケットに遭遇したら中断</span>
+<a id="__codelineno-14-40" name="__codelineno-14-40" href="#__codelineno-14-40"></a><span class="w">        </span><span class="c1">// 線形プロービングを行い、空バケットに達したら終了</span>
 <a id="__codelineno-14-41" name="__codelineno-14-41" href="#__codelineno-14-41"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-42" name="__codelineno-14-42" href="#__codelineno-14-42"></a><span class="w">            </span><span class="c1">// keyに遭遇した場合、対応するバケットインデックスを返却</span>
+<a id="__codelineno-14-42" name="__codelineno-14-42" href="#__codelineno-14-42"></a><span class="w">            </span><span class="c1">// key が見つかったら、対応するバケットのインデックスを返す</span>
 <a id="__codelineno-14-43" name="__codelineno-14-43" href="#__codelineno-14-43"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-44" name="__codelineno-14-44" href="#__codelineno-14-44"></a><span class="w">                </span><span class="c1">// 以前に削除マークに遭遇していた場合、キー値ペアをそのインデックスに移動</span>
+<a id="__codelineno-14-44" name="__codelineno-14-44" href="#__codelineno-14-44"></a><span class="w">                </span><span class="c1">// 以前に削除マークが見つかっていれば、そのインデックスへキーと値のペアを移動</span>
 <a id="__codelineno-14-45" name="__codelineno-14-45" href="#__codelineno-14-45"></a><span class="w">                </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">-1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-46" name="__codelineno-14-46" href="#__codelineno-14-46"></a><span class="w">                    </span><span class="n">buckets</span><span class="p">[</span><span class="n">firstTombstone</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
 <a id="__codelineno-14-47" name="__codelineno-14-47" href="#__codelineno-14-47"></a><span class="w">                    </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">;</span>
-<a id="__codelineno-14-48" name="__codelineno-14-48" href="#__codelineno-14-48"></a><span class="w">                    </span><span class="k">return</span><span class="w"> </span><span class="n">firstTombstone</span><span class="p">;</span><span class="w"> </span><span class="c1">// 移動されたバケットインデックスを返却</span>
+<a id="__codelineno-14-48" name="__codelineno-14-48" href="#__codelineno-14-48"></a><span class="w">                    </span><span class="k">return</span><span class="w"> </span><span class="n">firstTombstone</span><span class="p">;</span><span class="w"> </span><span class="c1">// 移動後のバケットインデックスを返す</span>
 <a id="__codelineno-14-49" name="__codelineno-14-49" href="#__codelineno-14-49"></a><span class="w">                </span><span class="p">}</span>
-<a id="__codelineno-14-50" name="__codelineno-14-50" href="#__codelineno-14-50"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="c1">// バケットインデックスを返却</span>
+<a id="__codelineno-14-50" name="__codelineno-14-50" href="#__codelineno-14-50"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="c1">// バケットのインデックスを返す</span>
 <a id="__codelineno-14-51" name="__codelineno-14-51" href="#__codelineno-14-51"></a><span class="w">            </span><span class="p">}</span>
-<a id="__codelineno-14-52" name="__codelineno-14-52" href="#__codelineno-14-52"></a><span class="w">            </span><span class="c1">// 最初に遭遇した削除マークを記録</span>
+<a id="__codelineno-14-52" name="__codelineno-14-52" href="#__codelineno-14-52"></a><span class="w">            </span><span class="c1">// 最初に見つかった削除マークを記録</span>
 <a id="__codelineno-14-53" name="__codelineno-14-53" href="#__codelineno-14-53"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">-1</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-54" name="__codelineno-14-54" href="#__codelineno-14-54"></a><span class="w">                </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
 <a id="__codelineno-14-55" name="__codelineno-14-55" href="#__codelineno-14-55"></a><span class="w">            </span><span class="p">}</span>
-<a id="__codelineno-14-56" name="__codelineno-14-56" href="#__codelineno-14-56"></a><span class="w">            </span><span class="c1">// バケットインデックスを計算、末尾を超えた場合は先頭に戻る</span>
+<a id="__codelineno-14-56" name="__codelineno-14-56" href="#__codelineno-14-56"></a><span class="w">            </span><span class="c1">// バケットのインデックスを計算し、末尾を越えたら先頭に戻る</span>
 <a id="__codelineno-14-57" name="__codelineno-14-57" href="#__codelineno-14-57"></a><span class="w">            </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
 <a id="__codelineno-14-58" name="__codelineno-14-58" href="#__codelineno-14-58"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-14-59" name="__codelineno-14-59" href="#__codelineno-14-59"></a><span class="w">        </span><span class="c1">// keyが存在しない場合、挿入ポイントのインデックスを返却</span>
+<a id="__codelineno-14-59" name="__codelineno-14-59" href="#__codelineno-14-59"></a><span class="w">        </span><span class="c1">// key が存在しない場合は追加位置のインデックスを返す</span>
 <a id="__codelineno-14-60" name="__codelineno-14-60" href="#__codelineno-14-60"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">-1</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">firstTombstone</span><span class="p">;</span>
 <a id="__codelineno-14-61" name="__codelineno-14-61" href="#__codelineno-14-61"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-62" name="__codelineno-14-62" href="#__codelineno-14-62"></a>
-<a id="__codelineno-14-63" name="__codelineno-14-63" href="#__codelineno-14-63"></a><span class="w">    </span><span class="cm">/* クエリ操作 */</span>
+<a id="__codelineno-14-63" name="__codelineno-14-63" href="#__codelineno-14-63"></a><span class="w">    </span><span class="cm">/* 検索操作 */</span>
 <a id="__codelineno-14-64" name="__codelineno-14-64" href="#__codelineno-14-64"></a><span class="w">    </span><span class="n">string</span><span class="w"> </span><span class="n">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-65" name="__codelineno-14-65" href="#__codelineno-14-65"></a><span class="w">        </span><span class="c1">// keyに対応するバケットインデックスを検索</span>
+<a id="__codelineno-14-65" name="__codelineno-14-65" href="#__codelineno-14-65"></a><span class="w">        </span><span class="c1">// key に対応するバケットインデックスを探す</span>
 <a id="__codelineno-14-66" name="__codelineno-14-66" href="#__codelineno-14-66"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
-<a id="__codelineno-14-67" name="__codelineno-14-67" href="#__codelineno-14-67"></a><span class="w">        </span><span class="c1">// キー値ペアが見つかった場合、対応するvalを返却</span>
+<a id="__codelineno-14-67" name="__codelineno-14-67" href="#__codelineno-14-67"></a><span class="w">        </span><span class="c1">// キーと値の組が見つかったら、対応する val を返す</span>
 <a id="__codelineno-14-68" name="__codelineno-14-68" href="#__codelineno-14-68"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-69" name="__codelineno-14-69" href="#__codelineno-14-69"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
 <a id="__codelineno-14-70" name="__codelineno-14-70" href="#__codelineno-14-70"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-14-71" name="__codelineno-14-71" href="#__codelineno-14-71"></a><span class="w">        </span><span class="c1">// キー値ペアが存在しない場合、空文字列を返却</span>
+<a id="__codelineno-14-71" name="__codelineno-14-71" href="#__codelineno-14-71"></a><span class="w">        </span><span class="c1">// キーと値の組が存在しない場合は空文字列を返す</span>
 <a id="__codelineno-14-72" name="__codelineno-14-72" href="#__codelineno-14-72"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="s">&quot;&quot;</span><span class="p">;</span>
 <a id="__codelineno-14-73" name="__codelineno-14-73" href="#__codelineno-14-73"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-74" name="__codelineno-14-74" href="#__codelineno-14-74"></a>
 <a id="__codelineno-14-75" name="__codelineno-14-75" href="#__codelineno-14-75"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
 <a id="__codelineno-14-76" name="__codelineno-14-76" href="#__codelineno-14-76"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-77" name="__codelineno-14-77" href="#__codelineno-14-77"></a><span class="w">        </span><span class="c1">// 負荷率が閾値を超えた場合、拡張を実行</span>
+<a id="__codelineno-14-77" name="__codelineno-14-77" href="#__codelineno-14-77"></a><span class="w">        </span><span class="c1">// 負荷率がしきい値を超えたら、リサイズを実行</span>
 <a id="__codelineno-14-78" name="__codelineno-14-78" href="#__codelineno-14-78"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">loadThres</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-79" name="__codelineno-14-79" href="#__codelineno-14-79"></a><span class="w">            </span><span class="n">extend</span><span class="p">();</span>
 <a id="__codelineno-14-80" name="__codelineno-14-80" href="#__codelineno-14-80"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-14-81" name="__codelineno-14-81" href="#__codelineno-14-81"></a><span class="w">        </span><span class="c1">// keyに対応するバケットインデックスを検索</span>
+<a id="__codelineno-14-81" name="__codelineno-14-81" href="#__codelineno-14-81"></a><span class="w">        </span><span class="c1">// key に対応するバケットインデックスを探す</span>
 <a id="__codelineno-14-82" name="__codelineno-14-82" href="#__codelineno-14-82"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
-<a id="__codelineno-14-83" name="__codelineno-14-83" href="#__codelineno-14-83"></a><span class="w">        </span><span class="c1">// キー値ペアが見つかった場合、valを上書きして返却</span>
+<a id="__codelineno-14-83" name="__codelineno-14-83" href="#__codelineno-14-83"></a><span class="w">        </span><span class="c1">// キーと値の組が見つかったら、val を上書きして返す</span>
 <a id="__codelineno-14-84" name="__codelineno-14-84" href="#__codelineno-14-84"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-85" name="__codelineno-14-85" href="#__codelineno-14-85"></a><span class="w">            </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
 <a id="__codelineno-14-86" name="__codelineno-14-86" href="#__codelineno-14-86"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-14-87" name="__codelineno-14-87" href="#__codelineno-14-87"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-14-88" name="__codelineno-14-88" href="#__codelineno-14-88"></a><span class="w">        </span><span class="c1">// キー値ペアが存在しない場合、キー値ペアを追加</span>
+<a id="__codelineno-14-88" name="__codelineno-14-88" href="#__codelineno-14-88"></a><span class="w">        </span><span class="c1">// キーと値の組が存在しない場合は、その組を追加する</span>
 <a id="__codelineno-14-89" name="__codelineno-14-89" href="#__codelineno-14-89"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
 <a id="__codelineno-14-90" name="__codelineno-14-90" href="#__codelineno-14-90"></a><span class="w">        </span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
 <a id="__codelineno-14-91" name="__codelineno-14-91" href="#__codelineno-14-91"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-92" name="__codelineno-14-92" href="#__codelineno-14-92"></a>
 <a id="__codelineno-14-93" name="__codelineno-14-93" href="#__codelineno-14-93"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
 <a id="__codelineno-14-94" name="__codelineno-14-94" href="#__codelineno-14-94"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-95" name="__codelineno-14-95" href="#__codelineno-14-95"></a><span class="w">        </span><span class="c1">// keyに対応するバケットインデックスを検索</span>
+<a id="__codelineno-14-95" name="__codelineno-14-95" href="#__codelineno-14-95"></a><span class="w">        </span><span class="c1">// key に対応するバケットインデックスを探す</span>
 <a id="__codelineno-14-96" name="__codelineno-14-96" href="#__codelineno-14-96"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
-<a id="__codelineno-14-97" name="__codelineno-14-97" href="#__codelineno-14-97"></a><span class="w">        </span><span class="c1">// キー値ペアが見つかった場合、削除マークで覆う</span>
+<a id="__codelineno-14-97" name="__codelineno-14-97" href="#__codelineno-14-97"></a><span class="w">        </span><span class="c1">// キーと値の組が見つかったら、削除マーカーで上書きする</span>
 <a id="__codelineno-14-98" name="__codelineno-14-98" href="#__codelineno-14-98"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-99" name="__codelineno-14-99" href="#__codelineno-14-99"></a><span class="w">            </span><span class="k">delete</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
 <a id="__codelineno-14-100" name="__codelineno-14-100" href="#__codelineno-14-100"></a><span class="w">            </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">;</span>
@@ -5073,11 +6181,11 @@
 <a id="__codelineno-14-106" name="__codelineno-14-106" href="#__codelineno-14-106"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">extend</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-107" name="__codelineno-14-107" href="#__codelineno-14-107"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルを一時保存</span>
 <a id="__codelineno-14-108" name="__codelineno-14-108" href="#__codelineno-14-108"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Pair</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span>
-<a id="__codelineno-14-109" name="__codelineno-14-109" href="#__codelineno-14-109"></a><span class="w">        </span><span class="c1">// 拡張された新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-14-109" name="__codelineno-14-109" href="#__codelineno-14-109"></a><span class="w">        </span><span class="c1">// リサイズ後の新しいハッシュテーブルを初期化</span>
 <a id="__codelineno-14-110" name="__codelineno-14-110" href="#__codelineno-14-110"></a><span class="w">        </span><span class="n">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span>
 <a id="__codelineno-14-111" name="__codelineno-14-111" href="#__codelineno-14-111"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Pair</span><span class="w"> </span><span class="o">*&gt;</span><span class="p">(</span><span class="n">capacity</span><span class="p">,</span><span class="w"> </span><span class="k">nullptr</span><span class="p">);</span>
 <a id="__codelineno-14-112" name="__codelineno-14-112" href="#__codelineno-14-112"></a><span class="w">        </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-14-113" name="__codelineno-14-113" href="#__codelineno-14-113"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルから新しいハッシュテーブルにキー値ペアを移動</span>
+<a id="__codelineno-14-113" name="__codelineno-14-113" href="#__codelineno-14-113"></a><span class="w">        </span><span class="c1">// キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
 <a id="__codelineno-14-114" name="__codelineno-14-114" href="#__codelineno-14-114"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-115" name="__codelineno-14-115" href="#__codelineno-14-115"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-116" name="__codelineno-14-116" href="#__codelineno-14-116"></a><span class="w">                </span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
@@ -5086,7 +6194,7 @@
 <a id="__codelineno-14-119" name="__codelineno-14-119" href="#__codelineno-14-119"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-14-120" name="__codelineno-14-120" href="#__codelineno-14-120"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-121" name="__codelineno-14-121" href="#__codelineno-14-121"></a>
-<a id="__codelineno-14-122" name="__codelineno-14-122" href="#__codelineno-14-122"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを印刷 */</span>
+<a id="__codelineno-14-122" name="__codelineno-14-122" href="#__codelineno-14-122"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを出力 */</span>
 <a id="__codelineno-14-123" name="__codelineno-14-123" href="#__codelineno-14-123"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-124" name="__codelineno-14-124" href="#__codelineno-14-124"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-125" name="__codelineno-14-125" href="#__codelineno-14-125"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
@@ -5104,12 +6212,12 @@
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">hash_map_open_addressing.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* オープンアドレス法ハッシュテーブル */</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kd">class</span> <span class="nc">HashMapOpenAddressing</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="c1">// キー値ペアの数</span>
-<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">4</span><span class="p">;</span><span class="w"> </span><span class="c1">// ハッシュテーブルの容量</span>
-<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">final</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">loadThres</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3.0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 拡張をトリガーする負荷率の閾値</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="c1">// キーと値のペア数</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">4</span><span class="p">;</span><span class="w"> </span><span class="c1">// ハッシュテーブル容量</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">final</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">loadThres</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3.0</span><span class="p">;</span><span class="w"> </span><span class="c1">// リサイズを発動する負荷率のしきい値</span>
 <a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 拡張倍率</span>
 <a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="n">Pair</span><span class="o">[]</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span><span class="w"> </span><span class="c1">// バケット配列</span>
-<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">final</span><span class="w"> </span><span class="n">Pair</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;-1&quot;</span><span class="p">);</span><span class="w"> </span><span class="c1">// 削除マーク</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">final</span><span class="w"> </span><span class="n">Pair</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;-1&quot;</span><span class="p">);</span><span class="w"> </span><span class="c1">// 削除済みマーク</span>
 <a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a>
 <a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
 <a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">HashMapOpenAddressing</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
@@ -5127,68 +6235,68 @@
 <a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
 <a id="__codelineno-15-24" name="__codelineno-15-24" href="#__codelineno-15-24"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></a>
-<a id="__codelineno-15-26" name="__codelineno-15-26" href="#__codelineno-15-26"></a><span class="w">    </span><span class="cm">/* keyに対応するバケットインデックスを検索 */</span>
+<a id="__codelineno-15-26" name="__codelineno-15-26" href="#__codelineno-15-26"></a><span class="w">    </span><span class="cm">/* key に対応するバケットインデックスを探す */</span>
 <a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">findBucket</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-28" name="__codelineno-15-28" href="#__codelineno-15-28"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
 <a id="__codelineno-15-29" name="__codelineno-15-29" href="#__codelineno-15-29"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-15-30" name="__codelineno-15-30" href="#__codelineno-15-30"></a><span class="w">        </span><span class="c1">// 線形探査、空のバケットに遭遇したら終了</span>
+<a id="__codelineno-15-30" name="__codelineno-15-30" href="#__codelineno-15-30"></a><span class="w">        </span><span class="c1">// 線形プロービングを行い、空バケットに達したら終了</span>
 <a id="__codelineno-15-31" name="__codelineno-15-31" href="#__codelineno-15-31"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-32" name="__codelineno-15-32" href="#__codelineno-15-32"></a><span class="w">            </span><span class="c1">// keyに遭遇した場合、対応するバケットインデックスを返す</span>
+<a id="__codelineno-15-32" name="__codelineno-15-32" href="#__codelineno-15-32"></a><span class="w">            </span><span class="c1">// key が見つかったら、対応するバケットのインデックスを返す</span>
 <a id="__codelineno-15-33" name="__codelineno-15-33" href="#__codelineno-15-33"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-34" name="__codelineno-15-34" href="#__codelineno-15-34"></a><span class="w">                </span><span class="c1">// 以前に削除マークに遭遇していた場合、キー値ペアをそのインデックスに移動</span>
+<a id="__codelineno-15-34" name="__codelineno-15-34" href="#__codelineno-15-34"></a><span class="w">                </span><span class="c1">// 以前に削除マークが見つかっていれば、そのインデックスへキーと値のペアを移動</span>
 <a id="__codelineno-15-35" name="__codelineno-15-35" href="#__codelineno-15-35"></a><span class="w">                </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-36" name="__codelineno-15-36" href="#__codelineno-15-36"></a><span class="w">                    </span><span class="n">buckets</span><span class="o">[</span><span class="n">firstTombstone</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-15-37" name="__codelineno-15-37" href="#__codelineno-15-37"></a><span class="w">                    </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">;</span>
 <a id="__codelineno-15-38" name="__codelineno-15-38" href="#__codelineno-15-38"></a><span class="w">                    </span><span class="k">return</span><span class="w"> </span><span class="n">firstTombstone</span><span class="p">;</span><span class="w"> </span><span class="c1">// 移動後のバケットインデックスを返す</span>
 <a id="__codelineno-15-39" name="__codelineno-15-39" href="#__codelineno-15-39"></a><span class="w">                </span><span class="p">}</span>
-<a id="__codelineno-15-40" name="__codelineno-15-40" href="#__codelineno-15-40"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="c1">// バケットインデックスを返す</span>
+<a id="__codelineno-15-40" name="__codelineno-15-40" href="#__codelineno-15-40"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="c1">// バケットのインデックスを返す</span>
 <a id="__codelineno-15-41" name="__codelineno-15-41" href="#__codelineno-15-41"></a><span class="w">            </span><span class="p">}</span>
-<a id="__codelineno-15-42" name="__codelineno-15-42" href="#__codelineno-15-42"></a><span class="w">            </span><span class="c1">// 最初に遭遇した削除マークを記録</span>
+<a id="__codelineno-15-42" name="__codelineno-15-42" href="#__codelineno-15-42"></a><span class="w">            </span><span class="c1">// 最初に見つかった削除マークを記録</span>
 <a id="__codelineno-15-43" name="__codelineno-15-43" href="#__codelineno-15-43"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-44" name="__codelineno-15-44" href="#__codelineno-15-44"></a><span class="w">                </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
 <a id="__codelineno-15-45" name="__codelineno-15-45" href="#__codelineno-15-45"></a><span class="w">            </span><span class="p">}</span>
-<a id="__codelineno-15-46" name="__codelineno-15-46" href="#__codelineno-15-46"></a><span class="w">            </span><span class="c1">// バケットインデックスを計算、末尾を超えた場合は先頭に戻る</span>
+<a id="__codelineno-15-46" name="__codelineno-15-46" href="#__codelineno-15-46"></a><span class="w">            </span><span class="c1">// バケットのインデックスを計算し、末尾を越えたら先頭に戻る</span>
 <a id="__codelineno-15-47" name="__codelineno-15-47" href="#__codelineno-15-47"></a><span class="w">            </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
 <a id="__codelineno-15-48" name="__codelineno-15-48" href="#__codelineno-15-48"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-15-49" name="__codelineno-15-49" href="#__codelineno-15-49"></a><span class="w">        </span><span class="c1">// keyが存在しない場合、挿入ポイントのインデックスを返す</span>
+<a id="__codelineno-15-49" name="__codelineno-15-49" href="#__codelineno-15-49"></a><span class="w">        </span><span class="c1">// key が存在しない場合は追加位置のインデックスを返す</span>
 <a id="__codelineno-15-50" name="__codelineno-15-50" href="#__codelineno-15-50"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">firstTombstone</span><span class="p">;</span>
 <a id="__codelineno-15-51" name="__codelineno-15-51" href="#__codelineno-15-51"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-52" name="__codelineno-15-52" href="#__codelineno-15-52"></a>
-<a id="__codelineno-15-53" name="__codelineno-15-53" href="#__codelineno-15-53"></a><span class="w">    </span><span class="cm">/* クエリ操作 */</span>
+<a id="__codelineno-15-53" name="__codelineno-15-53" href="#__codelineno-15-53"></a><span class="w">    </span><span class="cm">/* 検索操作 */</span>
 <a id="__codelineno-15-54" name="__codelineno-15-54" href="#__codelineno-15-54"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-55" name="__codelineno-15-55" href="#__codelineno-15-55"></a><span class="w">        </span><span class="c1">// keyに対応するバケットインデックスを検索</span>
+<a id="__codelineno-15-55" name="__codelineno-15-55" href="#__codelineno-15-55"></a><span class="w">        </span><span class="c1">// key に対応するバケットインデックスを探す</span>
 <a id="__codelineno-15-56" name="__codelineno-15-56" href="#__codelineno-15-56"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
-<a id="__codelineno-15-57" name="__codelineno-15-57" href="#__codelineno-15-57"></a><span class="w">        </span><span class="c1">// キー値ペアが見つかった場合、対応するvalを返す</span>
+<a id="__codelineno-15-57" name="__codelineno-15-57" href="#__codelineno-15-57"></a><span class="w">        </span><span class="c1">// キーと値の組が見つかったら、対応する val を返す</span>
 <a id="__codelineno-15-58" name="__codelineno-15-58" href="#__codelineno-15-58"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-59" name="__codelineno-15-59" href="#__codelineno-15-59"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
 <a id="__codelineno-15-60" name="__codelineno-15-60" href="#__codelineno-15-60"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-15-61" name="__codelineno-15-61" href="#__codelineno-15-61"></a><span class="w">        </span><span class="c1">// キー値ペアが存在しない場合、nullを返す</span>
+<a id="__codelineno-15-61" name="__codelineno-15-61" href="#__codelineno-15-61"></a><span class="w">        </span><span class="c1">// キーと値の組が存在しなければ null を返す</span>
 <a id="__codelineno-15-62" name="__codelineno-15-62" href="#__codelineno-15-62"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
 <a id="__codelineno-15-63" name="__codelineno-15-63" href="#__codelineno-15-63"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-64" name="__codelineno-15-64" href="#__codelineno-15-64"></a>
 <a id="__codelineno-15-65" name="__codelineno-15-65" href="#__codelineno-15-65"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
 <a id="__codelineno-15-66" name="__codelineno-15-66" href="#__codelineno-15-66"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-67" name="__codelineno-15-67" href="#__codelineno-15-67"></a><span class="w">        </span><span class="c1">// 負荷率が閾値を超えた場合、拡張を実行</span>
+<a id="__codelineno-15-67" name="__codelineno-15-67" href="#__codelineno-15-67"></a><span class="w">        </span><span class="c1">// 負荷率がしきい値を超えたら、リサイズを実行</span>
 <a id="__codelineno-15-68" name="__codelineno-15-68" href="#__codelineno-15-68"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">loadThres</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-69" name="__codelineno-15-69" href="#__codelineno-15-69"></a><span class="w">            </span><span class="n">extend</span><span class="p">();</span>
 <a id="__codelineno-15-70" name="__codelineno-15-70" href="#__codelineno-15-70"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-15-71" name="__codelineno-15-71" href="#__codelineno-15-71"></a><span class="w">        </span><span class="c1">// keyに対応するバケットインデックスを検索</span>
+<a id="__codelineno-15-71" name="__codelineno-15-71" href="#__codelineno-15-71"></a><span class="w">        </span><span class="c1">// key に対応するバケットインデックスを探す</span>
 <a id="__codelineno-15-72" name="__codelineno-15-72" href="#__codelineno-15-72"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
-<a id="__codelineno-15-73" name="__codelineno-15-73" href="#__codelineno-15-73"></a><span class="w">        </span><span class="c1">// キー値ペアが見つかった場合、valを上書きして戻る</span>
+<a id="__codelineno-15-73" name="__codelineno-15-73" href="#__codelineno-15-73"></a><span class="w">        </span><span class="c1">// キーと値の組が見つかったら、val を上書きして返す</span>
 <a id="__codelineno-15-74" name="__codelineno-15-74" href="#__codelineno-15-74"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-75" name="__codelineno-15-75" href="#__codelineno-15-75"></a><span class="w">            </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
 <a id="__codelineno-15-76" name="__codelineno-15-76" href="#__codelineno-15-76"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-15-77" name="__codelineno-15-77" href="#__codelineno-15-77"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-15-78" name="__codelineno-15-78" href="#__codelineno-15-78"></a><span class="w">        </span><span class="c1">// キー値ペアが存在しない場合、キー値ペアを追加</span>
+<a id="__codelineno-15-78" name="__codelineno-15-78" href="#__codelineno-15-78"></a><span class="w">        </span><span class="c1">// キーと値の組が存在しない場合は、その組を追加する</span>
 <a id="__codelineno-15-79" name="__codelineno-15-79" href="#__codelineno-15-79"></a><span class="w">        </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
 <a id="__codelineno-15-80" name="__codelineno-15-80" href="#__codelineno-15-80"></a><span class="w">        </span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
 <a id="__codelineno-15-81" name="__codelineno-15-81" href="#__codelineno-15-81"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-82" name="__codelineno-15-82" href="#__codelineno-15-82"></a>
 <a id="__codelineno-15-83" name="__codelineno-15-83" href="#__codelineno-15-83"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
 <a id="__codelineno-15-84" name="__codelineno-15-84" href="#__codelineno-15-84"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-85" name="__codelineno-15-85" href="#__codelineno-15-85"></a><span class="w">        </span><span class="c1">// keyに対応するバケットインデックスを検索</span>
+<a id="__codelineno-15-85" name="__codelineno-15-85" href="#__codelineno-15-85"></a><span class="w">        </span><span class="c1">// key に対応するバケットインデックスを探す</span>
 <a id="__codelineno-15-86" name="__codelineno-15-86" href="#__codelineno-15-86"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
-<a id="__codelineno-15-87" name="__codelineno-15-87" href="#__codelineno-15-87"></a><span class="w">        </span><span class="c1">// キー値ペアが見つかった場合、削除マークで覆う</span>
+<a id="__codelineno-15-87" name="__codelineno-15-87" href="#__codelineno-15-87"></a><span class="w">        </span><span class="c1">// キーと値の組が見つかったら、削除マーカーで上書きする</span>
 <a id="__codelineno-15-88" name="__codelineno-15-88" href="#__codelineno-15-88"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-89" name="__codelineno-15-89" href="#__codelineno-15-89"></a><span class="w">            </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">;</span>
 <a id="__codelineno-15-90" name="__codelineno-15-90" href="#__codelineno-15-90"></a><span class="w">            </span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
@@ -5197,13 +6305,13 @@
 <a id="__codelineno-15-93" name="__codelineno-15-93" href="#__codelineno-15-93"></a>
 <a id="__codelineno-15-94" name="__codelineno-15-94" href="#__codelineno-15-94"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを拡張 */</span>
 <a id="__codelineno-15-95" name="__codelineno-15-95" href="#__codelineno-15-95"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">extend</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-96" name="__codelineno-15-96" href="#__codelineno-15-96"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルを一時的に保存</span>
+<a id="__codelineno-15-96" name="__codelineno-15-96" href="#__codelineno-15-96"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルを一時保存</span>
 <a id="__codelineno-15-97" name="__codelineno-15-97" href="#__codelineno-15-97"></a><span class="w">        </span><span class="n">Pair</span><span class="o">[]</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span>
-<a id="__codelineno-15-98" name="__codelineno-15-98" href="#__codelineno-15-98"></a><span class="w">        </span><span class="c1">// 拡張された新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-15-98" name="__codelineno-15-98" href="#__codelineno-15-98"></a><span class="w">        </span><span class="c1">// リサイズ後の新しいハッシュテーブルを初期化</span>
 <a id="__codelineno-15-99" name="__codelineno-15-99" href="#__codelineno-15-99"></a><span class="w">        </span><span class="n">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span>
 <a id="__codelineno-15-100" name="__codelineno-15-100" href="#__codelineno-15-100"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="o">[</span><span class="n">capacity</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-15-101" name="__codelineno-15-101" href="#__codelineno-15-101"></a><span class="w">        </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-15-102" name="__codelineno-15-102" href="#__codelineno-15-102"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルから新しいハッシュテーブルにキー値ペアを移動</span>
+<a id="__codelineno-15-102" name="__codelineno-15-102" href="#__codelineno-15-102"></a><span class="w">        </span><span class="c1">// キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
 <a id="__codelineno-15-103" name="__codelineno-15-103" href="#__codelineno-15-103"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-104" name="__codelineno-15-104" href="#__codelineno-15-104"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-105" name="__codelineno-15-105" href="#__codelineno-15-105"></a><span class="w">                </span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
@@ -5211,7 +6319,7 @@
 <a id="__codelineno-15-107" name="__codelineno-15-107" href="#__codelineno-15-107"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-15-108" name="__codelineno-15-108" href="#__codelineno-15-108"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-109" name="__codelineno-15-109" href="#__codelineno-15-109"></a>
-<a id="__codelineno-15-110" name="__codelineno-15-110" href="#__codelineno-15-110"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを印刷 */</span>
+<a id="__codelineno-15-110" name="__codelineno-15-110" href="#__codelineno-15-110"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを出力 */</span>
 <a id="__codelineno-15-111" name="__codelineno-15-111" href="#__codelineno-15-111"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-112" name="__codelineno-15-112" href="#__codelineno-15-112"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-113" name="__codelineno-15-113" href="#__codelineno-15-113"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
@@ -5227,76 +6335,1370 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map_open_addressing.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">HashMapOpenAddressing</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">hash_map_open_addressing.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* オープンアドレス法ハッシュテーブル */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">HashMapOpenAddressing</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="c1">// キーと値のペア数</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">4</span><span class="p">;</span><span class="w"> </span><span class="c1">// ハッシュテーブル容量</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="kt">double</span><span class="w"> </span><span class="n">loadThres</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3.0</span><span class="p">;</span><span class="w"> </span><span class="c1">// リサイズを発動する負荷率のしきい値</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 拡張倍率</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="n">Pair</span><span class="p">[]</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span><span class="w"> </span><span class="c1">// バケット配列</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="n">Pair</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;-1&quot;</span><span class="p">);</span><span class="w"> </span><span class="c1">// 削除済みマーク</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nf">HashMapOpenAddressing</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">        </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">[</span><span class="n">capacity</span><span class="p">];</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="nf">HashFunc</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="w">    </span><span class="cm">/* 負荷率 */</span>
+<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="w">    </span><span class="kt">double</span><span class="w"> </span><span class="nf">LoadFactor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="n">size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-16-24" name="__codelineno-16-24" href="#__codelineno-16-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-25" name="__codelineno-16-25" href="#__codelineno-16-25"></a>
+<a id="__codelineno-16-26" name="__codelineno-16-26" href="#__codelineno-16-26"></a><span class="w">    </span><span class="cm">/* key に対応するバケットインデックスを探す */</span>
+<a id="__codelineno-16-27" name="__codelineno-16-27" href="#__codelineno-16-27"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="nf">FindBucket</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-28" name="__codelineno-16-28" href="#__codelineno-16-28"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-16-29" name="__codelineno-16-29" href="#__codelineno-16-29"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-16-30" name="__codelineno-16-30" href="#__codelineno-16-30"></a><span class="w">        </span><span class="c1">// 線形プロービングを行い、空バケットに達したら終了</span>
+<a id="__codelineno-16-31" name="__codelineno-16-31" href="#__codelineno-16-31"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-32" name="__codelineno-16-32" href="#__codelineno-16-32"></a><span class="w">            </span><span class="c1">// key が見つかったら、対応するバケットのインデックスを返す</span>
+<a id="__codelineno-16-33" name="__codelineno-16-33" href="#__codelineno-16-33"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-34" name="__codelineno-16-34" href="#__codelineno-16-34"></a><span class="w">                </span><span class="c1">// 以前に削除マークが見つかっていれば、そのインデックスへキーと値のペアを移動</span>
+<a id="__codelineno-16-35" name="__codelineno-16-35" href="#__codelineno-16-35"></a><span class="w">                </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-36" name="__codelineno-16-36" href="#__codelineno-16-36"></a><span class="w">                    </span><span class="n">buckets</span><span class="p">[</span><span class="n">firstTombstone</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-16-37" name="__codelineno-16-37" href="#__codelineno-16-37"></a><span class="w">                    </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">;</span>
+<a id="__codelineno-16-38" name="__codelineno-16-38" href="#__codelineno-16-38"></a><span class="w">                    </span><span class="k">return</span><span class="w"> </span><span class="n">firstTombstone</span><span class="p">;</span><span class="w"> </span><span class="c1">// 移動後のバケットインデックスを返す</span>
+<a id="__codelineno-16-39" name="__codelineno-16-39" href="#__codelineno-16-39"></a><span class="w">                </span><span class="p">}</span>
+<a id="__codelineno-16-40" name="__codelineno-16-40" href="#__codelineno-16-40"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="c1">// バケットのインデックスを返す</span>
+<a id="__codelineno-16-41" name="__codelineno-16-41" href="#__codelineno-16-41"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-16-42" name="__codelineno-16-42" href="#__codelineno-16-42"></a><span class="w">            </span><span class="c1">// 最初に見つかった削除マークを記録</span>
+<a id="__codelineno-16-43" name="__codelineno-16-43" href="#__codelineno-16-43"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-44" name="__codelineno-16-44" href="#__codelineno-16-44"></a><span class="w">                </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
+<a id="__codelineno-16-45" name="__codelineno-16-45" href="#__codelineno-16-45"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-16-46" name="__codelineno-16-46" href="#__codelineno-16-46"></a><span class="w">            </span><span class="c1">// バケットのインデックスを計算し、末尾を越えたら先頭に戻る</span>
+<a id="__codelineno-16-47" name="__codelineno-16-47" href="#__codelineno-16-47"></a><span class="w">            </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-16-48" name="__codelineno-16-48" href="#__codelineno-16-48"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-49" name="__codelineno-16-49" href="#__codelineno-16-49"></a><span class="w">        </span><span class="c1">// key が存在しない場合は追加位置のインデックスを返す</span>
+<a id="__codelineno-16-50" name="__codelineno-16-50" href="#__codelineno-16-50"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">firstTombstone</span><span class="p">;</span>
+<a id="__codelineno-16-51" name="__codelineno-16-51" href="#__codelineno-16-51"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-52" name="__codelineno-16-52" href="#__codelineno-16-52"></a>
+<a id="__codelineno-16-53" name="__codelineno-16-53" href="#__codelineno-16-53"></a><span class="w">    </span><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-16-54" name="__codelineno-16-54" href="#__codelineno-16-54"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">string?</span><span class="w"> </span><span class="n">Get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-55" name="__codelineno-16-55" href="#__codelineno-16-55"></a><span class="w">        </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-16-56" name="__codelineno-16-56" href="#__codelineno-16-56"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">FindBucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-16-57" name="__codelineno-16-57" href="#__codelineno-16-57"></a><span class="w">        </span><span class="c1">// キーと値の組が見つかったら、対応する val を返す</span>
+<a id="__codelineno-16-58" name="__codelineno-16-58" href="#__codelineno-16-58"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-59" name="__codelineno-16-59" href="#__codelineno-16-59"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-16-60" name="__codelineno-16-60" href="#__codelineno-16-60"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-61" name="__codelineno-16-61" href="#__codelineno-16-61"></a><span class="w">        </span><span class="c1">// キーと値の組が存在しなければ null を返す</span>
+<a id="__codelineno-16-62" name="__codelineno-16-62" href="#__codelineno-16-62"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
+<a id="__codelineno-16-63" name="__codelineno-16-63" href="#__codelineno-16-63"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-64" name="__codelineno-16-64" href="#__codelineno-16-64"></a>
+<a id="__codelineno-16-65" name="__codelineno-16-65" href="#__codelineno-16-65"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-16-66" name="__codelineno-16-66" href="#__codelineno-16-66"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">Put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="kt">string</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-67" name="__codelineno-16-67" href="#__codelineno-16-67"></a><span class="w">        </span><span class="c1">// 負荷率がしきい値を超えたら、リサイズを実行</span>
+<a id="__codelineno-16-68" name="__codelineno-16-68" href="#__codelineno-16-68"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">LoadFactor</span><span class="p">()</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">loadThres</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-69" name="__codelineno-16-69" href="#__codelineno-16-69"></a><span class="w">            </span><span class="n">Extend</span><span class="p">();</span>
+<a id="__codelineno-16-70" name="__codelineno-16-70" href="#__codelineno-16-70"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-71" name="__codelineno-16-71" href="#__codelineno-16-71"></a><span class="w">        </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-16-72" name="__codelineno-16-72" href="#__codelineno-16-72"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">FindBucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-16-73" name="__codelineno-16-73" href="#__codelineno-16-73"></a><span class="w">        </span><span class="c1">// キーと値の組が見つかったら、val を上書きして返す</span>
+<a id="__codelineno-16-74" name="__codelineno-16-74" href="#__codelineno-16-74"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-75" name="__codelineno-16-75" href="#__codelineno-16-75"></a><span class="w">            </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-16-76" name="__codelineno-16-76" href="#__codelineno-16-76"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-16-77" name="__codelineno-16-77" href="#__codelineno-16-77"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-78" name="__codelineno-16-78" href="#__codelineno-16-78"></a><span class="w">        </span><span class="c1">// キーと値の組が存在しない場合は、その組を追加する</span>
+<a id="__codelineno-16-79" name="__codelineno-16-79" href="#__codelineno-16-79"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-16-80" name="__codelineno-16-80" href="#__codelineno-16-80"></a><span class="w">        </span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-16-81" name="__codelineno-16-81" href="#__codelineno-16-81"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-82" name="__codelineno-16-82" href="#__codelineno-16-82"></a>
+<a id="__codelineno-16-83" name="__codelineno-16-83" href="#__codelineno-16-83"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-16-84" name="__codelineno-16-84" href="#__codelineno-16-84"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">Remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-85" name="__codelineno-16-85" href="#__codelineno-16-85"></a><span class="w">        </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-16-86" name="__codelineno-16-86" href="#__codelineno-16-86"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">FindBucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-16-87" name="__codelineno-16-87" href="#__codelineno-16-87"></a><span class="w">        </span><span class="c1">// キーと値の組が見つかったら、削除マーカーで上書きする</span>
+<a id="__codelineno-16-88" name="__codelineno-16-88" href="#__codelineno-16-88"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-89" name="__codelineno-16-89" href="#__codelineno-16-89"></a><span class="w">            </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">;</span>
+<a id="__codelineno-16-90" name="__codelineno-16-90" href="#__codelineno-16-90"></a><span class="w">            </span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-16-91" name="__codelineno-16-91" href="#__codelineno-16-91"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-92" name="__codelineno-16-92" href="#__codelineno-16-92"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-93" name="__codelineno-16-93" href="#__codelineno-16-93"></a>
+<a id="__codelineno-16-94" name="__codelineno-16-94" href="#__codelineno-16-94"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを拡張 */</span>
+<a id="__codelineno-16-95" name="__codelineno-16-95" href="#__codelineno-16-95"></a><span class="w">    </span><span class="k">void</span><span class="w"> </span><span class="nf">Extend</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-96" name="__codelineno-16-96" href="#__codelineno-16-96"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルを一時保存</span>
+<a id="__codelineno-16-97" name="__codelineno-16-97" href="#__codelineno-16-97"></a><span class="w">        </span><span class="n">Pair</span><span class="p">[]</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span>
+<a id="__codelineno-16-98" name="__codelineno-16-98" href="#__codelineno-16-98"></a><span class="w">        </span><span class="c1">// リサイズ後の新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-16-99" name="__codelineno-16-99" href="#__codelineno-16-99"></a><span class="w">        </span><span class="n">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span>
+<a id="__codelineno-16-100" name="__codelineno-16-100" href="#__codelineno-16-100"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">[</span><span class="n">capacity</span><span class="p">];</span>
+<a id="__codelineno-16-101" name="__codelineno-16-101" href="#__codelineno-16-101"></a><span class="w">        </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-16-102" name="__codelineno-16-102" href="#__codelineno-16-102"></a><span class="w">        </span><span class="c1">// キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
+<a id="__codelineno-16-103" name="__codelineno-16-103" href="#__codelineno-16-103"></a><span class="w">        </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-104" name="__codelineno-16-104" href="#__codelineno-16-104"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-105" name="__codelineno-16-105" href="#__codelineno-16-105"></a><span class="w">                </span><span class="n">Put</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-16-106" name="__codelineno-16-106" href="#__codelineno-16-106"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-16-107" name="__codelineno-16-107" href="#__codelineno-16-107"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-108" name="__codelineno-16-108" href="#__codelineno-16-108"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-109" name="__codelineno-16-109" href="#__codelineno-16-109"></a>
+<a id="__codelineno-16-110" name="__codelineno-16-110" href="#__codelineno-16-110"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-16-111" name="__codelineno-16-111" href="#__codelineno-16-111"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">Print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-112" name="__codelineno-16-112" href="#__codelineno-16-112"></a><span class="w">        </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-113" name="__codelineno-16-113" href="#__codelineno-16-113"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-114" name="__codelineno-16-114" href="#__codelineno-16-114"></a><span class="w">                </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="s">&quot;null&quot;</span><span class="p">);</span>
+<a id="__codelineno-16-115" name="__codelineno-16-115" href="#__codelineno-16-115"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-116" name="__codelineno-16-116" href="#__codelineno-16-116"></a><span class="w">                </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="s">&quot;TOMBSTONE&quot;</span><span class="p">);</span>
+<a id="__codelineno-16-117" name="__codelineno-16-117" href="#__codelineno-16-117"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-118" name="__codelineno-16-118" href="#__codelineno-16-118"></a><span class="w">                </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-16-119" name="__codelineno-16-119" href="#__codelineno-16-119"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-16-120" name="__codelineno-16-120" href="#__codelineno-16-120"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-121" name="__codelineno-16-121" href="#__codelineno-16-121"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-122" name="__codelineno-16-122" href="#__codelineno-16-122"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map_open_addressing.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">hashMapOpenAddressing</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">hash_map_open_addressing.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* オープンアドレス法ハッシュテーブル */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">hashMapOpenAddressing</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="nx">size</span><span class="w">        </span><span class="kt">int</span><span class="w">     </span><span class="c1">// キーと値のペア数</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="nx">capacity</span><span class="w">    </span><span class="kt">int</span><span class="w">     </span><span class="c1">// ハッシュテーブル容量</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">    </span><span class="nx">loadThres</span><span class="w">   </span><span class="kt">float64</span><span class="w"> </span><span class="c1">// リサイズを発動する負荷率のしきい値</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">    </span><span class="nx">extendRatio</span><span class="w"> </span><span class="kt">int</span><span class="w">     </span><span class="c1">// 拡張倍率</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">    </span><span class="nx">buckets</span><span class="w">     </span><span class="p">[]</span><span class="o">*</span><span class="nx">pair</span><span class="w"> </span><span class="c1">// バケット配列</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">    </span><span class="nx">TOMBSTONE</span><span class="w">   </span><span class="o">*</span><span class="nx">pair</span><span class="w">   </span><span class="c1">// 削除済みマーク</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="p">}</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="kd">func</span><span class="w"> </span><span class="nx">newHashMapOpenAddressing</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="nx">hashMapOpenAddressing</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">hashMapOpenAddressing</span><span class="p">{</span>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w">        </span><span class="nx">size</span><span class="p">:</span><span class="w">        </span><span class="mi">0</span><span class="p">,</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">        </span><span class="nx">capacity</span><span class="p">:</span><span class="w">    </span><span class="mi">4</span><span class="p">,</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w">        </span><span class="nx">loadThres</span><span class="p">:</span><span class="w">   </span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3.0</span><span class="p">,</span>
+<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="w">        </span><span class="nx">extendRatio</span><span class="p">:</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span>
+<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="w">        </span><span class="nx">buckets</span><span class="p">:</span><span class="w">     </span><span class="nb">make</span><span class="p">([]</span><span class="o">*</span><span class="nx">pair</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">),</span>
+<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="w">        </span><span class="nx">TOMBSTONE</span><span class="p">:</span><span class="w">   </span><span class="o">&amp;</span><span class="nx">pair</span><span class="p">{</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;-1&quot;</span><span class="p">},</span>
+<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></a><span class="p">}</span>
+<a id="__codelineno-17-22" name="__codelineno-17-22" href="#__codelineno-17-22"></a>
+<a id="__codelineno-17-23" name="__codelineno-17-23" href="#__codelineno-17-23"></a><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-17-24" name="__codelineno-17-24" href="#__codelineno-17-24"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">hashMapOpenAddressing</span><span class="p">)</span><span class="w"> </span><span class="nx">hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-25" name="__codelineno-17-25" href="#__codelineno-17-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">capacity</span><span class="w"> </span><span class="c1">// キーに基づいてハッシュ値を計算</span>
+<a id="__codelineno-17-26" name="__codelineno-17-26" href="#__codelineno-17-26"></a><span class="p">}</span>
+<a id="__codelineno-17-27" name="__codelineno-17-27" href="#__codelineno-17-27"></a>
+<a id="__codelineno-17-28" name="__codelineno-17-28" href="#__codelineno-17-28"></a><span class="cm">/* 負荷率 */</span>
+<a id="__codelineno-17-29" name="__codelineno-17-29" href="#__codelineno-17-29"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">hashMapOpenAddressing</span><span class="p">)</span><span class="w"> </span><span class="nx">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="kt">float64</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-30" name="__codelineno-17-30" href="#__codelineno-17-30"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">h</span><span class="p">.</span><span class="nx">size</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">h</span><span class="p">.</span><span class="nx">capacity</span><span class="p">)</span><span class="w"> </span><span class="c1">// 現在の負荷率を計算</span>
+<a id="__codelineno-17-31" name="__codelineno-17-31" href="#__codelineno-17-31"></a><span class="p">}</span>
+<a id="__codelineno-17-32" name="__codelineno-17-32" href="#__codelineno-17-32"></a>
+<a id="__codelineno-17-33" name="__codelineno-17-33" href="#__codelineno-17-33"></a><span class="cm">/* key に対応するバケットインデックスを探す */</span>
+<a id="__codelineno-17-34" name="__codelineno-17-34" href="#__codelineno-17-34"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">hashMapOpenAddressing</span><span class="p">)</span><span class="w"> </span><span class="nx">findBucket</span><span class="p">(</span><span class="nx">key</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-35" name="__codelineno-17-35" href="#__codelineno-17-35"></a><span class="w">    </span><span class="nx">index</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="c1">// 初期インデックスを取得</span>
+<a id="__codelineno-17-36" name="__codelineno-17-36" href="#__codelineno-17-36"></a><span class="w">    </span><span class="nx">firstTombstone</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w">     </span><span class="c1">// 最初に遭遇した `TOMBSTONE` の位置を記録する</span>
+<a id="__codelineno-17-37" name="__codelineno-17-37" href="#__codelineno-17-37"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-38" name="__codelineno-17-38" href="#__codelineno-17-38"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">].</span><span class="nx">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">key</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-39" name="__codelineno-17-39" href="#__codelineno-17-39"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="nx">firstTombstone</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-40" name="__codelineno-17-40" href="#__codelineno-17-40"></a><span class="w">                </span><span class="c1">// 以前に削除マークが見つかっていれば、そのインデックスへキーと値のペアを移動</span>
+<a id="__codelineno-17-41" name="__codelineno-17-41" href="#__codelineno-17-41"></a><span class="w">                </span><span class="nx">h</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">firstTombstone</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span>
+<a id="__codelineno-17-42" name="__codelineno-17-42" href="#__codelineno-17-42"></a><span class="w">                </span><span class="nx">h</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">TOMBSTONE</span>
+<a id="__codelineno-17-43" name="__codelineno-17-43" href="#__codelineno-17-43"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="nx">firstTombstone</span><span class="w"> </span><span class="c1">// 移動後のバケットインデックスを返す</span>
+<a id="__codelineno-17-44" name="__codelineno-17-44" href="#__codelineno-17-44"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-17-45" name="__codelineno-17-45" href="#__codelineno-17-45"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="c1">// 見つかったインデックスを返す</span>
+<a id="__codelineno-17-46" name="__codelineno-17-46" href="#__codelineno-17-46"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-17-47" name="__codelineno-17-47" href="#__codelineno-17-47"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">TOMBSTONE</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-48" name="__codelineno-17-48" href="#__codelineno-17-48"></a><span class="w">            </span><span class="nx">firstTombstone</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="c1">// 最初に遭遇した削除マークの位置を記録する</span>
+<a id="__codelineno-17-49" name="__codelineno-17-49" href="#__codelineno-17-49"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-17-50" name="__codelineno-17-50" href="#__codelineno-17-50"></a><span class="w">        </span><span class="nx">index</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="nx">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">capacity</span><span class="w"> </span><span class="c1">// 線形探索を行い、末尾を越えたら先頭に戻る</span>
+<a id="__codelineno-17-51" name="__codelineno-17-51" href="#__codelineno-17-51"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-52" name="__codelineno-17-52" href="#__codelineno-17-52"></a><span class="w">    </span><span class="c1">// key が存在しない場合は追加位置のインデックスを返す</span>
+<a id="__codelineno-17-53" name="__codelineno-17-53" href="#__codelineno-17-53"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">firstTombstone</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-54" name="__codelineno-17-54" href="#__codelineno-17-54"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">firstTombstone</span>
+<a id="__codelineno-17-55" name="__codelineno-17-55" href="#__codelineno-17-55"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-56" name="__codelineno-17-56" href="#__codelineno-17-56"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">index</span>
+<a id="__codelineno-17-57" name="__codelineno-17-57" href="#__codelineno-17-57"></a><span class="p">}</span>
+<a id="__codelineno-17-58" name="__codelineno-17-58" href="#__codelineno-17-58"></a>
+<a id="__codelineno-17-59" name="__codelineno-17-59" href="#__codelineno-17-59"></a><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-17-60" name="__codelineno-17-60" href="#__codelineno-17-60"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">hashMapOpenAddressing</span><span class="p">)</span><span class="w"> </span><span class="nx">get</span><span class="p">(</span><span class="nx">key</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">string</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-61" name="__codelineno-17-61" href="#__codelineno-17-61"></a><span class="w">    </span><span class="nx">index</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">findBucket</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-17-62" name="__codelineno-17-62" href="#__codelineno-17-62"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">TOMBSTONE</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-63" name="__codelineno-17-63" href="#__codelineno-17-63"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">].</span><span class="nx">val</span><span class="w"> </span><span class="c1">// キーと値の組が見つかったら、対応する val を返す</span>
+<a id="__codelineno-17-64" name="__codelineno-17-64" href="#__codelineno-17-64"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-65" name="__codelineno-17-65" href="#__codelineno-17-65"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="s">&quot;&quot;</span><span class="w"> </span><span class="c1">// キーと値のペアが存在しない場合は `&quot;&quot;` を返す</span>
+<a id="__codelineno-17-66" name="__codelineno-17-66" href="#__codelineno-17-66"></a><span class="p">}</span>
+<a id="__codelineno-17-67" name="__codelineno-17-67" href="#__codelineno-17-67"></a>
+<a id="__codelineno-17-68" name="__codelineno-17-68" href="#__codelineno-17-68"></a><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-17-69" name="__codelineno-17-69" href="#__codelineno-17-69"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">hashMapOpenAddressing</span><span class="p">)</span><span class="w"> </span><span class="nx">put</span><span class="p">(</span><span class="nx">key</span><span class="w"> </span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-70" name="__codelineno-17-70" href="#__codelineno-17-70"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">loadThres</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-71" name="__codelineno-17-71" href="#__codelineno-17-71"></a><span class="w">        </span><span class="nx">h</span><span class="p">.</span><span class="nx">extend</span><span class="p">()</span><span class="w"> </span><span class="c1">// 負荷率がしきい値を超えたら、リサイズを実行</span>
+<a id="__codelineno-17-72" name="__codelineno-17-72" href="#__codelineno-17-72"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-73" name="__codelineno-17-73" href="#__codelineno-17-73"></a><span class="w">    </span><span class="nx">index</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">findBucket</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-17-74" name="__codelineno-17-74" href="#__codelineno-17-74"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">TOMBSTONE</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-75" name="__codelineno-17-75" href="#__codelineno-17-75"></a><span class="w">        </span><span class="nx">h</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">pair</span><span class="p">{</span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">}</span><span class="w"> </span><span class="c1">// キーと値の組が存在しない場合は、その組を追加する</span>
+<a id="__codelineno-17-76" name="__codelineno-17-76" href="#__codelineno-17-76"></a><span class="w">        </span><span class="nx">h</span><span class="p">.</span><span class="nx">size</span><span class="o">++</span>
+<a id="__codelineno-17-77" name="__codelineno-17-77" href="#__codelineno-17-77"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-78" name="__codelineno-17-78" href="#__codelineno-17-78"></a><span class="w">        </span><span class="nx">h</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">].</span><span class="nx">val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="c1">// キーと値のペアが見つかった場合は、`val` を上書きする</span>
+<a id="__codelineno-17-79" name="__codelineno-17-79" href="#__codelineno-17-79"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-80" name="__codelineno-17-80" href="#__codelineno-17-80"></a><span class="p">}</span>
+<a id="__codelineno-17-81" name="__codelineno-17-81" href="#__codelineno-17-81"></a>
+<a id="__codelineno-17-82" name="__codelineno-17-82" href="#__codelineno-17-82"></a><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-17-83" name="__codelineno-17-83" href="#__codelineno-17-83"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">hashMapOpenAddressing</span><span class="p">)</span><span class="w"> </span><span class="nx">remove</span><span class="p">(</span><span class="nx">key</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-84" name="__codelineno-17-84" href="#__codelineno-17-84"></a><span class="w">    </span><span class="nx">index</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">findBucket</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-17-85" name="__codelineno-17-85" href="#__codelineno-17-85"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">TOMBSTONE</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-86" name="__codelineno-17-86" href="#__codelineno-17-86"></a><span class="w">        </span><span class="nx">h</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">TOMBSTONE</span><span class="w"> </span><span class="c1">// キーと値の組が見つかったら、削除マーカーで上書きする</span>
+<a id="__codelineno-17-87" name="__codelineno-17-87" href="#__codelineno-17-87"></a><span class="w">        </span><span class="nx">h</span><span class="p">.</span><span class="nx">size</span><span class="o">--</span>
+<a id="__codelineno-17-88" name="__codelineno-17-88" href="#__codelineno-17-88"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-89" name="__codelineno-17-89" href="#__codelineno-17-89"></a><span class="p">}</span>
+<a id="__codelineno-17-90" name="__codelineno-17-90" href="#__codelineno-17-90"></a>
+<a id="__codelineno-17-91" name="__codelineno-17-91" href="#__codelineno-17-91"></a><span class="cm">/* ハッシュテーブルを拡張 */</span>
+<a id="__codelineno-17-92" name="__codelineno-17-92" href="#__codelineno-17-92"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">hashMapOpenAddressing</span><span class="p">)</span><span class="w"> </span><span class="nx">extend</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-93" name="__codelineno-17-93" href="#__codelineno-17-93"></a><span class="w">    </span><span class="nx">oldBuckets</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">buckets</span><span class="w">               </span><span class="c1">// 元のハッシュテーブルを一時保存</span>
+<a id="__codelineno-17-94" name="__codelineno-17-94" href="#__codelineno-17-94"></a><span class="w">    </span><span class="nx">h</span><span class="p">.</span><span class="nx">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">extendRatio</span><span class="w">           </span><span class="c1">// 容量を更新</span>
+<a id="__codelineno-17-95" name="__codelineno-17-95" href="#__codelineno-17-95"></a><span class="w">    </span><span class="nx">h</span><span class="p">.</span><span class="nx">buckets</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="o">*</span><span class="nx">pair</span><span class="p">,</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">capacity</span><span class="p">)</span><span class="w"> </span><span class="c1">// リサイズ後の新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-17-96" name="__codelineno-17-96" href="#__codelineno-17-96"></a><span class="w">    </span><span class="nx">h</span><span class="p">.</span><span class="nx">size</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span><span class="w">                            </span><span class="c1">// サイズをリセットする</span>
+<a id="__codelineno-17-97" name="__codelineno-17-97" href="#__codelineno-17-97"></a><span class="w">    </span><span class="c1">// キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
+<a id="__codelineno-17-98" name="__codelineno-17-98" href="#__codelineno-17-98"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">oldBuckets</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-99" name="__codelineno-17-99" href="#__codelineno-17-99"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">TOMBSTONE</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-100" name="__codelineno-17-100" href="#__codelineno-17-100"></a><span class="w">            </span><span class="nx">h</span><span class="p">.</span><span class="nx">put</span><span class="p">(</span><span class="nx">pair</span><span class="p">.</span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="p">)</span>
+<a id="__codelineno-17-101" name="__codelineno-17-101" href="#__codelineno-17-101"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-17-102" name="__codelineno-17-102" href="#__codelineno-17-102"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-103" name="__codelineno-17-103" href="#__codelineno-17-103"></a><span class="p">}</span>
+<a id="__codelineno-17-104" name="__codelineno-17-104" href="#__codelineno-17-104"></a>
+<a id="__codelineno-17-105" name="__codelineno-17-105" href="#__codelineno-17-105"></a><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-17-106" name="__codelineno-17-106" href="#__codelineno-17-106"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">hashMapOpenAddressing</span><span class="p">)</span><span class="w"> </span><span class="nb">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-107" name="__codelineno-17-107" href="#__codelineno-17-107"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">buckets</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-108" name="__codelineno-17-108" href="#__codelineno-17-108"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-109" name="__codelineno-17-109" href="#__codelineno-17-109"></a><span class="w">            </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="s">&quot;nil&quot;</span><span class="p">)</span>
+<a id="__codelineno-17-110" name="__codelineno-17-110" href="#__codelineno-17-110"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">TOMBSTONE</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-111" name="__codelineno-17-111" href="#__codelineno-17-111"></a><span class="w">            </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="s">&quot;TOMBSTONE&quot;</span><span class="p">)</span>
+<a id="__codelineno-17-112" name="__codelineno-17-112" href="#__codelineno-17-112"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-113" name="__codelineno-17-113" href="#__codelineno-17-113"></a><span class="w">            </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Printf</span><span class="p">(</span><span class="s">&quot;%d -&gt; %s\n&quot;</span><span class="p">,</span><span class="w"> </span><span class="nx">pair</span><span class="p">.</span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="p">)</span>
+<a id="__codelineno-17-114" name="__codelineno-17-114" href="#__codelineno-17-114"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-17-115" name="__codelineno-17-115" href="#__codelineno-17-115"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-116" name="__codelineno-17-116" href="#__codelineno-17-116"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map_open_addressing.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">HashMapOpenAddressing</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">hash_map_open_addressing.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* オープンアドレス法ハッシュテーブル */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">HashMapOpenAddressing</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">size</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// キーと値のペア数</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">capacity</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// ハッシュテーブル容量</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">loadThres</span><span class="p">:</span><span class="w"> </span><span class="nb">Double</span><span class="w"> </span><span class="c1">// リサイズを発動する負荷率のしきい値</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">extendRatio</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// 拡張倍率</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">buckets</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="n">Pair</span><span class="p">?]</span><span class="w"> </span><span class="c1">// バケット配列</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">TOMBSTONE</span><span class="p">:</span><span class="w"> </span><span class="n">Pair</span><span class="w"> </span><span class="c1">// 削除済みマーク</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w">    </span><span class="kd">init</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w">        </span><span class="n">size</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w">        </span><span class="n">capacity</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">4</span>
+<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="w">        </span><span class="n">loadThres</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3.0</span>
+<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w">        </span><span class="n">extendRatio</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span>
+<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="w">        </span><span class="n">TOMBSTONE</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="s">&quot;-1&quot;</span><span class="p">)</span>
+<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a>
+<a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-22" name="__codelineno-18-22" href="#__codelineno-18-22"></a><span class="w">        </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span>
+<a id="__codelineno-18-23" name="__codelineno-18-23" href="#__codelineno-18-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-24" name="__codelineno-18-24" href="#__codelineno-18-24"></a>
+<a id="__codelineno-18-25" name="__codelineno-18-25" href="#__codelineno-18-25"></a><span class="w">    </span><span class="cm">/* 負荷率 */</span>
+<a id="__codelineno-18-26" name="__codelineno-18-26" href="#__codelineno-18-26"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Double</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-27" name="__codelineno-18-27" href="#__codelineno-18-27"></a><span class="w">        </span><span class="nb">Double</span><span class="p">(</span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nb">Double</span><span class="p">(</span><span class="n">capacity</span><span class="p">)</span>
+<a id="__codelineno-18-28" name="__codelineno-18-28" href="#__codelineno-18-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-29" name="__codelineno-18-29" href="#__codelineno-18-29"></a>
+<a id="__codelineno-18-30" name="__codelineno-18-30" href="#__codelineno-18-30"></a><span class="w">    </span><span class="cm">/* key に対応するバケットインデックスを探す */</span>
+<a id="__codelineno-18-31" name="__codelineno-18-31" href="#__codelineno-18-31"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-32" name="__codelineno-18-32" href="#__codelineno-18-32"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">index</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-18-33" name="__codelineno-18-33" href="#__codelineno-18-33"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">firstTombstone</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-18-34" name="__codelineno-18-34" href="#__codelineno-18-34"></a><span class="w">        </span><span class="c1">// 線形プロービングを行い、空バケットに達したら終了</span>
+<a id="__codelineno-18-35" name="__codelineno-18-35" href="#__codelineno-18-35"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-36" name="__codelineno-18-36" href="#__codelineno-18-36"></a><span class="w">            </span><span class="c1">// key が見つかったら、対応するバケットのインデックスを返す</span>
+<a id="__codelineno-18-37" name="__codelineno-18-37" href="#__codelineno-18-37"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">!</span><span class="p">.</span><span class="n">key</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-38" name="__codelineno-18-38" href="#__codelineno-18-38"></a><span class="w">                </span><span class="c1">// 以前に削除マークが見つかっていれば、そのインデックスへキーと値のペアを移動</span>
+<a id="__codelineno-18-39" name="__codelineno-18-39" href="#__codelineno-18-39"></a><span class="w">                </span><span class="k">if</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-40" name="__codelineno-18-40" href="#__codelineno-18-40"></a><span class="w">                    </span><span class="n">buckets</span><span class="p">[</span><span class="n">firstTombstone</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
+<a id="__codelineno-18-41" name="__codelineno-18-41" href="#__codelineno-18-41"></a><span class="w">                    </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">TOMBSTONE</span>
+<a id="__codelineno-18-42" name="__codelineno-18-42" href="#__codelineno-18-42"></a><span class="w">                    </span><span class="k">return</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="c1">// 移動後のバケットインデックスを返す</span>
+<a id="__codelineno-18-43" name="__codelineno-18-43" href="#__codelineno-18-43"></a><span class="w">                </span><span class="p">}</span>
+<a id="__codelineno-18-44" name="__codelineno-18-44" href="#__codelineno-18-44"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="c1">// バケットのインデックスを返す</span>
+<a id="__codelineno-18-45" name="__codelineno-18-45" href="#__codelineno-18-45"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-18-46" name="__codelineno-18-46" href="#__codelineno-18-46"></a><span class="w">            </span><span class="c1">// 最初に見つかった削除マークを記録</span>
+<a id="__codelineno-18-47" name="__codelineno-18-47" href="#__codelineno-18-47"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-48" name="__codelineno-18-48" href="#__codelineno-18-48"></a><span class="w">                </span><span class="n">firstTombstone</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">index</span>
+<a id="__codelineno-18-49" name="__codelineno-18-49" href="#__codelineno-18-49"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-18-50" name="__codelineno-18-50" href="#__codelineno-18-50"></a><span class="w">            </span><span class="c1">// バケットのインデックスを計算し、末尾を越えたら先頭に戻る</span>
+<a id="__codelineno-18-51" name="__codelineno-18-51" href="#__codelineno-18-51"></a><span class="w">            </span><span class="n">index</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span>
+<a id="__codelineno-18-52" name="__codelineno-18-52" href="#__codelineno-18-52"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-53" name="__codelineno-18-53" href="#__codelineno-18-53"></a><span class="w">        </span><span class="c1">// key が存在しない場合は追加位置のインデックスを返す</span>
+<a id="__codelineno-18-54" name="__codelineno-18-54" href="#__codelineno-18-54"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">?</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">firstTombstone</span>
+<a id="__codelineno-18-55" name="__codelineno-18-55" href="#__codelineno-18-55"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-56" name="__codelineno-18-56" href="#__codelineno-18-56"></a>
+<a id="__codelineno-18-57" name="__codelineno-18-57" href="#__codelineno-18-57"></a><span class="w">    </span><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-18-58" name="__codelineno-18-58" href="#__codelineno-18-58"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">String</span><span class="p">?</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-59" name="__codelineno-18-59" href="#__codelineno-18-59"></a><span class="w">        </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-18-60" name="__codelineno-18-60" href="#__codelineno-18-60"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">index</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-18-61" name="__codelineno-18-61" href="#__codelineno-18-61"></a><span class="w">        </span><span class="c1">// キーと値の組が見つかったら、対応する val を返す</span>
+<a id="__codelineno-18-62" name="__codelineno-18-62" href="#__codelineno-18-62"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-63" name="__codelineno-18-63" href="#__codelineno-18-63"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">!</span><span class="p">.</span><span class="n">val</span>
+<a id="__codelineno-18-64" name="__codelineno-18-64" href="#__codelineno-18-64"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-65" name="__codelineno-18-65" href="#__codelineno-18-65"></a><span class="w">        </span><span class="c1">// キーと値の組が存在しなければ null を返す</span>
+<a id="__codelineno-18-66" name="__codelineno-18-66" href="#__codelineno-18-66"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-18-67" name="__codelineno-18-67" href="#__codelineno-18-67"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-68" name="__codelineno-18-68" href="#__codelineno-18-68"></a>
+<a id="__codelineno-18-69" name="__codelineno-18-69" href="#__codelineno-18-69"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-18-70" name="__codelineno-18-70" href="#__codelineno-18-70"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="nb">String</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-71" name="__codelineno-18-71" href="#__codelineno-18-71"></a><span class="w">        </span><span class="c1">// 負荷率がしきい値を超えたら、リサイズを実行</span>
+<a id="__codelineno-18-72" name="__codelineno-18-72" href="#__codelineno-18-72"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">loadThres</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-73" name="__codelineno-18-73" href="#__codelineno-18-73"></a><span class="w">            </span><span class="bp">extend</span><span class="p">()</span>
+<a id="__codelineno-18-74" name="__codelineno-18-74" href="#__codelineno-18-74"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-75" name="__codelineno-18-75" href="#__codelineno-18-75"></a><span class="w">        </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-18-76" name="__codelineno-18-76" href="#__codelineno-18-76"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">index</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-18-77" name="__codelineno-18-77" href="#__codelineno-18-77"></a><span class="w">        </span><span class="c1">// キーと値の組が見つかったら、val を上書きして返す</span>
+<a id="__codelineno-18-78" name="__codelineno-18-78" href="#__codelineno-18-78"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-79" name="__codelineno-18-79" href="#__codelineno-18-79"></a><span class="w">            </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">!</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">val</span>
+<a id="__codelineno-18-80" name="__codelineno-18-80" href="#__codelineno-18-80"></a><span class="w">            </span><span class="k">return</span>
+<a id="__codelineno-18-81" name="__codelineno-18-81" href="#__codelineno-18-81"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-82" name="__codelineno-18-82" href="#__codelineno-18-82"></a><span class="w">        </span><span class="c1">// キーと値の組が存在しない場合は、その組を追加する</span>
+<a id="__codelineno-18-83" name="__codelineno-18-83" href="#__codelineno-18-83"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-18-84" name="__codelineno-18-84" href="#__codelineno-18-84"></a><span class="w">        </span><span class="n">size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-18-85" name="__codelineno-18-85" href="#__codelineno-18-85"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-86" name="__codelineno-18-86" href="#__codelineno-18-86"></a>
+<a id="__codelineno-18-87" name="__codelineno-18-87" href="#__codelineno-18-87"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-18-88" name="__codelineno-18-88" href="#__codelineno-18-88"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-89" name="__codelineno-18-89" href="#__codelineno-18-89"></a><span class="w">        </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-18-90" name="__codelineno-18-90" href="#__codelineno-18-90"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">index</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-18-91" name="__codelineno-18-91" href="#__codelineno-18-91"></a><span class="w">        </span><span class="c1">// キーと値の組が見つかったら、削除マーカーで上書きする</span>
+<a id="__codelineno-18-92" name="__codelineno-18-92" href="#__codelineno-18-92"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-93" name="__codelineno-18-93" href="#__codelineno-18-93"></a><span class="w">            </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">TOMBSTONE</span>
+<a id="__codelineno-18-94" name="__codelineno-18-94" href="#__codelineno-18-94"></a><span class="w">            </span><span class="n">size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-18-95" name="__codelineno-18-95" href="#__codelineno-18-95"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-96" name="__codelineno-18-96" href="#__codelineno-18-96"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-97" name="__codelineno-18-97" href="#__codelineno-18-97"></a>
+<a id="__codelineno-18-98" name="__codelineno-18-98" href="#__codelineno-18-98"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを拡張 */</span>
+<a id="__codelineno-18-99" name="__codelineno-18-99" href="#__codelineno-18-99"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">extend</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-100" name="__codelineno-18-100" href="#__codelineno-18-100"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルを一時保存</span>
+<a id="__codelineno-18-101" name="__codelineno-18-101" href="#__codelineno-18-101"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">bucketsTmp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">buckets</span>
+<a id="__codelineno-18-102" name="__codelineno-18-102" href="#__codelineno-18-102"></a><span class="w">        </span><span class="c1">// リサイズ後の新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-18-103" name="__codelineno-18-103" href="#__codelineno-18-103"></a><span class="w">        </span><span class="n">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="n">extendRatio</span>
+<a id="__codelineno-18-104" name="__codelineno-18-104" href="#__codelineno-18-104"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span>
+<a id="__codelineno-18-105" name="__codelineno-18-105" href="#__codelineno-18-105"></a><span class="w">        </span><span class="n">size</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-18-106" name="__codelineno-18-106" href="#__codelineno-18-106"></a><span class="w">        </span><span class="c1">// キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
+<a id="__codelineno-18-107" name="__codelineno-18-107" href="#__codelineno-18-107"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-108" name="__codelineno-18-108" href="#__codelineno-18-108"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">pair</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-109" name="__codelineno-18-109" href="#__codelineno-18-109"></a><span class="w">                </span><span class="n">put</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-18-110" name="__codelineno-18-110" href="#__codelineno-18-110"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-18-111" name="__codelineno-18-111" href="#__codelineno-18-111"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-112" name="__codelineno-18-112" href="#__codelineno-18-112"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-113" name="__codelineno-18-113" href="#__codelineno-18-113"></a>
+<a id="__codelineno-18-114" name="__codelineno-18-114" href="#__codelineno-18-114"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-18-115" name="__codelineno-18-115" href="#__codelineno-18-115"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-116" name="__codelineno-18-116" href="#__codelineno-18-116"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-117" name="__codelineno-18-117" href="#__codelineno-18-117"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-118" name="__codelineno-18-118" href="#__codelineno-18-118"></a><span class="w">                </span><span class="n">Swift</span><span class="p">.</span><span class="bp">print</span><span class="p">(</span><span class="s">&quot;null&quot;</span><span class="p">)</span>
+<a id="__codelineno-18-119" name="__codelineno-18-119" href="#__codelineno-18-119"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-120" name="__codelineno-18-120" href="#__codelineno-18-120"></a><span class="w">                </span><span class="n">Swift</span><span class="p">.</span><span class="bp">print</span><span class="p">(</span><span class="s">&quot;TOMBSTONE&quot;</span><span class="p">)</span>
+<a id="__codelineno-18-121" name="__codelineno-18-121" href="#__codelineno-18-121"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-122" name="__codelineno-18-122" href="#__codelineno-18-122"></a><span class="w">                </span><span class="n">Swift</span><span class="p">.</span><span class="bp">print</span><span class="p">(</span><span class="s">&quot;</span><span class="si">\(</span><span class="n">pair</span><span class="p">!.</span><span class="n">key</span><span class="si">)</span><span class="s"> -&gt; </span><span class="si">\(</span><span class="n">pair</span><span class="p">!.</span><span class="n">val</span><span class="si">)</span><span class="s">&quot;</span><span class="p">)</span>
+<a id="__codelineno-18-123" name="__codelineno-18-123" href="#__codelineno-18-123"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-18-124" name="__codelineno-18-124" href="#__codelineno-18-124"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-125" name="__codelineno-18-125" href="#__codelineno-18-125"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-126" name="__codelineno-18-126" href="#__codelineno-18-126"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map_open_addressing.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">HashMapOpenAddressing</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">hash_map_open_addressing.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* オープンアドレス法ハッシュテーブル */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">HashMapOpenAddressing</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="n">#size</span><span class="p">;</span><span class="w"> </span><span class="c1">// キーと値のペア数</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="n">#capacity</span><span class="p">;</span><span class="w"> </span><span class="c1">// ハッシュテーブル容量</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">    </span><span class="n">#loadThres</span><span class="p">;</span><span class="w"> </span><span class="c1">// リサイズを発動する負荷率のしきい値</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">    </span><span class="n">#extendRatio</span><span class="p">;</span><span class="w"> </span><span class="c1">// 拡張倍率</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">    </span><span class="n">#buckets</span><span class="p">;</span><span class="w"> </span><span class="c1">// バケット配列</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">    </span><span class="n">#TOMBSTONE</span><span class="p">;</span><span class="w"> </span><span class="c1">// 削除済みマーク</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// キーと値のペア数</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">4</span><span class="p">;</span><span class="w"> </span><span class="c1">// ハッシュテーブル容量</span>
+<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#loadThres</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3.0</span><span class="p">;</span><span class="w"> </span><span class="c1">// リサイズを発動する負荷率のしきい値</span>
+<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 拡張倍率</span>
+<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#capacity</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="kc">null</span><span class="p">);</span><span class="w"> </span><span class="c1">// バケット配列</span>
+<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#TOMBSTONE</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">Pair</span><span class="p">(</span><span class="o">-</span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;-1&#39;</span><span class="p">);</span><span class="w"> </span><span class="c1">// 削除済みマーク</span>
+<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a>
+<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a><span class="w">    </span><span class="n">#hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-22" name="__codelineno-19-22" href="#__codelineno-19-22"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#capacity</span><span class="p">;</span>
+<a id="__codelineno-19-23" name="__codelineno-19-23" href="#__codelineno-19-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-24" name="__codelineno-19-24" href="#__codelineno-19-24"></a>
+<a id="__codelineno-19-25" name="__codelineno-19-25" href="#__codelineno-19-25"></a><span class="w">    </span><span class="cm">/* 負荷率 */</span>
+<a id="__codelineno-19-26" name="__codelineno-19-26" href="#__codelineno-19-26"></a><span class="w">    </span><span class="n">#loadFactor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-27" name="__codelineno-19-27" href="#__codelineno-19-27"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#capacity</span><span class="p">;</span>
+<a id="__codelineno-19-28" name="__codelineno-19-28" href="#__codelineno-19-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-29" name="__codelineno-19-29" href="#__codelineno-19-29"></a>
+<a id="__codelineno-19-30" name="__codelineno-19-30" href="#__codelineno-19-30"></a><span class="w">    </span><span class="cm">/* key に対応するバケットインデックスを探す */</span>
+<a id="__codelineno-19-31" name="__codelineno-19-31" href="#__codelineno-19-31"></a><span class="w">    </span><span class="n">#findBucket</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-32" name="__codelineno-19-32" href="#__codelineno-19-32"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">);</span>
+<a id="__codelineno-19-33" name="__codelineno-19-33" href="#__codelineno-19-33"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-19-34" name="__codelineno-19-34" href="#__codelineno-19-34"></a><span class="w">        </span><span class="c1">// 線形プロービングを行い、空バケットに達したら終了</span>
+<a id="__codelineno-19-35" name="__codelineno-19-35" href="#__codelineno-19-35"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-36" name="__codelineno-19-36" href="#__codelineno-19-36"></a><span class="w">            </span><span class="c1">// key が見つかったら、対応するバケットのインデックスを返す</span>
+<a id="__codelineno-19-37" name="__codelineno-19-37" href="#__codelineno-19-37"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">].</span><span class="nx">key</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-38" name="__codelineno-19-38" href="#__codelineno-19-38"></a><span class="w">                </span><span class="c1">// 以前に削除マークが見つかっていれば、そのインデックスへキーと値のペアを移動</span>
+<a id="__codelineno-19-39" name="__codelineno-19-39" href="#__codelineno-19-39"></a><span class="w">                </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">firstTombstone</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-40" name="__codelineno-19-40" href="#__codelineno-19-40"></a><span class="w">                    </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">firstTombstone</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">];</span>
+<a id="__codelineno-19-41" name="__codelineno-19-41" href="#__codelineno-19-41"></a><span class="w">                    </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#TOMBSTONE</span><span class="p">;</span>
+<a id="__codelineno-19-42" name="__codelineno-19-42" href="#__codelineno-19-42"></a><span class="w">                    </span><span class="k">return</span><span class="w"> </span><span class="nx">firstTombstone</span><span class="p">;</span><span class="w"> </span><span class="c1">// 移動後のバケットインデックスを返す</span>
+<a id="__codelineno-19-43" name="__codelineno-19-43" href="#__codelineno-19-43"></a><span class="w">                </span><span class="p">}</span>
+<a id="__codelineno-19-44" name="__codelineno-19-44" href="#__codelineno-19-44"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="nx">index</span><span class="p">;</span><span class="w"> </span><span class="c1">// バケットのインデックスを返す</span>
+<a id="__codelineno-19-45" name="__codelineno-19-45" href="#__codelineno-19-45"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-19-46" name="__codelineno-19-46" href="#__codelineno-19-46"></a><span class="w">            </span><span class="c1">// 最初に見つかった削除マークを記録</span>
+<a id="__codelineno-19-47" name="__codelineno-19-47" href="#__codelineno-19-47"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span>
+<a id="__codelineno-19-48" name="__codelineno-19-48" href="#__codelineno-19-48"></a><span class="w">                </span><span class="nx">firstTombstone</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="w"> </span><span class="o">&amp;&amp;</span>
+<a id="__codelineno-19-49" name="__codelineno-19-49" href="#__codelineno-19-49"></a><span class="w">                </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#TOMBSTONE</span>
+<a id="__codelineno-19-50" name="__codelineno-19-50" href="#__codelineno-19-50"></a><span class="w">            </span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-51" name="__codelineno-19-51" href="#__codelineno-19-51"></a><span class="w">                </span><span class="nx">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">index</span><span class="p">;</span>
+<a id="__codelineno-19-52" name="__codelineno-19-52" href="#__codelineno-19-52"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-19-53" name="__codelineno-19-53" href="#__codelineno-19-53"></a><span class="w">            </span><span class="c1">// バケットのインデックスを計算し、末尾を越えたら先頭に戻る</span>
+<a id="__codelineno-19-54" name="__codelineno-19-54" href="#__codelineno-19-54"></a><span class="w">            </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="nx">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#capacity</span><span class="p">;</span>
+<a id="__codelineno-19-55" name="__codelineno-19-55" href="#__codelineno-19-55"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-56" name="__codelineno-19-56" href="#__codelineno-19-56"></a><span class="w">        </span><span class="c1">// key が存在しない場合は追加位置のインデックスを返す</span>
+<a id="__codelineno-19-57" name="__codelineno-19-57" href="#__codelineno-19-57"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">firstTombstone</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">firstTombstone</span><span class="p">;</span>
+<a id="__codelineno-19-58" name="__codelineno-19-58" href="#__codelineno-19-58"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-59" name="__codelineno-19-59" href="#__codelineno-19-59"></a>
+<a id="__codelineno-19-60" name="__codelineno-19-60" href="#__codelineno-19-60"></a><span class="w">    </span><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-19-61" name="__codelineno-19-61" href="#__codelineno-19-61"></a><span class="w">    </span><span class="nx">get</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-62" name="__codelineno-19-62" href="#__codelineno-19-62"></a><span class="w">        </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-19-63" name="__codelineno-19-63" href="#__codelineno-19-63"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#findBucket</span><span class="p">(</span><span class="nx">key</span><span class="p">);</span>
+<a id="__codelineno-19-64" name="__codelineno-19-64" href="#__codelineno-19-64"></a><span class="w">        </span><span class="c1">// キーと値の組が見つかったら、対応する val を返す</span>
+<a id="__codelineno-19-65" name="__codelineno-19-65" href="#__codelineno-19-65"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span>
+<a id="__codelineno-19-66" name="__codelineno-19-66" href="#__codelineno-19-66"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span>
+<a id="__codelineno-19-67" name="__codelineno-19-67" href="#__codelineno-19-67"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#TOMBSTONE</span>
+<a id="__codelineno-19-68" name="__codelineno-19-68" href="#__codelineno-19-68"></a><span class="w">        </span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-69" name="__codelineno-19-69" href="#__codelineno-19-69"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">].</span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-19-70" name="__codelineno-19-70" href="#__codelineno-19-70"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-71" name="__codelineno-19-71" href="#__codelineno-19-71"></a><span class="w">        </span><span class="c1">// キーと値の組が存在しなければ null を返す</span>
+<a id="__codelineno-19-72" name="__codelineno-19-72" href="#__codelineno-19-72"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-19-73" name="__codelineno-19-73" href="#__codelineno-19-73"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-74" name="__codelineno-19-74" href="#__codelineno-19-74"></a>
+<a id="__codelineno-19-75" name="__codelineno-19-75" href="#__codelineno-19-75"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-19-76" name="__codelineno-19-76" href="#__codelineno-19-76"></a><span class="w">    </span><span class="nx">put</span><span class="p">(</span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-77" name="__codelineno-19-77" href="#__codelineno-19-77"></a><span class="w">        </span><span class="c1">// 負荷率がしきい値を超えたら、リサイズを実行</span>
+<a id="__codelineno-19-78" name="__codelineno-19-78" href="#__codelineno-19-78"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#loadFactor</span><span class="p">()</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#loadThres</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-79" name="__codelineno-19-79" href="#__codelineno-19-79"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#extend</span><span class="p">();</span>
+<a id="__codelineno-19-80" name="__codelineno-19-80" href="#__codelineno-19-80"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-81" name="__codelineno-19-81" href="#__codelineno-19-81"></a><span class="w">        </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-19-82" name="__codelineno-19-82" href="#__codelineno-19-82"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#findBucket</span><span class="p">(</span><span class="nx">key</span><span class="p">);</span>
+<a id="__codelineno-19-83" name="__codelineno-19-83" href="#__codelineno-19-83"></a><span class="w">        </span><span class="c1">// キーと値の組が見つかったら、val を上書きして返す</span>
+<a id="__codelineno-19-84" name="__codelineno-19-84" href="#__codelineno-19-84"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span>
+<a id="__codelineno-19-85" name="__codelineno-19-85" href="#__codelineno-19-85"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span>
+<a id="__codelineno-19-86" name="__codelineno-19-86" href="#__codelineno-19-86"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#TOMBSTONE</span>
+<a id="__codelineno-19-87" name="__codelineno-19-87" href="#__codelineno-19-87"></a><span class="w">        </span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-88" name="__codelineno-19-88" href="#__codelineno-19-88"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">].</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-19-89" name="__codelineno-19-89" href="#__codelineno-19-89"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-19-90" name="__codelineno-19-90" href="#__codelineno-19-90"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-91" name="__codelineno-19-91" href="#__codelineno-19-91"></a><span class="w">        </span><span class="c1">// キーと値の組が存在しない場合は、その組を追加する</span>
+<a id="__codelineno-19-92" name="__codelineno-19-92" href="#__codelineno-19-92"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">Pair</span><span class="p">(</span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-19-93" name="__codelineno-19-93" href="#__codelineno-19-93"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-19-94" name="__codelineno-19-94" href="#__codelineno-19-94"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-95" name="__codelineno-19-95" href="#__codelineno-19-95"></a>
+<a id="__codelineno-19-96" name="__codelineno-19-96" href="#__codelineno-19-96"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-19-97" name="__codelineno-19-97" href="#__codelineno-19-97"></a><span class="w">    </span><span class="nx">remove</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-98" name="__codelineno-19-98" href="#__codelineno-19-98"></a><span class="w">        </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-19-99" name="__codelineno-19-99" href="#__codelineno-19-99"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#findBucket</span><span class="p">(</span><span class="nx">key</span><span class="p">);</span>
+<a id="__codelineno-19-100" name="__codelineno-19-100" href="#__codelineno-19-100"></a><span class="w">        </span><span class="c1">// キーと値の組が見つかったら、削除マーカーで上書きする</span>
+<a id="__codelineno-19-101" name="__codelineno-19-101" href="#__codelineno-19-101"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span>
+<a id="__codelineno-19-102" name="__codelineno-19-102" href="#__codelineno-19-102"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span>
+<a id="__codelineno-19-103" name="__codelineno-19-103" href="#__codelineno-19-103"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#TOMBSTONE</span>
+<a id="__codelineno-19-104" name="__codelineno-19-104" href="#__codelineno-19-104"></a><span class="w">        </span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-105" name="__codelineno-19-105" href="#__codelineno-19-105"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#TOMBSTONE</span><span class="p">;</span>
+<a id="__codelineno-19-106" name="__codelineno-19-106" href="#__codelineno-19-106"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-19-107" name="__codelineno-19-107" href="#__codelineno-19-107"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-108" name="__codelineno-19-108" href="#__codelineno-19-108"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-109" name="__codelineno-19-109" href="#__codelineno-19-109"></a>
+<a id="__codelineno-19-110" name="__codelineno-19-110" href="#__codelineno-19-110"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを拡張 */</span>
+<a id="__codelineno-19-111" name="__codelineno-19-111" href="#__codelineno-19-111"></a><span class="w">    </span><span class="n">#extend</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-112" name="__codelineno-19-112" href="#__codelineno-19-112"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルを一時保存</span>
+<a id="__codelineno-19-113" name="__codelineno-19-113" href="#__codelineno-19-113"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">bucketsTmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">;</span>
+<a id="__codelineno-19-114" name="__codelineno-19-114" href="#__codelineno-19-114"></a><span class="w">        </span><span class="c1">// リサイズ後の新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-19-115" name="__codelineno-19-115" href="#__codelineno-19-115"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#extendRatio</span><span class="p">;</span>
+<a id="__codelineno-19-116" name="__codelineno-19-116" href="#__codelineno-19-116"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#capacity</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="kc">null</span><span class="p">);</span>
+<a id="__codelineno-19-117" name="__codelineno-19-117" href="#__codelineno-19-117"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-19-118" name="__codelineno-19-118" href="#__codelineno-19-118"></a><span class="w">        </span><span class="c1">// キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
+<a id="__codelineno-19-119" name="__codelineno-19-119" href="#__codelineno-19-119"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">bucketsTmp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-120" name="__codelineno-19-120" href="#__codelineno-19-120"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">pair</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-121" name="__codelineno-19-121" href="#__codelineno-19-121"></a><span class="w">                </span><span class="k">this</span><span class="p">.</span><span class="nx">put</span><span class="p">(</span><span class="nx">pair</span><span class="p">.</span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-19-122" name="__codelineno-19-122" href="#__codelineno-19-122"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-19-123" name="__codelineno-19-123" href="#__codelineno-19-123"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-124" name="__codelineno-19-124" href="#__codelineno-19-124"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-125" name="__codelineno-19-125" href="#__codelineno-19-125"></a>
+<a id="__codelineno-19-126" name="__codelineno-19-126" href="#__codelineno-19-126"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-19-127" name="__codelineno-19-127" href="#__codelineno-19-127"></a><span class="w">    </span><span class="nx">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-128" name="__codelineno-19-128" href="#__codelineno-19-128"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-129" name="__codelineno-19-129" href="#__codelineno-19-129"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">pair</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-130" name="__codelineno-19-130" href="#__codelineno-19-130"></a><span class="w">                </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="s1">&#39;null&#39;</span><span class="p">);</span>
+<a id="__codelineno-19-131" name="__codelineno-19-131" href="#__codelineno-19-131"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">pair</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-132" name="__codelineno-19-132" href="#__codelineno-19-132"></a><span class="w">                </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="s1">&#39;TOMBSTONE&#39;</span><span class="p">);</span>
+<a id="__codelineno-19-133" name="__codelineno-19-133" href="#__codelineno-19-133"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-134" name="__codelineno-19-134" href="#__codelineno-19-134"></a><span class="w">                </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="nx">pair</span><span class="p">.</span><span class="nx">key</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s1">&#39; -&gt; &#39;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-19-135" name="__codelineno-19-135" href="#__codelineno-19-135"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-19-136" name="__codelineno-19-136" href="#__codelineno-19-136"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-137" name="__codelineno-19-137" href="#__codelineno-19-137"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-138" name="__codelineno-19-138" href="#__codelineno-19-138"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map_open_addressing.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">HashMapOpenAddressing</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">hash_map_open_addressing.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* オープンアドレス法ハッシュテーブル */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">HashMapOpenAddressing</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">size</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// キーと値のペア数</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">capacity</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// ハッシュテーブル容量</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">loadThres</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// リサイズを発動する負荷率のしきい値</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">extendRatio</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// 拡張倍率</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">buckets</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="nx">Pair</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="o">&gt;</span><span class="p">;</span><span class="w"> </span><span class="c1">// バケット配列</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">TOMBSTONE</span><span class="o">:</span><span class="w"> </span><span class="kt">Pair</span><span class="p">;</span><span class="w"> </span><span class="c1">// 削除済みマーク</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// キーと値のペア数</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">4</span><span class="p">;</span><span class="w"> </span><span class="c1">// ハッシュテーブル容量</span>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">loadThres</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3.0</span><span class="p">;</span><span class="w"> </span><span class="c1">// リサイズを発動する負荷率のしきい値</span>
+<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 拡張倍率</span>
+<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="kc">null</span><span class="p">);</span><span class="w"> </span><span class="c1">// バケット配列</span>
+<a id="__codelineno-20-17" name="__codelineno-20-17" href="#__codelineno-20-17"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">TOMBSTONE</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">Pair</span><span class="p">(</span><span class="o">-</span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;-1&#39;</span><span class="p">);</span><span class="w"> </span><span class="c1">// 削除済みマーク</span>
+<a id="__codelineno-20-18" name="__codelineno-20-18" href="#__codelineno-20-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-19" name="__codelineno-20-19" href="#__codelineno-20-19"></a>
+<a id="__codelineno-20-20" name="__codelineno-20-20" href="#__codelineno-20-20"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-20-21" name="__codelineno-20-21" href="#__codelineno-20-21"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-22" name="__codelineno-20-22" href="#__codelineno-20-22"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="p">;</span>
+<a id="__codelineno-20-23" name="__codelineno-20-23" href="#__codelineno-20-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-24" name="__codelineno-20-24" href="#__codelineno-20-24"></a>
+<a id="__codelineno-20-25" name="__codelineno-20-25" href="#__codelineno-20-25"></a><span class="w">    </span><span class="cm">/* 負荷率 */</span>
+<a id="__codelineno-20-26" name="__codelineno-20-26" href="#__codelineno-20-26"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">loadFactor</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-27" name="__codelineno-20-27" href="#__codelineno-20-27"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="p">;</span>
+<a id="__codelineno-20-28" name="__codelineno-20-28" href="#__codelineno-20-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-29" name="__codelineno-20-29" href="#__codelineno-20-29"></a>
+<a id="__codelineno-20-30" name="__codelineno-20-30" href="#__codelineno-20-30"></a><span class="w">    </span><span class="cm">/* key に対応するバケットインデックスを探す */</span>
+<a id="__codelineno-20-31" name="__codelineno-20-31" href="#__codelineno-20-31"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">findBucket</span><span class="p">(</span><span class="nx">key</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-32" name="__codelineno-20-32" href="#__codelineno-20-32"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">);</span>
+<a id="__codelineno-20-33" name="__codelineno-20-33" href="#__codelineno-20-33"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-20-34" name="__codelineno-20-34" href="#__codelineno-20-34"></a><span class="w">        </span><span class="c1">// 線形プロービングを行い、空バケットに達したら終了</span>
+<a id="__codelineno-20-35" name="__codelineno-20-35" href="#__codelineno-20-35"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-36" name="__codelineno-20-36" href="#__codelineno-20-36"></a><span class="w">            </span><span class="c1">// key が見つかったら、対応するバケットのインデックスを返す</span>
+<a id="__codelineno-20-37" name="__codelineno-20-37" href="#__codelineno-20-37"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="o">!</span><span class="p">.</span><span class="nx">key</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-38" name="__codelineno-20-38" href="#__codelineno-20-38"></a><span class="w">                </span><span class="c1">// 以前に削除マークが見つかっていれば、そのインデックスへキーと値のペアを移動</span>
+<a id="__codelineno-20-39" name="__codelineno-20-39" href="#__codelineno-20-39"></a><span class="w">                </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">firstTombstone</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-40" name="__codelineno-20-40" href="#__codelineno-20-40"></a><span class="w">                    </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">firstTombstone</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">];</span>
+<a id="__codelineno-20-41" name="__codelineno-20-41" href="#__codelineno-20-41"></a><span class="w">                    </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">TOMBSTONE</span><span class="p">;</span>
+<a id="__codelineno-20-42" name="__codelineno-20-42" href="#__codelineno-20-42"></a><span class="w">                    </span><span class="k">return</span><span class="w"> </span><span class="nx">firstTombstone</span><span class="p">;</span><span class="w"> </span><span class="c1">// 移動後のバケットインデックスを返す</span>
+<a id="__codelineno-20-43" name="__codelineno-20-43" href="#__codelineno-20-43"></a><span class="w">                </span><span class="p">}</span>
+<a id="__codelineno-20-44" name="__codelineno-20-44" href="#__codelineno-20-44"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="nx">index</span><span class="p">;</span><span class="w"> </span><span class="c1">// バケットのインデックスを返す</span>
+<a id="__codelineno-20-45" name="__codelineno-20-45" href="#__codelineno-20-45"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-20-46" name="__codelineno-20-46" href="#__codelineno-20-46"></a><span class="w">            </span><span class="c1">// 最初に見つかった削除マークを記録</span>
+<a id="__codelineno-20-47" name="__codelineno-20-47" href="#__codelineno-20-47"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span>
+<a id="__codelineno-20-48" name="__codelineno-20-48" href="#__codelineno-20-48"></a><span class="w">                </span><span class="nx">firstTombstone</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="w"> </span><span class="o">&amp;&amp;</span>
+<a id="__codelineno-20-49" name="__codelineno-20-49" href="#__codelineno-20-49"></a><span class="w">                </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">TOMBSTONE</span>
+<a id="__codelineno-20-50" name="__codelineno-20-50" href="#__codelineno-20-50"></a><span class="w">            </span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-51" name="__codelineno-20-51" href="#__codelineno-20-51"></a><span class="w">                </span><span class="nx">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">index</span><span class="p">;</span>
+<a id="__codelineno-20-52" name="__codelineno-20-52" href="#__codelineno-20-52"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-20-53" name="__codelineno-20-53" href="#__codelineno-20-53"></a><span class="w">            </span><span class="c1">// バケットのインデックスを計算し、末尾を越えたら先頭に戻る</span>
+<a id="__codelineno-20-54" name="__codelineno-20-54" href="#__codelineno-20-54"></a><span class="w">            </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="nx">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="p">;</span>
+<a id="__codelineno-20-55" name="__codelineno-20-55" href="#__codelineno-20-55"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-56" name="__codelineno-20-56" href="#__codelineno-20-56"></a><span class="w">        </span><span class="c1">// key が存在しない場合は追加位置のインデックスを返す</span>
+<a id="__codelineno-20-57" name="__codelineno-20-57" href="#__codelineno-20-57"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">firstTombstone</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">firstTombstone</span><span class="p">;</span>
+<a id="__codelineno-20-58" name="__codelineno-20-58" href="#__codelineno-20-58"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-59" name="__codelineno-20-59" href="#__codelineno-20-59"></a>
+<a id="__codelineno-20-60" name="__codelineno-20-60" href="#__codelineno-20-60"></a><span class="w">    </span><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-20-61" name="__codelineno-20-61" href="#__codelineno-20-61"></a><span class="w">    </span><span class="nx">get</span><span class="p">(</span><span class="nx">key</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-62" name="__codelineno-20-62" href="#__codelineno-20-62"></a><span class="w">        </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-20-63" name="__codelineno-20-63" href="#__codelineno-20-63"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">findBucket</span><span class="p">(</span><span class="nx">key</span><span class="p">);</span>
+<a id="__codelineno-20-64" name="__codelineno-20-64" href="#__codelineno-20-64"></a><span class="w">        </span><span class="c1">// キーと値の組が見つかったら、対応する val を返す</span>
+<a id="__codelineno-20-65" name="__codelineno-20-65" href="#__codelineno-20-65"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span>
+<a id="__codelineno-20-66" name="__codelineno-20-66" href="#__codelineno-20-66"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span>
+<a id="__codelineno-20-67" name="__codelineno-20-67" href="#__codelineno-20-67"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">TOMBSTONE</span>
+<a id="__codelineno-20-68" name="__codelineno-20-68" href="#__codelineno-20-68"></a><span class="w">        </span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-69" name="__codelineno-20-69" href="#__codelineno-20-69"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="o">!</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-20-70" name="__codelineno-20-70" href="#__codelineno-20-70"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-71" name="__codelineno-20-71" href="#__codelineno-20-71"></a><span class="w">        </span><span class="c1">// キーと値の組が存在しなければ null を返す</span>
+<a id="__codelineno-20-72" name="__codelineno-20-72" href="#__codelineno-20-72"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-20-73" name="__codelineno-20-73" href="#__codelineno-20-73"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-74" name="__codelineno-20-74" href="#__codelineno-20-74"></a>
+<a id="__codelineno-20-75" name="__codelineno-20-75" href="#__codelineno-20-75"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-20-76" name="__codelineno-20-76" href="#__codelineno-20-76"></a><span class="w">    </span><span class="nx">put</span><span class="p">(</span><span class="nx">key</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-77" name="__codelineno-20-77" href="#__codelineno-20-77"></a><span class="w">        </span><span class="c1">// 負荷率がしきい値を超えたら、リサイズを実行</span>
+<a id="__codelineno-20-78" name="__codelineno-20-78" href="#__codelineno-20-78"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">loadThres</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-79" name="__codelineno-20-79" href="#__codelineno-20-79"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">extend</span><span class="p">();</span>
+<a id="__codelineno-20-80" name="__codelineno-20-80" href="#__codelineno-20-80"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-81" name="__codelineno-20-81" href="#__codelineno-20-81"></a><span class="w">        </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-20-82" name="__codelineno-20-82" href="#__codelineno-20-82"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">findBucket</span><span class="p">(</span><span class="nx">key</span><span class="p">);</span>
+<a id="__codelineno-20-83" name="__codelineno-20-83" href="#__codelineno-20-83"></a><span class="w">        </span><span class="c1">// キーと値の組が見つかったら、val を上書きして返す</span>
+<a id="__codelineno-20-84" name="__codelineno-20-84" href="#__codelineno-20-84"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span>
+<a id="__codelineno-20-85" name="__codelineno-20-85" href="#__codelineno-20-85"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span>
+<a id="__codelineno-20-86" name="__codelineno-20-86" href="#__codelineno-20-86"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">TOMBSTONE</span>
+<a id="__codelineno-20-87" name="__codelineno-20-87" href="#__codelineno-20-87"></a><span class="w">        </span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-88" name="__codelineno-20-88" href="#__codelineno-20-88"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="o">!</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-20-89" name="__codelineno-20-89" href="#__codelineno-20-89"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-20-90" name="__codelineno-20-90" href="#__codelineno-20-90"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-91" name="__codelineno-20-91" href="#__codelineno-20-91"></a><span class="w">        </span><span class="c1">// キーと値の組が存在しない場合は、その組を追加する</span>
+<a id="__codelineno-20-92" name="__codelineno-20-92" href="#__codelineno-20-92"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">Pair</span><span class="p">(</span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-20-93" name="__codelineno-20-93" href="#__codelineno-20-93"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-20-94" name="__codelineno-20-94" href="#__codelineno-20-94"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-95" name="__codelineno-20-95" href="#__codelineno-20-95"></a>
+<a id="__codelineno-20-96" name="__codelineno-20-96" href="#__codelineno-20-96"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-20-97" name="__codelineno-20-97" href="#__codelineno-20-97"></a><span class="w">    </span><span class="nx">remove</span><span class="p">(</span><span class="nx">key</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-98" name="__codelineno-20-98" href="#__codelineno-20-98"></a><span class="w">        </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-20-99" name="__codelineno-20-99" href="#__codelineno-20-99"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">findBucket</span><span class="p">(</span><span class="nx">key</span><span class="p">);</span>
+<a id="__codelineno-20-100" name="__codelineno-20-100" href="#__codelineno-20-100"></a><span class="w">        </span><span class="c1">// キーと値の組が見つかったら、削除マーカーで上書きする</span>
+<a id="__codelineno-20-101" name="__codelineno-20-101" href="#__codelineno-20-101"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span>
+<a id="__codelineno-20-102" name="__codelineno-20-102" href="#__codelineno-20-102"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span>
+<a id="__codelineno-20-103" name="__codelineno-20-103" href="#__codelineno-20-103"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">TOMBSTONE</span>
+<a id="__codelineno-20-104" name="__codelineno-20-104" href="#__codelineno-20-104"></a><span class="w">        </span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-105" name="__codelineno-20-105" href="#__codelineno-20-105"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">TOMBSTONE</span><span class="p">;</span>
+<a id="__codelineno-20-106" name="__codelineno-20-106" href="#__codelineno-20-106"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-20-107" name="__codelineno-20-107" href="#__codelineno-20-107"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-108" name="__codelineno-20-108" href="#__codelineno-20-108"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-109" name="__codelineno-20-109" href="#__codelineno-20-109"></a>
+<a id="__codelineno-20-110" name="__codelineno-20-110" href="#__codelineno-20-110"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを拡張 */</span>
+<a id="__codelineno-20-111" name="__codelineno-20-111" href="#__codelineno-20-111"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">extend</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-112" name="__codelineno-20-112" href="#__codelineno-20-112"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルを一時保存</span>
+<a id="__codelineno-20-113" name="__codelineno-20-113" href="#__codelineno-20-113"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">bucketsTmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">;</span>
+<a id="__codelineno-20-114" name="__codelineno-20-114" href="#__codelineno-20-114"></a><span class="w">        </span><span class="c1">// リサイズ後の新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-20-115" name="__codelineno-20-115" href="#__codelineno-20-115"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">extendRatio</span><span class="p">;</span>
+<a id="__codelineno-20-116" name="__codelineno-20-116" href="#__codelineno-20-116"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="kc">null</span><span class="p">);</span>
+<a id="__codelineno-20-117" name="__codelineno-20-117" href="#__codelineno-20-117"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-20-118" name="__codelineno-20-118" href="#__codelineno-20-118"></a><span class="w">        </span><span class="c1">// キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
+<a id="__codelineno-20-119" name="__codelineno-20-119" href="#__codelineno-20-119"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">bucketsTmp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-120" name="__codelineno-20-120" href="#__codelineno-20-120"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">pair</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-121" name="__codelineno-20-121" href="#__codelineno-20-121"></a><span class="w">                </span><span class="k">this</span><span class="p">.</span><span class="nx">put</span><span class="p">(</span><span class="nx">pair</span><span class="p">.</span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-20-122" name="__codelineno-20-122" href="#__codelineno-20-122"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-20-123" name="__codelineno-20-123" href="#__codelineno-20-123"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-124" name="__codelineno-20-124" href="#__codelineno-20-124"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-125" name="__codelineno-20-125" href="#__codelineno-20-125"></a>
+<a id="__codelineno-20-126" name="__codelineno-20-126" href="#__codelineno-20-126"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-20-127" name="__codelineno-20-127" href="#__codelineno-20-127"></a><span class="w">    </span><span class="nx">print</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-128" name="__codelineno-20-128" href="#__codelineno-20-128"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-129" name="__codelineno-20-129" href="#__codelineno-20-129"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">pair</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-130" name="__codelineno-20-130" href="#__codelineno-20-130"></a><span class="w">                </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="s1">&#39;null&#39;</span><span class="p">);</span>
+<a id="__codelineno-20-131" name="__codelineno-20-131" href="#__codelineno-20-131"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">pair</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-132" name="__codelineno-20-132" href="#__codelineno-20-132"></a><span class="w">                </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="s1">&#39;TOMBSTONE&#39;</span><span class="p">);</span>
+<a id="__codelineno-20-133" name="__codelineno-20-133" href="#__codelineno-20-133"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-134" name="__codelineno-20-134" href="#__codelineno-20-134"></a><span class="w">                </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="nx">pair</span><span class="p">.</span><span class="nx">key</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s1">&#39; -&gt; &#39;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-20-135" name="__codelineno-20-135" href="#__codelineno-20-135"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-20-136" name="__codelineno-20-136" href="#__codelineno-20-136"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-137" name="__codelineno-20-137" href="#__codelineno-20-137"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-138" name="__codelineno-20-138" href="#__codelineno-20-138"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map_open_addressing.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">HashMapOpenAddressing</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">hash_map_open_addressing.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* オープンアドレス法ハッシュテーブル */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">HashMapOpenAddressing</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="kd">late</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">_size</span><span class="p">;</span><span class="w"> </span><span class="c1">// キーと値のペア数</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">_capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">4</span><span class="p">;</span><span class="w"> </span><span class="c1">// ハッシュテーブル容量</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">  </span><span class="kt">double</span><span class="w"> </span><span class="n">_loadThres</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">3.0</span><span class="p">;</span><span class="w"> </span><span class="c1">// リサイズを発動する負荷率のしきい値</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">_extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 拡張倍率</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">  </span><span class="kd">late</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">?&gt;</span><span class="w"> </span><span class="n">_buckets</span><span class="p">;</span><span class="w"> </span><span class="c1">// バケット配列</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">  </span><span class="n">Pair</span><span class="w"> </span><span class="n">_TOMBSTONE</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="o">-</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="s2">&quot;-1&quot;</span><span class="p">);</span><span class="w"> </span><span class="c1">// 削除済みマーク</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="w">  </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="w">  </span><span class="n">HashMapOpenAddressing</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w">    </span><span class="n">_size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">    </span><span class="n">_buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">generate</span><span class="p">(</span><span class="n">_capacity</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="kc">null</span><span class="p">);</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a>
+<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="w">  </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-21-17" name="__codelineno-21-17" href="#__codelineno-21-17"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-18" name="__codelineno-21-18" href="#__codelineno-21-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">_capacity</span><span class="p">;</span>
+<a id="__codelineno-21-19" name="__codelineno-21-19" href="#__codelineno-21-19"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-20" name="__codelineno-21-20" href="#__codelineno-21-20"></a>
+<a id="__codelineno-21-21" name="__codelineno-21-21" href="#__codelineno-21-21"></a><span class="w">  </span><span class="cm">/* 負荷率 */</span>
+<a id="__codelineno-21-22" name="__codelineno-21-22" href="#__codelineno-21-22"></a><span class="w">  </span><span class="kt">double</span><span class="w"> </span><span class="n">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-23" name="__codelineno-21-23" href="#__codelineno-21-23"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">_capacity</span><span class="p">;</span>
+<a id="__codelineno-21-24" name="__codelineno-21-24" href="#__codelineno-21-24"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-25" name="__codelineno-21-25" href="#__codelineno-21-25"></a>
+<a id="__codelineno-21-26" name="__codelineno-21-26" href="#__codelineno-21-26"></a><span class="w">  </span><span class="cm">/* key に対応するバケットインデックスを探す */</span>
+<a id="__codelineno-21-27" name="__codelineno-21-27" href="#__codelineno-21-27"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-28" name="__codelineno-21-28" href="#__codelineno-21-28"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-21-29" name="__codelineno-21-29" href="#__codelineno-21-29"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-21-30" name="__codelineno-21-30" href="#__codelineno-21-30"></a><span class="w">    </span><span class="c1">// 線形プロービングを行い、空バケットに達したら終了</span>
+<a id="__codelineno-21-31" name="__codelineno-21-31" href="#__codelineno-21-31"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">_buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-32" name="__codelineno-21-32" href="#__codelineno-21-32"></a><span class="w">      </span><span class="c1">// key が見つかったら、対応するバケットのインデックスを返す</span>
+<a id="__codelineno-21-33" name="__codelineno-21-33" href="#__codelineno-21-33"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">!</span><span class="p">.</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-34" name="__codelineno-21-34" href="#__codelineno-21-34"></a><span class="w">        </span><span class="c1">// 以前に削除マークが見つかっていれば、そのインデックスへキーと値のペアを移動</span>
+<a id="__codelineno-21-35" name="__codelineno-21-35" href="#__codelineno-21-35"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-36" name="__codelineno-21-36" href="#__codelineno-21-36"></a><span class="w">          </span><span class="n">_buckets</span><span class="p">[</span><span class="n">firstTombstone</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-21-37" name="__codelineno-21-37" href="#__codelineno-21-37"></a><span class="w">          </span><span class="n">_buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_TOMBSTONE</span><span class="p">;</span>
+<a id="__codelineno-21-38" name="__codelineno-21-38" href="#__codelineno-21-38"></a><span class="w">          </span><span class="k">return</span><span class="w"> </span><span class="n">firstTombstone</span><span class="p">;</span><span class="w"> </span><span class="c1">// 移動後のバケットインデックスを返す</span>
+<a id="__codelineno-21-39" name="__codelineno-21-39" href="#__codelineno-21-39"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-21-40" name="__codelineno-21-40" href="#__codelineno-21-40"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="c1">// バケットのインデックスを返す</span>
+<a id="__codelineno-21-41" name="__codelineno-21-41" href="#__codelineno-21-41"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-21-42" name="__codelineno-21-42" href="#__codelineno-21-42"></a><span class="w">      </span><span class="c1">// 最初に見つかった削除マークを記録</span>
+<a id="__codelineno-21-43" name="__codelineno-21-43" href="#__codelineno-21-43"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">_buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">_TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-44" name="__codelineno-21-44" href="#__codelineno-21-44"></a><span class="w">        </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
+<a id="__codelineno-21-45" name="__codelineno-21-45" href="#__codelineno-21-45"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-21-46" name="__codelineno-21-46" href="#__codelineno-21-46"></a><span class="w">      </span><span class="c1">// バケットのインデックスを計算し、末尾を越えたら先頭に戻る</span>
+<a id="__codelineno-21-47" name="__codelineno-21-47" href="#__codelineno-21-47"></a><span class="w">      </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">_capacity</span><span class="p">;</span>
+<a id="__codelineno-21-48" name="__codelineno-21-48" href="#__codelineno-21-48"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-49" name="__codelineno-21-49" href="#__codelineno-21-49"></a><span class="w">    </span><span class="c1">// key が存在しない場合は追加位置のインデックスを返す</span>
+<a id="__codelineno-21-50" name="__codelineno-21-50" href="#__codelineno-21-50"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">firstTombstone</span><span class="p">;</span>
+<a id="__codelineno-21-51" name="__codelineno-21-51" href="#__codelineno-21-51"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-52" name="__codelineno-21-52" href="#__codelineno-21-52"></a>
+<a id="__codelineno-21-53" name="__codelineno-21-53" href="#__codelineno-21-53"></a><span class="w">  </span><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-21-54" name="__codelineno-21-54" href="#__codelineno-21-54"></a><span class="w">  </span><span class="kt">String</span><span class="o">?</span><span class="w"> </span><span class="kd">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-55" name="__codelineno-21-55" href="#__codelineno-21-55"></a><span class="w">    </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-21-56" name="__codelineno-21-56" href="#__codelineno-21-56"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-21-57" name="__codelineno-21-57" href="#__codelineno-21-57"></a><span class="w">    </span><span class="c1">// キーと値の組が見つかったら、対応する val を返す</span>
+<a id="__codelineno-21-58" name="__codelineno-21-58" href="#__codelineno-21-58"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">_buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">_TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-59" name="__codelineno-21-59" href="#__codelineno-21-59"></a><span class="w">      </span><span class="k">return</span><span class="w"> </span><span class="n">_buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">!</span><span class="p">.</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-21-60" name="__codelineno-21-60" href="#__codelineno-21-60"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-61" name="__codelineno-21-61" href="#__codelineno-21-61"></a><span class="w">    </span><span class="c1">// キーと値の組が存在しなければ null を返す</span>
+<a id="__codelineno-21-62" name="__codelineno-21-62" href="#__codelineno-21-62"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-21-63" name="__codelineno-21-63" href="#__codelineno-21-63"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-64" name="__codelineno-21-64" href="#__codelineno-21-64"></a>
+<a id="__codelineno-21-65" name="__codelineno-21-65" href="#__codelineno-21-65"></a><span class="w">  </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-21-66" name="__codelineno-21-66" href="#__codelineno-21-66"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="kt">String</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-67" name="__codelineno-21-67" href="#__codelineno-21-67"></a><span class="w">    </span><span class="c1">// 負荷率がしきい値を超えたら、リサイズを実行</span>
+<a id="__codelineno-21-68" name="__codelineno-21-68" href="#__codelineno-21-68"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">_loadThres</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-69" name="__codelineno-21-69" href="#__codelineno-21-69"></a><span class="w">      </span><span class="n">extend</span><span class="p">();</span>
+<a id="__codelineno-21-70" name="__codelineno-21-70" href="#__codelineno-21-70"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-71" name="__codelineno-21-71" href="#__codelineno-21-71"></a><span class="w">    </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-21-72" name="__codelineno-21-72" href="#__codelineno-21-72"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-21-73" name="__codelineno-21-73" href="#__codelineno-21-73"></a><span class="w">    </span><span class="c1">// キーと値の組が見つかったら、val を上書きして返す</span>
+<a id="__codelineno-21-74" name="__codelineno-21-74" href="#__codelineno-21-74"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">_buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">_TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-75" name="__codelineno-21-75" href="#__codelineno-21-75"></a><span class="w">      </span><span class="n">_buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">!</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-21-76" name="__codelineno-21-76" href="#__codelineno-21-76"></a><span class="w">      </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-21-77" name="__codelineno-21-77" href="#__codelineno-21-77"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-78" name="__codelineno-21-78" href="#__codelineno-21-78"></a><span class="w">    </span><span class="c1">// キーと値の組が存在しない場合は、その組を追加する</span>
+<a id="__codelineno-21-79" name="__codelineno-21-79" href="#__codelineno-21-79"></a><span class="w">    </span><span class="n">_buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-21-80" name="__codelineno-21-80" href="#__codelineno-21-80"></a><span class="w">    </span><span class="n">_size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-21-81" name="__codelineno-21-81" href="#__codelineno-21-81"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-82" name="__codelineno-21-82" href="#__codelineno-21-82"></a>
+<a id="__codelineno-21-83" name="__codelineno-21-83" href="#__codelineno-21-83"></a><span class="w">  </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-21-84" name="__codelineno-21-84" href="#__codelineno-21-84"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-85" name="__codelineno-21-85" href="#__codelineno-21-85"></a><span class="w">    </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-21-86" name="__codelineno-21-86" href="#__codelineno-21-86"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-21-87" name="__codelineno-21-87" href="#__codelineno-21-87"></a><span class="w">    </span><span class="c1">// キーと値の組が見つかったら、削除マーカーで上書きする</span>
+<a id="__codelineno-21-88" name="__codelineno-21-88" href="#__codelineno-21-88"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">_buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">_TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-89" name="__codelineno-21-89" href="#__codelineno-21-89"></a><span class="w">      </span><span class="n">_buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_TOMBSTONE</span><span class="p">;</span>
+<a id="__codelineno-21-90" name="__codelineno-21-90" href="#__codelineno-21-90"></a><span class="w">      </span><span class="n">_size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-21-91" name="__codelineno-21-91" href="#__codelineno-21-91"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-92" name="__codelineno-21-92" href="#__codelineno-21-92"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-93" name="__codelineno-21-93" href="#__codelineno-21-93"></a>
+<a id="__codelineno-21-94" name="__codelineno-21-94" href="#__codelineno-21-94"></a><span class="w">  </span><span class="cm">/* ハッシュテーブルを拡張 */</span>
+<a id="__codelineno-21-95" name="__codelineno-21-95" href="#__codelineno-21-95"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">extend</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-96" name="__codelineno-21-96" href="#__codelineno-21-96"></a><span class="w">    </span><span class="c1">// 元のハッシュテーブルを一時保存</span>
+<a id="__codelineno-21-97" name="__codelineno-21-97" href="#__codelineno-21-97"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">?&gt;</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_buckets</span><span class="p">;</span>
+<a id="__codelineno-21-98" name="__codelineno-21-98" href="#__codelineno-21-98"></a><span class="w">    </span><span class="c1">// リサイズ後の新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-21-99" name="__codelineno-21-99" href="#__codelineno-21-99"></a><span class="w">    </span><span class="n">_capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="n">_extendRatio</span><span class="p">;</span>
+<a id="__codelineno-21-100" name="__codelineno-21-100" href="#__codelineno-21-100"></a><span class="w">    </span><span class="n">_buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">generate</span><span class="p">(</span><span class="n">_capacity</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="kc">null</span><span class="p">);</span>
+<a id="__codelineno-21-101" name="__codelineno-21-101" href="#__codelineno-21-101"></a><span class="w">    </span><span class="n">_size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-21-102" name="__codelineno-21-102" href="#__codelineno-21-102"></a><span class="w">    </span><span class="c1">// キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
+<a id="__codelineno-21-103" name="__codelineno-21-103" href="#__codelineno-21-103"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="o">?</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-104" name="__codelineno-21-104" href="#__codelineno-21-104"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">_TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-105" name="__codelineno-21-105" href="#__codelineno-21-105"></a><span class="w">        </span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-21-106" name="__codelineno-21-106" href="#__codelineno-21-106"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-21-107" name="__codelineno-21-107" href="#__codelineno-21-107"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-108" name="__codelineno-21-108" href="#__codelineno-21-108"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-109" name="__codelineno-21-109" href="#__codelineno-21-109"></a>
+<a id="__codelineno-21-110" name="__codelineno-21-110" href="#__codelineno-21-110"></a><span class="w">  </span><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-21-111" name="__codelineno-21-111" href="#__codelineno-21-111"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">printHashMap</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-112" name="__codelineno-21-112" href="#__codelineno-21-112"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="o">?</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">_buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-113" name="__codelineno-21-113" href="#__codelineno-21-113"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-114" name="__codelineno-21-114" href="#__codelineno-21-114"></a><span class="w">        </span><span class="n">print</span><span class="p">(</span><span class="s2">&quot;null&quot;</span><span class="p">);</span>
+<a id="__codelineno-21-115" name="__codelineno-21-115" href="#__codelineno-21-115"></a><span class="w">      </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">_TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-116" name="__codelineno-21-116" href="#__codelineno-21-116"></a><span class="w">        </span><span class="n">print</span><span class="p">(</span><span class="s2">&quot;TOMBSTONE&quot;</span><span class="p">);</span>
+<a id="__codelineno-21-117" name="__codelineno-21-117" href="#__codelineno-21-117"></a><span class="w">      </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-118" name="__codelineno-21-118" href="#__codelineno-21-118"></a><span class="w">        </span><span class="n">print</span><span class="p">(</span><span class="s2">&quot;</span><span class="si">${</span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="si">}</span><span class="s2"> -&gt; </span><span class="si">${</span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">);</span>
+<a id="__codelineno-21-119" name="__codelineno-21-119" href="#__codelineno-21-119"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-21-120" name="__codelineno-21-120" href="#__codelineno-21-120"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-121" name="__codelineno-21-121" href="#__codelineno-21-121"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-122" name="__codelineno-21-122" href="#__codelineno-21-122"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map_open_addressing.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">HashMapOpenAddressing</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">hash_map_open_addressing.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* オープンアドレス法ハッシュテーブル */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">HashMapOpenAddressing</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="n">size</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w">                </span><span class="c1">// キーと値のペア数</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="n">capacity</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w">            </span><span class="c1">// ハッシュテーブル容量</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">    </span><span class="n">load_thres</span><span class="p">:</span><span class="w"> </span><span class="kt">f64</span><span class="p">,</span><span class="w">            </span><span class="c1">// リサイズを発動する負荷率のしきい値</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w">    </span><span class="n">extend_ratio</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w">        </span><span class="c1">// 拡張倍率</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">    </span><span class="n">buckets</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="c1">// バケット配列</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">    </span><span class="n">TOMBSTONE</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="p">,</span><span class="w">    </span><span class="c1">// 削除済みマーク</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="p">}</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="k">impl</span><span class="w"> </span><span class="n">HashMapOpenAddressing</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">new</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">        </span><span class="bp">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="w">            </span><span class="n">size</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span>
+<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="w">            </span><span class="n">capacity</span><span class="p">:</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span>
+<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="w">            </span><span class="n">load_thres</span><span class="p">:</span><span class="w"> </span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3.0</span><span class="p">,</span>
+<a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="w">            </span><span class="n">extend_ratio</span><span class="p">:</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span>
+<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="w">            </span><span class="n">buckets</span><span class="p">:</span><span class="w"> </span><span class="nc">vec</span><span class="o">!</span><span class="p">[</span><span class="nb">None</span><span class="p">;</span><span class="w"> </span><span class="mi">4</span><span class="p">],</span>
+<a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a><span class="w">            </span><span class="n">TOMBSTONE</span><span class="p">:</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-21" name="__codelineno-22-21" href="#__codelineno-22-21"></a><span class="w">                </span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">,</span>
+<a id="__codelineno-22-22" name="__codelineno-22-22" href="#__codelineno-22-22"></a><span class="w">                </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="s">&quot;-1&quot;</span><span class="p">.</span><span class="n">to_string</span><span class="p">(),</span>
+<a id="__codelineno-22-23" name="__codelineno-22-23" href="#__codelineno-22-23"></a><span class="w">            </span><span class="p">}),</span>
+<a id="__codelineno-22-24" name="__codelineno-22-24" href="#__codelineno-22-24"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-25" name="__codelineno-22-25" href="#__codelineno-22-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-26" name="__codelineno-22-26" href="#__codelineno-22-26"></a>
+<a id="__codelineno-22-27" name="__codelineno-22-27" href="#__codelineno-22-27"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-22-28" name="__codelineno-22-28" href="#__codelineno-22-28"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">hash_func</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-29" name="__codelineno-22-29" href="#__codelineno-22-29"></a><span class="w">        </span><span class="p">(</span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">capacity</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span>
+<a id="__codelineno-22-30" name="__codelineno-22-30" href="#__codelineno-22-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-31" name="__codelineno-22-31" href="#__codelineno-22-31"></a>
+<a id="__codelineno-22-32" name="__codelineno-22-32" href="#__codelineno-22-32"></a><span class="w">    </span><span class="cm">/* 負荷率 */</span>
+<a id="__codelineno-22-33" name="__codelineno-22-33" href="#__codelineno-22-33"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">load_factor</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">f64</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-34" name="__codelineno-22-34" href="#__codelineno-22-34"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">f64</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">capacity</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">f64</span>
+<a id="__codelineno-22-35" name="__codelineno-22-35" href="#__codelineno-22-35"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-36" name="__codelineno-22-36" href="#__codelineno-22-36"></a>
+<a id="__codelineno-22-37" name="__codelineno-22-37" href="#__codelineno-22-37"></a><span class="w">    </span><span class="cm">/* key に対応するバケットインデックスを探す */</span>
+<a id="__codelineno-22-38" name="__codelineno-22-38" href="#__codelineno-22-38"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">find_bucket</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-39" name="__codelineno-22-39" href="#__codelineno-22-39"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-22-40" name="__codelineno-22-40" href="#__codelineno-22-40"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">first_tombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-22-41" name="__codelineno-22-41" href="#__codelineno-22-41"></a><span class="w">        </span><span class="c1">// 線形プロービングを行い、空バケットに達したら終了</span>
+<a id="__codelineno-22-42" name="__codelineno-22-42" href="#__codelineno-22-42"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">is_some</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-43" name="__codelineno-22-43" href="#__codelineno-22-43"></a><span class="w">            </span><span class="c1">// `key` に遭遇したら、対応するバケットのインデックスを返す</span>
+<a id="__codelineno-22-44" name="__codelineno-22-44" href="#__codelineno-22-44"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">as_ref</span><span class="p">().</span><span class="n">unwrap</span><span class="p">().</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-45" name="__codelineno-22-45" href="#__codelineno-22-45"></a><span class="w">                </span><span class="c1">// 以前に削除マークに遭遇していた場合は、キーと値のペアをそのインデックスへ移動する</span>
+<a id="__codelineno-22-46" name="__codelineno-22-46" href="#__codelineno-22-46"></a><span class="w">                </span><span class="k">if</span><span class="w"> </span><span class="n">first_tombstone</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-47" name="__codelineno-22-47" href="#__codelineno-22-47"></a><span class="w">                    </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">first_tombstone</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">take</span><span class="p">();</span>
+<a id="__codelineno-22-48" name="__codelineno-22-48" href="#__codelineno-22-48"></a><span class="w">                    </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">TOMBSTONE</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-22-49" name="__codelineno-22-49" href="#__codelineno-22-49"></a><span class="w">                    </span><span class="k">return</span><span class="w"> </span><span class="n">first_tombstone</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">;</span><span class="w"> </span><span class="c1">// 移動後のバケットインデックスを返す</span>
+<a id="__codelineno-22-50" name="__codelineno-22-50" href="#__codelineno-22-50"></a><span class="w">                </span><span class="p">}</span>
+<a id="__codelineno-22-51" name="__codelineno-22-51" href="#__codelineno-22-51"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="c1">// バケットのインデックスを返す</span>
+<a id="__codelineno-22-52" name="__codelineno-22-52" href="#__codelineno-22-52"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-22-53" name="__codelineno-22-53" href="#__codelineno-22-53"></a><span class="w">            </span><span class="c1">// 最初に見つかった削除マークを記録</span>
+<a id="__codelineno-22-54" name="__codelineno-22-54" href="#__codelineno-22-54"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">first_tombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">TOMBSTONE</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-55" name="__codelineno-22-55" href="#__codelineno-22-55"></a><span class="w">                </span><span class="n">first_tombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">;</span>
+<a id="__codelineno-22-56" name="__codelineno-22-56" href="#__codelineno-22-56"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-22-57" name="__codelineno-22-57" href="#__codelineno-22-57"></a><span class="w">            </span><span class="c1">// バケットのインデックスを計算し、末尾を越えたら先頭に戻る</span>
+<a id="__codelineno-22-58" name="__codelineno-22-58" href="#__codelineno-22-58"></a><span class="w">            </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-22-59" name="__codelineno-22-59" href="#__codelineno-22-59"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-60" name="__codelineno-22-60" href="#__codelineno-22-60"></a><span class="w">        </span><span class="c1">// key が存在しない場合は追加位置のインデックスを返す</span>
+<a id="__codelineno-22-61" name="__codelineno-22-61" href="#__codelineno-22-61"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">first_tombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-62" name="__codelineno-22-62" href="#__codelineno-22-62"></a><span class="w">            </span><span class="n">index</span>
+<a id="__codelineno-22-63" name="__codelineno-22-63" href="#__codelineno-22-63"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-64" name="__codelineno-22-64" href="#__codelineno-22-64"></a><span class="w">            </span><span class="n">first_tombstone</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span>
+<a id="__codelineno-22-65" name="__codelineno-22-65" href="#__codelineno-22-65"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-66" name="__codelineno-22-66" href="#__codelineno-22-66"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-67" name="__codelineno-22-67" href="#__codelineno-22-67"></a>
+<a id="__codelineno-22-68" name="__codelineno-22-68" href="#__codelineno-22-68"></a><span class="w">    </span><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-22-69" name="__codelineno-22-69" href="#__codelineno-22-69"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="kt">str</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-70" name="__codelineno-22-70" href="#__codelineno-22-70"></a><span class="w">        </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-22-71" name="__codelineno-22-71" href="#__codelineno-22-71"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">find_bucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-22-72" name="__codelineno-22-72" href="#__codelineno-22-72"></a><span class="w">        </span><span class="c1">// キーと値の組が見つかったら、対応する val を返す</span>
+<a id="__codelineno-22-73" name="__codelineno-22-73" href="#__codelineno-22-73"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">is_some</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">TOMBSTONE</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-74" name="__codelineno-22-74" href="#__codelineno-22-74"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">as_ref</span><span class="p">().</span><span class="n">map</span><span class="p">(</span><span class="o">|</span><span class="n">pair</span><span class="o">|</span><span class="w"> </span><span class="o">&amp;</span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="o">&amp;</span><span class="kt">str</span><span class="p">);</span>
+<a id="__codelineno-22-75" name="__codelineno-22-75" href="#__codelineno-22-75"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-76" name="__codelineno-22-76" href="#__codelineno-22-76"></a><span class="w">        </span><span class="c1">// キーと値の組が存在しなければ null を返す</span>
+<a id="__codelineno-22-77" name="__codelineno-22-77" href="#__codelineno-22-77"></a><span class="w">        </span><span class="nb">None</span>
+<a id="__codelineno-22-78" name="__codelineno-22-78" href="#__codelineno-22-78"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-79" name="__codelineno-22-79" href="#__codelineno-22-79"></a>
+<a id="__codelineno-22-80" name="__codelineno-22-80" href="#__codelineno-22-80"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-22-81" name="__codelineno-22-81" href="#__codelineno-22-81"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="nb">String</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-82" name="__codelineno-22-82" href="#__codelineno-22-82"></a><span class="w">        </span><span class="c1">// 負荷率がしきい値を超えたら、リサイズを実行</span>
+<a id="__codelineno-22-83" name="__codelineno-22-83" href="#__codelineno-22-83"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">load_factor</span><span class="p">()</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">load_thres</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-84" name="__codelineno-22-84" href="#__codelineno-22-84"></a><span class="w">            </span><span class="bp">self</span><span class="p">.</span><span class="n">extend</span><span class="p">();</span>
+<a id="__codelineno-22-85" name="__codelineno-22-85" href="#__codelineno-22-85"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-86" name="__codelineno-22-86" href="#__codelineno-22-86"></a><span class="w">        </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-22-87" name="__codelineno-22-87" href="#__codelineno-22-87"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">find_bucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-22-88" name="__codelineno-22-88" href="#__codelineno-22-88"></a><span class="w">        </span><span class="c1">// キーと値の組が見つかったら、val を上書きして返す</span>
+<a id="__codelineno-22-89" name="__codelineno-22-89" href="#__codelineno-22-89"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">is_some</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">TOMBSTONE</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-90" name="__codelineno-22-90" href="#__codelineno-22-90"></a><span class="w">            </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">as_mut</span><span class="p">().</span><span class="n">unwrap</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-22-91" name="__codelineno-22-91" href="#__codelineno-22-91"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-22-92" name="__codelineno-22-92" href="#__codelineno-22-92"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-93" name="__codelineno-22-93" href="#__codelineno-22-93"></a><span class="w">        </span><span class="c1">// キーと値の組が存在しない場合は、その組を追加する</span>
+<a id="__codelineno-22-94" name="__codelineno-22-94" href="#__codelineno-22-94"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="p">});</span>
+<a id="__codelineno-22-95" name="__codelineno-22-95" href="#__codelineno-22-95"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-22-96" name="__codelineno-22-96" href="#__codelineno-22-96"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-97" name="__codelineno-22-97" href="#__codelineno-22-97"></a>
+<a id="__codelineno-22-98" name="__codelineno-22-98" href="#__codelineno-22-98"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-22-99" name="__codelineno-22-99" href="#__codelineno-22-99"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-100" name="__codelineno-22-100" href="#__codelineno-22-100"></a><span class="w">        </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-22-101" name="__codelineno-22-101" href="#__codelineno-22-101"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">find_bucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-22-102" name="__codelineno-22-102" href="#__codelineno-22-102"></a><span class="w">        </span><span class="c1">// キーと値の組が見つかったら、削除マーカーで上書きする</span>
+<a id="__codelineno-22-103" name="__codelineno-22-103" href="#__codelineno-22-103"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">is_some</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">TOMBSTONE</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-104" name="__codelineno-22-104" href="#__codelineno-22-104"></a><span class="w">            </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">TOMBSTONE</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-22-105" name="__codelineno-22-105" href="#__codelineno-22-105"></a><span class="w">            </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-22-106" name="__codelineno-22-106" href="#__codelineno-22-106"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-107" name="__codelineno-22-107" href="#__codelineno-22-107"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-108" name="__codelineno-22-108" href="#__codelineno-22-108"></a>
+<a id="__codelineno-22-109" name="__codelineno-22-109" href="#__codelineno-22-109"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを拡張 */</span>
+<a id="__codelineno-22-110" name="__codelineno-22-110" href="#__codelineno-22-110"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">extend</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-111" name="__codelineno-22-111" href="#__codelineno-22-111"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルを一時保存</span>
+<a id="__codelineno-22-112" name="__codelineno-22-112" href="#__codelineno-22-112"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">buckets_tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-22-113" name="__codelineno-22-113" href="#__codelineno-22-113"></a><span class="w">        </span><span class="c1">// リサイズ後の新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-22-114" name="__codelineno-22-114" href="#__codelineno-22-114"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">extend_ratio</span><span class="p">;</span>
+<a id="__codelineno-22-115" name="__codelineno-22-115" href="#__codelineno-22-115"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="nb">None</span><span class="p">;</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">capacity</span><span class="p">];</span>
+<a id="__codelineno-22-116" name="__codelineno-22-116" href="#__codelineno-22-116"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-22-117" name="__codelineno-22-117" href="#__codelineno-22-117"></a>
+<a id="__codelineno-22-118" name="__codelineno-22-118" href="#__codelineno-22-118"></a><span class="w">        </span><span class="c1">// キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
+<a id="__codelineno-22-119" name="__codelineno-22-119" href="#__codelineno-22-119"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets_tmp</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-120" name="__codelineno-22-120" href="#__codelineno-22-120"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">TOMBSTONE</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-121" name="__codelineno-22-121" href="#__codelineno-22-121"></a><span class="w">                </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-22-122" name="__codelineno-22-122" href="#__codelineno-22-122"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-22-123" name="__codelineno-22-123" href="#__codelineno-22-123"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">unwrap</span><span class="p">();</span>
+<a id="__codelineno-22-124" name="__codelineno-22-124" href="#__codelineno-22-124"></a>
+<a id="__codelineno-22-125" name="__codelineno-22-125" href="#__codelineno-22-125"></a><span class="w">            </span><span class="bp">self</span><span class="p">.</span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-22-126" name="__codelineno-22-126" href="#__codelineno-22-126"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-127" name="__codelineno-22-127" href="#__codelineno-22-127"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-128" name="__codelineno-22-128" href="#__codelineno-22-128"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-22-129" name="__codelineno-22-129" href="#__codelineno-22-129"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">print</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-130" name="__codelineno-22-130" href="#__codelineno-22-130"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="o">&amp;</span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-131" name="__codelineno-22-131" href="#__codelineno-22-131"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-132" name="__codelineno-22-132" href="#__codelineno-22-132"></a><span class="w">                </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;null&quot;</span><span class="p">);</span>
+<a id="__codelineno-22-133" name="__codelineno-22-133" href="#__codelineno-22-133"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">&amp;</span><span class="bp">self</span><span class="p">.</span><span class="n">TOMBSTONE</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-134" name="__codelineno-22-134" href="#__codelineno-22-134"></a><span class="w">                </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;TOMBSTONE&quot;</span><span class="p">);</span>
+<a id="__codelineno-22-135" name="__codelineno-22-135" href="#__codelineno-22-135"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-136" name="__codelineno-22-136" href="#__codelineno-22-136"></a><span class="w">                </span><span class="kd">let</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">as_ref</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span>
+<a id="__codelineno-22-137" name="__codelineno-22-137" href="#__codelineno-22-137"></a><span class="w">                </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{} -&gt; {}&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-22-138" name="__codelineno-22-138" href="#__codelineno-22-138"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-22-139" name="__codelineno-22-139" href="#__codelineno-22-139"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-140" name="__codelineno-22-140" href="#__codelineno-22-140"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-141" name="__codelineno-22-141" href="#__codelineno-22-141"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map_open_addressing.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">HashMapOpenAddressing</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">hash_map_open_addressing.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* オープンアドレス法ハッシュテーブル */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w">         </span><span class="c1">// キーと値のペア数</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span><span class="w">     </span><span class="c1">// ハッシュテーブル容量</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">    </span><span class="kt">double</span><span class="w"> </span><span class="n">loadThres</span><span class="p">;</span><span class="w"> </span><span class="c1">// リサイズを発動する負荷率のしきい値</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span><span class="w">  </span><span class="c1">// 拡張倍率</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w">    </span><span class="n">Pair</span><span class="w"> </span><span class="o">**</span><span class="n">buckets</span><span class="p">;</span><span class="w">   </span><span class="c1">// バケット配列</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w">    </span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">TOMBSTONE</span><span class="p">;</span><span class="w">  </span><span class="c1">// 削除済みマーク</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="p">}</span><span class="w"> </span><span class="n">HashMapOpenAddressing</span><span class="p">;</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="n">HashMapOpenAddressing</span><span class="w"> </span><span class="o">*</span><span class="nf">newHashMapOpenAddressing</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w">    </span><span class="n">HashMapOpenAddressing</span><span class="w"> </span><span class="o">*</span><span class="n">hashMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">HashMapOpenAddressing</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">HashMapOpenAddressing</span><span class="p">));</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w">    </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="w">    </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">4</span><span class="p">;</span>
+<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="w">    </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">loadThres</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3.0</span><span class="p">;</span>
+<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="w">    </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="w">    </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">**</span><span class="p">)</span><span class="n">calloc</span><span class="p">(</span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="p">));</span>
+<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="w">    </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">TOMBSTONE</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">Pair</span><span class="p">));</span>
+<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="w">    </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">TOMBSTONE</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a><span class="w">    </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">TOMBSTONE</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;-1&quot;</span><span class="p">;</span>
+<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a>
+<a id="__codelineno-23-23" name="__codelineno-23-23" href="#__codelineno-23-23"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">hashMap</span><span class="p">;</span>
+<a id="__codelineno-23-24" name="__codelineno-23-24" href="#__codelineno-23-24"></a><span class="p">}</span>
+<a id="__codelineno-23-25" name="__codelineno-23-25" href="#__codelineno-23-25"></a>
+<a id="__codelineno-23-26" name="__codelineno-23-26" href="#__codelineno-23-26"></a><span class="cm">/* デストラクタ */</span>
+<a id="__codelineno-23-27" name="__codelineno-23-27" href="#__codelineno-23-27"></a><span class="kt">void</span><span class="w"> </span><span class="nf">delHashMapOpenAddressing</span><span class="p">(</span><span class="n">HashMapOpenAddressing</span><span class="w"> </span><span class="o">*</span><span class="n">hashMap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-28" name="__codelineno-23-28" href="#__codelineno-23-28"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-29" name="__codelineno-23-29" href="#__codelineno-23-29"></a><span class="w">        </span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-23-30" name="__codelineno-23-30" href="#__codelineno-23-30"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-31" name="__codelineno-23-31" href="#__codelineno-23-31"></a><span class="w">            </span><span class="n">free</span><span class="p">(</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-23-32" name="__codelineno-23-32" href="#__codelineno-23-32"></a><span class="w">            </span><span class="n">free</span><span class="p">(</span><span class="n">pair</span><span class="p">);</span>
+<a id="__codelineno-23-33" name="__codelineno-23-33" href="#__codelineno-23-33"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-34" name="__codelineno-23-34" href="#__codelineno-23-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-35" name="__codelineno-23-35" href="#__codelineno-23-35"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">);</span>
+<a id="__codelineno-23-36" name="__codelineno-23-36" href="#__codelineno-23-36"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">TOMBSTONE</span><span class="p">);</span>
+<a id="__codelineno-23-37" name="__codelineno-23-37" href="#__codelineno-23-37"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">hashMap</span><span class="p">);</span>
+<a id="__codelineno-23-38" name="__codelineno-23-38" href="#__codelineno-23-38"></a><span class="p">}</span>
+<a id="__codelineno-23-39" name="__codelineno-23-39" href="#__codelineno-23-39"></a>
+<a id="__codelineno-23-40" name="__codelineno-23-40" href="#__codelineno-23-40"></a><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-23-41" name="__codelineno-23-41" href="#__codelineno-23-41"></a><span class="kt">int</span><span class="w"> </span><span class="nf">hashFunc</span><span class="p">(</span><span class="n">HashMapOpenAddressing</span><span class="w"> </span><span class="o">*</span><span class="n">hashMap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-42" name="__codelineno-23-42" href="#__codelineno-23-42"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-23-43" name="__codelineno-23-43" href="#__codelineno-23-43"></a><span class="p">}</span>
+<a id="__codelineno-23-44" name="__codelineno-23-44" href="#__codelineno-23-44"></a>
+<a id="__codelineno-23-45" name="__codelineno-23-45" href="#__codelineno-23-45"></a><span class="cm">/* 負荷率 */</span>
+<a id="__codelineno-23-46" name="__codelineno-23-46" href="#__codelineno-23-46"></a><span class="kt">double</span><span class="w"> </span><span class="nf">loadFactor</span><span class="p">(</span><span class="n">HashMapOpenAddressing</span><span class="w"> </span><span class="o">*</span><span class="n">hashMap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-47" name="__codelineno-23-47" href="#__codelineno-23-47"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-23-48" name="__codelineno-23-48" href="#__codelineno-23-48"></a><span class="p">}</span>
+<a id="__codelineno-23-49" name="__codelineno-23-49" href="#__codelineno-23-49"></a>
+<a id="__codelineno-23-50" name="__codelineno-23-50" href="#__codelineno-23-50"></a><span class="cm">/* key に対応するバケットインデックスを探す */</span>
+<a id="__codelineno-23-51" name="__codelineno-23-51" href="#__codelineno-23-51"></a><span class="kt">int</span><span class="w"> </span><span class="nf">findBucket</span><span class="p">(</span><span class="n">HashMapOpenAddressing</span><span class="w"> </span><span class="o">*</span><span class="n">hashMap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-52" name="__codelineno-23-52" href="#__codelineno-23-52"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">hashMap</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-23-53" name="__codelineno-23-53" href="#__codelineno-23-53"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-23-54" name="__codelineno-23-54" href="#__codelineno-23-54"></a><span class="w">    </span><span class="c1">// 線形プロービングを行い、空バケットに達したら終了</span>
+<a id="__codelineno-23-55" name="__codelineno-23-55" href="#__codelineno-23-55"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-56" name="__codelineno-23-56" href="#__codelineno-23-56"></a><span class="w">        </span><span class="c1">// key が見つかったら、対応するバケットのインデックスを返す</span>
+<a id="__codelineno-23-57" name="__codelineno-23-57" href="#__codelineno-23-57"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-58" name="__codelineno-23-58" href="#__codelineno-23-58"></a><span class="w">            </span><span class="c1">// 以前に削除マークが見つかっていれば、そのインデックスへキーと値のペアを移動</span>
+<a id="__codelineno-23-59" name="__codelineno-23-59" href="#__codelineno-23-59"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">-1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-60" name="__codelineno-23-60" href="#__codelineno-23-60"></a><span class="w">                </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">firstTombstone</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-23-61" name="__codelineno-23-61" href="#__codelineno-23-61"></a><span class="w">                </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">TOMBSTONE</span><span class="p">;</span>
+<a id="__codelineno-23-62" name="__codelineno-23-62" href="#__codelineno-23-62"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="n">firstTombstone</span><span class="p">;</span><span class="w"> </span><span class="c1">// 移動後のバケットインデックスを返す</span>
+<a id="__codelineno-23-63" name="__codelineno-23-63" href="#__codelineno-23-63"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-23-64" name="__codelineno-23-64" href="#__codelineno-23-64"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="c1">// バケットのインデックスを返す</span>
+<a id="__codelineno-23-65" name="__codelineno-23-65" href="#__codelineno-23-65"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-66" name="__codelineno-23-66" href="#__codelineno-23-66"></a><span class="w">        </span><span class="c1">// 最初に見つかった削除マークを記録</span>
+<a id="__codelineno-23-67" name="__codelineno-23-67" href="#__codelineno-23-67"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">-1</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-68" name="__codelineno-23-68" href="#__codelineno-23-68"></a><span class="w">            </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
+<a id="__codelineno-23-69" name="__codelineno-23-69" href="#__codelineno-23-69"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-70" name="__codelineno-23-70" href="#__codelineno-23-70"></a><span class="w">        </span><span class="c1">// バケットのインデックスを計算し、末尾を越えたら先頭に戻る</span>
+<a id="__codelineno-23-71" name="__codelineno-23-71" href="#__codelineno-23-71"></a><span class="w">        </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-23-72" name="__codelineno-23-72" href="#__codelineno-23-72"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-73" name="__codelineno-23-73" href="#__codelineno-23-73"></a><span class="w">    </span><span class="c1">// key が存在しない場合は追加位置のインデックスを返す</span>
+<a id="__codelineno-23-74" name="__codelineno-23-74" href="#__codelineno-23-74"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">-1</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">firstTombstone</span><span class="p">;</span>
+<a id="__codelineno-23-75" name="__codelineno-23-75" href="#__codelineno-23-75"></a><span class="p">}</span>
+<a id="__codelineno-23-76" name="__codelineno-23-76" href="#__codelineno-23-76"></a>
+<a id="__codelineno-23-77" name="__codelineno-23-77" href="#__codelineno-23-77"></a><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-23-78" name="__codelineno-23-78" href="#__codelineno-23-78"></a><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="nf">get</span><span class="p">(</span><span class="n">HashMapOpenAddressing</span><span class="w"> </span><span class="o">*</span><span class="n">hashMap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-79" name="__codelineno-23-79" href="#__codelineno-23-79"></a><span class="w">    </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-23-80" name="__codelineno-23-80" href="#__codelineno-23-80"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">hashMap</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-23-81" name="__codelineno-23-81" href="#__codelineno-23-81"></a><span class="w">    </span><span class="c1">// キーと値の組が見つかったら、対応する val を返す</span>
+<a id="__codelineno-23-82" name="__codelineno-23-82" href="#__codelineno-23-82"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-83" name="__codelineno-23-83" href="#__codelineno-23-83"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-23-84" name="__codelineno-23-84" href="#__codelineno-23-84"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-85" name="__codelineno-23-85" href="#__codelineno-23-85"></a><span class="w">    </span><span class="c1">// キーと値の組が存在しない場合は空文字列を返す</span>
+<a id="__codelineno-23-86" name="__codelineno-23-86" href="#__codelineno-23-86"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="s">&quot;&quot;</span><span class="p">;</span>
+<a id="__codelineno-23-87" name="__codelineno-23-87" href="#__codelineno-23-87"></a><span class="p">}</span>
+<a id="__codelineno-23-88" name="__codelineno-23-88" href="#__codelineno-23-88"></a>
+<a id="__codelineno-23-89" name="__codelineno-23-89" href="#__codelineno-23-89"></a><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-23-90" name="__codelineno-23-90" href="#__codelineno-23-90"></a><span class="kt">void</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="n">HashMapOpenAddressing</span><span class="w"> </span><span class="o">*</span><span class="n">hashMap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-91" name="__codelineno-23-91" href="#__codelineno-23-91"></a><span class="w">    </span><span class="c1">// 負荷率がしきい値を超えたら、リサイズを実行</span>
+<a id="__codelineno-23-92" name="__codelineno-23-92" href="#__codelineno-23-92"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">loadFactor</span><span class="p">(</span><span class="n">hashMap</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">loadThres</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-93" name="__codelineno-23-93" href="#__codelineno-23-93"></a><span class="w">        </span><span class="n">extend</span><span class="p">(</span><span class="n">hashMap</span><span class="p">);</span>
+<a id="__codelineno-23-94" name="__codelineno-23-94" href="#__codelineno-23-94"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-95" name="__codelineno-23-95" href="#__codelineno-23-95"></a><span class="w">    </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-23-96" name="__codelineno-23-96" href="#__codelineno-23-96"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">hashMap</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-23-97" name="__codelineno-23-97" href="#__codelineno-23-97"></a><span class="w">    </span><span class="c1">// キーと値の組が見つかったら、val を上書きして返す</span>
+<a id="__codelineno-23-98" name="__codelineno-23-98" href="#__codelineno-23-98"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-99" name="__codelineno-23-99" href="#__codelineno-23-99"></a><span class="w">        </span><span class="n">free</span><span class="p">(</span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-23-100" name="__codelineno-23-100" href="#__codelineno-23-100"></a><span class="w">        </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">strlen</span><span class="p">(</span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">));</span>
+<a id="__codelineno-23-101" name="__codelineno-23-101" href="#__codelineno-23-101"></a><span class="w">        </span><span class="n">strcpy</span><span class="p">(</span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-23-102" name="__codelineno-23-102" href="#__codelineno-23-102"></a><span class="w">        </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">[</span><span class="n">strlen</span><span class="p">(</span><span class="n">val</span><span class="p">)]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="sc">&#39;\0&#39;</span><span class="p">;</span>
+<a id="__codelineno-23-103" name="__codelineno-23-103" href="#__codelineno-23-103"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-23-104" name="__codelineno-23-104" href="#__codelineno-23-104"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-105" name="__codelineno-23-105" href="#__codelineno-23-105"></a><span class="w">    </span><span class="c1">// キーと値の組が存在しない場合は、その組を追加する</span>
+<a id="__codelineno-23-106" name="__codelineno-23-106" href="#__codelineno-23-106"></a><span class="w">    </span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">Pair</span><span class="p">));</span>
+<a id="__codelineno-23-107" name="__codelineno-23-107" href="#__codelineno-23-107"></a><span class="w">    </span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="p">;</span>
+<a id="__codelineno-23-108" name="__codelineno-23-108" href="#__codelineno-23-108"></a><span class="w">    </span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">strlen</span><span class="p">(</span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">));</span>
+<a id="__codelineno-23-109" name="__codelineno-23-109" href="#__codelineno-23-109"></a><span class="w">    </span><span class="n">strcpy</span><span class="p">(</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-23-110" name="__codelineno-23-110" href="#__codelineno-23-110"></a><span class="w">    </span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">[</span><span class="n">strlen</span><span class="p">(</span><span class="n">val</span><span class="p">)]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="sc">&#39;\0&#39;</span><span class="p">;</span>
+<a id="__codelineno-23-111" name="__codelineno-23-111" href="#__codelineno-23-111"></a>
+<a id="__codelineno-23-112" name="__codelineno-23-112" href="#__codelineno-23-112"></a><span class="w">    </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pair</span><span class="p">;</span>
+<a id="__codelineno-23-113" name="__codelineno-23-113" href="#__codelineno-23-113"></a><span class="w">    </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-23-114" name="__codelineno-23-114" href="#__codelineno-23-114"></a><span class="p">}</span>
+<a id="__codelineno-23-115" name="__codelineno-23-115" href="#__codelineno-23-115"></a>
+<a id="__codelineno-23-116" name="__codelineno-23-116" href="#__codelineno-23-116"></a><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-23-117" name="__codelineno-23-117" href="#__codelineno-23-117"></a><span class="kt">void</span><span class="w"> </span><span class="nf">removeItem</span><span class="p">(</span><span class="n">HashMapOpenAddressing</span><span class="w"> </span><span class="o">*</span><span class="n">hashMap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-118" name="__codelineno-23-118" href="#__codelineno-23-118"></a><span class="w">    </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-23-119" name="__codelineno-23-119" href="#__codelineno-23-119"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">hashMap</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-23-120" name="__codelineno-23-120" href="#__codelineno-23-120"></a><span class="w">    </span><span class="c1">// キーと値の組が見つかったら、削除マーカーで上書きする</span>
+<a id="__codelineno-23-121" name="__codelineno-23-121" href="#__codelineno-23-121"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-122" name="__codelineno-23-122" href="#__codelineno-23-122"></a><span class="w">        </span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-23-123" name="__codelineno-23-123" href="#__codelineno-23-123"></a><span class="w">        </span><span class="n">free</span><span class="p">(</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-23-124" name="__codelineno-23-124" href="#__codelineno-23-124"></a><span class="w">        </span><span class="n">free</span><span class="p">(</span><span class="n">pair</span><span class="p">);</span>
+<a id="__codelineno-23-125" name="__codelineno-23-125" href="#__codelineno-23-125"></a><span class="w">        </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">TOMBSTONE</span><span class="p">;</span>
+<a id="__codelineno-23-126" name="__codelineno-23-126" href="#__codelineno-23-126"></a><span class="w">        </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-23-127" name="__codelineno-23-127" href="#__codelineno-23-127"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-128" name="__codelineno-23-128" href="#__codelineno-23-128"></a><span class="p">}</span>
+<a id="__codelineno-23-129" name="__codelineno-23-129" href="#__codelineno-23-129"></a>
+<a id="__codelineno-23-130" name="__codelineno-23-130" href="#__codelineno-23-130"></a><span class="cm">/* ハッシュテーブルを拡張 */</span>
+<a id="__codelineno-23-131" name="__codelineno-23-131" href="#__codelineno-23-131"></a><span class="kt">void</span><span class="w"> </span><span class="nf">extend</span><span class="p">(</span><span class="n">HashMapOpenAddressing</span><span class="w"> </span><span class="o">*</span><span class="n">hashMap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-132" name="__codelineno-23-132" href="#__codelineno-23-132"></a><span class="w">    </span><span class="c1">// 元のハッシュテーブルを一時保存</span>
+<a id="__codelineno-23-133" name="__codelineno-23-133" href="#__codelineno-23-133"></a><span class="w">    </span><span class="n">Pair</span><span class="w"> </span><span class="o">**</span><span class="n">bucketsTmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">;</span>
+<a id="__codelineno-23-134" name="__codelineno-23-134" href="#__codelineno-23-134"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">oldCapacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-23-135" name="__codelineno-23-135" href="#__codelineno-23-135"></a><span class="w">    </span><span class="c1">// リサイズ後の新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-23-136" name="__codelineno-23-136" href="#__codelineno-23-136"></a><span class="w">    </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">extendRatio</span><span class="p">;</span>
+<a id="__codelineno-23-137" name="__codelineno-23-137" href="#__codelineno-23-137"></a><span class="w">    </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">**</span><span class="p">)</span><span class="n">calloc</span><span class="p">(</span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="p">));</span>
+<a id="__codelineno-23-138" name="__codelineno-23-138" href="#__codelineno-23-138"></a><span class="w">    </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-23-139" name="__codelineno-23-139" href="#__codelineno-23-139"></a><span class="w">    </span><span class="c1">// キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
+<a id="__codelineno-23-140" name="__codelineno-23-140" href="#__codelineno-23-140"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">oldCapacity</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-141" name="__codelineno-23-141" href="#__codelineno-23-141"></a><span class="w">        </span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-23-142" name="__codelineno-23-142" href="#__codelineno-23-142"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-143" name="__codelineno-23-143" href="#__codelineno-23-143"></a><span class="w">            </span><span class="n">put</span><span class="p">(</span><span class="n">hashMap</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-23-144" name="__codelineno-23-144" href="#__codelineno-23-144"></a><span class="w">            </span><span class="n">free</span><span class="p">(</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-23-145" name="__codelineno-23-145" href="#__codelineno-23-145"></a><span class="w">            </span><span class="n">free</span><span class="p">(</span><span class="n">pair</span><span class="p">);</span>
+<a id="__codelineno-23-146" name="__codelineno-23-146" href="#__codelineno-23-146"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-147" name="__codelineno-23-147" href="#__codelineno-23-147"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-148" name="__codelineno-23-148" href="#__codelineno-23-148"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">bucketsTmp</span><span class="p">);</span>
+<a id="__codelineno-23-149" name="__codelineno-23-149" href="#__codelineno-23-149"></a><span class="p">}</span>
+<a id="__codelineno-23-150" name="__codelineno-23-150" href="#__codelineno-23-150"></a>
+<a id="__codelineno-23-151" name="__codelineno-23-151" href="#__codelineno-23-151"></a><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-23-152" name="__codelineno-23-152" href="#__codelineno-23-152"></a><span class="kt">void</span><span class="w"> </span><span class="nf">print</span><span class="p">(</span><span class="n">HashMapOpenAddressing</span><span class="w"> </span><span class="o">*</span><span class="n">hashMap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-153" name="__codelineno-23-153" href="#__codelineno-23-153"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-154" name="__codelineno-23-154" href="#__codelineno-23-154"></a><span class="w">        </span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-23-155" name="__codelineno-23-155" href="#__codelineno-23-155"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-156" name="__codelineno-23-156" href="#__codelineno-23-156"></a><span class="w">            </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;NULL</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">);</span>
+<a id="__codelineno-23-157" name="__codelineno-23-157" href="#__codelineno-23-157"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-158" name="__codelineno-23-158" href="#__codelineno-23-158"></a><span class="w">            </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;TOMBSTONE</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">);</span>
+<a id="__codelineno-23-159" name="__codelineno-23-159" href="#__codelineno-23-159"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-160" name="__codelineno-23-160" href="#__codelineno-23-160"></a><span class="w">            </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d -&gt; %s</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-23-161" name="__codelineno-23-161" href="#__codelineno-23-161"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-162" name="__codelineno-23-162" href="#__codelineno-23-162"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-163" name="__codelineno-23-163" href="#__codelineno-23-163"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map_open_addressing.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">HashMapOpenAddressing</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">hash_map_open_addressing.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* オープンアドレス法ハッシュテーブル */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">HashMapOpenAddressing</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">size</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w">               </span><span class="c1">// キーと値のペア数</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">capacity</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w">           </span><span class="c1">// ハッシュテーブル容量</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">loadThres</span><span class="p">:</span><span class="w"> </span><span class="kt">Double</span><span class="w">       </span><span class="c1">// リサイズを発動する負荷率のしきい値</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">extendRatio</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w">        </span><span class="c1">// 拡張倍率</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">buckets</span><span class="p">:</span><span class="w"> </span><span class="n">Array</span><span class="o">&lt;</span><span class="n">Pair?&gt;</span><span class="w">   </span><span class="c1">// バケット配列</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">TOMBSTONE</span><span class="p">:</span><span class="w"> </span><span class="n">Pair</span><span class="w">         </span><span class="c1">// 削除済みマーク</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="w">    </span><span class="k">init</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">        </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w">        </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">4</span>
+<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w">        </span><span class="n">loadThres</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">3.0</span>
+<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="w">        </span><span class="n">extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2</span>
+<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arrayOfNulls</span><span class="p">(</span><span class="n">capacity</span><span class="p">)</span>
+<a id="__codelineno-24-17" name="__codelineno-24-17" href="#__codelineno-24-17"></a><span class="w">        </span><span class="n">TOMBSTONE</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="o">-</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;-1&quot;</span><span class="p">)</span>
+<a id="__codelineno-24-18" name="__codelineno-24-18" href="#__codelineno-24-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-19" name="__codelineno-24-19" href="#__codelineno-24-19"></a>
+<a id="__codelineno-24-20" name="__codelineno-24-20" href="#__codelineno-24-20"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-24-21" name="__codelineno-24-21" href="#__codelineno-24-21"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-22" name="__codelineno-24-22" href="#__codelineno-24-22"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span>
+<a id="__codelineno-24-23" name="__codelineno-24-23" href="#__codelineno-24-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-24" name="__codelineno-24-24" href="#__codelineno-24-24"></a>
+<a id="__codelineno-24-25" name="__codelineno-24-25" href="#__codelineno-24-25"></a><span class="w">    </span><span class="cm">/* 負荷率 */</span>
+<a id="__codelineno-24-26" name="__codelineno-24-26" href="#__codelineno-24-26"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">loadFactor</span><span class="p">():</span><span class="w"> </span><span class="kt">Double</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-27" name="__codelineno-24-27" href="#__codelineno-24-27"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">capacity</span><span class="p">).</span><span class="na">toDouble</span><span class="p">()</span>
+<a id="__codelineno-24-28" name="__codelineno-24-28" href="#__codelineno-24-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-29" name="__codelineno-24-29" href="#__codelineno-24-29"></a>
+<a id="__codelineno-24-30" name="__codelineno-24-30" href="#__codelineno-24-30"></a><span class="w">    </span><span class="cm">/* key に対応するバケットインデックスを探す */</span>
+<a id="__codelineno-24-31" name="__codelineno-24-31" href="#__codelineno-24-31"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-32" name="__codelineno-24-32" href="#__codelineno-24-32"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-24-33" name="__codelineno-24-33" href="#__codelineno-24-33"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="m">1</span>
+<a id="__codelineno-24-34" name="__codelineno-24-34" href="#__codelineno-24-34"></a><span class="w">        </span><span class="c1">// 線形プロービングを行い、空バケットに達したら終了</span>
+<a id="__codelineno-24-35" name="__codelineno-24-35" href="#__codelineno-24-35"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-36" name="__codelineno-24-36" href="#__codelineno-24-36"></a><span class="w">            </span><span class="c1">// key が見つかったら、対応するバケットのインデックスを返す</span>
+<a id="__codelineno-24-37" name="__codelineno-24-37" href="#__codelineno-24-37"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]?.</span><span class="na">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-38" name="__codelineno-24-38" href="#__codelineno-24-38"></a><span class="w">                </span><span class="c1">// 以前に削除マークが見つかっていれば、そのインデックスへキーと値のペアを移動</span>
+<a id="__codelineno-24-39" name="__codelineno-24-39" href="#__codelineno-24-39"></a><span class="w">                </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-40" name="__codelineno-24-40" href="#__codelineno-24-40"></a><span class="w">                    </span><span class="n">buckets</span><span class="o">[</span><span class="n">firstTombstone</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span>
+<a id="__codelineno-24-41" name="__codelineno-24-41" href="#__codelineno-24-41"></a><span class="w">                    </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TOMBSTONE</span>
+<a id="__codelineno-24-42" name="__codelineno-24-42" href="#__codelineno-24-42"></a><span class="w">                    </span><span class="k">return</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="c1">// 移動後のバケットインデックスを返す</span>
+<a id="__codelineno-24-43" name="__codelineno-24-43" href="#__codelineno-24-43"></a><span class="w">                </span><span class="p">}</span>
+<a id="__codelineno-24-44" name="__codelineno-24-44" href="#__codelineno-24-44"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="c1">// バケットのインデックスを返す</span>
+<a id="__codelineno-24-45" name="__codelineno-24-45" href="#__codelineno-24-45"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-24-46" name="__codelineno-24-46" href="#__codelineno-24-46"></a><span class="w">            </span><span class="c1">// 最初に見つかった削除マークを記録</span>
+<a id="__codelineno-24-47" name="__codelineno-24-47" href="#__codelineno-24-47"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-48" name="__codelineno-24-48" href="#__codelineno-24-48"></a><span class="w">                </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span>
+<a id="__codelineno-24-49" name="__codelineno-24-49" href="#__codelineno-24-49"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-24-50" name="__codelineno-24-50" href="#__codelineno-24-50"></a><span class="w">            </span><span class="c1">// バケットのインデックスを計算し、末尾を越えたら先頭に戻る</span>
+<a id="__codelineno-24-51" name="__codelineno-24-51" href="#__codelineno-24-51"></a><span class="w">            </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span>
+<a id="__codelineno-24-52" name="__codelineno-24-52" href="#__codelineno-24-52"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-24-53" name="__codelineno-24-53" href="#__codelineno-24-53"></a><span class="w">        </span><span class="c1">// key が存在しない場合は追加位置のインデックスを返す</span>
+<a id="__codelineno-24-54" name="__codelineno-24-54" href="#__codelineno-24-54"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="n">firstTombstone</span>
+<a id="__codelineno-24-55" name="__codelineno-24-55" href="#__codelineno-24-55"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-56" name="__codelineno-24-56" href="#__codelineno-24-56"></a>
+<a id="__codelineno-24-57" name="__codelineno-24-57" href="#__codelineno-24-57"></a><span class="w">    </span><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-24-58" name="__codelineno-24-58" href="#__codelineno-24-58"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">String?</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-59" name="__codelineno-24-59" href="#__codelineno-24-59"></a><span class="w">        </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-24-60" name="__codelineno-24-60" href="#__codelineno-24-60"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-24-61" name="__codelineno-24-61" href="#__codelineno-24-61"></a><span class="w">        </span><span class="c1">// キーと値の組が見つかったら、対応する val を返す</span>
+<a id="__codelineno-24-62" name="__codelineno-24-62" href="#__codelineno-24-62"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-63" name="__codelineno-24-63" href="#__codelineno-24-63"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]?.</span><span class="na">_val</span>
+<a id="__codelineno-24-64" name="__codelineno-24-64" href="#__codelineno-24-64"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-24-65" name="__codelineno-24-65" href="#__codelineno-24-65"></a><span class="w">        </span><span class="c1">// キーと値の組が存在しなければ null を返す</span>
+<a id="__codelineno-24-66" name="__codelineno-24-66" href="#__codelineno-24-66"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span>
+<a id="__codelineno-24-67" name="__codelineno-24-67" href="#__codelineno-24-67"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-68" name="__codelineno-24-68" href="#__codelineno-24-68"></a>
+<a id="__codelineno-24-69" name="__codelineno-24-69" href="#__codelineno-24-69"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-24-70" name="__codelineno-24-70" href="#__codelineno-24-70"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">:</span><span class="w"> </span><span class="kt">String</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-71" name="__codelineno-24-71" href="#__codelineno-24-71"></a><span class="w">        </span><span class="c1">// 負荷率がしきい値を超えたら、リサイズを実行</span>
+<a id="__codelineno-24-72" name="__codelineno-24-72" href="#__codelineno-24-72"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">loadThres</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-73" name="__codelineno-24-73" href="#__codelineno-24-73"></a><span class="w">            </span><span class="n">extend</span><span class="p">()</span>
+<a id="__codelineno-24-74" name="__codelineno-24-74" href="#__codelineno-24-74"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-24-75" name="__codelineno-24-75" href="#__codelineno-24-75"></a><span class="w">        </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-24-76" name="__codelineno-24-76" href="#__codelineno-24-76"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-24-77" name="__codelineno-24-77" href="#__codelineno-24-77"></a><span class="w">        </span><span class="c1">// キーと値の組が見つかったら、val を上書きして返す</span>
+<a id="__codelineno-24-78" name="__codelineno-24-78" href="#__codelineno-24-78"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-79" name="__codelineno-24-79" href="#__codelineno-24-79"></a><span class="w">            </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]!!</span><span class="p">.</span><span class="na">_val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_val</span>
+<a id="__codelineno-24-80" name="__codelineno-24-80" href="#__codelineno-24-80"></a><span class="w">            </span><span class="k">return</span>
+<a id="__codelineno-24-81" name="__codelineno-24-81" href="#__codelineno-24-81"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-24-82" name="__codelineno-24-82" href="#__codelineno-24-82"></a><span class="w">        </span><span class="c1">// キーと値の組が存在しない場合は、その組を追加する</span>
+<a id="__codelineno-24-83" name="__codelineno-24-83" href="#__codelineno-24-83"></a><span class="w">        </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">)</span>
+<a id="__codelineno-24-84" name="__codelineno-24-84" href="#__codelineno-24-84"></a><span class="w">        </span><span class="n">size</span><span class="o">++</span>
+<a id="__codelineno-24-85" name="__codelineno-24-85" href="#__codelineno-24-85"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-86" name="__codelineno-24-86" href="#__codelineno-24-86"></a>
+<a id="__codelineno-24-87" name="__codelineno-24-87" href="#__codelineno-24-87"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-24-88" name="__codelineno-24-88" href="#__codelineno-24-88"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-89" name="__codelineno-24-89" href="#__codelineno-24-89"></a><span class="w">        </span><span class="c1">// key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-24-90" name="__codelineno-24-90" href="#__codelineno-24-90"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-24-91" name="__codelineno-24-91" href="#__codelineno-24-91"></a><span class="w">        </span><span class="c1">// キーと値の組が見つかったら、削除マーカーで上書きする</span>
+<a id="__codelineno-24-92" name="__codelineno-24-92" href="#__codelineno-24-92"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-93" name="__codelineno-24-93" href="#__codelineno-24-93"></a><span class="w">            </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TOMBSTONE</span>
+<a id="__codelineno-24-94" name="__codelineno-24-94" href="#__codelineno-24-94"></a><span class="w">            </span><span class="n">size</span><span class="o">--</span>
+<a id="__codelineno-24-95" name="__codelineno-24-95" href="#__codelineno-24-95"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-24-96" name="__codelineno-24-96" href="#__codelineno-24-96"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-97" name="__codelineno-24-97" href="#__codelineno-24-97"></a>
+<a id="__codelineno-24-98" name="__codelineno-24-98" href="#__codelineno-24-98"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを拡張 */</span>
+<a id="__codelineno-24-99" name="__codelineno-24-99" href="#__codelineno-24-99"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">extend</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-100" name="__codelineno-24-100" href="#__codelineno-24-100"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルを一時保存</span>
+<a id="__codelineno-24-101" name="__codelineno-24-101" href="#__codelineno-24-101"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">bucketsTmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span>
+<a id="__codelineno-24-102" name="__codelineno-24-102" href="#__codelineno-24-102"></a><span class="w">        </span><span class="c1">// リサイズ後の新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-24-103" name="__codelineno-24-103" href="#__codelineno-24-103"></a><span class="w">        </span><span class="n">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="n">extendRatio</span>
+<a id="__codelineno-24-104" name="__codelineno-24-104" href="#__codelineno-24-104"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arrayOfNulls</span><span class="p">(</span><span class="n">capacity</span><span class="p">)</span>
+<a id="__codelineno-24-105" name="__codelineno-24-105" href="#__codelineno-24-105"></a><span class="w">        </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-24-106" name="__codelineno-24-106" href="#__codelineno-24-106"></a><span class="w">        </span><span class="c1">// キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
+<a id="__codelineno-24-107" name="__codelineno-24-107" href="#__codelineno-24-107"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-108" name="__codelineno-24-108" href="#__codelineno-24-108"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-109" name="__codelineno-24-109" href="#__codelineno-24-109"></a><span class="w">                </span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">_val</span><span class="p">)</span>
+<a id="__codelineno-24-110" name="__codelineno-24-110" href="#__codelineno-24-110"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-24-111" name="__codelineno-24-111" href="#__codelineno-24-111"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-24-112" name="__codelineno-24-112" href="#__codelineno-24-112"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-113" name="__codelineno-24-113" href="#__codelineno-24-113"></a>
+<a id="__codelineno-24-114" name="__codelineno-24-114" href="#__codelineno-24-114"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-24-115" name="__codelineno-24-115" href="#__codelineno-24-115"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-116" name="__codelineno-24-116" href="#__codelineno-24-116"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-117" name="__codelineno-24-117" href="#__codelineno-24-117"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-118" name="__codelineno-24-118" href="#__codelineno-24-118"></a><span class="w">                </span><span class="n">println</span><span class="p">(</span><span class="s">&quot;null&quot;</span><span class="p">)</span>
+<a id="__codelineno-24-119" name="__codelineno-24-119" href="#__codelineno-24-119"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-120" name="__codelineno-24-120" href="#__codelineno-24-120"></a><span class="w">                </span><span class="n">println</span><span class="p">(</span><span class="s">&quot;TOMESTOME&quot;</span><span class="p">)</span>
+<a id="__codelineno-24-121" name="__codelineno-24-121" href="#__codelineno-24-121"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-122" name="__codelineno-24-122" href="#__codelineno-24-122"></a><span class="w">                </span><span class="n">println</span><span class="p">(</span><span class="s">&quot;</span><span class="si">${</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="si">}</span><span class="s"> -&gt; </span><span class="si">${</span><span class="n">pair</span><span class="p">.</span><span class="na">_val</span><span class="si">}</span><span class="s">&quot;</span><span class="p">)</span>
+<a id="__codelineno-24-123" name="__codelineno-24-123" href="#__codelineno-24-123"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-24-124" name="__codelineno-24-124" href="#__codelineno-24-124"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-24-125" name="__codelineno-24-125" href="#__codelineno-24-125"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-126" name="__codelineno-24-126" href="#__codelineno-24-126"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map_open_addressing.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">HashMapOpenAddressing</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">hash_map_open_addressing.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### オープンアドレス法ハッシュテーブル ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">HashMapOpenAddressing</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="no">TOMBSTONE</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">Pair</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;-1&#39;</span><span class="p">)</span><span class="w"> </span><span class="c1"># 削除済みマーク</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">  </span><span class="c1">### コンストラクタ ###</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1"># キーと値のペア数</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w">    </span><span class="vi">@capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">4</span><span class="w"> </span><span class="c1"># ハッシュテーブル容量</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">    </span><span class="vi">@load_thres</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="o">.</span><span class="mi">0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">3</span><span class="o">.</span><span class="mi">0</span><span class="w"> </span><span class="c1"># リサイズを発動する負荷率のしきい値</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w">    </span><span class="vi">@extend_ratio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1"># 拡張倍率</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w">    </span><span class="vi">@buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="vi">@capacity</span><span class="p">)</span><span class="w"> </span><span class="c1"># バケット配列</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a>
+<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w">  </span><span class="c1">### ハッシュ関数 ###</span>
+<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w">    </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="vi">@capacity</span>
+<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a>
+<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="w">  </span><span class="c1">### 負荷率 ###</span>
+<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">load_factor</span>
+<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="vi">@capacity</span>
+<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a>
+<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a><span class="w">  </span><span class="c1">### key に対応するバケットインデックスを検索 ###</span>
+<a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">find_bucket</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></a><span class="w">    </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-25-27" name="__codelineno-25-27" href="#__codelineno-25-27"></a><span class="w">    </span><span class="n">first_tombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-25-28" name="__codelineno-25-28" href="#__codelineno-25-28"></a><span class="w">    </span><span class="c1"># 線形プロービングを行い、空バケットに達したら終了</span>
+<a id="__codelineno-25-29" name="__codelineno-25-29" href="#__codelineno-25-29"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="vi">@buckets</span><span class="o">[</span><span class="n">index</span><span class="o">].</span><span class="n">nil?</span>
+<a id="__codelineno-25-30" name="__codelineno-25-30" href="#__codelineno-25-30"></a><span class="w">      </span><span class="c1"># key が見つかったら、対応するバケットのインデックスを返す</span>
+<a id="__codelineno-25-31" name="__codelineno-25-31" href="#__codelineno-25-31"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="vi">@buckets</span><span class="o">[</span><span class="n">index</span><span class="o">].</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span>
+<a id="__codelineno-25-32" name="__codelineno-25-32" href="#__codelineno-25-32"></a><span class="w">        </span><span class="c1"># 以前に削除マークが見つかっていれば、そのインデックスへキーと値のペアを移動</span>
+<a id="__codelineno-25-33" name="__codelineno-25-33" href="#__codelineno-25-33"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">first_tombstone</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-25-34" name="__codelineno-25-34" href="#__codelineno-25-34"></a><span class="w">          </span><span class="vi">@buckets</span><span class="o">[</span><span class="n">first_tombstone</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span>
+<a id="__codelineno-25-35" name="__codelineno-25-35" href="#__codelineno-25-35"></a><span class="w">          </span><span class="vi">@buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">TOMBSTONE</span>
+<a id="__codelineno-25-36" name="__codelineno-25-36" href="#__codelineno-25-36"></a><span class="w">          </span><span class="k">return</span><span class="w"> </span><span class="n">first_tombstone</span><span class="w"> </span><span class="c1"># 移動後のバケットインデックスを返す</span>
+<a id="__codelineno-25-37" name="__codelineno-25-37" href="#__codelineno-25-37"></a><span class="w">        </span><span class="k">end</span>
+<a id="__codelineno-25-38" name="__codelineno-25-38" href="#__codelineno-25-38"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="c1"># バケットのインデックスを返す</span>
+<a id="__codelineno-25-39" name="__codelineno-25-39" href="#__codelineno-25-39"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-25-40" name="__codelineno-25-40" href="#__codelineno-25-40"></a><span class="w">      </span><span class="c1"># 最初に見つかった削除マークを記録</span>
+<a id="__codelineno-25-41" name="__codelineno-25-41" href="#__codelineno-25-41"></a><span class="w">      </span><span class="n">first_tombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">first_tombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="vi">@buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="no">TOMBSTONE</span>
+<a id="__codelineno-25-42" name="__codelineno-25-42" href="#__codelineno-25-42"></a><span class="w">      </span><span class="c1"># バケットのインデックスを計算し、末尾を越えたら先頭に戻る</span>
+<a id="__codelineno-25-43" name="__codelineno-25-43" href="#__codelineno-25-43"></a><span class="w">      </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="vi">@capacity</span>
+<a id="__codelineno-25-44" name="__codelineno-25-44" href="#__codelineno-25-44"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-25-45" name="__codelineno-25-45" href="#__codelineno-25-45"></a><span class="w">    </span><span class="c1"># key が存在しない場合は追加位置のインデックスを返す</span>
+<a id="__codelineno-25-46" name="__codelineno-25-46" href="#__codelineno-25-46"></a><span class="w">    </span><span class="n">first_tombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">first_tombstone</span>
+<a id="__codelineno-25-47" name="__codelineno-25-47" href="#__codelineno-25-47"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-48" name="__codelineno-25-48" href="#__codelineno-25-48"></a>
+<a id="__codelineno-25-49" name="__codelineno-25-49" href="#__codelineno-25-49"></a><span class="w">  </span><span class="c1">### 検索操作 ###</span>
+<a id="__codelineno-25-50" name="__codelineno-25-50" href="#__codelineno-25-50"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-25-51" name="__codelineno-25-51" href="#__codelineno-25-51"></a><span class="w">    </span><span class="c1"># key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-25-52" name="__codelineno-25-52" href="#__codelineno-25-52"></a><span class="w">    </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">find_bucket</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-25-53" name="__codelineno-25-53" href="#__codelineno-25-53"></a><span class="w">    </span><span class="c1"># キーと値の組が見つかったら、対応する val を返す</span>
+<a id="__codelineno-25-54" name="__codelineno-25-54" href="#__codelineno-25-54"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="vi">@buckets</span><span class="o">[</span><span class="n">index</span><span class="o">].</span><span class="n">val</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="o">[</span><span class="kp">nil</span><span class="p">,</span><span class="w"> </span><span class="no">TOMBSTONE</span><span class="o">].</span><span class="n">include?</span><span class="p">(</span><span class="vi">@buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-25-55" name="__codelineno-25-55" href="#__codelineno-25-55"></a><span class="w">    </span><span class="c1"># キーと値のペアが存在しない場合は `nil` を返す</span>
+<a id="__codelineno-25-56" name="__codelineno-25-56" href="#__codelineno-25-56"></a><span class="w">    </span><span class="kp">nil</span>
+<a id="__codelineno-25-57" name="__codelineno-25-57" href="#__codelineno-25-57"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-58" name="__codelineno-25-58" href="#__codelineno-25-58"></a>
+<a id="__codelineno-25-59" name="__codelineno-25-59" href="#__codelineno-25-59"></a><span class="w">  </span><span class="c1">### 追加操作 ###</span>
+<a id="__codelineno-25-60" name="__codelineno-25-60" href="#__codelineno-25-60"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-25-61" name="__codelineno-25-61" href="#__codelineno-25-61"></a><span class="w">    </span><span class="c1"># 負荷率がしきい値を超えたら、リサイズを実行</span>
+<a id="__codelineno-25-62" name="__codelineno-25-62" href="#__codelineno-25-62"></a><span class="w">    </span><span class="kp">extend</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">load_factor</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="vi">@load_thres</span>
+<a id="__codelineno-25-63" name="__codelineno-25-63" href="#__codelineno-25-63"></a><span class="w">    </span><span class="c1"># key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-25-64" name="__codelineno-25-64" href="#__codelineno-25-64"></a><span class="w">    </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">find_bucket</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-25-65" name="__codelineno-25-65" href="#__codelineno-25-65"></a><span class="w">    </span><span class="c1"># キーと値のペアが見つかった場合は、`val` を上書きして返す</span>
+<a id="__codelineno-25-66" name="__codelineno-25-66" href="#__codelineno-25-66"></a><span class="w">    </span><span class="k">unless</span><span class="w"> </span><span class="o">[</span><span class="kp">nil</span><span class="p">,</span><span class="w"> </span><span class="no">TOMBSTONE</span><span class="o">].</span><span class="n">include?</span><span class="p">(</span><span class="vi">@buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-25-67" name="__codelineno-25-67" href="#__codelineno-25-67"></a><span class="w">      </span><span class="vi">@buckets</span><span class="o">[</span><span class="n">index</span><span class="o">].</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span>
+<a id="__codelineno-25-68" name="__codelineno-25-68" href="#__codelineno-25-68"></a><span class="w">      </span><span class="k">return</span>
+<a id="__codelineno-25-69" name="__codelineno-25-69" href="#__codelineno-25-69"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-25-70" name="__codelineno-25-70" href="#__codelineno-25-70"></a><span class="w">    </span><span class="c1"># キーと値の組が存在しない場合は、その組を追加する</span>
+<a id="__codelineno-25-71" name="__codelineno-25-71" href="#__codelineno-25-71"></a><span class="w">    </span><span class="vi">@buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">Pair</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-25-72" name="__codelineno-25-72" href="#__codelineno-25-72"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-25-73" name="__codelineno-25-73" href="#__codelineno-25-73"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-74" name="__codelineno-25-74" href="#__codelineno-25-74"></a>
+<a id="__codelineno-25-75" name="__codelineno-25-75" href="#__codelineno-25-75"></a><span class="w">  </span><span class="c1">### 削除操作 ###</span>
+<a id="__codelineno-25-76" name="__codelineno-25-76" href="#__codelineno-25-76"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-25-77" name="__codelineno-25-77" href="#__codelineno-25-77"></a><span class="w">    </span><span class="c1"># key に対応するバケットインデックスを探す</span>
+<a id="__codelineno-25-78" name="__codelineno-25-78" href="#__codelineno-25-78"></a><span class="w">    </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">find_bucket</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-25-79" name="__codelineno-25-79" href="#__codelineno-25-79"></a><span class="w">    </span><span class="c1"># キーと値の組が見つかったら、削除マーカーで上書きする</span>
+<a id="__codelineno-25-80" name="__codelineno-25-80" href="#__codelineno-25-80"></a><span class="w">    </span><span class="k">unless</span><span class="w"> </span><span class="o">[</span><span class="kp">nil</span><span class="p">,</span><span class="w"> </span><span class="no">TOMBSTONE</span><span class="o">].</span><span class="n">include?</span><span class="p">(</span><span class="vi">@buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-25-81" name="__codelineno-25-81" href="#__codelineno-25-81"></a><span class="w">      </span><span class="vi">@buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">TOMBSTONE</span>
+<a id="__codelineno-25-82" name="__codelineno-25-82" href="#__codelineno-25-82"></a><span class="w">      </span><span class="vi">@size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-25-83" name="__codelineno-25-83" href="#__codelineno-25-83"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-25-84" name="__codelineno-25-84" href="#__codelineno-25-84"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-85" name="__codelineno-25-85" href="#__codelineno-25-85"></a>
+<a id="__codelineno-25-86" name="__codelineno-25-86" href="#__codelineno-25-86"></a><span class="w">  </span><span class="c1">### ハッシュテーブルを拡張 ###</span>
+<a id="__codelineno-25-87" name="__codelineno-25-87" href="#__codelineno-25-87"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">extend</span>
+<a id="__codelineno-25-88" name="__codelineno-25-88" href="#__codelineno-25-88"></a><span class="w">    </span><span class="c1"># 元のハッシュテーブルを一時保存</span>
+<a id="__codelineno-25-89" name="__codelineno-25-89" href="#__codelineno-25-89"></a><span class="w">    </span><span class="n">buckets_tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@buckets</span>
+<a id="__codelineno-25-90" name="__codelineno-25-90" href="#__codelineno-25-90"></a><span class="w">    </span><span class="c1"># リサイズ後の新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-25-91" name="__codelineno-25-91" href="#__codelineno-25-91"></a><span class="w">    </span><span class="vi">@capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="vi">@extend_ratio</span>
+<a id="__codelineno-25-92" name="__codelineno-25-92" href="#__codelineno-25-92"></a><span class="w">    </span><span class="vi">@buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="vi">@capacity</span><span class="p">)</span>
+<a id="__codelineno-25-93" name="__codelineno-25-93" href="#__codelineno-25-93"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-25-94" name="__codelineno-25-94" href="#__codelineno-25-94"></a><span class="w">    </span><span class="c1"># キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す</span>
+<a id="__codelineno-25-95" name="__codelineno-25-95" href="#__codelineno-25-95"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets_tmp</span>
+<a id="__codelineno-25-96" name="__codelineno-25-96" href="#__codelineno-25-96"></a><span class="w">      </span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="o">[</span><span class="kp">nil</span><span class="p">,</span><span class="w"> </span><span class="no">TOMBSTONE</span><span class="o">].</span><span class="n">include?</span><span class="p">(</span><span class="n">pair</span><span class="p">)</span>
+<a id="__codelineno-25-97" name="__codelineno-25-97" href="#__codelineno-25-97"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-25-98" name="__codelineno-25-98" href="#__codelineno-25-98"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-99" name="__codelineno-25-99" href="#__codelineno-25-99"></a>
+<a id="__codelineno-25-100" name="__codelineno-25-100" href="#__codelineno-25-100"></a><span class="w">  </span><span class="c1">### ハッシュテーブルを出力 ###</span>
+<a id="__codelineno-25-101" name="__codelineno-25-101" href="#__codelineno-25-101"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">print</span>
+<a id="__codelineno-25-102" name="__codelineno-25-102" href="#__codelineno-25-102"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="vi">@buckets</span>
+<a id="__codelineno-25-103" name="__codelineno-25-103" href="#__codelineno-25-103"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="n">pair</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-25-104" name="__codelineno-25-104" href="#__codelineno-25-104"></a><span class="w">        </span><span class="nb">puts</span><span class="w"> </span><span class="s2">&quot;Nil&quot;</span>
+<a id="__codelineno-25-105" name="__codelineno-25-105" href="#__codelineno-25-105"></a><span class="w">      </span><span class="k">elsif</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="no">TOMBSTONE</span>
+<a id="__codelineno-25-106" name="__codelineno-25-106" href="#__codelineno-25-106"></a><span class="w">        </span><span class="nb">puts</span><span class="w"> </span><span class="s2">&quot;TOMBSTONE&quot;</span>
+<a id="__codelineno-25-107" name="__codelineno-25-107" href="#__codelineno-25-107"></a><span class="w">      </span><span class="k">else</span>
+<a id="__codelineno-25-108" name="__codelineno-25-108" href="#__codelineno-25-108"></a><span class="w">        </span><span class="nb">puts</span><span class="w"> </span><span class="s2">&quot;</span><span class="si">#{</span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="si">}</span><span class="s2"> -&gt; </span><span class="si">#{</span><span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="si">}</span><span class="s2">&quot;</span>
+<a id="__codelineno-25-109" name="__codelineno-25-109" href="#__codelineno-25-109"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-25-110" name="__codelineno-25-110" href="#__codelineno-25-110"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-25-111" name="__codelineno-25-111" href="#__codelineno-25-111"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-112" name="__codelineno-25-112" href="#__codelineno-25-112"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h3 id="2">2. &nbsp; 二次プローブ<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>二次プローブは線形プローブに似ており、オープンアドレス法の一般的な戦略の1つです。衝突が発生した場合、二次プローブは単純に固定ステップ数をスキップするのではなく、「プローブ回数の二乗」に等しいステップ数、つまり<span class="arithmatex">\(1, 4, 9, \dots\)</span>ステップをスキップします。</p>
-<p>二次プローブには以下の利点があります：</p>
+<h3 id="2">2. &nbsp; 二次探索<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>二次探索は線形探索に似ており、オープンアドレッシングの一般的な戦略の 1 つです。衝突が発生したとき、二次探索では単純に固定歩数を飛ばすのではなく、「探索回数の二乗」に相当する歩数、すなわち <span class="arithmatex">\(1, 4, 9, \dots\)</span> 歩を飛ばします。</p>
+<p>二次探索には主に次の利点があります。</p>
 <ul>
-<li>二次プローブは、プローブ回数の二乗の距離をスキップすることで、線形プローブのクラスタリング効果を軽減しようとします。</li>
-<li>二次プローブはより大きな距離をスキップして空の位置を見つけ、データをより均等に分散するのに役立ちます。</li>
+<li>二次探索は、探索回数の二乗の距離を飛ばすことで、線形探索のクラスタリング効果を緩和しようとします。</li>
+<li>二次探索はより大きな距離を飛ばして空き位置を探すため、データ分布がより均一になるのに役立ちます。</li>
 </ul>
-<p>しかし、二次プローブは完璧ではありません：</p>
+<p>しかし、二次探索は完璧ではありません。</p>
 <ul>
-<li>クラスタリングは依然として存在し、つまり一部の位置は他の位置よりも占有される可能性が高いです。</li>
-<li>二乗の成長により、二次プローブはハッシュ表全体をプローブできない可能性があり、ハッシュ表に空のバケットがあっても、二次プローブがアクセスできない可能性があります。</li>
+<li>依然としてクラスタリング現象は存在し、ある位置が他の位置より占有されやすいことがあります。</li>
+<li>二乗の増加により、二次探索はハッシュテーブル全体を探索できない可能性があります。これは、ハッシュテーブルに空バケットがあっても、二次探索ではそこに到達できないことがあることを意味します。</li>
 </ul>
-<h3 id="3">3. &nbsp; 二重ハッシュ<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
-<p>名前が示すように、二重ハッシュ法は複数のハッシュ関数<span class="arithmatex">\(f_1(x)\)</span>、<span class="arithmatex">\(f_2(x)\)</span>、<span class="arithmatex">\(f_3(x)\)</span>、<span class="arithmatex">\(\dots\)</span>をプローブに使用します。</p>
+<h3 id="3">3. &nbsp; 多重ハッシュ<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
+<p>その名のとおり、多重ハッシュ法では複数のハッシュ関数 <span class="arithmatex">\(f_1(x)\)</span>、<span class="arithmatex">\(f_2(x)\)</span>、<span class="arithmatex">\(f_3(x)\)</span>、<span class="arithmatex">\(\dots\)</span> を使って探索を行います。</p>
 <ul>
-<li><strong>要素の挿入</strong>: ハッシュ関数<span class="arithmatex">\(f_1(x)\)</span>が衝突に遭遇した場合、<span class="arithmatex">\(f_2(x)\)</span>を試し、以下同様に、空の位置が見つかって要素が挿入されるまで続けます。</li>
-<li><strong>要素の検索</strong>: 同じハッシュ関数の順序で検索し、ターゲット要素が見つかって返されるまで、または空の位置に遭遇するかすべてのハッシュ関数が試されるまで続け、要素がハッシュ表にないことを示し、<code>None</code>を返します。</li>
+<li><strong>要素の挿入</strong>：ハッシュ関数 <span class="arithmatex">\(f_1(x)\)</span> で衝突が発生した場合は、<span class="arithmatex">\(f_2(x)\)</span> を試し、以下同様に、空き位置が見つかるまで続けてから要素を挿入します。</li>
+<li><strong>要素の検索</strong>：同じハッシュ関数の順序で探索し、対象要素が見つかった時点で返します。空き位置に遭遇するか、すべてのハッシュ関数を試しても見つからない場合は、ハッシュテーブル内にその要素は存在しないため、 <code>None</code> を返します。</li>
 </ul>
-<p>線形プローブと比較して、二重ハッシュ法はクラスタリングが起こりにくいですが、複数のハッシュ関数は追加の計算オーバーヘッドを導入します。</p>
+<p>線形探索と比べると、多重ハッシュ法はクラスタリングを起こしにくい一方で、複数のハッシュ関数により追加の計算量が発生します。</p>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>オープンアドレス法（線形プローブ、二次プローブ、二重ハッシュ）ハッシュ表はすべて「要素を直接削除できない」という問題があることに注意してください。</p>
+<p>注意してください。オープンアドレッシング（線形探索、二次探索、多重ハッシュ）のハッシュテーブルには、いずれも「要素を直接削除できない」という問題があります。</p>
 </div>
 <h2 id="623">6.2.3 &nbsp; プログラミング言語の選択<a class="headerlink" href="#623" title="Permanent link">&para;</a></h2>
-<p>異なるプログラミング言語は異なるハッシュ表実装戦略を採用しています。以下にいくつかの例を示します：</p>
+<p>各種プログラミング言語は異なるハッシュテーブル実装戦略を採用しています。以下にいくつか例を挙げます。</p>
 <ul>
-<li>Pythonはオープンアドレス法を使用します。<code>dict</code>辞書はプローブに疑似乱数を使用します。</li>
-<li>Javaは連鎖法を使用します。JDK 1.8以降、<code>HashMap</code>の配列長が64に達し、連結リストの長さが8に達すると、連結リストは検索性能を向上させるために赤黒木に変換されます。</li>
-<li>Goは連鎖法を使用します。Goは各バケットが最大8つのキー値ペアを格納できることを規定し、容量を超えた場合はオーバーフローバケットが連結されます。オーバーフローバケットが多すぎる場合、性能を確保するために特別な等容量リサイズ操作が実行されます。</li>
+<li>Python はオープンアドレッシングを採用しています。辞書 <code>dict</code> は疑似乱数を用いて探索します。</li>
+<li>Java はチェイン法を採用しています。JDK 1.8 以降、<code>HashMap</code> 内の配列長が 64 に達し、かつ連結リスト長が 8 に達すると、連結リストは検索性能を高めるため赤黒木に変換されます。</li>
+<li>Go はチェイン法を採用しています。Go では各バケットに最大 8 個のキーと値のペアを格納でき、容量を超えるとオーバーフローバケットを連結します。オーバーフローバケットが多すぎる場合は、性能を確保するために特殊な等量拡張操作を実行します。</li>
 </ul>
 
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@@ -5320,7 +7722,7 @@ aria-label="フッター"
   <a
     href="../hash_map/"
     class="md-footer__link md-footer__link--prev"
-    aria-label="前: 6.1 &amp;nbsp; ハッシュ表"
+    aria-label="前: 6.1 &amp;nbsp; ハッシュテーブル"
     rel="prev"
   >
     <div class="md-footer__button md-icon">
@@ -5332,7 +7734,7 @@ aria-label="フッター"
         前
       </span>
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-        6.1 &nbsp; ハッシュ表
+        6.1 &nbsp; ハッシュテーブル
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@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -39,7 +39,7 @@
     
     
       
-        <title>6.1 ハッシュ表 - Hello アルゴリズム</title>
+        <title>6.1 ハッシュテーブル - Hello アルゴリズム</title>
       
     
     
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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         <div class="md-header__topic" data-md-component="header-topic">
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-              6.1 &nbsp; ハッシュ表
+              6.1 &nbsp; ハッシュテーブル
             
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-    序
+    はじめに
   
 
     
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+    はじめに
   
 
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-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
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-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
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-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
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-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
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-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
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-        6.1.1 &nbsp; ハッシュ表の一般的な操作
+        6.1.1 &nbsp; ハッシュテーブルの基本操作
       
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-        6.1.2 &nbsp; ハッシュ表の簡単な実装
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-        6.1.3 &nbsp; ハッシュ衝突とリサイズ
+        6.1.3 &nbsp; ハッシュ衝突と拡張
       
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@@ -2188,7 +2188,7 @@
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-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2574,7 +2574,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2630,7 +2630,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2658,7 +2658,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3196,7 +3196,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3252,7 +3252,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3280,7 +3280,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3473,7 +3473,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3501,7 +3501,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3642,7 +3642,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3670,7 +3670,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3698,7 +3698,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3726,7 +3726,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3919,7 +3919,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4164,7 +4164,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4310,7 +4310,7 @@
   <a href="#611" class="md-nav__link">
     <span class="md-ellipsis">
       
-        6.1.1 &nbsp; ハッシュ表の一般的な操作
+        6.1.1 &nbsp; ハッシュテーブルの基本操作
       
     </span>
   </a>
@@ -4321,7 +4321,7 @@
   <a href="#612" class="md-nav__link">
     <span class="md-ellipsis">
       
-        6.1.2 &nbsp; ハッシュ表の簡単な実装
+        6.1.2 &nbsp; ハッシュテーブルの簡単な実装
       
     </span>
   </a>
@@ -4332,7 +4332,7 @@
   <a href="#613" class="md-nav__link">
     <span class="md-ellipsis">
       
-        6.1.3 &nbsp; ハッシュ衝突とリサイズ
+        6.1.3 &nbsp; ハッシュ衝突と拡張
       
     </span>
   </a>
@@ -4376,19 +4376,19 @@
 
 
 <!-- Page content -->
-<h1 id="61">6.1 &nbsp; ハッシュ表<a class="headerlink" href="#61" title="Permanent link">&para;</a></h1>
-<p><u>ハッシュ表</u>は<u>ハッシュマップ</u>とも呼ばれ、キーと値の間のマッピングを確立し、効率的な要素の取得を可能にするデータ構造です。具体的には、ハッシュ表に<code>key</code>を入力すると、<span class="arithmatex">\(O(1)\)</span>の時間計算量で対応する<code>value</code>を取得できます。</p>
-<p>下図に示すように、<span class="arithmatex">\(n\)</span>人の学生がいて、各学生には「名前」と「学籍番号」の2つのデータフィールドがあるとします。学籍番号を入力として対応する名前を返すクエリ機能を実装したい場合、下図に示すハッシュ表を使用できます。</p>
-<p><img alt="ハッシュ表の抽象的な表現" class="animation-figure" src="../hash_map.assets/hash_table_lookup.png" /></p>
-<p align="center"> 図 6-1 &nbsp; ハッシュ表の抽象的な表現 </p>
+<h1 id="61">6.1 &nbsp; ハッシュテーブル<a class="headerlink" href="#61" title="Permanent link">&para;</a></h1>
+<p><u>ハッシュテーブル（hash table）</u>は、<u>散列表</u>とも呼ばれ、キー <code>key</code> と値 <code>value</code> の対応関係を構築することで、高効率な要素検索を実現します。具体的には、ハッシュテーブルにキー <code>key</code> を入力すると、対応する値 <code>value</code> を <span class="arithmatex">\(O(1)\)</span> 時間で取得できます。</p>
+<p>以下の図に示すように、<span class="arithmatex">\(n\)</span> 人の学生がいるとし、各学生は「名前」と「学籍番号」の 2 つの情報を持っています。もし「学籍番号を入力すると対応する名前を返す」という検索機能を実現したいなら、下図のようなハッシュテーブルを用いることができます。</p>
+<p><img alt="ハッシュテーブルの抽象表現" class="animation-figure" src="../hash_map.assets/hash_table_lookup.png" /></p>
+<p align="center"> 図 6-1 &nbsp; ハッシュテーブルの抽象表現 </p>
 
-<p>ハッシュ表に加えて、配列や連結リストもクエリ機能の実装に使用できますが、時間計算量が異なります。効率は以下の表で比較されています：</p>
+<p>ハッシュテーブルのほかに、配列や連結リストでも検索機能を実現できます。それらの効率比較を次の表に示します。</p>
 <ul>
-<li><strong>要素の挿入</strong>: 配列（または連結リスト）の末尾に要素を追加するだけです。この操作の時間計算量は<span class="arithmatex">\(O(1)\)</span>です。</li>
-<li><strong>要素の検索</strong>: 配列（または連結リスト）がソートされていないため、要素を検索するにはすべての要素を走査する必要があります。この操作の時間計算量は<span class="arithmatex">\(O(n)\)</span>です。</li>
-<li><strong>要素の削除</strong>: 要素を削除するには、まずその要素を見つけてから、配列（または連結リスト）から削除します。この操作の時間計算量は<span class="arithmatex">\(O(n)\)</span>です。</li>
+<li><strong>要素の追加</strong>：要素を配列（連結リスト）の末尾に追加するだけでよく、<span class="arithmatex">\(O(1)\)</span> 時間です。</li>
+<li><strong>要素の検索</strong>：配列（連結リスト）は無秩序なので、すべての要素を走査する必要があり、<span class="arithmatex">\(O(n)\)</span> 時間かかります。</li>
+<li><strong>要素の削除</strong>：先に要素を検索してから配列（連結リスト）から削除する必要があり、<span class="arithmatex">\(O(n)\)</span> 時間かかります。</li>
 </ul>
-<p align="center"> 表 6-1 &nbsp; 一般的な操作の時間効率の比較 </p>
+<p align="center"> 表 6-1 &nbsp; 要素検索効率の比較 </p>
 
 <div class="center-table">
 <table>
@@ -4397,7 +4397,7 @@
 <th></th>
 <th>配列</th>
 <th>連結リスト</th>
-<th>ハッシュ表</th>
+<th>ハッシュテーブル</th>
 </tr>
 </thead>
 <tbody>
@@ -4408,7 +4408,7 @@
 <td><span class="arithmatex">\(O(1)\)</span></td>
 </tr>
 <tr>
-<td>要素の挿入</td>
+<td>要素の追加</td>
 <td><span class="arithmatex">\(O(1)\)</span></td>
 <td><span class="arithmatex">\(O(1)\)</span></td>
 <td><span class="arithmatex">\(O(1)\)</span></td>
@@ -4422,770 +4422,1670 @@
 </tbody>
 </table>
 </div>
-<p>観察されるように、**ハッシュ表における操作（挿入、削除、検索、変更）の時間計算量は<span class="arithmatex">\(O(1)\)</span>**で、非常に効率的です。</p>
-<h2 id="611">6.1.1 &nbsp; ハッシュ表の一般的な操作<a class="headerlink" href="#611" title="Permanent link">&para;</a></h2>
-<p>ハッシュ表の一般的な操作には、初期化、クエリ、キー値ペアの追加、キー値ペアの削除があります。以下はコード例です：</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="1:12"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label></div>
+<p>以上から分かるように、<strong>ハッシュテーブルにおける追加・削除・検索・更新の時間計算量はいずれも <span class="arithmatex">\(O(1)\)</span></strong> であり、非常に高効率です。</p>
+<h2 id="611">6.1.1 &nbsp; ハッシュテーブルの基本操作<a class="headerlink" href="#611" title="Permanent link">&para;</a></h2>
+<p>ハッシュテーブルの一般的な操作には、初期化、検索、キーと値のペアの追加、キーと値のペアの削除などがあります。コード例は以下のとおりです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># ハッシュ表を初期化</span>
+<div class="highlight"><span class="filename">hash_map.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># ハッシュテーブルを初期化</span>
 <a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="n">hmap</span><span class="p">:</span> <span class="nb">dict</span> <span class="o">=</span> <span class="p">{}</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="c1"># 追加操作</span>
-<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="c1"># ハッシュ表にキー値ペア (key, value) を追加</span>
-<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="n">hmap</span><span class="p">[</span><span class="mi">12836</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;小哈&quot;</span>
-<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="n">hmap</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;小啰&quot;</span>
-<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="n">hmap</span><span class="p">[</span><span class="mi">16750</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;小算&quot;</span>
-<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="n">hmap</span><span class="p">[</span><span class="mi">13276</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;小法&quot;</span>
-<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="n">hmap</span><span class="p">[</span><span class="mi">10583</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;小鸭&quot;</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="c1"># ハッシュテーブルにキーと値のペア (key, value) を追加</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="n">hmap</span><span class="p">[</span><span class="mi">12836</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;シャオハ&quot;</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="n">hmap</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;シャオルオ&quot;</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="n">hmap</span><span class="p">[</span><span class="mi">16750</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;シャオスワン&quot;</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="n">hmap</span><span class="p">[</span><span class="mi">13276</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;シャオファ&quot;</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="n">hmap</span><span class="p">[</span><span class="mi">10583</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;シャオヤー&quot;</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>
-<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="c1"># クエリ操作</span>
-<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="c1"># ハッシュ表にキーを入力し、値を取得</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="c1"># 検索操作</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="c1"># ハッシュテーブルにキー key を入力し、値 value を取得</span>
 <a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a><span class="n">name</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="n">hmap</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span>
 <a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>
 <a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a><span class="c1"># 削除操作</span>
-<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a><span class="c1"># ハッシュ表からキー値ペア (key, value) を削除</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a><span class="c1"># ハッシュテーブルからキーと値のペア (key, value) を削除</span>
 <a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a><span class="n">hmap</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="mi">10583</span><span class="p">)</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* ハッシュ表を初期化 */</span>
+<div class="highlight"><span class="filename">hash_map.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* ハッシュテーブルを初期化 */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="n">unordered_map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="o">&gt;</span><span class="w"> </span><span class="n">map</span><span class="p">;</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="cm">/* 追加操作 */</span>
-<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="c1">// ハッシュ表にキー値ペア (key, value) を追加</span>
-<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="n">map</span><span class="p">[</span><span class="mi">12836</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;小哈&quot;</span><span class="p">;</span>
-<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="n">map</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;小啰&quot;</span><span class="p">;</span>
-<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="n">map</span><span class="p">[</span><span class="mi">16750</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;小算&quot;</span><span class="p">;</span>
-<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="n">map</span><span class="p">[</span><span class="mi">13276</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;小法&quot;</span><span class="p">;</span>
-<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="n">map</span><span class="p">[</span><span class="mi">10583</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;小鸭&quot;</span><span class="p">;</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="c1">// ハッシュテーブルにキーと値のペア (key, value) を追加</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="n">map</span><span class="p">[</span><span class="mi">12836</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;シャオハ&quot;</span><span class="p">;</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="n">map</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;シャオルオ&quot;</span><span class="p">;</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="n">map</span><span class="p">[</span><span class="mi">16750</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;シャオスワン&quot;</span><span class="p">;</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="n">map</span><span class="p">[</span><span class="mi">13276</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;シャオファ&quot;</span><span class="p">;</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="n">map</span><span class="p">[</span><span class="mi">10583</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;シャオヤー&quot;</span><span class="p">;</span>
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a>
-<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="cm">/* クエリ操作 */</span>
-<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="c1">// ハッシュ表にキーを入力し、値を取得</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="c1">// ハッシュテーブルにキー key を入力し、値 value を取得</span>
 <a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="n">string</span><span class="w"> </span><span class="n">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">[</span><span class="mi">15937</span><span class="p">];</span>
 <a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a>
 <a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="cm">/* 削除操作 */</span>
-<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="c1">// ハッシュ表からキー値ペア (key, value) を削除</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="c1">// ハッシュテーブルからキーと値のペア (key, value) を削除</span>
 <a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="n">map</span><span class="p">.</span><span class="n">erase</span><span class="p">(</span><span class="mi">10583</span><span class="p">);</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* ハッシュ表を初期化 */</span>
+<div class="highlight"><span class="filename">hash_map.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* ハッシュテーブルを初期化 */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="n">Map</span><span class="o">&lt;</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashMap</span><span class="o">&lt;&gt;</span><span class="p">();</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="cm">/* 追加操作 */</span>
-<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="c1">// ハッシュ表にキー値ペア (key, value) を追加</span>
-<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">12836</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小哈&quot;</span><span class="p">);</span>
-<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">15937</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小啰&quot;</span><span class="p">);</span>
-<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">16750</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小算&quot;</span><span class="p">);</span>
-<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">13276</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小法&quot;</span><span class="p">);</span>
-<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">10583</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小鸭&quot;</span><span class="p">);</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="c1">// ハッシュテーブルにキーと値のペア (key, value) を追加</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">12836</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;シャオハ&quot;</span><span class="p">);</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">15937</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;シャオルオ&quot;</span><span class="p">);</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">16750</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;シャオスワン&quot;</span><span class="p">);</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">13276</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;シャオファ&quot;</span><span class="p">);</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">10583</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;シャオヤー&quot;</span><span class="p">);</span>
 <a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a>
-<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="cm">/* クエリ操作 */</span>
-<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="c1">// ハッシュ表にキーを入力し、値を取得</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="c1">// ハッシュテーブルにキー key を入力し、値 value を取得</span>
 <a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="n">String</span><span class="w"> </span><span class="n">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="mi">15937</span><span class="p">);</span>
 <a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a>
 <a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="cm">/* 削除操作 */</span>
-<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="c1">// ハッシュ表からキー値ペア (key, value) を削除</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="c1">// ハッシュテーブルからキーと値のペア (key, value) を削除</span>
 <a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="n">map</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="mi">10583</span><span class="p">);</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* ハッシュ表を初期化 */</span>
+<div class="highlight"><span class="filename">hash_map.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* ハッシュテーブルを初期化 */</span>
 <a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="n">Dictionary</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">string</span><span class="o">&gt;</span><span class="w"> </span><span class="n">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
-<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="c1">// ハッシュ表にキー値ペア (key, value) を追加</span>
-<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="p">{</span><span class="w"> </span><span class="mi">12836</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小哈&quot;</span><span class="w"> </span><span class="p">},</span>
-<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="p">{</span><span class="w"> </span><span class="mi">15937</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小啰&quot;</span><span class="w"> </span><span class="p">},</span>
-<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="p">{</span><span class="w"> </span><span class="mi">16750</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小算&quot;</span><span class="w"> </span><span class="p">},</span>
-<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="p">{</span><span class="w"> </span><span class="mi">13276</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小法&quot;</span><span class="w"> </span><span class="p">},</span>
-<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="p">{</span><span class="w"> </span><span class="mi">10583</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小鸭&quot;</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="c1">// ハッシュテーブルにキーと値のペア (key, value) を追加</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="p">{</span><span class="w"> </span><span class="mi">12836</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;シャオハ&quot;</span><span class="w"> </span><span class="p">},</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="p">{</span><span class="w"> </span><span class="mi">15937</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;シャオルオ&quot;</span><span class="w"> </span><span class="p">},</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="p">{</span><span class="w"> </span><span class="mi">16750</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;シャオスワン&quot;</span><span class="w"> </span><span class="p">},</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="p">{</span><span class="w"> </span><span class="mi">13276</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;シャオファ&quot;</span><span class="w"> </span><span class="p">},</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="p">{</span><span class="w"> </span><span class="mi">10583</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;シャオヤー&quot;</span><span class="w"> </span><span class="p">}</span>
 <a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="p">};</span>
 <a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a>
-<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="cm">/* クエリ操作 */</span>
-<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="c1">// ハッシュ表にキーを入力し、値を取得</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="c1">// ハッシュテーブルにキー key を入力し、値 value を取得</span>
 <a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="kt">string</span><span class="w"> </span><span class="n">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">[</span><span class="mi">15937</span><span class="p">];</span>
 <a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a>
 <a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="cm">/* 削除操作 */</span>
-<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="c1">// ハッシュ表からキー値ペア (key, value) を削除</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="c1">// ハッシュテーブルからキーと値のペア (key, value) を削除</span>
 <a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="n">map</span><span class="p">.</span><span class="n">Remove</span><span class="p">(</span><span class="mi">10583</span><span class="p">);</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map_test.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* ハッシュ表を初期化 */</span>
+<div class="highlight"><span class="filename">hash_map_test.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* ハッシュテーブルを初期化 */</span>
 <a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="nx">hmap</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">(</span><span class="kd">map</span><span class="p">[</span><span class="kt">int</span><span class="p">]</span><span class="kt">string</span><span class="p">)</span>
 <a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a>
 <a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="cm">/* 追加操作 */</span>
-<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="c1">// ハッシュ表にキー値ペア (key, value) を追加</span>
-<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="nx">hmap</span><span class="p">[</span><span class="mi">12836</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;小哈&quot;</span>
-<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="nx">hmap</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;小啰&quot;</span>
-<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="nx">hmap</span><span class="p">[</span><span class="mi">16750</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;小算&quot;</span>
-<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="nx">hmap</span><span class="p">[</span><span class="mi">13276</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;小法&quot;</span>
-<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="nx">hmap</span><span class="p">[</span><span class="mi">10583</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;小鸭&quot;</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="c1">// ハッシュテーブルにキーと値のペア (key, value) を追加</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="nx">hmap</span><span class="p">[</span><span class="mi">12836</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;シャオハ&quot;</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="nx">hmap</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;シャオルオ&quot;</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="nx">hmap</span><span class="p">[</span><span class="mi">16750</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;シャオスワン&quot;</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="nx">hmap</span><span class="p">[</span><span class="mi">13276</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;シャオファ&quot;</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="nx">hmap</span><span class="p">[</span><span class="mi">10583</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;シャオヤー&quot;</span>
 <a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a>
-<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="cm">/* クエリ操作 */</span>
-<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="c1">// ハッシュ表にキーを入力し、値を取得</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="c1">// ハッシュテーブルにキー key を入力し、値 value を取得</span>
 <a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="nx">name</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">hmap</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span>
 <a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a>
 <a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="cm">/* 削除操作 */</span>
-<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="c1">// ハッシュ表からキー値ペア (key, value) を削除</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="c1">// ハッシュテーブルからキーと値のペア (key, value) を削除</span>
 <a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="nb">delete</span><span class="p">(</span><span class="nx">hmap</span><span class="p">,</span><span class="w"> </span><span class="mi">10583</span><span class="p">)</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* ハッシュ表を初期化 */</span>
+<div class="highlight"><span class="filename">hash_map.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* ハッシュテーブルを初期化 */</span>
 <a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">var</span><span class="w"> </span><span class="nv">map</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">:</span><span class="w"> </span><span class="nb">String</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[:]</span>
 <a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a>
 <a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="cm">/* 追加操作 */</span>
-<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="c1">// ハッシュ表にキー値ペア (key, value) を追加</span>
-<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="bp">map</span><span class="p">[</span><span class="mi">12836</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;小哈&quot;</span>
-<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="bp">map</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;小啰&quot;</span>
-<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="bp">map</span><span class="p">[</span><span class="mi">16750</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;小算&quot;</span>
-<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="bp">map</span><span class="p">[</span><span class="mi">13276</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;小法&quot;</span>
-<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="bp">map</span><span class="p">[</span><span class="mi">10583</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;小鸭&quot;</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="c1">// ハッシュテーブルにキーと値のペア (key, value) を追加</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="bp">map</span><span class="p">[</span><span class="mi">12836</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;シャオハ&quot;</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="bp">map</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;シャオルオ&quot;</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="bp">map</span><span class="p">[</span><span class="mi">16750</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;シャオスワン&quot;</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="bp">map</span><span class="p">[</span><span class="mi">13276</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;シャオファ&quot;</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="bp">map</span><span class="p">[</span><span class="mi">10583</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;シャオヤー&quot;</span>
 <a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a>
-<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="cm">/* クエリ操作 */</span>
-<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="c1">// ハッシュ表にキーを入力し、値を取得</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="c1">// ハッシュテーブルにキー key を入力し、値 value を取得</span>
 <a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="kd">let</span><span class="w"> </span><span class="nv">name</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">map</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span><span class="o">!</span>
 <a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a>
 <a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="cm">/* 削除操作 */</span>
-<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="c1">// ハッシュ表からキー値ペア (key, value) を削除</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="c1">// ハッシュテーブルからキーと値のペア (key, value) を削除</span>
 <a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="bp">map</span><span class="p">.</span><span class="n">removeValue</span><span class="p">(</span><span class="n">forKey</span><span class="p">:</span><span class="w"> </span><span class="mi">10583</span><span class="p">)</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* ハッシュ表を初期化 */</span>
+<div class="highlight"><span class="filename">hash_map.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* ハッシュテーブルを初期化 */</span>
 <a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Map</span><span class="p">();</span>
 <a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="cm">/* 追加操作 */</span>
-<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="c1">// ハッシュ表にキー値ペア (key, value) を追加</span>
-<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">12836</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;小哈&#39;</span><span class="p">);</span>
-<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">15937</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;小啰&#39;</span><span class="p">);</span>
-<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">16750</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;小算&#39;</span><span class="p">);</span>
-<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">13276</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;小法&#39;</span><span class="p">);</span>
-<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">10583</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;小鸭&#39;</span><span class="p">);</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="c1">// ハッシュテーブルにキーと値のペア (key, value) を追加</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">12836</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;シャオハ&#39;</span><span class="p">);</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">15937</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;シャオルオ&#39;</span><span class="p">);</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">16750</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;シャオスワン&#39;</span><span class="p">);</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">13276</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;シャオファ&#39;</span><span class="p">);</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">10583</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;シャオヤー&#39;</span><span class="p">);</span>
 <a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a>
-<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="cm">/* クエリ操作 */</span>
-<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="c1">// ハッシュ表にキーを入力し、値を取得</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="c1">// ハッシュテーブルにキー key を入力し、値 value を取得</span>
 <a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="kd">let</span><span class="w"> </span><span class="nx">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="mf">15937</span><span class="p">);</span>
 <a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a>
 <a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="cm">/* 削除操作 */</span>
-<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="c1">// ハッシュ表からキー値ペア (key, value) を削除</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="c1">// ハッシュテーブルからキーと値のペア (key, value) を削除</span>
 <a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="nx">map</span><span class="p">.</span><span class="ow">delete</span><span class="p">(</span><span class="mf">10583</span><span class="p">);</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* ハッシュ表を初期化 */</span>
+<div class="highlight"><span class="filename">hash_map.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* ハッシュテーブルを初期化 */</span>
 <a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Map</span><span class="o">&lt;</span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="kt">string</span><span class="o">&gt;</span><span class="p">();</span>
 <a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="cm">/* 追加操作 */</span>
-<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="c1">// ハッシュ表にキー値ペア (key, value) を追加</span>
-<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">12836</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;小哈&#39;</span><span class="p">);</span>
-<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">15937</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;小啰&#39;</span><span class="p">);</span>
-<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">16750</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;小算&#39;</span><span class="p">);</span>
-<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">13276</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;小法&#39;</span><span class="p">);</span>
-<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">10583</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;小鸭&#39;</span><span class="p">);</span>
-<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\n追加後、ハッシュ表は\nKey -&gt; Value&#39;</span><span class="p">);</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="c1">// ハッシュテーブルにキーと値のペア (key, value) を追加</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">12836</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;シャオハ&#39;</span><span class="p">);</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">15937</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;シャオルオ&#39;</span><span class="p">);</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">16750</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;シャオスワン&#39;</span><span class="p">);</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">13276</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;シャオファ&#39;</span><span class="p">);</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">10583</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;シャオヤー&#39;</span><span class="p">);</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\n追加後のハッシュテーブルは次のとおりです\nKey -&gt; Value&#39;</span><span class="p">);</span>
 <a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">map</span><span class="p">);</span>
 <a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a>
-<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="cm">/* クエリ操作 */</span>
-<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="c1">// ハッシュ表にキーを入力し、値を取得</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="c1">// ハッシュテーブルにキー key を入力し、値 value を取得</span>
 <a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="kd">let</span><span class="w"> </span><span class="nx">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="mf">15937</span><span class="p">);</span>
-<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\n学籍番号15937を入力、名前を問い合わせ &#39;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">name</span><span class="p">);</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\n学籍番号 15937 を入力し、名前を検索: &#39;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">name</span><span class="p">);</span>
 <a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a>
 <a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="cm">/* 削除操作 */</span>
-<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="c1">// ハッシュ表からキー値ペア (key, value) を削除</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="c1">// ハッシュテーブルからキーと値のペア (key, value) を削除</span>
 <a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="nx">map</span><span class="p">.</span><span class="ow">delete</span><span class="p">(</span><span class="mf">10583</span><span class="p">);</span>
-<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\n10583を削除後、ハッシュ表は\nKey -&gt; Value&#39;</span><span class="p">);</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\n10583 を削除した後のハッシュテーブル\nKey -&gt; Value&#39;</span><span class="p">);</span>
 <a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">map</span><span class="p">);</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* ハッシュ表を初期化 */</span>
+<div class="highlight"><span class="filename">hash_map.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* ハッシュテーブルを初期化 */</span>
 <a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="n">Map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{};</span>
 <a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a>
 <a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="cm">/* 追加操作 */</span>
-<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="c1">// ハッシュ表にキー値ペア (key, value) を追加</span>
-<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="n">map</span><span class="p">[</span><span class="m">12836</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;小哈&quot;</span><span class="p">;</span>
-<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="n">map</span><span class="p">[</span><span class="m">15937</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;小啰&quot;</span><span class="p">;</span>
-<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="n">map</span><span class="p">[</span><span class="m">16750</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;小算&quot;</span><span class="p">;</span>
-<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="n">map</span><span class="p">[</span><span class="m">13276</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;小法&quot;</span><span class="p">;</span>
-<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="n">map</span><span class="p">[</span><span class="m">10583</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;小鸭&quot;</span><span class="p">;</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="c1">// ハッシュテーブルにキーと値のペア (key, value) を追加</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="n">map</span><span class="p">[</span><span class="m">12836</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;シャオハ&quot;</span><span class="p">;</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="n">map</span><span class="p">[</span><span class="m">15937</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;シャオルオ&quot;</span><span class="p">;</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="n">map</span><span class="p">[</span><span class="m">16750</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;シャオスワン&quot;</span><span class="p">;</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="n">map</span><span class="p">[</span><span class="m">13276</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;シャオファ&quot;</span><span class="p">;</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="n">map</span><span class="p">[</span><span class="m">10583</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;シャオヤー&quot;</span><span class="p">;</span>
 <a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a>
-<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="cm">/* クエリ操作 */</span>
-<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="c1">// ハッシュ表にキーを入力し、値を取得</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="c1">// ハッシュテーブルにキー key を入力し、値 value を取得</span>
 <a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="kt">String</span><span class="w"> </span><span class="n">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">[</span><span class="m">15937</span><span class="p">];</span>
 <a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a>
 <a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="cm">/* 削除操作 */</span>
-<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="c1">// ハッシュ表からキー値ペア (key, value) を削除</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="c1">// ハッシュテーブルからキーと値のペア (key, value) を削除</span>
 <a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="n">map</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="m">10583</span><span class="p">);</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">hash_map.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">collections</span><span class="p">::</span><span class="n">HashMap</span><span class="p">;</span>
 <a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
-<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="cm">/* ハッシュ表を初期化 */</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="cm">/* ハッシュテーブルを初期化 */</span>
 <a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">map</span><span class="p">:</span><span class="w"> </span><span class="nc">HashMap</span><span class="o">&lt;</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="nb">String</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashMap</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
 <a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a>
 <a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="cm">/* 追加操作 */</span>
-<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="c1">// ハッシュ表にキー値ペア (key, value) を追加</span>
-<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="n">map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">12836</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小哈&quot;</span><span class="p">.</span><span class="n">to_string</span><span class="p">());</span>
-<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="n">map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">15937</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小啰&quot;</span><span class="p">.</span><span class="n">to_string</span><span class="p">());</span>
-<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="n">map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">16750</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小算&quot;</span><span class="p">.</span><span class="n">to_string</span><span class="p">());</span>
-<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="n">map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">13279</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小法&quot;</span><span class="p">.</span><span class="n">to_string</span><span class="p">());</span>
-<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="n">map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">10583</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小鸭&quot;</span><span class="p">.</span><span class="n">to_string</span><span class="p">());</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="c1">// ハッシュテーブルにキーと値のペア (key, value) を追加</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="n">map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">12836</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;シャオハ&quot;</span><span class="p">.</span><span class="n">to_string</span><span class="p">());</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="n">map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">15937</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;シャオルオ&quot;</span><span class="p">.</span><span class="n">to_string</span><span class="p">());</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="n">map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">16750</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;シャオスワン&quot;</span><span class="p">.</span><span class="n">to_string</span><span class="p">());</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="n">map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">13279</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;シャオファ&quot;</span><span class="p">.</span><span class="n">to_string</span><span class="p">());</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="n">map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">10583</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;シャオヤー&quot;</span><span class="p">.</span><span class="n">to_string</span><span class="p">());</span>
 <a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a>
-<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="cm">/* クエリ操作 */</span>
-<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="c1">// ハッシュ表にキーを入力し、値を取得</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="c1">// ハッシュテーブルにキー key を入力し、値 value を取得</span>
 <a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="kd">let</span><span class="w"> </span><span class="n">_name</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="nb">String</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">get</span><span class="p">(</span><span class="o">&amp;</span><span class="mi">15937</span><span class="p">);</span>
 <a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a>
 <a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="cm">/* 削除操作 */</span>
-<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="c1">// ハッシュ表からキー値ペア (key, value) を削除</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="c1">// ハッシュテーブルからキーと値のペア (key, value) を削除</span>
 <a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="kd">let</span><span class="w"> </span><span class="n">_removed_value</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="nb">String</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="o">&amp;</span><span class="mi">10583</span><span class="p">);</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// Cには組み込みのハッシュ表が提供されていません</span>
+<div class="highlight"><span class="filename">hash_map.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// C には組み込みのハッシュテーブルはありません</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
+<div class="highlight"><span class="filename">hash_map.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* ハッシュテーブルを初期化 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">val</span><span class="w"> </span><span class="nv">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashMap</span><span class="o">&lt;</span><span class="kt">Int</span><span class="p">,</span><span class="kt">String</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="c1">// ハッシュテーブルにキーと値のペア (key, value) を追加</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="n">map</span><span class="o">[</span><span class="m">12836</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;シャオハ&quot;</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="n">map</span><span class="o">[</span><span class="m">15937</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;シャオルオ&quot;</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="n">map</span><span class="o">[</span><span class="m">16750</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;シャオスワン&quot;</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="n">map</span><span class="o">[</span><span class="m">13276</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;シャオファ&quot;</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="n">map</span><span class="o">[</span><span class="m">10583</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;シャオヤー&quot;</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="c1">// ハッシュテーブルにキー key を入力し、値 value を取得</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="kd">val</span><span class="w"> </span><span class="nv">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="o">[</span><span class="m">15937</span><span class="o">]</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="c1">// ハッシュテーブルからキーと値のペア (key, value) を削除</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="n">map</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="m">10583</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1"># ハッシュテーブルを初期化</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="n">hmap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{}</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="c1"># 追加操作</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="c1"># ハッシュテーブルにキーと値のペア (key, value) を追加</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="n">hmap</span><span class="o">[</span><span class="mi">12836</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;シャオハ&quot;</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="n">hmap</span><span class="o">[</span><span class="mi">15937</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;シャオルオ&quot;</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="n">hmap</span><span class="o">[</span><span class="mi">16750</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;シャオスワン&quot;</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="n">hmap</span><span class="o">[</span><span class="mi">13276</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;シャオファ&quot;</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="n">hmap</span><span class="o">[</span><span class="mi">10583</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;シャオヤー&quot;</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="c1"># 検索操作</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="c1"># ハッシュテーブルにキー key を入力し、値 value を取得</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="nb">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hmap</span><span class="o">[</span><span class="mi">15937</span><span class="o">]</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="c1"># 削除操作</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="c1"># ハッシュテーブルからキーと値のペア (key, value) を削除</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="n">hmap</span><span class="o">.</span><span class="n">delete</span><span class="p">(</span><span class="mi">10583</span><span class="p">)</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>ハッシュ表を走査する一般的な方法は3つあります：キー値ペアの走査、キーの走査、値の走査。以下はコード例です：</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="2:12"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label></div>
+<details class="pythontutor">
+<summary>可視化実行</summary>
+<p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%93%88%E5%B8%8C%E8%A1%A8%0A%20%20%20%20hmap%20%3D%20%7B%7D%0A%20%20%20%20%0A%20%20%20%20%23%20%E6%B7%BB%E5%8A%A0%E6%93%8D%E4%BD%9C%0A%20%20%20%20%23%20%E5%9C%A8%E5%93%88%E5%B8%8C%E8%A1%A8%E4%B8%AD%E6%B7%BB%E5%8A%A0%E9%94%AE%E5%80%BC%E5%AF%B9%20%28key,%20value%29%0A%20%20%20%20hmap%5B12836%5D%20%3D%20%22%E5%B0%8F%E5%93%88%22%0A%20%20%20%20hmap%5B15937%5D%20%3D%20%22%E5%B0%8F%E5%95%B0%22%0A%20%20%20%20hmap%5B16750%5D%20%3D%20%22%E5%B0%8F%E7%AE%97%22%0A%20%20%20%20hmap%5B13276%5D%20%3D%20%22%E5%B0%8F%E6%B3%95%22%0A%20%20%20%20hmap%5B10583%5D%20%3D%20%22%E5%B0%8F%E9%B8%AD%22%0A%20%20%20%20%0A%20%20%20%20%23%20%E6%9F%A5%E8%AF%A2%E6%93%8D%E4%BD%9C%0A%20%20%20%20%23%20%E5%90%91%E5%93%88%E5%B8%8C%E8%A1%A8%E4%B8%AD%E8%BE%93%E5%85%A5%E9%94%AE%20key%20%EF%BC%8C%E5%BE%97%E5%88%B0%E5%80%BC%20value%0A%20%20%20%20name%20%3D%20hmap%5B15937%5D%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%88%A0%E9%99%A4%E6%93%8D%E4%BD%9C%0A%20%20%20%20%23%20%E5%9C%A8%E5%93%88%E5%B8%8C%E8%A1%A8%E4%B8%AD%E5%88%A0%E9%99%A4%E9%94%AE%E5%80%BC%E5%AF%B9%20%28key,%20value%29%0A%20%20%20%20hmap.pop%2810583%29&amp;cumulative=false&amp;curInstr=2&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>
+</details>
+<p>ハッシュテーブルには、キーと値のペア、キー、値を走査する 3 つの一般的な方法があります。コード例は以下のとおりです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map.py</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1"># ハッシュ表を走査</span>
-<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="c1"># キー値ペア key-&gt;value を走査</span>
-<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="k">for</span> <span class="n">key</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="n">hmap</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>    <span class="nb">print</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="s2">&quot;-&gt;&quot;</span><span class="p">,</span> <span class="n">value</span><span class="p">)</span>
-<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="c1"># キーのみを走査</span>
-<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="k">for</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">hmap</span><span class="o">.</span><span class="n">keys</span><span class="p">():</span>
-<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a>    <span class="nb">print</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
-<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="c1"># 値のみを走査</span>
-<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="k">for</span> <span class="n">value</span> <span class="ow">in</span> <span class="n">hmap</span><span class="o">.</span><span class="n">values</span><span class="p">():</span>
-<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a>    <span class="nb">print</span><span class="p">(</span><span class="n">value</span><span class="p">)</span>
+<div class="highlight"><span class="filename">hash_map.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="c1"># ハッシュテーブルを走査</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="c1"># キーと値のペア key-&gt;value を走査</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="k">for</span> <span class="n">key</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="n">hmap</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="nb">print</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="s2">&quot;-&gt;&quot;</span><span class="p">,</span> <span class="n">value</span><span class="p">)</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="c1"># キー key のみを走査</span>
+<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="k">for</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">hmap</span><span class="o">.</span><span class="n">keys</span><span class="p">():</span>
+<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>    <span class="nb">print</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="c1"># 値 value のみを走査</span>
+<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="k">for</span> <span class="n">value</span> <span class="ow">in</span> <span class="n">hmap</span><span class="o">.</span><span class="n">values</span><span class="p">():</span>
+<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>    <span class="nb">print</span><span class="p">(</span><span class="n">value</span><span class="p">)</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map.cpp</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="cm">/* ハッシュ表を走査 */</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="c1">// キー値ペア key-&gt;value を走査</span>
-<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="n">kv</span><span class="o">:</span><span class="w"> </span><span class="n">map</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="w">    </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">kv</span><span class="p">.</span><span class="n">first</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">kv</span><span class="p">.</span><span class="n">second</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
-<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="p">}</span>
-<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="c1">// イテレータを使用してキー値ペア key-&gt;value を走査</span>
-<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="n">iter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">begin</span><span class="p">();</span><span class="w"> </span><span class="n">iter</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">end</span><span class="p">();</span><span class="w"> </span><span class="n">iter</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="w">    </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">iter</span><span class="o">-&gt;</span><span class="n">first</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;-&gt;&quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">iter</span><span class="o">-&gt;</span><span class="n">second</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
-<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="p">}</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map.java</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* ハッシュ表を走査 */</span>
-<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="c1">// キー値ペア key-&gt;value を走査</span>
-<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Map</span><span class="p">.</span><span class="na">Entry</span><span class="o">&lt;</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">kv</span><span class="p">:</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="na">entrySet</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">kv</span><span class="p">.</span><span class="na">getKey</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">kv</span><span class="p">.</span><span class="na">getValue</span><span class="p">());</span>
+<div class="highlight"><span class="filename">hash_map.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* ハッシュテーブルを走査 */</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="c1">// キーと値のペア key-&gt;value を走査</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="n">kv</span><span class="o">:</span><span class="w"> </span><span class="n">map</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">kv</span><span class="p">.</span><span class="n">first</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">kv</span><span class="p">.</span><span class="n">second</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
 <a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="p">}</span>
-<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="c1">// キーのみを走査</span>
-<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="na">keySet</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">    </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="c1">// イテレータを使って key-&gt;value を走査</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="n">iter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">begin</span><span class="p">();</span><span class="w"> </span><span class="n">iter</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">end</span><span class="p">();</span><span class="w"> </span><span class="n">iter</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">    </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">iter</span><span class="o">-&gt;</span><span class="n">first</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;-&gt;&quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">iter</span><span class="o">-&gt;</span><span class="n">second</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
 <a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="p">}</span>
-<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="c1">// 値のみを走査</span>
-<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="na">values</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">    </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
-<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map.cs</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* ハッシュ表を走査 */</span>
-<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="c1">// キー値ペア Key-&gt;Value を走査</span>
-<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">var</span><span class="w"> </span><span class="n">kv</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">map</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="n">kv</span><span class="p">.</span><span class="n">Key</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">kv</span><span class="p">.</span><span class="n">Value</span><span class="p">);</span>
+<div class="highlight"><span class="filename">hash_map.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* ハッシュテーブルを走査 */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="c1">// キーと値のペア key-&gt;value を走査</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Map</span><span class="p">.</span><span class="na">Entry</span><span class="w"> </span><span class="o">&lt;</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">kv</span><span class="p">:</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="na">entrySet</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">kv</span><span class="p">.</span><span class="na">getKey</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">kv</span><span class="p">.</span><span class="na">getValue</span><span class="p">());</span>
 <a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="p">}</span>
-<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="c1">// キーのみを走査</span>
-<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">Keys</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="c1">// キー key のみを走査</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="na">keySet</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
 <a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="p">}</span>
-<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="c1">// 値のみを走査</span>
-<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">string</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">Values</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">    </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="c1">// 値 value のみを走査</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="na">values</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">    </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
 <a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map_test.go</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* ハッシュ表を走査 */</span>
-<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="c1">// キー値ペア key-&gt;value を走査</span>
-<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="k">for</span><span class="w"> </span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="nx">value</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">hmap</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;-&gt;&quot;</span><span class="p">,</span><span class="w"> </span><span class="nx">value</span><span class="p">)</span>
+<div class="highlight"><span class="filename">hash_map.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* ハッシュテーブルを走査 */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="c1">// キーと値のペア Key-&gt;Value を走査</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">var</span><span class="w"> </span><span class="n">kv</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">map</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="n">kv</span><span class="p">.</span><span class="n">Key</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">kv</span><span class="p">.</span><span class="n">Value</span><span class="p">);</span>
 <a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="p">}</span>
-<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="c1">// キーのみを走査</span>
-<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="k">for</span><span class="w"> </span><span class="nx">key</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">hmap</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="c1">// キー key のみを走査</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">Keys</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
 <a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="p">}</span>
-<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="c1">// 値のみを走査</span>
-<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">value</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">hmap</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">value</span><span class="p">)</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="c1">// 値 value のみを走査</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">string</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">Values</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">    </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
 <a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map.swift</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* ハッシュ表を走査 */</span>
-<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="c1">// キー値ペア Key-&gt;Value を走査</span>
-<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">value</span><span class="p">)</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="bp">map</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="bp">print</span><span class="p">(</span><span class="s">&quot;</span><span class="si">\(</span><span class="n">key</span><span class="si">)</span><span class="s"> -&gt; </span><span class="si">\(</span><span class="n">value</span><span class="si">)</span><span class="s">&quot;</span><span class="p">)</span>
+<div class="highlight"><span class="filename">hash_map_test.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* ハッシュテーブルを走査 */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="c1">// キーと値のペア key-&gt;value を走査</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="k">for</span><span class="w"> </span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="nx">value</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">hmap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;-&gt;&quot;</span><span class="p">,</span><span class="w"> </span><span class="nx">value</span><span class="p">)</span>
 <a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="p">}</span>
-<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="c1">// キーのみを走査</span>
-<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="k">for</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="bp">map</span><span class="p">.</span><span class="n">keys</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">    </span><span class="bp">print</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="c1">// キー key のみを走査</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="k">for</span><span class="w"> </span><span class="nx">key</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">hmap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span>
 <a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="p">}</span>
-<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="c1">// 値のみを走査</span>
-<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="k">for</span><span class="w"> </span><span class="n">value</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="bp">map</span><span class="p">.</span><span class="n">values</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">    </span><span class="bp">print</span><span class="p">(</span><span class="n">value</span><span class="p">)</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="c1">// 値 value のみを走査</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">value</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">hmap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">value</span><span class="p">)</span>
 <a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map.js</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* ハッシュ表を走査 */</span>
-<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\nキー値ペア Key-&gt;Value を走査&#39;</span><span class="p">);</span>
-<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="p">[</span><span class="nx">k</span><span class="p">,</span><span class="w"> </span><span class="nx">v</span><span class="p">]</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">entries</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">k</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s1">&#39; -&gt; &#39;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">v</span><span class="p">);</span>
+<div class="highlight"><span class="filename">hash_map.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* ハッシュテーブルを走査 */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="c1">// キーと値のペア Key-&gt;Value を走査</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">value</span><span class="p">)</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="bp">map</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="bp">print</span><span class="p">(</span><span class="s">&quot;</span><span class="si">\(</span><span class="n">key</span><span class="si">)</span><span class="s"> -&gt; </span><span class="si">\(</span><span class="n">value</span><span class="si">)</span><span class="s">&quot;</span><span class="p">)</span>
 <a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="p">}</span>
-<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\nキーのみを走査 Key&#39;</span><span class="p">);</span>
-<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">keys</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">    </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">k</span><span class="p">);</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="c1">// キー Key のみを走査</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="k">for</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="bp">map</span><span class="p">.</span><span class="n">keys</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">    </span><span class="bp">print</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
 <a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="p">}</span>
-<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\n値のみを走査 Value&#39;</span><span class="p">);</span>
-<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">v</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">values</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w">    </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">v</span><span class="p">);</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="c1">// 値 Value のみを走査</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="k">for</span><span class="w"> </span><span class="n">value</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="bp">map</span><span class="p">.</span><span class="n">values</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w">    </span><span class="bp">print</span><span class="p">(</span><span class="n">value</span><span class="p">)</span>
 <a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map.ts</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* ハッシュ表を走査 */</span>
-<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\nキー値ペア Key-&gt;Value を走査&#39;</span><span class="p">);</span>
+<div class="highlight"><span class="filename">hash_map.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* ハッシュテーブルを走査 */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\nキーと値のペア Key-&gt;Value を走査&#39;</span><span class="p">);</span>
 <a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="p">[</span><span class="nx">k</span><span class="p">,</span><span class="w"> </span><span class="nx">v</span><span class="p">]</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">entries</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">k</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s1">&#39; -&gt; &#39;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">v</span><span class="p">);</span>
 <a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="p">}</span>
-<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\nキーのみを走査 Key&#39;</span><span class="p">);</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\nキー Key のみを走査&#39;</span><span class="p">);</span>
 <a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">keys</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">    </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">k</span><span class="p">);</span>
 <a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="p">}</span>
-<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\n値のみを走査 Value&#39;</span><span class="p">);</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\n値 Value のみを走査&#39;</span><span class="p">);</span>
 <a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">v</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">values</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">    </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">v</span><span class="p">);</span>
 <a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map.dart</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* ハッシュ表を走査 */</span>
-<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="c1">// キー値ペア Key-&gt;Value を走査</span>
-<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="n">map</span><span class="p">.</span><span class="n">forEach</span><span class="p">((</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">value</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="n">print</span><span class="p">(</span><span class="s1">&#39;</span><span class="si">$</span><span class="n">key</span><span class="s1"> -&gt; </span><span class="si">$</span><span class="n">value</span><span class="s1">&#39;</span><span class="p">);</span>
-<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="p">});</span>
-<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a>
-<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="c1">// キーのみを走査 Key</span>
-<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="n">map</span><span class="p">.</span><span class="n">keys</span><span class="p">.</span><span class="n">forEach</span><span class="p">((</span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="n">print</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
-<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="p">});</span>
-<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a>
-<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="c1">// 値のみを走査 Value</span>
-<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="n">map</span><span class="p">.</span><span class="n">values</span><span class="p">.</span><span class="n">forEach</span><span class="p">((</span><span class="n">value</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="n">print</span><span class="p">(</span><span class="n">value</span><span class="p">);</span>
-<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="p">});</span>
+<div class="highlight"><span class="filename">hash_map.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* ハッシュテーブルを走査 */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\nキーと値のペア Key-&gt;Value を走査&#39;</span><span class="p">);</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="p">[</span><span class="nx">k</span><span class="p">,</span><span class="w"> </span><span class="nx">v</span><span class="p">]</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">entries</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">k</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s1">&#39; -&gt; &#39;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">v</span><span class="p">);</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="p">}</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\nキー Key のみを走査&#39;</span><span class="p">);</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">keys</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">    </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">k</span><span class="p">);</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="p">}</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\n値 Value のみを走査&#39;</span><span class="p">);</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">v</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">values</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">    </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">v</span><span class="p">);</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map.rs</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* ハッシュ表を走査 */</span>
-<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="c1">// キー値ペア Key-&gt;Value を走査</span>
-<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">value</span><span class="p">)</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="o">&amp;</span><span class="n">map</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">    </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{key} -&gt; {value}&quot;</span><span class="p">);</span>
-<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">hash_map.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* ハッシュテーブルを走査 */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="c1">// キーと値のペア Key-&gt;Value を走査</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="n">map</span><span class="p">.</span><span class="n">forEach</span><span class="p">((</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">value</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="n">print</span><span class="p">(</span><span class="s1">&#39;</span><span class="si">$</span><span class="n">key</span><span class="s1"> -&gt; </span><span class="si">$</span><span class="n">value</span><span class="s1">&#39;</span><span class="p">);</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="p">});</span>
 <a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a>
-<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="c1">// キーのみを走査 Key</span>
-<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="k">for</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">keys</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">    </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{key}&quot;</span><span class="p">);</span>
-<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="p">}</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="c1">// キー Key のみを走査</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="n">map</span><span class="p">.</span><span class="n">keys</span><span class="p">.</span><span class="n">forEach</span><span class="p">((</span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">  </span><span class="n">print</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="p">});</span>
 <a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a>
-<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="c1">// 値のみを走査 Value</span>
-<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="k">for</span><span class="w"> </span><span class="n">value</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">values</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w">    </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{value}&quot;</span><span class="p">);</span>
-<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="p">}</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="c1">// 値 Value のみを走査</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="n">map</span><span class="p">.</span><span class="n">values</span><span class="p">.</span><span class="n">forEach</span><span class="p">((</span><span class="n">value</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w">  </span><span class="n">print</span><span class="p">(</span><span class="n">value</span><span class="p">);</span>
+<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="p">});</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map.c</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="c1">// Cには組み込みのハッシュ表が提供されていません</span>
+<div class="highlight"><span class="filename">hash_map.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* ハッシュテーブルを走査 */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="c1">// キーと値のペア Key-&gt;Value を走査</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">value</span><span class="p">)</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="o">&amp;</span><span class="n">map</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{key} -&gt; {value}&quot;</span><span class="p">);</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="p">}</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="c1">// キー Key のみを走査</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="k">for</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">keys</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">    </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{key}&quot;</span><span class="p">);</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="p">}</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="c1">// 値 Value のみを走査</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="k">for</span><span class="w"> </span><span class="n">value</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">values</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">    </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{value}&quot;</span><span class="p">);</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">hash_map.kt</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a>
+<div class="highlight"><span class="filename">hash_map.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="c1">// C には組み込みのハッシュテーブルはありません</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* ハッシュテーブルを走査 */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="c1">// キーと値のペア key-&gt;value を走査</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="k">for</span><span class="w"> </span><span class="p">((</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">value</span><span class="p">)</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">map</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="n">println</span><span class="p">(</span><span class="s">&quot;</span><span class="si">$</span><span class="n">key</span><span class="s"> -&gt; </span><span class="si">$</span><span class="n">value</span><span class="s">&quot;</span><span class="p">)</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="p">}</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="c1">// キー key のみを走査</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">key</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="na">keys</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w">    </span><span class="n">println</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="p">}</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="c1">// 値 value のみを走査</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">_val</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="na">values</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">    </span><span class="n">println</span><span class="p">(</span><span class="n">_val</span><span class="p">)</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1"># ハッシュテーブルを走査</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="c1"># キーと値のペア key-&gt;value を走査</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="n">hmap</span><span class="o">.</span><span class="n">entries</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">value</span><span class="o">|</span><span class="w"> </span><span class="nb">puts</span><span class="w"> </span><span class="s2">&quot;</span><span class="si">#{</span><span class="n">key</span><span class="si">}</span><span class="s2"> -&gt; </span><span class="si">#{</span><span class="n">value</span><span class="si">}</span><span class="s2">&quot;</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="c1"># キー key のみを走査</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="n">hmap</span><span class="o">.</span><span class="n">keys</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">key</span><span class="o">|</span><span class="w"> </span><span class="nb">puts</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="c1"># 値 value のみを走査</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="n">hmap</span><span class="o">.</span><span class="n">values</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">val</span><span class="o">|</span><span class="w"> </span><span class="nb">puts</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="p">}</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h2 id="612">6.1.2 &nbsp; ハッシュ表の簡単な実装<a class="headerlink" href="#612" title="Permanent link">&para;</a></h2>
-<p>まず、最も簡単なケースを考えてみましょう：<strong>配列のみを使ってハッシュ表を実装すること</strong>。ハッシュ表において、配列の各空きスロットは<u>バケット</u>と呼ばれ、各バケットはキー値ペアを格納できます。したがって、クエリ操作は<code>key</code>に対応するバケットを見つけ、そこから<code>value</code>を取得することになります。</p>
-<p>では、<code>key</code>に基づいて対応するバケットをどのように特定するのでしょうか？これは<u>ハッシュ関数</u>によって実現されます。ハッシュ関数の役割は、より大きな入力空間をより小さな出力空間にマッピングすることです。ハッシュ表では、入力空間はすべてのキーで構成され、出力空間はすべてのバケット（配列インデックス）で構成されます。つまり、<code>key</code>が与えられた場合、<strong>ハッシュ関数を使用して対応するキー値ペアの配列内の格納位置を決定できます</strong>。</p>
-<p>与えられた<code>key</code>に対して、ハッシュ関数の計算は2つのステップで構成されます：</p>
+<details class="pythontutor">
+<summary>可視化実行</summary>
+<p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%93%88%E5%B8%8C%E8%A1%A8%0A%20%20%20%20hmap%20%3D%20%7B%7D%0A%20%20%20%20%0A%20%20%20%20%23%20%E6%B7%BB%E5%8A%A0%E6%93%8D%E4%BD%9C%0A%20%20%20%20%23%20%E5%9C%A8%E5%93%88%E5%B8%8C%E8%A1%A8%E4%B8%AD%E6%B7%BB%E5%8A%A0%E9%94%AE%E5%80%BC%E5%AF%B9%20%28key,%20value%29%0A%20%20%20%20hmap%5B12836%5D%20%3D%20%22%E5%B0%8F%E5%93%88%22%0A%20%20%20%20hmap%5B15937%5D%20%3D%20%22%E5%B0%8F%E5%95%B0%22%0A%20%20%20%20hmap%5B16750%5D%20%3D%20%22%E5%B0%8F%E7%AE%97%22%0A%20%20%20%20hmap%5B13276%5D%20%3D%20%22%E5%B0%8F%E6%B3%95%22%0A%20%20%20%20hmap%5B10583%5D%20%3D%20%22%E5%B0%8F%E9%B8%AD%22%0A%20%20%20%20%0A%20%20%20%20%23%20%E9%81%8D%E5%8E%86%E5%93%88%E5%B8%8C%E8%A1%A8%0A%20%20%20%20%23%20%E9%81%8D%E5%8E%86%E9%94%AE%E5%80%BC%E5%AF%B9%20key-%3Evalue%0A%20%20%20%20for%20key,%20value%20in%20hmap.items%28%29%3A%0A%20%20%20%20%20%20%20%20print%28key,%20%22-%3E%22,%20value%29%0A%20%20%20%20%23%20%E5%8D%95%E7%8B%AC%E9%81%8D%E5%8E%86%E9%94%AE%20key%0A%20%20%20%20for%20key%20in%20hmap.keys%28%29%3A%0A%20%20%20%20%20%20%20%20print%28key%29%0A%20%20%20%20%23%20%E5%8D%95%E7%8B%AC%E9%81%8D%E5%8E%86%E5%80%BC%20value%0A%20%20%20%20for%20value%20in%20hmap.values%28%29%3A%0A%20%20%20%20%20%20%20%20print%28value%29&amp;cumulative=false&amp;curInstr=8&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>
+</details>
+<h2 id="612">6.1.2 &nbsp; ハッシュテーブルの簡単な実装<a class="headerlink" href="#612" title="Permanent link">&para;</a></h2>
+<p>まずは最も単純なケースとして、**1 つの配列だけでハッシュテーブルを実装する**ことを考えます。ハッシュテーブルでは、配列中の各空き位置を<u>バケット（bucket）</u>と呼び、各バケットには 1 つのキーと値のペアを格納できます。したがって、検索操作とは <code>key</code> に対応するバケットを見つけ、そのバケットから <code>value</code> を取得することです。</p>
+<p>では、<code>key</code> に基づいて対応するバケットをどのように特定するのでしょうか。これは<u>ハッシュ関数（hash function）</u>によって実現されます。ハッシュ関数の役割は、大きな入力空間をより小さな出力空間に写像することです。ハッシュテーブルでは、入力空間はすべての <code>key</code> 、出力空間はすべてのバケット（配列インデックス）です。言い換えると、<code>key</code> を入力すると、<strong>ハッシュ関数によってその <code>key</code> に対応するキーと値のペアの配列内での格納位置を求められます</strong>。</p>
+<p><code>key</code> を入力したとき、ハッシュ関数の計算過程は次の 2 段階に分かれます。</p>
 <ol>
-<li>特定のハッシュアルゴリズム<code>hash()</code>を使用してハッシュ値を計算します。</li>
-<li>ハッシュ値をバケット数（配列長）<code>capacity</code>で剰余を取り、キーに対応する配列<code>index</code>を取得します。</li>
+<li>あるハッシュアルゴリズム <code>hash()</code> を用いてハッシュ値を計算します。</li>
+<li>ハッシュ値をバケット数（配列長）<code>capacity</code> で剰余し、その <code>key</code> に対応するバケット（配列インデックス）<code>index</code> を求めます。</li>
 </ol>
-<div class="highlight"><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="nv">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span>hash<span class="o">(</span>key<span class="o">)</span><span class="w"> </span>%<span class="w"> </span>capacity
+<div class="highlight"><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="nv">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span>hash<span class="o">(</span>key<span class="o">)</span><span class="w"> </span>%<span class="w"> </span>capacity
 </code></pre></div>
-<p>その後、<code>index</code>を使用してハッシュ表内の対応するバケットにアクセスし、<code>value</code>を取得できます。</p>
-<p>配列長が<code>capacity = 100</code>で、ハッシュアルゴリズムが<code>hash(key) = key</code>として定義されているとします。したがって、ハッシュ関数は<code>key % 100</code>として表現できます。以下の図は、<code>key</code>を学籍番号、<code>value</code>を名前として、ハッシュ関数の動作原理を示しています。</p>
+<p>その後、<code>index</code> を使ってハッシュテーブル内の対応するバケットにアクセスし、<code>value</code> を取得できます。</p>
+<p>配列長を <code>capacity = 100</code> 、ハッシュアルゴリズムを <code>hash(key) = key</code> とすると、ハッシュ関数は <code>key % 100</code> となります。次の図では、<code>key</code> を学籍番号、<code>value</code> を名前の例として、ハッシュ関数の動作原理を示します。</p>
 <p><img alt="ハッシュ関数の動作原理" class="animation-figure" src="../hash_map.assets/hash_function.png" /></p>
 <p align="center"> 図 6-2 &nbsp; ハッシュ関数の動作原理 </p>
 
-<p>以下のコードは簡単なハッシュ表を実装しています。ここでは、<code>key</code>と<code>value</code>を<code>Pair</code>クラスにカプセル化してキー値ペアを表現しています。</p>
+<p>以下のコードは、単純なハッシュテーブルを実装したものです。ここでは、キーと値のペアを表すために <code>key</code> と <code>value</code> をクラス <code>Pair</code> にまとめています。</p>
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 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_hash_map.py</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">Pair</span><span class="p">:</span>
-<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;キー値ペア&quot;&quot;&quot;</span>
-<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a>
-<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">str</span><span class="p">):</span>
-<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">key</span> <span class="o">=</span> <span class="n">key</span>
-<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">val</span> <span class="o">=</span> <span class="n">val</span>
-<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a>
-<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayHashMap</span><span class="p">:</span>
-<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;配列実装に基づくハッシュテーブル&quot;&quot;&quot;</span>
-<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a>
-<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
-<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a>        <span class="c1"># 100個のバケットを含む配列を初期化</span>
-<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">Pair</span> <span class="o">|</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="kc">None</span><span class="p">]</span> <span class="o">*</span> <span class="mi">100</span>
-<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a>
-<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">hash_func</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;ハッシュ関数&quot;&quot;&quot;</span>
-<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a>        <span class="n">index</span> <span class="o">=</span> <span class="n">key</span> <span class="o">%</span> <span class="mi">100</span>
-<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a>        <span class="k">return</span> <span class="n">index</span>
-<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a>
-<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">str</span><span class="p">:</span>
-<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;照会操作&quot;&quot;&quot;</span>
-<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a>        <span class="n">index</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
-<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a>        <span class="n">pair</span><span class="p">:</span> <span class="n">Pair</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
-<a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a>        <span class="k">if</span> <span class="n">pair</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></a>            <span class="k">return</span> <span class="kc">None</span>
-<a id="__codelineno-25-27" name="__codelineno-25-27" href="#__codelineno-25-27"></a>        <span class="k">return</span> <span class="n">pair</span><span class="o">.</span><span class="n">val</span>
-<a id="__codelineno-25-28" name="__codelineno-25-28" href="#__codelineno-25-28"></a>
-<a id="__codelineno-25-29" name="__codelineno-25-29" href="#__codelineno-25-29"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">str</span><span class="p">):</span>
-<a id="__codelineno-25-30" name="__codelineno-25-30" href="#__codelineno-25-30"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;追加操作&quot;&quot;&quot;</span>
-<a id="__codelineno-25-31" name="__codelineno-25-31" href="#__codelineno-25-31"></a>        <span class="n">pair</span> <span class="o">=</span> <span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
-<a id="__codelineno-25-32" name="__codelineno-25-32" href="#__codelineno-25-32"></a>        <span class="n">index</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
-<a id="__codelineno-25-33" name="__codelineno-25-33" href="#__codelineno-25-33"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">pair</span>
-<a id="__codelineno-25-34" name="__codelineno-25-34" href="#__codelineno-25-34"></a>
-<a id="__codelineno-25-35" name="__codelineno-25-35" href="#__codelineno-25-35"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-25-36" name="__codelineno-25-36" href="#__codelineno-25-36"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;削除操作&quot;&quot;&quot;</span>
-<a id="__codelineno-25-37" name="__codelineno-25-37" href="#__codelineno-25-37"></a>        <span class="n">index</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
-<a id="__codelineno-25-38" name="__codelineno-25-38" href="#__codelineno-25-38"></a>        <span class="c1"># None に設定し、削除を表現</span>
-<a id="__codelineno-25-39" name="__codelineno-25-39" href="#__codelineno-25-39"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span>
-<a id="__codelineno-25-40" name="__codelineno-25-40" href="#__codelineno-25-40"></a>
-<a id="__codelineno-25-41" name="__codelineno-25-41" href="#__codelineno-25-41"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">entry_set</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="n">Pair</span><span class="p">]:</span>
-<a id="__codelineno-25-42" name="__codelineno-25-42" href="#__codelineno-25-42"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;すべてのキー値ペアを取得&quot;&quot;&quot;</span>
-<a id="__codelineno-25-43" name="__codelineno-25-43" href="#__codelineno-25-43"></a>        <span class="n">result</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">Pair</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
-<a id="__codelineno-25-44" name="__codelineno-25-44" href="#__codelineno-25-44"></a>        <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span>
-<a id="__codelineno-25-45" name="__codelineno-25-45" href="#__codelineno-25-45"></a>            <span class="k">if</span> <span class="n">pair</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-25-46" name="__codelineno-25-46" href="#__codelineno-25-46"></a>                <span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">pair</span><span class="p">)</span>
-<a id="__codelineno-25-47" name="__codelineno-25-47" href="#__codelineno-25-47"></a>        <span class="k">return</span> <span class="n">result</span>
-<a id="__codelineno-25-48" name="__codelineno-25-48" href="#__codelineno-25-48"></a>
-<a id="__codelineno-25-49" name="__codelineno-25-49" href="#__codelineno-25-49"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">key_set</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
-<a id="__codelineno-25-50" name="__codelineno-25-50" href="#__codelineno-25-50"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;すべてのキーを取得&quot;&quot;&quot;</span>
-<a id="__codelineno-25-51" name="__codelineno-25-51" href="#__codelineno-25-51"></a>        <span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
-<a id="__codelineno-25-52" name="__codelineno-25-52" href="#__codelineno-25-52"></a>        <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span>
-<a id="__codelineno-25-53" name="__codelineno-25-53" href="#__codelineno-25-53"></a>            <span class="k">if</span> <span class="n">pair</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-25-54" name="__codelineno-25-54" href="#__codelineno-25-54"></a>                <span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="p">)</span>
-<a id="__codelineno-25-55" name="__codelineno-25-55" href="#__codelineno-25-55"></a>        <span class="k">return</span> <span class="n">result</span>
-<a id="__codelineno-25-56" name="__codelineno-25-56" href="#__codelineno-25-56"></a>
-<a id="__codelineno-25-57" name="__codelineno-25-57" href="#__codelineno-25-57"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">value_set</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">str</span><span class="p">]:</span>
-<a id="__codelineno-25-58" name="__codelineno-25-58" href="#__codelineno-25-58"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;すべての値を取得&quot;&quot;&quot;</span>
-<a id="__codelineno-25-59" name="__codelineno-25-59" href="#__codelineno-25-59"></a>        <span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
-<a id="__codelineno-25-60" name="__codelineno-25-60" href="#__codelineno-25-60"></a>        <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span>
-<a id="__codelineno-25-61" name="__codelineno-25-61" href="#__codelineno-25-61"></a>            <span class="k">if</span> <span class="n">pair</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-25-62" name="__codelineno-25-62" href="#__codelineno-25-62"></a>                <span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
-<a id="__codelineno-25-63" name="__codelineno-25-63" href="#__codelineno-25-63"></a>        <span class="k">return</span> <span class="n">result</span>
-<a id="__codelineno-25-64" name="__codelineno-25-64" href="#__codelineno-25-64"></a>
-<a id="__codelineno-25-65" name="__codelineno-25-65" href="#__codelineno-25-65"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">print</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<a id="__codelineno-25-66" name="__codelineno-25-66" href="#__codelineno-25-66"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;ハッシュテーブルを出力&quot;&quot;&quot;</span>
-<a id="__codelineno-25-67" name="__codelineno-25-67" href="#__codelineno-25-67"></a>        <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span>
-<a id="__codelineno-25-68" name="__codelineno-25-68" href="#__codelineno-25-68"></a>            <span class="k">if</span> <span class="n">pair</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-25-69" name="__codelineno-25-69" href="#__codelineno-25-69"></a>                <span class="nb">print</span><span class="p">(</span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="p">,</span> <span class="s2">&quot;-&gt;&quot;</span><span class="p">,</span> <span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">array_hash_map.cpp</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="cm">/* キー値ペア */</span>
-<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">Pair</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
-<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">;</span>
-<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w">    </span><span class="n">string</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
-<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w">    </span><span class="n">Pair</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="w">        </span><span class="k">this</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="p">;</span>
-<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="w">        </span><span class="k">this</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
-<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="p">};</span>
-<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a>
-<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="cm">/* 配列実装に基づくハッシュテーブル */</span>
-<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayHashMap</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
-<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Pair</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span>
-<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a>
-<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
-<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a><span class="w">    </span><span class="n">ArrayHashMap</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a><span class="w">        </span><span class="c1">// 配列を初期化、100個のバケットを含む</span>
-<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Pair</span><span class="w"> </span><span class="o">*&gt;</span><span class="p">(</span><span class="mi">100</span><span class="p">);</span>
-<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a>
-<a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a><span class="w">    </span><span class="o">~</span><span class="n">ArrayHashMap</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-24" name="__codelineno-26-24" href="#__codelineno-26-24"></a><span class="w">        </span><span class="c1">// メモリを解放</span>
-<a id="__codelineno-26-25" name="__codelineno-26-25" href="#__codelineno-26-25"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="o">&amp;</span><span class="n">bucket</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-26" name="__codelineno-26-26" href="#__codelineno-26-26"></a><span class="w">            </span><span class="k">delete</span><span class="w"> </span><span class="n">bucket</span><span class="p">;</span>
-<a id="__codelineno-26-27" name="__codelineno-26-27" href="#__codelineno-26-27"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-26-28" name="__codelineno-26-28" href="#__codelineno-26-28"></a><span class="w">        </span><span class="n">buckets</span><span class="p">.</span><span class="n">clear</span><span class="p">();</span>
-<a id="__codelineno-26-29" name="__codelineno-26-29" href="#__codelineno-26-29"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-30" name="__codelineno-26-30" href="#__codelineno-26-30"></a>
-<a id="__codelineno-26-31" name="__codelineno-26-31" href="#__codelineno-26-31"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
-<a id="__codelineno-26-32" name="__codelineno-26-32" href="#__codelineno-26-32"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-33" name="__codelineno-26-33" href="#__codelineno-26-33"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">100</span><span class="p">;</span>
-<a id="__codelineno-26-34" name="__codelineno-26-34" href="#__codelineno-26-34"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
-<a id="__codelineno-26-35" name="__codelineno-26-35" href="#__codelineno-26-35"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-36" name="__codelineno-26-36" href="#__codelineno-26-36"></a>
-<a id="__codelineno-26-37" name="__codelineno-26-37" href="#__codelineno-26-37"></a><span class="w">    </span><span class="cm">/* クエリ操作 */</span>
-<a id="__codelineno-26-38" name="__codelineno-26-38" href="#__codelineno-26-38"></a><span class="w">    </span><span class="n">string</span><span class="w"> </span><span class="n">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-39" name="__codelineno-26-39" href="#__codelineno-26-39"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
-<a id="__codelineno-26-40" name="__codelineno-26-40" href="#__codelineno-26-40"></a><span class="w">        </span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
-<a id="__codelineno-26-41" name="__codelineno-26-41" href="#__codelineno-26-41"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
-<a id="__codelineno-26-42" name="__codelineno-26-42" href="#__codelineno-26-42"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="s">&quot;&quot;</span><span class="p">;</span>
-<a id="__codelineno-26-43" name="__codelineno-26-43" href="#__codelineno-26-43"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
-<a id="__codelineno-26-44" name="__codelineno-26-44" href="#__codelineno-26-44"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-45" name="__codelineno-26-45" href="#__codelineno-26-45"></a>
-<a id="__codelineno-26-46" name="__codelineno-26-46" href="#__codelineno-26-46"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
-<a id="__codelineno-26-47" name="__codelineno-26-47" href="#__codelineno-26-47"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-48" name="__codelineno-26-48" href="#__codelineno-26-48"></a><span class="w">        </span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
-<a id="__codelineno-26-49" name="__codelineno-26-49" href="#__codelineno-26-49"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
-<a id="__codelineno-26-50" name="__codelineno-26-50" href="#__codelineno-26-50"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pair</span><span class="p">;</span>
-<a id="__codelineno-26-51" name="__codelineno-26-51" href="#__codelineno-26-51"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-52" name="__codelineno-26-52" href="#__codelineno-26-52"></a>
-<a id="__codelineno-26-53" name="__codelineno-26-53" href="#__codelineno-26-53"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
-<a id="__codelineno-26-54" name="__codelineno-26-54" href="#__codelineno-26-54"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-55" name="__codelineno-26-55" href="#__codelineno-26-55"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
-<a id="__codelineno-26-56" name="__codelineno-26-56" href="#__codelineno-26-56"></a><span class="w">        </span><span class="c1">// メモリを解放してnullptrに設定</span>
-<a id="__codelineno-26-57" name="__codelineno-26-57" href="#__codelineno-26-57"></a><span class="w">        </span><span class="k">delete</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
-<a id="__codelineno-26-58" name="__codelineno-26-58" href="#__codelineno-26-58"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
-<a id="__codelineno-26-59" name="__codelineno-26-59" href="#__codelineno-26-59"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-60" name="__codelineno-26-60" href="#__codelineno-26-60"></a>
-<a id="__codelineno-26-61" name="__codelineno-26-61" href="#__codelineno-26-61"></a><span class="w">    </span><span class="cm">/* すべてのキー値ペアを取得 */</span>
-<a id="__codelineno-26-62" name="__codelineno-26-62" href="#__codelineno-26-62"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Pair</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">pairSet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-63" name="__codelineno-26-63" href="#__codelineno-26-63"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Pair</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">pairSet</span><span class="p">;</span>
-<a id="__codelineno-26-64" name="__codelineno-26-64" href="#__codelineno-26-64"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-65" name="__codelineno-26-65" href="#__codelineno-26-65"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-66" name="__codelineno-26-66" href="#__codelineno-26-66"></a><span class="w">                </span><span class="n">pairSet</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">pair</span><span class="p">);</span>
-<a id="__codelineno-26-67" name="__codelineno-26-67" href="#__codelineno-26-67"></a><span class="w">            </span><span class="p">}</span>
-<a id="__codelineno-26-68" name="__codelineno-26-68" href="#__codelineno-26-68"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-26-69" name="__codelineno-26-69" href="#__codelineno-26-69"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pairSet</span><span class="p">;</span>
-<a id="__codelineno-26-70" name="__codelineno-26-70" href="#__codelineno-26-70"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-71" name="__codelineno-26-71" href="#__codelineno-26-71"></a>
-<a id="__codelineno-26-72" name="__codelineno-26-72" href="#__codelineno-26-72"></a><span class="w">    </span><span class="cm">/* すべてのキーを取得 */</span>
-<a id="__codelineno-26-73" name="__codelineno-26-73" href="#__codelineno-26-73"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">keySet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-74" name="__codelineno-26-74" href="#__codelineno-26-74"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">keySet</span><span class="p">;</span>
-<a id="__codelineno-26-75" name="__codelineno-26-75" href="#__codelineno-26-75"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-76" name="__codelineno-26-76" href="#__codelineno-26-76"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-77" name="__codelineno-26-77" href="#__codelineno-26-77"></a><span class="w">                </span><span class="n">keySet</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">key</span><span class="p">);</span>
-<a id="__codelineno-26-78" name="__codelineno-26-78" href="#__codelineno-26-78"></a><span class="w">            </span><span class="p">}</span>
-<a id="__codelineno-26-79" name="__codelineno-26-79" href="#__codelineno-26-79"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-26-80" name="__codelineno-26-80" href="#__codelineno-26-80"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">keySet</span><span class="p">;</span>
-<a id="__codelineno-26-81" name="__codelineno-26-81" href="#__codelineno-26-81"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-82" name="__codelineno-26-82" href="#__codelineno-26-82"></a>
-<a id="__codelineno-26-83" name="__codelineno-26-83" href="#__codelineno-26-83"></a><span class="w">    </span><span class="cm">/* すべての値を取得 */</span>
-<a id="__codelineno-26-84" name="__codelineno-26-84" href="#__codelineno-26-84"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">string</span><span class="o">&gt;</span><span class="w"> </span><span class="n">valueSet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-85" name="__codelineno-26-85" href="#__codelineno-26-85"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">string</span><span class="o">&gt;</span><span class="w"> </span><span class="n">valueSet</span><span class="p">;</span>
-<a id="__codelineno-26-86" name="__codelineno-26-86" href="#__codelineno-26-86"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-87" name="__codelineno-26-87" href="#__codelineno-26-87"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-88" name="__codelineno-26-88" href="#__codelineno-26-88"></a><span class="w">                </span><span class="n">valueSet</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
-<a id="__codelineno-26-89" name="__codelineno-26-89" href="#__codelineno-26-89"></a><span class="w">            </span><span class="p">}</span>
-<a id="__codelineno-26-90" name="__codelineno-26-90" href="#__codelineno-26-90"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-26-91" name="__codelineno-26-91" href="#__codelineno-26-91"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">valueSet</span><span class="p">;</span>
-<a id="__codelineno-26-92" name="__codelineno-26-92" href="#__codelineno-26-92"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-93" name="__codelineno-26-93" href="#__codelineno-26-93"></a>
-<a id="__codelineno-26-94" name="__codelineno-26-94" href="#__codelineno-26-94"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを印刷 */</span>
-<a id="__codelineno-26-95" name="__codelineno-26-95" href="#__codelineno-26-95"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-96" name="__codelineno-26-96" href="#__codelineno-26-96"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">kv</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">pairSet</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-97" name="__codelineno-26-97" href="#__codelineno-26-97"></a><span class="w">            </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">kv</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">kv</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
-<a id="__codelineno-26-98" name="__codelineno-26-98" href="#__codelineno-26-98"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-26-99" name="__codelineno-26-99" href="#__codelineno-26-99"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-100" name="__codelineno-26-100" href="#__codelineno-26-100"></a><span class="p">};</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">array_hash_map.java</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* キー値ペア */</span>
-<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="kd">class</span> <span class="nc">Pair</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">;</span>
-<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
-<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a>
-<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">Pair</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="p">;</span>
-<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
-<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a><span class="p">}</span>
-<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a>
-<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="cm">/* 配列実装に基づくハッシュテーブル */</span>
-<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="kd">class</span> <span class="nc">ArrayHashMap</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span>
+<div class="highlight"><span class="filename">array_hash_map.py</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">Pair</span><span class="p">:</span>
+<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;キーと値の組&quot;&quot;&quot;</span>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a>
+<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">str</span><span class="p">):</span>
+<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">key</span> <span class="o">=</span> <span class="n">key</span>
+<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">val</span> <span class="o">=</span> <span class="n">val</span>
+<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a>
+<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayHashMap</span><span class="p">:</span>
+<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;配列ベースのハッシュテーブル&quot;&quot;&quot;</span>
+<a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a>
+<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
+<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a>        <span class="c1"># 100 個のバケットを含む配列を初期化</span>
+<a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">Pair</span> <span class="o">|</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="kc">None</span><span class="p">]</span> <span class="o">*</span> <span class="mi">100</span>
 <a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a>
-<a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">ArrayHashMap</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-17" name="__codelineno-27-17" href="#__codelineno-27-17"></a><span class="w">        </span><span class="c1">// 100個のバケットを含む配列を初期化</span>
-<a id="__codelineno-27-18" name="__codelineno-27-18" href="#__codelineno-27-18"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
-<a id="__codelineno-27-19" name="__codelineno-27-19" href="#__codelineno-27-19"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">100</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-20" name="__codelineno-27-20" href="#__codelineno-27-20"></a><span class="w">            </span><span class="n">buckets</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="kc">null</span><span class="p">);</span>
-<a id="__codelineno-27-21" name="__codelineno-27-21" href="#__codelineno-27-21"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-27-22" name="__codelineno-27-22" href="#__codelineno-27-22"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-23" name="__codelineno-27-23" href="#__codelineno-27-23"></a>
-<a id="__codelineno-27-24" name="__codelineno-27-24" href="#__codelineno-27-24"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
-<a id="__codelineno-27-25" name="__codelineno-27-25" href="#__codelineno-27-25"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">hashFunc</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-26" name="__codelineno-27-26" href="#__codelineno-27-26"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">100</span><span class="p">;</span>
-<a id="__codelineno-27-27" name="__codelineno-27-27" href="#__codelineno-27-27"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
-<a id="__codelineno-27-28" name="__codelineno-27-28" href="#__codelineno-27-28"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-29" name="__codelineno-27-29" href="#__codelineno-27-29"></a>
-<a id="__codelineno-27-30" name="__codelineno-27-30" href="#__codelineno-27-30"></a><span class="w">    </span><span class="cm">/* クエリ操作 */</span>
-<a id="__codelineno-27-31" name="__codelineno-27-31" href="#__codelineno-27-31"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-32" name="__codelineno-27-32" href="#__codelineno-27-32"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
-<a id="__codelineno-27-33" name="__codelineno-27-33" href="#__codelineno-27-33"></a><span class="w">        </span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
-<a id="__codelineno-27-34" name="__codelineno-27-34" href="#__codelineno-27-34"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
-<a id="__codelineno-27-35" name="__codelineno-27-35" href="#__codelineno-27-35"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
-<a id="__codelineno-27-36" name="__codelineno-27-36" href="#__codelineno-27-36"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
-<a id="__codelineno-27-37" name="__codelineno-27-37" href="#__codelineno-27-37"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-38" name="__codelineno-27-38" href="#__codelineno-27-38"></a>
-<a id="__codelineno-27-39" name="__codelineno-27-39" href="#__codelineno-27-39"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
-<a id="__codelineno-27-40" name="__codelineno-27-40" href="#__codelineno-27-40"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-41" name="__codelineno-27-41" href="#__codelineno-27-41"></a><span class="w">        </span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
-<a id="__codelineno-27-42" name="__codelineno-27-42" href="#__codelineno-27-42"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
-<a id="__codelineno-27-43" name="__codelineno-27-43" href="#__codelineno-27-43"></a><span class="w">        </span><span class="n">buckets</span><span class="p">.</span><span class="na">set</span><span class="p">(</span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">);</span>
-<a id="__codelineno-27-44" name="__codelineno-27-44" href="#__codelineno-27-44"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-45" name="__codelineno-27-45" href="#__codelineno-27-45"></a>
-<a id="__codelineno-27-46" name="__codelineno-27-46" href="#__codelineno-27-46"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
-<a id="__codelineno-27-47" name="__codelineno-27-47" href="#__codelineno-27-47"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-48" name="__codelineno-27-48" href="#__codelineno-27-48"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
-<a id="__codelineno-27-49" name="__codelineno-27-49" href="#__codelineno-27-49"></a><span class="w">        </span><span class="c1">// nullに設定して削除を示す</span>
-<a id="__codelineno-27-50" name="__codelineno-27-50" href="#__codelineno-27-50"></a><span class="w">        </span><span class="n">buckets</span><span class="p">.</span><span class="na">set</span><span class="p">(</span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">);</span>
-<a id="__codelineno-27-51" name="__codelineno-27-51" href="#__codelineno-27-51"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-52" name="__codelineno-27-52" href="#__codelineno-27-52"></a>
-<a id="__codelineno-27-53" name="__codelineno-27-53" href="#__codelineno-27-53"></a><span class="w">    </span><span class="cm">/* すべてのキー値ペアを取得 */</span>
-<a id="__codelineno-27-54" name="__codelineno-27-54" href="#__codelineno-27-54"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">pairSet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-55" name="__codelineno-27-55" href="#__codelineno-27-55"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">pairSet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
-<a id="__codelineno-27-56" name="__codelineno-27-56" href="#__codelineno-27-56"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-57" name="__codelineno-27-57" href="#__codelineno-27-57"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
-<a id="__codelineno-27-58" name="__codelineno-27-58" href="#__codelineno-27-58"></a><span class="w">                </span><span class="n">pairSet</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">pair</span><span class="p">);</span>
-<a id="__codelineno-27-59" name="__codelineno-27-59" href="#__codelineno-27-59"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-27-60" name="__codelineno-27-60" href="#__codelineno-27-60"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pairSet</span><span class="p">;</span>
-<a id="__codelineno-27-61" name="__codelineno-27-61" href="#__codelineno-27-61"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-62" name="__codelineno-27-62" href="#__codelineno-27-62"></a>
-<a id="__codelineno-27-63" name="__codelineno-27-63" href="#__codelineno-27-63"></a><span class="w">    </span><span class="cm">/* すべてのキーを取得 */</span>
-<a id="__codelineno-27-64" name="__codelineno-27-64" href="#__codelineno-27-64"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">keySet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-65" name="__codelineno-27-65" href="#__codelineno-27-65"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">keySet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
-<a id="__codelineno-27-66" name="__codelineno-27-66" href="#__codelineno-27-66"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-67" name="__codelineno-27-67" href="#__codelineno-27-67"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
-<a id="__codelineno-27-68" name="__codelineno-27-68" href="#__codelineno-27-68"></a><span class="w">                </span><span class="n">keySet</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="p">);</span>
-<a id="__codelineno-27-69" name="__codelineno-27-69" href="#__codelineno-27-69"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-27-70" name="__codelineno-27-70" href="#__codelineno-27-70"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">keySet</span><span class="p">;</span>
-<a id="__codelineno-27-71" name="__codelineno-27-71" href="#__codelineno-27-71"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-72" name="__codelineno-27-72" href="#__codelineno-27-72"></a>
-<a id="__codelineno-27-73" name="__codelineno-27-73" href="#__codelineno-27-73"></a><span class="w">    </span><span class="cm">/* すべての値を取得 */</span>
-<a id="__codelineno-27-74" name="__codelineno-27-74" href="#__codelineno-27-74"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">valueSet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-75" name="__codelineno-27-75" href="#__codelineno-27-75"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">valueSet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
-<a id="__codelineno-27-76" name="__codelineno-27-76" href="#__codelineno-27-76"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-77" name="__codelineno-27-77" href="#__codelineno-27-77"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
-<a id="__codelineno-27-78" name="__codelineno-27-78" href="#__codelineno-27-78"></a><span class="w">                </span><span class="n">valueSet</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
-<a id="__codelineno-27-79" name="__codelineno-27-79" href="#__codelineno-27-79"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-27-80" name="__codelineno-27-80" href="#__codelineno-27-80"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">valueSet</span><span class="p">;</span>
-<a id="__codelineno-27-81" name="__codelineno-27-81" href="#__codelineno-27-81"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-82" name="__codelineno-27-82" href="#__codelineno-27-82"></a>
-<a id="__codelineno-27-83" name="__codelineno-27-83" href="#__codelineno-27-83"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを印刷 */</span>
-<a id="__codelineno-27-84" name="__codelineno-27-84" href="#__codelineno-27-84"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-85" name="__codelineno-27-85" href="#__codelineno-27-85"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">kv</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">pairSet</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-86" name="__codelineno-27-86" href="#__codelineno-27-86"></a><span class="w">            </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">kv</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">kv</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
-<a id="__codelineno-27-87" name="__codelineno-27-87" href="#__codelineno-27-87"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-27-88" name="__codelineno-27-88" href="#__codelineno-27-88"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-89" name="__codelineno-27-89" href="#__codelineno-27-89"></a><span class="p">}</span>
+<a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">hash_func</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-27-17" name="__codelineno-27-17" href="#__codelineno-27-17"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;ハッシュ関数&quot;&quot;&quot;</span>
+<a id="__codelineno-27-18" name="__codelineno-27-18" href="#__codelineno-27-18"></a>        <span class="n">index</span> <span class="o">=</span> <span class="n">key</span> <span class="o">%</span> <span class="mi">100</span>
+<a id="__codelineno-27-19" name="__codelineno-27-19" href="#__codelineno-27-19"></a>        <span class="k">return</span> <span class="n">index</span>
+<a id="__codelineno-27-20" name="__codelineno-27-20" href="#__codelineno-27-20"></a>
+<a id="__codelineno-27-21" name="__codelineno-27-21" href="#__codelineno-27-21"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">str</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-27-22" name="__codelineno-27-22" href="#__codelineno-27-22"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;検索操作&quot;&quot;&quot;</span>
+<a id="__codelineno-27-23" name="__codelineno-27-23" href="#__codelineno-27-23"></a>        <span class="n">index</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-27-24" name="__codelineno-27-24" href="#__codelineno-27-24"></a>        <span class="n">pair</span><span class="p">:</span> <span class="n">Pair</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
+<a id="__codelineno-27-25" name="__codelineno-27-25" href="#__codelineno-27-25"></a>        <span class="k">if</span> <span class="n">pair</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-27-26" name="__codelineno-27-26" href="#__codelineno-27-26"></a>            <span class="k">return</span> <span class="kc">None</span>
+<a id="__codelineno-27-27" name="__codelineno-27-27" href="#__codelineno-27-27"></a>        <span class="k">return</span> <span class="n">pair</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-27-28" name="__codelineno-27-28" href="#__codelineno-27-28"></a>
+<a id="__codelineno-27-29" name="__codelineno-27-29" href="#__codelineno-27-29"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">str</span><span class="p">):</span>
+<a id="__codelineno-27-30" name="__codelineno-27-30" href="#__codelineno-27-30"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;追加と更新の操作&quot;&quot;&quot;</span>
+<a id="__codelineno-27-31" name="__codelineno-27-31" href="#__codelineno-27-31"></a>        <span class="n">pair</span> <span class="o">=</span> <span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-27-32" name="__codelineno-27-32" href="#__codelineno-27-32"></a>        <span class="n">index</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-27-33" name="__codelineno-27-33" href="#__codelineno-27-33"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">pair</span>
+<a id="__codelineno-27-34" name="__codelineno-27-34" href="#__codelineno-27-34"></a>
+<a id="__codelineno-27-35" name="__codelineno-27-35" href="#__codelineno-27-35"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-27-36" name="__codelineno-27-36" href="#__codelineno-27-36"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;削除操作&quot;&quot;&quot;</span>
+<a id="__codelineno-27-37" name="__codelineno-27-37" href="#__codelineno-27-37"></a>        <span class="n">index</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-27-38" name="__codelineno-27-38" href="#__codelineno-27-38"></a>        <span class="c1"># None に設定し、削除を表す</span>
+<a id="__codelineno-27-39" name="__codelineno-27-39" href="#__codelineno-27-39"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span>
+<a id="__codelineno-27-40" name="__codelineno-27-40" href="#__codelineno-27-40"></a>
+<a id="__codelineno-27-41" name="__codelineno-27-41" href="#__codelineno-27-41"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">entry_set</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="n">Pair</span><span class="p">]:</span>
+<a id="__codelineno-27-42" name="__codelineno-27-42" href="#__codelineno-27-42"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;すべてのキーと値のペアを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-27-43" name="__codelineno-27-43" href="#__codelineno-27-43"></a>        <span class="n">result</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">Pair</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-27-44" name="__codelineno-27-44" href="#__codelineno-27-44"></a>        <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span>
+<a id="__codelineno-27-45" name="__codelineno-27-45" href="#__codelineno-27-45"></a>            <span class="k">if</span> <span class="n">pair</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-27-46" name="__codelineno-27-46" href="#__codelineno-27-46"></a>                <span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">pair</span><span class="p">)</span>
+<a id="__codelineno-27-47" name="__codelineno-27-47" href="#__codelineno-27-47"></a>        <span class="k">return</span> <span class="n">result</span>
+<a id="__codelineno-27-48" name="__codelineno-27-48" href="#__codelineno-27-48"></a>
+<a id="__codelineno-27-49" name="__codelineno-27-49" href="#__codelineno-27-49"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">key_set</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-27-50" name="__codelineno-27-50" href="#__codelineno-27-50"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;すべてのキーを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-27-51" name="__codelineno-27-51" href="#__codelineno-27-51"></a>        <span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-27-52" name="__codelineno-27-52" href="#__codelineno-27-52"></a>        <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span>
+<a id="__codelineno-27-53" name="__codelineno-27-53" href="#__codelineno-27-53"></a>            <span class="k">if</span> <span class="n">pair</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-27-54" name="__codelineno-27-54" href="#__codelineno-27-54"></a>                <span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-27-55" name="__codelineno-27-55" href="#__codelineno-27-55"></a>        <span class="k">return</span> <span class="n">result</span>
+<a id="__codelineno-27-56" name="__codelineno-27-56" href="#__codelineno-27-56"></a>
+<a id="__codelineno-27-57" name="__codelineno-27-57" href="#__codelineno-27-57"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">value_set</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">str</span><span class="p">]:</span>
+<a id="__codelineno-27-58" name="__codelineno-27-58" href="#__codelineno-27-58"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;すべての値を取得&quot;&quot;&quot;</span>
+<a id="__codelineno-27-59" name="__codelineno-27-59" href="#__codelineno-27-59"></a>        <span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-27-60" name="__codelineno-27-60" href="#__codelineno-27-60"></a>        <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span>
+<a id="__codelineno-27-61" name="__codelineno-27-61" href="#__codelineno-27-61"></a>            <span class="k">if</span> <span class="n">pair</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-27-62" name="__codelineno-27-62" href="#__codelineno-27-62"></a>                <span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-27-63" name="__codelineno-27-63" href="#__codelineno-27-63"></a>        <span class="k">return</span> <span class="n">result</span>
+<a id="__codelineno-27-64" name="__codelineno-27-64" href="#__codelineno-27-64"></a>
+<a id="__codelineno-27-65" name="__codelineno-27-65" href="#__codelineno-27-65"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">print</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<a id="__codelineno-27-66" name="__codelineno-27-66" href="#__codelineno-27-66"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;ハッシュテーブルを出力&quot;&quot;&quot;</span>
+<a id="__codelineno-27-67" name="__codelineno-27-67" href="#__codelineno-27-67"></a>        <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span>
+<a id="__codelineno-27-68" name="__codelineno-27-68" href="#__codelineno-27-68"></a>            <span class="k">if</span> <span class="n">pair</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-27-69" name="__codelineno-27-69" href="#__codelineno-27-69"></a>                <span class="nb">print</span><span class="p">(</span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="p">,</span> <span class="s2">&quot;-&gt;&quot;</span><span class="p">,</span> <span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_hash_map.cs</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">Pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
-<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a>
-<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">ArrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_hash_map.cpp</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* キーと値の組 */</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">Pair</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">;</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">    </span><span class="n">string</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w">    </span><span class="n">Pair</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">        </span><span class="k">this</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="p">;</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">        </span><span class="k">this</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="p">};</span>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a>
+<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a><span class="cm">/* 配列ベースのハッシュテーブル */</span>
+<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayHashMap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
+<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Pair</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span>
+<a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a>
+<a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
+<a id="__codelineno-28-18" name="__codelineno-28-18" href="#__codelineno-28-18"></a><span class="w">    </span><span class="n">ArrayHashMap</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-19" name="__codelineno-28-19" href="#__codelineno-28-19"></a><span class="w">        </span><span class="c1">// 100 個のバケットを含む配列を初期化</span>
+<a id="__codelineno-28-20" name="__codelineno-28-20" href="#__codelineno-28-20"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Pair</span><span class="w"> </span><span class="o">*&gt;</span><span class="p">(</span><span class="mi">100</span><span class="p">);</span>
+<a id="__codelineno-28-21" name="__codelineno-28-21" href="#__codelineno-28-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-22" name="__codelineno-28-22" href="#__codelineno-28-22"></a>
+<a id="__codelineno-28-23" name="__codelineno-28-23" href="#__codelineno-28-23"></a><span class="w">    </span><span class="o">~</span><span class="n">ArrayHashMap</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-24" name="__codelineno-28-24" href="#__codelineno-28-24"></a><span class="w">        </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-28-25" name="__codelineno-28-25" href="#__codelineno-28-25"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="o">&amp;</span><span class="n">bucket</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-26" name="__codelineno-28-26" href="#__codelineno-28-26"></a><span class="w">            </span><span class="k">delete</span><span class="w"> </span><span class="n">bucket</span><span class="p">;</span>
+<a id="__codelineno-28-27" name="__codelineno-28-27" href="#__codelineno-28-27"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-28-28" name="__codelineno-28-28" href="#__codelineno-28-28"></a><span class="w">        </span><span class="n">buckets</span><span class="p">.</span><span class="n">clear</span><span class="p">();</span>
+<a id="__codelineno-28-29" name="__codelineno-28-29" href="#__codelineno-28-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-30" name="__codelineno-28-30" href="#__codelineno-28-30"></a>
+<a id="__codelineno-28-31" name="__codelineno-28-31" href="#__codelineno-28-31"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-28-32" name="__codelineno-28-32" href="#__codelineno-28-32"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-33" name="__codelineno-28-33" href="#__codelineno-28-33"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">100</span><span class="p">;</span>
+<a id="__codelineno-28-34" name="__codelineno-28-34" href="#__codelineno-28-34"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
+<a id="__codelineno-28-35" name="__codelineno-28-35" href="#__codelineno-28-35"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-36" name="__codelineno-28-36" href="#__codelineno-28-36"></a>
+<a id="__codelineno-28-37" name="__codelineno-28-37" href="#__codelineno-28-37"></a><span class="w">    </span><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-28-38" name="__codelineno-28-38" href="#__codelineno-28-38"></a><span class="w">    </span><span class="n">string</span><span class="w"> </span><span class="n">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-39" name="__codelineno-28-39" href="#__codelineno-28-39"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-28-40" name="__codelineno-28-40" href="#__codelineno-28-40"></a><span class="w">        </span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-28-41" name="__codelineno-28-41" href="#__codelineno-28-41"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
+<a id="__codelineno-28-42" name="__codelineno-28-42" href="#__codelineno-28-42"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="s">&quot;&quot;</span><span class="p">;</span>
+<a id="__codelineno-28-43" name="__codelineno-28-43" href="#__codelineno-28-43"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-28-44" name="__codelineno-28-44" href="#__codelineno-28-44"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-45" name="__codelineno-28-45" href="#__codelineno-28-45"></a>
+<a id="__codelineno-28-46" name="__codelineno-28-46" href="#__codelineno-28-46"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-28-47" name="__codelineno-28-47" href="#__codelineno-28-47"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-48" name="__codelineno-28-48" href="#__codelineno-28-48"></a><span class="w">        </span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-28-49" name="__codelineno-28-49" href="#__codelineno-28-49"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-28-50" name="__codelineno-28-50" href="#__codelineno-28-50"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pair</span><span class="p">;</span>
+<a id="__codelineno-28-51" name="__codelineno-28-51" href="#__codelineno-28-51"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-52" name="__codelineno-28-52" href="#__codelineno-28-52"></a>
+<a id="__codelineno-28-53" name="__codelineno-28-53" href="#__codelineno-28-53"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-28-54" name="__codelineno-28-54" href="#__codelineno-28-54"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-55" name="__codelineno-28-55" href="#__codelineno-28-55"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-28-56" name="__codelineno-28-56" href="#__codelineno-28-56"></a><span class="w">        </span><span class="c1">// メモリを解放して nullptr に設定する</span>
+<a id="__codelineno-28-57" name="__codelineno-28-57" href="#__codelineno-28-57"></a><span class="w">        </span><span class="k">delete</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-28-58" name="__codelineno-28-58" href="#__codelineno-28-58"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
+<a id="__codelineno-28-59" name="__codelineno-28-59" href="#__codelineno-28-59"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-60" name="__codelineno-28-60" href="#__codelineno-28-60"></a>
+<a id="__codelineno-28-61" name="__codelineno-28-61" href="#__codelineno-28-61"></a><span class="w">    </span><span class="cm">/* すべてのキーと値のペアを取得 */</span>
+<a id="__codelineno-28-62" name="__codelineno-28-62" href="#__codelineno-28-62"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Pair</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">pairSet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-63" name="__codelineno-28-63" href="#__codelineno-28-63"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Pair</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">pairSet</span><span class="p">;</span>
+<a id="__codelineno-28-64" name="__codelineno-28-64" href="#__codelineno-28-64"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-65" name="__codelineno-28-65" href="#__codelineno-28-65"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-66" name="__codelineno-28-66" href="#__codelineno-28-66"></a><span class="w">                </span><span class="n">pairSet</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">pair</span><span class="p">);</span>
+<a id="__codelineno-28-67" name="__codelineno-28-67" href="#__codelineno-28-67"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-28-68" name="__codelineno-28-68" href="#__codelineno-28-68"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-28-69" name="__codelineno-28-69" href="#__codelineno-28-69"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pairSet</span><span class="p">;</span>
+<a id="__codelineno-28-70" name="__codelineno-28-70" href="#__codelineno-28-70"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-71" name="__codelineno-28-71" href="#__codelineno-28-71"></a>
+<a id="__codelineno-28-72" name="__codelineno-28-72" href="#__codelineno-28-72"></a><span class="w">    </span><span class="cm">/* すべてのキーを取得 */</span>
+<a id="__codelineno-28-73" name="__codelineno-28-73" href="#__codelineno-28-73"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">keySet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-74" name="__codelineno-28-74" href="#__codelineno-28-74"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">keySet</span><span class="p">;</span>
+<a id="__codelineno-28-75" name="__codelineno-28-75" href="#__codelineno-28-75"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-76" name="__codelineno-28-76" href="#__codelineno-28-76"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-77" name="__codelineno-28-77" href="#__codelineno-28-77"></a><span class="w">                </span><span class="n">keySet</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-28-78" name="__codelineno-28-78" href="#__codelineno-28-78"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-28-79" name="__codelineno-28-79" href="#__codelineno-28-79"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-28-80" name="__codelineno-28-80" href="#__codelineno-28-80"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">keySet</span><span class="p">;</span>
+<a id="__codelineno-28-81" name="__codelineno-28-81" href="#__codelineno-28-81"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-82" name="__codelineno-28-82" href="#__codelineno-28-82"></a>
+<a id="__codelineno-28-83" name="__codelineno-28-83" href="#__codelineno-28-83"></a><span class="w">    </span><span class="cm">/* すべての値を取得 */</span>
+<a id="__codelineno-28-84" name="__codelineno-28-84" href="#__codelineno-28-84"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">string</span><span class="o">&gt;</span><span class="w"> </span><span class="n">valueSet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-85" name="__codelineno-28-85" href="#__codelineno-28-85"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">string</span><span class="o">&gt;</span><span class="w"> </span><span class="n">valueSet</span><span class="p">;</span>
+<a id="__codelineno-28-86" name="__codelineno-28-86" href="#__codelineno-28-86"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-87" name="__codelineno-28-87" href="#__codelineno-28-87"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-88" name="__codelineno-28-88" href="#__codelineno-28-88"></a><span class="w">                </span><span class="n">valueSet</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-28-89" name="__codelineno-28-89" href="#__codelineno-28-89"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-28-90" name="__codelineno-28-90" href="#__codelineno-28-90"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-28-91" name="__codelineno-28-91" href="#__codelineno-28-91"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">valueSet</span><span class="p">;</span>
+<a id="__codelineno-28-92" name="__codelineno-28-92" href="#__codelineno-28-92"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-93" name="__codelineno-28-93" href="#__codelineno-28-93"></a>
+<a id="__codelineno-28-94" name="__codelineno-28-94" href="#__codelineno-28-94"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-28-95" name="__codelineno-28-95" href="#__codelineno-28-95"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-96" name="__codelineno-28-96" href="#__codelineno-28-96"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">kv</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">pairSet</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-97" name="__codelineno-28-97" href="#__codelineno-28-97"></a><span class="w">            </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">kv</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">kv</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
+<a id="__codelineno-28-98" name="__codelineno-28-98" href="#__codelineno-28-98"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-28-99" name="__codelineno-28-99" href="#__codelineno-28-99"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-100" name="__codelineno-28-100" href="#__codelineno-28-100"></a><span class="p">};</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_hash_map.go</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
-<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a>
-<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">arrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_hash_map.java</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* キーと値の組 */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kd">class</span> <span class="nc">Pair</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">;</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">Pair</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="p">;</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="p">}</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="cm">/* 配列ベースのハッシュテーブル */</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="kd">class</span> <span class="nc">ArrayHashMap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">ArrayHashMap</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="w">        </span><span class="c1">// 100 個のバケットを含む配列を初期化</span>
+<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">100</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-20" name="__codelineno-29-20" href="#__codelineno-29-20"></a><span class="w">            </span><span class="n">buckets</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="kc">null</span><span class="p">);</span>
+<a id="__codelineno-29-21" name="__codelineno-29-21" href="#__codelineno-29-21"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-22" name="__codelineno-29-22" href="#__codelineno-29-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-23" name="__codelineno-29-23" href="#__codelineno-29-23"></a>
+<a id="__codelineno-29-24" name="__codelineno-29-24" href="#__codelineno-29-24"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-29-25" name="__codelineno-29-25" href="#__codelineno-29-25"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">hashFunc</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-26" name="__codelineno-29-26" href="#__codelineno-29-26"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">100</span><span class="p">;</span>
+<a id="__codelineno-29-27" name="__codelineno-29-27" href="#__codelineno-29-27"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
+<a id="__codelineno-29-28" name="__codelineno-29-28" href="#__codelineno-29-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-29" name="__codelineno-29-29" href="#__codelineno-29-29"></a>
+<a id="__codelineno-29-30" name="__codelineno-29-30" href="#__codelineno-29-30"></a><span class="w">    </span><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-29-31" name="__codelineno-29-31" href="#__codelineno-29-31"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-32" name="__codelineno-29-32" href="#__codelineno-29-32"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-29-33" name="__codelineno-29-33" href="#__codelineno-29-33"></a><span class="w">        </span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
+<a id="__codelineno-29-34" name="__codelineno-29-34" href="#__codelineno-29-34"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-29-35" name="__codelineno-29-35" href="#__codelineno-29-35"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-29-36" name="__codelineno-29-36" href="#__codelineno-29-36"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
+<a id="__codelineno-29-37" name="__codelineno-29-37" href="#__codelineno-29-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-38" name="__codelineno-29-38" href="#__codelineno-29-38"></a>
+<a id="__codelineno-29-39" name="__codelineno-29-39" href="#__codelineno-29-39"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-29-40" name="__codelineno-29-40" href="#__codelineno-29-40"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-41" name="__codelineno-29-41" href="#__codelineno-29-41"></a><span class="w">        </span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-29-42" name="__codelineno-29-42" href="#__codelineno-29-42"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-29-43" name="__codelineno-29-43" href="#__codelineno-29-43"></a><span class="w">        </span><span class="n">buckets</span><span class="p">.</span><span class="na">set</span><span class="p">(</span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">);</span>
+<a id="__codelineno-29-44" name="__codelineno-29-44" href="#__codelineno-29-44"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-45" name="__codelineno-29-45" href="#__codelineno-29-45"></a>
+<a id="__codelineno-29-46" name="__codelineno-29-46" href="#__codelineno-29-46"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-29-47" name="__codelineno-29-47" href="#__codelineno-29-47"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-48" name="__codelineno-29-48" href="#__codelineno-29-48"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-29-49" name="__codelineno-29-49" href="#__codelineno-29-49"></a><span class="w">        </span><span class="c1">// null に設定し、削除を表す</span>
+<a id="__codelineno-29-50" name="__codelineno-29-50" href="#__codelineno-29-50"></a><span class="w">        </span><span class="n">buckets</span><span class="p">.</span><span class="na">set</span><span class="p">(</span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">);</span>
+<a id="__codelineno-29-51" name="__codelineno-29-51" href="#__codelineno-29-51"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-52" name="__codelineno-29-52" href="#__codelineno-29-52"></a>
+<a id="__codelineno-29-53" name="__codelineno-29-53" href="#__codelineno-29-53"></a><span class="w">    </span><span class="cm">/* すべてのキーと値のペアを取得 */</span>
+<a id="__codelineno-29-54" name="__codelineno-29-54" href="#__codelineno-29-54"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">pairSet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-55" name="__codelineno-29-55" href="#__codelineno-29-55"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">pairSet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-29-56" name="__codelineno-29-56" href="#__codelineno-29-56"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-57" name="__codelineno-29-57" href="#__codelineno-29-57"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-29-58" name="__codelineno-29-58" href="#__codelineno-29-58"></a><span class="w">                </span><span class="n">pairSet</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">pair</span><span class="p">);</span>
+<a id="__codelineno-29-59" name="__codelineno-29-59" href="#__codelineno-29-59"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-60" name="__codelineno-29-60" href="#__codelineno-29-60"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pairSet</span><span class="p">;</span>
+<a id="__codelineno-29-61" name="__codelineno-29-61" href="#__codelineno-29-61"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-62" name="__codelineno-29-62" href="#__codelineno-29-62"></a>
+<a id="__codelineno-29-63" name="__codelineno-29-63" href="#__codelineno-29-63"></a><span class="w">    </span><span class="cm">/* すべてのキーを取得 */</span>
+<a id="__codelineno-29-64" name="__codelineno-29-64" href="#__codelineno-29-64"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">keySet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-65" name="__codelineno-29-65" href="#__codelineno-29-65"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">keySet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-29-66" name="__codelineno-29-66" href="#__codelineno-29-66"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-67" name="__codelineno-29-67" href="#__codelineno-29-67"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-29-68" name="__codelineno-29-68" href="#__codelineno-29-68"></a><span class="w">                </span><span class="n">keySet</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="p">);</span>
+<a id="__codelineno-29-69" name="__codelineno-29-69" href="#__codelineno-29-69"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-70" name="__codelineno-29-70" href="#__codelineno-29-70"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">keySet</span><span class="p">;</span>
+<a id="__codelineno-29-71" name="__codelineno-29-71" href="#__codelineno-29-71"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-72" name="__codelineno-29-72" href="#__codelineno-29-72"></a>
+<a id="__codelineno-29-73" name="__codelineno-29-73" href="#__codelineno-29-73"></a><span class="w">    </span><span class="cm">/* すべての値を取得 */</span>
+<a id="__codelineno-29-74" name="__codelineno-29-74" href="#__codelineno-29-74"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">valueSet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-75" name="__codelineno-29-75" href="#__codelineno-29-75"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">valueSet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-29-76" name="__codelineno-29-76" href="#__codelineno-29-76"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-77" name="__codelineno-29-77" href="#__codelineno-29-77"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-29-78" name="__codelineno-29-78" href="#__codelineno-29-78"></a><span class="w">                </span><span class="n">valueSet</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
+<a id="__codelineno-29-79" name="__codelineno-29-79" href="#__codelineno-29-79"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-80" name="__codelineno-29-80" href="#__codelineno-29-80"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">valueSet</span><span class="p">;</span>
+<a id="__codelineno-29-81" name="__codelineno-29-81" href="#__codelineno-29-81"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-82" name="__codelineno-29-82" href="#__codelineno-29-82"></a>
+<a id="__codelineno-29-83" name="__codelineno-29-83" href="#__codelineno-29-83"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-29-84" name="__codelineno-29-84" href="#__codelineno-29-84"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-85" name="__codelineno-29-85" href="#__codelineno-29-85"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">kv</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">pairSet</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-86" name="__codelineno-29-86" href="#__codelineno-29-86"></a><span class="w">            </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">kv</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">kv</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
+<a id="__codelineno-29-87" name="__codelineno-29-87" href="#__codelineno-29-87"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-88" name="__codelineno-29-88" href="#__codelineno-29-88"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-89" name="__codelineno-29-89" href="#__codelineno-29-89"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_hash_map.swift</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="p">[</span><span class="n">file</span><span class="p">]{</span><span class="n">utils</span><span class="o">/</span><span class="n">pair</span><span class="p">.</span><span class="n">swift</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">Pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
-<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a>
-<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">ArrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_hash_map.cs</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* キーと値の組 int-&gt;string */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="k">class</span><span class="w"> </span><span class="nf">Pair</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="kt">string</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="p">;</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">string</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="p">}</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="cm">/* 配列ベースのハッシュテーブル */</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayHashMap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">?&gt;</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nf">ArrayHashMap</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w">        </span><span class="c1">// 100 個のバケットを含む配列を初期化</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">100</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w">            </span><span class="n">buckets</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="k">null</span><span class="p">);</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a>
+<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="nf">HashFunc</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">100</span><span class="p">;</span>
+<a id="__codelineno-30-21" name="__codelineno-30-21" href="#__codelineno-30-21"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
+<a id="__codelineno-30-22" name="__codelineno-30-22" href="#__codelineno-30-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-23" name="__codelineno-30-23" href="#__codelineno-30-23"></a>
+<a id="__codelineno-30-24" name="__codelineno-30-24" href="#__codelineno-30-24"></a><span class="w">    </span><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-30-25" name="__codelineno-30-25" href="#__codelineno-30-25"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">string?</span><span class="w"> </span><span class="n">Get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-26" name="__codelineno-30-26" href="#__codelineno-30-26"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-30-27" name="__codelineno-30-27" href="#__codelineno-30-27"></a><span class="w">        </span><span class="n">Pair</span><span class="o">?</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-30-28" name="__codelineno-30-28" href="#__codelineno-30-28"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
+<a id="__codelineno-30-29" name="__codelineno-30-29" href="#__codelineno-30-29"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-30-30" name="__codelineno-30-30" href="#__codelineno-30-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-31" name="__codelineno-30-31" href="#__codelineno-30-31"></a>
+<a id="__codelineno-30-32" name="__codelineno-30-32" href="#__codelineno-30-32"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-30-33" name="__codelineno-30-33" href="#__codelineno-30-33"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">Put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="kt">string</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-34" name="__codelineno-30-34" href="#__codelineno-30-34"></a><span class="w">        </span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-30-35" name="__codelineno-30-35" href="#__codelineno-30-35"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-30-36" name="__codelineno-30-36" href="#__codelineno-30-36"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pair</span><span class="p">;</span>
+<a id="__codelineno-30-37" name="__codelineno-30-37" href="#__codelineno-30-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-38" name="__codelineno-30-38" href="#__codelineno-30-38"></a>
+<a id="__codelineno-30-39" name="__codelineno-30-39" href="#__codelineno-30-39"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-30-40" name="__codelineno-30-40" href="#__codelineno-30-40"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">Remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-41" name="__codelineno-30-41" href="#__codelineno-30-41"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-30-42" name="__codelineno-30-42" href="#__codelineno-30-42"></a><span class="w">        </span><span class="c1">// null に設定し、削除を表す</span>
+<a id="__codelineno-30-43" name="__codelineno-30-43" href="#__codelineno-30-43"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
+<a id="__codelineno-30-44" name="__codelineno-30-44" href="#__codelineno-30-44"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-45" name="__codelineno-30-45" href="#__codelineno-30-45"></a>
+<a id="__codelineno-30-46" name="__codelineno-30-46" href="#__codelineno-30-46"></a><span class="w">    </span><span class="cm">/* すべてのキーと値のペアを取得 */</span>
+<a id="__codelineno-30-47" name="__codelineno-30-47" href="#__codelineno-30-47"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">PairSet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-48" name="__codelineno-30-48" href="#__codelineno-30-48"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">pairSet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-30-49" name="__codelineno-30-49" href="#__codelineno-30-49"></a><span class="w">        </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="o">?</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-50" name="__codelineno-30-50" href="#__codelineno-30-50"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="p">)</span>
+<a id="__codelineno-30-51" name="__codelineno-30-51" href="#__codelineno-30-51"></a><span class="w">                </span><span class="n">pairSet</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">pair</span><span class="p">);</span>
+<a id="__codelineno-30-52" name="__codelineno-30-52" href="#__codelineno-30-52"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-30-53" name="__codelineno-30-53" href="#__codelineno-30-53"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pairSet</span><span class="p">;</span>
+<a id="__codelineno-30-54" name="__codelineno-30-54" href="#__codelineno-30-54"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-55" name="__codelineno-30-55" href="#__codelineno-30-55"></a>
+<a id="__codelineno-30-56" name="__codelineno-30-56" href="#__codelineno-30-56"></a><span class="w">    </span><span class="cm">/* すべてのキーを取得 */</span>
+<a id="__codelineno-30-57" name="__codelineno-30-57" href="#__codelineno-30-57"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">KeySet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-58" name="__codelineno-30-58" href="#__codelineno-30-58"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">keySet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-30-59" name="__codelineno-30-59" href="#__codelineno-30-59"></a><span class="w">        </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="o">?</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-60" name="__codelineno-30-60" href="#__codelineno-30-60"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="p">)</span>
+<a id="__codelineno-30-61" name="__codelineno-30-61" href="#__codelineno-30-61"></a><span class="w">                </span><span class="n">keySet</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-30-62" name="__codelineno-30-62" href="#__codelineno-30-62"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-30-63" name="__codelineno-30-63" href="#__codelineno-30-63"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">keySet</span><span class="p">;</span>
+<a id="__codelineno-30-64" name="__codelineno-30-64" href="#__codelineno-30-64"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-65" name="__codelineno-30-65" href="#__codelineno-30-65"></a>
+<a id="__codelineno-30-66" name="__codelineno-30-66" href="#__codelineno-30-66"></a><span class="w">    </span><span class="cm">/* すべての値を取得 */</span>
+<a id="__codelineno-30-67" name="__codelineno-30-67" href="#__codelineno-30-67"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">string</span><span class="o">&gt;</span><span class="w"> </span><span class="n">ValueSet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-68" name="__codelineno-30-68" href="#__codelineno-30-68"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">string</span><span class="o">&gt;</span><span class="w"> </span><span class="n">valueSet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-30-69" name="__codelineno-30-69" href="#__codelineno-30-69"></a><span class="w">        </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="o">?</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-70" name="__codelineno-30-70" href="#__codelineno-30-70"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="p">)</span>
+<a id="__codelineno-30-71" name="__codelineno-30-71" href="#__codelineno-30-71"></a><span class="w">                </span><span class="n">valueSet</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-30-72" name="__codelineno-30-72" href="#__codelineno-30-72"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-30-73" name="__codelineno-30-73" href="#__codelineno-30-73"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">valueSet</span><span class="p">;</span>
+<a id="__codelineno-30-74" name="__codelineno-30-74" href="#__codelineno-30-74"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-75" name="__codelineno-30-75" href="#__codelineno-30-75"></a>
+<a id="__codelineno-30-76" name="__codelineno-30-76" href="#__codelineno-30-76"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-30-77" name="__codelineno-30-77" href="#__codelineno-30-77"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">Print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-78" name="__codelineno-30-78" href="#__codelineno-30-78"></a><span class="w">        </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">kv</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">PairSet</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-79" name="__codelineno-30-79" href="#__codelineno-30-79"></a><span class="w">            </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="n">kv</span><span class="p">.</span><span class="n">key</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">kv</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-30-80" name="__codelineno-30-80" href="#__codelineno-30-80"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-30-81" name="__codelineno-30-81" href="#__codelineno-30-81"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-82" name="__codelineno-30-82" href="#__codelineno-30-82"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_hash_map.js</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">Pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
-<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a>
-<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_hash_map.go</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* キーと値の組 */</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w">    </span><span class="nx">key</span><span class="w"> </span><span class="kt">int</span>
+<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w">    </span><span class="nx">val</span><span class="w"> </span><span class="kt">string</span>
+<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="p">}</span>
+<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a>
+<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="cm">/* 配列ベースのハッシュテーブル */</span>
+<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="kd">type</span><span class="w"> </span><span class="nx">arrayHashMap</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="w">    </span><span class="nx">buckets</span><span class="w"> </span><span class="p">[]</span><span class="o">*</span><span class="nx">pair</span>
+<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a><span class="p">}</span>
+<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a>
+<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="cm">/* ハッシュテーブルを初期化 */</span>
+<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a><span class="kd">func</span><span class="w"> </span><span class="nx">newArrayHashMap</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayHashMap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a><span class="w">    </span><span class="c1">// 100 個のバケットを含む配列を初期化</span>
+<a id="__codelineno-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></a><span class="w">    </span><span class="nx">buckets</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="o">*</span><span class="nx">pair</span><span class="p">,</span><span class="w"> </span><span class="mi">100</span><span class="p">)</span>
+<a id="__codelineno-31-16" name="__codelineno-31-16" href="#__codelineno-31-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">arrayHashMap</span><span class="p">{</span><span class="nx">buckets</span><span class="p">:</span><span class="w"> </span><span class="nx">buckets</span><span class="p">}</span>
+<a id="__codelineno-31-17" name="__codelineno-31-17" href="#__codelineno-31-17"></a><span class="p">}</span>
+<a id="__codelineno-31-18" name="__codelineno-31-18" href="#__codelineno-31-18"></a>
+<a id="__codelineno-31-19" name="__codelineno-31-19" href="#__codelineno-31-19"></a><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-31-20" name="__codelineno-31-20" href="#__codelineno-31-20"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">a</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayHashMap</span><span class="p">)</span><span class="w"> </span><span class="nx">hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-21" name="__codelineno-31-21" href="#__codelineno-31-21"></a><span class="w">    </span><span class="nx">index</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">100</span>
+<a id="__codelineno-31-22" name="__codelineno-31-22" href="#__codelineno-31-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">index</span>
+<a id="__codelineno-31-23" name="__codelineno-31-23" href="#__codelineno-31-23"></a><span class="p">}</span>
+<a id="__codelineno-31-24" name="__codelineno-31-24" href="#__codelineno-31-24"></a>
+<a id="__codelineno-31-25" name="__codelineno-31-25" href="#__codelineno-31-25"></a><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-31-26" name="__codelineno-31-26" href="#__codelineno-31-26"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">a</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayHashMap</span><span class="p">)</span><span class="w"> </span><span class="nx">get</span><span class="p">(</span><span class="nx">key</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">string</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-27" name="__codelineno-31-27" href="#__codelineno-31-27"></a><span class="w">    </span><span class="nx">index</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">a</span><span class="p">.</span><span class="nx">hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span>
+<a id="__codelineno-31-28" name="__codelineno-31-28" href="#__codelineno-31-28"></a><span class="w">    </span><span class="nx">pair</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">a</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span>
+<a id="__codelineno-31-29" name="__codelineno-31-29" href="#__codelineno-31-29"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-30" name="__codelineno-31-30" href="#__codelineno-31-30"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="s">&quot;Not Found&quot;</span>
+<a id="__codelineno-31-31" name="__codelineno-31-31" href="#__codelineno-31-31"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-32" name="__codelineno-31-32" href="#__codelineno-31-32"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span>
+<a id="__codelineno-31-33" name="__codelineno-31-33" href="#__codelineno-31-33"></a><span class="p">}</span>
+<a id="__codelineno-31-34" name="__codelineno-31-34" href="#__codelineno-31-34"></a>
+<a id="__codelineno-31-35" name="__codelineno-31-35" href="#__codelineno-31-35"></a><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-31-36" name="__codelineno-31-36" href="#__codelineno-31-36"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">a</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayHashMap</span><span class="p">)</span><span class="w"> </span><span class="nx">put</span><span class="p">(</span><span class="nx">key</span><span class="w"> </span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-37" name="__codelineno-31-37" href="#__codelineno-31-37"></a><span class="w">    </span><span class="nx">pair</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">pair</span><span class="p">{</span><span class="nx">key</span><span class="p">:</span><span class="w"> </span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">:</span><span class="w"> </span><span class="nx">val</span><span class="p">}</span>
+<a id="__codelineno-31-38" name="__codelineno-31-38" href="#__codelineno-31-38"></a><span class="w">    </span><span class="nx">index</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">a</span><span class="p">.</span><span class="nx">hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span>
+<a id="__codelineno-31-39" name="__codelineno-31-39" href="#__codelineno-31-39"></a><span class="w">    </span><span class="nx">a</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">pair</span>
+<a id="__codelineno-31-40" name="__codelineno-31-40" href="#__codelineno-31-40"></a><span class="p">}</span>
+<a id="__codelineno-31-41" name="__codelineno-31-41" href="#__codelineno-31-41"></a>
+<a id="__codelineno-31-42" name="__codelineno-31-42" href="#__codelineno-31-42"></a><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-31-43" name="__codelineno-31-43" href="#__codelineno-31-43"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">a</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayHashMap</span><span class="p">)</span><span class="w"> </span><span class="nx">remove</span><span class="p">(</span><span class="nx">key</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-44" name="__codelineno-31-44" href="#__codelineno-31-44"></a><span class="w">    </span><span class="nx">index</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">a</span><span class="p">.</span><span class="nx">hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span>
+<a id="__codelineno-31-45" name="__codelineno-31-45" href="#__codelineno-31-45"></a><span class="w">    </span><span class="c1">// nil に設定し、削除を表す</span>
+<a id="__codelineno-31-46" name="__codelineno-31-46" href="#__codelineno-31-46"></a><span class="w">    </span><span class="nx">a</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-31-47" name="__codelineno-31-47" href="#__codelineno-31-47"></a><span class="p">}</span>
+<a id="__codelineno-31-48" name="__codelineno-31-48" href="#__codelineno-31-48"></a>
+<a id="__codelineno-31-49" name="__codelineno-31-49" href="#__codelineno-31-49"></a><span class="cm">/* すべてのキーのペアを取得する */</span>
+<a id="__codelineno-31-50" name="__codelineno-31-50" href="#__codelineno-31-50"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">a</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayHashMap</span><span class="p">)</span><span class="w"> </span><span class="nx">pairSet</span><span class="p">()</span><span class="w"> </span><span class="p">[]</span><span class="o">*</span><span class="nx">pair</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-51" name="__codelineno-31-51" href="#__codelineno-31-51"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">pairs</span><span class="w"> </span><span class="p">[]</span><span class="o">*</span><span class="nx">pair</span>
+<a id="__codelineno-31-52" name="__codelineno-31-52" href="#__codelineno-31-52"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">a</span><span class="p">.</span><span class="nx">buckets</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-53" name="__codelineno-31-53" href="#__codelineno-31-53"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-54" name="__codelineno-31-54" href="#__codelineno-31-54"></a><span class="w">            </span><span class="nx">pairs</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">pairs</span><span class="p">,</span><span class="w"> </span><span class="nx">pair</span><span class="p">)</span>
+<a id="__codelineno-31-55" name="__codelineno-31-55" href="#__codelineno-31-55"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-31-56" name="__codelineno-31-56" href="#__codelineno-31-56"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-57" name="__codelineno-31-57" href="#__codelineno-31-57"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">pairs</span>
+<a id="__codelineno-31-58" name="__codelineno-31-58" href="#__codelineno-31-58"></a><span class="p">}</span>
+<a id="__codelineno-31-59" name="__codelineno-31-59" href="#__codelineno-31-59"></a>
+<a id="__codelineno-31-60" name="__codelineno-31-60" href="#__codelineno-31-60"></a><span class="cm">/* すべてのキーを取得 */</span>
+<a id="__codelineno-31-61" name="__codelineno-31-61" href="#__codelineno-31-61"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">a</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayHashMap</span><span class="p">)</span><span class="w"> </span><span class="nx">keySet</span><span class="p">()</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-62" name="__codelineno-31-62" href="#__codelineno-31-62"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">keys</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span>
+<a id="__codelineno-31-63" name="__codelineno-31-63" href="#__codelineno-31-63"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">a</span><span class="p">.</span><span class="nx">buckets</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-64" name="__codelineno-31-64" href="#__codelineno-31-64"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-65" name="__codelineno-31-65" href="#__codelineno-31-65"></a><span class="w">            </span><span class="nx">keys</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">keys</span><span class="p">,</span><span class="w"> </span><span class="nx">pair</span><span class="p">.</span><span class="nx">key</span><span class="p">)</span>
+<a id="__codelineno-31-66" name="__codelineno-31-66" href="#__codelineno-31-66"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-31-67" name="__codelineno-31-67" href="#__codelineno-31-67"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-68" name="__codelineno-31-68" href="#__codelineno-31-68"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">keys</span>
+<a id="__codelineno-31-69" name="__codelineno-31-69" href="#__codelineno-31-69"></a><span class="p">}</span>
+<a id="__codelineno-31-70" name="__codelineno-31-70" href="#__codelineno-31-70"></a>
+<a id="__codelineno-31-71" name="__codelineno-31-71" href="#__codelineno-31-71"></a><span class="cm">/* すべての値を取得 */</span>
+<a id="__codelineno-31-72" name="__codelineno-31-72" href="#__codelineno-31-72"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">a</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayHashMap</span><span class="p">)</span><span class="w"> </span><span class="nx">valueSet</span><span class="p">()</span><span class="w"> </span><span class="p">[]</span><span class="kt">string</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-73" name="__codelineno-31-73" href="#__codelineno-31-73"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">values</span><span class="w"> </span><span class="p">[]</span><span class="kt">string</span>
+<a id="__codelineno-31-74" name="__codelineno-31-74" href="#__codelineno-31-74"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">a</span><span class="p">.</span><span class="nx">buckets</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-75" name="__codelineno-31-75" href="#__codelineno-31-75"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-76" name="__codelineno-31-76" href="#__codelineno-31-76"></a><span class="w">            </span><span class="nx">values</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">values</span><span class="p">,</span><span class="w"> </span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="p">)</span>
+<a id="__codelineno-31-77" name="__codelineno-31-77" href="#__codelineno-31-77"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-31-78" name="__codelineno-31-78" href="#__codelineno-31-78"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-79" name="__codelineno-31-79" href="#__codelineno-31-79"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">values</span>
+<a id="__codelineno-31-80" name="__codelineno-31-80" href="#__codelineno-31-80"></a><span class="p">}</span>
+<a id="__codelineno-31-81" name="__codelineno-31-81" href="#__codelineno-31-81"></a>
+<a id="__codelineno-31-82" name="__codelineno-31-82" href="#__codelineno-31-82"></a><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-31-83" name="__codelineno-31-83" href="#__codelineno-31-83"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">a</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayHashMap</span><span class="p">)</span><span class="w"> </span><span class="nb">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-84" name="__codelineno-31-84" href="#__codelineno-31-84"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">a</span><span class="p">.</span><span class="nx">buckets</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-85" name="__codelineno-31-85" href="#__codelineno-31-85"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-86" name="__codelineno-31-86" href="#__codelineno-31-86"></a><span class="w">            </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">pair</span><span class="p">.</span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;-&gt;&quot;</span><span class="p">,</span><span class="w"> </span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="p">)</span>
+<a id="__codelineno-31-87" name="__codelineno-31-87" href="#__codelineno-31-87"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-31-88" name="__codelineno-31-88" href="#__codelineno-31-88"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-89" name="__codelineno-31-89" href="#__codelineno-31-89"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_hash_map.ts</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">Pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
-<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a>
-<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_hash_map.swift</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* キーと値の組 */</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">Pair</span><span class="p">:</span><span class="w"> </span><span class="nb">Equatable</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">key</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span>
+<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">val</span><span class="p">:</span><span class="w"> </span><span class="nb">String</span>
+<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a>
+<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kd">init</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="nb">String</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="w">        </span><span class="kc">self</span><span class="p">.</span><span class="n">key</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">key</span>
+<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w">        </span><span class="kc">self</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">val</span>
+<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-10" name="__codelineno-32-10" href="#__codelineno-32-10"></a>
+<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kd">static</span><span class="w"> </span><span class="kd">func</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="p">(</span><span class="n">lhs</span><span class="p">:</span><span class="w"> </span><span class="n">Pair</span><span class="p">,</span><span class="w"> </span><span class="n">rhs</span><span class="p">:</span><span class="w"> </span><span class="n">Pair</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a><span class="w">        </span><span class="n">lhs</span><span class="p">.</span><span class="n">key</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">rhs</span><span class="p">.</span><span class="n">key</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">lhs</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">rhs</span><span class="p">.</span><span class="n">val</span>
+<a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-14" name="__codelineno-32-14" href="#__codelineno-32-14"></a><span class="p">}</span>
+<a id="__codelineno-32-15" name="__codelineno-32-15" href="#__codelineno-32-15"></a>
+<a id="__codelineno-32-16" name="__codelineno-32-16" href="#__codelineno-32-16"></a><span class="cm">/* 配列ベースのハッシュテーブル */</span>
+<a id="__codelineno-32-17" name="__codelineno-32-17" href="#__codelineno-32-17"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ArrayHashMap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-18" name="__codelineno-32-18" href="#__codelineno-32-18"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">buckets</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="n">Pair</span><span class="p">?]</span>
+<a id="__codelineno-32-19" name="__codelineno-32-19" href="#__codelineno-32-19"></a>
+<a id="__codelineno-32-20" name="__codelineno-32-20" href="#__codelineno-32-20"></a><span class="w">    </span><span class="kd">init</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-21" name="__codelineno-32-21" href="#__codelineno-32-21"></a><span class="w">        </span><span class="c1">// 100 個のバケットを含む配列を初期化</span>
+<a id="__codelineno-32-22" name="__codelineno-32-22" href="#__codelineno-32-22"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="mi">100</span><span class="p">)</span>
+<a id="__codelineno-32-23" name="__codelineno-32-23" href="#__codelineno-32-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-24" name="__codelineno-32-24" href="#__codelineno-32-24"></a>
+<a id="__codelineno-32-25" name="__codelineno-32-25" href="#__codelineno-32-25"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-32-26" name="__codelineno-32-26" href="#__codelineno-32-26"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">func</span><span class="w"> </span><span class="nf">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-27" name="__codelineno-32-27" href="#__codelineno-32-27"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">index</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">100</span>
+<a id="__codelineno-32-28" name="__codelineno-32-28" href="#__codelineno-32-28"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">index</span>
+<a id="__codelineno-32-29" name="__codelineno-32-29" href="#__codelineno-32-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-30" name="__codelineno-32-30" href="#__codelineno-32-30"></a>
+<a id="__codelineno-32-31" name="__codelineno-32-31" href="#__codelineno-32-31"></a><span class="w">    </span><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-32-32" name="__codelineno-32-32" href="#__codelineno-32-32"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">String</span><span class="p">?</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-33" name="__codelineno-32-33" href="#__codelineno-32-33"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">index</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-32-34" name="__codelineno-32-34" href="#__codelineno-32-34"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">pair</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
+<a id="__codelineno-32-35" name="__codelineno-32-35" href="#__codelineno-32-35"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pair</span><span class="p">?.</span><span class="n">val</span>
+<a id="__codelineno-32-36" name="__codelineno-32-36" href="#__codelineno-32-36"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-37" name="__codelineno-32-37" href="#__codelineno-32-37"></a>
+<a id="__codelineno-32-38" name="__codelineno-32-38" href="#__codelineno-32-38"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-32-39" name="__codelineno-32-39" href="#__codelineno-32-39"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="nb">String</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-40" name="__codelineno-32-40" href="#__codelineno-32-40"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">pair</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-32-41" name="__codelineno-32-41" href="#__codelineno-32-41"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">index</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-32-42" name="__codelineno-32-42" href="#__codelineno-32-42"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">pair</span>
+<a id="__codelineno-32-43" name="__codelineno-32-43" href="#__codelineno-32-43"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-44" name="__codelineno-32-44" href="#__codelineno-32-44"></a>
+<a id="__codelineno-32-45" name="__codelineno-32-45" href="#__codelineno-32-45"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-32-46" name="__codelineno-32-46" href="#__codelineno-32-46"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-47" name="__codelineno-32-47" href="#__codelineno-32-47"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">index</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-32-48" name="__codelineno-32-48" href="#__codelineno-32-48"></a><span class="w">        </span><span class="c1">// nil に設定し、削除を表す</span>
+<a id="__codelineno-32-49" name="__codelineno-32-49" href="#__codelineno-32-49"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-32-50" name="__codelineno-32-50" href="#__codelineno-32-50"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-51" name="__codelineno-32-51" href="#__codelineno-32-51"></a>
+<a id="__codelineno-32-52" name="__codelineno-32-52" href="#__codelineno-32-52"></a><span class="w">    </span><span class="cm">/* すべてのキーと値のペアを取得 */</span>
+<a id="__codelineno-32-53" name="__codelineno-32-53" href="#__codelineno-32-53"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">pairSet</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="n">Pair</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-54" name="__codelineno-32-54" href="#__codelineno-32-54"></a><span class="w">        </span><span class="n">buckets</span><span class="p">.</span><span class="n">compactMap</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nv">$0</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-32-55" name="__codelineno-32-55" href="#__codelineno-32-55"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-56" name="__codelineno-32-56" href="#__codelineno-32-56"></a>
+<a id="__codelineno-32-57" name="__codelineno-32-57" href="#__codelineno-32-57"></a><span class="w">    </span><span class="cm">/* すべてのキーを取得 */</span>
+<a id="__codelineno-32-58" name="__codelineno-32-58" href="#__codelineno-32-58"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">keySet</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-59" name="__codelineno-32-59" href="#__codelineno-32-59"></a><span class="w">        </span><span class="n">buckets</span><span class="p">.</span><span class="n">compactMap</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nv">$0</span><span class="p">?.</span><span class="n">key</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-32-60" name="__codelineno-32-60" href="#__codelineno-32-60"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-61" name="__codelineno-32-61" href="#__codelineno-32-61"></a>
+<a id="__codelineno-32-62" name="__codelineno-32-62" href="#__codelineno-32-62"></a><span class="w">    </span><span class="cm">/* すべての値を取得 */</span>
+<a id="__codelineno-32-63" name="__codelineno-32-63" href="#__codelineno-32-63"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">valueSet</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="nb">String</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-64" name="__codelineno-32-64" href="#__codelineno-32-64"></a><span class="w">        </span><span class="n">buckets</span><span class="p">.</span><span class="n">compactMap</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nv">$0</span><span class="p">?.</span><span class="n">val</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-32-65" name="__codelineno-32-65" href="#__codelineno-32-65"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-66" name="__codelineno-32-66" href="#__codelineno-32-66"></a>
+<a id="__codelineno-32-67" name="__codelineno-32-67" href="#__codelineno-32-67"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-32-68" name="__codelineno-32-68" href="#__codelineno-32-68"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-69" name="__codelineno-32-69" href="#__codelineno-32-69"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">pairSet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-70" name="__codelineno-32-70" href="#__codelineno-32-70"></a><span class="w">            </span><span class="n">Swift</span><span class="p">.</span><span class="bp">print</span><span class="p">(</span><span class="s">&quot;</span><span class="si">\(</span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="si">)</span><span class="s"> -&gt; </span><span class="si">\(</span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="si">)</span><span class="s">&quot;</span><span class="p">)</span>
+<a id="__codelineno-32-71" name="__codelineno-32-71" href="#__codelineno-32-71"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-32-72" name="__codelineno-32-72" href="#__codelineno-32-72"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-73" name="__codelineno-32-73" href="#__codelineno-32-73"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_hash_map.dart</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">Pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
-<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a>
-<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_hash_map.js</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* キーと値の組 Number -&gt; String */</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">Pair</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">key</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">key</span><span class="p">;</span>
+<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="p">}</span>
+<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a>
+<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="cm">/* 配列ベースのハッシュテーブル */</span>
+<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a><span class="kd">class</span><span class="w"> </span><span class="nx">ArrayHashMap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="w">    </span><span class="n">#buckets</span><span class="p">;</span>
+<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a><span class="w">        </span><span class="c1">// 100 個のバケットを含む配列を初期化</span>
+<a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mf">100</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="kc">null</span><span class="p">);</span>
+<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-16" name="__codelineno-33-16" href="#__codelineno-33-16"></a>
+<a id="__codelineno-33-17" name="__codelineno-33-17" href="#__codelineno-33-17"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-33-18" name="__codelineno-33-18" href="#__codelineno-33-18"></a><span class="w">    </span><span class="n">#hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-19" name="__codelineno-33-19" href="#__codelineno-33-19"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mf">100</span><span class="p">;</span>
+<a id="__codelineno-33-20" name="__codelineno-33-20" href="#__codelineno-33-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-21" name="__codelineno-33-21" href="#__codelineno-33-21"></a>
+<a id="__codelineno-33-22" name="__codelineno-33-22" href="#__codelineno-33-22"></a><span class="w">    </span><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-33-23" name="__codelineno-33-23" href="#__codelineno-33-23"></a><span class="w">    </span><span class="nx">get</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-24" name="__codelineno-33-24" href="#__codelineno-33-24"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">);</span>
+<a id="__codelineno-33-25" name="__codelineno-33-25" href="#__codelineno-33-25"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">];</span>
+<a id="__codelineno-33-26" name="__codelineno-33-26" href="#__codelineno-33-26"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">pair</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-33-27" name="__codelineno-33-27" href="#__codelineno-33-27"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-33-28" name="__codelineno-33-28" href="#__codelineno-33-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-29" name="__codelineno-33-29" href="#__codelineno-33-29"></a>
+<a id="__codelineno-33-30" name="__codelineno-33-30" href="#__codelineno-33-30"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-33-31" name="__codelineno-33-31" href="#__codelineno-33-31"></a><span class="w">    </span><span class="nx">set</span><span class="p">(</span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-32" name="__codelineno-33-32" href="#__codelineno-33-32"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">);</span>
+<a id="__codelineno-33-33" name="__codelineno-33-33" href="#__codelineno-33-33"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">Pair</span><span class="p">(</span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-33-34" name="__codelineno-33-34" href="#__codelineno-33-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-35" name="__codelineno-33-35" href="#__codelineno-33-35"></a>
+<a id="__codelineno-33-36" name="__codelineno-33-36" href="#__codelineno-33-36"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-33-37" name="__codelineno-33-37" href="#__codelineno-33-37"></a><span class="w">    </span><span class="ow">delete</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-38" name="__codelineno-33-38" href="#__codelineno-33-38"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">);</span>
+<a id="__codelineno-33-39" name="__codelineno-33-39" href="#__codelineno-33-39"></a><span class="w">        </span><span class="c1">// null に設定し、削除を表す</span>
+<a id="__codelineno-33-40" name="__codelineno-33-40" href="#__codelineno-33-40"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-33-41" name="__codelineno-33-41" href="#__codelineno-33-41"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-42" name="__codelineno-33-42" href="#__codelineno-33-42"></a>
+<a id="__codelineno-33-43" name="__codelineno-33-43" href="#__codelineno-33-43"></a><span class="w">    </span><span class="cm">/* すべてのキーと値のペアを取得 */</span>
+<a id="__codelineno-33-44" name="__codelineno-33-44" href="#__codelineno-33-44"></a><span class="w">    </span><span class="nx">entries</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-45" name="__codelineno-33-45" href="#__codelineno-33-45"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-33-46" name="__codelineno-33-46" href="#__codelineno-33-46"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-47" name="__codelineno-33-47" href="#__codelineno-33-47"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-48" name="__codelineno-33-48" href="#__codelineno-33-48"></a><span class="w">                </span><span class="nx">arr</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">i</span><span class="p">]);</span>
+<a id="__codelineno-33-49" name="__codelineno-33-49" href="#__codelineno-33-49"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-33-50" name="__codelineno-33-50" href="#__codelineno-33-50"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-33-51" name="__codelineno-33-51" href="#__codelineno-33-51"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">arr</span><span class="p">;</span>
+<a id="__codelineno-33-52" name="__codelineno-33-52" href="#__codelineno-33-52"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-53" name="__codelineno-33-53" href="#__codelineno-33-53"></a>
+<a id="__codelineno-33-54" name="__codelineno-33-54" href="#__codelineno-33-54"></a><span class="w">    </span><span class="cm">/* すべてのキーを取得 */</span>
+<a id="__codelineno-33-55" name="__codelineno-33-55" href="#__codelineno-33-55"></a><span class="w">    </span><span class="nx">keys</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-56" name="__codelineno-33-56" href="#__codelineno-33-56"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-33-57" name="__codelineno-33-57" href="#__codelineno-33-57"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-58" name="__codelineno-33-58" href="#__codelineno-33-58"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-59" name="__codelineno-33-59" href="#__codelineno-33-59"></a><span class="w">                </span><span class="nx">arr</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">i</span><span class="p">].</span><span class="nx">key</span><span class="p">);</span>
+<a id="__codelineno-33-60" name="__codelineno-33-60" href="#__codelineno-33-60"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-33-61" name="__codelineno-33-61" href="#__codelineno-33-61"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-33-62" name="__codelineno-33-62" href="#__codelineno-33-62"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">arr</span><span class="p">;</span>
+<a id="__codelineno-33-63" name="__codelineno-33-63" href="#__codelineno-33-63"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-64" name="__codelineno-33-64" href="#__codelineno-33-64"></a>
+<a id="__codelineno-33-65" name="__codelineno-33-65" href="#__codelineno-33-65"></a><span class="w">    </span><span class="cm">/* すべての値を取得 */</span>
+<a id="__codelineno-33-66" name="__codelineno-33-66" href="#__codelineno-33-66"></a><span class="w">    </span><span class="nx">values</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-67" name="__codelineno-33-67" href="#__codelineno-33-67"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-33-68" name="__codelineno-33-68" href="#__codelineno-33-68"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-69" name="__codelineno-33-69" href="#__codelineno-33-69"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-70" name="__codelineno-33-70" href="#__codelineno-33-70"></a><span class="w">                </span><span class="nx">arr</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#buckets</span><span class="p">[</span><span class="nx">i</span><span class="p">].</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-33-71" name="__codelineno-33-71" href="#__codelineno-33-71"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-33-72" name="__codelineno-33-72" href="#__codelineno-33-72"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-33-73" name="__codelineno-33-73" href="#__codelineno-33-73"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">arr</span><span class="p">;</span>
+<a id="__codelineno-33-74" name="__codelineno-33-74" href="#__codelineno-33-74"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-75" name="__codelineno-33-75" href="#__codelineno-33-75"></a>
+<a id="__codelineno-33-76" name="__codelineno-33-76" href="#__codelineno-33-76"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-33-77" name="__codelineno-33-77" href="#__codelineno-33-77"></a><span class="w">    </span><span class="nx">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-78" name="__codelineno-33-78" href="#__codelineno-33-78"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">pairSet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">entries</span><span class="p">();</span>
+<a id="__codelineno-33-79" name="__codelineno-33-79" href="#__codelineno-33-79"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">pairSet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-80" name="__codelineno-33-80" href="#__codelineno-33-80"></a><span class="w">            </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="sb">`</span><span class="si">${</span><span class="nx">pair</span><span class="p">.</span><span class="nx">key</span><span class="si">}</span><span class="sb"> -&gt; </span><span class="si">${</span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="si">}</span><span class="sb">`</span><span class="p">);</span>
+<a id="__codelineno-33-81" name="__codelineno-33-81" href="#__codelineno-33-81"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-33-82" name="__codelineno-33-82" href="#__codelineno-33-82"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-83" name="__codelineno-33-83" href="#__codelineno-33-83"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_hash_map.rs</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">Pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
-<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a>
-<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_hash_map.ts</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* キーと値の組 Number -&gt; String */</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">Pair</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nx">key</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span>
+<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">;</span>
+<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a>
+<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">key</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">key</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">key</span><span class="p">;</span>
+<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-10" name="__codelineno-34-10" href="#__codelineno-34-10"></a><span class="p">}</span>
+<a id="__codelineno-34-11" name="__codelineno-34-11" href="#__codelineno-34-11"></a>
+<a id="__codelineno-34-12" name="__codelineno-34-12" href="#__codelineno-34-12"></a><span class="cm">/* 配列ベースのハッシュテーブル */</span>
+<a id="__codelineno-34-13" name="__codelineno-34-13" href="#__codelineno-34-13"></a><span class="kd">class</span><span class="w"> </span><span class="nx">ArrayHashMap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-14" name="__codelineno-34-14" href="#__codelineno-34-14"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="k">readonly</span><span class="w"> </span><span class="nx">buckets</span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="nx">Pair</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)[];</span>
+<a id="__codelineno-34-15" name="__codelineno-34-15" href="#__codelineno-34-15"></a>
+<a id="__codelineno-34-16" name="__codelineno-34-16" href="#__codelineno-34-16"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-17" name="__codelineno-34-17" href="#__codelineno-34-17"></a><span class="w">        </span><span class="c1">// 100 個のバケットを含む配列を初期化</span>
+<a id="__codelineno-34-18" name="__codelineno-34-18" href="#__codelineno-34-18"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mf">100</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="kc">null</span><span class="p">);</span>
+<a id="__codelineno-34-19" name="__codelineno-34-19" href="#__codelineno-34-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-20" name="__codelineno-34-20" href="#__codelineno-34-20"></a>
+<a id="__codelineno-34-21" name="__codelineno-34-21" href="#__codelineno-34-21"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-34-22" name="__codelineno-34-22" href="#__codelineno-34-22"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-23" name="__codelineno-34-23" href="#__codelineno-34-23"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mf">100</span><span class="p">;</span>
+<a id="__codelineno-34-24" name="__codelineno-34-24" href="#__codelineno-34-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-25" name="__codelineno-34-25" href="#__codelineno-34-25"></a>
+<a id="__codelineno-34-26" name="__codelineno-34-26" href="#__codelineno-34-26"></a><span class="w">    </span><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-34-27" name="__codelineno-34-27" href="#__codelineno-34-27"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nx">get</span><span class="p">(</span><span class="nx">key</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-28" name="__codelineno-34-28" href="#__codelineno-34-28"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">);</span>
+<a id="__codelineno-34-29" name="__codelineno-34-29" href="#__codelineno-34-29"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">];</span>
+<a id="__codelineno-34-30" name="__codelineno-34-30" href="#__codelineno-34-30"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">pair</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-34-31" name="__codelineno-34-31" href="#__codelineno-34-31"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-34-32" name="__codelineno-34-32" href="#__codelineno-34-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-33" name="__codelineno-34-33" href="#__codelineno-34-33"></a>
+<a id="__codelineno-34-34" name="__codelineno-34-34" href="#__codelineno-34-34"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-34-35" name="__codelineno-34-35" href="#__codelineno-34-35"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nx">set</span><span class="p">(</span><span class="nx">key</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-36" name="__codelineno-34-36" href="#__codelineno-34-36"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">);</span>
+<a id="__codelineno-34-37" name="__codelineno-34-37" href="#__codelineno-34-37"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">Pair</span><span class="p">(</span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-34-38" name="__codelineno-34-38" href="#__codelineno-34-38"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-39" name="__codelineno-34-39" href="#__codelineno-34-39"></a>
+<a id="__codelineno-34-40" name="__codelineno-34-40" href="#__codelineno-34-40"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-34-41" name="__codelineno-34-41" href="#__codelineno-34-41"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="ow">delete</span><span class="p">(</span><span class="nx">key</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-42" name="__codelineno-34-42" href="#__codelineno-34-42"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">);</span>
+<a id="__codelineno-34-43" name="__codelineno-34-43" href="#__codelineno-34-43"></a><span class="w">        </span><span class="c1">// null に設定し、削除を表す</span>
+<a id="__codelineno-34-44" name="__codelineno-34-44" href="#__codelineno-34-44"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-34-45" name="__codelineno-34-45" href="#__codelineno-34-45"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-46" name="__codelineno-34-46" href="#__codelineno-34-46"></a>
+<a id="__codelineno-34-47" name="__codelineno-34-47" href="#__codelineno-34-47"></a><span class="w">    </span><span class="cm">/* すべてのキーと値のペアを取得 */</span>
+<a id="__codelineno-34-48" name="__codelineno-34-48" href="#__codelineno-34-48"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nx">entries</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="nx">Pair</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)[]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-49" name="__codelineno-34-49" href="#__codelineno-34-49"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">arr</span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="nx">Pair</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-34-50" name="__codelineno-34-50" href="#__codelineno-34-50"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-51" name="__codelineno-34-51" href="#__codelineno-34-51"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-52" name="__codelineno-34-52" href="#__codelineno-34-52"></a><span class="w">                </span><span class="nx">arr</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">i</span><span class="p">]);</span>
+<a id="__codelineno-34-53" name="__codelineno-34-53" href="#__codelineno-34-53"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-34-54" name="__codelineno-34-54" href="#__codelineno-34-54"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-34-55" name="__codelineno-34-55" href="#__codelineno-34-55"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">arr</span><span class="p">;</span>
+<a id="__codelineno-34-56" name="__codelineno-34-56" href="#__codelineno-34-56"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-57" name="__codelineno-34-57" href="#__codelineno-34-57"></a>
+<a id="__codelineno-34-58" name="__codelineno-34-58" href="#__codelineno-34-58"></a><span class="w">    </span><span class="cm">/* すべてのキーを取得 */</span>
+<a id="__codelineno-34-59" name="__codelineno-34-59" href="#__codelineno-34-59"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nx">keys</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="kt">number</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">undefined</span><span class="p">)[]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-60" name="__codelineno-34-60" href="#__codelineno-34-60"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">arr</span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="kt">number</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">undefined</span><span class="p">)[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-34-61" name="__codelineno-34-61" href="#__codelineno-34-61"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-62" name="__codelineno-34-62" href="#__codelineno-34-62"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-63" name="__codelineno-34-63" href="#__codelineno-34-63"></a><span class="w">                </span><span class="nx">arr</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">i</span><span class="p">].</span><span class="nx">key</span><span class="p">);</span>
+<a id="__codelineno-34-64" name="__codelineno-34-64" href="#__codelineno-34-64"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-34-65" name="__codelineno-34-65" href="#__codelineno-34-65"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-34-66" name="__codelineno-34-66" href="#__codelineno-34-66"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">arr</span><span class="p">;</span>
+<a id="__codelineno-34-67" name="__codelineno-34-67" href="#__codelineno-34-67"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-68" name="__codelineno-34-68" href="#__codelineno-34-68"></a>
+<a id="__codelineno-34-69" name="__codelineno-34-69" href="#__codelineno-34-69"></a><span class="w">    </span><span class="cm">/* すべての値を取得 */</span>
+<a id="__codelineno-34-70" name="__codelineno-34-70" href="#__codelineno-34-70"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nx">values</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="kt">string</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">undefined</span><span class="p">)[]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-71" name="__codelineno-34-71" href="#__codelineno-34-71"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">arr</span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="kt">string</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">undefined</span><span class="p">)[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-34-72" name="__codelineno-34-72" href="#__codelineno-34-72"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-73" name="__codelineno-34-73" href="#__codelineno-34-73"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-74" name="__codelineno-34-74" href="#__codelineno-34-74"></a><span class="w">                </span><span class="nx">arr</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">i</span><span class="p">].</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-34-75" name="__codelineno-34-75" href="#__codelineno-34-75"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-34-76" name="__codelineno-34-76" href="#__codelineno-34-76"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-34-77" name="__codelineno-34-77" href="#__codelineno-34-77"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">arr</span><span class="p">;</span>
+<a id="__codelineno-34-78" name="__codelineno-34-78" href="#__codelineno-34-78"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-79" name="__codelineno-34-79" href="#__codelineno-34-79"></a>
+<a id="__codelineno-34-80" name="__codelineno-34-80" href="#__codelineno-34-80"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-34-81" name="__codelineno-34-81" href="#__codelineno-34-81"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nx">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-82" name="__codelineno-34-82" href="#__codelineno-34-82"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">pairSet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">entries</span><span class="p">();</span>
+<a id="__codelineno-34-83" name="__codelineno-34-83" href="#__codelineno-34-83"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">pairSet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-84" name="__codelineno-34-84" href="#__codelineno-34-84"></a><span class="w">            </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="sb">`</span><span class="si">${</span><span class="nx">pair</span><span class="p">.</span><span class="nx">key</span><span class="si">}</span><span class="sb"> -&gt; </span><span class="si">${</span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="si">}</span><span class="sb">`</span><span class="p">);</span>
+<a id="__codelineno-34-85" name="__codelineno-34-85" href="#__codelineno-34-85"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-34-86" name="__codelineno-34-86" href="#__codelineno-34-86"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-87" name="__codelineno-34-87" href="#__codelineno-34-87"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_hash_map.c</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">Pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
-<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a>
-<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_hash_map.dart</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* キーと値の組 */</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">Pair</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">;</span>
+<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="w">  </span><span class="kt">String</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="w">  </span><span class="n">Pair</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="p">}</span>
+<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a>
+<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="cm">/* 配列ベースのハッシュテーブル */</span>
+<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ArrayHashMap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="w">  </span><span class="kd">late</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">?&gt;</span><span class="w"> </span><span class="n">_buckets</span><span class="p">;</span>
+<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a>
+<a id="__codelineno-35-12" name="__codelineno-35-12" href="#__codelineno-35-12"></a><span class="w">  </span><span class="n">ArrayHashMap</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-13" name="__codelineno-35-13" href="#__codelineno-35-13"></a><span class="w">    </span><span class="c1">// 100 個のバケットを含む配列を初期化</span>
+<a id="__codelineno-35-14" name="__codelineno-35-14" href="#__codelineno-35-14"></a><span class="w">    </span><span class="n">_buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="m">100</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">);</span>
+<a id="__codelineno-35-15" name="__codelineno-35-15" href="#__codelineno-35-15"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-35-16" name="__codelineno-35-16" href="#__codelineno-35-16"></a>
+<a id="__codelineno-35-17" name="__codelineno-35-17" href="#__codelineno-35-17"></a><span class="w">  </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-35-18" name="__codelineno-35-18" href="#__codelineno-35-18"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">_hashFunc</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-19" name="__codelineno-35-19" href="#__codelineno-35-19"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="m">100</span><span class="p">;</span>
+<a id="__codelineno-35-20" name="__codelineno-35-20" href="#__codelineno-35-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
+<a id="__codelineno-35-21" name="__codelineno-35-21" href="#__codelineno-35-21"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-35-22" name="__codelineno-35-22" href="#__codelineno-35-22"></a>
+<a id="__codelineno-35-23" name="__codelineno-35-23" href="#__codelineno-35-23"></a><span class="w">  </span><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-35-24" name="__codelineno-35-24" href="#__codelineno-35-24"></a><span class="w">  </span><span class="kt">String</span><span class="o">?</span><span class="w"> </span><span class="kd">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-25" name="__codelineno-35-25" href="#__codelineno-35-25"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-35-26" name="__codelineno-35-26" href="#__codelineno-35-26"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="n">Pair</span><span class="o">?</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-35-27" name="__codelineno-35-27" href="#__codelineno-35-27"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-28" name="__codelineno-35-28" href="#__codelineno-35-28"></a><span class="w">      </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-35-29" name="__codelineno-35-29" href="#__codelineno-35-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-30" name="__codelineno-35-30" href="#__codelineno-35-30"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-35-31" name="__codelineno-35-31" href="#__codelineno-35-31"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-35-32" name="__codelineno-35-32" href="#__codelineno-35-32"></a>
+<a id="__codelineno-35-33" name="__codelineno-35-33" href="#__codelineno-35-33"></a><span class="w">  </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-35-34" name="__codelineno-35-34" href="#__codelineno-35-34"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="kt">String</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-35" name="__codelineno-35-35" href="#__codelineno-35-35"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-35-36" name="__codelineno-35-36" href="#__codelineno-35-36"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-35-37" name="__codelineno-35-37" href="#__codelineno-35-37"></a><span class="w">    </span><span class="n">_buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pair</span><span class="p">;</span>
+<a id="__codelineno-35-38" name="__codelineno-35-38" href="#__codelineno-35-38"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-35-39" name="__codelineno-35-39" href="#__codelineno-35-39"></a>
+<a id="__codelineno-35-40" name="__codelineno-35-40" href="#__codelineno-35-40"></a><span class="w">  </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-35-41" name="__codelineno-35-41" href="#__codelineno-35-41"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-42" name="__codelineno-35-42" href="#__codelineno-35-42"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-35-43" name="__codelineno-35-43" href="#__codelineno-35-43"></a><span class="w">    </span><span class="n">_buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-35-44" name="__codelineno-35-44" href="#__codelineno-35-44"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-35-45" name="__codelineno-35-45" href="#__codelineno-35-45"></a>
+<a id="__codelineno-35-46" name="__codelineno-35-46" href="#__codelineno-35-46"></a><span class="w">  </span><span class="cm">/* すべてのキーと値のペアを取得 */</span>
+<a id="__codelineno-35-47" name="__codelineno-35-47" href="#__codelineno-35-47"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">pairSet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-48" name="__codelineno-35-48" href="#__codelineno-35-48"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">pairSet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-35-49" name="__codelineno-35-49" href="#__codelineno-35-49"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">final</span><span class="w"> </span><span class="n">Pair</span><span class="o">?</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">_buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-50" name="__codelineno-35-50" href="#__codelineno-35-50"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-51" name="__codelineno-35-51" href="#__codelineno-35-51"></a><span class="w">        </span><span class="n">pairSet</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">pair</span><span class="p">);</span>
+<a id="__codelineno-35-52" name="__codelineno-35-52" href="#__codelineno-35-52"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-35-53" name="__codelineno-35-53" href="#__codelineno-35-53"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-54" name="__codelineno-35-54" href="#__codelineno-35-54"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">pairSet</span><span class="p">;</span>
+<a id="__codelineno-35-55" name="__codelineno-35-55" href="#__codelineno-35-55"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-35-56" name="__codelineno-35-56" href="#__codelineno-35-56"></a>
+<a id="__codelineno-35-57" name="__codelineno-35-57" href="#__codelineno-35-57"></a><span class="w">  </span><span class="cm">/* すべてのキーを取得 */</span>
+<a id="__codelineno-35-58" name="__codelineno-35-58" href="#__codelineno-35-58"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">keySet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-59" name="__codelineno-35-59" href="#__codelineno-35-59"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">keySet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-35-60" name="__codelineno-35-60" href="#__codelineno-35-60"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">final</span><span class="w"> </span><span class="n">Pair</span><span class="o">?</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">_buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-61" name="__codelineno-35-61" href="#__codelineno-35-61"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-62" name="__codelineno-35-62" href="#__codelineno-35-62"></a><span class="w">        </span><span class="n">keySet</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-35-63" name="__codelineno-35-63" href="#__codelineno-35-63"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-35-64" name="__codelineno-35-64" href="#__codelineno-35-64"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-65" name="__codelineno-35-65" href="#__codelineno-35-65"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">keySet</span><span class="p">;</span>
+<a id="__codelineno-35-66" name="__codelineno-35-66" href="#__codelineno-35-66"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-35-67" name="__codelineno-35-67" href="#__codelineno-35-67"></a>
+<a id="__codelineno-35-68" name="__codelineno-35-68" href="#__codelineno-35-68"></a><span class="w">  </span><span class="cm">/* すべての値を取得 */</span>
+<a id="__codelineno-35-69" name="__codelineno-35-69" href="#__codelineno-35-69"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">values</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-70" name="__codelineno-35-70" href="#__codelineno-35-70"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">valueSet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-35-71" name="__codelineno-35-71" href="#__codelineno-35-71"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">final</span><span class="w"> </span><span class="n">Pair</span><span class="o">?</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">_buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-72" name="__codelineno-35-72" href="#__codelineno-35-72"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-73" name="__codelineno-35-73" href="#__codelineno-35-73"></a><span class="w">        </span><span class="n">valueSet</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-35-74" name="__codelineno-35-74" href="#__codelineno-35-74"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-35-75" name="__codelineno-35-75" href="#__codelineno-35-75"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-76" name="__codelineno-35-76" href="#__codelineno-35-76"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">valueSet</span><span class="p">;</span>
+<a id="__codelineno-35-77" name="__codelineno-35-77" href="#__codelineno-35-77"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-35-78" name="__codelineno-35-78" href="#__codelineno-35-78"></a>
+<a id="__codelineno-35-79" name="__codelineno-35-79" href="#__codelineno-35-79"></a><span class="w">  </span><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-35-80" name="__codelineno-35-80" href="#__codelineno-35-80"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">printHashMap</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-81" name="__codelineno-35-81" href="#__codelineno-35-81"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">final</span><span class="w"> </span><span class="n">Pair</span><span class="w"> </span><span class="n">kv</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">pairSet</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-82" name="__codelineno-35-82" href="#__codelineno-35-82"></a><span class="w">      </span><span class="n">print</span><span class="p">(</span><span class="s2">&quot;</span><span class="si">${</span><span class="n">kv</span><span class="p">.</span><span class="n">key</span><span class="si">}</span><span class="s2"> -&gt; </span><span class="si">${</span><span class="n">kv</span><span class="p">.</span><span class="n">val</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">);</span>
+<a id="__codelineno-35-83" name="__codelineno-35-83" href="#__codelineno-35-83"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-84" name="__codelineno-35-84" href="#__codelineno-35-84"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-35-85" name="__codelineno-35-85" href="#__codelineno-35-85"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_hash_map.kt</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">Pair</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
-<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a>
-<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">ArrayHashMap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">array_hash_map.rs</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* キーと値の組 */</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="cp">#[derive(Debug, Clone, PartialEq)]</span>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="k">pub</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">Pair</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span>
+<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="nb">String</span><span class="p">,</span>
+<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="p">}</span>
+<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a>
+<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="cm">/* 配列ベースのハッシュテーブル */</span>
+<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="k">pub</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">ArrayHashMap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a><span class="w">    </span><span class="n">buckets</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a><span class="p">}</span>
+<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a>
+<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></a><span class="k">impl</span><span class="w"> </span><span class="n">ArrayHashMap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-14" name="__codelineno-36-14" href="#__codelineno-36-14"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">new</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">ArrayHashMap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-15" name="__codelineno-36-15" href="#__codelineno-36-15"></a><span class="w">        </span><span class="c1">// 100 個のバケットを含む配列を初期化</span>
+<a id="__codelineno-36-16" name="__codelineno-36-16" href="#__codelineno-36-16"></a><span class="w">        </span><span class="bp">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-17" name="__codelineno-36-17" href="#__codelineno-36-17"></a><span class="w">            </span><span class="n">buckets</span><span class="p">:</span><span class="w"> </span><span class="nc">vec</span><span class="o">!</span><span class="p">[</span><span class="nb">None</span><span class="p">;</span><span class="w"> </span><span class="mi">100</span><span class="p">],</span>
+<a id="__codelineno-36-18" name="__codelineno-36-18" href="#__codelineno-36-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-36-19" name="__codelineno-36-19" href="#__codelineno-36-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-20" name="__codelineno-36-20" href="#__codelineno-36-20"></a>
+<a id="__codelineno-36-21" name="__codelineno-36-21" href="#__codelineno-36-21"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-36-22" name="__codelineno-36-22" href="#__codelineno-36-22"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">hash_func</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-23" name="__codelineno-36-23" href="#__codelineno-36-23"></a><span class="w">        </span><span class="n">key</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">100</span>
+<a id="__codelineno-36-24" name="__codelineno-36-24" href="#__codelineno-36-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-25" name="__codelineno-36-25" href="#__codelineno-36-25"></a>
+<a id="__codelineno-36-26" name="__codelineno-36-26" href="#__codelineno-36-26"></a><span class="w">    </span><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-36-27" name="__codelineno-36-27" href="#__codelineno-36-27"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="nb">String</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-28" name="__codelineno-36-28" href="#__codelineno-36-28"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-36-29" name="__codelineno-36-29" href="#__codelineno-36-29"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">as_ref</span><span class="p">().</span><span class="n">map</span><span class="p">(</span><span class="o">|</span><span class="n">pair</span><span class="o">|</span><span class="w"> </span><span class="o">&amp;</span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-36-30" name="__codelineno-36-30" href="#__codelineno-36-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-31" name="__codelineno-36-31" href="#__codelineno-36-31"></a>
+<a id="__codelineno-36-32" name="__codelineno-36-32" href="#__codelineno-36-32"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-36-33" name="__codelineno-36-33" href="#__codelineno-36-33"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="kt">str</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-34" name="__codelineno-36-34" href="#__codelineno-36-34"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-36-35" name="__codelineno-36-35" href="#__codelineno-36-35"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-36" name="__codelineno-36-36" href="#__codelineno-36-36"></a><span class="w">            </span><span class="n">key</span><span class="p">,</span>
+<a id="__codelineno-36-37" name="__codelineno-36-37" href="#__codelineno-36-37"></a><span class="w">            </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="nc">val</span><span class="p">.</span><span class="n">to_string</span><span class="p">(),</span>
+<a id="__codelineno-36-38" name="__codelineno-36-38" href="#__codelineno-36-38"></a><span class="w">        </span><span class="p">});</span>
+<a id="__codelineno-36-39" name="__codelineno-36-39" href="#__codelineno-36-39"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-40" name="__codelineno-36-40" href="#__codelineno-36-40"></a>
+<a id="__codelineno-36-41" name="__codelineno-36-41" href="#__codelineno-36-41"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-36-42" name="__codelineno-36-42" href="#__codelineno-36-42"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-43" name="__codelineno-36-43" href="#__codelineno-36-43"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-36-44" name="__codelineno-36-44" href="#__codelineno-36-44"></a><span class="w">        </span><span class="c1">// None に設定し、削除を表す</span>
+<a id="__codelineno-36-45" name="__codelineno-36-45" href="#__codelineno-36-45"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">None</span><span class="p">;</span>
+<a id="__codelineno-36-46" name="__codelineno-36-46" href="#__codelineno-36-46"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-47" name="__codelineno-36-47" href="#__codelineno-36-47"></a>
+<a id="__codelineno-36-48" name="__codelineno-36-48" href="#__codelineno-36-48"></a><span class="w">    </span><span class="cm">/* すべてのキーと値のペアを取得 */</span>
+<a id="__codelineno-36-49" name="__codelineno-36-49" href="#__codelineno-36-49"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">entry_set</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;&amp;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-50" name="__codelineno-36-50" href="#__codelineno-36-50"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span>
+<a id="__codelineno-36-51" name="__codelineno-36-51" href="#__codelineno-36-51"></a><span class="w">            </span><span class="p">.</span><span class="n">iter</span><span class="p">()</span>
+<a id="__codelineno-36-52" name="__codelineno-36-52" href="#__codelineno-36-52"></a><span class="w">            </span><span class="p">.</span><span class="n">filter_map</span><span class="p">(</span><span class="o">|</span><span class="n">pair</span><span class="o">|</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">as_ref</span><span class="p">())</span>
+<a id="__codelineno-36-53" name="__codelineno-36-53" href="#__codelineno-36-53"></a><span class="w">            </span><span class="p">.</span><span class="n">collect</span><span class="p">()</span>
+<a id="__codelineno-36-54" name="__codelineno-36-54" href="#__codelineno-36-54"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-55" name="__codelineno-36-55" href="#__codelineno-36-55"></a>
+<a id="__codelineno-36-56" name="__codelineno-36-56" href="#__codelineno-36-56"></a><span class="w">    </span><span class="cm">/* すべてのキーを取得 */</span>
+<a id="__codelineno-36-57" name="__codelineno-36-57" href="#__codelineno-36-57"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">key_set</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;&amp;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-58" name="__codelineno-36-58" href="#__codelineno-36-58"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span>
+<a id="__codelineno-36-59" name="__codelineno-36-59" href="#__codelineno-36-59"></a><span class="w">            </span><span class="p">.</span><span class="n">iter</span><span class="p">()</span>
+<a id="__codelineno-36-60" name="__codelineno-36-60" href="#__codelineno-36-60"></a><span class="w">            </span><span class="p">.</span><span class="n">filter_map</span><span class="p">(</span><span class="o">|</span><span class="n">pair</span><span class="o">|</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">as_ref</span><span class="p">().</span><span class="n">map</span><span class="p">(</span><span class="o">|</span><span class="n">pair</span><span class="o">|</span><span class="w"> </span><span class="o">&amp;</span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="p">))</span>
+<a id="__codelineno-36-61" name="__codelineno-36-61" href="#__codelineno-36-61"></a><span class="w">            </span><span class="p">.</span><span class="n">collect</span><span class="p">()</span>
+<a id="__codelineno-36-62" name="__codelineno-36-62" href="#__codelineno-36-62"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-63" name="__codelineno-36-63" href="#__codelineno-36-63"></a>
+<a id="__codelineno-36-64" name="__codelineno-36-64" href="#__codelineno-36-64"></a><span class="w">    </span><span class="cm">/* すべての値を取得 */</span>
+<a id="__codelineno-36-65" name="__codelineno-36-65" href="#__codelineno-36-65"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">value_set</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;&amp;</span><span class="nb">String</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-66" name="__codelineno-36-66" href="#__codelineno-36-66"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span>
+<a id="__codelineno-36-67" name="__codelineno-36-67" href="#__codelineno-36-67"></a><span class="w">            </span><span class="p">.</span><span class="n">iter</span><span class="p">()</span>
+<a id="__codelineno-36-68" name="__codelineno-36-68" href="#__codelineno-36-68"></a><span class="w">            </span><span class="p">.</span><span class="n">filter_map</span><span class="p">(</span><span class="o">|</span><span class="n">pair</span><span class="o">|</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">as_ref</span><span class="p">().</span><span class="n">map</span><span class="p">(</span><span class="o">|</span><span class="n">pair</span><span class="o">|</span><span class="w"> </span><span class="o">&amp;</span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">))</span>
+<a id="__codelineno-36-69" name="__codelineno-36-69" href="#__codelineno-36-69"></a><span class="w">            </span><span class="p">.</span><span class="n">collect</span><span class="p">()</span>
+<a id="__codelineno-36-70" name="__codelineno-36-70" href="#__codelineno-36-70"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-71" name="__codelineno-36-71" href="#__codelineno-36-71"></a>
+<a id="__codelineno-36-72" name="__codelineno-36-72" href="#__codelineno-36-72"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-36-73" name="__codelineno-36-73" href="#__codelineno-36-73"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">print</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-74" name="__codelineno-36-74" href="#__codelineno-36-74"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">entry_set</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-75" name="__codelineno-36-75" href="#__codelineno-36-75"></a><span class="w">            </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{} -&gt; {}&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-36-76" name="__codelineno-36-76" href="#__codelineno-36-76"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-36-77" name="__codelineno-36-77" href="#__codelineno-36-77"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-78" name="__codelineno-36-78" href="#__codelineno-36-78"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_hash_map.rb</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">Pair</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
-<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a>
-<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">ArrayHashMap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">array_hash_map.c</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* キーと値の組 int-&gt;string */</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">;</span>
+<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w">    </span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="p">}</span><span class="w"> </span><span class="n">Pair</span><span class="p">;</span>
+<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a>
+<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="cm">/* 配列ベースのハッシュテーブル */</span>
+<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="w">    </span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">buckets</span><span class="p">[</span><span class="n">MAX_SIZE</span><span class="p">];</span>
+<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="p">}</span><span class="w"> </span><span class="n">ArrayHashMap</span><span class="p">;</span>
+<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a>
+<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a><span class="n">ArrayHashMap</span><span class="w"> </span><span class="o">*</span><span class="nf">newArrayHashMap</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-14" name="__codelineno-37-14" href="#__codelineno-37-14"></a><span class="w">    </span><span class="n">ArrayHashMap</span><span class="w"> </span><span class="o">*</span><span class="n">hmap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">ArrayHashMap</span><span class="p">));</span>
+<a id="__codelineno-37-15" name="__codelineno-37-15" href="#__codelineno-37-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-16" name="__codelineno-37-16" href="#__codelineno-37-16"></a><span class="w">        </span><span class="n">hmap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-37-17" name="__codelineno-37-17" href="#__codelineno-37-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-18" name="__codelineno-37-18" href="#__codelineno-37-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">hmap</span><span class="p">;</span>
+<a id="__codelineno-37-19" name="__codelineno-37-19" href="#__codelineno-37-19"></a><span class="p">}</span>
+<a id="__codelineno-37-20" name="__codelineno-37-20" href="#__codelineno-37-20"></a>
+<a id="__codelineno-37-21" name="__codelineno-37-21" href="#__codelineno-37-21"></a><span class="cm">/* デストラクタ */</span>
+<a id="__codelineno-37-22" name="__codelineno-37-22" href="#__codelineno-37-22"></a><span class="kt">void</span><span class="w"> </span><span class="nf">delArrayHashMap</span><span class="p">(</span><span class="n">ArrayHashMap</span><span class="w"> </span><span class="o">*</span><span class="n">hmap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-23" name="__codelineno-37-23" href="#__codelineno-37-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-24" name="__codelineno-37-24" href="#__codelineno-37-24"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">hmap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-25" name="__codelineno-37-25" href="#__codelineno-37-25"></a><span class="w">            </span><span class="n">free</span><span class="p">(</span><span class="n">hmap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-37-26" name="__codelineno-37-26" href="#__codelineno-37-26"></a><span class="w">            </span><span class="n">free</span><span class="p">(</span><span class="n">hmap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-37-27" name="__codelineno-37-27" href="#__codelineno-37-27"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-37-28" name="__codelineno-37-28" href="#__codelineno-37-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-29" name="__codelineno-37-29" href="#__codelineno-37-29"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">hmap</span><span class="p">);</span>
+<a id="__codelineno-37-30" name="__codelineno-37-30" href="#__codelineno-37-30"></a><span class="p">}</span>
+<a id="__codelineno-37-31" name="__codelineno-37-31" href="#__codelineno-37-31"></a>
+<a id="__codelineno-37-32" name="__codelineno-37-32" href="#__codelineno-37-32"></a><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-37-33" name="__codelineno-37-33" href="#__codelineno-37-33"></a><span class="kt">void</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="n">ArrayHashMap</span><span class="w"> </span><span class="o">*</span><span class="n">hmap</span><span class="p">,</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-34" name="__codelineno-37-34" href="#__codelineno-37-34"></a><span class="w">    </span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">Pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">Pair</span><span class="p">));</span>
+<a id="__codelineno-37-35" name="__codelineno-37-35" href="#__codelineno-37-35"></a><span class="w">    </span><span class="n">Pair</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="p">;</span>
+<a id="__codelineno-37-36" name="__codelineno-37-36" href="#__codelineno-37-36"></a><span class="w">    </span><span class="n">Pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="n">strlen</span><span class="p">(</span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-37-37" name="__codelineno-37-37" href="#__codelineno-37-37"></a><span class="w">    </span><span class="n">strcpy</span><span class="p">(</span><span class="n">Pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-37-38" name="__codelineno-37-38" href="#__codelineno-37-38"></a>
+<a id="__codelineno-37-39" name="__codelineno-37-39" href="#__codelineno-37-39"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-37-40" name="__codelineno-37-40" href="#__codelineno-37-40"></a><span class="w">    </span><span class="n">hmap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Pair</span><span class="p">;</span>
+<a id="__codelineno-37-41" name="__codelineno-37-41" href="#__codelineno-37-41"></a><span class="p">}</span>
+<a id="__codelineno-37-42" name="__codelineno-37-42" href="#__codelineno-37-42"></a>
+<a id="__codelineno-37-43" name="__codelineno-37-43" href="#__codelineno-37-43"></a><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-37-44" name="__codelineno-37-44" href="#__codelineno-37-44"></a><span class="kt">void</span><span class="w"> </span><span class="nf">removeItem</span><span class="p">(</span><span class="n">ArrayHashMap</span><span class="w"> </span><span class="o">*</span><span class="n">hmap</span><span class="p">,</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-45" name="__codelineno-37-45" href="#__codelineno-37-45"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-37-46" name="__codelineno-37-46" href="#__codelineno-37-46"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">hmap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-37-47" name="__codelineno-37-47" href="#__codelineno-37-47"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">hmap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]);</span>
+<a id="__codelineno-37-48" name="__codelineno-37-48" href="#__codelineno-37-48"></a><span class="w">    </span><span class="n">hmap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-37-49" name="__codelineno-37-49" href="#__codelineno-37-49"></a><span class="p">}</span>
+<a id="__codelineno-37-50" name="__codelineno-37-50" href="#__codelineno-37-50"></a>
+<a id="__codelineno-37-51" name="__codelineno-37-51" href="#__codelineno-37-51"></a><span class="cm">/* すべてのキーと値のペアを取得 */</span>
+<a id="__codelineno-37-52" name="__codelineno-37-52" href="#__codelineno-37-52"></a><span class="kt">void</span><span class="w"> </span><span class="nf">pairSet</span><span class="p">(</span><span class="n">ArrayHashMap</span><span class="w"> </span><span class="o">*</span><span class="n">hmap</span><span class="p">,</span><span class="w"> </span><span class="n">MapSet</span><span class="w"> </span><span class="o">*</span><span class="n">set</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-53" name="__codelineno-37-53" href="#__codelineno-37-53"></a><span class="w">    </span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">entries</span><span class="p">;</span>
+<a id="__codelineno-37-54" name="__codelineno-37-54" href="#__codelineno-37-54"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-37-55" name="__codelineno-37-55" href="#__codelineno-37-55"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-37-56" name="__codelineno-37-56" href="#__codelineno-37-56"></a><span class="w">    </span><span class="cm">/* 有効なキーと値のペア数を集計 */</span>
+<a id="__codelineno-37-57" name="__codelineno-37-57" href="#__codelineno-37-57"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-58" name="__codelineno-37-58" href="#__codelineno-37-58"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">hmap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-59" name="__codelineno-37-59" href="#__codelineno-37-59"></a><span class="w">            </span><span class="n">total</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-37-60" name="__codelineno-37-60" href="#__codelineno-37-60"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-37-61" name="__codelineno-37-61" href="#__codelineno-37-61"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-62" name="__codelineno-37-62" href="#__codelineno-37-62"></a><span class="w">    </span><span class="n">entries</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">Pair</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">total</span><span class="p">);</span>
+<a id="__codelineno-37-63" name="__codelineno-37-63" href="#__codelineno-37-63"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-64" name="__codelineno-37-64" href="#__codelineno-37-64"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">hmap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-65" name="__codelineno-37-65" href="#__codelineno-37-65"></a><span class="w">            </span><span class="n">entries</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">key</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hmap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">key</span><span class="p">;</span>
+<a id="__codelineno-37-66" name="__codelineno-37-66" href="#__codelineno-37-66"></a><span class="w">            </span><span class="n">entries</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="n">strlen</span><span class="p">(</span><span class="n">hmap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-37-67" name="__codelineno-37-67" href="#__codelineno-37-67"></a><span class="w">            </span><span class="n">strcpy</span><span class="p">(</span><span class="n">entries</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">hmap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-37-68" name="__codelineno-37-68" href="#__codelineno-37-68"></a><span class="w">            </span><span class="n">index</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-37-69" name="__codelineno-37-69" href="#__codelineno-37-69"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-37-70" name="__codelineno-37-70" href="#__codelineno-37-70"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-71" name="__codelineno-37-71" href="#__codelineno-37-71"></a><span class="w">    </span><span class="n">set</span><span class="o">-&gt;</span><span class="n">set</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">entries</span><span class="p">;</span>
+<a id="__codelineno-37-72" name="__codelineno-37-72" href="#__codelineno-37-72"></a><span class="w">    </span><span class="n">set</span><span class="o">-&gt;</span><span class="n">len</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">total</span><span class="p">;</span>
+<a id="__codelineno-37-73" name="__codelineno-37-73" href="#__codelineno-37-73"></a><span class="p">}</span>
+<a id="__codelineno-37-74" name="__codelineno-37-74" href="#__codelineno-37-74"></a>
+<a id="__codelineno-37-75" name="__codelineno-37-75" href="#__codelineno-37-75"></a><span class="cm">/* すべてのキーを取得 */</span>
+<a id="__codelineno-37-76" name="__codelineno-37-76" href="#__codelineno-37-76"></a><span class="kt">void</span><span class="w"> </span><span class="nf">keySet</span><span class="p">(</span><span class="n">ArrayHashMap</span><span class="w"> </span><span class="o">*</span><span class="n">hmap</span><span class="p">,</span><span class="w"> </span><span class="n">MapSet</span><span class="w"> </span><span class="o">*</span><span class="n">set</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-77" name="__codelineno-37-77" href="#__codelineno-37-77"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">keys</span><span class="p">;</span>
+<a id="__codelineno-37-78" name="__codelineno-37-78" href="#__codelineno-37-78"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-37-79" name="__codelineno-37-79" href="#__codelineno-37-79"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-37-80" name="__codelineno-37-80" href="#__codelineno-37-80"></a><span class="w">    </span><span class="cm">/* 有効なキーと値のペア数を集計 */</span>
+<a id="__codelineno-37-81" name="__codelineno-37-81" href="#__codelineno-37-81"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-82" name="__codelineno-37-82" href="#__codelineno-37-82"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">hmap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-83" name="__codelineno-37-83" href="#__codelineno-37-83"></a><span class="w">            </span><span class="n">total</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-37-84" name="__codelineno-37-84" href="#__codelineno-37-84"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-37-85" name="__codelineno-37-85" href="#__codelineno-37-85"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-86" name="__codelineno-37-86" href="#__codelineno-37-86"></a><span class="w">    </span><span class="n">keys</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="n">total</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-37-87" name="__codelineno-37-87" href="#__codelineno-37-87"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-88" name="__codelineno-37-88" href="#__codelineno-37-88"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">hmap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-89" name="__codelineno-37-89" href="#__codelineno-37-89"></a><span class="w">            </span><span class="n">keys</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hmap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">key</span><span class="p">;</span>
+<a id="__codelineno-37-90" name="__codelineno-37-90" href="#__codelineno-37-90"></a><span class="w">            </span><span class="n">index</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-37-91" name="__codelineno-37-91" href="#__codelineno-37-91"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-37-92" name="__codelineno-37-92" href="#__codelineno-37-92"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-93" name="__codelineno-37-93" href="#__codelineno-37-93"></a><span class="w">    </span><span class="n">set</span><span class="o">-&gt;</span><span class="n">set</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">keys</span><span class="p">;</span>
+<a id="__codelineno-37-94" name="__codelineno-37-94" href="#__codelineno-37-94"></a><span class="w">    </span><span class="n">set</span><span class="o">-&gt;</span><span class="n">len</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">total</span><span class="p">;</span>
+<a id="__codelineno-37-95" name="__codelineno-37-95" href="#__codelineno-37-95"></a><span class="p">}</span>
+<a id="__codelineno-37-96" name="__codelineno-37-96" href="#__codelineno-37-96"></a>
+<a id="__codelineno-37-97" name="__codelineno-37-97" href="#__codelineno-37-97"></a><span class="cm">/* すべての値を取得 */</span>
+<a id="__codelineno-37-98" name="__codelineno-37-98" href="#__codelineno-37-98"></a><span class="kt">void</span><span class="w"> </span><span class="nf">valueSet</span><span class="p">(</span><span class="n">ArrayHashMap</span><span class="w"> </span><span class="o">*</span><span class="n">hmap</span><span class="p">,</span><span class="w"> </span><span class="n">MapSet</span><span class="w"> </span><span class="o">*</span><span class="n">set</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-99" name="__codelineno-37-99" href="#__codelineno-37-99"></a><span class="w">    </span><span class="kt">char</span><span class="w"> </span><span class="o">**</span><span class="n">vals</span><span class="p">;</span>
+<a id="__codelineno-37-100" name="__codelineno-37-100" href="#__codelineno-37-100"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-37-101" name="__codelineno-37-101" href="#__codelineno-37-101"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-37-102" name="__codelineno-37-102" href="#__codelineno-37-102"></a><span class="w">    </span><span class="cm">/* 有効なキーと値のペア数を集計 */</span>
+<a id="__codelineno-37-103" name="__codelineno-37-103" href="#__codelineno-37-103"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-104" name="__codelineno-37-104" href="#__codelineno-37-104"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">hmap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-105" name="__codelineno-37-105" href="#__codelineno-37-105"></a><span class="w">            </span><span class="n">total</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-37-106" name="__codelineno-37-106" href="#__codelineno-37-106"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-37-107" name="__codelineno-37-107" href="#__codelineno-37-107"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-108" name="__codelineno-37-108" href="#__codelineno-37-108"></a><span class="w">    </span><span class="n">vals</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="n">total</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="p">));</span>
+<a id="__codelineno-37-109" name="__codelineno-37-109" href="#__codelineno-37-109"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-110" name="__codelineno-37-110" href="#__codelineno-37-110"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">hmap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-111" name="__codelineno-37-111" href="#__codelineno-37-111"></a><span class="w">            </span><span class="n">vals</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hmap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-37-112" name="__codelineno-37-112" href="#__codelineno-37-112"></a><span class="w">            </span><span class="n">index</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-37-113" name="__codelineno-37-113" href="#__codelineno-37-113"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-37-114" name="__codelineno-37-114" href="#__codelineno-37-114"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-115" name="__codelineno-37-115" href="#__codelineno-37-115"></a><span class="w">    </span><span class="n">set</span><span class="o">-&gt;</span><span class="n">set</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vals</span><span class="p">;</span>
+<a id="__codelineno-37-116" name="__codelineno-37-116" href="#__codelineno-37-116"></a><span class="w">    </span><span class="n">set</span><span class="o">-&gt;</span><span class="n">len</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">total</span><span class="p">;</span>
+<a id="__codelineno-37-117" name="__codelineno-37-117" href="#__codelineno-37-117"></a><span class="p">}</span>
+<a id="__codelineno-37-118" name="__codelineno-37-118" href="#__codelineno-37-118"></a>
+<a id="__codelineno-37-119" name="__codelineno-37-119" href="#__codelineno-37-119"></a><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-37-120" name="__codelineno-37-120" href="#__codelineno-37-120"></a><span class="kt">void</span><span class="w"> </span><span class="nf">print</span><span class="p">(</span><span class="n">ArrayHashMap</span><span class="w"> </span><span class="o">*</span><span class="n">hmap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-121" name="__codelineno-37-121" href="#__codelineno-37-121"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-37-122" name="__codelineno-37-122" href="#__codelineno-37-122"></a><span class="w">    </span><span class="n">MapSet</span><span class="w"> </span><span class="n">set</span><span class="p">;</span>
+<a id="__codelineno-37-123" name="__codelineno-37-123" href="#__codelineno-37-123"></a><span class="w">    </span><span class="n">pairSet</span><span class="p">(</span><span class="n">hmap</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="n">set</span><span class="p">);</span>
+<a id="__codelineno-37-124" name="__codelineno-37-124" href="#__codelineno-37-124"></a><span class="w">    </span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">entries</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">set</span><span class="p">.</span><span class="n">set</span><span class="p">;</span>
+<a id="__codelineno-37-125" name="__codelineno-37-125" href="#__codelineno-37-125"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">set</span><span class="p">.</span><span class="n">len</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-126" name="__codelineno-37-126" href="#__codelineno-37-126"></a><span class="w">        </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d -&gt; %s</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">entries</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">entries</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-37-127" name="__codelineno-37-127" href="#__codelineno-37-127"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-128" name="__codelineno-37-128" href="#__codelineno-37-128"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">set</span><span class="p">.</span><span class="n">set</span><span class="p">);</span>
+<a id="__codelineno-37-129" name="__codelineno-37-129" href="#__codelineno-37-129"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_hash_map.kt</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="cm">/* キーと値の組 */</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">Pair</span><span class="p">(</span>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">key</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span>
+<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">_val</span><span class="p">:</span><span class="w"> </span><span class="kt">String</span>
+<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="p">)</span>
+<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a>
+<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="cm">/* 配列ベースのハッシュテーブル */</span>
+<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ArrayHashMap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="w">    </span><span class="c1">// 100 個のバケットを含む配列を初期化</span>
+<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arrayOfNulls</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="p">(</span><span class="m">100</span><span class="p">)</span>
+<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a>
+<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="m">100</span>
+<a id="__codelineno-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">index</span>
+<a id="__codelineno-38-16" name="__codelineno-38-16" href="#__codelineno-38-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-38-17" name="__codelineno-38-17" href="#__codelineno-38-17"></a>
+<a id="__codelineno-38-18" name="__codelineno-38-18" href="#__codelineno-38-18"></a><span class="w">    </span><span class="cm">/* 検索操作 */</span>
+<a id="__codelineno-38-19" name="__codelineno-38-19" href="#__codelineno-38-19"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">String?</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-38-20" name="__codelineno-38-20" href="#__codelineno-38-20"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-38-21" name="__codelineno-38-21" href="#__codelineno-38-21"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">?:</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span>
+<a id="__codelineno-38-22" name="__codelineno-38-22" href="#__codelineno-38-22"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">_val</span>
+<a id="__codelineno-38-23" name="__codelineno-38-23" href="#__codelineno-38-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-38-24" name="__codelineno-38-24" href="#__codelineno-38-24"></a>
+<a id="__codelineno-38-25" name="__codelineno-38-25" href="#__codelineno-38-25"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-38-26" name="__codelineno-38-26" href="#__codelineno-38-26"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">:</span><span class="w"> </span><span class="kt">String</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-38-27" name="__codelineno-38-27" href="#__codelineno-38-27"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">)</span>
+<a id="__codelineno-38-28" name="__codelineno-38-28" href="#__codelineno-38-28"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-38-29" name="__codelineno-38-29" href="#__codelineno-38-29"></a><span class="w">        </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pair</span>
+<a id="__codelineno-38-30" name="__codelineno-38-30" href="#__codelineno-38-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-38-31" name="__codelineno-38-31" href="#__codelineno-38-31"></a>
+<a id="__codelineno-38-32" name="__codelineno-38-32" href="#__codelineno-38-32"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-38-33" name="__codelineno-38-33" href="#__codelineno-38-33"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-38-34" name="__codelineno-38-34" href="#__codelineno-38-34"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-38-35" name="__codelineno-38-35" href="#__codelineno-38-35"></a><span class="w">        </span><span class="c1">// null に設定し、削除を表す</span>
+<a id="__codelineno-38-36" name="__codelineno-38-36" href="#__codelineno-38-36"></a><span class="w">        </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span>
+<a id="__codelineno-38-37" name="__codelineno-38-37" href="#__codelineno-38-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-38-38" name="__codelineno-38-38" href="#__codelineno-38-38"></a>
+<a id="__codelineno-38-39" name="__codelineno-38-39" href="#__codelineno-38-39"></a><span class="w">    </span><span class="cm">/* すべてのキーと値のペアを取得 */</span>
+<a id="__codelineno-38-40" name="__codelineno-38-40" href="#__codelineno-38-40"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">pairSet</span><span class="p">():</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-38-41" name="__codelineno-38-41" href="#__codelineno-38-41"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">pairSet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-38-42" name="__codelineno-38-42" href="#__codelineno-38-42"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-38-43" name="__codelineno-38-43" href="#__codelineno-38-43"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-38-44" name="__codelineno-38-44" href="#__codelineno-38-44"></a><span class="w">                </span><span class="n">pairSet</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">pair</span><span class="p">)</span>
+<a id="__codelineno-38-45" name="__codelineno-38-45" href="#__codelineno-38-45"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-38-46" name="__codelineno-38-46" href="#__codelineno-38-46"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pairSet</span>
+<a id="__codelineno-38-47" name="__codelineno-38-47" href="#__codelineno-38-47"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-38-48" name="__codelineno-38-48" href="#__codelineno-38-48"></a>
+<a id="__codelineno-38-49" name="__codelineno-38-49" href="#__codelineno-38-49"></a><span class="w">    </span><span class="cm">/* すべてのキーを取得 */</span>
+<a id="__codelineno-38-50" name="__codelineno-38-50" href="#__codelineno-38-50"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">keySet</span><span class="p">():</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-38-51" name="__codelineno-38-51" href="#__codelineno-38-51"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">keySet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-38-52" name="__codelineno-38-52" href="#__codelineno-38-52"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-38-53" name="__codelineno-38-53" href="#__codelineno-38-53"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-38-54" name="__codelineno-38-54" href="#__codelineno-38-54"></a><span class="w">                </span><span class="n">keySet</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="p">)</span>
+<a id="__codelineno-38-55" name="__codelineno-38-55" href="#__codelineno-38-55"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-38-56" name="__codelineno-38-56" href="#__codelineno-38-56"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">keySet</span>
+<a id="__codelineno-38-57" name="__codelineno-38-57" href="#__codelineno-38-57"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-38-58" name="__codelineno-38-58" href="#__codelineno-38-58"></a>
+<a id="__codelineno-38-59" name="__codelineno-38-59" href="#__codelineno-38-59"></a><span class="w">    </span><span class="cm">/* すべての値を取得 */</span>
+<a id="__codelineno-38-60" name="__codelineno-38-60" href="#__codelineno-38-60"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">valueSet</span><span class="p">():</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">String</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-38-61" name="__codelineno-38-61" href="#__codelineno-38-61"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">valueSet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="kt">String</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-38-62" name="__codelineno-38-62" href="#__codelineno-38-62"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-38-63" name="__codelineno-38-63" href="#__codelineno-38-63"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-38-64" name="__codelineno-38-64" href="#__codelineno-38-64"></a><span class="w">                </span><span class="n">valueSet</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">_val</span><span class="p">)</span>
+<a id="__codelineno-38-65" name="__codelineno-38-65" href="#__codelineno-38-65"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-38-66" name="__codelineno-38-66" href="#__codelineno-38-66"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">valueSet</span>
+<a id="__codelineno-38-67" name="__codelineno-38-67" href="#__codelineno-38-67"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-38-68" name="__codelineno-38-68" href="#__codelineno-38-68"></a>
+<a id="__codelineno-38-69" name="__codelineno-38-69" href="#__codelineno-38-69"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを出力 */</span>
+<a id="__codelineno-38-70" name="__codelineno-38-70" href="#__codelineno-38-70"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-38-71" name="__codelineno-38-71" href="#__codelineno-38-71"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">kv</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">pairSet</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-38-72" name="__codelineno-38-72" href="#__codelineno-38-72"></a><span class="w">            </span><span class="kd">val</span><span class="w"> </span><span class="nv">key</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">kv</span><span class="p">.</span><span class="na">key</span>
+<a id="__codelineno-38-73" name="__codelineno-38-73" href="#__codelineno-38-73"></a><span class="w">            </span><span class="kd">val</span><span class="w"> </span><span class="nv">_val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">kv</span><span class="p">.</span><span class="na">_val</span>
+<a id="__codelineno-38-74" name="__codelineno-38-74" href="#__codelineno-38-74"></a><span class="w">            </span><span class="n">println</span><span class="p">(</span><span class="s">&quot;</span><span class="si">$</span><span class="n">key</span><span class="s"> -&gt; </span><span class="si">$</span><span class="n">_val</span><span class="s">&quot;</span><span class="p">)</span>
+<a id="__codelineno-38-75" name="__codelineno-38-75" href="#__codelineno-38-75"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-38-76" name="__codelineno-38-76" href="#__codelineno-38-76"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-38-77" name="__codelineno-38-77" href="#__codelineno-38-77"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_hash_map.rb</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="c1">### キーと値のペア ###</span>
+<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">Pair</span>
+<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="w">  </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:key</span><span class="p">,</span><span class="w"> </span><span class="ss">:val</span>
+<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a>
+<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a><span class="w">    </span><span class="vi">@key</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span>
+<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a><span class="w">    </span><span class="vi">@val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span>
+<a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a><span class="k">end</span>
+<a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a>
+<a id="__codelineno-39-11" name="__codelineno-39-11" href="#__codelineno-39-11"></a><span class="c1">### 配列で実装したハッシュテーブル ###</span>
+<a id="__codelineno-39-12" name="__codelineno-39-12" href="#__codelineno-39-12"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayHashMap</span>
+<a id="__codelineno-39-13" name="__codelineno-39-13" href="#__codelineno-39-13"></a><span class="w">  </span><span class="c1">### コンストラクタ ###</span>
+<a id="__codelineno-39-14" name="__codelineno-39-14" href="#__codelineno-39-14"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span>
+<a id="__codelineno-39-15" name="__codelineno-39-15" href="#__codelineno-39-15"></a><span class="w">    </span><span class="c1"># 100 個のバケットを含む配列を初期化</span>
+<a id="__codelineno-39-16" name="__codelineno-39-16" href="#__codelineno-39-16"></a><span class="w">    </span><span class="vi">@buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">100</span><span class="p">)</span>
+<a id="__codelineno-39-17" name="__codelineno-39-17" href="#__codelineno-39-17"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-39-18" name="__codelineno-39-18" href="#__codelineno-39-18"></a>
+<a id="__codelineno-39-19" name="__codelineno-39-19" href="#__codelineno-39-19"></a><span class="w">  </span><span class="c1">### ハッシュ関数 ###</span>
+<a id="__codelineno-39-20" name="__codelineno-39-20" href="#__codelineno-39-20"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-39-21" name="__codelineno-39-21" href="#__codelineno-39-21"></a><span class="w">    </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">100</span>
+<a id="__codelineno-39-22" name="__codelineno-39-22" href="#__codelineno-39-22"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-39-23" name="__codelineno-39-23" href="#__codelineno-39-23"></a>
+<a id="__codelineno-39-24" name="__codelineno-39-24" href="#__codelineno-39-24"></a><span class="w">  </span><span class="c1">### 検索操作 ###</span>
+<a id="__codelineno-39-25" name="__codelineno-39-25" href="#__codelineno-39-25"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-39-26" name="__codelineno-39-26" href="#__codelineno-39-26"></a><span class="w">    </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-39-27" name="__codelineno-39-27" href="#__codelineno-39-27"></a><span class="w">    </span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span>
+<a id="__codelineno-39-28" name="__codelineno-39-28" href="#__codelineno-39-28"></a>
+<a id="__codelineno-39-29" name="__codelineno-39-29" href="#__codelineno-39-29"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">pair</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-39-30" name="__codelineno-39-30" href="#__codelineno-39-30"></a><span class="w">    </span><span class="n">pair</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-39-31" name="__codelineno-39-31" href="#__codelineno-39-31"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-39-32" name="__codelineno-39-32" href="#__codelineno-39-32"></a>
+<a id="__codelineno-39-33" name="__codelineno-39-33" href="#__codelineno-39-33"></a><span class="w">  </span><span class="c1">### 追加操作 ###</span>
+<a id="__codelineno-39-34" name="__codelineno-39-34" href="#__codelineno-39-34"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-39-35" name="__codelineno-39-35" href="#__codelineno-39-35"></a><span class="w">    </span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">Pair</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-39-36" name="__codelineno-39-36" href="#__codelineno-39-36"></a><span class="w">    </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-39-37" name="__codelineno-39-37" href="#__codelineno-39-37"></a><span class="w">    </span><span class="vi">@buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pair</span>
+<a id="__codelineno-39-38" name="__codelineno-39-38" href="#__codelineno-39-38"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-39-39" name="__codelineno-39-39" href="#__codelineno-39-39"></a>
+<a id="__codelineno-39-40" name="__codelineno-39-40" href="#__codelineno-39-40"></a><span class="w">  </span><span class="c1">### 削除操作 ###</span>
+<a id="__codelineno-39-41" name="__codelineno-39-41" href="#__codelineno-39-41"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-39-42" name="__codelineno-39-42" href="#__codelineno-39-42"></a><span class="w">    </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-39-43" name="__codelineno-39-43" href="#__codelineno-39-43"></a><span class="w">    </span><span class="c1"># nil に設定し、削除を表す</span>
+<a id="__codelineno-39-44" name="__codelineno-39-44" href="#__codelineno-39-44"></a><span class="w">    </span><span class="vi">@buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kp">nil</span>
+<a id="__codelineno-39-45" name="__codelineno-39-45" href="#__codelineno-39-45"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-39-46" name="__codelineno-39-46" href="#__codelineno-39-46"></a>
+<a id="__codelineno-39-47" name="__codelineno-39-47" href="#__codelineno-39-47"></a><span class="w">  </span><span class="c1">### すべてのキーと値のペアを取得 ###</span>
+<a id="__codelineno-39-48" name="__codelineno-39-48" href="#__codelineno-39-48"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">entry_set</span>
+<a id="__codelineno-39-49" name="__codelineno-39-49" href="#__codelineno-39-49"></a><span class="w">    </span><span class="n">result</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-39-50" name="__codelineno-39-50" href="#__codelineno-39-50"></a><span class="w">    </span><span class="vi">@buckets</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">pair</span><span class="o">|</span><span class="w"> </span><span class="n">result</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">pair</span><span class="o">.</span><span class="n">nil?</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-39-51" name="__codelineno-39-51" href="#__codelineno-39-51"></a><span class="w">    </span><span class="n">result</span>
+<a id="__codelineno-39-52" name="__codelineno-39-52" href="#__codelineno-39-52"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-39-53" name="__codelineno-39-53" href="#__codelineno-39-53"></a>
+<a id="__codelineno-39-54" name="__codelineno-39-54" href="#__codelineno-39-54"></a><span class="w">  </span><span class="c1">### すべてのキーを取得 ###</span>
+<a id="__codelineno-39-55" name="__codelineno-39-55" href="#__codelineno-39-55"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">key_set</span>
+<a id="__codelineno-39-56" name="__codelineno-39-56" href="#__codelineno-39-56"></a><span class="w">    </span><span class="n">result</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-39-57" name="__codelineno-39-57" href="#__codelineno-39-57"></a><span class="w">    </span><span class="vi">@buckets</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">pair</span><span class="o">|</span><span class="w"> </span><span class="n">result</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">pair</span><span class="o">.</span><span class="n">nil?</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-39-58" name="__codelineno-39-58" href="#__codelineno-39-58"></a><span class="w">    </span><span class="n">result</span>
+<a id="__codelineno-39-59" name="__codelineno-39-59" href="#__codelineno-39-59"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-39-60" name="__codelineno-39-60" href="#__codelineno-39-60"></a>
+<a id="__codelineno-39-61" name="__codelineno-39-61" href="#__codelineno-39-61"></a><span class="w">  </span><span class="c1">### すべての値を取得 ###</span>
+<a id="__codelineno-39-62" name="__codelineno-39-62" href="#__codelineno-39-62"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">value_set</span>
+<a id="__codelineno-39-63" name="__codelineno-39-63" href="#__codelineno-39-63"></a><span class="w">    </span><span class="n">result</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-39-64" name="__codelineno-39-64" href="#__codelineno-39-64"></a><span class="w">    </span><span class="vi">@buckets</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">pair</span><span class="o">|</span><span class="w"> </span><span class="n">result</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">pair</span><span class="o">.</span><span class="n">nil?</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-39-65" name="__codelineno-39-65" href="#__codelineno-39-65"></a><span class="w">    </span><span class="n">result</span>
+<a id="__codelineno-39-66" name="__codelineno-39-66" href="#__codelineno-39-66"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-39-67" name="__codelineno-39-67" href="#__codelineno-39-67"></a>
+<a id="__codelineno-39-68" name="__codelineno-39-68" href="#__codelineno-39-68"></a><span class="w">  </span><span class="c1">### ハッシュテーブルを出力 ###</span>
+<a id="__codelineno-39-69" name="__codelineno-39-69" href="#__codelineno-39-69"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">print</span>
+<a id="__codelineno-39-70" name="__codelineno-39-70" href="#__codelineno-39-70"></a><span class="w">    </span><span class="vi">@buckets</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">pair</span><span class="o">|</span><span class="w"> </span><span class="nb">puts</span><span class="w"> </span><span class="s2">&quot;</span><span class="si">#{</span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="si">}</span><span class="s2"> -&gt; </span><span class="si">#{</span><span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="si">}</span><span class="s2">&quot;</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">pair</span><span class="o">.</span><span class="n">nil?</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-39-71" name="__codelineno-39-71" href="#__codelineno-39-71"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-39-72" name="__codelineno-39-72" href="#__codelineno-39-72"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h2 id="613">6.1.3 &nbsp; ハッシュ衝突とリサイズ<a class="headerlink" href="#613" title="Permanent link">&para;</a></h2>
-<p>本質的に、ハッシュ関数の役割は、すべてのキーの入力空間全体を、すべての配列インデックスの出力空間にマッピングすることです。しかし、入力空間は出力空間よりもはるかに大きいことがよくあります。したがって、<strong>理論的には、「複数の入力が同じ出力に対応する」ケースが常に存在します</strong>。</p>
-<p>上記の例では、与えられたハッシュ関数で、入力<code>key</code>の下二桁が同じ場合、ハッシュ関数は同じ出力を生成します。例えば、学籍番号12836と20336の2人の学生をクエリすると、以下のことがわかります：</p>
-<div class="highlight"><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="m">12836</span><span class="w"> </span>%<span class="w"> </span><span class="nv">100</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">36</span>
-<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="m">20336</span><span class="w"> </span>%<span class="w"> </span><span class="nv">100</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">36</span>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20Pair%3A%0A%0A%20%20%20%20def%20__init__%28self%2C%20key%3A%20int%2C%20val%3A%20str%29%3A%0A%20%20%20%20%20%20%20%20self.key%20%3D%20key%0A%20%20%20%20%20%20%20%20self.val%20%3D%20val%0A%0Aclass%20ArrayHashMap%3A%0A%0A%20%20%20%20def%20__init__%28self%29%3A%0A%20%20%20%20%20%20%20%20self.buckets%3A%20list%5BPair%20%7C%20None%5D%20%3D%20%5BNone%5D%20%2A%2020%0A%0A%20%20%20%20def%20hash_func%28self%2C%20key%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20index%20%3D%20key%20%25%2020%0A%20%20%20%20%20%20%20%20return%20index%0A%0A%20%20%20%20def%20get%28self%2C%20key%3A%20int%29%20-%3E%20str%3A%0A%20%20%20%20%20%20%20%20index%3A%20int%20%3D%20self.hash_func%28key%29%0A%20%20%20%20%20%20%20%20pair%3A%20Pair%20%3D%20self.buckets%5Bindex%5D%0A%20%20%20%20%20%20%20%20if%20pair%20is%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%20%20%20%20return%20pair.val%0A%0A%20%20%20%20def%20put%28self%2C%20key%3A%20int%2C%20val%3A%20str%29%3A%0A%20%20%20%20%20%20%20%20pair%20%3D%20Pair%28key%2C%20val%29%0A%20%20%20%20%20%20%20%20index%3A%20int%20%3D%20self.hash_func%28key%29%0A%20%20%20%20%20%20%20%20self.buckets%5Bindex%5D%20%3D%20pair%0A%0A%20%20%20%20def%20remove%28self%2C%20key%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20index%3A%20int%20%3D%20self.hash_func%28key%29%0A%20%20%20%20%20%20%20%20self.buckets%5Bindex%5D%20%3D%20None%0A%0A%20%20%20%20def%20entry_set%28self%29%20-%3E%20list%5BPair%5D%3A%0A%20%20%20%20%20%20%20%20result%3A%20list%5BPair%5D%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20for%20pair%20in%20self.buckets%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20pair%20is%20not%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20result.append%28pair%29%0A%20%20%20%20%20%20%20%20return%20result%0A%0A%20%20%20%20def%20key_set%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20result%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20for%20pair%20in%20self.buckets%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20pair%20is%20not%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20result.append%28pair.key%29%0A%20%20%20%20%20%20%20%20return%20result%0A%0A%20%20%20%20def%20value_set%28self%29%20-%3E%20list%5Bstr%5D%3A%0A%20%20%20%20%20%20%20%20result%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20for%20pair%20in%20self.buckets%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20pair%20is%20not%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20result.append%28pair.val%29%0A%20%20%20%20%20%20%20%20return%20result%0A%0A%20%20%20%20def%20print%28self%29%3A%0A%20%20%20%20%20%20%20%20for%20pair%20in%20self.buckets%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20pair%20is%20not%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20print%28pair.key%2C%20%27-%3E%27%2C%20pair.val%29%0Aif%20__name__%20%3D%3D%20%27__main__%27%3A%0A%20%20%20%20hmap%20%3D%20ArrayHashMap%28%29%0A%20%20%20%20hmap.put%2812836%2C%20%27%E3%82%B7%E3%83%A3%E3%82%AA%E3%83%8F%E3%83%BC%27%29%0A%20%20%20%20hmap.put%2815937%2C%20%27%E3%82%B7%E3%83%A3%E3%82%AA%E3%83%AB%E3%82%AA%27%29%0A%20%20%20%20hmap.put%2816750%2C%20%27%E3%82%B7%E3%83%A3%E3%82%AA%E3%82%B9%E3%83%AF%E3%83%B3%27%29%0A%20%20%20%20hmap.put%2813276%2C%20%27%E3%82%B7%E3%83%A3%E3%82%AA%E3%83%95%E3%82%A1%E3%83%BC%27%29%0A%20%20%20%20hmap.put%2810583%2C%20%27%E3%82%B7%E3%83%A3%E3%82%AA%E3%83%A4%E3%83%BC%27%29%0A%20%20%20%20name%20%3D%20hmap.get%2815937%29%0A%20%20%20%20hmap.remove%2810583%29%0A%20%20%20%20print%28%27%5Cn%E3%82%AD%E3%83%BC%E3%81%A8%E5%80%A4%E3%81%AE%E3%83%9A%E3%82%A2%20Key-%3EValue%20%E3%82%92%E8%B5%B0%E6%9F%BB%27%29%0A%20%20%20%20for%20pair%20in%20hmap.entry_set%28%29%3A%0A%20%20%20%20%20%20%20%20print%28pair.key%2C%20%27-%3E%27%2C%20pair.val%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20Pair%3A%0A%0A%20%20%20%20def%20__init__%28self%2C%20key%3A%20int%2C%20val%3A%20str%29%3A%0A%20%20%20%20%20%20%20%20self.key%20%3D%20key%0A%20%20%20%20%20%20%20%20self.val%20%3D%20val%0A%0Aclass%20ArrayHashMap%3A%0A%0A%20%20%20%20def%20__init__%28self%29%3A%0A%20%20%20%20%20%20%20%20self.buckets%3A%20list%5BPair%20%7C%20None%5D%20%3D%20%5BNone%5D%20%2A%2020%0A%0A%20%20%20%20def%20hash_func%28self%2C%20key%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20index%20%3D%20key%20%25%2020%0A%20%20%20%20%20%20%20%20return%20index%0A%0A%20%20%20%20def%20get%28self%2C%20key%3A%20int%29%20-%3E%20str%3A%0A%20%20%20%20%20%20%20%20index%3A%20int%20%3D%20self.hash_func%28key%29%0A%20%20%20%20%20%20%20%20pair%3A%20Pair%20%3D%20self.buckets%5Bindex%5D%0A%20%20%20%20%20%20%20%20if%20pair%20is%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%20%20%20%20return%20pair.val%0A%0A%20%20%20%20def%20put%28self%2C%20key%3A%20int%2C%20val%3A%20str%29%3A%0A%20%20%20%20%20%20%20%20pair%20%3D%20Pair%28key%2C%20val%29%0A%20%20%20%20%20%20%20%20index%3A%20int%20%3D%20self.hash_func%28key%29%0A%20%20%20%20%20%20%20%20self.buckets%5Bindex%5D%20%3D%20pair%0A%0A%20%20%20%20def%20remove%28self%2C%20key%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20index%3A%20int%20%3D%20self.hash_func%28key%29%0A%20%20%20%20%20%20%20%20self.buckets%5Bindex%5D%20%3D%20None%0A%0A%20%20%20%20def%20entry_set%28self%29%20-%3E%20list%5BPair%5D%3A%0A%20%20%20%20%20%20%20%20result%3A%20list%5BPair%5D%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20for%20pair%20in%20self.buckets%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20pair%20is%20not%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20result.append%28pair%29%0A%20%20%20%20%20%20%20%20return%20result%0A%0A%20%20%20%20def%20key_set%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20result%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20for%20pair%20in%20self.buckets%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20pair%20is%20not%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20result.append%28pair.key%29%0A%20%20%20%20%20%20%20%20return%20result%0A%0A%20%20%20%20def%20value_set%28self%29%20-%3E%20list%5Bstr%5D%3A%0A%20%20%20%20%20%20%20%20result%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20for%20pair%20in%20self.buckets%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20pair%20is%20not%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20result.append%28pair.val%29%0A%20%20%20%20%20%20%20%20return%20result%0A%0A%20%20%20%20def%20print%28self%29%3A%0A%20%20%20%20%20%20%20%20for%20pair%20in%20self.buckets%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20pair%20is%20not%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20print%28pair.key%2C%20%27-%3E%27%2C%20pair.val%29%0Aif%20__name__%20%3D%3D%20%27__main__%27%3A%0A%20%20%20%20hmap%20%3D%20ArrayHashMap%28%29%0A%20%20%20%20hmap.put%2812836%2C%20%27%E3%82%B7%E3%83%A3%E3%82%AA%E3%83%8F%E3%83%BC%27%29%0A%20%20%20%20hmap.put%2815937%2C%20%27%E3%82%B7%E3%83%A3%E3%82%AA%E3%83%AB%E3%82%AA%27%29%0A%20%20%20%20hmap.put%2816750%2C%20%27%E3%82%B7%E3%83%A3%E3%82%AA%E3%82%B9%E3%83%AF%E3%83%B3%27%29%0A%20%20%20%20hmap.put%2813276%2C%20%27%E3%82%B7%E3%83%A3%E3%82%AA%E3%83%95%E3%82%A1%E3%83%BC%27%29%0A%20%20%20%20hmap.put%2810583%2C%20%27%E3%82%B7%E3%83%A3%E3%82%AA%E3%83%A4%E3%83%BC%27%29%0A%20%20%20%20name%20%3D%20hmap.get%2815937%29%0A%20%20%20%20hmap.remove%2810583%29%0A%20%20%20%20print%28%27%5Cn%E3%82%AD%E3%83%BC%E3%81%A8%E5%80%A4%E3%81%AE%E3%83%9A%E3%82%A2%20Key-%3EValue%20%E3%82%92%E8%B5%B0%E6%9F%BB%27%29%0A%20%20%20%20for%20pair%20in%20hmap.entry_set%28%29%3A%0A%20%20%20%20%20%20%20%20print%28pair.key%2C%20%27-%3E%27%2C%20pair.val%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h2 id="613">6.1.3 &nbsp; ハッシュ衝突と拡張<a class="headerlink" href="#613" title="Permanent link">&para;</a></h2>
+<p>本質的には、ハッシュ関数の役割は、すべての <code>key</code> からなる入力空間を、配列のすべてのインデックスからなる出力空間に写像することです。しかし、入力空間は多くの場合、出力空間よりはるかに大きいため、<strong>理論上は必ず「複数の入力が同じ出力に対応する」状況が存在します</strong>。</p>
+<p>上の例のハッシュ関数では、入力 <code>key</code> の下 2 桁が同じであれば、出力結果も同じになります。たとえば、学籍番号 12836 と 20336 の 2 人の学生を検索すると、次の結果を得ます：</p>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="m">12836</span><span class="w"> </span>%<span class="w"> </span><span class="nv">100</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">36</span>
+<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="m">20336</span><span class="w"> </span>%<span class="w"> </span><span class="nv">100</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">36</span>
 </code></pre></div>
-<p>下図に示すように、両方の学籍番号が同じ名前を指しており、これは明らかに間違っています。この複数の入力が同じ出力に対応する状況を<u>ハッシュ衝突</u>と呼びます。</p>
+<p>次の図に示すように、2 つの学籍番号が同じ名前を指してしまっており、これは明らかに誤りです。このような、複数の入力が同じ出力に対応する状況を<u>ハッシュ衝突（hash collision）</u>と呼びます。</p>
 <p><img alt="ハッシュ衝突の例" class="animation-figure" src="../hash_map.assets/hash_collision.png" /></p>
 <p align="center"> 図 6-3 &nbsp; ハッシュ衝突の例 </p>
 
-<p>ハッシュ表の容量<span class="arithmatex">\(n\)</span>が増加するにつれて、複数のキーが同じバケットに割り当てられる確率が減少し、衝突が少なくなることは理解しやすいです。したがって、<strong>ハッシュ表をリサイズすることでハッシュ衝突を減らすことができます</strong>。</p>
-<p>下図に示すように、リサイズ前は、キー値ペア<code>(136, A)</code>と<code>(236, D)</code>が衝突していました。しかし、リサイズ後は衝突が解決されています。</p>
-<p><img alt="ハッシュ表のリサイズ" class="animation-figure" src="../hash_map.assets/hash_table_reshash.png" /></p>
-<p align="center"> 図 6-4 &nbsp; ハッシュ表のリサイズ </p>
+<p>容易に分かるように、ハッシュテーブルの容量 <span class="arithmatex">\(n\)</span> が大きいほど、複数の <code>key</code> が同じバケットに割り当てられる確率は低くなり、衝突も少なくなります。したがって、<strong>ハッシュテーブルを拡張することでハッシュ衝突を減らせます</strong>。</p>
+<p>次の図に示すように、拡張前はキーと値のペア <code>(136, A)</code> と <code>(236, D)</code> が衝突していますが、拡張後は衝突が解消されます。</p>
+<p><img alt="ハッシュテーブルの拡張" class="animation-figure" src="../hash_map.assets/hash_table_reshash.png" /></p>
+<p align="center"> 図 6-4 &nbsp; ハッシュテーブルの拡張 </p>
 
-<p>配列の拡張と同様に、ハッシュ表のリサイズにはすべてのキー値ペアを元のハッシュ表から新しいものに移行する必要があり、時間がかかります。さらに、ハッシュ表の<code>capacity</code>が変更されるため、ハッシュ関数を使用してすべてのキー値ペアの格納位置を再計算する必要があり、リサイズプロセスの計算オーバーヘッドがさらに増加します。したがって、プログラミング言語は頻繁なリサイズを防ぐために、ハッシュ表に十分大きな容量を割り当てることがよくあります。</p>
-<p><u>負荷率</u>はハッシュ表の重要な概念です。ハッシュ表内の要素数とバケット数の比率として定義されます。ハッシュ衝突の深刻度を測定するために使用され、<strong>しばしばハッシュ表のリサイズのトリガーとしても機能します</strong>。例えば、Javaでは、負荷率が<span class="arithmatex">\(0.75\)</span>を超えると、システムはハッシュ表を元のサイズの2倍にリサイズします。</p>
+<p>配列の拡張と同様に、ハッシュテーブルの拡張ではすべてのキーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移し替える必要があり、非常に時間がかかります。また、ハッシュテーブルの容量 <code>capacity</code> が変わるため、ハッシュ関数を使ってすべてのキーと値のペアの格納位置を再計算しなければならず、これによって拡張過程の計算コストがさらに増加します。そのため、プログラミング言語では通常、頻繁な拡張を防ぐために十分大きなハッシュテーブル容量をあらかじめ確保します。</p>
+<p><u>負荷率（load factor）</u>はハッシュテーブルにおける重要な概念であり、ハッシュテーブル内の要素数をバケット数で割ったものとして定義され、ハッシュ衝突の深刻さを測るために用いられます。<strong>また、ハッシュテーブル拡張の発動条件としてもよく使われます</strong>。例えば Java では、負荷率が <span class="arithmatex">\(0.75\)</span> を超えると、システムはハッシュテーブルを元の <span class="arithmatex">\(2\)</span> 倍に拡張します。</p>
 
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@@ -5208,7 +6108,7 @@ aria-label="フッター"
   <a
     href="../"
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-    aria-label="前: 第 6 章 &amp;nbsp; ハッシュ表"
+    aria-label="前: 第 6 章 &amp;nbsp; ハッシュテーブル"
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@@ -6,7 +6,7 @@
       <meta charset="utf-8">
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-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
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@@ -39,7 +39,7 @@
     
     
       
-        <title>第 6 章 ハッシュ表 - Hello アルゴリズム</title>
+        <title>第 6 章 ハッシュテーブル - Hello アルゴリズム</title>
       
     
     
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             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
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+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
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 <!-- Page content -->
-<h1 id="6">第 6 章 &nbsp; ハッシュ表<a class="headerlink" href="#6" title="Permanent link">&para;</a></h1>
-<p><img alt="ハッシュ表" class="cover-image" src="../assets/covers/chapter_hashing.jpg" /></p>
+<h1 id="6">第 6 章 &nbsp; ハッシュテーブル<a class="headerlink" href="#6" title="Permanent link">&para;</a></h1>
+<p><img alt="ハッシュテーブル" class="cover-image" src="../assets/covers/chapter_hashing.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>コンピューティングの世界において、ハッシュ表は賢い司書のようなものです。</p>
-<p>インデックス番号の計算方法を理解し、目的の本を迅速に取得することを可能にします。</p>
+<p>コンピュータの世界では、ハッシュテーブルは聡明な図書館員のような存在です。</p>
+<p>彼は請求記号の計算方法を知っており、そのため目的の本を素早く見つけられます。</p>
 </div>
 <h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
-<li><a href="hash_map/">6.1 &nbsp; ハッシュ表</a></li>
+<li><a href="hash_map/">6.1 &nbsp; ハッシュテーブル</a></li>
 <li><a href="hash_collision/">6.2 &nbsp; ハッシュ衝突</a></li>
 <li><a href="hash_algorithm/">6.3 &nbsp; ハッシュアルゴリズム</a></li>
 <li><a href="summary/">6.4 &nbsp; まとめ</a></li>
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     class="md-footer__link md-footer__link--next"
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       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
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             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
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 <!-- Page content -->
 <h1 id="64">6.4 &nbsp; まとめ<a class="headerlink" href="#64" title="Permanent link">&para;</a></h1>
-<h3 id="1">1. &nbsp; 重要なポイント<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<h3 id="1">1. &nbsp; 重要ポイントの振り返り<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
-<li>入力<code>key</code>が与えられると、ハッシュ表は<span class="arithmatex">\(O(1)\)</span>の時間で対応する<code>value</code>を取得でき、非常に効率的です。</li>
-<li>一般的なハッシュ表の操作には、クエリ、キー値ペアの追加、キー値ペアの削除、ハッシュ表の走査があります。</li>
-<li>ハッシュ関数は<code>key</code>を配列インデックスにマッピングし、対応するバケットにアクセスして<code>value</code>を取得できるようにします。</li>
-<li>2つの異なるキーがハッシュ化後に同じ配列インデックスになる場合があり、誤ったクエリ結果につながります。この現象はハッシュ衝突として知られています。</li>
-<li>ハッシュ表の容量が大きいほど、ハッシュ衝突の確率は低くなります。したがって、ハッシュ表のリサイズはハッシュ衝突を緩和できます。配列のリサイズと同様に、ハッシュ表のリサイズはコストが高いです。</li>
-<li>要素数をバケット数で割った負荷率は、ハッシュ衝突の深刻度を反映し、しばしばハッシュ表リサイズのトリガー条件として使用されます。</li>
-<li>連鎖法は各要素を連結リストに変換し、衝突するすべての要素を同じリストに格納することでハッシュ衝突に対処します。ただし、過度に長いリストはクエリ効率を低下させる可能性があり、リストを赤黒木に変換することで改善できます。</li>
-<li>オープンアドレス法は複数回のプローブを通してハッシュ衝突を処理します。線形プローブは固定ステップサイズを使用しますが、要素を削除できず、クラスタリングを起こしやすい傾向があります。多重ハッシュはプローブに複数のハッシュ関数を使用し、線形プローブと比較してクラスタリングを減らしますが、計算オーバーヘッドが増加します。</li>
-<li>異なるプログラミング言語はさまざまなハッシュ表実装を採用しています。例えば、Javaの<code>HashMap</code>は連鎖法を使用し、Pythonの<code>dict</code>はオープンアドレス法を採用しています。</li>
-<li>ハッシュ表では、決定性、高効率、均等分散を持つハッシュアルゴリズムが望まれます。暗号化では、ハッシュアルゴリズムは衝突耐性と雪崩効果も持つべきです。</li>
-<li>ハッシュアルゴリズムは通常、ハッシュ値の均等分散を保証し、ハッシュ衝突を減らすために、大きな素数を剰余として使用します。</li>
-<li>一般的なハッシュアルゴリズムには、MD5、SHA-1、SHA-2、SHA-3があります。MD5はファイル整合性チェックによく使用され、SHA-2は安全なアプリケーションとプロトコルで一般的に使用されます。</li>
-<li>プログラミング言語は通常、ハッシュ表のバケットインデックスを計算するために、データ型に対して組み込みのハッシュアルゴリズムを提供します。一般的に、不変オブジェクトのみがハッシュ可能です。</li>
+<li><code>key</code> を入力すると、ハッシュテーブルは <span class="arithmatex">\(O(1)\)</span> 時間で <code>value</code> を検索でき、非常に高効率である。</li>
+<li>一般的なハッシュテーブルの操作には、検索、キーと値のペアの追加、キーと値のペアの削除、ハッシュテーブルの走査などがある。</li>
+<li>ハッシュ関数は <code>key</code> を配列インデックスに写像し、それによって対応するバケットにアクセスして <code>value</code> を取得する。</li>
+<li>異なる 2 つの <code>key</code> が、ハッシュ関数を通した後に同じ配列インデックスになることがあり、検索結果の誤りを引き起こす。この現象をハッシュ衝突と呼ぶ。</li>
+<li>ハッシュテーブルの容量が大きいほど、ハッシュ衝突の確率は低くなる。そのため、ハッシュテーブルを拡張することでハッシュ衝突を緩和できる。配列の拡張と同様に、ハッシュテーブルの拡張操作のコストは大きい。</li>
+<li>負荷率は、ハッシュテーブル内の要素数をバケット数で割ったものと定義され、ハッシュ衝突の深刻さを反映する。ハッシュテーブル拡張を発動する条件としてよく用いられる。</li>
+<li>連鎖方式では、単一要素を連結リストに変換し、衝突したすべての要素を同じ連結リストに格納する。しかし、連結リストが長すぎると検索効率が低下するため、さらに連結リストを赤黒木に変換して効率を高めることができる。</li>
+<li>オープンアドレス法は複数回の探索によってハッシュ衝突を処理する。線形探索は固定のステップ幅を用いるが、要素を削除できず、クラスタリングが発生しやすいという欠点がある。二重ハッシュは複数のハッシュ関数を用いて探索するため、線形探索に比べてクラスタリングが起きにくいが、複数のハッシュ関数によって計算量が増える。</li>
+<li>プログラミング言語ごとに、異なるハッシュテーブル実装が採用されている。たとえば、Java の <code>HashMap</code> は連鎖方式を使用し、Python の <code>Dict</code> はオープンアドレス法を採用している。</li>
+<li>ハッシュテーブルでは、ハッシュアルゴリズムに決定性、高効率、均一分布という特徴が求められる。暗号学では、ハッシュアルゴリズムはさらに耐衝突性とアバランシェ効果も備えるべきである。</li>
+<li>ハッシュアルゴリズムは通常、大きな素数を法として用い、ハッシュ値の均一分布を最大限に保証してハッシュ衝突を減らす。</li>
+<li>一般的なハッシュアルゴリズムには MD5、SHA-1、SHA-2、SHA-3 などがある。MD5 はファイル完全性の検証によく用いられ、SHA-2 はセキュリティ用途やプロトコルでよく用いられる。</li>
+<li>プログラミング言語は通常、データ型に対して組み込みのハッシュアルゴリズムを提供し、ハッシュテーブル内のバケットインデックスの計算に用いる。通常、ハッシュ可能なのは不変オブジェクトだけである。</li>
 </ul>
 <h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
-<p><strong>Q</strong>: ハッシュ表の時間計算量が<span class="arithmatex">\(O(n)\)</span>に悪化するのはいつですか？</p>
-<p>ハッシュ表の時間計算量は、ハッシュ衝突が深刻な場合に<span class="arithmatex">\(O(n)\)</span>に悪化する可能性があります。ハッシュ関数が適切に設計され、容量が適切に設定され、衝突が均等に分散されている場合、時間計算量は<span class="arithmatex">\(O(1)\)</span>です。プログラミング言語の組み込みハッシュ表を使用する場合、通常は時間計算量を<span class="arithmatex">\(O(1)\)</span>と考えます。</p>
-<p><strong>Q</strong>: なぜハッシュ関数<span class="arithmatex">\(f(x) = x\)</span>を使用しないのですか？これなら衝突を排除できます。</p>
-<p>ハッシュ関数<span class="arithmatex">\(f(x) = x\)</span>では、各要素が一意のバケットインデックスに対応し、これは配列と同等です。しかし、入力空間は通常出力空間（配列長）よりもはるかに大きいため、ハッシュ関数の最後のステップは配列長の剰余を取ることがよくあります。言い換えると、ハッシュ表の目標は、<span class="arithmatex">\(O(1)\)</span>のクエリ効率を提供しながら、より大きな状態空間をより小さなものにマッピングすることです。</p>
-<p><strong>Q</strong>: ハッシュ表がこれらの構造を使って実装されているにもかかわらず、なぜ配列、連結リスト、二分木よりも効率的になれるのですか？</p>
-<p>まず、ハッシュ表は時間効率が高いですが、空間効率は低いです。ハッシュ表のメモリの大部分は未使用のままです。</p>
-<p>次に、ハッシュ表は特定のユースケースでのみ時間効率が高いです。配列や連結リストを使用して同じ時間計算量で機能を実装できる場合、通常はハッシュ表を使用するよりも高速です。これは、ハッシュ関数の計算がオーバーヘッドを発生させ、時間計算量の定数因子が大きくなるためです。</p>
-<p>最後に、ハッシュ表の時間計算量は悪化する可能性があります。例えば、連鎖法では、連結リストや赤黒木で検索操作を実行し、これは依然として<span class="arithmatex">\(O(n)\)</span>時間に悪化するリスクがあります。</p>
-<p><strong>Q</strong>: 多重ハッシュにも要素を直接削除できないという欠陥がありますか？削除としてマークされた空間は再利用できますか？</p>
-<p>多重ハッシュはオープンアドレス法の一形態であり、すべてのオープンアドレス法には要素を直接削除できないという欠点があります。要素を削除済みとしてマークする必要があります。マークされた空間は再利用できます。ハッシュ表に新しい要素を挿入する際、ハッシュ関数が削除済みとしてマークされた位置を指している場合、その位置は新しい要素によって使用できます。これにより、ハッシュ表のプローブシーケンスを維持しながら、空間の効率的な使用が保証されます。</p>
-<p><strong>Q</strong>: なぜ線形プローブの検索プロセス中にハッシュ衝突が発生するのですか？</p>
-<p>検索プロセス中、ハッシュ関数は対応するバケットとキー値ペアを指します。<code>key</code>が一致しない場合、ハッシュ衝突を示します。したがって、線形プローブは正しいキー値ペアが見つかるか検索が失敗するまで、事前に決められたステップサイズで下方向に検索します。</p>
-<p><strong>Q</strong>: なぜハッシュ表のリサイズがハッシュ衝突を緩和できるのですか？</p>
-<p>ハッシュ関数の最後のステップは、出力を配列インデックス範囲内に保つために、配列長<span class="arithmatex">\(n\)</span>の剰余を取ることがよくあります。リサイズ時、配列長<span class="arithmatex">\(n\)</span>が変化し、キーに対応するインデックスも変化する可能性があります。以前に同じバケットにマッピングされていたキーが、リサイズ後に複数のバケットに分散される可能性があり、それによってハッシュ衝突が緩和されます。</p>
+<p><strong>Q</strong>：ハッシュテーブルの時間計算量が <span class="arithmatex">\(O(n)\)</span> になるのはどのような場合ですか？</p>
+<p>ハッシュ衝突が深刻な場合、ハッシュテーブルの時間計算量は <span class="arithmatex">\(O(n)\)</span> に劣化する。ハッシュ関数の設計が適切で、容量設定が合理的で、衝突が比較的均等な場合、時間計算量は <span class="arithmatex">\(O(1)\)</span> である。プログラミング言語組み込みのハッシュテーブルを使うとき、通常は時間計算量を <span class="arithmatex">\(O(1)\)</span> とみなす。</p>
+<p><strong>Q</strong>：なぜハッシュ関数 <span class="arithmatex">\(f(x) = x\)</span> を使わないのですか？ そうすれば衝突は起きません。</p>
+<p><span class="arithmatex">\(f(x) = x\)</span> というハッシュ関数では、各要素は一意のバケットインデックスに対応し、これは配列と等価である。しかし、入力空間は通常、出力空間（配列長）よりはるかに大きいため、ハッシュ関数の最後のステップはたいてい配列長での剰余になる。言い換えると、ハッシュテーブルの目的は、大きな状態空間をより小さな空間に写像し、<span class="arithmatex">\(O(1)\)</span> の検索効率を提供することである。</p>
+<p><strong>Q</strong>：ハッシュテーブルの基礎実装は配列、連結リスト、二分木なのに、なぜそれらより高効率になり得るのですか？</p>
+<p>まず、ハッシュテーブルは時間効率が高くなる一方で、空間効率は低くなる。ハッシュテーブルには、かなりの部分で未使用のメモリが存在する。</p>
+<p>次に、時間効率が高くなるのは特定の利用場面に限られる。ある機能が同じ時間計算量で配列や連結リストによって実装できるなら、通常はハッシュテーブルより速い。これは、ハッシュ関数の計算にコストがかかり、時間計算量の定数項がより大きいからである。</p>
+<p>最後に、ハッシュテーブルの時間計算量は劣化する可能性がある。たとえば連鎖方式では、連結リストや赤黒木で検索操作を行うため、なお <span class="arithmatex">\(O(n)\)</span> 時間に劣化するリスクがある。</p>
+<p><strong>Q</strong>：二重ハッシュにも要素を直接削除できない欠点がありますか？ 削除済みとマークした領域は再利用できますか？</p>
+<p>二重ハッシュはオープンアドレス法の一種であり、オープンアドレス法はいずれも要素を直接削除できないという欠点があるため、削除のマーク付けが必要になる。削除済みとマークされた領域は再利用できる。新しい要素をハッシュテーブルに挿入し、ハッシュ関数によって削除済みとマークされた位置を見つけた場合、その位置は新しい要素に使用できる。こうすることで、ハッシュテーブルの探索系列を変えずに保ちつつ、空間利用率も確保できる。</p>
+<p><strong>Q</strong>：なぜ線形探索では、要素を探すときにハッシュ衝突が発生するのですか？</p>
+<p>探索時には、ハッシュ関数で対応するバケットとキーと値のペアを見つけ、<code>key</code> が一致しないことが分かると、それはハッシュ衝突を意味する。そのため、線形探索法では事前に設定したステップ幅に従って順に探索し、正しいキーと値のペアを見つけるか、見つからずに終了するまで続ける。</p>
+<p><strong>Q</strong>：なぜハッシュテーブルの拡張でハッシュ衝突を緩和できるのですか？</p>
+<p>ハッシュ関数の最後のステップは、たいてい配列長 <span class="arithmatex">\(n\)</span> での剰余を取り、出力値を配列インデックスの範囲内に収めることである。拡張後は配列長 <span class="arithmatex">\(n\)</span> が変化し、<code>key</code> に対応するインデックスも変化する可能性がある。もともと同じバケットに入っていた複数の <code>key</code> は、拡張後には複数のバケットに割り当てられる可能性があり、それによってハッシュ衝突が緩和される。</p>
+<p><strong>Q</strong>：高効率な読み書きのためなら、配列を直接使えばよいのではないですか？</p>
+<p>データの <code>key</code> が連続した小範囲の整数であれば、配列を直接使えばよく、単純で高効率である。しかし <code>key</code> が別の型（たとえば文字列）の場合は、ハッシュ関数を用いて <code>key</code> を配列インデックスに写像し、さらにバケット配列を通じて要素を格納する必要がある。このような構造がハッシュテーブルである。</p>
 
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+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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+    8.2 &nbsp; ヒープ構築
   
 
     
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   <a href="#821" class="md-nav__link">
     <span class="md-ellipsis">
       
-        8.2.1 &nbsp; ヒープ挿入操作による実装
+        8.2.1 &nbsp; ヒープへの挿入操作による実現
       
     </span>
   </a>
@@ -2175,7 +2175,7 @@
   <a href="#822" class="md-nav__link">
     <span class="md-ellipsis">
       
-        8.2.2 &nbsp; 走査によるヒープ化の実装
+        8.2.2 &nbsp; 走査によるヒープ化で実現
       
     </span>
   </a>
@@ -2186,7 +2186,7 @@
   <a href="#823" class="md-nav__link">
     <span class="md-ellipsis">
       
-        8.2.3 &nbsp; 計算量分析
+        8.2.3 &nbsp; 計算量の分析
       
     </span>
   </a>
@@ -2574,7 +2574,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2630,7 +2630,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2658,7 +2658,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3196,7 +3196,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3252,7 +3252,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3280,7 +3280,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3473,7 +3473,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3501,7 +3501,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3642,7 +3642,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3670,7 +3670,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3698,7 +3698,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3726,7 +3726,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3919,7 +3919,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4164,7 +4164,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4310,7 +4310,7 @@
   <a href="#821" class="md-nav__link">
     <span class="md-ellipsis">
       
-        8.2.1 &nbsp; ヒープ挿入操作による実装
+        8.2.1 &nbsp; ヒープへの挿入操作による実現
       
     </span>
   </a>
@@ -4321,7 +4321,7 @@
   <a href="#822" class="md-nav__link">
     <span class="md-ellipsis">
       
-        8.2.2 &nbsp; 走査によるヒープ化の実装
+        8.2.2 &nbsp; 走査によるヒープ化で実現
       
     </span>
   </a>
@@ -4332,7 +4332,7 @@
   <a href="#823" class="md-nav__link">
     <span class="md-ellipsis">
       
-        8.2.3 &nbsp; 計算量分析
+        8.2.3 &nbsp; 計算量の分析
       
     </span>
   </a>
@@ -4376,39 +4376,39 @@
 
 
 <!-- Page content -->
-<h1 id="82">8.2 &nbsp; ヒープ構築操作<a class="headerlink" href="#82" title="Permanent link">&para;</a></h1>
-<p>場合によっては、リストのすべての要素を使用してヒープを構築したいことがあり、このプロセスは「ヒープ構築操作」として知られています。</p>
-<h2 id="821">8.2.1 &nbsp; ヒープ挿入操作による実装<a class="headerlink" href="#821" title="Permanent link">&para;</a></h2>
-<p>まず、空のヒープを作成し、次にリストを反復処理して、各要素に対して順番に「ヒープ挿入操作」を実行します。これは、要素をヒープの末尾に追加し、次に下から上に「ヒープ化」することを意味します。</p>
-<p>ヒープに要素が追加されるたびに、ヒープの長さは1つずつ増加します。ノードは二分木に上から下に追加されるため、ヒープは「上から下に」構築されます。</p>
-<p>要素数を<span class="arithmatex">\(n\)</span>とすると、各要素の挿入操作は<span class="arithmatex">\(O(\log{n})\)</span>時間かかるため、このヒープ構築方法の時間計算量は<span class="arithmatex">\(O(n \log n)\)</span>です。</p>
-<h2 id="822">8.2.2 &nbsp; 走査によるヒープ化の実装<a class="headerlink" href="#822" title="Permanent link">&para;</a></h2>
-<p>実際には、2つのステップでより効率的なヒープ構築方法を実装できます。</p>
+<h1 id="82">8.2 &nbsp; ヒープ構築<a class="headerlink" href="#82" title="Permanent link">&para;</a></h1>
+<p>場合によっては、リスト内のすべての要素を使ってヒープを構築したいことがあります。この過程を「ヒープ構築」と呼びます。</p>
+<h2 id="821">8.2.1 &nbsp; ヒープへの挿入操作による実現<a class="headerlink" href="#821" title="Permanent link">&para;</a></h2>
+<p>まず空のヒープを作成し、次にリストを走査して、各要素に対して順に「ヒープへの挿入操作」を実行します。つまり、要素をヒープの末尾に追加してから、その要素に対して「下から上へ」のヒープ化を行います。</p>
+<p>要素が1つヒープに挿入されるたびに、ヒープの長さは1増加します。ノードは上から下へ順に二分木へ追加されるため、ヒープは「上から下へ」構築されます。</p>
+<p>要素数を <span class="arithmatex">\(n\)</span> とすると、各要素のヒープへの挿入操作には <span class="arithmatex">\(O(\log{n})\)</span> の時間がかかるため、このヒープ構築法の時間計算量は <span class="arithmatex">\(O(n \log n)\)</span> です。</p>
+<h2 id="822">8.2.2 &nbsp; 走査によるヒープ化で実現<a class="headerlink" href="#822" title="Permanent link">&para;</a></h2>
+<p>実際には、より効率的なヒープ構築法を実現でき、全体は2つの手順に分かれます。</p>
 <ol>
 <li>リストのすべての要素をそのままヒープに追加します。この時点では、ヒープの性質はまだ満たされていません。</li>
-<li>ヒープを逆順（レベル順走査の逆）で走査し、各非葉ノードに対して「上から下のヒープ化」を実行します。</li>
+<li>ヒープを逆順で走査し（レベル順走査の逆順）、各非葉ノードに対して順に「上から下へ」のヒープ化を実行します。</li>
 </ol>
-<p><strong>ノードをヒープ化した後、そのノードを根とする部分木は有効な部分ヒープになります</strong>。走査が逆順であるため、ヒープは「下から上に」構築されます。</p>
-<p>逆走査を選択する理由は、現在のノードの下の部分木がすでに有効な部分ヒープであることを保証し、現在のノードのヒープ化を効果的にするためです。</p>
-<p>言及する価値があるのは、**葉ノードは子を持たないため、自然に有効な部分ヒープを形成し、ヒープ化する必要がない**ということです。以下のコードに示すように、最後の非葉ノードは最後のノードの親です。そこから開始して逆順に走査してヒープ化を実行します：</p>
+<p><strong>あるノードをヒープ化するたびに、そのノードを根とする部分木は合法な部分ヒープになります</strong>。また、逆順で走査するため、ヒープは「下から上へ」構築されます。</p>
+<p>逆順走査を選ぶのは、この方法なら現在のノードの下にある部分木がすでに合法な部分ヒープであることを保証でき、そのうえで現在のノードをヒープ化してはじめて有効になるからです。</p>
+<p>なお、<strong>葉ノードには子ノードがないため、それ自体が自然に合法な部分ヒープであり、ヒープ化は不要です</strong>。以下のコードが示すように、最後の非葉ノードは最後のノードの親ノードであり、そこから逆順に走査してヒープ化を実行します。</p>
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 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">my_heap.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;コンストラクタ、入力リストに基づいてヒープを構築&quot;&quot;&quot;</span>
-<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># すべてのリスト要素をヒープに追加</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;コンストラクタ。入力リストに基づいてヒープを構築する&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># リスト要素をそのままヒープに追加</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span> <span class="o">=</span> <span class="n">nums</span>
-<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="c1"># 葉以外のすべてのノードをヒープ化</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="c1"># 葉ノード以外のすべてのノードをヒープ化</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">parent</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">),</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">sift_down</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* コンストラクタ、入力リストに基づいてヒープを構築 */</span>
+<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* コンストラクタ。入力リストに基づいてヒープを構築する */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="n">MaxHeap</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// すべてのリスト要素をヒープに追加</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// リスト要素をそのままヒープに追加</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="n">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
-<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="c1">// 葉以外のすべてのノードをヒープ化</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="c1">// 葉ノード以外のすべてのノードをヒープ化</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">        </span><span class="n">siftDown</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="p">}</span>
@@ -4416,11 +4416,11 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* コンストラクタ、入力リストに基づいてヒープを構築 */</span>
+<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* コンストラクタ。入力リストに基づいてヒープを構築する */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="n">MaxHeap</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// すべてのリスト要素をヒープに追加</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// リスト要素をそのままヒープに追加</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="n">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">nums</span><span class="p">);</span>
-<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="c1">// 葉を除くすべてのノードをヒープ化</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="c1">// 葉ノード以外のすべてのノードをヒープ化</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="n">siftDown</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="p">}</span>
@@ -4428,74 +4428,274 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* コンストラクタ。入力リストに基づいてヒープを構築 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="n">MaxHeap</span><span class="p">(</span><span class="n">IEnumerable</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="c1">// リスト要素をそのままヒープに追加</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="n">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">(</span><span class="n">nums</span><span class="p">);</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="c1">// 葉ノード以外のすべてのノードをヒープ化</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="kt">var</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Parent</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">Size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">        </span><span class="n">SiftDown</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">maxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">newMaxHeap</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* コンストラクタ。スライスからヒープを構築する */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">newMaxHeap</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// リスト要素をそのままヒープに追加</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">h</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">maxHeap</span><span class="p">{</span><span class="nx">data</span><span class="p">:</span><span class="w"> </span><span class="nx">nums</span><span class="p">}</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">parent</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">        </span><span class="c1">// 葉ノード以外のすべてのノードをヒープ化</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">        </span><span class="nx">h</span><span class="p">.</span><span class="nx">siftDown</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">h</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="kd">init</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* コンストラクタ。入力リストに基づいてヒープを構築する */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">init</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// リスト要素をそのままヒープに追加</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="n">maxHeap</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="c1">// 葉ノード以外のすべてのノードをヒープ化</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)).</span><span class="n">reversed</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">        </span><span class="n">siftDown</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="kr">constructor</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* コンストラクタ。空のヒープを作成するか、入力リストからヒープを構築する */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kr">constructor</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="c1">// リスト要素をそのままヒープに追加</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="n">#maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="p">[]</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="p">[...</span><span class="nx">nums</span><span class="p">];</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="c1">// 葉ノード以外のすべてのノードをヒープ化</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#parent</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#siftDown</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="kr">constructor</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* コンストラクタ。空のヒープを作成するか、入力リストからヒープを構築する */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kr">constructor</span><span class="p">(</span><span class="nx">nums?</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="c1">// リスト要素をそのままヒープに追加</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="p">[]</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="p">[...</span><span class="nx">nums</span><span class="p">];</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="c1">// 葉ノード以外のすべてのノードをヒープ化</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">parent</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">siftDown</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* コンストラクタ。入力リストに基づいてヒープを構築する */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="n">MaxHeap</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="c1">// リスト要素をそのままヒープに追加</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="n">_maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="c1">// 葉ノード以外のすべてのノードをヒープ化</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_parent</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">    </span><span class="n">siftDown</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">new</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* コンストラクタ。入力リストに基づいてヒープを構築する */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">new</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="c1">// リスト要素をそのままヒープに追加</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MaxHeap</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">max_heap</span><span class="p">:</span><span class="w"> </span><span class="nc">nums</span><span class="w"> </span><span class="p">};</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="c1">// 葉ノード以外のすべてのノードをヒープ化</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">..=</span><span class="bp">Self</span><span class="p">::</span><span class="n">parent</span><span class="p">(</span><span class="n">heap</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)).</span><span class="n">rev</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">        </span><span class="n">heap</span><span class="p">.</span><span class="n">sift_down</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">    </span><span class="n">heap</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">newMaxHeap</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* コンストラクタ。スライスからヒープを構築する */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="nf">newMaxHeap</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="c1">// すべての要素をヒープに入れる</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">MaxHeap</span><span class="p">));</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">    </span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="p">;</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="n">memcpy</span><span class="p">(</span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">        </span><span class="c1">// 葉ノード以外のすべてのノードをヒープ化</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">        </span><span class="n">siftDown</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">;</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">my_heap.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 最大ヒープ */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">MaxHeap</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;?</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="c1">// 配列ではなくリストを使うことで、拡張を考慮する必要がない</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="cm">/* コンストラクタ。入力リストに基づいてヒープを構築する */</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">    </span><span class="k">init</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">        </span><span class="c1">// リスト要素をそのままヒープに追加</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">        </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">addAll</span><span class="p">(</span><span class="n">nums</span><span class="o">!!</span><span class="p">)</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">        </span><span class="c1">// 葉ノード以外のすべてのノードをヒープ化</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="n">downTo</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">            </span><span class="n">siftDown</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">    </span><span class="cm">/* 左子ノードのインデックスを取得 */</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">fun</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="w">    </span><span class="cm">/* 右子ノードのインデックスを取得 */</span>
+<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">fun</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">2</span>
+<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a>
+<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="w">    </span><span class="cm">/* 親ノードのインデックスを取得 */</span>
+<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">fun</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="c1">// 切り捨て除算</span>
+<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-30" name="__codelineno-11-30" href="#__codelineno-11-30"></a>
+<a id="__codelineno-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></a><span class="w">    </span><span class="cm">/* 要素を交換 */</span>
+<a id="__codelineno-11-32" name="__codelineno-11-32" href="#__codelineno-11-32"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">fun</span><span class="w"> </span><span class="nf">swap</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-33" name="__codelineno-11-33" href="#__codelineno-11-33"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-11-34" name="__codelineno-11-34" href="#__codelineno-11-34"></a><span class="w">        </span><span class="n">maxHeap</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-11-35" name="__codelineno-11-35" href="#__codelineno-11-35"></a><span class="w">        </span><span class="n">maxHeap</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span>
+<a id="__codelineno-11-36" name="__codelineno-11-36" href="#__codelineno-11-36"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-37" name="__codelineno-11-37" href="#__codelineno-11-37"></a>
+<a id="__codelineno-11-38" name="__codelineno-11-38" href="#__codelineno-11-38"></a><span class="w">    </span><span class="cm">/* ヒープのサイズを取得 */</span>
+<a id="__codelineno-11-39" name="__codelineno-11-39" href="#__codelineno-11-39"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">size</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-40" name="__codelineno-11-40" href="#__codelineno-11-40"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-11-41" name="__codelineno-11-41" href="#__codelineno-11-41"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-42" name="__codelineno-11-42" href="#__codelineno-11-42"></a>
+<a id="__codelineno-11-43" name="__codelineno-11-43" href="#__codelineno-11-43"></a><span class="w">    </span><span class="cm">/* ヒープが空かどうかを判定 */</span>
+<a id="__codelineno-11-44" name="__codelineno-11-44" href="#__codelineno-11-44"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">():</span><span class="w"> </span><span class="kt">Boolean</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-45" name="__codelineno-11-45" href="#__codelineno-11-45"></a><span class="w">        </span><span class="cm">/* ヒープが空かどうかを判定 */</span>
+<a id="__codelineno-11-46" name="__codelineno-11-46" href="#__codelineno-11-46"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-11-47" name="__codelineno-11-47" href="#__codelineno-11-47"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-48" name="__codelineno-11-48" href="#__codelineno-11-48"></a>
+<a id="__codelineno-11-49" name="__codelineno-11-49" href="#__codelineno-11-49"></a><span class="w">    </span><span class="cm">/* ヒープ先頭要素にアクセス */</span>
+<a id="__codelineno-11-50" name="__codelineno-11-50" href="#__codelineno-11-50"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">peek</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-51" name="__codelineno-11-51" href="#__codelineno-11-51"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">[</span><span class="m">0</span><span class="o">]</span>
+<a id="__codelineno-11-52" name="__codelineno-11-52" href="#__codelineno-11-52"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-53" name="__codelineno-11-53" href="#__codelineno-11-53"></a>
+<a id="__codelineno-11-54" name="__codelineno-11-54" href="#__codelineno-11-54"></a><span class="w">    </span><span class="cm">/* 要素をヒープに追加 */</span>
+<a id="__codelineno-11-55" name="__codelineno-11-55" href="#__codelineno-11-55"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">_val</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-56" name="__codelineno-11-56" href="#__codelineno-11-56"></a><span class="w">        </span><span class="c1">// ノードを追加</span>
+<a id="__codelineno-11-57" name="__codelineno-11-57" href="#__codelineno-11-57"></a><span class="w">        </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">_val</span><span class="p">)</span>
+<a id="__codelineno-11-58" name="__codelineno-11-58" href="#__codelineno-11-58"></a><span class="w">        </span><span class="c1">// 下から上へヒープ化</span>
+<a id="__codelineno-11-59" name="__codelineno-11-59" href="#__codelineno-11-59"></a><span class="w">        </span><span class="n">siftUp</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-11-60" name="__codelineno-11-60" href="#__codelineno-11-60"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-61" name="__codelineno-11-61" href="#__codelineno-11-61"></a>
+<a id="__codelineno-11-62" name="__codelineno-11-62" href="#__codelineno-11-62"></a><span class="w">    </span><span class="cm">/* ノード i から始めて、下から上へヒープ化 */</span>
+<a id="__codelineno-11-63" name="__codelineno-11-63" href="#__codelineno-11-63"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">fun</span><span class="w"> </span><span class="nf">siftUp</span><span class="p">(</span><span class="nb">it</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-64" name="__codelineno-11-64" href="#__codelineno-11-64"></a><span class="w">        </span><span class="c1">// Kotlin の関数引数は不変のため、一時変数を作成する</span>
+<a id="__codelineno-11-65" name="__codelineno-11-65" href="#__codelineno-11-65"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">it</span>
+<a id="__codelineno-11-66" name="__codelineno-11-66" href="#__codelineno-11-66"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-67" name="__codelineno-11-67" href="#__codelineno-11-67"></a><span class="w">            </span><span class="c1">// ノード i の親ノードを取得</span>
+<a id="__codelineno-11-68" name="__codelineno-11-68" href="#__codelineno-11-68"></a><span class="w">            </span><span class="kd">val</span><span class="w"> </span><span class="nv">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-11-69" name="__codelineno-11-69" href="#__codelineno-11-69"></a><span class="w">            </span><span class="c1">// 「根ノードを越えた」または「ノードの修復が不要」になったらヒープ化を終了</span>
+<a id="__codelineno-11-70" name="__codelineno-11-70" href="#__codelineno-11-70"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">[</span><span class="n">p</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="k">break</span>
+<a id="__codelineno-11-71" name="__codelineno-11-71" href="#__codelineno-11-71"></a><span class="w">            </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-11-72" name="__codelineno-11-72" href="#__codelineno-11-72"></a><span class="w">            </span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">)</span>
+<a id="__codelineno-11-73" name="__codelineno-11-73" href="#__codelineno-11-73"></a><span class="w">            </span><span class="c1">// ループで下から上へヒープ化</span>
+<a id="__codelineno-11-74" name="__codelineno-11-74" href="#__codelineno-11-74"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span>
+<a id="__codelineno-11-75" name="__codelineno-11-75" href="#__codelineno-11-75"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-76" name="__codelineno-11-76" href="#__codelineno-11-76"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-77" name="__codelineno-11-77" href="#__codelineno-11-77"></a>
+<a id="__codelineno-11-78" name="__codelineno-11-78" href="#__codelineno-11-78"></a><span class="w">    </span><span class="cm">/* 要素をヒープから取り出す */</span>
+<a id="__codelineno-11-79" name="__codelineno-11-79" href="#__codelineno-11-79"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">pop</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-80" name="__codelineno-11-80" href="#__codelineno-11-80"></a><span class="w">        </span><span class="c1">// 空判定の処理</span>
+<a id="__codelineno-11-81" name="__codelineno-11-81" href="#__codelineno-11-81"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">()</span>
+<a id="__codelineno-11-82" name="__codelineno-11-82" href="#__codelineno-11-82"></a><span class="w">        </span><span class="c1">// 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
+<a id="__codelineno-11-83" name="__codelineno-11-83" href="#__codelineno-11-83"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-11-84" name="__codelineno-11-84" href="#__codelineno-11-84"></a><span class="w">        </span><span class="c1">// ノードを削除</span>
+<a id="__codelineno-11-85" name="__codelineno-11-85" href="#__codelineno-11-85"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">_val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">removeAt</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-11-86" name="__codelineno-11-86" href="#__codelineno-11-86"></a><span class="w">        </span><span class="c1">// 上から下へヒープ化</span>
+<a id="__codelineno-11-87" name="__codelineno-11-87" href="#__codelineno-11-87"></a><span class="w">        </span><span class="n">siftDown</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
+<a id="__codelineno-11-88" name="__codelineno-11-88" href="#__codelineno-11-88"></a><span class="w">        </span><span class="c1">// ヒープ先頭要素を返す</span>
+<a id="__codelineno-11-89" name="__codelineno-11-89" href="#__codelineno-11-89"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">_val</span>
+<a id="__codelineno-11-90" name="__codelineno-11-90" href="#__codelineno-11-90"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-91" name="__codelineno-11-91" href="#__codelineno-11-91"></a>
+<a id="__codelineno-11-92" name="__codelineno-11-92" href="#__codelineno-11-92"></a><span class="w">    </span><span class="cm">/* ノード i から始めて、上から下へヒープ化 */</span>
+<a id="__codelineno-11-93" name="__codelineno-11-93" href="#__codelineno-11-93"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">fun</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="nb">it</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-94" name="__codelineno-11-94" href="#__codelineno-11-94"></a><span class="w">        </span><span class="c1">// Kotlin の関数引数は不変のため、一時変数を作成する</span>
+<a id="__codelineno-11-95" name="__codelineno-11-95" href="#__codelineno-11-95"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">it</span>
+<a id="__codelineno-11-96" name="__codelineno-11-96" href="#__codelineno-11-96"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-97" name="__codelineno-11-97" href="#__codelineno-11-97"></a><span class="w">            </span><span class="c1">// ノード i, l, r のうち値が最大のノードを ma とする</span>
+<a id="__codelineno-11-98" name="__codelineno-11-98" href="#__codelineno-11-98"></a><span class="w">            </span><span class="kd">val</span><span class="w"> </span><span class="nv">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-11-99" name="__codelineno-11-99" href="#__codelineno-11-99"></a><span class="w">            </span><span class="kd">val</span><span class="w"> </span><span class="nv">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-11-100" name="__codelineno-11-100" href="#__codelineno-11-100"></a><span class="w">            </span><span class="kd">var</span><span class="w"> </span><span class="nv">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-11-101" name="__codelineno-11-101" href="#__codelineno-11-101"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">[</span><span class="n">l</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span>
+<a id="__codelineno-11-102" name="__codelineno-11-102" href="#__codelineno-11-102"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">[</span><span class="n">r</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span>
+<a id="__codelineno-11-103" name="__codelineno-11-103" href="#__codelineno-11-103"></a><span class="w">            </span><span class="c1">// ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
+<a id="__codelineno-11-104" name="__codelineno-11-104" href="#__codelineno-11-104"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">break</span>
+<a id="__codelineno-11-105" name="__codelineno-11-105" href="#__codelineno-11-105"></a><span class="w">            </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-11-106" name="__codelineno-11-106" href="#__codelineno-11-106"></a><span class="w">            </span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">)</span>
+<a id="__codelineno-11-107" name="__codelineno-11-107" href="#__codelineno-11-107"></a><span class="w">            </span><span class="c1">// ループで上から下へヒープ化</span>
+<a id="__codelineno-11-108" name="__codelineno-11-108" href="#__codelineno-11-108"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span>
+<a id="__codelineno-11-109" name="__codelineno-11-109" href="#__codelineno-11-109"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-110" name="__codelineno-11-110" href="#__codelineno-11-110"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-111" name="__codelineno-11-111" href="#__codelineno-11-111"></a>
+<a id="__codelineno-11-112" name="__codelineno-11-112" href="#__codelineno-11-112"></a><span class="w">    </span><span class="cm">/* ヒープ（二分木）を出力 */</span>
+<a id="__codelineno-11-113" name="__codelineno-11-113" href="#__codelineno-11-113"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-114" name="__codelineno-11-114" href="#__codelineno-11-114"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">a</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="o">-&gt;</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-11-115" name="__codelineno-11-115" href="#__codelineno-11-115"></a><span class="w">        </span><span class="n">queue</span><span class="p">.</span><span class="na">addAll</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">)</span>
+<a id="__codelineno-11-116" name="__codelineno-11-116" href="#__codelineno-11-116"></a><span class="w">        </span><span class="n">printHeap</span><span class="p">(</span><span class="n">queue</span><span class="p">)</span>
+<a id="__codelineno-11-117" name="__codelineno-11-117" href="#__codelineno-11-117"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-118" name="__codelineno-11-118" href="#__codelineno-11-118"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="kp">initialize</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### コンストラクタ。入力リストに基づいてヒープを構築 ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># リスト要素をそのままヒープに追加</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="vi">@max_heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="c1"># 葉ノード以外のすべてのノードをヒープ化</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="n">parent</span><span class="p">(</span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">    </span><span class="n">sift_down</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h2 id="823">8.2.3 &nbsp; 計算量分析<a class="headerlink" href="#823" title="Permanent link">&para;</a></h2>
-<p>次に、この第2のヒープ構築方法の時間計算量を計算してみましょう。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" 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</iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20MaxHeap%3A%0A%20%20%20%20%22%22%22%E6%9C%80%E5%A4%A7%E3%83%92%E3%83%BC%E3%83%97%22%22%22%0A%0A%20%20%20%20def%20__init__%28self%2C%20nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%82%B3%E3%83%B3%E3%82%B9%E3%83%88%E3%83%A9%E3%82%AF%E3%82%BF%E3%80%82%E5%85%A5%E5%8A%9B%E3%83%AA%E3%82%B9%E3%83%88%E3%81%AB%E5%9F%BA%E3%81%A5%E3%81%84%E3%81%A6%E3%83%92%E3%83%BC%E3%83%97%E3%82%92%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E3%83%AA%E3%82%B9%E3%83%88%E8%A6%81%E7%B4%A0%E3%82%92%E3%81%9D%E3%81%AE%E3%81%BE%E3%81%BE%E3%83%92%E3%83%BC%E3%83%97%E3%81%AB%E8%BF%BD%E5%8A%A0%0A%20%20%20%20%20%20%20%20self.max_heap%20%3D%20nums%0A%20%20%20%20%20%20%20%20%23%20%E8%91%89%E3%83%8E%E3%83%BC%E3%83%89%E4%BB%A5%E5%A4%96%E3%81%AE%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E3%83%92%E3%83%BC%E3%83%97%E5%8C%96%0A%20%20%20%20%20%20%20%20for%20i%20in%20range%28self.parent%28self.size%28%29%20-%201%29%2C%20-1%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.sift_down%28i%29%0A%0A%20%20%20%20def%20left%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%B7%A6%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E5%8F%96%E5%BE%97%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%8F%B3%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E5%8F%96%E5%BE%97%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%A6%AA%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E5%8F%96%E5%BE%97%22%22%22%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20%2F%2F%202%20%20%23%20%E5%88%87%E3%82%8A%E6%8D%A8%E3%81%A6%E9%99%A4%E7%AE%97%0A%0A%20%20%20%20def%20swap%28self%2C%20i%3A%20int%2C%20j%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%A6%81%E7%B4%A0%E3%82%92%E4%BA%A4%E6%8F%9B%22%22%22%0A%20%20%20%20%20%20%20%20self.max_heap%5Bi%5D%2C%20self.max_heap%5Bj%5D%20%3D%20self.max_heap%5Bj%5D%2C%20self.max_heap%5Bi%5D%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%83%92%E3%83%BC%E3%83%97%E3%81%AE%E3%82%B5%E3%82%A4%E3%82%BA%E3%82%92%E5%8F%96%E5%BE%97%22%22%22%0A%20%20%20%20%20%20%20%20return%20len%28self.max_heap%29%0A%0A%20%20%20%20def%20sift_down%28self%2C%20i%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%83%8E%E3%83%BC%E3%83%89%20i%20%E3%81%8B%E3%82%89%E5%A7%8B%E3%82%81%E3%81%A6%E3%80%81%E4%B8%8A%E3%81%8B%E3%82%89%E4%B8%8B%E3%81%B8%E3%83%92%E3%83%BC%E3%83%97%E5%8C%96%22%22%22%0A%20%20%20%20%20%20%20%20while%20True%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%20i%2C%20l%2C%20r%20%E3%81%AE%E3%81%86%E3%81%A1%E5%80%A4%E3%81%8C%E6%9C%80%E5%A4%A7%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%20ma%20%E3%81%A8%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20l%2C%20r%2C%20ma%20%3D%20self.left%28i%29%2C%20self.right%28i%29%2C%20i%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20l%20%3C%20self.size%28%29%20and%20self.max_heap%5Bl%5D%20%3E%20self.max_heap%5Bma%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20ma%20%3D%20l%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20r%20%3C%20self.size%28%29%20and%20self.max_heap%5Br%5D%20%3E%20self.max_heap%5Bma%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20ma%20%3D%20r%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%20i%20%E3%81%8C%E6%9C%80%E5%A4%A7%E3%80%81%E3%81%BE%E3%81%9F%E3%81%AF%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20l%2C%20r%20%E3%81%8C%E7%AF%84%E5%9B%B2%E5%A4%96%E3%81%AA%E3%82%89%E3%80%81%E3%83%92%E3%83%BC%E3%83%97%E5%8C%96%E3%81%AF%E4%B8%8D%E8%A6%81%E3%81%AA%E3%81%AE%E3%81%A7%E6%8A%9C%E3%81%91%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20ma%20%3D%3D%20i%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%202%20%E3%81%A4%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E4%BA%A4%E6%8F%9B%0A%20%20%20%20%20%20%20%20%20%20%20%20self.swap%28i%2C%20ma%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%97%E3%81%A7%E4%B8%8A%E3%81%8B%E3%82%89%E4%B8%8B%E3%81%B8%E3%83%92%E3%83%BC%E3%83%97%E5%8C%96%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%3D%20ma%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E6%9C%80%E5%A4%A7%E3%83%92%E3%83%BC%E3%83%97%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20max_heap%20%3D%20MaxHeap%28%5B1%2C%202%2C%203%2C%204%2C%205%5D%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h2 id="823">8.2.3 &nbsp; 計算量の分析<a class="headerlink" href="#823" title="Permanent link">&para;</a></h2>
+<p>以下では、2つ目のヒープ構築法の時間計算量を求めてみましょう。</p>
 <ul>
-<li>完備二分木のノード数を<span class="arithmatex">\(n\)</span>と仮定すると、葉ノードの数は<span class="arithmatex">\((n + 1) / 2\)</span>です。ここで<span class="arithmatex">\(/\)</span> は整数除算です。したがって、ヒープ化が必要なノードの数は<span class="arithmatex">\((n - 1) / 2\)</span>です。</li>
-<li>「上から下のヒープ化」のプロセスでは、各ノードは最大で葉ノードまでヒープ化されるため、最大反復回数は二分木の高さ<span class="arithmatex">\(\log n\)</span>です。</li>
+<li>完全二分木のノード数を <span class="arithmatex">\(n\)</span> とすると、葉ノード数は <span class="arithmatex">\((n + 1) / 2\)</span> です。ここで <span class="arithmatex">\(/\)</span> は切り捨て除算を表します。したがって、ヒープ化が必要なノード数は <span class="arithmatex">\((n - 1) / 2\)</span> です。</li>
+<li>上から下へのヒープ化の過程では、各ノードは最大で葉ノードまでヒープ化されるため、最大反復回数は二分木の高さ <span class="arithmatex">\(\log n\)</span> です。</li>
 </ul>
-<p>この2つを掛け合わせると、ヒープ構築プロセスの時間計算量は<span class="arithmatex">\(O(n \log n)\)</span>となります。<strong>しかし、この推定は正確ではありません。二分木の下位レベルには上位よりもはるかに多くのノードがあるという性質を考慮していないからです。</strong></p>
-<p>より正確な計算を行いましょう。計算を簡素化するため、<span class="arithmatex">\(n\)</span>個のノードと高さ<span class="arithmatex">\(h\)</span>を持つ「完全二分木」を仮定します。この仮定は結果の正確性に影響しません。</p>
-<p><img alt="完全二分木の各レベルのノード数" class="animation-figure" src="../build_heap.assets/heapify_operations_count.png" /></p>
-<p align="center"> 図 8-5 &nbsp; 完全二分木の各レベルのノード数 </p>
+<p>上の2つを掛け合わせると、ヒープ構築過程の時間計算量は <span class="arithmatex">\(O(n \log n)\)</span> となります。<strong>しかし、この見積もりは正確ではありません。二分木では下層のノード数が上層よりはるかに多いという性質を考慮していないためです</strong>。</p>
+<p>次に、より正確な計算を行います。計算を簡単にするため、ノード数が <span class="arithmatex">\(n\)</span> 、高さが <span class="arithmatex">\(h\)</span> の「満二分木」を仮定します。この仮定は計算結果の正しさに影響しません。</p>
+<p><img alt="満二分木の各層のノード数" class="animation-figure" src="../build_heap.assets/heapify_operations_count.png" /></p>
+<p align="center"> 図 8-5 &nbsp; 満二分木の各層のノード数 </p>
 
-<p>上図に示すように、ノードが「上から下にヒープ化される」最大反復回数は、そのノードから葉ノードまでの距離と等しく、これは正確に「ノードの高さ」です。したがって、各レベルで「ノード数×ノードの高さ」を合計して、**すべてのノードの総ヒープ化反復回数を得る**ことができます。</p>
+<p>上図に示すように、ノードを「上から下へヒープ化」する最大反復回数は、そのノードから葉ノードまでの距離に等しく、この距離こそが「ノードの高さ」です。したがって、各層の「ノード数 <span class="arithmatex">\(\times\)</span> ノードの高さ」を合計すれば、**すべてのノードのヒープ化反復回数の総和**が得られます。</p>
 <div class="arithmatex">\[
 T(h) = 2^0h + 2^1(h-1) + 2^2(h-2) + \dots + 2^{(h-1)}\times1
 \]</div>
-<p>上記の方程式を簡素化するために、高校の数列の知識を使用する必要があります。まず<span class="arithmatex">\(T(h)\)</span>に<span class="arithmatex">\(2\)</span>を掛けて以下を得ます：</p>
+<p>上式を簡約するには中学の数列の知識を用います。まず <span class="arithmatex">\(T(h)\)</span> に <span class="arithmatex">\(2\)</span> を掛けると、次のようになります。</p>
 <div class="arithmatex">\[
 \begin{aligned}
 T(h) &amp; = 2^0h + 2^1(h-1) + 2^2(h-2) + \dots + 2^{h-1}\times1 \newline
-2T(h) &amp; = 2^1h + 2^2(h-1) + 2^3(h-2) + \dots + 2^h\times1 \newline
+2 T(h) &amp; = 2^1h + 2^2(h-1) + 2^3(h-2) + \dots + 2^{h}\times1 \newline
 \end{aligned}
 \]</div>
-<p>変位法を使用して<span class="arithmatex">\(2T(h)\)</span>から<span class="arithmatex">\(T(h)\)</span>を減算すると、以下を得ます：</p>
+<p>ずらして引く方法を用い、下式の <span class="arithmatex">\(2 T(h)\)</span> から上式の <span class="arithmatex">\(T(h)\)</span> を引くと、次が得られます。</p>
 <div class="arithmatex">\[
 2T(h) - T(h) = T(h) = -2^0h + 2^1 + 2^2 + \dots + 2^{h-1} + 2^h
 \]</div>
-<p>方程式を観察すると、<span class="arithmatex">\(T(h)\)</span>は等比数列であり、和の公式を使用して直接計算でき、時間計算量は以下になります：</p>
+<p>上式を見ると、<span class="arithmatex">\(T(h)\)</span> は等比数列であることがわかるため、和の公式を直接用いて、時間計算量は次のように求められます。</p>
 <div class="arithmatex">\[
 \begin{aligned}
 T(h) &amp; = 2 \frac{1 - 2^h}{1 - 2} - h \newline
@@ -4503,7 +4703,7 @@ T(h) &amp; = 2 \frac{1 - 2^h}{1 - 2} - h \newline
 &amp; = O(2^h)
 \end{aligned}
 \]</div>
-<p>さらに、高さ<span class="arithmatex">\(h\)</span>の完全二分木は<span class="arithmatex">\(n = 2^{h+1} - 1\)</span>個のノードを持つため、計算量は<span class="arithmatex">\(O(2^h) = O(n)\)</span>です。この計算は、**リストを入力してヒープを構築する時間計算量が<span class="arithmatex">\(O(n)\)</span>であり、非常に効率的である**ことを示しています。</p>
+<p>さらに、高さ <span class="arithmatex">\(h\)</span> の満二分木のノード数は <span class="arithmatex">\(n = 2^{h+1} - 1\)</span> であるため、計算量は容易に <span class="arithmatex">\(O(2^h) = O(n)\)</span> とわかります。以上の導出は、**入力リストからヒープを構築する時間計算量が <span class="arithmatex">\(O(n)\)</span> であり、非常に効率的である**ことを示しています。</p>
 
 <!-- Source file information -->
 
diff --git a/ja/chapter_heap/heap/index.html b/ja/chapter_heap/heap/index.html
index 12bb63f1d..d0606f160 100644
--- a/ja/chapter_heap/heap/index.html
+++ b/ja/chapter_heap/heap/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
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-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1613,7 +1613,7 @@
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1635,7 +1635,7 @@
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-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1942,7 +1942,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2136,7 +2136,7 @@
   <a href="#811" class="md-nav__link">
     <span class="md-ellipsis">
       
-        8.1.1 &nbsp; ヒープの一般的な操作
+        8.1.1 &nbsp; ヒープの基本操作
       
     </span>
   </a>
@@ -2170,7 +2170,7 @@
   <a href="#2" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2. &nbsp; ヒープの先頭要素へのアクセス
+        2. &nbsp; ヒープ頂点の要素にアクセス
       
     </span>
   </a>
@@ -2181,7 +2181,7 @@
   <a href="#3" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3. &nbsp; ヒープへの要素挿入
+        3. &nbsp; 要素をヒープに追加
       
     </span>
   </a>
@@ -2192,7 +2192,7 @@
   <a href="#4" class="md-nav__link">
     <span class="md-ellipsis">
       
-        4. &nbsp; ヒープからの先頭要素削除
+        4. &nbsp; ヒープ頂点の要素を取り出す
       
     </span>
   </a>
@@ -2208,7 +2208,7 @@
   <a href="#813" class="md-nav__link">
     <span class="md-ellipsis">
       
-        8.1.3 &nbsp; ヒープの一般的な応用
+        8.1.3 &nbsp; ヒープの代表的な応用
       
     </span>
   </a>
@@ -2238,7 +2238,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2624,7 +2624,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2680,7 +2680,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2708,7 +2708,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3246,7 +3246,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3302,7 +3302,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3330,7 +3330,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3523,7 +3523,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3551,7 +3551,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3692,7 +3692,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3720,7 +3720,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3748,7 +3748,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3776,7 +3776,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3969,7 +3969,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4214,7 +4214,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4360,7 +4360,7 @@
   <a href="#811" class="md-nav__link">
     <span class="md-ellipsis">
       
-        8.1.1 &nbsp; ヒープの一般的な操作
+        8.1.1 &nbsp; ヒープの基本操作
       
     </span>
   </a>
@@ -4394,7 +4394,7 @@
   <a href="#2" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2. &nbsp; ヒープの先頭要素へのアクセス
+        2. &nbsp; ヒープ頂点の要素にアクセス
       
     </span>
   </a>
@@ -4405,7 +4405,7 @@
   <a href="#3" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3. &nbsp; ヒープへの要素挿入
+        3. &nbsp; 要素をヒープに追加
       
     </span>
   </a>
@@ -4416,7 +4416,7 @@
   <a href="#4" class="md-nav__link">
     <span class="md-ellipsis">
       
-        4. &nbsp; ヒープからの先頭要素削除
+        4. &nbsp; ヒープ頂点の要素を取り出す
       
     </span>
   </a>
@@ -4432,7 +4432,7 @@
   <a href="#813" class="md-nav__link">
     <span class="md-ellipsis">
       
-        8.1.3 &nbsp; ヒープの一般的な応用
+        8.1.3 &nbsp; ヒープの代表的な応用
       
     </span>
   </a>
@@ -4477,25 +4477,25 @@
 
 <!-- Page content -->
 <h1 id="81">8.1 &nbsp; ヒープ<a class="headerlink" href="#81" title="Permanent link">&para;</a></h1>
-<p><u>ヒープ</u>は特定の条件を満たす完備二分木で、主に次の2つのタイプに分類されます（下図参照）。</p>
+<p><u>ヒープ（heap）</u>は、特定の条件を満たす完全二分木であり、主に次の 2 種類に分けられます。</p>
 <ul>
-<li><u>最小ヒープ</u>：任意のノードの値 <span class="arithmatex">\(\leq\)</span> その子ノードの値。</li>
-<li><u>最大ヒープ</u>：任意のノードの値 <span class="arithmatex">\(\geq\)</span> その子ノードの値。</li>
+<li><u>最小ヒープ（min heap）</u>：任意のノードの値 <span class="arithmatex">\(\leq\)</span> その子ノードの値。</li>
+<li><u>最大ヒープ（max heap）</u>：任意のノードの値 <span class="arithmatex">\(\geq\)</span> その子ノードの値。</li>
 </ul>
 <p><img alt="最小ヒープと最大ヒープ" class="animation-figure" src="../heap.assets/min_heap_and_max_heap.png" /></p>
 <p align="center"> 図 8-1 &nbsp; 最小ヒープと最大ヒープ </p>
 
-<p>完備二分木の特別なケースとして、ヒープには以下の特性があります：</p>
+<p>ヒープは完全二分木の特殊な例であり、次の性質を持ちます。</p>
 <ul>
-<li>最下位層のノードは左から右に埋められ、他の層のノードは完全に埋められています。</li>
-<li>二分木の根ノードをヒープの「先頭」と呼び、最も右下のノードをヒープの「末尾」と呼びます。</li>
-<li>最大ヒープ（最小ヒープ）の場合、先頭要素（根）の値はすべての要素の中で最大（最小）です。</li>
+<li>最下層のノードは左から順に埋められ、ほかの層のノードはすべて埋まっています。</li>
+<li>二分木の根ノードを「ヒープ頂点」、最下層で最も右にあるノードを「ヒープ底」と呼びます。</li>
+<li>最大ヒープ（最小ヒープ）では、ヒープ頂点の要素（根ノード）の値が最大（最小）です。</li>
 </ul>
-<h2 id="811">8.1.1 &nbsp; ヒープの一般的な操作<a class="headerlink" href="#811" title="Permanent link">&para;</a></h2>
-<p>多くのプログラミング言語が<u>優先度キュー</u>を提供していることに注意してください。これは優先度付きソートを持つキューとして定義される抽象データ構造です。</p>
-<p>実際には、<strong>ヒープは優先度キューを実装するためによく使用されます。最大ヒープは、要素が降順でデキューされる優先度キューに対応します</strong>。使用の観点から、「優先度キュー」と「ヒープ」を同等のデータ構造と考えることができます。したがって、この本では両者を特別に区別せず、統一して「ヒープ」と呼びます。</p>
-<p>ヒープの一般的な操作を下表に示します。メソッド名はプログラミング言語によって異なる場合があります。</p>
-<p align="center"> 表 8-1 &nbsp; ヒープ操作の効率 </p>
+<h2 id="811">8.1.1 &nbsp; ヒープの基本操作<a class="headerlink" href="#811" title="Permanent link">&para;</a></h2>
+<p>ここで注意したいのは、多くのプログラミング言語が提供しているのは<u>優先度付きキュー（priority queue）</u>であり、これは優先度順に並ぶキューとして定義される抽象データ構造だということです。</p>
+<p>実際には、<strong>ヒープは通常、優先度付きキューの実装に用いられ、最大ヒープは要素が大きい順に取り出される優先度付きキューに相当します</strong>。利用の観点では、「優先度付きキュー」と「ヒープ」は等価なデータ構造とみなせます。そのため、本書では両者を特に区別せず、まとめて「ヒープ」と呼びます。</p>
+<p>ヒープの基本操作を以下の表に示します。メソッド名はプログラミング言語によって異なります。</p>
+<p align="center"> 表 8-1 &nbsp; ヒープの操作効率 </p>
 
 <div class="center-table">
 <table>
@@ -4509,17 +4509,17 @@
 <tbody>
 <tr>
 <td><code>push()</code></td>
-<td>ヒープに要素を追加</td>
+<td>要素をヒープに追加</td>
 <td><span class="arithmatex">\(O(\log n)\)</span></td>
 </tr>
 <tr>
 <td><code>pop()</code></td>
-<td>ヒープから先頭要素を削除</td>
+<td>ヒープ頂点の要素を取り出す</td>
 <td><span class="arithmatex">\(O(\log n)\)</span></td>
 </tr>
 <tr>
 <td><code>peek()</code></td>
-<td>先頭要素にアクセス（最大/最小ヒープの場合、最大/最小値）</td>
+<td>ヒープ頂点の要素にアクセス（最大 / 最小ヒープではそれぞれ最大 / 最小値）</td>
 <td><span class="arithmatex">\(O(1)\)</span></td>
 </tr>
 <tr>
@@ -4529,38 +4529,38 @@
 </tr>
 <tr>
 <td><code>isEmpty()</code></td>
-<td>ヒープが空かどうかをチェック</td>
+<td>ヒープが空かどうかを判定</td>
 <td><span class="arithmatex">\(O(1)\)</span></td>
 </tr>
 </tbody>
 </table>
 </div>
-<p>実際には、プログラミング言語によって提供されるヒープクラス（または優先度キュークラス）を直接使用できます。</p>
-<p>ソートアルゴリズムで「昇順」と「降順」があるように、<code>flag</code>を設定するか<code>Comparator</code>を変更することで「最小ヒープ」と「最大ヒープ」を切り替えることができます。コードは以下の通りです：</p>
+<p>実際の応用では、プログラミング言語が提供するヒープクラス（または優先度付きキュークラス）をそのまま使えます。</p>
+<p>ソートアルゴリズムにおける「昇順」と「降順」と同様に、<code>flag</code> を設定したり <code>Comparator</code> を変更したりすることで、「最小ヒープ」と「最大ヒープ」を切り替えられます。コードは以下のとおりです：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">heap.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 最小ヒープの初期化</span>
+<div class="highlight"><span class="filename">heap.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 最小ヒープを初期化</span>
 <a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="n">min_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">=</span> <span class="p">[],</span> <span class="mi">1</span>
-<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="c1"># 最大ヒープの初期化</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="c1"># 最大ヒープを初期化</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">=</span> <span class="p">[],</span> <span class="o">-</span><span class="mi">1</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>
-<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="c1"># Pythonのheapqモジュールはデフォルトで最小ヒープを実装</span>
-<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="c1"># 要素をヒープにプッシュする前に負の値にすることで、順序を反転させ、最大ヒープを実装</span>
-<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="c1"># この例では、flag = 1は最小ヒープに対応し、flag = -1は最大ヒープに対応</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="c1"># Python の heapq モジュールはデフォルトで最小ヒープを実装している</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="c1"># 「要素を負にして」からヒープに追加すると、大小関係を反転させて最大ヒープを実現できる</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="c1"># この例では、flag = 1 のときは最小ヒープ、flag = -1 のときは最大ヒープに対応する</span>
 <a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>
-<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="c1"># ヒープに要素をプッシュ</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="c1"># 要素をヒープに追加</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">*</span> <span class="mi">1</span><span class="p">)</span>
 <a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">*</span> <span class="mi">3</span><span class="p">)</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">*</span> <span class="mi">2</span><span class="p">)</span>
 <a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">*</span> <span class="mi">5</span><span class="p">)</span>
 <a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">*</span> <span class="mi">4</span><span class="p">)</span>
 <a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>
-<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a><span class="c1"># ヒープの先頭要素を取得</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a><span class="c1"># ヒープ頂点の要素を取得</span>
 <a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a><span class="n">peek</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">max_heap</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="c1"># 5</span>
 <a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>
-<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a><span class="c1"># ヒープの先頭要素をポップ</span>
-<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="c1"># ポップされた要素は降順のシーケンスを形成</span>
+<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a><span class="c1"># ヒープ頂点の要素を取り出す</span>
+<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="c1"># 取り出された要素は大きい順の列になる</span>
 <a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="n">val</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">heapq</span><span class="o">.</span><span class="n">heappop</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span> <span class="c1"># 5</span>
 <a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a><span class="n">val</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">heapq</span><span class="o">.</span><span class="n">heappop</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span> <span class="c1"># 4</span>
 <a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a><span class="n">val</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">heapq</span><span class="o">.</span><span class="n">heappop</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span> <span class="c1"># 3</span>
@@ -4570,33 +4570,33 @@
 <a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a><span class="c1"># ヒープのサイズを取得</span>
 <a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a><span class="n">size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span>
 <a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a>
-<a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a><span class="c1"># ヒープが空かどうかをチェック</span>
+<a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a><span class="c1"># ヒープが空かどうかを判定</span>
 <a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a><span class="n">is_empty</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="ow">not</span> <span class="n">max_heap</span>
 <a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a>
-<a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a><span class="c1"># リストからヒープを作成</span>
+<a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a><span class="c1"># 入力リストからヒープを構築</span>
 <a id="__codelineno-0-35" name="__codelineno-0-35" href="#__codelineno-0-35"></a><span class="n">min_heap</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">4</span><span class="p">]</span>
 <a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heapify</span><span class="p">(</span><span class="n">min_heap</span><span class="p">)</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">heap.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* ヒープの初期化 */</span>
-<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// 最小ヒープの初期化</span>
+<div class="highlight"><span class="filename">heap.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* ヒープを初期化 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// 最小ヒープを初期化</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="n">priority_queue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">greater</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">minHeap</span><span class="p">;</span>
-<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="c1">// 最大ヒープの初期化</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="c1">// 最大ヒープを初期化</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="n">priority_queue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">less</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">;</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a>
-<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="cm">/* ヒープに要素をプッシュ */</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="cm">/* 要素をヒープに追加 */</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a>
-<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="cm">/* ヒープの先頭要素を取得 */</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="cm">/* ヒープ頂点の要素を取得 */</span>
 <a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">top</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
 <a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a>
-<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="cm">/* ヒープの先頭要素をポップ */</span>
-<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="c1">// ポップされた要素は降順のシーケンスを形成</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="cm">/* ヒープ頂点の要素を取り出す */</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="c1">// 取り出された要素は大きい順の列になる</span>
 <a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
 <a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 4</span>
 <a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 3</span>
@@ -4606,33 +4606,33 @@
 <a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="cm">/* ヒープのサイズを取得 */</span>
 <a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
 <a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a>
-<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="cm">/* ヒープが空かどうかをチェック */</span>
+<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="cm">/* ヒープが空かどうかを判定 */</span>
 <a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">empty</span><span class="p">();</span>
 <a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a>
-<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="cm">/* リストからヒープを作成 */</span>
+<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="cm">/* 入力リストからヒープを構築 */</span>
 <a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">input</span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">};</span>
 <a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="n">priority_queue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">greater</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">minHeap</span><span class="p">(</span><span class="n">input</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">input</span><span class="p">.</span><span class="n">end</span><span class="p">());</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">heap.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* ヒープの初期化 */</span>
-<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="c1">// 最小ヒープの初期化</span>
+<div class="highlight"><span class="filename">heap.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* ヒープを初期化 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="c1">// 最小ヒープを初期化</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="n">Queue</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">minHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="o">&lt;&gt;</span><span class="p">();</span>
-<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="c1">// 最大ヒープの初期化（ラムダ式でComparatorを変更するだけ）</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="c1">// 最大ヒープを初期化（lambda 式で Comparator を変更すればよい）</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="n">Queue</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="o">&lt;&gt;</span><span class="p">((</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">)</span><span class="w"> </span><span class="o">-&gt;</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">a</span><span class="p">);</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a>
-<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="cm">/* ヒープに要素をプッシュ */</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="cm">/* 要素をヒープに追加 */</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
 <a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
 <a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a>
-<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="cm">/* ヒープの先頭要素を取得 */</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="cm">/* ヒープ頂点の要素を取得 */</span>
 <a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">peek</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
 <a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a>
-<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="cm">/* ヒープの先頭要素をポップ */</span>
-<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="c1">// ポップされた要素は降順のシーケンスを形成</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="cm">/* ヒープ頂点の要素を取り出す */</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="c1">// 取り出された要素は大きい順の列になる</span>
 <a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
 <a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// 4</span>
 <a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// 3</span>
@@ -4642,32 +4642,32 @@
 <a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="cm">/* ヒープのサイズを取得 */</span>
 <a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
 <a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a>
-<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="cm">/* ヒープが空かどうかをチェック */</span>
+<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="cm">/* ヒープが空かどうかを判定 */</span>
 <a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="kt">boolean</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">();</span>
 <a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a>
-<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="cm">/* リストからヒープを作成 */</span>
+<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="cm">/* 入力リストからヒープを構築 */</span>
 <a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="n">minHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">Arrays</span><span class="p">.</span><span class="na">asList</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">));</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">heap.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* ヒープの初期化 */</span>
-<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="c1">// 最小ヒープの初期化</span>
+<div class="highlight"><span class="filename">heap.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* ヒープを初期化 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="c1">// 最小ヒープを初期化</span>
 <a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="n">PriorityQueue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">minHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">();</span>
-<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="c1">// 最大ヒープの初期化（ラムダ式でComparatorを変更するだけ）</span>
-<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="n">PriorityQueue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="n">Comparer</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">.</span><span class="n">Create</span><span class="p">((</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">y</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">y</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">x</span><span class="p">));</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="c1">// 最大ヒープを初期化（lambda 式で Comparer を変更すればよい）</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="n">PriorityQueue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="n">Comparer</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">.</span><span class="n">Create</span><span class="p">((</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">y</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">y</span><span class="p">.</span><span class="n">CompareTo</span><span class="p">(</span><span class="n">x</span><span class="p">)));</span>
 <a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a>
-<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="cm">/* ヒープに要素をプッシュ */</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="cm">/* 要素をヒープに追加 */</span>
 <a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">);</span>
 <a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
 <a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">);</span>
 <a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">);</span>
 <a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a>
-<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="cm">/* ヒープの先頭要素を取得 */</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="cm">/* ヒープ頂点の要素を取得 */</span>
 <a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Peek</span><span class="p">();</span><span class="c1">//5</span>
 <a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a>
-<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="cm">/* ヒープの先頭要素をポップ */</span>
-<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="c1">// ポップされた要素は降順のシーケンスを形成</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="cm">/* ヒープ頂点の要素を取り出す */</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="c1">// 取り出された要素は大きい順の列になる</span>
 <a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w">  </span><span class="c1">// 5</span>
 <a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w">  </span><span class="c1">// 4</span>
 <a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w">  </span><span class="c1">// 3</span>
@@ -4677,74 +4677,74 @@
 <a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="cm">/* ヒープのサイズを取得 */</span>
 <a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Count</span><span class="p">;</span>
 <a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a>
-<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a><span class="cm">/* ヒープが空かどうかをチェック */</span>
+<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a><span class="cm">/* ヒープが空かどうかを判定 */</span>
 <a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a>
-<a id="__codelineno-3-31" name="__codelineno-3-31" href="#__codelineno-3-31"></a><span class="cm">/* リストからヒープを作成 */</span>
+<a id="__codelineno-3-31" name="__codelineno-3-31" href="#__codelineno-3-31"></a><span class="cm">/* 入力リストからヒープを構築 */</span>
 <a id="__codelineno-3-32" name="__codelineno-3-32" href="#__codelineno-3-32"></a><span class="n">minHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="p">([(</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">),</span><span class="w"> </span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">),</span><span class="w"> </span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">),</span><span class="w"> </span><span class="p">(</span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">),</span><span class="w"> </span><span class="p">(</span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">)]);</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">heap.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="c1">// Goでは、heap.Interfaceを実装することで整数の最大ヒープを構築できます</span>
-<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="c1">// heap.Interfaceを実装するには、sort.Interfaceも実装する必要があります</span>
+<div class="highlight"><span class="filename">heap.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="c1">// Go では、heap.Interface を実装することで整数の最大ヒープを構築できる</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="c1">// heap.Interface を実装するには、同時に sort.Interface も実装する必要がある</span>
 <a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="kd">type</span><span class="w"> </span><span class="nx">intHeap</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span>
 <a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a>
-<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="c1">// heap.InterfaceのPushメソッド、要素をヒープにプッシュ</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="c1">// Push は heap.Interface のメソッドで、要素をヒープに追加する</span>
 <a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Push</span><span class="p">(</span><span class="nx">x</span><span class="w"> </span><span class="kt">any</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="c1">// PushとPopの両方でポインタレシーバーを使用</span>
-<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">    </span><span class="c1">// スライスの要素を調整するだけでなく、その長さも変更するため</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="c1">// Push と Pop は pointer receiver を引数に取る</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">    </span><span class="c1">// スライスの内容を調整するだけでなく、スライスの長さも変更するため。</span>
 <a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="o">*</span><span class="nx">h</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">,</span><span class="w"> </span><span class="nx">x</span><span class="p">.(</span><span class="kt">int</span><span class="p">))</span>
 <a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="p">}</span>
 <a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a>
-<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="c1">// heap.InterfaceのPopメソッド、ヒープの先頭要素を削除</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="c1">// Pop は heap.Interface のメソッドで、ヒープ頂点の要素を取り出す</span>
 <a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Pop</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">    </span><span class="c1">// ヒープからポップする要素は末尾に格納</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">    </span><span class="c1">// 取り出す要素は末尾に格納されている</span>
 <a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">    </span><span class="nx">last</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
 <a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">    </span><span class="o">*</span><span class="nx">h</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[:</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
 <a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">last</span>
 <a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="p">}</span>
 <a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a>
-<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="c1">// sort.InterfaceのLenメソッド</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="c1">// Len は sort.Interface のメソッド</span>
 <a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Len</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)</span>
 <a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="p">}</span>
 <a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a>
-<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="c1">// sort.InterfaceのLessメソッド</span>
+<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="c1">// Less は sort.Interface のメソッド</span>
 <a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Less</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w">    </span><span class="c1">// 最小ヒープを実装したい場合は、これを小なり比較に変更</span>
+<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w">    </span><span class="c1">// 最小ヒープを実装する場合は、不等号を小なりに変更する</span>
 <a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">i</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">j</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span>
 <a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="p">}</span>
 <a id="__codelineno-4-30" name="__codelineno-4-30" href="#__codelineno-4-30"></a>
-<a id="__codelineno-4-31" name="__codelineno-4-31" href="#__codelineno-4-31"></a><span class="c1">// sort.InterfaceのSwapメソッド</span>
+<a id="__codelineno-4-31" name="__codelineno-4-31" href="#__codelineno-4-31"></a><span class="c1">// Swap は sort.Interface のメソッド</span>
 <a id="__codelineno-4-32" name="__codelineno-4-32" href="#__codelineno-4-32"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-4-33" name="__codelineno-4-33" href="#__codelineno-4-33"></a><span class="w">    </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">j</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span>
 <a id="__codelineno-4-34" name="__codelineno-4-34" href="#__codelineno-4-34"></a><span class="p">}</span>
 <a id="__codelineno-4-35" name="__codelineno-4-35" href="#__codelineno-4-35"></a>
-<a id="__codelineno-4-36" name="__codelineno-4-36" href="#__codelineno-4-36"></a><span class="c1">// Top ヒープの先頭要素を取得</span>
+<a id="__codelineno-4-36" name="__codelineno-4-36" href="#__codelineno-4-36"></a><span class="c1">// Top はヒープ頂点の要素を取得</span>
 <a id="__codelineno-4-37" name="__codelineno-4-37" href="#__codelineno-4-37"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Top</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-4-38" name="__codelineno-4-38" href="#__codelineno-4-38"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
 <a id="__codelineno-4-39" name="__codelineno-4-39" href="#__codelineno-4-39"></a><span class="p">}</span>
 <a id="__codelineno-4-40" name="__codelineno-4-40" href="#__codelineno-4-40"></a>
-<a id="__codelineno-4-41" name="__codelineno-4-41" href="#__codelineno-4-41"></a><span class="cm">/* ドライバーコード */</span>
+<a id="__codelineno-4-41" name="__codelineno-4-41" href="#__codelineno-4-41"></a><span class="cm">/* Driver Code */</span>
 <a id="__codelineno-4-42" name="__codelineno-4-42" href="#__codelineno-4-42"></a><span class="kd">func</span><span class="w"> </span><span class="nx">TestHeap</span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">testing</span><span class="p">.</span><span class="nx">T</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-4-43" name="__codelineno-4-43" href="#__codelineno-4-43"></a><span class="w">    </span><span class="cm">/* ヒープの初期化 */</span>
-<a id="__codelineno-4-44" name="__codelineno-4-44" href="#__codelineno-4-44"></a><span class="w">    </span><span class="c1">// 最大ヒープの初期化</span>
+<a id="__codelineno-4-43" name="__codelineno-4-43" href="#__codelineno-4-43"></a><span class="w">    </span><span class="cm">/* ヒープを初期化 */</span>
+<a id="__codelineno-4-44" name="__codelineno-4-44" href="#__codelineno-4-44"></a><span class="w">    </span><span class="c1">// 最大ヒープを初期化</span>
 <a id="__codelineno-4-45" name="__codelineno-4-45" href="#__codelineno-4-45"></a><span class="w">    </span><span class="nx">maxHeap</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">intHeap</span><span class="p">{}</span>
 <a id="__codelineno-4-46" name="__codelineno-4-46" href="#__codelineno-4-46"></a><span class="w">    </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Init</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span>
-<a id="__codelineno-4-47" name="__codelineno-4-47" href="#__codelineno-4-47"></a><span class="w">    </span><span class="cm">/* ヒープに要素をプッシュ */</span>
-<a id="__codelineno-4-48" name="__codelineno-4-48" href="#__codelineno-4-48"></a><span class="w">    </span><span class="c1">// heap.Interfaceのメソッドを呼び出して要素を追加</span>
+<a id="__codelineno-4-47" name="__codelineno-4-47" href="#__codelineno-4-47"></a><span class="w">    </span><span class="cm">/* 要素をヒープに追加 */</span>
+<a id="__codelineno-4-48" name="__codelineno-4-48" href="#__codelineno-4-48"></a><span class="w">    </span><span class="c1">// heap.Interface のメソッドを呼び出して要素を追加する</span>
 <a id="__codelineno-4-49" name="__codelineno-4-49" href="#__codelineno-4-49"></a><span class="w">    </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
 <a id="__codelineno-4-50" name="__codelineno-4-50" href="#__codelineno-4-50"></a><span class="w">    </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span>
 <a id="__codelineno-4-51" name="__codelineno-4-51" href="#__codelineno-4-51"></a><span class="w">    </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
 <a id="__codelineno-4-52" name="__codelineno-4-52" href="#__codelineno-4-52"></a><span class="w">    </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span>
 <a id="__codelineno-4-53" name="__codelineno-4-53" href="#__codelineno-4-53"></a><span class="w">    </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span>
 <a id="__codelineno-4-54" name="__codelineno-4-54" href="#__codelineno-4-54"></a>
-<a id="__codelineno-4-55" name="__codelineno-4-55" href="#__codelineno-4-55"></a><span class="w">    </span><span class="cm">/* ヒープの先頭要素を取得 */</span>
+<a id="__codelineno-4-55" name="__codelineno-4-55" href="#__codelineno-4-55"></a><span class="w">    </span><span class="cm">/* ヒープ頂点の要素を取得 */</span>
 <a id="__codelineno-4-56" name="__codelineno-4-56" href="#__codelineno-4-56"></a><span class="w">    </span><span class="nx">top</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">Top</span><span class="p">()</span>
-<a id="__codelineno-4-57" name="__codelineno-4-57" href="#__codelineno-4-57"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Printf</span><span class="p">(</span><span class="s">&quot;ヒープの先頭要素は %d\n&quot;</span><span class="p">,</span><span class="w"> </span><span class="nx">top</span><span class="p">)</span>
+<a id="__codelineno-4-57" name="__codelineno-4-57" href="#__codelineno-4-57"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Printf</span><span class="p">(</span><span class="s">&quot;ヒープ頂点の要素は %d\n&quot;</span><span class="p">,</span><span class="w"> </span><span class="nx">top</span><span class="p">)</span>
 <a id="__codelineno-4-58" name="__codelineno-4-58" href="#__codelineno-4-58"></a>
-<a id="__codelineno-4-59" name="__codelineno-4-59" href="#__codelineno-4-59"></a><span class="w">    </span><span class="cm">/* ヒープの先頭要素をポップ */</span>
-<a id="__codelineno-4-60" name="__codelineno-4-60" href="#__codelineno-4-60"></a><span class="w">    </span><span class="c1">// heap.Interfaceのメソッドを呼び出して要素を削除</span>
+<a id="__codelineno-4-59" name="__codelineno-4-59" href="#__codelineno-4-59"></a><span class="w">    </span><span class="cm">/* ヒープ頂点の要素を取り出す */</span>
+<a id="__codelineno-4-60" name="__codelineno-4-60" href="#__codelineno-4-60"></a><span class="w">    </span><span class="c1">// heap.Interface のメソッドを呼び出して要素を削除する</span>
 <a id="__codelineno-4-61" name="__codelineno-4-61" href="#__codelineno-4-61"></a><span class="w">    </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Pop</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="c1">// 5</span>
 <a id="__codelineno-4-62" name="__codelineno-4-62" href="#__codelineno-4-62"></a><span class="w">    </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Pop</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="c1">// 4</span>
 <a id="__codelineno-4-63" name="__codelineno-4-63" href="#__codelineno-4-63"></a><span class="w">    </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Pop</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="c1">// 3</span>
@@ -4755,28 +4755,28 @@
 <a id="__codelineno-4-68" name="__codelineno-4-68" href="#__codelineno-4-68"></a><span class="w">    </span><span class="nx">size</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span>
 <a id="__codelineno-4-69" name="__codelineno-4-69" href="#__codelineno-4-69"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Printf</span><span class="p">(</span><span class="s">&quot;ヒープ内の要素数は %d\n&quot;</span><span class="p">,</span><span class="w"> </span><span class="nx">size</span><span class="p">)</span>
 <a id="__codelineno-4-70" name="__codelineno-4-70" href="#__codelineno-4-70"></a>
-<a id="__codelineno-4-71" name="__codelineno-4-71" href="#__codelineno-4-71"></a><span class="w">    </span><span class="cm">/* ヒープが空かどうかをチェック */</span>
+<a id="__codelineno-4-71" name="__codelineno-4-71" href="#__codelineno-4-71"></a><span class="w">    </span><span class="cm">/* ヒープが空かどうかを判定 */</span>
 <a id="__codelineno-4-72" name="__codelineno-4-72" href="#__codelineno-4-72"></a><span class="w">    </span><span class="nx">isEmpty</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
-<a id="__codelineno-4-73" name="__codelineno-4-73" href="#__codelineno-4-73"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Printf</span><span class="p">(</span><span class="s">&quot;ヒープは空ですか？ %t\n&quot;</span><span class="p">,</span><span class="w"> </span><span class="nx">isEmpty</span><span class="p">)</span>
+<a id="__codelineno-4-73" name="__codelineno-4-73" href="#__codelineno-4-73"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Printf</span><span class="p">(</span><span class="s">&quot;ヒープは空か %t\n&quot;</span><span class="p">,</span><span class="w"> </span><span class="nx">isEmpty</span><span class="p">)</span>
 <a id="__codelineno-4-74" name="__codelineno-4-74" href="#__codelineno-4-74"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">heap.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* ヒープの初期化 */</span>
-<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="c1">// SwiftのHeap型は最大ヒープと最小ヒープの両方をサポートし、swift-collectionsライブラリが必要</span>
+<div class="highlight"><span class="filename">heap.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* ヒープを初期化 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="c1">// Swift の Heap 型は最大ヒープと最小ヒープの両方をサポートしており、swift-collections の導入が必要</span>
 <a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">var</span><span class="w"> </span><span class="nv">heap</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Heap</span><span class="p">&lt;</span><span class="nb">Int</span><span class="p">&gt;()</span>
 <a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>
-<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="cm">/* ヒープに要素をプッシュ */</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="cm">/* 要素をヒープに追加 */</span>
 <a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="n">heap</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
 <a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="n">heap</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
 <a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="n">heap</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
 <a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="n">heap</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
 <a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="n">heap</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
 <a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a>
-<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="cm">/* ヒープの先頭要素を取得 */</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="cm">/* ヒープ頂点の要素を取得 */</span>
 <a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="kd">var</span><span class="w"> </span><span class="nv">peek</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">heap</span><span class="p">.</span><span class="bp">max</span><span class="p">()</span><span class="o">!</span>
 <a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a>
-<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="cm">/* ヒープの先頭要素をポップ */</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="cm">/* ヒープ頂点の要素を取り出す */</span>
 <a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="n">peek</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">heap</span><span class="p">.</span><span class="n">removeMax</span><span class="p">()</span><span class="w"> </span><span class="c1">// 5</span>
 <a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="n">peek</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">heap</span><span class="p">.</span><span class="n">removeMax</span><span class="p">()</span><span class="w"> </span><span class="c1">// 4</span>
 <a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="n">peek</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">heap</span><span class="p">.</span><span class="n">removeMax</span><span class="p">()</span><span class="w"> </span><span class="c1">// 3</span>
@@ -4786,47 +4786,47 @@
 <a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="cm">/* ヒープのサイズを取得 */</span>
 <a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="kd">let</span><span class="w"> </span><span class="nv">size</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">heap</span><span class="p">.</span><span class="bp">count</span>
 <a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a>
-<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="cm">/* ヒープが空かどうかをチェック */</span>
+<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="cm">/* ヒープが空かどうかを判定 */</span>
 <a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a><span class="kd">let</span><span class="w"> </span><span class="nv">isEmpty</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">heap</span><span class="p">.</span><span class="bp">isEmpty</span>
 <a id="__codelineno-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a>
-<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a><span class="cm">/* リストからヒープを作成 */</span>
+<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a><span class="cm">/* 入力リストからヒープを構築 */</span>
 <a id="__codelineno-5-29" name="__codelineno-5-29" href="#__codelineno-5-29"></a><span class="kd">let</span><span class="w"> </span><span class="nv">heap2</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Heap</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">])</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">heap.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="c1">// JavaScriptは組み込みのHeapクラスを提供していません</span>
+<div class="highlight"><span class="filename">heap.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="c1">// JavaScript には組み込みの Heap クラスがない</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">heap.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="c1">// TypeScriptは組み込みのHeapクラスを提供していません</span>
+<div class="highlight"><span class="filename">heap.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="c1">// TypeScript には組み込みの Heap クラスがない</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">heap.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="c1">// Dartは組み込みのHeapクラスを提供していません</span>
+<div class="highlight"><span class="filename">heap.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="c1">// Dart には組み込みの Heap クラスがない</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">heap.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">collections</span><span class="p">::</span><span class="n">BinaryHeap</span><span class="p">;</span>
 <a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">Reverse</span><span class="p">;</span>
 <a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a>
-<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="cm">/* ヒープの初期化 */</span>
-<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="c1">// 最小ヒープの初期化</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="cm">/* ヒープを初期化 */</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="c1">// 最小ヒープを初期化</span>
 <a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">min_heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BinaryHeap</span><span class="p">::</span><span class="o">&lt;</span><span class="n">Reverse</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
-<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="c1">// 最大ヒープの初期化</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="c1">// 最大ヒープを初期化</span>
 <a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">max_heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BinaryHeap</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
 <a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a>
-<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="cm">/* ヒープに要素をプッシュ */</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="cm">/* 要素をヒープに追加 */</span>
 <a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
 <a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
 <a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
 <a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
 <a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a>
-<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="cm">/* ヒープの先頭要素を取得 */</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="cm">/* ヒープ頂点の要素を取得 */</span>
 <a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">peek</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w">  </span><span class="c1">// 5</span>
 <a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a>
-<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="cm">/* ヒープの先頭要素をポップ */</span>
-<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="c1">// ポップされた要素は降順のシーケンスを形成</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="cm">/* ヒープ頂点の要素を取り出す */</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="c1">// 取り出された要素は大きい順の列になる</span>
 <a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w">   </span><span class="c1">// 5</span>
 <a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w">   </span><span class="c1">// 4</span>
 <a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w">   </span><span class="c1">// 3</span>
@@ -4836,36 +4836,36 @@
 <a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a><span class="cm">/* ヒープのサイズを取得 */</span>
 <a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="kd">let</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
 <a id="__codelineno-9-30" name="__codelineno-9-30" href="#__codelineno-9-30"></a>
-<a id="__codelineno-9-31" name="__codelineno-9-31" href="#__codelineno-9-31"></a><span class="cm">/* ヒープが空かどうかをチェック */</span>
+<a id="__codelineno-9-31" name="__codelineno-9-31" href="#__codelineno-9-31"></a><span class="cm">/* ヒープが空かどうかを判定 */</span>
 <a id="__codelineno-9-32" name="__codelineno-9-32" href="#__codelineno-9-32"></a><span class="kd">let</span><span class="w"> </span><span class="n">is_empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">is_empty</span><span class="p">();</span>
 <a id="__codelineno-9-33" name="__codelineno-9-33" href="#__codelineno-9-33"></a>
-<a id="__codelineno-9-34" name="__codelineno-9-34" href="#__codelineno-9-34"></a><span class="cm">/* リストからヒープを作成 */</span>
+<a id="__codelineno-9-34" name="__codelineno-9-34" href="#__codelineno-9-34"></a><span class="cm">/* 入力リストからヒープを構築 */</span>
 <a id="__codelineno-9-35" name="__codelineno-9-35" href="#__codelineno-9-35"></a><span class="kd">let</span><span class="w"> </span><span class="n">min_heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BinaryHeap</span><span class="p">::</span><span class="n">from</span><span class="p">(</span><span class="fm">vec!</span><span class="p">[</span><span class="n">Reverse</span><span class="p">(</span><span class="mi">1</span><span class="p">),</span><span class="w"> </span><span class="n">Reverse</span><span class="p">(</span><span class="mi">3</span><span class="p">),</span><span class="w"> </span><span class="n">Reverse</span><span class="p">(</span><span class="mi">2</span><span class="p">),</span><span class="w"> </span><span class="n">Reverse</span><span class="p">(</span><span class="mi">5</span><span class="p">),</span><span class="w"> </span><span class="n">Reverse</span><span class="p">(</span><span class="mi">4</span><span class="p">)]);</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">heap.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// Cは組み込みのHeapクラスを提供していません</span>
+<div class="highlight"><span class="filename">heap.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// C には組み込みの Heap クラスがない</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">heap.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* ヒープの初期化 */</span>
-<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="c1">// 最小ヒープの初期化</span>
+<div class="highlight"><span class="filename">heap.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* ヒープを初期化 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="c1">// 最小ヒープを初期化</span>
 <a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="kd">var</span><span class="w"> </span><span class="nv">minHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">()</span>
-<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="c1">// 最大ヒープの初期化（ラムダ式でComparatorを変更するだけ）</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="c1">// 最大ヒープを初期化（lambda 式で Comparator を変更すればよい）</span>
 <a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="kd">val</span><span class="w"> </span><span class="nv">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">a</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="o">-&gt;</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">}</span>
 <a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a>
-<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="cm">/* ヒープに要素をプッシュ */</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="cm">/* 要素をヒープに追加 */</span>
 <a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="m">1</span><span class="p">)</span>
 <a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="m">3</span><span class="p">)</span>
 <a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="m">2</span><span class="p">)</span>
 <a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="m">5</span><span class="p">)</span>
 <a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="m">4</span><span class="p">)</span>
 <a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a>
-<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="cm">/* ヒープの先頭要素を取得 */</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="cm">/* ヒープ頂点の要素を取得 */</span>
 <a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="kd">var</span><span class="w"> </span><span class="nv">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">peek</span><span class="p">()</span><span class="w"> </span><span class="c1">// 5</span>
 <a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a>
-<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="cm">/* ヒープの先頭要素をポップ */</span>
-<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="c1">// ポップされた要素は降順のシーケンスを形成</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="cm">/* ヒープ頂点の要素を取り出す */</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="c1">// 取り出された要素は大きい順の列になる</span>
 <a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">()</span><span class="w"> </span><span class="c1">// 5</span>
 <a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">()</span><span class="w"> </span><span class="c1">// 4</span>
 <a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">()</span><span class="w"> </span><span class="c1">// 3</span>
@@ -4875,234 +4875,364 @@
 <a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="cm">/* ヒープのサイズを取得 */</span>
 <a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="kd">val</span><span class="w"> </span><span class="nv">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">size</span>
 <a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a>
-<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="cm">/* ヒープが空かどうかをチェック */</span>
+<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="cm">/* ヒープが空かどうかを判定 */</span>
 <a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a><span class="kd">val</span><span class="w"> </span><span class="nv">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">()</span>
 <a id="__codelineno-11-30" name="__codelineno-11-30" href="#__codelineno-11-30"></a>
-<a id="__codelineno-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></a><span class="cm">/* リストからヒープを作成 */</span>
+<a id="__codelineno-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></a><span class="cm">/* 入力リストからヒープを構築 */</span>
 <a id="__codelineno-11-32" name="__codelineno-11-32" href="#__codelineno-11-32"></a><span class="n">minHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="p">(</span><span class="n">mutableListOf</span><span class="p">(</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">))</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">heap.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a>
+<div class="highlight"><span class="filename">heap.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1"># Ruby には組み込みの Heap クラスがない</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>実行を可視化</summary>
+<p>https://pythontutor.com/render.html#code=import%20heapq%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%B0%8F%E9%A1%B6%E5%A0%86%0A%20%20%20%20min_heap,%20flag%20%3D%20%5B%5D,%201%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20max_heap,%20flag%20%3D%20%5B%5D,%20-1%0A%20%20%20%20%0A%20%20%20%20%23%20Python%20%E7%9A%84%20heapq%20%E6%A8%A1%E5%9D%97%E9%BB%98%E8%AE%A4%E5%AE%9E%E7%8E%B0%E5%B0%8F%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E8%80%83%E8%99%91%E5%B0%86%E2%80%9C%E5%85%83%E7%B4%A0%E5%8F%96%E8%B4%9F%E2%80%9D%E5%90%8E%E5%86%8D%E5%85%A5%E5%A0%86%EF%BC%8C%E8%BF%99%E6%A0%B7%E5%B0%B1%E5%8F%AF%E4%BB%A5%E5%B0%86%E5%A4%A7%E5%B0%8F%E5%85%B3%E7%B3%BB%E9%A2%A0%E5%80%92%EF%BC%8C%E4%BB%8E%E8%80%8C%E5%AE%9E%E7%8E%B0%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E5%9C%A8%E6%9C%AC%E7%A4%BA%E4%BE%8B%E4%B8%AD%EF%BC%8Cflag%20%3D%201%20%E6%97%B6%E5%AF%B9%E5%BA%94%E5%B0%8F%E9%A1%B6%E5%A0%86%EF%BC%8Cflag%20%3D%20-1%20%E6%97%B6%E5%AF%B9%E5%BA%94%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%85%A5%E5%A0%86%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%201%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%203%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%202%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%205%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%204%29%0A%20%20%20%20%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%0A%20%20%20%20peek%20%3D%20flag%20*%20max_heap%5B0%5D%20%23%205%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%E5%87%BA%E5%A0%86%0A%20%20%20%20%23%20%E5%87%BA%E5%A0%86%E5%85%83%E7%B4%A0%E4%BC%9A%E5%BD%A2%E6%88%90%E4%B8%80%E4%B8%AA%E4%BB%8E%E5%A4%A7%E5%88%B0%E5%B0%8F%E7%9A%84%E5%BA%8F%E5%88%97%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%205%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%204%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%203%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%202%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%201%0A%20%20%20%20%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E5%A0%86%E5%A4%A7%E5%B0%8F%0A%20%20%20%20size%20%3D%20len%28max_heap%29%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%88%A4%E6%96%AD%E5%A0%86%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%0A%20%20%20%20is_empty%20%3D%20not%20max_heap%0A%20%20%20%20%0A%20%20%20%20%23%20%E8%BE%93%E5%85%A5%E5%88%97%E8%A1%A8%E5%B9%B6%E5%BB%BA%E5%A0%86%0A%20%20%20%20min_heap%20%3D%20%5B1,%203,%202,%205,%204%5D%0A%20%20%20%20heapq.heapify%28min_heap%29&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>
+</details>
 <h2 id="812">8.1.2 &nbsp; ヒープの実装<a class="headerlink" href="#812" title="Permanent link">&para;</a></h2>
-<p>以下の実装は最大ヒープです。最小ヒープに変換するには、すべてのサイズ論理比較を反転させるだけです（例えば、<span class="arithmatex">\(\geq\)</span>を<span class="arithmatex">\(\leq\)</span>に置き換える）。興味のある読者は自分で実装することをお勧めします。</p>
+<p>以下では最大ヒープを実装します。最小ヒープに変換したい場合は、すべての大小比較ロジックを反転させるだけです（たとえば、<span class="arithmatex">\(\geq\)</span> を <span class="arithmatex">\(\leq\)</span> に置き換えます）。興味のある読者は自分で実装してみてください。</p>
 <h3 id="1">1. &nbsp; ヒープの格納と表現<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>「二分木」の節で述べたように、完備二分木は配列表現に非常に適しています。ヒープは完備二分木の一種なので、<strong>配列を使用してヒープを格納します</strong>。</p>
-<p>配列を使用して二分木を表現する場合、要素はノード値を表し、インデックスは二分木内のノード位置を表します。<strong>ノードポインタはインデックスマッピング公式を通じて実装されます</strong>。</p>
-<p>下図に示すように、インデックス<span class="arithmatex">\(i\)</span>が与えられた場合、その左の子のインデックスは<span class="arithmatex">\(2i + 1\)</span>、右の子のインデックスは<span class="arithmatex">\(2i + 2\)</span>、親のインデックスは<span class="arithmatex">\((i - 1) / 2\)</span>（床除算）です。インデックスが範囲外の場合、nullノードまたはノードが存在しないことを意味します。</p>
+<p>「二分木」の章で述べたように、完全二分木は配列で表現するのに非常に適しています。ヒープはまさに完全二分木の一種なので、<strong>ここでは配列を使ってヒープを格納します</strong>。</p>
+<p>配列で二分木を表す場合、要素はノードの値を表し、インデックスは二分木におけるノードの位置を表します。<strong>ノード間の参照関係はインデックスの対応式によって実現できます</strong>。</p>
+<p>次の図に示すように、インデックス <span class="arithmatex">\(i\)</span> に対して、左子ノードのインデックスは <span class="arithmatex">\(2i + 1\)</span> 、右子ノードのインデックスは <span class="arithmatex">\(2i + 2\)</span> 、親ノードのインデックスは <span class="arithmatex">\((i - 1) / 2\)</span>（切り捨て除算）です。インデックスが範囲外であれば、空ノードまたはノードが存在しないことを表します。</p>
 <p><img alt="ヒープの表現と格納" class="animation-figure" src="../heap.assets/representation_of_heap.png" /></p>
 <p align="center"> 図 8-2 &nbsp; ヒープの表現と格納 </p>
 
-<p>後で便利に使用するため、インデックスマッピング公式を関数にカプセル化できます：</p>
+<p>インデックスの対応式は関数にまとめておくと、後続で使いやすくなります：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">my_heap.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;左の子ノードのインデックスを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;左子ノードのインデックスを取得&quot;&quot;&quot;</span>
 <a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="k">return</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span>
 <a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>
 <a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="k">def</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;右の子ノードのインデックスを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;右子ノードのインデックスを取得&quot;&quot;&quot;</span>
 <a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>    <span class="k">return</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">2</span>
 <a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>
 <a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="k">def</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
 <a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;親ノードのインデックスを取得&quot;&quot;&quot;</span>
-<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>    <span class="k">return</span> <span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>  <span class="c1"># 整数除算で切り下げ</span>
+<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>    <span class="k">return</span> <span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>  <span class="c1"># 切り捨て除算</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 左の子ノードのインデックスを取得 */</span>
+<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 左子ノードのインデックスを取得 */</span>
 <a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="p">}</span>
 <a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>
-<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="cm">/* 右の子ノードのインデックスを取得 */</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="cm">/* 右子ノードのインデックスを取得 */</span>
 <a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="kt">int</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
 <a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="p">}</span>
 <a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>
 <a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="cm">/* 親ノードのインデックスを取得 */</span>
 <a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 整数除算で切り下げ</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 切り捨て除算</span>
 <a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 左の子ノードのインデックスを取得 */</span>
+<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 左子ノードのインデックスを取得 */</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="p">}</span>
 <a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a>
-<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="cm">/* 右の子ノードのインデックスを取得 */</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="cm">/* 右子ノードのインデックスを取得 */</span>
 <a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="kt">int</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
 <a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="p">}</span>
 <a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a>
 <a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="cm">/* 親ノードのインデックスを取得 */</span>
 <a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 整数除算で切り下げ</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 切り捨て除算</span>
 <a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Left</span><span class="p">}</span>
-<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a>
-<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Right</span><span class="p">}</span>
-<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a>
-<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="na">[class]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Parent</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 左子ノードのインデックスを取得 */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="p">}</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="cm">/* 右子ノードのインデックスを取得 */</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="p">}</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="cm">/* 親ノードのインデックスを取得 */</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 切り捨て除算</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">maxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">left</span><span class="p">}</span>
-<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a>
-<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">maxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">right</span><span class="p">}</span>
-<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a>
-<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">maxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">parent</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 左子ノードのインデックスを取得 */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="o">*</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="p">}</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="cm">/* 右子ノードのインデックスを取得 */</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="o">*</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="p">}</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="cm">/* 親ノードのインデックスを取得 */</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w">    </span><span class="c1">// 切り捨て除算</span>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="kr">left</span><span class="p">}</span>
-<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a>
-<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="kr">right</span><span class="p">}</span>
-<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a>
-<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">parent</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 左子ノードのインデックスを取得 */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="p">}</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="cm">/* 右子ノードのインデックスを取得 */</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="kd">func</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">    </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="p">}</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="cm">/* 親ノードのインデックスを取得 */</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="kd">func</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w">    </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1">// 切り捨て除算</span>
+<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">left</span><span class="p">}</span>
-<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a>
-<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">right</span><span class="p">}</span>
-<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a>
-<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">parent</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 左子ノードのインデックスを取得 */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="n">#left</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="p">}</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="cm">/* 右子ノードのインデックスを取得 */</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="n">#right</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="p">}</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="cm">/* 親ノードのインデックスを取得 */</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="n">#parent</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">((</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 切り捨て除算</span>
+<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">left</span><span class="p">}</span>
-<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a>
-<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">right</span><span class="p">}</span>
-<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a>
-<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">parent</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 左子ノードのインデックスを取得 */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="p">}</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="cm">/* 右子ノードのインデックスを取得 */</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="p">}</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="cm">/* 親ノードのインデックスを取得 */</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">((</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 切り捨て除算</span>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">_left</span><span class="p">}</span>
-<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a>
-<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">_right</span><span class="p">}</span>
-<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a>
-<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">_parent</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 左子ノードのインデックスを取得 */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">_left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="p">}</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="cm">/* 右子ノードのインデックスを取得 */</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="kt">int</span><span class="w"> </span><span class="n">_right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="p">}</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="cm">/* 親ノードのインデックスを取得 */</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="kt">int</span><span class="w"> </span><span class="n">_parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 切り捨て除算</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">left</span><span class="p">}</span>
-<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a>
-<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">right</span><span class="p">}</span>
-<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a>
-<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">parent</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 左子ノードのインデックスを取得 */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="p">}</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="cm">/* 右子ノードのインデックスを取得 */</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="k">fn</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">    </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="p">}</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="cm">/* 親ノードのインデックスを取得 */</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="k">fn</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">    </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1">// 切り捨て除算</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">left</span><span class="p">}</span>
-<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a>
-<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">right</span><span class="p">}</span>
-<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a>
-<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">parent</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 左子ノードのインデックスを取得 */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="p">}</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="cm">/* 右子ノードのインデックスを取得 */</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="kt">int</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="p">}</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="cm">/* 親ノードのインデックスを取得 */</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 切り捨て</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">left</span><span class="p">}</span>
-<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a>
-<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">right</span><span class="p">}</span>
-<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a>
-<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">parent</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 左子ノードのインデックスを取得 */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="p">}</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="cm">/* 右子ノードのインデックスを取得 */</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">2</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="p">}</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="cm">/* 親ノードのインデックスを取得 */</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="c1">// 切り捨て除算</span>
+<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">left</span><span class="p">}</span>
-<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a>
-<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">right</span><span class="p">}</span>
-<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a>
-<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">parent</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### 左子ノードのインデックスを取得 ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="k">end</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="c1">### 右子ノードのインデックスを取得 ###</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="k">def</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w">  </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="k">end</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="c1">### 親ノードのインデックスを取得 ###</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="k">def</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w">  </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="w">     </span><span class="c1"># 切り捨て除算</span>
+<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h3 id="2">2. &nbsp; ヒープの先頭要素へのアクセス<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>ヒープの先頭要素は二分木の根ノードで、リストの最初の要素でもあります：</p>
+<h3 id="2">2. &nbsp; ヒープ頂点の要素にアクセス<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>ヒープ頂点の要素は二分木の根ノード、すなわちリストの先頭要素です：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">my_heap.py</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ヒープの先頭要素にアクセス&quot;&quot;&quot;</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ヒープ先頭要素にアクセス&quot;&quot;&quot;</span>
 <a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>    <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* ヒープの先頭要素にアクセス */</span>
+<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* ヒープ先頭要素にアクセス */</span>
 <a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span>
 <a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* ヒープの先頭要素にアクセス */</span>
+<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* ヒープ先頭要素にアクセス */</span>
 <a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Peek</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* ヒープ先頭要素にアクセス */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">maxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">peek</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* ヒープ先頭要素にアクセス */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">peek</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">peek</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* ヒープ先頭要素にアクセス */</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w">    </span><span class="n">maxHeap</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">peek</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* ヒープ先頭要素にアクセス */</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="nx">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#maxHeap</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span>
+<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">peek</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* ヒープ先頭要素にアクセス */</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="nx">peek</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span>
+<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">peek</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* ヒープ先頭要素にアクセス */</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="m">0</span><span class="p">];</span>
+<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">peek</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* ヒープ先頭要素にアクセス */</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w">    </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="n">first</span><span class="p">().</span><span class="n">copied</span><span class="p">()</span>
+<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">peek</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* ヒープ先頭要素にアクセス */</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">peek</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* ヒープ先頭要素にアクセス */</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">peek</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">[</span><span class="m">0</span><span class="o">]</span>
+<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">peek</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="c1">### ヒープ先頭要素を参照 ###</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">peek</span>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w">  </span><span class="vi">@max_heap</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span>
+<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h3 id="3">3. &nbsp; ヒープへの要素挿入<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
-<p>要素<code>val</code>が与えられた場合、まずそれをヒープの底に追加します。追加後、<code>val</code>がヒープ内の他の要素より大きい可能性があるため、ヒープの完全性が損なわれる可能性があります。<strong>したがって、挿入されたノードから根ノードまでのパスを修復する必要があります</strong>。この操作は<u>ヒープ化</u>と呼ばれます。</p>
-<p>挿入されたノードから開始して、<strong>下から上にヒープ化を実行します</strong>。下図に示すように、挿入されたノードの値をその親ノードと比較し、挿入されたノードが大きい場合はそれらを交換します。次にこの操作を続行し、根に到達するか、交換が不要なノードに遭遇するまで、下から上にヒープ内の各ノードを修復します。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20MaxHeap%3A%0A%20%20%20%20%22%22%22%E6%9C%80%E5%A4%A7%E3%83%92%E3%83%BC%E3%83%97%22%22%22%0A%0A%20%20%20%20def%20__init__%28self%2C%20nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%82%B3%E3%83%B3%E3%82%B9%E3%83%88%E3%83%A9%E3%82%AF%E3%82%BF%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E3%83%AA%E3%82%B9%E3%83%88%E8%A6%81%E7%B4%A0%E3%82%92%E3%81%9D%E3%81%AE%E3%81%BE%E3%81%BE%E3%83%92%E3%83%BC%E3%83%97%E3%81%AB%E8%BF%BD%E5%8A%A0%0A%20%20%20%20%20%20%20%20self.max_heap%20%3D%20nums%0A%0A%20%20%20%20def%20left%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%B7%A6%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E5%8F%96%E5%BE%97%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%8F%B3%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E5%8F%96%E5%BE%97%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%A6%AA%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E5%8F%96%E5%BE%97%22%22%22%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20%2F%2F%202%20%20%23%20%E5%88%87%E3%82%8A%E6%8D%A8%E3%81%A6%E9%99%A4%E7%AE%97%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%83%92%E3%83%BC%E3%83%97%E3%81%AE%E3%82%B5%E3%82%A4%E3%82%BA%E3%82%92%E5%8F%96%E5%BE%97%22%22%22%0A%20%20%20%20%20%20%20%20return%20len%28self.max_heap%29%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%83%92%E3%83%BC%E3%83%97%E3%81%8C%E7%A9%BA%E3%81%8B%E3%81%A9%E3%81%86%E3%81%8B%E3%82%92%E5%88%A4%E5%AE%9A%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.size%28%29%20%3D%3D%200%0A%0A%20%20%20%20def%20peek%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%83%92%E3%83%BC%E3%83%97%E5%85%88%E9%A0%AD%E8%A6%81%E7%B4%A0%E3%81%AB%E3%82%A2%E3%82%AF%E3%82%BB%E3%82%B9%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.max_heap%5B0%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E6%9C%80%E5%A4%A7%E3%83%92%E3%83%BC%E3%83%97%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20%23%20%E5%85%A5%E5%8A%9B%E9%85%8D%E5%88%97%E3%81%AF%E3%81%99%E3%81%A7%E3%81%AB%E6%AD%A3%E5%BD%93%E3%81%AA%E3%83%92%E3%83%BC%E3%83%97%E3%81%A7%E3%81%82%E3%82%8B%E7%82%B9%E3%81%AB%E6%B3%A8%E6%84%8F%0A%20%20%20%20max_heap%20%3D%20MaxHeap%28%5B9%2C%208%2C%206%2C%206%2C%207%2C%205%2C%202%2C%201%2C%204%2C%203%2C%206%2C%202%5D%29%0A%0A%20%20%20%20%23%20%E3%83%92%E3%83%BC%E3%83%97%E9%A0%82%E7%82%B9%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E5%8F%96%E5%BE%97%0A%20%20%20%20peek%20%3D%20max_heap.peek%28%29%0A%20%20%20%20print%28f%22%5Cn%E3%83%92%E3%83%BC%E3%83%97%E5%85%88%E9%A0%AD%E8%A6%81%E7%B4%A0%E3%81%AF%20%7Bpeek%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=7&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20MaxHeap%3A%0A%20%20%20%20%22%22%22%E6%9C%80%E5%A4%A7%E3%83%92%E3%83%BC%E3%83%97%22%22%22%0A%0A%20%20%20%20def%20__init__%28self%2C%20nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%82%B3%E3%83%B3%E3%82%B9%E3%83%88%E3%83%A9%E3%82%AF%E3%82%BF%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E3%83%AA%E3%82%B9%E3%83%88%E8%A6%81%E7%B4%A0%E3%82%92%E3%81%9D%E3%81%AE%E3%81%BE%E3%81%BE%E3%83%92%E3%83%BC%E3%83%97%E3%81%AB%E8%BF%BD%E5%8A%A0%0A%20%20%20%20%20%20%20%20self.max_heap%20%3D%20nums%0A%0A%20%20%20%20def%20left%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%B7%A6%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E5%8F%96%E5%BE%97%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%8F%B3%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E5%8F%96%E5%BE%97%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%A6%AA%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E5%8F%96%E5%BE%97%22%22%22%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20%2F%2F%202%20%20%23%20%E5%88%87%E3%82%8A%E6%8D%A8%E3%81%A6%E9%99%A4%E7%AE%97%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%83%92%E3%83%BC%E3%83%97%E3%81%AE%E3%82%B5%E3%82%A4%E3%82%BA%E3%82%92%E5%8F%96%E5%BE%97%22%22%22%0A%20%20%20%20%20%20%20%20return%20len%28self.max_heap%29%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%83%92%E3%83%BC%E3%83%97%E3%81%8C%E7%A9%BA%E3%81%8B%E3%81%A9%E3%81%86%E3%81%8B%E3%82%92%E5%88%A4%E5%AE%9A%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.size%28%29%20%3D%3D%200%0A%0A%20%20%20%20def%20peek%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%83%92%E3%83%BC%E3%83%97%E5%85%88%E9%A0%AD%E8%A6%81%E7%B4%A0%E3%81%AB%E3%82%A2%E3%82%AF%E3%82%BB%E3%82%B9%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.max_heap%5B0%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E6%9C%80%E5%A4%A7%E3%83%92%E3%83%BC%E3%83%97%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20%23%20%E5%85%A5%E5%8A%9B%E9%85%8D%E5%88%97%E3%81%AF%E3%81%99%E3%81%A7%E3%81%AB%E6%AD%A3%E5%BD%93%E3%81%AA%E3%83%92%E3%83%BC%E3%83%97%E3%81%A7%E3%81%82%E3%82%8B%E7%82%B9%E3%81%AB%E6%B3%A8%E6%84%8F%0A%20%20%20%20max_heap%20%3D%20MaxHeap%28%5B9%2C%208%2C%206%2C%206%2C%207%2C%205%2C%202%2C%201%2C%204%2C%203%2C%206%2C%202%5D%29%0A%0A%20%20%20%20%23%20%E3%83%92%E3%83%BC%E3%83%97%E9%A0%82%E7%82%B9%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E5%8F%96%E5%BE%97%0A%20%20%20%20peek%20%3D%20max_heap.peek%28%29%0A%20%20%20%20print%28f%22%5Cn%E3%83%92%E3%83%BC%E3%83%97%E5%85%88%E9%A0%AD%E8%A6%81%E7%B4%A0%E3%81%AF%20%7Bpeek%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=7&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h3 id="3">3. &nbsp; 要素をヒープに追加<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
+<p>与えられた要素 <code>val</code> を、まずヒープの底に追加します。追加後、<code>val</code> がヒープ内のほかの要素より大きい可能性があるため、ヒープ条件が崩れているかもしれません。<strong>そのため、挿入ノードから根ノードまでの経路上にある各ノードを修復する必要があります</strong>。この操作を<u>ヒープ化（heapify）</u>と呼びます。</p>
+<p>ヒープへ追加したノードから始めて、**下から上へヒープ化**を行います。次の図のように、挿入ノードとその親ノードの値を比較し、挿入ノードのほうが大きければそれらを交換します。その後もこの操作を繰り返し、下から上へ各ノードを修復して、根ノードを越えるか交換不要のノードに達した時点で終了します。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="4:9"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">&lt;1&gt;</label><label for="__tabbed_4_2">&lt;2&gt;</label><label for="__tabbed_4_3">&lt;3&gt;</label><label for="__tabbed_4_4">&lt;4&gt;</label><label for="__tabbed_4_5">&lt;5&gt;</label><label for="__tabbed_4_6">&lt;6&gt;</label><label for="__tabbed_4_7">&lt;7&gt;</label><label for="__tabbed_4_8">&lt;8&gt;</label><label for="__tabbed_4_9">&lt;9&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="ヒープへの要素挿入の手順" class="animation-figure" src="../heap.assets/heap_push_step1.png" /></p>
+<p><img alt="要素をヒープに追加する手順" class="animation-figure" src="../heap.assets/heap_push_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="heap_push_step2" class="animation-figure" src="../heap.assets/heap_push_step2.png" /></p>
@@ -5130,35 +5260,35 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 8-3 &nbsp; ヒープへの要素挿入の手順 </p>
+<p align="center"> 図 8-3 &nbsp; 要素をヒープに追加する手順 </p>
 
-<p>総ノード数を<span class="arithmatex">\(n\)</span>とすると、木の高さは<span class="arithmatex">\(O(\log n)\)</span>です。したがって、ヒープ化操作のループ反復回数は最大<span class="arithmatex">\(O(\log n)\)</span>で、<strong>要素挿入操作の時間計算量は<span class="arithmatex">\(O(\log n)\)</span>になります</strong>。コードは以下の通りです：</p>
+<p>ノード総数を <span class="arithmatex">\(n\)</span> とすると、木の高さは <span class="arithmatex">\(O(\log n)\)</span> です。したがって、ヒープ化操作のループ回数は高々 <span class="arithmatex">\(O(\log n)\)</span> であり、<strong>要素をヒープに追加する操作の時間計算量は <span class="arithmatex">\(O(\log n)\)</span></strong> です。コードは以下のとおりです：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="5:13"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">my_heap.py</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ヒープに要素をプッシュ&quot;&quot;&quot;</span>
+<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;要素をヒープに追加&quot;&quot;&quot;</span>
 <a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a>    <span class="c1"># ノードを追加</span>
 <a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
 <a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a>    <span class="c1"># 下から上へヒープ化</span>
 <a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">sift_up</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
 <a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a>
 <a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">sift_up</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ノードiから開始して、下から上へヒープ化&quot;&quot;&quot;</span>
+<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ノード i から始めて、下から上へヒープ化&quot;&quot;&quot;</span>
 <a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a>    <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
-<a id="__codelineno-39-11" name="__codelineno-39-11" href="#__codelineno-39-11"></a>        <span class="c1"># ノードiの親ノードを取得</span>
+<a id="__codelineno-39-11" name="__codelineno-39-11" href="#__codelineno-39-11"></a>        <span class="c1"># ノード i の親ノードを取得</span>
 <a id="__codelineno-39-12" name="__codelineno-39-12" href="#__codelineno-39-12"></a>        <span class="n">p</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
-<a id="__codelineno-39-13" name="__codelineno-39-13" href="#__codelineno-39-13"></a>        <span class="c1"># 「ルートノードを越える」または「ノードが修復不要」の場合、ヒープ化を終了</span>
+<a id="__codelineno-39-13" name="__codelineno-39-13" href="#__codelineno-39-13"></a>        <span class="c1"># 「根ノードを越えた」または「ノードの修復が不要」になったらヒープ化を終了</span>
 <a id="__codelineno-39-14" name="__codelineno-39-14" href="#__codelineno-39-14"></a>        <span class="k">if</span> <span class="n">p</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&lt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">p</span><span class="p">]:</span>
 <a id="__codelineno-39-15" name="__codelineno-39-15" href="#__codelineno-39-15"></a>            <span class="k">break</span>
-<a id="__codelineno-39-16" name="__codelineno-39-16" href="#__codelineno-39-16"></a>        <span class="c1"># 2つのノードを交換</span>
+<a id="__codelineno-39-16" name="__codelineno-39-16" href="#__codelineno-39-16"></a>        <span class="c1"># 2 つのノードを交換</span>
 <a id="__codelineno-39-17" name="__codelineno-39-17" href="#__codelineno-39-17"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">p</span><span class="p">)</span>
-<a id="__codelineno-39-18" name="__codelineno-39-18" href="#__codelineno-39-18"></a>        <span class="c1"># 上向きのループヒープ化</span>
+<a id="__codelineno-39-18" name="__codelineno-39-18" href="#__codelineno-39-18"></a>        <span class="c1"># ループで下から上へヒープ化</span>
 <a id="__codelineno-39-19" name="__codelineno-39-19" href="#__codelineno-39-19"></a>        <span class="n">i</span> <span class="o">=</span> <span class="n">p</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* ヒープに要素をプッシュ */</span>
+<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* 要素をヒープに追加 */</span>
 <a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w">    </span><span class="c1">// ノードを追加</span>
 <a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w">    </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
@@ -5166,24 +5296,24 @@
 <a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w">    </span><span class="n">siftUp</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="p">}</span>
 <a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a>
-<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="cm">/* ノードiから上向きにヒープ化を開始 */</span>
+<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="cm">/* ノード i から始めて、下から上へヒープ化 */</span>
 <a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftUp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nb">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w">        </span><span class="c1">// ノードiの親ノードを取得</span>
+<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w">        </span><span class="c1">// ノード i の親ノードを取得</span>
 <a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
-<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="w">        </span><span class="c1">// 「ルートノードを超える」または「ノードが修復不要」の場合、ヒープ化を終了</span>
+<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="w">        </span><span class="c1">// 「根ノードを越えた」または「ノードの修復が不要」になったらヒープ化を終了</span>
 <a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">p</span><span class="p">])</span>
 <a id="__codelineno-40-16" name="__codelineno-40-16" href="#__codelineno-40-16"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
-<a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="w">        </span><span class="c1">// 2つのノードを交換</span>
+<a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
 <a id="__codelineno-40-18" name="__codelineno-40-18" href="#__codelineno-40-18"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">p</span><span class="p">]);</span>
-<a id="__codelineno-40-19" name="__codelineno-40-19" href="#__codelineno-40-19"></a><span class="w">        </span><span class="c1">// 上向きにループしてヒープ化</span>
+<a id="__codelineno-40-19" name="__codelineno-40-19" href="#__codelineno-40-19"></a><span class="w">        </span><span class="c1">// ループで下から上へヒープ化</span>
 <a id="__codelineno-40-20" name="__codelineno-40-20" href="#__codelineno-40-20"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
 <a id="__codelineno-40-21" name="__codelineno-40-21" href="#__codelineno-40-21"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-40-22" name="__codelineno-40-22" href="#__codelineno-40-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 要素をヒープにプッシュ */</span>
+<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 要素をヒープに追加 */</span>
 <a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w">    </span><span class="c1">// ノードを追加</span>
 <a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w">    </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
@@ -5191,96 +5321,306 @@
 <a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a><span class="w">    </span><span class="n">siftUp</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="p">}</span>
 <a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a>
-<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="cm">/* ノード i から上向きにヒープ化を開始 */</span>
+<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="cm">/* ノード i から始めて、下から上へヒープ化 */</span>
 <a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftUp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a><span class="w">        </span><span class="c1">// ノード i の親ノードを取得</span>
 <a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
-<a id="__codelineno-41-14" name="__codelineno-41-14" href="#__codelineno-41-14"></a><span class="w">        </span><span class="c1">// 「根ノードを越える」または「ノードが修復不要」の場合、ヒープ化を終了</span>
+<a id="__codelineno-41-14" name="__codelineno-41-14" href="#__codelineno-41-14"></a><span class="w">        </span><span class="c1">// 「根ノードを越えた」または「ノードの修復が不要」になったらヒープ化を終了</span>
 <a id="__codelineno-41-15" name="__codelineno-41-15" href="#__codelineno-41-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">p</span><span class="p">))</span>
 <a id="__codelineno-41-16" name="__codelineno-41-16" href="#__codelineno-41-16"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
-<a id="__codelineno-41-17" name="__codelineno-41-17" href="#__codelineno-41-17"></a><span class="w">        </span><span class="c1">// 2つのノードを交換</span>
+<a id="__codelineno-41-17" name="__codelineno-41-17" href="#__codelineno-41-17"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
 <a id="__codelineno-41-18" name="__codelineno-41-18" href="#__codelineno-41-18"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
-<a id="__codelineno-41-19" name="__codelineno-41-19" href="#__codelineno-41-19"></a><span class="w">        </span><span class="c1">// 上向きにヒープ化をループ</span>
+<a id="__codelineno-41-19" name="__codelineno-41-19" href="#__codelineno-41-19"></a><span class="w">        </span><span class="c1">// ループで下から上へヒープ化</span>
 <a id="__codelineno-41-20" name="__codelineno-41-20" href="#__codelineno-41-20"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
 <a id="__codelineno-41-21" name="__codelineno-41-21" href="#__codelineno-41-21"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-41-22" name="__codelineno-41-22" href="#__codelineno-41-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Push</span><span class="p">}</span>
-<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a>
-<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">SiftUp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="cm">/* 要素をヒープに追加 */</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="w">    </span><span class="c1">// ノードを追加</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w">    </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="w">    </span><span class="c1">// 下から上へヒープ化</span>
+<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a><span class="w">    </span><span class="n">SiftUp</span><span class="p">(</span><span class="n">Size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="p">}</span>
+<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a>
+<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="cm">/* ノード i から始めて、下から上へヒープ化 */</span>
+<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a><span class="k">void</span><span class="w"> </span><span class="nf">SiftUp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="k">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a><span class="w">        </span><span class="c1">// ノード i の親ノードを取得</span>
+<a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-42-14" name="__codelineno-42-14" href="#__codelineno-42-14"></a><span class="w">        </span><span class="c1">// 「根ノードを越えた」または「ノードの修復が不要」な場合は、ヒープ化を終了する</span>
+<a id="__codelineno-42-15" name="__codelineno-42-15" href="#__codelineno-42-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">p</span><span class="p">])</span>
+<a id="__codelineno-42-16" name="__codelineno-42-16" href="#__codelineno-42-16"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-42-17" name="__codelineno-42-17" href="#__codelineno-42-17"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-42-18" name="__codelineno-42-18" href="#__codelineno-42-18"></a><span class="w">        </span><span class="n">Swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
+<a id="__codelineno-42-19" name="__codelineno-42-19" href="#__codelineno-42-19"></a><span class="w">        </span><span class="c1">// ループで下から上へヒープ化</span>
+<a id="__codelineno-42-20" name="__codelineno-42-20" href="#__codelineno-42-20"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
+<a id="__codelineno-42-21" name="__codelineno-42-21" href="#__codelineno-42-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-42-22" name="__codelineno-42-22" href="#__codelineno-42-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">maxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">push</span><span class="p">}</span>
-<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a>
-<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">maxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">siftUp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* 要素をヒープに追加 */</span>
+<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="kt">any</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w">    </span><span class="c1">// ノードを追加</span>
+<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">    </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">)</span>
+<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w">    </span><span class="c1">// 下から上へヒープ化</span>
+<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w">    </span><span class="nx">h</span><span class="p">.</span><span class="nx">siftUp</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="p">}</span>
+<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a>
+<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="cm">/* ノード i から始めて、下から上へヒープ化 */</span>
+<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">siftUp</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">true</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w">        </span><span class="c1">// ノード i の親ノードを取得</span>
+<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="w">        </span><span class="nx">p</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span>
+<a id="__codelineno-43-14" name="__codelineno-43-14" href="#__codelineno-43-14"></a><span class="w">        </span><span class="c1">// 「根ノードを越えた」または「ノードの修復が不要」になったらヒープ化を終了</span>
+<a id="__codelineno-43-15" name="__codelineno-43-15" href="#__codelineno-43-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">p</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">i</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">p</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-16" name="__codelineno-43-16" href="#__codelineno-43-16"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-43-17" name="__codelineno-43-17" href="#__codelineno-43-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-43-18" name="__codelineno-43-18" href="#__codelineno-43-18"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-43-19" name="__codelineno-43-19" href="#__codelineno-43-19"></a><span class="w">        </span><span class="nx">h</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">p</span><span class="p">)</span>
+<a id="__codelineno-43-20" name="__codelineno-43-20" href="#__codelineno-43-20"></a><span class="w">        </span><span class="c1">// ループで下から上へヒープ化</span>
+<a id="__codelineno-43-21" name="__codelineno-43-21" href="#__codelineno-43-21"></a><span class="w">        </span><span class="nx">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">p</span>
+<a id="__codelineno-43-22" name="__codelineno-43-22" href="#__codelineno-43-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-23" name="__codelineno-43-23" href="#__codelineno-43-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">push</span><span class="p">}</span>
-<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a>
-<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">siftUp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* 要素をヒープに追加 */</span>
+<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w">    </span><span class="c1">// ノードを追加</span>
+<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">    </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w">    </span><span class="c1">// 下から上へヒープ化</span>
+<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w">    </span><span class="n">siftUp</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="p">}</span>
+<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a>
+<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="cm">/* ノード i から始めて、下から上へヒープ化 */</span>
+<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="kd">func</span><span class="w"> </span><span class="nf">siftUp</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="kc">true</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="w">        </span><span class="c1">// ノード i の親ノードを取得</span>
+<a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">p</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-44-15" name="__codelineno-44-15" href="#__codelineno-44-15"></a><span class="w">        </span><span class="c1">// 「根ノードを越えた」または「ノードの修復が不要」になったらヒープ化を終了</span>
+<a id="__codelineno-44-16" name="__codelineno-44-16" href="#__codelineno-44-16"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">p</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-17" name="__codelineno-44-17" href="#__codelineno-44-17"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-44-18" name="__codelineno-44-18" href="#__codelineno-44-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-44-19" name="__codelineno-44-19" href="#__codelineno-44-19"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-44-20" name="__codelineno-44-20" href="#__codelineno-44-20"></a><span class="w">        </span><span class="bp">swap</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="n">p</span><span class="p">)</span>
+<a id="__codelineno-44-21" name="__codelineno-44-21" href="#__codelineno-44-21"></a><span class="w">        </span><span class="c1">// ループで下から上へヒープ化</span>
+<a id="__codelineno-44-22" name="__codelineno-44-22" href="#__codelineno-44-22"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">p</span>
+<a id="__codelineno-44-23" name="__codelineno-44-23" href="#__codelineno-44-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-24" name="__codelineno-44-24" href="#__codelineno-44-24"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">push</span><span class="p">}</span>
-<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a>
-<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">siftUp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="cm">/* 要素をヒープに追加 */</span>
+<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w">    </span><span class="c1">// ノードを追加</span>
+<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="n">#maxHeap</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w">    </span><span class="c1">// 下から上へヒープ化</span>
+<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="n">#siftUp</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="p">}</span>
+<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a>
+<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="cm">/* ノード i から始めて、下から上へヒープ化 */</span>
+<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="n">#siftUp</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w">        </span><span class="c1">// ノード i の親ノードを取得</span>
+<a id="__codelineno-45-13" name="__codelineno-45-13" href="#__codelineno-45-13"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#parent</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
+<a id="__codelineno-45-14" name="__codelineno-45-14" href="#__codelineno-45-14"></a><span class="w">        </span><span class="c1">// 「根ノードを越えた」または「ノードの修復が不要」になったらヒープ化を終了</span>
+<a id="__codelineno-45-15" name="__codelineno-45-15" href="#__codelineno-45-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">p</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#maxHeap</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#maxHeap</span><span class="p">[</span><span class="nx">p</span><span class="p">])</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-45-16" name="__codelineno-45-16" href="#__codelineno-45-16"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-45-17" name="__codelineno-45-17" href="#__codelineno-45-17"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">p</span><span class="p">);</span>
+<a id="__codelineno-45-18" name="__codelineno-45-18" href="#__codelineno-45-18"></a><span class="w">        </span><span class="c1">// ループで下から上へヒープ化</span>
+<a id="__codelineno-45-19" name="__codelineno-45-19" href="#__codelineno-45-19"></a><span class="w">        </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">p</span><span class="p">;</span>
+<a id="__codelineno-45-20" name="__codelineno-45-20" href="#__codelineno-45-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-45-21" name="__codelineno-45-21" href="#__codelineno-45-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">push</span><span class="p">}</span>
-<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a>
-<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">siftUp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="cm">/* 要素をヒープに追加 */</span>
+<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w">    </span><span class="c1">// ノードを追加</span>
+<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="w">    </span><span class="c1">// 下から上へヒープ化</span>
+<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="nx">siftUp</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></a><span class="p">}</span>
+<a id="__codelineno-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a>
+<a id="__codelineno-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></a><span class="cm">/* ノード i から始めて、下から上へヒープ化 */</span>
+<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a><span class="nx">siftUp</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-12" name="__codelineno-46-12" href="#__codelineno-46-12"></a><span class="w">        </span><span class="c1">// ノード i の親ノードを取得</span>
+<a id="__codelineno-46-13" name="__codelineno-46-13" href="#__codelineno-46-13"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
+<a id="__codelineno-46-14" name="__codelineno-46-14" href="#__codelineno-46-14"></a><span class="w">        </span><span class="c1">// 「根ノードを越えた」または「ノードの修復が不要」になったらヒープ化を終了</span>
+<a id="__codelineno-46-15" name="__codelineno-46-15" href="#__codelineno-46-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">p</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">p</span><span class="p">])</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-46-16" name="__codelineno-46-16" href="#__codelineno-46-16"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-46-17" name="__codelineno-46-17" href="#__codelineno-46-17"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">p</span><span class="p">);</span>
+<a id="__codelineno-46-18" name="__codelineno-46-18" href="#__codelineno-46-18"></a><span class="w">        </span><span class="c1">// ループで下から上へヒープ化</span>
+<a id="__codelineno-46-19" name="__codelineno-46-19" href="#__codelineno-46-19"></a><span class="w">        </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">p</span><span class="p">;</span>
+<a id="__codelineno-46-20" name="__codelineno-46-20" href="#__codelineno-46-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-46-21" name="__codelineno-46-21" href="#__codelineno-46-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">push</span><span class="p">}</span>
-<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a>
-<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">siftUp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* 要素をヒープに追加 */</span>
+<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w">  </span><span class="c1">// ノードを追加</span>
+<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w">  </span><span class="n">_maxHeap</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="w">  </span><span class="c1">// 下から上へヒープ化</span>
+<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a><span class="w">  </span><span class="n">siftUp</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="p">}</span>
+<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a>
+<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="cm">/* ノード i から始めて、下から上へヒープ化 */</span>
+<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="kt">void</span><span class="w"> </span><span class="n">siftUp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a><span class="w">    </span><span class="c1">// ノード i の親ノードを取得</span>
+<a id="__codelineno-47-13" name="__codelineno-47-13" href="#__codelineno-47-13"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-47-14" name="__codelineno-47-14" href="#__codelineno-47-14"></a><span class="w">    </span><span class="c1">// 「根ノードを越えた」または「ノードの修復が不要」になったらヒープ化を終了</span>
+<a id="__codelineno-47-15" name="__codelineno-47-15" href="#__codelineno-47-15"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="n">p</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-16" name="__codelineno-47-16" href="#__codelineno-47-16"></a><span class="w">      </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-47-17" name="__codelineno-47-17" href="#__codelineno-47-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-47-18" name="__codelineno-47-18" href="#__codelineno-47-18"></a><span class="w">    </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-47-19" name="__codelineno-47-19" href="#__codelineno-47-19"></a><span class="w">    </span><span class="n">_swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
+<a id="__codelineno-47-20" name="__codelineno-47-20" href="#__codelineno-47-20"></a><span class="w">    </span><span class="c1">// ループで下から上へヒープ化</span>
+<a id="__codelineno-47-21" name="__codelineno-47-21" href="#__codelineno-47-21"></a><span class="w">    </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
+<a id="__codelineno-47-22" name="__codelineno-47-22" href="#__codelineno-47-22"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-47-23" name="__codelineno-47-23" href="#__codelineno-47-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">push</span><span class="p">}</span>
-<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a>
-<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">sift_up</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="cm">/* 要素をヒープに追加 */</span>
+<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="w">    </span><span class="c1">// ノードを追加</span>
+<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a><span class="w">    </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a><span class="w">    </span><span class="c1">// 下から上へヒープ化</span>
+<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a><span class="w">    </span><span class="bp">self</span><span class="p">.</span><span class="n">sift_up</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a><span class="p">}</span>
+<a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a>
+<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a><span class="cm">/* ノード i から始めて、下から上へヒープ化 */</span>
+<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a><span class="k">fn</span><span class="w"> </span><span class="nf">sift_up</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-11" name="__codelineno-48-11" href="#__codelineno-48-11"></a><span class="w">    </span><span class="k">loop</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-12" name="__codelineno-48-12" href="#__codelineno-48-12"></a><span class="w">        </span><span class="c1">// ノード i はすでにヒープの先頭ノードなので、ヒープ化を終了する</span>
+<a id="__codelineno-48-13" name="__codelineno-48-13" href="#__codelineno-48-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-14" name="__codelineno-48-14" href="#__codelineno-48-14"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-48-15" name="__codelineno-48-15" href="#__codelineno-48-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-48-16" name="__codelineno-48-16" href="#__codelineno-48-16"></a><span class="w">        </span><span class="c1">// ノード i の親ノードを取得</span>
+<a id="__codelineno-48-17" name="__codelineno-48-17" href="#__codelineno-48-17"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span><span class="p">::</span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-48-18" name="__codelineno-48-18" href="#__codelineno-48-18"></a><span class="w">        </span><span class="c1">// 「ノードの修復が不要」になったら、ヒープ化を終了</span>
+<a id="__codelineno-48-19" name="__codelineno-48-19" href="#__codelineno-48-19"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">p</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-20" name="__codelineno-48-20" href="#__codelineno-48-20"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-48-21" name="__codelineno-48-21" href="#__codelineno-48-21"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-48-22" name="__codelineno-48-22" href="#__codelineno-48-22"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-48-23" name="__codelineno-48-23" href="#__codelineno-48-23"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
+<a id="__codelineno-48-24" name="__codelineno-48-24" href="#__codelineno-48-24"></a><span class="w">        </span><span class="c1">// ループで下から上へヒープ化</span>
+<a id="__codelineno-48-25" name="__codelineno-48-25" href="#__codelineno-48-25"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
+<a id="__codelineno-48-26" name="__codelineno-48-26" href="#__codelineno-48-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-48-27" name="__codelineno-48-27" href="#__codelineno-48-27"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">push</span><span class="p">}</span>
-<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a>
-<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">siftUp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* 要素をヒープに追加 */</span>
+<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="w">    </span><span class="c1">// 通常は、これほど多くのノードを追加すべきではない</span>
+<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="w">        </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;heap is full!&quot;</span><span class="p">);</span>
+<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="w">    </span><span class="c1">// ノードを追加</span>
+<a id="__codelineno-49-9" name="__codelineno-49-9" href="#__codelineno-49-9"></a><span class="w">    </span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-49-10" name="__codelineno-49-10" href="#__codelineno-49-10"></a><span class="w">    </span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-49-11" name="__codelineno-49-11" href="#__codelineno-49-11"></a>
+<a id="__codelineno-49-12" name="__codelineno-49-12" href="#__codelineno-49-12"></a><span class="w">    </span><span class="c1">// 下から上へヒープ化</span>
+<a id="__codelineno-49-13" name="__codelineno-49-13" href="#__codelineno-49-13"></a><span class="w">    </span><span class="n">siftUp</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-49-14" name="__codelineno-49-14" href="#__codelineno-49-14"></a><span class="p">}</span>
+<a id="__codelineno-49-15" name="__codelineno-49-15" href="#__codelineno-49-15"></a>
+<a id="__codelineno-49-16" name="__codelineno-49-16" href="#__codelineno-49-16"></a><span class="cm">/* ノード i から始めて、下から上へヒープ化 */</span>
+<a id="__codelineno-49-17" name="__codelineno-49-17" href="#__codelineno-49-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftUp</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-18" name="__codelineno-49-18" href="#__codelineno-49-18"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nb">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-19" name="__codelineno-49-19" href="#__codelineno-49-19"></a><span class="w">        </span><span class="c1">// ノード i の親ノードを取得</span>
+<a id="__codelineno-49-20" name="__codelineno-49-20" href="#__codelineno-49-20"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-49-21" name="__codelineno-49-21" href="#__codelineno-49-21"></a><span class="w">        </span><span class="c1">// 「根ノードを越えた」または「ノードの修復が不要」になったらヒープ化を終了</span>
+<a id="__codelineno-49-22" name="__codelineno-49-22" href="#__codelineno-49-22"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="n">p</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-23" name="__codelineno-49-23" href="#__codelineno-49-23"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-49-24" name="__codelineno-49-24" href="#__codelineno-49-24"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-49-25" name="__codelineno-49-25" href="#__codelineno-49-25"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-49-26" name="__codelineno-49-26" href="#__codelineno-49-26"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
+<a id="__codelineno-49-27" name="__codelineno-49-27" href="#__codelineno-49-27"></a><span class="w">        </span><span class="c1">// ループで下から上へヒープ化</span>
+<a id="__codelineno-49-28" name="__codelineno-49-28" href="#__codelineno-49-28"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
+<a id="__codelineno-49-29" name="__codelineno-49-29" href="#__codelineno-49-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-49-30" name="__codelineno-49-30" href="#__codelineno-49-30"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.kt</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">push</span><span class="p">}</span>
-<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a>
-<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">siftUp</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.kt</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* 要素をヒープに追加 */</span>
+<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">_val</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w">    </span><span class="c1">// ノードを追加</span>
+<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w">    </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">_val</span><span class="p">)</span>
+<a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="w">    </span><span class="c1">// 下から上へヒープ化</span>
+<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a><span class="w">    </span><span class="n">siftUp</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="p">}</span>
+<a id="__codelineno-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a>
+<a id="__codelineno-50-9" name="__codelineno-50-9" href="#__codelineno-50-9"></a><span class="cm">/* ノード i から始めて、下から上へヒープ化 */</span>
+<a id="__codelineno-50-10" name="__codelineno-50-10" href="#__codelineno-50-10"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">siftUp</span><span class="p">(</span><span class="nb">it</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-11" name="__codelineno-50-11" href="#__codelineno-50-11"></a><span class="w">    </span><span class="c1">// Kotlin の関数引数は不変のため、一時変数を作成する</span>
+<a id="__codelineno-50-12" name="__codelineno-50-12" href="#__codelineno-50-12"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">it</span>
+<a id="__codelineno-50-13" name="__codelineno-50-13" href="#__codelineno-50-13"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-14" name="__codelineno-50-14" href="#__codelineno-50-14"></a><span class="w">        </span><span class="c1">// ノード i の親ノードを取得</span>
+<a id="__codelineno-50-15" name="__codelineno-50-15" href="#__codelineno-50-15"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-50-16" name="__codelineno-50-16" href="#__codelineno-50-16"></a><span class="w">        </span><span class="c1">// 「根ノードを越えた」または「ノードの修復が不要」になったらヒープ化を終了</span>
+<a id="__codelineno-50-17" name="__codelineno-50-17" href="#__codelineno-50-17"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">[</span><span class="n">p</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="k">break</span>
+<a id="__codelineno-50-18" name="__codelineno-50-18" href="#__codelineno-50-18"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-50-19" name="__codelineno-50-19" href="#__codelineno-50-19"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">)</span>
+<a id="__codelineno-50-20" name="__codelineno-50-20" href="#__codelineno-50-20"></a><span class="w">        </span><span class="c1">// ループで下から上へヒープ化</span>
+<a id="__codelineno-50-21" name="__codelineno-50-21" href="#__codelineno-50-21"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span>
+<a id="__codelineno-50-22" name="__codelineno-50-22" href="#__codelineno-50-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-50-23" name="__codelineno-50-23" href="#__codelineno-50-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.rb</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">push</span><span class="p">}</span>
-<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a>
-<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">sift_up</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.rb</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="c1">### 要素をヒープに挿入 ###</span>
+<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w">  </span><span class="c1"># ノードを追加</span>
+<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a><span class="w">  </span><span class="vi">@max_heap</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span>
+<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w">  </span><span class="c1"># 下から上へヒープ化</span>
+<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a><span class="w">  </span><span class="n">sift_up</span><span class="p">(</span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="k">end</span>
+<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a>
+<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a><span class="c1">### ノード i から下から上へヒープ化 ###</span>
+<a id="__codelineno-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></a><span class="k">def</span><span class="w"> </span><span class="nf">sift_up</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-51-11" name="__codelineno-51-11" href="#__codelineno-51-11"></a><span class="w">  </span><span class="kp">loop</span><span class="w"> </span><span class="k">do</span>
+<a id="__codelineno-51-12" name="__codelineno-51-12" href="#__codelineno-51-12"></a><span class="w">    </span><span class="c1"># ノード i の親ノードを取得</span>
+<a id="__codelineno-51-13" name="__codelineno-51-13" href="#__codelineno-51-13"></a><span class="w">    </span><span class="nb">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-51-14" name="__codelineno-51-14" href="#__codelineno-51-14"></a><span class="w">    </span><span class="c1"># 「根ノードを越えた」または「ノードの修復が不要」になったらヒープ化を終了</span>
+<a id="__codelineno-51-15" name="__codelineno-51-15" href="#__codelineno-51-15"></a><span class="w">    </span><span class="k">break</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nb">p</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="vi">@max_heap</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="vi">@max_heap</span><span class="o">[</span><span class="nb">p</span><span class="o">]</span>
+<a id="__codelineno-51-16" name="__codelineno-51-16" href="#__codelineno-51-16"></a><span class="w">    </span><span class="c1"># 2 つのノードを交換</span>
+<a id="__codelineno-51-17" name="__codelineno-51-17" href="#__codelineno-51-17"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="nb">p</span><span class="p">)</span>
+<a id="__codelineno-51-18" name="__codelineno-51-18" href="#__codelineno-51-18"></a><span class="w">    </span><span class="c1"># ループで下から上へヒープ化</span>
+<a id="__codelineno-51-19" name="__codelineno-51-19" href="#__codelineno-51-19"></a><span class="w">    </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">p</span>
+<a id="__codelineno-51-20" name="__codelineno-51-20" href="#__codelineno-51-20"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-51-21" name="__codelineno-51-21" href="#__codelineno-51-21"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h3 id="4">4. &nbsp; ヒープからの先頭要素削除<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
-<p>ヒープの先頭要素は二分木の根ノード、つまりリストの最初の要素です。リストから最初の要素を直接削除すると、二分木内のすべてのノードインデックスが変更され、後続の修復にヒープ化を使用することが困難になります。要素インデックスの変更を最小限に抑えるため、次の手順を使用します。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" 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</iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20MaxHeap%3A%0A%20%20%20%20%22%22%22%E6%9C%80%E5%A4%A7%E3%83%92%E3%83%BC%E3%83%97%22%22%22%0A%0A%20%20%20%20def%20__init__%28self%2C%20nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%82%B3%E3%83%B3%E3%82%B9%E3%83%88%E3%83%A9%E3%82%AF%E3%82%BF%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E3%83%AA%E3%82%B9%E3%83%88%E8%A6%81%E7%B4%A0%E3%82%92%E3%81%9D%E3%81%AE%E3%81%BE%E3%81%BE%E3%83%92%E3%83%BC%E3%83%97%E3%81%AB%E8%BF%BD%E5%8A%A0%0A%20%20%20%20%20%20%20%20self.max_heap%20%3D%20nums%0A%0A%20%20%20%20def%20left%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%B7%A6%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E5%8F%96%E5%BE%97%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%8F%B3%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E5%8F%96%E5%BE%97%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%A6%AA%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E5%8F%96%E5%BE%97%22%22%22%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20%2F%2F%202%20%20%23%20%E5%88%87%E3%82%8A%E6%8D%A8%E3%81%A6%E9%99%A4%E7%AE%97%0A%0A%20%20%20%20def%20swap%28self%2C%20i%3A%20int%2C%20j%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%A6%81%E7%B4%A0%E3%82%92%E4%BA%A4%E6%8F%9B%22%22%22%0A%20%20%20%20%20%20%20%20self.max_heap%5Bi%5D%2C%20self.max_heap%5Bj%5D%20%3D%20self.max_heap%5Bj%5D%2C%20self.max_heap%5Bi%5D%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%83%92%E3%83%BC%E3%83%97%E3%81%AE%E3%82%B5%E3%82%A4%E3%82%BA%E3%82%92%E5%8F%96%E5%BE%97%22%22%22%0A%20%20%20%20%20%20%20%20return%20len%28self.max_heap%29%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%83%92%E3%83%BC%E3%83%97%E3%81%8C%E7%A9%BA%E3%81%8B%E3%81%A9%E3%81%86%E3%81%8B%E3%82%92%E5%88%A4%E5%AE%9A%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.size%28%29%20%3D%3D%200%0A%0A%20%20%20%20def%20push%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%A6%81%E7%B4%A0%E3%82%92%E3%83%92%E3%83%BC%E3%83%97%E3%81%AB%E8%BF%BD%E5%8A%A0%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E8%BF%BD%E5%8A%A0%0A%20%20%20%20%20%20%20%20self.max_heap.append%28val%29%0A%20%20%20%20%20%20%20%20%23%20%E4%B8%8B%E3%81%8B%E3%82%89%E4%B8%8A%E3%81%B8%E3%83%92%E3%83%BC%E3%83%97%E5%8C%96%0A%20%20%20%20%20%20%20%20self.sift_up%28self.size%28%29%20-%201%29%0A%0A%20%20%20%20def%20sift_up%28self%2C%20i%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%83%8E%E3%83%BC%E3%83%89%20i%20%E3%81%8B%E3%82%89%E5%A7%8B%E3%82%81%E3%81%A6%E3%80%81%E4%B8%8B%E3%81%8B%E3%82%89%E4%B8%8A%E3%81%B8%E3%83%92%E3%83%BC%E3%83%97%E5%8C%96%22%22%22%0A%20%20%20%20%20%20%20%20while%20True%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%20i%20%E3%81%AE%E8%A6%AA%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E5%8F%96%E5%BE%97%0A%20%20%20%20%20%20%20%20%20%20%20%20p%20%3D%20self.parent%28i%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E3%80%8C%E6%A0%B9%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E8%B6%8A%E3%81%88%E3%81%9F%E3%80%8D%E3%81%BE%E3%81%9F%E3%81%AF%E3%80%8C%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AE%E4%BF%AE%E5%BE%A9%E3%81%8C%E4%B8%8D%E8%A6%81%E3%80%8D%E3%81%AB%E3%81%AA%E3%81%A3%E3%81%9F%E3%82%89%E3%83%92%E3%83%BC%E3%83%97%E5%8C%96%E3%82%92%E7%B5%82%E4%BA%86%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20p%20%3C%200%20or%20self.max_heap%5Bi%5D%20%3C%3D%20self.max_heap%5Bp%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%202%20%E3%81%A4%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E4%BA%A4%E6%8F%9B%0A%20%20%20%20%20%20%20%20%20%20%20%20self.swap%28i%2C%20p%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%97%E3%81%A7%E4%B8%8B%E3%81%8B%E3%82%89%E4%B8%8A%E3%81%B8%E3%83%92%E3%83%BC%E3%83%97%E5%8C%96%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%3D%20p%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E6%9C%80%E5%A4%A7%E3%83%92%E3%83%BC%E3%83%97%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20%23%20%E5%85%A5%E5%8A%9B%E9%85%8D%E5%88%97%E3%81%AF%E3%81%99%E3%81%A7%E3%81%AB%E6%AD%A3%E5%BD%93%E3%81%AA%E3%83%92%E3%83%BC%E3%83%97%E3%81%A7%E3%81%82%E3%82%8B%E7%82%B9%E3%81%AB%E6%B3%A8%E6%84%8F%0A%20%20%20%20max_heap%20%3D%20MaxHeap%28%5B9%2C%208%2C%206%2C%206%2C%207%2C%205%2C%202%2C%201%2C%204%2C%203%2C%206%2C%202%5D%29%0A%0A%20%20%20%20%23%20%E8%A6%81%E7%B4%A0%E3%82%92%E3%83%92%E3%83%BC%E3%83%97%E3%81%AB%E8%BF%BD%E5%8A%A0%0A%20%20%20%20val%20%3D%207%0A%20%20%20%20max_heap.push%28val%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=8&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h3 id="4">4. &nbsp; ヒープ頂点の要素を取り出す<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
+<p>ヒープ頂点の要素は二分木の根ノード、すなわちリストの先頭要素です。もし先頭要素をそのまま削除すると、二分木内のすべてのノードのインデックスが変化してしまい、その後のヒープ化による修復が困難になります。要素インデックスの変動をできるだけ小さくするため、次の手順を取ります。</p>
 <ol>
-<li>ヒープの先頭要素と底の要素を交換します（根ノードと最も右の葉ノードを交換）。</li>
-<li>交換後、リストからヒープの底を削除します（交換されているため、実際には元の先頭要素が削除される）。</li>
-<li>根ノードから開始して、<strong>上から下にヒープ化を実行します</strong>。</li>
+<li>ヒープ頂点の要素とヒープ底の要素を交換する（根ノードと最も右の葉ノードを交換する）。</li>
+<li>交換後、ヒープ底をリストから削除する（すでに交換済みであるため、実際に削除されるのは元のヒープ頂点の要素であることに注意）。</li>
+<li>根ノードから開始し、**上から下へヒープ化**を行う。</li>
 </ol>
-<p>下図に示すように、<strong>「上から下のヒープ化」の方向は「下から上のヒープ化」と反対です</strong>。根ノードの値をその2つの子と比較し、最大の子と交換します。次に、葉ノードに到達するか、交換が不要なノードに遭遇するまで、この操作を繰り返します。</p>
+<p>次の図のように、**「上から下へのヒープ化」の方向は「下から上へのヒープ化」と逆**です。根ノードの値を 2 つの子ノードと比較し、最大の子ノードと根ノードを交換します。その後、この操作を繰り返し、葉ノードを越えるか交換不要のノードに達した時点で終了します。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="6:10"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">&lt;1&gt;</label><label for="__tabbed_6_2">&lt;2&gt;</label><label for="__tabbed_6_3">&lt;3&gt;</label><label for="__tabbed_6_4">&lt;4&gt;</label><label for="__tabbed_6_5">&lt;5&gt;</label><label for="__tabbed_6_6">&lt;6&gt;</label><label for="__tabbed_6_7">&lt;7&gt;</label><label for="__tabbed_6_8">&lt;8&gt;</label><label for="__tabbed_6_9">&lt;9&gt;</label><label for="__tabbed_6_10">&lt;10&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="ヒープからの先頭要素削除の手順" class="animation-figure" src="../heap.assets/heap_pop_step1.png" /></p>
+<p><img alt="ヒープ頂点の要素を取り出す手順" class="animation-figure" src="../heap.assets/heap_pop_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="heap_pop_step2" class="animation-figure" src="../heap.assets/heap_pop_step2.png" /></p>
@@ -5311,52 +5651,52 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 8-4 &nbsp; ヒープからの先頭要素削除の手順 </p>
+<p align="center"> 図 8-4 &nbsp; ヒープ頂点の要素を取り出す手順 </p>
 
-<p>要素挿入操作と同様に、先頭要素削除操作の時間計算量も<span class="arithmatex">\(O(\log n)\)</span>です。コードは以下の通りです：</p>
+<p>要素をヒープに追加する操作と同様に、ヒープ頂点の要素を取り出す操作の時間計算量も <span class="arithmatex">\(O(\log n)\)</span> です。コードは以下のとおりです：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="7:13"><input checked="checked" id="__tabbed_7_1" name="__tabbed_7" type="radio" /><input id="__tabbed_7_2" name="__tabbed_7" type="radio" /><input id="__tabbed_7_3" name="__tabbed_7" type="radio" /><input id="__tabbed_7_4" name="__tabbed_7" type="radio" /><input id="__tabbed_7_5" name="__tabbed_7" type="radio" /><input id="__tabbed_7_6" name="__tabbed_7" type="radio" /><input id="__tabbed_7_7" name="__tabbed_7" type="radio" /><input id="__tabbed_7_8" name="__tabbed_7" type="radio" /><input id="__tabbed_7_9" name="__tabbed_7" type="radio" /><input id="__tabbed_7_10" name="__tabbed_7" type="radio" /><input id="__tabbed_7_11" name="__tabbed_7" type="radio" /><input id="__tabbed_7_12" name="__tabbed_7" type="radio" /><input id="__tabbed_7_13" name="__tabbed_7" type="radio" /><div class="tabbed-labels"><label for="__tabbed_7_1">Python</label><label for="__tabbed_7_2">C++</label><label for="__tabbed_7_3">Java</label><label for="__tabbed_7_4">C#</label><label for="__tabbed_7_5">Go</label><label for="__tabbed_7_6">Swift</label><label for="__tabbed_7_7">JS</label><label for="__tabbed_7_8">TS</label><label for="__tabbed_7_9">Dart</label><label for="__tabbed_7_10">Rust</label><label for="__tabbed_7_11">C</label><label for="__tabbed_7_12">Kotlin</label><label for="__tabbed_7_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">my_heap.py</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;要素をヒープから出す&quot;&quot;&quot;</span>
-<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a>    <span class="c1"># 空の処理</span>
+<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;要素をヒープから取り出す&quot;&quot;&quot;</span>
+<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a>    <span class="c1"># 空判定の処理</span>
 <a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a>    <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
-<a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a>        <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Heap is empty&quot;</span><span class="p">)</span>
-<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a>    <span class="c1"># ルートノードと最右端の葉ノードを交換（最初の要素と最後の要素を交換）</span>
+<a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a>        <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;ヒープが空です&quot;</span><span class="p">)</span>
+<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a>    <span class="c1"># 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
 <a id="__codelineno-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
 <a id="__codelineno-52-8" name="__codelineno-52-8" href="#__codelineno-52-8"></a>    <span class="c1"># ノードを削除</span>
 <a id="__codelineno-52-9" name="__codelineno-52-9" href="#__codelineno-52-9"></a>    <span class="n">val</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
 <a id="__codelineno-52-10" name="__codelineno-52-10" href="#__codelineno-52-10"></a>    <span class="c1"># 上から下へヒープ化</span>
 <a id="__codelineno-52-11" name="__codelineno-52-11" href="#__codelineno-52-11"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">sift_down</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
-<a id="__codelineno-52-12" name="__codelineno-52-12" href="#__codelineno-52-12"></a>    <span class="c1"># ヒープの先頭要素を返す</span>
+<a id="__codelineno-52-12" name="__codelineno-52-12" href="#__codelineno-52-12"></a>    <span class="c1"># ヒープ先頭要素を返す</span>
 <a id="__codelineno-52-13" name="__codelineno-52-13" href="#__codelineno-52-13"></a>    <span class="k">return</span> <span class="n">val</span>
 <a id="__codelineno-52-14" name="__codelineno-52-14" href="#__codelineno-52-14"></a>
 <a id="__codelineno-52-15" name="__codelineno-52-15" href="#__codelineno-52-15"></a><span class="k">def</span><span class="w"> </span><span class="nf">sift_down</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-52-16" name="__codelineno-52-16" href="#__codelineno-52-16"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ノードiから開始して、上から下へヒープ化&quot;&quot;&quot;</span>
+<a id="__codelineno-52-16" name="__codelineno-52-16" href="#__codelineno-52-16"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ノード i から始めて、上から下へヒープ化&quot;&quot;&quot;</span>
 <a id="__codelineno-52-17" name="__codelineno-52-17" href="#__codelineno-52-17"></a>    <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
-<a id="__codelineno-52-18" name="__codelineno-52-18" href="#__codelineno-52-18"></a>        <span class="c1"># i、l、rの中で最大のノードを決定し、maとする</span>
+<a id="__codelineno-52-18" name="__codelineno-52-18" href="#__codelineno-52-18"></a>        <span class="c1"># ノード i, l, r のうち値が最大のノードを ma とする</span>
 <a id="__codelineno-52-19" name="__codelineno-52-19" href="#__codelineno-52-19"></a>        <span class="n">l</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">ma</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="n">i</span>
 <a id="__codelineno-52-20" name="__codelineno-52-20" href="#__codelineno-52-20"></a>        <span class="k">if</span> <span class="n">l</span> <span class="o">&lt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span> <span class="o">&gt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">ma</span><span class="p">]:</span>
 <a id="__codelineno-52-21" name="__codelineno-52-21" href="#__codelineno-52-21"></a>            <span class="n">ma</span> <span class="o">=</span> <span class="n">l</span>
 <a id="__codelineno-52-22" name="__codelineno-52-22" href="#__codelineno-52-22"></a>        <span class="k">if</span> <span class="n">r</span> <span class="o">&lt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span> <span class="o">&gt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">ma</span><span class="p">]:</span>
 <a id="__codelineno-52-23" name="__codelineno-52-23" href="#__codelineno-52-23"></a>            <span class="n">ma</span> <span class="o">=</span> <span class="n">r</span>
-<a id="__codelineno-52-24" name="__codelineno-52-24" href="#__codelineno-52-24"></a>        <span class="c1"># ノードiが最大またはインデックスl、rが範囲外の場合、さらなるヒープ化は不要、ブレーク</span>
+<a id="__codelineno-52-24" name="__codelineno-52-24" href="#__codelineno-52-24"></a>        <span class="c1"># ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
 <a id="__codelineno-52-25" name="__codelineno-52-25" href="#__codelineno-52-25"></a>        <span class="k">if</span> <span class="n">ma</span> <span class="o">==</span> <span class="n">i</span><span class="p">:</span>
 <a id="__codelineno-52-26" name="__codelineno-52-26" href="#__codelineno-52-26"></a>            <span class="k">break</span>
-<a id="__codelineno-52-27" name="__codelineno-52-27" href="#__codelineno-52-27"></a>        <span class="c1"># 2つのノードを交換</span>
+<a id="__codelineno-52-27" name="__codelineno-52-27" href="#__codelineno-52-27"></a>        <span class="c1"># 2 つのノードを交換</span>
 <a id="__codelineno-52-28" name="__codelineno-52-28" href="#__codelineno-52-28"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">ma</span><span class="p">)</span>
-<a id="__codelineno-52-29" name="__codelineno-52-29" href="#__codelineno-52-29"></a>        <span class="c1"># 下向きのループヒープ化</span>
+<a id="__codelineno-52-29" name="__codelineno-52-29" href="#__codelineno-52-29"></a>        <span class="c1"># ループで上から下へヒープ化</span>
 <a id="__codelineno-52-30" name="__codelineno-52-30" href="#__codelineno-52-30"></a>        <span class="n">i</span> <span class="o">=</span> <span class="n">ma</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 要素がヒープから退出 */</span>
+<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 要素をヒープから取り出す */</span>
 <a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a><span class="w">    </span><span class="c1">// 空の処理</span>
+<a id="__codelineno-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a><span class="w">    </span><span class="c1">// 空判定の処理</span>
 <a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a><span class="w">        </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Heap is empty&quot;</span><span class="p">);</span>
+<a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a><span class="w">        </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;ヒープが空です&quot;</span><span class="p">);</span>
 <a id="__codelineno-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></a><span class="w">    </span><span class="c1">// ルートノードを最も右の葉ノードと交換（最初の要素と最後の要素を交換）</span>
+<a id="__codelineno-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></a><span class="w">    </span><span class="c1">// 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
 <a id="__codelineno-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
 <a id="__codelineno-53-9" name="__codelineno-53-9" href="#__codelineno-53-9"></a><span class="w">    </span><span class="c1">// ノードを削除</span>
 <a id="__codelineno-53-10" name="__codelineno-53-10" href="#__codelineno-53-10"></a><span class="w">    </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
@@ -5364,128 +5704,452 @@
 <a id="__codelineno-53-12" name="__codelineno-53-12" href="#__codelineno-53-12"></a><span class="w">    </span><span class="n">siftDown</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-53-13" name="__codelineno-53-13" href="#__codelineno-53-13"></a><span class="p">}</span>
 <a id="__codelineno-53-14" name="__codelineno-53-14" href="#__codelineno-53-14"></a>
-<a id="__codelineno-53-15" name="__codelineno-53-15" href="#__codelineno-53-15"></a><span class="cm">/* ノードiから下向きにヒープ化を開始 */</span>
+<a id="__codelineno-53-15" name="__codelineno-53-15" href="#__codelineno-53-15"></a><span class="cm">/* ノード i から始めて、上から下へヒープ化 */</span>
 <a id="__codelineno-53-16" name="__codelineno-53-16" href="#__codelineno-53-16"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-53-17" name="__codelineno-53-17" href="#__codelineno-53-17"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nb">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-53-18" name="__codelineno-53-18" href="#__codelineno-53-18"></a><span class="w">        </span><span class="c1">// i、l、rの中で最大のノードを決定し、maとして記録</span>
+<a id="__codelineno-53-18" name="__codelineno-53-18" href="#__codelineno-53-18"></a><span class="w">        </span><span class="c1">// ノード i, l, r のうち値が最大のノードを ma とする</span>
 <a id="__codelineno-53-19" name="__codelineno-53-19" href="#__codelineno-53-19"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
 <a id="__codelineno-53-20" name="__codelineno-53-20" href="#__codelineno-53-20"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
 <a id="__codelineno-53-21" name="__codelineno-53-21" href="#__codelineno-53-21"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
 <a id="__codelineno-53-22" name="__codelineno-53-22" href="#__codelineno-53-22"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
 <a id="__codelineno-53-23" name="__codelineno-53-23" href="#__codelineno-53-23"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
-<a id="__codelineno-53-24" name="__codelineno-53-24" href="#__codelineno-53-24"></a><span class="w">        </span><span class="c1">// ノードiが最大、またはインデックスl、rが範囲外の場合、これ以上のヒープ化は不要、ブレーク</span>
+<a id="__codelineno-53-24" name="__codelineno-53-24" href="#__codelineno-53-24"></a><span class="w">        </span><span class="c1">// ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
 <a id="__codelineno-53-25" name="__codelineno-53-25" href="#__codelineno-53-25"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
 <a id="__codelineno-53-26" name="__codelineno-53-26" href="#__codelineno-53-26"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
 <a id="__codelineno-53-27" name="__codelineno-53-27" href="#__codelineno-53-27"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">]);</span>
-<a id="__codelineno-53-28" name="__codelineno-53-28" href="#__codelineno-53-28"></a><span class="w">        </span><span class="c1">// 下向きにループしてヒープ化</span>
+<a id="__codelineno-53-28" name="__codelineno-53-28" href="#__codelineno-53-28"></a><span class="w">        </span><span class="c1">// ループで上から下へヒープ化</span>
 <a id="__codelineno-53-29" name="__codelineno-53-29" href="#__codelineno-53-29"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
 <a id="__codelineno-53-30" name="__codelineno-53-30" href="#__codelineno-53-30"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-53-31" name="__codelineno-53-31" href="#__codelineno-53-31"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="cm">/* 要素がヒープから退出 */</span>
+<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="cm">/* 要素をヒープから取り出す */</span>
 <a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w">    </span><span class="c1">// 空の処理</span>
+<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w">    </span><span class="c1">// 空判定の処理</span>
 <a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
 <a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w">        </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
-<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w">    </span><span class="c1">// 根ノードを最も右の葉ノードと交換（最初の要素を最後の要素と交換）</span>
+<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w">    </span><span class="c1">// 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
 <a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w">    </span><span class="c1">// ノードを削除</span>
 <a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-54-10" name="__codelineno-54-10" href="#__codelineno-54-10"></a><span class="w">    </span><span class="c1">// 上から下へヒープ化</span>
 <a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a><span class="w">    </span><span class="n">siftDown</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
-<a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="w">    </span><span class="c1">// ヒープの先頭要素を返す</span>
+<a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="w">    </span><span class="c1">// ヒープ先頭要素を返す</span>
 <a id="__codelineno-54-13" name="__codelineno-54-13" href="#__codelineno-54-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
 <a id="__codelineno-54-14" name="__codelineno-54-14" href="#__codelineno-54-14"></a><span class="p">}</span>
 <a id="__codelineno-54-15" name="__codelineno-54-15" href="#__codelineno-54-15"></a>
-<a id="__codelineno-54-16" name="__codelineno-54-16" href="#__codelineno-54-16"></a><span class="cm">/* ノード i から下向きにヒープ化を開始 */</span>
+<a id="__codelineno-54-16" name="__codelineno-54-16" href="#__codelineno-54-16"></a><span class="cm">/* ノード i から始めて、上から下へヒープ化 */</span>
 <a id="__codelineno-54-17" name="__codelineno-54-17" href="#__codelineno-54-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-54-18" name="__codelineno-54-18" href="#__codelineno-54-18"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-54-19" name="__codelineno-54-19" href="#__codelineno-54-19"></a><span class="w">        </span><span class="c1">// i、l、r の中で最大のノードを決定し、ma とする</span>
+<a id="__codelineno-54-19" name="__codelineno-54-19" href="#__codelineno-54-19"></a><span class="w">        </span><span class="c1">// ノード i, l, r のうち値が最大のノードを ma とする</span>
 <a id="__codelineno-54-20" name="__codelineno-54-20" href="#__codelineno-54-20"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
 <a id="__codelineno-54-21" name="__codelineno-54-21" href="#__codelineno-54-21"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">l</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">ma</span><span class="p">))</span>
 <a id="__codelineno-54-22" name="__codelineno-54-22" href="#__codelineno-54-22"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
 <a id="__codelineno-54-23" name="__codelineno-54-23" href="#__codelineno-54-23"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">ma</span><span class="p">))</span>
 <a id="__codelineno-54-24" name="__codelineno-54-24" href="#__codelineno-54-24"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
-<a id="__codelineno-54-25" name="__codelineno-54-25" href="#__codelineno-54-25"></a><span class="w">        </span><span class="c1">// ノード i が最大の場合、またはインデックス l、r が範囲外の場合、さらなるヒープ化は不要、終了</span>
+<a id="__codelineno-54-25" name="__codelineno-54-25" href="#__codelineno-54-25"></a><span class="w">        </span><span class="c1">// ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
 <a id="__codelineno-54-26" name="__codelineno-54-26" href="#__codelineno-54-26"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
 <a id="__codelineno-54-27" name="__codelineno-54-27" href="#__codelineno-54-27"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
-<a id="__codelineno-54-28" name="__codelineno-54-28" href="#__codelineno-54-28"></a><span class="w">        </span><span class="c1">// 2つのノードを交換</span>
+<a id="__codelineno-54-28" name="__codelineno-54-28" href="#__codelineno-54-28"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
 <a id="__codelineno-54-29" name="__codelineno-54-29" href="#__codelineno-54-29"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">);</span>
-<a id="__codelineno-54-30" name="__codelineno-54-30" href="#__codelineno-54-30"></a><span class="w">        </span><span class="c1">// 下向きにヒープ化をループ</span>
+<a id="__codelineno-54-30" name="__codelineno-54-30" href="#__codelineno-54-30"></a><span class="w">        </span><span class="c1">// ループで上から下へヒープ化</span>
 <a id="__codelineno-54-31" name="__codelineno-54-31" href="#__codelineno-54-31"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
 <a id="__codelineno-54-32" name="__codelineno-54-32" href="#__codelineno-54-32"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-54-33" name="__codelineno-54-33" href="#__codelineno-54-33"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Pop</span><span class="p">}</span>
-<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a>
-<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">SiftDown</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="cm">/* 要素をヒープから取り出す */</span>
+<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="w">    </span><span class="c1">// 空判定の処理</span>
+<a id="__codelineno-55-4" name="__codelineno-55-4" href="#__codelineno-55-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsEmpty</span><span class="p">())</span>
+<a id="__codelineno-55-5" name="__codelineno-55-5" href="#__codelineno-55-5"></a><span class="w">        </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="nf">IndexOutOfRangeException</span><span class="p">();</span>
+<a id="__codelineno-55-6" name="__codelineno-55-6" href="#__codelineno-55-6"></a><span class="w">    </span><span class="c1">// 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
+<a id="__codelineno-55-7" name="__codelineno-55-7" href="#__codelineno-55-7"></a><span class="w">    </span><span class="n">Swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">Size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-55-8" name="__codelineno-55-8" href="#__codelineno-55-8"></a><span class="w">    </span><span class="c1">// ノードを削除</span>
+<a id="__codelineno-55-9" name="__codelineno-55-9" href="#__codelineno-55-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Last</span><span class="p">();</span>
+<a id="__codelineno-55-10" name="__codelineno-55-10" href="#__codelineno-55-10"></a><span class="w">    </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="n">Size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-55-11" name="__codelineno-55-11" href="#__codelineno-55-11"></a><span class="w">    </span><span class="c1">// 上から下へヒープ化</span>
+<a id="__codelineno-55-12" name="__codelineno-55-12" href="#__codelineno-55-12"></a><span class="w">    </span><span class="n">SiftDown</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-55-13" name="__codelineno-55-13" href="#__codelineno-55-13"></a><span class="w">    </span><span class="c1">// ヒープ先頭要素を返す</span>
+<a id="__codelineno-55-14" name="__codelineno-55-14" href="#__codelineno-55-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-55-15" name="__codelineno-55-15" href="#__codelineno-55-15"></a><span class="p">}</span>
+<a id="__codelineno-55-16" name="__codelineno-55-16" href="#__codelineno-55-16"></a>
+<a id="__codelineno-55-17" name="__codelineno-55-17" href="#__codelineno-55-17"></a><span class="cm">/* ノード i から始めて、上から下へヒープ化 */</span>
+<a id="__codelineno-55-18" name="__codelineno-55-18" href="#__codelineno-55-18"></a><span class="k">void</span><span class="w"> </span><span class="nf">SiftDown</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-19" name="__codelineno-55-19" href="#__codelineno-55-19"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="k">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-20" name="__codelineno-55-20" href="#__codelineno-55-20"></a><span class="w">        </span><span class="c1">// ノード i, l, r のうち値が最大のノードを ma とする</span>
+<a id="__codelineno-55-21" name="__codelineno-55-21" href="#__codelineno-55-21"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-55-22" name="__codelineno-55-22" href="#__codelineno-55-22"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">Size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
+<a id="__codelineno-55-23" name="__codelineno-55-23" href="#__codelineno-55-23"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
+<a id="__codelineno-55-24" name="__codelineno-55-24" href="#__codelineno-55-24"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">Size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
+<a id="__codelineno-55-25" name="__codelineno-55-25" href="#__codelineno-55-25"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
+<a id="__codelineno-55-26" name="__codelineno-55-26" href="#__codelineno-55-26"></a><span class="w">        </span><span class="c1">// 「ノード i が最大」または「葉ノードを越えた」場合は、ヒープ化を終了する</span>
+<a id="__codelineno-55-27" name="__codelineno-55-27" href="#__codelineno-55-27"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-55-28" name="__codelineno-55-28" href="#__codelineno-55-28"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-55-29" name="__codelineno-55-29" href="#__codelineno-55-29"></a><span class="w">        </span><span class="n">Swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">);</span>
+<a id="__codelineno-55-30" name="__codelineno-55-30" href="#__codelineno-55-30"></a><span class="w">        </span><span class="c1">// ループで上から下へヒープ化</span>
+<a id="__codelineno-55-31" name="__codelineno-55-31" href="#__codelineno-55-31"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
+<a id="__codelineno-55-32" name="__codelineno-55-32" href="#__codelineno-55-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-55-33" name="__codelineno-55-33" href="#__codelineno-55-33"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">maxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">pop</span><span class="p">}</span>
-<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a>
-<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">maxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">siftDown</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="cm">/* 要素をヒープから取り出す */</span>
+<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">pop</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a><span class="w">    </span><span class="c1">// 空判定の処理</span>
+<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a><span class="w">        </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="s">&quot;error&quot;</span><span class="p">)</span>
+<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a><span class="w">    </span><span class="c1">// 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
+<a id="__codelineno-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></a><span class="w">    </span><span class="nx">h</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-56-10" name="__codelineno-56-10" href="#__codelineno-56-10"></a><span class="w">    </span><span class="c1">// ノードを削除</span>
+<a id="__codelineno-56-11" name="__codelineno-56-11" href="#__codelineno-56-11"></a><span class="w">    </span><span class="nx">val</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nb">len</span><span class="p">(</span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-56-12" name="__codelineno-56-12" href="#__codelineno-56-12"></a><span class="w">    </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[:</span><span class="nb">len</span><span class="p">(</span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-56-13" name="__codelineno-56-13" href="#__codelineno-56-13"></a><span class="w">    </span><span class="c1">// 上から下へヒープ化</span>
+<a id="__codelineno-56-14" name="__codelineno-56-14" href="#__codelineno-56-14"></a><span class="w">    </span><span class="nx">h</span><span class="p">.</span><span class="nx">siftDown</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-56-15" name="__codelineno-56-15" href="#__codelineno-56-15"></a>
+<a id="__codelineno-56-16" name="__codelineno-56-16" href="#__codelineno-56-16"></a><span class="w">    </span><span class="c1">// ヒープ先頭要素を返す</span>
+<a id="__codelineno-56-17" name="__codelineno-56-17" href="#__codelineno-56-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">val</span>
+<a id="__codelineno-56-18" name="__codelineno-56-18" href="#__codelineno-56-18"></a><span class="p">}</span>
+<a id="__codelineno-56-19" name="__codelineno-56-19" href="#__codelineno-56-19"></a>
+<a id="__codelineno-56-20" name="__codelineno-56-20" href="#__codelineno-56-20"></a><span class="cm">/* ノード i から始めて、上から下へヒープ化 */</span>
+<a id="__codelineno-56-21" name="__codelineno-56-21" href="#__codelineno-56-21"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">siftDown</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-22" name="__codelineno-56-22" href="#__codelineno-56-22"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">true</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-23" name="__codelineno-56-23" href="#__codelineno-56-23"></a><span class="w">        </span><span class="c1">// ノード i, l, r のうち値が最大のノードを max とする</span>
+<a id="__codelineno-56-24" name="__codelineno-56-24" href="#__codelineno-56-24"></a><span class="w">        </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">r</span><span class="p">,</span><span class="w"> </span><span class="nx">max</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span><span class="w"> </span><span class="nx">i</span>
+<a id="__codelineno-56-25" name="__codelineno-56-25" href="#__codelineno-56-25"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">l</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">max</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-26" name="__codelineno-56-26" href="#__codelineno-56-26"></a><span class="w">            </span><span class="nx">max</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">l</span>
+<a id="__codelineno-56-27" name="__codelineno-56-27" href="#__codelineno-56-27"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-56-28" name="__codelineno-56-28" href="#__codelineno-56-28"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">r</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">max</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-29" name="__codelineno-56-29" href="#__codelineno-56-29"></a><span class="w">            </span><span class="nx">max</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">r</span>
+<a id="__codelineno-56-30" name="__codelineno-56-30" href="#__codelineno-56-30"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-56-31" name="__codelineno-56-31" href="#__codelineno-56-31"></a><span class="w">        </span><span class="c1">// ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
+<a id="__codelineno-56-32" name="__codelineno-56-32" href="#__codelineno-56-32"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">max</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-33" name="__codelineno-56-33" href="#__codelineno-56-33"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-56-34" name="__codelineno-56-34" href="#__codelineno-56-34"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-56-35" name="__codelineno-56-35" href="#__codelineno-56-35"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-56-36" name="__codelineno-56-36" href="#__codelineno-56-36"></a><span class="w">        </span><span class="nx">h</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">max</span><span class="p">)</span>
+<a id="__codelineno-56-37" name="__codelineno-56-37" href="#__codelineno-56-37"></a><span class="w">        </span><span class="c1">// ループで上から下へヒープ化</span>
+<a id="__codelineno-56-38" name="__codelineno-56-38" href="#__codelineno-56-38"></a><span class="w">        </span><span class="nx">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">max</span>
+<a id="__codelineno-56-39" name="__codelineno-56-39" href="#__codelineno-56-39"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-56-40" name="__codelineno-56-40" href="#__codelineno-56-40"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">pop</span><span class="p">}</span>
-<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a>
-<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">siftDown</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 要素をヒープから取り出す */</span>
+<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="w">    </span><span class="c1">// 空判定の処理</span>
+<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="bp">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a><span class="w">        </span><span class="bp">fatalError</span><span class="p">(</span><span class="s">&quot;ヒープが空です&quot;</span><span class="p">)</span>
+<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></a><span class="w">    </span><span class="c1">// 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
+<a id="__codelineno-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w">    </span><span class="bp">swap</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="w">    </span><span class="c1">// ノードを削除</span>
+<a id="__codelineno-57-10" name="__codelineno-57-10" href="#__codelineno-57-10"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">at</span><span class="p">:</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-57-11" name="__codelineno-57-11" href="#__codelineno-57-11"></a><span class="w">    </span><span class="c1">// 上から下へヒープ化</span>
+<a id="__codelineno-57-12" name="__codelineno-57-12" href="#__codelineno-57-12"></a><span class="w">    </span><span class="n">siftDown</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-57-13" name="__codelineno-57-13" href="#__codelineno-57-13"></a><span class="w">    </span><span class="c1">// ヒープ先頭要素を返す</span>
+<a id="__codelineno-57-14" name="__codelineno-57-14" href="#__codelineno-57-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">val</span>
+<a id="__codelineno-57-15" name="__codelineno-57-15" href="#__codelineno-57-15"></a><span class="p">}</span>
+<a id="__codelineno-57-16" name="__codelineno-57-16" href="#__codelineno-57-16"></a>
+<a id="__codelineno-57-17" name="__codelineno-57-17" href="#__codelineno-57-17"></a><span class="cm">/* ノード i から始めて、上から下へヒープ化 */</span>
+<a id="__codelineno-57-18" name="__codelineno-57-18" href="#__codelineno-57-18"></a><span class="kd">func</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-19" name="__codelineno-57-19" href="#__codelineno-57-19"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-57-20" name="__codelineno-57-20" href="#__codelineno-57-20"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="kc">true</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-21" name="__codelineno-57-21" href="#__codelineno-57-21"></a><span class="w">        </span><span class="c1">// ノード i, l, r のうち値が最大のノードを ma とする</span>
+<a id="__codelineno-57-22" name="__codelineno-57-22" href="#__codelineno-57-22"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">l</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kr">left</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-57-23" name="__codelineno-57-23" href="#__codelineno-57-23"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">r</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kr">right</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-57-24" name="__codelineno-57-24" href="#__codelineno-57-24"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">ma</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-57-25" name="__codelineno-57-25" href="#__codelineno-57-25"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">(),</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-26" name="__codelineno-57-26" href="#__codelineno-57-26"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">l</span>
+<a id="__codelineno-57-27" name="__codelineno-57-27" href="#__codelineno-57-27"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-57-28" name="__codelineno-57-28" href="#__codelineno-57-28"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">(),</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-29" name="__codelineno-57-29" href="#__codelineno-57-29"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">r</span>
+<a id="__codelineno-57-30" name="__codelineno-57-30" href="#__codelineno-57-30"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-57-31" name="__codelineno-57-31" href="#__codelineno-57-31"></a><span class="w">        </span><span class="c1">// ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
+<a id="__codelineno-57-32" name="__codelineno-57-32" href="#__codelineno-57-32"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-33" name="__codelineno-57-33" href="#__codelineno-57-33"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-57-34" name="__codelineno-57-34" href="#__codelineno-57-34"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-57-35" name="__codelineno-57-35" href="#__codelineno-57-35"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-57-36" name="__codelineno-57-36" href="#__codelineno-57-36"></a><span class="w">        </span><span class="bp">swap</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="n">ma</span><span class="p">)</span>
+<a id="__codelineno-57-37" name="__codelineno-57-37" href="#__codelineno-57-37"></a><span class="w">        </span><span class="c1">// ループで上から下へヒープ化</span>
+<a id="__codelineno-57-38" name="__codelineno-57-38" href="#__codelineno-57-38"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ma</span>
+<a id="__codelineno-57-39" name="__codelineno-57-39" href="#__codelineno-57-39"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-57-40" name="__codelineno-57-40" href="#__codelineno-57-40"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">pop</span><span class="p">}</span>
-<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a>
-<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">siftDown</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 要素をヒープから取り出す */</span>
+<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="nx">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w">    </span><span class="c1">// 空判定の処理</span>
+<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;ヒープが空です&#39;</span><span class="p">);</span>
+<a id="__codelineno-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a><span class="w">    </span><span class="c1">// 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
+<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="n">#swap</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></a><span class="w">    </span><span class="c1">// ノードを削除</span>
+<a id="__codelineno-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#maxHeap</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></a><span class="w">    </span><span class="c1">// 上から下へヒープ化</span>
+<a id="__codelineno-58-10" name="__codelineno-58-10" href="#__codelineno-58-10"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="n">#siftDown</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-58-11" name="__codelineno-58-11" href="#__codelineno-58-11"></a><span class="w">    </span><span class="c1">// ヒープ先頭要素を返す</span>
+<a id="__codelineno-58-12" name="__codelineno-58-12" href="#__codelineno-58-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-58-13" name="__codelineno-58-13" href="#__codelineno-58-13"></a><span class="p">}</span>
+<a id="__codelineno-58-14" name="__codelineno-58-14" href="#__codelineno-58-14"></a>
+<a id="__codelineno-58-15" name="__codelineno-58-15" href="#__codelineno-58-15"></a><span class="cm">/* ノード i から始めて、上から下へヒープ化 */</span>
+<a id="__codelineno-58-16" name="__codelineno-58-16" href="#__codelineno-58-16"></a><span class="n">#siftDown</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-17" name="__codelineno-58-17" href="#__codelineno-58-17"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-18" name="__codelineno-58-18" href="#__codelineno-58-18"></a><span class="w">        </span><span class="c1">// ノード i, l, r のうち値が最大のノードを ma とする</span>
+<a id="__codelineno-58-19" name="__codelineno-58-19" href="#__codelineno-58-19"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#left</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span>
+<a id="__codelineno-58-20" name="__codelineno-58-20" href="#__codelineno-58-20"></a><span class="w">            </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#right</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
+<a id="__codelineno-58-21" name="__codelineno-58-21" href="#__codelineno-58-21"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-58-22" name="__codelineno-58-22" href="#__codelineno-58-22"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#maxHeap</span><span class="p">[</span><span class="nx">l</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#maxHeap</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">l</span><span class="p">;</span>
+<a id="__codelineno-58-23" name="__codelineno-58-23" href="#__codelineno-58-23"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#maxHeap</span><span class="p">[</span><span class="nx">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#maxHeap</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">r</span><span class="p">;</span>
+<a id="__codelineno-58-24" name="__codelineno-58-24" href="#__codelineno-58-24"></a><span class="w">        </span><span class="c1">// ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
+<a id="__codelineno-58-25" name="__codelineno-58-25" href="#__codelineno-58-25"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">ma</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-58-26" name="__codelineno-58-26" href="#__codelineno-58-26"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-58-27" name="__codelineno-58-27" href="#__codelineno-58-27"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">ma</span><span class="p">);</span>
+<a id="__codelineno-58-28" name="__codelineno-58-28" href="#__codelineno-58-28"></a><span class="w">        </span><span class="c1">// ループで上から下へヒープ化</span>
+<a id="__codelineno-58-29" name="__codelineno-58-29" href="#__codelineno-58-29"></a><span class="w">        </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">ma</span><span class="p">;</span>
+<a id="__codelineno-58-30" name="__codelineno-58-30" href="#__codelineno-58-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-58-31" name="__codelineno-58-31" href="#__codelineno-58-31"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">pop</span><span class="p">}</span>
-<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a>
-<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">siftDown</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="cm">/* 要素をヒープから取り出す */</span>
+<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a><span class="nx">pop</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="w">    </span><span class="c1">// 空判定の処理</span>
+<a id="__codelineno-59-4" name="__codelineno-59-4" href="#__codelineno-59-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">RangeError</span><span class="p">(</span><span class="s1">&#39;Heap is empty.&#39;</span><span class="p">);</span>
+<a id="__codelineno-59-5" name="__codelineno-59-5" href="#__codelineno-59-5"></a><span class="w">    </span><span class="c1">// 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
+<a id="__codelineno-59-6" name="__codelineno-59-6" href="#__codelineno-59-6"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-59-7" name="__codelineno-59-7" href="#__codelineno-59-7"></a><span class="w">    </span><span class="c1">// ノードを削除</span>
+<a id="__codelineno-59-8" name="__codelineno-59-8" href="#__codelineno-59-8"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-59-9" name="__codelineno-59-9" href="#__codelineno-59-9"></a><span class="w">    </span><span class="c1">// 上から下へヒープ化</span>
+<a id="__codelineno-59-10" name="__codelineno-59-10" href="#__codelineno-59-10"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="nx">siftDown</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-59-11" name="__codelineno-59-11" href="#__codelineno-59-11"></a><span class="w">    </span><span class="c1">// ヒープ先頭要素を返す</span>
+<a id="__codelineno-59-12" name="__codelineno-59-12" href="#__codelineno-59-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-59-13" name="__codelineno-59-13" href="#__codelineno-59-13"></a><span class="p">}</span>
+<a id="__codelineno-59-14" name="__codelineno-59-14" href="#__codelineno-59-14"></a>
+<a id="__codelineno-59-15" name="__codelineno-59-15" href="#__codelineno-59-15"></a><span class="cm">/* ノード i から始めて、上から下へヒープ化 */</span>
+<a id="__codelineno-59-16" name="__codelineno-59-16" href="#__codelineno-59-16"></a><span class="nx">siftDown</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-17" name="__codelineno-59-17" href="#__codelineno-59-17"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-18" name="__codelineno-59-18" href="#__codelineno-59-18"></a><span class="w">        </span><span class="c1">// ノード i, l, r のうち値が最大のノードを ma とする</span>
+<a id="__codelineno-59-19" name="__codelineno-59-19" href="#__codelineno-59-19"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span>
+<a id="__codelineno-59-20" name="__codelineno-59-20" href="#__codelineno-59-20"></a><span class="w">            </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
+<a id="__codelineno-59-21" name="__codelineno-59-21" href="#__codelineno-59-21"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-59-22" name="__codelineno-59-22" href="#__codelineno-59-22"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">l</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">l</span><span class="p">;</span>
+<a id="__codelineno-59-23" name="__codelineno-59-23" href="#__codelineno-59-23"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">r</span><span class="p">;</span>
+<a id="__codelineno-59-24" name="__codelineno-59-24" href="#__codelineno-59-24"></a><span class="w">        </span><span class="c1">// ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
+<a id="__codelineno-59-25" name="__codelineno-59-25" href="#__codelineno-59-25"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">ma</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-59-26" name="__codelineno-59-26" href="#__codelineno-59-26"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-59-27" name="__codelineno-59-27" href="#__codelineno-59-27"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">ma</span><span class="p">);</span>
+<a id="__codelineno-59-28" name="__codelineno-59-28" href="#__codelineno-59-28"></a><span class="w">        </span><span class="c1">// ループで上から下へヒープ化</span>
+<a id="__codelineno-59-29" name="__codelineno-59-29" href="#__codelineno-59-29"></a><span class="w">        </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">ma</span><span class="p">;</span>
+<a id="__codelineno-59-30" name="__codelineno-59-30" href="#__codelineno-59-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-59-31" name="__codelineno-59-31" href="#__codelineno-59-31"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">pop</span><span class="p">}</span>
-<a id="__codelineno-60-2" name="__codelineno-60-2" href="#__codelineno-60-2"></a>
-<a id="__codelineno-60-3" name="__codelineno-60-3" href="#__codelineno-60-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">siftDown</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="cm">/* 要素をヒープから取り出す */</span>
+<a id="__codelineno-60-2" name="__codelineno-60-2" href="#__codelineno-60-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-3" name="__codelineno-60-3" href="#__codelineno-60-3"></a><span class="w">  </span><span class="c1">// 空判定の処理</span>
+<a id="__codelineno-60-4" name="__codelineno-60-4" href="#__codelineno-60-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">Exception</span><span class="p">(</span><span class="s1">&#39;ヒープが空です&#39;</span><span class="p">);</span>
+<a id="__codelineno-60-5" name="__codelineno-60-5" href="#__codelineno-60-5"></a><span class="w">  </span><span class="c1">// 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
+<a id="__codelineno-60-6" name="__codelineno-60-6" href="#__codelineno-60-6"></a><span class="w">  </span><span class="n">_swap</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-60-7" name="__codelineno-60-7" href="#__codelineno-60-7"></a><span class="w">  </span><span class="c1">// ノードを削除</span>
+<a id="__codelineno-60-8" name="__codelineno-60-8" href="#__codelineno-60-8"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">.</span><span class="n">removeLast</span><span class="p">();</span>
+<a id="__codelineno-60-9" name="__codelineno-60-9" href="#__codelineno-60-9"></a><span class="w">  </span><span class="c1">// 上から下へヒープ化</span>
+<a id="__codelineno-60-10" name="__codelineno-60-10" href="#__codelineno-60-10"></a><span class="w">  </span><span class="n">siftDown</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-60-11" name="__codelineno-60-11" href="#__codelineno-60-11"></a><span class="w">  </span><span class="c1">// ヒープ先頭要素を返す</span>
+<a id="__codelineno-60-12" name="__codelineno-60-12" href="#__codelineno-60-12"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-60-13" name="__codelineno-60-13" href="#__codelineno-60-13"></a><span class="p">}</span>
+<a id="__codelineno-60-14" name="__codelineno-60-14" href="#__codelineno-60-14"></a>
+<a id="__codelineno-60-15" name="__codelineno-60-15" href="#__codelineno-60-15"></a><span class="cm">/* ノード i から始めて、上から下へヒープ化 */</span>
+<a id="__codelineno-60-16" name="__codelineno-60-16" href="#__codelineno-60-16"></a><span class="kt">void</span><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-17" name="__codelineno-60-17" href="#__codelineno-60-17"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-18" name="__codelineno-60-18" href="#__codelineno-60-18"></a><span class="w">    </span><span class="c1">// ノード i, l, r のうち値が最大のノードを ma とする</span>
+<a id="__codelineno-60-19" name="__codelineno-60-19" href="#__codelineno-60-19"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_left</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-60-20" name="__codelineno-60-20" href="#__codelineno-60-20"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_right</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-60-21" name="__codelineno-60-21" href="#__codelineno-60-21"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-60-22" name="__codelineno-60-22" href="#__codelineno-60-22"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
+<a id="__codelineno-60-23" name="__codelineno-60-23" href="#__codelineno-60-23"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
+<a id="__codelineno-60-24" name="__codelineno-60-24" href="#__codelineno-60-24"></a><span class="w">    </span><span class="c1">// ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
+<a id="__codelineno-60-25" name="__codelineno-60-25" href="#__codelineno-60-25"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-60-26" name="__codelineno-60-26" href="#__codelineno-60-26"></a><span class="w">    </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-60-27" name="__codelineno-60-27" href="#__codelineno-60-27"></a><span class="w">    </span><span class="n">_swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">);</span>
+<a id="__codelineno-60-28" name="__codelineno-60-28" href="#__codelineno-60-28"></a><span class="w">    </span><span class="c1">// ループで上から下へヒープ化</span>
+<a id="__codelineno-60-29" name="__codelineno-60-29" href="#__codelineno-60-29"></a><span class="w">    </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
+<a id="__codelineno-60-30" name="__codelineno-60-30" href="#__codelineno-60-30"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-60-31" name="__codelineno-60-31" href="#__codelineno-60-31"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">pop</span><span class="p">}</span>
-<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a>
-<a id="__codelineno-61-3" name="__codelineno-61-3" href="#__codelineno-61-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">sift_down</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="cm">/* 要素をヒープから取り出す */</span>
+<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-3" name="__codelineno-61-3" href="#__codelineno-61-3"></a><span class="w">    </span><span class="c1">// 空判定の処理</span>
+<a id="__codelineno-61-4" name="__codelineno-61-4" href="#__codelineno-61-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">is_empty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-5" name="__codelineno-61-5" href="#__codelineno-61-5"></a><span class="w">        </span><span class="fm">panic!</span><span class="p">(</span><span class="s">&quot;index out of bounds&quot;</span><span class="p">);</span>
+<a id="__codelineno-61-6" name="__codelineno-61-6" href="#__codelineno-61-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-61-7" name="__codelineno-61-7" href="#__codelineno-61-7"></a><span class="w">    </span><span class="c1">// 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
+<a id="__codelineno-61-8" name="__codelineno-61-8" href="#__codelineno-61-8"></a><span class="w">    </span><span class="bp">self</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-61-9" name="__codelineno-61-9" href="#__codelineno-61-9"></a><span class="w">    </span><span class="c1">// ノードを削除</span>
+<a id="__codelineno-61-10" name="__codelineno-61-10" href="#__codelineno-61-10"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span>
+<a id="__codelineno-61-11" name="__codelineno-61-11" href="#__codelineno-61-11"></a><span class="w">    </span><span class="c1">// 上から下へヒープ化</span>
+<a id="__codelineno-61-12" name="__codelineno-61-12" href="#__codelineno-61-12"></a><span class="w">    </span><span class="bp">self</span><span class="p">.</span><span class="n">sift_down</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-61-13" name="__codelineno-61-13" href="#__codelineno-61-13"></a><span class="w">    </span><span class="c1">// ヒープ先頭要素を返す</span>
+<a id="__codelineno-61-14" name="__codelineno-61-14" href="#__codelineno-61-14"></a><span class="w">    </span><span class="n">val</span>
+<a id="__codelineno-61-15" name="__codelineno-61-15" href="#__codelineno-61-15"></a><span class="p">}</span>
+<a id="__codelineno-61-16" name="__codelineno-61-16" href="#__codelineno-61-16"></a>
+<a id="__codelineno-61-17" name="__codelineno-61-17" href="#__codelineno-61-17"></a><span class="cm">/* ノード i から始めて、上から下へヒープ化 */</span>
+<a id="__codelineno-61-18" name="__codelineno-61-18" href="#__codelineno-61-18"></a><span class="k">fn</span><span class="w"> </span><span class="nf">sift_down</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-19" name="__codelineno-61-19" href="#__codelineno-61-19"></a><span class="w">    </span><span class="k">loop</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-20" name="__codelineno-61-20" href="#__codelineno-61-20"></a><span class="w">        </span><span class="c1">// ノード i, l, r のうち値が最大のノードを ma とする</span>
+<a id="__codelineno-61-21" name="__codelineno-61-21" href="#__codelineno-61-21"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">,</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">ma</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="bp">Self</span><span class="p">::</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="bp">Self</span><span class="p">::</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-61-22" name="__codelineno-61-22" href="#__codelineno-61-22"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-23" name="__codelineno-61-23" href="#__codelineno-61-23"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
+<a id="__codelineno-61-24" name="__codelineno-61-24" href="#__codelineno-61-24"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-61-25" name="__codelineno-61-25" href="#__codelineno-61-25"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-26" name="__codelineno-61-26" href="#__codelineno-61-26"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
+<a id="__codelineno-61-27" name="__codelineno-61-27" href="#__codelineno-61-27"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-61-28" name="__codelineno-61-28" href="#__codelineno-61-28"></a><span class="w">        </span><span class="c1">// ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
+<a id="__codelineno-61-29" name="__codelineno-61-29" href="#__codelineno-61-29"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-30" name="__codelineno-61-30" href="#__codelineno-61-30"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-61-31" name="__codelineno-61-31" href="#__codelineno-61-31"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-61-32" name="__codelineno-61-32" href="#__codelineno-61-32"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-61-33" name="__codelineno-61-33" href="#__codelineno-61-33"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">);</span>
+<a id="__codelineno-61-34" name="__codelineno-61-34" href="#__codelineno-61-34"></a><span class="w">        </span><span class="c1">// ループで上から下へヒープ化</span>
+<a id="__codelineno-61-35" name="__codelineno-61-35" href="#__codelineno-61-35"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
+<a id="__codelineno-61-36" name="__codelineno-61-36" href="#__codelineno-61-36"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-61-37" name="__codelineno-61-37" href="#__codelineno-61-37"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">pop</span><span class="p">}</span>
-<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a>
-<a id="__codelineno-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">siftDown</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="cm">/* 要素をヒープから取り出す */</span>
+<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></a><span class="w">    </span><span class="c1">// 空判定の処理</span>
+<a id="__codelineno-62-4" name="__codelineno-62-4" href="#__codelineno-62-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-5" name="__codelineno-62-5" href="#__codelineno-62-5"></a><span class="w">        </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;heap is empty!&quot;</span><span class="p">);</span>
+<a id="__codelineno-62-6" name="__codelineno-62-6" href="#__codelineno-62-6"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">;</span>
+<a id="__codelineno-62-7" name="__codelineno-62-7" href="#__codelineno-62-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-62-8" name="__codelineno-62-8" href="#__codelineno-62-8"></a><span class="w">    </span><span class="c1">// 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
+<a id="__codelineno-62-9" name="__codelineno-62-9" href="#__codelineno-62-9"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-62-10" name="__codelineno-62-10" href="#__codelineno-62-10"></a><span class="w">    </span><span class="c1">// ノードを削除</span>
+<a id="__codelineno-62-11" name="__codelineno-62-11" href="#__codelineno-62-11"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-62-12" name="__codelineno-62-12" href="#__codelineno-62-12"></a><span class="w">    </span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-62-13" name="__codelineno-62-13" href="#__codelineno-62-13"></a><span class="w">    </span><span class="c1">// 上から下へヒープ化</span>
+<a id="__codelineno-62-14" name="__codelineno-62-14" href="#__codelineno-62-14"></a><span class="w">    </span><span class="n">siftDown</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-62-15" name="__codelineno-62-15" href="#__codelineno-62-15"></a>
+<a id="__codelineno-62-16" name="__codelineno-62-16" href="#__codelineno-62-16"></a><span class="w">    </span><span class="c1">// ヒープ先頭要素を返す</span>
+<a id="__codelineno-62-17" name="__codelineno-62-17" href="#__codelineno-62-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-62-18" name="__codelineno-62-18" href="#__codelineno-62-18"></a><span class="p">}</span>
+<a id="__codelineno-62-19" name="__codelineno-62-19" href="#__codelineno-62-19"></a>
+<a id="__codelineno-62-20" name="__codelineno-62-20" href="#__codelineno-62-20"></a><span class="cm">/* ノード i から始めて、上から下へヒープ化 */</span>
+<a id="__codelineno-62-21" name="__codelineno-62-21" href="#__codelineno-62-21"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-22" name="__codelineno-62-22" href="#__codelineno-62-22"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nb">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-23" name="__codelineno-62-23" href="#__codelineno-62-23"></a><span class="w">        </span><span class="c1">// ノード i, l, r のうち値が最大のノードを max とする</span>
+<a id="__codelineno-62-24" name="__codelineno-62-24" href="#__codelineno-62-24"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-62-25" name="__codelineno-62-25" href="#__codelineno-62-25"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-62-26" name="__codelineno-62-26" href="#__codelineno-62-26"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-62-27" name="__codelineno-62-27" href="#__codelineno-62-27"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="n">max</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-28" name="__codelineno-62-28" href="#__codelineno-62-28"></a><span class="w">            </span><span class="n">max</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
+<a id="__codelineno-62-29" name="__codelineno-62-29" href="#__codelineno-62-29"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-62-30" name="__codelineno-62-30" href="#__codelineno-62-30"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="n">max</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-31" name="__codelineno-62-31" href="#__codelineno-62-31"></a><span class="w">            </span><span class="n">max</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
+<a id="__codelineno-62-32" name="__codelineno-62-32" href="#__codelineno-62-32"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-62-33" name="__codelineno-62-33" href="#__codelineno-62-33"></a><span class="w">        </span><span class="c1">// ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
+<a id="__codelineno-62-34" name="__codelineno-62-34" href="#__codelineno-62-34"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">max</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-35" name="__codelineno-62-35" href="#__codelineno-62-35"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-62-36" name="__codelineno-62-36" href="#__codelineno-62-36"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-62-37" name="__codelineno-62-37" href="#__codelineno-62-37"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-62-38" name="__codelineno-62-38" href="#__codelineno-62-38"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">max</span><span class="p">);</span>
+<a id="__codelineno-62-39" name="__codelineno-62-39" href="#__codelineno-62-39"></a><span class="w">        </span><span class="c1">// ループで上から下へヒープ化</span>
+<a id="__codelineno-62-40" name="__codelineno-62-40" href="#__codelineno-62-40"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">;</span>
+<a id="__codelineno-62-41" name="__codelineno-62-41" href="#__codelineno-62-41"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-62-42" name="__codelineno-62-42" href="#__codelineno-62-42"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.kt</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">pop</span><span class="p">}</span>
-<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a>
-<a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">siftDown</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.kt</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="cm">/* 要素をヒープから取り出す */</span>
+<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">pop</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a><span class="w">    </span><span class="c1">// 空判定の処理</span>
+<a id="__codelineno-63-4" name="__codelineno-63-4" href="#__codelineno-63-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">()</span>
+<a id="__codelineno-63-5" name="__codelineno-63-5" href="#__codelineno-63-5"></a><span class="w">    </span><span class="c1">// 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
+<a id="__codelineno-63-6" name="__codelineno-63-6" href="#__codelineno-63-6"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></a><span class="w">    </span><span class="c1">// ノードを削除</span>
+<a id="__codelineno-63-8" name="__codelineno-63-8" href="#__codelineno-63-8"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">_val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">removeAt</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-63-9" name="__codelineno-63-9" href="#__codelineno-63-9"></a><span class="w">    </span><span class="c1">// 上から下へヒープ化</span>
+<a id="__codelineno-63-10" name="__codelineno-63-10" href="#__codelineno-63-10"></a><span class="w">    </span><span class="n">siftDown</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
+<a id="__codelineno-63-11" name="__codelineno-63-11" href="#__codelineno-63-11"></a><span class="w">    </span><span class="c1">// ヒープ先頭要素を返す</span>
+<a id="__codelineno-63-12" name="__codelineno-63-12" href="#__codelineno-63-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_val</span>
+<a id="__codelineno-63-13" name="__codelineno-63-13" href="#__codelineno-63-13"></a><span class="p">}</span>
+<a id="__codelineno-63-14" name="__codelineno-63-14" href="#__codelineno-63-14"></a>
+<a id="__codelineno-63-15" name="__codelineno-63-15" href="#__codelineno-63-15"></a><span class="cm">/* ノード i から始めて、上から下へヒープ化 */</span>
+<a id="__codelineno-63-16" name="__codelineno-63-16" href="#__codelineno-63-16"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="nb">it</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-17" name="__codelineno-63-17" href="#__codelineno-63-17"></a><span class="w">    </span><span class="c1">// Kotlin の関数引数は不変のため、一時変数を作成する</span>
+<a id="__codelineno-63-18" name="__codelineno-63-18" href="#__codelineno-63-18"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">it</span>
+<a id="__codelineno-63-19" name="__codelineno-63-19" href="#__codelineno-63-19"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-20" name="__codelineno-63-20" href="#__codelineno-63-20"></a><span class="w">        </span><span class="c1">// ノード i, l, r のうち値が最大のノードを ma とする</span>
+<a id="__codelineno-63-21" name="__codelineno-63-21" href="#__codelineno-63-21"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-63-22" name="__codelineno-63-22" href="#__codelineno-63-22"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-63-23" name="__codelineno-63-23" href="#__codelineno-63-23"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-63-24" name="__codelineno-63-24" href="#__codelineno-63-24"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">[</span><span class="n">l</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span>
+<a id="__codelineno-63-25" name="__codelineno-63-25" href="#__codelineno-63-25"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">[</span><span class="n">r</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span>
+<a id="__codelineno-63-26" name="__codelineno-63-26" href="#__codelineno-63-26"></a><span class="w">        </span><span class="c1">// ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
+<a id="__codelineno-63-27" name="__codelineno-63-27" href="#__codelineno-63-27"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">break</span>
+<a id="__codelineno-63-28" name="__codelineno-63-28" href="#__codelineno-63-28"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-63-29" name="__codelineno-63-29" href="#__codelineno-63-29"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">)</span>
+<a id="__codelineno-63-30" name="__codelineno-63-30" href="#__codelineno-63-30"></a><span class="w">        </span><span class="c1">// ループで上から下へヒープ化</span>
+<a id="__codelineno-63-31" name="__codelineno-63-31" href="#__codelineno-63-31"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span>
+<a id="__codelineno-63-32" name="__codelineno-63-32" href="#__codelineno-63-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-63-33" name="__codelineno-63-33" href="#__codelineno-63-33"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">my_heap.rb</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">pop</span><span class="p">}</span>
-<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a>
-<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">sift_down</span><span class="p">}</span>
+<div class="highlight"><span class="filename">my_heap.rb</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="c1">### 要素をヒープから取り出す ###</span>
+<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">pop</span>
+<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a><span class="w">  </span><span class="c1"># 空判定の処理</span>
+<a id="__codelineno-64-4" name="__codelineno-64-4" href="#__codelineno-64-4"></a><span class="w">  </span><span class="k">raise</span><span class="w"> </span><span class="no">IndexError</span><span class="p">,</span><span class="w"> </span><span class="s2">&quot;ヒープが空です&quot;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_empty?</span>
+<a id="__codelineno-64-5" name="__codelineno-64-5" href="#__codelineno-64-5"></a><span class="w">  </span><span class="c1"># 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
+<a id="__codelineno-64-6" name="__codelineno-64-6" href="#__codelineno-64-6"></a><span class="w">  </span><span class="n">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-64-7" name="__codelineno-64-7" href="#__codelineno-64-7"></a><span class="w">  </span><span class="c1"># ノードを削除</span>
+<a id="__codelineno-64-8" name="__codelineno-64-8" href="#__codelineno-64-8"></a><span class="w">  </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@max_heap</span><span class="o">.</span><span class="n">pop</span>
+<a id="__codelineno-64-9" name="__codelineno-64-9" href="#__codelineno-64-9"></a><span class="w">  </span><span class="c1"># 上から下へヒープ化</span>
+<a id="__codelineno-64-10" name="__codelineno-64-10" href="#__codelineno-64-10"></a><span class="w">  </span><span class="n">sift_down</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-64-11" name="__codelineno-64-11" href="#__codelineno-64-11"></a><span class="w">  </span><span class="c1"># ヒープ先頭要素を返す</span>
+<a id="__codelineno-64-12" name="__codelineno-64-12" href="#__codelineno-64-12"></a><span class="w">  </span><span class="n">val</span>
+<a id="__codelineno-64-13" name="__codelineno-64-13" href="#__codelineno-64-13"></a><span class="k">end</span>
+<a id="__codelineno-64-14" name="__codelineno-64-14" href="#__codelineno-64-14"></a>
+<a id="__codelineno-64-15" name="__codelineno-64-15" href="#__codelineno-64-15"></a><span class="c1">### ノード i から上から下へヒープ化 ###</span>
+<a id="__codelineno-64-16" name="__codelineno-64-16" href="#__codelineno-64-16"></a><span class="k">def</span><span class="w"> </span><span class="nf">sift_down</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-64-17" name="__codelineno-64-17" href="#__codelineno-64-17"></a><span class="w">  </span><span class="kp">loop</span><span class="w"> </span><span class="k">do</span>
+<a id="__codelineno-64-18" name="__codelineno-64-18" href="#__codelineno-64-18"></a><span class="w">    </span><span class="c1"># ノード i, l, r のうち値が最大のノードを ma とする</span>
+<a id="__codelineno-64-19" name="__codelineno-64-19" href="#__codelineno-64-19"></a><span class="w">    </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-64-20" name="__codelineno-64-20" href="#__codelineno-64-20"></a><span class="w">    </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="vi">@max_heap</span><span class="o">[</span><span class="n">l</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="vi">@max_heap</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span>
+<a id="__codelineno-64-21" name="__codelineno-64-21" href="#__codelineno-64-21"></a><span class="w">    </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="vi">@max_heap</span><span class="o">[</span><span class="n">r</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="vi">@max_heap</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span>
+<a id="__codelineno-64-22" name="__codelineno-64-22" href="#__codelineno-64-22"></a>
+<a id="__codelineno-64-23" name="__codelineno-64-23" href="#__codelineno-64-23"></a><span class="w">    </span><span class="c1"># ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
+<a id="__codelineno-64-24" name="__codelineno-64-24" href="#__codelineno-64-24"></a><span class="w">    </span><span class="k">break</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-64-25" name="__codelineno-64-25" href="#__codelineno-64-25"></a>
+<a id="__codelineno-64-26" name="__codelineno-64-26" href="#__codelineno-64-26"></a><span class="w">    </span><span class="c1"># 2 つのノードを交換</span>
+<a id="__codelineno-64-27" name="__codelineno-64-27" href="#__codelineno-64-27"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">)</span>
+<a id="__codelineno-64-28" name="__codelineno-64-28" href="#__codelineno-64-28"></a><span class="w">    </span><span class="c1"># ループで上から下へヒープ化</span>
+<a id="__codelineno-64-29" name="__codelineno-64-29" href="#__codelineno-64-29"></a><span class="w">    </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span>
+<a id="__codelineno-64-30" name="__codelineno-64-30" href="#__codelineno-64-30"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-64-31" name="__codelineno-64-31" href="#__codelineno-64-31"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h2 id="813">8.1.3 &nbsp; ヒープの一般的な応用<a class="headerlink" href="#813" title="Permanent link">&para;</a></h2>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20MaxHeap%3A%0A%0A%20%20%20%20def%20__init__%28self%2C%20nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%20%20%20%20self.max_heap%20%3D%20nums%0A%0A%20%20%20%20def%20left%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20%2F%2F%202%0A%0A%20%20%20%20def%20swap%28self%2C%20i%3A%20int%2C%20j%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.max_heap%5Bi%5D%2C%20self.max_heap%5Bj%5D%20%3D%20%28self.max_heap%5Bj%5D%2C%20self.max_heap%5Bi%5D%29%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%20len%28self.max_heap%29%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20return%20self.size%28%29%20%3D%3D%200%0A%0A%20%20%20%20def%20pop%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20if%20self.is_empty%28%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%27%E3%83%92%E3%83%BC%E3%83%97%E3%81%8C%E7%A9%BA%E3%81%A7%E3%81%99%27%29%0A%20%20%20%20%20%20%20%20self.swap%280%2C%20self.size%28%29%20-%201%29%0A%20%20%20%20%20%20%20%20val%20%3D%20self.max_heap.pop%28%29%0A%20%20%20%20%20%20%20%20self.sift_down%280%29%0A%20%20%20%20%20%20%20%20return%20val%0A%0A%20%20%20%20def%20sift_down%28self%2C%20i%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20while%20True%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20l%2C%20r%2C%20ma%20%3D%20%28self.left%28i%29%2C%20self.right%28i%29%2C%20i%29%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20l%20%3C%20self.size%28%29%20and%20self.max_heap%5Bl%5D%20%3E%20self.max_heap%5Bma%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20ma%20%3D%20l%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20r%20%3C%20self.size%28%29%20and%20self.max_heap%5Br%5D%20%3E%20self.max_heap%5Bma%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20ma%20%3D%20r%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20ma%20%3D%3D%20i%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20%20%20%20%20self.swap%28i%2C%20ma%29%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%3D%20ma%0Aif%20__name__%20%3D%3D%20%27__main__%27%3A%0A%20%20%20%20max_heap%20%3D%20MaxHeap%28%5B9%2C%208%2C%207%2C%206%2C%207%2C%206%2C%202%2C%201%2C%204%2C%203%2C%206%2C%202%2C%205%5D%29%0A%20%20%20%20peek%20%3D%20max_heap.pop%28%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=8&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20MaxHeap%3A%0A%0A%20%20%20%20def%20__init__%28self%2C%20nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%20%20%20%20self.max_heap%20%3D%20nums%0A%0A%20%20%20%20def%20left%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20%2F%2F%202%0A%0A%20%20%20%20def%20swap%28self%2C%20i%3A%20int%2C%20j%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.max_heap%5Bi%5D%2C%20self.max_heap%5Bj%5D%20%3D%20%28self.max_heap%5Bj%5D%2C%20self.max_heap%5Bi%5D%29%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%20len%28self.max_heap%29%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20return%20self.size%28%29%20%3D%3D%200%0A%0A%20%20%20%20def%20pop%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20if%20self.is_empty%28%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%27%E3%83%92%E3%83%BC%E3%83%97%E3%81%8C%E7%A9%BA%E3%81%A7%E3%81%99%27%29%0A%20%20%20%20%20%20%20%20self.swap%280%2C%20self.size%28%29%20-%201%29%0A%20%20%20%20%20%20%20%20val%20%3D%20self.max_heap.pop%28%29%0A%20%20%20%20%20%20%20%20self.sift_down%280%29%0A%20%20%20%20%20%20%20%20return%20val%0A%0A%20%20%20%20def%20sift_down%28self%2C%20i%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20while%20True%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20l%2C%20r%2C%20ma%20%3D%20%28self.left%28i%29%2C%20self.right%28i%29%2C%20i%29%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20l%20%3C%20self.size%28%29%20and%20self.max_heap%5Bl%5D%20%3E%20self.max_heap%5Bma%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20ma%20%3D%20l%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20r%20%3C%20self.size%28%29%20and%20self.max_heap%5Br%5D%20%3E%20self.max_heap%5Bma%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20ma%20%3D%20r%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20ma%20%3D%3D%20i%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20%20%20%20%20self.swap%28i%2C%20ma%29%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%3D%20ma%0Aif%20__name__%20%3D%3D%20%27__main__%27%3A%0A%20%20%20%20max_heap%20%3D%20MaxHeap%28%5B9%2C%208%2C%207%2C%206%2C%207%2C%206%2C%202%2C%201%2C%204%2C%203%2C%206%2C%202%2C%205%5D%29%0A%20%20%20%20peek%20%3D%20max_heap.pop%28%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=8&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h2 id="813">8.1.3 &nbsp; ヒープの代表的な応用<a class="headerlink" href="#813" title="Permanent link">&para;</a></h2>
 <ul>
-<li><strong>優先度キュー</strong>：ヒープは優先度キューを実装するための好ましいデータ構造で、エンキュー操作とデキュー操作の両方の時間計算量が<span class="arithmatex">\(O(\log n)\)</span>、キュー構築の時間計算量が<span class="arithmatex">\(O(n)\)</span>で、すべて非常に効率的です。</li>
-<li><strong>ヒープソート</strong>：データセットが与えられた場合、それらからヒープを作成し、次に要素削除操作を継続的に実行して順序付けされたデータを取得できます。ただし、ヒープソートを実装するより洗練された方法があり、「ヒープソート」の章で説明されています。</li>
-<li><strong>最大<span class="arithmatex">\(k\)</span>個の要素の発見</strong>：これは古典的なアルゴリズム問題であり、一般的な使用例でもあります。Weiboホット検索のトップ10ホットニュースの選択や、トップ10の売れ筋商品の選択などです。</li>
+<li><strong>優先度付きキュー</strong>：ヒープは、優先度付きキューを実装するための代表的なデータ構造です。キューへの追加と取り出しの時間計算量はいずれも <span class="arithmatex">\(O(\log n)\)</span> で、ヒープ構築は <span class="arithmatex">\(O(n)\)</span> であり、これらの操作はいずれも非常に効率的です。</li>
+<li><strong>ヒープソート</strong>：与えられたデータ群からヒープを構築し、要素の取り出しを繰り返すことで整列済みデータを得られます。ただし、通常はより洗練された方法でヒープソートを実装します。詳しくは「ヒープソート」の章を参照してください。</li>
+<li><strong>最大の <span class="arithmatex">\(k\)</span> 個の要素を取得</strong>：これは古典的なアルゴリズム問題であると同時に、典型的な応用でもあります。たとえば、人気上位 10 件のニュースをホットトピックとして選んだり、売上上位 10 件の商品を選んだりする場面です。</li>
 </ul>
 
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-    aria-label="次: 8.2 &amp;nbsp; ヒープ構築操作"
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       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
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-    8.2 &nbsp; ヒープ構築操作
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-    10.2 &nbsp; 二分探索の挿入点
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-    10.4 &nbsp; ハッシュ最適化戦略
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
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+    12.3 &nbsp; 二分木の構築問題
   
 
     
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+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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+    13.4 &nbsp; n クイーン問題
   
 
     
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+    15.1 &nbsp; 貪欲法
   
 
     
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-    16.2 &nbsp; 一緒に創作に参加する
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@@ -4277,13 +4277,13 @@
 <p><img alt="ヒープ" class="cover-image" src="../assets/covers/chapter_heap.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>ヒープは山とその険しい峰のように、層をなして起伏し、それぞれが独特の形を持っています。</p>
-<p>各山の頂は散らばった高さで上下しますが、最も高いものが常に最初に注目を集めます。</p>
+<p>ヒープは連なる山々の峰のように、幾重にも重なり、さまざまな形をしている。</p>
+<p>いくつもの山の高さはまちまちだが、最も高い峰がいつも最初に目に入る。</p>
 </div>
 <h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
 <li><a href="heap/">8.1 &nbsp; ヒープ</a></li>
-<li><a href="build_heap/">8.2 &nbsp; ヒープ構築操作</a></li>
+<li><a href="build_heap/">8.2 &nbsp; ヒープ構築</a></li>
 <li><a href="top_k/">8.3 &nbsp; Top-k 問題</a></li>
 <li><a href="summary/">8.4 &nbsp; まとめ</a></li>
 </ul>
diff --git a/ja/chapter_heap/summary/index.html b/ja/chapter_heap/summary/index.html
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@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
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     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
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-    序
+    はじめに
   
 
     
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-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
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             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
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-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
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-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
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   <a href="#1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; 重要な復習
+        1. &nbsp; 重要なポイントの振り返り
       
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-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
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-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3241,7 +3241,7 @@
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
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-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3631,7 +3631,7 @@
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-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3659,7 +3659,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3687,7 +3687,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3715,7 +3715,7 @@
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-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3908,7 +3908,7 @@
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4153,7 +4153,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4299,7 +4299,7 @@
   <a href="#1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; 重要な復習
+        1. &nbsp; 重要なポイントの振り返り
       
     </span>
   </a>
@@ -4355,19 +4355,19 @@
 
 <!-- Page content -->
 <h1 id="84">8.4 &nbsp; まとめ<a class="headerlink" href="#84" title="Permanent link">&para;</a></h1>
-<h3 id="1">1. &nbsp; 重要な復習<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<h3 id="1">1. &nbsp; 重要なポイントの振り返り<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
-<li>ヒープは完備二分木で、その構築性質に基づいて最大ヒープまたは最小ヒープに分類できます。最大ヒープの先頭要素は最大で、最小ヒープの先頭要素は最小です。</li>
-<li>優先度キューは、デキューの優先度を持つキューとして定義され、通常ヒープを使用して実装されます。</li>
-<li>ヒープの一般的な操作とそれに対応する時間計算量には以下があります：ヒープへの要素挿入<span class="arithmatex">\(O(\log n)\)</span>、ヒープからの先頭要素削除<span class="arithmatex">\(O(\log n)\)</span>、ヒープの先頭要素へのアクセス<span class="arithmatex">\(O(1)\)</span>。</li>
-<li>完備二分木は配列で表現するのに適しているため、ヒープは一般的に配列を使用して格納されます。</li>
-<li>ヒープ化操作はヒープの性質を維持するために使用され、ヒープの挿入操作と削除操作の両方で使用されます。</li>
-<li><span class="arithmatex">\(n\)</span>個の要素が入力として与えられた場合のヒープ構築の時間計算量は<span class="arithmatex">\(O(n)\)</span>に最適化でき、これは非常に効率的です。</li>
-<li>Top-kは古典的なアルゴリズム問題で、ヒープデータ構造を使用して効率的に解決でき、時間計算量は<span class="arithmatex">\(O(n \log k)\)</span>です。</li>
+<li>ヒープは完全二分木であり、条件の違いによって最大ヒープと最小ヒープに分けられる。最大（最小）ヒープの根の要素は最大値（最小値）である。</li>
+<li>優先度付きキューとは、取り出し時に優先度が考慮されるキューであり、通常はヒープを用いて実装される。</li>
+<li>ヒープの代表的な操作とそれに対応する時間計算量には、要素の挿入 <span class="arithmatex">\(O(\log n)\)</span>、根の要素の削除 <span class="arithmatex">\(O(\log n)\)</span>、根の要素へのアクセス <span class="arithmatex">\(O(1)\)</span> などがある。</li>
+<li>完全二分木は配列で表現するのに非常に適しているため、通常は配列を使ってヒープを格納する。</li>
+<li>ヒープ化操作はヒープの性質を保つために用いられ、挿入操作と削除操作の両方で使用される。</li>
+<li><span class="arithmatex">\(n\)</span> 個の要素を入力してヒープを構築する時間計算量は <span class="arithmatex">\(O(n)\)</span> まで最適化でき、非常に効率的である。</li>
+<li>Top-k は古典的なアルゴリズム問題であり、ヒープ構造を用いることで効率的に解くことができ、時間計算量は <span class="arithmatex">\(O(n \log k)\)</span> である。</li>
 </ul>
 <h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
-<p><strong>Q</strong>: データ構造の「ヒープ」とメモリ管理の「ヒープ」は同じ概念ですか？</p>
-<p>この2つは、どちらも「ヒープ」と呼ばれますが、同じ概念ではありません。コンピュータシステムメモリのヒープは動的メモリ割り当ての一部で、プログラムが実行中にデータを格納するために使用できます。プログラムは、オブジェクトや配列などの複雑な構造を格納するために、一定量のヒープメモリを要求できます。割り当てられたデータが不要になったときは、メモリリークを防ぐためにプログラムがこのメモリを解放する必要があります。スタックメモリと比較して、ヒープメモリの管理と使用にはより多くの注意が必要で、不適切な使用はメモリリークやダングリングポインタにつながる可能性があります。</p>
+<p><strong>Q</strong>：データ構造の「ヒープ」とメモリ管理の「ヒープ」は同じ概念ですか？</p>
+<p>両者は同じ概念ではなく、たまたまどちらも「ヒープ」と呼ばれているだけである。コンピュータシステムのメモリにおけるヒープは動的メモリ割り当ての一部であり、プログラムは実行時にこれを使ってデータを格納できる。プログラムは一定量のヒープメモリを要求し、オブジェクトや配列などの複雑な構造を保存できる。これらのデータが不要になったときは、メモリリークを防ぐためにそのメモリを解放する必要がある。スタックメモリと比べると、ヒープメモリの管理と使用にはより慎重さが求められ、不適切に扱うとメモリリークやダングリングポインタなどの問題を引き起こす可能性がある。</p>
 
 <!-- Source file information -->
 
diff --git a/ja/chapter_heap/top_k/index.html b/ja/chapter_heap/top_k/index.html
index adc1d5fa3..48744757f 100644
--- a/ja/chapter_heap/top_k/index.html
+++ b/ja/chapter_heap/top_k/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -39,7 +39,7 @@
     
     
       
-        <title>8.3 Top-k問題 - Hello アルゴリズム</title>
+        <title>8.3 Top-k 問題 - Hello アルゴリズム</title>
       
     
     
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -152,7 +152,7 @@
         <div class="md-header__topic" data-md-component="header-topic">
           <span class="md-ellipsis">
             
-              8.3 &nbsp; Top-k問題
+              8.3 &nbsp; Top-k 問題
             
           </span>
         </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1635,7 +1635,7 @@
   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1942,7 +1942,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2107,7 +2107,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2189,10 +2189,10 @@
     <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
       
         <li class="md-nav__item">
-  <a href="#831-1" class="md-nav__link">
+  <a href="#831" class="md-nav__link">
     <span class="md-ellipsis">
       
-        8.3.1 &nbsp; 方法1：反復選択
+        8.3.1 &nbsp; 方法一：走査による選択
       
     </span>
   </a>
@@ -2200,10 +2200,10 @@
 </li>
       
         <li class="md-nav__item">
-  <a href="#832-2" class="md-nav__link">
+  <a href="#832" class="md-nav__link">
     <span class="md-ellipsis">
       
-        8.3.2 &nbsp; 方法2：ソート
+        8.3.2 &nbsp; 方法二：ソート
       
     </span>
   </a>
@@ -2211,10 +2211,10 @@
 </li>
       
         <li class="md-nav__item">
-  <a href="#833-3" class="md-nav__link">
+  <a href="#833" class="md-nav__link">
     <span class="md-ellipsis">
       
-        8.3.3 &nbsp; 方法3：ヒープ
+        8.3.3 &nbsp; 方法三：ヒープ
       
     </span>
   </a>
@@ -2574,7 +2574,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2630,7 +2630,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2658,7 +2658,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3196,7 +3196,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3252,7 +3252,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3280,7 +3280,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3473,7 +3473,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3501,7 +3501,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3642,7 +3642,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3670,7 +3670,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3698,7 +3698,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3726,7 +3726,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3919,7 +3919,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4164,7 +4164,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4307,10 +4307,10 @@
     <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
       
         <li class="md-nav__item">
-  <a href="#831-1" class="md-nav__link">
+  <a href="#831" class="md-nav__link">
     <span class="md-ellipsis">
       
-        8.3.1 &nbsp; 方法1：反復選択
+        8.3.1 &nbsp; 方法一：走査による選択
       
     </span>
   </a>
@@ -4318,10 +4318,10 @@
 </li>
       
         <li class="md-nav__item">
-  <a href="#832-2" class="md-nav__link">
+  <a href="#832" class="md-nav__link">
     <span class="md-ellipsis">
       
-        8.3.2 &nbsp; 方法2：ソート
+        8.3.2 &nbsp; 方法二：ソート
       
     </span>
   </a>
@@ -4329,10 +4329,10 @@
 </li>
       
         <li class="md-nav__item">
-  <a href="#833-3" class="md-nav__link">
+  <a href="#833" class="md-nav__link">
     <span class="md-ellipsis">
       
-        8.3.3 &nbsp; 方法3：ヒープ
+        8.3.3 &nbsp; 方法三：ヒープ
       
     </span>
   </a>
@@ -4376,40 +4376,40 @@
 
 
 <!-- Page content -->
-<h1 id="83-top-k">8.3 &nbsp; Top-k問題<a class="headerlink" href="#83-top-k" title="Permanent link">&para;</a></h1>
+<h1 id="83-top-k">8.3 &nbsp; Top-k 問題<a class="headerlink" href="#83-top-k" title="Permanent link">&para;</a></h1>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
-<p>長さ<span class="arithmatex">\(n\)</span>の順序付けられていない配列<code>nums</code>が与えられたとき、配列内の最大<span class="arithmatex">\(k\)</span>個の要素を返してください。</p>
+<p>長さ <span class="arithmatex">\(n\)</span> の未整列配列 <code>nums</code> が与えられたとき、配列内で最大の <span class="arithmatex">\(k\)</span> 個の要素を返してください。</p>
 </div>
-<p>この問題について、まず2つの直接的な解法を紹介し、次により効率的なヒープベースの方法を説明します。</p>
-<h2 id="831-1">8.3.1 &nbsp; 方法1：反復選択<a class="headerlink" href="#831-1" title="Permanent link">&para;</a></h2>
-<p>下図に示すように、<span class="arithmatex">\(k\)</span>回の反復を実行し、各回で<span class="arithmatex">\(1\)</span>番目、<span class="arithmatex">\(2\)</span>番目、<span class="arithmatex">\(\dots\)</span>、<span class="arithmatex">\(k\)</span>番目に大きい要素を抽出できます。時間計算量は<span class="arithmatex">\(O(nk)\)</span>です。</p>
-<p>この方法は<span class="arithmatex">\(k \ll n\)</span>の場合にのみ適しています。<span class="arithmatex">\(k\)</span>が<span class="arithmatex">\(n\)</span>に近い場合、時間計算量は<span class="arithmatex">\(O(n^2)\)</span>に近づき、非常に時間がかかります。</p>
-<p><img alt="最大k個の要素を反復的に見つける" class="animation-figure" src="../top_k.assets/top_k_traversal.png" /></p>
-<p align="center"> 図 8-6 &nbsp; 最大k個の要素を反復的に見つける </p>
+<p>この問題について、まずは発想が比較的直接的な 2 つの解法を紹介し、その後でより効率の高いヒープ解法を紹介します。</p>
+<h2 id="831">8.3.1 &nbsp; 方法一：走査による選択<a class="headerlink" href="#831" title="Permanent link">&para;</a></h2>
+<p>以下の図に示すように <span class="arithmatex">\(k\)</span> 回の走査を行い、各ラウンドでそれぞれ第 <span class="arithmatex">\(1\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(\dots\)</span>、<span class="arithmatex">\(k\)</span> 位の要素を取り出すことができます。時間計算量は <span class="arithmatex">\(O(nk)\)</span> です。</p>
+<p>この方法は <span class="arithmatex">\(k \ll n\)</span> の場合にしか適していません。<span class="arithmatex">\(k\)</span> が <span class="arithmatex">\(n\)</span> にかなり近いと、時間計算量は <span class="arithmatex">\(O(n^2)\)</span> に近づき、非常に時間がかかるためです。</p>
+<p><img alt="走査によって最大の k 個の要素を探す" class="animation-figure" src="../top_k.assets/top_k_traversal.png" /></p>
+<p align="center"> 図 8-6 &nbsp; 走査によって最大の k 個の要素を探す </p>
 
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p><span class="arithmatex">\(k = n\)</span>の場合、完全に順序付けられたシーケンスを得ることができ、これは「選択ソート」アルゴリズムと同等です。</p>
+<p><span class="arithmatex">\(k = n\)</span> のとき、完全な昇順列を得ることができ、この場合は「選択ソート」アルゴリズムと等価になります。</p>
 </div>
-<h2 id="832-2">8.3.2 &nbsp; 方法2：ソート<a class="headerlink" href="#832-2" title="Permanent link">&para;</a></h2>
-<p>下図に示すように、まず配列<code>nums</code>をソートし、次に最後の<span class="arithmatex">\(k\)</span>個の要素を返すことができます。時間計算量は<span class="arithmatex">\(O(n \log n)\)</span>です。</p>
-<p>明らかに、この方法はタスクを「やりすぎ」ています。最大<span class="arithmatex">\(k\)</span>個の要素を見つけるだけでよく、他の要素をソートする必要はありません。</p>
-<p><img alt="ソートによる最大k個の要素の発見" class="animation-figure" src="../top_k.assets/top_k_sorting.png" /></p>
-<p align="center"> 図 8-7 &nbsp; ソートによる最大k個の要素の発見 </p>
+<h2 id="832">8.3.2 &nbsp; 方法二：ソート<a class="headerlink" href="#832" title="Permanent link">&para;</a></h2>
+<p>以下の図に示すように、まず配列 <code>nums</code> をソートし、その後で右端の <span class="arithmatex">\(k\)</span> 個の要素を返すことができます。時間計算量は <span class="arithmatex">\(O(n \log n)\)</span> です。</p>
+<p>明らかに、この方法は必要以上の処理を行っています。なぜなら、必要なのは最大の <span class="arithmatex">\(k\)</span> 個の要素を見つけることだけであり、他の要素をソートする必要はないからです。</p>
+<p><img alt="ソートによって最大の k 個の要素を探す" class="animation-figure" src="../top_k.assets/top_k_sorting.png" /></p>
+<p align="center"> 図 8-7 &nbsp; ソートによって最大の k 個の要素を探す </p>
 
-<h2 id="833-3">8.3.3 &nbsp; 方法3：ヒープ<a class="headerlink" href="#833-3" title="Permanent link">&para;</a></h2>
-<p>以下のプロセスに示すように、ヒープに基づいてTop-k問題をより効率的に解決できます。</p>
+<h2 id="833">8.3.3 &nbsp; 方法三：ヒープ<a class="headerlink" href="#833" title="Permanent link">&para;</a></h2>
+<p>ヒープを用いることで、Top-k 問題をより効率的に解くことができます。手順は以下の図のとおりです。</p>
 <ol>
-<li>最小ヒープを初期化します。先頭要素が最小になります。</li>
-<li>まず、配列の最初の<span class="arithmatex">\(k\)</span>個の要素をヒープに挿入します。</li>
-<li><span class="arithmatex">\(k + 1\)</span>番目の要素から開始し、現在の要素がヒープの先頭要素より大きい場合、ヒープの先頭要素を削除し、現在の要素をヒープに挿入します。</li>
-<li>走査を完了した後、ヒープには最大<span class="arithmatex">\(k\)</span>個の要素が含まれています。</li>
+<li>最小ヒープを初期化し、そのヒープ頂点の要素が最小となるようにします。</li>
+<li>まず配列の先頭 <span class="arithmatex">\(k\)</span> 個の要素を順にヒープへ挿入します。</li>
+<li><span class="arithmatex">\(k + 1\)</span> 番目の要素から開始し、現在の要素がヒープ頂点の要素より大きければ、ヒープ頂点の要素を取り出し、現在の要素をヒープへ挿入します。</li>
+<li>走査が完了した後、ヒープに保持されているのが最大の <span class="arithmatex">\(k\)</span> 個の要素です。</li>
 </ol>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:9"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label><label for="__tabbed_1_5">&lt;5&gt;</label><label for="__tabbed_1_6">&lt;6&gt;</label><label for="__tabbed_1_7">&lt;7&gt;</label><label for="__tabbed_1_8">&lt;8&gt;</label><label for="__tabbed_1_9">&lt;9&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="ヒープに基づく最大k個の要素の発見" class="animation-figure" src="../top_k.assets/top_k_heap_step1.png" /></p>
+<p><img alt="ヒープに基づいて最大の k 個の要素を探す" class="animation-figure" src="../top_k.assets/top_k_heap_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="top_k_heap_step2" class="animation-figure" src="../top_k.assets/top_k_heap_step2.png" /></p>
@@ -4437,22 +4437,22 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 8-8 &nbsp; ヒープに基づく最大k個の要素の発見 </p>
+<p align="center"> 図 8-8 &nbsp; ヒープに基づいて最大の k 個の要素を探す </p>
 
-<p>サンプルコードは以下の通りです：</p>
+<p>サンプルコードは以下のとおりです。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">top_k.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">top_k_heap</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">k</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ヒープを使用して配列内の最大k個の要素を見つける&quot;&quot;&quot;</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ヒープに基づいて配列中の最大の k 個の要素を探す&quot;&quot;&quot;</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 最小ヒープを初期化</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">heap</span> <span class="o">=</span> <span class="p">[]</span>
-<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="c1"># 配列の最初のk個の要素をヒープに入力</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="c1"># 配列の先頭 k 個の要素をヒープに追加</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">k</span><span class="p">):</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">heap</span><span class="p">,</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
-<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="c1"># k+1番目の要素から、ヒープの長さをkに保つ</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="c1"># k+1 番目の要素から開始し、ヒープ長を k に保つ</span>
 <a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">k</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
-<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="c1"># 現在の要素がヒープの先頭要素より大きい場合、ヒープの先頭要素を削除し、現在の要素をヒープに入力</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="c1"># 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">heap</span><span class="p">[</span><span class="mi">0</span><span class="p">]:</span>
 <a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>            <span class="n">heapq</span><span class="o">.</span><span class="n">heappop</span><span class="p">(</span><span class="n">heap</span><span class="p">)</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>            <span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">heap</span><span class="p">,</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
@@ -4460,17 +4460,17 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">top_k.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* ヒープを使用して配列内の最大k個の要素を見つける */</span>
+<div class="highlight"><span class="filename">top_k.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* ヒープに基づいて配列中の最大の k 個の要素を探す */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="n">priority_queue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">greater</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">topKHeap</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 最小ヒープを初期化</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="n">priority_queue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">greater</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">heap</span><span class="p">;</span>
-<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="c1">// 配列の最初のk個の要素をヒープに入力</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="c1">// 配列の先頭 k 個の要素をヒープに追加</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">k</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">        </span><span class="n">heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="c1">// k+1番目の要素から、ヒープの長さをkに保つ</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="c1">// k+1 番目の要素から開始し、ヒープ長を k に保つ</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">k</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="c1">// 現在の要素がヒープの先頭要素より大きい場合、ヒープの先頭要素を削除し、現在の要素をヒープに入力</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="c1">// 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">heap</span><span class="p">.</span><span class="n">top</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">            </span><span class="n">heap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
 <a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">            </span><span class="n">heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
@@ -4481,17 +4481,17 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">top_k.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* ヒープを使用して配列内の最大 k 個の要素を検索 */</span>
+<div class="highlight"><span class="filename">top_k.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* ヒープに基づいて配列中の最大の k 個の要素を探す */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="n">Queue</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">topKHeap</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 最小ヒープを初期化</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="n">Queue</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="p">();</span>
-<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="c1">// 配列の最初の k 個の要素をヒープに入力</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="c1">// 配列の先頭 k 個の要素をヒープに追加</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">k</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="n">heap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">);</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="c1">// k+1 番目の要素から、ヒープの長さを k に保つ</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="c1">// k+1 番目の要素から開始し、ヒープ長を k に保つ</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">k</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="c1">// 現在の要素がヒープの先頭要素より大きい場合、ヒープの先頭要素を削除し、現在の要素をヒープに入力</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="c1">// 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する</span>
 <a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">heap</span><span class="p">.</span><span class="na">peek</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">            </span><span class="n">heap</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span>
 <a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">            </span><span class="n">heap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">);</span>
@@ -4502,73 +4502,316 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">top_k.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">top_k</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">TopKHeap</span><span class="p">}</span>
+<div class="highlight"><span class="filename">top_k.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* ヒープに基づいて配列中の最大の k 個の要素を探す */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="n">PriorityQueue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">TopKHeap</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="c1">// 最小ヒープを初期化</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="n">PriorityQueue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">();</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="c1">// 配列の先頭 k 個の要素をヒープに追加</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">k</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">        </span><span class="n">heap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="c1">// k+1 番目の要素から開始し、ヒープ長を k に保つ</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">k</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">        </span><span class="c1">// 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">heap</span><span class="p">.</span><span class="n">Peek</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">            </span><span class="n">heap</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">            </span><span class="n">heap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">heap</span><span class="p">;</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">top_k.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">topKHeap</span><span class="p">}</span>
+<div class="highlight"><span class="filename">top_k.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* ヒープに基づいて配列中の最大の k 個の要素を探す */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">topKHeap</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">minHeap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// 最小ヒープを初期化</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">h</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">minHeap</span><span class="p">{}</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Init</span><span class="p">(</span><span class="nx">h</span><span class="p">)</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="c1">// 配列の先頭 k 個の要素をヒープに追加</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">k</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">        </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">h</span><span class="p">,</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">    </span><span class="c1">// k+1 番目の要素から開始し、ヒープ長を k に保つ</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">k</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">        </span><span class="c1">// 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">Top</span><span class="p">().(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">            </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Pop</span><span class="p">(</span><span class="nx">h</span><span class="p">)</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">            </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">h</span><span class="p">,</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">h</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">top_k.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">topKHeap</span><span class="p">}</span>
+<div class="highlight"><span class="filename">top_k.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* ヒープに基づいて配列中の最大の k 個の要素を探す */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">topKHeap</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">k</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// 最小ヒープを初期化し、先頭 k 個の要素でヒープを構築する</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">heap</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Heap</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="kr">prefix</span><span class="p">(</span><span class="n">k</span><span class="p">))</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="c1">// k+1 番目の要素から開始し、ヒープ長を k に保つ</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="p">.</span><span class="bp">dropFirst</span><span class="p">(</span><span class="n">k</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">        </span><span class="c1">// 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">heap</span><span class="p">.</span><span class="bp">min</span><span class="p">()</span><span class="o">!</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">            </span><span class="kc">_</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">heap</span><span class="p">.</span><span class="n">removeMin</span><span class="p">()</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">            </span><span class="n">heap</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">heap</span><span class="p">.</span><span class="n">unordered</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">top_k.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">pushMinHeap</span><span class="p">}</span>
-<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
-<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">popMinHeap</span><span class="p">}</span>
-<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a>
-<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">peekMinHeap</span><span class="p">}</span>
+<div class="highlight"><span class="filename">top_k.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 要素をヒープに追加 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">pushMinHeap</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="c1">// 要素を反転する</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="o">-</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="p">}</span>
 <a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a>
-<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">getMinHeap</span><span class="p">}</span>
-<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a>
-<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">topKHeap</span><span class="p">}</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="cm">/* 要素をヒープから取り出す */</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="kd">function</span><span class="w"> </span><span class="nx">popMinHeap</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">    </span><span class="c1">// 要素を反転する</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="p">}</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="cm">/* ヒープ先頭要素にアクセス */</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="kd">function</span><span class="w"> </span><span class="nx">peekMinHeap</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">    </span><span class="c1">// 要素を反転する</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">peek</span><span class="p">();</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="p">}</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="cm">/* ヒープから要素を取り出す */</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="kd">function</span><span class="w"> </span><span class="nx">getMinHeap</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w">    </span><span class="c1">// 要素を反転する</span>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">getMaxHeap</span><span class="p">().</span><span class="nx">map</span><span class="p">((</span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="o">-</span><span class="nx">num</span><span class="p">);</span>
+<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="p">}</span>
+<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a>
+<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="cm">/* ヒープに基づいて配列中の最大の k 個の要素を探す */</span>
+<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="kd">function</span><span class="w"> </span><span class="nx">topKHeap</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">k</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-27" name="__codelineno-6-27" href="#__codelineno-6-27"></a><span class="w">    </span><span class="c1">// 最小ヒープを初期化する</span>
+<a id="__codelineno-6-28" name="__codelineno-6-28" href="#__codelineno-6-28"></a><span class="w">    </span><span class="c1">// 注意: ヒープ内の全要素を反転し、最大ヒープで最小ヒープをシミュレートする</span>
+<a id="__codelineno-6-29" name="__codelineno-6-29" href="#__codelineno-6-29"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">MaxHeap</span><span class="p">([]);</span>
+<a id="__codelineno-6-30" name="__codelineno-6-30" href="#__codelineno-6-30"></a><span class="w">    </span><span class="c1">// 配列の先頭 k 個の要素をヒープに追加</span>
+<a id="__codelineno-6-31" name="__codelineno-6-31" href="#__codelineno-6-31"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">k</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-32" name="__codelineno-6-32" href="#__codelineno-6-32"></a><span class="w">        </span><span class="nx">pushMinHeap</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]);</span>
+<a id="__codelineno-6-33" name="__codelineno-6-33" href="#__codelineno-6-33"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-34" name="__codelineno-6-34" href="#__codelineno-6-34"></a><span class="w">    </span><span class="c1">// k+1 番目の要素から開始し、ヒープ長を k に保つ</span>
+<a id="__codelineno-6-35" name="__codelineno-6-35" href="#__codelineno-6-35"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">k</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-36" name="__codelineno-6-36" href="#__codelineno-6-36"></a><span class="w">        </span><span class="c1">// 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する</span>
+<a id="__codelineno-6-37" name="__codelineno-6-37" href="#__codelineno-6-37"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">peekMinHeap</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-38" name="__codelineno-6-38" href="#__codelineno-6-38"></a><span class="w">            </span><span class="nx">popMinHeap</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">);</span>
+<a id="__codelineno-6-39" name="__codelineno-6-39" href="#__codelineno-6-39"></a><span class="w">            </span><span class="nx">pushMinHeap</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]);</span>
+<a id="__codelineno-6-40" name="__codelineno-6-40" href="#__codelineno-6-40"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-41" name="__codelineno-6-41" href="#__codelineno-6-41"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-42" name="__codelineno-6-42" href="#__codelineno-6-42"></a><span class="w">    </span><span class="c1">// ヒープ内の要素を返す</span>
+<a id="__codelineno-6-43" name="__codelineno-6-43" href="#__codelineno-6-43"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">getMinHeap</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">);</span>
+<a id="__codelineno-6-44" name="__codelineno-6-44" href="#__codelineno-6-44"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">top_k.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">pushMinHeap</span><span class="p">}</span>
-<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
-<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">popMinHeap</span><span class="p">}</span>
-<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a>
-<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">peekMinHeap</span><span class="p">}</span>
+<div class="highlight"><span class="filename">top_k.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 要素をヒープに追加 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">pushMinHeap</span><span class="p">(</span><span class="nx">maxHeap</span><span class="o">:</span><span class="w"> </span><span class="kt">MaxHeap</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="c1">// 要素を反転する</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="o">-</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="p">}</span>
 <a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a>
-<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">getMinHeap</span><span class="p">}</span>
-<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a>
-<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">topKHeap</span><span class="p">}</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="cm">/* 要素をヒープから取り出す */</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="kd">function</span><span class="w"> </span><span class="nx">popMinHeap</span><span class="p">(</span><span class="nx">maxHeap</span><span class="o">:</span><span class="w"> </span><span class="kt">MaxHeap</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="c1">// 要素を反転する</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="p">}</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="cm">/* ヒープ先頭要素にアクセス */</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="kd">function</span><span class="w"> </span><span class="nx">peekMinHeap</span><span class="p">(</span><span class="nx">maxHeap</span><span class="o">:</span><span class="w"> </span><span class="kt">MaxHeap</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">    </span><span class="c1">// 要素を反転する</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">peek</span><span class="p">();</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="p">}</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="cm">/* ヒープから要素を取り出す */</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="kd">function</span><span class="w"> </span><span class="nx">getMinHeap</span><span class="p">(</span><span class="nx">maxHeap</span><span class="o">:</span><span class="w"> </span><span class="kt">MaxHeap</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="w">    </span><span class="c1">// 要素を反転する</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">getMaxHeap</span><span class="p">().</span><span class="nx">map</span><span class="p">((</span><span class="nx">num</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="o">-</span><span class="nx">num</span><span class="p">);</span>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="p">}</span>
+<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="cm">/* ヒープに基づいて配列中の最大の k 個の要素を探す */</span>
+<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="kd">function</span><span class="w"> </span><span class="nx">topKHeap</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">k</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a><span class="w">    </span><span class="c1">// 最小ヒープを初期化する</span>
+<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a><span class="w">    </span><span class="c1">// 注意: ヒープ内の全要素を反転し、最大ヒープで最小ヒープをシミュレートする</span>
+<a id="__codelineno-7-29" name="__codelineno-7-29" href="#__codelineno-7-29"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">MaxHeap</span><span class="p">([]);</span>
+<a id="__codelineno-7-30" name="__codelineno-7-30" href="#__codelineno-7-30"></a><span class="w">    </span><span class="c1">// 配列の先頭 k 個の要素をヒープに追加</span>
+<a id="__codelineno-7-31" name="__codelineno-7-31" href="#__codelineno-7-31"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">k</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-32" name="__codelineno-7-32" href="#__codelineno-7-32"></a><span class="w">        </span><span class="nx">pushMinHeap</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]);</span>
+<a id="__codelineno-7-33" name="__codelineno-7-33" href="#__codelineno-7-33"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-34" name="__codelineno-7-34" href="#__codelineno-7-34"></a><span class="w">    </span><span class="c1">// k+1 番目の要素から開始し、ヒープ長を k に保つ</span>
+<a id="__codelineno-7-35" name="__codelineno-7-35" href="#__codelineno-7-35"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">k</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-36" name="__codelineno-7-36" href="#__codelineno-7-36"></a><span class="w">        </span><span class="c1">// 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する</span>
+<a id="__codelineno-7-37" name="__codelineno-7-37" href="#__codelineno-7-37"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">peekMinHeap</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-38" name="__codelineno-7-38" href="#__codelineno-7-38"></a><span class="w">            </span><span class="nx">popMinHeap</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">);</span>
+<a id="__codelineno-7-39" name="__codelineno-7-39" href="#__codelineno-7-39"></a><span class="w">            </span><span class="nx">pushMinHeap</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]);</span>
+<a id="__codelineno-7-40" name="__codelineno-7-40" href="#__codelineno-7-40"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-41" name="__codelineno-7-41" href="#__codelineno-7-41"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-42" name="__codelineno-7-42" href="#__codelineno-7-42"></a><span class="w">    </span><span class="c1">// ヒープ内の要素を返す</span>
+<a id="__codelineno-7-43" name="__codelineno-7-43" href="#__codelineno-7-43"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">getMinHeap</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">);</span>
+<a id="__codelineno-7-44" name="__codelineno-7-44" href="#__codelineno-7-44"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">top_k.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">topKHeap</span><span class="p">}</span>
+<div class="highlight"><span class="filename">top_k.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* ヒープに基づいて配列中の最大の k 個の要素を探す */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="n">MinHeap</span><span class="w"> </span><span class="n">topKHeap</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="c1">// 最小ヒープを初期化し、配列の先頭 k 個の要素をヒープに入れる</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="n">MinHeap</span><span class="w"> </span><span class="n">heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MinHeap</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">sublist</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">k</span><span class="p">));</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="c1">// k+1 番目の要素から開始し、ヒープ長を k に保つ</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">k</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">    </span><span class="c1">// 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">heap</span><span class="p">.</span><span class="n">peek</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">      </span><span class="n">heap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">      </span><span class="n">heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">heap</span><span class="p">;</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">top_k.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">top_k_heap</span><span class="p">}</span>
+<div class="highlight"><span class="filename">top_k.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* ヒープに基づいて配列中の最大の k 個の要素を探す */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">top_k_heap</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">k</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">BinaryHeap</span><span class="o">&lt;</span><span class="n">Reverse</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="c1">// BinaryHeap は最大ヒープであり、Reverse で要素の順序を反転することで最小ヒープを実現する</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BinaryHeap</span><span class="p">::</span><span class="o">&lt;</span><span class="n">Reverse</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="c1">// 配列の先頭 k 個の要素をヒープに追加</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="o">&amp;</span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">iter</span><span class="p">().</span><span class="n">take</span><span class="p">(</span><span class="n">k</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">        </span><span class="n">heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">Reverse</span><span class="p">(</span><span class="n">num</span><span class="p">));</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">    </span><span class="c1">// k+1 番目の要素から開始し、ヒープ長を k に保つ</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="o">&amp;</span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">iter</span><span class="p">().</span><span class="n">skip</span><span class="p">(</span><span class="n">k</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">        </span><span class="c1">// 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">heap</span><span class="p">.</span><span class="n">peek</span><span class="p">().</span><span class="n">unwrap</span><span class="p">().</span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">            </span><span class="n">heap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">            </span><span class="n">heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">Reverse</span><span class="p">(</span><span class="n">num</span><span class="p">));</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">    </span><span class="n">heap</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">top_k.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">pushMinHeap</span><span class="p">}</span>
-<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
-<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">popMinHeap</span><span class="p">}</span>
-<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a>
-<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">peekMinHeap</span><span class="p">}</span>
+<div class="highlight"><span class="filename">top_k.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 要素をヒープに追加 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">pushMinHeap</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="c1">// 要素を反転する</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="n">push</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="o">-</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="p">}</span>
 <a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a>
-<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">getMinHeap</span><span class="p">}</span>
-<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a>
-<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">topKHeap</span><span class="p">}</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="cm">/* 要素をヒープから取り出す */</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="kt">int</span><span class="w"> </span><span class="nf">popMinHeap</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">    </span><span class="c1">// 要素を反転する</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="n">pop</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">);</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="p">}</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="cm">/* ヒープ先頭要素にアクセス */</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="kt">int</span><span class="w"> </span><span class="nf">peekMinHeap</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">    </span><span class="c1">// 要素を反転する</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="n">peek</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">);</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="p">}</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="cm">/* ヒープから要素を取り出す */</span>
+<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="nf">getMinHeap</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="w">    </span><span class="c1">// ヒープ内のすべての要素を反転して res 配列に格納</span>
+<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="p">}</span>
+<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a>
+<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a><span class="cm">/* ヒープから要素を取り出す */</span>
+<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="nf">getMinHeap</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></a><span class="w">    </span><span class="c1">// ヒープ内のすべての要素を反転して res 配列に格納</span>
+<a id="__codelineno-10-32" name="__codelineno-10-32" href="#__codelineno-10-32"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-10-33" name="__codelineno-10-33" href="#__codelineno-10-33"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-34" name="__codelineno-10-34" href="#__codelineno-10-34"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-10-35" name="__codelineno-10-35" href="#__codelineno-10-35"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-36" name="__codelineno-10-36" href="#__codelineno-10-36"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-10-37" name="__codelineno-10-37" href="#__codelineno-10-37"></a><span class="p">}</span>
+<a id="__codelineno-10-38" name="__codelineno-10-38" href="#__codelineno-10-38"></a>
+<a id="__codelineno-10-39" name="__codelineno-10-39" href="#__codelineno-10-39"></a><span class="c1">// ヒープに基づいて配列中の最大の k 個の要素を求める関数</span>
+<a id="__codelineno-10-40" name="__codelineno-10-40" href="#__codelineno-10-40"></a><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="nf">topKHeap</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">sizeNums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-41" name="__codelineno-10-41" href="#__codelineno-10-41"></a><span class="w">    </span><span class="c1">// 最小ヒープを初期化する</span>
+<a id="__codelineno-10-42" name="__codelineno-10-42" href="#__codelineno-10-42"></a><span class="w">    </span><span class="c1">// 注意: ヒープ内の全要素を反転し、最大ヒープで最小ヒープをシミュレートする</span>
+<a id="__codelineno-10-43" name="__codelineno-10-43" href="#__codelineno-10-43"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-10-44" name="__codelineno-10-44" href="#__codelineno-10-44"></a><span class="w">    </span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newMaxHeap</span><span class="p">(</span><span class="n">empty</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-10-45" name="__codelineno-10-45" href="#__codelineno-10-45"></a><span class="w">    </span><span class="c1">// 配列の先頭 k 個の要素をヒープに追加</span>
+<a id="__codelineno-10-46" name="__codelineno-10-46" href="#__codelineno-10-46"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">k</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-47" name="__codelineno-10-47" href="#__codelineno-10-47"></a><span class="w">        </span><span class="n">pushMinHeap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-10-48" name="__codelineno-10-48" href="#__codelineno-10-48"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-49" name="__codelineno-10-49" href="#__codelineno-10-49"></a><span class="w">    </span><span class="c1">// k+1 番目の要素から開始し、ヒープ長を k に保つ</span>
+<a id="__codelineno-10-50" name="__codelineno-10-50" href="#__codelineno-10-50"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">k</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">sizeNums</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-51" name="__codelineno-10-51" href="#__codelineno-10-51"></a><span class="w">        </span><span class="c1">// 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する</span>
+<a id="__codelineno-10-52" name="__codelineno-10-52" href="#__codelineno-10-52"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">peekMinHeap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-53" name="__codelineno-10-53" href="#__codelineno-10-53"></a><span class="w">            </span><span class="n">popMinHeap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">);</span>
+<a id="__codelineno-10-54" name="__codelineno-10-54" href="#__codelineno-10-54"></a><span class="w">            </span><span class="n">pushMinHeap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-10-55" name="__codelineno-10-55" href="#__codelineno-10-55"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-56" name="__codelineno-10-56" href="#__codelineno-10-56"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-57" name="__codelineno-10-57" href="#__codelineno-10-57"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">getMinHeap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">);</span>
+<a id="__codelineno-10-58" name="__codelineno-10-58" href="#__codelineno-10-58"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-10-59" name="__codelineno-10-59" href="#__codelineno-10-59"></a><span class="w">    </span><span class="n">delMaxHeap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">);</span>
+<a id="__codelineno-10-60" name="__codelineno-10-60" href="#__codelineno-10-60"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-10-61" name="__codelineno-10-61" href="#__codelineno-10-61"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">top_k.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">topKHeap</span><span class="p">}</span>
+<div class="highlight"><span class="filename">top_k.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* ヒープに基づいて配列中の最大の k 個の要素を探す */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">topKHeap</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">k</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="n">Queue</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="c1">// 最小ヒープを初期化</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="c1">// 配列の先頭 k 個の要素をヒープに追加</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">k</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">        </span><span class="n">heap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">    </span><span class="c1">// k+1 番目の要素から開始し、ヒープ長を k に保つ</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">k</span><span class="p">..</span><span class="o">&lt;</span><span class="n">nums</span><span class="p">.</span><span class="na">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">        </span><span class="c1">// 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">heap</span><span class="p">.</span><span class="na">peek</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">            </span><span class="n">heap</span><span class="p">.</span><span class="na">poll</span><span class="p">()</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">            </span><span class="n">heap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">heap</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">top_k.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">top_k_heap</span><span class="p">}</span>
+<div class="highlight"><span class="filename">top_k.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### ヒープに基づいて配列中の最大 k 個の要素を探す ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">top_k_heap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">k</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># 最小ヒープを初期化する</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="c1"># 注意: ヒープ内の全要素を反転し、最大ヒープで最小ヒープをシミュレートする</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="n">max_heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">MaxHeap</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="o">[]</span><span class="p">)</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">  </span><span class="c1"># 配列の先頭 k 個の要素をヒープに追加</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">k</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">    </span><span class="n">push_min_heap</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">  </span><span class="c1"># k+1 番目の要素から開始し、ヒープ長を k に保つ</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">k</span><span class="o">...</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">    </span><span class="c1"># 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">peek_min_heap</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">      </span><span class="n">pop_min_heap</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">      </span><span class="n">push_min_heap</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w">  </span><span class="n">get_min_heap</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>合計<span class="arithmatex">\(n\)</span>回のヒープ挿入と削除が実行され、最大ヒープサイズが<span class="arithmatex">\(k\)</span>であるため、時間計算量は<span class="arithmatex">\(O(n \log k)\)</span>です。この方法は非常に効率的で、<span class="arithmatex">\(k\)</span>が小さい場合、時間計算量は<span class="arithmatex">\(O(n)\)</span>に近づき、<span class="arithmatex">\(k\)</span>が大きい場合でも、時間計算量は<span class="arithmatex">\(O(n \log n)\)</span>を超えません。</p>
-<p>さらに、この方法は動的データストリームのシナリオに適しています。データを継続的に追加することで、ヒープ内の要素を維持し、最大<span class="arithmatex">\(k\)</span>個の要素の動的更新を実現できます。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=import%20heapq%0A%0Adef%20top_k_heap%28nums%3A%20list%5Bint%5D%2C%20k%3A%20int%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%22%22%22%E3%83%92%E3%83%BC%E3%83%97%E3%81%AB%E5%9F%BA%E3%81%A5%E3%81%84%E3%81%A6%E9%85%8D%E5%88%97%E4%B8%AD%E3%81%AE%E6%9C%80%E5%A4%A7%E3%81%AE%20k%20%E5%80%8B%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E6%8E%A2%E3%81%99%22%22%22%0A%20%20%20%20%23%20%E6%9C%80%E5%B0%8F%E3%83%92%E3%83%BC%E3%83%97%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20heap%20%3D%20%5B%5D%0A%20%20%20%20%23%20%E9%85%8D%E5%88%97%E3%81%AE%E5%85%88%E9%A0%AD%20k%20%E5%80%8B%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E3%83%92%E3%83%BC%E3%83%97%E3%81%AB%E8%BF%BD%E5%8A%A0%0A%20%20%20%20for%20i%20in%20range%28k%29%3A%0A%20%20%20%20%20%20%20%20heapq.heappush%28heap%2C%20nums%5Bi%5D%29%0A%20%20%20%20%23%20k%2B1%20%E7%95%AA%E7%9B%AE%E3%81%AE%E8%A6%81%E7%B4%A0%E3%81%8B%E3%82%89%E9%96%8B%E5%A7%8B%E3%81%97%E3%80%81%E3%83%92%E3%83%BC%E3%83%97%E9%95%B7%E3%82%92%20k%20%E3%81%AB%E4%BF%9D%E3%81%A4%0A%20%20%20%20for%20i%20in%20range%28k%2C%20len%28nums%29%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E7%8F%BE%E5%9C%A8%E3%81%AE%E8%A6%81%E7%B4%A0%E3%81%8C%E3%83%92%E3%83%BC%E3%83%97%E5%85%88%E9%A0%AD%E3%82%88%E3%82%8A%E5%A4%A7%E3%81%8D%E3%81%91%E3%82%8C%E3%81%B0%E3%80%81%E3%83%92%E3%83%BC%E3%83%97%E5%85%88%E9%A0%AD%E3%82%92%E5%8F%96%E3%82%8A%E5%87%BA%E3%81%97%E3%81%A6%E7%8F%BE%E5%9C%A8%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E8%BF%BD%E5%8A%A0%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20if%20nums%5Bi%5D%20%3E%20heap%5B0%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20heapq.heappop%28heap%29%0A%20%20%20%20%20%20%20%20%20%20%20%20heapq.heappush%28heap%2C%20nums%5Bi%5D%29%0A%20%20%20%20return%20heap%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B1%2C%207%2C%206%2C%203%2C%202%5D%0A%20%20%20%20k%20%3D%203%0A%0A%20%20%20%20res%20%3D%20top_k_heap%28nums%2C%20k%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=import%20heapq%0A%0Adef%20top_k_heap%28nums%3A%20list%5Bint%5D%2C%20k%3A%20int%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%22%22%22%E3%83%92%E3%83%BC%E3%83%97%E3%81%AB%E5%9F%BA%E3%81%A5%E3%81%84%E3%81%A6%E9%85%8D%E5%88%97%E4%B8%AD%E3%81%AE%E6%9C%80%E5%A4%A7%E3%81%AE%20k%20%E5%80%8B%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E6%8E%A2%E3%81%99%22%22%22%0A%20%20%20%20%23%20%E6%9C%80%E5%B0%8F%E3%83%92%E3%83%BC%E3%83%97%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20heap%20%3D%20%5B%5D%0A%20%20%20%20%23%20%E9%85%8D%E5%88%97%E3%81%AE%E5%85%88%E9%A0%AD%20k%20%E5%80%8B%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E3%83%92%E3%83%BC%E3%83%97%E3%81%AB%E8%BF%BD%E5%8A%A0%0A%20%20%20%20for%20i%20in%20range%28k%29%3A%0A%20%20%20%20%20%20%20%20heapq.heappush%28heap%2C%20nums%5Bi%5D%29%0A%20%20%20%20%23%20k%2B1%20%E7%95%AA%E7%9B%AE%E3%81%AE%E8%A6%81%E7%B4%A0%E3%81%8B%E3%82%89%E9%96%8B%E5%A7%8B%E3%81%97%E3%80%81%E3%83%92%E3%83%BC%E3%83%97%E9%95%B7%E3%82%92%20k%20%E3%81%AB%E4%BF%9D%E3%81%A4%0A%20%20%20%20for%20i%20in%20range%28k%2C%20len%28nums%29%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E7%8F%BE%E5%9C%A8%E3%81%AE%E8%A6%81%E7%B4%A0%E3%81%8C%E3%83%92%E3%83%BC%E3%83%97%E5%85%88%E9%A0%AD%E3%82%88%E3%82%8A%E5%A4%A7%E3%81%8D%E3%81%91%E3%82%8C%E3%81%B0%E3%80%81%E3%83%92%E3%83%BC%E3%83%97%E5%85%88%E9%A0%AD%E3%82%92%E5%8F%96%E3%82%8A%E5%87%BA%E3%81%97%E3%81%A6%E7%8F%BE%E5%9C%A8%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E8%BF%BD%E5%8A%A0%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20if%20nums%5Bi%5D%20%3E%20heap%5B0%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20heapq.heappop%28heap%29%0A%20%20%20%20%20%20%20%20%20%20%20%20heapq.heappush%28heap%2C%20nums%5Bi%5D%29%0A%20%20%20%20return%20heap%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B1%2C%207%2C%206%2C%203%2C%202%5D%0A%20%20%20%20k%20%3D%203%0A%0A%20%20%20%20res%20%3D%20top_k_heap%28nums%2C%20k%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>合計で <span class="arithmatex">\(n\)</span> 回のヒープ挿入と取り出しを行い、ヒープの最大長は <span class="arithmatex">\(k\)</span> であるため、時間計算量は <span class="arithmatex">\(O(n \log k)\)</span> です。この方法は非常に効率が高く、<span class="arithmatex">\(k\)</span> が小さいときは時間計算量が <span class="arithmatex">\(O(n)\)</span> に近づき、<span class="arithmatex">\(k\)</span> が大きいときでも <span class="arithmatex">\(O(n \log n)\)</span> を超えることはありません。</p>
+<p>さらに、この方法は動的データストリームの利用シーンにも適しています。データが継続的に追加される場合でも、ヒープ内の要素を保ち続けることで、最大の <span class="arithmatex">\(k\)</span> 個の要素を動的に更新できます。</p>
 
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     class="md-footer__link md-footer__link--prev"
-    aria-label="前: 8.2 &amp;nbsp; ヒープ構築操作"
+    aria-label="前: 8.2 &amp;nbsp; ヒープ構築"
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       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
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         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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 <!-- Page content -->
 <h1 id="_1">はじめに<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h1>
-<p>数年前、私はLeetCodeで「剣指Offer」の問題解答を共有し、多くの読者から励ましとサポートを受けました。読者とのやり取りの中で、最もよく聞かれた質問は「アルゴリズムの勉強をどう始めたらよいか」でした。次第に、私はこの質問に強い関心を抱くようになりました。</p>
-<p>問題を直接解くことが最も人気のある方法のようです。これはシンプルで直接的で効果的です。しかし、問題解決はマインスイーパーをプレイするようなものです。自学自習の能力が高い人は、地雷を一つずつ回避していくことができますが、しっかりとした基礎がない人は、何度もつまずいて挫折しながら後退することになるかもしれません。教科書を読むことも一般的な方法ですが、就職活動中の人にとって、卒業論文の執筆、履歴書の提出、筆記試験や面接の準備が既にエネルギーの大部分を消費しており、分厚い本を読むことはしばしば困難な挑戦となります。</p>
-<p>もしあなたが同様の悩みを抱えているなら、この本があなたを見つけることができて幸運です。この本は、この質問に対する私の答えです。これが最良の解決策ではないかもしれませんが、少なくとも積極的な試みです。この本があなたに直接内定をもたらすことはできませんが、データ構造とアルゴリズムの「知識地図」を探索する手引きとなり、さまざまな「地雷」の形、大きさ、位置を理解し、さまざまな「地雷除去方法」をマスターできるようお手伝いします。これらのスキルがあれば、より快適に問題を解き、文献を読むことができ、徐々に知識体系を構築できると信じています。</p>
-<p>私は、ファインマン教授の言葉に深く同感します。「知識は無料ではありません。注意を払わなければならないのです。」この意味で、この本は完全に「無料」ではありません。この本に対するあなたの貴重な「注意」に応えるために、私は最善を尽くし、最大の「注意」を払ってこの本を書きます。</p>
-<p>自分の限界を認識しており、この本の内容が時間をかけて洗練されたにもかかわらず、間違いは確実に残っていることを理解しています。先生方や学生の皆様からの批評と訂正を心から歓迎いたします。</p>
-<p><img alt="Hello Algo" class="cover-image" src="../assets/covers/chapter_hello_algo.jpg" /></p>
+<p>数年前、私は LeetCode 中国版で「剣指 Offer」シリーズの解説を共有し、多くの読者から励ましと支持をいただきました。読者との交流の中で、最もよく聞かれた質問の一つが「アルゴリズムをどう学び始めればよいか」でした。次第に、私はこの問題に強い関心を抱くようになりました。</p>
+<p>手探りでひたすら問題を解くことは、最も人気のある方法のようです。単純で、直接的で、しかも効果的です。しかし問題演習は「マインスイーパー」を遊ぶことに似ており、独学力の高い人は地雷を一つずつうまく取り除ける一方で、基礎が十分でない人は大きな痛手を受け、挫折の中で少しずつ後退してしまいがちです。教材を通読するのもよくある方法ですが、就職を目指す人にとっては、卒業論文、履歴書の提出、筆記試験や面接の準備ですでに大半の力を使い果たしており、分厚い本を読み込むことはしばしば困難な挑戦になってしまいます。</p>
+<p>もしあなたも同じような悩みを抱えているなら、この本があなたのもとに“たどり着いた”のは幸運なことです。本書は、この問いに対して私が示す答えです。たとえ最良の解ではなくても、少なくとも前向きな試みではあります。本書だけで直接内定を得られるわけではありませんが、データ構造とアルゴリズムの「知識地図」を探る手助けをし、さまざまな「地雷」の形や大きさ、分布を理解し、いろいろな「地雷除去の方法」を身につけられるよう導きます。こうした力があれば、問題演習や文献読解をより自在に進め、やがて完整な知識体系を築いていけると信じています。</p>
+<p>私はファインマン教授の言葉に深く賛同しています。「Knowledge isn't free. You have to pay attention.」この意味において、本書は完全に「無料」ではありません。本書のためにあなたが払ってくれる貴重な「注意」に応えるため、私はできる限りの力を尽くし、最大限の「注意」を注いで本書を書き上げます。</p>
+<p>私は自らの学識と力量の浅さをよく承知しています。本書の内容はある程度磨きをかけてきたものの、なお多くの誤りが残っているはずです。先生方、そして学習者の皆さまからのご批判とご指摘を心よりお願いいたします。</p>
+<p><img alt="Hello アルゴリズム" class="cover-image" src="../assets/covers/chapter_hello_algo.jpg" /></p>
 <div style="text-align: center;">
-    <h2 style="margin-top: 0.8em; margin-bottom: 0.8em;">Hello, Algo!</h2>
+    <h2 style="margin-top: 0.8em; margin-bottom: 0.8em;">Hello、アルゴリズム！</h2>
 </div>
 
-<p>コンピュータの出現は世界に大きな変化をもたらしました。高速な計算能力と優れたプログラム可能性により、コンピュータはアルゴリズムを実行しデータを処理するための理想的な媒体となりました。ビデオゲームのリアルなグラフィックス、自動運転の知的な判断、AlphaGoの見事な囲碁ゲーム、ChatGPTの自然な対話など、これらのアプリケーションはすべて、コンピュータ上で動作するアルゴリズムの精巧な実演です。</p>
-<p>実際、コンピュータの出現以前から、アルゴリズムとデータ構造は世界の至る所に存在していました。初期のアルゴリズムは比較的シンプルで、古代の計数方法や道具作りの手順などがありました。文明が進歩するにつれて、アルゴリズムはより洗練され複雑になりました。職人の精巧な技術から、生産力を解放する工業製品、宇宙を支配する科学法則まで、ほぼすべての平凡または驚異的なことの背後には、アルゴリズムの巧妙な思考があります。</p>
-<p>同様に、データ構造は至る所にあります。ソーシャルネットワークから地下鉄路線まで、多くのシステムは「グラフ」としてモデル化できます。国から家族まで、社会組織の主要な形態は「木」の特徴を示します。冬服は「スタック」のようで、最初に着たものが最後に脱がれます。バドミントンのシャトル筒は「キュー」に似ており、一方の端で挿入し、もう一方の端で取り出します。辞書は「ハッシュテーブル」のようで、目標エントリを素早く検索できます。</p>
-<p>この本は、明確で理解しやすいアニメーション図解と実行可能なコード例を通じて、読者がアルゴリズムとデータ構造の核心概念を理解し、プログラミングを通じてそれらを実装できるようになることを目指しています。この基盤の上で、この本は複雑な世界におけるアルゴリズムの生き生きとした現れを明らかにし、アルゴリズムの美しさを示すことに努めています。この本があなたのお役に立てることを願っています！</p>
+<p>コンピュータの登場は世界に大きな変革をもたらしました。高速な計算能力と優れたプログラム可能性によって、アルゴリズムの実行とデータ処理の理想的な媒体となったのです。ビデオゲームのリアルな映像、自動運転の知的な意思決定、AlphaGo の見事な対局、ChatGPT の自然な対話に至るまで、これらの応用はいずれもコンピュータ上でアルゴリズムが巧みに表現されたものです。</p>
+<p>実際には、コンピュータが誕生する以前から、アルゴリズムとデータ構造は世界のいたるところに存在していました。初期のアルゴリズムは比較的単純で、たとえば古代の数え方や道具作りの手順などがそれに当たります。文明の進歩とともに、アルゴリズムは次第により精緻で複雑なものになっていきました。匠の巧みな技から、生産力を解放する工業製品、さらには宇宙の運行を支配する科学法則に至るまで、ほとんどあらゆる平凡なもの、あるいは驚嘆すべきものの背後には、精妙なアルゴリズムの思想が潜んでいます。</p>
+<p>同様に、データ構造も至るところに存在します。社会ネットワークのような大きなものから地下鉄路線のような小さなものまで、多くのシステムは「グラフ」としてモデル化できます。国家のような大きな単位から家庭のような小さな単位まで、社会の主な組織形態には「木」の特徴があります。冬服は「スタック」のように、最初に着たものが最後に脱がれます。バドミントンシャトルの筒は「キュー」のように、一方から入れて他方から取り出します。辞書は「ハッシュテーブル」のようなもので、目的の見出し語を素早く探せます。</p>
+<p>本書は、わかりやすいアニメーション図解と実行可能なコード例を通じて、読者がアルゴリズムとデータ構造の核心概念を理解し、さらにプログラミングによってそれらを実装できるようになることを目指しています。そのうえで、本書は複雑な世界の中にあるアルゴリズムの生き生きとした現れを明らかにし、アルゴリズムの美しさを示そうとしています。本書があなたの助けになれば幸いです。</p>
 
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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 <!-- Page content -->
-<h1 id="11">1.1 &nbsp; アルゴリズムは至る所にある<a class="headerlink" href="#11" title="Permanent link">&para;</a></h1>
-<p>「アルゴリズム」という言葉を聞くと、自然に数学を思い浮かべます。しかし、多くのアルゴリズムは複雑な数学を含まず、基本的な論理により多く依存しており、これは私たちの日常生活の至る所で見ることができます。</p>
-<p>アルゴリズムについて正式に議論を始める前に、興味深い事実を共有する価値があります。<strong>あなたは無意識のうちに多くのアルゴリズムを学び、日常生活でそれらを応用することに慣れています</strong>。ここで、この点を証明するためにいくつかの具体的な例を挙げます。</p>
-<p><strong>例1：辞書の引き方</strong>。英語の辞書では、単語がアルファベット順に並んでいます。<span class="arithmatex">\(r\)</span>で始まる単語を探していると仮定すると、通常は以下の方法で行います：</p>
+<h1 id="11">1.1 &nbsp; アルゴリズムは至るところにある<a class="headerlink" href="#11" title="Permanent link">&para;</a></h1>
+<p>「アルゴリズム」という言葉を聞くと、自然に数学を思い浮かべます。しかし実際には、多くのアルゴリズムは複雑な数学を必要とせず、むしろ基本的な論理に依存しており、その論理は私たちの日常生活のいたるところで見られます。</p>
+<p>アルゴリズムを本格的に議論する前に、ひとつ面白い事実を共有しておきます。<strong>あなたはすでに知らず知らずのうちに多くのアルゴリズムを身につけ、それらを日常生活に応用することに慣れているのです</strong>。以下では、いくつかの具体例を挙げてこれを示します。</p>
+<p><strong>例1：辞書を引く</strong>。辞書では、各漢字に対応するピンインがあり、辞書はピンインのアルファベット順に並んでいます。ピンインの先頭文字が <span class="arithmatex">\(r\)</span> の字を探すと仮定すると、通常は次の図のような方法で行います。</p>
 <ol>
-<li>辞書を大体半分ぐらいのところで開き、そのページの最初の語彙を確認します。例えば<span class="arithmatex">\(m\)</span>で始まる文字だとしましょう。</li>
-<li><span class="arithmatex">\(r\)</span>はアルファベットで<span class="arithmatex">\(m\)</span>の後に来るので、前半を無視して、探索空間を後半に絞ります。</li>
-<li><span class="arithmatex">\(r\)</span>で始まる単語を見つけるまで、ステップ<code>1.</code>と<code>2.</code>を繰り返します。</li>
+<li>辞書をおよそ半分のところまで開き、そのページの先頭文字を確認し、先頭文字が <span class="arithmatex">\(m\)</span> だとします。</li>
+<li>ピンインのアルファベット表では <span class="arithmatex">\(r\)</span> は <span class="arithmatex">\(m\)</span> の後にあるため、辞書の前半を除外し、探索範囲を後半に絞ります。</li>
+<li>ピンインの先頭文字が <span class="arithmatex">\(r\)</span> のページを見つけるまで、手順 <code>1.</code> と手順 <code>2.</code> を繰り返します。</li>
 </ol>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:5"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label><label for="__tabbed_1_5">&lt;5&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="辞書を引く過程" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step1.png" /></p>
+<p><img alt="辞書を引く手順" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step1.png" /></p>
 </div>
 <div class="tabbed-block">
-<p><img alt="辞書での二分探索ステップ2" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step2.png" /></p>
+<p><img alt="binary_search_dictionary_step2" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step2.png" /></p>
 </div>
 <div class="tabbed-block">
-<p><img alt="辞書での二分探索ステップ3" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step3.png" /></p>
+<p><img alt="binary_search_dictionary_step3" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step3.png" /></p>
 </div>
 <div class="tabbed-block">
-<p><img alt="辞書での二分探索ステップ4" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step4.png" /></p>
+<p><img alt="binary_search_dictionary_step4" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step4.png" /></p>
 </div>
 <div class="tabbed-block">
-<p><img alt="辞書での二分探索ステップ5" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step5.png" /></p>
+<p><img alt="binary_search_dictionary_step5" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step5.png" /></p>
 </div>
 </div>
 </div>
-<p align="center"> 図 1-1 &nbsp; 辞書を引く過程 </p>
+<p align="center"> 図 1-1 &nbsp; 辞書を引く手順 </p>
 
-<p>辞書を引くことは、小学生にとって必須のスキルですが、実際には有名な「二分探索」アルゴリズムです。データ構造の観点から、辞書をソートされた「配列」と考えることができます。アルゴリズムの観点から、辞書で単語を探すために取られる一連の行動は、「二分探索」アルゴリズムと見なすことができます。</p>
-<p><strong>例2：トランプの整理</strong>。トランプをプレイするとき、手札を昇順に並べる必要があります。以下の過程で示されます。</p>
+<p>辞書を引くという小学生の必須スキルは、実は有名な「二分探索」アルゴリズムそのものです。データ構造の観点では、辞書を整列済みの「配列」とみなせます。アルゴリズムの観点では、上記の一連の辞書引きの操作を「二分探索」とみなせます。</p>
+<p><strong>例2：トランプを整理する</strong>。カードゲームをするとき、毎回手札のトランプを小さい順に並べ替える必要があります。その流れは次の図のとおりです。</p>
 <ol>
-<li>トランプを「整列済み」と「未整列」のセクションに分けます。最初は一番左のカードが既に整列していると仮定します。</li>
-<li>未整列セクションからカードを1枚取り出し、整列済みセクションの正しい位置に挿入します。この後、左端の2枚のカードが整列します。</li>
-<li>すべてのカードが整列するまで、ステップ<code>2</code>を繰り返します。</li>
+<li>トランプを「整列済み」と「未整列」の2つの部分に分け、初期状態では一番左の1枚がすでに整列済みだとします。</li>
+<li>未整列部分から1枚のトランプを取り出し、整列済み部分の正しい位置に挿入します。完了すると、左端の2枚は整列済みになります。</li>
+<li>手順 <code>2.</code> を繰り返し、各ラウンドで未整列部分から1枚を整列済み部分へ挿入し、すべてのトランプが整列済みになるまで続けます。</li>
 </ol>
-<p><img alt="トランプの整理過程" class="animation-figure" src="../algorithms_are_everywhere.assets/playing_cards_sorting.png" /></p>
-<p align="center"> 図 1-2 &nbsp; トランプの整理過程 </p>
+<p><img alt="トランプを並べ替える手順" class="animation-figure" src="../algorithms_are_everywhere.assets/playing_cards_sorting.png" /></p>
+<p align="center"> 図 1-2 &nbsp; トランプを並べ替える手順 </p>
 
-<p>上記のトランプを整理する方法は、実質的に「挿入ソート」アルゴリズムであり、小さなデータセットに対して非常に効率的です。多くのプログラミング言語のソート関数には挿入ソートが含まれています。</p>
-<p><strong>例3：お釣りの計算</strong>。スーパーマーケットで<span class="arithmatex">\(69\)</span>の買い物をしたと仮定します。レジ係に<span class="arithmatex">\(100\)</span>を渡すと、<span class="arithmatex">\(31\)</span>のお釣りを提供する必要があります。この過程は以下の図で明確に理解できます。</p>
+<p>上記のトランプ整理の方法は、本質的には「挿入ソート」アルゴリズムです。これは小規模なデータ集合を処理する際に非常に効率的で、多くのプログラミング言語のソートライブラリ関数にも挿入ソートが使われています。</p>
+<p><strong>例3：お釣りを出す</strong>。スーパーで <span class="arithmatex">\(69\)</span> 元の商品を購入し、店員に <span class="arithmatex">\(100\)</span> 元渡したとすると、店員は <span class="arithmatex">\(31\)</span> 元のお釣りを返す必要があります。店員は自然に次の図のような考え方をします。</p>
 <ol>
-<li>選択肢は<span class="arithmatex">\(31\)</span>以下の価値のある通貨で、<span class="arithmatex">\(1\)</span>、<span class="arithmatex">\(5\)</span>、<span class="arithmatex">\(10\)</span>、<span class="arithmatex">\(20\)</span>が含まれます。</li>
-<li>選択肢から最大の<span class="arithmatex">\(20\)</span>を取り出し、<span class="arithmatex">\(31 - 20 = 11\)</span>が残ります。</li>
-<li>残りの選択肢から最大の<span class="arithmatex">\(10\)</span>を取り出し、<span class="arithmatex">\(11 - 10 = 1\)</span>が残ります。</li>
-<li>残りの選択肢から最大の<span class="arithmatex">\(1\)</span>を取り出し、<span class="arithmatex">\(1 - 1 = 0\)</span>が残ります。</li>
-<li>お釣りの計算が完了し、解答は<span class="arithmatex">\(20 + 10 + 1 = 31\)</span>です。</li>
+<li>選択肢は <span class="arithmatex">\(31\)</span> 元より小さい額面の貨幣で、<span class="arithmatex">\(1\)</span> 元、<span class="arithmatex">\(5\)</span> 元、<span class="arithmatex">\(10\)</span> 元、<span class="arithmatex">\(20\)</span> 元があります。</li>
+<li>選択肢の中から最大の <span class="arithmatex">\(20\)</span> 元を取り出すと、残りは <span class="arithmatex">\(31 - 20 = 11\)</span> 元です。</li>
+<li>残りの選択肢の中から最大の <span class="arithmatex">\(10\)</span> 元を取り出すと、残りは <span class="arithmatex">\(11 - 10 = 1\)</span> 元です。</li>
+<li>残りの選択肢の中から最大の <span class="arithmatex">\(1\)</span> 元を取り出すと、残りは <span class="arithmatex">\(1 - 1 = 0\)</span> 元です。</li>
+<li>お釣りは完了し、内訳は <span class="arithmatex">\(20 + 10 + 1 = 31\)</span> 元です。</li>
 </ol>
-<p><img alt="お釣りの計算過程" class="animation-figure" src="../algorithms_are_everywhere.assets/greedy_change.png" /></p>
-<p align="center"> 図 1-3 &nbsp; お釣りの計算過程 </p>
+<p><img alt="お釣りの過程" class="animation-figure" src="../algorithms_are_everywhere.assets/greedy_change.png" /></p>
+<p align="center"> 図 1-3 &nbsp; お釣りの過程 </p>
 
-<p>記述されたステップでは、利用可能な最大の額面を使用して各段階で最良の選択肢を選ぶことで、効果的なお釣り計算戦略につながります。データ構造とアルゴリズムの観点から、このアプローチは「貪欲」アルゴリズムとして知られています。</p>
-<p>料理の準備から宇宙旅行まで、ほぼすべての問題解決にはアルゴリズムが関わっています。コンピュータの出現により、メモリにデータ構造を格納し、CPUとGPUを呼び出してアルゴリズムを実行するコードを書くことができるようになりました。このようにして、現実世界の問題をコンピュータに移し、より効率的な方法でさまざまな複雑な問題を解決できます。</p>
+<p>以上の手順では、各ステップでその時点で最善と思われる選択肢を取っています。つまり、できるだけ額面の大きい貨幣を使い、最終的に実行可能なお釣りの方案を得ています。データ構造とアルゴリズムの観点から見ると、この方法は本質的に「貪欲法」です。</p>
+<p>料理を一品作ることから星間航行に至るまで、ほとんどあらゆる問題の解決にアルゴリズムは欠かせません。コンピュータの登場によって、プログラミングを通じてデータ構造をメモリに格納し、さらにコードを書いて CPU や GPU にアルゴリズムを実行させることが可能になりました。こうして、生活の中の問題をコンピュータに移し、より効率的な方法でさまざまな複雑な問題を解決できるのです。</p>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>データ構造、アルゴリズム、配列、二分探索などの概念についてまだ混乱している場合は、読み続けることをお勧めします。この本は、データ構造とアルゴリズムの理解の領域へと優しく導いてくれるでしょう。</p>
+<p>データ構造、アルゴリズム、配列、二分探索といった概念がまだ少し曖昧でも、そのまま読み進めてください。本書がデータ構造とアルゴリズムの知識の世界へと案内します。</p>
 </div>
 
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-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
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-        <title>第 1 章 アルゴリズムとの出会い - Hello アルゴリズム</title>
+        <title>第 1 章 アルゴリズム入門 - Hello アルゴリズム</title>
       
     
     
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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 <!-- Page content -->
-<h1 id="1">第 1 章 &nbsp; アルゴリズムとの出会い<a class="headerlink" href="#1" title="Permanent link">&para;</a></h1>
-<p><img alt="アルゴリズムとの出会い" class="cover-image" src="../assets/covers/chapter_introduction.jpg" /></p>
+<h1 id="1">第 1 章 &nbsp; アルゴリズム入門<a class="headerlink" href="#1" title="Permanent link">&para;</a></h1>
+<p><img alt="アルゴリズム入門" class="cover-image" src="../assets/covers/chapter_introduction.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>優雅な乙女が踊ります。データと絡み合い、アルゴリズムのメロディーに合わせてスカートをなびかせながら。</p>
-<p>彼女があなたをダンスに誘います。彼女のステップに従って、論理と美に満ちたアルゴリズムの世界に入りましょう。</p>
+<p>一人の少女が軽やかに舞い、データと織り重なり合いながら、スカートの裾にはアルゴリズムの旋律がたなびいています。</p>
+<p>彼女はあなたをこの舞いへと誘います。その足取りに続いて、論理と美しさに満ちたアルゴリズムの世界へ踏み入りましょう。</p>
 </div>
 <h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
-<li><a href="algorithms_are_everywhere/">1.1 &nbsp; アルゴリズムはどこにでもある</a></li>
-<li><a href="what_is_dsa/">1.2 &nbsp; アルゴリズムとは何か</a></li>
+<li><a href="algorithms_are_everywhere/">1.1 &nbsp; アルゴリズムは至るところにある</a></li>
+<li><a href="what_is_dsa/">1.2 &nbsp; アルゴリズムとは</a></li>
 <li><a href="summary/">1.3 &nbsp; まとめ</a></li>
 </ul>
 
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+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
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+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
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-    1.2 &nbsp; アルゴリズムとは何か
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+  <a href="#1" class="md-nav__link">
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-        1. &nbsp; Q &amp; A
+        1. &nbsp; 要点の振り返り
+      
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2-q-a" class="md-nav__link">
+    <span class="md-ellipsis">
+      
+        2. &nbsp; Q &amp; A
       
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-    12.1 &nbsp; 分割統治アルゴリズム
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+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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+    13.4 &nbsp; n クイーン問題
   
 
     
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+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4285,10 +4296,21 @@
     <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
       
         <li class="md-nav__item">
-  <a href="#1-q-a" class="md-nav__link">
+  <a href="#1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; Q &amp; A
+        1. &nbsp; 要点の振り返り
+      
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2-q-a" class="md-nav__link">
+    <span class="md-ellipsis">
+      
+        2. &nbsp; Q &amp; A
       
     </span>
   </a>
@@ -4333,24 +4355,25 @@
 
 <!-- Page content -->
 <h1 id="13">1.3 &nbsp; まとめ<a class="headerlink" href="#13" title="Permanent link">&para;</a></h1>
+<h3 id="1">1. &nbsp; 要点の振り返り<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
-<li>アルゴリズムは日常生活にありふれており、思っているほどアクセスしにくく複雑なものではありません。実際、私たちは既に無意識のうちに多くのアルゴリズムを学び、生活の様々な問題を解決するために使用しています。</li>
-<li>辞書で単語を引く原理は二分探索アルゴリズムと一致しています。二分探索アルゴリズムは分割統治という重要なアルゴリズム概念を体現しています。</li>
-<li>トランプを整理する過程は挿入ソートアルゴリズムと非常に似ています。挿入ソートアルゴリズムは小さなデータセットのソートに適しています。</li>
-<li>通貨でお釣りを計算するステップは本質的に貪欲アルゴリズムに従っており、各ステップでその時点での最良の選択をします。</li>
-<li>アルゴリズムは有限時間内で特定の問題を解決するための段階的な指示のセットですが、データ構造はコンピュータでのデータの組織化と保存方法を定義します。</li>
-<li>データ構造とアルゴリズムは密接に関連しています。データ構造はアルゴリズムの基礎であり、アルゴリズムはデータ構造の機能を活用するステージです。</li>
-<li>データ構造とアルゴリズムをブロックの組み立てに例えることができます。ブロックはデータを表し、ブロックの形状と接続方法はデータ構造を表し、ブロックを組み立てるステップはアルゴリズムに対応します。</li>
+<li>アルゴリズムは日常生活の至る所にあり、決して手の届かない難解な知識ではありません。実際、私たちは気づかないうちに多くのアルゴリズムを身につけ、生活のさまざまな問題を解決しています。</li>
+<li>辞書を引く原理は二分探索アルゴリズムと一致しています。二分探索アルゴリズムは分割統治という重要なアルゴリズム思想を体現しています。</li>
+<li>トランプを整理する過程は挿入ソートアルゴリズムと非常によく似ています。挿入ソートアルゴリズムは小規模なデータ集合のソートに適しています。</li>
+<li>貨幣の釣り銭を求める手順の本質は貪欲アルゴリズムであり、各ステップでその時点で最善と思われる選択を取ります。</li>
+<li>アルゴリズムとは、限られた時間内に特定の問題を解決するための一連の命令または操作手順であり、データ構造とは、コンピュータ内でデータを組織し保存する方法です。</li>
+<li>データ構造とアルゴリズムは密接に結びついています。データ構造はアルゴリズムの土台であり、アルゴリズムはデータ構造に生命を吹き込みます。</li>
+<li>データ構造とアルゴリズムは積み木の組み立てにたとえることができます。積み木はデータを表し、積み木の形や接続方法などはデータ構造を表し、積み木を組み立てる手順がアルゴリズムに対応します。</li>
 </ul>
-<h3 id="1-q-a">1. &nbsp; Q &amp; A<a class="headerlink" href="#1-q-a" title="Permanent link">&para;</a></h3>
-<p><strong>Q</strong>：プログラマーとして、日常の仕事でアルゴリズムを手動で実装する必要があることはめったにありません。最も一般的に使用されるアルゴリズムは、既にプログラミング言語とライブラリに組み込まれており、すぐに使用できます。これは、私たちが仕事で遭遇する問題が、カスタムアルゴリズム設計を必要とする複雑さのレベルにまだ達していないことを示唆していますか？</p>
-<p>特定の仕事スキルが武術の「技」のようなものだとすれば、基礎科目は「内功」のようなものです。</p>
-<p>アルゴリズム（およびその他の基礎科目）を学ぶ意義は、必ずしも仕事でそれらを一から実装することではなく、概念の確固たる理解に基づいて、より専門的な意思決定と問題解決を可能にし、それによって仕事の全体的な質を向上させることだと私は信じています。例えば、すべてのプログラミング言語には組み込みのソート関数があります：</p>
+<h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
+<p><strong>Q</strong>：プログラマーとして、私は日常業務でアルゴリズムを使って問題を解決したことがありません。よく使うアルゴリズムはプログラミング言語にすべてカプセル化されており、そのまま使えばよいです。これは、仕事上の問題がまだアルゴリズムを必要とする段階に達していないことを意味するのでしょうか？</p>
+<p>具体的な仕事のスキルを武術の「型」にたとえるなら、基礎科目はむしろ「内功」に近いものです。</p>
+<p>私は、アルゴリズム（およびその他の基礎科目）を学ぶ意義は、仕事でそれをゼロから実装することではなく、学んだ知識に基づいて問題解決の際に専門的な反応や判断を下せるようになり、その結果として仕事全体の品質を高めることにあると考えています。簡単な例を挙げると、どのプログラミング言語にもソート関数が組み込まれています。</p>
 <ul>
-<li>データ構造とアルゴリズムを学んでいない場合、どんなデータが与えられても、このソート関数に渡すだけかもしれません。スムーズに動作し、良いパフォーマンスを示し、問題がないように見えます。</li>
-<li>しかし、アルゴリズムを学んだことがあれば、組み込みのソート関数の時間複雑度は通常<span class="arithmatex">\(O(n \log n)\)</span>であることを理解しています。さらに、データが固定桁数の整数（学生IDなど）で構成されている場合、基数ソートのようなより効率的なアプローチを適用でき、時間複雑度をO(nk)に削減できます。ここでkは桁数です。大量のデータを処理する際、節約された時間は重要な価値に変わります — コストの削減、ユーザーエクスペリエンスの向上、システムパフォーマンスの向上。</li>
+<li>もしデータ構造とアルゴリズムを学んでいなければ、どんなデータが与えられても、そのソート関数に任せてしまうかもしれません。問題なく動き、性能も悪くなく、一見すると特に問題はありません。</li>
+<li>しかしアルゴリズムを学んでいれば、組み込みのソート関数の時間計算量が <span class="arithmatex">\(O(n \log n)\)</span> であることを知っています。さらに、与えられたデータが固定桁数の整数（例えば学籍番号）であれば、より効率の高い「基数ソート」を使って、時間計算量を <span class="arithmatex">\(O(nk)\)</span> に下げることができます。ここで <span class="arithmatex">\(k\)</span> は桁数です。データ量が非常に大きい場合、節約できた実行時間は大きな価値を生みます（コスト削減、体験向上など）。</li>
 </ul>
-<p>エンジニアリングでは、多くの問題を最適に解決することは困難です。ほとんどは「準最適」解決策で対処されます。問題の難しさは、その固有の複雑さだけでなく、それに取り組む人の知識と経験にも依存します。専門知識と経験が深いほど、分析がより徹底的になり、問題をより優雅に解決できます。</p>
+<p>工学分野では、多くの問題で最適解に到達することは難しく、少なくない問題は「だいたい」解決されているにすぎません。問題の難しさは、一方では問題そのものの性質に依存し、他方ではそれを観測する人の知識の蓄積にも依存します。知識が充実し、経験が豊富であるほど、問題分析はより深くなり、問題はより洗練された形で解決できるようになります。</p>
 
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@@ -4373,7 +4396,7 @@ aria-label="フッター"
   <a
     href="../what_is_dsa/"
     class="md-footer__link md-footer__link--prev"
-    aria-label="前: 1.2 &amp;nbsp; アルゴリズムとは何か"
+    aria-label="前: 1.2 &amp;nbsp; アルゴリズムとは"
     rel="prev"
   >
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@@ -4385,7 +4408,7 @@ aria-label="フッター"
         前
       </span>
       <div class="md-ellipsis">
-        1.2 &nbsp; アルゴリズムとは何か
+        1.2 &nbsp; アルゴリズムとは
       </div>
     </div>
   </a>
@@ -4397,7 +4420,7 @@ aria-label="フッター"
   <a
     href="../../chapter_computational_complexity/"
     class="md-footer__link md-footer__link--next"
-    aria-label="次: 第 2 章 &amp;nbsp; 複雑度解析"
+    aria-label="次: 第 2 章 &amp;nbsp; 計算量解析"
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         次
       </span>
       <div class="md-ellipsis">
-        第 2 章 &nbsp; 複雑度解析
+        第 2 章 &nbsp; 計算量解析
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     </div>
     <div class="md-footer__button md-icon">
diff --git a/ja/chapter_introduction/what_is_dsa/index.html b/ja/chapter_introduction/what_is_dsa/index.html
index 89768a20c..a39c5d4b6 100644
--- a/ja/chapter_introduction/what_is_dsa/index.html
+++ b/ja/chapter_introduction/what_is_dsa/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -39,7 +39,7 @@
     
     
       
-        <title>1.2 アルゴリズムとは何か - Hello アルゴリズム</title>
+        <title>1.2 アルゴリズムとは - Hello アルゴリズム</title>
       
     
     
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -152,7 +152,7 @@
         <div class="md-header__topic" data-md-component="header-topic">
           <span class="md-ellipsis">
             
-              1.2 &nbsp; アルゴリズムとは何か
+              1.2 &nbsp; アルゴリズムとは
             
           </span>
         </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
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-    序
+    はじめに
   
 
           </label>
@@ -620,7 +620,7 @@
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-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -657,7 +657,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -675,7 +675,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -866,7 +866,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1143,7 +1143,7 @@
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-    3.3 &nbsp; 数値の符号化 *
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+    12.1 &nbsp; 分割統治法
   
 
     
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-    15.1 &nbsp; 貪欲アルゴリズム
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
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 <!-- Page content -->
-<h1 id="12">1.2 &nbsp; アルゴリズムとは何か<a class="headerlink" href="#12" title="Permanent link">&para;</a></h1>
+<h1 id="12">1.2 &nbsp; アルゴリズムとは<a class="headerlink" href="#12" title="Permanent link">&para;</a></h1>
 <h2 id="121">1.2.1 &nbsp; アルゴリズムの定義<a class="headerlink" href="#121" title="Permanent link">&para;</a></h2>
-<p><u>アルゴリズム</u>は、有限時間内で特定の問題を解決するための一連の指示またはステップです。以下の特徴があります：</p>
+<p><u>アルゴリズム（algorithm）</u>とは、限られた時間内に特定の問題を解決するための一連の命令または操作手順であり、次のような特徴を持ちます。</p>
 <ul>
-<li>問題が明確に定義されており、入力と出力の明確な定義が含まれています。</li>
-<li>アルゴリズムは実行可能で、有限の回数のステップ、時間、メモリ空間内で完了できることを意味します。</li>
-<li>各ステップには明確な意味があります。同じ入力と条件の下で出力は一貫して同じです。</li>
+<li>問題が明確であり、入力と出力の定義がはっきりしています。</li>
+<li>実行可能であり、有限の手順、時間、メモリ空間で完了できます。</li>
+<li>各手順の意味が確定しており、同じ入力と実行条件では常に同じ出力になります。</li>
 </ul>
 <h2 id="122">1.2.2 &nbsp; データ構造の定義<a class="headerlink" href="#122" title="Permanent link">&para;</a></h2>
-<p><u>データ構造</u>は、コンピュータ内でデータを組織し保存する方法で、以下の設計目標があります：</p>
+<p><u>データ構造（data structure）</u>とは、データを整理して保存する方式であり、データの内容、データ間の関係、データの操作方法を含み、次のような設計目標があります。</p>
 <ul>
-<li>コンピュータのメモリを節約するために空間占有を最小化する。</li>
-<li>データ操作を可能な限り高速にし、データのアクセス、追加、削除、更新などをカバーする。</li>
-<li>効率的なアルゴリズム実行を可能にするために、簡潔なデータ表現と論理情報を提供する。</li>
+<li>使用する空間をできるだけ少なくし、コンピュータのメモリを節約します。</li>
+<li>データの操作をできるだけ高速にし、アクセス、追加、削除、更新などを含みます。</li>
+<li>簡潔なデータ表現と論理情報を提供し、アルゴリズムが効率よく動作できるようにします。</li>
 </ul>
-<p><strong>データ構造の設計はバランスを取る行為であり、しばしばトレードオフが必要です</strong>。一つの側面を改善したい場合、しばしば別の側面で妥協する必要があります。以下は2つの例です：</p>
+<p><strong>データ構造の設計はトレードオフに満ちた過程です</strong>。ある面を改善したい場合、別の面で妥協が必要になることがよくあります。以下に 2 つの例を示します。</p>
 <ul>
-<li>配列と比較して、連結リストはデータの追加と削除においてより便利ですが、データアクセス速度を犠牲にします。</li>
-<li>連結リストと比較して、グラフはより豊富な論理情報を提供しますが、より多くのメモリ空間が必要です。</li>
+<li>連結リストは配列に比べてデータの追加や削除がしやすい一方で、データアクセス速度を犠牲にしています。</li>
+<li>グラフは連結リストに比べてより豊富な論理情報を提供しますが、より大きなメモリ空間を必要とします。</li>
 </ul>
 <h2 id="123">1.2.3 &nbsp; データ構造とアルゴリズムの関係<a class="headerlink" href="#123" title="Permanent link">&para;</a></h2>
-<p>以下の図に示すように、データ構造とアルゴリズムは高度に関連し、密接に統合されており、具体的には以下の3つの側面があります：</p>
+<p>以下の図のように、データ構造とアルゴリズムは高度に関連し、密接に結び付いており、具体的には次の 3 つの点に表れます。</p>
 <ul>
-<li>データ構造はアルゴリズムの基礎です。構造化されたデータ保存とアルゴリズムのためのデータ操作方法を提供します。</li>
-<li>アルゴリズムはデータ構造に活力を注入します。データ構造だけではデータ情報を保存するだけです。アルゴリズムの応用によって、特定の問題を解決できます。</li>
-<li>アルゴリズムは異なるデータ構造に基づいて実装できることが多いですが、実行効率は大きく異なることがあります。適切なデータ構造を選択することが鍵です。</li>
+<li>データ構造はアルゴリズムの土台です。データ構造はアルゴリズムに対して、構造化して格納されたデータと、そのデータを操作する方法を提供します。</li>
+<li>アルゴリズムはデータ構造に命を吹き込みます。データ構造そのものはデータ情報を保存するだけであり、アルゴリズムと組み合わせて初めて特定の問題を解決できます。</li>
+<li>アルゴリズムは通常、異なるデータ構造に基づいて実装できますが、実行効率が大きく異なる場合があり、適切なデータ構造を選ぶことが重要です。</li>
 </ul>
 <p><img alt="データ構造とアルゴリズムの関係" class="animation-figure" src="../what_is_dsa.assets/relationship_between_data_structure_and_algorithm.png" /></p>
 <p align="center"> 図 1-4 &nbsp; データ構造とアルゴリズムの関係 </p>
 
-<p>データ構造とアルゴリズムは、以下の図に示すように、ブロックのセットに例えることができます。ブロックセットには多数のピースが含まれ、詳細な組み立て説明書が付いています。これらの説明書に段階的に従うことで、複雑なブロックモデルを構築できます。</p>
-<p><img alt="ブロックの組み立て" class="animation-figure" src="../what_is_dsa.assets/assembling_blocks.png" /></p>
-<p align="center"> 図 1-5 &nbsp; ブロックの組み立て </p>
+<p>データ構造とアルゴリズムは、以下の図に示す組み立てブロックのようなものです。1 セットのブロックには多くの部品が含まれるだけでなく、詳しい組み立て説明書も付いています。説明書に従って一歩ずつ操作すれば、精巧なブロック模型を組み立てられます。</p>
+<p><img alt="組み立てブロック" class="animation-figure" src="../what_is_dsa.assets/assembling_blocks.png" /></p>
+<p align="center"> 図 1-5 &nbsp; 組み立てブロック </p>
 
-<p>両者の詳細な対応関係は以下の表に示されています。</p>
-<p align="center"> 表 1-1 &nbsp; データ構造とアルゴリズムをブロックと比較 </p>
+<p>両者の詳細な対応関係を次の表に示します。</p>
+<p align="center"> 表 1-1 &nbsp; データ構造とアルゴリズムを組み立てブロックにたとえる </p>
 
 <div class="center-table">
 <table>
 <thead>
 <tr>
 <th>データ構造とアルゴリズム</th>
-<th>ブロック</th>
+<th>組み立てブロック</th>
 </tr>
 </thead>
 <tbody>
 <tr>
 <td>入力データ</td>
-<td>未組み立てのブロック</td>
+<td>まだ組み立てていないブロック</td>
 </tr>
 <tr>
 <td>データ構造</td>
-<td>ブロックの組織、形状、サイズ、接続などを含む</td>
+<td>ブロックの構成形式。形状、大きさ、接続方法などを含む</td>
 </tr>
 <tr>
 <td>アルゴリズム</td>
-<td>ブロックを望ましい形状に組み立てる一連のステップ</td>
+<td>ブロックを目標の形に組み上げる一連の操作手順</td>
 </tr>
 <tr>
 <td>出力データ</td>
-<td>完成したブロックモデル</td>
+<td>ブロック模型</td>
 </tr>
 </tbody>
 </table>
 </div>
-<p>データ構造とアルゴリズムはプログラミング言語から独立していることは注目に値します。この理由により、この本は複数のプログラミング言語での実装を提供できます。</p>
+<p>特筆すべき点として、データ構造とアルゴリズムはプログラミング言語から独立しています。だからこそ、本書では複数のプログラミング言語に基づく実装を提供できます。</p>
 <div class="admonition tip">
-<p class="admonition-title">慣習的な略語</p>
-<p>実生活の議論では、「データ構造とアルゴリズム」を単純に「アルゴリズム」と呼ぶことがよくあります。例えば、よく知られたLeetCodeアルゴリズム問題は、実際にはデータ構造とアルゴリズムの両方の知識をテストしています。</p>
+<p class="admonition-title">慣習的な略称</p>
+<p>実際の議論では、私たちは通常「データ構造とアルゴリズム」を略して「アルゴリズム」と呼びます。たとえば広く知られている LeetCode のアルゴリズム問題は、実際にはデータ構造とアルゴリズムの両方の知識を同時に問うています。</p>
 </div>
 
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   <a
     href="../algorithms_are_everywhere/"
     class="md-footer__link md-footer__link--prev"
-    aria-label="前: 1.1 &amp;nbsp; アルゴリズムはどこにでもある"
+    aria-label="前: 1.1 &amp;nbsp; アルゴリズムは至るところにある"
     rel="prev"
   >
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         前
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-        1.1 &nbsp; アルゴリズムはどこにでもある
+        1.1 &nbsp; アルゴリズムは至るところにある
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+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    1.2 &nbsp; アルゴリズムとは
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    1.3 &nbsp; まとめ
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4zm10 14.5-4-4-4 4V20h8zm-4-5 4-4V4H8v3.5zM10 6h4v.75l-2 2-2-2z"/></svg>
+  
+  <span class="md-ellipsis">
+    
+  
+    第 2 章 &nbsp; 計算量解析
+  
+
+    
+  </span>
+  
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            
+  
+    第 2 章 &nbsp; 計算量解析
+  
+
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    2.1 &nbsp; アルゴリズム効率の評価
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    2.2 &nbsp; 反復と再帰
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    2.3 &nbsp; 時間計算量
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    2.4 &nbsp; 空間計算量
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    2.5 &nbsp; まとめ
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_data_structure/" class="md-nav__link ">
+              
+  
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8zm-2 2H5v4h4zM12 2l5.5 9h-11zm0 3.86L10.08 9h3.84zM17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5"/></svg>
+  
+  <span class="md-ellipsis">
+    
+  
+    第 3 章 &nbsp; データ構造
+  
+
+    
+  </span>
+  
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            
+  
+    第 3 章 &nbsp; データ構造
+  
+
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    3.1 &nbsp; データ構造の分類
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    3.2 &nbsp; 基本データ型
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    3.3 &nbsp; 数値エンコーディング *
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    3.4 &nbsp; 文字エンコーディング *
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    3.5 &nbsp; まとめ
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5zm4 2v2H5V7zm-2 6v-2h2v2zm0 2h2v2H5zm13 2H9v-2h9zm0-4H9v-2h9zm0-4H9V7h9z"/></svg>
+  
+  <span class="md-ellipsis">
+    
+  
+    第 4 章 &nbsp; 配列と連結リスト
+  
+
+    
+  </span>
+  
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            
+  
+    第 4 章 &nbsp; 配列と連結リスト
+  
+
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    4.1 &nbsp; 配列
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    4.2 &nbsp; 連結リスト
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    4.3 &nbsp; リスト
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    4.4 &nbsp; メモリとキャッシュ *
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    4.5 &nbsp; まとめ
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38zM6.77 14.32l.37-1.76 8.79 1.85-.37 1.76zm1.16-4.21.76-1.61 8.14 3.78-.76 1.62zm2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37zm4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21zM6.59 18.41v-1.8h8.98v1.8z"/></svg>
+  
+  <span class="md-ellipsis">
+    
+  
+    第 5 章 &nbsp; スタックとキュー
+  
+
+    
+  </span>
+  
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            
+  
+    第 5 章 &nbsp; スタックとキュー
+  
+
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    5.1 &nbsp; スタック
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    5.2 &nbsp; キュー
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    5.3 &nbsp; 両端キュー
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    5.4 &nbsp; まとめ
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_hashing/" class="md-nav__link ">
+              
+  
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21zm-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54zM19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2"/></svg>
+  
+  <span class="md-ellipsis">
+    
+  
+    第 6 章 &nbsp; ハッシュテーブル
+  
+
+    
+  </span>
+  
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            
+  
+    第 6 章 &nbsp; ハッシュテーブル
+  
+
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    6.1 &nbsp; ハッシュテーブル
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    6.2 &nbsp; ハッシュ衝突
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    6.3 &nbsp; ハッシュアルゴリズム
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    6.4 &nbsp; まとめ
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
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+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_tree/" class="md-nav__link ">
+              
+  
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1"/></svg>
+  
+  <span class="md-ellipsis">
+    
+  
+    第 7 章 &nbsp; 木
+  
+
+    
+  </span>
+  
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            
+  
+    第 7 章 &nbsp; 木
+  
+
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    7.1 &nbsp; 二分木
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    7.2 &nbsp; 二分木の走査
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    7.3 &nbsp; 二分木の配列表現
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    7.4 &nbsp; 二分探索木
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    7.5 &nbsp; AVL 木 *
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    7.6 &nbsp; まとめ
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_heap/" class="md-nav__link ">
+              
+  
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1"/></svg>
+  
+  <span class="md-ellipsis">
+    
+  
+    第 8 章 &nbsp; ヒープ
+  
+
+    
+  </span>
+  
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            
+  
+    第 8 章 &nbsp; ヒープ
+  
+
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    8.1 &nbsp; ヒープ
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    8.2 &nbsp; ヒープ構築
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    8.3 &nbsp; Top-k 問題
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    8.4 &nbsp; まとめ
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_graph/" class="md-nav__link ">
+              
+  
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59zM6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43s.83.16 1.12.43l4.28-2.53zM12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68s1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25zm2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24z"/></svg>
+  
+  <span class="md-ellipsis">
+    
+  
+    第 9 章 &nbsp; グラフ
+  
+
+    
+  </span>
+  
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            
+  
+    第 9 章 &nbsp; グラフ
+  
+
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    9.1 &nbsp; グラフ
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    9.2 &nbsp; グラフの基本操作
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    9.3 &nbsp; グラフの走査
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    9.4 &nbsp; まとめ
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_searching/" class="md-nav__link ">
+              
+  
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4zM3 16v-2h6v2zm0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1z"/></svg>
+  
+  <span class="md-ellipsis">
+    
+  
+    第 10 章 &nbsp; 探索
+  
+
+    
+  </span>
+  
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            
+  
+    第 10 章 &nbsp; 探索
+  
+
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    10.1 &nbsp; 二分探索
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    10.2 &nbsp; 二分探索の挿入位置
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    10.3 &nbsp; 二分探索の境界
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    10.4 &nbsp; ハッシュによる最適化戦略
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    10.5 &nbsp; 探索アルゴリズム再考
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    10.6 &nbsp; まとめ
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_sorting/" class="md-nav__link ">
+              
+  
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2z"/></svg>
+  
+  <span class="md-ellipsis">
+    
+  
+    第 11 章 &nbsp; ソート
+  
+
+    
+  </span>
+  
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            
+  
+    第 11 章 &nbsp; ソート
+  
+
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    11.1 &nbsp; ソートアルゴリズム
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    11.2 &nbsp; 選択ソート
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    11.3 &nbsp; バブルソート
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    11.4 &nbsp; 挿入ソート
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    11.5 &nbsp; クイックソート
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    11.6 &nbsp; マージソート
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    11.7 &nbsp; ヒープソート
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    11.8 &nbsp; バケットソート
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    11.9 &nbsp; 計数ソート
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    11.10 &nbsp; 基数ソート
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    11.11 &nbsp; まとめ
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7zM2 9v6h5V9zm10 0v2H9v2h3v2l3-3zm5 2v2h5v-2zm0 4v2h5v-2z"/></svg>
+  
+  <span class="md-ellipsis">
+    
+  
+    第 12 章 &nbsp; 分割統治
+  
+
+    
+  </span>
+  
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            
+  
+    第 12 章 &nbsp; 分割統治
+  
+
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    12.1 &nbsp; 分割統治法
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    12.2 &nbsp; 分割統治探索戦略
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    12.3 &nbsp; 二分木の構築問題
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    12.4 &nbsp; ハノイの塔の問題
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    12.5 &nbsp; まとめ
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_backtracking/" class="md-nav__link ">
+              
+  
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2zm-4-6H5v-2h2z"/></svg>
+  
+  <span class="md-ellipsis">
+    
+  
+    第 13 章 &nbsp; バックトラッキング
+  
+
+    
+  </span>
+  
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            
+  
+    第 13 章 &nbsp; バックトラッキング
+  
+
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    13.2 &nbsp; 全順列問題
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    13.3 &nbsp; 部分和問題
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    13.4 &nbsp; n クイーン問題
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    13.5 &nbsp; まとめ
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3zm0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4zm0 2v4h4v-4zm4 10v-4H4v4zm6-12V4h-4v4zm6-4h-4v4h4z"/></svg>
+  
+  <span class="md-ellipsis">
+    
+  
+    第 14 章 &nbsp; 動的計画法
+  
+
+    
+  </span>
+  
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            
+  
+    第 14 章 &nbsp; 動的計画法
+  
+
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    14.1 &nbsp; 動的計画法入門
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    14.2 &nbsp; 動的計画法の問題特性
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    14.3 &nbsp; 動的計画法の問題解決の考え方
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    14.4 &nbsp; 0-1 ナップサック問題
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    14.5 &nbsp; 完全ナップサック問題
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    14.6 &nbsp; 編集距離問題
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    14.7 &nbsp; まとめ
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_greedy/" class="md-nav__link ">
+              
+  
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16z"/></svg>
+  
+  <span class="md-ellipsis">
+    
+  
+    第 15 章 &nbsp; 貪欲法
+  
+
+    
+  </span>
+  
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            
+  
+    第 15 章 &nbsp; 貪欲法
+  
+
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    15.1 &nbsp; 貪欲法
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    15.2 &nbsp; 分数ナップサック問題
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    15.3 &nbsp; 最大容量問題
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    15.4 &nbsp; 最大積分割問題
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    15.5 &nbsp; まとめ
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
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+          
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+        
+      
+        
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+        
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+    
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+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_appendix/" class="md-nav__link ">
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+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2zm1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4"/></svg>
+  
+  <span class="md-ellipsis">
+    
+  
+    第 16 章 &nbsp; 付録
+  
+
+    
+  </span>
+  
+  
+
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+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
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+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            
+  
+    第 16 章 &nbsp; 付録
+  
+
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+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    16.1 &nbsp; プログラミング環境のインストール
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
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+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    16.2 &nbsp; 一緒に制作に参加しましょう
+  
+
+    
+  </span>
+  
+  
+
+      </a>
+    </li>
+  
+
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    16.3 &nbsp; 用語集
+  
+
+    
+  </span>
+  
+  
+
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+    </li>
+  
+
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+        </nav>
+      
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+
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+  
+  <span class="md-ellipsis">
+    
+  
+    参考文献
+  
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+  </span>
+  
+  
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+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
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+            
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+</nav>
+                  </div>
+                </div>
+              </div>
+            
+            
+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
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+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#_2" class="md-nav__link">
+    <span class="md-ellipsis">
+      
+        長所と短所
+      
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#_3" class="md-nav__link">
+    <span class="md-ellipsis">
+      
+        購入リンク
+      
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#_4" class="md-nav__link">
+    <span class="md-ellipsis">
+      
+        あとがき
+      
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
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+          
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+              
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+                
+                  <!-- Tags -->
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+    <a
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+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path fill="currentColor" d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0M88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24z"/></svg>
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+  
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+<!-- Page content -->
+<h1 id="_1">紙の書籍<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h1>
+<p>長い時間をかけて磨き上げた『Hello アルゴリズム』の紙の書籍が、ついに発売されました！今の気持ちは、次の一節で表せます：</p>
+<p align="center">風を追い月を追って立ち止まるな、草原の果てには春の山がある。</p>
+
+<p><img alt="" class="animation-figure" src="index.assets/paper_book_overview.jpg" /></p>
+<p>以下の動画では紙の書籍を紹介しており、私の考えもいくつか含まれています：</p>
+<ul>
+<li>データ構造とアルゴリズムを学ぶ重要性。</li>
+<li>なぜ紙の書籍で Python を選んだのか。</li>
+<li>知識共有に対する理解。</li>
+</ul>
+<blockquote>
+<p>新人 UP 主ですので、ぜひ応援と高評価・チャンネル登録をお願いします～ありがとうございます！</p>
+</blockquote>
+<div class="video-container">
+    <iframe src="//player.bilibili.com/player.html?aid=1051597767&bvid=BV1QH4y157uC&cid=1462564112&p=1&autoplay=0" scrolling="no" border="0" frameborder="no" framespacing="0" allowfullscreen="true"> </iframe>
+</div>
+
+<p>紙の書籍のスナップショット：</p>
+<p><img alt="" class="animation-figure" src="index.assets/paper_book_chapter_heap.jpg" /></p>
+<p><img alt="" class="animation-figure" src="index.assets/paper_book_avl_tree.jpg" /></p>
+<h2 id="_2">長所と短所<a class="headerlink" href="#_2" title="Permanent link">&para;</a></h2>
+<p>紙の書籍ならではの魅力を、簡単にまとめると次のとおりです：</p>
+<ul>
+<li>フルカラー印刷を採用し、本書の「アニメーション図解」の強みをそのまま活かせます。</li>
+<li>紙の素材にもこだわり、色彩を高い精度で再現しつつ、紙の書籍ならではの質感も残しています。</li>
+<li>紙の書籍版は Web 版よりも書式が整っており、たとえば図中の数式には斜体を用いています。</li>
+<li>価格を上げずに、マインドマップの折り込みページやしおりも付属します。</li>
+<li>紙の書籍、Web 版、PDF 版で内容は同期しており、自由に切り替えて読めます。</li>
+</ul>
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>紙の書籍と Web 版を同期させるのは難しいため、細かな違いが生じる場合があります。ご了承ください！</p>
+</div>
+<p>もちろん、購入前に検討しておくべき点もいくつかあります：</p>
+<ul>
+<li>Python 言語を使用しているため、あなたの主言語と合わない可能性があります（Python は疑似コードと捉え、考え方の理解を重視してください）。</li>
+<li>フルカラー印刷は図解やコードの読みやすさを大きく高める一方で、白黒印刷より価格はやや高くなります。</li>
+</ul>
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>「印刷品質」と「価格」は、アルゴリズムにおける「時間効率」と「空間効率」のようなもので、両立は容易ではありません。そして私は、「印刷品質」は「時間効率」に当たるため、より重視すべきだと考えています。</p>
+</div>
+<h2 id="_3">購入リンク<a class="headerlink" href="#_3" title="Permanent link">&para;</a></h2>
+<p>紙の書籍に興味があれば、ぜひ一冊ご検討ください。新刊の 5 割引を用意していただきましたので、<a href="https://3.cn/1X-qmTD3">こちらのリンク</a>をご覧いただくか、以下の QR コードをスキャンしてください：</p>
+<p><img alt="" class="animation-figure" src="index.assets/book_jd_link.jpg" /></p>
+<h2 id="_4">あとがき<a class="headerlink" href="#_4" title="Permanent link">&para;</a></h2>
+<p>当初、私は紙の書籍出版に必要な作業量を甘く見ていて、オープンソースプロジェクトをきちんと保守していれば、紙の書籍版も何らかの自動化手段で生成できると思っていました。実際には、紙の書籍の制作フローとオープンソースプロジェクトの更新の仕組みには大きな違いがあり、その間をつなぐには多くの追加作業が必要でした。</p>
+<p>一冊の本の初稿と出版基準を満たす完成稿との間には、なお大きな隔たりがあります。出版社（企画、編集、デザイン、マーケティングなど）と著者が力を合わせ、長い時間をかけて磨き上げていく必要があります。ここで、図霊の企画編集者である王軍花さん、そして人民郵電出版社と図霊コミュニティで本書の出版工程に携わってくださったすべての皆さまに感謝いたします！</p>
+<p>この本があなたの助けになれば幸いです！</p>
+
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diff --git a/ja/chapter_preface/about_the_book/index.html b/ja/chapter_preface/about_the_book/index.html
index a92e17f70..57497669f 100644
--- a/ja/chapter_preface/about_the_book/index.html
+++ b/ja/chapter_preface/about_the_book/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -39,7 +39,7 @@
     
     
       
-        <title>0.1 この本について - Hello アルゴリズム</title>
+        <title>0.1 本書について - Hello アルゴリズム</title>
       
     
     
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -152,7 +152,7 @@
         <div class="md-header__topic" data-md-component="header-topic">
           <span class="md-ellipsis">
             
-              0.1 &nbsp; この本について
+              0.1 &nbsp; 本書について
             
           </span>
         </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -701,7 +701,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -729,7 +729,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -866,7 +866,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1143,7 +1143,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1171,7 +1171,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1674,7 +1674,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1696,7 +1696,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1718,7 +1718,7 @@
   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -2025,7 +2025,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2188,7 +2188,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2574,7 +2574,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2630,7 +2630,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2658,7 +2658,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3196,7 +3196,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3252,7 +3252,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3280,7 +3280,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3473,7 +3473,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3501,7 +3501,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3642,7 +3642,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3670,7 +3670,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3698,7 +3698,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3726,7 +3726,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3919,7 +3919,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4164,7 +4164,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4376,47 +4376,48 @@
 
 
 <!-- Page content -->
-<h1 id="01">0.1 &nbsp; この本について<a class="headerlink" href="#01" title="Permanent link">&para;</a></h1>
-<p>このオープンソースプロジェクトは、データ構造とアルゴリズムに関する無料で初心者にやさしいクラッシュコースの作成を目指しています。</p>
+<h1 id="01">0.1 &nbsp; 本書について<a class="headerlink" href="#01" title="Permanent link">&para;</a></h1>
+<p>本プロジェクトは、オープンソースで無料、かつ初心者にやさしいデータ構造とアルゴリズムの入門書を作ることを目的としています。</p>
 <ul>
-<li>アニメーション付きの図解、理解しやすい内容、滑らかな学習曲線により、初心者がデータ構造とアルゴリズムの「知識マップ」を探索するのに役立ちます。</li>
-<li>ワンクリックでコードを実行できるため、読者のプログラミングスキルの向上と、アルゴリズムの動作原理およびデータ構造の基礎実装の理解に役立ちます。</li>
-<li>教えることによる学習を促進し、質問や洞察の共有を自由に行ってください。議論を通じて一緒に成長しましょう。</li>
+<li>全編でアニメーション付きの図解を採用し、内容は明快で理解しやすく、学習曲線もなだらかで、初心者がデータ構造とアルゴリズムの知識地図を探求できるよう導きます。</li>
+<li>ソースコードはワンクリックで実行でき、読者が演習を通じてプログラミング能力を高め、アルゴリズムの動作原理とデータ構造の内部実装を理解する助けとなります。</li>
+<li>読者どうしの助け合いによる学習を推奨しており、コメント欄で質問や見解を共有し、対話と議論を通じてともに成長していくことを歓迎します。</li>
 </ul>
 <h2 id="011">0.1.1 &nbsp; 対象読者<a class="headerlink" href="#011" title="Permanent link">&para;</a></h2>
-<p>もしあなたがアルゴリズムに触れたばかりで経験が限られている場合、またはアルゴリズムである程度の経験を積んでいても、データ構造とアルゴリズムについて曖昧な理解しかなく、常に「分かった」と「うーん」の間を行き来している場合、この本はあなたのためのものです！</p>
-<p>すでにある程度の問題解決経験を積んでおり、ほとんどのタイプの問題に精通している場合、この本はアルゴリズムの知識体系を復習し整理するのに役立ちます。リポジトリのソースコードは「問題解決ツールキット」や「アルゴリズムチートシート」として使用できます。</p>
-<p>もしあなたがアルゴリズムの専門家であれば、貴重な提案をいただくか、<a href="https://www.hello-algo.com/chapter_appendix/contribution/">参加して協力</a>していただければと思います。</p>
+<p>もしあなたがアルゴリズム初心者で、これまでアルゴリズムに触れたことがない、あるいはすでに多少の問題演習の経験はあるものの、データ構造とアルゴリズムについてはまだ曖昧な理解にとどまり、できるかできないかの間を行き来しているなら、本書はまさにあなたのために作られています！</p>
+<p>もしすでに一定量の問題演習を積み、ほとんどの問題パターンに慣れているなら、本書はアルゴリズム知識体系の復習と整理に役立ちます。リポジトリのソースコードは「問題演習ツール集」や「アルゴリズム辞典」として活用できます。</p>
+<p>もしあなたがアルゴリズムの「達人」なら、貴重なご提案をいただけることを楽しみにしています。あるいは<a href="https://www.hello-algo.com/chapter_appendix/contribution/">一緒に執筆に参加</a>してください。</p>
 <div class="admonition success">
 <p class="admonition-title">前提条件</p>
-<p>少なくとも一つのプログラミング言語で簡単なコードを書いて読むことができる必要があります。</p>
+<p>少なくともいずれか一つの言語でのプログラミング基礎があり、簡単なコードを読んだり書いたりできる必要があります。</p>
 </div>
 <h2 id="012">0.1.2 &nbsp; 内容構成<a class="headerlink" href="#012" title="Permanent link">&para;</a></h2>
-<p>本書の主な内容を下図に示します。</p>
+<p>本書の主な内容は以下の図のとおりです。</p>
 <ul>
-<li><strong>計算量解析</strong>: データ構造とアルゴリズムを評価する側面と方法を探求します。時間計算量と空間計算量を導出する方法、および一般的なタイプと例を扱います。</li>
-<li><strong>データ構造</strong>: 基本的なデータ型、分類方法、定義、長所と短所、一般的な操作、タイプ、応用、および配列、連結リスト、スタック、キュー、ハッシュテーブル、木、ヒープ、グラフなどのデータ構造の実装方法に焦点を当てます。</li>
-<li><strong>アルゴリズム</strong>: アルゴリズムを定義し、その長所と短所、効率性、応用シナリオ、問題解決ステップについて議論し、検索、ソート、分割統治、バックトラッキング、動的プログラミング、貪欲アルゴリズムなど、さまざまなアルゴリズムのサンプル問題を含みます。</li>
+<li><strong>計算量解析</strong>：データ構造とアルゴリズムを評価する観点と方法。時間計算量と空間計算量の求め方、代表的な種類、例など。</li>
+<li><strong>データ構造</strong>：基本データ型とデータ構造の分類方法。配列、連結リスト、スタック、キュー、ハッシュテーブル、木、ヒープ、グラフなどのデータ構造の定義、長所と短所、基本操作、代表的な種類、典型的な応用、実装方法など。</li>
+<li><strong>アルゴリズム</strong>：探索、ソート、分割統治、バックトラッキング、動的計画法、貪欲法などのアルゴリズムの定義、長所と短所、効率、適用場面、問題を解く手順、例題など。</li>
 </ul>
 <p><img alt="本書の主な内容" class="animation-figure" src="../about_the_book.assets/hello_algo_mindmap.png" /></p>
 <p align="center"> 図 0-1 &nbsp; 本書の主な内容 </p>
 
 <h2 id="013">0.1.3 &nbsp; 謝辞<a class="headerlink" href="#013" title="Permanent link">&para;</a></h2>
-<p>本書は、オープンソースコミュニティの多数の貢献者による共同の努力のもと、継続的に改善されています。時間と労力を注いで執筆に携わってくださったすべての方々に感謝します。貢献者は以下のとおりです（GitHub により自動生成された順序）：krahets、coderonion、Gonglja、nuomi1、Reanon、justin-tse、hpstory、danielsss、curtishd、night-cruise、S-N-O-R-L-A-X、rongyi、msk397、gvenusleo、khoaxuantu、rivertwilight、K3v123、gyt95、zhuoqinyue、yuelinxin、Zuoxun、mingXta、Phoenix0415、FangYuan33、GN-Yu、longsizhuo、IsChristina、xBLACKICEx、guowei-gong、Cathay-Chen、pengchzn、QiLOL、magentaqin、hello-ikun、JoseHung、qualifier1024、thomasq0、sunshinesDL、L-Super、Guanngxu、Transmigration-zhou、WSL0809、Slone123c、lhxsm、yuan0221、what-is-me、Shyam-Chen、theNefelibatas、longranger2、codeberg-user、xiongsp、JeffersonHuang、prinpal、seven1240、Wonderdch、malone6、xiaomiusa87、gaofer、bluebean-cloud、a16su、SamJin98、hongyun-robot、nanlei、XiaChuerwu、yd-j、iron-irax、mgisr、steventimes、junminhong、heshuyue、danny900714、MolDuM、Nigh、Dr-XYZ、XC-Zero、reeswell、PXG-XPG、NI-SW、Horbin-Magician、Enlightenus、YangXuanyi、beatrix-chan、DullSword、xjr7670、jiaxianhua、qq909244296、iStig、boloboloda、hts0000、gledfish、wenjianmin、keshida、kilikilikid、lclc6、lwbaptx、linyejoe2、liuxjerry、llql1211、fbigm、echo1937、szu17dmy、dshlstarr、Yucao-cy、coderlef、czruby、bongbongbakudan、beintentional、ZongYangL、ZhongYuuu、ZhongGuanbin、hezhizhen、linzeyan、ZJKung、luluxia、xb534、ztkuaikuai、yw-1021、ElaBosak233、baagod、zhouLion、yishangzhang、yi427、yanedie、yabo083、weibk、wangwang105、th1nk3r-ing、tao363、4yDX3906、syd168、sslmj2020、smilelsb、siqyka、selear、sdshaoda、Xi-Row、popozhu、nuquist19、noobcodemaker、XiaoK29、chadyi、lyl625760、lucaswangdev、0130w、shanghai-Jerry、EJackYang、Javesun99、eltociear、lipusheng、KNChiu、BlindTerran、ShiMaRing、lovelock、FreddieLi、FloranceYeh、fanchenggang、gltianwen、goerll、nedchu、curly210102、CuB3y0nd、KraHsu、CarrotDLaw、youshaoXG、bubble9um、Asashishi、Asa0oo0o0o、fanenr、eagleanurag、akshiterate、52coder、foursevenlove、KorsChen、GaochaoZhu、hopkings2008、yang-le、realwujing、Evilrabbit520、Umer-Jahangir、Turing-1024-Lee、Suremotoo、paoxiaomooo、Chieko-Seren、Allen-Scai、ymmmas、Risuntsy、Richard-Zhang1019、RafaelCaso、qingpeng9802、primexiao、Urbaner3、zhongfq、nidhoggfgg、MwumLi、CreatorMetaSky、martinx、ZnYang2018、hugtyftg、logan-qiu、psychelzh、Keynman、KeiichiKasai、KawaiiAsh。</p>
-<p>この本のコードレビュー作業は、coderonion, Gonglja, gvenusleo, hpstory, justin‐tse, khoaxuantu, krahets, night-cruise, nuomi1, Reanon and rongyi（アルファベット順）によって完了されました。彼らの時間と努力に感謝し、様々な言語でのコードの標準化と統一性を確保してくださいました。</p>
-<p>本書の繁体字中国語版は Shyam-Chen および Dr-XYZ によってレビューされ、英語版は yuelinxin、K3v123、QiLOL、Phoenix0415、SamJin98、yanedie、RafaelCaso、pengchzn、thomasq0、magentaqin によってレビューされ、日本語版は eltociear によってレビューされました。彼らの継続的な貢献のおかげで、本書はより幅広い読者層に提供することができています。ここに深く感謝いたします。</p>
-<p>この本の制作過程において、多くの方々から貴重な支援をいただきました。これらに限定されませんが：</p>
+<p>本書は、オープンソースコミュニティの多くの貢献者による共同の努力のもとで、継続的に改善されています。時間と労力を注いでくださったすべての執筆者の皆さんに感謝します。お名前は次のとおりです（GitHub により自動生成された順序）：krahets、coderonion、Gonglja、nuomi1、Reanon、justin-tse、hpstory、danielsss、curtishd、night-cruise、S-N-O-R-L-A-X、rongyi、msk397、gvenusleo、khoaxuantu、rivertwilight、K3v123、gyt95、zhuoqinyue、yuelinxin、Zuoxun、mingXta、Phoenix0415、FangYuan33、GN-Yu、longsizhuo、IsChristina、xBLACKICEx、guowei-gong、Cathay-Chen、pengchzn、QiLOL、magentaqin、hello-ikun、JoseHung、qualifier1024、thomasq0、sunshinesDL、L-Super、Guanngxu、Transmigration-zhou、WSL0809、Slone123c、lhxsm、yuan0221、what-is-me、Shyam-Chen、theNefelibatas、longranger2、codeberg-user、xiongsp、JeffersonHuang、prinpal、seven1240、Wonderdch、malone6、xiaomiusa87、gaofer、bluebean-cloud、a16su、SamJin98、hongyun-robot、nanlei、XiaChuerwu、yd-j、iron-irax、mgisr、steventimes、junminhong、heshuyue、danny900714、MolDuM、Nigh、Dr-XYZ、XC-Zero、reeswell、PXG-XPG、NI-SW、Horbin-Magician、Enlightenus、YangXuanyi、beatrix-chan、DullSword、xjr7670、jiaxianhua、qq909244296、iStig、boloboloda、hts0000、gledfish、wenjianmin、keshida、kilikilikid、lclc6、lwbaptx、linyejoe2、liuxjerry、llql1211、fbigm、echo1937、szu17dmy、dshlstarr、Yucao-cy、coderlef、czruby、bongbongbakudan、beintentional、ZongYangL、ZhongYuuu、ZhongGuanbin、hezhizhen、linzeyan、ZJKung、luluxia、xb534、ztkuaikuai、yw-1021、ElaBosak233、baagod、zhouLion、yishangzhang、yi427、yanedie、yabo083、weibk、wangwang105、th1nk3r-ing、tao363、4yDX3906、syd168、sslmj2020、smilelsb、siqyka、selear、sdshaoda、Xi-Row、popozhu、nuquist19、noobcodemaker、XiaoK29、chadyi、lyl625760、lucaswangdev、0130w、shanghai-Jerry、EJackYang、Javesun99、eltociear、lipusheng、KNChiu、BlindTerran、ShiMaRing、lovelock、FreddieLi、FloranceYeh、fanchenggang、gltianwen、goerll、nedchu、curly210102、CuB3y0nd、KraHsu、CarrotDLaw、youshaoXG、bubble9um、Asashishi、Asa0oo0o0o、fanenr、eagleanurag、akshiterate、52coder、foursevenlove、KorsChen、GaochaoZhu、hopkings2008、yang-le、realwujing、Evilrabbit520、Umer-Jahangir、Turing-1024-Lee、Suremotoo、paoxiaomooo、Chieko-Seren、Allen-Scai、ymmmas、Risuntsy、Richard-Zhang1019、RafaelCaso、qingpeng9802、primexiao、Urbaner3、zhongfq、nidhoggfgg、MwumLi、CreatorMetaSky、martinx、ZnYang2018、hugtyftg、logan-qiu、psychelzh、Keynman、KeiichiKasai と KawaiiAsh。</p>
+<p>本書のコードレビューは coderonion、curtishd、Gonglja、gvenusleo、hpstory、justin-tse、khoaxuantu、krahets、night-cruise、nuomi1、Reanon と rongyi によって行われました（アルファベット順）。彼らが費やしてくれた時間と労力に感謝します。各言語のコードの規範性と統一性が保たれているのは、まさに彼らのおかげです。</p>
+<p>本書の繁体字中国語版は Shyam-Chen と Dr-XYZ がレビューし、英語版は yuelinxin、K3v123、QiLOL、Phoenix0415、SamJin98、yanedie、RafaelCaso、pengchzn、thomasq0 と magentaqin がレビューし、日本語版は eltociear がレビューしました。彼らの継続的な貢献があってこそ、本書はより幅広い読者に届けられています。感謝いたします。</p>
+<p>本書の ePub 電子書籍生成ツールは zhongfq によって開発されました。彼の貢献に感謝します。読者により自由な読書方法を提供してくれました。</p>
+<p>本書の執筆過程で、私は多くの方々の助けを得ました。</p>
 <ul>
-<li>会社でのメンター、李熙博士に感謝します。ある会話で「早く行動しろ」と励ましていただき、この本を書く決意を固めることができました。</li>
-<li>ガールフレンドのBubbleに感謝します。この本の最初の読者として、アルゴリズム初心者の視点から多くの貴重な提案をいただき、この本を初心者により適したものにしてくださいました。</li>
-<li>Tengbao、Qibao、Feibaoに感謝します。この本のクリエイティブな名前を考えてくださり、みんなが初めて「Hello World!」を書いた時の素晴らしい思い出を呼び起こしてくれました。</li>
-<li>Xiaoquanに感謝します。知的財産に関する専門的な支援を提供してくださり、このオープンソース本の開発において重要な役割を果たしてくださいました。</li>
-<li>Sutongに感謝します。この本の美しいカバーとロゴをデザインしてくださり、私の要求で何度も修正を辛抱強く行ってくださいました。</li>
-<li>@squidfunk に感謝します。執筆と組版の提案、および彼が開発したオープンソースドキュメントテーマ <a href="https://github.com/squidfunk/mkdocs-material/tree/master">Material-for-MkDocs</a> を提供してくださいました。</li>
+<li>会社での私の指導教員である李汐博士に感謝します。ある対話の中で「すぐに行動しよう」と励ましてくださり、この本を書く決意を固めることができました；</li>
+<li>私の恋人であり、本書の最初の読者でもある泡泡に感謝します。アルゴリズム初心者の視点から多くの貴重な提案をしてくれたおかげで、本書はより初心者に適したものになりました；</li>
+<li>腾宝、琦宝、飞宝が本書に創造性あふれる名前を付けてくれたことに感謝します。みんなが最初のコード行「Hello World!」を書いた美しい記憶を呼び起こしてくれました；</li>
+<li>校铨が知的財産の面で専門的な支援をしてくれたことに感謝します。これは本オープンソース書籍の改善に重要な役割を果たしました；</li>
+<li>苏潼が本書の美しい表紙と logo をデザインし、私の完璧主義につき合って何度も辛抱強く修正してくれたことに感謝します；</li>
+<li>@squidfunk が組版に関する助言を提供してくれたこと、そして彼が開発したオープンソースのドキュメントテーマ <a href="https://github.com/squidfunk/mkdocs-material/tree/master">Material-for-MkDocs</a> に感謝します。</li>
 </ul>
-<p>執筆の過程で、データ構造とアルゴリズムに関する多数の教科書や記事を深く研究しました。これらの作品は模範的なモデルとして機能し、この本の内容の正確性と品質を確保してくださいました。先人の方々の貴重な貢献に感謝いたします！</p>
-<p>この本は、理論と実践を組み合わせた学習を提唱しており、この点で <a href="https://github.com/d2l-ai/d2l-en">"Dive into Deep Learning"</a> からインスピレーションを受けています。この優れた本をすべての読者に強くお勧めします。</p>
-<p><strong>継続的な支援と励ましにより、この興味深い仕事をすることを可能にしてくださった両親に心から感謝いたします</strong>。</p>
+<p>執筆の過程で、私はデータ構造とアルゴリズムに関する多くの教材や記事を読みました。これらの作品は本書に優れた手本を与え、本書の内容の正確性と品質を支えてくれました。ここに、すべての先生方と先人たちの卓越した貢献に感謝します！</p>
+<p>本書は手と頭を同時に使う学習方法を提唱しています。この点で私は<a href="https://github.com/d2l-ai/d2l-zh">『手を動かして学ぶ深層学習』</a>から大きな啓発を受けました。ここで読者の皆さんにこの優れた著作を強くお勧めします。</p>
+<p><strong>心から両親に感謝します。いつも支え励ましてくれたからこそ、私はこの興味深いことに取り組む機会を得ることができました</strong>。</p>
 
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+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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-<p><img alt="序文" class="cover-image" src="../assets/covers/chapter_preface.jpg" /></p>
+<h1 id="0">第 0 章 &nbsp; はじめに<a class="headerlink" href="#0" title="Permanent link">&para;</a></h1>
+<p><img alt="はじめに" class="cover-image" src="../assets/covers/chapter_preface.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>アルゴリズムは美しい交響曲のようで、コードの一行一行がリズムのように流れています。</p>
-<p>この本があなたの心の中で静かに響き、独特で深い旋律を残すことを願っています。</p>
+<p>アルゴリズムは美しい交響曲のようであり、コードの一行一行が旋律のように流れていきます。</p>
+<p>この本があなたの心の中でそっと響き、独自で深い旋律を残してくれることを願っています。</p>
 </div>
 <h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
diff --git a/ja/chapter_preface/suggestions/index.html b/ja/chapter_preface/suggestions/index.html
index de11aa15c..75d70273f 100644
--- a/ja/chapter_preface/suggestions/index.html
+++ b/ja/chapter_preface/suggestions/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -39,7 +39,7 @@
     
     
       
-        <title>0.2 読み方 - Hello アルゴリズム</title>
+        <title>0.2 本書の使い方 - Hello アルゴリズム</title>
       
     
     
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -152,7 +152,7 @@
         <div class="md-header__topic" data-md-component="header-topic">
           <span class="md-ellipsis">
             
-              0.2 &nbsp; 読み方
+              0.2 &nbsp; 本書の使い方
             
           </span>
         </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -544,7 +544,7 @@
   <a href="#021" class="md-nav__link">
     <span class="md-ellipsis">
       
-        0.2.1 &nbsp; 記述規則
+        0.2.1 &nbsp; 文章スタイルの約束
       
     </span>
   </a>
@@ -555,7 +555,7 @@
   <a href="#022" class="md-nav__link">
     <span class="md-ellipsis">
       
-        0.2.2 &nbsp; アニメーション図解による効率的学習
+        0.2.2 &nbsp; アニメーション図解で効率よく学ぶ
       
     </span>
   </a>
@@ -566,7 +566,7 @@
   <a href="#023" class="md-nav__link">
     <span class="md-ellipsis">
       
-        0.2.3 &nbsp; コーディング実践による理解の深化
+        0.2.3 &nbsp; コード実践で理解を深める
       
     </span>
   </a>
@@ -577,7 +577,7 @@
   <a href="#024" class="md-nav__link">
     <span class="md-ellipsis">
       
-        0.2.4 &nbsp; 議論による共同学習
+        0.2.4 &nbsp; 質問と議論を通じてともに成長する
       
     </span>
   </a>
@@ -588,7 +588,7 @@
   <a href="#025" class="md-nav__link">
     <span class="md-ellipsis">
       
-        0.2.5 &nbsp; アルゴリズム学習パス
+        0.2.5 &nbsp; アルゴリズム学習ロードマップ
       
     </span>
   </a>
@@ -723,7 +723,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -751,7 +751,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -888,7 +888,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1165,7 +1165,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1193,7 +1193,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1696,7 +1696,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1718,7 +1718,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1740,7 +1740,7 @@
   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -2047,7 +2047,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2210,7 +2210,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2596,7 +2596,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2652,7 +2652,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2680,7 +2680,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3218,7 +3218,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3274,7 +3274,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3302,7 +3302,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3495,7 +3495,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3523,7 +3523,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3664,7 +3664,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3692,7 +3692,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3720,7 +3720,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3748,7 +3748,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3941,7 +3941,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4186,7 +4186,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4332,7 +4332,7 @@
   <a href="#021" class="md-nav__link">
     <span class="md-ellipsis">
       
-        0.2.1 &nbsp; 記述規則
+        0.2.1 &nbsp; 文章スタイルの約束
       
     </span>
   </a>
@@ -4343,7 +4343,7 @@
   <a href="#022" class="md-nav__link">
     <span class="md-ellipsis">
       
-        0.2.2 &nbsp; アニメーション図解による効率的学習
+        0.2.2 &nbsp; アニメーション図解で効率よく学ぶ
       
     </span>
   </a>
@@ -4354,7 +4354,7 @@
   <a href="#023" class="md-nav__link">
     <span class="md-ellipsis">
       
-        0.2.3 &nbsp; コーディング実践による理解の深化
+        0.2.3 &nbsp; コード実践で理解を深める
       
     </span>
   </a>
@@ -4365,7 +4365,7 @@
   <a href="#024" class="md-nav__link">
     <span class="md-ellipsis">
       
-        0.2.4 &nbsp; 議論による共同学習
+        0.2.4 &nbsp; 質問と議論を通じてともに成長する
       
     </span>
   </a>
@@ -4376,7 +4376,7 @@
   <a href="#025" class="md-nav__link">
     <span class="md-ellipsis">
       
-        0.2.5 &nbsp; アルゴリズム学習パス
+        0.2.5 &nbsp; アルゴリズム学習ロードマップ
       
     </span>
   </a>
@@ -4420,26 +4420,26 @@
 
 
 <!-- Page content -->
-<h1 id="02">0.2 &nbsp; 読み方<a class="headerlink" href="#02" title="Permanent link">&para;</a></h1>
+<h1 id="02">0.2 &nbsp; 本書の使い方<a class="headerlink" href="#02" title="Permanent link">&para;</a></h1>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>最良の読書体験のために、このセクションを通読することをお勧めします。</p>
+<p>最適な読書体験を得るために、本節の内容を一通り読むことをおすすめします。</p>
 </div>
-<h2 id="021">0.2.1 &nbsp; 記述規則<a class="headerlink" href="#021" title="Permanent link">&para;</a></h2>
+<h2 id="021">0.2.1 &nbsp; 文章スタイルの約束<a class="headerlink" href="#021" title="Permanent link">&para;</a></h2>
 <ul>
-<li>タイトルの後に「*」が付いた章は任意であり、比較的難易度の高い内容が含まれています。時間に制約がある場合は、これらをスキップすることをお勧めします。</li>
-<li>技術用語は太字（印刷版およびPDF版）または下線（Web版）で表示されます。例えば、<u>配列</u>などです。技術文書をより良く理解するために、これらに慣れることをお勧めします。</li>
-<li>**太字のテキスト**は重要な内容や要約文を示し、特別な注意を払う価値があります。</li>
-<li>特定の意味を持つ単語や句は「引用符」で示され、曖昧さを避けます。</li>
-<li>プログラミング言語間で一致しない用語については、この本はPythonに従います。例えば、<code>null</code>を意味するために<code>None</code>を使用します。</li>
-<li>この本は、よりコンパクトなコンテンツレイアウトと引き換えに、プログラミング言語のコメント規約を部分的に無視しています。コメントは主に3つのタイプで構成されています：タイトルコメント、内容コメント、複数行コメント。</li>
+<li>見出しの後に <code>*</code> が付いているのは選読章で、内容は比較的難しめです。時間が限られている場合は、先に読み飛ばしてもかまいません。</li>
+<li>専門用語は太字（紙書籍版と PDF 版）または下線付き（Web 版）で示します。たとえば<u>配列（array）</u>のようなものです。文献を読む際に役立つため、覚えておくことをおすすめします。</li>
+<li>重要な内容やまとめの文は <strong>太字</strong> で示します。これらの文章には特に注意してください。</li>
+<li>特定の意味を持つ語句には“引用符”を付け、曖昧さを避けます。</li>
+<li>プログラミング言語ごとに用語が一致しない場合、本書では Python を基準とします。たとえば、“空”を表すのに <code>None</code> を使います。</li>
+<li>本書では、よりコンパクトなレイアウトのために、言語ごとのコメント規約を一部省略しています。コメントは主に3種類あります。タイトルコメント、内容コメント、複数行コメントです。</li>
 </ul>
-<div class="tabbed-set tabbed-alternate" data-tabs="1:12"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label></div>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="sd">&quot;&quot;&quot;関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント&quot;&quot;&quot;</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="sd">&quot;&quot;&quot;タイトルコメント。関数、クラス、テストケースなどを示すために使います&quot;&quot;&quot;</span>
 <a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a>
-<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="c1"># 詳細を説明するためのコメント</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="c1"># 内容コメント。コードを詳しく説明するために使います</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="sd">&quot;&quot;&quot;</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="sd">複数行</span>
@@ -4448,9 +4448,9 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* タイトルコメント。関数、クラス、テストケースなどを示すために使います */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="c1">// 詳細を説明するためのコメント</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="c1">// 内容コメント。コードを詳しく説明するために使います</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="cm">/**</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="cm"> * 複数行</span>
@@ -4459,9 +4459,9 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* タイトルコメント。関数、クラス、テストケースなどを示すために使います */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="c1">// 詳細を説明するためのコメント</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="c1">// 内容コメント。コードを詳しく説明するために使います</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="cm">/**</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="cm"> * 複数行</span>
@@ -4470,9 +4470,9 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* タイトルコメント。関数、クラス、テストケースなどを示すために使います */</span>
 <a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
-<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="c1">// 詳細を説明するためのコメント</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="c1">// 内容コメント。コードを詳しく説明するために使います</span>
 <a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a>
 <a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="cm">/**</span>
 <a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="cm"> * 複数行</span>
@@ -4481,9 +4481,9 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* タイトルコメント。関数、クラス、テストケースなどを示すために使います */</span>
 <a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
-<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="c1">// 詳細を説明するためのコメント</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="c1">// 内容コメント。コードを詳しく説明するために使います</span>
 <a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a>
 <a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="cm">/**</span>
 <a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="cm"> * 複数行</span>
@@ -4492,9 +4492,9 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* タイトルコメント。関数、クラス、テストケースなどを示すために使います */</span>
 <a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
-<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="c1">// 詳細を説明するためのコメント</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="c1">// 内容コメント。コードを詳しく説明するために使います</span>
 <a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>
 <a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="cm">/**</span>
 <a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="cm"> * 複数行</span>
@@ -4503,9 +4503,9 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* タイトルコメント。関数、クラス、テストケースなどを示すために使います */</span>
 <a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
-<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="c1">// 詳細を説明するためのコメント</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="c1">// 内容コメント。コードを詳しく説明するために使います</span>
 <a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a>
 <a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="cm">/**</span>
 <a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="cm"> * 複数行</span>
@@ -4514,9 +4514,9 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* タイトルコメント。関数、クラス、テストケースなどを示すために使います */</span>
 <a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
-<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="c1">// 詳細を説明するためのコメント</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="c1">// 内容コメント。コードを詳しく説明するために使います</span>
 <a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a>
 <a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="cm">/**</span>
 <a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="cm"> * 複数行</span>
@@ -4525,9 +4525,9 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* タイトルコメント。関数、クラス、テストケースなどを示すために使います */</span>
 <a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
-<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="c1">// 詳細を説明するためのコメント</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="c1">// 内容コメント。コードを詳しく説明するために使います</span>
 <a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a>
 <a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="cm">/**</span>
 <a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="cm"> * 複数行</span>
@@ -4536,9 +4536,9 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* タイトルコメント。関数、クラス、テストケースなどを示すために使います */</span>
 <a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
-<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="c1">// 詳細を説明するためのコメント</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="c1">// 内容コメント。コードを詳しく説明するために使います</span>
 <a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a>
 <a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="sd">/**</span>
 <a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="sd"> * 複数行</span>
@@ -4547,9 +4547,9 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* タイトルコメント。関数、クラス、テストケースなどを示すために使います */</span>
 <a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
-<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="c1">// 詳細を説明するためのコメント</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="c1">// 内容コメント。コードを詳しく説明するために使います</span>
 <a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a>
 <a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="cm">/**</span>
 <a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="cm"> * 複数行</span>
@@ -4558,9 +4558,9 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* タイトルコメント。関数、クラス、テストケースなどを示すために使います */</span>
 <a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
-<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="c1">// 詳細を説明するためのコメント</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="c1">// 内容コメント。コードを詳しく説明するために使います</span>
 <a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a>
 <a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="cm">/**</span>
 <a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="cm"> * 複数行</span>
@@ -4568,51 +4568,63 @@
 <a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="cm"> */</span>
 </code></pre></div>
 </div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### タイトルコメント。関数、クラス、テストケースなどを示すために使います ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="c1"># 内容コメント。コードを詳しく説明するために使います</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="c1"># 複数行</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="c1"># コメント</span>
+</code></pre></div>
 </div>
 </div>
-<h2 id="022">0.2.2 &nbsp; アニメーション図解による効率的学習<a class="headerlink" href="#022" title="Permanent link">&para;</a></h2>
-<p>テキストと比較して、動画や画像は情報密度が高く、より構造化されており、理解しやすくなっています。この本では、<strong>重要で難しい概念は主にアニメーションと図解を通じて提示され</strong>、テキストは説明と補足として機能します。</p>
-<p>下図に示すようなアニメーションや図解のある内容に遭遇した場合、<strong>図の理解を優先し、テキストを補足として</strong>、両方を統合して包括的な理解を得てください。</p>
+</div>
+<h2 id="022">0.2.2 &nbsp; アニメーション図解で効率よく学ぶ<a class="headerlink" href="#022" title="Permanent link">&para;</a></h2>
+<p>文字と比べて、動画や画像は情報密度と構造化の度合いが高く、理解しやすいものです。本書では、<strong>重要かつ難解な知識は主にアニメーションによる図解で示し</strong>、文章は説明と補足を担います。</p>
+<p>本書を読んでいて、ある内容に以下の図のようなアニメーション図解がある場合は、<strong>図を主、文章を従として</strong>、両方を合わせて理解してください。</p>
 <p><img alt="アニメーション図解の例" class="animation-figure" src="../../index.assets/animation.gif" /></p>
 <p align="center"> 図 0-2 &nbsp; アニメーション図解の例 </p>
 
-<h2 id="023">0.2.3 &nbsp; コーディング実践による理解の深化<a class="headerlink" href="#023" title="Permanent link">&para;</a></h2>
-<p>この本のソースコードは<a href="https://github.com/krahets/hello-algo">GitHubリポジトリ</a>でホストされています。下図に示すように、<strong>ソースコードにはテスト例が付属しており、ワンクリックで実行できます</strong>。</p>
-<p>時間に余裕がある場合は、<strong>自分でコードをタイプすることをお勧めします</strong>。時間がない場合は、少なくともすべてのコードを読んで実行してください。</p>
-<p>コードを読むだけと比較して、コードを書くことは多くの場合、より多くの学習をもたらします。<strong>実践による学習こそが真の学習方法です。</strong></p>
+<h2 id="023">0.2.3 &nbsp; コード実践で理解を深める<a class="headerlink" href="#023" title="Permanent link">&para;</a></h2>
+<p>本書のサンプルコードは <a href="https://github.com/krahets/hello-algo">GitHub リポジトリ</a> で管理されています。以下の図のように、<strong>ソースコードにはテストケースが付いており、ワンクリックで実行できます</strong>。</p>
+<p>時間に余裕があれば、<strong>コードを見ながら自分で一度書いてみることをおすすめします</strong>。学習時間が限られている場合でも、少なくともすべてのコードに目を通し、実行してください。</p>
+<p>コードを読むのに比べて、書く過程のほうが得られるものは多いものです。<strong>手を動かしてこそ、本当に学んだことになります</strong>。</p>
 <p><img alt="コード実行例" class="animation-figure" src="../../index.assets/running_code.gif" /></p>
 <p align="center"> 図 0-3 &nbsp; コード実行例 </p>
 
-<p>コードを実行するための設定には、主に3つのステップが含まれます。</p>
-<p><strong>ステップ1：ローカルプログラミング環境をインストール</strong>。付録の<a href="https://www.hello-algo.com/chapter_appendix/installation/">チュートリアル</a>に従ってインストールするか、すでにインストールされている場合はこのステップをスキップしてください。</p>
-<p><strong>ステップ2：コードリポジトリをクローンまたはダウンロード</strong>。<a href="https://github.com/krahets/hello-algo">GitHubリポジトリ</a>を訪問してください。</p>
-<p><a href="https://git-scm.com/downloads">Git</a>がインストールされている場合は、次のコマンドを使用してリポジトリをクローンします：</p>
-<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a>git<span class="w"> </span>clone<span class="w"> </span>https://github.com/krahets/hello-algo.git
+<p>コードを実行する前準備は主に3ステップです。</p>
+<p><strong>第1ステップ：ローカルのプログラミング環境をインストールする</strong>。付録の<a href="https://www.hello-algo.com/chapter_appendix/installation/">チュートリアル</a>を参照してインストールしてください。すでにインストール済みであれば、この手順は省略できます。</p>
+<p><strong>第2ステップ：コードリポジトリをクローンまたはダウンロードする</strong>。 <a href="https://github.com/krahets/hello-algo">GitHub リポジトリ</a> にアクセスしてください。すでに <a href="https://git-scm.com/downloads">Git</a> をインストールしている場合は、次のコマンドでこのリポジトリをクローンできます：</p>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a>git<span class="w"> </span>clone<span class="w"> </span>https://github.com/krahets/hello-algo.git
 </code></pre></div>
-<p>または、下図に示す場所にある「Download ZIP」ボタンをクリックして、コードを圧縮ZIPファイルとして直接ダウンロードすることもできます。その後、ローカルで展開するだけです。</p>
+<p>もちろん、以下の図に示す場所で“Download ZIP”ボタンをクリックし、コードの圧縮ファイルを直接ダウンロードしてローカルで展開することもできます。</p>
 <p><img alt="リポジトリのクローンとコードのダウンロード" class="animation-figure" src="../suggestions.assets/download_code.png" /></p>
 <p align="center"> 図 0-4 &nbsp; リポジトリのクローンとコードのダウンロード </p>
 
-<p><strong>ステップ3：ソースコードを実行</strong>。下図に示すように、上部にファイル名が記載されたコードブロックについては、リポジトリの<code>codes</code>フォルダで対応するソースコードファイルを見つけることができます。これらのファイルはワンクリックで実行でき、不要なデバッグ時間を節約し、学習に集中できます。</p>
+<p><strong>第3ステップ：ソースコードを実行する</strong>。以下の図のように、上部にファイル名が表示されているコードブロックについては、リポジトリの <code>codes</code> フォルダ内に対応するソースコードファイルがあります。ソースコードファイルはワンクリックで実行できるため、不要なデバッグ時間を減らし、学習内容に集中できます。</p>
 <p><img alt="コードブロックと対応するソースコードファイル" class="animation-figure" src="../suggestions.assets/code_md_to_repo.png" /></p>
 <p align="center"> 図 0-5 &nbsp; コードブロックと対応するソースコードファイル </p>
 
-<h2 id="024">0.2.4 &nbsp; 議論による共同学習<a class="headerlink" href="#024" title="Permanent link">&para;</a></h2>
-<p>この本を読んでいる間、学べなかった点を飛ばさないでください。<strong>コメントセクションで気軽に質問してください</strong>。喜んでお答えし、通常2日以内に回答できます。</p>
-<p>下図に示すように、各章の下部にコメントセクションがあります。これらのコメントに注意を払うことをお勧めします。他の人が遭遇した問題を知ることで、知識のギャップを特定し、より深い思索を促すだけでなく、仲間の読者の質問に答えたり、洞察を共有したり、相互の向上を促進したりすることで寛大に貢献することも招待します。</p>
-<p><img alt="コメントセクションの例" class="animation-figure" src="../../index.assets/comment.gif" /></p>
-<p align="center"> 図 0-6 &nbsp; コメントセクションの例 </p>
+<p>ローカルでコードを実行するだけでなく、<strong>Web 版では Python コードの可視化実行にも対応しています</strong>（<a href="https://pythontutor.com/">pythontutor</a> を利用）。以下の図のように、コードブロックの下にある“可視化実行”をクリックすると表示を展開し、アルゴリズムコードの実行過程を観察できます。また、“全画面表示”をクリックすると、より見やすい閲覧体験が得られます。</p>
+<p><img alt="Python コードの可視化実行" class="animation-figure" src="../suggestions.assets/pythontutor_example.png" /></p>
+<p align="center"> 図 0-6 &nbsp; Python コードの可視化実行 </p>
 
-<h2 id="025">0.2.5 &nbsp; アルゴリズム学習パス<a class="headerlink" href="#025" title="Permanent link">&para;</a></h2>
-<p>全体的に、データ構造とアルゴリズムをマスターする旅は3つの段階に分けることができます：</p>
+<h2 id="024">0.2.4 &nbsp; 質問と議論を通じてともに成長する<a class="headerlink" href="#024" title="Permanent link">&para;</a></h2>
+<p>本書を読んでいて、理解できていない知識点を安易に読み飛ばさないでください。<strong>コメント欄で気軽に質問してください</strong>。私と仲間たちが誠意をもって回答し、通常は 2 日以内に返信します。</p>
+<p>以下の図のように、Web 版では各章の下部にコメント欄があります。ぜひコメント欄の内容にも目を通してください。一方では、みんなが直面した問題を知ることで知識の抜けを補い、より深い思考を促せます。もう一方では、ほかの仲間の質問にも積極的に答え、見解を共有し、互いの成長を助けてほしいと思います。</p>
+<p><img alt="コメント欄の例" class="animation-figure" src="../../index.assets/comment.gif" /></p>
+<p align="center"> 図 0-7 &nbsp; コメント欄の例 </p>
+
+<h2 id="025">0.2.5 &nbsp; アルゴリズム学習ロードマップ<a class="headerlink" href="#025" title="Permanent link">&para;</a></h2>
+<p>全体として見ると、データ構造とアルゴリズムの学習過程は 3 つの段階に分けられます。</p>
 <ol>
-<li><strong>段階1：アルゴリズムの入門</strong>。さまざまなデータ構造の特性と使用法に慣れ、異なるアルゴリズムの原理、プロセス、用途、効率について学ぶ必要があります。</li>
-<li><strong>段階2：アルゴリズム問題の練習</strong>。<a href="https://leetcode.cn/studyplan/coding-interviews/">Sword for Offer</a>や<a href="https://leetcode.cn/studyplan/top-100-liked/">LeetCode Hot 100</a>などの人気のある問題から始めることをお勧めし、少なくとも100問を蓄積して主流のアルゴリズム問題に慣れることです。練習を始めると忘却が課題になる可能性がありますが、これは正常なことですのでご安心ください。「エビングハウスの忘却曲線」に従って問題を復習することができ、通常3〜5回の反復の後、それらを覚えることができるでしょう。</li>
-<li><strong>段階3：知識体系の構築</strong>。学習の面では、アルゴリズムコラム記事、解法フレームワーク、アルゴリズム教科書を読んで知識体系を継続的に豊かにすることができます。練習の面では、トピック別分類、一つの問題に対する複数の解法、複数の問題に対する一つの解法など、高度な戦略を試すことができます。これらの戦略に関する洞察は、さまざまなコミュニティで見つけることができます。</li>
+<li><strong>第 1 段階：アルゴリズム入門</strong>。さまざまなデータ構造の特徴と使い方に慣れ、異なるアルゴリズムの原理、流れ、用途、効率などを学ぶ必要があります。</li>
+<li><strong>第 2 段階：アルゴリズム問題を解く</strong>。まずは人気の高い問題から取り組み、少なくとも 100 問は蓄積して、主流のアルゴリズム問題に慣れることをおすすめします。最初のうちは、“知識の忘却”が課題になるかもしれませんが、心配はいりません。これはごく自然なことです。“エビングハウスの忘却曲線”に沿って問題を復習すれば、通常は 3～5 回繰り返すことでしっかり記憶に定着します。おすすめの問題リストと学習計画は、この <a href="https://github.com/krahets/LeetCode-Book">GitHub リポジトリ</a> を参照してください。</li>
+<li><strong>第 3 段階：知識体系を構築する</strong>。学習面では、アルゴリズムの連載記事、解法フレームワーク、教材などを読むことで、知識体系を継続的に充実させられます。問題演習の面では、トピック別分類、1 問多解、1 解多題といった発展的な戦略も試せます。関連する学習ノウハウは各コミュニティで見つけられます。</li>
 </ol>
-<p>下図に示すように、この本は主に「段階1」をカバーしており、段階2と3により効率的に取り組むのに役立つことを目的としています。</p>
-<p><img alt="アルゴリズム学習パス" class="animation-figure" src="../suggestions.assets/learning_route.png" /></p>
-<p align="center"> 図 0-7 &nbsp; アルゴリズム学習パス </p>
+<p>以下の図のように、本書の内容は主に“第 1 段階”を扱っており、第 2 段階と第 3 段階の学習をより効率的に進める助けとなることを目的としています。</p>
+<p><img alt="アルゴリズム学習ロードマップ" class="animation-figure" src="../suggestions.assets/learning_route.png" /></p>
+<p align="center"> 図 0-8 &nbsp; アルゴリズム学習ロードマップ </p>
 
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diff --git a/ja/chapter_preface/summary/index.html b/ja/chapter_preface/summary/index.html
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@@ -6,7 +6,7 @@
       <meta charset="utf-8">
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-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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+    はじめに
   
 
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+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    0.3 &nbsp; まとめ
+  
+
+    
+  </span>
+  
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
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+        
+
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      
+        1. &nbsp; 重要ポイントの振り返り
+      
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
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+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      
+        1. &nbsp; 重要ポイントの振り返り
+      
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
 </nav>
                   </div>
                 </div>
@@ -4265,13 +4333,14 @@
 
 <!-- Page content -->
 <h1 id="03">0.3 &nbsp; まとめ<a class="headerlink" href="#03" title="Permanent link">&para;</a></h1>
+<h3 id="1">1. &nbsp; 重要ポイントの振り返り<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
-<li>この本の主な読者はアルゴリズムの初心者です。すでに基本的な知識をお持ちの場合、この本はアルゴリズムの知識を体系的に復習するのに役立ち、この本のソースコードは「コーディングツールキット」としても使用できます。</li>
-<li>この本は3つの主要なセクション、計算量解析、データ構造、アルゴリズムで構成されており、この分野のほとんどのトピックをカバーしています。</li>
-<li>アルゴリズムの初心者にとって、多くの回り道や一般的な落とし穴を避けるために、初期段階で入門書を読むことが重要です。</li>
-<li>本書内のアニメーションと図は通常、重要なポイントと難しい知識を紹介するために使用されます。本を読む際にはこれらにより多くの注意を払う必要があります。</li>
-<li>実践はプログラミングを学ぶ最良の方法です。ソースコードを実行し、自分でコードをタイプすることを強くお勧めします。</li>
-<li>この本のWeb版の各章には議論セクションがあり、いつでも質問や洞察を共有することを歓迎します。</li>
+<li>本書の主な対象読者はアルゴリズム初学者です。すでにある程度の基礎がある場合でも、本書はアルゴリズム知識を体系的に振り返る助けとなり、書中のソースコードは「問題演習用ツール集」としても利用できます。</li>
+<li>本書の内容は主に計算量解析、データ構造、アルゴリズムの三部からなり、この分野の大部分のテーマを網羅しています。</li>
+<li>アルゴリズム初心者にとって、学習初期の段階で入門書を読むことは非常に重要であり、多くの遠回りを避けられます。</li>
+<li>本書のアニメーション図解は通常、重要な知識や難しい知識を紹介するために用いられます。本書を読む際は、これらの内容により多く注意を払うべきです。</li>
+<li>実践はプログラミングを学ぶ最良の方法です。ソースコードを実行し、実際に自分でコードを書くことを強く勧めます。</li>
+<li>本書のWeb版の各章にはコメント欄が設けられており、疑問や見解をいつでも共有することを歓迎します。</li>
 </ul>
 
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-    aria-label="次: 第 1 章 &amp;nbsp; アルゴリズムとの出会い"
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diff --git a/ja/chapter_reference/index.html b/ja/chapter_reference/index.html
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       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -115,7 +115,7 @@
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+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
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@@ -4256,11 +4256,11 @@
 <p>[1] Thomas H. Cormen, et al. Introduction to Algorithms (3<sup>rd</sup> Edition).</p>
 <p>[2] Aditya Bhargava. Grokking Algorithms: An Illustrated Guide for Programmers and Other Curious People (1<sup>st</sup> Edition).</p>
 <p>[3] Robert Sedgewick, et al. Algorithms (4<sup>th</sup> Edition).</p>
-<p>[4] Yan Weimin. Data Structures (C Language Version).</p>
-<p>[5] Deng Junhui. Data Structures (C++ Language Version, Third Edition).</p>
-<p>[6] Mark Allen Weiss, translated by Chen Yue. Data Structures and Algorithm Analysis in Java (Third Edition).</p>
-<p>[7] Cheng Jie. Speaking of Data Structures.</p>
-<p>[8] Wang Zheng. The Beauty of Data Structures and Algorithms.</p>
+<p>[4] 严蔚敏. データ構造（C 言語版）.</p>
+<p>[5] 邓俊辉. データ構造（C++ 言語版、第3版）.</p>
+<p>[6] マーク・アレン・ワイス著，陈越訳. データ構造とアルゴリズム解析：Java言語による記述（第3版）.</p>
+<p>[7] 程杰. データ構造の話.</p>
+<p>[8] 王争. データ構造とアルゴリズムの美.</p>
 <p>[9] Gayle Laakmann McDowell. Cracking the Coding Interview: 189 Programming Questions and Solutions (6<sup>th</sup> Edition).</p>
 <p>[10] Aston Zhang, et al. Dive into Deep Learning.</p>
 
diff --git a/ja/chapter_searching/binary_search/index.html b/ja/chapter_searching/binary_search/index.html
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@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
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     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
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 <!-- Page content -->
 <h1 id="101">10.1 &nbsp; 二分探索<a class="headerlink" href="#101" title="Permanent link">&para;</a></h1>
-<p><u>二分探索</u>は分割統治戦略を用いる効率的な探索アルゴリズムです。配列内の要素の整列順序を利用し、各反復で探索区間を半分に減らしながら、目標要素が見つかるか探索区間が空になるまで続行します。</p>
+<p><u>二分探索（binary search）</u>は分割統治法に基づく効率的な探索アルゴリズムです。データが整列済みである性質を利用し、各ラウンドで探索範囲を半分に縮小し、目標要素を見つけるか探索区間が空になるまで続けます。</p>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
-<p>長さ<span class="arithmatex">\(n\)</span>の配列<code>nums</code>が与えられ、要素は重複なしで昇順に配列されています。この配列内の要素<code>target</code>のインデックスを見つけて返してください。配列に要素が含まれていない場合は<span class="arithmatex">\(-1\)</span>を返してください。例を下図に示します。</p>
+<p>長さ <span class="arithmatex">\(n\)</span> の配列 <code>nums</code> が与えられます。要素は小さい順に並んでおり、重複しません。要素 <code>target</code> がこの配列内にある場合はそのインデックスを返し、含まれない場合は <span class="arithmatex">\(-1\)</span> を返してください。例を次の図に示します。</p>
 </div>
-<p><img alt="Binary search example data" class="animation-figure" src="../binary_search.assets/binary_search_example.png" /></p>
-<p align="center"> 図 10-1 &nbsp; Binary search example data </p>
+<p><img alt="二分探索の例" class="animation-figure" src="../binary_search.assets/binary_search_example.png" /></p>
+<p align="center"> 図 10-1 &nbsp; 二分探索の例 </p>
 
-<p>下図に示すように、まず<span class="arithmatex">\(i = 0\)</span>と<span class="arithmatex">\(j = n - 1\)</span>でポインタを初期化し、それぞれ配列の最初と最後の要素を指します。これらはまた全体の探索区間<span class="arithmatex">\([0, n - 1]\)</span>を表します。角括弧は閉区間を示し、境界値自身も含むことに注意してください。</p>
-<p>そして、以下の2つのステップをループで実行する可能性があります。</p>
+<p>次の図に示すように、まずポインタ <span class="arithmatex">\(i = 0\)</span> と <span class="arithmatex">\(j = n - 1\)</span> を初期化し、それぞれ配列の先頭要素と末尾要素を指すようにして、探索区間 <span class="arithmatex">\([0, n - 1]\)</span> を表します。角括弧は閉区間を表し、境界値自体を含むことに注意してください。</p>
+<p>次に、以下の 2 つの手順を繰り返します。</p>
 <ol>
-<li>中点インデックス<span class="arithmatex">\(m = \lfloor {(i + j) / 2} \rfloor\)</span>を計算します。ここで<span class="arithmatex">\(\lfloor \: \rfloor\)</span>は床関数を表します。</li>
-<li><code>nums[m]</code>と<code>target</code>の比較に基づいて、以下の3つのケースのうち1つを選択して実行します。<ol>
-<li><code>nums[m] &lt; target</code>の場合、<code>target</code>は区間<span class="arithmatex">\([m + 1, j]\)</span>にあることを示すため、<span class="arithmatex">\(i = m + 1\)</span>とします。</li>
-<li><code>nums[m] &gt; target</code>の場合、<code>target</code>は区間<span class="arithmatex">\([i, m - 1]\)</span>にあることを示すため、<span class="arithmatex">\(j = m - 1\)</span>とします。</li>
-<li><code>nums[m] = target</code>の場合、<code>target</code>が見つかったことを示すため、インデックス<span class="arithmatex">\(m\)</span>を返します。</li>
+<li>中央のインデックス <span class="arithmatex">\(m = \lfloor {(i + j) / 2} \rfloor\)</span> を計算します。ここで <span class="arithmatex">\(\lfloor \: \rfloor\)</span> は切り捨てを表します。</li>
+<li><code>nums[m]</code> と <code>target</code> の大小関係を判定し、次の 3 つの場合に分かれます。<ol>
+<li><code>nums[m] &lt; target</code> のとき、<code>target</code> は区間 <span class="arithmatex">\([m + 1, j]\)</span> にあるため、<span class="arithmatex">\(i = m + 1\)</span> を実行します。</li>
+<li><code>nums[m] &gt; target</code> のとき、<code>target</code> は区間 <span class="arithmatex">\([i, m - 1]\)</span> にあるため、<span class="arithmatex">\(j = m - 1\)</span> を実行します。</li>
+<li><code>nums[m] = target</code> のとき、<code>target</code> が見つかったので、インデックス <span class="arithmatex">\(m\)</span> を返します。</li>
 </ol>
 </li>
 </ol>
-<p>配列に目標要素が含まれていない場合、探索区間は最終的に空になり、<span class="arithmatex">\(-1\)</span>を返して終了します。</p>
+<p>配列に目標要素が含まれない場合、探索区間は最終的に空まで縮小されます。このとき <span class="arithmatex">\(-1\)</span> を返します。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:7"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label><label for="__tabbed_1_5">&lt;5&gt;</label><label for="__tabbed_1_6">&lt;6&gt;</label><label for="__tabbed_1_7">&lt;7&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="Binary search process" class="animation-figure" src="../binary_search.assets/binary_search_step1.png" /></p>
+<p><img alt="二分探索の流れ" class="animation-figure" src="../binary_search.assets/binary_search_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="binary_search_step2" class="animation-figure" src="../binary_search.assets/binary_search_step2.png" /></p>
@@ -4400,152 +4400,342 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 10-2 &nbsp; Binary search process </p>
+<p align="center"> 図 10-2 &nbsp; 二分探索の流れ </p>
 
-<p><span class="arithmatex">\(i\)</span>と<span class="arithmatex">\(j\)</span>が両方とも<code>int</code>型であるため、**<span class="arithmatex">\(i + j\)</span>は<code>int</code>型の範囲を超える可能性がある**ことは注目に値します。大きな数のオーバーフローを避けるため、通常は式<span class="arithmatex">\(m = \lfloor {i + (j - i) / 2} \rfloor\)</span>を使用して中点を計算します。</p>
-<p>コードは以下の通りです：</p>
+<p>注意すべき点として、<span class="arithmatex">\(i\)</span> と <span class="arithmatex">\(j\)</span> はどちらも <code>int</code> 型であるため、<strong><span class="arithmatex">\(i + j\)</span> が <code>int</code> 型の範囲を超える可能性があります</strong>。大きな数によるオーバーフローを避けるため、通常は式 <span class="arithmatex">\(m = \lfloor {i + (j - i) / 2} \rfloor\)</span> を用いて中点を計算します。</p>
+<p>コードは次のとおりです。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_search.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">binary_search</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二分探索（両端閉区間）&quot;&quot;&quot;</span>
-<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 両端閉区間 [0, n-1] を初期化、すなわち i, j はそれぞれ配列の最初の要素と最後の要素を指す</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二分探索（両閉区間）&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>
-<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="c1"># 検索区間が空になるまでループ（i &gt; j のとき空）</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="c1"># ループし、探索区間が空になったら終了する（i &gt; j で空）</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;=</span> <span class="n">j</span><span class="p">:</span>
-<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="c1"># 理論的には、Pythonの数値は無限に大きくなることができる（メモリサイズに依存）ため、大きな数のオーバーフローを考慮する必要はない</span>
-<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="n">m</span> <span class="o">=</span> <span class="n">i</span> <span class="o">+</span> <span class="p">(</span><span class="n">j</span> <span class="o">-</span> <span class="n">i</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>  <span class="c1"># 中点インデックス m を計算</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="c1"># 理論上、Python の数値は無限に大きくできるため（メモリ容量に依存）、大きな数のオーバーフローを考慮する必要はない</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="n">m</span> <span class="o">=</span> <span class="p">(</span><span class="n">i</span> <span class="o">+</span> <span class="n">j</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>  <span class="c1"># 中点インデックス m を計算</span>
 <a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span> <span class="o">&lt;</span> <span class="n">target</span><span class="p">:</span>
-<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>            <span class="n">i</span> <span class="o">=</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span>  <span class="c1"># この場合、target は区間 [m+1, j] にあることを示す</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>            <span class="n">i</span> <span class="o">=</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span>  <span class="c1"># この場合、target は区間 [m+1, j] にある</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="k">elif</span> <span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">target</span><span class="p">:</span>
-<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>            <span class="n">j</span> <span class="o">=</span> <span class="n">m</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># この場合、target は区間 [i, m-1] にあることを示す</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>            <span class="n">j</span> <span class="o">=</span> <span class="n">m</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># この場合、target は区間 [i, m-1] にある</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="k">else</span><span class="p">:</span>
-<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>            <span class="k">return</span> <span class="n">m</span>  <span class="c1"># ターゲット要素が見つかったため、そのインデックスを返す</span>
-<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>  <span class="c1"># ターゲット要素が見つからなかったため、-1 を返す</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>            <span class="k">return</span> <span class="n">m</span>  <span class="c1"># 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>  <span class="c1"># 目標要素が見つからなければ -1 を返す</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 二分探索（両端閉区間） */</span>
+<div class="highlight"><span class="filename">binary_search.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 二分探索（両閉区間） */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearch</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 両端閉区間[0, n-1]を初期化、すなわちi、jはそれぞれ配列の最初の要素と最後の要素を指す</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="c1">// 探索区間が空になるまでループ（i &gt; jの時空になる）</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="c1">// ループし、探索区間が空になったら終了する（i &gt; j で空）</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックスmを計算</span>
-<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w">    </span><span class="c1">// この状況はtargetが区間[m+1, j]にあることを示す</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w">    </span><span class="c1">// この場合、target は区間 [m+1, j] にある</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この状況はtargetが区間[i, m-1]にあることを示す</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この場合、target は区間 [i, m-1] にある</span>
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="c1">// ターゲット要素が見つかったため、そのインデックスを返す</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
 <a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="c1">// ターゲット要素が見つからなかったため、-1を返す</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="c1">// 目標要素が見つからなければ -1 を返す</span>
 <a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
 <a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 二分探索（両端閉区間） */</span>
+<div class="highlight"><span class="filename">binary_search.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 二分探索（両閉区間） */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearch</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 両端閉区間 [0, n-1] を初期化、すなわち i, j はそれぞれ配列の最初の要素と最後の要素を指す</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="c1">// 探索区間が空になるまでループ（i &gt; j のとき空）</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="c1">// ループし、探索区間が空になったら終了する（i &gt; j で空）</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
-<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この状況は target が区間 [m+1, j] にあることを示す</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この場合、target は区間 [m+1, j] にある</span>
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この状況は target が区間 [i, m-1] にあることを示す</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この場合、target は区間 [i, m-1] にある</span>
 <a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="c1">// 目標要素を見つけたので、そのインデックスを返す</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
 <a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="c1">// 目標要素を見つけられなかったので、-1 を返す</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="c1">// 目標要素が見つからなければ -1 を返す</span>
 <a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_search</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BinarySearch</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 二分探索（両閉区間） */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">BinarySearch</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="c1">// 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="c1">// ループし、探索区間が空になったら終了する（i &gt; j で空）</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">   </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w">      </span><span class="c1">// この場合、target は区間 [m+1, j] にある</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="nf">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この場合、target は区間 [i, m-1] にある</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">        </span><span class="k">else</span><span class="w">                       </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">    </span><span class="c1">// 目標要素が見つからなければ -1 を返す</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">binarySearch</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 二分探索（両閉区間） */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">binarySearch</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="c1">// ループし、探索区間が空になったら終了する（i &gt; j で空）</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">        </span><span class="nx">m</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="o">-</span><span class="nx">i</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="w">      </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// この場合、target は区間 [m+1, j] にある</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">            </span><span class="nx">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// この場合、target は区間 [i, m-1] にある</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nx">m</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">    </span><span class="c1">// 目標要素が見つからなければ -1 を返す</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">binarySearch</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 二分探索（両閉区間） */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">binarySearch</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">startIndex</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">endIndex</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="c1">// ループし、探索区間が空になったら終了する（i &gt; j で空）</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// この場合、target は区間 [m+1, j] にある</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// この場合、target は区間 [i, m-1] にある</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">    </span><span class="c1">// 目標要素が見つからなければ -1 を返す</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearch</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 二分探索（両閉区間） */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">binarySearch</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="c1">// 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">        </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="c1">// ループし、探索区間が空になったら終了する（i &gt; j で空）</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">        </span><span class="c1">// 中点インデックス `m` を計算し、`parseInt()` で切り捨てる</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">parseInt</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">            </span><span class="c1">// この場合、target は区間 [m+1, j] にある</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">            </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">            </span><span class="c1">// この場合、target は区間 [i, m-1] にある</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w">    </span><span class="c1">// 目標要素が見つからなければ -1 を返す</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearch</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 二分探索（両閉区間） */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">binarySearch</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">target</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="c1">// 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">        </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="c1">// ループし、探索区間が空になったら終了する（i &gt; j で空）</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">        </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">            </span><span class="c1">// この場合、target は区間 [m+1, j] にある</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">            </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">            </span><span class="c1">// この場合、target は区間 [i, m-1] にある</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">            </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 目標要素が見つからなければ -1 を返す</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearch</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 二分探索（両閉区間） */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">binarySearch</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="c1">// 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="c1">// ループし、探索区間が空になったら終了する（i &gt; j で空）</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">      </span><span class="c1">// この場合、target は区間 [m+1, j] にある</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">      </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">      </span><span class="c1">// この場合、target は区間 [i, m-1] にある</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">      </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">      </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">      </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w">  </span><span class="c1">// 目標要素が見つからなければ -1 を返す</span>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binary_search</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 二分探索（両閉区間） */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">binary_search</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="c1">// 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="c1">// ループし、探索区間が空になったら終了する（i &gt; j で空）</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">            </span><span class="c1">// この場合、target は区間 [m+1, j] にある</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">            </span><span class="c1">// この場合、target は区間 [i, m-1] にある</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">            </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w">    </span><span class="c1">// 目標要素が見つからなければ -1 を返す</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearch</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 二分探索（両閉区間） */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearch</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">len</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="c1">// 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">len</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">    </span><span class="c1">// ループし、探索区間が空になったら終了する（i &gt; j で空）</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w">    </span><span class="c1">// この場合、target は区間 [m+1, j] にある</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この場合、target は区間 [i, m-1] にある</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">    </span><span class="c1">// 目標要素が見つからなければ -1 を返す</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binarySearch</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 二分探索（両閉区間） */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">binarySearch</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="c1">// 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="c1">// ループし、探索区間が空になったら終了する（i &gt; j で空）</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この場合、target は区間 [m+1, j] にある</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この場合、target は区間 [i, m-1] にある</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">        </span><span class="k">else</span><span class="w">  </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">    </span><span class="c1">// 目標要素が見つからなければ -1 を返す</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="m">1</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binary_search</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 二分探索（両閉区間） ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">binary_search</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="c1"># ループし、探索区間が空になったら終了する（i &gt; j で空）</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">    </span><span class="c1"># 理論上、Ruby の数値は無限に大きくできるため（メモリ容量に依存）、大きな数のオーバーフローを考慮する必要はない</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">    </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="w">   </span><span class="c1"># 中点インデックス m を計算</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">      </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># この場合、target は区間 [m+1, j] にある</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">    </span><span class="k">elsif</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">      </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># この場合、target は区間 [i, m-1] にある</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">      </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="w">  </span><span class="c1"># 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="w">  </span><span class="o">-</span><span class="mi">1</span><span class="w">  </span><span class="c1"># 目標要素が見つからなければ -1 を返す</span>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p><strong>時間計算量は<span class="arithmatex">\(O(\log n)\)</span>です</strong>：二分ループにおいて、区間は各ラウンドで半分に減少するため、反復回数は<span class="arithmatex">\(\log_2 n\)</span>となります。</p>
-<p><strong>空間計算量は<span class="arithmatex">\(O(1)\)</span>です</strong>：ポインタ<span class="arithmatex">\(i\)</span>と<span class="arithmatex">\(j\)</span>は定数サイズの空間を占有します。</p>
-<h2 id="1011">10.1.1 &nbsp; 区間表現方法<a class="headerlink" href="#1011" title="Permanent link">&para;</a></h2>
-<p>上記の閉区間の他に、もう一つの一般的な区間表現は「左閉右開」区間で、<span class="arithmatex">\([0, n)\)</span>として定義され、左境界は自身を含み、右境界は含みません。この表現では、<span class="arithmatex">\(i = j\)</span>のとき区間<span class="arithmatex">\([i, j)\)</span>は空になります。</p>
-<p>この表現に基づいて同じ機能を持つ二分探索アルゴリズムを実装できます：</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20binary_search%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%EF%BC%88%E4%B8%A1%E9%96%89%E5%8C%BA%E9%96%93%EF%BC%89%22%22%22%0A%20%20%20%20%23%20%E4%B8%A1%E9%96%89%E5%8C%BA%E9%96%93%20%5B0%2C%20n-1%5D%20%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%E3%80%82%E3%81%A4%E3%81%BE%E3%82%8A%20i%2C%20j%20%E3%81%AF%E3%81%9D%E3%82%8C%E3%81%9E%E3%82%8C%E9%85%8D%E5%88%97%E3%81%AE%E5%85%88%E9%A0%AD%E8%A6%81%E7%B4%A0%E3%81%A8%E6%9C%AB%E5%B0%BE%E8%A6%81%E7%B4%A0%E3%82%92%E6%8C%87%E3%81%99%0A%20%20%20%20i%2C%20j%20%3D%200%2C%20len%28nums%29%20-%201%0A%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%97%E3%81%97%E3%80%81%E6%8E%A2%E7%B4%A2%E5%8C%BA%E9%96%93%E3%81%8C%E7%A9%BA%E3%81%AB%E3%81%AA%E3%81%A3%E3%81%9F%E3%82%89%E7%B5%82%E4%BA%86%E3%81%99%E3%82%8B%EF%BC%88i%20%3E%20j%20%E3%81%A7%E7%A9%BA%EF%BC%89%0A%20%20%20%20while%20i%20%3C%3D%20j%3A%0A%20%20%20%20%20%20%20%20%23%20%E7%90%86%E8%AB%96%E4%B8%8A%E3%80%81Python%20%E3%81%AE%E6%95%B0%E5%80%A4%E3%81%AF%E7%84%A1%E9%99%90%E3%81%AB%E5%A4%A7%E3%81%8D%E3%81%8F%E3%81%A7%E3%81%8D%E3%82%8B%E3%81%9F%E3%82%81%EF%BC%88%E3%83%A1%E3%83%A2%E3%83%AA%E5%AE%B9%E9%87%8F%E3%81%AB%E4%BE%9D%E5%AD%98%EF%BC%89%E3%80%81%E5%A4%A7%E3%81%8D%E3%81%AA%E6%95%B0%E3%81%AE%E3%82%AA%E3%83%BC%E3%83%90%E3%83%BC%E3%83%95%E3%83%AD%E3%83%BC%E3%82%92%E8%80%83%E6%85%AE%E3%81%99%E3%82%8B%E5%BF%85%E8%A6%81%E3%81%AF%E3%81%AA%E3%81%84%0A%20%20%20%20%20%20%20%20m%20%3D%20%28i%20%2B%20j%29%20%2F%2F%202%20%20%23%20%E4%B8%AD%E7%82%B9%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20m%20%E3%82%92%E8%A8%88%E7%AE%97%0A%20%20%20%20%20%20%20%20if%20nums%5Bm%5D%20%3C%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%3D%20m%20%2B%201%20%20%23%20%E3%81%93%E3%81%AE%E5%A0%B4%E5%90%88%E3%80%81target%20%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bm%2B1%2C%20j%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20elif%20nums%5Bm%5D%20%3E%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20%3D%20m%20-%201%20%20%23%20%E3%81%93%E3%81%AE%E5%A0%B4%E5%90%88%E3%80%81target%20%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bi%2C%20m-1%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20m%20%20%23%20%E7%9B%AE%E6%A8%99%E8%A6%81%E7%B4%A0%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%81%A3%E3%81%9F%E3%82%89%E3%81%9D%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20-1%20%20%23%20%E7%9B%AE%E6%A8%99%E8%A6%81%E7%B4%A0%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%82%89%E3%81%AA%E3%81%91%E3%82%8C%E3%81%B0%20-1%20%E3%82%92%E8%BF%94%E3%81%99%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20target%20%3D%206%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%206%2C%208%2C%2012%2C%2015%2C%2023%2C%2026%2C%2031%2C%2035%5D%0A%0A%20%20%20%20%23%20%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%EF%BC%88%E4%B8%A1%E9%96%89%E5%8C%BA%E9%96%93%EF%BC%89%0A%20%20%20%20index%20%3D%20binary_search%28nums%2C%20target%29%0A%20%20%20%20print%28%22%E5%AF%BE%E8%B1%A1%E8%A6%81%E7%B4%A0%206%20%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20%3D%20%22%2C%20index%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20binary_search%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%EF%BC%88%E4%B8%A1%E9%96%89%E5%8C%BA%E9%96%93%EF%BC%89%22%22%22%0A%20%20%20%20%23%20%E4%B8%A1%E9%96%89%E5%8C%BA%E9%96%93%20%5B0%2C%20n-1%5D%20%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%E3%80%82%E3%81%A4%E3%81%BE%E3%82%8A%20i%2C%20j%20%E3%81%AF%E3%81%9D%E3%82%8C%E3%81%9E%E3%82%8C%E9%85%8D%E5%88%97%E3%81%AE%E5%85%88%E9%A0%AD%E8%A6%81%E7%B4%A0%E3%81%A8%E6%9C%AB%E5%B0%BE%E8%A6%81%E7%B4%A0%E3%82%92%E6%8C%87%E3%81%99%0A%20%20%20%20i%2C%20j%20%3D%200%2C%20len%28nums%29%20-%201%0A%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%97%E3%81%97%E3%80%81%E6%8E%A2%E7%B4%A2%E5%8C%BA%E9%96%93%E3%81%8C%E7%A9%BA%E3%81%AB%E3%81%AA%E3%81%A3%E3%81%9F%E3%82%89%E7%B5%82%E4%BA%86%E3%81%99%E3%82%8B%EF%BC%88i%20%3E%20j%20%E3%81%A7%E7%A9%BA%EF%BC%89%0A%20%20%20%20while%20i%20%3C%3D%20j%3A%0A%20%20%20%20%20%20%20%20%23%20%E7%90%86%E8%AB%96%E4%B8%8A%E3%80%81Python%20%E3%81%AE%E6%95%B0%E5%80%A4%E3%81%AF%E7%84%A1%E9%99%90%E3%81%AB%E5%A4%A7%E3%81%8D%E3%81%8F%E3%81%A7%E3%81%8D%E3%82%8B%E3%81%9F%E3%82%81%EF%BC%88%E3%83%A1%E3%83%A2%E3%83%AA%E5%AE%B9%E9%87%8F%E3%81%AB%E4%BE%9D%E5%AD%98%EF%BC%89%E3%80%81%E5%A4%A7%E3%81%8D%E3%81%AA%E6%95%B0%E3%81%AE%E3%82%AA%E3%83%BC%E3%83%90%E3%83%BC%E3%83%95%E3%83%AD%E3%83%BC%E3%82%92%E8%80%83%E6%85%AE%E3%81%99%E3%82%8B%E5%BF%85%E8%A6%81%E3%81%AF%E3%81%AA%E3%81%84%0A%20%20%20%20%20%20%20%20m%20%3D%20%28i%20%2B%20j%29%20%2F%2F%202%20%20%23%20%E4%B8%AD%E7%82%B9%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20m%20%E3%82%92%E8%A8%88%E7%AE%97%0A%20%20%20%20%20%20%20%20if%20nums%5Bm%5D%20%3C%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%3D%20m%20%2B%201%20%20%23%20%E3%81%93%E3%81%AE%E5%A0%B4%E5%90%88%E3%80%81target%20%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bm%2B1%2C%20j%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20elif%20nums%5Bm%5D%20%3E%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20%3D%20m%20-%201%20%20%23%20%E3%81%93%E3%81%AE%E5%A0%B4%E5%90%88%E3%80%81target%20%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bi%2C%20m-1%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20m%20%20%23%20%E7%9B%AE%E6%A8%99%E8%A6%81%E7%B4%A0%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%81%A3%E3%81%9F%E3%82%89%E3%81%9D%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20-1%20%20%23%20%E7%9B%AE%E6%A8%99%E8%A6%81%E7%B4%A0%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%82%89%E3%81%AA%E3%81%91%E3%82%8C%E3%81%B0%20-1%20%E3%82%92%E8%BF%94%E3%81%99%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20target%20%3D%206%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%206%2C%208%2C%2012%2C%2015%2C%2023%2C%2026%2C%2031%2C%2035%5D%0A%0A%20%20%20%20%23%20%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%EF%BC%88%E4%B8%A1%E9%96%89%E5%8C%BA%E9%96%93%EF%BC%89%0A%20%20%20%20index%20%3D%20binary_search%28nums%2C%20target%29%0A%20%20%20%20print%28%22%E5%AF%BE%E8%B1%A1%E8%A6%81%E7%B4%A0%206%20%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20%3D%20%22%2C%20index%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p><strong>時間計算量は <span class="arithmatex">\(O(\log n)\)</span></strong> ：二分探索のループでは各ラウンドで区間が半分になるため、ループ回数は <span class="arithmatex">\(\log_2 n\)</span> です。</p>
+<p><strong>空間計算量は <span class="arithmatex">\(O(1)\)</span></strong> ：ポインタ <span class="arithmatex">\(i\)</span> と <span class="arithmatex">\(j\)</span> に必要なのは定数サイズの空間だけです。</p>
+<h2 id="1011">10.1.1 &nbsp; 区間の表し方<a class="headerlink" href="#1011" title="Permanent link">&para;</a></h2>
+<p>上記の両閉区間のほかに、一般的な区間表現として「左閉右開」区間があり、<span class="arithmatex">\([0, n)\)</span> と定義されます。つまり左端は含み、右端は含みません。この表現では、区間 <span class="arithmatex">\([i, j)\)</span> は <span class="arithmatex">\(i = j\)</span> のとき空です。</p>
+<p>この表現に基づいて、同じ機能を持つ二分探索アルゴリズムを実装できます。</p>
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 <div class="highlight"><span class="filename">binary_search.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">binary_search_lcro</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
 <a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二分探索（左閉右開区間）&quot;&quot;&quot;</span>
-<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="c1"># 左閉右開区間 [0, n) を初期化、すなわち i, j はそれぞれ配列の最初の要素と最後の要素+1を指す</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="c1"># 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す</span>
 <a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
-<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># 検索区間が空になるまでループ（i = j のとき空）</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># ループし、探索区間が空になったら終了する（i = j で空）</span>
 <a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>    <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="n">j</span><span class="p">:</span>
-<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>        <span class="n">m</span> <span class="o">=</span> <span class="n">i</span> <span class="o">+</span> <span class="p">(</span><span class="n">j</span> <span class="o">-</span> <span class="n">i</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>  <span class="c1"># 中点インデックス m を計算</span>
+<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>        <span class="n">m</span> <span class="o">=</span> <span class="p">(</span><span class="n">i</span> <span class="o">+</span> <span class="n">j</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>  <span class="c1"># 中点インデックス m を計算</span>
 <a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>        <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span> <span class="o">&lt;</span> <span class="n">target</span><span class="p">:</span>
-<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>            <span class="n">i</span> <span class="o">=</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span>  <span class="c1"># この場合、target は区間 [m+1, j) にあることを示す</span>
+<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>            <span class="n">i</span> <span class="o">=</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span>  <span class="c1"># この場合、target は区間 [m+1, j) にある</span>
 <a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>        <span class="k">elif</span> <span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">target</span><span class="p">:</span>
-<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>            <span class="n">j</span> <span class="o">=</span> <span class="n">m</span>  <span class="c1"># この場合、target は区間 [i, m) にあることを示す</span>
+<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>            <span class="n">j</span> <span class="o">=</span> <span class="n">m</span>  <span class="c1"># この場合、target は区間 [i, m) にある</span>
 <a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>        <span class="k">else</span><span class="p">:</span>
-<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a>            <span class="k">return</span> <span class="n">m</span>  <span class="c1"># ターゲット要素が見つかったため、そのインデックスを返す</span>
-<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>    <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>  <span class="c1"># ターゲット要素が見つからなかったため、-1 を返す</span>
+<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a>            <span class="k">return</span> <span class="n">m</span>  <span class="c1"># 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>    <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>  <span class="c1"># 目標要素が見つからなければ -1 を返す</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_search.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 二分探索（左閉右開区間） */</span>
 <a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearchLCRO</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="c1">// 左閉右開区間[0, n)を初期化、すなわちi、jはそれぞれ配列の最初の要素と最後の要素+1を指す</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="c1">// 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す</span>
 <a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
-<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="c1">// 探索区間が空になるまでループ（i = jの時空になる）</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="c1">// ループし、探索区間が空になったら終了する（i = j で空）</span>
 <a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックスmを計算</span>
-<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w">    </span><span class="c1">// この状況はtargetが区間[m+1, j)にあることを示す</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w">    </span><span class="c1">// この場合、target は区間 [m+1, j) にある</span>
 <a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この状況はtargetが区間[i, m)にあることを示す</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この場合、target は区間 [i, m) にある</span>
 <a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
-<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="c1">// ターゲット要素が見つかったため、そのインデックスを返す</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
 <a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
 <a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">    </span><span class="c1">// ターゲット要素が見つからなかったため、-1を返す</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">    </span><span class="c1">// 目標要素が見つからなければ -1 を返す</span>
 <a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
 <a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="p">}</span>
 </code></pre></div>
@@ -4553,81 +4743,272 @@
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_search.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 二分探索（左閉右開区間） */</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearchLCRO</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 左閉右開区間 [0, n) を初期化、すなわち i, j はそれぞれ配列の最初の要素と最後の要素+1を指す</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す</span>
 <a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
-<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="c1">// 探索区間が空になるまでループ（i = j のとき空）</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="c1">// ループし、探索区間が空になったら終了する（i = j で空）</span>
 <a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
-<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この状況は target が区間 [m+1, j) にあることを示す</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この場合、target は区間 [m+1, j) にある</span>
 <a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この状況は target が区間 [i, m) にあることを示す</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この場合、target は区間 [i, m) にある</span>
 <a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
-<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="c1">// 目標要素を見つけたので、そのインデックスを返す</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
 <a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
 <a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="c1">// 目標要素を見つけられなかったので、-1 を返す</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="c1">// 目標要素が見つからなければ -1 を返す</span>
 <a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_search</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BinarySearchLCRO</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 二分探索（左閉右開区間） */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">BinarySearchLCRO</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="c1">// 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="c1">// ループし、探索区間が空になったら終了する（i = j で空）</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">   </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w">      </span><span class="c1">// この場合、target は区間 [m+1, j) にある</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="nf">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この場合、target は区間 [i, m) にある</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">        </span><span class="k">else</span><span class="w">                       </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">    </span><span class="c1">// 目標要素が見つからなければ -1 を返す</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">binarySearchLCRO</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 二分探索（左閉右開区間） */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">binarySearchLCRO</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="c1">// 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">    </span><span class="c1">// ループし、探索区間が空になったら終了する（i = j で空）</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">        </span><span class="nx">m</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="o">-</span><span class="nx">i</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="w">      </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// この場合、target は区間 [m+1, j) にある</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">            </span><span class="nx">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// この場合、target は区間 [i, m) にある</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">m</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nx">m</span>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w">    </span><span class="c1">// 目標要素が見つからなければ -1 を返す</span>
+<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">binarySearchLCRO</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 二分探索（左閉右開区間） */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">binarySearchLCRO</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="c1">// 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">startIndex</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">endIndex</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">    </span><span class="c1">// ループし、探索区間が空になったら終了する（i = j で空）</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// この場合、target は区間 [m+1, j) にある</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// この場合、target は区間 [i, m) にある</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">m</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span>
+<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="w">    </span><span class="c1">// 目標要素が見つからなければ -1 を返す</span>
+<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearchLCRO</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 二分探索（左閉右開区間） */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">binarySearchLCRO</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="c1">// 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">        </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">    </span><span class="c1">// ループし、探索区間が空になったら終了する（i = j で空）</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">        </span><span class="c1">// 中点インデックス `m` を計算し、`parseInt()` で切り捨てる</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">parseInt</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w">            </span><span class="c1">// この場合、target は区間 [m+1, j) にある</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">            </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span>
+<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w">            </span><span class="c1">// この場合、target は区間 [i, m) にある</span>
+<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span>
+<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a><span class="w">        </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span>
+<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a><span class="w">    </span><span class="c1">// 目標要素が見つからなければ -1 を返す</span>
+<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearchLCRO</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 二分探索（左閉右開区間） */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">binarySearchLCRO</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">target</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="c1">// 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">        </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">    </span><span class="c1">// ループし、探索区間が空になったら終了する（i = j で空）</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">        </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w">            </span><span class="c1">// この場合、target は区間 [m+1, j) にある</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">            </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w">            </span><span class="c1">// この場合、target は区間 [i, m) にある</span>
+<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span>
+<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-17" name="__codelineno-20-17" href="#__codelineno-20-17"></a><span class="w">            </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-20-18" name="__codelineno-20-18" href="#__codelineno-20-18"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span>
+<a id="__codelineno-20-19" name="__codelineno-20-19" href="#__codelineno-20-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-20" name="__codelineno-20-20" href="#__codelineno-20-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-21" name="__codelineno-20-21" href="#__codelineno-20-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 目標要素が見つからなければ -1 を返す</span>
+<a id="__codelineno-20-22" name="__codelineno-20-22" href="#__codelineno-20-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearchLCRO</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 二分探索（左閉右開区間） */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">binarySearchLCRO</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="c1">// 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">  </span><span class="c1">// ループし、探索区間が空になったら終了する（i = j で空）</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">      </span><span class="c1">// この場合、target は区間 [m+1, j) にある</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="w">      </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w">      </span><span class="c1">// この場合、target は区間 [i, m) にある</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">      </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w">      </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="w">      </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
+<a id="__codelineno-21-17" name="__codelineno-21-17" href="#__codelineno-21-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-18" name="__codelineno-21-18" href="#__codelineno-21-18"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-19" name="__codelineno-21-19" href="#__codelineno-21-19"></a><span class="w">  </span><span class="c1">// 目標要素が見つからなければ -1 を返す</span>
+<a id="__codelineno-21-20" name="__codelineno-21-20" href="#__codelineno-21-20"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-21-21" name="__codelineno-21-21" href="#__codelineno-21-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binary_search_lcro</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 二分探索（左閉右開区間） */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">binary_search_lcro</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="c1">// 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">;</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w">    </span><span class="c1">// ループし、探索区間が空になったら終了する（i = j で空）</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w">            </span><span class="c1">// この場合、target は区間 [m+1, j) にある</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">            </span><span class="c1">// この場合、target は区間 [i, m) にある</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="w">            </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
+<a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a><span class="w">    </span><span class="c1">// 目標要素が見つからなければ -1 を返す</span>
+<a id="__codelineno-22-21" name="__codelineno-22-21" href="#__codelineno-22-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-22-22" name="__codelineno-22-22" href="#__codelineno-22-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearchLCRO</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 二分探索（左閉右開区間） */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearchLCRO</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">len</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="c1">// 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">len</span><span class="p">;</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">    </span><span class="c1">// ループし、探索区間が空になったら終了する（i = j で空）</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w">    </span><span class="c1">// この場合、target は区間 [m+1, j) にある</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この場合、target は区間 [i, m) にある</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="w">    </span><span class="c1">// 目標要素が見つからなければ -1 を返す</span>
+<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binarySearchLCRO</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 二分探索（左閉右開区間） */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">binarySearchLCRO</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="c1">// 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">    </span><span class="c1">// ループし、探索区間が空になったら終了する（i = j で空）</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この場合、target は区間 [m+1, j) にある</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この場合、target は区間 [i, m) にある</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w">        </span><span class="k">else</span><span class="w">  </span><span class="c1">// 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span>
+<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="w">    </span><span class="c1">// 目標要素が見つからなければ -1 を返す</span>
+<a id="__codelineno-24-17" name="__codelineno-24-17" href="#__codelineno-24-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="m">1</span>
+<a id="__codelineno-24-18" name="__codelineno-24-18" href="#__codelineno-24-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binary_search_lcro</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### 二分探索（左閉右開区間） ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">binary_search_lcro</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="c1"># 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">  </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">  </span><span class="c1"># ループし、探索区間が空になったら終了する（i = j で空）</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w">    </span><span class="c1"># 中点インデックス m を計算</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">    </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w">      </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># この場合、target は区間 [m+1, j) にある</span>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w">    </span><span class="k">elsif</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span>
+<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w">      </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># この場合、target は区間 [i, m) にある</span>
+<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w">      </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="w">  </span><span class="c1"># 目標要素が見つかったらそのインデックスを返す</span>
+<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a>
+<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a><span class="w">  </span><span class="o">-</span><span class="mi">1</span><span class="w">  </span><span class="c1"># 目標要素が見つからなければ -1 を返す</span>
+<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>下図に示すように、2つの区間表現タイプにおいて、二分探索アルゴリズムの初期化、ループ条件、区間縮小操作が異なります。</p>
-<p>「閉区間」表現では両方の境界が包含的であるため、ポインタ<span class="arithmatex">\(i\)</span>と<span class="arithmatex">\(j\)</span>による区間縮小操作も対称的です。これによりエラーが発生しにくくなるため、<strong>一般的に「閉区間」アプローチの使用が推奨されます</strong>。</p>
-<p><img alt="Two types of interval definitions" class="animation-figure" src="../binary_search.assets/binary_search_ranges.png" /></p>
-<p align="center"> 図 10-3 &nbsp; Two types of interval definitions </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20binary_search_lcro%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%EF%BC%88%E5%B7%A6%E9%96%89%E5%8F%B3%E9%96%8B%E5%8C%BA%E9%96%93%EF%BC%89%22%22%22%0A%20%20%20%20%23%20%E5%B7%A6%E9%96%89%E5%8F%B3%E9%96%8B%E5%8C%BA%E9%96%93%20%5B0%2C%20n%29%20%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%E3%80%82%E3%81%A4%E3%81%BE%E3%82%8A%20i%2C%20j%20%E3%81%AF%E3%81%9D%E3%82%8C%E3%81%9E%E3%82%8C%E9%85%8D%E5%88%97%E3%81%AE%E5%85%88%E9%A0%AD%E8%A6%81%E7%B4%A0%E3%81%A8%E6%9C%AB%E5%B0%BE%E8%A6%81%E7%B4%A0%2B1%E3%82%92%E6%8C%87%E3%81%99%0A%20%20%20%20i%2C%20j%20%3D%200%2C%20len%28nums%29%0A%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%97%E3%81%97%E3%80%81%E6%8E%A2%E7%B4%A2%E5%8C%BA%E9%96%93%E3%81%8C%E7%A9%BA%E3%81%AB%E3%81%AA%E3%81%A3%E3%81%9F%E3%82%89%E7%B5%82%E4%BA%86%E3%81%99%E3%82%8B%EF%BC%88i%20%3D%20j%20%E3%81%A7%E7%A9%BA%EF%BC%89%0A%20%20%20%20while%20i%20%3C%20j%3A%0A%20%20%20%20%20%20%20%20m%20%3D%20%28i%20%2B%20j%29%20%2F%2F%202%20%20%23%20%E4%B8%AD%E7%82%B9%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20m%20%E3%82%92%E8%A8%88%E7%AE%97%0A%20%20%20%20%20%20%20%20if%20nums%5Bm%5D%20%3C%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%3D%20m%20%2B%201%20%20%23%20%E3%81%93%E3%81%AE%E5%A0%B4%E5%90%88%E3%80%81target%20%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bm%2B1%2C%20j%29%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20elif%20nums%5Bm%5D%20%3E%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20%3D%20m%20%20%23%20%E3%81%93%E3%81%AE%E5%A0%B4%E5%90%88%E3%80%81target%20%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bi%2C%20m%29%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20m%20%20%23%20%E7%9B%AE%E6%A8%99%E8%A6%81%E7%B4%A0%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%81%A3%E3%81%9F%E3%82%89%E3%81%9D%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20-1%20%20%23%20%E7%9B%AE%E6%A8%99%E8%A6%81%E7%B4%A0%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%82%89%E3%81%AA%E3%81%91%E3%82%8C%E3%81%B0%20-1%20%E3%82%92%E8%BF%94%E3%81%99%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20target%20%3D%206%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%206%2C%208%2C%2012%2C%2015%2C%2023%2C%2026%2C%2031%2C%2035%5D%0A%0A%20%20%20%20%23%20%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%EF%BC%88%E5%B7%A6%E9%96%89%E5%8F%B3%E9%96%8B%E5%8C%BA%E9%96%93%EF%BC%89%0A%20%20%20%20index%20%3D%20binary_search_lcro%28nums%2C%20target%29%0A%20%20%20%20print%28%22%E5%AF%BE%E8%B1%A1%E8%A6%81%E7%B4%A0%206%20%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20%3D%20%22%2C%20index%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20binary_search_lcro%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%EF%BC%88%E5%B7%A6%E9%96%89%E5%8F%B3%E9%96%8B%E5%8C%BA%E9%96%93%EF%BC%89%22%22%22%0A%20%20%20%20%23%20%E5%B7%A6%E9%96%89%E5%8F%B3%E9%96%8B%E5%8C%BA%E9%96%93%20%5B0%2C%20n%29%20%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%E3%80%82%E3%81%A4%E3%81%BE%E3%82%8A%20i%2C%20j%20%E3%81%AF%E3%81%9D%E3%82%8C%E3%81%9E%E3%82%8C%E9%85%8D%E5%88%97%E3%81%AE%E5%85%88%E9%A0%AD%E8%A6%81%E7%B4%A0%E3%81%A8%E6%9C%AB%E5%B0%BE%E8%A6%81%E7%B4%A0%2B1%E3%82%92%E6%8C%87%E3%81%99%0A%20%20%20%20i%2C%20j%20%3D%200%2C%20len%28nums%29%0A%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%97%E3%81%97%E3%80%81%E6%8E%A2%E7%B4%A2%E5%8C%BA%E9%96%93%E3%81%8C%E7%A9%BA%E3%81%AB%E3%81%AA%E3%81%A3%E3%81%9F%E3%82%89%E7%B5%82%E4%BA%86%E3%81%99%E3%82%8B%EF%BC%88i%20%3D%20j%20%E3%81%A7%E7%A9%BA%EF%BC%89%0A%20%20%20%20while%20i%20%3C%20j%3A%0A%20%20%20%20%20%20%20%20m%20%3D%20%28i%20%2B%20j%29%20%2F%2F%202%20%20%23%20%E4%B8%AD%E7%82%B9%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20m%20%E3%82%92%E8%A8%88%E7%AE%97%0A%20%20%20%20%20%20%20%20if%20nums%5Bm%5D%20%3C%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%3D%20m%20%2B%201%20%20%23%20%E3%81%93%E3%81%AE%E5%A0%B4%E5%90%88%E3%80%81target%20%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bm%2B1%2C%20j%29%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20elif%20nums%5Bm%5D%20%3E%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20%3D%20m%20%20%23%20%E3%81%93%E3%81%AE%E5%A0%B4%E5%90%88%E3%80%81target%20%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bi%2C%20m%29%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20m%20%20%23%20%E7%9B%AE%E6%A8%99%E8%A6%81%E7%B4%A0%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%81%A3%E3%81%9F%E3%82%89%E3%81%9D%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20-1%20%20%23%20%E7%9B%AE%E6%A8%99%E8%A6%81%E7%B4%A0%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%82%89%E3%81%AA%E3%81%91%E3%82%8C%E3%81%B0%20-1%20%E3%82%92%E8%BF%94%E3%81%99%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20target%20%3D%206%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%206%2C%208%2C%2012%2C%2015%2C%2023%2C%2026%2C%2031%2C%2035%5D%0A%0A%20%20%20%20%23%20%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%EF%BC%88%E5%B7%A6%E9%96%89%E5%8F%B3%E9%96%8B%E5%8C%BA%E9%96%93%EF%BC%89%0A%20%20%20%20index%20%3D%20binary_search_lcro%28nums%2C%20target%29%0A%20%20%20%20print%28%22%E5%AF%BE%E8%B1%A1%E8%A6%81%E7%B4%A0%206%20%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20%3D%20%22%2C%20index%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>次の図に示すように、2 種類の区間表現では、二分探索アルゴリズムの初期化、ループ条件、区間の縮小操作がそれぞれ異なります。</p>
+<p>「両閉区間」の表現では左右の境界がどちらも閉区間として定義されるため、ポインタ <span class="arithmatex">\(i\)</span> とポインタ <span class="arithmatex">\(j\)</span> による区間縮小の操作も対称になります。このほうがミスをしにくいため、<strong>一般には「両閉区間」の書き方を推奨します</strong>。</p>
+<p><img alt="2 種類の区間定義" class="animation-figure" src="../binary_search.assets/binary_search_ranges.png" /></p>
+<p align="center"> 図 10-3 &nbsp; 2 種類の区間定義 </p>
 
-<h2 id="1012">10.1.2 &nbsp; 利点と制限<a class="headerlink" href="#1012" title="Permanent link">&para;</a></h2>
-<p>二分探索は時間と空間の両方の面で良好な性能を示します。</p>
+<h2 id="1012">10.1.2 &nbsp; 利点と限界<a class="headerlink" href="#1012" title="Permanent link">&para;</a></h2>
+<p>二分探索は時間と空間の両面で優れた性能を持ちます。</p>
 <ul>
-<li>二分探索は時間効率が良いです。大きなデータセットでは、対数時間計算量が大きな利点を提供します。例えば、サイズ<span class="arithmatex">\(n = 2^{20}\)</span>のデータセットが与えられた場合、線形探索は<span class="arithmatex">\(2^{20} = 1048576\)</span>回の反復が必要ですが、二分探索は<span class="arithmatex">\(\log_2 2^{20} = 20\)</span>回のループのみで済みます。</li>
-<li>二分探索には追加の空間が必要ありません。追加の空間に依存する探索アルゴリズム（ハッシュ探索など）と比較して、二分探索はより空間効率的です。</li>
+<li>二分探索は時間効率が高いです。データ量が大きい場合、対数時間計算量は大きな優位性を持ちます。たとえば、データサイズ <span class="arithmatex">\(n = 2^{20}\)</span> のとき、線形探索では <span class="arithmatex">\(2^{20} = 1048576\)</span> 回のループが必要ですが、二分探索では <span class="arithmatex">\(\log_2 2^{20} = 20\)</span> 回で済みます。</li>
+<li>二分探索は追加の空間を必要としません。追加領域を要する探索アルゴリズム（たとえばハッシュ探索）と比べて、二分探索はより省メモリです。</li>
 </ul>
-<p>しかし、二分探索は以下の懸念により、すべてのシナリオに適しているとは限りません。</p>
+<p>しかし、二分探索があらゆる状況に適しているわけではなく、主な理由は次のとおりです。</p>
 <ul>
-<li>二分探索はソート済みデータにのみ適用できます。未ソートのデータは二分探索を適用する前にソートする必要があり、ソートアルゴリズムは通常<span class="arithmatex">\(O(n \log n)\)</span>の時間計算量を持つため、これは価値がないかもしれません。このコストは線形探索よりも高く、二分探索自体は言うまでもありません。頻繁な挿入があるシナリオでは、配列を順序に保つコストは非常に高く、特定の位置に新しい要素を挿入する時間計算量は<span class="arithmatex">\(O(n)\)</span>です。</li>
-<li>二分探索は配列のみを使用できます。二分探索には非連続（ジャンプ）要素アクセスが必要で、これは連結リストでは非効率的です。そのため、連結リストや連結リストに基づくデータ構造はこのアルゴリズムに適していない可能性があります。</li>
-<li>線形探索は小さなデータセットでより良い性能を示します。線形探索では各反復で1つの判定操作のみが必要ですが、二分探索では1つの加算、1つの除算、1つから3つの判定操作、1つの加算（減算）を含み、合計4つから6つの操作が必要です。そのため、データサイズ<span class="arithmatex">\(n\)</span>が小さい場合、線形探索は二分探索よりも高速です。</li>
+<li>二分探索は整列済みデータにしか適用できません。入力データが無秩序な場合、二分探索を使うためだけにソートするのは割に合いません。ソートアルゴリズムの時間計算量は通常 <span class="arithmatex">\(O(n \log n)\)</span> であり、線形探索や二分探索よりも高いからです。要素を頻繁に挿入する場面では、配列の整列性を保つために特定位置へ挿入する必要があり、その時間計算量は <span class="arithmatex">\(O(n)\)</span> と高コストです。</li>
+<li>二分探索は配列にしか適していません。二分探索では要素へ飛び飛びにアクセスする必要がありますが、連結リストでそのようなアクセスを行う効率は低いため、連結リストやそれを基に実装されたデータ構造には向きません。</li>
+<li>データ量が小さい場合は線形探索のほうが高性能です。線形探索では各ラウンドで 1 回の比較だけで済みますが、二分探索では 1 回の加算、1 回の除算、1 ~ 3 回の比較、1 回の加算（減算）が必要で、合計 4 ~ 6 個の基本操作になります。したがって、データ量 <span class="arithmatex">\(n\)</span> が小さいときは、線形探索のほうがかえって速くなります。</li>
 </ul>
 
 <!-- Source file information -->
@@ -4675,7 +5056,7 @@ aria-label="フッター"
   <a
     href="../binary_search_insertion/"
     class="md-footer__link md-footer__link--next"
-    aria-label="次: 10.2 &amp;nbsp; 二分探索の挿入点"
+    aria-label="次: 10.2 &amp;nbsp; 二分探索の挿入位置"
     rel="next"
   >
     <div class="md-footer__title">
@@ -4683,7 +5064,7 @@ aria-label="フッター"
         次
       </span>
       <div class="md-ellipsis">
-        10.2 &nbsp; 二分探索の挿入点
+        10.2 &nbsp; 二分探索の挿入位置
       </div>
     </div>
     <div class="md-footer__button md-icon">
diff --git a/ja/chapter_searching/binary_search_edge/index.html b/ja/chapter_searching/binary_search_edge/index.html
index 12681e0a1..48968baa4 100644
--- a/ja/chapter_searching/binary_search_edge/index.html
+++ b/ja/chapter_searching/binary_search_edge/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1635,7 +1635,7 @@
   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1942,7 +1942,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2105,7 +2105,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2493,7 +2493,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2578,7 +2578,7 @@
   <a href="#1031" class="md-nav__link">
     <span class="md-ellipsis">
       
-        10.3.1 &nbsp; 左境界を見つける
+        10.3.1 &nbsp; 左端境界を探す
       
     </span>
   </a>
@@ -2589,19 +2589,19 @@
   <a href="#1032" class="md-nav__link">
     <span class="md-ellipsis">
       
-        10.3.2 &nbsp; 右境界を見つける
+        10.3.2 &nbsp; 右端境界を探す
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="10.3.2 右境界を見つける">
+    <nav class="md-nav" aria-label="10.3.2 右端境界を探す">
       <ul class="md-nav__list">
         
           <li class="md-nav__item">
   <a href="#1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; 左境界探索を再利用する
+        1. &nbsp; 左端境界探索を再利用する
       
     </span>
   </a>
@@ -2647,7 +2647,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2675,7 +2675,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3213,7 +3213,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3269,7 +3269,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3297,7 +3297,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3490,7 +3490,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3518,7 +3518,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3659,7 +3659,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3687,7 +3687,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3715,7 +3715,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3743,7 +3743,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3936,7 +3936,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4181,7 +4181,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4327,7 +4327,7 @@
   <a href="#1031" class="md-nav__link">
     <span class="md-ellipsis">
       
-        10.3.1 &nbsp; 左境界を見つける
+        10.3.1 &nbsp; 左端境界を探す
       
     </span>
   </a>
@@ -4338,19 +4338,19 @@
   <a href="#1032" class="md-nav__link">
     <span class="md-ellipsis">
       
-        10.3.2 &nbsp; 右境界を見つける
+        10.3.2 &nbsp; 右端境界を探す
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="10.3.2 右境界を見つける">
+    <nav class="md-nav" aria-label="10.3.2 右端境界を探す">
       <ul class="md-nav__list">
         
           <li class="md-nav__item">
   <a href="#1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; 左境界探索を再利用する
+        1. &nbsp; 左端境界探索を再利用する
       
     </span>
   </a>
@@ -4411,42 +4411,42 @@
 
 <!-- Page content -->
 <h1 id="103">10.3 &nbsp; 二分探索の境界<a class="headerlink" href="#103" title="Permanent link">&para;</a></h1>
-<h2 id="1031">10.3.1 &nbsp; 左境界を見つける<a class="headerlink" href="#1031" title="Permanent link">&para;</a></h2>
+<h2 id="1031">10.3.1 &nbsp; 左端境界を探す<a class="headerlink" href="#1031" title="Permanent link">&para;</a></h2>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
-<p>重複要素を含む可能性がある長さ<span class="arithmatex">\(n\)</span>のソート済み配列<code>nums</code>が与えられ、最も左の要素<code>target</code>のインデックスを返してください。要素が配列に存在しない場合は、<span class="arithmatex">\(-1\)</span>を返してください。</p>
+<p>長さ <span class="arithmatex">\(n\)</span> のソート済み配列 <code>nums</code> が与えられ、その中には重複要素が含まれる可能性があります。配列内で最も左にある要素 <code>target</code> のインデックスを返してください。配列にこの要素が含まれない場合は、<span class="arithmatex">\(-1\)</span> を返します。</p>
 </div>
-<p>挿入位置の二分探索方法を思い出すと、探索完了後、インデックス<span class="arithmatex">\(i\)</span>は<code>target</code>の最も左の出現を指します。したがって、<strong>挿入位置の探索は本質的に最も左の<code>target</code>のインデックスを見つけることと同じです</strong>。</p>
-<p>挿入位置を見つける関数を使用して<code>target</code>の左境界を見つけることができます。配列に<code>target</code>が含まれていない可能性があることに注意してください。これは以下の2つの結果につながる可能性があります：</p>
+<p>二分探索で挿入位置を求める方法を思い出すと、探索完了後に <span class="arithmatex">\(i\)</span> は最も左にある <code>target</code> を指します。<strong>したがって、挿入位置を探すことの本質は、最も左にある <code>target</code> のインデックスを探すことです</strong>。</p>
+<p>挿入位置を探す関数を使って左端境界を求めることを考えます。なお、配列に <code>target</code> が含まれない場合があり、そのときは次の 2 つの結果が起こりえます。</p>
 <ul>
-<li>挿入位置のインデックス<span class="arithmatex">\(i\)</span>が範囲外です。</li>
-<li>要素<code>nums[i]</code>が<code>target</code>と等しくありません。</li>
+<li>挿入位置のインデックス <span class="arithmatex">\(i\)</span> が範囲外になる。</li>
+<li>要素 <code>nums[i]</code> が <code>target</code> と等しくない。</li>
 </ul>
-<p>これらの場合、単に<span class="arithmatex">\(-1\)</span>を返します。コードは以下の通りです：</p>
+<p>上の 2 つの状況に当てはまる場合は、直接 <span class="arithmatex">\(-1\)</span> を返せば十分です。コードは以下のとおりです：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_search_edge.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">binary_search_left_edge</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;最左端のターゲットの二分探索&quot;&quot;&quot;</span>
-<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># ターゲットの挿入位置を見つけることと同等</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;最も左の target を二分探索&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># target の挿入位置を探すのと等価</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">i</span> <span class="o">=</span> <span class="n">binary_search_insertion</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">target</span><span class="p">)</span>
-<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="c1"># ターゲットが見つからなかった場合、-1 を返す</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="c1"># target が見つからなければ、-1 を返す</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="ow">or</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">!=</span> <span class="n">target</span><span class="p">:</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>
-<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="c1"># ターゲットが見つかった場合、インデックス i を返す</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="c1"># target が見つかったら、インデックス i を返す</span>
 <a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="k">return</span> <span class="n">i</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_edge.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 最左のターゲットの二分探索 */</span>
+<div class="highlight"><span class="filename">binary_search_edge.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 最も左の target を二分探索 */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearchLeftEdge</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// targetの挿入ポイントを見つけることと等価</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// target の挿入位置を探すのと等価</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">binarySearchInsertion</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">);</span>
-<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="c1">// targetが見つからなかったため、-1を返す</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="c1">// target が見つからなければ、-1 を返す</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="c1">// targetが見つかったため、インデックスiを返す</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="c1">// target が見つかったら、インデックス i を返す</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="p">}</span>
 </code></pre></div>
@@ -4454,97 +4454,201 @@
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_search_edge.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 最も左の target を二分探索 */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearchLeftEdge</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// target の挿入点を見つけることと等価</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// target の挿入位置を探すのと等価</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">binary_search_insertion</span><span class="p">.</span><span class="na">binarySearchInsertion</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">);</span>
-<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="c1">// target を見つけられなかったので、-1 を返す</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="c1">// target が見つからなければ、-1 を返す</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="c1">// target を見つけたので、インデックス i を返す</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="c1">// target が見つかったら、インデックス i を返す</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
 <a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_edge.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_search_edge</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BinarySearchLeftEdge</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_edge.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 最も左の target を二分探索 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">BinarySearchLeftEdge</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="c1">// target の挿入位置を探すのと等価</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">binary_search_insertion</span><span class="p">.</span><span class="n">BinarySearchInsertion</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">);</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="c1">// target が見つからなければ、-1 を返す</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="c1">// target が見つかったら、インデックス i を返す</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_edge.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">binarySearchLeftEdge</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_edge.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 最も左の target を二分探索 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">binarySearchLeftEdge</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// target の挿入位置を探すのと等価</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">binarySearchInsertion</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="c1">// target が見つからなければ、-1 を返す</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="c1">// target が見つかったら、インデックス i を返す</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_edge.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">binarySearchLeftEdge</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_edge.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 最も左の target を二分探索 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">binarySearchLeftEdge</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// target の挿入位置を探すのと等価</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">binarySearchInsertion</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="c1">// target が見つからなければ、-1 を返す</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">endIndex</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">    </span><span class="c1">// target が見つかったら、インデックス i を返す</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_edge.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearchLeftEdge</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_edge.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 最も左の target を二分探索 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">binarySearchLeftEdge</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="c1">// target の挿入位置を探すのと等価</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">binarySearchInsertion</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">);</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="c1">// target が見つからなければ、-1 を返す</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">    </span><span class="c1">// target が見つかったら、インデックス i を返す</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_edge.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearchLeftEdge</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_edge.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 最も左の target を二分探索 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">binarySearchLeftEdge</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="c1">// target の挿入位置を探すのと等価</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">binarySearchInsertion</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">);</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="c1">// target が見つからなければ、-1 を返す</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="c1">// target が見つかったら、インデックス i を返す</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_edge.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearchLeftEdge</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_edge.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 最も左の target を二分探索 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">binarySearchLeftEdge</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="c1">// target の挿入位置を探すのと等価</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">binarySearchInsertion</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">);</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="c1">// target が見つからなければ、-1 を返す</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">  </span><span class="c1">// target が見つかったら、インデックス i を返す</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_edge.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binary_search_left_edge</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_edge.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 最も左の target を二分探索 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">binary_search_left_edge</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="c1">// target の挿入位置を探すのと等価</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">binary_search_insertion</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">);</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="c1">// target が見つからなければ、-1 を返す</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">    </span><span class="c1">// target が見つかったら、インデックス i を返す</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">    </span><span class="n">i</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_edge.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearchLeftEdge</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_edge.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 最も左の target を二分探索 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearchLeftEdge</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">numSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="c1">// target の挿入位置を探すのと等価</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">binarySearchInsertion</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">numSize</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">);</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">    </span><span class="c1">// target が見つからなければ、-1 を返す</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">numSize</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">    </span><span class="c1">// target が見つかったら、インデックス i を返す</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_edge.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binarySearchLeftEdge</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_edge.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 最も左の target を二分探索 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">binarySearchLeftEdge</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="c1">// target の挿入位置を探すのと等価</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">binarySearchInsertion</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="c1">// target が見つからなければ、-1 を返す</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="m">1</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">    </span><span class="c1">// target が見つかったら、インデックス i を返す</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_edge.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binary_search_left_edge</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_edge.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### target の最左位置を二分探索 ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">binary_search_left_edge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># target の挿入位置を探すのと等価</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">binary_search_insertion</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="c1"># target が見つからなければ、-1 を返す</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">target</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">  </span><span class="n">i</span><span class="w"> </span><span class="c1"># target が見つかったら、インデックス i を返す</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h2 id="1032">10.3.2 &nbsp; 右境界を見つける<a class="headerlink" href="#1032" title="Permanent link">&para;</a></h2>
-<p><code>target</code>の最も右の出現をどのように見つけるでしょうか？最も直接的な方法は、<code>nums[m] == target</code>の場合に探索境界を調整する方法を変更して、従来の二分探索ロジックを修正することです。コードはここでは省略されています。興味がある場合は、自分でコードを実装してみてください。</p>
-<p>以下では、さらに2つの巧妙な方法を紹介します。</p>
-<h3 id="1">1. &nbsp; 左境界探索を再利用する<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p><code>target</code>の最も右の出現を見つけるには、最も左の<code>target</code>を見つけるために使用された関数を再利用できます。具体的には、最も右のターゲットの探索を最も左のターゲット + 1の探索に変換します。</p>
-<p>下図に示すように、探索完了後、ポインタ<span class="arithmatex">\(i\)</span>は最も左の<code>target + 1</code>（存在する場合）を指し、ポインタ<span class="arithmatex">\(j\)</span>は<code>target</code>の最も右の出現を指します。したがって、<span class="arithmatex">\(j\)</span>を返すことで右境界が得られます。</p>
-<p><img alt="Transforming the search for the right boundary into the search for the left boundary" class="animation-figure" src="../binary_search_edge.assets/binary_search_right_edge_by_left_edge.png" /></p>
-<p align="center"> 図 10-7 &nbsp; Transforming the search for the right boundary into the search for the left boundary </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20binary_search_insertion%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%E3%81%A7%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%82%92%E6%8E%A2%E3%81%99%EF%BC%88%E9%87%8D%E8%A4%87%E8%A6%81%E7%B4%A0%E3%81%82%E3%82%8A%EF%BC%89%22%22%22%0A%20%20%20%20i%2C%20j%20%3D%200%2C%20len%28nums%29%20-%201%20%20%23%20%E4%B8%A1%E9%96%89%E5%8C%BA%E9%96%93%20%5B0%2C%20n-1%5D%20%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20while%20i%20%3C%3D%20j%3A%0A%20%20%20%20%20%20%20%20m%20%3D%20%28i%20%2B%20j%29%20%2F%2F%202%20%20%23%20%E4%B8%AD%E7%82%B9%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20m%20%E3%82%92%E8%A8%88%E7%AE%97%0A%20%20%20%20%20%20%20%20if%20nums%5Bm%5D%20%3C%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%3D%20m%20%2B%201%20%20%23%20target%20%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bm%2B1%2C%20j%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20elif%20nums%5Bm%5D%20%3E%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20%3D%20m%20-%201%20%20%23%20target%20%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bi%2C%20m-1%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20%3D%20m%20-%201%20%20%23%20target%20%E3%82%88%E3%82%8A%E5%B0%8F%E3%81%95%E3%81%84%E6%9C%80%E5%88%9D%E3%81%AE%E8%A6%81%E7%B4%A0%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bi%2C%20m-1%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%23%20%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%20i%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20i%0A%0Adef%20binary_search_left_edge%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E6%9C%80%E3%82%82%E5%B7%A6%E3%81%AE%20target%20%E3%82%92%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%22%22%22%0A%20%20%20%20%23%20target%20%E3%81%AE%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%82%92%E6%8E%A2%E3%81%99%E3%81%AE%E3%81%A8%E7%AD%89%E4%BE%A1%0A%20%20%20%20i%20%3D%20binary_search_insertion%28nums%2C%20target%29%0A%20%20%20%20%23%20target%20%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%82%89%E3%81%AA%E3%81%91%E3%82%8C%E3%81%B0%E3%80%81-1%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20if%20i%20%3D%3D%20len%28nums%29%20or%20nums%5Bi%5D%20%21%3D%20target%3A%0A%20%20%20%20%20%20%20%20return%20-1%0A%20%20%20%20%23%20target%20%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%81%A3%E3%81%9F%E3%82%89%E3%80%81%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20i%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20i%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%87%8D%E8%A4%87%E8%A6%81%E7%B4%A0%E3%82%92%E5%90%AB%E3%82%80%E9%85%8D%E5%88%97%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%206%2C%206%2C%206%2C%206%2C%206%2C%2010%2C%2012%2C%2015%5D%0A%20%20%20%20%23%20%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%E3%81%A7%E5%B7%A6%E7%AB%AF%E3%81%A8%E5%8F%B3%E7%AB%AF%E3%82%92%E6%8E%A2%E3%81%99%0A%20%20%20%20target%20%3D%206%0A%20%20%20%20index%20%3D%20binary_search_left_edge%28nums%2C%20target%29%0A%20%20%20%20print%28f%22%E5%B7%A6%E7%AB%AF%E3%81%AE%E8%A6%81%E7%B4%A0%20%7Btarget%7D%20%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%AF%20%7Bindex%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20binary_search_insertion%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%E3%81%A7%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%82%92%E6%8E%A2%E3%81%99%EF%BC%88%E9%87%8D%E8%A4%87%E8%A6%81%E7%B4%A0%E3%81%82%E3%82%8A%EF%BC%89%22%22%22%0A%20%20%20%20i%2C%20j%20%3D%200%2C%20len%28nums%29%20-%201%20%20%23%20%E4%B8%A1%E9%96%89%E5%8C%BA%E9%96%93%20%5B0%2C%20n-1%5D%20%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20while%20i%20%3C%3D%20j%3A%0A%20%20%20%20%20%20%20%20m%20%3D%20%28i%20%2B%20j%29%20%2F%2F%202%20%20%23%20%E4%B8%AD%E7%82%B9%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20m%20%E3%82%92%E8%A8%88%E7%AE%97%0A%20%20%20%20%20%20%20%20if%20nums%5Bm%5D%20%3C%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%3D%20m%20%2B%201%20%20%23%20target%20%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bm%2B1%2C%20j%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20elif%20nums%5Bm%5D%20%3E%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20%3D%20m%20-%201%20%20%23%20target%20%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bi%2C%20m-1%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20%3D%20m%20-%201%20%20%23%20target%20%E3%82%88%E3%82%8A%E5%B0%8F%E3%81%95%E3%81%84%E6%9C%80%E5%88%9D%E3%81%AE%E8%A6%81%E7%B4%A0%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bi%2C%20m-1%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%23%20%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%20i%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20i%0A%0Adef%20binary_search_left_edge%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E6%9C%80%E3%82%82%E5%B7%A6%E3%81%AE%20target%20%E3%82%92%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%22%22%22%0A%20%20%20%20%23%20target%20%E3%81%AE%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%82%92%E6%8E%A2%E3%81%99%E3%81%AE%E3%81%A8%E7%AD%89%E4%BE%A1%0A%20%20%20%20i%20%3D%20binary_search_insertion%28nums%2C%20target%29%0A%20%20%20%20%23%20target%20%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%82%89%E3%81%AA%E3%81%91%E3%82%8C%E3%81%B0%E3%80%81-1%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20if%20i%20%3D%3D%20len%28nums%29%20or%20nums%5Bi%5D%20%21%3D%20target%3A%0A%20%20%20%20%20%20%20%20return%20-1%0A%20%20%20%20%23%20target%20%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%81%A3%E3%81%9F%E3%82%89%E3%80%81%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20i%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20i%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%87%8D%E8%A4%87%E8%A6%81%E7%B4%A0%E3%82%92%E5%90%AB%E3%82%80%E9%85%8D%E5%88%97%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%206%2C%206%2C%206%2C%206%2C%206%2C%2010%2C%2012%2C%2015%5D%0A%20%20%20%20%23%20%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%E3%81%A7%E5%B7%A6%E7%AB%AF%E3%81%A8%E5%8F%B3%E7%AB%AF%E3%82%92%E6%8E%A2%E3%81%99%0A%20%20%20%20target%20%3D%206%0A%20%20%20%20index%20%3D%20binary_search_left_edge%28nums%2C%20target%29%0A%20%20%20%20print%28f%22%E5%B7%A6%E7%AB%AF%E3%81%AE%E8%A6%81%E7%B4%A0%20%7Btarget%7D%20%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%AF%20%7Bindex%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h2 id="1032">10.3.2 &nbsp; 右端境界を探す<a class="headerlink" href="#1032" title="Permanent link">&para;</a></h2>
+<p>では、最も右にある <code>target</code> はどのように探せるでしょうか。最も直接的な方法はコードを修正し、<code>nums[m] == target</code> の場合のポインタの縮小操作を置き換えることです。ここではコードを省略するので、興味があれば自分で実装してみてください。</p>
+<p>ここでは、より巧妙な 2 つの方法を紹介します。</p>
+<h3 id="1">1. &nbsp; 左端境界探索を再利用する<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>実際には、最も左の要素を探す関数を利用して最も右の要素を探せます。具体的には、<strong>最も右にある <code>target</code> を探すことを、最も左にある <code>target + 1</code> を探すことに変換します</strong>。</p>
+<p>下図のように、探索完了後、ポインタ <span class="arithmatex">\(i\)</span> は最も左にある <code>target + 1</code>（存在する場合）を指し、<span class="arithmatex">\(j\)</span> は最も右にある <code>target</code> を指します。<strong>したがって <span class="arithmatex">\(j\)</span> を返せばよいです</strong>。</p>
+<p><img alt="右端境界の探索を左端境界の探索に変換する" class="animation-figure" src="../binary_search_edge.assets/binary_search_right_edge_by_left_edge.png" /></p>
+<p align="center"> 図 10-7 &nbsp; 右端境界の探索を左端境界の探索に変換する </p>
 
-<p>返される挿入位置は<span class="arithmatex">\(i\)</span>であることに注意してください。したがって、<span class="arithmatex">\(j\)</span>を得るためには1を引く必要があります：</p>
+<p>返される挿入位置は <span class="arithmatex">\(i\)</span> なので、そこから <span class="arithmatex">\(1\)</span> を引いて <span class="arithmatex">\(j\)</span> を得る必要があることに注意してください：</p>
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 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_search_edge.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">binary_search_right_edge</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;最右端のターゲットの二分探索&quot;&quot;&quot;</span>
-<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="c1"># 最左端のターゲット + 1 を見つけることに変換</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;最も右の target を二分探索&quot;&quot;&quot;</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="c1"># 最左の target + 1 を探す問題に変換する</span>
 <a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="n">i</span> <span class="o">=</span> <span class="n">binary_search_insertion</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">target</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># j は最右端のターゲットを指し、i はターゲットより大きい最初の要素を指す</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># j は最も右の target を指し、i は target より大きい最初の要素を指す</span>
 <a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>    <span class="n">j</span> <span class="o">=</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span>
-<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>    <span class="c1"># ターゲットが見つからなかった場合、-1 を返す</span>
+<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>    <span class="c1"># target が見つからなければ、-1 を返す</span>
 <a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>    <span class="k">if</span> <span class="n">j</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span> <span class="ow">or</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">!=</span> <span class="n">target</span><span class="p">:</span>
 <a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>        <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>
-<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>    <span class="c1"># ターゲットが見つかった場合、インデックス j を返す</span>
+<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>    <span class="c1"># target が見つかったら、インデックス j を返す</span>
 <a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>    <span class="k">return</span> <span class="n">j</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_edge.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 最右のターゲットの二分探索 */</span>
+<div class="highlight"><span class="filename">binary_search_edge.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 最も右の target を二分探索 */</span>
 <a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearchRightEdge</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="c1">// 最左のtarget + 1を見つけることに変換</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="c1">// 最左の target + 1 を探す問題に変換する</span>
 <a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">binarySearchInsertion</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="c1">// jは最右のターゲットを指し、iはtargetより大きい最初の要素を指す</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="c1">// j は最も右の target を指し、i は target より大きい最初の要素を指す</span>
 <a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">    </span><span class="c1">// targetが見つからなかったため、-1を返す</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">    </span><span class="c1">// target が見つからなければ、-1 を返す</span>
 <a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">-1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
 <a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">    </span><span class="c1">// targetが見つかったため、インデックスjを返す</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">    </span><span class="c1">// target が見つかったら、インデックス j を返す</span>
 <a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
 <a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="p">}</span>
 </code></pre></div>
@@ -4552,75 +4656,200 @@
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_search_edge.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 最も右の target を二分探索 */</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearchRightEdge</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 最も左の target + 1 を見つけることに変換</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 最左の target + 1 を探す問題に変換する</span>
 <a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">binary_search_insertion</span><span class="p">.</span><span class="na">binarySearchInsertion</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="c1">// j は最も右の target を指し、i は target より大きい最初の要素を指す</span>
 <a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="c1">// target を見つけられなかったので、-1 を返す</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="c1">// target が見つからなければ、-1 を返す</span>
 <a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">    </span><span class="c1">// target を見つけたので、インデックス j を返す</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">    </span><span class="c1">// target が見つかったら、インデックス j を返す</span>
 <a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
 <a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_edge.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_search_edge</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BinarySearchRightEdge</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_edge.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 最も右の target を二分探索 */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">BinarySearchRightEdge</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="c1">// 最左の target + 1 を探す問題に変換する</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">binary_search_insertion</span><span class="p">.</span><span class="n">BinarySearchInsertion</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="c1">// j は最も右の target を指し、i は target より大きい最初の要素を指す</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="c1">// target が見つからなければ、-1 を返す</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">    </span><span class="c1">// target が見つかったら、インデックス j を返す</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_edge.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">binarySearchRightEdge</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_edge.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 最も右の target を二分探索 */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">binarySearchRightEdge</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="c1">// 最左の target + 1 を探す問題に変換する</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">binarySearchInsertion</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">    </span><span class="c1">// j は最も右の target を指し、i は target より大きい最初の要素を指す</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">    </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">    </span><span class="c1">// target が見つからなければ、-1 を返す</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w">    </span><span class="c1">// target が見つかったら、インデックス j を返す</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">j</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_edge.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">binarySearchRightEdge</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_edge.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 最も右の target を二分探索 */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">binarySearchRightEdge</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="c1">// 最左の target + 1 を探す問題に変換する</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">binarySearchInsertion</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">    </span><span class="c1">// j は最も右の target を指し、i は target より大きい最初の要素を指す</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">    </span><span class="c1">// target が見つからなければ、-1 を返す</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w">    </span><span class="c1">// target が見つかったら、インデックス j を返す</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">j</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_edge.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearchRightEdge</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_edge.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 最も右の target を二分探索 */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">binarySearchRightEdge</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="c1">// 最左の target + 1 を探す問題に変換する</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">binarySearchInsertion</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">    </span><span class="c1">// j は最も右の target を指し、i は target より大きい最初の要素を指す</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">    </span><span class="c1">// target が見つからなければ、-1 を返す</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w">    </span><span class="c1">// target が見つかったら、インデックス j を返す</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">j</span><span class="p">;</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_edge.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearchRightEdge</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_edge.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 最も右の target を二分探索 */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">binarySearchRightEdge</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="c1">// 最左の target + 1 を探す問題に変換する</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">binarySearchInsertion</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">    </span><span class="c1">// j は最も右の target を指し、i は target より大きい最初の要素を指す</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">    </span><span class="c1">// target が見つからなければ、-1 を返す</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w">    </span><span class="c1">// target が見つかったら、インデックス j を返す</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">j</span><span class="p">;</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_edge.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearchRightEdge</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_edge.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 最も右の target を二分探索 */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">binarySearchRightEdge</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="c1">// 最左の target + 1 を探す問題に変換する</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">binarySearchInsertion</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">  </span><span class="c1">// j は最も右の target を指し、i は target より大きい最初の要素を指す</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">  </span><span class="c1">// target が見つからなければ、-1 を返す</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="w">  </span><span class="c1">// target が見つかったら、インデックス j を返す</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_edge.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binary_search_right_edge</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_edge.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 最も右の target を二分探索 */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">binary_search_right_edge</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="c1">// 最左の target + 1 を探す問題に変換する</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">binary_search_insertion</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">    </span><span class="c1">// j は最も右の target を指し、i は target より大きい最初の要素を指す</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">    </span><span class="c1">// target が見つからなければ、-1 を返す</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w">    </span><span class="c1">// target が見つかったら、インデックス j を返す</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">    </span><span class="n">j</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_edge.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearchRightEdge</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_edge.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 最も右の target を二分探索 */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearchRightEdge</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">numSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="c1">// 最左の target + 1 を探す問題に変換する</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">binarySearchInsertion</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">numSize</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">    </span><span class="c1">// j は最も右の target を指し、i は target より大きい最初の要素を指す</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w">    </span><span class="c1">// target が見つからなければ、-1 を返す</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">-1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w">    </span><span class="c1">// target が見つかったら、インデックス j を返す</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_edge.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binarySearchRightEdge</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_edge.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 最も右の target を二分探索 */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">binarySearchRightEdge</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="c1">// 最左の target + 1 を探す問題に変換する</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">binarySearchInsertion</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">    </span><span class="c1">// j は最も右の target を指し、i は target より大きい最初の要素を指す</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w">    </span><span class="c1">// target が見つからなければ、-1 を返す</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="m">1</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="w">    </span><span class="c1">// target が見つかったら、インデックス j を返す</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">j</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_edge.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binary_search_right_edge</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_edge.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### target の最右位置を二分探索 ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">binary_search_right_edge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="c1"># 最左の target + 1 を探す問題に変換する</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">  </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">binary_search_insertion</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">  </span><span class="c1"># j は最も右の target を指し、i は target より大きい最初の要素を指す</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">  </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">  </span><span class="c1"># target が見つからなければ、-1 を返す</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">target</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w">  </span><span class="n">j</span><span class="w"> </span><span class="c1"># target が見つかったら、インデックス j を返す</span>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20binary_search_insertion%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%E3%81%A7%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%82%92%E6%8E%A2%E3%81%99%EF%BC%88%E9%87%8D%E8%A4%87%E8%A6%81%E7%B4%A0%E3%81%82%E3%82%8A%EF%BC%89%22%22%22%0A%20%20%20%20i%2C%20j%20%3D%200%2C%20len%28nums%29%20-%201%20%20%23%20%E4%B8%A1%E9%96%89%E5%8C%BA%E9%96%93%20%5B0%2C%20n-1%5D%20%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20while%20i%20%3C%3D%20j%3A%0A%20%20%20%20%20%20%20%20m%20%3D%20%28i%20%2B%20j%29%20%2F%2F%202%20%20%23%20%E4%B8%AD%E7%82%B9%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20m%20%E3%82%92%E8%A8%88%E7%AE%97%0A%20%20%20%20%20%20%20%20if%20nums%5Bm%5D%20%3C%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%3D%20m%20%2B%201%20%20%23%20target%20%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bm%2B1%2C%20j%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20elif%20nums%5Bm%5D%20%3E%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20%3D%20m%20-%201%20%20%23%20target%20%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bi%2C%20m-1%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20%3D%20m%20-%201%20%20%23%20target%20%E3%82%88%E3%82%8A%E5%B0%8F%E3%81%95%E3%81%84%E6%9C%80%E5%88%9D%E3%81%AE%E8%A6%81%E7%B4%A0%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bi%2C%20m-1%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%23%20%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%20i%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20i%0A%0Adef%20binary_search_right_edge%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E6%9C%80%E3%82%82%E5%8F%B3%E3%81%AE%20target%20%E3%82%92%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%22%22%22%0A%20%20%20%20%23%20%E6%9C%80%E5%B7%A6%E3%81%AE%20target%20%2B%201%20%E3%82%92%E6%8E%A2%E3%81%99%E5%95%8F%E9%A1%8C%E3%81%AB%E5%A4%89%E6%8F%9B%E3%81%99%E3%82%8B%0A%20%20%20%20i%20%3D%20binary_search_insertion%28nums%2C%20target%20%2B%201%29%0A%20%20%20%20%23%20j%20%E3%81%AF%E6%9C%80%E3%82%82%E5%8F%B3%E3%81%AE%20target%20%E3%82%92%E6%8C%87%E3%81%97%E3%80%81i%20%E3%81%AF%20target%20%E3%82%88%E3%82%8A%E5%A4%A7%E3%81%8D%E3%81%84%E6%9C%80%E5%88%9D%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E6%8C%87%E3%81%99%0A%20%20%20%20j%20%3D%20i%20-%201%0A%20%20%20%20%23%20target%20%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%82%89%E3%81%AA%E3%81%91%E3%82%8C%E3%81%B0%E3%80%81-1%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20if%20j%20%3D%3D%20-1%20or%20nums%5Bj%5D%20%21%3D%20target%3A%0A%20%20%20%20%20%20%20%20return%20-1%0A%20%20%20%20%23%20target%20%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%81%A3%E3%81%9F%E3%82%89%E3%80%81%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20j%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20j%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%87%8D%E8%A4%87%E8%A6%81%E7%B4%A0%E3%82%92%E5%90%AB%E3%82%80%E9%85%8D%E5%88%97%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%206%2C%206%2C%206%2C%206%2C%206%2C%2010%2C%2012%2C%2015%5D%0A%20%20%20%20%23%20%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%E3%81%A7%E5%B7%A6%E7%AB%AF%E3%81%A8%E5%8F%B3%E7%AB%AF%E3%82%92%E6%8E%A2%E3%81%99%0A%20%20%20%20target%20%3D%206%0A%20%20%20%20index%20%3D%20binary_search_right_edge%28nums%2C%20target%29%0A%20%20%20%20print%28f%22%E5%8F%B3%E7%AB%AF%E3%81%AE%E8%A6%81%E7%B4%A0%20%7Btarget%7D%20%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%AF%20%7Bindex%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20binary_search_insertion%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%E3%81%A7%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%82%92%E6%8E%A2%E3%81%99%EF%BC%88%E9%87%8D%E8%A4%87%E8%A6%81%E7%B4%A0%E3%81%82%E3%82%8A%EF%BC%89%22%22%22%0A%20%20%20%20i%2C%20j%20%3D%200%2C%20len%28nums%29%20-%201%20%20%23%20%E4%B8%A1%E9%96%89%E5%8C%BA%E9%96%93%20%5B0%2C%20n-1%5D%20%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20while%20i%20%3C%3D%20j%3A%0A%20%20%20%20%20%20%20%20m%20%3D%20%28i%20%2B%20j%29%20%2F%2F%202%20%20%23%20%E4%B8%AD%E7%82%B9%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20m%20%E3%82%92%E8%A8%88%E7%AE%97%0A%20%20%20%20%20%20%20%20if%20nums%5Bm%5D%20%3C%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%3D%20m%20%2B%201%20%20%23%20target%20%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bm%2B1%2C%20j%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20elif%20nums%5Bm%5D%20%3E%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20%3D%20m%20-%201%20%20%23%20target%20%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bi%2C%20m-1%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20%3D%20m%20-%201%20%20%23%20target%20%E3%82%88%E3%82%8A%E5%B0%8F%E3%81%95%E3%81%84%E6%9C%80%E5%88%9D%E3%81%AE%E8%A6%81%E7%B4%A0%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bi%2C%20m-1%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%23%20%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%20i%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20i%0A%0Adef%20binary_search_right_edge%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E6%9C%80%E3%82%82%E5%8F%B3%E3%81%AE%20target%20%E3%82%92%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%22%22%22%0A%20%20%20%20%23%20%E6%9C%80%E5%B7%A6%E3%81%AE%20target%20%2B%201%20%E3%82%92%E6%8E%A2%E3%81%99%E5%95%8F%E9%A1%8C%E3%81%AB%E5%A4%89%E6%8F%9B%E3%81%99%E3%82%8B%0A%20%20%20%20i%20%3D%20binary_search_insertion%28nums%2C%20target%20%2B%201%29%0A%20%20%20%20%23%20j%20%E3%81%AF%E6%9C%80%E3%82%82%E5%8F%B3%E3%81%AE%20target%20%E3%82%92%E6%8C%87%E3%81%97%E3%80%81i%20%E3%81%AF%20target%20%E3%82%88%E3%82%8A%E5%A4%A7%E3%81%8D%E3%81%84%E6%9C%80%E5%88%9D%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E6%8C%87%E3%81%99%0A%20%20%20%20j%20%3D%20i%20-%201%0A%20%20%20%20%23%20target%20%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%82%89%E3%81%AA%E3%81%91%E3%82%8C%E3%81%B0%E3%80%81-1%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20if%20j%20%3D%3D%20-1%20or%20nums%5Bj%5D%20%21%3D%20target%3A%0A%20%20%20%20%20%20%20%20return%20-1%0A%20%20%20%20%23%20target%20%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%81%A3%E3%81%9F%E3%82%89%E3%80%81%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20j%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20j%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%87%8D%E8%A4%87%E8%A6%81%E7%B4%A0%E3%82%92%E5%90%AB%E3%82%80%E9%85%8D%E5%88%97%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%206%2C%206%2C%206%2C%206%2C%206%2C%2010%2C%2012%2C%2015%5D%0A%20%20%20%20%23%20%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%E3%81%A7%E5%B7%A6%E7%AB%AF%E3%81%A8%E5%8F%B3%E7%AB%AF%E3%82%92%E6%8E%A2%E3%81%99%0A%20%20%20%20target%20%3D%206%0A%20%20%20%20index%20%3D%20binary_search_right_edge%28nums%2C%20target%29%0A%20%20%20%20print%28f%22%E5%8F%B3%E7%AB%AF%E3%81%AE%E8%A6%81%E7%B4%A0%20%7Btarget%7D%20%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%AF%20%7Bindex%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 <h3 id="2">2. &nbsp; 要素探索に変換する<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>配列に<code>target</code>が含まれていない場合、<span class="arithmatex">\(i\)</span>と<span class="arithmatex">\(j\)</span>は最終的に<code>target</code>より大きい最初の要素と小さい最初の要素をそれぞれ指します。</p>
-<p>したがって、下図に示すように、配列に存在しない要素を構築して、左と右の境界を探索できます。</p>
+<p>配列に <code>target</code> が含まれない場合、最終的に <span class="arithmatex">\(i\)</span> と <span class="arithmatex">\(j\)</span> はそれぞれ <code>target</code> より大きい最初の要素と、<code>target</code> より小さい最初の要素を指すことになります。</p>
+<p>したがって、下図のように、配列中に存在しない要素を構成して、それを使って左右の境界を探せます。</p>
 <ul>
-<li>最も左の<code>target</code>を見つけるには：<code>target - 0.5</code>を探索することに変換でき、ポインタ<span class="arithmatex">\(i\)</span>を返します。</li>
-<li>最も右の<code>target</code>を見つけるには：<code>target + 0.5</code>を探索することに変換でき、ポインタ<span class="arithmatex">\(j\)</span>を返します。</li>
+<li>最も左にある <code>target</code> の探索：<code>target - 0.5</code> を探すことに変換でき、ポインタ <span class="arithmatex">\(i\)</span> を返します。</li>
+<li>最も右にある <code>target</code> の探索：<code>target + 0.5</code> を探すことに変換でき、ポインタ <span class="arithmatex">\(j\)</span> を返します。</li>
 </ul>
-<p><img alt="Transforming the search for boundaries into the search for an element" class="animation-figure" src="../binary_search_edge.assets/binary_search_edge_by_element.png" /></p>
-<p align="center"> 図 10-8 &nbsp; Transforming the search for boundaries into the search for an element </p>
+<p><img alt="境界の探索を要素の探索に変換する" class="animation-figure" src="../binary_search_edge.assets/binary_search_edge_by_element.png" /></p>
+<p align="center"> 図 10-8 &nbsp; 境界の探索を要素の探索に変換する </p>
 
-<p>コードはここでは省略されていますが、このアプローチについて注意すべき2つの重要な点があります。</p>
+<p>ここではコードを省略しますが、次の 2 点に注意が必要です。</p>
 <ul>
-<li>与えられた配列<code>nums</code>には小数が含まれていないため、等しい場合の処理は心配ありません。</li>
-<li>ただし、このアプローチで小数を導入するには、<code>target</code>変数を浮動小数点型に変更する必要があります（Pythonでは変更は不要です）。</li>
+<li>与えられた配列には小数が含まれないため、等しい場合をどう処理するかを気にする必要はありません。</li>
+<li>この方法では小数を導入するため、関数内の変数 <code>target</code> を浮動小数点数型に変更する必要があります（Python は変更不要です）。</li>
 </ul>
 
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@@ -4644,7 +4873,7 @@ aria-label="フッター"
   <a
     href="../binary_search_insertion/"
     class="md-footer__link md-footer__link--prev"
-    aria-label="前: 10.2 &amp;nbsp; 二分探索の挿入点"
+    aria-label="前: 10.2 &amp;nbsp; 二分探索の挿入位置"
     rel="prev"
   >
     <div class="md-footer__button md-icon">
@@ -4656,7 +4885,7 @@ aria-label="フッター"
         前
       </span>
       <div class="md-ellipsis">
-        10.2 &nbsp; 二分探索の挿入点
+        10.2 &nbsp; 二分探索の挿入位置
       </div>
     </div>
   </a>
@@ -4668,7 +4897,7 @@ aria-label="フッター"
   <a
     href="../replace_linear_by_hashing/"
     class="md-footer__link md-footer__link--next"
-    aria-label="次: 10.4 &amp;nbsp; ハッシュ最適化戦略"
+    aria-label="次: 10.4 &amp;nbsp; ハッシュによる最適化戦略"
     rel="next"
   >
     <div class="md-footer__title">
@@ -4676,7 +4905,7 @@ aria-label="フッター"
         次
       </span>
       <div class="md-ellipsis">
-        10.4 &nbsp; ハッシュ最適化戦略
+        10.4 &nbsp; ハッシュによる最適化戦略
       </div>
     </div>
     <div class="md-footer__button md-icon">
diff --git a/ja/chapter_searching/binary_search_insertion/index.html b/ja/chapter_searching/binary_search_insertion/index.html
index 7ffa205a2..a06233183 100644
--- a/ja/chapter_searching/binary_search_insertion/index.html
+++ b/ja/chapter_searching/binary_search_insertion/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -39,7 +39,7 @@
     
     
       
-        <title>10.2 二分探索による挿入 - Hello アルゴリズム</title>
+        <title>10.2 二分探索の挿入位置 - Hello アルゴリズム</title>
       
     
     
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -152,7 +152,7 @@
         <div class="md-header__topic" data-md-component="header-topic">
           <span class="md-ellipsis">
             
-              10.2 &nbsp; 二分探索による挿入
+              10.2 &nbsp; 二分探索の挿入位置
             
           </span>
         </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
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@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
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   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
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   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
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   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
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             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
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-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
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   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
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   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2502,7 +2502,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2619,7 +2619,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2647,7 +2647,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
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-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
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-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
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-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
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-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
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-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4354,63 +4354,63 @@
 
 
 <!-- Page content -->
-<h1 id="102">10.2 &nbsp; 二分探索による挿入<a class="headerlink" href="#102" title="Permanent link">&para;</a></h1>
-<p>二分探索は目標要素を探索するだけでなく、目標要素の挿入位置を探索するなど、多くの変種問題を解決するためにも使用されます。</p>
+<h1 id="102">10.2 &nbsp; 二分探索の挿入位置<a class="headerlink" href="#102" title="Permanent link">&para;</a></h1>
+<p>二分探索は目標要素の検索だけでなく、目標要素の挿入位置を探すなど、多くの派生問題の解決にも利用できます。</p>
 <h2 id="1021">10.2.1 &nbsp; 重複要素がない場合<a class="headerlink" href="#1021" title="Permanent link">&para;</a></h2>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
-<p>一意の要素を持つ長さ<span class="arithmatex">\(n\)</span>のソート済み配列<code>nums</code>と要素<code>target</code>が与えられ、ソート順を維持しながら<code>target</code>を<code>nums</code>に挿入します。<code>target</code>が配列にすでに存在する場合は、既存の要素の左側に挿入します。挿入後の配列における<code>target</code>のインデックスを返してください。下図に示す例を参照してください。</p>
+<p>長さ <span class="arithmatex">\(n\)</span> の整列済み配列 <code>nums</code> と要素 <code>target</code> が与えられます。配列には重複要素は存在しません。ここで <code>target</code> を配列 <code>nums</code> に挿入し、その順序を保ちます。配列中にすでに要素 <code>target</code> が存在する場合は、その左側に挿入します。挿入後の配列における <code>target</code> のインデックスを返してください。例を以下の図に示します。</p>
 </div>
-<p><img alt="Example data for binary search insertion point" class="animation-figure" src="../binary_search_insertion.assets/binary_search_insertion_example.png" /></p>
-<p align="center"> 図 10-4 &nbsp; Example data for binary search insertion point </p>
+<p><img alt="二分探索の挿入位置の例データ" class="animation-figure" src="../binary_search_insertion.assets/binary_search_insertion_example.png" /></p>
+<p align="center"> 図 10-4 &nbsp; 二分探索の挿入位置の例データ </p>
 
-<p>前のセクションの二分探索コードを再利用したい場合、以下の2つの質問に答える必要があります。</p>
-<p><strong>質問1</strong>：配列にすでに<code>target</code>が含まれている場合、挿入位置は既存要素のインデックスになりますか？</p>
-<p><code>target</code>を等しい要素の左側に挿入するという要件は、新しく挿入される<code>target</code>が元の<code>target</code>の位置を置き換えることを意味します。つまり、<strong>配列に<code>target</code>が含まれている場合、挿入位置は確かにその<code>target</code>のインデックスです</strong>。</p>
-<p><strong>質問2</strong>：配列に<code>target</code>が含まれていない場合、どのインデックスに挿入されますか？</p>
-<p>二分探索プロセスをさらに考えてみましょう：<code>nums[m] &lt; target</code>のとき、ポインタ<span class="arithmatex">\(i\)</span>が移動します。これは、ポインタ<span class="arithmatex">\(i\)</span>が<code>target</code>以上の要素に近づいていることを意味します。同様に、ポインタ<span class="arithmatex">\(j\)</span>は常に<code>target</code>以下の要素に近づいています。</p>
-<p>したがって、二分の終了時には確実に：<span class="arithmatex">\(i\)</span>は<code>target</code>より大きい最初の要素を指し、<span class="arithmatex">\(j\)</span>は<code>target</code>より小さい最初の要素を指します。<strong>配列に<code>target</code>が含まれていない場合、挿入位置は<span class="arithmatex">\(i\)</span>であることは明らかです</strong>。コードは以下の通りです：</p>
+<p>前節の二分探索コードを再利用したい場合は、次の二つの問題に答える必要があります。</p>
+<p><strong>問題 1</strong>：配列に <code>target</code> が含まれる場合、挿入位置のインデックスはその要素のインデックスですか？</p>
+<p>問題では <code>target</code> を等しい要素の左側に挿入するよう求めているため、新しく挿入された <code>target</code> は元の <code>target</code> の位置に入ります。つまり、<strong>配列に <code>target</code> が含まれる場合、挿入位置のインデックスはその <code>target</code> のインデックスです</strong>。</p>
+<p><strong>問題 2</strong>：配列に <code>target</code> が存在しない場合、挿入位置はどの要素のインデックスですか？</p>
+<p>二分探索の過程をさらに考えると、<code>nums[m] &lt; target</code> のときは <span class="arithmatex">\(i\)</span> が移動します。これは、ポインタ <span class="arithmatex">\(i\)</span> が <code>target</code> 以上の要素へ近づいていることを意味します。同様に、ポインタ <span class="arithmatex">\(j\)</span> は常に <code>target</code> 以下の要素へ近づいています。</p>
+<p>したがって二分探索の終了時には、<span class="arithmatex">\(i\)</span> は最初の <code>target</code> より大きい要素を指し、<span class="arithmatex">\(j\)</span> は最初の <code>target</code> より小さい要素を指します。<strong>よって、配列に <code>target</code> が含まれない場合、挿入インデックスは <span class="arithmatex">\(i\)</span> です</strong>。コードは次のとおりです：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_search_insertion.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">binary_search_insertion_simple</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;挿入位置の二分探索（重複要素なし）&quot;&quot;&quot;</span>
-<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># 両端閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二分探索で挿入位置を探す（重複要素なし）&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># 両閉区間 [0, n-1] を初期化</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;=</span> <span class="n">j</span><span class="p">:</span>
-<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="n">m</span> <span class="o">=</span> <span class="n">i</span> <span class="o">+</span> <span class="p">(</span><span class="n">j</span> <span class="o">-</span> <span class="n">i</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>  <span class="c1"># 中点インデックス m を計算</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="n">m</span> <span class="o">=</span> <span class="p">(</span><span class="n">i</span> <span class="o">+</span> <span class="n">j</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>  <span class="c1"># 中点インデックス m を計算</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span> <span class="o">&lt;</span> <span class="n">target</span><span class="p">:</span>
-<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>            <span class="n">i</span> <span class="o">=</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span>  <span class="c1"># ターゲットは区間 [m+1, j] にある</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>            <span class="n">i</span> <span class="o">=</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span>  <span class="c1"># target は区間 [m+1, j] にある</span>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="k">elif</span> <span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">target</span><span class="p">:</span>
-<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>            <span class="n">j</span> <span class="o">=</span> <span class="n">m</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># ターゲットは区間 [i, m-1] にある</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>            <span class="n">j</span> <span class="o">=</span> <span class="n">m</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># target は区間 [i, m-1] にある</span>
 <a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="k">else</span><span class="p">:</span>
-<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>            <span class="k">return</span> <span class="n">m</span>  <span class="c1"># ターゲットが見つかった場合、挿入位置 m を返す</span>
-<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="c1"># ターゲットが見つからなかった場合、挿入位置 i を返す</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>            <span class="k">return</span> <span class="n">m</span>  <span class="c1"># target が見つかったら、挿入位置 m を返す</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="c1"># target が見つからなければ、挿入位置 i を返す</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="k">return</span> <span class="n">i</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_insertion.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 挿入ポイントの二分探索（重複要素なし） */</span>
+<div class="highlight"><span class="filename">binary_search_insertion.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 二分探索で挿入位置を探す（重複要素なし） */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearchInsertionSimple</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端閉区間[0, n-1]を初期化</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両閉区間 [0, n-1] を初期化</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックスmを計算</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// ターゲットは区間[m+1, j]にある</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [m+1, j] にある</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// ターゲットは区間[i, m-1]にある</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [i, m-1] にある</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="c1">// ターゲットが見つかったため、挿入ポイントmを返す</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="c1">// target が見つかったら、挿入位置 m を返す</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="c1">// ターゲットが見つからなかったため、挿入ポイントiを返す</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="c1">// target が見つからなければ、挿入位置 i を返す</span>
 <a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
 <a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_insertion.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 挿入点の二分探索（重複要素なし） */</span>
+<div class="highlight"><span class="filename">binary_search_insertion.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 二分探索で挿入位置を探す（重複要素なし） */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearchInsertionSimple</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両閉区間 [0, n-1] を初期化</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
@@ -4418,81 +4418,253 @@
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [i, m-1] にある</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="c1">// target を見つけたので、挿入点 m を返す</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="c1">// target が見つかったら、挿入位置 m を返す</span>
 <a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="c1">// target を見つけられなかったので、挿入点 i を返す</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="c1">// target が見つからなければ、挿入位置 i を返す</span>
 <a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
 <a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_insertion.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_search_insertion</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BinarySearchInsertionSimple</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_insertion.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 二分探索で挿入位置を探す（重複要素なし） */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">BinarySearchInsertionSimple</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [m+1, j] にある</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [i, m-1] にある</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="c1">// target が見つかったら、挿入位置 m を返す</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">    </span><span class="c1">// target が見つからなければ、挿入位置 i を返す</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_insertion.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">binarySearchInsertionSimple</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_insertion.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 二分探索で挿入位置を探す（重複要素なし） */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">binarySearchInsertionSimple</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// 両閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">        </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">        </span><span class="nx">m</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="o">-</span><span class="nx">i</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">            </span><span class="c1">// target は区間 [m+1, j] にある</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">            </span><span class="nx">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">            </span><span class="c1">// target は区間 [i, m-1] にある</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">            </span><span class="c1">// target が見つかったら、挿入位置 m を返す</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nx">m</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w">    </span><span class="c1">// target が見つからなければ、挿入位置 i を返す</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_insertion.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">binarySearchInsertionSimple</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_insertion.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 二分探索で挿入位置を探す（重複要素なし） */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">binarySearchInsertionSimple</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// 両閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">startIndex</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">endIndex</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// target は区間 [m+1, j] にある</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// target は区間 [i, m-1] にある</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="c1">// target が見つかったら、挿入位置 m を返す</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">    </span><span class="c1">// target が見つからなければ、挿入位置 i を返す</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_insertion.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearchInsertionSimple</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_insertion.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 二分探索で挿入位置を探す（重複要素なし） */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">binarySearchInsertionSimple</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">        </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算し、Math.floor() で切り捨てる</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">            </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [m+1, j] にある</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [i, m-1] にある</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="c1">// target が見つかったら、挿入位置 m を返す</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">    </span><span class="c1">// target が見つからなければ、挿入位置 i を返す</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_insertion.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearchInsertionSimple</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_insertion.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 二分探索で挿入位置を探す（重複要素なし） */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">binarySearchInsertionSimple</span><span class="p">(</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="nx">target</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">        </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算し、Math.floor() で切り捨てる</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">            </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [m+1, j] にある</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [i, m-1] にある</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="c1">// target が見つかったら、挿入位置 m を返す</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">    </span><span class="c1">// target が見つからなければ、挿入位置 i を返す</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_insertion.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearchInsertionSimple</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_insertion.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 二分探索で挿入位置を探す（重複要素なし） */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">binarySearchInsertionSimple</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">      </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [m+1, j] にある</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">      </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [i, m-1] にある</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">      </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="c1">// target が見つかったら、挿入位置 m を返す</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">  </span><span class="c1">// target が見つからなければ、挿入位置 i を返す</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_insertion.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binary_search_insertion_simple</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_insertion.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 二分探索で挿入位置を探す（重複要素なし） */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">binary_search_insertion_simple</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="p">(</span><span class="k">mut</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span><span class="w"> </span><span class="c1">// 両閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [m+1, j] にある</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [i, m-1] にある</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">    </span><span class="c1">// target が見つからなければ、挿入位置 i を返す</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">    </span><span class="n">i</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_insertion.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearchInsertionSimple</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_insertion.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 二分探索で挿入位置を探す（重複要素なし） */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearchInsertionSimple</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">numSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">numSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [m+1, j] にある</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [i, m-1] にある</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="c1">// target が見つかったら、挿入位置 m を返す</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">    </span><span class="c1">// target が見つからなければ、挿入位置 i を返す</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_insertion.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binarySearchInsertionSimple</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_insertion.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 二分探索で挿入位置を探す（重複要素なし） */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">binarySearchInsertionSimple</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="c1">// 両閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="c1">// target は区間 [m+1, j] にある</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="c1">// target は区間 [i, m-1] にある</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="c1">// target が見つかったら、挿入位置 m を返す</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">    </span><span class="c1">// target が見つからなければ、挿入位置 i を返す</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_insertion.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binary_search_insertion_simple</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_insertion.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 二分探索の挿入位置（重複要素なし） ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">binary_search_insertion_simple</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># 両閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">    </span><span class="c1"># 中点インデックス m を計算</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">    </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">      </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># target は区間 [m+1, j] にある</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">    </span><span class="k">elsif</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">      </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># target は区間 [i, m-1] にある</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">      </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="w">  </span><span class="c1"># target が見つかったら、挿入位置 m を返す</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w">  </span><span class="n">i</span><span class="w"> </span><span class="c1"># target が見つからなければ、挿入位置 i を返す</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20binary_search_insertion_simple%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%E3%81%A7%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%82%92%E6%8E%A2%E3%81%99%EF%BC%88%E9%87%8D%E8%A4%87%E8%A6%81%E7%B4%A0%E3%81%AA%E3%81%97%EF%BC%89%22%22%22%0A%20%20%20%20i%2C%20j%20%3D%200%2C%20len%28nums%29%20-%201%20%20%23%20%E4%B8%A1%E9%96%89%E5%8C%BA%E9%96%93%20%5B0%2C%20n-1%5D%20%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20while%20i%20%3C%3D%20j%3A%0A%20%20%20%20%20%20%20%20m%20%3D%20%28i%20%2B%20j%29%20%2F%2F%202%20%20%23%20%E4%B8%AD%E7%82%B9%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20m%20%E3%82%92%E8%A8%88%E7%AE%97%0A%20%20%20%20%20%20%20%20if%20nums%5Bm%5D%20%3C%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%3D%20m%20%2B%201%20%20%23%20target%20%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bm%2B1%2C%20j%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20elif%20nums%5Bm%5D%20%3E%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20%3D%20m%20-%201%20%20%23%20target%20%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bi%2C%20m-1%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20m%20%20%23%20target%20%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%81%A3%E3%81%9F%E3%82%89%E3%80%81%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%20m%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20%23%20target%20%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%82%89%E3%81%AA%E3%81%91%E3%82%8C%E3%81%B0%E3%80%81%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%20i%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20i%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%87%8D%E8%A4%87%E8%A6%81%E7%B4%A0%E3%81%AE%E3%81%AA%E3%81%84%E9%85%8D%E5%88%97%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%206%2C%208%2C%2012%2C%2015%2C%2023%2C%2026%2C%2031%2C%2035%5D%0A%20%20%20%20%23%20%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%E3%81%A7%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%82%92%E6%8E%A2%E3%81%99%0A%20%20%20%20target%20%3D%206%0A%20%20%20%20index%20%3D%20binary_search_insertion_simple%28nums%2C%20target%29%0A%20%20%20%20print%28f%22%E8%A6%81%E7%B4%A0%20%7Btarget%7D%20%E3%81%AE%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%AF%20%7Bindex%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20binary_search_insertion_simple%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%E3%81%A7%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%82%92%E6%8E%A2%E3%81%99%EF%BC%88%E9%87%8D%E8%A4%87%E8%A6%81%E7%B4%A0%E3%81%AA%E3%81%97%EF%BC%89%22%22%22%0A%20%20%20%20i%2C%20j%20%3D%200%2C%20len%28nums%29%20-%201%20%20%23%20%E4%B8%A1%E9%96%89%E5%8C%BA%E9%96%93%20%5B0%2C%20n-1%5D%20%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20while%20i%20%3C%3D%20j%3A%0A%20%20%20%20%20%20%20%20m%20%3D%20%28i%20%2B%20j%29%20%2F%2F%202%20%20%23%20%E4%B8%AD%E7%82%B9%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20m%20%E3%82%92%E8%A8%88%E7%AE%97%0A%20%20%20%20%20%20%20%20if%20nums%5Bm%5D%20%3C%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%3D%20m%20%2B%201%20%20%23%20target%20%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bm%2B1%2C%20j%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20elif%20nums%5Bm%5D%20%3E%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20%3D%20m%20-%201%20%20%23%20target%20%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bi%2C%20m-1%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20m%20%20%23%20target%20%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%81%A3%E3%81%9F%E3%82%89%E3%80%81%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%20m%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20%23%20target%20%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%82%89%E3%81%AA%E3%81%91%E3%82%8C%E3%81%B0%E3%80%81%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%20i%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20i%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%87%8D%E8%A4%87%E8%A6%81%E7%B4%A0%E3%81%AE%E3%81%AA%E3%81%84%E9%85%8D%E5%88%97%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%206%2C%208%2C%2012%2C%2015%2C%2023%2C%2026%2C%2031%2C%2035%5D%0A%20%20%20%20%23%20%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%E3%81%A7%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%82%92%E6%8E%A2%E3%81%99%0A%20%20%20%20target%20%3D%206%0A%20%20%20%20index%20%3D%20binary_search_insertion_simple%28nums%2C%20target%29%0A%20%20%20%20print%28f%22%E8%A6%81%E7%B4%A0%20%7Btarget%7D%20%E3%81%AE%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%AF%20%7Bindex%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 <h2 id="1022">10.2.2 &nbsp; 重複要素がある場合<a class="headerlink" href="#1022" title="Permanent link">&para;</a></h2>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
-<p>前の質問に基づいて、配列に重複要素が含まれている可能性があると仮定し、他はすべて同じとします。</p>
+<p>前問を踏まえ、配列には重複要素が含まれる可能性があるものとし、それ以外の条件は変わりません。</p>
 </div>
-<p>配列に<code>target</code>の複数の出現がある場合、通常の二分探索は<code>target</code>の1つの出現のインデックスのみを返すことができ、<strong>その位置の左右に<code>target</code>の出現がいくつあるかを特定することはできません</strong>。</p>
-<p>問題では目標要素を最も左の位置に挿入することが要求されているため、<strong>配列内の最も左の<code>target</code>のインデックスを見つける必要があります</strong>。最初に下図に示すステップを通してこれを実装することを考えてみましょう。</p>
+<p>配列中に複数の <code>target</code> が存在する場合、通常の二分探索ではそのうち一つの <code>target</code> のインデックスしか返せず、<strong>その要素の左側と右側にあといくつ <code>target</code> があるかは分かりません</strong>。</p>
+<p>問題では目標要素を最も左に挿入する必要があるため、<strong>配列中で最も左にある <code>target</code> のインデックスを探す必要があります</strong>。まずは以下の図に示す手順で実現することを考えます。</p>
 <ol>
-<li>二分探索を実行して<code>target</code>の任意のインデックス、例えば<span class="arithmatex">\(k\)</span>を見つけます。</li>
-<li>インデックス<span class="arithmatex">\(k\)</span>から開始して、最も左の<code>target</code>の出現が見つかるまで左に線形探索を行い、このインデックスを返します。</li>
+<li>二分探索を実行し、任意の <code>target</code> のインデックスを得て、これを <span class="arithmatex">\(k\)</span> とします。</li>
+<li>インデックス <span class="arithmatex">\(k\)</span> から始めて左へ線形探索し、最も左の <code>target</code> を見つけたら返します。</li>
 </ol>
-<p><img alt="Linear search for the insertion point of duplicate elements" class="animation-figure" src="../binary_search_insertion.assets/binary_search_insertion_naive.png" /></p>
-<p align="center"> 図 10-5 &nbsp; Linear search for the insertion point of duplicate elements </p>
+<p><img alt="線形探索による重複要素の挿入位置" class="animation-figure" src="../binary_search_insertion.assets/binary_search_insertion_naive.png" /></p>
+<p align="center"> 図 10-5 &nbsp; 線形探索による重複要素の挿入位置 </p>
 
-<p>この方法は実現可能ですが、線形探索を含むため、時間計算量は<span class="arithmatex">\(O(n)\)</span>です。この方法は、配列に多くの重複する<code>target</code>が含まれている場合に非効率です。</p>
-<p>今度は二分探索コードを拡張することを考えてみましょう。下図に示すように、全体的なプロセスは同じままです。各ラウンドで、まず中間インデックス<span class="arithmatex">\(m\)</span>を計算し、次に<code>target</code>と<code>nums[m]</code>の値を比較して、以下のケースになります。</p>
+<p>この方法は使用できますが、線形探索を含むため、時間計算量は <span class="arithmatex">\(O(n)\)</span> です。配列中に重複した <code>target</code> が多い場合、この方法の効率は低くなります。</p>
+<p>次に、二分探索のコードを拡張することを考えます。以下の図に示すように、全体の流れは変えず、各反復でまず中点インデックス <span class="arithmatex">\(m\)</span> を計算し、その後 <code>target</code> と <code>nums[m]</code> の大小関係を判定して、次のいくつかの状況に分けます。</p>
 <ul>
-<li><code>nums[m] &lt; target</code>または<code>nums[m] &gt; target</code>のとき、これは<code>target</code>がまだ見つかっていないことを意味するため、通常の二分探索を使用して探索範囲を狭め、<strong>ポインタ<span class="arithmatex">\(i\)</span>と<span class="arithmatex">\(j\)</span>を<code>target</code>に近づけます</strong>。</li>
-<li><code>nums[m] == target</code>のとき、これは<code>target</code>より小さい要素が範囲<span class="arithmatex">\([i, m - 1]\)</span>にあることを示すため、<span class="arithmatex">\(j = m - 1\)</span>を使用して範囲を狭め、<strong>ポインタ<span class="arithmatex">\(j\)</span>を<code>target</code>より小さい要素に近づけます</strong>。</li>
+<li><code>nums[m] &lt; target</code> または <code>nums[m] &gt; target</code> のときは、まだ <code>target</code> を見つけていないことを意味するため、通常の二分探索と同じ区間縮小を行い、<strong>ポインタ <span class="arithmatex">\(i\)</span> と <span class="arithmatex">\(j\)</span> を <code>target</code> に近づけます</strong>。</li>
+<li><code>nums[m] == target</code> のときは、<code>target</code> より小さい要素が区間 <span class="arithmatex">\([i, m - 1]\)</span> にあることを意味するため、<span class="arithmatex">\(j = m - 1\)</span> として区間を縮小し、<strong>ポインタ <span class="arithmatex">\(j\)</span> を <code>target</code> より小さい要素に近づけます</strong>。</li>
 </ul>
-<p>ループ後、<span class="arithmatex">\(i\)</span>は最も左の<code>target</code>を指し、<span class="arithmatex">\(j\)</span>は<code>target</code>より小さい最初の要素を指すため、<strong>インデックス<span class="arithmatex">\(i\)</span>が挿入位置です</strong>。</p>
+<p>ループ終了後、<span class="arithmatex">\(i\)</span> は最も左の <code>target</code> を指し、<span class="arithmatex">\(j\)</span> は最初の <code>target</code> より小さい要素を指すため、<strong>インデックス <span class="arithmatex">\(i\)</span> が挿入位置です</strong>。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:8"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">&lt;1&gt;</label><label for="__tabbed_2_2">&lt;2&gt;</label><label for="__tabbed_2_3">&lt;3&gt;</label><label for="__tabbed_2_4">&lt;4&gt;</label><label for="__tabbed_2_5">&lt;5&gt;</label><label for="__tabbed_2_6">&lt;6&gt;</label><label for="__tabbed_2_7">&lt;7&gt;</label><label for="__tabbed_2_8">&lt;8&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="Steps for binary search insertion point of duplicate elements" class="animation-figure" src="../binary_search_insertion.assets/binary_search_insertion_step1.png" /></p>
+<p><img alt="重複要素に対する二分探索の挿入位置の手順" class="animation-figure" src="../binary_search_insertion.assets/binary_search_insertion_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="binary_search_insertion_step2" class="animation-figure" src="../binary_search_insertion.assets/binary_search_insertion_step2.png" /></p>
@@ -4517,51 +4689,51 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 10-6 &nbsp; Steps for binary search insertion point of duplicate elements </p>
+<p align="center"> 図 10-6 &nbsp; 重複要素に対する二分探索の挿入位置の手順 </p>
 
-<p>以下のコードを観察してください。分岐<code>nums[m] &gt; target</code>と<code>nums[m] == target</code>の操作は同じであるため、これら2つの分岐をマージできます。</p>
-<p>それでも、ロジックがより明確になり、可読性が向上するため、条件を展開したままにしておくことができます。</p>
+<p>以下のコードを観察すると、分岐 <code>nums[m] &gt; target</code> と <code>nums[m] == target</code> の処理は同じであるため、両者はまとめることができます。</p>
+<p>それでも、判定条件を分けたままにしておくことは可能であり、そのほうがロジックがより明確で、可読性も高くなります。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_search_insertion.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">binary_search_insertion</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;挿入位置の二分探索（重複要素あり）&quot;&quot;&quot;</span>
-<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># 両端閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二分探索で挿入位置を探す（重複要素あり）&quot;&quot;&quot;</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># 両閉区間 [0, n-1] を初期化</span>
 <a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;=</span> <span class="n">j</span><span class="p">:</span>
-<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>        <span class="n">m</span> <span class="o">=</span> <span class="n">i</span> <span class="o">+</span> <span class="p">(</span><span class="n">j</span> <span class="o">-</span> <span class="n">i</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>  <span class="c1"># 中点インデックス m を計算</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>        <span class="n">m</span> <span class="o">=</span> <span class="p">(</span><span class="n">i</span> <span class="o">+</span> <span class="n">j</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>  <span class="c1"># 中点インデックス m を計算</span>
 <a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>        <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span> <span class="o">&lt;</span> <span class="n">target</span><span class="p">:</span>
-<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>            <span class="n">i</span> <span class="o">=</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span>  <span class="c1"># ターゲットは区間 [m+1, j] にある</span>
+<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>            <span class="n">i</span> <span class="o">=</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span>  <span class="c1"># target は区間 [m+1, j] にある</span>
 <a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>        <span class="k">elif</span> <span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">target</span><span class="p">:</span>
-<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>            <span class="n">j</span> <span class="o">=</span> <span class="n">m</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># ターゲットは区間 [i, m-1] にある</span>
+<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>            <span class="n">j</span> <span class="o">=</span> <span class="n">m</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># target は区間 [i, m-1] にある</span>
 <a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>        <span class="k">else</span><span class="p">:</span>
-<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>            <span class="n">j</span> <span class="o">=</span> <span class="n">m</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># ターゲット未満の最初の要素は区間 [i, m-1] にある</span>
+<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>            <span class="n">j</span> <span class="o">=</span> <span class="n">m</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># target より小さい最初の要素は区間 [i, m-1] にある</span>
 <a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>    <span class="c1"># 挿入位置 i を返す</span>
 <a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a>    <span class="k">return</span> <span class="n">i</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_insertion.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 挿入ポイントの二分探索（重複要素あり） */</span>
+<div class="highlight"><span class="filename">binary_search_insertion.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 二分探索で挿入位置を探す（重複要素あり） */</span>
 <a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearchInsertion</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端閉区間[0, n-1]を初期化</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両閉区間 [0, n-1] を初期化</span>
 <a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックスmを計算</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
 <a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// ターゲットは区間[m+1, j]にある</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [m+1, j] にある</span>
 <a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// ターゲットは区間[i, m-1]にある</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [i, m-1] にある</span>
 <a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// ターゲット未満の最初の要素は区間[i, m-1]にある</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target より小さい最初の要素は区間 [i, m-1] にある</span>
 <a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">    </span><span class="c1">// 挿入ポイントiを返す</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">    </span><span class="c1">// 挿入位置 i を返す</span>
 <a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
 <a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_insertion.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 挿入点の二分探索（重複要素あり） */</span>
+<div class="highlight"><span class="filename">binary_search_insertion.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 二分探索で挿入位置を探す（重複要素あり） */</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearchInsertion</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両閉区間 [0, n-1] を初期化</span>
 <a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
 <a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
@@ -4572,59 +4744,228 @@
 <a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target より小さい最初の要素は区間 [i, m-1] にある</span>
 <a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">    </span><span class="c1">// 挿入点 i を返す</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">    </span><span class="c1">// 挿入位置 i を返す</span>
 <a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
 <a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_insertion.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_search_insertion</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BinarySearchInsertion</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_insertion.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 二分探索で挿入位置を探す（重複要素あり） */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">BinarySearchInsertion</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [m+1, j] にある</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [i, m-1] にある</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target より小さい最初の要素は区間 [i, m-1] にある</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">    </span><span class="c1">// 挿入位置 i を返す</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_insertion.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">binarySearchInsertion</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_insertion.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 二分探索で挿入位置を探す（重複要素あり） */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">binarySearchInsertion</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="c1">// 両閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">        </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">        </span><span class="nx">m</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="o">-</span><span class="nx">i</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">            </span><span class="c1">// target は区間 [m+1, j] にある</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">            </span><span class="nx">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">            </span><span class="c1">// target は区間 [i, m-1] にある</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">            </span><span class="c1">// target より小さい最初の要素は区間 [i, m-1] にある</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="w">    </span><span class="c1">// 挿入位置 i を返す</span>
+<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span>
+<a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_insertion.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">binarySearchInsertion</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_insertion.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 二分探索で挿入位置を探す（重複要素あり） */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">binarySearchInsertion</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="c1">// 両閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">startIndex</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">endIndex</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// target は区間 [m+1, j] にある</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// target は区間 [i, m-1] にある</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// target より小さい最初の要素は区間 [i, m-1] にある</span>
+<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="w">    </span><span class="c1">// 挿入位置 i を返す</span>
+<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_insertion.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearchInsertion</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_insertion.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 二分探索で挿入位置を探す（重複要素あり） */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">binarySearchInsertion</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">        </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算し、Math.floor() で切り捨てる</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">            </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [m+1, j] にある</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [i, m-1] にある</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target より小さい最初の要素は区間 [i, m-1] にある</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w">    </span><span class="c1">// 挿入位置 i を返す</span>
+<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_insertion.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearchInsertion</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_insertion.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 二分探索で挿入位置を探す（重複要素あり） */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">binarySearchInsertion</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">        </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算し、Math.floor() で切り捨てる</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">            </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [m+1, j] にある</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [i, m-1] にある</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target より小さい最初の要素は区間 [i, m-1] にある</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w">    </span><span class="c1">// 挿入位置 i を返す</span>
+<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-20-17" name="__codelineno-20-17" href="#__codelineno-20-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_insertion.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearchInsertion</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_insertion.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 二分探索で挿入位置を探す（重複要素あり） */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">binarySearchInsertion</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">      </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [m+1, j] にある</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">      </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [i, m-1] にある</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="w">      </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target より小さい最初の要素は区間 [i, m-1] にある</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w">  </span><span class="c1">// 挿入位置 i を返す</span>
+<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_insertion.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binary_search_insertion</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_insertion.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 二分探索で挿入位置を探す（重複要素あり） */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">binary_search_insertion</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="p">(</span><span class="k">mut</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span><span class="w"> </span><span class="c1">// 両閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [m+1, j] にある</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [i, m-1] にある</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target より小さい最初の要素は区間 [i, m-1] にある</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">    </span><span class="c1">// 挿入位置 i を返す</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="w">    </span><span class="n">i</span>
+<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_insertion.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearchInsertion</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_insertion.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 二分探索で挿入位置を探す（重複要素あり） */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearchInsertion</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">numSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">numSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [m+1, j] にある</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [i, m-1] にある</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target より小さい最初の要素は区間 [i, m-1] にある</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w">    </span><span class="c1">// 挿入位置 i を返す</span>
+<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_insertion.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binarySearchInsertion</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_insertion.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 二分探索で挿入位置を探す（重複要素あり） */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">binarySearchInsertion</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="c1">// 両閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="c1">// target は区間 [m+1, j] にある</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="c1">// target は区間 [i, m-1] にある</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="c1">// target より小さい最初の要素は区間 [i, m-1] にある</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="w">    </span><span class="c1">// 挿入位置 i を返す</span>
+<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-24-17" name="__codelineno-24-17" href="#__codelineno-24-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_insertion.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binary_search_insertion</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_insertion.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### 二分探索の挿入位置（重複要素あり） ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">binary_search_insertion</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="c1"># 両閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">  </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">    </span><span class="c1"># 中点インデックス m を計算</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w">    </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w">      </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># target は区間 [m+1, j] にある</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w">    </span><span class="k">elsif</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w">      </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># target は区間 [i, m-1] にある</span>
+<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w">      </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># target より小さい最初の要素は区間 [i, m-1] にある</span>
+<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a>
+<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="w">  </span><span class="n">i</span><span class="w"> </span><span class="c1"># 挿入位置 i を返す</span>
+<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20binary_search_insertion%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%E3%81%A7%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%82%92%E6%8E%A2%E3%81%99%EF%BC%88%E9%87%8D%E8%A4%87%E8%A6%81%E7%B4%A0%E3%81%82%E3%82%8A%EF%BC%89%22%22%22%0A%20%20%20%20i%2C%20j%20%3D%200%2C%20len%28nums%29%20-%201%20%20%23%20%E4%B8%A1%E9%96%89%E5%8C%BA%E9%96%93%20%5B0%2C%20n-1%5D%20%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20while%20i%20%3C%3D%20j%3A%0A%20%20%20%20%20%20%20%20m%20%3D%20%28i%20%2B%20j%29%20%2F%2F%202%20%20%23%20%E4%B8%AD%E7%82%B9%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20m%20%E3%82%92%E8%A8%88%E7%AE%97%0A%20%20%20%20%20%20%20%20if%20nums%5Bm%5D%20%3C%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%3D%20m%20%2B%201%20%20%23%20target%20%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bm%2B1%2C%20j%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20elif%20nums%5Bm%5D%20%3E%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20%3D%20m%20-%201%20%20%23%20target%20%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bi%2C%20m-1%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20%3D%20m%20-%201%20%20%23%20target%20%E3%82%88%E3%82%8A%E5%B0%8F%E3%81%95%E3%81%84%E6%9C%80%E5%88%9D%E3%81%AE%E8%A6%81%E7%B4%A0%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bi%2C%20m-1%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%23%20%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%20i%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20i%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%87%8D%E8%A4%87%E8%A6%81%E7%B4%A0%E3%82%92%E5%90%AB%E3%82%80%E9%85%8D%E5%88%97%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%206%2C%206%2C%206%2C%206%2C%206%2C%2010%2C%2012%2C%2015%5D%0A%20%20%20%20%23%20%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%E3%81%A7%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%82%92%E6%8E%A2%E3%81%99%0A%20%20%20%20target%20%3D%206%0A%20%20%20%20index%20%3D%20binary_search_insertion%28nums%2C%20target%29%0A%20%20%20%20print%28f%22%E8%A6%81%E7%B4%A0%20%7Btarget%7D%20%E3%81%AE%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%AF%20%7Bindex%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20binary_search_insertion%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%E3%81%A7%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%82%92%E6%8E%A2%E3%81%99%EF%BC%88%E9%87%8D%E8%A4%87%E8%A6%81%E7%B4%A0%E3%81%82%E3%82%8A%EF%BC%89%22%22%22%0A%20%20%20%20i%2C%20j%20%3D%200%2C%20len%28nums%29%20-%201%20%20%23%20%E4%B8%A1%E9%96%89%E5%8C%BA%E9%96%93%20%5B0%2C%20n-1%5D%20%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20while%20i%20%3C%3D%20j%3A%0A%20%20%20%20%20%20%20%20m%20%3D%20%28i%20%2B%20j%29%20%2F%2F%202%20%20%23%20%E4%B8%AD%E7%82%B9%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20m%20%E3%82%92%E8%A8%88%E7%AE%97%0A%20%20%20%20%20%20%20%20if%20nums%5Bm%5D%20%3C%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%3D%20m%20%2B%201%20%20%23%20target%20%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bm%2B1%2C%20j%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20elif%20nums%5Bm%5D%20%3E%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20%3D%20m%20-%201%20%20%23%20target%20%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bi%2C%20m-1%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20%3D%20m%20-%201%20%20%23%20target%20%E3%82%88%E3%82%8A%E5%B0%8F%E3%81%95%E3%81%84%E6%9C%80%E5%88%9D%E3%81%AE%E8%A6%81%E7%B4%A0%E3%81%AF%E5%8C%BA%E9%96%93%20%5Bi%2C%20m-1%5D%20%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%23%20%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%20i%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20i%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E9%87%8D%E8%A4%87%E8%A6%81%E7%B4%A0%E3%82%92%E5%90%AB%E3%82%80%E9%85%8D%E5%88%97%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%206%2C%206%2C%206%2C%206%2C%206%2C%2010%2C%2012%2C%2015%5D%0A%20%20%20%20%23%20%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%E3%81%A7%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%82%92%E6%8E%A2%E3%81%99%0A%20%20%20%20target%20%3D%206%0A%20%20%20%20index%20%3D%20binary_search_insertion%28nums%2C%20target%29%0A%20%20%20%20print%28f%22%E8%A6%81%E7%B4%A0%20%7Btarget%7D%20%E3%81%AE%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%AF%20%7Bindex%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>このセクションのコードは「閉区間」を使用しています。「左閉右開」に興味がある場合は、自分でコードを実装してみてください。</p>
+<p>本節のコードはすべて「両閉区間」の書き方です。興味のある読者は「左閉右開」の書き方を自分で実装してみてください。</p>
 </div>
-<p>要約すると、二分探索は本質的にポインタ<span class="arithmatex">\(i\)</span>と<span class="arithmatex">\(j\)</span>の探索目標を設定することです。これらの目標は特定の要素（<code>target</code>など）または要素の範囲（<code>target</code>より小さいものなど）である可能性があります。</p>
-<p>二分探索の連続ループにおいて、ポインタ<span class="arithmatex">\(i\)</span>と<span class="arithmatex">\(j\)</span>は段階的に事前定義された目標に近づきます。最終的に、それらは答えを見つけるか、境界を越えた後に停止します。</p>
+<p>要するに、二分探索とはポインタ <span class="arithmatex">\(i\)</span> と <span class="arithmatex">\(j\)</span> にそれぞれ探索目標を設定することにほかなりません。目標は具体的な要素（たとえば <code>target</code>）である場合もあれば、要素の範囲（たとえば <code>target</code> より小さい要素）である場合もあります。</p>
+<p>繰り返される二分のループの中で、ポインタ <span class="arithmatex">\(i\)</span> と <span class="arithmatex">\(j\)</span> はどちらも事前に定めた目標へ徐々に近づいていきます。最終的に、それらは答えを見つけるか、境界を越えたところで停止します。</p>
 
 <!-- Source file information -->
 
diff --git a/ja/chapter_searching/index.html b/ja/chapter_searching/index.html
index 340152269..86712363d 100644
--- a/ja/chapter_searching/index.html
+++ b/ja/chapter_searching/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
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             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
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-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
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           </label>
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+    6.1 &nbsp; ハッシュテーブル
   
 
     
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2105,7 +2105,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2493,7 +2493,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2549,7 +2549,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
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   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3115,7 +3115,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3171,7 +3171,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3199,7 +3199,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3392,7 +3392,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3420,7 +3420,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3561,7 +3561,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3589,7 +3589,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3617,7 +3617,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3645,7 +3645,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3838,7 +3838,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4083,7 +4083,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4274,19 +4274,19 @@
 
 <!-- Page content -->
 <h1 id="10">第 10 章 &nbsp; 探索<a class="headerlink" href="#10" title="Permanent link">&para;</a></h1>
-<p><img alt="Searching" class="cover-image" src="../assets/covers/chapter_searching.jpg" /></p>
+<p><img alt="探索" class="cover-image" src="../assets/covers/chapter_searching.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>探索は未知への冒険です。神秘的な空間の隅々まで巡る必要があるかもしれませんし、あるいはすぐに目標を見つけることができるかもしれません。</p>
-<p>この発見の旅において、それぞれの探査は予期しない答えで終わるかもしれません。</p>
+<p>探索は未知の冒険であり、私たちは神秘的な空間の隅々まで歩き回る必要があるかもしれず、あるいは素早く目標を特定できるかもしれません。</p>
+<p>この探索の旅において、すべての探求が思いもよらなかった答えをもたらすかもしれません。</p>
 </div>
 <h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
 <li><a href="binary_search/">10.1 &nbsp; 二分探索</a></li>
-<li><a href="binary_search_insertion/">10.2 &nbsp; 二分探索の挿入点</a></li>
+<li><a href="binary_search_insertion/">10.2 &nbsp; 二分探索の挿入位置</a></li>
 <li><a href="binary_search_edge/">10.3 &nbsp; 二分探索の境界</a></li>
-<li><a href="replace_linear_by_hashing/">10.4 &nbsp; ハッシュ最適化戦略</a></li>
-<li><a href="searching_algorithm_revisited/">10.5 &nbsp; 探索アルゴリズムの再認識</a></li>
+<li><a href="replace_linear_by_hashing/">10.4 &nbsp; ハッシュによる最適化戦略</a></li>
+<li><a href="searching_algorithm_revisited/">10.5 &nbsp; 探索アルゴリズム再考</a></li>
 <li><a href="summary/">10.6 &nbsp; まとめ</a></li>
 </ul>
 
diff --git a/ja/chapter_searching/replace_linear_by_hashing/index.html b/ja/chapter_searching/replace_linear_by_hashing/index.html
index 094a0ca1f..3473e9f64 100644
--- a/ja/chapter_searching/replace_linear_by_hashing/index.html
+++ b/ja/chapter_searching/replace_linear_by_hashing/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -39,7 +39,7 @@
     
     
       
-        <title>10.4 ハッシュ最適化戦略 - Hello アルゴリズム</title>
+        <title>10.4 ハッシュによる最適化戦略 - Hello アルゴリズム</title>
       
     
     
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -152,7 +152,7 @@
         <div class="md-header__topic" data-md-component="header-topic">
           <span class="md-ellipsis">
             
-              10.4 &nbsp; ハッシュ最適化戦略
+              10.4 &nbsp; ハッシュによる最適化戦略
             
           </span>
         </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1635,7 +1635,7 @@
   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1942,7 +1942,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2105,7 +2105,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2493,7 +2493,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2558,7 +2558,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2576,7 +2576,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2606,7 +2606,7 @@
   <a href="#1041" class="md-nav__link">
     <span class="md-ellipsis">
       
-        10.4.1 &nbsp; 線形探索：時間を空間と交換
+        10.4.1 &nbsp; 線形探索：時間と引き換えに空間を節約
       
     </span>
   </a>
@@ -2617,7 +2617,7 @@
   <a href="#1042" class="md-nav__link">
     <span class="md-ellipsis">
       
-        10.4.2 &nbsp; ハッシュ探索：空間を時間と交換
+        10.4.2 &nbsp; ハッシュ探索：空間と引き換えに時間を節約
       
     </span>
   </a>
@@ -2647,7 +2647,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3185,7 +3185,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3241,7 +3241,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3269,7 +3269,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3462,7 +3462,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3490,7 +3490,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3631,7 +3631,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3659,7 +3659,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3687,7 +3687,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3715,7 +3715,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3908,7 +3908,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4153,7 +4153,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4299,7 +4299,7 @@
   <a href="#1041" class="md-nav__link">
     <span class="md-ellipsis">
       
-        10.4.1 &nbsp; 線形探索：時間を空間と交換
+        10.4.1 &nbsp; 線形探索：時間と引き換えに空間を節約
       
     </span>
   </a>
@@ -4310,7 +4310,7 @@
   <a href="#1042" class="md-nav__link">
     <span class="md-ellipsis">
       
-        10.4.2 &nbsp; ハッシュ探索：空間を時間と交換
+        10.4.2 &nbsp; ハッシュ探索：空間と引き換えに時間を節約
       
     </span>
   </a>
@@ -4354,24 +4354,24 @@
 
 
 <!-- Page content -->
-<h1 id="104">10.4 &nbsp; ハッシュ最適化戦略<a class="headerlink" href="#104" title="Permanent link">&para;</a></h1>
-<p>アルゴリズム問題において、<strong>線形探索をハッシュベースの探索に置き換えることで、アルゴリズムの時間計算量を削減することがよくあります</strong>。アルゴリズム問題を使用して理解を深めましょう。</p>
+<h1 id="104">10.4 &nbsp; ハッシュによる最適化戦略<a class="headerlink" href="#104" title="Permanent link">&para;</a></h1>
+<p>アルゴリズムの問題では，<strong>線形探索をハッシュ探索に置き換えることでアルゴリズムの時間計算量を下げることがよくあります</strong>。ここでは，あるアルゴリズム問題を通じて理解を深めましょう。</p>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
-<p>整数配列<code>nums</code>と目標要素<code>target</code>が与えられ、配列内で「和」が<code>target</code>に等しい2つの要素を探索し、それらの配列インデックスを返してください。任意の解が受け入れられます。</p>
+<p>整数配列 <code>nums</code> と目標要素 <code>target</code> が与えられたとき，配列内から和が <code>target</code> となる 2 つの要素を探索し，それらの配列インデックスを返してください。任意の 1 つの解を返せば十分です。</p>
 </div>
-<h2 id="1041">10.4.1 &nbsp; 線形探索：時間を空間と交換<a class="headerlink" href="#1041" title="Permanent link">&para;</a></h2>
-<p>すべての可能な組み合わせを直接横断することを考えてみます。下図に示すように、ネストしたループを開始し、各反復で2つの整数の和が<code>target</code>に等しいかどうかを判断します。そうであれば、それらのインデックスを返します。</p>
-<p><img alt="Linear search solution for two-sum problem" class="animation-figure" src="../replace_linear_by_hashing.assets/two_sum_brute_force.png" /></p>
-<p align="center"> 図 10-9 &nbsp; Linear search solution for two-sum problem </p>
+<h2 id="1041">10.4.1 &nbsp; 線形探索：時間と引き換えに空間を節約<a class="headerlink" href="#1041" title="Permanent link">&para;</a></h2>
+<p>考えられるすべての組み合わせを直接走査することを考えます。次の図に示すように，2 重ループを開始し，各ラウンドで 2 つの整数の和が <code>target</code> であるかを判定します。そうであれば，それらのインデックスを返します。</p>
+<p><img alt="線形探索で 2 数の和を求める" class="animation-figure" src="../replace_linear_by_hashing.assets/two_sum_brute_force.png" /></p>
+<p align="center"> 図 10-9 &nbsp; 線形探索で 2 数の和を求める </p>
 
-<p>コードは以下の通りです：</p>
+<p>コードは次のとおりです：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">two_sum.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">two_sum_brute_force</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;方法一：ブルートフォース列挙&quot;&quot;&quot;</span>
-<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 二重ループ、時間計算量は O(n^2)</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;方法 1：総当たり列挙&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 2重ループのため、時間計算量は O(n^2)</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>            <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">+</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">==</span> <span class="n">target</span><span class="p">:</span>
@@ -4380,10 +4380,10 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">two_sum.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 方法一：ブルートフォース列挙 */</span>
+<div class="highlight"><span class="filename">two_sum.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 方法 1：総当たり列挙 */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">twoSumBruteForce</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
-<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// 二重ループ、時間計算量はO(n^2)</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// 2重ループのため、時間計算量は O(n^2)</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
@@ -4395,10 +4395,10 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">two_sum.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 方法一: 暴力列挙 */</span>
+<div class="highlight"><span class="filename">two_sum.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 方法 1：総当たり列挙 */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">twoSumBruteForce</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
-<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// 二重ループ、時間計算量は O(n^2)</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// 2重ループのため、時間計算量は O(n^2)</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
@@ -4410,58 +4410,177 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">two_sum.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">two_sum</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">TwoSumBruteForce</span><span class="p">}</span>
+<div class="highlight"><span class="filename">two_sum.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 方法 1：総当たり列挙 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="nf">TwoSumBruteForce</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="c1">// 2重ループのため、時間計算量は O(n^2)</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">two_sum.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">twoSumBruteForce</span><span class="p">}</span>
+<div class="highlight"><span class="filename">two_sum.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 方法 1：総当たり列挙 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">twoSumBruteForce</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="nx">size</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="c1">// 2重ループのため、時間計算量は O(n^2)</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">size</span><span class="o">-</span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">size</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="o">+</span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">{</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">}</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">two_sum.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">twoSumBruteForce</span><span class="p">}</span>
+<div class="highlight"><span class="filename">two_sum.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 方法 1：総当たり列挙 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">twoSumBruteForce</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// 2重ループのため、時間計算量は O(n^2)</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="p">.</span><span class="bp">dropLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="p">.</span><span class="bp">dropFirst</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">two_sum.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">twoSumBruteForce</span><span class="p">}</span>
+<div class="highlight"><span class="filename">two_sum.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 方法 1：総当たり列挙 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">twoSumBruteForce</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="c1">// 2重ループのため、時間計算量は O(n^2)</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">two_sum.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">twoSumBruteForce</span><span class="p">}</span>
+<div class="highlight"><span class="filename">two_sum.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 方法 1：総当たり列挙 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">twoSumBruteForce</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">target</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="c1">// 2重ループのため、時間計算量は O(n^2)</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">two_sum.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">twoSumBruteForce</span><span class="p">}</span>
+<div class="highlight"><span class="filename">two_sum.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 方法1: 総当たり列挙 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">twoSumBruteForce</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="c1">// 2重ループのため、時間計算量は O(n^2)</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="m">0</span><span class="p">];</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">two_sum.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">two_sum_brute_force</span><span class="p">}</span>
+<div class="highlight"><span class="filename">two_sum.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 方法 1：総当たり列挙 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">two_sum_brute_force</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="c1">// 2重ループのため、時間計算量は O(n^2)</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">..</span><span class="n">size</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="fm">vec!</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">]);</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">    </span><span class="nb">None</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">two_sum.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">twoSumBruteForce</span><span class="p">}</span>
+<div class="highlight"><span class="filename">two_sum.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 方法 1：総当たり列挙 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="nf">twoSumBruteForce</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">numsSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">returnSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">numsSize</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">numsSize</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">                </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">                </span><span class="n">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">                </span><span class="o">*</span><span class="n">returnSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">    </span><span class="o">*</span><span class="n">returnSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">two_sum.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">twoSumBruteForce</span><span class="p">}</span>
+<div class="highlight"><span class="filename">two_sum.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 方法 1：総当たり列挙 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">twoSumBruteForce</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="n">IntArray</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="c1">// 2重ループのため、時間計算量は O(n^2)</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">intArrayOf</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">two_sum.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">two_sum_brute_force</span><span class="p">}</span>
+<div class="highlight"><span class="filename">two_sum.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 方法1：総当たり列挙 ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">two_sum_brute_force</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># 2重ループのため、時間計算量は O(n^2)</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="p">(</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">...</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">      </span><span class="k">return</span><span class="w"> </span><span class="o">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">  </span><span class="o">[]</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>この方法の時間計算量は<span class="arithmatex">\(O(n^2)\)</span>、空間計算量は<span class="arithmatex">\(O(1)\)</span>で、大容量データでは非常に時間がかかる可能性があります。</p>
-<h2 id="1042">10.4.2 &nbsp; ハッシュ探索：空間を時間と交換<a class="headerlink" href="#1042" title="Permanent link">&para;</a></h2>
-<p>ハッシュテーブルの使用を考えてみましょう。キーと値のペアはそれぞれ配列要素とそのインデックスです。配列をループし、各反復中に下図に示すステップを実行します。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 423px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20two_sum_brute_force%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%22%22%22%E6%96%B9%E6%B3%95%201%EF%BC%9A%E7%B7%8F%E5%BD%93%E3%81%9F%E3%82%8A%E5%88%97%E6%8C%99%22%22%22%0A%20%20%20%20%23%202%E9%87%8D%E3%83%AB%E3%83%BC%E3%83%97%E3%81%AE%E3%81%9F%E3%82%81%E3%80%81%E6%99%82%E9%96%93%E8%A8%88%E7%AE%97%E9%87%8F%E3%81%AF%20O%28n%5E2%29%0A%20%20%20%20for%20i%20in%20range%28len%28nums%29%20-%201%29%3A%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28i%20%2B%201%2C%20len%28nums%29%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20nums%5Bi%5D%20%2B%20nums%5Bj%5D%20%3D%3D%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20return%20%5Bi%2C%20j%5D%0A%20%20%20%20return%20%5B%5D%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B2%2C%207%2C%2011%2C%2015%5D%0A%20%20%20%20target%20%3D%2013%0A%20%20%20%20res%20%3D%20two_sum_brute_force%28nums%2C%20target%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20two_sum_brute_force%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%22%22%22%E6%96%B9%E6%B3%95%201%EF%BC%9A%E7%B7%8F%E5%BD%93%E3%81%9F%E3%82%8A%E5%88%97%E6%8C%99%22%22%22%0A%20%20%20%20%23%202%E9%87%8D%E3%83%AB%E3%83%BC%E3%83%97%E3%81%AE%E3%81%9F%E3%82%81%E3%80%81%E6%99%82%E9%96%93%E8%A8%88%E7%AE%97%E9%87%8F%E3%81%AF%20O%28n%5E2%29%0A%20%20%20%20for%20i%20in%20range%28len%28nums%29%20-%201%29%3A%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28i%20%2B%201%2C%20len%28nums%29%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20nums%5Bi%5D%20%2B%20nums%5Bj%5D%20%3D%3D%20target%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20return%20%5Bi%2C%20j%5D%0A%20%20%20%20return%20%5B%5D%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B2%2C%207%2C%2011%2C%2015%5D%0A%20%20%20%20target%20%3D%2013%0A%20%20%20%20res%20%3D%20two_sum_brute_force%28nums%2C%20target%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>この方法の時間計算量は <span class="arithmatex">\(O(n^2)\)</span> ，空間計算量は <span class="arithmatex">\(O(1)\)</span> であり，大規模データでは非常に時間がかかります。</p>
+<h2 id="1042">10.4.2 &nbsp; ハッシュ探索：空間と引き換えに時間を節約<a class="headerlink" href="#1042" title="Permanent link">&para;</a></h2>
+<p>ハッシュテーブルを利用し，キーと値をそれぞれ配列要素と要素のインデックスにします。配列をループで走査し，各ラウンドで次の図に示す手順を実行します。</p>
 <ol>
-<li>数値<code>target - nums[i]</code>がハッシュテーブルにあるかどうかを確認します。ある場合は、これら2つの要素のインデックスを直接返します。</li>
-<li>キーと値のペア<code>nums[i]</code>とインデックス<code>i</code>をハッシュテーブルに追加します。</li>
+<li>数値 <code>target - nums[i]</code> がハッシュテーブル内にあるかを判定します。あれば，この 2 つの要素のインデックスを直接返します。</li>
+<li>キーと値の組 <code>nums[i]</code> とインデックス <code>i</code> をハッシュテーブルに追加します。</li>
 </ol>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:3"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">&lt;1&gt;</label><label for="__tabbed_2_2">&lt;2&gt;</label><label for="__tabbed_2_3">&lt;3&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="Help hash table solve two-sum" class="animation-figure" src="../replace_linear_by_hashing.assets/two_sum_hashtable_step1.png" /></p>
+<p><img alt="補助ハッシュテーブルで 2 数の和を求める" class="animation-figure" src="../replace_linear_by_hashing.assets/two_sum_hashtable_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="two_sum_hashtable_step2" class="animation-figure" src="../replace_linear_by_hashing.assets/two_sum_hashtable_step2.png" /></p>
@@ -4471,17 +4590,17 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 10-10 &nbsp; Help hash table solve two-sum </p>
+<p align="center"> 図 10-10 &nbsp; 補助ハッシュテーブルで 2 数の和を求める </p>
 
-<p>実装コードは以下に示され、単一のループのみが必要です：</p>
+<p>実装コードは次のとおりで，単一ループだけで済みます：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">two_sum.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">two_sum_hash_table</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;方法二：補助ハッシュテーブル&quot;&quot;&quot;</span>
-<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="c1"># 補助ハッシュテーブル、空間計算量は O(n)</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;方法 2：補助ハッシュテーブル&quot;&quot;&quot;</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="c1"># 補助ハッシュテーブルを使用し、空間計算量は O(n)</span>
 <a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="n">dic</span> <span class="o">=</span> <span class="p">{}</span>
-<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># 単一ループ、時間計算量は O(n)</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># 単一ループで、時間計算量は O(n)</span>
 <a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
 <a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>        <span class="k">if</span> <span class="n">target</span> <span class="o">-</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="ow">in</span> <span class="n">dic</span><span class="p">:</span>
 <a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>            <span class="k">return</span> <span class="p">[</span><span class="n">dic</span><span class="p">[</span><span class="n">target</span> <span class="o">-</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]],</span> <span class="n">i</span><span class="p">]</span>
@@ -4490,12 +4609,12 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">two_sum.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 方法二：補助ハッシュテーブル */</span>
+<div class="highlight"><span class="filename">two_sum.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 方法 2：補助ハッシュテーブル */</span>
 <a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">twoSumHashTable</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
-<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="c1">// 補助ハッシュテーブル、空間計算量はO(n)</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="c1">// 補助ハッシュテーブルを使用し、空間計算量は O(n)</span>
 <a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="n">unordered_map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dic</span><span class="p">;</span>
-<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="c1">// 単層ループ、時間計算量はO(n)</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="c1">// 単一ループで、時間計算量は O(n)</span>
 <a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">dic</span><span class="p">.</span><span class="n">find</span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">])</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">dic</span><span class="p">.</span><span class="n">end</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="p">{</span><span class="n">dic</span><span class="p">[</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]],</span><span class="w"> </span><span class="n">i</span><span class="p">};</span>
@@ -4507,12 +4626,12 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">two_sum.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 方法二: 補助ハッシュテーブル */</span>
+<div class="highlight"><span class="filename">two_sum.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 方法 2：補助ハッシュテーブル */</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">twoSumHashTable</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
-<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="c1">// 補助ハッシュテーブル、空間計算量は O(n)</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="c1">// 補助ハッシュテーブルを使用し、空間計算量は O(n)</span>
 <a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="n">Map</span><span class="o">&lt;</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dic</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashMap</span><span class="o">&lt;&gt;</span><span class="p">();</span>
-<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="c1">// 単一層ループ、時間計算量は O(n)</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="c1">// 単一ループで、時間計算量は O(n)</span>
 <a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">dic</span><span class="p">.</span><span class="na">containsKey</span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">dic</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">),</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">};</span>
@@ -4524,51 +4643,209 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">two_sum.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">two_sum</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">TwoSumHashTable</span><span class="p">}</span>
+<div class="highlight"><span class="filename">two_sum.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 方法 2：補助ハッシュテーブル */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="nf">TwoSumHashTable</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="c1">// 補助ハッシュテーブルを使用し、空間計算量は O(n)</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="n">Dictionary</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dic</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="c1">// 単一ループで、時間計算量は O(n)</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">dic</span><span class="p">.</span><span class="n">ContainsKey</span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="n">dic</span><span class="p">[</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]],</span><span class="w"> </span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">        </span><span class="n">dic</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">two_sum.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">twoSumHashTable</span><span class="p">}</span>
+<div class="highlight"><span class="filename">two_sum.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 方法 2：補助ハッシュテーブル */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">twoSumHashTable</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="c1">// 補助ハッシュテーブルを使用し、空間計算量は O(n)</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="nx">hashTable</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="kd">map</span><span class="p">[</span><span class="kt">int</span><span class="p">]</span><span class="kt">int</span><span class="p">{}</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">    </span><span class="c1">// 単一ループで、時間計算量は O(n)</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">idx</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">preIdx</span><span class="p">,</span><span class="w"> </span><span class="nx">ok</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">hashTable</span><span class="p">[</span><span class="nx">target</span><span class="o">-</span><span class="nx">val</span><span class="p">];</span><span class="w"> </span><span class="nx">ok</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">{</span><span class="nx">preIdx</span><span class="p">,</span><span class="w"> </span><span class="nx">idx</span><span class="p">}</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">        </span><span class="nx">hashTable</span><span class="p">[</span><span class="nx">val</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">idx</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">two_sum.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">twoSumHashTable</span><span class="p">}</span>
+<div class="highlight"><span class="filename">two_sum.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 方法 2：補助ハッシュテーブル */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">twoSumHashTable</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="c1">// 補助ハッシュテーブルを使用し、空間計算量は O(n)</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">dic</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[:]</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">    </span><span class="c1">// 単一ループで、時間計算量は O(n)</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dic</span><span class="p">[</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="n">j</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">        </span><span class="n">dic</span><span class="p">[</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">two_sum.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">twoSumHashTable</span><span class="p">}</span>
+<div class="highlight"><span class="filename">two_sum.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 方法 2：補助ハッシュテーブル */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">twoSumHashTable</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="c1">// 補助ハッシュテーブルを使用し、空間計算量は O(n)</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{};</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">    </span><span class="c1">// 単一ループで、時間計算量は O(n)</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">m</span><span class="p">[</span><span class="nx">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">undefined</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="nx">m</span><span class="p">[</span><span class="nx">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]],</span><span class="w"> </span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w">            </span><span class="nx">m</span><span class="p">[</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">two_sum.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">twoSumHashTable</span><span class="p">}</span>
+<div class="highlight"><span class="filename">two_sum.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 方法 2：補助ハッシュテーブル */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">twoSumHashTable</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">target</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="c1">// 補助ハッシュテーブルを使用し、空間計算量は O(n)</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">m</span><span class="o">:</span><span class="w"> </span><span class="kt">Map</span><span class="o">&lt;</span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="kt">number</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Map</span><span class="p">();</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">    </span><span class="c1">// 単一ループで、時間計算量は O(n)</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]);</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">index</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">undefined</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="nx">index</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w">            </span><span class="nx">m</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">i</span><span class="p">);</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">two_sum.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">twoSumHashTable</span><span class="p">}</span>
+<div class="highlight"><span class="filename">two_sum.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 方法2: 補助ハッシュテーブル */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">twoSumHashTable</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="c1">// 補助ハッシュテーブルを使用し、空間計算量は O(n)</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">  </span><span class="n">Map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dic</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashMap</span><span class="p">();</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">  </span><span class="c1">// 単一ループで、時間計算量は O(n)</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">dic</span><span class="p">.</span><span class="n">containsKey</span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">      </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="n">dic</span><span class="p">[</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span><span class="o">!</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="w">    </span><span class="n">dic</span><span class="p">.</span><span class="n">putIfAbsent</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="m">0</span><span class="p">];</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">two_sum.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">two_sum_hash_table</span><span class="p">}</span>
+<div class="highlight"><span class="filename">two_sum.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 方法 2：補助ハッシュテーブル */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">two_sum_hash_table</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="c1">// 補助ハッシュテーブルを使用し、空間計算量は O(n)</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">dic</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashMap</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">    </span><span class="c1">// 単一ループで、時間計算量は O(n)</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">iter</span><span class="p">().</span><span class="n">enumerate</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">        </span><span class="k">match</span><span class="w"> </span><span class="n">dic</span><span class="p">.</span><span class="n">get</span><span class="p">(</span><span class="o">&amp;</span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">num</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">            </span><span class="nb">Some</span><span class="p">(</span><span class="n">v</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="fm">vec!</span><span class="p">[</span><span class="o">*</span><span class="n">v</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">]),</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">            </span><span class="nb">None</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">dic</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">),</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w">        </span><span class="p">};</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">    </span><span class="nb">None</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">two_sum.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">HashTable</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
-<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a>
-<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">twoSumHashTable</span><span class="p">}</span>
+<div class="highlight"><span class="filename">two_sum.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* ハッシュテーブル */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">;</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">    </span><span class="n">UT_hash_handle</span><span class="w"> </span><span class="n">hh</span><span class="p">;</span><span class="w"> </span><span class="c1">// uthash.h を用いて実装</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="p">}</span><span class="w"> </span><span class="n">HashTable</span><span class="p">;</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="cm">/* ハッシュテーブルを検索する */</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="n">HashTable</span><span class="w"> </span><span class="o">*</span><span class="nf">find</span><span class="p">(</span><span class="n">HashTable</span><span class="w"> </span><span class="o">*</span><span class="n">h</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w">    </span><span class="n">HashTable</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w">    </span><span class="n">HASH_FIND_INT</span><span class="p">(</span><span class="n">h</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">tmp</span><span class="p">);</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="p">}</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a>
+<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="cm">/* ハッシュテーブルに要素を挿入する */</span>
+<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">HashTable</span><span class="w"> </span><span class="o">**</span><span class="n">h</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="w">    </span><span class="n">HashTable</span><span class="w"> </span><span class="o">*</span><span class="n">t</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">find</span><span class="p">(</span><span class="o">*</span><span class="n">h</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">t</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="w">        </span><span class="n">HashTable</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">HashTable</span><span class="p">));</span>
+<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="w">        </span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a><span class="w">        </span><span class="n">HASH_ADD_INT</span><span class="p">(</span><span class="o">*</span><span class="n">h</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">tmp</span><span class="p">);</span>
+<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-23" name="__codelineno-23-23" href="#__codelineno-23-23"></a><span class="w">        </span><span class="n">t</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-23-24" name="__codelineno-23-24" href="#__codelineno-23-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-25" name="__codelineno-23-25" href="#__codelineno-23-25"></a><span class="p">}</span>
+<a id="__codelineno-23-26" name="__codelineno-23-26" href="#__codelineno-23-26"></a>
+<a id="__codelineno-23-27" name="__codelineno-23-27" href="#__codelineno-23-27"></a><span class="cm">/* 方法 2：補助ハッシュテーブル */</span>
+<a id="__codelineno-23-28" name="__codelineno-23-28" href="#__codelineno-23-28"></a><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="nf">twoSumHashTable</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">numsSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">returnSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-29" name="__codelineno-23-29" href="#__codelineno-23-29"></a><span class="w">    </span><span class="n">HashTable</span><span class="w"> </span><span class="o">*</span><span class="n">hashtable</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-23-30" name="__codelineno-23-30" href="#__codelineno-23-30"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">numsSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-31" name="__codelineno-23-31" href="#__codelineno-23-31"></a><span class="w">        </span><span class="n">HashTable</span><span class="w"> </span><span class="o">*</span><span class="n">t</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">find</span><span class="p">(</span><span class="n">hashtable</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-23-32" name="__codelineno-23-32" href="#__codelineno-23-32"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">t</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-33" name="__codelineno-23-33" href="#__codelineno-23-33"></a><span class="w">            </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-23-34" name="__codelineno-23-34" href="#__codelineno-23-34"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">t</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-23-35" name="__codelineno-23-35" href="#__codelineno-23-35"></a><span class="w">            </span><span class="o">*</span><span class="n">returnSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-23-36" name="__codelineno-23-36" href="#__codelineno-23-36"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-23-37" name="__codelineno-23-37" href="#__codelineno-23-37"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-38" name="__codelineno-23-38" href="#__codelineno-23-38"></a><span class="w">        </span><span class="n">insert</span><span class="p">(</span><span class="o">&amp;</span><span class="n">hashtable</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-23-39" name="__codelineno-23-39" href="#__codelineno-23-39"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-40" name="__codelineno-23-40" href="#__codelineno-23-40"></a><span class="w">    </span><span class="o">*</span><span class="n">returnSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-23-41" name="__codelineno-23-41" href="#__codelineno-23-41"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-23-42" name="__codelineno-23-42" href="#__codelineno-23-42"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">two_sum.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">twoSumHashTable</span><span class="p">}</span>
+<div class="highlight"><span class="filename">two_sum.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 方法 2：補助ハッシュテーブル */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">twoSumHashTable</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="n">IntArray</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="c1">// 補助ハッシュテーブルを使用し、空間計算量は O(n)</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">dic</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashMap</span><span class="o">&lt;</span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">    </span><span class="c1">// 単一ループで、時間計算量は O(n)</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">dic</span><span class="p">.</span><span class="na">containsKey</span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">intArrayOf</span><span class="p">(</span><span class="n">dic</span><span class="o">[</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]]!!</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="w">        </span><span class="n">dic</span><span class="o">[</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
+<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">two_sum.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">two_sum_hash_table</span><span class="p">}</span>
+<div class="highlight"><span class="filename">two_sum.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### 方法2：補助ハッシュテーブル ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">two_sum_hash_table</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="c1"># 補助ハッシュテーブルを使用し、空間計算量は O(n)</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">  </span><span class="n">dic</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{}</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">  </span><span class="c1"># 単一ループで、時間計算量は O(n)</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">[</span><span class="n">dic</span><span class="o">[</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]]</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">dic</span><span class="o">.</span><span class="n">has_key?</span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">    </span><span class="n">dic</span><span class="o">[</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w">  </span><span class="o">[]</span>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>この方法は、ハッシュ探索を使用することで時間計算量を<span class="arithmatex">\(O(n^2)\)</span>から<span class="arithmatex">\(O(n)\)</span>に削減し、実行時効率を大幅に向上させます。</p>
-<p>追加のハッシュテーブルを維持する必要があるため、空間計算量は<span class="arithmatex">\(O(n)\)</span>です。<strong>それにもかかわらず、この方法は全体的により均衡のとれた時空間効率を持ち、この問題の最適解となります</strong>。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 459px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20two_sum_hash_table%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%22%22%22%E6%96%B9%E6%B3%95%202%EF%BC%9A%E8%A3%9C%E5%8A%A9%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%22%22%22%0A%20%20%20%20%23%20%E8%A3%9C%E5%8A%A9%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E4%BD%BF%E7%94%A8%E3%81%97%E3%80%81%E7%A9%BA%E9%96%93%E8%A8%88%E7%AE%97%E9%87%8F%E3%81%AF%20O%28n%29%0A%20%20%20%20dic%20%3D%20%7B%7D%0A%20%20%20%20%23%20%E5%8D%98%E4%B8%80%E3%83%AB%E3%83%BC%E3%83%97%E3%81%A7%E3%80%81%E6%99%82%E9%96%93%E8%A8%88%E7%AE%97%E9%87%8F%E3%81%AF%20O%28n%29%0A%20%20%20%20for%20i%20in%20range%28len%28nums%29%29%3A%0A%20%20%20%20%20%20%20%20if%20target%20-%20nums%5Bi%5D%20in%20dic%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20%5Bdic%5Btarget%20-%20nums%5Bi%5D%5D%2C%20i%5D%0A%20%20%20%20%20%20%20%20dic%5Bnums%5Bi%5D%5D%20%3D%20i%0A%20%20%20%20return%20%5B%5D%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B2%2C%207%2C%2011%2C%2015%5D%0A%20%20%20%20target%20%3D%2013%0A%20%20%20%20res%20%3D%20two_sum_hash_table%28nums%2C%20target%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20two_sum_hash_table%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%22%22%22%E6%96%B9%E6%B3%95%202%EF%BC%9A%E8%A3%9C%E5%8A%A9%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%22%22%22%0A%20%20%20%20%23%20%E8%A3%9C%E5%8A%A9%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E4%BD%BF%E7%94%A8%E3%81%97%E3%80%81%E7%A9%BA%E9%96%93%E8%A8%88%E7%AE%97%E9%87%8F%E3%81%AF%20O%28n%29%0A%20%20%20%20dic%20%3D%20%7B%7D%0A%20%20%20%20%23%20%E5%8D%98%E4%B8%80%E3%83%AB%E3%83%BC%E3%83%97%E3%81%A7%E3%80%81%E6%99%82%E9%96%93%E8%A8%88%E7%AE%97%E9%87%8F%E3%81%AF%20O%28n%29%0A%20%20%20%20for%20i%20in%20range%28len%28nums%29%29%3A%0A%20%20%20%20%20%20%20%20if%20target%20-%20nums%5Bi%5D%20in%20dic%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20%5Bdic%5Btarget%20-%20nums%5Bi%5D%5D%2C%20i%5D%0A%20%20%20%20%20%20%20%20dic%5Bnums%5Bi%5D%5D%20%3D%20i%0A%20%20%20%20return%20%5B%5D%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B2%2C%207%2C%2011%2C%2015%5D%0A%20%20%20%20target%20%3D%2013%0A%20%20%20%20res%20%3D%20two_sum_hash_table%28nums%2C%20target%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>この方法ではハッシュ探索によって時間計算量を <span class="arithmatex">\(O(n^2)\)</span> から <span class="arithmatex">\(O(n)\)</span> に下げ，実行効率を大幅に向上させます。</p>
+<p>追加のハッシュテーブルを維持する必要があるため，空間計算量は <span class="arithmatex">\(O(n)\)</span> です。<strong>それでも，この方法は全体として時間と空間の効率のバランスがより良く，本問の最適解です</strong>。</p>
 
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     class="md-footer__link md-footer__link--next"
-    aria-label="次: 10.5 &amp;nbsp; 探索アルゴリズムの再認識"
+    aria-label="次: 10.5 &amp;nbsp; 探索アルゴリズム再考"
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   >
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@@ -4623,7 +4900,7 @@ aria-label="フッター"
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-        10.5 &nbsp; 探索アルゴリズムの再認識
+        10.5 &nbsp; 探索アルゴリズム再考
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index 2dfe28d49..e57e6e075 100644
--- a/ja/chapter_searching/searching_algorithm_revisited/index.html
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@@ -6,7 +6,7 @@
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         <meta name="author" content="krahets">
@@ -39,7 +39,7 @@
     
     
       
-        <title>10.5 探索アルゴリズムの再検討 - Hello アルゴリズム</title>
+        <title>10.5 探索アルゴリズム再考 - Hello アルゴリズム</title>
       
     
     
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -152,7 +152,7 @@
         <div class="md-header__topic" data-md-component="header-topic">
           <span class="md-ellipsis">
             
-              10.5 &nbsp; 探索アルゴリズムの再検討
+              10.5 &nbsp; 探索アルゴリズム再考
             
           </span>
         </div>
@@ -341,7 +341,7 @@
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-    序
+    はじめに
   
 
     
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-    序
+    はじめに
   
 
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-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
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-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
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-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
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-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
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-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
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-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
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-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
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-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
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-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
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   <a href="#1052" class="md-nav__link">
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-        10.5.2 &nbsp; 適応的探索
+        10.5.2 &nbsp; 適応的な探索
       
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   <a href="#1053" class="md-nav__link">
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-        10.5.3 &nbsp; 探索方法の選択
+        10.5.3 &nbsp; 探索手法の選択
       
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
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-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
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-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
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-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
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-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
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-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
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   <a href="#1052" class="md-nav__link">
     <span class="md-ellipsis">
       
-        10.5.2 &nbsp; 適応的探索
+        10.5.2 &nbsp; 適応的な探索
       
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@@ -4332,7 +4332,7 @@
   <a href="#1053" class="md-nav__link">
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-        10.5.3 &nbsp; 探索方法の選択
+        10.5.3 &nbsp; 探索手法の選択
       
     </span>
   </a>
@@ -4376,42 +4376,42 @@
 
 
 <!-- Page content -->
-<h1 id="105">10.5 &nbsp; 探索アルゴリズムの再検討<a class="headerlink" href="#105" title="Permanent link">&para;</a></h1>
-<p><u>探索アルゴリズム（検索アルゴリズム）</u>は、配列、連結リスト、木、グラフなどのデータ構造内で特定の基準を満たす1つ以上の要素を取得するために使用されます。</p>
-<p>探索アルゴリズムは、そのアプローチに基づいて以下の2つのカテゴリに分けることができます。</p>
+<h1 id="105">10.5 &nbsp; 探索アルゴリズム再考<a class="headerlink" href="#105" title="Permanent link">&para;</a></h1>
+<p><u>探索アルゴリズム（searching algorithm）</u>は、データ構造（配列、連結リスト、木、グラフなど）の中から、特定の条件を満たす 1 つまたは複数の要素を探索するために用いられます。</p>
+<p>探索アルゴリズムは、実装の考え方に応じて次の 2 種類に分けられます。</p>
 <ul>
-<li><strong>データ構造を横断することで目標要素を特定する</strong>：配列、連結リスト、木、グラフの横断など。</li>
-<li><strong>データの組織構造や既存のデータを使用して効率的な要素探索を実現する</strong>：二分探索、ハッシュ探索、二分探索木探索など。</li>
+<li><strong>データ構造を走査して目標要素を特定する方法</strong>。配列、連結リスト、木、グラフの走査などがこれに当たります。</li>
+<li><strong>データの構成やデータに含まれる事前情報を利用して、要素を効率よく探す方法</strong>。二分探索、ハッシュ探索、二分探索木による探索などがこれに当たります。</li>
 </ul>
-<p>これらのトピックは前の章で紹介されたため、私たちには馴染みのないものではありません。このセクションでは、より体系的な観点から探索アルゴリズムを再検討します。</p>
+<p>これらのトピックはすでに前の章で扱っているため、探索アルゴリズムは私たちにとって見慣れたものです。本節では、より体系的な視点から探索アルゴリズムをあらためて見直します。</p>
 <h2 id="1051">10.5.1 &nbsp; 総当たり探索<a class="headerlink" href="#1051" title="Permanent link">&para;</a></h2>
-<p>総当たり探索は、データ構造のすべての要素を横断することで目標要素を特定します。</p>
+<p>総当たり探索は、データ構造の各要素を順に調べて目標要素を特定します。</p>
 <ul>
-<li>「線形探索」は配列や連結リストなどの線形データ構造に適しています。データ構造の一端から開始し、目標要素が見つかるか、目標要素を見つけることなく他端に到達するまで、各要素に一つずつアクセスします。</li>
-<li>「幅優先探索」と「深さ優先探索」は、グラフと木の2つの横断戦略です。幅優先探索は初期ノードから開始し、層ごと（左から右へ）に探索し、近くから遠くのノードにアクセスします。深さ優先探索は初期ノードから開始し、パスの終端（上から下へ）まで追跡し、その後バックトラックして他のパスを試し、データ構造全体が横断されるまで続行します。</li>
+<li>“線形探索”は配列や連結リストなどの線形データ構造に適しています。データ構造の一端から始めて、要素を 1 つずつ調べ、目標要素が見つかるか、もう一方の端に達しても見つからないまで続けます。</li>
+<li>“幅優先探索”と“深さ優先探索”は、グラフと木における 2 つの走査戦略です。幅優先探索は初期ノードから始めて層ごとに探索し、近いところから遠いところへ各ノードを訪れます。深さ優先探索は初期ノードから始めて 1 本の経路を最後までたどり、その後でバックトラックしてほかの経路を試し、データ構造全体を走査し終えるまで続けます。</li>
 </ul>
-<p>総当たり探索の利点は、その単純さと汎用性であり、**データの前処理や追加のデータ構造の助けが不要**です。</p>
-<p>ただし、**このタイプのアルゴリズムの時間計算量は<span class="arithmatex">\(O(n)\)</span>**で、<span class="arithmatex">\(n\)</span>は要素数であるため、大規模なデータセットでは性能が悪くなります。</p>
-<h2 id="1052">10.5.2 &nbsp; 適応的探索<a class="headerlink" href="#1052" title="Permanent link">&para;</a></h2>
-<p>適応的探索は、データの固有の性質（順序など）を使用して探索プロセスを最適化し、それにより目標要素をより効率的に特定します。</p>
+<p>総当たり探索の利点は、単純で汎用性が高く、**データの前処理や追加のデータ構造を必要としない**ことです。</p>
+<p>しかし、<strong>この種のアルゴリズムの時間計算量は <span class="arithmatex">\(O(n)\)</span> です</strong>。ここで <span class="arithmatex">\(n\)</span> は要素数であり、そのためデータ量が大きい場合は性能が低くなります。</p>
+<h2 id="1052">10.5.2 &nbsp; 適応的な探索<a class="headerlink" href="#1052" title="Permanent link">&para;</a></h2>
+<p>適応的な探索は、データが持つ固有の性質（整列性など）を利用して探索過程を最適化し、目標要素をより効率よく特定します。</p>
 <ul>
-<li>「二分探索」はデータの整列性を使用して効率的な探索を実現し、配列にのみ適用可能です。</li>
-<li>「ハッシュ探索」はハッシュテーブルを使用して探索データと目標データの間にキーと値のマッピングを確立し、それによりクエリ操作を実装します。</li>
-<li>特定の木構造（二分探索木など）での「木探索」は、ノード値の比較に基づいてノードを迅速に除外し、それにより目標要素を特定します。</li>
+<li>“二分探索”は、データの順序性を利用して効率的な探索を行う方法で、配列にしか適用できません。</li>
+<li>“ハッシュ探索”は、ハッシュ表を用いて探索対象のデータと目標データをキーと値の対応にし、問い合わせ操作を実現します。</li>
+<li>“木探索”は、特定の木構造（たとえば二分探索木）の中で、ノード値の比較に基づいて不要なノードをすばやく除外し、目標要素を特定します。</li>
 </ul>
-<p>これらのアルゴリズムの利点は高効率であり、<strong>時間計算量が<span class="arithmatex">\(O(\log n)\)</span>または<span class="arithmatex">\(O(1)\)</span>にまで達します</strong>。</p>
-<p>ただし、<strong>これらのアルゴリズムを使用するには、多くの場合データの前処理が必要です</strong>。例えば、二分探索では事前に配列をソートする必要があり、ハッシュ探索と木探索の両方で追加のデータ構造の助けが必要です。これらの構造を維持することも、時間と空間の面でより多くのオーバーヘッドが必要です。</p>
+<p>この種のアルゴリズムの利点は効率が高く、**時間計算量が <span class="arithmatex">\(O(\log n)\)</span> あるいは <span class="arithmatex">\(O(1)\)</span> に達する**ことです。</p>
+<p>しかし、<strong>これらのアルゴリズムを使うには、たいていデータの前処理が必要です</strong>。たとえば、二分探索では事前に配列をソートする必要があり、ハッシュ探索と木探索では追加のデータ構造が必要です。これらのデータ構造を維持するにも、追加の時間と空間のコストがかかります。</p>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>適応的探索アルゴリズムは、多くの場合探索アルゴリズムと呼ばれ、<strong>主に特定のデータ構造内で目標要素を迅速に取得するために使用されます</strong>。</p>
+<p>適応的な探索アルゴリズムは、しばしば検索アルゴリズムとも呼ばれ、<strong>主に特定のデータ構造の中で目標要素を高速に取得するために用いられます</strong>。</p>
 </div>
-<h2 id="1053">10.5.3 &nbsp; 探索方法の選択<a class="headerlink" href="#1053" title="Permanent link">&para;</a></h2>
-<p>サイズ<span class="arithmatex">\(n\)</span>のデータセットが与えられた場合、線形探索、二分探索、木探索、ハッシュ探索、またはその他の方法を使用して目標要素を取得できます。これらの方法の動作原理を下図に示します。</p>
-<p><img alt="Various search strategies" class="animation-figure" src="../searching_algorithm_revisited.assets/searching_algorithms.png" /></p>
-<p align="center"> 図 10-11 &nbsp; Various search strategies </p>
+<h2 id="1053">10.5.3 &nbsp; 探索手法の選択<a class="headerlink" href="#1053" title="Permanent link">&para;</a></h2>
+<p>大きさ <span class="arithmatex">\(n\)</span> のデータ集合が与えられたとき、線形探索、二分探索、木探索、ハッシュ探索など、さまざまな方法で目標要素を探索できます。各手法の動作原理を下図に示します。</p>
+<p><img alt="複数の探索戦略" class="animation-figure" src="../searching_algorithm_revisited.assets/searching_algorithms.png" /></p>
+<p align="center"> 図 10-11 &nbsp; 複数の探索戦略 </p>
 
-<p>前述の方法の特性と操作効率を以下の表に示します。</p>
-<p align="center"> 表 10-1 &nbsp; 探索アルゴリズム効率の比較 </p>
+<p>上記のいくつかの手法について、操作効率と特性を次の表に示します。</p>
+<p align="center"> 表 10-1 &nbsp; 探索アルゴリズムの効率比較 </p>
 
 <div class="center-table">
 <table>
@@ -4447,7 +4447,7 @@
 <td><span class="arithmatex">\(O(1)\)</span></td>
 </tr>
 <tr>
-<td>追加空間</td>
+<td>追加領域</td>
 <td><span class="arithmatex">\(O(1)\)</span></td>
 <td><span class="arithmatex">\(O(1)\)</span></td>
 <td><span class="arithmatex">\(O(n)\)</span></td>
@@ -4458,44 +4458,44 @@
 <td>/</td>
 <td>ソート <span class="arithmatex">\(O(n \log n)\)</span></td>
 <td>木構築 <span class="arithmatex">\(O(n \log n)\)</span></td>
-<td>ハッシュテーブル構築 <span class="arithmatex">\(O(n)\)</span></td>
+<td>ハッシュ表構築 <span class="arithmatex">\(O(n)\)</span></td>
 </tr>
 <tr>
-<td>データ順序性</td>
-<td>無順序</td>
-<td>順序</td>
-<td>順序</td>
-<td>無順序</td>
+<td>データの順序性</td>
+<td>なし</td>
+<td>あり</td>
+<td>あり</td>
+<td>なし</td>
 </tr>
 </tbody>
 </table>
 </div>
-<p>探索アルゴリズムの選択は、データ量、探索性能要件、データクエリと更新の頻度などにも依存します。</p>
+<p>探索アルゴリズムの選択は、規模、探索性能の要求、データの問い合わせ頻度や更新頻度などにも左右されます。</p>
 <p><strong>線形探索</strong></p>
 <ul>
-<li>汎用性が良く、データ前処理操作が不要です。データを一度だけクエリする必要がある場合、他の3つの方法のデータ前処理時間は線形探索の時間よりも長くなります。</li>
-<li>小容量のデータに適しており、時間計算量が効率に与える影響は小さいです。</li>
-<li>データ更新が非常に頻繁なシナリオに適しています。この方法はデータの追加メンテナンスを必要としないためです。</li>
+<li>汎用性が高く、データの前処理をまったく必要としません。データを 1 回だけ問い合わせればよい場合、ほか 3 つの手法では前処理にかかる時間のほうが、線形探索そのものより長くなることがあります。</li>
+<li>規模の小さいデータに適しています。この場合、時間計算量が効率に与える影響は比較的小さいです。</li>
+<li>データ更新頻度が高い場面に適しています。この手法では、データに対する追加の保守が不要だからです。</li>
 </ul>
 <p><strong>二分探索</strong></p>
 <ul>
-<li>より大きなデータ量に適しており、安定した性能と最悪ケースの時間計算量<span class="arithmatex">\(O(\log n)\)</span>を持ちます。</li>
-<li>ただし、データ量が大きすぎることはできません。配列の保存には連続したメモリ空間が必要だからです。</li>
-<li>頻繁な追加と削除があるシナリオには適していません。順序付き配列の維持に多くのオーバーヘッドが発生するためです。</li>
+<li>大規模データに適しており、効率が安定しています。最悪時間計算量は <span class="arithmatex">\(O(\log n)\)</span> です。</li>
+<li>データ量が大きすぎる場合には向きません。配列の格納には連続したメモリ領域が必要だからです。</li>
+<li>頻繁な挿入・削除がある場面には向きません。整列配列を維持するコストが高いためです。</li>
 </ul>
 <p><strong>ハッシュ探索</strong></p>
 <ul>
-<li>高速クエリ性能が不可欠なシナリオに適しており、平均時間計算量は<span class="arithmatex">\(O(1)\)</span>です。</li>
-<li>順序付きデータや範囲探索が必要なシナリオには適していません。ハッシュテーブルはデータの順序性を維持できないためです。</li>
+<li>問い合わせ性能への要求が高い場面に適しており、平均時間計算量は <span class="arithmatex">\(O(1)\)</span> です。</li>
+<li>順序付きデータや範囲探索が必要な場面には向きません。ハッシュ表ではデータの順序性を維持できないからです。</li>
 <li>ハッシュ関数とハッシュ衝突処理戦略への依存度が高く、性能劣化のリスクが大きいです。</li>
-<li>過度に大容量のデータには適していません。ハッシュテーブルは衝突を最小化し、良好なクエリ性能を提供するために追加の空間が必要だからです。</li>
+<li>データ量が大きすぎる場合には向きません。ハッシュ表は衝突をできるだけ減らして良好な問い合わせ性能を出すために、追加の空間を必要とするからです。</li>
 </ul>
 <p><strong>木探索</strong></p>
 <ul>
-<li>大容量データに適しています。木ノードはメモリ内に分散して保存されるためです。</li>
-<li>順序付きデータの維持や範囲探索に適しています。</li>
-<li>ノードの継続的な追加と削除により、二分探索木は偏る可能性があり、時間計算量が<span class="arithmatex">\(O(n)\)</span>に劣化する可能性があります。</li>
-<li>AVL木や赤黒木を使用する場合、操作は<span class="arithmatex">\(O(\log n)\)</span>効率で安定して実行できますが、木のバランスを維持する操作により追加のオーバーヘッドが追加されます。</li>
+<li>巨大データに適しています。木ノードはメモリ上に分散して格納されるためです。</li>
+<li>順序付きデータの維持や範囲探索が必要な場面に適しています。</li>
+<li>ノードの挿入・削除を続ける過程で、二分探索木は偏ることがあり、時間計算量は <span class="arithmatex">\(O(n)\)</span> まで劣化する可能性があります。</li>
+<li>AVL 木や赤黒木を使えば、各種操作を <span class="arithmatex">\(O(\log n)\)</span> の効率で安定して実行できますが、木の平衡を保つ処理による追加コストが発生します。</li>
 </ul>
 
 <!-- Source file information -->
@@ -4519,7 +4519,7 @@ aria-label="フッター"
   <a
     href="../replace_linear_by_hashing/"
     class="md-footer__link md-footer__link--prev"
-    aria-label="前: 10.4 &amp;nbsp; ハッシュ最適化戦略"
+    aria-label="前: 10.4 &amp;nbsp; ハッシュによる最適化戦略"
     rel="prev"
   >
     <div class="md-footer__button md-icon">
@@ -4531,7 +4531,7 @@ aria-label="フッター"
         前
       </span>
       <div class="md-ellipsis">
-        10.4 &nbsp; ハッシュ最適化戦略
+        10.4 &nbsp; ハッシュによる最適化戦略
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index 53c7d772e..861da1e76 100644
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@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
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     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
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   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
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-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
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   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
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-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2105,7 +2105,7 @@
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-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2493,7 +2493,7 @@
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-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
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-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -2607,6 +2607,24 @@
         
       
       
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  
+  <span class="md-ellipsis">
+    
+  
+    10.6 &nbsp; まとめ
+  
+
+    
+  </span>
+  
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
       <a href="././" class="md-nav__link md-nav__link--active">
         
   
@@ -2624,6 +2642,37 @@
 
       </a>
       
+        
+
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      
+        1. &nbsp; 要点の振り返り
+      
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
     </li>
   
 
@@ -3125,7 +3174,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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-    13.3 &nbsp; 部分集合和問題
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-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
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-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
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-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
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-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3655,7 +3704,7 @@
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-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3848,7 +3897,7 @@
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4093,7 +4142,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4229,6 +4278,25 @@
     
   
   
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      
+        1. &nbsp; 要点の振り返り
+      
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
 </nav>
                   </div>
                 </div>
@@ -4265,13 +4333,14 @@
 
 <!-- Page content -->
 <h1 id="106">10.6 &nbsp; まとめ<a class="headerlink" href="#106" title="Permanent link">&para;</a></h1>
+<h3 id="1">1. &nbsp; 要点の振り返り<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
-<li>二分探索はデータの順序に依存し、探索区間を反復的に半分にすることで探索を実行します。入力データがソート済みである必要があり、配列または配列ベースのデータ構造にのみ適用可能です。</li>
-<li>無順序データセット内のエントリを見つけるには、総当たり探索が必要な場合があります。データ構造に基づいて異なる探索アルゴリズムを適用できます：線形探索は配列と連結リストに適しており、幅優先探索（BFS）と深さ優先探索（DFS）はグラフと木に適しています。これらのアルゴリズムは非常に汎用性が高く、データの前処理が不要ですが、<span class="arithmatex">\(O(n)\)</span>という高い時間計算量を持ちます。</li>
-<li>ハッシュ探索、木探索、二分探索は効率的な探索方法で、特定のデータ構造内で目標要素を迅速に特定できます。これらのアルゴリズムは非常に効率的で、時間計算量が<span class="arithmatex">\(O(\log n)\)</span>または<span class="arithmatex">\(O(1)\)</span>にまで達しますが、通常は追加のデータ構造を収容するために追加の空間が必要です。</li>
-<li>実際には、データ量、探索性能要件、データクエリと更新頻度などの要因を分析して、適切な探索方法を選択する必要があります。</li>
-<li>線形探索は小さなデータや頻繁に更新される（変動性の高い）データに理想的です。二分探索は大きくてソート済みのデータに適しています。ハッシュ探索は高いクエリ効率が必要で範囲クエリが不要なデータに適しています。木探索は順序を維持し、範囲クエリをサポートする必要がある大きな動的データに最も適しています。</li>
-<li>線形探索をハッシュ探索に置き換えることは、実行時性能を最適化する一般的な戦略で、時間計算量を<span class="arithmatex">\(O(n)\)</span>から<span class="arithmatex">\(O(1)\)</span>に削減します。</li>
+<li>二分探索はデータの順序性に依存し、ループによって探索区間を半分ずつ縮小しながら探索を行う。入力データがソート済みであることを前提とし、配列または配列ベースで実装されたデータ構造にのみ適用できる。</li>
+<li>総当たり探索はデータ構造を走査してデータを特定する。線形探索は配列と連結リストに適しており、幅優先探索と深さ優先探索はグラフと木に適している。この種のアルゴリズムは汎用性が高く、データの前処理を必要としないが、時間計算量 <span class="arithmatex">\(O(n)\)</span> は高い。</li>
+<li>ハッシュ探索、木探索、二分探索は高効率な探索手法であり、特定のデータ構造内で目的の要素を高速に特定できる。この種のアルゴリズムは効率が高く、時間計算量は <span class="arithmatex">\(O(\log n)\)</span> あるいは <span class="arithmatex">\(O(1)\)</span> に達するが、通常は追加のデータ構造を必要とする。</li>
+<li>実際には、データ規模、探索性能の要件、データの問い合わせ頻度や更新頻度などの要因を具体的に分析し、そのうえで適切な探索手法を選択する必要がある。</li>
+<li>線形探索は小規模または頻繁に更新されるデータに適している。二分探索は大規模でソート済みのデータに適している。ハッシュ探索は問い合わせ効率への要求が高く、範囲検索を必要としないデータに適している。木探索は順序の維持と範囲検索のサポートが必要な大規模動的データに適している。</li>
+<li>ハッシュ探索で線形探索を置き換えることは、実行時間を最適化するための一般的な戦略であり、時間計算量を <span class="arithmatex">\(O(n)\)</span> から <span class="arithmatex">\(O(1)\)</span> へと下げられる。</li>
 </ul>
 
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@@ -4295,7 +4364,7 @@ aria-label="フッター"
   <a
     href="../searching_algorithm_revisited/"
     class="md-footer__link md-footer__link--prev"
-    aria-label="前: 10.5 &amp;nbsp; 探索アルゴリズムの再認識"
+    aria-label="前: 10.5 &amp;nbsp; 探索アルゴリズム再考"
     rel="prev"
   >
     <div class="md-footer__button md-icon">
@@ -4307,7 +4376,7 @@ aria-label="フッター"
         前
       </span>
       <div class="md-ellipsis">
-        10.5 &nbsp; 探索アルゴリズムの再認識
+        10.5 &nbsp; 探索アルゴリズム再考
       </div>
     </div>
   </a>
diff --git a/ja/chapter_sorting/bubble_sort/index.html b/ja/chapter_sorting/bubble_sort/index.html
index 4b9ea9ac6..b0662a216 100644
--- a/ja/chapter_sorting/bubble_sort/index.html
+++ b/ja/chapter_sorting/bubble_sort/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
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     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1635,7 +1635,7 @@
   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1942,7 +1942,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2105,7 +2105,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2491,7 +2491,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2547,7 +2547,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2575,7 +2575,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -2839,7 +2839,7 @@
   <a href="#1131" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.3.1 &nbsp; アルゴリズムプロセス
+        11.3.1 &nbsp; アルゴリズムの流れ
       
     </span>
   </a>
@@ -2861,7 +2861,7 @@
   <a href="#1133" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.3.3 &nbsp; アルゴリズムの特性
+        11.3.3 &nbsp; アルゴリズムの特徴
       
     </span>
   </a>
@@ -3196,7 +3196,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3252,7 +3252,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3280,7 +3280,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3473,7 +3473,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3501,7 +3501,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3642,7 +3642,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3670,7 +3670,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3698,7 +3698,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3726,7 +3726,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3919,7 +3919,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4164,7 +4164,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4310,7 +4310,7 @@
   <a href="#1131" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.3.1 &nbsp; アルゴリズムプロセス
+        11.3.1 &nbsp; アルゴリズムの流れ
       
     </span>
   </a>
@@ -4332,7 +4332,7 @@
   <a href="#1133" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.3.3 &nbsp; アルゴリズムの特性
+        11.3.3 &nbsp; アルゴリズムの特徴
       
     </span>
   </a>
@@ -4377,12 +4377,12 @@
 
 <!-- Page content -->
 <h1 id="113">11.3 &nbsp; バブルソート<a class="headerlink" href="#113" title="Permanent link">&para;</a></h1>
-<p><u>バブルソート</u>は、隣接する要素を継続的に比較し交換することで動作します。このプロセスは泡が底から上に上昇するようなものなので、「バブルソート」と名付けられました。</p>
-<p>下図に示すように、バブリングプロセスは要素交換を使用してシミュレートできます：配列の左端から開始して右に移動し、隣接する要素の各ペアを比較します。左の要素が右の要素より大きい場合は、それらを交換します。横断後、最大要素は配列の右端にバブルアップします。</p>
+<p><u>バブルソート（bubble sort）</u>は、隣接する要素を繰り返し比較して交換することで整列を行います。この過程が泡のように下から上へ浮かび上がることから、バブルソートと呼ばれます。</p>
+<p>次の図に示すように、バブル処理は要素の交換操作によってシミュレートできます。配列の最も左の端から右へ走査し、隣接する要素の大小を順に比較して、「左要素 &gt; 右要素」であれば両者を交換します。走査が終わると、最大の要素は配列の最も右端へ移動します。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:7"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label><label for="__tabbed_1_5">&lt;5&gt;</label><label for="__tabbed_1_6">&lt;6&gt;</label><label for="__tabbed_1_7">&lt;7&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="Simulating bubble process using element swap" class="animation-figure" src="../bubble_sort.assets/bubble_operation_step1.png" /></p>
+<p><img alt="要素の交換操作でバブル処理をシミュレート" class="animation-figure" src="../bubble_sort.assets/bubble_operation_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="bubble_operation_step2" class="animation-figure" src="../bubble_sort.assets/bubble_operation_step2.png" /></p>
@@ -4404,29 +4404,29 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 11-4 &nbsp; Simulating bubble process using element swap </p>
+<p align="center"> 図 11-4 &nbsp; 要素の交換操作でバブル処理をシミュレート </p>
 
-<h2 id="1131">11.3.1 &nbsp; アルゴリズムプロセス<a class="headerlink" href="#1131" title="Permanent link">&para;</a></h2>
-<p>配列の長さを<span class="arithmatex">\(n\)</span>とします。バブルソートのステップは下図に示されます：</p>
+<h2 id="1131">11.3.1 &nbsp; アルゴリズムの流れ<a class="headerlink" href="#1131" title="Permanent link">&para;</a></h2>
+<p>配列の長さを <span class="arithmatex">\(n\)</span> とすると、バブルソートの手順は次の図のとおりです。</p>
 <ol>
-<li>まず、<span class="arithmatex">\(n\)</span>個の要素に対して1回の「バブル」パスを実行し、<strong>最大要素を正しい位置に交換します</strong>。</li>
-<li>次に、残りの<span class="arithmatex">\(n - 1\)</span>個の要素に対して「バブル」パスを実行し、<strong>2番目に大きい要素を正しい位置に交換します</strong>。</li>
-<li>この方法で続行します；<span class="arithmatex">\(n - 1\)</span>回のパスの後、<strong>最大<span class="arithmatex">\(n - 1\)</span>個の要素が正しい位置に移動されます</strong>。</li>
-<li>残りの唯一の要素は**必ず**最小であるため、**さらなる**ソートは必要ありません。この時点で、配列はソートされます。</li>
+<li>まず、<span class="arithmatex">\(n\)</span> 個の要素に対して「バブル処理」を行い、<strong>配列中の最大要素を正しい位置へ交換します</strong>。</li>
+<li>次に、残りの <span class="arithmatex">\(n - 1\)</span> 個の要素に対して「バブル処理」を行い、<strong>2 番目に大きい要素を正しい位置へ交換します</strong>。</li>
+<li>このようにして、<span class="arithmatex">\(n - 1\)</span> 回の「バブル処理」を終えると、<strong>大きいほうから <span class="arithmatex">\(n - 1\)</span> 個の要素がすべて正しい位置へ交換されます</strong>。</li>
+<li>残った 1 つの要素は必ず最小要素なので、並べ替える必要はなく、これで配列のソートが完了します。</li>
 </ol>
-<p><img alt="Bubble sort process" class="animation-figure" src="../bubble_sort.assets/bubble_sort_overview.png" /></p>
-<p align="center"> 図 11-5 &nbsp; Bubble sort process </p>
+<p><img alt="バブルソートの流れ" class="animation-figure" src="../bubble_sort.assets/bubble_sort_overview.png" /></p>
+<p align="center"> 図 11-5 &nbsp; バブルソートの流れ </p>
 
-<p>コード例は以下の通りです：</p>
+<p>コード例は次のとおりです。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">bubble_sort.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
 <a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バブルソート&quot;&quot;&quot;</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
-<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="c1"># 外側のループ：未ソート範囲は [0, i]</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="c1"># 外側のループ：未ソート区間は [0, i]</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
-<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="c1"># 内側のループ：未ソート範囲 [0, i] の最大要素を範囲の右端に移動</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="c1"># 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">i</span><span class="p">):</span>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>            <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]:</span>
 <a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>                <span class="c1"># nums[j] と nums[j + 1] を交換</span>
@@ -4436,13 +4436,13 @@
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">bubble_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* バブルソート */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">bubbleSort</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 外側ループ：未ソート範囲は[0, i]</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="c1">// 内側ループ：未ソート範囲[0, i]内の最大要素を範囲の右端に交換</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">                </span><span class="c1">// nums[j]とnums[j + 1]を交換</span>
-<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">                </span><span class="c1">// ここではstdのswapを使用</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換する</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">                </span><span class="c1">// ここでは std::swap() 関数を使用する</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">                </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="p">}</span>
@@ -4453,9 +4453,9 @@
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">bubble_sort.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* バブルソート */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">bubbleSort</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 外側ループ: 未ソート範囲は [0, i]</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="c1">// 内側ループ: 未ソート範囲 [0, i] の最大要素を範囲の右端に交換</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
@@ -4469,159 +4469,482 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bubble_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">bubble_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BubbleSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bubble_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* バブルソート */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">BubbleSort</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">                </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bubble_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">bubbleSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bubble_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* バブルソート */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">bubbleSort</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">                </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="o">+</span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bubble_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">bubbleSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bubble_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* バブルソート */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">bubbleSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="p">.</span><span class="bp">dropFirst</span><span class="p">().</span><span class="n">reversed</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">                </span><span class="n">nums</span><span class="p">.</span><span class="n">swapAt</span><span class="p">(</span><span class="n">j</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bubble_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">bubbleSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bubble_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* バブルソート */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">bubbleSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">                </span><span class="kd">let</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">                </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">                </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">;</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bubble_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">bubbleSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bubble_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* バブルソート */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">bubbleSort</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">                </span><span class="kd">let</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">                </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">                </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">;</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bubble_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bubbleSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bubble_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* バブルソート */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">bubbleSort</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">    </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">        </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">];</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bubble_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bubble_sort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bubble_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* バブルソート */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">..</span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()).</span><span class="n">rev</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">i</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">                </span><span class="n">nums</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="n">j</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bubble_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bubbleSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bubble_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* バブルソート */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">bubbleSort</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">                </span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">                </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">                </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bubble_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">bubbleSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bubble_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* バブルソート */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">bubbleSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="n">downTo</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">                </span><span class="kd">val</span><span class="w"> </span><span class="nv">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">                </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="o">]</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">                </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bubble_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">bubble_sort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bubble_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### バブルソート ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="c1"># 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">    </span><span class="c1"># 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">i</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">        </span><span class="c1"># nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 459px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20bubble_sort%28nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%22%22%22%E3%83%90%E3%83%96%E3%83%AB%E3%82%BD%E3%83%BC%E3%83%88%22%22%22%0A%20%20%20%20n%20%3D%20len%28nums%29%0A%20%20%20%20%23%20%E5%A4%96%E5%81%B4%E3%81%AE%E3%83%AB%E3%83%BC%E3%83%97%EF%BC%9A%E6%9C%AA%E3%82%BD%E3%83%BC%E3%83%88%E5%8C%BA%E9%96%93%E3%81%AF%20%5B0%2C%20i%5D%0A%20%20%20%20for%20i%20in%20range%28n%20-%201%2C%200%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E5%86%85%E5%81%B4%E3%81%AE%E3%83%AB%E3%83%BC%E3%83%97%EF%BC%9A%E6%9C%AA%E3%82%BD%E3%83%BC%E3%83%88%E5%8C%BA%E9%96%93%20%5B0%2C%20i%5D%20%E3%81%AE%E6%9C%80%E5%A4%A7%E8%A6%81%E7%B4%A0%E3%82%92%E3%81%9D%E3%81%AE%E5%8C%BA%E9%96%93%E3%81%AE%E6%9C%80%E5%8F%B3%E7%AB%AF%E3%81%B8%E4%BA%A4%E6%8F%9B%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28i%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20nums%5Bj%5D%20%3E%20nums%5Bj%20%2B%201%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20nums%5Bj%5D%20%E3%81%A8%20nums%5Bj%20%2B%201%5D%20%E3%82%92%E4%BA%A4%E6%8F%9B%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20nums%5Bj%5D%2C%20nums%5Bj%20%2B%201%5D%20%3D%20nums%5Bj%20%2B%201%5D%2C%20nums%5Bj%5D%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B4%2C%201%2C%203%2C%201%2C%205%2C%202%5D%0A%20%20%20%20bubble_sort%28nums%29%0A%20%20%20%20print%28%22%E3%83%90%E3%83%96%E3%83%AB%E3%82%BD%E3%83%BC%E3%83%88%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%22%2C%20nums%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20bubble_sort%28nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%22%22%22%E3%83%90%E3%83%96%E3%83%AB%E3%82%BD%E3%83%BC%E3%83%88%22%22%22%0A%20%20%20%20n%20%3D%20len%28nums%29%0A%20%20%20%20%23%20%E5%A4%96%E5%81%B4%E3%81%AE%E3%83%AB%E3%83%BC%E3%83%97%EF%BC%9A%E6%9C%AA%E3%82%BD%E3%83%BC%E3%83%88%E5%8C%BA%E9%96%93%E3%81%AF%20%5B0%2C%20i%5D%0A%20%20%20%20for%20i%20in%20range%28n%20-%201%2C%200%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E5%86%85%E5%81%B4%E3%81%AE%E3%83%AB%E3%83%BC%E3%83%97%EF%BC%9A%E6%9C%AA%E3%82%BD%E3%83%BC%E3%83%88%E5%8C%BA%E9%96%93%20%5B0%2C%20i%5D%20%E3%81%AE%E6%9C%80%E5%A4%A7%E8%A6%81%E7%B4%A0%E3%82%92%E3%81%9D%E3%81%AE%E5%8C%BA%E9%96%93%E3%81%AE%E6%9C%80%E5%8F%B3%E7%AB%AF%E3%81%B8%E4%BA%A4%E6%8F%9B%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28i%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20nums%5Bj%5D%20%3E%20nums%5Bj%20%2B%201%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20nums%5Bj%5D%20%E3%81%A8%20nums%5Bj%20%2B%201%5D%20%E3%82%92%E4%BA%A4%E6%8F%9B%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20nums%5Bj%5D%2C%20nums%5Bj%20%2B%201%5D%20%3D%20nums%5Bj%20%2B%201%5D%2C%20nums%5Bj%5D%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B4%2C%201%2C%203%2C%201%2C%205%2C%202%5D%0A%20%20%20%20bubble_sort%28nums%29%0A%20%20%20%20print%28%22%E3%83%90%E3%83%96%E3%83%AB%E3%82%BD%E3%83%BC%E3%83%88%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%22%2C%20nums%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 <h2 id="1132">11.3.2 &nbsp; 効率の最適化<a class="headerlink" href="#1132" title="Permanent link">&para;</a></h2>
-<p>「バブリング」のラウンド中に交換が発生しない場合、配列はすでにソートされているため、すぐに戻ることができます。これを検出するために、<code>flag</code>変数を追加できます；パスで交換が行われない場合は、フラグを設定して早期に戻ります。</p>
-<p>この最適化があっても、バブルソートの最悪時間計算量と平均時間計算量は<span class="arithmatex">\(O(n^2)\)</span>のままです。ただし、入力配列がすでにソートされている場合、最良ケース時間計算量は<span class="arithmatex">\(O(n)\)</span>まで低くなる可能性があります。</p>
+<p>ある回の「バブル処理」で交換操作が一度も行われなければ、配列はすでにソート済みであり、結果をそのまま返せることがわかります。したがって、この状況を検出するためのフラグ <code>flag</code> を追加し、発生した時点で直ちに返すようにできます。</p>
+<p>最適化後も、バブルソートの最悪時間計算量と平均時間計算量は依然として <span class="arithmatex">\(O(n^2)\)</span> です。ただし、入力配列が完全に整列済みであれば、最良時間計算量は <span class="arithmatex">\(O(n)\)</span> に達します。</p>
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 <div class="highlight"><span class="filename">bubble_sort.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">bubble_sort_with_flag</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バブルソート（フラグによる最適化）&quot;&quot;&quot;</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バブルソート（フラグ最適化）&quot;&quot;&quot;</span>
 <a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
-<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="c1"># 外側のループ：未ソート範囲は [0, i]</span>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="c1"># 外側のループ：未ソート区間は [0, i]</span>
 <a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
-<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>        <span class="n">flag</span> <span class="o">=</span> <span class="kc">False</span>  <span class="c1"># フラグを初期化</span>
-<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>        <span class="c1"># 内側のループ：未ソート範囲 [0, i] の最大要素を範囲の右端に移動</span>
+<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>        <span class="n">flag</span> <span class="o">=</span> <span class="kc">False</span>  <span class="c1"># フラグを初期化する</span>
+<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>        <span class="c1"># 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
 <a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">i</span><span class="p">):</span>
 <a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>            <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]:</span>
 <a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>                <span class="c1"># nums[j] と nums[j + 1] を交換</span>
 <a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>                <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
-<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>                <span class="n">flag</span> <span class="o">=</span> <span class="kc">True</span>  <span class="c1"># 要素を交換したことを記録</span>
+<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>                <span class="n">flag</span> <span class="o">=</span> <span class="kc">True</span>  <span class="c1"># 交換する要素を記録</span>
 <a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a>        <span class="k">if</span> <span class="ow">not</span> <span class="n">flag</span><span class="p">:</span>
-<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>            <span class="k">break</span>  <span class="c1"># この回の「バブリング」で要素が交換されなかった場合、終了</span>
+<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>            <span class="k">break</span>  <span class="c1"># このバブル処理で要素交換が一度もなければそのまま終了</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bubble_sort.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* バブルソート（フラグ最適化版）*/</span>
+<div class="highlight"><span class="filename">bubble_sort.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* バブルソート（フラグ最適化） */</span>
 <a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">bubbleSortWithFlag</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="c1">// 外側ループ：未ソート範囲は[0, i]</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
 <a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">        </span><span class="kt">bool</span><span class="w"> </span><span class="n">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">false</span><span class="p">;</span><span class="w"> </span><span class="c1">// フラグを初期化</span>
-<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">        </span><span class="c1">// 内側ループ：未ソート範囲[0, i]内の最大要素を範囲の右端に交換</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">        </span><span class="kt">bool</span><span class="w"> </span><span class="n">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">false</span><span class="p">;</span><span class="w"> </span><span class="c1">// フラグを初期化する</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
 <a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">                </span><span class="c1">// nums[j]とnums[j + 1]を交換</span>
-<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">                </span><span class="c1">// ここではstdのswapを使用</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換する</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">                </span><span class="c1">// ここでは std::swap() 関数を使用する</span>
 <a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">                </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
-<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">                </span><span class="n">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">true</span><span class="p">;</span><span class="w"> </span><span class="c1">// 交換された要素を記録</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">                </span><span class="n">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">true</span><span class="p">;</span><span class="w"> </span><span class="c1">// 交換する要素を記録</span>
 <a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">flag</span><span class="p">)</span>
-<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span><span class="w"> </span><span class="c1">// この回の「バブリング」で要素が交換されなかった場合、終了</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span><span class="w"> </span><span class="c1">// このバブル処理で要素交換が一度もなければそのまま終了</span>
 <a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bubble_sort.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* バブルソート（フラグによる最適化） */</span>
+<div class="highlight"><span class="filename">bubble_sort.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* バブルソート（フラグ最適化） */</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">bubbleSortWithFlag</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 外側ループ: 未ソート範囲は [0, i]</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
 <a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">        </span><span class="kt">boolean</span><span class="w"> </span><span class="n">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span><span class="w"> </span><span class="c1">// フラグを初期化</span>
-<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">        </span><span class="c1">// 内側ループ: 未ソート範囲 [0, i] の最大要素を範囲の右端に交換</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">        </span><span class="kt">boolean</span><span class="w"> </span><span class="n">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span><span class="w"> </span><span class="c1">// フラグを初期化する</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
 <a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
 <a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">                </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">                </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">                </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
-<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">                </span><span class="n">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span><span class="w"> </span><span class="c1">// 交換された要素を記録</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">                </span><span class="n">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span><span class="w"> </span><span class="c1">// 交換する要素を記録</span>
 <a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">flag</span><span class="p">)</span>
-<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span><span class="w"> </span><span class="c1">// この「バブリング」ラウンドで要素が交換されなかった場合、終了</span>
+<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span><span class="w"> </span><span class="c1">// このバブル処理で要素交換が一度もなければそのまま終了</span>
 <a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bubble_sort.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">bubble_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BubbleSortWithFlag</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bubble_sort.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* バブルソート（フラグ最適化） */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">BubbleSortWithFlag</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">        </span><span class="kt">bool</span><span class="w"> </span><span class="n">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">false</span><span class="p">;</span><span class="w"> </span><span class="c1">// フラグを初期化する</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">                </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">                </span><span class="n">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">true</span><span class="p">;</span><span class="w">  </span><span class="c1">// 交換する要素を記録</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">flag</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span><span class="w">     </span><span class="c1">// このバブル処理で要素交換が一度もなければそのまま終了</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bubble_sort.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">bubbleSortWithFlag</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bubble_sort.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* バブルソート（フラグ最適化） */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">bubbleSortWithFlag</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">        </span><span class="nx">flag</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="kc">false</span><span class="w"> </span><span class="c1">// フラグを初期化する</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">                </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="o">+</span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w">                </span><span class="nx">flag</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">true</span><span class="w"> </span><span class="c1">// 交換する要素を記録</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">flag</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">false</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// このバブル処理で要素交換が一度もなければそのまま終了</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bubble_sort.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">bubbleSortWithFlag</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bubble_sort.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* バブルソート（フラグ最適化） */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">bubbleSortWithFlag</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="p">.</span><span class="bp">dropFirst</span><span class="p">().</span><span class="n">reversed</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">flag</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">false</span><span class="w"> </span><span class="c1">// フラグを初期化する</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">                </span><span class="n">nums</span><span class="p">.</span><span class="n">swapAt</span><span class="p">(</span><span class="n">j</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">                </span><span class="n">flag</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">true</span><span class="w"> </span><span class="c1">// 交換する要素を記録</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="o">!</span><span class="n">flag</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// このバブル処理で要素交換が一度もなければそのまま終了</span>
+<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bubble_sort.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">bubbleSortWithFlag</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bubble_sort.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* バブルソート（フラグ最適化） */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">bubbleSortWithFlag</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span><span class="w"> </span><span class="c1">// フラグを初期化する</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w">                </span><span class="kd">let</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w">                </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">                </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">;</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w">                </span><span class="nx">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span><span class="w"> </span><span class="c1">// 交換する要素を記録</span>
+<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="nx">flag</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span><span class="w"> </span><span class="c1">// このバブル処理で要素交換が一度もなければそのまま終了</span>
+<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bubble_sort.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">bubbleSortWithFlag</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bubble_sort.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* バブルソート（フラグ最適化） */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">bubbleSortWithFlag</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span><span class="w"> </span><span class="c1">// フラグを初期化する</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">                </span><span class="kd">let</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w">                </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">                </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">;</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w">                </span><span class="nx">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span><span class="w"> </span><span class="c1">// 交換する要素を記録</span>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="nx">flag</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span><span class="w"> </span><span class="c1">// このバブル処理で要素交換が一度もなければそのまま終了</span>
+<a id="__codelineno-20-17" name="__codelineno-20-17" href="#__codelineno-20-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-18" name="__codelineno-20-18" href="#__codelineno-20-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bubble_sort.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bubbleSortWithFlag</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bubble_sort.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* バブルソート（フラグ最適化） */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">bubbleSortWithFlag</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">    </span><span class="kt">bool</span><span class="w"> </span><span class="n">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span><span class="w"> </span><span class="c1">// フラグを初期化する</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">    </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">        </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">];</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">        </span><span class="n">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span><span class="w"> </span><span class="c1">// 交換する要素を記録</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">flag</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span><span class="w"> </span><span class="c1">// このバブル処理で要素交換が一度もなければそのまま終了</span>
+<a id="__codelineno-21-17" name="__codelineno-21-17" href="#__codelineno-21-17"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-18" name="__codelineno-21-18" href="#__codelineno-21-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bubble_sort.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bubble_sort_with_flag</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bubble_sort.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* バブルソート（フラグ最適化） */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">bubble_sort_with_flag</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">..</span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()).</span><span class="n">rev</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span><span class="w"> </span><span class="c1">// フラグを初期化する</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">i</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w">                </span><span class="n">nums</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="n">j</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w">                </span><span class="n">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span><span class="w"> </span><span class="c1">// 交換する要素を記録</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="o">!</span><span class="n">flag</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span><span class="w"> </span><span class="c1">// このバブル処理で要素交換が一度もなければそのまま終了</span>
+<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="w">        </span><span class="p">};</span>
+<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bubble_sort.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bubbleSortWithFlag</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bubble_sort.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* バブルソート（フラグ最適化） */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">bubbleSortWithFlag</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">        </span><span class="kt">bool</span><span class="w"> </span><span class="n">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">false</span><span class="p">;</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w">                </span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w">                </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w">                </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w">                </span><span class="n">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">true</span><span class="p">;</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">flag</span><span class="p">)</span>
+<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bubble_sort.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">bubbleSortWithFlag</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bubble_sort.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* バブルソート（フラグ最適化） */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">bubbleSortWithFlag</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="c1">// 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="n">downTo</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="w"> </span><span class="c1">// フラグを初期化する</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w">                </span><span class="kd">val</span><span class="w"> </span><span class="nv">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="w">                </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="o">]</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">                </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w">                </span><span class="n">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="w"> </span><span class="c1">// 交換する要素を記録</span>
+<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">flag</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="w"> </span><span class="c1">// このバブル処理で要素交換が一度もなければそのまま終了</span>
+<a id="__codelineno-24-17" name="__codelineno-24-17" href="#__codelineno-24-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-18" name="__codelineno-24-18" href="#__codelineno-24-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bubble_sort.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">bubble_sort_with_flag</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bubble_sort.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### バブルソート ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">  </span><span class="c1"># 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">    </span><span class="c1"># 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">i</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">        </span><span class="c1"># nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="k">end</span>
+<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a>
+<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="c1"># ## バブルソート（フラグ最適化）###</span>
+<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="k">def</span><span class="w"> </span><span class="nf">bubble_sort_with_flag</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a><span class="w">  </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="w">  </span><span class="c1"># 外側のループ：未ソート区間は [0, i]</span>
+<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="w">    </span><span class="n">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kp">false</span><span class="w"> </span><span class="c1"># フラグを初期化する</span>
+<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a>
+<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="w">    </span><span class="c1"># 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換</span>
+<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">i</span>
+<a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
+<a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></a><span class="w">        </span><span class="c1"># nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-25-27" name="__codelineno-25-27" href="#__codelineno-25-27"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-25-28" name="__codelineno-25-28" href="#__codelineno-25-28"></a><span class="w">        </span><span class="n">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kp">true</span><span class="w"> </span><span class="c1"># 交換する要素を記録</span>
+<a id="__codelineno-25-29" name="__codelineno-25-29" href="#__codelineno-25-29"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-25-30" name="__codelineno-25-30" href="#__codelineno-25-30"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-25-31" name="__codelineno-25-31" href="#__codelineno-25-31"></a>
+<a id="__codelineno-25-32" name="__codelineno-25-32" href="#__codelineno-25-32"></a><span class="w">    </span><span class="k">break</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">flag</span><span class="w"> </span><span class="c1"># このバブル処理で要素交換が一度もなければそのまま終了</span>
+<a id="__codelineno-25-33" name="__codelineno-25-33" href="#__codelineno-25-33"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-34" name="__codelineno-25-34" href="#__codelineno-25-34"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h2 id="1133">11.3.3 &nbsp; アルゴリズムの特性<a class="headerlink" href="#1133" title="Permanent link">&para;</a></h2>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 531px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20bubble_sort_with_flag%28nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%22%22%22%E3%83%90%E3%83%96%E3%83%AB%E3%82%BD%E3%83%BC%E3%83%88%EF%BC%88%E3%83%95%E3%83%A9%E3%82%B0%E6%9C%80%E9%81%A9%E5%8C%96%EF%BC%89%22%22%22%0A%20%20%20%20n%20%3D%20len%28nums%29%0A%20%20%20%20%23%20%E5%A4%96%E5%81%B4%E3%81%AE%E3%83%AB%E3%83%BC%E3%83%97%EF%BC%9A%E6%9C%AA%E3%82%BD%E3%83%BC%E3%83%88%E5%8C%BA%E9%96%93%E3%81%AF%20%5B0%2C%20i%5D%0A%20%20%20%20for%20i%20in%20range%28n%20-%201%2C%200%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20flag%20%3D%20False%20%20%23%20%E3%83%95%E3%83%A9%E3%82%B0%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20%23%20%E5%86%85%E5%81%B4%E3%81%AE%E3%83%AB%E3%83%BC%E3%83%97%EF%BC%9A%E6%9C%AA%E3%82%BD%E3%83%BC%E3%83%88%E5%8C%BA%E9%96%93%20%5B0%2C%20i%5D%20%E3%81%AE%E6%9C%80%E5%A4%A7%E8%A6%81%E7%B4%A0%E3%82%92%E3%81%9D%E3%81%AE%E5%8C%BA%E9%96%93%E3%81%AE%E6%9C%80%E5%8F%B3%E7%AB%AF%E3%81%B8%E4%BA%A4%E6%8F%9B%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28i%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20nums%5Bj%5D%20%3E%20nums%5Bj%20%2B%201%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20nums%5Bj%5D%20%E3%81%A8%20nums%5Bj%20%2B%201%5D%20%E3%82%92%E4%BA%A4%E6%8F%9B%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20nums%5Bj%5D%2C%20nums%5Bj%20%2B%201%5D%20%3D%20nums%5Bj%20%2B%201%5D%2C%20nums%5Bj%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20flag%20%3D%20True%20%20%23%20%E4%BA%A4%E6%8F%9B%E3%81%99%E3%82%8B%E8%A6%81%E7%B4%A0%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20%20%20%20%20if%20not%20flag%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20break%20%20%23%20%E3%81%93%E3%81%AE%E3%83%90%E3%83%96%E3%83%AB%E5%87%A6%E7%90%86%E3%81%A7%E8%A6%81%E7%B4%A0%E4%BA%A4%E6%8F%9B%E3%81%8C%E4%B8%80%E5%BA%A6%E3%82%82%E3%81%AA%E3%81%91%E3%82%8C%E3%81%B0%E3%81%9D%E3%81%AE%E3%81%BE%E3%81%BE%E7%B5%82%E4%BA%86%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B4%2C%201%2C%203%2C%201%2C%205%2C%202%5D%0A%20%20%20%20bubble_sort_with_flag%28nums%29%0A%20%20%20%20print%28%22%E3%83%90%E3%83%96%E3%83%AB%E3%82%BD%E3%83%BC%E3%83%88%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%22%2C%20nums%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20bubble_sort_with_flag%28nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%22%22%22%E3%83%90%E3%83%96%E3%83%AB%E3%82%BD%E3%83%BC%E3%83%88%EF%BC%88%E3%83%95%E3%83%A9%E3%82%B0%E6%9C%80%E9%81%A9%E5%8C%96%EF%BC%89%22%22%22%0A%20%20%20%20n%20%3D%20len%28nums%29%0A%20%20%20%20%23%20%E5%A4%96%E5%81%B4%E3%81%AE%E3%83%AB%E3%83%BC%E3%83%97%EF%BC%9A%E6%9C%AA%E3%82%BD%E3%83%BC%E3%83%88%E5%8C%BA%E9%96%93%E3%81%AF%20%5B0%2C%20i%5D%0A%20%20%20%20for%20i%20in%20range%28n%20-%201%2C%200%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20flag%20%3D%20False%20%20%23%20%E3%83%95%E3%83%A9%E3%82%B0%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20%23%20%E5%86%85%E5%81%B4%E3%81%AE%E3%83%AB%E3%83%BC%E3%83%97%EF%BC%9A%E6%9C%AA%E3%82%BD%E3%83%BC%E3%83%88%E5%8C%BA%E9%96%93%20%5B0%2C%20i%5D%20%E3%81%AE%E6%9C%80%E5%A4%A7%E8%A6%81%E7%B4%A0%E3%82%92%E3%81%9D%E3%81%AE%E5%8C%BA%E9%96%93%E3%81%AE%E6%9C%80%E5%8F%B3%E7%AB%AF%E3%81%B8%E4%BA%A4%E6%8F%9B%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28i%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20nums%5Bj%5D%20%3E%20nums%5Bj%20%2B%201%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20nums%5Bj%5D%20%E3%81%A8%20nums%5Bj%20%2B%201%5D%20%E3%82%92%E4%BA%A4%E6%8F%9B%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20nums%5Bj%5D%2C%20nums%5Bj%20%2B%201%5D%20%3D%20nums%5Bj%20%2B%201%5D%2C%20nums%5Bj%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20flag%20%3D%20True%20%20%23%20%E4%BA%A4%E6%8F%9B%E3%81%99%E3%82%8B%E8%A6%81%E7%B4%A0%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20%20%20%20%20if%20not%20flag%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20break%20%20%23%20%E3%81%93%E3%81%AE%E3%83%90%E3%83%96%E3%83%AB%E5%87%A6%E7%90%86%E3%81%A7%E8%A6%81%E7%B4%A0%E4%BA%A4%E6%8F%9B%E3%81%8C%E4%B8%80%E5%BA%A6%E3%82%82%E3%81%AA%E3%81%91%E3%82%8C%E3%81%B0%E3%81%9D%E3%81%AE%E3%81%BE%E3%81%BE%E7%B5%82%E4%BA%86%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B4%2C%201%2C%203%2C%201%2C%205%2C%202%5D%0A%20%20%20%20bubble_sort_with_flag%28nums%29%0A%20%20%20%20print%28%22%E3%83%90%E3%83%96%E3%83%AB%E3%82%BD%E3%83%BC%E3%83%88%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%22%2C%20nums%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h2 id="1133">11.3.3 &nbsp; アルゴリズムの特徴<a class="headerlink" href="#1133" title="Permanent link">&para;</a></h2>
 <ul>
-<li><strong><span class="arithmatex">\(O(n^2)\)</span>の時間計算量、適応ソート。</strong> 各「バブリング」ラウンドは長さ<span class="arithmatex">\(n - 1\)</span>、<span class="arithmatex">\(n - 2\)</span>、<span class="arithmatex">\(\dots\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(1\)</span>の配列セグメントを横断し、合計は<span class="arithmatex">\((n - 1) n / 2\)</span>となります。<code>flag</code>最適化により、配列がすでにソートされている場合、最良ケース時間計算量は<span class="arithmatex">\(O(n)\)</span>に達する可能性があります。</li>
-<li><strong><span class="arithmatex">\(O(1)\)</span>の空間計算量、インプレースソート。</strong> ポインタ<span class="arithmatex">\(i\)</span>と<span class="arithmatex">\(j\)</span>によって定数量の追加空間のみが使用されます。</li>
-<li><strong>安定ソート。</strong> 等しい要素は「バブリング」中に交換されないため、元の順序が保持され、これは安定ソートになります。</li>
+<li><strong>時間計算量は <span class="arithmatex">\(O(n^2)\)</span>、適応的ソート</strong>：各回の「バブル処理」で走査する配列の長さは順に <span class="arithmatex">\(n - 1\)</span>、<span class="arithmatex">\(n - 2\)</span>、<span class="arithmatex">\(\dots\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(1\)</span> であり、その総和は <span class="arithmatex">\((n - 1) n / 2\)</span> です。<code>flag</code> による最適化を導入すると、最良時間計算量は <span class="arithmatex">\(O(n)\)</span> に達します。</li>
+<li><strong>空間計算量は <span class="arithmatex">\(O(1)\)</span>、インプレースソート</strong>：ポインタ <span class="arithmatex">\(i\)</span> と <span class="arithmatex">\(j\)</span> は定数サイズの追加領域しか使用しません。</li>
+<li><strong>安定ソート</strong>：「バブル処理」では等しい要素に出会っても交換しないためです。</li>
 </ul>
 
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diff --git a/ja/chapter_sorting/bucket_sort/index.html b/ja/chapter_sorting/bucket_sort/index.html
index c17400622..d23ede207 100644
--- a/ja/chapter_sorting/bucket_sort/index.html
+++ b/ja/chapter_sorting/bucket_sort/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
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             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
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-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2105,7 +2105,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2491,7 +2491,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2547,7 +2547,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2575,7 +2575,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -2979,7 +2979,7 @@
   <a href="#1181" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.8.1 &nbsp; アルゴリズムの過程
+        11.8.1 &nbsp; アルゴリズムの流れ
       
     </span>
   </a>
@@ -2990,7 +2990,7 @@
   <a href="#1182" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.8.2 &nbsp; アルゴリズムの特徴
+        11.8.2 &nbsp; アルゴリズムの特性
       
     </span>
   </a>
@@ -3001,7 +3001,7 @@
   <a href="#1183" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.8.3 &nbsp; 均等分散を達成する方法
+        11.8.3 &nbsp; 均等な分配を実現するには
       
     </span>
   </a>
@@ -3196,7 +3196,7 @@
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
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-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
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-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
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-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
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-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
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-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4310,7 +4310,7 @@
   <a href="#1181" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.8.1 &nbsp; アルゴリズムの過程
+        11.8.1 &nbsp; アルゴリズムの流れ
       
     </span>
   </a>
@@ -4321,7 +4321,7 @@
   <a href="#1182" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.8.2 &nbsp; アルゴリズムの特徴
+        11.8.2 &nbsp; アルゴリズムの特性
       
     </span>
   </a>
@@ -4332,7 +4332,7 @@
   <a href="#1183" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.8.3 &nbsp; 均等分散を達成する方法
+        11.8.3 &nbsp; 均等な分配を実現するには
       
     </span>
   </a>
@@ -4377,38 +4377,38 @@
 
 <!-- Page content -->
 <h1 id="118">11.8 &nbsp; バケットソート<a class="headerlink" href="#118" title="Permanent link">&para;</a></h1>
-<p>前述のソートアルゴリズムはすべて「比較ベースのソートアルゴリズム」で、値を比較することで要素をソートします。このようなソートアルゴリズムは <span class="arithmatex">\(O(n \log n)\)</span> より良い時間計算量を持つことはできません。次に、線形時間計算量を達成できるいくつかの「非比較ソートアルゴリズム」について議論します。</p>
-<p><u>バケットソート</u>は分割統治戦略の典型的な応用です。一連の順序付けられたバケットを設定し、各バケットがデータの範囲を含み、入力データをこれらのバケットに均等に分散させることで動作します。そして、各バケット内のデータを個別にソートします。最後に、すべてのバケットからのソート済みデータを順次マージして最終結果を生成します。</p>
-<h2 id="1181">11.8.1 &nbsp; アルゴリズムの過程<a class="headerlink" href="#1181" title="Permanent link">&para;</a></h2>
-<p>長さ <span class="arithmatex">\(n\)</span> の配列で、<span class="arithmatex">\([0, 1)\)</span> の範囲の浮動小数点数を考えてみます。バケットソートの過程は以下の図に示されています。</p>
+<p>前述のいくつかのソートアルゴリズムは、いずれも「比較ベースのソートアルゴリズム」に属し、要素間の大小を比較することで整列を実現します。この種のソートアルゴリズムの時間計算量は <span class="arithmatex">\(O(n \log n)\)</span> を超えられません。続いて、時間計算量が線形オーダーに達しうる「非比較ソートアルゴリズム」をいくつか見ていきます。</p>
+<p><u>バケットソート（bucket sort）</u>は分割統治戦略の典型的な応用です。大小関係をもつ複数のバケットを用意し、各バケットがあるデータ範囲に対応するようにして、データを各バケットへ均等に分配します。その後、各バケット内でそれぞれソートを行い、最後にバケットの順序に従ってすべてのデータを結合します。</p>
+<h2 id="1181">11.8.1 &nbsp; アルゴリズムの流れ<a class="headerlink" href="#1181" title="Permanent link">&para;</a></h2>
+<p>長さ <span class="arithmatex">\(n\)</span> の配列を考え、その要素は範囲 <span class="arithmatex">\([0, 1)\)</span> の浮動小数点数であるとします。バケットソートの流れを以下の図に示します。</p>
 <ol>
-<li><span class="arithmatex">\(k\)</span> 個のバケットを初期化し、<span class="arithmatex">\(n\)</span> 個の要素をこれらの <span class="arithmatex">\(k\)</span> 個のバケットに分散させます。</li>
-<li>各バケットを個別にソートします（プログラミング言語の組み込みソート関数を使用）。</li>
-<li>最小から最大のバケットの順序で結果をマージします。</li>
+<li><span class="arithmatex">\(k\)</span> 個のバケットを初期化し、<span class="arithmatex">\(n\)</span> 個の要素を <span class="arithmatex">\(k\)</span> 個のバケットに分配します。</li>
+<li>各バケットに対してそれぞれソートを実行します（ここではプログラミング言語の組み込みソート関数を用います）。</li>
+<li>バケットを小さい順にたどって結果を結合します。</li>
 </ol>
-<p><img alt="バケットソートアルゴリズムの過程" class="animation-figure" src="../bucket_sort.assets/bucket_sort_overview.png" /></p>
-<p align="center"> 図 11-13 &nbsp; バケットソートアルゴリズムの過程 </p>
+<p><img alt="バケットソートの流れ" class="animation-figure" src="../bucket_sort.assets/bucket_sort_overview.png" /></p>
+<p align="center"> 図 11-13 &nbsp; バケットソートの流れ </p>
 
-<p>コードは以下の通りです：</p>
+<p>コードは以下のとおりです：</p>
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 <div class="highlight"><span class="filename">bucket_sort.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">bucket_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">float</span><span class="p">]):</span>
 <a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バケットソート&quot;&quot;&quot;</span>
-<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># k = n/2 個のバケットを初期化、各バケットに平均2個の要素を配置することを期待</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># k = n/2 個のバケットを初期化し、各バケットに 2 要素ずつ割り当てる想定とする</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">k</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="n">buckets</span> <span class="o">=</span> <span class="p">[[]</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">k</span><span class="p">)]</span>
-<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 1. 配列要素を各バケットに分散</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 1. 配列要素を各バケットに振り分ける</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">nums</span><span class="p">:</span>
-<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="c1"># 入力データ範囲は [0, 1)、num * k を使用してインデックス範囲 [0, k-1] にマッピング</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="c1"># 入力データの範囲は [0, 1) であり、num * k を用いてインデックス範囲 [0, k-1] に写像する</span>
 <a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="n">i</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">num</span> <span class="o">*</span> <span class="n">k</span><span class="p">)</span>
 <a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="c1"># num をバケット i に追加</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
-<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="c1"># 2. 各バケットをソート</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="c1"># 2. 各バケットをソートする</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="k">for</span> <span class="n">bucket</span> <span class="ow">in</span> <span class="n">buckets</span><span class="p">:</span>
-<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>        <span class="c1"># 組み込みソート関数を使用、他のソートアルゴリズムに置き換えることも可能</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>        <span class="c1"># 組み込みのソート関数を使う。他のソートアルゴリズムに置き換えてもよい</span>
 <a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>        <span class="n">bucket</span><span class="o">.</span><span class="n">sort</span><span class="p">()</span>
-<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>    <span class="c1"># 3. バケットを走査して結果をマージ</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>    <span class="c1"># 3. バケットを走査して結果を結合</span>
 <a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>    <span class="n">i</span> <span class="o">=</span> <span class="mi">0</span>
 <a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>    <span class="k">for</span> <span class="n">bucket</span> <span class="ow">in</span> <span class="n">buckets</span><span class="p">:</span>
 <a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>        <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">bucket</span><span class="p">:</span>
@@ -4419,22 +4419,22 @@
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">bucket_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* バケットソート */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">bucketSort</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">float</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// k = n/2個のバケットを初期化、各バケットに2つの要素を割り当てることを期待</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// k = n/2 個のバケットを初期化し、各バケットに 2 要素ずつ割り当てる想定とする</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">float</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">buckets</span><span class="p">(</span><span class="n">k</span><span class="p">);</span>
-<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// 1. 配列要素を各バケットに分配</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// 1. 配列要素を各バケットに振り分ける</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">        </span><span class="c1">// 入力データ範囲は[0, 1)、num * kを使用してインデックス範囲[0, k-1]にマップ</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">        </span><span class="c1">// 入力データの範囲は [0, 1) であり、num * k を用いてインデックス範囲 [0, k-1] に写像する</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">k</span><span class="p">;</span>
-<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="c1">// bucket_idxバケットに数値を追加</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="c1">// num をバケット bucket_idx に追加</span>
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">push_back</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="c1">// 2. 各バケットをソート</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="c1">// 2. 各バケットをソートする</span>
 <a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">float</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">bucket</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="c1">// 組み込みソート関数を使用、他のソートアルゴリズムに置き換えることも可能</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="c1">// 組み込みのソート関数を使う。他のソートアルゴリズムに置き換えてもよい</span>
 <a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">        </span><span class="n">sort</span><span class="p">(</span><span class="n">bucket</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">bucket</span><span class="p">.</span><span class="n">end</span><span class="p">());</span>
 <a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="c1">// 3. バケットを走査して結果をマージ</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="c1">// 3. バケットを走査して結果を結合</span>
 <a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">float</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">bucket</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
@@ -4447,25 +4447,25 @@
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">bucket_sort.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* バケットソート */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">bucketSort</span><span class="p">(</span><span class="kt">float</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// k = n/2 個のバケットを初期化、各バケットに期待される要素数は 2 個</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// k = n/2 個のバケットを初期化し、各バケットに 2 要素ずつ割り当てる想定とする</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Float</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">k</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="n">buckets</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">());</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="c1">// 1. 配列要素を各バケットに分散</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="c1">// 1. 配列要素を各バケットに振り分ける</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="c1">// 入力データ範囲は [0, 1)、num * k を使ってインデックス範囲 [0, k-1] にマッピング</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="c1">// 入力データの範囲は [0, 1) であり、num * k を用いてインデックス範囲 [0, k-1] に写像する</span>
 <a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">k</span><span class="p">);</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="c1">// num をバケット i に追加</span>
 <a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">        </span><span class="n">buckets</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">i</span><span class="p">).</span><span class="na">add</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
 <a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="c1">// 2. 各バケットをソート</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="c1">// 2. 各バケットをソートする</span>
 <a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Float</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">        </span><span class="c1">// 組み込みソート関数を使用、他のソートアルゴリズムに置き換えることも可能</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">        </span><span class="c1">// 組み込みのソート関数を使う。他のソートアルゴリズムに置き換えてもよい</span>
 <a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">        </span><span class="n">Collections</span><span class="p">.</span><span class="na">sort</span><span class="p">(</span><span class="n">bucket</span><span class="p">);</span>
 <a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">    </span><span class="c1">// 3. バケットを走査して結果をマージ</span>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">    </span><span class="c1">// 3. バケットを走査して結果を結合</span>
 <a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Float</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
@@ -4476,65 +4476,336 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bucket_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">bucket_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BucketSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bucket_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* バケットソート */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">BucketSort</span><span class="p">(</span><span class="kt">float</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="c1">// k = n/2 個のバケットを初期化し、各バケットに 2 要素ずつ割り当てる想定とする</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">float</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">k</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">        </span><span class="n">buckets</span><span class="p">.</span><span class="n">Add</span><span class="p">([]);</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="c1">// 1. 配列要素を各バケットに振り分ける</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">        </span><span class="c1">// 入力データの範囲は [0, 1) であり、num * k を用いてインデックス範囲 [0, k-1] に写像する</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)(</span><span class="n">num</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">k</span><span class="p">);</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">        </span><span class="c1">// num をバケット i に追加</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">Add</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">    </span><span class="c1">// 2. 各バケットをソートする</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">float</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">        </span><span class="c1">// 組み込みのソート関数を使う。他のソートアルゴリズムに置き換えてもよい</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w">        </span><span class="n">bucket</span><span class="p">.</span><span class="n">Sort</span><span class="p">();</span>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w">    </span><span class="c1">// 3. バケットを走査して結果を結合</span>
+<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">float</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="w">        </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="w">            </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bucket_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">bucketSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bucket_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* バケットソート */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">bucketSort</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">float64</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// k = n/2 個のバケットを初期化し、各バケットに 2 要素ずつ割り当てる想定とする</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">k</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="nx">buckets</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="kt">float64</span><span class="p">,</span><span class="w"> </span><span class="nx">k</span><span class="p">)</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">k</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">        </span><span class="nx">buckets</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">float64</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="c1">// 1. 配列要素を各バケットに振り分ける</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">        </span><span class="c1">// 入力データの範囲は [0, 1) であり、num * k を用いてインデックス範囲 [0, k-1] に写像する</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">        </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">num</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">k</span><span class="p">))</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">        </span><span class="c1">// num をバケット i に追加</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">        </span><span class="nx">buckets</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">    </span><span class="c1">// 2. 各バケットをソートする</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">k</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w">        </span><span class="c1">// 組み込みのスライスソート関数を使う。ほかのソートアルゴリズムに置き換えてもよい</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w">        </span><span class="nx">sort</span><span class="p">.</span><span class="nx">Float64s</span><span class="p">(</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w">    </span><span class="c1">// 3. バケットを走査して結果を結合</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w">    </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">buckets</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="w">            </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">num</span>
+<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="w">            </span><span class="nx">i</span><span class="o">++</span>
+<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bucket_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">bucketSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bucket_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* バケットソート */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">bucketSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Double</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// k = n/2 個のバケットを初期化し、各バケットに 2 要素ずつ割り当てる想定とする</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">k</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">count</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">buckets</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">k</span><span class="p">).</span><span class="bp">map</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">[</span><span class="nb">Double</span><span class="p">]()</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="c1">// 1. 配列要素を各バケットに振り分ける</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">        </span><span class="c1">// 入力データの範囲は [0, 1) であり、num * k を用いてインデックス範囲 [0, k-1] に写像する</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Int</span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">Double</span><span class="p">(</span><span class="n">k</span><span class="p">))</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">        </span><span class="c1">// num をバケット i に追加</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">append</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">    </span><span class="c1">// 2. 各バケットをソートする</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="p">.</span><span class="bp">indices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">        </span><span class="c1">// 組み込みのソート関数を使う。他のソートアルゴリズムに置き換えてもよい</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="bp">sort</span><span class="p">()</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">    </span><span class="c1">// 3. バケットを走査して結果を結合</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">startIndex</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="w">            </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bucket_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">bucketSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bucket_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* バケットソート */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">bucketSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="c1">// k = n/2 個のバケットを初期化し、各バケットに 2 要素ずつ割り当てる想定とする</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">k</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">        </span><span class="nx">buckets</span><span class="p">.</span><span class="nx">push</span><span class="p">([]);</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">    </span><span class="c1">// 1. 配列要素を各バケットに振り分ける</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">        </span><span class="c1">// 入力データの範囲は [0, 1) であり、num * k を用いてインデックス範囲 [0, k-1] に写像する</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nx">num</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">k</span><span class="p">);</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">        </span><span class="c1">// num をバケット i に追加</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">        </span><span class="nx">buckets</span><span class="p">[</span><span class="nx">i</span><span class="p">].</span><span class="nx">push</span><span class="p">(</span><span class="nx">num</span><span class="p">);</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w">    </span><span class="c1">// 2. 各バケットをソートする</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w">        </span><span class="c1">// 組み込みのソート関数を使う。他のソートアルゴリズムに置き換えてもよい</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">        </span><span class="nx">bucket</span><span class="p">.</span><span class="nx">sort</span><span class="p">((</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">b</span><span class="p">);</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w">    </span><span class="c1">// 3. バケットを走査して結果を結合</span>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="w">            </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-27" name="__codelineno-6-27" href="#__codelineno-6-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-28" name="__codelineno-6-28" href="#__codelineno-6-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bucket_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">bucketSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bucket_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* バケットソート */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">bucketSort</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="c1">// k = n/2 個のバケットを初期化し、各バケットに 2 要素ずつ割り当てる想定とする</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">buckets</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[][]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">k</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">        </span><span class="nx">buckets</span><span class="p">.</span><span class="nx">push</span><span class="p">([]);</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="c1">// 1. 配列要素を各バケットに振り分ける</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">        </span><span class="c1">// 入力データの範囲は [0, 1) であり、num * k を用いてインデックス範囲 [0, k-1] に写像する</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nx">num</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">k</span><span class="p">);</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">        </span><span class="c1">// num をバケット i に追加</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">        </span><span class="nx">buckets</span><span class="p">[</span><span class="nx">i</span><span class="p">].</span><span class="nx">push</span><span class="p">(</span><span class="nx">num</span><span class="p">);</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">    </span><span class="c1">// 2. 各バケットをソートする</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">        </span><span class="c1">// 組み込みのソート関数を使う。他のソートアルゴリズムに置き換えてもよい</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">        </span><span class="nx">bucket</span><span class="p">.</span><span class="nx">sort</span><span class="p">((</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">b</span><span class="p">);</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="w">    </span><span class="c1">// 3. バケットを走査して結果を結合</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="w">            </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bucket_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bucketSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bucket_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* バケットソート */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">bucketSort</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">double</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="c1">// k = n/2 個のバケットを初期化し、各バケットに 2 要素ずつ割り当てる想定とする</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">double</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">generate</span><span class="p">(</span><span class="n">k</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">[]);</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="c1">// 1. 配列要素を各バケットに振り分ける</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="w"> </span><span class="n">_num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">    </span><span class="c1">// 入力データの範囲は [0, 1) であり、_num * k を用いてインデックス範囲 [0, k-1] に写像する</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">_num</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">k</span><span class="p">).</span><span class="n">toInt</span><span class="p">();</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">    </span><span class="c1">// _num をバケット bucket_idx に追加</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">    </span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">add</span><span class="p">(</span><span class="n">_num</span><span class="p">);</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">  </span><span class="c1">// 2. 各バケットをソートする</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">double</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">    </span><span class="n">bucket</span><span class="p">.</span><span class="n">sort</span><span class="p">();</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w">  </span><span class="c1">// 3. バケットを走査して結果を結合</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">double</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="w"> </span><span class="n">_num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="w">      </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_num</span><span class="p">;</span>
+<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bucket_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bucket_sort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bucket_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* バケットソート */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">bucket_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">f64</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="c1">// k = n/2 個のバケットを初期化し、各バケットに 2 要素ずつ割り当てる想定とする</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="fm">vec!</span><span class="p">[];</span><span class="w"> </span><span class="n">k</span><span class="p">];</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="c1">// 1. 配列要素を各バケットに振り分ける</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="o">&amp;</span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">iter</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">        </span><span class="c1">// 入力データの範囲は [0, 1) であり、num * k を用いてインデックス範囲 [0, k-1] に写像する</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">f64</span><span class="p">)</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">;</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">        </span><span class="c1">// num をバケット i に追加</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">    </span><span class="c1">// 2. 各バケットをソートする</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">buckets</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">        </span><span class="c1">// 組み込みのソート関数を使う。他のソートアルゴリズムに置き換えてもよい</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">        </span><span class="n">bucket</span><span class="p">.</span><span class="n">sort_by</span><span class="p">(</span><span class="o">|</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="o">|</span><span class="w"> </span><span class="n">a</span><span class="p">.</span><span class="n">partial_cmp</span><span class="p">(</span><span class="n">b</span><span class="p">).</span><span class="n">unwrap</span><span class="p">());</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">    </span><span class="c1">// 3. バケットを走査して結果を結合</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="p">.</span><span class="n">iter</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="o">&amp;</span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span><span class="p">.</span><span class="n">iter</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="w">            </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bucket_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bucketSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bucket_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* バケットソート */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">bucketSort</span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">nums</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">                                 </span><span class="c1">// k = n/2 個のバケットを初期化する</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">sizes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="n">k</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span><span class="w">          </span><span class="c1">// 各バケットのサイズを記録する</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">    </span><span class="kt">float</span><span class="w"> </span><span class="o">**</span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="n">k</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="o">*</span><span class="p">));</span><span class="w"> </span><span class="c1">// 動的配列の配列（バケット）</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="c1">// 各バケットに十分な容量を事前確保する</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">k</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">float</span><span class="p">));</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">        </span><span class="n">sizes</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="c1">// 1. 配列要素を各バケットに振り分ける</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">idx</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">k</span><span class="p">);</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">idx</span><span class="p">][</span><span class="n">sizes</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">    </span><span class="c1">// 2. 各バケットをソートする</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">k</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">        </span><span class="n">qsort</span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">sizes</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">float</span><span class="p">),</span><span class="w"> </span><span class="n">compare</span><span class="p">);</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="w">    </span><span class="c1">// 3. ソート済みのバケットを結合する</span>
+<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">idx</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">k</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">sizes</span><span class="p">[</span><span class="n">i</span><span class="p">];</span><span class="w"> </span><span class="o">++</span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="w">            </span><span class="n">nums</span><span class="p">[</span><span class="n">idx</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="w">        </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="w">        </span><span class="n">free</span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bucket_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">bucketSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bucket_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* バケットソート */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">bucketSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">FloatArray</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="c1">// k = n/2 個のバケットを初期化し、各バケットに 2 要素ずつ割り当てる想定とする</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Float</span><span class="o">&gt;&gt;</span><span class="p">()</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">k</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">        </span><span class="n">buckets</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">mutableListOf</span><span class="p">())</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">    </span><span class="c1">// 1. 配列要素を各バケットに振り分ける</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">        </span><span class="c1">// 入力データの範囲は [0, 1) であり、num * k を用いてインデックス範囲 [0, k-1] に写像する</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">k</span><span class="p">).</span><span class="na">toInt</span><span class="p">()</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">        </span><span class="c1">// num をバケット i に追加</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">        </span><span class="n">buckets</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">    </span><span class="c1">// 2. 各バケットをソートする</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">bucket</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">        </span><span class="c1">// 組み込みのソート関数を使う。他のソートアルゴリズムに置き換えてもよい</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w">        </span><span class="n">bucket</span><span class="p">.</span><span class="na">sort</span><span class="p">()</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="w">    </span><span class="c1">// 3. バケットを走査して結果を結合</span>
+<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">bucket</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="w">            </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">++]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bucket_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">bucket_sort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bucket_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### バケットソート ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">bucket_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># k = n/2 個のバケットを初期化し、各バケットに 2 要素ずつ割り当てる想定とする</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">k</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">[]</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">  </span><span class="c1"># 1. 配列要素を各バケットに振り分ける</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">  </span><span class="n">nums</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="o">|</span><span class="n">num</span><span class="o">|</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">    </span><span class="c1"># 入力データの範囲は [0, 1) であり、num * k を用いてインデックス範囲 [0, k-1] に写像する</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">    </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">k</span><span class="p">)</span><span class="o">.</span><span class="n">to_i</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">    </span><span class="c1"># num をバケット i に追加</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">    </span><span class="n">buckets</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">  </span><span class="c1"># 2. 各バケットをソートする</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">  </span><span class="n">buckets</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="o">|</span><span class="n">bucket</span><span class="o">|</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">    </span><span class="c1"># 組み込みのソート関数を使う。他のソートアルゴリズムに置き換えてもよい</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w">    </span><span class="n">bucket</span><span class="o">.</span><span class="n">sort!</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w">  </span><span class="c1"># 3. バケットを走査して結果を結合</span>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w">  </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="w">  </span><span class="n">buckets</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="o">|</span><span class="n">bucket</span><span class="o">|</span>
+<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a><span class="w">    </span><span class="n">bucket</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="o">|</span><span class="n">num</span><span class="o">|</span>
+<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="w">      </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a><span class="w">      </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h2 id="1182">11.8.2 &nbsp; アルゴリズムの特徴<a class="headerlink" href="#1182" title="Permanent link">&para;</a></h2>
-<p>バケットソートは非常に大きなデータセットの処理に適しています。例えば、入力データに100万個の要素が含まれ、システムメモリの制限によりすべてのデータを同時にロードできない場合、データを1,000個のバケットに分割し、各バケットを個別にソートしてから結果をマージできます。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20bucket_sort%28nums%3A%20list%5Bfloat%5D%29%3A%0A%20%20%20%20%22%22%22%E3%83%90%E3%82%B1%E3%83%83%E3%83%88%E3%82%BD%E3%83%BC%E3%83%88%22%22%22%0A%20%20%20%20%23%20k%20%3D%20n%2F2%20%E5%80%8B%E3%81%AE%E3%83%90%E3%82%B1%E3%83%83%E3%83%88%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%97%E3%80%81%E5%90%84%E3%83%90%E3%82%B1%E3%83%83%E3%83%88%E3%81%AB%202%20%E8%A6%81%E7%B4%A0%E3%81%9A%E3%81%A4%E5%89%B2%E3%82%8A%E5%BD%93%E3%81%A6%E3%82%8B%E6%83%B3%E5%AE%9A%E3%81%A8%E3%81%99%E3%82%8B%0A%20%20%20%20k%20%3D%20len%28nums%29%20%2F%2F%202%0A%20%20%20%20buckets%20%3D%20%5B%5B%5D%20for%20_%20in%20range%28k%29%5D%0A%20%20%20%20%23%201.%20%E9%85%8D%E5%88%97%E8%A6%81%E7%B4%A0%E3%82%92%E5%90%84%E3%83%90%E3%82%B1%E3%83%83%E3%83%88%E3%81%AB%E6%8C%AF%E3%82%8A%E5%88%86%E3%81%91%E3%82%8B%0A%20%20%20%20for%20num%20in%20nums%3A%0A%20%20%20%20%20%20%20%20%23%20%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%81%AE%E7%AF%84%E5%9B%B2%E3%81%AF%20%5B0%2C%201%29%20%E3%81%A7%E3%81%82%E3%82%8A%E3%80%81num%20%2A%20k%20%E3%82%92%E7%94%A8%E3%81%84%E3%81%A6%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E7%AF%84%E5%9B%B2%20%5B0%2C%20k-1%5D%20%E3%81%AB%E5%86%99%E5%83%8F%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20i%20%3D%20int%28num%20%2A%20k%29%0A%20%20%20%20%20%20%20%20%23%20num%20%E3%82%92%E3%83%90%E3%82%B1%E3%83%83%E3%83%88%20i%20%E3%81%AB%E8%BF%BD%E5%8A%A0%0A%20%20%20%20%20%20%20%20buckets%5Bi%5D.append%28num%29%0A%20%20%20%20%23%202.%20%E5%90%84%E3%83%90%E3%82%B1%E3%83%83%E3%83%88%E3%82%92%E3%82%BD%E3%83%BC%E3%83%88%E3%81%99%E3%82%8B%0A%20%20%20%20for%20bucket%20in%20buckets%3A%0A%20%20%20%20%20%20%20%20%23%20%E7%B5%84%E3%81%BF%E8%BE%BC%E3%81%BF%E3%81%AE%E3%82%BD%E3%83%BC%E3%83%88%E9%96%A2%E6%95%B0%E3%82%92%E4%BD%BF%E3%81%86%E3%80%82%E4%BB%96%E3%81%AE%E3%82%BD%E3%83%BC%E3%83%88%E3%82%A2%E3%83%AB%E3%82%B4%E3%83%AA%E3%82%BA%E3%83%A0%E3%81%AB%E7%BD%AE%E3%81%8D%E6%8F%9B%E3%81%88%E3%81%A6%E3%82%82%E3%82%88%E3%81%84%0A%20%20%20%20%20%20%20%20bucket.sort%28%29%0A%20%20%20%20%23%203.%20%E3%83%90%E3%82%B1%E3%83%83%E3%83%88%E3%82%92%E8%B5%B0%E6%9F%BB%E3%81%97%E3%81%A6%E7%B5%90%E6%9E%9C%E3%82%92%E7%B5%90%E5%90%88%0A%20%20%20%20i%20%3D%200%0A%20%20%20%20for%20bucket%20in%20buckets%3A%0A%20%20%20%20%20%20%20%20for%20num%20in%20bucket%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20nums%5Bi%5D%20%3D%20num%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%2B%3D%201%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%81%AF%E7%AF%84%E5%9B%B2%20%5B0%2C%201%29%20%E3%81%AE%E6%B5%AE%E5%8B%95%E5%B0%8F%E6%95%B0%E7%82%B9%E6%95%B0%E3%81%A8%E3%81%99%E3%82%8B%0A%20%20%20%20nums%20%3D%20%5B0.49%2C%200.96%2C%200.82%2C%200.09%2C%200.57%2C%200.43%2C%200.91%2C%200.75%2C%200.15%2C%200.37%5D%0A%20%20%20%20bucket_sort%28nums%29%0A%20%20%20%20print%28%22%E3%83%90%E3%82%B1%E3%83%83%E3%83%88%E3%82%BD%E3%83%BC%E3%83%88%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%22%2C%20nums%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20bucket_sort%28nums%3A%20list%5Bfloat%5D%29%3A%0A%20%20%20%20%22%22%22%E3%83%90%E3%82%B1%E3%83%83%E3%83%88%E3%82%BD%E3%83%BC%E3%83%88%22%22%22%0A%20%20%20%20%23%20k%20%3D%20n%2F2%20%E5%80%8B%E3%81%AE%E3%83%90%E3%82%B1%E3%83%83%E3%83%88%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%97%E3%80%81%E5%90%84%E3%83%90%E3%82%B1%E3%83%83%E3%83%88%E3%81%AB%202%20%E8%A6%81%E7%B4%A0%E3%81%9A%E3%81%A4%E5%89%B2%E3%82%8A%E5%BD%93%E3%81%A6%E3%82%8B%E6%83%B3%E5%AE%9A%E3%81%A8%E3%81%99%E3%82%8B%0A%20%20%20%20k%20%3D%20len%28nums%29%20%2F%2F%202%0A%20%20%20%20buckets%20%3D%20%5B%5B%5D%20for%20_%20in%20range%28k%29%5D%0A%20%20%20%20%23%201.%20%E9%85%8D%E5%88%97%E8%A6%81%E7%B4%A0%E3%82%92%E5%90%84%E3%83%90%E3%82%B1%E3%83%83%E3%83%88%E3%81%AB%E6%8C%AF%E3%82%8A%E5%88%86%E3%81%91%E3%82%8B%0A%20%20%20%20for%20num%20in%20nums%3A%0A%20%20%20%20%20%20%20%20%23%20%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%81%AE%E7%AF%84%E5%9B%B2%E3%81%AF%20%5B0%2C%201%29%20%E3%81%A7%E3%81%82%E3%82%8A%E3%80%81num%20%2A%20k%20%E3%82%92%E7%94%A8%E3%81%84%E3%81%A6%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E7%AF%84%E5%9B%B2%20%5B0%2C%20k-1%5D%20%E3%81%AB%E5%86%99%E5%83%8F%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20i%20%3D%20int%28num%20%2A%20k%29%0A%20%20%20%20%20%20%20%20%23%20num%20%E3%82%92%E3%83%90%E3%82%B1%E3%83%83%E3%83%88%20i%20%E3%81%AB%E8%BF%BD%E5%8A%A0%0A%20%20%20%20%20%20%20%20buckets%5Bi%5D.append%28num%29%0A%20%20%20%20%23%202.%20%E5%90%84%E3%83%90%E3%82%B1%E3%83%83%E3%83%88%E3%82%92%E3%82%BD%E3%83%BC%E3%83%88%E3%81%99%E3%82%8B%0A%20%20%20%20for%20bucket%20in%20buckets%3A%0A%20%20%20%20%20%20%20%20%23%20%E7%B5%84%E3%81%BF%E8%BE%BC%E3%81%BF%E3%81%AE%E3%82%BD%E3%83%BC%E3%83%88%E9%96%A2%E6%95%B0%E3%82%92%E4%BD%BF%E3%81%86%E3%80%82%E4%BB%96%E3%81%AE%E3%82%BD%E3%83%BC%E3%83%88%E3%82%A2%E3%83%AB%E3%82%B4%E3%83%AA%E3%82%BA%E3%83%A0%E3%81%AB%E7%BD%AE%E3%81%8D%E6%8F%9B%E3%81%88%E3%81%A6%E3%82%82%E3%82%88%E3%81%84%0A%20%20%20%20%20%20%20%20bucket.sort%28%29%0A%20%20%20%20%23%203.%20%E3%83%90%E3%82%B1%E3%83%83%E3%83%88%E3%82%92%E8%B5%B0%E6%9F%BB%E3%81%97%E3%81%A6%E7%B5%90%E6%9E%9C%E3%82%92%E7%B5%90%E5%90%88%0A%20%20%20%20i%20%3D%200%0A%20%20%20%20for%20bucket%20in%20buckets%3A%0A%20%20%20%20%20%20%20%20for%20num%20in%20bucket%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20nums%5Bi%5D%20%3D%20num%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%2B%3D%201%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%81%AF%E7%AF%84%E5%9B%B2%20%5B0%2C%201%29%20%E3%81%AE%E6%B5%AE%E5%8B%95%E5%B0%8F%E6%95%B0%E7%82%B9%E6%95%B0%E3%81%A8%E3%81%99%E3%82%8B%0A%20%20%20%20nums%20%3D%20%5B0.49%2C%200.96%2C%200.82%2C%200.09%2C%200.57%2C%200.43%2C%200.91%2C%200.75%2C%200.15%2C%200.37%5D%0A%20%20%20%20bucket_sort%28nums%29%0A%20%20%20%20print%28%22%E3%83%90%E3%82%B1%E3%83%83%E3%83%88%E3%82%BD%E3%83%BC%E3%83%88%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%22%2C%20nums%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h2 id="1182">11.8.2 &nbsp; アルゴリズムの特性<a class="headerlink" href="#1182" title="Permanent link">&para;</a></h2>
+<p>バケットソートは、非常に大規模なデータの処理に適しています。たとえば、入力データに 100 万個の要素が含まれ、空間の制約によりシステムメモリへすべてのデータを一度に読み込めない場合です。このとき、データを 1000 個のバケットに分け、それぞれのバケットを個別にソートしてから、最後に結果を結合できます。</p>
 <ul>
-<li><strong>時間計算量は <span class="arithmatex">\(O(n + k)\)</span></strong>：要素がバケット間で均等に分散されていると仮定すると、各バケット内の要素数は <span class="arithmatex">\(n/k\)</span> です。単一のバケットのソートに <span class="arithmatex">\(O(n/k \log(n/k))\)</span> 時間がかかると仮定すると、すべてのバケットのソートに <span class="arithmatex">\(O(n \log(n/k))\)</span> 時間がかかります。<strong>バケット数 <span class="arithmatex">\(k\)</span> が比較的大きいとき、時間計算量は <span class="arithmatex">\(O(n)\)</span> に近づきます</strong>。結果のマージには、すべてのバケットと要素を走査する必要があり、<span class="arithmatex">\(O(n + k)\)</span> 時間がかかります。最悪の場合、すべてのデータが単一のバケットに分散され、そのバケットのソートには <span class="arithmatex">\(O(n^2)\)</span> 時間がかかります。</li>
-<li><strong>空間計算量は <span class="arithmatex">\(O(n + k)\)</span>、非インプレースソート</strong>：<span class="arithmatex">\(k\)</span> 個のバケットと合計 <span class="arithmatex">\(n\)</span> 個の要素のための追加スペースが必要です。</li>
-<li>バケットソートが安定かどうかは、各バケット内で使用されるソートアルゴリズムが安定かどうかに依存します。</li>
+<li><strong>時間計算量は <span class="arithmatex">\(O(n + k)\)</span></strong> ：要素が各バケット内に平均的に分布していると仮定すると、各バケット内の要素数は <span class="arithmatex">\(\frac{n}{k}\)</span> です。1 つのバケットをソートするのに <span class="arithmatex">\(O(\frac{n}{k} \log\frac{n}{k})\)</span> の時間がかかるなら、すべてのバケットのソートには <span class="arithmatex">\(O(n \log\frac{n}{k})\)</span> の時間がかかります。<strong>バケット数 <span class="arithmatex">\(k\)</span> が十分大きいとき、時間計算量は <span class="arithmatex">\(O(n)\)</span> に近づきます</strong>。結果を結合する際には、すべてのバケットと要素を走査する必要があり、<span class="arithmatex">\(O(n + k)\)</span> の時間を要します。最悪の場合、すべてのデータが 1 つのバケットに割り当てられ、そのバケットのソートに <span class="arithmatex">\(O(n^2)\)</span> の時間がかかります。</li>
+<li><strong>空間計算量は <span class="arithmatex">\(O(n + k)\)</span>、非インプレースソート</strong>：<span class="arithmatex">\(k\)</span> 個のバケットと合計 <span class="arithmatex">\(n\)</span> 個の要素ぶんの追加領域が必要です。</li>
+<li>バケットソートが安定かどうかは、バケット内要素のソートに用いるアルゴリズムが安定かどうかに依存します。</li>
 </ul>
-<h2 id="1183">11.8.3 &nbsp; 均等分散を達成する方法<a class="headerlink" href="#1183" title="Permanent link">&para;</a></h2>
-<p>バケットソートの理論的時間計算量は <span class="arithmatex">\(O(n)\)</span> に達することができます。<strong>重要なことは、すべてのバケットに要素を均等に分散させることです</strong>。実世界のデータはしばしば均一に分散されていないからです。例えば、eBayのすべての商品を価格範囲で10個のバケットに均等に分散させたいとします。しかし、商品価格の分散は均等でない可能性があり、100ドル未満の商品が多く、500ドル以上の商品が少ないかもしれません。価格範囲を均等に10分割すると、各バケットの商品数の差が大きくなります。</p>
-<p>均等分散を達成するために、最初におおよその境界を設定して、データを3つのバケットに大まかに分割できます。<strong>分散が完了した後、より多くのアイテムを持つバケットをさらに3つのバケットに分割し、すべてのバケットの要素数がほぼ等しくなるまで続けます</strong>。</p>
-<p>以下の図に示すように、この方法は本質的に再帰木を構築し、葉ノードの要素数ができるだけ均等になることを目指します。もちろん、各ラウンドでデータを3つのバケットに分割する必要はありません - 分割戦略はデータの独特な特性に適応的に調整できます。</p>
-<p><img alt="バケットの再帰的分割" class="animation-figure" src="../bucket_sort.assets/scatter_in_buckets_recursively.png" /></p>
-<p align="center"> 図 11-14 &nbsp; バケットの再帰的分割 </p>
+<h2 id="1183">11.8.3 &nbsp; 均等な分配を実現するには<a class="headerlink" href="#1183" title="Permanent link">&para;</a></h2>
+<p>バケットソートの時間計算量は理論上 <span class="arithmatex">\(O(n)\)</span> に達しますが、<strong>鍵は要素を各バケットへ均等に分配すること</strong> にあります。実際のデータは均一に分布していないことが多いからです。たとえば、Taobao 上のすべての商品を価格帯ごとに 10 個のバケットへ均等に分けたいとしても、商品の価格分布は偏っており、100 元未満は非常に多く、1000 元超は非常に少ないかもしれません。価格区間を単純に 10 等分すると、各バケットの商品数には大きな差が生じます。</p>
+<p>均等な分配を実現するために、まず大まかな境界線を設定し、データをひとまず 3 個のバケットに粗く振り分けます。<strong>分配後は、商品数の多いバケットをさらに 3 個のバケットに分割し、すべてのバケット内の要素数がおおむね等しくなるまでこれを続けます</strong>。</p>
+<p>以下の図に示すように、この方法の本質は再帰木を構築することにあり、目標は葉ノードの値をできるだけ均等にすることです。もちろん、毎回データを 3 個のバケットに分割する必要はなく、具体的な分け方はデータの特徴に応じて柔軟に選べます。</p>
+<p><img alt="再帰的にバケットを分割" class="animation-figure" src="../bucket_sort.assets/scatter_in_buckets_recursively.png" /></p>
+<p align="center"> 図 11-14 &nbsp; 再帰的にバケットを分割 </p>
 
-<p>商品価格の確率分布を事前に知っている場合、<strong>データの確率分布に基づいて各バケットの価格境界を設定できます</strong>。データ分布を具体的に計算する必要は必ずしもなく、代わりに確率モデルを使用してデータ特性に基づいて近似できることに注意してください。</p>
-<p>以下の図に示すように、商品価格が正規分布に従うと仮定すると、バケット間でアイテムの分散のバランスを取るために合理的な価格区間を定義できます。</p>
-<p><img alt="確率分布に基づくバケット分割" class="animation-figure" src="../bucket_sort.assets/scatter_in_buckets_distribution.png" /></p>
-<p align="center"> 図 11-15 &nbsp; 確率分布に基づくバケット分割 </p>
+<p>商品価格の確率分布をあらかじめ把握しているなら、<strong>データの確率分布に基づいて各バケットの価格境界を設定できます</strong>。なお、データ分布は必ずしも特別に統計を取る必要はなく、データの特徴に応じて何らかの確率モデルで近似することもできます。</p>
+<p>以下の図に示すように、商品価格が正規分布に従うと仮定すれば、価格区間を合理的に設定でき、それによって商品を各バケットへ均等に分配できます。</p>
+<p><img alt="確率分布に基づいてバケットを分割" class="animation-figure" src="../bucket_sort.assets/scatter_in_buckets_distribution.png" /></p>
+<p align="center"> 図 11-15 &nbsp; 確率分布に基づいてバケットを分割 </p>
 
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       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1635,7 +1635,7 @@
   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1942,7 +1942,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2105,7 +2105,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2491,7 +2491,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2547,7 +2547,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2575,7 +2575,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3007,7 +3007,7 @@
   <a href="#1191" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.9.1 &nbsp; 簡単な実装
+        11.9.1 &nbsp; 単純な実装
       
     </span>
   </a>
@@ -3029,7 +3029,7 @@
   <a href="#1193" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.9.3 &nbsp; アルゴリズムの特徴
+        11.9.3 &nbsp; アルゴリズムの特性
       
     </span>
   </a>
@@ -3040,7 +3040,7 @@
   <a href="#1194" class="md-nav__link">
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-        11.9.4 &nbsp; 制限事項
+        11.9.4 &nbsp; 制約
       
     </span>
   </a>
@@ -3207,7 +3207,7 @@
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3263,7 +3263,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3291,7 +3291,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3484,7 +3484,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3512,7 +3512,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3653,7 +3653,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3681,7 +3681,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3709,7 +3709,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3737,7 +3737,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3930,7 +3930,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4175,7 +4175,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4321,7 +4321,7 @@
   <a href="#1191" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.9.1 &nbsp; 簡単な実装
+        11.9.1 &nbsp; 単純な実装
       
     </span>
   </a>
@@ -4343,7 +4343,7 @@
   <a href="#1193" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.9.3 &nbsp; アルゴリズムの特徴
+        11.9.3 &nbsp; アルゴリズムの特性
       
     </span>
   </a>
@@ -4354,7 +4354,7 @@
   <a href="#1194" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.9.4 &nbsp; 制限事項
+        11.9.4 &nbsp; 制約
       
     </span>
   </a>
@@ -4399,57 +4399,55 @@
 
 <!-- Page content -->
 <h1 id="119">11.9 &nbsp; 計数ソート<a class="headerlink" href="#119" title="Permanent link">&para;</a></h1>
-<p><u>計数ソート</u>は要素の数をカウントすることでソートを実現し、通常は整数配列に適用されます。</p>
-<h2 id="1191">11.9.1 &nbsp; 簡単な実装<a class="headerlink" href="#1191" title="Permanent link">&para;</a></h2>
-<p>簡単な例から始めましょう。長さ <span class="arithmatex">\(n\)</span> の配列 <code>nums</code> が与えられ、すべての要素が「非負整数」である場合、計数ソートの全体的な過程は以下の図に示されています。</p>
+<p><u>計数ソート（counting sort）</u>は要素数を集計することでソートを実現し、通常は整数配列に適用されます。</p>
+<h2 id="1191">11.9.1 &nbsp; 単純な実装<a class="headerlink" href="#1191" title="Permanent link">&para;</a></h2>
+<p>まず簡単な例を見てみましょう。長さ <span class="arithmatex">\(n\)</span> の配列 <code>nums</code> が与えられ、その要素はすべて「非負整数」であるとします。計数ソートの全体的な流れを以下の図に示します。</p>
 <ol>
-<li>配列を走査して最大数を見つけ、それを <span class="arithmatex">\(m\)</span> とし、長さ <span class="arithmatex">\(m + 1\)</span> の補助配列 <code>counter</code> を作成します。</li>
-<li><strong><code>counter</code> を使用して <code>nums</code> 内の各数の出現回数をカウントします</strong>。ここで <code>counter[num]</code> は数 <code>num</code> の出現回数に対応します。カウント方法は簡単で、<code>nums</code> を走査し（現在の数を <code>num</code> とする）、各ラウンドで <code>counter[num]</code> を <span class="arithmatex">\(1\)</span> 増やします。</li>
-<li><strong><code>counter</code> のインデックスは自然に順序付けられているため、すべての数は本質的にすでにソートされています</strong>。次に、<code>counter</code> を走査し、出現順に <code>nums</code> を昇順で埋めます。</li>
+<li>配列を走査し、その中の最大値を見つけて <span class="arithmatex">\(m\)</span> とし、続いて長さ <span class="arithmatex">\(m + 1\)</span> の補助配列 <code>counter</code> を作成します。</li>
+<li><strong><code>counter</code> を用いて <code>nums</code> 内の各数値の出現回数を集計します</strong>。ここで <code>counter[num]</code> は数値 <code>num</code> の出現回数に対応します。集計方法は非常に簡単で、<code>nums</code> を走査し（現在の数値を <code>num</code> とする）、各回で <code>counter[num]</code> を <span class="arithmatex">\(1\)</span> 増やせばよいです。</li>
+<li><strong><code>counter</code> の各インデックスは自然に順序づけられているため、すべての数値はすでに整列された状態とみなせます</strong>。続いて <code>counter</code> を走査し、各数値の出現回数に応じて小さい順に <code>nums</code> へ書き戻せば完了です。</li>
 </ol>
-<p><img alt="計数ソートの過程" class="animation-figure" src="../counting_sort.assets/counting_sort_overview.png" /></p>
-<p align="center"> 図 11-16 &nbsp; 計数ソートの過程 </p>
+<p><img alt="計数ソートの流れ" class="animation-figure" src="../counting_sort.assets/counting_sort_overview.png" /></p>
+<p align="center"> 図 11-16 &nbsp; 計数ソートの流れ </p>
 
-<p>コードは以下の通りです：</p>
+<p>コードは以下のとおりです：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">counting_sort.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">counting_sort_naive</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
 <a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;計数ソート&quot;&quot;&quot;</span>
-<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># シンプルな実装、オブジェクトのソートには使用できない</span>
-<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="c1"># 1. 配列内の最大要素 m を統計</span>
-<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="n">m</span> <span class="o">=</span> <span class="mi">0</span>
-<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">nums</span><span class="p">:</span>
-<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="n">m</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">num</span><span class="p">)</span>
-<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="c1"># 2. 各数字の出現回数を統計</span>
-<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="c1"># counter[num] は num の出現回数を表す</span>
-<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="n">counter</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">nums</span><span class="p">:</span>
-<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
-<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="c1"># 3. counter を走査し、各要素を元の配列 nums に埋め戻し</span>
-<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="n">i</span> <span class="o">=</span> <span class="mi">0</span>
-<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
-<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>        <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]):</span>
-<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>            <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>
-<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>            <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 簡易版。オブジェクトのソートには使えない</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="c1"># 1. 配列の最大要素 m を求める</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="n">m</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 2. 各数値の出現回数を数える</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="c1"># counter[num] は num の出現回数を表す</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="n">counter</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">nums</span><span class="p">:</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="c1"># 3. counter を走査し、各要素を元の配列 nums に書き戻す</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="n">i</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>        <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]):</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>            <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>            <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* カウントソート */</span>
-<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// 簡単な実装、オブジェクトのソートには使用できない</span>
+<div class="highlight"><span class="filename">counting_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 計数ソート */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// 簡易実装のため、オブジェクトのソートには使えない</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="kt">void</span><span class="w"> </span><span class="nf">countingSortNaive</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素mを統計</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素 m を求める</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">        </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">);</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="c1">// 2. 各数字の出現回数を統計</span>
-<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="c1">// counter[num]はnumの出現回数を表す</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="c1">// 2. 各数値の出現回数を数える</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="c1">// counter[num] は num の出現回数を表す</span>
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">counter</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span><span class="o">++</span><span class="p">;</span>
 <a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="c1">// 3. counterを走査し、各要素を元の配列numsに戻す</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="c1">// 3. counter を走査し、各要素を元の配列 nums に書き戻す</span>
 <a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">num</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">];</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
@@ -4461,20 +4459,20 @@
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">counting_sort.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 計数ソート */</span>
-<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="c1">// 簡単な実装、オブジェクトのソートには使用できない</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="c1">// 簡易実装のため、オブジェクトのソートには使えない</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="kt">void</span><span class="w"> </span><span class="nf">countingSortNaive</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素 m を統計</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素 m を求める</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">max</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">);</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="c1">// 2. 各数字の出現回数を統計</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="c1">// 2. 各数値の出現回数を数える</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="c1">// counter[num] は num の出現回数を表す</span>
 <a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="n">counter</span><span class="o">[</span><span class="n">num</span><span class="o">]++</span><span class="p">;</span>
 <a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="c1">// 3. counter を走査し、各要素を元の配列 nums に戻す</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="c1">// 3. counter を走査し、各要素を元の配列 nums に書き戻す</span>
 <a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">num</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">counter</span><span class="o">[</span><span class="n">num</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
@@ -4485,67 +4483,278 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">counting_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">CountingSortNaive</span><span class="p">}</span>
+<div class="highlight"><span class="filename">counting_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 計数ソート */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="c1">// 簡易実装のため、オブジェクトのソートには使えない</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="k">void</span><span class="w"> </span><span class="nf">CountingSortNaive</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素 m を求める</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">        </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Max</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="c1">// 2. 各数値の出現回数を数える</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">    </span><span class="c1">// counter[num] は num の出現回数を表す</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">    </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">    </span><span class="c1">// 3. counter を走査し、各要素を元の配列 nums に書き戻す</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">num</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">];</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w">            </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">countingSortNaive</span><span class="p">}</span>
+<div class="highlight"><span class="filename">counting_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 計数ソート */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="c1">// 簡易実装のため、オブジェクトのソートには使えない</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="kd">func</span><span class="w"> </span><span class="nx">countingSortNaive</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素 m を求める</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="nx">m</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">            </span><span class="nx">m</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">num</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">    </span><span class="c1">// 2. 各数値の出現回数を数える</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">    </span><span class="c1">// counter[num] は num の出現回数を表す</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">    </span><span class="nx">counter</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">        </span><span class="nx">counter</span><span class="p">[</span><span class="nx">num</span><span class="p">]</span><span class="o">++</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">    </span><span class="c1">// 3. counter を走査し、各要素を元の配列 nums に書き戻す</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="o">+</span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">num</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">counter</span><span class="p">[</span><span class="nx">num</span><span class="p">];</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w">            </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">num</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w">            </span><span class="nx">i</span><span class="o">++</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">countingSortNaive</span><span class="p">}</span>
+<div class="highlight"><span class="filename">counting_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 計数ソート */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="c1">// 簡易実装のため、オブジェクトのソートには使えない</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">func</span><span class="w"> </span><span class="nf">countingSortNaive</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素 m を求める</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">max</span><span class="p">()</span><span class="o">!</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="c1">// 2. 各数値の出現回数を数える</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="c1">// counter[num] は num の出現回数を表す</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">counter</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">    </span><span class="c1">// 3. counter を走査し、各要素を元の配列 nums に書き戻す</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">            </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">countingSortNaive</span><span class="p">}</span>
+<div class="highlight"><span class="filename">counting_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 計数ソート */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="c1">// 簡易実装のため、オブジェクトのソートには使えない</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="kd">function</span><span class="w"> </span><span class="nx">countingSortNaive</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素 m を求める</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">max</span><span class="p">(...</span><span class="nx">nums</span><span class="p">);</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="c1">// 2. 各数値の出現回数を数える</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="c1">// counter[num] は num の出現回数を表す</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">        </span><span class="nx">counter</span><span class="p">[</span><span class="nx">num</span><span class="p">]</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">    </span><span class="c1">// 3. counter を走査し、各要素を元の配列 nums に書き戻す</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">num</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">counter</span><span class="p">[</span><span class="nx">num</span><span class="p">];</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w">            </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">countingSortNaive</span><span class="p">}</span>
+<div class="highlight"><span class="filename">counting_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 計数ソート */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="c1">// 簡易実装のため、オブジェクトのソートには使えない</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="kd">function</span><span class="w"> </span><span class="nx">countingSortNaive</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素 m を求める</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">m</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">max</span><span class="p">(...</span><span class="nx">nums</span><span class="p">);</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="c1">// 2. 各数値の出現回数を数える</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="c1">// counter[num] は num の出現回数を表す</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">counter</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">(</span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">        </span><span class="nx">counter</span><span class="p">[</span><span class="nx">num</span><span class="p">]</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">    </span><span class="c1">// 3. counter を走査し、各要素を元の配列 nums に書き戻す</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">num</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">counter</span><span class="p">[</span><span class="nx">num</span><span class="p">];</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">            </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">countingSortNaive</span><span class="p">}</span>
+<div class="highlight"><span class="filename">counting_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 計数ソート */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="c1">// 簡易実装のため、オブジェクトのソートには使えない</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="kt">void</span><span class="w"> </span><span class="n">countingSortNaive</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="c1">// 1. 配列の最大要素 m を求める</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">    </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">_num</span><span class="p">);</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">  </span><span class="c1">// 2. 各数値の出現回数を数える</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">  </span><span class="c1">// counter[_num] は _num の出現回数を表す</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">    </span><span class="n">counter</span><span class="p">[</span><span class="n">_num</span><span class="p">]</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">  </span><span class="c1">// 3. counter を走査し、各要素を元の配列 nums に書き戻す</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">_num</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">_num</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">_num</span><span class="p">];</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w">      </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_num</span><span class="p">;</span>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">counting_sort_naive</span><span class="p">}</span>
+<div class="highlight"><span class="filename">counting_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 計数ソート */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="c1">// 簡易実装のため、オブジェクトのソートには使えない</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="k">fn</span><span class="w"> </span><span class="nf">counting_sort_naive</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素 m を求める</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">.</span><span class="n">iter</span><span class="p">().</span><span class="n">max</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="c1">// 2. 各数値の出現回数を数える</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="c1">// counter[num] は num の出現回数を表す</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="o">&amp;</span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">iter</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">    </span><span class="c1">// 3. counter を走査し、各要素を元の配列 nums に書き戻す</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">            </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">countingSortNaive</span><span class="p">}</span>
+<div class="highlight"><span class="filename">counting_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 計数ソート */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="c1">// 簡易実装のため、オブジェクトのソートには使えない</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="kt">void</span><span class="w"> </span><span class="nf">countingSortNaive</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素 m を求める</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">            </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="c1">// 2. 各数値の出現回数を数える</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">    </span><span class="c1">// counter[num] は num の出現回数を表す</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">calloc</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">    </span><span class="c1">// 3. counter を走査し、各要素を元の配列 nums に書き戻す</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">num</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">];</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="w">            </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="w">    </span><span class="c1">// 4. メモリを解放する</span>
+<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">counter</span><span class="p">);</span>
+<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">countingSortNaive</span><span class="p">}</span>
+<div class="highlight"><span class="filename">counting_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 計数ソート */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="c1">// 簡易実装のため、オブジェクトのソートには使えない</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">countingSortNaive</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素 m を求める</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">        </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">    </span><span class="c1">// 2. 各数値の出現回数を数える</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">    </span><span class="c1">// counter[num] は num の出現回数を表す</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">        </span><span class="n">counter</span><span class="o">[</span><span class="n">num</span><span class="o">]++</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">    </span><span class="c1">// 3. counter を走査し、各要素を元の配列 nums に書き戻す</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">counter</span><span class="o">[</span><span class="n">num</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w">            </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="w">            </span><span class="n">j</span><span class="o">++</span>
+<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span>
+<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">counting_sort_naive</span><span class="p">}</span>
+<div class="highlight"><span class="filename">counting_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 計数ソート ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">counting_sort_naive</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># 簡易版。オブジェクトのソートには使えない</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="c1"># 1. 配列の最大要素 m を求める</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="n">nums</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">num</span><span class="o">|</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="o">].</span><span class="n">max</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">  </span><span class="c1"># 2. 各数値の出現回数を数える</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">  </span><span class="c1"># counter[num] は num の出現回数を表す</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">  </span><span class="n">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">  </span><span class="n">nums</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">num</span><span class="o">|</span><span class="w"> </span><span class="n">counter</span><span class="o">[</span><span class="n">num</span><span class="o">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">  </span><span class="c1"># 3. counter を走査し、各要素を元の配列 nums に書き戻す</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">  </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">    </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">counter</span><span class="o">[</span><span class="n">num</span><span class="o">]</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">      </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">      </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20counting_sort_naive%28nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%22%22%22%E8%A8%88%E6%95%B0%E3%82%BD%E3%83%BC%E3%83%88%22%22%22%0A%20%20%20%20%23%20%E7%B0%A1%E6%98%93%E7%89%88%E3%80%82%E3%82%AA%E3%83%96%E3%82%B8%E3%82%A7%E3%82%AF%E3%83%88%E3%81%AE%E3%82%BD%E3%83%BC%E3%83%88%E3%81%AB%E3%81%AF%E4%BD%BF%E3%81%88%E3%81%AA%E3%81%84%0A%20%20%20%20%23%201.%20%E9%85%8D%E5%88%97%E3%81%AE%E6%9C%80%E5%A4%A7%E8%A6%81%E7%B4%A0%20m%20%E3%82%92%E6%B1%82%E3%82%81%E3%82%8B%0A%20%20%20%20m%20%3D%200%0A%20%20%20%20for%20num%20in%20nums%3A%0A%20%20%20%20%20%20%20%20m%20%3D%20max%28m%2C%20num%29%0A%20%20%20%20%23%202.%20%E5%90%84%E6%95%B0%E5%80%A4%E3%81%AE%E5%87%BA%E7%8F%BE%E5%9B%9E%E6%95%B0%E3%82%92%E6%95%B0%E3%81%88%E3%82%8B%0A%20%20%20%20%23%20counter%5Bnum%5D%20%E3%81%AF%20num%20%E3%81%AE%E5%87%BA%E7%8F%BE%E5%9B%9E%E6%95%B0%E3%82%92%E8%A1%A8%E3%81%99%0A%20%20%20%20counter%20%3D%20%5B0%5D%20%2A%20%28m%20%2B%201%29%0A%20%20%20%20for%20num%20in%20nums%3A%0A%20%20%20%20%20%20%20%20counter%5Bnum%5D%20%2B%3D%201%0A%20%20%20%20%23%203.%20counter%20%E3%82%92%E8%B5%B0%E6%9F%BB%E3%81%97%E3%80%81%E5%90%84%E8%A6%81%E7%B4%A0%E3%82%92%E5%85%83%E3%81%AE%E9%85%8D%E5%88%97%20nums%20%E3%81%AB%E6%9B%B8%E3%81%8D%E6%88%BB%E3%81%99%0A%20%20%20%20i%20%3D%200%0A%20%20%20%20for%20num%20in%20range%28m%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20for%20_%20in%20range%28counter%5Bnum%5D%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20nums%5Bi%5D%20%3D%20num%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%2B%3D%201%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B1%2C%200%2C%201%2C%202%2C%200%2C%204%2C%200%2C%202%2C%202%2C%204%5D%0A%20%20%20%20counting_sort_naive%28nums%29%0A%20%20%20%20print%28f%22%E8%A8%88%E6%95%B0%E3%82%BD%E3%83%BC%E3%83%88%EF%BC%88%E3%82%AA%E3%83%96%E3%82%B8%E3%82%A7%E3%82%AF%E3%83%88%E3%81%AF%E3%82%BD%E3%83%BC%E3%83%88%E4%B8%8D%E5%8F%AF%EF%BC%89%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%20%7Bnums%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20counting_sort_naive%28nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%22%22%22%E8%A8%88%E6%95%B0%E3%82%BD%E3%83%BC%E3%83%88%22%22%22%0A%20%20%20%20%23%20%E7%B0%A1%E6%98%93%E7%89%88%E3%80%82%E3%82%AA%E3%83%96%E3%82%B8%E3%82%A7%E3%82%AF%E3%83%88%E3%81%AE%E3%82%BD%E3%83%BC%E3%83%88%E3%81%AB%E3%81%AF%E4%BD%BF%E3%81%88%E3%81%AA%E3%81%84%0A%20%20%20%20%23%201.%20%E9%85%8D%E5%88%97%E3%81%AE%E6%9C%80%E5%A4%A7%E8%A6%81%E7%B4%A0%20m%20%E3%82%92%E6%B1%82%E3%82%81%E3%82%8B%0A%20%20%20%20m%20%3D%200%0A%20%20%20%20for%20num%20in%20nums%3A%0A%20%20%20%20%20%20%20%20m%20%3D%20max%28m%2C%20num%29%0A%20%20%20%20%23%202.%20%E5%90%84%E6%95%B0%E5%80%A4%E3%81%AE%E5%87%BA%E7%8F%BE%E5%9B%9E%E6%95%B0%E3%82%92%E6%95%B0%E3%81%88%E3%82%8B%0A%20%20%20%20%23%20counter%5Bnum%5D%20%E3%81%AF%20num%20%E3%81%AE%E5%87%BA%E7%8F%BE%E5%9B%9E%E6%95%B0%E3%82%92%E8%A1%A8%E3%81%99%0A%20%20%20%20counter%20%3D%20%5B0%5D%20%2A%20%28m%20%2B%201%29%0A%20%20%20%20for%20num%20in%20nums%3A%0A%20%20%20%20%20%20%20%20counter%5Bnum%5D%20%2B%3D%201%0A%20%20%20%20%23%203.%20counter%20%E3%82%92%E8%B5%B0%E6%9F%BB%E3%81%97%E3%80%81%E5%90%84%E8%A6%81%E7%B4%A0%E3%82%92%E5%85%83%E3%81%AE%E9%85%8D%E5%88%97%20nums%20%E3%81%AB%E6%9B%B8%E3%81%8D%E6%88%BB%E3%81%99%0A%20%20%20%20i%20%3D%200%0A%20%20%20%20for%20num%20in%20range%28m%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20for%20_%20in%20range%28counter%5Bnum%5D%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20nums%5Bi%5D%20%3D%20num%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%2B%3D%201%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B1%2C%200%2C%201%2C%202%2C%200%2C%204%2C%200%2C%202%2C%202%2C%204%5D%0A%20%20%20%20counting_sort_naive%28nums%29%0A%20%20%20%20print%28f%22%E8%A8%88%E6%95%B0%E3%82%BD%E3%83%BC%E3%83%88%EF%BC%88%E3%82%AA%E3%83%96%E3%82%B8%E3%82%A7%E3%82%AF%E3%83%88%E3%81%AF%E3%82%BD%E3%83%BC%E3%83%88%E4%B8%8D%E5%8F%AF%EF%BC%89%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%20%7Bnums%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 <div class="admonition note">
 <p class="admonition-title">計数ソートとバケットソートの関係</p>
-<p>バケットソートの観点から、計数ソートにおける計数配列 <code>counter</code> の各インデックスをバケットと考え、カウントの過程を要素を対応するバケットに分散させることと考えることができます。本質的に、計数ソートは整数データのためのバケットソートの特別なケースです。</p>
+<p>バケットソートの観点から見ると、計数ソートにおける計数配列 <code>counter</code> の各インデックスを 1 つのバケットとみなし、個数を数える過程を各要素を対応するバケットへ振り分ける操作とみなせます。本質的には、計数ソートは整数データにおけるバケットソートの特殊な一例です。</p>
 </div>
 <h2 id="1192">11.9.2 &nbsp; 完全な実装<a class="headerlink" href="#1192" title="Permanent link">&para;</a></h2>
-<p>注意深い読者は気付くかもしれませんが、<strong>入力データがオブジェクトの場合、上記の手順 <code>3.</code> は無効です</strong>。入力データが商品オブジェクトで、価格（クラスメンバ変数）で商品をソートしたいとします。しかし、上記のアルゴリズムは結果としてソート済みの価格のみを提供できます。</p>
-<p>では、元のデータのソート結果をどのように取得できるでしょうか？まず、<code>counter</code> の「前置和」を計算します。名前が示すように、インデックス <code>i</code> での前置和 <code>prefix[i]</code> は、配列の最初の <code>i</code> 個の要素の和に等しいです：</p>
+<p>注意深い読者なら、**入力データがオブジェクトである場合、上記の手順 <code>3.</code> は機能しない**ことに気づくかもしれません。入力データが商品オブジェクトであり、商品価格（クラスのメンバ変数）に基づいて商品をソートしたいとします。しかし上記のアルゴリズムが返せるのは価格のソート結果だけです。</p>
+<p>では、元のデータのソート結果を得るにはどうすればよいのでしょうか。まず <code>counter</code> の「累積和」を計算します。名前のとおり、インデックス <code>i</code> における累積和 <code>prefix[i]</code> は、配列の先頭から <code>i</code> 番目までの要素の総和に等しくなります：</p>
 <div class="arithmatex">\[
 \text{prefix}[i] = \sum_{j=0}^i \text{counter[j]}
 \]</div>
-<p><strong>前置和には明確な意味があります。<code>prefix[num] - 1</code> は結果配列 <code>res</code> における要素 <code>num</code> の最後の出現のインデックスを表します</strong>。この情報は重要で、各要素が結果配列のどこに現れるべきかを教えてくれます。次に、元の配列 <code>nums</code> の各要素 <code>num</code> を逆順で走査し、各反復で以下の2つの手順を実行します。</p>
+<p><strong>累積和には明確な意味があり、<code>prefix[num] - 1</code> は要素 <code>num</code> が結果配列 <code>res</code> に最後に現れるインデックスを表します</strong>。この情報は非常に重要で、各要素が結果配列のどの位置に現れるべきかを示してくれます。続いて元の配列 <code>nums</code> を逆順に走査し、各要素 <code>num</code> に対して各反復で次の 2 つの手順を行います。</p>
 <ol>
-<li>インデックス <code>prefix[num] - 1</code> で配列 <code>res</code> に <code>num</code> を埋めます。</li>
-<li>前置和 <code>prefix[num]</code> を <span class="arithmatex">\(1\)</span> 減らして、<code>num</code> を配置する次のインデックスを取得します。</li>
+<li><code>num</code> を配列 <code>res</code> のインデックス <code>prefix[num] - 1</code> に格納します。</li>
+<li>累積和 <code>prefix[num]</code> を <span class="arithmatex">\(1\)</span> 減らし、次に <code>num</code> を配置するインデックスを得ます。</li>
 </ol>
-<p>走査後、配列 <code>res</code> にはソートされた結果が含まれ、最後に <code>res</code> が元の配列 <code>nums</code> を置き換えます。完全な計数ソートの過程は以下の図に示されています。</p>
+<p>走査が完了すると、配列 <code>res</code> にソート済みの結果が格納されます。最後に <code>res</code> で元の配列 <code>nums</code> を上書きすれば完了です。以下の図は完全な計数ソートの流れを示しています。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:8"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">&lt;1&gt;</label><label for="__tabbed_2_2">&lt;2&gt;</label><label for="__tabbed_2_3">&lt;3&gt;</label><label for="__tabbed_2_4">&lt;4&gt;</label><label for="__tabbed_2_5">&lt;5&gt;</label><label for="__tabbed_2_6">&lt;6&gt;</label><label for="__tabbed_2_7">&lt;7&gt;</label><label for="__tabbed_2_8">&lt;8&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="計数ソートの過程" class="animation-figure" src="../counting_sort.assets/counting_sort_step1.png" /></p>
+<p><img alt="計数ソートの手順" class="animation-figure" src="../counting_sort.assets/counting_sort_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="counting_sort_step2" class="animation-figure" src="../counting_sort.assets/counting_sort_step2.png" /></p>
@@ -4570,103 +4779,103 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 11-17 &nbsp; 計数ソートの過程 </p>
+<p align="center"> 図 11-17 &nbsp; 計数ソートの手順 </p>
 
-<p>計数ソートの実装コードは以下の通りです：</p>
+<p>計数ソートの実装コードは以下のとおりです：</p>
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 <div class="highlight"><span class="filename">counting_sort.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">counting_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
 <a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;計数ソート&quot;&quot;&quot;</span>
-<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="c1"># 完全な実装、オブジェクトのソートが可能で、安定ソート</span>
-<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="c1"># 1. 配列内の最大要素 m を統計</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="c1"># 完全版。オブジェクトをソートでき、かつ安定ソートである</span>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="c1"># 1. 配列の最大要素 m を求める</span>
 <a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="n">m</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
-<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>    <span class="c1"># 2. 各数字の出現回数を統計</span>
+<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>    <span class="c1"># 2. 各数値の出現回数を数える</span>
 <a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>    <span class="c1"># counter[num] は num の出現回数を表す</span>
 <a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>    <span class="n">counter</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
 <a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>    <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">nums</span><span class="p">:</span>
 <a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>        <span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
-<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>    <span class="c1"># 3. counter の前置和を計算し、「出現回数」を「末尾インデックス」に変換</span>
-<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>    <span class="c1"># counter[num]-1 は res において num が最後に出現するインデックス</span>
+<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>    <span class="c1"># 3. counter の累積和を求めて、「出現回数」を「末尾インデックス」に変換する</span>
+<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>    <span class="c1"># つまり counter[num]-1 は、num が res に最後に現れるインデックス</span>
 <a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">m</span><span class="p">):</span>
 <a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>        <span class="n">counter</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">+=</span> <span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
-<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a>    <span class="c1"># 4. nums を逆順に走査し、各要素を結果配列 res に配置</span>
+<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a>    <span class="c1"># 4. nums を逆順に走査し、各要素を結果配列 res に格納する</span>
 <a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a>    <span class="c1"># 結果を記録するための配列 res を初期化</span>
 <a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
 <a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span>
 <a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a>        <span class="n">num</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
 <a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a>        <span class="n">res</span><span class="p">[</span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>  <span class="c1"># num を対応するインデックスに配置</span>
-<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a>        <span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span> <span class="o">-=</span> <span class="mi">1</span>  <span class="c1"># 前置和を1減らし、num を配置する次のインデックスを取得</span>
-<a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a>    <span class="c1"># 結果配列 res を使用して元の配列 nums を上書き</span>
+<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a>        <span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span> <span class="o">-=</span> <span class="mi">1</span>  <span class="c1"># 累積和を 1 減らして、次に num を配置するインデックスを得る</span>
+<a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a>    <span class="c1"># 結果配列 res で元の配列 nums を上書きする</span>
 <a id="__codelineno-13-24" name="__codelineno-13-24" href="#__codelineno-13-24"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
 <a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a>        <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* カウントソート */</span>
-<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="c1">// 完全な実装、オブジェクトのソートが可能で安定ソート</span>
+<div class="highlight"><span class="filename">counting_sort.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 計数ソート */</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="c1">// 完全な実装で、オブジェクトをソートでき、かつ安定ソートである</span>
 <a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="kt">void</span><span class="w"> </span><span class="nf">countingSort</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素mを統計</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素 m を求める</span>
 <a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">        </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">);</span>
 <a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">    </span><span class="c1">// 2. 各数字の出現回数を統計</span>
-<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">    </span><span class="c1">// counter[num]はnumの出現回数を表す</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">    </span><span class="c1">// 2. 各数値の出現回数を数える</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">    </span><span class="c1">// counter[num] は num の出現回数を表す</span>
 <a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">counter</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span><span class="o">++</span><span class="p">;</span>
 <a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">    </span><span class="c1">// 3. counterの前缀和を計算し、「出現回数」を「末尾インデックス」に変換</span>
-<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">    </span><span class="c1">// counter[num]-1はnumがresで現れる最後のインデックス</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">    </span><span class="c1">// 3. counter の累積和を求めて、「出現回数」を「末尾インデックス」に変換する</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">    </span><span class="c1">// つまり counter[num]-1 は、num が res に最後に現れるインデックス</span>
 <a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
 <a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w">    </span><span class="c1">// 4. numsを逆順で走査し、各要素を結果配列resに配置</span>
-<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a><span class="w">    </span><span class="c1">// 結果を記録する配列resを初期化</span>
+<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w">    </span><span class="c1">// 4. nums を逆順に走査し、各要素を結果配列 res に格納する</span>
+<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a><span class="w">    </span><span class="c1">// 結果を記録するための配列 res を初期化</span>
 <a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
 <a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
 <a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
-<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span><span class="w"> </span><span class="c1">// numを対応するインデックスに配置</span>
-<a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span><span class="o">--</span><span class="p">;</span><span class="w">              </span><span class="c1">// 前缀和を1減らし、numを配置する次のインデックスを取得</span>
+<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span><span class="w"> </span><span class="c1">// num を対応するインデックスに配置</span>
+<a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span><span class="o">--</span><span class="p">;</span><span class="w">              </span><span class="c1">// 累積和を 1 減らして、次に num を配置するインデックスを得る</span>
 <a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></a><span class="w">    </span><span class="c1">// 結果配列resで元の配列numsを上書き</span>
+<a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></a><span class="w">    </span><span class="c1">// 結果配列 res で元の配列 nums を上書きする</span>
 <a id="__codelineno-14-30" name="__codelineno-14-30" href="#__codelineno-14-30"></a><span class="w">    </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
 <a id="__codelineno-14-31" name="__codelineno-14-31" href="#__codelineno-14-31"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">counting_sort.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 計数ソート */</span>
-<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="c1">// 完全な実装、オブジェクトをソートでき、安定ソート</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="c1">// 完全な実装で、オブジェクトをソートでき、かつ安定ソートである</span>
 <a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="kt">void</span><span class="w"> </span><span class="nf">countingSort</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素 m を統計</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素 m を求める</span>
 <a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">        </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">max</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">);</span>
 <a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">    </span><span class="c1">// 2. 各数字の出現回数を統計</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">    </span><span class="c1">// 2. 各数値の出現回数を数える</span>
 <a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="c1">// counter[num] は num の出現回数を表す</span>
 <a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">        </span><span class="n">counter</span><span class="o">[</span><span class="n">num</span><span class="o">]++</span><span class="p">;</span>
 <a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="c1">// 3. counter の累積和を計算し、「出現回数」を「尻尾インデックス」に変換</span>
-<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">    </span><span class="c1">// counter[num]-1 は res 内で num が出現する最後のインデックス</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="c1">// 3. counter の累積和を求めて、「出現回数」を「末尾インデックス」に変換する</span>
+<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">    </span><span class="c1">// つまり counter[num]-1 は、num が res に最後に現れるインデックス</span>
 <a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">        </span><span class="n">counter</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">counter</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w">    </span><span class="c1">// 4. nums を逆順に走査し、各要素を結果配列 res に配置</span>
-<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="w">    </span><span class="c1">// 結果を記録する配列 res を初期化</span>
+<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w">    </span><span class="c1">// 4. nums を逆順に走査し、各要素を結果配列 res に格納する</span>
+<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="w">    </span><span class="c1">// 結果を記録するための配列 res を初期化</span>
 <a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
 <a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-15-24" name="__codelineno-15-24" href="#__codelineno-15-24"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-15-26" name="__codelineno-15-26" href="#__codelineno-15-26"></a><span class="w">        </span><span class="n">res</span><span class="o">[</span><span class="n">counter</span><span class="o">[</span><span class="n">num</span><span class="o">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span><span class="w"> </span><span class="c1">// num を対応するインデックスに配置</span>
-<a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></a><span class="w">        </span><span class="n">counter</span><span class="o">[</span><span class="n">num</span><span class="o">]--</span><span class="p">;</span><span class="w"> </span><span class="c1">// 累積和を 1 減算し、num を配置する次のインデックスを取得</span>
+<a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></a><span class="w">        </span><span class="n">counter</span><span class="o">[</span><span class="n">num</span><span class="o">]--</span><span class="p">;</span><span class="w"> </span><span class="c1">// 累積和を 1 減らして、次に num を配置するインデックスを得る</span>
 <a id="__codelineno-15-28" name="__codelineno-15-28" href="#__codelineno-15-28"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-15-29" name="__codelineno-15-29" href="#__codelineno-15-29"></a><span class="w">    </span><span class="c1">// 結果配列 res を使って元の配列 nums を上書き</span>
+<a id="__codelineno-15-29" name="__codelineno-15-29" href="#__codelineno-15-29"></a><span class="w">    </span><span class="c1">// 結果配列 res で元の配列 nums を上書きする</span>
 <a id="__codelineno-15-30" name="__codelineno-15-30" href="#__codelineno-15-30"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-31" name="__codelineno-15-31" href="#__codelineno-15-31"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-15-32" name="__codelineno-15-32" href="#__codelineno-15-32"></a><span class="w">    </span><span class="p">}</span>
@@ -4674,57 +4883,360 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">counting_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">CountingSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">counting_sort.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 計数ソート */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="c1">// 完全な実装で、オブジェクトをソートでき、かつ安定ソートである</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="k">void</span><span class="w"> </span><span class="nf">CountingSort</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素 m を求める</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">        </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Max</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">    </span><span class="c1">// 2. 各数値の出現回数を数える</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="c1">// counter[num] は num の出現回数を表す</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">    </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">    </span><span class="c1">// 3. counter の累積和を求めて、「出現回数」を「末尾インデックス」に変換する</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">    </span><span class="c1">// つまり counter[num]-1 は、num が res に最後に現れるインデックス</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w">    </span><span class="c1">// 4. nums を逆順に走査し、各要素を結果配列 res に格納する</span>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="w">    </span><span class="c1">// 結果を記録するための配列 res を初期化</span>
+<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
+<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="w">    </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-16-24" name="__codelineno-16-24" href="#__codelineno-16-24"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-25" name="__codelineno-16-25" href="#__codelineno-16-25"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-16-26" name="__codelineno-16-26" href="#__codelineno-16-26"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span><span class="w"> </span><span class="c1">// num を対応するインデックスに配置</span>
+<a id="__codelineno-16-27" name="__codelineno-16-27" href="#__codelineno-16-27"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// 累積和を 1 減らして、次に num を配置するインデックスを得る</span>
+<a id="__codelineno-16-28" name="__codelineno-16-28" href="#__codelineno-16-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-29" name="__codelineno-16-29" href="#__codelineno-16-29"></a><span class="w">    </span><span class="c1">// 結果配列 res で元の配列 nums を上書きする</span>
+<a id="__codelineno-16-30" name="__codelineno-16-30" href="#__codelineno-16-30"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-31" name="__codelineno-16-31" href="#__codelineno-16-31"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-16-32" name="__codelineno-16-32" href="#__codelineno-16-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-33" name="__codelineno-16-33" href="#__codelineno-16-33"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">countingSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">counting_sort.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 計数ソート */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="c1">// 完全な実装で、オブジェクトをソートでき、かつ安定ソートである</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="kd">func</span><span class="w"> </span><span class="nx">countingSort</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素 m を求める</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">    </span><span class="nx">m</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">            </span><span class="nx">m</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">num</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w">    </span><span class="c1">// 2. 各数値の出現回数を数える</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">    </span><span class="c1">// counter[num] は num の出現回数を表す</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w">    </span><span class="nx">counter</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">        </span><span class="nx">counter</span><span class="p">[</span><span class="nx">num</span><span class="p">]</span><span class="o">++</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="w">    </span><span class="c1">// 3. counter の累積和を求めて、「出現回数」を「末尾インデックス」に変換する</span>
+<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="w">    </span><span class="c1">// つまり counter[num]-1 は、num が res に最後に現れるインデックス</span>
+<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a><span class="w">        </span><span class="nx">counter</span><span class="p">[</span><span class="nx">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">counter</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
+<a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-22" name="__codelineno-17-22" href="#__codelineno-17-22"></a><span class="w">    </span><span class="c1">// 4. nums を逆順に走査し、各要素を結果配列 res に格納する</span>
+<a id="__codelineno-17-23" name="__codelineno-17-23" href="#__codelineno-17-23"></a><span class="w">    </span><span class="c1">// 結果を記録するための配列 res を初期化</span>
+<a id="__codelineno-17-24" name="__codelineno-17-24" href="#__codelineno-17-24"></a><span class="w">    </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span>
+<a id="__codelineno-17-25" name="__codelineno-17-25" href="#__codelineno-17-25"></a><span class="w">    </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
+<a id="__codelineno-17-26" name="__codelineno-17-26" href="#__codelineno-17-26"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-27" name="__codelineno-17-27" href="#__codelineno-17-27"></a><span class="w">        </span><span class="nx">num</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
+<a id="__codelineno-17-28" name="__codelineno-17-28" href="#__codelineno-17-28"></a><span class="w">        </span><span class="c1">// num を対応するインデックスに配置</span>
+<a id="__codelineno-17-29" name="__codelineno-17-29" href="#__codelineno-17-29"></a><span class="w">        </span><span class="nx">res</span><span class="p">[</span><span class="nx">counter</span><span class="p">[</span><span class="nx">num</span><span class="p">]</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">num</span>
+<a id="__codelineno-17-30" name="__codelineno-17-30" href="#__codelineno-17-30"></a><span class="w">        </span><span class="c1">// 累積和を 1 減らして、次に num を配置するインデックスを得る</span>
+<a id="__codelineno-17-31" name="__codelineno-17-31" href="#__codelineno-17-31"></a><span class="w">        </span><span class="nx">counter</span><span class="p">[</span><span class="nx">num</span><span class="p">]</span><span class="o">--</span>
+<a id="__codelineno-17-32" name="__codelineno-17-32" href="#__codelineno-17-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-33" name="__codelineno-17-33" href="#__codelineno-17-33"></a><span class="w">    </span><span class="c1">// 結果配列 res で元の配列 nums を上書きする</span>
+<a id="__codelineno-17-34" name="__codelineno-17-34" href="#__codelineno-17-34"></a><span class="w">    </span><span class="nb">copy</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
+<a id="__codelineno-17-35" name="__codelineno-17-35" href="#__codelineno-17-35"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">countingSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">counting_sort.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 計数ソート */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="c1">// 完全な実装で、オブジェクトをソートでき、かつ安定ソートである</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="kd">func</span><span class="w"> </span><span class="nf">countingSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素 m を求める</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">max</span><span class="p">()</span><span class="o">!</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">    </span><span class="c1">// 2. 各数値の出現回数を数える</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">    </span><span class="c1">// counter[num] は num の出現回数を表す</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">counter</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w">    </span><span class="c1">// 3. counter の累積和を求めて、「出現回数」を「末尾インデックス」に変換する</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w">    </span><span class="c1">// つまり counter[num]-1 は、num が res に最後に現れるインデックス</span>
+<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="w">    </span><span class="c1">// 4. nums を逆順に走査し、各要素を結果配列 res に格納する</span>
+<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="w">    </span><span class="c1">// 結果を記録するための配列 res を初期化</span>
+<a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">count</span><span class="p">)</span>
+<a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="p">.</span><span class="n">reversed</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">num</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-18-22" name="__codelineno-18-22" href="#__codelineno-18-22"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="c1">// num を対応するインデックスに配置</span>
+<a id="__codelineno-18-23" name="__codelineno-18-23" href="#__codelineno-18-23"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// 累積和を 1 減らして、次に num を配置するインデックスを得る</span>
+<a id="__codelineno-18-24" name="__codelineno-18-24" href="#__codelineno-18-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-25" name="__codelineno-18-25" href="#__codelineno-18-25"></a><span class="w">    </span><span class="c1">// 結果配列 res で元の配列 nums を上書きする</span>
+<a id="__codelineno-18-26" name="__codelineno-18-26" href="#__codelineno-18-26"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-27" name="__codelineno-18-27" href="#__codelineno-18-27"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-18-28" name="__codelineno-18-28" href="#__codelineno-18-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-29" name="__codelineno-18-29" href="#__codelineno-18-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">countingSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">counting_sort.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 計数ソート */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="c1">// 完全な実装で、オブジェクトをソートでき、かつ安定ソートである</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="kd">function</span><span class="w"> </span><span class="nx">countingSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素 m を求める</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">max</span><span class="p">(...</span><span class="nx">nums</span><span class="p">);</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">    </span><span class="c1">// 2. 各数値の出現回数を数える</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">    </span><span class="c1">// counter[num] は num の出現回数を表す</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w">        </span><span class="nx">counter</span><span class="p">[</span><span class="nx">num</span><span class="p">]</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">    </span><span class="c1">// 3. counter の累積和を求めて、「出現回数」を「末尾インデックス」に変換する</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w">    </span><span class="c1">// つまり counter[num]-1 は、num が res に最後に現れるインデックス</span>
+<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w">        </span><span class="nx">counter</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">counter</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="w">    </span><span class="c1">// 4. nums を逆順に走査し、各要素を結果配列 res に格納する</span>
+<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a><span class="w">    </span><span class="c1">// 結果を記録するための配列 res を初期化</span>
+<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">);</span>
+<a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-22" name="__codelineno-19-22" href="#__codelineno-19-22"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-19-23" name="__codelineno-19-23" href="#__codelineno-19-23"></a><span class="w">        </span><span class="nx">res</span><span class="p">[</span><span class="nx">counter</span><span class="p">[</span><span class="nx">num</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span><span class="w"> </span><span class="c1">// num を対応するインデックスに配置</span>
+<a id="__codelineno-19-24" name="__codelineno-19-24" href="#__codelineno-19-24"></a><span class="w">        </span><span class="nx">counter</span><span class="p">[</span><span class="nx">num</span><span class="p">]</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// 累積和を 1 減らして、次に num を配置するインデックスを得る</span>
+<a id="__codelineno-19-25" name="__codelineno-19-25" href="#__codelineno-19-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-26" name="__codelineno-19-26" href="#__codelineno-19-26"></a><span class="w">    </span><span class="c1">// 結果配列 res で元の配列 nums を上書きする</span>
+<a id="__codelineno-19-27" name="__codelineno-19-27" href="#__codelineno-19-27"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-28" name="__codelineno-19-28" href="#__codelineno-19-28"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">res</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-19-29" name="__codelineno-19-29" href="#__codelineno-19-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-30" name="__codelineno-19-30" href="#__codelineno-19-30"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">countingSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">counting_sort.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 計数ソート */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="c1">// 完全な実装で、オブジェクトをソートでき、かつ安定ソートである</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="kd">function</span><span class="w"> </span><span class="nx">countingSort</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素 m を求める</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">m</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">max</span><span class="p">(...</span><span class="nx">nums</span><span class="p">);</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">    </span><span class="c1">// 2. 各数値の出現回数を数える</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">    </span><span class="c1">// counter[num] は num の出現回数を表す</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">counter</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">(</span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">        </span><span class="nx">counter</span><span class="p">[</span><span class="nx">num</span><span class="p">]</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">    </span><span class="c1">// 3. counter の累積和を求めて、「出現回数」を「末尾インデックス」に変換する</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w">    </span><span class="c1">// つまり counter[num]-1 は、num が res に最後に現れるインデックス</span>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w">        </span><span class="nx">counter</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">counter</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-17" name="__codelineno-20-17" href="#__codelineno-20-17"></a><span class="w">    </span><span class="c1">// 4. nums を逆順に走査し、各要素を結果配列 res に格納する</span>
+<a id="__codelineno-20-18" name="__codelineno-20-18" href="#__codelineno-20-18"></a><span class="w">    </span><span class="c1">// 結果を記録するための配列 res を初期化</span>
+<a id="__codelineno-20-19" name="__codelineno-20-19" href="#__codelineno-20-19"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-20-20" name="__codelineno-20-20" href="#__codelineno-20-20"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">(</span><span class="nx">n</span><span class="p">);</span>
+<a id="__codelineno-20-21" name="__codelineno-20-21" href="#__codelineno-20-21"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-22" name="__codelineno-20-22" href="#__codelineno-20-22"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-20-23" name="__codelineno-20-23" href="#__codelineno-20-23"></a><span class="w">        </span><span class="nx">res</span><span class="p">[</span><span class="nx">counter</span><span class="p">[</span><span class="nx">num</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span><span class="w"> </span><span class="c1">// num を対応するインデックスに配置</span>
+<a id="__codelineno-20-24" name="__codelineno-20-24" href="#__codelineno-20-24"></a><span class="w">        </span><span class="nx">counter</span><span class="p">[</span><span class="nx">num</span><span class="p">]</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// 累積和を 1 減らして、次に num を配置するインデックスを得る</span>
+<a id="__codelineno-20-25" name="__codelineno-20-25" href="#__codelineno-20-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-26" name="__codelineno-20-26" href="#__codelineno-20-26"></a><span class="w">    </span><span class="c1">// 結果配列 res で元の配列 nums を上書きする</span>
+<a id="__codelineno-20-27" name="__codelineno-20-27" href="#__codelineno-20-27"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-28" name="__codelineno-20-28" href="#__codelineno-20-28"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">res</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-20-29" name="__codelineno-20-29" href="#__codelineno-20-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-30" name="__codelineno-20-30" href="#__codelineno-20-30"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">countingSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">counting_sort.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 計数ソート */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="c1">// 完全な実装で、オブジェクトをソートでき、かつ安定ソートである</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="kt">void</span><span class="w"> </span><span class="n">countingSort</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="c1">// 1. 配列の最大要素 m を求める</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">    </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">_num</span><span class="p">);</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">  </span><span class="c1">// 2. 各数値の出現回数を数える</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="w">  </span><span class="c1">// counter[_num] は _num の出現回数を表す</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">    </span><span class="n">counter</span><span class="p">[</span><span class="n">_num</span><span class="p">]</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w">  </span><span class="c1">// 3. counter の累積和を求め、「出現回数」を「末尾インデックス」に変換する</span>
+<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="w">  </span><span class="c1">// つまり counter[_num]-1 は、res において _num が最後に出現する位置のインデックスである</span>
+<a id="__codelineno-21-17" name="__codelineno-21-17" href="#__codelineno-21-17"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-18" name="__codelineno-21-18" href="#__codelineno-21-18"></a><span class="w">    </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-21-19" name="__codelineno-21-19" href="#__codelineno-21-19"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-20" name="__codelineno-21-20" href="#__codelineno-21-20"></a><span class="w">  </span><span class="c1">// 4. nums を逆順に走査し、各要素を結果配列 res に格納する</span>
+<a id="__codelineno-21-21" name="__codelineno-21-21" href="#__codelineno-21-21"></a><span class="w">  </span><span class="c1">// 結果を記録するための配列 res を初期化</span>
+<a id="__codelineno-21-22" name="__codelineno-21-22" href="#__codelineno-21-22"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-21-23" name="__codelineno-21-23" href="#__codelineno-21-23"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-21-24" name="__codelineno-21-24" href="#__codelineno-21-24"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-25" name="__codelineno-21-25" href="#__codelineno-21-25"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-21-26" name="__codelineno-21-26" href="#__codelineno-21-26"></a><span class="w">    </span><span class="n">res</span><span class="p">[</span><span class="n">counter</span><span class="p">[</span><span class="n">_num</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_num</span><span class="p">;</span><span class="w"> </span><span class="c1">// _num を対応する添字に配置</span>
+<a id="__codelineno-21-27" name="__codelineno-21-27" href="#__codelineno-21-27"></a><span class="w">    </span><span class="n">counter</span><span class="p">[</span><span class="n">_num</span><span class="p">]</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// 累積和を 1 減らし、次に _num を配置するインデックスを得る</span>
+<a id="__codelineno-21-28" name="__codelineno-21-28" href="#__codelineno-21-28"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-29" name="__codelineno-21-29" href="#__codelineno-21-29"></a><span class="w">  </span><span class="c1">// 結果配列 res で元の配列 nums を上書きする</span>
+<a id="__codelineno-21-30" name="__codelineno-21-30" href="#__codelineno-21-30"></a><span class="w">  </span><span class="n">nums</span><span class="p">.</span><span class="n">setAll</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-21-31" name="__codelineno-21-31" href="#__codelineno-21-31"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">counting_sort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">counting_sort.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 計数ソート */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="c1">// 完全な実装で、オブジェクトをソートでき、かつ安定ソートである</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="k">fn</span><span class="w"> </span><span class="nf">counting_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素 m を求める</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">.</span><span class="n">iter</span><span class="p">().</span><span class="n">max</span><span class="p">().</span><span class="n">unwrap</span><span class="p">()</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">;</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w">    </span><span class="c1">// 2. 各数値の出現回数を数える</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">    </span><span class="c1">// counter[num] は num の出現回数を表す</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="o">&amp;</span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">iter</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">    </span><span class="c1">// 3. counter の累積和を求めて、「出現回数」を「末尾インデックス」に変換する</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">    </span><span class="c1">// つまり counter[num]-1 は、num が res に最後に現れるインデックス</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="w">    </span><span class="c1">// 4. nums を逆順に走査し、各要素を結果配列 res に格納する</span>
+<a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="w">    </span><span class="c1">// 結果を記録するための配列 res を初期化</span>
+<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
+<a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-22-21" name="__codelineno-22-21" href="#__codelineno-22-21"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="p">).</span><span class="n">rev</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-22" name="__codelineno-22-22" href="#__codelineno-22-22"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-22-23" name="__codelineno-22-23" href="#__codelineno-22-23"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span><span class="w"> </span><span class="c1">// num を対応するインデックスに配置</span>
+<a id="__codelineno-22-24" name="__codelineno-22-24" href="#__codelineno-22-24"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 累積和を 1 減らして、次に num を配置するインデックスを得る</span>
+<a id="__codelineno-22-25" name="__codelineno-22-25" href="#__codelineno-22-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-26" name="__codelineno-22-26" href="#__codelineno-22-26"></a><span class="w">    </span><span class="c1">// 結果配列 res で元の配列 nums を上書きする</span>
+<a id="__codelineno-22-27" name="__codelineno-22-27" href="#__codelineno-22-27"></a><span class="w">    </span><span class="n">nums</span><span class="p">.</span><span class="n">copy_from_slice</span><span class="p">(</span><span class="o">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-22-28" name="__codelineno-22-28" href="#__codelineno-22-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">countingSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">counting_sort.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 計数ソート */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="c1">// 完全な実装で、オブジェクトをソートでき、かつ安定ソートである</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="kt">void</span><span class="w"> </span><span class="nf">countingSort</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素 m を求める</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w">            </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w">    </span><span class="c1">// 2. 各数値の出現回数を数える</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w">    </span><span class="c1">// counter[num] は num の出現回数を表す</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">calloc</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="w">    </span><span class="c1">// 3. counter の累積和を求めて、「出現回数」を「末尾インデックス」に変換する</span>
+<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="w">    </span><span class="c1">// つまり counter[num]-1 は、num が res に最後に現れるインデックス</span>
+<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a><span class="w">    </span><span class="c1">// 4. nums を逆順に走査し、各要素を結果配列 res に格納する</span>
+<a id="__codelineno-23-23" name="__codelineno-23-23" href="#__codelineno-23-23"></a><span class="w">    </span><span class="c1">// 結果を記録するための配列 res を初期化</span>
+<a id="__codelineno-23-24" name="__codelineno-23-24" href="#__codelineno-23-24"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">size</span><span class="p">);</span>
+<a id="__codelineno-23-25" name="__codelineno-23-25" href="#__codelineno-23-25"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-26" name="__codelineno-23-26" href="#__codelineno-23-26"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-23-27" name="__codelineno-23-27" href="#__codelineno-23-27"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span><span class="w"> </span><span class="c1">// num を対応するインデックスに配置</span>
+<a id="__codelineno-23-28" name="__codelineno-23-28" href="#__codelineno-23-28"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span><span class="o">--</span><span class="p">;</span><span class="w">              </span><span class="c1">// 累積和を 1 減らして、次に num を配置するインデックスを得る</span>
+<a id="__codelineno-23-29" name="__codelineno-23-29" href="#__codelineno-23-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-30" name="__codelineno-23-30" href="#__codelineno-23-30"></a><span class="w">    </span><span class="c1">// 結果配列 res で元の配列 nums を上書きする</span>
+<a id="__codelineno-23-31" name="__codelineno-23-31" href="#__codelineno-23-31"></a><span class="w">    </span><span class="n">memcpy</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-23-32" name="__codelineno-23-32" href="#__codelineno-23-32"></a><span class="w">    </span><span class="c1">// 5. メモリを解放する</span>
+<a id="__codelineno-23-33" name="__codelineno-23-33" href="#__codelineno-23-33"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-23-34" name="__codelineno-23-34" href="#__codelineno-23-34"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">counter</span><span class="p">);</span>
+<a id="__codelineno-23-35" name="__codelineno-23-35" href="#__codelineno-23-35"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">countingSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">counting_sort.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 計数ソート */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="c1">// 完全な実装で、オブジェクトをソートでき、かつ安定ソートである</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">countingSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素 m を求める</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w">        </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w">    </span><span class="c1">// 2. 各数値の出現回数を数える</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w">    </span><span class="c1">// counter[num] は num の出現回数を表す</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w">        </span><span class="n">counter</span><span class="o">[</span><span class="n">num</span><span class="o">]++</span>
+<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="w">    </span><span class="c1">// 3. counter の累積和を求めて、「出現回数」を「末尾インデックス」に変換する</span>
+<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="w">    </span><span class="c1">// つまり counter[num]-1 は、num が res に最後に現れるインデックス</span>
+<a id="__codelineno-24-17" name="__codelineno-24-17" href="#__codelineno-24-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-18" name="__codelineno-24-18" href="#__codelineno-24-18"></a><span class="w">        </span><span class="n">counter</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">counter</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-24-19" name="__codelineno-24-19" href="#__codelineno-24-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-20" name="__codelineno-24-20" href="#__codelineno-24-20"></a><span class="w">    </span><span class="c1">// 4. nums を逆順に走査し、各要素を結果配列 res に格納する</span>
+<a id="__codelineno-24-21" name="__codelineno-24-21" href="#__codelineno-24-21"></a><span class="w">    </span><span class="c1">// 結果を記録するための配列 res を初期化</span>
+<a id="__codelineno-24-22" name="__codelineno-24-22" href="#__codelineno-24-22"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-24-23" name="__codelineno-24-23" href="#__codelineno-24-23"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-24-24" name="__codelineno-24-24" href="#__codelineno-24-24"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="n">downTo</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-25" name="__codelineno-24-25" href="#__codelineno-24-25"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-24-26" name="__codelineno-24-26" href="#__codelineno-24-26"></a><span class="w">        </span><span class="n">res</span><span class="o">[</span><span class="n">counter</span><span class="o">[</span><span class="n">num</span><span class="o">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="c1">// num を対応するインデックスに配置</span>
+<a id="__codelineno-24-27" name="__codelineno-24-27" href="#__codelineno-24-27"></a><span class="w">        </span><span class="n">counter</span><span class="o">[</span><span class="n">num</span><span class="o">]--</span><span class="w"> </span><span class="c1">// 累積和を 1 減らして、次に num を配置するインデックスを得る</span>
+<a id="__codelineno-24-28" name="__codelineno-24-28" href="#__codelineno-24-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-29" name="__codelineno-24-29" href="#__codelineno-24-29"></a><span class="w">    </span><span class="c1">// 結果配列 res で元の配列 nums を上書きする</span>
+<a id="__codelineno-24-30" name="__codelineno-24-30" href="#__codelineno-24-30"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-31" name="__codelineno-24-31" href="#__codelineno-24-31"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-24-32" name="__codelineno-24-32" href="#__codelineno-24-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-33" name="__codelineno-24-33" href="#__codelineno-24-33"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">counting_sort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">counting_sort.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### 計数ソート ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">counting_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="c1"># 完全版。オブジェクトをソートでき、かつ安定ソートである</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">  </span><span class="c1"># 1. 配列の最大要素 m を求める</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">  </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">.</span><span class="n">max</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">  </span><span class="c1"># 2. 各数値の出現回数を数える</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">  </span><span class="c1"># counter[num] は num の出現回数を表す</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w">  </span><span class="n">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">  </span><span class="n">nums</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">num</span><span class="o">|</span><span class="w"> </span><span class="n">counter</span><span class="o">[</span><span class="n">num</span><span class="o">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w">  </span><span class="c1"># 3. counter の累積和を求めて、「出現回数」を「末尾インデックス」に変換する</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w">  </span><span class="c1"># つまり counter[num]-1 は、num が res に最後に現れるインデックス</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w">  </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">m</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">counter</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">counter</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w">  </span><span class="c1"># 4. nums を逆順に走査し、各要素を結果配列 res に格納する</span>
+<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w">  </span><span class="c1"># 結果を記録するための配列 res を初期化する</span>
+<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w">  </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="w">  </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span>
+<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a><span class="w">    </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="w">    </span><span class="n">res</span><span class="o">[</span><span class="n">counter</span><span class="o">[</span><span class="n">num</span><span class="o">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="c1"># num を対応するインデックスに配置</span>
+<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a><span class="w">    </span><span class="n">counter</span><span class="o">[</span><span class="n">num</span><span class="o">]</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># 累積和を 1 減らして、次に num を配置するインデックスを得る</span>
+<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a><span class="w">  </span><span class="c1"># 結果配列 res で元の配列 nums を上書きする</span>
+<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="w">  </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h2 id="1193">11.9.3 &nbsp; アルゴリズムの特徴<a class="headerlink" href="#1193" title="Permanent link">&para;</a></h2>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20counting_sort%28nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%22%22%22%E8%A8%88%E6%95%B0%E3%82%BD%E3%83%BC%E3%83%88%22%22%22%0A%20%20%20%20%23%20%E5%AE%8C%E5%85%A8%E7%89%88%E3%80%82%E3%82%AA%E3%83%96%E3%82%B8%E3%82%A7%E3%82%AF%E3%83%88%E3%82%92%E3%82%BD%E3%83%BC%E3%83%88%E3%81%A7%E3%81%8D%E3%80%81%E3%81%8B%E3%81%A4%E5%AE%89%E5%AE%9A%E3%82%BD%E3%83%BC%E3%83%88%E3%81%A7%E3%81%82%E3%82%8B%0A%20%20%20%20%23%201.%20%E9%85%8D%E5%88%97%E3%81%AE%E6%9C%80%E5%A4%A7%E8%A6%81%E7%B4%A0%20m%20%E3%82%92%E6%B1%82%E3%82%81%E3%82%8B%0A%20%20%20%20m%20%3D%20max%28nums%29%0A%20%20%20%20%23%202.%20%E5%90%84%E6%95%B0%E5%80%A4%E3%81%AE%E5%87%BA%E7%8F%BE%E5%9B%9E%E6%95%B0%E3%82%92%E6%95%B0%E3%81%88%E3%82%8B%0A%20%20%20%20%23%20counter%5Bnum%5D%20%E3%81%AF%20num%20%E3%81%AE%E5%87%BA%E7%8F%BE%E5%9B%9E%E6%95%B0%E3%82%92%E8%A1%A8%E3%81%99%0A%20%20%20%20counter%20%3D%20%5B0%5D%20%2A%20%28m%20%2B%201%29%0A%20%20%20%20for%20num%20in%20nums%3A%0A%20%20%20%20%20%20%20%20counter%5Bnum%5D%20%2B%3D%201%0A%20%20%20%20%23%203.%20counter%20%E3%81%AE%E7%B4%AF%E7%A9%8D%E5%92%8C%E3%82%92%E6%B1%82%E3%82%81%E3%81%A6%E3%80%81%E3%80%8C%E5%87%BA%E7%8F%BE%E5%9B%9E%E6%95%B0%E3%80%8D%E3%82%92%E3%80%8C%E6%9C%AB%E5%B0%BE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%80%8D%E3%81%AB%E5%A4%89%E6%8F%9B%E3%81%99%E3%82%8B%0A%20%20%20%20%23%20%E3%81%A4%E3%81%BE%E3%82%8A%20counter%5Bnum%5D-1%20%E3%81%AF%E3%80%81num%20%E3%81%8C%20res%20%E3%81%AB%E6%9C%80%E5%BE%8C%E3%81%AB%E7%8F%BE%E3%82%8C%E3%82%8B%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%0A%20%20%20%20for%20i%20in%20range%28m%29%3A%0A%20%20%20%20%20%20%20%20counter%5Bi%20%2B%201%5D%20%2B%3D%20counter%5Bi%5D%0A%20%20%20%20%23%204.%20nums%20%E3%82%92%E9%80%86%E9%A0%86%E3%81%AB%E8%B5%B0%E6%9F%BB%E3%81%97%E3%80%81%E5%90%84%E8%A6%81%E7%B4%A0%E3%82%92%E7%B5%90%E6%9E%9C%E9%85%8D%E5%88%97%20res%20%E3%81%AB%E6%A0%BC%E7%B4%8D%E3%81%99%E3%82%8B%0A%20%20%20%20%23%20%E7%B5%90%E6%9E%9C%E3%82%92%E8%A8%98%E9%8C%B2%E3%81%99%E3%82%8B%E3%81%9F%E3%82%81%E3%81%AE%E9%85%8D%E5%88%97%20res%20%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20n%20%3D%20len%28nums%29%0A%20%20%20%20res%20%3D%20%5B0%5D%20%2A%20n%0A%20%20%20%20for%20i%20in%20range%28n%20-%201%2C%20-1%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20num%20%3D%20nums%5Bi%5D%0A%20%20%20%20%20%20%20%20res%5Bcounter%5Bnum%5D%20-%201%5D%20%3D%20num%20%20%23%20num%20%E3%82%92%E5%AF%BE%E5%BF%9C%E3%81%99%E3%82%8B%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%AB%E9%85%8D%E7%BD%AE%0A%20%20%20%20%20%20%20%20counter%5Bnum%5D%20-%3D%201%20%20%23%20%E7%B4%AF%E7%A9%8D%E5%92%8C%E3%82%92%201%20%E6%B8%9B%E3%82%89%E3%81%97%E3%81%A6%E3%80%81%E6%AC%A1%E3%81%AB%20num%20%E3%82%92%E9%85%8D%E7%BD%AE%E3%81%99%E3%82%8B%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E5%BE%97%E3%82%8B%0A%20%20%20%20%23%20%E7%B5%90%E6%9E%9C%E9%85%8D%E5%88%97%20res%20%E3%81%A7%E5%85%83%E3%81%AE%E9%85%8D%E5%88%97%20nums%20%E3%82%92%E4%B8%8A%E6%9B%B8%E3%81%8D%E3%81%99%E3%82%8B%0A%20%20%20%20for%20i%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20nums%5Bi%5D%20%3D%20res%5Bi%5D%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B1%2C%200%2C%201%2C%202%2C%200%2C%204%2C%200%2C%202%2C%202%2C%204%5D%0A%20%20%20%20counting_sort%28nums%29%0A%20%20%20%20print%28f%22%E3%82%AB%E3%82%A6%E3%83%B3%E3%83%88%E3%82%BD%E3%83%BC%E3%83%88%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%20%7Bnums%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20counting_sort%28nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%22%22%22%E8%A8%88%E6%95%B0%E3%82%BD%E3%83%BC%E3%83%88%22%22%22%0A%20%20%20%20%23%20%E5%AE%8C%E5%85%A8%E7%89%88%E3%80%82%E3%82%AA%E3%83%96%E3%82%B8%E3%82%A7%E3%82%AF%E3%83%88%E3%82%92%E3%82%BD%E3%83%BC%E3%83%88%E3%81%A7%E3%81%8D%E3%80%81%E3%81%8B%E3%81%A4%E5%AE%89%E5%AE%9A%E3%82%BD%E3%83%BC%E3%83%88%E3%81%A7%E3%81%82%E3%82%8B%0A%20%20%20%20%23%201.%20%E9%85%8D%E5%88%97%E3%81%AE%E6%9C%80%E5%A4%A7%E8%A6%81%E7%B4%A0%20m%20%E3%82%92%E6%B1%82%E3%82%81%E3%82%8B%0A%20%20%20%20m%20%3D%20max%28nums%29%0A%20%20%20%20%23%202.%20%E5%90%84%E6%95%B0%E5%80%A4%E3%81%AE%E5%87%BA%E7%8F%BE%E5%9B%9E%E6%95%B0%E3%82%92%E6%95%B0%E3%81%88%E3%82%8B%0A%20%20%20%20%23%20counter%5Bnum%5D%20%E3%81%AF%20num%20%E3%81%AE%E5%87%BA%E7%8F%BE%E5%9B%9E%E6%95%B0%E3%82%92%E8%A1%A8%E3%81%99%0A%20%20%20%20counter%20%3D%20%5B0%5D%20%2A%20%28m%20%2B%201%29%0A%20%20%20%20for%20num%20in%20nums%3A%0A%20%20%20%20%20%20%20%20counter%5Bnum%5D%20%2B%3D%201%0A%20%20%20%20%23%203.%20counter%20%E3%81%AE%E7%B4%AF%E7%A9%8D%E5%92%8C%E3%82%92%E6%B1%82%E3%82%81%E3%81%A6%E3%80%81%E3%80%8C%E5%87%BA%E7%8F%BE%E5%9B%9E%E6%95%B0%E3%80%8D%E3%82%92%E3%80%8C%E6%9C%AB%E5%B0%BE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%80%8D%E3%81%AB%E5%A4%89%E6%8F%9B%E3%81%99%E3%82%8B%0A%20%20%20%20%23%20%E3%81%A4%E3%81%BE%E3%82%8A%20counter%5Bnum%5D-1%20%E3%81%AF%E3%80%81num%20%E3%81%8C%20res%20%E3%81%AB%E6%9C%80%E5%BE%8C%E3%81%AB%E7%8F%BE%E3%82%8C%E3%82%8B%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%0A%20%20%20%20for%20i%20in%20range%28m%29%3A%0A%20%20%20%20%20%20%20%20counter%5Bi%20%2B%201%5D%20%2B%3D%20counter%5Bi%5D%0A%20%20%20%20%23%204.%20nums%20%E3%82%92%E9%80%86%E9%A0%86%E3%81%AB%E8%B5%B0%E6%9F%BB%E3%81%97%E3%80%81%E5%90%84%E8%A6%81%E7%B4%A0%E3%82%92%E7%B5%90%E6%9E%9C%E9%85%8D%E5%88%97%20res%20%E3%81%AB%E6%A0%BC%E7%B4%8D%E3%81%99%E3%82%8B%0A%20%20%20%20%23%20%E7%B5%90%E6%9E%9C%E3%82%92%E8%A8%98%E9%8C%B2%E3%81%99%E3%82%8B%E3%81%9F%E3%82%81%E3%81%AE%E9%85%8D%E5%88%97%20res%20%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20n%20%3D%20len%28nums%29%0A%20%20%20%20res%20%3D%20%5B0%5D%20%2A%20n%0A%20%20%20%20for%20i%20in%20range%28n%20-%201%2C%20-1%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20num%20%3D%20nums%5Bi%5D%0A%20%20%20%20%20%20%20%20res%5Bcounter%5Bnum%5D%20-%201%5D%20%3D%20num%20%20%23%20num%20%E3%82%92%E5%AF%BE%E5%BF%9C%E3%81%99%E3%82%8B%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%AB%E9%85%8D%E7%BD%AE%0A%20%20%20%20%20%20%20%20counter%5Bnum%5D%20-%3D%201%20%20%23%20%E7%B4%AF%E7%A9%8D%E5%92%8C%E3%82%92%201%20%E6%B8%9B%E3%82%89%E3%81%97%E3%81%A6%E3%80%81%E6%AC%A1%E3%81%AB%20num%20%E3%82%92%E9%85%8D%E7%BD%AE%E3%81%99%E3%82%8B%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E5%BE%97%E3%82%8B%0A%20%20%20%20%23%20%E7%B5%90%E6%9E%9C%E9%85%8D%E5%88%97%20res%20%E3%81%A7%E5%85%83%E3%81%AE%E9%85%8D%E5%88%97%20nums%20%E3%82%92%E4%B8%8A%E6%9B%B8%E3%81%8D%E3%81%99%E3%82%8B%0A%20%20%20%20for%20i%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20nums%5Bi%5D%20%3D%20res%5Bi%5D%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B1%2C%200%2C%201%2C%202%2C%200%2C%204%2C%200%2C%202%2C%202%2C%204%5D%0A%20%20%20%20counting_sort%28nums%29%0A%20%20%20%20print%28f%22%E3%82%AB%E3%82%A6%E3%83%B3%E3%83%88%E3%82%BD%E3%83%BC%E3%83%88%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%20%7Bnums%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h2 id="1193">11.9.3 &nbsp; アルゴリズムの特性<a class="headerlink" href="#1193" title="Permanent link">&para;</a></h2>
 <ul>
-<li><strong>時間計算量は <span class="arithmatex">\(O(n + m)\)</span>、非適応ソート</strong>：<code>nums</code> と <code>counter</code> の走査が含まれ、どちらも線形時間を使用します。一般的に、<span class="arithmatex">\(n \gg m\)</span> であり、時間計算量は <span class="arithmatex">\(O(n)\)</span> に近づきます。</li>
-<li><strong>空間計算量は <span class="arithmatex">\(O(n + m)\)</span>、非インプレースソート</strong>：長さ <span class="arithmatex">\(n\)</span> の配列 <code>res</code> と長さ <span class="arithmatex">\(m\)</span> の配列 <code>counter</code> をそれぞれ使用します。</li>
-<li><strong>安定ソート</strong>：要素が「右から左」の順序で <code>res</code> に埋められるため、<code>nums</code> の走査を逆順にすることで、等しい要素間の相対位置の変化を防ぎ、安定したソートを実現できます。実際、<code>nums</code> を順番に走査しても正しいソート結果を生成できますが、結果は不安定です。</li>
+<li><strong>時間計算量は <span class="arithmatex">\(O(n + m)\)</span>、非適応ソート</strong> ：<code>nums</code> の走査と <code>counter</code> の走査が含まれ、いずれも線形時間です。一般には <span class="arithmatex">\(n \gg m\)</span> であり、時間計算量は <span class="arithmatex">\(O(n)\)</span> に近づきます。</li>
+<li><strong>空間計算量は <span class="arithmatex">\(O(n + m)\)</span>、非インプレースソート</strong>：長さがそれぞれ <span class="arithmatex">\(n\)</span> と <span class="arithmatex">\(m\)</span> の配列 <code>res</code> と <code>counter</code> を利用します。</li>
+<li><strong>安定ソート</strong>：<code>res</code> に要素を埋める順序が「右から左」であるため、<code>nums</code> を逆順に走査することで等しい要素どうしの相対位置が変化するのを防ぎ、安定ソートを実現できます。実際には、<code>nums</code> を順方向に走査しても正しいソート結果は得られますが、その結果は安定ではありません。</li>
 </ul>
-<h2 id="1194">11.9.4 &nbsp; 制限事項<a class="headerlink" href="#1194" title="Permanent link">&para;</a></h2>
-<p>今までに、計数ソートは非常に巧妙だと感じるかもしれません。単に量をカウントするだけで効率的なソートを実現できるからです。しかし、計数ソートを使用するための前提条件は比較的厳しいです。</p>
-<p><strong>計数ソートは非負整数にのみ適用できます</strong>。他のタイプのデータに適用したい場合、これらのデータが要素の元の順序を変更することなく非負整数に変換できることを保証する必要があります。例えば、負の整数を含む配列の場合、最初にすべての数に定数を加えて、すべてを正の数に変換し、ソート完了後に元に戻すことができます。</p>
-<p><strong>計数ソートは値の範囲が小さい大きなデータセットに適しています</strong>。例えば、上記の例では、<span class="arithmatex">\(m\)</span> は大きすぎるべきではありません。そうでなければ、あまりにも多くのスペースを占有してしまいます。そして <span class="arithmatex">\(n \ll m\)</span> の場合、計数ソートは <span class="arithmatex">\(O(m)\)</span> 時間を使用し、<span class="arithmatex">\(O(n \log n)\)</span> ソートアルゴリズムより遅い可能性があります。</p>
+<h2 id="1194">11.9.4 &nbsp; 制約<a class="headerlink" href="#1194" title="Permanent link">&para;</a></h2>
+<p>ここまで読むと、計数ソートは非常に巧妙で、個数を数えるだけで効率的なソートを実現できると感じるかもしれません。しかし、計数ソートを利用するための前提条件は比較的厳格です。</p>
+<p><strong>計数ソートは非負整数にしか適用できません</strong>。ほかの型のデータに適用したい場合は、それらのデータを非負整数に変換でき、かつ変換の過程で要素間の相対的な大小関係が変わらないことを保証する必要があります。たとえば、負数を含む整数配列に対しては、すべての数値に定数を加えて正数へ変換し、ソート後に元へ戻すことができます。</p>
+<p><strong>計数ソートはデータ量が多く、値域が小さい場合に適しています</strong>。たとえば上記の例では <span class="arithmatex">\(m\)</span> が大きすぎてはならず、そうでないと過剰な空間を消費します。また、<span class="arithmatex">\(n \ll m\)</span> のとき、計数ソートは <span class="arithmatex">\(O(m)\)</span> 時間を要するため、<span class="arithmatex">\(O(n \log n)\)</span> のソートアルゴリズムより遅くなる可能性があります。</p>
 
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diff --git a/ja/chapter_sorting/heap_sort/index.html b/ja/chapter_sorting/heap_sort/index.html
index ee143032d..7fade06ba 100644
--- a/ja/chapter_sorting/heap_sort/index.html
+++ b/ja/chapter_sorting/heap_sort/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
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@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1635,7 +1635,7 @@
   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1942,7 +1942,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2105,7 +2105,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2491,7 +2491,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2547,7 +2547,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2575,7 +2575,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
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   <a href="#1172" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.7.2 &nbsp; アルゴリズムの特徴
+        11.7.2 &nbsp; アルゴリズムの特性
       
     </span>
   </a>
@@ -3185,7 +3185,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
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   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
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   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
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   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
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   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
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   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3715,7 +3715,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3908,7 +3908,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4153,7 +4153,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4310,7 +4310,7 @@
   <a href="#1172" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.7.2 &nbsp; アルゴリズムの特徴
+        11.7.2 &nbsp; アルゴリズムの特性
       
     </span>
   </a>
@@ -4357,30 +4357,30 @@
 <h1 id="117">11.7 &nbsp; ヒープソート<a class="headerlink" href="#117" title="Permanent link">&para;</a></h1>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>この節を読む前に、「ヒープ」の章を必ず完了させてください。</p>
+<p>本節を読む前に、「ヒープ」の章を学習済みであることを確認してください。</p>
 </div>
-<p><u>ヒープソート</u>は、ヒープデータ構造に基づく効率的なソートアルゴリズムです。すでに学習した「ヒープの構築」と「要素の抽出」操作を使用してヒープソートを実装できます。</p>
+<p><u>ヒープソート（heap sort）</u>は、ヒープデータ構造に基づいて実装される効率的なソートアルゴリズムです。すでに学んだ「ヒープ構築操作」と「要素の取り出し操作」を利用してヒープソートを実現できます。</p>
 <ol>
-<li>配列を入力し、最小ヒープを構築します。ここで、最小要素がヒープの頂上に位置します。</li>
-<li>継続的に抽出操作を実行し、抽出された要素を順次記録して、最小から最大までのソート済みリストを取得します。</li>
+<li>配列を入力して最小ヒープを構築すると、このとき最小要素はヒープの頂点にあります。</li>
+<li>取り出し操作を繰り返し実行し、取り出された要素を順に記録すれば、昇順に並んだ列が得られます。</li>
 </ol>
-<p>上記の方法は実現可能ですが、ポップされた要素を格納するための追加の配列が必要で、やや空間を消費します。実際には、通常、より優雅な実装を使用します。</p>
+<p>以上の方法でも実行できますが、取り出した要素を保存するために追加の配列が必要となり、空間をやや無駄にします。実際には、通常はより洗練された実装方法を用います。</p>
 <h2 id="1171">11.7.1 &nbsp; アルゴリズムの流れ<a class="headerlink" href="#1171" title="Permanent link">&para;</a></h2>
-<p>配列の長さを <span class="arithmatex">\(n\)</span> とすると、ヒープソートの過程は以下の通りです。</p>
+<p>配列の長さを <span class="arithmatex">\(n\)</span> とすると、ヒープソートの流れは次図のとおりです。</p>
 <ol>
-<li>配列を入力し、最大ヒープを構築します。この手順の後、最大要素がヒープの頂上に位置します。</li>
-<li>ヒープの頂上要素（最初の要素）とヒープの底部要素（最後の要素）を交換します。この交換の後、ヒープの長さを <span class="arithmatex">\(1\)</span> 減らし、ソート済み要素の数を <span class="arithmatex">\(1\)</span> 増やします。</li>
-<li>ヒープの頂上から開始して、上から下へのsift-down操作を実行します。sift-downの後、ヒープの性質が復元されます。</li>
-<li>手順 <code>2.</code> と <code>3.</code> を繰り返します。<span class="arithmatex">\(n - 1\)</span> ラウンドループして、配列のソートを完了します。</li>
+<li>配列を入力して最大ヒープを構築します。完了後、最大要素はヒープの頂点にあります。</li>
+<li>ヒープ頂点の要素（最初の要素）とヒープ末尾の要素（最後の要素）を交換します。交換後、ヒープの長さは <span class="arithmatex">\(1\)</span> 減少し、整列済み要素数は <span class="arithmatex">\(1\)</span> 増加します。</li>
+<li>ヒープ頂点の要素から始めて、上から下へヒープ化操作（sift down）を実行します。ヒープ化が完了すると、ヒープの性質が回復します。</li>
+<li>第 <code>2.</code> ステップと第 <code>3.</code> ステップを繰り返し実行します。これを <span class="arithmatex">\(n - 1\)</span> 回繰り返すと、配列の整列が完了します。</li>
 </ol>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>実際、要素抽出操作も手順 <code>2.</code> と <code>3.</code> を含み、抽出された要素をヒープから削除する追加の手順があります。</p>
+<p>実際には、要素の取り出し操作にも第 <code>2.</code> ステップと第 <code>3.</code> ステップが含まれており、要素を取り出す処理が 1 つ加わるだけです。</p>
 </div>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:12"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label><label for="__tabbed_1_5">&lt;5&gt;</label><label for="__tabbed_1_6">&lt;6&gt;</label><label for="__tabbed_1_7">&lt;7&gt;</label><label for="__tabbed_1_8">&lt;8&gt;</label><label for="__tabbed_1_9">&lt;9&gt;</label><label for="__tabbed_1_10">&lt;10&gt;</label><label for="__tabbed_1_11">&lt;11&gt;</label><label for="__tabbed_1_12">&lt;12&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="ヒープソートの過程" class="animation-figure" src="../heap_sort.assets/heap_sort_step1.png" /></p>
+<p><img alt="ヒープソートの手順" class="animation-figure" src="../heap_sort.assets/heap_sort_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="heap_sort_step2" class="animation-figure" src="../heap_sort.assets/heap_sort_step2.png" /></p>
@@ -4417,16 +4417,16 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 11-12 &nbsp; ヒープソートの過程 </p>
+<p align="center"> 図 11-12 &nbsp; ヒープソートの手順 </p>
 
-<p>コードの実装では、「ヒープ」の章からのsift-down関数 <code>sift_down()</code> を使用しました。最大要素が抽出されるにつれてヒープの長さが減少するため、<code>sift_down()</code> 関数に長さパラメータ <span class="arithmatex">\(n\)</span> を追加して、ヒープの現在の有効長を指定する必要があることに注意することが重要です。コードは以下の通りです：</p>
+<p>コード実装では、「ヒープ」の章と同じ上から下へのヒープ化 <code>sift_down()</code> 関数を使用します。注意すべき点として、ヒープの長さは最大要素を取り出すたびに短くなるため、<code>sift_down()</code> 関数に長さパラメータ <span class="arithmatex">\(n\)</span> を追加し、ヒープの現在の有効な長さを指定する必要があります。コードは以下のとおりです。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">heap_sort.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">sift_down</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ヒープの長さが n、ノード i から上から下へヒープ化を開始&quot;&quot;&quot;</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ヒープの長さは n。ノード i から下方向にヒープ化&quot;&quot;&quot;</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
-<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>        <span class="c1"># i、l、r の中で最大のノードを判定し、ma とする</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>        <span class="c1"># ノード i, l, r のうち値が最大のノードを ma とする</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="n">l</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="n">r</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">2</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="n">ma</span> <span class="o">=</span> <span class="n">i</span>
@@ -4434,32 +4434,32 @@
 <a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>            <span class="n">ma</span> <span class="o">=</span> <span class="n">l</span>
 <a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="k">if</span> <span class="n">r</span> <span class="o">&lt;</span> <span class="n">n</span> <span class="ow">and</span> <span class="n">nums</span><span class="p">[</span><span class="n">r</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">]:</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>            <span class="n">ma</span> <span class="o">=</span> <span class="n">r</span>
-<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="c1"># ノード i が最大または l、r のインデックスが範囲外の場合、さらなるヒープ化は不要、ループを抜ける</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="c1"># ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="k">if</span> <span class="n">ma</span> <span class="o">==</span> <span class="n">i</span><span class="p">:</span>
 <a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>            <span class="k">break</span>
-<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>        <span class="c1"># 2つのノードを交換</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>        <span class="c1"># 2 つのノードを交換</span>
 <a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>        <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
-<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>        <span class="c1"># 下向きにヒープ化をループ</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>        <span class="c1"># ループで上から下へヒープ化</span>
 <a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>        <span class="n">i</span> <span class="o">=</span> <span class="n">ma</span>
 <a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>
 <a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a><span class="k">def</span><span class="w"> </span><span class="nf">heap_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
 <a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ヒープソート&quot;&quot;&quot;</span>
-<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>    <span class="c1"># ヒープ構築操作：葉ノード以外のすべてのノードをヒープ化</span>
+<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>    <span class="c1"># ヒープ構築：葉ノード以外のすべてのノードをヒープ化する</span>
 <a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>        <span class="n">sift_down</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">),</span> <span class="n">i</span><span class="p">)</span>
-<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>    <span class="c1"># ヒープから最大要素を抽出し、n-1 回繰り返す</span>
+<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>    <span class="c1"># ヒープから最大要素を取り出し、n-1 回繰り返す</span>
 <a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
-<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>        <span class="c1"># ルートノードと最も右の葉ノードを交換（最初の要素と最後の要素を交換）</span>
+<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>        <span class="c1"># 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
 <a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a>        <span class="n">nums</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
-<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a>        <span class="c1"># ルートノードから上から下へヒープ化を開始</span>
+<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a>        <span class="c1"># 根ノードを起点に、上から下へヒープ化</span>
 <a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a>        <span class="n">sift_down</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">heap_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* ヒープの長さはn、ノードiから上から下へヒープ化を開始 */</span>
+<div class="highlight"><span class="filename">heap_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* ヒープの長さは n。ノード i から下方向にヒープ化 */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nb">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">        </span><span class="c1">// i、l、r の中で最大のノードを決定し、maとして記録</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">        </span><span class="c1">// ノード i, l, r のうち値が最大のノードを ma とする</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
@@ -4467,38 +4467,38 @@
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
-<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="c1">// ノードiが最大か、インデックスl、rが境界外の場合、それ以上のヒープ化は不要で終了</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="c1">// ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
 <a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">        </span><span class="c1">// 二つのノードを交換</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
 <a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">]);</span>
-<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">        </span><span class="c1">// 下向きにヒープ化をループ</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">        </span><span class="c1">// ループで上から下へヒープ化</span>
 <a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
 <a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="p">}</span>
 <a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a>
 <a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="cm">/* ヒープソート */</span>
 <a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="kt">void</span><span class="w"> </span><span class="nf">heapSort</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w">    </span><span class="c1">// ヒープ構築操作：葉以外のすべてのノードをヒープ化</span>
+<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w">    </span><span class="c1">// ヒープ構築：葉ノード以外のすべてのノードをヒープ化する</span>
 <a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="o">--</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a><span class="w">        </span><span class="n">siftDown</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">(),</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
 <a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="w">    </span><span class="c1">// ヒープから最大要素を抽出し、n-1回繰り返す</span>
+<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="w">    </span><span class="c1">// ヒープから最大要素を取り出し、n-1 回繰り返す</span>
 <a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="o">--</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="w">        </span><span class="c1">// ルートノードを最右葉ノードと交換（最初の要素を最後の要素と交換）</span>
+<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="w">        </span><span class="c1">// 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
 <a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
-<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="w">        </span><span class="c1">// ルートノードから上から下へヒープ化を開始</span>
+<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="w">        </span><span class="c1">// 根ノードを起点に、上から下へヒープ化</span>
 <a id="__codelineno-1-34" name="__codelineno-1-34" href="#__codelineno-1-34"></a><span class="w">        </span><span class="n">siftDown</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-1-35" name="__codelineno-1-35" href="#__codelineno-1-35"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-1-36" name="__codelineno-1-36" href="#__codelineno-1-36"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">heap_sort.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* ヒープの長さは n、ノード i から上から下へヒープ化開始 */</span>
+<div class="highlight"><span class="filename">heap_sort.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* ヒープの長さは n。ノード i から下方向にヒープ化 */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">        </span><span class="c1">// i, l, r の中で最大のノードを判定し、ma とする</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">        </span><span class="c1">// ノード i, l, r のうち値が最大のノードを ma とする</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
@@ -4506,103 +4506,452 @@
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">r</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span><span class="p">)</span>
 <a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
-<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="c1">// ノード i が最大、またはインデックス l, r が範囲外の場合、さらなるヒープ化は不要、ブレーク</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="c1">// ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
 <a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
-<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="c1">// 2つのノードを交換</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
 <a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span>
-<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">        </span><span class="c1">// 下向きにヒープ化をループ</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">        </span><span class="c1">// ループで上から下へヒープ化</span>
 <a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
 <a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="p">}</span>
 <a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a>
 <a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="cm">/* ヒープソート */</span>
 <a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="kt">void</span><span class="w"> </span><span class="nf">heapSort</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w">    </span><span class="c1">// ヒープ構築操作: 葉ノード以外のすべてのノードをヒープ化</span>
+<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w">    </span><span class="c1">// ヒープ構築：葉ノード以外のすべてのノードをヒープ化する</span>
 <a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="w">        </span><span class="n">siftDown</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
 <a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a><span class="w">    </span><span class="c1">// ヒープから最大要素を抽出し、n-1 回繰り返し</span>
+<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a><span class="w">    </span><span class="c1">// ヒープから最大要素を取り出し、n-1 回繰り返す</span>
 <a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="w">        </span><span class="c1">// ルートノードと最も右の葉ノードを交換（最初の要素と最後の要素を交換）</span>
+<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="w">        </span><span class="c1">// 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
 <a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
-<a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a><span class="w">        </span><span class="c1">// ルートノードから上から下へヒープ化開始</span>
+<a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a><span class="w">        </span><span class="c1">// 根ノードを起点に、上から下へヒープ化</span>
 <a id="__codelineno-2-37" name="__codelineno-2-37" href="#__codelineno-2-37"></a><span class="w">        </span><span class="n">siftDown</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-2-38" name="__codelineno-2-38" href="#__codelineno-2-38"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-2-39" name="__codelineno-2-39" href="#__codelineno-2-39"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">heap_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">heap_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">SiftDown</span><span class="p">}</span>
-<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
-<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">heap_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">HeapSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">heap_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* ヒープの長さは n。ノード i から下方向にヒープ化 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">SiftDown</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="k">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">        </span><span class="c1">// ノード i, l, r のうち値が最大のノードを ma とする</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">        </span><span class="c1">// ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">        </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">])</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">]);</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">        </span><span class="c1">// ループで上から下へヒープ化</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="p">}</span>
+<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a>
+<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="cm">/* ヒープソート */</span>
+<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="k">void</span><span class="w"> </span><span class="nf">HeapSort</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="w">    </span><span class="c1">// ヒープ構築：葉ノード以外のすべてのノードをヒープ化する</span>
+<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="w">        </span><span class="n">SiftDown</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a><span class="w">    </span><span class="c1">// ヒープから最大要素を取り出し、n-1 回繰り返す</span>
+<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a><span class="w">        </span><span class="c1">// 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
+<a id="__codelineno-3-31" name="__codelineno-3-31" href="#__codelineno-3-31"></a><span class="w">        </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-3-32" name="__codelineno-3-32" href="#__codelineno-3-32"></a><span class="w">        </span><span class="c1">// 根ノードを起点に、上から下へヒープ化</span>
+<a id="__codelineno-3-33" name="__codelineno-3-33" href="#__codelineno-3-33"></a><span class="w">        </span><span class="n">SiftDown</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-3-34" name="__codelineno-3-34" href="#__codelineno-3-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-35" name="__codelineno-3-35" href="#__codelineno-3-35"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">heap_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">siftDown</span><span class="p">}</span>
-<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
-<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">heapSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">heap_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* ヒープの長さは n。ノード i から下方向にヒープ化 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">siftDown</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">true</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">        </span><span class="c1">// ノード i, l, r のうち値が最大のノードを ma とする</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">        </span><span class="nx">l</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">2</span><span class="o">*</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">        </span><span class="nx">r</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">2</span><span class="o">*</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">        </span><span class="nx">ma</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">i</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">l</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">ma</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">            </span><span class="nx">ma</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">l</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">r</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">ma</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">            </span><span class="nx">ma</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">r</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">        </span><span class="c1">// ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w">        </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">ma</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">ma</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w">        </span><span class="c1">// ループで上から下へヒープ化</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w">        </span><span class="nx">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">ma</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="p">}</span>
+<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a>
+<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="cm">/* ヒープソート */</span>
+<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="kd">func</span><span class="w"> </span><span class="nx">heapSort</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w">    </span><span class="c1">// ヒープ構築：葉ノード以外のすべてのノードをヒープ化する</span>
+<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="w">        </span><span class="nx">siftDown</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">),</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span>
+<a id="__codelineno-4-30" name="__codelineno-4-30" href="#__codelineno-4-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-31" name="__codelineno-4-31" href="#__codelineno-4-31"></a><span class="w">    </span><span class="c1">// ヒープから最大要素を取り出し、n-1 回繰り返す</span>
+<a id="__codelineno-4-32" name="__codelineno-4-32" href="#__codelineno-4-32"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-33" name="__codelineno-4-33" href="#__codelineno-4-33"></a><span class="w">        </span><span class="c1">// 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
+<a id="__codelineno-4-34" name="__codelineno-4-34" href="#__codelineno-4-34"></a><span class="w">        </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-4-35" name="__codelineno-4-35" href="#__codelineno-4-35"></a><span class="w">        </span><span class="c1">// 根ノードを起点に、上から下へヒープ化</span>
+<a id="__codelineno-4-36" name="__codelineno-4-36" href="#__codelineno-4-36"></a><span class="w">        </span><span class="nx">siftDown</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-4-37" name="__codelineno-4-37" href="#__codelineno-4-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-38" name="__codelineno-4-38" href="#__codelineno-4-38"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">heap_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">siftDown</span><span class="p">}</span>
-<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
-<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">heapSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">heap_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* ヒープの長さは n。ノード i から下方向にヒープ化 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="kc">true</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">        </span><span class="c1">// ノード i, l, r のうち値が最大のノードを ma とする</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">l</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">r</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">ma</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">l</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">r</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">        </span><span class="c1">// ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="w">        </span><span class="n">nums</span><span class="p">.</span><span class="n">swapAt</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">)</span>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w">        </span><span class="c1">// ループで上から下へヒープ化</span>
+<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ma</span>
+<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="p">}</span>
+<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a>
+<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a><span class="cm">/* ヒープソート */</span>
+<a id="__codelineno-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a><span class="kd">func</span><span class="w"> </span><span class="nf">heapSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a><span class="w">    </span><span class="c1">// ヒープ構築：葉ノード以外のすべてのノードをヒープ化する</span>
+<a id="__codelineno-5-29" name="__codelineno-5-29" href="#__codelineno-5-29"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">count</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">through</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">by</span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-30" name="__codelineno-5-30" href="#__codelineno-5-30"></a><span class="w">        </span><span class="n">siftDown</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">count</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-5-31" name="__codelineno-5-31" href="#__codelineno-5-31"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-32" name="__codelineno-5-32" href="#__codelineno-5-32"></a><span class="w">    </span><span class="c1">// ヒープから最大要素を取り出し、n-1 回繰り返す</span>
+<a id="__codelineno-5-33" name="__codelineno-5-33" href="#__codelineno-5-33"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="p">.</span><span class="bp">dropFirst</span><span class="p">().</span><span class="n">reversed</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-34" name="__codelineno-5-34" href="#__codelineno-5-34"></a><span class="w">        </span><span class="c1">// 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
+<a id="__codelineno-5-35" name="__codelineno-5-35" href="#__codelineno-5-35"></a><span class="w">        </span><span class="n">nums</span><span class="p">.</span><span class="n">swapAt</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-5-36" name="__codelineno-5-36" href="#__codelineno-5-36"></a><span class="w">        </span><span class="c1">// 根ノードを起点に、上から下へヒープ化</span>
+<a id="__codelineno-5-37" name="__codelineno-5-37" href="#__codelineno-5-37"></a><span class="w">        </span><span class="n">siftDown</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-5-38" name="__codelineno-5-38" href="#__codelineno-5-38"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-39" name="__codelineno-5-39" href="#__codelineno-5-39"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">heap_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">siftDown</span><span class="p">}</span>
-<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
-<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">heapSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">heap_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* ヒープの長さは n。ノード i から下方向にヒープ化 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">siftDown</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">        </span><span class="c1">// ノード i, l, r のうち値が最大のノードを ma とする</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">l</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">            </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">l</span><span class="p">;</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">            </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">r</span><span class="p">;</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">        </span><span class="c1">// ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">ma</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">        </span><span class="p">[</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">ma</span><span class="p">]]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">nums</span><span class="p">[</span><span class="nx">ma</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]];</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w">        </span><span class="c1">// ループで上から下へヒープ化</span>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w">        </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">ma</span><span class="p">;</span>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="p">}</span>
+<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a>
+<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="cm">/* ヒープソート */</span>
+<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="kd">function</span><span class="w"> </span><span class="nx">heapSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-27" name="__codelineno-6-27" href="#__codelineno-6-27"></a><span class="w">    </span><span class="c1">// ヒープ構築：葉ノード以外のすべてのノードをヒープ化する</span>
+<a id="__codelineno-6-28" name="__codelineno-6-28" href="#__codelineno-6-28"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-29" name="__codelineno-6-29" href="#__codelineno-6-29"></a><span class="w">        </span><span class="nx">siftDown</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">);</span>
+<a id="__codelineno-6-30" name="__codelineno-6-30" href="#__codelineno-6-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-31" name="__codelineno-6-31" href="#__codelineno-6-31"></a><span class="w">    </span><span class="c1">// ヒープから最大要素を取り出し、n-1 回繰り返す</span>
+<a id="__codelineno-6-32" name="__codelineno-6-32" href="#__codelineno-6-32"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-33" name="__codelineno-6-33" href="#__codelineno-6-33"></a><span class="w">        </span><span class="c1">// 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
+<a id="__codelineno-6-34" name="__codelineno-6-34" href="#__codelineno-6-34"></a><span class="w">        </span><span class="p">[</span><span class="nx">nums</span><span class="p">[</span><span class="mf">0</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="mf">0</span><span class="p">]];</span>
+<a id="__codelineno-6-35" name="__codelineno-6-35" href="#__codelineno-6-35"></a><span class="w">        </span><span class="c1">// 根ノードを起点に、上から下へヒープ化</span>
+<a id="__codelineno-6-36" name="__codelineno-6-36" href="#__codelineno-6-36"></a><span class="w">        </span><span class="nx">siftDown</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-6-37" name="__codelineno-6-37" href="#__codelineno-6-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-38" name="__codelineno-6-38" href="#__codelineno-6-38"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">heap_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">siftDown</span><span class="p">}</span>
-<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
-<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">heapSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">heap_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* ヒープの長さは n。ノード i から下方向にヒープ化 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">siftDown</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">        </span><span class="c1">// ノード i, l, r のうち値が最大のノードを ma とする</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">l</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">            </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">l</span><span class="p">;</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">            </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">r</span><span class="p">;</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">        </span><span class="c1">// ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">ma</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">        </span><span class="p">[</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">ma</span><span class="p">]]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">nums</span><span class="p">[</span><span class="nx">ma</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]];</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w">        </span><span class="c1">// ループで上から下へヒープ化</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="w">        </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">ma</span><span class="p">;</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="p">}</span>
+<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="cm">/* ヒープソート */</span>
+<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="kd">function</span><span class="w"> </span><span class="nx">heapSort</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a><span class="w">    </span><span class="c1">// ヒープ構築：葉ノード以外のすべてのノードをヒープ化する</span>
+<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-29" name="__codelineno-7-29" href="#__codelineno-7-29"></a><span class="w">        </span><span class="nx">siftDown</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">);</span>
+<a id="__codelineno-7-30" name="__codelineno-7-30" href="#__codelineno-7-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-31" name="__codelineno-7-31" href="#__codelineno-7-31"></a><span class="w">    </span><span class="c1">// ヒープから最大要素を取り出し、n-1 回繰り返す</span>
+<a id="__codelineno-7-32" name="__codelineno-7-32" href="#__codelineno-7-32"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-33" name="__codelineno-7-33" href="#__codelineno-7-33"></a><span class="w">        </span><span class="c1">// 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
+<a id="__codelineno-7-34" name="__codelineno-7-34" href="#__codelineno-7-34"></a><span class="w">        </span><span class="p">[</span><span class="nx">nums</span><span class="p">[</span><span class="mf">0</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="mf">0</span><span class="p">]];</span>
+<a id="__codelineno-7-35" name="__codelineno-7-35" href="#__codelineno-7-35"></a><span class="w">        </span><span class="c1">// 根ノードを起点に、上から下へヒープ化</span>
+<a id="__codelineno-7-36" name="__codelineno-7-36" href="#__codelineno-7-36"></a><span class="w">        </span><span class="nx">siftDown</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-7-37" name="__codelineno-7-37" href="#__codelineno-7-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-38" name="__codelineno-7-38" href="#__codelineno-7-38"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">heap_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">siftDown</span><span class="p">}</span>
-<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
-<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">heapSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">heap_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* ヒープの長さは n。ノード i から下方向にヒープ化 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">    </span><span class="c1">// ノード i, l, r のうち値が最大のノードを ma とする</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">    </span><span class="c1">// ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">    </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">    </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">];</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">    </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">    </span><span class="c1">// ループで上から下へヒープ化</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">    </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="p">}</span>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a>
+<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="cm">/* ヒープソート */</span>
+<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="kt">void</span><span class="w"> </span><span class="n">heapSort</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a><span class="w">  </span><span class="c1">// ヒープ構築：葉ノード以外のすべてのノードをヒープ化する</span>
+<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a><span class="w">    </span><span class="n">siftDown</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-8-26" name="__codelineno-8-26" href="#__codelineno-8-26"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-27" name="__codelineno-8-27" href="#__codelineno-8-27"></a><span class="w">  </span><span class="c1">// ヒープから最大要素を取り出し、n-1 回繰り返す</span>
+<a id="__codelineno-8-28" name="__codelineno-8-28" href="#__codelineno-8-28"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-29" name="__codelineno-8-29" href="#__codelineno-8-29"></a><span class="w">    </span><span class="c1">// 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
+<a id="__codelineno-8-30" name="__codelineno-8-30" href="#__codelineno-8-30"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="m">0</span><span class="p">];</span>
+<a id="__codelineno-8-31" name="__codelineno-8-31" href="#__codelineno-8-31"></a><span class="w">    </span><span class="n">nums</span><span class="p">[</span><span class="m">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-8-32" name="__codelineno-8-32" href="#__codelineno-8-32"></a><span class="w">    </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-8-33" name="__codelineno-8-33" href="#__codelineno-8-33"></a><span class="w">    </span><span class="c1">// 根ノードを起点に、上から下へヒープ化</span>
+<a id="__codelineno-8-34" name="__codelineno-8-34" href="#__codelineno-8-34"></a><span class="w">    </span><span class="n">siftDown</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-8-35" name="__codelineno-8-35" href="#__codelineno-8-35"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-36" name="__codelineno-8-36" href="#__codelineno-8-36"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">heap_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">sift_down</span><span class="p">}</span>
-<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
-<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">heap_sort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">heap_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* ヒープの長さは n。ノード i から下方向にヒープ化 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">sift_down</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="k">loop</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">        </span><span class="c1">// ノード i, l, r のうち値が最大のノードを ma とする</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">        </span><span class="c1">// ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">        </span><span class="n">nums</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">);</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w">        </span><span class="c1">// ループで上から下へヒープ化</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
+<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="p">}</span>
+<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a>
+<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="cm">/* ヒープソート */</span>
+<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="k">fn</span><span class="w"> </span><span class="nf">heap_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="w">    </span><span class="c1">// ヒープ構築：葉ノード以外のすべてのノードをヒープ化する</span>
+<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">..</span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">).</span><span class="n">rev</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="w">        </span><span class="n">sift_down</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">(),</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-9-30" name="__codelineno-9-30" href="#__codelineno-9-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-31" name="__codelineno-9-31" href="#__codelineno-9-31"></a><span class="w">    </span><span class="c1">// ヒープから最大要素を取り出し、n-1 回繰り返す</span>
+<a id="__codelineno-9-32" name="__codelineno-9-32" href="#__codelineno-9-32"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">..</span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()).</span><span class="n">rev</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-33" name="__codelineno-9-33" href="#__codelineno-9-33"></a><span class="w">        </span><span class="c1">// 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
+<a id="__codelineno-9-34" name="__codelineno-9-34" href="#__codelineno-9-34"></a><span class="w">        </span><span class="n">nums</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-9-35" name="__codelineno-9-35" href="#__codelineno-9-35"></a><span class="w">        </span><span class="c1">// 根ノードを起点に、上から下へヒープ化</span>
+<a id="__codelineno-9-36" name="__codelineno-9-36" href="#__codelineno-9-36"></a><span class="w">        </span><span class="n">sift_down</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-9-37" name="__codelineno-9-37" href="#__codelineno-9-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-38" name="__codelineno-9-38" href="#__codelineno-9-38"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">heap_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">siftDown</span><span class="p">}</span>
-<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
-<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">heapSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">heap_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* ヒープの長さは n。ノード i から下方向にヒープ化 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">        </span><span class="c1">// ノード i, l, r のうち値が最大のノードを ma とする</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">        </span><span class="c1">// ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">];</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span>
+<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="w">        </span><span class="c1">// ループで上から下へヒープ化</span>
+<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
+<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="p">}</span>
+<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a>
+<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="cm">/* ヒープソート */</span>
+<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="kt">void</span><span class="w"> </span><span class="nf">heapSort</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="w">    </span><span class="c1">// ヒープ構築：葉ノード以外のすべてのノードをヒープ化する</span>
+<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="o">--</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a><span class="w">        </span><span class="n">siftDown</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></a><span class="w">    </span><span class="c1">// ヒープから最大要素を取り出し、n-1 回繰り返す</span>
+<a id="__codelineno-10-32" name="__codelineno-10-32" href="#__codelineno-10-32"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="o">--</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-33" name="__codelineno-10-33" href="#__codelineno-10-33"></a><span class="w">        </span><span class="c1">// 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
+<a id="__codelineno-10-34" name="__codelineno-10-34" href="#__codelineno-10-34"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-10-35" name="__codelineno-10-35" href="#__codelineno-10-35"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-10-36" name="__codelineno-10-36" href="#__codelineno-10-36"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-10-37" name="__codelineno-10-37" href="#__codelineno-10-37"></a><span class="w">        </span><span class="c1">// 根ノードを起点に、上から下へヒープ化</span>
+<a id="__codelineno-10-38" name="__codelineno-10-38" href="#__codelineno-10-38"></a><span class="w">        </span><span class="n">siftDown</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-10-39" name="__codelineno-10-39" href="#__codelineno-10-39"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-40" name="__codelineno-10-40" href="#__codelineno-10-40"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">heap_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">siftDown</span><span class="p">}</span>
-<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
-<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">heapSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">heap_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* ヒープの長さは n。ノード i から下方向にヒープ化 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">li</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">li</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">        </span><span class="c1">// ノード i, l, r のうち値が最大のノードを ma とする</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">2</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">l</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span><span class="p">)</span><span class="w"> </span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">r</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span><span class="p">)</span><span class="w"> </span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">        </span><span class="c1">// ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">        </span><span class="c1">// 2 つのノードを交換</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w">        </span><span class="c1">// ループで上から下へヒープ化</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span>
+<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="p">}</span>
+<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a>
+<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="cm">/* ヒープソート */</span>
+<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">heapSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a><span class="w">    </span><span class="c1">// ヒープ構築：葉ノード以外のすべてのノードをヒープ化する</span>
+<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="n">downTo</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a><span class="w">        </span><span class="n">siftDown</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-11-30" name="__codelineno-11-30" href="#__codelineno-11-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></a><span class="w">    </span><span class="c1">// ヒープから最大要素を取り出し、n-1 回繰り返す</span>
+<a id="__codelineno-11-32" name="__codelineno-11-32" href="#__codelineno-11-32"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="n">downTo</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-33" name="__codelineno-11-33" href="#__codelineno-11-33"></a><span class="w">        </span><span class="c1">// 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
+<a id="__codelineno-11-34" name="__codelineno-11-34" href="#__codelineno-11-34"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="m">0</span><span class="o">]</span>
+<a id="__codelineno-11-35" name="__codelineno-11-35" href="#__codelineno-11-35"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="m">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-11-36" name="__codelineno-11-36" href="#__codelineno-11-36"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span>
+<a id="__codelineno-11-37" name="__codelineno-11-37" href="#__codelineno-11-37"></a><span class="w">        </span><span class="c1">// 根ノードを起点に、上から下へヒープ化</span>
+<a id="__codelineno-11-38" name="__codelineno-11-38" href="#__codelineno-11-38"></a><span class="w">        </span><span class="n">siftDown</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">)</span>
+<a id="__codelineno-11-39" name="__codelineno-11-39" href="#__codelineno-11-39"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-40" name="__codelineno-11-40" href="#__codelineno-11-40"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">heap_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">sift_down</span><span class="p">}</span>
-<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
-<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">heap_sort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">heap_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### ヒープ長 n で、ノード i から上から下へヒープ化 ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">sift_down</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="kp">true</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">    </span><span class="c1"># ノード i, l, r のうち値が最大のノードを ma とする</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">    </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">    </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">    </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">    </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">l</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">    </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">r</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">    </span><span class="c1"># ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">    </span><span class="k">break</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">    </span><span class="c1"># 2 つのノードを交換</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">    </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">    </span><span class="c1"># ループで上から下へヒープ化</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">    </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="k">end</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="c1">### ヒープソート ###</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="k">def</span><span class="w"> </span><span class="nf">heap_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w">  </span><span class="c1"># ヒープ構築：葉ノード以外のすべてのノードをヒープ化する</span>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w">  </span><span class="p">(</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span>
+<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="w">    </span><span class="n">sift_down</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="w">  </span><span class="c1"># ヒープから最大要素を取り出し、n-1 回繰り返す</span>
+<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a><span class="w">  </span><span class="p">(</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span>
+<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a><span class="w">    </span><span class="c1"># 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）</span>
+<a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a><span class="w">    </span><span class="n">nums</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span>
+<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a><span class="w">    </span><span class="c1"># 根ノードを起点に、上から下へヒープ化</span>
+<a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a><span class="w">    </span><span class="n">sift_down</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-12-31" name="__codelineno-12-31" href="#__codelineno-12-31"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-32" name="__codelineno-12-32" href="#__codelineno-12-32"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h2 id="1172">11.7.2 &nbsp; アルゴリズムの特徴<a class="headerlink" href="#1172" title="Permanent link">&para;</a></h2>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20sift_down%28nums%3A%20list%5Bint%5D%2C%20n%3A%20int%2C%20i%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E3%83%92%E3%83%BC%E3%83%97%E3%81%AE%E9%95%B7%E3%81%95%E3%81%AF%20n%E3%80%82%E3%83%8E%E3%83%BC%E3%83%89%20i%20%E3%81%8B%E3%82%89%E4%B8%8B%E6%96%B9%E5%90%91%E3%81%AB%E3%83%92%E3%83%BC%E3%83%97%E5%8C%96%22%22%22%0A%20%20%20%20while%20True%3A%0A%20%20%20%20%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%20i%2C%20l%2C%20r%20%E3%81%AE%E3%81%86%E3%81%A1%E5%80%A4%E3%81%8C%E6%9C%80%E5%A4%A7%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%20ma%20%E3%81%A8%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20l%20%3D%202%20%2A%20i%20%2B%201%0A%20%20%20%20%20%20%20%20r%20%3D%202%20%2A%20i%20%2B%202%0A%20%20%20%20%20%20%20%20ma%20%3D%20i%0A%20%20%20%20%20%20%20%20if%20l%20%3C%20n%20and%20nums%5Bl%5D%20%3E%20nums%5Bma%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20ma%20%3D%20l%0A%20%20%20%20%20%20%20%20if%20r%20%3C%20n%20and%20nums%5Br%5D%20%3E%20nums%5Bma%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20ma%20%3D%20r%0A%20%20%20%20%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%20i%20%E3%81%8C%E6%9C%80%E5%A4%A7%E3%80%81%E3%81%BE%E3%81%9F%E3%81%AF%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20l%2C%20r%20%E3%81%8C%E7%AF%84%E5%9B%B2%E5%A4%96%E3%81%AA%E3%82%89%E3%80%81%E3%83%92%E3%83%BC%E3%83%97%E5%8C%96%E3%81%AF%E4%B8%8D%E8%A6%81%E3%81%AA%E3%81%AE%E3%81%A7%E6%8A%9C%E3%81%91%E3%82%8B%0A%20%20%20%20%20%20%20%20if%20ma%20%3D%3D%20i%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20%23%202%20%E3%81%A4%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E4%BA%A4%E6%8F%9B%0A%20%20%20%20%20%20%20%20nums%5Bi%5D%2C%20nums%5Bma%5D%20%3D%20nums%5Bma%5D%2C%20nums%5Bi%5D%0A%20%20%20%20%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%97%E3%81%A7%E4%B8%8A%E3%81%8B%E3%82%89%E4%B8%8B%E3%81%B8%E3%83%92%E3%83%BC%E3%83%97%E5%8C%96%0A%20%20%20%20%20%20%20%20i%20%3D%20ma%0A%0Adef%20heap_sort%28nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%22%22%22%E3%83%92%E3%83%BC%E3%83%97%E3%82%BD%E3%83%BC%E3%83%88%22%22%22%0A%20%20%20%20%23%20%E3%83%92%E3%83%BC%E3%83%97%E6%A7%8B%E7%AF%89%EF%BC%9A%E8%91%89%E3%83%8E%E3%83%BC%E3%83%89%E4%BB%A5%E5%A4%96%E3%81%AE%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E3%83%92%E3%83%BC%E3%83%97%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20for%20i%20in%20range%28len%28nums%29%20%2F%2F%202%20-%201%2C%20-1%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20sift_down%28nums%2C%20len%28nums%29%2C%20i%29%0A%20%20%20%20%23%20%E3%83%92%E3%83%BC%E3%83%97%E3%81%8B%E3%82%89%E6%9C%80%E5%A4%A7%E8%A6%81%E7%B4%A0%E3%82%92%E5%8F%96%E3%82%8A%E5%87%BA%E3%81%97%E3%80%81n-1%20%E5%9B%9E%E7%B9%B0%E3%82%8A%E8%BF%94%E3%81%99%0A%20%20%20%20for%20i%20in%20range%28len%28nums%29%20-%201%2C%200%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E6%A0%B9%E3%83%8E%E3%83%BC%E3%83%89%E3%81%A8%E6%9C%80%E3%82%82%E5%8F%B3%E3%81%AE%E8%91%89%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E4%BA%A4%E6%8F%9B%EF%BC%88%E5%85%88%E9%A0%AD%E8%A6%81%E7%B4%A0%E3%81%A8%E6%9C%AB%E5%B0%BE%E8%A6%81%E7%B4%A0%E3%82%92%E4%BA%A4%E6%8F%9B%EF%BC%89%0A%20%20%20%20%20%20%20%20nums%5B0%5D%2C%20nums%5Bi%5D%20%3D%20nums%5Bi%5D%2C%20nums%5B0%5D%0A%20%20%20%20%20%20%20%20%23%20%E6%A0%B9%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E8%B5%B7%E7%82%B9%E3%81%AB%E3%80%81%E4%B8%8A%E3%81%8B%E3%82%89%E4%B8%8B%E3%81%B8%E3%83%92%E3%83%BC%E3%83%97%E5%8C%96%0A%20%20%20%20%20%20%20%20sift_down%28nums%2C%20i%2C%200%29%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B4%2C%201%2C%203%2C%201%2C%205%2C%202%5D%0A%20%20%20%20heap_sort%28nums%29%0A%20%20%20%20print%28%22%E3%83%92%E3%83%BC%E3%83%97%E3%82%BD%E3%83%BC%E3%83%88%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%22%2C%20nums%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20sift_down%28nums%3A%20list%5Bint%5D%2C%20n%3A%20int%2C%20i%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E3%83%92%E3%83%BC%E3%83%97%E3%81%AE%E9%95%B7%E3%81%95%E3%81%AF%20n%E3%80%82%E3%83%8E%E3%83%BC%E3%83%89%20i%20%E3%81%8B%E3%82%89%E4%B8%8B%E6%96%B9%E5%90%91%E3%81%AB%E3%83%92%E3%83%BC%E3%83%97%E5%8C%96%22%22%22%0A%20%20%20%20while%20True%3A%0A%20%20%20%20%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%20i%2C%20l%2C%20r%20%E3%81%AE%E3%81%86%E3%81%A1%E5%80%A4%E3%81%8C%E6%9C%80%E5%A4%A7%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%20ma%20%E3%81%A8%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20l%20%3D%202%20%2A%20i%20%2B%201%0A%20%20%20%20%20%20%20%20r%20%3D%202%20%2A%20i%20%2B%202%0A%20%20%20%20%20%20%20%20ma%20%3D%20i%0A%20%20%20%20%20%20%20%20if%20l%20%3C%20n%20and%20nums%5Bl%5D%20%3E%20nums%5Bma%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20ma%20%3D%20l%0A%20%20%20%20%20%20%20%20if%20r%20%3C%20n%20and%20nums%5Br%5D%20%3E%20nums%5Bma%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20ma%20%3D%20r%0A%20%20%20%20%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%20i%20%E3%81%8C%E6%9C%80%E5%A4%A7%E3%80%81%E3%81%BE%E3%81%9F%E3%81%AF%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%20l%2C%20r%20%E3%81%8C%E7%AF%84%E5%9B%B2%E5%A4%96%E3%81%AA%E3%82%89%E3%80%81%E3%83%92%E3%83%BC%E3%83%97%E5%8C%96%E3%81%AF%E4%B8%8D%E8%A6%81%E3%81%AA%E3%81%AE%E3%81%A7%E6%8A%9C%E3%81%91%E3%82%8B%0A%20%20%20%20%20%20%20%20if%20ma%20%3D%3D%20i%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20%23%202%20%E3%81%A4%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E4%BA%A4%E6%8F%9B%0A%20%20%20%20%20%20%20%20nums%5Bi%5D%2C%20nums%5Bma%5D%20%3D%20nums%5Bma%5D%2C%20nums%5Bi%5D%0A%20%20%20%20%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%97%E3%81%A7%E4%B8%8A%E3%81%8B%E3%82%89%E4%B8%8B%E3%81%B8%E3%83%92%E3%83%BC%E3%83%97%E5%8C%96%0A%20%20%20%20%20%20%20%20i%20%3D%20ma%0A%0Adef%20heap_sort%28nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%22%22%22%E3%83%92%E3%83%BC%E3%83%97%E3%82%BD%E3%83%BC%E3%83%88%22%22%22%0A%20%20%20%20%23%20%E3%83%92%E3%83%BC%E3%83%97%E6%A7%8B%E7%AF%89%EF%BC%9A%E8%91%89%E3%83%8E%E3%83%BC%E3%83%89%E4%BB%A5%E5%A4%96%E3%81%AE%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E3%83%92%E3%83%BC%E3%83%97%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20for%20i%20in%20range%28len%28nums%29%20%2F%2F%202%20-%201%2C%20-1%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20sift_down%28nums%2C%20len%28nums%29%2C%20i%29%0A%20%20%20%20%23%20%E3%83%92%E3%83%BC%E3%83%97%E3%81%8B%E3%82%89%E6%9C%80%E5%A4%A7%E8%A6%81%E7%B4%A0%E3%82%92%E5%8F%96%E3%82%8A%E5%87%BA%E3%81%97%E3%80%81n-1%20%E5%9B%9E%E7%B9%B0%E3%82%8A%E8%BF%94%E3%81%99%0A%20%20%20%20for%20i%20in%20range%28len%28nums%29%20-%201%2C%200%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E6%A0%B9%E3%83%8E%E3%83%BC%E3%83%89%E3%81%A8%E6%9C%80%E3%82%82%E5%8F%B3%E3%81%AE%E8%91%89%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E4%BA%A4%E6%8F%9B%EF%BC%88%E5%85%88%E9%A0%AD%E8%A6%81%E7%B4%A0%E3%81%A8%E6%9C%AB%E5%B0%BE%E8%A6%81%E7%B4%A0%E3%82%92%E4%BA%A4%E6%8F%9B%EF%BC%89%0A%20%20%20%20%20%20%20%20nums%5B0%5D%2C%20nums%5Bi%5D%20%3D%20nums%5Bi%5D%2C%20nums%5B0%5D%0A%20%20%20%20%20%20%20%20%23%20%E6%A0%B9%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E8%B5%B7%E7%82%B9%E3%81%AB%E3%80%81%E4%B8%8A%E3%81%8B%E3%82%89%E4%B8%8B%E3%81%B8%E3%83%92%E3%83%BC%E3%83%97%E5%8C%96%0A%20%20%20%20%20%20%20%20sift_down%28nums%2C%20i%2C%200%29%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B4%2C%201%2C%203%2C%201%2C%205%2C%202%5D%0A%20%20%20%20heap_sort%28nums%29%0A%20%20%20%20print%28%22%E3%83%92%E3%83%BC%E3%83%97%E3%82%BD%E3%83%BC%E3%83%88%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%22%2C%20nums%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h2 id="1172">11.7.2 &nbsp; アルゴリズムの特性<a class="headerlink" href="#1172" title="Permanent link">&para;</a></h2>
 <ul>
-<li><strong>時間計算量は <span class="arithmatex">\(O(n \log n)\)</span>、非適応ソート</strong>：ヒープの構築は <span class="arithmatex">\(O(n)\)</span> 時間を使用します。ヒープから最大要素を抽出するには <span class="arithmatex">\(O(\log n)\)</span> 時間がかかり、<span class="arithmatex">\(n - 1\)</span> ラウンドループします。</li>
-<li><strong>空間計算量は <span class="arithmatex">\(O(1)\)</span>、インプレースソート</strong>：いくつかのポインタ変数が <span class="arithmatex">\(O(1)\)</span> 空間を使用します。要素の交換とヒープ化操作は元の配列で実行されます。</li>
-<li><strong>非安定ソート</strong>：ヒープの頂上と底部要素の交換中に、等しい要素の相対位置が変わる可能性があります。</li>
+<li><strong>時間計算量は <span class="arithmatex">\(O(n \log n)\)</span>、非適応ソート</strong>：ヒープ構築操作には <span class="arithmatex">\(O(n)\)</span> の時間がかかります。ヒープから最大要素を取り出す時間計算量は <span class="arithmatex">\(O(\log n)\)</span> であり、これを合計 <span class="arithmatex">\(n - 1\)</span> 回繰り返します。</li>
+<li><strong>空間計算量は <span class="arithmatex">\(O(1)\)</span>、インプレースソート</strong>：いくつかのポインタ変数が使う空間は <span class="arithmatex">\(O(1)\)</span> です。要素の交換とヒープ化操作はいずれも元の配列上で行われます。</li>
+<li><strong>非安定ソート</strong>：ヒープ頂点の要素とヒープ末尾の要素を交換する際、等しい要素どうしの相対位置が変化する可能性があります。</li>
 </ul>
 
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--- a/ja/chapter_sorting/index.html
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@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
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-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1635,7 +1635,7 @@
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-    6.1 &nbsp; ハッシュ表
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@@ -1942,7 +1942,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
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   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
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   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
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   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
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   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
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   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
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-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
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-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
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   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3617,7 +3617,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3645,7 +3645,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3838,7 +3838,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4083,7 +4083,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4274,11 +4274,11 @@
 
 <!-- Page content -->
 <h1 id="11">第 11 章 &nbsp; ソート<a class="headerlink" href="#11" title="Permanent link">&para;</a></h1>
-<p><img alt="Sorting" class="cover-image" src="../assets/covers/chapter_sorting.jpg" /></p>
+<p><img alt="ソート" class="cover-image" src="../assets/covers/chapter_sorting.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>ソートは混沌を秩序に変える魔法の鍵のようなもので、データをより効率的に理解し処理することを可能にします。</p>
-<p>単純な昇順であろうと複雑なカテゴリ配列であろうと、ソートはデータの調和美を明らかにします。</p>
+<p>ソートは、混沌を秩序へと変える魔法の鍵のようなものであり、データをより効率的に理解し処理することを可能にします。</p>
+<p>単純な昇順であれ、複雑な分類配列であれ、ソートはデータの調和のとれた美しさを私たちに示してくれます。</p>
 </div>
 <h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
diff --git a/ja/chapter_sorting/insertion_sort/index.html b/ja/chapter_sorting/insertion_sort/index.html
index 4635819cd..7c8994e99 100644
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+++ b/ja/chapter_sorting/insertion_sort/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
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-    序
+    はじめに
   
 
     
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-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
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-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2491,7 +2491,7 @@
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+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
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   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -2867,7 +2867,7 @@
   <a href="#1141" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.4.1 &nbsp; アルゴリズムプロセス
+        11.4.1 &nbsp; アルゴリズムの流れ
       
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   <a href="#1142" class="md-nav__link">
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-        11.4.2 &nbsp; アルゴリズムの特性
+        11.4.2 &nbsp; アルゴリズムの特徴
       
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@@ -3196,7 +3196,7 @@
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
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   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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+    13.3 &nbsp; 部分和問題
   
 
     
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-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3642,7 +3642,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3670,7 +3670,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3698,7 +3698,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3726,7 +3726,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3919,7 +3919,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4164,7 +4164,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4310,7 +4310,7 @@
   <a href="#1141" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.4.1 &nbsp; アルゴリズムプロセス
+        11.4.1 &nbsp; アルゴリズムの流れ
       
     </span>
   </a>
@@ -4321,7 +4321,7 @@
   <a href="#1142" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.4.2 &nbsp; アルゴリズムの特性
+        11.4.2 &nbsp; アルゴリズムの特徴
       
     </span>
   </a>
@@ -4377,52 +4377,52 @@
 
 <!-- Page content -->
 <h1 id="114">11.4 &nbsp; 挿入ソート<a class="headerlink" href="#114" title="Permanent link">&para;</a></h1>
-<p><u>挿入ソート</u>は、トランプのデッキを手動でソートするプロセスによく似た動作をするシンプルなソートアルゴリズムです。</p>
-<p>具体的には、未ソート区間からベース要素を選択し、その左側のソート済み区間の要素と比較して、要素を正しい位置に挿入します。</p>
-<p>下図は、要素が配列に挿入される方法を示しています。ベース要素を<code>base</code>とすると、ターゲットインデックスから<code>base</code>までのすべての要素を右に1つずつシフトし、その後<code>base</code>をターゲットインデックスに割り当てる必要があります。</p>
-<p><img alt="Single insertion operation" class="animation-figure" src="../insertion_sort.assets/insertion_operation.png" /></p>
-<p align="center"> 図 11-6 &nbsp; Single insertion operation </p>
+<p><u>挿入ソート（insertion sort）</u>は単純なソートアルゴリズムであり、その動作原理は手作業でトランプの山を整える過程と非常によく似ています。</p>
+<p>具体的には、未ソート区間から基準要素を 1 つ選び、その要素を左側の整列済み区間の要素と 1 つずつ比較し、正しい位置に挿入します。</p>
+<p>以下の図は、配列に要素を挿入する操作の流れを示しています。基準要素を <code>base</code> とすると、目的のインデックスから <code>base</code> までのすべての要素を 1 つずつ右に移動し、その後 <code>base</code> を目的のインデックスに代入する必要があります。</p>
+<p><img alt="1 回の挿入操作" class="animation-figure" src="../insertion_sort.assets/insertion_operation.png" /></p>
+<p align="center"> 図 11-6 &nbsp; 1 回の挿入操作 </p>
 
-<h2 id="1141">11.4.1 &nbsp; アルゴリズムプロセス<a class="headerlink" href="#1141" title="Permanent link">&para;</a></h2>
-<p>挿入ソートの全体的なプロセスは下図に示されます。</p>
+<h2 id="1141">11.4.1 &nbsp; アルゴリズムの流れ<a class="headerlink" href="#1141" title="Permanent link">&para;</a></h2>
+<p>挿入ソート全体の流れを以下の図に示します。</p>
 <ol>
-<li>配列の最初の要素をソート済みとみなします。</li>
-<li>2番目の要素を<code>base</code>として選択し、正しい位置に挿入して、<strong>最初の2つの要素をソート済みにします</strong>。</li>
-<li>3番目の要素を<code>base</code>として選択し、正しい位置に挿入して、<strong>最初の3つの要素をソート済みにします</strong>。</li>
-<li>この方法で続行し、最後の反復では、最後の要素を<code>base</code>として取り、正しい位置に挿入した後、<strong>すべての要素がソートされます</strong>。</li>
+<li>初期状態では、配列の 1 番目の要素はすでに整列済みです。</li>
+<li>配列の 2 番目の要素を <code>base</code> として選び、正しい位置に挿入すると、**配列の先頭 2 要素が整列済み**になります。</li>
+<li>3 番目の要素を <code>base</code> として選び、正しい位置に挿入すると、**配列の先頭 3 要素が整列済み**になります。</li>
+<li>このように繰り返し、最後のラウンドで最後の要素を <code>base</code> として選んで正しい位置に挿入すると、**すべての要素が整列済み**になります。</li>
 </ol>
-<p><img alt="Insertion sort process" class="animation-figure" src="../insertion_sort.assets/insertion_sort_overview.png" /></p>
-<p align="center"> 図 11-7 &nbsp; Insertion sort process </p>
+<p><img alt="挿入ソートの流れ" class="animation-figure" src="../insertion_sort.assets/insertion_sort_overview.png" /></p>
+<p align="center"> 図 11-7 &nbsp; 挿入ソートの流れ </p>
 
-<p>コード例は以下の通りです：</p>
+<p>コード例は以下のとおりです。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">insertion_sort.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">insertion_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
 <a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;挿入ソート&quot;&quot;&quot;</span>
-<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 外側のループ：ソート済み範囲は [0, i-1]</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 外側ループ：整列済み区間は [0, i-1]</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="n">base</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="n">j</span> <span class="o">=</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span>
-<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="c1"># 内側のループ：base をソート済み範囲 [0, i-1] の正しい位置に挿入</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="c1"># 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する</span>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="k">while</span> <span class="n">j</span> <span class="o">&gt;=</span> <span class="mi">0</span> <span class="ow">and</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">base</span><span class="p">:</span>
-<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>            <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>  <span class="c1"># nums[j] を右に1つ移動</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>            <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>  <span class="c1"># nums[j] を 1 つ右へ移動する</span>
 <a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>            <span class="n">j</span> <span class="o">-=</span> <span class="mi">1</span>
-<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">base</span>  <span class="c1"># base を正しい位置に代入</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">base</span>  <span class="c1"># base を正しい位置に配置する</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">insertion_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 挿入ソート */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insertionSort</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 外側ループ：ソート済み範囲は[0, i-1]</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 外側ループ：整列済み区間は [0, i-1]</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="c1">// 内側ループ：baseをソート済み範囲[0, i-1]内の正しい位置に挿入</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="c1">// 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">base</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">            </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span><span class="w"> </span><span class="c1">// nums[j]を一つ右に移動</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">            </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span><span class="w"> </span><span class="c1">// nums[j] を 1 つ右へ移動する</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w"> </span><span class="c1">// baseを正しい位置に代入</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w"> </span><span class="c1">// base を正しい位置に配置する</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="p">}</span>
 </code></pre></div>
@@ -4430,76 +4430,210 @@
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">insertion_sort.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 挿入ソート */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insertionSort</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 外側ループ: ソート済み範囲は [0, i-1]</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 外側ループ：整列済み区間は [0, i-1]</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="c1">// 内側ループ: base をソート済み範囲 [0, i-1] の正しい位置に挿入</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="c1">// 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">base</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">            </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="c1">// nums[j] を右に1つ移動</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">            </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="c1">// nums[j] を 1 つ右へ移動する</span>
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w">        </span><span class="c1">// base を正しい位置に代入</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w">        </span><span class="c1">// base を正しい位置に配置する</span>
 <a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">insertion_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">insertion_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">InsertionSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">insertion_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 挿入ソート */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">InsertionSort</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="c1">// 外側ループ：整列済み区間は [0, i-1]</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">bas</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">        </span><span class="c1">// 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">bas</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">            </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span><span class="w"> </span><span class="c1">// nums[j] を 1 つ右へ移動する</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bas</span><span class="p">;</span><span class="w">         </span><span class="c1">// base を正しい位置に配置する</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">insertion_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">insertionSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">insertion_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 挿入ソート */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">insertionSort</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// 外側ループ：整列済み区間は [0, i-1]</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">        </span><span class="nx">base</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">        </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">        </span><span class="c1">// 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">base</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">            </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="c1">// nums[j] を 1 つ右へ移動する</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">            </span><span class="nx">j</span><span class="o">--</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">base</span><span class="w"> </span><span class="c1">// base を正しい位置に配置する</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">insertion_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">insertionSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">insertion_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 挿入ソート */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">insertionSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// 外側ループ：整列済み区間は [0, i-1]</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="p">.</span><span class="bp">dropFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">base</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">        </span><span class="c1">// 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">            </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="c1">// nums[j] を 1 つ右へ移動する</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="c1">// base を正しい位置に配置する</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">insertion_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">insertionSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">insertion_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 挿入ソート */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">insertionSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="c1">// 外側ループ：整列済み区間は [0, i-1]</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">        </span><span class="c1">// 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">base</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">            </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">];</span><span class="w"> </span><span class="c1">// nums[j] を 1 つ右へ移動する</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">            </span><span class="nx">j</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">base</span><span class="p">;</span><span class="w"> </span><span class="c1">// base を正しい位置に配置する</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">insertion_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">insertionSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">insertion_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 挿入ソート */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">insertionSort</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="c1">// 外側ループ：整列済み区間は [0, i-1]</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">        </span><span class="c1">// 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">base</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">            </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">];</span><span class="w"> </span><span class="c1">// nums[j] を 1 つ右へ移動する</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">            </span><span class="nx">j</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">base</span><span class="p">;</span><span class="w"> </span><span class="c1">// base を正しい位置に配置する</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">insertion_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insertionSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">insertion_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 挿入ソート */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">insertionSort</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="c1">// 外側ループ：整列済み区間は [0, i-1]</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">    </span><span class="c1">// 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">base</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">      </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span><span class="w"> </span><span class="c1">// nums[j] を 1 つ右へ移動する</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">      </span><span class="n">j</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">    </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w"> </span><span class="c1">// base を正しい位置に配置する</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">insertion_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insertion_sort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">insertion_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 挿入ソート */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">insertion_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="c1">// 外側ループ：整列済み区間は [0, i-1]</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..</span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="p">(</span><span class="n">base</span><span class="p">,</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">);</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">        </span><span class="c1">// 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">            </span><span class="n">nums</span><span class="p">[(</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">];</span><span class="w"> </span><span class="c1">// nums[j] を 1 つ右へ移動する</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">        </span><span class="n">nums</span><span class="p">[(</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w"> </span><span class="c1">// base を正しい位置に配置する</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">insertion_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insertionSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">insertion_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 挿入ソート */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insertionSort</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="c1">// 外側ループ：整列済み区間は [0, i-1]</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">        </span><span class="c1">// 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">base</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">            </span><span class="c1">// nums[j] を 1 つ右へ移動する</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">            </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">        </span><span class="c1">// base を正しい位置に配置する</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">base</span><span class="p">;</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">insertion_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insertionSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">insertion_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 挿入ソート */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">insertionSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="c1">// 外側ループ: ソート済み要素は 1, 2, ..., n</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">indices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">        </span><span class="c1">// 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">base</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">            </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="c1">// nums[j] を 1 つ右へ移動する</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">base</span><span class="w">        </span><span class="c1">// base を正しい位置に配置する</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">insertion_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insertion_sort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">insertion_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 挿入ソート ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">insertion_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="c1"># 外側ループ：整列済み区間は [0, i-1]</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="n">n</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">    </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">    </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">    </span><span class="c1"># 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">base</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">      </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="c1"># nums[j] を 1 つ右へ移動する</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">      </span><span class="n">j</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">    </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="c1"># base を正しい位置に配置する</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h2 id="1142">11.4.2 &nbsp; アルゴリズムの特性<a class="headerlink" href="#1142" title="Permanent link">&para;</a></h2>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 495px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20insertion_sort%28nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%22%22%22%E6%8C%BF%E5%85%A5%E3%82%BD%E3%83%BC%E3%83%88%22%22%22%0A%20%20%20%20%23%20%E5%A4%96%E5%81%B4%E3%83%AB%E3%83%BC%E3%83%97%EF%BC%9A%E6%95%B4%E5%88%97%E6%B8%88%E3%81%BF%E5%8C%BA%E9%96%93%E3%81%AF%20%5B0%2C%20i-1%5D%0A%20%20%20%20for%20i%20in%20range%281%2C%20len%28nums%29%29%3A%0A%20%20%20%20%20%20%20%20base%20%3D%20nums%5Bi%5D%0A%20%20%20%20%20%20%20%20j%20%3D%20i%20-%201%0A%20%20%20%20%20%20%20%20%23%20%E5%86%85%E5%81%B4%E3%83%AB%E3%83%BC%E3%83%97%3A%20base%20%E3%82%92%E3%82%BD%E3%83%BC%E3%83%88%E6%B8%88%E3%81%BF%E5%8C%BA%E9%96%93%20%5B0%2C%20i-1%5D%20%E3%81%AE%E6%AD%A3%E3%81%97%E3%81%84%E4%BD%8D%E7%BD%AE%E3%81%AB%E6%8C%BF%E5%85%A5%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20while%20j%20%3E%3D%200%20and%20nums%5Bj%5D%20%3E%20base%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20nums%5Bj%20%2B%201%5D%20%3D%20nums%5Bj%5D%20%20%23%20nums%5Bj%5D%20%E3%82%92%201%20%E3%81%A4%E5%8F%B3%E3%81%B8%E7%A7%BB%E5%8B%95%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20-%3D%201%0A%20%20%20%20%20%20%20%20nums%5Bj%20%2B%201%5D%20%3D%20base%20%20%23%20base%20%E3%82%92%E6%AD%A3%E3%81%97%E3%81%84%E4%BD%8D%E7%BD%AE%E3%81%AB%E9%85%8D%E7%BD%AE%E3%81%99%E3%82%8B%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B4%2C%201%2C%203%2C%201%2C%205%2C%202%5D%0A%20%20%20%20insertion_sort%28nums%29%0A%20%20%20%20print%28%22%E6%8C%BF%E5%85%A5%E3%82%BD%E3%83%BC%E3%83%88%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%22%2C%20nums%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20insertion_sort%28nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%22%22%22%E6%8C%BF%E5%85%A5%E3%82%BD%E3%83%BC%E3%83%88%22%22%22%0A%20%20%20%20%23%20%E5%A4%96%E5%81%B4%E3%83%AB%E3%83%BC%E3%83%97%EF%BC%9A%E6%95%B4%E5%88%97%E6%B8%88%E3%81%BF%E5%8C%BA%E9%96%93%E3%81%AF%20%5B0%2C%20i-1%5D%0A%20%20%20%20for%20i%20in%20range%281%2C%20len%28nums%29%29%3A%0A%20%20%20%20%20%20%20%20base%20%3D%20nums%5Bi%5D%0A%20%20%20%20%20%20%20%20j%20%3D%20i%20-%201%0A%20%20%20%20%20%20%20%20%23%20%E5%86%85%E5%81%B4%E3%83%AB%E3%83%BC%E3%83%97%3A%20base%20%E3%82%92%E3%82%BD%E3%83%BC%E3%83%88%E6%B8%88%E3%81%BF%E5%8C%BA%E9%96%93%20%5B0%2C%20i-1%5D%20%E3%81%AE%E6%AD%A3%E3%81%97%E3%81%84%E4%BD%8D%E7%BD%AE%E3%81%AB%E6%8C%BF%E5%85%A5%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20while%20j%20%3E%3D%200%20and%20nums%5Bj%5D%20%3E%20base%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20nums%5Bj%20%2B%201%5D%20%3D%20nums%5Bj%5D%20%20%23%20nums%5Bj%5D%20%E3%82%92%201%20%E3%81%A4%E5%8F%B3%E3%81%B8%E7%A7%BB%E5%8B%95%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20-%3D%201%0A%20%20%20%20%20%20%20%20nums%5Bj%20%2B%201%5D%20%3D%20base%20%20%23%20base%20%E3%82%92%E6%AD%A3%E3%81%97%E3%81%84%E4%BD%8D%E7%BD%AE%E3%81%AB%E9%85%8D%E7%BD%AE%E3%81%99%E3%82%8B%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B4%2C%201%2C%203%2C%201%2C%205%2C%202%5D%0A%20%20%20%20insertion_sort%28nums%29%0A%20%20%20%20print%28%22%E6%8C%BF%E5%85%A5%E3%82%BD%E3%83%BC%E3%83%88%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%22%2C%20nums%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h2 id="1142">11.4.2 &nbsp; アルゴリズムの特徴<a class="headerlink" href="#1142" title="Permanent link">&para;</a></h2>
 <ul>
-<li><strong>時間計算量は<span class="arithmatex">\(O(n^2)\)</span>、適応ソート</strong>：最悪の場合、各挿入操作には<span class="arithmatex">\(n - 1\)</span>、<span class="arithmatex">\(n-2\)</span>、...、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(1\)</span>のループが必要で、合計は<span class="arithmatex">\((n - 1) n / 2\)</span>となり、時間計算量は<span class="arithmatex">\(O(n^2)\)</span>です。順序付きデータの場合、挿入操作は早期に終了します。入力配列が完全に順序付けられている場合、挿入ソートは最良時間計算量<span class="arithmatex">\(O(n)\)</span>を実現します。</li>
-<li><strong>空間計算量は<span class="arithmatex">\(O(1)\)</span>、インプレースソート</strong>：ポインタ<span class="arithmatex">\(i\)</span>と<span class="arithmatex">\(j\)</span>は定数量の追加空間を使用します。</li>
-<li><strong>安定ソート</strong>：挿入操作中、等しい要素の右側に要素を挿入し、順序を変更しません。</li>
+<li><strong>計算量は <span class="arithmatex">\(O(n^2)\)</span>、適応的ソート</strong>：最悪の場合、各挿入操作ではそれぞれ <span class="arithmatex">\(n - 1\)</span>、<span class="arithmatex">\(n-2\)</span>、<span class="arithmatex">\(\dots\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(1\)</span> 回のループが必要であり、合計は <span class="arithmatex">\((n - 1) n / 2\)</span> となるため、時間計算量は <span class="arithmatex">\(O(n^2)\)</span> です。データが整列済みであれば、挿入操作は早期に終了します。入力配列が完全に整列済みである場合、挿入ソートは最良の時間計算量 <span class="arithmatex">\(O(n)\)</span> に達します。</li>
+<li><strong>空間計算量は <span class="arithmatex">\(O(1)\)</span>、インプレースソート</strong>：ポインタ <span class="arithmatex">\(i\)</span> と <span class="arithmatex">\(j\)</span> は定数サイズの追加領域しか使用しません。</li>
+<li><strong>安定ソート</strong>：挿入操作の過程では、要素を等しい要素の右側に挿入するため、それらの順序は変化しません。</li>
 </ul>
 <h2 id="1143">11.4.3 &nbsp; 挿入ソートの利点<a class="headerlink" href="#1143" title="Permanent link">&para;</a></h2>
-<p>挿入ソートの時間計算量は<span class="arithmatex">\(O(n^2)\)</span>で、次に学習するクイックソートの時間計算量は<span class="arithmatex">\(O(n \log n)\)</span>です。挿入ソートはより高い時間計算量を持ちますが、<strong>小さな入力サイズでは通常より高速です</strong>。</p>
-<p>この結論は線形探索と二分探索の結論と似ています。時間計算量が<span class="arithmatex">\(O(n \log n)\)</span>で分割統治戦略に基づくクイックソートなどのアルゴリズムは、多くの場合より多くの単位操作を含みます。小さな入力サイズでは、<span class="arithmatex">\(n^2\)</span>と<span class="arithmatex">\(n \log n\)</span>の数値は近く、計算量が支配的でなく、ラウンドあたりの単位操作数が決定的な役割を果たします。</p>
-<p>実際、多くのプログラミング言語（Javaなど）は、組み込みソート関数内で挿入ソートを使用しています。一般的なアプローチは：長い配列に対しては、クイックソートなどの分割統治戦略に基づくソートアルゴリズムを使用し、短い配列に対しては挿入ソートを直接使用します。</p>
-<p>バブルソート、選択ソート、挿入ソートはすべて時間計算量<span class="arithmatex">\(O(n^2)\)</span>を持ちますが、実際には、<strong>挿入ソートはバブルソートや選択ソートよりも一般的に使用されます</strong>。主な理由は以下の通りです。</p>
+<p>挿入ソートの時間計算量は <span class="arithmatex">\(O(n^2)\)</span> であり、これから学ぶクイックソートの時間計算量は <span class="arithmatex">\(O(n \log n)\)</span> です。挿入ソートの時間計算量のほうが大きいにもかかわらず、**データ量が小さい場合には、挿入ソートのほうが通常は高速**です。</p>
+<p>この結論は、線形探索と二分探索の適用条件に関する結論と似ています。クイックソートのような <span class="arithmatex">\(O(n \log n)\)</span> のアルゴリズムは分割統治法に基づくソートアルゴリズムであり、一般により多くの基本演算を含みます。一方、データ量が小さい場合は、<span class="arithmatex">\(n^2\)</span> と <span class="arithmatex">\(n \log n\)</span> の値は比較的近く、計算量が支配的ではなくなり、各ラウンドにおける基本演算の回数が決定的な役割を果たします。</p>
+<p>実際、多くのプログラミング言語（たとえば Java）の組み込みソート関数では挿入ソートが採用されており、その大まかな考え方は次のとおりです。長い配列にはクイックソートなどの分割統治法に基づくソートアルゴリズムを使い、短い配列には直接挿入ソートを使います。</p>
+<p>バブルソート、選択ソート、挿入ソートはいずれも時間計算量が <span class="arithmatex">\(O(n^2)\)</span> ですが、実際には、<strong>挿入ソートはバブルソートや選択ソートよりもはるかに高い頻度で使われます</strong>。主な理由は次のとおりです。</p>
 <ul>
-<li>バブルソートは要素交換に基づき、一時変数の使用が必要で、3つの単位操作を含みます；挿入ソートは要素代入に基づき、1つの単位操作のみが必要です。したがって、<strong>バブルソートの計算オーバーヘッドは一般的に挿入ソートよりも高くなります</strong>。</li>
-<li>選択ソートの時間計算量は常に<span class="arithmatex">\(O(n^2)\)</span>です。<strong>部分的に順序付けられたデータのセットが与えられた場合、挿入ソートは通常選択ソートよりも効率的です</strong>。</li>
-<li>選択ソートは不安定で、マルチレベルソートに適用できません。</li>
+<li>バブルソートは要素の交換によって実装され、1 つの一時変数を必要とするため、合計で 3 回の基本演算が関わります。これに対して、挿入ソートは要素の代入に基づいており、必要な基本演算は 1 回だけです。したがって、<strong>バブルソートの計算コストは通常、挿入ソートより高くなります</strong>。</li>
+<li>選択ソートの時間計算量はどのような場合でも <span class="arithmatex">\(O(n^2)\)</span> です。**部分的に整列されたデータが与えられた場合、挿入ソートは通常、選択ソートより効率的**です。</li>
+<li>選択ソートは安定ではないため、多段ソートには適用できません。</li>
 </ul>
 
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diff --git a/ja/chapter_sorting/merge_sort/index.html b/ja/chapter_sorting/merge_sort/index.html
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@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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-    序
+    はじめに
   
 
     
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+    はじめに
   
 
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-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
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-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
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-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
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-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
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-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
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-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
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-    10.2 &nbsp; 二分探索の挿入点
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-    10.5 &nbsp; 探索アルゴリズムの再認識
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-        11.6.1 &nbsp; アルゴリズムワークフロー
+        11.6.1 &nbsp; アルゴリズムの流れ
       
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-    12.3 &nbsp; 木の構築問題
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+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
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+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
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   <a href="#1161" class="md-nav__link">
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-        11.6.1 &nbsp; アルゴリズムワークフロー
+        11.6.1 &nbsp; アルゴリズムの流れ
       
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 <!-- Page content -->
 <h1 id="116">11.6 &nbsp; マージソート<a class="headerlink" href="#116" title="Permanent link">&para;</a></h1>
-<p><u>マージソート</u>は分割統治戦略に基づくソートアルゴリズムで、下図に示す「分割」と「マージ」フェーズを含みます。</p>
+<p><u>マージソート（merge sort）</u>は分割統治戦略に基づくソートアルゴリズムであり、以下の図に示す「分割」と「マージ」の段階から構成されます。</p>
 <ol>
-<li><strong>分割フェーズ</strong>：中点から配列を再帰的に分割し、長い配列のソート問題をより短い配列に変換します。</li>
-<li><strong>マージフェーズ</strong>：サブ配列の長さが1になったときに分割を停止し、その後マージを開始します。2つの短いソート済み配列を連続的により長いソート済み配列にマージし、プロセスが完了するまで続行します。</li>
+<li><strong>分割段階</strong>：再帰によって配列を中点で繰り返し分割し、長い配列のソート問題を短い配列のソート問題へ変換します。</li>
+<li><strong>マージ段階</strong>：部分配列の長さが 1 になったら分割を終了し、マージを開始して、左右 2 つの短いソート済み配列をより長いソート済み配列へと繰り返しマージしていきます。</li>
 </ol>
-<p><img alt="The divide and merge phases of merge sort" class="animation-figure" src="../merge_sort.assets/merge_sort_overview.png" /></p>
-<p align="center"> 図 11-10 &nbsp; The divide and merge phases of merge sort </p>
+<p><img alt="マージソートの分割とマージの段階" class="animation-figure" src="../merge_sort.assets/merge_sort_overview.png" /></p>
+<p align="center"> 図 11-10 &nbsp; マージソートの分割とマージの段階 </p>
 
-<h2 id="1161">11.6.1 &nbsp; アルゴリズムワークフロー<a class="headerlink" href="#1161" title="Permanent link">&para;</a></h2>
-<p>下図に示すように、「分割フェーズ」は中点から配列を上から下に2つのサブ配列に再帰的に分割します。</p>
+<h2 id="1161">11.6.1 &nbsp; アルゴリズムの流れ<a class="headerlink" href="#1161" title="Permanent link">&para;</a></h2>
+<p>以下の図に示すように、「分割段階」では配列を上から下へ再帰的に中点で 2 つの部分配列へ分割します。</p>
 <ol>
-<li>中点<code>mid</code>を計算し、左サブ配列（区間<code>[left, mid]</code>）と右サブ配列（区間<code>[mid + 1, right]</code>）を再帰的に分割します。</li>
-<li>サブ配列の長さが1になるまでステップ<code>1.</code>を再帰的に続行し、その後停止します。</li>
+<li>配列の中点 <code>mid</code> を計算し、左部分配列（区間 <code>[left, mid]</code> ）と右部分配列（区間 <code>[mid + 1, right]</code> ）を再帰的に分割します。</li>
+<li>手順 <code>1.</code> を再帰的に実行し、部分配列区間の長さが 1 になった時点で終了します。</li>
 </ol>
-<p>「マージフェーズ」は左と右のサブ配列を下から上にソート済み配列に結合します。重要なのは、マージが長さ1のサブ配列から開始され、マージフェーズ中に各サブ配列がソートされることです。</p>
+<p>「マージ段階」では左部分配列と右部分配列を下から上へとマージし、1 つのソート済み配列にします。長さ 1 の部分配列からマージを始めるため、この段階の各部分配列はすでに整列されています。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:10"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label><label for="__tabbed_1_5">&lt;5&gt;</label><label for="__tabbed_1_6">&lt;6&gt;</label><label for="__tabbed_1_7">&lt;7&gt;</label><label for="__tabbed_1_8">&lt;8&gt;</label><label for="__tabbed_1_9">&lt;9&gt;</label><label for="__tabbed_1_10">&lt;10&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="Merge sort process" class="animation-figure" src="../merge_sort.assets/merge_sort_step1.png" /></p>
+<p><img alt="マージソートの手順" class="animation-figure" src="../merge_sort.assets/merge_sort_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="merge_sort_step2" class="animation-figure" src="../merge_sort.assets/merge_sort_step2.png" /></p>
@@ -4426,25 +4426,25 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 11-11 &nbsp; Merge sort process </p>
+<p align="center"> 図 11-11 &nbsp; マージソートの手順 </p>
 
-<p>マージソートの再帰順序は二分木の後順横断と一致することが観察できます。</p>
+<p>観察すると、マージソートの再帰順序は二分木の後順走査と一致していることがわかります。</p>
 <ul>
-<li><strong>後順横断</strong>：まず左のサブツリーを再帰的に横断し、次に右のサブツリーを横断し、最後にルートノードを処理します。</li>
-<li><strong>マージソート</strong>：まず左のサブ配列を再帰的に処理し、次に右のサブ配列を処理し、最後にマージを実行します。</li>
+<li><strong>後順走査</strong>：まず左部分木を再帰し、次に右部分木を再帰し、最後に根ノードを処理します。</li>
+<li><strong>マージソート</strong>：まず左部分配列を再帰し、次に右部分配列を再帰し、最後にマージを処理します。</li>
 </ul>
-<p>マージソートの実装は以下のコードに示されます。<code>nums</code>でマージされる区間は<code>[left, right]</code>で、<code>tmp</code>の対応する区間は<code>[0, right - left]</code>であることに注意してください。</p>
+<p>マージソートの実装を以下のコードに示します。注意として、<code>nums</code> のマージ対象区間は <code>[left, right]</code> であり、<code>tmp</code> の対応区間は <code>[0, right - left]</code> です。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">merge_sort.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">mid</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;左サブ配列と右サブ配列をマージ&quot;&quot;&quot;</span>
-<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 左サブ配列区間は [left, mid]、右サブ配列区間は [mid+1, right]</span>
-<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="c1"># 一時配列 tmp を作成してマージ結果を格納</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;左部分配列と右部分配列をマージ&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="c1"># マージ結果を格納する一時配列 tmp を作成</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="n">tmp</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">right</span> <span class="o">-</span> <span class="n">left</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 左右サブ配列の開始インデックスを初期化</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 左右の部分配列の開始インデックスを初期化する</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">,</span> <span class="n">k</span> <span class="o">=</span> <span class="n">left</span><span class="p">,</span> <span class="n">mid</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span>
-<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="c1"># 両方のサブ配列に要素が残っている間、より小さい要素を一時配列にコピー</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="c1"># 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする</span>
 <a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;=</span> <span class="n">mid</span> <span class="ow">and</span> <span class="n">j</span> <span class="o">&lt;=</span> <span class="n">right</span><span class="p">:</span>
 <a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&lt;=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]:</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>            <span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
@@ -4453,7 +4453,7 @@
 <a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>            <span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
 <a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>            <span class="n">j</span> <span class="o">+=</span> <span class="mi">1</span>
 <a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>        <span class="n">k</span> <span class="o">+=</span> <span class="mi">1</span>
-<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>    <span class="c1"># 残った左右サブ配列の要素を一時配列にコピー</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>    <span class="c1"># 左右の部分配列の残り要素を一時配列にコピーする</span>
 <a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>    <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;=</span> <span class="n">mid</span><span class="p">:</span>
 <a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>        <span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
 <a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>        <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
@@ -4462,7 +4462,7 @@
 <a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a>        <span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
 <a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>        <span class="n">j</span> <span class="o">+=</span> <span class="mi">1</span>
 <a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>        <span class="n">k</span> <span class="o">+=</span> <span class="mi">1</span>
-<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a>    <span class="c1"># 一時配列 tmp の要素を元の配列 nums の対応する区間にコピーバック</span>
+<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a>    <span class="c1"># 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする</span>
 <a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>    <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">tmp</span><span class="p">)):</span>
 <a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a>        <span class="n">nums</span><span class="p">[</span><span class="n">left</span> <span class="o">+</span> <span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">]</span>
 <a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a>
@@ -4470,38 +4470,38 @@
 <a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;マージソート&quot;&quot;&quot;</span>
 <a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a>    <span class="c1"># 終了条件</span>
 <a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a>    <span class="k">if</span> <span class="n">left</span> <span class="o">&gt;=</span> <span class="n">right</span><span class="p">:</span>
-<a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a>        <span class="k">return</span>  <span class="c1"># サブ配列の長さが1のときに再帰を終了</span>
-<a id="__codelineno-0-35" name="__codelineno-0-35" href="#__codelineno-0-35"></a>    <span class="c1"># 分割段階</span>
-<a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a>    <span class="n">mid</span> <span class="o">=</span> <span class="n">left</span> <span class="o">+</span> <span class="p">(</span><span class="n">right</span> <span class="o">-</span> <span class="n">left</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>  <span class="c1"># 中点を計算</span>
-<a id="__codelineno-0-37" name="__codelineno-0-37" href="#__codelineno-0-37"></a>    <span class="n">merge_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">left</span><span class="p">,</span> <span class="n">mid</span><span class="p">)</span>  <span class="c1"># 左サブ配列を再帰的に処理</span>
-<a id="__codelineno-0-38" name="__codelineno-0-38" href="#__codelineno-0-38"></a>    <span class="n">merge_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">mid</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">right</span><span class="p">)</span>  <span class="c1"># 右サブ配列を再帰的に処理</span>
-<a id="__codelineno-0-39" name="__codelineno-0-39" href="#__codelineno-0-39"></a>    <span class="c1"># マージ段階</span>
+<a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a>        <span class="k">return</span>  <span class="c1"># 部分配列の長さが 1 になったら再帰を終了</span>
+<a id="__codelineno-0-35" name="__codelineno-0-35" href="#__codelineno-0-35"></a>    <span class="c1"># 分割フェーズ</span>
+<a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a>    <span class="n">mid</span> <span class="o">=</span> <span class="p">(</span><span class="n">left</span> <span class="o">+</span> <span class="n">right</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span> <span class="c1"># 中点を計算</span>
+<a id="__codelineno-0-37" name="__codelineno-0-37" href="#__codelineno-0-37"></a>    <span class="n">merge_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">left</span><span class="p">,</span> <span class="n">mid</span><span class="p">)</span>  <span class="c1"># 左部分配列を再帰処理</span>
+<a id="__codelineno-0-38" name="__codelineno-0-38" href="#__codelineno-0-38"></a>    <span class="n">merge_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">mid</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">right</span><span class="p">)</span>  <span class="c1"># 右部分配列を再帰処理</span>
+<a id="__codelineno-0-39" name="__codelineno-0-39" href="#__codelineno-0-39"></a>    <span class="c1"># マージフェーズ</span>
 <a id="__codelineno-0-40" name="__codelineno-0-40" href="#__codelineno-0-40"></a>    <span class="n">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">left</span><span class="p">,</span> <span class="n">mid</span><span class="p">,</span> <span class="n">right</span><span class="p">)</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">merge_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 左サブ配列と右サブ配列をマージ */</span>
+<div class="highlight"><span class="filename">merge_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 左部分配列と右部分配列をマージ */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">merge</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 左サブ配列の区間は[left, mid]、右サブ配列の区間は[mid+1, right]</span>
-<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// マージ結果を保存する一時配列tmpを作成</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// マージ結果を格納する一時配列 tmp を作成</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tmp</span><span class="p">(</span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// 左右サブ配列の開始インデックスを初期化</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// 左右の部分配列の開始インデックスを初期化する</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="c1">// 両サブ配列に要素がある間、小さい方の要素を一時配列にコピー</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="c1">// 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">])</span>
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">            </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="o">++</span><span class="p">];</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="k">else</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">            </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="o">++</span><span class="p">];</span>
 <a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="c1">// 左右サブ配列の残りの要素を一時配列にコピー</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="c1">// 左右の部分配列の残り要素を一時配列にコピーする</span>
 <a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">mid</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">        </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="o">++</span><span class="p">];</span>
 <a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">        </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="o">++</span><span class="p">];</span>
 <a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w">    </span><span class="c1">// 一時配列tmpの要素を元の配列numsの対応する区間にコピー</span>
+<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w">    </span><span class="c1">// 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする</span>
 <a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">k</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">];</span>
 <a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w">    </span><span class="p">}</span>
@@ -4511,12 +4511,12 @@
 <a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="kt">void</span><span class="w"> </span><span class="nf">mergeSort</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="w">    </span><span class="c1">// 終了条件</span>
 <a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
-<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span><span class="w"> </span><span class="c1">// サブ配列の長さが1の時、再帰を終了</span>
-<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="w">    </span><span class="c1">// 分割段階</span>
+<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span><span class="w"> </span><span class="c1">// 部分配列の長さが 1 になったら再帰を終了</span>
+<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="w">    </span><span class="c1">// 分割フェーズ</span>
 <a id="__codelineno-1-34" name="__codelineno-1-34" href="#__codelineno-1-34"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">    </span><span class="c1">// 中点を計算</span>
-<a id="__codelineno-1-35" name="__codelineno-1-35" href="#__codelineno-1-35"></a><span class="w">    </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">);</span><span class="w">      </span><span class="c1">// 左サブ配列を再帰的に処理</span>
-<a id="__codelineno-1-36" name="__codelineno-1-36" href="#__codelineno-1-36"></a><span class="w">    </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右サブ配列を再帰的に処理</span>
-<a id="__codelineno-1-37" name="__codelineno-1-37" href="#__codelineno-1-37"></a><span class="w">    </span><span class="c1">// マージ段階</span>
+<a id="__codelineno-1-35" name="__codelineno-1-35" href="#__codelineno-1-35"></a><span class="w">    </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">);</span><span class="w">      </span><span class="c1">// 左部分配列を再帰処理</span>
+<a id="__codelineno-1-36" name="__codelineno-1-36" href="#__codelineno-1-36"></a><span class="w">    </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右部分配列を再帰処理</span>
+<a id="__codelineno-1-37" name="__codelineno-1-37" href="#__codelineno-1-37"></a><span class="w">    </span><span class="c1">// マージフェーズ</span>
 <a id="__codelineno-1-38" name="__codelineno-1-38" href="#__codelineno-1-38"></a><span class="w">    </span><span class="n">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
 <a id="__codelineno-1-39" name="__codelineno-1-39" href="#__codelineno-1-39"></a><span class="p">}</span>
 </code></pre></div>
@@ -4524,26 +4524,26 @@
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">merge_sort.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 左部分配列と右部分配列をマージ */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">merge</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 左部分配列区間は [left, mid]、右部分配列区間は [mid+1, right]</span>
-<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// 一時配列 tmp を作成してマージ結果を格納</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// マージ結果を格納する一時配列 tmp を作成</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// 左右部分配列の開始インデックスを初期化</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// 左右の部分配列の開始インデックスを初期化する</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="c1">// 両部分配列にまだ要素がある間、比較してより小さい要素を一時配列にコピー</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="c1">// 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする</span>
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">)</span>
 <a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">            </span><span class="n">tmp</span><span class="o">[</span><span class="n">k</span><span class="o">++]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">++]</span><span class="p">;</span>
 <a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="k">else</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">            </span><span class="n">tmp</span><span class="o">[</span><span class="n">k</span><span class="o">++]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">++]</span><span class="p">;</span>
 <a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="c1">// 左右部分配列の残りの要素を一時配列にコピー</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="c1">// 左右の部分配列の残り要素を一時配列にコピーする</span>
 <a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">mid</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">        </span><span class="n">tmp</span><span class="o">[</span><span class="n">k</span><span class="o">++]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">++]</span><span class="p">;</span>
 <a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">        </span><span class="n">tmp</span><span class="o">[</span><span class="n">k</span><span class="o">++]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">++]</span><span class="p">;</span>
 <a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w">    </span><span class="c1">// 一時配列 tmp の要素を元の配列 nums の対応する区間にコピーバック</span>
+<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w">    </span><span class="c1">// 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする</span>
 <a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">k</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">k</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="w">    </span><span class="p">}</span>
@@ -4553,91 +4553,501 @@
 <a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="kt">void</span><span class="w"> </span><span class="nf">mergeSort</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a><span class="w">    </span><span class="c1">// 終了条件</span>
 <a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
-<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span><span class="w"> </span><span class="c1">// 部分配列の長さが 1 のとき再帰を終了</span>
-<a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a><span class="w">    </span><span class="c1">// 分割段階</span>
+<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span><span class="w"> </span><span class="c1">// 部分配列の長さが 1 になったら再帰を終了</span>
+<a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a><span class="w">    </span><span class="c1">// 分割フェーズ</span>
 <a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点を計算</span>
-<a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a><span class="w">    </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">);</span><span class="w"> </span><span class="c1">// 左部分配列を再帰的に処理</span>
-<a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a><span class="w">    </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右部分配列を再帰的に処理</span>
-<a id="__codelineno-2-37" name="__codelineno-2-37" href="#__codelineno-2-37"></a><span class="w">    </span><span class="c1">// マージ段階</span>
+<a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a><span class="w">    </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">);</span><span class="w"> </span><span class="c1">// 左部分配列を再帰処理</span>
+<a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a><span class="w">    </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右部分配列を再帰処理</span>
+<a id="__codelineno-2-37" name="__codelineno-2-37" href="#__codelineno-2-37"></a><span class="w">    </span><span class="c1">// マージフェーズ</span>
 <a id="__codelineno-2-38" name="__codelineno-2-38" href="#__codelineno-2-38"></a><span class="w">    </span><span class="n">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
 <a id="__codelineno-2-39" name="__codelineno-2-39" href="#__codelineno-2-39"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">merge_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">merge_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Merge</span><span class="p">}</span>
-<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
-<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">merge_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MergeSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">merge_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 左部分配列と右部分配列をマージ */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Merge</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="c1">// 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="c1">// マージ結果を格納する一時配列 tmp を作成</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="c1">// 左右の部分配列の開始インデックスを初期化する</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="c1">// 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">])</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">            </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="o">++</span><span class="p">];</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">        </span><span class="k">else</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">            </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="o">++</span><span class="p">];</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">    </span><span class="c1">// 左右の部分配列の残り要素を一時配列にコピーする</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">mid</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">        </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="o">++</span><span class="p">];</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w">        </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="o">++</span><span class="p">];</span>
+<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="w">    </span><span class="c1">// 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする</span>
+<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">k</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">];</span>
+<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="p">}</span>
+<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a>
+<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a><span class="cm">/* マージソート */</span>
+<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a><span class="k">void</span><span class="w"> </span><span class="nf">MergeSort</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-3-31" name="__codelineno-3-31" href="#__codelineno-3-31"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span><span class="w">       </span><span class="c1">// 部分配列の長さが 1 になったら再帰を終了</span>
+<a id="__codelineno-3-32" name="__codelineno-3-32" href="#__codelineno-3-32"></a><span class="w">    </span><span class="c1">// 分割フェーズ</span>
+<a id="__codelineno-3-33" name="__codelineno-3-33" href="#__codelineno-3-33"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">    </span><span class="c1">// 中点を計算</span>
+<a id="__codelineno-3-34" name="__codelineno-3-34" href="#__codelineno-3-34"></a><span class="w">    </span><span class="n">MergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">);</span><span class="w">      </span><span class="c1">// 左部分配列を再帰処理</span>
+<a id="__codelineno-3-35" name="__codelineno-3-35" href="#__codelineno-3-35"></a><span class="w">    </span><span class="n">MergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右部分配列を再帰処理</span>
+<a id="__codelineno-3-36" name="__codelineno-3-36" href="#__codelineno-3-36"></a><span class="w">    </span><span class="c1">// マージフェーズ</span>
+<a id="__codelineno-3-37" name="__codelineno-3-37" href="#__codelineno-3-37"></a><span class="w">    </span><span class="n">Merge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-3-38" name="__codelineno-3-38" href="#__codelineno-3-38"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">merge_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">merge</span><span class="p">}</span>
-<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
-<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">mergeSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">merge_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 左部分配列と右部分配列をマージ */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">merge</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="c1">// マージ結果を格納する一時配列 tmp を作成</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="nx">tmp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="o">-</span><span class="nx">left</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="c1">// 左右の部分配列の開始インデックスを初期化する</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">,</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">    </span><span class="c1">// 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">            </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">k</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">            </span><span class="nx">i</span><span class="o">++</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">            </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">k</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">            </span><span class="nx">j</span><span class="o">++</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">        </span><span class="nx">k</span><span class="o">++</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w">    </span><span class="c1">// 左右の部分配列の残り要素を一時配列にコピーする</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w">        </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">k</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w">        </span><span class="nx">i</span><span class="o">++</span>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="w">        </span><span class="nx">k</span><span class="o">++</span>
+<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="w">        </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">k</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span>
+<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w">        </span><span class="nx">j</span><span class="o">++</span>
+<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="w">        </span><span class="nx">k</span><span class="o">++</span>
+<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-30" name="__codelineno-4-30" href="#__codelineno-4-30"></a><span class="w">    </span><span class="c1">// 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする</span>
+<a id="__codelineno-4-31" name="__codelineno-4-31" href="#__codelineno-4-31"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">tmp</span><span class="p">);</span><span class="w"> </span><span class="nx">k</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-32" name="__codelineno-4-32" href="#__codelineno-4-32"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">left</span><span class="o">+</span><span class="nx">k</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">k</span><span class="p">]</span>
+<a id="__codelineno-4-33" name="__codelineno-4-33" href="#__codelineno-4-33"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-34" name="__codelineno-4-34" href="#__codelineno-4-34"></a><span class="p">}</span>
+<a id="__codelineno-4-35" name="__codelineno-4-35" href="#__codelineno-4-35"></a>
+<a id="__codelineno-4-36" name="__codelineno-4-36" href="#__codelineno-4-36"></a><span class="cm">/* マージソート */</span>
+<a id="__codelineno-4-37" name="__codelineno-4-37" href="#__codelineno-4-37"></a><span class="kd">func</span><span class="w"> </span><span class="nx">mergeSort</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-38" name="__codelineno-4-38" href="#__codelineno-4-38"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-4-39" name="__codelineno-4-39" href="#__codelineno-4-39"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-40" name="__codelineno-4-40" href="#__codelineno-4-40"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-4-41" name="__codelineno-4-41" href="#__codelineno-4-41"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-42" name="__codelineno-4-42" href="#__codelineno-4-42"></a><span class="w">    </span><span class="c1">// 分割フェーズ</span>
+<a id="__codelineno-4-43" name="__codelineno-4-43" href="#__codelineno-4-43"></a><span class="w">    </span><span class="nx">mid</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="nx">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">left</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-4-44" name="__codelineno-4-44" href="#__codelineno-4-44"></a><span class="w">    </span><span class="nx">mergeSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="p">)</span>
+<a id="__codelineno-4-45" name="__codelineno-4-45" href="#__codelineno-4-45"></a><span class="w">    </span><span class="nx">mergeSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span>
+<a id="__codelineno-4-46" name="__codelineno-4-46" href="#__codelineno-4-46"></a><span class="w">    </span><span class="c1">// マージフェーズ</span>
+<a id="__codelineno-4-47" name="__codelineno-4-47" href="#__codelineno-4-47"></a><span class="w">    </span><span class="nx">merge</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span>
+<a id="__codelineno-4-48" name="__codelineno-4-48" href="#__codelineno-4-48"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">merge_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">merge</span><span class="p">}</span>
-<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
-<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">mergeSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">merge_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 左部分配列と右部分配列をマージ */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="kr">left</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="kr">right</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="c1">// マージ結果を格納する一時配列 tmp を作成</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">tmp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="kr">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="kr">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="c1">// 左右の部分配列の開始インデックスを初期化する</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kr">left</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">    </span><span class="c1">// 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="kr">right</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">            </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">            </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">        </span><span class="n">k</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w">    </span><span class="c1">// 左右の部分配列の残り要素を一時配列にコピーする</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w">        </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="w">        </span><span class="n">k</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="kr">right</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a><span class="w">        </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a><span class="w">        </span><span class="n">j</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a><span class="w">        </span><span class="n">k</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-29" name="__codelineno-5-29" href="#__codelineno-5-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-30" name="__codelineno-5-30" href="#__codelineno-5-30"></a><span class="w">    </span><span class="c1">// 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする</span>
+<a id="__codelineno-5-31" name="__codelineno-5-31" href="#__codelineno-5-31"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="bp">indices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-32" name="__codelineno-5-32" href="#__codelineno-5-32"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="kr">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">]</span>
+<a id="__codelineno-5-33" name="__codelineno-5-33" href="#__codelineno-5-33"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-34" name="__codelineno-5-34" href="#__codelineno-5-34"></a><span class="p">}</span>
+<a id="__codelineno-5-35" name="__codelineno-5-35" href="#__codelineno-5-35"></a>
+<a id="__codelineno-5-36" name="__codelineno-5-36" href="#__codelineno-5-36"></a><span class="cm">/* マージソート */</span>
+<a id="__codelineno-5-37" name="__codelineno-5-37" href="#__codelineno-5-37"></a><span class="kd">func</span><span class="w"> </span><span class="nf">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="kr">left</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="kr">right</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-38" name="__codelineno-5-38" href="#__codelineno-5-38"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-5-39" name="__codelineno-5-39" href="#__codelineno-5-39"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="kr">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="kr">right</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 部分配列の長さが 1 になったら再帰を終了</span>
+<a id="__codelineno-5-40" name="__codelineno-5-40" href="#__codelineno-5-40"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-5-41" name="__codelineno-5-41" href="#__codelineno-5-41"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-42" name="__codelineno-5-42" href="#__codelineno-5-42"></a><span class="w">    </span><span class="c1">// 分割フェーズ</span>
+<a id="__codelineno-5-43" name="__codelineno-5-43" href="#__codelineno-5-43"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">mid</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kr">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="kr">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="kr">left</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1">// 中点を計算</span>
+<a id="__codelineno-5-44" name="__codelineno-5-44" href="#__codelineno-5-44"></a><span class="w">    </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kr">left</span><span class="p">:</span><span class="w"> </span><span class="kr">left</span><span class="p">,</span><span class="w"> </span><span class="kr">right</span><span class="p">:</span><span class="w"> </span><span class="n">mid</span><span class="p">)</span><span class="w"> </span><span class="c1">// 左部分配列を再帰処理</span>
+<a id="__codelineno-5-45" name="__codelineno-5-45" href="#__codelineno-5-45"></a><span class="w">    </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kr">left</span><span class="p">:</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="kr">right</span><span class="p">:</span><span class="w"> </span><span class="kr">right</span><span class="p">)</span><span class="w"> </span><span class="c1">// 右部分配列を再帰処理</span>
+<a id="__codelineno-5-46" name="__codelineno-5-46" href="#__codelineno-5-46"></a><span class="w">    </span><span class="c1">// マージフェーズ</span>
+<a id="__codelineno-5-47" name="__codelineno-5-47" href="#__codelineno-5-47"></a><span class="w">    </span><span class="n">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kr">left</span><span class="p">:</span><span class="w"> </span><span class="kr">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">:</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="kr">right</span><span class="p">:</span><span class="w"> </span><span class="kr">right</span><span class="p">)</span>
+<a id="__codelineno-5-48" name="__codelineno-5-48" href="#__codelineno-5-48"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">merge_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">merge</span><span class="p">}</span>
-<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
-<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">mergeSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">merge_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 左部分配列と右部分配列をマージ */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">merge</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="c1">// 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="c1">// マージ結果を格納する一時配列 tmp を作成</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="c1">// 左右の部分配列の開始インデックスを初期化する</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">        </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">        </span><span class="nx">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">    </span><span class="c1">// 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">            </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="o">++</span><span class="p">];</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">            </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="o">++</span><span class="p">];</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w">    </span><span class="c1">// 左右の部分配列の残り要素を一時配列にコピーする</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">mid</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w">        </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="o">++</span><span class="p">];</span>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="w">        </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="o">++</span><span class="p">];</span>
+<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="w">    </span><span class="c1">// 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする</span>
+<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="nx">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">tmp</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">k</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-27" name="__codelineno-6-27" href="#__codelineno-6-27"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">k</span><span class="p">];</span>
+<a id="__codelineno-6-28" name="__codelineno-6-28" href="#__codelineno-6-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-29" name="__codelineno-6-29" href="#__codelineno-6-29"></a><span class="p">}</span>
+<a id="__codelineno-6-30" name="__codelineno-6-30" href="#__codelineno-6-30"></a>
+<a id="__codelineno-6-31" name="__codelineno-6-31" href="#__codelineno-6-31"></a><span class="cm">/* マージソート */</span>
+<a id="__codelineno-6-32" name="__codelineno-6-32" href="#__codelineno-6-32"></a><span class="kd">function</span><span class="w"> </span><span class="nx">mergeSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-33" name="__codelineno-6-33" href="#__codelineno-6-33"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-6-34" name="__codelineno-6-34" href="#__codelineno-6-34"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span><span class="w"> </span><span class="c1">// 部分配列の長さが 1 になったら再帰を終了</span>
+<a id="__codelineno-6-35" name="__codelineno-6-35" href="#__codelineno-6-35"></a><span class="w">    </span><span class="c1">// 分割フェーズ</span>
+<a id="__codelineno-6-36" name="__codelineno-6-36" href="#__codelineno-6-36"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nx">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="nx">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">left</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 中点を計算</span>
+<a id="__codelineno-6-37" name="__codelineno-6-37" href="#__codelineno-6-37"></a><span class="w">    </span><span class="nx">mergeSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="p">);</span><span class="w"> </span><span class="c1">// 左部分配列を再帰処理</span>
+<a id="__codelineno-6-38" name="__codelineno-6-38" href="#__codelineno-6-38"></a><span class="w">    </span><span class="nx">mergeSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右部分配列を再帰処理</span>
+<a id="__codelineno-6-39" name="__codelineno-6-39" href="#__codelineno-6-39"></a><span class="w">    </span><span class="c1">// マージフェーズ</span>
+<a id="__codelineno-6-40" name="__codelineno-6-40" href="#__codelineno-6-40"></a><span class="w">    </span><span class="nx">merge</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">);</span>
+<a id="__codelineno-6-41" name="__codelineno-6-41" href="#__codelineno-6-41"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">merge_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">merge</span><span class="p">}</span>
-<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
-<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">mergeSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">merge_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 左部分配列と右部分配列をマージ */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">merge</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">left</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="c1">// 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="c1">// マージ結果を格納する一時配列 tmp を作成</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="c1">// 左右の部分配列の開始インデックスを初期化する</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">        </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">        </span><span class="nx">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">    </span><span class="c1">// 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">            </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="o">++</span><span class="p">];</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">            </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="o">++</span><span class="p">];</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">    </span><span class="c1">// 左右の部分配列の残り要素を一時配列にコピーする</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">mid</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w">        </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="o">++</span><span class="p">];</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="w">        </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="o">++</span><span class="p">];</span>
+<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="w">    </span><span class="c1">// 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする</span>
+<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="nx">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">tmp</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">k</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">k</span><span class="p">];</span>
+<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-29" name="__codelineno-7-29" href="#__codelineno-7-29"></a><span class="p">}</span>
+<a id="__codelineno-7-30" name="__codelineno-7-30" href="#__codelineno-7-30"></a>
+<a id="__codelineno-7-31" name="__codelineno-7-31" href="#__codelineno-7-31"></a><span class="cm">/* マージソート */</span>
+<a id="__codelineno-7-32" name="__codelineno-7-32" href="#__codelineno-7-32"></a><span class="kd">function</span><span class="w"> </span><span class="nx">mergeSort</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">left</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-33" name="__codelineno-7-33" href="#__codelineno-7-33"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-7-34" name="__codelineno-7-34" href="#__codelineno-7-34"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span><span class="w"> </span><span class="c1">// 部分配列の長さが 1 になったら再帰を終了</span>
+<a id="__codelineno-7-35" name="__codelineno-7-35" href="#__codelineno-7-35"></a><span class="w">    </span><span class="c1">// 分割フェーズ</span>
+<a id="__codelineno-7-36" name="__codelineno-7-36" href="#__codelineno-7-36"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nx">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="nx">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">left</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 中点を計算</span>
+<a id="__codelineno-7-37" name="__codelineno-7-37" href="#__codelineno-7-37"></a><span class="w">    </span><span class="nx">mergeSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="p">);</span><span class="w"> </span><span class="c1">// 左部分配列を再帰処理</span>
+<a id="__codelineno-7-38" name="__codelineno-7-38" href="#__codelineno-7-38"></a><span class="w">    </span><span class="nx">mergeSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右部分配列を再帰処理</span>
+<a id="__codelineno-7-39" name="__codelineno-7-39" href="#__codelineno-7-39"></a><span class="w">    </span><span class="c1">// マージフェーズ</span>
+<a id="__codelineno-7-40" name="__codelineno-7-40" href="#__codelineno-7-40"></a><span class="w">    </span><span class="nx">merge</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">);</span>
+<a id="__codelineno-7-41" name="__codelineno-7-41" href="#__codelineno-7-41"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">merge_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">merge</span><span class="p">}</span>
-<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
-<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">mergeSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">merge_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 左部分配列と右部分配列をマージ */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">merge</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="c1">// 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="c1">// マージ結果を格納する一時配列 tmp を作成</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="c1">// 左右の部分配列の開始インデックスを初期化する</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">  </span><span class="c1">// 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">])</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">      </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="o">++</span><span class="p">];</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">      </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="o">++</span><span class="p">];</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">  </span><span class="c1">// 左右の部分配列の残り要素を一時配列にコピーする</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">mid</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">    </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="o">++</span><span class="p">];</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="w">    </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="o">++</span><span class="p">];</span>
+<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="w">  </span><span class="c1">// 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする</span>
+<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">k</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a><span class="w">    </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">];</span>
+<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-26" name="__codelineno-8-26" href="#__codelineno-8-26"></a><span class="p">}</span>
+<a id="__codelineno-8-27" name="__codelineno-8-27" href="#__codelineno-8-27"></a>
+<a id="__codelineno-8-28" name="__codelineno-8-28" href="#__codelineno-8-28"></a><span class="cm">/* マージソート */</span>
+<a id="__codelineno-8-29" name="__codelineno-8-29" href="#__codelineno-8-29"></a><span class="kt">void</span><span class="w"> </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-30" name="__codelineno-8-30" href="#__codelineno-8-30"></a><span class="w">  </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-8-31" name="__codelineno-8-31" href="#__codelineno-8-31"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span><span class="w"> </span><span class="c1">// 部分配列の長さが 1 になったら再帰を終了</span>
+<a id="__codelineno-8-32" name="__codelineno-8-32" href="#__codelineno-8-32"></a><span class="w">  </span><span class="c1">// 分割フェーズ</span>
+<a id="__codelineno-8-33" name="__codelineno-8-33" href="#__codelineno-8-33"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点を計算</span>
+<a id="__codelineno-8-34" name="__codelineno-8-34" href="#__codelineno-8-34"></a><span class="w">  </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">);</span><span class="w"> </span><span class="c1">// 左部分配列を再帰処理</span>
+<a id="__codelineno-8-35" name="__codelineno-8-35" href="#__codelineno-8-35"></a><span class="w">  </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右部分配列を再帰処理</span>
+<a id="__codelineno-8-36" name="__codelineno-8-36" href="#__codelineno-8-36"></a><span class="w">  </span><span class="c1">// マージフェーズ</span>
+<a id="__codelineno-8-37" name="__codelineno-8-37" href="#__codelineno-8-37"></a><span class="w">  </span><span class="n">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-8-38" name="__codelineno-8-38" href="#__codelineno-8-38"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">merge_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">merge</span><span class="p">}</span>
-<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
-<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">merge_sort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">merge_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 左部分配列と右部分配列をマージ */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">left</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="c1">// 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="c1">// マージ結果を格納する一時配列 tmp を作成</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">tmp_size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">tmp_size</span><span class="p">];</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="c1">// 左右の部分配列の開始インデックスを初期化する</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="p">(</span><span class="k">mut</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">j</span><span class="p">,</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">k</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">    </span><span class="c1">// 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">            </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">            </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">        </span><span class="n">k</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w">    </span><span class="c1">// 左右の部分配列の残り要素を一時配列にコピーする</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="w">        </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="w">        </span><span class="n">k</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="w">        </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a><span class="w">        </span><span class="n">k</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="w">        </span><span class="n">j</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-30" name="__codelineno-9-30" href="#__codelineno-9-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-31" name="__codelineno-9-31" href="#__codelineno-9-31"></a><span class="w">    </span><span class="c1">// 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする</span>
+<a id="__codelineno-9-32" name="__codelineno-9-32" href="#__codelineno-9-32"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">tmp_size</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-33" name="__codelineno-9-33" href="#__codelineno-9-33"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">];</span>
+<a id="__codelineno-9-34" name="__codelineno-9-34" href="#__codelineno-9-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-35" name="__codelineno-9-35" href="#__codelineno-9-35"></a><span class="p">}</span>
+<a id="__codelineno-9-36" name="__codelineno-9-36" href="#__codelineno-9-36"></a>
+<a id="__codelineno-9-37" name="__codelineno-9-37" href="#__codelineno-9-37"></a><span class="cm">/* マージソート */</span>
+<a id="__codelineno-9-38" name="__codelineno-9-38" href="#__codelineno-9-38"></a><span class="k">fn</span><span class="w"> </span><span class="nf">merge_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">left</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-39" name="__codelineno-9-39" href="#__codelineno-9-39"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-9-40" name="__codelineno-9-40" href="#__codelineno-9-40"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-41" name="__codelineno-9-41" href="#__codelineno-9-41"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span><span class="w"> </span><span class="c1">// 部分配列の長さが 1 になったら再帰を終了</span>
+<a id="__codelineno-9-42" name="__codelineno-9-42" href="#__codelineno-9-42"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-43" name="__codelineno-9-43" href="#__codelineno-9-43"></a>
+<a id="__codelineno-9-44" name="__codelineno-9-44" href="#__codelineno-9-44"></a><span class="w">    </span><span class="c1">// 分割フェーズ</span>
+<a id="__codelineno-9-45" name="__codelineno-9-45" href="#__codelineno-9-45"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点を計算</span>
+<a id="__codelineno-9-46" name="__codelineno-9-46" href="#__codelineno-9-46"></a><span class="w">    </span><span class="n">merge_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">);</span><span class="w"> </span><span class="c1">// 左部分配列を再帰処理</span>
+<a id="__codelineno-9-47" name="__codelineno-9-47" href="#__codelineno-9-47"></a><span class="w">    </span><span class="n">merge_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右部分配列を再帰処理</span>
+<a id="__codelineno-9-48" name="__codelineno-9-48" href="#__codelineno-9-48"></a>
+<a id="__codelineno-9-49" name="__codelineno-9-49" href="#__codelineno-9-49"></a><span class="w">    </span><span class="c1">// マージフェーズ</span>
+<a id="__codelineno-9-50" name="__codelineno-9-50" href="#__codelineno-9-50"></a><span class="w">    </span><span class="n">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-9-51" name="__codelineno-9-51" href="#__codelineno-9-51"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">merge_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">merge</span><span class="p">}</span>
-<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
-<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">mergeSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">merge_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 左部分配列と右部分配列をマージ */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">merge</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="c1">// 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="c1">// マージ結果を格納する一時配列 tmp を作成</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">tmpSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="n">tmpSize</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">    </span><span class="c1">// 左右の部分配列の開始インデックスを初期化する</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">    </span><span class="c1">// 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">            </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="o">++</span><span class="p">];</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">            </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="o">++</span><span class="p">];</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">    </span><span class="c1">// 左右の部分配列の残り要素を一時配列にコピーする</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">mid</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w">        </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="o">++</span><span class="p">];</span>
+<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w">        </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="o">++</span><span class="p">];</span>
+<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="w">    </span><span class="c1">// 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする</span>
+<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">tmpSize</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">k</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">];</span>
+<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">tmp</span><span class="p">);</span>
+<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="p">}</span>
+<a id="__codelineno-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></a>
+<a id="__codelineno-10-32" name="__codelineno-10-32" href="#__codelineno-10-32"></a><span class="cm">/* マージソート */</span>
+<a id="__codelineno-10-33" name="__codelineno-10-33" href="#__codelineno-10-33"></a><span class="kt">void</span><span class="w"> </span><span class="nf">mergeSort</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-34" name="__codelineno-10-34" href="#__codelineno-10-34"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-10-35" name="__codelineno-10-35" href="#__codelineno-10-35"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-10-36" name="__codelineno-10-36" href="#__codelineno-10-36"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span><span class="w"> </span><span class="c1">// 部分配列の長さが 1 になったら再帰を終了</span>
+<a id="__codelineno-10-37" name="__codelineno-10-37" href="#__codelineno-10-37"></a><span class="w">    </span><span class="c1">// 分割フェーズ</span>
+<a id="__codelineno-10-38" name="__codelineno-10-38" href="#__codelineno-10-38"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">    </span><span class="c1">// 中点を計算</span>
+<a id="__codelineno-10-39" name="__codelineno-10-39" href="#__codelineno-10-39"></a><span class="w">    </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">);</span><span class="w">      </span><span class="c1">// 左部分配列を再帰処理</span>
+<a id="__codelineno-10-40" name="__codelineno-10-40" href="#__codelineno-10-40"></a><span class="w">    </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右部分配列を再帰処理</span>
+<a id="__codelineno-10-41" name="__codelineno-10-41" href="#__codelineno-10-41"></a><span class="w">    </span><span class="c1">// マージフェーズ</span>
+<a id="__codelineno-10-42" name="__codelineno-10-42" href="#__codelineno-10-42"></a><span class="w">    </span><span class="n">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-10-43" name="__codelineno-10-43" href="#__codelineno-10-43"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">merge_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">merge</span><span class="p">}</span>
-<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
-<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">mergeSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">merge_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 左部分配列と右部分配列をマージ */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="c1">// 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="c1">// マージ結果を格納する一時配列 tmp を作成</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="c1">// 左右の部分配列の開始インデックスを初期化する</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">    </span><span class="c1">// 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">            </span><span class="n">tmp</span><span class="o">[</span><span class="n">k</span><span class="o">++]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">++]</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">        </span><span class="k">else</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">            </span><span class="n">tmp</span><span class="o">[</span><span class="n">k</span><span class="o">++]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">++]</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">    </span><span class="c1">// 左右の部分配列の残り要素を一時配列にコピーする</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">mid</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w">        </span><span class="n">tmp</span><span class="o">[</span><span class="n">k</span><span class="o">++]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">++]</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="w">        </span><span class="n">tmp</span><span class="o">[</span><span class="n">k</span><span class="o">++]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">++]</span>
+<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="w">    </span><span class="c1">// 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする</span>
+<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="na">indices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">l</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">[</span><span class="n">l</span><span class="o">]</span>
+<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="p">}</span>
+<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a>
+<a id="__codelineno-11-30" name="__codelineno-11-30" href="#__codelineno-11-30"></a><span class="cm">/* マージソート */</span>
+<a id="__codelineno-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-32" name="__codelineno-11-32" href="#__codelineno-11-32"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-11-33" name="__codelineno-11-33" href="#__codelineno-11-33"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w">  </span><span class="c1">// 部分配列の長さが 1 になったら再帰を終了</span>
+<a id="__codelineno-11-34" name="__codelineno-11-34" href="#__codelineno-11-34"></a><span class="w">    </span><span class="c1">// 分割フェーズ</span>
+<a id="__codelineno-11-35" name="__codelineno-11-35" href="#__codelineno-11-35"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">mid</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="c1">// 中点を計算</span>
+<a id="__codelineno-11-36" name="__codelineno-11-36" href="#__codelineno-11-36"></a><span class="w">    </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">)</span><span class="w"> </span><span class="c1">// 左部分配列を再帰処理</span>
+<a id="__codelineno-11-37" name="__codelineno-11-37" href="#__codelineno-11-37"></a><span class="w">    </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="c1">// 右部分配列を再帰処理</span>
+<a id="__codelineno-11-38" name="__codelineno-11-38" href="#__codelineno-11-38"></a><span class="w">    </span><span class="c1">// マージフェーズ</span>
+<a id="__codelineno-11-39" name="__codelineno-11-39" href="#__codelineno-11-39"></a><span class="w">    </span><span class="n">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-11-40" name="__codelineno-11-40" href="#__codelineno-11-40"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">merge_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">merge</span><span class="p">}</span>
-<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
-<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">merge_sort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">merge_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 左部分配列と右部分配列をマージ ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="c1"># マージ結果を格納する一時配列 tmp を作成</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="c1"># 左右の部分配列の開始インデックスを初期化する</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">  </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">,</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">  </span><span class="c1"># 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">right</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">      </span><span class="n">tmp</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">      </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">      </span><span class="n">tmp</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">      </span><span class="n">j</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">    </span><span class="n">k</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w">  </span><span class="c1"># 左右の部分配列の残り要素を一時配列にコピーする</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">mid</span>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w">    </span><span class="n">tmp</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w">    </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="w">    </span><span class="n">k</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">right</span>
+<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a><span class="w">    </span><span class="n">tmp</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a><span class="w">    </span><span class="n">j</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a><span class="w">    </span><span class="n">k</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a><span class="w">  </span><span class="c1"># 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする</span>
+<a id="__codelineno-12-31" name="__codelineno-12-31" href="#__codelineno-12-31"></a><span class="w">  </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">tmp</span><span class="o">.</span><span class="n">length</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="o">|</span><span class="n">k</span><span class="o">|</span>
+<a id="__codelineno-12-32" name="__codelineno-12-32" href="#__codelineno-12-32"></a><span class="w">    </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">k</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">[</span><span class="n">k</span><span class="o">]</span>
+<a id="__codelineno-12-33" name="__codelineno-12-33" href="#__codelineno-12-33"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-34" name="__codelineno-12-34" href="#__codelineno-12-34"></a><span class="k">end</span>
+<a id="__codelineno-12-35" name="__codelineno-12-35" href="#__codelineno-12-35"></a>
+<a id="__codelineno-12-36" name="__codelineno-12-36" href="#__codelineno-12-36"></a><span class="c1">### マージソート ###</span>
+<a id="__codelineno-12-37" name="__codelineno-12-37" href="#__codelineno-12-37"></a><span class="k">def</span><span class="w"> </span><span class="nf">merge_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-12-38" name="__codelineno-12-38" href="#__codelineno-12-38"></a><span class="w">  </span><span class="c1"># 終了条件</span>
+<a id="__codelineno-12-39" name="__codelineno-12-39" href="#__codelineno-12-39"></a><span class="w">  </span><span class="c1"># 部分配列の長さが 1 になったら再帰を終了する</span>
+<a id="__codelineno-12-40" name="__codelineno-12-40" href="#__codelineno-12-40"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">right</span>
+<a id="__codelineno-12-41" name="__codelineno-12-41" href="#__codelineno-12-41"></a><span class="w">  </span><span class="c1"># 分割フェーズ</span>
+<a id="__codelineno-12-42" name="__codelineno-12-42" href="#__codelineno-12-42"></a><span class="w">  </span><span class="n">mid</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1"># 中点を計算</span>
+<a id="__codelineno-12-43" name="__codelineno-12-43" href="#__codelineno-12-43"></a><span class="w">  </span><span class="n">merge_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">)</span><span class="w"> </span><span class="c1"># 左部分配列を再帰処理</span>
+<a id="__codelineno-12-44" name="__codelineno-12-44" href="#__codelineno-12-44"></a><span class="w">  </span><span class="n">merge_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="c1"># 右部分配列を再帰処理</span>
+<a id="__codelineno-12-45" name="__codelineno-12-45" href="#__codelineno-12-45"></a><span class="w">  </span><span class="c1"># マージフェーズ</span>
+<a id="__codelineno-12-46" name="__codelineno-12-46" href="#__codelineno-12-46"></a><span class="w">  </span><span class="n">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-12-47" name="__codelineno-12-47" href="#__codelineno-12-47"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20merge%28nums%3A%20list%5Bint%5D%2C%20left%3A%20int%2C%20mid%3A%20int%2C%20right%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E5%B7%A6%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%A8%E5%8F%B3%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%82%92%E3%83%9E%E3%83%BC%E3%82%B8%22%22%22%0A%20%20%20%20%23%20%E5%B7%A6%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AE%E5%8C%BA%E9%96%93%E3%81%AF%20%5Bleft%2C%20mid%5D%E3%80%81%E5%8F%B3%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AE%E5%8C%BA%E9%96%93%E3%81%AF%20%5Bmid%2B1%2C%20right%5D%0A%20%20%20%20%23%20%E3%83%9E%E3%83%BC%E3%82%B8%E7%B5%90%E6%9E%9C%E3%82%92%E6%A0%BC%E7%B4%8D%E3%81%99%E3%82%8B%E4%B8%80%E6%99%82%E9%85%8D%E5%88%97%20tmp%20%E3%82%92%E4%BD%9C%E6%88%90%0A%20%20%20%20tmp%20%3D%20%5B0%5D%20%2A%20%28right%20-%20left%20%2B%201%29%0A%20%20%20%20%23%20%E5%B7%A6%E5%8F%B3%E3%81%AE%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AE%E9%96%8B%E5%A7%8B%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20i%2C%20j%2C%20k%20%3D%20left%2C%20mid%20%2B%201%2C%200%0A%20%20%20%20%23%20%E5%B7%A6%E5%8F%B3%E3%81%AE%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AB%E3%81%BE%E3%81%A0%E8%A6%81%E7%B4%A0%E3%81%8C%E3%81%82%E3%82%8B%E9%96%93%E3%81%AF%E6%AF%94%E8%BC%83%E3%81%97%E3%80%81%E5%B0%8F%E3%81%95%E3%81%84%E3%81%BB%E3%81%86%E3%82%92%E4%B8%80%E6%99%82%E9%85%8D%E5%88%97%E3%81%AB%E3%82%B3%E3%83%94%E3%83%BC%E3%81%99%E3%82%8B%0A%20%20%20%20while%20i%20%3C%3D%20mid%20and%20j%20%3C%3D%20right%3A%0A%20%20%20%20%20%20%20%20if%20nums%5Bi%5D%20%3C%3D%20nums%5Bj%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20tmp%5Bk%5D%20%3D%20nums%5Bi%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%2B%3D%201%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20tmp%5Bk%5D%20%3D%20nums%5Bj%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20%2B%3D%201%0A%20%20%20%20%20%20%20%20k%20%2B%3D%201%0A%20%20%20%20%23%20%E5%B7%A6%E5%8F%B3%E3%81%AE%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AE%E6%AE%8B%E3%82%8A%E8%A6%81%E7%B4%A0%E3%82%92%E4%B8%80%E6%99%82%E9%85%8D%E5%88%97%E3%81%AB%E3%82%B3%E3%83%94%E3%83%BC%E3%81%99%E3%82%8B%0A%20%20%20%20while%20i%20%3C%3D%20mid%3A%0A%20%20%20%20%20%20%20%20tmp%5Bk%5D%20%3D%20nums%5Bi%5D%0A%20%20%20%20%20%20%20%20i%20%2B%3D%201%0A%20%20%20%20%20%20%20%20k%20%2B%3D%201%0A%20%20%20%20while%20j%20%3C%3D%20right%3A%0A%20%20%20%20%20%20%20%20tmp%5Bk%5D%20%3D%20nums%5Bj%5D%0A%20%20%20%20%20%20%20%20j%20%2B%3D%201%0A%20%20%20%20%20%20%20%20k%20%2B%3D%201%0A%20%20%20%20%23%20%E4%B8%80%E6%99%82%E9%85%8D%E5%88%97%20tmp%20%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E5%85%83%E3%81%AE%E9%85%8D%E5%88%97%20nums%20%E3%81%AE%E5%AF%BE%E5%BF%9C%E5%8C%BA%E9%96%93%E3%81%AB%E3%82%B3%E3%83%94%E3%83%BC%E3%81%99%E3%82%8B%0A%20%20%20%20for%20k%20in%20range%280%2C%20len%28tmp%29%29%3A%0A%20%20%20%20%20%20%20%20nums%5Bleft%20%2B%20k%5D%20%3D%20tmp%5Bk%5D%0A%0A%0Adef%20merge_sort%28nums%3A%20list%5Bint%5D%2C%20left%3A%20int%2C%20right%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E3%83%9E%E3%83%BC%E3%82%B8%E3%82%BD%E3%83%BC%E3%83%88%22%22%22%0A%20%20%20%20%23%20%E7%B5%82%E4%BA%86%E6%9D%A1%E4%BB%B6%0A%20%20%20%20if%20left%20%3E%3D%20right%3A%0A%20%20%20%20%20%20%20%20return%20%20%23%20%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AE%E9%95%B7%E3%81%95%E3%81%8C%201%20%E3%81%AB%E3%81%AA%E3%81%A3%E3%81%9F%E3%82%89%E5%86%8D%E5%B8%B0%E3%82%92%E7%B5%82%E4%BA%86%0A%20%20%20%20%23%20%E5%88%86%E5%89%B2%E3%83%95%E3%82%A7%E3%83%BC%E3%82%BA%0A%20%20%20%20mid%20%3D%20%28left%20%2B%20right%29%20%2F%2F%202%20%20%23%20%E4%B8%AD%E7%82%B9%E3%82%92%E8%A8%88%E7%AE%97%0A%20%20%20%20merge_sort%28nums%2C%20left%2C%20mid%29%20%20%23%20%E5%B7%A6%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%82%92%E5%86%8D%E5%B8%B0%E5%87%A6%E7%90%86%0A%20%20%20%20merge_sort%28nums%2C%20mid%20%2B%201%2C%20right%29%20%20%23%20%E5%8F%B3%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%82%92%E5%86%8D%E5%B8%B0%E5%87%A6%E7%90%86%0A%20%20%20%20%23%20%E3%83%9E%E3%83%BC%E3%82%B8%E3%83%95%E3%82%A7%E3%83%BC%E3%82%BA%0A%20%20%20%20merge%28nums%2C%20left%2C%20mid%2C%20right%29%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B7%2C%203%2C%202%2C%206%2C%200%2C%201%2C%205%2C%204%5D%0A%20%20%20%20merge_sort%28nums%2C%200%2C%20len%28nums%29%20-%201%29%0A%20%20%20%20print%28%22%E3%83%9E%E3%83%BC%E3%82%B8%E3%82%BD%E3%83%BC%E3%83%88%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%22%2C%20nums%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20merge%28nums%3A%20list%5Bint%5D%2C%20left%3A%20int%2C%20mid%3A%20int%2C%20right%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E5%B7%A6%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%A8%E5%8F%B3%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%82%92%E3%83%9E%E3%83%BC%E3%82%B8%22%22%22%0A%20%20%20%20%23%20%E5%B7%A6%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AE%E5%8C%BA%E9%96%93%E3%81%AF%20%5Bleft%2C%20mid%5D%E3%80%81%E5%8F%B3%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AE%E5%8C%BA%E9%96%93%E3%81%AF%20%5Bmid%2B1%2C%20right%5D%0A%20%20%20%20%23%20%E3%83%9E%E3%83%BC%E3%82%B8%E7%B5%90%E6%9E%9C%E3%82%92%E6%A0%BC%E7%B4%8D%E3%81%99%E3%82%8B%E4%B8%80%E6%99%82%E9%85%8D%E5%88%97%20tmp%20%E3%82%92%E4%BD%9C%E6%88%90%0A%20%20%20%20tmp%20%3D%20%5B0%5D%20%2A%20%28right%20-%20left%20%2B%201%29%0A%20%20%20%20%23%20%E5%B7%A6%E5%8F%B3%E3%81%AE%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AE%E9%96%8B%E5%A7%8B%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20i%2C%20j%2C%20k%20%3D%20left%2C%20mid%20%2B%201%2C%200%0A%20%20%20%20%23%20%E5%B7%A6%E5%8F%B3%E3%81%AE%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AB%E3%81%BE%E3%81%A0%E8%A6%81%E7%B4%A0%E3%81%8C%E3%81%82%E3%82%8B%E9%96%93%E3%81%AF%E6%AF%94%E8%BC%83%E3%81%97%E3%80%81%E5%B0%8F%E3%81%95%E3%81%84%E3%81%BB%E3%81%86%E3%82%92%E4%B8%80%E6%99%82%E9%85%8D%E5%88%97%E3%81%AB%E3%82%B3%E3%83%94%E3%83%BC%E3%81%99%E3%82%8B%0A%20%20%20%20while%20i%20%3C%3D%20mid%20and%20j%20%3C%3D%20right%3A%0A%20%20%20%20%20%20%20%20if%20nums%5Bi%5D%20%3C%3D%20nums%5Bj%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20tmp%5Bk%5D%20%3D%20nums%5Bi%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%2B%3D%201%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20tmp%5Bk%5D%20%3D%20nums%5Bj%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20%2B%3D%201%0A%20%20%20%20%20%20%20%20k%20%2B%3D%201%0A%20%20%20%20%23%20%E5%B7%A6%E5%8F%B3%E3%81%AE%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AE%E6%AE%8B%E3%82%8A%E8%A6%81%E7%B4%A0%E3%82%92%E4%B8%80%E6%99%82%E9%85%8D%E5%88%97%E3%81%AB%E3%82%B3%E3%83%94%E3%83%BC%E3%81%99%E3%82%8B%0A%20%20%20%20while%20i%20%3C%3D%20mid%3A%0A%20%20%20%20%20%20%20%20tmp%5Bk%5D%20%3D%20nums%5Bi%5D%0A%20%20%20%20%20%20%20%20i%20%2B%3D%201%0A%20%20%20%20%20%20%20%20k%20%2B%3D%201%0A%20%20%20%20while%20j%20%3C%3D%20right%3A%0A%20%20%20%20%20%20%20%20tmp%5Bk%5D%20%3D%20nums%5Bj%5D%0A%20%20%20%20%20%20%20%20j%20%2B%3D%201%0A%20%20%20%20%20%20%20%20k%20%2B%3D%201%0A%20%20%20%20%23%20%E4%B8%80%E6%99%82%E9%85%8D%E5%88%97%20tmp%20%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E5%85%83%E3%81%AE%E9%85%8D%E5%88%97%20nums%20%E3%81%AE%E5%AF%BE%E5%BF%9C%E5%8C%BA%E9%96%93%E3%81%AB%E3%82%B3%E3%83%94%E3%83%BC%E3%81%99%E3%82%8B%0A%20%20%20%20for%20k%20in%20range%280%2C%20len%28tmp%29%29%3A%0A%20%20%20%20%20%20%20%20nums%5Bleft%20%2B%20k%5D%20%3D%20tmp%5Bk%5D%0A%0A%0Adef%20merge_sort%28nums%3A%20list%5Bint%5D%2C%20left%3A%20int%2C%20right%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E3%83%9E%E3%83%BC%E3%82%B8%E3%82%BD%E3%83%BC%E3%83%88%22%22%22%0A%20%20%20%20%23%20%E7%B5%82%E4%BA%86%E6%9D%A1%E4%BB%B6%0A%20%20%20%20if%20left%20%3E%3D%20right%3A%0A%20%20%20%20%20%20%20%20return%20%20%23%20%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AE%E9%95%B7%E3%81%95%E3%81%8C%201%20%E3%81%AB%E3%81%AA%E3%81%A3%E3%81%9F%E3%82%89%E5%86%8D%E5%B8%B0%E3%82%92%E7%B5%82%E4%BA%86%0A%20%20%20%20%23%20%E5%88%86%E5%89%B2%E3%83%95%E3%82%A7%E3%83%BC%E3%82%BA%0A%20%20%20%20mid%20%3D%20%28left%20%2B%20right%29%20%2F%2F%202%20%20%23%20%E4%B8%AD%E7%82%B9%E3%82%92%E8%A8%88%E7%AE%97%0A%20%20%20%20merge_sort%28nums%2C%20left%2C%20mid%29%20%20%23%20%E5%B7%A6%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%82%92%E5%86%8D%E5%B8%B0%E5%87%A6%E7%90%86%0A%20%20%20%20merge_sort%28nums%2C%20mid%20%2B%201%2C%20right%29%20%20%23%20%E5%8F%B3%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%82%92%E5%86%8D%E5%B8%B0%E5%87%A6%E7%90%86%0A%20%20%20%20%23%20%E3%83%9E%E3%83%BC%E3%82%B8%E3%83%95%E3%82%A7%E3%83%BC%E3%82%BA%0A%20%20%20%20merge%28nums%2C%20left%2C%20mid%2C%20right%29%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B7%2C%203%2C%202%2C%206%2C%200%2C%201%2C%205%2C%204%5D%0A%20%20%20%20merge_sort%28nums%2C%200%2C%20len%28nums%29%20-%201%29%0A%20%20%20%20print%28%22%E3%83%9E%E3%83%BC%E3%82%B8%E3%82%BD%E3%83%BC%E3%83%88%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%22%2C%20nums%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 <h2 id="1162">11.6.2 &nbsp; アルゴリズムの特性<a class="headerlink" href="#1162" title="Permanent link">&para;</a></h2>
 <ul>
-<li><strong><span class="arithmatex">\(O(n \log n)\)</span>の時間計算量、非適応ソート</strong>：分割により高さ<span class="arithmatex">\(\log n\)</span>の再帰ツリーが作成され、各層で合計<span class="arithmatex">\(n\)</span>回の操作をマージし、全体的な時間計算量は<span class="arithmatex">\(O(n \log n)\)</span>となります。</li>
-<li><strong><span class="arithmatex">\(O(n)\)</span>の空間計算量、非インプレースソート</strong>：再帰深度は<span class="arithmatex">\(\log n\)</span>で、<span class="arithmatex">\(O(\log n)\)</span>のスタックフレーム空間を使用します。マージ操作には補助配列が必要で、追加の<span class="arithmatex">\(O(n)\)</span>空間を使用します。</li>
-<li><strong>安定ソート</strong>：マージプロセス中、等しい要素の順序は変更されません。</li>
+<li><strong>時間計算量は <span class="arithmatex">\(O(n \log n)\)</span>、非適応型ソート</strong>：分割によって高さ <span class="arithmatex">\(\log n\)</span> の再帰木が生成され、各層でのマージ操作の総数は <span class="arithmatex">\(n\)</span> であるため、全体の時間計算量は <span class="arithmatex">\(O(n \log n)\)</span> です。</li>
+<li><strong>空間計算量は <span class="arithmatex">\(O(n)\)</span>、インプレースではないソート</strong>：再帰の深さは <span class="arithmatex">\(\log n\)</span> であり、サイズ <span class="arithmatex">\(O(\log n)\)</span> のスタックフレーム領域を使用します。マージ操作は補助配列を用いて実装する必要があり、サイズ <span class="arithmatex">\(O(n)\)</span> の追加領域を使用します。</li>
+<li><strong>安定ソート</strong>：マージの過程では、等しい要素の順序は変化しません。</li>
 </ul>
 <h2 id="1163">11.6.3 &nbsp; 連結リストのソート<a class="headerlink" href="#1163" title="Permanent link">&para;</a></h2>
-<p>連結リストの場合、マージソートは他のソートアルゴリズムよりも大きな利点があります。<strong>連結リストソートタスクの空間計算量を<span class="arithmatex">\(O(1)\)</span>に最適化できます</strong>。</p>
+<p>連結リストに対しては、マージソートは他のソートアルゴリズムと比べて顕著な利点があり、<strong>連結リストのソート問題の空間計算量を <span class="arithmatex">\(O(1)\)</span> まで最適化できます</strong> 。</p>
 <ul>
-<li><strong>分割フェーズ</strong>：「再帰」の代わりに「反復」を使用して連結リスト分割作業を実行できるため、再帰で使用されるスタックフレーム空間を節約できます。</li>
-<li><strong>マージフェーズ</strong>：連結リストでは、ノードの挿入と削除操作は参照（ポインタ）を変更することで実現できるため、マージフェーズ（2つの短い順序付きリストを1つの長い順序付きリストに結合）中に追加のリストを作成する必要がありません。</li>
+<li><strong>分割段階</strong>：連結リストの分割は「再帰」の代わりに「反復」で実装できるため、再帰で使用するスタックフレーム領域を省けます。</li>
+<li><strong>マージ段階</strong>：連結リストでは、ノードの追加や削除は参照（ポインタ）を変更するだけで実現できるため、マージ段階（2 つの短いソート済み連結リストを 1 つの長いソート済み連結リストにマージすること）では追加の連結リストを作成する必要がありません。</li>
 </ul>
-<p>実装の詳細は比較的複雑で、興味のある読者は関連資料を参照して学習してください。</p>
+<p>具体的な実装の詳細は比較的複雑なので、興味のある読者は関連資料を参照して学習してください。</p>
 
 <!-- Source file information -->
 
diff --git a/ja/chapter_sorting/quick_sort/index.html b/ja/chapter_sorting/quick_sort/index.html
index e9317a25f..2e9959c38 100644
--- a/ja/chapter_sorting/quick_sort/index.html
+++ b/ja/chapter_sorting/quick_sort/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
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-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1942,7 +1942,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2105,7 +2105,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2491,7 +2491,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2547,7 +2547,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
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   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
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   <a href="#1151" class="md-nav__link">
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-        11.5.1 &nbsp; アルゴリズムプロセス
+        11.5.1 &nbsp; アルゴリズムの流れ
       
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@@ -2906,7 +2906,7 @@
   <a href="#1152" class="md-nav__link">
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-        11.5.2 &nbsp; アルゴリズムの特徴
+        11.5.2 &nbsp; アルゴリズムの特性
       
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@@ -2917,7 +2917,7 @@
   <a href="#1153" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.5.3 &nbsp; なぜクイックソートは高速なのか
+        11.5.3 &nbsp; クイックソートが速い理由
       
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@@ -2928,7 +2928,7 @@
   <a href="#1154" class="md-nav__link">
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-        11.5.4 &nbsp; ピボット最適化
+        11.5.4 &nbsp; 基準数の最適化
       
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   <a href="#1155" class="md-nav__link">
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-        11.5.5 &nbsp; 末尾再帰最適化
+        11.5.5 &nbsp; 再帰の深さの最適化
       
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
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-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
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-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
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-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
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-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
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-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4186,7 +4186,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4332,7 +4332,7 @@
   <a href="#1151" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.5.1 &nbsp; アルゴリズムプロセス
+        11.5.1 &nbsp; アルゴリズムの流れ
       
     </span>
   </a>
@@ -4343,7 +4343,7 @@
   <a href="#1152" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.5.2 &nbsp; アルゴリズムの特徴
+        11.5.2 &nbsp; アルゴリズムの特性
       
     </span>
   </a>
@@ -4354,7 +4354,7 @@
   <a href="#1153" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.5.3 &nbsp; なぜクイックソートは高速なのか
+        11.5.3 &nbsp; クイックソートが速い理由
       
     </span>
   </a>
@@ -4365,7 +4365,7 @@
   <a href="#1154" class="md-nav__link">
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-        11.5.4 &nbsp; ピボット最適化
+        11.5.4 &nbsp; 基準数の最適化
       
     </span>
   </a>
@@ -4376,7 +4376,7 @@
   <a href="#1155" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.5.5 &nbsp; 末尾再帰最適化
+        11.5.5 &nbsp; 再帰の深さの最適化
       
     </span>
   </a>
@@ -4421,17 +4421,17 @@
 
 <!-- Page content -->
 <h1 id="115">11.5 &nbsp; クイックソート<a class="headerlink" href="#115" title="Permanent link">&para;</a></h1>
-<p><u>クイックソート</u>は分割統治戦略に基づくソートアルゴリズムで、その効率性と幅広い応用で知られています。</p>
-<p>クイックソートのコア操作は「ピボット分割」で、配列から要素を「ピボット」として選択し、ピボットより小さいすべての要素をその左側に移動し、ピボットより大きいすべての要素をその右側に移動することを目的としています。具体的に、ピボット分割のプロセスは下図に示されます。</p>
+<p><u>クイックソート（quick sort）</u>は分割統治戦略に基づくソートアルゴリズムであり、実行効率が高く、広く利用されています。</p>
+<p>クイックソートの中核操作は「パーティション」であり、その目的は、配列内のある要素を「基準数」として選び、基準数より小さいすべての要素を左側へ、大きい要素を右側へ移動することです。具体的には、パーティションの流れを下図に示します。</p>
 <ol>
-<li>配列の最も左の要素をピボットとして選択し、2つのポインタ<code>i</code>と<code>j</code>を初期化して配列の両端をそれぞれ指すようにします。</li>
-<li>各ラウンドで<code>i</code>（<code>j</code>）を使用してピボットより大きい（小さい）最初の要素を探索し、次にこれら2つの要素を交換するループを設定します。</li>
-<li><code>i</code>と<code>j</code>が出会うまでステップ<code>2.</code>を繰り返し、最後にピボットを2つのサブ配列の境界に交換します。</li>
+<li>配列の最左端の要素を基準数として選び、2 つのポインタ <code>i</code> と <code>j</code> を初期化して、それぞれ配列の両端を指すようにします。</li>
+<li>ループを設定し、各ラウンドで <code>i</code>（<code>j</code>）を使ってそれぞれ基準数より大きい（小さい）最初の要素を探し、その後この 2 つの要素を交換します。</li>
+<li><code>i</code> と <code>j</code> が出会うまでステップ <code>2.</code> を繰り返し、最後に基準数を 2 つの部分配列の境界へ交換します。</li>
 </ol>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:9"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label><label for="__tabbed_1_5">&lt;5&gt;</label><label for="__tabbed_1_6">&lt;6&gt;</label><label for="__tabbed_1_7">&lt;7&gt;</label><label for="__tabbed_1_8">&lt;8&gt;</label><label for="__tabbed_1_9">&lt;9&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="Pivot division process" class="animation-figure" src="../quick_sort.assets/pivot_division_step1.png" /></p>
+<p><img alt="パーティションの手順" class="animation-figure" src="../quick_sort.assets/pivot_division_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="pivot_division_step2" class="animation-figure" src="../quick_sort.assets/pivot_division_step2.png" /></p>
@@ -4459,148 +4459,336 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 11-8 &nbsp; Pivot division process </p>
+<p align="center"> 図 11-8 &nbsp; パーティションの手順 </p>
 
-<p>ピボット分割後、元の配列は3つの部分に分割されます：左サブ配列、ピボット、右サブ配列で、「左サブ配列の任意の要素 <span class="arithmatex">\(\leq\)</span> ピボット <span class="arithmatex">\(\leq\)</span> 右サブ配列の任意の要素」を満たします。したがって、これら2つのサブ配列のみをソートすればよいのです。</p>
+<p>パーティションが完了すると、元の配列は左部分配列、基準数、右部分配列の 3 つに分けられ、「左部分配列の任意の要素 <span class="arithmatex">\(\leq\)</span> 基準数 <span class="arithmatex">\(\leq\)</span> 右部分配列の任意の要素」を満たします。したがって、次はこの 2 つの部分配列だけをソートすれば済みます。</p>
 <div class="admonition note">
 <p class="admonition-title">クイックソートの分割統治戦略</p>
-<p>ピボット分割の本質は、より長い配列のソート問題をより短い2つの配列に簡素化することです。</p>
+<p>パーティションの本質は、長い配列のソート問題を 2 つの短い配列のソート問題へ簡略化することです。</p>
 </div>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">quick_sort.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">partition</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;分割&quot;&quot;&quot;</span>
-<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># nums[left] をピボットとして使用</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;番兵分割&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># nums[left] を基準値とする</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="n">left</span><span class="p">,</span> <span class="n">right</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="n">j</span><span class="p">:</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="n">j</span> <span class="ow">and</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">&gt;=</span> <span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">]:</span>
-<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>            <span class="n">j</span> <span class="o">-=</span> <span class="mi">1</span>  <span class="c1"># 右から左へピボットより小さい最初の要素を探す</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>            <span class="n">j</span> <span class="o">-=</span> <span class="mi">1</span>  <span class="c1"># 右から左へ基準値未満の最初の要素を探す</span>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="n">j</span> <span class="ow">and</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&lt;=</span> <span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">]:</span>
-<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>            <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>  <span class="c1"># 左から右へピボットより大きい最初の要素を探す</span>
-<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="c1"># 要素を交換</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>            <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>  <span class="c1"># 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="c1"># 要素の交換</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
-<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="c1"># ピボットを2つのサブ配列の境界に交換</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="c1"># 基準値を 2 つの部分配列の境界へ交換する</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
-<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="k">return</span> <span class="n">i</span>  <span class="c1"># ピボットのインデックスを返す</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="k">return</span> <span class="n">i</span>  <span class="c1"># 基準値のインデックスを返す</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 分割 */</span>
+<div class="highlight"><span class="filename">quick_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 番兵分割 */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">partition</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// nums[left]をピボットとして使用</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// nums[left] を基準値とする</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">;</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">])</span>
-<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右から左へピボットより小さい最初の要素を検索</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span><span class="w">                </span><span class="c1">// 右から左へ基準値未満の最初の要素を探す</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">])</span>
-<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w">          </span><span class="c1">// 左から右へピボットより大きい最初の要素を検索</span>
-<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span><span class="w"> </span><span class="c1">// これら二つの要素を交換</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w">                </span><span class="c1">// 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]);</span><span class="w"> </span><span class="c1">// この 2 つの要素を交換</span>
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">);</span><span class="w"> </span><span class="c1">// ピボットを二つのサブ配列の境界に交換</span>
-<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w">            </span><span class="c1">// ピボットのインデックスを返す</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">]);</span><span class="w">  </span><span class="c1">// 基準値を 2 つの部分配列の境界へ交換する</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w">                   </span><span class="c1">// 基準値のインデックスを返す</span>
 <a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 要素を交換 */</span>
+<div class="highlight"><span class="filename">quick_sort.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 要素の交換 */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">swap</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="p">}</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a>
-<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="cm">/* 分割 */</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="cm">/* 番兵分割 */</span>
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="kt">int</span><span class="w"> </span><span class="nf">partition</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="c1">// nums[left] を基準値として使用</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="c1">// nums[left] を基準値とする</span>
 <a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">;</span>
 <a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span><span class="p">)</span>
-<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span><span class="w">          </span><span class="c1">// 右から左へ、基準値より小さい最初の要素を検索</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span><span class="w">          </span><span class="c1">// 右から左へ基準値未満の最初の要素を探す</span>
 <a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span><span class="p">)</span>
-<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w">          </span><span class="c1">// 左から右へ、基準値より大きい最初の要素を検索</span>
-<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span><span class="w"> </span><span class="c1">// これら2つの要素を交換</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w">          </span><span class="c1">// 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span><span class="w"> </span><span class="c1">// この 2 つの要素を交換</span>
 <a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">);</span><span class="w">  </span><span class="c1">// 基準値を2つの部分配列の境界に交換</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">);</span><span class="w">  </span><span class="c1">// 基準値を 2 つの部分配列の境界へ交換する</span>
 <a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w">             </span><span class="c1">// 基準値のインデックスを返す</span>
 <a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">quickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Swap</span><span class="p">}</span>
-<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
-<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">quickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Partition</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 要素の交換 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Swap</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">])</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]);</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="p">}</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="cm">/* 番兵分割 */</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Partition</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="c1">// nums[left] を基準値とする</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">])</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span><span class="w">          </span><span class="c1">// 右から左へ基準値未満の最初の要素を探す</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">])</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w">          </span><span class="c1">// 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">        </span><span class="n">Swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span><span class="w"> </span><span class="c1">// この 2 つの要素を交換</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">    </span><span class="n">Swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">);</span><span class="w">  </span><span class="c1">// 基準値を 2 つの部分配列の境界へ交換する</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w">             </span><span class="c1">// 基準値のインデックスを返す</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">quickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">partition</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 番兵分割 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">q</span><span class="w"> </span><span class="o">*</span><span class="nx">quickSort</span><span class="p">)</span><span class="w"> </span><span class="nx">partition</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// nums[left] を基準値とする</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">left</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">            </span><span class="nx">j</span><span class="o">--</span><span class="w"> </span><span class="c1">// 右から左へ基準値未満の最初の要素を探す</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">left</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">            </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="c1">// 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">        </span><span class="c1">// 要素の交換</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">    </span><span class="c1">// 基準値を 2 つの部分配列の境界へ交換する</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">    </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">left</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">left</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="c1">// 基準値のインデックスを返す</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="bp">partition</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 番兵分割 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="kr">left</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="kr">right</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// nums[left] を基準値とする</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kr">left</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kr">right</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="kr">left</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// 右から左へ基準値未満の最初の要素を探す</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="kr">left</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">        </span><span class="n">nums</span><span class="p">.</span><span class="n">swapAt</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="c1">// この 2 つの要素を交換</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">    </span><span class="n">nums</span><span class="p">.</span><span class="n">swapAt</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kr">left</span><span class="p">)</span><span class="w"> </span><span class="c1">// 基準値を 2 つの部分配列の境界へ交換する</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="c1">// 基準値のインデックスを返す</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">QuickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">swap</span><span class="p">}</span>
-<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
-<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">QuickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">partition</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 要素の交換 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="nx">swap</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">;</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="p">}</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="cm">/* 番兵分割 */</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="nx">partition</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">    </span><span class="c1">// nums[left] を基準値とする</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">        </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">right</span><span class="p">;</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">left</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右から左へ基準値未満の最初の要素を探す</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">left</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w">            </span><span class="nx">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w">        </span><span class="c1">// 要素の交換</span>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">);</span><span class="w"> </span><span class="c1">// この 2 つの要素を交換</span>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">);</span><span class="w"> </span><span class="c1">// 基準値を 2 つの部分配列の境界へ交換する</span>
+<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span><span class="w"> </span><span class="c1">// 基準値のインデックスを返す</span>
+<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">QuickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">swap</span><span class="p">}</span>
-<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
-<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">QuickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">partition</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 要素の交換 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="nx">swap</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">];</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">;</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="p">}</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="cm">/* 番兵分割 */</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="nx">partition</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">left</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">    </span><span class="c1">// nums[left] を基準値とする</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">        </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">right</span><span class="p">;</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">left</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右から左へ基準値未満の最初の要素を探す</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">left</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">            </span><span class="nx">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w">        </span><span class="c1">// 要素の交換</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">);</span><span class="w"> </span><span class="c1">// この 2 つの要素を交換</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">);</span><span class="w"> </span><span class="c1">// 基準値を 2 つの部分配列の境界へ交換する</span>
+<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span><span class="w"> </span><span class="c1">// 基準値のインデックスを返す</span>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">_swap</span><span class="p">}</span>
-<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
-<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">_partition</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 要素の交換 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">_swap</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="p">}</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="cm">/* 番兵分割 */</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="kt">int</span><span class="w"> </span><span class="n">_partition</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">  </span><span class="c1">// nums[left] を基準値とする</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">])</span><span class="w"> </span><span class="n">j</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右から左へ基準値未満の最初の要素を探す</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">])</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">    </span><span class="n">_swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span><span class="w"> </span><span class="c1">// この 2 つの要素を交換</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">  </span><span class="n">_swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">);</span><span class="w"> </span><span class="c1">// 基準値を 2 つの部分配列の境界へ交換する</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="c1">// 基準値のインデックスを返す</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">partition</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 番兵分割 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">left</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="c1">// nums[left] を基準値とする</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="p">(</span><span class="k">mut</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右から左へ基準値未満の最初の要素を探す</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">        </span><span class="n">nums</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span><span class="w"> </span><span class="c1">// この 2 つの要素を交換</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">    </span><span class="n">nums</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">);</span><span class="w"> </span><span class="c1">// 基準値を 2 つの部分配列の境界へ交換する</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">    </span><span class="n">i</span><span class="w"> </span><span class="c1">// 基準値のインデックスを返す</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">swap</span><span class="p">}</span>
-<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
-<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">partition</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 要素の交換 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">swap</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">    </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="p">}</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="cm">/* 番兵分割 */</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="kt">int</span><span class="w"> </span><span class="nf">partition</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="c1">// nums[left] を基準値とする</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右から左へ基準値未満の最初の要素を探す</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w">        </span><span class="c1">// この 2 つの要素を交換</span>
+<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span>
+<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w">    </span><span class="c1">// 基準値を 2 つの部分配列の境界へ交換する</span>
+<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">);</span>
+<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="w">    </span><span class="c1">// 基準値のインデックスを返す</span>
+<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">swap</span><span class="p">}</span>
-<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
-<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">partition</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 要素の交換 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="p">}</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="cm">/* 番兵分割 */</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">    </span><span class="c1">// nums[left] を基準値とする</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="w">           </span><span class="c1">// 右から左へ基準値未満の最初の要素を探す</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span><span class="w">           </span><span class="c1">// 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w">  </span><span class="c1">// この 2 つの要素を交換</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">)</span><span class="w">   </span><span class="c1">// 基準値を 2 つの部分配列の境界へ交換する</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="w">              </span><span class="c1">// 基準値のインデックスを返す</span>
+<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">QuickSort</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">partition</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 番兵分割 ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># nums[left] を基準値とする</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">      </span><span class="n">j</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># 右から左へ基準値未満の最初の要素を探す</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">      </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">    </span><span class="c1"># 要素の交換</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">    </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">  </span><span class="c1"># 基準値を 2 つの部分配列の境界へ交換する</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">  </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">  </span><span class="n">i</span><span class="w"> </span><span class="c1"># 基準値のインデックスを返す</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h2 id="1151">11.5.1 &nbsp; アルゴリズムプロセス<a class="headerlink" href="#1151" title="Permanent link">&para;</a></h2>
-<p>クイックソートの全体的なプロセスは下図に示されます。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20partition%28nums%3A%20list%5Bint%5D%2C%20left%3A%20int%2C%20right%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%95%AA%E5%85%B5%E5%88%86%E5%89%B2%22%22%22%0A%20%20%20%20%23%20nums%5Bleft%5D%20%E3%82%92%E5%9F%BA%E6%BA%96%E5%80%A4%E3%81%A8%E3%81%99%E3%82%8B%0A%20%20%20%20i%2C%20j%20%3D%20left%2C%20right%0A%20%20%20%20while%20i%20%3C%20j%3A%0A%20%20%20%20%20%20%20%20while%20i%20%3C%20j%20and%20nums%5Bj%5D%20%3E%3D%20nums%5Bleft%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20-%3D%201%20%20%23%20%E5%8F%B3%E3%81%8B%E3%82%89%E5%B7%A6%E3%81%B8%E5%9F%BA%E6%BA%96%E5%80%A4%E6%9C%AA%E6%BA%80%E3%81%AE%E6%9C%80%E5%88%9D%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E6%8E%A2%E3%81%99%0A%20%20%20%20%20%20%20%20while%20i%20%3C%20j%20and%20nums%5Bi%5D%20%3C%3D%20nums%5Bleft%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%2B%3D%201%20%20%23%20%E5%B7%A6%E3%81%8B%E3%82%89%E5%8F%B3%E3%81%B8%E5%9F%BA%E6%BA%96%E5%80%A4%E3%82%88%E3%82%8A%E5%A4%A7%E3%81%8D%E3%81%84%E6%9C%80%E5%88%9D%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E6%8E%A2%E3%81%99%0A%20%20%20%20%20%20%20%20%23%20%E8%A6%81%E7%B4%A0%E3%81%AE%E4%BA%A4%E6%8F%9B%0A%20%20%20%20%20%20%20%20nums%5Bi%5D%2C%20nums%5Bj%5D%20%3D%20nums%5Bj%5D%2C%20nums%5Bi%5D%0A%20%20%20%20%23%20%E5%9F%BA%E6%BA%96%E5%80%A4%E3%82%92%202%20%E3%81%A4%E3%81%AE%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AE%E5%A2%83%E7%95%8C%E3%81%B8%E4%BA%A4%E6%8F%9B%E3%81%99%E3%82%8B%0A%20%20%20%20nums%5Bi%5D%2C%20nums%5Bleft%5D%20%3D%20nums%5Bleft%5D%2C%20nums%5Bi%5D%0A%20%20%20%20return%20i%20%20%23%20%E5%9F%BA%E6%BA%96%E5%80%A4%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E8%BF%94%E3%81%99%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B2%2C%204%2C%201%2C%200%2C%203%2C%205%5D%0A%20%20%20%20partition%28nums%2C%200%2C%20len%28nums%29%20-%201%29%0A%20%20%20%20print%28%22%E7%95%AA%E5%85%B5%E5%88%86%E5%89%B2%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%22%2C%20nums%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20partition%28nums%3A%20list%5Bint%5D%2C%20left%3A%20int%2C%20right%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%95%AA%E5%85%B5%E5%88%86%E5%89%B2%22%22%22%0A%20%20%20%20%23%20nums%5Bleft%5D%20%E3%82%92%E5%9F%BA%E6%BA%96%E5%80%A4%E3%81%A8%E3%81%99%E3%82%8B%0A%20%20%20%20i%2C%20j%20%3D%20left%2C%20right%0A%20%20%20%20while%20i%20%3C%20j%3A%0A%20%20%20%20%20%20%20%20while%20i%20%3C%20j%20and%20nums%5Bj%5D%20%3E%3D%20nums%5Bleft%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20-%3D%201%20%20%23%20%E5%8F%B3%E3%81%8B%E3%82%89%E5%B7%A6%E3%81%B8%E5%9F%BA%E6%BA%96%E5%80%A4%E6%9C%AA%E6%BA%80%E3%81%AE%E6%9C%80%E5%88%9D%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E6%8E%A2%E3%81%99%0A%20%20%20%20%20%20%20%20while%20i%20%3C%20j%20and%20nums%5Bi%5D%20%3C%3D%20nums%5Bleft%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%2B%3D%201%20%20%23%20%E5%B7%A6%E3%81%8B%E3%82%89%E5%8F%B3%E3%81%B8%E5%9F%BA%E6%BA%96%E5%80%A4%E3%82%88%E3%82%8A%E5%A4%A7%E3%81%8D%E3%81%84%E6%9C%80%E5%88%9D%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E6%8E%A2%E3%81%99%0A%20%20%20%20%20%20%20%20%23%20%E8%A6%81%E7%B4%A0%E3%81%AE%E4%BA%A4%E6%8F%9B%0A%20%20%20%20%20%20%20%20nums%5Bi%5D%2C%20nums%5Bj%5D%20%3D%20nums%5Bj%5D%2C%20nums%5Bi%5D%0A%20%20%20%20%23%20%E5%9F%BA%E6%BA%96%E5%80%A4%E3%82%92%202%20%E3%81%A4%E3%81%AE%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AE%E5%A2%83%E7%95%8C%E3%81%B8%E4%BA%A4%E6%8F%9B%E3%81%99%E3%82%8B%0A%20%20%20%20nums%5Bi%5D%2C%20nums%5Bleft%5D%20%3D%20nums%5Bleft%5D%2C%20nums%5Bi%5D%0A%20%20%20%20return%20i%20%20%23%20%E5%9F%BA%E6%BA%96%E5%80%A4%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E8%BF%94%E3%81%99%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B2%2C%204%2C%201%2C%200%2C%203%2C%205%5D%0A%20%20%20%20partition%28nums%2C%200%2C%20len%28nums%29%20-%201%29%0A%20%20%20%20print%28%22%E7%95%AA%E5%85%B5%E5%88%86%E5%89%B2%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%22%2C%20nums%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h2 id="1151">11.5.1 &nbsp; アルゴリズムの流れ<a class="headerlink" href="#1151" title="Permanent link">&para;</a></h2>
+<p>クイックソート全体の流れを下図に示します。</p>
 <ol>
-<li>まず、元の配列に対して「ピボット分割」を実行し、未ソートの左と右のサブ配列を取得します。</li>
-<li>次に、左と右のサブ配列に対してそれぞれ再帰的に「ピボット分割」を実行します。</li>
-<li>サブ配列の長さが1になるまで再帰を続け、配列全体のソートを完了します。</li>
+<li>まず、元の配列に対して 1 回「パーティション」を実行し、未ソートの左部分配列と右部分配列を得ます。</li>
+<li>次に、左部分配列と右部分配列に対してそれぞれ再帰的に「パーティション」を実行します。</li>
+<li>部分配列の長さが 1 になるまで再帰を続け、配列全体のソートを完了します。</li>
 </ol>
-<p><img alt="Quick sort process" class="animation-figure" src="../quick_sort.assets/quick_sort_overview.png" /></p>
-<p align="center"> 図 11-9 &nbsp; Quick sort process </p>
+<p><img alt="クイックソートの流れ" class="animation-figure" src="../quick_sort.assets/quick_sort_overview.png" /></p>
+<p align="center"> 図 11-9 &nbsp; クイックソートの流れ </p>
 
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 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">quick_sort.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">quick_sort</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
 <a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;クイックソート&quot;&quot;&quot;</span>
-<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="c1"># サブ配列の長さが1のときに再帰を終了</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="c1"># 部分配列の長さが 1 なら再帰を終了する</span>
 <a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="k">if</span> <span class="n">left</span> <span class="o">&gt;=</span> <span class="n">right</span><span class="p">:</span>
 <a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>        <span class="k">return</span>
-<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>    <span class="c1"># 分割</span>
+<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>    <span class="c1"># 番兵分割</span>
 <a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>    <span class="n">pivot</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">left</span><span class="p">,</span> <span class="n">right</span><span class="p">)</span>
-<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>    <span class="c1"># 左サブ配列と右サブ配列を再帰的に処理</span>
+<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>    <span class="c1"># 左右の部分配列を再帰処理</span>
 <a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">quick_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">left</span><span class="p">,</span> <span class="n">pivot</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
 <a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">quick_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">pivot</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">right</span><span class="p">)</span>
 </code></pre></div>
@@ -4608,12 +4796,12 @@
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">quick_sort.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* クイックソート */</span>
 <a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">quickSort</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="c1">// サブ配列の長さが1の時、再帰を終了</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="c1">// 部分配列の長さが 1 なら再帰を終了する</span>
 <a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
 <a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="c1">// 分割</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="c1">// 番兵分割</span>
 <a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
-<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">    </span><span class="c1">// 左サブ配列と右サブ配列を再帰的に処理</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">    </span><span class="c1">// 左右の部分配列を再帰処理</span>
 <a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">    </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">    </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
 <a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="p">}</span>
@@ -4622,83 +4810,191 @@
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">quick_sort.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* クイックソート */</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">quickSort</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 部分配列の長さが 1 のとき再帰を終了</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 部分配列の長さが 1 なら再帰を終了する</span>
 <a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
 <a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="c1">// 分割</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="c1">// 番兵分割</span>
 <a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
-<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="c1">// 左部分配列と右部分配列を再帰的に処理</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="c1">// 左右の部分配列を再帰処理</span>
 <a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">    </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
 <a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">quickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">QuickSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* クイックソート */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">QuickSort</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="c1">// 部分配列の長さが 1 なら再帰を終了する</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="c1">// 番兵分割</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="c1">// 左右の部分配列を再帰処理</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">    </span><span class="n">QuickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="n">QuickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">quickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">quickSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* クイックソート */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">q</span><span class="w"> </span><span class="o">*</span><span class="nx">quickSort</span><span class="p">)</span><span class="w"> </span><span class="nx">quickSort</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="c1">// 部分配列の長さが 1 なら再帰を終了する</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">    </span><span class="c1">// 番兵分割</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">    </span><span class="nx">pivot</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">partition</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">    </span><span class="c1">// 左右の部分配列を再帰処理</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">    </span><span class="nx">q</span><span class="p">.</span><span class="nx">quickSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">pivot</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w">    </span><span class="nx">q</span><span class="p">.</span><span class="nx">quickSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">pivot</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">quickSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* クイックソート */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="kr">left</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="kr">right</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="c1">// 部分配列の長さが 1 なら再帰を終了する</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="kr">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="kr">right</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">    </span><span class="c1">// 番兵分割</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">pivot</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kr">left</span><span class="p">:</span><span class="w"> </span><span class="kr">left</span><span class="p">,</span><span class="w"> </span><span class="kr">right</span><span class="p">:</span><span class="w"> </span><span class="kr">right</span><span class="p">)</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">    </span><span class="c1">// 左右の部分配列を再帰処理</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">    </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kr">left</span><span class="p">:</span><span class="w"> </span><span class="kr">left</span><span class="p">,</span><span class="w"> </span><span class="kr">right</span><span class="p">:</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w">    </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kr">left</span><span class="p">:</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="kr">right</span><span class="p">:</span><span class="w"> </span><span class="kr">right</span><span class="p">)</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">QuickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">quickSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* クイックソート */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="nx">quickSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="c1">// 部分配列の長さが 1 なら再帰を終了する</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">    </span><span class="c1">// 番兵分割</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">pivot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">partition</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">);</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">    </span><span class="c1">// 左右の部分配列を再帰処理</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="nx">quickSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="nx">quickSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">);</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">QuickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">quickSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* クイックソート */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="nx">quickSort</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">left</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="c1">// 部分配列の長さが 1 なら再帰を終了する</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">    </span><span class="c1">// 番兵分割</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">pivot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">partition</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">);</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">    </span><span class="c1">// 左右の部分配列を再帰処理</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="nx">quickSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="nx">quickSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">);</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quickSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* クイックソート */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">quickSort</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="c1">// 部分配列の長さが 1 なら再帰を終了する</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">  </span><span class="c1">// 番兵分割</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">  </span><span class="c1">// 左右の部分配列を再帰処理</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">  </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">  </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quick_sort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* クイックソート */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">quick_sort</span><span class="p">(</span><span class="n">left</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="c1">// 部分配列の長さが 1 なら再帰を終了する</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">    </span><span class="c1">// 番兵分割</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span><span class="p">::</span><span class="n">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">;</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">    </span><span class="c1">// 左右の部分配列を再帰処理</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w">    </span><span class="bp">Self</span><span class="p">::</span><span class="n">quick_sort</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">);</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w">    </span><span class="bp">Self</span><span class="p">::</span><span class="n">quick_sort</span><span class="p">(</span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">);</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quickSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* クイックソート */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">quickSort</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="c1">// 部分配列の長さが 1 なら再帰を終了する</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w">    </span><span class="c1">// 番兵分割</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w">    </span><span class="c1">// 左右の部分配列を再帰処理</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w">    </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w">    </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">quickSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* クイックソート */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="c1">// 部分配列の長さが 1 なら再帰を終了する</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="k">return</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">    </span><span class="c1">// 番兵分割</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">pivot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w">    </span><span class="c1">// 左右の部分配列を再帰処理</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w">    </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w">    </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">QuickSort</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">quick_sort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### クイックソートクラス ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">quick_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="c1"># 部分配列の長さが 1 でない場合は再帰する</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">right</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">    </span><span class="c1"># 番兵分割</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">    </span><span class="n">pivot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">    </span><span class="c1"># 左右の部分配列を再帰処理</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w">    </span><span class="n">quick_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">    </span><span class="n">quick_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w">  </span><span class="n">nums</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h2 id="1152">11.5.2 &nbsp; アルゴリズムの特徴<a class="headerlink" href="#1152" title="Permanent link">&para;</a></h2>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20partition%28nums%3A%20list%5Bint%5D%2C%20left%3A%20int%2C%20right%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%95%AA%E5%85%B5%E5%88%86%E5%89%B2%22%22%22%0A%20%20%20%20%23%20nums%5Bleft%5D%20%E3%82%92%E5%9F%BA%E6%BA%96%E5%80%A4%E3%81%A8%E3%81%99%E3%82%8B%0A%20%20%20%20i%2C%20j%20%3D%20left%2C%20right%0A%20%20%20%20while%20i%20%3C%20j%3A%0A%20%20%20%20%20%20%20%20while%20i%20%3C%20j%20and%20nums%5Bj%5D%20%3E%3D%20nums%5Bleft%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20-%3D%201%20%20%23%20%E5%8F%B3%E3%81%8B%E3%82%89%E5%B7%A6%E3%81%B8%E5%9F%BA%E6%BA%96%E5%80%A4%E6%9C%AA%E6%BA%80%E3%81%AE%E6%9C%80%E5%88%9D%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E6%8E%A2%E3%81%99%0A%20%20%20%20%20%20%20%20while%20i%20%3C%20j%20and%20nums%5Bi%5D%20%3C%3D%20nums%5Bleft%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%2B%3D%201%20%20%23%20%E5%B7%A6%E3%81%8B%E3%82%89%E5%8F%B3%E3%81%B8%E5%9F%BA%E6%BA%96%E5%80%A4%E3%82%88%E3%82%8A%E5%A4%A7%E3%81%8D%E3%81%84%E6%9C%80%E5%88%9D%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E6%8E%A2%E3%81%99%0A%20%20%20%20%20%20%20%20%23%20%E8%A6%81%E7%B4%A0%E3%81%AE%E4%BA%A4%E6%8F%9B%0A%20%20%20%20%20%20%20%20nums%5Bi%5D%2C%20nums%5Bj%5D%20%3D%20nums%5Bj%5D%2C%20nums%5Bi%5D%0A%20%20%20%20%23%20%E5%9F%BA%E6%BA%96%E5%80%A4%E3%82%92%202%20%E3%81%A4%E3%81%AE%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AE%E5%A2%83%E7%95%8C%E3%81%B8%E4%BA%A4%E6%8F%9B%E3%81%99%E3%82%8B%0A%20%20%20%20nums%5Bi%5D%2C%20nums%5Bleft%5D%20%3D%20nums%5Bleft%5D%2C%20nums%5Bi%5D%0A%20%20%20%20return%20i%20%20%23%20%E5%9F%BA%E6%BA%96%E5%80%A4%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E8%BF%94%E3%81%99%0A%0Adef%20quick_sort%28nums%3A%20list%5Bint%5D%2C%20left%3A%20int%2C%20right%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E3%82%AF%E3%82%A4%E3%83%83%E3%82%AF%E3%82%BD%E3%83%BC%E3%83%88%22%22%22%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AE%E9%95%B7%E3%81%95%E3%81%8C%201%20%E3%81%AA%E3%82%89%E5%86%8D%E5%B8%B0%E3%82%92%E7%B5%82%E4%BA%86%E3%81%99%E3%82%8B%0A%20%20%20%20if%20left%20%3E%3D%20right%3A%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20%23%20%E7%95%AA%E5%85%B5%E5%88%86%E5%89%B2%0A%20%20%20%20pivot%20%3D%20partition%28nums%2C%20left%2C%20right%29%0A%20%20%20%20%23%20%E5%B7%A6%E5%8F%B3%E3%81%AE%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%82%92%E5%86%8D%E5%B8%B0%E5%87%A6%E7%90%86%0A%20%20%20%20quick_sort%28nums%2C%20left%2C%20pivot%20-%201%29%0A%20%20%20%20quick_sort%28nums%2C%20pivot%20%2B%201%2C%20right%29%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E3%82%AF%E3%82%A4%E3%83%83%E3%82%AF%E3%82%BD%E3%83%BC%E3%83%88%0A%20%20%20%20nums%20%3D%20%5B2%2C%204%2C%201%2C%200%2C%203%2C%205%5D%0A%20%20%20%20quick_sort%28nums%2C%200%2C%20len%28nums%29%20-%201%29%0A%20%20%20%20print%28%22%E3%82%AF%E3%82%A4%E3%83%83%E3%82%AF%E3%82%BD%E3%83%BC%E3%83%88%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%22%2C%20nums%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20partition%28nums%3A%20list%5Bint%5D%2C%20left%3A%20int%2C%20right%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%95%AA%E5%85%B5%E5%88%86%E5%89%B2%22%22%22%0A%20%20%20%20%23%20nums%5Bleft%5D%20%E3%82%92%E5%9F%BA%E6%BA%96%E5%80%A4%E3%81%A8%E3%81%99%E3%82%8B%0A%20%20%20%20i%2C%20j%20%3D%20left%2C%20right%0A%20%20%20%20while%20i%20%3C%20j%3A%0A%20%20%20%20%20%20%20%20while%20i%20%3C%20j%20and%20nums%5Bj%5D%20%3E%3D%20nums%5Bleft%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20-%3D%201%20%20%23%20%E5%8F%B3%E3%81%8B%E3%82%89%E5%B7%A6%E3%81%B8%E5%9F%BA%E6%BA%96%E5%80%A4%E6%9C%AA%E6%BA%80%E3%81%AE%E6%9C%80%E5%88%9D%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E6%8E%A2%E3%81%99%0A%20%20%20%20%20%20%20%20while%20i%20%3C%20j%20and%20nums%5Bi%5D%20%3C%3D%20nums%5Bleft%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%2B%3D%201%20%20%23%20%E5%B7%A6%E3%81%8B%E3%82%89%E5%8F%B3%E3%81%B8%E5%9F%BA%E6%BA%96%E5%80%A4%E3%82%88%E3%82%8A%E5%A4%A7%E3%81%8D%E3%81%84%E6%9C%80%E5%88%9D%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E6%8E%A2%E3%81%99%0A%20%20%20%20%20%20%20%20%23%20%E8%A6%81%E7%B4%A0%E3%81%AE%E4%BA%A4%E6%8F%9B%0A%20%20%20%20%20%20%20%20nums%5Bi%5D%2C%20nums%5Bj%5D%20%3D%20nums%5Bj%5D%2C%20nums%5Bi%5D%0A%20%20%20%20%23%20%E5%9F%BA%E6%BA%96%E5%80%A4%E3%82%92%202%20%E3%81%A4%E3%81%AE%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AE%E5%A2%83%E7%95%8C%E3%81%B8%E4%BA%A4%E6%8F%9B%E3%81%99%E3%82%8B%0A%20%20%20%20nums%5Bi%5D%2C%20nums%5Bleft%5D%20%3D%20nums%5Bleft%5D%2C%20nums%5Bi%5D%0A%20%20%20%20return%20i%20%20%23%20%E5%9F%BA%E6%BA%96%E5%80%A4%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E8%BF%94%E3%81%99%0A%0Adef%20quick_sort%28nums%3A%20list%5Bint%5D%2C%20left%3A%20int%2C%20right%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E3%82%AF%E3%82%A4%E3%83%83%E3%82%AF%E3%82%BD%E3%83%BC%E3%83%88%22%22%22%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AE%E9%95%B7%E3%81%95%E3%81%8C%201%20%E3%81%AA%E3%82%89%E5%86%8D%E5%B8%B0%E3%82%92%E7%B5%82%E4%BA%86%E3%81%99%E3%82%8B%0A%20%20%20%20if%20left%20%3E%3D%20right%3A%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20%23%20%E7%95%AA%E5%85%B5%E5%88%86%E5%89%B2%0A%20%20%20%20pivot%20%3D%20partition%28nums%2C%20left%2C%20right%29%0A%20%20%20%20%23%20%E5%B7%A6%E5%8F%B3%E3%81%AE%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%82%92%E5%86%8D%E5%B8%B0%E5%87%A6%E7%90%86%0A%20%20%20%20quick_sort%28nums%2C%20left%2C%20pivot%20-%201%29%0A%20%20%20%20quick_sort%28nums%2C%20pivot%20%2B%201%2C%20right%29%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E3%82%AF%E3%82%A4%E3%83%83%E3%82%AF%E3%82%BD%E3%83%BC%E3%83%88%0A%20%20%20%20nums%20%3D%20%5B2%2C%204%2C%201%2C%200%2C%203%2C%205%5D%0A%20%20%20%20quick_sort%28nums%2C%200%2C%20len%28nums%29%20-%201%29%0A%20%20%20%20print%28%22%E3%82%AF%E3%82%A4%E3%83%83%E3%82%AF%E3%82%BD%E3%83%BC%E3%83%88%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%22%2C%20nums%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h2 id="1152">11.5.2 &nbsp; アルゴリズムの特性<a class="headerlink" href="#1152" title="Permanent link">&para;</a></h2>
 <ul>
-<li><strong><span class="arithmatex">\(O(n \log n)\)</span>の時間計算量、非適応ソート</strong>：平均的なケースでは、ピボット分割の再帰レベルは<span class="arithmatex">\(\log n\)</span>で、レベルあたりのループの総数は<span class="arithmatex">\(n\)</span>であり、全体で<span class="arithmatex">\(O(n \log n)\)</span>の時間を使用します。最悪の場合、各ラウンドのピボット分割は長さ<span class="arithmatex">\(n\)</span>の配列を長さ<span class="arithmatex">\(0\)</span>と<span class="arithmatex">\(n - 1\)</span>の2つのサブ配列に分割し、再帰レベル数が<span class="arithmatex">\(n\)</span>に達すると、各レベルのループ数は<span class="arithmatex">\(n\)</span>で、使用される総時間は<span class="arithmatex">\(O(n^2)\)</span>です。</li>
-<li><strong><span class="arithmatex">\(O(n)\)</span>の空間計算量、インプレースソート</strong>：入力配列が完全に逆順の場合、最悪の再帰深度は<span class="arithmatex">\(n\)</span>に達し、<span class="arithmatex">\(O(n)\)</span>のスタックフレーム空間を使用します。ソート操作は追加の配列の助けなしに元の配列で実行されます。</li>
-<li><strong>非安定ソート</strong>：ピボット分割の最終ステップで、ピボットは等しい要素の右側に交換される可能性があります。</li>
+<li><strong>時間計算量は <span class="arithmatex">\(O(n \log n)\)</span>、非適応型ソート</strong>：平均的な場合、パーティションの再帰の深さは <span class="arithmatex">\(\log n\)</span> で、各層の総ループ回数は <span class="arithmatex">\(n\)</span> のため、全体で <span class="arithmatex">\(O(n \log n)\)</span> 時間を要します。最悪の場合、各回のパーティション操作で長さ <span class="arithmatex">\(n\)</span> の配列が長さ <span class="arithmatex">\(0\)</span> と <span class="arithmatex">\(n - 1\)</span> の 2 つの部分配列に分割され、このとき再帰の深さは <span class="arithmatex">\(n\)</span> に達し、各層のループ回数は <span class="arithmatex">\(n\)</span> となるため、全体で <span class="arithmatex">\(O(n^2)\)</span> 時間を要します。</li>
+<li><strong>空間計算量は <span class="arithmatex">\(O(n)\)</span>、インプレースソート</strong>：入力配列が完全な逆順の場合、最悪の再帰深さ <span class="arithmatex">\(n\)</span> に達し、<span class="arithmatex">\(O(n)\)</span> のスタックフレーム空間を使用します。ソート操作は元の配列上で行われ、追加の配列は用いません。</li>
+<li><strong>非安定ソート</strong>：パーティションの最後のステップで、基準数が等しい要素の右側へ交換される可能性があります。</li>
 </ul>
-<h2 id="1153">11.5.3 &nbsp; なぜクイックソートは高速なのか<a class="headerlink" href="#1153" title="Permanent link">&para;</a></h2>
-<p>名前が示すように、クイックソートは効率性の面で一定の利点を持つべきです。クイックソートの平均時間計算量は「マージソート」や「ヒープソート」と同じですが、以下の理由で一般的により効率的です。</p>
+<h2 id="1153">11.5.3 &nbsp; クイックソートが速い理由<a class="headerlink" href="#1153" title="Permanent link">&para;</a></h2>
+<p>名前からも分かるように、クイックソートは効率面で一定の優位性を持っています。クイックソートの平均時間計算量は「マージソート」や「ヒープソート」と同じですが、通常はクイックソートのほうが高効率であり、主な理由は次のとおりです。</p>
 <ul>
-<li><strong>最悪ケースシナリオの低い確率</strong>：クイックソートの最悪時間計算量は<span class="arithmatex">\(O(n^2)\)</span>で、マージソートほど安定していませんが、ほとんどの場合、クイックソートは<span class="arithmatex">\(O(n \log n)\)</span>の時間計算量で動作できます。</li>
-<li><strong>高いキャッシュ利用率</strong>：ピボット分割操作中、システムはサブ配列全体をキャッシュにロードできるため、要素により効率的にアクセスできます。対照的に、「ヒープソート」などのアルゴリズムは要素にジャンプ方式でアクセスする必要があり、この特徴を欠いています。</li>
-<li><strong>計算量の小さな定数係数</strong>：上記3つのアルゴリズムの中で、クイックソートは比較、代入、交換などの操作の総数が最も少ないです。これは「挿入ソート」が「バブルソート」よりも高速な理由と似ています。</li>
+<li><strong>最悪ケースが起こる確率が低い</strong>：クイックソートの最悪時間計算量は <span class="arithmatex">\(O(n^2)\)</span> で、「マージソート」ほど安定ではありませんが、大半のケースでは <span class="arithmatex">\(O(n \log n)\)</span> の時間計算量で動作します。</li>
+<li><strong>キャッシュ利用効率が高い</strong>：パーティション操作の実行時には、システムが部分配列全体をキャッシュに読み込めるため、要素アクセスの効率が高くなります。一方、「ヒープソート」のようなアルゴリズムは要素へ飛び飛びにアクセスする必要があり、この性質を持ちません。</li>
+<li><strong>計算量の定数係数が小さい</strong>：上記 3 つのアルゴリズムの中で、クイックソートは比較、代入、交換などの操作総数が最も少なくなります。これは「挿入ソート」が「バブルソート」より速い理由と似ています。</li>
 </ul>
-<h2 id="1154">11.5.4 &nbsp; ピボット最適化<a class="headerlink" href="#1154" title="Permanent link">&para;</a></h2>
-<p><strong>クイックソートの時間効率は特定の入力で劣化する可能性があります</strong>。例えば、入力配列が完全に逆順の場合、最も左の要素をピボットとして選択するため、ピボット分割後、ピボットは配列の右端に交換され、左サブ配列の長さが<span class="arithmatex">\(n - 1\)</span>、右サブ配列の長さが<span class="arithmatex">\(0\)</span>になります。この方法を続けると、各ラウンドのピボット分割でサブ配列の長さが<span class="arithmatex">\(0\)</span>になり、分割統治戦略が失敗し、クイックソートは「バブルソート」に似た形に劣化します。</p>
-<p>この状況を避けるため、<strong>ピボット分割でピボット選択戦略を最適化できます</strong>。例えば、要素をランダムに選択してピボットとすることができます。ただし、運が悪く、一貫して最適でないピボットを選択した場合、効率はまだ満足できません。</p>
-<p>プログラミング言語は通常「疑似乱数」を生成することに注意することが重要です。疑似乱数シーケンスに対して特定のテストケースを構築すると、クイックソートの効率はまだ劣化する可能性があります。</p>
-<p>さらなる改善のため、3つの候補要素（通常は配列の最初、最後、中点の要素）を選択し、**これら3つの候補要素の中央値をピボットとして使用**できます。この方法で、ピボットが「小さすぎず大きすぎない」確率が大幅に増加します。もちろん、さらに多くの候補要素を選択してアルゴリズムの堅牢性をさらに向上させることもできます。この方法により、時間計算量が<span class="arithmatex">\(O(n^2)\)</span>に劣化する確率が大幅に削減されます。</p>
-<p>サンプルコードは以下の通りです：</p>
+<h2 id="1154">11.5.4 &nbsp; 基準数の最適化<a class="headerlink" href="#1154" title="Permanent link">&para;</a></h2>
+<p><strong>クイックソートは、入力によっては時間効率が低下する可能性があります</strong>。極端な例として、入力配列が完全な逆順であるとします。最左端の要素を基準数として選ぶため、パーティション完了後には基準数が配列の最右端へ交換され、左部分配列の長さが <span class="arithmatex">\(n - 1\)</span>、右部分配列の長さが <span class="arithmatex">\(0\)</span> になります。この再帰を続けると、各回のパーティション後に必ず一方の部分配列の長さが <span class="arithmatex">\(0\)</span> となり、分割統治戦略が機能せず、クイックソートは「バブルソート」に近い形へ退化します。</p>
+<p>この状況をできるだけ避けるため、<strong>パーティションにおける基準数の選び方を最適化できます</strong>。たとえば、ランダムに 1 つの要素を選んで基準数にできます。しかし、運が悪く毎回望ましくない基準数を選んでしまうと、効率は依然として十分ではありません。</p>
+<p>注意すべき点として、プログラミング言語が通常生成するのは「疑似乱数」です。疑似乱数列に合わせて特定のテストケースを構築すると、クイックソートの効率はやはり劣化する可能性があります。</p>
+<p>さらに改善するために、配列から 3 つの候補要素（通常は先頭、末尾、中間の要素）を選び、**その 3 つの候補要素の中央値を基準数とする**ことができます。こうすると、基準数が「小さすぎず大きすぎもしない」確率が大幅に上がります。もちろん、候補要素をさらに増やして、アルゴリズムの頑健性をいっそう高めることも可能です。この方法を採用すると、時間計算量が <span class="arithmatex">\(O(n^2)\)</span> まで劣化する確率は大きく下がります。</p>
+<p>コード例を以下に示します。</p>
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 <div class="highlight"><span class="filename">quick_sort.py</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">median_three</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">mid</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;3つの候補要素の中央値を選択&quot;&quot;&quot;</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;3つの候補要素の中央値を選ぶ&quot;&quot;&quot;</span>
 <a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>    <span class="n">l</span><span class="p">,</span> <span class="n">m</span><span class="p">,</span> <span class="n">r</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">mid</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">right</span><span class="p">]</span>
 <a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>    <span class="k">if</span> <span class="p">(</span><span class="n">l</span> <span class="o">&lt;=</span> <span class="n">m</span> <span class="o">&lt;=</span> <span class="n">r</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="n">r</span> <span class="o">&lt;=</span> <span class="n">m</span> <span class="o">&lt;=</span> <span class="n">l</span><span class="p">):</span>
 <a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a>        <span class="k">return</span> <span class="n">mid</span>  <span class="c1"># m は l と r の間</span>
@@ -4707,58 +5003,58 @@
 <a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>    <span class="k">return</span> <span class="n">right</span>
 <a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a>
 <a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="k">def</span><span class="w"> </span><span class="nf">partition</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;分割（三点中央値）&quot;&quot;&quot;</span>
-<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a>    <span class="c1"># nums[left] をピボットとして使用</span>
+<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;番兵による分割処理（3 点中央値）&quot;&quot;&quot;</span>
+<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a>    <span class="c1"># nums[left] を基準値とする</span>
 <a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a>    <span class="n">med</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">median_three</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">left</span><span class="p">,</span> <span class="p">(</span><span class="n">left</span> <span class="o">+</span> <span class="n">right</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span><span class="p">,</span> <span class="n">right</span><span class="p">)</span>
-<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a>    <span class="c1"># 中央値を配列の最左端に交換</span>
+<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a>    <span class="c1"># 中央値を配列の最左端に交換する</span>
 <a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a>    <span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">med</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">med</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">]</span>
-<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a>    <span class="c1"># nums[left] をピボットとして使用</span>
+<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a>    <span class="c1"># nums[left] を基準値とする</span>
 <a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a>    <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="n">left</span><span class="p">,</span> <span class="n">right</span>
 <a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a>    <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="n">j</span><span class="p">:</span>
 <a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a>        <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="n">j</span> <span class="ow">and</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">&gt;=</span> <span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">]:</span>
-<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a>            <span class="n">j</span> <span class="o">-=</span> <span class="mi">1</span>  <span class="c1"># 右から左へピボットより小さい最初の要素を探す</span>
+<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a>            <span class="n">j</span> <span class="o">-=</span> <span class="mi">1</span>  <span class="c1"># 右から左へ基準値未満の最初の要素を探す</span>
 <a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a>        <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="n">j</span> <span class="ow">and</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&lt;=</span> <span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">]:</span>
-<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a>            <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>  <span class="c1"># 左から右へピボットより大きい最初の要素を探す</span>
-<a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a>        <span class="c1"># 要素を交換</span>
+<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a>            <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>  <span class="c1"># 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a>        <span class="c1"># 要素の交換</span>
 <a id="__codelineno-26-24" name="__codelineno-26-24" href="#__codelineno-26-24"></a>        <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
-<a id="__codelineno-26-25" name="__codelineno-26-25" href="#__codelineno-26-25"></a>    <span class="c1"># ピボットを2つのサブ配列の境界に交換</span>
+<a id="__codelineno-26-25" name="__codelineno-26-25" href="#__codelineno-26-25"></a>    <span class="c1"># 基準値を 2 つの部分配列の境界へ交換する</span>
 <a id="__codelineno-26-26" name="__codelineno-26-26" href="#__codelineno-26-26"></a>    <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
-<a id="__codelineno-26-27" name="__codelineno-26-27" href="#__codelineno-26-27"></a>    <span class="k">return</span> <span class="n">i</span>  <span class="c1"># ピボットのインデックスを返す</span>
+<a id="__codelineno-26-27" name="__codelineno-26-27" href="#__codelineno-26-27"></a>    <span class="k">return</span> <span class="n">i</span>  <span class="c1"># 基準値のインデックスを返す</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* 三つの候補要素の中央値を選択 */</span>
+<div class="highlight"><span class="filename">quick_sort.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* 3つの候補要素の中央値を選ぶ */</span>
 <a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">medianThree</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">],</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">mid</span><span class="p">],</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">right</span><span class="p">];</span>
 <a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">((</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">l</span><span class="p">))</span>
-<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mid</span><span class="p">;</span><span class="w"> </span><span class="c1">// mはlとrの間</span>
+<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mid</span><span class="p">;</span><span class="w"> </span><span class="c1">// m は l と r の間</span>
 <a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">((</span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">))</span>
-<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// lはmとrの間</span>
+<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// l は m と r の間</span>
 <a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">right</span><span class="p">;</span>
 <a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="p">}</span>
 <a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a>
-<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="cm">/* 分割（三つの中央値） */</span>
+<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="cm">/* 番兵による分割処理（3 点中央値） */</span>
 <a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">partition</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w">    </span><span class="c1">// 三つの候補要素の中央値を選択</span>
+<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w">    </span><span class="c1">// 3つの候補要素の中央値を選ぶ</span>
 <a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">med</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">medianThree</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
-<a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="w">    </span><span class="c1">// 中央値を配列の最左位置に交換</span>
-<a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">med</span><span class="p">);</span>
-<a id="__codelineno-27-17" name="__codelineno-27-17" href="#__codelineno-27-17"></a><span class="w">    </span><span class="c1">// nums[left]をピボットとして使用</span>
+<a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="w">    </span><span class="c1">// 中央値を配列の最左端に交換する</span>
+<a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">med</span><span class="p">]);</span>
+<a id="__codelineno-27-17" name="__codelineno-27-17" href="#__codelineno-27-17"></a><span class="w">    </span><span class="c1">// nums[left] を基準値とする</span>
 <a id="__codelineno-27-18" name="__codelineno-27-18" href="#__codelineno-27-18"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">;</span>
 <a id="__codelineno-27-19" name="__codelineno-27-19" href="#__codelineno-27-19"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-20" name="__codelineno-27-20" href="#__codelineno-27-20"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">])</span>
-<a id="__codelineno-27-21" name="__codelineno-27-21" href="#__codelineno-27-21"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右から左へピボットより小さい最初の要素を検索</span>
+<a id="__codelineno-27-21" name="__codelineno-27-21" href="#__codelineno-27-21"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span><span class="w">                </span><span class="c1">// 右から左へ基準値未満の最初の要素を探す</span>
 <a id="__codelineno-27-22" name="__codelineno-27-22" href="#__codelineno-27-22"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">])</span>
-<a id="__codelineno-27-23" name="__codelineno-27-23" href="#__codelineno-27-23"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w">          </span><span class="c1">// 左から右へピボットより大きい最初の要素を検索</span>
-<a id="__codelineno-27-24" name="__codelineno-27-24" href="#__codelineno-27-24"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span><span class="w"> </span><span class="c1">// これら二つの要素を交換</span>
+<a id="__codelineno-27-23" name="__codelineno-27-23" href="#__codelineno-27-23"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w">                </span><span class="c1">// 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-27-24" name="__codelineno-27-24" href="#__codelineno-27-24"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]);</span><span class="w"> </span><span class="c1">// この 2 つの要素を交換</span>
 <a id="__codelineno-27-25" name="__codelineno-27-25" href="#__codelineno-27-25"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-26" name="__codelineno-27-26" href="#__codelineno-27-26"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">);</span><span class="w"> </span><span class="c1">// ピボットを二つのサブ配列の境界に交換</span>
-<a id="__codelineno-27-27" name="__codelineno-27-27" href="#__codelineno-27-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w">            </span><span class="c1">// ピボットのインデックスを返す</span>
+<a id="__codelineno-27-26" name="__codelineno-27-26" href="#__codelineno-27-26"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">]);</span><span class="w">  </span><span class="c1">// 基準値を 2 つの部分配列の境界へ交換する</span>
+<a id="__codelineno-27-27" name="__codelineno-27-27" href="#__codelineno-27-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w">                   </span><span class="c1">// 基準値のインデックスを返す</span>
 <a id="__codelineno-27-28" name="__codelineno-27-28" href="#__codelineno-27-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 3つの候補要素の中央値を選択 */</span>
+<div class="highlight"><span class="filename">quick_sort.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 3つの候補要素の中央値を選ぶ */</span>
 <a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">medianThree</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">mid</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">right</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">((</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">l</span><span class="p">))</span>
@@ -4768,190 +5064,668 @@
 <a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">right</span><span class="p">;</span>
 <a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="p">}</span>
 <a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a>
-<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="cm">/* 分割（3つの中央値） */</span>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="cm">/* 番兵による分割処理（3 点中央値） */</span>
 <a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">partition</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w">    </span><span class="c1">// 3つの候補要素の中央値を選択</span>
+<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w">    </span><span class="c1">// 3つの候補要素の中央値を選ぶ</span>
 <a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">med</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">medianThree</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
-<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="w">    </span><span class="c1">// 中央値を配列の最左端の位置に交換</span>
+<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="w">    </span><span class="c1">// 中央値を配列の最左端に交換する</span>
 <a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">med</span><span class="p">);</span>
-<a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a><span class="w">    </span><span class="c1">// nums[left] を基準値として使用</span>
+<a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a><span class="w">    </span><span class="c1">// nums[left] を基準値とする</span>
 <a id="__codelineno-28-18" name="__codelineno-28-18" href="#__codelineno-28-18"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">;</span>
 <a id="__codelineno-28-19" name="__codelineno-28-19" href="#__codelineno-28-19"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-20" name="__codelineno-28-20" href="#__codelineno-28-20"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span><span class="p">)</span>
-<a id="__codelineno-28-21" name="__codelineno-28-21" href="#__codelineno-28-21"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span><span class="w">          </span><span class="c1">// 右から左へ、基準値より小さい最初の要素を検索</span>
+<a id="__codelineno-28-21" name="__codelineno-28-21" href="#__codelineno-28-21"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span><span class="w">          </span><span class="c1">// 右から左へ基準値未満の最初の要素を探す</span>
 <a id="__codelineno-28-22" name="__codelineno-28-22" href="#__codelineno-28-22"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span><span class="p">)</span>
-<a id="__codelineno-28-23" name="__codelineno-28-23" href="#__codelineno-28-23"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w">          </span><span class="c1">// 左から右へ、基準値より大きい最初の要素を検索</span>
-<a id="__codelineno-28-24" name="__codelineno-28-24" href="#__codelineno-28-24"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span><span class="w"> </span><span class="c1">// これら2つの要素を交換</span>
+<a id="__codelineno-28-23" name="__codelineno-28-23" href="#__codelineno-28-23"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w">          </span><span class="c1">// 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-28-24" name="__codelineno-28-24" href="#__codelineno-28-24"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span><span class="w"> </span><span class="c1">// この 2 つの要素を交換</span>
 <a id="__codelineno-28-25" name="__codelineno-28-25" href="#__codelineno-28-25"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-28-26" name="__codelineno-28-26" href="#__codelineno-28-26"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">);</span><span class="w">  </span><span class="c1">// 基準値を2つの部分配列の境界に交換</span>
+<a id="__codelineno-28-26" name="__codelineno-28-26" href="#__codelineno-28-26"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">);</span><span class="w">  </span><span class="c1">// 基準値を 2 つの部分配列の境界へ交換する</span>
 <a id="__codelineno-28-27" name="__codelineno-28-27" href="#__codelineno-28-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w">             </span><span class="c1">// 基準値のインデックスを返す</span>
 <a id="__codelineno-28-28" name="__codelineno-28-28" href="#__codelineno-28-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">QuickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MedianThree</span><span class="p">}</span>
-<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a>
-<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">QuickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Partition</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 3つの候補要素の中央値を選ぶ */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">MedianThree</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">],</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">mid</span><span class="p">],</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">right</span><span class="p">];</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">((</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">l</span><span class="p">))</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mid</span><span class="p">;</span><span class="w"> </span><span class="c1">// m は l と r の間</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">((</span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">))</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// l は m と r の間</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="p">}</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="cm">/* 番兵による分割処理（3 点中央値） */</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Partition</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w">    </span><span class="c1">// 3つの候補要素の中央値を選ぶ</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">med</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MedianThree</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="w">    </span><span class="c1">// 中央値を配列の最左端に交換する</span>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w">    </span><span class="n">Swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">med</span><span class="p">);</span>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="w">    </span><span class="c1">// nums[left] を基準値とする</span>
+<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-20" name="__codelineno-29-20" href="#__codelineno-29-20"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">])</span>
+<a id="__codelineno-29-21" name="__codelineno-29-21" href="#__codelineno-29-21"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span><span class="w">          </span><span class="c1">// 右から左へ基準値未満の最初の要素を探す</span>
+<a id="__codelineno-29-22" name="__codelineno-29-22" href="#__codelineno-29-22"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">])</span>
+<a id="__codelineno-29-23" name="__codelineno-29-23" href="#__codelineno-29-23"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w">          </span><span class="c1">// 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-29-24" name="__codelineno-29-24" href="#__codelineno-29-24"></a><span class="w">        </span><span class="n">Swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span><span class="w"> </span><span class="c1">// この 2 つの要素を交換</span>
+<a id="__codelineno-29-25" name="__codelineno-29-25" href="#__codelineno-29-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-26" name="__codelineno-29-26" href="#__codelineno-29-26"></a><span class="w">    </span><span class="n">Swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">);</span><span class="w">  </span><span class="c1">// 基準値を 2 つの部分配列の境界へ交換する</span>
+<a id="__codelineno-29-27" name="__codelineno-29-27" href="#__codelineno-29-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w">             </span><span class="c1">// 基準値のインデックスを返す</span>
+<a id="__codelineno-29-28" name="__codelineno-29-28" href="#__codelineno-29-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">quickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">medianThree</span><span class="p">}</span>
-<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a>
-<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">quickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">partition</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 3つの候補要素の中央値を選ぶ */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">q</span><span class="w"> </span><span class="o">*</span><span class="nx">quickSortMedian</span><span class="p">)</span><span class="w"> </span><span class="nx">medianThree</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="p">,</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">left</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">mid</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">right</span><span class="p">]</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">l</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="c1">// m は l と r の間</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="c1">// l は m と r の間</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">right</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="p">}</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="cm">/* 番兵による分割処理（3 点中央値） */</span>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">q</span><span class="w"> </span><span class="o">*</span><span class="nx">quickSortMedian</span><span class="p">)</span><span class="w"> </span><span class="nx">partition</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w">    </span><span class="c1">// nums[left] を基準値とする</span>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w">    </span><span class="nx">med</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">medianThree</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="nx">left</span><span class="o">+</span><span class="nx">right</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span>
+<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="w">    </span><span class="c1">// 中央値を配列の最左端に交換する</span>
+<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a><span class="w">    </span><span class="nx">nums</span><span class="p">[</span><span class="nx">left</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">med</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">med</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">left</span><span class="p">]</span>
+<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="w">    </span><span class="c1">// nums[left] を基準値とする</span>
+<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></a><span class="w">    </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span>
+<a id="__codelineno-30-21" name="__codelineno-30-21" href="#__codelineno-30-21"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-22" name="__codelineno-30-22" href="#__codelineno-30-22"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">left</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-23" name="__codelineno-30-23" href="#__codelineno-30-23"></a><span class="w">            </span><span class="nx">j</span><span class="o">--</span><span class="w"> </span><span class="c1">// 右から左へ基準値未満の最初の要素を探す</span>
+<a id="__codelineno-30-24" name="__codelineno-30-24" href="#__codelineno-30-24"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-30-25" name="__codelineno-30-25" href="#__codelineno-30-25"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">left</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-26" name="__codelineno-30-26" href="#__codelineno-30-26"></a><span class="w">            </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="c1">// 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-30-27" name="__codelineno-30-27" href="#__codelineno-30-27"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-30-28" name="__codelineno-30-28" href="#__codelineno-30-28"></a><span class="w">        </span><span class="c1">// 要素の交換</span>
+<a id="__codelineno-30-29" name="__codelineno-30-29" href="#__codelineno-30-29"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
+<a id="__codelineno-30-30" name="__codelineno-30-30" href="#__codelineno-30-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-31" name="__codelineno-30-31" href="#__codelineno-30-31"></a><span class="w">    </span><span class="c1">// 基準値を 2 つの部分配列の境界へ交換する</span>
+<a id="__codelineno-30-32" name="__codelineno-30-32" href="#__codelineno-30-32"></a><span class="w">    </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">left</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">left</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
+<a id="__codelineno-30-33" name="__codelineno-30-33" href="#__codelineno-30-33"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="c1">// 基準値のインデックスを返す</span>
+<a id="__codelineno-30-34" name="__codelineno-30-34" href="#__codelineno-30-34"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">medianThree</span><span class="p">}</span>
-<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a>
-<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">partitionMedian</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* 3つの候補要素の中央値を選ぶ */</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">medianThree</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="kr">left</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="kr">right</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">l</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="kr">left</span><span class="p">]</span>
+<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">mid</span><span class="p">]</span>
+<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">r</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="kr">right</span><span class="p">]</span>
+<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">l</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="c1">// m は l と r の間</span>
+<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kr">left</span><span class="w"> </span><span class="c1">// l は m と r の間</span>
+<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="kr">right</span>
+<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a><span class="p">}</span>
+<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a>
+<a id="__codelineno-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></a><span class="cm">/* 番兵による分割処理（3 点中央値） */</span>
+<a id="__codelineno-31-16" name="__codelineno-31-16" href="#__codelineno-31-16"></a><span class="kd">func</span><span class="w"> </span><span class="nf">partitionMedian</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="kr">left</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="kr">right</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-17" name="__codelineno-31-17" href="#__codelineno-31-17"></a><span class="w">    </span><span class="c1">// 3つの候補要素の中央値を選ぶ</span>
+<a id="__codelineno-31-18" name="__codelineno-31-18" href="#__codelineno-31-18"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">med</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">medianThree</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kr">left</span><span class="p">:</span><span class="w"> </span><span class="kr">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">:</span><span class="w"> </span><span class="kr">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="kr">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="kr">left</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="kr">right</span><span class="p">:</span><span class="w"> </span><span class="kr">right</span><span class="p">)</span>
+<a id="__codelineno-31-19" name="__codelineno-31-19" href="#__codelineno-31-19"></a><span class="w">    </span><span class="c1">// 中央値を配列の最左端に交換する</span>
+<a id="__codelineno-31-20" name="__codelineno-31-20" href="#__codelineno-31-20"></a><span class="w">    </span><span class="n">nums</span><span class="p">.</span><span class="n">swapAt</span><span class="p">(</span><span class="kr">left</span><span class="p">,</span><span class="w"> </span><span class="n">med</span><span class="p">)</span>
+<a id="__codelineno-31-21" name="__codelineno-31-21" href="#__codelineno-31-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="bp">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kr">left</span><span class="p">:</span><span class="w"> </span><span class="kr">left</span><span class="p">,</span><span class="w"> </span><span class="kr">right</span><span class="p">:</span><span class="w"> </span><span class="kr">right</span><span class="p">)</span>
+<a id="__codelineno-31-22" name="__codelineno-31-22" href="#__codelineno-31-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">QuickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">medianThree</span><span class="p">}</span>
-<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a>
-<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">QuickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">partition</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* 3つの候補要素の中央値を選ぶ */</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="nx">medianThree</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">left</span><span class="p">],</span>
+<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="w">        </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">mid</span><span class="p">],</span>
+<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="w">        </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">right</span><span class="p">];</span>
+<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="w">    </span><span class="c1">// m は l と r の間</span>
+<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">((</span><span class="nx">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">l</span><span class="p">))</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">mid</span><span class="p">;</span>
+<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w">    </span><span class="c1">// l は m と r の間</span>
+<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">((</span><span class="nx">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">))</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">left</span><span class="p">;</span>
+<a id="__codelineno-32-10" name="__codelineno-32-10" href="#__codelineno-32-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">right</span><span class="p">;</span>
+<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a><span class="p">}</span>
+<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a>
+<a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a><span class="cm">/* 番兵による分割処理（3 点中央値） */</span>
+<a id="__codelineno-32-14" name="__codelineno-32-14" href="#__codelineno-32-14"></a><span class="nx">partition</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-15" name="__codelineno-32-15" href="#__codelineno-32-15"></a><span class="w">    </span><span class="c1">// 3つの候補要素の中央値を選ぶ</span>
+<a id="__codelineno-32-16" name="__codelineno-32-16" href="#__codelineno-32-16"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">med</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">medianThree</span><span class="p">(</span>
+<a id="__codelineno-32-17" name="__codelineno-32-17" href="#__codelineno-32-17"></a><span class="w">        </span><span class="nx">nums</span><span class="p">,</span>
+<a id="__codelineno-32-18" name="__codelineno-32-18" href="#__codelineno-32-18"></a><span class="w">        </span><span class="nx">left</span><span class="p">,</span>
+<a id="__codelineno-32-19" name="__codelineno-32-19" href="#__codelineno-32-19"></a><span class="w">        </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">((</span><span class="nx">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">),</span>
+<a id="__codelineno-32-20" name="__codelineno-32-20" href="#__codelineno-32-20"></a><span class="w">        </span><span class="nx">right</span>
+<a id="__codelineno-32-21" name="__codelineno-32-21" href="#__codelineno-32-21"></a><span class="w">    </span><span class="p">);</span>
+<a id="__codelineno-32-22" name="__codelineno-32-22" href="#__codelineno-32-22"></a><span class="w">    </span><span class="c1">// 中央値を配列の最左端に交換する</span>
+<a id="__codelineno-32-23" name="__codelineno-32-23" href="#__codelineno-32-23"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">med</span><span class="p">);</span>
+<a id="__codelineno-32-24" name="__codelineno-32-24" href="#__codelineno-32-24"></a><span class="w">    </span><span class="c1">// nums[left] を基準値とする</span>
+<a id="__codelineno-32-25" name="__codelineno-32-25" href="#__codelineno-32-25"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span>
+<a id="__codelineno-32-26" name="__codelineno-32-26" href="#__codelineno-32-26"></a><span class="w">        </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">right</span><span class="p">;</span>
+<a id="__codelineno-32-27" name="__codelineno-32-27" href="#__codelineno-32-27"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-28" name="__codelineno-32-28" href="#__codelineno-32-28"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">left</span><span class="p">])</span><span class="w"> </span><span class="nx">j</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右から左へ基準値未満の最初の要素を探す</span>
+<a id="__codelineno-32-29" name="__codelineno-32-29" href="#__codelineno-32-29"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">left</span><span class="p">])</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-32-30" name="__codelineno-32-30" href="#__codelineno-32-30"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">);</span><span class="w"> </span><span class="c1">// この 2 つの要素を交換</span>
+<a id="__codelineno-32-31" name="__codelineno-32-31" href="#__codelineno-32-31"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-32" name="__codelineno-32-32" href="#__codelineno-32-32"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">);</span><span class="w"> </span><span class="c1">// 基準値を 2 つの部分配列の境界へ交換する</span>
+<a id="__codelineno-32-33" name="__codelineno-32-33" href="#__codelineno-32-33"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span><span class="w"> </span><span class="c1">// 基準値のインデックスを返す</span>
+<a id="__codelineno-32-34" name="__codelineno-32-34" href="#__codelineno-32-34"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">QuickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">medianThree</span><span class="p">}</span>
-<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a>
-<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">QuickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">partition</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* 3つの候補要素の中央値を選ぶ */</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="nx">medianThree</span><span class="p">(</span>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w">    </span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span>
+<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w">    </span><span class="nx">left</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span>
+<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w">    </span><span class="nx">mid</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span>
+<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="w">    </span><span class="nx">right</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span>
+<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">left</span><span class="p">],</span>
+<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="w">        </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">mid</span><span class="p">],</span>
+<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a><span class="w">        </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">right</span><span class="p">];</span>
+<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="w">    </span><span class="c1">// m は l と r の間</span>
+<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">((</span><span class="nx">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">l</span><span class="p">))</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">mid</span><span class="p">;</span>
+<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a><span class="w">    </span><span class="c1">// l は m と r の間</span>
+<a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">((</span><span class="nx">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">))</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">left</span><span class="p">;</span>
+<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">right</span><span class="p">;</span>
+<a id="__codelineno-33-16" name="__codelineno-33-16" href="#__codelineno-33-16"></a><span class="p">}</span>
+<a id="__codelineno-33-17" name="__codelineno-33-17" href="#__codelineno-33-17"></a>
+<a id="__codelineno-33-18" name="__codelineno-33-18" href="#__codelineno-33-18"></a><span class="cm">/* 番兵による分割処理（3 点中央値） */</span>
+<a id="__codelineno-33-19" name="__codelineno-33-19" href="#__codelineno-33-19"></a><span class="nx">partition</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">left</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-20" name="__codelineno-33-20" href="#__codelineno-33-20"></a><span class="w">    </span><span class="c1">// 3つの候補要素の中央値を選ぶ</span>
+<a id="__codelineno-33-21" name="__codelineno-33-21" href="#__codelineno-33-21"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">med</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">medianThree</span><span class="p">(</span>
+<a id="__codelineno-33-22" name="__codelineno-33-22" href="#__codelineno-33-22"></a><span class="w">        </span><span class="nx">nums</span><span class="p">,</span>
+<a id="__codelineno-33-23" name="__codelineno-33-23" href="#__codelineno-33-23"></a><span class="w">        </span><span class="nx">left</span><span class="p">,</span>
+<a id="__codelineno-33-24" name="__codelineno-33-24" href="#__codelineno-33-24"></a><span class="w">        </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">((</span><span class="nx">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">),</span>
+<a id="__codelineno-33-25" name="__codelineno-33-25" href="#__codelineno-33-25"></a><span class="w">        </span><span class="nx">right</span>
+<a id="__codelineno-33-26" name="__codelineno-33-26" href="#__codelineno-33-26"></a><span class="w">    </span><span class="p">);</span>
+<a id="__codelineno-33-27" name="__codelineno-33-27" href="#__codelineno-33-27"></a><span class="w">    </span><span class="c1">// 中央値を配列の最左端に交換する</span>
+<a id="__codelineno-33-28" name="__codelineno-33-28" href="#__codelineno-33-28"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">med</span><span class="p">);</span>
+<a id="__codelineno-33-29" name="__codelineno-33-29" href="#__codelineno-33-29"></a><span class="w">    </span><span class="c1">// nums[left] を基準値とする</span>
+<a id="__codelineno-33-30" name="__codelineno-33-30" href="#__codelineno-33-30"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span>
+<a id="__codelineno-33-31" name="__codelineno-33-31" href="#__codelineno-33-31"></a><span class="w">        </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">right</span><span class="p">;</span>
+<a id="__codelineno-33-32" name="__codelineno-33-32" href="#__codelineno-33-32"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-33" name="__codelineno-33-33" href="#__codelineno-33-33"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">left</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-34" name="__codelineno-33-34" href="#__codelineno-33-34"></a><span class="w">            </span><span class="nx">j</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右から左へ基準値未満の最初の要素を探す</span>
+<a id="__codelineno-33-35" name="__codelineno-33-35" href="#__codelineno-33-35"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-33-36" name="__codelineno-33-36" href="#__codelineno-33-36"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">left</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-37" name="__codelineno-33-37" href="#__codelineno-33-37"></a><span class="w">            </span><span class="nx">i</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-33-38" name="__codelineno-33-38" href="#__codelineno-33-38"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-33-39" name="__codelineno-33-39" href="#__codelineno-33-39"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">);</span><span class="w"> </span><span class="c1">// この 2 つの要素を交換</span>
+<a id="__codelineno-33-40" name="__codelineno-33-40" href="#__codelineno-33-40"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-41" name="__codelineno-33-41" href="#__codelineno-33-41"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">);</span><span class="w"> </span><span class="c1">// 基準値を 2 つの部分配列の境界へ交換する</span>
+<a id="__codelineno-33-42" name="__codelineno-33-42" href="#__codelineno-33-42"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span><span class="w"> </span><span class="c1">// 基準値のインデックスを返す</span>
+<a id="__codelineno-33-43" name="__codelineno-33-43" href="#__codelineno-33-43"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">_medianThree</span><span class="p">}</span>
-<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a>
-<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">_partition</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* 3つの候補要素の中央値を選ぶ */</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">_medianThree</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">],</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">mid</span><span class="p">],</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">right</span><span class="p">];</span>
+<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">((</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">l</span><span class="p">))</span>
+<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">mid</span><span class="p">;</span><span class="w"> </span><span class="c1">// m は l と r の間</span>
+<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">((</span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">))</span>
+<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// l は m と r の間</span>
+<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="p">}</span>
+<a id="__codelineno-34-10" name="__codelineno-34-10" href="#__codelineno-34-10"></a>
+<a id="__codelineno-34-11" name="__codelineno-34-11" href="#__codelineno-34-11"></a><span class="cm">/* 番兵による分割処理（3 点中央値） */</span>
+<a id="__codelineno-34-12" name="__codelineno-34-12" href="#__codelineno-34-12"></a><span class="kt">int</span><span class="w"> </span><span class="n">_partition</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-13" name="__codelineno-34-13" href="#__codelineno-34-13"></a><span class="w">  </span><span class="c1">// 3つの候補要素の中央値を選ぶ</span>
+<a id="__codelineno-34-14" name="__codelineno-34-14" href="#__codelineno-34-14"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">med</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_medianThree</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-34-15" name="__codelineno-34-15" href="#__codelineno-34-15"></a><span class="w">  </span><span class="c1">// 中央値を配列の最左端に交換する</span>
+<a id="__codelineno-34-16" name="__codelineno-34-16" href="#__codelineno-34-16"></a><span class="w">  </span><span class="n">_swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">med</span><span class="p">);</span>
+<a id="__codelineno-34-17" name="__codelineno-34-17" href="#__codelineno-34-17"></a><span class="w">  </span><span class="c1">// nums[left] を基準値とする</span>
+<a id="__codelineno-34-18" name="__codelineno-34-18" href="#__codelineno-34-18"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-34-19" name="__codelineno-34-19" href="#__codelineno-34-19"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-20" name="__codelineno-34-20" href="#__codelineno-34-20"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">])</span><span class="w"> </span><span class="n">j</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右から左へ基準値未満の最初の要素を探す</span>
+<a id="__codelineno-34-21" name="__codelineno-34-21" href="#__codelineno-34-21"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">])</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-34-22" name="__codelineno-34-22" href="#__codelineno-34-22"></a><span class="w">    </span><span class="n">_swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span><span class="w"> </span><span class="c1">// この 2 つの要素を交換</span>
+<a id="__codelineno-34-23" name="__codelineno-34-23" href="#__codelineno-34-23"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-24" name="__codelineno-34-24" href="#__codelineno-34-24"></a><span class="w">  </span><span class="n">_swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">);</span><span class="w"> </span><span class="c1">// 基準値を 2 つの部分配列の境界へ交換する</span>
+<a id="__codelineno-34-25" name="__codelineno-34-25" href="#__codelineno-34-25"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="c1">// 基準値のインデックスを返す</span>
+<a id="__codelineno-34-26" name="__codelineno-34-26" href="#__codelineno-34-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">median_three</span><span class="p">}</span>
-<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a>
-<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">partition</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* 3つの候補要素の中央値を選ぶ */</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">median_three</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">left</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">mid</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">right</span><span class="p">]);</span>
+<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">l</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mid</span><span class="p">;</span><span class="w"> </span><span class="c1">// m は l と r の間</span>
+<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// l は m と r の間</span>
+<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="w">    </span><span class="n">right</span>
+<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a><span class="p">}</span>
+<a id="__codelineno-35-12" name="__codelineno-35-12" href="#__codelineno-35-12"></a>
+<a id="__codelineno-35-13" name="__codelineno-35-13" href="#__codelineno-35-13"></a><span class="cm">/* 番兵による分割処理（3 点中央値） */</span>
+<a id="__codelineno-35-14" name="__codelineno-35-14" href="#__codelineno-35-14"></a><span class="k">fn</span><span class="w"> </span><span class="nf">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">left</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-15" name="__codelineno-35-15" href="#__codelineno-35-15"></a><span class="w">    </span><span class="c1">// 3つの候補要素の中央値を選ぶ</span>
+<a id="__codelineno-35-16" name="__codelineno-35-16" href="#__codelineno-35-16"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">med</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span><span class="p">::</span><span class="n">median_three</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-35-17" name="__codelineno-35-17" href="#__codelineno-35-17"></a><span class="w">    </span><span class="c1">// 中央値を配列の最左端に交換する</span>
+<a id="__codelineno-35-18" name="__codelineno-35-18" href="#__codelineno-35-18"></a><span class="w">    </span><span class="n">nums</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">med</span><span class="p">);</span>
+<a id="__codelineno-35-19" name="__codelineno-35-19" href="#__codelineno-35-19"></a><span class="w">    </span><span class="c1">// nums[left] を基準値とする</span>
+<a id="__codelineno-35-20" name="__codelineno-35-20" href="#__codelineno-35-20"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="p">(</span><span class="k">mut</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-35-21" name="__codelineno-35-21" href="#__codelineno-35-21"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-22" name="__codelineno-35-22" href="#__codelineno-35-22"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-23" name="__codelineno-35-23" href="#__codelineno-35-23"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右から左へ基準値未満の最初の要素を探す</span>
+<a id="__codelineno-35-24" name="__codelineno-35-24" href="#__codelineno-35-24"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-35-25" name="__codelineno-35-25" href="#__codelineno-35-25"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-26" name="__codelineno-35-26" href="#__codelineno-35-26"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-35-27" name="__codelineno-35-27" href="#__codelineno-35-27"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-35-28" name="__codelineno-35-28" href="#__codelineno-35-28"></a><span class="w">        </span><span class="n">nums</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span><span class="w"> </span><span class="c1">// この 2 つの要素を交換</span>
+<a id="__codelineno-35-29" name="__codelineno-35-29" href="#__codelineno-35-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-30" name="__codelineno-35-30" href="#__codelineno-35-30"></a><span class="w">    </span><span class="n">nums</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">);</span><span class="w"> </span><span class="c1">// 基準値を 2 つの部分配列の境界へ交換する</span>
+<a id="__codelineno-35-31" name="__codelineno-35-31" href="#__codelineno-35-31"></a><span class="w">    </span><span class="n">i</span><span class="w"> </span><span class="c1">// 基準値のインデックスを返す</span>
+<a id="__codelineno-35-32" name="__codelineno-35-32" href="#__codelineno-35-32"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">medianThree</span><span class="p">}</span>
-<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a>
-<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">partitionMedian</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* 3つの候補要素の中央値を選ぶ */</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">medianThree</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">],</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">mid</span><span class="p">],</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">right</span><span class="p">];</span>
+<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">((</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">l</span><span class="p">))</span>
+<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mid</span><span class="p">;</span><span class="w"> </span><span class="c1">// m は l と r の間</span>
+<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">((</span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">))</span>
+<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// l は m と r の間</span>
+<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="p">}</span>
+<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a>
+<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a><span class="cm">/* 番兵による分割処理（3 点中央値） */</span>
+<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">partitionMedian</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></a><span class="w">    </span><span class="c1">// 3つの候補要素の中央値を選ぶ</span>
+<a id="__codelineno-36-14" name="__codelineno-36-14" href="#__codelineno-36-14"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">med</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">medianThree</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-36-15" name="__codelineno-36-15" href="#__codelineno-36-15"></a><span class="w">    </span><span class="c1">// 中央値を配列の最左端に交換する</span>
+<a id="__codelineno-36-16" name="__codelineno-36-16" href="#__codelineno-36-16"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">med</span><span class="p">);</span>
+<a id="__codelineno-36-17" name="__codelineno-36-17" href="#__codelineno-36-17"></a><span class="w">    </span><span class="c1">// nums[left] を基準値とする</span>
+<a id="__codelineno-36-18" name="__codelineno-36-18" href="#__codelineno-36-18"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-36-19" name="__codelineno-36-19" href="#__codelineno-36-19"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-20" name="__codelineno-36-20" href="#__codelineno-36-20"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">])</span>
+<a id="__codelineno-36-21" name="__codelineno-36-21" href="#__codelineno-36-21"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右から左へ基準値未満の最初の要素を探す</span>
+<a id="__codelineno-36-22" name="__codelineno-36-22" href="#__codelineno-36-22"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">])</span>
+<a id="__codelineno-36-23" name="__codelineno-36-23" href="#__codelineno-36-23"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w">          </span><span class="c1">// 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-36-24" name="__codelineno-36-24" href="#__codelineno-36-24"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span><span class="w"> </span><span class="c1">// この 2 つの要素を交換</span>
+<a id="__codelineno-36-25" name="__codelineno-36-25" href="#__codelineno-36-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-26" name="__codelineno-36-26" href="#__codelineno-36-26"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">);</span><span class="w"> </span><span class="c1">// 基準値を 2 つの部分配列の境界へ交換する</span>
+<a id="__codelineno-36-27" name="__codelineno-36-27" href="#__codelineno-36-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w">            </span><span class="c1">// 基準値のインデックスを返す</span>
+<a id="__codelineno-36-28" name="__codelineno-36-28" href="#__codelineno-36-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">medianThree</span><span class="p">}</span>
-<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a>
-<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">partitionMedian</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* 3つの候補要素の中央値を選ぶ */</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">medianThree</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span>
+<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">mid</span><span class="o">]</span>
+<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">right</span><span class="o">]</span>
+<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">((</span><span class="n">m</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">l</span><span class="p">..</span><span class="na">r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">r</span><span class="p">..</span><span class="na">l</span><span class="p">))</span>
+<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mid</span><span class="w">  </span><span class="c1">// m は l と r の間</span>
+<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">((</span><span class="n">l</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">m</span><span class="p">..</span><span class="na">r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">r</span><span class="p">..</span><span class="na">m</span><span class="p">))</span>
+<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="c1">// l は m と r の間</span>
+<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">right</span>
+<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a><span class="p">}</span>
+<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a>
+<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a><span class="cm">/* 番兵による分割処理（3 点中央値） */</span>
+<a id="__codelineno-37-14" name="__codelineno-37-14" href="#__codelineno-37-14"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">partitionMedian</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-15" name="__codelineno-37-15" href="#__codelineno-37-15"></a><span class="w">    </span><span class="c1">// 3つの候補要素の中央値を選ぶ</span>
+<a id="__codelineno-37-16" name="__codelineno-37-16" href="#__codelineno-37-16"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">med</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">medianThree</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-37-17" name="__codelineno-37-17" href="#__codelineno-37-17"></a><span class="w">    </span><span class="c1">// 中央値を配列の最左端に交換する</span>
+<a id="__codelineno-37-18" name="__codelineno-37-18" href="#__codelineno-37-18"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">med</span><span class="p">)</span>
+<a id="__codelineno-37-19" name="__codelineno-37-19" href="#__codelineno-37-19"></a><span class="w">    </span><span class="c1">// nums[left] を基準値とする</span>
+<a id="__codelineno-37-20" name="__codelineno-37-20" href="#__codelineno-37-20"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span>
+<a id="__codelineno-37-21" name="__codelineno-37-21" href="#__codelineno-37-21"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span>
+<a id="__codelineno-37-22" name="__codelineno-37-22" href="#__codelineno-37-22"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-23" name="__codelineno-37-23" href="#__codelineno-37-23"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-37-24" name="__codelineno-37-24" href="#__codelineno-37-24"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="w">                      </span><span class="c1">// 右から左へ基準値未満の最初の要素を探す</span>
+<a id="__codelineno-37-25" name="__codelineno-37-25" href="#__codelineno-37-25"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-37-26" name="__codelineno-37-26" href="#__codelineno-37-26"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span><span class="w">                      </span><span class="c1">// 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-37-27" name="__codelineno-37-27" href="#__codelineno-37-27"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w">             </span><span class="c1">// この 2 つの要素を交換</span>
+<a id="__codelineno-37-28" name="__codelineno-37-28" href="#__codelineno-37-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-29" name="__codelineno-37-29" href="#__codelineno-37-29"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">)</span><span class="w">              </span><span class="c1">// 基準値を 2 つの部分配列の境界へ交換する</span>
+<a id="__codelineno-37-30" name="__codelineno-37-30" href="#__codelineno-37-30"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="w">                         </span><span class="c1">// 基準値のインデックスを返す</span>
+<a id="__codelineno-37-31" name="__codelineno-37-31" href="#__codelineno-37-31"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">QuickSortMedian</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">median_three</span><span class="p">}</span>
-<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a>
-<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">QuickSortMedian</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">partition</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="c1">### 3 つの候補要素の中央値を選ぶ ###</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">median_three</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w">  </span><span class="c1"># 3つの候補要素の中央値を選ぶ</span>
+<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w">  </span><span class="n">_l</span><span class="p">,</span><span class="w"> </span><span class="n">_m</span><span class="p">,</span><span class="w"> </span><span class="n">_r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">mid</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">right</span><span class="o">]</span>
+<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="w">  </span><span class="c1"># m は l と r の間</span>
+<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">_m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">_m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">_r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="n">_r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">_m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">_m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">_l</span><span class="p">)</span>
+<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="w">  </span><span class="c1"># l は m と r の間</span>
+<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">_l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">_l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">_r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="n">_r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">_l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">_l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">_m</span><span class="p">)</span>
+<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">right</span>
+<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a><span class="k">end</span>
+<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a>
+<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a><span class="c1">### 3 つの候補要素の中央値を選ぶ ###</span>
+<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a><span class="k">def</span><span class="w"> </span><span class="nf">median_three</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a><span class="w">  </span><span class="c1"># 3つの候補要素の中央値を選ぶ</span>
+<a id="__codelineno-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a><span class="w">  </span><span class="n">_l</span><span class="p">,</span><span class="w"> </span><span class="n">_m</span><span class="p">,</span><span class="w"> </span><span class="n">_r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">mid</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">right</span><span class="o">]</span>
+<a id="__codelineno-38-16" name="__codelineno-38-16" href="#__codelineno-38-16"></a><span class="w">  </span><span class="c1"># m は l と r の間</span>
+<a id="__codelineno-38-17" name="__codelineno-38-17" href="#__codelineno-38-17"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">_m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">_m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">_r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="n">_r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">_m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">_m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">_l</span><span class="p">)</span>
+<a id="__codelineno-38-18" name="__codelineno-38-18" href="#__codelineno-38-18"></a><span class="w">  </span><span class="c1"># l は m と r の間</span>
+<a id="__codelineno-38-19" name="__codelineno-38-19" href="#__codelineno-38-19"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">_l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">_l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">_r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="n">_r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">_l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">_l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">_m</span><span class="p">)</span>
+<a id="__codelineno-38-20" name="__codelineno-38-20" href="#__codelineno-38-20"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">right</span>
+<a id="__codelineno-38-21" name="__codelineno-38-21" href="#__codelineno-38-21"></a><span class="k">end</span>
+<a id="__codelineno-38-22" name="__codelineno-38-22" href="#__codelineno-38-22"></a>
+<a id="__codelineno-38-23" name="__codelineno-38-23" href="#__codelineno-38-23"></a><span class="c1"># ## 番兵分割（三数中央値）###</span>
+<a id="__codelineno-38-24" name="__codelineno-38-24" href="#__codelineno-38-24"></a><span class="k">def</span><span class="w"> </span><span class="nf">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-38-25" name="__codelineno-38-25" href="#__codelineno-38-25"></a><span class="w">  </span><span class="c1"># ## nums[left] を基準値とする</span>
+<a id="__codelineno-38-26" name="__codelineno-38-26" href="#__codelineno-38-26"></a><span class="w">  </span><span class="n">med</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">median_three</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-38-27" name="__codelineno-38-27" href="#__codelineno-38-27"></a><span class="w">  </span><span class="c1"># 中央値を配列の最左端に交換する</span>
+<a id="__codelineno-38-28" name="__codelineno-38-28" href="#__codelineno-38-28"></a><span class="w">  </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">med</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">med</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span>
+<a id="__codelineno-38-29" name="__codelineno-38-29" href="#__codelineno-38-29"></a><span class="w">  </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span>
+<a id="__codelineno-38-30" name="__codelineno-38-30" href="#__codelineno-38-30"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span>
+<a id="__codelineno-38-31" name="__codelineno-38-31" href="#__codelineno-38-31"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span>
+<a id="__codelineno-38-32" name="__codelineno-38-32" href="#__codelineno-38-32"></a><span class="w">      </span><span class="n">j</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># 右から左へ基準値未満の最初の要素を探す</span>
+<a id="__codelineno-38-33" name="__codelineno-38-33" href="#__codelineno-38-33"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-38-34" name="__codelineno-38-34" href="#__codelineno-38-34"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span>
+<a id="__codelineno-38-35" name="__codelineno-38-35" href="#__codelineno-38-35"></a><span class="w">      </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-38-36" name="__codelineno-38-36" href="#__codelineno-38-36"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-38-37" name="__codelineno-38-37" href="#__codelineno-38-37"></a><span class="w">    </span><span class="c1"># 要素の交換</span>
+<a id="__codelineno-38-38" name="__codelineno-38-38" href="#__codelineno-38-38"></a><span class="w">    </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-38-39" name="__codelineno-38-39" href="#__codelineno-38-39"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-40" name="__codelineno-38-40" href="#__codelineno-38-40"></a><span class="w">  </span><span class="c1"># 基準値を 2 つの部分配列の境界へ交換する</span>
+<a id="__codelineno-38-41" name="__codelineno-38-41" href="#__codelineno-38-41"></a><span class="w">  </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-38-42" name="__codelineno-38-42" href="#__codelineno-38-42"></a><span class="w">  </span><span class="n">i</span><span class="w"> </span><span class="c1"># 基準値のインデックスを返す</span>
+<a id="__codelineno-38-43" name="__codelineno-38-43" href="#__codelineno-38-43"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h2 id="1155">11.5.5 &nbsp; 末尾再帰最適化<a class="headerlink" href="#1155" title="Permanent link">&para;</a></h2>
-<p><strong>特定の入力では、クイックソートはより多くの空間を占有する可能性があります</strong>。例えば、完全に順序付けられた入力配列を考えてみましょう。再帰でのサブ配列の長さを<span class="arithmatex">\(m\)</span>とします。各ラウンドのピボット分割で、長さ<span class="arithmatex">\(0\)</span>の左サブ配列と長さ<span class="arithmatex">\(m - 1\)</span>の右サブ配列が生成されます。これは、再帰呼び出しごとに問題サイズが1つの要素のみ減少することを意味し、各レベルの再帰での削減が非常に小さくなります。
-結果として、再帰ツリーの高さは<span class="arithmatex">\(n − 1\)</span>に達する可能性があり、これには<span class="arithmatex">\(O(n)\)</span>のスタックフレーム空間が必要です。</p>
-<p>スタックフレーム空間の蓄積を防ぐため、各ラウンドのピボットソート後に2つのサブ配列の長さを比較し、**より短いサブ配列のみを再帰的にソート**できます。より短いサブ配列の長さは<span class="arithmatex">\(n / 2\)</span>を超えないため、この方法は再帰深度が<span class="arithmatex">\(\log n\)</span>を超えないことを保証し、最悪空間計算量を<span class="arithmatex">\(O(\log n)\)</span>に最適化します。コードは以下の通りです：</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20median_three%28nums%3A%20list%5Bint%5D%2C%20left%3A%20int%2C%20mid%3A%20int%2C%20right%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%223%E3%81%A4%E3%81%AE%E5%80%99%E8%A3%9C%E8%A6%81%E7%B4%A0%E3%81%AE%E4%B8%AD%E5%A4%AE%E5%80%A4%E3%82%92%E9%81%B8%E3%81%B6%22%22%22%0A%20%20%20%20l%2C%20m%2C%20r%20%3D%20nums%5Bleft%5D%2C%20nums%5Bmid%5D%2C%20nums%5Bright%5D%0A%20%20%20%20if%20%28l%20%3C%3D%20m%20%3C%3D%20r%29%20or%20%28r%20%3C%3D%20m%20%3C%3D%20l%29%3A%0A%20%20%20%20%20%20%20%20return%20mid%20%20%23%20m%20%E3%81%AF%20l%20%E3%81%A8%20r%20%E3%81%AE%E9%96%93%0A%20%20%20%20if%20%28m%20%3C%3D%20l%20%3C%3D%20r%29%20or%20%28r%20%3C%3D%20l%20%3C%3D%20m%29%3A%0A%20%20%20%20%20%20%20%20return%20left%20%20%23%20l%20%E3%81%AF%20m%20%E3%81%A8%20r%20%E3%81%AE%E9%96%93%0A%20%20%20%20return%20right%0A%0Adef%20partition%28nums%3A%20list%5Bint%5D%2C%20left%3A%20int%2C%20right%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%95%AA%E5%85%B5%E3%81%AB%E3%82%88%E3%82%8B%E5%88%86%E5%89%B2%E5%87%A6%E7%90%86%EF%BC%883%20%E7%82%B9%E4%B8%AD%E5%A4%AE%E5%80%A4%EF%BC%89%22%22%22%0A%20%20%20%20%23%20nums%5Bleft%5D%20%E3%82%92%E5%9F%BA%E6%BA%96%E5%80%A4%E3%81%A8%E3%81%99%E3%82%8B%0A%20%20%20%20med%20%3D%20median_three%28nums%2C%20left%2C%20%28left%20%2B%20right%29%20%2F%2F%202%2C%20right%29%0A%20%20%20%20%23%20%E4%B8%AD%E5%A4%AE%E5%80%A4%E3%82%92%E9%85%8D%E5%88%97%E3%81%AE%E6%9C%80%E5%B7%A6%E7%AB%AF%E3%81%AB%E4%BA%A4%E6%8F%9B%E3%81%99%E3%82%8B%0A%20%20%20%20nums%5Bleft%5D%2C%20nums%5Bmed%5D%20%3D%20nums%5Bmed%5D%2C%20nums%5Bleft%5D%0A%20%20%20%20%23%20nums%5Bleft%5D%20%E3%82%92%E5%9F%BA%E6%BA%96%E5%80%A4%E3%81%A8%E3%81%99%E3%82%8B%0A%20%20%20%20i%2C%20j%20%3D%20left%2C%20right%0A%20%20%20%20while%20i%20%3C%20j%3A%0A%20%20%20%20%20%20%20%20while%20i%20%3C%20j%20and%20nums%5Bj%5D%20%3E%3D%20nums%5Bleft%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20-%3D%201%20%20%23%20%E5%8F%B3%E3%81%8B%E3%82%89%E5%B7%A6%E3%81%B8%E5%9F%BA%E6%BA%96%E5%80%A4%E6%9C%AA%E6%BA%80%E3%81%AE%E6%9C%80%E5%88%9D%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E6%8E%A2%E3%81%99%0A%20%20%20%20%20%20%20%20while%20i%20%3C%20j%20and%20nums%5Bi%5D%20%3C%3D%20nums%5Bleft%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%2B%3D%201%20%20%23%20%E5%B7%A6%E3%81%8B%E3%82%89%E5%8F%B3%E3%81%B8%E5%9F%BA%E6%BA%96%E5%80%A4%E3%82%88%E3%82%8A%E5%A4%A7%E3%81%8D%E3%81%84%E6%9C%80%E5%88%9D%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E6%8E%A2%E3%81%99%0A%20%20%20%20%20%20%20%20%23%20%E8%A6%81%E7%B4%A0%E3%81%AE%E4%BA%A4%E6%8F%9B%0A%20%20%20%20%20%20%20%20nums%5Bi%5D%2C%20nums%5Bj%5D%20%3D%20nums%5Bj%5D%2C%20nums%5Bi%5D%0A%20%20%20%20%23%20%E5%9F%BA%E6%BA%96%E5%80%A4%E3%82%92%202%20%E3%81%A4%E3%81%AE%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AE%E5%A2%83%E7%95%8C%E3%81%B8%E4%BA%A4%E6%8F%9B%E3%81%99%E3%82%8B%0A%20%20%20%20nums%5Bi%5D%2C%20nums%5Bleft%5D%20%3D%20nums%5Bleft%5D%2C%20nums%5Bi%5D%0A%20%20%20%20return%20i%20%20%23%20%E5%9F%BA%E6%BA%96%E5%80%A4%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E8%BF%94%E3%81%99%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E4%B8%AD%E5%A4%AE%E5%80%A4%E3%83%94%E3%83%9C%E3%83%83%E3%83%88%E6%9C%80%E9%81%A9%E5%8C%96%0A%20%20%20%20nums%20%3D%20%5B2%2C%204%2C%201%2C%200%2C%203%2C%205%5D%0A%20%20%20%20partition%28nums%2C%200%2C%20len%28nums%29%20-%201%29%0A%20%20%20%20print%28%22%E7%95%AA%E5%85%B5%E5%88%86%E5%89%B2%EF%BC%88%E4%B8%AD%E5%A4%AE%E5%80%A4%E3%83%94%E3%83%9C%E3%83%83%E3%83%88%E6%9C%80%E9%81%A9%E5%8C%96%EF%BC%89%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%22%2C%20nums%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20median_three%28nums%3A%20list%5Bint%5D%2C%20left%3A%20int%2C%20mid%3A%20int%2C%20right%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%223%E3%81%A4%E3%81%AE%E5%80%99%E8%A3%9C%E8%A6%81%E7%B4%A0%E3%81%AE%E4%B8%AD%E5%A4%AE%E5%80%A4%E3%82%92%E9%81%B8%E3%81%B6%22%22%22%0A%20%20%20%20l%2C%20m%2C%20r%20%3D%20nums%5Bleft%5D%2C%20nums%5Bmid%5D%2C%20nums%5Bright%5D%0A%20%20%20%20if%20%28l%20%3C%3D%20m%20%3C%3D%20r%29%20or%20%28r%20%3C%3D%20m%20%3C%3D%20l%29%3A%0A%20%20%20%20%20%20%20%20return%20mid%20%20%23%20m%20%E3%81%AF%20l%20%E3%81%A8%20r%20%E3%81%AE%E9%96%93%0A%20%20%20%20if%20%28m%20%3C%3D%20l%20%3C%3D%20r%29%20or%20%28r%20%3C%3D%20l%20%3C%3D%20m%29%3A%0A%20%20%20%20%20%20%20%20return%20left%20%20%23%20l%20%E3%81%AF%20m%20%E3%81%A8%20r%20%E3%81%AE%E9%96%93%0A%20%20%20%20return%20right%0A%0Adef%20partition%28nums%3A%20list%5Bint%5D%2C%20left%3A%20int%2C%20right%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%95%AA%E5%85%B5%E3%81%AB%E3%82%88%E3%82%8B%E5%88%86%E5%89%B2%E5%87%A6%E7%90%86%EF%BC%883%20%E7%82%B9%E4%B8%AD%E5%A4%AE%E5%80%A4%EF%BC%89%22%22%22%0A%20%20%20%20%23%20nums%5Bleft%5D%20%E3%82%92%E5%9F%BA%E6%BA%96%E5%80%A4%E3%81%A8%E3%81%99%E3%82%8B%0A%20%20%20%20med%20%3D%20median_three%28nums%2C%20left%2C%20%28left%20%2B%20right%29%20%2F%2F%202%2C%20right%29%0A%20%20%20%20%23%20%E4%B8%AD%E5%A4%AE%E5%80%A4%E3%82%92%E9%85%8D%E5%88%97%E3%81%AE%E6%9C%80%E5%B7%A6%E7%AB%AF%E3%81%AB%E4%BA%A4%E6%8F%9B%E3%81%99%E3%82%8B%0A%20%20%20%20nums%5Bleft%5D%2C%20nums%5Bmed%5D%20%3D%20nums%5Bmed%5D%2C%20nums%5Bleft%5D%0A%20%20%20%20%23%20nums%5Bleft%5D%20%E3%82%92%E5%9F%BA%E6%BA%96%E5%80%A4%E3%81%A8%E3%81%99%E3%82%8B%0A%20%20%20%20i%2C%20j%20%3D%20left%2C%20right%0A%20%20%20%20while%20i%20%3C%20j%3A%0A%20%20%20%20%20%20%20%20while%20i%20%3C%20j%20and%20nums%5Bj%5D%20%3E%3D%20nums%5Bleft%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20-%3D%201%20%20%23%20%E5%8F%B3%E3%81%8B%E3%82%89%E5%B7%A6%E3%81%B8%E5%9F%BA%E6%BA%96%E5%80%A4%E6%9C%AA%E6%BA%80%E3%81%AE%E6%9C%80%E5%88%9D%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E6%8E%A2%E3%81%99%0A%20%20%20%20%20%20%20%20while%20i%20%3C%20j%20and%20nums%5Bi%5D%20%3C%3D%20nums%5Bleft%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%2B%3D%201%20%20%23%20%E5%B7%A6%E3%81%8B%E3%82%89%E5%8F%B3%E3%81%B8%E5%9F%BA%E6%BA%96%E5%80%A4%E3%82%88%E3%82%8A%E5%A4%A7%E3%81%8D%E3%81%84%E6%9C%80%E5%88%9D%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E6%8E%A2%E3%81%99%0A%20%20%20%20%20%20%20%20%23%20%E8%A6%81%E7%B4%A0%E3%81%AE%E4%BA%A4%E6%8F%9B%0A%20%20%20%20%20%20%20%20nums%5Bi%5D%2C%20nums%5Bj%5D%20%3D%20nums%5Bj%5D%2C%20nums%5Bi%5D%0A%20%20%20%20%23%20%E5%9F%BA%E6%BA%96%E5%80%A4%E3%82%92%202%20%E3%81%A4%E3%81%AE%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AE%E5%A2%83%E7%95%8C%E3%81%B8%E4%BA%A4%E6%8F%9B%E3%81%99%E3%82%8B%0A%20%20%20%20nums%5Bi%5D%2C%20nums%5Bleft%5D%20%3D%20nums%5Bleft%5D%2C%20nums%5Bi%5D%0A%20%20%20%20return%20i%20%20%23%20%E5%9F%BA%E6%BA%96%E5%80%A4%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E8%BF%94%E3%81%99%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E4%B8%AD%E5%A4%AE%E5%80%A4%E3%83%94%E3%83%9C%E3%83%83%E3%83%88%E6%9C%80%E9%81%A9%E5%8C%96%0A%20%20%20%20nums%20%3D%20%5B2%2C%204%2C%201%2C%200%2C%203%2C%205%5D%0A%20%20%20%20partition%28nums%2C%200%2C%20len%28nums%29%20-%201%29%0A%20%20%20%20print%28%22%E7%95%AA%E5%85%B5%E5%88%86%E5%89%B2%EF%BC%88%E4%B8%AD%E5%A4%AE%E5%80%A4%E3%83%94%E3%83%9C%E3%83%83%E3%83%88%E6%9C%80%E9%81%A9%E5%8C%96%EF%BC%89%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%22%2C%20nums%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h2 id="1155">11.5.5 &nbsp; 再帰の深さの最適化<a class="headerlink" href="#1155" title="Permanent link">&para;</a></h2>
+<p><strong>一部の入力では、クイックソートは多くの空間を消費する可能性があります</strong>。完全に整列済みの入力配列を例にとり、再帰中の部分配列の長さを <span class="arithmatex">\(m\)</span> とします。各回のパーティション操作では長さ <span class="arithmatex">\(0\)</span> の左部分配列と長さ <span class="arithmatex">\(m - 1\)</span> の右部分配列が生成されます。これは、各再帰呼び出しで減る問題サイズが非常に小さいこと（要素が 1 つ減るだけ）を意味し、再帰木の高さは <span class="arithmatex">\(n - 1\)</span> に達するため、このとき <span class="arithmatex">\(O(n)\)</span> のスタックフレーム空間を占有します。</p>
+<p>スタックフレーム空間の蓄積を防ぐために、各回のパーティション完了後に 2 つの部分配列の長さを比較し、**短いほうの部分配列に対してのみ再帰**を行えます。短い部分配列の長さは <span class="arithmatex">\(n / 2\)</span> を超えないため、この方法なら再帰の深さを <span class="arithmatex">\(\log n\)</span> 以下に抑えられ、最悪時の空間計算量を <span class="arithmatex">\(O(\log n)\)</span> まで最適化できます。コードを以下に示します。</p>
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 <div class="highlight"><span class="filename">quick_sort.py</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">quick_sort</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;クイックソート（末尾再帰最適化）&quot;&quot;&quot;</span>
-<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a>    <span class="c1"># サブ配列の長さが1のときに終了</span>
+<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;クイックソート（再帰深度最適化）&quot;&quot;&quot;</span>
+<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a>    <span class="c1"># 部分配列の長さが 1 なら終了</span>
 <a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a>    <span class="k">while</span> <span class="n">left</span> <span class="o">&lt;</span> <span class="n">right</span><span class="p">:</span>
-<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a>        <span class="c1"># 分割操作</span>
+<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a>        <span class="c1"># 番兵による分割処理</span>
 <a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a>        <span class="n">pivot</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">left</span><span class="p">,</span> <span class="n">right</span><span class="p">)</span>
-<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a>        <span class="c1"># 2つのサブ配列のうち短い方に対してクイックソートを実行</span>
+<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a>        <span class="c1"># 2 つの部分配列のうち短いほうにクイックソートを適用する</span>
 <a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a>        <span class="k">if</span> <span class="n">pivot</span> <span class="o">-</span> <span class="n">left</span> <span class="o">&lt;</span> <span class="n">right</span> <span class="o">-</span> <span class="n">pivot</span><span class="p">:</span>
-<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">quick_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">left</span><span class="p">,</span> <span class="n">pivot</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>  <span class="c1"># 左サブ配列を再帰的にソート</span>
-<a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a>            <span class="n">left</span> <span class="o">=</span> <span class="n">pivot</span> <span class="o">+</span> <span class="mi">1</span>  <span class="c1"># 残りの未ソート区間は [pivot + 1, right]</span>
+<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">quick_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">left</span><span class="p">,</span> <span class="n">pivot</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>  <span class="c1"># 左部分配列を再帰的にソート</span>
+<a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a>            <span class="n">left</span> <span class="o">=</span> <span class="n">pivot</span> <span class="o">+</span> <span class="mi">1</span>  <span class="c1"># 未ソート区間の残りは [pivot + 1, right]</span>
 <a id="__codelineno-39-11" name="__codelineno-39-11" href="#__codelineno-39-11"></a>        <span class="k">else</span><span class="p">:</span>
-<a id="__codelineno-39-12" name="__codelineno-39-12" href="#__codelineno-39-12"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">quick_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">pivot</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">right</span><span class="p">)</span>  <span class="c1"># 右サブ配列を再帰的にソート</span>
-<a id="__codelineno-39-13" name="__codelineno-39-13" href="#__codelineno-39-13"></a>            <span class="n">right</span> <span class="o">=</span> <span class="n">pivot</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># 残りの未ソート区間は [left, pivot - 1]</span>
+<a id="__codelineno-39-12" name="__codelineno-39-12" href="#__codelineno-39-12"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">quick_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">pivot</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">right</span><span class="p">)</span>  <span class="c1"># 右部分配列を再帰的にソート</span>
+<a id="__codelineno-39-13" name="__codelineno-39-13" href="#__codelineno-39-13"></a>            <span class="n">right</span> <span class="o">=</span> <span class="n">pivot</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># 未ソート区間の残りは [left, pivot - 1]</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.cpp</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* クイックソート（末尾再帰最適化） */</span>
+<div class="highlight"><span class="filename">quick_sort.cpp</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* クイックソート（再帰深度最適化） */</span>
 <a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">quickSort</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w">    </span><span class="c1">// サブ配列の長さが1の時終了</span>
+<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w">    </span><span class="c1">// 部分配列の長さが 1 なら終了</span>
 <a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w">        </span><span class="c1">// 分割操作</span>
+<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w">        </span><span class="c1">// 番兵による分割処理</span>
 <a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
-<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w">        </span><span class="c1">// 二つのサブ配列のうち短い方でクイックソートを実行</span>
+<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w">        </span><span class="c1">// 2 つの部分配列のうち短いほうにクイックソートを適用する</span>
 <a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">pivot</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w">            </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span><span class="w"> </span><span class="c1">// 左サブ配列を再帰的にソート</span>
-<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w">            </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">                 </span><span class="c1">// 残りの未ソート区間は[pivot + 1, right]</span>
+<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w">            </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span><span class="w"> </span><span class="c1">// 左部分配列を再帰的にソート</span>
+<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w">            </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">                 </span><span class="c1">// 未ソート区間の残りは [pivot + 1, right]</span>
 <a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w">            </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右サブ配列を再帰的にソート</span>
-<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w">            </span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">                 </span><span class="c1">// 残りの未ソート区間は[left, pivot - 1]</span>
+<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w">            </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右部分配列を再帰的にソート</span>
+<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w">            </span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">                 </span><span class="c1">// 未ソート区間の残りは [left, pivot - 1]</span>
 <a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-40-16" name="__codelineno-40-16" href="#__codelineno-40-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.java</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* クイックソート（末尾再帰最適化） */</span>
+<div class="highlight"><span class="filename">quick_sort.java</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* クイックソート（再帰深度最適化） */</span>
 <a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">quickSort</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w">    </span><span class="c1">// 部分配列の長さが 1 のとき終了</span>
+<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w">    </span><span class="c1">// 部分配列の長さが 1 なら終了</span>
 <a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="w">        </span><span class="c1">// 分割操作</span>
+<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="w">        </span><span class="c1">// 番兵による分割処理</span>
 <a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
-<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="w">        </span><span class="c1">// 2つの部分配列のうち短い方にクイックソートを実行</span>
+<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="w">        </span><span class="c1">// 2 つの部分配列のうち短いほうにクイックソートを適用する</span>
 <a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">pivot</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="w">            </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span><span class="w"> </span><span class="c1">// 左部分配列を再帰的にソート</span>
-<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="w">            </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 残りの未ソート区間は [pivot + 1, right]</span>
+<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="w">            </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 未ソート区間の残りは [pivot + 1, right]</span>
 <a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a><span class="w">            </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右部分配列を再帰的にソート</span>
-<a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a><span class="w">            </span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 残りの未ソート区間は [left, pivot - 1]</span>
+<a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a><span class="w">            </span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 未ソート区間の残りは [left, pivot - 1]</span>
 <a id="__codelineno-41-14" name="__codelineno-41-14" href="#__codelineno-41-14"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-41-15" name="__codelineno-41-15" href="#__codelineno-41-15"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-41-16" name="__codelineno-41-16" href="#__codelineno-41-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.cs</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">QuickSortTailCall</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">QuickSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.cs</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="cm">/* クイックソート（再帰深度最適化） */</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">QuickSort</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="w">    </span><span class="c1">// 部分配列の長さが 1 なら終了</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="w">        </span><span class="c1">// 番兵による分割処理</span>
+<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="w">        </span><span class="c1">// 2 つの部分配列のうち短いほうにクイックソートを適用する</span>
+<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">pivot</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="w">            </span><span class="n">QuickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span><span class="w">  </span><span class="c1">// 左部分配列を再帰的にソート</span>
+<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a><span class="w">            </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// 未ソート区間の残りは [pivot + 1, right]</span>
+<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a><span class="w">            </span><span class="n">QuickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右部分配列を再帰的にソート</span>
+<a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a><span class="w">            </span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 未ソート区間の残りは [left, pivot - 1]</span>
+<a id="__codelineno-42-14" name="__codelineno-42-14" href="#__codelineno-42-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-42-15" name="__codelineno-42-15" href="#__codelineno-42-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-42-16" name="__codelineno-42-16" href="#__codelineno-42-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.go</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">quickSortTailCall</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">quickSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.go</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* クイックソート（再帰深度最適化） */</span>
+<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">q</span><span class="w"> </span><span class="o">*</span><span class="nx">quickSortTailCall</span><span class="p">)</span><span class="w"> </span><span class="nx">quickSort</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w">    </span><span class="c1">// 部分配列の長さが 1 なら終了</span>
+<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w">        </span><span class="c1">// 番兵による分割処理</span>
+<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w">        </span><span class="nx">pivot</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">partition</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span>
+<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="w">        </span><span class="c1">// 2 つの部分配列のうち短いほうにクイックソートを適用する</span>
+<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">pivot</span><span class="o">-</span><span class="nx">left</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">right</span><span class="o">-</span><span class="nx">pivot</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w">            </span><span class="nx">q</span><span class="p">.</span><span class="nx">quickSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">pivot</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="c1">// 左部分配列を再帰的にソート</span>
+<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w">            </span><span class="nx">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w">                 </span><span class="c1">// 未ソート区間の残りは [pivot + 1, right]</span>
+<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w">            </span><span class="nx">q</span><span class="p">.</span><span class="nx">quickSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">pivot</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="c1">// 右部分配列を再帰的にソート</span>
+<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="w">            </span><span class="nx">right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w">                 </span><span class="c1">// 未ソート区間の残りは [left, pivot - 1]</span>
+<a id="__codelineno-43-14" name="__codelineno-43-14" href="#__codelineno-43-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-43-15" name="__codelineno-43-15" href="#__codelineno-43-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-16" name="__codelineno-43-16" href="#__codelineno-43-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.swift</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">quickSortTailCall</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.swift</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* クイックソート（再帰深度最適化） */</span>
+<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">quickSortTailCall</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="kr">left</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="kr">right</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kr">left</span>
+<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kr">right</span>
+<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w">    </span><span class="c1">// 部分配列の長さが 1 なら終了</span>
+<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="kr">left</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="kr">right</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w">        </span><span class="c1">// 番兵による分割処理</span>
+<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">pivot</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kr">left</span><span class="p">:</span><span class="w"> </span><span class="kr">left</span><span class="p">,</span><span class="w"> </span><span class="kr">right</span><span class="p">:</span><span class="w"> </span><span class="kr">right</span><span class="p">)</span>
+<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w">        </span><span class="c1">// 2 つの部分配列のうち短いほうにクイックソートを適用する</span>
+<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="kr">left</span><span class="p">)</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="p">(</span><span class="kr">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">pivot</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w">            </span><span class="n">quickSortTailCall</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kr">left</span><span class="p">:</span><span class="w"> </span><span class="kr">left</span><span class="p">,</span><span class="w"> </span><span class="kr">right</span><span class="p">:</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="c1">// 左部分配列を再帰的にソート</span>
+<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w">            </span><span class="kr">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// 未ソート区間の残りは [pivot + 1, right]</span>
+<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a><span class="w">            </span><span class="n">quickSortTailCall</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kr">left</span><span class="p">:</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="kr">right</span><span class="p">:</span><span class="w"> </span><span class="kr">right</span><span class="p">)</span><span class="w"> </span><span class="c1">// 右部分配列を再帰的にソート</span>
+<a id="__codelineno-44-15" name="__codelineno-44-15" href="#__codelineno-44-15"></a><span class="w">            </span><span class="kr">right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// 未ソート区間の残りは [left, pivot - 1]</span>
+<a id="__codelineno-44-16" name="__codelineno-44-16" href="#__codelineno-44-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-44-17" name="__codelineno-44-17" href="#__codelineno-44-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-18" name="__codelineno-44-18" href="#__codelineno-44-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.js</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">QuickSortTailCall</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">quickSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.js</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="cm">/* クイックソート（再帰深度最適化） */</span>
+<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="nx">quickSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w">    </span><span class="c1">// 部分配列の長さが 1 なら終了</span>
+<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">left</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w">        </span><span class="c1">// 番兵による分割処理</span>
+<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">pivot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">partition</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">);</span>
+<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="w">        </span><span class="c1">// 2 つの部分配列のうち短いほうにクイックソートを適用する</span>
+<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">pivot</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">quickSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span><span class="w"> </span><span class="c1">// 左部分配列を再帰的にソート</span>
+<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="w">            </span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 未ソート区間の残りは [pivot + 1, right]</span>
+<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">quickSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右部分配列を再帰的にソート</span>
+<a id="__codelineno-45-13" name="__codelineno-45-13" href="#__codelineno-45-13"></a><span class="w">            </span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 未ソート区間の残りは [left, pivot - 1]</span>
+<a id="__codelineno-45-14" name="__codelineno-45-14" href="#__codelineno-45-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-45-15" name="__codelineno-45-15" href="#__codelineno-45-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-45-16" name="__codelineno-45-16" href="#__codelineno-45-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.ts</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">QuickSortTailCall</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">quickSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.ts</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="cm">/* クイックソート（再帰深度最適化） */</span>
+<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="nx">quickSort</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">left</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w">    </span><span class="c1">// 部分配列の長さが 1 なら終了</span>
+<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">left</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="w">        </span><span class="c1">// 番兵による分割処理</span>
+<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">pivot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">partition</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">);</span>
+<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></a><span class="w">        </span><span class="c1">// 2 つの部分配列のうち短いほうにクイックソートを適用する</span>
+<a id="__codelineno-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">pivot</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">quickSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span><span class="w"> </span><span class="c1">// 左部分配列を再帰的にソート</span>
+<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a><span class="w">            </span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 未ソート区間の残りは [pivot + 1, right]</span>
+<a id="__codelineno-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-12" name="__codelineno-46-12" href="#__codelineno-46-12"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">quickSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右部分配列を再帰的にソート</span>
+<a id="__codelineno-46-13" name="__codelineno-46-13" href="#__codelineno-46-13"></a><span class="w">            </span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 未ソート区間の残りは [left, pivot - 1]</span>
+<a id="__codelineno-46-14" name="__codelineno-46-14" href="#__codelineno-46-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-46-15" name="__codelineno-46-15" href="#__codelineno-46-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-46-16" name="__codelineno-46-16" href="#__codelineno-46-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.dart</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSortTailCall</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quickSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.dart</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* クイックソート（再帰深度最適化） */</span>
+<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">quickSort</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w">  </span><span class="c1">// 部分配列の長さが 1 なら終了</span>
+<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="w">    </span><span class="c1">// 番兵による分割処理</span>
+<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="w">    </span><span class="c1">// 2 つの部分配列のうち短いほうにクイックソートを適用する</span>
+<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">pivot</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="w">      </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span><span class="w"> </span><span class="c1">// 左部分配列を再帰的にソート</span>
+<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="w">      </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 未ソート区間の残りは [pivot + 1, right]</span>
+<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a><span class="w">      </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右部分配列を再帰的にソート</span>
+<a id="__codelineno-47-13" name="__codelineno-47-13" href="#__codelineno-47-13"></a><span class="w">      </span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 未ソート区間の残りは [left, pivot - 1]</span>
+<a id="__codelineno-47-14" name="__codelineno-47-14" href="#__codelineno-47-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-47-15" name="__codelineno-47-15" href="#__codelineno-47-15"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-47-16" name="__codelineno-47-16" href="#__codelineno-47-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.rs</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSortTailCall</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quick_sort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.rs</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="cm">/* クイックソート（再帰深度最適化） */</span>
+<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">quick_sort</span><span class="p">(</span><span class="k">mut</span><span class="w"> </span><span class="n">left</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">right</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="w">    </span><span class="c1">// 部分配列の長さが 1 なら終了</span>
+<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a><span class="w">        </span><span class="c1">// 番兵による分割処理</span>
+<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span><span class="p">::</span><span class="n">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">;</span>
+<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a><span class="w">        </span><span class="c1">// 2 つの部分配列のうち短いほうにクイックソートを適用する</span>
+<a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a><span class="w">            </span><span class="bp">Self</span><span class="p">::</span><span class="n">quick_sort</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">);</span><span class="w"> </span><span class="c1">// 左部分配列を再帰的にソート</span>
+<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a><span class="w">            </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 未ソート区間の残りは [pivot + 1, right]</span>
+<a id="__codelineno-48-11" name="__codelineno-48-11" href="#__codelineno-48-11"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-12" name="__codelineno-48-12" href="#__codelineno-48-12"></a><span class="w">            </span><span class="bp">Self</span><span class="p">::</span><span class="n">quick_sort</span><span class="p">(</span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右部分配列を再帰的にソート</span>
+<a id="__codelineno-48-13" name="__codelineno-48-13" href="#__codelineno-48-13"></a><span class="w">            </span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 未ソート区間の残りは [left, pivot - 1]</span>
+<a id="__codelineno-48-14" name="__codelineno-48-14" href="#__codelineno-48-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-48-15" name="__codelineno-48-15" href="#__codelineno-48-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-48-16" name="__codelineno-48-16" href="#__codelineno-48-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.c</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quickSortTailCall</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.c</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* クイックソート（再帰深度最適化） */</span>
+<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">quickSortTailCall</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="w">    </span><span class="c1">// 部分配列の長さが 1 なら終了</span>
+<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="w">        </span><span class="c1">// 番兵による分割処理</span>
+<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="w">        </span><span class="c1">// 2 つの部分配列のうち短いほうにクイックソートを適用する</span>
+<a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">pivot</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-9" name="__codelineno-49-9" href="#__codelineno-49-9"></a><span class="w">            </span><span class="c1">// 左部分配列を再帰的にソート</span>
+<a id="__codelineno-49-10" name="__codelineno-49-10" href="#__codelineno-49-10"></a><span class="w">            </span><span class="n">quickSortTailCall</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-49-11" name="__codelineno-49-11" href="#__codelineno-49-11"></a><span class="w">            </span><span class="c1">// 未ソート区間の残りは [pivot + 1, right]</span>
+<a id="__codelineno-49-12" name="__codelineno-49-12" href="#__codelineno-49-12"></a><span class="w">            </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-49-13" name="__codelineno-49-13" href="#__codelineno-49-13"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-14" name="__codelineno-49-14" href="#__codelineno-49-14"></a><span class="w">            </span><span class="c1">// 右部分配列を再帰的にソート</span>
+<a id="__codelineno-49-15" name="__codelineno-49-15" href="#__codelineno-49-15"></a><span class="w">            </span><span class="n">quickSortTailCall</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-49-16" name="__codelineno-49-16" href="#__codelineno-49-16"></a><span class="w">            </span><span class="c1">// 未ソート区間の残りは [left, pivot - 1]</span>
+<a id="__codelineno-49-17" name="__codelineno-49-17" href="#__codelineno-49-17"></a><span class="w">            </span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-49-18" name="__codelineno-49-18" href="#__codelineno-49-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-49-19" name="__codelineno-49-19" href="#__codelineno-49-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-49-20" name="__codelineno-49-20" href="#__codelineno-49-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.kt</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">quickSortTailCall</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.kt</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* クイックソート（再帰深度最適化） */</span>
+<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">quickSortTailCall</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w">    </span><span class="c1">// 部分配列の長さが 1 なら終了</span>
+<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span>
+<a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span>
+<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="w">        </span><span class="c1">// 番兵による分割処理</span>
+<a id="__codelineno-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">pivot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">)</span>
+<a id="__codelineno-50-9" name="__codelineno-50-9" href="#__codelineno-50-9"></a><span class="w">        </span><span class="c1">// 2 つの部分配列のうち短いほうにクイックソートを適用する</span>
+<a id="__codelineno-50-10" name="__codelineno-50-10" href="#__codelineno-50-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">pivot</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-11" name="__codelineno-50-11" href="#__codelineno-50-11"></a><span class="w">            </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="c1">// 左部分配列を再帰的にソート</span>
+<a id="__codelineno-50-12" name="__codelineno-50-12" href="#__codelineno-50-12"></a><span class="w">            </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="c1">// 未ソート区間の残りは [pivot + 1, right]</span>
+<a id="__codelineno-50-13" name="__codelineno-50-13" href="#__codelineno-50-13"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-14" name="__codelineno-50-14" href="#__codelineno-50-14"></a><span class="w">            </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="c1">// 右部分配列を再帰的にソート</span>
+<a id="__codelineno-50-15" name="__codelineno-50-15" href="#__codelineno-50-15"></a><span class="w">            </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="c1">// 未ソート区間の残りは [left, pivot - 1]</span>
+<a id="__codelineno-50-16" name="__codelineno-50-16" href="#__codelineno-50-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-50-17" name="__codelineno-50-17" href="#__codelineno-50-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-50-18" name="__codelineno-50-18" href="#__codelineno-50-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.rb</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">QuickSortTailCall</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">quick_sort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">quick_sort.rb</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="c1">### 番兵分割 ###</span>
+<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w">  </span><span class="c1"># nums[left] を基準値とする</span>
+<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a><span class="w">  </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span>
+<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w">  </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span>
+<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span>
+<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span>
+<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="w">      </span><span class="n">j</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># 右から左へ基準値未満の最初の要素を探す</span>
+<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span>
+<a id="__codelineno-51-11" name="__codelineno-51-11" href="#__codelineno-51-11"></a><span class="w">      </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># 左から右へ基準値より大きい最初の要素を探す</span>
+<a id="__codelineno-51-12" name="__codelineno-51-12" href="#__codelineno-51-12"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-51-13" name="__codelineno-51-13" href="#__codelineno-51-13"></a><span class="w">    </span><span class="c1"># 要素の交換</span>
+<a id="__codelineno-51-14" name="__codelineno-51-14" href="#__codelineno-51-14"></a><span class="w">    </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-51-15" name="__codelineno-51-15" href="#__codelineno-51-15"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-51-16" name="__codelineno-51-16" href="#__codelineno-51-16"></a><span class="w">  </span><span class="c1"># 基準値を 2 つの部分配列の境界へ交換する</span>
+<a id="__codelineno-51-17" name="__codelineno-51-17" href="#__codelineno-51-17"></a><span class="w">  </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-51-18" name="__codelineno-51-18" href="#__codelineno-51-18"></a><span class="w">  </span><span class="n">i</span><span class="w"> </span><span class="c1"># 基準値のインデックスを返す</span>
+<a id="__codelineno-51-19" name="__codelineno-51-19" href="#__codelineno-51-19"></a><span class="k">end</span>
+<a id="__codelineno-51-20" name="__codelineno-51-20" href="#__codelineno-51-20"></a>
+<a id="__codelineno-51-21" name="__codelineno-51-21" href="#__codelineno-51-21"></a><span class="c1"># ## クイックソート（再帰深度最適化）###</span>
+<a id="__codelineno-51-22" name="__codelineno-51-22" href="#__codelineno-51-22"></a><span class="k">def</span><span class="w"> </span><span class="nf">quick_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-51-23" name="__codelineno-51-23" href="#__codelineno-51-23"></a><span class="w">  </span><span class="c1"># 部分配列の長さが 1 でない場合は再帰する</span>
+<a id="__codelineno-51-24" name="__codelineno-51-24" href="#__codelineno-51-24"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">right</span>
+<a id="__codelineno-51-25" name="__codelineno-51-25" href="#__codelineno-51-25"></a><span class="w">    </span><span class="c1"># 番兵分割</span>
+<a id="__codelineno-51-26" name="__codelineno-51-26" href="#__codelineno-51-26"></a><span class="w">    </span><span class="n">pivot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-51-27" name="__codelineno-51-27" href="#__codelineno-51-27"></a><span class="w">    </span><span class="c1"># 2 つの部分配列のうち短いほうにクイックソートを適用する</span>
+<a id="__codelineno-51-28" name="__codelineno-51-28" href="#__codelineno-51-28"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">pivot</span>
+<a id="__codelineno-51-29" name="__codelineno-51-29" href="#__codelineno-51-29"></a><span class="w">      </span><span class="n">quick_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-51-30" name="__codelineno-51-30" href="#__codelineno-51-30"></a><span class="w">      </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># 未ソート区間の残りは [pivot + 1, right]</span>
+<a id="__codelineno-51-31" name="__codelineno-51-31" href="#__codelineno-51-31"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-51-32" name="__codelineno-51-32" href="#__codelineno-51-32"></a><span class="w">      </span><span class="n">quick_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-51-33" name="__codelineno-51-33" href="#__codelineno-51-33"></a><span class="w">      </span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># 未ソート区間の残りは [left, pivot - 1]</span>
+<a id="__codelineno-51-34" name="__codelineno-51-34" href="#__codelineno-51-34"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-51-35" name="__codelineno-51-35" href="#__codelineno-51-35"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-51-36" name="__codelineno-51-36" href="#__codelineno-51-36"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20partition%28nums%3A%20list%5Bint%5D%2C%20left%3A%20int%2C%20right%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%95%AA%E5%85%B5%E5%88%86%E5%89%B2%22%22%22%0A%20%20%20%20%23%20nums%5Bleft%5D%20%E3%82%92%E5%9F%BA%E6%BA%96%E5%80%A4%E3%81%A8%E3%81%99%E3%82%8B%0A%20%20%20%20i%2C%20j%20%3D%20left%2C%20right%0A%20%20%20%20while%20i%20%3C%20j%3A%0A%20%20%20%20%20%20%20%20while%20i%20%3C%20j%20and%20nums%5Bj%5D%20%3E%3D%20nums%5Bleft%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20-%3D%201%20%20%23%20%E5%8F%B3%E3%81%8B%E3%82%89%E5%B7%A6%E3%81%B8%E5%9F%BA%E6%BA%96%E5%80%A4%E6%9C%AA%E6%BA%80%E3%81%AE%E6%9C%80%E5%88%9D%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E6%8E%A2%E3%81%99%0A%20%20%20%20%20%20%20%20while%20i%20%3C%20j%20and%20nums%5Bi%5D%20%3C%3D%20nums%5Bleft%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%2B%3D%201%20%20%23%20%E5%B7%A6%E3%81%8B%E3%82%89%E5%8F%B3%E3%81%B8%E5%9F%BA%E6%BA%96%E5%80%A4%E3%82%88%E3%82%8A%E5%A4%A7%E3%81%8D%E3%81%84%E6%9C%80%E5%88%9D%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E6%8E%A2%E3%81%99%0A%20%20%20%20%20%20%20%20%23%20%E8%A6%81%E7%B4%A0%E3%81%AE%E4%BA%A4%E6%8F%9B%0A%20%20%20%20%20%20%20%20nums%5Bi%5D%2C%20nums%5Bj%5D%20%3D%20nums%5Bj%5D%2C%20nums%5Bi%5D%0A%20%20%20%20%23%20%E5%9F%BA%E6%BA%96%E5%80%A4%E3%82%92%202%20%E3%81%A4%E3%81%AE%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AE%E5%A2%83%E7%95%8C%E3%81%B8%E4%BA%A4%E6%8F%9B%E3%81%99%E3%82%8B%0A%20%20%20%20nums%5Bi%5D%2C%20nums%5Bleft%5D%20%3D%20nums%5Bleft%5D%2C%20nums%5Bi%5D%0A%20%20%20%20return%20i%20%20%23%20%E5%9F%BA%E6%BA%96%E5%80%A4%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E8%BF%94%E3%81%99%0A%0Adef%20quick_sort%28nums%3A%20list%5Bint%5D%2C%20left%3A%20int%2C%20right%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E3%82%AF%E3%82%A4%E3%83%83%E3%82%AF%E3%82%BD%E3%83%BC%E3%83%88%EF%BC%88%E6%9C%AB%E5%B0%BE%E5%86%8D%E5%B8%B0%E6%9C%80%E9%81%A9%E5%8C%96%EF%BC%89%22%22%22%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AE%E9%95%B7%E3%81%95%E3%81%8C%201%20%E3%81%AA%E3%82%89%E7%B5%82%E4%BA%86%0A%20%20%20%20while%20left%20%3C%20right%3A%0A%20%20%20%20%20%20%20%20%23%20%E7%95%AA%E5%85%B5%E3%81%AB%E3%82%88%E3%82%8B%E5%88%86%E5%89%B2%E5%87%A6%E7%90%86%0A%20%20%20%20%20%20%20%20pivot%20%3D%20partition%28nums%2C%20left%2C%20right%29%0A%20%20%20%20%20%20%20%20%23%202%20%E3%81%A4%E3%81%AE%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AE%E3%81%86%E3%81%A1%E7%9F%AD%E3%81%84%E3%81%BB%E3%81%86%E3%81%AB%E3%82%AF%E3%82%A4%E3%83%83%E3%82%AF%E3%82%BD%E3%83%BC%E3%83%88%E3%82%92%E9%81%A9%E7%94%A8%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20if%20pivot%20-%20left%20%3C%20right%20-%20pivot%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20quick_sort%28nums%2C%20left%2C%20pivot%20-%201%29%20%20%23%20%E5%B7%A6%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%82%92%E5%86%8D%E5%B8%B0%E7%9A%84%E3%81%AB%E3%82%BD%E3%83%BC%E3%83%88%0A%20%20%20%20%20%20%20%20%20%20%20%20left%20%3D%20pivot%20%2B%201%20%20%23%20%E6%9C%AA%E3%82%BD%E3%83%BC%E3%83%88%E5%8C%BA%E9%96%93%E3%81%AE%E6%AE%8B%E3%82%8A%E3%81%AF%20%5Bpivot%20%2B%201%2C%20right%5D%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20quick_sort%28nums%2C%20pivot%20%2B%201%2C%20right%29%20%20%23%20%E5%8F%B3%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%82%92%E5%86%8D%E5%B8%B0%E7%9A%84%E3%81%AB%E3%82%BD%E3%83%BC%E3%83%88%0A%20%20%20%20%20%20%20%20%20%20%20%20right%20%3D%20pivot%20-%201%20%20%23%20%E6%9C%AA%E3%82%BD%E3%83%BC%E3%83%88%E5%8C%BA%E9%96%93%E3%81%AE%E6%AE%8B%E3%82%8A%E3%81%AF%20%5Bleft%2C%20pivot%20-%201%5D%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E3%82%AF%E3%82%A4%E3%83%83%E3%82%AF%E3%82%BD%E3%83%BC%E3%83%88%EF%BC%88%E6%9C%AB%E5%B0%BE%E5%86%8D%E5%B8%B0%E6%9C%80%E9%81%A9%E5%8C%96%EF%BC%89%0A%20%20%20%20nums%20%3D%20%5B2%2C%204%2C%201%2C%200%2C%203%2C%205%5D%0A%20%20%20%20quick_sort%28nums%2C%200%2C%20len%28nums%29%20-%201%29%0A%20%20%20%20print%28%22%E3%82%AF%E3%82%A4%E3%83%83%E3%82%AF%E3%82%BD%E3%83%BC%E3%83%88%EF%BC%88%E6%9C%AB%E5%B0%BE%E5%86%8D%E5%B8%B0%E6%9C%80%E9%81%A9%E5%8C%96%EF%BC%89%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%22%2C%20nums%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20partition%28nums%3A%20list%5Bint%5D%2C%20left%3A%20int%2C%20right%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%95%AA%E5%85%B5%E5%88%86%E5%89%B2%22%22%22%0A%20%20%20%20%23%20nums%5Bleft%5D%20%E3%82%92%E5%9F%BA%E6%BA%96%E5%80%A4%E3%81%A8%E3%81%99%E3%82%8B%0A%20%20%20%20i%2C%20j%20%3D%20left%2C%20right%0A%20%20%20%20while%20i%20%3C%20j%3A%0A%20%20%20%20%20%20%20%20while%20i%20%3C%20j%20and%20nums%5Bj%5D%20%3E%3D%20nums%5Bleft%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20-%3D%201%20%20%23%20%E5%8F%B3%E3%81%8B%E3%82%89%E5%B7%A6%E3%81%B8%E5%9F%BA%E6%BA%96%E5%80%A4%E6%9C%AA%E6%BA%80%E3%81%AE%E6%9C%80%E5%88%9D%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E6%8E%A2%E3%81%99%0A%20%20%20%20%20%20%20%20while%20i%20%3C%20j%20and%20nums%5Bi%5D%20%3C%3D%20nums%5Bleft%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%2B%3D%201%20%20%23%20%E5%B7%A6%E3%81%8B%E3%82%89%E5%8F%B3%E3%81%B8%E5%9F%BA%E6%BA%96%E5%80%A4%E3%82%88%E3%82%8A%E5%A4%A7%E3%81%8D%E3%81%84%E6%9C%80%E5%88%9D%E3%81%AE%E8%A6%81%E7%B4%A0%E3%82%92%E6%8E%A2%E3%81%99%0A%20%20%20%20%20%20%20%20%23%20%E8%A6%81%E7%B4%A0%E3%81%AE%E4%BA%A4%E6%8F%9B%0A%20%20%20%20%20%20%20%20nums%5Bi%5D%2C%20nums%5Bj%5D%20%3D%20nums%5Bj%5D%2C%20nums%5Bi%5D%0A%20%20%20%20%23%20%E5%9F%BA%E6%BA%96%E5%80%A4%E3%82%92%202%20%E3%81%A4%E3%81%AE%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AE%E5%A2%83%E7%95%8C%E3%81%B8%E4%BA%A4%E6%8F%9B%E3%81%99%E3%82%8B%0A%20%20%20%20nums%5Bi%5D%2C%20nums%5Bleft%5D%20%3D%20nums%5Bleft%5D%2C%20nums%5Bi%5D%0A%20%20%20%20return%20i%20%20%23%20%E5%9F%BA%E6%BA%96%E5%80%A4%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E8%BF%94%E3%81%99%0A%0Adef%20quick_sort%28nums%3A%20list%5Bint%5D%2C%20left%3A%20int%2C%20right%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E3%82%AF%E3%82%A4%E3%83%83%E3%82%AF%E3%82%BD%E3%83%BC%E3%83%88%EF%BC%88%E6%9C%AB%E5%B0%BE%E5%86%8D%E5%B8%B0%E6%9C%80%E9%81%A9%E5%8C%96%EF%BC%89%22%22%22%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AE%E9%95%B7%E3%81%95%E3%81%8C%201%20%E3%81%AA%E3%82%89%E7%B5%82%E4%BA%86%0A%20%20%20%20while%20left%20%3C%20right%3A%0A%20%20%20%20%20%20%20%20%23%20%E7%95%AA%E5%85%B5%E3%81%AB%E3%82%88%E3%82%8B%E5%88%86%E5%89%B2%E5%87%A6%E7%90%86%0A%20%20%20%20%20%20%20%20pivot%20%3D%20partition%28nums%2C%20left%2C%20right%29%0A%20%20%20%20%20%20%20%20%23%202%20%E3%81%A4%E3%81%AE%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%81%AE%E3%81%86%E3%81%A1%E7%9F%AD%E3%81%84%E3%81%BB%E3%81%86%E3%81%AB%E3%82%AF%E3%82%A4%E3%83%83%E3%82%AF%E3%82%BD%E3%83%BC%E3%83%88%E3%82%92%E9%81%A9%E7%94%A8%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20if%20pivot%20-%20left%20%3C%20right%20-%20pivot%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20quick_sort%28nums%2C%20left%2C%20pivot%20-%201%29%20%20%23%20%E5%B7%A6%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%82%92%E5%86%8D%E5%B8%B0%E7%9A%84%E3%81%AB%E3%82%BD%E3%83%BC%E3%83%88%0A%20%20%20%20%20%20%20%20%20%20%20%20left%20%3D%20pivot%20%2B%201%20%20%23%20%E6%9C%AA%E3%82%BD%E3%83%BC%E3%83%88%E5%8C%BA%E9%96%93%E3%81%AE%E6%AE%8B%E3%82%8A%E3%81%AF%20%5Bpivot%20%2B%201%2C%20right%5D%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20quick_sort%28nums%2C%20pivot%20%2B%201%2C%20right%29%20%20%23%20%E5%8F%B3%E9%83%A8%E5%88%86%E9%85%8D%E5%88%97%E3%82%92%E5%86%8D%E5%B8%B0%E7%9A%84%E3%81%AB%E3%82%BD%E3%83%BC%E3%83%88%0A%20%20%20%20%20%20%20%20%20%20%20%20right%20%3D%20pivot%20-%201%20%20%23%20%E6%9C%AA%E3%82%BD%E3%83%BC%E3%83%88%E5%8C%BA%E9%96%93%E3%81%AE%E6%AE%8B%E3%82%8A%E3%81%AF%20%5Bleft%2C%20pivot%20-%201%5D%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E3%82%AF%E3%82%A4%E3%83%83%E3%82%AF%E3%82%BD%E3%83%BC%E3%83%88%EF%BC%88%E6%9C%AB%E5%B0%BE%E5%86%8D%E5%B8%B0%E6%9C%80%E9%81%A9%E5%8C%96%EF%BC%89%0A%20%20%20%20nums%20%3D%20%5B2%2C%204%2C%201%2C%200%2C%203%2C%205%5D%0A%20%20%20%20quick_sort%28nums%2C%200%2C%20len%28nums%29%20-%201%29%0A%20%20%20%20print%28%22%E3%82%AF%E3%82%A4%E3%83%83%E3%82%AF%E3%82%BD%E3%83%BC%E3%83%88%EF%BC%88%E6%9C%AB%E5%B0%BE%E5%86%8D%E5%B8%B0%E6%9C%80%E9%81%A9%E5%8C%96%EF%BC%89%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%22%2C%20nums%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 
 <!-- Source file information -->
 
diff --git a/ja/chapter_sorting/radix_sort/index.html b/ja/chapter_sorting/radix_sort/index.html
index e60293b7c..f73d9162f 100644
--- a/ja/chapter_sorting/radix_sort/index.html
+++ b/ja/chapter_sorting/radix_sort/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1635,7 +1635,7 @@
   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1942,7 +1942,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2105,7 +2105,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2491,7 +2491,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2547,7 +2547,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2575,7 +2575,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3035,7 +3035,7 @@
   <a href="#11101" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.10.1 &nbsp; アルゴリズムの過程
+        11.10.1 &nbsp; アルゴリズムの流れ
       
     </span>
   </a>
@@ -3185,7 +3185,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3241,7 +3241,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3269,7 +3269,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3462,7 +3462,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3490,7 +3490,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3631,7 +3631,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3659,7 +3659,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3687,7 +3687,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3715,7 +3715,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3908,7 +3908,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4153,7 +4153,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4299,7 +4299,7 @@
   <a href="#11101" class="md-nav__link">
     <span class="md-ellipsis">
       
-        11.10.1 &nbsp; アルゴリズムの過程
+        11.10.1 &nbsp; アルゴリズムの流れ
       
     </span>
   </a>
@@ -4355,262 +4355,709 @@
 
 <!-- Page content -->
 <h1 id="1110">11.10 &nbsp; 基数ソート<a class="headerlink" href="#1110" title="Permanent link">&para;</a></h1>
-<p>前の節では計数ソートを紹介しました。これは、データサイズ <span class="arithmatex">\(n\)</span> が大きいがデータ範囲 <span class="arithmatex">\(m\)</span> が小さいシナリオに適しています。<span class="arithmatex">\(n = 10^6\)</span> の学生IDをソートする必要があり、各IDが <span class="arithmatex">\(8\)</span> 桁の数字であるとします。これは、データ範囲 <span class="arithmatex">\(m = 10^8\)</span> が非常に大きいことを意味します。この場合、計数ソートを使用すると、大量のメモリスペースが必要になります。基数ソートはこの状況を回避できます。</p>
-<p><u>基数ソート</u>は計数ソートと同じ核心概念を共有し、要素の頻度をカウントすることでソートします。同時に、基数ソートは数字の桁間の漸進的関係を利用してこれを基盤としています。桁を一度に一つずつ処理してソートし、最終的なソート順序を達成します。</p>
-<h2 id="11101">11.10.1 &nbsp; アルゴリズムの過程<a class="headerlink" href="#11101" title="Permanent link">&para;</a></h2>
-<p>学生IDデータを例として、最下位桁を <span class="arithmatex">\(1\)</span> 番目、最上位桁を <span class="arithmatex">\(8\)</span> 番目とすると、基数ソートの過程は以下の図に示されています。</p>
+<p>前節では計数ソートを紹介しました。これは、データ量 <span class="arithmatex">\(n\)</span> が大きく、データ範囲 <span class="arithmatex">\(m\)</span> が小さい場合に適しています。<span class="arithmatex">\(n = 10^6\)</span> 個の学籍番号をソートすると仮定すると、学籍番号は <span class="arithmatex">\(8\)</span> 桁の数字なので、データ範囲 <span class="arithmatex">\(m = 10^8\)</span> は非常に大きくなります。計数ソートでは大量のメモリ空間を確保する必要がありますが、基数ソートではこの問題を回避できます。</p>
+<p><u>基数ソート（radix sort）</u>の基本的な考え方は計数ソートと同じで、個数を数えることによってソートを実現します。そのうえで、基数ソートは各桁の段階的な関係を利用し、各桁を順にソートすることで、最終的なソート結果を得ます。</p>
+<h2 id="11101">11.10.1 &nbsp; アルゴリズムの流れ<a class="headerlink" href="#11101" title="Permanent link">&para;</a></h2>
+<p>学籍番号データを例にすると、数字の最下位桁を第 <span class="arithmatex">\(1\)</span> 位、最上位桁を第 <span class="arithmatex">\(8\)</span> 位としたとき、基数ソートの流れは次図のようになります。</p>
 <ol>
-<li>桁 <span class="arithmatex">\(k = 1\)</span> を初期化します。</li>
-<li>学生IDの <span class="arithmatex">\(k\)</span> 番目の桁に対して「計数ソート」を実行します。完了後、データは <span class="arithmatex">\(k\)</span> 番目の桁に基づいて最小から最大までソートされます。</li>
-<li><span class="arithmatex">\(k\)</span> を <span class="arithmatex">\(1\)</span> 増やし、手順 <code>2.</code> に戻って反復を続け、すべての桁がソートされるまで続けます。この時点で過程が終了します。</li>
+<li>桁番号 <span class="arithmatex">\(k = 1\)</span> を初期化します。</li>
+<li>学籍番号の第 <span class="arithmatex">\(k\)</span> 位に対して「計数ソート」を実行します。完了すると、データは第 <span class="arithmatex">\(k\)</span> 位に従って昇順に並びます。</li>
+<li><span class="arithmatex">\(k\)</span> を <span class="arithmatex">\(1\)</span> 増やし、手順 <code>2.</code> に戻って反復を続けます。すべての桁のソートが完了したら終了します。</li>
 </ol>
-<p><img alt="基数ソートアルゴリズムの過程" class="animation-figure" src="../radix_sort.assets/radix_sort_overview.png" /></p>
-<p align="center"> 図 11-18 &nbsp; 基数ソートアルゴリズムの過程 </p>
+<p><img alt="基数ソートのアルゴリズムの流れ" class="animation-figure" src="../radix_sort.assets/radix_sort_overview.png" /></p>
+<p align="center"> 図 11-18 &nbsp; 基数ソートのアルゴリズムの流れ </p>
 
-<p>以下、コード実装を詳しく見てみます。基数 <span class="arithmatex">\(d\)</span> での数 <span class="arithmatex">\(x\)</span> に対して、その <span class="arithmatex">\(k\)</span> 番目の桁 <span class="arithmatex">\(x_k\)</span> を取得するには、以下の計算式を使用できます：</p>
+<p>以下ではコード実装を分解して見ていきます。<span class="arithmatex">\(d\)</span> 進数の数値 <span class="arithmatex">\(x\)</span> について、その第 <span class="arithmatex">\(k\)</span> 位 <span class="arithmatex">\(x_k\)</span> を取得するには、次の計算式を用います。</p>
 <div class="arithmatex">\[
 x_k = \lfloor\frac{x}{d^{k-1}}\rfloor \bmod d
 \]</div>
-<p>ここで <span class="arithmatex">\(\lfloor a \rfloor\)</span> は浮動小数点数 <span class="arithmatex">\(a\)</span> の切り捨てを表し、<span class="arithmatex">\(\bmod \: d\)</span> は <span class="arithmatex">\(d\)</span> による剰余を表します。学生IDデータの場合、<span class="arithmatex">\(d = 10\)</span> で <span class="arithmatex">\(k \in [1, 8]\)</span> です。</p>
-<p>さらに、<span class="arithmatex">\(k\)</span> 番目の桁に基づいてソートできるように、計数ソートのコードを少し修正する必要があります：</p>
+<p>ここで、<span class="arithmatex">\(\lfloor a \rfloor\)</span> は浮動小数点数 <span class="arithmatex">\(a\)</span> の切り捨てを表し、<span class="arithmatex">\(\bmod \: d\)</span> は <span class="arithmatex">\(d\)</span> による剰余を表します。学籍番号データでは、<span class="arithmatex">\(d = 10\)</span> かつ <span class="arithmatex">\(k \in [1, 8]\)</span> です。</p>
+<p>さらに、数字の第 <span class="arithmatex">\(k\)</span> 位に基づいてソートできるように、計数ソートのコードを少し変更する必要があります。</p>
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 <div class="highlight"><span class="filename">radix_sort.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">digit</span><span class="p">(</span><span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">exp</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;要素 num の k 番目の桁を取得、exp = 10^(k-1)&quot;&quot;&quot;</span>
-<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># k の代わりに exp を渡すことで、ここでコストの高い累乗計算を避けることができる</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;要素 num の下から k 桁目を取得（exp = 10^(k-1)）&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># ここで高コストな累乗計算を繰り返さないよう、k ではなく exp を渡す</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">return</span> <span class="p">(</span><span class="n">num</span> <span class="o">//</span> <span class="n">exp</span><span class="p">)</span> <span class="o">%</span> <span class="mi">10</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="k">def</span><span class="w"> </span><span class="nf">counting_sort_digit</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">exp</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;計数ソート（nums の k 番目の桁に基づく）&quot;&quot;&quot;</span>
-<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="c1"># 10進数の桁の範囲は 0~9、したがって長さ10のバケット配列が必要</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;計数ソート（nums の k 桁目でソート）&quot;&quot;&quot;</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="c1"># 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要</span>
 <a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="n">counter</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">10</span>
 <a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
-<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="c1"># 数字 0~9 の出現回数を統計</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="c1"># 0~9 の各数字の出現回数を集計する</span>
 <a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
-<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="n">d</span> <span class="o">=</span> <span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">exp</span><span class="p">)</span>  <span class="c1"># nums[i] の k 番目の桁を取得、d とする</span>
-<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>        <span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>  <span class="c1"># 数字 d の出現回数を統計</span>
-<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="c1"># 前置和を計算し、「出現回数」を「配列インデックス」に変換</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="n">d</span> <span class="o">=</span> <span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">exp</span><span class="p">)</span>  <span class="c1"># nums[i] の第 k 位を取得し、d とする</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>        <span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>  <span class="c1"># 数字 d の出現回数を数える</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="c1"># 累積和を求め、「出現回数」を「配列インデックス」に変換する</span>
 <a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">):</span>
 <a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>        <span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">+=</span> <span class="n">counter</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span>
-<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>    <span class="c1"># 逆順に走査し、バケット統計に基づいて各要素を res に配置</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>    <span class="c1"># 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する</span>
 <a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span>
 <a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
 <a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>        <span class="n">d</span> <span class="o">=</span> <span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">exp</span><span class="p">)</span>
-<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>        <span class="n">j</span> <span class="o">=</span> <span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># 配列内の d のインデックス j を取得</span>
-<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a>        <span class="n">res</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>  <span class="c1"># 現在の要素をインデックス j に配置</span>
-<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>        <span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span> <span class="o">-=</span> <span class="mi">1</span>  <span class="c1"># d の数を1減らす</span>
-<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>    <span class="c1"># 結果を使用して元の配列 nums を上書き</span>
+<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>        <span class="n">j</span> <span class="o">=</span> <span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># d の配列内インデックス j を取得する</span>
+<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a>        <span class="n">res</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>  <span class="c1"># 現在の要素をインデックス j に格納する</span>
+<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>        <span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span> <span class="o">-=</span> <span class="mi">1</span>  <span class="c1"># d の個数を 1 減らす</span>
+<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>    <span class="c1"># 結果で元の配列 nums を上書きする</span>
 <a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
 <a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>        <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
 <a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a>
 <a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a><span class="k">def</span><span class="w"> </span><span class="nf">radix_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
 <a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;基数ソート&quot;&quot;&quot;</span>
-<a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a>    <span class="c1"># 配列の最大要素を取得し、最大桁数を判定するために使用</span>
+<a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a>    <span class="c1"># 最大桁数の判定用に配列の最大要素を取得</span>
 <a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a>    <span class="n">m</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
-<a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a>    <span class="c1"># 最下位桁から最上位桁まで走査</span>
+<a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a>    <span class="c1"># 下位桁から上位桁の順に走査する</span>
 <a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a>    <span class="n">exp</span> <span class="o">=</span> <span class="mi">1</span>
 <a id="__codelineno-0-35" name="__codelineno-0-35" href="#__codelineno-0-35"></a>    <span class="k">while</span> <span class="n">exp</span> <span class="o">&lt;=</span> <span class="n">m</span><span class="p">:</span>
-<a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a>        <span class="c1"># 配列要素の k 番目の桁に対して計数ソートを実行</span>
+<a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a>        <span class="c1"># 配列要素の k 桁目に対して計数ソートを行う</span>
 <a id="__codelineno-0-37" name="__codelineno-0-37" href="#__codelineno-0-37"></a>        <span class="c1"># k = 1 -&gt; exp = 1</span>
 <a id="__codelineno-0-38" name="__codelineno-0-38" href="#__codelineno-0-38"></a>        <span class="c1"># k = 2 -&gt; exp = 10</span>
-<a id="__codelineno-0-39" name="__codelineno-0-39" href="#__codelineno-0-39"></a>        <span class="c1"># つまり、exp = 10^(k-1)</span>
+<a id="__codelineno-0-39" name="__codelineno-0-39" href="#__codelineno-0-39"></a>        <span class="c1"># つまり exp = 10^(k-1)</span>
 <a id="__codelineno-0-40" name="__codelineno-0-40" href="#__codelineno-0-40"></a>        <span class="n">counting_sort_digit</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">exp</span><span class="p">)</span>
 <a id="__codelineno-0-41" name="__codelineno-0-41" href="#__codelineno-0-41"></a>        <span class="n">exp</span> <span class="o">*=</span> <span class="mi">10</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">radix_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 要素numのk番目の桁を取得、exp = 10^(k-1) */</span>
+<div class="highlight"><span class="filename">radix_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 要素 num の下から k 桁目を取得（exp = 10^(k-1)） */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">digit</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// kの代わりにexpを渡すことで、ここで繰り返される高価な冪乗計算を避けることができる</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// ここで高コストな累乗計算を繰り返さないよう、k ではなく exp を渡す</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">10</span><span class="p">;</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="p">}</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a>
-<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="cm">/* カウントソート（numsのk番目の桁に基づく） */</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="cm">/* 計数ソート（nums の k 桁目でソート） */</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="kt">void</span><span class="w"> </span><span class="nf">countingSortDigit</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="c1">// 10進数の桁範囲は0~9なので、長さ10のバケット配列が必要</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="c1">// 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">counter</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
-<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="c1">// 数字0~9の出現回数を統計</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="c1">// 0~9 の各数字の出現回数を集計する</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span><span class="w"> </span><span class="c1">// nums[i]のk番目の桁を取得、dとして記録</span>
-<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="o">++</span><span class="p">;</span><span class="w">                </span><span class="c1">// 数字dの出現回数を統計</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span><span class="w"> </span><span class="c1">// nums[i] の第 k 位を取得し、d とする</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="o">++</span><span class="p">;</span><span class="w">                </span><span class="c1">// 数字 d の出現回数を数える</span>
 <a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="c1">// 前缀和を計算し、「出現回数」を「配列インデックス」に変換</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="c1">// 累積和を求め、「出現回数」を「配列インデックス」に変換する</span>
 <a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">10</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
 <a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">    </span><span class="c1">// 逆順で走査し、バケット統計に基づいて各要素をresに配置</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">    </span><span class="c1">// 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する</span>
 <a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
 <a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span>
-<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// dが配列内にあるインデックスjを取得</span>
-<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span><span class="w">       </span><span class="c1">// 現在の要素をインデックスjに配置</span>
-<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="o">--</span><span class="p">;</span><span class="w">           </span><span class="c1">// dのカウントを1減らす</span>
+<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// d の配列内インデックス j を取得する</span>
+<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span><span class="w">       </span><span class="c1">// 現在の要素をインデックス j に格納する</span>
+<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="o">--</span><span class="p">;</span><span class="w">           </span><span class="c1">// d の個数を 1 減らす</span>
 <a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="w">    </span><span class="c1">// 結果で元の配列numsを上書き</span>
+<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="w">    </span><span class="c1">// 結果で元の配列 nums を上書きする</span>
 <a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
 <a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
 <a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="p">}</span>
 <a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a>
 <a id="__codelineno-1-34" name="__codelineno-1-34" href="#__codelineno-1-34"></a><span class="cm">/* 基数ソート */</span>
 <a id="__codelineno-1-35" name="__codelineno-1-35" href="#__codelineno-1-35"></a><span class="kt">void</span><span class="w"> </span><span class="nf">radixSort</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-36" name="__codelineno-1-36" href="#__codelineno-1-36"></a><span class="w">    </span><span class="c1">// 配列の最大要素を取得、最大桁数を判定するために使用</span>
+<a id="__codelineno-1-36" name="__codelineno-1-36" href="#__codelineno-1-36"></a><span class="w">    </span><span class="c1">// 最大桁数の判定用に配列の最大要素を取得</span>
 <a id="__codelineno-1-37" name="__codelineno-1-37" href="#__codelineno-1-37"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">*</span><span class="n">max_element</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">end</span><span class="p">());</span>
-<a id="__codelineno-1-38" name="__codelineno-1-38" href="#__codelineno-1-38"></a><span class="w">    </span><span class="c1">// 最下位桁から最上位桁まで走査</span>
+<a id="__codelineno-1-38" name="__codelineno-1-38" href="#__codelineno-1-38"></a><span class="w">    </span><span class="c1">// 下位桁から上位桁の順に走査する</span>
 <a id="__codelineno-1-39" name="__codelineno-1-39" href="#__codelineno-1-39"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span>
-<a id="__codelineno-1-40" name="__codelineno-1-40" href="#__codelineno-1-40"></a><span class="w">        </span><span class="c1">// 配列要素のk番目の桁でカウントソートを実行</span>
+<a id="__codelineno-1-40" name="__codelineno-1-40" href="#__codelineno-1-40"></a><span class="w">        </span><span class="c1">// 配列要素の k 桁目に対して計数ソートを行う</span>
 <a id="__codelineno-1-41" name="__codelineno-1-41" href="#__codelineno-1-41"></a><span class="w">        </span><span class="c1">// k = 1 -&gt; exp = 1</span>
 <a id="__codelineno-1-42" name="__codelineno-1-42" href="#__codelineno-1-42"></a><span class="w">        </span><span class="c1">// k = 2 -&gt; exp = 10</span>
-<a id="__codelineno-1-43" name="__codelineno-1-43" href="#__codelineno-1-43"></a><span class="w">        </span><span class="c1">// つまり、exp = 10^(k-1)</span>
+<a id="__codelineno-1-43" name="__codelineno-1-43" href="#__codelineno-1-43"></a><span class="w">        </span><span class="c1">// つまり exp = 10^(k-1)</span>
 <a id="__codelineno-1-44" name="__codelineno-1-44" href="#__codelineno-1-44"></a><span class="w">        </span><span class="n">countingSortDigit</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span>
 <a id="__codelineno-1-45" name="__codelineno-1-45" href="#__codelineno-1-45"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">radix_sort.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 要素 num の k 番目の桁を取得、exp = 10^(k-1) */</span>
+<div class="highlight"><span class="filename">radix_sort.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 要素 num の下から k 桁目を取得（exp = 10^(k-1)） */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">digit</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// k の代わりに exp を渡すことで、ここでコストの高い累乗計算の繰り返しを避けることができる</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// ここで高コストな累乗計算を繰り返さないよう、k ではなく exp を渡す</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">10</span><span class="p">;</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="p">}</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a>
-<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="cm">/* 計数ソート（nums の k 番目の桁に基づく） */</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="cm">/* 計数ソート（nums の k 桁目でソート） */</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="kt">void</span><span class="w"> </span><span class="nf">countingSortDigit</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="c1">// 10進数の桁の範囲は 0~9、したがって長さ 10 のバケット配列が必要</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="c1">// 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="mi">10</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
-<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="c1">// 桁 0~9 の出現回数を統計</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="c1">// 0~9 の各数字の出現回数を集計する</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span><span class="w"> </span><span class="c1">// nums[i] の k 番目の桁を取得、d とする</span>
-<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="n">counter</span><span class="o">[</span><span class="n">d</span><span class="o">]++</span><span class="p">;</span><span class="w">                </span><span class="c1">// 桁 d の出現回数を統計</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span><span class="w"> </span><span class="c1">// nums[i] の第 k 位を取得し、d とする</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="n">counter</span><span class="o">[</span><span class="n">d</span><span class="o">]++</span><span class="p">;</span><span class="w">                </span><span class="c1">// 数字 d の出現回数を数える</span>
 <a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">    </span><span class="c1">// 累積和を計算し、「出現回数」を「配列インデックス」に変換</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">    </span><span class="c1">// 累積和を求め、「出現回数」を「配列インデックス」に変換する</span>
 <a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">10</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">        </span><span class="n">counter</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">counter</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">    </span><span class="c1">// 逆順に走査し、バケット統計に基づいて各要素を res に配置</span>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">    </span><span class="c1">// 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する</span>
 <a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span>
-<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">counter</span><span class="o">[</span><span class="n">d</span><span class="o">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 配列内での d のインデックス j を取得</span>
-<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w">        </span><span class="n">res</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span><span class="w">       </span><span class="c1">// 現在の要素をインデックス j に配置</span>
-<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w">        </span><span class="n">counter</span><span class="o">[</span><span class="n">d</span><span class="o">]--</span><span class="p">;</span><span class="w">           </span><span class="c1">// d のカウントを 1 減らす</span>
+<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">counter</span><span class="o">[</span><span class="n">d</span><span class="o">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// d の配列内インデックス j を取得する</span>
+<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w">        </span><span class="n">res</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span><span class="w">       </span><span class="c1">// 現在の要素をインデックス j に格納する</span>
+<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w">        </span><span class="n">counter</span><span class="o">[</span><span class="n">d</span><span class="o">]--</span><span class="p">;</span><span class="w">           </span><span class="c1">// d の個数を 1 減らす</span>
 <a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="w">    </span><span class="c1">// 結果で元の配列 nums を上書き</span>
+<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="w">    </span><span class="c1">// 結果で元の配列 nums を上書きする</span>
 <a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
 <a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="p">}</span>
 <a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a>
 <a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a><span class="cm">/* 基数ソート */</span>
 <a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a><span class="kt">void</span><span class="w"> </span><span class="nf">radixSort</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a><span class="w">    </span><span class="c1">// 配列の最大要素を取得し、最大桁数を判定するために使用</span>
+<a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a><span class="w">    </span><span class="c1">// 最大桁数の判定用に配列の最大要素を取得</span>
 <a id="__codelineno-2-37" name="__codelineno-2-37" href="#__codelineno-2-37"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Integer</span><span class="p">.</span><span class="na">MIN_VALUE</span><span class="p">;</span>
 <a id="__codelineno-2-38" name="__codelineno-2-38" href="#__codelineno-2-38"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span>
 <a id="__codelineno-2-39" name="__codelineno-2-39" href="#__codelineno-2-39"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">m</span><span class="p">)</span>
 <a id="__codelineno-2-40" name="__codelineno-2-40" href="#__codelineno-2-40"></a><span class="w">            </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-2-41" name="__codelineno-2-41" href="#__codelineno-2-41"></a><span class="w">    </span><span class="c1">// 最下位桁から最上位桁まで走査</span>
+<a id="__codelineno-2-41" name="__codelineno-2-41" href="#__codelineno-2-41"></a><span class="w">    </span><span class="c1">// 下位桁から上位桁の順に走査する</span>
 <a id="__codelineno-2-42" name="__codelineno-2-42" href="#__codelineno-2-42"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-43" name="__codelineno-2-43" href="#__codelineno-2-43"></a><span class="w">        </span><span class="c1">// 配列要素の k 番目の桁に対して計数ソートを実行</span>
+<a id="__codelineno-2-43" name="__codelineno-2-43" href="#__codelineno-2-43"></a><span class="w">        </span><span class="c1">// 配列要素の k 桁目に対して計数ソートを行う</span>
 <a id="__codelineno-2-44" name="__codelineno-2-44" href="#__codelineno-2-44"></a><span class="w">        </span><span class="c1">// k = 1 -&gt; exp = 1</span>
 <a id="__codelineno-2-45" name="__codelineno-2-45" href="#__codelineno-2-45"></a><span class="w">        </span><span class="c1">// k = 2 -&gt; exp = 10</span>
-<a id="__codelineno-2-46" name="__codelineno-2-46" href="#__codelineno-2-46"></a><span class="w">        </span><span class="c1">// すなわち exp = 10^(k-1)</span>
+<a id="__codelineno-2-46" name="__codelineno-2-46" href="#__codelineno-2-46"></a><span class="w">        </span><span class="c1">// つまり exp = 10^(k-1)</span>
 <a id="__codelineno-2-47" name="__codelineno-2-47" href="#__codelineno-2-47"></a><span class="w">        </span><span class="n">countingSortDigit</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span>
 <a id="__codelineno-2-48" name="__codelineno-2-48" href="#__codelineno-2-48"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-2-49" name="__codelineno-2-49" href="#__codelineno-2-49"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">radix_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">radix_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Digit</span><span class="p">}</span>
-<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
-<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">radix_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">CountingSortDigit</span><span class="p">}</span>
-<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a>
-<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="na">[class]</span><span class="p">{</span><span class="n">radix_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">RadixSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">radix_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 要素 num の下から k 桁目を取得（exp = 10^(k-1)） */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Digit</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="c1">// ここで高コストな累乗計算を繰り返さないよう、k ではなく exp を渡す</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">10</span><span class="p">;</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="p">}</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="cm">/* 計数ソート（nums の k 桁目でソート） */</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="k">void</span><span class="w"> </span><span class="nf">CountingSortDigit</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="c1">// 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">    </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="mi">10</span><span class="p">];</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">    </span><span class="c1">// 0~9 の各数字の出現回数を集計する</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Digit</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span><span class="w"> </span><span class="c1">// nums[i] の第 k 位を取得し、d とする</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="o">++</span><span class="p">;</span><span class="w">                </span><span class="c1">// 数字 d の出現回数を数える</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">    </span><span class="c1">// 累積和を求め、「出現回数」を「配列インデックス」に変換する</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">10</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w">    </span><span class="c1">// 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する</span>
+<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="w">    </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Digit</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span>
+<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// d の配列内インデックス j を取得する</span>
+<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span><span class="w">       </span><span class="c1">// 現在の要素をインデックス j に格納する</span>
+<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="o">--</span><span class="p">;</span><span class="w">           </span><span class="c1">// d の個数を 1 減らす</span>
+<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a><span class="w">    </span><span class="c1">// 結果で元の配列 nums を上書きする</span>
+<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-31" name="__codelineno-3-31" href="#__codelineno-3-31"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-3-32" name="__codelineno-3-32" href="#__codelineno-3-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-33" name="__codelineno-3-33" href="#__codelineno-3-33"></a><span class="p">}</span>
+<a id="__codelineno-3-34" name="__codelineno-3-34" href="#__codelineno-3-34"></a>
+<a id="__codelineno-3-35" name="__codelineno-3-35" href="#__codelineno-3-35"></a><span class="cm">/* 基数ソート */</span>
+<a id="__codelineno-3-36" name="__codelineno-3-36" href="#__codelineno-3-36"></a><span class="k">void</span><span class="w"> </span><span class="nf">RadixSort</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-37" name="__codelineno-3-37" href="#__codelineno-3-37"></a><span class="w">    </span><span class="c1">// 最大桁数の判定用に配列の最大要素を取得</span>
+<a id="__codelineno-3-38" name="__codelineno-3-38" href="#__codelineno-3-38"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kt">int</span><span class="p">.</span><span class="n">MinValue</span><span class="p">;</span>
+<a id="__codelineno-3-39" name="__codelineno-3-39" href="#__codelineno-3-39"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-40" name="__codelineno-3-40" href="#__codelineno-3-40"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-3-41" name="__codelineno-3-41" href="#__codelineno-3-41"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-42" name="__codelineno-3-42" href="#__codelineno-3-42"></a><span class="w">    </span><span class="c1">// 下位桁から上位桁の順に走査する</span>
+<a id="__codelineno-3-43" name="__codelineno-3-43" href="#__codelineno-3-43"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-44" name="__codelineno-3-44" href="#__codelineno-3-44"></a><span class="w">        </span><span class="c1">// 配列要素の k 桁目に対して計数ソートを行う</span>
+<a id="__codelineno-3-45" name="__codelineno-3-45" href="#__codelineno-3-45"></a><span class="w">        </span><span class="c1">// k = 1 -&gt; exp = 1</span>
+<a id="__codelineno-3-46" name="__codelineno-3-46" href="#__codelineno-3-46"></a><span class="w">        </span><span class="c1">// k = 2 -&gt; exp = 10</span>
+<a id="__codelineno-3-47" name="__codelineno-3-47" href="#__codelineno-3-47"></a><span class="w">        </span><span class="c1">// つまり exp = 10^(k-1)</span>
+<a id="__codelineno-3-48" name="__codelineno-3-48" href="#__codelineno-3-48"></a><span class="w">        </span><span class="n">CountingSortDigit</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span>
+<a id="__codelineno-3-49" name="__codelineno-3-49" href="#__codelineno-3-49"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-50" name="__codelineno-3-50" href="#__codelineno-3-50"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">radix_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">digit</span><span class="p">}</span>
-<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
-<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">countingSortDigit</span><span class="p">}</span>
-<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a>
-<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">radixSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">radix_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 要素 num の下から k 桁目を取得（exp = 10^(k-1)） */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">digit</span><span class="p">(</span><span class="nx">num</span><span class="p">,</span><span class="w"> </span><span class="nx">exp</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// ここで高コストな累乗計算を繰り返さないよう、k ではなく exp を渡す</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="nx">num</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nx">exp</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">10</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="p">}</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="cm">/* 計数ソート（nums の k 桁目でソート） */</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="kd">func</span><span class="w"> </span><span class="nx">countingSortDigit</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">exp</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="c1">// 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">    </span><span class="nx">counter</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">    </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">    </span><span class="c1">// 0~9 の各数字の出現回数を集計する</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">        </span><span class="nx">d</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">digit</span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">exp</span><span class="p">)</span><span class="w"> </span><span class="c1">// nums[i] の第 k 位を取得し、d とする</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">        </span><span class="nx">counter</span><span class="p">[</span><span class="nx">d</span><span class="p">]</span><span class="o">++</span><span class="w">             </span><span class="c1">// 数字 d の出現回数を数える</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">    </span><span class="c1">// 累積和を求め、「出現回数」を「配列インデックス」に変換する</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">10</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w">        </span><span class="nx">counter</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">counter</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w">    </span><span class="c1">// 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w">    </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="w">        </span><span class="nx">d</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">digit</span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">exp</span><span class="p">)</span>
+<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="w">        </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">counter</span><span class="p">[</span><span class="nx">d</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// d の配列内インデックス j を取得する</span>
+<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="w">        </span><span class="nx">res</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w">    </span><span class="c1">// 現在の要素をインデックス j に格納する</span>
+<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w">        </span><span class="nx">counter</span><span class="p">[</span><span class="nx">d</span><span class="p">]</span><span class="o">--</span><span class="w">        </span><span class="c1">// d の個数を 1 減らす</span>
+<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="w">    </span><span class="c1">// 結果で元の配列 nums を上書きする</span>
+<a id="__codelineno-4-30" name="__codelineno-4-30" href="#__codelineno-4-30"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-31" name="__codelineno-4-31" href="#__codelineno-4-31"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">res</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
+<a id="__codelineno-4-32" name="__codelineno-4-32" href="#__codelineno-4-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-33" name="__codelineno-4-33" href="#__codelineno-4-33"></a><span class="p">}</span>
+<a id="__codelineno-4-34" name="__codelineno-4-34" href="#__codelineno-4-34"></a>
+<a id="__codelineno-4-35" name="__codelineno-4-35" href="#__codelineno-4-35"></a><span class="cm">/* 基数ソート */</span>
+<a id="__codelineno-4-36" name="__codelineno-4-36" href="#__codelineno-4-36"></a><span class="kd">func</span><span class="w"> </span><span class="nx">radixSort</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-37" name="__codelineno-4-37" href="#__codelineno-4-37"></a><span class="w">    </span><span class="c1">// 最大桁数の判定用に配列の最大要素を取得</span>
+<a id="__codelineno-4-38" name="__codelineno-4-38" href="#__codelineno-4-38"></a><span class="w">    </span><span class="nx">max</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">MinInt</span>
+<a id="__codelineno-4-39" name="__codelineno-4-39" href="#__codelineno-4-39"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-40" name="__codelineno-4-40" href="#__codelineno-4-40"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">max</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-41" name="__codelineno-4-41" href="#__codelineno-4-41"></a><span class="w">            </span><span class="nx">max</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">num</span>
+<a id="__codelineno-4-42" name="__codelineno-4-42" href="#__codelineno-4-42"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-43" name="__codelineno-4-43" href="#__codelineno-4-43"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-44" name="__codelineno-4-44" href="#__codelineno-4-44"></a><span class="w">    </span><span class="c1">// 下位桁から上位桁の順に走査する</span>
+<a id="__codelineno-4-45" name="__codelineno-4-45" href="#__codelineno-4-45"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">exp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">max</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">exp</span><span class="p">;</span><span class="w"> </span><span class="nx">exp</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">10</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-46" name="__codelineno-4-46" href="#__codelineno-4-46"></a><span class="w">        </span><span class="c1">// 配列要素の k 桁目に対して計数ソートを行う</span>
+<a id="__codelineno-4-47" name="__codelineno-4-47" href="#__codelineno-4-47"></a><span class="w">        </span><span class="c1">// k = 1 -&gt; exp = 1</span>
+<a id="__codelineno-4-48" name="__codelineno-4-48" href="#__codelineno-4-48"></a><span class="w">        </span><span class="c1">// k = 2 -&gt; exp = 10</span>
+<a id="__codelineno-4-49" name="__codelineno-4-49" href="#__codelineno-4-49"></a><span class="w">        </span><span class="c1">// つまり exp = 10^(k-1)</span>
+<a id="__codelineno-4-50" name="__codelineno-4-50" href="#__codelineno-4-50"></a><span class="w">        </span><span class="nx">countingSortDigit</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">exp</span><span class="p">)</span>
+<a id="__codelineno-4-51" name="__codelineno-4-51" href="#__codelineno-4-51"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-52" name="__codelineno-4-52" href="#__codelineno-4-52"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">radix_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">digit</span><span class="p">}</span>
-<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
-<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">countingSortDigit</span><span class="p">}</span>
-<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>
-<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">radixSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">radix_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 要素 num の下から k 桁目を取得（exp = 10^(k-1)） */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">digit</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// ここで高コストな累乗計算を繰り返さないよう、k ではなく exp を渡す</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">10</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="p">}</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="cm">/* 計数ソート（nums の k 桁目でソート） */</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="kd">func</span><span class="w"> </span><span class="nf">countingSortDigit</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">exp</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">    </span><span class="c1">// 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">counter</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">    </span><span class="c1">// 0~9 の各数字の出現回数を集計する</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">d</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">exp</span><span class="p">:</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="c1">// nums[i] の第 k 位を取得し、d とする</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// 数字 d の出現回数を数える</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">    </span><span class="c1">// 累積和を求め、「出現回数」を「配列インデックス」に変換する</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="mi">10</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="w">    </span><span class="c1">// 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する</span>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">count</span><span class="p">)</span>
+<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="p">.</span><span class="n">reversed</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">d</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">exp</span><span class="p">:</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span>
+<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// d の配列内インデックス j を取得する</span>
+<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="c1">// 現在の要素をインデックス j に格納する</span>
+<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// d の個数を 1 減らす</span>
+<a id="__codelineno-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a><span class="w">    </span><span class="c1">// 結果で元の配列 nums を上書きする</span>
+<a id="__codelineno-5-29" name="__codelineno-5-29" href="#__codelineno-5-29"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-30" name="__codelineno-5-30" href="#__codelineno-5-30"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-5-31" name="__codelineno-5-31" href="#__codelineno-5-31"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-32" name="__codelineno-5-32" href="#__codelineno-5-32"></a><span class="p">}</span>
+<a id="__codelineno-5-33" name="__codelineno-5-33" href="#__codelineno-5-33"></a>
+<a id="__codelineno-5-34" name="__codelineno-5-34" href="#__codelineno-5-34"></a><span class="cm">/* 基数ソート */</span>
+<a id="__codelineno-5-35" name="__codelineno-5-35" href="#__codelineno-5-35"></a><span class="kd">func</span><span class="w"> </span><span class="nf">radixSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-36" name="__codelineno-5-36" href="#__codelineno-5-36"></a><span class="w">    </span><span class="c1">// 最大桁数の判定用に配列の最大要素を取得</span>
+<a id="__codelineno-5-37" name="__codelineno-5-37" href="#__codelineno-5-37"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Int</span><span class="p">.</span><span class="bp">min</span>
+<a id="__codelineno-5-38" name="__codelineno-5-38" href="#__codelineno-5-38"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-39" name="__codelineno-5-39" href="#__codelineno-5-39"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-40" name="__codelineno-5-40" href="#__codelineno-5-40"></a><span class="w">            </span><span class="n">m</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-5-41" name="__codelineno-5-41" href="#__codelineno-5-41"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-42" name="__codelineno-5-42" href="#__codelineno-5-42"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-43" name="__codelineno-5-43" href="#__codelineno-5-43"></a><span class="w">    </span><span class="c1">// 下位桁から上位桁の順に走査する</span>
+<a id="__codelineno-5-44" name="__codelineno-5-44" href="#__codelineno-5-44"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">sequence</span><span class="p">(</span><span class="bp">first</span><span class="p">:</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="p">(</span><span class="nv">$0</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span><span class="w"> </span><span class="p">?</span><span class="w"> </span><span class="nv">$0</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">10</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">})</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-45" name="__codelineno-5-45" href="#__codelineno-5-45"></a><span class="w">        </span><span class="c1">// 配列要素の k 桁目に対して計数ソートを行う</span>
+<a id="__codelineno-5-46" name="__codelineno-5-46" href="#__codelineno-5-46"></a><span class="w">        </span><span class="c1">// k = 1 -&gt; exp = 1</span>
+<a id="__codelineno-5-47" name="__codelineno-5-47" href="#__codelineno-5-47"></a><span class="w">        </span><span class="c1">// k = 2 -&gt; exp = 10</span>
+<a id="__codelineno-5-48" name="__codelineno-5-48" href="#__codelineno-5-48"></a><span class="w">        </span><span class="c1">// つまり exp = 10^(k-1)</span>
+<a id="__codelineno-5-49" name="__codelineno-5-49" href="#__codelineno-5-49"></a><span class="w">        </span><span class="n">countingSortDigit</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">:</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span>
+<a id="__codelineno-5-50" name="__codelineno-5-50" href="#__codelineno-5-50"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-51" name="__codelineno-5-51" href="#__codelineno-5-51"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">radix_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">digit</span><span class="p">}</span>
-<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
-<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">countingSortDigit</span><span class="p">}</span>
-<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a>
-<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">radixSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">radix_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 要素 num の下から k 桁目を取得（exp = 10^(k-1)） */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">digit</span><span class="p">(</span><span class="nx">num</span><span class="p">,</span><span class="w"> </span><span class="nx">exp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="c1">// ここで高コストな累乗計算を繰り返さないよう、k ではなく exp を渡す</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nx">num</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nx">exp</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mf">10</span><span class="p">;</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="p">}</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="cm">/* 計数ソート（nums の k 桁目でソート） */</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="kd">function</span><span class="w"> </span><span class="nx">countingSortDigit</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">exp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">    </span><span class="c1">// 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mf">10</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">    </span><span class="c1">// 0~9 の各数字の出現回数を集計する</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">digit</span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">exp</span><span class="p">);</span><span class="w"> </span><span class="c1">// nums[i] の第 k 位を取得し、d とする</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">        </span><span class="nx">counter</span><span class="p">[</span><span class="nx">d</span><span class="p">]</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// 数字 d の出現回数を数える</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w">    </span><span class="c1">// 累積和を求め、「出現回数」を「配列インデックス」に変換する</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">10</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">        </span><span class="nx">counter</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">counter</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w">    </span><span class="c1">// 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する</span>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">digit</span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">exp</span><span class="p">);</span>
+<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">counter</span><span class="p">[</span><span class="nx">d</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// d の配列内インデックス j を取得する</span>
+<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="w">        </span><span class="nx">res</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span><span class="w"> </span><span class="c1">// 現在の要素をインデックス j に格納する</span>
+<a id="__codelineno-6-27" name="__codelineno-6-27" href="#__codelineno-6-27"></a><span class="w">        </span><span class="nx">counter</span><span class="p">[</span><span class="nx">d</span><span class="p">]</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// d の個数を 1 減らす</span>
+<a id="__codelineno-6-28" name="__codelineno-6-28" href="#__codelineno-6-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-29" name="__codelineno-6-29" href="#__codelineno-6-29"></a><span class="w">    </span><span class="c1">// 結果で元の配列 nums を上書きする</span>
+<a id="__codelineno-6-30" name="__codelineno-6-30" href="#__codelineno-6-30"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-31" name="__codelineno-6-31" href="#__codelineno-6-31"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">res</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-6-32" name="__codelineno-6-32" href="#__codelineno-6-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-33" name="__codelineno-6-33" href="#__codelineno-6-33"></a><span class="p">}</span>
+<a id="__codelineno-6-34" name="__codelineno-6-34" href="#__codelineno-6-34"></a>
+<a id="__codelineno-6-35" name="__codelineno-6-35" href="#__codelineno-6-35"></a><span class="cm">/* 基数ソート */</span>
+<a id="__codelineno-6-36" name="__codelineno-6-36" href="#__codelineno-6-36"></a><span class="kd">function</span><span class="w"> </span><span class="nx">radixSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-37" name="__codelineno-6-37" href="#__codelineno-6-37"></a><span class="w">    </span><span class="c1">// 最大桁数の判定用に配列の最大要素を取得</span>
+<a id="__codelineno-6-38" name="__codelineno-6-38" href="#__codelineno-6-38"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">max</span><span class="p">(...</span><span class="w"> </span><span class="nx">nums</span><span class="p">);</span>
+<a id="__codelineno-6-39" name="__codelineno-6-39" href="#__codelineno-6-39"></a><span class="w">    </span><span class="c1">// 下位桁から上位桁の順に走査する</span>
+<a id="__codelineno-6-40" name="__codelineno-6-40" href="#__codelineno-6-40"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">exp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">exp</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">exp</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mf">10</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-41" name="__codelineno-6-41" href="#__codelineno-6-41"></a><span class="w">        </span><span class="c1">// 配列要素の k 桁目に対して計数ソートを行う</span>
+<a id="__codelineno-6-42" name="__codelineno-6-42" href="#__codelineno-6-42"></a><span class="w">        </span><span class="c1">// k = 1 -&gt; exp = 1</span>
+<a id="__codelineno-6-43" name="__codelineno-6-43" href="#__codelineno-6-43"></a><span class="w">        </span><span class="c1">// k = 2 -&gt; exp = 10</span>
+<a id="__codelineno-6-44" name="__codelineno-6-44" href="#__codelineno-6-44"></a><span class="w">        </span><span class="c1">// つまり exp = 10^(k-1)</span>
+<a id="__codelineno-6-45" name="__codelineno-6-45" href="#__codelineno-6-45"></a><span class="w">        </span><span class="nx">countingSortDigit</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">exp</span><span class="p">);</span>
+<a id="__codelineno-6-46" name="__codelineno-6-46" href="#__codelineno-6-46"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-47" name="__codelineno-6-47" href="#__codelineno-6-47"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">radix_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">digit</span><span class="p">}</span>
-<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
-<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">countingSortDigit</span><span class="p">}</span>
-<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a>
-<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">radixSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">radix_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 要素 num の下から k 桁目を取得（exp = 10^(k-1)） */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">digit</span><span class="p">(</span><span class="nx">num</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">exp</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="c1">// ここで高コストな累乗計算を繰り返さないよう、k ではなく exp を渡す</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nx">num</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nx">exp</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mf">10</span><span class="p">;</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="p">}</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="cm">/* 計数ソート（nums の k 桁目でソート） */</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="kd">function</span><span class="w"> </span><span class="nx">countingSortDigit</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">exp</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="c1">// 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mf">10</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">    </span><span class="c1">// 0~9 の各数字の出現回数を集計する</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">digit</span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">exp</span><span class="p">);</span><span class="w"> </span><span class="c1">// nums[i] の第 k 位を取得し、d とする</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">        </span><span class="nx">counter</span><span class="p">[</span><span class="nx">d</span><span class="p">]</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// 数字 d の出現回数を数える</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">    </span><span class="c1">// 累積和を求め、「出現回数」を「配列インデックス」に変換する</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">10</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">        </span><span class="nx">counter</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">counter</span><span class="p">[</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="w">    </span><span class="c1">// 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">digit</span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">exp</span><span class="p">);</span>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">counter</span><span class="p">[</span><span class="nx">d</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// d の配列内インデックス j を取得する</span>
+<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="w">        </span><span class="nx">res</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span><span class="w"> </span><span class="c1">// 現在の要素をインデックス j に格納する</span>
+<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a><span class="w">        </span><span class="nx">counter</span><span class="p">[</span><span class="nx">d</span><span class="p">]</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// d の個数を 1 減らす</span>
+<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-29" name="__codelineno-7-29" href="#__codelineno-7-29"></a><span class="w">    </span><span class="c1">// 結果で元の配列 nums を上書きする</span>
+<a id="__codelineno-7-30" name="__codelineno-7-30" href="#__codelineno-7-30"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-31" name="__codelineno-7-31" href="#__codelineno-7-31"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">res</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-7-32" name="__codelineno-7-32" href="#__codelineno-7-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-33" name="__codelineno-7-33" href="#__codelineno-7-33"></a><span class="p">}</span>
+<a id="__codelineno-7-34" name="__codelineno-7-34" href="#__codelineno-7-34"></a>
+<a id="__codelineno-7-35" name="__codelineno-7-35" href="#__codelineno-7-35"></a><span class="cm">/* 基数ソート */</span>
+<a id="__codelineno-7-36" name="__codelineno-7-36" href="#__codelineno-7-36"></a><span class="kd">function</span><span class="w"> </span><span class="nx">radixSort</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-37" name="__codelineno-7-37" href="#__codelineno-7-37"></a><span class="w">    </span><span class="c1">// 最大桁数の判定用に配列の最大要素を取得</span>
+<a id="__codelineno-7-38" name="__codelineno-7-38" href="#__codelineno-7-38"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">m</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">max</span><span class="p">(...</span><span class="w"> </span><span class="nx">nums</span><span class="p">);</span>
+<a id="__codelineno-7-39" name="__codelineno-7-39" href="#__codelineno-7-39"></a><span class="w">    </span><span class="c1">// 下位桁から上位桁の順に走査する</span>
+<a id="__codelineno-7-40" name="__codelineno-7-40" href="#__codelineno-7-40"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">exp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">exp</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">exp</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mf">10</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-41" name="__codelineno-7-41" href="#__codelineno-7-41"></a><span class="w">        </span><span class="c1">// 配列要素の k 桁目に対して計数ソートを行う</span>
+<a id="__codelineno-7-42" name="__codelineno-7-42" href="#__codelineno-7-42"></a><span class="w">        </span><span class="c1">// k = 1 -&gt; exp = 1</span>
+<a id="__codelineno-7-43" name="__codelineno-7-43" href="#__codelineno-7-43"></a><span class="w">        </span><span class="c1">// k = 2 -&gt; exp = 10</span>
+<a id="__codelineno-7-44" name="__codelineno-7-44" href="#__codelineno-7-44"></a><span class="w">        </span><span class="c1">// つまり exp = 10^(k-1)</span>
+<a id="__codelineno-7-45" name="__codelineno-7-45" href="#__codelineno-7-45"></a><span class="w">        </span><span class="nx">countingSortDigit</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">exp</span><span class="p">);</span>
+<a id="__codelineno-7-46" name="__codelineno-7-46" href="#__codelineno-7-46"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-47" name="__codelineno-7-47" href="#__codelineno-7-47"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">radix_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">digit</span><span class="p">}</span>
-<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
-<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">countingSortDigit</span><span class="p">}</span>
-<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a>
-<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">radixSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">radix_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 要素 `_num` の第 k 桁を取得する。ここで `exp = 10^(k-1)` */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="c1">// ここで高コストな累乗計算を繰り返さないよう、k ではなく exp を渡す</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">_num</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="m">10</span><span class="p">;</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="p">}</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="cm">/* 計数ソート（nums の k 桁目でソート） */</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="kt">void</span><span class="w"> </span><span class="n">countingSortDigit</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">  </span><span class="c1">// 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="m">10</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">  </span><span class="c1">// 0~9 の各数字の出現回数を集計する</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span><span class="w"> </span><span class="c1">// nums[i] の第 k 位を取得し、d とする</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">    </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// 数字 d の出現回数を数える</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">  </span><span class="c1">// 累積和を求め、「出現回数」を「配列インデックス」に変換する</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">10</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w">    </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">];</span>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="w">  </span><span class="c1">// 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する</span>
+<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span>
+<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// d の配列内インデックス j を取得する</span>
+<a id="__codelineno-8-26" name="__codelineno-8-26" href="#__codelineno-8-26"></a><span class="w">    </span><span class="n">res</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span><span class="w"> </span><span class="c1">// 現在の要素をインデックス j に格納する</span>
+<a id="__codelineno-8-27" name="__codelineno-8-27" href="#__codelineno-8-27"></a><span class="w">    </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// d の個数を 1 減らす</span>
+<a id="__codelineno-8-28" name="__codelineno-8-28" href="#__codelineno-8-28"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-29" name="__codelineno-8-29" href="#__codelineno-8-29"></a><span class="w">  </span><span class="c1">// 結果で元の配列 nums を上書きする</span>
+<a id="__codelineno-8-30" name="__codelineno-8-30" href="#__codelineno-8-30"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-8-31" name="__codelineno-8-31" href="#__codelineno-8-31"></a><span class="p">}</span>
+<a id="__codelineno-8-32" name="__codelineno-8-32" href="#__codelineno-8-32"></a>
+<a id="__codelineno-8-33" name="__codelineno-8-33" href="#__codelineno-8-33"></a><span class="cm">/* 基数ソート */</span>
+<a id="__codelineno-8-34" name="__codelineno-8-34" href="#__codelineno-8-34"></a><span class="kt">void</span><span class="w"> </span><span class="n">radixSort</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-35" name="__codelineno-8-35" href="#__codelineno-8-35"></a><span class="w">  </span><span class="c1">// 最大桁数の判定用に配列の最大要素を取得する</span>
+<a id="__codelineno-8-36" name="__codelineno-8-36" href="#__codelineno-8-36"></a><span class="w">  </span><span class="c1">// dart の `int` の長さは 64 ビット</span>
+<a id="__codelineno-8-37" name="__codelineno-8-37" href="#__codelineno-8-37"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="m">63</span><span class="p">;</span>
+<a id="__codelineno-8-38" name="__codelineno-8-38" href="#__codelineno-8-38"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_num</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_num</span><span class="p">;</span>
+<a id="__codelineno-8-39" name="__codelineno-8-39" href="#__codelineno-8-39"></a><span class="w">  </span><span class="c1">// 下位桁から上位桁の順に走査する</span>
+<a id="__codelineno-8-40" name="__codelineno-8-40" href="#__codelineno-8-40"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="m">10</span><span class="p">)</span>
+<a id="__codelineno-8-41" name="__codelineno-8-41" href="#__codelineno-8-41"></a><span class="w">    </span><span class="c1">// 配列要素の k 桁目に対して計数ソートを行う</span>
+<a id="__codelineno-8-42" name="__codelineno-8-42" href="#__codelineno-8-42"></a><span class="w">    </span><span class="c1">// k = 1 -&gt; exp = 1</span>
+<a id="__codelineno-8-43" name="__codelineno-8-43" href="#__codelineno-8-43"></a><span class="w">    </span><span class="c1">// k = 2 -&gt; exp = 10</span>
+<a id="__codelineno-8-44" name="__codelineno-8-44" href="#__codelineno-8-44"></a><span class="w">    </span><span class="c1">// つまり exp = 10^(k-1)</span>
+<a id="__codelineno-8-45" name="__codelineno-8-45" href="#__codelineno-8-45"></a><span class="w">    </span><span class="n">countingSortDigit</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span>
+<a id="__codelineno-8-46" name="__codelineno-8-46" href="#__codelineno-8-46"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">radix_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">digit</span><span class="p">}</span>
-<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
-<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">counting_sort_digit</span><span class="p">}</span>
-<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a>
-<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">radix_sort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">radix_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 要素 num の下から k 桁目を取得（exp = 10^(k-1)） */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">digit</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="c1">// ここで高コストな累乗計算を繰り返さないよう、k ではなく exp を渡す</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">((</span><span class="n">num</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">;</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="p">}</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="cm">/* 計数ソート（nums の k 桁目でソート） */</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="k">fn</span><span class="w"> </span><span class="nf">counting_sort_digit</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">exp</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">    </span><span class="c1">// 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="mi">10</span><span class="p">];</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">    </span><span class="c1">// 0~9 の各数字の出現回数を集計する</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span><span class="w"> </span><span class="c1">// nums[i] の第 k 位を取得し、d とする</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 数字 d の出現回数を数える</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">    </span><span class="c1">// 累積和を求め、「出現回数」を「配列インデックス」に変換する</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..</span><span class="mi">10</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w">    </span><span class="c1">// 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する</span>
+<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="p">).</span><span class="n">rev</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span>
+<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// d の配列内インデックス j を取得する</span>
+<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span><span class="w"> </span><span class="c1">// 現在の要素をインデックス j に格納する</span>
+<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// d の個数を 1 減らす</span>
+<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="w">    </span><span class="c1">// 結果で元の配列 nums を上書きする</span>
+<a id="__codelineno-9-30" name="__codelineno-9-30" href="#__codelineno-9-30"></a><span class="w">    </span><span class="n">nums</span><span class="p">.</span><span class="n">copy_from_slice</span><span class="p">(</span><span class="o">&amp;</span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-9-31" name="__codelineno-9-31" href="#__codelineno-9-31"></a><span class="p">}</span>
+<a id="__codelineno-9-32" name="__codelineno-9-32" href="#__codelineno-9-32"></a>
+<a id="__codelineno-9-33" name="__codelineno-9-33" href="#__codelineno-9-33"></a><span class="cm">/* 基数ソート */</span>
+<a id="__codelineno-9-34" name="__codelineno-9-34" href="#__codelineno-9-34"></a><span class="k">fn</span><span class="w"> </span><span class="nf">radix_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-35" name="__codelineno-9-35" href="#__codelineno-9-35"></a><span class="w">    </span><span class="c1">// 最大桁数の判定用に配列の最大要素を取得</span>
+<a id="__codelineno-9-36" name="__codelineno-9-36" href="#__codelineno-9-36"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">.</span><span class="n">into_iter</span><span class="p">().</span><span class="n">max</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span>
+<a id="__codelineno-9-37" name="__codelineno-9-37" href="#__codelineno-9-37"></a><span class="w">    </span><span class="c1">// 下位桁から上位桁の順に走査する</span>
+<a id="__codelineno-9-38" name="__codelineno-9-38" href="#__codelineno-9-38"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-9-39" name="__codelineno-9-39" href="#__codelineno-9-39"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-40" name="__codelineno-9-40" href="#__codelineno-9-40"></a><span class="w">        </span><span class="n">counting_sort_digit</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span>
+<a id="__codelineno-9-41" name="__codelineno-9-41" href="#__codelineno-9-41"></a><span class="w">        </span><span class="n">exp</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">10</span><span class="p">;</span>
+<a id="__codelineno-9-42" name="__codelineno-9-42" href="#__codelineno-9-42"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-43" name="__codelineno-9-43" href="#__codelineno-9-43"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">radix_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">digit</span><span class="p">}</span>
-<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
-<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">countingSortDigit</span><span class="p">}</span>
-<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a>
-<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">radixSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">radix_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 要素 num の下から k 桁目を取得（exp = 10^(k-1)） */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">digit</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="c1">// ここで高コストな累乗計算を繰り返さないよう、k ではなく exp を渡す</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">10</span><span class="p">;</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="p">}</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="cm">/* 計数ソート（nums の k 桁目でソート） */</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="kt">void</span><span class="w"> </span><span class="nf">countingSortDigit</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">    </span><span class="c1">// 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">((</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">10</span><span class="p">));</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="n">memset</span><span class="p">(</span><span class="n">counter</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">10</span><span class="p">);</span><span class="w"> </span><span class="c1">// 後続のメモリ解放に備えて 0 で初期化する</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">    </span><span class="c1">// 0~9 の各数字の出現回数を集計する</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">        </span><span class="c1">// nums[i] の第 k 位を取得し、d とする</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">        </span><span class="c1">// 数字 d の出現回数を数える</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w">    </span><span class="c1">// 累積和を求め、「出現回数」を「配列インデックス」に変換する</span>
+<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">10</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w">    </span><span class="c1">// 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する</span>
+<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">size</span><span class="p">);</span>
+<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span>
+<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// d の配列内インデックス j を取得する</span>
+<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span><span class="w">       </span><span class="c1">// 現在の要素をインデックス j に格納する</span>
+<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="o">--</span><span class="p">;</span><span class="w">           </span><span class="c1">// d の個数を 1 減らす</span>
+<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></a><span class="w">    </span><span class="c1">// 結果で元の配列 nums を上書きする</span>
+<a id="__codelineno-10-32" name="__codelineno-10-32" href="#__codelineno-10-32"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-33" name="__codelineno-10-33" href="#__codelineno-10-33"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-10-34" name="__codelineno-10-34" href="#__codelineno-10-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-35" name="__codelineno-10-35" href="#__codelineno-10-35"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-10-36" name="__codelineno-10-36" href="#__codelineno-10-36"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-10-37" name="__codelineno-10-37" href="#__codelineno-10-37"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">counter</span><span class="p">);</span>
+<a id="__codelineno-10-38" name="__codelineno-10-38" href="#__codelineno-10-38"></a><span class="p">}</span>
+<a id="__codelineno-10-39" name="__codelineno-10-39" href="#__codelineno-10-39"></a>
+<a id="__codelineno-10-40" name="__codelineno-10-40" href="#__codelineno-10-40"></a><span class="cm">/* 基数ソート */</span>
+<a id="__codelineno-10-41" name="__codelineno-10-41" href="#__codelineno-10-41"></a><span class="kt">void</span><span class="w"> </span><span class="nf">radixSort</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-42" name="__codelineno-10-42" href="#__codelineno-10-42"></a><span class="w">    </span><span class="c1">// 最大桁数の判定用に配列の最大要素を取得</span>
+<a id="__codelineno-10-43" name="__codelineno-10-43" href="#__codelineno-10-43"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">INT32_MIN</span><span class="p">;</span>
+<a id="__codelineno-10-44" name="__codelineno-10-44" href="#__codelineno-10-44"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-45" name="__codelineno-10-45" href="#__codelineno-10-45"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">max</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-46" name="__codelineno-10-46" href="#__codelineno-10-46"></a><span class="w">            </span><span class="n">max</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-10-47" name="__codelineno-10-47" href="#__codelineno-10-47"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-48" name="__codelineno-10-48" href="#__codelineno-10-48"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-49" name="__codelineno-10-49" href="#__codelineno-10-49"></a><span class="w">    </span><span class="c1">// 下位桁から上位桁の順に走査する</span>
+<a id="__codelineno-10-50" name="__codelineno-10-50" href="#__codelineno-10-50"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">exp</span><span class="p">;</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span>
+<a id="__codelineno-10-51" name="__codelineno-10-51" href="#__codelineno-10-51"></a><span class="w">        </span><span class="c1">// 配列要素の k 桁目に対して計数ソートを行う</span>
+<a id="__codelineno-10-52" name="__codelineno-10-52" href="#__codelineno-10-52"></a><span class="w">        </span><span class="c1">// k = 1 -&gt; exp = 1</span>
+<a id="__codelineno-10-53" name="__codelineno-10-53" href="#__codelineno-10-53"></a><span class="w">        </span><span class="c1">// k = 2 -&gt; exp = 10</span>
+<a id="__codelineno-10-54" name="__codelineno-10-54" href="#__codelineno-10-54"></a><span class="w">        </span><span class="c1">// つまり exp = 10^(k-1)</span>
+<a id="__codelineno-10-55" name="__codelineno-10-55" href="#__codelineno-10-55"></a><span class="w">        </span><span class="n">countingSortDigit</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span>
+<a id="__codelineno-10-56" name="__codelineno-10-56" href="#__codelineno-10-56"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">radix_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">digit</span><span class="p">}</span>
-<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
-<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">countingSortDigit</span><span class="p">}</span>
-<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a>
-<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">radixSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">radix_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 要素 num の下から k 桁目を取得（exp = 10^(k-1)） */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">digit</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="c1">// ここで高コストな累乗計算を繰り返さないよう、k ではなく exp を渡す</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="m">10</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="p">}</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="cm">/* 計数ソート（nums の k 桁目でソート） */</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">countingSortDigit</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">    </span><span class="c1">// 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="m">10</span><span class="p">)</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">    </span><span class="c1">// 0~9 の各数字の出現回数を集計する</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="c1">// nums[i] の第 k 位を取得し、d とする</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">        </span><span class="n">counter</span><span class="o">[</span><span class="n">d</span><span class="o">]++</span><span class="w">                </span><span class="c1">// 数字 d の出現回数を数える</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">    </span><span class="c1">// 累積和を求め、「出現回数」を「配列インデックス」に変換する</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="m">9</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w">        </span><span class="n">counter</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">counter</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="w">    </span><span class="c1">// 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する</span>
+<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="n">downTo</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span>
+<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">counter</span><span class="o">[</span><span class="n">d</span><span class="o">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="c1">// d の配列内インデックス j を取得する</span>
+<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="w">        </span><span class="n">res</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w">       </span><span class="c1">// 現在の要素をインデックス j に格納する</span>
+<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a><span class="w">        </span><span class="n">counter</span><span class="o">[</span><span class="n">d</span><span class="o">]--</span><span class="w">           </span><span class="c1">// d の個数を 1 減らす</span>
+<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a><span class="w">    </span><span class="c1">// 結果で元の配列 nums を上書きする</span>
+<a id="__codelineno-11-30" name="__codelineno-11-30" href="#__codelineno-11-30"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-11-32" name="__codelineno-11-32" href="#__codelineno-11-32"></a><span class="p">}</span>
+<a id="__codelineno-11-33" name="__codelineno-11-33" href="#__codelineno-11-33"></a>
+<a id="__codelineno-11-34" name="__codelineno-11-34" href="#__codelineno-11-34"></a><span class="cm">/* 基数ソート */</span>
+<a id="__codelineno-11-35" name="__codelineno-11-35" href="#__codelineno-11-35"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">radixSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-36" name="__codelineno-11-36" href="#__codelineno-11-36"></a><span class="w">    </span><span class="c1">// 最大桁数の判定用に配列の最大要素を取得</span>
+<a id="__codelineno-11-37" name="__codelineno-11-37" href="#__codelineno-11-37"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kt">Int</span><span class="p">.</span><span class="na">MIN_VALUE</span>
+<a id="__codelineno-11-38" name="__codelineno-11-38" href="#__codelineno-11-38"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-11-39" name="__codelineno-11-39" href="#__codelineno-11-39"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">exp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-11-40" name="__codelineno-11-40" href="#__codelineno-11-40"></a><span class="w">    </span><span class="c1">// 下位桁から上位桁の順に走査する</span>
+<a id="__codelineno-11-41" name="__codelineno-11-41" href="#__codelineno-11-41"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">exp</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-42" name="__codelineno-11-42" href="#__codelineno-11-42"></a><span class="w">        </span><span class="c1">// 配列要素の k 桁目に対して計数ソートを行う</span>
+<a id="__codelineno-11-43" name="__codelineno-11-43" href="#__codelineno-11-43"></a><span class="w">        </span><span class="c1">// k = 1 -&gt; exp = 1</span>
+<a id="__codelineno-11-44" name="__codelineno-11-44" href="#__codelineno-11-44"></a><span class="w">        </span><span class="c1">// k = 2 -&gt; exp = 10</span>
+<a id="__codelineno-11-45" name="__codelineno-11-45" href="#__codelineno-11-45"></a><span class="w">        </span><span class="c1">// つまり exp = 10^(k-1)</span>
+<a id="__codelineno-11-46" name="__codelineno-11-46" href="#__codelineno-11-46"></a><span class="w">        </span><span class="n">countingSortDigit</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span>
+<a id="__codelineno-11-47" name="__codelineno-11-47" href="#__codelineno-11-47"></a><span class="w">        </span><span class="n">exp</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="m">10</span>
+<a id="__codelineno-11-48" name="__codelineno-11-48" href="#__codelineno-11-48"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-49" name="__codelineno-11-49" href="#__codelineno-11-49"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">radix_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">digit</span><span class="p">}</span>
-<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
-<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">counting_sort_digit</span><span class="p">}</span>
-<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
-<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">radix_sort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">radix_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### num の第 k 桁を取得する。ここで exp = 10^(k-1) ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">digit</span><span class="p">(</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># k ではなく exp を渡すことで、ここで高コストな累乗計算を繰り返し実行するのを避けられる</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">10</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="k">end</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="c1">### num の第 k 桁を取得する。ここで exp = 10^(k-1) ###</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">digit</span><span class="p">(</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">  </span><span class="c1"># k ではなく exp を渡すことで、ここで高コストな累乗計算を繰り返し実行するのを避けられる</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">  </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">10</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="k">end</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="c1"># ## 計数ソート（nums の k 桁目でソート）###</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="k">def</span><span class="w"> </span><span class="nf">counting_sort_digit</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">  </span><span class="c1"># 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">  </span><span class="n">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">  </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w">  </span><span class="c1"># 0~9 の各数字の出現回数を集計する</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="w">    </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="c1"># nums[i] の第 k 位を取得し、d とする</span>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w">    </span><span class="n">counter</span><span class="o">[</span><span class="n">d</span><span class="o">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># 数字 d の出現回数を数える</span>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="w">  </span><span class="c1"># 累積和を求め、「出現回数」を「配列インデックス」に変換する</span>
+<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a><span class="w">  </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="mi">10</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">counter</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">counter</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="w">  </span><span class="c1"># 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する</span>
+<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a><span class="w">    </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span>
+<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a><span class="w">    </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">counter</span><span class="o">[</span><span class="n">d</span><span class="o">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># d の配列内インデックス j を取得する</span>
+<a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a><span class="w">    </span><span class="n">res</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="c1"># 現在の要素をインデックス j に格納する</span>
+<a id="__codelineno-12-31" name="__codelineno-12-31" href="#__codelineno-12-31"></a><span class="w">    </span><span class="n">counter</span><span class="o">[</span><span class="n">d</span><span class="o">]</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># d の個数を 1 減らす</span>
+<a id="__codelineno-12-32" name="__codelineno-12-32" href="#__codelineno-12-32"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-33" name="__codelineno-12-33" href="#__codelineno-12-33"></a><span class="w">  </span><span class="c1"># 結果で元の配列 nums を上書きする</span>
+<a id="__codelineno-12-34" name="__codelineno-12-34" href="#__codelineno-12-34"></a><span class="w">  </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-12-35" name="__codelineno-12-35" href="#__codelineno-12-35"></a><span class="k">end</span>
+<a id="__codelineno-12-36" name="__codelineno-12-36" href="#__codelineno-12-36"></a>
+<a id="__codelineno-12-37" name="__codelineno-12-37" href="#__codelineno-12-37"></a><span class="c1">### 基数ソート ###</span>
+<a id="__codelineno-12-38" name="__codelineno-12-38" href="#__codelineno-12-38"></a><span class="k">def</span><span class="w"> </span><span class="nf">radix_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-12-39" name="__codelineno-12-39" href="#__codelineno-12-39"></a><span class="w">  </span><span class="c1"># 最大桁数の判定用に配列の最大要素を取得</span>
+<a id="__codelineno-12-40" name="__codelineno-12-40" href="#__codelineno-12-40"></a><span class="w">  </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">.</span><span class="n">max</span>
+<a id="__codelineno-12-41" name="__codelineno-12-41" href="#__codelineno-12-41"></a><span class="w">  </span><span class="c1"># 下位桁から上位桁の順に走査する</span>
+<a id="__codelineno-12-42" name="__codelineno-12-42" href="#__codelineno-12-42"></a><span class="w">  </span><span class="n">exp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-43" name="__codelineno-12-43" href="#__codelineno-12-43"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span>
+<a id="__codelineno-12-44" name="__codelineno-12-44" href="#__codelineno-12-44"></a><span class="w">    </span><span class="c1"># 配列要素の k 桁目に対して計数ソートを行う</span>
+<a id="__codelineno-12-45" name="__codelineno-12-45" href="#__codelineno-12-45"></a><span class="w">    </span><span class="c1"># k = 1 -&gt; exp = 1</span>
+<a id="__codelineno-12-46" name="__codelineno-12-46" href="#__codelineno-12-46"></a><span class="w">    </span><span class="c1"># k = 2 -&gt; exp = 10</span>
+<a id="__codelineno-12-47" name="__codelineno-12-47" href="#__codelineno-12-47"></a><span class="w">    </span><span class="c1"># つまり exp = 10^(k-1)</span>
+<a id="__codelineno-12-48" name="__codelineno-12-48" href="#__codelineno-12-48"></a><span class="w">    </span><span class="n">counting_sort_digit</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span>
+<a id="__codelineno-12-49" name="__codelineno-12-49" href="#__codelineno-12-49"></a><span class="w">    </span><span class="n">exp</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">10</span>
+<a id="__codelineno-12-50" name="__codelineno-12-50" href="#__codelineno-12-50"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-51" name="__codelineno-12-51" href="#__codelineno-12-51"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" 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target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 <div class="admonition question">
-<p class="admonition-title">なぜ最下位桁から開始するのか？</p>
-<p>連続するソートラウンドでは、後のラウンドの結果が前のラウンドの結果を上書きします。例えば、最初のラウンドの結果が <span class="arithmatex">\(a &lt; b\)</span> で、2番目のラウンドが <span class="arithmatex">\(a &gt; b\)</span> の場合、2番目のラウンドの結果が最初のラウンドの結果を置き換えます。上位桁は下位桁より優先されるため、上位桁の前に下位桁をソートすることが理にかなっています。</p>
+<p class="admonition-title">なぜ最下位桁からソートするのですか？</p>
+<p>連続するソートの各ラウンドでは、後のラウンドの結果が前のラウンドの結果を上書きします。たとえば、第1ラウンドで <span class="arithmatex">\(a &lt; b\)</span> となっていても、第2ラウンドで <span class="arithmatex">\(a &gt; b\)</span> となれば、第2ラウンドの結果が優先されます。数字では高位の優先度が低位より高いため、先に低位をソートし、その後で高位をソートする必要があります。</p>
 </div>
 <h2 id="11102">11.10.2 &nbsp; アルゴリズムの特徴<a class="headerlink" href="#11102" title="Permanent link">&para;</a></h2>
-<p>計数ソートと比較して、基数ソートはより大きな数値範囲に適していますが、<strong>データが固定桁数で表現でき、桁数があまり大きくないことを前提としています</strong>。例えば、浮動小数点数は桁数 <span class="arithmatex">\(k\)</span> が大きい可能性があり、時間計算量 <span class="arithmatex">\(O(nk) \gg O(n^2)\)</span> につながる可能性があるため、基数ソートには適していません。</p>
+<p>計数ソートと比べると、基数ソートは値の範囲が大きい場合に適しています。<strong>ただし、データが固定桁数の形式で表せること、かつ桁数が大きすぎないことが前提です</strong>。たとえば、浮動小数点数は基数ソートに適していません。桁数 <span class="arithmatex">\(k\)</span> が大きすぎて、時間計算量が <span class="arithmatex">\(O(nk) \gg O(n^2)\)</span> になる可能性があるためです。</p>
 <ul>
-<li><strong>時間計算量は <span class="arithmatex">\(O(nk)\)</span>、非適応ソート</strong>：データサイズを <span class="arithmatex">\(n\)</span>、データが基数 <span class="arithmatex">\(d\)</span>、最大桁数を <span class="arithmatex">\(k\)</span> とすると、単一桁のソートには <span class="arithmatex">\(O(n + d)\)</span> 時間がかかり、すべての <span class="arithmatex">\(k\)</span> 桁のソートには <span class="arithmatex">\(O((n + d)k)\)</span> 時間がかかります。一般的に、<span class="arithmatex">\(d\)</span> と <span class="arithmatex">\(k\)</span> はどちらも比較的小さく、時間計算量は <span class="arithmatex">\(O(n)\)</span> に近づきます。</li>
-<li><strong>空間計算量は <span class="arithmatex">\(O(n + d)\)</span>、非インプレースソート</strong>：計数ソートと同様に、基数ソートは長さ <span class="arithmatex">\(n\)</span> と <span class="arithmatex">\(d\)</span> の配列 <code>res</code> と <code>counter</code> にそれぞれ依存します。</li>
-<li><strong>安定ソート</strong>：計数ソートが安定な場合、基数ソートも安定です。計数ソートが不安定な場合、基数ソートは正しいソート順序を保証できません。</li>
+<li><strong>時間計算量は <span class="arithmatex">\(O(nk)\)</span>、非適応ソート</strong>：データ量を <span class="arithmatex">\(n\)</span>、データが <span class="arithmatex">\(d\)</span> 進数、最大桁数を <span class="arithmatex">\(k\)</span> とすると、ある1桁に対して計数ソートを実行する時間は <span class="arithmatex">\(O(n + d)\)</span> であり、全 <span class="arithmatex">\(k\)</span> 桁をソートする時間は <span class="arithmatex">\(O((n + d)k)\)</span> です。通常、<span class="arithmatex">\(d\)</span> と <span class="arithmatex">\(k\)</span> はどちらも比較的小さいため、時間計算量は <span class="arithmatex">\(O(n)\)</span> に近づきます。</li>
+<li><strong>空間計算量は <span class="arithmatex">\(O(n + d)\)</span>、非原地ソート</strong>：計数ソートと同様に、基数ソートでは長さ <span class="arithmatex">\(n\)</span> と <span class="arithmatex">\(d\)</span> の配列 <code>res</code> と <code>counter</code> を補助的に用います。</li>
+<li><strong>安定ソート</strong>：計数ソートが安定であれば基数ソートも安定です。計数ソートが不安定な場合、基数ソートでは正しいソート結果を保証できません。</li>
 </ul>
 
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diff --git a/ja/chapter_sorting/selection_sort/index.html b/ja/chapter_sorting/selection_sort/index.html
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+++ b/ja/chapter_sorting/selection_sort/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
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-    序
+    はじめに
   
 
     
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-    序
+    はじめに
   
 
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@@ -618,7 +618,7 @@
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-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
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-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
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   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
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-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
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-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
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-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
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-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
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   <a href="#1121" class="md-nav__link">
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-        11.2.1 &nbsp; アルゴリズムの特性
+        11.2.1 &nbsp; アルゴリズムの特徴
       
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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+    13.4 &nbsp; n クイーン問題
   
 
     
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-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
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   <a href="#1121" class="md-nav__link">
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-        11.2.1 &nbsp; アルゴリズムの特性
+        11.2.1 &nbsp; アルゴリズムの特徴
       
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 <!-- Page content -->
 <h1 id="112">11.2 &nbsp; 選択ソート<a class="headerlink" href="#112" title="Permanent link">&para;</a></h1>
-<p><u>選択ソート</u>は非常にシンプルな原理で動作します：各反復で未ソート区間から最小要素を選択し、ソート済みセクションの末尾に移動するループを使用します。</p>
-<p>配列の長さを<span class="arithmatex">\(n\)</span>とすると、選択ソートのステップは下図に示されます。</p>
+<p><u>選択ソート（selection sort）</u>の仕組みは非常に単純です。ループを開始し、各ラウンドで未ソート区間から最小の要素を選び、整列済み区間の末尾に配置します。</p>
+<p>配列の長さを <span class="arithmatex">\(n\)</span> とすると、選択ソートの手順は次の図のようになります。</p>
 <ol>
-<li>最初に、すべての要素は未ソートで、つまり未ソート（インデックス）区間は<span class="arithmatex">\([0, n-1]\)</span>です。</li>
-<li>区間<span class="arithmatex">\([0, n-1]\)</span>の最小要素を選択し、インデックス<span class="arithmatex">\(0\)</span>の要素と交換します。この後、配列の最初の要素がソートされます。</li>
-<li>区間<span class="arithmatex">\([1, n-1]\)</span>の最小要素を選択し、インデックス<span class="arithmatex">\(1\)</span>の要素と交換します。この後、配列の最初の2つの要素がソートされます。</li>
-<li>この方法で続行します。<span class="arithmatex">\(n - 1\)</span>ラウンドの選択と交換の後、最初の<span class="arithmatex">\(n - 1\)</span>個の要素がソートされます。</li>
-<li>残りの唯一の要素は結果的に最大要素であり、ソートする必要がないため、配列はソートされます。</li>
+<li>初期状態では、すべての要素が未ソートであり、未ソートな（インデックス）区間は <span class="arithmatex">\([0, n-1]\)</span> です。</li>
+<li>区間 <span class="arithmatex">\([0, n-1]\)</span> 内の最小要素を選び、インデックス <span class="arithmatex">\(0\)</span> の要素と交換します。これにより、配列の先頭 1 要素が整列済みになります。</li>
+<li>区間 <span class="arithmatex">\([1, n-1]\)</span> 内の最小要素を選び、インデックス <span class="arithmatex">\(1\)</span> の要素と交換します。これにより、配列の先頭 2 要素が整列済みになります。</li>
+<li>これを繰り返します。<span class="arithmatex">\(n - 1\)</span> 回の選択と交換を経ると、配列の先頭 <span class="arithmatex">\(n - 1\)</span> 要素が整列済みになります。</li>
+<li>残った 1 つの要素は必ず最大要素なので、ソートは不要です。これで配列のソートは完了します。</li>
 </ol>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:11"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label><label for="__tabbed_1_5">&lt;5&gt;</label><label for="__tabbed_1_6">&lt;6&gt;</label><label for="__tabbed_1_7">&lt;7&gt;</label><label for="__tabbed_1_8">&lt;8&gt;</label><label for="__tabbed_1_9">&lt;9&gt;</label><label for="__tabbed_1_10">&lt;10&gt;</label><label for="__tabbed_1_11">&lt;11&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="Selection sort process" class="animation-figure" src="../selection_sort.assets/selection_sort_step1.png" /></p>
+<p><img alt="選択ソートの手順" class="animation-figure" src="../selection_sort.assets/selection_sort_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="selection_sort_step2" class="animation-figure" src="../selection_sort.assets/selection_sort_step2.png" /></p>
@@ -4379,23 +4379,23 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 11-2 &nbsp; Selection sort process </p>
+<p align="center"> 図 11-2 &nbsp; 選択ソートの手順 </p>
 
-<p>コードでは、<span class="arithmatex">\(k\)</span>を使用して未ソート区間内の最小要素を記録します：</p>
+<p>コードでは、<span class="arithmatex">\(k\)</span> を用いて未ソート区間内の最小要素を記録します。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">selection_sort.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">selection_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
 <a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;選択ソート&quot;&quot;&quot;</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
-<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="c1"># 外側のループ：未ソート範囲は [i, n-1]</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="c1"># 外側ループ：未整列区間は [i, n-1]</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
-<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="c1"># 内側のループ：未ソート範囲内で最小要素を見つける</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="c1"># 内側のループ：未ソート区間の最小要素を見つける</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="n">k</span> <span class="o">=</span> <span class="n">i</span>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
 <a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>            <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">&lt;</span> <span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]:</span>
 <a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>                <span class="n">k</span> <span class="o">=</span> <span class="n">j</span>  <span class="c1"># 最小要素のインデックスを記録</span>
-<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="c1"># 最小要素を未ソート範囲の先頭要素と交換</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="c1"># その最小要素を未整列区間の先頭要素と交換する</span>
 <a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
 </code></pre></div>
 </div>
@@ -4403,15 +4403,15 @@
 <div class="highlight"><span class="filename">selection_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 選択ソート */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">selectionSort</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
-<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// 外側ループ：未ソート範囲は[i, n-1]</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// 外側ループ：未整列区間は [i, n-1]</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="c1">// 内側ループ：未ソート範囲内で最小要素を見つける</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間の最小要素を見つける</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">])</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">                </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span><span class="w"> </span><span class="c1">// 最小要素のインデックスを記録</span>
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="c1">// 最小要素を未ソート範囲の最初の要素と交換</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="c1">// その最小要素を未整列区間の先頭要素と交換する</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]);</span>
 <a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="p">}</span>
@@ -4421,15 +4421,15 @@
 <div class="highlight"><span class="filename">selection_sort.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 選択ソート */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">selectionSort</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
-<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// 外側ループ: 未ソート範囲は [i, n-1]</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// 外側ループ：未整列区間は [i, n-1]</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="c1">// 内側ループ: 未ソート範囲内で最小要素を見つける</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間の最小要素を見つける</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="p">)</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">                </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span><span class="w"> </span><span class="c1">// 最小要素のインデックスを記録</span>
 <a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="c1">// 最小要素と未ソート範囲の最初の要素を交換</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="c1">// その最小要素を未整列区間の先頭要素と交換する</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span>
@@ -4438,55 +4438,214 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">selection_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">selection_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">SelectionSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">selection_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 選択ソート */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">SelectionSort</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="c1">// 外側ループ：未整列区間は [i, n-1]</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間の最小要素を見つける</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">])</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">                </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span><span class="w"> </span><span class="c1">// 最小要素のインデックスを記録</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">        </span><span class="c1">// その最小要素を未整列区間の先頭要素と交換する</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">        </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">])</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]);</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">selection_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">selectionSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">selection_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 選択ソート */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">selectionSort</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="c1">// 外側ループ：未整列区間は [i, n-1]</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="o">-</span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間の最小要素を見つける</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">        </span><span class="nx">k</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">i</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">k</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">                </span><span class="c1">// 最小要素のインデックスを記録</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">                </span><span class="nx">k</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">j</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">        </span><span class="c1">// その最小要素を未整列区間の先頭要素と交換する</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">        </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">k</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">k</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">selection_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">selectionSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">selection_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 選択ソート */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">selectionSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// 外側ループ：未整列区間は [i, n-1]</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="p">.</span><span class="bp">dropLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間の最小要素を見つける</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">k</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="p">.</span><span class="bp">dropFirst</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">                </span><span class="n">k</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="c1">// 最小要素のインデックスを記録</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">        </span><span class="c1">// その最小要素を未整列区間の先頭要素と交換する</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">        </span><span class="n">nums</span><span class="p">.</span><span class="n">swapAt</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">k</span><span class="p">)</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">selection_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">selectionSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">selection_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 選択ソート */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">selectionSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="c1">// 外側ループ：未整列区間は [i, n-1]</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間の最小要素を見つける</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">k</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">                </span><span class="nx">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">j</span><span class="p">;</span><span class="w"> </span><span class="c1">// 最小要素のインデックスを記録</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">        </span><span class="c1">// その最小要素を未整列区間の先頭要素と交換する</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">        </span><span class="p">[</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">k</span><span class="p">]]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">nums</span><span class="p">[</span><span class="nx">k</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]];</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">selection_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">selectionSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">selection_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 選択ソート */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">selectionSort</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="c1">// 外側ループ：未整列区間は [i, n-1]</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間の最小要素を見つける</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">k</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">                </span><span class="nx">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">j</span><span class="p">;</span><span class="w"> </span><span class="c1">// 最小要素のインデックスを記録</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">        </span><span class="c1">// その最小要素を未整列区間の先頭要素と交換する</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">        </span><span class="p">[</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">k</span><span class="p">]]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">nums</span><span class="p">[</span><span class="nx">k</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]];</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">selection_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">selectionSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">selection_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 選択ソート */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">selectionSort</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="c1">// 外側ループ：未整列区間は [i, n-1]</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">    </span><span class="c1">// 内側のループ：未ソート区間の最小要素を見つける</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">])</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span><span class="w"> </span><span class="c1">// 最小要素のインデックスを記録</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">    </span><span class="c1">// その最小要素を未整列区間の先頭要素と交換する</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">    </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">];</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">    </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">selection_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">selection_sort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">selection_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 選択ソート */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">selection_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">is_empty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="c1">// 外側ループ：未整列区間は [i, n-1]</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間の最小要素を見つける</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">                </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span><span class="w"> </span><span class="c1">// 最小要素のインデックスを記録</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">        </span><span class="c1">// その最小要素を未整列区間の先頭要素と交換する</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">        </span><span class="n">nums</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">k</span><span class="p">);</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">selection_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">selectionSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">selection_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 選択ソート */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">selectionSort</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="c1">// 外側ループ：未整列区間は [i, n-1]</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間の最小要素を見つける</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">])</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">                </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span><span class="w"> </span><span class="c1">// 最小要素のインデックスを記録</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">        </span><span class="c1">// その最小要素を未整列区間の先頭要素と交換する</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">];</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">selection_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">selectionSort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">selection_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 選択ソート */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">selectionSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="c1">// 外側ループ：未整列区間は [i, n-1]</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">        </span><span class="c1">// 内側のループ：未ソート区間の最小要素を見つける</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">                </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="c1">// 最小要素のインデックスを記録</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">        </span><span class="c1">// その最小要素を未整列区間の先頭要素と交換する</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">k</span><span class="o">]</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">selection_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">selection_sort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">selection_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 選択ソート ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">selection_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="c1"># 外側ループ：未整列区間は [i, n-1]</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">    </span><span class="c1"># 内側のループ：未ソート区間の最小要素を見つける</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">    </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">...</span><span class="n">n</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">k</span><span class="o">]</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">        </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="c1"># 最小要素のインデックスを記録</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">    </span><span class="c1"># その最小要素を未整列区間の先頭要素と交換する</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">    </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h2 id="1121">11.2.1 &nbsp; アルゴリズムの特性<a class="headerlink" href="#1121" title="Permanent link">&para;</a></h2>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 513px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20selection_sort%28nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%22%22%22%E9%81%B8%E6%8A%9E%E3%82%BD%E3%83%BC%E3%83%88%22%22%22%0A%20%20%20%20n%20%3D%20len%28nums%29%0A%20%20%20%20%23%20%E5%A4%96%E5%81%B4%E3%83%AB%E3%83%BC%E3%83%97%EF%BC%9A%E6%9C%AA%E6%95%B4%E5%88%97%E5%8C%BA%E9%96%93%E3%81%AF%20%5Bi%2C%20n-1%5D%0A%20%20%20%20for%20i%20in%20range%28n%20-%201%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E5%86%85%E5%81%B4%E3%81%AE%E3%83%AB%E3%83%BC%E3%83%97%EF%BC%9A%E6%9C%AA%E3%82%BD%E3%83%BC%E3%83%88%E5%8C%BA%E9%96%93%E3%81%AE%E6%9C%80%E5%B0%8F%E8%A6%81%E7%B4%A0%E3%82%92%E8%A6%8B%E3%81%A4%E3%81%91%E3%82%8B%0A%20%20%20%20%20%20%20%20k%20%3D%20i%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28i%20%2B%201%2C%20n%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20nums%5Bj%5D%20%3C%20nums%5Bk%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20k%20%3D%20j%20%20%23%20%E6%9C%80%E5%B0%8F%E8%A6%81%E7%B4%A0%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20%20%20%20%20%23%20%E3%81%9D%E3%81%AE%E6%9C%80%E5%B0%8F%E8%A6%81%E7%B4%A0%E3%82%92%E6%9C%AA%E6%95%B4%E5%88%97%E5%8C%BA%E9%96%93%E3%81%AE%E5%85%88%E9%A0%AD%E8%A6%81%E7%B4%A0%E3%81%A8%E4%BA%A4%E6%8F%9B%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20nums%5Bi%5D%2C%20nums%5Bk%5D%20%3D%20nums%5Bk%5D%2C%20nums%5Bi%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B4%2C%201%2C%203%2C%201%2C%205%2C%202%5D%0A%20%20%20%20selection_sort%28nums%29%0A%20%20%20%20print%28%22%E9%81%B8%E6%8A%9E%E3%82%BD%E3%83%BC%E3%83%88%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%22%2C%20nums%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20selection_sort%28nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%22%22%22%E9%81%B8%E6%8A%9E%E3%82%BD%E3%83%BC%E3%83%88%22%22%22%0A%20%20%20%20n%20%3D%20len%28nums%29%0A%20%20%20%20%23%20%E5%A4%96%E5%81%B4%E3%83%AB%E3%83%BC%E3%83%97%EF%BC%9A%E6%9C%AA%E6%95%B4%E5%88%97%E5%8C%BA%E9%96%93%E3%81%AF%20%5Bi%2C%20n-1%5D%0A%20%20%20%20for%20i%20in%20range%28n%20-%201%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E5%86%85%E5%81%B4%E3%81%AE%E3%83%AB%E3%83%BC%E3%83%97%EF%BC%9A%E6%9C%AA%E3%82%BD%E3%83%BC%E3%83%88%E5%8C%BA%E9%96%93%E3%81%AE%E6%9C%80%E5%B0%8F%E8%A6%81%E7%B4%A0%E3%82%92%E8%A6%8B%E3%81%A4%E3%81%91%E3%82%8B%0A%20%20%20%20%20%20%20%20k%20%3D%20i%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28i%20%2B%201%2C%20n%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20nums%5Bj%5D%20%3C%20nums%5Bk%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20k%20%3D%20j%20%20%23%20%E6%9C%80%E5%B0%8F%E8%A6%81%E7%B4%A0%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%82%92%E8%A8%98%E9%8C%B2%0A%20%20%20%20%20%20%20%20%23%20%E3%81%9D%E3%81%AE%E6%9C%80%E5%B0%8F%E8%A6%81%E7%B4%A0%E3%82%92%E6%9C%AA%E6%95%B4%E5%88%97%E5%8C%BA%E9%96%93%E3%81%AE%E5%85%88%E9%A0%AD%E8%A6%81%E7%B4%A0%E3%81%A8%E4%BA%A4%E6%8F%9B%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20nums%5Bi%5D%2C%20nums%5Bk%5D%20%3D%20nums%5Bk%5D%2C%20nums%5Bi%5D%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B4%2C%201%2C%203%2C%201%2C%205%2C%202%5D%0A%20%20%20%20selection_sort%28nums%29%0A%20%20%20%20print%28%22%E9%81%B8%E6%8A%9E%E3%82%BD%E3%83%BC%E3%83%88%E5%AE%8C%E4%BA%86%E5%BE%8C%20nums%20%3D%22%2C%20nums%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h2 id="1121">11.2.1 &nbsp; アルゴリズムの特徴<a class="headerlink" href="#1121" title="Permanent link">&para;</a></h2>
 <ul>
-<li><strong><span class="arithmatex">\(O(n^2)\)</span>の時間計算量、非適応ソート</strong>：外側ループに<span class="arithmatex">\(n - 1\)</span>回の反復があり、未ソートセクションの長さは最初の反復で<span class="arithmatex">\(n\)</span>から始まり、最後の反復で<span class="arithmatex">\(2\)</span>まで減少します。つまり、各外側ループ反復にはそれぞれ<span class="arithmatex">\(n\)</span>、<span class="arithmatex">\(n - 1\)</span>、<span class="arithmatex">\(\dots\)</span>、<span class="arithmatex">\(3\)</span>、<span class="arithmatex">\(2\)</span>回の内側ループ反復が含まれ、合計は<span class="arithmatex">\(\frac{(n - 1)(n + 2)}{2}\)</span>となります。</li>
-<li><strong><span class="arithmatex">\(O(1)\)</span>の空間計算量、インプレースソート</strong>：ポインタ<span class="arithmatex">\(i\)</span>と<span class="arithmatex">\(j\)</span>で定数の追加空間を使用します。</li>
-<li><strong>非安定ソート</strong>：下図に示すように、要素<code>nums[i]</code>は等しい要素の右側に交換される可能性があり、相対順序が変わる原因となります。</li>
+<li><strong>時間計算量は <span class="arithmatex">\(O(n^2)\)</span>、非適応ソート</strong>：外側のループは合計 <span class="arithmatex">\(n - 1\)</span> 回です。最初のラウンドの未ソート区間の長さは <span class="arithmatex">\(n\)</span>、最後のラウンドでは <span class="arithmatex">\(2\)</span> であり、各ラウンドの内側のループ回数はそれぞれ <span class="arithmatex">\(n\)</span>、<span class="arithmatex">\(n - 1\)</span>、<span class="arithmatex">\(\dots\)</span>、<span class="arithmatex">\(3\)</span>、<span class="arithmatex">\(2\)</span> となります。総和は <span class="arithmatex">\(\frac{(n - 1)(n + 2)}{2}\)</span> です。</li>
+<li><strong>空間計算量は <span class="arithmatex">\(O(1)\)</span>、インプレースソート</strong>：ポインタ <span class="arithmatex">\(i\)</span> と <span class="arithmatex">\(j\)</span> は定数サイズの追加領域しか使用しません。</li>
+<li><strong>不安定ソート</strong>：次の図のように、要素 <code>nums[i]</code> がそれと等しい要素の右側へ交換され、両者の相対的な順序が変わる可能性があります。</li>
 </ul>
-<p><img alt="Selection sort instability example" class="animation-figure" src="../selection_sort.assets/selection_sort_instability.png" /></p>
-<p align="center"> 図 11-3 &nbsp; Selection sort instability example </p>
+<p><img alt="選択ソートの不安定な例" class="animation-figure" src="../selection_sort.assets/selection_sort_instability.png" /></p>
+<p align="center"> 図 11-3 &nbsp; 選択ソートの不安定な例 </p>
 
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       <meta charset="utf-8">
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-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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-    1.1 &nbsp; アルゴリズムはどこにでもある
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-    1.2 &nbsp; アルゴリズムとは何か
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-    2.1 &nbsp; アルゴリズムの効率評価
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-    3.3 &nbsp; 数値の符号化 *
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-    15.1 &nbsp; 貪欲アルゴリズム
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 <!-- Page content -->
 <h1 id="111">11.1 &nbsp; ソートアルゴリズム<a class="headerlink" href="#111" title="Permanent link">&para;</a></h1>
-<p><u>ソートアルゴリズム</u>は、データセットを特定の順序で配列するために使用されます。ソートアルゴリズムは、順序付けられたデータは通常、より効率的に探索、分析、処理できるため、幅広い応用があります。</p>
-<p>下図に示すように、ソートアルゴリズムのデータ型は整数、浮動小数点数、文字、文字列などです。ソート基準は、数値サイズ、文字ASCII順序、またはカスタム基準など、必要に応じて設定できます。</p>
-<p><img alt="Data types and comparator examples" class="animation-figure" src="../sorting_algorithm.assets/sorting_examples.png" /></p>
-<p align="center"> 図 11-1 &nbsp; Data types and comparator examples </p>
+<p><u>ソートアルゴリズム（sorting algorithm）</u>は、データの集合を特定の順序に従って並べ替えるために用いられます。ソートアルゴリズムは幅広く応用されており、整列済みデータは通常、より効率的に検索、分析、処理できるためです。</p>
+<p>下図に示すように、ソートアルゴリズムにおけるデータ型は整数、浮動小数点数、文字、文字列などです。ソートの判定規則は、数値の大小、文字の ASCII コード順、またはカスタムルールなど、要件に応じて設定できます。</p>
+<p><img alt="データ型と判定規則の例" class="animation-figure" src="../sorting_algorithm.assets/sorting_examples.png" /></p>
+<p align="center"> 図 11-1 &nbsp; データ型と判定規則の例 </p>
 
-<h2 id="1111">11.1.1 &nbsp; 評価次元<a class="headerlink" href="#1111" title="Permanent link">&para;</a></h2>
-<p><strong>実行効率</strong>：ソートアルゴリズムの時間計算量ができるだけ低いことを期待し、全体的な操作数も少ないこと（時間計算量の定数項を下げる）を望みます。大容量データでは、実行効率が特に重要です。</p>
-<p><strong>インプレース性</strong>：名前が示すとおり、<u>インプレースソート</u>は元の配列を直接操作することで実現され、追加のヘルパー配列が不要であるため、メモリを節約します。一般的に、インプレースソートはデータ移動操作が少なく、高速です。</p>
-<p><strong>安定性</strong>：<u>安定ソート</u>は、ソート後に配列内の等しい要素の相対順序が変わらないことを保証します。</p>
-<p>安定ソートは、マルチキーソートシナリオにおいて必要条件です。学生情報を格納するテーブルがあり、第1列と第2列がそれぞれ名前と年齢であるとします。この場合、<u>不安定ソート</u>は入力データの順序を失う可能性があります：</p>
-<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 入力データは名前でソート済み</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="c1"># (名前, 年齢)</span>
+<h2 id="1111">11.1.1 &nbsp; 評価軸<a class="headerlink" href="#1111" title="Permanent link">&para;</a></h2>
+<p><strong>実行効率</strong>：ソートアルゴリズムの時間計算量はできるだけ低く、かつ全体の操作回数も少ないこと（時間計算量における定数項が小さいこと）が望まれます。大量データの場合、実行効率はとりわけ重要です。</p>
+<p><strong>インプレース性</strong>：その名のとおり、<u>インプレースソート</u>は元の配列を直接操作して並べ替えを行うため、追加の補助配列を必要とせず、メモリを節約できます。通常、インプレースソートはデータの移動操作が少なく、実行速度もより高速です。</p>
+<p><strong>安定性</strong>：<u>安定ソート</u>は、並べ替え完了後も、等しい要素の配列内での相対順序が変化しません。</p>
+<p>安定ソートは多段ソートの場面で必要条件となります。学生情報を保存した表があり、第 1 列と第 2 列がそれぞれ氏名と年齢であると仮定します。この場合、<u>不安定ソート</u>によって入力データの順序性が失われる可能性があります。</p>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 入力データは氏名順にソートされている</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="c1"># (name, age)</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="w">  </span><span class="o">(</span><span class="s1">&#39;A&#39;</span>,<span class="w"> </span><span class="m">19</span><span class="o">)</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="w">  </span><span class="o">(</span><span class="s1">&#39;B&#39;</span>,<span class="w"> </span><span class="m">18</span><span class="o">)</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="w">  </span><span class="o">(</span><span class="s1">&#39;C&#39;</span>,<span class="w"> </span><span class="m">21</span><span class="o">)</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="w">  </span><span class="o">(</span><span class="s1">&#39;D&#39;</span>,<span class="w"> </span><span class="m">19</span><span class="o">)</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="w">  </span><span class="o">(</span><span class="s1">&#39;E&#39;</span>,<span class="w"> </span><span class="m">23</span><span class="o">)</span>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>
-<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="c1"># 不安定ソートアルゴリズムを使用してリストを年齢でソートすると仮定すると、</span>
-<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="c1"># 結果は(&#39;D&#39;, 19)と(&#39;A&#39;, 19)の相対位置を変更し、</span>
-<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a><span class="c1"># 入力データが名前でソート済みであるという性質が失われる</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="c1"># 不安定ソートアルゴリズムで年齢順にリストを並べ替えると仮定すると、</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="c1"># 結果では (&#39;D&#39;, 19) と (&#39;A&#39;, 19) の相対位置が変わり、</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a><span class="c1"># 入力データが氏名順である性質が失われる</span>
 <a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="w">  </span><span class="o">(</span><span class="s1">&#39;B&#39;</span>,<span class="w"> </span><span class="m">18</span><span class="o">)</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="w">  </span><span class="o">(</span><span class="s1">&#39;D&#39;</span>,<span class="w"> </span><span class="m">19</span><span class="o">)</span>
 <a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a><span class="w">  </span><span class="o">(</span><span class="s1">&#39;A&#39;</span>,<span class="w"> </span><span class="m">19</span><span class="o">)</span>
 <a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="w">  </span><span class="o">(</span><span class="s1">&#39;C&#39;</span>,<span class="w"> </span><span class="m">21</span><span class="o">)</span>
 <a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a><span class="w">  </span><span class="o">(</span><span class="s1">&#39;E&#39;</span>,<span class="w"> </span><span class="m">23</span><span class="o">)</span>
 </code></pre></div>
-<p><strong>適応性</strong>：<u>適応ソート</u>は入力データ内の既存の順序情報を活用して計算負荷を削減し、より最適な時間効率を実現します。適応ソートアルゴリズムの最良ケース時間計算量は、通常平均ケース時間計算量よりも優れています。</p>
-<p><strong>比較ベースまたは非比較ベース</strong>：<u>比較ベースソート</u>は比較演算子（<span class="arithmatex">\(&lt;\)</span>、<span class="arithmatex">\(=\)</span>、<span class="arithmatex">\(&gt;\)</span>）に依存して要素の相対順序を決定し、配列全体をソートします。理論的最適時間計算量は<span class="arithmatex">\(O(n \log n)\)</span>です。一方、<u>非比較ソート</u>は比較演算子を使用せず、<span class="arithmatex">\(O(n)\)</span>の時間計算量を実現できますが、汎用性は比較的劣ります。</p>
+<p><strong>適応性</strong>：<u>適応的ソート</u>は、入力データに既に存在する順序情報を利用して計算量を減らし、より優れた時間効率を実現できます。適応的ソートアルゴリズムの最良時間計算量は、通常、平均時間計算量より優れています。</p>
+<p><strong>比較ベースかどうか</strong>：<u>比較ベースのソート</u>は、比較演算子（<span class="arithmatex">\(&lt;\)</span>、<span class="arithmatex">\(=\)</span>、<span class="arithmatex">\(&gt;\)</span>）に依存して要素の相対順序を判定し、それによって配列全体をソートします。理論上の最良時間計算量は <span class="arithmatex">\(O(n \log n)\)</span> です。一方、<u>非比較ソート</u>は比較演算子を使用せず、時間計算量は <span class="arithmatex">\(O(n)\)</span> に達しますが、汎用性は相対的に低くなります。</p>
 <h2 id="1112">11.1.2 &nbsp; 理想的なソートアルゴリズム<a class="headerlink" href="#1112" title="Permanent link">&para;</a></h2>
-<p><strong>高速実行、インプレース、安定、適応、汎用</strong>。明らかに、これらのすべての特徴を組み合わせたソートアルゴリズムは今日まで見つかっていません。したがって、ソートアルゴリズムを選択する際は、データの特定の特徴と問題の要件に基づいて決定する必要があります。</p>
-<p>次に、さまざまなソートアルゴリズムを一緒に学び、上記の評価次元に基づいてそれぞれの利点と欠点を分析します。</p>
+<p><strong>高速、インプレース、安定、適応的、高い汎用性</strong>。明らかに、これまでのところ、以上のすべての特性を兼ね備えたソートアルゴリズムはまだ見つかっていません。そのため、ソートアルゴリズムを選択する際には、具体的なデータの特徴と問題の要件に応じて判断する必要があります。</p>
+<p>次に、さまざまなソートアルゴリズムを一緒に学び、上記の評価軸に基づいて各ソートアルゴリズムの長所と短所を分析していきます。</p>
 
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@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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 <!-- Page content -->
 <h1 id="1111">11.11 &nbsp; まとめ<a class="headerlink" href="#1111" title="Permanent link">&para;</a></h1>
-<h3 id="1">1. &nbsp; 重要な復習<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<h3 id="1">1. &nbsp; 重要なポイントの振り返り<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
-<li>バブルソートは隣接する要素を交換することで動作します。フラグを追加して早期リターンを可能にすることで、バブルソートの最良ケースの時間計算量を <span class="arithmatex">\(O(n)\)</span> に最適化できます。</li>
-<li>挿入ソートは、未ソート区間から要素を取り出してソート済み区間の正しい位置に挿入することで各ラウンドをソートします。挿入ソートの時間計算量は <span class="arithmatex">\(O(n^2)\)</span> ですが、単位あたりの操作が比較的少ないため、少量のデータのソートでは非常に人気があります。</li>
-<li>クイックソートは歩哨分割操作に基づいています。歩哨分割では、常に最悪のピボットを選ぶ可能性があり、時間計算量が <span class="arithmatex">\(O(n^2)\)</span> に劣化する可能性があります。中央値やランダムピボットを導入することで、そのような劣化の確率を減らすことができます。末尾再帰は再帰の深さを効果的に減らし、空間計算量を <span class="arithmatex">\(O(\log n)\)</span> に最適化します。</li>
-<li>マージソートには分割とマージの2つの段階があり、通常分割統治戦略を体現しています。マージソートでは、配列のソートには補助配列の作成が必要で、空間計算量は <span class="arithmatex">\(O(n)\)</span> になります。しかし、リストのソートの空間計算量は <span class="arithmatex">\(O(1)\)</span> に最適化できます。</li>
-<li>バケットソートは3つの手順から構成されます：データをバケットに分散、各バケット内でのソート、バケット順での結果のマージ。これも分割統治戦略を体現し、非常に大きなデータセットに適しています。バケットソートの鍵はデータの均等分散です。</li>
-<li>計数ソートはバケットソートの変形で、各データポイントの出現回数をカウントすることでソートします。計数ソートは限られた範囲のデータを持つ大きなデータセットに適しており、データを正の整数に変換する必要があります。</li>
-<li>基数ソートは桁ごとにソートすることでデータを処理し、データが固定長の数値として表現される必要があります。</li>
-<li>全体的に、私たちは高効率、安定性、インプレース操作、適応性を持つソートアルゴリズムを求めています。しかし、他のデータ構造やアルゴリズムと同様に、これらすべての条件を同時に満たすソートアルゴリズムは存在しません。実際の応用では、データの特性に基づいて適切なソートアルゴリズムを選択する必要があります。</li>
-<li>以下の図は、効率性、安定性、インプレース性、適応性の観点から主流のソートアルゴリズムを比較しています。</li>
+<li>バブルソートは隣接する要素を交換することで整列を行います。フラグを追加して早期リターンを可能にすると、バブルソートの最良時間計算量を <span class="arithmatex">\(O(n)\)</span> に最適化できます。</li>
+<li>挿入ソートは各ラウンドで未整列区間の要素を整列済み区間の正しい位置に挿入することで整列を完了します。挿入ソートの時間計算量は <span class="arithmatex">\(O(n^2)\)</span> ですが、基本操作が比較的少ないため、小規模データのソート処理で非常に人気があります。</li>
+<li>クイックソートは番兵分割操作に基づいて整列を行います。番兵分割では毎回最悪の基準値を選んでしまう可能性があり、その結果、時間計算量は <span class="arithmatex">\(O(n^2)\)</span> まで劣化することがあります。中央値の基準値やランダムな基準値を導入すると、この劣化の確率を下げられます。短い部分配列を優先して再帰すれば、再帰の深さを効果的に抑え、空間計算量を <span class="arithmatex">\(O(\log n)\)</span> に最適化できます。</li>
+<li>マージソートは分割とマージという 2 つの段階からなり、分割統治戦略を典型的に体現しています。マージソートでは配列を整列する際に補助配列の作成が必要で、空間計算量は <span class="arithmatex">\(O(n)\)</span> です。一方、連結リストを整列する場合の空間計算量は <span class="arithmatex">\(O(1)\)</span> まで最適化できます。</li>
+<li>バケットソートはデータのバケット分配、バケット内ソート、結果の結合という 3 つの手順を含みます。これも分割統治戦略を体現しており、データ量が非常に大きい場合に適しています。バケットソートの鍵は、データを平均的に分配することにあります。</li>
+<li>カウントソートはバケットソートの特例であり、データの出現回数を数えることで整列を行います。カウントソートはデータ量が大きく、かつデータ範囲が限られている場合に適しており、データを正の整数に変換できることが前提です。</li>
+<li>基数ソートは各桁ごとの整列によってデータを整列し、データが固定桁数の数値として表せることを前提とします。</li>
+<li>総じて言えば、私たちは高効率で、安定で、インプレースで、さらに適応的であるといった利点を備えたソートアルゴリズムを見つけたいと考えます。しかし、ほかのデータ構造やアルゴリズムと同様に、これらすべての条件を同時に満たせるソートアルゴリズムは存在しません。実際の応用では、データの特性に応じて適切なソートアルゴリズムを選ぶ必要があります。</li>
+<li>下図では、主流のソートアルゴリズムについて、効率、安定性、インプレース性、適応性などを比較しています。</li>
 </ul>
 <p><img alt="ソートアルゴリズムの比較" class="animation-figure" src="../summary.assets/sorting_algorithms_comparison.png" /></p>
 <p align="center"> 図 11-19 &nbsp; ソートアルゴリズムの比較 </p>
 
 <h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
-<p><strong>Q</strong>: ソートアルゴリズムの安定性はいつ必要ですか？</p>
-<p>実際には、オブジェクトの一つの属性に基づいてソートする場合があります。例えば、学生は名前と身長の属性を持ち、多段階ソートを実装することを目指します：最初に名前で <code>(A, 180) (B, 185) (C, 170) (D, 170)</code> を取得し、次に身長で。ソートアルゴリズムが不安定なため、<code>(D, 170) (C, 170) (A, 180) (B, 185)</code> になってしまう可能性があります。</p>
-<p>学生DとCの位置が交換され、名前の順序性が破られているのが分かります。これは望ましくありません。</p>
-<p><strong>Q</strong>: 歩哨分割での「右から左への検索」と「左から右への検索」の順序を交換できますか？</p>
-<p>いいえ、最左要素をピボットとして使用する場合、最初に「右から左への検索」を行い、次に「左から右への検索」を行う必要があります。この結論はやや直観に反するので、理由を分析してみましょう。</p>
-<p>歩哨分割 <code>partition()</code> の最後のステップは <code>nums[left]</code> と <code>nums[i]</code> を交換することです。交換後、ピボットの左側の要素はすべてピボット以下になります。<strong>これには最後の交換前に <code>nums[left] &gt;= nums[i]</code> が成り立つ必要があります</strong>。「左から右への検索」を最初に行い、ピボットより大きい要素が見つからない場合、<strong><code>i == j</code> でループを終了し、<code>nums[j] == nums[i] &gt; nums[left]</code> となる可能性があります</strong>。つまり、最終交換操作はピボットより大きい要素を配列の左端に交換し、歩哨分割を失敗させます。</p>
-<p>例えば、配列 <code>[0, 0, 0, 0, 1]</code> が与えられた場合、最初に「左から右への検索」を行うと、歩哨分割後の配列は <code>[1, 0, 0, 0, 0]</code> となり、これは正しくありません。</p>
-<p>さらに考えると、<code>nums[right]</code> をピボットとして選択する場合、まったく逆で、最初に「左から右への検索」を行う必要があります。</p>
-<p><strong>Q</strong>: 末尾再帰最適化について、短い配列を選択することで再帰の深さが <span class="arithmatex">\(\log n\)</span> を超えないことを保証するのはなぜですか？</p>
-<p>再帰の深さは現在リターンしていない再帰メソッドの数です。歩哨分割の各ラウンドは元の配列を2つの副配列に分割します。末尾再帰最適化により、再帰的に続行する副配列の長さは最大でも元の配列長の半分です。最悪の場合常に長さを半分にすると仮定すると、最終的な再帰の深さは <span class="arithmatex">\(\log n\)</span> になります。</p>
-<p>元のクイックソートを見直すと、より大きな配列を継続的に再帰処理する可能性があり、最悪の場合 <span class="arithmatex">\(n\)</span>、<span class="arithmatex">\(n - 1\)</span>、...、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(1\)</span> で、再帰の深さは <span class="arithmatex">\(n\)</span> になります。末尾再帰最適化はこのシナリオを回避できます。</p>
-<p><strong>Q</strong>: 配列のすべての要素が等しい場合、クイックソートの時間計算量は <span class="arithmatex">\(O(n^2)\)</span> ですか？この劣化ケースをどう処理すべきですか？</p>
-<p>はい。この状況については、歩哨分割を使用して配列をピボットより小さい、等しい、大きいの3つの部分に分割することを検討してください。小さい部分と大きい部分のみを再帰的に進めます。この方法では、すべての入力要素が等しい配列を1ラウンドの歩哨分割だけでソートできます。</p>
-<p><strong>Q</strong>: なぜバケットソートの最悪ケース時間計算量は <span class="arithmatex">\(O(n^2)\)</span> ですか？</p>
-<p>最悪の場合、すべての要素が同じバケットに配置されます。これらの要素をソートするために <span class="arithmatex">\(O(n^2)\)</span> アルゴリズムを使用する場合、時間計算量は <span class="arithmatex">\(O(n^2)\)</span> になります。</p>
+<p><strong>Q</strong>：ソートアルゴリズムの安定性は、どのような場合に必須ですか？</p>
+<p>現実には、オブジェクトのある属性に基づいて整列することがあります。たとえば、学生には氏名と身長という 2 つの属性があり、多段階のソートを行いたいとします。まず氏名で整列して <code>(A, 180) (B, 185) (C, 170) (D, 170)</code> を得て、その後に身長で整列します。ソートアルゴリズムが不安定である場合、結果は <code>(D, 170) (C, 170) (A, 180) (B, 185)</code> になる可能性があります。</p>
+<p>このように、学生 D と C の位置が入れ替わり、氏名に関する順序性が壊れてしまいます。これは望ましくありません。</p>
+<p><strong>Q</strong>：番兵分割において、「右から左へ探索する」順序と「左から右へ探索する」順序は入れ替えられますか？</p>
+<p>できません。最も左端の要素を基準値とする場合は、必ず先に「右から左へ探索する」を行い、その後に「左から右へ探索する」を行う必要があります。この結論はやや直感に反するので、理由を分析してみましょう。</p>
+<p>番兵分割 <code>partition()</code> の最後の手順は、<code>nums[left]</code> と <code>nums[i]</code> を交換することです。交換が終わると、基準値の左側にある要素はすべて基準値 <code>&lt;=</code> になります。<strong>したがって、最後の交換の前に <code>nums[left] &gt;= nums[i]</code> が必ず成り立っていなければなりません</strong>。仮に先に「左から右へ探索する」を行うと、基準値より大きい要素が見つからない場合、<strong><code>i == j</code> の時点でループを抜け、このとき <code>nums[j] == nums[i] &gt; nums[left]</code> となる可能性があります</strong>。つまり、この最後の交換によって、基準値より大きい要素が配列の最左端へ移されてしまい、番兵分割は失敗します。</p>
+<p>たとえば、配列 <code>[0, 0, 0, 0, 1]</code> が与えられたとき、先に「左から右へ探索する」を行うと、番兵分割後の配列は <code>[1, 0, 0, 0, 0]</code> になります。これは誤った結果です。</p>
+<p>さらに考えると、<code>nums[right]</code> を基準値に選ぶ場合はちょうど逆になり、必ず先に「左から右へ探索する」を行う必要があります。</p>
+<p><strong>Q</strong>：クイックソートの再帰深度最適化について、短い配列を選ぶとなぜ再帰深度が <span class="arithmatex">\(\log n\)</span> を超えないと保証できるのですか？</p>
+<p>再帰深度とは、現在まだ戻っていない再帰呼び出しの数のことです。各ラウンドの番兵分割では、元の配列を 2 つの部分配列に分けます。再帰深度の最適化後は、下方向に再帰する部分配列の長さは最大でも元の配列長の半分です。最悪の場合でも毎回半分の長さになると仮定すれば、最終的な再帰深度は <span class="arithmatex">\(\log n\)</span> になります。</p>
+<p>元のクイックソートを振り返ると、長いほうの配列に対して連続して再帰してしまう可能性があり、最悪の場合は <span class="arithmatex">\(n\)</span>、<span class="arithmatex">\(n - 1\)</span>、<span class="arithmatex">\(\dots\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(1\)</span> と続き、再帰深度は <span class="arithmatex">\(n\)</span> になります。再帰深度の最適化により、このような状況を避けられます。</p>
+<p><strong>Q</strong>：配列内のすべての要素が等しい場合、クイックソートの時間計算量は <span class="arithmatex">\(O(n^2)\)</span> になりますか？このような退化はどう処理すべきですか？</p>
+<p>はい。この場合は、番兵分割によって配列を「基準値より小さい」「基準値に等しい」「基準値より大きい」の 3 つの部分に分ける方法を検討できます。下方向に再帰するのは、小さい部分と大きい部分だけです。この方法では、入力要素がすべて等しい配列は、1 回の番兵分割だけで整列を完了できます。</p>
+<p><strong>Q</strong>：バケットソートの最悪時間計算量が <span class="arithmatex">\(O(n^2)\)</span> なのはなぜですか？</p>
+<p>最悪の場合、すべての要素が同じバケットに振り分けられます。その要素群を整列するのに <span class="arithmatex">\(O(n^2)\)</span> のアルゴリズムを使えば、時間計算量は <span class="arithmatex">\(O(n^2)\)</span> になります。</p>
 
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diff --git a/ja/chapter_stack_and_queue/deque/index.html b/ja/chapter_stack_and_queue/deque/index.html
index b98556e41..60eb9d891 100644
--- a/ja/chapter_stack_and_queue/deque/index.html
+++ b/ja/chapter_stack_and_queue/deque/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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-    序
+    はじめに
   
 
     
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-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
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-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
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   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
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-    3.4 &nbsp; 文字の符号化 *
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-        5.3.1 &nbsp; 両端キューの一般的な操作
+        5.3.1 &nbsp; 両端キューの基本操作
       
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-    第 6 章 &nbsp; ハッシュ表
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
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+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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+    15.1 &nbsp; 貪欲法
   
 
     
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
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-        5.3.1 &nbsp; 両端キューの一般的な操作
+        5.3.1 &nbsp; 両端キューの基本操作
       
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 <!-- Page content -->
 <h1 id="53">5.3 &nbsp; 両端キュー<a class="headerlink" href="#53" title="Permanent link">&para;</a></h1>
-<p>キューでは、先頭からの要素の削除や末尾への要素の追加のみが可能です。下図に示すように、<u>両端キュー（deque）</u>はより柔軟性を提供し、先頭と末尾の両方で要素の追加や削除を可能にします。</p>
+<p>キューでは、先頭要素を削除するか末尾に要素を追加することしかできません。次の図に示すように、<u>両端キュー（double-ended queue）</u>はより高い柔軟性を備えており、先頭と末尾の両方で要素の追加や削除を行えます。</p>
 <p><img alt="両端キューの操作" class="animation-figure" src="../deque.assets/deque_operations.png" /></p>
 <p align="center"> 図 5-7 &nbsp; 両端キューの操作 </p>
 
-<h2 id="531">5.3.1 &nbsp; 両端キューの一般的な操作<a class="headerlink" href="#531" title="Permanent link">&para;</a></h2>
-<p>両端キューの一般的な操作は以下の通りです。具体的なメソッド名は使用するプログラミング言語によって異なります。</p>
+<h2 id="531">5.3.1 &nbsp; 両端キューの基本操作<a class="headerlink" href="#531" title="Permanent link">&para;</a></h2>
+<p>両端キューの基本操作を次の表に示します。具体的なメソッド名は、使用するプログラミング言語によって異なります。</p>
 <p align="center"> 表 5-3 &nbsp; 両端キューの操作効率 </p>
 
 <div class="center-table">
@@ -4452,40 +4452,40 @@
 </thead>
 <tbody>
 <tr>
-<td><code>pushFirst()</code></td>
+<td><code>push_first()</code></td>
 <td>先頭に要素を追加</td>
 <td><span class="arithmatex">\(O(1)\)</span></td>
 </tr>
 <tr>
-<td><code>pushLast()</code></td>
+<td><code>push_last()</code></td>
 <td>末尾に要素を追加</td>
 <td><span class="arithmatex">\(O(1)\)</span></td>
 </tr>
 <tr>
-<td><code>popFirst()</code></td>
+<td><code>pop_first()</code></td>
 <td>先頭要素を削除</td>
 <td><span class="arithmatex">\(O(1)\)</span></td>
 </tr>
 <tr>
-<td><code>popLast()</code></td>
+<td><code>pop_last()</code></td>
 <td>末尾要素を削除</td>
 <td><span class="arithmatex">\(O(1)\)</span></td>
 </tr>
 <tr>
-<td><code>peekFirst()</code></td>
+<td><code>peek_first()</code></td>
 <td>先頭要素にアクセス</td>
 <td><span class="arithmatex">\(O(1)\)</span></td>
 </tr>
 <tr>
-<td><code>peekLast()</code></td>
+<td><code>peek_last()</code></td>
 <td>末尾要素にアクセス</td>
 <td><span class="arithmatex">\(O(1)\)</span></td>
 </tr>
 </tbody>
 </table>
 </div>
-<p>同様に、プログラミング言語で実装された両端キュークラスを直接使用することができます：</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="1:12"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label></div>
+<p>同様に、プログラミング言語に組み込み実装されている両端キューのクラスを直接使うこともできます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">deque.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="kn">from</span><span class="w"> </span><span class="nn">collections</span><span class="w"> </span><span class="kn">import</span> <span class="n">deque</span>
@@ -4511,7 +4511,7 @@
 <a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="c1"># 両端キューの長さを取得</span>
 <a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="n">size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">deq</span><span class="p">)</span>
 <a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a>
-<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a><span class="c1"># 両端キューが空かどうかを確認</span>
+<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a><span class="c1"># 両端キューが空かどうかを判定</span>
 <a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a><span class="n">is_empty</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">deq</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span>
 </code></pre></div>
 </div>
@@ -4537,7 +4537,7 @@
 <a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="cm">/* 両端キューの長さを取得 */</span>
 <a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
 <a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a>
-<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="cm">/* 両端キューが空かどうかを確認 */</span>
+<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="cm">/* 両端キューが空かどうかを判定 */</span>
 <a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="kt">bool</span><span class="w"> </span><span class="n">empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">empty</span><span class="p">();</span>
 </code></pre></div>
 </div>
@@ -4563,13 +4563,13 @@
 <a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="cm">/* 両端キューの長さを取得 */</span>
 <a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
 <a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a>
-<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="cm">/* 両端キューが空かどうかを確認 */</span>
+<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="cm">/* 両端キューが空かどうかを判定 */</span>
 <a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="kt">boolean</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">();</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">deque.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 両端キューを初期化 */</span>
-<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="c1">// C#では、LinkedListを両端キューとして使用</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="c1">// C# では、連結リスト LinkedList を両端キューとして使用する</span>
 <a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="n">LinkedList</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">deque</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">();</span>
 <a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a>
 <a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="cm">/* 要素をエンキュー */</span>
@@ -4590,13 +4590,13 @@
 <a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="cm">/* 両端キューの長さを取得 */</span>
 <a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">Count</span><span class="p">;</span>
 <a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a>
-<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="cm">/* 両端キューが空かどうかを確認 */</span>
+<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="cm">/* 両端キューが空かどうかを判定 */</span>
 <a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">deque_test.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 両端キューを初期化 */</span>
-<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="c1">// Goでは、listを両端キューとして使用</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="c1">// Go では、list を両端キューとして使用する</span>
 <a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="nx">deque</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">list</span><span class="p">.</span><span class="nx">New</span><span class="p">()</span>
 <a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a>
 <a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="cm">/* 要素をエンキュー */</span>
@@ -4617,13 +4617,13 @@
 <a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="cm">/* 両端キューの長さを取得 */</span>
 <a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="nx">size</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">Len</span><span class="p">()</span>
 <a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a>
-<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="cm">/* 両端キューが空かどうかを確認 */</span>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="cm">/* 両端キューが空かどうかを判定 */</span>
 <a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="nx">isEmpty</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">Len</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">deque.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 両端キューを初期化 */</span>
-<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="c1">// Swiftには組み込みの両端キュークラスがないため、Arrayを両端キューとして使用</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="c1">// Swift には組み込みの両端キュークラスがないため、Array を両端キューとして使用する</span>
 <a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">var</span><span class="w"> </span><span class="nv">deque</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
 <a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>
 <a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="cm">/* 要素をエンキュー */</span>
@@ -4635,81 +4635,81 @@
 <a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a>
 <a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="cm">/* 要素にアクセス */</span>
 <a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="kd">let</span><span class="w"> </span><span class="nv">peekFirst</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="bp">first</span><span class="p">!</span><span class="w"> </span><span class="c1">// 先頭要素</span>
-<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="kd">let</span><span class="w"> </span><span class="nv">peekLast</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="bp">last</span><span class="p">!</span><span class="w">   </span><span class="c1">// 末尾要素</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="kd">let</span><span class="w"> </span><span class="nv">peekLast</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="bp">last</span><span class="p">!</span><span class="w"> </span><span class="c1">// 末尾要素</span>
 <a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a>
 <a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="cm">/* 要素をデキュー */</span>
-<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="c1">// Arrayを使用する場合、popFirstの計算量はO(n)</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="c1">// Array で模擬する場合、popFirst の計算量は O(n)</span>
 <a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="kd">let</span><span class="w"> </span><span class="nv">popFirst</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">removeFirst</span><span class="p">()</span><span class="w"> </span><span class="c1">// 先頭要素をデキュー</span>
-<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="kd">let</span><span class="w"> </span><span class="nv">popLast</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="bp">removeLast</span><span class="p">()</span><span class="w">   </span><span class="c1">// 末尾要素をデキュー</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="kd">let</span><span class="w"> </span><span class="nv">popLast</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="bp">removeLast</span><span class="p">()</span><span class="w"> </span><span class="c1">// 末尾要素をデキュー</span>
 <a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a>
 <a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="cm">/* 両端キューの長さを取得 */</span>
 <a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="kd">let</span><span class="w"> </span><span class="nv">size</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="bp">count</span>
 <a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a>
-<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="cm">/* 両端キューが空かどうかを確認 */</span>
+<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="cm">/* 両端キューが空かどうかを判定 */</span>
 <a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="kd">let</span><span class="w"> </span><span class="nv">isEmpty</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="bp">isEmpty</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">deque.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 両端キューを初期化 */</span>
-<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="c1">// JavaScriptには組み込みの両端キューがないため、Arrayを両端キューとして使用</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="c1">// JavaScript には組み込みの両端キューがないため、Array を両端キューとして使用するしかない</span>
 <a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="kd">const</span><span class="w"> </span><span class="nx">deque</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
 <a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a>
 <a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="cm">/* 要素をエンキュー */</span>
 <a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">2</span><span class="p">);</span>
 <a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
 <a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">4</span><span class="p">);</span>
-<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="c1">// 注意：unshift()は配列のため時間計算量がO(n)</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="c1">// 配列であるため、unshift() メソッドの時間計算量は O(n) です</span>
 <a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">unshift</span><span class="p">(</span><span class="mf">3</span><span class="p">);</span>
 <a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">unshift</span><span class="p">(</span><span class="mf">1</span><span class="p">);</span>
 <a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a>
 <a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="cm">/* 要素にアクセス */</span>
-<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peekFirst</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span><span class="w"> </span><span class="c1">// 先頭要素</span>
-<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peekLast</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">[</span><span class="nx">deque</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span><span class="w"> </span><span class="c1">// 末尾要素</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peekFirst</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peekLast</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">[</span><span class="nx">deque</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
 <a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a>
 <a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="cm">/* 要素をデキュー */</span>
-<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="c1">// 注意：shift()は配列のため時間計算量がO(n)</span>
-<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="kd">const</span><span class="w"> </span><span class="nx">popFront</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">shift</span><span class="p">();</span><span class="w"> </span><span class="c1">// 先頭要素をデキュー</span>
-<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="kd">const</span><span class="w"> </span><span class="nx">popBack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span><span class="w">    </span><span class="c1">// 末尾要素をデキュー</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="c1">// 配列であるため、shift() メソッドの時間計算量は O(n) です</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="kd">const</span><span class="w"> </span><span class="nx">popFront</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">shift</span><span class="p">();</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="kd">const</span><span class="w"> </span><span class="nx">popBack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
 <a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a>
 <a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="cm">/* 両端キューの長さを取得 */</span>
 <a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="kd">const</span><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
 <a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a>
-<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="cm">/* 両端キューが空かどうかを確認 */</span>
+<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="cm">/* 両端キューが空かどうかを判定 */</span>
 <a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="kd">const</span><span class="w"> </span><span class="nx">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">deque.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 両端キューを初期化 */</span>
-<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="c1">// TypeScriptには組み込みの両端キューがないため、Arrayを両端キューとして使用</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="c1">// TypeScript には組み込みの両端キューがないため、Array を両端キューとして使用するしかない</span>
 <a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="kd">const</span><span class="w"> </span><span class="nx">deque</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
 <a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a>
 <a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="cm">/* 要素をエンキュー */</span>
 <a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">2</span><span class="p">);</span>
 <a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
 <a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">4</span><span class="p">);</span>
-<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="c1">// 注意：unshift()は配列のため時間計算量がO(n)</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="c1">// 配列であるため、unshift() メソッドの時間計算量は O(n) です</span>
 <a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">unshift</span><span class="p">(</span><span class="mf">3</span><span class="p">);</span>
 <a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">unshift</span><span class="p">(</span><span class="mf">1</span><span class="p">);</span>
 <a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a>
 <a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="cm">/* 要素にアクセス */</span>
-<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peekFirst</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span><span class="w"> </span><span class="c1">// 先頭要素</span>
-<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peekLast</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">[</span><span class="nx">deque</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span><span class="w"> </span><span class="c1">// 末尾要素</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peekFirst</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peekLast</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">[</span><span class="nx">deque</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
 <a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a>
 <a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="cm">/* 要素をデキュー */</span>
-<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="c1">// 注意：shift()は配列のため時間計算量がO(n)</span>
-<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="kd">const</span><span class="w"> </span><span class="nx">popFront</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">shift</span><span class="p">()</span><span class="w"> </span><span class="kr">as</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭要素をデキュー</span>
-<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="kd">const</span><span class="w"> </span><span class="nx">popBack</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">pop</span><span class="p">()</span><span class="w"> </span><span class="kr">as</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w">    </span><span class="c1">// 末尾要素をデキュー</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="c1">// 配列であるため、shift() メソッドの時間計算量は O(n) です</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="kd">const</span><span class="w"> </span><span class="nx">popFront</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">shift</span><span class="p">()</span><span class="w"> </span><span class="kr">as</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="kd">const</span><span class="w"> </span><span class="nx">popBack</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">pop</span><span class="p">()</span><span class="w"> </span><span class="kr">as</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span>
 <a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a>
 <a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="cm">/* 両端キューの長さを取得 */</span>
 <a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="kd">const</span><span class="w"> </span><span class="nx">size</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
 <a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a>
-<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="cm">/* 両端キューが空かどうかを確認 */</span>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="cm">/* 両端キューが空かどうかを判定 */</span>
 <a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="kd">const</span><span class="w"> </span><span class="nx">isEmpty</span><span class="o">:</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">deque.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 両端キューを初期化 */</span>
-<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="c1">// Dartでは、Queueが両端キューとして定義される</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="c1">// Dart では、Queue は両端キューとして定義されています</span>
 <a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="n">Queue</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">deque</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Queue</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">();</span>
 <a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a>
 <a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="cm">/* 要素をエンキュー */</span>
@@ -4730,7 +4730,7 @@
 <a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="cm">/* 両端キューの長さを取得 */</span>
 <a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
 <a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a>
-<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a><span class="cm">/* 両端キューが空かどうかを確認 */</span>
+<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a><span class="cm">/* 両端キューが空かどうかを判定 */</span>
 <a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">isEmpty</span><span class="p">;</span>
 </code></pre></div>
 </div>
@@ -4760,30 +4760,85 @@
 <a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="cm">/* 両端キューの長さを取得 */</span>
 <a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="kd">let</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
 <a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a>
-<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="cm">/* 両端キューが空かどうかを確認 */</span>
+<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="cm">/* 両端キューが空かどうかを判定 */</span>
 <a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="kd">let</span><span class="w"> </span><span class="n">is_empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">is_empty</span><span class="p">();</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">deque.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// Cには組み込みの両端キューが提供されていません</span>
+<div class="highlight"><span class="filename">deque.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// C には組み込みの両端キューがありません</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">deque.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
+<div class="highlight"><span class="filename">deque.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 両端キューを初期化 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">val</span><span class="w"> </span><span class="nv">deque</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">LinkedList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="cm">/* 要素をエンキュー */</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="n">deque</span><span class="p">.</span><span class="na">offerLast</span><span class="p">(</span><span class="m">2</span><span class="p">)</span><span class="w">  </span><span class="c1">// 末尾に追加</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="n">deque</span><span class="p">.</span><span class="na">offerLast</span><span class="p">(</span><span class="m">5</span><span class="p">)</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="n">deque</span><span class="p">.</span><span class="na">offerLast</span><span class="p">(</span><span class="m">4</span><span class="p">)</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="n">deque</span><span class="p">.</span><span class="na">offerFirst</span><span class="p">(</span><span class="m">3</span><span class="p">)</span><span class="w"> </span><span class="c1">// 先頭に追加</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="n">deque</span><span class="p">.</span><span class="na">offerFirst</span><span class="p">(</span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="kd">val</span><span class="w"> </span><span class="nv">peekFirst</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="na">peekFirst</span><span class="p">()</span><span class="w"> </span><span class="c1">// 先頭要素</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="kd">val</span><span class="w"> </span><span class="nv">peekLast</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="na">peekLast</span><span class="p">()</span><span class="w">   </span><span class="c1">// 末尾要素</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="cm">/* 要素をデキュー */</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="kd">val</span><span class="w"> </span><span class="nv">popFirst</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="na">pollFirst</span><span class="p">()</span><span class="w"> </span><span class="c1">// 先頭要素をデキュー</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="kd">val</span><span class="w"> </span><span class="nv">popLast</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="na">pollLast</span><span class="p">()</span><span class="w">   </span><span class="c1">// 末尾要素をデキュー</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="kd">val</span><span class="w"> </span><span class="nv">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a>
+<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="cm">/* 両端キューが空かどうかを判定 */</span>
+<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="kd">val</span><span class="w"> </span><span class="nv">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">()</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">deque.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1"># 両端キューを初期化</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="c1"># Ruby には組み込みの両端キューがないため、Array を両端キューとして使用するしかありません</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="n">deque</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="c1"># 要素をエンキュー</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="n">deque</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="n">deque</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">5</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="n">deque</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">4</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="c1"># 配列であるため、Array#unshift メソッドの時間計算量は O(n) です</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="n">deque</span><span class="o">.</span><span class="n">unshift</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="n">deque</span><span class="o">.</span><span class="n">unshift</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="c1"># 要素にアクセス</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="n">peek_first</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="o">.</span><span class="n">first</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="n">peek_last</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="o">.</span><span class="n">last</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="c1"># 要素をデキュー</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="c1"># 配列であるため、 Array#shift メソッドの時間計算量は O(n) です</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="n">pop_front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="o">.</span><span class="n">shift</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="n">pop_back</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="o">.</span><span class="n">pop</span>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="c1"># 両端キューの長さを取得</span>
+<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a>
+<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="c1"># 両端キューが空かどうかを判定</span>
+<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a><span class="n">is_empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="o">.</span><span class="n">zero?</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>実行の可視化</summary>
+<p>https://pythontutor.com/render.html#code=from%20collections%20import%20deque%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%0A%20%20%20%20deq%20%3D%20deque%28%29%0A%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%85%A5%E9%98%9F%0A%20%20%20%20deq.append%282%29%20%20%23%20%E6%B7%BB%E5%8A%A0%E8%87%B3%E9%98%9F%E5%B0%BE%0A%20%20%20%20deq.append%285%29%0A%20%20%20%20deq.append%284%29%0A%20%20%20%20deq.appendleft%283%29%20%20%23%20%E6%B7%BB%E5%8A%A0%E8%87%B3%E9%98%9F%E9%A6%96%0A%20%20%20%20deq.appendleft%281%29%0A%20%20%20%20print%28%22%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%20deque%20%3D%22,%20deq%29%0A%0A%20%20%20%20%23%20%E8%AE%BF%E9%97%AE%E5%85%83%E7%B4%A0%0A%20%20%20%20front%20%3D%20deq%5B0%5D%20%20%23%20%E9%98%9F%E9%A6%96%E5%85%83%E7%B4%A0%0A%20%20%20%20print%28%22%E9%98%9F%E9%A6%96%E5%85%83%E7%B4%A0%20front%20%3D%22,%20front%29%0A%20%20%20%20rear%20%3D%20deq%5B-1%5D%20%20%23%20%E9%98%9F%E5%B0%BE%E5%85%83%E7%B4%A0%0A%20%20%20%20print%28%22%E9%98%9F%E5%B0%BE%E5%85%83%E7%B4%A0%20rear%20%3D%22,%20rear%29%0A%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%87%BA%E9%98%9F%0A%20%20%20%20pop_front%20%3D%20deq.popleft%28%29%20%20%23%20%E9%98%9F%E9%A6%96%E5%85%83%E7%B4%A0%E5%87%BA%E9%98%9F%0A%20%20%20%20print%28%22%E9%98%9F%E9%A6%96%E5%87%BA%E9%98%9F%E5%85%83%E7%B4%A0%20%20pop_front%20%3D%22,%20pop_front%29%0A%20%20%20%20print%28%22%E9%98%9F%E9%A6%96%E5%87%BA%E9%98%9F%E5%90%8E%20deque%20%3D%22,%20deq%29%0A%20%20%20%20pop_rear%20%3D%20deq.pop%28%29%20%20%23%20%E9%98%9F%E5%B0%BE%E5%85%83%E7%B4%A0%E5%87%BA%E9%98%9F%0A%20%20%20%20print%28%22%E9%98%9F%E5%B0%BE%E5%87%BA%E9%98%9F%E5%85%83%E7%B4%A0%20%20pop_rear%20%3D%22,%20pop_rear%29%0A%20%20%20%20print%28%22%E9%98%9F%E5%B0%BE%E5%87%BA%E9%98%9F%E5%90%8E%20deque%20%3D%22,%20deq%29%0A%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%E7%9A%84%E9%95%BF%E5%BA%A6%0A%20%20%20%20size%20%3D%20len%28deq%29%0A%20%20%20%20print%28%22%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%E9%95%BF%E5%BA%A6%20size%20%3D%22,%20size%29%0A%0A%20%20%20%20%23%20%E5%88%A4%E6%96%AD%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%0A%20%20%20%20is_empty%20%3D%20len%28deq%29%20%3D%3D%200%0A%20%20%20%20print%28%22%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%20%3D%22,%20is_empty%29&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>
+</details>
 <h2 id="532">5.3.2 &nbsp; 両端キューの実装 *<a class="headerlink" href="#532" title="Permanent link">&para;</a></h2>
-<p>両端キューの実装は通常のキューの実装と似ており、連結リストまたは配列を基盤となるデータ構造として使用できます。</p>
+<p>両端キューの実装はキューと似ており、連結リストまたは配列を基盤となるデータ構造として選べます。</p>
 <h3 id="1">1. &nbsp; 双方向連結リストに基づく実装<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>前節で、通常の単一連結リストを使ってキューを実装したことを思い出してください。これは先頭からの削除（デキュー操作に対応）と末尾への新しい要素の追加（エンキュー操作に対応）を便利に行えるためでした。</p>
-<p>両端キューでは、先頭と末尾の両方でエンキューとデキュー操作を実行できます。つまり、両端キューは逆方向の操作も実装する必要があります。このため、両端キューの基盤となるデータ構造として「双方向連結リスト」を使用します。</p>
-<p>下図に示すように、双方向連結リストの先頭ノードと末尾ノードをそれぞれ両端キューの前端と後端として扱い、両端でのノードの追加と削除機能を実装します。</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="2:5"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">LinkedListDeque</label><label for="__tabbed_2_2">pushLast()</label><label for="__tabbed_2_3">pushFirst()</label><label for="__tabbed_2_4">popLast()</label><label for="__tabbed_2_5">popFirst()</label></div>
+<p>前節を振り返ると、通常の単方向連結リストを使ってキューを実装しました。これは、先頭ノードの削除（デキューに対応）と末尾ノードの後ろへの新規ノード追加（エンキューに対応）を容易に行えるためです。</p>
+<p>両端キューでは、先頭と末尾のどちらでもエンキューとデキューを行えます。言い換えると、両端キューではもう一方の対称方向の操作も実装する必要があります。そのため、両端キューの基盤データ構造として「双方向連結リスト」を採用します。</p>
+<p>次の図に示すように、双方向連結リストの先頭ノードと末尾ノードを両端キューの先頭と末尾と見なし、両端でノードを追加および削除する機能を実現します。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:5"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">LinkedListDeque</label><label for="__tabbed_2_2">push_last()</label><label for="__tabbed_2_3">push_first()</label><label for="__tabbed_2_4">pop_last()</label><label for="__tabbed_2_5">pop_first()</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="双方向連結リストによる両端キューのエンキューとデキュー操作の実装" class="animation-figure" src="../deque.assets/linkedlist_deque_step1.png" /></p>
+<p><img alt="連結リストによる両端キューのエンキューとデキュー" class="animation-figure" src="../deque.assets/linkedlist_deque_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="linkedlist_deque_push_last" class="animation-figure" src="../deque.assets/linkedlist_deque_step2_push_last.png" /></p>
@@ -4799,461 +4854,1718 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 5-8 &nbsp; 双方向連結リストによる両端キューのエンキューとデキュー操作の実装 </p>
+<p align="center"> 図 5-8 &nbsp; 連結リストによる両端キューのエンキューとデキュー </p>
 
-<p>実装コードは以下の通りです：</p>
+<p>実装コードは次のとおりです：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_deque.py</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">ListNode</span><span class="p">:</span>
-<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;双方向連結リストノード&quot;&quot;&quot;</span>
-<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a>
-<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
-<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">val</span>
-<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">next</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># 後続ノードへの参照</span>
-<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">prev</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># 前駆ノードへの参照</span>
-<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a>
-<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="k">class</span><span class="w"> </span><span class="nc">LinkedListDeque</span><span class="p">:</span>
-<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;双方向連結リストベースの双端キュークラス&quot;&quot;&quot;</span>
-<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a>
-<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
-<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># ヘッドノード front</span>
-<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># テールノード rear</span>
-<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># 双端キューの長さ</span>
-<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a>
-<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;双端キューの長さを取得&quot;&quot;&quot;</span>
-<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span>
-<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a>
-<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">is_empty</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
-<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;双端キューが空かどうかを判定&quot;&quot;&quot;</span>
-<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="mi">0</span>
-<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a>
-<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">is_front</span><span class="p">:</span> <span class="nb">bool</span><span class="p">):</span>
-<a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;エンキュー操作&quot;&quot;&quot;</span>
-<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a>        <span class="n">node</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
-<a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a>        <span class="c1"># リストが空の場合、front と rear の両方を node に向ける</span>
-<a id="__codelineno-12-31" name="__codelineno-12-31" href="#__codelineno-12-31"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
-<a id="__codelineno-12-32" name="__codelineno-12-32" href="#__codelineno-12-32"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span> <span class="o">=</span> <span class="n">node</span>
-<a id="__codelineno-12-33" name="__codelineno-12-33" href="#__codelineno-12-33"></a>        <span class="c1"># 前端エンキュー操作</span>
-<a id="__codelineno-12-34" name="__codelineno-12-34" href="#__codelineno-12-34"></a>        <span class="k">elif</span> <span class="n">is_front</span><span class="p">:</span>
-<a id="__codelineno-12-35" name="__codelineno-12-35" href="#__codelineno-12-35"></a>            <span class="c1"># ノードをリストの先頭に追加</span>
-<a id="__codelineno-12-36" name="__codelineno-12-36" href="#__codelineno-12-36"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="o">.</span><span class="n">prev</span> <span class="o">=</span> <span class="n">node</span>
-<a id="__codelineno-12-37" name="__codelineno-12-37" href="#__codelineno-12-37"></a>            <span class="n">node</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span>
-<a id="__codelineno-12-38" name="__codelineno-12-38" href="#__codelineno-12-38"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">=</span> <span class="n">node</span>  <span class="c1"># ヘッドノードを更新</span>
-<a id="__codelineno-12-39" name="__codelineno-12-39" href="#__codelineno-12-39"></a>        <span class="c1"># 後端エンキュー操作</span>
-<a id="__codelineno-12-40" name="__codelineno-12-40" href="#__codelineno-12-40"></a>        <span class="k">else</span><span class="p">:</span>
-<a id="__codelineno-12-41" name="__codelineno-12-41" href="#__codelineno-12-41"></a>            <span class="c1"># ノードをリストの末尾に追加</span>
-<a id="__codelineno-12-42" name="__codelineno-12-42" href="#__codelineno-12-42"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">node</span>
-<a id="__codelineno-12-43" name="__codelineno-12-43" href="#__codelineno-12-43"></a>            <span class="n">node</span><span class="o">.</span><span class="n">prev</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span>
-<a id="__codelineno-12-44" name="__codelineno-12-44" href="#__codelineno-12-44"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span> <span class="o">=</span> <span class="n">node</span>  <span class="c1"># テールノードを更新</span>
-<a id="__codelineno-12-45" name="__codelineno-12-45" href="#__codelineno-12-45"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">+=</span> <span class="mi">1</span>  <span class="c1"># キューの長さを更新</span>
-<a id="__codelineno-12-46" name="__codelineno-12-46" href="#__codelineno-12-46"></a>
-<a id="__codelineno-12-47" name="__codelineno-12-47" href="#__codelineno-12-47"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push_first</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-12-48" name="__codelineno-12-48" href="#__codelineno-12-48"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;前端エンキュー&quot;&quot;&quot;</span>
-<a id="__codelineno-12-49" name="__codelineno-12-49" href="#__codelineno-12-49"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span> <span class="kc">True</span><span class="p">)</span>
-<a id="__codelineno-12-50" name="__codelineno-12-50" href="#__codelineno-12-50"></a>
-<a id="__codelineno-12-51" name="__codelineno-12-51" href="#__codelineno-12-51"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push_last</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-12-52" name="__codelineno-12-52" href="#__codelineno-12-52"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;後端エンキュー&quot;&quot;&quot;</span>
-<a id="__codelineno-12-53" name="__codelineno-12-53" href="#__codelineno-12-53"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span> <span class="kc">False</span><span class="p">)</span>
-<a id="__codelineno-12-54" name="__codelineno-12-54" href="#__codelineno-12-54"></a>
-<a id="__codelineno-12-55" name="__codelineno-12-55" href="#__codelineno-12-55"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">is_front</span><span class="p">:</span> <span class="nb">bool</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-12-56" name="__codelineno-12-56" href="#__codelineno-12-56"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;デキュー操作&quot;&quot;&quot;</span>
-<a id="__codelineno-12-57" name="__codelineno-12-57" href="#__codelineno-12-57"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
-<a id="__codelineno-12-58" name="__codelineno-12-58" href="#__codelineno-12-58"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Double-ended queue is empty&quot;</span><span class="p">)</span>
-<a id="__codelineno-12-59" name="__codelineno-12-59" href="#__codelineno-12-59"></a>        <span class="c1"># 前端デキュー操作</span>
-<a id="__codelineno-12-60" name="__codelineno-12-60" href="#__codelineno-12-60"></a>        <span class="k">if</span> <span class="n">is_front</span><span class="p">:</span>
-<a id="__codelineno-12-61" name="__codelineno-12-61" href="#__codelineno-12-61"></a>            <span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="o">.</span><span class="n">val</span>  <span class="c1"># ヘッドノードの値を一時的に保存</span>
-<a id="__codelineno-12-62" name="__codelineno-12-62" href="#__codelineno-12-62"></a>            <span class="c1"># ヘッドノードを削除</span>
-<a id="__codelineno-12-63" name="__codelineno-12-63" href="#__codelineno-12-63"></a>            <span class="n">fnext</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="o">.</span><span class="n">next</span>
-<a id="__codelineno-12-64" name="__codelineno-12-64" href="#__codelineno-12-64"></a>            <span class="k">if</span> <span class="n">fnext</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-12-65" name="__codelineno-12-65" href="#__codelineno-12-65"></a>                <span class="n">fnext</span><span class="o">.</span><span class="n">prev</span> <span class="o">=</span> <span class="kc">None</span>
-<a id="__codelineno-12-66" name="__codelineno-12-66" href="#__codelineno-12-66"></a>                <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="kc">None</span>
-<a id="__codelineno-12-67" name="__codelineno-12-67" href="#__codelineno-12-67"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">=</span> <span class="n">fnext</span>  <span class="c1"># ヘッドノードを更新</span>
-<a id="__codelineno-12-68" name="__codelineno-12-68" href="#__codelineno-12-68"></a>        <span class="c1"># 後端デキュー操作</span>
-<a id="__codelineno-12-69" name="__codelineno-12-69" href="#__codelineno-12-69"></a>        <span class="k">else</span><span class="p">:</span>
-<a id="__codelineno-12-70" name="__codelineno-12-70" href="#__codelineno-12-70"></a>            <span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span><span class="o">.</span><span class="n">val</span>  <span class="c1"># テールノードの値を一時的に保存</span>
-<a id="__codelineno-12-71" name="__codelineno-12-71" href="#__codelineno-12-71"></a>            <span class="c1"># テールノードを削除</span>
-<a id="__codelineno-12-72" name="__codelineno-12-72" href="#__codelineno-12-72"></a>            <span class="n">rprev</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span><span class="o">.</span><span class="n">prev</span>
-<a id="__codelineno-12-73" name="__codelineno-12-73" href="#__codelineno-12-73"></a>            <span class="k">if</span> <span class="n">rprev</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-12-74" name="__codelineno-12-74" href="#__codelineno-12-74"></a>                <span class="n">rprev</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="kc">None</span>
-<a id="__codelineno-12-75" name="__codelineno-12-75" href="#__codelineno-12-75"></a>                <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span><span class="o">.</span><span class="n">prev</span> <span class="o">=</span> <span class="kc">None</span>
-<a id="__codelineno-12-76" name="__codelineno-12-76" href="#__codelineno-12-76"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span> <span class="o">=</span> <span class="n">rprev</span>  <span class="c1"># テールノードを更新</span>
-<a id="__codelineno-12-77" name="__codelineno-12-77" href="#__codelineno-12-77"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-=</span> <span class="mi">1</span>  <span class="c1"># キューの長さを更新</span>
-<a id="__codelineno-12-78" name="__codelineno-12-78" href="#__codelineno-12-78"></a>        <span class="k">return</span> <span class="n">val</span>
-<a id="__codelineno-12-79" name="__codelineno-12-79" href="#__codelineno-12-79"></a>
-<a id="__codelineno-12-80" name="__codelineno-12-80" href="#__codelineno-12-80"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop_first</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-12-81" name="__codelineno-12-81" href="#__codelineno-12-81"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;前端デキュー&quot;&quot;&quot;</span>
-<a id="__codelineno-12-82" name="__codelineno-12-82" href="#__codelineno-12-82"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
-<a id="__codelineno-12-83" name="__codelineno-12-83" href="#__codelineno-12-83"></a>
-<a id="__codelineno-12-84" name="__codelineno-12-84" href="#__codelineno-12-84"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop_last</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-12-85" name="__codelineno-12-85" href="#__codelineno-12-85"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;後端デキュー&quot;&quot;&quot;</span>
-<a id="__codelineno-12-86" name="__codelineno-12-86" href="#__codelineno-12-86"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
-<a id="__codelineno-12-87" name="__codelineno-12-87" href="#__codelineno-12-87"></a>
-<a id="__codelineno-12-88" name="__codelineno-12-88" href="#__codelineno-12-88"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">peek_first</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-12-89" name="__codelineno-12-89" href="#__codelineno-12-89"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;前端要素にアクセス&quot;&quot;&quot;</span>
-<a id="__codelineno-12-90" name="__codelineno-12-90" href="#__codelineno-12-90"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
-<a id="__codelineno-12-91" name="__codelineno-12-91" href="#__codelineno-12-91"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Double-ended queue is empty&quot;</span><span class="p">)</span>
-<a id="__codelineno-12-92" name="__codelineno-12-92" href="#__codelineno-12-92"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="o">.</span><span class="n">val</span>
-<a id="__codelineno-12-93" name="__codelineno-12-93" href="#__codelineno-12-93"></a>
-<a id="__codelineno-12-94" name="__codelineno-12-94" href="#__codelineno-12-94"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">peek_last</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-12-95" name="__codelineno-12-95" href="#__codelineno-12-95"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;後端要素にアクセス&quot;&quot;&quot;</span>
-<a id="__codelineno-12-96" name="__codelineno-12-96" href="#__codelineno-12-96"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
-<a id="__codelineno-12-97" name="__codelineno-12-97" href="#__codelineno-12-97"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Double-ended queue is empty&quot;</span><span class="p">)</span>
-<a id="__codelineno-12-98" name="__codelineno-12-98" href="#__codelineno-12-98"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span><span class="o">.</span><span class="n">val</span>
-<a id="__codelineno-12-99" name="__codelineno-12-99" href="#__codelineno-12-99"></a>
-<a id="__codelineno-12-100" name="__codelineno-12-100" href="#__codelineno-12-100"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">to_array</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
-<a id="__codelineno-12-101" name="__codelineno-12-101" href="#__codelineno-12-101"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;出力用の配列を返す&quot;&quot;&quot;</span>
-<a id="__codelineno-12-102" name="__codelineno-12-102" href="#__codelineno-12-102"></a>        <span class="n">node</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span>
-<a id="__codelineno-12-103" name="__codelineno-12-103" href="#__codelineno-12-103"></a>        <span class="n">res</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span>
-<a id="__codelineno-12-104" name="__codelineno-12-104" href="#__codelineno-12-104"></a>        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()):</span>
-<a id="__codelineno-12-105" name="__codelineno-12-105" href="#__codelineno-12-105"></a>            <span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">node</span><span class="o">.</span><span class="n">val</span>
-<a id="__codelineno-12-106" name="__codelineno-12-106" href="#__codelineno-12-106"></a>            <span class="n">node</span> <span class="o">=</span> <span class="n">node</span><span class="o">.</span><span class="n">next</span>
-<a id="__codelineno-12-107" name="__codelineno-12-107" href="#__codelineno-12-107"></a>        <span class="k">return</span> <span class="n">res</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_deque.cpp</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="cm">/* 双方向連結リストノード */</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">DoublyListNode</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">              </span><span class="c1">// ノードの値</span>
-<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="w">    </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">next</span><span class="p">;</span><span class="w"> </span><span class="c1">// 後続ノードへのポインタ</span>
-<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="w">    </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">prev</span><span class="p">;</span><span class="w"> </span><span class="c1">// 前続ノードへのポインタ</span>
-<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="w">    </span><span class="n">DoublyListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">val</span><span class="p">),</span><span class="w"> </span><span class="n">prev</span><span class="p">(</span><span class="k">nullptr</span><span class="p">),</span><span class="w"> </span><span class="n">next</span><span class="p">(</span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="p">};</span>
+<div class="highlight"><span class="filename">linkedlist_deque.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">ListNode</span><span class="p">:</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;双方向連結リストノード&quot;&quot;&quot;</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
+<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">val</span>
+<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">next</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># 後続ノードへの参照</span>
+<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">prev</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># 前駆ノードへの参照</span>
 <a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>
-<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a><span class="cm">/* 双方向連結リストに基づく両端キュークラス */</span>
-<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="k">class</span><span class="w"> </span><span class="nc">LinkedListDeque</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
-<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a><span class="w">    </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">front</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">rear</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードfront、末尾ノードrear</span>
-<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">              </span><span class="c1">// 両端キューの長さ</span>
-<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a>
-<a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
-<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
-<a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a><span class="w">    </span><span class="n">LinkedListDeque</span><span class="p">()</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">front</span><span class="p">(</span><span class="k">nullptr</span><span class="p">),</span><span class="w"> </span><span class="n">rear</span><span class="p">(</span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a>
-<a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a><span class="w">    </span><span class="cm">/* デストラクタ */</span>
-<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a><span class="w">    </span><span class="o">~</span><span class="n">LinkedListDeque</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a><span class="w">        </span><span class="c1">// 連結リストを走査、ノードを削除、メモリを解放</span>
-<a id="__codelineno-13-24" name="__codelineno-13-24" href="#__codelineno-13-24"></a><span class="w">        </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">pre</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
-<a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-26" name="__codelineno-13-26" href="#__codelineno-13-26"></a><span class="w">            </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
-<a id="__codelineno-13-27" name="__codelineno-13-27" href="#__codelineno-13-27"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
-<a id="__codelineno-13-28" name="__codelineno-13-28" href="#__codelineno-13-28"></a><span class="w">            </span><span class="k">delete</span><span class="w"> </span><span class="n">pre</span><span class="p">;</span>
-<a id="__codelineno-13-29" name="__codelineno-13-29" href="#__codelineno-13-29"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-13-30" name="__codelineno-13-30" href="#__codelineno-13-30"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-31" name="__codelineno-13-31" href="#__codelineno-13-31"></a>
-<a id="__codelineno-13-32" name="__codelineno-13-32" href="#__codelineno-13-32"></a><span class="w">    </span><span class="cm">/* 両端キューの長さを取得 */</span>
-<a id="__codelineno-13-33" name="__codelineno-13-33" href="#__codelineno-13-33"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-34" name="__codelineno-13-34" href="#__codelineno-13-34"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
-<a id="__codelineno-13-35" name="__codelineno-13-35" href="#__codelineno-13-35"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-36" name="__codelineno-13-36" href="#__codelineno-13-36"></a>
-<a id="__codelineno-13-37" name="__codelineno-13-37" href="#__codelineno-13-37"></a><span class="w">    </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
-<a id="__codelineno-13-38" name="__codelineno-13-38" href="#__codelineno-13-38"></a><span class="w">    </span><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-39" name="__codelineno-13-39" href="#__codelineno-13-39"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-13-40" name="__codelineno-13-40" href="#__codelineno-13-40"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-41" name="__codelineno-13-41" href="#__codelineno-13-41"></a>
-<a id="__codelineno-13-42" name="__codelineno-13-42" href="#__codelineno-13-42"></a><span class="w">    </span><span class="cm">/* エンキュー操作 */</span>
-<a id="__codelineno-13-43" name="__codelineno-13-43" href="#__codelineno-13-43"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-44" name="__codelineno-13-44" href="#__codelineno-13-44"></a><span class="w">        </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">DoublyListNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
-<a id="__codelineno-13-45" name="__codelineno-13-45" href="#__codelineno-13-45"></a><span class="w">        </span><span class="c1">// リストが空の場合、frontとrearの両方をnodeに向ける</span>
-<a id="__codelineno-13-46" name="__codelineno-13-46" href="#__codelineno-13-46"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
-<a id="__codelineno-13-47" name="__codelineno-13-47" href="#__codelineno-13-47"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
-<a id="__codelineno-13-48" name="__codelineno-13-48" href="#__codelineno-13-48"></a><span class="w">        </span><span class="c1">// 先頭エンキュー操作</span>
-<a id="__codelineno-13-49" name="__codelineno-13-49" href="#__codelineno-13-49"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-50" name="__codelineno-13-50" href="#__codelineno-13-50"></a><span class="w">            </span><span class="c1">// ノードをリストの先頭に追加</span>
-<a id="__codelineno-13-51" name="__codelineno-13-51" href="#__codelineno-13-51"></a><span class="w">            </span><span class="n">front</span><span class="o">-&gt;</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
-<a id="__codelineno-13-52" name="__codelineno-13-52" href="#__codelineno-13-52"></a><span class="w">            </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
-<a id="__codelineno-13-53" name="__codelineno-13-53" href="#__codelineno-13-53"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードを更新</span>
-<a id="__codelineno-13-54" name="__codelineno-13-54" href="#__codelineno-13-54"></a><span class="w">        </span><span class="c1">// 末尾エンキュー操作</span>
-<a id="__codelineno-13-55" name="__codelineno-13-55" href="#__codelineno-13-55"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-56" name="__codelineno-13-56" href="#__codelineno-13-56"></a><span class="w">            </span><span class="c1">// ノードをリストの末尾に追加</span>
-<a id="__codelineno-13-57" name="__codelineno-13-57" href="#__codelineno-13-57"></a><span class="w">            </span><span class="n">rear</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
-<a id="__codelineno-13-58" name="__codelineno-13-58" href="#__codelineno-13-58"></a><span class="w">            </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="p">;</span>
-<a id="__codelineno-13-59" name="__codelineno-13-59" href="#__codelineno-13-59"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノードを更新</span>
-<a id="__codelineno-13-60" name="__codelineno-13-60" href="#__codelineno-13-60"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-13-61" name="__codelineno-13-61" href="#__codelineno-13-61"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// キュー長を更新</span>
-<a id="__codelineno-13-62" name="__codelineno-13-62" href="#__codelineno-13-62"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-63" name="__codelineno-13-63" href="#__codelineno-13-63"></a>
-<a id="__codelineno-13-64" name="__codelineno-13-64" href="#__codelineno-13-64"></a><span class="w">    </span><span class="cm">/* 先頭エンキュー */</span>
-<a id="__codelineno-13-65" name="__codelineno-13-65" href="#__codelineno-13-65"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">pushFirst</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-66" name="__codelineno-13-66" href="#__codelineno-13-66"></a><span class="w">        </span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="nb">true</span><span class="p">);</span>
-<a id="__codelineno-13-67" name="__codelineno-13-67" href="#__codelineno-13-67"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-68" name="__codelineno-13-68" href="#__codelineno-13-68"></a>
-<a id="__codelineno-13-69" name="__codelineno-13-69" href="#__codelineno-13-69"></a><span class="w">    </span><span class="cm">/* 末尾エンキュー */</span>
-<a id="__codelineno-13-70" name="__codelineno-13-70" href="#__codelineno-13-70"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">pushLast</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-71" name="__codelineno-13-71" href="#__codelineno-13-71"></a><span class="w">        </span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="nb">false</span><span class="p">);</span>
-<a id="__codelineno-13-72" name="__codelineno-13-72" href="#__codelineno-13-72"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-73" name="__codelineno-13-73" href="#__codelineno-13-73"></a>
-<a id="__codelineno-13-74" name="__codelineno-13-74" href="#__codelineno-13-74"></a><span class="w">    </span><span class="cm">/* デキュー操作 */</span>
-<a id="__codelineno-13-75" name="__codelineno-13-75" href="#__codelineno-13-75"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="kt">bool</span><span class="w"> </span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-76" name="__codelineno-13-76" href="#__codelineno-13-76"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
-<a id="__codelineno-13-77" name="__codelineno-13-77" href="#__codelineno-13-77"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Queue is empty&quot;</span><span class="p">);</span>
-<a id="__codelineno-13-78" name="__codelineno-13-78" href="#__codelineno-13-78"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
-<a id="__codelineno-13-79" name="__codelineno-13-79" href="#__codelineno-13-79"></a><span class="w">        </span><span class="c1">// 先頭デキュー操作</span>
-<a id="__codelineno-13-80" name="__codelineno-13-80" href="#__codelineno-13-80"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-81" name="__codelineno-13-81" href="#__codelineno-13-81"></a><span class="w">            </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードの値を一時保存</span>
-<a id="__codelineno-13-82" name="__codelineno-13-82" href="#__codelineno-13-82"></a><span class="w">            </span><span class="c1">// 先頭ノードを削除</span>
-<a id="__codelineno-13-83" name="__codelineno-13-83" href="#__codelineno-13-83"></a><span class="w">            </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">fNext</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
-<a id="__codelineno-13-84" name="__codelineno-13-84" href="#__codelineno-13-84"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">fNext</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-85" name="__codelineno-13-85" href="#__codelineno-13-85"></a><span class="w">                </span><span class="n">fNext</span><span class="o">-&gt;</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
-<a id="__codelineno-13-86" name="__codelineno-13-86" href="#__codelineno-13-86"></a><span class="w">                </span><span class="n">front</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
-<a id="__codelineno-13-87" name="__codelineno-13-87" href="#__codelineno-13-87"></a><span class="w">            </span><span class="p">}</span>
-<a id="__codelineno-13-88" name="__codelineno-13-88" href="#__codelineno-13-88"></a><span class="w">            </span><span class="k">delete</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
-<a id="__codelineno-13-89" name="__codelineno-13-89" href="#__codelineno-13-89"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fNext</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードを更新</span>
-<a id="__codelineno-13-90" name="__codelineno-13-90" href="#__codelineno-13-90"></a><span class="w">        </span><span class="c1">// 末尾デキュー操作</span>
-<a id="__codelineno-13-91" name="__codelineno-13-91" href="#__codelineno-13-91"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-92" name="__codelineno-13-92" href="#__codelineno-13-92"></a><span class="w">            </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノードの値を一時保存</span>
-<a id="__codelineno-13-93" name="__codelineno-13-93" href="#__codelineno-13-93"></a><span class="w">            </span><span class="c1">// 末尾ノードを削除</span>
-<a id="__codelineno-13-94" name="__codelineno-13-94" href="#__codelineno-13-94"></a><span class="w">            </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">rPrev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="o">-&gt;</span><span class="n">prev</span><span class="p">;</span>
-<a id="__codelineno-13-95" name="__codelineno-13-95" href="#__codelineno-13-95"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">rPrev</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-96" name="__codelineno-13-96" href="#__codelineno-13-96"></a><span class="w">                </span><span class="n">rPrev</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
-<a id="__codelineno-13-97" name="__codelineno-13-97" href="#__codelineno-13-97"></a><span class="w">                </span><span class="n">rear</span><span class="o">-&gt;</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
-<a id="__codelineno-13-98" name="__codelineno-13-98" href="#__codelineno-13-98"></a><span class="w">            </span><span class="p">}</span>
-<a id="__codelineno-13-99" name="__codelineno-13-99" href="#__codelineno-13-99"></a><span class="w">            </span><span class="k">delete</span><span class="w"> </span><span class="n">rear</span><span class="p">;</span>
-<a id="__codelineno-13-100" name="__codelineno-13-100" href="#__codelineno-13-100"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rPrev</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノードを更新</span>
-<a id="__codelineno-13-101" name="__codelineno-13-101" href="#__codelineno-13-101"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-13-102" name="__codelineno-13-102" href="#__codelineno-13-102"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// キュー長を更新</span>
-<a id="__codelineno-13-103" name="__codelineno-13-103" href="#__codelineno-13-103"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
-<a id="__codelineno-13-104" name="__codelineno-13-104" href="#__codelineno-13-104"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-105" name="__codelineno-13-105" href="#__codelineno-13-105"></a>
-<a id="__codelineno-13-106" name="__codelineno-13-106" href="#__codelineno-13-106"></a><span class="w">    </span><span class="cm">/* 先頭デキュー */</span>
-<a id="__codelineno-13-107" name="__codelineno-13-107" href="#__codelineno-13-107"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">popFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-108" name="__codelineno-13-108" href="#__codelineno-13-108"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="nb">true</span><span class="p">);</span>
-<a id="__codelineno-13-109" name="__codelineno-13-109" href="#__codelineno-13-109"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-110" name="__codelineno-13-110" href="#__codelineno-13-110"></a>
-<a id="__codelineno-13-111" name="__codelineno-13-111" href="#__codelineno-13-111"></a><span class="w">    </span><span class="cm">/* 末尾デキュー */</span>
-<a id="__codelineno-13-112" name="__codelineno-13-112" href="#__codelineno-13-112"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">popLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-113" name="__codelineno-13-113" href="#__codelineno-13-113"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="nb">false</span><span class="p">);</span>
-<a id="__codelineno-13-114" name="__codelineno-13-114" href="#__codelineno-13-114"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-115" name="__codelineno-13-115" href="#__codelineno-13-115"></a>
-<a id="__codelineno-13-116" name="__codelineno-13-116" href="#__codelineno-13-116"></a><span class="w">    </span><span class="cm">/* 先頭要素にアクセス */</span>
-<a id="__codelineno-13-117" name="__codelineno-13-117" href="#__codelineno-13-117"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">peekFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-118" name="__codelineno-13-118" href="#__codelineno-13-118"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
-<a id="__codelineno-13-119" name="__codelineno-13-119" href="#__codelineno-13-119"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Double-ended queue is empty&quot;</span><span class="p">);</span>
-<a id="__codelineno-13-120" name="__codelineno-13-120" href="#__codelineno-13-120"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">front</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
-<a id="__codelineno-13-121" name="__codelineno-13-121" href="#__codelineno-13-121"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-122" name="__codelineno-13-122" href="#__codelineno-13-122"></a>
-<a id="__codelineno-13-123" name="__codelineno-13-123" href="#__codelineno-13-123"></a><span class="w">    </span><span class="cm">/* 末尾要素にアクセス */</span>
-<a id="__codelineno-13-124" name="__codelineno-13-124" href="#__codelineno-13-124"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">peekLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-125" name="__codelineno-13-125" href="#__codelineno-13-125"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
-<a id="__codelineno-13-126" name="__codelineno-13-126" href="#__codelineno-13-126"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Double-ended queue is empty&quot;</span><span class="p">);</span>
-<a id="__codelineno-13-127" name="__codelineno-13-127" href="#__codelineno-13-127"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">rear</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
-<a id="__codelineno-13-128" name="__codelineno-13-128" href="#__codelineno-13-128"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-129" name="__codelineno-13-129" href="#__codelineno-13-129"></a>
-<a id="__codelineno-13-130" name="__codelineno-13-130" href="#__codelineno-13-130"></a><span class="w">    </span><span class="cm">/* 印刷用に配列を返却 */</span>
-<a id="__codelineno-13-131" name="__codelineno-13-131" href="#__codelineno-13-131"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toVector</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-132" name="__codelineno-13-132" href="#__codelineno-13-132"></a><span class="w">        </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
-<a id="__codelineno-13-133" name="__codelineno-13-133" href="#__codelineno-13-133"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">(</span><span class="n">size</span><span class="p">());</span>
-<a id="__codelineno-13-134" name="__codelineno-13-134" href="#__codelineno-13-134"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-135" name="__codelineno-13-135" href="#__codelineno-13-135"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
-<a id="__codelineno-13-136" name="__codelineno-13-136" href="#__codelineno-13-136"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
-<a id="__codelineno-13-137" name="__codelineno-13-137" href="#__codelineno-13-137"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-13-138" name="__codelineno-13-138" href="#__codelineno-13-138"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
-<a id="__codelineno-13-139" name="__codelineno-13-139" href="#__codelineno-13-139"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-140" name="__codelineno-13-140" href="#__codelineno-13-140"></a><span class="p">};</span>
+<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a><span class="k">class</span><span class="w"> </span><span class="nc">LinkedListDeque</span><span class="p">:</span>
+<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;双方向連結リストベースの両端キュー&quot;&quot;&quot;</span>
+<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>
+<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
+<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># 先頭ノード front</span>
+<a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># 末尾ノード rear</span>
+<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># 両端キューの長さ</span>
+<a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a>
+<a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;両端キューの長さを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span>
+<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a>
+<a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">is_empty</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
+<a id="__codelineno-13-24" name="__codelineno-13-24" href="#__codelineno-13-24"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;両端キューが空かどうかを判定&quot;&quot;&quot;</span>
+<a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="mi">0</span>
+<a id="__codelineno-13-26" name="__codelineno-13-26" href="#__codelineno-13-26"></a>
+<a id="__codelineno-13-27" name="__codelineno-13-27" href="#__codelineno-13-27"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">is_front</span><span class="p">:</span> <span class="nb">bool</span><span class="p">):</span>
+<a id="__codelineno-13-28" name="__codelineno-13-28" href="#__codelineno-13-28"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;エンキュー操作&quot;&quot;&quot;</span>
+<a id="__codelineno-13-29" name="__codelineno-13-29" href="#__codelineno-13-29"></a>        <span class="n">node</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-13-30" name="__codelineno-13-30" href="#__codelineno-13-30"></a>        <span class="c1"># 連結リストが空なら、front と rear の両方を node に向ける</span>
+<a id="__codelineno-13-31" name="__codelineno-13-31" href="#__codelineno-13-31"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
+<a id="__codelineno-13-32" name="__codelineno-13-32" href="#__codelineno-13-32"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span> <span class="o">=</span> <span class="n">node</span>
+<a id="__codelineno-13-33" name="__codelineno-13-33" href="#__codelineno-13-33"></a>        <span class="c1"># 先頭へのエンキュー操作</span>
+<a id="__codelineno-13-34" name="__codelineno-13-34" href="#__codelineno-13-34"></a>        <span class="k">elif</span> <span class="n">is_front</span><span class="p">:</span>
+<a id="__codelineno-13-35" name="__codelineno-13-35" href="#__codelineno-13-35"></a>            <span class="c1"># node を連結リストの先頭に追加</span>
+<a id="__codelineno-13-36" name="__codelineno-13-36" href="#__codelineno-13-36"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="o">.</span><span class="n">prev</span> <span class="o">=</span> <span class="n">node</span>
+<a id="__codelineno-13-37" name="__codelineno-13-37" href="#__codelineno-13-37"></a>            <span class="n">node</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span>
+<a id="__codelineno-13-38" name="__codelineno-13-38" href="#__codelineno-13-38"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">=</span> <span class="n">node</span>  <span class="c1"># 先頭ノードを更新する</span>
+<a id="__codelineno-13-39" name="__codelineno-13-39" href="#__codelineno-13-39"></a>        <span class="c1"># 末尾へのエンキュー操作</span>
+<a id="__codelineno-13-40" name="__codelineno-13-40" href="#__codelineno-13-40"></a>        <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-13-41" name="__codelineno-13-41" href="#__codelineno-13-41"></a>            <span class="c1"># node を連結リストの末尾に追加</span>
+<a id="__codelineno-13-42" name="__codelineno-13-42" href="#__codelineno-13-42"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">node</span>
+<a id="__codelineno-13-43" name="__codelineno-13-43" href="#__codelineno-13-43"></a>            <span class="n">node</span><span class="o">.</span><span class="n">prev</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span>
+<a id="__codelineno-13-44" name="__codelineno-13-44" href="#__codelineno-13-44"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span> <span class="o">=</span> <span class="n">node</span>  <span class="c1"># 末尾ノードを更新する</span>
+<a id="__codelineno-13-45" name="__codelineno-13-45" href="#__codelineno-13-45"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">+=</span> <span class="mi">1</span>  <span class="c1"># キューの長さを更新</span>
+<a id="__codelineno-13-46" name="__codelineno-13-46" href="#__codelineno-13-46"></a>
+<a id="__codelineno-13-47" name="__codelineno-13-47" href="#__codelineno-13-47"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push_first</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-13-48" name="__codelineno-13-48" href="#__codelineno-13-48"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キュー先頭にエンキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-13-49" name="__codelineno-13-49" href="#__codelineno-13-49"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span> <span class="kc">True</span><span class="p">)</span>
+<a id="__codelineno-13-50" name="__codelineno-13-50" href="#__codelineno-13-50"></a>
+<a id="__codelineno-13-51" name="__codelineno-13-51" href="#__codelineno-13-51"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push_last</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-13-52" name="__codelineno-13-52" href="#__codelineno-13-52"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キュー末尾にエンキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-13-53" name="__codelineno-13-53" href="#__codelineno-13-53"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span> <span class="kc">False</span><span class="p">)</span>
+<a id="__codelineno-13-54" name="__codelineno-13-54" href="#__codelineno-13-54"></a>
+<a id="__codelineno-13-55" name="__codelineno-13-55" href="#__codelineno-13-55"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">is_front</span><span class="p">:</span> <span class="nb">bool</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-56" name="__codelineno-13-56" href="#__codelineno-13-56"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;デキュー操作&quot;&quot;&quot;</span>
+<a id="__codelineno-13-57" name="__codelineno-13-57" href="#__codelineno-13-57"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
+<a id="__codelineno-13-58" name="__codelineno-13-58" href="#__codelineno-13-58"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;両端キューが空です&quot;</span><span class="p">)</span>
+<a id="__codelineno-13-59" name="__codelineno-13-59" href="#__codelineno-13-59"></a>        <span class="c1"># キュー先頭からの取り出し</span>
+<a id="__codelineno-13-60" name="__codelineno-13-60" href="#__codelineno-13-60"></a>        <span class="k">if</span> <span class="n">is_front</span><span class="p">:</span>
+<a id="__codelineno-13-61" name="__codelineno-13-61" href="#__codelineno-13-61"></a>            <span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="o">.</span><span class="n">val</span>  <span class="c1"># 先頭ノードの値を一時保存</span>
+<a id="__codelineno-13-62" name="__codelineno-13-62" href="#__codelineno-13-62"></a>            <span class="c1"># 先頭ノードを削除</span>
+<a id="__codelineno-13-63" name="__codelineno-13-63" href="#__codelineno-13-63"></a>            <span class="n">fnext</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-13-64" name="__codelineno-13-64" href="#__codelineno-13-64"></a>            <span class="k">if</span> <span class="n">fnext</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-13-65" name="__codelineno-13-65" href="#__codelineno-13-65"></a>                <span class="n">fnext</span><span class="o">.</span><span class="n">prev</span> <span class="o">=</span> <span class="kc">None</span>
+<a id="__codelineno-13-66" name="__codelineno-13-66" href="#__codelineno-13-66"></a>                <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="kc">None</span>
+<a id="__codelineno-13-67" name="__codelineno-13-67" href="#__codelineno-13-67"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">=</span> <span class="n">fnext</span>  <span class="c1"># 先頭ノードを更新する</span>
+<a id="__codelineno-13-68" name="__codelineno-13-68" href="#__codelineno-13-68"></a>        <span class="c1"># キュー末尾からの取り出し</span>
+<a id="__codelineno-13-69" name="__codelineno-13-69" href="#__codelineno-13-69"></a>        <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-13-70" name="__codelineno-13-70" href="#__codelineno-13-70"></a>            <span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span><span class="o">.</span><span class="n">val</span>  <span class="c1"># 末尾ノードの値を一時保存</span>
+<a id="__codelineno-13-71" name="__codelineno-13-71" href="#__codelineno-13-71"></a>            <span class="c1"># 末尾ノードを削除</span>
+<a id="__codelineno-13-72" name="__codelineno-13-72" href="#__codelineno-13-72"></a>            <span class="n">rprev</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span><span class="o">.</span><span class="n">prev</span>
+<a id="__codelineno-13-73" name="__codelineno-13-73" href="#__codelineno-13-73"></a>            <span class="k">if</span> <span class="n">rprev</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-13-74" name="__codelineno-13-74" href="#__codelineno-13-74"></a>                <span class="n">rprev</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="kc">None</span>
+<a id="__codelineno-13-75" name="__codelineno-13-75" href="#__codelineno-13-75"></a>                <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span><span class="o">.</span><span class="n">prev</span> <span class="o">=</span> <span class="kc">None</span>
+<a id="__codelineno-13-76" name="__codelineno-13-76" href="#__codelineno-13-76"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span> <span class="o">=</span> <span class="n">rprev</span>  <span class="c1"># 末尾ノードを更新する</span>
+<a id="__codelineno-13-77" name="__codelineno-13-77" href="#__codelineno-13-77"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-=</span> <span class="mi">1</span>  <span class="c1"># キューの長さを更新</span>
+<a id="__codelineno-13-78" name="__codelineno-13-78" href="#__codelineno-13-78"></a>        <span class="k">return</span> <span class="n">val</span>
+<a id="__codelineno-13-79" name="__codelineno-13-79" href="#__codelineno-13-79"></a>
+<a id="__codelineno-13-80" name="__codelineno-13-80" href="#__codelineno-13-80"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop_first</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-81" name="__codelineno-13-81" href="#__codelineno-13-81"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キュー先頭からデキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-13-82" name="__codelineno-13-82" href="#__codelineno-13-82"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
+<a id="__codelineno-13-83" name="__codelineno-13-83" href="#__codelineno-13-83"></a>
+<a id="__codelineno-13-84" name="__codelineno-13-84" href="#__codelineno-13-84"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop_last</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-85" name="__codelineno-13-85" href="#__codelineno-13-85"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キュー末尾からデキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-13-86" name="__codelineno-13-86" href="#__codelineno-13-86"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
+<a id="__codelineno-13-87" name="__codelineno-13-87" href="#__codelineno-13-87"></a>
+<a id="__codelineno-13-88" name="__codelineno-13-88" href="#__codelineno-13-88"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">peek_first</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-89" name="__codelineno-13-89" href="#__codelineno-13-89"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キュー先頭の要素にアクセス&quot;&quot;&quot;</span>
+<a id="__codelineno-13-90" name="__codelineno-13-90" href="#__codelineno-13-90"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
+<a id="__codelineno-13-91" name="__codelineno-13-91" href="#__codelineno-13-91"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;両端キューが空です&quot;</span><span class="p">)</span>
+<a id="__codelineno-13-92" name="__codelineno-13-92" href="#__codelineno-13-92"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-13-93" name="__codelineno-13-93" href="#__codelineno-13-93"></a>
+<a id="__codelineno-13-94" name="__codelineno-13-94" href="#__codelineno-13-94"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">peek_last</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-95" name="__codelineno-13-95" href="#__codelineno-13-95"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キュー末尾の要素にアクセス&quot;&quot;&quot;</span>
+<a id="__codelineno-13-96" name="__codelineno-13-96" href="#__codelineno-13-96"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
+<a id="__codelineno-13-97" name="__codelineno-13-97" href="#__codelineno-13-97"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;両端キューが空です&quot;</span><span class="p">)</span>
+<a id="__codelineno-13-98" name="__codelineno-13-98" href="#__codelineno-13-98"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-13-99" name="__codelineno-13-99" href="#__codelineno-13-99"></a>
+<a id="__codelineno-13-100" name="__codelineno-13-100" href="#__codelineno-13-100"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">to_array</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-13-101" name="__codelineno-13-101" href="#__codelineno-13-101"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;出力用の配列を返す&quot;&quot;&quot;</span>
+<a id="__codelineno-13-102" name="__codelineno-13-102" href="#__codelineno-13-102"></a>        <span class="n">node</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span>
+<a id="__codelineno-13-103" name="__codelineno-13-103" href="#__codelineno-13-103"></a>        <span class="n">res</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span>
+<a id="__codelineno-13-104" name="__codelineno-13-104" href="#__codelineno-13-104"></a>        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()):</span>
+<a id="__codelineno-13-105" name="__codelineno-13-105" href="#__codelineno-13-105"></a>            <span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">node</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-13-106" name="__codelineno-13-106" href="#__codelineno-13-106"></a>            <span class="n">node</span> <span class="o">=</span> <span class="n">node</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-13-107" name="__codelineno-13-107" href="#__codelineno-13-107"></a>        <span class="k">return</span> <span class="n">res</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_deque.java</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 双方向連結リストノード */</span>
-<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kd">class</span> <span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// ノード値</span>
-<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">next</span><span class="p">;</span><span class="w"> </span><span class="c1">// 後続ノードへの参照</span>
-<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">prev</span><span class="p">;</span><span class="w"> </span><span class="c1">// 前任ノードへの参照</span>
-<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>
-<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">    </span><span class="n">ListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
-<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">        </span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
-<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="p">}</span>
-<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a>
-<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="cm">/* 双方向連結リストに基づく両端キュークラス */</span>
-<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="kd">class</span> <span class="nc">LinkedListDeque</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="n">front</span><span class="p">,</span><span class="w"> </span><span class="n">rear</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノード front、末尾ノード rear</span>
-<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端キューの長さ</span>
-<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a>
-<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">LinkedListDeque</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
-<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a>
-<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a><span class="w">    </span><span class="cm">/* 両端キューの長さを取得 */</span>
-<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
-<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a>
-<a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a><span class="w">    </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
-<a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<div class="highlight"><span class="filename">linkedlist_deque.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 双方向連結リストノード */</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">DoublyListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">              </span><span class="c1">// ノード値</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">next</span><span class="p">;</span><span class="w"> </span><span class="c1">// 後継ノードへのポインタ</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">prev</span><span class="p">;</span><span class="w"> </span><span class="c1">// 前駆ノードへのポインタ</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="n">DoublyListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">val</span><span class="p">),</span><span class="w"> </span><span class="n">prev</span><span class="p">(</span><span class="k">nullptr</span><span class="p">),</span><span class="w"> </span><span class="n">next</span><span class="p">(</span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="p">};</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="cm">/* 双方向連結リストベースの両端キュー */</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="k">class</span><span class="w"> </span><span class="nc">LinkedListDeque</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">    </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">front</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">rear</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノード front、末尾ノード rear</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">              </span><span class="c1">// 両端キューの長さ</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
+<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w">    </span><span class="n">LinkedListDeque</span><span class="p">()</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">front</span><span class="p">(</span><span class="k">nullptr</span><span class="p">),</span><span class="w"> </span><span class="n">rear</span><span class="p">(</span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a>
+<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a><span class="w">    </span><span class="cm">/* デストラクタメソッド */</span>
+<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a><span class="w">    </span><span class="o">~</span><span class="n">LinkedListDeque</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a><span class="w">        </span><span class="c1">// 連結リストを走査してノードを削除し、メモリを解放する</span>
+<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a><span class="w">        </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">pre</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a><span class="w">            </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
+<a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a><span class="w">            </span><span class="k">delete</span><span class="w"> </span><span class="n">pre</span><span class="p">;</span>
+<a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-14-30" name="__codelineno-14-30" href="#__codelineno-14-30"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-31" name="__codelineno-14-31" href="#__codelineno-14-31"></a>
-<a id="__codelineno-14-32" name="__codelineno-14-32" href="#__codelineno-14-32"></a><span class="w">    </span><span class="cm">/* エンキュー操作 */</span>
-<a id="__codelineno-14-33" name="__codelineno-14-33" href="#__codelineno-14-33"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-34" name="__codelineno-14-34" href="#__codelineno-14-34"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
-<a id="__codelineno-14-35" name="__codelineno-14-35" href="#__codelineno-14-35"></a><span class="w">        </span><span class="c1">// リストが空の場合、front と rear の両方を node に指す</span>
-<a id="__codelineno-14-36" name="__codelineno-14-36" href="#__codelineno-14-36"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
-<a id="__codelineno-14-37" name="__codelineno-14-37" href="#__codelineno-14-37"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
-<a id="__codelineno-14-38" name="__codelineno-14-38" href="#__codelineno-14-38"></a><span class="w">        </span><span class="c1">// 先頭エンキュー操作</span>
-<a id="__codelineno-14-39" name="__codelineno-14-39" href="#__codelineno-14-39"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-40" name="__codelineno-14-40" href="#__codelineno-14-40"></a><span class="w">            </span><span class="c1">// node をリストの先頭に追加</span>
-<a id="__codelineno-14-41" name="__codelineno-14-41" href="#__codelineno-14-41"></a><span class="w">            </span><span class="n">front</span><span class="p">.</span><span class="na">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
-<a id="__codelineno-14-42" name="__codelineno-14-42" href="#__codelineno-14-42"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
-<a id="__codelineno-14-43" name="__codelineno-14-43" href="#__codelineno-14-43"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// front を更新</span>
-<a id="__codelineno-14-44" name="__codelineno-14-44" href="#__codelineno-14-44"></a><span class="w">        </span><span class="c1">// 末尾エンキュー操作</span>
-<a id="__codelineno-14-45" name="__codelineno-14-45" href="#__codelineno-14-45"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-46" name="__codelineno-14-46" href="#__codelineno-14-46"></a><span class="w">            </span><span class="c1">// node をリストの末尾に追加</span>
-<a id="__codelineno-14-47" name="__codelineno-14-47" href="#__codelineno-14-47"></a><span class="w">            </span><span class="n">rear</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
-<a id="__codelineno-14-48" name="__codelineno-14-48" href="#__codelineno-14-48"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="na">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="p">;</span>
-<a id="__codelineno-14-49" name="__codelineno-14-49" href="#__codelineno-14-49"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// rear を更新</span>
-<a id="__codelineno-14-50" name="__codelineno-14-50" href="#__codelineno-14-50"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-14-51" name="__codelineno-14-51" href="#__codelineno-14-51"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// 長さを更新</span>
-<a id="__codelineno-14-52" name="__codelineno-14-52" href="#__codelineno-14-52"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-53" name="__codelineno-14-53" href="#__codelineno-14-53"></a>
-<a id="__codelineno-14-54" name="__codelineno-14-54" href="#__codelineno-14-54"></a><span class="w">    </span><span class="cm">/* 先頭エンキュー */</span>
-<a id="__codelineno-14-55" name="__codelineno-14-55" href="#__codelineno-14-55"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">pushFirst</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-56" name="__codelineno-14-56" href="#__codelineno-14-56"></a><span class="w">        </span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kc">true</span><span class="p">);</span>
-<a id="__codelineno-14-57" name="__codelineno-14-57" href="#__codelineno-14-57"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-58" name="__codelineno-14-58" href="#__codelineno-14-58"></a>
-<a id="__codelineno-14-59" name="__codelineno-14-59" href="#__codelineno-14-59"></a><span class="w">    </span><span class="cm">/* 末尾エンキュー */</span>
-<a id="__codelineno-14-60" name="__codelineno-14-60" href="#__codelineno-14-60"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">pushLast</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-61" name="__codelineno-14-61" href="#__codelineno-14-61"></a><span class="w">        </span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kc">false</span><span class="p">);</span>
+<a id="__codelineno-14-32" name="__codelineno-14-32" href="#__codelineno-14-32"></a><span class="w">    </span><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-14-33" name="__codelineno-14-33" href="#__codelineno-14-33"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-34" name="__codelineno-14-34" href="#__codelineno-14-34"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-14-35" name="__codelineno-14-35" href="#__codelineno-14-35"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-36" name="__codelineno-14-36" href="#__codelineno-14-36"></a>
+<a id="__codelineno-14-37" name="__codelineno-14-37" href="#__codelineno-14-37"></a><span class="w">    </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
+<a id="__codelineno-14-38" name="__codelineno-14-38" href="#__codelineno-14-38"></a><span class="w">    </span><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-39" name="__codelineno-14-39" href="#__codelineno-14-39"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-14-40" name="__codelineno-14-40" href="#__codelineno-14-40"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-41" name="__codelineno-14-41" href="#__codelineno-14-41"></a>
+<a id="__codelineno-14-42" name="__codelineno-14-42" href="#__codelineno-14-42"></a><span class="w">    </span><span class="cm">/* エンキュー操作 */</span>
+<a id="__codelineno-14-43" name="__codelineno-14-43" href="#__codelineno-14-43"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-44" name="__codelineno-14-44" href="#__codelineno-14-44"></a><span class="w">        </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">DoublyListNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-14-45" name="__codelineno-14-45" href="#__codelineno-14-45"></a><span class="w">        </span><span class="c1">// 連結リストが空なら、front と rear の両方を node に向ける</span>
+<a id="__codelineno-14-46" name="__codelineno-14-46" href="#__codelineno-14-46"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-14-47" name="__codelineno-14-47" href="#__codelineno-14-47"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-14-48" name="__codelineno-14-48" href="#__codelineno-14-48"></a><span class="w">        </span><span class="c1">// 先頭へのエンキュー操作</span>
+<a id="__codelineno-14-49" name="__codelineno-14-49" href="#__codelineno-14-49"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-50" name="__codelineno-14-50" href="#__codelineno-14-50"></a><span class="w">            </span><span class="c1">// node を連結リストの先頭に追加</span>
+<a id="__codelineno-14-51" name="__codelineno-14-51" href="#__codelineno-14-51"></a><span class="w">            </span><span class="n">front</span><span class="o">-&gt;</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-14-52" name="__codelineno-14-52" href="#__codelineno-14-52"></a><span class="w">            </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-14-53" name="__codelineno-14-53" href="#__codelineno-14-53"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードを更新する</span>
+<a id="__codelineno-14-54" name="__codelineno-14-54" href="#__codelineno-14-54"></a><span class="w">        </span><span class="c1">// 末尾へのエンキュー操作</span>
+<a id="__codelineno-14-55" name="__codelineno-14-55" href="#__codelineno-14-55"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-56" name="__codelineno-14-56" href="#__codelineno-14-56"></a><span class="w">            </span><span class="c1">// node を連結リストの末尾に追加</span>
+<a id="__codelineno-14-57" name="__codelineno-14-57" href="#__codelineno-14-57"></a><span class="w">            </span><span class="n">rear</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-14-58" name="__codelineno-14-58" href="#__codelineno-14-58"></a><span class="w">            </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="p">;</span>
+<a id="__codelineno-14-59" name="__codelineno-14-59" href="#__codelineno-14-59"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノードを更新する</span>
+<a id="__codelineno-14-60" name="__codelineno-14-60" href="#__codelineno-14-60"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-14-61" name="__codelineno-14-61" href="#__codelineno-14-61"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの長さを更新</span>
 <a id="__codelineno-14-62" name="__codelineno-14-62" href="#__codelineno-14-62"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-63" name="__codelineno-14-63" href="#__codelineno-14-63"></a>
-<a id="__codelineno-14-64" name="__codelineno-14-64" href="#__codelineno-14-64"></a><span class="w">    </span><span class="cm">/* デキュー操作 */</span>
-<a id="__codelineno-14-65" name="__codelineno-14-65" href="#__codelineno-14-65"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="kt">boolean</span><span class="w"> </span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-66" name="__codelineno-14-66" href="#__codelineno-14-66"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
-<a id="__codelineno-14-67" name="__codelineno-14-67" href="#__codelineno-14-67"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
-<a id="__codelineno-14-68" name="__codelineno-14-68" href="#__codelineno-14-68"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
-<a id="__codelineno-14-69" name="__codelineno-14-69" href="#__codelineno-14-69"></a><span class="w">        </span><span class="c1">// 先頭デキュー操作</span>
-<a id="__codelineno-14-70" name="__codelineno-14-70" href="#__codelineno-14-70"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-71" name="__codelineno-14-71" href="#__codelineno-14-71"></a><span class="w">            </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">.</span><span class="na">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 一時的に先頭ノード値を保存</span>
-<a id="__codelineno-14-72" name="__codelineno-14-72" href="#__codelineno-14-72"></a><span class="w">            </span><span class="c1">// 次のノードを削除</span>
-<a id="__codelineno-14-73" name="__codelineno-14-73" href="#__codelineno-14-73"></a><span class="w">            </span><span class="n">ListNode</span><span class="w"> </span><span class="n">fNext</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
-<a id="__codelineno-14-74" name="__codelineno-14-74" href="#__codelineno-14-74"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">fNext</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-75" name="__codelineno-14-75" href="#__codelineno-14-75"></a><span class="w">                </span><span class="n">fNext</span><span class="p">.</span><span class="na">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
-<a id="__codelineno-14-76" name="__codelineno-14-76" href="#__codelineno-14-76"></a><span class="w">                </span><span class="n">front</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
-<a id="__codelineno-14-77" name="__codelineno-14-77" href="#__codelineno-14-77"></a><span class="w">            </span><span class="p">}</span>
-<a id="__codelineno-14-78" name="__codelineno-14-78" href="#__codelineno-14-78"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fNext</span><span class="p">;</span><span class="w"> </span><span class="c1">// front を更新</span>
-<a id="__codelineno-14-79" name="__codelineno-14-79" href="#__codelineno-14-79"></a><span class="w">        </span><span class="c1">// 末尾デキュー操作</span>
-<a id="__codelineno-14-80" name="__codelineno-14-80" href="#__codelineno-14-80"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-81" name="__codelineno-14-81" href="#__codelineno-14-81"></a><span class="w">            </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="p">.</span><span class="na">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 一時的に末尾ノード値を保存</span>
-<a id="__codelineno-14-82" name="__codelineno-14-82" href="#__codelineno-14-82"></a><span class="w">            </span><span class="c1">// 前のノードを削除</span>
-<a id="__codelineno-14-83" name="__codelineno-14-83" href="#__codelineno-14-83"></a><span class="w">            </span><span class="n">ListNode</span><span class="w"> </span><span class="n">rPrev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="p">.</span><span class="na">prev</span><span class="p">;</span>
-<a id="__codelineno-14-84" name="__codelineno-14-84" href="#__codelineno-14-84"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">rPrev</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-85" name="__codelineno-14-85" href="#__codelineno-14-85"></a><span class="w">                </span><span class="n">rPrev</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
-<a id="__codelineno-14-86" name="__codelineno-14-86" href="#__codelineno-14-86"></a><span class="w">                </span><span class="n">rear</span><span class="p">.</span><span class="na">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-14-64" name="__codelineno-14-64" href="#__codelineno-14-64"></a><span class="w">    </span><span class="cm">/* キュー先頭にエンキュー */</span>
+<a id="__codelineno-14-65" name="__codelineno-14-65" href="#__codelineno-14-65"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">pushFirst</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-66" name="__codelineno-14-66" href="#__codelineno-14-66"></a><span class="w">        </span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="nb">true</span><span class="p">);</span>
+<a id="__codelineno-14-67" name="__codelineno-14-67" href="#__codelineno-14-67"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-68" name="__codelineno-14-68" href="#__codelineno-14-68"></a>
+<a id="__codelineno-14-69" name="__codelineno-14-69" href="#__codelineno-14-69"></a><span class="w">    </span><span class="cm">/* キュー末尾にエンキュー */</span>
+<a id="__codelineno-14-70" name="__codelineno-14-70" href="#__codelineno-14-70"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">pushLast</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-71" name="__codelineno-14-71" href="#__codelineno-14-71"></a><span class="w">        </span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="nb">false</span><span class="p">);</span>
+<a id="__codelineno-14-72" name="__codelineno-14-72" href="#__codelineno-14-72"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-73" name="__codelineno-14-73" href="#__codelineno-14-73"></a>
+<a id="__codelineno-14-74" name="__codelineno-14-74" href="#__codelineno-14-74"></a><span class="w">    </span><span class="cm">/* デキュー操作 */</span>
+<a id="__codelineno-14-75" name="__codelineno-14-75" href="#__codelineno-14-75"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="kt">bool</span><span class="w"> </span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-76" name="__codelineno-14-76" href="#__codelineno-14-76"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-14-77" name="__codelineno-14-77" href="#__codelineno-14-77"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;キューが空です&quot;</span><span class="p">);</span>
+<a id="__codelineno-14-78" name="__codelineno-14-78" href="#__codelineno-14-78"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-14-79" name="__codelineno-14-79" href="#__codelineno-14-79"></a><span class="w">        </span><span class="c1">// キュー先頭からの取り出し</span>
+<a id="__codelineno-14-80" name="__codelineno-14-80" href="#__codelineno-14-80"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-81" name="__codelineno-14-81" href="#__codelineno-14-81"></a><span class="w">            </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードの値を一時保存</span>
+<a id="__codelineno-14-82" name="__codelineno-14-82" href="#__codelineno-14-82"></a><span class="w">            </span><span class="c1">// 先頭ノードを削除</span>
+<a id="__codelineno-14-83" name="__codelineno-14-83" href="#__codelineno-14-83"></a><span class="w">            </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">fNext</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-14-84" name="__codelineno-14-84" href="#__codelineno-14-84"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">fNext</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-85" name="__codelineno-14-85" href="#__codelineno-14-85"></a><span class="w">                </span><span class="n">fNext</span><span class="o">-&gt;</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
+<a id="__codelineno-14-86" name="__codelineno-14-86" href="#__codelineno-14-86"></a><span class="w">                </span><span class="n">front</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
 <a id="__codelineno-14-87" name="__codelineno-14-87" href="#__codelineno-14-87"></a><span class="w">            </span><span class="p">}</span>
-<a id="__codelineno-14-88" name="__codelineno-14-88" href="#__codelineno-14-88"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rPrev</span><span class="p">;</span><span class="w"> </span><span class="c1">// rear を更新</span>
-<a id="__codelineno-14-89" name="__codelineno-14-89" href="#__codelineno-14-89"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-14-90" name="__codelineno-14-90" href="#__codelineno-14-90"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// 長さを更新</span>
-<a id="__codelineno-14-91" name="__codelineno-14-91" href="#__codelineno-14-91"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
-<a id="__codelineno-14-92" name="__codelineno-14-92" href="#__codelineno-14-92"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-93" name="__codelineno-14-93" href="#__codelineno-14-93"></a>
-<a id="__codelineno-14-94" name="__codelineno-14-94" href="#__codelineno-14-94"></a><span class="w">    </span><span class="cm">/* 先頭デキュー */</span>
-<a id="__codelineno-14-95" name="__codelineno-14-95" href="#__codelineno-14-95"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">popFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-96" name="__codelineno-14-96" href="#__codelineno-14-96"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="kc">true</span><span class="p">);</span>
-<a id="__codelineno-14-97" name="__codelineno-14-97" href="#__codelineno-14-97"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-98" name="__codelineno-14-98" href="#__codelineno-14-98"></a>
-<a id="__codelineno-14-99" name="__codelineno-14-99" href="#__codelineno-14-99"></a><span class="w">    </span><span class="cm">/* 末尾デキュー */</span>
-<a id="__codelineno-14-100" name="__codelineno-14-100" href="#__codelineno-14-100"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">popLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-101" name="__codelineno-14-101" href="#__codelineno-14-101"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="kc">false</span><span class="p">);</span>
-<a id="__codelineno-14-102" name="__codelineno-14-102" href="#__codelineno-14-102"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-103" name="__codelineno-14-103" href="#__codelineno-14-103"></a>
-<a id="__codelineno-14-104" name="__codelineno-14-104" href="#__codelineno-14-104"></a><span class="w">    </span><span class="cm">/* 先頭要素にアクセス */</span>
-<a id="__codelineno-14-105" name="__codelineno-14-105" href="#__codelineno-14-105"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">peekFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-106" name="__codelineno-14-106" href="#__codelineno-14-106"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
-<a id="__codelineno-14-107" name="__codelineno-14-107" href="#__codelineno-14-107"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
-<a id="__codelineno-14-108" name="__codelineno-14-108" href="#__codelineno-14-108"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">front</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
+<a id="__codelineno-14-88" name="__codelineno-14-88" href="#__codelineno-14-88"></a><span class="w">            </span><span class="k">delete</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-14-89" name="__codelineno-14-89" href="#__codelineno-14-89"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fNext</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードを更新する</span>
+<a id="__codelineno-14-90" name="__codelineno-14-90" href="#__codelineno-14-90"></a><span class="w">        </span><span class="c1">// キュー末尾からの取り出し</span>
+<a id="__codelineno-14-91" name="__codelineno-14-91" href="#__codelineno-14-91"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-92" name="__codelineno-14-92" href="#__codelineno-14-92"></a><span class="w">            </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノードの値を一時保存</span>
+<a id="__codelineno-14-93" name="__codelineno-14-93" href="#__codelineno-14-93"></a><span class="w">            </span><span class="c1">// 末尾ノードを削除</span>
+<a id="__codelineno-14-94" name="__codelineno-14-94" href="#__codelineno-14-94"></a><span class="w">            </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">rPrev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="o">-&gt;</span><span class="n">prev</span><span class="p">;</span>
+<a id="__codelineno-14-95" name="__codelineno-14-95" href="#__codelineno-14-95"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">rPrev</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-96" name="__codelineno-14-96" href="#__codelineno-14-96"></a><span class="w">                </span><span class="n">rPrev</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
+<a id="__codelineno-14-97" name="__codelineno-14-97" href="#__codelineno-14-97"></a><span class="w">                </span><span class="n">rear</span><span class="o">-&gt;</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
+<a id="__codelineno-14-98" name="__codelineno-14-98" href="#__codelineno-14-98"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-14-99" name="__codelineno-14-99" href="#__codelineno-14-99"></a><span class="w">            </span><span class="k">delete</span><span class="w"> </span><span class="n">rear</span><span class="p">;</span>
+<a id="__codelineno-14-100" name="__codelineno-14-100" href="#__codelineno-14-100"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rPrev</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノードを更新する</span>
+<a id="__codelineno-14-101" name="__codelineno-14-101" href="#__codelineno-14-101"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-14-102" name="__codelineno-14-102" href="#__codelineno-14-102"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの長さを更新</span>
+<a id="__codelineno-14-103" name="__codelineno-14-103" href="#__codelineno-14-103"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-14-104" name="__codelineno-14-104" href="#__codelineno-14-104"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-105" name="__codelineno-14-105" href="#__codelineno-14-105"></a>
+<a id="__codelineno-14-106" name="__codelineno-14-106" href="#__codelineno-14-106"></a><span class="w">    </span><span class="cm">/* キュー先頭からデキュー */</span>
+<a id="__codelineno-14-107" name="__codelineno-14-107" href="#__codelineno-14-107"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">popFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-108" name="__codelineno-14-108" href="#__codelineno-14-108"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="nb">true</span><span class="p">);</span>
 <a id="__codelineno-14-109" name="__codelineno-14-109" href="#__codelineno-14-109"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-110" name="__codelineno-14-110" href="#__codelineno-14-110"></a>
-<a id="__codelineno-14-111" name="__codelineno-14-111" href="#__codelineno-14-111"></a><span class="w">    </span><span class="cm">/* 末尾要素にアクセス */</span>
-<a id="__codelineno-14-112" name="__codelineno-14-112" href="#__codelineno-14-112"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">peekLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-113" name="__codelineno-14-113" href="#__codelineno-14-113"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
-<a id="__codelineno-14-114" name="__codelineno-14-114" href="#__codelineno-14-114"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
-<a id="__codelineno-14-115" name="__codelineno-14-115" href="#__codelineno-14-115"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">rear</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
-<a id="__codelineno-14-116" name="__codelineno-14-116" href="#__codelineno-14-116"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-117" name="__codelineno-14-117" href="#__codelineno-14-117"></a>
-<a id="__codelineno-14-118" name="__codelineno-14-118" href="#__codelineno-14-118"></a><span class="w">    </span><span class="cm">/* 配列を返す */</span>
-<a id="__codelineno-14-119" name="__codelineno-14-119" href="#__codelineno-14-119"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-120" name="__codelineno-14-120" href="#__codelineno-14-120"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
-<a id="__codelineno-14-121" name="__codelineno-14-121" href="#__codelineno-14-121"></a><span class="w">        </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">size</span><span class="p">()</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-14-122" name="__codelineno-14-122" href="#__codelineno-14-122"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-123" name="__codelineno-14-123" href="#__codelineno-14-123"></a><span class="w">            </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
-<a id="__codelineno-14-124" name="__codelineno-14-124" href="#__codelineno-14-124"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
-<a id="__codelineno-14-125" name="__codelineno-14-125" href="#__codelineno-14-125"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-14-126" name="__codelineno-14-126" href="#__codelineno-14-126"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
-<a id="__codelineno-14-127" name="__codelineno-14-127" href="#__codelineno-14-127"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-128" name="__codelineno-14-128" href="#__codelineno-14-128"></a><span class="p">}</span>
+<a id="__codelineno-14-111" name="__codelineno-14-111" href="#__codelineno-14-111"></a><span class="w">    </span><span class="cm">/* キュー末尾からデキュー */</span>
+<a id="__codelineno-14-112" name="__codelineno-14-112" href="#__codelineno-14-112"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">popLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-113" name="__codelineno-14-113" href="#__codelineno-14-113"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="nb">false</span><span class="p">);</span>
+<a id="__codelineno-14-114" name="__codelineno-14-114" href="#__codelineno-14-114"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-115" name="__codelineno-14-115" href="#__codelineno-14-115"></a>
+<a id="__codelineno-14-116" name="__codelineno-14-116" href="#__codelineno-14-116"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-14-117" name="__codelineno-14-117" href="#__codelineno-14-117"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">peekFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-118" name="__codelineno-14-118" href="#__codelineno-14-118"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-14-119" name="__codelineno-14-119" href="#__codelineno-14-119"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;両端キューが空です&quot;</span><span class="p">);</span>
+<a id="__codelineno-14-120" name="__codelineno-14-120" href="#__codelineno-14-120"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">front</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-14-121" name="__codelineno-14-121" href="#__codelineno-14-121"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-122" name="__codelineno-14-122" href="#__codelineno-14-122"></a>
+<a id="__codelineno-14-123" name="__codelineno-14-123" href="#__codelineno-14-123"></a><span class="w">    </span><span class="cm">/* キュー末尾の要素にアクセス */</span>
+<a id="__codelineno-14-124" name="__codelineno-14-124" href="#__codelineno-14-124"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">peekLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-125" name="__codelineno-14-125" href="#__codelineno-14-125"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-14-126" name="__codelineno-14-126" href="#__codelineno-14-126"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;両端キューが空です&quot;</span><span class="p">);</span>
+<a id="__codelineno-14-127" name="__codelineno-14-127" href="#__codelineno-14-127"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">rear</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-14-128" name="__codelineno-14-128" href="#__codelineno-14-128"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-129" name="__codelineno-14-129" href="#__codelineno-14-129"></a>
+<a id="__codelineno-14-130" name="__codelineno-14-130" href="#__codelineno-14-130"></a><span class="w">    </span><span class="cm">/* 出力用の配列を返す */</span>
+<a id="__codelineno-14-131" name="__codelineno-14-131" href="#__codelineno-14-131"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toVector</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-132" name="__codelineno-14-132" href="#__codelineno-14-132"></a><span class="w">        </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-14-133" name="__codelineno-14-133" href="#__codelineno-14-133"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">(</span><span class="n">size</span><span class="p">());</span>
+<a id="__codelineno-14-134" name="__codelineno-14-134" href="#__codelineno-14-134"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-135" name="__codelineno-14-135" href="#__codelineno-14-135"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-14-136" name="__codelineno-14-136" href="#__codelineno-14-136"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-14-137" name="__codelineno-14-137" href="#__codelineno-14-137"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-14-138" name="__codelineno-14-138" href="#__codelineno-14-138"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-14-139" name="__codelineno-14-139" href="#__codelineno-14-139"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-140" name="__codelineno-14-140" href="#__codelineno-14-140"></a><span class="p">};</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_deque.cs</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">ListNode</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
-<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a>
-<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">LinkedListDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">linkedlist_deque.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 双方向連結リストノード */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kd">class</span> <span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// ノード値</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">next</span><span class="p">;</span><span class="w"> </span><span class="c1">// 後続ノードへの参照</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">prev</span><span class="p">;</span><span class="w"> </span><span class="c1">// 前駆ノードへの参照</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="n">ListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">        </span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="p">}</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="cm">/* 双方向連結リストベースの両端キュー */</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="kd">class</span> <span class="nc">LinkedListDeque</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="n">front</span><span class="p">,</span><span class="w"> </span><span class="n">rear</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノード front、末尾ノード rear</span>
+<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端キューの長さ</span>
+<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a>
+<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">LinkedListDeque</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a>
+<a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="w">    </span><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-24" name="__codelineno-15-24" href="#__codelineno-15-24"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-26" name="__codelineno-15-26" href="#__codelineno-15-26"></a>
+<a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></a><span class="w">    </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
+<a id="__codelineno-15-28" name="__codelineno-15-28" href="#__codelineno-15-28"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-29" name="__codelineno-15-29" href="#__codelineno-15-29"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-15-30" name="__codelineno-15-30" href="#__codelineno-15-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-31" name="__codelineno-15-31" href="#__codelineno-15-31"></a>
+<a id="__codelineno-15-32" name="__codelineno-15-32" href="#__codelineno-15-32"></a><span class="w">    </span><span class="cm">/* エンキュー操作 */</span>
+<a id="__codelineno-15-33" name="__codelineno-15-33" href="#__codelineno-15-33"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-34" name="__codelineno-15-34" href="#__codelineno-15-34"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-15-35" name="__codelineno-15-35" href="#__codelineno-15-35"></a><span class="w">        </span><span class="c1">// 連結リストが空なら、front と rear の両方を node に向ける</span>
+<a id="__codelineno-15-36" name="__codelineno-15-36" href="#__codelineno-15-36"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-15-37" name="__codelineno-15-37" href="#__codelineno-15-37"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-15-38" name="__codelineno-15-38" href="#__codelineno-15-38"></a><span class="w">        </span><span class="c1">// 先頭へのエンキュー操作</span>
+<a id="__codelineno-15-39" name="__codelineno-15-39" href="#__codelineno-15-39"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-40" name="__codelineno-15-40" href="#__codelineno-15-40"></a><span class="w">            </span><span class="c1">// node を連結リストの先頭に追加</span>
+<a id="__codelineno-15-41" name="__codelineno-15-41" href="#__codelineno-15-41"></a><span class="w">            </span><span class="n">front</span><span class="p">.</span><span class="na">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-15-42" name="__codelineno-15-42" href="#__codelineno-15-42"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-15-43" name="__codelineno-15-43" href="#__codelineno-15-43"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードを更新する</span>
+<a id="__codelineno-15-44" name="__codelineno-15-44" href="#__codelineno-15-44"></a><span class="w">        </span><span class="c1">// 末尾へのエンキュー操作</span>
+<a id="__codelineno-15-45" name="__codelineno-15-45" href="#__codelineno-15-45"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-46" name="__codelineno-15-46" href="#__codelineno-15-46"></a><span class="w">            </span><span class="c1">// node を連結リストの末尾に追加</span>
+<a id="__codelineno-15-47" name="__codelineno-15-47" href="#__codelineno-15-47"></a><span class="w">            </span><span class="n">rear</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-15-48" name="__codelineno-15-48" href="#__codelineno-15-48"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="na">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="p">;</span>
+<a id="__codelineno-15-49" name="__codelineno-15-49" href="#__codelineno-15-49"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノードを更新する</span>
+<a id="__codelineno-15-50" name="__codelineno-15-50" href="#__codelineno-15-50"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-51" name="__codelineno-15-51" href="#__codelineno-15-51"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの長さを更新</span>
+<a id="__codelineno-15-52" name="__codelineno-15-52" href="#__codelineno-15-52"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-53" name="__codelineno-15-53" href="#__codelineno-15-53"></a>
+<a id="__codelineno-15-54" name="__codelineno-15-54" href="#__codelineno-15-54"></a><span class="w">    </span><span class="cm">/* キュー先頭にエンキュー */</span>
+<a id="__codelineno-15-55" name="__codelineno-15-55" href="#__codelineno-15-55"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">pushFirst</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-56" name="__codelineno-15-56" href="#__codelineno-15-56"></a><span class="w">        </span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kc">true</span><span class="p">);</span>
+<a id="__codelineno-15-57" name="__codelineno-15-57" href="#__codelineno-15-57"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-58" name="__codelineno-15-58" href="#__codelineno-15-58"></a>
+<a id="__codelineno-15-59" name="__codelineno-15-59" href="#__codelineno-15-59"></a><span class="w">    </span><span class="cm">/* キュー末尾にエンキュー */</span>
+<a id="__codelineno-15-60" name="__codelineno-15-60" href="#__codelineno-15-60"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">pushLast</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-61" name="__codelineno-15-61" href="#__codelineno-15-61"></a><span class="w">        </span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kc">false</span><span class="p">);</span>
+<a id="__codelineno-15-62" name="__codelineno-15-62" href="#__codelineno-15-62"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-63" name="__codelineno-15-63" href="#__codelineno-15-63"></a>
+<a id="__codelineno-15-64" name="__codelineno-15-64" href="#__codelineno-15-64"></a><span class="w">    </span><span class="cm">/* デキュー操作 */</span>
+<a id="__codelineno-15-65" name="__codelineno-15-65" href="#__codelineno-15-65"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="kt">boolean</span><span class="w"> </span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-66" name="__codelineno-15-66" href="#__codelineno-15-66"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-15-67" name="__codelineno-15-67" href="#__codelineno-15-67"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
+<a id="__codelineno-15-68" name="__codelineno-15-68" href="#__codelineno-15-68"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-15-69" name="__codelineno-15-69" href="#__codelineno-15-69"></a><span class="w">        </span><span class="c1">// キュー先頭からの取り出し</span>
+<a id="__codelineno-15-70" name="__codelineno-15-70" href="#__codelineno-15-70"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-71" name="__codelineno-15-71" href="#__codelineno-15-71"></a><span class="w">            </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">.</span><span class="na">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードの値を一時保存</span>
+<a id="__codelineno-15-72" name="__codelineno-15-72" href="#__codelineno-15-72"></a><span class="w">            </span><span class="c1">// 先頭ノードを削除</span>
+<a id="__codelineno-15-73" name="__codelineno-15-73" href="#__codelineno-15-73"></a><span class="w">            </span><span class="n">ListNode</span><span class="w"> </span><span class="n">fNext</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
+<a id="__codelineno-15-74" name="__codelineno-15-74" href="#__codelineno-15-74"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">fNext</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-75" name="__codelineno-15-75" href="#__codelineno-15-75"></a><span class="w">                </span><span class="n">fNext</span><span class="p">.</span><span class="na">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-15-76" name="__codelineno-15-76" href="#__codelineno-15-76"></a><span class="w">                </span><span class="n">front</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-15-77" name="__codelineno-15-77" href="#__codelineno-15-77"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-15-78" name="__codelineno-15-78" href="#__codelineno-15-78"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fNext</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードを更新する</span>
+<a id="__codelineno-15-79" name="__codelineno-15-79" href="#__codelineno-15-79"></a><span class="w">        </span><span class="c1">// キュー末尾からの取り出し</span>
+<a id="__codelineno-15-80" name="__codelineno-15-80" href="#__codelineno-15-80"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-81" name="__codelineno-15-81" href="#__codelineno-15-81"></a><span class="w">            </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="p">.</span><span class="na">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノードの値を一時保存</span>
+<a id="__codelineno-15-82" name="__codelineno-15-82" href="#__codelineno-15-82"></a><span class="w">            </span><span class="c1">// 末尾ノードを削除</span>
+<a id="__codelineno-15-83" name="__codelineno-15-83" href="#__codelineno-15-83"></a><span class="w">            </span><span class="n">ListNode</span><span class="w"> </span><span class="n">rPrev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="p">.</span><span class="na">prev</span><span class="p">;</span>
+<a id="__codelineno-15-84" name="__codelineno-15-84" href="#__codelineno-15-84"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">rPrev</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-85" name="__codelineno-15-85" href="#__codelineno-15-85"></a><span class="w">                </span><span class="n">rPrev</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-15-86" name="__codelineno-15-86" href="#__codelineno-15-86"></a><span class="w">                </span><span class="n">rear</span><span class="p">.</span><span class="na">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-15-87" name="__codelineno-15-87" href="#__codelineno-15-87"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-15-88" name="__codelineno-15-88" href="#__codelineno-15-88"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rPrev</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノードを更新する</span>
+<a id="__codelineno-15-89" name="__codelineno-15-89" href="#__codelineno-15-89"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-90" name="__codelineno-15-90" href="#__codelineno-15-90"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの長さを更新</span>
+<a id="__codelineno-15-91" name="__codelineno-15-91" href="#__codelineno-15-91"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-15-92" name="__codelineno-15-92" href="#__codelineno-15-92"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-93" name="__codelineno-15-93" href="#__codelineno-15-93"></a>
+<a id="__codelineno-15-94" name="__codelineno-15-94" href="#__codelineno-15-94"></a><span class="w">    </span><span class="cm">/* キュー先頭からデキュー */</span>
+<a id="__codelineno-15-95" name="__codelineno-15-95" href="#__codelineno-15-95"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">popFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-96" name="__codelineno-15-96" href="#__codelineno-15-96"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="kc">true</span><span class="p">);</span>
+<a id="__codelineno-15-97" name="__codelineno-15-97" href="#__codelineno-15-97"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-98" name="__codelineno-15-98" href="#__codelineno-15-98"></a>
+<a id="__codelineno-15-99" name="__codelineno-15-99" href="#__codelineno-15-99"></a><span class="w">    </span><span class="cm">/* キュー末尾からデキュー */</span>
+<a id="__codelineno-15-100" name="__codelineno-15-100" href="#__codelineno-15-100"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">popLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-101" name="__codelineno-15-101" href="#__codelineno-15-101"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="kc">false</span><span class="p">);</span>
+<a id="__codelineno-15-102" name="__codelineno-15-102" href="#__codelineno-15-102"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-103" name="__codelineno-15-103" href="#__codelineno-15-103"></a>
+<a id="__codelineno-15-104" name="__codelineno-15-104" href="#__codelineno-15-104"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-15-105" name="__codelineno-15-105" href="#__codelineno-15-105"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">peekFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-106" name="__codelineno-15-106" href="#__codelineno-15-106"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-15-107" name="__codelineno-15-107" href="#__codelineno-15-107"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
+<a id="__codelineno-15-108" name="__codelineno-15-108" href="#__codelineno-15-108"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">front</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
+<a id="__codelineno-15-109" name="__codelineno-15-109" href="#__codelineno-15-109"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-110" name="__codelineno-15-110" href="#__codelineno-15-110"></a>
+<a id="__codelineno-15-111" name="__codelineno-15-111" href="#__codelineno-15-111"></a><span class="w">    </span><span class="cm">/* キュー末尾の要素にアクセス */</span>
+<a id="__codelineno-15-112" name="__codelineno-15-112" href="#__codelineno-15-112"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">peekLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-113" name="__codelineno-15-113" href="#__codelineno-15-113"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-15-114" name="__codelineno-15-114" href="#__codelineno-15-114"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
+<a id="__codelineno-15-115" name="__codelineno-15-115" href="#__codelineno-15-115"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">rear</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
+<a id="__codelineno-15-116" name="__codelineno-15-116" href="#__codelineno-15-116"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-117" name="__codelineno-15-117" href="#__codelineno-15-117"></a>
+<a id="__codelineno-15-118" name="__codelineno-15-118" href="#__codelineno-15-118"></a><span class="w">    </span><span class="cm">/* 出力用の配列を返す */</span>
+<a id="__codelineno-15-119" name="__codelineno-15-119" href="#__codelineno-15-119"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-120" name="__codelineno-15-120" href="#__codelineno-15-120"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-15-121" name="__codelineno-15-121" href="#__codelineno-15-121"></a><span class="w">        </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">size</span><span class="p">()</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-15-122" name="__codelineno-15-122" href="#__codelineno-15-122"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-123" name="__codelineno-15-123" href="#__codelineno-15-123"></a><span class="w">            </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
+<a id="__codelineno-15-124" name="__codelineno-15-124" href="#__codelineno-15-124"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
+<a id="__codelineno-15-125" name="__codelineno-15-125" href="#__codelineno-15-125"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-126" name="__codelineno-15-126" href="#__codelineno-15-126"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-15-127" name="__codelineno-15-127" href="#__codelineno-15-127"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-128" name="__codelineno-15-128" href="#__codelineno-15-128"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_deque.go</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">linkedListDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">linkedlist_deque.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 双方向連結リストノード */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="k">class</span><span class="w"> </span><span class="nf">ListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">       </span><span class="c1">// ノード値</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">null</span><span class="p">;</span><span class="w"> </span><span class="c1">// 後続ノードへの参照</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">null</span><span class="p">;</span><span class="w"> </span><span class="c1">// 前駆ノードへの参照</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="p">}</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="cm">/* 双方向連結リストベースの両端キュー */</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="k">class</span><span class="w"> </span><span class="nc">LinkedListDeque</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">front</span><span class="p">,</span><span class="w"> </span><span class="n">rear</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノード front、末尾ノード rear</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">      </span><span class="c1">// 両端キューの長さ</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nf">LinkedListDeque</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">        </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">    </span><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a>
+<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="w">    </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
+<a id="__codelineno-16-24" name="__codelineno-16-24" href="#__codelineno-16-24"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="nf">IsEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-25" name="__codelineno-16-25" href="#__codelineno-16-25"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nf">Size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-16-26" name="__codelineno-16-26" href="#__codelineno-16-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-27" name="__codelineno-16-27" href="#__codelineno-16-27"></a>
+<a id="__codelineno-16-28" name="__codelineno-16-28" href="#__codelineno-16-28"></a><span class="w">    </span><span class="cm">/* エンキュー操作 */</span>
+<a id="__codelineno-16-29" name="__codelineno-16-29" href="#__codelineno-16-29"></a><span class="w">    </span><span class="k">void</span><span class="w"> </span><span class="nf">Push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-30" name="__codelineno-16-30" href="#__codelineno-16-30"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-16-31" name="__codelineno-16-31" href="#__codelineno-16-31"></a><span class="w">        </span><span class="c1">// 連結リストが空なら、front と rear の両方を node に向ける</span>
+<a id="__codelineno-16-32" name="__codelineno-16-32" href="#__codelineno-16-32"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-33" name="__codelineno-16-33" href="#__codelineno-16-33"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-16-34" name="__codelineno-16-34" href="#__codelineno-16-34"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-16-35" name="__codelineno-16-35" href="#__codelineno-16-35"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-36" name="__codelineno-16-36" href="#__codelineno-16-36"></a><span class="w">        </span><span class="c1">// 先頭へのエンキュー操作</span>
+<a id="__codelineno-16-37" name="__codelineno-16-37" href="#__codelineno-16-37"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="nf">if</span><span class="w"> </span><span class="p">(</span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-38" name="__codelineno-16-38" href="#__codelineno-16-38"></a><span class="w">            </span><span class="c1">// node を連結リストの先頭に追加</span>
+<a id="__codelineno-16-39" name="__codelineno-16-39" href="#__codelineno-16-39"></a><span class="w">            </span><span class="n">front</span><span class="o">!</span><span class="p">.</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-16-40" name="__codelineno-16-40" href="#__codelineno-16-40"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-16-41" name="__codelineno-16-41" href="#__codelineno-16-41"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードを更新する</span>
+<a id="__codelineno-16-42" name="__codelineno-16-42" href="#__codelineno-16-42"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-43" name="__codelineno-16-43" href="#__codelineno-16-43"></a><span class="w">        </span><span class="c1">// 末尾へのエンキュー操作</span>
+<a id="__codelineno-16-44" name="__codelineno-16-44" href="#__codelineno-16-44"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-45" name="__codelineno-16-45" href="#__codelineno-16-45"></a><span class="w">            </span><span class="c1">// node を連結リストの末尾に追加</span>
+<a id="__codelineno-16-46" name="__codelineno-16-46" href="#__codelineno-16-46"></a><span class="w">            </span><span class="n">rear</span><span class="o">!</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-16-47" name="__codelineno-16-47" href="#__codelineno-16-47"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="p">;</span>
+<a id="__codelineno-16-48" name="__codelineno-16-48" href="#__codelineno-16-48"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w">  </span><span class="c1">// 末尾ノードを更新する</span>
+<a id="__codelineno-16-49" name="__codelineno-16-49" href="#__codelineno-16-49"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-50" name="__codelineno-16-50" href="#__codelineno-16-50"></a>
+<a id="__codelineno-16-51" name="__codelineno-16-51" href="#__codelineno-16-51"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの長さを更新</span>
+<a id="__codelineno-16-52" name="__codelineno-16-52" href="#__codelineno-16-52"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-53" name="__codelineno-16-53" href="#__codelineno-16-53"></a>
+<a id="__codelineno-16-54" name="__codelineno-16-54" href="#__codelineno-16-54"></a><span class="w">    </span><span class="cm">/* キュー先頭にエンキュー */</span>
+<a id="__codelineno-16-55" name="__codelineno-16-55" href="#__codelineno-16-55"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">PushFirst</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-56" name="__codelineno-16-56" href="#__codelineno-16-56"></a><span class="w">        </span><span class="n">Push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="k">true</span><span class="p">);</span>
+<a id="__codelineno-16-57" name="__codelineno-16-57" href="#__codelineno-16-57"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-58" name="__codelineno-16-58" href="#__codelineno-16-58"></a>
+<a id="__codelineno-16-59" name="__codelineno-16-59" href="#__codelineno-16-59"></a><span class="w">    </span><span class="cm">/* キュー末尾にエンキュー */</span>
+<a id="__codelineno-16-60" name="__codelineno-16-60" href="#__codelineno-16-60"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">PushLast</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-61" name="__codelineno-16-61" href="#__codelineno-16-61"></a><span class="w">        </span><span class="n">Push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="k">false</span><span class="p">);</span>
+<a id="__codelineno-16-62" name="__codelineno-16-62" href="#__codelineno-16-62"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-63" name="__codelineno-16-63" href="#__codelineno-16-63"></a>
+<a id="__codelineno-16-64" name="__codelineno-16-64" href="#__codelineno-16-64"></a><span class="w">    </span><span class="cm">/* デキュー操作 */</span>
+<a id="__codelineno-16-65" name="__codelineno-16-65" href="#__codelineno-16-65"></a><span class="w">    </span><span class="kt">int?</span><span class="w"> </span><span class="n">Pop</span><span class="p">(</span><span class="kt">bool</span><span class="w"> </span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-66" name="__codelineno-16-66" href="#__codelineno-16-66"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsEmpty</span><span class="p">())</span>
+<a id="__codelineno-16-67" name="__codelineno-16-67" href="#__codelineno-16-67"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="nf">Exception</span><span class="p">();</span>
+<a id="__codelineno-16-68" name="__codelineno-16-68" href="#__codelineno-16-68"></a><span class="w">        </span><span class="kt">int?</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-16-69" name="__codelineno-16-69" href="#__codelineno-16-69"></a><span class="w">        </span><span class="c1">// キュー先頭からの取り出し</span>
+<a id="__codelineno-16-70" name="__codelineno-16-70" href="#__codelineno-16-70"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-71" name="__codelineno-16-71" href="#__codelineno-16-71"></a><span class="w">            </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="o">?.</span><span class="n">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードの値を一時保存</span>
+<a id="__codelineno-16-72" name="__codelineno-16-72" href="#__codelineno-16-72"></a><span class="w">            </span><span class="c1">// 先頭ノードを削除</span>
+<a id="__codelineno-16-73" name="__codelineno-16-73" href="#__codelineno-16-73"></a><span class="w">            </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">fNext</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="o">?.</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-16-74" name="__codelineno-16-74" href="#__codelineno-16-74"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">fNext</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-75" name="__codelineno-16-75" href="#__codelineno-16-75"></a><span class="w">                </span><span class="n">fNext</span><span class="p">.</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
+<a id="__codelineno-16-76" name="__codelineno-16-76" href="#__codelineno-16-76"></a><span class="w">                </span><span class="n">front</span><span class="o">!</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
+<a id="__codelineno-16-77" name="__codelineno-16-77" href="#__codelineno-16-77"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-16-78" name="__codelineno-16-78" href="#__codelineno-16-78"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fNext</span><span class="p">;</span><span class="w">   </span><span class="c1">// 先頭ノードを更新する</span>
+<a id="__codelineno-16-79" name="__codelineno-16-79" href="#__codelineno-16-79"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-80" name="__codelineno-16-80" href="#__codelineno-16-80"></a><span class="w">        </span><span class="c1">// キュー末尾からの取り出し</span>
+<a id="__codelineno-16-81" name="__codelineno-16-81" href="#__codelineno-16-81"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-82" name="__codelineno-16-82" href="#__codelineno-16-82"></a><span class="w">            </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="o">?.</span><span class="n">val</span><span class="p">;</span><span class="w">  </span><span class="c1">// 末尾ノードの値を一時保存</span>
+<a id="__codelineno-16-83" name="__codelineno-16-83" href="#__codelineno-16-83"></a><span class="w">            </span><span class="c1">// 末尾ノードを削除</span>
+<a id="__codelineno-16-84" name="__codelineno-16-84" href="#__codelineno-16-84"></a><span class="w">            </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">rPrev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="o">?.</span><span class="n">prev</span><span class="p">;</span>
+<a id="__codelineno-16-85" name="__codelineno-16-85" href="#__codelineno-16-85"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">rPrev</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-86" name="__codelineno-16-86" href="#__codelineno-16-86"></a><span class="w">                </span><span class="n">rPrev</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
+<a id="__codelineno-16-87" name="__codelineno-16-87" href="#__codelineno-16-87"></a><span class="w">                </span><span class="n">rear</span><span class="o">!</span><span class="p">.</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
+<a id="__codelineno-16-88" name="__codelineno-16-88" href="#__codelineno-16-88"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-16-89" name="__codelineno-16-89" href="#__codelineno-16-89"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rPrev</span><span class="p">;</span><span class="w">    </span><span class="c1">// 末尾ノードを更新する</span>
+<a id="__codelineno-16-90" name="__codelineno-16-90" href="#__codelineno-16-90"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-91" name="__codelineno-16-91" href="#__codelineno-16-91"></a>
+<a id="__codelineno-16-92" name="__codelineno-16-92" href="#__codelineno-16-92"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの長さを更新</span>
+<a id="__codelineno-16-93" name="__codelineno-16-93" href="#__codelineno-16-93"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-16-94" name="__codelineno-16-94" href="#__codelineno-16-94"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-95" name="__codelineno-16-95" href="#__codelineno-16-95"></a>
+<a id="__codelineno-16-96" name="__codelineno-16-96" href="#__codelineno-16-96"></a><span class="w">    </span><span class="cm">/* キュー先頭からデキュー */</span>
+<a id="__codelineno-16-97" name="__codelineno-16-97" href="#__codelineno-16-97"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int?</span><span class="w"> </span><span class="n">PopFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-98" name="__codelineno-16-98" href="#__codelineno-16-98"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nf">Pop</span><span class="p">(</span><span class="k">true</span><span class="p">);</span>
+<a id="__codelineno-16-99" name="__codelineno-16-99" href="#__codelineno-16-99"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-100" name="__codelineno-16-100" href="#__codelineno-16-100"></a>
+<a id="__codelineno-16-101" name="__codelineno-16-101" href="#__codelineno-16-101"></a><span class="w">    </span><span class="cm">/* キュー末尾からデキュー */</span>
+<a id="__codelineno-16-102" name="__codelineno-16-102" href="#__codelineno-16-102"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int?</span><span class="w"> </span><span class="n">PopLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-103" name="__codelineno-16-103" href="#__codelineno-16-103"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nf">Pop</span><span class="p">(</span><span class="k">false</span><span class="p">);</span>
+<a id="__codelineno-16-104" name="__codelineno-16-104" href="#__codelineno-16-104"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-105" name="__codelineno-16-105" href="#__codelineno-16-105"></a>
+<a id="__codelineno-16-106" name="__codelineno-16-106" href="#__codelineno-16-106"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-16-107" name="__codelineno-16-107" href="#__codelineno-16-107"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int?</span><span class="w"> </span><span class="n">PeekFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-108" name="__codelineno-16-108" href="#__codelineno-16-108"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsEmpty</span><span class="p">())</span>
+<a id="__codelineno-16-109" name="__codelineno-16-109" href="#__codelineno-16-109"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="nf">Exception</span><span class="p">();</span>
+<a id="__codelineno-16-110" name="__codelineno-16-110" href="#__codelineno-16-110"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">front</span><span class="o">?.</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-16-111" name="__codelineno-16-111" href="#__codelineno-16-111"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-112" name="__codelineno-16-112" href="#__codelineno-16-112"></a>
+<a id="__codelineno-16-113" name="__codelineno-16-113" href="#__codelineno-16-113"></a><span class="w">    </span><span class="cm">/* キュー末尾の要素にアクセス */</span>
+<a id="__codelineno-16-114" name="__codelineno-16-114" href="#__codelineno-16-114"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int?</span><span class="w"> </span><span class="n">PeekLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-115" name="__codelineno-16-115" href="#__codelineno-16-115"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsEmpty</span><span class="p">())</span>
+<a id="__codelineno-16-116" name="__codelineno-16-116" href="#__codelineno-16-116"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="nf">Exception</span><span class="p">();</span>
+<a id="__codelineno-16-117" name="__codelineno-16-117" href="#__codelineno-16-117"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">rear</span><span class="o">?.</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-16-118" name="__codelineno-16-118" href="#__codelineno-16-118"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-119" name="__codelineno-16-119" href="#__codelineno-16-119"></a>
+<a id="__codelineno-16-120" name="__codelineno-16-120" href="#__codelineno-16-120"></a><span class="w">    </span><span class="cm">/* 出力用の配列を返す */</span>
+<a id="__codelineno-16-121" name="__codelineno-16-121" href="#__codelineno-16-121"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int?</span><span class="p">[]</span><span class="w"> </span><span class="n">ToArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-122" name="__codelineno-16-122" href="#__codelineno-16-122"></a><span class="w">        </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-16-123" name="__codelineno-16-123" href="#__codelineno-16-123"></a><span class="w">        </span><span class="kt">int?</span><span class="p">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int?</span><span class="p">[</span><span class="n">Size</span><span class="p">()];</span>
+<a id="__codelineno-16-124" name="__codelineno-16-124" href="#__codelineno-16-124"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-125" name="__codelineno-16-125" href="#__codelineno-16-125"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">?.</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-16-126" name="__codelineno-16-126" href="#__codelineno-16-126"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">?.</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-16-127" name="__codelineno-16-127" href="#__codelineno-16-127"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-128" name="__codelineno-16-128" href="#__codelineno-16-128"></a>
+<a id="__codelineno-16-129" name="__codelineno-16-129" href="#__codelineno-16-129"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-16-130" name="__codelineno-16-130" href="#__codelineno-16-130"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-131" name="__codelineno-16-131" href="#__codelineno-16-131"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_deque.swift</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">ListNode</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
-<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a>
-<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">LinkedListDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">linkedlist_deque.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 双方向連結リストベースの両端キュー */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">linkedListDeque</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="c1">// 組み込みパッケージ list を使う</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="nx">data</span><span class="w"> </span><span class="o">*</span><span class="nx">list</span><span class="p">.</span><span class="nx">List</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="p">}</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="cm">/* 両端キューを初期化する */</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="kd">func</span><span class="w"> </span><span class="nx">newLinkedListDeque</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="nx">linkedListDeque</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">linkedListDeque</span><span class="p">{</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">        </span><span class="nx">data</span><span class="p">:</span><span class="w"> </span><span class="nx">list</span><span class="p">.</span><span class="nx">New</span><span class="p">(),</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="p">}</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="cm">/* キュー先頭に要素を追加する */</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">linkedListDeque</span><span class="p">)</span><span class="w"> </span><span class="nx">pushFirst</span><span class="p">(</span><span class="nx">value</span><span class="w"> </span><span class="kt">any</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w">    </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">.</span><span class="nx">PushFront</span><span class="p">(</span><span class="nx">value</span><span class="p">)</span>
+<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="p">}</span>
+<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a>
+<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="cm">/* キュー末尾に要素を追加する */</span>
+<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">linkedListDeque</span><span class="p">)</span><span class="w"> </span><span class="nx">pushLast</span><span class="p">(</span><span class="nx">value</span><span class="w"> </span><span class="kt">any</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></a><span class="w">    </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">.</span><span class="nx">PushBack</span><span class="p">(</span><span class="nx">value</span><span class="p">)</span>
+<a id="__codelineno-17-22" name="__codelineno-17-22" href="#__codelineno-17-22"></a><span class="p">}</span>
+<a id="__codelineno-17-23" name="__codelineno-17-23" href="#__codelineno-17-23"></a>
+<a id="__codelineno-17-24" name="__codelineno-17-24" href="#__codelineno-17-24"></a><span class="cm">/* 先頭要素を取り出す */</span>
+<a id="__codelineno-17-25" name="__codelineno-17-25" href="#__codelineno-17-25"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">linkedListDeque</span><span class="p">)</span><span class="w"> </span><span class="nx">popFirst</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-26" name="__codelineno-17-26" href="#__codelineno-17-26"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-27" name="__codelineno-17-27" href="#__codelineno-17-27"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-17-28" name="__codelineno-17-28" href="#__codelineno-17-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-29" name="__codelineno-17-29" href="#__codelineno-17-29"></a><span class="w">    </span><span class="nx">e</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">.</span><span class="nx">Front</span><span class="p">()</span>
+<a id="__codelineno-17-30" name="__codelineno-17-30" href="#__codelineno-17-30"></a><span class="w">    </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">.</span><span class="nx">Remove</span><span class="p">(</span><span class="nx">e</span><span class="p">)</span>
+<a id="__codelineno-17-31" name="__codelineno-17-31" href="#__codelineno-17-31"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">e</span><span class="p">.</span><span class="nx">Value</span>
+<a id="__codelineno-17-32" name="__codelineno-17-32" href="#__codelineno-17-32"></a><span class="p">}</span>
+<a id="__codelineno-17-33" name="__codelineno-17-33" href="#__codelineno-17-33"></a>
+<a id="__codelineno-17-34" name="__codelineno-17-34" href="#__codelineno-17-34"></a><span class="cm">/* 末尾要素を取り出す */</span>
+<a id="__codelineno-17-35" name="__codelineno-17-35" href="#__codelineno-17-35"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">linkedListDeque</span><span class="p">)</span><span class="w"> </span><span class="nx">popLast</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-36" name="__codelineno-17-36" href="#__codelineno-17-36"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-37" name="__codelineno-17-37" href="#__codelineno-17-37"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-17-38" name="__codelineno-17-38" href="#__codelineno-17-38"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-39" name="__codelineno-17-39" href="#__codelineno-17-39"></a><span class="w">    </span><span class="nx">e</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">.</span><span class="nx">Back</span><span class="p">()</span>
+<a id="__codelineno-17-40" name="__codelineno-17-40" href="#__codelineno-17-40"></a><span class="w">    </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">.</span><span class="nx">Remove</span><span class="p">(</span><span class="nx">e</span><span class="p">)</span>
+<a id="__codelineno-17-41" name="__codelineno-17-41" href="#__codelineno-17-41"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">e</span><span class="p">.</span><span class="nx">Value</span>
+<a id="__codelineno-17-42" name="__codelineno-17-42" href="#__codelineno-17-42"></a><span class="p">}</span>
+<a id="__codelineno-17-43" name="__codelineno-17-43" href="#__codelineno-17-43"></a>
+<a id="__codelineno-17-44" name="__codelineno-17-44" href="#__codelineno-17-44"></a><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-17-45" name="__codelineno-17-45" href="#__codelineno-17-45"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">linkedListDeque</span><span class="p">)</span><span class="w"> </span><span class="nx">peekFirst</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-46" name="__codelineno-17-46" href="#__codelineno-17-46"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-47" name="__codelineno-17-47" href="#__codelineno-17-47"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-17-48" name="__codelineno-17-48" href="#__codelineno-17-48"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-49" name="__codelineno-17-49" href="#__codelineno-17-49"></a><span class="w">    </span><span class="nx">e</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">.</span><span class="nx">Front</span><span class="p">()</span>
+<a id="__codelineno-17-50" name="__codelineno-17-50" href="#__codelineno-17-50"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">e</span><span class="p">.</span><span class="nx">Value</span>
+<a id="__codelineno-17-51" name="__codelineno-17-51" href="#__codelineno-17-51"></a><span class="p">}</span>
+<a id="__codelineno-17-52" name="__codelineno-17-52" href="#__codelineno-17-52"></a>
+<a id="__codelineno-17-53" name="__codelineno-17-53" href="#__codelineno-17-53"></a><span class="cm">/* キュー末尾の要素にアクセス */</span>
+<a id="__codelineno-17-54" name="__codelineno-17-54" href="#__codelineno-17-54"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">linkedListDeque</span><span class="p">)</span><span class="w"> </span><span class="nx">peekLast</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-55" name="__codelineno-17-55" href="#__codelineno-17-55"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-56" name="__codelineno-17-56" href="#__codelineno-17-56"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-17-57" name="__codelineno-17-57" href="#__codelineno-17-57"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-58" name="__codelineno-17-58" href="#__codelineno-17-58"></a><span class="w">    </span><span class="nx">e</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">.</span><span class="nx">Back</span><span class="p">()</span>
+<a id="__codelineno-17-59" name="__codelineno-17-59" href="#__codelineno-17-59"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">e</span><span class="p">.</span><span class="nx">Value</span>
+<a id="__codelineno-17-60" name="__codelineno-17-60" href="#__codelineno-17-60"></a><span class="p">}</span>
+<a id="__codelineno-17-61" name="__codelineno-17-61" href="#__codelineno-17-61"></a>
+<a id="__codelineno-17-62" name="__codelineno-17-62" href="#__codelineno-17-62"></a><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-17-63" name="__codelineno-17-63" href="#__codelineno-17-63"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">linkedListDeque</span><span class="p">)</span><span class="w"> </span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-64" name="__codelineno-17-64" href="#__codelineno-17-64"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">.</span><span class="nx">Len</span><span class="p">()</span>
+<a id="__codelineno-17-65" name="__codelineno-17-65" href="#__codelineno-17-65"></a><span class="p">}</span>
+<a id="__codelineno-17-66" name="__codelineno-17-66" href="#__codelineno-17-66"></a>
+<a id="__codelineno-17-67" name="__codelineno-17-67" href="#__codelineno-17-67"></a><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-17-68" name="__codelineno-17-68" href="#__codelineno-17-68"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">linkedListDeque</span><span class="p">)</span><span class="w"> </span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-69" name="__codelineno-17-69" href="#__codelineno-17-69"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">.</span><span class="nx">Len</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-17-70" name="__codelineno-17-70" href="#__codelineno-17-70"></a><span class="p">}</span>
+<a id="__codelineno-17-71" name="__codelineno-17-71" href="#__codelineno-17-71"></a>
+<a id="__codelineno-17-72" name="__codelineno-17-72" href="#__codelineno-17-72"></a><span class="cm">/* 表示用に List を取得 */</span>
+<a id="__codelineno-17-73" name="__codelineno-17-73" href="#__codelineno-17-73"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">linkedListDeque</span><span class="p">)</span><span class="w"> </span><span class="nx">toList</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="nx">list</span><span class="p">.</span><span class="nx">List</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-74" name="__codelineno-17-74" href="#__codelineno-17-74"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span>
+<a id="__codelineno-17-75" name="__codelineno-17-75" href="#__codelineno-17-75"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_deque.js</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ListNode</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
-<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a>
-<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">LinkedListDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">linkedlist_deque.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 双方向連結リストノード */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">val</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// ノード値</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">next</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 後続ノードへの参照</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">    </span><span class="kr">weak</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">prev</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 前駆ノードへの参照</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">    </span><span class="kd">init</span><span class="p">(</span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">        </span><span class="kc">self</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">val</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="p">}</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="cm">/* 双方向連結リストベースの両端キュー */</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="kd">class</span><span class="w"> </span><span class="nc">LinkedListDeque</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">front</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 先頭ノード front</span>
+<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">rear</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 末尾ノード rear</span>
+<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">_size</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// 両端キューの長さ</span>
+<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a>
+<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="w">    </span><span class="kd">init</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a><span class="w">        </span><span class="n">_size</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></a>
+<a id="__codelineno-18-22" name="__codelineno-18-22" href="#__codelineno-18-22"></a><span class="w">    </span><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-18-23" name="__codelineno-18-23" href="#__codelineno-18-23"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-24" name="__codelineno-18-24" href="#__codelineno-18-24"></a><span class="w">        </span><span class="n">_size</span>
+<a id="__codelineno-18-25" name="__codelineno-18-25" href="#__codelineno-18-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-26" name="__codelineno-18-26" href="#__codelineno-18-26"></a>
+<a id="__codelineno-18-27" name="__codelineno-18-27" href="#__codelineno-18-27"></a><span class="w">    </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
+<a id="__codelineno-18-28" name="__codelineno-18-28" href="#__codelineno-18-28"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-29" name="__codelineno-18-29" href="#__codelineno-18-29"></a><span class="w">        </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-18-30" name="__codelineno-18-30" href="#__codelineno-18-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-31" name="__codelineno-18-31" href="#__codelineno-18-31"></a>
+<a id="__codelineno-18-32" name="__codelineno-18-32" href="#__codelineno-18-32"></a><span class="w">    </span><span class="cm">/* エンキュー操作 */</span>
+<a id="__codelineno-18-33" name="__codelineno-18-33" href="#__codelineno-18-33"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">func</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">isFront</span><span class="p">:</span><span class="w"> </span><span class="nb">Bool</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-34" name="__codelineno-18-34" href="#__codelineno-18-34"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-18-35" name="__codelineno-18-35" href="#__codelineno-18-35"></a><span class="w">        </span><span class="c1">// 連結リストが空なら、front と rear の両方を node に向ける</span>
+<a id="__codelineno-18-36" name="__codelineno-18-36" href="#__codelineno-18-36"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-37" name="__codelineno-18-37" href="#__codelineno-18-37"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-18-38" name="__codelineno-18-38" href="#__codelineno-18-38"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-18-39" name="__codelineno-18-39" href="#__codelineno-18-39"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-40" name="__codelineno-18-40" href="#__codelineno-18-40"></a><span class="w">        </span><span class="c1">// 先頭へのエンキュー操作</span>
+<a id="__codelineno-18-41" name="__codelineno-18-41" href="#__codelineno-18-41"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">isFront</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-42" name="__codelineno-18-42" href="#__codelineno-18-42"></a><span class="w">            </span><span class="c1">// node を連結リストの先頭に追加</span>
+<a id="__codelineno-18-43" name="__codelineno-18-43" href="#__codelineno-18-43"></a><span class="w">            </span><span class="n">front</span><span class="p">?.</span><span class="n">prev</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-18-44" name="__codelineno-18-44" href="#__codelineno-18-44"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">front</span>
+<a id="__codelineno-18-45" name="__codelineno-18-45" href="#__codelineno-18-45"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="c1">// 先頭ノードを更新する</span>
+<a id="__codelineno-18-46" name="__codelineno-18-46" href="#__codelineno-18-46"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-47" name="__codelineno-18-47" href="#__codelineno-18-47"></a><span class="w">        </span><span class="c1">// 末尾へのエンキュー操作</span>
+<a id="__codelineno-18-48" name="__codelineno-18-48" href="#__codelineno-18-48"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-49" name="__codelineno-18-49" href="#__codelineno-18-49"></a><span class="w">            </span><span class="c1">// node を連結リストの末尾に追加</span>
+<a id="__codelineno-18-50" name="__codelineno-18-50" href="#__codelineno-18-50"></a><span class="w">            </span><span class="n">rear</span><span class="p">?.</span><span class="n">next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-18-51" name="__codelineno-18-51" href="#__codelineno-18-51"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="n">prev</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">rear</span>
+<a id="__codelineno-18-52" name="__codelineno-18-52" href="#__codelineno-18-52"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="c1">// 末尾ノードを更新する</span>
+<a id="__codelineno-18-53" name="__codelineno-18-53" href="#__codelineno-18-53"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-54" name="__codelineno-18-54" href="#__codelineno-18-54"></a><span class="w">        </span><span class="n">_size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// キューの長さを更新</span>
+<a id="__codelineno-18-55" name="__codelineno-18-55" href="#__codelineno-18-55"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-56" name="__codelineno-18-56" href="#__codelineno-18-56"></a>
+<a id="__codelineno-18-57" name="__codelineno-18-57" href="#__codelineno-18-57"></a><span class="w">    </span><span class="cm">/* キュー先頭にエンキュー */</span>
+<a id="__codelineno-18-58" name="__codelineno-18-58" href="#__codelineno-18-58"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">pushFirst</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-59" name="__codelineno-18-59" href="#__codelineno-18-59"></a><span class="w">        </span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="n">isFront</span><span class="p">:</span><span class="w"> </span><span class="kc">true</span><span class="p">)</span>
+<a id="__codelineno-18-60" name="__codelineno-18-60" href="#__codelineno-18-60"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-61" name="__codelineno-18-61" href="#__codelineno-18-61"></a>
+<a id="__codelineno-18-62" name="__codelineno-18-62" href="#__codelineno-18-62"></a><span class="w">    </span><span class="cm">/* キュー末尾にエンキュー */</span>
+<a id="__codelineno-18-63" name="__codelineno-18-63" href="#__codelineno-18-63"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">pushLast</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-64" name="__codelineno-18-64" href="#__codelineno-18-64"></a><span class="w">        </span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="n">isFront</span><span class="p">:</span><span class="w"> </span><span class="kc">false</span><span class="p">)</span>
+<a id="__codelineno-18-65" name="__codelineno-18-65" href="#__codelineno-18-65"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-66" name="__codelineno-18-66" href="#__codelineno-18-66"></a>
+<a id="__codelineno-18-67" name="__codelineno-18-67" href="#__codelineno-18-67"></a><span class="w">    </span><span class="cm">/* デキュー操作 */</span>
+<a id="__codelineno-18-68" name="__codelineno-18-68" href="#__codelineno-18-68"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">func</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="n">isFront</span><span class="p">:</span><span class="w"> </span><span class="nb">Bool</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-69" name="__codelineno-18-69" href="#__codelineno-18-69"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-70" name="__codelineno-18-70" href="#__codelineno-18-70"></a><span class="w">            </span><span class="bp">fatalError</span><span class="p">(</span><span class="s">&quot;両端キューが空です&quot;</span><span class="p">)</span>
+<a id="__codelineno-18-71" name="__codelineno-18-71" href="#__codelineno-18-71"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-72" name="__codelineno-18-72" href="#__codelineno-18-72"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">val</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span>
+<a id="__codelineno-18-73" name="__codelineno-18-73" href="#__codelineno-18-73"></a><span class="w">        </span><span class="c1">// キュー先頭からの取り出し</span>
+<a id="__codelineno-18-74" name="__codelineno-18-74" href="#__codelineno-18-74"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">isFront</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-75" name="__codelineno-18-75" href="#__codelineno-18-75"></a><span class="w">            </span><span class="n">val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">front</span><span class="p">!.</span><span class="n">val</span><span class="w"> </span><span class="c1">// 先頭ノードの値を一時保存</span>
+<a id="__codelineno-18-76" name="__codelineno-18-76" href="#__codelineno-18-76"></a><span class="w">            </span><span class="c1">// 先頭ノードを削除</span>
+<a id="__codelineno-18-77" name="__codelineno-18-77" href="#__codelineno-18-77"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="nv">fNext</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">front</span><span class="p">?.</span><span class="n">next</span>
+<a id="__codelineno-18-78" name="__codelineno-18-78" href="#__codelineno-18-78"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">fNext</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-79" name="__codelineno-18-79" href="#__codelineno-18-79"></a><span class="w">                </span><span class="n">fNext</span><span class="p">?.</span><span class="n">prev</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-18-80" name="__codelineno-18-80" href="#__codelineno-18-80"></a><span class="w">                </span><span class="n">front</span><span class="p">?.</span><span class="n">next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-18-81" name="__codelineno-18-81" href="#__codelineno-18-81"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-18-82" name="__codelineno-18-82" href="#__codelineno-18-82"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">fNext</span><span class="w"> </span><span class="c1">// 先頭ノードを更新する</span>
+<a id="__codelineno-18-83" name="__codelineno-18-83" href="#__codelineno-18-83"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-84" name="__codelineno-18-84" href="#__codelineno-18-84"></a><span class="w">        </span><span class="c1">// キュー末尾からの取り出し</span>
+<a id="__codelineno-18-85" name="__codelineno-18-85" href="#__codelineno-18-85"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-86" name="__codelineno-18-86" href="#__codelineno-18-86"></a><span class="w">            </span><span class="n">val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">rear</span><span class="p">!.</span><span class="n">val</span><span class="w"> </span><span class="c1">// 末尾ノードの値を一時保存</span>
+<a id="__codelineno-18-87" name="__codelineno-18-87" href="#__codelineno-18-87"></a><span class="w">            </span><span class="c1">// 末尾ノードを削除</span>
+<a id="__codelineno-18-88" name="__codelineno-18-88" href="#__codelineno-18-88"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="nv">rPrev</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">rear</span><span class="p">?.</span><span class="n">prev</span>
+<a id="__codelineno-18-89" name="__codelineno-18-89" href="#__codelineno-18-89"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">rPrev</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-90" name="__codelineno-18-90" href="#__codelineno-18-90"></a><span class="w">                </span><span class="n">rPrev</span><span class="p">?.</span><span class="n">next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-18-91" name="__codelineno-18-91" href="#__codelineno-18-91"></a><span class="w">                </span><span class="n">rear</span><span class="p">?.</span><span class="n">prev</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-18-92" name="__codelineno-18-92" href="#__codelineno-18-92"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-18-93" name="__codelineno-18-93" href="#__codelineno-18-93"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">rPrev</span><span class="w"> </span><span class="c1">// 末尾ノードを更新する</span>
+<a id="__codelineno-18-94" name="__codelineno-18-94" href="#__codelineno-18-94"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-95" name="__codelineno-18-95" href="#__codelineno-18-95"></a><span class="w">        </span><span class="n">_size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// キューの長さを更新</span>
+<a id="__codelineno-18-96" name="__codelineno-18-96" href="#__codelineno-18-96"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">val</span>
+<a id="__codelineno-18-97" name="__codelineno-18-97" href="#__codelineno-18-97"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-98" name="__codelineno-18-98" href="#__codelineno-18-98"></a>
+<a id="__codelineno-18-99" name="__codelineno-18-99" href="#__codelineno-18-99"></a><span class="w">    </span><span class="cm">/* キュー先頭からデキュー */</span>
+<a id="__codelineno-18-100" name="__codelineno-18-100" href="#__codelineno-18-100"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">popFirst</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-101" name="__codelineno-18-101" href="#__codelineno-18-101"></a><span class="w">        </span><span class="n">pop</span><span class="p">(</span><span class="n">isFront</span><span class="p">:</span><span class="w"> </span><span class="kc">true</span><span class="p">)</span>
+<a id="__codelineno-18-102" name="__codelineno-18-102" href="#__codelineno-18-102"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-103" name="__codelineno-18-103" href="#__codelineno-18-103"></a>
+<a id="__codelineno-18-104" name="__codelineno-18-104" href="#__codelineno-18-104"></a><span class="w">    </span><span class="cm">/* キュー末尾からデキュー */</span>
+<a id="__codelineno-18-105" name="__codelineno-18-105" href="#__codelineno-18-105"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">popLast</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-106" name="__codelineno-18-106" href="#__codelineno-18-106"></a><span class="w">        </span><span class="n">pop</span><span class="p">(</span><span class="n">isFront</span><span class="p">:</span><span class="w"> </span><span class="kc">false</span><span class="p">)</span>
+<a id="__codelineno-18-107" name="__codelineno-18-107" href="#__codelineno-18-107"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-108" name="__codelineno-18-108" href="#__codelineno-18-108"></a>
+<a id="__codelineno-18-109" name="__codelineno-18-109" href="#__codelineno-18-109"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-18-110" name="__codelineno-18-110" href="#__codelineno-18-110"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">peekFirst</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-111" name="__codelineno-18-111" href="#__codelineno-18-111"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-112" name="__codelineno-18-112" href="#__codelineno-18-112"></a><span class="w">            </span><span class="bp">fatalError</span><span class="p">(</span><span class="s">&quot;両端キューが空です&quot;</span><span class="p">)</span>
+<a id="__codelineno-18-113" name="__codelineno-18-113" href="#__codelineno-18-113"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-114" name="__codelineno-18-114" href="#__codelineno-18-114"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">front</span><span class="p">!.</span><span class="n">val</span>
+<a id="__codelineno-18-115" name="__codelineno-18-115" href="#__codelineno-18-115"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-116" name="__codelineno-18-116" href="#__codelineno-18-116"></a>
+<a id="__codelineno-18-117" name="__codelineno-18-117" href="#__codelineno-18-117"></a><span class="w">    </span><span class="cm">/* キュー末尾の要素にアクセス */</span>
+<a id="__codelineno-18-118" name="__codelineno-18-118" href="#__codelineno-18-118"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">peekLast</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-119" name="__codelineno-18-119" href="#__codelineno-18-119"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-120" name="__codelineno-18-120" href="#__codelineno-18-120"></a><span class="w">            </span><span class="bp">fatalError</span><span class="p">(</span><span class="s">&quot;両端キューが空です&quot;</span><span class="p">)</span>
+<a id="__codelineno-18-121" name="__codelineno-18-121" href="#__codelineno-18-121"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-122" name="__codelineno-18-122" href="#__codelineno-18-122"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">rear</span><span class="p">!.</span><span class="n">val</span>
+<a id="__codelineno-18-123" name="__codelineno-18-123" href="#__codelineno-18-123"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-124" name="__codelineno-18-124" href="#__codelineno-18-124"></a>
+<a id="__codelineno-18-125" name="__codelineno-18-125" href="#__codelineno-18-125"></a><span class="w">    </span><span class="cm">/* 出力用の配列を返す */</span>
+<a id="__codelineno-18-126" name="__codelineno-18-126" href="#__codelineno-18-126"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-127" name="__codelineno-18-127" href="#__codelineno-18-127"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">front</span>
+<a id="__codelineno-18-128" name="__codelineno-18-128" href="#__codelineno-18-128"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
+<a id="__codelineno-18-129" name="__codelineno-18-129" href="#__codelineno-18-129"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="bp">indices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-130" name="__codelineno-18-130" href="#__codelineno-18-130"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span><span class="p">!.</span><span class="n">val</span>
+<a id="__codelineno-18-131" name="__codelineno-18-131" href="#__codelineno-18-131"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span><span class="p">?.</span><span class="n">next</span>
+<a id="__codelineno-18-132" name="__codelineno-18-132" href="#__codelineno-18-132"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-133" name="__codelineno-18-133" href="#__codelineno-18-133"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-18-134" name="__codelineno-18-134" href="#__codelineno-18-134"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-135" name="__codelineno-18-135" href="#__codelineno-18-135"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_deque.ts</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ListNode</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
-<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a>
-<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">LinkedListDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">linkedlist_deque.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 双方向連結リストノード */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="nx">prev</span><span class="p">;</span><span class="w"> </span><span class="c1">// 前駆ノードへの参照（ポインタ）</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="nx">next</span><span class="p">;</span><span class="w"> </span><span class="c1">// 後継ノードへの参照（ポインタ）</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">    </span><span class="nx">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// ノード値</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="p">}</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a>
+<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="cm">/* 双方向連結リストベースの両端キュー */</span>
+<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="kd">class</span><span class="w"> </span><span class="nx">LinkedListDeque</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a><span class="w">    </span><span class="n">#front</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノード front</span>
+<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="w">    </span><span class="n">#rear</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノード rear</span>
+<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a><span class="w">    </span><span class="n">#queSize</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端キューの長さ</span>
+<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a>
+<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-19-22" name="__codelineno-19-22" href="#__codelineno-19-22"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-19-23" name="__codelineno-19-23" href="#__codelineno-19-23"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-19-24" name="__codelineno-19-24" href="#__codelineno-19-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-25" name="__codelineno-19-25" href="#__codelineno-19-25"></a>
+<a id="__codelineno-19-26" name="__codelineno-19-26" href="#__codelineno-19-26"></a><span class="w">    </span><span class="cm">/* 末尾へのエンキュー操作 */</span>
+<a id="__codelineno-19-27" name="__codelineno-19-27" href="#__codelineno-19-27"></a><span class="w">    </span><span class="nx">pushLast</span><span class="p">(</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-28" name="__codelineno-19-28" href="#__codelineno-19-28"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-19-29" name="__codelineno-19-29" href="#__codelineno-19-29"></a><span class="w">        </span><span class="c1">// 連結リストが空なら、front と rear の両方を node に向ける</span>
+<a id="__codelineno-19-30" name="__codelineno-19-30" href="#__codelineno-19-30"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-31" name="__codelineno-19-31" href="#__codelineno-19-31"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-19-32" name="__codelineno-19-32" href="#__codelineno-19-32"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-19-33" name="__codelineno-19-33" href="#__codelineno-19-33"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-34" name="__codelineno-19-34" href="#__codelineno-19-34"></a><span class="w">            </span><span class="c1">// node を連結リストの末尾に追加</span>
+<a id="__codelineno-19-35" name="__codelineno-19-35" href="#__codelineno-19-35"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#rear</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-19-36" name="__codelineno-19-36" href="#__codelineno-19-36"></a><span class="w">            </span><span class="nx">node</span><span class="p">.</span><span class="nx">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#rear</span><span class="p">;</span>
+<a id="__codelineno-19-37" name="__codelineno-19-37" href="#__codelineno-19-37"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノードを更新する</span>
+<a id="__codelineno-19-38" name="__codelineno-19-38" href="#__codelineno-19-38"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-39" name="__codelineno-19-39" href="#__codelineno-19-39"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-19-40" name="__codelineno-19-40" href="#__codelineno-19-40"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-41" name="__codelineno-19-41" href="#__codelineno-19-41"></a>
+<a id="__codelineno-19-42" name="__codelineno-19-42" href="#__codelineno-19-42"></a><span class="w">    </span><span class="cm">/* 先頭へのエンキュー操作 */</span>
+<a id="__codelineno-19-43" name="__codelineno-19-43" href="#__codelineno-19-43"></a><span class="w">    </span><span class="nx">pushFirst</span><span class="p">(</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-44" name="__codelineno-19-44" href="#__codelineno-19-44"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-19-45" name="__codelineno-19-45" href="#__codelineno-19-45"></a><span class="w">        </span><span class="c1">// 連結リストが空なら、front と rear の両方を node に向ける</span>
+<a id="__codelineno-19-46" name="__codelineno-19-46" href="#__codelineno-19-46"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-47" name="__codelineno-19-47" href="#__codelineno-19-47"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-19-48" name="__codelineno-19-48" href="#__codelineno-19-48"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-19-49" name="__codelineno-19-49" href="#__codelineno-19-49"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-50" name="__codelineno-19-50" href="#__codelineno-19-50"></a><span class="w">            </span><span class="c1">// node を連結リストの先頭に追加</span>
+<a id="__codelineno-19-51" name="__codelineno-19-51" href="#__codelineno-19-51"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="p">.</span><span class="nx">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-19-52" name="__codelineno-19-52" href="#__codelineno-19-52"></a><span class="w">            </span><span class="nx">node</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="p">;</span>
+<a id="__codelineno-19-53" name="__codelineno-19-53" href="#__codelineno-19-53"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードを更新する</span>
+<a id="__codelineno-19-54" name="__codelineno-19-54" href="#__codelineno-19-54"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-55" name="__codelineno-19-55" href="#__codelineno-19-55"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-19-56" name="__codelineno-19-56" href="#__codelineno-19-56"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-57" name="__codelineno-19-57" href="#__codelineno-19-57"></a>
+<a id="__codelineno-19-58" name="__codelineno-19-58" href="#__codelineno-19-58"></a><span class="w">    </span><span class="cm">/* キュー末尾からの取り出し */</span>
+<a id="__codelineno-19-59" name="__codelineno-19-59" href="#__codelineno-19-59"></a><span class="w">    </span><span class="nx">popLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-60" name="__codelineno-19-60" href="#__codelineno-19-60"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-61" name="__codelineno-19-61" href="#__codelineno-19-61"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-19-62" name="__codelineno-19-62" href="#__codelineno-19-62"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-63" name="__codelineno-19-63" href="#__codelineno-19-63"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">value</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#rear</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノードの値を保存する</span>
+<a id="__codelineno-19-64" name="__codelineno-19-64" href="#__codelineno-19-64"></a><span class="w">        </span><span class="c1">// 末尾ノードを削除</span>
+<a id="__codelineno-19-65" name="__codelineno-19-65" href="#__codelineno-19-65"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#rear</span><span class="p">.</span><span class="nx">prev</span><span class="p">;</span>
+<a id="__codelineno-19-66" name="__codelineno-19-66" href="#__codelineno-19-66"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">temp</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-67" name="__codelineno-19-67" href="#__codelineno-19-67"></a><span class="w">            </span><span class="nx">temp</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-19-68" name="__codelineno-19-68" href="#__codelineno-19-68"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#rear</span><span class="p">.</span><span class="nx">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-19-69" name="__codelineno-19-69" href="#__codelineno-19-69"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-70" name="__codelineno-19-70" href="#__codelineno-19-70"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">temp</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノードを更新する</span>
+<a id="__codelineno-19-71" name="__codelineno-19-71" href="#__codelineno-19-71"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-19-72" name="__codelineno-19-72" href="#__codelineno-19-72"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">value</span><span class="p">;</span>
+<a id="__codelineno-19-73" name="__codelineno-19-73" href="#__codelineno-19-73"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-74" name="__codelineno-19-74" href="#__codelineno-19-74"></a>
+<a id="__codelineno-19-75" name="__codelineno-19-75" href="#__codelineno-19-75"></a><span class="w">    </span><span class="cm">/* キュー先頭からの取り出し */</span>
+<a id="__codelineno-19-76" name="__codelineno-19-76" href="#__codelineno-19-76"></a><span class="w">    </span><span class="nx">popFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-77" name="__codelineno-19-77" href="#__codelineno-19-77"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-78" name="__codelineno-19-78" href="#__codelineno-19-78"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-19-79" name="__codelineno-19-79" href="#__codelineno-19-79"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-80" name="__codelineno-19-80" href="#__codelineno-19-80"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">value</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノードの値を保存する</span>
+<a id="__codelineno-19-81" name="__codelineno-19-81" href="#__codelineno-19-81"></a><span class="w">        </span><span class="c1">// 先頭ノードを削除</span>
+<a id="__codelineno-19-82" name="__codelineno-19-82" href="#__codelineno-19-82"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="p">.</span><span class="nx">next</span><span class="p">;</span>
+<a id="__codelineno-19-83" name="__codelineno-19-83" href="#__codelineno-19-83"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">temp</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-84" name="__codelineno-19-84" href="#__codelineno-19-84"></a><span class="w">            </span><span class="nx">temp</span><span class="p">.</span><span class="nx">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-19-85" name="__codelineno-19-85" href="#__codelineno-19-85"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-19-86" name="__codelineno-19-86" href="#__codelineno-19-86"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-87" name="__codelineno-19-87" href="#__codelineno-19-87"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">temp</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードを更新する</span>
+<a id="__codelineno-19-88" name="__codelineno-19-88" href="#__codelineno-19-88"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-19-89" name="__codelineno-19-89" href="#__codelineno-19-89"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">value</span><span class="p">;</span>
+<a id="__codelineno-19-90" name="__codelineno-19-90" href="#__codelineno-19-90"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-91" name="__codelineno-19-91" href="#__codelineno-19-91"></a>
+<a id="__codelineno-19-92" name="__codelineno-19-92" href="#__codelineno-19-92"></a><span class="w">    </span><span class="cm">/* キュー末尾の要素にアクセス */</span>
+<a id="__codelineno-19-93" name="__codelineno-19-93" href="#__codelineno-19-93"></a><span class="w">    </span><span class="nx">peekLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-94" name="__codelineno-19-94" href="#__codelineno-19-94"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#rear</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-19-95" name="__codelineno-19-95" href="#__codelineno-19-95"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-96" name="__codelineno-19-96" href="#__codelineno-19-96"></a>
+<a id="__codelineno-19-97" name="__codelineno-19-97" href="#__codelineno-19-97"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-19-98" name="__codelineno-19-98" href="#__codelineno-19-98"></a><span class="w">    </span><span class="nx">peekFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-99" name="__codelineno-19-99" href="#__codelineno-19-99"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-19-100" name="__codelineno-19-100" href="#__codelineno-19-100"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-101" name="__codelineno-19-101" href="#__codelineno-19-101"></a>
+<a id="__codelineno-19-102" name="__codelineno-19-102" href="#__codelineno-19-102"></a><span class="w">    </span><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-19-103" name="__codelineno-19-103" href="#__codelineno-19-103"></a><span class="w">    </span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-104" name="__codelineno-19-104" href="#__codelineno-19-104"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="p">;</span>
+<a id="__codelineno-19-105" name="__codelineno-19-105" href="#__codelineno-19-105"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-106" name="__codelineno-19-106" href="#__codelineno-19-106"></a>
+<a id="__codelineno-19-107" name="__codelineno-19-107" href="#__codelineno-19-107"></a><span class="w">    </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
+<a id="__codelineno-19-108" name="__codelineno-19-108" href="#__codelineno-19-108"></a><span class="w">    </span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-109" name="__codelineno-19-109" href="#__codelineno-19-109"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-19-110" name="__codelineno-19-110" href="#__codelineno-19-110"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-111" name="__codelineno-19-111" href="#__codelineno-19-111"></a>
+<a id="__codelineno-19-112" name="__codelineno-19-112" href="#__codelineno-19-112"></a><span class="w">    </span><span class="cm">/* 両端キューを出力する */</span>
+<a id="__codelineno-19-113" name="__codelineno-19-113" href="#__codelineno-19-113"></a><span class="w">    </span><span class="nx">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-114" name="__codelineno-19-114" href="#__codelineno-19-114"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-19-115" name="__codelineno-19-115" href="#__codelineno-19-115"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="p">;</span>
+<a id="__codelineno-19-116" name="__codelineno-19-116" href="#__codelineno-19-116"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">temp</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-117" name="__codelineno-19-117" href="#__codelineno-19-117"></a><span class="w">            </span><span class="nx">arr</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">temp</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-19-118" name="__codelineno-19-118" href="#__codelineno-19-118"></a><span class="w">            </span><span class="nx">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">temp</span><span class="p">.</span><span class="nx">next</span><span class="p">;</span>
+<a id="__codelineno-19-119" name="__codelineno-19-119" href="#__codelineno-19-119"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-120" name="__codelineno-19-120" href="#__codelineno-19-120"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="s1">&#39;[&#39;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">arr</span><span class="p">.</span><span class="nx">join</span><span class="p">(</span><span class="s1">&#39;, &#39;</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s1">&#39;]&#39;</span><span class="p">);</span>
+<a id="__codelineno-19-121" name="__codelineno-19-121" href="#__codelineno-19-121"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-122" name="__codelineno-19-122" href="#__codelineno-19-122"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_deque.dart</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ListNode</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
-<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a>
-<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">LinkedListDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">linkedlist_deque.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 双方向連結リストノード */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="nx">prev</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="p">;</span><span class="w"> </span><span class="c1">// 前駆ノードへの参照（ポインタ）</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="nx">next</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="p">;</span><span class="w"> </span><span class="c1">// 後継ノードへの参照（ポインタ）</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">    </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// ノード値</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="p">}</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="cm">/* 双方向連結リストベースの両端キュー */</span>
+<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="kd">class</span><span class="w"> </span><span class="nx">LinkedListDeque</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">front</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノード front</span>
+<a id="__codelineno-20-17" name="__codelineno-20-17" href="#__codelineno-20-17"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">rear</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノード rear</span>
+<a id="__codelineno-20-18" name="__codelineno-20-18" href="#__codelineno-20-18"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">queSize</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端キューの長さ</span>
+<a id="__codelineno-20-19" name="__codelineno-20-19" href="#__codelineno-20-19"></a>
+<a id="__codelineno-20-20" name="__codelineno-20-20" href="#__codelineno-20-20"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-21" name="__codelineno-20-21" href="#__codelineno-20-21"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-20-22" name="__codelineno-20-22" href="#__codelineno-20-22"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-20-23" name="__codelineno-20-23" href="#__codelineno-20-23"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-20-24" name="__codelineno-20-24" href="#__codelineno-20-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-25" name="__codelineno-20-25" href="#__codelineno-20-25"></a>
+<a id="__codelineno-20-26" name="__codelineno-20-26" href="#__codelineno-20-26"></a><span class="w">    </span><span class="cm">/* 末尾へのエンキュー操作 */</span>
+<a id="__codelineno-20-27" name="__codelineno-20-27" href="#__codelineno-20-27"></a><span class="w">    </span><span class="nx">pushLast</span><span class="p">(</span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-28" name="__codelineno-20-28" href="#__codelineno-20-28"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">node</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-20-29" name="__codelineno-20-29" href="#__codelineno-20-29"></a><span class="w">        </span><span class="c1">// 連結リストが空なら、front と rear の両方を node に向ける</span>
+<a id="__codelineno-20-30" name="__codelineno-20-30" href="#__codelineno-20-30"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-31" name="__codelineno-20-31" href="#__codelineno-20-31"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-20-32" name="__codelineno-20-32" href="#__codelineno-20-32"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-20-33" name="__codelineno-20-33" href="#__codelineno-20-33"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-34" name="__codelineno-20-34" href="#__codelineno-20-34"></a><span class="w">            </span><span class="c1">// node を連結リストの末尾に追加</span>
+<a id="__codelineno-20-35" name="__codelineno-20-35" href="#__codelineno-20-35"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">rear</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-20-36" name="__codelineno-20-36" href="#__codelineno-20-36"></a><span class="w">            </span><span class="nx">node</span><span class="p">.</span><span class="nx">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">rear</span><span class="p">;</span>
+<a id="__codelineno-20-37" name="__codelineno-20-37" href="#__codelineno-20-37"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノードを更新する</span>
+<a id="__codelineno-20-38" name="__codelineno-20-38" href="#__codelineno-20-38"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-39" name="__codelineno-20-39" href="#__codelineno-20-39"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-20-40" name="__codelineno-20-40" href="#__codelineno-20-40"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-41" name="__codelineno-20-41" href="#__codelineno-20-41"></a>
+<a id="__codelineno-20-42" name="__codelineno-20-42" href="#__codelineno-20-42"></a><span class="w">    </span><span class="cm">/* 先頭へのエンキュー操作 */</span>
+<a id="__codelineno-20-43" name="__codelineno-20-43" href="#__codelineno-20-43"></a><span class="w">    </span><span class="nx">pushFirst</span><span class="p">(</span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-44" name="__codelineno-20-44" href="#__codelineno-20-44"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">node</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-20-45" name="__codelineno-20-45" href="#__codelineno-20-45"></a><span class="w">        </span><span class="c1">// 連結リストが空なら、front と rear の両方を node に向ける</span>
+<a id="__codelineno-20-46" name="__codelineno-20-46" href="#__codelineno-20-46"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-47" name="__codelineno-20-47" href="#__codelineno-20-47"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-20-48" name="__codelineno-20-48" href="#__codelineno-20-48"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-20-49" name="__codelineno-20-49" href="#__codelineno-20-49"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-50" name="__codelineno-20-50" href="#__codelineno-20-50"></a><span class="w">            </span><span class="c1">// node を連結リストの先頭に追加</span>
+<a id="__codelineno-20-51" name="__codelineno-20-51" href="#__codelineno-20-51"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="p">.</span><span class="nx">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-20-52" name="__codelineno-20-52" href="#__codelineno-20-52"></a><span class="w">            </span><span class="nx">node</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="p">;</span>
+<a id="__codelineno-20-53" name="__codelineno-20-53" href="#__codelineno-20-53"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードを更新する</span>
+<a id="__codelineno-20-54" name="__codelineno-20-54" href="#__codelineno-20-54"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-55" name="__codelineno-20-55" href="#__codelineno-20-55"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-20-56" name="__codelineno-20-56" href="#__codelineno-20-56"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-57" name="__codelineno-20-57" href="#__codelineno-20-57"></a>
+<a id="__codelineno-20-58" name="__codelineno-20-58" href="#__codelineno-20-58"></a><span class="w">    </span><span class="cm">/* キュー末尾からの取り出し */</span>
+<a id="__codelineno-20-59" name="__codelineno-20-59" href="#__codelineno-20-59"></a><span class="w">    </span><span class="nx">popLast</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-60" name="__codelineno-20-60" href="#__codelineno-20-60"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-61" name="__codelineno-20-61" href="#__codelineno-20-61"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-20-62" name="__codelineno-20-62" href="#__codelineno-20-62"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-63" name="__codelineno-20-63" href="#__codelineno-20-63"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">value</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">rear</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノードの値を保存する</span>
+<a id="__codelineno-20-64" name="__codelineno-20-64" href="#__codelineno-20-64"></a><span class="w">        </span><span class="c1">// 末尾ノードを削除</span>
+<a id="__codelineno-20-65" name="__codelineno-20-65" href="#__codelineno-20-65"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">temp</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">rear</span><span class="p">.</span><span class="nx">prev</span><span class="p">;</span>
+<a id="__codelineno-20-66" name="__codelineno-20-66" href="#__codelineno-20-66"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">temp</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-67" name="__codelineno-20-67" href="#__codelineno-20-67"></a><span class="w">            </span><span class="nx">temp</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-20-68" name="__codelineno-20-68" href="#__codelineno-20-68"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">rear</span><span class="p">.</span><span class="nx">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-20-69" name="__codelineno-20-69" href="#__codelineno-20-69"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-70" name="__codelineno-20-70" href="#__codelineno-20-70"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">temp</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノードを更新する</span>
+<a id="__codelineno-20-71" name="__codelineno-20-71" href="#__codelineno-20-71"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-20-72" name="__codelineno-20-72" href="#__codelineno-20-72"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">value</span><span class="p">;</span>
+<a id="__codelineno-20-73" name="__codelineno-20-73" href="#__codelineno-20-73"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-74" name="__codelineno-20-74" href="#__codelineno-20-74"></a>
+<a id="__codelineno-20-75" name="__codelineno-20-75" href="#__codelineno-20-75"></a><span class="w">    </span><span class="cm">/* キュー先頭からの取り出し */</span>
+<a id="__codelineno-20-76" name="__codelineno-20-76" href="#__codelineno-20-76"></a><span class="w">    </span><span class="nx">popFirst</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-77" name="__codelineno-20-77" href="#__codelineno-20-77"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-78" name="__codelineno-20-78" href="#__codelineno-20-78"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-20-79" name="__codelineno-20-79" href="#__codelineno-20-79"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-80" name="__codelineno-20-80" href="#__codelineno-20-80"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">value</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノードの値を保存する</span>
+<a id="__codelineno-20-81" name="__codelineno-20-81" href="#__codelineno-20-81"></a><span class="w">        </span><span class="c1">// 先頭ノードを削除</span>
+<a id="__codelineno-20-82" name="__codelineno-20-82" href="#__codelineno-20-82"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">temp</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="p">.</span><span class="nx">next</span><span class="p">;</span>
+<a id="__codelineno-20-83" name="__codelineno-20-83" href="#__codelineno-20-83"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">temp</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-84" name="__codelineno-20-84" href="#__codelineno-20-84"></a><span class="w">            </span><span class="nx">temp</span><span class="p">.</span><span class="nx">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-20-85" name="__codelineno-20-85" href="#__codelineno-20-85"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-20-86" name="__codelineno-20-86" href="#__codelineno-20-86"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-87" name="__codelineno-20-87" href="#__codelineno-20-87"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">temp</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードを更新する</span>
+<a id="__codelineno-20-88" name="__codelineno-20-88" href="#__codelineno-20-88"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-20-89" name="__codelineno-20-89" href="#__codelineno-20-89"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">value</span><span class="p">;</span>
+<a id="__codelineno-20-90" name="__codelineno-20-90" href="#__codelineno-20-90"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-91" name="__codelineno-20-91" href="#__codelineno-20-91"></a>
+<a id="__codelineno-20-92" name="__codelineno-20-92" href="#__codelineno-20-92"></a><span class="w">    </span><span class="cm">/* キュー末尾の要素にアクセス */</span>
+<a id="__codelineno-20-93" name="__codelineno-20-93" href="#__codelineno-20-93"></a><span class="w">    </span><span class="nx">peekLast</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-94" name="__codelineno-20-94" href="#__codelineno-20-94"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">this.rear.val</span><span class="p">;</span>
+<a id="__codelineno-20-95" name="__codelineno-20-95" href="#__codelineno-20-95"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-96" name="__codelineno-20-96" href="#__codelineno-20-96"></a>
+<a id="__codelineno-20-97" name="__codelineno-20-97" href="#__codelineno-20-97"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-20-98" name="__codelineno-20-98" href="#__codelineno-20-98"></a><span class="w">    </span><span class="nx">peekFirst</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-99" name="__codelineno-20-99" href="#__codelineno-20-99"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">this.front.val</span><span class="p">;</span>
+<a id="__codelineno-20-100" name="__codelineno-20-100" href="#__codelineno-20-100"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-101" name="__codelineno-20-101" href="#__codelineno-20-101"></a>
+<a id="__codelineno-20-102" name="__codelineno-20-102" href="#__codelineno-20-102"></a><span class="w">    </span><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-20-103" name="__codelineno-20-103" href="#__codelineno-20-103"></a><span class="w">    </span><span class="nx">size</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-104" name="__codelineno-20-104" href="#__codelineno-20-104"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="p">;</span>
+<a id="__codelineno-20-105" name="__codelineno-20-105" href="#__codelineno-20-105"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-106" name="__codelineno-20-106" href="#__codelineno-20-106"></a>
+<a id="__codelineno-20-107" name="__codelineno-20-107" href="#__codelineno-20-107"></a><span class="w">    </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
+<a id="__codelineno-20-108" name="__codelineno-20-108" href="#__codelineno-20-108"></a><span class="w">    </span><span class="nx">isEmpty</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-109" name="__codelineno-20-109" href="#__codelineno-20-109"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-20-110" name="__codelineno-20-110" href="#__codelineno-20-110"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-111" name="__codelineno-20-111" href="#__codelineno-20-111"></a>
+<a id="__codelineno-20-112" name="__codelineno-20-112" href="#__codelineno-20-112"></a><span class="w">    </span><span class="cm">/* 両端キューを出力する */</span>
+<a id="__codelineno-20-113" name="__codelineno-20-113" href="#__codelineno-20-113"></a><span class="w">    </span><span class="nx">print</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-114" name="__codelineno-20-114" href="#__codelineno-20-114"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">arr</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-20-115" name="__codelineno-20-115" href="#__codelineno-20-115"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">temp</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="p">;</span>
+<a id="__codelineno-20-116" name="__codelineno-20-116" href="#__codelineno-20-116"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">temp</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-117" name="__codelineno-20-117" href="#__codelineno-20-117"></a><span class="w">            </span><span class="nx">arr</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">temp</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-20-118" name="__codelineno-20-118" href="#__codelineno-20-118"></a><span class="w">            </span><span class="nx">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">temp</span><span class="p">.</span><span class="nx">next</span><span class="p">;</span>
+<a id="__codelineno-20-119" name="__codelineno-20-119" href="#__codelineno-20-119"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-120" name="__codelineno-20-120" href="#__codelineno-20-120"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="s1">&#39;[&#39;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">arr</span><span class="p">.</span><span class="nx">join</span><span class="p">(</span><span class="s1">&#39;, &#39;</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s1">&#39;]&#39;</span><span class="p">);</span>
+<a id="__codelineno-20-121" name="__codelineno-20-121" href="#__codelineno-20-121"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-122" name="__codelineno-20-122" href="#__codelineno-20-122"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_deque.rs</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ListNode</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
-<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a>
-<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">LinkedListDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">linkedlist_deque.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 双方向連結リストノード */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// ノード値</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">next</span><span class="p">;</span><span class="w"> </span><span class="c1">// 後続ノードへの参照</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">  </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">prev</span><span class="p">;</span><span class="w"> </span><span class="c1">// 前駆ノードへの参照</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">  </span><span class="n">ListNode</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="p">{</span><span class="k">this</span><span class="p">.</span><span class="n">next</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">prev</span><span class="p">});</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="p">}</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="cm">/* 双方向連結リストに基づく双方向キュー */</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="kd">class</span><span class="w"> </span><span class="nc">LinkedListDeque</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w">  </span><span class="kd">late</span><span class="w"> </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">_front</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノード _front</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">  </span><span class="kd">late</span><span class="w"> </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">_rear</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノード _rear</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">_queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端キューの長さ</span>
+<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a>
+<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="w">  </span><span class="n">LinkedListDeque</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-17" name="__codelineno-21-17" href="#__codelineno-21-17"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="n">_front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-21-18" name="__codelineno-21-18" href="#__codelineno-21-18"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="n">_rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-21-19" name="__codelineno-21-19" href="#__codelineno-21-19"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-20" name="__codelineno-21-20" href="#__codelineno-21-20"></a>
+<a id="__codelineno-21-21" name="__codelineno-21-21" href="#__codelineno-21-21"></a><span class="w">  </span><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-21-22" name="__codelineno-21-22" href="#__codelineno-21-22"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-23" name="__codelineno-21-23" href="#__codelineno-21-23"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">_queSize</span><span class="p">;</span>
+<a id="__codelineno-21-24" name="__codelineno-21-24" href="#__codelineno-21-24"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-25" name="__codelineno-21-25" href="#__codelineno-21-25"></a>
+<a id="__codelineno-21-26" name="__codelineno-21-26" href="#__codelineno-21-26"></a><span class="w">  </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
+<a id="__codelineno-21-27" name="__codelineno-21-27" href="#__codelineno-21-27"></a><span class="w">  </span><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-28" name="__codelineno-21-28" href="#__codelineno-21-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-21-29" name="__codelineno-21-29" href="#__codelineno-21-29"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-30" name="__codelineno-21-30" href="#__codelineno-21-30"></a>
+<a id="__codelineno-21-31" name="__codelineno-21-31" href="#__codelineno-21-31"></a><span class="w">  </span><span class="cm">/* エンキュー操作 */</span>
+<a id="__codelineno-21-32" name="__codelineno-21-32" href="#__codelineno-21-32"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="p">,</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-33" name="__codelineno-21-33" href="#__codelineno-21-33"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">_num</span><span class="p">);</span>
+<a id="__codelineno-21-34" name="__codelineno-21-34" href="#__codelineno-21-34"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-35" name="__codelineno-21-35" href="#__codelineno-21-35"></a><span class="w">      </span><span class="c1">// 連結リストが空なら、`_front` と `_rear` の両方を `node` に向ける</span>
+<a id="__codelineno-21-36" name="__codelineno-21-36" href="#__codelineno-21-36"></a><span class="w">      </span><span class="n">_front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-21-37" name="__codelineno-21-37" href="#__codelineno-21-37"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-38" name="__codelineno-21-38" href="#__codelineno-21-38"></a><span class="w">      </span><span class="c1">// 先頭へのエンキュー操作</span>
+<a id="__codelineno-21-39" name="__codelineno-21-39" href="#__codelineno-21-39"></a><span class="w">      </span><span class="c1">// node を連結リストの先頭に追加する</span>
+<a id="__codelineno-21-40" name="__codelineno-21-40" href="#__codelineno-21-40"></a><span class="w">      </span><span class="n">_front</span><span class="o">!</span><span class="p">.</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-21-41" name="__codelineno-21-41" href="#__codelineno-21-41"></a><span class="w">      </span><span class="n">node</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_front</span><span class="p">;</span>
+<a id="__codelineno-21-42" name="__codelineno-21-42" href="#__codelineno-21-42"></a><span class="w">      </span><span class="n">_front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードを更新する</span>
+<a id="__codelineno-21-43" name="__codelineno-21-43" href="#__codelineno-21-43"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-44" name="__codelineno-21-44" href="#__codelineno-21-44"></a><span class="w">      </span><span class="c1">// 末尾へのエンキュー操作</span>
+<a id="__codelineno-21-45" name="__codelineno-21-45" href="#__codelineno-21-45"></a><span class="w">      </span><span class="c1">// node を連結リストの末尾に追加する</span>
+<a id="__codelineno-21-46" name="__codelineno-21-46" href="#__codelineno-21-46"></a><span class="w">      </span><span class="n">_rear</span><span class="o">!</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-21-47" name="__codelineno-21-47" href="#__codelineno-21-47"></a><span class="w">      </span><span class="n">node</span><span class="p">.</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_rear</span><span class="p">;</span>
+<a id="__codelineno-21-48" name="__codelineno-21-48" href="#__codelineno-21-48"></a><span class="w">      </span><span class="n">_rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノードを更新する</span>
+<a id="__codelineno-21-49" name="__codelineno-21-49" href="#__codelineno-21-49"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-50" name="__codelineno-21-50" href="#__codelineno-21-50"></a><span class="w">    </span><span class="n">_queSize</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの長さを更新</span>
+<a id="__codelineno-21-51" name="__codelineno-21-51" href="#__codelineno-21-51"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-52" name="__codelineno-21-52" href="#__codelineno-21-52"></a>
+<a id="__codelineno-21-53" name="__codelineno-21-53" href="#__codelineno-21-53"></a><span class="w">  </span><span class="cm">/* キュー先頭にエンキュー */</span>
+<a id="__codelineno-21-54" name="__codelineno-21-54" href="#__codelineno-21-54"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">pushFirst</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-55" name="__codelineno-21-55" href="#__codelineno-21-55"></a><span class="w">    </span><span class="n">push</span><span class="p">(</span><span class="n">_num</span><span class="p">,</span><span class="w"> </span><span class="kc">true</span><span class="p">);</span>
+<a id="__codelineno-21-56" name="__codelineno-21-56" href="#__codelineno-21-56"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-57" name="__codelineno-21-57" href="#__codelineno-21-57"></a>
+<a id="__codelineno-21-58" name="__codelineno-21-58" href="#__codelineno-21-58"></a><span class="w">  </span><span class="cm">/* キュー末尾にエンキュー */</span>
+<a id="__codelineno-21-59" name="__codelineno-21-59" href="#__codelineno-21-59"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">pushLast</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-60" name="__codelineno-21-60" href="#__codelineno-21-60"></a><span class="w">    </span><span class="n">push</span><span class="p">(</span><span class="n">_num</span><span class="p">,</span><span class="w"> </span><span class="kc">false</span><span class="p">);</span>
+<a id="__codelineno-21-61" name="__codelineno-21-61" href="#__codelineno-21-61"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-62" name="__codelineno-21-62" href="#__codelineno-21-62"></a>
+<a id="__codelineno-21-63" name="__codelineno-21-63" href="#__codelineno-21-63"></a><span class="w">  </span><span class="cm">/* デキュー操作 */</span>
+<a id="__codelineno-21-64" name="__codelineno-21-64" href="#__codelineno-21-64"></a><span class="w">  </span><span class="kt">int</span><span class="o">?</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="kt">bool</span><span class="w"> </span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-65" name="__codelineno-21-65" href="#__codelineno-21-65"></a><span class="w">    </span><span class="c1">// キューが空なら、そのまま `null` を返す</span>
+<a id="__codelineno-21-66" name="__codelineno-21-66" href="#__codelineno-21-66"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-67" name="__codelineno-21-67" href="#__codelineno-21-67"></a><span class="w">      </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-21-68" name="__codelineno-21-68" href="#__codelineno-21-68"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-69" name="__codelineno-21-69" href="#__codelineno-21-69"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-21-70" name="__codelineno-21-70" href="#__codelineno-21-70"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-71" name="__codelineno-21-71" href="#__codelineno-21-71"></a><span class="w">      </span><span class="c1">// キュー先頭からの取り出し</span>
+<a id="__codelineno-21-72" name="__codelineno-21-72" href="#__codelineno-21-72"></a><span class="w">      </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_front</span><span class="o">!</span><span class="p">.</span><span class="n">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードの値を一時保存</span>
+<a id="__codelineno-21-73" name="__codelineno-21-73" href="#__codelineno-21-73"></a><span class="w">      </span><span class="c1">// 先頭ノードを削除</span>
+<a id="__codelineno-21-74" name="__codelineno-21-74" href="#__codelineno-21-74"></a><span class="w">      </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">fNext</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_front</span><span class="o">!</span><span class="p">.</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-21-75" name="__codelineno-21-75" href="#__codelineno-21-75"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">fNext</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-76" name="__codelineno-21-76" href="#__codelineno-21-76"></a><span class="w">        </span><span class="n">fNext</span><span class="p">.</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-21-77" name="__codelineno-21-77" href="#__codelineno-21-77"></a><span class="w">        </span><span class="n">_front</span><span class="o">!</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-21-78" name="__codelineno-21-78" href="#__codelineno-21-78"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-21-79" name="__codelineno-21-79" href="#__codelineno-21-79"></a><span class="w">      </span><span class="n">_front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fNext</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードを更新する</span>
+<a id="__codelineno-21-80" name="__codelineno-21-80" href="#__codelineno-21-80"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-81" name="__codelineno-21-81" href="#__codelineno-21-81"></a><span class="w">      </span><span class="c1">// キュー末尾からの取り出し</span>
+<a id="__codelineno-21-82" name="__codelineno-21-82" href="#__codelineno-21-82"></a><span class="w">      </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_rear</span><span class="o">!</span><span class="p">.</span><span class="n">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノードの値を一時保存</span>
+<a id="__codelineno-21-83" name="__codelineno-21-83" href="#__codelineno-21-83"></a><span class="w">      </span><span class="c1">// 末尾ノードを削除</span>
+<a id="__codelineno-21-84" name="__codelineno-21-84" href="#__codelineno-21-84"></a><span class="w">      </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">rPrev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_rear</span><span class="o">!</span><span class="p">.</span><span class="n">prev</span><span class="p">;</span>
+<a id="__codelineno-21-85" name="__codelineno-21-85" href="#__codelineno-21-85"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">rPrev</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-86" name="__codelineno-21-86" href="#__codelineno-21-86"></a><span class="w">        </span><span class="n">rPrev</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-21-87" name="__codelineno-21-87" href="#__codelineno-21-87"></a><span class="w">        </span><span class="n">_rear</span><span class="o">!</span><span class="p">.</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-21-88" name="__codelineno-21-88" href="#__codelineno-21-88"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-21-89" name="__codelineno-21-89" href="#__codelineno-21-89"></a><span class="w">      </span><span class="n">_rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rPrev</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノードを更新する</span>
+<a id="__codelineno-21-90" name="__codelineno-21-90" href="#__codelineno-21-90"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-91" name="__codelineno-21-91" href="#__codelineno-21-91"></a><span class="w">    </span><span class="n">_queSize</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの長さを更新</span>
+<a id="__codelineno-21-92" name="__codelineno-21-92" href="#__codelineno-21-92"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-21-93" name="__codelineno-21-93" href="#__codelineno-21-93"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-94" name="__codelineno-21-94" href="#__codelineno-21-94"></a>
+<a id="__codelineno-21-95" name="__codelineno-21-95" href="#__codelineno-21-95"></a><span class="w">  </span><span class="cm">/* キュー先頭からデキュー */</span>
+<a id="__codelineno-21-96" name="__codelineno-21-96" href="#__codelineno-21-96"></a><span class="w">  </span><span class="kt">int</span><span class="o">?</span><span class="w"> </span><span class="n">popFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-97" name="__codelineno-21-97" href="#__codelineno-21-97"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="kc">true</span><span class="p">);</span>
+<a id="__codelineno-21-98" name="__codelineno-21-98" href="#__codelineno-21-98"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-99" name="__codelineno-21-99" href="#__codelineno-21-99"></a>
+<a id="__codelineno-21-100" name="__codelineno-21-100" href="#__codelineno-21-100"></a><span class="w">  </span><span class="cm">/* キュー末尾からデキュー */</span>
+<a id="__codelineno-21-101" name="__codelineno-21-101" href="#__codelineno-21-101"></a><span class="w">  </span><span class="kt">int</span><span class="o">?</span><span class="w"> </span><span class="n">popLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-102" name="__codelineno-21-102" href="#__codelineno-21-102"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="kc">false</span><span class="p">);</span>
+<a id="__codelineno-21-103" name="__codelineno-21-103" href="#__codelineno-21-103"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-104" name="__codelineno-21-104" href="#__codelineno-21-104"></a>
+<a id="__codelineno-21-105" name="__codelineno-21-105" href="#__codelineno-21-105"></a><span class="w">  </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-21-106" name="__codelineno-21-106" href="#__codelineno-21-106"></a><span class="w">  </span><span class="kt">int</span><span class="o">?</span><span class="w"> </span><span class="n">peekFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-107" name="__codelineno-21-107" href="#__codelineno-21-107"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_front</span><span class="o">?</span><span class="p">.</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-21-108" name="__codelineno-21-108" href="#__codelineno-21-108"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-109" name="__codelineno-21-109" href="#__codelineno-21-109"></a>
+<a id="__codelineno-21-110" name="__codelineno-21-110" href="#__codelineno-21-110"></a><span class="w">  </span><span class="cm">/* キュー末尾の要素にアクセス */</span>
+<a id="__codelineno-21-111" name="__codelineno-21-111" href="#__codelineno-21-111"></a><span class="w">  </span><span class="kt">int</span><span class="o">?</span><span class="w"> </span><span class="n">peekLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-112" name="__codelineno-21-112" href="#__codelineno-21-112"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_rear</span><span class="o">?</span><span class="p">.</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-21-113" name="__codelineno-21-113" href="#__codelineno-21-113"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-114" name="__codelineno-21-114" href="#__codelineno-21-114"></a>
+<a id="__codelineno-21-115" name="__codelineno-21-115" href="#__codelineno-21-115"></a><span class="w">  </span><span class="cm">/* 出力用の配列を返す */</span>
+<a id="__codelineno-21-116" name="__codelineno-21-116" href="#__codelineno-21-116"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-117" name="__codelineno-21-117" href="#__codelineno-21-117"></a><span class="w">    </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_front</span><span class="p">;</span>
+<a id="__codelineno-21-118" name="__codelineno-21-118" href="#__codelineno-21-118"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-21-119" name="__codelineno-21-119" href="#__codelineno-21-119"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">_queSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-120" name="__codelineno-21-120" href="#__codelineno-21-120"></a><span class="w">      </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">node</span><span class="o">!</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-21-121" name="__codelineno-21-121" href="#__codelineno-21-121"></a><span class="w">      </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-21-122" name="__codelineno-21-122" href="#__codelineno-21-122"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-123" name="__codelineno-21-123" href="#__codelineno-21-123"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-21-124" name="__codelineno-21-124" href="#__codelineno-21-124"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-125" name="__codelineno-21-125" href="#__codelineno-21-125"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_deque.c</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">DoublyListNode</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
-<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a>
-<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">LinkedListDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">linkedlist_deque.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 双方向連結リストノード */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">pub</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="nc">T</span><span class="p">,</span><span class="w">                                 </span><span class="c1">// ノード値</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="c1">// 後継ノードへのポインタ</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="n">prev</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="c1">// 前駆ノードへのポインタ</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="p">}</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="k">impl</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">new</span><span class="p">(</span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="nc">T</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w">        </span><span class="n">Rc</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">RefCell</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w">            </span><span class="n">val</span><span class="p">,</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">            </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">            </span><span class="n">prev</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">        </span><span class="p">}))</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="p">}</span>
+<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a>
+<a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="cm">/* 双方向連結リストベースの両端キュー */</span>
+<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="cp">#[allow(dead_code)]</span>
+<a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a><span class="k">pub</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">LinkedListDeque</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-21" name="__codelineno-22-21" href="#__codelineno-22-21"></a><span class="w">    </span><span class="n">front</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="c1">// 先頭ノード front</span>
+<a id="__codelineno-22-22" name="__codelineno-22-22" href="#__codelineno-22-22"></a><span class="w">    </span><span class="n">rear</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;&gt;</span><span class="p">,</span><span class="w">  </span><span class="c1">// 末尾ノード rear</span>
+<a id="__codelineno-22-23" name="__codelineno-22-23" href="#__codelineno-22-23"></a><span class="w">    </span><span class="n">que_size</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w">                         </span><span class="c1">// 両端キューの長さ</span>
+<a id="__codelineno-22-24" name="__codelineno-22-24" href="#__codelineno-22-24"></a><span class="p">}</span>
+<a id="__codelineno-22-25" name="__codelineno-22-25" href="#__codelineno-22-25"></a>
+<a id="__codelineno-22-26" name="__codelineno-22-26" href="#__codelineno-22-26"></a><span class="k">impl</span><span class="o">&lt;</span><span class="n">T</span><span class="p">:</span><span class="w"> </span><span class="nb">Copy</span><span class="o">&gt;</span><span class="w"> </span><span class="n">LinkedListDeque</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-27" name="__codelineno-22-27" href="#__codelineno-22-27"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">new</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-28" name="__codelineno-22-28" href="#__codelineno-22-28"></a><span class="w">        </span><span class="bp">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-29" name="__codelineno-22-29" href="#__codelineno-22-29"></a><span class="w">            </span><span class="n">front</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span>
+<a id="__codelineno-22-30" name="__codelineno-22-30" href="#__codelineno-22-30"></a><span class="w">            </span><span class="n">rear</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span>
+<a id="__codelineno-22-31" name="__codelineno-22-31" href="#__codelineno-22-31"></a><span class="w">            </span><span class="n">que_size</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span>
+<a id="__codelineno-22-32" name="__codelineno-22-32" href="#__codelineno-22-32"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-33" name="__codelineno-22-33" href="#__codelineno-22-33"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-34" name="__codelineno-22-34" href="#__codelineno-22-34"></a>
+<a id="__codelineno-22-35" name="__codelineno-22-35" href="#__codelineno-22-35"></a><span class="w">    </span><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-22-36" name="__codelineno-22-36" href="#__codelineno-22-36"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-37" name="__codelineno-22-37" href="#__codelineno-22-37"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="p">;</span>
+<a id="__codelineno-22-38" name="__codelineno-22-38" href="#__codelineno-22-38"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-39" name="__codelineno-22-39" href="#__codelineno-22-39"></a>
+<a id="__codelineno-22-40" name="__codelineno-22-40" href="#__codelineno-22-40"></a><span class="w">    </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
+<a id="__codelineno-22-41" name="__codelineno-22-41" href="#__codelineno-22-41"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">is_empty</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-42" name="__codelineno-22-42" href="#__codelineno-22-42"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-22-43" name="__codelineno-22-43" href="#__codelineno-22-43"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-44" name="__codelineno-22-44" href="#__codelineno-22-44"></a>
+<a id="__codelineno-22-45" name="__codelineno-22-45" href="#__codelineno-22-45"></a><span class="w">    </span><span class="cm">/* エンキュー操作 */</span>
+<a id="__codelineno-22-46" name="__codelineno-22-46" href="#__codelineno-22-46"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nc">T</span><span class="p">,</span><span class="w"> </span><span class="n">is_front</span><span class="p">:</span><span class="w"> </span><span class="kt">bool</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-47" name="__codelineno-22-47" href="#__codelineno-22-47"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-22-48" name="__codelineno-22-48" href="#__codelineno-22-48"></a><span class="w">        </span><span class="c1">// 先頭へのエンキュー操作</span>
+<a id="__codelineno-22-49" name="__codelineno-22-49" href="#__codelineno-22-49"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">is_front</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-50" name="__codelineno-22-50" href="#__codelineno-22-50"></a><span class="w">            </span><span class="k">match</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="p">.</span><span class="n">take</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-51" name="__codelineno-22-51" href="#__codelineno-22-51"></a><span class="w">                </span><span class="c1">// 連結リストが空なら、front と rear の両方を node に向ける</span>
+<a id="__codelineno-22-52" name="__codelineno-22-52" href="#__codelineno-22-52"></a><span class="w">                </span><span class="nb">None</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-53" name="__codelineno-22-53" href="#__codelineno-22-53"></a><span class="w">                    </span><span class="bp">self</span><span class="p">.</span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-22-54" name="__codelineno-22-54" href="#__codelineno-22-54"></a><span class="w">                    </span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-22-55" name="__codelineno-22-55" href="#__codelineno-22-55"></a><span class="w">                </span><span class="p">}</span>
+<a id="__codelineno-22-56" name="__codelineno-22-56" href="#__codelineno-22-56"></a><span class="w">                </span><span class="c1">// node を連結リストの先頭に追加</span>
+<a id="__codelineno-22-57" name="__codelineno-22-57" href="#__codelineno-22-57"></a><span class="w">                </span><span class="nb">Some</span><span class="p">(</span><span class="n">old_front</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-58" name="__codelineno-22-58" href="#__codelineno-22-58"></a><span class="w">                    </span><span class="n">old_front</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-22-59" name="__codelineno-22-59" href="#__codelineno-22-59"></a><span class="w">                    </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">old_front</span><span class="p">);</span>
+<a id="__codelineno-22-60" name="__codelineno-22-60" href="#__codelineno-22-60"></a><span class="w">                    </span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// 先頭ノードを更新する</span>
+<a id="__codelineno-22-61" name="__codelineno-22-61" href="#__codelineno-22-61"></a><span class="w">                </span><span class="p">}</span>
+<a id="__codelineno-22-62" name="__codelineno-22-62" href="#__codelineno-22-62"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-22-63" name="__codelineno-22-63" href="#__codelineno-22-63"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-64" name="__codelineno-22-64" href="#__codelineno-22-64"></a><span class="w">        </span><span class="c1">// 末尾へのエンキュー操作</span>
+<a id="__codelineno-22-65" name="__codelineno-22-65" href="#__codelineno-22-65"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-66" name="__codelineno-22-66" href="#__codelineno-22-66"></a><span class="w">            </span><span class="k">match</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">rear</span><span class="p">.</span><span class="n">take</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-67" name="__codelineno-22-67" href="#__codelineno-22-67"></a><span class="w">                </span><span class="c1">// 連結リストが空なら、front と rear の両方を node に向ける</span>
+<a id="__codelineno-22-68" name="__codelineno-22-68" href="#__codelineno-22-68"></a><span class="w">                </span><span class="nb">None</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-69" name="__codelineno-22-69" href="#__codelineno-22-69"></a><span class="w">                    </span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-22-70" name="__codelineno-22-70" href="#__codelineno-22-70"></a><span class="w">                    </span><span class="bp">self</span><span class="p">.</span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-22-71" name="__codelineno-22-71" href="#__codelineno-22-71"></a><span class="w">                </span><span class="p">}</span>
+<a id="__codelineno-22-72" name="__codelineno-22-72" href="#__codelineno-22-72"></a><span class="w">                </span><span class="c1">// node を連結リストの末尾に追加</span>
+<a id="__codelineno-22-73" name="__codelineno-22-73" href="#__codelineno-22-73"></a><span class="w">                </span><span class="nb">Some</span><span class="p">(</span><span class="n">old_rear</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-74" name="__codelineno-22-74" href="#__codelineno-22-74"></a><span class="w">                    </span><span class="n">old_rear</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-22-75" name="__codelineno-22-75" href="#__codelineno-22-75"></a><span class="w">                    </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">old_rear</span><span class="p">);</span>
+<a id="__codelineno-22-76" name="__codelineno-22-76" href="#__codelineno-22-76"></a><span class="w">                    </span><span class="bp">self</span><span class="p">.</span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// 末尾ノードを更新する</span>
+<a id="__codelineno-22-77" name="__codelineno-22-77" href="#__codelineno-22-77"></a><span class="w">                </span><span class="p">}</span>
+<a id="__codelineno-22-78" name="__codelineno-22-78" href="#__codelineno-22-78"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-22-79" name="__codelineno-22-79" href="#__codelineno-22-79"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-80" name="__codelineno-22-80" href="#__codelineno-22-80"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの長さを更新</span>
+<a id="__codelineno-22-81" name="__codelineno-22-81" href="#__codelineno-22-81"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-82" name="__codelineno-22-82" href="#__codelineno-22-82"></a>
+<a id="__codelineno-22-83" name="__codelineno-22-83" href="#__codelineno-22-83"></a><span class="w">    </span><span class="cm">/* キュー先頭にエンキュー */</span>
+<a id="__codelineno-22-84" name="__codelineno-22-84" href="#__codelineno-22-84"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">push_first</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nc">T</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-85" name="__codelineno-22-85" href="#__codelineno-22-85"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kc">true</span><span class="p">);</span>
+<a id="__codelineno-22-86" name="__codelineno-22-86" href="#__codelineno-22-86"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-87" name="__codelineno-22-87" href="#__codelineno-22-87"></a>
+<a id="__codelineno-22-88" name="__codelineno-22-88" href="#__codelineno-22-88"></a><span class="w">    </span><span class="cm">/* キュー末尾にエンキュー */</span>
+<a id="__codelineno-22-89" name="__codelineno-22-89" href="#__codelineno-22-89"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">push_last</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nc">T</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-90" name="__codelineno-22-90" href="#__codelineno-22-90"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kc">false</span><span class="p">);</span>
+<a id="__codelineno-22-91" name="__codelineno-22-91" href="#__codelineno-22-91"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-92" name="__codelineno-22-92" href="#__codelineno-22-92"></a>
+<a id="__codelineno-22-93" name="__codelineno-22-93" href="#__codelineno-22-93"></a><span class="w">    </span><span class="cm">/* デキュー操作 */</span>
+<a id="__codelineno-22-94" name="__codelineno-22-94" href="#__codelineno-22-94"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">is_front</span><span class="p">:</span><span class="w"> </span><span class="kt">bool</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-95" name="__codelineno-22-95" href="#__codelineno-22-95"></a><span class="w">        </span><span class="c1">// キューが空なら、そのまま `None` を返す</span>
+<a id="__codelineno-22-96" name="__codelineno-22-96" href="#__codelineno-22-96"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">is_empty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-97" name="__codelineno-22-97" href="#__codelineno-22-97"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nb">None</span><span class="p">;</span>
+<a id="__codelineno-22-98" name="__codelineno-22-98" href="#__codelineno-22-98"></a><span class="w">        </span><span class="p">};</span>
+<a id="__codelineno-22-99" name="__codelineno-22-99" href="#__codelineno-22-99"></a><span class="w">        </span><span class="c1">// キュー先頭からの取り出し</span>
+<a id="__codelineno-22-100" name="__codelineno-22-100" href="#__codelineno-22-100"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">is_front</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-101" name="__codelineno-22-101" href="#__codelineno-22-101"></a><span class="w">            </span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="p">.</span><span class="n">take</span><span class="p">().</span><span class="n">map</span><span class="p">(</span><span class="o">|</span><span class="n">old_front</span><span class="o">|</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-102" name="__codelineno-22-102" href="#__codelineno-22-102"></a><span class="w">                </span><span class="k">match</span><span class="w"> </span><span class="n">old_front</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="p">.</span><span class="n">take</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-103" name="__codelineno-22-103" href="#__codelineno-22-103"></a><span class="w">                    </span><span class="nb">Some</span><span class="p">(</span><span class="n">new_front</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-104" name="__codelineno-22-104" href="#__codelineno-22-104"></a><span class="w">                        </span><span class="n">new_front</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">prev</span><span class="p">.</span><span class="n">take</span><span class="p">();</span>
+<a id="__codelineno-22-105" name="__codelineno-22-105" href="#__codelineno-22-105"></a><span class="w">                        </span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">new_front</span><span class="p">);</span><span class="w"> </span><span class="c1">// 先頭ノードを更新する</span>
+<a id="__codelineno-22-106" name="__codelineno-22-106" href="#__codelineno-22-106"></a><span class="w">                    </span><span class="p">}</span>
+<a id="__codelineno-22-107" name="__codelineno-22-107" href="#__codelineno-22-107"></a><span class="w">                    </span><span class="nb">None</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-108" name="__codelineno-22-108" href="#__codelineno-22-108"></a><span class="w">                        </span><span class="bp">self</span><span class="p">.</span><span class="n">rear</span><span class="p">.</span><span class="n">take</span><span class="p">();</span>
+<a id="__codelineno-22-109" name="__codelineno-22-109" href="#__codelineno-22-109"></a><span class="w">                    </span><span class="p">}</span>
+<a id="__codelineno-22-110" name="__codelineno-22-110" href="#__codelineno-22-110"></a><span class="w">                </span><span class="p">}</span>
+<a id="__codelineno-22-111" name="__codelineno-22-111" href="#__codelineno-22-111"></a><span class="w">                </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの長さを更新</span>
+<a id="__codelineno-22-112" name="__codelineno-22-112" href="#__codelineno-22-112"></a><span class="w">                </span><span class="n">old_front</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span>
+<a id="__codelineno-22-113" name="__codelineno-22-113" href="#__codelineno-22-113"></a><span class="w">            </span><span class="p">})</span>
+<a id="__codelineno-22-114" name="__codelineno-22-114" href="#__codelineno-22-114"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-115" name="__codelineno-22-115" href="#__codelineno-22-115"></a><span class="w">        </span><span class="c1">// キュー末尾からの取り出し</span>
+<a id="__codelineno-22-116" name="__codelineno-22-116" href="#__codelineno-22-116"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-117" name="__codelineno-22-117" href="#__codelineno-22-117"></a><span class="w">            </span><span class="bp">self</span><span class="p">.</span><span class="n">rear</span><span class="p">.</span><span class="n">take</span><span class="p">().</span><span class="n">map</span><span class="p">(</span><span class="o">|</span><span class="n">old_rear</span><span class="o">|</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-118" name="__codelineno-22-118" href="#__codelineno-22-118"></a><span class="w">                </span><span class="k">match</span><span class="w"> </span><span class="n">old_rear</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">prev</span><span class="p">.</span><span class="n">take</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-119" name="__codelineno-22-119" href="#__codelineno-22-119"></a><span class="w">                    </span><span class="nb">Some</span><span class="p">(</span><span class="n">new_rear</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-120" name="__codelineno-22-120" href="#__codelineno-22-120"></a><span class="w">                        </span><span class="n">new_rear</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="p">.</span><span class="n">take</span><span class="p">();</span>
+<a id="__codelineno-22-121" name="__codelineno-22-121" href="#__codelineno-22-121"></a><span class="w">                        </span><span class="bp">self</span><span class="p">.</span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">new_rear</span><span class="p">);</span><span class="w"> </span><span class="c1">// 末尾ノードを更新する</span>
+<a id="__codelineno-22-122" name="__codelineno-22-122" href="#__codelineno-22-122"></a><span class="w">                    </span><span class="p">}</span>
+<a id="__codelineno-22-123" name="__codelineno-22-123" href="#__codelineno-22-123"></a><span class="w">                    </span><span class="nb">None</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-124" name="__codelineno-22-124" href="#__codelineno-22-124"></a><span class="w">                        </span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="p">.</span><span class="n">take</span><span class="p">();</span>
+<a id="__codelineno-22-125" name="__codelineno-22-125" href="#__codelineno-22-125"></a><span class="w">                    </span><span class="p">}</span>
+<a id="__codelineno-22-126" name="__codelineno-22-126" href="#__codelineno-22-126"></a><span class="w">                </span><span class="p">}</span>
+<a id="__codelineno-22-127" name="__codelineno-22-127" href="#__codelineno-22-127"></a><span class="w">                </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの長さを更新</span>
+<a id="__codelineno-22-128" name="__codelineno-22-128" href="#__codelineno-22-128"></a><span class="w">                </span><span class="n">old_rear</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span>
+<a id="__codelineno-22-129" name="__codelineno-22-129" href="#__codelineno-22-129"></a><span class="w">            </span><span class="p">})</span>
+<a id="__codelineno-22-130" name="__codelineno-22-130" href="#__codelineno-22-130"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-131" name="__codelineno-22-131" href="#__codelineno-22-131"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-132" name="__codelineno-22-132" href="#__codelineno-22-132"></a>
+<a id="__codelineno-22-133" name="__codelineno-22-133" href="#__codelineno-22-133"></a><span class="w">    </span><span class="cm">/* キュー先頭からデキュー */</span>
+<a id="__codelineno-22-134" name="__codelineno-22-134" href="#__codelineno-22-134"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">pop_first</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-135" name="__codelineno-22-135" href="#__codelineno-22-135"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">pop</span><span class="p">(</span><span class="kc">true</span><span class="p">);</span>
+<a id="__codelineno-22-136" name="__codelineno-22-136" href="#__codelineno-22-136"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-137" name="__codelineno-22-137" href="#__codelineno-22-137"></a>
+<a id="__codelineno-22-138" name="__codelineno-22-138" href="#__codelineno-22-138"></a><span class="w">    </span><span class="cm">/* キュー末尾からデキュー */</span>
+<a id="__codelineno-22-139" name="__codelineno-22-139" href="#__codelineno-22-139"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">pop_last</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-140" name="__codelineno-22-140" href="#__codelineno-22-140"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">pop</span><span class="p">(</span><span class="kc">false</span><span class="p">);</span>
+<a id="__codelineno-22-141" name="__codelineno-22-141" href="#__codelineno-22-141"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-142" name="__codelineno-22-142" href="#__codelineno-22-142"></a>
+<a id="__codelineno-22-143" name="__codelineno-22-143" href="#__codelineno-22-143"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-22-144" name="__codelineno-22-144" href="#__codelineno-22-144"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">peek_first</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-145" name="__codelineno-22-145" href="#__codelineno-22-145"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="p">.</span><span class="n">as_ref</span><span class="p">()</span>
+<a id="__codelineno-22-146" name="__codelineno-22-146" href="#__codelineno-22-146"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-147" name="__codelineno-22-147" href="#__codelineno-22-147"></a>
+<a id="__codelineno-22-148" name="__codelineno-22-148" href="#__codelineno-22-148"></a><span class="w">    </span><span class="cm">/* キュー末尾の要素にアクセス */</span>
+<a id="__codelineno-22-149" name="__codelineno-22-149" href="#__codelineno-22-149"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">peek_last</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-150" name="__codelineno-22-150" href="#__codelineno-22-150"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">rear</span><span class="p">.</span><span class="n">as_ref</span><span class="p">()</span>
+<a id="__codelineno-22-151" name="__codelineno-22-151" href="#__codelineno-22-151"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-152" name="__codelineno-22-152" href="#__codelineno-22-152"></a>
+<a id="__codelineno-22-153" name="__codelineno-22-153" href="#__codelineno-22-153"></a><span class="w">    </span><span class="cm">/* 出力用の配列を返す */</span>
+<a id="__codelineno-22-154" name="__codelineno-22-154" href="#__codelineno-22-154"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">to_array</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">head</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-155" name="__codelineno-22-155" href="#__codelineno-22-155"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-22-156" name="__codelineno-22-156" href="#__codelineno-22-156"></a><span class="w">        </span><span class="k">fn</span><span class="w"> </span><span class="nf">recur</span><span class="o">&lt;</span><span class="n">T</span><span class="p">:</span><span class="w"> </span><span class="nb">Copy</span><span class="o">&gt;</span><span class="p">(</span><span class="n">cur</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-157" name="__codelineno-22-157" href="#__codelineno-22-157"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">cur</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-158" name="__codelineno-22-158" href="#__codelineno-22-158"></a><span class="w">                </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-22-159" name="__codelineno-22-159" href="#__codelineno-22-159"></a><span class="w">                </span><span class="n">recur</span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">next</span><span class="p">.</span><span class="n">as_ref</span><span class="p">(),</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-22-160" name="__codelineno-22-160" href="#__codelineno-22-160"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-22-161" name="__codelineno-22-161" href="#__codelineno-22-161"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-162" name="__codelineno-22-162" href="#__codelineno-22-162"></a>
+<a id="__codelineno-22-163" name="__codelineno-22-163" href="#__codelineno-22-163"></a><span class="w">        </span><span class="n">recur</span><span class="p">(</span><span class="n">head</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-22-164" name="__codelineno-22-164" href="#__codelineno-22-164"></a><span class="w">        </span><span class="n">res</span>
+<a id="__codelineno-22-165" name="__codelineno-22-165" href="#__codelineno-22-165"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-166" name="__codelineno-22-166" href="#__codelineno-22-166"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_deque.kt</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">ListNode</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
-<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a>
-<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">LinkedListDeque</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">linkedlist_deque.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 双方向連結リストノード */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">DoublyListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">                     </span><span class="c1">// ノード値</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="k">struct</span><span class="w"> </span><span class="nc">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">next</span><span class="p">;</span><span class="w"> </span><span class="c1">// 後続ノード</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">    </span><span class="k">struct</span><span class="w"> </span><span class="nc">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">prev</span><span class="p">;</span><span class="w"> </span><span class="c1">// 前駆ノード</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="p">}</span><span class="w"> </span><span class="n">DoublyListNode</span><span class="p">;</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="nf">newDoublyListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w">    </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">new</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">DoublyListNode</span><span class="p">));</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w">    </span><span class="n">new</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w">    </span><span class="n">new</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w">    </span><span class="n">new</span><span class="o">-&gt;</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">new</span><span class="p">;</span>
+<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="p">}</span>
+<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a>
+<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="cm">/* デストラクタ */</span>
+<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="kt">void</span><span class="w"> </span><span class="nf">delDoublyListNode</span><span class="p">(</span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="p">}</span>
+<a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a>
+<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a><span class="cm">/* 双方向連結リストベースの両端キュー */</span>
+<a id="__codelineno-23-23" name="__codelineno-23-23" href="#__codelineno-23-23"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-24" name="__codelineno-23-24" href="#__codelineno-23-24"></a><span class="w">    </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">front</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">rear</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノード front、末尾ノード rear</span>
+<a id="__codelineno-23-25" name="__codelineno-23-25" href="#__codelineno-23-25"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w">                  </span><span class="c1">// 両端キューの長さ</span>
+<a id="__codelineno-23-26" name="__codelineno-23-26" href="#__codelineno-23-26"></a><span class="p">}</span><span class="w"> </span><span class="n">LinkedListDeque</span><span class="p">;</span>
+<a id="__codelineno-23-27" name="__codelineno-23-27" href="#__codelineno-23-27"></a>
+<a id="__codelineno-23-28" name="__codelineno-23-28" href="#__codelineno-23-28"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-23-29" name="__codelineno-23-29" href="#__codelineno-23-29"></a><span class="n">LinkedListDeque</span><span class="w"> </span><span class="o">*</span><span class="nf">newLinkedListDeque</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-30" name="__codelineno-23-30" href="#__codelineno-23-30"></a><span class="w">    </span><span class="n">LinkedListDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">LinkedListDeque</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">LinkedListDeque</span><span class="p">));</span>
+<a id="__codelineno-23-31" name="__codelineno-23-31" href="#__codelineno-23-31"></a><span class="w">    </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-23-32" name="__codelineno-23-32" href="#__codelineno-23-32"></a><span class="w">    </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-23-33" name="__codelineno-23-33" href="#__codelineno-23-33"></a><span class="w">    </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-23-34" name="__codelineno-23-34" href="#__codelineno-23-34"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">deque</span><span class="p">;</span>
+<a id="__codelineno-23-35" name="__codelineno-23-35" href="#__codelineno-23-35"></a><span class="p">}</span>
+<a id="__codelineno-23-36" name="__codelineno-23-36" href="#__codelineno-23-36"></a>
+<a id="__codelineno-23-37" name="__codelineno-23-37" href="#__codelineno-23-37"></a><span class="cm">/* デストラクタ */</span>
+<a id="__codelineno-23-38" name="__codelineno-23-38" href="#__codelineno-23-38"></a><span class="kt">void</span><span class="w"> </span><span class="nf">delLinkedListdeque</span><span class="p">(</span><span class="n">LinkedListDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-39" name="__codelineno-23-39" href="#__codelineno-23-39"></a><span class="w">    </span><span class="c1">// すべてのノードを解放</span>
+<a id="__codelineno-23-40" name="__codelineno-23-40" href="#__codelineno-23-40"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-41" name="__codelineno-23-41" href="#__codelineno-23-41"></a><span class="w">        </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-23-42" name="__codelineno-23-42" href="#__codelineno-23-42"></a><span class="w">        </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-23-43" name="__codelineno-23-43" href="#__codelineno-23-43"></a><span class="w">        </span><span class="n">free</span><span class="p">(</span><span class="n">tmp</span><span class="p">);</span>
+<a id="__codelineno-23-44" name="__codelineno-23-44" href="#__codelineno-23-44"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-45" name="__codelineno-23-45" href="#__codelineno-23-45"></a><span class="w">    </span><span class="c1">// deque 構造体を解放する</span>
+<a id="__codelineno-23-46" name="__codelineno-23-46" href="#__codelineno-23-46"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">deque</span><span class="p">);</span>
+<a id="__codelineno-23-47" name="__codelineno-23-47" href="#__codelineno-23-47"></a><span class="p">}</span>
+<a id="__codelineno-23-48" name="__codelineno-23-48" href="#__codelineno-23-48"></a>
+<a id="__codelineno-23-49" name="__codelineno-23-49" href="#__codelineno-23-49"></a><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-23-50" name="__codelineno-23-50" href="#__codelineno-23-50"></a><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="n">LinkedListDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-51" name="__codelineno-23-51" href="#__codelineno-23-51"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-23-52" name="__codelineno-23-52" href="#__codelineno-23-52"></a><span class="p">}</span>
+<a id="__codelineno-23-53" name="__codelineno-23-53" href="#__codelineno-23-53"></a>
+<a id="__codelineno-23-54" name="__codelineno-23-54" href="#__codelineno-23-54"></a><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-23-55" name="__codelineno-23-55" href="#__codelineno-23-55"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">empty</span><span class="p">(</span><span class="n">LinkedListDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-56" name="__codelineno-23-56" href="#__codelineno-23-56"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="p">(</span><span class="n">deque</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-23-57" name="__codelineno-23-57" href="#__codelineno-23-57"></a><span class="p">}</span>
+<a id="__codelineno-23-58" name="__codelineno-23-58" href="#__codelineno-23-58"></a>
+<a id="__codelineno-23-59" name="__codelineno-23-59" href="#__codelineno-23-59"></a><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-23-60" name="__codelineno-23-60" href="#__codelineno-23-60"></a><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">LinkedListDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-61" name="__codelineno-23-61" href="#__codelineno-23-61"></a><span class="w">    </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newDoublyListNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-23-62" name="__codelineno-23-62" href="#__codelineno-23-62"></a><span class="w">    </span><span class="c1">// 連結リストが空なら、`front` と `rear` の両方を `node` に向ける</span>
+<a id="__codelineno-23-63" name="__codelineno-23-63" href="#__codelineno-23-63"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">empty</span><span class="p">(</span><span class="n">deque</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-64" name="__codelineno-23-64" href="#__codelineno-23-64"></a><span class="w">        </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-23-65" name="__codelineno-23-65" href="#__codelineno-23-65"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-66" name="__codelineno-23-66" href="#__codelineno-23-66"></a><span class="w">    </span><span class="c1">// 先頭へのエンキュー操作</span>
+<a id="__codelineno-23-67" name="__codelineno-23-67" href="#__codelineno-23-67"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-68" name="__codelineno-23-68" href="#__codelineno-23-68"></a><span class="w">        </span><span class="c1">// node を連結リストの先頭に追加</span>
+<a id="__codelineno-23-69" name="__codelineno-23-69" href="#__codelineno-23-69"></a><span class="w">        </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="o">-&gt;</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-23-70" name="__codelineno-23-70" href="#__codelineno-23-70"></a><span class="w">        </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-23-71" name="__codelineno-23-71" href="#__codelineno-23-71"></a><span class="w">        </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードを更新する</span>
+<a id="__codelineno-23-72" name="__codelineno-23-72" href="#__codelineno-23-72"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-73" name="__codelineno-23-73" href="#__codelineno-23-73"></a><span class="w">    </span><span class="c1">// 末尾へのエンキュー操作</span>
+<a id="__codelineno-23-74" name="__codelineno-23-74" href="#__codelineno-23-74"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-75" name="__codelineno-23-75" href="#__codelineno-23-75"></a><span class="w">        </span><span class="c1">// node を連結リストの末尾に追加</span>
+<a id="__codelineno-23-76" name="__codelineno-23-76" href="#__codelineno-23-76"></a><span class="w">        </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">rear</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-23-77" name="__codelineno-23-77" href="#__codelineno-23-77"></a><span class="w">        </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">rear</span><span class="p">;</span>
+<a id="__codelineno-23-78" name="__codelineno-23-78" href="#__codelineno-23-78"></a><span class="w">        </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-23-79" name="__codelineno-23-79" href="#__codelineno-23-79"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-80" name="__codelineno-23-80" href="#__codelineno-23-80"></a><span class="w">    </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの長さを更新</span>
+<a id="__codelineno-23-81" name="__codelineno-23-81" href="#__codelineno-23-81"></a><span class="p">}</span>
+<a id="__codelineno-23-82" name="__codelineno-23-82" href="#__codelineno-23-82"></a>
+<a id="__codelineno-23-83" name="__codelineno-23-83" href="#__codelineno-23-83"></a><span class="cm">/* キュー先頭にエンキュー */</span>
+<a id="__codelineno-23-84" name="__codelineno-23-84" href="#__codelineno-23-84"></a><span class="kt">void</span><span class="w"> </span><span class="nf">pushFirst</span><span class="p">(</span><span class="n">LinkedListDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-85" name="__codelineno-23-85" href="#__codelineno-23-85"></a><span class="w">    </span><span class="n">push</span><span class="p">(</span><span class="n">deque</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="nb">true</span><span class="p">);</span>
+<a id="__codelineno-23-86" name="__codelineno-23-86" href="#__codelineno-23-86"></a><span class="p">}</span>
+<a id="__codelineno-23-87" name="__codelineno-23-87" href="#__codelineno-23-87"></a>
+<a id="__codelineno-23-88" name="__codelineno-23-88" href="#__codelineno-23-88"></a><span class="cm">/* キュー末尾にエンキュー */</span>
+<a id="__codelineno-23-89" name="__codelineno-23-89" href="#__codelineno-23-89"></a><span class="kt">void</span><span class="w"> </span><span class="nf">pushLast</span><span class="p">(</span><span class="n">LinkedListDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-90" name="__codelineno-23-90" href="#__codelineno-23-90"></a><span class="w">    </span><span class="n">push</span><span class="p">(</span><span class="n">deque</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="nb">false</span><span class="p">);</span>
+<a id="__codelineno-23-91" name="__codelineno-23-91" href="#__codelineno-23-91"></a><span class="p">}</span>
+<a id="__codelineno-23-92" name="__codelineno-23-92" href="#__codelineno-23-92"></a>
+<a id="__codelineno-23-93" name="__codelineno-23-93" href="#__codelineno-23-93"></a><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-23-94" name="__codelineno-23-94" href="#__codelineno-23-94"></a><span class="kt">int</span><span class="w"> </span><span class="nf">peekFirst</span><span class="p">(</span><span class="n">LinkedListDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-95" name="__codelineno-23-95" href="#__codelineno-23-95"></a><span class="w">    </span><span class="n">assert</span><span class="p">(</span><span class="n">size</span><span class="p">(</span><span class="n">deque</span><span class="p">)</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="p">);</span>
+<a id="__codelineno-23-96" name="__codelineno-23-96" href="#__codelineno-23-96"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-23-97" name="__codelineno-23-97" href="#__codelineno-23-97"></a><span class="p">}</span>
+<a id="__codelineno-23-98" name="__codelineno-23-98" href="#__codelineno-23-98"></a>
+<a id="__codelineno-23-99" name="__codelineno-23-99" href="#__codelineno-23-99"></a><span class="cm">/* キュー末尾の要素にアクセス */</span>
+<a id="__codelineno-23-100" name="__codelineno-23-100" href="#__codelineno-23-100"></a><span class="kt">int</span><span class="w"> </span><span class="nf">peekLast</span><span class="p">(</span><span class="n">LinkedListDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-101" name="__codelineno-23-101" href="#__codelineno-23-101"></a><span class="w">    </span><span class="n">assert</span><span class="p">(</span><span class="n">size</span><span class="p">(</span><span class="n">deque</span><span class="p">)</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">rear</span><span class="p">);</span>
+<a id="__codelineno-23-102" name="__codelineno-23-102" href="#__codelineno-23-102"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">rear</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-23-103" name="__codelineno-23-103" href="#__codelineno-23-103"></a><span class="p">}</span>
+<a id="__codelineno-23-104" name="__codelineno-23-104" href="#__codelineno-23-104"></a>
+<a id="__codelineno-23-105" name="__codelineno-23-105" href="#__codelineno-23-105"></a><span class="cm">/* デキュー */</span>
+<a id="__codelineno-23-106" name="__codelineno-23-106" href="#__codelineno-23-106"></a><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="n">LinkedListDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="p">,</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-107" name="__codelineno-23-107" href="#__codelineno-23-107"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">empty</span><span class="p">(</span><span class="n">deque</span><span class="p">))</span>
+<a id="__codelineno-23-108" name="__codelineno-23-108" href="#__codelineno-23-108"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-23-109" name="__codelineno-23-109" href="#__codelineno-23-109"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-23-110" name="__codelineno-23-110" href="#__codelineno-23-110"></a><span class="w">    </span><span class="c1">// キュー先頭からの取り出し</span>
+<a id="__codelineno-23-111" name="__codelineno-23-111" href="#__codelineno-23-111"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-112" name="__codelineno-23-112" href="#__codelineno-23-112"></a><span class="w">        </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peekFirst</span><span class="p">(</span><span class="n">deque</span><span class="p">);</span><span class="w"> </span><span class="c1">// 先頭ノードの値を一時保存</span>
+<a id="__codelineno-23-113" name="__codelineno-23-113" href="#__codelineno-23-113"></a><span class="w">        </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">fNext</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-23-114" name="__codelineno-23-114" href="#__codelineno-23-114"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">fNext</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-115" name="__codelineno-23-115" href="#__codelineno-23-115"></a><span class="w">            </span><span class="n">fNext</span><span class="o">-&gt;</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-23-116" name="__codelineno-23-116" href="#__codelineno-23-116"></a><span class="w">            </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-23-117" name="__codelineno-23-117" href="#__codelineno-23-117"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-118" name="__codelineno-23-118" href="#__codelineno-23-118"></a><span class="w">        </span><span class="n">delDoublyListNode</span><span class="p">(</span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="p">);</span>
+<a id="__codelineno-23-119" name="__codelineno-23-119" href="#__codelineno-23-119"></a><span class="w">        </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fNext</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードを更新する</span>
+<a id="__codelineno-23-120" name="__codelineno-23-120" href="#__codelineno-23-120"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-121" name="__codelineno-23-121" href="#__codelineno-23-121"></a><span class="w">    </span><span class="c1">// キュー末尾からの取り出し</span>
+<a id="__codelineno-23-122" name="__codelineno-23-122" href="#__codelineno-23-122"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-123" name="__codelineno-23-123" href="#__codelineno-23-123"></a><span class="w">        </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peekLast</span><span class="p">(</span><span class="n">deque</span><span class="p">);</span><span class="w"> </span><span class="c1">// 末尾ノードの値を一時保存</span>
+<a id="__codelineno-23-124" name="__codelineno-23-124" href="#__codelineno-23-124"></a><span class="w">        </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">rPrev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">rear</span><span class="o">-&gt;</span><span class="n">prev</span><span class="p">;</span>
+<a id="__codelineno-23-125" name="__codelineno-23-125" href="#__codelineno-23-125"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">rPrev</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-126" name="__codelineno-23-126" href="#__codelineno-23-126"></a><span class="w">            </span><span class="n">rPrev</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-23-127" name="__codelineno-23-127" href="#__codelineno-23-127"></a><span class="w">            </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">rear</span><span class="o">-&gt;</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-23-128" name="__codelineno-23-128" href="#__codelineno-23-128"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-129" name="__codelineno-23-129" href="#__codelineno-23-129"></a><span class="w">        </span><span class="n">delDoublyListNode</span><span class="p">(</span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">rear</span><span class="p">);</span>
+<a id="__codelineno-23-130" name="__codelineno-23-130" href="#__codelineno-23-130"></a><span class="w">        </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rPrev</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノードを更新する</span>
+<a id="__codelineno-23-131" name="__codelineno-23-131" href="#__codelineno-23-131"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-132" name="__codelineno-23-132" href="#__codelineno-23-132"></a><span class="w">    </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの長さを更新</span>
+<a id="__codelineno-23-133" name="__codelineno-23-133" href="#__codelineno-23-133"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-23-134" name="__codelineno-23-134" href="#__codelineno-23-134"></a><span class="p">}</span>
+<a id="__codelineno-23-135" name="__codelineno-23-135" href="#__codelineno-23-135"></a>
+<a id="__codelineno-23-136" name="__codelineno-23-136" href="#__codelineno-23-136"></a><span class="cm">/* キュー先頭からデキュー */</span>
+<a id="__codelineno-23-137" name="__codelineno-23-137" href="#__codelineno-23-137"></a><span class="kt">int</span><span class="w"> </span><span class="nf">popFirst</span><span class="p">(</span><span class="n">LinkedListDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-138" name="__codelineno-23-138" href="#__codelineno-23-138"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="n">deque</span><span class="p">,</span><span class="w"> </span><span class="nb">true</span><span class="p">);</span>
+<a id="__codelineno-23-139" name="__codelineno-23-139" href="#__codelineno-23-139"></a><span class="p">}</span>
+<a id="__codelineno-23-140" name="__codelineno-23-140" href="#__codelineno-23-140"></a>
+<a id="__codelineno-23-141" name="__codelineno-23-141" href="#__codelineno-23-141"></a><span class="cm">/* キュー末尾からデキュー */</span>
+<a id="__codelineno-23-142" name="__codelineno-23-142" href="#__codelineno-23-142"></a><span class="kt">int</span><span class="w"> </span><span class="nf">popLast</span><span class="p">(</span><span class="n">LinkedListDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-143" name="__codelineno-23-143" href="#__codelineno-23-143"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="n">deque</span><span class="p">,</span><span class="w"> </span><span class="nb">false</span><span class="p">);</span>
+<a id="__codelineno-23-144" name="__codelineno-23-144" href="#__codelineno-23-144"></a><span class="p">}</span>
+<a id="__codelineno-23-145" name="__codelineno-23-145" href="#__codelineno-23-145"></a>
+<a id="__codelineno-23-146" name="__codelineno-23-146" href="#__codelineno-23-146"></a><span class="cm">/* キューを出力する */</span>
+<a id="__codelineno-23-147" name="__codelineno-23-147" href="#__codelineno-23-147"></a><span class="kt">void</span><span class="w"> </span><span class="nf">printLinkedListDeque</span><span class="p">(</span><span class="n">LinkedListDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-148" name="__codelineno-23-148" href="#__codelineno-23-148"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="p">);</span>
+<a id="__codelineno-23-149" name="__codelineno-23-149" href="#__codelineno-23-149"></a><span class="w">    </span><span class="c1">// 連結リスト内のデータを配列にコピー</span>
+<a id="__codelineno-23-150" name="__codelineno-23-150" href="#__codelineno-23-150"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-23-151" name="__codelineno-23-151" href="#__codelineno-23-151"></a><span class="w">    </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-23-152" name="__codelineno-23-152" href="#__codelineno-23-152"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-153" name="__codelineno-23-153" href="#__codelineno-23-153"></a><span class="w">        </span><span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-23-154" name="__codelineno-23-154" href="#__codelineno-23-154"></a><span class="w">        </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-23-155" name="__codelineno-23-155" href="#__codelineno-23-155"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-156" name="__codelineno-23-156" href="#__codelineno-23-156"></a><span class="w">    </span><span class="n">printArray</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="p">);</span>
+<a id="__codelineno-23-157" name="__codelineno-23-157" href="#__codelineno-23-157"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">arr</span><span class="p">);</span>
+<a id="__codelineno-23-158" name="__codelineno-23-158" href="#__codelineno-23-158"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_deque.rb</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">ListNode</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
-<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a>
-<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">LinkedListDeque</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">linkedlist_deque.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 双方向連結リストノード */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ListNode</span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="nv">_val</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="c1">// ノード値</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">next</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="c1">// 後続ノードへの参照</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">prev</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="c1">// 前駆ノードへの参照</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="p">}</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="cm">/* 双方向連結リストベースの両端キュー */</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="kd">class</span><span class="w"> </span><span class="nc">LinkedListDeque</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">front</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="c1">// 先頭ノード front</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">rear</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="c1">// 末尾ノード rear</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">queSize</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="c1">// 両端キューの長さ</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a>
+<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w">    </span><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">size</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span>
+<a id="__codelineno-24-17" name="__codelineno-24-17" href="#__codelineno-24-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-18" name="__codelineno-24-18" href="#__codelineno-24-18"></a>
+<a id="__codelineno-24-19" name="__codelineno-24-19" href="#__codelineno-24-19"></a><span class="w">    </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
+<a id="__codelineno-24-20" name="__codelineno-24-20" href="#__codelineno-24-20"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">():</span><span class="w"> </span><span class="kt">Boolean</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-21" name="__codelineno-24-21" href="#__codelineno-24-21"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-24-22" name="__codelineno-24-22" href="#__codelineno-24-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-23" name="__codelineno-24-23" href="#__codelineno-24-23"></a>
+<a id="__codelineno-24-24" name="__codelineno-24-24" href="#__codelineno-24-24"></a><span class="w">    </span><span class="cm">/* エンキュー操作 */</span>
+<a id="__codelineno-24-25" name="__codelineno-24-25" href="#__codelineno-24-25"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">isFront</span><span class="p">:</span><span class="w"> </span><span class="kt">Boolean</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-26" name="__codelineno-24-26" href="#__codelineno-24-26"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-24-27" name="__codelineno-24-27" href="#__codelineno-24-27"></a><span class="w">        </span><span class="c1">// 連結リストが空なら、front と rear の両方を node に向ける</span>
+<a id="__codelineno-24-28" name="__codelineno-24-28" href="#__codelineno-24-28"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-29" name="__codelineno-24-29" href="#__codelineno-24-29"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-24-30" name="__codelineno-24-30" href="#__codelineno-24-30"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span>
+<a id="__codelineno-24-31" name="__codelineno-24-31" href="#__codelineno-24-31"></a><span class="w">            </span><span class="c1">// 先頭へのエンキュー操作</span>
+<a id="__codelineno-24-32" name="__codelineno-24-32" href="#__codelineno-24-32"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-33" name="__codelineno-24-33" href="#__codelineno-24-33"></a><span class="w">            </span><span class="c1">// node を連結リストの先頭に追加</span>
+<a id="__codelineno-24-34" name="__codelineno-24-34" href="#__codelineno-24-34"></a><span class="w">            </span><span class="n">front</span><span class="o">?.</span><span class="na">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-24-35" name="__codelineno-24-35" href="#__codelineno-24-35"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span>
+<a id="__codelineno-24-36" name="__codelineno-24-36" href="#__codelineno-24-36"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="c1">// 先頭ノードを更新する</span>
+<a id="__codelineno-24-37" name="__codelineno-24-37" href="#__codelineno-24-37"></a><span class="w">            </span><span class="c1">// 末尾へのエンキュー操作</span>
+<a id="__codelineno-24-38" name="__codelineno-24-38" href="#__codelineno-24-38"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-39" name="__codelineno-24-39" href="#__codelineno-24-39"></a><span class="w">            </span><span class="c1">// node を連結リストの末尾に追加</span>
+<a id="__codelineno-24-40" name="__codelineno-24-40" href="#__codelineno-24-40"></a><span class="w">            </span><span class="n">rear</span><span class="o">?.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-24-41" name="__codelineno-24-41" href="#__codelineno-24-41"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="na">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span>
+<a id="__codelineno-24-42" name="__codelineno-24-42" href="#__codelineno-24-42"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="c1">// 末尾ノードを更新する</span>
+<a id="__codelineno-24-43" name="__codelineno-24-43" href="#__codelineno-24-43"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-24-44" name="__codelineno-24-44" href="#__codelineno-24-44"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="w"> </span><span class="c1">// キューの長さを更新</span>
+<a id="__codelineno-24-45" name="__codelineno-24-45" href="#__codelineno-24-45"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-46" name="__codelineno-24-46" href="#__codelineno-24-46"></a>
+<a id="__codelineno-24-47" name="__codelineno-24-47" href="#__codelineno-24-47"></a><span class="w">    </span><span class="cm">/* キュー先頭にエンキュー */</span>
+<a id="__codelineno-24-48" name="__codelineno-24-48" href="#__codelineno-24-48"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">pushFirst</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-49" name="__codelineno-24-49" href="#__codelineno-24-49"></a><span class="w">        </span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kc">true</span><span class="p">)</span>
+<a id="__codelineno-24-50" name="__codelineno-24-50" href="#__codelineno-24-50"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-51" name="__codelineno-24-51" href="#__codelineno-24-51"></a>
+<a id="__codelineno-24-52" name="__codelineno-24-52" href="#__codelineno-24-52"></a><span class="w">    </span><span class="cm">/* キュー末尾にエンキュー */</span>
+<a id="__codelineno-24-53" name="__codelineno-24-53" href="#__codelineno-24-53"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">pushLast</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-54" name="__codelineno-24-54" href="#__codelineno-24-54"></a><span class="w">        </span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kc">false</span><span class="p">)</span>
+<a id="__codelineno-24-55" name="__codelineno-24-55" href="#__codelineno-24-55"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-56" name="__codelineno-24-56" href="#__codelineno-24-56"></a>
+<a id="__codelineno-24-57" name="__codelineno-24-57" href="#__codelineno-24-57"></a><span class="w">    </span><span class="cm">/* デキュー操作 */</span>
+<a id="__codelineno-24-58" name="__codelineno-24-58" href="#__codelineno-24-58"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="n">isFront</span><span class="p">:</span><span class="w"> </span><span class="kt">Boolean</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-59" name="__codelineno-24-59" href="#__codelineno-24-59"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span>
+<a id="__codelineno-24-60" name="__codelineno-24-60" href="#__codelineno-24-60"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">()</span>
+<a id="__codelineno-24-61" name="__codelineno-24-61" href="#__codelineno-24-61"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">_val</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span>
+<a id="__codelineno-24-62" name="__codelineno-24-62" href="#__codelineno-24-62"></a><span class="w">        </span><span class="c1">// キュー先頭からの取り出し</span>
+<a id="__codelineno-24-63" name="__codelineno-24-63" href="#__codelineno-24-63"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-64" name="__codelineno-24-64" href="#__codelineno-24-64"></a><span class="w">            </span><span class="n">_val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="o">!!</span><span class="p">.</span><span class="na">_val</span><span class="w"> </span><span class="c1">// 先頭ノードの値を一時保存</span>
+<a id="__codelineno-24-65" name="__codelineno-24-65" href="#__codelineno-24-65"></a><span class="w">            </span><span class="c1">// 先頭ノードを削除</span>
+<a id="__codelineno-24-66" name="__codelineno-24-66" href="#__codelineno-24-66"></a><span class="w">            </span><span class="kd">val</span><span class="w"> </span><span class="nv">fNext</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="o">!!</span><span class="p">.</span><span class="na">next</span>
+<a id="__codelineno-24-67" name="__codelineno-24-67" href="#__codelineno-24-67"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">fNext</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-68" name="__codelineno-24-68" href="#__codelineno-24-68"></a><span class="w">                </span><span class="n">fNext</span><span class="p">.</span><span class="na">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span>
+<a id="__codelineno-24-69" name="__codelineno-24-69" href="#__codelineno-24-69"></a><span class="w">                </span><span class="n">front</span><span class="o">!!</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span>
+<a id="__codelineno-24-70" name="__codelineno-24-70" href="#__codelineno-24-70"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-24-71" name="__codelineno-24-71" href="#__codelineno-24-71"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fNext</span><span class="w"> </span><span class="c1">// 先頭ノードを更新する</span>
+<a id="__codelineno-24-72" name="__codelineno-24-72" href="#__codelineno-24-72"></a><span class="w">            </span><span class="c1">// キュー末尾からの取り出し</span>
+<a id="__codelineno-24-73" name="__codelineno-24-73" href="#__codelineno-24-73"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-74" name="__codelineno-24-74" href="#__codelineno-24-74"></a><span class="w">            </span><span class="n">_val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="o">!!</span><span class="p">.</span><span class="na">_val</span><span class="w"> </span><span class="c1">// 末尾ノードの値を一時保存</span>
+<a id="__codelineno-24-75" name="__codelineno-24-75" href="#__codelineno-24-75"></a><span class="w">            </span><span class="c1">// 末尾ノードを削除</span>
+<a id="__codelineno-24-76" name="__codelineno-24-76" href="#__codelineno-24-76"></a><span class="w">            </span><span class="kd">val</span><span class="w"> </span><span class="nv">rPrev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="o">!!</span><span class="p">.</span><span class="na">prev</span>
+<a id="__codelineno-24-77" name="__codelineno-24-77" href="#__codelineno-24-77"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">rPrev</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-78" name="__codelineno-24-78" href="#__codelineno-24-78"></a><span class="w">                </span><span class="n">rPrev</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span>
+<a id="__codelineno-24-79" name="__codelineno-24-79" href="#__codelineno-24-79"></a><span class="w">                </span><span class="n">rear</span><span class="o">!!</span><span class="p">.</span><span class="na">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span>
+<a id="__codelineno-24-80" name="__codelineno-24-80" href="#__codelineno-24-80"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-24-81" name="__codelineno-24-81" href="#__codelineno-24-81"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rPrev</span><span class="w"> </span><span class="c1">// 末尾ノードを更新する</span>
+<a id="__codelineno-24-82" name="__codelineno-24-82" href="#__codelineno-24-82"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-24-83" name="__codelineno-24-83" href="#__codelineno-24-83"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="w"> </span><span class="c1">// キューの長さを更新</span>
+<a id="__codelineno-24-84" name="__codelineno-24-84" href="#__codelineno-24-84"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">_val</span>
+<a id="__codelineno-24-85" name="__codelineno-24-85" href="#__codelineno-24-85"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-86" name="__codelineno-24-86" href="#__codelineno-24-86"></a>
+<a id="__codelineno-24-87" name="__codelineno-24-87" href="#__codelineno-24-87"></a><span class="w">    </span><span class="cm">/* キュー先頭からデキュー */</span>
+<a id="__codelineno-24-88" name="__codelineno-24-88" href="#__codelineno-24-88"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">popFirst</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-89" name="__codelineno-24-89" href="#__codelineno-24-89"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="kc">true</span><span class="p">)</span>
+<a id="__codelineno-24-90" name="__codelineno-24-90" href="#__codelineno-24-90"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-91" name="__codelineno-24-91" href="#__codelineno-24-91"></a>
+<a id="__codelineno-24-92" name="__codelineno-24-92" href="#__codelineno-24-92"></a><span class="w">    </span><span class="cm">/* キュー末尾からデキュー */</span>
+<a id="__codelineno-24-93" name="__codelineno-24-93" href="#__codelineno-24-93"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">popLast</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-94" name="__codelineno-24-94" href="#__codelineno-24-94"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="kc">false</span><span class="p">)</span>
+<a id="__codelineno-24-95" name="__codelineno-24-95" href="#__codelineno-24-95"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-96" name="__codelineno-24-96" href="#__codelineno-24-96"></a>
+<a id="__codelineno-24-97" name="__codelineno-24-97" href="#__codelineno-24-97"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-24-98" name="__codelineno-24-98" href="#__codelineno-24-98"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">peekFirst</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-99" name="__codelineno-24-99" href="#__codelineno-24-99"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">()</span>
+<a id="__codelineno-24-100" name="__codelineno-24-100" href="#__codelineno-24-100"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">front</span><span class="o">!!</span><span class="p">.</span><span class="na">_val</span>
+<a id="__codelineno-24-101" name="__codelineno-24-101" href="#__codelineno-24-101"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-102" name="__codelineno-24-102" href="#__codelineno-24-102"></a>
+<a id="__codelineno-24-103" name="__codelineno-24-103" href="#__codelineno-24-103"></a><span class="w">    </span><span class="cm">/* キュー末尾の要素にアクセス */</span>
+<a id="__codelineno-24-104" name="__codelineno-24-104" href="#__codelineno-24-104"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">peekLast</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-105" name="__codelineno-24-105" href="#__codelineno-24-105"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">()</span>
+<a id="__codelineno-24-106" name="__codelineno-24-106" href="#__codelineno-24-106"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">rear</span><span class="o">!!</span><span class="p">.</span><span class="na">_val</span>
+<a id="__codelineno-24-107" name="__codelineno-24-107" href="#__codelineno-24-107"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-108" name="__codelineno-24-108" href="#__codelineno-24-108"></a>
+<a id="__codelineno-24-109" name="__codelineno-24-109" href="#__codelineno-24-109"></a><span class="w">    </span><span class="cm">/* 出力用の配列を返す */</span>
+<a id="__codelineno-24-110" name="__codelineno-24-110" href="#__codelineno-24-110"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">toArray</span><span class="p">():</span><span class="w"> </span><span class="n">IntArray</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-111" name="__codelineno-24-111" href="#__codelineno-24-111"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span>
+<a id="__codelineno-24-112" name="__codelineno-24-112" href="#__codelineno-24-112"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">size</span><span class="p">())</span>
+<a id="__codelineno-24-113" name="__codelineno-24-113" href="#__codelineno-24-113"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">indices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-114" name="__codelineno-24-114" href="#__codelineno-24-114"></a><span class="w">            </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">!!</span><span class="p">.</span><span class="na">_val</span>
+<a id="__codelineno-24-115" name="__codelineno-24-115" href="#__codelineno-24-115"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">next</span>
+<a id="__codelineno-24-116" name="__codelineno-24-116" href="#__codelineno-24-116"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-24-117" name="__codelineno-24-117" href="#__codelineno-24-117"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-24-118" name="__codelineno-24-118" href="#__codelineno-24-118"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-119" name="__codelineno-24-119" href="#__codelineno-24-119"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_deque.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="cm">=begin</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="cm">File: linkedlist_deque.rb</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="cm">Created Time: 2024-04-06</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="cm">Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="cm">=end</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="c1"># ## 双方向連結リストノード</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="k">class</span><span class="w"> </span><span class="nc">ListNode</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">  </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:val</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w">  </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:next</span><span class="w"> </span><span class="c1"># 後続ノードへの参照</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w">  </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:prev</span><span class="w"> </span><span class="c1"># 前ノードへの参照</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w">  </span><span class="c1">### コンストラクタ ###</span>
+<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w">    </span><span class="vi">@val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span>
+<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="k">end</span>
+<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a>
+<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="c1">### 双方向連結リストで実装した両端キュー ###</span>
+<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a><span class="k">class</span><span class="w"> </span><span class="nc">LinkedListDeque</span>
+<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="w">  </span><span class="c1">### 両端キューの長さを取得 ###</span>
+<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a><span class="w">  </span><span class="kp">attr_reader</span><span class="w"> </span><span class="ss">:size</span>
+<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a>
+<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a><span class="w">  </span><span class="c1">### コンストラクタ ###</span>
+<a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span>
+<a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></a><span class="w">    </span><span class="vi">@front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kp">nil</span><span class="w">  </span><span class="c1"># 先頭ノード front</span>
+<a id="__codelineno-25-27" name="__codelineno-25-27" href="#__codelineno-25-27"></a><span class="w">    </span><span class="vi">@rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kp">nil</span><span class="w">   </span><span class="c1"># 末尾ノード rear</span>
+<a id="__codelineno-25-28" name="__codelineno-25-28" href="#__codelineno-25-28"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w">     </span><span class="c1"># 両端キューの長さ</span>
+<a id="__codelineno-25-29" name="__codelineno-25-29" href="#__codelineno-25-29"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-30" name="__codelineno-25-30" href="#__codelineno-25-30"></a>
+<a id="__codelineno-25-31" name="__codelineno-25-31" href="#__codelineno-25-31"></a><span class="w">  </span><span class="c1">### 両端キューが空か判定 ###</span>
+<a id="__codelineno-25-32" name="__codelineno-25-32" href="#__codelineno-25-32"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">is_empty?</span>
+<a id="__codelineno-25-33" name="__codelineno-25-33" href="#__codelineno-25-33"></a><span class="w">    </span><span class="n">size</span><span class="o">.</span><span class="n">zero?</span>
+<a id="__codelineno-25-34" name="__codelineno-25-34" href="#__codelineno-25-34"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-35" name="__codelineno-25-35" href="#__codelineno-25-35"></a>
+<a id="__codelineno-25-36" name="__codelineno-25-36" href="#__codelineno-25-36"></a><span class="w">  </span><span class="c1">### エンキュー操作 ###</span>
+<a id="__codelineno-25-37" name="__codelineno-25-37" href="#__codelineno-25-37"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="n">is_front</span><span class="p">)</span>
+<a id="__codelineno-25-38" name="__codelineno-25-38" href="#__codelineno-25-38"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">ListNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-25-39" name="__codelineno-25-39" href="#__codelineno-25-39"></a><span class="w">    </span><span class="c1"># 連結リストが空なら、`front` と `rear` の両方を `node` に向ける</span>
+<a id="__codelineno-25-40" name="__codelineno-25-40" href="#__codelineno-25-40"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">is_empty?</span>
+<a id="__codelineno-25-41" name="__codelineno-25-41" href="#__codelineno-25-41"></a><span class="w">      </span><span class="vi">@front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-25-42" name="__codelineno-25-42" href="#__codelineno-25-42"></a><span class="w">    </span><span class="c1"># 先頭へのエンキュー操作</span>
+<a id="__codelineno-25-43" name="__codelineno-25-43" href="#__codelineno-25-43"></a><span class="w">    </span><span class="k">elsif</span><span class="w"> </span><span class="n">is_front</span>
+<a id="__codelineno-25-44" name="__codelineno-25-44" href="#__codelineno-25-44"></a><span class="w">      </span><span class="c1"># node を連結リストの先頭に追加</span>
+<a id="__codelineno-25-45" name="__codelineno-25-45" href="#__codelineno-25-45"></a><span class="w">      </span><span class="vi">@front</span><span class="o">.</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-25-46" name="__codelineno-25-46" href="#__codelineno-25-46"></a><span class="w">      </span><span class="n">node</span><span class="o">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@front</span>
+<a id="__codelineno-25-47" name="__codelineno-25-47" href="#__codelineno-25-47"></a><span class="w">      </span><span class="vi">@front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="c1"># 先頭ノードを更新する</span>
+<a id="__codelineno-25-48" name="__codelineno-25-48" href="#__codelineno-25-48"></a><span class="w">    </span><span class="c1"># 末尾へのエンキュー操作</span>
+<a id="__codelineno-25-49" name="__codelineno-25-49" href="#__codelineno-25-49"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-25-50" name="__codelineno-25-50" href="#__codelineno-25-50"></a><span class="w">      </span><span class="c1"># node を連結リストの末尾に追加</span>
+<a id="__codelineno-25-51" name="__codelineno-25-51" href="#__codelineno-25-51"></a><span class="w">      </span><span class="vi">@rear</span><span class="o">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-25-52" name="__codelineno-25-52" href="#__codelineno-25-52"></a><span class="w">      </span><span class="n">node</span><span class="o">.</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@rear</span>
+<a id="__codelineno-25-53" name="__codelineno-25-53" href="#__codelineno-25-53"></a><span class="w">      </span><span class="vi">@rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="c1"># 末尾ノードを更新する</span>
+<a id="__codelineno-25-54" name="__codelineno-25-54" href="#__codelineno-25-54"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-25-55" name="__codelineno-25-55" href="#__codelineno-25-55"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># キューの長さを更新</span>
+<a id="__codelineno-25-56" name="__codelineno-25-56" href="#__codelineno-25-56"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-57" name="__codelineno-25-57" href="#__codelineno-25-57"></a>
+<a id="__codelineno-25-58" name="__codelineno-25-58" href="#__codelineno-25-58"></a><span class="w">  </span><span class="c1">### キュー先頭に追加 ###</span>
+<a id="__codelineno-25-59" name="__codelineno-25-59" href="#__codelineno-25-59"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">push_first</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-25-60" name="__codelineno-25-60" href="#__codelineno-25-60"></a><span class="w">    </span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kp">true</span><span class="p">)</span>
+<a id="__codelineno-25-61" name="__codelineno-25-61" href="#__codelineno-25-61"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-62" name="__codelineno-25-62" href="#__codelineno-25-62"></a>
+<a id="__codelineno-25-63" name="__codelineno-25-63" href="#__codelineno-25-63"></a><span class="w">  </span><span class="c1">### キュー末尾に追加 ###</span>
+<a id="__codelineno-25-64" name="__codelineno-25-64" href="#__codelineno-25-64"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">push_last</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-25-65" name="__codelineno-25-65" href="#__codelineno-25-65"></a><span class="w">    </span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kp">false</span><span class="p">)</span>
+<a id="__codelineno-25-66" name="__codelineno-25-66" href="#__codelineno-25-66"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-67" name="__codelineno-25-67" href="#__codelineno-25-67"></a>
+<a id="__codelineno-25-68" name="__codelineno-25-68" href="#__codelineno-25-68"></a><span class="w">  </span><span class="c1">### デキュー操作 ###</span>
+<a id="__codelineno-25-69" name="__codelineno-25-69" href="#__codelineno-25-69"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="n">is_front</span><span class="p">)</span>
+<a id="__codelineno-25-70" name="__codelineno-25-70" href="#__codelineno-25-70"></a><span class="w">    </span><span class="k">raise</span><span class="w"> </span><span class="no">IndexError</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;両端キューは空です&#39;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_empty?</span>
+<a id="__codelineno-25-71" name="__codelineno-25-71" href="#__codelineno-25-71"></a>
+<a id="__codelineno-25-72" name="__codelineno-25-72" href="#__codelineno-25-72"></a><span class="w">    </span><span class="c1"># キュー先頭からの取り出し</span>
+<a id="__codelineno-25-73" name="__codelineno-25-73" href="#__codelineno-25-73"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">is_front</span>
+<a id="__codelineno-25-74" name="__codelineno-25-74" href="#__codelineno-25-74"></a><span class="w">      </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@front</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="c1"># 先頭ノードの値を一時保存</span>
+<a id="__codelineno-25-75" name="__codelineno-25-75" href="#__codelineno-25-75"></a><span class="w">      </span><span class="c1"># 先頭ノードを削除</span>
+<a id="__codelineno-25-76" name="__codelineno-25-76" href="#__codelineno-25-76"></a><span class="w">      </span><span class="n">fnext</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@front</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-25-77" name="__codelineno-25-77" href="#__codelineno-25-77"></a><span class="w">      </span><span class="k">unless</span><span class="w"> </span><span class="n">fnext</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-25-78" name="__codelineno-25-78" href="#__codelineno-25-78"></a><span class="w">        </span><span class="n">fnext</span><span class="o">.</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kp">nil</span>
+<a id="__codelineno-25-79" name="__codelineno-25-79" href="#__codelineno-25-79"></a><span class="w">        </span><span class="vi">@front</span><span class="o">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kp">nil</span>
+<a id="__codelineno-25-80" name="__codelineno-25-80" href="#__codelineno-25-80"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-25-81" name="__codelineno-25-81" href="#__codelineno-25-81"></a><span class="w">      </span><span class="vi">@front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fnext</span><span class="w"> </span><span class="c1"># 先頭ノードを更新する</span>
+<a id="__codelineno-25-82" name="__codelineno-25-82" href="#__codelineno-25-82"></a><span class="w">    </span><span class="c1"># キュー末尾からの取り出し</span>
+<a id="__codelineno-25-83" name="__codelineno-25-83" href="#__codelineno-25-83"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-25-84" name="__codelineno-25-84" href="#__codelineno-25-84"></a><span class="w">      </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@rear</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="c1"># 末尾ノードの値を一時保存</span>
+<a id="__codelineno-25-85" name="__codelineno-25-85" href="#__codelineno-25-85"></a><span class="w">      </span><span class="c1"># 末尾ノードを削除</span>
+<a id="__codelineno-25-86" name="__codelineno-25-86" href="#__codelineno-25-86"></a><span class="w">      </span><span class="n">rprev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@rear</span><span class="o">.</span><span class="n">prev</span>
+<a id="__codelineno-25-87" name="__codelineno-25-87" href="#__codelineno-25-87"></a><span class="w">      </span><span class="k">unless</span><span class="w"> </span><span class="n">rprev</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-25-88" name="__codelineno-25-88" href="#__codelineno-25-88"></a><span class="w">        </span><span class="n">rprev</span><span class="o">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kp">nil</span>
+<a id="__codelineno-25-89" name="__codelineno-25-89" href="#__codelineno-25-89"></a><span class="w">        </span><span class="vi">@rear</span><span class="o">.</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kp">nil</span>
+<a id="__codelineno-25-90" name="__codelineno-25-90" href="#__codelineno-25-90"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-25-91" name="__codelineno-25-91" href="#__codelineno-25-91"></a><span class="w">      </span><span class="vi">@rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rprev</span><span class="w"> </span><span class="c1"># 末尾ノードを更新する</span>
+<a id="__codelineno-25-92" name="__codelineno-25-92" href="#__codelineno-25-92"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-25-93" name="__codelineno-25-93" href="#__codelineno-25-93"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># キューの長さを更新</span>
+<a id="__codelineno-25-94" name="__codelineno-25-94" href="#__codelineno-25-94"></a>
+<a id="__codelineno-25-95" name="__codelineno-25-95" href="#__codelineno-25-95"></a><span class="w">    </span><span class="n">val</span>
+<a id="__codelineno-25-96" name="__codelineno-25-96" href="#__codelineno-25-96"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-97" name="__codelineno-25-97" href="#__codelineno-25-97"></a>
+<a id="__codelineno-25-98" name="__codelineno-25-98" href="#__codelineno-25-98"></a><span class="w">  </span><span class="c1">### キュー先頭から取り出す ###</span>
+<a id="__codelineno-25-99" name="__codelineno-25-99" href="#__codelineno-25-99"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">pop_first</span>
+<a id="__codelineno-25-100" name="__codelineno-25-100" href="#__codelineno-25-100"></a><span class="w">    </span><span class="n">pop</span><span class="p">(</span><span class="kp">true</span><span class="p">)</span>
+<a id="__codelineno-25-101" name="__codelineno-25-101" href="#__codelineno-25-101"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-102" name="__codelineno-25-102" href="#__codelineno-25-102"></a>
+<a id="__codelineno-25-103" name="__codelineno-25-103" href="#__codelineno-25-103"></a><span class="w">  </span><span class="c1">### キュー先頭から取り出す ###</span>
+<a id="__codelineno-25-104" name="__codelineno-25-104" href="#__codelineno-25-104"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">pop_last</span>
+<a id="__codelineno-25-105" name="__codelineno-25-105" href="#__codelineno-25-105"></a><span class="w">    </span><span class="n">pop</span><span class="p">(</span><span class="kp">false</span><span class="p">)</span>
+<a id="__codelineno-25-106" name="__codelineno-25-106" href="#__codelineno-25-106"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-107" name="__codelineno-25-107" href="#__codelineno-25-107"></a>
+<a id="__codelineno-25-108" name="__codelineno-25-108" href="#__codelineno-25-108"></a><span class="w">  </span><span class="c1">### 先頭要素にアクセス ###</span>
+<a id="__codelineno-25-109" name="__codelineno-25-109" href="#__codelineno-25-109"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">peek_first</span>
+<a id="__codelineno-25-110" name="__codelineno-25-110" href="#__codelineno-25-110"></a><span class="w">    </span><span class="k">raise</span><span class="w"> </span><span class="no">IndexError</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;両端キューは空です&#39;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_empty?</span>
+<a id="__codelineno-25-111" name="__codelineno-25-111" href="#__codelineno-25-111"></a>
+<a id="__codelineno-25-112" name="__codelineno-25-112" href="#__codelineno-25-112"></a><span class="w">    </span><span class="vi">@front</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-25-113" name="__codelineno-25-113" href="#__codelineno-25-113"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-114" name="__codelineno-25-114" href="#__codelineno-25-114"></a>
+<a id="__codelineno-25-115" name="__codelineno-25-115" href="#__codelineno-25-115"></a><span class="w">  </span><span class="c1">### キュー末尾要素を参照 ###</span>
+<a id="__codelineno-25-116" name="__codelineno-25-116" href="#__codelineno-25-116"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">peek_last</span>
+<a id="__codelineno-25-117" name="__codelineno-25-117" href="#__codelineno-25-117"></a><span class="w">    </span><span class="k">raise</span><span class="w"> </span><span class="no">IndexError</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;両端キューは空です&#39;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_empty?</span>
+<a id="__codelineno-25-118" name="__codelineno-25-118" href="#__codelineno-25-118"></a>
+<a id="__codelineno-25-119" name="__codelineno-25-119" href="#__codelineno-25-119"></a><span class="w">    </span><span class="vi">@rear</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-25-120" name="__codelineno-25-120" href="#__codelineno-25-120"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-121" name="__codelineno-25-121" href="#__codelineno-25-121"></a>
+<a id="__codelineno-25-122" name="__codelineno-25-122" href="#__codelineno-25-122"></a><span class="w">  </span><span class="c1">### 表示用の配列を返す ###</span>
+<a id="__codelineno-25-123" name="__codelineno-25-123" href="#__codelineno-25-123"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">to_array</span>
+<a id="__codelineno-25-124" name="__codelineno-25-124" href="#__codelineno-25-124"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@front</span>
+<a id="__codelineno-25-125" name="__codelineno-25-125" href="#__codelineno-25-125"></a><span class="w">    </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-25-126" name="__codelineno-25-126" href="#__codelineno-25-126"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">size</span>
+<a id="__codelineno-25-127" name="__codelineno-25-127" href="#__codelineno-25-127"></a><span class="w">      </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-25-128" name="__codelineno-25-128" href="#__codelineno-25-128"></a><span class="w">      </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-25-129" name="__codelineno-25-129" href="#__codelineno-25-129"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-25-130" name="__codelineno-25-130" href="#__codelineno-25-130"></a><span class="w">    </span><span class="n">res</span>
+<a id="__codelineno-25-131" name="__codelineno-25-131" href="#__codelineno-25-131"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-132" name="__codelineno-25-132" href="#__codelineno-25-132"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
 <h3 id="2">2. &nbsp; 配列に基づく実装<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>下図に示すように、配列でキューを実装するのと同様に、循環配列を使って両端キューを実装することもできます。</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="4:5"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">ArrayDeque</label><label for="__tabbed_4_2">pushLast()</label><label for="__tabbed_4_3">pushFirst()</label><label for="__tabbed_4_4">popLast()</label><label for="__tabbed_4_5">popFirst()</label></div>
+<p>次の図に示すように、配列によるキュー実装と同様に、循環配列を使って両端キューを実装することもできます。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="4:5"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">ArrayDeque</label><label for="__tabbed_4_2">push_last()</label><label for="__tabbed_4_3">push_first()</label><label for="__tabbed_4_4">pop_last()</label><label for="__tabbed_4_5">pop_first()</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="配列による両端キューのエンキューとデキュー操作の実装" class="animation-figure" src="../deque.assets/array_deque_step1.png" /></p>
+<p><img alt="配列による両端キューのエンキューとデキュー" class="animation-figure" src="../deque.assets/array_deque_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="array_deque_push_last" class="animation-figure" src="../deque.assets/array_deque_step2_push_last.png" /></p>
@@ -5269,359 +6581,1415 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 5-9 &nbsp; 配列による両端キューのエンキューとデキュー操作の実装 </p>
+<p align="center"> 図 5-9 &nbsp; 配列による両端キューのエンキューとデキュー </p>
 
-<p>実装では「前端エンキュー」と「後端デキュー」のメソッドを追加するだけです：</p>
+<p>キュー実装を土台として、「先頭へのエンキュー」と「末尾からのデキュー」のメソッドを追加するだけで済みます：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="5:13"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_deque.py</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayDeque</span><span class="p">:</span>
-<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;循環配列ベースの双端キュークラス&quot;&quot;&quot;</span>
-<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a>
-<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">capacity</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
-<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">capacity</span>
-<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>
-<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>
-<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a>
-<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">capacity</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;双端キューの容量を取得&quot;&quot;&quot;</span>
-<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a>        <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">)</span>
-<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a>
-<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;双端キューの長さを取得&quot;&quot;&quot;</span>
-<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span>
-<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a>
-<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">is_empty</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
-<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;双端キューが空かどうかを判定&quot;&quot;&quot;</span>
-<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="mi">0</span>
-<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a>
-<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">index</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;循環配列のインデックスを計算&quot;&quot;&quot;</span>
-<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a>        <span class="c1"># モジュロ演算によって循環配列を実装</span>
-<a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a>        <span class="c1"># i が配列の末尾を超えた場合、先頭に戻る</span>
-<a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></a>        <span class="c1"># i が配列の先頭を超えた場合、末尾に戻る</span>
-<a id="__codelineno-25-27" name="__codelineno-25-27" href="#__codelineno-25-27"></a>        <span class="k">return</span> <span class="p">(</span><span class="n">i</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">())</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">()</span>
-<a id="__codelineno-25-28" name="__codelineno-25-28" href="#__codelineno-25-28"></a>
-<a id="__codelineno-25-29" name="__codelineno-25-29" href="#__codelineno-25-29"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push_first</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-25-30" name="__codelineno-25-30" href="#__codelineno-25-30"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;前端エンキュー&quot;&quot;&quot;</span>
-<a id="__codelineno-25-31" name="__codelineno-25-31" href="#__codelineno-25-31"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">():</span>
-<a id="__codelineno-25-32" name="__codelineno-25-32" href="#__codelineno-25-32"></a>            <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;双端キューが満杯です&quot;</span><span class="p">)</span>
-<a id="__codelineno-25-33" name="__codelineno-25-33" href="#__codelineno-25-33"></a>            <span class="k">return</span>
-<a id="__codelineno-25-34" name="__codelineno-25-34" href="#__codelineno-25-34"></a>        <span class="c1"># フロントポインタを左に1つ移動</span>
-<a id="__codelineno-25-35" name="__codelineno-25-35" href="#__codelineno-25-35"></a>        <span class="c1"># モジュロ演算によってフロントが配列の先頭を超えて末尾に戻ることを実装</span>
-<a id="__codelineno-25-36" name="__codelineno-25-36" href="#__codelineno-25-36"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-25-37" name="__codelineno-25-37" href="#__codelineno-25-37"></a>        <span class="c1"># num を前端に追加</span>
-<a id="__codelineno-25-38" name="__codelineno-25-38" href="#__codelineno-25-38"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>
-<a id="__codelineno-25-39" name="__codelineno-25-39" href="#__codelineno-25-39"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">+=</span> <span class="mi">1</span>
-<a id="__codelineno-25-40" name="__codelineno-25-40" href="#__codelineno-25-40"></a>
-<a id="__codelineno-25-41" name="__codelineno-25-41" href="#__codelineno-25-41"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push_last</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-25-42" name="__codelineno-25-42" href="#__codelineno-25-42"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;後端エンキュー&quot;&quot;&quot;</span>
-<a id="__codelineno-25-43" name="__codelineno-25-43" href="#__codelineno-25-43"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">():</span>
-<a id="__codelineno-25-44" name="__codelineno-25-44" href="#__codelineno-25-44"></a>            <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;双端キューが満杯です&quot;</span><span class="p">)</span>
-<a id="__codelineno-25-45" name="__codelineno-25-45" href="#__codelineno-25-45"></a>            <span class="k">return</span>
-<a id="__codelineno-25-46" name="__codelineno-25-46" href="#__codelineno-25-46"></a>        <span class="c1"># リアポインタを計算、リアインデックス + 1 を指す</span>
-<a id="__codelineno-25-47" name="__codelineno-25-47" href="#__codelineno-25-47"></a>        <span class="n">rear</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">)</span>
-<a id="__codelineno-25-48" name="__codelineno-25-48" href="#__codelineno-25-48"></a>        <span class="c1"># num を後端に追加</span>
-<a id="__codelineno-25-49" name="__codelineno-25-49" href="#__codelineno-25-49"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">[</span><span class="n">rear</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>
-<a id="__codelineno-25-50" name="__codelineno-25-50" href="#__codelineno-25-50"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">+=</span> <span class="mi">1</span>
-<a id="__codelineno-25-51" name="__codelineno-25-51" href="#__codelineno-25-51"></a>
-<a id="__codelineno-25-52" name="__codelineno-25-52" href="#__codelineno-25-52"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop_first</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-25-53" name="__codelineno-25-53" href="#__codelineno-25-53"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;前端デキュー&quot;&quot;&quot;</span>
-<a id="__codelineno-25-54" name="__codelineno-25-54" href="#__codelineno-25-54"></a>        <span class="n">num</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">peek_first</span><span class="p">()</span>
-<a id="__codelineno-25-55" name="__codelineno-25-55" href="#__codelineno-25-55"></a>        <span class="c1"># フロントポインタを1つ後ろに移動</span>
-<a id="__codelineno-25-56" name="__codelineno-25-56" href="#__codelineno-25-56"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-25-57" name="__codelineno-25-57" href="#__codelineno-25-57"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-=</span> <span class="mi">1</span>
-<a id="__codelineno-25-58" name="__codelineno-25-58" href="#__codelineno-25-58"></a>        <span class="k">return</span> <span class="n">num</span>
-<a id="__codelineno-25-59" name="__codelineno-25-59" href="#__codelineno-25-59"></a>
-<a id="__codelineno-25-60" name="__codelineno-25-60" href="#__codelineno-25-60"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop_last</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-25-61" name="__codelineno-25-61" href="#__codelineno-25-61"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;後端デキュー&quot;&quot;&quot;</span>
-<a id="__codelineno-25-62" name="__codelineno-25-62" href="#__codelineno-25-62"></a>        <span class="n">num</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">peek_last</span><span class="p">()</span>
-<a id="__codelineno-25-63" name="__codelineno-25-63" href="#__codelineno-25-63"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-=</span> <span class="mi">1</span>
-<a id="__codelineno-25-64" name="__codelineno-25-64" href="#__codelineno-25-64"></a>        <span class="k">return</span> <span class="n">num</span>
-<a id="__codelineno-25-65" name="__codelineno-25-65" href="#__codelineno-25-65"></a>
-<a id="__codelineno-25-66" name="__codelineno-25-66" href="#__codelineno-25-66"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">peek_first</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-25-67" name="__codelineno-25-67" href="#__codelineno-25-67"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;前端要素にアクセス&quot;&quot;&quot;</span>
-<a id="__codelineno-25-68" name="__codelineno-25-68" href="#__codelineno-25-68"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
-<a id="__codelineno-25-69" name="__codelineno-25-69" href="#__codelineno-25-69"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Double-ended queue is empty&quot;</span><span class="p">)</span>
-<a id="__codelineno-25-70" name="__codelineno-25-70" href="#__codelineno-25-70"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="p">]</span>
-<a id="__codelineno-25-71" name="__codelineno-25-71" href="#__codelineno-25-71"></a>
-<a id="__codelineno-25-72" name="__codelineno-25-72" href="#__codelineno-25-72"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">peek_last</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-25-73" name="__codelineno-25-73" href="#__codelineno-25-73"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;後端要素にアクセス&quot;&quot;&quot;</span>
-<a id="__codelineno-25-74" name="__codelineno-25-74" href="#__codelineno-25-74"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
-<a id="__codelineno-25-75" name="__codelineno-25-75" href="#__codelineno-25-75"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Double-ended queue is empty&quot;</span><span class="p">)</span>
-<a id="__codelineno-25-76" name="__codelineno-25-76" href="#__codelineno-25-76"></a>        <span class="c1"># 後端要素のインデックスを計算</span>
-<a id="__codelineno-25-77" name="__codelineno-25-77" href="#__codelineno-25-77"></a>        <span class="n">last</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-25-78" name="__codelineno-25-78" href="#__codelineno-25-78"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">[</span><span class="n">last</span><span class="p">]</span>
-<a id="__codelineno-25-79" name="__codelineno-25-79" href="#__codelineno-25-79"></a>
-<a id="__codelineno-25-80" name="__codelineno-25-80" href="#__codelineno-25-80"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">to_array</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
-<a id="__codelineno-25-81" name="__codelineno-25-81" href="#__codelineno-25-81"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;出力用の配列を返す&quot;&quot;&quot;</span>
-<a id="__codelineno-25-82" name="__codelineno-25-82" href="#__codelineno-25-82"></a>        <span class="c1"># 有効な長さ範囲内の要素のみを変換</span>
-<a id="__codelineno-25-83" name="__codelineno-25-83" href="#__codelineno-25-83"></a>        <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
-<a id="__codelineno-25-84" name="__codelineno-25-84" href="#__codelineno-25-84"></a>        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">):</span>
-<a id="__codelineno-25-85" name="__codelineno-25-85" href="#__codelineno-25-85"></a>            <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">+</span> <span class="n">i</span><span class="p">)])</span>
-<a id="__codelineno-25-86" name="__codelineno-25-86" href="#__codelineno-25-86"></a>        <span class="k">return</span> <span class="n">res</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">array_deque.cpp</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="cm">/* 循環配列に基づく両端キュークラス */</span>
-<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayDeque</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
-<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端キューの要素を格納する配列</span>
-<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w">        </span><span class="c1">// 先頭ポインタ、先頭要素を指す</span>
-<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w">      </span><span class="c1">// 両端キューの長さ</span>
-<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a>
-<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
-<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
-<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="w">    </span><span class="n">ArrayDeque</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w">        </span><span class="n">nums</span><span class="p">.</span><span class="n">resize</span><span class="p">(</span><span class="n">capacity</span><span class="p">);</span>
-<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a>
-<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="w">    </span><span class="cm">/* 両端キューの容量を取得 */</span>
-<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
-<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a>
-<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a><span class="w">    </span><span class="cm">/* 両端キューの長さを取得 */</span>
-<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
-<a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-24" name="__codelineno-26-24" href="#__codelineno-26-24"></a>
-<a id="__codelineno-26-25" name="__codelineno-26-25" href="#__codelineno-26-25"></a><span class="w">    </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
-<a id="__codelineno-26-26" name="__codelineno-26-26" href="#__codelineno-26-26"></a><span class="w">    </span><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-27" name="__codelineno-26-27" href="#__codelineno-26-27"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-26-28" name="__codelineno-26-28" href="#__codelineno-26-28"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-29" name="__codelineno-26-29" href="#__codelineno-26-29"></a>
-<a id="__codelineno-26-30" name="__codelineno-26-30" href="#__codelineno-26-30"></a><span class="w">    </span><span class="cm">/* 循環配列のインデックスを計算 */</span>
-<a id="__codelineno-26-31" name="__codelineno-26-31" href="#__codelineno-26-31"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-32" name="__codelineno-26-32" href="#__codelineno-26-32"></a><span class="w">        </span><span class="c1">// 剰余演算で循環配列を実現</span>
-<a id="__codelineno-26-33" name="__codelineno-26-33" href="#__codelineno-26-33"></a><span class="w">        </span><span class="c1">// iが配列の末尾を超えた場合、先頭に戻る</span>
-<a id="__codelineno-26-34" name="__codelineno-26-34" href="#__codelineno-26-34"></a><span class="w">        </span><span class="c1">// iが配列の先頭を超えた場合、末尾に戻る</span>
-<a id="__codelineno-26-35" name="__codelineno-26-35" href="#__codelineno-26-35"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">();</span>
-<a id="__codelineno-26-36" name="__codelineno-26-36" href="#__codelineno-26-36"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-37" name="__codelineno-26-37" href="#__codelineno-26-37"></a>
-<a id="__codelineno-26-38" name="__codelineno-26-38" href="#__codelineno-26-38"></a><span class="w">    </span><span class="cm">/* 先頭エンキュー */</span>
-<a id="__codelineno-26-39" name="__codelineno-26-39" href="#__codelineno-26-39"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">pushFirst</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-40" name="__codelineno-26-40" href="#__codelineno-26-40"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-41" name="__codelineno-26-41" href="#__codelineno-26-41"></a><span class="w">            </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;Double-ended queue is full&quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
-<a id="__codelineno-26-42" name="__codelineno-26-42" href="#__codelineno-26-42"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-26-43" name="__codelineno-26-43" href="#__codelineno-26-43"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-26-44" name="__codelineno-26-44" href="#__codelineno-26-44"></a><span class="w">        </span><span class="c1">// 先頭ポインタを1つ左に移動</span>
-<a id="__codelineno-26-45" name="__codelineno-26-45" href="#__codelineno-26-45"></a><span class="w">        </span><span class="c1">// 剰余演算でfrontが配列の先頭を越えて末尾に戻ることを実現</span>
-<a id="__codelineno-26-46" name="__codelineno-26-46" href="#__codelineno-26-46"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-26-47" name="__codelineno-26-47" href="#__codelineno-26-47"></a><span class="w">        </span><span class="c1">// numを先頭に追加</span>
-<a id="__codelineno-26-48" name="__codelineno-26-48" href="#__codelineno-26-48"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">front</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-26-49" name="__codelineno-26-49" href="#__codelineno-26-49"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-26-50" name="__codelineno-26-50" href="#__codelineno-26-50"></a><span class="w">    </span><span class="p">}</span>
+<div class="highlight"><span class="filename">array_deque.py</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayDeque</span><span class="p">:</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;循環配列ベースの両端キュー&quot;&quot;&quot;</span>
+<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>
+<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">capacity</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
+<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">capacity</span>
+<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a>
+<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">capacity</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;両端キューの容量を取得&quot;&quot;&quot;</span>
+<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a>        <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">)</span>
+<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a>
+<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;両端キューの長さを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span>
+<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a>
+<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">is_empty</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
+<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;両端キューが空かどうかを判定&quot;&quot;&quot;</span>
+<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="mi">0</span>
+<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a>
+<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">index</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;循環配列のインデックスを計算&quot;&quot;&quot;</span>
+<a id="__codelineno-26-24" name="__codelineno-26-24" href="#__codelineno-26-24"></a>        <span class="c1"># 剰余演算により配列の先頭と末尾をつなげる</span>
+<a id="__codelineno-26-25" name="__codelineno-26-25" href="#__codelineno-26-25"></a>        <span class="c1"># i が配列の末尾を越えたら先頭に戻る</span>
+<a id="__codelineno-26-26" name="__codelineno-26-26" href="#__codelineno-26-26"></a>        <span class="c1"># i が配列の先頭を越えて前に出たら末尾に戻る</span>
+<a id="__codelineno-26-27" name="__codelineno-26-27" href="#__codelineno-26-27"></a>        <span class="k">return</span> <span class="p">(</span><span class="n">i</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">())</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">()</span>
+<a id="__codelineno-26-28" name="__codelineno-26-28" href="#__codelineno-26-28"></a>
+<a id="__codelineno-26-29" name="__codelineno-26-29" href="#__codelineno-26-29"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push_first</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-26-30" name="__codelineno-26-30" href="#__codelineno-26-30"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キュー先頭にエンキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-26-31" name="__codelineno-26-31" href="#__codelineno-26-31"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">():</span>
+<a id="__codelineno-26-32" name="__codelineno-26-32" href="#__codelineno-26-32"></a>            <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;両端キューがいっぱいです&quot;</span><span class="p">)</span>
+<a id="__codelineno-26-33" name="__codelineno-26-33" href="#__codelineno-26-33"></a>            <span class="k">return</span>
+<a id="__codelineno-26-34" name="__codelineno-26-34" href="#__codelineno-26-34"></a>        <span class="c1"># 先頭ポインタを左に 1 つ移動する</span>
+<a id="__codelineno-26-35" name="__codelineno-26-35" href="#__codelineno-26-35"></a>        <span class="c1"># 剰余演算により、front が配列先頭を越えた後に末尾へ戻るようにする</span>
+<a id="__codelineno-26-36" name="__codelineno-26-36" href="#__codelineno-26-36"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-26-37" name="__codelineno-26-37" href="#__codelineno-26-37"></a>        <span class="c1"># num をキュー先頭に追加</span>
+<a id="__codelineno-26-38" name="__codelineno-26-38" href="#__codelineno-26-38"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>
+<a id="__codelineno-26-39" name="__codelineno-26-39" href="#__codelineno-26-39"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-26-40" name="__codelineno-26-40" href="#__codelineno-26-40"></a>
+<a id="__codelineno-26-41" name="__codelineno-26-41" href="#__codelineno-26-41"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push_last</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-26-42" name="__codelineno-26-42" href="#__codelineno-26-42"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キュー末尾にエンキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-26-43" name="__codelineno-26-43" href="#__codelineno-26-43"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">():</span>
+<a id="__codelineno-26-44" name="__codelineno-26-44" href="#__codelineno-26-44"></a>            <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;両端キューがいっぱいです&quot;</span><span class="p">)</span>
+<a id="__codelineno-26-45" name="__codelineno-26-45" href="#__codelineno-26-45"></a>            <span class="k">return</span>
+<a id="__codelineno-26-46" name="__codelineno-26-46" href="#__codelineno-26-46"></a>        <span class="c1"># キュー末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-26-47" name="__codelineno-26-47" href="#__codelineno-26-47"></a>        <span class="n">rear</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">)</span>
+<a id="__codelineno-26-48" name="__codelineno-26-48" href="#__codelineno-26-48"></a>        <span class="c1"># num をキュー末尾に追加</span>
+<a id="__codelineno-26-49" name="__codelineno-26-49" href="#__codelineno-26-49"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">[</span><span class="n">rear</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>
+<a id="__codelineno-26-50" name="__codelineno-26-50" href="#__codelineno-26-50"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">+=</span> <span class="mi">1</span>
 <a id="__codelineno-26-51" name="__codelineno-26-51" href="#__codelineno-26-51"></a>
-<a id="__codelineno-26-52" name="__codelineno-26-52" href="#__codelineno-26-52"></a><span class="w">    </span><span class="cm">/* 末尾エンキュー */</span>
-<a id="__codelineno-26-53" name="__codelineno-26-53" href="#__codelineno-26-53"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">pushLast</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-54" name="__codelineno-26-54" href="#__codelineno-26-54"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-55" name="__codelineno-26-55" href="#__codelineno-26-55"></a><span class="w">            </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;Double-ended queue is full&quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
-<a id="__codelineno-26-56" name="__codelineno-26-56" href="#__codelineno-26-56"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-26-57" name="__codelineno-26-57" href="#__codelineno-26-57"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-26-58" name="__codelineno-26-58" href="#__codelineno-26-58"></a><span class="w">        </span><span class="c1">// 末尾ポインタを計算、末尾インデックス + 1を指す</span>
-<a id="__codelineno-26-59" name="__codelineno-26-59" href="#__codelineno-26-59"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">queSize</span><span class="p">);</span>
-<a id="__codelineno-26-60" name="__codelineno-26-60" href="#__codelineno-26-60"></a><span class="w">        </span><span class="c1">// numを末尾に追加</span>
-<a id="__codelineno-26-61" name="__codelineno-26-61" href="#__codelineno-26-61"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">rear</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-26-62" name="__codelineno-26-62" href="#__codelineno-26-62"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-26-63" name="__codelineno-26-63" href="#__codelineno-26-63"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-64" name="__codelineno-26-64" href="#__codelineno-26-64"></a>
-<a id="__codelineno-26-65" name="__codelineno-26-65" href="#__codelineno-26-65"></a><span class="w">    </span><span class="cm">/* 先頭デキュー */</span>
-<a id="__codelineno-26-66" name="__codelineno-26-66" href="#__codelineno-26-66"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">popFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-67" name="__codelineno-26-67" href="#__codelineno-26-67"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peekFirst</span><span class="p">();</span>
-<a id="__codelineno-26-68" name="__codelineno-26-68" href="#__codelineno-26-68"></a><span class="w">        </span><span class="c1">// 先頭ポインタを1つ後ろに移動</span>
-<a id="__codelineno-26-69" name="__codelineno-26-69" href="#__codelineno-26-69"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-26-70" name="__codelineno-26-70" href="#__codelineno-26-70"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
-<a id="__codelineno-26-71" name="__codelineno-26-71" href="#__codelineno-26-71"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-26-72" name="__codelineno-26-72" href="#__codelineno-26-72"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-73" name="__codelineno-26-73" href="#__codelineno-26-73"></a>
-<a id="__codelineno-26-74" name="__codelineno-26-74" href="#__codelineno-26-74"></a><span class="w">    </span><span class="cm">/* 末尾デキュー */</span>
-<a id="__codelineno-26-75" name="__codelineno-26-75" href="#__codelineno-26-75"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">popLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-76" name="__codelineno-26-76" href="#__codelineno-26-76"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peekLast</span><span class="p">();</span>
-<a id="__codelineno-26-77" name="__codelineno-26-77" href="#__codelineno-26-77"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
-<a id="__codelineno-26-78" name="__codelineno-26-78" href="#__codelineno-26-78"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-26-79" name="__codelineno-26-79" href="#__codelineno-26-79"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-80" name="__codelineno-26-80" href="#__codelineno-26-80"></a>
-<a id="__codelineno-26-81" name="__codelineno-26-81" href="#__codelineno-26-81"></a><span class="w">    </span><span class="cm">/* 先頭要素にアクセス */</span>
-<a id="__codelineno-26-82" name="__codelineno-26-82" href="#__codelineno-26-82"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">peekFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-83" name="__codelineno-26-83" href="#__codelineno-26-83"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
-<a id="__codelineno-26-84" name="__codelineno-26-84" href="#__codelineno-26-84"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Double-ended queue is empty&quot;</span><span class="p">);</span>
-<a id="__codelineno-26-85" name="__codelineno-26-85" href="#__codelineno-26-85"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">front</span><span class="p">];</span>
-<a id="__codelineno-26-86" name="__codelineno-26-86" href="#__codelineno-26-86"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-87" name="__codelineno-26-87" href="#__codelineno-26-87"></a>
-<a id="__codelineno-26-88" name="__codelineno-26-88" href="#__codelineno-26-88"></a><span class="w">    </span><span class="cm">/* 末尾要素にアクセス */</span>
-<a id="__codelineno-26-89" name="__codelineno-26-89" href="#__codelineno-26-89"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">peekLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-90" name="__codelineno-26-90" href="#__codelineno-26-90"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
-<a id="__codelineno-26-91" name="__codelineno-26-91" href="#__codelineno-26-91"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Double-ended queue is empty&quot;</span><span class="p">);</span>
-<a id="__codelineno-26-92" name="__codelineno-26-92" href="#__codelineno-26-92"></a><span class="w">        </span><span class="c1">// 末尾要素のインデックスを計算</span>
-<a id="__codelineno-26-93" name="__codelineno-26-93" href="#__codelineno-26-93"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">last</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-26-94" name="__codelineno-26-94" href="#__codelineno-26-94"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">last</span><span class="p">];</span>
-<a id="__codelineno-26-95" name="__codelineno-26-95" href="#__codelineno-26-95"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-96" name="__codelineno-26-96" href="#__codelineno-26-96"></a>
-<a id="__codelineno-26-97" name="__codelineno-26-97" href="#__codelineno-26-97"></a><span class="w">    </span><span class="cm">/* 印刷用に配列を返却 */</span>
-<a id="__codelineno-26-98" name="__codelineno-26-98" href="#__codelineno-26-98"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toVector</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-99" name="__codelineno-26-99" href="#__codelineno-26-99"></a><span class="w">        </span><span class="c1">// 有効な長さ範囲内の要素のみを変換</span>
-<a id="__codelineno-26-100" name="__codelineno-26-100" href="#__codelineno-26-100"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">(</span><span class="n">queSize</span><span class="p">);</span>
-<a id="__codelineno-26-101" name="__codelineno-26-101" href="#__codelineno-26-101"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-102" name="__codelineno-26-102" href="#__codelineno-26-102"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">index</span><span class="p">(</span><span class="n">j</span><span class="p">)];</span>
-<a id="__codelineno-26-103" name="__codelineno-26-103" href="#__codelineno-26-103"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-26-104" name="__codelineno-26-104" href="#__codelineno-26-104"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
-<a id="__codelineno-26-105" name="__codelineno-26-105" href="#__codelineno-26-105"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-106" name="__codelineno-26-106" href="#__codelineno-26-106"></a><span class="p">};</span>
+<a id="__codelineno-26-52" name="__codelineno-26-52" href="#__codelineno-26-52"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop_first</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-26-53" name="__codelineno-26-53" href="#__codelineno-26-53"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キュー先頭からデキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-26-54" name="__codelineno-26-54" href="#__codelineno-26-54"></a>        <span class="n">num</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">peek_first</span><span class="p">()</span>
+<a id="__codelineno-26-55" name="__codelineno-26-55" href="#__codelineno-26-55"></a>        <span class="c1"># 先頭ポインタを 1 つ後ろへ進める</span>
+<a id="__codelineno-26-56" name="__codelineno-26-56" href="#__codelineno-26-56"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-26-57" name="__codelineno-26-57" href="#__codelineno-26-57"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-=</span> <span class="mi">1</span>
+<a id="__codelineno-26-58" name="__codelineno-26-58" href="#__codelineno-26-58"></a>        <span class="k">return</span> <span class="n">num</span>
+<a id="__codelineno-26-59" name="__codelineno-26-59" href="#__codelineno-26-59"></a>
+<a id="__codelineno-26-60" name="__codelineno-26-60" href="#__codelineno-26-60"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop_last</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-26-61" name="__codelineno-26-61" href="#__codelineno-26-61"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キュー末尾からデキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-26-62" name="__codelineno-26-62" href="#__codelineno-26-62"></a>        <span class="n">num</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">peek_last</span><span class="p">()</span>
+<a id="__codelineno-26-63" name="__codelineno-26-63" href="#__codelineno-26-63"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-=</span> <span class="mi">1</span>
+<a id="__codelineno-26-64" name="__codelineno-26-64" href="#__codelineno-26-64"></a>        <span class="k">return</span> <span class="n">num</span>
+<a id="__codelineno-26-65" name="__codelineno-26-65" href="#__codelineno-26-65"></a>
+<a id="__codelineno-26-66" name="__codelineno-26-66" href="#__codelineno-26-66"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">peek_first</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-26-67" name="__codelineno-26-67" href="#__codelineno-26-67"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キュー先頭の要素にアクセス&quot;&quot;&quot;</span>
+<a id="__codelineno-26-68" name="__codelineno-26-68" href="#__codelineno-26-68"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
+<a id="__codelineno-26-69" name="__codelineno-26-69" href="#__codelineno-26-69"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;両端キューが空です&quot;</span><span class="p">)</span>
+<a id="__codelineno-26-70" name="__codelineno-26-70" href="#__codelineno-26-70"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="p">]</span>
+<a id="__codelineno-26-71" name="__codelineno-26-71" href="#__codelineno-26-71"></a>
+<a id="__codelineno-26-72" name="__codelineno-26-72" href="#__codelineno-26-72"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">peek_last</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-26-73" name="__codelineno-26-73" href="#__codelineno-26-73"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キュー末尾の要素にアクセス&quot;&quot;&quot;</span>
+<a id="__codelineno-26-74" name="__codelineno-26-74" href="#__codelineno-26-74"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
+<a id="__codelineno-26-75" name="__codelineno-26-75" href="#__codelineno-26-75"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;両端キューが空です&quot;</span><span class="p">)</span>
+<a id="__codelineno-26-76" name="__codelineno-26-76" href="#__codelineno-26-76"></a>        <span class="c1"># 末尾要素のインデックスを計算</span>
+<a id="__codelineno-26-77" name="__codelineno-26-77" href="#__codelineno-26-77"></a>        <span class="n">last</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-26-78" name="__codelineno-26-78" href="#__codelineno-26-78"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">[</span><span class="n">last</span><span class="p">]</span>
+<a id="__codelineno-26-79" name="__codelineno-26-79" href="#__codelineno-26-79"></a>
+<a id="__codelineno-26-80" name="__codelineno-26-80" href="#__codelineno-26-80"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">to_array</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-26-81" name="__codelineno-26-81" href="#__codelineno-26-81"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;出力用の配列を返す&quot;&quot;&quot;</span>
+<a id="__codelineno-26-82" name="__codelineno-26-82" href="#__codelineno-26-82"></a>        <span class="c1"># 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-26-83" name="__codelineno-26-83" href="#__codelineno-26-83"></a>        <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-26-84" name="__codelineno-26-84" href="#__codelineno-26-84"></a>        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">):</span>
+<a id="__codelineno-26-85" name="__codelineno-26-85" href="#__codelineno-26-85"></a>            <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">+</span> <span class="n">i</span><span class="p">)])</span>
+<a id="__codelineno-26-86" name="__codelineno-26-86" href="#__codelineno-26-86"></a>        <span class="k">return</span> <span class="n">res</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_deque.java</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* 循環配列に基づく両端キュークラス */</span>
-<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="kd">class</span> <span class="nc">ArrayDeque</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端キューの要素を格納する配列</span>
-<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ポインタ、先頭要素を指す</span>
-<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端キューの長さ</span>
-<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a>
-<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
-<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">ArrayDeque</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="na">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">capacity</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a>
-<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w">    </span><span class="cm">/* 両端キューの容量を取得 */</span>
-<a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
-<a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-17" name="__codelineno-27-17" href="#__codelineno-27-17"></a>
-<a id="__codelineno-27-18" name="__codelineno-27-18" href="#__codelineno-27-18"></a><span class="w">    </span><span class="cm">/* 両端キューの長さを取得 */</span>
-<a id="__codelineno-27-19" name="__codelineno-27-19" href="#__codelineno-27-19"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-20" name="__codelineno-27-20" href="#__codelineno-27-20"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
-<a id="__codelineno-27-21" name="__codelineno-27-21" href="#__codelineno-27-21"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-22" name="__codelineno-27-22" href="#__codelineno-27-22"></a>
-<a id="__codelineno-27-23" name="__codelineno-27-23" href="#__codelineno-27-23"></a><span class="w">    </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
-<a id="__codelineno-27-24" name="__codelineno-27-24" href="#__codelineno-27-24"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-25" name="__codelineno-27-25" href="#__codelineno-27-25"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-27-26" name="__codelineno-27-26" href="#__codelineno-27-26"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-27" name="__codelineno-27-27" href="#__codelineno-27-27"></a>
-<a id="__codelineno-27-28" name="__codelineno-27-28" href="#__codelineno-27-28"></a><span class="w">    </span><span class="cm">/* 循環配列インデックスを計算 */</span>
-<a id="__codelineno-27-29" name="__codelineno-27-29" href="#__codelineno-27-29"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">index</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-30" name="__codelineno-27-30" href="#__codelineno-27-30"></a><span class="w">        </span><span class="c1">// モジュロ演算により循環配列を実装</span>
-<a id="__codelineno-27-31" name="__codelineno-27-31" href="#__codelineno-27-31"></a><span class="w">        </span><span class="c1">// i が配列の末尾を超える場合、先頭に戻る</span>
-<a id="__codelineno-27-32" name="__codelineno-27-32" href="#__codelineno-27-32"></a><span class="w">        </span><span class="c1">// i が配列の先頭を超える場合、末尾に戻る</span>
-<a id="__codelineno-27-33" name="__codelineno-27-33" href="#__codelineno-27-33"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">();</span>
-<a id="__codelineno-27-34" name="__codelineno-27-34" href="#__codelineno-27-34"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-35" name="__codelineno-27-35" href="#__codelineno-27-35"></a>
-<a id="__codelineno-27-36" name="__codelineno-27-36" href="#__codelineno-27-36"></a><span class="w">    </span><span class="cm">/* 先頭エンキュー */</span>
-<a id="__codelineno-27-37" name="__codelineno-27-37" href="#__codelineno-27-37"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">pushFirst</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-38" name="__codelineno-27-38" href="#__codelineno-27-38"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-39" name="__codelineno-27-39" href="#__codelineno-27-39"></a><span class="w">            </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">&quot;両端キューが満杯です&quot;</span><span class="p">);</span>
-<a id="__codelineno-27-40" name="__codelineno-27-40" href="#__codelineno-27-40"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-27-41" name="__codelineno-27-41" href="#__codelineno-27-41"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-27-42" name="__codelineno-27-42" href="#__codelineno-27-42"></a><span class="w">        </span><span class="c1">// 先頭ポインタを左に移動し、境界を越える場合は配列の末尾に回る</span>
-<a id="__codelineno-27-43" name="__codelineno-27-43" href="#__codelineno-27-43"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-27-44" name="__codelineno-27-44" href="#__codelineno-27-44"></a><span class="w">        </span><span class="c1">// 先頭に num を追加</span>
-<a id="__codelineno-27-45" name="__codelineno-27-45" href="#__codelineno-27-45"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">front</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-27-46" name="__codelineno-27-46" href="#__codelineno-27-46"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-27-47" name="__codelineno-27-47" href="#__codelineno-27-47"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-48" name="__codelineno-27-48" href="#__codelineno-27-48"></a>
-<a id="__codelineno-27-49" name="__codelineno-27-49" href="#__codelineno-27-49"></a><span class="w">    </span><span class="cm">/* 末尾エンキュー */</span>
-<a id="__codelineno-27-50" name="__codelineno-27-50" href="#__codelineno-27-50"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">pushLast</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-51" name="__codelineno-27-51" href="#__codelineno-27-51"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-52" name="__codelineno-27-52" href="#__codelineno-27-52"></a><span class="w">            </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">&quot;両端キューが満杯です&quot;</span><span class="p">);</span>
-<a id="__codelineno-27-53" name="__codelineno-27-53" href="#__codelineno-27-53"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-27-54" name="__codelineno-27-54" href="#__codelineno-27-54"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-27-55" name="__codelineno-27-55" href="#__codelineno-27-55"></a><span class="w">        </span><span class="c1">// 末尾ポインタを計算し、末尾に要素を追加</span>
-<a id="__codelineno-27-56" name="__codelineno-27-56" href="#__codelineno-27-56"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">queSize</span><span class="p">);</span>
-<a id="__codelineno-27-57" name="__codelineno-27-57" href="#__codelineno-27-57"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">rear</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-27-58" name="__codelineno-27-58" href="#__codelineno-27-58"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-27-59" name="__codelineno-27-59" href="#__codelineno-27-59"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-60" name="__codelineno-27-60" href="#__codelineno-27-60"></a>
-<a id="__codelineno-27-61" name="__codelineno-27-61" href="#__codelineno-27-61"></a><span class="w">    </span><span class="cm">/* 先頭デキュー */</span>
-<a id="__codelineno-27-62" name="__codelineno-27-62" href="#__codelineno-27-62"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">popFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-63" name="__codelineno-27-63" href="#__codelineno-27-63"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peekFirst</span><span class="p">();</span>
-<a id="__codelineno-27-64" name="__codelineno-27-64" href="#__codelineno-27-64"></a><span class="w">        </span><span class="c1">// 先頭ポインタを右に移動</span>
-<a id="__codelineno-27-65" name="__codelineno-27-65" href="#__codelineno-27-65"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-27-66" name="__codelineno-27-66" href="#__codelineno-27-66"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
-<a id="__codelineno-27-67" name="__codelineno-27-67" href="#__codelineno-27-67"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-27-68" name="__codelineno-27-68" href="#__codelineno-27-68"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-69" name="__codelineno-27-69" href="#__codelineno-27-69"></a>
-<a id="__codelineno-27-70" name="__codelineno-27-70" href="#__codelineno-27-70"></a><span class="w">    </span><span class="cm">/* 末尾デキュー */</span>
-<a id="__codelineno-27-71" name="__codelineno-27-71" href="#__codelineno-27-71"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">popLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-72" name="__codelineno-27-72" href="#__codelineno-27-72"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peekLast</span><span class="p">();</span>
-<a id="__codelineno-27-73" name="__codelineno-27-73" href="#__codelineno-27-73"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
-<a id="__codelineno-27-74" name="__codelineno-27-74" href="#__codelineno-27-74"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-27-75" name="__codelineno-27-75" href="#__codelineno-27-75"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-76" name="__codelineno-27-76" href="#__codelineno-27-76"></a>
-<a id="__codelineno-27-77" name="__codelineno-27-77" href="#__codelineno-27-77"></a><span class="w">    </span><span class="cm">/* 先頭要素にアクセス */</span>
-<a id="__codelineno-27-78" name="__codelineno-27-78" href="#__codelineno-27-78"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">peekFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-79" name="__codelineno-27-79" href="#__codelineno-27-79"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
-<a id="__codelineno-27-80" name="__codelineno-27-80" href="#__codelineno-27-80"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
-<a id="__codelineno-27-81" name="__codelineno-27-81" href="#__codelineno-27-81"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">front</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-27-82" name="__codelineno-27-82" href="#__codelineno-27-82"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-83" name="__codelineno-27-83" href="#__codelineno-27-83"></a>
-<a id="__codelineno-27-84" name="__codelineno-27-84" href="#__codelineno-27-84"></a><span class="w">    </span><span class="cm">/* 末尾要素にアクセス */</span>
-<a id="__codelineno-27-85" name="__codelineno-27-85" href="#__codelineno-27-85"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">peekLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-86" name="__codelineno-27-86" href="#__codelineno-27-86"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
-<a id="__codelineno-27-87" name="__codelineno-27-87" href="#__codelineno-27-87"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
-<a id="__codelineno-27-88" name="__codelineno-27-88" href="#__codelineno-27-88"></a><span class="w">        </span><span class="c1">// 末尾要素のインデックスを計算</span>
-<a id="__codelineno-27-89" name="__codelineno-27-89" href="#__codelineno-27-89"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">last</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-27-90" name="__codelineno-27-90" href="#__codelineno-27-90"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">last</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-27-91" name="__codelineno-27-91" href="#__codelineno-27-91"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-92" name="__codelineno-27-92" href="#__codelineno-27-92"></a>
-<a id="__codelineno-27-93" name="__codelineno-27-93" href="#__codelineno-27-93"></a><span class="w">    </span><span class="cm">/* 配列を返す */</span>
-<a id="__codelineno-27-94" name="__codelineno-27-94" href="#__codelineno-27-94"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-95" name="__codelineno-27-95" href="#__codelineno-27-95"></a><span class="w">        </span><span class="c1">// front から開始して queSize 個の要素のみをコピー</span>
-<a id="__codelineno-27-96" name="__codelineno-27-96" href="#__codelineno-27-96"></a><span class="w">        </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">queSize</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-27-97" name="__codelineno-27-97" href="#__codelineno-27-97"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-98" name="__codelineno-27-98" href="#__codelineno-27-98"></a><span class="w">            </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">index</span><span class="p">(</span><span class="n">j</span><span class="p">)</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-27-99" name="__codelineno-27-99" href="#__codelineno-27-99"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-27-100" name="__codelineno-27-100" href="#__codelineno-27-100"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
-<a id="__codelineno-27-101" name="__codelineno-27-101" href="#__codelineno-27-101"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-102" name="__codelineno-27-102" href="#__codelineno-27-102"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">array_deque.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* 循環配列ベースの両端キュー */</span>
+<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayDeque</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
+<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端キューの要素を格納する配列</span>
+<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w">        </span><span class="c1">// 先頭ポインタ。先頭要素を指す</span>
+<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w">      </span><span class="c1">// 両端キューの長さ</span>
+<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a>
+<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
+<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a><span class="w">    </span><span class="n">ArrayDeque</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="w">        </span><span class="n">nums</span><span class="p">.</span><span class="n">resize</span><span class="p">(</span><span class="n">capacity</span><span class="p">);</span>
+<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a>
+<a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="w">    </span><span class="cm">/* 両端キューの容量を取得 */</span>
+<a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-17" name="__codelineno-27-17" href="#__codelineno-27-17"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-27-18" name="__codelineno-27-18" href="#__codelineno-27-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-19" name="__codelineno-27-19" href="#__codelineno-27-19"></a>
+<a id="__codelineno-27-20" name="__codelineno-27-20" href="#__codelineno-27-20"></a><span class="w">    </span><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-27-21" name="__codelineno-27-21" href="#__codelineno-27-21"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-22" name="__codelineno-27-22" href="#__codelineno-27-22"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-27-23" name="__codelineno-27-23" href="#__codelineno-27-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-24" name="__codelineno-27-24" href="#__codelineno-27-24"></a>
+<a id="__codelineno-27-25" name="__codelineno-27-25" href="#__codelineno-27-25"></a><span class="w">    </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
+<a id="__codelineno-27-26" name="__codelineno-27-26" href="#__codelineno-27-26"></a><span class="w">    </span><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-27" name="__codelineno-27-27" href="#__codelineno-27-27"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-27-28" name="__codelineno-27-28" href="#__codelineno-27-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-29" name="__codelineno-27-29" href="#__codelineno-27-29"></a>
+<a id="__codelineno-27-30" name="__codelineno-27-30" href="#__codelineno-27-30"></a><span class="w">    </span><span class="cm">/* 循環配列のインデックスを計算 */</span>
+<a id="__codelineno-27-31" name="__codelineno-27-31" href="#__codelineno-27-31"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-32" name="__codelineno-27-32" href="#__codelineno-27-32"></a><span class="w">        </span><span class="c1">// 剰余演算により配列の先頭と末尾をつなげる</span>
+<a id="__codelineno-27-33" name="__codelineno-27-33" href="#__codelineno-27-33"></a><span class="w">        </span><span class="c1">// i が配列の末尾を越えたら先頭に戻る</span>
+<a id="__codelineno-27-34" name="__codelineno-27-34" href="#__codelineno-27-34"></a><span class="w">        </span><span class="c1">// i が配列の先頭を越えて前に出たら末尾に戻る</span>
+<a id="__codelineno-27-35" name="__codelineno-27-35" href="#__codelineno-27-35"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">();</span>
+<a id="__codelineno-27-36" name="__codelineno-27-36" href="#__codelineno-27-36"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-37" name="__codelineno-27-37" href="#__codelineno-27-37"></a>
+<a id="__codelineno-27-38" name="__codelineno-27-38" href="#__codelineno-27-38"></a><span class="w">    </span><span class="cm">/* キュー先頭にエンキュー */</span>
+<a id="__codelineno-27-39" name="__codelineno-27-39" href="#__codelineno-27-39"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">pushFirst</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-40" name="__codelineno-27-40" href="#__codelineno-27-40"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-41" name="__codelineno-27-41" href="#__codelineno-27-41"></a><span class="w">            </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;両端キューがいっぱいです&quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
+<a id="__codelineno-27-42" name="__codelineno-27-42" href="#__codelineno-27-42"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-27-43" name="__codelineno-27-43" href="#__codelineno-27-43"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-27-44" name="__codelineno-27-44" href="#__codelineno-27-44"></a><span class="w">        </span><span class="c1">// 先頭ポインタを左に 1 つ移動する</span>
+<a id="__codelineno-27-45" name="__codelineno-27-45" href="#__codelineno-27-45"></a><span class="w">        </span><span class="c1">// 剰余演算により、front が配列先頭を越えた後に末尾へ戻るようにする</span>
+<a id="__codelineno-27-46" name="__codelineno-27-46" href="#__codelineno-27-46"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-27-47" name="__codelineno-27-47" href="#__codelineno-27-47"></a><span class="w">        </span><span class="c1">// num をキュー先頭に追加</span>
+<a id="__codelineno-27-48" name="__codelineno-27-48" href="#__codelineno-27-48"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">front</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-27-49" name="__codelineno-27-49" href="#__codelineno-27-49"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-27-50" name="__codelineno-27-50" href="#__codelineno-27-50"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-51" name="__codelineno-27-51" href="#__codelineno-27-51"></a>
+<a id="__codelineno-27-52" name="__codelineno-27-52" href="#__codelineno-27-52"></a><span class="w">    </span><span class="cm">/* キュー末尾にエンキュー */</span>
+<a id="__codelineno-27-53" name="__codelineno-27-53" href="#__codelineno-27-53"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">pushLast</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-54" name="__codelineno-27-54" href="#__codelineno-27-54"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-55" name="__codelineno-27-55" href="#__codelineno-27-55"></a><span class="w">            </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;両端キューがいっぱいです&quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
+<a id="__codelineno-27-56" name="__codelineno-27-56" href="#__codelineno-27-56"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-27-57" name="__codelineno-27-57" href="#__codelineno-27-57"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-27-58" name="__codelineno-27-58" href="#__codelineno-27-58"></a><span class="w">        </span><span class="c1">// キュー末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-27-59" name="__codelineno-27-59" href="#__codelineno-27-59"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">queSize</span><span class="p">);</span>
+<a id="__codelineno-27-60" name="__codelineno-27-60" href="#__codelineno-27-60"></a><span class="w">        </span><span class="c1">// num をキュー末尾に追加</span>
+<a id="__codelineno-27-61" name="__codelineno-27-61" href="#__codelineno-27-61"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">rear</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-27-62" name="__codelineno-27-62" href="#__codelineno-27-62"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-27-63" name="__codelineno-27-63" href="#__codelineno-27-63"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-64" name="__codelineno-27-64" href="#__codelineno-27-64"></a>
+<a id="__codelineno-27-65" name="__codelineno-27-65" href="#__codelineno-27-65"></a><span class="w">    </span><span class="cm">/* キュー先頭からデキュー */</span>
+<a id="__codelineno-27-66" name="__codelineno-27-66" href="#__codelineno-27-66"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">popFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-67" name="__codelineno-27-67" href="#__codelineno-27-67"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peekFirst</span><span class="p">();</span>
+<a id="__codelineno-27-68" name="__codelineno-27-68" href="#__codelineno-27-68"></a><span class="w">        </span><span class="c1">// 先頭ポインタを 1 つ後ろへ進める</span>
+<a id="__codelineno-27-69" name="__codelineno-27-69" href="#__codelineno-27-69"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-27-70" name="__codelineno-27-70" href="#__codelineno-27-70"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-27-71" name="__codelineno-27-71" href="#__codelineno-27-71"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-27-72" name="__codelineno-27-72" href="#__codelineno-27-72"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-73" name="__codelineno-27-73" href="#__codelineno-27-73"></a>
+<a id="__codelineno-27-74" name="__codelineno-27-74" href="#__codelineno-27-74"></a><span class="w">    </span><span class="cm">/* キュー末尾からデキュー */</span>
+<a id="__codelineno-27-75" name="__codelineno-27-75" href="#__codelineno-27-75"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">popLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-76" name="__codelineno-27-76" href="#__codelineno-27-76"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peekLast</span><span class="p">();</span>
+<a id="__codelineno-27-77" name="__codelineno-27-77" href="#__codelineno-27-77"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-27-78" name="__codelineno-27-78" href="#__codelineno-27-78"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-27-79" name="__codelineno-27-79" href="#__codelineno-27-79"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-80" name="__codelineno-27-80" href="#__codelineno-27-80"></a>
+<a id="__codelineno-27-81" name="__codelineno-27-81" href="#__codelineno-27-81"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-27-82" name="__codelineno-27-82" href="#__codelineno-27-82"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">peekFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-83" name="__codelineno-27-83" href="#__codelineno-27-83"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-27-84" name="__codelineno-27-84" href="#__codelineno-27-84"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;両端キューが空です&quot;</span><span class="p">);</span>
+<a id="__codelineno-27-85" name="__codelineno-27-85" href="#__codelineno-27-85"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">front</span><span class="p">];</span>
+<a id="__codelineno-27-86" name="__codelineno-27-86" href="#__codelineno-27-86"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-87" name="__codelineno-27-87" href="#__codelineno-27-87"></a>
+<a id="__codelineno-27-88" name="__codelineno-27-88" href="#__codelineno-27-88"></a><span class="w">    </span><span class="cm">/* キュー末尾の要素にアクセス */</span>
+<a id="__codelineno-27-89" name="__codelineno-27-89" href="#__codelineno-27-89"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">peekLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-90" name="__codelineno-27-90" href="#__codelineno-27-90"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-27-91" name="__codelineno-27-91" href="#__codelineno-27-91"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;両端キューが空です&quot;</span><span class="p">);</span>
+<a id="__codelineno-27-92" name="__codelineno-27-92" href="#__codelineno-27-92"></a><span class="w">        </span><span class="c1">// 末尾要素のインデックスを計算</span>
+<a id="__codelineno-27-93" name="__codelineno-27-93" href="#__codelineno-27-93"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">last</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-27-94" name="__codelineno-27-94" href="#__codelineno-27-94"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">last</span><span class="p">];</span>
+<a id="__codelineno-27-95" name="__codelineno-27-95" href="#__codelineno-27-95"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-96" name="__codelineno-27-96" href="#__codelineno-27-96"></a>
+<a id="__codelineno-27-97" name="__codelineno-27-97" href="#__codelineno-27-97"></a><span class="w">    </span><span class="cm">/* 出力用の配列を返す */</span>
+<a id="__codelineno-27-98" name="__codelineno-27-98" href="#__codelineno-27-98"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toVector</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-99" name="__codelineno-27-99" href="#__codelineno-27-99"></a><span class="w">        </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-27-100" name="__codelineno-27-100" href="#__codelineno-27-100"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">(</span><span class="n">queSize</span><span class="p">);</span>
+<a id="__codelineno-27-101" name="__codelineno-27-101" href="#__codelineno-27-101"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-102" name="__codelineno-27-102" href="#__codelineno-27-102"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">index</span><span class="p">(</span><span class="n">j</span><span class="p">)];</span>
+<a id="__codelineno-27-103" name="__codelineno-27-103" href="#__codelineno-27-103"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-27-104" name="__codelineno-27-104" href="#__codelineno-27-104"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-27-105" name="__codelineno-27-105" href="#__codelineno-27-105"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-106" name="__codelineno-27-106" href="#__codelineno-27-106"></a><span class="p">};</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_deque.cs</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">ArrayDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_deque.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 循環配列ベースの両端キュー */</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="kd">class</span> <span class="nc">ArrayDeque</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端キューの要素を格納する配列</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ポインタ。先頭要素を指す</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端キューの長さ</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">ArrayDeque</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="na">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">capacity</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a>
+<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w">    </span><span class="cm">/* 両端キューの容量を取得 */</span>
+<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
+<a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a>
+<a id="__codelineno-28-18" name="__codelineno-28-18" href="#__codelineno-28-18"></a><span class="w">    </span><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-28-19" name="__codelineno-28-19" href="#__codelineno-28-19"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-20" name="__codelineno-28-20" href="#__codelineno-28-20"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-28-21" name="__codelineno-28-21" href="#__codelineno-28-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-22" name="__codelineno-28-22" href="#__codelineno-28-22"></a>
+<a id="__codelineno-28-23" name="__codelineno-28-23" href="#__codelineno-28-23"></a><span class="w">    </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
+<a id="__codelineno-28-24" name="__codelineno-28-24" href="#__codelineno-28-24"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-25" name="__codelineno-28-25" href="#__codelineno-28-25"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-28-26" name="__codelineno-28-26" href="#__codelineno-28-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-27" name="__codelineno-28-27" href="#__codelineno-28-27"></a>
+<a id="__codelineno-28-28" name="__codelineno-28-28" href="#__codelineno-28-28"></a><span class="w">    </span><span class="cm">/* 循環配列のインデックスを計算 */</span>
+<a id="__codelineno-28-29" name="__codelineno-28-29" href="#__codelineno-28-29"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">index</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-30" name="__codelineno-28-30" href="#__codelineno-28-30"></a><span class="w">        </span><span class="c1">// 剰余演算により配列の先頭と末尾をつなげる</span>
+<a id="__codelineno-28-31" name="__codelineno-28-31" href="#__codelineno-28-31"></a><span class="w">        </span><span class="c1">// i が配列の末尾を越えたら先頭に戻る</span>
+<a id="__codelineno-28-32" name="__codelineno-28-32" href="#__codelineno-28-32"></a><span class="w">        </span><span class="c1">// i が配列の先頭を越えて前に出たら末尾に戻る</span>
+<a id="__codelineno-28-33" name="__codelineno-28-33" href="#__codelineno-28-33"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">();</span>
+<a id="__codelineno-28-34" name="__codelineno-28-34" href="#__codelineno-28-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-35" name="__codelineno-28-35" href="#__codelineno-28-35"></a>
+<a id="__codelineno-28-36" name="__codelineno-28-36" href="#__codelineno-28-36"></a><span class="w">    </span><span class="cm">/* キュー先頭にエンキュー */</span>
+<a id="__codelineno-28-37" name="__codelineno-28-37" href="#__codelineno-28-37"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">pushFirst</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-38" name="__codelineno-28-38" href="#__codelineno-28-38"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-39" name="__codelineno-28-39" href="#__codelineno-28-39"></a><span class="w">            </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">&quot;双方向キューは満杯です&quot;</span><span class="p">);</span>
+<a id="__codelineno-28-40" name="__codelineno-28-40" href="#__codelineno-28-40"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-28-41" name="__codelineno-28-41" href="#__codelineno-28-41"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-28-42" name="__codelineno-28-42" href="#__codelineno-28-42"></a><span class="w">        </span><span class="c1">// 先頭ポインタを左に 1 つ移動する</span>
+<a id="__codelineno-28-43" name="__codelineno-28-43" href="#__codelineno-28-43"></a><span class="w">        </span><span class="c1">// 剰余演算により、front が配列先頭を越えた後に末尾へ戻るようにする</span>
+<a id="__codelineno-28-44" name="__codelineno-28-44" href="#__codelineno-28-44"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-28-45" name="__codelineno-28-45" href="#__codelineno-28-45"></a><span class="w">        </span><span class="c1">// num をキュー先頭に追加</span>
+<a id="__codelineno-28-46" name="__codelineno-28-46" href="#__codelineno-28-46"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">front</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-28-47" name="__codelineno-28-47" href="#__codelineno-28-47"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-28-48" name="__codelineno-28-48" href="#__codelineno-28-48"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-49" name="__codelineno-28-49" href="#__codelineno-28-49"></a>
+<a id="__codelineno-28-50" name="__codelineno-28-50" href="#__codelineno-28-50"></a><span class="w">    </span><span class="cm">/* キュー末尾にエンキュー */</span>
+<a id="__codelineno-28-51" name="__codelineno-28-51" href="#__codelineno-28-51"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">pushLast</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-52" name="__codelineno-28-52" href="#__codelineno-28-52"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-53" name="__codelineno-28-53" href="#__codelineno-28-53"></a><span class="w">            </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">&quot;双方向キューは満杯です&quot;</span><span class="p">);</span>
+<a id="__codelineno-28-54" name="__codelineno-28-54" href="#__codelineno-28-54"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-28-55" name="__codelineno-28-55" href="#__codelineno-28-55"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-28-56" name="__codelineno-28-56" href="#__codelineno-28-56"></a><span class="w">        </span><span class="c1">// キュー末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-28-57" name="__codelineno-28-57" href="#__codelineno-28-57"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">queSize</span><span class="p">);</span>
+<a id="__codelineno-28-58" name="__codelineno-28-58" href="#__codelineno-28-58"></a><span class="w">        </span><span class="c1">// num をキュー末尾に追加</span>
+<a id="__codelineno-28-59" name="__codelineno-28-59" href="#__codelineno-28-59"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">rear</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-28-60" name="__codelineno-28-60" href="#__codelineno-28-60"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-28-61" name="__codelineno-28-61" href="#__codelineno-28-61"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-62" name="__codelineno-28-62" href="#__codelineno-28-62"></a>
+<a id="__codelineno-28-63" name="__codelineno-28-63" href="#__codelineno-28-63"></a><span class="w">    </span><span class="cm">/* キュー先頭からデキュー */</span>
+<a id="__codelineno-28-64" name="__codelineno-28-64" href="#__codelineno-28-64"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">popFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-65" name="__codelineno-28-65" href="#__codelineno-28-65"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peekFirst</span><span class="p">();</span>
+<a id="__codelineno-28-66" name="__codelineno-28-66" href="#__codelineno-28-66"></a><span class="w">        </span><span class="c1">// 先頭ポインタを 1 つ後ろへ進める</span>
+<a id="__codelineno-28-67" name="__codelineno-28-67" href="#__codelineno-28-67"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-28-68" name="__codelineno-28-68" href="#__codelineno-28-68"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-28-69" name="__codelineno-28-69" href="#__codelineno-28-69"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-28-70" name="__codelineno-28-70" href="#__codelineno-28-70"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-71" name="__codelineno-28-71" href="#__codelineno-28-71"></a>
+<a id="__codelineno-28-72" name="__codelineno-28-72" href="#__codelineno-28-72"></a><span class="w">    </span><span class="cm">/* キュー末尾からデキュー */</span>
+<a id="__codelineno-28-73" name="__codelineno-28-73" href="#__codelineno-28-73"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">popLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-74" name="__codelineno-28-74" href="#__codelineno-28-74"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peekLast</span><span class="p">();</span>
+<a id="__codelineno-28-75" name="__codelineno-28-75" href="#__codelineno-28-75"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-28-76" name="__codelineno-28-76" href="#__codelineno-28-76"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-28-77" name="__codelineno-28-77" href="#__codelineno-28-77"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-78" name="__codelineno-28-78" href="#__codelineno-28-78"></a>
+<a id="__codelineno-28-79" name="__codelineno-28-79" href="#__codelineno-28-79"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-28-80" name="__codelineno-28-80" href="#__codelineno-28-80"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">peekFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-81" name="__codelineno-28-81" href="#__codelineno-28-81"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-28-82" name="__codelineno-28-82" href="#__codelineno-28-82"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
+<a id="__codelineno-28-83" name="__codelineno-28-83" href="#__codelineno-28-83"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">front</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-28-84" name="__codelineno-28-84" href="#__codelineno-28-84"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-85" name="__codelineno-28-85" href="#__codelineno-28-85"></a>
+<a id="__codelineno-28-86" name="__codelineno-28-86" href="#__codelineno-28-86"></a><span class="w">    </span><span class="cm">/* キュー末尾の要素にアクセス */</span>
+<a id="__codelineno-28-87" name="__codelineno-28-87" href="#__codelineno-28-87"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">peekLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-88" name="__codelineno-28-88" href="#__codelineno-28-88"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-28-89" name="__codelineno-28-89" href="#__codelineno-28-89"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
+<a id="__codelineno-28-90" name="__codelineno-28-90" href="#__codelineno-28-90"></a><span class="w">        </span><span class="c1">// 末尾要素のインデックスを計算</span>
+<a id="__codelineno-28-91" name="__codelineno-28-91" href="#__codelineno-28-91"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">last</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-28-92" name="__codelineno-28-92" href="#__codelineno-28-92"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">last</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-28-93" name="__codelineno-28-93" href="#__codelineno-28-93"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-94" name="__codelineno-28-94" href="#__codelineno-28-94"></a>
+<a id="__codelineno-28-95" name="__codelineno-28-95" href="#__codelineno-28-95"></a><span class="w">    </span><span class="cm">/* 出力用の配列を返す */</span>
+<a id="__codelineno-28-96" name="__codelineno-28-96" href="#__codelineno-28-96"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-97" name="__codelineno-28-97" href="#__codelineno-28-97"></a><span class="w">        </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-28-98" name="__codelineno-28-98" href="#__codelineno-28-98"></a><span class="w">        </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">queSize</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-28-99" name="__codelineno-28-99" href="#__codelineno-28-99"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-100" name="__codelineno-28-100" href="#__codelineno-28-100"></a><span class="w">            </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">index</span><span class="p">(</span><span class="n">j</span><span class="p">)</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-28-101" name="__codelineno-28-101" href="#__codelineno-28-101"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-28-102" name="__codelineno-28-102" href="#__codelineno-28-102"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-28-103" name="__codelineno-28-103" href="#__codelineno-28-103"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-104" name="__codelineno-28-104" href="#__codelineno-28-104"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_deque.go</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">arrayDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_deque.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 循環配列ベースの両端キュー */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayDeque</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span><span class="w">  </span><span class="c1">// 両端キューの要素を格納する配列</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w">   </span><span class="c1">// 先頭ポインタ。先頭要素を指す</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端キューの長さ</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nf">ArrayDeque</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">        </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">capacity</span><span class="p">];</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w">    </span><span class="cm">/* 両端キューの容量を取得 */</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="nf">Capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a>
+<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w">    </span><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-20" name="__codelineno-29-20" href="#__codelineno-29-20"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-29-21" name="__codelineno-29-21" href="#__codelineno-29-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-22" name="__codelineno-29-22" href="#__codelineno-29-22"></a>
+<a id="__codelineno-29-23" name="__codelineno-29-23" href="#__codelineno-29-23"></a><span class="w">    </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
+<a id="__codelineno-29-24" name="__codelineno-29-24" href="#__codelineno-29-24"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="nf">IsEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-25" name="__codelineno-29-25" href="#__codelineno-29-25"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-29-26" name="__codelineno-29-26" href="#__codelineno-29-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-27" name="__codelineno-29-27" href="#__codelineno-29-27"></a>
+<a id="__codelineno-29-28" name="__codelineno-29-28" href="#__codelineno-29-28"></a><span class="w">    </span><span class="cm">/* 循環配列のインデックスを計算 */</span>
+<a id="__codelineno-29-29" name="__codelineno-29-29" href="#__codelineno-29-29"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="nf">Index</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-30" name="__codelineno-29-30" href="#__codelineno-29-30"></a><span class="w">        </span><span class="c1">// 剰余演算により配列の先頭と末尾をつなげる</span>
+<a id="__codelineno-29-31" name="__codelineno-29-31" href="#__codelineno-29-31"></a><span class="w">        </span><span class="c1">// i が配列の末尾を越えたら先頭に戻る</span>
+<a id="__codelineno-29-32" name="__codelineno-29-32" href="#__codelineno-29-32"></a><span class="w">        </span><span class="c1">// i が配列の先頭を越えて前に出たら末尾に戻る</span>
+<a id="__codelineno-29-33" name="__codelineno-29-33" href="#__codelineno-29-33"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">Capacity</span><span class="p">())</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">Capacity</span><span class="p">();</span>
+<a id="__codelineno-29-34" name="__codelineno-29-34" href="#__codelineno-29-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-35" name="__codelineno-29-35" href="#__codelineno-29-35"></a>
+<a id="__codelineno-29-36" name="__codelineno-29-36" href="#__codelineno-29-36"></a><span class="w">    </span><span class="cm">/* キュー先頭にエンキュー */</span>
+<a id="__codelineno-29-37" name="__codelineno-29-37" href="#__codelineno-29-37"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">PushFirst</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-38" name="__codelineno-29-38" href="#__codelineno-29-38"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">Capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-39" name="__codelineno-29-39" href="#__codelineno-29-39"></a><span class="w">            </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="s">&quot;両端キューは満杯です&quot;</span><span class="p">);</span>
+<a id="__codelineno-29-40" name="__codelineno-29-40" href="#__codelineno-29-40"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-29-41" name="__codelineno-29-41" href="#__codelineno-29-41"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-42" name="__codelineno-29-42" href="#__codelineno-29-42"></a><span class="w">        </span><span class="c1">// 先頭ポインタを左に 1 つ移動する</span>
+<a id="__codelineno-29-43" name="__codelineno-29-43" href="#__codelineno-29-43"></a><span class="w">        </span><span class="c1">// 剰余演算により、front が配列先頭を越えた後に末尾へ戻るようにする</span>
+<a id="__codelineno-29-44" name="__codelineno-29-44" href="#__codelineno-29-44"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-29-45" name="__codelineno-29-45" href="#__codelineno-29-45"></a><span class="w">        </span><span class="c1">// num をキュー先頭に追加</span>
+<a id="__codelineno-29-46" name="__codelineno-29-46" href="#__codelineno-29-46"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">front</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-29-47" name="__codelineno-29-47" href="#__codelineno-29-47"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-29-48" name="__codelineno-29-48" href="#__codelineno-29-48"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-49" name="__codelineno-29-49" href="#__codelineno-29-49"></a>
+<a id="__codelineno-29-50" name="__codelineno-29-50" href="#__codelineno-29-50"></a><span class="w">    </span><span class="cm">/* キュー末尾にエンキュー */</span>
+<a id="__codelineno-29-51" name="__codelineno-29-51" href="#__codelineno-29-51"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">PushLast</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-52" name="__codelineno-29-52" href="#__codelineno-29-52"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">Capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-53" name="__codelineno-29-53" href="#__codelineno-29-53"></a><span class="w">            </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="s">&quot;両端キューは満杯です&quot;</span><span class="p">);</span>
+<a id="__codelineno-29-54" name="__codelineno-29-54" href="#__codelineno-29-54"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-29-55" name="__codelineno-29-55" href="#__codelineno-29-55"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-56" name="__codelineno-29-56" href="#__codelineno-29-56"></a><span class="w">        </span><span class="c1">// キュー末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-29-57" name="__codelineno-29-57" href="#__codelineno-29-57"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">queSize</span><span class="p">);</span>
+<a id="__codelineno-29-58" name="__codelineno-29-58" href="#__codelineno-29-58"></a><span class="w">        </span><span class="c1">// num をキュー末尾に追加</span>
+<a id="__codelineno-29-59" name="__codelineno-29-59" href="#__codelineno-29-59"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">rear</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-29-60" name="__codelineno-29-60" href="#__codelineno-29-60"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-29-61" name="__codelineno-29-61" href="#__codelineno-29-61"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-62" name="__codelineno-29-62" href="#__codelineno-29-62"></a>
+<a id="__codelineno-29-63" name="__codelineno-29-63" href="#__codelineno-29-63"></a><span class="w">    </span><span class="cm">/* キュー先頭からデキュー */</span>
+<a id="__codelineno-29-64" name="__codelineno-29-64" href="#__codelineno-29-64"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">PopFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-65" name="__codelineno-29-65" href="#__codelineno-29-65"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">PeekFirst</span><span class="p">();</span>
+<a id="__codelineno-29-66" name="__codelineno-29-66" href="#__codelineno-29-66"></a><span class="w">        </span><span class="c1">// 先頭ポインタを 1 つ後ろへ進める</span>
+<a id="__codelineno-29-67" name="__codelineno-29-67" href="#__codelineno-29-67"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-29-68" name="__codelineno-29-68" href="#__codelineno-29-68"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-29-69" name="__codelineno-29-69" href="#__codelineno-29-69"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-29-70" name="__codelineno-29-70" href="#__codelineno-29-70"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-71" name="__codelineno-29-71" href="#__codelineno-29-71"></a>
+<a id="__codelineno-29-72" name="__codelineno-29-72" href="#__codelineno-29-72"></a><span class="w">    </span><span class="cm">/* キュー末尾からデキュー */</span>
+<a id="__codelineno-29-73" name="__codelineno-29-73" href="#__codelineno-29-73"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">PopLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-74" name="__codelineno-29-74" href="#__codelineno-29-74"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">PeekLast</span><span class="p">();</span>
+<a id="__codelineno-29-75" name="__codelineno-29-75" href="#__codelineno-29-75"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-29-76" name="__codelineno-29-76" href="#__codelineno-29-76"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-29-77" name="__codelineno-29-77" href="#__codelineno-29-77"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-78" name="__codelineno-29-78" href="#__codelineno-29-78"></a>
+<a id="__codelineno-29-79" name="__codelineno-29-79" href="#__codelineno-29-79"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-29-80" name="__codelineno-29-80" href="#__codelineno-29-80"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">PeekFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-81" name="__codelineno-29-81" href="#__codelineno-29-81"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-82" name="__codelineno-29-82" href="#__codelineno-29-82"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="nf">InvalidOperationException</span><span class="p">();</span>
+<a id="__codelineno-29-83" name="__codelineno-29-83" href="#__codelineno-29-83"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-84" name="__codelineno-29-84" href="#__codelineno-29-84"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">front</span><span class="p">];</span>
+<a id="__codelineno-29-85" name="__codelineno-29-85" href="#__codelineno-29-85"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-86" name="__codelineno-29-86" href="#__codelineno-29-86"></a>
+<a id="__codelineno-29-87" name="__codelineno-29-87" href="#__codelineno-29-87"></a><span class="w">    </span><span class="cm">/* キュー末尾の要素にアクセス */</span>
+<a id="__codelineno-29-88" name="__codelineno-29-88" href="#__codelineno-29-88"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">PeekLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-89" name="__codelineno-29-89" href="#__codelineno-29-89"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-90" name="__codelineno-29-90" href="#__codelineno-29-90"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="nf">InvalidOperationException</span><span class="p">();</span>
+<a id="__codelineno-29-91" name="__codelineno-29-91" href="#__codelineno-29-91"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-92" name="__codelineno-29-92" href="#__codelineno-29-92"></a><span class="w">        </span><span class="c1">// 末尾要素のインデックスを計算</span>
+<a id="__codelineno-29-93" name="__codelineno-29-93" href="#__codelineno-29-93"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">last</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-29-94" name="__codelineno-29-94" href="#__codelineno-29-94"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">last</span><span class="p">];</span>
+<a id="__codelineno-29-95" name="__codelineno-29-95" href="#__codelineno-29-95"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-96" name="__codelineno-29-96" href="#__codelineno-29-96"></a>
+<a id="__codelineno-29-97" name="__codelineno-29-97" href="#__codelineno-29-97"></a><span class="w">    </span><span class="cm">/* 出力用の配列を返す */</span>
+<a id="__codelineno-29-98" name="__codelineno-29-98" href="#__codelineno-29-98"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="nf">ToArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-99" name="__codelineno-29-99" href="#__codelineno-29-99"></a><span class="w">        </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-29-100" name="__codelineno-29-100" href="#__codelineno-29-100"></a><span class="w">        </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">queSize</span><span class="p">];</span>
+<a id="__codelineno-29-101" name="__codelineno-29-101" href="#__codelineno-29-101"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-102" name="__codelineno-29-102" href="#__codelineno-29-102"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">Index</span><span class="p">(</span><span class="n">j</span><span class="p">)];</span>
+<a id="__codelineno-29-103" name="__codelineno-29-103" href="#__codelineno-29-103"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-104" name="__codelineno-29-104" href="#__codelineno-29-104"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-29-105" name="__codelineno-29-105" href="#__codelineno-29-105"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-106" name="__codelineno-29-106" href="#__codelineno-29-106"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_deque.swift</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">ArrayDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_deque.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 循環配列ベースの両端キュー */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">arrayDeque</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="nx">nums</span><span class="w">        </span><span class="p">[]</span><span class="kt">int</span><span class="w"> </span><span class="c1">// 両端キューの要素を格納する配列</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="nx">front</span><span class="w">       </span><span class="kt">int</span><span class="w">   </span><span class="c1">// 先頭ポインタ。先頭要素を指す</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">    </span><span class="nx">queSize</span><span class="w">     </span><span class="kt">int</span><span class="w">   </span><span class="c1">// 両端キューの長さ</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="nx">queCapacity</span><span class="w"> </span><span class="kt">int</span><span class="w">   </span><span class="c1">// キュー容量（格納できる要素数の上限）</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="p">}</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="cm">/* キューを初期化 */</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="kd">func</span><span class="w"> </span><span class="nx">newArrayDeque</span><span class="p">(</span><span class="nx">queCapacity</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayDeque</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">arrayDeque</span><span class="p">{</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w">        </span><span class="nx">nums</span><span class="p">:</span><span class="w">        </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">queCapacity</span><span class="p">),</span>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w">        </span><span class="nx">queCapacity</span><span class="p">:</span><span class="w"> </span><span class="nx">queCapacity</span><span class="p">,</span>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w">        </span><span class="nx">front</span><span class="p">:</span><span class="w">       </span><span class="mi">0</span><span class="p">,</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w">        </span><span class="nx">queSize</span><span class="p">:</span><span class="w">     </span><span class="mi">0</span><span class="p">,</span>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="p">}</span>
+<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a>
+<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">q</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayDeque</span><span class="p">)</span><span class="w"> </span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-21" name="__codelineno-30-21" href="#__codelineno-30-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">queSize</span>
+<a id="__codelineno-30-22" name="__codelineno-30-22" href="#__codelineno-30-22"></a><span class="p">}</span>
+<a id="__codelineno-30-23" name="__codelineno-30-23" href="#__codelineno-30-23"></a>
+<a id="__codelineno-30-24" name="__codelineno-30-24" href="#__codelineno-30-24"></a><span class="cm">/* 両端キューが空かどうかを判定 */</span>
+<a id="__codelineno-30-25" name="__codelineno-30-25" href="#__codelineno-30-25"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">q</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayDeque</span><span class="p">)</span><span class="w"> </span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-26" name="__codelineno-30-26" href="#__codelineno-30-26"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-30-27" name="__codelineno-30-27" href="#__codelineno-30-27"></a><span class="p">}</span>
+<a id="__codelineno-30-28" name="__codelineno-30-28" href="#__codelineno-30-28"></a>
+<a id="__codelineno-30-29" name="__codelineno-30-29" href="#__codelineno-30-29"></a><span class="cm">/* 循環配列のインデックスを計算 */</span>
+<a id="__codelineno-30-30" name="__codelineno-30-30" href="#__codelineno-30-30"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">q</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayDeque</span><span class="p">)</span><span class="w"> </span><span class="nx">index</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-31" name="__codelineno-30-31" href="#__codelineno-30-31"></a><span class="w">    </span><span class="c1">// 剰余演算により配列の先頭と末尾をつなげる</span>
+<a id="__codelineno-30-32" name="__codelineno-30-32" href="#__codelineno-30-32"></a><span class="w">    </span><span class="c1">// i が配列の末尾を越えたら先頭に戻る</span>
+<a id="__codelineno-30-33" name="__codelineno-30-33" href="#__codelineno-30-33"></a><span class="w">    </span><span class="c1">// i が配列の先頭を越えて前に出たら末尾に戻る</span>
+<a id="__codelineno-30-34" name="__codelineno-30-34" href="#__codelineno-30-34"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">queCapacity</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">queCapacity</span>
+<a id="__codelineno-30-35" name="__codelineno-30-35" href="#__codelineno-30-35"></a><span class="p">}</span>
+<a id="__codelineno-30-36" name="__codelineno-30-36" href="#__codelineno-30-36"></a>
+<a id="__codelineno-30-37" name="__codelineno-30-37" href="#__codelineno-30-37"></a><span class="cm">/* キュー先頭にエンキュー */</span>
+<a id="__codelineno-30-38" name="__codelineno-30-38" href="#__codelineno-30-38"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">q</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayDeque</span><span class="p">)</span><span class="w"> </span><span class="nx">pushFirst</span><span class="p">(</span><span class="nx">num</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-39" name="__codelineno-30-39" href="#__codelineno-30-39"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">queCapacity</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-40" name="__codelineno-30-40" href="#__codelineno-30-40"></a><span class="w">        </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="s">&quot;両端キューは満杯です&quot;</span><span class="p">)</span>
+<a id="__codelineno-30-41" name="__codelineno-30-41" href="#__codelineno-30-41"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-30-42" name="__codelineno-30-42" href="#__codelineno-30-42"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-43" name="__codelineno-30-43" href="#__codelineno-30-43"></a><span class="w">    </span><span class="c1">// 先頭ポインタを左に 1 つ移動する</span>
+<a id="__codelineno-30-44" name="__codelineno-30-44" href="#__codelineno-30-44"></a><span class="w">    </span><span class="c1">// 剰余演算により、front が配列先頭を越えた後に末尾へ戻るようにする</span>
+<a id="__codelineno-30-45" name="__codelineno-30-45" href="#__codelineno-30-45"></a><span class="w">    </span><span class="nx">q</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">index</span><span class="p">(</span><span class="nx">q</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-30-46" name="__codelineno-30-46" href="#__codelineno-30-46"></a><span class="w">    </span><span class="c1">// num をキュー先頭に追加</span>
+<a id="__codelineno-30-47" name="__codelineno-30-47" href="#__codelineno-30-47"></a><span class="w">    </span><span class="nx">q</span><span class="p">.</span><span class="nx">nums</span><span class="p">[</span><span class="nx">q</span><span class="p">.</span><span class="nx">front</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">num</span>
+<a id="__codelineno-30-48" name="__codelineno-30-48" href="#__codelineno-30-48"></a><span class="w">    </span><span class="nx">q</span><span class="p">.</span><span class="nx">queSize</span><span class="o">++</span>
+<a id="__codelineno-30-49" name="__codelineno-30-49" href="#__codelineno-30-49"></a><span class="p">}</span>
+<a id="__codelineno-30-50" name="__codelineno-30-50" href="#__codelineno-30-50"></a>
+<a id="__codelineno-30-51" name="__codelineno-30-51" href="#__codelineno-30-51"></a><span class="cm">/* キュー末尾にエンキュー */</span>
+<a id="__codelineno-30-52" name="__codelineno-30-52" href="#__codelineno-30-52"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">q</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayDeque</span><span class="p">)</span><span class="w"> </span><span class="nx">pushLast</span><span class="p">(</span><span class="nx">num</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-53" name="__codelineno-30-53" href="#__codelineno-30-53"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">queCapacity</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-54" name="__codelineno-30-54" href="#__codelineno-30-54"></a><span class="w">        </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="s">&quot;両端キューは満杯です&quot;</span><span class="p">)</span>
+<a id="__codelineno-30-55" name="__codelineno-30-55" href="#__codelineno-30-55"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-30-56" name="__codelineno-30-56" href="#__codelineno-30-56"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-57" name="__codelineno-30-57" href="#__codelineno-30-57"></a><span class="w">    </span><span class="c1">// キュー末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-30-58" name="__codelineno-30-58" href="#__codelineno-30-58"></a><span class="w">    </span><span class="nx">rear</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">index</span><span class="p">(</span><span class="nx">q</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">queSize</span><span class="p">)</span>
+<a id="__codelineno-30-59" name="__codelineno-30-59" href="#__codelineno-30-59"></a><span class="w">    </span><span class="c1">// num をキュー末尾に追加</span>
+<a id="__codelineno-30-60" name="__codelineno-30-60" href="#__codelineno-30-60"></a><span class="w">    </span><span class="nx">q</span><span class="p">.</span><span class="nx">nums</span><span class="p">[</span><span class="nx">rear</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">num</span>
+<a id="__codelineno-30-61" name="__codelineno-30-61" href="#__codelineno-30-61"></a><span class="w">    </span><span class="nx">q</span><span class="p">.</span><span class="nx">queSize</span><span class="o">++</span>
+<a id="__codelineno-30-62" name="__codelineno-30-62" href="#__codelineno-30-62"></a><span class="p">}</span>
+<a id="__codelineno-30-63" name="__codelineno-30-63" href="#__codelineno-30-63"></a>
+<a id="__codelineno-30-64" name="__codelineno-30-64" href="#__codelineno-30-64"></a><span class="cm">/* キュー先頭からデキュー */</span>
+<a id="__codelineno-30-65" name="__codelineno-30-65" href="#__codelineno-30-65"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">q</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayDeque</span><span class="p">)</span><span class="w"> </span><span class="nx">popFirst</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-66" name="__codelineno-30-66" href="#__codelineno-30-66"></a><span class="w">    </span><span class="nx">num</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">peekFirst</span><span class="p">()</span>
+<a id="__codelineno-30-67" name="__codelineno-30-67" href="#__codelineno-30-67"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-68" name="__codelineno-30-68" href="#__codelineno-30-68"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-30-69" name="__codelineno-30-69" href="#__codelineno-30-69"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-70" name="__codelineno-30-70" href="#__codelineno-30-70"></a><span class="w">    </span><span class="c1">// 先頭ポインタを 1 つ後ろへ進める</span>
+<a id="__codelineno-30-71" name="__codelineno-30-71" href="#__codelineno-30-71"></a><span class="w">    </span><span class="nx">q</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">index</span><span class="p">(</span><span class="nx">q</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-30-72" name="__codelineno-30-72" href="#__codelineno-30-72"></a><span class="w">    </span><span class="nx">q</span><span class="p">.</span><span class="nx">queSize</span><span class="o">--</span>
+<a id="__codelineno-30-73" name="__codelineno-30-73" href="#__codelineno-30-73"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">num</span>
+<a id="__codelineno-30-74" name="__codelineno-30-74" href="#__codelineno-30-74"></a><span class="p">}</span>
+<a id="__codelineno-30-75" name="__codelineno-30-75" href="#__codelineno-30-75"></a>
+<a id="__codelineno-30-76" name="__codelineno-30-76" href="#__codelineno-30-76"></a><span class="cm">/* キュー末尾からデキュー */</span>
+<a id="__codelineno-30-77" name="__codelineno-30-77" href="#__codelineno-30-77"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">q</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayDeque</span><span class="p">)</span><span class="w"> </span><span class="nx">popLast</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-78" name="__codelineno-30-78" href="#__codelineno-30-78"></a><span class="w">    </span><span class="nx">num</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">peekLast</span><span class="p">()</span>
+<a id="__codelineno-30-79" name="__codelineno-30-79" href="#__codelineno-30-79"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-80" name="__codelineno-30-80" href="#__codelineno-30-80"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-30-81" name="__codelineno-30-81" href="#__codelineno-30-81"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-82" name="__codelineno-30-82" href="#__codelineno-30-82"></a><span class="w">    </span><span class="nx">q</span><span class="p">.</span><span class="nx">queSize</span><span class="o">--</span>
+<a id="__codelineno-30-83" name="__codelineno-30-83" href="#__codelineno-30-83"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">num</span>
+<a id="__codelineno-30-84" name="__codelineno-30-84" href="#__codelineno-30-84"></a><span class="p">}</span>
+<a id="__codelineno-30-85" name="__codelineno-30-85" href="#__codelineno-30-85"></a>
+<a id="__codelineno-30-86" name="__codelineno-30-86" href="#__codelineno-30-86"></a><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-30-87" name="__codelineno-30-87" href="#__codelineno-30-87"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">q</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayDeque</span><span class="p">)</span><span class="w"> </span><span class="nx">peekFirst</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-88" name="__codelineno-30-88" href="#__codelineno-30-88"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-89" name="__codelineno-30-89" href="#__codelineno-30-89"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-30-90" name="__codelineno-30-90" href="#__codelineno-30-90"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-91" name="__codelineno-30-91" href="#__codelineno-30-91"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">nums</span><span class="p">[</span><span class="nx">q</span><span class="p">.</span><span class="nx">front</span><span class="p">]</span>
+<a id="__codelineno-30-92" name="__codelineno-30-92" href="#__codelineno-30-92"></a><span class="p">}</span>
+<a id="__codelineno-30-93" name="__codelineno-30-93" href="#__codelineno-30-93"></a>
+<a id="__codelineno-30-94" name="__codelineno-30-94" href="#__codelineno-30-94"></a><span class="cm">/* キュー末尾の要素にアクセス */</span>
+<a id="__codelineno-30-95" name="__codelineno-30-95" href="#__codelineno-30-95"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">q</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayDeque</span><span class="p">)</span><span class="w"> </span><span class="nx">peekLast</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-96" name="__codelineno-30-96" href="#__codelineno-30-96"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-97" name="__codelineno-30-97" href="#__codelineno-30-97"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-30-98" name="__codelineno-30-98" href="#__codelineno-30-98"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-99" name="__codelineno-30-99" href="#__codelineno-30-99"></a><span class="w">    </span><span class="c1">// 末尾要素のインデックスを計算</span>
+<a id="__codelineno-30-100" name="__codelineno-30-100" href="#__codelineno-30-100"></a><span class="w">    </span><span class="nx">last</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">index</span><span class="p">(</span><span class="nx">q</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">queSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-30-101" name="__codelineno-30-101" href="#__codelineno-30-101"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">nums</span><span class="p">[</span><span class="nx">last</span><span class="p">]</span>
+<a id="__codelineno-30-102" name="__codelineno-30-102" href="#__codelineno-30-102"></a><span class="p">}</span>
+<a id="__codelineno-30-103" name="__codelineno-30-103" href="#__codelineno-30-103"></a>
+<a id="__codelineno-30-104" name="__codelineno-30-104" href="#__codelineno-30-104"></a><span class="cm">/* 表示用に Slice を取得 */</span>
+<a id="__codelineno-30-105" name="__codelineno-30-105" href="#__codelineno-30-105"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">q</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayDeque</span><span class="p">)</span><span class="w"> </span><span class="nx">toSlice</span><span class="p">()</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-106" name="__codelineno-30-106" href="#__codelineno-30-106"></a><span class="w">    </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-30-107" name="__codelineno-30-107" href="#__codelineno-30-107"></a><span class="w">    </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">queSize</span><span class="p">)</span>
+<a id="__codelineno-30-108" name="__codelineno-30-108" href="#__codelineno-30-108"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">front</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">queSize</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-109" name="__codelineno-30-109" href="#__codelineno-30-109"></a><span class="w">        </span><span class="nx">res</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">nums</span><span class="p">[</span><span class="nx">q</span><span class="p">.</span><span class="nx">index</span><span class="p">(</span><span class="nx">j</span><span class="p">)]</span>
+<a id="__codelineno-30-110" name="__codelineno-30-110" href="#__codelineno-30-110"></a><span class="w">        </span><span class="nx">j</span><span class="o">++</span>
+<a id="__codelineno-30-111" name="__codelineno-30-111" href="#__codelineno-30-111"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-112" name="__codelineno-30-112" href="#__codelineno-30-112"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
+<a id="__codelineno-30-113" name="__codelineno-30-113" href="#__codelineno-30-113"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_deque.js</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_deque.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* 循環配列ベースの両端キュー */</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ArrayDeque</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="c1">// 両端キューの要素を格納する配列</span>
+<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">front</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// 先頭ポインタ。先頭要素を指す</span>
+<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">_size</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// 両端キューの長さ</span>
+<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a>
+<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w">    </span><span class="kd">init</span><span class="p">(</span><span class="n">capacity</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="w">        </span><span class="n">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span>
+<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="w">        </span><span class="n">_size</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a>
+<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a><span class="w">    </span><span class="cm">/* 両端キューの容量を取得 */</span>
+<a id="__codelineno-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-16" name="__codelineno-31-16" href="#__codelineno-31-16"></a><span class="w">        </span><span class="n">nums</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-31-17" name="__codelineno-31-17" href="#__codelineno-31-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-18" name="__codelineno-31-18" href="#__codelineno-31-18"></a>
+<a id="__codelineno-31-19" name="__codelineno-31-19" href="#__codelineno-31-19"></a><span class="w">    </span><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-31-20" name="__codelineno-31-20" href="#__codelineno-31-20"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-21" name="__codelineno-31-21" href="#__codelineno-31-21"></a><span class="w">        </span><span class="n">_size</span>
+<a id="__codelineno-31-22" name="__codelineno-31-22" href="#__codelineno-31-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-23" name="__codelineno-31-23" href="#__codelineno-31-23"></a>
+<a id="__codelineno-31-24" name="__codelineno-31-24" href="#__codelineno-31-24"></a><span class="w">    </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
+<a id="__codelineno-31-25" name="__codelineno-31-25" href="#__codelineno-31-25"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-26" name="__codelineno-31-26" href="#__codelineno-31-26"></a><span class="w">        </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-31-27" name="__codelineno-31-27" href="#__codelineno-31-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-28" name="__codelineno-31-28" href="#__codelineno-31-28"></a>
+<a id="__codelineno-31-29" name="__codelineno-31-29" href="#__codelineno-31-29"></a><span class="w">    </span><span class="cm">/* 循環配列のインデックスを計算 */</span>
+<a id="__codelineno-31-30" name="__codelineno-31-30" href="#__codelineno-31-30"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">func</span><span class="w"> </span><span class="nf">index</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-31" name="__codelineno-31-31" href="#__codelineno-31-31"></a><span class="w">        </span><span class="c1">// 剰余演算により配列の先頭と末尾をつなげる</span>
+<a id="__codelineno-31-32" name="__codelineno-31-32" href="#__codelineno-31-32"></a><span class="w">        </span><span class="c1">// i が配列の末尾を越えたら先頭に戻る</span>
+<a id="__codelineno-31-33" name="__codelineno-31-33" href="#__codelineno-31-33"></a><span class="w">        </span><span class="c1">// i が配列の先頭を越えて前に出たら末尾に戻る</span>
+<a id="__codelineno-31-34" name="__codelineno-31-34" href="#__codelineno-31-34"></a><span class="w">        </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span>
+<a id="__codelineno-31-35" name="__codelineno-31-35" href="#__codelineno-31-35"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-36" name="__codelineno-31-36" href="#__codelineno-31-36"></a>
+<a id="__codelineno-31-37" name="__codelineno-31-37" href="#__codelineno-31-37"></a><span class="w">    </span><span class="cm">/* キュー先頭にエンキュー */</span>
+<a id="__codelineno-31-38" name="__codelineno-31-38" href="#__codelineno-31-38"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">pushFirst</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-39" name="__codelineno-31-39" href="#__codelineno-31-39"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-40" name="__codelineno-31-40" href="#__codelineno-31-40"></a><span class="w">            </span><span class="bp">print</span><span class="p">(</span><span class="s">&quot;両端キューがいっぱいです&quot;</span><span class="p">)</span>
+<a id="__codelineno-31-41" name="__codelineno-31-41" href="#__codelineno-31-41"></a><span class="w">            </span><span class="k">return</span>
+<a id="__codelineno-31-42" name="__codelineno-31-42" href="#__codelineno-31-42"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-31-43" name="__codelineno-31-43" href="#__codelineno-31-43"></a><span class="w">        </span><span class="c1">// 先頭ポインタを左に 1 つ移動する</span>
+<a id="__codelineno-31-44" name="__codelineno-31-44" href="#__codelineno-31-44"></a><span class="w">        </span><span class="c1">// 剰余演算により、front が配列先頭を越えた後に末尾へ戻るようにする</span>
+<a id="__codelineno-31-45" name="__codelineno-31-45" href="#__codelineno-31-45"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">front</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-31-46" name="__codelineno-31-46" href="#__codelineno-31-46"></a><span class="w">        </span><span class="c1">// num をキュー先頭に追加</span>
+<a id="__codelineno-31-47" name="__codelineno-31-47" href="#__codelineno-31-47"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">front</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-31-48" name="__codelineno-31-48" href="#__codelineno-31-48"></a><span class="w">        </span><span class="n">_size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-31-49" name="__codelineno-31-49" href="#__codelineno-31-49"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-50" name="__codelineno-31-50" href="#__codelineno-31-50"></a>
+<a id="__codelineno-31-51" name="__codelineno-31-51" href="#__codelineno-31-51"></a><span class="w">    </span><span class="cm">/* キュー末尾にエンキュー */</span>
+<a id="__codelineno-31-52" name="__codelineno-31-52" href="#__codelineno-31-52"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">pushLast</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-53" name="__codelineno-31-53" href="#__codelineno-31-53"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-54" name="__codelineno-31-54" href="#__codelineno-31-54"></a><span class="w">            </span><span class="bp">print</span><span class="p">(</span><span class="s">&quot;両端キューがいっぱいです&quot;</span><span class="p">)</span>
+<a id="__codelineno-31-55" name="__codelineno-31-55" href="#__codelineno-31-55"></a><span class="w">            </span><span class="k">return</span>
+<a id="__codelineno-31-56" name="__codelineno-31-56" href="#__codelineno-31-56"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-31-57" name="__codelineno-31-57" href="#__codelineno-31-57"></a><span class="w">        </span><span class="c1">// キュー末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-31-58" name="__codelineno-31-58" href="#__codelineno-31-58"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">rear</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
+<a id="__codelineno-31-59" name="__codelineno-31-59" href="#__codelineno-31-59"></a><span class="w">        </span><span class="c1">// num をキュー末尾に追加</span>
+<a id="__codelineno-31-60" name="__codelineno-31-60" href="#__codelineno-31-60"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">rear</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-31-61" name="__codelineno-31-61" href="#__codelineno-31-61"></a><span class="w">        </span><span class="n">_size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-31-62" name="__codelineno-31-62" href="#__codelineno-31-62"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-63" name="__codelineno-31-63" href="#__codelineno-31-63"></a>
+<a id="__codelineno-31-64" name="__codelineno-31-64" href="#__codelineno-31-64"></a><span class="w">    </span><span class="cm">/* キュー先頭からデキュー */</span>
+<a id="__codelineno-31-65" name="__codelineno-31-65" href="#__codelineno-31-65"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">popFirst</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-66" name="__codelineno-31-66" href="#__codelineno-31-66"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">num</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">peekFirst</span><span class="p">()</span>
+<a id="__codelineno-31-67" name="__codelineno-31-67" href="#__codelineno-31-67"></a><span class="w">        </span><span class="c1">// 先頭ポインタを 1 つ後ろへ進める</span>
+<a id="__codelineno-31-68" name="__codelineno-31-68" href="#__codelineno-31-68"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-31-69" name="__codelineno-31-69" href="#__codelineno-31-69"></a><span class="w">        </span><span class="n">_size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-31-70" name="__codelineno-31-70" href="#__codelineno-31-70"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-31-71" name="__codelineno-31-71" href="#__codelineno-31-71"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-72" name="__codelineno-31-72" href="#__codelineno-31-72"></a>
+<a id="__codelineno-31-73" name="__codelineno-31-73" href="#__codelineno-31-73"></a><span class="w">    </span><span class="cm">/* キュー末尾からデキュー */</span>
+<a id="__codelineno-31-74" name="__codelineno-31-74" href="#__codelineno-31-74"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">popLast</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-75" name="__codelineno-31-75" href="#__codelineno-31-75"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">num</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">peekLast</span><span class="p">()</span>
+<a id="__codelineno-31-76" name="__codelineno-31-76" href="#__codelineno-31-76"></a><span class="w">        </span><span class="n">_size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-31-77" name="__codelineno-31-77" href="#__codelineno-31-77"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-31-78" name="__codelineno-31-78" href="#__codelineno-31-78"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-79" name="__codelineno-31-79" href="#__codelineno-31-79"></a>
+<a id="__codelineno-31-80" name="__codelineno-31-80" href="#__codelineno-31-80"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-31-81" name="__codelineno-31-81" href="#__codelineno-31-81"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">peekFirst</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-82" name="__codelineno-31-82" href="#__codelineno-31-82"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-83" name="__codelineno-31-83" href="#__codelineno-31-83"></a><span class="w">            </span><span class="bp">fatalError</span><span class="p">(</span><span class="s">&quot;両端キューが空です&quot;</span><span class="p">)</span>
+<a id="__codelineno-31-84" name="__codelineno-31-84" href="#__codelineno-31-84"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-31-85" name="__codelineno-31-85" href="#__codelineno-31-85"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">front</span><span class="p">]</span>
+<a id="__codelineno-31-86" name="__codelineno-31-86" href="#__codelineno-31-86"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-87" name="__codelineno-31-87" href="#__codelineno-31-87"></a>
+<a id="__codelineno-31-88" name="__codelineno-31-88" href="#__codelineno-31-88"></a><span class="w">    </span><span class="cm">/* キュー末尾の要素にアクセス */</span>
+<a id="__codelineno-31-89" name="__codelineno-31-89" href="#__codelineno-31-89"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">peekLast</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-90" name="__codelineno-31-90" href="#__codelineno-31-90"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-91" name="__codelineno-31-91" href="#__codelineno-31-91"></a><span class="w">            </span><span class="bp">fatalError</span><span class="p">(</span><span class="s">&quot;両端キューが空です&quot;</span><span class="p">)</span>
+<a id="__codelineno-31-92" name="__codelineno-31-92" href="#__codelineno-31-92"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-31-93" name="__codelineno-31-93" href="#__codelineno-31-93"></a><span class="w">        </span><span class="c1">// 末尾要素のインデックスを計算</span>
+<a id="__codelineno-31-94" name="__codelineno-31-94" href="#__codelineno-31-94"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">last</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-31-95" name="__codelineno-31-95" href="#__codelineno-31-95"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="bp">last</span><span class="p">]</span>
+<a id="__codelineno-31-96" name="__codelineno-31-96" href="#__codelineno-31-96"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-97" name="__codelineno-31-97" href="#__codelineno-31-97"></a>
+<a id="__codelineno-31-98" name="__codelineno-31-98" href="#__codelineno-31-98"></a><span class="w">    </span><span class="cm">/* 出力用の配列を返す */</span>
+<a id="__codelineno-31-99" name="__codelineno-31-99" href="#__codelineno-31-99"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-100" name="__codelineno-31-100" href="#__codelineno-31-100"></a><span class="w">        </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-31-101" name="__codelineno-31-101" href="#__codelineno-31-101"></a><span class="w">        </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">size</span><span class="p">()).</span><span class="bp">map</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">index</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nv">$0</span><span class="p">)]</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-31-102" name="__codelineno-31-102" href="#__codelineno-31-102"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-103" name="__codelineno-31-103" href="#__codelineno-31-103"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_deque.ts</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_deque.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* 循環配列ベースの両端キュー */</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">ArrayDeque</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w">    </span><span class="n">#nums</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端キューの要素を格納する配列</span>
+<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="w">    </span><span class="n">#front</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ポインタ。先頭要素を指す</span>
+<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="w">    </span><span class="n">#queSize</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端キューの長さ</span>
+<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a>
+<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">capacity</span><span class="p">);</span>
+<a id="__codelineno-32-10" name="__codelineno-32-10" href="#__codelineno-32-10"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a>
+<a id="__codelineno-32-14" name="__codelineno-32-14" href="#__codelineno-32-14"></a><span class="w">    </span><span class="cm">/* 両端キューの容量を取得 */</span>
+<a id="__codelineno-32-15" name="__codelineno-32-15" href="#__codelineno-32-15"></a><span class="w">    </span><span class="nx">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-16" name="__codelineno-32-16" href="#__codelineno-32-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-32-17" name="__codelineno-32-17" href="#__codelineno-32-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-18" name="__codelineno-32-18" href="#__codelineno-32-18"></a>
+<a id="__codelineno-32-19" name="__codelineno-32-19" href="#__codelineno-32-19"></a><span class="w">    </span><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-32-20" name="__codelineno-32-20" href="#__codelineno-32-20"></a><span class="w">    </span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-21" name="__codelineno-32-21" href="#__codelineno-32-21"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="p">;</span>
+<a id="__codelineno-32-22" name="__codelineno-32-22" href="#__codelineno-32-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-23" name="__codelineno-32-23" href="#__codelineno-32-23"></a>
+<a id="__codelineno-32-24" name="__codelineno-32-24" href="#__codelineno-32-24"></a><span class="w">    </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
+<a id="__codelineno-32-25" name="__codelineno-32-25" href="#__codelineno-32-25"></a><span class="w">    </span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-26" name="__codelineno-32-26" href="#__codelineno-32-26"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-32-27" name="__codelineno-32-27" href="#__codelineno-32-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-28" name="__codelineno-32-28" href="#__codelineno-32-28"></a>
+<a id="__codelineno-32-29" name="__codelineno-32-29" href="#__codelineno-32-29"></a><span class="w">    </span><span class="cm">/* 循環配列のインデックスを計算 */</span>
+<a id="__codelineno-32-30" name="__codelineno-32-30" href="#__codelineno-32-30"></a><span class="w">    </span><span class="nx">index</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-31" name="__codelineno-32-31" href="#__codelineno-32-31"></a><span class="w">        </span><span class="c1">// 剰余演算により配列の先頭と末尾をつなげる</span>
+<a id="__codelineno-32-32" name="__codelineno-32-32" href="#__codelineno-32-32"></a><span class="w">        </span><span class="c1">// i が配列の末尾を越えたら先頭に戻る</span>
+<a id="__codelineno-32-33" name="__codelineno-32-33" href="#__codelineno-32-33"></a><span class="w">        </span><span class="c1">// i が配列の先頭を越えて前に出たら末尾に戻る</span>
+<a id="__codelineno-32-34" name="__codelineno-32-34" href="#__codelineno-32-34"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="p">())</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="p">();</span>
+<a id="__codelineno-32-35" name="__codelineno-32-35" href="#__codelineno-32-35"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-36" name="__codelineno-32-36" href="#__codelineno-32-36"></a>
+<a id="__codelineno-32-37" name="__codelineno-32-37" href="#__codelineno-32-37"></a><span class="w">    </span><span class="cm">/* キュー先頭にエンキュー */</span>
+<a id="__codelineno-32-38" name="__codelineno-32-38" href="#__codelineno-32-38"></a><span class="w">    </span><span class="nx">pushFirst</span><span class="p">(</span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-39" name="__codelineno-32-39" href="#__codelineno-32-39"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-40" name="__codelineno-32-40" href="#__codelineno-32-40"></a><span class="w">            </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="s1">&#39;両端キューがいっぱいです&#39;</span><span class="p">);</span>
+<a id="__codelineno-32-41" name="__codelineno-32-41" href="#__codelineno-32-41"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-32-42" name="__codelineno-32-42" href="#__codelineno-32-42"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-32-43" name="__codelineno-32-43" href="#__codelineno-32-43"></a><span class="w">        </span><span class="c1">// 先頭ポインタを左に 1 つ移動する</span>
+<a id="__codelineno-32-44" name="__codelineno-32-44" href="#__codelineno-32-44"></a><span class="w">        </span><span class="c1">// 剰余演算により、front が配列先頭を越えた後に末尾へ戻るようにする</span>
+<a id="__codelineno-32-45" name="__codelineno-32-45" href="#__codelineno-32-45"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">index</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-32-46" name="__codelineno-32-46" href="#__codelineno-32-46"></a><span class="w">        </span><span class="c1">// num をキュー先頭に追加</span>
+<a id="__codelineno-32-47" name="__codelineno-32-47" href="#__codelineno-32-47"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#nums</span><span class="p">[</span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-32-48" name="__codelineno-32-48" href="#__codelineno-32-48"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-32-49" name="__codelineno-32-49" href="#__codelineno-32-49"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-50" name="__codelineno-32-50" href="#__codelineno-32-50"></a>
+<a id="__codelineno-32-51" name="__codelineno-32-51" href="#__codelineno-32-51"></a><span class="w">    </span><span class="cm">/* キュー末尾にエンキュー */</span>
+<a id="__codelineno-32-52" name="__codelineno-32-52" href="#__codelineno-32-52"></a><span class="w">    </span><span class="nx">pushLast</span><span class="p">(</span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-53" name="__codelineno-32-53" href="#__codelineno-32-53"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-54" name="__codelineno-32-54" href="#__codelineno-32-54"></a><span class="w">            </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="s1">&#39;両端キューがいっぱいです&#39;</span><span class="p">);</span>
+<a id="__codelineno-32-55" name="__codelineno-32-55" href="#__codelineno-32-55"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-32-56" name="__codelineno-32-56" href="#__codelineno-32-56"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-32-57" name="__codelineno-32-57" href="#__codelineno-32-57"></a><span class="w">        </span><span class="c1">// キュー末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-32-58" name="__codelineno-32-58" href="#__codelineno-32-58"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">index</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="p">);</span>
+<a id="__codelineno-32-59" name="__codelineno-32-59" href="#__codelineno-32-59"></a><span class="w">        </span><span class="c1">// num をキュー末尾に追加</span>
+<a id="__codelineno-32-60" name="__codelineno-32-60" href="#__codelineno-32-60"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#nums</span><span class="p">[</span><span class="nx">rear</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-32-61" name="__codelineno-32-61" href="#__codelineno-32-61"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-32-62" name="__codelineno-32-62" href="#__codelineno-32-62"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-63" name="__codelineno-32-63" href="#__codelineno-32-63"></a>
+<a id="__codelineno-32-64" name="__codelineno-32-64" href="#__codelineno-32-64"></a><span class="w">    </span><span class="cm">/* キュー先頭からデキュー */</span>
+<a id="__codelineno-32-65" name="__codelineno-32-65" href="#__codelineno-32-65"></a><span class="w">    </span><span class="nx">popFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-66" name="__codelineno-32-66" href="#__codelineno-32-66"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">peekFirst</span><span class="p">();</span>
+<a id="__codelineno-32-67" name="__codelineno-32-67" href="#__codelineno-32-67"></a><span class="w">        </span><span class="c1">// 先頭ポインタを 1 つ後ろへ進める</span>
+<a id="__codelineno-32-68" name="__codelineno-32-68" href="#__codelineno-32-68"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">index</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-32-69" name="__codelineno-32-69" href="#__codelineno-32-69"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-32-70" name="__codelineno-32-70" href="#__codelineno-32-70"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-32-71" name="__codelineno-32-71" href="#__codelineno-32-71"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-72" name="__codelineno-32-72" href="#__codelineno-32-72"></a>
+<a id="__codelineno-32-73" name="__codelineno-32-73" href="#__codelineno-32-73"></a><span class="w">    </span><span class="cm">/* キュー末尾からデキュー */</span>
+<a id="__codelineno-32-74" name="__codelineno-32-74" href="#__codelineno-32-74"></a><span class="w">    </span><span class="nx">popLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-75" name="__codelineno-32-75" href="#__codelineno-32-75"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">peekLast</span><span class="p">();</span>
+<a id="__codelineno-32-76" name="__codelineno-32-76" href="#__codelineno-32-76"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-32-77" name="__codelineno-32-77" href="#__codelineno-32-77"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-32-78" name="__codelineno-32-78" href="#__codelineno-32-78"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-79" name="__codelineno-32-79" href="#__codelineno-32-79"></a>
+<a id="__codelineno-32-80" name="__codelineno-32-80" href="#__codelineno-32-80"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-32-81" name="__codelineno-32-81" href="#__codelineno-32-81"></a><span class="w">    </span><span class="nx">peekFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-82" name="__codelineno-32-82" href="#__codelineno-32-82"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;The Deque Is Empty.&#39;</span><span class="p">);</span>
+<a id="__codelineno-32-83" name="__codelineno-32-83" href="#__codelineno-32-83"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#nums</span><span class="p">[</span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="p">];</span>
+<a id="__codelineno-32-84" name="__codelineno-32-84" href="#__codelineno-32-84"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-85" name="__codelineno-32-85" href="#__codelineno-32-85"></a>
+<a id="__codelineno-32-86" name="__codelineno-32-86" href="#__codelineno-32-86"></a><span class="w">    </span><span class="cm">/* キュー末尾の要素にアクセス */</span>
+<a id="__codelineno-32-87" name="__codelineno-32-87" href="#__codelineno-32-87"></a><span class="w">    </span><span class="nx">peekLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-88" name="__codelineno-32-88" href="#__codelineno-32-88"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;The Deque Is Empty.&#39;</span><span class="p">);</span>
+<a id="__codelineno-32-89" name="__codelineno-32-89" href="#__codelineno-32-89"></a><span class="w">        </span><span class="c1">// 末尾要素のインデックスを計算</span>
+<a id="__codelineno-32-90" name="__codelineno-32-90" href="#__codelineno-32-90"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">last</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">index</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-32-91" name="__codelineno-32-91" href="#__codelineno-32-91"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#nums</span><span class="p">[</span><span class="nx">last</span><span class="p">];</span>
+<a id="__codelineno-32-92" name="__codelineno-32-92" href="#__codelineno-32-92"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-93" name="__codelineno-32-93" href="#__codelineno-32-93"></a>
+<a id="__codelineno-32-94" name="__codelineno-32-94" href="#__codelineno-32-94"></a><span class="w">    </span><span class="cm">/* 出力用の配列を返す */</span>
+<a id="__codelineno-32-95" name="__codelineno-32-95" href="#__codelineno-32-95"></a><span class="w">    </span><span class="nx">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-96" name="__codelineno-32-96" href="#__codelineno-32-96"></a><span class="w">        </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-32-97" name="__codelineno-32-97" href="#__codelineno-32-97"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-32-98" name="__codelineno-32-98" href="#__codelineno-32-98"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-99" name="__codelineno-32-99" href="#__codelineno-32-99"></a><span class="w">            </span><span class="nx">res</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#nums</span><span class="p">[</span><span class="k">this</span><span class="p">.</span><span class="nx">index</span><span class="p">(</span><span class="nx">j</span><span class="p">)];</span>
+<a id="__codelineno-32-100" name="__codelineno-32-100" href="#__codelineno-32-100"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-32-101" name="__codelineno-32-101" href="#__codelineno-32-101"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-32-102" name="__codelineno-32-102" href="#__codelineno-32-102"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-103" name="__codelineno-32-103" href="#__codelineno-32-103"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_deque.dart</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_deque.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* 循環配列ベースの両端キュー */</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">ArrayDeque</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[];</span><span class="w"> </span><span class="c1">// 両端キューの要素を格納する配列</span>
+<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">front</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ポインタ。先頭要素を指す</span>
+<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">queSize</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端キューの長さ</span>
+<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a>
+<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">capacity</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">capacity</span><span class="p">);</span>
+<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a>
+<a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a><span class="w">    </span><span class="cm">/* 両端キューの容量を取得 */</span>
+<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a><span class="w">    </span><span class="nx">capacity</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-16" name="__codelineno-33-16" href="#__codelineno-33-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-33-17" name="__codelineno-33-17" href="#__codelineno-33-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-18" name="__codelineno-33-18" href="#__codelineno-33-18"></a>
+<a id="__codelineno-33-19" name="__codelineno-33-19" href="#__codelineno-33-19"></a><span class="w">    </span><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-33-20" name="__codelineno-33-20" href="#__codelineno-33-20"></a><span class="w">    </span><span class="nx">size</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-21" name="__codelineno-33-21" href="#__codelineno-33-21"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="p">;</span>
+<a id="__codelineno-33-22" name="__codelineno-33-22" href="#__codelineno-33-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-23" name="__codelineno-33-23" href="#__codelineno-33-23"></a>
+<a id="__codelineno-33-24" name="__codelineno-33-24" href="#__codelineno-33-24"></a><span class="w">    </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
+<a id="__codelineno-33-25" name="__codelineno-33-25" href="#__codelineno-33-25"></a><span class="w">    </span><span class="nx">isEmpty</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-26" name="__codelineno-33-26" href="#__codelineno-33-26"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-33-27" name="__codelineno-33-27" href="#__codelineno-33-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-28" name="__codelineno-33-28" href="#__codelineno-33-28"></a>
+<a id="__codelineno-33-29" name="__codelineno-33-29" href="#__codelineno-33-29"></a><span class="w">    </span><span class="cm">/* 循環配列のインデックスを計算 */</span>
+<a id="__codelineno-33-30" name="__codelineno-33-30" href="#__codelineno-33-30"></a><span class="w">    </span><span class="nx">index</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-31" name="__codelineno-33-31" href="#__codelineno-33-31"></a><span class="w">        </span><span class="c1">// 剰余演算により配列の先頭と末尾をつなげる</span>
+<a id="__codelineno-33-32" name="__codelineno-33-32" href="#__codelineno-33-32"></a><span class="w">        </span><span class="c1">// i が配列の末尾を越えたら先頭に戻る</span>
+<a id="__codelineno-33-33" name="__codelineno-33-33" href="#__codelineno-33-33"></a><span class="w">        </span><span class="c1">// i が配列の先頭を越えて前に出たら末尾に戻る</span>
+<a id="__codelineno-33-34" name="__codelineno-33-34" href="#__codelineno-33-34"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="p">())</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="p">();</span>
+<a id="__codelineno-33-35" name="__codelineno-33-35" href="#__codelineno-33-35"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-36" name="__codelineno-33-36" href="#__codelineno-33-36"></a>
+<a id="__codelineno-33-37" name="__codelineno-33-37" href="#__codelineno-33-37"></a><span class="w">    </span><span class="cm">/* キュー先頭にエンキュー */</span>
+<a id="__codelineno-33-38" name="__codelineno-33-38" href="#__codelineno-33-38"></a><span class="w">    </span><span class="nx">pushFirst</span><span class="p">(</span><span class="nx">num</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-39" name="__codelineno-33-39" href="#__codelineno-33-39"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-40" name="__codelineno-33-40" href="#__codelineno-33-40"></a><span class="w">            </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="s1">&#39;両端キューは満杯です&#39;</span><span class="p">);</span>
+<a id="__codelineno-33-41" name="__codelineno-33-41" href="#__codelineno-33-41"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-33-42" name="__codelineno-33-42" href="#__codelineno-33-42"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-33-43" name="__codelineno-33-43" href="#__codelineno-33-43"></a><span class="w">        </span><span class="c1">// 先頭ポインタを左に 1 つ移動する</span>
+<a id="__codelineno-33-44" name="__codelineno-33-44" href="#__codelineno-33-44"></a><span class="w">        </span><span class="c1">// 剰余演算により、front が配列先頭を越えた後に末尾へ戻るようにする</span>
+<a id="__codelineno-33-45" name="__codelineno-33-45" href="#__codelineno-33-45"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">index</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-33-46" name="__codelineno-33-46" href="#__codelineno-33-46"></a><span class="w">        </span><span class="c1">// num をキュー先頭に追加</span>
+<a id="__codelineno-33-47" name="__codelineno-33-47" href="#__codelineno-33-47"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">nums</span><span class="p">[</span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-33-48" name="__codelineno-33-48" href="#__codelineno-33-48"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-33-49" name="__codelineno-33-49" href="#__codelineno-33-49"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-50" name="__codelineno-33-50" href="#__codelineno-33-50"></a>
+<a id="__codelineno-33-51" name="__codelineno-33-51" href="#__codelineno-33-51"></a><span class="w">    </span><span class="cm">/* キュー末尾にエンキュー */</span>
+<a id="__codelineno-33-52" name="__codelineno-33-52" href="#__codelineno-33-52"></a><span class="w">    </span><span class="nx">pushLast</span><span class="p">(</span><span class="nx">num</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-53" name="__codelineno-33-53" href="#__codelineno-33-53"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-54" name="__codelineno-33-54" href="#__codelineno-33-54"></a><span class="w">            </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="s1">&#39;両端キューは満杯です&#39;</span><span class="p">);</span>
+<a id="__codelineno-33-55" name="__codelineno-33-55" href="#__codelineno-33-55"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-33-56" name="__codelineno-33-56" href="#__codelineno-33-56"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-33-57" name="__codelineno-33-57" href="#__codelineno-33-57"></a><span class="w">        </span><span class="c1">// キュー末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-33-58" name="__codelineno-33-58" href="#__codelineno-33-58"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">rear</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">index</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="p">);</span>
+<a id="__codelineno-33-59" name="__codelineno-33-59" href="#__codelineno-33-59"></a><span class="w">        </span><span class="c1">// num をキュー末尾に追加</span>
+<a id="__codelineno-33-60" name="__codelineno-33-60" href="#__codelineno-33-60"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">nums</span><span class="p">[</span><span class="nx">rear</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-33-61" name="__codelineno-33-61" href="#__codelineno-33-61"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-33-62" name="__codelineno-33-62" href="#__codelineno-33-62"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-63" name="__codelineno-33-63" href="#__codelineno-33-63"></a>
+<a id="__codelineno-33-64" name="__codelineno-33-64" href="#__codelineno-33-64"></a><span class="w">    </span><span class="cm">/* キュー先頭からデキュー */</span>
+<a id="__codelineno-33-65" name="__codelineno-33-65" href="#__codelineno-33-65"></a><span class="w">    </span><span class="nx">popFirst</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-66" name="__codelineno-33-66" href="#__codelineno-33-66"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">peekFirst</span><span class="p">();</span>
+<a id="__codelineno-33-67" name="__codelineno-33-67" href="#__codelineno-33-67"></a><span class="w">        </span><span class="c1">// 先頭ポインタを 1 つ後ろへ進める</span>
+<a id="__codelineno-33-68" name="__codelineno-33-68" href="#__codelineno-33-68"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">index</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-33-69" name="__codelineno-33-69" href="#__codelineno-33-69"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-33-70" name="__codelineno-33-70" href="#__codelineno-33-70"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-33-71" name="__codelineno-33-71" href="#__codelineno-33-71"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-72" name="__codelineno-33-72" href="#__codelineno-33-72"></a>
+<a id="__codelineno-33-73" name="__codelineno-33-73" href="#__codelineno-33-73"></a><span class="w">    </span><span class="cm">/* キュー末尾からデキュー */</span>
+<a id="__codelineno-33-74" name="__codelineno-33-74" href="#__codelineno-33-74"></a><span class="w">    </span><span class="nx">popLast</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-75" name="__codelineno-33-75" href="#__codelineno-33-75"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">peekLast</span><span class="p">();</span>
+<a id="__codelineno-33-76" name="__codelineno-33-76" href="#__codelineno-33-76"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-33-77" name="__codelineno-33-77" href="#__codelineno-33-77"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-33-78" name="__codelineno-33-78" href="#__codelineno-33-78"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-79" name="__codelineno-33-79" href="#__codelineno-33-79"></a>
+<a id="__codelineno-33-80" name="__codelineno-33-80" href="#__codelineno-33-80"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-33-81" name="__codelineno-33-81" href="#__codelineno-33-81"></a><span class="w">    </span><span class="nx">peekFirst</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-82" name="__codelineno-33-82" href="#__codelineno-33-82"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;The Deque Is Empty.&#39;</span><span class="p">);</span>
+<a id="__codelineno-33-83" name="__codelineno-33-83" href="#__codelineno-33-83"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">nums</span><span class="p">[</span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="p">];</span>
+<a id="__codelineno-33-84" name="__codelineno-33-84" href="#__codelineno-33-84"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-85" name="__codelineno-33-85" href="#__codelineno-33-85"></a>
+<a id="__codelineno-33-86" name="__codelineno-33-86" href="#__codelineno-33-86"></a><span class="w">    </span><span class="cm">/* キュー末尾の要素にアクセス */</span>
+<a id="__codelineno-33-87" name="__codelineno-33-87" href="#__codelineno-33-87"></a><span class="w">    </span><span class="nx">peekLast</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-88" name="__codelineno-33-88" href="#__codelineno-33-88"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;The Deque Is Empty.&#39;</span><span class="p">);</span>
+<a id="__codelineno-33-89" name="__codelineno-33-89" href="#__codelineno-33-89"></a><span class="w">        </span><span class="c1">// 末尾要素のインデックスを計算</span>
+<a id="__codelineno-33-90" name="__codelineno-33-90" href="#__codelineno-33-90"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">last</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">index</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-33-91" name="__codelineno-33-91" href="#__codelineno-33-91"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">nums</span><span class="p">[</span><span class="nx">last</span><span class="p">];</span>
+<a id="__codelineno-33-92" name="__codelineno-33-92" href="#__codelineno-33-92"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-93" name="__codelineno-33-93" href="#__codelineno-33-93"></a>
+<a id="__codelineno-33-94" name="__codelineno-33-94" href="#__codelineno-33-94"></a><span class="w">    </span><span class="cm">/* 出力用の配列を返す */</span>
+<a id="__codelineno-33-95" name="__codelineno-33-95" href="#__codelineno-33-95"></a><span class="w">    </span><span class="nx">toArray</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-96" name="__codelineno-33-96" href="#__codelineno-33-96"></a><span class="w">        </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-33-97" name="__codelineno-33-97" href="#__codelineno-33-97"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-33-98" name="__codelineno-33-98" href="#__codelineno-33-98"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-99" name="__codelineno-33-99" href="#__codelineno-33-99"></a><span class="w">            </span><span class="nx">res</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">nums</span><span class="p">[</span><span class="k">this</span><span class="p">.</span><span class="nx">index</span><span class="p">(</span><span class="nx">j</span><span class="p">)];</span>
+<a id="__codelineno-33-100" name="__codelineno-33-100" href="#__codelineno-33-100"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-33-101" name="__codelineno-33-101" href="#__codelineno-33-101"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-33-102" name="__codelineno-33-102" href="#__codelineno-33-102"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-103" name="__codelineno-33-103" href="#__codelineno-33-103"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_deque.rs</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_deque.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* 循環配列ベースの両端キュー */</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ArrayDeque</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w">  </span><span class="kd">late</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">_nums</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端キューの要素を格納する配列</span>
+<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w">  </span><span class="kd">late</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">_front</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ポインタ。先頭要素を指す</span>
+<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w">  </span><span class="kd">late</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">_queSize</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端キューの長さ</span>
+<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a>
+<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w">  </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w">  </span><span class="n">ArrayDeque</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="n">_nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">capacity</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-34-10" name="__codelineno-34-10" href="#__codelineno-34-10"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="n">_front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">_queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-34-11" name="__codelineno-34-11" href="#__codelineno-34-11"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-12" name="__codelineno-34-12" href="#__codelineno-34-12"></a>
+<a id="__codelineno-34-13" name="__codelineno-34-13" href="#__codelineno-34-13"></a><span class="w">  </span><span class="cm">/* 両端キューの容量を取得 */</span>
+<a id="__codelineno-34-14" name="__codelineno-34-14" href="#__codelineno-34-14"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-15" name="__codelineno-34-15" href="#__codelineno-34-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_nums</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-34-16" name="__codelineno-34-16" href="#__codelineno-34-16"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-17" name="__codelineno-34-17" href="#__codelineno-34-17"></a>
+<a id="__codelineno-34-18" name="__codelineno-34-18" href="#__codelineno-34-18"></a><span class="w">  </span><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-34-19" name="__codelineno-34-19" href="#__codelineno-34-19"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-20" name="__codelineno-34-20" href="#__codelineno-34-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_queSize</span><span class="p">;</span>
+<a id="__codelineno-34-21" name="__codelineno-34-21" href="#__codelineno-34-21"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-22" name="__codelineno-34-22" href="#__codelineno-34-22"></a>
+<a id="__codelineno-34-23" name="__codelineno-34-23" href="#__codelineno-34-23"></a><span class="w">  </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
+<a id="__codelineno-34-24" name="__codelineno-34-24" href="#__codelineno-34-24"></a><span class="w">  </span><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-25" name="__codelineno-34-25" href="#__codelineno-34-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-34-26" name="__codelineno-34-26" href="#__codelineno-34-26"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-27" name="__codelineno-34-27" href="#__codelineno-34-27"></a>
+<a id="__codelineno-34-28" name="__codelineno-34-28" href="#__codelineno-34-28"></a><span class="w">  </span><span class="cm">/* 循環配列のインデックスを計算 */</span>
+<a id="__codelineno-34-29" name="__codelineno-34-29" href="#__codelineno-34-29"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-30" name="__codelineno-34-30" href="#__codelineno-34-30"></a><span class="w">    </span><span class="c1">// 剰余演算により配列の先頭と末尾をつなげる</span>
+<a id="__codelineno-34-31" name="__codelineno-34-31" href="#__codelineno-34-31"></a><span class="w">    </span><span class="c1">// i が配列の末尾を越えたら先頭に戻る</span>
+<a id="__codelineno-34-32" name="__codelineno-34-32" href="#__codelineno-34-32"></a><span class="w">    </span><span class="c1">// i が配列の先頭を越えて前に出たら末尾に戻る</span>
+<a id="__codelineno-34-33" name="__codelineno-34-33" href="#__codelineno-34-33"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">();</span>
+<a id="__codelineno-34-34" name="__codelineno-34-34" href="#__codelineno-34-34"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-35" name="__codelineno-34-35" href="#__codelineno-34-35"></a>
+<a id="__codelineno-34-36" name="__codelineno-34-36" href="#__codelineno-34-36"></a><span class="w">  </span><span class="cm">/* キュー先頭にエンキュー */</span>
+<a id="__codelineno-34-37" name="__codelineno-34-37" href="#__codelineno-34-37"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">pushFirst</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-38" name="__codelineno-34-38" href="#__codelineno-34-38"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-39" name="__codelineno-34-39" href="#__codelineno-34-39"></a><span class="w">      </span><span class="k">throw</span><span class="w"> </span><span class="n">Exception</span><span class="p">(</span><span class="s2">&quot;両端キューがいっぱいです&quot;</span><span class="p">);</span>
+<a id="__codelineno-34-40" name="__codelineno-34-40" href="#__codelineno-34-40"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-41" name="__codelineno-34-41" href="#__codelineno-34-41"></a><span class="w">    </span><span class="c1">// 先頭ポインタを左に 1 つ移動する</span>
+<a id="__codelineno-34-42" name="__codelineno-34-42" href="#__codelineno-34-42"></a><span class="w">    </span><span class="c1">// 剰余演算により _front が配列の先頭を越えたあと末尾に戻るようにする</span>
+<a id="__codelineno-34-43" name="__codelineno-34-43" href="#__codelineno-34-43"></a><span class="w">    </span><span class="n">_front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">_front</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-34-44" name="__codelineno-34-44" href="#__codelineno-34-44"></a><span class="w">    </span><span class="c1">// _num をキューの先頭に追加</span>
+<a id="__codelineno-34-45" name="__codelineno-34-45" href="#__codelineno-34-45"></a><span class="w">    </span><span class="n">_nums</span><span class="p">[</span><span class="n">_front</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_num</span><span class="p">;</span>
+<a id="__codelineno-34-46" name="__codelineno-34-46" href="#__codelineno-34-46"></a><span class="w">    </span><span class="n">_queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-34-47" name="__codelineno-34-47" href="#__codelineno-34-47"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-48" name="__codelineno-34-48" href="#__codelineno-34-48"></a>
+<a id="__codelineno-34-49" name="__codelineno-34-49" href="#__codelineno-34-49"></a><span class="w">  </span><span class="cm">/* キュー末尾にエンキュー */</span>
+<a id="__codelineno-34-50" name="__codelineno-34-50" href="#__codelineno-34-50"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">pushLast</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-51" name="__codelineno-34-51" href="#__codelineno-34-51"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-52" name="__codelineno-34-52" href="#__codelineno-34-52"></a><span class="w">      </span><span class="k">throw</span><span class="w"> </span><span class="n">Exception</span><span class="p">(</span><span class="s2">&quot;両端キューがいっぱいです&quot;</span><span class="p">);</span>
+<a id="__codelineno-34-53" name="__codelineno-34-53" href="#__codelineno-34-53"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-54" name="__codelineno-34-54" href="#__codelineno-34-54"></a><span class="w">    </span><span class="c1">// キュー末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-34-55" name="__codelineno-34-55" href="#__codelineno-34-55"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">_front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">_queSize</span><span class="p">);</span>
+<a id="__codelineno-34-56" name="__codelineno-34-56" href="#__codelineno-34-56"></a><span class="w">    </span><span class="c1">// _num をキュー末尾に追加</span>
+<a id="__codelineno-34-57" name="__codelineno-34-57" href="#__codelineno-34-57"></a><span class="w">    </span><span class="n">_nums</span><span class="p">[</span><span class="n">rear</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_num</span><span class="p">;</span>
+<a id="__codelineno-34-58" name="__codelineno-34-58" href="#__codelineno-34-58"></a><span class="w">    </span><span class="n">_queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-34-59" name="__codelineno-34-59" href="#__codelineno-34-59"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-60" name="__codelineno-34-60" href="#__codelineno-34-60"></a>
+<a id="__codelineno-34-61" name="__codelineno-34-61" href="#__codelineno-34-61"></a><span class="w">  </span><span class="cm">/* キュー先頭からデキュー */</span>
+<a id="__codelineno-34-62" name="__codelineno-34-62" href="#__codelineno-34-62"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">popFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-63" name="__codelineno-34-63" href="#__codelineno-34-63"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peekFirst</span><span class="p">();</span>
+<a id="__codelineno-34-64" name="__codelineno-34-64" href="#__codelineno-34-64"></a><span class="w">    </span><span class="c1">// 先頭ポインタを右に 1 つ移動する</span>
+<a id="__codelineno-34-65" name="__codelineno-34-65" href="#__codelineno-34-65"></a><span class="w">    </span><span class="n">_front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">_front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-34-66" name="__codelineno-34-66" href="#__codelineno-34-66"></a><span class="w">    </span><span class="n">_queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-34-67" name="__codelineno-34-67" href="#__codelineno-34-67"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_num</span><span class="p">;</span>
+<a id="__codelineno-34-68" name="__codelineno-34-68" href="#__codelineno-34-68"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-69" name="__codelineno-34-69" href="#__codelineno-34-69"></a>
+<a id="__codelineno-34-70" name="__codelineno-34-70" href="#__codelineno-34-70"></a><span class="w">  </span><span class="cm">/* キュー末尾からデキュー */</span>
+<a id="__codelineno-34-71" name="__codelineno-34-71" href="#__codelineno-34-71"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">popLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-72" name="__codelineno-34-72" href="#__codelineno-34-72"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peekLast</span><span class="p">();</span>
+<a id="__codelineno-34-73" name="__codelineno-34-73" href="#__codelineno-34-73"></a><span class="w">    </span><span class="n">_queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-34-74" name="__codelineno-34-74" href="#__codelineno-34-74"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_num</span><span class="p">;</span>
+<a id="__codelineno-34-75" name="__codelineno-34-75" href="#__codelineno-34-75"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-76" name="__codelineno-34-76" href="#__codelineno-34-76"></a>
+<a id="__codelineno-34-77" name="__codelineno-34-77" href="#__codelineno-34-77"></a><span class="w">  </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-34-78" name="__codelineno-34-78" href="#__codelineno-34-78"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">peekFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-79" name="__codelineno-34-79" href="#__codelineno-34-79"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-80" name="__codelineno-34-80" href="#__codelineno-34-80"></a><span class="w">      </span><span class="k">throw</span><span class="w"> </span><span class="n">Exception</span><span class="p">(</span><span class="s2">&quot;両端キューが空です&quot;</span><span class="p">);</span>
+<a id="__codelineno-34-81" name="__codelineno-34-81" href="#__codelineno-34-81"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-82" name="__codelineno-34-82" href="#__codelineno-34-82"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_nums</span><span class="p">[</span><span class="n">_front</span><span class="p">];</span>
+<a id="__codelineno-34-83" name="__codelineno-34-83" href="#__codelineno-34-83"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-84" name="__codelineno-34-84" href="#__codelineno-34-84"></a>
+<a id="__codelineno-34-85" name="__codelineno-34-85" href="#__codelineno-34-85"></a><span class="w">  </span><span class="cm">/* キュー末尾の要素にアクセス */</span>
+<a id="__codelineno-34-86" name="__codelineno-34-86" href="#__codelineno-34-86"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">peekLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-87" name="__codelineno-34-87" href="#__codelineno-34-87"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-88" name="__codelineno-34-88" href="#__codelineno-34-88"></a><span class="w">      </span><span class="k">throw</span><span class="w"> </span><span class="n">Exception</span><span class="p">(</span><span class="s2">&quot;両端キューが空です&quot;</span><span class="p">);</span>
+<a id="__codelineno-34-89" name="__codelineno-34-89" href="#__codelineno-34-89"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-90" name="__codelineno-34-90" href="#__codelineno-34-90"></a><span class="w">    </span><span class="c1">// 末尾要素のインデックスを計算</span>
+<a id="__codelineno-34-91" name="__codelineno-34-91" href="#__codelineno-34-91"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">last</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">_front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">_queSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-34-92" name="__codelineno-34-92" href="#__codelineno-34-92"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_nums</span><span class="p">[</span><span class="n">last</span><span class="p">];</span>
+<a id="__codelineno-34-93" name="__codelineno-34-93" href="#__codelineno-34-93"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-94" name="__codelineno-34-94" href="#__codelineno-34-94"></a>
+<a id="__codelineno-34-95" name="__codelineno-34-95" href="#__codelineno-34-95"></a><span class="w">  </span><span class="cm">/* 出力用の配列を返す */</span>
+<a id="__codelineno-34-96" name="__codelineno-34-96" href="#__codelineno-34-96"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-97" name="__codelineno-34-97" href="#__codelineno-34-97"></a><span class="w">    </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-34-98" name="__codelineno-34-98" href="#__codelineno-34-98"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">_queSize</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-34-99" name="__codelineno-34-99" href="#__codelineno-34-99"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_front</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">_queSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-100" name="__codelineno-34-100" href="#__codelineno-34-100"></a><span class="w">      </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_nums</span><span class="p">[</span><span class="n">index</span><span class="p">(</span><span class="n">j</span><span class="p">)];</span>
+<a id="__codelineno-34-101" name="__codelineno-34-101" href="#__codelineno-34-101"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-102" name="__codelineno-34-102" href="#__codelineno-34-102"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-34-103" name="__codelineno-34-103" href="#__codelineno-34-103"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-104" name="__codelineno-34-104" href="#__codelineno-34-104"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_deque.c</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_deque.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* 循環配列ベースの両端キュー */</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">ArrayDeque</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w">    </span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="p">,</span><span class="w">    </span><span class="c1">// 両端キューの要素を格納する配列</span>
+<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="w">    </span><span class="n">front</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w">    </span><span class="c1">// 先頭ポインタ。先頭要素を指す</span>
+<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="w">    </span><span class="n">que_size</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="c1">// 両端キューの長さ</span>
+<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="p">}</span>
+<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a>
+<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="k">impl</span><span class="o">&lt;</span><span class="n">T</span><span class="p">:</span><span class="w"> </span><span class="nb">Copy</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nb">Default</span><span class="o">&gt;</span><span class="w"> </span><span class="n">ArrayDeque</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">new</span><span class="p">(</span><span class="n">capacity</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a><span class="w">        </span><span class="bp">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-12" name="__codelineno-35-12" href="#__codelineno-35-12"></a><span class="w">            </span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="nc">vec</span><span class="o">!</span><span class="p">[</span><span class="n">T</span><span class="p">::</span><span class="n">default</span><span class="p">();</span><span class="w"> </span><span class="n">capacity</span><span class="p">],</span>
+<a id="__codelineno-35-13" name="__codelineno-35-13" href="#__codelineno-35-13"></a><span class="w">            </span><span class="n">front</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span>
+<a id="__codelineno-35-14" name="__codelineno-35-14" href="#__codelineno-35-14"></a><span class="w">            </span><span class="n">que_size</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span>
+<a id="__codelineno-35-15" name="__codelineno-35-15" href="#__codelineno-35-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-35-16" name="__codelineno-35-16" href="#__codelineno-35-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-17" name="__codelineno-35-17" href="#__codelineno-35-17"></a>
+<a id="__codelineno-35-18" name="__codelineno-35-18" href="#__codelineno-35-18"></a><span class="w">    </span><span class="cm">/* 両端キューの容量を取得 */</span>
+<a id="__codelineno-35-19" name="__codelineno-35-19" href="#__codelineno-35-19"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">capacity</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-20" name="__codelineno-35-20" href="#__codelineno-35-20"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()</span>
+<a id="__codelineno-35-21" name="__codelineno-35-21" href="#__codelineno-35-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-22" name="__codelineno-35-22" href="#__codelineno-35-22"></a>
+<a id="__codelineno-35-23" name="__codelineno-35-23" href="#__codelineno-35-23"></a><span class="w">    </span><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-35-24" name="__codelineno-35-24" href="#__codelineno-35-24"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-25" name="__codelineno-35-25" href="#__codelineno-35-25"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span>
+<a id="__codelineno-35-26" name="__codelineno-35-26" href="#__codelineno-35-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-27" name="__codelineno-35-27" href="#__codelineno-35-27"></a>
+<a id="__codelineno-35-28" name="__codelineno-35-28" href="#__codelineno-35-28"></a><span class="w">    </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
+<a id="__codelineno-35-29" name="__codelineno-35-29" href="#__codelineno-35-29"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">is_empty</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-30" name="__codelineno-35-30" href="#__codelineno-35-30"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-35-31" name="__codelineno-35-31" href="#__codelineno-35-31"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-32" name="__codelineno-35-32" href="#__codelineno-35-32"></a>
+<a id="__codelineno-35-33" name="__codelineno-35-33" href="#__codelineno-35-33"></a><span class="w">    </span><span class="cm">/* 循環配列のインデックスを計算 */</span>
+<a id="__codelineno-35-34" name="__codelineno-35-34" href="#__codelineno-35-34"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">index</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-35" name="__codelineno-35-35" href="#__codelineno-35-35"></a><span class="w">        </span><span class="c1">// 剰余演算により配列の先頭と末尾をつなげる</span>
+<a id="__codelineno-35-36" name="__codelineno-35-36" href="#__codelineno-35-36"></a><span class="w">        </span><span class="c1">// i が配列の末尾を越えたら先頭に戻る</span>
+<a id="__codelineno-35-37" name="__codelineno-35-37" href="#__codelineno-35-37"></a><span class="w">        </span><span class="c1">// i が配列の先頭を越えて前に出たら末尾に戻る</span>
+<a id="__codelineno-35-38" name="__codelineno-35-38" href="#__codelineno-35-38"></a><span class="w">        </span><span class="p">((</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span>
+<a id="__codelineno-35-39" name="__codelineno-35-39" href="#__codelineno-35-39"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-40" name="__codelineno-35-40" href="#__codelineno-35-40"></a>
+<a id="__codelineno-35-41" name="__codelineno-35-41" href="#__codelineno-35-41"></a><span class="w">    </span><span class="cm">/* キュー先頭にエンキュー */</span>
+<a id="__codelineno-35-42" name="__codelineno-35-42" href="#__codelineno-35-42"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">push_first</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nc">T</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-43" name="__codelineno-35-43" href="#__codelineno-35-43"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-44" name="__codelineno-35-44" href="#__codelineno-35-44"></a><span class="w">            </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;両端キューがいっぱいです&quot;</span><span class="p">);</span>
+<a id="__codelineno-35-45" name="__codelineno-35-45" href="#__codelineno-35-45"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-35-46" name="__codelineno-35-46" href="#__codelineno-35-46"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-35-47" name="__codelineno-35-47" href="#__codelineno-35-47"></a><span class="w">        </span><span class="c1">// 先頭ポインタを左に 1 つ移動する</span>
+<a id="__codelineno-35-48" name="__codelineno-35-48" href="#__codelineno-35-48"></a><span class="w">        </span><span class="c1">// 剰余演算により、front が配列先頭を越えた後に末尾へ戻るようにする</span>
+<a id="__codelineno-35-49" name="__codelineno-35-49" href="#__codelineno-35-49"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-35-50" name="__codelineno-35-50" href="#__codelineno-35-50"></a><span class="w">        </span><span class="c1">// num をキュー先頭に追加</span>
+<a id="__codelineno-35-51" name="__codelineno-35-51" href="#__codelineno-35-51"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">nums</span><span class="p">[</span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-35-52" name="__codelineno-35-52" href="#__codelineno-35-52"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-35-53" name="__codelineno-35-53" href="#__codelineno-35-53"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-54" name="__codelineno-35-54" href="#__codelineno-35-54"></a>
+<a id="__codelineno-35-55" name="__codelineno-35-55" href="#__codelineno-35-55"></a><span class="w">    </span><span class="cm">/* キュー末尾にエンキュー */</span>
+<a id="__codelineno-35-56" name="__codelineno-35-56" href="#__codelineno-35-56"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">push_last</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nc">T</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-57" name="__codelineno-35-57" href="#__codelineno-35-57"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-58" name="__codelineno-35-58" href="#__codelineno-35-58"></a><span class="w">            </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;両端キューがいっぱいです&quot;</span><span class="p">);</span>
+<a id="__codelineno-35-59" name="__codelineno-35-59" href="#__codelineno-35-59"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-35-60" name="__codelineno-35-60" href="#__codelineno-35-60"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-35-61" name="__codelineno-35-61" href="#__codelineno-35-61"></a><span class="w">        </span><span class="c1">// キュー末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-35-62" name="__codelineno-35-62" href="#__codelineno-35-62"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">);</span>
+<a id="__codelineno-35-63" name="__codelineno-35-63" href="#__codelineno-35-63"></a><span class="w">        </span><span class="c1">// num をキュー末尾に追加</span>
+<a id="__codelineno-35-64" name="__codelineno-35-64" href="#__codelineno-35-64"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">nums</span><span class="p">[</span><span class="n">rear</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-35-65" name="__codelineno-35-65" href="#__codelineno-35-65"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-35-66" name="__codelineno-35-66" href="#__codelineno-35-66"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-67" name="__codelineno-35-67" href="#__codelineno-35-67"></a>
+<a id="__codelineno-35-68" name="__codelineno-35-68" href="#__codelineno-35-68"></a><span class="w">    </span><span class="cm">/* キュー先頭からデキュー */</span>
+<a id="__codelineno-35-69" name="__codelineno-35-69" href="#__codelineno-35-69"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">pop_first</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">T</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-70" name="__codelineno-35-70" href="#__codelineno-35-70"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">peek_first</span><span class="p">();</span>
+<a id="__codelineno-35-71" name="__codelineno-35-71" href="#__codelineno-35-71"></a><span class="w">        </span><span class="c1">// 先頭ポインタを 1 つ後ろへ進める</span>
+<a id="__codelineno-35-72" name="__codelineno-35-72" href="#__codelineno-35-72"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-35-73" name="__codelineno-35-73" href="#__codelineno-35-73"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-35-74" name="__codelineno-35-74" href="#__codelineno-35-74"></a><span class="w">        </span><span class="n">num</span>
+<a id="__codelineno-35-75" name="__codelineno-35-75" href="#__codelineno-35-75"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-76" name="__codelineno-35-76" href="#__codelineno-35-76"></a>
+<a id="__codelineno-35-77" name="__codelineno-35-77" href="#__codelineno-35-77"></a><span class="w">    </span><span class="cm">/* キュー末尾からデキュー */</span>
+<a id="__codelineno-35-78" name="__codelineno-35-78" href="#__codelineno-35-78"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">pop_last</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">T</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-79" name="__codelineno-35-79" href="#__codelineno-35-79"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">peek_last</span><span class="p">();</span>
+<a id="__codelineno-35-80" name="__codelineno-35-80" href="#__codelineno-35-80"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-35-81" name="__codelineno-35-81" href="#__codelineno-35-81"></a><span class="w">        </span><span class="n">num</span>
+<a id="__codelineno-35-82" name="__codelineno-35-82" href="#__codelineno-35-82"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-83" name="__codelineno-35-83" href="#__codelineno-35-83"></a>
+<a id="__codelineno-35-84" name="__codelineno-35-84" href="#__codelineno-35-84"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-35-85" name="__codelineno-35-85" href="#__codelineno-35-85"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">peek_first</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">T</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-86" name="__codelineno-35-86" href="#__codelineno-35-86"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">is_empty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-87" name="__codelineno-35-87" href="#__codelineno-35-87"></a><span class="w">            </span><span class="fm">panic!</span><span class="p">(</span><span class="s">&quot;両端キューが空です&quot;</span><span class="p">)</span>
+<a id="__codelineno-35-88" name="__codelineno-35-88" href="#__codelineno-35-88"></a><span class="w">        </span><span class="p">};</span>
+<a id="__codelineno-35-89" name="__codelineno-35-89" href="#__codelineno-35-89"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">nums</span><span class="p">[</span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="p">]</span>
+<a id="__codelineno-35-90" name="__codelineno-35-90" href="#__codelineno-35-90"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-91" name="__codelineno-35-91" href="#__codelineno-35-91"></a>
+<a id="__codelineno-35-92" name="__codelineno-35-92" href="#__codelineno-35-92"></a><span class="w">    </span><span class="cm">/* キュー末尾の要素にアクセス */</span>
+<a id="__codelineno-35-93" name="__codelineno-35-93" href="#__codelineno-35-93"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">peek_last</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">T</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-94" name="__codelineno-35-94" href="#__codelineno-35-94"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">is_empty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-95" name="__codelineno-35-95" href="#__codelineno-35-95"></a><span class="w">            </span><span class="fm">panic!</span><span class="p">(</span><span class="s">&quot;両端キューが空です&quot;</span><span class="p">)</span>
+<a id="__codelineno-35-96" name="__codelineno-35-96" href="#__codelineno-35-96"></a><span class="w">        </span><span class="p">};</span>
+<a id="__codelineno-35-97" name="__codelineno-35-97" href="#__codelineno-35-97"></a><span class="w">        </span><span class="c1">// 末尾要素のインデックスを計算</span>
+<a id="__codelineno-35-98" name="__codelineno-35-98" href="#__codelineno-35-98"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">last</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-35-99" name="__codelineno-35-99" href="#__codelineno-35-99"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">nums</span><span class="p">[</span><span class="n">last</span><span class="p">]</span>
+<a id="__codelineno-35-100" name="__codelineno-35-100" href="#__codelineno-35-100"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-101" name="__codelineno-35-101" href="#__codelineno-35-101"></a>
+<a id="__codelineno-35-102" name="__codelineno-35-102" href="#__codelineno-35-102"></a><span class="w">    </span><span class="cm">/* 出力用の配列を返す */</span>
+<a id="__codelineno-35-103" name="__codelineno-35-103" href="#__codelineno-35-103"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">to_array</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-104" name="__codelineno-35-104" href="#__codelineno-35-104"></a><span class="w">        </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-35-105" name="__codelineno-35-105" href="#__codelineno-35-105"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="n">T</span><span class="p">::</span><span class="n">default</span><span class="p">();</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="p">];</span>
+<a id="__codelineno-35-106" name="__codelineno-35-106" href="#__codelineno-35-106"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-35-107" name="__codelineno-35-107" href="#__codelineno-35-107"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-108" name="__codelineno-35-108" href="#__codelineno-35-108"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">nums</span><span class="p">[</span><span class="bp">self</span><span class="p">.</span><span class="n">index</span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">)];</span>
+<a id="__codelineno-35-109" name="__codelineno-35-109" href="#__codelineno-35-109"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-35-110" name="__codelineno-35-110" href="#__codelineno-35-110"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-35-111" name="__codelineno-35-111" href="#__codelineno-35-111"></a><span class="w">        </span><span class="n">res</span>
+<a id="__codelineno-35-112" name="__codelineno-35-112" href="#__codelineno-35-112"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-113" name="__codelineno-35-113" href="#__codelineno-35-113"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_deque.kt</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">ArrayDeque</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">array_deque.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* 循環配列ベースの両端キュー */</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">;</span><span class="w">       </span><span class="c1">// キュー要素を格納する配列</span>
+<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w">       </span><span class="c1">// 先頭ポインタ。先頭要素を指す</span>
+<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w">     </span><span class="c1">// 末尾ポインタ。キューの末尾 + 1 を指す</span>
+<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">queCapacity</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの容量</span>
+<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="p">}</span><span class="w"> </span><span class="n">ArrayDeque</span><span class="p">;</span>
+<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a>
+<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a><span class="n">ArrayDeque</span><span class="w"> </span><span class="o">*</span><span class="nf">newArrayDeque</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a><span class="w">    </span><span class="n">ArrayDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">ArrayDeque</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">ArrayDeque</span><span class="p">));</span>
+<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a><span class="w">    </span><span class="c1">// 配列を初期化</span>
+<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></a><span class="w">    </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queCapacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-36-14" name="__codelineno-36-14" href="#__codelineno-36-14"></a><span class="w">    </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queCapacity</span><span class="p">);</span>
+<a id="__codelineno-36-15" name="__codelineno-36-15" href="#__codelineno-36-15"></a><span class="w">    </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-36-16" name="__codelineno-36-16" href="#__codelineno-36-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">deque</span><span class="p">;</span>
+<a id="__codelineno-36-17" name="__codelineno-36-17" href="#__codelineno-36-17"></a><span class="p">}</span>
+<a id="__codelineno-36-18" name="__codelineno-36-18" href="#__codelineno-36-18"></a>
+<a id="__codelineno-36-19" name="__codelineno-36-19" href="#__codelineno-36-19"></a><span class="cm">/* デストラクタ */</span>
+<a id="__codelineno-36-20" name="__codelineno-36-20" href="#__codelineno-36-20"></a><span class="kt">void</span><span class="w"> </span><span class="nf">delArrayDeque</span><span class="p">(</span><span class="n">ArrayDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-21" name="__codelineno-36-21" href="#__codelineno-36-21"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">nums</span><span class="p">);</span>
+<a id="__codelineno-36-22" name="__codelineno-36-22" href="#__codelineno-36-22"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">deque</span><span class="p">);</span>
+<a id="__codelineno-36-23" name="__codelineno-36-23" href="#__codelineno-36-23"></a><span class="p">}</span>
+<a id="__codelineno-36-24" name="__codelineno-36-24" href="#__codelineno-36-24"></a>
+<a id="__codelineno-36-25" name="__codelineno-36-25" href="#__codelineno-36-25"></a><span class="cm">/* 両端キューの容量を取得 */</span>
+<a id="__codelineno-36-26" name="__codelineno-36-26" href="#__codelineno-36-26"></a><span class="kt">int</span><span class="w"> </span><span class="nf">capacity</span><span class="p">(</span><span class="n">ArrayDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-27" name="__codelineno-36-27" href="#__codelineno-36-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queCapacity</span><span class="p">;</span>
+<a id="__codelineno-36-28" name="__codelineno-36-28" href="#__codelineno-36-28"></a><span class="p">}</span>
+<a id="__codelineno-36-29" name="__codelineno-36-29" href="#__codelineno-36-29"></a>
+<a id="__codelineno-36-30" name="__codelineno-36-30" href="#__codelineno-36-30"></a><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-36-31" name="__codelineno-36-31" href="#__codelineno-36-31"></a><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="n">ArrayDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-32" name="__codelineno-36-32" href="#__codelineno-36-32"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-36-33" name="__codelineno-36-33" href="#__codelineno-36-33"></a><span class="p">}</span>
+<a id="__codelineno-36-34" name="__codelineno-36-34" href="#__codelineno-36-34"></a>
+<a id="__codelineno-36-35" name="__codelineno-36-35" href="#__codelineno-36-35"></a><span class="cm">/* 両端キューが空かどうかを判定 */</span>
+<a id="__codelineno-36-36" name="__codelineno-36-36" href="#__codelineno-36-36"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">empty</span><span class="p">(</span><span class="n">ArrayDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-37" name="__codelineno-36-37" href="#__codelineno-36-37"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-36-38" name="__codelineno-36-38" href="#__codelineno-36-38"></a><span class="p">}</span>
+<a id="__codelineno-36-39" name="__codelineno-36-39" href="#__codelineno-36-39"></a>
+<a id="__codelineno-36-40" name="__codelineno-36-40" href="#__codelineno-36-40"></a><span class="cm">/* 循環配列のインデックスを計算 */</span>
+<a id="__codelineno-36-41" name="__codelineno-36-41" href="#__codelineno-36-41"></a><span class="kt">int</span><span class="w"> </span><span class="nf">dequeIndex</span><span class="p">(</span><span class="n">ArrayDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-42" name="__codelineno-36-42" href="#__codelineno-36-42"></a><span class="w">    </span><span class="c1">// 剰余演算により配列の先頭と末尾をつなげる</span>
+<a id="__codelineno-36-43" name="__codelineno-36-43" href="#__codelineno-36-43"></a><span class="w">    </span><span class="c1">// i が配列の末尾を越えたら先頭に戻る</span>
+<a id="__codelineno-36-44" name="__codelineno-36-44" href="#__codelineno-36-44"></a><span class="w">    </span><span class="c1">// i が配列の先頭を越えたら末尾に戻る</span>
+<a id="__codelineno-36-45" name="__codelineno-36-45" href="#__codelineno-36-45"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">((</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">capacity</span><span class="p">(</span><span class="n">deque</span><span class="p">))</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">(</span><span class="n">deque</span><span class="p">));</span>
+<a id="__codelineno-36-46" name="__codelineno-36-46" href="#__codelineno-36-46"></a><span class="p">}</span>
+<a id="__codelineno-36-47" name="__codelineno-36-47" href="#__codelineno-36-47"></a>
+<a id="__codelineno-36-48" name="__codelineno-36-48" href="#__codelineno-36-48"></a><span class="cm">/* キュー先頭にエンキュー */</span>
+<a id="__codelineno-36-49" name="__codelineno-36-49" href="#__codelineno-36-49"></a><span class="kt">void</span><span class="w"> </span><span class="nf">pushFirst</span><span class="p">(</span><span class="n">ArrayDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-50" name="__codelineno-36-50" href="#__codelineno-36-50"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">(</span><span class="n">deque</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-51" name="__codelineno-36-51" href="#__codelineno-36-51"></a><span class="w">        </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;両端キューがいっぱいです</span><span class="se">\r\n</span><span class="s">&quot;</span><span class="p">);</span>
+<a id="__codelineno-36-52" name="__codelineno-36-52" href="#__codelineno-36-52"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-36-53" name="__codelineno-36-53" href="#__codelineno-36-53"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-54" name="__codelineno-36-54" href="#__codelineno-36-54"></a><span class="w">    </span><span class="c1">// 先頭ポインタを左に 1 つ移動する</span>
+<a id="__codelineno-36-55" name="__codelineno-36-55" href="#__codelineno-36-55"></a><span class="w">    </span><span class="c1">// 剰余演算により front が配列の先頭を越えたあと末尾に戻るようにする</span>
+<a id="__codelineno-36-56" name="__codelineno-36-56" href="#__codelineno-36-56"></a><span class="w">    </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dequeIndex</span><span class="p">(</span><span class="n">deque</span><span class="p">,</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-36-57" name="__codelineno-36-57" href="#__codelineno-36-57"></a><span class="w">    </span><span class="c1">// num をキューの先頭に追加</span>
+<a id="__codelineno-36-58" name="__codelineno-36-58" href="#__codelineno-36-58"></a><span class="w">    </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">nums</span><span class="p">[</span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-36-59" name="__codelineno-36-59" href="#__codelineno-36-59"></a><span class="w">    </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-36-60" name="__codelineno-36-60" href="#__codelineno-36-60"></a><span class="p">}</span>
+<a id="__codelineno-36-61" name="__codelineno-36-61" href="#__codelineno-36-61"></a>
+<a id="__codelineno-36-62" name="__codelineno-36-62" href="#__codelineno-36-62"></a><span class="cm">/* キュー末尾にエンキュー */</span>
+<a id="__codelineno-36-63" name="__codelineno-36-63" href="#__codelineno-36-63"></a><span class="kt">void</span><span class="w"> </span><span class="nf">pushLast</span><span class="p">(</span><span class="n">ArrayDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-64" name="__codelineno-36-64" href="#__codelineno-36-64"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">(</span><span class="n">deque</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-65" name="__codelineno-36-65" href="#__codelineno-36-65"></a><span class="w">        </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;両端キューがいっぱいです</span><span class="se">\r\n</span><span class="s">&quot;</span><span class="p">);</span>
+<a id="__codelineno-36-66" name="__codelineno-36-66" href="#__codelineno-36-66"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-36-67" name="__codelineno-36-67" href="#__codelineno-36-67"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-68" name="__codelineno-36-68" href="#__codelineno-36-68"></a><span class="w">    </span><span class="c1">// キュー末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-36-69" name="__codelineno-36-69" href="#__codelineno-36-69"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dequeIndex</span><span class="p">(</span><span class="n">deque</span><span class="p">,</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="p">);</span>
+<a id="__codelineno-36-70" name="__codelineno-36-70" href="#__codelineno-36-70"></a><span class="w">    </span><span class="c1">// num をキュー末尾に追加</span>
+<a id="__codelineno-36-71" name="__codelineno-36-71" href="#__codelineno-36-71"></a><span class="w">    </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">nums</span><span class="p">[</span><span class="n">rear</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-36-72" name="__codelineno-36-72" href="#__codelineno-36-72"></a><span class="w">    </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-36-73" name="__codelineno-36-73" href="#__codelineno-36-73"></a><span class="p">}</span>
+<a id="__codelineno-36-74" name="__codelineno-36-74" href="#__codelineno-36-74"></a>
+<a id="__codelineno-36-75" name="__codelineno-36-75" href="#__codelineno-36-75"></a><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-36-76" name="__codelineno-36-76" href="#__codelineno-36-76"></a><span class="kt">int</span><span class="w"> </span><span class="nf">peekFirst</span><span class="p">(</span><span class="n">ArrayDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-77" name="__codelineno-36-77" href="#__codelineno-36-77"></a><span class="w">    </span><span class="c1">// アクセス例外：双方向キューが空です</span>
+<a id="__codelineno-36-78" name="__codelineno-36-78" href="#__codelineno-36-78"></a><span class="w">    </span><span class="n">assert</span><span class="p">(</span><span class="n">empty</span><span class="p">(</span><span class="n">deque</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-36-79" name="__codelineno-36-79" href="#__codelineno-36-79"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">nums</span><span class="p">[</span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="p">];</span>
+<a id="__codelineno-36-80" name="__codelineno-36-80" href="#__codelineno-36-80"></a><span class="p">}</span>
+<a id="__codelineno-36-81" name="__codelineno-36-81" href="#__codelineno-36-81"></a>
+<a id="__codelineno-36-82" name="__codelineno-36-82" href="#__codelineno-36-82"></a><span class="cm">/* キュー末尾の要素にアクセス */</span>
+<a id="__codelineno-36-83" name="__codelineno-36-83" href="#__codelineno-36-83"></a><span class="kt">int</span><span class="w"> </span><span class="nf">peekLast</span><span class="p">(</span><span class="n">ArrayDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-84" name="__codelineno-36-84" href="#__codelineno-36-84"></a><span class="w">    </span><span class="c1">// アクセス例外：双方向キューが空です</span>
+<a id="__codelineno-36-85" name="__codelineno-36-85" href="#__codelineno-36-85"></a><span class="w">    </span><span class="n">assert</span><span class="p">(</span><span class="n">empty</span><span class="p">(</span><span class="n">deque</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-36-86" name="__codelineno-36-86" href="#__codelineno-36-86"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">last</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dequeIndex</span><span class="p">(</span><span class="n">deque</span><span class="p">,</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-36-87" name="__codelineno-36-87" href="#__codelineno-36-87"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">nums</span><span class="p">[</span><span class="n">last</span><span class="p">];</span>
+<a id="__codelineno-36-88" name="__codelineno-36-88" href="#__codelineno-36-88"></a><span class="p">}</span>
+<a id="__codelineno-36-89" name="__codelineno-36-89" href="#__codelineno-36-89"></a>
+<a id="__codelineno-36-90" name="__codelineno-36-90" href="#__codelineno-36-90"></a><span class="cm">/* キュー先頭からデキュー */</span>
+<a id="__codelineno-36-91" name="__codelineno-36-91" href="#__codelineno-36-91"></a><span class="kt">int</span><span class="w"> </span><span class="nf">popFirst</span><span class="p">(</span><span class="n">ArrayDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-92" name="__codelineno-36-92" href="#__codelineno-36-92"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peekFirst</span><span class="p">(</span><span class="n">deque</span><span class="p">);</span>
+<a id="__codelineno-36-93" name="__codelineno-36-93" href="#__codelineno-36-93"></a><span class="w">    </span><span class="c1">// 先頭ポインタを 1 つ後ろへ進める</span>
+<a id="__codelineno-36-94" name="__codelineno-36-94" href="#__codelineno-36-94"></a><span class="w">    </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dequeIndex</span><span class="p">(</span><span class="n">deque</span><span class="p">,</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-36-95" name="__codelineno-36-95" href="#__codelineno-36-95"></a><span class="w">    </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-36-96" name="__codelineno-36-96" href="#__codelineno-36-96"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-36-97" name="__codelineno-36-97" href="#__codelineno-36-97"></a><span class="p">}</span>
+<a id="__codelineno-36-98" name="__codelineno-36-98" href="#__codelineno-36-98"></a>
+<a id="__codelineno-36-99" name="__codelineno-36-99" href="#__codelineno-36-99"></a><span class="cm">/* キュー末尾からデキュー */</span>
+<a id="__codelineno-36-100" name="__codelineno-36-100" href="#__codelineno-36-100"></a><span class="kt">int</span><span class="w"> </span><span class="nf">popLast</span><span class="p">(</span><span class="n">ArrayDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-101" name="__codelineno-36-101" href="#__codelineno-36-101"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peekLast</span><span class="p">(</span><span class="n">deque</span><span class="p">);</span>
+<a id="__codelineno-36-102" name="__codelineno-36-102" href="#__codelineno-36-102"></a><span class="w">    </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-36-103" name="__codelineno-36-103" href="#__codelineno-36-103"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-36-104" name="__codelineno-36-104" href="#__codelineno-36-104"></a><span class="p">}</span>
+<a id="__codelineno-36-105" name="__codelineno-36-105" href="#__codelineno-36-105"></a>
+<a id="__codelineno-36-106" name="__codelineno-36-106" href="#__codelineno-36-106"></a><span class="cm">/* 出力用の配列を返す */</span>
+<a id="__codelineno-36-107" name="__codelineno-36-107" href="#__codelineno-36-107"></a><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="nf">toArray</span><span class="p">(</span><span class="n">ArrayDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">queSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-108" name="__codelineno-36-108" href="#__codelineno-36-108"></a><span class="w">    </span><span class="o">*</span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-36-109" name="__codelineno-36-109" href="#__codelineno-36-109"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">calloc</span><span class="p">(</span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-36-110" name="__codelineno-36-110" href="#__codelineno-36-110"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-36-111" name="__codelineno-36-111" href="#__codelineno-36-111"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-112" name="__codelineno-36-112" href="#__codelineno-36-112"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">deque</span><span class="o">-&gt;</span><span class="n">queCapacity</span><span class="p">];</span>
+<a id="__codelineno-36-113" name="__codelineno-36-113" href="#__codelineno-36-113"></a><span class="w">        </span><span class="n">j</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-36-114" name="__codelineno-36-114" href="#__codelineno-36-114"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-115" name="__codelineno-36-115" href="#__codelineno-36-115"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-36-116" name="__codelineno-36-116" href="#__codelineno-36-116"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_deque.rb</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">ArrayDeque</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">array_deque.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ArrayDeque</span><span class="p">(</span><span class="n">capacity</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">capacity</span><span class="p">)</span><span class="w"> </span><span class="c1">// 両端キューの要素を格納する配列</span>
+<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">front</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="c1">// 先頭ポインタ。先頭要素を指す</span>
+<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">queSize</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="c1">// 両端キューの長さ</span>
+<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a>
+<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w">    </span><span class="cm">/* 両端キューの容量を取得 */</span>
+<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">capacity</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a>
+<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a><span class="w">    </span><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">size</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-14" name="__codelineno-37-14" href="#__codelineno-37-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span>
+<a id="__codelineno-37-15" name="__codelineno-37-15" href="#__codelineno-37-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-16" name="__codelineno-37-16" href="#__codelineno-37-16"></a>
+<a id="__codelineno-37-17" name="__codelineno-37-17" href="#__codelineno-37-17"></a><span class="w">    </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
+<a id="__codelineno-37-18" name="__codelineno-37-18" href="#__codelineno-37-18"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">():</span><span class="w"> </span><span class="kt">Boolean</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-19" name="__codelineno-37-19" href="#__codelineno-37-19"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-37-20" name="__codelineno-37-20" href="#__codelineno-37-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-21" name="__codelineno-37-21" href="#__codelineno-37-21"></a>
+<a id="__codelineno-37-22" name="__codelineno-37-22" href="#__codelineno-37-22"></a><span class="w">    </span><span class="cm">/* 循環配列のインデックスを計算 */</span>
+<a id="__codelineno-37-23" name="__codelineno-37-23" href="#__codelineno-37-23"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">fun</span><span class="w"> </span><span class="nf">index</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-24" name="__codelineno-37-24" href="#__codelineno-37-24"></a><span class="w">        </span><span class="c1">// 剰余演算により配列の先頭と末尾をつなげる</span>
+<a id="__codelineno-37-25" name="__codelineno-37-25" href="#__codelineno-37-25"></a><span class="w">        </span><span class="c1">// i が配列の末尾を越えたら先頭に戻る</span>
+<a id="__codelineno-37-26" name="__codelineno-37-26" href="#__codelineno-37-26"></a><span class="w">        </span><span class="c1">// i が配列の先頭を越えて前に出たら末尾に戻る</span>
+<a id="__codelineno-37-27" name="__codelineno-37-27" href="#__codelineno-37-27"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span>
+<a id="__codelineno-37-28" name="__codelineno-37-28" href="#__codelineno-37-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-29" name="__codelineno-37-29" href="#__codelineno-37-29"></a>
+<a id="__codelineno-37-30" name="__codelineno-37-30" href="#__codelineno-37-30"></a><span class="w">    </span><span class="cm">/* キュー先頭にエンキュー */</span>
+<a id="__codelineno-37-31" name="__codelineno-37-31" href="#__codelineno-37-31"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">pushFirst</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-32" name="__codelineno-37-32" href="#__codelineno-37-32"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-33" name="__codelineno-37-33" href="#__codelineno-37-33"></a><span class="w">            </span><span class="n">println</span><span class="p">(</span><span class="s">&quot;双方向キューは満杯です&quot;</span><span class="p">)</span>
+<a id="__codelineno-37-34" name="__codelineno-37-34" href="#__codelineno-37-34"></a><span class="w">            </span><span class="k">return</span>
+<a id="__codelineno-37-35" name="__codelineno-37-35" href="#__codelineno-37-35"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-37-36" name="__codelineno-37-36" href="#__codelineno-37-36"></a><span class="w">        </span><span class="c1">// 先頭ポインタを左に 1 つ移動する</span>
+<a id="__codelineno-37-37" name="__codelineno-37-37" href="#__codelineno-37-37"></a><span class="w">        </span><span class="c1">// 剰余演算により、front が配列先頭を越えた後に末尾へ戻るようにする</span>
+<a id="__codelineno-37-38" name="__codelineno-37-38" href="#__codelineno-37-38"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-37-39" name="__codelineno-37-39" href="#__codelineno-37-39"></a><span class="w">        </span><span class="c1">// num をキュー先頭に追加</span>
+<a id="__codelineno-37-40" name="__codelineno-37-40" href="#__codelineno-37-40"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">front</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-37-41" name="__codelineno-37-41" href="#__codelineno-37-41"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span>
+<a id="__codelineno-37-42" name="__codelineno-37-42" href="#__codelineno-37-42"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-43" name="__codelineno-37-43" href="#__codelineno-37-43"></a>
+<a id="__codelineno-37-44" name="__codelineno-37-44" href="#__codelineno-37-44"></a><span class="w">    </span><span class="cm">/* キュー末尾にエンキュー */</span>
+<a id="__codelineno-37-45" name="__codelineno-37-45" href="#__codelineno-37-45"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">pushLast</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-46" name="__codelineno-37-46" href="#__codelineno-37-46"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-47" name="__codelineno-37-47" href="#__codelineno-37-47"></a><span class="w">            </span><span class="n">println</span><span class="p">(</span><span class="s">&quot;双方向キューは満杯です&quot;</span><span class="p">)</span>
+<a id="__codelineno-37-48" name="__codelineno-37-48" href="#__codelineno-37-48"></a><span class="w">            </span><span class="k">return</span>
+<a id="__codelineno-37-49" name="__codelineno-37-49" href="#__codelineno-37-49"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-37-50" name="__codelineno-37-50" href="#__codelineno-37-50"></a><span class="w">        </span><span class="c1">// キュー末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-37-51" name="__codelineno-37-51" href="#__codelineno-37-51"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">queSize</span><span class="p">)</span>
+<a id="__codelineno-37-52" name="__codelineno-37-52" href="#__codelineno-37-52"></a><span class="w">        </span><span class="c1">// num をキュー末尾に追加</span>
+<a id="__codelineno-37-53" name="__codelineno-37-53" href="#__codelineno-37-53"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">rear</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-37-54" name="__codelineno-37-54" href="#__codelineno-37-54"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span>
+<a id="__codelineno-37-55" name="__codelineno-37-55" href="#__codelineno-37-55"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-56" name="__codelineno-37-56" href="#__codelineno-37-56"></a>
+<a id="__codelineno-37-57" name="__codelineno-37-57" href="#__codelineno-37-57"></a><span class="w">    </span><span class="cm">/* キュー先頭からデキュー */</span>
+<a id="__codelineno-37-58" name="__codelineno-37-58" href="#__codelineno-37-58"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">popFirst</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-59" name="__codelineno-37-59" href="#__codelineno-37-59"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peekFirst</span><span class="p">()</span>
+<a id="__codelineno-37-60" name="__codelineno-37-60" href="#__codelineno-37-60"></a><span class="w">        </span><span class="c1">// 先頭ポインタを 1 つ後ろへ進める</span>
+<a id="__codelineno-37-61" name="__codelineno-37-61" href="#__codelineno-37-61"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-37-62" name="__codelineno-37-62" href="#__codelineno-37-62"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span>
+<a id="__codelineno-37-63" name="__codelineno-37-63" href="#__codelineno-37-63"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-37-64" name="__codelineno-37-64" href="#__codelineno-37-64"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-65" name="__codelineno-37-65" href="#__codelineno-37-65"></a>
+<a id="__codelineno-37-66" name="__codelineno-37-66" href="#__codelineno-37-66"></a><span class="w">    </span><span class="cm">/* キュー末尾からデキュー */</span>
+<a id="__codelineno-37-67" name="__codelineno-37-67" href="#__codelineno-37-67"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">popLast</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-68" name="__codelineno-37-68" href="#__codelineno-37-68"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peekLast</span><span class="p">()</span>
+<a id="__codelineno-37-69" name="__codelineno-37-69" href="#__codelineno-37-69"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span>
+<a id="__codelineno-37-70" name="__codelineno-37-70" href="#__codelineno-37-70"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-37-71" name="__codelineno-37-71" href="#__codelineno-37-71"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-72" name="__codelineno-37-72" href="#__codelineno-37-72"></a>
+<a id="__codelineno-37-73" name="__codelineno-37-73" href="#__codelineno-37-73"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-37-74" name="__codelineno-37-74" href="#__codelineno-37-74"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">peekFirst</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-75" name="__codelineno-37-75" href="#__codelineno-37-75"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">()</span>
+<a id="__codelineno-37-76" name="__codelineno-37-76" href="#__codelineno-37-76"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">front</span><span class="o">]</span>
+<a id="__codelineno-37-77" name="__codelineno-37-77" href="#__codelineno-37-77"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-78" name="__codelineno-37-78" href="#__codelineno-37-78"></a>
+<a id="__codelineno-37-79" name="__codelineno-37-79" href="#__codelineno-37-79"></a><span class="w">    </span><span class="cm">/* キュー末尾の要素にアクセス */</span>
+<a id="__codelineno-37-80" name="__codelineno-37-80" href="#__codelineno-37-80"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">peekLast</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-81" name="__codelineno-37-81" href="#__codelineno-37-81"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">()</span>
+<a id="__codelineno-37-82" name="__codelineno-37-82" href="#__codelineno-37-82"></a><span class="w">        </span><span class="c1">// 末尾要素のインデックスを計算</span>
+<a id="__codelineno-37-83" name="__codelineno-37-83" href="#__codelineno-37-83"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">last</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-37-84" name="__codelineno-37-84" href="#__codelineno-37-84"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">last</span><span class="o">]</span>
+<a id="__codelineno-37-85" name="__codelineno-37-85" href="#__codelineno-37-85"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-86" name="__codelineno-37-86" href="#__codelineno-37-86"></a>
+<a id="__codelineno-37-87" name="__codelineno-37-87" href="#__codelineno-37-87"></a><span class="w">    </span><span class="cm">/* 出力用の配列を返す */</span>
+<a id="__codelineno-37-88" name="__codelineno-37-88" href="#__codelineno-37-88"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">toArray</span><span class="p">():</span><span class="w"> </span><span class="n">IntArray</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-89" name="__codelineno-37-89" href="#__codelineno-37-89"></a><span class="w">        </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-37-90" name="__codelineno-37-90" href="#__codelineno-37-90"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">queSize</span><span class="p">)</span>
+<a id="__codelineno-37-91" name="__codelineno-37-91" href="#__codelineno-37-91"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-37-92" name="__codelineno-37-92" href="#__codelineno-37-92"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span>
+<a id="__codelineno-37-93" name="__codelineno-37-93" href="#__codelineno-37-93"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">queSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-94" name="__codelineno-37-94" href="#__codelineno-37-94"></a><span class="w">            </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">index</span><span class="p">(</span><span class="n">j</span><span class="p">)</span><span class="o">]</span>
+<a id="__codelineno-37-95" name="__codelineno-37-95" href="#__codelineno-37-95"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span>
+<a id="__codelineno-37-96" name="__codelineno-37-96" href="#__codelineno-37-96"></a><span class="w">            </span><span class="n">j</span><span class="o">++</span>
+<a id="__codelineno-37-97" name="__codelineno-37-97" href="#__codelineno-37-97"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-37-98" name="__codelineno-37-98" href="#__codelineno-37-98"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-37-99" name="__codelineno-37-99" href="#__codelineno-37-99"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-100" name="__codelineno-37-100" href="#__codelineno-37-100"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_deque.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="c1">### 循環配列で実装した両端キュー ###</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayDeque</span>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w">  </span><span class="c1">### 両端キューの長さを取得 ###</span>
+<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w">  </span><span class="kp">attr_reader</span><span class="w"> </span><span class="ss">:size</span>
+<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a>
+<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w">  </span><span class="c1">### コンストラクタ ###</span>
+<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">capacity</span><span class="p">)</span>
+<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="w">    </span><span class="vi">@nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">capacity</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="w">    </span><span class="vi">@front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a>
+<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a><span class="w">  </span><span class="c1">### 両端キューの容量を取得 ###</span>
+<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">capacity</span>
+<a id="__codelineno-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a><span class="w">    </span><span class="vi">@nums</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-38-16" name="__codelineno-38-16" href="#__codelineno-38-16"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-17" name="__codelineno-38-17" href="#__codelineno-38-17"></a>
+<a id="__codelineno-38-18" name="__codelineno-38-18" href="#__codelineno-38-18"></a><span class="w">  </span><span class="c1">### 両端キューが空か判定 ###</span>
+<a id="__codelineno-38-19" name="__codelineno-38-19" href="#__codelineno-38-19"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">is_empty?</span>
+<a id="__codelineno-38-20" name="__codelineno-38-20" href="#__codelineno-38-20"></a><span class="w">    </span><span class="n">size</span><span class="o">.</span><span class="n">zero?</span>
+<a id="__codelineno-38-21" name="__codelineno-38-21" href="#__codelineno-38-21"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-22" name="__codelineno-38-22" href="#__codelineno-38-22"></a>
+<a id="__codelineno-38-23" name="__codelineno-38-23" href="#__codelineno-38-23"></a><span class="w">  </span><span class="c1">### キュー先頭に追加 ###</span>
+<a id="__codelineno-38-24" name="__codelineno-38-24" href="#__codelineno-38-24"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">push_first</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-38-25" name="__codelineno-38-25" href="#__codelineno-38-25"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span>
+<a id="__codelineno-38-26" name="__codelineno-38-26" href="#__codelineno-38-26"></a><span class="w">      </span><span class="nb">puts</span><span class="w"> </span><span class="s1">&#39;両端キューがいっぱいです&#39;</span>
+<a id="__codelineno-38-27" name="__codelineno-38-27" href="#__codelineno-38-27"></a><span class="w">      </span><span class="k">return</span>
+<a id="__codelineno-38-28" name="__codelineno-38-28" href="#__codelineno-38-28"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-38-29" name="__codelineno-38-29" href="#__codelineno-38-29"></a>
+<a id="__codelineno-38-30" name="__codelineno-38-30" href="#__codelineno-38-30"></a><span class="w">    </span><span class="c1"># 先頭ポインタを左に 1 つ移動する</span>
+<a id="__codelineno-38-31" name="__codelineno-38-31" href="#__codelineno-38-31"></a><span class="w">    </span><span class="c1"># 剰余演算により、front が配列先頭を越えた後に末尾へ戻るようにする</span>
+<a id="__codelineno-38-32" name="__codelineno-38-32" href="#__codelineno-38-32"></a><span class="w">    </span><span class="vi">@front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="vi">@front</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-38-33" name="__codelineno-38-33" href="#__codelineno-38-33"></a><span class="w">    </span><span class="c1"># num をキュー先頭に追加</span>
+<a id="__codelineno-38-34" name="__codelineno-38-34" href="#__codelineno-38-34"></a><span class="w">    </span><span class="vi">@nums</span><span class="o">[</span><span class="vi">@front</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-38-35" name="__codelineno-38-35" href="#__codelineno-38-35"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-38-36" name="__codelineno-38-36" href="#__codelineno-38-36"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-37" name="__codelineno-38-37" href="#__codelineno-38-37"></a>
+<a id="__codelineno-38-38" name="__codelineno-38-38" href="#__codelineno-38-38"></a><span class="w">  </span><span class="c1">### キュー末尾に追加 ###</span>
+<a id="__codelineno-38-39" name="__codelineno-38-39" href="#__codelineno-38-39"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">push_last</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-38-40" name="__codelineno-38-40" href="#__codelineno-38-40"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span>
+<a id="__codelineno-38-41" name="__codelineno-38-41" href="#__codelineno-38-41"></a><span class="w">      </span><span class="nb">puts</span><span class="w"> </span><span class="s1">&#39;両端キューがいっぱいです&#39;</span>
+<a id="__codelineno-38-42" name="__codelineno-38-42" href="#__codelineno-38-42"></a><span class="w">      </span><span class="k">return</span>
+<a id="__codelineno-38-43" name="__codelineno-38-43" href="#__codelineno-38-43"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-38-44" name="__codelineno-38-44" href="#__codelineno-38-44"></a>
+<a id="__codelineno-38-45" name="__codelineno-38-45" href="#__codelineno-38-45"></a><span class="w">    </span><span class="c1"># キュー末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-38-46" name="__codelineno-38-46" href="#__codelineno-38-46"></a><span class="w">    </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="vi">@front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">size</span><span class="p">)</span>
+<a id="__codelineno-38-47" name="__codelineno-38-47" href="#__codelineno-38-47"></a><span class="w">    </span><span class="c1"># num をキュー末尾に追加</span>
+<a id="__codelineno-38-48" name="__codelineno-38-48" href="#__codelineno-38-48"></a><span class="w">    </span><span class="vi">@nums</span><span class="o">[</span><span class="n">rear</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-38-49" name="__codelineno-38-49" href="#__codelineno-38-49"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-38-50" name="__codelineno-38-50" href="#__codelineno-38-50"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-51" name="__codelineno-38-51" href="#__codelineno-38-51"></a>
+<a id="__codelineno-38-52" name="__codelineno-38-52" href="#__codelineno-38-52"></a><span class="w">  </span><span class="c1">### キュー先頭から取り出す ###</span>
+<a id="__codelineno-38-53" name="__codelineno-38-53" href="#__codelineno-38-53"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">pop_first</span>
+<a id="__codelineno-38-54" name="__codelineno-38-54" href="#__codelineno-38-54"></a><span class="w">    </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek_first</span>
+<a id="__codelineno-38-55" name="__codelineno-38-55" href="#__codelineno-38-55"></a><span class="w">    </span><span class="c1"># 先頭ポインタを 1 つ後ろへ進める</span>
+<a id="__codelineno-38-56" name="__codelineno-38-56" href="#__codelineno-38-56"></a><span class="w">    </span><span class="vi">@front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="vi">@front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-38-57" name="__codelineno-38-57" href="#__codelineno-38-57"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-38-58" name="__codelineno-38-58" href="#__codelineno-38-58"></a><span class="w">    </span><span class="n">num</span>
+<a id="__codelineno-38-59" name="__codelineno-38-59" href="#__codelineno-38-59"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-60" name="__codelineno-38-60" href="#__codelineno-38-60"></a>
+<a id="__codelineno-38-61" name="__codelineno-38-61" href="#__codelineno-38-61"></a><span class="w">  </span><span class="c1">### キューの末尾から取り出す ###</span>
+<a id="__codelineno-38-62" name="__codelineno-38-62" href="#__codelineno-38-62"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">pop_last</span>
+<a id="__codelineno-38-63" name="__codelineno-38-63" href="#__codelineno-38-63"></a><span class="w">    </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek_last</span>
+<a id="__codelineno-38-64" name="__codelineno-38-64" href="#__codelineno-38-64"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-38-65" name="__codelineno-38-65" href="#__codelineno-38-65"></a><span class="w">    </span><span class="n">num</span>
+<a id="__codelineno-38-66" name="__codelineno-38-66" href="#__codelineno-38-66"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-67" name="__codelineno-38-67" href="#__codelineno-38-67"></a>
+<a id="__codelineno-38-68" name="__codelineno-38-68" href="#__codelineno-38-68"></a><span class="w">  </span><span class="c1">### 先頭要素にアクセス ###</span>
+<a id="__codelineno-38-69" name="__codelineno-38-69" href="#__codelineno-38-69"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">peek_first</span>
+<a id="__codelineno-38-70" name="__codelineno-38-70" href="#__codelineno-38-70"></a><span class="w">    </span><span class="k">raise</span><span class="w"> </span><span class="no">IndexError</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;両端キューは空です&#39;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_empty?</span>
+<a id="__codelineno-38-71" name="__codelineno-38-71" href="#__codelineno-38-71"></a>
+<a id="__codelineno-38-72" name="__codelineno-38-72" href="#__codelineno-38-72"></a><span class="w">    </span><span class="vi">@nums</span><span class="o">[</span><span class="vi">@front</span><span class="o">]</span>
+<a id="__codelineno-38-73" name="__codelineno-38-73" href="#__codelineno-38-73"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-74" name="__codelineno-38-74" href="#__codelineno-38-74"></a>
+<a id="__codelineno-38-75" name="__codelineno-38-75" href="#__codelineno-38-75"></a><span class="w">  </span><span class="c1">### キュー末尾要素を参照 ###</span>
+<a id="__codelineno-38-76" name="__codelineno-38-76" href="#__codelineno-38-76"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">peek_last</span>
+<a id="__codelineno-38-77" name="__codelineno-38-77" href="#__codelineno-38-77"></a><span class="w">    </span><span class="k">raise</span><span class="w"> </span><span class="no">IndexError</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;両端キューは空です&#39;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_empty?</span>
+<a id="__codelineno-38-78" name="__codelineno-38-78" href="#__codelineno-38-78"></a>
+<a id="__codelineno-38-79" name="__codelineno-38-79" href="#__codelineno-38-79"></a><span class="w">    </span><span class="c1"># 末尾要素のインデックスを計算</span>
+<a id="__codelineno-38-80" name="__codelineno-38-80" href="#__codelineno-38-80"></a><span class="w">    </span><span class="n">last</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="vi">@front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-38-81" name="__codelineno-38-81" href="#__codelineno-38-81"></a><span class="w">    </span><span class="vi">@nums</span><span class="o">[</span><span class="n">last</span><span class="o">]</span>
+<a id="__codelineno-38-82" name="__codelineno-38-82" href="#__codelineno-38-82"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-83" name="__codelineno-38-83" href="#__codelineno-38-83"></a>
+<a id="__codelineno-38-84" name="__codelineno-38-84" href="#__codelineno-38-84"></a><span class="w">  </span><span class="c1">### 表示用の配列を返す ###</span>
+<a id="__codelineno-38-85" name="__codelineno-38-85" href="#__codelineno-38-85"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">to_array</span>
+<a id="__codelineno-38-86" name="__codelineno-38-86" href="#__codelineno-38-86"></a><span class="w">    </span><span class="c1"># 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-38-87" name="__codelineno-38-87" href="#__codelineno-38-87"></a><span class="w">    </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-38-88" name="__codelineno-38-88" href="#__codelineno-38-88"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">size</span>
+<a id="__codelineno-38-89" name="__codelineno-38-89" href="#__codelineno-38-89"></a><span class="w">      </span><span class="n">res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="vi">@nums</span><span class="o">[</span><span class="n">index</span><span class="p">(</span><span class="vi">@front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="o">]</span>
+<a id="__codelineno-38-90" name="__codelineno-38-90" href="#__codelineno-38-90"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-38-91" name="__codelineno-38-91" href="#__codelineno-38-91"></a><span class="w">    </span><span class="n">res</span>
+<a id="__codelineno-38-92" name="__codelineno-38-92" href="#__codelineno-38-92"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-93" name="__codelineno-38-93" href="#__codelineno-38-93"></a>
+<a id="__codelineno-38-94" name="__codelineno-38-94" href="#__codelineno-38-94"></a><span class="w">  </span><span class="kp">private</span>
+<a id="__codelineno-38-95" name="__codelineno-38-95" href="#__codelineno-38-95"></a>
+<a id="__codelineno-38-96" name="__codelineno-38-96" href="#__codelineno-38-96"></a><span class="w">  </span><span class="c1">### 循環配列のインデックスを計算 ###</span>
+<a id="__codelineno-38-97" name="__codelineno-38-97" href="#__codelineno-38-97"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">index</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-38-98" name="__codelineno-38-98" href="#__codelineno-38-98"></a><span class="w">    </span><span class="c1"># 剰余演算により配列の先頭と末尾をつなげる</span>
+<a id="__codelineno-38-99" name="__codelineno-38-99" href="#__codelineno-38-99"></a><span class="w">    </span><span class="c1"># i が配列の末尾を越えたら先頭に戻る</span>
+<a id="__codelineno-38-100" name="__codelineno-38-100" href="#__codelineno-38-100"></a><span class="w">    </span><span class="c1"># i が配列の先頭を越えて前に出たら末尾に戻る</span>
+<a id="__codelineno-38-101" name="__codelineno-38-101" href="#__codelineno-38-101"></a><span class="w">    </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span>
+<a id="__codelineno-38-102" name="__codelineno-38-102" href="#__codelineno-38-102"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-103" name="__codelineno-38-103" href="#__codelineno-38-103"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
 <h2 id="533">5.3.3 &nbsp; 両端キューの応用<a class="headerlink" href="#533" title="Permanent link">&para;</a></h2>
-<p>両端キューはスタックとキューの両方のロジックを組み合わせているため、<strong>それぞれのすべてのユースケースを実装でき、より大きな柔軟性を提供します</strong>。</p>
-<p>ソフトウェアの「元に戻す」機能は通常スタックを使って実装されることを知っています：システムは各変更操作をスタックに<code>push</code>し、次に<code>pop</code>して元に戻すことを実装します。しかし、システムリソースの制限を考慮して、ソフトウェアは元に戻すステップの数を制限することがよくあります（例えば、最後の50ステップのみを許可）。スタックの長さが50を超えた場合、ソフトウェアはスタックの底部（キューの前端）で削除操作を実行する必要があります。<strong>しかし、通常のスタックではこの機能を実行できないため、両端キューが必要になります</strong>。「元に戻す」のコアロジックは依然としてスタックの後入れ先出し原則に従いますが、両端キューはより柔軟にいくつかの追加ロジックを実装できることに注意してください。</p>
+<p>両端キューはスタックとキューの両方の論理を備えているため、<strong>これら 2 つのすべての応用場面を実現でき、さらに高い自由度を提供します</strong>。</p>
+<p>私たちが知っているように、ソフトウェアの「元に戻す」機能は通常スタックを使って実装されます。システムは変更操作を毎回スタックに <code>push</code> し、その後 <code>pop</code> によって取り消しを実現します。しかし、システム資源の制約を考慮すると、通常ソフトウェアは取り消し可能な手数を制限します（たとえば <span class="arithmatex">\(50\)</span> 手まで保存可能）。スタックの長さが <span class="arithmatex">\(50\)</span> を超えると、ソフトウェアはスタックの底部（先頭）で削除操作を行う必要があります。<strong>しかしスタックではこの機能を実現できないため、この場合はスタックの代わりに両端キューを使用する必要があります</strong>。なお、「元に戻す」の中核ロジック自体は依然としてスタックの後入れ先出し原則に従っており、両端キューは追加のロジックをより柔軟に実装できるだけです。</p>
 
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diff --git a/ja/chapter_stack_and_queue/index.html b/ja/chapter_stack_and_queue/index.html
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--- a/ja/chapter_stack_and_queue/index.html
+++ b/ja/chapter_stack_and_queue/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
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+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
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-    序
+    はじめに
   
 
           </label>
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   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
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-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
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   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
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-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
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-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
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+    6.1 &nbsp; ハッシュテーブル
   
 
     
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2107,7 +2107,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2493,7 +2493,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2577,7 +2577,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3115,7 +3115,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3171,7 +3171,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3199,7 +3199,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3392,7 +3392,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3420,7 +3420,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3561,7 +3561,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3589,7 +3589,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3617,7 +3617,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3645,7 +3645,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3838,7 +3838,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4083,7 +4083,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4277,8 +4277,8 @@
 <p><img alt="スタックとキュー" class="cover-image" src="../assets/covers/chapter_stack_and_queue.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>スタックは積み重ねられた猫のようなもので、キューは一列に並んだ猫のようなものです。</p>
-<p>それらはそれぞれ、後入先出（LIFO）と先入先出（FIFO）の論理関係を表しています。</p>
+<p>スタックは猫を積み重ねるようなもので、キューは猫が列に並ぶようなものです。</p>
+<p>両者はそれぞれ、後入れ先出しと先入れ先出しの論理関係を表します。</p>
 </div>
 <h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
diff --git a/ja/chapter_stack_and_queue/queue/index.html b/ja/chapter_stack_and_queue/queue/index.html
index 5c16c8de6..4ac5563b8 100644
--- a/ja/chapter_stack_and_queue/queue/index.html
+++ b/ja/chapter_stack_and_queue/queue/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
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   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
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-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
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-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1531,7 +1531,7 @@
   <a href="#521" class="md-nav__link">
     <span class="md-ellipsis">
       
-        5.2.1 &nbsp; キューの一般的な操作
+        5.2.1 &nbsp; キューの基本操作
       
     </span>
   </a>
@@ -1554,7 +1554,7 @@
   <a href="#1" class="md-nav__link">
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-        1. &nbsp; 連結リストベースの実装
+        1. &nbsp; 連結リストに基づく実装
       
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@@ -1565,7 +1565,7 @@
   <a href="#2" class="md-nav__link">
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-        2. &nbsp; 配列ベースの実装
+        2. &nbsp; 配列に基づく実装
       
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@@ -3726,7 +3726,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3754,7 +3754,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3947,7 +3947,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4192,7 +4192,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4338,7 +4338,7 @@
   <a href="#521" class="md-nav__link">
     <span class="md-ellipsis">
       
-        5.2.1 &nbsp; キューの一般的な操作
+        5.2.1 &nbsp; キューの基本操作
       
     </span>
   </a>
@@ -4361,7 +4361,7 @@
   <a href="#1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; 連結リストベースの実装
+        1. &nbsp; 連結リストに基づく実装
       
     </span>
   </a>
@@ -4372,7 +4372,7 @@
   <a href="#2" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2. &nbsp; 配列ベースの実装
+        2. &nbsp; 配列に基づく実装
       
     </span>
   </a>
@@ -4433,13 +4433,13 @@
 
 <!-- Page content -->
 <h1 id="52">5.2 &nbsp; キュー<a class="headerlink" href="#52" title="Permanent link">&para;</a></h1>
-<p><u>キュー</u>は、先入先出（FIFO）ルールに従う線形データ構造です。名前が示すように、キューは行列の現象をシミュレートし、新参者は列の後ろに並び、前の人が最初に列を離れます。</p>
-<p>下図に示すように、キューの前面を「ヘッド」、後面を「テール」と呼びます。キューの後ろに要素を追加する操作を「エンキュー」、前から要素を削除する操作を「デキュー」と呼びます。</p>
-<p><img alt="キューの先入先出ルール" class="animation-figure" src="../queue.assets/queue_operations.png" /></p>
-<p align="center"> 図 5-4 &nbsp; キューの先入先出ルール </p>
+<p><u>キュー（queue）</u>は、先入れ先出しの規則に従う線形データ構造です。名前のとおり、キューは順番待ちの現象を模したもので、新しく来た人は絶えずキュー末尾に加わり、キュー先頭にいる人から順に離れていきます。</p>
+<p>下図のように、キューの先頭を「キュー先頭」、末尾を「キュー末尾」と呼びます。要素をキュー末尾に加える操作を「エンキュー」、キュー先頭の要素を削除する操作を「デキュー」と呼びます。</p>
+<p><img alt="キューの先入れ先出し規則" class="animation-figure" src="../queue.assets/queue_operations.png" /></p>
+<p align="center"> 図 5-4 &nbsp; キューの先入れ先出し規則 </p>
 
-<h2 id="521">5.2.1 &nbsp; キューの一般的な操作<a class="headerlink" href="#521" title="Permanent link">&para;</a></h2>
-<p>キューの一般的な操作を下表に示します。メソッド名はプログラミング言語によって異なる場合があることに注意してください。ここでは、スタックで使用したのと同じ命名規則を使用します。</p>
+<h2 id="521">5.2.1 &nbsp; キューの基本操作<a class="headerlink" href="#521" title="Permanent link">&para;</a></h2>
+<p>キューの基本操作を以下の表に示します。なお、メソッド名はプログラミング言語によって異なる場合があります。ここではスタックと同じ命名を採用します。</p>
 <p align="center"> 表 5-2 &nbsp; キュー操作の効率 </p>
 
 <div class="center-table">
@@ -4454,31 +4454,31 @@
 <tbody>
 <tr>
 <td><code>push()</code></td>
-<td>要素をエンキュー、テールに追加</td>
+<td>要素をエンキューし、キュー末尾に追加する</td>
 <td><span class="arithmatex">\(O(1)\)</span></td>
 </tr>
 <tr>
 <td><code>pop()</code></td>
-<td>ヘッド要素をデキュー</td>
+<td>キュー先頭の要素をデキューする</td>
 <td><span class="arithmatex">\(O(1)\)</span></td>
 </tr>
 <tr>
 <td><code>peek()</code></td>
-<td>ヘッド要素にアクセス</td>
+<td>キュー先頭の要素にアクセスする</td>
 <td><span class="arithmatex">\(O(1)\)</span></td>
 </tr>
 </tbody>
 </table>
 </div>
-<p>プログラミング言語で用意されているキュークラスを直接使用できます：</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="1:12"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label></div>
+<p>プログラミング言語に用意された既存のキュークラスをそのまま利用できます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">queue.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="kn">from</span><span class="w"> </span><span class="nn">collections</span><span class="w"> </span><span class="kn">import</span> <span class="n">deque</span>
 <a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="c1"># キューを初期化</span>
-<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="c1"># Pythonでは、一般的にdequeクラスをキューとして使用します</span>
-<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="c1"># queue.Queue()は純粋なキュークラスですが、使いにくいため推奨されません</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="c1"># Python では、通常は双方向キュークラス deque をキューとして使用する</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="c1"># queue.Queue() は純粋なキュークラスだが、やや使いにくいため非推奨</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="n">que</span><span class="p">:</span> <span class="n">deque</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="n">deque</span><span class="p">()</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="c1"># 要素をエンキュー</span>
@@ -4488,7 +4488,7 @@
 <a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="n">que</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="n">que</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
 <a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>
-<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="c1"># 最初の要素にアクセス</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="c1"># キュー先頭の要素にアクセス</span>
 <a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a><span class="n">front</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">que</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
 <a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>
 <a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a><span class="c1"># 要素をデキュー</span>
@@ -4497,7 +4497,7 @@
 <a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="c1"># キューの長さを取得</span>
 <a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="n">size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">que</span><span class="p">)</span>
 <a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a>
-<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a><span class="c1"># キューが空かどうかチェック</span>
+<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a><span class="c1"># キューが空かどうかを判定</span>
 <a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a><span class="n">is_empty</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">que</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span>
 </code></pre></div>
 </div>
@@ -4512,7 +4512,7 @@
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="n">queue</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="n">queue</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a>
-<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="cm">/* 最初の要素にアクセス */</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="cm">/* キュー先頭の要素にアクセス */</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="kt">int</span><span class="w"> </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">front</span><span class="p">();</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a>
 <a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="cm">/* 要素をデキュー */</span>
@@ -4521,7 +4521,7 @@
 <a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="cm">/* キューの長さを取得 */</span>
 <a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
 <a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a>
-<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="cm">/* キューが空かどうかチェック */</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="cm">/* キューが空かどうかを判定 */</span>
 <a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="kt">bool</span><span class="w"> </span><span class="n">empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">empty</span><span class="p">();</span>
 </code></pre></div>
 </div>
@@ -4536,7 +4536,7 @@
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="n">queue</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="n">queue</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a>
-<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="cm">/* 最初の要素にアクセス */</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="cm">/* キュー先頭の要素にアクセス */</span>
 <a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="na">peek</span><span class="p">();</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a>
 <a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="cm">/* 要素をデキュー */</span>
@@ -4545,7 +4545,7 @@
 <a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="cm">/* キューの長さを取得 */</span>
 <a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
 <a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a>
-<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="cm">/* キューが空かどうかチェック */</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="cm">/* キューが空かどうかを判定 */</span>
 <a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="kt">boolean</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">();</span>
 </code></pre></div>
 </div>
@@ -4560,7 +4560,7 @@
 <a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="n">queue</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
 <a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="n">queue</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
 <a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a>
-<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="cm">/* 最初の要素にアクセス */</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="cm">/* キュー先頭の要素にアクセス */</span>
 <a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">Peek</span><span class="p">();</span>
 <a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a>
 <a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="cm">/* 要素をデキュー */</span>
@@ -4569,13 +4569,13 @@
 <a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="cm">/* キューの長さを取得 */</span>
 <a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">Count</span><span class="p">;</span>
 <a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a>
-<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="cm">/* キューが空かどうかチェック */</span>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="cm">/* キューが空かどうかを判定 */</span>
 <a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">queue_test.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* キューを初期化 */</span>
-<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="c1">// Goでは、listをキューとして使用</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="c1">// Go では、list をキューとして使用する</span>
 <a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="nx">queue</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">list</span><span class="p">.</span><span class="nx">New</span><span class="p">()</span>
 <a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a>
 <a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="cm">/* 要素をエンキュー */</span>
@@ -4585,7 +4585,7 @@
 <a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="nx">queue</span><span class="p">.</span><span class="nx">PushBack</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
 <a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="nx">queue</span><span class="p">.</span><span class="nx">PushBack</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
 <a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a>
-<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="cm">/* 最初の要素にアクセス */</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="cm">/* キュー先頭の要素にアクセス */</span>
 <a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="nx">peek</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">queue</span><span class="p">.</span><span class="nx">Front</span><span class="p">()</span>
 <a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a>
 <a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="cm">/* 要素をデキュー */</span>
@@ -4595,13 +4595,13 @@
 <a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="cm">/* キューの長さを取得 */</span>
 <a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="nx">size</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">queue</span><span class="p">.</span><span class="nx">Len</span><span class="p">()</span>
 <a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a>
-<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="cm">/* キューが空かどうかチェック */</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="cm">/* キューが空かどうかを判定 */</span>
 <a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="nx">isEmpty</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">queue</span><span class="p">.</span><span class="nx">Len</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">queue.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* キューを初期化 */</span>
-<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="c1">// Swiftには組み込みのキュークラスがないため、Arrayをキューとして使用</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="c1">// Swift には組み込みのキュークラスがないため、Array をキューとして使える</span>
 <a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">var</span><span class="w"> </span><span class="nv">queue</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
 <a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>
 <a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="cm">/* 要素をエンキュー */</span>
@@ -4611,23 +4611,23 @@
 <a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="n">queue</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
 <a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="n">queue</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
 <a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a>
-<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="cm">/* 最初の要素にアクセス */</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="cm">/* キュー先頭の要素にアクセス */</span>
 <a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="kd">let</span><span class="w"> </span><span class="nv">peek</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="bp">first</span><span class="p">!</span>
 <a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a>
 <a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="cm">/* 要素をデキュー */</span>
-<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="c1">// 配列なので、removeFirstの計算量はO(n)</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="c1">// 配列であるため、removeFirst の計算量は O(n)</span>
 <a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="kd">let</span><span class="w"> </span><span class="nv">pool</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">removeFirst</span><span class="p">()</span>
 <a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a>
 <a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="cm">/* キューの長さを取得 */</span>
 <a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="kd">let</span><span class="w"> </span><span class="nv">size</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="bp">count</span>
 <a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a>
-<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="cm">/* キューが空かどうかチェック */</span>
+<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="cm">/* キューが空かどうかを判定 */</span>
 <a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="kd">let</span><span class="w"> </span><span class="nv">isEmpty</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="bp">isEmpty</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">queue.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* キューを初期化 */</span>
-<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="c1">// JavaScriptには組み込みのキューがないため、Arrayをキューとして使用</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="c1">// JavaScript には組み込みのキューがないため、Array をキューとして使える</span>
 <a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="kd">const</span><span class="w"> </span><span class="nx">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
 <a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a>
 <a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="cm">/* 要素をエンキュー */</span>
@@ -4637,23 +4637,23 @@
 <a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="nx">queue</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
 <a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="nx">queue</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">4</span><span class="p">);</span>
 <a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a>
-<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="cm">/* 最初の要素にアクセス */</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="cm">/* キュー先頭の要素にアクセス */</span>
 <a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">queue</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span>
 <a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a>
 <a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="cm">/* 要素をデキュー */</span>
-<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="c1">// 基礎構造が配列なので、shift()メソッドの時間計算量はO(n)</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="c1">// 基盤は配列であるため、shift() メソッドの時間計算量は O(n)</span>
 <a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="kd">const</span><span class="w"> </span><span class="nx">pop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">queue</span><span class="p">.</span><span class="nx">shift</span><span class="p">();</span>
 <a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a>
 <a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="cm">/* キューの長さを取得 */</span>
 <a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="kd">const</span><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">queue</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
 <a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a>
-<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="cm">/* キューが空かどうかチェック */</span>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="cm">/* キューが空かどうかを判定 */</span>
 <a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="kd">const</span><span class="w"> </span><span class="nx">empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">queue</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">queue.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* キューを初期化 */</span>
-<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="c1">// TypeScriptには組み込みのキューがないため、Arrayをキューとして使用</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="c1">// TypeScript には組み込みのキューがないため、Array をキューとして使える</span>
 <a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="kd">const</span><span class="w"> </span><span class="nx">queue</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
 <a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a>
 <a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="cm">/* 要素をエンキュー */</span>
@@ -4663,23 +4663,23 @@
 <a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="nx">queue</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
 <a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="nx">queue</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">4</span><span class="p">);</span>
 <a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a>
-<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="cm">/* 最初の要素にアクセス */</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="cm">/* キュー先頭の要素にアクセス */</span>
 <a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">queue</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span>
 <a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a>
 <a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="cm">/* 要素をデキュー */</span>
-<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="c1">// 基礎構造が配列なので、shift()メソッドの時間計算量はO(n)</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="c1">// 基盤は配列であるため、shift() メソッドの時間計算量は O(n)</span>
 <a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="kd">const</span><span class="w"> </span><span class="nx">pop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">queue</span><span class="p">.</span><span class="nx">shift</span><span class="p">();</span>
 <a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a>
 <a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="cm">/* キューの長さを取得 */</span>
 <a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="kd">const</span><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">queue</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
 <a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a>
-<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="cm">/* キューが空かどうかチェック */</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="cm">/* キューが空かどうかを判定 */</span>
 <a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="kd">const</span><span class="w"> </span><span class="nx">empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">queue</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">queue.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* キューを初期化 */</span>
-<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="c1">// DartのQueueクラスは双方向キューですが、キューとして使用できます</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="c1">// Dart では、キュークラス Qeque は双方向キューであり、キューとしても使用できる</span>
 <a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="n">Queue</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Queue</span><span class="p">();</span>
 <a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a>
 <a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="cm">/* 要素をエンキュー */</span>
@@ -4689,7 +4689,7 @@
 <a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="n">queue</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">5</span><span class="p">);</span>
 <a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="n">queue</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">4</span><span class="p">);</span>
 <a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a>
-<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="cm">/* 最初の要素にアクセス */</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="cm">/* キュー先頭の要素にアクセス */</span>
 <a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">first</span><span class="p">;</span>
 <a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a>
 <a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="cm">/* 要素をデキュー */</span>
@@ -4698,13 +4698,13 @@
 <a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="cm">/* キューの長さを取得 */</span>
 <a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
 <a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a>
-<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="cm">/* キューが空かどうかチェック */</span>
+<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="cm">/* キューが空かどうかを判定 */</span>
 <a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">isEmpty</span><span class="p">;</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">queue.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 双方向キューを初期化 */</span>
-<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="c1">// Rustでは、双方向キューを通常のキューとして使用</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="c1">// Rust では双方向キューを通常のキューとして使う</span>
 <a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">deque</span><span class="p">:</span><span class="w"> </span><span class="nc">VecDeque</span><span class="o">&lt;</span><span class="kt">u32</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">VecDeque</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
 <a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a>
 <a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="cm">/* 要素をエンキュー */</span>
@@ -4714,7 +4714,7 @@
 <a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
 <a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
 <a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a>
-<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="cm">/* 最初の要素にアクセス */</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="cm">/* キュー先頭の要素にアクセス */</span>
 <a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">front</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">front</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="p">}</span>
 <a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a>
@@ -4725,28 +4725,78 @@
 <a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="cm">/* キューの長さを取得 */</span>
 <a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="kd">let</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
 <a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a>
-<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="cm">/* キューが空かどうかチェック */</span>
+<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="cm">/* キューが空かどうかを判定 */</span>
 <a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="kd">let</span><span class="w"> </span><span class="n">is_empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">is_empty</span><span class="p">();</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">queue.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// Cは組み込みのキューを提供していません</span>
+<div class="highlight"><span class="filename">queue.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// C には組み込みのキューがない</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">queue.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
+<div class="highlight"><span class="filename">queue.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* キューを初期化 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">val</span><span class="w"> </span><span class="nv">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">LinkedList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="cm">/* 要素をエンキュー */</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="n">queue</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="n">queue</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="m">3</span><span class="p">)</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="n">queue</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="m">2</span><span class="p">)</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="n">queue</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="m">5</span><span class="p">)</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="n">queue</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="m">4</span><span class="p">)</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="kd">val</span><span class="w"> </span><span class="nv">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="na">peek</span><span class="p">()</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="cm">/* 要素をデキュー */</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="kd">val</span><span class="w"> </span><span class="nv">pop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="na">poll</span><span class="p">()</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="kd">val</span><span class="w"> </span><span class="nv">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="kd">val</span><span class="w"> </span><span class="nv">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">()</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">queue.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1"># キューを初期化</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="c1"># Ruby 組み込みのキュー（Thread::Queue) には peek と走査メソッドがないため、Array をキューとして使える</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="n">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="c1"># 要素をエンキュー</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="n">queue</span><span class="o">.</span><span class="n">push</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="n">queue</span><span class="o">.</span><span class="n">push</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="n">queue</span><span class="o">.</span><span class="n">push</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="n">queue</span><span class="o">.</span><span class="n">push</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="n">queue</span><span class="o">.</span><span class="n">push</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="c1"># キュー先頭の要素にアクセス</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">.</span><span class="n">first</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="c1"># 要素をデキュー</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="c1"># 注意：配列であるため、Array#shift メソッドの時間計算量は O(n)</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="n">pop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">.</span><span class="n">shift</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="c1"># キューの長さを取得</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="c1"># キューが空かどうかを判定</span>
+<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="n">is_empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">.</span><span class="n">empty?</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>可視化実行</summary>
+<p>https://pythontutor.com/render.html#code=from%20collections%20import%20deque%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E9%98%9F%E5%88%97%0A%20%20%20%20%23%20%E5%9C%A8%20Python%20%E4%B8%AD%EF%BC%8C%E6%88%91%E4%BB%AC%E4%B8%80%E8%88%AC%E5%B0%86%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%E7%B1%BB%20deque%20%E7%9C%8B%E4%BD%9C%E9%98%9F%E5%88%97%E4%BD%BF%E7%94%A8%0A%20%20%20%20%23%20%E8%99%BD%E7%84%B6%20queue.Queue%28%29%20%E6%98%AF%E7%BA%AF%E6%AD%A3%E7%9A%84%E9%98%9F%E5%88%97%E7%B1%BB%EF%BC%8C%E4%BD%86%E4%B8%8D%E5%A4%AA%E5%A5%BD%E7%94%A8%0A%20%20%20%20que%20%3D%20deque%28%29%0A%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%85%A5%E9%98%9F%0A%20%20%20%20que.append%281%29%0A%20%20%20%20que.append%283%29%0A%20%20%20%20que.append%282%29%0A%20%20%20%20que.append%285%29%0A%20%20%20%20que.append%284%29%0A%20%20%20%20print%28%22%E9%98%9F%E5%88%97%20que%20%3D%22,%20que%29%0A%0A%20%20%20%20%23%20%E8%AE%BF%E9%97%AE%E9%98%9F%E9%A6%96%E5%85%83%E7%B4%A0%0A%20%20%20%20front%20%3D%20que%5B0%5D%0A%20%20%20%20print%28%22%E9%98%9F%E9%A6%96%E5%85%83%E7%B4%A0%20front%20%3D%22,%20front%29%0A%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%87%BA%E9%98%9F%0A%20%20%20%20pop%20%3D%20que.popleft%28%29%0A%20%20%20%20print%28%22%E5%87%BA%E9%98%9F%E5%85%83%E7%B4%A0%20pop%20%3D%22,%20pop%29%0A%20%20%20%20print%28%22%E5%87%BA%E9%98%9F%E5%90%8E%20que%20%3D%22,%20que%29%0A%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E9%98%9F%E5%88%97%E7%9A%84%E9%95%BF%E5%BA%A6%0A%20%20%20%20size%20%3D%20len%28que%29%0A%20%20%20%20print%28%22%E9%98%9F%E5%88%97%E9%95%BF%E5%BA%A6%20size%20%3D%22,%20size%29%0A%0A%20%20%20%20%23%20%E5%88%A4%E6%96%AD%E9%98%9F%E5%88%97%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%0A%20%20%20%20is_empty%20%3D%20len%28que%29%20%3D%3D%200%0A%20%20%20%20print%28%22%E9%98%9F%E5%88%97%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%20%3D%22,%20is_empty%29&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>
+</details>
 <h2 id="522">5.2.2 &nbsp; キューの実装<a class="headerlink" href="#522" title="Permanent link">&para;</a></h2>
-<p>キューを実装するには、一方の端で要素を追加し、もう一方の端で要素を削除できるデータ構造が必要です。連結リストと配列の両方がこの要件を満たします。</p>
-<h3 id="1">1. &nbsp; 連結リストベースの実装<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>下図に示すように、連結リストの「ヘッドノード」と「テールノード」をそれぞれキューの「フロント」と「リア」と考えることができます。ノードは後ろでのみ追加でき、前でのみ削除できるように規定されています。</p>
+<p>キューを実装するには、一方の端で要素を追加し、もう一方の端で要素を削除できるデータ構造が必要です。連結リストと配列はいずれもこの条件を満たします。</p>
+<h3 id="1">1. &nbsp; 連結リストに基づく実装<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>下図のように、連結リストの「先頭ノード」と「末尾ノード」をそれぞれ「キュー先頭」と「キュー末尾」とみなし、キュー末尾ではノードの追加のみ、キュー先頭ではノードの削除のみを行うようにします。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:3"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">LinkedListQueue</label><label for="__tabbed_2_2">push()</label><label for="__tabbed_2_3">pop()</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="連結リストによるキュー実装のエンキューとデキュー操作" class="animation-figure" src="../queue.assets/linkedlist_queue_step1.png" /></p>
+<p><img alt="連結リストでキューを実装したエンキューとデキュー操作" class="animation-figure" src="../queue.assets/linkedlist_queue_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="linkedlist_queue_push" class="animation-figure" src="../queue.assets/linkedlist_queue_step2_push.png" /></p>
@@ -4756,266 +4806,924 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 5-5 &nbsp; 連結リストによるキュー実装のエンキューとデキュー操作 </p>
+<p align="center"> 図 5-5 &nbsp; 連結リストでキューを実装したエンキューとデキュー操作 </p>
 
-<p>以下は、連結リストを使用してキューを実装するコードです：</p>
+<p>以下は連結リストでキューを実装するコードです：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_queue.py</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">LinkedListQueue</span><span class="p">:</span>
-<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;連結リストベースのキュークラス&quot;&quot;&quot;</span>
-<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a>
-<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
-<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># ヘッドノード front</span>
-<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># テールノード rear</span>
-<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>
-<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a>
-<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キューの長さを取得&quot;&quot;&quot;</span>
-<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span>
-<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a>
-<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">is_empty</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
-<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キューが空かどうかを判定&quot;&quot;&quot;</span>
-<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="mi">0</span>
-<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a>
-<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;エンキュー&quot;&quot;&quot;</span>
-<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a>        <span class="c1"># テールノードの後ろに num を追加</span>
-<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a>        <span class="n">node</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
-<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a>        <span class="c1"># キューが空の場合、ヘッドとテールノードの両方をそのノードに向ける</span>
-<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">=</span> <span class="n">node</span>
-<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span> <span class="o">=</span> <span class="n">node</span>
-<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a>        <span class="c1"># キューが空でない場合、そのノードをテールノードの後ろに追加</span>
-<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a>        <span class="k">else</span><span class="p">:</span>
-<a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">node</span>
-<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span> <span class="o">=</span> <span class="n">node</span>
-<a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">+=</span> <span class="mi">1</span>
-<a id="__codelineno-12-31" name="__codelineno-12-31" href="#__codelineno-12-31"></a>
-<a id="__codelineno-12-32" name="__codelineno-12-32" href="#__codelineno-12-32"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-12-33" name="__codelineno-12-33" href="#__codelineno-12-33"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;デキュー&quot;&quot;&quot;</span>
-<a id="__codelineno-12-34" name="__codelineno-12-34" href="#__codelineno-12-34"></a>        <span class="n">num</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">peek</span><span class="p">()</span>
-<a id="__codelineno-12-35" name="__codelineno-12-35" href="#__codelineno-12-35"></a>        <span class="c1"># ヘッドノードを削除</span>
-<a id="__codelineno-12-36" name="__codelineno-12-36" href="#__codelineno-12-36"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="o">.</span><span class="n">next</span>
-<a id="__codelineno-12-37" name="__codelineno-12-37" href="#__codelineno-12-37"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-=</span> <span class="mi">1</span>
-<a id="__codelineno-12-38" name="__codelineno-12-38" href="#__codelineno-12-38"></a>        <span class="k">return</span> <span class="n">num</span>
-<a id="__codelineno-12-39" name="__codelineno-12-39" href="#__codelineno-12-39"></a>
-<a id="__codelineno-12-40" name="__codelineno-12-40" href="#__codelineno-12-40"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-12-41" name="__codelineno-12-41" href="#__codelineno-12-41"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;フロント要素にアクセス&quot;&quot;&quot;</span>
-<a id="__codelineno-12-42" name="__codelineno-12-42" href="#__codelineno-12-42"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
-<a id="__codelineno-12-43" name="__codelineno-12-43" href="#__codelineno-12-43"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Queue is empty&quot;</span><span class="p">)</span>
-<a id="__codelineno-12-44" name="__codelineno-12-44" href="#__codelineno-12-44"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="o">.</span><span class="n">val</span>
-<a id="__codelineno-12-45" name="__codelineno-12-45" href="#__codelineno-12-45"></a>
-<a id="__codelineno-12-46" name="__codelineno-12-46" href="#__codelineno-12-46"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">to_list</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
-<a id="__codelineno-12-47" name="__codelineno-12-47" href="#__codelineno-12-47"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;出力用のリストに変換&quot;&quot;&quot;</span>
-<a id="__codelineno-12-48" name="__codelineno-12-48" href="#__codelineno-12-48"></a>        <span class="n">queue</span> <span class="o">=</span> <span class="p">[]</span>
-<a id="__codelineno-12-49" name="__codelineno-12-49" href="#__codelineno-12-49"></a>        <span class="n">temp</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span>
-<a id="__codelineno-12-50" name="__codelineno-12-50" href="#__codelineno-12-50"></a>        <span class="k">while</span> <span class="n">temp</span><span class="p">:</span>
-<a id="__codelineno-12-51" name="__codelineno-12-51" href="#__codelineno-12-51"></a>            <span class="n">queue</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">temp</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
-<a id="__codelineno-12-52" name="__codelineno-12-52" href="#__codelineno-12-52"></a>            <span class="n">temp</span> <span class="o">=</span> <span class="n">temp</span><span class="o">.</span><span class="n">next</span>
-<a id="__codelineno-12-53" name="__codelineno-12-53" href="#__codelineno-12-53"></a>        <span class="k">return</span> <span class="n">queue</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_queue.cpp</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="cm">/* 連結リストに基づくキュークラス */</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">LinkedListQueue</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
-<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">front</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">rear</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードfront、末尾ノードrear</span>
-<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
-<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>
-<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
-<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="w">    </span><span class="n">LinkedListQueue</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
-<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a><span class="w">        </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
-<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="w">        </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a><span class="w">    </span><span class="p">}</span>
+<div class="highlight"><span class="filename">linkedlist_queue.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">LinkedListQueue</span><span class="p">:</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;連結リストベースのキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
+<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># 先頭ノード front</span>
+<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># 末尾ノード rear</span>
+<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>
+<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キューの長さを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span>
 <a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a>
-<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a><span class="w">    </span><span class="o">~</span><span class="n">LinkedListQueue</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a><span class="w">        </span><span class="c1">// 連結リストを走査、ノードを削除、メモリを解放</span>
-<a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a><span class="w">        </span><span class="n">freeMemoryLinkedList</span><span class="p">(</span><span class="n">front</span><span class="p">);</span>
-<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a>
-<a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a><span class="w">    </span><span class="cm">/* キューの長さを取得 */</span>
-<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
-<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a>
-<a id="__codelineno-13-24" name="__codelineno-13-24" href="#__codelineno-13-24"></a><span class="w">    </span><span class="cm">/* キューが空かどうかを判定 */</span>
-<a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a><span class="w">    </span><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-26" name="__codelineno-13-26" href="#__codelineno-13-26"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-13-27" name="__codelineno-13-27" href="#__codelineno-13-27"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-28" name="__codelineno-13-28" href="#__codelineno-13-28"></a>
-<a id="__codelineno-13-29" name="__codelineno-13-29" href="#__codelineno-13-29"></a><span class="w">    </span><span class="cm">/* エンキュー */</span>
-<a id="__codelineno-13-30" name="__codelineno-13-30" href="#__codelineno-13-30"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-31" name="__codelineno-13-31" href="#__codelineno-13-31"></a><span class="w">        </span><span class="c1">// 末尾ノードの後ろにnumを追加</span>
-<a id="__codelineno-13-32" name="__codelineno-13-32" href="#__codelineno-13-32"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
-<a id="__codelineno-13-33" name="__codelineno-13-33" href="#__codelineno-13-33"></a><span class="w">        </span><span class="c1">// キューが空の場合、先頭と末尾ノードの両方をそのノードに向ける</span>
-<a id="__codelineno-13-34" name="__codelineno-13-34" href="#__codelineno-13-34"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-35" name="__codelineno-13-35" href="#__codelineno-13-35"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
-<a id="__codelineno-13-36" name="__codelineno-13-36" href="#__codelineno-13-36"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
-<a id="__codelineno-13-37" name="__codelineno-13-37" href="#__codelineno-13-37"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-13-38" name="__codelineno-13-38" href="#__codelineno-13-38"></a><span class="w">        </span><span class="c1">// キューが空でない場合、そのノードを末尾ノードの後ろに追加</span>
-<a id="__codelineno-13-39" name="__codelineno-13-39" href="#__codelineno-13-39"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-40" name="__codelineno-13-40" href="#__codelineno-13-40"></a><span class="w">            </span><span class="n">rear</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
-<a id="__codelineno-13-41" name="__codelineno-13-41" href="#__codelineno-13-41"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
-<a id="__codelineno-13-42" name="__codelineno-13-42" href="#__codelineno-13-42"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-13-43" name="__codelineno-13-43" href="#__codelineno-13-43"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-13-44" name="__codelineno-13-44" href="#__codelineno-13-44"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">is_empty</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
+<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キューが空かどうかを判定&quot;&quot;&quot;</span>
+<a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="mi">0</span>
+<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>
+<a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;エンキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a>        <span class="c1"># 末尾ノードの後ろに num を追加</span>
+<a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a>        <span class="n">node</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a>        <span class="c1"># キューが空なら、先頭・末尾ノードをともにそのノードに設定</span>
+<a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-13-24" name="__codelineno-13-24" href="#__codelineno-13-24"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">=</span> <span class="n">node</span>
+<a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span> <span class="o">=</span> <span class="n">node</span>
+<a id="__codelineno-13-26" name="__codelineno-13-26" href="#__codelineno-13-26"></a>        <span class="c1"># キューが空でなければ、そのノードを末尾ノードの後ろに追加</span>
+<a id="__codelineno-13-27" name="__codelineno-13-27" href="#__codelineno-13-27"></a>        <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-13-28" name="__codelineno-13-28" href="#__codelineno-13-28"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">node</span>
+<a id="__codelineno-13-29" name="__codelineno-13-29" href="#__codelineno-13-29"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span> <span class="o">=</span> <span class="n">node</span>
+<a id="__codelineno-13-30" name="__codelineno-13-30" href="#__codelineno-13-30"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-13-31" name="__codelineno-13-31" href="#__codelineno-13-31"></a>
+<a id="__codelineno-13-32" name="__codelineno-13-32" href="#__codelineno-13-32"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-33" name="__codelineno-13-33" href="#__codelineno-13-33"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;デキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-13-34" name="__codelineno-13-34" href="#__codelineno-13-34"></a>        <span class="n">num</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">peek</span><span class="p">()</span>
+<a id="__codelineno-13-35" name="__codelineno-13-35" href="#__codelineno-13-35"></a>        <span class="c1"># 先頭ノードを削除</span>
+<a id="__codelineno-13-36" name="__codelineno-13-36" href="#__codelineno-13-36"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-13-37" name="__codelineno-13-37" href="#__codelineno-13-37"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-=</span> <span class="mi">1</span>
+<a id="__codelineno-13-38" name="__codelineno-13-38" href="#__codelineno-13-38"></a>        <span class="k">return</span> <span class="n">num</span>
+<a id="__codelineno-13-39" name="__codelineno-13-39" href="#__codelineno-13-39"></a>
+<a id="__codelineno-13-40" name="__codelineno-13-40" href="#__codelineno-13-40"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-41" name="__codelineno-13-41" href="#__codelineno-13-41"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キュー先頭の要素にアクセス&quot;&quot;&quot;</span>
+<a id="__codelineno-13-42" name="__codelineno-13-42" href="#__codelineno-13-42"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
+<a id="__codelineno-13-43" name="__codelineno-13-43" href="#__codelineno-13-43"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;キューが空です&quot;</span><span class="p">)</span>
+<a id="__codelineno-13-44" name="__codelineno-13-44" href="#__codelineno-13-44"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="o">.</span><span class="n">val</span>
 <a id="__codelineno-13-45" name="__codelineno-13-45" href="#__codelineno-13-45"></a>
-<a id="__codelineno-13-46" name="__codelineno-13-46" href="#__codelineno-13-46"></a><span class="w">    </span><span class="cm">/* デキュー */</span>
-<a id="__codelineno-13-47" name="__codelineno-13-47" href="#__codelineno-13-47"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-48" name="__codelineno-13-48" href="#__codelineno-13-48"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span><span class="p">();</span>
-<a id="__codelineno-13-49" name="__codelineno-13-49" href="#__codelineno-13-49"></a><span class="w">        </span><span class="c1">// 先頭ノードを削除</span>
-<a id="__codelineno-13-50" name="__codelineno-13-50" href="#__codelineno-13-50"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
-<a id="__codelineno-13-51" name="__codelineno-13-51" href="#__codelineno-13-51"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
-<a id="__codelineno-13-52" name="__codelineno-13-52" href="#__codelineno-13-52"></a><span class="w">        </span><span class="c1">// メモリを解放</span>
-<a id="__codelineno-13-53" name="__codelineno-13-53" href="#__codelineno-13-53"></a><span class="w">        </span><span class="k">delete</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
-<a id="__codelineno-13-54" name="__codelineno-13-54" href="#__codelineno-13-54"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
-<a id="__codelineno-13-55" name="__codelineno-13-55" href="#__codelineno-13-55"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-13-56" name="__codelineno-13-56" href="#__codelineno-13-56"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-57" name="__codelineno-13-57" href="#__codelineno-13-57"></a>
-<a id="__codelineno-13-58" name="__codelineno-13-58" href="#__codelineno-13-58"></a><span class="w">    </span><span class="cm">/* 先頭要素にアクセス */</span>
-<a id="__codelineno-13-59" name="__codelineno-13-59" href="#__codelineno-13-59"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-60" name="__codelineno-13-60" href="#__codelineno-13-60"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
-<a id="__codelineno-13-61" name="__codelineno-13-61" href="#__codelineno-13-61"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Queue is empty&quot;</span><span class="p">);</span>
-<a id="__codelineno-13-62" name="__codelineno-13-62" href="#__codelineno-13-62"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">front</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
-<a id="__codelineno-13-63" name="__codelineno-13-63" href="#__codelineno-13-63"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-64" name="__codelineno-13-64" href="#__codelineno-13-64"></a>
-<a id="__codelineno-13-65" name="__codelineno-13-65" href="#__codelineno-13-65"></a><span class="w">    </span><span class="cm">/* 連結リストをVectorに変換して返却 */</span>
-<a id="__codelineno-13-66" name="__codelineno-13-66" href="#__codelineno-13-66"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toVector</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-67" name="__codelineno-13-67" href="#__codelineno-13-67"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
-<a id="__codelineno-13-68" name="__codelineno-13-68" href="#__codelineno-13-68"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">(</span><span class="n">size</span><span class="p">());</span>
-<a id="__codelineno-13-69" name="__codelineno-13-69" href="#__codelineno-13-69"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-70" name="__codelineno-13-70" href="#__codelineno-13-70"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
-<a id="__codelineno-13-71" name="__codelineno-13-71" href="#__codelineno-13-71"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
-<a id="__codelineno-13-72" name="__codelineno-13-72" href="#__codelineno-13-72"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-13-73" name="__codelineno-13-73" href="#__codelineno-13-73"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
-<a id="__codelineno-13-74" name="__codelineno-13-74" href="#__codelineno-13-74"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-75" name="__codelineno-13-75" href="#__codelineno-13-75"></a><span class="p">};</span>
+<a id="__codelineno-13-46" name="__codelineno-13-46" href="#__codelineno-13-46"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">to_list</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-13-47" name="__codelineno-13-47" href="#__codelineno-13-47"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;表示用にリストへ変換&quot;&quot;&quot;</span>
+<a id="__codelineno-13-48" name="__codelineno-13-48" href="#__codelineno-13-48"></a>        <span class="n">queue</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-13-49" name="__codelineno-13-49" href="#__codelineno-13-49"></a>        <span class="n">temp</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span>
+<a id="__codelineno-13-50" name="__codelineno-13-50" href="#__codelineno-13-50"></a>        <span class="k">while</span> <span class="n">temp</span><span class="p">:</span>
+<a id="__codelineno-13-51" name="__codelineno-13-51" href="#__codelineno-13-51"></a>            <span class="n">queue</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">temp</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-13-52" name="__codelineno-13-52" href="#__codelineno-13-52"></a>            <span class="n">temp</span> <span class="o">=</span> <span class="n">temp</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-13-53" name="__codelineno-13-53" href="#__codelineno-13-53"></a>        <span class="k">return</span> <span class="n">queue</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_queue.java</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 連結リストに基づくキュークラス */</span>
-<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kd">class</span> <span class="nc">LinkedListQueue</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="n">front</span><span class="p">,</span><span class="w"> </span><span class="n">rear</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノード front、末尾ノード rear</span>
-<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>
-<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">LinkedListQueue</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
-<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">        </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
-<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>
-<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">    </span><span class="cm">/* キューの長さを取得 */</span>
-<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
-<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a>
-<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">    </span><span class="cm">/* キューが空かどうかを判定 */</span>
-<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a>
-<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a><span class="w">    </span><span class="cm">/* エンキュー */</span>
-<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a><span class="w">        </span><span class="c1">// 末尾ノードの後ろに num を追加</span>
-<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
-<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a><span class="w">        </span><span class="c1">// キューが空の場合、先頭と末尾ノードの両方をそのノードにポイント</span>
-<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
-<a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
-<a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></a><span class="w">        </span><span class="c1">// キューが空でない場合、そのノードを末尾ノードの後ろに追加</span>
-<a id="__codelineno-14-30" name="__codelineno-14-30" href="#__codelineno-14-30"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-31" name="__codelineno-14-31" href="#__codelineno-14-31"></a><span class="w">            </span><span class="n">rear</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
-<a id="__codelineno-14-32" name="__codelineno-14-32" href="#__codelineno-14-32"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
-<a id="__codelineno-14-33" name="__codelineno-14-33" href="#__codelineno-14-33"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-14-34" name="__codelineno-14-34" href="#__codelineno-14-34"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-14-35" name="__codelineno-14-35" href="#__codelineno-14-35"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-36" name="__codelineno-14-36" href="#__codelineno-14-36"></a>
-<a id="__codelineno-14-37" name="__codelineno-14-37" href="#__codelineno-14-37"></a><span class="w">    </span><span class="cm">/* デキュー */</span>
-<a id="__codelineno-14-38" name="__codelineno-14-38" href="#__codelineno-14-38"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-39" name="__codelineno-14-39" href="#__codelineno-14-39"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span><span class="p">();</span>
-<a id="__codelineno-14-40" name="__codelineno-14-40" href="#__codelineno-14-40"></a><span class="w">        </span><span class="c1">// 先頭ノードを削除</span>
-<a id="__codelineno-14-41" name="__codelineno-14-41" href="#__codelineno-14-41"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
-<a id="__codelineno-14-42" name="__codelineno-14-42" href="#__codelineno-14-42"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
-<a id="__codelineno-14-43" name="__codelineno-14-43" href="#__codelineno-14-43"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<div class="highlight"><span class="filename">linkedlist_queue.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 連結リストベースのキュー */</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">LinkedListQueue</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">front</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">rear</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノード front、末尾ノード rear</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">    </span><span class="n">LinkedListQueue</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">        </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">        </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">    </span><span class="o">~</span><span class="n">LinkedListQueue</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">        </span><span class="c1">// 連結リストを走査してノードを削除し、メモリを解放する</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">        </span><span class="n">freeMemoryLinkedList</span><span class="p">(</span><span class="n">front</span><span class="p">);</span>
+<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a>
+<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w">    </span><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a>
+<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a><span class="w">    </span><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a><span class="w">    </span><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a>
+<a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></a><span class="w">    </span><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-14-30" name="__codelineno-14-30" href="#__codelineno-14-30"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-31" name="__codelineno-14-31" href="#__codelineno-14-31"></a><span class="w">        </span><span class="c1">// 末尾ノードの後ろに num を追加</span>
+<a id="__codelineno-14-32" name="__codelineno-14-32" href="#__codelineno-14-32"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-14-33" name="__codelineno-14-33" href="#__codelineno-14-33"></a><span class="w">        </span><span class="c1">// キューが空なら、先頭・末尾ノードをともにそのノードに設定</span>
+<a id="__codelineno-14-34" name="__codelineno-14-34" href="#__codelineno-14-34"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-35" name="__codelineno-14-35" href="#__codelineno-14-35"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-14-36" name="__codelineno-14-36" href="#__codelineno-14-36"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-14-37" name="__codelineno-14-37" href="#__codelineno-14-37"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-14-38" name="__codelineno-14-38" href="#__codelineno-14-38"></a><span class="w">        </span><span class="c1">// キューが空でなければ、そのノードを末尾ノードの後ろに追加</span>
+<a id="__codelineno-14-39" name="__codelineno-14-39" href="#__codelineno-14-39"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-40" name="__codelineno-14-40" href="#__codelineno-14-40"></a><span class="w">            </span><span class="n">rear</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-14-41" name="__codelineno-14-41" href="#__codelineno-14-41"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-14-42" name="__codelineno-14-42" href="#__codelineno-14-42"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-14-43" name="__codelineno-14-43" href="#__codelineno-14-43"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
 <a id="__codelineno-14-44" name="__codelineno-14-44" href="#__codelineno-14-44"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-45" name="__codelineno-14-45" href="#__codelineno-14-45"></a>
-<a id="__codelineno-14-46" name="__codelineno-14-46" href="#__codelineno-14-46"></a><span class="w">    </span><span class="cm">/* 先頭要素にアクセス */</span>
-<a id="__codelineno-14-47" name="__codelineno-14-47" href="#__codelineno-14-47"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-48" name="__codelineno-14-48" href="#__codelineno-14-48"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
-<a id="__codelineno-14-49" name="__codelineno-14-49" href="#__codelineno-14-49"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
-<a id="__codelineno-14-50" name="__codelineno-14-50" href="#__codelineno-14-50"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">front</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
-<a id="__codelineno-14-51" name="__codelineno-14-51" href="#__codelineno-14-51"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-52" name="__codelineno-14-52" href="#__codelineno-14-52"></a>
-<a id="__codelineno-14-53" name="__codelineno-14-53" href="#__codelineno-14-53"></a><span class="w">    </span><span class="cm">/* 連結リストを配列に変換して返す */</span>
-<a id="__codelineno-14-54" name="__codelineno-14-54" href="#__codelineno-14-54"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-55" name="__codelineno-14-55" href="#__codelineno-14-55"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
-<a id="__codelineno-14-56" name="__codelineno-14-56" href="#__codelineno-14-56"></a><span class="w">        </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">size</span><span class="p">()</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-14-57" name="__codelineno-14-57" href="#__codelineno-14-57"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-58" name="__codelineno-14-58" href="#__codelineno-14-58"></a><span class="w">            </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
-<a id="__codelineno-14-59" name="__codelineno-14-59" href="#__codelineno-14-59"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
-<a id="__codelineno-14-60" name="__codelineno-14-60" href="#__codelineno-14-60"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-14-61" name="__codelineno-14-61" href="#__codelineno-14-61"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
-<a id="__codelineno-14-62" name="__codelineno-14-62" href="#__codelineno-14-62"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-63" name="__codelineno-14-63" href="#__codelineno-14-63"></a><span class="p">}</span>
+<a id="__codelineno-14-46" name="__codelineno-14-46" href="#__codelineno-14-46"></a><span class="w">    </span><span class="cm">/* デキュー */</span>
+<a id="__codelineno-14-47" name="__codelineno-14-47" href="#__codelineno-14-47"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-48" name="__codelineno-14-48" href="#__codelineno-14-48"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span><span class="p">();</span>
+<a id="__codelineno-14-49" name="__codelineno-14-49" href="#__codelineno-14-49"></a><span class="w">        </span><span class="c1">// 先頭ノードを削除</span>
+<a id="__codelineno-14-50" name="__codelineno-14-50" href="#__codelineno-14-50"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-14-51" name="__codelineno-14-51" href="#__codelineno-14-51"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-14-52" name="__codelineno-14-52" href="#__codelineno-14-52"></a><span class="w">        </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-14-53" name="__codelineno-14-53" href="#__codelineno-14-53"></a><span class="w">        </span><span class="k">delete</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-14-54" name="__codelineno-14-54" href="#__codelineno-14-54"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-14-55" name="__codelineno-14-55" href="#__codelineno-14-55"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-14-56" name="__codelineno-14-56" href="#__codelineno-14-56"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-57" name="__codelineno-14-57" href="#__codelineno-14-57"></a>
+<a id="__codelineno-14-58" name="__codelineno-14-58" href="#__codelineno-14-58"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-14-59" name="__codelineno-14-59" href="#__codelineno-14-59"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-60" name="__codelineno-14-60" href="#__codelineno-14-60"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-14-61" name="__codelineno-14-61" href="#__codelineno-14-61"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;キューが空です&quot;</span><span class="p">);</span>
+<a id="__codelineno-14-62" name="__codelineno-14-62" href="#__codelineno-14-62"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">front</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-14-63" name="__codelineno-14-63" href="#__codelineno-14-63"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-64" name="__codelineno-14-64" href="#__codelineno-14-64"></a>
+<a id="__codelineno-14-65" name="__codelineno-14-65" href="#__codelineno-14-65"></a><span class="w">    </span><span class="cm">/* 連結リストを Vector に変換して返す */</span>
+<a id="__codelineno-14-66" name="__codelineno-14-66" href="#__codelineno-14-66"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toVector</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-67" name="__codelineno-14-67" href="#__codelineno-14-67"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-14-68" name="__codelineno-14-68" href="#__codelineno-14-68"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">(</span><span class="n">size</span><span class="p">());</span>
+<a id="__codelineno-14-69" name="__codelineno-14-69" href="#__codelineno-14-69"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-70" name="__codelineno-14-70" href="#__codelineno-14-70"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-14-71" name="__codelineno-14-71" href="#__codelineno-14-71"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-14-72" name="__codelineno-14-72" href="#__codelineno-14-72"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-14-73" name="__codelineno-14-73" href="#__codelineno-14-73"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-14-74" name="__codelineno-14-74" href="#__codelineno-14-74"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-75" name="__codelineno-14-75" href="#__codelineno-14-75"></a><span class="p">};</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_queue.cs</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">LinkedListQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">linkedlist_queue.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 連結リストベースのキュー */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kd">class</span> <span class="nc">LinkedListQueue</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="n">front</span><span class="p">,</span><span class="w"> </span><span class="n">rear</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノード front、末尾ノード rear</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">LinkedListQueue</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">        </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">    </span><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a>
+<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">    </span><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a>
+<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="w">    </span><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="w">        </span><span class="c1">// 末尾ノードの後ろに num を追加</span>
+<a id="__codelineno-15-24" name="__codelineno-15-24" href="#__codelineno-15-24"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></a><span class="w">        </span><span class="c1">// キューが空なら、先頭・末尾ノードをともにそのノードに設定</span>
+<a id="__codelineno-15-26" name="__codelineno-15-26" href="#__codelineno-15-26"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-15-28" name="__codelineno-15-28" href="#__codelineno-15-28"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-15-29" name="__codelineno-15-29" href="#__codelineno-15-29"></a><span class="w">        </span><span class="c1">// キューが空でなければ、そのノードを末尾ノードの後ろに追加</span>
+<a id="__codelineno-15-30" name="__codelineno-15-30" href="#__codelineno-15-30"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-31" name="__codelineno-15-31" href="#__codelineno-15-31"></a><span class="w">            </span><span class="n">rear</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-15-32" name="__codelineno-15-32" href="#__codelineno-15-32"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-15-33" name="__codelineno-15-33" href="#__codelineno-15-33"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-34" name="__codelineno-15-34" href="#__codelineno-15-34"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-15-35" name="__codelineno-15-35" href="#__codelineno-15-35"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-36" name="__codelineno-15-36" href="#__codelineno-15-36"></a>
+<a id="__codelineno-15-37" name="__codelineno-15-37" href="#__codelineno-15-37"></a><span class="w">    </span><span class="cm">/* デキュー */</span>
+<a id="__codelineno-15-38" name="__codelineno-15-38" href="#__codelineno-15-38"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-39" name="__codelineno-15-39" href="#__codelineno-15-39"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span><span class="p">();</span>
+<a id="__codelineno-15-40" name="__codelineno-15-40" href="#__codelineno-15-40"></a><span class="w">        </span><span class="c1">// 先頭ノードを削除</span>
+<a id="__codelineno-15-41" name="__codelineno-15-41" href="#__codelineno-15-41"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
+<a id="__codelineno-15-42" name="__codelineno-15-42" href="#__codelineno-15-42"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-15-43" name="__codelineno-15-43" href="#__codelineno-15-43"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-15-44" name="__codelineno-15-44" href="#__codelineno-15-44"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-45" name="__codelineno-15-45" href="#__codelineno-15-45"></a>
+<a id="__codelineno-15-46" name="__codelineno-15-46" href="#__codelineno-15-46"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-15-47" name="__codelineno-15-47" href="#__codelineno-15-47"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-48" name="__codelineno-15-48" href="#__codelineno-15-48"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-15-49" name="__codelineno-15-49" href="#__codelineno-15-49"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
+<a id="__codelineno-15-50" name="__codelineno-15-50" href="#__codelineno-15-50"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">front</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
+<a id="__codelineno-15-51" name="__codelineno-15-51" href="#__codelineno-15-51"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-52" name="__codelineno-15-52" href="#__codelineno-15-52"></a>
+<a id="__codelineno-15-53" name="__codelineno-15-53" href="#__codelineno-15-53"></a><span class="w">    </span><span class="cm">/* 連結リストを Array に変換して返す */</span>
+<a id="__codelineno-15-54" name="__codelineno-15-54" href="#__codelineno-15-54"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-55" name="__codelineno-15-55" href="#__codelineno-15-55"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-15-56" name="__codelineno-15-56" href="#__codelineno-15-56"></a><span class="w">        </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">size</span><span class="p">()</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-15-57" name="__codelineno-15-57" href="#__codelineno-15-57"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-58" name="__codelineno-15-58" href="#__codelineno-15-58"></a><span class="w">            </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
+<a id="__codelineno-15-59" name="__codelineno-15-59" href="#__codelineno-15-59"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
+<a id="__codelineno-15-60" name="__codelineno-15-60" href="#__codelineno-15-60"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-61" name="__codelineno-15-61" href="#__codelineno-15-61"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-15-62" name="__codelineno-15-62" href="#__codelineno-15-62"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-63" name="__codelineno-15-63" href="#__codelineno-15-63"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_queue.go</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">linkedListQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">linkedlist_queue.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 連結リストベースのキュー */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">LinkedListQueue</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">front</span><span class="p">,</span><span class="w"> </span><span class="n">rear</span><span class="p">;</span><span class="w">  </span><span class="c1">// 先頭ノード front、末尾ノード rear</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nf">LinkedListQueue</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">        </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">    </span><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">    </span><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="nf">IsEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nf">Size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="w">    </span><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">Push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="w">        </span><span class="c1">// 末尾ノードの後ろに num を追加</span>
+<a id="__codelineno-16-24" name="__codelineno-16-24" href="#__codelineno-16-24"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-16-25" name="__codelineno-16-25" href="#__codelineno-16-25"></a><span class="w">        </span><span class="c1">// キューが空なら、先頭・末尾ノードをともにそのノードに設定</span>
+<a id="__codelineno-16-26" name="__codelineno-16-26" href="#__codelineno-16-26"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-27" name="__codelineno-16-27" href="#__codelineno-16-27"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-16-28" name="__codelineno-16-28" href="#__codelineno-16-28"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-16-29" name="__codelineno-16-29" href="#__codelineno-16-29"></a><span class="w">            </span><span class="c1">// キューが空でなければ、そのノードを末尾ノードの後ろに追加</span>
+<a id="__codelineno-16-30" name="__codelineno-16-30" href="#__codelineno-16-30"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">rear</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-31" name="__codelineno-16-31" href="#__codelineno-16-31"></a><span class="w">            </span><span class="n">rear</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-16-32" name="__codelineno-16-32" href="#__codelineno-16-32"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-16-33" name="__codelineno-16-33" href="#__codelineno-16-33"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-34" name="__codelineno-16-34" href="#__codelineno-16-34"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-16-35" name="__codelineno-16-35" href="#__codelineno-16-35"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-36" name="__codelineno-16-36" href="#__codelineno-16-36"></a>
+<a id="__codelineno-16-37" name="__codelineno-16-37" href="#__codelineno-16-37"></a><span class="w">    </span><span class="cm">/* デキュー */</span>
+<a id="__codelineno-16-38" name="__codelineno-16-38" href="#__codelineno-16-38"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-39" name="__codelineno-16-39" href="#__codelineno-16-39"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Peek</span><span class="p">();</span>
+<a id="__codelineno-16-40" name="__codelineno-16-40" href="#__codelineno-16-40"></a><span class="w">        </span><span class="c1">// 先頭ノードを削除</span>
+<a id="__codelineno-16-41" name="__codelineno-16-41" href="#__codelineno-16-41"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="o">?.</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-16-42" name="__codelineno-16-42" href="#__codelineno-16-42"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-16-43" name="__codelineno-16-43" href="#__codelineno-16-43"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-16-44" name="__codelineno-16-44" href="#__codelineno-16-44"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-45" name="__codelineno-16-45" href="#__codelineno-16-45"></a>
+<a id="__codelineno-16-46" name="__codelineno-16-46" href="#__codelineno-16-46"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-16-47" name="__codelineno-16-47" href="#__codelineno-16-47"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-48" name="__codelineno-16-48" href="#__codelineno-16-48"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsEmpty</span><span class="p">())</span>
+<a id="__codelineno-16-49" name="__codelineno-16-49" href="#__codelineno-16-49"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="nf">Exception</span><span class="p">();</span>
+<a id="__codelineno-16-50" name="__codelineno-16-50" href="#__codelineno-16-50"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">front</span><span class="o">!</span><span class="p">.</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-16-51" name="__codelineno-16-51" href="#__codelineno-16-51"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-52" name="__codelineno-16-52" href="#__codelineno-16-52"></a>
+<a id="__codelineno-16-53" name="__codelineno-16-53" href="#__codelineno-16-53"></a><span class="w">    </span><span class="cm">/* 連結リストを Array に変換して返す */</span>
+<a id="__codelineno-16-54" name="__codelineno-16-54" href="#__codelineno-16-54"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="nf">ToArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-55" name="__codelineno-16-55" href="#__codelineno-16-55"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span>
+<a id="__codelineno-16-56" name="__codelineno-16-56" href="#__codelineno-16-56"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-16-57" name="__codelineno-16-57" href="#__codelineno-16-57"></a>
+<a id="__codelineno-16-58" name="__codelineno-16-58" href="#__codelineno-16-58"></a><span class="w">        </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-16-59" name="__codelineno-16-59" href="#__codelineno-16-59"></a><span class="w">        </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">Size</span><span class="p">()];</span>
+<a id="__codelineno-16-60" name="__codelineno-16-60" href="#__codelineno-16-60"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-61" name="__codelineno-16-61" href="#__codelineno-16-61"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">!</span><span class="p">.</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-16-62" name="__codelineno-16-62" href="#__codelineno-16-62"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-16-63" name="__codelineno-16-63" href="#__codelineno-16-63"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-64" name="__codelineno-16-64" href="#__codelineno-16-64"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-16-65" name="__codelineno-16-65" href="#__codelineno-16-65"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-66" name="__codelineno-16-66" href="#__codelineno-16-66"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_queue.swift</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">LinkedListQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">linkedlist_queue.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 連結リストベースのキュー */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">linkedListQueue</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="c1">// 組み込みパッケージ list でキューを実装する</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="nx">data</span><span class="w"> </span><span class="o">*</span><span class="nx">list</span><span class="p">.</span><span class="nx">List</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="p">}</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="cm">/* キューを初期化 */</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="kd">func</span><span class="w"> </span><span class="nx">newLinkedListQueue</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="nx">linkedListQueue</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">linkedListQueue</span><span class="p">{</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">        </span><span class="nx">data</span><span class="p">:</span><span class="w"> </span><span class="nx">list</span><span class="p">.</span><span class="nx">New</span><span class="p">(),</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="p">}</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">linkedListQueue</span><span class="p">)</span><span class="w"> </span><span class="nx">push</span><span class="p">(</span><span class="nx">value</span><span class="w"> </span><span class="kt">any</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w">    </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">.</span><span class="nx">PushBack</span><span class="p">(</span><span class="nx">value</span><span class="p">)</span>
+<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="p">}</span>
+<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a>
+<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="cm">/* デキュー */</span>
+<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">linkedListQueue</span><span class="p">)</span><span class="w"> </span><span class="nx">pop</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-22" name="__codelineno-17-22" href="#__codelineno-17-22"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-17-23" name="__codelineno-17-23" href="#__codelineno-17-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-24" name="__codelineno-17-24" href="#__codelineno-17-24"></a><span class="w">    </span><span class="nx">e</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">.</span><span class="nx">Front</span><span class="p">()</span>
+<a id="__codelineno-17-25" name="__codelineno-17-25" href="#__codelineno-17-25"></a><span class="w">    </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">.</span><span class="nx">Remove</span><span class="p">(</span><span class="nx">e</span><span class="p">)</span>
+<a id="__codelineno-17-26" name="__codelineno-17-26" href="#__codelineno-17-26"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">e</span><span class="p">.</span><span class="nx">Value</span>
+<a id="__codelineno-17-27" name="__codelineno-17-27" href="#__codelineno-17-27"></a><span class="p">}</span>
+<a id="__codelineno-17-28" name="__codelineno-17-28" href="#__codelineno-17-28"></a>
+<a id="__codelineno-17-29" name="__codelineno-17-29" href="#__codelineno-17-29"></a><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-17-30" name="__codelineno-17-30" href="#__codelineno-17-30"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">linkedListQueue</span><span class="p">)</span><span class="w"> </span><span class="nx">peek</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-31" name="__codelineno-17-31" href="#__codelineno-17-31"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-32" name="__codelineno-17-32" href="#__codelineno-17-32"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-17-33" name="__codelineno-17-33" href="#__codelineno-17-33"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-34" name="__codelineno-17-34" href="#__codelineno-17-34"></a><span class="w">    </span><span class="nx">e</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">.</span><span class="nx">Front</span><span class="p">()</span>
+<a id="__codelineno-17-35" name="__codelineno-17-35" href="#__codelineno-17-35"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">e</span><span class="p">.</span><span class="nx">Value</span>
+<a id="__codelineno-17-36" name="__codelineno-17-36" href="#__codelineno-17-36"></a><span class="p">}</span>
+<a id="__codelineno-17-37" name="__codelineno-17-37" href="#__codelineno-17-37"></a>
+<a id="__codelineno-17-38" name="__codelineno-17-38" href="#__codelineno-17-38"></a><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-17-39" name="__codelineno-17-39" href="#__codelineno-17-39"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">linkedListQueue</span><span class="p">)</span><span class="w"> </span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-40" name="__codelineno-17-40" href="#__codelineno-17-40"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">.</span><span class="nx">Len</span><span class="p">()</span>
+<a id="__codelineno-17-41" name="__codelineno-17-41" href="#__codelineno-17-41"></a><span class="p">}</span>
+<a id="__codelineno-17-42" name="__codelineno-17-42" href="#__codelineno-17-42"></a>
+<a id="__codelineno-17-43" name="__codelineno-17-43" href="#__codelineno-17-43"></a><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-17-44" name="__codelineno-17-44" href="#__codelineno-17-44"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">linkedListQueue</span><span class="p">)</span><span class="w"> </span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-45" name="__codelineno-17-45" href="#__codelineno-17-45"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">.</span><span class="nx">Len</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-17-46" name="__codelineno-17-46" href="#__codelineno-17-46"></a><span class="p">}</span>
+<a id="__codelineno-17-47" name="__codelineno-17-47" href="#__codelineno-17-47"></a>
+<a id="__codelineno-17-48" name="__codelineno-17-48" href="#__codelineno-17-48"></a><span class="cm">/* 表示用に List を取得 */</span>
+<a id="__codelineno-17-49" name="__codelineno-17-49" href="#__codelineno-17-49"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">linkedListQueue</span><span class="p">)</span><span class="w"> </span><span class="nx">toList</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="nx">list</span><span class="p">.</span><span class="nx">List</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-50" name="__codelineno-17-50" href="#__codelineno-17-50"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span>
+<a id="__codelineno-17-51" name="__codelineno-17-51" href="#__codelineno-17-51"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_queue.js</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">LinkedListQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">linkedlist_queue.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 連結リストベースのキュー */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">LinkedListQueue</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">front</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 先頭ノード</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">rear</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 末尾ノード</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">_size</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">    </span><span class="kd">init</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">        </span><span class="n">_size</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w">    </span><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w">        </span><span class="n">_size</span>
+<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a>
+<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="w">    </span><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="w">        </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a>
+<a id="__codelineno-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></a><span class="w">    </span><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-18-22" name="__codelineno-18-22" href="#__codelineno-18-22"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-23" name="__codelineno-18-23" href="#__codelineno-18-23"></a><span class="w">        </span><span class="c1">// 末尾ノードの後ろに num を追加</span>
+<a id="__codelineno-18-24" name="__codelineno-18-24" href="#__codelineno-18-24"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-18-25" name="__codelineno-18-25" href="#__codelineno-18-25"></a><span class="w">        </span><span class="c1">// キューが空なら、先頭・末尾ノードをともにそのノードに設定</span>
+<a id="__codelineno-18-26" name="__codelineno-18-26" href="#__codelineno-18-26"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">front</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-27" name="__codelineno-18-27" href="#__codelineno-18-27"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-18-28" name="__codelineno-18-28" href="#__codelineno-18-28"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-18-29" name="__codelineno-18-29" href="#__codelineno-18-29"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-30" name="__codelineno-18-30" href="#__codelineno-18-30"></a><span class="w">        </span><span class="c1">// キューが空でなければ、そのノードを末尾ノードの後ろに追加</span>
+<a id="__codelineno-18-31" name="__codelineno-18-31" href="#__codelineno-18-31"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-32" name="__codelineno-18-32" href="#__codelineno-18-32"></a><span class="w">            </span><span class="n">rear</span><span class="p">?.</span><span class="n">next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-18-33" name="__codelineno-18-33" href="#__codelineno-18-33"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-18-34" name="__codelineno-18-34" href="#__codelineno-18-34"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-35" name="__codelineno-18-35" href="#__codelineno-18-35"></a><span class="w">        </span><span class="n">_size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-18-36" name="__codelineno-18-36" href="#__codelineno-18-36"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-37" name="__codelineno-18-37" href="#__codelineno-18-37"></a>
+<a id="__codelineno-18-38" name="__codelineno-18-38" href="#__codelineno-18-38"></a><span class="w">    </span><span class="cm">/* デキュー */</span>
+<a id="__codelineno-18-39" name="__codelineno-18-39" href="#__codelineno-18-39"></a><span class="w">    </span><span class="p">@</span><span class="n">discardableResult</span>
+<a id="__codelineno-18-40" name="__codelineno-18-40" href="#__codelineno-18-40"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-41" name="__codelineno-18-41" href="#__codelineno-18-41"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">num</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">peek</span><span class="p">()</span>
+<a id="__codelineno-18-42" name="__codelineno-18-42" href="#__codelineno-18-42"></a><span class="w">        </span><span class="c1">// 先頭ノードを削除</span>
+<a id="__codelineno-18-43" name="__codelineno-18-43" href="#__codelineno-18-43"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">front</span><span class="p">?.</span><span class="n">next</span>
+<a id="__codelineno-18-44" name="__codelineno-18-44" href="#__codelineno-18-44"></a><span class="w">        </span><span class="n">_size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-18-45" name="__codelineno-18-45" href="#__codelineno-18-45"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-18-46" name="__codelineno-18-46" href="#__codelineno-18-46"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-47" name="__codelineno-18-47" href="#__codelineno-18-47"></a>
+<a id="__codelineno-18-48" name="__codelineno-18-48" href="#__codelineno-18-48"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-18-49" name="__codelineno-18-49" href="#__codelineno-18-49"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-50" name="__codelineno-18-50" href="#__codelineno-18-50"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-51" name="__codelineno-18-51" href="#__codelineno-18-51"></a><span class="w">            </span><span class="bp">fatalError</span><span class="p">(</span><span class="s">&quot;キューが空です&quot;</span><span class="p">)</span>
+<a id="__codelineno-18-52" name="__codelineno-18-52" href="#__codelineno-18-52"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-53" name="__codelineno-18-53" href="#__codelineno-18-53"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">front</span><span class="p">!.</span><span class="n">val</span>
+<a id="__codelineno-18-54" name="__codelineno-18-54" href="#__codelineno-18-54"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-55" name="__codelineno-18-55" href="#__codelineno-18-55"></a>
+<a id="__codelineno-18-56" name="__codelineno-18-56" href="#__codelineno-18-56"></a><span class="w">    </span><span class="cm">/* 連結リストを Array に変換して返す */</span>
+<a id="__codelineno-18-57" name="__codelineno-18-57" href="#__codelineno-18-57"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-58" name="__codelineno-18-58" href="#__codelineno-18-58"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">front</span>
+<a id="__codelineno-18-59" name="__codelineno-18-59" href="#__codelineno-18-59"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
+<a id="__codelineno-18-60" name="__codelineno-18-60" href="#__codelineno-18-60"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="bp">indices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-61" name="__codelineno-18-61" href="#__codelineno-18-61"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span><span class="p">!.</span><span class="n">val</span>
+<a id="__codelineno-18-62" name="__codelineno-18-62" href="#__codelineno-18-62"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span><span class="p">?.</span><span class="n">next</span>
+<a id="__codelineno-18-63" name="__codelineno-18-63" href="#__codelineno-18-63"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-64" name="__codelineno-18-64" href="#__codelineno-18-64"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-18-65" name="__codelineno-18-65" href="#__codelineno-18-65"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-66" name="__codelineno-18-66" href="#__codelineno-18-66"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_queue.ts</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">LinkedListQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">linkedlist_queue.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 連結リストベースのキュー */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">LinkedListQueue</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="n">#front</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノード #front</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="n">#rear</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノード #rear</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">    </span><span class="n">#queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">    </span><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w">    </span><span class="nx">get</span><span class="w"> </span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="p">;</span>
+<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a>
+<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="w">    </span><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a><span class="w">    </span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a>
+<a id="__codelineno-19-22" name="__codelineno-19-22" href="#__codelineno-19-22"></a><span class="w">    </span><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-19-23" name="__codelineno-19-23" href="#__codelineno-19-23"></a><span class="w">    </span><span class="nx">push</span><span class="p">(</span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-24" name="__codelineno-19-24" href="#__codelineno-19-24"></a><span class="w">        </span><span class="c1">// 末尾ノードの後ろに num を追加</span>
+<a id="__codelineno-19-25" name="__codelineno-19-25" href="#__codelineno-19-25"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="nx">num</span><span class="p">);</span>
+<a id="__codelineno-19-26" name="__codelineno-19-26" href="#__codelineno-19-26"></a><span class="w">        </span><span class="c1">// キューが空なら、先頭・末尾ノードをともにそのノードに設定</span>
+<a id="__codelineno-19-27" name="__codelineno-19-27" href="#__codelineno-19-27"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-28" name="__codelineno-19-28" href="#__codelineno-19-28"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-19-29" name="__codelineno-19-29" href="#__codelineno-19-29"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-19-30" name="__codelineno-19-30" href="#__codelineno-19-30"></a><span class="w">            </span><span class="c1">// キューが空でなければ、そのノードを末尾ノードの後ろに追加</span>
+<a id="__codelineno-19-31" name="__codelineno-19-31" href="#__codelineno-19-31"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-32" name="__codelineno-19-32" href="#__codelineno-19-32"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#rear</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-19-33" name="__codelineno-19-33" href="#__codelineno-19-33"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="n">#rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-19-34" name="__codelineno-19-34" href="#__codelineno-19-34"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-35" name="__codelineno-19-35" href="#__codelineno-19-35"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-19-36" name="__codelineno-19-36" href="#__codelineno-19-36"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-37" name="__codelineno-19-37" href="#__codelineno-19-37"></a>
+<a id="__codelineno-19-38" name="__codelineno-19-38" href="#__codelineno-19-38"></a><span class="w">    </span><span class="cm">/* デキュー */</span>
+<a id="__codelineno-19-39" name="__codelineno-19-39" href="#__codelineno-19-39"></a><span class="w">    </span><span class="nx">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-40" name="__codelineno-19-40" href="#__codelineno-19-40"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">peek</span><span class="p">();</span>
+<a id="__codelineno-19-41" name="__codelineno-19-41" href="#__codelineno-19-41"></a><span class="w">        </span><span class="c1">// 先頭ノードを削除</span>
+<a id="__codelineno-19-42" name="__codelineno-19-42" href="#__codelineno-19-42"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="p">.</span><span class="nx">next</span><span class="p">;</span>
+<a id="__codelineno-19-43" name="__codelineno-19-43" href="#__codelineno-19-43"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-19-44" name="__codelineno-19-44" href="#__codelineno-19-44"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-19-45" name="__codelineno-19-45" href="#__codelineno-19-45"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-46" name="__codelineno-19-46" href="#__codelineno-19-46"></a>
+<a id="__codelineno-19-47" name="__codelineno-19-47" href="#__codelineno-19-47"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-19-48" name="__codelineno-19-48" href="#__codelineno-19-48"></a><span class="w">    </span><span class="nx">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-49" name="__codelineno-19-49" href="#__codelineno-19-49"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;キューが空&#39;</span><span class="p">);</span>
+<a id="__codelineno-19-50" name="__codelineno-19-50" href="#__codelineno-19-50"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-19-51" name="__codelineno-19-51" href="#__codelineno-19-51"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-52" name="__codelineno-19-52" href="#__codelineno-19-52"></a>
+<a id="__codelineno-19-53" name="__codelineno-19-53" href="#__codelineno-19-53"></a><span class="w">    </span><span class="cm">/* 連結リストを Array に変換して返す */</span>
+<a id="__codelineno-19-54" name="__codelineno-19-54" href="#__codelineno-19-54"></a><span class="w">    </span><span class="nx">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-55" name="__codelineno-19-55" href="#__codelineno-19-55"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="p">;</span>
+<a id="__codelineno-19-56" name="__codelineno-19-56" href="#__codelineno-19-56"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">);</span>
+<a id="__codelineno-19-57" name="__codelineno-19-57" href="#__codelineno-19-57"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-58" name="__codelineno-19-58" href="#__codelineno-19-58"></a><span class="w">            </span><span class="nx">res</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-19-59" name="__codelineno-19-59" href="#__codelineno-19-59"></a><span class="w">            </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">next</span><span class="p">;</span>
+<a id="__codelineno-19-60" name="__codelineno-19-60" href="#__codelineno-19-60"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-61" name="__codelineno-19-61" href="#__codelineno-19-61"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-19-62" name="__codelineno-19-62" href="#__codelineno-19-62"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-63" name="__codelineno-19-63" href="#__codelineno-19-63"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_queue.dart</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">LinkedListQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">linkedlist_queue.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 連結リストベースのキュー */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">LinkedListQueue</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">front</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノード front</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">rear</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノード rear</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">queSize</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">    </span><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w">    </span><span class="nx">get</span><span class="w"> </span><span class="nx">size</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="p">;</span>
+<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a>
+<a id="__codelineno-20-17" name="__codelineno-20-17" href="#__codelineno-20-17"></a><span class="w">    </span><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-20-18" name="__codelineno-20-18" href="#__codelineno-20-18"></a><span class="w">    </span><span class="nx">isEmpty</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-19" name="__codelineno-20-19" href="#__codelineno-20-19"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-20-20" name="__codelineno-20-20" href="#__codelineno-20-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-21" name="__codelineno-20-21" href="#__codelineno-20-21"></a>
+<a id="__codelineno-20-22" name="__codelineno-20-22" href="#__codelineno-20-22"></a><span class="w">    </span><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-20-23" name="__codelineno-20-23" href="#__codelineno-20-23"></a><span class="w">    </span><span class="nx">push</span><span class="p">(</span><span class="nx">num</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-24" name="__codelineno-20-24" href="#__codelineno-20-24"></a><span class="w">        </span><span class="c1">// 末尾ノードの後ろに num を追加</span>
+<a id="__codelineno-20-25" name="__codelineno-20-25" href="#__codelineno-20-25"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="nx">num</span><span class="p">);</span>
+<a id="__codelineno-20-26" name="__codelineno-20-26" href="#__codelineno-20-26"></a><span class="w">        </span><span class="c1">// キューが空なら、先頭・末尾ノードをともにそのノードに設定</span>
+<a id="__codelineno-20-27" name="__codelineno-20-27" href="#__codelineno-20-27"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-28" name="__codelineno-20-28" href="#__codelineno-20-28"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-20-29" name="__codelineno-20-29" href="#__codelineno-20-29"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-20-30" name="__codelineno-20-30" href="#__codelineno-20-30"></a><span class="w">            </span><span class="c1">// キューが空でなければ、そのノードを末尾ノードの後ろに追加</span>
+<a id="__codelineno-20-31" name="__codelineno-20-31" href="#__codelineno-20-31"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-32" name="__codelineno-20-32" href="#__codelineno-20-32"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">rear</span><span class="o">!</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-20-33" name="__codelineno-20-33" href="#__codelineno-20-33"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-20-34" name="__codelineno-20-34" href="#__codelineno-20-34"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-35" name="__codelineno-20-35" href="#__codelineno-20-35"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-20-36" name="__codelineno-20-36" href="#__codelineno-20-36"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-37" name="__codelineno-20-37" href="#__codelineno-20-37"></a>
+<a id="__codelineno-20-38" name="__codelineno-20-38" href="#__codelineno-20-38"></a><span class="w">    </span><span class="cm">/* デキュー */</span>
+<a id="__codelineno-20-39" name="__codelineno-20-39" href="#__codelineno-20-39"></a><span class="w">    </span><span class="nx">pop</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-40" name="__codelineno-20-40" href="#__codelineno-20-40"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">peek</span><span class="p">();</span>
+<a id="__codelineno-20-41" name="__codelineno-20-41" href="#__codelineno-20-41"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="p">)</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;キューが空です&#39;</span><span class="p">);</span>
+<a id="__codelineno-20-42" name="__codelineno-20-42" href="#__codelineno-20-42"></a><span class="w">        </span><span class="c1">// 先頭ノードを削除</span>
+<a id="__codelineno-20-43" name="__codelineno-20-43" href="#__codelineno-20-43"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="p">.</span><span class="nx">next</span><span class="p">;</span>
+<a id="__codelineno-20-44" name="__codelineno-20-44" href="#__codelineno-20-44"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-20-45" name="__codelineno-20-45" href="#__codelineno-20-45"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-20-46" name="__codelineno-20-46" href="#__codelineno-20-46"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-47" name="__codelineno-20-47" href="#__codelineno-20-47"></a>
+<a id="__codelineno-20-48" name="__codelineno-20-48" href="#__codelineno-20-48"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-20-49" name="__codelineno-20-49" href="#__codelineno-20-49"></a><span class="w">    </span><span class="nx">peek</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-50" name="__codelineno-20-50" href="#__codelineno-20-50"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;キューが空です&#39;</span><span class="p">);</span>
+<a id="__codelineno-20-51" name="__codelineno-20-51" href="#__codelineno-20-51"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="o">!</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-20-52" name="__codelineno-20-52" href="#__codelineno-20-52"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-53" name="__codelineno-20-53" href="#__codelineno-20-53"></a>
+<a id="__codelineno-20-54" name="__codelineno-20-54" href="#__codelineno-20-54"></a><span class="w">    </span><span class="cm">/* 連結リストを Array に変換して返す */</span>
+<a id="__codelineno-20-55" name="__codelineno-20-55" href="#__codelineno-20-55"></a><span class="w">    </span><span class="nx">toArray</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-56" name="__codelineno-20-56" href="#__codelineno-20-56"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="p">;</span>
+<a id="__codelineno-20-57" name="__codelineno-20-57" href="#__codelineno-20-57"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">);</span>
+<a id="__codelineno-20-58" name="__codelineno-20-58" href="#__codelineno-20-58"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-59" name="__codelineno-20-59" href="#__codelineno-20-59"></a><span class="w">            </span><span class="nx">res</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="o">!</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-20-60" name="__codelineno-20-60" href="#__codelineno-20-60"></a><span class="w">            </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="o">!</span><span class="p">.</span><span class="nx">next</span><span class="p">;</span>
+<a id="__codelineno-20-61" name="__codelineno-20-61" href="#__codelineno-20-61"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-62" name="__codelineno-20-62" href="#__codelineno-20-62"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-20-63" name="__codelineno-20-63" href="#__codelineno-20-63"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-64" name="__codelineno-20-64" href="#__codelineno-20-64"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_queue.rs</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">LinkedListQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">linkedlist_queue.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 連結リストベースのキュー */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">LinkedListQueue</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">_front</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノード _front</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">_rear</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノード _rear</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">_queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの長さ</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">  </span><span class="n">LinkedListQueue</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">    </span><span class="n">_front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">    </span><span class="n">_rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w">  </span><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_queSize</span><span class="p">;</span>
+<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a>
+<a id="__codelineno-21-17" name="__codelineno-21-17" href="#__codelineno-21-17"></a><span class="w">  </span><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-21-18" name="__codelineno-21-18" href="#__codelineno-21-18"></a><span class="w">  </span><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-19" name="__codelineno-21-19" href="#__codelineno-21-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-21-20" name="__codelineno-21-20" href="#__codelineno-21-20"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-21" name="__codelineno-21-21" href="#__codelineno-21-21"></a>
+<a id="__codelineno-21-22" name="__codelineno-21-22" href="#__codelineno-21-22"></a><span class="w">  </span><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-21-23" name="__codelineno-21-23" href="#__codelineno-21-23"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-24" name="__codelineno-21-24" href="#__codelineno-21-24"></a><span class="w">    </span><span class="c1">// 末尾ノードの後ろに _num を追加</span>
+<a id="__codelineno-21-25" name="__codelineno-21-25" href="#__codelineno-21-25"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">_num</span><span class="p">);</span>
+<a id="__codelineno-21-26" name="__codelineno-21-26" href="#__codelineno-21-26"></a><span class="w">    </span><span class="c1">// キューが空なら、先頭・末尾ノードをともにそのノードに設定</span>
+<a id="__codelineno-21-27" name="__codelineno-21-27" href="#__codelineno-21-27"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_front</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-28" name="__codelineno-21-28" href="#__codelineno-21-28"></a><span class="w">      </span><span class="n">_front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-21-29" name="__codelineno-21-29" href="#__codelineno-21-29"></a><span class="w">      </span><span class="n">_rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-21-30" name="__codelineno-21-30" href="#__codelineno-21-30"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-31" name="__codelineno-21-31" href="#__codelineno-21-31"></a><span class="w">      </span><span class="c1">// キューが空でなければ、そのノードを末尾ノードの後ろに追加</span>
+<a id="__codelineno-21-32" name="__codelineno-21-32" href="#__codelineno-21-32"></a><span class="w">      </span><span class="n">_rear</span><span class="o">!</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-21-33" name="__codelineno-21-33" href="#__codelineno-21-33"></a><span class="w">      </span><span class="n">_rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-21-34" name="__codelineno-21-34" href="#__codelineno-21-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-35" name="__codelineno-21-35" href="#__codelineno-21-35"></a><span class="w">    </span><span class="n">_queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-21-36" name="__codelineno-21-36" href="#__codelineno-21-36"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-37" name="__codelineno-21-37" href="#__codelineno-21-37"></a>
+<a id="__codelineno-21-38" name="__codelineno-21-38" href="#__codelineno-21-38"></a><span class="w">  </span><span class="cm">/* デキュー */</span>
+<a id="__codelineno-21-39" name="__codelineno-21-39" href="#__codelineno-21-39"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-40" name="__codelineno-21-40" href="#__codelineno-21-40"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span><span class="p">();</span>
+<a id="__codelineno-21-41" name="__codelineno-21-41" href="#__codelineno-21-41"></a><span class="w">    </span><span class="c1">// 先頭ノードを削除</span>
+<a id="__codelineno-21-42" name="__codelineno-21-42" href="#__codelineno-21-42"></a><span class="w">    </span><span class="n">_front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_front</span><span class="o">!</span><span class="p">.</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-21-43" name="__codelineno-21-43" href="#__codelineno-21-43"></a><span class="w">    </span><span class="n">_queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-21-44" name="__codelineno-21-44" href="#__codelineno-21-44"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_num</span><span class="p">;</span>
+<a id="__codelineno-21-45" name="__codelineno-21-45" href="#__codelineno-21-45"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-46" name="__codelineno-21-46" href="#__codelineno-21-46"></a>
+<a id="__codelineno-21-47" name="__codelineno-21-47" href="#__codelineno-21-47"></a><span class="w">  </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-21-48" name="__codelineno-21-48" href="#__codelineno-21-48"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-49" name="__codelineno-21-49" href="#__codelineno-21-49"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-50" name="__codelineno-21-50" href="#__codelineno-21-50"></a><span class="w">      </span><span class="k">throw</span><span class="w"> </span><span class="n">Exception</span><span class="p">(</span><span class="s1">&#39;キューが空です&#39;</span><span class="p">);</span>
+<a id="__codelineno-21-51" name="__codelineno-21-51" href="#__codelineno-21-51"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-52" name="__codelineno-21-52" href="#__codelineno-21-52"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_front</span><span class="o">!</span><span class="p">.</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-21-53" name="__codelineno-21-53" href="#__codelineno-21-53"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-54" name="__codelineno-21-54" href="#__codelineno-21-54"></a>
+<a id="__codelineno-21-55" name="__codelineno-21-55" href="#__codelineno-21-55"></a><span class="w">  </span><span class="cm">/* 連結リストを Array に変換して返す */</span>
+<a id="__codelineno-21-56" name="__codelineno-21-56" href="#__codelineno-21-56"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-57" name="__codelineno-21-57" href="#__codelineno-21-57"></a><span class="w">    </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_front</span><span class="p">;</span>
+<a id="__codelineno-21-58" name="__codelineno-21-58" href="#__codelineno-21-58"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-21-59" name="__codelineno-21-59" href="#__codelineno-21-59"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-60" name="__codelineno-21-60" href="#__codelineno-21-60"></a><span class="w">      </span><span class="n">queue</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-21-61" name="__codelineno-21-61" href="#__codelineno-21-61"></a><span class="w">      </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-21-62" name="__codelineno-21-62" href="#__codelineno-21-62"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-63" name="__codelineno-21-63" href="#__codelineno-21-63"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">queue</span><span class="p">;</span>
+<a id="__codelineno-21-64" name="__codelineno-21-64" href="#__codelineno-21-64"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-65" name="__codelineno-21-65" href="#__codelineno-21-65"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_queue.c</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">LinkedListQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">linkedlist_queue.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 連結リストベースのキュー */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="cp">#[allow(dead_code)]</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="k">pub</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">LinkedListQueue</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="n">front</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="c1">// 先頭ノード front</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">    </span><span class="n">rear</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;&gt;</span><span class="p">,</span><span class="w">  </span><span class="c1">// 末尾ノード rear</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w">    </span><span class="n">que_size</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w">                         </span><span class="c1">// キューの長さ</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="p">}</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="k">impl</span><span class="o">&lt;</span><span class="n">T</span><span class="p">:</span><span class="w"> </span><span class="nb">Copy</span><span class="o">&gt;</span><span class="w"> </span><span class="n">LinkedListQueue</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">new</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w">        </span><span class="bp">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">            </span><span class="n">front</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">            </span><span class="n">rear</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">            </span><span class="n">que_size</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a>
+<a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="w">    </span><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="p">;</span>
+<a id="__codelineno-22-21" name="__codelineno-22-21" href="#__codelineno-22-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-22" name="__codelineno-22-22" href="#__codelineno-22-22"></a>
+<a id="__codelineno-22-23" name="__codelineno-22-23" href="#__codelineno-22-23"></a><span class="w">    </span><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-22-24" name="__codelineno-22-24" href="#__codelineno-22-24"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">is_empty</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-25" name="__codelineno-22-25" href="#__codelineno-22-25"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-22-26" name="__codelineno-22-26" href="#__codelineno-22-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-27" name="__codelineno-22-27" href="#__codelineno-22-27"></a>
+<a id="__codelineno-22-28" name="__codelineno-22-28" href="#__codelineno-22-28"></a><span class="w">    </span><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-22-29" name="__codelineno-22-29" href="#__codelineno-22-29"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nc">T</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-30" name="__codelineno-22-30" href="#__codelineno-22-30"></a><span class="w">        </span><span class="c1">// 末尾ノードの後ろに num を追加</span>
+<a id="__codelineno-22-31" name="__codelineno-22-31" href="#__codelineno-22-31"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">new_rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-22-32" name="__codelineno-22-32" href="#__codelineno-22-32"></a><span class="w">        </span><span class="k">match</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">rear</span><span class="p">.</span><span class="n">take</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-33" name="__codelineno-22-33" href="#__codelineno-22-33"></a><span class="w">            </span><span class="c1">// キューが空でなければ、そのノードを末尾ノードの後ろに追加</span>
+<a id="__codelineno-22-34" name="__codelineno-22-34" href="#__codelineno-22-34"></a><span class="w">            </span><span class="nb">Some</span><span class="p">(</span><span class="n">old_rear</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-35" name="__codelineno-22-35" href="#__codelineno-22-35"></a><span class="w">                </span><span class="n">old_rear</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">new_rear</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-22-36" name="__codelineno-22-36" href="#__codelineno-22-36"></a><span class="w">                </span><span class="bp">self</span><span class="p">.</span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">new_rear</span><span class="p">);</span>
+<a id="__codelineno-22-37" name="__codelineno-22-37" href="#__codelineno-22-37"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-22-38" name="__codelineno-22-38" href="#__codelineno-22-38"></a><span class="w">            </span><span class="c1">// キューが空なら、先頭・末尾ノードをともにそのノードに設定</span>
+<a id="__codelineno-22-39" name="__codelineno-22-39" href="#__codelineno-22-39"></a><span class="w">            </span><span class="nb">None</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-40" name="__codelineno-22-40" href="#__codelineno-22-40"></a><span class="w">                </span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">new_rear</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-22-41" name="__codelineno-22-41" href="#__codelineno-22-41"></a><span class="w">                </span><span class="bp">self</span><span class="p">.</span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">new_rear</span><span class="p">);</span>
+<a id="__codelineno-22-42" name="__codelineno-22-42" href="#__codelineno-22-42"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-22-43" name="__codelineno-22-43" href="#__codelineno-22-43"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-44" name="__codelineno-22-44" href="#__codelineno-22-44"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-22-45" name="__codelineno-22-45" href="#__codelineno-22-45"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-46" name="__codelineno-22-46" href="#__codelineno-22-46"></a>
+<a id="__codelineno-22-47" name="__codelineno-22-47" href="#__codelineno-22-47"></a><span class="w">    </span><span class="cm">/* デキュー */</span>
+<a id="__codelineno-22-48" name="__codelineno-22-48" href="#__codelineno-22-48"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-49" name="__codelineno-22-49" href="#__codelineno-22-49"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="p">.</span><span class="n">take</span><span class="p">().</span><span class="n">map</span><span class="p">(</span><span class="o">|</span><span class="n">old_front</span><span class="o">|</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-50" name="__codelineno-22-50" href="#__codelineno-22-50"></a><span class="w">            </span><span class="k">match</span><span class="w"> </span><span class="n">old_front</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="p">.</span><span class="n">take</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-51" name="__codelineno-22-51" href="#__codelineno-22-51"></a><span class="w">                </span><span class="nb">Some</span><span class="p">(</span><span class="n">new_front</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-52" name="__codelineno-22-52" href="#__codelineno-22-52"></a><span class="w">                    </span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">new_front</span><span class="p">);</span>
+<a id="__codelineno-22-53" name="__codelineno-22-53" href="#__codelineno-22-53"></a><span class="w">                </span><span class="p">}</span>
+<a id="__codelineno-22-54" name="__codelineno-22-54" href="#__codelineno-22-54"></a><span class="w">                </span><span class="nb">None</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-55" name="__codelineno-22-55" href="#__codelineno-22-55"></a><span class="w">                    </span><span class="bp">self</span><span class="p">.</span><span class="n">rear</span><span class="p">.</span><span class="n">take</span><span class="p">();</span>
+<a id="__codelineno-22-56" name="__codelineno-22-56" href="#__codelineno-22-56"></a><span class="w">                </span><span class="p">}</span>
+<a id="__codelineno-22-57" name="__codelineno-22-57" href="#__codelineno-22-57"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-22-58" name="__codelineno-22-58" href="#__codelineno-22-58"></a><span class="w">            </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-22-59" name="__codelineno-22-59" href="#__codelineno-22-59"></a><span class="w">            </span><span class="n">old_front</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span>
+<a id="__codelineno-22-60" name="__codelineno-22-60" href="#__codelineno-22-60"></a><span class="w">        </span><span class="p">})</span>
+<a id="__codelineno-22-61" name="__codelineno-22-61" href="#__codelineno-22-61"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-62" name="__codelineno-22-62" href="#__codelineno-22-62"></a>
+<a id="__codelineno-22-63" name="__codelineno-22-63" href="#__codelineno-22-63"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-22-64" name="__codelineno-22-64" href="#__codelineno-22-64"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-65" name="__codelineno-22-65" href="#__codelineno-22-65"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="p">.</span><span class="n">as_ref</span><span class="p">()</span>
+<a id="__codelineno-22-66" name="__codelineno-22-66" href="#__codelineno-22-66"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-67" name="__codelineno-22-67" href="#__codelineno-22-67"></a>
+<a id="__codelineno-22-68" name="__codelineno-22-68" href="#__codelineno-22-68"></a><span class="w">    </span><span class="cm">/* 連結リストを Array に変換して返す */</span>
+<a id="__codelineno-22-69" name="__codelineno-22-69" href="#__codelineno-22-69"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">to_array</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">head</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-70" name="__codelineno-22-70" href="#__codelineno-22-70"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-22-71" name="__codelineno-22-71" href="#__codelineno-22-71"></a>
+<a id="__codelineno-22-72" name="__codelineno-22-72" href="#__codelineno-22-72"></a><span class="w">        </span><span class="k">fn</span><span class="w"> </span><span class="nf">recur</span><span class="o">&lt;</span><span class="n">T</span><span class="p">:</span><span class="w"> </span><span class="nb">Copy</span><span class="o">&gt;</span><span class="p">(</span><span class="n">cur</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-73" name="__codelineno-22-73" href="#__codelineno-22-73"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">cur</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-74" name="__codelineno-22-74" href="#__codelineno-22-74"></a><span class="w">                </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-22-75" name="__codelineno-22-75" href="#__codelineno-22-75"></a><span class="w">                </span><span class="n">recur</span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">next</span><span class="p">.</span><span class="n">as_ref</span><span class="p">(),</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-22-76" name="__codelineno-22-76" href="#__codelineno-22-76"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-22-77" name="__codelineno-22-77" href="#__codelineno-22-77"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-78" name="__codelineno-22-78" href="#__codelineno-22-78"></a>
+<a id="__codelineno-22-79" name="__codelineno-22-79" href="#__codelineno-22-79"></a><span class="w">        </span><span class="n">recur</span><span class="p">(</span><span class="n">head</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-22-80" name="__codelineno-22-80" href="#__codelineno-22-80"></a>
+<a id="__codelineno-22-81" name="__codelineno-22-81" href="#__codelineno-22-81"></a><span class="w">        </span><span class="n">res</span>
+<a id="__codelineno-22-82" name="__codelineno-22-82" href="#__codelineno-22-82"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-83" name="__codelineno-22-83" href="#__codelineno-22-83"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_queue.kt</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">LinkedListQueue</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">linkedlist_queue.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 連結リストベースのキュー */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">front</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">rear</span><span class="p">;</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="p">}</span><span class="w"> </span><span class="n">LinkedListQueue</span><span class="p">;</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="n">LinkedListQueue</span><span class="w"> </span><span class="o">*</span><span class="nf">newLinkedListQueue</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w">    </span><span class="n">LinkedListQueue</span><span class="w"> </span><span class="o">*</span><span class="n">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">LinkedListQueue</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">LinkedListQueue</span><span class="p">));</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w">    </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w">    </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w">    </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">queue</span><span class="p">;</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="p">}</span>
+<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a>
+<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="cm">/* デストラクタ */</span>
+<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">delLinkedListQueue</span><span class="p">(</span><span class="n">LinkedListQueue</span><span class="w"> </span><span class="o">*</span><span class="n">queue</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="w">    </span><span class="c1">// すべてのノードを解放</span>
+<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a><span class="w">        </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a><span class="w">        </span><span class="n">free</span><span class="p">(</span><span class="n">tmp</span><span class="p">);</span>
+<a id="__codelineno-23-23" name="__codelineno-23-23" href="#__codelineno-23-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-24" name="__codelineno-23-24" href="#__codelineno-23-24"></a><span class="w">    </span><span class="c1">// queue 構造体を解放する</span>
+<a id="__codelineno-23-25" name="__codelineno-23-25" href="#__codelineno-23-25"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">queue</span><span class="p">);</span>
+<a id="__codelineno-23-26" name="__codelineno-23-26" href="#__codelineno-23-26"></a><span class="p">}</span>
+<a id="__codelineno-23-27" name="__codelineno-23-27" href="#__codelineno-23-27"></a>
+<a id="__codelineno-23-28" name="__codelineno-23-28" href="#__codelineno-23-28"></a><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-23-29" name="__codelineno-23-29" href="#__codelineno-23-29"></a><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="n">LinkedListQueue</span><span class="w"> </span><span class="o">*</span><span class="n">queue</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-30" name="__codelineno-23-30" href="#__codelineno-23-30"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-23-31" name="__codelineno-23-31" href="#__codelineno-23-31"></a><span class="p">}</span>
+<a id="__codelineno-23-32" name="__codelineno-23-32" href="#__codelineno-23-32"></a>
+<a id="__codelineno-23-33" name="__codelineno-23-33" href="#__codelineno-23-33"></a><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-23-34" name="__codelineno-23-34" href="#__codelineno-23-34"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">empty</span><span class="p">(</span><span class="n">LinkedListQueue</span><span class="w"> </span><span class="o">*</span><span class="n">queue</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-35" name="__codelineno-23-35" href="#__codelineno-23-35"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="p">(</span><span class="n">queue</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-23-36" name="__codelineno-23-36" href="#__codelineno-23-36"></a><span class="p">}</span>
+<a id="__codelineno-23-37" name="__codelineno-23-37" href="#__codelineno-23-37"></a>
+<a id="__codelineno-23-38" name="__codelineno-23-38" href="#__codelineno-23-38"></a><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-23-39" name="__codelineno-23-39" href="#__codelineno-23-39"></a><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">LinkedListQueue</span><span class="w"> </span><span class="o">*</span><span class="n">queue</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-40" name="__codelineno-23-40" href="#__codelineno-23-40"></a><span class="w">    </span><span class="c1">// 末尾ノードに node を追加</span>
+<a id="__codelineno-23-41" name="__codelineno-23-41" href="#__codelineno-23-41"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newListNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-23-42" name="__codelineno-23-42" href="#__codelineno-23-42"></a><span class="w">    </span><span class="c1">// キューが空なら、先頭・末尾ノードをともにそのノードに設定</span>
+<a id="__codelineno-23-43" name="__codelineno-23-43" href="#__codelineno-23-43"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-44" name="__codelineno-23-44" href="#__codelineno-23-44"></a><span class="w">        </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-23-45" name="__codelineno-23-45" href="#__codelineno-23-45"></a><span class="w">        </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-23-46" name="__codelineno-23-46" href="#__codelineno-23-46"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-47" name="__codelineno-23-47" href="#__codelineno-23-47"></a><span class="w">    </span><span class="c1">// キューが空でなければ、そのノードを末尾ノードの後ろに追加</span>
+<a id="__codelineno-23-48" name="__codelineno-23-48" href="#__codelineno-23-48"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-49" name="__codelineno-23-49" href="#__codelineno-23-49"></a><span class="w">        </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">rear</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-23-50" name="__codelineno-23-50" href="#__codelineno-23-50"></a><span class="w">        </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-23-51" name="__codelineno-23-51" href="#__codelineno-23-51"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-52" name="__codelineno-23-52" href="#__codelineno-23-52"></a><span class="w">    </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-23-53" name="__codelineno-23-53" href="#__codelineno-23-53"></a><span class="p">}</span>
+<a id="__codelineno-23-54" name="__codelineno-23-54" href="#__codelineno-23-54"></a>
+<a id="__codelineno-23-55" name="__codelineno-23-55" href="#__codelineno-23-55"></a><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-23-56" name="__codelineno-23-56" href="#__codelineno-23-56"></a><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="n">LinkedListQueue</span><span class="w"> </span><span class="o">*</span><span class="n">queue</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-57" name="__codelineno-23-57" href="#__codelineno-23-57"></a><span class="w">    </span><span class="n">assert</span><span class="p">(</span><span class="n">size</span><span class="p">(</span><span class="n">queue</span><span class="p">)</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="p">);</span>
+<a id="__codelineno-23-58" name="__codelineno-23-58" href="#__codelineno-23-58"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-23-59" name="__codelineno-23-59" href="#__codelineno-23-59"></a><span class="p">}</span>
+<a id="__codelineno-23-60" name="__codelineno-23-60" href="#__codelineno-23-60"></a>
+<a id="__codelineno-23-61" name="__codelineno-23-61" href="#__codelineno-23-61"></a><span class="cm">/* デキュー */</span>
+<a id="__codelineno-23-62" name="__codelineno-23-62" href="#__codelineno-23-62"></a><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="n">LinkedListQueue</span><span class="w"> </span><span class="o">*</span><span class="n">queue</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-63" name="__codelineno-23-63" href="#__codelineno-23-63"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span><span class="p">(</span><span class="n">queue</span><span class="p">);</span>
+<a id="__codelineno-23-64" name="__codelineno-23-64" href="#__codelineno-23-64"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-23-65" name="__codelineno-23-65" href="#__codelineno-23-65"></a><span class="w">    </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-23-66" name="__codelineno-23-66" href="#__codelineno-23-66"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">tmp</span><span class="p">);</span>
+<a id="__codelineno-23-67" name="__codelineno-23-67" href="#__codelineno-23-67"></a><span class="w">    </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-23-68" name="__codelineno-23-68" href="#__codelineno-23-68"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-23-69" name="__codelineno-23-69" href="#__codelineno-23-69"></a><span class="p">}</span>
+<a id="__codelineno-23-70" name="__codelineno-23-70" href="#__codelineno-23-70"></a>
+<a id="__codelineno-23-71" name="__codelineno-23-71" href="#__codelineno-23-71"></a><span class="cm">/* キューを出力する */</span>
+<a id="__codelineno-23-72" name="__codelineno-23-72" href="#__codelineno-23-72"></a><span class="kt">void</span><span class="w"> </span><span class="nf">printLinkedListQueue</span><span class="p">(</span><span class="n">LinkedListQueue</span><span class="w"> </span><span class="o">*</span><span class="n">queue</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-73" name="__codelineno-23-73" href="#__codelineno-23-73"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="p">);</span>
+<a id="__codelineno-23-74" name="__codelineno-23-74" href="#__codelineno-23-74"></a><span class="w">    </span><span class="c1">// 連結リスト内のデータを配列にコピー</span>
+<a id="__codelineno-23-75" name="__codelineno-23-75" href="#__codelineno-23-75"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-23-76" name="__codelineno-23-76" href="#__codelineno-23-76"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-23-77" name="__codelineno-23-77" href="#__codelineno-23-77"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-78" name="__codelineno-23-78" href="#__codelineno-23-78"></a><span class="w">        </span><span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-23-79" name="__codelineno-23-79" href="#__codelineno-23-79"></a><span class="w">        </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-23-80" name="__codelineno-23-80" href="#__codelineno-23-80"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-81" name="__codelineno-23-81" href="#__codelineno-23-81"></a><span class="w">    </span><span class="n">printArray</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="p">);</span>
+<a id="__codelineno-23-82" name="__codelineno-23-82" href="#__codelineno-23-82"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">arr</span><span class="p">);</span>
+<a id="__codelineno-23-83" name="__codelineno-23-83" href="#__codelineno-23-83"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_queue.rb</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">LinkedListQueue</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">linkedlist_queue.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 連結リストベースのキュー */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">LinkedListQueue</span><span class="p">(</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="c1">// 先頭ノード front、末尾ノード rear</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">front</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">rear</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">queSize</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w">    </span><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">size</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a>
+<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w">    </span><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">():</span><span class="w"> </span><span class="kt">Boolean</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-24-17" name="__codelineno-24-17" href="#__codelineno-24-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-18" name="__codelineno-24-18" href="#__codelineno-24-18"></a>
+<a id="__codelineno-24-19" name="__codelineno-24-19" href="#__codelineno-24-19"></a><span class="w">    </span><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-24-20" name="__codelineno-24-20" href="#__codelineno-24-20"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-21" name="__codelineno-24-21" href="#__codelineno-24-21"></a><span class="w">        </span><span class="c1">// 末尾ノードの後ろに num を追加</span>
+<a id="__codelineno-24-22" name="__codelineno-24-22" href="#__codelineno-24-22"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-24-23" name="__codelineno-24-23" href="#__codelineno-24-23"></a><span class="w">        </span><span class="c1">// キューが空なら、先頭・末尾ノードをともにそのノードに設定</span>
+<a id="__codelineno-24-24" name="__codelineno-24-24" href="#__codelineno-24-24"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-25" name="__codelineno-24-25" href="#__codelineno-24-25"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-24-26" name="__codelineno-24-26" href="#__codelineno-24-26"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-24-27" name="__codelineno-24-27" href="#__codelineno-24-27"></a><span class="w">            </span><span class="c1">// キューが空でなければ、そのノードを末尾ノードの後ろに追加</span>
+<a id="__codelineno-24-28" name="__codelineno-24-28" href="#__codelineno-24-28"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-29" name="__codelineno-24-29" href="#__codelineno-24-29"></a><span class="w">            </span><span class="n">rear</span><span class="o">?.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-24-30" name="__codelineno-24-30" href="#__codelineno-24-30"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-24-31" name="__codelineno-24-31" href="#__codelineno-24-31"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-24-32" name="__codelineno-24-32" href="#__codelineno-24-32"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span>
+<a id="__codelineno-24-33" name="__codelineno-24-33" href="#__codelineno-24-33"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-34" name="__codelineno-24-34" href="#__codelineno-24-34"></a>
+<a id="__codelineno-24-35" name="__codelineno-24-35" href="#__codelineno-24-35"></a><span class="w">    </span><span class="cm">/* デキュー */</span>
+<a id="__codelineno-24-36" name="__codelineno-24-36" href="#__codelineno-24-36"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">pop</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-37" name="__codelineno-24-37" href="#__codelineno-24-37"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span><span class="p">()</span>
+<a id="__codelineno-24-38" name="__codelineno-24-38" href="#__codelineno-24-38"></a><span class="w">        </span><span class="c1">// 先頭ノードを削除</span>
+<a id="__codelineno-24-39" name="__codelineno-24-39" href="#__codelineno-24-39"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="o">?.</span><span class="na">next</span>
+<a id="__codelineno-24-40" name="__codelineno-24-40" href="#__codelineno-24-40"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span>
+<a id="__codelineno-24-41" name="__codelineno-24-41" href="#__codelineno-24-41"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-24-42" name="__codelineno-24-42" href="#__codelineno-24-42"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-43" name="__codelineno-24-43" href="#__codelineno-24-43"></a>
+<a id="__codelineno-24-44" name="__codelineno-24-44" href="#__codelineno-24-44"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-24-45" name="__codelineno-24-45" href="#__codelineno-24-45"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">peek</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-46" name="__codelineno-24-46" href="#__codelineno-24-46"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">()</span>
+<a id="__codelineno-24-47" name="__codelineno-24-47" href="#__codelineno-24-47"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">front</span><span class="o">!!</span><span class="p">.</span><span class="na">_val</span>
+<a id="__codelineno-24-48" name="__codelineno-24-48" href="#__codelineno-24-48"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-49" name="__codelineno-24-49" href="#__codelineno-24-49"></a>
+<a id="__codelineno-24-50" name="__codelineno-24-50" href="#__codelineno-24-50"></a><span class="w">    </span><span class="cm">/* 連結リストを Array に変換して返す */</span>
+<a id="__codelineno-24-51" name="__codelineno-24-51" href="#__codelineno-24-51"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">toArray</span><span class="p">():</span><span class="w"> </span><span class="n">IntArray</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-52" name="__codelineno-24-52" href="#__codelineno-24-52"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span>
+<a id="__codelineno-24-53" name="__codelineno-24-53" href="#__codelineno-24-53"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">size</span><span class="p">())</span>
+<a id="__codelineno-24-54" name="__codelineno-24-54" href="#__codelineno-24-54"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">indices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-55" name="__codelineno-24-55" href="#__codelineno-24-55"></a><span class="w">            </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">!!</span><span class="p">.</span><span class="na">_val</span>
+<a id="__codelineno-24-56" name="__codelineno-24-56" href="#__codelineno-24-56"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">next</span>
+<a id="__codelineno-24-57" name="__codelineno-24-57" href="#__codelineno-24-57"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-24-58" name="__codelineno-24-58" href="#__codelineno-24-58"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-24-59" name="__codelineno-24-59" href="#__codelineno-24-59"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-60" name="__codelineno-24-60" href="#__codelineno-24-60"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_queue.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### 連結リストで実装したキュー ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">LinkedListQueue</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="c1">### キューの長さを取得 ###</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">  </span><span class="kp">attr_reader</span><span class="w"> </span><span class="ss">:size</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">  </span><span class="c1">### コンストラクタ ###</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w">    </span><span class="vi">@front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kp">nil</span><span class="w">  </span><span class="c1"># 先頭ノード front</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">    </span><span class="vi">@rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kp">nil</span><span class="w">   </span><span class="c1"># 末尾ノード rear</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w">  </span><span class="c1">### キューが空か判定 ###</span>
+<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">is_empty?</span>
+<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w">    </span><span class="vi">@front</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a>
+<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a><span class="w">  </span><span class="c1">### エンキュー ###</span>
+<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a><span class="w">    </span><span class="c1"># 末尾ノードの後ろに num を追加</span>
+<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">ListNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a>
+<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="w">    </span><span class="c1"># キューが空なら、先頭ノードと末尾ノードの両方をそのノードに向ける</span>
+<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="vi">@front</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a><span class="w">      </span><span class="vi">@front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></a><span class="w">      </span><span class="vi">@rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-25-27" name="__codelineno-25-27" href="#__codelineno-25-27"></a><span class="w">    </span><span class="c1"># キューが空でなければ、そのノードを末尾ノードの後ろに追加する</span>
+<a id="__codelineno-25-28" name="__codelineno-25-28" href="#__codelineno-25-28"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-25-29" name="__codelineno-25-29" href="#__codelineno-25-29"></a><span class="w">      </span><span class="vi">@rear</span><span class="o">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-25-30" name="__codelineno-25-30" href="#__codelineno-25-30"></a><span class="w">      </span><span class="vi">@rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-25-31" name="__codelineno-25-31" href="#__codelineno-25-31"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-25-32" name="__codelineno-25-32" href="#__codelineno-25-32"></a>
+<a id="__codelineno-25-33" name="__codelineno-25-33" href="#__codelineno-25-33"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-25-34" name="__codelineno-25-34" href="#__codelineno-25-34"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-35" name="__codelineno-25-35" href="#__codelineno-25-35"></a>
+<a id="__codelineno-25-36" name="__codelineno-25-36" href="#__codelineno-25-36"></a><span class="w">  </span><span class="c1">### デキュー ###</span>
+<a id="__codelineno-25-37" name="__codelineno-25-37" href="#__codelineno-25-37"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">pop</span>
+<a id="__codelineno-25-38" name="__codelineno-25-38" href="#__codelineno-25-38"></a><span class="w">    </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span>
+<a id="__codelineno-25-39" name="__codelineno-25-39" href="#__codelineno-25-39"></a><span class="w">    </span><span class="c1"># 先頭ノードを削除</span>
+<a id="__codelineno-25-40" name="__codelineno-25-40" href="#__codelineno-25-40"></a><span class="w">    </span><span class="vi">@front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@front</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-25-41" name="__codelineno-25-41" href="#__codelineno-25-41"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-25-42" name="__codelineno-25-42" href="#__codelineno-25-42"></a><span class="w">    </span><span class="n">num</span>
+<a id="__codelineno-25-43" name="__codelineno-25-43" href="#__codelineno-25-43"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-44" name="__codelineno-25-44" href="#__codelineno-25-44"></a>
+<a id="__codelineno-25-45" name="__codelineno-25-45" href="#__codelineno-25-45"></a><span class="w">  </span><span class="c1">### 先頭要素にアクセス ###</span>
+<a id="__codelineno-25-46" name="__codelineno-25-46" href="#__codelineno-25-46"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">peek</span>
+<a id="__codelineno-25-47" name="__codelineno-25-47" href="#__codelineno-25-47"></a><span class="w">    </span><span class="k">raise</span><span class="w"> </span><span class="no">IndexError</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;キューは空です&#39;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_empty?</span>
+<a id="__codelineno-25-48" name="__codelineno-25-48" href="#__codelineno-25-48"></a>
+<a id="__codelineno-25-49" name="__codelineno-25-49" href="#__codelineno-25-49"></a><span class="w">    </span><span class="vi">@front</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-25-50" name="__codelineno-25-50" href="#__codelineno-25-50"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-51" name="__codelineno-25-51" href="#__codelineno-25-51"></a>
+<a id="__codelineno-25-52" name="__codelineno-25-52" href="#__codelineno-25-52"></a><span class="w">  </span><span class="c1">### 連結リストを Array に変換して返す ###</span>
+<a id="__codelineno-25-53" name="__codelineno-25-53" href="#__codelineno-25-53"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">to_array</span>
+<a id="__codelineno-25-54" name="__codelineno-25-54" href="#__codelineno-25-54"></a><span class="w">    </span><span class="n">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-25-55" name="__codelineno-25-55" href="#__codelineno-25-55"></a><span class="w">    </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@front</span>
+<a id="__codelineno-25-56" name="__codelineno-25-56" href="#__codelineno-25-56"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">temp</span>
+<a id="__codelineno-25-57" name="__codelineno-25-57" href="#__codelineno-25-57"></a><span class="w">      </span><span class="n">queue</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">temp</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-25-58" name="__codelineno-25-58" href="#__codelineno-25-58"></a><span class="w">      </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-25-59" name="__codelineno-25-59" href="#__codelineno-25-59"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-25-60" name="__codelineno-25-60" href="#__codelineno-25-60"></a><span class="w">    </span><span class="n">queue</span>
+<a id="__codelineno-25-61" name="__codelineno-25-61" href="#__codelineno-25-61"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-62" name="__codelineno-25-62" href="#__codelineno-25-62"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h3 id="2">2. &nbsp; 配列ベースの実装<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>配列の最初の要素を削除する時間計算量は<span class="arithmatex">\(O(n)\)</span>で、デキュー操作が非効率になります。しかし、この問題は以下のように巧妙に回避できます。</p>
-<p>変数<code>front</code>を使用してフロント要素のインデックスを示し、変数<code>size</code>を維持してキューの長さを記録します。<code>rear = front + size</code>を定義し、これはテール要素の直後の位置を指します。</p>
-<p>この設計により、<strong>配列内の要素の有効な間隔は<code>[front, rear - 1]</code>です</strong>。各操作の実装方法を下図に示します。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20ListNode%3A%0A%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%0A%0Aclass%20LinkedListQueue%3A%0A%0A%20%20%20%20def%20__init__%28self%29%3A%0A%20%20%20%20%20%20%20%20self._front%3A%20ListNode%20%7C%20None%20%3D%20None%0A%20%20%20%20%20%20%20%20self._rear%3A%20ListNode%20%7C%20None%20%3D%20None%0A%20%20%20%20%20%20%20%20self._size%3A%20int%20%3D%200%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%20self._size%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20return%20not%20self._front%0A%0A%20%20%20%20def%20push%28self%2C%20num%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20node%20%3D%20ListNode%28num%29%0A%20%20%20%20%20%20%20%20if%20self._front%20is%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self._front%20%3D%20node%0A%20%20%20%20%20%20%20%20%20%20%20%20self._rear%20%3D%20node%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self._rear.next%20%3D%20node%0A%20%20%20%20%20%20%20%20%20%20%20%20self._rear%20%3D%20node%0A%20%20%20%20%20%20%20%20self._size%20%2B%3D%201%0A%0A%20%20%20%20def%20pop%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20num%20%3D%20self.peek%28%29%0A%20%20%20%20%20%20%20%20self._front%20%3D%20self._front.next%0A%20%20%20%20%20%20%20%20self._size%20-%3D%201%0A%20%20%20%20%20%20%20%20return%20num%0A%0A%20%20%20%20def%20peek%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20if%20self.is_empty%28%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%27%E3%82%AD%E3%83%A5%E3%83%BC%E3%81%8C%E7%A9%BA%E3%81%A7%E3%81%99%27%29%0A%20%20%20%20%20%20%20%20return%20self._front.val%0A%0A%20%20%20%20def%20to_list%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20queue%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20temp%20%3D%20self._front%0A%20%20%20%20%20%20%20%20while%20temp%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20queue.append%28temp.val%29%0A%20%20%20%20%20%20%20%20%20%20%20%20temp%20%3D%20temp.next%0A%20%20%20%20%20%20%20%20return%20queue%0Aif%20__name__%20%3D%3D%20%27__main__%27%3A%0A%20%20%20%20queue%20%3D%20LinkedListQueue%28%29%0A%20%20%20%20queue.push%281%29%0A%20%20%20%20queue.push%283%29%0A%20%20%20%20queue.push%282%29%0A%20%20%20%20queue.push%285%29%0A%20%20%20%20queue.push%284%29%0A%20%20%20%20print%28%27%E3%82%AD%E3%83%A5%E3%83%BC%20queue%20%3D%27%2C%20queue.to_list%28%29%29%0A%20%20%20%20peek%20%3D%20queue.peek%28%29%0A%20%20%20%20print%28%27%E5%85%88%E9%A0%AD%E8%A6%81%E7%B4%A0%20front%20%3D%27%2C%20peek%29%0A%20%20%20%20pop_front%20%3D%20queue.pop%28%29%0A%20%20%20%20print%28%27%E5%8F%96%E3%82%8A%E5%87%BA%E3%81%97%E3%81%9F%E8%A6%81%E7%B4%A0%20pop%20%3D%27%2C%20pop_front%29%0A%20%20%20%20print%28%27%E5%8F%96%E3%82%8A%E5%87%BA%E3%81%97%E3%81%9F%E5%BE%8C%20queue%20%3D%27%2C%20queue.to_list%28%29%29%0A%20%20%20%20size%20%3D%20queue.size%28%29%0A%20%20%20%20print%28%27%E3%82%AD%E3%83%A5%E3%83%BC%E3%81%AE%E9%95%B7%E3%81%95%20size%20%3D%27%2C%20size%29%0A%20%20%20%20is_empty%20%3D%20queue.is_empty%28%29%0A%20%20%20%20print%28%27%E3%82%AD%E3%83%A5%E3%83%BC%E3%81%8C%E7%A9%BA%E3%81%8B%E3%81%A9%E3%81%86%E3%81%8B%20%3D%27%2C%20is_empty%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20ListNode%3A%0A%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%0A%0Aclass%20LinkedListQueue%3A%0A%0A%20%20%20%20def%20__init__%28self%29%3A%0A%20%20%20%20%20%20%20%20self._front%3A%20ListNode%20%7C%20None%20%3D%20None%0A%20%20%20%20%20%20%20%20self._rear%3A%20ListNode%20%7C%20None%20%3D%20None%0A%20%20%20%20%20%20%20%20self._size%3A%20int%20%3D%200%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%20self._size%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20return%20not%20self._front%0A%0A%20%20%20%20def%20push%28self%2C%20num%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20node%20%3D%20ListNode%28num%29%0A%20%20%20%20%20%20%20%20if%20self._front%20is%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self._front%20%3D%20node%0A%20%20%20%20%20%20%20%20%20%20%20%20self._rear%20%3D%20node%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self._rear.next%20%3D%20node%0A%20%20%20%20%20%20%20%20%20%20%20%20self._rear%20%3D%20node%0A%20%20%20%20%20%20%20%20self._size%20%2B%3D%201%0A%0A%20%20%20%20def%20pop%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20num%20%3D%20self.peek%28%29%0A%20%20%20%20%20%20%20%20self._front%20%3D%20self._front.next%0A%20%20%20%20%20%20%20%20self._size%20-%3D%201%0A%20%20%20%20%20%20%20%20return%20num%0A%0A%20%20%20%20def%20peek%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20if%20self.is_empty%28%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%27%E3%82%AD%E3%83%A5%E3%83%BC%E3%81%8C%E7%A9%BA%E3%81%A7%E3%81%99%27%29%0A%20%20%20%20%20%20%20%20return%20self._front.val%0A%0A%20%20%20%20def%20to_list%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20queue%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20temp%20%3D%20self._front%0A%20%20%20%20%20%20%20%20while%20temp%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20queue.append%28temp.val%29%0A%20%20%20%20%20%20%20%20%20%20%20%20temp%20%3D%20temp.next%0A%20%20%20%20%20%20%20%20return%20queue%0Aif%20__name__%20%3D%3D%20%27__main__%27%3A%0A%20%20%20%20queue%20%3D%20LinkedListQueue%28%29%0A%20%20%20%20queue.push%281%29%0A%20%20%20%20queue.push%283%29%0A%20%20%20%20queue.push%282%29%0A%20%20%20%20queue.push%285%29%0A%20%20%20%20queue.push%284%29%0A%20%20%20%20print%28%27%E3%82%AD%E3%83%A5%E3%83%BC%20queue%20%3D%27%2C%20queue.to_list%28%29%29%0A%20%20%20%20peek%20%3D%20queue.peek%28%29%0A%20%20%20%20print%28%27%E5%85%88%E9%A0%AD%E8%A6%81%E7%B4%A0%20front%20%3D%27%2C%20peek%29%0A%20%20%20%20pop_front%20%3D%20queue.pop%28%29%0A%20%20%20%20print%28%27%E5%8F%96%E3%82%8A%E5%87%BA%E3%81%97%E3%81%9F%E8%A6%81%E7%B4%A0%20pop%20%3D%27%2C%20pop_front%29%0A%20%20%20%20print%28%27%E5%8F%96%E3%82%8A%E5%87%BA%E3%81%97%E3%81%9F%E5%BE%8C%20queue%20%3D%27%2C%20queue.to_list%28%29%29%0A%20%20%20%20size%20%3D%20queue.size%28%29%0A%20%20%20%20print%28%27%E3%82%AD%E3%83%A5%E3%83%BC%E3%81%AE%E9%95%B7%E3%81%95%20size%20%3D%27%2C%20size%29%0A%20%20%20%20is_empty%20%3D%20queue.is_empty%28%29%0A%20%20%20%20print%28%27%E3%82%AD%E3%83%A5%E3%83%BC%E3%81%8C%E7%A9%BA%E3%81%8B%E3%81%A9%E3%81%86%E3%81%8B%20%3D%27%2C%20is_empty%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h3 id="2">2. &nbsp; 配列に基づく実装<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>配列で先頭要素を削除する時間計算量は <span class="arithmatex">\(O(n)\)</span> であり、そのままではデキュー操作の効率が低くなります。しかし、次の巧妙な方法によってこの問題を回避できます。</p>
+<p>変数 <code>front</code> を用いてキュー先頭要素のインデックスを指し、さらに変数 <code>size</code> でキューの長さを記録できます。<code>rear = front + size</code> と定義すると、この式で得られる <code>rear</code> はキュー末尾要素の次の位置を指します。</p>
+<p>この設計に基づくと、<strong>配列内で要素を含む有効区間は <code>[front, rear - 1]</code></strong> となります。各種操作の実装方法を下図に示します。</p>
 <ul>
-<li>エンキュー操作：入力要素を<code>rear</code>インデックスに割り当て、<code>size</code>を1増加させます。</li>
-<li>デキュー操作：単に<code>front</code>を1増加させ、<code>size</code>を1減少させます。</li>
+<li>エンキュー操作：入力要素を <code>rear</code> の位置に代入し、<code>size</code> を 1 増やします。</li>
+<li>デキュー操作：<code>front</code> を 1 増やし、<code>size</code> を 1 減らすだけです。</li>
 </ul>
-<p>エンキューとデキュー操作は両方とも単一の操作のみを必要とし、それぞれの時間計算量は<span class="arithmatex">\(O(1)\)</span>です。</p>
+<p>このように、エンキューとデキューはいずれも 1 回の操作だけで済み、時間計算量はともに <span class="arithmatex">\(O(1)\)</span> です。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="4:3"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">ArrayQueue</label><label for="__tabbed_4_2">push()</label><label for="__tabbed_4_3">pop()</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="配列によるキュー実装のエンキューとデキュー操作" class="animation-figure" src="../queue.assets/array_queue_step1.png" /></p>
+<p><img alt="配列でキューを実装したエンキューとデキュー操作" class="animation-figure" src="../queue.assets/array_queue_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="array_queue_push" class="animation-figure" src="../queue.assets/array_queue_step2_push.png" /></p>
@@ -5025,264 +5733,941 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 5-6 &nbsp; 配列によるキュー実装のエンキューとデキュー操作 </p>
+<p align="center"> 図 5-6 &nbsp; 配列でキューを実装したエンキューとデキュー操作 </p>
 
-<p>問題に気づくかもしれません：エンキューとデキュー操作が継続的に実行されると、<code>front</code>と<code>rear</code>の両方が右に移動し、<strong>最終的に配列の末尾に到達してそれ以上移動できなくなります</strong>。これを解決するために、配列を「循環配列」として扱い、配列の末尾を先頭に接続します。</p>
-<p>循環配列では、<code>front</code>または<code>rear</code>が末尾に到達すると、配列の先頭にループバックする必要があります。この循環パターンは、以下のコードに示すように「剰余演算」で実現できます：</p>
+<p>ここで 1 つ問題があります。エンキューとデキューを繰り返すと、<code>front</code> と <code>rear</code> はどちらも右へ移動し続け、<strong>配列の末尾に達するとそれ以上進めなくなります</strong>。この問題を解決するために、配列を先頭と末尾がつながった「環状配列」とみなします。</p>
+<p>環状配列では、<code>front</code> または <code>rear</code> が配列末尾を越えたときに、直ちに配列先頭へ戻って走査を続けられるようにする必要があります。この周期的な規則は「剰余演算」によって実現できます。コードは次のとおりです：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="5:13"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_queue.py</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayQueue</span><span class="p">:</span>
-<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;循環配列ベースのキュークラス&quot;&quot;&quot;</span>
-<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a>
-<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">size</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
-<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">size</span>  <span class="c1"># キュー要素を格納する配列</span>
-<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># フロントポインタ、フロント要素を指す</span>
-<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># キューの長さ</span>
-<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a>
-<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">capacity</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キューの容量を取得&quot;&quot;&quot;</span>
-<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a>        <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">)</span>
-<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a>
-<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キューの長さを取得&quot;&quot;&quot;</span>
-<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span>
-<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a>
-<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">is_empty</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
-<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キューが空かどうかを判定&quot;&quot;&quot;</span>
-<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="mi">0</span>
-<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a>
-<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;エンキュー&quot;&quot;&quot;</span>
-<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">():</span>
-<a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Queue is full&quot;</span><span class="p">)</span>
-<a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></a>        <span class="c1"># リアポインタを計算、リアインデックス + 1 を指す</span>
-<a id="__codelineno-25-27" name="__codelineno-25-27" href="#__codelineno-25-27"></a>        <span class="c1"># モジュロ演算を使用してリアポインタを配列の末尾から先頭に戻す</span>
-<a id="__codelineno-25-28" name="__codelineno-25-28" href="#__codelineno-25-28"></a>        <span class="n">rear</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">)</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">()</span>
-<a id="__codelineno-25-29" name="__codelineno-25-29" href="#__codelineno-25-29"></a>        <span class="c1"># num をリアに追加</span>
-<a id="__codelineno-25-30" name="__codelineno-25-30" href="#__codelineno-25-30"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">[</span><span class="n">rear</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>
-<a id="__codelineno-25-31" name="__codelineno-25-31" href="#__codelineno-25-31"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">+=</span> <span class="mi">1</span>
-<a id="__codelineno-25-32" name="__codelineno-25-32" href="#__codelineno-25-32"></a>
-<a id="__codelineno-25-33" name="__codelineno-25-33" href="#__codelineno-25-33"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-25-34" name="__codelineno-25-34" href="#__codelineno-25-34"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;デキュー&quot;&quot;&quot;</span>
-<a id="__codelineno-25-35" name="__codelineno-25-35" href="#__codelineno-25-35"></a>        <span class="n">num</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">peek</span><span class="p">()</span>
-<a id="__codelineno-25-36" name="__codelineno-25-36" href="#__codelineno-25-36"></a>        <span class="c1"># フロントポインタを1つ後ろに移動、末尾を超えた場合は配列の先頭に戻る</span>
-<a id="__codelineno-25-37" name="__codelineno-25-37" href="#__codelineno-25-37"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">()</span>
-<a id="__codelineno-25-38" name="__codelineno-25-38" href="#__codelineno-25-38"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-=</span> <span class="mi">1</span>
-<a id="__codelineno-25-39" name="__codelineno-25-39" href="#__codelineno-25-39"></a>        <span class="k">return</span> <span class="n">num</span>
-<a id="__codelineno-25-40" name="__codelineno-25-40" href="#__codelineno-25-40"></a>
-<a id="__codelineno-25-41" name="__codelineno-25-41" href="#__codelineno-25-41"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-25-42" name="__codelineno-25-42" href="#__codelineno-25-42"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;フロント要素にアクセス&quot;&quot;&quot;</span>
-<a id="__codelineno-25-43" name="__codelineno-25-43" href="#__codelineno-25-43"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
-<a id="__codelineno-25-44" name="__codelineno-25-44" href="#__codelineno-25-44"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Queue is empty&quot;</span><span class="p">)</span>
-<a id="__codelineno-25-45" name="__codelineno-25-45" href="#__codelineno-25-45"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="p">]</span>
-<a id="__codelineno-25-46" name="__codelineno-25-46" href="#__codelineno-25-46"></a>
-<a id="__codelineno-25-47" name="__codelineno-25-47" href="#__codelineno-25-47"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">to_list</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
-<a id="__codelineno-25-48" name="__codelineno-25-48" href="#__codelineno-25-48"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;出力用の配列を返す&quot;&quot;&quot;</span>
-<a id="__codelineno-25-49" name="__codelineno-25-49" href="#__codelineno-25-49"></a>        <span class="n">res</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span>
-<a id="__codelineno-25-50" name="__codelineno-25-50" href="#__codelineno-25-50"></a>        <span class="n">j</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span>
-<a id="__codelineno-25-51" name="__codelineno-25-51" href="#__codelineno-25-51"></a>        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()):</span>
-<a id="__codelineno-25-52" name="__codelineno-25-52" href="#__codelineno-25-52"></a>            <span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">[(</span><span class="n">j</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">())]</span>
-<a id="__codelineno-25-53" name="__codelineno-25-53" href="#__codelineno-25-53"></a>            <span class="n">j</span> <span class="o">+=</span> <span class="mi">1</span>
-<a id="__codelineno-25-54" name="__codelineno-25-54" href="#__codelineno-25-54"></a>        <span class="k">return</span> <span class="n">res</span>
+<div class="highlight"><span class="filename">array_queue.py</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayQueue</span><span class="p">:</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;循環配列ベースのキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>
+<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">size</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
+<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">size</span>  <span class="c1"># キュー要素を格納する配列</span>
+<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># 先頭ポインタ。先頭要素を指す</span>
+<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># キューの長さ</span>
+<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a>
+<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">capacity</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キューの容量を取得&quot;&quot;&quot;</span>
+<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a>        <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">)</span>
+<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a>
+<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キューの長さを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span>
+<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a>
+<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">is_empty</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
+<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キューが空かどうかを判定&quot;&quot;&quot;</span>
+<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="mi">0</span>
+<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a>
+<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;エンキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-26-24" name="__codelineno-26-24" href="#__codelineno-26-24"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">():</span>
+<a id="__codelineno-26-25" name="__codelineno-26-25" href="#__codelineno-26-25"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;キューがいっぱいです&quot;</span><span class="p">)</span>
+<a id="__codelineno-26-26" name="__codelineno-26-26" href="#__codelineno-26-26"></a>        <span class="c1"># 末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-26-27" name="__codelineno-26-27" href="#__codelineno-26-27"></a>        <span class="c1"># 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする</span>
+<a id="__codelineno-26-28" name="__codelineno-26-28" href="#__codelineno-26-28"></a>        <span class="n">rear</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">)</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">()</span>
+<a id="__codelineno-26-29" name="__codelineno-26-29" href="#__codelineno-26-29"></a>        <span class="c1"># num をキュー末尾に追加</span>
+<a id="__codelineno-26-30" name="__codelineno-26-30" href="#__codelineno-26-30"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">[</span><span class="n">rear</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>
+<a id="__codelineno-26-31" name="__codelineno-26-31" href="#__codelineno-26-31"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-26-32" name="__codelineno-26-32" href="#__codelineno-26-32"></a>
+<a id="__codelineno-26-33" name="__codelineno-26-33" href="#__codelineno-26-33"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-26-34" name="__codelineno-26-34" href="#__codelineno-26-34"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;デキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-26-35" name="__codelineno-26-35" href="#__codelineno-26-35"></a>        <span class="n">num</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">peek</span><span class="p">()</span>
+<a id="__codelineno-26-36" name="__codelineno-26-36" href="#__codelineno-26-36"></a>        <span class="c1"># 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す</span>
+<a id="__codelineno-26-37" name="__codelineno-26-37" href="#__codelineno-26-37"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">()</span>
+<a id="__codelineno-26-38" name="__codelineno-26-38" href="#__codelineno-26-38"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-=</span> <span class="mi">1</span>
+<a id="__codelineno-26-39" name="__codelineno-26-39" href="#__codelineno-26-39"></a>        <span class="k">return</span> <span class="n">num</span>
+<a id="__codelineno-26-40" name="__codelineno-26-40" href="#__codelineno-26-40"></a>
+<a id="__codelineno-26-41" name="__codelineno-26-41" href="#__codelineno-26-41"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-26-42" name="__codelineno-26-42" href="#__codelineno-26-42"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キュー先頭の要素にアクセス&quot;&quot;&quot;</span>
+<a id="__codelineno-26-43" name="__codelineno-26-43" href="#__codelineno-26-43"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
+<a id="__codelineno-26-44" name="__codelineno-26-44" href="#__codelineno-26-44"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;キューが空です&quot;</span><span class="p">)</span>
+<a id="__codelineno-26-45" name="__codelineno-26-45" href="#__codelineno-26-45"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="p">]</span>
+<a id="__codelineno-26-46" name="__codelineno-26-46" href="#__codelineno-26-46"></a>
+<a id="__codelineno-26-47" name="__codelineno-26-47" href="#__codelineno-26-47"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">to_list</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-26-48" name="__codelineno-26-48" href="#__codelineno-26-48"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;表示用のリストを返す&quot;&quot;&quot;</span>
+<a id="__codelineno-26-49" name="__codelineno-26-49" href="#__codelineno-26-49"></a>        <span class="n">res</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span>
+<a id="__codelineno-26-50" name="__codelineno-26-50" href="#__codelineno-26-50"></a>        <span class="n">j</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span>
+<a id="__codelineno-26-51" name="__codelineno-26-51" href="#__codelineno-26-51"></a>        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()):</span>
+<a id="__codelineno-26-52" name="__codelineno-26-52" href="#__codelineno-26-52"></a>            <span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">[(</span><span class="n">j</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">())]</span>
+<a id="__codelineno-26-53" name="__codelineno-26-53" href="#__codelineno-26-53"></a>            <span class="n">j</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-26-54" name="__codelineno-26-54" href="#__codelineno-26-54"></a>        <span class="k">return</span> <span class="n">res</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_queue.cpp</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="cm">/* 循環配列に基づくキュークラス */</span>
-<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayQueue</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
-<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">;</span><span class="w">       </span><span class="c1">// キュー要素を格納する配列</span>
-<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w">       </span><span class="c1">// 先頭ポインタ、先頭要素を指す</span>
-<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w">     </span><span class="c1">// キューの長さ</span>
-<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">queCapacity</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの容量</span>
-<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>
-<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
-<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="w">    </span><span class="n">ArrayQueue</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w">        </span><span class="c1">// 配列を初期化</span>
-<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="w">        </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">capacity</span><span class="p">];</span>
-<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="w">        </span><span class="n">queCapacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
-<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a>
-<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a><span class="w">    </span><span class="o">~</span><span class="n">ArrayQueue</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a><span class="w">        </span><span class="k">delete</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
-<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a>
-<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a><span class="w">    </span><span class="cm">/* キューの容量を取得 */</span>
-<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queCapacity</span><span class="p">;</span>
-<a id="__codelineno-26-24" name="__codelineno-26-24" href="#__codelineno-26-24"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-25" name="__codelineno-26-25" href="#__codelineno-26-25"></a>
-<a id="__codelineno-26-26" name="__codelineno-26-26" href="#__codelineno-26-26"></a><span class="w">    </span><span class="cm">/* キューの長さを取得 */</span>
-<a id="__codelineno-26-27" name="__codelineno-26-27" href="#__codelineno-26-27"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-28" name="__codelineno-26-28" href="#__codelineno-26-28"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
-<a id="__codelineno-26-29" name="__codelineno-26-29" href="#__codelineno-26-29"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-30" name="__codelineno-26-30" href="#__codelineno-26-30"></a>
-<a id="__codelineno-26-31" name="__codelineno-26-31" href="#__codelineno-26-31"></a><span class="w">    </span><span class="cm">/* キューが空かどうかを判定 */</span>
-<a id="__codelineno-26-32" name="__codelineno-26-32" href="#__codelineno-26-32"></a><span class="w">    </span><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-33" name="__codelineno-26-33" href="#__codelineno-26-33"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-26-34" name="__codelineno-26-34" href="#__codelineno-26-34"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-35" name="__codelineno-26-35" href="#__codelineno-26-35"></a>
-<a id="__codelineno-26-36" name="__codelineno-26-36" href="#__codelineno-26-36"></a><span class="w">    </span><span class="cm">/* エンキュー */</span>
-<a id="__codelineno-26-37" name="__codelineno-26-37" href="#__codelineno-26-37"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-38" name="__codelineno-26-38" href="#__codelineno-26-38"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">queCapacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-39" name="__codelineno-26-39" href="#__codelineno-26-39"></a><span class="w">            </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;Queue is full&quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
-<a id="__codelineno-26-40" name="__codelineno-26-40" href="#__codelineno-26-40"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-26-41" name="__codelineno-26-41" href="#__codelineno-26-41"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-26-42" name="__codelineno-26-42" href="#__codelineno-26-42"></a><span class="w">        </span><span class="c1">// 末尾ポインタを計算、末尾インデックス + 1を指す</span>
-<a id="__codelineno-26-43" name="__codelineno-26-43" href="#__codelineno-26-43"></a><span class="w">        </span><span class="c1">// 剰余演算を使用して末尾ポインタが配列の末尾から先頭に戻るようにラップ</span>
-<a id="__codelineno-26-44" name="__codelineno-26-44" href="#__codelineno-26-44"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">queSize</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">queCapacity</span><span class="p">;</span>
-<a id="__codelineno-26-45" name="__codelineno-26-45" href="#__codelineno-26-45"></a><span class="w">        </span><span class="c1">// numを末尾に追加</span>
-<a id="__codelineno-26-46" name="__codelineno-26-46" href="#__codelineno-26-46"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">rear</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-26-47" name="__codelineno-26-47" href="#__codelineno-26-47"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-26-48" name="__codelineno-26-48" href="#__codelineno-26-48"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-49" name="__codelineno-26-49" href="#__codelineno-26-49"></a>
-<a id="__codelineno-26-50" name="__codelineno-26-50" href="#__codelineno-26-50"></a><span class="w">    </span><span class="cm">/* デキュー */</span>
-<a id="__codelineno-26-51" name="__codelineno-26-51" href="#__codelineno-26-51"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-52" name="__codelineno-26-52" href="#__codelineno-26-52"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span><span class="p">();</span>
-<a id="__codelineno-26-53" name="__codelineno-26-53" href="#__codelineno-26-53"></a><span class="w">        </span><span class="c1">// 先頭ポインタを1つ後ろに移動、末尾を超えた場合は配列の先頭に戻る</span>
-<a id="__codelineno-26-54" name="__codelineno-26-54" href="#__codelineno-26-54"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">queCapacity</span><span class="p">;</span>
-<a id="__codelineno-26-55" name="__codelineno-26-55" href="#__codelineno-26-55"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
-<a id="__codelineno-26-56" name="__codelineno-26-56" href="#__codelineno-26-56"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-26-57" name="__codelineno-26-57" href="#__codelineno-26-57"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-58" name="__codelineno-26-58" href="#__codelineno-26-58"></a>
-<a id="__codelineno-26-59" name="__codelineno-26-59" href="#__codelineno-26-59"></a><span class="w">    </span><span class="cm">/* 先頭要素にアクセス */</span>
-<a id="__codelineno-26-60" name="__codelineno-26-60" href="#__codelineno-26-60"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-61" name="__codelineno-26-61" href="#__codelineno-26-61"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
-<a id="__codelineno-26-62" name="__codelineno-26-62" href="#__codelineno-26-62"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Queue is empty&quot;</span><span class="p">);</span>
-<a id="__codelineno-26-63" name="__codelineno-26-63" href="#__codelineno-26-63"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">front</span><span class="p">];</span>
-<a id="__codelineno-26-64" name="__codelineno-26-64" href="#__codelineno-26-64"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-65" name="__codelineno-26-65" href="#__codelineno-26-65"></a>
-<a id="__codelineno-26-66" name="__codelineno-26-66" href="#__codelineno-26-66"></a><span class="w">    </span><span class="cm">/* 配列をVectorに変換して返却 */</span>
-<a id="__codelineno-26-67" name="__codelineno-26-67" href="#__codelineno-26-67"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toVector</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-68" name="__codelineno-26-68" href="#__codelineno-26-68"></a><span class="w">        </span><span class="c1">// 有効な長さ範囲内の要素のみを変換</span>
-<a id="__codelineno-26-69" name="__codelineno-26-69" href="#__codelineno-26-69"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">arr</span><span class="p">(</span><span class="n">queSize</span><span class="p">);</span>
-<a id="__codelineno-26-70" name="__codelineno-26-70" href="#__codelineno-26-70"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-71" name="__codelineno-26-71" href="#__codelineno-26-71"></a><span class="w">            </span><span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">queCapacity</span><span class="p">];</span>
-<a id="__codelineno-26-72" name="__codelineno-26-72" href="#__codelineno-26-72"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-26-73" name="__codelineno-26-73" href="#__codelineno-26-73"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">arr</span><span class="p">;</span>
-<a id="__codelineno-26-74" name="__codelineno-26-74" href="#__codelineno-26-74"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-75" name="__codelineno-26-75" href="#__codelineno-26-75"></a><span class="p">};</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">array_queue.java</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* 配列に基づくキュークラス */</span>
-<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="kd">class</span> <span class="nc">ArrayQueue</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span><span class="w"> </span><span class="c1">// 要素を格納する配列</span>
-<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューヘッドポインタ、最初の要素を指す</span>
-<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの長さ</span>
-<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a>
-<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">ArrayQueue</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w">        </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">capacity</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a>
-<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="w">    </span><span class="cm">/* キューの容量を取得 */</span>
-<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
+<div class="highlight"><span class="filename">array_queue.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* 循環配列ベースのキュー */</span>
+<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayQueue</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
+<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">;</span><span class="w">       </span><span class="c1">// キュー要素を格納する配列</span>
+<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w">       </span><span class="c1">// 先頭ポインタ。先頭要素を指す</span>
+<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w">     </span><span class="c1">// キューの長さ</span>
+<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">queCapacity</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの容量</span>
+<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a>
+<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
+<a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a><span class="w">    </span><span class="n">ArrayQueue</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="w">        </span><span class="c1">// 配列を初期化</span>
+<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="w">        </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">capacity</span><span class="p">];</span>
+<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w">        </span><span class="n">queCapacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></a>
-<a id="__codelineno-27-17" name="__codelineno-27-17" href="#__codelineno-27-17"></a><span class="w">    </span><span class="cm">/* キューの長さを取得 */</span>
-<a id="__codelineno-27-18" name="__codelineno-27-18" href="#__codelineno-27-18"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-19" name="__codelineno-27-19" href="#__codelineno-27-19"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
-<a id="__codelineno-27-20" name="__codelineno-27-20" href="#__codelineno-27-20"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-21" name="__codelineno-27-21" href="#__codelineno-27-21"></a>
-<a id="__codelineno-27-22" name="__codelineno-27-22" href="#__codelineno-27-22"></a><span class="w">    </span><span class="cm">/* キューが空かどうかを判定 */</span>
-<a id="__codelineno-27-23" name="__codelineno-27-23" href="#__codelineno-27-23"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-24" name="__codelineno-27-24" href="#__codelineno-27-24"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-27-25" name="__codelineno-27-25" href="#__codelineno-27-25"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-26" name="__codelineno-27-26" href="#__codelineno-27-26"></a>
-<a id="__codelineno-27-27" name="__codelineno-27-27" href="#__codelineno-27-27"></a><span class="w">    </span><span class="cm">/* エンキュー */</span>
-<a id="__codelineno-27-28" name="__codelineno-27-28" href="#__codelineno-27-28"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-29" name="__codelineno-27-29" href="#__codelineno-27-29"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-30" name="__codelineno-27-30" href="#__codelineno-27-30"></a><span class="w">            </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">&quot;キューが満杯です&quot;</span><span class="p">);</span>
-<a id="__codelineno-27-31" name="__codelineno-27-31" href="#__codelineno-27-31"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-27-32" name="__codelineno-27-32" href="#__codelineno-27-32"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-27-33" name="__codelineno-27-33" href="#__codelineno-27-33"></a><span class="w">        </span><span class="c1">// リアポインタを計算：front + queSize</span>
-<a id="__codelineno-27-34" name="__codelineno-27-34" href="#__codelineno-27-34"></a><span class="w">        </span><span class="c1">// モジュロ操作により rear が配列の長さを超えることを回避</span>
-<a id="__codelineno-27-35" name="__codelineno-27-35" href="#__codelineno-27-35"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">queSize</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">();</span>
-<a id="__codelineno-27-36" name="__codelineno-27-36" href="#__codelineno-27-36"></a><span class="w">        </span><span class="c1">// 要素をキューリアに追加</span>
-<a id="__codelineno-27-37" name="__codelineno-27-37" href="#__codelineno-27-37"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">rear</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-27-38" name="__codelineno-27-38" href="#__codelineno-27-38"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-27-39" name="__codelineno-27-39" href="#__codelineno-27-39"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-40" name="__codelineno-27-40" href="#__codelineno-27-40"></a>
-<a id="__codelineno-27-41" name="__codelineno-27-41" href="#__codelineno-27-41"></a><span class="w">    </span><span class="cm">/* デキュー */</span>
-<a id="__codelineno-27-42" name="__codelineno-27-42" href="#__codelineno-27-42"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-43" name="__codelineno-27-43" href="#__codelineno-27-43"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span><span class="p">();</span>
-<a id="__codelineno-27-44" name="__codelineno-27-44" href="#__codelineno-27-44"></a><span class="w">        </span><span class="c1">// キューヘッドポインタを後ろに1つ移動、モジュロ操作により範囲を超えることを回避</span>
-<a id="__codelineno-27-45" name="__codelineno-27-45" href="#__codelineno-27-45"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">();</span>
-<a id="__codelineno-27-46" name="__codelineno-27-46" href="#__codelineno-27-46"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
-<a id="__codelineno-27-47" name="__codelineno-27-47" href="#__codelineno-27-47"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-27-17" name="__codelineno-27-17" href="#__codelineno-27-17"></a><span class="w">    </span><span class="o">~</span><span class="n">ArrayQueue</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-18" name="__codelineno-27-18" href="#__codelineno-27-18"></a><span class="w">        </span><span class="k">delete</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
+<a id="__codelineno-27-19" name="__codelineno-27-19" href="#__codelineno-27-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-20" name="__codelineno-27-20" href="#__codelineno-27-20"></a>
+<a id="__codelineno-27-21" name="__codelineno-27-21" href="#__codelineno-27-21"></a><span class="w">    </span><span class="cm">/* キューの容量を取得 */</span>
+<a id="__codelineno-27-22" name="__codelineno-27-22" href="#__codelineno-27-22"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-23" name="__codelineno-27-23" href="#__codelineno-27-23"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queCapacity</span><span class="p">;</span>
+<a id="__codelineno-27-24" name="__codelineno-27-24" href="#__codelineno-27-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-25" name="__codelineno-27-25" href="#__codelineno-27-25"></a>
+<a id="__codelineno-27-26" name="__codelineno-27-26" href="#__codelineno-27-26"></a><span class="w">    </span><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-27-27" name="__codelineno-27-27" href="#__codelineno-27-27"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-28" name="__codelineno-27-28" href="#__codelineno-27-28"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-27-29" name="__codelineno-27-29" href="#__codelineno-27-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-30" name="__codelineno-27-30" href="#__codelineno-27-30"></a>
+<a id="__codelineno-27-31" name="__codelineno-27-31" href="#__codelineno-27-31"></a><span class="w">    </span><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-27-32" name="__codelineno-27-32" href="#__codelineno-27-32"></a><span class="w">    </span><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-33" name="__codelineno-27-33" href="#__codelineno-27-33"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-27-34" name="__codelineno-27-34" href="#__codelineno-27-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-35" name="__codelineno-27-35" href="#__codelineno-27-35"></a>
+<a id="__codelineno-27-36" name="__codelineno-27-36" href="#__codelineno-27-36"></a><span class="w">    </span><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-27-37" name="__codelineno-27-37" href="#__codelineno-27-37"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-38" name="__codelineno-27-38" href="#__codelineno-27-38"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">queCapacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-39" name="__codelineno-27-39" href="#__codelineno-27-39"></a><span class="w">            </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;キューがいっぱいです&quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
+<a id="__codelineno-27-40" name="__codelineno-27-40" href="#__codelineno-27-40"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-27-41" name="__codelineno-27-41" href="#__codelineno-27-41"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-27-42" name="__codelineno-27-42" href="#__codelineno-27-42"></a><span class="w">        </span><span class="c1">// 末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-27-43" name="__codelineno-27-43" href="#__codelineno-27-43"></a><span class="w">        </span><span class="c1">// 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする</span>
+<a id="__codelineno-27-44" name="__codelineno-27-44" href="#__codelineno-27-44"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">queSize</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">queCapacity</span><span class="p">;</span>
+<a id="__codelineno-27-45" name="__codelineno-27-45" href="#__codelineno-27-45"></a><span class="w">        </span><span class="c1">// num をキュー末尾に追加</span>
+<a id="__codelineno-27-46" name="__codelineno-27-46" href="#__codelineno-27-46"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">rear</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-27-47" name="__codelineno-27-47" href="#__codelineno-27-47"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
 <a id="__codelineno-27-48" name="__codelineno-27-48" href="#__codelineno-27-48"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-27-49" name="__codelineno-27-49" href="#__codelineno-27-49"></a>
-<a id="__codelineno-27-50" name="__codelineno-27-50" href="#__codelineno-27-50"></a><span class="w">    </span><span class="cm">/* キューヘッド要素にアクセス */</span>
-<a id="__codelineno-27-51" name="__codelineno-27-51" href="#__codelineno-27-51"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-52" name="__codelineno-27-52" href="#__codelineno-27-52"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
-<a id="__codelineno-27-53" name="__codelineno-27-53" href="#__codelineno-27-53"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
-<a id="__codelineno-27-54" name="__codelineno-27-54" href="#__codelineno-27-54"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">front</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-27-55" name="__codelineno-27-55" href="#__codelineno-27-55"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-56" name="__codelineno-27-56" href="#__codelineno-27-56"></a>
-<a id="__codelineno-27-57" name="__codelineno-27-57" href="#__codelineno-27-57"></a><span class="w">    </span><span class="cm">/* 配列を返す */</span>
-<a id="__codelineno-27-58" name="__codelineno-27-58" href="#__codelineno-27-58"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-59" name="__codelineno-27-59" href="#__codelineno-27-59"></a><span class="w">        </span><span class="c1">// front から開始して queSize 個の要素のみをコピー</span>
-<a id="__codelineno-27-60" name="__codelineno-27-60" href="#__codelineno-27-60"></a><span class="w">        </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">queSize</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-27-61" name="__codelineno-27-61" href="#__codelineno-27-61"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-62" name="__codelineno-27-62" href="#__codelineno-27-62"></a><span class="w">            </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-27-63" name="__codelineno-27-63" href="#__codelineno-27-63"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-27-64" name="__codelineno-27-64" href="#__codelineno-27-64"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
-<a id="__codelineno-27-65" name="__codelineno-27-65" href="#__codelineno-27-65"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-66" name="__codelineno-27-66" href="#__codelineno-27-66"></a><span class="p">}</span>
+<a id="__codelineno-27-50" name="__codelineno-27-50" href="#__codelineno-27-50"></a><span class="w">    </span><span class="cm">/* デキュー */</span>
+<a id="__codelineno-27-51" name="__codelineno-27-51" href="#__codelineno-27-51"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-52" name="__codelineno-27-52" href="#__codelineno-27-52"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span><span class="p">();</span>
+<a id="__codelineno-27-53" name="__codelineno-27-53" href="#__codelineno-27-53"></a><span class="w">        </span><span class="c1">// 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す</span>
+<a id="__codelineno-27-54" name="__codelineno-27-54" href="#__codelineno-27-54"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">queCapacity</span><span class="p">;</span>
+<a id="__codelineno-27-55" name="__codelineno-27-55" href="#__codelineno-27-55"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-27-56" name="__codelineno-27-56" href="#__codelineno-27-56"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-27-57" name="__codelineno-27-57" href="#__codelineno-27-57"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-58" name="__codelineno-27-58" href="#__codelineno-27-58"></a>
+<a id="__codelineno-27-59" name="__codelineno-27-59" href="#__codelineno-27-59"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-27-60" name="__codelineno-27-60" href="#__codelineno-27-60"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-61" name="__codelineno-27-61" href="#__codelineno-27-61"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-27-62" name="__codelineno-27-62" href="#__codelineno-27-62"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;キューが空です&quot;</span><span class="p">);</span>
+<a id="__codelineno-27-63" name="__codelineno-27-63" href="#__codelineno-27-63"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">front</span><span class="p">];</span>
+<a id="__codelineno-27-64" name="__codelineno-27-64" href="#__codelineno-27-64"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-65" name="__codelineno-27-65" href="#__codelineno-27-65"></a>
+<a id="__codelineno-27-66" name="__codelineno-27-66" href="#__codelineno-27-66"></a><span class="w">    </span><span class="cm">/* 配列を Vector に変換して返す */</span>
+<a id="__codelineno-27-67" name="__codelineno-27-67" href="#__codelineno-27-67"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toVector</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-68" name="__codelineno-27-68" href="#__codelineno-27-68"></a><span class="w">        </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-27-69" name="__codelineno-27-69" href="#__codelineno-27-69"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">arr</span><span class="p">(</span><span class="n">queSize</span><span class="p">);</span>
+<a id="__codelineno-27-70" name="__codelineno-27-70" href="#__codelineno-27-70"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-71" name="__codelineno-27-71" href="#__codelineno-27-71"></a><span class="w">            </span><span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">queCapacity</span><span class="p">];</span>
+<a id="__codelineno-27-72" name="__codelineno-27-72" href="#__codelineno-27-72"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-27-73" name="__codelineno-27-73" href="#__codelineno-27-73"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">arr</span><span class="p">;</span>
+<a id="__codelineno-27-74" name="__codelineno-27-74" href="#__codelineno-27-74"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-75" name="__codelineno-27-75" href="#__codelineno-27-75"></a><span class="p">};</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_queue.cs</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">ArrayQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_queue.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 循環配列ベースのキュー */</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="kd">class</span> <span class="nc">ArrayQueue</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span><span class="w"> </span><span class="c1">// キュー要素を格納する配列</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ポインタ。先頭要素を指す</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの長さ</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">ArrayQueue</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">        </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">capacity</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a>
+<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a><span class="w">    </span><span class="cm">/* キューの容量を取得 */</span>
+<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
+<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a>
+<a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a><span class="w">    </span><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-28-18" name="__codelineno-28-18" href="#__codelineno-28-18"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-19" name="__codelineno-28-19" href="#__codelineno-28-19"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-28-20" name="__codelineno-28-20" href="#__codelineno-28-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-21" name="__codelineno-28-21" href="#__codelineno-28-21"></a>
+<a id="__codelineno-28-22" name="__codelineno-28-22" href="#__codelineno-28-22"></a><span class="w">    </span><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-28-23" name="__codelineno-28-23" href="#__codelineno-28-23"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-24" name="__codelineno-28-24" href="#__codelineno-28-24"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-28-25" name="__codelineno-28-25" href="#__codelineno-28-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-26" name="__codelineno-28-26" href="#__codelineno-28-26"></a>
+<a id="__codelineno-28-27" name="__codelineno-28-27" href="#__codelineno-28-27"></a><span class="w">    </span><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-28-28" name="__codelineno-28-28" href="#__codelineno-28-28"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-29" name="__codelineno-28-29" href="#__codelineno-28-29"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-30" name="__codelineno-28-30" href="#__codelineno-28-30"></a><span class="w">            </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">&quot;キューは満杯です&quot;</span><span class="p">);</span>
+<a id="__codelineno-28-31" name="__codelineno-28-31" href="#__codelineno-28-31"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-28-32" name="__codelineno-28-32" href="#__codelineno-28-32"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-28-33" name="__codelineno-28-33" href="#__codelineno-28-33"></a><span class="w">        </span><span class="c1">// 末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-28-34" name="__codelineno-28-34" href="#__codelineno-28-34"></a><span class="w">        </span><span class="c1">// 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする</span>
+<a id="__codelineno-28-35" name="__codelineno-28-35" href="#__codelineno-28-35"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">queSize</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">();</span>
+<a id="__codelineno-28-36" name="__codelineno-28-36" href="#__codelineno-28-36"></a><span class="w">        </span><span class="c1">// num をキュー末尾に追加</span>
+<a id="__codelineno-28-37" name="__codelineno-28-37" href="#__codelineno-28-37"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">rear</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-28-38" name="__codelineno-28-38" href="#__codelineno-28-38"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-28-39" name="__codelineno-28-39" href="#__codelineno-28-39"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-40" name="__codelineno-28-40" href="#__codelineno-28-40"></a>
+<a id="__codelineno-28-41" name="__codelineno-28-41" href="#__codelineno-28-41"></a><span class="w">    </span><span class="cm">/* デキュー */</span>
+<a id="__codelineno-28-42" name="__codelineno-28-42" href="#__codelineno-28-42"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-43" name="__codelineno-28-43" href="#__codelineno-28-43"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span><span class="p">();</span>
+<a id="__codelineno-28-44" name="__codelineno-28-44" href="#__codelineno-28-44"></a><span class="w">        </span><span class="c1">// 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す</span>
+<a id="__codelineno-28-45" name="__codelineno-28-45" href="#__codelineno-28-45"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">();</span>
+<a id="__codelineno-28-46" name="__codelineno-28-46" href="#__codelineno-28-46"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-28-47" name="__codelineno-28-47" href="#__codelineno-28-47"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-28-48" name="__codelineno-28-48" href="#__codelineno-28-48"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-49" name="__codelineno-28-49" href="#__codelineno-28-49"></a>
+<a id="__codelineno-28-50" name="__codelineno-28-50" href="#__codelineno-28-50"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-28-51" name="__codelineno-28-51" href="#__codelineno-28-51"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-52" name="__codelineno-28-52" href="#__codelineno-28-52"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-28-53" name="__codelineno-28-53" href="#__codelineno-28-53"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
+<a id="__codelineno-28-54" name="__codelineno-28-54" href="#__codelineno-28-54"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">front</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-28-55" name="__codelineno-28-55" href="#__codelineno-28-55"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-56" name="__codelineno-28-56" href="#__codelineno-28-56"></a>
+<a id="__codelineno-28-57" name="__codelineno-28-57" href="#__codelineno-28-57"></a><span class="w">    </span><span class="cm">/* 配列を返す */</span>
+<a id="__codelineno-28-58" name="__codelineno-28-58" href="#__codelineno-28-58"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-59" name="__codelineno-28-59" href="#__codelineno-28-59"></a><span class="w">        </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-28-60" name="__codelineno-28-60" href="#__codelineno-28-60"></a><span class="w">        </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">queSize</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-28-61" name="__codelineno-28-61" href="#__codelineno-28-61"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-62" name="__codelineno-28-62" href="#__codelineno-28-62"></a><span class="w">            </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-28-63" name="__codelineno-28-63" href="#__codelineno-28-63"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-28-64" name="__codelineno-28-64" href="#__codelineno-28-64"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-28-65" name="__codelineno-28-65" href="#__codelineno-28-65"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-66" name="__codelineno-28-66" href="#__codelineno-28-66"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_queue.go</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">arrayQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_queue.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 循環配列ベースのキュー */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayQueue</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span><span class="w">  </span><span class="c1">// キュー要素を格納する配列</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w">   </span><span class="c1">// 先頭ポインタ。先頭要素を指す</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの長さ</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nf">ArrayQueue</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">        </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">capacity</span><span class="p">];</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="w">    </span><span class="cm">/* キューの容量を取得 */</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="nf">Capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="w">    </span><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-29-20" name="__codelineno-29-20" href="#__codelineno-29-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-21" name="__codelineno-29-21" href="#__codelineno-29-21"></a>
+<a id="__codelineno-29-22" name="__codelineno-29-22" href="#__codelineno-29-22"></a><span class="w">    </span><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-29-23" name="__codelineno-29-23" href="#__codelineno-29-23"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="nf">IsEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-24" name="__codelineno-29-24" href="#__codelineno-29-24"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-29-25" name="__codelineno-29-25" href="#__codelineno-29-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-26" name="__codelineno-29-26" href="#__codelineno-29-26"></a>
+<a id="__codelineno-29-27" name="__codelineno-29-27" href="#__codelineno-29-27"></a><span class="w">    </span><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-29-28" name="__codelineno-29-28" href="#__codelineno-29-28"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">Push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-29" name="__codelineno-29-29" href="#__codelineno-29-29"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">Capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-30" name="__codelineno-29-30" href="#__codelineno-29-30"></a><span class="w">            </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="s">&quot;キューは満杯です&quot;</span><span class="p">);</span>
+<a id="__codelineno-29-31" name="__codelineno-29-31" href="#__codelineno-29-31"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-29-32" name="__codelineno-29-32" href="#__codelineno-29-32"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-33" name="__codelineno-29-33" href="#__codelineno-29-33"></a><span class="w">        </span><span class="c1">// 末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-29-34" name="__codelineno-29-34" href="#__codelineno-29-34"></a><span class="w">        </span><span class="c1">// 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする</span>
+<a id="__codelineno-29-35" name="__codelineno-29-35" href="#__codelineno-29-35"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">queSize</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">Capacity</span><span class="p">();</span>
+<a id="__codelineno-29-36" name="__codelineno-29-36" href="#__codelineno-29-36"></a><span class="w">        </span><span class="c1">// num をキュー末尾に追加</span>
+<a id="__codelineno-29-37" name="__codelineno-29-37" href="#__codelineno-29-37"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">rear</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-29-38" name="__codelineno-29-38" href="#__codelineno-29-38"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-29-39" name="__codelineno-29-39" href="#__codelineno-29-39"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-40" name="__codelineno-29-40" href="#__codelineno-29-40"></a>
+<a id="__codelineno-29-41" name="__codelineno-29-41" href="#__codelineno-29-41"></a><span class="w">    </span><span class="cm">/* デキュー */</span>
+<a id="__codelineno-29-42" name="__codelineno-29-42" href="#__codelineno-29-42"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-43" name="__codelineno-29-43" href="#__codelineno-29-43"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Peek</span><span class="p">();</span>
+<a id="__codelineno-29-44" name="__codelineno-29-44" href="#__codelineno-29-44"></a><span class="w">        </span><span class="c1">// 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す</span>
+<a id="__codelineno-29-45" name="__codelineno-29-45" href="#__codelineno-29-45"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">Capacity</span><span class="p">();</span>
+<a id="__codelineno-29-46" name="__codelineno-29-46" href="#__codelineno-29-46"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-29-47" name="__codelineno-29-47" href="#__codelineno-29-47"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-29-48" name="__codelineno-29-48" href="#__codelineno-29-48"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-49" name="__codelineno-29-49" href="#__codelineno-29-49"></a>
+<a id="__codelineno-29-50" name="__codelineno-29-50" href="#__codelineno-29-50"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-29-51" name="__codelineno-29-51" href="#__codelineno-29-51"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-52" name="__codelineno-29-52" href="#__codelineno-29-52"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsEmpty</span><span class="p">())</span>
+<a id="__codelineno-29-53" name="__codelineno-29-53" href="#__codelineno-29-53"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="nf">Exception</span><span class="p">();</span>
+<a id="__codelineno-29-54" name="__codelineno-29-54" href="#__codelineno-29-54"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">front</span><span class="p">];</span>
+<a id="__codelineno-29-55" name="__codelineno-29-55" href="#__codelineno-29-55"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-56" name="__codelineno-29-56" href="#__codelineno-29-56"></a>
+<a id="__codelineno-29-57" name="__codelineno-29-57" href="#__codelineno-29-57"></a><span class="w">    </span><span class="cm">/* 配列を返す */</span>
+<a id="__codelineno-29-58" name="__codelineno-29-58" href="#__codelineno-29-58"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="nf">ToArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-59" name="__codelineno-29-59" href="#__codelineno-29-59"></a><span class="w">        </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-29-60" name="__codelineno-29-60" href="#__codelineno-29-60"></a><span class="w">        </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">queSize</span><span class="p">];</span>
+<a id="__codelineno-29-61" name="__codelineno-29-61" href="#__codelineno-29-61"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-62" name="__codelineno-29-62" href="#__codelineno-29-62"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">Capacity</span><span class="p">()];</span>
+<a id="__codelineno-29-63" name="__codelineno-29-63" href="#__codelineno-29-63"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-64" name="__codelineno-29-64" href="#__codelineno-29-64"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-29-65" name="__codelineno-29-65" href="#__codelineno-29-65"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-66" name="__codelineno-29-66" href="#__codelineno-29-66"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_queue.swift</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">ArrayQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_queue.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 循環配列ベースのキュー */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">arrayQueue</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="nx">nums</span><span class="w">        </span><span class="p">[]</span><span class="kt">int</span><span class="w"> </span><span class="c1">// キュー要素を格納する配列</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="nx">front</span><span class="w">       </span><span class="kt">int</span><span class="w">   </span><span class="c1">// 先頭ポインタ。先頭要素を指す</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">    </span><span class="nx">queSize</span><span class="w">     </span><span class="kt">int</span><span class="w">   </span><span class="c1">// キューの長さ</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="nx">queCapacity</span><span class="w"> </span><span class="kt">int</span><span class="w">   </span><span class="c1">// キュー容量（格納できる要素数の上限）</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="p">}</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="cm">/* キューを初期化 */</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="kd">func</span><span class="w"> </span><span class="nx">newArrayQueue</span><span class="p">(</span><span class="nx">queCapacity</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayQueue</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">arrayQueue</span><span class="p">{</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w">        </span><span class="nx">nums</span><span class="p">:</span><span class="w">        </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">queCapacity</span><span class="p">),</span>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w">        </span><span class="nx">queCapacity</span><span class="p">:</span><span class="w"> </span><span class="nx">queCapacity</span><span class="p">,</span>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w">        </span><span class="nx">front</span><span class="p">:</span><span class="w">       </span><span class="mi">0</span><span class="p">,</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w">        </span><span class="nx">queSize</span><span class="p">:</span><span class="w">     </span><span class="mi">0</span><span class="p">,</span>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="p">}</span>
+<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a>
+<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">q</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayQueue</span><span class="p">)</span><span class="w"> </span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-21" name="__codelineno-30-21" href="#__codelineno-30-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">queSize</span>
+<a id="__codelineno-30-22" name="__codelineno-30-22" href="#__codelineno-30-22"></a><span class="p">}</span>
+<a id="__codelineno-30-23" name="__codelineno-30-23" href="#__codelineno-30-23"></a>
+<a id="__codelineno-30-24" name="__codelineno-30-24" href="#__codelineno-30-24"></a><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-30-25" name="__codelineno-30-25" href="#__codelineno-30-25"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">q</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayQueue</span><span class="p">)</span><span class="w"> </span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-26" name="__codelineno-30-26" href="#__codelineno-30-26"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-30-27" name="__codelineno-30-27" href="#__codelineno-30-27"></a><span class="p">}</span>
+<a id="__codelineno-30-28" name="__codelineno-30-28" href="#__codelineno-30-28"></a>
+<a id="__codelineno-30-29" name="__codelineno-30-29" href="#__codelineno-30-29"></a><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-30-30" name="__codelineno-30-30" href="#__codelineno-30-30"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">q</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayQueue</span><span class="p">)</span><span class="w"> </span><span class="nx">push</span><span class="p">(</span><span class="nx">num</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-31" name="__codelineno-30-31" href="#__codelineno-30-31"></a><span class="w">    </span><span class="c1">// rear == queCapacity のときキューは満杯</span>
+<a id="__codelineno-30-32" name="__codelineno-30-32" href="#__codelineno-30-32"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">queCapacity</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-33" name="__codelineno-30-33" href="#__codelineno-30-33"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-30-34" name="__codelineno-30-34" href="#__codelineno-30-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-35" name="__codelineno-30-35" href="#__codelineno-30-35"></a><span class="w">    </span><span class="c1">// 末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-30-36" name="__codelineno-30-36" href="#__codelineno-30-36"></a><span class="w">    </span><span class="c1">// 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする</span>
+<a id="__codelineno-30-37" name="__codelineno-30-37" href="#__codelineno-30-37"></a><span class="w">    </span><span class="nx">rear</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">(</span><span class="nx">q</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">queSize</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">queCapacity</span>
+<a id="__codelineno-30-38" name="__codelineno-30-38" href="#__codelineno-30-38"></a><span class="w">    </span><span class="c1">// num をキュー末尾に追加</span>
+<a id="__codelineno-30-39" name="__codelineno-30-39" href="#__codelineno-30-39"></a><span class="w">    </span><span class="nx">q</span><span class="p">.</span><span class="nx">nums</span><span class="p">[</span><span class="nx">rear</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">num</span>
+<a id="__codelineno-30-40" name="__codelineno-30-40" href="#__codelineno-30-40"></a><span class="w">    </span><span class="nx">q</span><span class="p">.</span><span class="nx">queSize</span><span class="o">++</span>
+<a id="__codelineno-30-41" name="__codelineno-30-41" href="#__codelineno-30-41"></a><span class="p">}</span>
+<a id="__codelineno-30-42" name="__codelineno-30-42" href="#__codelineno-30-42"></a>
+<a id="__codelineno-30-43" name="__codelineno-30-43" href="#__codelineno-30-43"></a><span class="cm">/* デキュー */</span>
+<a id="__codelineno-30-44" name="__codelineno-30-44" href="#__codelineno-30-44"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">q</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayQueue</span><span class="p">)</span><span class="w"> </span><span class="nx">pop</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-45" name="__codelineno-30-45" href="#__codelineno-30-45"></a><span class="w">    </span><span class="nx">num</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">peek</span><span class="p">()</span>
+<a id="__codelineno-30-46" name="__codelineno-30-46" href="#__codelineno-30-46"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-47" name="__codelineno-30-47" href="#__codelineno-30-47"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-30-48" name="__codelineno-30-48" href="#__codelineno-30-48"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-49" name="__codelineno-30-49" href="#__codelineno-30-49"></a>
+<a id="__codelineno-30-50" name="__codelineno-30-50" href="#__codelineno-30-50"></a><span class="w">    </span><span class="c1">// 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す</span>
+<a id="__codelineno-30-51" name="__codelineno-30-51" href="#__codelineno-30-51"></a><span class="w">    </span><span class="nx">q</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="nx">q</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">queCapacity</span>
+<a id="__codelineno-30-52" name="__codelineno-30-52" href="#__codelineno-30-52"></a><span class="w">    </span><span class="nx">q</span><span class="p">.</span><span class="nx">queSize</span><span class="o">--</span>
+<a id="__codelineno-30-53" name="__codelineno-30-53" href="#__codelineno-30-53"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">num</span>
+<a id="__codelineno-30-54" name="__codelineno-30-54" href="#__codelineno-30-54"></a><span class="p">}</span>
+<a id="__codelineno-30-55" name="__codelineno-30-55" href="#__codelineno-30-55"></a>
+<a id="__codelineno-30-56" name="__codelineno-30-56" href="#__codelineno-30-56"></a><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-30-57" name="__codelineno-30-57" href="#__codelineno-30-57"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">q</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayQueue</span><span class="p">)</span><span class="w"> </span><span class="nx">peek</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-58" name="__codelineno-30-58" href="#__codelineno-30-58"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-59" name="__codelineno-30-59" href="#__codelineno-30-59"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-30-60" name="__codelineno-30-60" href="#__codelineno-30-60"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-61" name="__codelineno-30-61" href="#__codelineno-30-61"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">nums</span><span class="p">[</span><span class="nx">q</span><span class="p">.</span><span class="nx">front</span><span class="p">]</span>
+<a id="__codelineno-30-62" name="__codelineno-30-62" href="#__codelineno-30-62"></a><span class="p">}</span>
+<a id="__codelineno-30-63" name="__codelineno-30-63" href="#__codelineno-30-63"></a>
+<a id="__codelineno-30-64" name="__codelineno-30-64" href="#__codelineno-30-64"></a><span class="cm">/* 表示用に Slice を取得 */</span>
+<a id="__codelineno-30-65" name="__codelineno-30-65" href="#__codelineno-30-65"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">q</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayQueue</span><span class="p">)</span><span class="w"> </span><span class="nx">toSlice</span><span class="p">()</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-66" name="__codelineno-30-66" href="#__codelineno-30-66"></a><span class="w">    </span><span class="nx">rear</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">(</span><span class="nx">q</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">queSize</span><span class="p">)</span>
+<a id="__codelineno-30-67" name="__codelineno-30-67" href="#__codelineno-30-67"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">rear</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">queCapacity</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-68" name="__codelineno-30-68" href="#__codelineno-30-68"></a><span class="w">        </span><span class="nx">rear</span><span class="w"> </span><span class="o">%=</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">queCapacity</span>
+<a id="__codelineno-30-69" name="__codelineno-30-69" href="#__codelineno-30-69"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">q</span><span class="p">.</span><span class="nx">nums</span><span class="p">[</span><span class="nx">q</span><span class="p">.</span><span class="nx">front</span><span class="p">:],</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">nums</span><span class="p">[:</span><span class="nx">rear</span><span class="p">]</span><span class="o">...</span><span class="p">)</span>
+<a id="__codelineno-30-70" name="__codelineno-30-70" href="#__codelineno-30-70"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-71" name="__codelineno-30-71" href="#__codelineno-30-71"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">q</span><span class="p">.</span><span class="nx">nums</span><span class="p">[</span><span class="nx">q</span><span class="p">.</span><span class="nx">front</span><span class="p">:</span><span class="nx">rear</span><span class="p">]</span>
+<a id="__codelineno-30-72" name="__codelineno-30-72" href="#__codelineno-30-72"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_queue.js</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_queue.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* 循環配列ベースのキュー */</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ArrayQueue</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">nums</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="c1">// キュー要素を格納する配列</span>
+<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">front</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// 先頭ポインタ。先頭要素を指す</span>
+<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">_size</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// キューの長さ</span>
+<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a>
+<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w">    </span><span class="kd">init</span><span class="p">(</span><span class="n">capacity</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w">        </span><span class="c1">// 配列を初期化</span>
+<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="w">        </span><span class="n">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span>
+<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="w">        </span><span class="n">_size</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a>
+<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a><span class="w">    </span><span class="cm">/* キューの容量を取得 */</span>
+<a id="__codelineno-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-16" name="__codelineno-31-16" href="#__codelineno-31-16"></a><span class="w">        </span><span class="n">nums</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-31-17" name="__codelineno-31-17" href="#__codelineno-31-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-18" name="__codelineno-31-18" href="#__codelineno-31-18"></a>
+<a id="__codelineno-31-19" name="__codelineno-31-19" href="#__codelineno-31-19"></a><span class="w">    </span><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-31-20" name="__codelineno-31-20" href="#__codelineno-31-20"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-21" name="__codelineno-31-21" href="#__codelineno-31-21"></a><span class="w">        </span><span class="n">_size</span>
+<a id="__codelineno-31-22" name="__codelineno-31-22" href="#__codelineno-31-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-23" name="__codelineno-31-23" href="#__codelineno-31-23"></a>
+<a id="__codelineno-31-24" name="__codelineno-31-24" href="#__codelineno-31-24"></a><span class="w">    </span><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-31-25" name="__codelineno-31-25" href="#__codelineno-31-25"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-26" name="__codelineno-31-26" href="#__codelineno-31-26"></a><span class="w">        </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-31-27" name="__codelineno-31-27" href="#__codelineno-31-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-28" name="__codelineno-31-28" href="#__codelineno-31-28"></a>
+<a id="__codelineno-31-29" name="__codelineno-31-29" href="#__codelineno-31-29"></a><span class="w">    </span><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-31-30" name="__codelineno-31-30" href="#__codelineno-31-30"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-31" name="__codelineno-31-31" href="#__codelineno-31-31"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-32" name="__codelineno-31-32" href="#__codelineno-31-32"></a><span class="w">            </span><span class="bp">print</span><span class="p">(</span><span class="s">&quot;キューがいっぱいです&quot;</span><span class="p">)</span>
+<a id="__codelineno-31-33" name="__codelineno-31-33" href="#__codelineno-31-33"></a><span class="w">            </span><span class="k">return</span>
+<a id="__codelineno-31-34" name="__codelineno-31-34" href="#__codelineno-31-34"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-31-35" name="__codelineno-31-35" href="#__codelineno-31-35"></a><span class="w">        </span><span class="c1">// 末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-31-36" name="__codelineno-31-36" href="#__codelineno-31-36"></a><span class="w">        </span><span class="c1">// 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする</span>
+<a id="__codelineno-31-37" name="__codelineno-31-37" href="#__codelineno-31-37"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">rear</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">size</span><span class="p">())</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span>
+<a id="__codelineno-31-38" name="__codelineno-31-38" href="#__codelineno-31-38"></a><span class="w">        </span><span class="c1">// num をキュー末尾に追加</span>
+<a id="__codelineno-31-39" name="__codelineno-31-39" href="#__codelineno-31-39"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">rear</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-31-40" name="__codelineno-31-40" href="#__codelineno-31-40"></a><span class="w">        </span><span class="n">_size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-31-41" name="__codelineno-31-41" href="#__codelineno-31-41"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-42" name="__codelineno-31-42" href="#__codelineno-31-42"></a>
+<a id="__codelineno-31-43" name="__codelineno-31-43" href="#__codelineno-31-43"></a><span class="w">    </span><span class="cm">/* デキュー */</span>
+<a id="__codelineno-31-44" name="__codelineno-31-44" href="#__codelineno-31-44"></a><span class="w">    </span><span class="p">@</span><span class="n">discardableResult</span>
+<a id="__codelineno-31-45" name="__codelineno-31-45" href="#__codelineno-31-45"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-46" name="__codelineno-31-46" href="#__codelineno-31-46"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">num</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">peek</span><span class="p">()</span>
+<a id="__codelineno-31-47" name="__codelineno-31-47" href="#__codelineno-31-47"></a><span class="w">        </span><span class="c1">// 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す</span>
+<a id="__codelineno-31-48" name="__codelineno-31-48" href="#__codelineno-31-48"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span>
+<a id="__codelineno-31-49" name="__codelineno-31-49" href="#__codelineno-31-49"></a><span class="w">        </span><span class="n">_size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-31-50" name="__codelineno-31-50" href="#__codelineno-31-50"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-31-51" name="__codelineno-31-51" href="#__codelineno-31-51"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-52" name="__codelineno-31-52" href="#__codelineno-31-52"></a>
+<a id="__codelineno-31-53" name="__codelineno-31-53" href="#__codelineno-31-53"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-31-54" name="__codelineno-31-54" href="#__codelineno-31-54"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-55" name="__codelineno-31-55" href="#__codelineno-31-55"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-56" name="__codelineno-31-56" href="#__codelineno-31-56"></a><span class="w">            </span><span class="bp">fatalError</span><span class="p">(</span><span class="s">&quot;キューが空です&quot;</span><span class="p">)</span>
+<a id="__codelineno-31-57" name="__codelineno-31-57" href="#__codelineno-31-57"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-31-58" name="__codelineno-31-58" href="#__codelineno-31-58"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">front</span><span class="p">]</span>
+<a id="__codelineno-31-59" name="__codelineno-31-59" href="#__codelineno-31-59"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-60" name="__codelineno-31-60" href="#__codelineno-31-60"></a>
+<a id="__codelineno-31-61" name="__codelineno-31-61" href="#__codelineno-31-61"></a><span class="w">    </span><span class="cm">/* 配列を返す */</span>
+<a id="__codelineno-31-62" name="__codelineno-31-62" href="#__codelineno-31-62"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-63" name="__codelineno-31-63" href="#__codelineno-31-63"></a><span class="w">        </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-31-64" name="__codelineno-31-64" href="#__codelineno-31-64"></a><span class="w">        </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">size</span><span class="p">()).</span><span class="bp">map</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="nv">$0</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">()]</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-31-65" name="__codelineno-31-65" href="#__codelineno-31-65"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-66" name="__codelineno-31-66" href="#__codelineno-31-66"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_queue.ts</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_queue.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* 循環配列ベースのキュー */</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">ArrayQueue</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w">    </span><span class="n">#nums</span><span class="p">;</span><span class="w"> </span><span class="c1">// キュー要素を格納する配列</span>
+<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="w">    </span><span class="n">#front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ポインタ。先頭要素を指す</span>
+<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="w">    </span><span class="n">#queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの長さ</span>
+<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a>
+<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">capacity</span><span class="p">);</span>
+<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-10" name="__codelineno-32-10" href="#__codelineno-32-10"></a>
+<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a><span class="w">    </span><span class="cm">/* キューの容量を取得 */</span>
+<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a><span class="w">    </span><span class="nx">get</span><span class="w"> </span><span class="nx">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-32-14" name="__codelineno-32-14" href="#__codelineno-32-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-15" name="__codelineno-32-15" href="#__codelineno-32-15"></a>
+<a id="__codelineno-32-16" name="__codelineno-32-16" href="#__codelineno-32-16"></a><span class="w">    </span><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-32-17" name="__codelineno-32-17" href="#__codelineno-32-17"></a><span class="w">    </span><span class="nx">get</span><span class="w"> </span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-18" name="__codelineno-32-18" href="#__codelineno-32-18"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="p">;</span>
+<a id="__codelineno-32-19" name="__codelineno-32-19" href="#__codelineno-32-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-20" name="__codelineno-32-20" href="#__codelineno-32-20"></a>
+<a id="__codelineno-32-21" name="__codelineno-32-21" href="#__codelineno-32-21"></a><span class="w">    </span><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-32-22" name="__codelineno-32-22" href="#__codelineno-32-22"></a><span class="w">    </span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-23" name="__codelineno-32-23" href="#__codelineno-32-23"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-32-24" name="__codelineno-32-24" href="#__codelineno-32-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-25" name="__codelineno-32-25" href="#__codelineno-32-25"></a>
+<a id="__codelineno-32-26" name="__codelineno-32-26" href="#__codelineno-32-26"></a><span class="w">    </span><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-32-27" name="__codelineno-32-27" href="#__codelineno-32-27"></a><span class="w">    </span><span class="nx">push</span><span class="p">(</span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-28" name="__codelineno-32-28" href="#__codelineno-32-28"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-29" name="__codelineno-32-29" href="#__codelineno-32-29"></a><span class="w">            </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="s1">&#39;キューがいっぱいです&#39;</span><span class="p">);</span>
+<a id="__codelineno-32-30" name="__codelineno-32-30" href="#__codelineno-32-30"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-32-31" name="__codelineno-32-31" href="#__codelineno-32-31"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-32-32" name="__codelineno-32-32" href="#__codelineno-32-32"></a><span class="w">        </span><span class="c1">// 末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-32-33" name="__codelineno-32-33" href="#__codelineno-32-33"></a><span class="w">        </span><span class="c1">// 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする</span>
+<a id="__codelineno-32-34" name="__codelineno-32-34" href="#__codelineno-32-34"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="p">;</span>
+<a id="__codelineno-32-35" name="__codelineno-32-35" href="#__codelineno-32-35"></a><span class="w">        </span><span class="c1">// num をキュー末尾に追加</span>
+<a id="__codelineno-32-36" name="__codelineno-32-36" href="#__codelineno-32-36"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#nums</span><span class="p">[</span><span class="nx">rear</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-32-37" name="__codelineno-32-37" href="#__codelineno-32-37"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-32-38" name="__codelineno-32-38" href="#__codelineno-32-38"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-39" name="__codelineno-32-39" href="#__codelineno-32-39"></a>
+<a id="__codelineno-32-40" name="__codelineno-32-40" href="#__codelineno-32-40"></a><span class="w">    </span><span class="cm">/* デキュー */</span>
+<a id="__codelineno-32-41" name="__codelineno-32-41" href="#__codelineno-32-41"></a><span class="w">    </span><span class="nx">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-42" name="__codelineno-32-42" href="#__codelineno-32-42"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">peek</span><span class="p">();</span>
+<a id="__codelineno-32-43" name="__codelineno-32-43" href="#__codelineno-32-43"></a><span class="w">        </span><span class="c1">// 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す</span>
+<a id="__codelineno-32-44" name="__codelineno-32-44" href="#__codelineno-32-44"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="p">;</span>
+<a id="__codelineno-32-45" name="__codelineno-32-45" href="#__codelineno-32-45"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-32-46" name="__codelineno-32-46" href="#__codelineno-32-46"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-32-47" name="__codelineno-32-47" href="#__codelineno-32-47"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-48" name="__codelineno-32-48" href="#__codelineno-32-48"></a>
+<a id="__codelineno-32-49" name="__codelineno-32-49" href="#__codelineno-32-49"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-32-50" name="__codelineno-32-50" href="#__codelineno-32-50"></a><span class="w">    </span><span class="nx">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-51" name="__codelineno-32-51" href="#__codelineno-32-51"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;キューが空です&#39;</span><span class="p">);</span>
+<a id="__codelineno-32-52" name="__codelineno-32-52" href="#__codelineno-32-52"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#nums</span><span class="p">[</span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="p">];</span>
+<a id="__codelineno-32-53" name="__codelineno-32-53" href="#__codelineno-32-53"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-54" name="__codelineno-32-54" href="#__codelineno-32-54"></a>
+<a id="__codelineno-32-55" name="__codelineno-32-55" href="#__codelineno-32-55"></a><span class="w">    </span><span class="cm">/* Array を返す */</span>
+<a id="__codelineno-32-56" name="__codelineno-32-56" href="#__codelineno-32-56"></a><span class="w">    </span><span class="nx">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-57" name="__codelineno-32-57" href="#__codelineno-32-57"></a><span class="w">        </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-32-58" name="__codelineno-32-58" href="#__codelineno-32-58"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">);</span>
+<a id="__codelineno-32-59" name="__codelineno-32-59" href="#__codelineno-32-59"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#front</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-60" name="__codelineno-32-60" href="#__codelineno-32-60"></a><span class="w">            </span><span class="nx">arr</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="p">];</span>
+<a id="__codelineno-32-61" name="__codelineno-32-61" href="#__codelineno-32-61"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-32-62" name="__codelineno-32-62" href="#__codelineno-32-62"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">arr</span><span class="p">;</span>
+<a id="__codelineno-32-63" name="__codelineno-32-63" href="#__codelineno-32-63"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-64" name="__codelineno-32-64" href="#__codelineno-32-64"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_queue.dart</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_queue.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* 循環配列ベースのキュー */</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">ArrayQueue</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[];</span><span class="w"> </span><span class="c1">// キュー要素を格納する配列</span>
+<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">front</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ポインタ。先頭要素を指す</span>
+<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">queSize</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの長さ</span>
+<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a>
+<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">capacity</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">capacity</span><span class="p">);</span>
+<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a>
+<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="w">    </span><span class="cm">/* キューの容量を取得 */</span>
+<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a><span class="w">    </span><span class="nx">get</span><span class="w"> </span><span class="nx">capacity</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-16" name="__codelineno-33-16" href="#__codelineno-33-16"></a>
+<a id="__codelineno-33-17" name="__codelineno-33-17" href="#__codelineno-33-17"></a><span class="w">    </span><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-33-18" name="__codelineno-33-18" href="#__codelineno-33-18"></a><span class="w">    </span><span class="nx">get</span><span class="w"> </span><span class="nx">size</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-19" name="__codelineno-33-19" href="#__codelineno-33-19"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="p">;</span>
+<a id="__codelineno-33-20" name="__codelineno-33-20" href="#__codelineno-33-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-21" name="__codelineno-33-21" href="#__codelineno-33-21"></a>
+<a id="__codelineno-33-22" name="__codelineno-33-22" href="#__codelineno-33-22"></a><span class="w">    </span><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-33-23" name="__codelineno-33-23" href="#__codelineno-33-23"></a><span class="w">    </span><span class="nx">isEmpty</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-24" name="__codelineno-33-24" href="#__codelineno-33-24"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-33-25" name="__codelineno-33-25" href="#__codelineno-33-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-26" name="__codelineno-33-26" href="#__codelineno-33-26"></a>
+<a id="__codelineno-33-27" name="__codelineno-33-27" href="#__codelineno-33-27"></a><span class="w">    </span><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-33-28" name="__codelineno-33-28" href="#__codelineno-33-28"></a><span class="w">    </span><span class="nx">push</span><span class="p">(</span><span class="nx">num</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-29" name="__codelineno-33-29" href="#__codelineno-33-29"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-30" name="__codelineno-33-30" href="#__codelineno-33-30"></a><span class="w">            </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="s1">&#39;キューは満杯です&#39;</span><span class="p">);</span>
+<a id="__codelineno-33-31" name="__codelineno-33-31" href="#__codelineno-33-31"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-33-32" name="__codelineno-33-32" href="#__codelineno-33-32"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-33-33" name="__codelineno-33-33" href="#__codelineno-33-33"></a><span class="w">        </span><span class="c1">// 末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-33-34" name="__codelineno-33-34" href="#__codelineno-33-34"></a><span class="w">        </span><span class="c1">// 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする</span>
+<a id="__codelineno-33-35" name="__codelineno-33-35" href="#__codelineno-33-35"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="p">;</span>
+<a id="__codelineno-33-36" name="__codelineno-33-36" href="#__codelineno-33-36"></a><span class="w">        </span><span class="c1">// num をキュー末尾に追加</span>
+<a id="__codelineno-33-37" name="__codelineno-33-37" href="#__codelineno-33-37"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">nums</span><span class="p">[</span><span class="nx">rear</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-33-38" name="__codelineno-33-38" href="#__codelineno-33-38"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-33-39" name="__codelineno-33-39" href="#__codelineno-33-39"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-40" name="__codelineno-33-40" href="#__codelineno-33-40"></a>
+<a id="__codelineno-33-41" name="__codelineno-33-41" href="#__codelineno-33-41"></a><span class="w">    </span><span class="cm">/* デキュー */</span>
+<a id="__codelineno-33-42" name="__codelineno-33-42" href="#__codelineno-33-42"></a><span class="w">    </span><span class="nx">pop</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-43" name="__codelineno-33-43" href="#__codelineno-33-43"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">peek</span><span class="p">();</span>
+<a id="__codelineno-33-44" name="__codelineno-33-44" href="#__codelineno-33-44"></a><span class="w">        </span><span class="c1">// 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す</span>
+<a id="__codelineno-33-45" name="__codelineno-33-45" href="#__codelineno-33-45"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="p">;</span>
+<a id="__codelineno-33-46" name="__codelineno-33-46" href="#__codelineno-33-46"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-33-47" name="__codelineno-33-47" href="#__codelineno-33-47"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-33-48" name="__codelineno-33-48" href="#__codelineno-33-48"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-49" name="__codelineno-33-49" href="#__codelineno-33-49"></a>
+<a id="__codelineno-33-50" name="__codelineno-33-50" href="#__codelineno-33-50"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-33-51" name="__codelineno-33-51" href="#__codelineno-33-51"></a><span class="w">    </span><span class="nx">peek</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-52" name="__codelineno-33-52" href="#__codelineno-33-52"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;キューが空です&#39;</span><span class="p">);</span>
+<a id="__codelineno-33-53" name="__codelineno-33-53" href="#__codelineno-33-53"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">nums</span><span class="p">[</span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="p">];</span>
+<a id="__codelineno-33-54" name="__codelineno-33-54" href="#__codelineno-33-54"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-55" name="__codelineno-33-55" href="#__codelineno-33-55"></a>
+<a id="__codelineno-33-56" name="__codelineno-33-56" href="#__codelineno-33-56"></a><span class="w">    </span><span class="cm">/* Array を返す */</span>
+<a id="__codelineno-33-57" name="__codelineno-33-57" href="#__codelineno-33-57"></a><span class="w">    </span><span class="nx">toArray</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-58" name="__codelineno-33-58" href="#__codelineno-33-58"></a><span class="w">        </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-33-59" name="__codelineno-33-59" href="#__codelineno-33-59"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">);</span>
+<a id="__codelineno-33-60" name="__codelineno-33-60" href="#__codelineno-33-60"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-61" name="__codelineno-33-61" href="#__codelineno-33-61"></a><span class="w">            </span><span class="nx">arr</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="p">];</span>
+<a id="__codelineno-33-62" name="__codelineno-33-62" href="#__codelineno-33-62"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-33-63" name="__codelineno-33-63" href="#__codelineno-33-63"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">arr</span><span class="p">;</span>
+<a id="__codelineno-33-64" name="__codelineno-33-64" href="#__codelineno-33-64"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-65" name="__codelineno-33-65" href="#__codelineno-33-65"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_queue.rs</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_queue.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* 循環配列ベースのキュー */</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ArrayQueue</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w">  </span><span class="kd">late</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">_nums</span><span class="p">;</span><span class="w"> </span><span class="c1">// キュー要素を格納する配列</span>
+<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w">  </span><span class="kd">late</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">_front</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ポインタ。先頭要素を指す</span>
+<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w">  </span><span class="kd">late</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">_queSize</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの長さ</span>
+<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a>
+<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w">  </span><span class="n">ArrayQueue</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w">    </span><span class="n">_nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">capacity</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="w">    </span><span class="n">_front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-34-10" name="__codelineno-34-10" href="#__codelineno-34-10"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-11" name="__codelineno-34-11" href="#__codelineno-34-11"></a>
+<a id="__codelineno-34-12" name="__codelineno-34-12" href="#__codelineno-34-12"></a><span class="w">  </span><span class="cm">/* キューの容量を取得 */</span>
+<a id="__codelineno-34-13" name="__codelineno-34-13" href="#__codelineno-34-13"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">capaCity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-14" name="__codelineno-34-14" href="#__codelineno-34-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_nums</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-34-15" name="__codelineno-34-15" href="#__codelineno-34-15"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-16" name="__codelineno-34-16" href="#__codelineno-34-16"></a>
+<a id="__codelineno-34-17" name="__codelineno-34-17" href="#__codelineno-34-17"></a><span class="w">  </span><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-34-18" name="__codelineno-34-18" href="#__codelineno-34-18"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-19" name="__codelineno-34-19" href="#__codelineno-34-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_queSize</span><span class="p">;</span>
+<a id="__codelineno-34-20" name="__codelineno-34-20" href="#__codelineno-34-20"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-21" name="__codelineno-34-21" href="#__codelineno-34-21"></a>
+<a id="__codelineno-34-22" name="__codelineno-34-22" href="#__codelineno-34-22"></a><span class="w">  </span><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-34-23" name="__codelineno-34-23" href="#__codelineno-34-23"></a><span class="w">  </span><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-24" name="__codelineno-34-24" href="#__codelineno-34-24"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-34-25" name="__codelineno-34-25" href="#__codelineno-34-25"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-26" name="__codelineno-34-26" href="#__codelineno-34-26"></a>
+<a id="__codelineno-34-27" name="__codelineno-34-27" href="#__codelineno-34-27"></a><span class="w">  </span><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-34-28" name="__codelineno-34-28" href="#__codelineno-34-28"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-29" name="__codelineno-34-29" href="#__codelineno-34-29"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capaCity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-30" name="__codelineno-34-30" href="#__codelineno-34-30"></a><span class="w">      </span><span class="k">throw</span><span class="w"> </span><span class="n">Exception</span><span class="p">(</span><span class="s2">&quot;キューは満杯です&quot;</span><span class="p">);</span>
+<a id="__codelineno-34-31" name="__codelineno-34-31" href="#__codelineno-34-31"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-32" name="__codelineno-34-32" href="#__codelineno-34-32"></a><span class="w">    </span><span class="c1">// 末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-34-33" name="__codelineno-34-33" href="#__codelineno-34-33"></a><span class="w">    </span><span class="c1">// 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする</span>
+<a id="__codelineno-34-34" name="__codelineno-34-34" href="#__codelineno-34-34"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">_front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">_queSize</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capaCity</span><span class="p">();</span>
+<a id="__codelineno-34-35" name="__codelineno-34-35" href="#__codelineno-34-35"></a><span class="w">    </span><span class="c1">// _num をキュー末尾に追加</span>
+<a id="__codelineno-34-36" name="__codelineno-34-36" href="#__codelineno-34-36"></a><span class="w">    </span><span class="n">_nums</span><span class="p">[</span><span class="n">rear</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_num</span><span class="p">;</span>
+<a id="__codelineno-34-37" name="__codelineno-34-37" href="#__codelineno-34-37"></a><span class="w">    </span><span class="n">_queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-34-38" name="__codelineno-34-38" href="#__codelineno-34-38"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-39" name="__codelineno-34-39" href="#__codelineno-34-39"></a>
+<a id="__codelineno-34-40" name="__codelineno-34-40" href="#__codelineno-34-40"></a><span class="w">  </span><span class="cm">/* デキュー */</span>
+<a id="__codelineno-34-41" name="__codelineno-34-41" href="#__codelineno-34-41"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-42" name="__codelineno-34-42" href="#__codelineno-34-42"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span><span class="p">();</span>
+<a id="__codelineno-34-43" name="__codelineno-34-43" href="#__codelineno-34-43"></a><span class="w">    </span><span class="c1">// 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す</span>
+<a id="__codelineno-34-44" name="__codelineno-34-44" href="#__codelineno-34-44"></a><span class="w">    </span><span class="n">_front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">_front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capaCity</span><span class="p">();</span>
+<a id="__codelineno-34-45" name="__codelineno-34-45" href="#__codelineno-34-45"></a><span class="w">    </span><span class="n">_queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-34-46" name="__codelineno-34-46" href="#__codelineno-34-46"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_num</span><span class="p">;</span>
+<a id="__codelineno-34-47" name="__codelineno-34-47" href="#__codelineno-34-47"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-48" name="__codelineno-34-48" href="#__codelineno-34-48"></a>
+<a id="__codelineno-34-49" name="__codelineno-34-49" href="#__codelineno-34-49"></a><span class="w">  </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-34-50" name="__codelineno-34-50" href="#__codelineno-34-50"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-51" name="__codelineno-34-51" href="#__codelineno-34-51"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-52" name="__codelineno-34-52" href="#__codelineno-34-52"></a><span class="w">      </span><span class="k">throw</span><span class="w"> </span><span class="n">Exception</span><span class="p">(</span><span class="s2">&quot;キューが空です&quot;</span><span class="p">);</span>
+<a id="__codelineno-34-53" name="__codelineno-34-53" href="#__codelineno-34-53"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-54" name="__codelineno-34-54" href="#__codelineno-34-54"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_nums</span><span class="p">[</span><span class="n">_front</span><span class="p">];</span>
+<a id="__codelineno-34-55" name="__codelineno-34-55" href="#__codelineno-34-55"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-56" name="__codelineno-34-56" href="#__codelineno-34-56"></a>
+<a id="__codelineno-34-57" name="__codelineno-34-57" href="#__codelineno-34-57"></a><span class="w">  </span><span class="cm">/* Array を返す */</span>
+<a id="__codelineno-34-58" name="__codelineno-34-58" href="#__codelineno-34-58"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-59" name="__codelineno-34-59" href="#__codelineno-34-59"></a><span class="w">    </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-34-60" name="__codelineno-34-60" href="#__codelineno-34-60"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">_queSize</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-34-61" name="__codelineno-34-61" href="#__codelineno-34-61"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_front</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">_queSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-62" name="__codelineno-34-62" href="#__codelineno-34-62"></a><span class="w">      </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capaCity</span><span class="p">()];</span>
+<a id="__codelineno-34-63" name="__codelineno-34-63" href="#__codelineno-34-63"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-64" name="__codelineno-34-64" href="#__codelineno-34-64"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-34-65" name="__codelineno-34-65" href="#__codelineno-34-65"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-66" name="__codelineno-34-66" href="#__codelineno-34-66"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_queue.c</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_queue.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* 循環配列ベースのキュー */</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">ArrayQueue</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w">    </span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="p">,</span><span class="w">      </span><span class="c1">// キュー要素を格納する配列</span>
+<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="w">    </span><span class="n">front</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w">        </span><span class="c1">// 先頭ポインタ。先頭要素を指す</span>
+<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="w">    </span><span class="n">que_size</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w">     </span><span class="c1">// キューの長さ</span>
+<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="w">    </span><span class="n">que_capacity</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="c1">// キューの容量</span>
+<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="p">}</span>
+<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a>
+<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="k">impl</span><span class="o">&lt;</span><span class="n">T</span><span class="p">:</span><span class="w"> </span><span class="nb">Copy</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nb">Default</span><span class="o">&gt;</span><span class="w"> </span><span class="n">ArrayQueue</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">new</span><span class="p">(</span><span class="n">capacity</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">ArrayQueue</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-12" name="__codelineno-35-12" href="#__codelineno-35-12"></a><span class="w">        </span><span class="n">ArrayQueue</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-13" name="__codelineno-35-13" href="#__codelineno-35-13"></a><span class="w">            </span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="nc">vec</span><span class="o">!</span><span class="p">[</span><span class="n">T</span><span class="p">::</span><span class="n">default</span><span class="p">();</span><span class="w"> </span><span class="n">capacity</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">],</span>
+<a id="__codelineno-35-14" name="__codelineno-35-14" href="#__codelineno-35-14"></a><span class="w">            </span><span class="n">front</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span>
+<a id="__codelineno-35-15" name="__codelineno-35-15" href="#__codelineno-35-15"></a><span class="w">            </span><span class="n">que_size</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span>
+<a id="__codelineno-35-16" name="__codelineno-35-16" href="#__codelineno-35-16"></a><span class="w">            </span><span class="n">que_capacity</span><span class="p">:</span><span class="w"> </span><span class="nc">capacity</span><span class="p">,</span>
+<a id="__codelineno-35-17" name="__codelineno-35-17" href="#__codelineno-35-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-35-18" name="__codelineno-35-18" href="#__codelineno-35-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-19" name="__codelineno-35-19" href="#__codelineno-35-19"></a>
+<a id="__codelineno-35-20" name="__codelineno-35-20" href="#__codelineno-35-20"></a><span class="w">    </span><span class="cm">/* キューの容量を取得 */</span>
+<a id="__codelineno-35-21" name="__codelineno-35-21" href="#__codelineno-35-21"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">capacity</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-22" name="__codelineno-35-22" href="#__codelineno-35-22"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">que_capacity</span>
+<a id="__codelineno-35-23" name="__codelineno-35-23" href="#__codelineno-35-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-24" name="__codelineno-35-24" href="#__codelineno-35-24"></a>
+<a id="__codelineno-35-25" name="__codelineno-35-25" href="#__codelineno-35-25"></a><span class="w">    </span><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-35-26" name="__codelineno-35-26" href="#__codelineno-35-26"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-27" name="__codelineno-35-27" href="#__codelineno-35-27"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span>
+<a id="__codelineno-35-28" name="__codelineno-35-28" href="#__codelineno-35-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-29" name="__codelineno-35-29" href="#__codelineno-35-29"></a>
+<a id="__codelineno-35-30" name="__codelineno-35-30" href="#__codelineno-35-30"></a><span class="w">    </span><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-35-31" name="__codelineno-35-31" href="#__codelineno-35-31"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">is_empty</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-32" name="__codelineno-35-32" href="#__codelineno-35-32"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-35-33" name="__codelineno-35-33" href="#__codelineno-35-33"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-34" name="__codelineno-35-34" href="#__codelineno-35-34"></a>
+<a id="__codelineno-35-35" name="__codelineno-35-35" href="#__codelineno-35-35"></a><span class="w">    </span><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-35-36" name="__codelineno-35-36" href="#__codelineno-35-36"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nc">T</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-37" name="__codelineno-35-37" href="#__codelineno-35-37"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-38" name="__codelineno-35-38" href="#__codelineno-35-38"></a><span class="w">            </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;キューがいっぱいです&quot;</span><span class="p">);</span>
+<a id="__codelineno-35-39" name="__codelineno-35-39" href="#__codelineno-35-39"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-35-40" name="__codelineno-35-40" href="#__codelineno-35-40"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-35-41" name="__codelineno-35-41" href="#__codelineno-35-41"></a><span class="w">        </span><span class="c1">// 末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-35-42" name="__codelineno-35-42" href="#__codelineno-35-42"></a><span class="w">        </span><span class="c1">// 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする</span>
+<a id="__codelineno-35-43" name="__codelineno-35-43" href="#__codelineno-35-43"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">que_capacity</span><span class="p">;</span>
+<a id="__codelineno-35-44" name="__codelineno-35-44" href="#__codelineno-35-44"></a><span class="w">        </span><span class="c1">// num をキュー末尾に追加</span>
+<a id="__codelineno-35-45" name="__codelineno-35-45" href="#__codelineno-35-45"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">nums</span><span class="p">[</span><span class="n">rear</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-35-46" name="__codelineno-35-46" href="#__codelineno-35-46"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-35-47" name="__codelineno-35-47" href="#__codelineno-35-47"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-48" name="__codelineno-35-48" href="#__codelineno-35-48"></a>
+<a id="__codelineno-35-49" name="__codelineno-35-49" href="#__codelineno-35-49"></a><span class="w">    </span><span class="cm">/* デキュー */</span>
+<a id="__codelineno-35-50" name="__codelineno-35-50" href="#__codelineno-35-50"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">T</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-51" name="__codelineno-35-51" href="#__codelineno-35-51"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">peek</span><span class="p">();</span>
+<a id="__codelineno-35-52" name="__codelineno-35-52" href="#__codelineno-35-52"></a><span class="w">        </span><span class="c1">// 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す</span>
+<a id="__codelineno-35-53" name="__codelineno-35-53" href="#__codelineno-35-53"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">que_capacity</span><span class="p">;</span>
+<a id="__codelineno-35-54" name="__codelineno-35-54" href="#__codelineno-35-54"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-35-55" name="__codelineno-35-55" href="#__codelineno-35-55"></a><span class="w">        </span><span class="n">num</span>
+<a id="__codelineno-35-56" name="__codelineno-35-56" href="#__codelineno-35-56"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-57" name="__codelineno-35-57" href="#__codelineno-35-57"></a>
+<a id="__codelineno-35-58" name="__codelineno-35-58" href="#__codelineno-35-58"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-35-59" name="__codelineno-35-59" href="#__codelineno-35-59"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">T</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-60" name="__codelineno-35-60" href="#__codelineno-35-60"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">is_empty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-61" name="__codelineno-35-61" href="#__codelineno-35-61"></a><span class="w">            </span><span class="fm">panic!</span><span class="p">(</span><span class="s">&quot;index out of bounds&quot;</span><span class="p">);</span>
+<a id="__codelineno-35-62" name="__codelineno-35-62" href="#__codelineno-35-62"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-35-63" name="__codelineno-35-63" href="#__codelineno-35-63"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">nums</span><span class="p">[</span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span>
+<a id="__codelineno-35-64" name="__codelineno-35-64" href="#__codelineno-35-64"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-65" name="__codelineno-35-65" href="#__codelineno-35-65"></a>
+<a id="__codelineno-35-66" name="__codelineno-35-66" href="#__codelineno-35-66"></a><span class="w">    </span><span class="cm">/* 配列を返す */</span>
+<a id="__codelineno-35-67" name="__codelineno-35-67" href="#__codelineno-35-67"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">to_vector</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-68" name="__codelineno-35-68" href="#__codelineno-35-68"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">que_capacity</span><span class="p">;</span>
+<a id="__codelineno-35-69" name="__codelineno-35-69" href="#__codelineno-35-69"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-35-70" name="__codelineno-35-70" href="#__codelineno-35-70"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="n">T</span><span class="p">::</span><span class="n">default</span><span class="p">();</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">];</span>
+<a id="__codelineno-35-71" name="__codelineno-35-71" href="#__codelineno-35-71"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="bp">self</span><span class="p">.</span><span class="n">que_size</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-72" name="__codelineno-35-72" href="#__codelineno-35-72"></a><span class="w">            </span><span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">nums</span><span class="p">[(</span><span class="n">j</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">];</span>
+<a id="__codelineno-35-73" name="__codelineno-35-73" href="#__codelineno-35-73"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-35-74" name="__codelineno-35-74" href="#__codelineno-35-74"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-35-75" name="__codelineno-35-75" href="#__codelineno-35-75"></a><span class="w">        </span><span class="n">arr</span>
+<a id="__codelineno-35-76" name="__codelineno-35-76" href="#__codelineno-35-76"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-77" name="__codelineno-35-77" href="#__codelineno-35-77"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_queue.kt</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">ArrayQueue</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">array_queue.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* 循環配列ベースのキュー */</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">;</span><span class="w">       </span><span class="c1">// キュー要素を格納する配列</span>
+<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w">       </span><span class="c1">// 先頭ポインタ。先頭要素を指す</span>
+<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w">     </span><span class="c1">// 末尾ポインタ。キューの末尾 + 1 を指す</span>
+<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">queCapacity</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの容量</span>
+<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="p">}</span><span class="w"> </span><span class="n">ArrayQueue</span><span class="p">;</span>
+<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a>
+<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a><span class="n">ArrayQueue</span><span class="w"> </span><span class="o">*</span><span class="nf">newArrayQueue</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a><span class="w">    </span><span class="n">ArrayQueue</span><span class="w"> </span><span class="o">*</span><span class="n">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">ArrayQueue</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">ArrayQueue</span><span class="p">));</span>
+<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a><span class="w">    </span><span class="c1">// 配列を初期化</span>
+<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></a><span class="w">    </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queCapacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-36-14" name="__codelineno-36-14" href="#__codelineno-36-14"></a><span class="w">    </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queCapacity</span><span class="p">);</span>
+<a id="__codelineno-36-15" name="__codelineno-36-15" href="#__codelineno-36-15"></a><span class="w">    </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-36-16" name="__codelineno-36-16" href="#__codelineno-36-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">queue</span><span class="p">;</span>
+<a id="__codelineno-36-17" name="__codelineno-36-17" href="#__codelineno-36-17"></a><span class="p">}</span>
+<a id="__codelineno-36-18" name="__codelineno-36-18" href="#__codelineno-36-18"></a>
+<a id="__codelineno-36-19" name="__codelineno-36-19" href="#__codelineno-36-19"></a><span class="cm">/* デストラクタ */</span>
+<a id="__codelineno-36-20" name="__codelineno-36-20" href="#__codelineno-36-20"></a><span class="kt">void</span><span class="w"> </span><span class="nf">delArrayQueue</span><span class="p">(</span><span class="n">ArrayQueue</span><span class="w"> </span><span class="o">*</span><span class="n">queue</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-21" name="__codelineno-36-21" href="#__codelineno-36-21"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">nums</span><span class="p">);</span>
+<a id="__codelineno-36-22" name="__codelineno-36-22" href="#__codelineno-36-22"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">queue</span><span class="p">);</span>
+<a id="__codelineno-36-23" name="__codelineno-36-23" href="#__codelineno-36-23"></a><span class="p">}</span>
+<a id="__codelineno-36-24" name="__codelineno-36-24" href="#__codelineno-36-24"></a>
+<a id="__codelineno-36-25" name="__codelineno-36-25" href="#__codelineno-36-25"></a><span class="cm">/* キューの容量を取得 */</span>
+<a id="__codelineno-36-26" name="__codelineno-36-26" href="#__codelineno-36-26"></a><span class="kt">int</span><span class="w"> </span><span class="nf">capacity</span><span class="p">(</span><span class="n">ArrayQueue</span><span class="w"> </span><span class="o">*</span><span class="n">queue</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-27" name="__codelineno-36-27" href="#__codelineno-36-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queCapacity</span><span class="p">;</span>
+<a id="__codelineno-36-28" name="__codelineno-36-28" href="#__codelineno-36-28"></a><span class="p">}</span>
+<a id="__codelineno-36-29" name="__codelineno-36-29" href="#__codelineno-36-29"></a>
+<a id="__codelineno-36-30" name="__codelineno-36-30" href="#__codelineno-36-30"></a><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-36-31" name="__codelineno-36-31" href="#__codelineno-36-31"></a><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="n">ArrayQueue</span><span class="w"> </span><span class="o">*</span><span class="n">queue</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-32" name="__codelineno-36-32" href="#__codelineno-36-32"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-36-33" name="__codelineno-36-33" href="#__codelineno-36-33"></a><span class="p">}</span>
+<a id="__codelineno-36-34" name="__codelineno-36-34" href="#__codelineno-36-34"></a>
+<a id="__codelineno-36-35" name="__codelineno-36-35" href="#__codelineno-36-35"></a><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-36-36" name="__codelineno-36-36" href="#__codelineno-36-36"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">empty</span><span class="p">(</span><span class="n">ArrayQueue</span><span class="w"> </span><span class="o">*</span><span class="n">queue</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-37" name="__codelineno-36-37" href="#__codelineno-36-37"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-36-38" name="__codelineno-36-38" href="#__codelineno-36-38"></a><span class="p">}</span>
+<a id="__codelineno-36-39" name="__codelineno-36-39" href="#__codelineno-36-39"></a>
+<a id="__codelineno-36-40" name="__codelineno-36-40" href="#__codelineno-36-40"></a><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-36-41" name="__codelineno-36-41" href="#__codelineno-36-41"></a><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="n">ArrayQueue</span><span class="w"> </span><span class="o">*</span><span class="n">queue</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-42" name="__codelineno-36-42" href="#__codelineno-36-42"></a><span class="w">    </span><span class="n">assert</span><span class="p">(</span><span class="n">size</span><span class="p">(</span><span class="n">queue</span><span class="p">)</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-36-43" name="__codelineno-36-43" href="#__codelineno-36-43"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">nums</span><span class="p">[</span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="p">];</span>
+<a id="__codelineno-36-44" name="__codelineno-36-44" href="#__codelineno-36-44"></a><span class="p">}</span>
+<a id="__codelineno-36-45" name="__codelineno-36-45" href="#__codelineno-36-45"></a>
+<a id="__codelineno-36-46" name="__codelineno-36-46" href="#__codelineno-36-46"></a><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-36-47" name="__codelineno-36-47" href="#__codelineno-36-47"></a><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">ArrayQueue</span><span class="w"> </span><span class="o">*</span><span class="n">queue</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-48" name="__codelineno-36-48" href="#__codelineno-36-48"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="p">(</span><span class="n">queue</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">(</span><span class="n">queue</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-49" name="__codelineno-36-49" href="#__codelineno-36-49"></a><span class="w">        </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;キューは満杯です</span><span class="se">\r\n</span><span class="s">&quot;</span><span class="p">);</span>
+<a id="__codelineno-36-50" name="__codelineno-36-50" href="#__codelineno-36-50"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-36-51" name="__codelineno-36-51" href="#__codelineno-36-51"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-52" name="__codelineno-36-52" href="#__codelineno-36-52"></a><span class="w">    </span><span class="c1">// 末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-36-53" name="__codelineno-36-53" href="#__codelineno-36-53"></a><span class="w">    </span><span class="c1">// 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする</span>
+<a id="__codelineno-36-54" name="__codelineno-36-54" href="#__codelineno-36-54"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queCapacity</span><span class="p">;</span>
+<a id="__codelineno-36-55" name="__codelineno-36-55" href="#__codelineno-36-55"></a><span class="w">    </span><span class="c1">// num をキュー末尾に追加</span>
+<a id="__codelineno-36-56" name="__codelineno-36-56" href="#__codelineno-36-56"></a><span class="w">    </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">nums</span><span class="p">[</span><span class="n">rear</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-36-57" name="__codelineno-36-57" href="#__codelineno-36-57"></a><span class="w">    </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-36-58" name="__codelineno-36-58" href="#__codelineno-36-58"></a><span class="p">}</span>
+<a id="__codelineno-36-59" name="__codelineno-36-59" href="#__codelineno-36-59"></a>
+<a id="__codelineno-36-60" name="__codelineno-36-60" href="#__codelineno-36-60"></a><span class="cm">/* デキュー */</span>
+<a id="__codelineno-36-61" name="__codelineno-36-61" href="#__codelineno-36-61"></a><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="n">ArrayQueue</span><span class="w"> </span><span class="o">*</span><span class="n">queue</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-62" name="__codelineno-36-62" href="#__codelineno-36-62"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span><span class="p">(</span><span class="n">queue</span><span class="p">);</span>
+<a id="__codelineno-36-63" name="__codelineno-36-63" href="#__codelineno-36-63"></a><span class="w">    </span><span class="c1">// 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す</span>
+<a id="__codelineno-36-64" name="__codelineno-36-64" href="#__codelineno-36-64"></a><span class="w">    </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queCapacity</span><span class="p">;</span>
+<a id="__codelineno-36-65" name="__codelineno-36-65" href="#__codelineno-36-65"></a><span class="w">    </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-36-66" name="__codelineno-36-66" href="#__codelineno-36-66"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-36-67" name="__codelineno-36-67" href="#__codelineno-36-67"></a><span class="p">}</span>
+<a id="__codelineno-36-68" name="__codelineno-36-68" href="#__codelineno-36-68"></a>
+<a id="__codelineno-36-69" name="__codelineno-36-69" href="#__codelineno-36-69"></a><span class="cm">/* 出力用の配列を返す */</span>
+<a id="__codelineno-36-70" name="__codelineno-36-70" href="#__codelineno-36-70"></a><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="nf">toArray</span><span class="p">(</span><span class="n">ArrayQueue</span><span class="w"> </span><span class="o">*</span><span class="n">queue</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">queSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-71" name="__codelineno-36-71" href="#__codelineno-36-71"></a><span class="w">    </span><span class="o">*</span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-36-72" name="__codelineno-36-72" href="#__codelineno-36-72"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">calloc</span><span class="p">(</span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
+<a id="__codelineno-36-73" name="__codelineno-36-73" href="#__codelineno-36-73"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-36-74" name="__codelineno-36-74" href="#__codelineno-36-74"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-75" name="__codelineno-36-75" href="#__codelineno-36-75"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queCapacity</span><span class="p">];</span>
+<a id="__codelineno-36-76" name="__codelineno-36-76" href="#__codelineno-36-76"></a><span class="w">        </span><span class="n">j</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-36-77" name="__codelineno-36-77" href="#__codelineno-36-77"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-78" name="__codelineno-36-78" href="#__codelineno-36-78"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-36-79" name="__codelineno-36-79" href="#__codelineno-36-79"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_queue.rb</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">ArrayQueue</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">array_queue.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* 循環配列ベースのキュー */</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ArrayQueue</span><span class="p">(</span><span class="n">capacity</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">nums</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">capacity</span><span class="p">)</span><span class="w"> </span><span class="c1">// キュー要素を格納する配列</span>
+<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">front</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="c1">// 先頭ポインタ。先頭要素を指す</span>
+<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">queSize</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="c1">// キューの長さ</span>
+<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a>
+<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w">    </span><span class="cm">/* キューの容量を取得 */</span>
+<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">capacity</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a>
+<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a><span class="w">    </span><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">size</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-14" name="__codelineno-37-14" href="#__codelineno-37-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span>
+<a id="__codelineno-37-15" name="__codelineno-37-15" href="#__codelineno-37-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-16" name="__codelineno-37-16" href="#__codelineno-37-16"></a>
+<a id="__codelineno-37-17" name="__codelineno-37-17" href="#__codelineno-37-17"></a><span class="w">    </span><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-37-18" name="__codelineno-37-18" href="#__codelineno-37-18"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">():</span><span class="w"> </span><span class="kt">Boolean</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-19" name="__codelineno-37-19" href="#__codelineno-37-19"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-37-20" name="__codelineno-37-20" href="#__codelineno-37-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-21" name="__codelineno-37-21" href="#__codelineno-37-21"></a>
+<a id="__codelineno-37-22" name="__codelineno-37-22" href="#__codelineno-37-22"></a><span class="w">    </span><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-37-23" name="__codelineno-37-23" href="#__codelineno-37-23"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-24" name="__codelineno-37-24" href="#__codelineno-37-24"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-25" name="__codelineno-37-25" href="#__codelineno-37-25"></a><span class="w">            </span><span class="n">println</span><span class="p">(</span><span class="s">&quot;キューは満杯です&quot;</span><span class="p">)</span>
+<a id="__codelineno-37-26" name="__codelineno-37-26" href="#__codelineno-37-26"></a><span class="w">            </span><span class="k">return</span>
+<a id="__codelineno-37-27" name="__codelineno-37-27" href="#__codelineno-37-27"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-37-28" name="__codelineno-37-28" href="#__codelineno-37-28"></a><span class="w">        </span><span class="c1">// 末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-37-29" name="__codelineno-37-29" href="#__codelineno-37-29"></a><span class="w">        </span><span class="c1">// 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする</span>
+<a id="__codelineno-37-30" name="__codelineno-37-30" href="#__codelineno-37-30"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">queSize</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span>
+<a id="__codelineno-37-31" name="__codelineno-37-31" href="#__codelineno-37-31"></a><span class="w">        </span><span class="c1">// num をキュー末尾に追加</span>
+<a id="__codelineno-37-32" name="__codelineno-37-32" href="#__codelineno-37-32"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">rear</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-37-33" name="__codelineno-37-33" href="#__codelineno-37-33"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span>
+<a id="__codelineno-37-34" name="__codelineno-37-34" href="#__codelineno-37-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-35" name="__codelineno-37-35" href="#__codelineno-37-35"></a>
+<a id="__codelineno-37-36" name="__codelineno-37-36" href="#__codelineno-37-36"></a><span class="w">    </span><span class="cm">/* デキュー */</span>
+<a id="__codelineno-37-37" name="__codelineno-37-37" href="#__codelineno-37-37"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">pop</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-38" name="__codelineno-37-38" href="#__codelineno-37-38"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span><span class="p">()</span>
+<a id="__codelineno-37-39" name="__codelineno-37-39" href="#__codelineno-37-39"></a><span class="w">        </span><span class="c1">// 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す</span>
+<a id="__codelineno-37-40" name="__codelineno-37-40" href="#__codelineno-37-40"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span>
+<a id="__codelineno-37-41" name="__codelineno-37-41" href="#__codelineno-37-41"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span>
+<a id="__codelineno-37-42" name="__codelineno-37-42" href="#__codelineno-37-42"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-37-43" name="__codelineno-37-43" href="#__codelineno-37-43"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-44" name="__codelineno-37-44" href="#__codelineno-37-44"></a>
+<a id="__codelineno-37-45" name="__codelineno-37-45" href="#__codelineno-37-45"></a><span class="w">    </span><span class="cm">/* キュー先頭の要素にアクセス */</span>
+<a id="__codelineno-37-46" name="__codelineno-37-46" href="#__codelineno-37-46"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">peek</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-47" name="__codelineno-37-47" href="#__codelineno-37-47"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">()</span>
+<a id="__codelineno-37-48" name="__codelineno-37-48" href="#__codelineno-37-48"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">front</span><span class="o">]</span>
+<a id="__codelineno-37-49" name="__codelineno-37-49" href="#__codelineno-37-49"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-50" name="__codelineno-37-50" href="#__codelineno-37-50"></a>
+<a id="__codelineno-37-51" name="__codelineno-37-51" href="#__codelineno-37-51"></a><span class="w">    </span><span class="cm">/* 配列を返す */</span>
+<a id="__codelineno-37-52" name="__codelineno-37-52" href="#__codelineno-37-52"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">toArray</span><span class="p">():</span><span class="w"> </span><span class="n">IntArray</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-53" name="__codelineno-37-53" href="#__codelineno-37-53"></a><span class="w">        </span><span class="c1">// 有効長の範囲内のリスト要素のみを変換</span>
+<a id="__codelineno-37-54" name="__codelineno-37-54" href="#__codelineno-37-54"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">queSize</span><span class="p">)</span>
+<a id="__codelineno-37-55" name="__codelineno-37-55" href="#__codelineno-37-55"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-37-56" name="__codelineno-37-56" href="#__codelineno-37-56"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span>
+<a id="__codelineno-37-57" name="__codelineno-37-57" href="#__codelineno-37-57"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">queSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-58" name="__codelineno-37-58" href="#__codelineno-37-58"></a><span class="w">            </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="o">]</span>
+<a id="__codelineno-37-59" name="__codelineno-37-59" href="#__codelineno-37-59"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span>
+<a id="__codelineno-37-60" name="__codelineno-37-60" href="#__codelineno-37-60"></a><span class="w">            </span><span class="n">j</span><span class="o">++</span>
+<a id="__codelineno-37-61" name="__codelineno-37-61" href="#__codelineno-37-61"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-37-62" name="__codelineno-37-62" href="#__codelineno-37-62"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-37-63" name="__codelineno-37-63" href="#__codelineno-37-63"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-64" name="__codelineno-37-64" href="#__codelineno-37-64"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_queue.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="c1">### 循環配列で実装したキュー ###</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayQueue</span>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w">  </span><span class="c1">### キューの長さを取得 ###</span>
+<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w">  </span><span class="kp">attr_reader</span><span class="w"> </span><span class="ss">:size</span>
+<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a>
+<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w">  </span><span class="c1">### コンストラクタ ###</span>
+<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">size</span><span class="p">)</span>
+<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="w">    </span><span class="vi">@nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="c1"># キュー要素を格納する配列</span>
+<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="w">    </span><span class="vi">@front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1"># 先頭ポインタ。先頭要素を指す</span>
+<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1"># キューの長さ</span>
+<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a>
+<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a><span class="w">  </span><span class="c1">### キューの容量を取得 ###</span>
+<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">capacity</span>
+<a id="__codelineno-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a><span class="w">    </span><span class="vi">@nums</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-38-16" name="__codelineno-38-16" href="#__codelineno-38-16"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-17" name="__codelineno-38-17" href="#__codelineno-38-17"></a>
+<a id="__codelineno-38-18" name="__codelineno-38-18" href="#__codelineno-38-18"></a><span class="w">  </span><span class="c1">### キューが空か判定 ###</span>
+<a id="__codelineno-38-19" name="__codelineno-38-19" href="#__codelineno-38-19"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">is_empty?</span>
+<a id="__codelineno-38-20" name="__codelineno-38-20" href="#__codelineno-38-20"></a><span class="w">    </span><span class="n">size</span><span class="o">.</span><span class="n">zero?</span>
+<a id="__codelineno-38-21" name="__codelineno-38-21" href="#__codelineno-38-21"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-22" name="__codelineno-38-22" href="#__codelineno-38-22"></a>
+<a id="__codelineno-38-23" name="__codelineno-38-23" href="#__codelineno-38-23"></a><span class="w">  </span><span class="c1">### エンキュー ###</span>
+<a id="__codelineno-38-24" name="__codelineno-38-24" href="#__codelineno-38-24"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-38-25" name="__codelineno-38-25" href="#__codelineno-38-25"></a><span class="w">    </span><span class="k">raise</span><span class="w"> </span><span class="no">IndexError</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;キューがいっぱいです&#39;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span>
+<a id="__codelineno-38-26" name="__codelineno-38-26" href="#__codelineno-38-26"></a>
+<a id="__codelineno-38-27" name="__codelineno-38-27" href="#__codelineno-38-27"></a><span class="w">    </span><span class="c1"># 末尾ポインタを計算し、末尾インデックス + 1 を指す</span>
+<a id="__codelineno-38-28" name="__codelineno-38-28" href="#__codelineno-38-28"></a><span class="w">    </span><span class="c1"># 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする</span>
+<a id="__codelineno-38-29" name="__codelineno-38-29" href="#__codelineno-38-29"></a><span class="w">    </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="vi">@front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span>
+<a id="__codelineno-38-30" name="__codelineno-38-30" href="#__codelineno-38-30"></a><span class="w">    </span><span class="c1"># num をキュー末尾に追加</span>
+<a id="__codelineno-38-31" name="__codelineno-38-31" href="#__codelineno-38-31"></a><span class="w">    </span><span class="vi">@nums</span><span class="o">[</span><span class="n">rear</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-38-32" name="__codelineno-38-32" href="#__codelineno-38-32"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-38-33" name="__codelineno-38-33" href="#__codelineno-38-33"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-34" name="__codelineno-38-34" href="#__codelineno-38-34"></a>
+<a id="__codelineno-38-35" name="__codelineno-38-35" href="#__codelineno-38-35"></a><span class="w">  </span><span class="c1">### デキュー ###</span>
+<a id="__codelineno-38-36" name="__codelineno-38-36" href="#__codelineno-38-36"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">pop</span>
+<a id="__codelineno-38-37" name="__codelineno-38-37" href="#__codelineno-38-37"></a><span class="w">    </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span>
+<a id="__codelineno-38-38" name="__codelineno-38-38" href="#__codelineno-38-38"></a><span class="w">    </span><span class="c1"># 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す</span>
+<a id="__codelineno-38-39" name="__codelineno-38-39" href="#__codelineno-38-39"></a><span class="w">    </span><span class="vi">@front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="vi">@front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span>
+<a id="__codelineno-38-40" name="__codelineno-38-40" href="#__codelineno-38-40"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-38-41" name="__codelineno-38-41" href="#__codelineno-38-41"></a><span class="w">    </span><span class="n">num</span>
+<a id="__codelineno-38-42" name="__codelineno-38-42" href="#__codelineno-38-42"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-43" name="__codelineno-38-43" href="#__codelineno-38-43"></a>
+<a id="__codelineno-38-44" name="__codelineno-38-44" href="#__codelineno-38-44"></a><span class="w">  </span><span class="c1">### 先頭要素にアクセス ###</span>
+<a id="__codelineno-38-45" name="__codelineno-38-45" href="#__codelineno-38-45"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">peek</span>
+<a id="__codelineno-38-46" name="__codelineno-38-46" href="#__codelineno-38-46"></a><span class="w">    </span><span class="k">raise</span><span class="w"> </span><span class="no">IndexError</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;キューは空です&#39;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_empty?</span>
+<a id="__codelineno-38-47" name="__codelineno-38-47" href="#__codelineno-38-47"></a>
+<a id="__codelineno-38-48" name="__codelineno-38-48" href="#__codelineno-38-48"></a><span class="w">    </span><span class="vi">@nums</span><span class="o">[</span><span class="vi">@front</span><span class="o">]</span>
+<a id="__codelineno-38-49" name="__codelineno-38-49" href="#__codelineno-38-49"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-50" name="__codelineno-38-50" href="#__codelineno-38-50"></a>
+<a id="__codelineno-38-51" name="__codelineno-38-51" href="#__codelineno-38-51"></a><span class="w">  </span><span class="c1">### 表示用のリストを返す ###</span>
+<a id="__codelineno-38-52" name="__codelineno-38-52" href="#__codelineno-38-52"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">to_array</span>
+<a id="__codelineno-38-53" name="__codelineno-38-53" href="#__codelineno-38-53"></a><span class="w">    </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-38-54" name="__codelineno-38-54" href="#__codelineno-38-54"></a><span class="w">    </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@front</span>
+<a id="__codelineno-38-55" name="__codelineno-38-55" href="#__codelineno-38-55"></a>
+<a id="__codelineno-38-56" name="__codelineno-38-56" href="#__codelineno-38-56"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">size</span>
+<a id="__codelineno-38-57" name="__codelineno-38-57" href="#__codelineno-38-57"></a><span class="w">      </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="o">]</span>
+<a id="__codelineno-38-58" name="__codelineno-38-58" href="#__codelineno-38-58"></a><span class="w">      </span><span class="n">j</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-38-59" name="__codelineno-38-59" href="#__codelineno-38-59"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-38-60" name="__codelineno-38-60" href="#__codelineno-38-60"></a>
+<a id="__codelineno-38-61" name="__codelineno-38-61" href="#__codelineno-38-61"></a><span class="w">    </span><span class="n">res</span>
+<a id="__codelineno-38-62" name="__codelineno-38-62" href="#__codelineno-38-62"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-63" name="__codelineno-38-63" href="#__codelineno-38-63"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>上記のキュー実装にはまだ制限があります：長さが固定されています。しかし、この問題は解決が困難ではありません。配列を必要に応じて自動拡張できる動的配列に置き換えることができます。興味のある読者は自分で実装してみてください。</p>
-<p>2つの実装の比較はスタックの場合と一貫しており、ここでは繰り返しません。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20ArrayQueue%3A%0A%0A%20%20%20%20def%20__init__%28self%2C%20size%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self._nums%3A%20list%5Bint%5D%20%3D%20%5B0%5D%20%2A%20size%0A%20%20%20%20%20%20%20%20self._front%3A%20int%20%3D%200%0A%20%20%20%20%20%20%20%20self._size%3A%20int%20%3D%200%0A%0A%20%20%20%20def%20capacity%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%20len%28self._nums%29%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%20self._size%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20return%20self._size%20%3D%3D%200%0A%0A%20%20%20%20def%20push%28self%2C%20num%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20if%20self._size%20%3D%3D%20self.capacity%28%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%27%E3%82%AD%E3%83%A5%E3%83%BC%E3%81%8C%E3%81%84%E3%81%A3%E3%81%B1%E3%81%84%E3%81%A7%E3%81%99%27%29%0A%20%20%20%20%20%20%20%20rear%3A%20int%20%3D%20%28self._front%20%2B%20self._size%29%20%25%20self.capacity%28%29%0A%20%20%20%20%20%20%20%20self._nums%5Brear%5D%20%3D%20num%0A%20%20%20%20%20%20%20%20self._size%20%2B%3D%201%0A%0A%20%20%20%20def%20pop%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20num%3A%20int%20%3D%20self.peek%28%29%0A%20%20%20%20%20%20%20%20self._front%20%3D%20%28self._front%20%2B%201%29%20%25%20self.capacity%28%29%0A%20%20%20%20%20%20%20%20self._size%20-%3D%201%0A%20%20%20%20%20%20%20%20return%20num%0A%0A%20%20%20%20def%20peek%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20if%20self.is_empty%28%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%27%E3%82%AD%E3%83%A5%E3%83%BC%E3%81%8C%E7%A9%BA%E3%81%A7%E3%81%99%27%29%0A%20%20%20%20%20%20%20%20return%20self._nums%5Bself._front%5D%0A%0A%20%20%20%20def%20to_list%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20res%20%3D%20%5B0%5D%20%2A%20self.size%28%29%0A%20%20%20%20%20%20%20%20j%3A%20int%20%3D%20self._front%0A%20%20%20%20%20%20%20%20for%20i%20in%20range%28self.size%28%29%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20res%5Bi%5D%20%3D%20self._nums%5Bj%20%25%20self.capacity%28%29%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20%2B%3D%201%0A%20%20%20%20%20%20%20%20return%20res%0Aif%20__name__%20%3D%3D%20%27__main__%27%3A%0A%20%20%20%20queue%20%3D%20ArrayQueue%2810%29%0A%20%20%20%20queue.push%281%29%0A%20%20%20%20queue.push%283%29%0A%20%20%20%20queue.push%282%29%0A%20%20%20%20queue.push%285%29%0A%20%20%20%20queue.push%284%29%0A%20%20%20%20peek%20%3D%20queue.peek%28%29%0A%20%20%20%20print%28%27%E5%85%88%E9%A0%AD%E8%A6%81%E7%B4%A0%20peek%20%3D%27%2C%20peek%29%0A%20%20%20%20pop%20%3D%20queue.pop%28%29%0A%20%20%20%20print%28%27%E5%8F%96%E3%82%8A%E5%87%BA%E3%81%97%E3%81%9F%E8%A6%81%E7%B4%A0%20pop%20%3D%27%2C%20pop%29%0A%20%20%20%20size%20%3D%20queue.size%28%29%0A%20%20%20%20print%28%27%E3%82%AD%E3%83%A5%E3%83%BC%E3%81%AE%E9%95%B7%E3%81%95%20size%20%3D%27%2C%20size%29%0A%20%20%20%20is_empty%20%3D%20queue.is_empty%28%29%0A%20%20%20%20print%28%27%E3%82%AD%E3%83%A5%E3%83%BC%E3%81%8C%E7%A9%BA%E3%81%8B%E3%81%A9%E3%81%86%E3%81%8B%20%3D%27%2C%20is_empty%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20ArrayQueue%3A%0A%0A%20%20%20%20def%20__init__%28self%2C%20size%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self._nums%3A%20list%5Bint%5D%20%3D%20%5B0%5D%20%2A%20size%0A%20%20%20%20%20%20%20%20self._front%3A%20int%20%3D%200%0A%20%20%20%20%20%20%20%20self._size%3A%20int%20%3D%200%0A%0A%20%20%20%20def%20capacity%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%20len%28self._nums%29%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%20self._size%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20return%20self._size%20%3D%3D%200%0A%0A%20%20%20%20def%20push%28self%2C%20num%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20if%20self._size%20%3D%3D%20self.capacity%28%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%27%E3%82%AD%E3%83%A5%E3%83%BC%E3%81%8C%E3%81%84%E3%81%A3%E3%81%B1%E3%81%84%E3%81%A7%E3%81%99%27%29%0A%20%20%20%20%20%20%20%20rear%3A%20int%20%3D%20%28self._front%20%2B%20self._size%29%20%25%20self.capacity%28%29%0A%20%20%20%20%20%20%20%20self._nums%5Brear%5D%20%3D%20num%0A%20%20%20%20%20%20%20%20self._size%20%2B%3D%201%0A%0A%20%20%20%20def%20pop%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20num%3A%20int%20%3D%20self.peek%28%29%0A%20%20%20%20%20%20%20%20self._front%20%3D%20%28self._front%20%2B%201%29%20%25%20self.capacity%28%29%0A%20%20%20%20%20%20%20%20self._size%20-%3D%201%0A%20%20%20%20%20%20%20%20return%20num%0A%0A%20%20%20%20def%20peek%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20if%20self.is_empty%28%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%27%E3%82%AD%E3%83%A5%E3%83%BC%E3%81%8C%E7%A9%BA%E3%81%A7%E3%81%99%27%29%0A%20%20%20%20%20%20%20%20return%20self._nums%5Bself._front%5D%0A%0A%20%20%20%20def%20to_list%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20res%20%3D%20%5B0%5D%20%2A%20self.size%28%29%0A%20%20%20%20%20%20%20%20j%3A%20int%20%3D%20self._front%0A%20%20%20%20%20%20%20%20for%20i%20in%20range%28self.size%28%29%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20res%5Bi%5D%20%3D%20self._nums%5Bj%20%25%20self.capacity%28%29%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20%2B%3D%201%0A%20%20%20%20%20%20%20%20return%20res%0Aif%20__name__%20%3D%3D%20%27__main__%27%3A%0A%20%20%20%20queue%20%3D%20ArrayQueue%2810%29%0A%20%20%20%20queue.push%281%29%0A%20%20%20%20queue.push%283%29%0A%20%20%20%20queue.push%282%29%0A%20%20%20%20queue.push%285%29%0A%20%20%20%20queue.push%284%29%0A%20%20%20%20peek%20%3D%20queue.peek%28%29%0A%20%20%20%20print%28%27%E5%85%88%E9%A0%AD%E8%A6%81%E7%B4%A0%20peek%20%3D%27%2C%20peek%29%0A%20%20%20%20pop%20%3D%20queue.pop%28%29%0A%20%20%20%20print%28%27%E5%8F%96%E3%82%8A%E5%87%BA%E3%81%97%E3%81%9F%E8%A6%81%E7%B4%A0%20pop%20%3D%27%2C%20pop%29%0A%20%20%20%20size%20%3D%20queue.size%28%29%0A%20%20%20%20print%28%27%E3%82%AD%E3%83%A5%E3%83%BC%E3%81%AE%E9%95%B7%E3%81%95%20size%20%3D%27%2C%20size%29%0A%20%20%20%20is_empty%20%3D%20queue.is_empty%28%29%0A%20%20%20%20print%28%27%E3%82%AD%E3%83%A5%E3%83%BC%E3%81%8C%E7%A9%BA%E3%81%8B%E3%81%A9%E3%81%86%E3%81%8B%20%3D%27%2C%20is_empty%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>上記の実装によるキューにも制約があり、長さを可変にできません。しかし、この問題の解決は難しくなく、配列を動的配列に置き換えれば容量拡張の仕組みを導入できます。興味があれば自分で実装してみてください。</p>
+<p>2 つの実装の比較に関する結論はスタックの場合と同じなので、ここでは繰り返しません。</p>
 <h2 id="523">5.2.3 &nbsp; キューの典型的な応用<a class="headerlink" href="#523" title="Permanent link">&para;</a></h2>
 <ul>
-<li><strong>Amazonの注文</strong>：買い物客が注文を行った後、これらの注文はキューに参加し、システムは順番に処理します。独身の日などのイベント中は、短時間で大量の注文が生成され、高い同時実行性がエンジニアにとって重要な課題となります。</li>
-<li><strong>様々なToDoリスト</strong>：「先着順」機能が必要なシナリオ、例えばプリンターのタスクキューやレストランの配達キューなど、キューで処理順序を効果的に維持できます。</li>
+<li><strong>淘宝の注文</strong>。購入者が注文すると、その注文はキューに追加され、システムは順番に従って注文を処理します。ダブルイレブンの期間には短時間で膨大な注文が発生するため、高並行性がエンジニアにとって重点的に解決すべき課題になります。</li>
+<li><strong>各種の待機事項</strong>。先着順の機能を実現する必要があるあらゆる場面、たとえばプリンターのジョブキューや飲食店の配膳キューなどでは、キューによって処理順序を効果的に維持できます。</li>
 </ul>
 
 <!-- Source file information -->
diff --git a/ja/chapter_stack_and_queue/stack/index.html b/ja/chapter_stack_and_queue/stack/index.html
index cfa421119..88d4a75ba 100644
--- a/ja/chapter_stack_and_queue/stack/index.html
+++ b/ja/chapter_stack_and_queue/stack/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
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             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
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-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
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-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
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   <a href="#511" class="md-nav__link">
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-        5.1.1 &nbsp; スタックの一般的な操作
+        5.1.1 &nbsp; スタックの基本操作
       
     </span>
   </a>
@@ -1526,7 +1526,7 @@
   <a href="#1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; 連結リストベースの実装
+        1. &nbsp; 連結リストによる実装
       
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@@ -1537,7 +1537,7 @@
   <a href="#2" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2. &nbsp; 配列ベースの実装
+        2. &nbsp; 配列による実装
       
     </span>
   </a>
@@ -1713,7 +1713,7 @@
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
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-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
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-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2227,7 +2227,7 @@
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-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2613,7 +2613,7 @@
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-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
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-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3235,7 +3235,7 @@
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3291,7 +3291,7 @@
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
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-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
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-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
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-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
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-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
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-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
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-        5.1.1 &nbsp; スタックの一般的な操作
+        5.1.1 &nbsp; スタックの基本操作
       
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-        1. &nbsp; 連結リストベースの実装
+        1. &nbsp; 連結リストによる実装
       
     </span>
   </a>
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   <a href="#2" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2. &nbsp; 配列ベースの実装
+        2. &nbsp; 配列による実装
       
     </span>
   </a>
@@ -4455,15 +4455,15 @@
 
 <!-- Page content -->
 <h1 id="51">5.1 &nbsp; スタック<a class="headerlink" href="#51" title="Permanent link">&para;</a></h1>
-<p><u>スタック</u>は、後入先出（LIFO）の原則に従う線形データ構造です。</p>
-<p>スタックをテーブル上の皿の山に例えることができます。底の皿にアクセスするには、まず上の皿を取り除く必要があります。皿を様々な種類の要素（整数、文字、オブジェクトなど）に置き換えることで、スタックと呼ばれるデータ構造を得ることができます。</p>
-<p>下図に示すように、要素の山の上部を「スタックのトップ」、下部を「スタックのボトム」と呼びます。スタックのトップに要素を追加する操作を「プッシュ」、トップ要素を削除する操作を「ポップ」と呼びます。</p>
-<p><img alt="スタックの後入先出ルール" class="animation-figure" src="../stack.assets/stack_operations.png" /></p>
-<p align="center"> 図 5-1 &nbsp; スタックの後入先出ルール </p>
+<p><u>スタック（stack）</u>は、後入れ先出しの論理に従う線形データ構造です。</p>
+<p>スタックは机の上に積まれた皿の山にたとえられます。1回に1枚の皿しか動かせないとすると、いちばん下の皿を取り出すには、上にある皿を順番にどかす必要があります。この皿をさまざまな型の要素（整数、文字、オブジェクトなど）に置き換えたものが、スタックというデータ構造です。</p>
+<p>下図のように、積み重なった要素の上端を「スタックトップ」、下端を「スタックボトム」と呼びます。要素をスタックトップに追加する操作を「プッシュ」、スタックトップの要素を削除する操作を「ポップ」と呼びます。</p>
+<p><img alt="スタックの後入れ先出しの規則" class="animation-figure" src="../stack.assets/stack_operations.png" /></p>
+<p align="center"> 図 5-1 &nbsp; スタックの後入れ先出しの規則 </p>
 
-<h2 id="511">5.1.1 &nbsp; スタックの一般的な操作<a class="headerlink" href="#511" title="Permanent link">&para;</a></h2>
-<p>スタックの一般的な操作を下表に示します。具体的なメソッド名は使用するプログラミング言語によって異なります。ここでは、例として<code>push()</code>、<code>pop()</code>、<code>peek()</code>を使用します。</p>
-<p align="center"> 表 5-1 &nbsp; スタック操作の効率 </p>
+<h2 id="511">5.1.1 &nbsp; スタックの基本操作<a class="headerlink" href="#511" title="Permanent link">&para;</a></h2>
+<p>スタックの基本操作を以下の表に示します。具体的なメソッド名は使用するプログラミング言語によって異なります。ここでは、一般的な <code>push()</code>、<code>pop()</code>、<code>peek()</code> を例に挙げます。</p>
+<p align="center"> 表 5-1 &nbsp; スタックの操作効率 </p>
 
 <div class="center-table">
 <table>
@@ -4477,47 +4477,47 @@
 <tbody>
 <tr>
 <td><code>push()</code></td>
-<td>要素をスタックにプッシュ（トップに追加）</td>
+<td>要素をプッシュする（スタックトップに追加）</td>
 <td><span class="arithmatex">\(O(1)\)</span></td>
 </tr>
 <tr>
 <td><code>pop()</code></td>
-<td>スタックからトップ要素をポップ</td>
+<td>スタックトップの要素をポップする</td>
 <td><span class="arithmatex">\(O(1)\)</span></td>
 </tr>
 <tr>
 <td><code>peek()</code></td>
-<td>スタックのトップ要素にアクセス</td>
+<td>スタックトップの要素にアクセスする</td>
 <td><span class="arithmatex">\(O(1)\)</span></td>
 </tr>
 </tbody>
 </table>
 </div>
-<p>通常、プログラミング言語に組み込まれているスタッククラスを直接使用できます。ただし、一部の言語では具体的にスタッククラスを提供していない場合があります。これらの場合、言語の「配列」または「連結リスト」をスタックとして使用し、プログラムでスタックロジックに関連しない操作を無視できます。</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="1:12"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label></div>
+<p>通常は、プログラミング言語に組み込まれているスタッククラスをそのまま利用できます。ただし、専用のスタッククラスが用意されていない言語もあります。その場合は、その言語の「配列」や「連結リスト」をスタックとして用い、プログラムのロジック上でスタックに無関係な操作を無視します。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">stack.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># スタックを初期化</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="c1"># Pythonには組み込みのスタッククラスがないため、listをスタックとして使用</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="c1"># Python には組み込みのスタッククラスがないため、list をスタックとして使用できる</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="n">stack</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>
-<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="c1"># 要素をスタックにプッシュ</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="c1"># 要素をプッシュ</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="n">stack</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="n">stack</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="n">stack</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
 <a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="n">stack</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
 <a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="n">stack</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>
-<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="c1"># スタックのトップ要素にアクセス</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="c1"># スタックトップの要素にアクセス</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="n">peek</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">stack</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
 <a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>
-<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="c1"># スタックから要素をポップ</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="c1"># 要素をポップ</span>
 <a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a><span class="n">pop</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">stack</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
 <a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>
 <a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a><span class="c1"># スタックの長さを取得</span>
 <a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a><span class="n">size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">stack</span><span class="p">)</span>
 <a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>
-<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="c1"># スタックが空かどうかチェック</span>
+<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="c1"># 空かどうかを判定</span>
 <a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="n">is_empty</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">stack</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span>
 </code></pre></div>
 </div>
@@ -4525,23 +4525,23 @@
 <div class="highlight"><span class="filename">stack.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* スタックを初期化 */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="n">stack</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">stack</span><span class="p">;</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a>
-<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="cm">/* 要素をスタックにプッシュ */</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="cm">/* 要素をプッシュ */</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="n">stack</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="n">stack</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="n">stack</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="n">stack</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="n">stack</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a>
-<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="cm">/* スタックのトップ要素にアクセス */</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="cm">/* スタックトップの要素にアクセス */</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="kt">int</span><span class="w"> </span><span class="n">top</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">top</span><span class="p">();</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a>
-<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="cm">/* スタックから要素をポップ */</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="cm">/* 要素をポップ */</span>
 <a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="n">stack</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 戻り値なし</span>
 <a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a>
 <a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="cm">/* スタックの長さを取得 */</span>
 <a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
 <a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a>
-<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="cm">/* スタックが空かどうかチェック */</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="cm">/* 空かどうかを判定 */</span>
 <a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="kt">bool</span><span class="w"> </span><span class="n">empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">empty</span><span class="p">();</span>
 </code></pre></div>
 </div>
@@ -4549,23 +4549,23 @@
 <div class="highlight"><span class="filename">stack.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* スタックを初期化 */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="n">Stack</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Stack</span><span class="o">&lt;&gt;</span><span class="p">();</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a>
-<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="cm">/* 要素をスタックにプッシュ */</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="cm">/* 要素をプッシュ */</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="n">stack</span><span class="p">.</span><span class="na">push</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="n">stack</span><span class="p">.</span><span class="na">push</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="n">stack</span><span class="p">.</span><span class="na">push</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="n">stack</span><span class="p">.</span><span class="na">push</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="n">stack</span><span class="p">.</span><span class="na">push</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a>
-<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="cm">/* スタックのトップ要素にアクセス */</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="cm">/* スタックトップの要素にアクセス */</span>
 <a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">peek</span><span class="p">();</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a>
-<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="cm">/* スタックから要素をポップ */</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="cm">/* 要素をポップ */</span>
 <a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">pop</span><span class="p">();</span>
 <a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a>
 <a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="cm">/* スタックの長さを取得 */</span>
 <a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
 <a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a>
-<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="cm">/* スタックが空かどうかチェック */</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="cm">/* 空かどうかを判定 */</span>
 <a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="kt">boolean</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">();</span>
 </code></pre></div>
 </div>
@@ -4573,197 +4573,246 @@
 <div class="highlight"><span class="filename">stack.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* スタックを初期化 */</span>
 <a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="n">Stack</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">();</span>
 <a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a>
-<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="cm">/* 要素をスタックにプッシュ */</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="cm">/* 要素をプッシュ */</span>
 <a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="n">stack</span><span class="p">.</span><span class="n">Push</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="n">stack</span><span class="p">.</span><span class="n">Push</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
 <a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="n">stack</span><span class="p">.</span><span class="n">Push</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
 <a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="n">stack</span><span class="p">.</span><span class="n">Push</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
 <a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="n">stack</span><span class="p">.</span><span class="n">Push</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
 <a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a>
-<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="cm">/* スタックのトップ要素にアクセス */</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="cm">/* スタックトップの要素にアクセス */</span>
 <a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">Peek</span><span class="p">();</span>
 <a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a>
-<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="cm">/* スタックから要素をポップ */</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="cm">/* 要素をポップ */</span>
 <a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">Pop</span><span class="p">();</span>
 <a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a>
 <a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="cm">/* スタックの長さを取得 */</span>
 <a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">Count</span><span class="p">;</span>
 <a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a>
-<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="cm">/* スタックが空かどうかチェック */</span>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="cm">/* 空かどうかを判定 */</span>
 <a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">stack_test.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* スタックを初期化 */</span>
-<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="c1">// Goでは、Sliceをスタックとして使用することが推奨されます</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="c1">// Go では、Slice をスタックとして使うのが一般的</span>
 <a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="kd">var</span><span class="w"> </span><span class="nx">stack</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span>
 <a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a>
-<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="cm">/* 要素をスタックにプッシュ */</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="cm">/* 要素をプッシュ */</span>
 <a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="nx">stack</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">stack</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
 <a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="nx">stack</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">stack</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span>
 <a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="nx">stack</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">stack</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
 <a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="nx">stack</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">stack</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span>
 <a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="nx">stack</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">stack</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span>
 <a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a>
-<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="cm">/* スタックのトップ要素にアクセス */</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="cm">/* スタックトップの要素にアクセス */</span>
 <a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="nx">peek</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">stack</span><span class="p">[</span><span class="nb">len</span><span class="p">(</span><span class="nx">stack</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
 <a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a>
-<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="cm">/* スタックから要素をポップ */</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="cm">/* 要素をポップ */</span>
 <a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="nx">pop</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">stack</span><span class="p">[</span><span class="nb">len</span><span class="p">(</span><span class="nx">stack</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
 <a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="nx">stack</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">stack</span><span class="p">[:</span><span class="nb">len</span><span class="p">(</span><span class="nx">stack</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
 <a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a>
 <a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="cm">/* スタックの長さを取得 */</span>
 <a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="nx">size</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">stack</span><span class="p">)</span>
 <a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a>
-<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="cm">/* スタックが空かどうかチェック */</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="cm">/* 空かどうかを判定 */</span>
 <a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="nx">isEmpty</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">stack</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">stack.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* スタックを初期化 */</span>
-<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="c1">// Swiftには組み込みのスタッククラスがないため、Arrayをスタックとして使用</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="c1">// Swift には組み込みのスタッククラスがないため、Array をスタックとして使用できる</span>
 <a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">var</span><span class="w"> </span><span class="nv">stack</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
 <a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>
-<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="cm">/* 要素をスタックにプッシュ */</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="cm">/* 要素をプッシュ */</span>
 <a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="n">stack</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
 <a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="n">stack</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
 <a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="n">stack</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
 <a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="n">stack</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
 <a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="n">stack</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
 <a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a>
-<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="cm">/* スタックのトップ要素にアクセス */</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="cm">/* スタックトップの要素にアクセス */</span>
 <a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="kd">let</span><span class="w"> </span><span class="nv">peek</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="bp">last</span><span class="p">!</span>
 <a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a>
-<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="cm">/* スタックから要素をポップ */</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="cm">/* 要素をポップ */</span>
 <a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="kd">let</span><span class="w"> </span><span class="nv">pop</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="bp">removeLast</span><span class="p">()</span>
 <a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a>
 <a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="cm">/* スタックの長さを取得 */</span>
 <a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="kd">let</span><span class="w"> </span><span class="nv">size</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="bp">count</span>
 <a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a>
-<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="cm">/* スタックが空かどうかチェック */</span>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="cm">/* 空かどうかを判定 */</span>
 <a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="kd">let</span><span class="w"> </span><span class="nv">isEmpty</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="bp">isEmpty</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">stack.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* スタックを初期化 */</span>
-<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="c1">// JavaScriptには組み込みのスタッククラスがないため、Arrayをスタックとして使用</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="c1">// JavaScript には組み込みのスタッククラスがないため、Array をスタックとして使用できる</span>
 <a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="kd">const</span><span class="w"> </span><span class="nx">stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
 <a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a>
-<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="cm">/* 要素をスタックにプッシュ */</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="cm">/* 要素をプッシュ */</span>
 <a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="nx">stack</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">1</span><span class="p">);</span>
 <a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="nx">stack</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">3</span><span class="p">);</span>
 <a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="nx">stack</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">2</span><span class="p">);</span>
 <a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="nx">stack</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
 <a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="nx">stack</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">4</span><span class="p">);</span>
 <a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a>
-<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="cm">/* スタックのトップ要素にアクセス */</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="cm">/* スタックトップの要素にアクセス */</span>
 <a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">stack</span><span class="p">[</span><span class="nx">stack</span><span class="p">.</span><span class="nx">length</span><span class="o">-</span><span class="mf">1</span><span class="p">];</span>
 <a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a>
-<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="cm">/* スタックから要素をポップ */</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="cm">/* 要素をポップ */</span>
 <a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="kd">const</span><span class="w"> </span><span class="nx">pop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">stack</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
 <a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a>
 <a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="cm">/* スタックの長さを取得 */</span>
 <a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="kd">const</span><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">stack</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
 <a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a>
-<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="cm">/* スタックが空かどうかチェック */</span>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="cm">/* 空かどうかを判定 */</span>
 <a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="kd">const</span><span class="w"> </span><span class="nx">is_empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">stack</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">stack.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* スタックを初期化 */</span>
-<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="c1">// TypeScriptには組み込みのスタッククラスがないため、Arrayをスタックとして使用</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="c1">// TypeScript には組み込みのスタッククラスがないため、Array をスタックとして使用できる</span>
 <a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="kd">const</span><span class="w"> </span><span class="nx">stack</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
 <a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a>
-<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="cm">/* 要素をスタックにプッシュ */</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="cm">/* 要素をプッシュ */</span>
 <a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="nx">stack</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">1</span><span class="p">);</span>
 <a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="nx">stack</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">3</span><span class="p">);</span>
 <a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="nx">stack</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">2</span><span class="p">);</span>
 <a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="nx">stack</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
 <a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="nx">stack</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">4</span><span class="p">);</span>
 <a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a>
-<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="cm">/* スタックのトップ要素にアクセス */</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="cm">/* スタックトップの要素にアクセス */</span>
 <a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">stack</span><span class="p">[</span><span class="nx">stack</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
 <a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a>
-<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="cm">/* スタックから要素をポップ */</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="cm">/* 要素をポップ */</span>
 <a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="kd">const</span><span class="w"> </span><span class="nx">pop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">stack</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
 <a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a>
 <a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="cm">/* スタックの長さを取得 */</span>
 <a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="kd">const</span><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">stack</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
 <a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a>
-<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="cm">/* スタックが空かどうかチェック */</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="cm">/* 空かどうかを判定 */</span>
 <a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="kd">const</span><span class="w"> </span><span class="nx">is_empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">stack</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">stack.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* スタックを初期化 */</span>
-<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="c1">// Dartには組み込みのスタッククラスがないため、Listをスタックとして使用</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="c1">// Dart には組み込みのスタッククラスがないため、List をスタックとして使用できる</span>
 <a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
 <a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a>
-<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="cm">/* 要素をスタックにプッシュ */</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="cm">/* 要素をプッシュ */</span>
 <a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="n">stack</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">1</span><span class="p">);</span>
 <a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="n">stack</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">3</span><span class="p">);</span>
 <a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="n">stack</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">2</span><span class="p">);</span>
 <a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="n">stack</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">5</span><span class="p">);</span>
 <a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="n">stack</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">4</span><span class="p">);</span>
 <a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a>
-<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="cm">/* スタックのトップ要素にアクセス */</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="cm">/* スタックトップの要素にアクセス */</span>
 <a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">last</span><span class="p">;</span>
 <a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a>
-<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="cm">/* スタックから要素をポップ */</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="cm">/* 要素をポップ */</span>
 <a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">removeLast</span><span class="p">();</span>
 <a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a>
 <a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="cm">/* スタックの長さを取得 */</span>
 <a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
 <a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a>
-<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="cm">/* スタックが空かどうかチェック */</span>
+<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="cm">/* 空かどうかを判定 */</span>
 <a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">isEmpty</span><span class="p">;</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">stack.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* スタックを初期化 */</span>
-<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="c1">// Vecをスタックとして使用</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="c1">// Vec をスタックとして使用する</span>
 <a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">stack</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
 <a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a>
-<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="cm">/* 要素をスタックにプッシュ */</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="cm">/* 要素をプッシュ */</span>
 <a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="n">stack</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="n">stack</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
 <a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="n">stack</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
 <a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="n">stack</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
 <a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="n">stack</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
 <a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a>
-<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="cm">/* スタックのトップ要素にアクセス */</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="cm">/* スタックトップの要素にアクセス */</span>
 <a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="kd">let</span><span class="w"> </span><span class="n">top</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">last</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span>
 <a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a>
-<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="cm">/* スタックから要素をポップ */</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="cm">/* 要素をポップ */</span>
 <a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="kd">let</span><span class="w"> </span><span class="n">pop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span>
 <a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a>
 <a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="cm">/* スタックの長さを取得 */</span>
 <a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="kd">let</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
 <a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a>
-<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="cm">/* スタックが空かどうかチェック */</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="cm">/* 空かどうかを判定 */</span>
 <a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="kd">let</span><span class="w"> </span><span class="n">is_empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">is_empty</span><span class="p">();</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">stack.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// Cは組み込みのスタックを提供していません</span>
+<div class="highlight"><span class="filename">stack.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// C には組み込みのスタックがない</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">stack.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
+<div class="highlight"><span class="filename">stack.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* スタックを初期化 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">val</span><span class="w"> </span><span class="nv">stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Stack</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="cm">/* 要素をプッシュ */</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="n">stack</span><span class="p">.</span><span class="na">push</span><span class="p">(</span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="n">stack</span><span class="p">.</span><span class="na">push</span><span class="p">(</span><span class="m">3</span><span class="p">)</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="n">stack</span><span class="p">.</span><span class="na">push</span><span class="p">(</span><span class="m">2</span><span class="p">)</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="n">stack</span><span class="p">.</span><span class="na">push</span><span class="p">(</span><span class="m">5</span><span class="p">)</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="n">stack</span><span class="p">.</span><span class="na">push</span><span class="p">(</span><span class="m">4</span><span class="p">)</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="cm">/* スタックトップの要素にアクセス */</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="kd">val</span><span class="w"> </span><span class="nv">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">peek</span><span class="p">()</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="cm">/* 要素をポップ */</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="kd">val</span><span class="w"> </span><span class="nv">pop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">pop</span><span class="p">()</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="kd">val</span><span class="w"> </span><span class="nv">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="cm">/* 空かどうかを判定 */</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="kd">val</span><span class="w"> </span><span class="nv">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">()</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">stack.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1"># スタックを初期化</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="c1"># Ruby には組み込みのスタッククラスがないため、Array をスタックとして使用できる</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="n">stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="c1"># 要素をプッシュ</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="n">stack</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="n">stack</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">3</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="n">stack</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="n">stack</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">5</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="n">stack</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">4</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="c1"># スタックトップの要素にアクセス</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="o">.</span><span class="n">last</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="c1"># 要素をポップ</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="n">pop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="o">.</span><span class="n">pop</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="c1"># スタックの長さを取得</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="c1"># 空かどうかを判定</span>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="n">is_empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="o">.</span><span class="n">empty?</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>実行の可視化</summary>
+<p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E6%A0%88%0A%20%20%20%20%23%20Python%20%E6%B2%A1%E6%9C%89%E5%86%85%E7%BD%AE%E7%9A%84%E6%A0%88%E7%B1%BB%EF%BC%8C%E5%8F%AF%E4%BB%A5%E6%8A%8A%20list%20%E5%BD%93%E4%BD%9C%E6%A0%88%E6%9D%A5%E4%BD%BF%E7%94%A8%0A%20%20%20%20stack%20%3D%20%5B%5D%0A%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%85%A5%E6%A0%88%0A%20%20%20%20stack.append%281%29%0A%20%20%20%20stack.append%283%29%0A%20%20%20%20stack.append%282%29%0A%20%20%20%20stack.append%285%29%0A%20%20%20%20stack.append%284%29%0A%20%20%20%20print%28%22%E6%A0%88%20stack%20%3D%22,%20stack%29%0A%0A%20%20%20%20%23%20%E8%AE%BF%E9%97%AE%E6%A0%88%E9%A1%B6%E5%85%83%E7%B4%A0%0A%20%20%20%20peek%20%3D%20stack%5B-1%5D%0A%20%20%20%20print%28%22%E6%A0%88%E9%A1%B6%E5%85%83%E7%B4%A0%20peek%20%3D%22,%20peek%29%0A%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%87%BA%E6%A0%88%0A%20%20%20%20pop%20%3D%20stack.pop%28%29%0A%20%20%20%20print%28%22%E5%87%BA%E6%A0%88%E5%85%83%E7%B4%A0%20pop%20%3D%22,%20pop%29%0A%20%20%20%20print%28%22%E5%87%BA%E6%A0%88%E5%90%8E%20stack%20%3D%22,%20stack%29%0A%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E6%A0%88%E7%9A%84%E9%95%BF%E5%BA%A6%0A%20%20%20%20size%20%3D%20len%28stack%29%0A%20%20%20%20print%28%22%E6%A0%88%E7%9A%84%E9%95%BF%E5%BA%A6%20size%20%3D%22,%20size%29%0A%0A%20%20%20%20%23%20%E5%88%A4%E6%96%AD%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%0A%20%20%20%20is_empty%20%3D%20len%28stack%29%20%3D%3D%200%0A%20%20%20%20print%28%22%E6%A0%88%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%20%3D%22,%20is_empty%29&amp;cumulative=false&amp;curInstr=2&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>
+</details>
 <h2 id="512">5.1.2 &nbsp; スタックの実装<a class="headerlink" href="#512" title="Permanent link">&para;</a></h2>
-<p>スタックがどのように動作するかをより深く理解するために、自分でスタッククラスを実装してみましょう。</p>
-<p>スタックは後入先出の原則に従うため、スタックのトップでのみ要素を追加または削除できます。しかし、配列と連結リストの両方は任意の位置で要素を追加・削除できるため、<strong>スタックは制限された配列または連結リストと見なすことができます</strong>。言い換えれば、配列や連結リストの特定の無関係な操作を「遮蔽」して、外部の動作をスタックの特性に合わせることができます。</p>
-<h3 id="1">1. &nbsp; 連結リストベースの実装<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>連結リストを使用してスタックを実装する場合、リストのヘッドノードをスタックのトップ、テールノードをスタックのボトムと考えることができます。</p>
-<p>下図に示すように、プッシュ操作では、単に連結リストのヘッドに要素を挿入します。このノード挿入方法は「ヘッド挿入」として知られています。ポップ操作では、リストからヘッドノードを削除するだけです。</p>
+<p>スタックの動作の仕組みをより深く理解するために、自分でスタッククラスを実装してみましょう。</p>
+<p>スタックは後入れ先出しの原則に従うため、要素の追加や削除はスタックトップでしか行えません。一方、配列や連結リストでは任意の位置で要素を追加・削除できます。<strong>つまり、スタックは制限付きの配列または連結リストとみなせます。</strong> 言い換えると、配列や連結リストのうち無関係な操作を「隠蔽」することで、外から見た振る舞いをスタックの特性に合わせられます。</p>
+<h3 id="1">1. &nbsp; 連結リストによる実装<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>連結リストでスタックを実装する場合、連結リストの先頭ノードをスタックトップ、末尾ノードをスタックボトムとみなせます。</p>
+<p>下図のように、プッシュ操作では要素を連結リストの先頭に挿入するだけでよく、このノード挿入方法は「頭部挿入法」と呼ばれます。ポップ操作では、先頭ノードを連結リストから削除するだけです。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:3"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">LinkedListStack</label><label for="__tabbed_2_2">push()</label><label for="__tabbed_2_3">pop()</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="連結リストによるスタック実装のプッシュとポップ操作" class="animation-figure" src="../stack.assets/linkedlist_stack_step1.png" /></p>
+<p><img alt="連結リストによるスタック実装のプッシュ・ポップ操作" class="animation-figure" src="../stack.assets/linkedlist_stack_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="linkedlist_stack_push" class="animation-figure" src="../stack.assets/linkedlist_stack_step2_push.png" /></p>
@@ -4773,230 +4822,769 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 5-2 &nbsp; 連結リストによるスタック実装のプッシュとポップ操作 </p>
+<p align="center"> 図 5-2 &nbsp; 連結リストによるスタック実装のプッシュ・ポップ操作 </p>
 
-<p>以下は、連結リストに基づくスタック実装のサンプルコードです：</p>
+<p>以下は、連結リストによってスタックを実装したコード例です：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_stack.py</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">LinkedListStack</span><span class="p">:</span>
-<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;連結リストベースのスタッククラス&quot;&quot;&quot;</span>
-<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a>
-<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
-<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_peek</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>
-<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>
-<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a>
-<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;スタックの長さを取得&quot;&quot;&quot;</span>
-<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span>
-<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a>
-<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">is_empty</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
-<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;スタックが空かどうかを判定&quot;&quot;&quot;</span>
-<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="mi">0</span>
-<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a>
-<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;プッシュ&quot;&quot;&quot;</span>
-<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a>        <span class="n">node</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
-<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a>        <span class="n">node</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_peek</span>
-<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_peek</span> <span class="o">=</span> <span class="n">node</span>
-<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">+=</span> <span class="mi">1</span>
-<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a>
-<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;ポップ&quot;&quot;&quot;</span>
-<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a>        <span class="n">num</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">peek</span><span class="p">()</span>
-<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_peek</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_peek</span><span class="o">.</span><span class="n">next</span>
-<a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-=</span> <span class="mi">1</span>
-<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a>        <span class="k">return</span> <span class="n">num</span>
-<a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a>
-<a id="__codelineno-12-31" name="__codelineno-12-31" href="#__codelineno-12-31"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-12-32" name="__codelineno-12-32" href="#__codelineno-12-32"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;スタックトップ要素にアクセス&quot;&quot;&quot;</span>
-<a id="__codelineno-12-33" name="__codelineno-12-33" href="#__codelineno-12-33"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
-<a id="__codelineno-12-34" name="__codelineno-12-34" href="#__codelineno-12-34"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Stack is empty&quot;</span><span class="p">)</span>
-<a id="__codelineno-12-35" name="__codelineno-12-35" href="#__codelineno-12-35"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_peek</span><span class="o">.</span><span class="n">val</span>
-<a id="__codelineno-12-36" name="__codelineno-12-36" href="#__codelineno-12-36"></a>
-<a id="__codelineno-12-37" name="__codelineno-12-37" href="#__codelineno-12-37"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">to_list</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
-<a id="__codelineno-12-38" name="__codelineno-12-38" href="#__codelineno-12-38"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;出力用のリストに変換&quot;&quot;&quot;</span>
-<a id="__codelineno-12-39" name="__codelineno-12-39" href="#__codelineno-12-39"></a>        <span class="n">arr</span> <span class="o">=</span> <span class="p">[]</span>
-<a id="__codelineno-12-40" name="__codelineno-12-40" href="#__codelineno-12-40"></a>        <span class="n">node</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_peek</span>
-<a id="__codelineno-12-41" name="__codelineno-12-41" href="#__codelineno-12-41"></a>        <span class="k">while</span> <span class="n">node</span><span class="p">:</span>
-<a id="__codelineno-12-42" name="__codelineno-12-42" href="#__codelineno-12-42"></a>            <span class="n">arr</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
-<a id="__codelineno-12-43" name="__codelineno-12-43" href="#__codelineno-12-43"></a>            <span class="n">node</span> <span class="o">=</span> <span class="n">node</span><span class="o">.</span><span class="n">next</span>
-<a id="__codelineno-12-44" name="__codelineno-12-44" href="#__codelineno-12-44"></a>        <span class="n">arr</span><span class="o">.</span><span class="n">reverse</span><span class="p">()</span>
-<a id="__codelineno-12-45" name="__codelineno-12-45" href="#__codelineno-12-45"></a>        <span class="k">return</span> <span class="n">arr</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_stack.cpp</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="cm">/* 連結リストに基づくスタッククラス */</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">LinkedListStack</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
-<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">stackTop</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードをスタックトップとして使用</span>
-<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">stkSize</span><span class="p">;</span><span class="w">        </span><span class="c1">// スタックの長さ</span>
-<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>
-<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
-<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="w">    </span><span class="n">LinkedListStack</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="w">        </span><span class="n">stackTop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
-<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a><span class="w">        </span><span class="n">stkSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="w">    </span><span class="p">}</span>
+<div class="highlight"><span class="filename">linkedlist_stack.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">LinkedListStack</span><span class="p">:</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;連結リストベースのスタック&quot;&quot;&quot;</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
+<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_peek</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>
+<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>
+<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;スタックの長さを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span>
 <a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>
-<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a><span class="w">    </span><span class="o">~</span><span class="n">LinkedListStack</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a><span class="w">        </span><span class="c1">// 連結リストを走査、ノードを削除、メモリを解放</span>
-<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a><span class="w">        </span><span class="n">freeMemoryLinkedList</span><span class="p">(</span><span class="n">stackTop</span><span class="p">);</span>
-<a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>
-<a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a><span class="w">    </span><span class="cm">/* スタックの長さを取得 */</span>
-<a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stkSize</span><span class="p">;</span>
-<a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a>
-<a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a><span class="w">    </span><span class="cm">/* スタックが空かどうかを判定 */</span>
-<a id="__codelineno-13-24" name="__codelineno-13-24" href="#__codelineno-13-24"></a><span class="w">    </span><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-13-26" name="__codelineno-13-26" href="#__codelineno-13-26"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-27" name="__codelineno-13-27" href="#__codelineno-13-27"></a>
-<a id="__codelineno-13-28" name="__codelineno-13-28" href="#__codelineno-13-28"></a><span class="w">    </span><span class="cm">/* プッシュ */</span>
-<a id="__codelineno-13-29" name="__codelineno-13-29" href="#__codelineno-13-29"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-30" name="__codelineno-13-30" href="#__codelineno-13-30"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
-<a id="__codelineno-13-31" name="__codelineno-13-31" href="#__codelineno-13-31"></a><span class="w">        </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackTop</span><span class="p">;</span>
-<a id="__codelineno-13-32" name="__codelineno-13-32" href="#__codelineno-13-32"></a><span class="w">        </span><span class="n">stackTop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
-<a id="__codelineno-13-33" name="__codelineno-13-33" href="#__codelineno-13-33"></a><span class="w">        </span><span class="n">stkSize</span><span class="o">++</span><span class="p">;</span>
-<a id="__codelineno-13-34" name="__codelineno-13-34" href="#__codelineno-13-34"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-35" name="__codelineno-13-35" href="#__codelineno-13-35"></a>
-<a id="__codelineno-13-36" name="__codelineno-13-36" href="#__codelineno-13-36"></a><span class="w">    </span><span class="cm">/* ポップ */</span>
-<a id="__codelineno-13-37" name="__codelineno-13-37" href="#__codelineno-13-37"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-38" name="__codelineno-13-38" href="#__codelineno-13-38"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">top</span><span class="p">();</span>
-<a id="__codelineno-13-39" name="__codelineno-13-39" href="#__codelineno-13-39"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackTop</span><span class="p">;</span>
-<a id="__codelineno-13-40" name="__codelineno-13-40" href="#__codelineno-13-40"></a><span class="w">        </span><span class="n">stackTop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackTop</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
-<a id="__codelineno-13-41" name="__codelineno-13-41" href="#__codelineno-13-41"></a><span class="w">        </span><span class="c1">// メモリを解放</span>
-<a id="__codelineno-13-42" name="__codelineno-13-42" href="#__codelineno-13-42"></a><span class="w">        </span><span class="k">delete</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
-<a id="__codelineno-13-43" name="__codelineno-13-43" href="#__codelineno-13-43"></a><span class="w">        </span><span class="n">stkSize</span><span class="o">--</span><span class="p">;</span>
-<a id="__codelineno-13-44" name="__codelineno-13-44" href="#__codelineno-13-44"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-13-45" name="__codelineno-13-45" href="#__codelineno-13-45"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-46" name="__codelineno-13-46" href="#__codelineno-13-46"></a>
-<a id="__codelineno-13-47" name="__codelineno-13-47" href="#__codelineno-13-47"></a><span class="w">    </span><span class="cm">/* スタックトップ要素にアクセス */</span>
-<a id="__codelineno-13-48" name="__codelineno-13-48" href="#__codelineno-13-48"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">top</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-49" name="__codelineno-13-49" href="#__codelineno-13-49"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
-<a id="__codelineno-13-50" name="__codelineno-13-50" href="#__codelineno-13-50"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Stack is empty&quot;</span><span class="p">);</span>
-<a id="__codelineno-13-51" name="__codelineno-13-51" href="#__codelineno-13-51"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stackTop</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
-<a id="__codelineno-13-52" name="__codelineno-13-52" href="#__codelineno-13-52"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-53" name="__codelineno-13-53" href="#__codelineno-13-53"></a>
-<a id="__codelineno-13-54" name="__codelineno-13-54" href="#__codelineno-13-54"></a><span class="w">    </span><span class="cm">/* リストを配列に変換して返却 */</span>
-<a id="__codelineno-13-55" name="__codelineno-13-55" href="#__codelineno-13-55"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toVector</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-56" name="__codelineno-13-56" href="#__codelineno-13-56"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackTop</span><span class="p">;</span>
-<a id="__codelineno-13-57" name="__codelineno-13-57" href="#__codelineno-13-57"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">(</span><span class="n">size</span><span class="p">());</span>
-<a id="__codelineno-13-58" name="__codelineno-13-58" href="#__codelineno-13-58"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-59" name="__codelineno-13-59" href="#__codelineno-13-59"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
-<a id="__codelineno-13-60" name="__codelineno-13-60" href="#__codelineno-13-60"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
-<a id="__codelineno-13-61" name="__codelineno-13-61" href="#__codelineno-13-61"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-13-62" name="__codelineno-13-62" href="#__codelineno-13-62"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
-<a id="__codelineno-13-63" name="__codelineno-13-63" href="#__codelineno-13-63"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-64" name="__codelineno-13-64" href="#__codelineno-13-64"></a><span class="p">};</span>
+<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">is_empty</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
+<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;スタックが空かどうかを判定&quot;&quot;&quot;</span>
+<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="mi">0</span>
+<a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a>
+<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;プッシュ&quot;&quot;&quot;</span>
+<a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a>        <span class="n">node</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a>        <span class="n">node</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_peek</span>
+<a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_peek</span> <span class="o">=</span> <span class="n">node</span>
+<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a>
+<a id="__codelineno-13-24" name="__codelineno-13-24" href="#__codelineno-13-24"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;ポップ&quot;&quot;&quot;</span>
+<a id="__codelineno-13-26" name="__codelineno-13-26" href="#__codelineno-13-26"></a>        <span class="n">num</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">peek</span><span class="p">()</span>
+<a id="__codelineno-13-27" name="__codelineno-13-27" href="#__codelineno-13-27"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_peek</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_peek</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-13-28" name="__codelineno-13-28" href="#__codelineno-13-28"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-=</span> <span class="mi">1</span>
+<a id="__codelineno-13-29" name="__codelineno-13-29" href="#__codelineno-13-29"></a>        <span class="k">return</span> <span class="n">num</span>
+<a id="__codelineno-13-30" name="__codelineno-13-30" href="#__codelineno-13-30"></a>
+<a id="__codelineno-13-31" name="__codelineno-13-31" href="#__codelineno-13-31"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-32" name="__codelineno-13-32" href="#__codelineno-13-32"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;スタックトップの要素にアクセス&quot;&quot;&quot;</span>
+<a id="__codelineno-13-33" name="__codelineno-13-33" href="#__codelineno-13-33"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
+<a id="__codelineno-13-34" name="__codelineno-13-34" href="#__codelineno-13-34"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;スタックが空です&quot;</span><span class="p">)</span>
+<a id="__codelineno-13-35" name="__codelineno-13-35" href="#__codelineno-13-35"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_peek</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-13-36" name="__codelineno-13-36" href="#__codelineno-13-36"></a>
+<a id="__codelineno-13-37" name="__codelineno-13-37" href="#__codelineno-13-37"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">to_list</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-13-38" name="__codelineno-13-38" href="#__codelineno-13-38"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;表示用にリストへ変換&quot;&quot;&quot;</span>
+<a id="__codelineno-13-39" name="__codelineno-13-39" href="#__codelineno-13-39"></a>        <span class="n">arr</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-13-40" name="__codelineno-13-40" href="#__codelineno-13-40"></a>        <span class="n">node</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_peek</span>
+<a id="__codelineno-13-41" name="__codelineno-13-41" href="#__codelineno-13-41"></a>        <span class="k">while</span> <span class="n">node</span><span class="p">:</span>
+<a id="__codelineno-13-42" name="__codelineno-13-42" href="#__codelineno-13-42"></a>            <span class="n">arr</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-13-43" name="__codelineno-13-43" href="#__codelineno-13-43"></a>            <span class="n">node</span> <span class="o">=</span> <span class="n">node</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-13-44" name="__codelineno-13-44" href="#__codelineno-13-44"></a>        <span class="n">arr</span><span class="o">.</span><span class="n">reverse</span><span class="p">()</span>
+<a id="__codelineno-13-45" name="__codelineno-13-45" href="#__codelineno-13-45"></a>        <span class="k">return</span> <span class="n">arr</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_stack.java</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 連結リストに基づくスタッククラス */</span>
-<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kd">class</span> <span class="nc">LinkedListStack</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="n">stackPeek</span><span class="p">;</span><span class="w"> </span><span class="c1">// ヘッドノードをスタックトップとして使用</span>
-<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">stkSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// スタックの長さ</span>
-<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>
-<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">LinkedListStack</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">        </span><span class="n">stackPeek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
-<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>
-<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">    </span><span class="cm">/* スタックの長さを取得 */</span>
-<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stkSize</span><span class="p">;</span>
-<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a>
-<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">    </span><span class="cm">/* スタックが空かどうかを判定 */</span>
-<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a>
-<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w">    </span><span class="cm">/* プッシュ */</span>
-<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
-<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a><span class="w">        </span><span class="n">node</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackPeek</span><span class="p">;</span>
-<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a><span class="w">        </span><span class="n">stackPeek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
-<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a><span class="w">        </span><span class="n">stkSize</span><span class="o">++</span><span class="p">;</span>
+<div class="highlight"><span class="filename">linkedlist_stack.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 連結リストベースのスタック */</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">LinkedListStack</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">stackTop</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードをスタックトップとする</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">stkSize</span><span class="p">;</span><span class="w">        </span><span class="c1">// スタックの長さ</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">    </span><span class="n">LinkedListStack</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">        </span><span class="n">stackTop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">        </span><span class="n">stkSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">    </span><span class="o">~</span><span class="n">LinkedListStack</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">        </span><span class="c1">// 連結リストを走査してノードを削除し、メモリを解放する</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">        </span><span class="n">freeMemoryLinkedList</span><span class="p">(</span><span class="n">stackTop</span><span class="p">);</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a>
+<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w">    </span><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stkSize</span><span class="p">;</span>
+<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a>
+<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a><span class="w">    </span><span class="cm">/* スタックが空かどうかを判定 */</span>
+<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a><span class="w">    </span><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a>
-<a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a><span class="w">    </span><span class="cm">/* ポップ */</span>
-<a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-30" name="__codelineno-14-30" href="#__codelineno-14-30"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span><span class="p">();</span>
-<a id="__codelineno-14-31" name="__codelineno-14-31" href="#__codelineno-14-31"></a><span class="w">        </span><span class="n">stackPeek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackPeek</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
-<a id="__codelineno-14-32" name="__codelineno-14-32" href="#__codelineno-14-32"></a><span class="w">        </span><span class="n">stkSize</span><span class="o">--</span><span class="p">;</span>
-<a id="__codelineno-14-33" name="__codelineno-14-33" href="#__codelineno-14-33"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a><span class="w">    </span><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-30" name="__codelineno-14-30" href="#__codelineno-14-30"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-14-31" name="__codelineno-14-31" href="#__codelineno-14-31"></a><span class="w">        </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackTop</span><span class="p">;</span>
+<a id="__codelineno-14-32" name="__codelineno-14-32" href="#__codelineno-14-32"></a><span class="w">        </span><span class="n">stackTop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-14-33" name="__codelineno-14-33" href="#__codelineno-14-33"></a><span class="w">        </span><span class="n">stkSize</span><span class="o">++</span><span class="p">;</span>
 <a id="__codelineno-14-34" name="__codelineno-14-34" href="#__codelineno-14-34"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-35" name="__codelineno-14-35" href="#__codelineno-14-35"></a>
-<a id="__codelineno-14-36" name="__codelineno-14-36" href="#__codelineno-14-36"></a><span class="w">    </span><span class="cm">/* スタックトップ要素にアクセス */</span>
-<a id="__codelineno-14-37" name="__codelineno-14-37" href="#__codelineno-14-37"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-38" name="__codelineno-14-38" href="#__codelineno-14-38"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
-<a id="__codelineno-14-39" name="__codelineno-14-39" href="#__codelineno-14-39"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
-<a id="__codelineno-14-40" name="__codelineno-14-40" href="#__codelineno-14-40"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stackPeek</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
-<a id="__codelineno-14-41" name="__codelineno-14-41" href="#__codelineno-14-41"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-42" name="__codelineno-14-42" href="#__codelineno-14-42"></a>
-<a id="__codelineno-14-43" name="__codelineno-14-43" href="#__codelineno-14-43"></a><span class="w">    </span><span class="cm">/* List を Array に変換して返す */</span>
-<a id="__codelineno-14-44" name="__codelineno-14-44" href="#__codelineno-14-44"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-45" name="__codelineno-14-45" href="#__codelineno-14-45"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackPeek</span><span class="p">;</span>
-<a id="__codelineno-14-46" name="__codelineno-14-46" href="#__codelineno-14-46"></a><span class="w">        </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">size</span><span class="p">()</span><span class="o">]</span><span class="p">;</span>
-<a id="__codelineno-14-47" name="__codelineno-14-47" href="#__codelineno-14-47"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-48" name="__codelineno-14-48" href="#__codelineno-14-48"></a><span class="w">            </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
-<a id="__codelineno-14-49" name="__codelineno-14-49" href="#__codelineno-14-49"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
-<a id="__codelineno-14-50" name="__codelineno-14-50" href="#__codelineno-14-50"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-14-51" name="__codelineno-14-51" href="#__codelineno-14-51"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-14-36" name="__codelineno-14-36" href="#__codelineno-14-36"></a><span class="w">    </span><span class="cm">/* ポップ */</span>
+<a id="__codelineno-14-37" name="__codelineno-14-37" href="#__codelineno-14-37"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-38" name="__codelineno-14-38" href="#__codelineno-14-38"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">top</span><span class="p">();</span>
+<a id="__codelineno-14-39" name="__codelineno-14-39" href="#__codelineno-14-39"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackTop</span><span class="p">;</span>
+<a id="__codelineno-14-40" name="__codelineno-14-40" href="#__codelineno-14-40"></a><span class="w">        </span><span class="n">stackTop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackTop</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-14-41" name="__codelineno-14-41" href="#__codelineno-14-41"></a><span class="w">        </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-14-42" name="__codelineno-14-42" href="#__codelineno-14-42"></a><span class="w">        </span><span class="k">delete</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-14-43" name="__codelineno-14-43" href="#__codelineno-14-43"></a><span class="w">        </span><span class="n">stkSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-14-44" name="__codelineno-14-44" href="#__codelineno-14-44"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-14-45" name="__codelineno-14-45" href="#__codelineno-14-45"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-46" name="__codelineno-14-46" href="#__codelineno-14-46"></a>
+<a id="__codelineno-14-47" name="__codelineno-14-47" href="#__codelineno-14-47"></a><span class="w">    </span><span class="cm">/* スタックトップの要素にアクセス */</span>
+<a id="__codelineno-14-48" name="__codelineno-14-48" href="#__codelineno-14-48"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">top</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-49" name="__codelineno-14-49" href="#__codelineno-14-49"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-14-50" name="__codelineno-14-50" href="#__codelineno-14-50"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;スタックが空です&quot;</span><span class="p">);</span>
+<a id="__codelineno-14-51" name="__codelineno-14-51" href="#__codelineno-14-51"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stackTop</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
 <a id="__codelineno-14-52" name="__codelineno-14-52" href="#__codelineno-14-52"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-14-53" name="__codelineno-14-53" href="#__codelineno-14-53"></a><span class="p">}</span>
+<a id="__codelineno-14-53" name="__codelineno-14-53" href="#__codelineno-14-53"></a>
+<a id="__codelineno-14-54" name="__codelineno-14-54" href="#__codelineno-14-54"></a><span class="w">    </span><span class="cm">/* List を Array に変換して返す */</span>
+<a id="__codelineno-14-55" name="__codelineno-14-55" href="#__codelineno-14-55"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toVector</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-56" name="__codelineno-14-56" href="#__codelineno-14-56"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackTop</span><span class="p">;</span>
+<a id="__codelineno-14-57" name="__codelineno-14-57" href="#__codelineno-14-57"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">(</span><span class="n">size</span><span class="p">());</span>
+<a id="__codelineno-14-58" name="__codelineno-14-58" href="#__codelineno-14-58"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-59" name="__codelineno-14-59" href="#__codelineno-14-59"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-14-60" name="__codelineno-14-60" href="#__codelineno-14-60"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-14-61" name="__codelineno-14-61" href="#__codelineno-14-61"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-14-62" name="__codelineno-14-62" href="#__codelineno-14-62"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-14-63" name="__codelineno-14-63" href="#__codelineno-14-63"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-64" name="__codelineno-14-64" href="#__codelineno-14-64"></a><span class="p">};</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_stack.cs</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">LinkedListStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">linkedlist_stack.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 連結リストベースのスタック */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kd">class</span> <span class="nc">LinkedListStack</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="n">stackPeek</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードをスタックトップとする</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">stkSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// スタックの長さ</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">LinkedListStack</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">        </span><span class="n">stackPeek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stkSize</span><span class="p">;</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="cm">/* スタックが空かどうかを判定 */</span>
+<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a>
+<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w">    </span><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="w">        </span><span class="n">node</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackPeek</span><span class="p">;</span>
+<a id="__codelineno-15-24" name="__codelineno-15-24" href="#__codelineno-15-24"></a><span class="w">        </span><span class="n">stackPeek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></a><span class="w">        </span><span class="n">stkSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-15-26" name="__codelineno-15-26" href="#__codelineno-15-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></a>
+<a id="__codelineno-15-28" name="__codelineno-15-28" href="#__codelineno-15-28"></a><span class="w">    </span><span class="cm">/* ポップ */</span>
+<a id="__codelineno-15-29" name="__codelineno-15-29" href="#__codelineno-15-29"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-30" name="__codelineno-15-30" href="#__codelineno-15-30"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span><span class="p">();</span>
+<a id="__codelineno-15-31" name="__codelineno-15-31" href="#__codelineno-15-31"></a><span class="w">        </span><span class="n">stackPeek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackPeek</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
+<a id="__codelineno-15-32" name="__codelineno-15-32" href="#__codelineno-15-32"></a><span class="w">        </span><span class="n">stkSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-15-33" name="__codelineno-15-33" href="#__codelineno-15-33"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-15-34" name="__codelineno-15-34" href="#__codelineno-15-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-35" name="__codelineno-15-35" href="#__codelineno-15-35"></a>
+<a id="__codelineno-15-36" name="__codelineno-15-36" href="#__codelineno-15-36"></a><span class="w">    </span><span class="cm">/* スタックトップの要素にアクセス */</span>
+<a id="__codelineno-15-37" name="__codelineno-15-37" href="#__codelineno-15-37"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-38" name="__codelineno-15-38" href="#__codelineno-15-38"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-15-39" name="__codelineno-15-39" href="#__codelineno-15-39"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
+<a id="__codelineno-15-40" name="__codelineno-15-40" href="#__codelineno-15-40"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stackPeek</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
+<a id="__codelineno-15-41" name="__codelineno-15-41" href="#__codelineno-15-41"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-42" name="__codelineno-15-42" href="#__codelineno-15-42"></a>
+<a id="__codelineno-15-43" name="__codelineno-15-43" href="#__codelineno-15-43"></a><span class="w">    </span><span class="cm">/* List を Array に変換して返す */</span>
+<a id="__codelineno-15-44" name="__codelineno-15-44" href="#__codelineno-15-44"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-45" name="__codelineno-15-45" href="#__codelineno-15-45"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackPeek</span><span class="p">;</span>
+<a id="__codelineno-15-46" name="__codelineno-15-46" href="#__codelineno-15-46"></a><span class="w">        </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">size</span><span class="p">()</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-15-47" name="__codelineno-15-47" href="#__codelineno-15-47"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-48" name="__codelineno-15-48" href="#__codelineno-15-48"></a><span class="w">            </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
+<a id="__codelineno-15-49" name="__codelineno-15-49" href="#__codelineno-15-49"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
+<a id="__codelineno-15-50" name="__codelineno-15-50" href="#__codelineno-15-50"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-51" name="__codelineno-15-51" href="#__codelineno-15-51"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-15-52" name="__codelineno-15-52" href="#__codelineno-15-52"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-53" name="__codelineno-15-53" href="#__codelineno-15-53"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_stack.go</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">linkedListStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">linkedlist_stack.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 連結リストベースのスタック */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">LinkedListStack</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">stackPeek</span><span class="p">;</span><span class="w">  </span><span class="c1">// 先頭ノードをスタックトップとする</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">stkSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">   </span><span class="c1">// スタックの長さ</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nf">LinkedListStack</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">        </span><span class="n">stackPeek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stkSize</span><span class="p">;</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">    </span><span class="cm">/* スタックが空かどうかを判定 */</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="nf">IsEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nf">Size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w">    </span><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">Push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="w">            </span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackPeek</span>
+<a id="__codelineno-16-24" name="__codelineno-16-24" href="#__codelineno-16-24"></a><span class="w">        </span><span class="p">};</span>
+<a id="__codelineno-16-25" name="__codelineno-16-25" href="#__codelineno-16-25"></a><span class="w">        </span><span class="n">stackPeek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-16-26" name="__codelineno-16-26" href="#__codelineno-16-26"></a><span class="w">        </span><span class="n">stkSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-16-27" name="__codelineno-16-27" href="#__codelineno-16-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-28" name="__codelineno-16-28" href="#__codelineno-16-28"></a>
+<a id="__codelineno-16-29" name="__codelineno-16-29" href="#__codelineno-16-29"></a><span class="w">    </span><span class="cm">/* ポップ */</span>
+<a id="__codelineno-16-30" name="__codelineno-16-30" href="#__codelineno-16-30"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-31" name="__codelineno-16-31" href="#__codelineno-16-31"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Peek</span><span class="p">();</span>
+<a id="__codelineno-16-32" name="__codelineno-16-32" href="#__codelineno-16-32"></a><span class="w">        </span><span class="n">stackPeek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackPeek</span><span class="o">!</span><span class="p">.</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-16-33" name="__codelineno-16-33" href="#__codelineno-16-33"></a><span class="w">        </span><span class="n">stkSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-16-34" name="__codelineno-16-34" href="#__codelineno-16-34"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-16-35" name="__codelineno-16-35" href="#__codelineno-16-35"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-36" name="__codelineno-16-36" href="#__codelineno-16-36"></a>
+<a id="__codelineno-16-37" name="__codelineno-16-37" href="#__codelineno-16-37"></a><span class="w">    </span><span class="cm">/* スタックトップの要素にアクセス */</span>
+<a id="__codelineno-16-38" name="__codelineno-16-38" href="#__codelineno-16-38"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-39" name="__codelineno-16-39" href="#__codelineno-16-39"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsEmpty</span><span class="p">())</span>
+<a id="__codelineno-16-40" name="__codelineno-16-40" href="#__codelineno-16-40"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="nf">Exception</span><span class="p">();</span>
+<a id="__codelineno-16-41" name="__codelineno-16-41" href="#__codelineno-16-41"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stackPeek</span><span class="o">!</span><span class="p">.</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-16-42" name="__codelineno-16-42" href="#__codelineno-16-42"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-43" name="__codelineno-16-43" href="#__codelineno-16-43"></a>
+<a id="__codelineno-16-44" name="__codelineno-16-44" href="#__codelineno-16-44"></a><span class="w">    </span><span class="cm">/* List を Array に変換して返す */</span>
+<a id="__codelineno-16-45" name="__codelineno-16-45" href="#__codelineno-16-45"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="nf">ToArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-46" name="__codelineno-16-46" href="#__codelineno-16-46"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">stackPeek</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span>
+<a id="__codelineno-16-47" name="__codelineno-16-47" href="#__codelineno-16-47"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-16-48" name="__codelineno-16-48" href="#__codelineno-16-48"></a>
+<a id="__codelineno-16-49" name="__codelineno-16-49" href="#__codelineno-16-49"></a><span class="w">        </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackPeek</span><span class="p">;</span>
+<a id="__codelineno-16-50" name="__codelineno-16-50" href="#__codelineno-16-50"></a><span class="w">        </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">Size</span><span class="p">()];</span>
+<a id="__codelineno-16-51" name="__codelineno-16-51" href="#__codelineno-16-51"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-52" name="__codelineno-16-52" href="#__codelineno-16-52"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">!</span><span class="p">.</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-16-53" name="__codelineno-16-53" href="#__codelineno-16-53"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-16-54" name="__codelineno-16-54" href="#__codelineno-16-54"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-55" name="__codelineno-16-55" href="#__codelineno-16-55"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-16-56" name="__codelineno-16-56" href="#__codelineno-16-56"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-57" name="__codelineno-16-57" href="#__codelineno-16-57"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_stack.swift</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">LinkedListStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">linkedlist_stack.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 連結リストベースのスタック */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">linkedListStack</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="c1">// 組み込みパッケージ list でスタックを実装する</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="nx">data</span><span class="w"> </span><span class="o">*</span><span class="nx">list</span><span class="p">.</span><span class="nx">List</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="p">}</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="cm">/* スタックを初期化 */</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="kd">func</span><span class="w"> </span><span class="nx">newLinkedListStack</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="nx">linkedListStack</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">linkedListStack</span><span class="p">{</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">        </span><span class="nx">data</span><span class="p">:</span><span class="w"> </span><span class="nx">list</span><span class="p">.</span><span class="nx">New</span><span class="p">(),</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="p">}</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">linkedListStack</span><span class="p">)</span><span class="w"> </span><span class="nx">push</span><span class="p">(</span><span class="nx">value</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w">    </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">.</span><span class="nx">PushBack</span><span class="p">(</span><span class="nx">value</span><span class="p">)</span>
+<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="p">}</span>
+<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a>
+<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="cm">/* ポップ */</span>
+<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">linkedListStack</span><span class="p">)</span><span class="w"> </span><span class="nx">pop</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-22" name="__codelineno-17-22" href="#__codelineno-17-22"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-17-23" name="__codelineno-17-23" href="#__codelineno-17-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-24" name="__codelineno-17-24" href="#__codelineno-17-24"></a><span class="w">    </span><span class="nx">e</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">.</span><span class="nx">Back</span><span class="p">()</span>
+<a id="__codelineno-17-25" name="__codelineno-17-25" href="#__codelineno-17-25"></a><span class="w">    </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">.</span><span class="nx">Remove</span><span class="p">(</span><span class="nx">e</span><span class="p">)</span>
+<a id="__codelineno-17-26" name="__codelineno-17-26" href="#__codelineno-17-26"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">e</span><span class="p">.</span><span class="nx">Value</span>
+<a id="__codelineno-17-27" name="__codelineno-17-27" href="#__codelineno-17-27"></a><span class="p">}</span>
+<a id="__codelineno-17-28" name="__codelineno-17-28" href="#__codelineno-17-28"></a>
+<a id="__codelineno-17-29" name="__codelineno-17-29" href="#__codelineno-17-29"></a><span class="cm">/* スタックトップの要素にアクセス */</span>
+<a id="__codelineno-17-30" name="__codelineno-17-30" href="#__codelineno-17-30"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">linkedListStack</span><span class="p">)</span><span class="w"> </span><span class="nx">peek</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-31" name="__codelineno-17-31" href="#__codelineno-17-31"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-32" name="__codelineno-17-32" href="#__codelineno-17-32"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-17-33" name="__codelineno-17-33" href="#__codelineno-17-33"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-34" name="__codelineno-17-34" href="#__codelineno-17-34"></a><span class="w">    </span><span class="nx">e</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">.</span><span class="nx">Back</span><span class="p">()</span>
+<a id="__codelineno-17-35" name="__codelineno-17-35" href="#__codelineno-17-35"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">e</span><span class="p">.</span><span class="nx">Value</span>
+<a id="__codelineno-17-36" name="__codelineno-17-36" href="#__codelineno-17-36"></a><span class="p">}</span>
+<a id="__codelineno-17-37" name="__codelineno-17-37" href="#__codelineno-17-37"></a>
+<a id="__codelineno-17-38" name="__codelineno-17-38" href="#__codelineno-17-38"></a><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-17-39" name="__codelineno-17-39" href="#__codelineno-17-39"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">linkedListStack</span><span class="p">)</span><span class="w"> </span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-40" name="__codelineno-17-40" href="#__codelineno-17-40"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">.</span><span class="nx">Len</span><span class="p">()</span>
+<a id="__codelineno-17-41" name="__codelineno-17-41" href="#__codelineno-17-41"></a><span class="p">}</span>
+<a id="__codelineno-17-42" name="__codelineno-17-42" href="#__codelineno-17-42"></a>
+<a id="__codelineno-17-43" name="__codelineno-17-43" href="#__codelineno-17-43"></a><span class="cm">/* スタックが空かどうかを判定 */</span>
+<a id="__codelineno-17-44" name="__codelineno-17-44" href="#__codelineno-17-44"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">linkedListStack</span><span class="p">)</span><span class="w"> </span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-45" name="__codelineno-17-45" href="#__codelineno-17-45"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">.</span><span class="nx">Len</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-17-46" name="__codelineno-17-46" href="#__codelineno-17-46"></a><span class="p">}</span>
+<a id="__codelineno-17-47" name="__codelineno-17-47" href="#__codelineno-17-47"></a>
+<a id="__codelineno-17-48" name="__codelineno-17-48" href="#__codelineno-17-48"></a><span class="cm">/* 表示用に List を取得 */</span>
+<a id="__codelineno-17-49" name="__codelineno-17-49" href="#__codelineno-17-49"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">linkedListStack</span><span class="p">)</span><span class="w"> </span><span class="nx">toList</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="nx">list</span><span class="p">.</span><span class="nx">List</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-50" name="__codelineno-17-50" href="#__codelineno-17-50"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span>
+<a id="__codelineno-17-51" name="__codelineno-17-51" href="#__codelineno-17-51"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_stack.js</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">LinkedListStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">linkedlist_stack.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 連結リストベースのスタック */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">LinkedListStack</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">_peek</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 先頭ノードをスタックトップとする</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">_size</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// スタックの長さ</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">    </span><span class="kd">init</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">        </span><span class="n">_size</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">    </span><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w">        </span><span class="n">_size</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a>
+<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w">    </span><span class="cm">/* スタックが空かどうかを判定 */</span>
+<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="w">        </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a>
+<a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a><span class="w">    </span><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-22" name="__codelineno-18-22" href="#__codelineno-18-22"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-18-23" name="__codelineno-18-23" href="#__codelineno-18-23"></a><span class="w">        </span><span class="n">node</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">_peek</span>
+<a id="__codelineno-18-24" name="__codelineno-18-24" href="#__codelineno-18-24"></a><span class="w">        </span><span class="n">_peek</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-18-25" name="__codelineno-18-25" href="#__codelineno-18-25"></a><span class="w">        </span><span class="n">_size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-18-26" name="__codelineno-18-26" href="#__codelineno-18-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-27" name="__codelineno-18-27" href="#__codelineno-18-27"></a>
+<a id="__codelineno-18-28" name="__codelineno-18-28" href="#__codelineno-18-28"></a><span class="w">    </span><span class="cm">/* ポップ */</span>
+<a id="__codelineno-18-29" name="__codelineno-18-29" href="#__codelineno-18-29"></a><span class="w">    </span><span class="p">@</span><span class="n">discardableResult</span>
+<a id="__codelineno-18-30" name="__codelineno-18-30" href="#__codelineno-18-30"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-31" name="__codelineno-18-31" href="#__codelineno-18-31"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">num</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">peek</span><span class="p">()</span>
+<a id="__codelineno-18-32" name="__codelineno-18-32" href="#__codelineno-18-32"></a><span class="w">        </span><span class="n">_peek</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">_peek</span><span class="p">?.</span><span class="n">next</span>
+<a id="__codelineno-18-33" name="__codelineno-18-33" href="#__codelineno-18-33"></a><span class="w">        </span><span class="n">_size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-18-34" name="__codelineno-18-34" href="#__codelineno-18-34"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-18-35" name="__codelineno-18-35" href="#__codelineno-18-35"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-36" name="__codelineno-18-36" href="#__codelineno-18-36"></a>
+<a id="__codelineno-18-37" name="__codelineno-18-37" href="#__codelineno-18-37"></a><span class="w">    </span><span class="cm">/* スタックトップの要素にアクセス */</span>
+<a id="__codelineno-18-38" name="__codelineno-18-38" href="#__codelineno-18-38"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-39" name="__codelineno-18-39" href="#__codelineno-18-39"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-40" name="__codelineno-18-40" href="#__codelineno-18-40"></a><span class="w">            </span><span class="bp">fatalError</span><span class="p">(</span><span class="s">&quot;スタックが空です&quot;</span><span class="p">)</span>
+<a id="__codelineno-18-41" name="__codelineno-18-41" href="#__codelineno-18-41"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-42" name="__codelineno-18-42" href="#__codelineno-18-42"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">_peek</span><span class="p">!.</span><span class="n">val</span>
+<a id="__codelineno-18-43" name="__codelineno-18-43" href="#__codelineno-18-43"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-44" name="__codelineno-18-44" href="#__codelineno-18-44"></a>
+<a id="__codelineno-18-45" name="__codelineno-18-45" href="#__codelineno-18-45"></a><span class="w">    </span><span class="cm">/* List を Array に変換して返す */</span>
+<a id="__codelineno-18-46" name="__codelineno-18-46" href="#__codelineno-18-46"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-47" name="__codelineno-18-47" href="#__codelineno-18-47"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">_peek</span>
+<a id="__codelineno-18-48" name="__codelineno-18-48" href="#__codelineno-18-48"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
+<a id="__codelineno-18-49" name="__codelineno-18-49" href="#__codelineno-18-49"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="bp">indices</span><span class="p">.</span><span class="n">reversed</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-50" name="__codelineno-18-50" href="#__codelineno-18-50"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span><span class="p">!.</span><span class="n">val</span>
+<a id="__codelineno-18-51" name="__codelineno-18-51" href="#__codelineno-18-51"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span><span class="p">?.</span><span class="n">next</span>
+<a id="__codelineno-18-52" name="__codelineno-18-52" href="#__codelineno-18-52"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-53" name="__codelineno-18-53" href="#__codelineno-18-53"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-18-54" name="__codelineno-18-54" href="#__codelineno-18-54"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-55" name="__codelineno-18-55" href="#__codelineno-18-55"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_stack.ts</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">LinkedListStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">linkedlist_stack.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 連結リストベースのスタック */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">LinkedListStack</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="n">#stackPeek</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードをスタックトップとする</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="n">#stkSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// スタックの長さ</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#stackPeek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w">    </span><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w">    </span><span class="nx">get</span><span class="w"> </span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#stkSize</span><span class="p">;</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a>
+<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w">    </span><span class="cm">/* スタックが空かどうかを判定 */</span>
+<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a><span class="w">    </span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a>
+<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a><span class="w">    </span><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a><span class="w">    </span><span class="nx">push</span><span class="p">(</span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-22" name="__codelineno-19-22" href="#__codelineno-19-22"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="nx">num</span><span class="p">);</span>
+<a id="__codelineno-19-23" name="__codelineno-19-23" href="#__codelineno-19-23"></a><span class="w">        </span><span class="nx">node</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#stackPeek</span><span class="p">;</span>
+<a id="__codelineno-19-24" name="__codelineno-19-24" href="#__codelineno-19-24"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#stackPeek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-19-25" name="__codelineno-19-25" href="#__codelineno-19-25"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#stkSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-19-26" name="__codelineno-19-26" href="#__codelineno-19-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-27" name="__codelineno-19-27" href="#__codelineno-19-27"></a>
+<a id="__codelineno-19-28" name="__codelineno-19-28" href="#__codelineno-19-28"></a><span class="w">    </span><span class="cm">/* ポップ */</span>
+<a id="__codelineno-19-29" name="__codelineno-19-29" href="#__codelineno-19-29"></a><span class="w">    </span><span class="nx">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-30" name="__codelineno-19-30" href="#__codelineno-19-30"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">peek</span><span class="p">();</span>
+<a id="__codelineno-19-31" name="__codelineno-19-31" href="#__codelineno-19-31"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#stackPeek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#stackPeek</span><span class="p">.</span><span class="nx">next</span><span class="p">;</span>
+<a id="__codelineno-19-32" name="__codelineno-19-32" href="#__codelineno-19-32"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#stkSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-19-33" name="__codelineno-19-33" href="#__codelineno-19-33"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-19-34" name="__codelineno-19-34" href="#__codelineno-19-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-35" name="__codelineno-19-35" href="#__codelineno-19-35"></a>
+<a id="__codelineno-19-36" name="__codelineno-19-36" href="#__codelineno-19-36"></a><span class="w">    </span><span class="cm">/* スタックトップの要素にアクセス */</span>
+<a id="__codelineno-19-37" name="__codelineno-19-37" href="#__codelineno-19-37"></a><span class="w">    </span><span class="nx">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-38" name="__codelineno-19-38" href="#__codelineno-19-38"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="k">this</span><span class="p">.</span><span class="n">#stackPeek</span><span class="p">)</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;スタックが空&#39;</span><span class="p">);</span>
+<a id="__codelineno-19-39" name="__codelineno-19-39" href="#__codelineno-19-39"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#stackPeek</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-19-40" name="__codelineno-19-40" href="#__codelineno-19-40"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-41" name="__codelineno-19-41" href="#__codelineno-19-41"></a>
+<a id="__codelineno-19-42" name="__codelineno-19-42" href="#__codelineno-19-42"></a><span class="w">    </span><span class="cm">/* 連結リストを Array に変換して返す */</span>
+<a id="__codelineno-19-43" name="__codelineno-19-43" href="#__codelineno-19-43"></a><span class="w">    </span><span class="nx">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-44" name="__codelineno-19-44" href="#__codelineno-19-44"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#stackPeek</span><span class="p">;</span>
+<a id="__codelineno-19-45" name="__codelineno-19-45" href="#__codelineno-19-45"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">);</span>
+<a id="__codelineno-19-46" name="__codelineno-19-46" href="#__codelineno-19-46"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-47" name="__codelineno-19-47" href="#__codelineno-19-47"></a><span class="w">            </span><span class="nx">res</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-19-48" name="__codelineno-19-48" href="#__codelineno-19-48"></a><span class="w">            </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">next</span><span class="p">;</span>
+<a id="__codelineno-19-49" name="__codelineno-19-49" href="#__codelineno-19-49"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-50" name="__codelineno-19-50" href="#__codelineno-19-50"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-19-51" name="__codelineno-19-51" href="#__codelineno-19-51"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-52" name="__codelineno-19-52" href="#__codelineno-19-52"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_stack.dart</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">LinkedListStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">linkedlist_stack.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 連結リストベースのスタック */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">LinkedListStack</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">stackPeek</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードをスタックトップとする</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">stkSize</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// スタックの長さ</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">stackPeek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">    </span><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w">    </span><span class="nx">get</span><span class="w"> </span><span class="nx">size</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">stkSize</span><span class="p">;</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a>
+<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w">    </span><span class="cm">/* スタックが空かどうかを判定 */</span>
+<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a><span class="w">    </span><span class="nx">isEmpty</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-17" name="__codelineno-20-17" href="#__codelineno-20-17"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-20-18" name="__codelineno-20-18" href="#__codelineno-20-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-19" name="__codelineno-20-19" href="#__codelineno-20-19"></a>
+<a id="__codelineno-20-20" name="__codelineno-20-20" href="#__codelineno-20-20"></a><span class="w">    </span><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-20-21" name="__codelineno-20-21" href="#__codelineno-20-21"></a><span class="w">    </span><span class="nx">push</span><span class="p">(</span><span class="nx">num</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-22" name="__codelineno-20-22" href="#__codelineno-20-22"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="nx">num</span><span class="p">);</span>
+<a id="__codelineno-20-23" name="__codelineno-20-23" href="#__codelineno-20-23"></a><span class="w">        </span><span class="nx">node</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">stackPeek</span><span class="p">;</span>
+<a id="__codelineno-20-24" name="__codelineno-20-24" href="#__codelineno-20-24"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">stackPeek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-20-25" name="__codelineno-20-25" href="#__codelineno-20-25"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">stkSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-20-26" name="__codelineno-20-26" href="#__codelineno-20-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-27" name="__codelineno-20-27" href="#__codelineno-20-27"></a>
+<a id="__codelineno-20-28" name="__codelineno-20-28" href="#__codelineno-20-28"></a><span class="w">    </span><span class="cm">/* ポップ */</span>
+<a id="__codelineno-20-29" name="__codelineno-20-29" href="#__codelineno-20-29"></a><span class="w">    </span><span class="nx">pop</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-30" name="__codelineno-20-30" href="#__codelineno-20-30"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">peek</span><span class="p">();</span>
+<a id="__codelineno-20-31" name="__codelineno-20-31" href="#__codelineno-20-31"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="k">this</span><span class="p">.</span><span class="nx">stackPeek</span><span class="p">)</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;スタックが空です&#39;</span><span class="p">);</span>
+<a id="__codelineno-20-32" name="__codelineno-20-32" href="#__codelineno-20-32"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">stackPeek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">stackPeek</span><span class="p">.</span><span class="nx">next</span><span class="p">;</span>
+<a id="__codelineno-20-33" name="__codelineno-20-33" href="#__codelineno-20-33"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">stkSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-20-34" name="__codelineno-20-34" href="#__codelineno-20-34"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-20-35" name="__codelineno-20-35" href="#__codelineno-20-35"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-36" name="__codelineno-20-36" href="#__codelineno-20-36"></a>
+<a id="__codelineno-20-37" name="__codelineno-20-37" href="#__codelineno-20-37"></a><span class="w">    </span><span class="cm">/* スタックトップの要素にアクセス */</span>
+<a id="__codelineno-20-38" name="__codelineno-20-38" href="#__codelineno-20-38"></a><span class="w">    </span><span class="nx">peek</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-39" name="__codelineno-20-39" href="#__codelineno-20-39"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="k">this</span><span class="p">.</span><span class="nx">stackPeek</span><span class="p">)</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;スタックが空です&#39;</span><span class="p">);</span>
+<a id="__codelineno-20-40" name="__codelineno-20-40" href="#__codelineno-20-40"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">stackPeek</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-20-41" name="__codelineno-20-41" href="#__codelineno-20-41"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-42" name="__codelineno-20-42" href="#__codelineno-20-42"></a>
+<a id="__codelineno-20-43" name="__codelineno-20-43" href="#__codelineno-20-43"></a><span class="w">    </span><span class="cm">/* 連結リストを Array に変換して返す */</span>
+<a id="__codelineno-20-44" name="__codelineno-20-44" href="#__codelineno-20-44"></a><span class="w">    </span><span class="nx">toArray</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-45" name="__codelineno-20-45" href="#__codelineno-20-45"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">stackPeek</span><span class="p">;</span>
+<a id="__codelineno-20-46" name="__codelineno-20-46" href="#__codelineno-20-46"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">);</span>
+<a id="__codelineno-20-47" name="__codelineno-20-47" href="#__codelineno-20-47"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-48" name="__codelineno-20-48" href="#__codelineno-20-48"></a><span class="w">            </span><span class="nx">res</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="o">!</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-20-49" name="__codelineno-20-49" href="#__codelineno-20-49"></a><span class="w">            </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="o">!</span><span class="p">.</span><span class="nx">next</span><span class="p">;</span>
+<a id="__codelineno-20-50" name="__codelineno-20-50" href="#__codelineno-20-50"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-51" name="__codelineno-20-51" href="#__codelineno-20-51"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-20-52" name="__codelineno-20-52" href="#__codelineno-20-52"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-53" name="__codelineno-20-53" href="#__codelineno-20-53"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_stack.rs</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">LinkedListStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">linkedlist_stack.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 連結リストクラスに基づくスタック */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">LinkedListStack</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">_stackPeek</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードをスタックトップとする</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">_stkSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// スタックの長さ</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">  </span><span class="n">LinkedListStack</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">    </span><span class="n">_stackPeek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="w">  </span><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_stkSize</span><span class="p">;</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a>
+<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w">  </span><span class="cm">/* スタックが空かどうかを判定 */</span>
+<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="w">  </span><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-17" name="__codelineno-21-17" href="#__codelineno-21-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_stkSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-21-18" name="__codelineno-21-18" href="#__codelineno-21-18"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-19" name="__codelineno-21-19" href="#__codelineno-21-19"></a>
+<a id="__codelineno-21-20" name="__codelineno-21-20" href="#__codelineno-21-20"></a><span class="w">  </span><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-21-21" name="__codelineno-21-21" href="#__codelineno-21-21"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-22" name="__codelineno-21-22" href="#__codelineno-21-22"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">_num</span><span class="p">);</span>
+<a id="__codelineno-21-23" name="__codelineno-21-23" href="#__codelineno-21-23"></a><span class="w">    </span><span class="n">node</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_stackPeek</span><span class="p">;</span>
+<a id="__codelineno-21-24" name="__codelineno-21-24" href="#__codelineno-21-24"></a><span class="w">    </span><span class="n">_stackPeek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-21-25" name="__codelineno-21-25" href="#__codelineno-21-25"></a><span class="w">    </span><span class="n">_stkSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-21-26" name="__codelineno-21-26" href="#__codelineno-21-26"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-27" name="__codelineno-21-27" href="#__codelineno-21-27"></a>
+<a id="__codelineno-21-28" name="__codelineno-21-28" href="#__codelineno-21-28"></a><span class="w">  </span><span class="cm">/* ポップ */</span>
+<a id="__codelineno-21-29" name="__codelineno-21-29" href="#__codelineno-21-29"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-30" name="__codelineno-21-30" href="#__codelineno-21-30"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span><span class="p">();</span>
+<a id="__codelineno-21-31" name="__codelineno-21-31" href="#__codelineno-21-31"></a><span class="w">    </span><span class="n">_stackPeek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_stackPeek</span><span class="o">!</span><span class="p">.</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-21-32" name="__codelineno-21-32" href="#__codelineno-21-32"></a><span class="w">    </span><span class="n">_stkSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-21-33" name="__codelineno-21-33" href="#__codelineno-21-33"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_num</span><span class="p">;</span>
+<a id="__codelineno-21-34" name="__codelineno-21-34" href="#__codelineno-21-34"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-35" name="__codelineno-21-35" href="#__codelineno-21-35"></a>
+<a id="__codelineno-21-36" name="__codelineno-21-36" href="#__codelineno-21-36"></a><span class="w">  </span><span class="cm">/* スタックトップの要素にアクセス */</span>
+<a id="__codelineno-21-37" name="__codelineno-21-37" href="#__codelineno-21-37"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-38" name="__codelineno-21-38" href="#__codelineno-21-38"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_stackPeek</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-39" name="__codelineno-21-39" href="#__codelineno-21-39"></a><span class="w">      </span><span class="k">throw</span><span class="w"> </span><span class="n">Exception</span><span class="p">(</span><span class="s2">&quot;スタックが空です&quot;</span><span class="p">);</span>
+<a id="__codelineno-21-40" name="__codelineno-21-40" href="#__codelineno-21-40"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-41" name="__codelineno-21-41" href="#__codelineno-21-41"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_stackPeek</span><span class="o">!</span><span class="p">.</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-21-42" name="__codelineno-21-42" href="#__codelineno-21-42"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-43" name="__codelineno-21-43" href="#__codelineno-21-43"></a>
+<a id="__codelineno-21-44" name="__codelineno-21-44" href="#__codelineno-21-44"></a><span class="w">  </span><span class="cm">/* 連結リストを List に変換して返す */</span>
+<a id="__codelineno-21-45" name="__codelineno-21-45" href="#__codelineno-21-45"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toList</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-46" name="__codelineno-21-46" href="#__codelineno-21-46"></a><span class="w">    </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_stackPeek</span><span class="p">;</span>
+<a id="__codelineno-21-47" name="__codelineno-21-47" href="#__codelineno-21-47"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">list</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-21-48" name="__codelineno-21-48" href="#__codelineno-21-48"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-49" name="__codelineno-21-49" href="#__codelineno-21-49"></a><span class="w">      </span><span class="n">list</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-21-50" name="__codelineno-21-50" href="#__codelineno-21-50"></a><span class="w">      </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-21-51" name="__codelineno-21-51" href="#__codelineno-21-51"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-52" name="__codelineno-21-52" href="#__codelineno-21-52"></a><span class="w">    </span><span class="n">list</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">list</span><span class="p">.</span><span class="n">reversed</span><span class="p">.</span><span class="n">toList</span><span class="p">();</span>
+<a id="__codelineno-21-53" name="__codelineno-21-53" href="#__codelineno-21-53"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">list</span><span class="p">;</span>
+<a id="__codelineno-21-54" name="__codelineno-21-54" href="#__codelineno-21-54"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-55" name="__codelineno-21-55" href="#__codelineno-21-55"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_stack.c</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">LinkedListStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">linkedlist_stack.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 連結リストベースのスタック */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="cp">#[allow(dead_code)]</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="k">pub</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">LinkedListStack</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="n">stack_peek</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="c1">// 先頭ノードをスタックトップとする</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">    </span><span class="n">stk_size</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w">                              </span><span class="c1">// スタックの長さ</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="p">}</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="k">impl</span><span class="o">&lt;</span><span class="n">T</span><span class="p">:</span><span class="w"> </span><span class="nb">Copy</span><span class="o">&gt;</span><span class="w"> </span><span class="n">LinkedListStack</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">new</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w">        </span><span class="bp">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w">            </span><span class="n">stack_peek</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">            </span><span class="n">stk_size</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a>
+<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="w">    </span><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">stk_size</span><span class="p">;</span>
+<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a>
+<a id="__codelineno-22-21" name="__codelineno-22-21" href="#__codelineno-22-21"></a><span class="w">    </span><span class="cm">/* スタックが空かどうかを判定 */</span>
+<a id="__codelineno-22-22" name="__codelineno-22-22" href="#__codelineno-22-22"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">is_empty</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-23" name="__codelineno-22-23" href="#__codelineno-22-23"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-22-24" name="__codelineno-22-24" href="#__codelineno-22-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-25" name="__codelineno-22-25" href="#__codelineno-22-25"></a>
+<a id="__codelineno-22-26" name="__codelineno-22-26" href="#__codelineno-22-26"></a><span class="w">    </span><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-22-27" name="__codelineno-22-27" href="#__codelineno-22-27"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nc">T</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-28" name="__codelineno-22-28" href="#__codelineno-22-28"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-22-29" name="__codelineno-22-29" href="#__codelineno-22-29"></a><span class="w">        </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">stack_peek</span><span class="p">.</span><span class="n">take</span><span class="p">();</span>
+<a id="__codelineno-22-30" name="__codelineno-22-30" href="#__codelineno-22-30"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">stack_peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-22-31" name="__codelineno-22-31" href="#__codelineno-22-31"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">stk_size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-22-32" name="__codelineno-22-32" href="#__codelineno-22-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-33" name="__codelineno-22-33" href="#__codelineno-22-33"></a>
+<a id="__codelineno-22-34" name="__codelineno-22-34" href="#__codelineno-22-34"></a><span class="w">    </span><span class="cm">/* ポップ */</span>
+<a id="__codelineno-22-35" name="__codelineno-22-35" href="#__codelineno-22-35"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-36" name="__codelineno-22-36" href="#__codelineno-22-36"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">stack_peek</span><span class="p">.</span><span class="n">take</span><span class="p">().</span><span class="n">map</span><span class="p">(</span><span class="o">|</span><span class="n">old_head</span><span class="o">|</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-37" name="__codelineno-22-37" href="#__codelineno-22-37"></a><span class="w">            </span><span class="bp">self</span><span class="p">.</span><span class="n">stack_peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">old_head</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="p">.</span><span class="n">take</span><span class="p">();</span>
+<a id="__codelineno-22-38" name="__codelineno-22-38" href="#__codelineno-22-38"></a><span class="w">            </span><span class="bp">self</span><span class="p">.</span><span class="n">stk_size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-22-39" name="__codelineno-22-39" href="#__codelineno-22-39"></a>
+<a id="__codelineno-22-40" name="__codelineno-22-40" href="#__codelineno-22-40"></a><span class="w">            </span><span class="n">old_head</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span>
+<a id="__codelineno-22-41" name="__codelineno-22-41" href="#__codelineno-22-41"></a><span class="w">        </span><span class="p">})</span>
+<a id="__codelineno-22-42" name="__codelineno-22-42" href="#__codelineno-22-42"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-43" name="__codelineno-22-43" href="#__codelineno-22-43"></a>
+<a id="__codelineno-22-44" name="__codelineno-22-44" href="#__codelineno-22-44"></a><span class="w">    </span><span class="cm">/* スタックトップの要素にアクセス */</span>
+<a id="__codelineno-22-45" name="__codelineno-22-45" href="#__codelineno-22-45"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-46" name="__codelineno-22-46" href="#__codelineno-22-46"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">stack_peek</span><span class="p">.</span><span class="n">as_ref</span><span class="p">()</span>
+<a id="__codelineno-22-47" name="__codelineno-22-47" href="#__codelineno-22-47"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-48" name="__codelineno-22-48" href="#__codelineno-22-48"></a>
+<a id="__codelineno-22-49" name="__codelineno-22-49" href="#__codelineno-22-49"></a><span class="w">    </span><span class="cm">/* List を Array に変換して返す */</span>
+<a id="__codelineno-22-50" name="__codelineno-22-50" href="#__codelineno-22-50"></a><span class="w">    </span><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">to_array</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-51" name="__codelineno-22-51" href="#__codelineno-22-51"></a><span class="w">        </span><span class="k">fn</span><span class="w"> </span><span class="nf">_to_array</span><span class="o">&lt;</span><span class="n">T</span><span class="p">:</span><span class="w"> </span><span class="nb">Sized</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nb">Copy</span><span class="o">&gt;</span><span class="p">(</span><span class="n">head</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;&gt;&gt;&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-52" name="__codelineno-22-52" href="#__codelineno-22-52"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-53" name="__codelineno-22-53" href="#__codelineno-22-53"></a><span class="w">                </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_to_array</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">next</span><span class="p">.</span><span class="n">as_ref</span><span class="p">());</span>
+<a id="__codelineno-22-54" name="__codelineno-22-54" href="#__codelineno-22-54"></a><span class="w">                </span><span class="n">nums</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-22-55" name="__codelineno-22-55" href="#__codelineno-22-55"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
+<a id="__codelineno-22-56" name="__codelineno-22-56" href="#__codelineno-22-56"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-22-57" name="__codelineno-22-57" href="#__codelineno-22-57"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-22-58" name="__codelineno-22-58" href="#__codelineno-22-58"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-59" name="__codelineno-22-59" href="#__codelineno-22-59"></a>
+<a id="__codelineno-22-60" name="__codelineno-22-60" href="#__codelineno-22-60"></a><span class="w">        </span><span class="n">_to_array</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">peek</span><span class="p">())</span>
+<a id="__codelineno-22-61" name="__codelineno-22-61" href="#__codelineno-22-61"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-62" name="__codelineno-22-62" href="#__codelineno-22-62"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_stack.kt</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">LinkedListStack</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">linkedlist_stack.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 連結リストベースのスタック */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">top</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードをスタックトップとする</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w">      </span><span class="c1">// スタックの長さ</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="p">}</span><span class="w"> </span><span class="n">LinkedListStack</span><span class="p">;</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="n">LinkedListStack</span><span class="w"> </span><span class="o">*</span><span class="nf">newLinkedListStack</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w">    </span><span class="n">LinkedListStack</span><span class="w"> </span><span class="o">*</span><span class="n">s</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">LinkedListStack</span><span class="p">));</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w">    </span><span class="n">s</span><span class="o">-&gt;</span><span class="n">top</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w">    </span><span class="n">s</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">s</span><span class="p">;</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="p">}</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a>
+<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="cm">/* デストラクタ */</span>
+<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="kt">void</span><span class="w"> </span><span class="nf">delLinkedListStack</span><span class="p">(</span><span class="n">LinkedListStack</span><span class="w"> </span><span class="o">*</span><span class="n">s</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="o">-&gt;</span><span class="n">top</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="o">-&gt;</span><span class="n">top</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="w">        </span><span class="n">free</span><span class="p">(</span><span class="n">s</span><span class="o">-&gt;</span><span class="n">top</span><span class="p">);</span>
+<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="w">        </span><span class="n">s</span><span class="o">-&gt;</span><span class="n">top</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
+<a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">s</span><span class="p">);</span>
+<a id="__codelineno-23-23" name="__codelineno-23-23" href="#__codelineno-23-23"></a><span class="p">}</span>
+<a id="__codelineno-23-24" name="__codelineno-23-24" href="#__codelineno-23-24"></a>
+<a id="__codelineno-23-25" name="__codelineno-23-25" href="#__codelineno-23-25"></a><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-23-26" name="__codelineno-23-26" href="#__codelineno-23-26"></a><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="n">LinkedListStack</span><span class="w"> </span><span class="o">*</span><span class="n">s</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-27" name="__codelineno-23-27" href="#__codelineno-23-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">s</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">;</span>
+<a id="__codelineno-23-28" name="__codelineno-23-28" href="#__codelineno-23-28"></a><span class="p">}</span>
+<a id="__codelineno-23-29" name="__codelineno-23-29" href="#__codelineno-23-29"></a>
+<a id="__codelineno-23-30" name="__codelineno-23-30" href="#__codelineno-23-30"></a><span class="cm">/* スタックが空かどうかを判定 */</span>
+<a id="__codelineno-23-31" name="__codelineno-23-31" href="#__codelineno-23-31"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">(</span><span class="n">LinkedListStack</span><span class="w"> </span><span class="o">*</span><span class="n">s</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-32" name="__codelineno-23-32" href="#__codelineno-23-32"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">s</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-23-33" name="__codelineno-23-33" href="#__codelineno-23-33"></a><span class="p">}</span>
+<a id="__codelineno-23-34" name="__codelineno-23-34" href="#__codelineno-23-34"></a>
+<a id="__codelineno-23-35" name="__codelineno-23-35" href="#__codelineno-23-35"></a><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-23-36" name="__codelineno-23-36" href="#__codelineno-23-36"></a><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">LinkedListStack</span><span class="w"> </span><span class="o">*</span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-37" name="__codelineno-23-37" href="#__codelineno-23-37"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">ListNode</span><span class="p">));</span>
+<a id="__codelineno-23-38" name="__codelineno-23-38" href="#__codelineno-23-38"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="o">-&gt;</span><span class="n">top</span><span class="p">;</span><span class="w"> </span><span class="c1">// 新しく追加したノードのポインタフィールドを更新</span>
+<a id="__codelineno-23-39" name="__codelineno-23-39" href="#__codelineno-23-39"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span><span class="w">     </span><span class="c1">// 新しく追加したノードのデータフィールドを更新</span>
+<a id="__codelineno-23-40" name="__codelineno-23-40" href="#__codelineno-23-40"></a><span class="w">    </span><span class="n">s</span><span class="o">-&gt;</span><span class="n">top</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w">       </span><span class="c1">// スタックトップを更新</span>
+<a id="__codelineno-23-41" name="__codelineno-23-41" href="#__codelineno-23-41"></a><span class="w">    </span><span class="n">s</span><span class="o">-&gt;</span><span class="n">size</span><span class="o">++</span><span class="p">;</span><span class="w">           </span><span class="c1">// スタックサイズを更新</span>
+<a id="__codelineno-23-42" name="__codelineno-23-42" href="#__codelineno-23-42"></a><span class="p">}</span>
+<a id="__codelineno-23-43" name="__codelineno-23-43" href="#__codelineno-23-43"></a>
+<a id="__codelineno-23-44" name="__codelineno-23-44" href="#__codelineno-23-44"></a><span class="cm">/* スタックトップの要素にアクセス */</span>
+<a id="__codelineno-23-45" name="__codelineno-23-45" href="#__codelineno-23-45"></a><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="n">LinkedListStack</span><span class="w"> </span><span class="o">*</span><span class="n">s</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-46" name="__codelineno-23-46" href="#__codelineno-23-46"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-47" name="__codelineno-23-47" href="#__codelineno-23-47"></a><span class="w">        </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;スタックは空です</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">);</span>
+<a id="__codelineno-23-48" name="__codelineno-23-48" href="#__codelineno-23-48"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">;</span>
+<a id="__codelineno-23-49" name="__codelineno-23-49" href="#__codelineno-23-49"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-50" name="__codelineno-23-50" href="#__codelineno-23-50"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">s</span><span class="o">-&gt;</span><span class="n">top</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-23-51" name="__codelineno-23-51" href="#__codelineno-23-51"></a><span class="p">}</span>
+<a id="__codelineno-23-52" name="__codelineno-23-52" href="#__codelineno-23-52"></a>
+<a id="__codelineno-23-53" name="__codelineno-23-53" href="#__codelineno-23-53"></a><span class="cm">/* ポップ */</span>
+<a id="__codelineno-23-54" name="__codelineno-23-54" href="#__codelineno-23-54"></a><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="n">LinkedListStack</span><span class="w"> </span><span class="o">*</span><span class="n">s</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-55" name="__codelineno-23-55" href="#__codelineno-23-55"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span><span class="p">(</span><span class="n">s</span><span class="p">);</span>
+<a id="__codelineno-23-56" name="__codelineno-23-56" href="#__codelineno-23-56"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="o">-&gt;</span><span class="n">top</span><span class="p">;</span>
+<a id="__codelineno-23-57" name="__codelineno-23-57" href="#__codelineno-23-57"></a><span class="w">    </span><span class="n">s</span><span class="o">-&gt;</span><span class="n">top</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="o">-&gt;</span><span class="n">top</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-23-58" name="__codelineno-23-58" href="#__codelineno-23-58"></a><span class="w">    </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-23-59" name="__codelineno-23-59" href="#__codelineno-23-59"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">tmp</span><span class="p">);</span>
+<a id="__codelineno-23-60" name="__codelineno-23-60" href="#__codelineno-23-60"></a><span class="w">    </span><span class="n">s</span><span class="o">-&gt;</span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-23-61" name="__codelineno-23-61" href="#__codelineno-23-61"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-23-62" name="__codelineno-23-62" href="#__codelineno-23-62"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">linkedlist_stack.rb</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">LinkedListStack</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">linkedlist_stack.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 連結リストベースのスタック */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">LinkedListStack</span><span class="p">(</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">stackPeek</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="c1">// 先頭ノードをスタックトップとする</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">stkSize</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="c1">// スタックの長さ</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w">    </span><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">size</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stkSize</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">    </span><span class="cm">/* スタックが空かどうかを判定 */</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">():</span><span class="w"> </span><span class="kt">Boolean</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a>
+<a id="__codelineno-24-17" name="__codelineno-24-17" href="#__codelineno-24-17"></a><span class="w">    </span><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-24-18" name="__codelineno-24-18" href="#__codelineno-24-18"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-19" name="__codelineno-24-19" href="#__codelineno-24-19"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-24-20" name="__codelineno-24-20" href="#__codelineno-24-20"></a><span class="w">        </span><span class="n">node</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackPeek</span>
+<a id="__codelineno-24-21" name="__codelineno-24-21" href="#__codelineno-24-21"></a><span class="w">        </span><span class="n">stackPeek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-24-22" name="__codelineno-24-22" href="#__codelineno-24-22"></a><span class="w">        </span><span class="n">stkSize</span><span class="o">++</span>
+<a id="__codelineno-24-23" name="__codelineno-24-23" href="#__codelineno-24-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-24" name="__codelineno-24-24" href="#__codelineno-24-24"></a>
+<a id="__codelineno-24-25" name="__codelineno-24-25" href="#__codelineno-24-25"></a><span class="w">    </span><span class="cm">/* ポップ */</span>
+<a id="__codelineno-24-26" name="__codelineno-24-26" href="#__codelineno-24-26"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">pop</span><span class="p">():</span><span class="w"> </span><span class="kt">Int?</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-27" name="__codelineno-24-27" href="#__codelineno-24-27"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span><span class="p">()</span>
+<a id="__codelineno-24-28" name="__codelineno-24-28" href="#__codelineno-24-28"></a><span class="w">        </span><span class="n">stackPeek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackPeek</span><span class="o">?.</span><span class="na">next</span>
+<a id="__codelineno-24-29" name="__codelineno-24-29" href="#__codelineno-24-29"></a><span class="w">        </span><span class="n">stkSize</span><span class="o">--</span>
+<a id="__codelineno-24-30" name="__codelineno-24-30" href="#__codelineno-24-30"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-24-31" name="__codelineno-24-31" href="#__codelineno-24-31"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-32" name="__codelineno-24-32" href="#__codelineno-24-32"></a>
+<a id="__codelineno-24-33" name="__codelineno-24-33" href="#__codelineno-24-33"></a><span class="w">    </span><span class="cm">/* スタックトップの要素にアクセス */</span>
+<a id="__codelineno-24-34" name="__codelineno-24-34" href="#__codelineno-24-34"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">peek</span><span class="p">():</span><span class="w"> </span><span class="kt">Int?</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-35" name="__codelineno-24-35" href="#__codelineno-24-35"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">()</span>
+<a id="__codelineno-24-36" name="__codelineno-24-36" href="#__codelineno-24-36"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stackPeek</span><span class="o">?.</span><span class="na">_val</span>
+<a id="__codelineno-24-37" name="__codelineno-24-37" href="#__codelineno-24-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-38" name="__codelineno-24-38" href="#__codelineno-24-38"></a>
+<a id="__codelineno-24-39" name="__codelineno-24-39" href="#__codelineno-24-39"></a><span class="w">    </span><span class="cm">/* List を Array に変換して返す */</span>
+<a id="__codelineno-24-40" name="__codelineno-24-40" href="#__codelineno-24-40"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">toArray</span><span class="p">():</span><span class="w"> </span><span class="n">IntArray</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-41" name="__codelineno-24-41" href="#__codelineno-24-41"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackPeek</span>
+<a id="__codelineno-24-42" name="__codelineno-24-42" href="#__codelineno-24-42"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">size</span><span class="p">())</span>
+<a id="__codelineno-24-43" name="__codelineno-24-43" href="#__codelineno-24-43"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="n">downTo</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-44" name="__codelineno-24-44" href="#__codelineno-24-44"></a><span class="w">            </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">?.</span><span class="na">_val</span><span class="o">!!</span>
+<a id="__codelineno-24-45" name="__codelineno-24-45" href="#__codelineno-24-45"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">next</span>
+<a id="__codelineno-24-46" name="__codelineno-24-46" href="#__codelineno-24-46"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-24-47" name="__codelineno-24-47" href="#__codelineno-24-47"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-24-48" name="__codelineno-24-48" href="#__codelineno-24-48"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-49" name="__codelineno-24-49" href="#__codelineno-24-49"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_stack.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### 連結リストで実装したスタック ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">LinkedListStack</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="kp">attr_reader</span><span class="w"> </span><span class="ss">:size</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">  </span><span class="c1">### コンストラクタ ###</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w">  </span><span class="c1">### スタックが空か判定 ###</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">is_empty?</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w">    </span><span class="vi">@peek</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a>
+<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w">  </span><span class="c1">### プッシュ ###</span>
+<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">ListNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a><span class="w">    </span><span class="n">node</span><span class="o">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@peek</span>
+<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="w">    </span><span class="vi">@peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a>
+<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="w">  </span><span class="c1">### ポップ ###</span>
+<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">pop</span>
+<a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a><span class="w">    </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span>
+<a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></a><span class="w">    </span><span class="vi">@peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@peek</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-25-27" name="__codelineno-25-27" href="#__codelineno-25-27"></a><span class="w">    </span><span class="vi">@size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-25-28" name="__codelineno-25-28" href="#__codelineno-25-28"></a><span class="w">    </span><span class="n">num</span>
+<a id="__codelineno-25-29" name="__codelineno-25-29" href="#__codelineno-25-29"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-30" name="__codelineno-25-30" href="#__codelineno-25-30"></a>
+<a id="__codelineno-25-31" name="__codelineno-25-31" href="#__codelineno-25-31"></a><span class="w">  </span><span class="c1">### スタックトップ要素を参照 ###</span>
+<a id="__codelineno-25-32" name="__codelineno-25-32" href="#__codelineno-25-32"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">peek</span>
+<a id="__codelineno-25-33" name="__codelineno-25-33" href="#__codelineno-25-33"></a><span class="w">    </span><span class="k">raise</span><span class="w"> </span><span class="no">IndexError</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;スタックは空です&#39;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_empty?</span>
+<a id="__codelineno-25-34" name="__codelineno-25-34" href="#__codelineno-25-34"></a>
+<a id="__codelineno-25-35" name="__codelineno-25-35" href="#__codelineno-25-35"></a><span class="w">    </span><span class="vi">@peek</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-25-36" name="__codelineno-25-36" href="#__codelineno-25-36"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-37" name="__codelineno-25-37" href="#__codelineno-25-37"></a>
+<a id="__codelineno-25-38" name="__codelineno-25-38" href="#__codelineno-25-38"></a><span class="w">  </span><span class="c1">### 連結リストを Array に変換して返す ###</span>
+<a id="__codelineno-25-39" name="__codelineno-25-39" href="#__codelineno-25-39"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">to_array</span>
+<a id="__codelineno-25-40" name="__codelineno-25-40" href="#__codelineno-25-40"></a><span class="w">    </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-25-41" name="__codelineno-25-41" href="#__codelineno-25-41"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@peek</span>
+<a id="__codelineno-25-42" name="__codelineno-25-42" href="#__codelineno-25-42"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-25-43" name="__codelineno-25-43" href="#__codelineno-25-43"></a><span class="w">      </span><span class="n">arr</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-25-44" name="__codelineno-25-44" href="#__codelineno-25-44"></a><span class="w">      </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-25-45" name="__codelineno-25-45" href="#__codelineno-25-45"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-25-46" name="__codelineno-25-46" href="#__codelineno-25-46"></a><span class="w">    </span><span class="n">arr</span><span class="o">.</span><span class="n">reverse</span>
+<a id="__codelineno-25-47" name="__codelineno-25-47" href="#__codelineno-25-47"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-48" name="__codelineno-25-48" href="#__codelineno-25-48"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h3 id="2">2. &nbsp; 配列ベースの実装<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>配列を使用してスタックを実装する場合、配列の末尾をスタックのトップと考えることができます。下図に示すように、プッシュとポップ操作は、それぞれ配列の末尾での要素の追加と削除に対応し、どちらも時間計算量<span class="arithmatex">\(O(1)\)</span>です。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" 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target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h3 id="2">2. &nbsp; 配列による実装<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>配列でスタックを実装する場合、配列の末尾をスタックトップとして扱えます。下図のように、プッシュとポップはそれぞれ配列末尾への要素追加と削除に対応し、どちらの時間計算量も <span class="arithmatex">\(O(1)\)</span> です。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="4:3"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">ArrayStack</label><label for="__tabbed_4_2">push()</label><label for="__tabbed_4_3">pop()</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="配列によるスタック実装のプッシュとポップ操作" class="animation-figure" src="../stack.assets/array_stack_step1.png" /></p>
+<p><img alt="配列によるスタック実装のプッシュ・ポップ操作" class="animation-figure" src="../stack.assets/array_stack_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="array_stack_push" class="animation-figure" src="../stack.assets/array_stack_step2_push.png" /></p>
@@ -5006,198 +5594,631 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 5-3 &nbsp; 配列によるスタック実装のプッシュとポップ操作 </p>
+<p align="center"> 図 5-3 &nbsp; 配列によるスタック実装のプッシュ・ポップ操作 </p>
 
-<p>スタックにプッシュされる要素が継続的に増加する可能性があるため、動的配列を使用でき、配列拡張を自分で処理する必要がありません。以下はサンプルコードです：</p>
+<p>プッシュされる要素は際限なく増える可能性があるため、動的配列を使えば、配列の拡張を自前で処理する必要がありません。以下にコード例を示します：</p>
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-<div class="highlight"><span class="filename">array_stack.py</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayStack</span><span class="p">:</span>
-<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;配列ベースのスタッククラス&quot;&quot;&quot;</span>
-<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a>
-<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
-<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_stack</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
-<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a>
-<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;スタックの長さを取得&quot;&quot;&quot;</span>
-<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a>        <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_stack</span><span class="p">)</span>
-<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a>
-<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">is_empty</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
-<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;スタックが空かどうかを判定&quot;&quot;&quot;</span>
-<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="o">==</span> <span class="mi">0</span>
-<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a>
-<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">item</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;プッシュ&quot;&quot;&quot;</span>
-<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_stack</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">item</span><span class="p">)</span>
-<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a>
-<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;ポップ&quot;&quot;&quot;</span>
-<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
-<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Stack is empty&quot;</span><span class="p">)</span>
-<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_stack</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
-<a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a>
-<a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-25-27" name="__codelineno-25-27" href="#__codelineno-25-27"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;スタックトップ要素にアクセス&quot;&quot;&quot;</span>
-<a id="__codelineno-25-28" name="__codelineno-25-28" href="#__codelineno-25-28"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
-<a id="__codelineno-25-29" name="__codelineno-25-29" href="#__codelineno-25-29"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Stack is empty&quot;</span><span class="p">)</span>
-<a id="__codelineno-25-30" name="__codelineno-25-30" href="#__codelineno-25-30"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_stack</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
-<a id="__codelineno-25-31" name="__codelineno-25-31" href="#__codelineno-25-31"></a>
-<a id="__codelineno-25-32" name="__codelineno-25-32" href="#__codelineno-25-32"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">to_list</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
-<a id="__codelineno-25-33" name="__codelineno-25-33" href="#__codelineno-25-33"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;出力用の配列を返す&quot;&quot;&quot;</span>
-<a id="__codelineno-25-34" name="__codelineno-25-34" href="#__codelineno-25-34"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_stack</span>
-</code></pre></div>
-</div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">array_stack.cpp</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="cm">/* 配列に基づくスタッククラス */</span>
-<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayStack</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
-<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">stack</span><span class="p">;</span>
-<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a>
-<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
-<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="w">    </span><span class="cm">/* スタックの長さを取得 */</span>
-<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
-<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="w">    </span><span class="p">}</span>
+<div class="highlight"><span class="filename">array_stack.py</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayStack</span><span class="p">:</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;配列ベースのスタック&quot;&quot;&quot;</span>
+<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>
+<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
+<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_stack</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a>
+<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;スタックの長さを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a>        <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_stack</span><span class="p">)</span>
 <a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a>
-<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="w">    </span><span class="cm">/* スタックが空かどうかを判定 */</span>
-<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="w">    </span><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a>
-<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a><span class="w">    </span><span class="cm">/* プッシュ */</span>
-<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a><span class="w">        </span><span class="n">stack</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
-<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a>
-<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a><span class="w">    </span><span class="cm">/* ポップ */</span>
-<a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-24" name="__codelineno-26-24" href="#__codelineno-26-24"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">top</span><span class="p">();</span>
-<a id="__codelineno-26-25" name="__codelineno-26-25" href="#__codelineno-26-25"></a><span class="w">        </span><span class="n">stack</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
-<a id="__codelineno-26-26" name="__codelineno-26-26" href="#__codelineno-26-26"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
-<a id="__codelineno-26-27" name="__codelineno-26-27" href="#__codelineno-26-27"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-28" name="__codelineno-26-28" href="#__codelineno-26-28"></a>
-<a id="__codelineno-26-29" name="__codelineno-26-29" href="#__codelineno-26-29"></a><span class="w">    </span><span class="cm">/* スタックトップ要素にアクセス */</span>
-<a id="__codelineno-26-30" name="__codelineno-26-30" href="#__codelineno-26-30"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">top</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-31" name="__codelineno-26-31" href="#__codelineno-26-31"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
-<a id="__codelineno-26-32" name="__codelineno-26-32" href="#__codelineno-26-32"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Stack is empty&quot;</span><span class="p">);</span>
-<a id="__codelineno-26-33" name="__codelineno-26-33" href="#__codelineno-26-33"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">back</span><span class="p">();</span>
-<a id="__codelineno-26-34" name="__codelineno-26-34" href="#__codelineno-26-34"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-35" name="__codelineno-26-35" href="#__codelineno-26-35"></a>
-<a id="__codelineno-26-36" name="__codelineno-26-36" href="#__codelineno-26-36"></a><span class="w">    </span><span class="cm">/* Vectorを返却 */</span>
-<a id="__codelineno-26-37" name="__codelineno-26-37" href="#__codelineno-26-37"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toVector</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-26-38" name="__codelineno-26-38" href="#__codelineno-26-38"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">;</span>
-<a id="__codelineno-26-39" name="__codelineno-26-39" href="#__codelineno-26-39"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-26-40" name="__codelineno-26-40" href="#__codelineno-26-40"></a><span class="p">};</span>
+<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">is_empty</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
+<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;スタックが空かどうかを判定&quot;&quot;&quot;</span>
+<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="o">==</span> <span class="mi">0</span>
+<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a>
+<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">item</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;プッシュ&quot;&quot;&quot;</span>
+<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_stack</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">item</span><span class="p">)</span>
+<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a>
+<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;ポップ&quot;&quot;&quot;</span>
+<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
+<a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;スタックが空です&quot;</span><span class="p">)</span>
+<a id="__codelineno-26-24" name="__codelineno-26-24" href="#__codelineno-26-24"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_stack</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
+<a id="__codelineno-26-25" name="__codelineno-26-25" href="#__codelineno-26-25"></a>
+<a id="__codelineno-26-26" name="__codelineno-26-26" href="#__codelineno-26-26"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-26-27" name="__codelineno-26-27" href="#__codelineno-26-27"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;スタックトップの要素にアクセス&quot;&quot;&quot;</span>
+<a id="__codelineno-26-28" name="__codelineno-26-28" href="#__codelineno-26-28"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
+<a id="__codelineno-26-29" name="__codelineno-26-29" href="#__codelineno-26-29"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;スタックが空です&quot;</span><span class="p">)</span>
+<a id="__codelineno-26-30" name="__codelineno-26-30" href="#__codelineno-26-30"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_stack</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-26-31" name="__codelineno-26-31" href="#__codelineno-26-31"></a>
+<a id="__codelineno-26-32" name="__codelineno-26-32" href="#__codelineno-26-32"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">to_list</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-26-33" name="__codelineno-26-33" href="#__codelineno-26-33"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;表示用のリストを返す&quot;&quot;&quot;</span>
+<a id="__codelineno-26-34" name="__codelineno-26-34" href="#__codelineno-26-34"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_stack</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_stack.java</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* 配列に基づくスタッククラス */</span>
-<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="kd">class</span> <span class="nc">ArrayStack</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">stack</span><span class="p">;</span>
-<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a>
-<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">ArrayStack</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w">        </span><span class="c1">// リスト（動的配列）を初期化</span>
-<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">        </span><span class="n">stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
-<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a>
-<a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a><span class="w">    </span><span class="cm">/* スタックの長さを取得 */</span>
-<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
-<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a>
-<a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="w">    </span><span class="cm">/* スタックが空かどうかを判定 */</span>
-<a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-17" name="__codelineno-27-17" href="#__codelineno-27-17"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-27-18" name="__codelineno-27-18" href="#__codelineno-27-18"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-19" name="__codelineno-27-19" href="#__codelineno-27-19"></a>
-<a id="__codelineno-27-20" name="__codelineno-27-20" href="#__codelineno-27-20"></a><span class="w">    </span><span class="cm">/* プッシュ */</span>
-<a id="__codelineno-27-21" name="__codelineno-27-21" href="#__codelineno-27-21"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-22" name="__codelineno-27-22" href="#__codelineno-27-22"></a><span class="w">        </span><span class="n">stack</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
-<a id="__codelineno-27-23" name="__codelineno-27-23" href="#__codelineno-27-23"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-24" name="__codelineno-27-24" href="#__codelineno-27-24"></a>
-<a id="__codelineno-27-25" name="__codelineno-27-25" href="#__codelineno-27-25"></a><span class="w">    </span><span class="cm">/* ポップ */</span>
-<a id="__codelineno-27-26" name="__codelineno-27-26" href="#__codelineno-27-26"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-27" name="__codelineno-27-27" href="#__codelineno-27-27"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
-<a id="__codelineno-27-28" name="__codelineno-27-28" href="#__codelineno-27-28"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
-<a id="__codelineno-27-29" name="__codelineno-27-29" href="#__codelineno-27-29"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-27-30" name="__codelineno-27-30" href="#__codelineno-27-30"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-31" name="__codelineno-27-31" href="#__codelineno-27-31"></a>
-<a id="__codelineno-27-32" name="__codelineno-27-32" href="#__codelineno-27-32"></a><span class="w">    </span><span class="cm">/* スタックトップ要素にアクセス */</span>
-<a id="__codelineno-27-33" name="__codelineno-27-33" href="#__codelineno-27-33"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-34" name="__codelineno-27-34" href="#__codelineno-27-34"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
-<a id="__codelineno-27-35" name="__codelineno-27-35" href="#__codelineno-27-35"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
-<a id="__codelineno-27-36" name="__codelineno-27-36" href="#__codelineno-27-36"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
-<a id="__codelineno-27-37" name="__codelineno-27-37" href="#__codelineno-27-37"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-38" name="__codelineno-27-38" href="#__codelineno-27-38"></a>
-<a id="__codelineno-27-39" name="__codelineno-27-39" href="#__codelineno-27-39"></a><span class="w">    </span><span class="cm">/* List を Array に変換して返す */</span>
-<a id="__codelineno-27-40" name="__codelineno-27-40" href="#__codelineno-27-40"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">Object</span><span class="o">[]</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-41" name="__codelineno-27-41" href="#__codelineno-27-41"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">toArray</span><span class="p">();</span>
-<a id="__codelineno-27-42" name="__codelineno-27-42" href="#__codelineno-27-42"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-43" name="__codelineno-27-43" href="#__codelineno-27-43"></a><span class="p">}</span>
+<div class="highlight"><span class="filename">array_stack.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* 配列ベースのスタック */</span>
+<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayStack</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
+<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">stack</span><span class="p">;</span>
+<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a>
+<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
+<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">    </span><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a>
+<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="w">    </span><span class="cm">/* スタックが空かどうかを判定 */</span>
+<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w">    </span><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></a>
+<a id="__codelineno-27-17" name="__codelineno-27-17" href="#__codelineno-27-17"></a><span class="w">    </span><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-27-18" name="__codelineno-27-18" href="#__codelineno-27-18"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-19" name="__codelineno-27-19" href="#__codelineno-27-19"></a><span class="w">        </span><span class="n">stack</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-27-20" name="__codelineno-27-20" href="#__codelineno-27-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-21" name="__codelineno-27-21" href="#__codelineno-27-21"></a>
+<a id="__codelineno-27-22" name="__codelineno-27-22" href="#__codelineno-27-22"></a><span class="w">    </span><span class="cm">/* ポップ */</span>
+<a id="__codelineno-27-23" name="__codelineno-27-23" href="#__codelineno-27-23"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-24" name="__codelineno-27-24" href="#__codelineno-27-24"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">top</span><span class="p">();</span>
+<a id="__codelineno-27-25" name="__codelineno-27-25" href="#__codelineno-27-25"></a><span class="w">        </span><span class="n">stack</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
+<a id="__codelineno-27-26" name="__codelineno-27-26" href="#__codelineno-27-26"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-27-27" name="__codelineno-27-27" href="#__codelineno-27-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-28" name="__codelineno-27-28" href="#__codelineno-27-28"></a>
+<a id="__codelineno-27-29" name="__codelineno-27-29" href="#__codelineno-27-29"></a><span class="w">    </span><span class="cm">/* スタックトップの要素にアクセス */</span>
+<a id="__codelineno-27-30" name="__codelineno-27-30" href="#__codelineno-27-30"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">top</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-31" name="__codelineno-27-31" href="#__codelineno-27-31"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-27-32" name="__codelineno-27-32" href="#__codelineno-27-32"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;スタックが空です&quot;</span><span class="p">);</span>
+<a id="__codelineno-27-33" name="__codelineno-27-33" href="#__codelineno-27-33"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">back</span><span class="p">();</span>
+<a id="__codelineno-27-34" name="__codelineno-27-34" href="#__codelineno-27-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-35" name="__codelineno-27-35" href="#__codelineno-27-35"></a>
+<a id="__codelineno-27-36" name="__codelineno-27-36" href="#__codelineno-27-36"></a><span class="w">    </span><span class="cm">/* Vector を返す */</span>
+<a id="__codelineno-27-37" name="__codelineno-27-37" href="#__codelineno-27-37"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toVector</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-38" name="__codelineno-27-38" href="#__codelineno-27-38"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">;</span>
+<a id="__codelineno-27-39" name="__codelineno-27-39" href="#__codelineno-27-39"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-40" name="__codelineno-27-40" href="#__codelineno-27-40"></a><span class="p">};</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_stack.cs</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">ArrayStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_stack.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 配列ベースのスタック */</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="kd">class</span> <span class="nc">ArrayStack</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">stack</span><span class="p">;</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">ArrayStack</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w">        </span><span class="c1">// リスト（動的配列）を初期化する</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">        </span><span class="n">stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a>
+<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="w">    </span><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
+<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a>
+<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="w">    </span><span class="cm">/* スタックが空かどうかを判定 */</span>
+<a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-28-18" name="__codelineno-28-18" href="#__codelineno-28-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-19" name="__codelineno-28-19" href="#__codelineno-28-19"></a>
+<a id="__codelineno-28-20" name="__codelineno-28-20" href="#__codelineno-28-20"></a><span class="w">    </span><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-28-21" name="__codelineno-28-21" href="#__codelineno-28-21"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-22" name="__codelineno-28-22" href="#__codelineno-28-22"></a><span class="w">        </span><span class="n">stack</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-28-23" name="__codelineno-28-23" href="#__codelineno-28-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-24" name="__codelineno-28-24" href="#__codelineno-28-24"></a>
+<a id="__codelineno-28-25" name="__codelineno-28-25" href="#__codelineno-28-25"></a><span class="w">    </span><span class="cm">/* ポップ */</span>
+<a id="__codelineno-28-26" name="__codelineno-28-26" href="#__codelineno-28-26"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-27" name="__codelineno-28-27" href="#__codelineno-28-27"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-28-28" name="__codelineno-28-28" href="#__codelineno-28-28"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
+<a id="__codelineno-28-29" name="__codelineno-28-29" href="#__codelineno-28-29"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-28-30" name="__codelineno-28-30" href="#__codelineno-28-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-31" name="__codelineno-28-31" href="#__codelineno-28-31"></a>
+<a id="__codelineno-28-32" name="__codelineno-28-32" href="#__codelineno-28-32"></a><span class="w">    </span><span class="cm">/* スタックトップの要素にアクセス */</span>
+<a id="__codelineno-28-33" name="__codelineno-28-33" href="#__codelineno-28-33"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-34" name="__codelineno-28-34" href="#__codelineno-28-34"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-28-35" name="__codelineno-28-35" href="#__codelineno-28-35"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
+<a id="__codelineno-28-36" name="__codelineno-28-36" href="#__codelineno-28-36"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-28-37" name="__codelineno-28-37" href="#__codelineno-28-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-38" name="__codelineno-28-38" href="#__codelineno-28-38"></a>
+<a id="__codelineno-28-39" name="__codelineno-28-39" href="#__codelineno-28-39"></a><span class="w">    </span><span class="cm">/* List を Array に変換して返す */</span>
+<a id="__codelineno-28-40" name="__codelineno-28-40" href="#__codelineno-28-40"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">Object</span><span class="o">[]</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-41" name="__codelineno-28-41" href="#__codelineno-28-41"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">toArray</span><span class="p">();</span>
+<a id="__codelineno-28-42" name="__codelineno-28-42" href="#__codelineno-28-42"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-43" name="__codelineno-28-43" href="#__codelineno-28-43"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_stack.go</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">arrayStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_stack.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 配列ベースのスタック */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayStack</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">stack</span><span class="p">;</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="nf">ArrayStack</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">        </span><span class="c1">// リスト（動的配列）を初期化する</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">        </span><span class="n">stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">    </span><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">Count</span><span class="p">;</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w">    </span><span class="cm">/* スタックが空かどうかを判定 */</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="nf">IsEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nf">Size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a>
+<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="w">    </span><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-29-20" name="__codelineno-29-20" href="#__codelineno-29-20"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">Push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-21" name="__codelineno-29-21" href="#__codelineno-29-21"></a><span class="w">        </span><span class="n">stack</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-29-22" name="__codelineno-29-22" href="#__codelineno-29-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-23" name="__codelineno-29-23" href="#__codelineno-29-23"></a>
+<a id="__codelineno-29-24" name="__codelineno-29-24" href="#__codelineno-29-24"></a><span class="w">    </span><span class="cm">/* ポップ */</span>
+<a id="__codelineno-29-25" name="__codelineno-29-25" href="#__codelineno-29-25"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-26" name="__codelineno-29-26" href="#__codelineno-29-26"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsEmpty</span><span class="p">())</span>
+<a id="__codelineno-29-27" name="__codelineno-29-27" href="#__codelineno-29-27"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="nf">Exception</span><span class="p">();</span>
+<a id="__codelineno-29-28" name="__codelineno-29-28" href="#__codelineno-29-28"></a><span class="w">        </span><span class="kt">var</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Peek</span><span class="p">();</span>
+<a id="__codelineno-29-29" name="__codelineno-29-29" href="#__codelineno-29-29"></a><span class="w">        </span><span class="n">stack</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="n">Size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-29-30" name="__codelineno-29-30" href="#__codelineno-29-30"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-29-31" name="__codelineno-29-31" href="#__codelineno-29-31"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-32" name="__codelineno-29-32" href="#__codelineno-29-32"></a>
+<a id="__codelineno-29-33" name="__codelineno-29-33" href="#__codelineno-29-33"></a><span class="w">    </span><span class="cm">/* スタックトップの要素にアクセス */</span>
+<a id="__codelineno-29-34" name="__codelineno-29-34" href="#__codelineno-29-34"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-35" name="__codelineno-29-35" href="#__codelineno-29-35"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsEmpty</span><span class="p">())</span>
+<a id="__codelineno-29-36" name="__codelineno-29-36" href="#__codelineno-29-36"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="nf">Exception</span><span class="p">();</span>
+<a id="__codelineno-29-37" name="__codelineno-29-37" href="#__codelineno-29-37"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">[</span><span class="n">Size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-29-38" name="__codelineno-29-38" href="#__codelineno-29-38"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-39" name="__codelineno-29-39" href="#__codelineno-29-39"></a>
+<a id="__codelineno-29-40" name="__codelineno-29-40" href="#__codelineno-29-40"></a><span class="w">    </span><span class="cm">/* List を Array に変換して返す */</span>
+<a id="__codelineno-29-41" name="__codelineno-29-41" href="#__codelineno-29-41"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="nf">ToArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-42" name="__codelineno-29-42" href="#__codelineno-29-42"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">[..</span><span class="w"> </span><span class="n">stack</span><span class="p">];</span>
+<a id="__codelineno-29-43" name="__codelineno-29-43" href="#__codelineno-29-43"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-44" name="__codelineno-29-44" href="#__codelineno-29-44"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_stack.swift</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">ArrayStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_stack.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 配列ベースのスタック */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">arrayStack</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="nx">data</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="w"> </span><span class="c1">// データ</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="p">}</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="cm">/* スタックを初期化 */</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="kd">func</span><span class="w"> </span><span class="nx">newArrayStack</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayStack</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">arrayStack</span><span class="p">{</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w">        </span><span class="c1">// スタックの長さを 0、容量を 16 に設定</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w">        </span><span class="nx">data</span><span class="p">:</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">16</span><span class="p">),</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="p">}</span>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="cm">/* スタックの長さ */</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayStack</span><span class="p">)</span><span class="w"> </span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">)</span>
+<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="p">}</span>
+<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a>
+<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="cm">/* スタックが空かどうか */</span>
+<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayStack</span><span class="p">)</span><span class="w"> </span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-21" name="__codelineno-30-21" href="#__codelineno-30-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-30-22" name="__codelineno-30-22" href="#__codelineno-30-22"></a><span class="p">}</span>
+<a id="__codelineno-30-23" name="__codelineno-30-23" href="#__codelineno-30-23"></a>
+<a id="__codelineno-30-24" name="__codelineno-30-24" href="#__codelineno-30-24"></a><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-30-25" name="__codelineno-30-25" href="#__codelineno-30-25"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayStack</span><span class="p">)</span><span class="w"> </span><span class="nx">push</span><span class="p">(</span><span class="nx">v</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-26" name="__codelineno-30-26" href="#__codelineno-30-26"></a><span class="w">    </span><span class="c1">// スライスは自動で拡張される</span>
+<a id="__codelineno-30-27" name="__codelineno-30-27" href="#__codelineno-30-27"></a><span class="w">    </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">,</span><span class="w"> </span><span class="nx">v</span><span class="p">)</span>
+<a id="__codelineno-30-28" name="__codelineno-30-28" href="#__codelineno-30-28"></a><span class="p">}</span>
+<a id="__codelineno-30-29" name="__codelineno-30-29" href="#__codelineno-30-29"></a>
+<a id="__codelineno-30-30" name="__codelineno-30-30" href="#__codelineno-30-30"></a><span class="cm">/* ポップ */</span>
+<a id="__codelineno-30-31" name="__codelineno-30-31" href="#__codelineno-30-31"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayStack</span><span class="p">)</span><span class="w"> </span><span class="nx">pop</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-32" name="__codelineno-30-32" href="#__codelineno-30-32"></a><span class="w">    </span><span class="nx">val</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">peek</span><span class="p">()</span>
+<a id="__codelineno-30-33" name="__codelineno-30-33" href="#__codelineno-30-33"></a><span class="w">    </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">[:</span><span class="nb">len</span><span class="p">(</span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-30-34" name="__codelineno-30-34" href="#__codelineno-30-34"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">val</span>
+<a id="__codelineno-30-35" name="__codelineno-30-35" href="#__codelineno-30-35"></a><span class="p">}</span>
+<a id="__codelineno-30-36" name="__codelineno-30-36" href="#__codelineno-30-36"></a>
+<a id="__codelineno-30-37" name="__codelineno-30-37" href="#__codelineno-30-37"></a><span class="cm">/* スタックトップ要素を取得する */</span>
+<a id="__codelineno-30-38" name="__codelineno-30-38" href="#__codelineno-30-38"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayStack</span><span class="p">)</span><span class="w"> </span><span class="nx">peek</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-39" name="__codelineno-30-39" href="#__codelineno-30-39"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-40" name="__codelineno-30-40" href="#__codelineno-30-40"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-30-41" name="__codelineno-30-41" href="#__codelineno-30-41"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-42" name="__codelineno-30-42" href="#__codelineno-30-42"></a><span class="w">    </span><span class="nx">val</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nb">len</span><span class="p">(</span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-30-43" name="__codelineno-30-43" href="#__codelineno-30-43"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">val</span>
+<a id="__codelineno-30-44" name="__codelineno-30-44" href="#__codelineno-30-44"></a><span class="p">}</span>
+<a id="__codelineno-30-45" name="__codelineno-30-45" href="#__codelineno-30-45"></a>
+<a id="__codelineno-30-46" name="__codelineno-30-46" href="#__codelineno-30-46"></a><span class="cm">/* 表示用に Slice を取得 */</span>
+<a id="__codelineno-30-47" name="__codelineno-30-47" href="#__codelineno-30-47"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayStack</span><span class="p">)</span><span class="w"> </span><span class="nx">toSlice</span><span class="p">()</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-48" name="__codelineno-30-48" href="#__codelineno-30-48"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">data</span>
+<a id="__codelineno-30-49" name="__codelineno-30-49" href="#__codelineno-30-49"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_stack.js</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_stack.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* 配列ベースのスタック */</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ArrayStack</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">stack</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span>
+<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a>
+<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w">    </span><span class="kd">init</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w">        </span><span class="c1">// リスト（動的配列）を初期化する</span>
+<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w">        </span><span class="n">stack</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
+<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a>
+<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a><span class="w">    </span><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="w">        </span><span class="n">stack</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a>
+<a id="__codelineno-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></a><span class="w">    </span><span class="cm">/* スタックが空かどうかを判定 */</span>
+<a id="__codelineno-31-16" name="__codelineno-31-16" href="#__codelineno-31-16"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-17" name="__codelineno-31-17" href="#__codelineno-31-17"></a><span class="w">        </span><span class="n">stack</span><span class="p">.</span><span class="bp">isEmpty</span>
+<a id="__codelineno-31-18" name="__codelineno-31-18" href="#__codelineno-31-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-19" name="__codelineno-31-19" href="#__codelineno-31-19"></a>
+<a id="__codelineno-31-20" name="__codelineno-31-20" href="#__codelineno-31-20"></a><span class="w">    </span><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-31-21" name="__codelineno-31-21" href="#__codelineno-31-21"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-22" name="__codelineno-31-22" href="#__codelineno-31-22"></a><span class="w">        </span><span class="n">stack</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-31-23" name="__codelineno-31-23" href="#__codelineno-31-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-24" name="__codelineno-31-24" href="#__codelineno-31-24"></a>
+<a id="__codelineno-31-25" name="__codelineno-31-25" href="#__codelineno-31-25"></a><span class="w">    </span><span class="cm">/* ポップ */</span>
+<a id="__codelineno-31-26" name="__codelineno-31-26" href="#__codelineno-31-26"></a><span class="w">    </span><span class="p">@</span><span class="n">discardableResult</span>
+<a id="__codelineno-31-27" name="__codelineno-31-27" href="#__codelineno-31-27"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-28" name="__codelineno-31-28" href="#__codelineno-31-28"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-29" name="__codelineno-31-29" href="#__codelineno-31-29"></a><span class="w">            </span><span class="bp">fatalError</span><span class="p">(</span><span class="s">&quot;スタックが空です&quot;</span><span class="p">)</span>
+<a id="__codelineno-31-30" name="__codelineno-31-30" href="#__codelineno-31-30"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-31-31" name="__codelineno-31-31" href="#__codelineno-31-31"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="bp">removeLast</span><span class="p">()</span>
+<a id="__codelineno-31-32" name="__codelineno-31-32" href="#__codelineno-31-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-33" name="__codelineno-31-33" href="#__codelineno-31-33"></a>
+<a id="__codelineno-31-34" name="__codelineno-31-34" href="#__codelineno-31-34"></a><span class="w">    </span><span class="cm">/* スタックトップの要素にアクセス */</span>
+<a id="__codelineno-31-35" name="__codelineno-31-35" href="#__codelineno-31-35"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-36" name="__codelineno-31-36" href="#__codelineno-31-36"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-37" name="__codelineno-31-37" href="#__codelineno-31-37"></a><span class="w">            </span><span class="bp">fatalError</span><span class="p">(</span><span class="s">&quot;スタックが空です&quot;</span><span class="p">)</span>
+<a id="__codelineno-31-38" name="__codelineno-31-38" href="#__codelineno-31-38"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-31-39" name="__codelineno-31-39" href="#__codelineno-31-39"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="bp">last</span><span class="p">!</span>
+<a id="__codelineno-31-40" name="__codelineno-31-40" href="#__codelineno-31-40"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-41" name="__codelineno-31-41" href="#__codelineno-31-41"></a>
+<a id="__codelineno-31-42" name="__codelineno-31-42" href="#__codelineno-31-42"></a><span class="w">    </span><span class="cm">/* List を Array に変換して返す */</span>
+<a id="__codelineno-31-43" name="__codelineno-31-43" href="#__codelineno-31-43"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-44" name="__codelineno-31-44" href="#__codelineno-31-44"></a><span class="w">        </span><span class="n">stack</span>
+<a id="__codelineno-31-45" name="__codelineno-31-45" href="#__codelineno-31-45"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-46" name="__codelineno-31-46" href="#__codelineno-31-46"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_stack.ts</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_stack.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* 配列ベースのスタック */</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">ArrayStack</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w">    </span><span class="n">#stack</span><span class="p">;</span>
+<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a>
+<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w">    </span><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="w">    </span><span class="nx">get</span><span class="w"> </span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-10" name="__codelineno-32-10" href="#__codelineno-32-10"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#stack</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a>
+<a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a><span class="w">    </span><span class="cm">/* スタックが空かどうかを判定 */</span>
+<a id="__codelineno-32-14" name="__codelineno-32-14" href="#__codelineno-32-14"></a><span class="w">    </span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-15" name="__codelineno-32-15" href="#__codelineno-32-15"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#stack</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-32-16" name="__codelineno-32-16" href="#__codelineno-32-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-17" name="__codelineno-32-17" href="#__codelineno-32-17"></a>
+<a id="__codelineno-32-18" name="__codelineno-32-18" href="#__codelineno-32-18"></a><span class="w">    </span><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-32-19" name="__codelineno-32-19" href="#__codelineno-32-19"></a><span class="w">    </span><span class="nx">push</span><span class="p">(</span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-20" name="__codelineno-32-20" href="#__codelineno-32-20"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#stack</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">num</span><span class="p">);</span>
+<a id="__codelineno-32-21" name="__codelineno-32-21" href="#__codelineno-32-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-22" name="__codelineno-32-22" href="#__codelineno-32-22"></a>
+<a id="__codelineno-32-23" name="__codelineno-32-23" href="#__codelineno-32-23"></a><span class="w">    </span><span class="cm">/* ポップ */</span>
+<a id="__codelineno-32-24" name="__codelineno-32-24" href="#__codelineno-32-24"></a><span class="w">    </span><span class="nx">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-25" name="__codelineno-32-25" href="#__codelineno-32-25"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;スタックが空&#39;</span><span class="p">);</span>
+<a id="__codelineno-32-26" name="__codelineno-32-26" href="#__codelineno-32-26"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#stack</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-32-27" name="__codelineno-32-27" href="#__codelineno-32-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-28" name="__codelineno-32-28" href="#__codelineno-32-28"></a>
+<a id="__codelineno-32-29" name="__codelineno-32-29" href="#__codelineno-32-29"></a><span class="w">    </span><span class="cm">/* スタックトップの要素にアクセス */</span>
+<a id="__codelineno-32-30" name="__codelineno-32-30" href="#__codelineno-32-30"></a><span class="w">    </span><span class="nx">top</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-31" name="__codelineno-32-31" href="#__codelineno-32-31"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;スタックが空&#39;</span><span class="p">);</span>
+<a id="__codelineno-32-32" name="__codelineno-32-32" href="#__codelineno-32-32"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#stack</span><span class="p">[</span><span class="k">this</span><span class="p">.</span><span class="n">#stack</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-32-33" name="__codelineno-32-33" href="#__codelineno-32-33"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-34" name="__codelineno-32-34" href="#__codelineno-32-34"></a>
+<a id="__codelineno-32-35" name="__codelineno-32-35" href="#__codelineno-32-35"></a><span class="w">    </span><span class="cm">/* Array を返す */</span>
+<a id="__codelineno-32-36" name="__codelineno-32-36" href="#__codelineno-32-36"></a><span class="w">    </span><span class="nx">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-37" name="__codelineno-32-37" href="#__codelineno-32-37"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#stack</span><span class="p">;</span>
+<a id="__codelineno-32-38" name="__codelineno-32-38" href="#__codelineno-32-38"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-39" name="__codelineno-32-39" href="#__codelineno-32-39"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_stack.dart</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_stack.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* 配列ベースのスタック */</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">ArrayStack</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w">    </span><span class="k">private</span><span class="w"> </span><span class="nx">stack</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[];</span>
+<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a>
+<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w">    </span><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="w">    </span><span class="nx">get</span><span class="w"> </span><span class="nx">size</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">stack</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a>
+<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a><span class="w">    </span><span class="cm">/* スタックが空かどうかを判定 */</span>
+<a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a><span class="w">    </span><span class="nx">isEmpty</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">stack</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-33-16" name="__codelineno-33-16" href="#__codelineno-33-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-17" name="__codelineno-33-17" href="#__codelineno-33-17"></a>
+<a id="__codelineno-33-18" name="__codelineno-33-18" href="#__codelineno-33-18"></a><span class="w">    </span><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-33-19" name="__codelineno-33-19" href="#__codelineno-33-19"></a><span class="w">    </span><span class="nx">push</span><span class="p">(</span><span class="nx">num</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-20" name="__codelineno-33-20" href="#__codelineno-33-20"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">stack</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">num</span><span class="p">);</span>
+<a id="__codelineno-33-21" name="__codelineno-33-21" href="#__codelineno-33-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-22" name="__codelineno-33-22" href="#__codelineno-33-22"></a>
+<a id="__codelineno-33-23" name="__codelineno-33-23" href="#__codelineno-33-23"></a><span class="w">    </span><span class="cm">/* ポップ */</span>
+<a id="__codelineno-33-24" name="__codelineno-33-24" href="#__codelineno-33-24"></a><span class="w">    </span><span class="nx">pop</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-25" name="__codelineno-33-25" href="#__codelineno-33-25"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;スタックが空です&#39;</span><span class="p">);</span>
+<a id="__codelineno-33-26" name="__codelineno-33-26" href="#__codelineno-33-26"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">stack</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-33-27" name="__codelineno-33-27" href="#__codelineno-33-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-28" name="__codelineno-33-28" href="#__codelineno-33-28"></a>
+<a id="__codelineno-33-29" name="__codelineno-33-29" href="#__codelineno-33-29"></a><span class="w">    </span><span class="cm">/* スタックトップの要素にアクセス */</span>
+<a id="__codelineno-33-30" name="__codelineno-33-30" href="#__codelineno-33-30"></a><span class="w">    </span><span class="nx">top</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-31" name="__codelineno-33-31" href="#__codelineno-33-31"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;スタックが空です&#39;</span><span class="p">);</span>
+<a id="__codelineno-33-32" name="__codelineno-33-32" href="#__codelineno-33-32"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">stack</span><span class="p">[</span><span class="k">this</span><span class="p">.</span><span class="nx">stack</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-33-33" name="__codelineno-33-33" href="#__codelineno-33-33"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-34" name="__codelineno-33-34" href="#__codelineno-33-34"></a>
+<a id="__codelineno-33-35" name="__codelineno-33-35" href="#__codelineno-33-35"></a><span class="w">    </span><span class="cm">/* Array を返す */</span>
+<a id="__codelineno-33-36" name="__codelineno-33-36" href="#__codelineno-33-36"></a><span class="w">    </span><span class="nx">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-37" name="__codelineno-33-37" href="#__codelineno-33-37"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">stack</span><span class="p">;</span>
+<a id="__codelineno-33-38" name="__codelineno-33-38" href="#__codelineno-33-38"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-39" name="__codelineno-33-39" href="#__codelineno-33-39"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_stack.rs</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_stack.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* 配列ベースのスタック */</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ArrayStack</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w">  </span><span class="kd">late</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">_stack</span><span class="p">;</span>
+<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w">  </span><span class="n">ArrayStack</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w">    </span><span class="n">_stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a>
+<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w">  </span><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-10" name="__codelineno-34-10" href="#__codelineno-34-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_stack</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-34-11" name="__codelineno-34-11" href="#__codelineno-34-11"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-12" name="__codelineno-34-12" href="#__codelineno-34-12"></a>
+<a id="__codelineno-34-13" name="__codelineno-34-13" href="#__codelineno-34-13"></a><span class="w">  </span><span class="cm">/* スタックが空かどうかを判定 */</span>
+<a id="__codelineno-34-14" name="__codelineno-34-14" href="#__codelineno-34-14"></a><span class="w">  </span><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-15" name="__codelineno-34-15" href="#__codelineno-34-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_stack</span><span class="p">.</span><span class="n">isEmpty</span><span class="p">;</span>
+<a id="__codelineno-34-16" name="__codelineno-34-16" href="#__codelineno-34-16"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-17" name="__codelineno-34-17" href="#__codelineno-34-17"></a>
+<a id="__codelineno-34-18" name="__codelineno-34-18" href="#__codelineno-34-18"></a><span class="w">  </span><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-34-19" name="__codelineno-34-19" href="#__codelineno-34-19"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-20" name="__codelineno-34-20" href="#__codelineno-34-20"></a><span class="w">    </span><span class="n">_stack</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">_num</span><span class="p">);</span>
+<a id="__codelineno-34-21" name="__codelineno-34-21" href="#__codelineno-34-21"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-22" name="__codelineno-34-22" href="#__codelineno-34-22"></a>
+<a id="__codelineno-34-23" name="__codelineno-34-23" href="#__codelineno-34-23"></a><span class="w">  </span><span class="cm">/* ポップ */</span>
+<a id="__codelineno-34-24" name="__codelineno-34-24" href="#__codelineno-34-24"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-25" name="__codelineno-34-25" href="#__codelineno-34-25"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-26" name="__codelineno-34-26" href="#__codelineno-34-26"></a><span class="w">      </span><span class="k">throw</span><span class="w"> </span><span class="n">Exception</span><span class="p">(</span><span class="s2">&quot;スタックが空です&quot;</span><span class="p">);</span>
+<a id="__codelineno-34-27" name="__codelineno-34-27" href="#__codelineno-34-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-28" name="__codelineno-34-28" href="#__codelineno-34-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_stack</span><span class="p">.</span><span class="n">removeLast</span><span class="p">();</span>
+<a id="__codelineno-34-29" name="__codelineno-34-29" href="#__codelineno-34-29"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-30" name="__codelineno-34-30" href="#__codelineno-34-30"></a>
+<a id="__codelineno-34-31" name="__codelineno-34-31" href="#__codelineno-34-31"></a><span class="w">  </span><span class="cm">/* スタックトップの要素にアクセス */</span>
+<a id="__codelineno-34-32" name="__codelineno-34-32" href="#__codelineno-34-32"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-33" name="__codelineno-34-33" href="#__codelineno-34-33"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-34" name="__codelineno-34-34" href="#__codelineno-34-34"></a><span class="w">      </span><span class="k">throw</span><span class="w"> </span><span class="n">Exception</span><span class="p">(</span><span class="s2">&quot;スタックが空です&quot;</span><span class="p">);</span>
+<a id="__codelineno-34-35" name="__codelineno-34-35" href="#__codelineno-34-35"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-36" name="__codelineno-34-36" href="#__codelineno-34-36"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_stack</span><span class="p">.</span><span class="n">last</span><span class="p">;</span>
+<a id="__codelineno-34-37" name="__codelineno-34-37" href="#__codelineno-34-37"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-38" name="__codelineno-34-38" href="#__codelineno-34-38"></a>
+<a id="__codelineno-34-39" name="__codelineno-34-39" href="#__codelineno-34-39"></a><span class="w">  </span><span class="cm">/* スタックを Array に変換して返す */</span>
+<a id="__codelineno-34-40" name="__codelineno-34-40" href="#__codelineno-34-40"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toArray</span><span class="p">()</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">_stack</span><span class="p">;</span>
+<a id="__codelineno-34-41" name="__codelineno-34-41" href="#__codelineno-34-41"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_stack.c</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_stack.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* 配列ベースのスタック */</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">ArrayStack</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w">    </span><span class="n">stack</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="p">}</span>
+<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a>
+<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="k">impl</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="n">ArrayStack</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="w">    </span><span class="cm">/* スタックを初期化 */</span>
+<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">new</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">ArrayStack</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="w">        </span><span class="n">ArrayStack</span><span class="p">::</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="w">            </span><span class="n">stack</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="p">::</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="p">::</span><span class="n">new</span><span class="p">(),</span>
+<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-35-12" name="__codelineno-35-12" href="#__codelineno-35-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-13" name="__codelineno-35-13" href="#__codelineno-35-13"></a>
+<a id="__codelineno-35-14" name="__codelineno-35-14" href="#__codelineno-35-14"></a><span class="w">    </span><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-35-15" name="__codelineno-35-15" href="#__codelineno-35-15"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-16" name="__codelineno-35-16" href="#__codelineno-35-16"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">stack</span><span class="p">.</span><span class="n">len</span><span class="p">()</span>
+<a id="__codelineno-35-17" name="__codelineno-35-17" href="#__codelineno-35-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-18" name="__codelineno-35-18" href="#__codelineno-35-18"></a>
+<a id="__codelineno-35-19" name="__codelineno-35-19" href="#__codelineno-35-19"></a><span class="w">    </span><span class="cm">/* スタックが空かどうかを判定 */</span>
+<a id="__codelineno-35-20" name="__codelineno-35-20" href="#__codelineno-35-20"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">is_empty</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-21" name="__codelineno-35-21" href="#__codelineno-35-21"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-35-22" name="__codelineno-35-22" href="#__codelineno-35-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-23" name="__codelineno-35-23" href="#__codelineno-35-23"></a>
+<a id="__codelineno-35-24" name="__codelineno-35-24" href="#__codelineno-35-24"></a><span class="w">    </span><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-35-25" name="__codelineno-35-25" href="#__codelineno-35-25"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nc">T</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-26" name="__codelineno-35-26" href="#__codelineno-35-26"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">stack</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-35-27" name="__codelineno-35-27" href="#__codelineno-35-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-28" name="__codelineno-35-28" href="#__codelineno-35-28"></a>
+<a id="__codelineno-35-29" name="__codelineno-35-29" href="#__codelineno-35-29"></a><span class="w">    </span><span class="cm">/* ポップ */</span>
+<a id="__codelineno-35-30" name="__codelineno-35-30" href="#__codelineno-35-30"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-31" name="__codelineno-35-31" href="#__codelineno-35-31"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">stack</span><span class="p">.</span><span class="n">pop</span><span class="p">()</span>
+<a id="__codelineno-35-32" name="__codelineno-35-32" href="#__codelineno-35-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-33" name="__codelineno-35-33" href="#__codelineno-35-33"></a>
+<a id="__codelineno-35-34" name="__codelineno-35-34" href="#__codelineno-35-34"></a><span class="w">    </span><span class="cm">/* スタックトップの要素にアクセス */</span>
+<a id="__codelineno-35-35" name="__codelineno-35-35" href="#__codelineno-35-35"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-36" name="__codelineno-35-36" href="#__codelineno-35-36"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">is_empty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-37" name="__codelineno-35-37" href="#__codelineno-35-37"></a><span class="w">            </span><span class="fm">panic!</span><span class="p">(</span><span class="s">&quot;スタックが空です&quot;</span><span class="p">)</span>
+<a id="__codelineno-35-38" name="__codelineno-35-38" href="#__codelineno-35-38"></a><span class="w">        </span><span class="p">};</span>
+<a id="__codelineno-35-39" name="__codelineno-35-39" href="#__codelineno-35-39"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">stack</span><span class="p">.</span><span class="n">last</span><span class="p">()</span>
+<a id="__codelineno-35-40" name="__codelineno-35-40" href="#__codelineno-35-40"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-41" name="__codelineno-35-41" href="#__codelineno-35-41"></a>
+<a id="__codelineno-35-42" name="__codelineno-35-42" href="#__codelineno-35-42"></a><span class="w">    </span><span class="cm">/* &amp;Vec を返す */</span>
+<a id="__codelineno-35-43" name="__codelineno-35-43" href="#__codelineno-35-43"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">to_array</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kp">&amp;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-44" name="__codelineno-35-44" href="#__codelineno-35-44"></a><span class="w">        </span><span class="o">&amp;</span><span class="bp">self</span><span class="p">.</span><span class="n">stack</span>
+<a id="__codelineno-35-45" name="__codelineno-35-45" href="#__codelineno-35-45"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-46" name="__codelineno-35-46" href="#__codelineno-35-46"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_stack.kt</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">ArrayStack</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">array_stack.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* 配列ベースのスタック */</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">data</span><span class="p">;</span>
+<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span>
+<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="p">}</span><span class="w"> </span><span class="n">ArrayStack</span><span class="p">;</span>
+<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a>
+<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="n">ArrayStack</span><span class="w"> </span><span class="o">*</span><span class="nf">newArrayStack</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="w">    </span><span class="n">ArrayStack</span><span class="w"> </span><span class="o">*</span><span class="n">stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">ArrayStack</span><span class="p">));</span>
+<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a><span class="w">    </span><span class="c1">// 大きめの容量で初期化し、拡張を避ける</span>
+<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a><span class="w">    </span><span class="n">stack</span><span class="o">-&gt;</span><span class="n">data</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">);</span>
+<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a><span class="w">    </span><span class="n">stack</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">;</span>
+<a id="__codelineno-36-14" name="__codelineno-36-14" href="#__codelineno-36-14"></a><span class="p">}</span>
+<a id="__codelineno-36-15" name="__codelineno-36-15" href="#__codelineno-36-15"></a>
+<a id="__codelineno-36-16" name="__codelineno-36-16" href="#__codelineno-36-16"></a><span class="cm">/* デストラクタ */</span>
+<a id="__codelineno-36-17" name="__codelineno-36-17" href="#__codelineno-36-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">delArrayStack</span><span class="p">(</span><span class="n">ArrayStack</span><span class="w"> </span><span class="o">*</span><span class="n">stack</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-18" name="__codelineno-36-18" href="#__codelineno-36-18"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">stack</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">);</span>
+<a id="__codelineno-36-19" name="__codelineno-36-19" href="#__codelineno-36-19"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">stack</span><span class="p">);</span>
+<a id="__codelineno-36-20" name="__codelineno-36-20" href="#__codelineno-36-20"></a><span class="p">}</span>
+<a id="__codelineno-36-21" name="__codelineno-36-21" href="#__codelineno-36-21"></a>
+<a id="__codelineno-36-22" name="__codelineno-36-22" href="#__codelineno-36-22"></a><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-36-23" name="__codelineno-36-23" href="#__codelineno-36-23"></a><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="n">ArrayStack</span><span class="w"> </span><span class="o">*</span><span class="n">stack</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-24" name="__codelineno-36-24" href="#__codelineno-36-24"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">;</span>
+<a id="__codelineno-36-25" name="__codelineno-36-25" href="#__codelineno-36-25"></a><span class="p">}</span>
+<a id="__codelineno-36-26" name="__codelineno-36-26" href="#__codelineno-36-26"></a>
+<a id="__codelineno-36-27" name="__codelineno-36-27" href="#__codelineno-36-27"></a><span class="cm">/* スタックが空かどうかを判定 */</span>
+<a id="__codelineno-36-28" name="__codelineno-36-28" href="#__codelineno-36-28"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">(</span><span class="n">ArrayStack</span><span class="w"> </span><span class="o">*</span><span class="n">stack</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-29" name="__codelineno-36-29" href="#__codelineno-36-29"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-36-30" name="__codelineno-36-30" href="#__codelineno-36-30"></a><span class="p">}</span>
+<a id="__codelineno-36-31" name="__codelineno-36-31" href="#__codelineno-36-31"></a>
+<a id="__codelineno-36-32" name="__codelineno-36-32" href="#__codelineno-36-32"></a><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-36-33" name="__codelineno-36-33" href="#__codelineno-36-33"></a><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">ArrayStack</span><span class="w"> </span><span class="o">*</span><span class="n">stack</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-34" name="__codelineno-36-34" href="#__codelineno-36-34"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">stack</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-35" name="__codelineno-36-35" href="#__codelineno-36-35"></a><span class="w">        </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;スタックは満杯です</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">);</span>
+<a id="__codelineno-36-36" name="__codelineno-36-36" href="#__codelineno-36-36"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-36-37" name="__codelineno-36-37" href="#__codelineno-36-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-38" name="__codelineno-36-38" href="#__codelineno-36-38"></a><span class="w">    </span><span class="n">stack</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="n">stack</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-36-39" name="__codelineno-36-39" href="#__codelineno-36-39"></a><span class="w">    </span><span class="n">stack</span><span class="o">-&gt;</span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-36-40" name="__codelineno-36-40" href="#__codelineno-36-40"></a><span class="p">}</span>
+<a id="__codelineno-36-41" name="__codelineno-36-41" href="#__codelineno-36-41"></a>
+<a id="__codelineno-36-42" name="__codelineno-36-42" href="#__codelineno-36-42"></a><span class="cm">/* スタックトップの要素にアクセス */</span>
+<a id="__codelineno-36-43" name="__codelineno-36-43" href="#__codelineno-36-43"></a><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="n">ArrayStack</span><span class="w"> </span><span class="o">*</span><span class="n">stack</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-44" name="__codelineno-36-44" href="#__codelineno-36-44"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">stack</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-45" name="__codelineno-36-45" href="#__codelineno-36-45"></a><span class="w">        </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;スタックは空です</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">);</span>
+<a id="__codelineno-36-46" name="__codelineno-36-46" href="#__codelineno-36-46"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">;</span>
+<a id="__codelineno-36-47" name="__codelineno-36-47" href="#__codelineno-36-47"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-48" name="__codelineno-36-48" href="#__codelineno-36-48"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="n">stack</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-36-49" name="__codelineno-36-49" href="#__codelineno-36-49"></a><span class="p">}</span>
+<a id="__codelineno-36-50" name="__codelineno-36-50" href="#__codelineno-36-50"></a>
+<a id="__codelineno-36-51" name="__codelineno-36-51" href="#__codelineno-36-51"></a><span class="cm">/* ポップ */</span>
+<a id="__codelineno-36-52" name="__codelineno-36-52" href="#__codelineno-36-52"></a><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="n">ArrayStack</span><span class="w"> </span><span class="o">*</span><span class="n">stack</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-53" name="__codelineno-36-53" href="#__codelineno-36-53"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span><span class="p">(</span><span class="n">stack</span><span class="p">);</span>
+<a id="__codelineno-36-54" name="__codelineno-36-54" href="#__codelineno-36-54"></a><span class="w">    </span><span class="n">stack</span><span class="o">-&gt;</span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-36-55" name="__codelineno-36-55" href="#__codelineno-36-55"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-36-56" name="__codelineno-36-56" href="#__codelineno-36-56"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_stack.rb</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">ArrayStack</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">array_stack.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* 配列ベースのスタック */</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ArrayStack</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w">    </span><span class="c1">// リスト（動的配列）を初期化する</span>
+<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a>
+<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="w">    </span><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">size</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a>
+<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a><span class="w">    </span><span class="cm">/* スタックが空かどうかを判定 */</span>
+<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">():</span><span class="w"> </span><span class="kt">Boolean</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-37-14" name="__codelineno-37-14" href="#__codelineno-37-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-15" name="__codelineno-37-15" href="#__codelineno-37-15"></a>
+<a id="__codelineno-37-16" name="__codelineno-37-16" href="#__codelineno-37-16"></a><span class="w">    </span><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-37-17" name="__codelineno-37-17" href="#__codelineno-37-17"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-18" name="__codelineno-37-18" href="#__codelineno-37-18"></a><span class="w">        </span><span class="n">stack</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-37-19" name="__codelineno-37-19" href="#__codelineno-37-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-20" name="__codelineno-37-20" href="#__codelineno-37-20"></a>
+<a id="__codelineno-37-21" name="__codelineno-37-21" href="#__codelineno-37-21"></a><span class="w">    </span><span class="cm">/* ポップ */</span>
+<a id="__codelineno-37-22" name="__codelineno-37-22" href="#__codelineno-37-22"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">pop</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-23" name="__codelineno-37-23" href="#__codelineno-37-23"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">()</span>
+<a id="__codelineno-37-24" name="__codelineno-37-24" href="#__codelineno-37-24"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">removeAt</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-37-25" name="__codelineno-37-25" href="#__codelineno-37-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-26" name="__codelineno-37-26" href="#__codelineno-37-26"></a>
+<a id="__codelineno-37-27" name="__codelineno-37-27" href="#__codelineno-37-27"></a><span class="w">    </span><span class="cm">/* スタックトップの要素にアクセス */</span>
+<a id="__codelineno-37-28" name="__codelineno-37-28" href="#__codelineno-37-28"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">peek</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-29" name="__codelineno-37-29" href="#__codelineno-37-29"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">()</span>
+<a id="__codelineno-37-30" name="__codelineno-37-30" href="#__codelineno-37-30"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="o">[</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span>
+<a id="__codelineno-37-31" name="__codelineno-37-31" href="#__codelineno-37-31"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-32" name="__codelineno-37-32" href="#__codelineno-37-32"></a>
+<a id="__codelineno-37-33" name="__codelineno-37-33" href="#__codelineno-37-33"></a><span class="w">    </span><span class="cm">/* List を Array に変換して返す */</span>
+<a id="__codelineno-37-34" name="__codelineno-37-34" href="#__codelineno-37-34"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">toArray</span><span class="p">():</span><span class="w"> </span><span class="n">Array</span><span class="o">&lt;</span><span class="kt">Any</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-35" name="__codelineno-37-35" href="#__codelineno-37-35"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">toTypedArray</span><span class="p">()</span>
+<a id="__codelineno-37-36" name="__codelineno-37-36" href="#__codelineno-37-36"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-37" name="__codelineno-37-37" href="#__codelineno-37-37"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_stack.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="c1">### 配列で実装したスタック ###</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayStack</span>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w">  </span><span class="c1">### コンストラクタ ###</span>
+<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span>
+<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="w">    </span><span class="vi">@stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a>
+<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="w">  </span><span class="c1">### スタックの長さを取得 ###</span>
+<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">size</span>
+<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a><span class="w">    </span><span class="vi">@stack</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a>
+<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a><span class="w">  </span><span class="c1">### スタックが空か判定 ###</span>
+<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">is_empty?</span>
+<a id="__codelineno-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a><span class="w">    </span><span class="vi">@stack</span><span class="o">.</span><span class="n">empty?</span>
+<a id="__codelineno-38-16" name="__codelineno-38-16" href="#__codelineno-38-16"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-17" name="__codelineno-38-17" href="#__codelineno-38-17"></a>
+<a id="__codelineno-38-18" name="__codelineno-38-18" href="#__codelineno-38-18"></a><span class="w">  </span><span class="c1">### プッシュ ###</span>
+<a id="__codelineno-38-19" name="__codelineno-38-19" href="#__codelineno-38-19"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">item</span><span class="p">)</span>
+<a id="__codelineno-38-20" name="__codelineno-38-20" href="#__codelineno-38-20"></a><span class="w">    </span><span class="vi">@stack</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">item</span>
+<a id="__codelineno-38-21" name="__codelineno-38-21" href="#__codelineno-38-21"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-22" name="__codelineno-38-22" href="#__codelineno-38-22"></a>
+<a id="__codelineno-38-23" name="__codelineno-38-23" href="#__codelineno-38-23"></a><span class="w">  </span><span class="c1">### ポップ ###</span>
+<a id="__codelineno-38-24" name="__codelineno-38-24" href="#__codelineno-38-24"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">pop</span>
+<a id="__codelineno-38-25" name="__codelineno-38-25" href="#__codelineno-38-25"></a><span class="w">    </span><span class="k">raise</span><span class="w"> </span><span class="no">IndexError</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;スタックは空です&#39;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_empty?</span>
+<a id="__codelineno-38-26" name="__codelineno-38-26" href="#__codelineno-38-26"></a>
+<a id="__codelineno-38-27" name="__codelineno-38-27" href="#__codelineno-38-27"></a><span class="w">    </span><span class="vi">@stack</span><span class="o">.</span><span class="n">pop</span>
+<a id="__codelineno-38-28" name="__codelineno-38-28" href="#__codelineno-38-28"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-29" name="__codelineno-38-29" href="#__codelineno-38-29"></a>
+<a id="__codelineno-38-30" name="__codelineno-38-30" href="#__codelineno-38-30"></a><span class="w">  </span><span class="c1">### スタックトップ要素を参照 ###</span>
+<a id="__codelineno-38-31" name="__codelineno-38-31" href="#__codelineno-38-31"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">peek</span>
+<a id="__codelineno-38-32" name="__codelineno-38-32" href="#__codelineno-38-32"></a><span class="w">    </span><span class="k">raise</span><span class="w"> </span><span class="no">IndexError</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;スタックは空です&#39;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_empty?</span>
+<a id="__codelineno-38-33" name="__codelineno-38-33" href="#__codelineno-38-33"></a>
+<a id="__codelineno-38-34" name="__codelineno-38-34" href="#__codelineno-38-34"></a><span class="w">    </span><span class="vi">@stack</span><span class="o">.</span><span class="n">last</span>
+<a id="__codelineno-38-35" name="__codelineno-38-35" href="#__codelineno-38-35"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-36" name="__codelineno-38-36" href="#__codelineno-38-36"></a>
+<a id="__codelineno-38-37" name="__codelineno-38-37" href="#__codelineno-38-37"></a><span class="w">  </span><span class="c1">### 表示用のリストを返す ###</span>
+<a id="__codelineno-38-38" name="__codelineno-38-38" href="#__codelineno-38-38"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">to_array</span>
+<a id="__codelineno-38-39" name="__codelineno-38-39" href="#__codelineno-38-39"></a><span class="w">    </span><span class="vi">@stack</span>
+<a id="__codelineno-38-40" name="__codelineno-38-40" href="#__codelineno-38-40"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-41" name="__codelineno-38-41" href="#__codelineno-38-41"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20ArrayStack%3A%0A%20%20%20%20%22%22%22%E9%85%8D%E5%88%97%E3%83%99%E3%83%BC%E3%82%B9%E3%81%AE%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%22%22%22%0A%0A%20%20%20%20def%20__init__%28self%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%82%B3%E3%83%B3%E3%82%B9%E3%83%88%E3%83%A9%E3%82%AF%E3%82%BF%22%22%22%0A%20%20%20%20%20%20%20%20self._stack%3A%20list%5Bint%5D%20%3D%20%5B%5D%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%81%AE%E9%95%B7%E3%81%95%E3%82%92%E5%8F%96%E5%BE%97%22%22%22%0A%20%20%20%20%20%20%20%20return%20len%28self._stack%29%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%81%8C%E7%A9%BA%E3%81%8B%E3%81%A9%E3%81%86%E3%81%8B%E3%82%92%E5%88%A4%E5%AE%9A%22%22%22%0A%20%20%20%20%20%20%20%20return%20self._stack%20%3D%3D%20%5B%5D%0A%0A%20%20%20%20def%20push%28self%2C%20item%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%83%97%E3%83%83%E3%82%B7%E3%83%A5%22%22%22%0A%20%20%20%20%20%20%20%20self._stack.append%28item%29%0A%0A%20%20%20%20def%20pop%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%83%9D%E3%83%83%E3%83%97%22%22%22%0A%20%20%20%20%20%20%20%20if%20self.is_empty%28%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%22%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%81%8C%E7%A9%BA%E3%81%A7%E3%81%99%22%29%0A%20%20%20%20%20%20%20%20return%20self._stack.pop%28%29%0A%0A%20%20%20%20def%20peek%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%83%88%E3%83%83%E3%83%97%E3%81%AE%E8%A6%81%E7%B4%A0%E3%81%AB%E3%82%A2%E3%82%AF%E3%82%BB%E3%82%B9%22%22%22%0A%20%20%20%20%20%20%20%20if%20self.is_empty%28%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%22%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%81%8C%E7%A9%BA%E3%81%A7%E3%81%99%22%29%0A%20%20%20%20%20%20%20%20return%20self._stack%5B-1%5D%0A%0A%20%20%20%20def%20to_list%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%A1%A8%E7%A4%BA%E7%94%A8%E3%81%AE%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E8%BF%94%E3%81%99%22%22%22%0A%20%20%20%20%20%20%20%20return%20self._stack%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20stack%20%3D%20ArrayStack%28%29%0A%0A%20%20%20%20%23%20%E8%A6%81%E7%B4%A0%E3%82%92%E3%83%97%E3%83%83%E3%82%B7%E3%83%A5%0A%20%20%20%20stack.push%281%29%0A%20%20%20%20stack.push%283%29%0A%20%20%20%20stack.push%282%29%0A%20%20%20%20stack.push%285%29%0A%20%20%20%20stack.push%284%29%0A%20%20%20%20print%28%22%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%20stack%20%3D%22%2C%20stack.to_list%28%29%29%0A%0A%20%20%20%20%23%20%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%83%88%E3%83%83%E3%83%97%E3%81%AE%E8%A6%81%E7%B4%A0%E3%81%AB%E3%82%A2%E3%82%AF%E3%82%BB%E3%82%B9%0A%20%20%20%20peek%20%3D%20stack.peek%28%29%0A%20%20%20%20print%28%22%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%83%88%E3%83%83%E3%83%97%E8%A6%81%E7%B4%A0%20peek%20%3D%22%2C%20peek%29%0A%0A%20%20%20%20%23%20%E8%A6%81%E7%B4%A0%E3%82%92%E3%83%9D%E3%83%83%E3%83%97%0A%20%20%20%20pop%20%3D%20stack.pop%28%29%0A%20%20%20%20print%28%22%E3%83%9D%E3%83%83%E3%83%97%E3%81%97%E3%81%9F%E8%A6%81%E7%B4%A0%20pop%20%3D%22%2C%20pop%29%0A%20%20%20%20print%28%22%E3%83%9D%E3%83%83%E3%83%97%E5%BE%8C%20stack%20%3D%22%2C%20stack.to_list%28%29%29%0A%0A%20%20%20%20%23%20%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%81%AE%E9%95%B7%E3%81%95%E3%82%92%E5%8F%96%E5%BE%97%0A%20%20%20%20size%20%3D%20stack.size%28%29%0A%20%20%20%20print%28%22%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%81%AE%E9%95%B7%E3%81%95%20size%20%3D%22%2C%20size%29%0A%0A%20%20%20%20%23%20%E7%A9%BA%E3%81%8B%E3%81%A9%E3%81%86%E3%81%8B%E3%82%92%E5%88%A4%E5%AE%9A%0A%20%20%20%20is_empty%20%3D%20stack.is_empty%28%29%0A%20%20%20%20print%28%22%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%81%8C%E7%A9%BA%E3%81%8B%E3%81%A9%E3%81%86%E3%81%8B%20%3D%22%2C%20is_empty%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20ArrayStack%3A%0A%20%20%20%20%22%22%22%E9%85%8D%E5%88%97%E3%83%99%E3%83%BC%E3%82%B9%E3%81%AE%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%22%22%22%0A%0A%20%20%20%20def%20__init__%28self%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%82%B3%E3%83%B3%E3%82%B9%E3%83%88%E3%83%A9%E3%82%AF%E3%82%BF%22%22%22%0A%20%20%20%20%20%20%20%20self._stack%3A%20list%5Bint%5D%20%3D%20%5B%5D%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%81%AE%E9%95%B7%E3%81%95%E3%82%92%E5%8F%96%E5%BE%97%22%22%22%0A%20%20%20%20%20%20%20%20return%20len%28self._stack%29%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%81%8C%E7%A9%BA%E3%81%8B%E3%81%A9%E3%81%86%E3%81%8B%E3%82%92%E5%88%A4%E5%AE%9A%22%22%22%0A%20%20%20%20%20%20%20%20return%20self._stack%20%3D%3D%20%5B%5D%0A%0A%20%20%20%20def%20push%28self%2C%20item%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%83%97%E3%83%83%E3%82%B7%E3%83%A5%22%22%22%0A%20%20%20%20%20%20%20%20self._stack.append%28item%29%0A%0A%20%20%20%20def%20pop%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%83%9D%E3%83%83%E3%83%97%22%22%22%0A%20%20%20%20%20%20%20%20if%20self.is_empty%28%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%22%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%81%8C%E7%A9%BA%E3%81%A7%E3%81%99%22%29%0A%20%20%20%20%20%20%20%20return%20self._stack.pop%28%29%0A%0A%20%20%20%20def%20peek%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%83%88%E3%83%83%E3%83%97%E3%81%AE%E8%A6%81%E7%B4%A0%E3%81%AB%E3%82%A2%E3%82%AF%E3%82%BB%E3%82%B9%22%22%22%0A%20%20%20%20%20%20%20%20if%20self.is_empty%28%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%22%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%81%8C%E7%A9%BA%E3%81%A7%E3%81%99%22%29%0A%20%20%20%20%20%20%20%20return%20self._stack%5B-1%5D%0A%0A%20%20%20%20def%20to_list%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%A1%A8%E7%A4%BA%E7%94%A8%E3%81%AE%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E8%BF%94%E3%81%99%22%22%22%0A%20%20%20%20%20%20%20%20return%20self._stack%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20stack%20%3D%20ArrayStack%28%29%0A%0A%20%20%20%20%23%20%E8%A6%81%E7%B4%A0%E3%82%92%E3%83%97%E3%83%83%E3%82%B7%E3%83%A5%0A%20%20%20%20stack.push%281%29%0A%20%20%20%20stack.push%283%29%0A%20%20%20%20stack.push%282%29%0A%20%20%20%20stack.push%285%29%0A%20%20%20%20stack.push%284%29%0A%20%20%20%20print%28%22%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%20stack%20%3D%22%2C%20stack.to_list%28%29%29%0A%0A%20%20%20%20%23%20%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%83%88%E3%83%83%E3%83%97%E3%81%AE%E8%A6%81%E7%B4%A0%E3%81%AB%E3%82%A2%E3%82%AF%E3%82%BB%E3%82%B9%0A%20%20%20%20peek%20%3D%20stack.peek%28%29%0A%20%20%20%20print%28%22%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%83%88%E3%83%83%E3%83%97%E8%A6%81%E7%B4%A0%20peek%20%3D%22%2C%20peek%29%0A%0A%20%20%20%20%23%20%E8%A6%81%E7%B4%A0%E3%82%92%E3%83%9D%E3%83%83%E3%83%97%0A%20%20%20%20pop%20%3D%20stack.pop%28%29%0A%20%20%20%20print%28%22%E3%83%9D%E3%83%83%E3%83%97%E3%81%97%E3%81%9F%E8%A6%81%E7%B4%A0%20pop%20%3D%22%2C%20pop%29%0A%20%20%20%20print%28%22%E3%83%9D%E3%83%83%E3%83%97%E5%BE%8C%20stack%20%3D%22%2C%20stack.to_list%28%29%29%0A%0A%20%20%20%20%23%20%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%81%AE%E9%95%B7%E3%81%95%E3%82%92%E5%8F%96%E5%BE%97%0A%20%20%20%20size%20%3D%20stack.size%28%29%0A%20%20%20%20print%28%22%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%81%AE%E9%95%B7%E3%81%95%20size%20%3D%22%2C%20size%29%0A%0A%20%20%20%20%23%20%E7%A9%BA%E3%81%8B%E3%81%A9%E3%81%86%E3%81%8B%E3%82%92%E5%88%A4%E5%AE%9A%0A%20%20%20%20is_empty%20%3D%20stack.is_empty%28%29%0A%20%20%20%20print%28%22%E3%82%B9%E3%82%BF%E3%83%83%E3%82%AF%E3%81%8C%E7%A9%BA%E3%81%8B%E3%81%A9%E3%81%86%E3%81%8B%20%3D%22%2C%20is_empty%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 <h2 id="513-2">5.1.3 &nbsp; 2つの実装の比較<a class="headerlink" href="#513-2" title="Permanent link">&para;</a></h2>
-<p><strong>サポートされる操作</strong></p>
-<p>両方の実装は、スタックで定義されたすべての操作をサポートします。配列実装はさらにランダムアクセスをサポートしますが、これはスタック定義の範囲を超えており、一般的には使用されません。</p>
+<p><strong>対応する操作</strong></p>
+<p>どちらの実装も、スタックの定義に含まれる各種操作をサポートします。配列ベースの実装はランダムアクセスも可能ですが、これはスタックの定義範囲を超えているため、通常は利用しません。</p>
 <p><strong>時間効率</strong></p>
-<p>配列ベースの実装では、プッシュとポップ操作の両方が事前に割り当てられた連続メモリで発生し、良好なキャッシュ局所性があるため効率が高くなります。しかし、プッシュ操作が配列容量を超える場合、リサイズメカニズムがトリガーされ、そのプッシュ操作の時間計算量は<span class="arithmatex">\(O(n)\)</span>になります。</p>
-<p>連結リスト実装では、リスト拡張は非常に柔軟で、配列拡張のような効率低下の問題はありません。しかし、プッシュ操作にはノードオブジェクトの初期化とポインタの変更が必要なため、効率は比較的低くなります。プッシュされる要素がすでにノードオブジェクトの場合、初期化ステップをスキップでき、効率が向上します。</p>
-<p>したがって、プッシュとポップ操作の要素が<code>int</code>や<code>double</code>などの基本データ型の場合、以下の結論を導くことができます：</p>
+<p>配列ベースの実装では、プッシュとポップの両方があらかじめ確保された連続メモリ上で行われるため、キャッシュ局所性が高く、効率に優れます。ただし、プッシュ時に配列容量を超えると拡張処理が発生し、その1回のプッシュの時間計算量は <span class="arithmatex">\(O(n)\)</span> になります。</p>
+<p>連結リストベースの実装では、サイズ拡張が非常に柔軟であり、前述のような配列拡張による効率低下はありません。ただし、プッシュ時にはノードオブジェクトの初期化とポインタの更新が必要になるため、効率は相対的に低くなります。もっとも、プッシュする要素自体がノードオブジェクトであれば、初期化の手間を省けるため、効率を高められます。</p>
+<p>以上を踏まえると、プッシュおよびポップの対象が <code>int</code> や <code>double</code> のような基本データ型である場合、次の結論が得られます。</p>
 <ul>
-<li>配列ベースのスタック実装は拡張時に効率が低下しますが、拡張は低頻度操作であるため、平均効率は高くなります。</li>
-<li>連結リストベースのスタック実装はより安定した効率パフォーマンスを提供します。</li>
+<li>配列ベースのスタックは拡張時に効率が低下しますが、拡張は低頻度の操作であるため、平均効率はより高くなります。</li>
+<li>連結リストベースのスタックは、より安定した効率を提供できます。</li>
 </ul>
 <p><strong>空間効率</strong></p>
-<p>リストを初期化する際、システムは「初期容量」を割り当てますが、これは実際の必要量を超える可能性があります。さらに、拡張メカニズムは通常、特定の係数（2倍など）で容量を増加させ、これも実際の必要量を超える可能性があります。したがって、<strong>配列ベースのスタックは一部の空間を無駄にする可能性があります</strong>。</p>
-<p>しかし、連結リストノードはポインタを格納するための追加空間が必要なため、<strong>連結リストノードが占有する空間は比較的大きくなります</strong>。</p>
-<p>まとめると、どちらの実装がよりメモリ効率的かを単純に判断することはできません。特定の状況に基づく分析が必要です。</p>
+<p>リストを初期化するとき、システムは「初期容量」を割り当てますが、この容量は実際の必要量を上回ることがあります。また、拡張は通常、一定の倍率（たとえば2倍）で行われるため、拡張後の容量も実際の必要量を超える可能性があります。したがって、<strong>配列ベースのスタックは一定のメモリ浪費を招く可能性があります。</strong></p>
+<p>一方で、連結リストのノードはポインタを追加で保持する必要があるため、<strong>連結リストノードは相対的に大きな領域を占有します。</strong></p>
+<p>以上より、どちらの実装がより省メモリかを単純に断定することはできず、具体的な状況に応じて分析する必要があります。</p>
 <h2 id="514">5.1.4 &nbsp; スタックの典型的な応用<a class="headerlink" href="#514" title="Permanent link">&para;</a></h2>
 <ul>
-<li><strong>ブラウザの戻ると進む、ソフトウェアの元に戻すとやり直し</strong>。新しいWebページを開くたびに、ブラウザは前のページをスタックにプッシュし、戻る操作（本質的にはポップ操作）を通じて前のページに戻ることができます。戻ると進むの両方をサポートするには、2つのスタックが連携して動作する必要があります。</li>
-<li><strong>プログラムのメモリ管理</strong>。関数が呼び出されるたびに、システムはスタックのトップにスタックフレームを追加して関数のコンテキスト情報を記録します。再帰関数では、下方向の再帰フェーズはスタックへのプッシュを続け、上方向のバックトラッキングフェーズはスタックからのポップを続けます。</li>
+<li><strong>ブラウザにおける戻ると進む、ソフトウェアにおける取り消しとやり直し</strong>。新しいWebページを開くたびに、ブラウザは直前のページをスタックにプッシュするため、戻る操作によって前のページに戻れます。戻る操作は実際にはポップに相当します。戻ると進むを同時にサポートするには、2つのスタックを組み合わせて実現する必要があります。</li>
+<li><strong>プログラムのメモリ管理</strong>。関数を呼び出すたびに、システムはスタックトップにスタックフレームを追加し、関数のコンテキスト情報を記録します。再帰関数では、下向きに再帰していく段階でプッシュが繰り返され、上向きにバックトラックする段階でポップが繰り返されます。</li>
 </ul>
 
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index c3a8c9d02..d890afd34 100644
--- a/ja/chapter_stack_and_queue/summary/index.html
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@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
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+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
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-    序
+    はじめに
   
 
     
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-    序
+    はじめに
   
 
           </label>
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   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
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-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
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   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
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-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
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   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
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   <a href="#1" class="md-nav__link">
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-        1. &nbsp; 重要なポイント
+        1. &nbsp; 要点の振り返り
       
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-    第 6 章 &nbsp; ハッシュ表
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
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-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
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-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2647,7 +2647,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3185,7 +3185,7 @@
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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-    13.3 &nbsp; 部分集合和問題
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-    13.4 &nbsp; Nクイーン問題
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-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
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-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
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-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4299,7 +4299,7 @@
   <a href="#1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; 重要なポイント
+        1. &nbsp; 要点の振り返り
       
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 <!-- Page content -->
 <h1 id="54">5.4 &nbsp; まとめ<a class="headerlink" href="#54" title="Permanent link">&para;</a></h1>
-<h3 id="1">1. &nbsp; 重要なポイント<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<h3 id="1">1. &nbsp; 要点の振り返り<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
-<li>スタックは後入れ先出し（LIFO）の原則に従うデータ構造で、配列または連結リストを使って実装できます。</li>
-<li>時間効率の観点では、スタックの配列実装の方が平均的な効率が高いです。ただし、拡張時には単一のプッシュ操作の時間計算量が<span class="arithmatex">\(O(n)\)</span>に悪化する可能性があります。対照的に、スタックの連結リスト実装はより安定した効率を提供します。</li>
-<li>空間効率に関しては、スタックの配列実装は一定程度の空間の無駄につながる可能性があります。ただし、連結リストのノードが占有するメモリ空間は一般的に配列の要素よりも大きいことに注意することが重要です。</li>
-<li>キューは先入れ先出し（FIFO）の原則に従うデータ構造で、同様に配列または連結リストを使って実装できます。キューの時間と空間効率に関する結論は、スタックと似ています。</li>
-<li>両端キュー（deque）はより柔軟なキューの種類で、両端での要素の追加と削除を可能にします。</li>
+<li>スタックは後入れ先出しの原則に従うデータ構造であり、配列または連結リストで実装できます。</li>
+<li>時間効率の面では、スタックの配列実装は平均効率が高い一方、拡張時には 1 回のプッシュ操作の時間計算量が <span class="arithmatex">\(O(n)\)</span> まで悪化します。これに対して、スタックの連結リスト実装はより安定した効率を示します。</li>
+<li>空間効率の面では、スタックの配列実装はある程度の領域の無駄を生む可能性があります。ただし、連結リストのノードが占有するメモリは配列要素よりも大きい点に注意が必要です。</li>
+<li>キューは先入れ先出しの原則に従うデータ構造であり、同様に配列または連結リストで実装できます。時間効率と空間効率の比較における結論は、前述のスタックの場合と似ています。</li>
+<li>両端キューはより高い自由度を持つキューであり、両端で要素の追加と削除を行えます。</li>
 </ul>
 <h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
-<p><strong>Q</strong>: ブラウザの進む・戻る機能は双方向連結リストで実装されているのですか？</p>
-<p>ブラウザの進む・戻るナビゲーションは本質的に「スタック」概念の現れです。ユーザーが新しいページを訪問すると、そのページがスタックの先頭に追加されます。戻るボタンをクリックすると、ページがスタックの先頭からポップされます。両端キュー（deque）は、「両端キュー」の章で述べたように、いくつかの追加操作を便利に実装できます。</p>
-<p><strong>Q</strong>: スタックからポップした後、ポップされたノードのメモリを解放する必要がありますか？</p>
-<p>ポップされたノードが後で使用される場合は、そのメモリを解放する必要はありません。自動ガベージコレクションを持つJavaやPythonなどの言語では、手動のメモリ解放は必要ありません。CやC++では、手動のメモリ解放が必要です。</p>
-<p><strong>Q</strong>: 両端キューは2つのスタックを結合したもののように見えます。その用途は何ですか？</p>
-<p>両端キューは、スタックとキューの組み合わせまたは2つのスタックを結合したもので、スタックとキューの両方のロジックを示します。したがって、スタックとキューのすべてのアプリケーションを実装でき、より大きな柔軟性を提供します。</p>
-<p><strong>Q</strong>: 元に戻すとやり直しは具体的にどのように実装されるのですか？</p>
-<p>元に戻すとやり直しの操作は2つのスタックを使って実装されます：元に戻す用のスタック<code>A</code>とやり直し用のスタック<code>B</code>です。</p>
+<p><strong>Q</strong>：ブラウザの進む・戻るは双方向連結リストで実装されているのですか？</p>
+<p>ブラウザの進む・戻る機能の本質は「スタック」の表れです。ユーザーが新しいページにアクセスすると、そのページはスタックの先頭に追加されます。ユーザーが戻るボタンをクリックすると、そのページはスタックの先頭から取り出されます。両端キューを使うといくつかの追加操作を簡単に実装でき、この点は「両端キュー」の章で触れています。</p>
+<p><strong>Q</strong>：ポップした後、そのノードのメモリを解放する必要はありますか？</p>
+<p>後で取り出したノードを引き続き使うのであれば、メモリを解放する必要はありません。以降そのノードを使わない場合でも、<code>Java</code> や <code>Python</code> などの言語には自動ガベージコレクション機構があるため、手動でメモリを解放する必要はありません。一方、<code>C</code> と <code>C++</code> では手動でメモリを解放する必要があります。</p>
+<p><strong>Q</strong>：両端キューは 2 つのスタックをつなげたように見えますが、用途は何ですか？</p>
+<p>両端キューは、スタックとキューの組み合わせ、あるいは 2 つのスタックをつなげたもののような構造です。表しているのはスタック + キューのロジックなので、スタックとキューのすべての応用を実現でき、しかもより柔軟です。</p>
+<p><strong>Q</strong>：取り消し（undo）とやり直し（redo）は具体的にどのように実装されますか？</p>
+<p>2 つのスタックを使い、スタック <code>A</code> を取り消し用、スタック <code>B</code> をやり直し用に使います。</p>
 <ol>
-<li>ユーザーが操作を実行するたびに、それがスタック<code>A</code>にプッシュされ、スタック<code>B</code>がクリアされます。</li>
-<li>ユーザーが「元に戻す」を実行すると、最新の操作がスタック<code>A</code>からポップされ、スタック<code>B</code>にプッシュされます。</li>
-<li>ユーザーが「やり直し」を実行すると、最新の操作がスタック<code>B</code>からポップされ、スタック<code>A</code>に戻されます。</li>
+<li>ユーザーが操作を 1 つ実行するたびに、その操作をスタック <code>A</code> にプッシュし、スタック <code>B</code> を空にします。</li>
+<li>ユーザーが「取り消し」を実行したときは、スタック <code>A</code> から直近の操作をポップし、それをスタック <code>B</code> にプッシュします。</li>
+<li>ユーザーが「やり直し」を実行したときは、スタック <code>B</code> から直近の操作をポップし、それをスタック <code>A</code> にプッシュします。</li>
 </ol>
 
 <!-- Source file information -->
@@ -4423,7 +4423,7 @@ aria-label="フッター"
   <a
     href="../../chapter_hashing/"
     class="md-footer__link md-footer__link--next"
-    aria-label="次: 第 6 章 &amp;nbsp; ハッシュ表"
+    aria-label="次: 第 6 章 &amp;nbsp; ハッシュテーブル"
     rel="next"
   >
     <div class="md-footer__title">
@@ -4431,7 +4431,7 @@ aria-label="フッター"
         次
       </span>
       <div class="md-ellipsis">
-        第 6 章 &nbsp; ハッシュ表
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diff --git a/ja/chapter_tree/array_representation_of_tree/index.html b/ja/chapter_tree/array_representation_of_tree/index.html
index 35afcc992..06ea5653f 100644
--- a/ja/chapter_tree/array_representation_of_tree/index.html
+++ b/ja/chapter_tree/array_representation_of_tree/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
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     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
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+    はじめに
   
 
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@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
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   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
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+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1945,7 +1945,7 @@
   <a href="#731" class="md-nav__link">
     <span class="md-ellipsis">
       
-        7.3.1 &nbsp; 完全二分木の表現
+        7.3.1 &nbsp; 充足二分木を表現する
       
     </span>
   </a>
@@ -1956,7 +1956,7 @@
   <a href="#732" class="md-nav__link">
     <span class="md-ellipsis">
       
-        7.3.2 &nbsp; 任意の二分木の表現
+        7.3.2 &nbsp; 任意の二分木を表現する
       
     </span>
   </a>
@@ -1967,7 +1967,7 @@
   <a href="#733" class="md-nav__link">
     <span class="md-ellipsis">
       
-        7.3.3 &nbsp; 利点と制限
+        7.3.3 &nbsp; 利点と制約
       
     </span>
   </a>
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
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-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
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-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
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-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
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-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
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-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
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-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
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-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
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-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
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-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
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-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
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-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
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-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
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+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
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   <a href="#731" class="md-nav__link">
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-        7.3.1 &nbsp; 完全二分木の表現
+        7.3.1 &nbsp; 充足二分木を表現する
       
     </span>
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   <a href="#732" class="md-nav__link">
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-        7.3.2 &nbsp; 任意の二分木の表現
+        7.3.2 &nbsp; 任意の二分木を表現する
       
     </span>
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   <a href="#733" class="md-nav__link">
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-        7.3.3 &nbsp; 利点と制限
+        7.3.3 &nbsp; 利点と制約
       
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@@ -4377,162 +4377,164 @@
 
 <!-- Page content -->
 <h1 id="73">7.3 &nbsp; 二分木の配列表現<a class="headerlink" href="#73" title="Permanent link">&para;</a></h1>
-<p>連結リスト表現では、二分木の格納単位はノード<code>TreeNode</code>であり、ノードはポインタによって接続されます。連結リスト表現での二分木の基本操作については前の節で紹介しました。</p>
-<p>では、配列を使って二分木を表現することはできるでしょうか？答えはイエスです。</p>
-<h2 id="731">7.3.1 &nbsp; 完全二分木の表現<a class="headerlink" href="#731" title="Permanent link">&para;</a></h2>
-<p>まず簡単なケースから分析してみましょう。完全二分木が与えられたとき、レベル順探索の順序に従ってすべてのノードを配列に格納し、各ノードは一意の配列インデックスに対応します。</p>
-<p>レベル順探索の特性に基づいて、親ノードのインデックスとその子ノードの間の「マッピング公式」を導き出すことができます：<strong>ノードのインデックスが<span class="arithmatex">\(i\)</span>の場合、その左の子のインデックスは<span class="arithmatex">\(2i + 1\)</span>、右の子のインデックスは<span class="arithmatex">\(2i + 2\)</span>です</strong>。下図は、さまざまなノードのインデックス間のマッピング関係を示しています。</p>
-<p><img alt="完全二分木の配列表現" class="animation-figure" src="../array_representation_of_tree.assets/array_representation_binary_tree.png" /></p>
-<p align="center"> 図 7-12 &nbsp; 完全二分木の配列表現 </p>
+<p>連結リスト表現では、二分木の記憶単位はノード <code>TreeNode</code> であり、ノード同士はポインタによって接続されます。前節では、連結リスト表現における二分木の各種基本操作を紹介しました。</p>
+<p>では、配列で二分木を表現できるでしょうか？答えはもちろん可能です。</p>
+<h2 id="731">7.3.1 &nbsp; 充足二分木を表現する<a class="headerlink" href="#731" title="Permanent link">&para;</a></h2>
+<p>まずは簡単な例を考えます。与えられた 1 本の充足二分木について、すべてのノードをレベル順走査の順に配列へ格納すると、各ノードは一意な配列インデックスに対応します。</p>
+<p>レベル順走査の性質に基づくと、親ノードのインデックスと子ノードのインデックスの間にある「対応式」を導けます。<strong>あるノードのインデックスが <span class="arithmatex">\(i\)</span> なら、その左子ノードのインデックスは <span class="arithmatex">\(2i + 1\)</span> 、右子ノードのインデックスは <span class="arithmatex">\(2i + 2\)</span> です</strong>。以下の図は、各ノードインデックス間の対応関係を示しています。</p>
+<p><img alt="充足二分木の配列表現" class="animation-figure" src="../array_representation_of_tree.assets/array_representation_binary_tree.png" /></p>
+<p align="center"> 図 7-12 &nbsp; 充足二分木の配列表現 </p>
 
-<p><strong>マッピング公式は、連結リストのノード参照（ポインタ）と同様の役割を果たします</strong>。配列内の任意のノードが与えられたとき、マッピング公式を使用してその左（右）の子ノードにアクセスできます。</p>
-<h2 id="732">7.3.2 &nbsp; 任意の二分木の表現<a class="headerlink" href="#732" title="Permanent link">&para;</a></h2>
-<p>完全二分木は特別なケースです。二分木の中間レベルには多くの<code>None</code>値が存在することがよくあります。レベル順探索のシーケンスにはこれらの<code>None</code>値が含まれないため、このシーケンスだけに依存して<code>None</code>値の数と分布を推測することはできません。<strong>つまり、複数の二分木構造が同じレベル順探索シーケンスと一致する可能性があります</strong>。</p>
-<p>下図に示すように、完全でない二分木が与えられた場合、上記の配列表現方法は失敗します。</p>
-<p><img alt="レベル順探索シーケンスが複数の二分木の可能性に対応" class="animation-figure" src="../array_representation_of_tree.assets/array_representation_without_empty.png" /></p>
-<p align="center"> 図 7-13 &nbsp; レベル順探索シーケンスが複数の二分木の可能性に対応 </p>
+<p><strong>対応式は、連結リストにおけるノード参照（ポインタ）と同じ役割を果たします</strong>。与えられた配列内の任意のノードについて、この対応式を使えばその左（右）子ノードにアクセスできます。</p>
+<h2 id="732">7.3.2 &nbsp; 任意の二分木を表現する<a class="headerlink" href="#732" title="Permanent link">&para;</a></h2>
+<p>充足二分木は特殊なケースであり、一般の二分木では中間層に多数の <code>None</code> が存在することがよくあります。レベル順走査の列にはこれらの <code>None</code> が含まれないため、その列だけから <code>None</code> の数や分布位置を推定することはできません。<strong>つまり、このレベル順走査列に一致する二分木構造は複数存在し得ます</strong>。</p>
+<p>次の図のように、非充足二分木が与えられると、上記の配列表現はすでに成り立ちません。</p>
+<p><img alt="レベル順走査列に対応する複数の二分木の可能性" class="animation-figure" src="../array_representation_of_tree.assets/array_representation_without_empty.png" /></p>
+<p align="center"> 図 7-13 &nbsp; レベル順走査列に対応する複数の二分木の可能性 </p>
 
-<p>この問題を解決するために、<strong>レベル順探索シーケンスですべての<code>None</code>値を明示的に書き出すことを検討できます</strong>。下図に示すように、この処理後、レベル順探索シーケンスは二分木を一意に表現できます。サンプルコードは以下の通りです：</p>
+<p>この問題を解決するために、**レベル順走査列にすべての <code>None</code> を明示的に書き込む**ことを考えられます。次の図のように、このように処理すればレベル順走査列で二分木を一意に表現できます。コード例は以下のとおりです：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 二分木の配列表現</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="c1"># Noneを使用して空のスロットを表現</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="c1"># 空き位置を表すために None を使う</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="n">tree</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="mi">12</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="mi">15</span><span class="p">]</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 二分木の配列表現 */</span>
-<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// 最大整数値INT_MAXを使用して空のスロットをマーク</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// int の最大値 INT_MAX を使って空き位置を示す</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">15</span><span class="p">};</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 二分木の配列表現 */</span>
-<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="c1">// Integerラッパークラスを使用してnullで空のスロットをマーク</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="c1">// int のラッパークラス Integer を使えば、null で空き位置を示せる</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="n">Integer</span><span class="o">[]</span><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mi">15</span><span class="w"> </span><span class="p">};</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 二分木の配列表現 */</span>
-<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="c1">// nullable int (int?)を使用してnullで空のスロットをマーク</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="c1">// nullable な int? 型を使えば、null で空き位置を示せる</span>
 <a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="kt">int?</span><span class="p">[]</span><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="k">null</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="k">null</span><span class="p">,</span><span class="w"> </span><span class="k">null</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="k">null</span><span class="p">,</span><span class="w"> </span><span class="k">null</span><span class="p">,</span><span class="w"> </span><span class="mi">15</span><span class="p">];</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 二分木の配列表現 */</span>
-<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="c1">// any型スライスを使用してnilで空のスロットをマーク</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="c1">// any 型のスライスを使えば、nil で空き位置を示せる</span>
 <a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="nx">tree</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">15</span><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 二分木の配列表現 */</span>
-<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="c1">// optional Int (Int?)を使用してnilで空のスロットをマーク</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="c1">// nullable な Int? 型を使えば、nil で空き位置を示せる</span>
 <a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">let</span><span class="w"> </span><span class="nv">tree</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">?]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">15</span><span class="p">]</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 二分木の配列表現 */</span>
-<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="c1">// nullを使用して空のスロットを表現</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="c1">// null を使って空き位置を表す</span>
 <a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="kd">let</span><span class="w"> </span><span class="nx">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span><span class="w"> </span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">4</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mf">6</span><span class="p">,</span><span class="w"> </span><span class="mf">7</span><span class="p">,</span><span class="w"> </span><span class="mf">8</span><span class="p">,</span><span class="w"> </span><span class="mf">9</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mf">12</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mf">15</span><span class="p">];</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 二分木の配列表現 */</span>
-<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="c1">// nullを使用して空のスロットを表現</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="c1">// null を使って空き位置を表す</span>
 <a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="kd">let</span><span class="w"> </span><span class="nx">tree</span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="kt">number</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span><span class="w"> </span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">4</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mf">6</span><span class="p">,</span><span class="w"> </span><span class="mf">7</span><span class="p">,</span><span class="w"> </span><span class="mf">8</span><span class="p">,</span><span class="w"> </span><span class="mf">9</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mf">12</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mf">15</span><span class="p">];</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 二分木の配列表現 */</span>
-<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="c1">// nullable int (int?)を使用してnullで空のスロットをマーク</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="c1">// nullable な int? 型を使えば、null で空き位置を示せる</span>
 <a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">?&gt;</span><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">6</span><span class="p">,</span><span class="w"> </span><span class="m">7</span><span class="p">,</span><span class="w"> </span><span class="m">8</span><span class="p">,</span><span class="w"> </span><span class="m">9</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">12</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">15</span><span class="p">];</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 二分木の配列表現 */</span>
-<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="c1">// Noneを使用して空のスロットをマーク</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="c1">// None を使って空き位置を示す</span>
 <a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="kd">let</span><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nb">Some</span><span class="p">(</span><span class="mi">1</span><span class="p">),</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">2</span><span class="p">),</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">3</span><span class="p">),</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">4</span><span class="p">),</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">6</span><span class="p">),</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">7</span><span class="p">),</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">8</span><span class="p">),</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">9</span><span class="p">),</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">12</span><span class="p">),</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">15</span><span class="p">)];</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 二分木の配列表現 */</span>
-<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="c1">// 最大int値を使用して空のスロットをマーク、したがってノード値はINT_MAXであってはならない</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="c1">// int の最大値で空き位置を示すため、ノード値は INT_MAX であってはならない</span>
 <a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="kt">int</span><span class="w"> </span><span class="n">tree</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">15</span><span class="p">};</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 二分木の配列表現 */</span>
-<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="c1">// nullを使用して空のスロットを表現</span>
-<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="kd">val</span><span class="w"> </span><span class="nv">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="p">(</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">6</span><span class="p">,</span><span class="w"> </span><span class="m">7</span><span class="p">,</span><span class="w"> </span><span class="m">8</span><span class="p">,</span><span class="w"> </span><span class="m">9</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">12</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">15</span><span class="w"> </span><span class="p">)</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="c1">// null を使って空き位置を表す</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="kd">val</span><span class="w"> </span><span class="nv">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arrayOf</span><span class="p">(</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">6</span><span class="p">,</span><span class="w"> </span><span class="m">7</span><span class="p">,</span><span class="w"> </span><span class="m">8</span><span class="p">,</span><span class="w"> </span><span class="m">9</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">12</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">15</span><span class="w"> </span><span class="p">)</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 二分木の配列表現 ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="c1"># nil を使って空き位置を表す</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="kp">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="kp">nil</span><span class="p">,</span><span class="w"> </span><span class="kp">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="kp">nil</span><span class="p">,</span><span class="w"> </span><span class="kp">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">15</span><span class="o">]</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p><img alt="任意の種類の二分木の配列表現" class="animation-figure" src="../array_representation_of_tree.assets/array_representation_with_empty.png" /></p>
-<p align="center"> 図 7-14 &nbsp; 任意の種類の二分木の配列表現 </p>
+<p><img alt="任意の二分木の配列表現" class="animation-figure" src="../array_representation_of_tree.assets/array_representation_with_empty.png" /></p>
+<p align="center"> 図 7-14 &nbsp; 任意の二分木の配列表現 </p>
 
-<p>注目すべきは、<strong>完備二分木は配列表現に非常に適している**ということです。完備二分木の定義を思い出すと、<code>None</code>は最下位レベルでのみ、かつ右側に向かって現れます。**つまり、すべての<code>None</code>値は確実にレベル順探索シーケンスの最後に現れます</strong>。</p>
-<p>これは、配列を使用して完備二分木を表現する際、すべての<code>None</code>値の格納を省略できることを意味し、非常に便利です。下図に例を示します。</p>
-<p><img alt="完備二分木の配列表現" class="animation-figure" src="../array_representation_of_tree.assets/array_representation_complete_binary_tree.png" /></p>
-<p align="center"> 図 7-15 &nbsp; 完備二分木の配列表現 </p>
+<p>補足すると、<strong>完全二分木は配列による表現に非常に適しています</strong>。完全二分木の定義を振り返ると、<code>None</code> は最下層の右側にしか現れないため、<strong>すべての <code>None</code> は必ずレベル順走査列の末尾に現れます</strong>。</p>
+<p>つまり、完全二分木を配列で表す場合は、すべての <code>None</code> の格納を省略できるため、非常に便利です。次の図に例を示します。</p>
+<p><img alt="完全二分木の配列表現" class="animation-figure" src="../array_representation_of_tree.assets/array_representation_complete_binary_tree.png" /></p>
+<p align="center"> 図 7-15 &nbsp; 完全二分木の配列表現 </p>
 
-<p>以下のコードは、配列表現に基づく二分木を実装し、次の操作を含みます：</p>
+<p>以下のコードでは、配列ベースで表現した二分木を実装しており、次の操作を含みます。</p>
 <ul>
-<li>ノードが与えられたとき、その値、左（右）の子ノード、および親ノードを取得する。</li>
-<li>前順、中順、後順、およびレベル順探索シーケンスを取得する。</li>
+<li>あるノードが与えられたとき、その値、左（右）子ノード、親ノードを取得する。</li>
+<li>前順走査、中順走査、後順走査、レベル順走査の列を取得する。</li>
 </ul>
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 <div class="highlight"><span class="filename">array_binary_tree.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayBinaryTree</span><span class="p">:</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;配列ベースの二分木クラス&quot;&quot;&quot;</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;配列表現による二分木クラス&quot;&quot;&quot;</span>
 <a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>
 <a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span> <span class="o">|</span> <span class="kc">None</span><span class="p">]):</span>
 <a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
 <a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_tree</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
 <a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>
 <a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;リストの容量&quot;&quot;&quot;</span>
+<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;リスト容量&quot;&quot;&quot;</span>
 <a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>        <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_tree</span><span class="p">)</span>
 <a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>
 <a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">val</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;インデックスiのノードの値を取得&quot;&quot;&quot;</span>
-<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>        <span class="c1"># インデックスが範囲外の場合、Noneを返し、空席を表す</span>
+<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;インデックス i のノードの値を取得&quot;&quot;&quot;</span>
+<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>        <span class="c1"># インデックスが範囲外なら、空きを表す None を返す</span>
 <a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a>        <span class="k">if</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">i</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">():</span>
 <a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a>            <span class="k">return</span> <span class="kc">None</span>
 <a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_tree</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
 <a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a>
 <a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;インデックスiのノードの左の子のインデックスを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;インデックス i のノードの左子ノードのインデックスを取得&quot;&quot;&quot;</span>
 <a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a>        <span class="k">return</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span>
 <a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a>
 <a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-13-24" name="__codelineno-13-24" href="#__codelineno-13-24"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;インデックスiのノードの右の子のインデックスを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-13-24" name="__codelineno-13-24" href="#__codelineno-13-24"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;インデックス i のノードの右子ノードのインデックスを取得&quot;&quot;&quot;</span>
 <a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a>        <span class="k">return</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">2</span>
 <a id="__codelineno-13-26" name="__codelineno-13-26" href="#__codelineno-13-26"></a>
 <a id="__codelineno-13-27" name="__codelineno-13-27" href="#__codelineno-13-27"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-13-28" name="__codelineno-13-28" href="#__codelineno-13-28"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;インデックスiのノードの親のインデックスを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-13-28" name="__codelineno-13-28" href="#__codelineno-13-28"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;インデックス i のノードの親ノードのインデックスを取得&quot;&quot;&quot;</span>
 <a id="__codelineno-13-29" name="__codelineno-13-29" href="#__codelineno-13-29"></a>        <span class="k">return</span> <span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>
 <a id="__codelineno-13-30" name="__codelineno-13-30" href="#__codelineno-13-30"></a>
 <a id="__codelineno-13-31" name="__codelineno-13-31" href="#__codelineno-13-31"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">level_order</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
 <a id="__codelineno-13-32" name="__codelineno-13-32" href="#__codelineno-13-32"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;レベル順走査&quot;&quot;&quot;</span>
 <a id="__codelineno-13-33" name="__codelineno-13-33" href="#__codelineno-13-33"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
-<a id="__codelineno-13-34" name="__codelineno-13-34" href="#__codelineno-13-34"></a>        <span class="c1"># 配列を走査</span>
+<a id="__codelineno-13-34" name="__codelineno-13-34" href="#__codelineno-13-34"></a>        <span class="c1"># 配列を直接走査する</span>
 <a id="__codelineno-13-35" name="__codelineno-13-35" href="#__codelineno-13-35"></a>        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()):</span>
 <a id="__codelineno-13-36" name="__codelineno-13-36" href="#__codelineno-13-36"></a>            <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-13-37" name="__codelineno-13-37" href="#__codelineno-13-37"></a>                <span class="bp">self</span><span class="o">.</span><span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
 <a id="__codelineno-13-38" name="__codelineno-13-38" href="#__codelineno-13-38"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">res</span>
 <a id="__codelineno-13-39" name="__codelineno-13-39" href="#__codelineno-13-39"></a>
 <a id="__codelineno-13-40" name="__codelineno-13-40" href="#__codelineno-13-40"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">order</span><span class="p">:</span> <span class="nb">str</span><span class="p">):</span>
-<a id="__codelineno-13-41" name="__codelineno-13-41" href="#__codelineno-13-41"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;深さ優先走査&quot;&quot;&quot;</span>
+<a id="__codelineno-13-41" name="__codelineno-13-41" href="#__codelineno-13-41"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;深さ優先探索&quot;&quot;&quot;</span>
 <a id="__codelineno-13-42" name="__codelineno-13-42" href="#__codelineno-13-42"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-13-43" name="__codelineno-13-43" href="#__codelineno-13-43"></a>            <span class="k">return</span>
-<a id="__codelineno-13-44" name="__codelineno-13-44" href="#__codelineno-13-44"></a>        <span class="c1"># 前順走査</span>
+<a id="__codelineno-13-44" name="__codelineno-13-44" href="#__codelineno-13-44"></a>        <span class="c1"># 先行順走査</span>
 <a id="__codelineno-13-45" name="__codelineno-13-45" href="#__codelineno-13-45"></a>        <span class="k">if</span> <span class="n">order</span> <span class="o">==</span> <span class="s2">&quot;pre&quot;</span><span class="p">:</span>
 <a id="__codelineno-13-46" name="__codelineno-13-46" href="#__codelineno-13-46"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
 <a id="__codelineno-13-47" name="__codelineno-13-47" href="#__codelineno-13-47"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">dfs</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="n">order</span><span class="p">)</span>
@@ -4545,7 +4547,7 @@
 <a id="__codelineno-13-54" name="__codelineno-13-54" href="#__codelineno-13-54"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
 <a id="__codelineno-13-55" name="__codelineno-13-55" href="#__codelineno-13-55"></a>
 <a id="__codelineno-13-56" name="__codelineno-13-56" href="#__codelineno-13-56"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
-<a id="__codelineno-13-57" name="__codelineno-13-57" href="#__codelineno-13-57"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;前順走査&quot;&quot;&quot;</span>
+<a id="__codelineno-13-57" name="__codelineno-13-57" href="#__codelineno-13-57"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;先行順走査&quot;&quot;&quot;</span>
 <a id="__codelineno-13-58" name="__codelineno-13-58" href="#__codelineno-13-58"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
 <a id="__codelineno-13-59" name="__codelineno-13-59" href="#__codelineno-13-59"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="s2">&quot;pre&quot;</span><span class="p">)</span>
 <a id="__codelineno-13-60" name="__codelineno-13-60" href="#__codelineno-13-60"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">res</span>
@@ -4564,7 +4566,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_binary_tree.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 配列ベースの二分木クラス */</span>
+<div class="highlight"><span class="filename">array_binary_tree.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 配列表現による二分木クラス */</span>
 <a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayBinaryTree</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
 <a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
@@ -4572,30 +4574,30 @@
 <a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">        </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">;</span>
 <a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>
-<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">    </span><span class="cm">/* リストの容量 */</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">    </span><span class="cm">/* リスト容量 */</span>
 <a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
 <a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a>
 <a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの値を取得 */</span>
 <a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">        </span><span class="c1">// インデックスが範囲外の場合、INT_MAX を返す（null を表す）</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">        </span><span class="c1">// インデックスが範囲外なら、空きを表す INT_MAX を返す</span>
 <a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
 <a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">;</span>
 <a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
 <a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a>
-<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの左の子のインデックスを取得 */</span>
+<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの左子ノードのインデックスを取得 */</span>
 <a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a>
-<a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの右の子のインデックスを取得 */</span>
+<a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの右子ノードのインデックスを取得 */</span>
 <a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
 <a id="__codelineno-14-30" name="__codelineno-14-30" href="#__codelineno-14-30"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-31" name="__codelineno-14-31" href="#__codelineno-14-31"></a>
-<a id="__codelineno-14-32" name="__codelineno-14-32" href="#__codelineno-14-32"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの親のインデックスを取得 */</span>
+<a id="__codelineno-14-32" name="__codelineno-14-32" href="#__codelineno-14-32"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの親ノードのインデックスを取得 */</span>
 <a id="__codelineno-14-33" name="__codelineno-14-33" href="#__codelineno-14-33"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-34" name="__codelineno-14-34" href="#__codelineno-14-34"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
 <a id="__codelineno-14-35" name="__codelineno-14-35" href="#__codelineno-14-35"></a><span class="w">    </span><span class="p">}</span>
@@ -4603,7 +4605,7 @@
 <a id="__codelineno-14-37" name="__codelineno-14-37" href="#__codelineno-14-37"></a><span class="w">    </span><span class="cm">/* レベル順走査 */</span>
 <a id="__codelineno-14-38" name="__codelineno-14-38" href="#__codelineno-14-38"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">levelOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-39" name="__codelineno-14-39" href="#__codelineno-14-39"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
-<a id="__codelineno-14-40" name="__codelineno-14-40" href="#__codelineno-14-40"></a><span class="w">        </span><span class="c1">// 配列を走査</span>
+<a id="__codelineno-14-40" name="__codelineno-14-40" href="#__codelineno-14-40"></a><span class="w">        </span><span class="c1">// 配列を直接走査する</span>
 <a id="__codelineno-14-41" name="__codelineno-14-41" href="#__codelineno-14-41"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-42" name="__codelineno-14-42" href="#__codelineno-14-42"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">)</span>
 <a id="__codelineno-14-43" name="__codelineno-14-43" href="#__codelineno-14-43"></a><span class="w">                </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
@@ -4611,7 +4613,7 @@
 <a id="__codelineno-14-45" name="__codelineno-14-45" href="#__codelineno-14-45"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
 <a id="__codelineno-14-46" name="__codelineno-14-46" href="#__codelineno-14-46"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-47" name="__codelineno-14-47" href="#__codelineno-14-47"></a>
-<a id="__codelineno-14-48" name="__codelineno-14-48" href="#__codelineno-14-48"></a><span class="w">    </span><span class="cm">/* 前順走査 */</span>
+<a id="__codelineno-14-48" name="__codelineno-14-48" href="#__codelineno-14-48"></a><span class="w">    </span><span class="cm">/* 先行順走査 */</span>
 <a id="__codelineno-14-49" name="__codelineno-14-49" href="#__codelineno-14-49"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">preOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-50" name="__codelineno-14-50" href="#__codelineno-14-50"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
 <a id="__codelineno-14-51" name="__codelineno-14-51" href="#__codelineno-14-51"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;pre&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
@@ -4635,12 +4637,12 @@
 <a id="__codelineno-14-69" name="__codelineno-14-69" href="#__codelineno-14-69"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
 <a id="__codelineno-14-70" name="__codelineno-14-70" href="#__codelineno-14-70"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tree</span><span class="p">;</span>
 <a id="__codelineno-14-71" name="__codelineno-14-71" href="#__codelineno-14-71"></a>
-<a id="__codelineno-14-72" name="__codelineno-14-72" href="#__codelineno-14-72"></a><span class="w">    </span><span class="cm">/* 深さ優先走査 */</span>
+<a id="__codelineno-14-72" name="__codelineno-14-72" href="#__codelineno-14-72"></a><span class="w">    </span><span class="cm">/* 深さ優先探索 */</span>
 <a id="__codelineno-14-73" name="__codelineno-14-73" href="#__codelineno-14-73"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-74" name="__codelineno-14-74" href="#__codelineno-14-74"></a><span class="w">        </span><span class="c1">// 空の位置の場合、戻る</span>
+<a id="__codelineno-14-74" name="__codelineno-14-74" href="#__codelineno-14-74"></a><span class="w">        </span><span class="c1">// 空きスロットなら返す</span>
 <a id="__codelineno-14-75" name="__codelineno-14-75" href="#__codelineno-14-75"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">)</span>
 <a id="__codelineno-14-76" name="__codelineno-14-76" href="#__codelineno-14-76"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-14-77" name="__codelineno-14-77" href="#__codelineno-14-77"></a><span class="w">        </span><span class="c1">// 前順走査</span>
+<a id="__codelineno-14-77" name="__codelineno-14-77" href="#__codelineno-14-77"></a><span class="w">        </span><span class="c1">// 先行順走査</span>
 <a id="__codelineno-14-78" name="__codelineno-14-78" href="#__codelineno-14-78"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">&quot;pre&quot;</span><span class="p">)</span>
 <a id="__codelineno-14-79" name="__codelineno-14-79" href="#__codelineno-14-79"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
 <a id="__codelineno-14-80" name="__codelineno-14-80" href="#__codelineno-14-80"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
@@ -4656,7 +4658,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_binary_tree.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 配列ベースの二分木クラス */</span>
+<div class="highlight"><span class="filename">array_binary_tree.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 配列表現による二分木クラス */</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kd">class</span> <span class="nc">ArrayBinaryTree</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tree</span><span class="p">;</span>
 <a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a>
@@ -4665,30 +4667,30 @@
 <a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">        </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">arr</span><span class="p">);</span>
 <a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a>
-<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="cm">/* リストの容量 */</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="cm">/* リスト容量 */</span>
 <a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
 <a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a>
 <a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの値を取得 */</span>
 <a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">Integer</span><span class="w"> </span><span class="nf">val</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">        </span><span class="c1">// インデックスが範囲外の場合、null を返す（空の位置を表す）</span>
+<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">        </span><span class="c1">// インデックスが範囲外なら、空きを表す null を返す</span>
 <a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
 <a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
 <a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
 <a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a>
-<a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの左の子のインデックスを取得 */</span>
+<a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの左子ノードのインデックスを取得 */</span>
 <a id="__codelineno-15-24" name="__codelineno-15-24" href="#__codelineno-15-24"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">Integer</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-15-26" name="__codelineno-15-26" href="#__codelineno-15-26"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></a>
-<a id="__codelineno-15-28" name="__codelineno-15-28" href="#__codelineno-15-28"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの右の子のインデックスを取得 */</span>
+<a id="__codelineno-15-28" name="__codelineno-15-28" href="#__codelineno-15-28"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの右子ノードのインデックスを取得 */</span>
 <a id="__codelineno-15-29" name="__codelineno-15-29" href="#__codelineno-15-29"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">Integer</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-30" name="__codelineno-15-30" href="#__codelineno-15-30"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
 <a id="__codelineno-15-31" name="__codelineno-15-31" href="#__codelineno-15-31"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-32" name="__codelineno-15-32" href="#__codelineno-15-32"></a>
-<a id="__codelineno-15-33" name="__codelineno-15-33" href="#__codelineno-15-33"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの親のインデックスを取得 */</span>
+<a id="__codelineno-15-33" name="__codelineno-15-33" href="#__codelineno-15-33"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの親ノードのインデックスを取得 */</span>
 <a id="__codelineno-15-34" name="__codelineno-15-34" href="#__codelineno-15-34"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">Integer</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-35" name="__codelineno-15-35" href="#__codelineno-15-35"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
 <a id="__codelineno-15-36" name="__codelineno-15-36" href="#__codelineno-15-36"></a><span class="w">    </span><span class="p">}</span>
@@ -4696,7 +4698,7 @@
 <a id="__codelineno-15-38" name="__codelineno-15-38" href="#__codelineno-15-38"></a><span class="w">    </span><span class="cm">/* レベル順走査 */</span>
 <a id="__codelineno-15-39" name="__codelineno-15-39" href="#__codelineno-15-39"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">levelOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-40" name="__codelineno-15-40" href="#__codelineno-15-40"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
-<a id="__codelineno-15-41" name="__codelineno-15-41" href="#__codelineno-15-41"></a><span class="w">        </span><span class="c1">// 配列を走査</span>
+<a id="__codelineno-15-41" name="__codelineno-15-41" href="#__codelineno-15-41"></a><span class="w">        </span><span class="c1">// 配列を直接走査する</span>
 <a id="__codelineno-15-42" name="__codelineno-15-42" href="#__codelineno-15-42"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-43" name="__codelineno-15-43" href="#__codelineno-15-43"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
 <a id="__codelineno-15-44" name="__codelineno-15-44" href="#__codelineno-15-44"></a><span class="w">                </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
@@ -4704,12 +4706,12 @@
 <a id="__codelineno-15-46" name="__codelineno-15-46" href="#__codelineno-15-46"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
 <a id="__codelineno-15-47" name="__codelineno-15-47" href="#__codelineno-15-47"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-48" name="__codelineno-15-48" href="#__codelineno-15-48"></a>
-<a id="__codelineno-15-49" name="__codelineno-15-49" href="#__codelineno-15-49"></a><span class="w">    </span><span class="cm">/* 深さ優先走査 */</span>
+<a id="__codelineno-15-49" name="__codelineno-15-49" href="#__codelineno-15-49"></a><span class="w">    </span><span class="cm">/* 深さ優先探索 */</span>
 <a id="__codelineno-15-50" name="__codelineno-15-50" href="#__codelineno-15-50"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">Integer</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-51" name="__codelineno-15-51" href="#__codelineno-15-51"></a><span class="w">        </span><span class="c1">// 空の位置の場合、戻る</span>
+<a id="__codelineno-15-51" name="__codelineno-15-51" href="#__codelineno-15-51"></a><span class="w">        </span><span class="c1">// 空きスロットなら返す</span>
 <a id="__codelineno-15-52" name="__codelineno-15-52" href="#__codelineno-15-52"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
 <a id="__codelineno-15-53" name="__codelineno-15-53" href="#__codelineno-15-53"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-15-54" name="__codelineno-15-54" href="#__codelineno-15-54"></a><span class="w">        </span><span class="c1">// 前順走査</span>
+<a id="__codelineno-15-54" name="__codelineno-15-54" href="#__codelineno-15-54"></a><span class="w">        </span><span class="c1">// 先行順走査</span>
 <a id="__codelineno-15-55" name="__codelineno-15-55" href="#__codelineno-15-55"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="s">&quot;pre&quot;</span><span class="p">.</span><span class="na">equals</span><span class="p">(</span><span class="n">order</span><span class="p">))</span>
 <a id="__codelineno-15-56" name="__codelineno-15-56" href="#__codelineno-15-56"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
 <a id="__codelineno-15-57" name="__codelineno-15-57" href="#__codelineno-15-57"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
@@ -4722,7 +4724,7 @@
 <a id="__codelineno-15-64" name="__codelineno-15-64" href="#__codelineno-15-64"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
 <a id="__codelineno-15-65" name="__codelineno-15-65" href="#__codelineno-15-65"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-66" name="__codelineno-15-66" href="#__codelineno-15-66"></a>
-<a id="__codelineno-15-67" name="__codelineno-15-67" href="#__codelineno-15-67"></a><span class="w">    </span><span class="cm">/* 前順走査 */</span>
+<a id="__codelineno-15-67" name="__codelineno-15-67" href="#__codelineno-15-67"></a><span class="w">    </span><span class="cm">/* 先行順走査 */</span>
 <a id="__codelineno-15-68" name="__codelineno-15-68" href="#__codelineno-15-68"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-69" name="__codelineno-15-69" href="#__codelineno-15-69"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
 <a id="__codelineno-15-70" name="__codelineno-15-70" href="#__codelineno-15-70"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;pre&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
@@ -4746,59 +4748,916 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_binary_tree.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_binary_tree.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 配列表現による二分木クラス */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="k">class</span><span class="w"> </span><span class="nf">ArrayBinaryTree</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int?</span><span class="o">&gt;</span><span class="w"> </span><span class="n">arr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int?</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="n">arr</span><span class="p">);</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="cm">/* リスト容量 */</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">.</span><span class="n">Count</span><span class="p">;</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの値を取得 */</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int?</span><span class="w"> </span><span class="n">Val</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">        </span><span class="c1">// インデックスが範囲外なら、空きを表す null を返す</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">Size</span><span class="p">())</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの左子ノードのインデックスを取得 */</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a>
+<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの右子ノードのインデックスを取得 */</span>
+<a id="__codelineno-16-24" name="__codelineno-16-24" href="#__codelineno-16-24"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-25" name="__codelineno-16-25" href="#__codelineno-16-25"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-16-26" name="__codelineno-16-26" href="#__codelineno-16-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-27" name="__codelineno-16-27" href="#__codelineno-16-27"></a>
+<a id="__codelineno-16-28" name="__codelineno-16-28" href="#__codelineno-16-28"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの親ノードのインデックスを取得 */</span>
+<a id="__codelineno-16-29" name="__codelineno-16-29" href="#__codelineno-16-29"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-30" name="__codelineno-16-30" href="#__codelineno-16-30"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-16-31" name="__codelineno-16-31" href="#__codelineno-16-31"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-32" name="__codelineno-16-32" href="#__codelineno-16-32"></a>
+<a id="__codelineno-16-33" name="__codelineno-16-33" href="#__codelineno-16-33"></a><span class="w">    </span><span class="cm">/* レベル順走査 */</span>
+<a id="__codelineno-16-34" name="__codelineno-16-34" href="#__codelineno-16-34"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">LevelOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-35" name="__codelineno-16-35" href="#__codelineno-16-35"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-16-36" name="__codelineno-16-36" href="#__codelineno-16-36"></a><span class="w">        </span><span class="c1">// 配列を直接走査する</span>
+<a id="__codelineno-16-37" name="__codelineno-16-37" href="#__codelineno-16-37"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">Size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-38" name="__codelineno-16-38" href="#__codelineno-16-38"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">Val</span><span class="p">(</span><span class="n">i</span><span class="p">).</span><span class="n">HasValue</span><span class="p">)</span>
+<a id="__codelineno-16-39" name="__codelineno-16-39" href="#__codelineno-16-39"></a><span class="w">                </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">Val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">!</span><span class="p">.</span><span class="n">Value</span><span class="p">);</span>
+<a id="__codelineno-16-40" name="__codelineno-16-40" href="#__codelineno-16-40"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-41" name="__codelineno-16-41" href="#__codelineno-16-41"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-16-42" name="__codelineno-16-42" href="#__codelineno-16-42"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-43" name="__codelineno-16-43" href="#__codelineno-16-43"></a>
+<a id="__codelineno-16-44" name="__codelineno-16-44" href="#__codelineno-16-44"></a><span class="w">    </span><span class="cm">/* 深さ優先探索 */</span>
+<a id="__codelineno-16-45" name="__codelineno-16-45" href="#__codelineno-16-45"></a><span class="w">    </span><span class="k">void</span><span class="w"> </span><span class="nf">DFS</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">string</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-46" name="__codelineno-16-46" href="#__codelineno-16-46"></a><span class="w">        </span><span class="c1">// 空きスロットなら返す</span>
+<a id="__codelineno-16-47" name="__codelineno-16-47" href="#__codelineno-16-47"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">Val</span><span class="p">(</span><span class="n">i</span><span class="p">).</span><span class="n">HasValue</span><span class="p">)</span>
+<a id="__codelineno-16-48" name="__codelineno-16-48" href="#__codelineno-16-48"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-16-49" name="__codelineno-16-49" href="#__codelineno-16-49"></a><span class="w">        </span><span class="c1">// 先行順走査</span>
+<a id="__codelineno-16-50" name="__codelineno-16-50" href="#__codelineno-16-50"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">&quot;pre&quot;</span><span class="p">)</span>
+<a id="__codelineno-16-51" name="__codelineno-16-51" href="#__codelineno-16-51"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">Val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">!</span><span class="p">.</span><span class="n">Value</span><span class="p">);</span>
+<a id="__codelineno-16-52" name="__codelineno-16-52" href="#__codelineno-16-52"></a><span class="w">        </span><span class="n">DFS</span><span class="p">(</span><span class="n">Left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-16-53" name="__codelineno-16-53" href="#__codelineno-16-53"></a><span class="w">        </span><span class="c1">// 中順走査</span>
+<a id="__codelineno-16-54" name="__codelineno-16-54" href="#__codelineno-16-54"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">&quot;in&quot;</span><span class="p">)</span>
+<a id="__codelineno-16-55" name="__codelineno-16-55" href="#__codelineno-16-55"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">Val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">!</span><span class="p">.</span><span class="n">Value</span><span class="p">);</span>
+<a id="__codelineno-16-56" name="__codelineno-16-56" href="#__codelineno-16-56"></a><span class="w">        </span><span class="n">DFS</span><span class="p">(</span><span class="n">Right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-16-57" name="__codelineno-16-57" href="#__codelineno-16-57"></a><span class="w">        </span><span class="c1">// 後順走査</span>
+<a id="__codelineno-16-58" name="__codelineno-16-58" href="#__codelineno-16-58"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">&quot;post&quot;</span><span class="p">)</span>
+<a id="__codelineno-16-59" name="__codelineno-16-59" href="#__codelineno-16-59"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">Val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">!</span><span class="p">.</span><span class="n">Value</span><span class="p">);</span>
+<a id="__codelineno-16-60" name="__codelineno-16-60" href="#__codelineno-16-60"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-61" name="__codelineno-16-61" href="#__codelineno-16-61"></a>
+<a id="__codelineno-16-62" name="__codelineno-16-62" href="#__codelineno-16-62"></a><span class="w">    </span><span class="cm">/* 先行順走査 */</span>
+<a id="__codelineno-16-63" name="__codelineno-16-63" href="#__codelineno-16-63"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">PreOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-64" name="__codelineno-16-64" href="#__codelineno-16-64"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-16-65" name="__codelineno-16-65" href="#__codelineno-16-65"></a><span class="w">        </span><span class="n">DFS</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;pre&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-16-66" name="__codelineno-16-66" href="#__codelineno-16-66"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-16-67" name="__codelineno-16-67" href="#__codelineno-16-67"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-68" name="__codelineno-16-68" href="#__codelineno-16-68"></a>
+<a id="__codelineno-16-69" name="__codelineno-16-69" href="#__codelineno-16-69"></a><span class="w">    </span><span class="cm">/* 中順走査 */</span>
+<a id="__codelineno-16-70" name="__codelineno-16-70" href="#__codelineno-16-70"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">InOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-71" name="__codelineno-16-71" href="#__codelineno-16-71"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-16-72" name="__codelineno-16-72" href="#__codelineno-16-72"></a><span class="w">        </span><span class="n">DFS</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;in&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-16-73" name="__codelineno-16-73" href="#__codelineno-16-73"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-16-74" name="__codelineno-16-74" href="#__codelineno-16-74"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-75" name="__codelineno-16-75" href="#__codelineno-16-75"></a>
+<a id="__codelineno-16-76" name="__codelineno-16-76" href="#__codelineno-16-76"></a><span class="w">    </span><span class="cm">/* 後順走査 */</span>
+<a id="__codelineno-16-77" name="__codelineno-16-77" href="#__codelineno-16-77"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">PostOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-78" name="__codelineno-16-78" href="#__codelineno-16-78"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-16-79" name="__codelineno-16-79" href="#__codelineno-16-79"></a><span class="w">        </span><span class="n">DFS</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;post&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-16-80" name="__codelineno-16-80" href="#__codelineno-16-80"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-16-81" name="__codelineno-16-81" href="#__codelineno-16-81"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-82" name="__codelineno-16-82" href="#__codelineno-16-82"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_binary_tree.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">arrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_binary_tree.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 配列表現による二分木クラス */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">arrayBinaryTree</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="nx">tree</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="p">}</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="kd">func</span><span class="w"> </span><span class="nx">newArrayBinaryTree</span><span class="p">(</span><span class="nx">arr</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayBinaryTree</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">arrayBinaryTree</span><span class="p">{</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">        </span><span class="nx">tree</span><span class="p">:</span><span class="w"> </span><span class="nx">arr</span><span class="p">,</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="p">}</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="cm">/* リスト容量 */</span>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">abt</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayBinaryTree</span><span class="p">)</span><span class="w"> </span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">abt</span><span class="p">.</span><span class="nx">tree</span><span class="p">)</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="p">}</span>
+<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a>
+<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="cm">/* インデックス i のノードの値を取得 */</span>
+<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">abt</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayBinaryTree</span><span class="p">)</span><span class="w"> </span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a><span class="w">    </span><span class="c1">// インデックスが範囲外なら、空きを表す null を返す</span>
+<a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">abt</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-22" name="__codelineno-17-22" href="#__codelineno-17-22"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-17-23" name="__codelineno-17-23" href="#__codelineno-17-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-24" name="__codelineno-17-24" href="#__codelineno-17-24"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">abt</span><span class="p">.</span><span class="nx">tree</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
+<a id="__codelineno-17-25" name="__codelineno-17-25" href="#__codelineno-17-25"></a><span class="p">}</span>
+<a id="__codelineno-17-26" name="__codelineno-17-26" href="#__codelineno-17-26"></a>
+<a id="__codelineno-17-27" name="__codelineno-17-27" href="#__codelineno-17-27"></a><span class="cm">/* インデックス i のノードの左子ノードのインデックスを取得 */</span>
+<a id="__codelineno-17-28" name="__codelineno-17-28" href="#__codelineno-17-28"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">abt</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayBinaryTree</span><span class="p">)</span><span class="w"> </span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-29" name="__codelineno-17-29" href="#__codelineno-17-29"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="o">*</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-17-30" name="__codelineno-17-30" href="#__codelineno-17-30"></a><span class="p">}</span>
+<a id="__codelineno-17-31" name="__codelineno-17-31" href="#__codelineno-17-31"></a>
+<a id="__codelineno-17-32" name="__codelineno-17-32" href="#__codelineno-17-32"></a><span class="cm">/* インデックス i のノードの右子ノードのインデックスを取得 */</span>
+<a id="__codelineno-17-33" name="__codelineno-17-33" href="#__codelineno-17-33"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">abt</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayBinaryTree</span><span class="p">)</span><span class="w"> </span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-34" name="__codelineno-17-34" href="#__codelineno-17-34"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="o">*</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-17-35" name="__codelineno-17-35" href="#__codelineno-17-35"></a><span class="p">}</span>
+<a id="__codelineno-17-36" name="__codelineno-17-36" href="#__codelineno-17-36"></a>
+<a id="__codelineno-17-37" name="__codelineno-17-37" href="#__codelineno-17-37"></a><span class="cm">/* インデックス i のノードの親ノードのインデックスを取得 */</span>
+<a id="__codelineno-17-38" name="__codelineno-17-38" href="#__codelineno-17-38"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">abt</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayBinaryTree</span><span class="p">)</span><span class="w"> </span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-39" name="__codelineno-17-39" href="#__codelineno-17-39"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-17-40" name="__codelineno-17-40" href="#__codelineno-17-40"></a><span class="p">}</span>
+<a id="__codelineno-17-41" name="__codelineno-17-41" href="#__codelineno-17-41"></a>
+<a id="__codelineno-17-42" name="__codelineno-17-42" href="#__codelineno-17-42"></a><span class="cm">/* レベル順走査 */</span>
+<a id="__codelineno-17-43" name="__codelineno-17-43" href="#__codelineno-17-43"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">abt</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayBinaryTree</span><span class="p">)</span><span class="w"> </span><span class="nx">levelOrder</span><span class="p">()</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-44" name="__codelineno-17-44" href="#__codelineno-17-44"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span>
+<a id="__codelineno-17-45" name="__codelineno-17-45" href="#__codelineno-17-45"></a><span class="w">    </span><span class="c1">// 配列を直接走査する</span>
+<a id="__codelineno-17-46" name="__codelineno-17-46" href="#__codelineno-17-46"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">abt</span><span class="p">.</span><span class="nx">size</span><span class="p">();</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-47" name="__codelineno-17-47" href="#__codelineno-17-47"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">abt</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-48" name="__codelineno-17-48" href="#__codelineno-17-48"></a><span class="w">            </span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">abt</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">))</span>
+<a id="__codelineno-17-49" name="__codelineno-17-49" href="#__codelineno-17-49"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-17-50" name="__codelineno-17-50" href="#__codelineno-17-50"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-51" name="__codelineno-17-51" href="#__codelineno-17-51"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
+<a id="__codelineno-17-52" name="__codelineno-17-52" href="#__codelineno-17-52"></a><span class="p">}</span>
+<a id="__codelineno-17-53" name="__codelineno-17-53" href="#__codelineno-17-53"></a>
+<a id="__codelineno-17-54" name="__codelineno-17-54" href="#__codelineno-17-54"></a><span class="cm">/* 深さ優先探索 */</span>
+<a id="__codelineno-17-55" name="__codelineno-17-55" href="#__codelineno-17-55"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">abt</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayBinaryTree</span><span class="p">)</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">order</span><span class="w"> </span><span class="kt">string</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="kt">any</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-56" name="__codelineno-17-56" href="#__codelineno-17-56"></a><span class="w">    </span><span class="c1">// 空きスロットなら返す</span>
+<a id="__codelineno-17-57" name="__codelineno-17-57" href="#__codelineno-17-57"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">abt</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-58" name="__codelineno-17-58" href="#__codelineno-17-58"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-17-59" name="__codelineno-17-59" href="#__codelineno-17-59"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-60" name="__codelineno-17-60" href="#__codelineno-17-60"></a><span class="w">    </span><span class="c1">// 先行順走査</span>
+<a id="__codelineno-17-61" name="__codelineno-17-61" href="#__codelineno-17-61"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">&quot;pre&quot;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-62" name="__codelineno-17-62" href="#__codelineno-17-62"></a><span class="w">        </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">abt</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">))</span>
+<a id="__codelineno-17-63" name="__codelineno-17-63" href="#__codelineno-17-63"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-64" name="__codelineno-17-64" href="#__codelineno-17-64"></a><span class="w">    </span><span class="nx">abt</span><span class="p">.</span><span class="nx">dfs</span><span class="p">(</span><span class="nx">abt</span><span class="p">.</span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span><span class="w"> </span><span class="nx">order</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
+<a id="__codelineno-17-65" name="__codelineno-17-65" href="#__codelineno-17-65"></a><span class="w">    </span><span class="c1">// 中順走査</span>
+<a id="__codelineno-17-66" name="__codelineno-17-66" href="#__codelineno-17-66"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">&quot;in&quot;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-67" name="__codelineno-17-67" href="#__codelineno-17-67"></a><span class="w">        </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">abt</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">))</span>
+<a id="__codelineno-17-68" name="__codelineno-17-68" href="#__codelineno-17-68"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-69" name="__codelineno-17-69" href="#__codelineno-17-69"></a><span class="w">    </span><span class="nx">abt</span><span class="p">.</span><span class="nx">dfs</span><span class="p">(</span><span class="nx">abt</span><span class="p">.</span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span><span class="w"> </span><span class="nx">order</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
+<a id="__codelineno-17-70" name="__codelineno-17-70" href="#__codelineno-17-70"></a><span class="w">    </span><span class="c1">// 後順走査</span>
+<a id="__codelineno-17-71" name="__codelineno-17-71" href="#__codelineno-17-71"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">&quot;post&quot;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-72" name="__codelineno-17-72" href="#__codelineno-17-72"></a><span class="w">        </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">abt</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">))</span>
+<a id="__codelineno-17-73" name="__codelineno-17-73" href="#__codelineno-17-73"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-74" name="__codelineno-17-74" href="#__codelineno-17-74"></a><span class="p">}</span>
+<a id="__codelineno-17-75" name="__codelineno-17-75" href="#__codelineno-17-75"></a>
+<a id="__codelineno-17-76" name="__codelineno-17-76" href="#__codelineno-17-76"></a><span class="cm">/* 先行順走査 */</span>
+<a id="__codelineno-17-77" name="__codelineno-17-77" href="#__codelineno-17-77"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">abt</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayBinaryTree</span><span class="p">)</span><span class="w"> </span><span class="nx">preOrder</span><span class="p">()</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-78" name="__codelineno-17-78" href="#__codelineno-17-78"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span>
+<a id="__codelineno-17-79" name="__codelineno-17-79" href="#__codelineno-17-79"></a><span class="w">    </span><span class="nx">abt</span><span class="p">.</span><span class="nx">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;pre&quot;</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">res</span><span class="p">)</span>
+<a id="__codelineno-17-80" name="__codelineno-17-80" href="#__codelineno-17-80"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
+<a id="__codelineno-17-81" name="__codelineno-17-81" href="#__codelineno-17-81"></a><span class="p">}</span>
+<a id="__codelineno-17-82" name="__codelineno-17-82" href="#__codelineno-17-82"></a>
+<a id="__codelineno-17-83" name="__codelineno-17-83" href="#__codelineno-17-83"></a><span class="cm">/* 中順走査 */</span>
+<a id="__codelineno-17-84" name="__codelineno-17-84" href="#__codelineno-17-84"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">abt</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayBinaryTree</span><span class="p">)</span><span class="w"> </span><span class="nx">inOrder</span><span class="p">()</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-85" name="__codelineno-17-85" href="#__codelineno-17-85"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span>
+<a id="__codelineno-17-86" name="__codelineno-17-86" href="#__codelineno-17-86"></a><span class="w">    </span><span class="nx">abt</span><span class="p">.</span><span class="nx">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;in&quot;</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">res</span><span class="p">)</span>
+<a id="__codelineno-17-87" name="__codelineno-17-87" href="#__codelineno-17-87"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
+<a id="__codelineno-17-88" name="__codelineno-17-88" href="#__codelineno-17-88"></a><span class="p">}</span>
+<a id="__codelineno-17-89" name="__codelineno-17-89" href="#__codelineno-17-89"></a>
+<a id="__codelineno-17-90" name="__codelineno-17-90" href="#__codelineno-17-90"></a><span class="cm">/* 後順走査 */</span>
+<a id="__codelineno-17-91" name="__codelineno-17-91" href="#__codelineno-17-91"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">abt</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayBinaryTree</span><span class="p">)</span><span class="w"> </span><span class="nx">postOrder</span><span class="p">()</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-92" name="__codelineno-17-92" href="#__codelineno-17-92"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span>
+<a id="__codelineno-17-93" name="__codelineno-17-93" href="#__codelineno-17-93"></a><span class="w">    </span><span class="nx">abt</span><span class="p">.</span><span class="nx">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;post&quot;</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">res</span><span class="p">)</span>
+<a id="__codelineno-17-94" name="__codelineno-17-94" href="#__codelineno-17-94"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
+<a id="__codelineno-17-95" name="__codelineno-17-95" href="#__codelineno-17-95"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_binary_tree.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_binary_tree.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 配列表現による二分木クラス */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ArrayBinaryTree</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">tree</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">?]</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">    </span><span class="kd">init</span><span class="p">(</span><span class="n">arr</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">?])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">        </span><span class="n">tree</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">arr</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">    </span><span class="cm">/* リスト容量 */</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w">        </span><span class="n">tree</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a>
+<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの値を取得 */</span>
+<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">val</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="p">?</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="w">        </span><span class="c1">// インデックスが範囲外なら、空きを表す null を返す</span>
+<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-18-22" name="__codelineno-18-22" href="#__codelineno-18-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-23" name="__codelineno-18-23" href="#__codelineno-18-23"></a>
+<a id="__codelineno-18-24" name="__codelineno-18-24" href="#__codelineno-18-24"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの左子ノードのインデックスを取得 */</span>
+<a id="__codelineno-18-25" name="__codelineno-18-25" href="#__codelineno-18-25"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-26" name="__codelineno-18-26" href="#__codelineno-18-26"></a><span class="w">        </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-18-27" name="__codelineno-18-27" href="#__codelineno-18-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-28" name="__codelineno-18-28" href="#__codelineno-18-28"></a>
+<a id="__codelineno-18-29" name="__codelineno-18-29" href="#__codelineno-18-29"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの右子ノードのインデックスを取得 */</span>
+<a id="__codelineno-18-30" name="__codelineno-18-30" href="#__codelineno-18-30"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-31" name="__codelineno-18-31" href="#__codelineno-18-31"></a><span class="w">        </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-18-32" name="__codelineno-18-32" href="#__codelineno-18-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-33" name="__codelineno-18-33" href="#__codelineno-18-33"></a>
+<a id="__codelineno-18-34" name="__codelineno-18-34" href="#__codelineno-18-34"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの親ノードのインデックスを取得 */</span>
+<a id="__codelineno-18-35" name="__codelineno-18-35" href="#__codelineno-18-35"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-36" name="__codelineno-18-36" href="#__codelineno-18-36"></a><span class="w">        </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-18-37" name="__codelineno-18-37" href="#__codelineno-18-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-38" name="__codelineno-18-38" href="#__codelineno-18-38"></a>
+<a id="__codelineno-18-39" name="__codelineno-18-39" href="#__codelineno-18-39"></a><span class="w">    </span><span class="cm">/* レベル順走査 */</span>
+<a id="__codelineno-18-40" name="__codelineno-18-40" href="#__codelineno-18-40"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">levelOrder</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-41" name="__codelineno-18-41" href="#__codelineno-18-41"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
+<a id="__codelineno-18-42" name="__codelineno-18-42" href="#__codelineno-18-42"></a><span class="w">        </span><span class="c1">// 配列を直接走査する</span>
+<a id="__codelineno-18-43" name="__codelineno-18-43" href="#__codelineno-18-43"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-44" name="__codelineno-18-44" href="#__codelineno-18-44"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-45" name="__codelineno-18-45" href="#__codelineno-18-45"></a><span class="w">                </span><span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-18-46" name="__codelineno-18-46" href="#__codelineno-18-46"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-18-47" name="__codelineno-18-47" href="#__codelineno-18-47"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-48" name="__codelineno-18-48" href="#__codelineno-18-48"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-18-49" name="__codelineno-18-49" href="#__codelineno-18-49"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-50" name="__codelineno-18-50" href="#__codelineno-18-50"></a>
+<a id="__codelineno-18-51" name="__codelineno-18-51" href="#__codelineno-18-51"></a><span class="w">    </span><span class="cm">/* 深さ優先探索 */</span>
+<a id="__codelineno-18-52" name="__codelineno-18-52" href="#__codelineno-18-52"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">func</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">order</span><span class="p">:</span><span class="w"> </span><span class="nb">String</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-53" name="__codelineno-18-53" href="#__codelineno-18-53"></a><span class="w">        </span><span class="c1">// 空きスロットなら返す</span>
+<a id="__codelineno-18-54" name="__codelineno-18-54" href="#__codelineno-18-54"></a><span class="w">        </span><span class="k">guard</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-55" name="__codelineno-18-55" href="#__codelineno-18-55"></a><span class="w">            </span><span class="k">return</span>
+<a id="__codelineno-18-56" name="__codelineno-18-56" href="#__codelineno-18-56"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-57" name="__codelineno-18-57" href="#__codelineno-18-57"></a><span class="w">        </span><span class="c1">// 先行順走査</span>
+<a id="__codelineno-18-58" name="__codelineno-18-58" href="#__codelineno-18-58"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="s">&quot;pre&quot;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-59" name="__codelineno-18-59" href="#__codelineno-18-59"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-18-60" name="__codelineno-18-60" href="#__codelineno-18-60"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-61" name="__codelineno-18-61" href="#__codelineno-18-61"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kr">left</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">:</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-18-62" name="__codelineno-18-62" href="#__codelineno-18-62"></a><span class="w">        </span><span class="c1">// 中順走査</span>
+<a id="__codelineno-18-63" name="__codelineno-18-63" href="#__codelineno-18-63"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="s">&quot;in&quot;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-64" name="__codelineno-18-64" href="#__codelineno-18-64"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-18-65" name="__codelineno-18-65" href="#__codelineno-18-65"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-66" name="__codelineno-18-66" href="#__codelineno-18-66"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kr">right</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">:</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-18-67" name="__codelineno-18-67" href="#__codelineno-18-67"></a><span class="w">        </span><span class="c1">// 後順走査</span>
+<a id="__codelineno-18-68" name="__codelineno-18-68" href="#__codelineno-18-68"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="s">&quot;post&quot;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-69" name="__codelineno-18-69" href="#__codelineno-18-69"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-18-70" name="__codelineno-18-70" href="#__codelineno-18-70"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-71" name="__codelineno-18-71" href="#__codelineno-18-71"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-72" name="__codelineno-18-72" href="#__codelineno-18-72"></a>
+<a id="__codelineno-18-73" name="__codelineno-18-73" href="#__codelineno-18-73"></a><span class="w">    </span><span class="cm">/* 先行順走査 */</span>
+<a id="__codelineno-18-74" name="__codelineno-18-74" href="#__codelineno-18-74"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-75" name="__codelineno-18-75" href="#__codelineno-18-75"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
+<a id="__codelineno-18-76" name="__codelineno-18-76" href="#__codelineno-18-76"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">order</span><span class="p">:</span><span class="w"> </span><span class="s">&quot;pre&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-18-77" name="__codelineno-18-77" href="#__codelineno-18-77"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-18-78" name="__codelineno-18-78" href="#__codelineno-18-78"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-79" name="__codelineno-18-79" href="#__codelineno-18-79"></a>
+<a id="__codelineno-18-80" name="__codelineno-18-80" href="#__codelineno-18-80"></a><span class="w">    </span><span class="cm">/* 中順走査 */</span>
+<a id="__codelineno-18-81" name="__codelineno-18-81" href="#__codelineno-18-81"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">inOrder</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-82" name="__codelineno-18-82" href="#__codelineno-18-82"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
+<a id="__codelineno-18-83" name="__codelineno-18-83" href="#__codelineno-18-83"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">order</span><span class="p">:</span><span class="w"> </span><span class="s">&quot;in&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-18-84" name="__codelineno-18-84" href="#__codelineno-18-84"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-18-85" name="__codelineno-18-85" href="#__codelineno-18-85"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-86" name="__codelineno-18-86" href="#__codelineno-18-86"></a>
+<a id="__codelineno-18-87" name="__codelineno-18-87" href="#__codelineno-18-87"></a><span class="w">    </span><span class="cm">/* 後順走査 */</span>
+<a id="__codelineno-18-88" name="__codelineno-18-88" href="#__codelineno-18-88"></a><span class="w">    </span><span class="kd">func</span><span class="w"> </span><span class="nf">postOrder</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-89" name="__codelineno-18-89" href="#__codelineno-18-89"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
+<a id="__codelineno-18-90" name="__codelineno-18-90" href="#__codelineno-18-90"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">order</span><span class="p">:</span><span class="w"> </span><span class="s">&quot;post&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-18-91" name="__codelineno-18-91" href="#__codelineno-18-91"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-18-92" name="__codelineno-18-92" href="#__codelineno-18-92"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-93" name="__codelineno-18-93" href="#__codelineno-18-93"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_binary_tree.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_binary_tree.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 配列表現による二分木クラス */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">ArrayBinaryTree</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="n">#tree</span><span class="p">;</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">arr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">arr</span><span class="p">;</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w">    </span><span class="cm">/* リスト容量 */</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w">    </span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#tree</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a>
+<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの値を取得 */</span>
+<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a><span class="w">    </span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="w">        </span><span class="c1">// インデックスが範囲外なら、空きを表す null を返す</span>
+<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">())</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#tree</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a>
+<a id="__codelineno-19-22" name="__codelineno-19-22" href="#__codelineno-19-22"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの左子ノードのインデックスを取得 */</span>
+<a id="__codelineno-19-23" name="__codelineno-19-23" href="#__codelineno-19-23"></a><span class="w">    </span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-24" name="__codelineno-19-24" href="#__codelineno-19-24"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-19-25" name="__codelineno-19-25" href="#__codelineno-19-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-26" name="__codelineno-19-26" href="#__codelineno-19-26"></a>
+<a id="__codelineno-19-27" name="__codelineno-19-27" href="#__codelineno-19-27"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの右子ノードのインデックスを取得 */</span>
+<a id="__codelineno-19-28" name="__codelineno-19-28" href="#__codelineno-19-28"></a><span class="w">    </span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-29" name="__codelineno-19-29" href="#__codelineno-19-29"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
+<a id="__codelineno-19-30" name="__codelineno-19-30" href="#__codelineno-19-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-31" name="__codelineno-19-31" href="#__codelineno-19-31"></a>
+<a id="__codelineno-19-32" name="__codelineno-19-32" href="#__codelineno-19-32"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの親ノードのインデックスを取得 */</span>
+<a id="__codelineno-19-33" name="__codelineno-19-33" href="#__codelineno-19-33"></a><span class="w">    </span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-34" name="__codelineno-19-34" href="#__codelineno-19-34"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">((</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 切り捨て除算</span>
+<a id="__codelineno-19-35" name="__codelineno-19-35" href="#__codelineno-19-35"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-36" name="__codelineno-19-36" href="#__codelineno-19-36"></a>
+<a id="__codelineno-19-37" name="__codelineno-19-37" href="#__codelineno-19-37"></a><span class="w">    </span><span class="cm">/* レベル順走査 */</span>
+<a id="__codelineno-19-38" name="__codelineno-19-38" href="#__codelineno-19-38"></a><span class="w">    </span><span class="nx">levelOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-39" name="__codelineno-19-39" href="#__codelineno-19-39"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-19-40" name="__codelineno-19-40" href="#__codelineno-19-40"></a><span class="w">        </span><span class="c1">// 配列を直接走査する</span>
+<a id="__codelineno-19-41" name="__codelineno-19-41" href="#__codelineno-19-41"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">();</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-42" name="__codelineno-19-42" href="#__codelineno-19-42"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">));</span>
+<a id="__codelineno-19-43" name="__codelineno-19-43" href="#__codelineno-19-43"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-19-44" name="__codelineno-19-44" href="#__codelineno-19-44"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-19-45" name="__codelineno-19-45" href="#__codelineno-19-45"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-46" name="__codelineno-19-46" href="#__codelineno-19-46"></a>
+<a id="__codelineno-19-47" name="__codelineno-19-47" href="#__codelineno-19-47"></a><span class="w">    </span><span class="cm">/* 深さ優先探索 */</span>
+<a id="__codelineno-19-48" name="__codelineno-19-48" href="#__codelineno-19-48"></a><span class="w">    </span><span class="n">#dfs</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">order</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-49" name="__codelineno-19-49" href="#__codelineno-19-49"></a><span class="w">        </span><span class="c1">// 空きスロットなら返す</span>
+<a id="__codelineno-19-50" name="__codelineno-19-50" href="#__codelineno-19-50"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-19-51" name="__codelineno-19-51" href="#__codelineno-19-51"></a><span class="w">        </span><span class="c1">// 先行順走査</span>
+<a id="__codelineno-19-52" name="__codelineno-19-52" href="#__codelineno-19-52"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">order</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="s1">&#39;pre&#39;</span><span class="p">)</span><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">));</span>
+<a id="__codelineno-19-53" name="__codelineno-19-53" href="#__codelineno-19-53"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#dfs</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span><span class="w"> </span><span class="nx">order</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-19-54" name="__codelineno-19-54" href="#__codelineno-19-54"></a><span class="w">        </span><span class="c1">// 中順走査</span>
+<a id="__codelineno-19-55" name="__codelineno-19-55" href="#__codelineno-19-55"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">order</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="s1">&#39;in&#39;</span><span class="p">)</span><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">));</span>
+<a id="__codelineno-19-56" name="__codelineno-19-56" href="#__codelineno-19-56"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#dfs</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span><span class="w"> </span><span class="nx">order</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-19-57" name="__codelineno-19-57" href="#__codelineno-19-57"></a><span class="w">        </span><span class="c1">// 後順走査</span>
+<a id="__codelineno-19-58" name="__codelineno-19-58" href="#__codelineno-19-58"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">order</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="s1">&#39;post&#39;</span><span class="p">)</span><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">));</span>
+<a id="__codelineno-19-59" name="__codelineno-19-59" href="#__codelineno-19-59"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-60" name="__codelineno-19-60" href="#__codelineno-19-60"></a>
+<a id="__codelineno-19-61" name="__codelineno-19-61" href="#__codelineno-19-61"></a><span class="w">    </span><span class="cm">/* 先行順走査 */</span>
+<a id="__codelineno-19-62" name="__codelineno-19-62" href="#__codelineno-19-62"></a><span class="w">    </span><span class="nx">preOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-63" name="__codelineno-19-63" href="#__codelineno-19-63"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-19-64" name="__codelineno-19-64" href="#__codelineno-19-64"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#dfs</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;pre&#39;</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-19-65" name="__codelineno-19-65" href="#__codelineno-19-65"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-19-66" name="__codelineno-19-66" href="#__codelineno-19-66"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-67" name="__codelineno-19-67" href="#__codelineno-19-67"></a>
+<a id="__codelineno-19-68" name="__codelineno-19-68" href="#__codelineno-19-68"></a><span class="w">    </span><span class="cm">/* 中順走査 */</span>
+<a id="__codelineno-19-69" name="__codelineno-19-69" href="#__codelineno-19-69"></a><span class="w">    </span><span class="nx">inOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-70" name="__codelineno-19-70" href="#__codelineno-19-70"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-19-71" name="__codelineno-19-71" href="#__codelineno-19-71"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#dfs</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;in&#39;</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-19-72" name="__codelineno-19-72" href="#__codelineno-19-72"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-19-73" name="__codelineno-19-73" href="#__codelineno-19-73"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-74" name="__codelineno-19-74" href="#__codelineno-19-74"></a>
+<a id="__codelineno-19-75" name="__codelineno-19-75" href="#__codelineno-19-75"></a><span class="w">    </span><span class="cm">/* 後順走査 */</span>
+<a id="__codelineno-19-76" name="__codelineno-19-76" href="#__codelineno-19-76"></a><span class="w">    </span><span class="nx">postOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-77" name="__codelineno-19-77" href="#__codelineno-19-77"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-19-78" name="__codelineno-19-78" href="#__codelineno-19-78"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#dfs</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;post&#39;</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-19-79" name="__codelineno-19-79" href="#__codelineno-19-79"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-19-80" name="__codelineno-19-80" href="#__codelineno-19-80"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-81" name="__codelineno-19-81" href="#__codelineno-19-81"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_binary_tree.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_binary_tree.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 配列表現による二分木クラス */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">ArrayBinaryTree</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="n">#tree</span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="kt">number</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)[];</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">arr</span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="kt">number</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)[])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">arr</span><span class="p">;</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">    </span><span class="cm">/* リスト容量 */</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w">    </span><span class="nx">size</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#tree</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a>
+<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの値を取得 */</span>
+<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a><span class="w">    </span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-17" name="__codelineno-20-17" href="#__codelineno-20-17"></a><span class="w">        </span><span class="c1">// インデックスが範囲外なら、空きを表す null を返す</span>
+<a id="__codelineno-20-18" name="__codelineno-20-18" href="#__codelineno-20-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">())</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-20-19" name="__codelineno-20-19" href="#__codelineno-20-19"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#tree</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-20-20" name="__codelineno-20-20" href="#__codelineno-20-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-21" name="__codelineno-20-21" href="#__codelineno-20-21"></a>
+<a id="__codelineno-20-22" name="__codelineno-20-22" href="#__codelineno-20-22"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの左子ノードのインデックスを取得 */</span>
+<a id="__codelineno-20-23" name="__codelineno-20-23" href="#__codelineno-20-23"></a><span class="w">    </span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-24" name="__codelineno-20-24" href="#__codelineno-20-24"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-20-25" name="__codelineno-20-25" href="#__codelineno-20-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-26" name="__codelineno-20-26" href="#__codelineno-20-26"></a>
+<a id="__codelineno-20-27" name="__codelineno-20-27" href="#__codelineno-20-27"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの右子ノードのインデックスを取得 */</span>
+<a id="__codelineno-20-28" name="__codelineno-20-28" href="#__codelineno-20-28"></a><span class="w">    </span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-29" name="__codelineno-20-29" href="#__codelineno-20-29"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
+<a id="__codelineno-20-30" name="__codelineno-20-30" href="#__codelineno-20-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-31" name="__codelineno-20-31" href="#__codelineno-20-31"></a>
+<a id="__codelineno-20-32" name="__codelineno-20-32" href="#__codelineno-20-32"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの親ノードのインデックスを取得 */</span>
+<a id="__codelineno-20-33" name="__codelineno-20-33" href="#__codelineno-20-33"></a><span class="w">    </span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-34" name="__codelineno-20-34" href="#__codelineno-20-34"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">((</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 切り捨て除算</span>
+<a id="__codelineno-20-35" name="__codelineno-20-35" href="#__codelineno-20-35"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-36" name="__codelineno-20-36" href="#__codelineno-20-36"></a>
+<a id="__codelineno-20-37" name="__codelineno-20-37" href="#__codelineno-20-37"></a><span class="w">    </span><span class="cm">/* レベル順走査 */</span>
+<a id="__codelineno-20-38" name="__codelineno-20-38" href="#__codelineno-20-38"></a><span class="w">    </span><span class="nx">levelOrder</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-39" name="__codelineno-20-39" href="#__codelineno-20-39"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-20-40" name="__codelineno-20-40" href="#__codelineno-20-40"></a><span class="w">        </span><span class="c1">// 配列を直接走査する</span>
+<a id="__codelineno-20-41" name="__codelineno-20-41" href="#__codelineno-20-41"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">();</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-42" name="__codelineno-20-42" href="#__codelineno-20-42"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">));</span>
+<a id="__codelineno-20-43" name="__codelineno-20-43" href="#__codelineno-20-43"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-20-44" name="__codelineno-20-44" href="#__codelineno-20-44"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-20-45" name="__codelineno-20-45" href="#__codelineno-20-45"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-46" name="__codelineno-20-46" href="#__codelineno-20-46"></a>
+<a id="__codelineno-20-47" name="__codelineno-20-47" href="#__codelineno-20-47"></a><span class="w">    </span><span class="cm">/* 深さ優先探索 */</span>
+<a id="__codelineno-20-48" name="__codelineno-20-48" href="#__codelineno-20-48"></a><span class="w">    </span><span class="n">#dfs</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">order</span><span class="o">:</span><span class="w"> </span><span class="kt">Order</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="kt">number</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-49" name="__codelineno-20-49" href="#__codelineno-20-49"></a><span class="w">        </span><span class="c1">// 空きスロットなら返す</span>
+<a id="__codelineno-20-50" name="__codelineno-20-50" href="#__codelineno-20-50"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-20-51" name="__codelineno-20-51" href="#__codelineno-20-51"></a><span class="w">        </span><span class="c1">// 先行順走査</span>
+<a id="__codelineno-20-52" name="__codelineno-20-52" href="#__codelineno-20-52"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">order</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="s1">&#39;pre&#39;</span><span class="p">)</span><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">));</span>
+<a id="__codelineno-20-53" name="__codelineno-20-53" href="#__codelineno-20-53"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#dfs</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span><span class="w"> </span><span class="nx">order</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-20-54" name="__codelineno-20-54" href="#__codelineno-20-54"></a><span class="w">        </span><span class="c1">// 中順走査</span>
+<a id="__codelineno-20-55" name="__codelineno-20-55" href="#__codelineno-20-55"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">order</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="s1">&#39;in&#39;</span><span class="p">)</span><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">));</span>
+<a id="__codelineno-20-56" name="__codelineno-20-56" href="#__codelineno-20-56"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#dfs</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span><span class="w"> </span><span class="nx">order</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-20-57" name="__codelineno-20-57" href="#__codelineno-20-57"></a><span class="w">        </span><span class="c1">// 後順走査</span>
+<a id="__codelineno-20-58" name="__codelineno-20-58" href="#__codelineno-20-58"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">order</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="s1">&#39;post&#39;</span><span class="p">)</span><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">));</span>
+<a id="__codelineno-20-59" name="__codelineno-20-59" href="#__codelineno-20-59"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-60" name="__codelineno-20-60" href="#__codelineno-20-60"></a>
+<a id="__codelineno-20-61" name="__codelineno-20-61" href="#__codelineno-20-61"></a><span class="w">    </span><span class="cm">/* 先行順走査 */</span>
+<a id="__codelineno-20-62" name="__codelineno-20-62" href="#__codelineno-20-62"></a><span class="w">    </span><span class="nx">preOrder</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="kt">number</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)[]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-63" name="__codelineno-20-63" href="#__codelineno-20-63"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-20-64" name="__codelineno-20-64" href="#__codelineno-20-64"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#dfs</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;pre&#39;</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-20-65" name="__codelineno-20-65" href="#__codelineno-20-65"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-20-66" name="__codelineno-20-66" href="#__codelineno-20-66"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-67" name="__codelineno-20-67" href="#__codelineno-20-67"></a>
+<a id="__codelineno-20-68" name="__codelineno-20-68" href="#__codelineno-20-68"></a><span class="w">    </span><span class="cm">/* 中順走査 */</span>
+<a id="__codelineno-20-69" name="__codelineno-20-69" href="#__codelineno-20-69"></a><span class="w">    </span><span class="nx">inOrder</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="kt">number</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)[]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-70" name="__codelineno-20-70" href="#__codelineno-20-70"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-20-71" name="__codelineno-20-71" href="#__codelineno-20-71"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#dfs</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;in&#39;</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-20-72" name="__codelineno-20-72" href="#__codelineno-20-72"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-20-73" name="__codelineno-20-73" href="#__codelineno-20-73"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-74" name="__codelineno-20-74" href="#__codelineno-20-74"></a>
+<a id="__codelineno-20-75" name="__codelineno-20-75" href="#__codelineno-20-75"></a><span class="w">    </span><span class="cm">/* 後順走査 */</span>
+<a id="__codelineno-20-76" name="__codelineno-20-76" href="#__codelineno-20-76"></a><span class="w">    </span><span class="nx">postOrder</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="kt">number</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)[]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-77" name="__codelineno-20-77" href="#__codelineno-20-77"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-20-78" name="__codelineno-20-78" href="#__codelineno-20-78"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="n">#dfs</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;post&#39;</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-20-79" name="__codelineno-20-79" href="#__codelineno-20-79"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
+<a id="__codelineno-20-80" name="__codelineno-20-80" href="#__codelineno-20-80"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-81" name="__codelineno-20-81" href="#__codelineno-20-81"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_binary_tree.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_binary_tree.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 配列表現による二分木クラス */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ArrayBinaryTree</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="kd">late</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">?&gt;</span><span class="w"> </span><span class="n">_tree</span><span class="p">;</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">  </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">  </span><span class="n">ArrayBinaryTree</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">_tree</span><span class="p">);</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">  </span><span class="cm">/* リスト容量 */</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_tree</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">  </span><span class="cm">/* インデックス i のノードの値を取得 */</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w">  </span><span class="kt">int</span><span class="o">?</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w">    </span><span class="c1">// インデックスが範囲外なら、空きを表す null を返す</span>
+<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-17" name="__codelineno-21-17" href="#__codelineno-21-17"></a><span class="w">      </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-21-18" name="__codelineno-21-18" href="#__codelineno-21-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-19" name="__codelineno-21-19" href="#__codelineno-21-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">_tree</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-21-20" name="__codelineno-21-20" href="#__codelineno-21-20"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-21" name="__codelineno-21-21" href="#__codelineno-21-21"></a>
+<a id="__codelineno-21-22" name="__codelineno-21-22" href="#__codelineno-21-22"></a><span class="w">  </span><span class="cm">/* インデックス i のノードの左子ノードのインデックスを取得 */</span>
+<a id="__codelineno-21-23" name="__codelineno-21-23" href="#__codelineno-21-23"></a><span class="w">  </span><span class="kt">int</span><span class="o">?</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-24" name="__codelineno-21-24" href="#__codelineno-21-24"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-21-25" name="__codelineno-21-25" href="#__codelineno-21-25"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-26" name="__codelineno-21-26" href="#__codelineno-21-26"></a>
+<a id="__codelineno-21-27" name="__codelineno-21-27" href="#__codelineno-21-27"></a><span class="w">  </span><span class="cm">/* インデックス i のノードの右子ノードのインデックスを取得 */</span>
+<a id="__codelineno-21-28" name="__codelineno-21-28" href="#__codelineno-21-28"></a><span class="w">  </span><span class="kt">int</span><span class="o">?</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-29" name="__codelineno-21-29" href="#__codelineno-21-29"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
+<a id="__codelineno-21-30" name="__codelineno-21-30" href="#__codelineno-21-30"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-31" name="__codelineno-21-31" href="#__codelineno-21-31"></a>
+<a id="__codelineno-21-32" name="__codelineno-21-32" href="#__codelineno-21-32"></a><span class="w">  </span><span class="cm">/* インデックス i のノードの親ノードのインデックスを取得 */</span>
+<a id="__codelineno-21-33" name="__codelineno-21-33" href="#__codelineno-21-33"></a><span class="w">  </span><span class="kt">int</span><span class="o">?</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-34" name="__codelineno-21-34" href="#__codelineno-21-34"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
+<a id="__codelineno-21-35" name="__codelineno-21-35" href="#__codelineno-21-35"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-36" name="__codelineno-21-36" href="#__codelineno-21-36"></a>
+<a id="__codelineno-21-37" name="__codelineno-21-37" href="#__codelineno-21-37"></a><span class="w">  </span><span class="cm">/* レベル順走査 */</span>
+<a id="__codelineno-21-38" name="__codelineno-21-38" href="#__codelineno-21-38"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">levelOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-39" name="__codelineno-21-39" href="#__codelineno-21-39"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-21-40" name="__codelineno-21-40" href="#__codelineno-21-40"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-41" name="__codelineno-21-41" href="#__codelineno-21-41"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-42" name="__codelineno-21-42" href="#__codelineno-21-42"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">!</span><span class="p">);</span>
+<a id="__codelineno-21-43" name="__codelineno-21-43" href="#__codelineno-21-43"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-21-44" name="__codelineno-21-44" href="#__codelineno-21-44"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-45" name="__codelineno-21-45" href="#__codelineno-21-45"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-21-46" name="__codelineno-21-46" href="#__codelineno-21-46"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-47" name="__codelineno-21-47" href="#__codelineno-21-47"></a>
+<a id="__codelineno-21-48" name="__codelineno-21-48" href="#__codelineno-21-48"></a><span class="w">  </span><span class="cm">/* 深さ優先探索 */</span>
+<a id="__codelineno-21-49" name="__codelineno-21-49" href="#__codelineno-21-49"></a><span class="w">  </span><span class="kt">void</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">String</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">?&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-50" name="__codelineno-21-50" href="#__codelineno-21-50"></a><span class="w">    </span><span class="c1">// 空きスロットなら返す</span>
+<a id="__codelineno-21-51" name="__codelineno-21-51" href="#__codelineno-21-51"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-52" name="__codelineno-21-52" href="#__codelineno-21-52"></a><span class="w">      </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-21-53" name="__codelineno-21-53" href="#__codelineno-21-53"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-54" name="__codelineno-21-54" href="#__codelineno-21-54"></a><span class="w">    </span><span class="c1">// 先行順走査</span>
+<a id="__codelineno-21-55" name="__codelineno-21-55" href="#__codelineno-21-55"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s1">&#39;pre&#39;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-56" name="__codelineno-21-56" href="#__codelineno-21-56"></a><span class="w">      </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-21-57" name="__codelineno-21-57" href="#__codelineno-21-57"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-58" name="__codelineno-21-58" href="#__codelineno-21-58"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">!</span><span class="p">,</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-21-59" name="__codelineno-21-59" href="#__codelineno-21-59"></a><span class="w">    </span><span class="c1">// 中順走査</span>
+<a id="__codelineno-21-60" name="__codelineno-21-60" href="#__codelineno-21-60"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s1">&#39;in&#39;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-61" name="__codelineno-21-61" href="#__codelineno-21-61"></a><span class="w">      </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-21-62" name="__codelineno-21-62" href="#__codelineno-21-62"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-63" name="__codelineno-21-63" href="#__codelineno-21-63"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">!</span><span class="p">,</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-21-64" name="__codelineno-21-64" href="#__codelineno-21-64"></a><span class="w">    </span><span class="c1">// 後順走査</span>
+<a id="__codelineno-21-65" name="__codelineno-21-65" href="#__codelineno-21-65"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s1">&#39;post&#39;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-66" name="__codelineno-21-66" href="#__codelineno-21-66"></a><span class="w">      </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-21-67" name="__codelineno-21-67" href="#__codelineno-21-67"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-21-68" name="__codelineno-21-68" href="#__codelineno-21-68"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-69" name="__codelineno-21-69" href="#__codelineno-21-69"></a>
+<a id="__codelineno-21-70" name="__codelineno-21-70" href="#__codelineno-21-70"></a><span class="w">  </span><span class="cm">/* 先行順走査 */</span>
+<a id="__codelineno-21-71" name="__codelineno-21-71" href="#__codelineno-21-71"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">?&gt;</span><span class="w"> </span><span class="n">preOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-72" name="__codelineno-21-72" href="#__codelineno-21-72"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">?&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-21-73" name="__codelineno-21-73" href="#__codelineno-21-73"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;pre&#39;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-21-74" name="__codelineno-21-74" href="#__codelineno-21-74"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-21-75" name="__codelineno-21-75" href="#__codelineno-21-75"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-76" name="__codelineno-21-76" href="#__codelineno-21-76"></a>
+<a id="__codelineno-21-77" name="__codelineno-21-77" href="#__codelineno-21-77"></a><span class="w">  </span><span class="cm">/* 中順走査 */</span>
+<a id="__codelineno-21-78" name="__codelineno-21-78" href="#__codelineno-21-78"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">?&gt;</span><span class="w"> </span><span class="n">inOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-79" name="__codelineno-21-79" href="#__codelineno-21-79"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">?&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-21-80" name="__codelineno-21-80" href="#__codelineno-21-80"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;in&#39;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-21-81" name="__codelineno-21-81" href="#__codelineno-21-81"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-21-82" name="__codelineno-21-82" href="#__codelineno-21-82"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-83" name="__codelineno-21-83" href="#__codelineno-21-83"></a>
+<a id="__codelineno-21-84" name="__codelineno-21-84" href="#__codelineno-21-84"></a><span class="w">  </span><span class="cm">/* 後順走査 */</span>
+<a id="__codelineno-21-85" name="__codelineno-21-85" href="#__codelineno-21-85"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">?&gt;</span><span class="w"> </span><span class="n">postOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-86" name="__codelineno-21-86" href="#__codelineno-21-86"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">?&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-21-87" name="__codelineno-21-87" href="#__codelineno-21-87"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;post&#39;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-21-88" name="__codelineno-21-88" href="#__codelineno-21-88"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-21-89" name="__codelineno-21-89" href="#__codelineno-21-89"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-90" name="__codelineno-21-90" href="#__codelineno-21-90"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_binary_tree.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_binary_tree.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 配列表現による二分木クラス */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">ArrayBinaryTree</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="n">tree</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Option</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="p">}</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="k">impl</span><span class="w"> </span><span class="n">ArrayBinaryTree</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">new</span><span class="p">(</span><span class="n">arr</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Option</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">        </span><span class="bp">Self</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">tree</span><span class="p">:</span><span class="w"> </span><span class="nc">arr</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">    </span><span class="cm">/* リスト容量 */</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">tree</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a>
+<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの値を取得 */</span>
+<a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">val</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="w">        </span><span class="c1">// インデックスが範囲外なら、空きを表す None を返す</span>
+<a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-21" name="__codelineno-22-21" href="#__codelineno-22-21"></a><span class="w">            </span><span class="nb">None</span>
+<a id="__codelineno-22-22" name="__codelineno-22-22" href="#__codelineno-22-22"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-23" name="__codelineno-22-23" href="#__codelineno-22-23"></a><span class="w">            </span><span class="bp">self</span><span class="p">.</span><span class="n">tree</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span>
+<a id="__codelineno-22-24" name="__codelineno-22-24" href="#__codelineno-22-24"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-25" name="__codelineno-22-25" href="#__codelineno-22-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-26" name="__codelineno-22-26" href="#__codelineno-22-26"></a>
+<a id="__codelineno-22-27" name="__codelineno-22-27" href="#__codelineno-22-27"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの左子ノードのインデックスを取得 */</span>
+<a id="__codelineno-22-28" name="__codelineno-22-28" href="#__codelineno-22-28"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-29" name="__codelineno-22-29" href="#__codelineno-22-29"></a><span class="w">        </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-22-30" name="__codelineno-22-30" href="#__codelineno-22-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-31" name="__codelineno-22-31" href="#__codelineno-22-31"></a>
+<a id="__codelineno-22-32" name="__codelineno-22-32" href="#__codelineno-22-32"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの右子ノードのインデックスを取得 */</span>
+<a id="__codelineno-22-33" name="__codelineno-22-33" href="#__codelineno-22-33"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-34" name="__codelineno-22-34" href="#__codelineno-22-34"></a><span class="w">        </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-22-35" name="__codelineno-22-35" href="#__codelineno-22-35"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-36" name="__codelineno-22-36" href="#__codelineno-22-36"></a>
+<a id="__codelineno-22-37" name="__codelineno-22-37" href="#__codelineno-22-37"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの親ノードのインデックスを取得 */</span>
+<a id="__codelineno-22-38" name="__codelineno-22-38" href="#__codelineno-22-38"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-39" name="__codelineno-22-39" href="#__codelineno-22-39"></a><span class="w">        </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-22-40" name="__codelineno-22-40" href="#__codelineno-22-40"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-41" name="__codelineno-22-41" href="#__codelineno-22-41"></a>
+<a id="__codelineno-22-42" name="__codelineno-22-42" href="#__codelineno-22-42"></a><span class="w">    </span><span class="cm">/* レベル順走査 */</span>
+<a id="__codelineno-22-43" name="__codelineno-22-43" href="#__codelineno-22-43"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">level_order</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-44" name="__codelineno-22-44" href="#__codelineno-22-44"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">tree</span><span class="p">.</span><span class="n">iter</span><span class="p">().</span><span class="n">filter_map</span><span class="p">(</span><span class="o">|&amp;</span><span class="n">x</span><span class="o">|</span><span class="w"> </span><span class="n">x</span><span class="p">).</span><span class="n">collect</span><span class="p">()</span>
+<a id="__codelineno-22-45" name="__codelineno-22-45" href="#__codelineno-22-45"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-46" name="__codelineno-22-46" href="#__codelineno-22-46"></a>
+<a id="__codelineno-22-47" name="__codelineno-22-47" href="#__codelineno-22-47"></a><span class="w">    </span><span class="cm">/* 深さ優先探索 */</span>
+<a id="__codelineno-22-48" name="__codelineno-22-48" href="#__codelineno-22-48"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">order</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="o">&#39;</span><span class="nb">static</span><span class="w"> </span><span class="kt">str</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-49" name="__codelineno-22-49" href="#__codelineno-22-49"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">).</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-50" name="__codelineno-22-50" href="#__codelineno-22-50"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-22-51" name="__codelineno-22-51" href="#__codelineno-22-51"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-52" name="__codelineno-22-52" href="#__codelineno-22-52"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">).</span><span class="n">unwrap</span><span class="p">();</span>
+<a id="__codelineno-22-53" name="__codelineno-22-53" href="#__codelineno-22-53"></a><span class="w">        </span><span class="c1">// 先行順走査</span>
+<a id="__codelineno-22-54" name="__codelineno-22-54" href="#__codelineno-22-54"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">&quot;pre&quot;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-55" name="__codelineno-22-55" href="#__codelineno-22-55"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-22-56" name="__codelineno-22-56" href="#__codelineno-22-56"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-57" name="__codelineno-22-57" href="#__codelineno-22-57"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">dfs</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-22-58" name="__codelineno-22-58" href="#__codelineno-22-58"></a><span class="w">        </span><span class="c1">// 中順走査</span>
+<a id="__codelineno-22-59" name="__codelineno-22-59" href="#__codelineno-22-59"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">&quot;in&quot;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-60" name="__codelineno-22-60" href="#__codelineno-22-60"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-22-61" name="__codelineno-22-61" href="#__codelineno-22-61"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-62" name="__codelineno-22-62" href="#__codelineno-22-62"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">dfs</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-22-63" name="__codelineno-22-63" href="#__codelineno-22-63"></a><span class="w">        </span><span class="c1">// 後順走査</span>
+<a id="__codelineno-22-64" name="__codelineno-22-64" href="#__codelineno-22-64"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">&quot;post&quot;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-65" name="__codelineno-22-65" href="#__codelineno-22-65"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-22-66" name="__codelineno-22-66" href="#__codelineno-22-66"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-67" name="__codelineno-22-67" href="#__codelineno-22-67"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-68" name="__codelineno-22-68" href="#__codelineno-22-68"></a>
+<a id="__codelineno-22-69" name="__codelineno-22-69" href="#__codelineno-22-69"></a><span class="w">    </span><span class="cm">/* 先行順走査 */</span>
+<a id="__codelineno-22-70" name="__codelineno-22-70" href="#__codelineno-22-70"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-71" name="__codelineno-22-71" href="#__codelineno-22-71"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span>
+<a id="__codelineno-22-72" name="__codelineno-22-72" href="#__codelineno-22-72"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;pre&quot;</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-22-73" name="__codelineno-22-73" href="#__codelineno-22-73"></a><span class="w">        </span><span class="n">res</span>
+<a id="__codelineno-22-74" name="__codelineno-22-74" href="#__codelineno-22-74"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-75" name="__codelineno-22-75" href="#__codelineno-22-75"></a>
+<a id="__codelineno-22-76" name="__codelineno-22-76" href="#__codelineno-22-76"></a><span class="w">    </span><span class="cm">/* 中順走査 */</span>
+<a id="__codelineno-22-77" name="__codelineno-22-77" href="#__codelineno-22-77"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">in_order</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-78" name="__codelineno-22-78" href="#__codelineno-22-78"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span>
+<a id="__codelineno-22-79" name="__codelineno-22-79" href="#__codelineno-22-79"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;in&quot;</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-22-80" name="__codelineno-22-80" href="#__codelineno-22-80"></a><span class="w">        </span><span class="n">res</span>
+<a id="__codelineno-22-81" name="__codelineno-22-81" href="#__codelineno-22-81"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-82" name="__codelineno-22-82" href="#__codelineno-22-82"></a>
+<a id="__codelineno-22-83" name="__codelineno-22-83" href="#__codelineno-22-83"></a><span class="w">    </span><span class="cm">/* 後順走査 */</span>
+<a id="__codelineno-22-84" name="__codelineno-22-84" href="#__codelineno-22-84"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">post_order</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-85" name="__codelineno-22-85" href="#__codelineno-22-85"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span>
+<a id="__codelineno-22-86" name="__codelineno-22-86" href="#__codelineno-22-86"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;post&quot;</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-22-87" name="__codelineno-22-87" href="#__codelineno-22-87"></a><span class="w">        </span><span class="n">res</span>
+<a id="__codelineno-22-88" name="__codelineno-22-88" href="#__codelineno-22-88"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-89" name="__codelineno-22-89" href="#__codelineno-22-89"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_binary_tree.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<div class="highlight"><span class="filename">array_binary_tree.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 配列表現による二分木の構造体 */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">tree</span><span class="p">;</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="p">}</span><span class="w"> </span><span class="n">ArrayBinaryTree</span><span class="p">;</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="n">ArrayBinaryTree</span><span class="w"> </span><span class="o">*</span><span class="nf">newArrayBinaryTree</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">arr</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">arrSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w">    </span><span class="n">ArrayBinaryTree</span><span class="w"> </span><span class="o">*</span><span class="n">abt</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">ArrayBinaryTree</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">ArrayBinaryTree</span><span class="p">));</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w">    </span><span class="n">abt</span><span class="o">-&gt;</span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">arrSize</span><span class="p">);</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w">    </span><span class="n">memcpy</span><span class="p">(</span><span class="n">abt</span><span class="o">-&gt;</span><span class="n">tree</span><span class="p">,</span><span class="w"> </span><span class="n">arr</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">arrSize</span><span class="p">);</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w">    </span><span class="n">abt</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arrSize</span><span class="p">;</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">abt</span><span class="p">;</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="p">}</span>
+<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a>
+<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="cm">/* デストラクタ */</span>
+<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">delArrayBinaryTree</span><span class="p">(</span><span class="n">ArrayBinaryTree</span><span class="w"> </span><span class="o">*</span><span class="n">abt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">abt</span><span class="o">-&gt;</span><span class="n">tree</span><span class="p">);</span>
+<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">abt</span><span class="p">);</span>
+<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="p">}</span>
+<a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a>
+<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a><span class="cm">/* リスト容量 */</span>
+<a id="__codelineno-23-23" name="__codelineno-23-23" href="#__codelineno-23-23"></a><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="n">ArrayBinaryTree</span><span class="w"> </span><span class="o">*</span><span class="n">abt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-24" name="__codelineno-23-24" href="#__codelineno-23-24"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">abt</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">;</span>
+<a id="__codelineno-23-25" name="__codelineno-23-25" href="#__codelineno-23-25"></a><span class="p">}</span>
+<a id="__codelineno-23-26" name="__codelineno-23-26" href="#__codelineno-23-26"></a>
+<a id="__codelineno-23-27" name="__codelineno-23-27" href="#__codelineno-23-27"></a><span class="cm">/* インデックス i のノードの値を取得 */</span>
+<a id="__codelineno-23-28" name="__codelineno-23-28" href="#__codelineno-23-28"></a><span class="kt">int</span><span class="w"> </span><span class="nf">val</span><span class="p">(</span><span class="n">ArrayBinaryTree</span><span class="w"> </span><span class="o">*</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-29" name="__codelineno-23-29" href="#__codelineno-23-29"></a><span class="w">    </span><span class="c1">// インデックスが範囲外なら、空きを表す INT_MAX を返す</span>
+<a id="__codelineno-23-30" name="__codelineno-23-30" href="#__codelineno-23-30"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">abt</span><span class="p">))</span>
+<a id="__codelineno-23-31" name="__codelineno-23-31" href="#__codelineno-23-31"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">;</span>
+<a id="__codelineno-23-32" name="__codelineno-23-32" href="#__codelineno-23-32"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">abt</span><span class="o">-&gt;</span><span class="n">tree</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-23-33" name="__codelineno-23-33" href="#__codelineno-23-33"></a><span class="p">}</span>
+<a id="__codelineno-23-34" name="__codelineno-23-34" href="#__codelineno-23-34"></a>
+<a id="__codelineno-23-35" name="__codelineno-23-35" href="#__codelineno-23-35"></a><span class="cm">/* レベル順走査 */</span>
+<a id="__codelineno-23-36" name="__codelineno-23-36" href="#__codelineno-23-36"></a><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="nf">levelOrder</span><span class="p">(</span><span class="n">ArrayBinaryTree</span><span class="w"> </span><span class="o">*</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">returnSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-37" name="__codelineno-23-37" href="#__codelineno-23-37"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">abt</span><span class="p">));</span>
+<a id="__codelineno-23-38" name="__codelineno-23-38" href="#__codelineno-23-38"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-23-39" name="__codelineno-23-39" href="#__codelineno-23-39"></a><span class="w">    </span><span class="c1">// 配列を直接走査する</span>
+<a id="__codelineno-23-40" name="__codelineno-23-40" href="#__codelineno-23-40"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">abt</span><span class="p">);</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-41" name="__codelineno-23-41" href="#__codelineno-23-41"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">)</span>
+<a id="__codelineno-23-42" name="__codelineno-23-42" href="#__codelineno-23-42"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">index</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-23-43" name="__codelineno-23-43" href="#__codelineno-23-43"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-44" name="__codelineno-23-44" href="#__codelineno-23-44"></a><span class="w">    </span><span class="o">*</span><span class="n">returnSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
+<a id="__codelineno-23-45" name="__codelineno-23-45" href="#__codelineno-23-45"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-23-46" name="__codelineno-23-46" href="#__codelineno-23-46"></a><span class="p">}</span>
+<a id="__codelineno-23-47" name="__codelineno-23-47" href="#__codelineno-23-47"></a>
+<a id="__codelineno-23-48" name="__codelineno-23-48" href="#__codelineno-23-48"></a><span class="cm">/* 深さ優先探索 */</span>
+<a id="__codelineno-23-49" name="__codelineno-23-49" href="#__codelineno-23-49"></a><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">ArrayBinaryTree</span><span class="w"> </span><span class="o">*</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-50" name="__codelineno-23-50" href="#__codelineno-23-50"></a><span class="w">    </span><span class="c1">// 空きスロットなら返す</span>
+<a id="__codelineno-23-51" name="__codelineno-23-51" href="#__codelineno-23-51"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">)</span>
+<a id="__codelineno-23-52" name="__codelineno-23-52" href="#__codelineno-23-52"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-23-53" name="__codelineno-23-53" href="#__codelineno-23-53"></a><span class="w">    </span><span class="c1">// 先行順走査</span>
+<a id="__codelineno-23-54" name="__codelineno-23-54" href="#__codelineno-23-54"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">strcmp</span><span class="p">(</span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;pre&quot;</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-23-55" name="__codelineno-23-55" href="#__codelineno-23-55"></a><span class="w">        </span><span class="n">res</span><span class="p">[(</span><span class="o">*</span><span class="n">index</span><span class="p">)</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-23-56" name="__codelineno-23-56" href="#__codelineno-23-56"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">index</span><span class="p">);</span>
+<a id="__codelineno-23-57" name="__codelineno-23-57" href="#__codelineno-23-57"></a><span class="w">    </span><span class="c1">// 中順走査</span>
+<a id="__codelineno-23-58" name="__codelineno-23-58" href="#__codelineno-23-58"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">strcmp</span><span class="p">(</span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;in&quot;</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-23-59" name="__codelineno-23-59" href="#__codelineno-23-59"></a><span class="w">        </span><span class="n">res</span><span class="p">[(</span><span class="o">*</span><span class="n">index</span><span class="p">)</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-23-60" name="__codelineno-23-60" href="#__codelineno-23-60"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">index</span><span class="p">);</span>
+<a id="__codelineno-23-61" name="__codelineno-23-61" href="#__codelineno-23-61"></a><span class="w">    </span><span class="c1">// 後順走査</span>
+<a id="__codelineno-23-62" name="__codelineno-23-62" href="#__codelineno-23-62"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">strcmp</span><span class="p">(</span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;post&quot;</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-23-63" name="__codelineno-23-63" href="#__codelineno-23-63"></a><span class="w">        </span><span class="n">res</span><span class="p">[(</span><span class="o">*</span><span class="n">index</span><span class="p">)</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-23-64" name="__codelineno-23-64" href="#__codelineno-23-64"></a><span class="p">}</span>
+<a id="__codelineno-23-65" name="__codelineno-23-65" href="#__codelineno-23-65"></a>
+<a id="__codelineno-23-66" name="__codelineno-23-66" href="#__codelineno-23-66"></a><span class="cm">/* 先行順走査 */</span>
+<a id="__codelineno-23-67" name="__codelineno-23-67" href="#__codelineno-23-67"></a><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="nf">preOrder</span><span class="p">(</span><span class="n">ArrayBinaryTree</span><span class="w"> </span><span class="o">*</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">returnSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-68" name="__codelineno-23-68" href="#__codelineno-23-68"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">abt</span><span class="p">));</span>
+<a id="__codelineno-23-69" name="__codelineno-23-69" href="#__codelineno-23-69"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-23-70" name="__codelineno-23-70" href="#__codelineno-23-70"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;pre&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="n">index</span><span class="p">);</span>
+<a id="__codelineno-23-71" name="__codelineno-23-71" href="#__codelineno-23-71"></a><span class="w">    </span><span class="o">*</span><span class="n">returnSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
+<a id="__codelineno-23-72" name="__codelineno-23-72" href="#__codelineno-23-72"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-23-73" name="__codelineno-23-73" href="#__codelineno-23-73"></a><span class="p">}</span>
+<a id="__codelineno-23-74" name="__codelineno-23-74" href="#__codelineno-23-74"></a>
+<a id="__codelineno-23-75" name="__codelineno-23-75" href="#__codelineno-23-75"></a><span class="cm">/* 中順走査 */</span>
+<a id="__codelineno-23-76" name="__codelineno-23-76" href="#__codelineno-23-76"></a><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="nf">inOrder</span><span class="p">(</span><span class="n">ArrayBinaryTree</span><span class="w"> </span><span class="o">*</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">returnSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-77" name="__codelineno-23-77" href="#__codelineno-23-77"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">abt</span><span class="p">));</span>
+<a id="__codelineno-23-78" name="__codelineno-23-78" href="#__codelineno-23-78"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-23-79" name="__codelineno-23-79" href="#__codelineno-23-79"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;in&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="n">index</span><span class="p">);</span>
+<a id="__codelineno-23-80" name="__codelineno-23-80" href="#__codelineno-23-80"></a><span class="w">    </span><span class="o">*</span><span class="n">returnSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
+<a id="__codelineno-23-81" name="__codelineno-23-81" href="#__codelineno-23-81"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-23-82" name="__codelineno-23-82" href="#__codelineno-23-82"></a><span class="p">}</span>
+<a id="__codelineno-23-83" name="__codelineno-23-83" href="#__codelineno-23-83"></a>
+<a id="__codelineno-23-84" name="__codelineno-23-84" href="#__codelineno-23-84"></a><span class="cm">/* 後順走査 */</span>
+<a id="__codelineno-23-85" name="__codelineno-23-85" href="#__codelineno-23-85"></a><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="nf">postOrder</span><span class="p">(</span><span class="n">ArrayBinaryTree</span><span class="w"> </span><span class="o">*</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">returnSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-86" name="__codelineno-23-86" href="#__codelineno-23-86"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">abt</span><span class="p">));</span>
+<a id="__codelineno-23-87" name="__codelineno-23-87" href="#__codelineno-23-87"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-23-88" name="__codelineno-23-88" href="#__codelineno-23-88"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;post&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="n">index</span><span class="p">);</span>
+<a id="__codelineno-23-89" name="__codelineno-23-89" href="#__codelineno-23-89"></a><span class="w">    </span><span class="o">*</span><span class="n">returnSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
+<a id="__codelineno-23-90" name="__codelineno-23-90" href="#__codelineno-23-90"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-23-91" name="__codelineno-23-91" href="#__codelineno-23-91"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_binary_tree.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">ArrayBinaryTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">array_binary_tree.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 配列表現による二分木クラス */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ArrayBinaryTree</span><span class="p">(</span><span class="kd">val</span><span class="w"> </span><span class="nv">tree</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="cm">/* リスト容量 */</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">size</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの値を取得 */</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">_val</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int?</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w">        </span><span class="c1">// インデックスが範囲外なら、空きを表す null を返す</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a>
+<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの左子ノードのインデックスを取得 */</span>
+<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-17" name="__codelineno-24-17" href="#__codelineno-24-17"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-24-18" name="__codelineno-24-18" href="#__codelineno-24-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-19" name="__codelineno-24-19" href="#__codelineno-24-19"></a>
+<a id="__codelineno-24-20" name="__codelineno-24-20" href="#__codelineno-24-20"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの右子ノードのインデックスを取得 */</span>
+<a id="__codelineno-24-21" name="__codelineno-24-21" href="#__codelineno-24-21"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-22" name="__codelineno-24-22" href="#__codelineno-24-22"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">2</span>
+<a id="__codelineno-24-23" name="__codelineno-24-23" href="#__codelineno-24-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-24" name="__codelineno-24-24" href="#__codelineno-24-24"></a>
+<a id="__codelineno-24-25" name="__codelineno-24-25" href="#__codelineno-24-25"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの親ノードのインデックスを取得 */</span>
+<a id="__codelineno-24-26" name="__codelineno-24-26" href="#__codelineno-24-26"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-27" name="__codelineno-24-27" href="#__codelineno-24-27"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span>
+<a id="__codelineno-24-28" name="__codelineno-24-28" href="#__codelineno-24-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-29" name="__codelineno-24-29" href="#__codelineno-24-29"></a>
+<a id="__codelineno-24-30" name="__codelineno-24-30" href="#__codelineno-24-30"></a><span class="w">    </span><span class="cm">/* レベル順走査 */</span>
+<a id="__codelineno-24-31" name="__codelineno-24-31" href="#__codelineno-24-31"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">levelOrder</span><span class="p">():</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-32" name="__codelineno-24-32" href="#__codelineno-24-32"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-24-33" name="__codelineno-24-33" href="#__codelineno-24-33"></a><span class="w">        </span><span class="c1">// 配列を直接走査する</span>
+<a id="__codelineno-24-34" name="__codelineno-24-34" href="#__codelineno-24-34"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">size</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-35" name="__codelineno-24-35" href="#__codelineno-24-35"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-24-36" name="__codelineno-24-36" href="#__codelineno-24-36"></a><span class="w">                </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">_val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
+<a id="__codelineno-24-37" name="__codelineno-24-37" href="#__codelineno-24-37"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-24-38" name="__codelineno-24-38" href="#__codelineno-24-38"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-24-39" name="__codelineno-24-39" href="#__codelineno-24-39"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-40" name="__codelineno-24-40" href="#__codelineno-24-40"></a>
+<a id="__codelineno-24-41" name="__codelineno-24-41" href="#__codelineno-24-41"></a><span class="w">    </span><span class="cm">/* 深さ優先探索 */</span>
+<a id="__codelineno-24-42" name="__codelineno-24-42" href="#__codelineno-24-42"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">order</span><span class="p">:</span><span class="w"> </span><span class="kt">String</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-43" name="__codelineno-24-43" href="#__codelineno-24-43"></a><span class="w">        </span><span class="c1">// 空きスロットなら返す</span>
+<a id="__codelineno-24-44" name="__codelineno-24-44" href="#__codelineno-24-44"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-24-45" name="__codelineno-24-45" href="#__codelineno-24-45"></a><span class="w">            </span><span class="k">return</span>
+<a id="__codelineno-24-46" name="__codelineno-24-46" href="#__codelineno-24-46"></a><span class="w">        </span><span class="c1">// 先行順走査</span>
+<a id="__codelineno-24-47" name="__codelineno-24-47" href="#__codelineno-24-47"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="s">&quot;pre&quot;</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">order</span><span class="p">)</span>
+<a id="__codelineno-24-48" name="__codelineno-24-48" href="#__codelineno-24-48"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">_val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
+<a id="__codelineno-24-49" name="__codelineno-24-49" href="#__codelineno-24-49"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-24-50" name="__codelineno-24-50" href="#__codelineno-24-50"></a><span class="w">        </span><span class="c1">// 中順走査</span>
+<a id="__codelineno-24-51" name="__codelineno-24-51" href="#__codelineno-24-51"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="s">&quot;in&quot;</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">order</span><span class="p">)</span>
+<a id="__codelineno-24-52" name="__codelineno-24-52" href="#__codelineno-24-52"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">_val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
+<a id="__codelineno-24-53" name="__codelineno-24-53" href="#__codelineno-24-53"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-24-54" name="__codelineno-24-54" href="#__codelineno-24-54"></a><span class="w">        </span><span class="c1">// 後順走査</span>
+<a id="__codelineno-24-55" name="__codelineno-24-55" href="#__codelineno-24-55"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="s">&quot;post&quot;</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">order</span><span class="p">)</span>
+<a id="__codelineno-24-56" name="__codelineno-24-56" href="#__codelineno-24-56"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">_val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
+<a id="__codelineno-24-57" name="__codelineno-24-57" href="#__codelineno-24-57"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-58" name="__codelineno-24-58" href="#__codelineno-24-58"></a>
+<a id="__codelineno-24-59" name="__codelineno-24-59" href="#__codelineno-24-59"></a><span class="w">    </span><span class="cm">/* 先行順走査 */</span>
+<a id="__codelineno-24-60" name="__codelineno-24-60" href="#__codelineno-24-60"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">():</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-61" name="__codelineno-24-61" href="#__codelineno-24-61"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-24-62" name="__codelineno-24-62" href="#__codelineno-24-62"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;pre&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-24-63" name="__codelineno-24-63" href="#__codelineno-24-63"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-24-64" name="__codelineno-24-64" href="#__codelineno-24-64"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-65" name="__codelineno-24-65" href="#__codelineno-24-65"></a>
+<a id="__codelineno-24-66" name="__codelineno-24-66" href="#__codelineno-24-66"></a><span class="w">    </span><span class="cm">/* 中順走査 */</span>
+<a id="__codelineno-24-67" name="__codelineno-24-67" href="#__codelineno-24-67"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">inOrder</span><span class="p">():</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-68" name="__codelineno-24-68" href="#__codelineno-24-68"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-24-69" name="__codelineno-24-69" href="#__codelineno-24-69"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;in&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-24-70" name="__codelineno-24-70" href="#__codelineno-24-70"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-24-71" name="__codelineno-24-71" href="#__codelineno-24-71"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-72" name="__codelineno-24-72" href="#__codelineno-24-72"></a>
+<a id="__codelineno-24-73" name="__codelineno-24-73" href="#__codelineno-24-73"></a><span class="w">    </span><span class="cm">/* 後順走査 */</span>
+<a id="__codelineno-24-74" name="__codelineno-24-74" href="#__codelineno-24-74"></a><span class="w">    </span><span class="kd">fun</span><span class="w"> </span><span class="nf">postOrder</span><span class="p">():</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-75" name="__codelineno-24-75" href="#__codelineno-24-75"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-24-76" name="__codelineno-24-76" href="#__codelineno-24-76"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;post&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-24-77" name="__codelineno-24-77" href="#__codelineno-24-77"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
+<a id="__codelineno-24-78" name="__codelineno-24-78" href="#__codelineno-24-78"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-79" name="__codelineno-24-79" href="#__codelineno-24-79"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">array_binary_tree.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">ArrayBinaryTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<div class="highlight"><span class="filename">array_binary_tree.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### 配列表現の二分木クラス ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayBinaryTree</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="c1">### コンストラクタ ###</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">    </span><span class="vi">@tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="o">.</span><span class="n">to_a</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w">  </span><span class="c1">### リスト容量 ###</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">size</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w">    </span><span class="vi">@tree</span><span class="o">.</span><span class="n">length</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w">  </span><span class="c1">### インデックス i のノードの値を取得 ###</span>
+<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w">    </span><span class="c1"># インデックスが範囲外なら `nil` を返し、空きスロットを表す</span>
+<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span>
+<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a>
+<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a><span class="w">    </span><span class="vi">@tree</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a>
+<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="w">  </span><span class="c1">### インデックス i のノードの左子ノードのインデックスを取得 ###</span>
+<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="w">    </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a>
+<a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></a><span class="w">  </span><span class="c1">### インデックス i のノードの右子ノードのインデックスを取得 ###</span>
+<a id="__codelineno-25-27" name="__codelineno-25-27" href="#__codelineno-25-27"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-25-28" name="__codelineno-25-28" href="#__codelineno-25-28"></a><span class="w">    </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-25-29" name="__codelineno-25-29" href="#__codelineno-25-29"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-30" name="__codelineno-25-30" href="#__codelineno-25-30"></a>
+<a id="__codelineno-25-31" name="__codelineno-25-31" href="#__codelineno-25-31"></a><span class="w">  </span><span class="c1">### インデックス i のノードの親ノードのインデックスを取得 ###</span>
+<a id="__codelineno-25-32" name="__codelineno-25-32" href="#__codelineno-25-32"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-25-33" name="__codelineno-25-33" href="#__codelineno-25-33"></a><span class="w">    </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-25-34" name="__codelineno-25-34" href="#__codelineno-25-34"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-35" name="__codelineno-25-35" href="#__codelineno-25-35"></a>
+<a id="__codelineno-25-36" name="__codelineno-25-36" href="#__codelineno-25-36"></a><span class="w">  </span><span class="c1">### レベル順走査 ###</span>
+<a id="__codelineno-25-37" name="__codelineno-25-37" href="#__codelineno-25-37"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">level_order</span>
+<a id="__codelineno-25-38" name="__codelineno-25-38" href="#__codelineno-25-38"></a><span class="w">    </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-25-39" name="__codelineno-25-39" href="#__codelineno-25-39"></a>
+<a id="__codelineno-25-40" name="__codelineno-25-40" href="#__codelineno-25-40"></a><span class="w">    </span><span class="c1"># 配列を直接走査する</span>
+<a id="__codelineno-25-41" name="__codelineno-25-41" href="#__codelineno-25-41"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">size</span>
+<a id="__codelineno-25-42" name="__codelineno-25-42" href="#__codelineno-25-42"></a><span class="w">      </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-25-43" name="__codelineno-25-43" href="#__codelineno-25-43"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-25-44" name="__codelineno-25-44" href="#__codelineno-25-44"></a>
+<a id="__codelineno-25-45" name="__codelineno-25-45" href="#__codelineno-25-45"></a><span class="w">    </span><span class="vi">@res</span>
+<a id="__codelineno-25-46" name="__codelineno-25-46" href="#__codelineno-25-46"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-47" name="__codelineno-25-47" href="#__codelineno-25-47"></a>
+<a id="__codelineno-25-48" name="__codelineno-25-48" href="#__codelineno-25-48"></a><span class="w">  </span><span class="c1">### 深さ優先探索 ###</span>
+<a id="__codelineno-25-49" name="__codelineno-25-49" href="#__codelineno-25-49"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">order</span><span class="p">)</span>
+<a id="__codelineno-25-50" name="__codelineno-25-50" href="#__codelineno-25-50"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-25-51" name="__codelineno-25-51" href="#__codelineno-25-51"></a><span class="w">    </span><span class="c1"># 先行順走査</span>
+<a id="__codelineno-25-52" name="__codelineno-25-52" href="#__codelineno-25-52"></a><span class="w">    </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="ss">:pre</span>
+<a id="__codelineno-25-53" name="__codelineno-25-53" href="#__codelineno-25-53"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">)</span>
+<a id="__codelineno-25-54" name="__codelineno-25-54" href="#__codelineno-25-54"></a><span class="w">    </span><span class="c1"># 中順走査</span>
+<a id="__codelineno-25-55" name="__codelineno-25-55" href="#__codelineno-25-55"></a><span class="w">    </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="ss">:in</span>
+<a id="__codelineno-25-56" name="__codelineno-25-56" href="#__codelineno-25-56"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">)</span>
+<a id="__codelineno-25-57" name="__codelineno-25-57" href="#__codelineno-25-57"></a><span class="w">    </span><span class="c1"># 後順走査</span>
+<a id="__codelineno-25-58" name="__codelineno-25-58" href="#__codelineno-25-58"></a><span class="w">    </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="ss">:post</span>
+<a id="__codelineno-25-59" name="__codelineno-25-59" href="#__codelineno-25-59"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-60" name="__codelineno-25-60" href="#__codelineno-25-60"></a>
+<a id="__codelineno-25-61" name="__codelineno-25-61" href="#__codelineno-25-61"></a><span class="w">  </span><span class="c1">### 前順走査 ###</span>
+<a id="__codelineno-25-62" name="__codelineno-25-62" href="#__codelineno-25-62"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span>
+<a id="__codelineno-25-63" name="__codelineno-25-63" href="#__codelineno-25-63"></a><span class="w">    </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-25-64" name="__codelineno-25-64" href="#__codelineno-25-64"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="ss">:pre</span><span class="p">)</span>
+<a id="__codelineno-25-65" name="__codelineno-25-65" href="#__codelineno-25-65"></a><span class="w">    </span><span class="vi">@res</span>
+<a id="__codelineno-25-66" name="__codelineno-25-66" href="#__codelineno-25-66"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-67" name="__codelineno-25-67" href="#__codelineno-25-67"></a>
+<a id="__codelineno-25-68" name="__codelineno-25-68" href="#__codelineno-25-68"></a><span class="w">  </span><span class="c1">### 中順走査 ###</span>
+<a id="__codelineno-25-69" name="__codelineno-25-69" href="#__codelineno-25-69"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">in_order</span>
+<a id="__codelineno-25-70" name="__codelineno-25-70" href="#__codelineno-25-70"></a><span class="w">    </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-25-71" name="__codelineno-25-71" href="#__codelineno-25-71"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="ss">:in</span><span class="p">)</span>
+<a id="__codelineno-25-72" name="__codelineno-25-72" href="#__codelineno-25-72"></a><span class="w">    </span><span class="vi">@res</span>
+<a id="__codelineno-25-73" name="__codelineno-25-73" href="#__codelineno-25-73"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-74" name="__codelineno-25-74" href="#__codelineno-25-74"></a>
+<a id="__codelineno-25-75" name="__codelineno-25-75" href="#__codelineno-25-75"></a><span class="w">  </span><span class="c1">### 後順走査 ###</span>
+<a id="__codelineno-25-76" name="__codelineno-25-76" href="#__codelineno-25-76"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">post_order</span>
+<a id="__codelineno-25-77" name="__codelineno-25-77" href="#__codelineno-25-77"></a><span class="w">    </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-25-78" name="__codelineno-25-78" href="#__codelineno-25-78"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="ss">:post</span><span class="p">)</span>
+<a id="__codelineno-25-79" name="__codelineno-25-79" href="#__codelineno-25-79"></a><span class="w">    </span><span class="vi">@res</span>
+<a id="__codelineno-25-80" name="__codelineno-25-80" href="#__codelineno-25-80"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-81" name="__codelineno-25-81" href="#__codelineno-25-81"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h2 id="733">7.3.3 &nbsp; 利点と制限<a class="headerlink" href="#733" title="Permanent link">&para;</a></h2>
-<p>二分木の配列表現には以下の利点があります：</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%0A%20%20%20%20def%20__init__%28self%2C%20val%29%3A%0A%20%20%20%20%20%20%20%20self.val%20%3D%20val%0A%20%20%20%20%20%20%20%20self.left%20%3D%20None%0A%20%20%20%20%20%20%20%20self.right%20%3D%20None%0A%0Aclass%20ArrayBinaryTree%3A%0A%0A%20%20%20%20def%20__init__%28self%2C%20arr%3A%20list%5Bint%20%7C%20None%5D%29%3A%0A%20%20%20%20%20%20%20%20self._tree%20%3D%20list%28arr%29%0A%0A%20%20%20%20def%20size%28self%29%3A%0A%20%20%20%20%20%20%20%20return%20len%28self._tree%29%0A%0A%20%20%20%20def%20val%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20if%20i%20%3C%200%20or%20i%20%3E%3D%20self.size%28%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%20%20%20%20return%20self._tree%5Bi%5D%0A%0A%20%20%20%20def%20left%28self%2C%20i%3A%20int%29%20-%3E%20int%20%7C%20None%3A%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self%2C%20i%3A%20int%29%20-%3E%20int%20%7C%20None%3A%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self%2C%20i%3A%20int%29%20-%3E%20int%20%7C%20None%3A%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20%2F%2F%202%0A%0A%20%20%20%20def%20level_order%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20self.res%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20for%20i%20in%20range%28self.size%28%29%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20self.val%28i%29%20is%20not%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20self.res.append%28self.val%28i%29%29%0A%20%20%20%20%20%20%20%20return%20self.res%0A%0A%20%20%20%20def%20dfs%28self%2C%20i%3A%20int%2C%20order%3A%20str%29%3A%0A%20%20%20%20%20%20%20%20if%20self.val%28i%29%20is%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%0A%20%20%20%20%20%20%20%20if%20order%20%3D%3D%20%27pre%27%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.res.append%28self.val%28i%29%29%0A%20%20%20%20%20%20%20%20self.dfs%28self.left%28i%29%2C%20order%29%0A%20%20%20%20%20%20%20%20if%20order%20%3D%3D%20%27in%27%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.res.append%28self.val%28i%29%29%0A%20%20%20%20%20%20%20%20self.dfs%28self.right%28i%29%2C%20order%29%0A%20%20%20%20%20%20%20%20if%20order%20%3D%3D%20%27post%27%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.res.append%28self.val%28i%29%29%0A%0A%20%20%20%20def%20pre_order%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20self.res%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20self.dfs%280%2C%20order%3D%27pre%27%29%0A%20%20%20%20%20%20%20%20return%20self.res%0A%0A%20%20%20%20def%20in_order%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20self.res%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20self.dfs%280%2C%20order%3D%27in%27%29%0A%20%20%20%20%20%20%20%20return%20self.res%0A%0A%20%20%20%20def%20post_order%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20self.res%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20self.dfs%280%2C%20order%3D%27post%27%29%0A%20%20%20%20%20%20%20%20return%20self.res%0Aif%20__name__%20%3D%3D%20%27__main__%27%3A%0A%20%20%20%20arr%20%3D%20%5B1%2C%202%2C%203%2C%204%2C%20None%2C%206%2C%20None%5D%0A%20%20%20%20abt%20%3D%20ArrayBinaryTree%28arr%29%0A%20%20%20%20i%20%3D%201%0A%20%20%20%20l%2C%20r%2C%20p%20%3D%20%28abt.left%28i%29%2C%20abt.right%28i%29%2C%20abt.parent%28i%29%29%0A%20%20%20%20res%20%3D%20abt.level_order%28%29%0A%20%20%20%20res%20%3D%20abt.pre_order%28%29%0A%20%20%20%20res%20%3D%20abt.in_order%28%29%0A%20%20%20%20res%20%3D%20abt.post_order%28%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%0A%20%20%20%20def%20__init__%28self%2C%20val%29%3A%0A%20%20%20%20%20%20%20%20self.val%20%3D%20val%0A%20%20%20%20%20%20%20%20self.left%20%3D%20None%0A%20%20%20%20%20%20%20%20self.right%20%3D%20None%0A%0Aclass%20ArrayBinaryTree%3A%0A%0A%20%20%20%20def%20__init__%28self%2C%20arr%3A%20list%5Bint%20%7C%20None%5D%29%3A%0A%20%20%20%20%20%20%20%20self._tree%20%3D%20list%28arr%29%0A%0A%20%20%20%20def%20size%28self%29%3A%0A%20%20%20%20%20%20%20%20return%20len%28self._tree%29%0A%0A%20%20%20%20def%20val%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20if%20i%20%3C%200%20or%20i%20%3E%3D%20self.size%28%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%20%20%20%20return%20self._tree%5Bi%5D%0A%0A%20%20%20%20def%20left%28self%2C%20i%3A%20int%29%20-%3E%20int%20%7C%20None%3A%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self%2C%20i%3A%20int%29%20-%3E%20int%20%7C%20None%3A%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self%2C%20i%3A%20int%29%20-%3E%20int%20%7C%20None%3A%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20%2F%2F%202%0A%0A%20%20%20%20def%20level_order%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20self.res%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20for%20i%20in%20range%28self.size%28%29%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20self.val%28i%29%20is%20not%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20self.res.append%28self.val%28i%29%29%0A%20%20%20%20%20%20%20%20return%20self.res%0A%0A%20%20%20%20def%20dfs%28self%2C%20i%3A%20int%2C%20order%3A%20str%29%3A%0A%20%20%20%20%20%20%20%20if%20self.val%28i%29%20is%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%0A%20%20%20%20%20%20%20%20if%20order%20%3D%3D%20%27pre%27%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.res.append%28self.val%28i%29%29%0A%20%20%20%20%20%20%20%20self.dfs%28self.left%28i%29%2C%20order%29%0A%20%20%20%20%20%20%20%20if%20order%20%3D%3D%20%27in%27%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.res.append%28self.val%28i%29%29%0A%20%20%20%20%20%20%20%20self.dfs%28self.right%28i%29%2C%20order%29%0A%20%20%20%20%20%20%20%20if%20order%20%3D%3D%20%27post%27%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.res.append%28self.val%28i%29%29%0A%0A%20%20%20%20def%20pre_order%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20self.res%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20self.dfs%280%2C%20order%3D%27pre%27%29%0A%20%20%20%20%20%20%20%20return%20self.res%0A%0A%20%20%20%20def%20in_order%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20self.res%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20self.dfs%280%2C%20order%3D%27in%27%29%0A%20%20%20%20%20%20%20%20return%20self.res%0A%0A%20%20%20%20def%20post_order%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20self.res%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20self.dfs%280%2C%20order%3D%27post%27%29%0A%20%20%20%20%20%20%20%20return%20self.res%0Aif%20__name__%20%3D%3D%20%27__main__%27%3A%0A%20%20%20%20arr%20%3D%20%5B1%2C%202%2C%203%2C%204%2C%20None%2C%206%2C%20None%5D%0A%20%20%20%20abt%20%3D%20ArrayBinaryTree%28arr%29%0A%20%20%20%20i%20%3D%201%0A%20%20%20%20l%2C%20r%2C%20p%20%3D%20%28abt.left%28i%29%2C%20abt.right%28i%29%2C%20abt.parent%28i%29%29%0A%20%20%20%20res%20%3D%20abt.level_order%28%29%0A%20%20%20%20res%20%3D%20abt.pre_order%28%29%0A%20%20%20%20res%20%3D%20abt.in_order%28%29%0A%20%20%20%20res%20%3D%20abt.post_order%28%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h2 id="733">7.3.3 &nbsp; 利点と制約<a class="headerlink" href="#733" title="Permanent link">&para;</a></h2>
+<p>二分木の配列表現には主に次の利点があります。</p>
 <ul>
-<li>配列は連続したメモリ空間に格納されるため、キャッシュフレンドリーで、より高速なアクセスと探索が可能です。</li>
-<li>ポインタを格納する必要がないため、スペースを節約できます。</li>
-<li>ノードへのランダムアクセスが可能です。</li>
+<li>配列は連続したメモリ空間に格納されるため、キャッシュ効率が高く、アクセスと走査が速い。</li>
+<li>ポインタを格納する必要がなく、比較的省スペースである。</li>
+<li>ノードへのランダムアクセスが可能である。</li>
 </ul>
-<p>しかし、配列表現にはいくつかの制限もあります：</p>
+<p>ただし、配列表現にはいくつかの制約もあります。</p>
 <ul>
-<li>配列格納には連続したメモリ空間が必要なため、大量のデータを持つ木の格納には適していません。</li>
-<li>ノードの追加や削除には配列の挿入や削除操作が必要で、効率が低くなります。</li>
-<li>二分木に多くの<code>None</code>値がある場合、配列に含まれるノードデータの割合が低くなり、空間利用率が低下します。</li>
+<li>配列による格納には連続したメモリ空間が必要なため、データ量が大きすぎる木の格納には向かない。</li>
+<li>ノードの追加と削除は配列の挿入・削除操作で実現する必要があり、効率は低い。</li>
+<li>二分木に大量の <code>None</code> が存在すると、配列に占める実ノードデータの比率が低くなり、空間利用率も低下する。</li>
 </ul>
 
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diff --git a/ja/chapter_tree/avl_tree/index.html b/ja/chapter_tree/avl_tree/index.html
index ad689e7d3..02d375913 100644
--- a/ja/chapter_tree/avl_tree/index.html
+++ b/ja/chapter_tree/avl_tree/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -39,7 +39,7 @@
     
     
       
-        <title>7.5 AVL木 * - Hello アルゴリズム</title>
+        <title>7.5 AVL 木 * - Hello アルゴリズム</title>
       
     
     
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -152,7 +152,7 @@
         <div class="md-header__topic" data-md-component="header-topic">
           <span class="md-ellipsis">
             
-              7.5 &nbsp; AVL木 *
+              7.5 &nbsp; AVL 木 *
             
           </span>
         </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
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   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1953,7 +1953,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -1971,7 +1971,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2001,12 +2001,12 @@
   <a href="#751-avl" class="md-nav__link">
     <span class="md-ellipsis">
       
-        7.5.1 &nbsp; AVL木の一般的な用語
+        7.5.1 &nbsp; AVL 木の基本用語
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="7.5.1 AVL木の一般的な用語">
+    <nav class="md-nav" aria-label="7.5.1 AVL 木の基本用語">
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           <li class="md-nav__item">
@@ -2024,7 +2024,7 @@
   <a href="#2" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2. &nbsp; ノードの平衡因子
+        2. &nbsp; ノードの平衡係数
       
     </span>
   </a>
@@ -2040,12 +2040,12 @@
   <a href="#752-avl" class="md-nav__link">
     <span class="md-ellipsis">
       
-        7.5.2 &nbsp; AVL木の回転
+        7.5.2 &nbsp; AVL 木の回転
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="7.5.2 AVL木の回転">
+    <nav class="md-nav" aria-label="7.5.2 AVL 木の回転">
       <ul class="md-nav__list">
         
           <li class="md-nav__item">
@@ -2074,7 +2074,7 @@
   <a href="#3" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3. &nbsp; 左右回転
+        3. &nbsp; 左回転してから右回転
       
     </span>
   </a>
@@ -2085,7 +2085,7 @@
   <a href="#4" class="md-nav__link">
     <span class="md-ellipsis">
       
-        4. &nbsp; 右左回転
+        4. &nbsp; 右回転してから左回転
       
     </span>
   </a>
@@ -2112,12 +2112,12 @@
   <a href="#753-avl" class="md-nav__link">
     <span class="md-ellipsis">
       
-        7.5.3 &nbsp; AVL木の一般的な操作
+        7.5.3 &nbsp; AVL 木の基本操作
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="7.5.3 AVL木の一般的な操作">
+    <nav class="md-nav" aria-label="7.5.3 AVL 木の基本操作">
       <ul class="md-nav__list">
         
           <li class="md-nav__item">
@@ -2146,7 +2146,7 @@
   <a href="#3_1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3. &nbsp; ノードの検索
+        3. &nbsp; ノードの探索
       
     </span>
   </a>
@@ -2162,7 +2162,7 @@
   <a href="#754-avl" class="md-nav__link">
     <span class="md-ellipsis">
       
-        7.5.4 &nbsp; AVL木の典型的な応用
+        7.5.4 &nbsp; AVL 木の代表的な応用
       
     </span>
   </a>
@@ -2327,7 +2327,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2713,7 +2713,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2769,7 +2769,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2797,7 +2797,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3335,7 +3335,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3391,7 +3391,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3419,7 +3419,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3612,7 +3612,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3640,7 +3640,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3781,7 +3781,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3809,7 +3809,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3837,7 +3837,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3865,7 +3865,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -4058,7 +4058,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4303,7 +4303,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4449,12 +4449,12 @@
   <a href="#751-avl" class="md-nav__link">
     <span class="md-ellipsis">
       
-        7.5.1 &nbsp; AVL木の一般的な用語
+        7.5.1 &nbsp; AVL 木の基本用語
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="7.5.1 AVL木の一般的な用語">
+    <nav class="md-nav" aria-label="7.5.1 AVL 木の基本用語">
       <ul class="md-nav__list">
         
           <li class="md-nav__item">
@@ -4472,7 +4472,7 @@
   <a href="#2" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2. &nbsp; ノードの平衡因子
+        2. &nbsp; ノードの平衡係数
       
     </span>
   </a>
@@ -4488,12 +4488,12 @@
   <a href="#752-avl" class="md-nav__link">
     <span class="md-ellipsis">
       
-        7.5.2 &nbsp; AVL木の回転
+        7.5.2 &nbsp; AVL 木の回転
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="7.5.2 AVL木の回転">
+    <nav class="md-nav" aria-label="7.5.2 AVL 木の回転">
       <ul class="md-nav__list">
         
           <li class="md-nav__item">
@@ -4522,7 +4522,7 @@
   <a href="#3" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3. &nbsp; 左右回転
+        3. &nbsp; 左回転してから右回転
       
     </span>
   </a>
@@ -4533,7 +4533,7 @@
   <a href="#4" class="md-nav__link">
     <span class="md-ellipsis">
       
-        4. &nbsp; 右左回転
+        4. &nbsp; 右回転してから左回転
       
     </span>
   </a>
@@ -4560,12 +4560,12 @@
   <a href="#753-avl" class="md-nav__link">
     <span class="md-ellipsis">
       
-        7.5.3 &nbsp; AVL木の一般的な操作
+        7.5.3 &nbsp; AVL 木の基本操作
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="7.5.3 AVL木の一般的な操作">
+    <nav class="md-nav" aria-label="7.5.3 AVL 木の基本操作">
       <ul class="md-nav__list">
         
           <li class="md-nav__item">
@@ -4594,7 +4594,7 @@
   <a href="#3_1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3. &nbsp; ノードの検索
+        3. &nbsp; ノードの探索
       
     </span>
   </a>
@@ -4610,7 +4610,7 @@
   <a href="#754-avl" class="md-nav__link">
     <span class="md-ellipsis">
       
-        7.5.4 &nbsp; AVL木の典型的な応用
+        7.5.4 &nbsp; AVL 木の代表的な応用
       
     </span>
   </a>
@@ -4654,83 +4654,83 @@
 
 
 <!-- Page content -->
-<h1 id="75-avl">7.5 &nbsp; AVL木 *<a class="headerlink" href="#75-avl" title="Permanent link">&para;</a></h1>
-<p>「二分探索木」の節では、複数の挿入と削除の後、二分探索木が連結リストに退化する可能性があることを述べました。このような場合、すべての操作の時間計算量が<span class="arithmatex">\(O(\log n)\)</span>から<span class="arithmatex">\(O(n)\)</span>に悪化します。</p>
-<p>下図に示すように、2つのノード削除操作の後、この二分探索木は連結リストに退化します。</p>
-<p><img alt="ノード削除後のAVL木の退化" class="animation-figure" src="../avl_tree.assets/avltree_degradation_from_removing_node.png" /></p>
-<p align="center"> 図 7-24 &nbsp; ノード削除後のAVL木の退化 </p>
+<h1 id="75-avl">7.5 &nbsp; AVL 木 *<a class="headerlink" href="#75-avl" title="Permanent link">&para;</a></h1>
+<p>「二分探索木」章で述べたように、挿入と削除を何度も繰り返すと、二分探索木は連結リストへ退化する可能性があります。この場合、すべての操作の時間計算量は <span class="arithmatex">\(O(\log n)\)</span> から <span class="arithmatex">\(O(n)\)</span> へ劣化します。</p>
+<p>以下の図に示すように、ノード削除を 2 回行うと、この二分探索木は連結リストへ退化します。</p>
+<p><img alt="AVL 木がノード削除後に退化する" class="animation-figure" src="../avl_tree.assets/avltree_degradation_from_removing_node.png" /></p>
+<p align="center"> 図 7-24 &nbsp; AVL 木がノード削除後に退化する </p>
 
-<p>例えば、下図に示す完全二分木では、2つのノードを挿入した後、木が左に大きく傾き、検索操作の時間計算量も悪化します。</p>
-<p><img alt="ノード挿入後のAVL木の退化" class="animation-figure" src="../avl_tree.assets/avltree_degradation_from_inserting_node.png" /></p>
-<p align="center"> 図 7-25 &nbsp; ノード挿入後のAVL木の退化 </p>
+<p>別の例として、以下の図に示す完全二分木に 2 つのノードを挿入すると、木は大きく左に傾き、探索操作の時間計算量もそれに伴って劣化します。</p>
+<p><img alt="AVL 木がノード挿入後に退化する" class="animation-figure" src="../avl_tree.assets/avltree_degradation_from_inserting_node.png" /></p>
+<p align="center"> 図 7-25 &nbsp; AVL 木がノード挿入後に退化する </p>
 
-<p>1962年、G. M. Adelson-VelskyとE. M. Landisが論文「An algorithm for the organization of information」で<u>AVL木</u>を提案しました。この論文では、ノードの継続的な追加と削除の後もAVL木が退化しないことを保証する一連の操作について詳述し、さまざまな操作の時間計算量を<span class="arithmatex">\(O(\log n)\)</span>レベルに維持しました。つまり、頻繁な追加、削除、検索、変更が必要なシナリオで、AVL木は常に効率的なデータ操作性能を維持でき、大きな応用価値があります。</p>
-<h2 id="751-avl">7.5.1 &nbsp; AVL木の一般的な用語<a class="headerlink" href="#751-avl" title="Permanent link">&para;</a></h2>
-<p>AVL木は二分探索木でありかつ平衡二分木でもあり、これら2つの種類の二分木のすべての性質を満たしているため、<u>平衡二分探索木</u>です。</p>
+<p>1962 年、G. M. Adelson-Velsky と E. M. Landis は論文“An algorithm for the organization of information”の中で <u>AVL 木</u> を提案しました。論文では一連の操作が詳しく説明されており、ノードの追加と削除を続けても AVL 木が退化しないようにして、各種操作の時間計算量を <span class="arithmatex">\(O(\log n)\)</span> の水準に保ちます。言い換えると、追加・削除・探索・更新を頻繁に行う場面でも、AVL 木は常に高いデータ操作性能を維持でき、実用価値の高い構造です。</p>
+<h2 id="751-avl">7.5.1 &nbsp; AVL 木の基本用語<a class="headerlink" href="#751-avl" title="Permanent link">&para;</a></h2>
+<p>AVL 木は二分探索木であると同時に平衡二分木でもあり、これら 2 種類の二分木の性質をすべて満たします。したがって、<u>平衡二分探索木（balanced binary search tree）</u>の一種です。</p>
 <h3 id="1">1. &nbsp; ノードの高さ<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>AVL木に関連する操作ではノードの高さを取得する必要があるため、ノードクラスに<code>height</code>変数を追加する必要があります：</p>
+<p>AVL 木の操作ではノードの高さを取得する必要があるため、ノードクラスに <code>height</code> 変数を追加します：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">TreeNode</span><span class="p">:</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;AVL木ノード&quot;&quot;&quot;</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;AVL 木ノードクラス&quot;&quot;&quot;</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">val</span>                 <span class="c1"># ノード値</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">height</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>                <span class="c1"># ノードの高さ</span>
-<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">left</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>   <span class="c1"># 左の子への参照</span>
-<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">right</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># 右の子への参照</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">left</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>   <span class="c1"># 左の子ノード参照</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">right</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># 右の子ノード参照</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* AVL木ノード */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* AVL 木ノードクラス */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">{};</span><span class="w">          </span><span class="c1">// ノード値</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">     </span><span class="c1">// ノードの高さ</span>
-<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">left</span><span class="p">{};</span><span class="w">   </span><span class="c1">// 左の子</span>
-<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">right</span><span class="p">{};</span><span class="w">  </span><span class="c1">// 右の子</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">left</span><span class="p">{};</span><span class="w">   </span><span class="c1">// 左の子ノード</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">right</span><span class="p">{};</span><span class="w">  </span><span class="c1">// 右の子ノード</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="n">TreeNode</span><span class="p">()</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">default</span><span class="p">;</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="k">explicit</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">x</span><span class="p">){}</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="p">};</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* AVL木ノード */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* AVL 木ノードクラス */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kd">class</span> <span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">        </span><span class="c1">// ノード値</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="p">;</span><span class="w">     </span><span class="c1">// ノードの高さ</span>
-<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w">  </span><span class="c1">// 左の子</span>
-<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右の子</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w">  </span><span class="c1">// 左の子ノード</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右の子ノード</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">TreeNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w"> </span><span class="p">}</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* AVL木ノード */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* AVL 木ノードクラス */</span>
 <a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">class</span><span class="w"> </span><span class="nf">TreeNode</span><span class="p">(</span><span class="kt">int?</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int?</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w">    </span><span class="c1">// ノード値</span>
 <a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="p">;</span><span class="w">      </span><span class="c1">// ノードの高さ</span>
-<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w">  </span><span class="c1">// 左の子への参照</span>
-<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右の子への参照</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w">  </span><span class="c1">// 左の子ノード参照</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右の子ノード参照</span>
 <a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* AVL木ノード */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* AVL 木ノード構造体 */</span>
 <a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="nx">Val</span><span class="w">    </span><span class="kt">int</span><span class="w">       </span><span class="c1">// ノード値</span>
 <a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">Height</span><span class="w"> </span><span class="kt">int</span><span class="w">       </span><span class="c1">// ノードの高さ</span>
-<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="nx">Left</span><span class="w">   </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="c1">// 左の子への参照</span>
-<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="nx">Right</span><span class="w">  </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="c1">// 右の子への参照</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="nx">Left</span><span class="w">   </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="c1">// 左の子ノード参照</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="nx">Right</span><span class="w">  </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="c1">// 右の子ノード参照</span>
 <a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* AVL木ノード */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* AVL 木ノードクラス */</span>
 <a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">val</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// ノード値</span>
 <a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">height</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// ノードの高さ</span>
-<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">left</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 左の子</span>
-<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">right</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 右の子</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">left</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 左の子ノード</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">right</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 右の子ノード</span>
 <a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a>
 <a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">    </span><span class="kd">init</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">        </span><span class="n">val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">x</span>
@@ -4740,12 +4740,12 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* AVL木ノード */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* AVL 木ノードクラス */</span>
 <a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="nx">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// ノード値</span>
-<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="nx">height</span><span class="p">;</span><span class="w"> </span><span class="c1">// ノードの高さ</span>
-<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="nx">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左の子ポインタ</span>
-<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="nx">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右の子ポインタ</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="nx">height</span><span class="p">;</span><span class="w"> </span><span class="c1">//ノードの高さ</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="nx">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左の子ノードポインタ</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="nx">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右の子ノードポインタ</span>
 <a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">,</span><span class="w"> </span><span class="nx">height</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span>
 <a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">height</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">height</span><span class="p">;</span>
@@ -4756,12 +4756,12 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* AVL木ノード */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* AVL 木ノードクラス */</span>
 <a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w">            </span><span class="c1">// ノード値</span>
 <a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="nx">height</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w">         </span><span class="c1">// ノードの高さ</span>
-<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="nx">left</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span><span class="w">  </span><span class="c1">// 左の子ポインタ</span>
-<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="nx">right</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右の子ポインタ</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="nx">left</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span><span class="w">  </span><span class="c1">// 左の子ノードポインタ</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="nx">right</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右の子ノードポインタ</span>
 <a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val?</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">height?</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">left?</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="nx">right?</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">val</span><span class="p">;</span>
 <a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">height</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">height</span><span class="p">;</span>
@@ -4772,12 +4772,12 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* AVL木ノード */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* AVL 木ノードクラス */</span>
 <a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">         </span><span class="c1">// ノード値</span>
 <a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="p">;</span><span class="w">      </span><span class="c1">// ノードの高さ</span>
-<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w">  </span><span class="c1">// 左の子</span>
-<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右の子</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w">  </span><span class="c1">// 左の子ノード</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右の子ノード</span>
 <a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="n">TreeNode</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="k">this</span><span class="p">.</span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">right</span><span class="p">]);</span>
 <a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="p">}</span>
 </code></pre></div>
@@ -4786,12 +4786,12 @@
 <div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">rc</span><span class="p">::</span><span class="n">Rc</span><span class="p">;</span>
 <a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cell</span><span class="p">::</span><span class="n">RefCell</span><span class="p">;</span>
 <a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a>
-<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="cm">/* AVL木ノード */</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="cm">/* AVL 木ノード構造体 */</span>
 <a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w">                               </span><span class="c1">// ノード値</span>
 <a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="n">height</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w">                            </span><span class="c1">// ノードの高さ</span>
-<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="n">left</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w">    </span><span class="c1">// 左の子</span>
-<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">    </span><span class="n">right</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w">   </span><span class="c1">// 右の子</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="n">left</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w">    </span><span class="c1">// 左の子ノード</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">    </span><span class="n">right</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w">   </span><span class="c1">// 右の子ノード</span>
 <a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="p">}</span>
 <a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a>
 <a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="k">impl</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="p">{</span>
@@ -4808,8 +4808,8 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* AVL木ノード */</span>
-<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* AVL 木ノード構造体 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
 <a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="p">;</span>
 <a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">    </span><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">left</span><span class="p">;</span>
@@ -4830,47 +4830,58 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* AVL木ノード */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* AVL 木ノードクラス */</span>
 <a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">TreeNode</span><span class="p">(</span><span class="kd">val</span><span class="w"> </span><span class="nv">_val</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// ノード値</span>
 <a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">height</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="w">          </span><span class="c1">// ノードの高さ</span>
-<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">left</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="w">   </span><span class="c1">// 左の子</span>
-<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">right</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="w">  </span><span class="c1">// 右の子</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">left</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="w">   </span><span class="c1">// 左の子ノード</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">right</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="w">  </span><span class="c1">// 右の子ノード</span>
 <a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### AVL 木ノードクラス ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">TreeNode</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:val</span><span class="w">    </span><span class="c1"># ノード値</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:height</span><span class="w"> </span><span class="c1"># ノードの高さ</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:left</span><span class="w">   </span><span class="c1"># 左の子ノード参照</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:right</span><span class="w">  </span><span class="c1"># 右の子ノード参照</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">    </span><span class="vi">@val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">    </span><span class="vi">@height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>「ノードの高さ」とは、そのノードから最も遠い葉ノードまでの距離、つまり通過する「辺」の数を指します。重要なのは、葉ノードの高さは<span class="arithmatex">\(0\)</span>で、nullノードの高さは<span class="arithmatex">\(-1\)</span>であることです。ノードの高さを取得し、更新するための2つのユーティリティ関数を作成します：</p>
+<p>「ノードの高さ」とは、そのノードから最も遠い葉ノードまでの距離、すなわち通過する「辺」の本数を指します。特に、葉ノードの高さは <span class="arithmatex">\(0\)</span>、空ノードの高さは <span class="arithmatex">\(-1\)</span> です。ここでは、ノードの高さを取得・更新するための 2 つの補助関数を用意します：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">height</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
 <a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ノードの高さを取得&quot;&quot;&quot;</span>
-<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="c1"># 空ノードの高さは-1、葉ノードの高さは0</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="c1"># 空ノードの高さは -1、葉ノードの高さは 0</span>
 <a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="k">if</span> <span class="n">node</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>        <span class="k">return</span> <span class="n">node</span><span class="o">.</span><span class="n">height</span>
 <a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>    <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>
 <a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>
 <a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">update_height</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">):</span>
-<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ノードの高さを更新&quot;&quot;&quot;</span>
-<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>    <span class="c1"># ノードの高さ = 最も高い部分木の高さ + 1</span>
+<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ノードの高さを更新する&quot;&quot;&quot;</span>
+<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>    <span class="c1"># ノードの高さは最も高い部分木の高さ + 1 に等しい</span>
 <a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>    <span class="n">node</span><span class="o">.</span><span class="n">height</span> <span class="o">=</span> <span class="nb">max</span><span class="p">([</span><span class="bp">self</span><span class="o">.</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)])</span> <span class="o">+</span> <span class="mi">1</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* ノードの高さを取得 */</span>
 <a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">height</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="c1">// 空ノードの高さは-1、葉ノードの高さは0</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="c1">// 空ノードの高さは -1、葉ノードの高さは 0</span>
 <a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="mi">-1</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">height</span><span class="p">;</span>
 <a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="p">}</span>
 <a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>
-<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="cm">/* ノードの高さを更新 */</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="cm">/* ノードの高さを更新する */</span>
 <a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="kt">void</span><span class="w"> </span><span class="nf">updateHeight</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">    </span><span class="c1">// ノードの高さ = 最も高い部分木の高さ + 1</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">    </span><span class="c1">// ノードの高さは最も高い部分木の高さ + 1 に等しい</span>
 <a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">),</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="p">}</span>
 </code></pre></div>
@@ -4882,162 +4893,340 @@
 <a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">height</span><span class="p">;</span>
 <a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="p">}</span>
 <a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a>
-<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="cm">/* ノードの高さを更新 */</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="cm">/* ノードの高さを更新する */</span>
 <a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="kt">void</span><span class="w"> </span><span class="nf">updateHeight</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">    </span><span class="c1">// ノードの高さは最も高い部分木の高さ + 1</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">    </span><span class="c1">// ノードの高さは最も高い部分木の高さ + 1 に等しい</span>
 <a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="n">node</span><span class="p">.</span><span class="na">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">max</span><span class="p">(</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">),</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Height</span><span class="p">}</span>
-<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a>
-<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">UpdateHeight</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* ノードの高さを取得 */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Height</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="c1">// 空ノードの高さは -1、葉ノードの高さは 0</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">height</span><span class="p">;</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="p">}</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="cm">/* ノードの高さを更新する */</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="k">void</span><span class="w"> </span><span class="nf">UpdateHeight</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">    </span><span class="c1">// ノードの高さは最も高い部分木の高さ + 1 に等しい</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="n">node</span><span class="p">.</span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Max</span><span class="p">(</span><span class="n">Height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">),</span><span class="w"> </span><span class="n">Height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">height</span><span class="p">}</span>
-<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a>
-<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">updateHeight</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* ノードの高さを取得 */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">aVLTree</span><span class="p">)</span><span class="w"> </span><span class="nx">height</span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="c1">// 空ノードの高さは -1、葉ノードの高さは 0</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Height</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="p">}</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="cm">/* ノードの高さを更新する */</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">aVLTree</span><span class="p">)</span><span class="w"> </span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">    </span><span class="nx">lh</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">height</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span><span class="p">)</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w">    </span><span class="nx">rh</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">height</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="p">)</span>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w">    </span><span class="c1">// ノードの高さは最も高い部分木の高さ + 1 に等しい</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">lh</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">rh</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w">        </span><span class="nx">node</span><span class="p">.</span><span class="nx">Height</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">lh</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="w">        </span><span class="nx">node</span><span class="p">.</span><span class="nx">Height</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">rh</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">height</span><span class="p">}</span>
-<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a>
-<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">updateHeight</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* ノードの高さを取得 */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">height</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="c1">// 空ノードの高さは -1、葉ノードの高さは 0</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="n">node</span><span class="p">?.</span><span class="n">height</span><span class="w"> </span><span class="p">??</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="p">}</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="cm">/* ノードの高さを更新する */</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="kd">func</span><span class="w"> </span><span class="nf">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">    </span><span class="c1">// ノードの高さは最も高い部分木の高さ + 1 に等しい</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">    </span><span class="n">node</span><span class="p">?.</span><span class="n">height</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">max</span><span class="p">(</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">?.</span><span class="kr">left</span><span class="p">),</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="p">))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">height</span><span class="p">}</span>
-<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a>
-<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">updateHeight</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* ノードの高さを取得 */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="nx">height</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="c1">// 空ノードの高さは -1、葉ノードの高さは 0</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">height</span><span class="p">;</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="p">}</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="cm">/* ノードの高さを更新する */</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="n">#updateHeight</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w">    </span><span class="c1">// ノードの高さは最も高い部分木の高さ + 1 に等しい</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w">    </span><span class="nx">node</span><span class="p">.</span><span class="nx">height</span><span class="w"> </span><span class="o">=</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w">        </span><span class="nb">Math</span><span class="p">.</span><span class="nx">max</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">height</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="p">),</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">height</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">height</span><span class="p">}</span>
-<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a>
-<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">updateHeight</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* ノードの高さを取得 */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="nx">height</span><span class="p">(</span><span class="nx">node</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="c1">// 空ノードの高さは -1、葉ノードの高さは 0</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="o">-</span><span class="nx">1</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">node.height</span><span class="p">;</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="p">}</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="cm">/* ノードの高さを更新する */</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">node</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">    </span><span class="c1">// ノードの高さは最も高い部分木の高さ + 1 に等しい</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">    </span><span class="nx">node</span><span class="p">.</span><span class="nx">height</span><span class="w"> </span><span class="o">=</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w">        </span><span class="nb">Math</span><span class="p">.</span><span class="nx">max</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">height</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="p">),</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">height</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">height</span><span class="p">}</span>
-<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a>
-<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">updateHeight</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* ノードの高さを取得 */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="c1">// 空ノードの高さは -1、葉ノードの高さは 0</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">height</span><span class="p">;</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="p">}</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="cm">/* ノードの高さを更新する */</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="kt">void</span><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">  </span><span class="c1">// ノードの高さは最も高い部分木の高さ + 1 に等しい</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="w">  </span><span class="n">node</span><span class="o">!</span><span class="p">.</span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">),</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">height</span><span class="p">}</span>
-<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a>
-<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">update_height</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* ノードの高さを取得 */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">height</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="nc">OptionTreeNodeRc</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="c1">// 空ノードの高さは -1、葉ノードの高さは 0</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="k">match</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">        </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">height</span><span class="p">,</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w">        </span><span class="nb">None</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">,</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="p">}</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="cm">/* ノードの高さを更新する */</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="k">fn</span><span class="w"> </span><span class="nf">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="nc">OptionTreeNodeRc</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="w">        </span><span class="c1">// ノードの高さは最も高い部分木の高さ + 1 に等しい</span>
+<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="w">        </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">max</span><span class="p">(</span><span class="bp">Self</span><span class="p">::</span><span class="n">height</span><span class="p">(</span><span class="n">left</span><span class="p">),</span><span class="w"> </span><span class="bp">Self</span><span class="p">::</span><span class="n">height</span><span class="p">(</span><span class="n">right</span><span class="p">))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">height</span><span class="p">}</span>
-<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a>
-<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">updateHeight</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* ノードの高さを取得 */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">height</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="c1">// 空ノードの高さは -1、葉ノードの高さは 0</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">height</span><span class="p">;</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="p">}</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="cm">/* ノードの高さを更新する */</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="kt">void</span><span class="w"> </span><span class="nf">updateHeight</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">lh</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">);</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">rh</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w">    </span><span class="c1">// ノードの高さは最も高い部分木の高さ + 1 に等しい</span>
+<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">lh</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">rh</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="w">        </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">lh</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="w">        </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rh</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">height</span><span class="p">}</span>
-<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a>
-<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">updateHeight</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* ノードの高さを取得 */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">height</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="c1">// 空ノードの高さは -1、葉ノードの高さは 0</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="o">?.</span><span class="na">height</span><span class="w"> </span><span class="o">?:</span><span class="w"> </span><span class="o">-</span><span class="m">1</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="p">}</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="cm">/* ノードの高さを更新する */</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w">    </span><span class="c1">// ノードの高さは最も高い部分木の高さ + 1 に等しい</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w">    </span><span class="n">node</span><span class="o">?.</span><span class="na">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">?.</span><span class="na">left</span><span class="p">),</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">?.</span><span class="na">right</span><span class="p">))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">height</span><span class="p">}</span>
-<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a>
-<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">update_height</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### ノードの高さを取得 ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="c1"># 空ノードの高さは -1、葉ノードの高さは 0</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">height</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">  </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="k">end</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="c1">### ノードの高さを更新 ###</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="k">def</span><span class="w"> </span><span class="nf">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w">  </span><span class="c1"># ノードの高さは最も高い部分木の高さ + 1 に等しい</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w">  </span><span class="n">node</span><span class="o">.</span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">),</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span><span class="o">].</span><span class="n">max</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h3 id="2">2. &nbsp; ノードの平衡因子<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>ノードの<u>平衡因子</u>は、そのノードの左部分木の高さから右部分木の高さを引いた値として定義され、nullノードの平衡因子は<span class="arithmatex">\(0\)</span>として定義されます。後で使いやすくするため、ノードの平衡因子を取得する機能も関数にカプセル化します：</p>
+<h3 id="2">2. &nbsp; ノードの平衡係数<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>ノードの<u>平衡係数（balance factor）</u>は、左部分木の高さから右部分木の高さを引いた値と定義し、空ノードの平衡係数は <span class="arithmatex">\(0\)</span> とします。同様に、ノードの平衡係数を取得する機能も関数にカプセル化して、後続で使いやすくします：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">balance_factor</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バランス因子を取得&quot;&quot;&quot;</span>
-<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>    <span class="c1"># 空ノードのバランス因子は0</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;平衡係数を取得&quot;&quot;&quot;</span>
+<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>    <span class="c1"># 空ノードの平衡係数は 0</span>
 <a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>    <span class="k">if</span> <span class="n">node</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a>        <span class="k">return</span> <span class="mi">0</span>
-<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a>    <span class="c1"># ノードのバランス因子 = 左部分木の高さ - 右部分木の高さ</span>
+<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a>    <span class="c1"># ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ</span>
 <a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a>    <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* 平衡因子を取得 */</span>
+<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* 平衡係数を取得 */</span>
 <a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">balanceFactor</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="c1">// 空ノードの平衡因子は0</span>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="c1">// 空ノードの平衡係数は 0</span>
 <a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
 <a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w">    </span><span class="c1">// ノードの平衡因子 = 左部分木の高さ - 右部分木の高さ</span>
+<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w">    </span><span class="c1">// ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ</span>
 <a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
 <a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 平衡因子を取得 */</span>
+<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 平衡係数を取得 */</span>
 <a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">balanceFactor</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="c1">// 空ノードの平衡因子は 0</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="c1">// 空ノードの平衡係数は 0</span>
 <a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
 <a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w">    </span><span class="c1">// ノードの平衡因子 = 左部分木の高さ - 右部分木の高さ</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w">    </span><span class="c1">// ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ</span>
 <a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">);</span>
 <a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BalanceFactor</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 平衡係数を取得 */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">BalanceFactor</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="c1">// 空ノードの平衡係数は 0</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">    </span><span class="c1">// ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nf">Height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">Height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">balanceFactor</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 平衡係数を取得 */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">aVLTree</span><span class="p">)</span><span class="w"> </span><span class="nx">balanceFactor</span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="c1">// 空ノードの平衡係数は 0</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">    </span><span class="c1">// ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">height</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">height</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="p">)</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">balanceFactor</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* 平衡係数を取得 */</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w">    </span><span class="c1">// 空ノードの平衡係数は 0</span>
+<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w">    </span><span class="k">guard</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w">    </span><span class="c1">// ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ</span>
+<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="kr">left</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="kr">right</span><span class="p">)</span>
+<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">balanceFactor</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* 平衡係数を取得 */</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="nx">balanceFactor</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w">    </span><span class="c1">// 空ノードの平衡係数は 0</span>
+<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="w">    </span><span class="c1">// ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ</span>
+<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">height</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">height</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">);</span>
+<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">balanceFactor</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* 平衡係数を取得 */</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="nx">balanceFactor</span><span class="p">(</span><span class="nx">node</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w">    </span><span class="c1">// 空ノードの平衡係数は 0</span>
+<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w">    </span><span class="c1">// ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ</span>
+<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">height</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">height</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">);</span>
+<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">balanceFactor</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* 平衡係数を取得 */</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w">  </span><span class="c1">// 空ノードの平衡係数は 0</span>
+<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w">  </span><span class="c1">// ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ</span>
+<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">balance_factor</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* 平衡係数を取得 */</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="nc">OptionTreeNodeRc</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w">    </span><span class="k">match</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="w">        </span><span class="c1">// 空ノードの平衡係数は 0</span>
+<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="w">        </span><span class="nb">None</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span>
+<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="w">        </span><span class="c1">// ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ</span>
+<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="w">        </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="w">            </span><span class="bp">Self</span><span class="p">::</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">())</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="bp">Self</span><span class="p">::</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">())</span>
+<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">balanceFactor</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* 平衡係数を取得 */</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">balanceFactor</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w">    </span><span class="c1">// 空ノードの平衡係数は 0</span>
+<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="w">    </span><span class="c1">// ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ</span>
+<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">balanceFactor</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* 平衡係数を取得 */</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w">    </span><span class="c1">// 空ノードの平衡係数は 0</span>
+<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">0</span>
+<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w">    </span><span class="c1">// ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ</span>
+<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">)</span>
+<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">balance_factor</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="c1">### 平衡係数を取得 ###</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w">  </span><span class="c1"># 空ノードの平衡係数は 0</span>
+<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a>
+<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w">  </span><span class="c1"># ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ</span>
+<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="w">  </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>平衡因子を<span class="arithmatex">\(f\)</span>とすると、AVL木の任意のノードの平衡因子は<span class="arithmatex">\(-1 \le f \le 1\)</span>を満たします。</p>
+<p>平衡係数を <span class="arithmatex">\(f\)</span> とすると、AVL 木の任意のノードの平衡係数は常に <span class="arithmatex">\(-1 \le f \le 1\)</span> を満たします。</p>
 </div>
-<h2 id="752-avl">7.5.2 &nbsp; AVL木の回転<a class="headerlink" href="#752-avl" title="Permanent link">&para;</a></h2>
-<p>AVL木の特徴的な機能は「回転」操作で、これは二分木の中順探索シーケンスに影響を与えることなく、不平衡なノードのバランスを回復できます。つまり、<strong>回転操作は「二分探索木」の性質を維持しながら、木を「平衡二分木」に戻すことができます</strong>。</p>
-<p>絶対平衡因子が<span class="arithmatex">\(&gt; 1\)</span>のノードを「不平衡ノード」と呼びます。不平衡のタイプに応じて、4種類の回転があります：右回転、左回転、右左回転、左右回転です。以下、これらの回転操作について詳しく説明します。</p>
+<h2 id="752-avl">7.5.2 &nbsp; AVL 木の回転<a class="headerlink" href="#752-avl" title="Permanent link">&para;</a></h2>
+<p>AVL 木の特徴は「回転」操作にあり、二分木の中順走査列を変えずに、不平衡ノードを再び平衡に戻せます。言い換えると、<strong>回転操作は「二分探索木」の性質を保ちながら、木を再び「平衡二分木」に戻すことができます</strong>。</p>
+<p>平衡係数の絶対値が <span class="arithmatex">\(&gt; 1\)</span> のノードを「不平衡ノード」と呼びます。ノードの不平衡の形に応じて、回転操作は 4 種類に分かれます。右回転、左回転、右回転してから左回転、左回転してから右回転です。以下でこれらを順に説明します。</p>
 <h3 id="1_1">1. &nbsp; 右回転<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
-<p>下図に示すように、二分木で下から上への最初の不平衡ノードは「ノード3」です。この不平衡ノードを根とする部分木に焦点を当て、これを<code>node</code>とし、その左の子を<code>child</code>として、「右回転」を実行します。右回転後、部分木は再びバランスが取れ、同時に二分探索木の性質も維持されます。</p>
+<p>以下の図では、ノードの下に平衡係数を示しています。下から上へ見ると、二分木で最初に不平衡になるのは「ノード 3」です。この不平衡ノードを根とする部分木に注目し、そのノードを <code>node</code>、左の子ノードを <code>child</code> として、「右回転」を行います。右回転後、部分木は平衡を回復し、なおかつ二分探索木の性質も保たれます。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="4:4"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">&lt;1&gt;</label><label for="__tabbed_4_2">&lt;2&gt;</label><label for="__tabbed_4_3">&lt;3&gt;</label><label for="__tabbed_4_4">&lt;4&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
@@ -5056,263 +5245,515 @@
 </div>
 <p align="center"> 図 7-26 &nbsp; 右回転の手順 </p>
 
-<p>下図に示すように、<code>child</code>ノードに右の子（<code>grand_child</code>と表記）がある場合、右回転で手順を追加する必要があります：<code>grand_child</code>を<code>node</code>の左の子に設定します。</p>
-<p><img alt="grand_childがある右回転" class="animation-figure" src="../avl_tree.assets/avltree_right_rotate_with_grandchild.png" /></p>
-<p align="center"> 図 7-27 &nbsp; grand_childがある右回転 </p>
+<p>以下の図に示すように、ノード <code>child</code> に右の子ノード（<code>grand_child</code> と記す）がある場合、右回転には 1 ステップ追加する必要があります。すなわち、<code>grand_child</code> を <code>node</code> の左の子ノードにします。</p>
+<p><img alt="grand_child を持つ右回転" class="animation-figure" src="../avl_tree.assets/avltree_right_rotate_with_grandchild.png" /></p>
+<p align="center"> 図 7-27 &nbsp; grand_child を持つ右回転 </p>
 
-<p>「右回転」は比喩的な用語で、実際にはノードポインタを変更することで実現されます。以下のコードで示されます：</p>
+<p>「右に回転する」というのはあくまでイメージしやすい表現であり、実際にはノードポインタを変更して実現します。コードは次のとおりです：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="5:13"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">right_rotate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;右回転操作&quot;&quot;&quot;</span>
+<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;右回転&quot;&quot;&quot;</span>
 <a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a>    <span class="n">child</span> <span class="o">=</span> <span class="n">node</span><span class="o">.</span><span class="n">left</span>
 <a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a>    <span class="n">grand_child</span> <span class="o">=</span> <span class="n">child</span><span class="o">.</span><span class="n">right</span>
-<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a>    <span class="c1"># childを中心にnodeを右に回転</span>
+<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a>    <span class="c1"># child を支点として node を右回転させる</span>
 <a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a>    <span class="n">child</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="n">node</span>
 <a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a>    <span class="n">node</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">grand_child</span>
-<a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a>    <span class="c1"># ノードの高さを更新</span>
+<a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a>    <span class="c1"># ノードの高さを更新する</span>
 <a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
 <a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">update_height</span><span class="p">(</span><span class="n">child</span><span class="p">)</span>
-<a id="__codelineno-39-11" name="__codelineno-39-11" href="#__codelineno-39-11"></a>    <span class="c1"># 回転後の部分木のルートを返す</span>
+<a id="__codelineno-39-11" name="__codelineno-39-11" href="#__codelineno-39-11"></a>    <span class="c1"># 回転後の部分木の根ノードを返す</span>
 <a id="__codelineno-39-12" name="__codelineno-39-12" href="#__codelineno-39-12"></a>    <span class="k">return</span> <span class="n">child</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* 右回転操作 */</span>
+<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* 右回転 */</span>
 <a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">rightRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">;</span>
 <a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
-<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w">    </span><span class="c1">// childを中心にnodeを右に回転</span>
+<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w">    </span><span class="c1">// child を支点として node を右回転させる</span>
 <a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w">    </span><span class="n">child</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
 <a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
-<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w">    </span><span class="c1">// ノードの高さを更新</span>
+<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w">    </span><span class="c1">// ノードの高さを更新する</span>
 <a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
 <a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">);</span>
-<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w">    </span><span class="c1">// 回転後の部分木のルートを返す</span>
+<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w">    </span><span class="c1">// 回転後の部分木の根ノードを返す</span>
 <a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
 <a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 右回転操作 */</span>
+<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 右回転 */</span>
 <a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">rightRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">;</span>
 <a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="na">right</span><span class="p">;</span>
-<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="w">    </span><span class="c1">// child を軸として node を右に回転</span>
+<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="w">    </span><span class="c1">// child を支点として node を右回転させる</span>
 <a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a><span class="w">    </span><span class="n">child</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
 <a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="w">    </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
-<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a><span class="w">    </span><span class="c1">// ノードの高さを更新</span>
+<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a><span class="w">    </span><span class="c1">// ノードの高さを更新する</span>
 <a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
 <a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">);</span>
-<a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a><span class="w">    </span><span class="c1">// 回転後の部分木の根を返す</span>
+<a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a><span class="w">    </span><span class="c1">// 回転後の部分木の根ノードを返す</span>
 <a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
 <a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">RightRotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="cm">/* 右回転 */</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">RightRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="w">    </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">?.</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w">    </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">?.</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="w">    </span><span class="c1">// child を支点として node を右回転させる</span>
+<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a><span class="w">    </span><span class="n">child</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="w">    </span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
+<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a><span class="w">    </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="w">    </span><span class="n">UpdateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a><span class="w">    </span><span class="n">UpdateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">);</span>
+<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a><span class="w">    </span><span class="c1">// 回転後の部分木の根ノードを返す</span>
+<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">rightRotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* 右回転 */</span>
+<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">aVLTree</span><span class="p">)</span><span class="w"> </span><span class="nx">rightRotate</span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w">    </span><span class="nx">child</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span>
+<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">    </span><span class="nx">grandChild</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">child</span><span class="p">.</span><span class="nx">Right</span>
+<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w">    </span><span class="c1">// child を支点として node を右回転させる</span>
+<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w">    </span><span class="nx">child</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">node</span>
+<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="w">    </span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">grandChild</span>
+<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w">    </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w">    </span><span class="nx">t</span><span class="p">.</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span>
+<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w">    </span><span class="nx">t</span><span class="p">.</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">child</span><span class="p">)</span>
+<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w">    </span><span class="c1">// 回転後の部分木の根ノードを返す</span>
+<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">child</span>
+<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">rightRotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* 右回転 */</span>
+<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">child</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span><span class="p">?.</span><span class="kr">left</span>
+<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">grandChild</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">child</span><span class="p">?.</span><span class="kr">right</span>
+<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w">    </span><span class="c1">// child を支点として node を右回転させる</span>
+<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w">    </span><span class="n">child</span><span class="p">?.</span><span class="kr">right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w">    </span><span class="n">node</span><span class="p">?.</span><span class="kr">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">grandChild</span>
+<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w">    </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">child</span><span class="p">)</span>
+<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w">    </span><span class="c1">// 回転後の部分木の根ノードを返す</span>
+<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">child</span>
+<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">rightRotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="cm">/* 右回転 */</span>
+<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="n">#rightRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span>
+<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">child</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
+<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w">    </span><span class="c1">// child を支点として node を右回転させる</span>
+<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w">    </span><span class="nx">child</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="w">    </span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">grandChild</span><span class="p">;</span>
+<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="w">    </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="n">#updateHeight</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
+<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="n">#updateHeight</span><span class="p">(</span><span class="nx">child</span><span class="p">);</span>
+<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w">    </span><span class="c1">// 回転後の部分木の根ノードを返す</span>
+<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">child</span><span class="p">;</span>
+<a id="__codelineno-45-13" name="__codelineno-45-13" href="#__codelineno-45-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">rightRotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="cm">/* 右回転 */</span>
+<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="nx">rightRotate</span><span class="p">(</span><span class="nx">node</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span>
+<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">child</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
+<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="w">    </span><span class="c1">// child を支点として node を右回転させる</span>
+<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a><span class="w">    </span><span class="nx">child</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></a><span class="w">    </span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">grandChild</span><span class="p">;</span>
+<a id="__codelineno-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a><span class="w">    </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
+<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">child</span><span class="p">);</span>
+<a id="__codelineno-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></a><span class="w">    </span><span class="c1">// 回転後の部分木の根ノードを返す</span>
+<a id="__codelineno-46-12" name="__codelineno-46-12" href="#__codelineno-46-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">child</span><span class="p">;</span>
+<a id="__codelineno-46-13" name="__codelineno-46-13" href="#__codelineno-46-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">rightRotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* 右回転 */</span>
+<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">!</span><span class="p">.</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">!</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="w">  </span><span class="c1">// child を支点として node を右回転させる</span>
+<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a><span class="w">  </span><span class="n">child</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="w">  </span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
+<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a><span class="w">  </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="w">  </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="w">  </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">);</span>
+<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="w">  </span><span class="c1">// 回転後の部分木の根ノードを返す</span>
+<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-47-13" name="__codelineno-47-13" href="#__codelineno-47-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">right_rotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="cm">/* 右回転 */</span>
+<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">right_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="nc">OptionTreeNodeRc</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">OptionTreeNodeRc</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="w">    </span><span class="k">match</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a><span class="w">        </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span>
+<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="n">grand_child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a><span class="w">            </span><span class="c1">// child を支点として node を右回転させる</span>
+<a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a><span class="w">            </span><span class="n">child</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grand_child</span><span class="p">;</span>
+<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a><span class="w">            </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-48-11" name="__codelineno-48-11" href="#__codelineno-48-11"></a><span class="w">            </span><span class="bp">Self</span><span class="p">::</span><span class="n">update_height</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">));</span>
+<a id="__codelineno-48-12" name="__codelineno-48-12" href="#__codelineno-48-12"></a><span class="w">            </span><span class="bp">Self</span><span class="p">::</span><span class="n">update_height</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">child</span><span class="p">.</span><span class="n">clone</span><span class="p">()));</span>
+<a id="__codelineno-48-13" name="__codelineno-48-13" href="#__codelineno-48-13"></a><span class="w">            </span><span class="c1">// 回転後の部分木の根ノードを返す</span>
+<a id="__codelineno-48-14" name="__codelineno-48-14" href="#__codelineno-48-14"></a><span class="w">            </span><span class="nb">Some</span><span class="p">(</span><span class="n">child</span><span class="p">)</span>
+<a id="__codelineno-48-15" name="__codelineno-48-15" href="#__codelineno-48-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-48-16" name="__codelineno-48-16" href="#__codelineno-48-16"></a><span class="w">        </span><span class="nb">None</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span>
+<a id="__codelineno-48-17" name="__codelineno-48-17" href="#__codelineno-48-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-48-18" name="__codelineno-48-18" href="#__codelineno-48-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">rightRotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* 右回転 */</span>
+<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">rightRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">child</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">grandChild</span><span class="p">;</span>
+<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w">    </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="w">    </span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a><span class="w">    </span><span class="c1">// child を支点として node を右回転させる</span>
+<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="w">    </span><span class="n">child</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
+<a id="__codelineno-49-9" name="__codelineno-49-9" href="#__codelineno-49-9"></a><span class="w">    </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-49-10" name="__codelineno-49-10" href="#__codelineno-49-10"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-49-11" name="__codelineno-49-11" href="#__codelineno-49-11"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">);</span>
+<a id="__codelineno-49-12" name="__codelineno-49-12" href="#__codelineno-49-12"></a><span class="w">    </span><span class="c1">// 回転後の部分木の根ノードを返す</span>
+<a id="__codelineno-49-13" name="__codelineno-49-13" href="#__codelineno-49-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-49-14" name="__codelineno-49-14" href="#__codelineno-49-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">rightRotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* 右回転 */</span>
+<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">!!</span><span class="p">.</span><span class="na">left</span>
+<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">!!</span><span class="p">.</span><span class="na">right</span>
+<a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="w">    </span><span class="c1">// child を支点として node を右回転させる</span>
+<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a><span class="w">    </span><span class="n">child</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="w">    </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span>
+<a id="__codelineno-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a><span class="w">    </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-50-9" name="__codelineno-50-9" href="#__codelineno-50-9"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-50-10" name="__codelineno-50-10" href="#__codelineno-50-10"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">)</span>
+<a id="__codelineno-50-11" name="__codelineno-50-11" href="#__codelineno-50-11"></a><span class="w">    </span><span class="c1">// 回転後の部分木の根ノードを返す</span>
+<a id="__codelineno-50-12" name="__codelineno-50-12" href="#__codelineno-50-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">child</span>
+<a id="__codelineno-50-13" name="__codelineno-50-13" href="#__codelineno-50-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">right_rotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="c1">### 右回転操作 ###</span>
+<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">right_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w">  </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span>
+<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a><span class="w">  </span><span class="n">grand_child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">.</span><span class="n">right</span>
+<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w">  </span><span class="c1"># child を支点として node を右回転させる</span>
+<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a><span class="w">  </span><span class="n">child</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="w">  </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grand_child</span>
+<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="w">  </span><span class="c1"># ノードの高さを更新する</span>
+<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a><span class="w">  </span><span class="n">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></a><span class="w">  </span><span class="n">update_height</span><span class="p">(</span><span class="n">child</span><span class="p">)</span>
+<a id="__codelineno-51-11" name="__codelineno-51-11" href="#__codelineno-51-11"></a><span class="w">  </span><span class="c1"># 回転後の部分木の根ノードを返す</span>
+<a id="__codelineno-51-12" name="__codelineno-51-12" href="#__codelineno-51-12"></a><span class="w">  </span><span class="n">child</span>
+<a id="__codelineno-51-13" name="__codelineno-51-13" href="#__codelineno-51-13"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
 <h3 id="2_1">2. &nbsp; 左回転<a class="headerlink" href="#2_1" title="Permanent link">&para;</a></h3>
-<p>対応して、上記の不平衡二分木の「鏡像」を考慮すると、下図に示す「左回転」操作を実行する必要があります。</p>
-<p><img alt="左回転操作" class="animation-figure" src="../avl_tree.assets/avltree_left_rotate.png" /></p>
-<p align="center"> 図 7-28 &nbsp; 左回転操作 </p>
+<p>対応する鏡像として、上記の不平衡二分木を左右反転して考えると、以下の図に示す「左回転」が必要になります。</p>
+<p><img alt="左回転" class="animation-figure" src="../avl_tree.assets/avltree_left_rotate.png" /></p>
+<p align="center"> 図 7-28 &nbsp; 左回転 </p>
 
-<p>同様に、下図に示すように、<code>child</code>ノードに左の子（<code>grand_child</code>と表記）がある場合、左回転で手順を追加する必要があります：<code>grand_child</code>を<code>node</code>の右の子に設定します。</p>
-<p><img alt="grand_childがある左回転" class="animation-figure" src="../avl_tree.assets/avltree_left_rotate_with_grandchild.png" /></p>
-<p align="center"> 図 7-29 &nbsp; grand_childがある左回転 </p>
+<p>同様に、以下の図に示すように、ノード <code>child</code> に左の子ノード（<code>grand_child</code> と記す）がある場合、左回転にも 1 ステップ追加する必要があります。すなわち、<code>grand_child</code> を <code>node</code> の右の子ノードにします。</p>
+<p><img alt="grand_child を持つ左回転" class="animation-figure" src="../avl_tree.assets/avltree_left_rotate_with_grandchild.png" /></p>
+<p align="center"> 図 7-29 &nbsp; grand_child を持つ左回転 </p>
 
-<p>**右回転と左回転の操作は論理的に対称であり、2つの対称的な不平衡タイプを解決します**ことが観察できます。対称性に基づいて、右回転の実装コードですべての<code>left</code>を<code>right</code>に、すべての<code>right</code>を<code>left</code>に置き換えることで、左回転の実装コードを得ることができます：</p>
+<p>分かるように、<strong>右回転と左回転は論理的に鏡像対称であり、それぞれが解決する 2 種類の不平衡も対称です</strong>。この対称性に基づけば、右回転の実装コードにあるすべての <code>left</code> を <code>right</code> に、すべての <code>right</code> を <code>left</code> に置き換えるだけで、左回転の実装コードが得られます：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="6:13"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><input id="__tabbed_6_13" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Kotlin</label><label for="__tabbed_6_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">left_rotate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;左回転操作&quot;&quot;&quot;</span>
+<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;左回転&quot;&quot;&quot;</span>
 <a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a>    <span class="n">child</span> <span class="o">=</span> <span class="n">node</span><span class="o">.</span><span class="n">right</span>
 <a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a>    <span class="n">grand_child</span> <span class="o">=</span> <span class="n">child</span><span class="o">.</span><span class="n">left</span>
-<a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a>    <span class="c1"># childを中心にnodeを左に回転</span>
+<a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a>    <span class="c1"># child を支点として node を左回転させる</span>
 <a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a>    <span class="n">child</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">node</span>
 <a id="__codelineno-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></a>    <span class="n">node</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="n">grand_child</span>
-<a id="__codelineno-52-8" name="__codelineno-52-8" href="#__codelineno-52-8"></a>    <span class="c1"># ノードの高さを更新</span>
+<a id="__codelineno-52-8" name="__codelineno-52-8" href="#__codelineno-52-8"></a>    <span class="c1"># ノードの高さを更新する</span>
 <a id="__codelineno-52-9" name="__codelineno-52-9" href="#__codelineno-52-9"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
 <a id="__codelineno-52-10" name="__codelineno-52-10" href="#__codelineno-52-10"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">update_height</span><span class="p">(</span><span class="n">child</span><span class="p">)</span>
-<a id="__codelineno-52-11" name="__codelineno-52-11" href="#__codelineno-52-11"></a>    <span class="c1"># 回転後の部分木のルートを返す</span>
+<a id="__codelineno-52-11" name="__codelineno-52-11" href="#__codelineno-52-11"></a>    <span class="c1"># 回転後の部分木の根ノードを返す</span>
 <a id="__codelineno-52-12" name="__codelineno-52-12" href="#__codelineno-52-12"></a>    <span class="k">return</span> <span class="n">child</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 左回転操作 */</span>
+<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 左回転 */</span>
 <a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">leftRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
 <a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">;</span>
-<a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a><span class="w">    </span><span class="c1">// childを中心にnodeを左に回転</span>
+<a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a><span class="w">    </span><span class="c1">// child を支点として node を左回転させる</span>
 <a id="__codelineno-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></a><span class="w">    </span><span class="n">child</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
 <a id="__codelineno-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
-<a id="__codelineno-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a><span class="w">    </span><span class="c1">// ノードの高さを更新</span>
+<a id="__codelineno-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a><span class="w">    </span><span class="c1">// ノードの高さを更新する</span>
 <a id="__codelineno-53-9" name="__codelineno-53-9" href="#__codelineno-53-9"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
 <a id="__codelineno-53-10" name="__codelineno-53-10" href="#__codelineno-53-10"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">);</span>
-<a id="__codelineno-53-11" name="__codelineno-53-11" href="#__codelineno-53-11"></a><span class="w">    </span><span class="c1">// 回転後の部分木のルートを返す</span>
+<a id="__codelineno-53-11" name="__codelineno-53-11" href="#__codelineno-53-11"></a><span class="w">    </span><span class="c1">// 回転後の部分木の根ノードを返す</span>
 <a id="__codelineno-53-12" name="__codelineno-53-12" href="#__codelineno-53-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
 <a id="__codelineno-53-13" name="__codelineno-53-13" href="#__codelineno-53-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="cm">/* 左回転操作 */</span>
+<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="cm">/* 左回転 */</span>
 <a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">leftRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">;</span>
 <a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="na">left</span><span class="p">;</span>
-<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w">    </span><span class="c1">// child を軸として node を左に回転</span>
+<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w">    </span><span class="c1">// child を支点として node を左回転させる</span>
 <a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w">    </span><span class="n">child</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
 <a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="w">    </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
-<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w">    </span><span class="c1">// ノードの高さを更新</span>
+<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w">    </span><span class="c1">// ノードの高さを更新する</span>
 <a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
 <a id="__codelineno-54-10" name="__codelineno-54-10" href="#__codelineno-54-10"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">);</span>
-<a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a><span class="w">    </span><span class="c1">// 回転後の部分木の根を返す</span>
+<a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a><span class="w">    </span><span class="c1">// 回転後の部分木の根ノードを返す</span>
 <a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
 <a id="__codelineno-54-13" name="__codelineno-54-13" href="#__codelineno-54-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">LeftRotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="cm">/* 左回転 */</span>
+<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">LeftRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="w">    </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">?.</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-55-4" name="__codelineno-55-4" href="#__codelineno-55-4"></a><span class="w">    </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">?.</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-55-5" name="__codelineno-55-5" href="#__codelineno-55-5"></a><span class="w">    </span><span class="c1">// child を支点として node を左回転させる</span>
+<a id="__codelineno-55-6" name="__codelineno-55-6" href="#__codelineno-55-6"></a><span class="w">    </span><span class="n">child</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-55-7" name="__codelineno-55-7" href="#__codelineno-55-7"></a><span class="w">    </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
+<a id="__codelineno-55-8" name="__codelineno-55-8" href="#__codelineno-55-8"></a><span class="w">    </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-55-9" name="__codelineno-55-9" href="#__codelineno-55-9"></a><span class="w">    </span><span class="n">UpdateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-55-10" name="__codelineno-55-10" href="#__codelineno-55-10"></a><span class="w">    </span><span class="n">UpdateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">);</span>
+<a id="__codelineno-55-11" name="__codelineno-55-11" href="#__codelineno-55-11"></a><span class="w">    </span><span class="c1">// 回転後の部分木の根ノードを返す</span>
+<a id="__codelineno-55-12" name="__codelineno-55-12" href="#__codelineno-55-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-55-13" name="__codelineno-55-13" href="#__codelineno-55-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">leftRotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="cm">/* 左回転 */</span>
+<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">aVLTree</span><span class="p">)</span><span class="w"> </span><span class="nx">leftRotate</span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a><span class="w">    </span><span class="nx">child</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span>
+<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a><span class="w">    </span><span class="nx">grandChild</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">child</span><span class="p">.</span><span class="nx">Left</span>
+<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a><span class="w">    </span><span class="c1">// child を支点として node を左回転させる</span>
+<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a><span class="w">    </span><span class="nx">child</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">node</span>
+<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a><span class="w">    </span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">grandChild</span>
+<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a><span class="w">    </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></a><span class="w">    </span><span class="nx">t</span><span class="p">.</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span>
+<a id="__codelineno-56-10" name="__codelineno-56-10" href="#__codelineno-56-10"></a><span class="w">    </span><span class="nx">t</span><span class="p">.</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">child</span><span class="p">)</span>
+<a id="__codelineno-56-11" name="__codelineno-56-11" href="#__codelineno-56-11"></a><span class="w">    </span><span class="c1">// 回転後の部分木の根ノードを返す</span>
+<a id="__codelineno-56-12" name="__codelineno-56-12" href="#__codelineno-56-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">child</span>
+<a id="__codelineno-56-13" name="__codelineno-56-13" href="#__codelineno-56-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">leftRotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 左回転 */</span>
+<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">child</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span><span class="p">?.</span><span class="kr">right</span>
+<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">grandChild</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">child</span><span class="p">?.</span><span class="kr">left</span>
+<a id="__codelineno-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a><span class="w">    </span><span class="c1">// child を支点として node を左回転させる</span>
+<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a><span class="w">    </span><span class="n">child</span><span class="p">?.</span><span class="kr">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></a><span class="w">    </span><span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">grandChild</span>
+<a id="__codelineno-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w">    </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-57-10" name="__codelineno-57-10" href="#__codelineno-57-10"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">child</span><span class="p">)</span>
+<a id="__codelineno-57-11" name="__codelineno-57-11" href="#__codelineno-57-11"></a><span class="w">    </span><span class="c1">// 回転後の部分木の根ノードを返す</span>
+<a id="__codelineno-57-12" name="__codelineno-57-12" href="#__codelineno-57-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">child</span>
+<a id="__codelineno-57-13" name="__codelineno-57-13" href="#__codelineno-57-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">leftRotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 左回転 */</span>
+<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="n">#leftRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
+<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">child</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span>
+<a id="__codelineno-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a><span class="w">    </span><span class="c1">// child を支点として node を左回転させる</span>
+<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a><span class="w">    </span><span class="nx">child</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></a><span class="w">    </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">grandChild</span><span class="p">;</span>
+<a id="__codelineno-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></a><span class="w">    </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="n">#updateHeight</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
+<a id="__codelineno-58-10" name="__codelineno-58-10" href="#__codelineno-58-10"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="n">#updateHeight</span><span class="p">(</span><span class="nx">child</span><span class="p">);</span>
+<a id="__codelineno-58-11" name="__codelineno-58-11" href="#__codelineno-58-11"></a><span class="w">    </span><span class="c1">// 回転後の部分木の根ノードを返す</span>
+<a id="__codelineno-58-12" name="__codelineno-58-12" href="#__codelineno-58-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">child</span><span class="p">;</span>
+<a id="__codelineno-58-13" name="__codelineno-58-13" href="#__codelineno-58-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">leftRotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="cm">/* 左回転 */</span>
+<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a><span class="nx">leftRotate</span><span class="p">(</span><span class="nx">node</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
+<a id="__codelineno-59-4" name="__codelineno-59-4" href="#__codelineno-59-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">child</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span>
+<a id="__codelineno-59-5" name="__codelineno-59-5" href="#__codelineno-59-5"></a><span class="w">    </span><span class="c1">// child を支点として node を左回転させる</span>
+<a id="__codelineno-59-6" name="__codelineno-59-6" href="#__codelineno-59-6"></a><span class="w">    </span><span class="nx">child</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-59-7" name="__codelineno-59-7" href="#__codelineno-59-7"></a><span class="w">    </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">grandChild</span><span class="p">;</span>
+<a id="__codelineno-59-8" name="__codelineno-59-8" href="#__codelineno-59-8"></a><span class="w">    </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-59-9" name="__codelineno-59-9" href="#__codelineno-59-9"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
+<a id="__codelineno-59-10" name="__codelineno-59-10" href="#__codelineno-59-10"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">child</span><span class="p">);</span>
+<a id="__codelineno-59-11" name="__codelineno-59-11" href="#__codelineno-59-11"></a><span class="w">    </span><span class="c1">// 回転後の部分木の根ノードを返す</span>
+<a id="__codelineno-59-12" name="__codelineno-59-12" href="#__codelineno-59-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">child</span><span class="p">;</span>
+<a id="__codelineno-59-13" name="__codelineno-59-13" href="#__codelineno-59-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">leftRotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="cm">/* 左回転 */</span>
+<a id="__codelineno-60-2" name="__codelineno-60-2" href="#__codelineno-60-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-60-3" name="__codelineno-60-3" href="#__codelineno-60-3"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">!</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-60-4" name="__codelineno-60-4" href="#__codelineno-60-4"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">!</span><span class="p">.</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-60-5" name="__codelineno-60-5" href="#__codelineno-60-5"></a><span class="w">  </span><span class="c1">// child を支点として node を左回転させる</span>
+<a id="__codelineno-60-6" name="__codelineno-60-6" href="#__codelineno-60-6"></a><span class="w">  </span><span class="n">child</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-60-7" name="__codelineno-60-7" href="#__codelineno-60-7"></a><span class="w">  </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
+<a id="__codelineno-60-8" name="__codelineno-60-8" href="#__codelineno-60-8"></a><span class="w">  </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-60-9" name="__codelineno-60-9" href="#__codelineno-60-9"></a><span class="w">  </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-60-10" name="__codelineno-60-10" href="#__codelineno-60-10"></a><span class="w">  </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">);</span>
+<a id="__codelineno-60-11" name="__codelineno-60-11" href="#__codelineno-60-11"></a><span class="w">  </span><span class="c1">// 回転後の部分木の根ノードを返す</span>
+<a id="__codelineno-60-12" name="__codelineno-60-12" href="#__codelineno-60-12"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-60-13" name="__codelineno-60-13" href="#__codelineno-60-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">left_rotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="cm">/* 左回転 */</span>
+<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">left_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="nc">OptionTreeNodeRc</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">OptionTreeNodeRc</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-3" name="__codelineno-61-3" href="#__codelineno-61-3"></a><span class="w">    </span><span class="k">match</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-4" name="__codelineno-61-4" href="#__codelineno-61-4"></a><span class="w">        </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-61-5" name="__codelineno-61-5" href="#__codelineno-61-5"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span>
+<a id="__codelineno-61-6" name="__codelineno-61-6" href="#__codelineno-61-6"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="n">grand_child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-61-7" name="__codelineno-61-7" href="#__codelineno-61-7"></a><span class="w">            </span><span class="c1">// child を支点として node を左回転させる</span>
+<a id="__codelineno-61-8" name="__codelineno-61-8" href="#__codelineno-61-8"></a><span class="w">            </span><span class="n">child</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-61-9" name="__codelineno-61-9" href="#__codelineno-61-9"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grand_child</span><span class="p">;</span>
+<a id="__codelineno-61-10" name="__codelineno-61-10" href="#__codelineno-61-10"></a><span class="w">            </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-61-11" name="__codelineno-61-11" href="#__codelineno-61-11"></a><span class="w">            </span><span class="bp">Self</span><span class="p">::</span><span class="n">update_height</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">));</span>
+<a id="__codelineno-61-12" name="__codelineno-61-12" href="#__codelineno-61-12"></a><span class="w">            </span><span class="bp">Self</span><span class="p">::</span><span class="n">update_height</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">child</span><span class="p">.</span><span class="n">clone</span><span class="p">()));</span>
+<a id="__codelineno-61-13" name="__codelineno-61-13" href="#__codelineno-61-13"></a><span class="w">            </span><span class="c1">// 回転後の部分木の根ノードを返す</span>
+<a id="__codelineno-61-14" name="__codelineno-61-14" href="#__codelineno-61-14"></a><span class="w">            </span><span class="nb">Some</span><span class="p">(</span><span class="n">child</span><span class="p">)</span>
+<a id="__codelineno-61-15" name="__codelineno-61-15" href="#__codelineno-61-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-61-16" name="__codelineno-61-16" href="#__codelineno-61-16"></a><span class="w">        </span><span class="nb">None</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span>
+<a id="__codelineno-61-17" name="__codelineno-61-17" href="#__codelineno-61-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-61-18" name="__codelineno-61-18" href="#__codelineno-61-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">leftRotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="cm">/* 左回転 */</span>
+<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">leftRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">child</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">grandChild</span><span class="p">;</span>
+<a id="__codelineno-62-4" name="__codelineno-62-4" href="#__codelineno-62-4"></a><span class="w">    </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-62-5" name="__codelineno-62-5" href="#__codelineno-62-5"></a><span class="w">    </span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-62-6" name="__codelineno-62-6" href="#__codelineno-62-6"></a><span class="w">    </span><span class="c1">// child を支点として node を左回転させる</span>
+<a id="__codelineno-62-7" name="__codelineno-62-7" href="#__codelineno-62-7"></a><span class="w">    </span><span class="n">child</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-62-8" name="__codelineno-62-8" href="#__codelineno-62-8"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
+<a id="__codelineno-62-9" name="__codelineno-62-9" href="#__codelineno-62-9"></a><span class="w">    </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-62-10" name="__codelineno-62-10" href="#__codelineno-62-10"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-62-11" name="__codelineno-62-11" href="#__codelineno-62-11"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">);</span>
+<a id="__codelineno-62-12" name="__codelineno-62-12" href="#__codelineno-62-12"></a><span class="w">    </span><span class="c1">// 回転後の部分木の根ノードを返す</span>
+<a id="__codelineno-62-13" name="__codelineno-62-13" href="#__codelineno-62-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-62-14" name="__codelineno-62-14" href="#__codelineno-62-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">leftRotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="cm">/* 左回転 */</span>
+<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">!!</span><span class="p">.</span><span class="na">right</span>
+<a id="__codelineno-63-4" name="__codelineno-63-4" href="#__codelineno-63-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">!!</span><span class="p">.</span><span class="na">left</span>
+<a id="__codelineno-63-5" name="__codelineno-63-5" href="#__codelineno-63-5"></a><span class="w">    </span><span class="c1">// child を支点として node を左回転させる</span>
+<a id="__codelineno-63-6" name="__codelineno-63-6" href="#__codelineno-63-6"></a><span class="w">    </span><span class="n">child</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></a><span class="w">    </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span>
+<a id="__codelineno-63-8" name="__codelineno-63-8" href="#__codelineno-63-8"></a><span class="w">    </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-63-9" name="__codelineno-63-9" href="#__codelineno-63-9"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-63-10" name="__codelineno-63-10" href="#__codelineno-63-10"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">)</span>
+<a id="__codelineno-63-11" name="__codelineno-63-11" href="#__codelineno-63-11"></a><span class="w">    </span><span class="c1">// 回転後の部分木の根ノードを返す</span>
+<a id="__codelineno-63-12" name="__codelineno-63-12" href="#__codelineno-63-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">child</span>
+<a id="__codelineno-63-13" name="__codelineno-63-13" href="#__codelineno-63-13"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">left_rotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="c1">### 左回転操作 ###</span>
+<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">left_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a><span class="w">  </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span>
+<a id="__codelineno-64-4" name="__codelineno-64-4" href="#__codelineno-64-4"></a><span class="w">  </span><span class="n">grand_child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">.</span><span class="n">left</span>
+<a id="__codelineno-64-5" name="__codelineno-64-5" href="#__codelineno-64-5"></a><span class="w">  </span><span class="c1"># child を支点として node を左回転させる</span>
+<a id="__codelineno-64-6" name="__codelineno-64-6" href="#__codelineno-64-6"></a><span class="w">  </span><span class="n">child</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-64-7" name="__codelineno-64-7" href="#__codelineno-64-7"></a><span class="w">  </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grand_child</span>
+<a id="__codelineno-64-8" name="__codelineno-64-8" href="#__codelineno-64-8"></a><span class="w">  </span><span class="c1"># ノードの高さを更新する</span>
+<a id="__codelineno-64-9" name="__codelineno-64-9" href="#__codelineno-64-9"></a><span class="w">  </span><span class="n">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-64-10" name="__codelineno-64-10" href="#__codelineno-64-10"></a><span class="w">  </span><span class="n">update_height</span><span class="p">(</span><span class="n">child</span><span class="p">)</span>
+<a id="__codelineno-64-11" name="__codelineno-64-11" href="#__codelineno-64-11"></a><span class="w">  </span><span class="c1"># 回転後の部分木の根ノードを返す</span>
+<a id="__codelineno-64-12" name="__codelineno-64-12" href="#__codelineno-64-12"></a><span class="w">  </span><span class="n">child</span>
+<a id="__codelineno-64-13" name="__codelineno-64-13" href="#__codelineno-64-13"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h3 id="3">3. &nbsp; 左右回転<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
-<p>下図に示す不平衡ノード3の場合、左回転または右回転のいずれかだけでは部分木のバランスを回復できません。この場合、まず<code>child</code>に対して「左回転」を実行し、次に<code>node</code>に対して「右回転」を実行する必要があります。</p>
-<p><img alt="左右回転" class="animation-figure" src="../avl_tree.assets/avltree_left_right_rotate.png" /></p>
-<p align="center"> 図 7-30 &nbsp; 左右回転 </p>
+<h3 id="3">3. &nbsp; 左回転してから右回転<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
+<p>以下の図の不平衡ノード 3 では、左回転だけでも右回転だけでも部分木を平衡に戻せません。この場合は、まず <code>child</code> に「左回転」を行い、次に <code>node</code> に「右回転」を行います。</p>
+<p><img alt="左回転してから右回転" class="animation-figure" src="../avl_tree.assets/avltree_left_right_rotate.png" /></p>
+<p align="center"> 図 7-30 &nbsp; 左回転してから右回転 </p>
 
-<h3 id="4">4. &nbsp; 右左回転<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
-<p>下図に示すように、上記の不平衡二分木の鏡像ケースでは、まず<code>child</code>に対して「右回転」を実行し、次に<code>node</code>に対して「左回転」を実行する必要があります。</p>
-<p><img alt="右左回転" class="animation-figure" src="../avl_tree.assets/avltree_right_left_rotate.png" /></p>
-<p align="center"> 図 7-31 &nbsp; 右左回転 </p>
+<h3 id="4">4. &nbsp; 右回転してから左回転<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
+<p>以下の図に示すように、上記の不平衡二分木の鏡像のケースでは、まず <code>child</code> に「右回転」を行い、次に <code>node</code> に「左回転」を行います。</p>
+<p><img alt="右回転してから左回転" class="animation-figure" src="../avl_tree.assets/avltree_right_left_rotate.png" /></p>
+<p align="center"> 図 7-31 &nbsp; 右回転してから左回転 </p>
 
 <h3 id="5">5. &nbsp; 回転の選択<a class="headerlink" href="#5" title="Permanent link">&para;</a></h3>
-<p>下図に示す4種類の不平衡は、それぞれ上記で説明したケースに対応し、右回転、左右回転、右左回転、左回転が必要です。</p>
-<p><img alt="AVL木の4つの回転ケース" class="animation-figure" src="../avl_tree.assets/avltree_rotation_cases.png" /></p>
-<p align="center"> 図 7-32 &nbsp; AVL木の4つの回転ケース </p>
+<p>以下の図に示す 4 種類の不平衡は、上の各ケースにそれぞれ対応しており、必要な操作は順に右回転、左回転してから右回転、右回転してから左回転、左回転です。</p>
+<p><img alt="AVL 木の 4 つの回転ケース" class="animation-figure" src="../avl_tree.assets/avltree_rotation_cases.png" /></p>
+<p align="center"> 図 7-32 &nbsp; AVL 木の 4 つの回転ケース </p>
 
-<p>下表に示すように、不平衡ノードの平衡因子とその高い側の子の平衡因子の符号を判断することで、不平衡ノードが上記のどのケースに属するかを決定します。</p>
-<p align="center"> 表 7-3 &nbsp; 4つの回転ケースの選択条件 </p>
+<p>以下の表に示すように、不平衡ノードの平衡係数と、高い側の子ノードの平衡係数の符号を判定することで、その不平衡ノードが上図のどのケースに属するかを判断できます。</p>
+<p align="center"> 表 7-3 &nbsp; 4 種類の回転ケースの選択条件 </p>
 
 <div class="center-table">
 <table>
 <thead>
 <tr>
-<th>不平衡ノードの平衡因子</th>
-<th>子ノードの平衡因子</th>
-<th>使用する回転方法</th>
+<th>不平衡ノードの平衡係数</th>
+<th>子ノードの平衡係数</th>
+<th>採用すべき回転方法</th>
 </tr>
 </thead>
 <tbody>
 <tr>
-<td><span class="arithmatex">\(&gt; 1\)</span>（左に傾いた木）</td>
+<td><span class="arithmatex">\(&gt; 1\)</span> （左に偏った木）</td>
 <td><span class="arithmatex">\(\geq 0\)</span></td>
 <td>右回転</td>
 </tr>
 <tr>
-<td><span class="arithmatex">\(&gt; 1\)</span>（左に傾いた木）</td>
+<td><span class="arithmatex">\(&gt; 1\)</span> （左に偏った木）</td>
 <td><span class="arithmatex">\(&lt;0\)</span></td>
 <td>左回転してから右回転</td>
 </tr>
 <tr>
-<td><span class="arithmatex">\(&lt; -1\)</span>（右に傾いた木）</td>
+<td><span class="arithmatex">\(&lt; -1\)</span> （右に偏った木）</td>
 <td><span class="arithmatex">\(\leq 0\)</span></td>
 <td>左回転</td>
 </tr>
 <tr>
-<td><span class="arithmatex">\(&lt; -1\)</span>（右に傾いた木）</td>
+<td><span class="arithmatex">\(&lt; -1\)</span> （右に偏った木）</td>
 <td><span class="arithmatex">\(&gt;0\)</span></td>
 <td>右回転してから左回転</td>
 </tr>
 </tbody>
 </table>
 </div>
-<p>便宜上、回転操作を関数にカプセル化します。<strong>この関数により、さまざまな種類の不平衡に対して回転を実行し、不平衡ノードのバランスを回復できます</strong>。コードは以下の通りです：</p>
+<p>使いやすくするために、回転操作を 1 つの関数にカプセル化します。<strong>この関数があれば、さまざまな不平衡ケースに対して回転を行い、不平衡ノードを再び平衡に戻せます</strong>。コードは次のとおりです：</p>
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 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">rotate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;回転操作を実行して部分木のバランスを復元&quot;&quot;&quot;</span>
-<a id="__codelineno-65-3" name="__codelineno-65-3" href="#__codelineno-65-3"></a>    <span class="c1"># nodeのバランス因子を取得</span>
+<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;回転操作を行い、この部分木の平衡を回復する&quot;&quot;&quot;</span>
+<a id="__codelineno-65-3" name="__codelineno-65-3" href="#__codelineno-65-3"></a>    <span class="c1"># ノード node の平衡係数を取得</span>
 <a id="__codelineno-65-4" name="__codelineno-65-4" href="#__codelineno-65-4"></a>    <span class="n">balance_factor</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
-<a id="__codelineno-65-5" name="__codelineno-65-5" href="#__codelineno-65-5"></a>    <span class="c1"># 左偏り木</span>
+<a id="__codelineno-65-5" name="__codelineno-65-5" href="#__codelineno-65-5"></a>    <span class="c1"># 左に偏った木</span>
 <a id="__codelineno-65-6" name="__codelineno-65-6" href="#__codelineno-65-6"></a>    <span class="k">if</span> <span class="n">balance_factor</span> <span class="o">&gt;</span> <span class="mi">1</span><span class="p">:</span>
 <a id="__codelineno-65-7" name="__codelineno-65-7" href="#__codelineno-65-7"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span> <span class="o">&gt;=</span> <span class="mi">0</span><span class="p">:</span>
 <a id="__codelineno-65-8" name="__codelineno-65-8" href="#__codelineno-65-8"></a>            <span class="c1"># 右回転</span>
@@ -5321,7 +5762,7 @@
 <a id="__codelineno-65-11" name="__codelineno-65-11" href="#__codelineno-65-11"></a>            <span class="c1"># 左回転してから右回転</span>
 <a id="__codelineno-65-12" name="__codelineno-65-12" href="#__codelineno-65-12"></a>            <span class="n">node</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">left_rotate</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
 <a id="__codelineno-65-13" name="__codelineno-65-13" href="#__codelineno-65-13"></a>            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">right_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
-<a id="__codelineno-65-14" name="__codelineno-65-14" href="#__codelineno-65-14"></a>    <span class="c1"># 右偏り木</span>
+<a id="__codelineno-65-14" name="__codelineno-65-14" href="#__codelineno-65-14"></a>    <span class="c1"># 右に偏った木</span>
 <a id="__codelineno-65-15" name="__codelineno-65-15" href="#__codelineno-65-15"></a>    <span class="k">elif</span> <span class="n">balance_factor</span> <span class="o">&lt;</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span>
 <a id="__codelineno-65-16" name="__codelineno-65-16" href="#__codelineno-65-16"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span> <span class="o">&lt;=</span> <span class="mi">0</span><span class="p">:</span>
 <a id="__codelineno-65-17" name="__codelineno-65-17" href="#__codelineno-65-17"></a>            <span class="c1"># 左回転</span>
@@ -5330,119 +5771,404 @@
 <a id="__codelineno-65-20" name="__codelineno-65-20" href="#__codelineno-65-20"></a>            <span class="c1"># 右回転してから左回転</span>
 <a id="__codelineno-65-21" name="__codelineno-65-21" href="#__codelineno-65-21"></a>            <span class="n">node</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">right_rotate</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
 <a id="__codelineno-65-22" name="__codelineno-65-22" href="#__codelineno-65-22"></a>            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">left_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
-<a id="__codelineno-65-23" name="__codelineno-65-23" href="#__codelineno-65-23"></a>    <span class="c1"># バランスの取れた木、回転不要、戻る</span>
+<a id="__codelineno-65-23" name="__codelineno-65-23" href="#__codelineno-65-23"></a>    <span class="c1"># 平衡木なので回転不要、そのまま返す</span>
 <a id="__codelineno-65-24" name="__codelineno-65-24" href="#__codelineno-65-24"></a>    <span class="k">return</span> <span class="n">node</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="cm">/* 回転操作を実行して部分木の平衡を回復 */</span>
+<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="cm">/* 回転操作を行い、この部分木の平衡を回復する */</span>
 <a id="__codelineno-66-2" name="__codelineno-66-2" href="#__codelineno-66-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">rotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-66-3" name="__codelineno-66-3" href="#__codelineno-66-3"></a><span class="w">    </span><span class="c1">// nodeの平衡因子を取得</span>
+<a id="__codelineno-66-3" name="__codelineno-66-3" href="#__codelineno-66-3"></a><span class="w">    </span><span class="c1">// ノード node の平衡係数を取得</span>
 <a id="__codelineno-66-4" name="__codelineno-66-4" href="#__codelineno-66-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">_balanceFactor</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
-<a id="__codelineno-66-5" name="__codelineno-66-5" href="#__codelineno-66-5"></a><span class="w">    </span><span class="c1">// 左に傾いた木</span>
+<a id="__codelineno-66-5" name="__codelineno-66-5" href="#__codelineno-66-5"></a><span class="w">    </span><span class="c1">// 左に偏った木</span>
 <a id="__codelineno-66-6" name="__codelineno-66-6" href="#__codelineno-66-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_balanceFactor</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-66-7" name="__codelineno-66-7" href="#__codelineno-66-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-66-8" name="__codelineno-66-8" href="#__codelineno-66-8"></a><span class="w">            </span><span class="c1">// 右回転</span>
 <a id="__codelineno-66-9" name="__codelineno-66-9" href="#__codelineno-66-9"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
 <a id="__codelineno-66-10" name="__codelineno-66-10" href="#__codelineno-66-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-66-11" name="__codelineno-66-11" href="#__codelineno-66-11"></a><span class="w">            </span><span class="c1">// 先に左回転、その後右回転</span>
+<a id="__codelineno-66-11" name="__codelineno-66-11" href="#__codelineno-66-11"></a><span class="w">            </span><span class="c1">// 左回転してから右回転</span>
 <a id="__codelineno-66-12" name="__codelineno-66-12" href="#__codelineno-66-12"></a><span class="w">            </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">);</span>
 <a id="__codelineno-66-13" name="__codelineno-66-13" href="#__codelineno-66-13"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
 <a id="__codelineno-66-14" name="__codelineno-66-14" href="#__codelineno-66-14"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-66-15" name="__codelineno-66-15" href="#__codelineno-66-15"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-66-16" name="__codelineno-66-16" href="#__codelineno-66-16"></a><span class="w">    </span><span class="c1">// 右に傾いた木</span>
+<a id="__codelineno-66-16" name="__codelineno-66-16" href="#__codelineno-66-16"></a><span class="w">    </span><span class="c1">// 右に偏った木</span>
 <a id="__codelineno-66-17" name="__codelineno-66-17" href="#__codelineno-66-17"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_balanceFactor</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">-1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-66-18" name="__codelineno-66-18" href="#__codelineno-66-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-66-19" name="__codelineno-66-19" href="#__codelineno-66-19"></a><span class="w">            </span><span class="c1">// 左回転</span>
 <a id="__codelineno-66-20" name="__codelineno-66-20" href="#__codelineno-66-20"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
 <a id="__codelineno-66-21" name="__codelineno-66-21" href="#__codelineno-66-21"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-66-22" name="__codelineno-66-22" href="#__codelineno-66-22"></a><span class="w">            </span><span class="c1">// 先に右回転、その後左回転</span>
+<a id="__codelineno-66-22" name="__codelineno-66-22" href="#__codelineno-66-22"></a><span class="w">            </span><span class="c1">// 右回転してから左回転</span>
 <a id="__codelineno-66-23" name="__codelineno-66-23" href="#__codelineno-66-23"></a><span class="w">            </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
 <a id="__codelineno-66-24" name="__codelineno-66-24" href="#__codelineno-66-24"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
 <a id="__codelineno-66-25" name="__codelineno-66-25" href="#__codelineno-66-25"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-66-26" name="__codelineno-66-26" href="#__codelineno-66-26"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-66-27" name="__codelineno-66-27" href="#__codelineno-66-27"></a><span class="w">    </span><span class="c1">// 平衡な木、回転不要、そのまま戻る</span>
+<a id="__codelineno-66-27" name="__codelineno-66-27" href="#__codelineno-66-27"></a><span class="w">    </span><span class="c1">// 平衡木なので回転不要、そのまま返す</span>
 <a id="__codelineno-66-28" name="__codelineno-66-28" href="#__codelineno-66-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
 <a id="__codelineno-66-29" name="__codelineno-66-29" href="#__codelineno-66-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="cm">/* 回転操作を実行して部分木の平衡を回復 */</span>
+<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="cm">/* 回転操作を行い、この部分木の平衡を回復する */</span>
 <a id="__codelineno-67-2" name="__codelineno-67-2" href="#__codelineno-67-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">rotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-67-3" name="__codelineno-67-3" href="#__codelineno-67-3"></a><span class="w">    </span><span class="c1">// node の平衡因子を取得</span>
+<a id="__codelineno-67-3" name="__codelineno-67-3" href="#__codelineno-67-3"></a><span class="w">    </span><span class="c1">// ノード node の平衡係数を取得</span>
 <a id="__codelineno-67-4" name="__codelineno-67-4" href="#__codelineno-67-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">balanceFactor</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
-<a id="__codelineno-67-5" name="__codelineno-67-5" href="#__codelineno-67-5"></a><span class="w">    </span><span class="c1">// 左傾斜の木</span>
+<a id="__codelineno-67-5" name="__codelineno-67-5" href="#__codelineno-67-5"></a><span class="w">    </span><span class="c1">// 左に偏った木</span>
 <a id="__codelineno-67-6" name="__codelineno-67-6" href="#__codelineno-67-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-67-7" name="__codelineno-67-7" href="#__codelineno-67-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-67-8" name="__codelineno-67-8" href="#__codelineno-67-8"></a><span class="w">            </span><span class="c1">// 右回転</span>
 <a id="__codelineno-67-9" name="__codelineno-67-9" href="#__codelineno-67-9"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
 <a id="__codelineno-67-10" name="__codelineno-67-10" href="#__codelineno-67-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-67-11" name="__codelineno-67-11" href="#__codelineno-67-11"></a><span class="w">            </span><span class="c1">// 先に左回転、その後右回転</span>
+<a id="__codelineno-67-11" name="__codelineno-67-11" href="#__codelineno-67-11"></a><span class="w">            </span><span class="c1">// 左回転してから右回転</span>
 <a id="__codelineno-67-12" name="__codelineno-67-12" href="#__codelineno-67-12"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">);</span>
 <a id="__codelineno-67-13" name="__codelineno-67-13" href="#__codelineno-67-13"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
 <a id="__codelineno-67-14" name="__codelineno-67-14" href="#__codelineno-67-14"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-67-15" name="__codelineno-67-15" href="#__codelineno-67-15"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-67-16" name="__codelineno-67-16" href="#__codelineno-67-16"></a><span class="w">    </span><span class="c1">// 右傾斜の木</span>
+<a id="__codelineno-67-16" name="__codelineno-67-16" href="#__codelineno-67-16"></a><span class="w">    </span><span class="c1">// 右に偏った木</span>
 <a id="__codelineno-67-17" name="__codelineno-67-17" href="#__codelineno-67-17"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-67-18" name="__codelineno-67-18" href="#__codelineno-67-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">)</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-67-19" name="__codelineno-67-19" href="#__codelineno-67-19"></a><span class="w">            </span><span class="c1">// 左回転</span>
 <a id="__codelineno-67-20" name="__codelineno-67-20" href="#__codelineno-67-20"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
 <a id="__codelineno-67-21" name="__codelineno-67-21" href="#__codelineno-67-21"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-67-22" name="__codelineno-67-22" href="#__codelineno-67-22"></a><span class="w">            </span><span class="c1">// 先に右回転、その後左回転</span>
+<a id="__codelineno-67-22" name="__codelineno-67-22" href="#__codelineno-67-22"></a><span class="w">            </span><span class="c1">// 右回転してから左回転</span>
 <a id="__codelineno-67-23" name="__codelineno-67-23" href="#__codelineno-67-23"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">);</span>
 <a id="__codelineno-67-24" name="__codelineno-67-24" href="#__codelineno-67-24"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
 <a id="__codelineno-67-25" name="__codelineno-67-25" href="#__codelineno-67-25"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-67-26" name="__codelineno-67-26" href="#__codelineno-67-26"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-67-27" name="__codelineno-67-27" href="#__codelineno-67-27"></a><span class="w">    </span><span class="c1">// 平衡木、回転は不要、戻る</span>
+<a id="__codelineno-67-27" name="__codelineno-67-27" href="#__codelineno-67-27"></a><span class="w">    </span><span class="c1">// 平衡木なので回転不要、そのまま返す</span>
 <a id="__codelineno-67-28" name="__codelineno-67-28" href="#__codelineno-67-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
 <a id="__codelineno-67-29" name="__codelineno-67-29" href="#__codelineno-67-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Rotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="cm">/* 回転操作を行い、この部分木の平衡を回復する */</span>
+<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">Rotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-68-3" name="__codelineno-68-3" href="#__codelineno-68-3"></a><span class="w">    </span><span class="c1">// ノード node の平衡係数を取得</span>
+<a id="__codelineno-68-4" name="__codelineno-68-4" href="#__codelineno-68-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">balanceFactorInt</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BalanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-68-5" name="__codelineno-68-5" href="#__codelineno-68-5"></a><span class="w">    </span><span class="c1">// 左に偏った木</span>
+<a id="__codelineno-68-6" name="__codelineno-68-6" href="#__codelineno-68-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactorInt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-68-7" name="__codelineno-68-7" href="#__codelineno-68-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">BalanceFactor</span><span class="p">(</span><span class="n">node</span><span class="o">?.</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-68-8" name="__codelineno-68-8" href="#__codelineno-68-8"></a><span class="w">            </span><span class="c1">// 右回転</span>
+<a id="__codelineno-68-9" name="__codelineno-68-9" href="#__codelineno-68-9"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nf">RightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-68-10" name="__codelineno-68-10" href="#__codelineno-68-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-68-11" name="__codelineno-68-11" href="#__codelineno-68-11"></a><span class="w">            </span><span class="c1">// 左回転してから右回転</span>
+<a id="__codelineno-68-12" name="__codelineno-68-12" href="#__codelineno-68-12"></a><span class="w">            </span><span class="n">node</span><span class="o">!</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">LeftRotate</span><span class="p">(</span><span class="n">node</span><span class="o">!</span><span class="p">.</span><span class="n">left</span><span class="p">);</span>
+<a id="__codelineno-68-13" name="__codelineno-68-13" href="#__codelineno-68-13"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nf">RightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-68-14" name="__codelineno-68-14" href="#__codelineno-68-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-68-15" name="__codelineno-68-15" href="#__codelineno-68-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-68-16" name="__codelineno-68-16" href="#__codelineno-68-16"></a><span class="w">    </span><span class="c1">// 右に偏った木</span>
+<a id="__codelineno-68-17" name="__codelineno-68-17" href="#__codelineno-68-17"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactorInt</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-68-18" name="__codelineno-68-18" href="#__codelineno-68-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">BalanceFactor</span><span class="p">(</span><span class="n">node</span><span class="o">?.</span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-68-19" name="__codelineno-68-19" href="#__codelineno-68-19"></a><span class="w">            </span><span class="c1">// 左回転</span>
+<a id="__codelineno-68-20" name="__codelineno-68-20" href="#__codelineno-68-20"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nf">LeftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-68-21" name="__codelineno-68-21" href="#__codelineno-68-21"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-68-22" name="__codelineno-68-22" href="#__codelineno-68-22"></a><span class="w">            </span><span class="c1">// 右回転してから左回転</span>
+<a id="__codelineno-68-23" name="__codelineno-68-23" href="#__codelineno-68-23"></a><span class="w">            </span><span class="n">node</span><span class="o">!</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">RightRotate</span><span class="p">(</span><span class="n">node</span><span class="o">!</span><span class="p">.</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-68-24" name="__codelineno-68-24" href="#__codelineno-68-24"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nf">LeftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-68-25" name="__codelineno-68-25" href="#__codelineno-68-25"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-68-26" name="__codelineno-68-26" href="#__codelineno-68-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-68-27" name="__codelineno-68-27" href="#__codelineno-68-27"></a><span class="w">    </span><span class="c1">// 平衡木なので回転不要、そのまま返す</span>
+<a id="__codelineno-68-28" name="__codelineno-68-28" href="#__codelineno-68-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-68-29" name="__codelineno-68-29" href="#__codelineno-68-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">rotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="cm">/* 回転操作を行い、この部分木の平衡を回復する */</span>
+<a id="__codelineno-69-2" name="__codelineno-69-2" href="#__codelineno-69-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">aVLTree</span><span class="p">)</span><span class="w"> </span><span class="nx">rotate</span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-3" name="__codelineno-69-3" href="#__codelineno-69-3"></a><span class="w">    </span><span class="c1">// ノード `node` の平衡係数を取得する</span>
+<a id="__codelineno-69-4" name="__codelineno-69-4" href="#__codelineno-69-4"></a><span class="w">    </span><span class="c1">// Go では短い変数名が推奨されるため、ここで `bf` は `t.balanceFactor` を表す</span>
+<a id="__codelineno-69-5" name="__codelineno-69-5" href="#__codelineno-69-5"></a><span class="w">    </span><span class="nx">bf</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">balanceFactor</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span>
+<a id="__codelineno-69-6" name="__codelineno-69-6" href="#__codelineno-69-6"></a><span class="w">    </span><span class="c1">// 左に偏った木</span>
+<a id="__codelineno-69-7" name="__codelineno-69-7" href="#__codelineno-69-7"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">bf</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-8" name="__codelineno-69-8" href="#__codelineno-69-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">balanceFactor</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-9" name="__codelineno-69-9" href="#__codelineno-69-9"></a><span class="w">            </span><span class="c1">// 右回転</span>
+<a id="__codelineno-69-10" name="__codelineno-69-10" href="#__codelineno-69-10"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">rightRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span>
+<a id="__codelineno-69-11" name="__codelineno-69-11" href="#__codelineno-69-11"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-12" name="__codelineno-69-12" href="#__codelineno-69-12"></a><span class="w">            </span><span class="c1">// 左回転してから右回転</span>
+<a id="__codelineno-69-13" name="__codelineno-69-13" href="#__codelineno-69-13"></a><span class="w">            </span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">leftRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span><span class="p">)</span>
+<a id="__codelineno-69-14" name="__codelineno-69-14" href="#__codelineno-69-14"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">rightRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span>
+<a id="__codelineno-69-15" name="__codelineno-69-15" href="#__codelineno-69-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-69-16" name="__codelineno-69-16" href="#__codelineno-69-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-69-17" name="__codelineno-69-17" href="#__codelineno-69-17"></a><span class="w">    </span><span class="c1">// 右に偏った木</span>
+<a id="__codelineno-69-18" name="__codelineno-69-18" href="#__codelineno-69-18"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">bf</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-19" name="__codelineno-69-19" href="#__codelineno-69-19"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">balanceFactor</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="p">)</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-20" name="__codelineno-69-20" href="#__codelineno-69-20"></a><span class="w">            </span><span class="c1">// 左回転</span>
+<a id="__codelineno-69-21" name="__codelineno-69-21" href="#__codelineno-69-21"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">leftRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span>
+<a id="__codelineno-69-22" name="__codelineno-69-22" href="#__codelineno-69-22"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-23" name="__codelineno-69-23" href="#__codelineno-69-23"></a><span class="w">            </span><span class="c1">// 右回転してから左回転</span>
+<a id="__codelineno-69-24" name="__codelineno-69-24" href="#__codelineno-69-24"></a><span class="w">            </span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">rightRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="p">)</span>
+<a id="__codelineno-69-25" name="__codelineno-69-25" href="#__codelineno-69-25"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">leftRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span>
+<a id="__codelineno-69-26" name="__codelineno-69-26" href="#__codelineno-69-26"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-69-27" name="__codelineno-69-27" href="#__codelineno-69-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-69-28" name="__codelineno-69-28" href="#__codelineno-69-28"></a><span class="w">    </span><span class="c1">// 平衡木なので回転不要、そのまま返す</span>
+<a id="__codelineno-69-29" name="__codelineno-69-29" href="#__codelineno-69-29"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span>
+<a id="__codelineno-69-30" name="__codelineno-69-30" href="#__codelineno-69-30"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">rotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="cm">/* 回転操作を行い、この部分木の平衡を回復する */</span>
+<a id="__codelineno-70-2" name="__codelineno-70-2" href="#__codelineno-70-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-3" name="__codelineno-70-3" href="#__codelineno-70-3"></a><span class="w">    </span><span class="c1">// ノード node の平衡係数を取得</span>
+<a id="__codelineno-70-4" name="__codelineno-70-4" href="#__codelineno-70-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">balanceFactor</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-70-5" name="__codelineno-70-5" href="#__codelineno-70-5"></a><span class="w">    </span><span class="c1">// 左に偏った木</span>
+<a id="__codelineno-70-6" name="__codelineno-70-6" href="#__codelineno-70-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">balanceFactor</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-7" name="__codelineno-70-7" href="#__codelineno-70-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="kc">self</span><span class="p">.</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">?.</span><span class="kr">left</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-8" name="__codelineno-70-8" href="#__codelineno-70-8"></a><span class="w">            </span><span class="c1">// 右回転</span>
+<a id="__codelineno-70-9" name="__codelineno-70-9" href="#__codelineno-70-9"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-70-10" name="__codelineno-70-10" href="#__codelineno-70-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-11" name="__codelineno-70-11" href="#__codelineno-70-11"></a><span class="w">            </span><span class="c1">// 左回転してから右回転</span>
+<a id="__codelineno-70-12" name="__codelineno-70-12" href="#__codelineno-70-12"></a><span class="w">            </span><span class="n">node</span><span class="p">?.</span><span class="kr">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">?.</span><span class="kr">left</span><span class="p">)</span>
+<a id="__codelineno-70-13" name="__codelineno-70-13" href="#__codelineno-70-13"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-70-14" name="__codelineno-70-14" href="#__codelineno-70-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-70-15" name="__codelineno-70-15" href="#__codelineno-70-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-70-16" name="__codelineno-70-16" href="#__codelineno-70-16"></a><span class="w">    </span><span class="c1">// 右に偏った木</span>
+<a id="__codelineno-70-17" name="__codelineno-70-17" href="#__codelineno-70-17"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">balanceFactor</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-18" name="__codelineno-70-18" href="#__codelineno-70-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="kc">self</span><span class="p">.</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="p">)</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-19" name="__codelineno-70-19" href="#__codelineno-70-19"></a><span class="w">            </span><span class="c1">// 左回転</span>
+<a id="__codelineno-70-20" name="__codelineno-70-20" href="#__codelineno-70-20"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-70-21" name="__codelineno-70-21" href="#__codelineno-70-21"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-22" name="__codelineno-70-22" href="#__codelineno-70-22"></a><span class="w">            </span><span class="c1">// 右回転してから左回転</span>
+<a id="__codelineno-70-23" name="__codelineno-70-23" href="#__codelineno-70-23"></a><span class="w">            </span><span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="p">)</span>
+<a id="__codelineno-70-24" name="__codelineno-70-24" href="#__codelineno-70-24"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-70-25" name="__codelineno-70-25" href="#__codelineno-70-25"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-70-26" name="__codelineno-70-26" href="#__codelineno-70-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-70-27" name="__codelineno-70-27" href="#__codelineno-70-27"></a><span class="w">    </span><span class="c1">// 平衡木なので回転不要、そのまま返す</span>
+<a id="__codelineno-70-28" name="__codelineno-70-28" href="#__codelineno-70-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-70-29" name="__codelineno-70-29" href="#__codelineno-70-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">rotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="cm">/* 回転操作を行い、この部分木の平衡を回復する */</span>
+<a id="__codelineno-71-2" name="__codelineno-71-2" href="#__codelineno-71-2"></a><span class="n">#rotate</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-3" name="__codelineno-71-3" href="#__codelineno-71-3"></a><span class="w">    </span><span class="c1">// ノード node の平衡係数を取得</span>
+<a id="__codelineno-71-4" name="__codelineno-71-4" href="#__codelineno-71-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">balanceFactor</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">balanceFactor</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
+<a id="__codelineno-71-5" name="__codelineno-71-5" href="#__codelineno-71-5"></a><span class="w">    </span><span class="c1">// 左に偏った木</span>
+<a id="__codelineno-71-6" name="__codelineno-71-6" href="#__codelineno-71-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">balanceFactor</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-7" name="__codelineno-71-7" href="#__codelineno-71-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">balanceFactor</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-8" name="__codelineno-71-8" href="#__codelineno-71-8"></a><span class="w">            </span><span class="c1">// 右回転</span>
+<a id="__codelineno-71-9" name="__codelineno-71-9" href="#__codelineno-71-9"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#rightRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
+<a id="__codelineno-71-10" name="__codelineno-71-10" href="#__codelineno-71-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-11" name="__codelineno-71-11" href="#__codelineno-71-11"></a><span class="w">            </span><span class="c1">// 左回転してから右回転</span>
+<a id="__codelineno-71-12" name="__codelineno-71-12" href="#__codelineno-71-12"></a><span class="w">            </span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#leftRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="p">);</span>
+<a id="__codelineno-71-13" name="__codelineno-71-13" href="#__codelineno-71-13"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#rightRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
+<a id="__codelineno-71-14" name="__codelineno-71-14" href="#__codelineno-71-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-71-15" name="__codelineno-71-15" href="#__codelineno-71-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-71-16" name="__codelineno-71-16" href="#__codelineno-71-16"></a><span class="w">    </span><span class="c1">// 右に偏った木</span>
+<a id="__codelineno-71-17" name="__codelineno-71-17" href="#__codelineno-71-17"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">balanceFactor</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-18" name="__codelineno-71-18" href="#__codelineno-71-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">balanceFactor</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-19" name="__codelineno-71-19" href="#__codelineno-71-19"></a><span class="w">            </span><span class="c1">// 左回転</span>
+<a id="__codelineno-71-20" name="__codelineno-71-20" href="#__codelineno-71-20"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#leftRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
+<a id="__codelineno-71-21" name="__codelineno-71-21" href="#__codelineno-71-21"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-22" name="__codelineno-71-22" href="#__codelineno-71-22"></a><span class="w">            </span><span class="c1">// 右回転してから左回転</span>
+<a id="__codelineno-71-23" name="__codelineno-71-23" href="#__codelineno-71-23"></a><span class="w">            </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#rightRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">);</span>
+<a id="__codelineno-71-24" name="__codelineno-71-24" href="#__codelineno-71-24"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#leftRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
+<a id="__codelineno-71-25" name="__codelineno-71-25" href="#__codelineno-71-25"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-71-26" name="__codelineno-71-26" href="#__codelineno-71-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-71-27" name="__codelineno-71-27" href="#__codelineno-71-27"></a><span class="w">    </span><span class="c1">// 平衡木なので回転不要、そのまま返す</span>
+<a id="__codelineno-71-28" name="__codelineno-71-28" href="#__codelineno-71-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-71-29" name="__codelineno-71-29" href="#__codelineno-71-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">rotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="cm">/* 回転操作を行い、この部分木の平衡を回復する */</span>
+<a id="__codelineno-72-2" name="__codelineno-72-2" href="#__codelineno-72-2"></a><span class="nx">rotate</span><span class="p">(</span><span class="nx">node</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-3" name="__codelineno-72-3" href="#__codelineno-72-3"></a><span class="w">    </span><span class="c1">// ノード node の平衡係数を取得</span>
+<a id="__codelineno-72-4" name="__codelineno-72-4" href="#__codelineno-72-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">balanceFactor</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">balanceFactor</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
+<a id="__codelineno-72-5" name="__codelineno-72-5" href="#__codelineno-72-5"></a><span class="w">    </span><span class="c1">// 左に偏った木</span>
+<a id="__codelineno-72-6" name="__codelineno-72-6" href="#__codelineno-72-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">balanceFactor</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-7" name="__codelineno-72-7" href="#__codelineno-72-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">balanceFactor</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-8" name="__codelineno-72-8" href="#__codelineno-72-8"></a><span class="w">            </span><span class="c1">// 右回転</span>
+<a id="__codelineno-72-9" name="__codelineno-72-9" href="#__codelineno-72-9"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">rightRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
+<a id="__codelineno-72-10" name="__codelineno-72-10" href="#__codelineno-72-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-11" name="__codelineno-72-11" href="#__codelineno-72-11"></a><span class="w">            </span><span class="c1">// 左回転してから右回転</span>
+<a id="__codelineno-72-12" name="__codelineno-72-12" href="#__codelineno-72-12"></a><span class="w">            </span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">leftRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="p">);</span>
+<a id="__codelineno-72-13" name="__codelineno-72-13" href="#__codelineno-72-13"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">rightRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
+<a id="__codelineno-72-14" name="__codelineno-72-14" href="#__codelineno-72-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-72-15" name="__codelineno-72-15" href="#__codelineno-72-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-72-16" name="__codelineno-72-16" href="#__codelineno-72-16"></a><span class="w">    </span><span class="c1">// 右に偏った木</span>
+<a id="__codelineno-72-17" name="__codelineno-72-17" href="#__codelineno-72-17"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">balanceFactor</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-18" name="__codelineno-72-18" href="#__codelineno-72-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">balanceFactor</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-19" name="__codelineno-72-19" href="#__codelineno-72-19"></a><span class="w">            </span><span class="c1">// 左回転</span>
+<a id="__codelineno-72-20" name="__codelineno-72-20" href="#__codelineno-72-20"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">leftRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
+<a id="__codelineno-72-21" name="__codelineno-72-21" href="#__codelineno-72-21"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-22" name="__codelineno-72-22" href="#__codelineno-72-22"></a><span class="w">            </span><span class="c1">// 右回転してから左回転</span>
+<a id="__codelineno-72-23" name="__codelineno-72-23" href="#__codelineno-72-23"></a><span class="w">            </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">rightRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">);</span>
+<a id="__codelineno-72-24" name="__codelineno-72-24" href="#__codelineno-72-24"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">leftRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
+<a id="__codelineno-72-25" name="__codelineno-72-25" href="#__codelineno-72-25"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-72-26" name="__codelineno-72-26" href="#__codelineno-72-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-72-27" name="__codelineno-72-27" href="#__codelineno-72-27"></a><span class="w">    </span><span class="c1">// 平衡木なので回転不要、そのまま返す</span>
+<a id="__codelineno-72-28" name="__codelineno-72-28" href="#__codelineno-72-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-72-29" name="__codelineno-72-29" href="#__codelineno-72-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">rotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="cm">/* 回転操作を行い、この部分木の平衡を回復する */</span>
+<a id="__codelineno-73-2" name="__codelineno-73-2" href="#__codelineno-73-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-73-3" name="__codelineno-73-3" href="#__codelineno-73-3"></a><span class="w">  </span><span class="c1">// ノード node の平衡係数を取得</span>
+<a id="__codelineno-73-4" name="__codelineno-73-4" href="#__codelineno-73-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">factor</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-73-5" name="__codelineno-73-5" href="#__codelineno-73-5"></a><span class="w">  </span><span class="c1">// 左に偏った木</span>
+<a id="__codelineno-73-6" name="__codelineno-73-6" href="#__codelineno-73-6"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">factor</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-73-7" name="__codelineno-73-7" href="#__codelineno-73-7"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="o">!</span><span class="p">.</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-73-8" name="__codelineno-73-8" href="#__codelineno-73-8"></a><span class="w">      </span><span class="c1">// 右回転</span>
+<a id="__codelineno-73-9" name="__codelineno-73-9" href="#__codelineno-73-9"></a><span class="w">      </span><span class="k">return</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-73-10" name="__codelineno-73-10" href="#__codelineno-73-10"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-73-11" name="__codelineno-73-11" href="#__codelineno-73-11"></a><span class="w">      </span><span class="c1">// 左回転してから右回転</span>
+<a id="__codelineno-73-12" name="__codelineno-73-12" href="#__codelineno-73-12"></a><span class="w">      </span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">);</span>
+<a id="__codelineno-73-13" name="__codelineno-73-13" href="#__codelineno-73-13"></a><span class="w">      </span><span class="k">return</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-73-14" name="__codelineno-73-14" href="#__codelineno-73-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-73-15" name="__codelineno-73-15" href="#__codelineno-73-15"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-73-16" name="__codelineno-73-16" href="#__codelineno-73-16"></a><span class="w">  </span><span class="c1">// 右に偏った木</span>
+<a id="__codelineno-73-17" name="__codelineno-73-17" href="#__codelineno-73-17"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">factor</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-73-18" name="__codelineno-73-18" href="#__codelineno-73-18"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="o">!</span><span class="p">.</span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-73-19" name="__codelineno-73-19" href="#__codelineno-73-19"></a><span class="w">      </span><span class="c1">// 左回転</span>
+<a id="__codelineno-73-20" name="__codelineno-73-20" href="#__codelineno-73-20"></a><span class="w">      </span><span class="k">return</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-73-21" name="__codelineno-73-21" href="#__codelineno-73-21"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-73-22" name="__codelineno-73-22" href="#__codelineno-73-22"></a><span class="w">      </span><span class="c1">// 右回転してから左回転</span>
+<a id="__codelineno-73-23" name="__codelineno-73-23" href="#__codelineno-73-23"></a><span class="w">      </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-73-24" name="__codelineno-73-24" href="#__codelineno-73-24"></a><span class="w">      </span><span class="k">return</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-73-25" name="__codelineno-73-25" href="#__codelineno-73-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-73-26" name="__codelineno-73-26" href="#__codelineno-73-26"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-73-27" name="__codelineno-73-27" href="#__codelineno-73-27"></a><span class="w">  </span><span class="c1">// 平衡木なので回転不要、そのまま返す</span>
+<a id="__codelineno-73-28" name="__codelineno-73-28" href="#__codelineno-73-28"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-73-29" name="__codelineno-73-29" href="#__codelineno-73-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">rotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="cm">/* 回転操作を行い、この部分木の平衡を回復する */</span>
+<a id="__codelineno-74-2" name="__codelineno-74-2" href="#__codelineno-74-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="nc">OptionTreeNodeRc</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">OptionTreeNodeRc</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-3" name="__codelineno-74-3" href="#__codelineno-74-3"></a><span class="w">    </span><span class="c1">// ノード node の平衡係数を取得</span>
+<a id="__codelineno-74-4" name="__codelineno-74-4" href="#__codelineno-74-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">balance_factor</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span><span class="p">::</span><span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-74-5" name="__codelineno-74-5" href="#__codelineno-74-5"></a><span class="w">    </span><span class="c1">// 左に偏った木</span>
+<a id="__codelineno-74-6" name="__codelineno-74-6" href="#__codelineno-74-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">balance_factor</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-7" name="__codelineno-74-7" href="#__codelineno-74-7"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">unwrap</span><span class="p">();</span>
+<a id="__codelineno-74-8" name="__codelineno-74-8" href="#__codelineno-74-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">Self</span><span class="p">::</span><span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">())</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-9" name="__codelineno-74-9" href="#__codelineno-74-9"></a><span class="w">            </span><span class="c1">// 右回転</span>
+<a id="__codelineno-74-10" name="__codelineno-74-10" href="#__codelineno-74-10"></a><span class="w">            </span><span class="bp">Self</span><span class="p">::</span><span class="n">right_rotate</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">))</span>
+<a id="__codelineno-74-11" name="__codelineno-74-11" href="#__codelineno-74-11"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-12" name="__codelineno-74-12" href="#__codelineno-74-12"></a><span class="w">            </span><span class="c1">// 左回転してから右回転</span>
+<a id="__codelineno-74-13" name="__codelineno-74-13" href="#__codelineno-74-13"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-74-14" name="__codelineno-74-14" href="#__codelineno-74-14"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span><span class="p">::</span><span class="n">left_rotate</span><span class="p">(</span><span class="n">left</span><span class="p">);</span>
+<a id="__codelineno-74-15" name="__codelineno-74-15" href="#__codelineno-74-15"></a><span class="w">            </span><span class="bp">Self</span><span class="p">::</span><span class="n">right_rotate</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">))</span>
+<a id="__codelineno-74-16" name="__codelineno-74-16" href="#__codelineno-74-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-74-17" name="__codelineno-74-17" href="#__codelineno-74-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-74-18" name="__codelineno-74-18" href="#__codelineno-74-18"></a><span class="w">    </span><span class="c1">// 右に偏った木</span>
+<a id="__codelineno-74-19" name="__codelineno-74-19" href="#__codelineno-74-19"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">balance_factor</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-20" name="__codelineno-74-20" href="#__codelineno-74-20"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">unwrap</span><span class="p">();</span>
+<a id="__codelineno-74-21" name="__codelineno-74-21" href="#__codelineno-74-21"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="bp">Self</span><span class="p">::</span><span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">())</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-22" name="__codelineno-74-22" href="#__codelineno-74-22"></a><span class="w">            </span><span class="c1">// 左回転</span>
+<a id="__codelineno-74-23" name="__codelineno-74-23" href="#__codelineno-74-23"></a><span class="w">            </span><span class="bp">Self</span><span class="p">::</span><span class="n">left_rotate</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">))</span>
+<a id="__codelineno-74-24" name="__codelineno-74-24" href="#__codelineno-74-24"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-25" name="__codelineno-74-25" href="#__codelineno-74-25"></a><span class="w">            </span><span class="c1">// 右回転してから左回転</span>
+<a id="__codelineno-74-26" name="__codelineno-74-26" href="#__codelineno-74-26"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-74-27" name="__codelineno-74-27" href="#__codelineno-74-27"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span><span class="p">::</span><span class="n">right_rotate</span><span class="p">(</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-74-28" name="__codelineno-74-28" href="#__codelineno-74-28"></a><span class="w">            </span><span class="bp">Self</span><span class="p">::</span><span class="n">left_rotate</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">))</span>
+<a id="__codelineno-74-29" name="__codelineno-74-29" href="#__codelineno-74-29"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-74-30" name="__codelineno-74-30" href="#__codelineno-74-30"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-74-31" name="__codelineno-74-31" href="#__codelineno-74-31"></a><span class="w">        </span><span class="c1">// 平衡木なので回転不要、そのまま返す</span>
+<a id="__codelineno-74-32" name="__codelineno-74-32" href="#__codelineno-74-32"></a><span class="w">        </span><span class="n">node</span>
+<a id="__codelineno-74-33" name="__codelineno-74-33" href="#__codelineno-74-33"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-74-34" name="__codelineno-74-34" href="#__codelineno-74-34"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">rotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="cm">/* 回転操作を行い、この部分木の平衡を回復する */</span>
+<a id="__codelineno-75-2" name="__codelineno-75-2" href="#__codelineno-75-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">rotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-75-3" name="__codelineno-75-3" href="#__codelineno-75-3"></a><span class="w">    </span><span class="c1">// ノード node の平衡係数を取得</span>
+<a id="__codelineno-75-4" name="__codelineno-75-4" href="#__codelineno-75-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">bf</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-75-5" name="__codelineno-75-5" href="#__codelineno-75-5"></a><span class="w">    </span><span class="c1">// 左に偏った木</span>
+<a id="__codelineno-75-6" name="__codelineno-75-6" href="#__codelineno-75-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">bf</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-75-7" name="__codelineno-75-7" href="#__codelineno-75-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-75-8" name="__codelineno-75-8" href="#__codelineno-75-8"></a><span class="w">            </span><span class="c1">// 右回転</span>
+<a id="__codelineno-75-9" name="__codelineno-75-9" href="#__codelineno-75-9"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-75-10" name="__codelineno-75-10" href="#__codelineno-75-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-75-11" name="__codelineno-75-11" href="#__codelineno-75-11"></a><span class="w">            </span><span class="c1">// 左回転してから右回転</span>
+<a id="__codelineno-75-12" name="__codelineno-75-12" href="#__codelineno-75-12"></a><span class="w">            </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">);</span>
+<a id="__codelineno-75-13" name="__codelineno-75-13" href="#__codelineno-75-13"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-75-14" name="__codelineno-75-14" href="#__codelineno-75-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-75-15" name="__codelineno-75-15" href="#__codelineno-75-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-75-16" name="__codelineno-75-16" href="#__codelineno-75-16"></a><span class="w">    </span><span class="c1">// 右に偏った木</span>
+<a id="__codelineno-75-17" name="__codelineno-75-17" href="#__codelineno-75-17"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">bf</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">-1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-75-18" name="__codelineno-75-18" href="#__codelineno-75-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-75-19" name="__codelineno-75-19" href="#__codelineno-75-19"></a><span class="w">            </span><span class="c1">// 左回転</span>
+<a id="__codelineno-75-20" name="__codelineno-75-20" href="#__codelineno-75-20"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-75-21" name="__codelineno-75-21" href="#__codelineno-75-21"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-75-22" name="__codelineno-75-22" href="#__codelineno-75-22"></a><span class="w">            </span><span class="c1">// 右回転してから左回転</span>
+<a id="__codelineno-75-23" name="__codelineno-75-23" href="#__codelineno-75-23"></a><span class="w">            </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-75-24" name="__codelineno-75-24" href="#__codelineno-75-24"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-75-25" name="__codelineno-75-25" href="#__codelineno-75-25"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-75-26" name="__codelineno-75-26" href="#__codelineno-75-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-75-27" name="__codelineno-75-27" href="#__codelineno-75-27"></a><span class="w">    </span><span class="c1">// 平衡木なので回転不要、そのまま返す</span>
+<a id="__codelineno-75-28" name="__codelineno-75-28" href="#__codelineno-75-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-75-29" name="__codelineno-75-29" href="#__codelineno-75-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">rotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="cm">/* 回転操作を行い、この部分木の平衡を回復する */</span>
+<a id="__codelineno-76-2" name="__codelineno-76-2" href="#__codelineno-76-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">):</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-76-3" name="__codelineno-76-3" href="#__codelineno-76-3"></a><span class="w">    </span><span class="c1">// ノード node の平衡係数を取得</span>
+<a id="__codelineno-76-4" name="__codelineno-76-4" href="#__codelineno-76-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">balanceFactor</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-76-5" name="__codelineno-76-5" href="#__codelineno-76-5"></a><span class="w">    </span><span class="c1">// 左に偏った木</span>
+<a id="__codelineno-76-6" name="__codelineno-76-6" href="#__codelineno-76-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-76-7" name="__codelineno-76-7" href="#__codelineno-76-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-76-8" name="__codelineno-76-8" href="#__codelineno-76-8"></a><span class="w">            </span><span class="c1">// 右回転</span>
+<a id="__codelineno-76-9" name="__codelineno-76-9" href="#__codelineno-76-9"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-76-10" name="__codelineno-76-10" href="#__codelineno-76-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-76-11" name="__codelineno-76-11" href="#__codelineno-76-11"></a><span class="w">            </span><span class="c1">// 左回転してから右回転</span>
+<a id="__codelineno-76-12" name="__codelineno-76-12" href="#__codelineno-76-12"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">)</span>
+<a id="__codelineno-76-13" name="__codelineno-76-13" href="#__codelineno-76-13"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-76-14" name="__codelineno-76-14" href="#__codelineno-76-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-76-15" name="__codelineno-76-15" href="#__codelineno-76-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-76-16" name="__codelineno-76-16" href="#__codelineno-76-16"></a><span class="w">    </span><span class="c1">// 右に偏った木</span>
+<a id="__codelineno-76-17" name="__codelineno-76-17" href="#__codelineno-76-17"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-76-18" name="__codelineno-76-18" href="#__codelineno-76-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">)</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-76-19" name="__codelineno-76-19" href="#__codelineno-76-19"></a><span class="w">            </span><span class="c1">// 左回転</span>
+<a id="__codelineno-76-20" name="__codelineno-76-20" href="#__codelineno-76-20"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-76-21" name="__codelineno-76-21" href="#__codelineno-76-21"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-76-22" name="__codelineno-76-22" href="#__codelineno-76-22"></a><span class="w">            </span><span class="c1">// 右回転してから左回転</span>
+<a id="__codelineno-76-23" name="__codelineno-76-23" href="#__codelineno-76-23"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">)</span>
+<a id="__codelineno-76-24" name="__codelineno-76-24" href="#__codelineno-76-24"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-76-25" name="__codelineno-76-25" href="#__codelineno-76-25"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-76-26" name="__codelineno-76-26" href="#__codelineno-76-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-76-27" name="__codelineno-76-27" href="#__codelineno-76-27"></a><span class="w">    </span><span class="c1">// 平衡木なので回転不要、そのまま返す</span>
+<a id="__codelineno-76-28" name="__codelineno-76-28" href="#__codelineno-76-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-76-29" name="__codelineno-76-29" href="#__codelineno-76-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">rotate</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="c1">### 回転操作を行い、この部分木の平衡を回復する ###</span>
+<a id="__codelineno-77-2" name="__codelineno-77-2" href="#__codelineno-77-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-77-3" name="__codelineno-77-3" href="#__codelineno-77-3"></a><span class="w">  </span><span class="c1"># ノード node の平衡係数を取得</span>
+<a id="__codelineno-77-4" name="__codelineno-77-4" href="#__codelineno-77-4"></a><span class="w">  </span><span class="n">balance_factor</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-77-5" name="__codelineno-77-5" href="#__codelineno-77-5"></a><span class="w">  </span><span class="c1"># 左部分木をたどる</span>
+<a id="__codelineno-77-6" name="__codelineno-77-6" href="#__codelineno-77-6"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="n">balance_factor</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-77-7" name="__codelineno-77-7" href="#__codelineno-77-7"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-77-8" name="__codelineno-77-8" href="#__codelineno-77-8"></a><span class="w">      </span><span class="c1"># 右回転</span>
+<a id="__codelineno-77-9" name="__codelineno-77-9" href="#__codelineno-77-9"></a><span class="w">      </span><span class="k">return</span><span class="w"> </span><span class="n">right_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-77-10" name="__codelineno-77-10" href="#__codelineno-77-10"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-77-11" name="__codelineno-77-11" href="#__codelineno-77-11"></a><span class="w">      </span><span class="c1"># 左回転してから右回転</span>
+<a id="__codelineno-77-12" name="__codelineno-77-12" href="#__codelineno-77-12"></a><span class="w">      </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left_rotate</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
+<a id="__codelineno-77-13" name="__codelineno-77-13" href="#__codelineno-77-13"></a><span class="w">      </span><span class="k">return</span><span class="w"> </span><span class="n">right_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-77-14" name="__codelineno-77-14" href="#__codelineno-77-14"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-77-15" name="__codelineno-77-15" href="#__codelineno-77-15"></a><span class="w">  </span><span class="c1"># 右に偏った木</span>
+<a id="__codelineno-77-16" name="__codelineno-77-16" href="#__codelineno-77-16"></a><span class="w">  </span><span class="k">elsif</span><span class="w"> </span><span class="n">balance_factor</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-77-17" name="__codelineno-77-17" href="#__codelineno-77-17"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-77-18" name="__codelineno-77-18" href="#__codelineno-77-18"></a><span class="w">      </span><span class="c1"># 左回転</span>
+<a id="__codelineno-77-19" name="__codelineno-77-19" href="#__codelineno-77-19"></a><span class="w">      </span><span class="k">return</span><span class="w"> </span><span class="n">left_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-77-20" name="__codelineno-77-20" href="#__codelineno-77-20"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-77-21" name="__codelineno-77-21" href="#__codelineno-77-21"></a><span class="w">      </span><span class="c1"># 右回転してから左回転</span>
+<a id="__codelineno-77-22" name="__codelineno-77-22" href="#__codelineno-77-22"></a><span class="w">      </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right_rotate</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-77-23" name="__codelineno-77-23" href="#__codelineno-77-23"></a><span class="w">      </span><span class="k">return</span><span class="w"> </span><span class="n">left_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-77-24" name="__codelineno-77-24" href="#__codelineno-77-24"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-77-25" name="__codelineno-77-25" href="#__codelineno-77-25"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-77-26" name="__codelineno-77-26" href="#__codelineno-77-26"></a><span class="w">  </span><span class="c1"># 平衡木なので回転不要、そのまま返す</span>
+<a id="__codelineno-77-27" name="__codelineno-77-27" href="#__codelineno-77-27"></a><span class="w">  </span><span class="n">node</span>
+<a id="__codelineno-77-28" name="__codelineno-77-28" href="#__codelineno-77-28"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h2 id="753-avl">7.5.3 &nbsp; AVL木の一般的な操作<a class="headerlink" href="#753-avl" title="Permanent link">&para;</a></h2>
+<h2 id="753-avl">7.5.3 &nbsp; AVL 木の基本操作<a class="headerlink" href="#753-avl" title="Permanent link">&para;</a></h2>
 <h3 id="1_2">1. &nbsp; ノードの挿入<a class="headerlink" href="#1_2" title="Permanent link">&para;</a></h3>
-<p>AVL木のノード挿入操作は二分探索木のそれと似ています。唯一の違いは、AVL木でノードを挿入した後、そのノードから根ノードまでのパス上に一連の不平衡ノードが現れる可能性があることです。したがって、<strong>このノードから始めて上向きに回転操作を実行し、すべての不平衡ノードのバランスを回復する必要があります</strong>。コードは以下の通りです：</p>
+<p>AVL 木のノード挿入は、基本的には二分探索木と同じです。唯一の違いは、AVL 木ではノード挿入後に、そのノードから根ノードまでの経路上に複数の不平衡ノードが現れる可能性があることです。したがって、<strong>このノードから開始して、下から上へ回転操作を行い、すべての不平衡ノードを平衡に戻す必要があります</strong>。コードは次のとおりです：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="8:13"><input checked="checked" id="__tabbed_8_1" name="__tabbed_8" type="radio" /><input id="__tabbed_8_2" name="__tabbed_8" type="radio" /><input id="__tabbed_8_3" name="__tabbed_8" type="radio" /><input id="__tabbed_8_4" name="__tabbed_8" type="radio" /><input id="__tabbed_8_5" name="__tabbed_8" type="radio" /><input id="__tabbed_8_6" name="__tabbed_8" type="radio" /><input id="__tabbed_8_7" name="__tabbed_8" type="radio" /><input id="__tabbed_8_8" name="__tabbed_8" type="radio" /><input id="__tabbed_8_9" name="__tabbed_8" type="radio" /><input id="__tabbed_8_10" name="__tabbed_8" type="radio" /><input id="__tabbed_8_11" name="__tabbed_8" type="radio" /><input id="__tabbed_8_12" name="__tabbed_8" type="radio" /><input id="__tabbed_8_13" name="__tabbed_8" type="radio" /><div class="tabbed-labels"><label for="__tabbed_8_1">Python</label><label for="__tabbed_8_2">C++</label><label for="__tabbed_8_3">Java</label><label for="__tabbed_8_4">C#</label><label for="__tabbed_8_5">Go</label><label for="__tabbed_8_6">Swift</label><label for="__tabbed_8_7">JS</label><label for="__tabbed_8_8">TS</label><label for="__tabbed_8_9">Dart</label><label for="__tabbed_8_10">Rust</label><label for="__tabbed_8_11">C</label><label for="__tabbed_8_12">Kotlin</label><label for="__tabbed_8_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
@@ -5451,20 +6177,20 @@
 <a id="__codelineno-78-3" name="__codelineno-78-3" href="#__codelineno-78-3"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">_root</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">insert_helper</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_root</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
 <a id="__codelineno-78-4" name="__codelineno-78-4" href="#__codelineno-78-4"></a>
 <a id="__codelineno-78-5" name="__codelineno-78-5" href="#__codelineno-78-5"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert_helper</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span><span class="p">:</span>
-<a id="__codelineno-78-6" name="__codelineno-78-6" href="#__codelineno-78-6"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;再帰的にノードを挿入（ヘルパーメソッド）&quot;&quot;&quot;</span>
+<a id="__codelineno-78-6" name="__codelineno-78-6" href="#__codelineno-78-6"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ノードを再帰的に挿入する（補助メソッド）&quot;&quot;&quot;</span>
 <a id="__codelineno-78-7" name="__codelineno-78-7" href="#__codelineno-78-7"></a>    <span class="k">if</span> <span class="n">node</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-78-8" name="__codelineno-78-8" href="#__codelineno-78-8"></a>        <span class="k">return</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
-<a id="__codelineno-78-9" name="__codelineno-78-9" href="#__codelineno-78-9"></a>    <span class="c1"># 1. 挿入位置を見つけてノードを挿入</span>
+<a id="__codelineno-78-9" name="__codelineno-78-9" href="#__codelineno-78-9"></a>    <span class="c1"># 1. 挿入位置を探索してノードを挿入</span>
 <a id="__codelineno-78-10" name="__codelineno-78-10" href="#__codelineno-78-10"></a>    <span class="k">if</span> <span class="n">val</span> <span class="o">&lt;</span> <span class="n">node</span><span class="o">.</span><span class="n">val</span><span class="p">:</span>
 <a id="__codelineno-78-11" name="__codelineno-78-11" href="#__codelineno-78-11"></a>        <span class="n">node</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">insert_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
 <a id="__codelineno-78-12" name="__codelineno-78-12" href="#__codelineno-78-12"></a>    <span class="k">elif</span> <span class="n">val</span> <span class="o">&gt;</span> <span class="n">node</span><span class="o">.</span><span class="n">val</span><span class="p">:</span>
 <a id="__codelineno-78-13" name="__codelineno-78-13" href="#__codelineno-78-13"></a>        <span class="n">node</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">insert_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
 <a id="__codelineno-78-14" name="__codelineno-78-14" href="#__codelineno-78-14"></a>    <span class="k">else</span><span class="p">:</span>
-<a id="__codelineno-78-15" name="__codelineno-78-15" href="#__codelineno-78-15"></a>        <span class="c1"># 重複ノードは挿入しない、戻る</span>
+<a id="__codelineno-78-15" name="__codelineno-78-15" href="#__codelineno-78-15"></a>        <span class="c1"># 重複ノードは挿入せず、そのまま返す</span>
 <a id="__codelineno-78-16" name="__codelineno-78-16" href="#__codelineno-78-16"></a>        <span class="k">return</span> <span class="n">node</span>
-<a id="__codelineno-78-17" name="__codelineno-78-17" href="#__codelineno-78-17"></a>    <span class="c1"># ノードの高さを更新</span>
+<a id="__codelineno-78-17" name="__codelineno-78-17" href="#__codelineno-78-17"></a>    <span class="c1"># ノードの高さを更新する</span>
 <a id="__codelineno-78-18" name="__codelineno-78-18" href="#__codelineno-78-18"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
-<a id="__codelineno-78-19" name="__codelineno-78-19" href="#__codelineno-78-19"></a>    <span class="c1"># 2. 回転操作を実行して部分木のバランスを復元</span>
+<a id="__codelineno-78-19" name="__codelineno-78-19" href="#__codelineno-78-19"></a>    <span class="c1"># 2. 回転操作を行い、部分木の平衡を回復する</span>
 <a id="__codelineno-78-20" name="__codelineno-78-20" href="#__codelineno-78-20"></a>    <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
 </code></pre></div>
 </div>
@@ -5474,21 +6200,21 @@
 <a id="__codelineno-79-3" name="__codelineno-79-3" href="#__codelineno-79-3"></a><span class="w">    </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
 <a id="__codelineno-79-4" name="__codelineno-79-4" href="#__codelineno-79-4"></a><span class="p">}</span>
 <a id="__codelineno-79-5" name="__codelineno-79-5" href="#__codelineno-79-5"></a>
-<a id="__codelineno-79-6" name="__codelineno-79-6" href="#__codelineno-79-6"></a><span class="cm">/* ノードを再帰的に挿入（ヘルパーメソッド） */</span>
+<a id="__codelineno-79-6" name="__codelineno-79-6" href="#__codelineno-79-6"></a><span class="cm">/* ノードを再帰的に挿入する（補助メソッド） */</span>
 <a id="__codelineno-79-7" name="__codelineno-79-7" href="#__codelineno-79-7"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">insertHelper</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-79-8" name="__codelineno-79-8" href="#__codelineno-79-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
 <a id="__codelineno-79-9" name="__codelineno-79-9" href="#__codelineno-79-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
-<a id="__codelineno-79-10" name="__codelineno-79-10" href="#__codelineno-79-10"></a><span class="w">    </span><span class="cm">/* 1. 挿入位置を見つけてノードを挿入 */</span>
+<a id="__codelineno-79-10" name="__codelineno-79-10" href="#__codelineno-79-10"></a><span class="w">    </span><span class="cm">/* 1. 挿入位置を探索してノードを挿入 */</span>
 <a id="__codelineno-79-11" name="__codelineno-79-11" href="#__codelineno-79-11"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">)</span>
 <a id="__codelineno-79-12" name="__codelineno-79-12" href="#__codelineno-79-12"></a><span class="w">        </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
 <a id="__codelineno-79-13" name="__codelineno-79-13" href="#__codelineno-79-13"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">)</span>
 <a id="__codelineno-79-14" name="__codelineno-79-14" href="#__codelineno-79-14"></a><span class="w">        </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
 <a id="__codelineno-79-15" name="__codelineno-79-15" href="#__codelineno-79-15"></a><span class="w">    </span><span class="k">else</span>
-<a id="__codelineno-79-16" name="__codelineno-79-16" href="#__codelineno-79-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w">    </span><span class="c1">// 重複ノードは挿入しない、そのまま戻る</span>
-<a id="__codelineno-79-17" name="__codelineno-79-17" href="#__codelineno-79-17"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// ノードの高さを更新</span>
-<a id="__codelineno-79-18" name="__codelineno-79-18" href="#__codelineno-79-18"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を実行して部分木の平衡を回復 */</span>
+<a id="__codelineno-79-16" name="__codelineno-79-16" href="#__codelineno-79-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w">    </span><span class="c1">// 重複ノードは挿入せず、そのまま返す</span>
+<a id="__codelineno-79-17" name="__codelineno-79-17" href="#__codelineno-79-17"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-79-18" name="__codelineno-79-18" href="#__codelineno-79-18"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を行い、部分木の平衡を回復する */</span>
 <a id="__codelineno-79-19" name="__codelineno-79-19" href="#__codelineno-79-19"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
-<a id="__codelineno-79-20" name="__codelineno-79-20" href="#__codelineno-79-20"></a><span class="w">    </span><span class="c1">// 部分木のルートノードを返す</span>
+<a id="__codelineno-79-20" name="__codelineno-79-20" href="#__codelineno-79-20"></a><span class="w">    </span><span class="c1">// 部分木の根ノードを返す</span>
 <a id="__codelineno-79-21" name="__codelineno-79-21" href="#__codelineno-79-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
 <a id="__codelineno-79-22" name="__codelineno-79-22" href="#__codelineno-79-22"></a><span class="p">}</span>
 </code></pre></div>
@@ -5499,19 +6225,19 @@
 <a id="__codelineno-80-3" name="__codelineno-80-3" href="#__codelineno-80-3"></a><span class="w">    </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
 <a id="__codelineno-80-4" name="__codelineno-80-4" href="#__codelineno-80-4"></a><span class="p">}</span>
 <a id="__codelineno-80-5" name="__codelineno-80-5" href="#__codelineno-80-5"></a>
-<a id="__codelineno-80-6" name="__codelineno-80-6" href="#__codelineno-80-6"></a><span class="cm">/* 再帰的にノードを挿入（補助メソッド） */</span>
+<a id="__codelineno-80-6" name="__codelineno-80-6" href="#__codelineno-80-6"></a><span class="cm">/* ノードを再帰的に挿入する（補助メソッド） */</span>
 <a id="__codelineno-80-7" name="__codelineno-80-7" href="#__codelineno-80-7"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">insertHelper</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-80-8" name="__codelineno-80-8" href="#__codelineno-80-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
 <a id="__codelineno-80-9" name="__codelineno-80-9" href="#__codelineno-80-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
-<a id="__codelineno-80-10" name="__codelineno-80-10" href="#__codelineno-80-10"></a><span class="w">    </span><span class="cm">/* 1. 挿入位置を見つけてノードを挿入 */</span>
+<a id="__codelineno-80-10" name="__codelineno-80-10" href="#__codelineno-80-10"></a><span class="w">    </span><span class="cm">/* 1. 挿入位置を探索してノードを挿入 */</span>
 <a id="__codelineno-80-11" name="__codelineno-80-11" href="#__codelineno-80-11"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">)</span>
 <a id="__codelineno-80-12" name="__codelineno-80-12" href="#__codelineno-80-12"></a><span class="w">        </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
 <a id="__codelineno-80-13" name="__codelineno-80-13" href="#__codelineno-80-13"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">)</span>
 <a id="__codelineno-80-14" name="__codelineno-80-14" href="#__codelineno-80-14"></a><span class="w">        </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
 <a id="__codelineno-80-15" name="__codelineno-80-15" href="#__codelineno-80-15"></a><span class="w">    </span><span class="k">else</span>
-<a id="__codelineno-80-16" name="__codelineno-80-16" href="#__codelineno-80-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 重複ノードは挿入しない、戻る</span>
-<a id="__codelineno-80-17" name="__codelineno-80-17" href="#__codelineno-80-17"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// ノードの高さを更新</span>
-<a id="__codelineno-80-18" name="__codelineno-80-18" href="#__codelineno-80-18"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を実行して部分木の平衡を回復 */</span>
+<a id="__codelineno-80-16" name="__codelineno-80-16" href="#__codelineno-80-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 重複ノードは挿入せず、そのまま返す</span>
+<a id="__codelineno-80-17" name="__codelineno-80-17" href="#__codelineno-80-17"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-80-18" name="__codelineno-80-18" href="#__codelineno-80-18"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を行い、部分木の平衡を回復する */</span>
 <a id="__codelineno-80-19" name="__codelineno-80-19" href="#__codelineno-80-19"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
 <a id="__codelineno-80-20" name="__codelineno-80-20" href="#__codelineno-80-20"></a><span class="w">    </span><span class="c1">// 部分木の根ノードを返す</span>
 <a id="__codelineno-80-21" name="__codelineno-80-21" href="#__codelineno-80-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
@@ -5519,69 +6245,287 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Insert</span><span class="p">}</span>
-<a id="__codelineno-81-2" name="__codelineno-81-2" href="#__codelineno-81-2"></a>
-<a id="__codelineno-81-3" name="__codelineno-81-3" href="#__codelineno-81-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">InsertHelper</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="cm">/* ノードを挿入 */</span>
+<a id="__codelineno-81-2" name="__codelineno-81-2" href="#__codelineno-81-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Insert</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-3" name="__codelineno-81-3" href="#__codelineno-81-3"></a><span class="w">    </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">InsertHelper</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-81-4" name="__codelineno-81-4" href="#__codelineno-81-4"></a><span class="p">}</span>
+<a id="__codelineno-81-5" name="__codelineno-81-5" href="#__codelineno-81-5"></a>
+<a id="__codelineno-81-6" name="__codelineno-81-6" href="#__codelineno-81-6"></a><span class="cm">/* ノードを再帰的に挿入する（補助メソッド） */</span>
+<a id="__codelineno-81-7" name="__codelineno-81-7" href="#__codelineno-81-7"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">InsertHelper</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-8" name="__codelineno-81-8" href="#__codelineno-81-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-81-9" name="__codelineno-81-9" href="#__codelineno-81-9"></a><span class="w">    </span><span class="cm">/* 1. 挿入位置を探索してノードを挿入 */</span>
+<a id="__codelineno-81-10" name="__codelineno-81-10" href="#__codelineno-81-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-81-11" name="__codelineno-81-11" href="#__codelineno-81-11"></a><span class="w">        </span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">InsertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-81-12" name="__codelineno-81-12" href="#__codelineno-81-12"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="nf">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-81-13" name="__codelineno-81-13" href="#__codelineno-81-13"></a><span class="w">        </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">InsertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-81-14" name="__codelineno-81-14" href="#__codelineno-81-14"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-81-15" name="__codelineno-81-15" href="#__codelineno-81-15"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w">     </span><span class="c1">// 重複ノードは挿入せず、そのまま返す</span>
+<a id="__codelineno-81-16" name="__codelineno-81-16" href="#__codelineno-81-16"></a><span class="w">    </span><span class="n">UpdateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w">  </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-81-17" name="__codelineno-81-17" href="#__codelineno-81-17"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を行い、部分木の平衡を回復する */</span>
+<a id="__codelineno-81-18" name="__codelineno-81-18" href="#__codelineno-81-18"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-81-19" name="__codelineno-81-19" href="#__codelineno-81-19"></a><span class="w">    </span><span class="c1">// 部分木の根ノードを返す</span>
+<a id="__codelineno-81-20" name="__codelineno-81-20" href="#__codelineno-81-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-81-21" name="__codelineno-81-21" href="#__codelineno-81-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">insert</span><span class="p">}</span>
-<a id="__codelineno-82-2" name="__codelineno-82-2" href="#__codelineno-82-2"></a>
-<a id="__codelineno-82-3" name="__codelineno-82-3" href="#__codelineno-82-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">insertHelper</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="cm">/* ノードを挿入 */</span>
+<a id="__codelineno-82-2" name="__codelineno-82-2" href="#__codelineno-82-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">aVLTree</span><span class="p">)</span><span class="w"> </span><span class="nx">insert</span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-3" name="__codelineno-82-3" href="#__codelineno-82-3"></a><span class="w">    </span><span class="nx">t</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">insertHelper</span><span class="p">(</span><span class="nx">t</span><span class="p">.</span><span class="nx">root</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">)</span>
+<a id="__codelineno-82-4" name="__codelineno-82-4" href="#__codelineno-82-4"></a><span class="p">}</span>
+<a id="__codelineno-82-5" name="__codelineno-82-5" href="#__codelineno-82-5"></a>
+<a id="__codelineno-82-6" name="__codelineno-82-6" href="#__codelineno-82-6"></a><span class="cm">/* ノードを再帰的に挿入する（補助関数） */</span>
+<a id="__codelineno-82-7" name="__codelineno-82-7" href="#__codelineno-82-7"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">aVLTree</span><span class="p">)</span><span class="w"> </span><span class="nx">insertHelper</span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-8" name="__codelineno-82-8" href="#__codelineno-82-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-9" name="__codelineno-82-9" href="#__codelineno-82-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">NewTreeNode</span><span class="p">(</span><span class="nx">val</span><span class="p">)</span>
+<a id="__codelineno-82-10" name="__codelineno-82-10" href="#__codelineno-82-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-82-11" name="__codelineno-82-11" href="#__codelineno-82-11"></a><span class="w">    </span><span class="cm">/* 1. 挿入位置を探索してノードを挿入 */</span>
+<a id="__codelineno-82-12" name="__codelineno-82-12" href="#__codelineno-82-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Val</span><span class="p">.(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-13" name="__codelineno-82-13" href="#__codelineno-82-13"></a><span class="w">        </span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">insertHelper</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">)</span>
+<a id="__codelineno-82-14" name="__codelineno-82-14" href="#__codelineno-82-14"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Val</span><span class="p">.(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-15" name="__codelineno-82-15" href="#__codelineno-82-15"></a><span class="w">        </span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">insertHelper</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">)</span>
+<a id="__codelineno-82-16" name="__codelineno-82-16" href="#__codelineno-82-16"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-17" name="__codelineno-82-17" href="#__codelineno-82-17"></a><span class="w">        </span><span class="c1">// 重複ノードは挿入せず、そのまま返す</span>
+<a id="__codelineno-82-18" name="__codelineno-82-18" href="#__codelineno-82-18"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span>
+<a id="__codelineno-82-19" name="__codelineno-82-19" href="#__codelineno-82-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-82-20" name="__codelineno-82-20" href="#__codelineno-82-20"></a><span class="w">    </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-82-21" name="__codelineno-82-21" href="#__codelineno-82-21"></a><span class="w">    </span><span class="nx">t</span><span class="p">.</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span>
+<a id="__codelineno-82-22" name="__codelineno-82-22" href="#__codelineno-82-22"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を行い、部分木の平衡を回復する */</span>
+<a id="__codelineno-82-23" name="__codelineno-82-23" href="#__codelineno-82-23"></a><span class="w">    </span><span class="nx">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">rotate</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span>
+<a id="__codelineno-82-24" name="__codelineno-82-24" href="#__codelineno-82-24"></a><span class="w">    </span><span class="c1">// 部分木の根ノードを返す</span>
+<a id="__codelineno-82-25" name="__codelineno-82-25" href="#__codelineno-82-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span>
+<a id="__codelineno-82-26" name="__codelineno-82-26" href="#__codelineno-82-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="bp">insert</span><span class="p">}</span>
-<a id="__codelineno-83-2" name="__codelineno-83-2" href="#__codelineno-83-2"></a>
-<a id="__codelineno-83-3" name="__codelineno-83-3" href="#__codelineno-83-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">insertHelper</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="cm">/* ノードを挿入 */</span>
+<a id="__codelineno-83-2" name="__codelineno-83-2" href="#__codelineno-83-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-3" name="__codelineno-83-3" href="#__codelineno-83-3"></a><span class="w">    </span><span class="n">root</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-83-4" name="__codelineno-83-4" href="#__codelineno-83-4"></a><span class="p">}</span>
+<a id="__codelineno-83-5" name="__codelineno-83-5" href="#__codelineno-83-5"></a>
+<a id="__codelineno-83-6" name="__codelineno-83-6" href="#__codelineno-83-6"></a><span class="cm">/* ノードを再帰的に挿入する（補助メソッド） */</span>
+<a id="__codelineno-83-7" name="__codelineno-83-7" href="#__codelineno-83-7"></a><span class="kd">func</span><span class="w"> </span><span class="nf">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-8" name="__codelineno-83-8" href="#__codelineno-83-8"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-83-9" name="__codelineno-83-9" href="#__codelineno-83-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-10" name="__codelineno-83-10" href="#__codelineno-83-10"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-83-11" name="__codelineno-83-11" href="#__codelineno-83-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-83-12" name="__codelineno-83-12" href="#__codelineno-83-12"></a><span class="w">    </span><span class="cm">/* 1. 挿入位置を探索してノードを挿入 */</span>
+<a id="__codelineno-83-13" name="__codelineno-83-13" href="#__codelineno-83-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="p">!.</span><span class="n">val</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-14" name="__codelineno-83-14" href="#__codelineno-83-14"></a><span class="w">        </span><span class="n">node</span><span class="p">?.</span><span class="kr">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">?.</span><span class="kr">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-83-15" name="__codelineno-83-15" href="#__codelineno-83-15"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="p">!.</span><span class="n">val</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-16" name="__codelineno-83-16" href="#__codelineno-83-16"></a><span class="w">        </span><span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-83-17" name="__codelineno-83-17" href="#__codelineno-83-17"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-18" name="__codelineno-83-18" href="#__codelineno-83-18"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="c1">// 重複ノードは挿入せず、そのまま返す</span>
+<a id="__codelineno-83-19" name="__codelineno-83-19" href="#__codelineno-83-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-83-20" name="__codelineno-83-20" href="#__codelineno-83-20"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-83-21" name="__codelineno-83-21" href="#__codelineno-83-21"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を行い、部分木の平衡を回復する */</span>
+<a id="__codelineno-83-22" name="__codelineno-83-22" href="#__codelineno-83-22"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-83-23" name="__codelineno-83-23" href="#__codelineno-83-23"></a><span class="w">    </span><span class="c1">// 部分木の根ノードを返す</span>
+<a id="__codelineno-83-24" name="__codelineno-83-24" href="#__codelineno-83-24"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-83-25" name="__codelineno-83-25" href="#__codelineno-83-25"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-84-1" name="__codelineno-84-1" href="#__codelineno-84-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">insert</span><span class="p">}</span>
-<a id="__codelineno-84-2" name="__codelineno-84-2" href="#__codelineno-84-2"></a>
-<a id="__codelineno-84-3" name="__codelineno-84-3" href="#__codelineno-84-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">insertHelper</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-84-1" name="__codelineno-84-1" href="#__codelineno-84-1"></a><span class="cm">/* ノードを挿入 */</span>
+<a id="__codelineno-84-2" name="__codelineno-84-2" href="#__codelineno-84-2"></a><span class="nx">insert</span><span class="p">(</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-3" name="__codelineno-84-3" href="#__codelineno-84-3"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#insertHelper</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-84-4" name="__codelineno-84-4" href="#__codelineno-84-4"></a><span class="p">}</span>
+<a id="__codelineno-84-5" name="__codelineno-84-5" href="#__codelineno-84-5"></a>
+<a id="__codelineno-84-6" name="__codelineno-84-6" href="#__codelineno-84-6"></a><span class="cm">/* ノードを再帰的に挿入する（補助メソッド） */</span>
+<a id="__codelineno-84-7" name="__codelineno-84-7" href="#__codelineno-84-7"></a><span class="n">#insertHelper</span><span class="p">(</span><span class="nx">node</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-8" name="__codelineno-84-8" href="#__codelineno-84-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-84-9" name="__codelineno-84-9" href="#__codelineno-84-9"></a><span class="w">    </span><span class="cm">/* 1. 挿入位置を探索してノードを挿入 */</span>
+<a id="__codelineno-84-10" name="__codelineno-84-10" href="#__codelineno-84-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#insertHelper</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-84-11" name="__codelineno-84-11" href="#__codelineno-84-11"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">val</span><span class="p">)</span>
+<a id="__codelineno-84-12" name="__codelineno-84-12" href="#__codelineno-84-12"></a><span class="w">        </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#insertHelper</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-84-13" name="__codelineno-84-13" href="#__codelineno-84-13"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 重複ノードは挿入せず、そのまま返す</span>
+<a id="__codelineno-84-14" name="__codelineno-84-14" href="#__codelineno-84-14"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="n">#updateHeight</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-84-15" name="__codelineno-84-15" href="#__codelineno-84-15"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を行い、部分木の平衡を回復する */</span>
+<a id="__codelineno-84-16" name="__codelineno-84-16" href="#__codelineno-84-16"></a><span class="w">    </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#rotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
+<a id="__codelineno-84-17" name="__codelineno-84-17" href="#__codelineno-84-17"></a><span class="w">    </span><span class="c1">// 部分木の根ノードを返す</span>
+<a id="__codelineno-84-18" name="__codelineno-84-18" href="#__codelineno-84-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-84-19" name="__codelineno-84-19" href="#__codelineno-84-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">insert</span><span class="p">}</span>
-<a id="__codelineno-85-2" name="__codelineno-85-2" href="#__codelineno-85-2"></a>
-<a id="__codelineno-85-3" name="__codelineno-85-3" href="#__codelineno-85-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">insertHelper</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="cm">/* ノードを挿入 */</span>
+<a id="__codelineno-85-2" name="__codelineno-85-2" href="#__codelineno-85-2"></a><span class="nx">insert</span><span class="p">(</span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-3" name="__codelineno-85-3" href="#__codelineno-85-3"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">insertHelper</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-85-4" name="__codelineno-85-4" href="#__codelineno-85-4"></a><span class="p">}</span>
+<a id="__codelineno-85-5" name="__codelineno-85-5" href="#__codelineno-85-5"></a>
+<a id="__codelineno-85-6" name="__codelineno-85-6" href="#__codelineno-85-6"></a><span class="cm">/* ノードを再帰的に挿入する（補助メソッド） */</span>
+<a id="__codelineno-85-7" name="__codelineno-85-7" href="#__codelineno-85-7"></a><span class="nx">insertHelper</span><span class="p">(</span><span class="nx">node</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-8" name="__codelineno-85-8" href="#__codelineno-85-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-85-9" name="__codelineno-85-9" href="#__codelineno-85-9"></a><span class="w">    </span><span class="cm">/* 1. 挿入位置を探索してノードを挿入 */</span>
+<a id="__codelineno-85-10" name="__codelineno-85-10" href="#__codelineno-85-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-11" name="__codelineno-85-11" href="#__codelineno-85-11"></a><span class="w">        </span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">insertHelper</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-85-12" name="__codelineno-85-12" href="#__codelineno-85-12"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-13" name="__codelineno-85-13" href="#__codelineno-85-13"></a><span class="w">        </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">insertHelper</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-85-14" name="__codelineno-85-14" href="#__codelineno-85-14"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-15" name="__codelineno-85-15" href="#__codelineno-85-15"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 重複ノードは挿入せず、そのまま返す</span>
+<a id="__codelineno-85-16" name="__codelineno-85-16" href="#__codelineno-85-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-85-17" name="__codelineno-85-17" href="#__codelineno-85-17"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-85-18" name="__codelineno-85-18" href="#__codelineno-85-18"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を行い、部分木の平衡を回復する */</span>
+<a id="__codelineno-85-19" name="__codelineno-85-19" href="#__codelineno-85-19"></a><span class="w">    </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">rotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
+<a id="__codelineno-85-20" name="__codelineno-85-20" href="#__codelineno-85-20"></a><span class="w">    </span><span class="c1">// 部分木の根ノードを返す</span>
+<a id="__codelineno-85-21" name="__codelineno-85-21" href="#__codelineno-85-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-85-22" name="__codelineno-85-22" href="#__codelineno-85-22"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
-<a id="__codelineno-86-2" name="__codelineno-86-2" href="#__codelineno-86-2"></a>
-<a id="__codelineno-86-3" name="__codelineno-86-3" href="#__codelineno-86-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insertHelper</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="cm">/* ノードを挿入 */</span>
+<a id="__codelineno-86-2" name="__codelineno-86-2" href="#__codelineno-86-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">insert</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-3" name="__codelineno-86-3" href="#__codelineno-86-3"></a><span class="w">  </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-86-4" name="__codelineno-86-4" href="#__codelineno-86-4"></a><span class="p">}</span>
+<a id="__codelineno-86-5" name="__codelineno-86-5" href="#__codelineno-86-5"></a>
+<a id="__codelineno-86-6" name="__codelineno-86-6" href="#__codelineno-86-6"></a><span class="cm">/* ノードを再帰的に挿入する（補助メソッド） */</span>
+<a id="__codelineno-86-7" name="__codelineno-86-7" href="#__codelineno-86-7"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-8" name="__codelineno-86-8" href="#__codelineno-86-8"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-86-9" name="__codelineno-86-9" href="#__codelineno-86-9"></a><span class="w">  </span><span class="cm">/* 1. 挿入位置を探索してノードを挿入 */</span>
+<a id="__codelineno-86-10" name="__codelineno-86-10" href="#__codelineno-86-10"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-86-11" name="__codelineno-86-11" href="#__codelineno-86-11"></a><span class="w">    </span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-86-12" name="__codelineno-86-12" href="#__codelineno-86-12"></a><span class="w">  </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-86-13" name="__codelineno-86-13" href="#__codelineno-86-13"></a><span class="w">    </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-86-14" name="__codelineno-86-14" href="#__codelineno-86-14"></a><span class="w">  </span><span class="k">else</span>
+<a id="__codelineno-86-15" name="__codelineno-86-15" href="#__codelineno-86-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 重複ノードは挿入せず、そのまま返す</span>
+<a id="__codelineno-86-16" name="__codelineno-86-16" href="#__codelineno-86-16"></a><span class="w">  </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-86-17" name="__codelineno-86-17" href="#__codelineno-86-17"></a><span class="w">  </span><span class="cm">/* 2. 回転操作を行い、部分木の平衡を回復する */</span>
+<a id="__codelineno-86-18" name="__codelineno-86-18" href="#__codelineno-86-18"></a><span class="w">  </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-86-19" name="__codelineno-86-19" href="#__codelineno-86-19"></a><span class="w">  </span><span class="c1">// 部分木の根ノードを返す</span>
+<a id="__codelineno-86-20" name="__codelineno-86-20" href="#__codelineno-86-20"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-86-21" name="__codelineno-86-21" href="#__codelineno-86-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-87-1" name="__codelineno-87-1" href="#__codelineno-87-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
-<a id="__codelineno-87-2" name="__codelineno-87-2" href="#__codelineno-87-2"></a>
-<a id="__codelineno-87-3" name="__codelineno-87-3" href="#__codelineno-87-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert_helper</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-87-1" name="__codelineno-87-1" href="#__codelineno-87-1"></a><span class="cm">/* ノードを挿入 */</span>
+<a id="__codelineno-87-2" name="__codelineno-87-2" href="#__codelineno-87-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-3" name="__codelineno-87-3" href="#__codelineno-87-3"></a><span class="w">    </span><span class="bp">self</span><span class="p">.</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span><span class="p">::</span><span class="n">insert_helper</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">root</span><span class="p">.</span><span class="n">clone</span><span class="p">(),</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-87-4" name="__codelineno-87-4" href="#__codelineno-87-4"></a><span class="p">}</span>
+<a id="__codelineno-87-5" name="__codelineno-87-5" href="#__codelineno-87-5"></a>
+<a id="__codelineno-87-6" name="__codelineno-87-6" href="#__codelineno-87-6"></a><span class="cm">/* ノードを再帰的に挿入する（補助メソッド） */</span>
+<a id="__codelineno-87-7" name="__codelineno-87-7" href="#__codelineno-87-7"></a><span class="k">fn</span><span class="w"> </span><span class="nf">insert_helper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="nc">OptionTreeNodeRc</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">OptionTreeNodeRc</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-8" name="__codelineno-87-8" href="#__codelineno-87-8"></a><span class="w">    </span><span class="k">match</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-9" name="__codelineno-87-9" href="#__codelineno-87-9"></a><span class="w">        </span><span class="nb">Some</span><span class="p">(</span><span class="k">mut</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-10" name="__codelineno-87-10" href="#__codelineno-87-10"></a><span class="w">            </span><span class="cm">/* 1. 挿入位置を探索してノードを挿入 */</span>
+<a id="__codelineno-87-11" name="__codelineno-87-11" href="#__codelineno-87-11"></a><span class="w">            </span><span class="k">match</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-12" name="__codelineno-87-12" href="#__codelineno-87-12"></a><span class="w">                </span><span class="kd">let</span><span class="w"> </span><span class="n">node_val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-87-13" name="__codelineno-87-13" href="#__codelineno-87-13"></a><span class="w">                </span><span class="n">node_val</span>
+<a id="__codelineno-87-14" name="__codelineno-87-14" href="#__codelineno-87-14"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-87-15" name="__codelineno-87-15" href="#__codelineno-87-15"></a><span class="w">            </span><span class="p">.</span><span class="n">cmp</span><span class="p">(</span><span class="o">&amp;</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-87-16" name="__codelineno-87-16" href="#__codelineno-87-16"></a><span class="w">            </span><span class="p">{</span>
+<a id="__codelineno-87-17" name="__codelineno-87-17" href="#__codelineno-87-17"></a><span class="w">                </span><span class="n">Ordering</span><span class="p">::</span><span class="n">Greater</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-18" name="__codelineno-87-18" href="#__codelineno-87-18"></a><span class="w">                    </span><span class="kd">let</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-87-19" name="__codelineno-87-19" href="#__codelineno-87-19"></a><span class="w">                    </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span><span class="p">::</span><span class="n">insert_helper</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-87-20" name="__codelineno-87-20" href="#__codelineno-87-20"></a><span class="w">                </span><span class="p">}</span>
+<a id="__codelineno-87-21" name="__codelineno-87-21" href="#__codelineno-87-21"></a><span class="w">                </span><span class="n">Ordering</span><span class="p">::</span><span class="n">Less</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-22" name="__codelineno-87-22" href="#__codelineno-87-22"></a><span class="w">                    </span><span class="kd">let</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-87-23" name="__codelineno-87-23" href="#__codelineno-87-23"></a><span class="w">                    </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span><span class="p">::</span><span class="n">insert_helper</span><span class="p">(</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-87-24" name="__codelineno-87-24" href="#__codelineno-87-24"></a><span class="w">                </span><span class="p">}</span>
+<a id="__codelineno-87-25" name="__codelineno-87-25" href="#__codelineno-87-25"></a><span class="w">                </span><span class="n">Ordering</span><span class="p">::</span><span class="n">Equal</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-26" name="__codelineno-87-26" href="#__codelineno-87-26"></a><span class="w">                    </span><span class="k">return</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// 重複ノードは挿入せず、そのまま返す</span>
+<a id="__codelineno-87-27" name="__codelineno-87-27" href="#__codelineno-87-27"></a><span class="w">                </span><span class="p">}</span>
+<a id="__codelineno-87-28" name="__codelineno-87-28" href="#__codelineno-87-28"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-87-29" name="__codelineno-87-29" href="#__codelineno-87-29"></a><span class="w">            </span><span class="bp">Self</span><span class="p">::</span><span class="n">update_height</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">()));</span><span class="w"> </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-87-30" name="__codelineno-87-30" href="#__codelineno-87-30"></a>
+<a id="__codelineno-87-31" name="__codelineno-87-31" href="#__codelineno-87-31"></a><span class="w">            </span><span class="cm">/* 2. 回転操作を行い、部分木の平衡を回復する */</span>
+<a id="__codelineno-87-32" name="__codelineno-87-32" href="#__codelineno-87-32"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span><span class="p">::</span><span class="n">rotate</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)).</span><span class="n">unwrap</span><span class="p">();</span>
+<a id="__codelineno-87-33" name="__codelineno-87-33" href="#__codelineno-87-33"></a><span class="w">            </span><span class="c1">// 部分木の根ノードを返す</span>
+<a id="__codelineno-87-34" name="__codelineno-87-34" href="#__codelineno-87-34"></a><span class="w">            </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-87-35" name="__codelineno-87-35" href="#__codelineno-87-35"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-87-36" name="__codelineno-87-36" href="#__codelineno-87-36"></a><span class="w">        </span><span class="nb">None</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">TreeNode</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">val</span><span class="p">)),</span>
+<a id="__codelineno-87-37" name="__codelineno-87-37" href="#__codelineno-87-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-87-38" name="__codelineno-87-38" href="#__codelineno-87-38"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-88-1" name="__codelineno-88-1" href="#__codelineno-88-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
-<a id="__codelineno-88-2" name="__codelineno-88-2" href="#__codelineno-88-2"></a>
-<a id="__codelineno-88-3" name="__codelineno-88-3" href="#__codelineno-88-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insertHelper</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-88-1" name="__codelineno-88-1" href="#__codelineno-88-1"></a><span class="cm">/* ノードを挿入 */</span>
+<a id="__codelineno-88-2" name="__codelineno-88-2" href="#__codelineno-88-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">AVLTree</span><span class="w"> </span><span class="o">*</span><span class="n">tree</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-3" name="__codelineno-88-3" href="#__codelineno-88-3"></a><span class="w">    </span><span class="n">tree</span><span class="o">-&gt;</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">tree</span><span class="o">-&gt;</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-88-4" name="__codelineno-88-4" href="#__codelineno-88-4"></a><span class="p">}</span>
+<a id="__codelineno-88-5" name="__codelineno-88-5" href="#__codelineno-88-5"></a>
+<a id="__codelineno-88-6" name="__codelineno-88-6" href="#__codelineno-88-6"></a><span class="cm">/* ノードを再帰的に挿入する（補助関数） */</span>
+<a id="__codelineno-88-7" name="__codelineno-88-7" href="#__codelineno-88-7"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">insertHelper</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-8" name="__codelineno-88-8" href="#__codelineno-88-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-9" name="__codelineno-88-9" href="#__codelineno-88-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">newTreeNode</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-88-10" name="__codelineno-88-10" href="#__codelineno-88-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-88-11" name="__codelineno-88-11" href="#__codelineno-88-11"></a><span class="w">    </span><span class="cm">/* 1. 挿入位置を探索してノードを挿入 */</span>
+<a id="__codelineno-88-12" name="__codelineno-88-12" href="#__codelineno-88-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-13" name="__codelineno-88-13" href="#__codelineno-88-13"></a><span class="w">        </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-88-14" name="__codelineno-88-14" href="#__codelineno-88-14"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-15" name="__codelineno-88-15" href="#__codelineno-88-15"></a><span class="w">        </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-88-16" name="__codelineno-88-16" href="#__codelineno-88-16"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-17" name="__codelineno-88-17" href="#__codelineno-88-17"></a><span class="w">        </span><span class="c1">// 重複ノードは挿入せず、そのまま返す</span>
+<a id="__codelineno-88-18" name="__codelineno-88-18" href="#__codelineno-88-18"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-88-19" name="__codelineno-88-19" href="#__codelineno-88-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-88-20" name="__codelineno-88-20" href="#__codelineno-88-20"></a><span class="w">    </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-88-21" name="__codelineno-88-21" href="#__codelineno-88-21"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-88-22" name="__codelineno-88-22" href="#__codelineno-88-22"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を行い、部分木の平衡を回復する */</span>
+<a id="__codelineno-88-23" name="__codelineno-88-23" href="#__codelineno-88-23"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-88-24" name="__codelineno-88-24" href="#__codelineno-88-24"></a><span class="w">    </span><span class="c1">// 部分木の根ノードを返す</span>
+<a id="__codelineno-88-25" name="__codelineno-88-25" href="#__codelineno-88-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-88-26" name="__codelineno-88-26" href="#__codelineno-88-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-89-1" name="__codelineno-89-1" href="#__codelineno-89-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert</span><span class="p">}</span>
-<a id="__codelineno-89-2" name="__codelineno-89-2" href="#__codelineno-89-2"></a>
-<a id="__codelineno-89-3" name="__codelineno-89-3" href="#__codelineno-89-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insertHelper</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-89-1" name="__codelineno-89-1" href="#__codelineno-89-1"></a><span class="cm">/* ノードを挿入 */</span>
+<a id="__codelineno-89-2" name="__codelineno-89-2" href="#__codelineno-89-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">_val</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-89-3" name="__codelineno-89-3" href="#__codelineno-89-3"></a><span class="w">    </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">)</span>
+<a id="__codelineno-89-4" name="__codelineno-89-4" href="#__codelineno-89-4"></a><span class="p">}</span>
+<a id="__codelineno-89-5" name="__codelineno-89-5" href="#__codelineno-89-5"></a>
+<a id="__codelineno-89-6" name="__codelineno-89-6" href="#__codelineno-89-6"></a><span class="cm">/* ノードを再帰的に挿入する（補助メソッド） */</span>
+<a id="__codelineno-89-7" name="__codelineno-89-7" href="#__codelineno-89-7"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">insertHelper</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?,</span><span class="w"> </span><span class="n">_val</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-89-8" name="__codelineno-89-8" href="#__codelineno-89-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-89-9" name="__codelineno-89-9" href="#__codelineno-89-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">_val</span><span class="p">)</span>
+<a id="__codelineno-89-10" name="__codelineno-89-10" href="#__codelineno-89-10"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span>
+<a id="__codelineno-89-11" name="__codelineno-89-11" href="#__codelineno-89-11"></a><span class="w">    </span><span class="cm">/* 1. 挿入位置を探索してノードを挿入 */</span>
+<a id="__codelineno-89-12" name="__codelineno-89-12" href="#__codelineno-89-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">_val</span><span class="p">)</span>
+<a id="__codelineno-89-13" name="__codelineno-89-13" href="#__codelineno-89-13"></a><span class="w">        </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">)</span>
+<a id="__codelineno-89-14" name="__codelineno-89-14" href="#__codelineno-89-14"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">_val</span><span class="p">)</span>
+<a id="__codelineno-89-15" name="__codelineno-89-15" href="#__codelineno-89-15"></a><span class="w">        </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">)</span>
+<a id="__codelineno-89-16" name="__codelineno-89-16" href="#__codelineno-89-16"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-89-17" name="__codelineno-89-17" href="#__codelineno-89-17"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="c1">// 重複ノードは挿入せず、そのまま返す</span>
+<a id="__codelineno-89-18" name="__codelineno-89-18" href="#__codelineno-89-18"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-89-19" name="__codelineno-89-19" href="#__codelineno-89-19"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を行い、部分木の平衡を回復する */</span>
+<a id="__codelineno-89-20" name="__codelineno-89-20" href="#__codelineno-89-20"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-89-21" name="__codelineno-89-21" href="#__codelineno-89-21"></a><span class="w">    </span><span class="c1">// 部分木の根ノードを返す</span>
+<a id="__codelineno-89-22" name="__codelineno-89-22" href="#__codelineno-89-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-89-23" name="__codelineno-89-23" href="#__codelineno-89-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-90-1" name="__codelineno-90-1" href="#__codelineno-90-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert</span><span class="p">}</span>
-<a id="__codelineno-90-2" name="__codelineno-90-2" href="#__codelineno-90-2"></a>
-<a id="__codelineno-90-3" name="__codelineno-90-3" href="#__codelineno-90-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert_helper</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-90-1" name="__codelineno-90-1" href="#__codelineno-90-1"></a><span class="c1">### ノードを挿入 ###</span>
+<a id="__codelineno-90-2" name="__codelineno-90-2" href="#__codelineno-90-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-90-3" name="__codelineno-90-3" href="#__codelineno-90-3"></a><span class="w">  </span><span class="vi">@root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insert_helper</span><span class="p">(</span><span class="vi">@root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-90-4" name="__codelineno-90-4" href="#__codelineno-90-4"></a><span class="k">end</span>
+<a id="__codelineno-90-5" name="__codelineno-90-5" href="#__codelineno-90-5"></a>
+<a id="__codelineno-90-6" name="__codelineno-90-6" href="#__codelineno-90-6"></a><span class="c1">### ノードを挿入 ###</span>
+<a id="__codelineno-90-7" name="__codelineno-90-7" href="#__codelineno-90-7"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-90-8" name="__codelineno-90-8" href="#__codelineno-90-8"></a><span class="w">  </span><span class="vi">@root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insert_helper</span><span class="p">(</span><span class="vi">@root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-90-9" name="__codelineno-90-9" href="#__codelineno-90-9"></a><span class="k">end</span>
+<a id="__codelineno-90-10" name="__codelineno-90-10" href="#__codelineno-90-10"></a>
+<a id="__codelineno-90-11" name="__codelineno-90-11" href="#__codelineno-90-11"></a><span class="c1"># ## ノードを再帰的に挿入（補助メソッド）###</span>
+<a id="__codelineno-90-12" name="__codelineno-90-12" href="#__codelineno-90-12"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert_helper</span><span class="p">(</span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-90-13" name="__codelineno-90-13" href="#__codelineno-90-13"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-90-14" name="__codelineno-90-14" href="#__codelineno-90-14"></a><span class="w">  </span><span class="c1"># 1. 挿入位置を探索してノードを挿入</span>
+<a id="__codelineno-90-15" name="__codelineno-90-15" href="#__codelineno-90-15"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-90-16" name="__codelineno-90-16" href="#__codelineno-90-16"></a><span class="w">    </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insert_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-90-17" name="__codelineno-90-17" href="#__codelineno-90-17"></a><span class="w">  </span><span class="k">elsif</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-90-18" name="__codelineno-90-18" href="#__codelineno-90-18"></a><span class="w">    </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insert_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-90-19" name="__codelineno-90-19" href="#__codelineno-90-19"></a><span class="w">  </span><span class="k">else</span>
+<a id="__codelineno-90-20" name="__codelineno-90-20" href="#__codelineno-90-20"></a><span class="w">    </span><span class="c1"># 重複ノードは挿入せず、そのまま返す</span>
+<a id="__codelineno-90-21" name="__codelineno-90-21" href="#__codelineno-90-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-90-22" name="__codelineno-90-22" href="#__codelineno-90-22"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-90-23" name="__codelineno-90-23" href="#__codelineno-90-23"></a><span class="w">  </span><span class="c1"># ノードの高さを更新する</span>
+<a id="__codelineno-90-24" name="__codelineno-90-24" href="#__codelineno-90-24"></a><span class="w">  </span><span class="n">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-90-25" name="__codelineno-90-25" href="#__codelineno-90-25"></a><span class="w">  </span><span class="c1"># 2. 回転操作を行い、部分木の平衡を回復する</span>
+<a id="__codelineno-90-26" name="__codelineno-90-26" href="#__codelineno-90-26"></a><span class="w">  </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-90-27" name="__codelineno-90-27" href="#__codelineno-90-27"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
 <h3 id="2_2">2. &nbsp; ノードの削除<a class="headerlink" href="#2_2" title="Permanent link">&para;</a></h3>
-<p>同様に、二分探索木でのノード削除方法に基づいて、下から上へ回転操作を実行してすべての不平衡ノードのバランスを回復する必要があります。コードは以下の通りです：</p>
+<p>同様に、二分探索木のノード削除メソッドを土台として、下から上へ回転操作を行い、すべての不平衡ノードを平衡に戻す必要があります。コードは次のとおりです：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="9:13"><input checked="checked" id="__tabbed_9_1" name="__tabbed_9" type="radio" /><input id="__tabbed_9_2" name="__tabbed_9" type="radio" /><input id="__tabbed_9_3" name="__tabbed_9" type="radio" /><input id="__tabbed_9_4" name="__tabbed_9" type="radio" /><input id="__tabbed_9_5" name="__tabbed_9" type="radio" /><input id="__tabbed_9_6" name="__tabbed_9" type="radio" /><input id="__tabbed_9_7" name="__tabbed_9" type="radio" /><input id="__tabbed_9_8" name="__tabbed_9" type="radio" /><input id="__tabbed_9_9" name="__tabbed_9" type="radio" /><input id="__tabbed_9_10" name="__tabbed_9" type="radio" /><input id="__tabbed_9_11" name="__tabbed_9" type="radio" /><input id="__tabbed_9_12" name="__tabbed_9" type="radio" /><input id="__tabbed_9_13" name="__tabbed_9" type="radio" /><div class="tabbed-labels"><label for="__tabbed_9_1">Python</label><label for="__tabbed_9_2">C++</label><label for="__tabbed_9_3">Java</label><label for="__tabbed_9_4">C#</label><label for="__tabbed_9_5">Go</label><label for="__tabbed_9_6">Swift</label><label for="__tabbed_9_7">JS</label><label for="__tabbed_9_8">TS</label><label for="__tabbed_9_9">Dart</label><label for="__tabbed_9_10">Rust</label><label for="__tabbed_9_11">C</label><label for="__tabbed_9_12">Kotlin</label><label for="__tabbed_9_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
@@ -5590,10 +6534,10 @@
 <a id="__codelineno-91-3" name="__codelineno-91-3" href="#__codelineno-91-3"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">_root</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">remove_helper</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_root</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
 <a id="__codelineno-91-4" name="__codelineno-91-4" href="#__codelineno-91-4"></a>
 <a id="__codelineno-91-5" name="__codelineno-91-5" href="#__codelineno-91-5"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove_helper</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-91-6" name="__codelineno-91-6" href="#__codelineno-91-6"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;再帰的にノードを削除（ヘルパーメソッド）&quot;&quot;&quot;</span>
+<a id="__codelineno-91-6" name="__codelineno-91-6" href="#__codelineno-91-6"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ノードを再帰的に削除する（補助メソッド）&quot;&quot;&quot;</span>
 <a id="__codelineno-91-7" name="__codelineno-91-7" href="#__codelineno-91-7"></a>    <span class="k">if</span> <span class="n">node</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-91-8" name="__codelineno-91-8" href="#__codelineno-91-8"></a>        <span class="k">return</span> <span class="kc">None</span>
-<a id="__codelineno-91-9" name="__codelineno-91-9" href="#__codelineno-91-9"></a>    <span class="c1"># 1. ノードを見つけて削除</span>
+<a id="__codelineno-91-9" name="__codelineno-91-9" href="#__codelineno-91-9"></a>    <span class="c1"># 1. ノードを探索して削除</span>
 <a id="__codelineno-91-10" name="__codelineno-91-10" href="#__codelineno-91-10"></a>    <span class="k">if</span> <span class="n">val</span> <span class="o">&lt;</span> <span class="n">node</span><span class="o">.</span><span class="n">val</span><span class="p">:</span>
 <a id="__codelineno-91-11" name="__codelineno-91-11" href="#__codelineno-91-11"></a>        <span class="n">node</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">remove_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
 <a id="__codelineno-91-12" name="__codelineno-91-12" href="#__codelineno-91-12"></a>    <span class="k">elif</span> <span class="n">val</span> <span class="o">&gt;</span> <span class="n">node</span><span class="o">.</span><span class="n">val</span><span class="p">:</span>
@@ -5601,22 +6545,22 @@
 <a id="__codelineno-91-14" name="__codelineno-91-14" href="#__codelineno-91-14"></a>    <span class="k">else</span><span class="p">:</span>
 <a id="__codelineno-91-15" name="__codelineno-91-15" href="#__codelineno-91-15"></a>        <span class="k">if</span> <span class="n">node</span><span class="o">.</span><span class="n">left</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">node</span><span class="o">.</span><span class="n">right</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-91-16" name="__codelineno-91-16" href="#__codelineno-91-16"></a>            <span class="n">child</span> <span class="o">=</span> <span class="n">node</span><span class="o">.</span><span class="n">left</span> <span class="ow">or</span> <span class="n">node</span><span class="o">.</span><span class="n">right</span>
-<a id="__codelineno-91-17" name="__codelineno-91-17" href="#__codelineno-91-17"></a>            <span class="c1"># 子ノード数 = 0、ノードを削除して戻る</span>
+<a id="__codelineno-91-17" name="__codelineno-91-17" href="#__codelineno-91-17"></a>            <span class="c1"># 子ノード数 = 0 の場合、node をそのまま削除して返す</span>
 <a id="__codelineno-91-18" name="__codelineno-91-18" href="#__codelineno-91-18"></a>            <span class="k">if</span> <span class="n">child</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-91-19" name="__codelineno-91-19" href="#__codelineno-91-19"></a>                <span class="k">return</span> <span class="kc">None</span>
-<a id="__codelineno-91-20" name="__codelineno-91-20" href="#__codelineno-91-20"></a>            <span class="c1"># 子ノード数 = 1、ノードを削除</span>
+<a id="__codelineno-91-20" name="__codelineno-91-20" href="#__codelineno-91-20"></a>            <span class="c1"># 子ノード数 = 1 の場合、node をそのまま削除する</span>
 <a id="__codelineno-91-21" name="__codelineno-91-21" href="#__codelineno-91-21"></a>            <span class="k">else</span><span class="p">:</span>
 <a id="__codelineno-91-22" name="__codelineno-91-22" href="#__codelineno-91-22"></a>                <span class="n">node</span> <span class="o">=</span> <span class="n">child</span>
 <a id="__codelineno-91-23" name="__codelineno-91-23" href="#__codelineno-91-23"></a>        <span class="k">else</span><span class="p">:</span>
-<a id="__codelineno-91-24" name="__codelineno-91-24" href="#__codelineno-91-24"></a>            <span class="c1"># 子ノード数 = 2、中順走査の次のノードを削除し、それで現在のノードを置き換え</span>
+<a id="__codelineno-91-24" name="__codelineno-91-24" href="#__codelineno-91-24"></a>            <span class="c1"># 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える</span>
 <a id="__codelineno-91-25" name="__codelineno-91-25" href="#__codelineno-91-25"></a>            <span class="n">temp</span> <span class="o">=</span> <span class="n">node</span><span class="o">.</span><span class="n">right</span>
 <a id="__codelineno-91-26" name="__codelineno-91-26" href="#__codelineno-91-26"></a>            <span class="k">while</span> <span class="n">temp</span><span class="o">.</span><span class="n">left</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-91-27" name="__codelineno-91-27" href="#__codelineno-91-27"></a>                <span class="n">temp</span> <span class="o">=</span> <span class="n">temp</span><span class="o">.</span><span class="n">left</span>
 <a id="__codelineno-91-28" name="__codelineno-91-28" href="#__codelineno-91-28"></a>            <span class="n">node</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">remove_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">,</span> <span class="n">temp</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
 <a id="__codelineno-91-29" name="__codelineno-91-29" href="#__codelineno-91-29"></a>            <span class="n">node</span><span class="o">.</span><span class="n">val</span> <span class="o">=</span> <span class="n">temp</span><span class="o">.</span><span class="n">val</span>
-<a id="__codelineno-91-30" name="__codelineno-91-30" href="#__codelineno-91-30"></a>    <span class="c1"># ノードの高さを更新</span>
+<a id="__codelineno-91-30" name="__codelineno-91-30" href="#__codelineno-91-30"></a>    <span class="c1"># ノードの高さを更新する</span>
 <a id="__codelineno-91-31" name="__codelineno-91-31" href="#__codelineno-91-31"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
-<a id="__codelineno-91-32" name="__codelineno-91-32" href="#__codelineno-91-32"></a>    <span class="c1"># 2. 回転操作を実行して部分木のバランスを復元</span>
+<a id="__codelineno-91-32" name="__codelineno-91-32" href="#__codelineno-91-32"></a>    <span class="c1"># 2. 回転操作を行い、部分木の平衡を回復する</span>
 <a id="__codelineno-91-33" name="__codelineno-91-33" href="#__codelineno-91-33"></a>    <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
 </code></pre></div>
 </div>
@@ -5626,11 +6570,11 @@
 <a id="__codelineno-92-3" name="__codelineno-92-3" href="#__codelineno-92-3"></a><span class="w">    </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
 <a id="__codelineno-92-4" name="__codelineno-92-4" href="#__codelineno-92-4"></a><span class="p">}</span>
 <a id="__codelineno-92-5" name="__codelineno-92-5" href="#__codelineno-92-5"></a>
-<a id="__codelineno-92-6" name="__codelineno-92-6" href="#__codelineno-92-6"></a><span class="cm">/* ノードを再帰的に削除（ヘルパーメソッド） */</span>
+<a id="__codelineno-92-6" name="__codelineno-92-6" href="#__codelineno-92-6"></a><span class="cm">/* ノードを再帰的に削除する（補助メソッド） */</span>
 <a id="__codelineno-92-7" name="__codelineno-92-7" href="#__codelineno-92-7"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">removeHelper</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-92-8" name="__codelineno-92-8" href="#__codelineno-92-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
 <a id="__codelineno-92-9" name="__codelineno-92-9" href="#__codelineno-92-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
-<a id="__codelineno-92-10" name="__codelineno-92-10" href="#__codelineno-92-10"></a><span class="w">    </span><span class="cm">/* 1. ノードを見つけて削除 */</span>
+<a id="__codelineno-92-10" name="__codelineno-92-10" href="#__codelineno-92-10"></a><span class="w">    </span><span class="cm">/* 1. ノードを探索して削除 */</span>
 <a id="__codelineno-92-11" name="__codelineno-92-11" href="#__codelineno-92-11"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">)</span>
 <a id="__codelineno-92-12" name="__codelineno-92-12" href="#__codelineno-92-12"></a><span class="w">        </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
 <a id="__codelineno-92-13" name="__codelineno-92-13" href="#__codelineno-92-13"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">)</span>
@@ -5638,18 +6582,18 @@
 <a id="__codelineno-92-15" name="__codelineno-92-15" href="#__codelineno-92-15"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-92-16" name="__codelineno-92-16" href="#__codelineno-92-16"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-92-17" name="__codelineno-92-17" href="#__codelineno-92-17"></a><span class="w">            </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
-<a id="__codelineno-92-18" name="__codelineno-92-18" href="#__codelineno-92-18"></a><span class="w">            </span><span class="c1">// 子ノード数 = 0、ノードを削除して戻る</span>
+<a id="__codelineno-92-18" name="__codelineno-92-18" href="#__codelineno-92-18"></a><span class="w">            </span><span class="c1">// 子ノード数 = 0 の場合、node をそのまま削除して返す</span>
 <a id="__codelineno-92-19" name="__codelineno-92-19" href="#__codelineno-92-19"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">child</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-92-20" name="__codelineno-92-20" href="#__codelineno-92-20"></a><span class="w">                </span><span class="k">delete</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
 <a id="__codelineno-92-21" name="__codelineno-92-21" href="#__codelineno-92-21"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
 <a id="__codelineno-92-22" name="__codelineno-92-22" href="#__codelineno-92-22"></a><span class="w">            </span><span class="p">}</span>
-<a id="__codelineno-92-23" name="__codelineno-92-23" href="#__codelineno-92-23"></a><span class="w">            </span><span class="c1">// 子ノード数 = 1、ノードを削除</span>
+<a id="__codelineno-92-23" name="__codelineno-92-23" href="#__codelineno-92-23"></a><span class="w">            </span><span class="c1">// 子ノード数 = 1 の場合、node をそのまま削除する</span>
 <a id="__codelineno-92-24" name="__codelineno-92-24" href="#__codelineno-92-24"></a><span class="w">            </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-92-25" name="__codelineno-92-25" href="#__codelineno-92-25"></a><span class="w">                </span><span class="k">delete</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
 <a id="__codelineno-92-26" name="__codelineno-92-26" href="#__codelineno-92-26"></a><span class="w">                </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
 <a id="__codelineno-92-27" name="__codelineno-92-27" href="#__codelineno-92-27"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-92-28" name="__codelineno-92-28" href="#__codelineno-92-28"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-92-29" name="__codelineno-92-29" href="#__codelineno-92-29"></a><span class="w">            </span><span class="c1">// 子ノード数 = 2、中順走査の次のノードを削除し、現在のノードと置き換える</span>
+<a id="__codelineno-92-29" name="__codelineno-92-29" href="#__codelineno-92-29"></a><span class="w">            </span><span class="c1">// 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える</span>
 <a id="__codelineno-92-30" name="__codelineno-92-30" href="#__codelineno-92-30"></a><span class="w">            </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
 <a id="__codelineno-92-31" name="__codelineno-92-31" href="#__codelineno-92-31"></a><span class="w">            </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">temp</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-92-32" name="__codelineno-92-32" href="#__codelineno-92-32"></a><span class="w">                </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">;</span>
@@ -5659,10 +6603,10 @@
 <a id="__codelineno-92-36" name="__codelineno-92-36" href="#__codelineno-92-36"></a><span class="w">            </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tempVal</span><span class="p">;</span>
 <a id="__codelineno-92-37" name="__codelineno-92-37" href="#__codelineno-92-37"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-92-38" name="__codelineno-92-38" href="#__codelineno-92-38"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-92-39" name="__codelineno-92-39" href="#__codelineno-92-39"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// ノードの高さを更新</span>
-<a id="__codelineno-92-40" name="__codelineno-92-40" href="#__codelineno-92-40"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を実行して部分木の平衡を回復 */</span>
+<a id="__codelineno-92-39" name="__codelineno-92-39" href="#__codelineno-92-39"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-92-40" name="__codelineno-92-40" href="#__codelineno-92-40"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を行い、部分木の平衡を回復する */</span>
 <a id="__codelineno-92-41" name="__codelineno-92-41" href="#__codelineno-92-41"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
-<a id="__codelineno-92-42" name="__codelineno-92-42" href="#__codelineno-92-42"></a><span class="w">    </span><span class="c1">// 部分木のルートノードを返す</span>
+<a id="__codelineno-92-42" name="__codelineno-92-42" href="#__codelineno-92-42"></a><span class="w">    </span><span class="c1">// 部分木の根ノードを返す</span>
 <a id="__codelineno-92-43" name="__codelineno-92-43" href="#__codelineno-92-43"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
 <a id="__codelineno-92-44" name="__codelineno-92-44" href="#__codelineno-92-44"></a><span class="p">}</span>
 </code></pre></div>
@@ -5673,11 +6617,11 @@
 <a id="__codelineno-93-3" name="__codelineno-93-3" href="#__codelineno-93-3"></a><span class="w">    </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
 <a id="__codelineno-93-4" name="__codelineno-93-4" href="#__codelineno-93-4"></a><span class="p">}</span>
 <a id="__codelineno-93-5" name="__codelineno-93-5" href="#__codelineno-93-5"></a>
-<a id="__codelineno-93-6" name="__codelineno-93-6" href="#__codelineno-93-6"></a><span class="cm">/* 再帰的にノードを削除（補助メソッド） */</span>
+<a id="__codelineno-93-6" name="__codelineno-93-6" href="#__codelineno-93-6"></a><span class="cm">/* ノードを再帰的に削除する（補助メソッド） */</span>
 <a id="__codelineno-93-7" name="__codelineno-93-7" href="#__codelineno-93-7"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">removeHelper</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-93-8" name="__codelineno-93-8" href="#__codelineno-93-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
 <a id="__codelineno-93-9" name="__codelineno-93-9" href="#__codelineno-93-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
-<a id="__codelineno-93-10" name="__codelineno-93-10" href="#__codelineno-93-10"></a><span class="w">    </span><span class="cm">/* 1. ノードを見つけて削除 */</span>
+<a id="__codelineno-93-10" name="__codelineno-93-10" href="#__codelineno-93-10"></a><span class="w">    </span><span class="cm">/* 1. ノードを探索して削除 */</span>
 <a id="__codelineno-93-11" name="__codelineno-93-11" href="#__codelineno-93-11"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">)</span>
 <a id="__codelineno-93-12" name="__codelineno-93-12" href="#__codelineno-93-12"></a><span class="w">        </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
 <a id="__codelineno-93-13" name="__codelineno-93-13" href="#__codelineno-93-13"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">)</span>
@@ -5685,14 +6629,14 @@
 <a id="__codelineno-93-15" name="__codelineno-93-15" href="#__codelineno-93-15"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-93-16" name="__codelineno-93-16" href="#__codelineno-93-16"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-93-17" name="__codelineno-93-17" href="#__codelineno-93-17"></a><span class="w">            </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">;</span>
-<a id="__codelineno-93-18" name="__codelineno-93-18" href="#__codelineno-93-18"></a><span class="w">            </span><span class="c1">// 子ノード数 = 0、ノードを削除して戻る</span>
+<a id="__codelineno-93-18" name="__codelineno-93-18" href="#__codelineno-93-18"></a><span class="w">            </span><span class="c1">// 子ノード数 = 0 の場合、node をそのまま削除して返す</span>
 <a id="__codelineno-93-19" name="__codelineno-93-19" href="#__codelineno-93-19"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">child</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
 <a id="__codelineno-93-20" name="__codelineno-93-20" href="#__codelineno-93-20"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
-<a id="__codelineno-93-21" name="__codelineno-93-21" href="#__codelineno-93-21"></a><span class="w">            </span><span class="c1">// 子ノード数 = 1、ノードを削除</span>
+<a id="__codelineno-93-21" name="__codelineno-93-21" href="#__codelineno-93-21"></a><span class="w">            </span><span class="c1">// 子ノード数 = 1 の場合、node をそのまま削除する</span>
 <a id="__codelineno-93-22" name="__codelineno-93-22" href="#__codelineno-93-22"></a><span class="w">            </span><span class="k">else</span>
 <a id="__codelineno-93-23" name="__codelineno-93-23" href="#__codelineno-93-23"></a><span class="w">                </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
 <a id="__codelineno-93-24" name="__codelineno-93-24" href="#__codelineno-93-24"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-93-25" name="__codelineno-93-25" href="#__codelineno-93-25"></a><span class="w">            </span><span class="c1">// 子ノード数 = 2、中順走査の次のノードを削除し、現在のノードをそれで置き換える</span>
+<a id="__codelineno-93-25" name="__codelineno-93-25" href="#__codelineno-93-25"></a><span class="w">            </span><span class="c1">// 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える</span>
 <a id="__codelineno-93-26" name="__codelineno-93-26" href="#__codelineno-93-26"></a><span class="w">            </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">;</span>
 <a id="__codelineno-93-27" name="__codelineno-93-27" href="#__codelineno-93-27"></a><span class="w">            </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">temp</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-93-28" name="__codelineno-93-28" href="#__codelineno-93-28"></a><span class="w">                </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="na">left</span><span class="p">;</span>
@@ -5701,8 +6645,8 @@
 <a id="__codelineno-93-31" name="__codelineno-93-31" href="#__codelineno-93-31"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
 <a id="__codelineno-93-32" name="__codelineno-93-32" href="#__codelineno-93-32"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-93-33" name="__codelineno-93-33" href="#__codelineno-93-33"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-93-34" name="__codelineno-93-34" href="#__codelineno-93-34"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// ノードの高さを更新</span>
-<a id="__codelineno-93-35" name="__codelineno-93-35" href="#__codelineno-93-35"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を実行して部分木の平衡を回復 */</span>
+<a id="__codelineno-93-34" name="__codelineno-93-34" href="#__codelineno-93-34"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-93-35" name="__codelineno-93-35" href="#__codelineno-93-35"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を行い、部分木の平衡を回復する */</span>
 <a id="__codelineno-93-36" name="__codelineno-93-36" href="#__codelineno-93-36"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
 <a id="__codelineno-93-37" name="__codelineno-93-37" href="#__codelineno-93-37"></a><span class="w">    </span><span class="c1">// 部分木の根ノードを返す</span>
 <a id="__codelineno-93-38" name="__codelineno-93-38" href="#__codelineno-93-38"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
@@ -5710,74 +6654,465 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-94-1" name="__codelineno-94-1" href="#__codelineno-94-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Remove</span><span class="p">}</span>
-<a id="__codelineno-94-2" name="__codelineno-94-2" href="#__codelineno-94-2"></a>
-<a id="__codelineno-94-3" name="__codelineno-94-3" href="#__codelineno-94-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">RemoveHelper</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-94-1" name="__codelineno-94-1" href="#__codelineno-94-1"></a><span class="cm">/* ノードを削除 */</span>
+<a id="__codelineno-94-2" name="__codelineno-94-2" href="#__codelineno-94-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-94-3" name="__codelineno-94-3" href="#__codelineno-94-3"></a><span class="w">    </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">RemoveHelper</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-94-4" name="__codelineno-94-4" href="#__codelineno-94-4"></a><span class="p">}</span>
+<a id="__codelineno-94-5" name="__codelineno-94-5" href="#__codelineno-94-5"></a>
+<a id="__codelineno-94-6" name="__codelineno-94-6" href="#__codelineno-94-6"></a><span class="cm">/* ノードを再帰的に削除する（補助メソッド） */</span>
+<a id="__codelineno-94-7" name="__codelineno-94-7" href="#__codelineno-94-7"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">RemoveHelper</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-94-8" name="__codelineno-94-8" href="#__codelineno-94-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
+<a id="__codelineno-94-9" name="__codelineno-94-9" href="#__codelineno-94-9"></a><span class="w">    </span><span class="cm">/* 1. ノードを探索して削除 */</span>
+<a id="__codelineno-94-10" name="__codelineno-94-10" href="#__codelineno-94-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-94-11" name="__codelineno-94-11" href="#__codelineno-94-11"></a><span class="w">        </span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">RemoveHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-94-12" name="__codelineno-94-12" href="#__codelineno-94-12"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="nf">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-94-13" name="__codelineno-94-13" href="#__codelineno-94-13"></a><span class="w">        </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">RemoveHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-94-14" name="__codelineno-94-14" href="#__codelineno-94-14"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-94-15" name="__codelineno-94-15" href="#__codelineno-94-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-94-16" name="__codelineno-94-16" href="#__codelineno-94-16"></a><span class="w">            </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">??</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-94-17" name="__codelineno-94-17" href="#__codelineno-94-17"></a><span class="w">            </span><span class="c1">// 子ノード数 = 0 の場合、node をそのまま削除して返す</span>
+<a id="__codelineno-94-18" name="__codelineno-94-18" href="#__codelineno-94-18"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">child</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span>
+<a id="__codelineno-94-19" name="__codelineno-94-19" href="#__codelineno-94-19"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
+<a id="__codelineno-94-20" name="__codelineno-94-20" href="#__codelineno-94-20"></a><span class="w">            </span><span class="c1">// 子ノード数 = 1 の場合、node をそのまま削除する</span>
+<a id="__codelineno-94-21" name="__codelineno-94-21" href="#__codelineno-94-21"></a><span class="w">            </span><span class="k">else</span>
+<a id="__codelineno-94-22" name="__codelineno-94-22" href="#__codelineno-94-22"></a><span class="w">                </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-94-23" name="__codelineno-94-23" href="#__codelineno-94-23"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-94-24" name="__codelineno-94-24" href="#__codelineno-94-24"></a><span class="w">            </span><span class="c1">// 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える</span>
+<a id="__codelineno-94-25" name="__codelineno-94-25" href="#__codelineno-94-25"></a><span class="w">            </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-94-26" name="__codelineno-94-26" href="#__codelineno-94-26"></a><span class="w">            </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">temp</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-94-27" name="__codelineno-94-27" href="#__codelineno-94-27"></a><span class="w">                </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-94-28" name="__codelineno-94-28" href="#__codelineno-94-28"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-94-29" name="__codelineno-94-29" href="#__codelineno-94-29"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">RemoveHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="n">val</span><span class="o">!</span><span class="p">.</span><span class="n">Value</span><span class="p">);</span>
+<a id="__codelineno-94-30" name="__codelineno-94-30" href="#__codelineno-94-30"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-94-31" name="__codelineno-94-31" href="#__codelineno-94-31"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-94-32" name="__codelineno-94-32" href="#__codelineno-94-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-94-33" name="__codelineno-94-33" href="#__codelineno-94-33"></a><span class="w">    </span><span class="n">UpdateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w">  </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-94-34" name="__codelineno-94-34" href="#__codelineno-94-34"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を行い、部分木の平衡を回復する */</span>
+<a id="__codelineno-94-35" name="__codelineno-94-35" href="#__codelineno-94-35"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-94-36" name="__codelineno-94-36" href="#__codelineno-94-36"></a><span class="w">    </span><span class="c1">// 部分木の根ノードを返す</span>
+<a id="__codelineno-94-37" name="__codelineno-94-37" href="#__codelineno-94-37"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-94-38" name="__codelineno-94-38" href="#__codelineno-94-38"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-95-1" name="__codelineno-95-1" href="#__codelineno-95-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">remove</span><span class="p">}</span>
-<a id="__codelineno-95-2" name="__codelineno-95-2" href="#__codelineno-95-2"></a>
-<a id="__codelineno-95-3" name="__codelineno-95-3" href="#__codelineno-95-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">removeHelper</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-95-1" name="__codelineno-95-1" href="#__codelineno-95-1"></a><span class="cm">/* ノードを削除 */</span>
+<a id="__codelineno-95-2" name="__codelineno-95-2" href="#__codelineno-95-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">aVLTree</span><span class="p">)</span><span class="w"> </span><span class="nx">remove</span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-95-3" name="__codelineno-95-3" href="#__codelineno-95-3"></a><span class="w">    </span><span class="nx">t</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">removeHelper</span><span class="p">(</span><span class="nx">t</span><span class="p">.</span><span class="nx">root</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">)</span>
+<a id="__codelineno-95-4" name="__codelineno-95-4" href="#__codelineno-95-4"></a><span class="p">}</span>
+<a id="__codelineno-95-5" name="__codelineno-95-5" href="#__codelineno-95-5"></a>
+<a id="__codelineno-95-6" name="__codelineno-95-6" href="#__codelineno-95-6"></a><span class="cm">/* ノードを再帰的に削除する（補助関数） */</span>
+<a id="__codelineno-95-7" name="__codelineno-95-7" href="#__codelineno-95-7"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">aVLTree</span><span class="p">)</span><span class="w"> </span><span class="nx">removeHelper</span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-95-8" name="__codelineno-95-8" href="#__codelineno-95-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-95-9" name="__codelineno-95-9" href="#__codelineno-95-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-95-10" name="__codelineno-95-10" href="#__codelineno-95-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-95-11" name="__codelineno-95-11" href="#__codelineno-95-11"></a><span class="w">    </span><span class="cm">/* 1. ノードを探索して削除 */</span>
+<a id="__codelineno-95-12" name="__codelineno-95-12" href="#__codelineno-95-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Val</span><span class="p">.(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-95-13" name="__codelineno-95-13" href="#__codelineno-95-13"></a><span class="w">        </span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">removeHelper</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">)</span>
+<a id="__codelineno-95-14" name="__codelineno-95-14" href="#__codelineno-95-14"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Val</span><span class="p">.(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-95-15" name="__codelineno-95-15" href="#__codelineno-95-15"></a><span class="w">        </span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">removeHelper</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">)</span>
+<a id="__codelineno-95-16" name="__codelineno-95-16" href="#__codelineno-95-16"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-95-17" name="__codelineno-95-17" href="#__codelineno-95-17"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-95-18" name="__codelineno-95-18" href="#__codelineno-95-18"></a><span class="w">            </span><span class="nx">child</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span>
+<a id="__codelineno-95-19" name="__codelineno-95-19" href="#__codelineno-95-19"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-95-20" name="__codelineno-95-20" href="#__codelineno-95-20"></a><span class="w">                </span><span class="nx">child</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span>
+<a id="__codelineno-95-21" name="__codelineno-95-21" href="#__codelineno-95-21"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-95-22" name="__codelineno-95-22" href="#__codelineno-95-22"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="nx">child</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-95-23" name="__codelineno-95-23" href="#__codelineno-95-23"></a><span class="w">                </span><span class="c1">// 子ノード数 = 0 の場合、node をそのまま削除して返す</span>
+<a id="__codelineno-95-24" name="__codelineno-95-24" href="#__codelineno-95-24"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-95-25" name="__codelineno-95-25" href="#__codelineno-95-25"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-95-26" name="__codelineno-95-26" href="#__codelineno-95-26"></a><span class="w">                </span><span class="c1">// 子ノード数 = 1 の場合、node をそのまま削除する</span>
+<a id="__codelineno-95-27" name="__codelineno-95-27" href="#__codelineno-95-27"></a><span class="w">                </span><span class="nx">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">child</span>
+<a id="__codelineno-95-28" name="__codelineno-95-28" href="#__codelineno-95-28"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-95-29" name="__codelineno-95-29" href="#__codelineno-95-29"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-95-30" name="__codelineno-95-30" href="#__codelineno-95-30"></a><span class="w">            </span><span class="c1">// 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える</span>
+<a id="__codelineno-95-31" name="__codelineno-95-31" href="#__codelineno-95-31"></a><span class="w">            </span><span class="nx">temp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span>
+<a id="__codelineno-95-32" name="__codelineno-95-32" href="#__codelineno-95-32"></a><span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="nx">temp</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-95-33" name="__codelineno-95-33" href="#__codelineno-95-33"></a><span class="w">                </span><span class="nx">temp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">temp</span><span class="p">.</span><span class="nx">Left</span>
+<a id="__codelineno-95-34" name="__codelineno-95-34" href="#__codelineno-95-34"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-95-35" name="__codelineno-95-35" href="#__codelineno-95-35"></a><span class="w">            </span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">removeHelper</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="p">,</span><span class="w"> </span><span class="nx">temp</span><span class="p">.</span><span class="nx">Val</span><span class="p">.(</span><span class="kt">int</span><span class="p">))</span>
+<a id="__codelineno-95-36" name="__codelineno-95-36" href="#__codelineno-95-36"></a><span class="w">            </span><span class="nx">node</span><span class="p">.</span><span class="nx">Val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">temp</span><span class="p">.</span><span class="nx">Val</span>
+<a id="__codelineno-95-37" name="__codelineno-95-37" href="#__codelineno-95-37"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-95-38" name="__codelineno-95-38" href="#__codelineno-95-38"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-95-39" name="__codelineno-95-39" href="#__codelineno-95-39"></a><span class="w">    </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-95-40" name="__codelineno-95-40" href="#__codelineno-95-40"></a><span class="w">    </span><span class="nx">t</span><span class="p">.</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span>
+<a id="__codelineno-95-41" name="__codelineno-95-41" href="#__codelineno-95-41"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を行い、部分木の平衡を回復する */</span>
+<a id="__codelineno-95-42" name="__codelineno-95-42" href="#__codelineno-95-42"></a><span class="w">    </span><span class="nx">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">rotate</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span>
+<a id="__codelineno-95-43" name="__codelineno-95-43" href="#__codelineno-95-43"></a><span class="w">    </span><span class="c1">// 部分木の根ノードを返す</span>
+<a id="__codelineno-95-44" name="__codelineno-95-44" href="#__codelineno-95-44"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span>
+<a id="__codelineno-95-45" name="__codelineno-95-45" href="#__codelineno-95-45"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-96-1" name="__codelineno-96-1" href="#__codelineno-96-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
-<a id="__codelineno-96-2" name="__codelineno-96-2" href="#__codelineno-96-2"></a>
-<a id="__codelineno-96-3" name="__codelineno-96-3" href="#__codelineno-96-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">removeHelper</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-96-1" name="__codelineno-96-1" href="#__codelineno-96-1"></a><span class="cm">/* ノードを削除 */</span>
+<a id="__codelineno-96-2" name="__codelineno-96-2" href="#__codelineno-96-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-96-3" name="__codelineno-96-3" href="#__codelineno-96-3"></a><span class="w">    </span><span class="n">root</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-96-4" name="__codelineno-96-4" href="#__codelineno-96-4"></a><span class="p">}</span>
+<a id="__codelineno-96-5" name="__codelineno-96-5" href="#__codelineno-96-5"></a>
+<a id="__codelineno-96-6" name="__codelineno-96-6" href="#__codelineno-96-6"></a><span class="cm">/* ノードを再帰的に削除する（補助メソッド） */</span>
+<a id="__codelineno-96-7" name="__codelineno-96-7" href="#__codelineno-96-7"></a><span class="kd">func</span><span class="w"> </span><span class="nf">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-96-8" name="__codelineno-96-8" href="#__codelineno-96-8"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-96-9" name="__codelineno-96-9" href="#__codelineno-96-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-96-10" name="__codelineno-96-10" href="#__codelineno-96-10"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-96-11" name="__codelineno-96-11" href="#__codelineno-96-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-96-12" name="__codelineno-96-12" href="#__codelineno-96-12"></a><span class="w">    </span><span class="cm">/* 1. ノードを探索して削除 */</span>
+<a id="__codelineno-96-13" name="__codelineno-96-13" href="#__codelineno-96-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="p">!.</span><span class="n">val</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-96-14" name="__codelineno-96-14" href="#__codelineno-96-14"></a><span class="w">        </span><span class="n">node</span><span class="p">?.</span><span class="kr">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">?.</span><span class="kr">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-96-15" name="__codelineno-96-15" href="#__codelineno-96-15"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="p">!.</span><span class="n">val</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-96-16" name="__codelineno-96-16" href="#__codelineno-96-16"></a><span class="w">        </span><span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-96-17" name="__codelineno-96-17" href="#__codelineno-96-17"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-96-18" name="__codelineno-96-18" href="#__codelineno-96-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="p">?.</span><span class="kr">left</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-96-19" name="__codelineno-96-19" href="#__codelineno-96-19"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="nv">child</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span><span class="p">?.</span><span class="kr">left</span><span class="w"> </span><span class="p">??</span><span class="w"> </span><span class="n">node</span><span class="p">?.</span><span class="kr">right</span>
+<a id="__codelineno-96-20" name="__codelineno-96-20" href="#__codelineno-96-20"></a><span class="w">            </span><span class="c1">// 子ノード数 = 0 の場合、node をそのまま削除して返す</span>
+<a id="__codelineno-96-21" name="__codelineno-96-21" href="#__codelineno-96-21"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-96-22" name="__codelineno-96-22" href="#__codelineno-96-22"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-96-23" name="__codelineno-96-23" href="#__codelineno-96-23"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-96-24" name="__codelineno-96-24" href="#__codelineno-96-24"></a><span class="w">            </span><span class="c1">// 子ノード数 = 1 の場合、node をそのまま削除する</span>
+<a id="__codelineno-96-25" name="__codelineno-96-25" href="#__codelineno-96-25"></a><span class="w">            </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-96-26" name="__codelineno-96-26" href="#__codelineno-96-26"></a><span class="w">                </span><span class="n">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">child</span>
+<a id="__codelineno-96-27" name="__codelineno-96-27" href="#__codelineno-96-27"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-96-28" name="__codelineno-96-28" href="#__codelineno-96-28"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-96-29" name="__codelineno-96-29" href="#__codelineno-96-29"></a><span class="w">            </span><span class="c1">// 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える</span>
+<a id="__codelineno-96-30" name="__codelineno-96-30" href="#__codelineno-96-30"></a><span class="w">            </span><span class="kd">var</span><span class="w"> </span><span class="nv">temp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span><span class="p">?.</span><span class="kr">right</span>
+<a id="__codelineno-96-31" name="__codelineno-96-31" href="#__codelineno-96-31"></a><span class="w">            </span><span class="k">while</span><span class="w"> </span><span class="n">temp</span><span class="p">?.</span><span class="kr">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-96-32" name="__codelineno-96-32" href="#__codelineno-96-32"></a><span class="w">                </span><span class="n">temp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">temp</span><span class="p">?.</span><span class="kr">left</span>
+<a id="__codelineno-96-33" name="__codelineno-96-33" href="#__codelineno-96-33"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-96-34" name="__codelineno-96-34" href="#__codelineno-96-34"></a><span class="w">            </span><span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="n">temp</span><span class="p">!.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-96-35" name="__codelineno-96-35" href="#__codelineno-96-35"></a><span class="w">            </span><span class="n">node</span><span class="p">?.</span><span class="n">val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">temp</span><span class="p">!.</span><span class="n">val</span>
+<a id="__codelineno-96-36" name="__codelineno-96-36" href="#__codelineno-96-36"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-96-37" name="__codelineno-96-37" href="#__codelineno-96-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-96-38" name="__codelineno-96-38" href="#__codelineno-96-38"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-96-39" name="__codelineno-96-39" href="#__codelineno-96-39"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を行い、部分木の平衡を回復する */</span>
+<a id="__codelineno-96-40" name="__codelineno-96-40" href="#__codelineno-96-40"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-96-41" name="__codelineno-96-41" href="#__codelineno-96-41"></a><span class="w">    </span><span class="c1">// 部分木の根ノードを返す</span>
+<a id="__codelineno-96-42" name="__codelineno-96-42" href="#__codelineno-96-42"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-96-43" name="__codelineno-96-43" href="#__codelineno-96-43"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-97-1" name="__codelineno-97-1" href="#__codelineno-97-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">remove</span><span class="p">}</span>
-<a id="__codelineno-97-2" name="__codelineno-97-2" href="#__codelineno-97-2"></a>
-<a id="__codelineno-97-3" name="__codelineno-97-3" href="#__codelineno-97-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">removeHelper</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-97-1" name="__codelineno-97-1" href="#__codelineno-97-1"></a><span class="cm">/* ノードを削除 */</span>
+<a id="__codelineno-97-2" name="__codelineno-97-2" href="#__codelineno-97-2"></a><span class="nx">remove</span><span class="p">(</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-97-3" name="__codelineno-97-3" href="#__codelineno-97-3"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#removeHelper</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-97-4" name="__codelineno-97-4" href="#__codelineno-97-4"></a><span class="p">}</span>
+<a id="__codelineno-97-5" name="__codelineno-97-5" href="#__codelineno-97-5"></a>
+<a id="__codelineno-97-6" name="__codelineno-97-6" href="#__codelineno-97-6"></a><span class="cm">/* ノードを再帰的に削除する（補助メソッド） */</span>
+<a id="__codelineno-97-7" name="__codelineno-97-7" href="#__codelineno-97-7"></a><span class="n">#removeHelper</span><span class="p">(</span><span class="nx">node</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-97-8" name="__codelineno-97-8" href="#__codelineno-97-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-97-9" name="__codelineno-97-9" href="#__codelineno-97-9"></a><span class="w">    </span><span class="cm">/* 1. ノードを探索して削除 */</span>
+<a id="__codelineno-97-10" name="__codelineno-97-10" href="#__codelineno-97-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#removeHelper</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-97-11" name="__codelineno-97-11" href="#__codelineno-97-11"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">val</span><span class="p">)</span>
+<a id="__codelineno-97-12" name="__codelineno-97-12" href="#__codelineno-97-12"></a><span class="w">        </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#removeHelper</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-97-13" name="__codelineno-97-13" href="#__codelineno-97-13"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-97-14" name="__codelineno-97-14" href="#__codelineno-97-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-97-15" name="__codelineno-97-15" href="#__codelineno-97-15"></a><span class="w">            </span><span class="kd">const</span><span class="w"> </span><span class="nx">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
+<a id="__codelineno-97-16" name="__codelineno-97-16" href="#__codelineno-97-16"></a><span class="w">            </span><span class="c1">// 子ノード数 = 0 の場合、node をそのまま削除して返す</span>
+<a id="__codelineno-97-17" name="__codelineno-97-17" href="#__codelineno-97-17"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">child</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-97-18" name="__codelineno-97-18" href="#__codelineno-97-18"></a><span class="w">            </span><span class="c1">// 子ノード数 = 1 の場合、node をそのまま削除する</span>
+<a id="__codelineno-97-19" name="__codelineno-97-19" href="#__codelineno-97-19"></a><span class="w">            </span><span class="k">else</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">child</span><span class="p">;</span>
+<a id="__codelineno-97-20" name="__codelineno-97-20" href="#__codelineno-97-20"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-97-21" name="__codelineno-97-21" href="#__codelineno-97-21"></a><span class="w">            </span><span class="c1">// 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える</span>
+<a id="__codelineno-97-22" name="__codelineno-97-22" href="#__codelineno-97-22"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="nx">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
+<a id="__codelineno-97-23" name="__codelineno-97-23" href="#__codelineno-97-23"></a><span class="w">            </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">temp</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-97-24" name="__codelineno-97-24" href="#__codelineno-97-24"></a><span class="w">                </span><span class="nx">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">temp</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span>
+<a id="__codelineno-97-25" name="__codelineno-97-25" href="#__codelineno-97-25"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-97-26" name="__codelineno-97-26" href="#__codelineno-97-26"></a><span class="w">            </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#removeHelper</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">,</span><span class="w"> </span><span class="nx">temp</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-97-27" name="__codelineno-97-27" href="#__codelineno-97-27"></a><span class="w">            </span><span class="nx">node</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">temp</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-97-28" name="__codelineno-97-28" href="#__codelineno-97-28"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-97-29" name="__codelineno-97-29" href="#__codelineno-97-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-97-30" name="__codelineno-97-30" href="#__codelineno-97-30"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="n">#updateHeight</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-97-31" name="__codelineno-97-31" href="#__codelineno-97-31"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を行い、部分木の平衡を回復する */</span>
+<a id="__codelineno-97-32" name="__codelineno-97-32" href="#__codelineno-97-32"></a><span class="w">    </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#rotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
+<a id="__codelineno-97-33" name="__codelineno-97-33" href="#__codelineno-97-33"></a><span class="w">    </span><span class="c1">// 部分木の根ノードを返す</span>
+<a id="__codelineno-97-34" name="__codelineno-97-34" href="#__codelineno-97-34"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-97-35" name="__codelineno-97-35" href="#__codelineno-97-35"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-98-1" name="__codelineno-98-1" href="#__codelineno-98-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">remove</span><span class="p">}</span>
-<a id="__codelineno-98-2" name="__codelineno-98-2" href="#__codelineno-98-2"></a>
-<a id="__codelineno-98-3" name="__codelineno-98-3" href="#__codelineno-98-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">removeHelper</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-98-1" name="__codelineno-98-1" href="#__codelineno-98-1"></a><span class="cm">/* ノードを削除 */</span>
+<a id="__codelineno-98-2" name="__codelineno-98-2" href="#__codelineno-98-2"></a><span class="nx">remove</span><span class="p">(</span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-98-3" name="__codelineno-98-3" href="#__codelineno-98-3"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">removeHelper</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-98-4" name="__codelineno-98-4" href="#__codelineno-98-4"></a><span class="p">}</span>
+<a id="__codelineno-98-5" name="__codelineno-98-5" href="#__codelineno-98-5"></a>
+<a id="__codelineno-98-6" name="__codelineno-98-6" href="#__codelineno-98-6"></a><span class="cm">/* ノードを再帰的に削除する（補助メソッド） */</span>
+<a id="__codelineno-98-7" name="__codelineno-98-7" href="#__codelineno-98-7"></a><span class="nx">removeHelper</span><span class="p">(</span><span class="nx">node</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-98-8" name="__codelineno-98-8" href="#__codelineno-98-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-98-9" name="__codelineno-98-9" href="#__codelineno-98-9"></a><span class="w">    </span><span class="cm">/* 1. ノードを探索して削除 */</span>
+<a id="__codelineno-98-10" name="__codelineno-98-10" href="#__codelineno-98-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-98-11" name="__codelineno-98-11" href="#__codelineno-98-11"></a><span class="w">        </span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">removeHelper</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-98-12" name="__codelineno-98-12" href="#__codelineno-98-12"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-98-13" name="__codelineno-98-13" href="#__codelineno-98-13"></a><span class="w">        </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">removeHelper</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-98-14" name="__codelineno-98-14" href="#__codelineno-98-14"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-98-15" name="__codelineno-98-15" href="#__codelineno-98-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-98-16" name="__codelineno-98-16" href="#__codelineno-98-16"></a><span class="w">            </span><span class="kd">const</span><span class="w"> </span><span class="nx">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">node.left</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">node.right</span><span class="p">;</span>
+<a id="__codelineno-98-17" name="__codelineno-98-17" href="#__codelineno-98-17"></a><span class="w">            </span><span class="c1">// 子ノード数 = 0 の場合、node をそのまま削除して返す</span>
+<a id="__codelineno-98-18" name="__codelineno-98-18" href="#__codelineno-98-18"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">child</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-98-19" name="__codelineno-98-19" href="#__codelineno-98-19"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-98-20" name="__codelineno-98-20" href="#__codelineno-98-20"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-98-21" name="__codelineno-98-21" href="#__codelineno-98-21"></a><span class="w">                </span><span class="c1">// 子ノード数 = 1 の場合、node をそのまま削除する</span>
+<a id="__codelineno-98-22" name="__codelineno-98-22" href="#__codelineno-98-22"></a><span class="w">                </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">child</span><span class="p">;</span>
+<a id="__codelineno-98-23" name="__codelineno-98-23" href="#__codelineno-98-23"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-98-24" name="__codelineno-98-24" href="#__codelineno-98-24"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-98-25" name="__codelineno-98-25" href="#__codelineno-98-25"></a><span class="w">            </span><span class="c1">// 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える</span>
+<a id="__codelineno-98-26" name="__codelineno-98-26" href="#__codelineno-98-26"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="nx">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
+<a id="__codelineno-98-27" name="__codelineno-98-27" href="#__codelineno-98-27"></a><span class="w">            </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">temp</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-98-28" name="__codelineno-98-28" href="#__codelineno-98-28"></a><span class="w">                </span><span class="nx">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">temp</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span>
+<a id="__codelineno-98-29" name="__codelineno-98-29" href="#__codelineno-98-29"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-98-30" name="__codelineno-98-30" href="#__codelineno-98-30"></a><span class="w">            </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">removeHelper</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">,</span><span class="w"> </span><span class="nx">temp</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-98-31" name="__codelineno-98-31" href="#__codelineno-98-31"></a><span class="w">            </span><span class="nx">node</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">temp</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-98-32" name="__codelineno-98-32" href="#__codelineno-98-32"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-98-33" name="__codelineno-98-33" href="#__codelineno-98-33"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-98-34" name="__codelineno-98-34" href="#__codelineno-98-34"></a><span class="w">    </span><span class="k">this</span><span class="p">.</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-98-35" name="__codelineno-98-35" href="#__codelineno-98-35"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を行い、部分木の平衡を回復する */</span>
+<a id="__codelineno-98-36" name="__codelineno-98-36" href="#__codelineno-98-36"></a><span class="w">    </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">rotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
+<a id="__codelineno-98-37" name="__codelineno-98-37" href="#__codelineno-98-37"></a><span class="w">    </span><span class="c1">// 部分木の根ノードを返す</span>
+<a id="__codelineno-98-38" name="__codelineno-98-38" href="#__codelineno-98-38"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-98-39" name="__codelineno-98-39" href="#__codelineno-98-39"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-99-1" name="__codelineno-99-1" href="#__codelineno-99-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
-<a id="__codelineno-99-2" name="__codelineno-99-2" href="#__codelineno-99-2"></a>
-<a id="__codelineno-99-3" name="__codelineno-99-3" href="#__codelineno-99-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">removeHelper</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-99-1" name="__codelineno-99-1" href="#__codelineno-99-1"></a><span class="cm">/* ノードを削除 */</span>
+<a id="__codelineno-99-2" name="__codelineno-99-2" href="#__codelineno-99-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-99-3" name="__codelineno-99-3" href="#__codelineno-99-3"></a><span class="w">  </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-99-4" name="__codelineno-99-4" href="#__codelineno-99-4"></a><span class="p">}</span>
+<a id="__codelineno-99-5" name="__codelineno-99-5" href="#__codelineno-99-5"></a>
+<a id="__codelineno-99-6" name="__codelineno-99-6" href="#__codelineno-99-6"></a><span class="cm">/* ノードを再帰的に削除する（補助メソッド） */</span>
+<a id="__codelineno-99-7" name="__codelineno-99-7" href="#__codelineno-99-7"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-99-8" name="__codelineno-99-8" href="#__codelineno-99-8"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-99-9" name="__codelineno-99-9" href="#__codelineno-99-9"></a><span class="w">  </span><span class="cm">/* 1. ノードを探索して削除 */</span>
+<a id="__codelineno-99-10" name="__codelineno-99-10" href="#__codelineno-99-10"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-99-11" name="__codelineno-99-11" href="#__codelineno-99-11"></a><span class="w">    </span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-99-12" name="__codelineno-99-12" href="#__codelineno-99-12"></a><span class="w">  </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-99-13" name="__codelineno-99-13" href="#__codelineno-99-13"></a><span class="w">    </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-99-14" name="__codelineno-99-14" href="#__codelineno-99-14"></a><span class="w">  </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-99-15" name="__codelineno-99-15" href="#__codelineno-99-15"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-99-16" name="__codelineno-99-16" href="#__codelineno-99-16"></a><span class="w">      </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">??</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-99-17" name="__codelineno-99-17" href="#__codelineno-99-17"></a><span class="w">      </span><span class="c1">// 子ノード数 = 0 の場合、node をそのまま削除して返す</span>
+<a id="__codelineno-99-18" name="__codelineno-99-18" href="#__codelineno-99-18"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">child</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-99-19" name="__codelineno-99-19" href="#__codelineno-99-19"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-99-20" name="__codelineno-99-20" href="#__codelineno-99-20"></a><span class="w">      </span><span class="c1">// 子ノード数 = 1 の場合、node をそのまま削除する</span>
+<a id="__codelineno-99-21" name="__codelineno-99-21" href="#__codelineno-99-21"></a><span class="w">      </span><span class="k">else</span>
+<a id="__codelineno-99-22" name="__codelineno-99-22" href="#__codelineno-99-22"></a><span class="w">        </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-99-23" name="__codelineno-99-23" href="#__codelineno-99-23"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-99-24" name="__codelineno-99-24" href="#__codelineno-99-24"></a><span class="w">      </span><span class="c1">// 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える</span>
+<a id="__codelineno-99-25" name="__codelineno-99-25" href="#__codelineno-99-25"></a><span class="w">      </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-99-26" name="__codelineno-99-26" href="#__codelineno-99-26"></a><span class="w">      </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">temp</span><span class="o">!</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-99-27" name="__codelineno-99-27" href="#__codelineno-99-27"></a><span class="w">        </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-99-28" name="__codelineno-99-28" href="#__codelineno-99-28"></a><span class="w">      </span><span class="p">}</span>
+<a id="__codelineno-99-29" name="__codelineno-99-29" href="#__codelineno-99-29"></a><span class="w">      </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-99-30" name="__codelineno-99-30" href="#__codelineno-99-30"></a><span class="w">      </span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-99-31" name="__codelineno-99-31" href="#__codelineno-99-31"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-99-32" name="__codelineno-99-32" href="#__codelineno-99-32"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-99-33" name="__codelineno-99-33" href="#__codelineno-99-33"></a><span class="w">  </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-99-34" name="__codelineno-99-34" href="#__codelineno-99-34"></a><span class="w">  </span><span class="cm">/* 2. 回転操作を行い、部分木の平衡を回復する */</span>
+<a id="__codelineno-99-35" name="__codelineno-99-35" href="#__codelineno-99-35"></a><span class="w">  </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-99-36" name="__codelineno-99-36" href="#__codelineno-99-36"></a><span class="w">  </span><span class="c1">// 部分木の根ノードを返す</span>
+<a id="__codelineno-99-37" name="__codelineno-99-37" href="#__codelineno-99-37"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-99-38" name="__codelineno-99-38" href="#__codelineno-99-38"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-100-1" name="__codelineno-100-1" href="#__codelineno-100-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
-<a id="__codelineno-100-2" name="__codelineno-100-2" href="#__codelineno-100-2"></a>
-<a id="__codelineno-100-3" name="__codelineno-100-3" href="#__codelineno-100-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">remove_helper</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-100-1" name="__codelineno-100-1" href="#__codelineno-100-1"></a><span class="cm">/* ノードを削除 */</span>
+<a id="__codelineno-100-2" name="__codelineno-100-2" href="#__codelineno-100-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-3" name="__codelineno-100-3" href="#__codelineno-100-3"></a><span class="w">    </span><span class="bp">Self</span><span class="p">::</span><span class="n">remove_helper</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">root</span><span class="p">.</span><span class="n">clone</span><span class="p">(),</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-100-4" name="__codelineno-100-4" href="#__codelineno-100-4"></a><span class="p">}</span>
+<a id="__codelineno-100-5" name="__codelineno-100-5" href="#__codelineno-100-5"></a>
+<a id="__codelineno-100-6" name="__codelineno-100-6" href="#__codelineno-100-6"></a><span class="cm">/* ノードを再帰的に削除する（補助メソッド） */</span>
+<a id="__codelineno-100-7" name="__codelineno-100-7" href="#__codelineno-100-7"></a><span class="k">fn</span><span class="w"> </span><span class="nf">remove_helper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="nc">OptionTreeNodeRc</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">OptionTreeNodeRc</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-8" name="__codelineno-100-8" href="#__codelineno-100-8"></a><span class="w">    </span><span class="k">match</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-9" name="__codelineno-100-9" href="#__codelineno-100-9"></a><span class="w">        </span><span class="nb">Some</span><span class="p">(</span><span class="k">mut</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-10" name="__codelineno-100-10" href="#__codelineno-100-10"></a><span class="w">            </span><span class="cm">/* 1. ノードを探索して削除 */</span>
+<a id="__codelineno-100-11" name="__codelineno-100-11" href="#__codelineno-100-11"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-12" name="__codelineno-100-12" href="#__codelineno-100-12"></a><span class="w">                </span><span class="kd">let</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-100-13" name="__codelineno-100-13" href="#__codelineno-100-13"></a><span class="w">                </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span><span class="p">::</span><span class="n">remove_helper</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-100-14" name="__codelineno-100-14" href="#__codelineno-100-14"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-15" name="__codelineno-100-15" href="#__codelineno-100-15"></a><span class="w">                </span><span class="kd">let</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-100-16" name="__codelineno-100-16" href="#__codelineno-100-16"></a><span class="w">                </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span><span class="p">::</span><span class="n">remove_helper</span><span class="p">(</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-100-17" name="__codelineno-100-17" href="#__codelineno-100-17"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-18" name="__codelineno-100-18" href="#__codelineno-100-18"></a><span class="w">                </span><span class="kd">let</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">is_some</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-19" name="__codelineno-100-19" href="#__codelineno-100-19"></a><span class="w">                    </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">()</span>
+<a id="__codelineno-100-20" name="__codelineno-100-20" href="#__codelineno-100-20"></a><span class="w">                </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-21" name="__codelineno-100-21" href="#__codelineno-100-21"></a><span class="w">                    </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">()</span>
+<a id="__codelineno-100-22" name="__codelineno-100-22" href="#__codelineno-100-22"></a><span class="w">                </span><span class="p">};</span>
+<a id="__codelineno-100-23" name="__codelineno-100-23" href="#__codelineno-100-23"></a><span class="w">                </span><span class="k">match</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-24" name="__codelineno-100-24" href="#__codelineno-100-24"></a><span class="w">                    </span><span class="c1">// 子ノード数 = 0 の場合、node をそのまま削除して返す</span>
+<a id="__codelineno-100-25" name="__codelineno-100-25" href="#__codelineno-100-25"></a><span class="w">                    </span><span class="nb">None</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-26" name="__codelineno-100-26" href="#__codelineno-100-26"></a><span class="w">                        </span><span class="k">return</span><span class="w"> </span><span class="nb">None</span><span class="p">;</span>
+<a id="__codelineno-100-27" name="__codelineno-100-27" href="#__codelineno-100-27"></a><span class="w">                    </span><span class="p">}</span>
+<a id="__codelineno-100-28" name="__codelineno-100-28" href="#__codelineno-100-28"></a><span class="w">                    </span><span class="c1">// 子ノード数 = 1 の場合、node をそのまま削除する</span>
+<a id="__codelineno-100-29" name="__codelineno-100-29" href="#__codelineno-100-29"></a><span class="w">                    </span><span class="nb">Some</span><span class="p">(</span><span class="n">child</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">,</span>
+<a id="__codelineno-100-30" name="__codelineno-100-30" href="#__codelineno-100-30"></a><span class="w">                </span><span class="p">}</span>
+<a id="__codelineno-100-31" name="__codelineno-100-31" href="#__codelineno-100-31"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-32" name="__codelineno-100-32" href="#__codelineno-100-32"></a><span class="w">                </span><span class="c1">// 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える</span>
+<a id="__codelineno-100-33" name="__codelineno-100-33" href="#__codelineno-100-33"></a><span class="w">                </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span>
+<a id="__codelineno-100-34" name="__codelineno-100-34" href="#__codelineno-100-34"></a><span class="w">                </span><span class="k">loop</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-35" name="__codelineno-100-35" href="#__codelineno-100-35"></a><span class="w">                    </span><span class="kd">let</span><span class="w"> </span><span class="n">temp_left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-100-36" name="__codelineno-100-36" href="#__codelineno-100-36"></a><span class="w">                    </span><span class="k">if</span><span class="w"> </span><span class="n">temp_left</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-37" name="__codelineno-100-37" href="#__codelineno-100-37"></a><span class="w">                        </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-100-38" name="__codelineno-100-38" href="#__codelineno-100-38"></a><span class="w">                    </span><span class="p">}</span>
+<a id="__codelineno-100-39" name="__codelineno-100-39" href="#__codelineno-100-39"></a><span class="w">                    </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp_left</span><span class="p">.</span><span class="n">unwrap</span><span class="p">();</span>
+<a id="__codelineno-100-40" name="__codelineno-100-40" href="#__codelineno-100-40"></a><span class="w">                </span><span class="p">}</span>
+<a id="__codelineno-100-41" name="__codelineno-100-41" href="#__codelineno-100-41"></a><span class="w">                </span><span class="kd">let</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-100-42" name="__codelineno-100-42" href="#__codelineno-100-42"></a><span class="w">                </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span><span class="p">::</span><span class="n">remove_helper</span><span class="p">(</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-100-43" name="__codelineno-100-43" href="#__codelineno-100-43"></a><span class="w">                </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-100-44" name="__codelineno-100-44" href="#__codelineno-100-44"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-100-45" name="__codelineno-100-45" href="#__codelineno-100-45"></a><span class="w">            </span><span class="bp">Self</span><span class="p">::</span><span class="n">update_height</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">()));</span><span class="w"> </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-100-46" name="__codelineno-100-46" href="#__codelineno-100-46"></a>
+<a id="__codelineno-100-47" name="__codelineno-100-47" href="#__codelineno-100-47"></a><span class="w">            </span><span class="cm">/* 2. 回転操作を行い、部分木の平衡を回復する */</span>
+<a id="__codelineno-100-48" name="__codelineno-100-48" href="#__codelineno-100-48"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span><span class="p">::</span><span class="n">rotate</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)).</span><span class="n">unwrap</span><span class="p">();</span>
+<a id="__codelineno-100-49" name="__codelineno-100-49" href="#__codelineno-100-49"></a><span class="w">            </span><span class="c1">// 部分木の根ノードを返す</span>
+<a id="__codelineno-100-50" name="__codelineno-100-50" href="#__codelineno-100-50"></a><span class="w">            </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-100-51" name="__codelineno-100-51" href="#__codelineno-100-51"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-100-52" name="__codelineno-100-52" href="#__codelineno-100-52"></a><span class="w">        </span><span class="nb">None</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span>
+<a id="__codelineno-100-53" name="__codelineno-100-53" href="#__codelineno-100-53"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-100-54" name="__codelineno-100-54" href="#__codelineno-100-54"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-101-1" name="__codelineno-101-1" href="#__codelineno-101-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">removeItem</span><span class="p">}</span>
-<a id="__codelineno-101-2" name="__codelineno-101-2" href="#__codelineno-101-2"></a>
-<a id="__codelineno-101-3" name="__codelineno-101-3" href="#__codelineno-101-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">removeHelper</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-101-1" name="__codelineno-101-1" href="#__codelineno-101-1"></a><span class="cm">/* ノードを削除 */</span>
+<a id="__codelineno-101-2" name="__codelineno-101-2" href="#__codelineno-101-2"></a><span class="c1">// stdio.h を導入しているため、ここでは remove 識別子を使えない</span>
+<a id="__codelineno-101-3" name="__codelineno-101-3" href="#__codelineno-101-3"></a><span class="kt">void</span><span class="w"> </span><span class="nf">removeItem</span><span class="p">(</span><span class="n">AVLTree</span><span class="w"> </span><span class="o">*</span><span class="n">tree</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-101-4" name="__codelineno-101-4" href="#__codelineno-101-4"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">tree</span><span class="o">-&gt;</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-101-5" name="__codelineno-101-5" href="#__codelineno-101-5"></a><span class="p">}</span>
+<a id="__codelineno-101-6" name="__codelineno-101-6" href="#__codelineno-101-6"></a>
+<a id="__codelineno-101-7" name="__codelineno-101-7" href="#__codelineno-101-7"></a><span class="cm">/* ノードを再帰的に削除する（補助関数） */</span>
+<a id="__codelineno-101-8" name="__codelineno-101-8" href="#__codelineno-101-8"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">removeHelper</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-101-9" name="__codelineno-101-9" href="#__codelineno-101-9"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">child</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">grandChild</span><span class="p">;</span>
+<a id="__codelineno-101-10" name="__codelineno-101-10" href="#__codelineno-101-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-101-11" name="__codelineno-101-11" href="#__codelineno-101-11"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-101-12" name="__codelineno-101-12" href="#__codelineno-101-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-101-13" name="__codelineno-101-13" href="#__codelineno-101-13"></a><span class="w">    </span><span class="cm">/* 1. ノードを探索して削除 */</span>
+<a id="__codelineno-101-14" name="__codelineno-101-14" href="#__codelineno-101-14"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-101-15" name="__codelineno-101-15" href="#__codelineno-101-15"></a><span class="w">        </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-101-16" name="__codelineno-101-16" href="#__codelineno-101-16"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-101-17" name="__codelineno-101-17" href="#__codelineno-101-17"></a><span class="w">        </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-101-18" name="__codelineno-101-18" href="#__codelineno-101-18"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-101-19" name="__codelineno-101-19" href="#__codelineno-101-19"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-101-20" name="__codelineno-101-20" href="#__codelineno-101-20"></a><span class="w">            </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-101-21" name="__codelineno-101-21" href="#__codelineno-101-21"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-101-22" name="__codelineno-101-22" href="#__codelineno-101-22"></a><span class="w">                </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-101-23" name="__codelineno-101-23" href="#__codelineno-101-23"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-101-24" name="__codelineno-101-24" href="#__codelineno-101-24"></a><span class="w">            </span><span class="c1">// 子ノード数 = 0 の場合、node をそのまま削除して返す</span>
+<a id="__codelineno-101-25" name="__codelineno-101-25" href="#__codelineno-101-25"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">child</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-101-26" name="__codelineno-101-26" href="#__codelineno-101-26"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-101-27" name="__codelineno-101-27" href="#__codelineno-101-27"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-101-28" name="__codelineno-101-28" href="#__codelineno-101-28"></a><span class="w">                </span><span class="c1">// 子ノード数 = 1 の場合、node をそのまま削除する</span>
+<a id="__codelineno-101-29" name="__codelineno-101-29" href="#__codelineno-101-29"></a><span class="w">                </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-101-30" name="__codelineno-101-30" href="#__codelineno-101-30"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-101-31" name="__codelineno-101-31" href="#__codelineno-101-31"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-101-32" name="__codelineno-101-32" href="#__codelineno-101-32"></a><span class="w">            </span><span class="c1">// 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える</span>
+<a id="__codelineno-101-33" name="__codelineno-101-33" href="#__codelineno-101-33"></a><span class="w">            </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-101-34" name="__codelineno-101-34" href="#__codelineno-101-34"></a><span class="w">            </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">temp</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-101-35" name="__codelineno-101-35" href="#__codelineno-101-35"></a><span class="w">                </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-101-36" name="__codelineno-101-36" href="#__codelineno-101-36"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-101-37" name="__codelineno-101-37" href="#__codelineno-101-37"></a><span class="w">            </span><span class="kt">int</span><span class="w"> </span><span class="n">tempVal</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-101-38" name="__codelineno-101-38" href="#__codelineno-101-38"></a><span class="w">            </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">temp</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-101-39" name="__codelineno-101-39" href="#__codelineno-101-39"></a><span class="w">            </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tempVal</span><span class="p">;</span>
+<a id="__codelineno-101-40" name="__codelineno-101-40" href="#__codelineno-101-40"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-101-41" name="__codelineno-101-41" href="#__codelineno-101-41"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-101-42" name="__codelineno-101-42" href="#__codelineno-101-42"></a><span class="w">    </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-101-43" name="__codelineno-101-43" href="#__codelineno-101-43"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-101-44" name="__codelineno-101-44" href="#__codelineno-101-44"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を行い、部分木の平衡を回復する */</span>
+<a id="__codelineno-101-45" name="__codelineno-101-45" href="#__codelineno-101-45"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-101-46" name="__codelineno-101-46" href="#__codelineno-101-46"></a><span class="w">    </span><span class="c1">// 部分木の根ノードを返す</span>
+<a id="__codelineno-101-47" name="__codelineno-101-47" href="#__codelineno-101-47"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-101-48" name="__codelineno-101-48" href="#__codelineno-101-48"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-102-1" name="__codelineno-102-1" href="#__codelineno-102-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove</span><span class="p">}</span>
-<a id="__codelineno-102-2" name="__codelineno-102-2" href="#__codelineno-102-2"></a>
-<a id="__codelineno-102-3" name="__codelineno-102-3" href="#__codelineno-102-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">removeHelper</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-102-1" name="__codelineno-102-1" href="#__codelineno-102-1"></a><span class="cm">/* ノードを削除 */</span>
+<a id="__codelineno-102-2" name="__codelineno-102-2" href="#__codelineno-102-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">_val</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-102-3" name="__codelineno-102-3" href="#__codelineno-102-3"></a><span class="w">    </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">)</span>
+<a id="__codelineno-102-4" name="__codelineno-102-4" href="#__codelineno-102-4"></a><span class="p">}</span>
+<a id="__codelineno-102-5" name="__codelineno-102-5" href="#__codelineno-102-5"></a>
+<a id="__codelineno-102-6" name="__codelineno-102-6" href="#__codelineno-102-6"></a><span class="cm">/* ノードを再帰的に削除する（補助メソッド） */</span>
+<a id="__codelineno-102-7" name="__codelineno-102-7" href="#__codelineno-102-7"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">removeHelper</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?,</span><span class="w"> </span><span class="n">_val</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="n">TreeNode? </span><span class="p">{</span>
+<a id="__codelineno-102-8" name="__codelineno-102-8" href="#__codelineno-102-8"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">?:</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span>
+<a id="__codelineno-102-9" name="__codelineno-102-9" href="#__codelineno-102-9"></a><span class="w">    </span><span class="cm">/* 1. ノードを探索して削除 */</span>
+<a id="__codelineno-102-10" name="__codelineno-102-10" href="#__codelineno-102-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">_val</span><span class="p">)</span>
+<a id="__codelineno-102-11" name="__codelineno-102-11" href="#__codelineno-102-11"></a><span class="w">        </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">)</span>
+<a id="__codelineno-102-12" name="__codelineno-102-12" href="#__codelineno-102-12"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">_val</span><span class="p">)</span>
+<a id="__codelineno-102-13" name="__codelineno-102-13" href="#__codelineno-102-13"></a><span class="w">        </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">)</span>
+<a id="__codelineno-102-14" name="__codelineno-102-14" href="#__codelineno-102-14"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-102-15" name="__codelineno-102-15" href="#__codelineno-102-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-102-16" name="__codelineno-102-16" href="#__codelineno-102-16"></a><span class="w">            </span><span class="kd">val</span><span class="w"> </span><span class="nv">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-102-17" name="__codelineno-102-17" href="#__codelineno-102-17"></a><span class="w">                </span><span class="n">node</span><span class="p">.</span><span class="na">left</span>
+<a id="__codelineno-102-18" name="__codelineno-102-18" href="#__codelineno-102-18"></a><span class="w">            </span><span class="k">else</span>
+<a id="__codelineno-102-19" name="__codelineno-102-19" href="#__codelineno-102-19"></a><span class="w">                </span><span class="n">node</span><span class="p">.</span><span class="na">right</span>
+<a id="__codelineno-102-20" name="__codelineno-102-20" href="#__codelineno-102-20"></a><span class="w">            </span><span class="c1">// 子ノード数 = 0 の場合、node をそのまま削除して返す</span>
+<a id="__codelineno-102-21" name="__codelineno-102-21" href="#__codelineno-102-21"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">child</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-102-22" name="__codelineno-102-22" href="#__codelineno-102-22"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span>
+<a id="__codelineno-102-23" name="__codelineno-102-23" href="#__codelineno-102-23"></a><span class="w">            </span><span class="c1">// 子ノード数 = 1 の場合、node をそのまま削除する</span>
+<a id="__codelineno-102-24" name="__codelineno-102-24" href="#__codelineno-102-24"></a><span class="w">            </span><span class="k">else</span>
+<a id="__codelineno-102-25" name="__codelineno-102-25" href="#__codelineno-102-25"></a><span class="w">                </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span>
+<a id="__codelineno-102-26" name="__codelineno-102-26" href="#__codelineno-102-26"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-102-27" name="__codelineno-102-27" href="#__codelineno-102-27"></a><span class="w">            </span><span class="c1">// 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える</span>
+<a id="__codelineno-102-28" name="__codelineno-102-28" href="#__codelineno-102-28"></a><span class="w">            </span><span class="kd">var</span><span class="w"> </span><span class="nv">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">right</span>
+<a id="__codelineno-102-29" name="__codelineno-102-29" href="#__codelineno-102-29"></a><span class="w">            </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">temp</span><span class="o">!!</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-102-30" name="__codelineno-102-30" href="#__codelineno-102-30"></a><span class="w">                </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="na">left</span>
+<a id="__codelineno-102-31" name="__codelineno-102-31" href="#__codelineno-102-31"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-102-32" name="__codelineno-102-32" href="#__codelineno-102-32"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">,</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="na">_val</span><span class="p">)</span>
+<a id="__codelineno-102-33" name="__codelineno-102-33" href="#__codelineno-102-33"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="na">_val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="na">_val</span>
+<a id="__codelineno-102-34" name="__codelineno-102-34" href="#__codelineno-102-34"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-102-35" name="__codelineno-102-35" href="#__codelineno-102-35"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-102-36" name="__codelineno-102-36" href="#__codelineno-102-36"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="c1">// ノードの高さを更新する</span>
+<a id="__codelineno-102-37" name="__codelineno-102-37" href="#__codelineno-102-37"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を行い、部分木の平衡を回復する */</span>
+<a id="__codelineno-102-38" name="__codelineno-102-38" href="#__codelineno-102-38"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-102-39" name="__codelineno-102-39" href="#__codelineno-102-39"></a><span class="w">    </span><span class="c1">// 部分木の根ノードを返す</span>
+<a id="__codelineno-102-40" name="__codelineno-102-40" href="#__codelineno-102-40"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-102-41" name="__codelineno-102-41" href="#__codelineno-102-41"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-103-1" name="__codelineno-103-1" href="#__codelineno-103-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove</span><span class="p">}</span>
-<a id="__codelineno-103-2" name="__codelineno-103-2" href="#__codelineno-103-2"></a>
-<a id="__codelineno-103-3" name="__codelineno-103-3" href="#__codelineno-103-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove_helper</span><span class="p">}</span>
+<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-103-1" name="__codelineno-103-1" href="#__codelineno-103-1"></a><span class="c1">### ノードを削除 ###</span>
+<a id="__codelineno-103-2" name="__codelineno-103-2" href="#__codelineno-103-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-103-3" name="__codelineno-103-3" href="#__codelineno-103-3"></a><span class="w">  </span><span class="vi">@root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">remove_helper</span><span class="p">(</span><span class="vi">@root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-103-4" name="__codelineno-103-4" href="#__codelineno-103-4"></a><span class="k">end</span>
+<a id="__codelineno-103-5" name="__codelineno-103-5" href="#__codelineno-103-5"></a>
+<a id="__codelineno-103-6" name="__codelineno-103-6" href="#__codelineno-103-6"></a><span class="c1">### ノードを削除 ###</span>
+<a id="__codelineno-103-7" name="__codelineno-103-7" href="#__codelineno-103-7"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-103-8" name="__codelineno-103-8" href="#__codelineno-103-8"></a><span class="w">  </span><span class="vi">@root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">remove_helper</span><span class="p">(</span><span class="vi">@root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-103-9" name="__codelineno-103-9" href="#__codelineno-103-9"></a><span class="k">end</span>
+<a id="__codelineno-103-10" name="__codelineno-103-10" href="#__codelineno-103-10"></a>
+<a id="__codelineno-103-11" name="__codelineno-103-11" href="#__codelineno-103-11"></a><span class="c1"># ## ノードを再帰的に削除（補助メソッド）###</span>
+<a id="__codelineno-103-12" name="__codelineno-103-12" href="#__codelineno-103-12"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove_helper</span><span class="p">(</span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-103-13" name="__codelineno-103-13" href="#__codelineno-103-13"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-103-14" name="__codelineno-103-14" href="#__codelineno-103-14"></a><span class="w">  </span><span class="c1"># 1. ノードを探索して削除</span>
+<a id="__codelineno-103-15" name="__codelineno-103-15" href="#__codelineno-103-15"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-103-16" name="__codelineno-103-16" href="#__codelineno-103-16"></a><span class="w">    </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">remove_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-103-17" name="__codelineno-103-17" href="#__codelineno-103-17"></a><span class="w">  </span><span class="k">elsif</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-103-18" name="__codelineno-103-18" href="#__codelineno-103-18"></a><span class="w">    </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">remove_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-103-19" name="__codelineno-103-19" href="#__codelineno-103-19"></a><span class="w">  </span><span class="k">else</span>
+<a id="__codelineno-103-20" name="__codelineno-103-20" href="#__codelineno-103-20"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="o">.</span><span class="n">nil?</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-103-21" name="__codelineno-103-21" href="#__codelineno-103-21"></a><span class="w">      </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span>
+<a id="__codelineno-103-22" name="__codelineno-103-22" href="#__codelineno-103-22"></a><span class="w">      </span><span class="c1"># 子ノード数 = 0 の場合、node をそのまま削除して返す</span>
+<a id="__codelineno-103-23" name="__codelineno-103-23" href="#__codelineno-103-23"></a><span class="w">      </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">child</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-103-24" name="__codelineno-103-24" href="#__codelineno-103-24"></a><span class="w">      </span><span class="c1"># 子ノード数 = 1 の場合、node をそのまま削除する</span>
+<a id="__codelineno-103-25" name="__codelineno-103-25" href="#__codelineno-103-25"></a><span class="w">      </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span>
+<a id="__codelineno-103-26" name="__codelineno-103-26" href="#__codelineno-103-26"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-103-27" name="__codelineno-103-27" href="#__codelineno-103-27"></a><span class="w">      </span><span class="c1"># 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える</span>
+<a id="__codelineno-103-28" name="__codelineno-103-28" href="#__codelineno-103-28"></a><span class="w">      </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span>
+<a id="__codelineno-103-29" name="__codelineno-103-29" href="#__codelineno-103-29"></a><span class="w">      </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">temp</span><span class="o">.</span><span class="n">left</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-103-30" name="__codelineno-103-30" href="#__codelineno-103-30"></a><span class="w">        </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="o">.</span><span class="n">left</span>
+<a id="__codelineno-103-31" name="__codelineno-103-31" href="#__codelineno-103-31"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-103-32" name="__codelineno-103-32" href="#__codelineno-103-32"></a><span class="w">      </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">remove_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">temp</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-103-33" name="__codelineno-103-33" href="#__codelineno-103-33"></a><span class="w">      </span><span class="n">node</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-103-34" name="__codelineno-103-34" href="#__codelineno-103-34"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-103-35" name="__codelineno-103-35" href="#__codelineno-103-35"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-103-36" name="__codelineno-103-36" href="#__codelineno-103-36"></a><span class="w">  </span><span class="c1"># ノードの高さを更新する</span>
+<a id="__codelineno-103-37" name="__codelineno-103-37" href="#__codelineno-103-37"></a><span class="w">  </span><span class="n">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-103-38" name="__codelineno-103-38" href="#__codelineno-103-38"></a><span class="w">  </span><span class="c1"># 2. 回転操作を行い、部分木の平衡を回復する</span>
+<a id="__codelineno-103-39" name="__codelineno-103-39" href="#__codelineno-103-39"></a><span class="w">  </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-103-40" name="__codelineno-103-40" href="#__codelineno-103-40"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h3 id="3_1">3. &nbsp; ノードの検索<a class="headerlink" href="#3_1" title="Permanent link">&para;</a></h3>
-<p>AVL木でのノード検索操作は二分探索木のそれと一致しており、ここでは詳述しません。</p>
-<h2 id="754-avl">7.5.4 &nbsp; AVL木の典型的な応用<a class="headerlink" href="#754-avl" title="Permanent link">&para;</a></h2>
+<h3 id="3_1">3. &nbsp; ノードの探索<a class="headerlink" href="#3_1" title="Permanent link">&para;</a></h3>
+<p>AVL 木のノード探索操作は二分探索木と同じなので、ここでは繰り返しません。</p>
+<h2 id="754-avl">7.5.4 &nbsp; AVL 木の代表的な応用<a class="headerlink" href="#754-avl" title="Permanent link">&para;</a></h2>
 <ul>
-<li>大量のデータの整理と格納に使用され、検索頻度が高く、挿入と削除の頻度が低いシナリオに適しています。</li>
-<li>データベースのインデックスシステムの構築に使用されます。</li>
-<li>赤黒木も一般的な平衡二分探索木の一種です。AVL木と比較して、赤黒木はより緩い平衡条件を持ち、ノードの挿入と削除にかかる回転数が少なく、ノードの追加と削除操作の平均効率が高くなります。</li>
+<li>大規模データの整理・格納に用いられ、高頻度の探索と低頻度の追加・削除に適しています。</li>
+<li>データベースのインデックスシステムの構築に使われます。</li>
+<li>赤黒木も代表的な平衡二分探索木の一つです。AVL 木と比べると、赤黒木は平衡条件がより緩く、ノードの挿入・削除に必要な回転操作が少ないため、平均的な更新効率はより高くなります。</li>
 </ul>
 
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diff --git a/ja/chapter_tree/binary_search_tree/index.html b/ja/chapter_tree/binary_search_tree/index.html
index dbd80dcff..35ca8d8ad 100644
--- a/ja/chapter_tree/binary_search_tree/index.html
+++ b/ja/chapter_tree/binary_search_tree/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1635,7 +1635,7 @@
   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1985,7 +1985,7 @@
   <a href="#1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; ノードの検索
+        1. &nbsp; ノードの探索
       
     </span>
   </a>
@@ -2018,7 +2018,7 @@
   <a href="#4" class="md-nav__link">
     <span class="md-ellipsis">
       
-        4. &nbsp; 中順走査は順序付けされている
+        4. &nbsp; 中順走査は昇順
       
     </span>
   </a>
@@ -2045,7 +2045,7 @@
   <a href="#743" class="md-nav__link">
     <span class="md-ellipsis">
       
-        7.4.3 &nbsp; 二分探索木の一般的な応用
+        7.4.3 &nbsp; 二分探索木の代表的な応用
       
     </span>
   </a>
@@ -2075,7 +2075,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2238,7 +2238,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2624,7 +2624,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2680,7 +2680,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2708,7 +2708,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3246,7 +3246,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3302,7 +3302,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3330,7 +3330,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3523,7 +3523,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3551,7 +3551,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3692,7 +3692,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3720,7 +3720,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3748,7 +3748,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3776,7 +3776,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3969,7 +3969,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4214,7 +4214,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4372,7 +4372,7 @@
   <a href="#1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; ノードの検索
+        1. &nbsp; ノードの探索
       
     </span>
   </a>
@@ -4405,7 +4405,7 @@
   <a href="#4" class="md-nav__link">
     <span class="md-ellipsis">
       
-        4. &nbsp; 中順走査は順序付けされている
+        4. &nbsp; 中順走査は昇順
       
     </span>
   </a>
@@ -4432,7 +4432,7 @@
   <a href="#743" class="md-nav__link">
     <span class="md-ellipsis">
       
-        7.4.3 &nbsp; 二分探索木の一般的な応用
+        7.4.3 &nbsp; 二分探索木の代表的な応用
       
     </span>
   </a>
@@ -4477,27 +4477,27 @@
 
 <!-- Page content -->
 <h1 id="74">7.4 &nbsp; 二分探索木<a class="headerlink" href="#74" title="Permanent link">&para;</a></h1>
-<p>下図に示すように、<u>二分探索木</u>は以下の条件を満たします。</p>
+<p>以下の図に示すように、<u>二分探索木（binary search tree）</u>は次の条件を満たします。</p>
 <ol>
 <li>根ノードについて、左部分木のすべてのノードの値 <span class="arithmatex">\(&lt;\)</span> 根ノードの値 <span class="arithmatex">\(&lt;\)</span> 右部分木のすべてのノードの値。</li>
-<li>任意のノードの左と右の部分木も二分探索木です。つまり、条件<code>1.</code>も満たします。</li>
+<li>任意のノードの左部分木と右部分木も二分探索木であり、すなわち条件 <code>1.</code> も満たします。</li>
 </ol>
 <p><img alt="二分探索木" class="animation-figure" src="../binary_search_tree.assets/binary_search_tree.png" /></p>
 <p align="center"> 図 7-16 &nbsp; 二分探索木 </p>
 
 <h2 id="741">7.4.1 &nbsp; 二分探索木の操作<a class="headerlink" href="#741" title="Permanent link">&para;</a></h2>
-<p>二分探索木をクラス<code>BinarySearchTree</code>としてカプセル化し、木の根ノードを指すメンバー変数<code>root</code>を宣言します。</p>
-<h3 id="1">1. &nbsp; ノードの検索<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>ターゲットノード値<code>num</code>が与えられた場合、二分探索木の性質に従って検索できます。下図に示すように、ノード<code>cur</code>を宣言し、二分木の根ノード<code>root</code>から開始し、ノード値<code>cur.val</code>と<code>num</code>のサイズを比較するループを行います。</p>
+<p>二分探索木をクラス <code>BinarySearchTree</code> としてカプセル化し、木の根ノードを指すメンバ変数 <code>root</code> を宣言します。</p>
+<h3 id="1">1. &nbsp; ノードの探索<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>目標ノードの値 <code>num</code> が与えられたら、二分探索木の性質に基づいて探索できます。以下の図に示すように、ノード <code>cur</code> を宣言し、二分木の根ノード <code>root</code> から出発して、ノード値 <code>cur.val</code> と <code>num</code> の大小関係を繰り返し比較します。</p>
 <ul>
-<li><code>cur.val &lt; num</code>の場合、ターゲットノードは<code>cur</code>の右部分木にあることを意味するため、<code>cur = cur.right</code>を実行します。</li>
-<li><code>cur.val &gt; num</code>の場合、ターゲットノードは<code>cur</code>の左部分木にあることを意味するため、<code>cur = cur.left</code>を実行します。</li>
-<li><code>cur.val = num</code>の場合、ターゲットノードが見つかったことを意味するため、ループを終了してノードを返します。</li>
+<li><code>cur.val &lt; num</code> の場合、目標ノードは <code>cur</code> の右部分木にあるため、<code>cur = cur.right</code> を実行します。</li>
+<li><code>cur.val &gt; num</code> の場合、目標ノードは <code>cur</code> の左部分木にあるため、<code>cur = cur.left</code> を実行します。</li>
+<li><code>cur.val = num</code> の場合、目標ノードが見つかったことを表し、ループを抜けてそのノードを返します。</li>
 </ul>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:4"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="二分探索木でのノード検索例" class="animation-figure" src="../binary_search_tree.assets/bst_search_step1.png" /></p>
+<p><img alt="二分探索木のノード探索例" class="animation-figure" src="../binary_search_tree.assets/bst_search_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="bst_search_step2" class="animation-figure" src="../binary_search_tree.assets/bst_search_step2.png" /></p>
@@ -4510,42 +4510,42 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 7-17 &nbsp; 二分探索木でのノード検索例 </p>
+<p align="center"> 図 7-17 &nbsp; 二分探索木のノード探索例 </p>
 
-<p>二分探索木での検索操作は二分探索アルゴリズムと同じ原理で動作し、各ラウンドでケースの半分を排除します。ループ数は最大で二分木の高さです。二分木が平衡している場合、<span class="arithmatex">\(O(\log n)\)</span>の時間を使用します。コード例は以下の通りです：</p>
+<p>二分探索木の探索操作は二分探索アルゴリズムと同じ原理で動作し、各ラウンドで半分の候補を除外します。ループ回数の上限は二分木の高さであり、二分木が平衡であれば <span class="arithmatex">\(O(\log n)\)</span> 時間です。コード例は次のとおりです。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_search_tree.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">search</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ノードを探索&quot;&quot;&quot;</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="n">cur</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_root</span>
-<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="c1"># ループで探索、葉ノードを通過した後にブレーク</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="c1"># ループで探索し、葉ノードを越えたら抜ける</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="k">while</span> <span class="n">cur</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="c1"># ターゲットノードはcurの右部分木にある</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="c1"># 目標ノードは cur の右部分木にある</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="k">if</span> <span class="n">cur</span><span class="o">.</span><span class="n">val</span> <span class="o">&lt;</span> <span class="n">num</span><span class="p">:</span>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>            <span class="n">cur</span> <span class="o">=</span> <span class="n">cur</span><span class="o">.</span><span class="n">right</span>
-<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="c1"># ターゲットノードはcurの左部分木にある</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="c1"># 目標ノードは cur の左部分木にある</span>
 <a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="k">elif</span> <span class="n">cur</span><span class="o">.</span><span class="n">val</span> <span class="o">&gt;</span> <span class="n">num</span><span class="p">:</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>            <span class="n">cur</span> <span class="o">=</span> <span class="n">cur</span><span class="o">.</span><span class="n">left</span>
-<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="c1"># ターゲットノードを発見、ループをブレーク</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="c1"># 目標ノードが見つかったらループを抜ける</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="k">else</span><span class="p">:</span>
 <a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>            <span class="k">break</span>
 <a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="k">return</span> <span class="n">cur</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* ノードを検索 */</span>
+<div class="highlight"><span class="filename">binary_search_tree.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* ノードを探索 */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">search</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
-<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// ループで検索、葉ノードを通り過ぎたら終了</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="c1">// 目標ノードはcurの右部分木にある</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="c1">// 目標ノードは cur の右部分木にある</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
-<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">        </span><span class="c1">// 目標ノードはcurの左部分木にある</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">        </span><span class="c1">// 目標ノードは cur の左部分木にある</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">;</span>
-<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="c1">// 目標ノードを見つけた、ループを抜ける</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="c1">// 目標ノードが見つかったらループを抜ける</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="k">else</span>
 <a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
 <a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="p">}</span>
@@ -4555,102 +4555,278 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* ノードを検索 */</span>
+<div class="highlight"><span class="filename">binary_search_tree.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* ノードを探索 */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">search</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
-<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// ループで検索、葉ノードを通過後に終了</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="c1">// 対象ノードは cur の右部分木にある</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="c1">// 目標ノードは cur の右部分木にある</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">right</span><span class="p">;</span>
-<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">        </span><span class="c1">// 対象ノードは cur の左部分木にある</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">        </span><span class="c1">// 目標ノードは cur の左部分木にある</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
 <a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">left</span><span class="p">;</span>
-<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="c1">// 対象ノードを見つけた、ループを終了</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="c1">// 目標ノードが見つかったらループを抜ける</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="k">else</span>
 <a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
 <a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="c1">// 対象ノードを返す</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="c1">// 目標ノードを返す</span>
 <a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
 <a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Search</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* ノードを探索 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">Search</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">        </span><span class="c1">// 目標ノードは cur の右部分木にある</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">            </span><span class="n">cur</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">        </span><span class="c1">// 目標ノードは cur の左部分木にある</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="nf">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">        </span><span class="c1">// 目標ノードが見つかったらループを抜ける</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">        </span><span class="k">else</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">    </span><span class="c1">// 目標ノードを返す</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">binarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">search</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* ノードを探索 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">bst</span><span class="w"> </span><span class="o">*</span><span class="nx">binarySearchTree</span><span class="p">)</span><span class="w"> </span><span class="nx">search</span><span class="p">(</span><span class="nx">num</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="nx">node</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">bst</span><span class="p">.</span><span class="nx">root</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Val</span><span class="p">.(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">            </span><span class="c1">// 目標ノードは cur の右部分木にある</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">            </span><span class="nx">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Val</span><span class="p">.(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">            </span><span class="c1">// 目標ノードは cur の左部分木にある</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">            </span><span class="nx">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">            </span><span class="c1">// 目標ノードが見つかったらループを抜ける</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">    </span><span class="c1">// 目標ノードを返す</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">search</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* ノードを探索 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">search</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">cur</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">root</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">        </span><span class="c1">// 目標ノードは cur の右部分木にある</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="p">!.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">cur</span><span class="p">?.</span><span class="kr">right</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">        </span><span class="c1">// 目標ノードは cur の左部分木にある</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="p">!.</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">cur</span><span class="p">?.</span><span class="kr">left</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">        </span><span class="c1">// 目標ノードが見つかったらループを抜ける</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w">    </span><span class="c1">// 目標ノードを返す</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">cur</span>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">search</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* ノードを探索 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="nx">search</span><span class="p">(</span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="p">;</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">        </span><span class="c1">// 目標ノードは cur の右部分木にある</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">        </span><span class="c1">// 目標ノードは cur の左部分木にある</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">        </span><span class="c1">// 目標ノードが見つかったらループを抜ける</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">    </span><span class="c1">// 目標ノードを返す</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">cur</span><span class="p">;</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">search</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* ノードを探索 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="nx">search</span><span class="p">(</span><span class="nx">num</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="p">;</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">        </span><span class="c1">// 目標ノードは cur の右部分木にある</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">        </span><span class="c1">// 目標ノードは cur の左部分木にある</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">        </span><span class="c1">// 目標ノードが見つかったらループを抜ける</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">    </span><span class="c1">// 目標ノードを返す</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">cur</span><span class="p">;</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">search</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* ノードを探索 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">search</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_root</span><span class="p">;</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">    </span><span class="c1">// 目標ノードは cur の右部分木にある</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">_num</span><span class="p">)</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">      </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">    </span><span class="c1">// 目標ノードは cur の左部分木にある</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">_num</span><span class="p">)</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">      </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">    </span><span class="c1">// 目標ノードが見つかったらループを抜ける</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">      </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">  </span><span class="c1">// 目標ノードを返す</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">search</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* ノードを探索 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">search</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">OptionTreeNodeRc</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">root</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">clone</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">        </span><span class="k">match</span><span class="w"> </span><span class="n">num</span><span class="p">.</span><span class="n">cmp</span><span class="p">(</span><span class="o">&amp;</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">            </span><span class="c1">// 目標ノードは cur の右部分木にある</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">            </span><span class="n">Ordering</span><span class="p">::</span><span class="n">Greater</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">(),</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">            </span><span class="c1">// 目標ノードは cur の左部分木にある</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">            </span><span class="n">Ordering</span><span class="p">::</span><span class="n">Less</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">(),</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">            </span><span class="c1">// 目標ノードが見つかったらループを抜ける</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">            </span><span class="n">Ordering</span><span class="p">::</span><span class="n">Equal</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="k">break</span><span class="p">,</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">    </span><span class="c1">// 目標ノードを返す</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">    </span><span class="n">cur</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">search</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* ノードを探索 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">search</span><span class="p">(</span><span class="n">BinarySearchTree</span><span class="w"> </span><span class="o">*</span><span class="n">bst</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bst</span><span class="o">-&gt;</span><span class="n">root</span><span class="p">;</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">            </span><span class="c1">// 目標ノードは cur の右部分木にある</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">            </span><span class="c1">// 目標ノードは cur の左部分木にある</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">            </span><span class="c1">// 目標ノードが見つかったらループを抜ける</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">    </span><span class="c1">// 目標ノードを返す</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">search</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* ノードを探索 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">search</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="n">TreeNode? </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">        </span><span class="c1">// 目標ノードは cur の右部分木にある</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">        </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">_val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">            </span><span class="n">cur</span><span class="p">.</span><span class="na">right</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">        </span><span class="c1">// 目標ノードは cur の左部分木にある</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">_val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">            </span><span class="n">cur</span><span class="p">.</span><span class="na">left</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">        </span><span class="c1">// 目標ノードが見つかったらループを抜ける</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">        </span><span class="k">else</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">    </span><span class="c1">// 目標ノードを返す</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">cur</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">BinarySearchTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">search</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### ノードを検索 ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">search</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@root</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="c1"># ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">cur</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">    </span><span class="c1"># 目標ノードは cur の右部分木にある</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">      </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">right</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">    </span><span class="c1"># 目標ノードは cur の左部分木にある</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">    </span><span class="k">elsif</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">      </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">left</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">    </span><span class="c1"># 目標ノードが見つかったらループを抜ける</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">      </span><span class="k">break</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w">  </span><span class="n">cur</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%29%3A%0A%20%20%20%20%20%20%20%20self.val%20%3D%20val%0A%20%20%20%20%20%20%20%20self.left%20%3D%20None%0A%20%20%20%20%20%20%20%20self.right%20%3D%20None%0A%0A%0Aclass%20BinarySearchTree%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%E6%9C%A8%22%22%22%0A%0A%20%20%20%20def%20__init__%28self%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%82%B3%E3%83%B3%E3%82%B9%E3%83%88%E3%83%A9%E3%82%AF%E3%82%BF%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E7%A9%BA%E3%81%AE%E6%9C%A8%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20self._root%20%3D%20None%0A%0A%20%20%20%20def%20search%28self%2C%20num%3A%20int%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%8E%A2%E7%B4%A2%22%22%22%0A%20%20%20%20%20%20%20%20cur%20%3D%20self._root%0A%20%20%20%20%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%97%E3%81%A7%E6%8E%A2%E7%B4%A2%E3%81%97%E3%80%81%E8%91%89%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E8%B6%8A%E3%81%88%E3%81%9F%E3%82%89%E6%8A%9C%E3%81%91%E3%82%8B%0A%20%20%20%20%20%20%20%20while%20cur%20is%20not%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E7%9B%AE%E6%A8%99%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AF%20cur%20%E3%81%AE%E5%8F%B3%E9%83%A8%E5%88%86%E6%9C%A8%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20cur.val%20%3C%20num%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20cur%20%3D%20cur.right%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E7%9B%AE%E6%A8%99%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AF%20cur%20%E3%81%AE%E5%B7%A6%E9%83%A8%E5%88%86%E6%9C%A8%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20elif%20cur.val%20%3E%20num%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20cur%20%3D%20cur.left%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E7%9B%AE%E6%A8%99%E3%83%8E%E3%83%BC%E3%83%89%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%81%A3%E3%81%9F%E3%82%89%E3%83%AB%E3%83%BC%E3%83%97%E3%82%92%E6%8A%9C%E3%81%91%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20return%20cur%0A%0A%20%20%20%20def%20insert%28self%2C%20num%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%8C%BF%E5%85%A5%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E6%9C%A8%E3%81%8C%E7%A9%BA%E3%81%AA%E3%82%89%E3%80%81%E6%A0%B9%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20if%20self._root%20is%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self._root%20%3D%20TreeNode%28num%29%0A%20%20%20%20%20%20%20%20%20%20%20%20return%0A%20%20%20%20%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%97%E3%81%A7%E6%8E%A2%E7%B4%A2%E3%81%97%E3%80%81%E8%91%89%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E8%B6%8A%E3%81%88%E3%81%9F%E3%82%89%E6%8A%9C%E3%81%91%E3%82%8B%0A%20%20%20%20%20%20%20%20cur%2C%20pre%20%3D%20self._root%2C%20None%0A%20%20%20%20%20%20%20%20while%20cur%20is%20not%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E9%87%8D%E8%A4%87%E3%83%8E%E3%83%BC%E3%83%89%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%81%A3%E3%81%9F%E3%82%89%E3%80%81%E7%9B%B4%E3%81%A1%E3%81%AB%E8%BF%94%E3%81%99%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20cur.val%20%3D%3D%20num%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20return%0A%20%20%20%20%20%20%20%20%20%20%20%20pre%20%3D%20cur%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%81%AF%20cur%20%E3%81%AE%E5%8F%B3%E9%83%A8%E5%88%86%E6%9C%A8%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20cur.val%20%3C%20num%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20cur%20%3D%20cur.right%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%81%AF%20cur%20%E3%81%AE%E5%B7%A6%E9%83%A8%E5%88%86%E6%9C%A8%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20cur%20%3D%20cur.left%0A%20%20%20%20%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%8C%BF%E5%85%A5%0A%20%20%20%20%20%20%20%20node%20%3D%20TreeNode%28num%29%0A%20%20%20%20%20%20%20%20if%20pre.val%20%3C%20num%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20pre.right%20%3D%20node%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20pre.left%20%3D%20node%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%E6%9C%A8%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20bst%20%3D%20BinarySearchTree%28%29%0A%20%20%20%20nums%20%3D%20%5B4%2C%202%2C%206%2C%201%2C%203%2C%205%2C%207%5D%0A%20%20%20%20for%20num%20in%20nums%3A%0A%20%20%20%20%20%20%20%20bst.insert%28num%29%0A%0A%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%8E%A2%E7%B4%A2%0A%20%20%20%20node%20%3D%20bst.search%287%29%0A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</iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%29%3A%0A%20%20%20%20%20%20%20%20self.val%20%3D%20val%0A%20%20%20%20%20%20%20%20self.left%20%3D%20None%0A%20%20%20%20%20%20%20%20self.right%20%3D%20None%0A%0A%0Aclass%20BinarySearchTree%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%E6%9C%A8%22%22%22%0A%0A%20%20%20%20def%20__init__%28self%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%82%B3%E3%83%B3%E3%82%B9%E3%83%88%E3%83%A9%E3%82%AF%E3%82%BF%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E7%A9%BA%E3%81%AE%E6%9C%A8%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20self._root%20%3D%20None%0A%0A%20%20%20%20def%20search%28self%2C%20num%3A%20int%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%8E%A2%E7%B4%A2%22%22%22%0A%20%20%20%20%20%20%20%20cur%20%3D%20self._root%0A%20%20%20%20%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%97%E3%81%A7%E6%8E%A2%E7%B4%A2%E3%81%97%E3%80%81%E8%91%89%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E8%B6%8A%E3%81%88%E3%81%9F%E3%82%89%E6%8A%9C%E3%81%91%E3%82%8B%0A%20%20%20%20%20%20%20%20while%20cur%20is%20not%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E7%9B%AE%E6%A8%99%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AF%20cur%20%E3%81%AE%E5%8F%B3%E9%83%A8%E5%88%86%E6%9C%A8%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20cur.val%20%3C%20num%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20cur%20%3D%20cur.right%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E7%9B%AE%E6%A8%99%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AF%20cur%20%E3%81%AE%E5%B7%A6%E9%83%A8%E5%88%86%E6%9C%A8%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20elif%20cur.val%20%3E%20num%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20cur%20%3D%20cur.left%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E7%9B%AE%E6%A8%99%E3%83%8E%E3%83%BC%E3%83%89%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%81%A3%E3%81%9F%E3%82%89%E3%83%AB%E3%83%BC%E3%83%97%E3%82%92%E6%8A%9C%E3%81%91%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20return%20cur%0A%0A%20%20%20%20def%20insert%28self%2C%20num%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%8C%BF%E5%85%A5%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E6%9C%A8%E3%81%8C%E7%A9%BA%E3%81%AA%E3%82%89%E3%80%81%E6%A0%B9%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20if%20self._root%20is%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self._root%20%3D%20TreeNode%28num%29%0A%20%20%20%20%20%20%20%20%20%20%20%20return%0A%20%20%20%20%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%97%E3%81%A7%E6%8E%A2%E7%B4%A2%E3%81%97%E3%80%81%E8%91%89%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E8%B6%8A%E3%81%88%E3%81%9F%E3%82%89%E6%8A%9C%E3%81%91%E3%82%8B%0A%20%20%20%20%20%20%20%20cur%2C%20pre%20%3D%20self._root%2C%20None%0A%20%20%20%20%20%20%20%20while%20cur%20is%20not%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E9%87%8D%E8%A4%87%E3%83%8E%E3%83%BC%E3%83%89%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%81%A3%E3%81%9F%E3%82%89%E3%80%81%E7%9B%B4%E3%81%A1%E3%81%AB%E8%BF%94%E3%81%99%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20cur.val%20%3D%3D%20num%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20return%0A%20%20%20%20%20%20%20%20%20%20%20%20pre%20%3D%20cur%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%81%AF%20cur%20%E3%81%AE%E5%8F%B3%E9%83%A8%E5%88%86%E6%9C%A8%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20cur.val%20%3C%20num%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20cur%20%3D%20cur.right%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%81%AF%20cur%20%E3%81%AE%E5%B7%A6%E9%83%A8%E5%88%86%E6%9C%A8%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20cur%20%3D%20cur.left%0A%20%20%20%20%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%8C%BF%E5%85%A5%0A%20%20%20%20%20%20%20%20node%20%3D%20TreeNode%28num%29%0A%20%20%20%20%20%20%20%20if%20pre.val%20%3C%20num%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20pre.right%20%3D%20node%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20pre.left%20%3D%20node%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%E6%9C%A8%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20bst%20%3D%20BinarySearchTree%28%29%0A%20%20%20%20nums%20%3D%20%5B4%2C%202%2C%206%2C%201%2C%203%2C%205%2C%207%5D%0A%20%20%20%20for%20num%20in%20nums%3A%0A%20%20%20%20%20%20%20%20bst.insert%28num%29%0A%0A%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%8E%A2%E7%B4%A2%0A%20%20%20%20node%20%3D%20bst.search%287%29%0A%20%20%20%20print%28%22%5Cn%E8%A6%8B%E3%81%A4%E3%81%8B%E3%81%A3%E3%81%9F%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AA%E3%83%96%E3%82%B8%E3%82%A7%E3%82%AF%E3%83%88%E3%81%AF%3A%20%7B%7D%E3%80%81%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AE%E5%80%A4%20%3D%20%7B%7D%22.format%28node%2C%20node.val%29%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=162&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 <h3 id="2">2. &nbsp; ノードの挿入<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>挿入する要素<code>num</code>が与えられた場合、二分探索木の性質「左部分木 &lt; 根ノード &lt; 右部分木」を維持するため、挿入操作は下図に示すように進行します。</p>
+<p>挿入する要素 <code>num</code> が与えられたとき、二分探索木の「左部分木 &lt; 根ノード &lt; 右部分木」という性質を保つため、挿入操作の流れは以下の図のようになります。</p>
 <ol>
-<li><strong>挿入位置を見つける</strong>: 検索操作と同様に、根ノードから開始し、現在のノード値と<code>num</code>のサイズ関係に従って下向きにループし、葉ノードを通過（<code>None</code>に走査）するまで、ループを終了します。</li>
-<li><strong>この位置にノードを挿入</strong>: ノード<code>num</code>を初期化し、<code>None</code>があった場所に配置します。</li>
+<li><strong>挿入位置を探索する</strong>：探索操作と同様に、根ノードから出発し、現在のノード値と <code>num</code> の大小関係に基づいて下方向へ探索を繰り返し、葉ノードを越えて（<code>None</code> まで到達して）ループを抜けます。</li>
+<li><strong>その位置にノードを挿入する</strong>：ノード <code>num</code> を初期化し、そのノードを <code>None</code> の位置に置きます。</li>
 </ol>
-<p><img alt="二分探索木へのノード挿入" class="animation-figure" src="../binary_search_tree.assets/bst_insert.png" /></p>
-<p align="center"> 図 7-18 &nbsp; 二分探索木へのノード挿入 </p>
+<p><img alt="二分探索木にノードを挿入する" class="animation-figure" src="../binary_search_tree.assets/bst_insert.png" /></p>
+<p align="center"> 図 7-18 &nbsp; 二分探索木にノードを挿入する </p>
 
-<p>コード実装では、以下の2点に注意してください。</p>
+<p>コード実装では、次の 2 点に注意が必要です。</p>
 <ul>
-<li>二分探索木は重複ノードの存在を許可しません。そうでなければ、その定義に違反します。したがって、挿入するノードが既に木に存在する場合、挿入は実行されず、ノードは直接戻ります。</li>
-<li>挿入操作を実行するには、前のループからのノードを保存するためにノード<code>pre</code>を使用する必要があります。このようにして、<code>None</code>に走査したときに、その親ノードを取得でき、ノード挿入操作を完了できます。</li>
+<li>二分探索木では重複ノードを許可しません。そうでないと定義に反するためです。したがって、挿入対象のノードが木内にすでに存在する場合は、挿入を行わずそのまま返します。</li>
+<li>ノード挿入を実現するために、ノード <code>pre</code> を用いて前回のループのノードを保持する必要があります。これにより、<code>None</code> までたどり着いたときにその親ノードを取得でき、ノード挿入を完了できます。</li>
 </ul>
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 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_search_tree.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
 <a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ノードを挿入&quot;&quot;&quot;</span>
-<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="c1"># 木が空の場合、ルートノードを初期化</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="c1"># 木が空なら、根ノードを初期化する</span>
 <a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_root</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_root</span> <span class="o">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
 <a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>        <span class="k">return</span>
-<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>    <span class="c1"># ループで探索、葉ノードを通過した後にブレーク</span>
+<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>    <span class="c1"># ループで探索し、葉ノードを越えたら抜ける</span>
 <a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>    <span class="n">cur</span><span class="p">,</span> <span class="n">pre</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_root</span><span class="p">,</span> <span class="kc">None</span>
 <a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>    <span class="k">while</span> <span class="n">cur</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>        <span class="c1"># 重複ノードを発見したため、戻る</span>
+<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>        <span class="c1"># 重複ノードが見つかったら、直ちに返す</span>
 <a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>        <span class="k">if</span> <span class="n">cur</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="n">num</span><span class="p">:</span>
 <a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>            <span class="k">return</span>
 <a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a>        <span class="n">pre</span> <span class="o">=</span> <span class="n">cur</span>
-<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>        <span class="c1"># 挿入位置はcurの右部分木にある</span>
+<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>        <span class="c1"># 挿入位置は cur の右部分木にある</span>
 <a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a>        <span class="k">if</span> <span class="n">cur</span><span class="o">.</span><span class="n">val</span> <span class="o">&lt;</span> <span class="n">num</span><span class="p">:</span>
 <a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a>            <span class="n">cur</span> <span class="o">=</span> <span class="n">cur</span><span class="o">.</span><span class="n">right</span>
-<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>        <span class="c1"># 挿入位置はcurの左部分木にある</span>
+<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>        <span class="c1"># 挿入位置は cur の左部分木にある</span>
 <a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a>        <span class="k">else</span><span class="p">:</span>
 <a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a>            <span class="n">cur</span> <span class="o">=</span> <span class="n">cur</span><span class="o">.</span><span class="n">left</span>
 <a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a>    <span class="c1"># ノードを挿入</span>
@@ -4664,22 +4840,22 @@
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_search_tree.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* ノードを挿入 */</span>
 <a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="c1">// 木が空の場合、ルートノードを初期化</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="c1">// 木が空なら、根ノードを初期化する</span>
 <a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">        </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
 <a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
-<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">    </span><span class="c1">// ループで検索、葉ノードを通り過ぎたら終了</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
 <a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">        </span><span class="c1">// 重複ノードを見つけた場合、戻る</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">        </span><span class="c1">// 重複ノードが見つかったら、直ちに返す</span>
 <a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
 <a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">        </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
-<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">        </span><span class="c1">// 挿入位置はcurの右部分木にある</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">        </span><span class="c1">// 挿入位置は cur の右部分木にある</span>
 <a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
 <a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
-<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w">        </span><span class="c1">// 挿入位置はcurの左部分木にある</span>
+<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w">        </span><span class="c1">// 挿入位置は cur の左部分木にある</span>
 <a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w">        </span><span class="k">else</span>
 <a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">;</span>
 <a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a><span class="w">    </span><span class="p">}</span>
@@ -4695,15 +4871,15 @@
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_search_tree.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* ノードを挿入 */</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 木が空の場合、根ノードを初期化</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 木が空なら、根ノードを初期化する</span>
 <a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">        </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
 <a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
-<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">    </span><span class="c1">// ループで検索、葉ノードを通過後に終了</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
 <a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">        </span><span class="c1">// 重複ノードを見つけた場合、戻る</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">        </span><span class="c1">// 重複ノードが見つかったら、直ちに返す</span>
 <a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
 <a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">        </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
@@ -4724,68 +4900,360 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* ノードを挿入 */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Insert</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="c1">// 木が空なら、根ノードを初期化する</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">        </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">        </span><span class="c1">// 重複ノードが見つかったら、直ちに返す</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">        </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">        </span><span class="c1">// 挿入位置は cur の右部分木にある</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">        </span><span class="c1">// 挿入位置は cur の左部分木にある</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w">        </span><span class="k">else</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a>
+<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="w">    </span><span class="c1">// ノードを挿入</span>
+<a id="__codelineno-16-24" name="__codelineno-16-24" href="#__codelineno-16-24"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-16-25" name="__codelineno-16-25" href="#__codelineno-16-25"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-26" name="__codelineno-16-26" href="#__codelineno-16-26"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-16-27" name="__codelineno-16-27" href="#__codelineno-16-27"></a><span class="w">            </span><span class="n">pre</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-16-28" name="__codelineno-16-28" href="#__codelineno-16-28"></a><span class="w">        </span><span class="k">else</span>
+<a id="__codelineno-16-29" name="__codelineno-16-29" href="#__codelineno-16-29"></a><span class="w">            </span><span class="n">pre</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-16-30" name="__codelineno-16-30" href="#__codelineno-16-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-31" name="__codelineno-16-31" href="#__codelineno-16-31"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">binarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* ノードを挿入 */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">bst</span><span class="w"> </span><span class="o">*</span><span class="nx">binarySearchTree</span><span class="p">)</span><span class="w"> </span><span class="nx">insert</span><span class="p">(</span><span class="nx">num</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="nx">cur</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">bst</span><span class="p">.</span><span class="nx">root</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="c1">// 木が空なら、根ノードを初期化する</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">        </span><span class="nx">bst</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">NewTreeNode</span><span class="p">(</span><span class="nx">num</span><span class="p">)</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">    </span><span class="c1">// 挿入対象ノードの直前のノード位置</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">pre</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w">            </span><span class="k">return</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w">        </span><span class="nx">pre</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">cur</span>
+<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Val</span><span class="p">.(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="w">            </span><span class="nx">cur</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Right</span>
+<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a><span class="w">            </span><span class="nx">cur</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Left</span>
+<a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-17-22" name="__codelineno-17-22" href="#__codelineno-17-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-23" name="__codelineno-17-23" href="#__codelineno-17-23"></a><span class="w">    </span><span class="c1">// ノードを挿入</span>
+<a id="__codelineno-17-24" name="__codelineno-17-24" href="#__codelineno-17-24"></a><span class="w">    </span><span class="nx">node</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewTreeNode</span><span class="p">(</span><span class="nx">num</span><span class="p">)</span>
+<a id="__codelineno-17-25" name="__codelineno-17-25" href="#__codelineno-17-25"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">pre</span><span class="p">.</span><span class="nx">Val</span><span class="p">.(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-26" name="__codelineno-17-26" href="#__codelineno-17-26"></a><span class="w">        </span><span class="nx">pre</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">node</span>
+<a id="__codelineno-17-27" name="__codelineno-17-27" href="#__codelineno-17-27"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-28" name="__codelineno-17-28" href="#__codelineno-17-28"></a><span class="w">        </span><span class="nx">pre</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">node</span>
+<a id="__codelineno-17-29" name="__codelineno-17-29" href="#__codelineno-17-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-30" name="__codelineno-17-30" href="#__codelineno-17-30"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="bp">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* ノードを挿入 */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="c1">// 木が空なら、根ノードを初期化する</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">        </span><span class="n">root</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">cur</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">root</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">pre</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w">        </span><span class="c1">// 重複ノードが見つかったら、直ちに返す</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="p">!.</span><span class="n">val</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="w">            </span><span class="k">return</span>
+<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="w">        </span><span class="n">pre</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">cur</span>
+<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="w">        </span><span class="c1">// 挿入位置は cur の右部分木にある</span>
+<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="p">!.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">cur</span><span class="p">?.</span><span class="kr">right</span>
+<a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></a><span class="w">        </span><span class="c1">// 挿入位置は cur の左部分木にある</span>
+<a id="__codelineno-18-22" name="__codelineno-18-22" href="#__codelineno-18-22"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-23" name="__codelineno-18-23" href="#__codelineno-18-23"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">cur</span><span class="p">?.</span><span class="kr">left</span>
+<a id="__codelineno-18-24" name="__codelineno-18-24" href="#__codelineno-18-24"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-18-25" name="__codelineno-18-25" href="#__codelineno-18-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-26" name="__codelineno-18-26" href="#__codelineno-18-26"></a><span class="w">    </span><span class="c1">// ノードを挿入</span>
+<a id="__codelineno-18-27" name="__codelineno-18-27" href="#__codelineno-18-27"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-18-28" name="__codelineno-18-28" href="#__codelineno-18-28"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">pre</span><span class="p">!.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-29" name="__codelineno-18-29" href="#__codelineno-18-29"></a><span class="w">        </span><span class="n">pre</span><span class="p">?.</span><span class="kr">right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-18-30" name="__codelineno-18-30" href="#__codelineno-18-30"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-31" name="__codelineno-18-31" href="#__codelineno-18-31"></a><span class="w">        </span><span class="n">pre</span><span class="p">?.</span><span class="kr">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-18-32" name="__codelineno-18-32" href="#__codelineno-18-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-33" name="__codelineno-18-33" href="#__codelineno-18-33"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* ノードを挿入 */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="nx">insert</span><span class="p">(</span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="c1">// 木が空なら、根ノードを初期化する</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="nx">num</span><span class="p">);</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="p">,</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w">        </span><span class="nx">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">        </span><span class="c1">// 重複ノードが見つかったら、直ちに返す</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w">        </span><span class="nx">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">;</span>
+<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w">        </span><span class="c1">// 挿入位置は cur の右部分木にある</span>
+<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
+<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="w">        </span><span class="c1">// 挿入位置は cur の左部分木にある</span>
+<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span>
+<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a><span class="w">    </span><span class="c1">// ノードを挿入</span>
+<a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="nx">num</span><span class="p">);</span>
+<a id="__codelineno-19-22" name="__codelineno-19-22" href="#__codelineno-19-22"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">pre</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="nx">pre</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-19-23" name="__codelineno-19-23" href="#__codelineno-19-23"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="nx">pre</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-19-24" name="__codelineno-19-24" href="#__codelineno-19-24"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* ノードを挿入 */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="nx">insert</span><span class="p">(</span><span class="nx">num</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="c1">// 木が空なら、根ノードを初期化する</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="nx">num</span><span class="p">);</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">cur</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="p">,</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">        </span><span class="nx">pre</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">        </span><span class="c1">// 重複ノードが見つかったら、直ちに返す</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w">        </span><span class="nx">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">;</span>
+<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w">        </span><span class="c1">// 挿入位置は cur の右部分木にある</span>
+<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
+<a id="__codelineno-20-17" name="__codelineno-20-17" href="#__codelineno-20-17"></a><span class="w">        </span><span class="c1">// 挿入位置は cur の左部分木にある</span>
+<a id="__codelineno-20-18" name="__codelineno-20-18" href="#__codelineno-20-18"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span>
+<a id="__codelineno-20-19" name="__codelineno-20-19" href="#__codelineno-20-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-20" name="__codelineno-20-20" href="#__codelineno-20-20"></a><span class="w">    </span><span class="c1">// ノードを挿入</span>
+<a id="__codelineno-20-21" name="__codelineno-20-21" href="#__codelineno-20-21"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="nx">num</span><span class="p">);</span>
+<a id="__codelineno-20-22" name="__codelineno-20-22" href="#__codelineno-20-22"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">pre</span><span class="o">!</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="nx">pre</span><span class="o">!</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-20-23" name="__codelineno-20-23" href="#__codelineno-20-23"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="nx">pre</span><span class="o">!</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
+<a id="__codelineno-20-24" name="__codelineno-20-24" href="#__codelineno-20-24"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* ノードを挿入 */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">insert</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="c1">// 木が空なら、根ノードを初期化する</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">    </span><span class="n">_root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">_num</span><span class="p">);</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">    </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_root</span><span class="p">;</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="w">  </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w">    </span><span class="c1">// 重複ノードが見つかったら、直ちに返す</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">_num</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w">    </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
+<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w">    </span><span class="c1">// 挿入位置は cur の右部分木にある</span>
+<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">_num</span><span class="p">)</span>
+<a id="__codelineno-21-17" name="__codelineno-21-17" href="#__codelineno-21-17"></a><span class="w">      </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-21-18" name="__codelineno-21-18" href="#__codelineno-21-18"></a><span class="w">    </span><span class="c1">// 挿入位置は cur の左部分木にある</span>
+<a id="__codelineno-21-19" name="__codelineno-21-19" href="#__codelineno-21-19"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-21-20" name="__codelineno-21-20" href="#__codelineno-21-20"></a><span class="w">      </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-21-21" name="__codelineno-21-21" href="#__codelineno-21-21"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-22" name="__codelineno-21-22" href="#__codelineno-21-22"></a><span class="w">  </span><span class="c1">// ノードを挿入</span>
+<a id="__codelineno-21-23" name="__codelineno-21-23" href="#__codelineno-21-23"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">_num</span><span class="p">);</span>
+<a id="__codelineno-21-24" name="__codelineno-21-24" href="#__codelineno-21-24"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="o">!</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">_num</span><span class="p">)</span>
+<a id="__codelineno-21-25" name="__codelineno-21-25" href="#__codelineno-21-25"></a><span class="w">    </span><span class="n">pre</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-21-26" name="__codelineno-21-26" href="#__codelineno-21-26"></a><span class="w">  </span><span class="k">else</span>
+<a id="__codelineno-21-27" name="__codelineno-21-27" href="#__codelineno-21-27"></a><span class="w">    </span><span class="n">pre</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-21-28" name="__codelineno-21-28" href="#__codelineno-21-28"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* ノードを挿入 */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="c1">// 木が空なら、根ノードを初期化する</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">root</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">        </span><span class="bp">self</span><span class="p">.</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">TreeNode</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">num</span><span class="p">));</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">root</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">None</span><span class="p">;</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">clone</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">        </span><span class="k">match</span><span class="w"> </span><span class="n">num</span><span class="p">.</span><span class="n">cmp</span><span class="p">(</span><span class="o">&amp;</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">            </span><span class="c1">// 重複ノードが見つかったら、直ちに返す</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">            </span><span class="n">Ordering</span><span class="p">::</span><span class="n">Equal</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="k">return</span><span class="p">,</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="w">            </span><span class="c1">// 挿入位置は cur の右部分木にある</span>
+<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="w">            </span><span class="n">Ordering</span><span class="p">::</span><span class="n">Greater</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="w">                </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="w">                </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a><span class="w">            </span><span class="c1">// 挿入位置は cur の左部分木にある</span>
+<a id="__codelineno-22-21" name="__codelineno-22-21" href="#__codelineno-22-21"></a><span class="w">            </span><span class="n">Ordering</span><span class="p">::</span><span class="n">Less</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-22" name="__codelineno-22-22" href="#__codelineno-22-22"></a><span class="w">                </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-22-23" name="__codelineno-22-23" href="#__codelineno-22-23"></a><span class="w">                </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-22-24" name="__codelineno-22-24" href="#__codelineno-22-24"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-22-25" name="__codelineno-22-25" href="#__codelineno-22-25"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-26" name="__codelineno-22-26" href="#__codelineno-22-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-27" name="__codelineno-22-27" href="#__codelineno-22-27"></a><span class="w">    </span><span class="c1">// ノードを挿入</span>
+<a id="__codelineno-22-28" name="__codelineno-22-28" href="#__codelineno-22-28"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="n">unwrap</span><span class="p">();</span>
+<a id="__codelineno-22-29" name="__codelineno-22-29" href="#__codelineno-22-29"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">TreeNode</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">num</span><span class="p">));</span>
+<a id="__codelineno-22-30" name="__codelineno-22-30" href="#__codelineno-22-30"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-31" name="__codelineno-22-31" href="#__codelineno-22-31"></a><span class="w">        </span><span class="n">pre</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-22-32" name="__codelineno-22-32" href="#__codelineno-22-32"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-33" name="__codelineno-22-33" href="#__codelineno-22-33"></a><span class="w">        </span><span class="n">pre</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-22-34" name="__codelineno-22-34" href="#__codelineno-22-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-35" name="__codelineno-22-35" href="#__codelineno-22-35"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* ノードを挿入 */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">BinarySearchTree</span><span class="w"> </span><span class="o">*</span><span class="n">bst</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="c1">// 木が空なら、根ノードを初期化する</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">bst</span><span class="o">-&gt;</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">        </span><span class="n">bst</span><span class="o">-&gt;</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newTreeNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bst</span><span class="o">-&gt;</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w">        </span><span class="c1">// 重複ノードが見つかったら、直ちに返す</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="w">        </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
+<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="w">            </span><span class="c1">// 挿入位置は cur の右部分木にある</span>
+<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="w">            </span><span class="c1">// 挿入位置は cur の左部分木にある</span>
+<a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-23-23" name="__codelineno-23-23" href="#__codelineno-23-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-24" name="__codelineno-23-24" href="#__codelineno-23-24"></a><span class="w">    </span><span class="c1">// ノードを挿入</span>
+<a id="__codelineno-23-25" name="__codelineno-23-25" href="#__codelineno-23-25"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newTreeNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-23-26" name="__codelineno-23-26" href="#__codelineno-23-26"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-27" name="__codelineno-23-27" href="#__codelineno-23-27"></a><span class="w">        </span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-23-28" name="__codelineno-23-28" href="#__codelineno-23-28"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-29" name="__codelineno-23-29" href="#__codelineno-23-29"></a><span class="w">        </span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-23-30" name="__codelineno-23-30" href="#__codelineno-23-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-31" name="__codelineno-23-31" href="#__codelineno-23-31"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* ノードを挿入 */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="c1">// 木が空なら、根ノードを初期化する</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">        </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">pre</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">        </span><span class="c1">// 重複ノードが見つかったら、直ちに返す</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">_val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w">            </span><span class="k">return</span>
+<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="w">        </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span>
+<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="w">        </span><span class="c1">// 挿入位置は cur の右部分木にある</span>
+<a id="__codelineno-24-17" name="__codelineno-24-17" href="#__codelineno-24-17"></a><span class="w">        </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">_val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-24-18" name="__codelineno-24-18" href="#__codelineno-24-18"></a><span class="w">            </span><span class="n">cur</span><span class="p">.</span><span class="na">right</span>
+<a id="__codelineno-24-19" name="__codelineno-24-19" href="#__codelineno-24-19"></a><span class="w">        </span><span class="c1">// 挿入位置は cur の左部分木にある</span>
+<a id="__codelineno-24-20" name="__codelineno-24-20" href="#__codelineno-24-20"></a><span class="w">        </span><span class="k">else</span>
+<a id="__codelineno-24-21" name="__codelineno-24-21" href="#__codelineno-24-21"></a><span class="w">            </span><span class="n">cur</span><span class="p">.</span><span class="na">left</span>
+<a id="__codelineno-24-22" name="__codelineno-24-22" href="#__codelineno-24-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-24-23" name="__codelineno-24-23" href="#__codelineno-24-23"></a><span class="w">    </span><span class="c1">// ノードを挿入</span>
+<a id="__codelineno-24-24" name="__codelineno-24-24" href="#__codelineno-24-24"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-24-25" name="__codelineno-24-25" href="#__codelineno-24-25"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="o">?.</span><span class="na">_val</span><span class="o">!!</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-24-26" name="__codelineno-24-26" href="#__codelineno-24-26"></a><span class="w">        </span><span class="n">pre</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-24-27" name="__codelineno-24-27" href="#__codelineno-24-27"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-24-28" name="__codelineno-24-28" href="#__codelineno-24-28"></a><span class="w">        </span><span class="n">pre</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-24-29" name="__codelineno-24-29" href="#__codelineno-24-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">BinarySearchTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### ノードを挿入 ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="c1"># 木が空なら、根ノードを初期化する</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="vi">@root</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">    </span><span class="vi">@root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">    </span><span class="k">return</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">  </span><span class="c1"># ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w">  </span><span class="n">cur</span><span class="p">,</span><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@root</span><span class="p">,</span><span class="w"> </span><span class="kp">nil</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">cur</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w">    </span><span class="c1"># 重複ノードが見つかったら、直ちに返す</span>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a>
+<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w">    </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span>
+<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w">    </span><span class="c1"># 挿入位置は cur の右部分木にある</span>
+<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a><span class="w">      </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">right</span>
+<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="w">    </span><span class="c1"># 挿入位置は cur の左部分木にある</span>
+<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="w">      </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">left</span>
+<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a>
+<a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a><span class="w">  </span><span class="c1"># ノードを挿入</span>
+<a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></a><span class="w">  </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-25-27" name="__codelineno-25-27" href="#__codelineno-25-27"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="n">pre</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-25-28" name="__codelineno-25-28" href="#__codelineno-25-28"></a><span class="w">    </span><span class="n">pre</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-25-29" name="__codelineno-25-29" href="#__codelineno-25-29"></a><span class="w">  </span><span class="k">else</span>
+<a id="__codelineno-25-30" name="__codelineno-25-30" href="#__codelineno-25-30"></a><span class="w">    </span><span class="n">pre</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
+<a id="__codelineno-25-31" name="__codelineno-25-31" href="#__codelineno-25-31"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-25-32" name="__codelineno-25-32" href="#__codelineno-25-32"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>ノードの検索と同様に、ノードの挿入には<span class="arithmatex">\(O(\log n)\)</span>の時間を使用します。</p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%29%3A%0A%20%20%20%20%20%20%20%20self.val%20%3D%20val%0A%20%20%20%20%20%20%20%20self.left%20%3D%20None%0A%20%20%20%20%20%20%20%20self.right%20%3D%20None%0A%0A%0Aclass%20BinarySearchTree%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%E6%9C%A8%22%22%22%0A%0A%20%20%20%20def%20__init__%28self%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%82%B3%E3%83%B3%E3%82%B9%E3%83%88%E3%83%A9%E3%82%AF%E3%82%BF%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E7%A9%BA%E3%81%AE%E6%9C%A8%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20self._root%20%3D%20None%0A%0A%20%20%20%20def%20insert%28self%2C%20num%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%8C%BF%E5%85%A5%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E6%9C%A8%E3%81%8C%E7%A9%BA%E3%81%AA%E3%82%89%E3%80%81%E6%A0%B9%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20if%20self._root%20is%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self._root%20%3D%20TreeNode%28num%29%0A%20%20%20%20%20%20%20%20%20%20%20%20return%0A%20%20%20%20%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%97%E3%81%A7%E6%8E%A2%E7%B4%A2%E3%81%97%E3%80%81%E8%91%89%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E8%B6%8A%E3%81%88%E3%81%9F%E3%82%89%E6%8A%9C%E3%81%91%E3%82%8B%0A%20%20%20%20%20%20%20%20cur%2C%20pre%20%3D%20self._root%2C%20None%0A%20%20%20%20%20%20%20%20while%20cur%20is%20not%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E9%87%8D%E8%A4%87%E3%83%8E%E3%83%BC%E3%83%89%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%81%A3%E3%81%9F%E3%82%89%E3%80%81%E7%9B%B4%E3%81%A1%E3%81%AB%E8%BF%94%E3%81%99%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20cur.val%20%3D%3D%20num%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20return%0A%20%20%20%20%20%20%20%20%20%20%20%20pre%20%3D%20cur%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%81%AF%20cur%20%E3%81%AE%E5%8F%B3%E9%83%A8%E5%88%86%E6%9C%A8%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20cur.val%20%3C%20num%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20cur%20%3D%20cur.right%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%81%AF%20cur%20%E3%81%AE%E5%B7%A6%E9%83%A8%E5%88%86%E6%9C%A8%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20cur%20%3D%20cur.left%0A%20%20%20%20%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%8C%BF%E5%85%A5%0A%20%20%20%20%20%20%20%20node%20%3D%20TreeNode%28num%29%0A%20%20%20%20%20%20%20%20if%20pre.val%20%3C%20num%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20pre.right%20%3D%20node%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20pre.left%20%3D%20node%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%E6%9C%A8%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20bst%20%3D%20BinarySearchTree%28%29%0A%20%20%20%20nums%20%3D%20%5B4%2C%202%2C%206%2C%201%2C%203%2C%205%2C%207%5D%0A%20%20%20%20for%20num%20in%20nums%3A%0A%20%20%20%20%20%20%20%20bst.insert%28num%29%0A%0A%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%8C%BF%E5%85%A5%0A%20%20%20%20bst.insert%2816%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=162&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%29%3A%0A%20%20%20%20%20%20%20%20self.val%20%3D%20val%0A%20%20%20%20%20%20%20%20self.left%20%3D%20None%0A%20%20%20%20%20%20%20%20self.right%20%3D%20None%0A%0A%0Aclass%20BinarySearchTree%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%E6%9C%A8%22%22%22%0A%0A%20%20%20%20def%20__init__%28self%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%82%B3%E3%83%B3%E3%82%B9%E3%83%88%E3%83%A9%E3%82%AF%E3%82%BF%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E7%A9%BA%E3%81%AE%E6%9C%A8%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20self._root%20%3D%20None%0A%0A%20%20%20%20def%20insert%28self%2C%20num%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%8C%BF%E5%85%A5%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E6%9C%A8%E3%81%8C%E7%A9%BA%E3%81%AA%E3%82%89%E3%80%81%E6%A0%B9%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20if%20self._root%20is%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self._root%20%3D%20TreeNode%28num%29%0A%20%20%20%20%20%20%20%20%20%20%20%20return%0A%20%20%20%20%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%97%E3%81%A7%E6%8E%A2%E7%B4%A2%E3%81%97%E3%80%81%E8%91%89%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E8%B6%8A%E3%81%88%E3%81%9F%E3%82%89%E6%8A%9C%E3%81%91%E3%82%8B%0A%20%20%20%20%20%20%20%20cur%2C%20pre%20%3D%20self._root%2C%20None%0A%20%20%20%20%20%20%20%20while%20cur%20is%20not%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E9%87%8D%E8%A4%87%E3%83%8E%E3%83%BC%E3%83%89%E3%81%8C%E8%A6%8B%E3%81%A4%E3%81%8B%E3%81%A3%E3%81%9F%E3%82%89%E3%80%81%E7%9B%B4%E3%81%A1%E3%81%AB%E8%BF%94%E3%81%99%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20cur.val%20%3D%3D%20num%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20return%0A%20%20%20%20%20%20%20%20%20%20%20%20pre%20%3D%20cur%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%81%AF%20cur%20%E3%81%AE%E5%8F%B3%E9%83%A8%E5%88%86%E6%9C%A8%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20cur.val%20%3C%20num%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20cur%20%3D%20cur.right%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%8C%BF%E5%85%A5%E4%BD%8D%E7%BD%AE%E3%81%AF%20cur%20%E3%81%AE%E5%B7%A6%E9%83%A8%E5%88%86%E6%9C%A8%E3%81%AB%E3%81%82%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20cur%20%3D%20cur.left%0A%20%20%20%20%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%8C%BF%E5%85%A5%0A%20%20%20%20%20%20%20%20node%20%3D%20TreeNode%28num%29%0A%20%20%20%20%20%20%20%20if%20pre.val%20%3C%20num%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20pre.right%20%3D%20node%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20pre.left%20%3D%20node%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E4%BA%8C%E5%88%86%E6%8E%A2%E7%B4%A2%E6%9C%A8%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20bst%20%3D%20BinarySearchTree%28%29%0A%20%20%20%20nums%20%3D%20%5B4%2C%202%2C%206%2C%201%2C%203%2C%205%2C%207%5D%0A%20%20%20%20for%20num%20in%20nums%3A%0A%20%20%20%20%20%20%20%20bst.insert%28num%29%0A%0A%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%8C%BF%E5%85%A5%0A%20%20%20%20bst.insert%2816%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=162&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<p>ノード探索と同様に、ノード挿入には <span class="arithmatex">\(O(\log n)\)</span> 時間を要します。</p>
 <h3 id="3">3. &nbsp; ノードの削除<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
-<p>まず、二分木でターゲットノードを見つけ、それを削除します。ノードの挿入と同様に、削除操作が完了した後も、二分探索木の性質「左部分木 &lt; 根ノード &lt; 右部分木」が満たされることを保証する必要があります。したがって、ターゲットノードの子ノード数に基づいて、0、1、2の3つのケースに分け、対応するノード削除操作を実行します。</p>
-<p>下図に示すように、削除するノードの次数が<span class="arithmatex">\(0\)</span>の場合、そのノードは葉ノードであることを意味し、直接削除できます。</p>
-<p><img alt="二分探索木でのノード削除（次数0）" class="animation-figure" src="../binary_search_tree.assets/bst_remove_case1.png" /></p>
-<p align="center"> 図 7-19 &nbsp; 二分探索木でのノード削除（次数0） </p>
+<p>まず二分木内で目標ノードを見つけ、その後で削除します。ノード挿入と同様に、削除操作の完了後も二分探索木の「左部分木 &lt; 根ノード &lt; 右部分木」という性質が保たれる必要があります。そのため、目標ノードの子ノード数に応じて、0、1、2 の 3 つのケースに分けて対応する削除操作を行います。</p>
+<p>以下の図に示すように、削除対象ノードの次数が <span class="arithmatex">\(0\)</span> のとき、そのノードは葉ノードであり、直接削除できます。</p>
+<p><img alt="二分探索木でノードを削除する（次数 0 ）" class="animation-figure" src="../binary_search_tree.assets/bst_remove_case1.png" /></p>
+<p align="center"> 図 7-19 &nbsp; 二分探索木でノードを削除する（次数 0 ） </p>
 
-<p>下図に示すように、削除するノードの次数が<span class="arithmatex">\(1\)</span>の場合、削除するノードをその子ノードで置き換えるだけで十分です。</p>
-<p><img alt="二分探索木でのノード削除（次数1）" class="animation-figure" src="../binary_search_tree.assets/bst_remove_case2.png" /></p>
-<p align="center"> 図 7-20 &nbsp; 二分探索木でのノード削除（次数1） </p>
+<p>以下の図に示すように、削除対象ノードの次数が <span class="arithmatex">\(1\)</span> のとき、削除対象ノードをその子ノードで置き換えれば十分です。</p>
+<p><img alt="二分探索木でノードを削除する（次数 1 ）" class="animation-figure" src="../binary_search_tree.assets/bst_remove_case2.png" /></p>
+<p align="center"> 図 7-20 &nbsp; 二分探索木でノードを削除する（次数 1 ） </p>
 
-<p>削除するノードの次数が<span class="arithmatex">\(2\)</span>の場合、直接削除することはできませんが、ノードを使用して置き換える必要があります。二分探索木の性質「左部分木 <span class="arithmatex">\(&lt;\)</span> 根ノード <span class="arithmatex">\(&lt;\)</span> 右部分木」を維持するため、<strong>このノードは右部分木の最小ノードまたは左部分木の最大ノードのいずれかです</strong>。</p>
-<p>右部分木の最小ノード（中順走査での次のノード）を選択すると仮定すると、削除操作は下図に示すように進行します。</p>
+<p>削除対象ノードの次数が <span class="arithmatex">\(2\)</span> のときは、直接削除できず、別のノードでそのノードを置き換える必要があります。二分探索木の「左部分木 <span class="arithmatex">\(&lt;\)</span> 根ノード <span class="arithmatex">\(&lt;\)</span> 右部分木」という性質を保つ必要があるため、<strong>このノードには右部分木の最小ノードまたは左部分木の最大ノードを使えます</strong>。</p>
+<p>右部分木の最小ノード（中順走査で次のノード）を選ぶと仮定すると、削除操作の流れは以下の図のようになります。</p>
 <ol>
-<li>削除するノードの「中順走査シーケンス」での次のノードを見つけ、<code>tmp</code>として示します。</li>
-<li>削除するノードの値を<code>tmp</code>の値で置き換え、木内でノード<code>tmp</code>を再帰的に削除します。</li>
+<li>削除対象ノードの「中順走査列」における次のノードを見つけ、<code>tmp</code> と記します。</li>
+<li><code>tmp</code> の値で削除対象ノードの値を上書きし、木の中でノード <code>tmp</code> を再帰的に削除します。</li>
 </ol>
 <div class="tabbed-set tabbed-alternate" data-tabs="4:4"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">&lt;1&gt;</label><label for="__tabbed_4_2">&lt;2&gt;</label><label for="__tabbed_4_3">&lt;3&gt;</label><label for="__tabbed_4_4">&lt;4&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="二分探索木でのノード削除（次数2）" class="animation-figure" src="../binary_search_tree.assets/bst_remove_case3_step1.png" /></p>
+<p><img alt="二分探索木でノードを削除する（次数 2 ）" class="animation-figure" src="../binary_search_tree.assets/bst_remove_case3_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="bst_remove_case3_step2" class="animation-figure" src="../binary_search_tree.assets/bst_remove_case3_step2.png" /></p>
@@ -4798,110 +5266,110 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 7-21 &nbsp; 二分探索木でのノード削除（次数2） </p>
+<p align="center"> 図 7-21 &nbsp; 二分探索木でノードを削除する（次数 2 ） </p>
 
-<p>ノードを削除する操作も<span class="arithmatex">\(O(\log n)\)</span>の時間を使用します。削除するノードを見つけるのに<span class="arithmatex">\(O(\log n)\)</span>の時間が必要で、中順走査の後継ノードを取得するのに<span class="arithmatex">\(O(\log n)\)</span>の時間が必要です。コード例は以下の通りです：</p>
+<p>ノード削除操作も同様に <span class="arithmatex">\(O(\log n)\)</span> 時間を要します。削除対象ノードの探索に <span class="arithmatex">\(O(\log n)\)</span> 時間、中順走査の後続ノードの取得に <span class="arithmatex">\(O(\log n)\)</span> 時間が必要です。コード例は次のとおりです。</p>
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 <div class="highlight"><span class="filename">binary_search_tree.py</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
 <a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ノードを削除&quot;&quot;&quot;</span>
-<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>    <span class="c1"># 木が空の場合、戻る</span>
+<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>    <span class="c1"># 木が空なら、そのまま早期リターンする</span>
 <a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>    <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_root</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a>        <span class="k">return</span>
-<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a>    <span class="c1"># ループで探索、葉ノードを通過した後にブレーク</span>
+<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a>    <span class="c1"># ループで探索し、葉ノードを越えたら抜ける</span>
 <a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a>    <span class="n">cur</span><span class="p">,</span> <span class="n">pre</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_root</span><span class="p">,</span> <span class="kc">None</span>
 <a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>    <span class="k">while</span> <span class="n">cur</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a>        <span class="c1"># 削除するノードを発見、ループをブレーク</span>
+<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a>        <span class="c1"># 削除対象のノードが見つかったら、ループを抜ける</span>
 <a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a>        <span class="k">if</span> <span class="n">cur</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="n">num</span><span class="p">:</span>
 <a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a>            <span class="k">break</span>
 <a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a>        <span class="n">pre</span> <span class="o">=</span> <span class="n">cur</span>
-<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a>        <span class="c1"># 削除するノードはcurの右部分木にある</span>
+<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a>        <span class="c1"># 削除対象ノードは cur の右部分木にある</span>
 <a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a>        <span class="k">if</span> <span class="n">cur</span><span class="o">.</span><span class="n">val</span> <span class="o">&lt;</span> <span class="n">num</span><span class="p">:</span>
 <a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a>            <span class="n">cur</span> <span class="o">=</span> <span class="n">cur</span><span class="o">.</span><span class="n">right</span>
-<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a>        <span class="c1"># 削除するノードはcurの左部分木にある</span>
+<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a>        <span class="c1"># 削除対象ノードは cur の左部分木にある</span>
 <a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a>        <span class="k">else</span><span class="p">:</span>
 <a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a>            <span class="n">cur</span> <span class="o">=</span> <span class="n">cur</span><span class="o">.</span><span class="n">left</span>
-<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a>    <span class="c1"># 削除するノードが存在しない場合、戻る</span>
+<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a>    <span class="c1"># 削除対象ノードがなければそのまま返す</span>
 <a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a>    <span class="k">if</span> <span class="n">cur</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a>        <span class="k">return</span>
 <a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a>
-<a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a>    <span class="c1"># 子ノード数 = 0 または 1</span>
+<a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a>    <span class="c1"># 子ノード数 = 0 or 1</span>
 <a id="__codelineno-26-24" name="__codelineno-26-24" href="#__codelineno-26-24"></a>    <span class="k">if</span> <span class="n">cur</span><span class="o">.</span><span class="n">left</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">cur</span><span class="o">.</span><span class="n">right</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-26-25" name="__codelineno-26-25" href="#__codelineno-26-25"></a>        <span class="c1"># 子ノード数 = 0/1の場合、child = null/その子ノード</span>
+<a id="__codelineno-26-25" name="__codelineno-26-25" href="#__codelineno-26-25"></a>        <span class="c1"># 子ノード数が 0 / 1 のとき、child = null / その子ノード</span>
 <a id="__codelineno-26-26" name="__codelineno-26-26" href="#__codelineno-26-26"></a>        <span class="n">child</span> <span class="o">=</span> <span class="n">cur</span><span class="o">.</span><span class="n">left</span> <span class="ow">or</span> <span class="n">cur</span><span class="o">.</span><span class="n">right</span>
-<a id="__codelineno-26-27" name="__codelineno-26-27" href="#__codelineno-26-27"></a>        <span class="c1"># ノードcurを削除</span>
+<a id="__codelineno-26-27" name="__codelineno-26-27" href="#__codelineno-26-27"></a>        <span class="c1"># ノード cur を削除する</span>
 <a id="__codelineno-26-28" name="__codelineno-26-28" href="#__codelineno-26-28"></a>        <span class="k">if</span> <span class="n">cur</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_root</span><span class="p">:</span>
 <a id="__codelineno-26-29" name="__codelineno-26-29" href="#__codelineno-26-29"></a>            <span class="k">if</span> <span class="n">pre</span><span class="o">.</span><span class="n">left</span> <span class="o">==</span> <span class="n">cur</span><span class="p">:</span>
 <a id="__codelineno-26-30" name="__codelineno-26-30" href="#__codelineno-26-30"></a>                <span class="n">pre</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">child</span>
 <a id="__codelineno-26-31" name="__codelineno-26-31" href="#__codelineno-26-31"></a>            <span class="k">else</span><span class="p">:</span>
 <a id="__codelineno-26-32" name="__codelineno-26-32" href="#__codelineno-26-32"></a>                <span class="n">pre</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="n">child</span>
 <a id="__codelineno-26-33" name="__codelineno-26-33" href="#__codelineno-26-33"></a>        <span class="k">else</span><span class="p">:</span>
-<a id="__codelineno-26-34" name="__codelineno-26-34" href="#__codelineno-26-34"></a>            <span class="c1"># 削除されるノードがルートの場合、ルートを再割り当て</span>
+<a id="__codelineno-26-34" name="__codelineno-26-34" href="#__codelineno-26-34"></a>            <span class="c1"># 削除ノードが根ノードなら、根ノードを再設定</span>
 <a id="__codelineno-26-35" name="__codelineno-26-35" href="#__codelineno-26-35"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_root</span> <span class="o">=</span> <span class="n">child</span>
 <a id="__codelineno-26-36" name="__codelineno-26-36" href="#__codelineno-26-36"></a>    <span class="c1"># 子ノード数 = 2</span>
 <a id="__codelineno-26-37" name="__codelineno-26-37" href="#__codelineno-26-37"></a>    <span class="k">else</span><span class="p">:</span>
-<a id="__codelineno-26-38" name="__codelineno-26-38" href="#__codelineno-26-38"></a>        <span class="c1"># curの中順走査の次のノードを取得</span>
+<a id="__codelineno-26-38" name="__codelineno-26-38" href="#__codelineno-26-38"></a>        <span class="c1"># 中順走査における cur の次ノードを取得</span>
 <a id="__codelineno-26-39" name="__codelineno-26-39" href="#__codelineno-26-39"></a>        <span class="n">tmp</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">=</span> <span class="n">cur</span><span class="o">.</span><span class="n">right</span>
 <a id="__codelineno-26-40" name="__codelineno-26-40" href="#__codelineno-26-40"></a>        <span class="k">while</span> <span class="n">tmp</span><span class="o">.</span><span class="n">left</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-26-41" name="__codelineno-26-41" href="#__codelineno-26-41"></a>            <span class="n">tmp</span> <span class="o">=</span> <span class="n">tmp</span><span class="o">.</span><span class="n">left</span>
-<a id="__codelineno-26-42" name="__codelineno-26-42" href="#__codelineno-26-42"></a>        <span class="c1"># 再帰的にノードtmpを削除</span>
+<a id="__codelineno-26-42" name="__codelineno-26-42" href="#__codelineno-26-42"></a>        <span class="c1"># ノード tmp を再帰的に削除</span>
 <a id="__codelineno-26-43" name="__codelineno-26-43" href="#__codelineno-26-43"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">tmp</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
-<a id="__codelineno-26-44" name="__codelineno-26-44" href="#__codelineno-26-44"></a>        <span class="c1"># curをtmpで置き換え</span>
+<a id="__codelineno-26-44" name="__codelineno-26-44" href="#__codelineno-26-44"></a>        <span class="c1"># tmp で cur を上書きする</span>
 <a id="__codelineno-26-45" name="__codelineno-26-45" href="#__codelineno-26-45"></a>        <span class="n">cur</span><span class="o">.</span><span class="n">val</span> <span class="o">=</span> <span class="n">tmp</span><span class="o">.</span><span class="n">val</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_search_tree.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* ノードを削除 */</span>
 <a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="c1">// 木が空の場合、戻る</span>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="c1">// 木が空なら、そのまま早期リターンする</span>
 <a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
 <a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
-<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">    </span><span class="c1">// ループで検索、葉ノードを通り過ぎたら終了</span>
+<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
 <a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="w">        </span><span class="c1">// 削除するノードを見つけた、ループを抜ける</span>
+<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="w">        </span><span class="c1">// 削除対象のノードが見つかったら、ループを抜ける</span>
 <a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
 <a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
 <a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="w">        </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
-<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w">        </span><span class="c1">// 削除するノードはcurの右部分木にある</span>
+<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w">        </span><span class="c1">// 削除対象ノードは cur の右部分木にある</span>
 <a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
 <a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
-<a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></a><span class="w">        </span><span class="c1">// 削除するノードはcurの左部分木にある</span>
+<a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></a><span class="w">        </span><span class="c1">// 削除対象ノードは cur の左部分木にある</span>
 <a id="__codelineno-27-17" name="__codelineno-27-17" href="#__codelineno-27-17"></a><span class="w">        </span><span class="k">else</span>
 <a id="__codelineno-27-18" name="__codelineno-27-18" href="#__codelineno-27-18"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">;</span>
 <a id="__codelineno-27-19" name="__codelineno-27-19" href="#__codelineno-27-19"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-27-20" name="__codelineno-27-20" href="#__codelineno-27-20"></a><span class="w">    </span><span class="c1">// 削除するノードがない場合、戻る</span>
+<a id="__codelineno-27-20" name="__codelineno-27-20" href="#__codelineno-27-20"></a><span class="w">    </span><span class="c1">// 削除対象ノードがなければそのまま返す</span>
 <a id="__codelineno-27-21" name="__codelineno-27-21" href="#__codelineno-27-21"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
 <a id="__codelineno-27-22" name="__codelineno-27-22" href="#__codelineno-27-22"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-27-23" name="__codelineno-27-23" href="#__codelineno-27-23"></a><span class="w">    </span><span class="c1">// 子ノード数 = 0 または 1</span>
+<a id="__codelineno-27-23" name="__codelineno-27-23" href="#__codelineno-27-23"></a><span class="w">    </span><span class="c1">// 子ノード数 = 0 or 1</span>
 <a id="__codelineno-27-24" name="__codelineno-27-24" href="#__codelineno-27-24"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-25" name="__codelineno-27-25" href="#__codelineno-27-25"></a><span class="w">        </span><span class="c1">// 子ノード数 = 0 / 1の場合、child = nullptr / その子ノード</span>
+<a id="__codelineno-27-25" name="__codelineno-27-25" href="#__codelineno-27-25"></a><span class="w">        </span><span class="c1">// 子ノード数 = 0 / 1 のとき、child = nullptr / その子ノード</span>
 <a id="__codelineno-27-26" name="__codelineno-27-26" href="#__codelineno-27-26"></a><span class="w">        </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
-<a id="__codelineno-27-27" name="__codelineno-27-27" href="#__codelineno-27-27"></a><span class="w">        </span><span class="c1">// ノードcurを削除</span>
+<a id="__codelineno-27-27" name="__codelineno-27-27" href="#__codelineno-27-27"></a><span class="w">        </span><span class="c1">// ノード cur を削除する</span>
 <a id="__codelineno-27-28" name="__codelineno-27-28" href="#__codelineno-27-28"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-29" name="__codelineno-27-29" href="#__codelineno-27-29"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">cur</span><span class="p">)</span>
 <a id="__codelineno-27-30" name="__codelineno-27-30" href="#__codelineno-27-30"></a><span class="w">                </span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
 <a id="__codelineno-27-31" name="__codelineno-27-31" href="#__codelineno-27-31"></a><span class="w">            </span><span class="k">else</span>
 <a id="__codelineno-27-32" name="__codelineno-27-32" href="#__codelineno-27-32"></a><span class="w">                </span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
 <a id="__codelineno-27-33" name="__codelineno-27-33" href="#__codelineno-27-33"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-34" name="__codelineno-27-34" href="#__codelineno-27-34"></a><span class="w">            </span><span class="c1">// 削除されるノードがルートの場合、ルートを再割り当て</span>
+<a id="__codelineno-27-34" name="__codelineno-27-34" href="#__codelineno-27-34"></a><span class="w">            </span><span class="c1">// 削除ノードが根ノードなら、根ノードを再設定</span>
 <a id="__codelineno-27-35" name="__codelineno-27-35" href="#__codelineno-27-35"></a><span class="w">            </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
 <a id="__codelineno-27-36" name="__codelineno-27-36" href="#__codelineno-27-36"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-27-37" name="__codelineno-27-37" href="#__codelineno-27-37"></a><span class="w">        </span><span class="c1">// メモリを解放</span>
+<a id="__codelineno-27-37" name="__codelineno-27-37" href="#__codelineno-27-37"></a><span class="w">        </span><span class="c1">// メモリを解放する</span>
 <a id="__codelineno-27-38" name="__codelineno-27-38" href="#__codelineno-27-38"></a><span class="w">        </span><span class="k">delete</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
 <a id="__codelineno-27-39" name="__codelineno-27-39" href="#__codelineno-27-39"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-27-40" name="__codelineno-27-40" href="#__codelineno-27-40"></a><span class="w">    </span><span class="c1">// 子ノード数 = 2</span>
 <a id="__codelineno-27-41" name="__codelineno-27-41" href="#__codelineno-27-41"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-27-42" name="__codelineno-27-42" href="#__codelineno-27-42"></a><span class="w">        </span><span class="c1">// curの中順走査の次のノードを取得</span>
+<a id="__codelineno-27-42" name="__codelineno-27-42" href="#__codelineno-27-42"></a><span class="w">        </span><span class="c1">// 中順走査における cur の次ノードを取得</span>
 <a id="__codelineno-27-43" name="__codelineno-27-43" href="#__codelineno-27-43"></a><span class="w">        </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
 <a id="__codelineno-27-44" name="__codelineno-27-44" href="#__codelineno-27-44"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-27-45" name="__codelineno-27-45" href="#__codelineno-27-45"></a><span class="w">            </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">;</span>
 <a id="__codelineno-27-46" name="__codelineno-27-46" href="#__codelineno-27-46"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-27-47" name="__codelineno-27-47" href="#__codelineno-27-47"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">tmpVal</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
-<a id="__codelineno-27-48" name="__codelineno-27-48" href="#__codelineno-27-48"></a><span class="w">        </span><span class="c1">// ノードtmpを再帰的に削除</span>
+<a id="__codelineno-27-48" name="__codelineno-27-48" href="#__codelineno-27-48"></a><span class="w">        </span><span class="c1">// ノード tmp を再帰的に削除</span>
 <a id="__codelineno-27-49" name="__codelineno-27-49" href="#__codelineno-27-49"></a><span class="w">        </span><span class="n">remove</span><span class="p">(</span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
-<a id="__codelineno-27-50" name="__codelineno-27-50" href="#__codelineno-27-50"></a><span class="w">        </span><span class="c1">// curをtmpで置き換え</span>
+<a id="__codelineno-27-50" name="__codelineno-27-50" href="#__codelineno-27-50"></a><span class="w">        </span><span class="c1">// tmp で cur を上書きする</span>
 <a id="__codelineno-27-51" name="__codelineno-27-51" href="#__codelineno-27-51"></a><span class="w">        </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmpVal</span><span class="p">;</span>
 <a id="__codelineno-27-52" name="__codelineno-27-52" href="#__codelineno-27-52"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-27-53" name="__codelineno-27-53" href="#__codelineno-27-53"></a><span class="p">}</span>
@@ -4910,107 +5378,629 @@
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_search_tree.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* ノードを削除 */</span>
 <a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="c1">// 木が空の場合、戻る</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="c1">// 木が空なら、そのまま早期リターンする</span>
 <a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
 <a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
-<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">    </span><span class="c1">// ループで検索、葉ノードを通過後に終了</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
 <a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="w">        </span><span class="c1">// 削除するノードを見つけた、ループを終了</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="w">        </span><span class="c1">// 削除対象のノードが見つかったら、ループを抜ける</span>
 <a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
 <a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
 <a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a><span class="w">        </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
-<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w">        </span><span class="c1">// 削除するノードは cur の右部分木にある</span>
+<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w">        </span><span class="c1">// 削除対象ノードは cur の右部分木にある</span>
 <a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
 <a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">right</span><span class="p">;</span>
-<a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a><span class="w">        </span><span class="c1">// 削除するノードは cur の左部分木にある</span>
+<a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a><span class="w">        </span><span class="c1">// 削除対象ノードは cur の左部分木にある</span>
 <a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a><span class="w">        </span><span class="k">else</span>
 <a id="__codelineno-28-18" name="__codelineno-28-18" href="#__codelineno-28-18"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">left</span><span class="p">;</span>
 <a id="__codelineno-28-19" name="__codelineno-28-19" href="#__codelineno-28-19"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-28-20" name="__codelineno-28-20" href="#__codelineno-28-20"></a><span class="w">    </span><span class="c1">// 削除するノードがない場合、戻る</span>
+<a id="__codelineno-28-20" name="__codelineno-28-20" href="#__codelineno-28-20"></a><span class="w">    </span><span class="c1">// 削除対象ノードがなければそのまま返す</span>
 <a id="__codelineno-28-21" name="__codelineno-28-21" href="#__codelineno-28-21"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
 <a id="__codelineno-28-22" name="__codelineno-28-22" href="#__codelineno-28-22"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-28-23" name="__codelineno-28-23" href="#__codelineno-28-23"></a><span class="w">    </span><span class="c1">// 子ノード数 = 0 または 1</span>
+<a id="__codelineno-28-23" name="__codelineno-28-23" href="#__codelineno-28-23"></a><span class="w">    </span><span class="c1">// 子ノード数 = 0 or 1</span>
 <a id="__codelineno-28-24" name="__codelineno-28-24" href="#__codelineno-28-24"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-28-25" name="__codelineno-28-25" href="#__codelineno-28-25"></a><span class="w">        </span><span class="c1">// 子ノード数 = 0/1 の場合、child = null/その子ノード</span>
+<a id="__codelineno-28-25" name="__codelineno-28-25" href="#__codelineno-28-25"></a><span class="w">        </span><span class="c1">// 子ノード数が 0 / 1 のとき、child = null / その子ノード</span>
 <a id="__codelineno-28-26" name="__codelineno-28-26" href="#__codelineno-28-26"></a><span class="w">        </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">right</span><span class="p">;</span>
-<a id="__codelineno-28-27" name="__codelineno-28-27" href="#__codelineno-28-27"></a><span class="w">        </span><span class="c1">// ノード cur を削除</span>
+<a id="__codelineno-28-27" name="__codelineno-28-27" href="#__codelineno-28-27"></a><span class="w">        </span><span class="c1">// ノード cur を削除する</span>
 <a id="__codelineno-28-28" name="__codelineno-28-28" href="#__codelineno-28-28"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-29" name="__codelineno-28-29" href="#__codelineno-28-29"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">cur</span><span class="p">)</span>
 <a id="__codelineno-28-30" name="__codelineno-28-30" href="#__codelineno-28-30"></a><span class="w">                </span><span class="n">pre</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
 <a id="__codelineno-28-31" name="__codelineno-28-31" href="#__codelineno-28-31"></a><span class="w">            </span><span class="k">else</span>
 <a id="__codelineno-28-32" name="__codelineno-28-32" href="#__codelineno-28-32"></a><span class="w">                </span><span class="n">pre</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
 <a id="__codelineno-28-33" name="__codelineno-28-33" href="#__codelineno-28-33"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-28-34" name="__codelineno-28-34" href="#__codelineno-28-34"></a><span class="w">            </span><span class="c1">// 削除されるノードが根の場合、根を再割り当て</span>
+<a id="__codelineno-28-34" name="__codelineno-28-34" href="#__codelineno-28-34"></a><span class="w">            </span><span class="c1">// 削除ノードが根ノードなら、根ノードを再設定</span>
 <a id="__codelineno-28-35" name="__codelineno-28-35" href="#__codelineno-28-35"></a><span class="w">            </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
 <a id="__codelineno-28-36" name="__codelineno-28-36" href="#__codelineno-28-36"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-28-37" name="__codelineno-28-37" href="#__codelineno-28-37"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-28-38" name="__codelineno-28-38" href="#__codelineno-28-38"></a><span class="w">    </span><span class="c1">// 子ノード数 = 2</span>
 <a id="__codelineno-28-39" name="__codelineno-28-39" href="#__codelineno-28-39"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-28-40" name="__codelineno-28-40" href="#__codelineno-28-40"></a><span class="w">        </span><span class="c1">// cur の中順走査の次のノードを取得</span>
+<a id="__codelineno-28-40" name="__codelineno-28-40" href="#__codelineno-28-40"></a><span class="w">        </span><span class="c1">// 中順走査における cur の次ノードを取得</span>
 <a id="__codelineno-28-41" name="__codelineno-28-41" href="#__codelineno-28-41"></a><span class="w">        </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">right</span><span class="p">;</span>
 <a id="__codelineno-28-42" name="__codelineno-28-42" href="#__codelineno-28-42"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">tmp</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-28-43" name="__codelineno-28-43" href="#__codelineno-28-43"></a><span class="w">            </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="na">left</span><span class="p">;</span>
 <a id="__codelineno-28-44" name="__codelineno-28-44" href="#__codelineno-28-44"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-28-45" name="__codelineno-28-45" href="#__codelineno-28-45"></a><span class="w">        </span><span class="c1">// 再帰的にノード tmp を削除</span>
+<a id="__codelineno-28-45" name="__codelineno-28-45" href="#__codelineno-28-45"></a><span class="w">        </span><span class="c1">// ノード tmp を再帰的に削除</span>
 <a id="__codelineno-28-46" name="__codelineno-28-46" href="#__codelineno-28-46"></a><span class="w">        </span><span class="n">remove</span><span class="p">(</span><span class="n">tmp</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
-<a id="__codelineno-28-47" name="__codelineno-28-47" href="#__codelineno-28-47"></a><span class="w">        </span><span class="c1">// cur を tmp で置き換える</span>
+<a id="__codelineno-28-47" name="__codelineno-28-47" href="#__codelineno-28-47"></a><span class="w">        </span><span class="c1">// tmp で cur を上書きする</span>
 <a id="__codelineno-28-48" name="__codelineno-28-48" href="#__codelineno-28-48"></a><span class="w">        </span><span class="n">cur</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
 <a id="__codelineno-28-49" name="__codelineno-28-49" href="#__codelineno-28-49"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-28-50" name="__codelineno-28-50" href="#__codelineno-28-50"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* ノードを削除 */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="c1">// 木が空なら、そのまま早期リターンする</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">        </span><span class="c1">// 削除対象のノードが見つかったら、ループを抜ける</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="w">        </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w">        </span><span class="c1">// 削除対象ノードは cur の右部分木にある</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w">        </span><span class="c1">// 削除対象ノードは cur の左部分木にある</span>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="w">        </span><span class="k">else</span>
+<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-20" name="__codelineno-29-20" href="#__codelineno-29-20"></a><span class="w">    </span><span class="c1">// 削除対象ノードがなければそのまま返す</span>
+<a id="__codelineno-29-21" name="__codelineno-29-21" href="#__codelineno-29-21"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span>
+<a id="__codelineno-29-22" name="__codelineno-29-22" href="#__codelineno-29-22"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-29-23" name="__codelineno-29-23" href="#__codelineno-29-23"></a><span class="w">    </span><span class="c1">// 子ノード数 = 0 or 1</span>
+<a id="__codelineno-29-24" name="__codelineno-29-24" href="#__codelineno-29-24"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-25" name="__codelineno-29-25" href="#__codelineno-29-25"></a><span class="w">        </span><span class="c1">// 子ノード数が 0 / 1 のとき、child = null / その子ノード</span>
+<a id="__codelineno-29-26" name="__codelineno-29-26" href="#__codelineno-29-26"></a><span class="w">        </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">??</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-29-27" name="__codelineno-29-27" href="#__codelineno-29-27"></a><span class="w">        </span><span class="c1">// ノード cur を削除する</span>
+<a id="__codelineno-29-28" name="__codelineno-29-28" href="#__codelineno-29-28"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-29" name="__codelineno-29-29" href="#__codelineno-29-29"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="o">!</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">cur</span><span class="p">)</span>
+<a id="__codelineno-29-30" name="__codelineno-29-30" href="#__codelineno-29-30"></a><span class="w">                </span><span class="n">pre</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-29-31" name="__codelineno-29-31" href="#__codelineno-29-31"></a><span class="w">            </span><span class="k">else</span>
+<a id="__codelineno-29-32" name="__codelineno-29-32" href="#__codelineno-29-32"></a><span class="w">                </span><span class="n">pre</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-29-33" name="__codelineno-29-33" href="#__codelineno-29-33"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-34" name="__codelineno-29-34" href="#__codelineno-29-34"></a><span class="w">            </span><span class="c1">// 削除ノードが根ノードなら、根ノードを再設定</span>
+<a id="__codelineno-29-35" name="__codelineno-29-35" href="#__codelineno-29-35"></a><span class="w">            </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-29-36" name="__codelineno-29-36" href="#__codelineno-29-36"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-37" name="__codelineno-29-37" href="#__codelineno-29-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-38" name="__codelineno-29-38" href="#__codelineno-29-38"></a><span class="w">    </span><span class="c1">// 子ノード数 = 2</span>
+<a id="__codelineno-29-39" name="__codelineno-29-39" href="#__codelineno-29-39"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-40" name="__codelineno-29-40" href="#__codelineno-29-40"></a><span class="w">        </span><span class="c1">// 中順走査における cur の次ノードを取得</span>
+<a id="__codelineno-29-41" name="__codelineno-29-41" href="#__codelineno-29-41"></a><span class="w">        </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-29-42" name="__codelineno-29-42" href="#__codelineno-29-42"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">tmp</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-43" name="__codelineno-29-43" href="#__codelineno-29-43"></a><span class="w">            </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-29-44" name="__codelineno-29-44" href="#__codelineno-29-44"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-45" name="__codelineno-29-45" href="#__codelineno-29-45"></a><span class="w">        </span><span class="c1">// ノード tmp を再帰的に削除</span>
+<a id="__codelineno-29-46" name="__codelineno-29-46" href="#__codelineno-29-46"></a><span class="w">        </span><span class="n">Remove</span><span class="p">(</span><span class="n">tmp</span><span class="p">.</span><span class="n">val</span><span class="o">!</span><span class="p">.</span><span class="n">Value</span><span class="p">);</span>
+<a id="__codelineno-29-47" name="__codelineno-29-47" href="#__codelineno-29-47"></a><span class="w">        </span><span class="c1">// tmp で cur を上書きする</span>
+<a id="__codelineno-29-48" name="__codelineno-29-48" href="#__codelineno-29-48"></a><span class="w">        </span><span class="n">cur</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-29-49" name="__codelineno-29-49" href="#__codelineno-29-49"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-50" name="__codelineno-29-50" href="#__codelineno-29-50"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">binarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* ノードを削除 */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">bst</span><span class="w"> </span><span class="o">*</span><span class="nx">binarySearchTree</span><span class="p">)</span><span class="w"> </span><span class="nx">remove</span><span class="p">(</span><span class="nx">num</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="nx">cur</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">bst</span><span class="p">.</span><span class="nx">root</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="c1">// 木が空なら、そのまま早期リターンする</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">    </span><span class="c1">// 削除対象ノードの直前のノード位置</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">pre</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w">        </span><span class="nx">pre</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">cur</span>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Val</span><span class="p">.(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="w">            </span><span class="c1">// 削除対象ノードは右部分木にある</span>
+<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a><span class="w">            </span><span class="nx">cur</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Right</span>
+<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></a><span class="w">            </span><span class="c1">// 削除対象ノードは左部分木にある</span>
+<a id="__codelineno-30-21" name="__codelineno-30-21" href="#__codelineno-30-21"></a><span class="w">            </span><span class="nx">cur</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Left</span>
+<a id="__codelineno-30-22" name="__codelineno-30-22" href="#__codelineno-30-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-30-23" name="__codelineno-30-23" href="#__codelineno-30-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-24" name="__codelineno-30-24" href="#__codelineno-30-24"></a><span class="w">    </span><span class="c1">// 削除対象ノードがなければそのまま返す</span>
+<a id="__codelineno-30-25" name="__codelineno-30-25" href="#__codelineno-30-25"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-26" name="__codelineno-30-26" href="#__codelineno-30-26"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-30-27" name="__codelineno-30-27" href="#__codelineno-30-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-28" name="__codelineno-30-28" href="#__codelineno-30-28"></a><span class="w">    </span><span class="c1">// 子ノード数は 0 または 1</span>
+<a id="__codelineno-30-29" name="__codelineno-30-29" href="#__codelineno-30-29"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-30" name="__codelineno-30-30" href="#__codelineno-30-30"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nx">child</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-30-31" name="__codelineno-30-31" href="#__codelineno-30-31"></a><span class="w">        </span><span class="c1">// 削除対象ノードの子ノードを取り出す</span>
+<a id="__codelineno-30-32" name="__codelineno-30-32" href="#__codelineno-30-32"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-33" name="__codelineno-30-33" href="#__codelineno-30-33"></a><span class="w">            </span><span class="nx">child</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Left</span>
+<a id="__codelineno-30-34" name="__codelineno-30-34" href="#__codelineno-30-34"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-35" name="__codelineno-30-35" href="#__codelineno-30-35"></a><span class="w">            </span><span class="nx">child</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Right</span>
+<a id="__codelineno-30-36" name="__codelineno-30-36" href="#__codelineno-30-36"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-30-37" name="__codelineno-30-37" href="#__codelineno-30-37"></a><span class="w">        </span><span class="c1">// ノード cur を削除する</span>
+<a id="__codelineno-30-38" name="__codelineno-30-38" href="#__codelineno-30-38"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nx">bst</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-39" name="__codelineno-30-39" href="#__codelineno-30-39"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="nx">pre</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-40" name="__codelineno-30-40" href="#__codelineno-30-40"></a><span class="w">                </span><span class="nx">pre</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">child</span>
+<a id="__codelineno-30-41" name="__codelineno-30-41" href="#__codelineno-30-41"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-42" name="__codelineno-30-42" href="#__codelineno-30-42"></a><span class="w">                </span><span class="nx">pre</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">child</span>
+<a id="__codelineno-30-43" name="__codelineno-30-43" href="#__codelineno-30-43"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-30-44" name="__codelineno-30-44" href="#__codelineno-30-44"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-45" name="__codelineno-30-45" href="#__codelineno-30-45"></a><span class="w">            </span><span class="c1">// 削除ノードが根ノードなら、根ノードを再設定</span>
+<a id="__codelineno-30-46" name="__codelineno-30-46" href="#__codelineno-30-46"></a><span class="w">            </span><span class="nx">bst</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">child</span>
+<a id="__codelineno-30-47" name="__codelineno-30-47" href="#__codelineno-30-47"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-30-48" name="__codelineno-30-48" href="#__codelineno-30-48"></a><span class="w">        </span><span class="c1">// 子ノード数は 2</span>
+<a id="__codelineno-30-49" name="__codelineno-30-49" href="#__codelineno-30-49"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-50" name="__codelineno-30-50" href="#__codelineno-30-50"></a><span class="w">        </span><span class="c1">// 中順走査で削除対象ノード `cur` の次のノードを取得する</span>
+<a id="__codelineno-30-51" name="__codelineno-30-51" href="#__codelineno-30-51"></a><span class="w">        </span><span class="nx">tmp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Right</span>
+<a id="__codelineno-30-52" name="__codelineno-30-52" href="#__codelineno-30-52"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">tmp</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-53" name="__codelineno-30-53" href="#__codelineno-30-53"></a><span class="w">            </span><span class="nx">tmp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">.</span><span class="nx">Left</span>
+<a id="__codelineno-30-54" name="__codelineno-30-54" href="#__codelineno-30-54"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-30-55" name="__codelineno-30-55" href="#__codelineno-30-55"></a><span class="w">        </span><span class="c1">// ノード tmp を再帰的に削除</span>
+<a id="__codelineno-30-56" name="__codelineno-30-56" href="#__codelineno-30-56"></a><span class="w">        </span><span class="nx">bst</span><span class="p">.</span><span class="nx">remove</span><span class="p">(</span><span class="nx">tmp</span><span class="p">.</span><span class="nx">Val</span><span class="p">.(</span><span class="kt">int</span><span class="p">))</span>
+<a id="__codelineno-30-57" name="__codelineno-30-57" href="#__codelineno-30-57"></a><span class="w">        </span><span class="c1">// tmp で cur を上書きする</span>
+<a id="__codelineno-30-58" name="__codelineno-30-58" href="#__codelineno-30-58"></a><span class="w">        </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">.</span><span class="nx">Val</span>
+<a id="__codelineno-30-59" name="__codelineno-30-59" href="#__codelineno-30-59"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-60" name="__codelineno-30-60" href="#__codelineno-30-60"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* ノードを削除 */</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w">    </span><span class="c1">// 木が空なら、そのまま早期リターンする</span>
+<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">cur</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">root</span>
+<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">pre</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?</span>
+<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="w">        </span><span class="c1">// 削除対象のノードが見つかったら、ループを抜ける</span>
+<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="p">!.</span><span class="n">val</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></a><span class="w">        </span><span class="n">pre</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">cur</span>
+<a id="__codelineno-31-16" name="__codelineno-31-16" href="#__codelineno-31-16"></a><span class="w">        </span><span class="c1">// 削除対象ノードは cur の右部分木にある</span>
+<a id="__codelineno-31-17" name="__codelineno-31-17" href="#__codelineno-31-17"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="p">!.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-18" name="__codelineno-31-18" href="#__codelineno-31-18"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">cur</span><span class="p">?.</span><span class="kr">right</span>
+<a id="__codelineno-31-19" name="__codelineno-31-19" href="#__codelineno-31-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-31-20" name="__codelineno-31-20" href="#__codelineno-31-20"></a><span class="w">        </span><span class="c1">// 削除対象ノードは cur の左部分木にある</span>
+<a id="__codelineno-31-21" name="__codelineno-31-21" href="#__codelineno-31-21"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-22" name="__codelineno-31-22" href="#__codelineno-31-22"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">cur</span><span class="p">?.</span><span class="kr">left</span>
+<a id="__codelineno-31-23" name="__codelineno-31-23" href="#__codelineno-31-23"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-31-24" name="__codelineno-31-24" href="#__codelineno-31-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-25" name="__codelineno-31-25" href="#__codelineno-31-25"></a><span class="w">    </span><span class="c1">// 削除対象ノードがなければそのまま返す</span>
+<a id="__codelineno-31-26" name="__codelineno-31-26" href="#__codelineno-31-26"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-27" name="__codelineno-31-27" href="#__codelineno-31-27"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-31-28" name="__codelineno-31-28" href="#__codelineno-31-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-29" name="__codelineno-31-29" href="#__codelineno-31-29"></a><span class="w">    </span><span class="c1">// 子ノード数 = 0 or 1</span>
+<a id="__codelineno-31-30" name="__codelineno-31-30" href="#__codelineno-31-30"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="p">?.</span><span class="kr">left</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">cur</span><span class="p">?.</span><span class="kr">right</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-31" name="__codelineno-31-31" href="#__codelineno-31-31"></a><span class="w">        </span><span class="c1">// 子ノード数が 0 / 1 のとき、child = null / その子ノード</span>
+<a id="__codelineno-31-32" name="__codelineno-31-32" href="#__codelineno-31-32"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">child</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">cur</span><span class="p">?.</span><span class="kr">left</span><span class="w"> </span><span class="p">??</span><span class="w"> </span><span class="n">cur</span><span class="p">?.</span><span class="kr">right</span>
+<a id="__codelineno-31-33" name="__codelineno-31-33" href="#__codelineno-31-33"></a><span class="w">        </span><span class="c1">// ノード cur を削除する</span>
+<a id="__codelineno-31-34" name="__codelineno-31-34" href="#__codelineno-31-34"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-35" name="__codelineno-31-35" href="#__codelineno-31-35"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">pre</span><span class="p">?.</span><span class="kr">left</span><span class="w"> </span><span class="p">===</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-36" name="__codelineno-31-36" href="#__codelineno-31-36"></a><span class="w">                </span><span class="n">pre</span><span class="p">?.</span><span class="kr">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">child</span>
+<a id="__codelineno-31-37" name="__codelineno-31-37" href="#__codelineno-31-37"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-38" name="__codelineno-31-38" href="#__codelineno-31-38"></a><span class="w">                </span><span class="n">pre</span><span class="p">?.</span><span class="kr">right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">child</span>
+<a id="__codelineno-31-39" name="__codelineno-31-39" href="#__codelineno-31-39"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-31-40" name="__codelineno-31-40" href="#__codelineno-31-40"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-41" name="__codelineno-31-41" href="#__codelineno-31-41"></a><span class="w">            </span><span class="c1">// 削除ノードが根ノードなら、根ノードを再設定</span>
+<a id="__codelineno-31-42" name="__codelineno-31-42" href="#__codelineno-31-42"></a><span class="w">            </span><span class="n">root</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">child</span>
+<a id="__codelineno-31-43" name="__codelineno-31-43" href="#__codelineno-31-43"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-31-44" name="__codelineno-31-44" href="#__codelineno-31-44"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-45" name="__codelineno-31-45" href="#__codelineno-31-45"></a><span class="w">    </span><span class="c1">// 子ノード数 = 2</span>
+<a id="__codelineno-31-46" name="__codelineno-31-46" href="#__codelineno-31-46"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-47" name="__codelineno-31-47" href="#__codelineno-31-47"></a><span class="w">        </span><span class="c1">// 中順走査における cur の次ノードを取得</span>
+<a id="__codelineno-31-48" name="__codelineno-31-48" href="#__codelineno-31-48"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">tmp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">cur</span><span class="p">?.</span><span class="kr">right</span>
+<a id="__codelineno-31-49" name="__codelineno-31-49" href="#__codelineno-31-49"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="n">tmp</span><span class="p">?.</span><span class="kr">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-50" name="__codelineno-31-50" href="#__codelineno-31-50"></a><span class="w">            </span><span class="n">tmp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">?.</span><span class="kr">left</span>
+<a id="__codelineno-31-51" name="__codelineno-31-51" href="#__codelineno-31-51"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-31-52" name="__codelineno-31-52" href="#__codelineno-31-52"></a><span class="w">        </span><span class="c1">// ノード tmp を再帰的に削除</span>
+<a id="__codelineno-31-53" name="__codelineno-31-53" href="#__codelineno-31-53"></a><span class="w">        </span><span class="n">remove</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="n">tmp</span><span class="p">!.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-31-54" name="__codelineno-31-54" href="#__codelineno-31-54"></a><span class="w">        </span><span class="c1">// tmp で cur を上書きする</span>
+<a id="__codelineno-31-55" name="__codelineno-31-55" href="#__codelineno-31-55"></a><span class="w">        </span><span class="n">cur</span><span class="p">?.</span><span class="n">val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">!.</span><span class="n">val</span>
+<a id="__codelineno-31-56" name="__codelineno-31-56" href="#__codelineno-31-56"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-57" name="__codelineno-31-57" href="#__codelineno-31-57"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* ノードを削除 */</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="nx">remove</span><span class="p">(</span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w">    </span><span class="c1">// 木が空なら、そのまま早期リターンする</span>
+<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="p">,</span>
+<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="w">        </span><span class="nx">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="w">        </span><span class="c1">// 削除対象のノードが見つかったら、ループを抜ける</span>
+<a id="__codelineno-32-10" name="__codelineno-32-10" href="#__codelineno-32-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a><span class="w">        </span><span class="nx">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">;</span>
+<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a><span class="w">        </span><span class="c1">// 削除対象ノードは cur の右部分木にある</span>
+<a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
+<a id="__codelineno-32-14" name="__codelineno-32-14" href="#__codelineno-32-14"></a><span class="w">        </span><span class="c1">// 削除対象ノードは cur の左部分木にある</span>
+<a id="__codelineno-32-15" name="__codelineno-32-15" href="#__codelineno-32-15"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span>
+<a id="__codelineno-32-16" name="__codelineno-32-16" href="#__codelineno-32-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-17" name="__codelineno-32-17" href="#__codelineno-32-17"></a><span class="w">    </span><span class="c1">// 削除対象ノードがなければそのまま返す</span>
+<a id="__codelineno-32-18" name="__codelineno-32-18" href="#__codelineno-32-18"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-32-19" name="__codelineno-32-19" href="#__codelineno-32-19"></a><span class="w">    </span><span class="c1">// 子ノード数 = 0 or 1</span>
+<a id="__codelineno-32-20" name="__codelineno-32-20" href="#__codelineno-32-20"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-21" name="__codelineno-32-21" href="#__codelineno-32-21"></a><span class="w">        </span><span class="c1">// 子ノード数が 0 / 1 のとき、child = null / その子ノード</span>
+<a id="__codelineno-32-22" name="__codelineno-32-22" href="#__codelineno-32-22"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
+<a id="__codelineno-32-23" name="__codelineno-32-23" href="#__codelineno-32-23"></a><span class="w">        </span><span class="c1">// ノード cur を削除する</span>
+<a id="__codelineno-32-24" name="__codelineno-32-24" href="#__codelineno-32-24"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-25" name="__codelineno-32-25" href="#__codelineno-32-25"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">pre</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">cur</span><span class="p">)</span><span class="w"> </span><span class="nx">pre</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">child</span><span class="p">;</span>
+<a id="__codelineno-32-26" name="__codelineno-32-26" href="#__codelineno-32-26"></a><span class="w">            </span><span class="k">else</span><span class="w"> </span><span class="nx">pre</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">child</span><span class="p">;</span>
+<a id="__codelineno-32-27" name="__codelineno-32-27" href="#__codelineno-32-27"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-28" name="__codelineno-32-28" href="#__codelineno-32-28"></a><span class="w">            </span><span class="c1">// 削除ノードが根ノードなら、根ノードを再設定</span>
+<a id="__codelineno-32-29" name="__codelineno-32-29" href="#__codelineno-32-29"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">child</span><span class="p">;</span>
+<a id="__codelineno-32-30" name="__codelineno-32-30" href="#__codelineno-32-30"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-32-31" name="__codelineno-32-31" href="#__codelineno-32-31"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-32" name="__codelineno-32-32" href="#__codelineno-32-32"></a><span class="w">    </span><span class="c1">// 子ノード数 = 2</span>
+<a id="__codelineno-32-33" name="__codelineno-32-33" href="#__codelineno-32-33"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-34" name="__codelineno-32-34" href="#__codelineno-32-34"></a><span class="w">        </span><span class="c1">// 中順走査における cur の次ノードを取得</span>
+<a id="__codelineno-32-35" name="__codelineno-32-35" href="#__codelineno-32-35"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
+<a id="__codelineno-32-36" name="__codelineno-32-36" href="#__codelineno-32-36"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">tmp</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-37" name="__codelineno-32-37" href="#__codelineno-32-37"></a><span class="w">            </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span>
+<a id="__codelineno-32-38" name="__codelineno-32-38" href="#__codelineno-32-38"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-32-39" name="__codelineno-32-39" href="#__codelineno-32-39"></a><span class="w">        </span><span class="c1">// ノード tmp を再帰的に削除</span>
+<a id="__codelineno-32-40" name="__codelineno-32-40" href="#__codelineno-32-40"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">remove</span><span class="p">(</span><span class="nx">tmp</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-32-41" name="__codelineno-32-41" href="#__codelineno-32-41"></a><span class="w">        </span><span class="c1">// tmp で cur を上書きする</span>
+<a id="__codelineno-32-42" name="__codelineno-32-42" href="#__codelineno-32-42"></a><span class="w">        </span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-32-43" name="__codelineno-32-43" href="#__codelineno-32-43"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-44" name="__codelineno-32-44" href="#__codelineno-32-44"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* ノードを削除 */</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="nx">remove</span><span class="p">(</span><span class="nx">num</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w">    </span><span class="c1">// 木が空なら、そのまま早期リターンする</span>
+<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">cur</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="p">,</span>
+<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="w">        </span><span class="nx">pre</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="w">        </span><span class="c1">// 削除対象のノードが見つかったら、ループを抜ける</span>
+<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="w">        </span><span class="nx">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">;</span>
+<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="w">        </span><span class="c1">// 削除対象ノードは cur の右部分木にある</span>
+<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
+<a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a><span class="w">        </span><span class="c1">// 削除対象ノードは cur の左部分木にある</span>
+<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span>
+<a id="__codelineno-33-16" name="__codelineno-33-16" href="#__codelineno-33-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-17" name="__codelineno-33-17" href="#__codelineno-33-17"></a><span class="w">    </span><span class="c1">// 削除対象ノードがなければそのまま返す</span>
+<a id="__codelineno-33-18" name="__codelineno-33-18" href="#__codelineno-33-18"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-33-19" name="__codelineno-33-19" href="#__codelineno-33-19"></a><span class="w">    </span><span class="c1">// 子ノード数 = 0 or 1</span>
+<a id="__codelineno-33-20" name="__codelineno-33-20" href="#__codelineno-33-20"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-21" name="__codelineno-33-21" href="#__codelineno-33-21"></a><span class="w">        </span><span class="c1">// 子ノード数が 0 / 1 のとき、child = null / その子ノード</span>
+<a id="__codelineno-33-22" name="__codelineno-33-22" href="#__codelineno-33-22"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">child</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">=</span>
+<a id="__codelineno-33-23" name="__codelineno-33-23" href="#__codelineno-33-23"></a><span class="w">            </span><span class="nx">cur</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">cur.left</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">cur.right</span><span class="p">;</span>
+<a id="__codelineno-33-24" name="__codelineno-33-24" href="#__codelineno-33-24"></a><span class="w">        </span><span class="c1">// ノード cur を削除する</span>
+<a id="__codelineno-33-25" name="__codelineno-33-25" href="#__codelineno-33-25"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-26" name="__codelineno-33-26" href="#__codelineno-33-26"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">pre</span><span class="o">!</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">cur</span><span class="p">)</span><span class="w"> </span><span class="nx">pre</span><span class="o">!</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">child</span><span class="p">;</span>
+<a id="__codelineno-33-27" name="__codelineno-33-27" href="#__codelineno-33-27"></a><span class="w">            </span><span class="k">else</span><span class="w"> </span><span class="nx">pre</span><span class="o">!</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">child</span><span class="p">;</span>
+<a id="__codelineno-33-28" name="__codelineno-33-28" href="#__codelineno-33-28"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-29" name="__codelineno-33-29" href="#__codelineno-33-29"></a><span class="w">            </span><span class="c1">// 削除ノードが根ノードなら、根ノードを再設定</span>
+<a id="__codelineno-33-30" name="__codelineno-33-30" href="#__codelineno-33-30"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">child</span><span class="p">;</span>
+<a id="__codelineno-33-31" name="__codelineno-33-31" href="#__codelineno-33-31"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-33-32" name="__codelineno-33-32" href="#__codelineno-33-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-33" name="__codelineno-33-33" href="#__codelineno-33-33"></a><span class="w">    </span><span class="c1">// 子ノード数 = 2</span>
+<a id="__codelineno-33-34" name="__codelineno-33-34" href="#__codelineno-33-34"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-35" name="__codelineno-33-35" href="#__codelineno-33-35"></a><span class="w">        </span><span class="c1">// 中順走査における cur の次ノードを取得</span>
+<a id="__codelineno-33-36" name="__codelineno-33-36" href="#__codelineno-33-36"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">tmp</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
+<a id="__codelineno-33-37" name="__codelineno-33-37" href="#__codelineno-33-37"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">tmp</span><span class="o">!</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-38" name="__codelineno-33-38" href="#__codelineno-33-38"></a><span class="w">            </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="o">!</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span>
+<a id="__codelineno-33-39" name="__codelineno-33-39" href="#__codelineno-33-39"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-33-40" name="__codelineno-33-40" href="#__codelineno-33-40"></a><span class="w">        </span><span class="c1">// ノード tmp を再帰的に削除</span>
+<a id="__codelineno-33-41" name="__codelineno-33-41" href="#__codelineno-33-41"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">remove</span><span class="p">(</span><span class="nx">tmp</span><span class="o">!</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-33-42" name="__codelineno-33-42" href="#__codelineno-33-42"></a><span class="w">        </span><span class="c1">// tmp で cur を上書きする</span>
+<a id="__codelineno-33-43" name="__codelineno-33-43" href="#__codelineno-33-43"></a><span class="w">        </span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="o">!</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-33-44" name="__codelineno-33-44" href="#__codelineno-33-44"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-45" name="__codelineno-33-45" href="#__codelineno-33-45"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* ノードを削除 */</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">_num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w">  </span><span class="c1">// 木が空なら、そのまま早期リターンする</span>
+<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_root</span><span class="p">;</span>
+<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w">  </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="w">    </span><span class="c1">// 削除対象のノードが見つかったら、ループを抜ける</span>
+<a id="__codelineno-34-10" name="__codelineno-34-10" href="#__codelineno-34-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">_num</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-34-11" name="__codelineno-34-11" href="#__codelineno-34-11"></a><span class="w">    </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
+<a id="__codelineno-34-12" name="__codelineno-34-12" href="#__codelineno-34-12"></a><span class="w">    </span><span class="c1">// 削除対象ノードは cur の右部分木にある</span>
+<a id="__codelineno-34-13" name="__codelineno-34-13" href="#__codelineno-34-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">_num</span><span class="p">)</span>
+<a id="__codelineno-34-14" name="__codelineno-34-14" href="#__codelineno-34-14"></a><span class="w">      </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-34-15" name="__codelineno-34-15" href="#__codelineno-34-15"></a><span class="w">    </span><span class="c1">// 削除対象ノードは cur の左部分木にある</span>
+<a id="__codelineno-34-16" name="__codelineno-34-16" href="#__codelineno-34-16"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-34-17" name="__codelineno-34-17" href="#__codelineno-34-17"></a><span class="w">      </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-34-18" name="__codelineno-34-18" href="#__codelineno-34-18"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-19" name="__codelineno-34-19" href="#__codelineno-34-19"></a><span class="w">  </span><span class="c1">// 削除対象ノードがない場合は、そのまま返す</span>
+<a id="__codelineno-34-20" name="__codelineno-34-20" href="#__codelineno-34-20"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-34-21" name="__codelineno-34-21" href="#__codelineno-34-21"></a><span class="w">  </span><span class="c1">// 子ノード数 = 0 or 1</span>
+<a id="__codelineno-34-22" name="__codelineno-34-22" href="#__codelineno-34-22"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-23" name="__codelineno-34-23" href="#__codelineno-34-23"></a><span class="w">    </span><span class="c1">// 子ノード数が 0 / 1 のとき、child = null / その子ノード</span>
+<a id="__codelineno-34-24" name="__codelineno-34-24" href="#__codelineno-34-24"></a><span class="w">    </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">??</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-34-25" name="__codelineno-34-25" href="#__codelineno-34-25"></a><span class="w">    </span><span class="c1">// ノード cur を削除する</span>
+<a id="__codelineno-34-26" name="__codelineno-34-26" href="#__codelineno-34-26"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">_root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-27" name="__codelineno-34-27" href="#__codelineno-34-27"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="o">!</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">cur</span><span class="p">)</span>
+<a id="__codelineno-34-28" name="__codelineno-34-28" href="#__codelineno-34-28"></a><span class="w">        </span><span class="n">pre</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-34-29" name="__codelineno-34-29" href="#__codelineno-34-29"></a><span class="w">      </span><span class="k">else</span>
+<a id="__codelineno-34-30" name="__codelineno-34-30" href="#__codelineno-34-30"></a><span class="w">        </span><span class="n">pre</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-34-31" name="__codelineno-34-31" href="#__codelineno-34-31"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-32" name="__codelineno-34-32" href="#__codelineno-34-32"></a><span class="w">      </span><span class="c1">// 削除ノードが根ノードなら、根ノードを再設定</span>
+<a id="__codelineno-34-33" name="__codelineno-34-33" href="#__codelineno-34-33"></a><span class="w">      </span><span class="n">_root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-34-34" name="__codelineno-34-34" href="#__codelineno-34-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-35" name="__codelineno-34-35" href="#__codelineno-34-35"></a><span class="w">  </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-36" name="__codelineno-34-36" href="#__codelineno-34-36"></a><span class="w">    </span><span class="c1">// 子ノード数 = 2</span>
+<a id="__codelineno-34-37" name="__codelineno-34-37" href="#__codelineno-34-37"></a><span class="w">    </span><span class="c1">// 中順走査における cur の次のノードを取得</span>
+<a id="__codelineno-34-38" name="__codelineno-34-38" href="#__codelineno-34-38"></a><span class="w">    </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-34-39" name="__codelineno-34-39" href="#__codelineno-34-39"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">tmp</span><span class="o">!</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-40" name="__codelineno-34-40" href="#__codelineno-34-40"></a><span class="w">      </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-34-41" name="__codelineno-34-41" href="#__codelineno-34-41"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-34-42" name="__codelineno-34-42" href="#__codelineno-34-42"></a><span class="w">    </span><span class="c1">// ノード tmp を再帰的に削除</span>
+<a id="__codelineno-34-43" name="__codelineno-34-43" href="#__codelineno-34-43"></a><span class="w">    </span><span class="n">remove</span><span class="p">(</span><span class="n">tmp</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-34-44" name="__codelineno-34-44" href="#__codelineno-34-44"></a><span class="w">    </span><span class="c1">// tmp で cur を上書きする</span>
+<a id="__codelineno-34-45" name="__codelineno-34-45" href="#__codelineno-34-45"></a><span class="w">    </span><span class="n">cur</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-34-46" name="__codelineno-34-46" href="#__codelineno-34-46"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-47" name="__codelineno-34-47" href="#__codelineno-34-47"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* ノードを削除 */</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w">    </span><span class="c1">// 木が空なら、そのまま早期リターンする</span>
+<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">root</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">root</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">None</span><span class="p">;</span>
+<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">clone</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a><span class="w">        </span><span class="k">match</span><span class="w"> </span><span class="n">num</span><span class="p">.</span><span class="n">cmp</span><span class="p">(</span><span class="o">&amp;</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-12" name="__codelineno-35-12" href="#__codelineno-35-12"></a><span class="w">            </span><span class="c1">// 削除対象のノードが見つかったら、ループを抜ける</span>
+<a id="__codelineno-35-13" name="__codelineno-35-13" href="#__codelineno-35-13"></a><span class="w">            </span><span class="n">Ordering</span><span class="p">::</span><span class="n">Equal</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="k">break</span><span class="p">,</span>
+<a id="__codelineno-35-14" name="__codelineno-35-14" href="#__codelineno-35-14"></a><span class="w">            </span><span class="c1">// 削除対象ノードは cur の右部分木にある</span>
+<a id="__codelineno-35-15" name="__codelineno-35-15" href="#__codelineno-35-15"></a><span class="w">            </span><span class="n">Ordering</span><span class="p">::</span><span class="n">Greater</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-16" name="__codelineno-35-16" href="#__codelineno-35-16"></a><span class="w">                </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-35-17" name="__codelineno-35-17" href="#__codelineno-35-17"></a><span class="w">                </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-35-18" name="__codelineno-35-18" href="#__codelineno-35-18"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-35-19" name="__codelineno-35-19" href="#__codelineno-35-19"></a><span class="w">            </span><span class="c1">// 削除対象ノードは cur の左部分木にある</span>
+<a id="__codelineno-35-20" name="__codelineno-35-20" href="#__codelineno-35-20"></a><span class="w">            </span><span class="n">Ordering</span><span class="p">::</span><span class="n">Less</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-21" name="__codelineno-35-21" href="#__codelineno-35-21"></a><span class="w">                </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-35-22" name="__codelineno-35-22" href="#__codelineno-35-22"></a><span class="w">                </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-35-23" name="__codelineno-35-23" href="#__codelineno-35-23"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-35-24" name="__codelineno-35-24" href="#__codelineno-35-24"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-35-25" name="__codelineno-35-25" href="#__codelineno-35-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-26" name="__codelineno-35-26" href="#__codelineno-35-26"></a><span class="w">    </span><span class="c1">// 削除対象ノードがなければそのまま返す</span>
+<a id="__codelineno-35-27" name="__codelineno-35-27" href="#__codelineno-35-27"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-28" name="__codelineno-35-28" href="#__codelineno-35-28"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-35-29" name="__codelineno-35-29" href="#__codelineno-35-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-30" name="__codelineno-35-30" href="#__codelineno-35-30"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">unwrap</span><span class="p">();</span>
+<a id="__codelineno-35-31" name="__codelineno-35-31" href="#__codelineno-35-31"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="p">(</span><span class="n">left_child</span><span class="p">,</span><span class="w"> </span><span class="n">right_child</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">(),</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-35-32" name="__codelineno-35-32" href="#__codelineno-35-32"></a><span class="w">    </span><span class="k">match</span><span class="w"> </span><span class="p">(</span><span class="n">left_child</span><span class="p">.</span><span class="n">clone</span><span class="p">(),</span><span class="w"> </span><span class="n">right_child</span><span class="p">.</span><span class="n">clone</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-33" name="__codelineno-35-33" href="#__codelineno-35-33"></a><span class="w">        </span><span class="c1">// 子ノード数 = 0 or 1</span>
+<a id="__codelineno-35-34" name="__codelineno-35-34" href="#__codelineno-35-34"></a><span class="w">        </span><span class="p">(</span><span class="nb">None</span><span class="p">,</span><span class="w"> </span><span class="nb">None</span><span class="p">)</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">_</span><span class="p">),</span><span class="w"> </span><span class="nb">None</span><span class="p">)</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="p">(</span><span class="nb">None</span><span class="p">,</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">_</span><span class="p">))</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-35" name="__codelineno-35-35" href="#__codelineno-35-35"></a><span class="w">            </span><span class="c1">// 子ノード数 = 0 / 1 のとき、child = nullptr / その子ノード</span>
+<a id="__codelineno-35-36" name="__codelineno-35-36" href="#__codelineno-35-36"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left_child</span><span class="p">.</span><span class="n">or</span><span class="p">(</span><span class="n">right_child</span><span class="p">);</span>
+<a id="__codelineno-35-37" name="__codelineno-35-37" href="#__codelineno-35-37"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="n">unwrap</span><span class="p">();</span>
+<a id="__codelineno-35-38" name="__codelineno-35-38" href="#__codelineno-35-38"></a><span class="w">            </span><span class="c1">// ノード cur を削除する</span>
+<a id="__codelineno-35-39" name="__codelineno-35-39" href="#__codelineno-35-39"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="o">!</span><span class="n">Rc</span><span class="p">::</span><span class="n">ptr_eq</span><span class="p">(</span><span class="o">&amp;</span><span class="n">cur</span><span class="p">,</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">root</span><span class="p">.</span><span class="n">as_ref</span><span class="p">().</span><span class="n">unwrap</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-40" name="__codelineno-35-40" href="#__codelineno-35-40"></a><span class="w">                </span><span class="kd">let</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-35-41" name="__codelineno-35-41" href="#__codelineno-35-41"></a><span class="w">                </span><span class="k">if</span><span class="w"> </span><span class="n">left</span><span class="p">.</span><span class="n">is_some</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">Rc</span><span class="p">::</span><span class="n">ptr_eq</span><span class="p">(</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">().</span><span class="n">unwrap</span><span class="p">(),</span><span class="w"> </span><span class="o">&amp;</span><span class="n">cur</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-42" name="__codelineno-35-42" href="#__codelineno-35-42"></a><span class="w">                    </span><span class="n">pre</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-35-43" name="__codelineno-35-43" href="#__codelineno-35-43"></a><span class="w">                </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-44" name="__codelineno-35-44" href="#__codelineno-35-44"></a><span class="w">                    </span><span class="n">pre</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-35-45" name="__codelineno-35-45" href="#__codelineno-35-45"></a><span class="w">                </span><span class="p">}</span>
+<a id="__codelineno-35-46" name="__codelineno-35-46" href="#__codelineno-35-46"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-47" name="__codelineno-35-47" href="#__codelineno-35-47"></a><span class="w">                </span><span class="c1">// 削除ノードが根ノードなら、根ノードを再設定</span>
+<a id="__codelineno-35-48" name="__codelineno-35-48" href="#__codelineno-35-48"></a><span class="w">                </span><span class="bp">self</span><span class="p">.</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-35-49" name="__codelineno-35-49" href="#__codelineno-35-49"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-35-50" name="__codelineno-35-50" href="#__codelineno-35-50"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-35-51" name="__codelineno-35-51" href="#__codelineno-35-51"></a><span class="w">        </span><span class="c1">// 子ノード数 = 2</span>
+<a id="__codelineno-35-52" name="__codelineno-35-52" href="#__codelineno-35-52"></a><span class="w">        </span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">_</span><span class="p">),</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">_</span><span class="p">))</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-53" name="__codelineno-35-53" href="#__codelineno-35-53"></a><span class="w">            </span><span class="c1">// 中順走査における cur の次ノードを取得</span>
+<a id="__codelineno-35-54" name="__codelineno-35-54" href="#__codelineno-35-54"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-35-55" name="__codelineno-35-55" href="#__codelineno-35-55"></a><span class="w">            </span><span class="k">while</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="n">clone</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-56" name="__codelineno-35-56" href="#__codelineno-35-56"></a><span class="w">                </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">is_some</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-57" name="__codelineno-35-57" href="#__codelineno-35-57"></a><span class="w">                    </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
+<a id="__codelineno-35-58" name="__codelineno-35-58" href="#__codelineno-35-58"></a><span class="w">                </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-59" name="__codelineno-35-59" href="#__codelineno-35-59"></a><span class="w">                    </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-35-60" name="__codelineno-35-60" href="#__codelineno-35-60"></a><span class="w">                </span><span class="p">}</span>
+<a id="__codelineno-35-61" name="__codelineno-35-61" href="#__codelineno-35-61"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-35-62" name="__codelineno-35-62" href="#__codelineno-35-62"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="n">tmp_val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-35-63" name="__codelineno-35-63" href="#__codelineno-35-63"></a><span class="w">            </span><span class="c1">// ノード tmp を再帰的に削除</span>
+<a id="__codelineno-35-64" name="__codelineno-35-64" href="#__codelineno-35-64"></a><span class="w">            </span><span class="bp">self</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">tmp_val</span><span class="p">);</span>
+<a id="__codelineno-35-65" name="__codelineno-35-65" href="#__codelineno-35-65"></a><span class="w">            </span><span class="c1">// tmp で cur を上書きする</span>
+<a id="__codelineno-35-66" name="__codelineno-35-66" href="#__codelineno-35-66"></a><span class="w">            </span><span class="n">cur</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp_val</span><span class="p">;</span>
+<a id="__codelineno-35-67" name="__codelineno-35-67" href="#__codelineno-35-67"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-35-68" name="__codelineno-35-68" href="#__codelineno-35-68"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-69" name="__codelineno-35-69" href="#__codelineno-35-69"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">removeItem</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* ノードを削除 */</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="c1">// stdio.h を導入しているため、ここでは remove 識別子を使えない</span>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="kt">void</span><span class="w"> </span><span class="nf">removeItem</span><span class="p">(</span><span class="n">BinarySearchTree</span><span class="w"> </span><span class="o">*</span><span class="n">bst</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w">    </span><span class="c1">// 木が空なら、そのまま早期リターンする</span>
+<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">bst</span><span class="o">-&gt;</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span>
+<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bst</span><span class="o">-&gt;</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a><span class="w">        </span><span class="c1">// 削除対象のノードが見つかったら、ループを抜ける</span>
+<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></a><span class="w">        </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
+<a id="__codelineno-36-14" name="__codelineno-36-14" href="#__codelineno-36-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-15" name="__codelineno-36-15" href="#__codelineno-36-15"></a><span class="w">            </span><span class="c1">// 削除対象ノードは root の右部分木にある</span>
+<a id="__codelineno-36-16" name="__codelineno-36-16" href="#__codelineno-36-16"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-36-17" name="__codelineno-36-17" href="#__codelineno-36-17"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-18" name="__codelineno-36-18" href="#__codelineno-36-18"></a><span class="w">            </span><span class="c1">// 削除対象ノードは root の左部分木にある</span>
+<a id="__codelineno-36-19" name="__codelineno-36-19" href="#__codelineno-36-19"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-36-20" name="__codelineno-36-20" href="#__codelineno-36-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-36-21" name="__codelineno-36-21" href="#__codelineno-36-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-22" name="__codelineno-36-22" href="#__codelineno-36-22"></a><span class="w">    </span><span class="c1">// 削除対象ノードがなければそのまま返す</span>
+<a id="__codelineno-36-23" name="__codelineno-36-23" href="#__codelineno-36-23"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span>
+<a id="__codelineno-36-24" name="__codelineno-36-24" href="#__codelineno-36-24"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-36-25" name="__codelineno-36-25" href="#__codelineno-36-25"></a><span class="w">    </span><span class="c1">// 削除対象ノードに子ノードがあるかを判定する</span>
+<a id="__codelineno-36-26" name="__codelineno-36-26" href="#__codelineno-36-26"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-27" name="__codelineno-36-27" href="#__codelineno-36-27"></a><span class="w">        </span><span class="cm">/* 子ノード数 = 0 or 1 */</span>
+<a id="__codelineno-36-28" name="__codelineno-36-28" href="#__codelineno-36-28"></a><span class="w">        </span><span class="c1">// 子ノード数 = 0 / 1 のとき、child = nullptr / その子ノード</span>
+<a id="__codelineno-36-29" name="__codelineno-36-29" href="#__codelineno-36-29"></a><span class="w">        </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-36-30" name="__codelineno-36-30" href="#__codelineno-36-30"></a><span class="w">        </span><span class="c1">// ノード cur を削除する</span>
+<a id="__codelineno-36-31" name="__codelineno-36-31" href="#__codelineno-36-31"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">cur</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-32" name="__codelineno-36-32" href="#__codelineno-36-32"></a><span class="w">            </span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-36-33" name="__codelineno-36-33" href="#__codelineno-36-33"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-34" name="__codelineno-36-34" href="#__codelineno-36-34"></a><span class="w">            </span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-36-35" name="__codelineno-36-35" href="#__codelineno-36-35"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-36-36" name="__codelineno-36-36" href="#__codelineno-36-36"></a><span class="w">        </span><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-36-37" name="__codelineno-36-37" href="#__codelineno-36-37"></a><span class="w">        </span><span class="n">free</span><span class="p">(</span><span class="n">cur</span><span class="p">);</span>
+<a id="__codelineno-36-38" name="__codelineno-36-38" href="#__codelineno-36-38"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-39" name="__codelineno-36-39" href="#__codelineno-36-39"></a><span class="w">        </span><span class="cm">/* 子ノード数 = 2 */</span>
+<a id="__codelineno-36-40" name="__codelineno-36-40" href="#__codelineno-36-40"></a><span class="w">        </span><span class="c1">// 中順走査における cur の次ノードを取得</span>
+<a id="__codelineno-36-41" name="__codelineno-36-41" href="#__codelineno-36-41"></a><span class="w">        </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-36-42" name="__codelineno-36-42" href="#__codelineno-36-42"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-43" name="__codelineno-36-43" href="#__codelineno-36-43"></a><span class="w">            </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-36-44" name="__codelineno-36-44" href="#__codelineno-36-44"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-36-45" name="__codelineno-36-45" href="#__codelineno-36-45"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">tmpVal</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-36-46" name="__codelineno-36-46" href="#__codelineno-36-46"></a><span class="w">        </span><span class="c1">// ノード tmp を再帰的に削除</span>
+<a id="__codelineno-36-47" name="__codelineno-36-47" href="#__codelineno-36-47"></a><span class="w">        </span><span class="n">removeItem</span><span class="p">(</span><span class="n">bst</span><span class="p">,</span><span class="w"> </span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-36-48" name="__codelineno-36-48" href="#__codelineno-36-48"></a><span class="w">        </span><span class="c1">// tmp で cur を上書きする</span>
+<a id="__codelineno-36-49" name="__codelineno-36-49" href="#__codelineno-36-49"></a><span class="w">        </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmpVal</span><span class="p">;</span>
+<a id="__codelineno-36-50" name="__codelineno-36-50" href="#__codelineno-36-50"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-51" name="__codelineno-36-51" href="#__codelineno-36-51"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* ノードを削除 */</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w">    </span><span class="c1">// 木が空なら、そのまま早期リターンする</span>
+<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span>
+<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">pre</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span>
+<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="w">    </span><span class="c1">// ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="w">        </span><span class="c1">// 削除対象のノードが見つかったら、ループを抜ける</span>
+<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">_val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a><span class="w">        </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span>
+<a id="__codelineno-37-14" name="__codelineno-37-14" href="#__codelineno-37-14"></a><span class="w">        </span><span class="c1">// 削除対象ノードは cur の右部分木にある</span>
+<a id="__codelineno-37-15" name="__codelineno-37-15" href="#__codelineno-37-15"></a><span class="w">        </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">_val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-37-16" name="__codelineno-37-16" href="#__codelineno-37-16"></a><span class="w">            </span><span class="n">cur</span><span class="p">.</span><span class="na">right</span>
+<a id="__codelineno-37-17" name="__codelineno-37-17" href="#__codelineno-37-17"></a><span class="w">        </span><span class="c1">// 削除対象ノードは cur の左部分木にある</span>
+<a id="__codelineno-37-18" name="__codelineno-37-18" href="#__codelineno-37-18"></a><span class="w">        </span><span class="k">else</span>
+<a id="__codelineno-37-19" name="__codelineno-37-19" href="#__codelineno-37-19"></a><span class="w">            </span><span class="n">cur</span><span class="p">.</span><span class="na">left</span>
+<a id="__codelineno-37-20" name="__codelineno-37-20" href="#__codelineno-37-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-21" name="__codelineno-37-21" href="#__codelineno-37-21"></a><span class="w">    </span><span class="c1">// 削除対象ノードがなければそのまま返す</span>
+<a id="__codelineno-37-22" name="__codelineno-37-22" href="#__codelineno-37-22"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-37-23" name="__codelineno-37-23" href="#__codelineno-37-23"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-37-24" name="__codelineno-37-24" href="#__codelineno-37-24"></a><span class="w">    </span><span class="c1">// 子ノード数 = 0 or 1</span>
+<a id="__codelineno-37-25" name="__codelineno-37-25" href="#__codelineno-37-25"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-26" name="__codelineno-37-26" href="#__codelineno-37-26"></a><span class="w">        </span><span class="c1">// 子ノード数が 0 / 1 のとき、child = null / その子ノード</span>
+<a id="__codelineno-37-27" name="__codelineno-37-27" href="#__codelineno-37-27"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-37-28" name="__codelineno-37-28" href="#__codelineno-37-28"></a><span class="w">            </span><span class="n">cur</span><span class="p">.</span><span class="na">left</span>
+<a id="__codelineno-37-29" name="__codelineno-37-29" href="#__codelineno-37-29"></a><span class="w">        </span><span class="k">else</span>
+<a id="__codelineno-37-30" name="__codelineno-37-30" href="#__codelineno-37-30"></a><span class="w">            </span><span class="n">cur</span><span class="p">.</span><span class="na">right</span>
+<a id="__codelineno-37-31" name="__codelineno-37-31" href="#__codelineno-37-31"></a><span class="w">        </span><span class="c1">// ノード cur を削除する</span>
+<a id="__codelineno-37-32" name="__codelineno-37-32" href="#__codelineno-37-32"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-33" name="__codelineno-37-33" href="#__codelineno-37-33"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="o">!!</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">cur</span><span class="p">)</span>
+<a id="__codelineno-37-34" name="__codelineno-37-34" href="#__codelineno-37-34"></a><span class="w">                </span><span class="n">pre</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span>
+<a id="__codelineno-37-35" name="__codelineno-37-35" href="#__codelineno-37-35"></a><span class="w">            </span><span class="k">else</span>
+<a id="__codelineno-37-36" name="__codelineno-37-36" href="#__codelineno-37-36"></a><span class="w">                </span><span class="n">pre</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span>
+<a id="__codelineno-37-37" name="__codelineno-37-37" href="#__codelineno-37-37"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-38" name="__codelineno-37-38" href="#__codelineno-37-38"></a><span class="w">            </span><span class="c1">// 削除ノードが根ノードなら、根ノードを再設定</span>
+<a id="__codelineno-37-39" name="__codelineno-37-39" href="#__codelineno-37-39"></a><span class="w">            </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span>
+<a id="__codelineno-37-40" name="__codelineno-37-40" href="#__codelineno-37-40"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-37-41" name="__codelineno-37-41" href="#__codelineno-37-41"></a><span class="w">        </span><span class="c1">// 子ノード数 = 2</span>
+<a id="__codelineno-37-42" name="__codelineno-37-42" href="#__codelineno-37-42"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-43" name="__codelineno-37-43" href="#__codelineno-37-43"></a><span class="w">        </span><span class="c1">// 中順走査における cur の次ノードを取得</span>
+<a id="__codelineno-37-44" name="__codelineno-37-44" href="#__codelineno-37-44"></a><span class="w">        </span><span class="kd">var</span><span class="w"> </span><span class="nv">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">right</span>
+<a id="__codelineno-37-45" name="__codelineno-37-45" href="#__codelineno-37-45"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">tmp</span><span class="o">!!</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-46" name="__codelineno-37-46" href="#__codelineno-37-46"></a><span class="w">            </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="na">left</span>
+<a id="__codelineno-37-47" name="__codelineno-37-47" href="#__codelineno-37-47"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-37-48" name="__codelineno-37-48" href="#__codelineno-37-48"></a><span class="w">        </span><span class="c1">// ノード tmp を再帰的に削除</span>
+<a id="__codelineno-37-49" name="__codelineno-37-49" href="#__codelineno-37-49"></a><span class="w">        </span><span class="n">remove</span><span class="p">(</span><span class="n">tmp</span><span class="p">.</span><span class="na">_val</span><span class="p">)</span>
+<a id="__codelineno-37-50" name="__codelineno-37-50" href="#__codelineno-37-50"></a><span class="w">        </span><span class="c1">// tmp で cur を上書きする</span>
+<a id="__codelineno-37-51" name="__codelineno-37-51" href="#__codelineno-37-51"></a><span class="w">        </span><span class="n">cur</span><span class="p">.</span><span class="na">_val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="na">_val</span>
+<a id="__codelineno-37-52" name="__codelineno-37-52" href="#__codelineno-37-52"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-37-53" name="__codelineno-37-53" href="#__codelineno-37-53"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">BinarySearchTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="c1">### ノードを削除 ###</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w">  </span><span class="c1"># 木が空なら、そのまま早期リターンする</span>
+<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="vi">@root</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a>
+<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w">  </span><span class="c1"># ループで探索し、葉ノードを越えたら抜ける</span>
+<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="w">  </span><span class="n">cur</span><span class="p">,</span><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@root</span><span class="p">,</span><span class="w"> </span><span class="kp">nil</span>
+<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">cur</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="w">    </span><span class="c1"># 削除対象のノードが見つかったら、ループを抜ける</span>
+<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a><span class="w">    </span><span class="k">break</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a>
+<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a><span class="w">    </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span>
+<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a><span class="w">    </span><span class="c1"># 削除対象ノードは cur の右部分木にある</span>
+<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a><span class="w">      </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">right</span>
+<a id="__codelineno-38-16" name="__codelineno-38-16" href="#__codelineno-38-16"></a><span class="w">    </span><span class="c1"># 削除対象ノードは cur の左部分木にある</span>
+<a id="__codelineno-38-17" name="__codelineno-38-17" href="#__codelineno-38-17"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-38-18" name="__codelineno-38-18" href="#__codelineno-38-18"></a><span class="w">      </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">left</span>
+<a id="__codelineno-38-19" name="__codelineno-38-19" href="#__codelineno-38-19"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-38-20" name="__codelineno-38-20" href="#__codelineno-38-20"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-21" name="__codelineno-38-21" href="#__codelineno-38-21"></a><span class="w">  </span><span class="c1"># 削除対象ノードがなければそのまま返す</span>
+<a id="__codelineno-38-22" name="__codelineno-38-22" href="#__codelineno-38-22"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-38-23" name="__codelineno-38-23" href="#__codelineno-38-23"></a>
+<a id="__codelineno-38-24" name="__codelineno-38-24" href="#__codelineno-38-24"></a><span class="w">  </span><span class="c1"># 子ノード数 = 0 or 1</span>
+<a id="__codelineno-38-25" name="__codelineno-38-25" href="#__codelineno-38-25"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">left</span><span class="o">.</span><span class="n">nil?</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">right</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-38-26" name="__codelineno-38-26" href="#__codelineno-38-26"></a><span class="w">    </span><span class="c1"># 子ノード数が 0 / 1 のとき、child = null / その子ノード</span>
+<a id="__codelineno-38-27" name="__codelineno-38-27" href="#__codelineno-38-27"></a><span class="w">    </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">right</span>
+<a id="__codelineno-38-28" name="__codelineno-38-28" href="#__codelineno-38-28"></a><span class="w">    </span><span class="c1"># ノード cur を削除する</span>
+<a id="__codelineno-38-29" name="__codelineno-38-29" href="#__codelineno-38-29"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="vi">@root</span>
+<a id="__codelineno-38-30" name="__codelineno-38-30" href="#__codelineno-38-30"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="n">pre</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">cur</span>
+<a id="__codelineno-38-31" name="__codelineno-38-31" href="#__codelineno-38-31"></a><span class="w">        </span><span class="n">pre</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span>
+<a id="__codelineno-38-32" name="__codelineno-38-32" href="#__codelineno-38-32"></a><span class="w">      </span><span class="k">else</span>
+<a id="__codelineno-38-33" name="__codelineno-38-33" href="#__codelineno-38-33"></a><span class="w">        </span><span class="n">pre</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span>
+<a id="__codelineno-38-34" name="__codelineno-38-34" href="#__codelineno-38-34"></a><span class="w">      </span><span class="k">end</span>
+<a id="__codelineno-38-35" name="__codelineno-38-35" href="#__codelineno-38-35"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-38-36" name="__codelineno-38-36" href="#__codelineno-38-36"></a><span class="w">      </span><span class="c1"># 削除ノードが根ノードなら、根ノードを再設定</span>
+<a id="__codelineno-38-37" name="__codelineno-38-37" href="#__codelineno-38-37"></a><span class="w">      </span><span class="vi">@root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span>
+<a id="__codelineno-38-38" name="__codelineno-38-38" href="#__codelineno-38-38"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-38-39" name="__codelineno-38-39" href="#__codelineno-38-39"></a><span class="w">  </span><span class="c1"># 子ノード数 = 2</span>
+<a id="__codelineno-38-40" name="__codelineno-38-40" href="#__codelineno-38-40"></a><span class="w">  </span><span class="k">else</span>
+<a id="__codelineno-38-41" name="__codelineno-38-41" href="#__codelineno-38-41"></a><span class="w">    </span><span class="c1"># 中順走査における cur の次ノードを取得</span>
+<a id="__codelineno-38-42" name="__codelineno-38-42" href="#__codelineno-38-42"></a><span class="w">    </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">right</span>
+<a id="__codelineno-38-43" name="__codelineno-38-43" href="#__codelineno-38-43"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">tmp</span><span class="o">.</span><span class="n">left</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-38-44" name="__codelineno-38-44" href="#__codelineno-38-44"></a><span class="w">      </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">.</span><span class="n">left</span>
+<a id="__codelineno-38-45" name="__codelineno-38-45" href="#__codelineno-38-45"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-38-46" name="__codelineno-38-46" href="#__codelineno-38-46"></a><span class="w">    </span><span class="c1"># ノード tmp を再帰的に削除</span>
+<a id="__codelineno-38-47" name="__codelineno-38-47" href="#__codelineno-38-47"></a><span class="w">    </span><span class="n">remove</span><span class="p">(</span><span class="n">tmp</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-38-48" name="__codelineno-38-48" href="#__codelineno-38-48"></a><span class="w">    </span><span class="c1"># tmp で cur を上書きする</span>
+<a id="__codelineno-38-49" name="__codelineno-38-49" href="#__codelineno-38-49"></a><span class="w">    </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-38-50" name="__codelineno-38-50" href="#__codelineno-38-50"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-38-51" name="__codelineno-38-51" href="#__codelineno-38-51"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h3 id="4">4. &nbsp; 中順走査は順序付けされている<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
-<p>下図に示すように、二分木の中順走査は「左 <span class="arithmatex">\(\rightarrow\)</span> 根 <span class="arithmatex">\(\rightarrow\)</span> 右」の走査順序に従い、二分探索木は「左子ノード <span class="arithmatex">\(&lt;\)</span> 根ノード <span class="arithmatex">\(&lt;\)</span> 右子ノード」のサイズ関係を満たします。</p>
-<p>これは、二分探索木で中順走査を実行するときに、常に次に小さいノードが最初に走査されることを意味し、重要な性質につながります：<strong>二分探索木の中順走査のシーケンスは昇順です</strong>。</p>
-<p>中順走査の昇順性質を使用して、二分探索木で順序付けされたデータを取得するには<span class="arithmatex">\(O(n)\)</span>の時間のみが必要で、追加のソート操作は不要であり、非常に効率的です。</p>
-<p><img alt="二分探索木の中順走査シーケンス" class="animation-figure" src="../binary_search_tree.assets/bst_inorder_traversal.png" /></p>
-<p align="center"> 図 7-22 &nbsp; 二分探索木の中順走査シーケンス </p>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" 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target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h3 id="4">4. &nbsp; 中順走査は昇順<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
+<p>以下の図に示すように、二分木の中順走査は「左 <span class="arithmatex">\(\rightarrow\)</span> 根 <span class="arithmatex">\(\rightarrow\)</span> 右」という順序に従い、二分探索木は「左子ノード <span class="arithmatex">\(&lt;\)</span> 根ノード <span class="arithmatex">\(&lt;\)</span> 右子ノード」という大小関係を満たします。</p>
+<p>これは、二分探索木で中順走査を行うと常に次の最小ノードが優先して走査されることを意味し、そこから重要な性質が導かれます。<strong>二分探索木の中順走査列は昇順です</strong>。</p>
+<p>中順走査が昇順になる性質を利用すれば、二分探索木から整列済みデータを取得するのに必要な時間は <span class="arithmatex">\(O(n)\)</span> のみで、追加のソート操作は不要です。非常に効率的です。</p>
+<p><img alt="二分探索木の中順走査列" class="animation-figure" src="../binary_search_tree.assets/bst_inorder_traversal.png" /></p>
+<p align="center"> 図 7-22 &nbsp; 二分探索木の中順走査列 </p>
 
 <h2 id="742">7.4.2 &nbsp; 二分探索木の効率<a class="headerlink" href="#742" title="Permanent link">&para;</a></h2>
-<p>データのセットが与えられた場合、配列または二分探索木を使用して格納することを検討します。下の表を観察すると、二分探索木のすべての操作は対数時間計算量を持ち、安定して効率的です。配列は、頻繁な追加と検索や削除の頻度が少ないシナリオでのみ、二分探索木よりも効率的です。</p>
+<p>あるデータ集合が与えられたとき、配列または二分探索木で格納する場合を考えます。次の表を見ると、二分探索木の各操作の時間計算量はいずれも対数オーダーであり、安定して高効率です。高頻度の追加と低頻度の探索・削除という場面でのみ、配列のほうが二分探索木より効率的です。</p>
 <p align="center"> 表 7-2 &nbsp; 配列と探索木の効率比較 </p>
 
 <div class="center-table">
@@ -5018,13 +6008,13 @@
 <thead>
 <tr>
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-<th>未ソート配列</th>
+<th>無秩序配列</th>
 <th>二分探索木</th>
 </tr>
 </thead>
 <tbody>
 <tr>
-<td>要素の検索</td>
+<td>要素の探索</td>
 <td><span class="arithmatex">\(O(n)\)</span></td>
 <td><span class="arithmatex">\(O(\log n)\)</span></td>
 </tr>
@@ -5041,16 +6031,16 @@
 </tbody>
 </table>
 </div>
-<p>理想的には、二分探索木は「平衡」しており、任意のノードを<span class="arithmatex">\(\log n\)</span>ループ内で見つけることができます。</p>
-<p>しかし、二分探索木で継続的にノードを挿入および削除すると、下図に示すように連結リストに退化する可能性があり、さまざまな操作の時間計算量も<span class="arithmatex">\(O(n)\)</span>に悪化します。</p>
+<p>理想的な状況では、二分探索木は「平衡」しており、その場合は <span class="arithmatex">\(\log n\)</span> 回のループ内で任意のノードを探索できます。</p>
+<p>しかし、二分探索木でノードの挿入と削除を繰り返すと、二分木が以下の図のような連結リストへ退化する可能性があり、このとき各操作の時間計算量も <span class="arithmatex">\(O(n)\)</span> に退化します。</p>
 <p><img alt="二分探索木の退化" class="animation-figure" src="../binary_search_tree.assets/bst_degradation.png" /></p>
 <p align="center"> 図 7-23 &nbsp; 二分探索木の退化 </p>
 
-<h2 id="743">7.4.3 &nbsp; 二分探索木の一般的な応用<a class="headerlink" href="#743" title="Permanent link">&para;</a></h2>
+<h2 id="743">7.4.3 &nbsp; 二分探索木の代表的な応用<a class="headerlink" href="#743" title="Permanent link">&para;</a></h2>
 <ul>
-<li>システムでの多レベルインデックスとして使用され、効率的な検索、挿入、削除操作を実装します。</li>
-<li>特定の検索アルゴリズムの基盤となるデータ構造として機能します。</li>
-<li>データストリームを格納して、その順序付けされた状態を維持するために使用されます。</li>
+<li>システム内の多段インデックスとして用いられ、効率的な探索、挿入、削除操作を実現します。</li>
+<li>一部の探索アルゴリズムの基盤データ構造として使われます。</li>
+<li>データストリームを格納し、その順序状態を保つために使われます。</li>
 </ul>
 
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-    aria-label="次: 7.5 &amp;nbsp; AVL木 *"
+    aria-label="次: 7.5 &amp;nbsp; AVL 木 *"
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       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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-    1.2 &nbsp; アルゴリズムとは何か
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-        7.1.1 &nbsp; 二分木の一般的な用語
+        7.1.1 &nbsp; 二分木のよく使われる用語
       
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-    <nav class="md-nav" aria-label="7.1.3 二分木の一般的な種類">
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+    7.5 &nbsp; AVL 木 *
   
 
     
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 <!-- Page content -->
 <h1 id="71">7.1 &nbsp; 二分木<a class="headerlink" href="#71" title="Permanent link">&para;</a></h1>
-<p><u>二分木</u>は、祖先と子孫の間の階層関係を表現し、「二つに分割する」分割統治法の論理を体現する非線形データ構造です。連結リストと同様に、二分木の基本単位はノードであり、各ノードは値、左の子ノードへの参照、右の子ノードへの参照を含みます。</p>
+<p><u>二分木（binary tree）</u>は非線形データ構造の一種であり、「祖先」と「子孫」の派生関係を表し、「一つを二つに分ける」分割統治の考え方を体現しています。連結リストと同様に、二分木の基本単位はノードであり、各ノードは値、左子ノードへの参照、右子ノードへの参照を含みます。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">TreeNode</span><span class="p">:</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二分木ノード&quot;&quot;&quot;</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二分木ノードクラス&quot;&quot;&quot;</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">val</span>                <span class="c1"># ノード値</span>
-<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">left</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># 左の子ノードへの参照</span>
-<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">right</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 右の子ノードへの参照</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">left</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># 左子ノード参照</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">right</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 右子ノード参照</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 二分木ノード */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 二分木ノード構造体 */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">          </span><span class="c1">// ノード値</span>
-<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">left</span><span class="p">;</span><span class="w">   </span><span class="c1">// 左の子ノードへのポインタ</span>
-<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">right</span><span class="p">;</span><span class="w">  </span><span class="c1">// 右の子ノードへのポインタ</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">left</span><span class="p">;</span><span class="w">   </span><span class="c1">// 左子ノードポインタ</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">right</span><span class="p">;</span><span class="w">  </span><span class="c1">// 右子ノードポインタ</span>
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="n">TreeNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">x</span><span class="p">),</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="k">nullptr</span><span class="p">),</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{}</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="p">};</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 二分木ノード */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 二分木ノードクラス */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kd">class</span> <span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">         </span><span class="c1">// ノード値</span>
-<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w">   </span><span class="c1">// 左の子ノードへの参照</span>
-<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w">  </span><span class="c1">// 右の子ノードへの参照</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w">   </span><span class="c1">// 左子ノード参照</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w">  </span><span class="c1">// 右子ノード参照</span>
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="n">TreeNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w"> </span><span class="p">}</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 二分木ノード */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 二分木ノードクラス */</span>
 <a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">class</span><span class="w"> </span><span class="nf">TreeNode</span><span class="p">(</span><span class="kt">int?</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int?</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w">    </span><span class="c1">// ノード値</span>
-<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w">  </span><span class="c1">// 左の子ノードへの参照</span>
-<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右の子ノードへの参照</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w">  </span><span class="c1">// 左子ノード参照</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右子ノード参照</span>
 <a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 二分木ノード */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 二分木ノード構造体 */</span>
 <a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="nx">Val</span><span class="w">   </span><span class="kt">int</span>
 <a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">Left</span><span class="w">  </span><span class="o">*</span><span class="nx">TreeNode</span>
@@ -4606,19 +4606,19 @@
 <a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="cm">/* コンストラクタ */</span>
 <a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="kd">func</span><span class="w"> </span><span class="nx">NewTreeNode</span><span class="p">(</span><span class="nx">v</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">TreeNode</span><span class="p">{</span>
-<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">        </span><span class="nx">Left</span><span class="p">:</span><span class="w">  </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="c1">// 左の子ノードへのポインタ</span>
-<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">        </span><span class="nx">Right</span><span class="p">:</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="c1">// 右の子ノードへのポインタ</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">        </span><span class="nx">Left</span><span class="p">:</span><span class="w">  </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="c1">// 左子ノードポインタ</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">        </span><span class="nx">Right</span><span class="p">:</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="c1">// 右子ノードポインタ</span>
 <a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">        </span><span class="nx">Val</span><span class="p">:</span><span class="w">   </span><span class="nx">v</span><span class="p">,</span><span class="w">   </span><span class="c1">// ノード値</span>
 <a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 二分木ノード */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 二分木ノードクラス */</span>
 <a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">val</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// ノード値</span>
-<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">left</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 左の子ノードへの参照</span>
-<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">right</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 右の子ノードへの参照</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">left</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 左子ノード参照</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">right</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 右子ノード参照</span>
 <a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a>
 <a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="kd">init</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">        </span><span class="n">val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">x</span>
@@ -4627,11 +4627,11 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 二分木ノード */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 二分木ノードクラス */</span>
 <a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="nx">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// ノード値</span>
-<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="nx">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左の子ノードへのポインタ</span>
-<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="nx">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右の子ノードへのポインタ</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="nx">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左子ノードポインタ</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="nx">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右子ノードポインタ</span>
 <a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span>
 <a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">left</span><span class="p">;</span>
@@ -4641,7 +4641,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 二分木ノード */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 二分木ノードクラス */</span>
 <a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span>
 <a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="nx">left</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
@@ -4649,18 +4649,18 @@
 <a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a>
 <a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val?</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">left?</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="nx">right?</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// ノード値</span>
-<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左の子ノードへの参照</span>
-<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右の子ノードへの参照</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左子ノード参照</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右子ノード参照</span>
 <a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 二分木ノード */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 二分木ノードクラス */</span>
 <a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">         </span><span class="c1">// ノード値</span>
-<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w">  </span><span class="c1">// 左の子ノードへの参照</span>
-<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右の子ノードへの参照</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w">  </span><span class="c1">// 左子ノード参照</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右子ノード参照</span>
 <a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="n">TreeNode</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="k">this</span><span class="p">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">right</span><span class="p">]);</span>
 <a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="p">}</span>
 </code></pre></div>
@@ -4669,11 +4669,11 @@
 <div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">rc</span><span class="p">::</span><span class="n">Rc</span><span class="p">;</span>
 <a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cell</span><span class="p">::</span><span class="n">RefCell</span><span class="p">;</span>
 <a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a>
-<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="cm">/* 二分木ノード */</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="cm">/* 二分木ノード構造体 */</span>
 <a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w">                               </span><span class="c1">// ノード値</span>
-<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="n">left</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w">    </span><span class="c1">// 左の子ノードへの参照</span>
-<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="n">right</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w">   </span><span class="c1">// 右の子ノードへの参照</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="n">left</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w">    </span><span class="c1">// 左子ノード参照</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="n">right</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w">   </span><span class="c1">// 右子ノード参照</span>
 <a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="p">}</span>
 <a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a>
 <a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="k">impl</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="p">{</span>
@@ -4689,12 +4689,12 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 二分木ノード */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 二分木ノード構造体 */</span>
 <a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">                </span><span class="c1">// ノード値</span>
 <a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="p">;</span><span class="w">             </span><span class="c1">// ノードの高さ</span>
-<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">    </span><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">left</span><span class="p">;</span><span class="w">  </span><span class="c1">// 左の子ノードへのポインタ</span>
-<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右の子ノードへのポインタ</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">    </span><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">left</span><span class="p">;</span><span class="w">  </span><span class="c1">// 左子ノードポインタ</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右子ノードポインタ</span>
 <a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="p">}</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">;</span>
 <a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a>
 <a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="cm">/* コンストラクタ */</span>
@@ -4711,57 +4711,66 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 二分木ノード */</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 二分木ノードクラス */</span>
 <a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">TreeNode</span><span class="p">(</span><span class="kd">val</span><span class="w"> </span><span class="nv">_val</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// ノード値</span>
-<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">left</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="w">   </span><span class="c1">// 左の子ノードへの参照</span>
-<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">right</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="w">  </span><span class="c1">// 右の子ノードへの参照</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">left</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="w">   </span><span class="c1">// 左子ノード参照</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">right</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="w">  </span><span class="c1">// 右子ノード参照</span>
 <a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 二分木ノードクラス ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">TreeNode</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:val</span><span class="w">    </span><span class="c1"># ノード値</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:left</span><span class="w">   </span><span class="c1"># 左子ノード参照</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:right</span><span class="w">  </span><span class="c1"># 右子ノード参照</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">  </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">    </span><span class="vi">@val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<p>各ノードは2つの参照（ポインタ）を持ち、それぞれ<u>左の子ノード</u>と<u>右の子ノード</u>を指しています。このノードは、これら2つの子ノードの<u>親ノード</u>と呼ばれます。二分木のノードが与えられたとき、このノードの左の子とその下にあるすべてのノードで形成される木を、このノードの<u>左部分木</u>と呼びます。同様に、<u>右部分木</u>も定義できます。</p>
-<p><strong>二分木では、葉ノードを除いて、他のすべてのノードは子ノードと空でない部分木を含みます。</strong> 下図に示すように、「ノード2」を親ノードとして見ると、その左と右の子ノードはそれぞれ「ノード4」と「ノード5」です。左部分木は「ノード4」とその下にあるすべてのノードで形成され、右部分木は「ノード5」とその下にあるすべてのノードで形成されます。</p>
+<p>各ノードは 2 つの参照（ポインタ）を持ち、それぞれ<u>左子ノード（left-child node）</u>と<u>右子ノード（right-child node）</u>を指します。このノードはこれら 2 つの子ノードの<u>親ノード（parent node）</u>と呼ばれます。二分木のあるノードが与えられたとき、そのノードの左子ノードとその配下のノードからなる木をそのノードの<u>左部分木（left subtree）</u>と呼び、同様に<u>右部分木（right subtree）</u>が定義されます。</p>
+<p><strong>二分木では、葉ノードを除くすべてのノードが子ノードと空でない部分木を持ちます</strong>。以下の図に示すように、「ノード 2」を親ノードとみなすと、その左子ノードと右子ノードはそれぞれ「ノード 4」と「ノード 5」であり、左部分木は「ノード 4 とその配下のノードからなる木」、右部分木は「ノード 5 とその配下のノードからなる木」です。</p>
 <p><img alt="親ノード、子ノード、部分木" class="animation-figure" src="../binary_tree.assets/binary_tree_definition.png" /></p>
 <p align="center"> 図 7-1 &nbsp; 親ノード、子ノード、部分木 </p>
 
-<h2 id="711">7.1.1 &nbsp; 二分木の一般的な用語<a class="headerlink" href="#711" title="Permanent link">&para;</a></h2>
-<p>二分木でよく使用される用語を下図に示します。</p>
+<h2 id="711">7.1.1 &nbsp; 二分木のよく使われる用語<a class="headerlink" href="#711" title="Permanent link">&para;</a></h2>
+<p>二分木でよく使われる用語を以下の図に示します。</p>
 <ul>
-<li><u>根ノード</u>：二分木の最上位レベルにあるノードで、親ノードを持ちません。</li>
-<li><u>葉ノード</u>：子ノードを持たないノードで、両方のポインタが<code>None</code>を指しています。</li>
-<li><u>辺</u>：2つのノードを結ぶ線分で、ノード間の参照（ポインタ）を表現します。</li>
-<li>ノードの<u>レベル</u>：上から下に向かって増加し、根ノードがレベル1です。</li>
-<li>ノードの<u>次数</u>：ノードが持つ子ノードの数です。二分木では、次数は0、1、または2になります。</li>
-<li>二分木の<u>高さ</u>：根ノードから最も遠い葉ノードまでの辺の数です。</li>
-<li>ノードの<u>深さ</u>：根ノードからそのノードまでの辺の数です。</li>
-<li>ノードの<u>高さ</u>：最も遠い葉ノードからそのノードまでの辺の数です。</li>
+<li><u>根ノード（root node）</u>：二分木の最上位にあるノードで、親ノードを持ちません。</li>
+<li><u>葉ノード（leaf node）</u>：子ノードを持たないノードで、2 本のポインタはいずれも <code>None</code> を指します。</li>
+<li><u>辺（edge）</u>：2 つのノードを結ぶ線分、すなわちノード参照（ポインタ）です。</li>
+<li>ノードが属する<u>レベル（level）</u>：上から下へ向かって増加し、根ノードのレベルは 1 です。</li>
+<li>ノードの<u>次数（degree）</u>：ノードの子ノードの数。二分木では次数の取り得る値は 0、1、2 です。</li>
+<li>二分木の<u>高さ（height）</u>：根ノードから最も遠い葉ノードまでに通る辺の数。</li>
+<li>ノードの<u>深さ（depth）</u>：根ノードからそのノードまでに通る辺の数。</li>
+<li>ノードの<u>高さ（height）</u>：そのノードから最も遠い葉ノードまでに通る辺の数。</li>
 </ul>
-<p><img alt="二分木の一般的な用語" class="animation-figure" src="../binary_tree.assets/binary_tree_terminology.png" /></p>
-<p align="center"> 図 7-2 &nbsp; 二分木の一般的な用語 </p>
+<p><img alt="二分木のよく使われる用語" class="animation-figure" src="../binary_tree.assets/binary_tree_terminology.png" /></p>
+<p align="center"> 図 7-2 &nbsp; 二分木のよく使われる用語 </p>
 
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>「高さ」と「深さ」は通常「通過する辺の数」として定義しますが、一部の問題や教科書では「通過するノードの数」として定義されることがあります。この場合、高さと深さの両方を1だけ増やす必要があります。</p>
+<p>なお、通常「高さ」と「深さ」は「通過した辺の数」と定義しますが、問題や教材によっては「通過したノードの数」と定義する場合もあります。その場合、高さと深さはいずれも 1 を加える必要があります。</p>
 </div>
 <h2 id="712">7.1.2 &nbsp; 二分木の基本操作<a class="headerlink" href="#712" title="Permanent link">&para;</a></h2>
-<h3 id="1">1. &nbsp; 二分木の初期化<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>連結リストと同様に、二分木の初期化では、まずノードを作成し、次にそれらの間の参照（ポインタ）を確立します。</p>
+<h3 id="1">1. &nbsp; 二分木を初期化する<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>連結リストと同様に、まずノードを初期化し、その後で参照（ポインタ）を構築します。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="c1"># 二分木の初期化</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="c1"># ノードの初期化</span>
+<div class="highlight"><span class="filename">binary_tree.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="c1"># 二分木を初期化する</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="c1"># ノードを初期化する</span>
 <a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="n">n1</span> <span class="o">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">val</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
 <a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="n">n2</span> <span class="o">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">val</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
 <a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="n">n3</span> <span class="o">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">val</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
 <a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="n">n4</span> <span class="o">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">val</span><span class="o">=</span><span class="mi">4</span><span class="p">)</span>
 <a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="n">n5</span> <span class="o">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">val</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
-<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="c1"># ノード間の参照（ポインタ）を結ぶ</span>
+<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="c1"># ノード間の参照（ポインタ）を構築する</span>
 <a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="n">n1</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">n2</span>
 <a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a><span class="n">n1</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="n">n3</span>
 <a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="n">n2</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">n4</span>
@@ -4769,14 +4778,14 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 二分木の初期化 */</span>
-<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="c1">// ノードの初期化</span>
+<div class="highlight"><span class="filename">binary_tree.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 二分木を初期化する */</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="c1">// ノードを初期化する</span>
 <a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="n">TreeNode</span><span class="o">*</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="n">TreeNode</span><span class="o">*</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
 <a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="n">TreeNode</span><span class="o">*</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
 <a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="n">TreeNode</span><span class="o">*</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
 <a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="n">TreeNode</span><span class="o">*</span><span class="w"> </span><span class="n">n5</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
-<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="c1">// ノード間の参照（ポインタ）を結ぶ</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="c1">// ノード間の参照（ポインタ）を構築する</span>
 <a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="n">n1</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
 <a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="n">n1</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
 <a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="n">n2</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
@@ -4784,13 +4793,13 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="c1">// ノードの初期化</span>
+<div class="highlight"><span class="filename">binary_tree.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="c1">// ノードを初期化する</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
 <a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
 <a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
 <a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n5</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
-<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="c1">// ノード間の参照（ポインタ）を結ぶ</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="c1">// ノード間の参照（ポインタ）を構築する</span>
 <a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="n">n1</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
 <a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="n">n1</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
 <a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="n">n2</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
@@ -4798,14 +4807,14 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 二分木の初期化 */</span>
-<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="c1">// ノードの初期化</span>
+<div class="highlight"><span class="filename">binary_tree.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 二分木を初期化する */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="c1">// ノードを初期化する</span>
 <a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
 <a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
 <a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
 <a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n5</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
-<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="c1">// ノード間の参照（ポインタ）を結ぶ</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="c1">// ノード間の参照（ポインタ）を構築する</span>
 <a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="n">n1</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
 <a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="n">n1</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
 <a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="n">n2</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
@@ -4813,14 +4822,14 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 二分木の初期化 */</span>
-<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="c1">// ノードの初期化</span>
+<div class="highlight"><span class="filename">binary_tree.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 二分木を初期化する */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="c1">// ノードを初期化する</span>
 <a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="nx">n1</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewTreeNode</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
 <a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="nx">n2</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewTreeNode</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
 <a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="nx">n3</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewTreeNode</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
 <a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="nx">n4</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewTreeNode</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
 <a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="nx">n5</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewTreeNode</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
-<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="c1">// ノード間の参照（ポインタ）を結ぶ</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="c1">// ノード間の参照（ポインタ）を構築する</span>
 <a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n2</span>
 <a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n3</span>
 <a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="nx">n2</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n4</span>
@@ -4828,13 +4837,13 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="c1">// ノードの初期化</span>
+<div class="highlight"><span class="filename">binary_tree.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="c1">// ノードを初期化する</span>
 <a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">let</span><span class="w"> </span><span class="nv">n1</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
 <a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="kd">let</span><span class="w"> </span><span class="nv">n2</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
 <a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="kd">let</span><span class="w"> </span><span class="nv">n3</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span>
 <a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="kd">let</span><span class="w"> </span><span class="nv">n4</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span>
 <a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="kd">let</span><span class="w"> </span><span class="nv">n5</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span>
-<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="c1">// ノード間の参照（ポインタ）を結ぶ</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="c1">// ノード間の参照（ポインタ）を構築する</span>
 <a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="n">n1</span><span class="p">.</span><span class="kr">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n2</span>
 <a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="n">n1</span><span class="p">.</span><span class="kr">right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n3</span>
 <a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="n">n2</span><span class="p">.</span><span class="kr">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n4</span>
@@ -4842,14 +4851,14 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 二分木の初期化 */</span>
-<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="c1">// ノードの初期化</span>
+<div class="highlight"><span class="filename">binary_tree.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 二分木を初期化する */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="c1">// ノードを初期化する</span>
 <a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="kd">let</span><span class="w"> </span><span class="nx">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">1</span><span class="p">),</span>
 <a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="nx">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">2</span><span class="p">),</span>
 <a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">    </span><span class="nx">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">3</span><span class="p">),</span>
 <a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">    </span><span class="nx">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">4</span><span class="p">),</span>
 <a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">    </span><span class="nx">n5</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
-<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="c1">// ノード間の参照（ポインタ）を結ぶ</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="c1">// ノード間の参照（ポインタ）を構築する</span>
 <a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n2</span><span class="p">;</span>
 <a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n3</span><span class="p">;</span>
 <a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="nx">n2</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n4</span><span class="p">;</span>
@@ -4857,14 +4866,14 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 二分木の初期化 */</span>
-<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="c1">// ノードの初期化</span>
+<div class="highlight"><span class="filename">binary_tree.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 二分木を初期化する */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="c1">// ノードを初期化する</span>
 <a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="kd">let</span><span class="w"> </span><span class="nx">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">1</span><span class="p">),</span>
 <a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="nx">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">2</span><span class="p">),</span>
 <a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">    </span><span class="nx">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">3</span><span class="p">),</span>
 <a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">    </span><span class="nx">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">4</span><span class="p">),</span>
 <a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">    </span><span class="nx">n5</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
-<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="c1">// ノード間の参照（ポインタ）を結ぶ</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="c1">// ノード間の参照（ポインタ）を構築する</span>
 <a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n2</span><span class="p">;</span>
 <a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n3</span><span class="p">;</span>
 <a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="nx">n2</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n4</span><span class="p">;</span>
@@ -4872,14 +4881,14 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 二分木の初期化 */</span>
-<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="c1">// ノードの初期化</span>
+<div class="highlight"><span class="filename">binary_tree.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 二分木を初期化する */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="c1">// ノードを初期化する</span>
 <a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">1</span><span class="p">);</span>
 <a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">2</span><span class="p">);</span>
 <a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">3</span><span class="p">);</span>
 <a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">4</span><span class="p">);</span>
 <a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n5</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">5</span><span class="p">);</span>
-<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="c1">// ノード間の参照（ポインタ）を結ぶ</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="c1">// ノード間の参照（ポインタ）を構築する</span>
 <a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="n">n1</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
 <a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="n">n1</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
 <a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="n">n2</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
@@ -4887,13 +4896,13 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="c1">// ノードの初期化</span>
+<div class="highlight"><span class="filename">binary_tree.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="c1">// ノードを初期化する</span>
 <a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="kd">let</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="kd">let</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
 <a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="kd">let</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
 <a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="kd">let</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
 <a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="kd">let</span><span class="w"> </span><span class="n">n5</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
-<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="c1">// ノード間の参照（ポインタ）を結ぶ</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="c1">// ノード間の参照（ポインタ）を構築する</span>
 <a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="n">n1</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">n2</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
 <a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="n">n1</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">n3</span><span class="p">);</span>
 <a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="n">n2</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">n4</span><span class="p">);</span>
@@ -4901,14 +4910,14 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 二分木の初期化 */</span>
-<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="c1">// ノードの初期化</span>
+<div class="highlight"><span class="filename">binary_tree.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 二分木を初期化する */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="c1">// ノードを初期化する</span>
 <a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newTreeNode</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newTreeNode</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
 <a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newTreeNode</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
 <a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newTreeNode</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
 <a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">n5</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newTreeNode</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
-<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="c1">// ノード間の参照（ポインタ）を結ぶ</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="c1">// ノード間の参照（ポインタ）を構築する</span>
 <a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="n">n1</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
 <a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="n">n1</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
 <a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="n">n2</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
@@ -4916,13 +4925,13 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="c1">// ノードの初期化</span>
+<div class="highlight"><span class="filename">binary_tree.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="c1">// ノードを初期化する</span>
 <a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">val</span><span class="w"> </span><span class="nv">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">1</span><span class="p">)</span>
 <a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="kd">val</span><span class="w"> </span><span class="nv">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">2</span><span class="p">)</span>
 <a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="kd">val</span><span class="w"> </span><span class="nv">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">3</span><span class="p">)</span>
 <a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="kd">val</span><span class="w"> </span><span class="nv">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">4</span><span class="p">)</span>
 <a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="kd">val</span><span class="w"> </span><span class="nv">n5</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">5</span><span class="p">)</span>
-<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="c1">// ノード間の参照（ポインタ）を結ぶ</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="c1">// ノード間の参照（ポインタ）を構築する</span>
 <a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="n">n1</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span>
 <a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="n">n1</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span>
 <a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="n">n2</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span>
@@ -4930,208 +4939,237 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a>
+<div class="highlight"><span class="filename">binary_tree.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1"># 二分木を初期化する</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="c1"># ノードを初期化する</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="n">n5</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="c1"># ノード間の参照（ポインタ）を構築する</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="n">n1</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="n">n1</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="n">n2</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="n">n2</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n5</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>実行の可視化</summary>
+<p>https://pythontutor.com/render.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%8F%89%E6%A0%91%E8%8A%82%E7%82%B9%E7%B1%BB%22%22%22%0A%20%20%20%20def%20__init__%28self,%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E8%8A%82%E7%82%B9%E5%80%BC%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%23%20%E5%8F%B3%E5%AD%90%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E4%BA%8C%E5%8F%89%E6%A0%91%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E8%8A%82%E7%82%B9%0A%20%20%20%20n1%20%3D%20TreeNode%28val%3D1%29%0A%20%20%20%20n2%20%3D%20TreeNode%28val%3D2%29%0A%20%20%20%20n3%20%3D%20TreeNode%28val%3D3%29%0A%20%20%20%20n4%20%3D%20TreeNode%28val%3D4%29%0A%20%20%20%20n5%20%3D%20TreeNode%28val%3D5%29%0A%20%20%20%20%23%20%E6%9E%84%E5%BB%BA%E8%8A%82%E7%82%B9%E4%B9%8B%E9%97%B4%E7%9A%84%E5%BC%95%E7%94%A8%EF%BC%88%E6%8C%87%E9%92%88%EF%BC%89%0A%20%20%20%20n1.left%20%3D%20n2%0A%20%20%20%20n1.right%20%3D%20n3%0A%20%20%20%20n2.left%20%3D%20n4%0A%20%20%20%20n2.right%20%3D%20n5&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>
+</details>
 <h3 id="2">2. &nbsp; ノードの挿入と削除<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>連結リストと同様に、二分木でのノードの挿入と削除はポインタを変更することで実現できます。下図に例を示します。</p>
-<p><img alt="二分木でのノードの挿入と削除" class="animation-figure" src="../binary_tree.assets/binary_tree_add_remove.png" /></p>
-<p align="center"> 図 7-3 &nbsp; 二分木でのノードの挿入と削除 </p>
+<p>連結リストと同様に、二分木でのノードの挿入と削除はポインタを変更することで実現できます。以下の図に 1 つの例を示します。</p>
+<p><img alt="二分木でノードを挿入・削除する" class="animation-figure" src="../binary_tree.assets/binary_tree_add_remove.png" /></p>
+<p align="center"> 図 7-3 &nbsp; 二分木でノードを挿入・削除する </p>
 
 <div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_tree.py</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1"># ノードの挿入と削除</span>
 <a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="n">p</span> <span class="o">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
-<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="c1"># n1 -&gt; n2の間にノードPを挿入</span>
+<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="c1"># n1 -&gt; n2 の間にノード P を挿入する</span>
 <a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="n">n1</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">p</span>
 <a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="n">p</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">n2</span>
-<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="c1"># ノードPを削除</span>
+<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="c1"># ノード P を削除する</span>
 <a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="n">n1</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">n2</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_tree.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* ノードの挿入と削除 */</span>
 <a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="n">TreeNode</span><span class="o">*</span><span class="w"> </span><span class="n">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
-<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="c1">// n1とn2の間にノードPを挿入</span>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="c1">// n1 -&gt; n2 の間にノード P を挿入する</span>
 <a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="n">n1</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="p">;</span>
 <a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="n">P</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
-<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="c1">// ノードPを削除</span>
+<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="c1">// ノード P を削除する</span>
 <a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="n">n1</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="k">delete</span><span class="w"> </span><span class="n">P</span><span class="p">;</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_tree.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
-<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="c1">// n1とn2の間にノードPを挿入</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="c1">// n1 -&gt; n2 の間にノード P を挿入する</span>
 <a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="n">n1</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="p">;</span>
 <a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="n">P</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
-<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="c1">// ノードPを削除</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="c1">// ノード P を削除する</span>
 <a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="n">n1</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_tree.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* ノードの挿入と削除 */</span>
 <a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
-<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="c1">// n1とn2の間にノードPを挿入</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="c1">// n1 -&gt; n2 の間にノード P を挿入する</span>
 <a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="n">n1</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="p">;</span>
 <a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="n">P</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
-<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="c1">// ノードPを削除</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="c1">// ノード P を削除する</span>
 <a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="n">n1</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_tree.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* ノードの挿入と削除 */</span>
-<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="c1">// n1とn2の間にノードPを挿入</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="c1">// n1 -&gt; n2 の間にノード P を挿入する</span>
 <a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="nx">p</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewTreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
 <a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">p</span>
 <a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="nx">p</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n2</span>
-<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="c1">// ノードPを削除</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="c1">// ノード P を削除する</span>
 <a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n2</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_tree.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="kd">let</span><span class="w"> </span><span class="nv">P</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
-<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="c1">// n1とn2の間にノードPを挿入</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="c1">// n1 -&gt; n2 の間にノード P を挿入する</span>
 <a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="n">n1</span><span class="p">.</span><span class="kr">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">P</span>
 <a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="n">P</span><span class="p">.</span><span class="kr">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n2</span>
-<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="c1">// ノードPを削除</span>
+<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="c1">// ノード P を削除する</span>
 <a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="n">n1</span><span class="p">.</span><span class="kr">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n2</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_tree.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* ノードの挿入と削除 */</span>
 <a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="kd">let</span><span class="w"> </span><span class="nx">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
-<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="c1">// n1とn2の間にノードPを挿入</span>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="c1">// n1 -&gt; n2 の間にノード P を挿入する</span>
 <a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">P</span><span class="p">;</span>
 <a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="nx">P</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n2</span><span class="p">;</span>
-<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="c1">// ノードPを削除</span>
+<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="c1">// ノード P を削除する</span>
 <a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n2</span><span class="p">;</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_tree.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* ノードの挿入と削除 */</span>
 <a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
-<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="c1">// n1とn2の間にノードPを挿入</span>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="c1">// n1 -&gt; n2 の間にノード P を挿入する</span>
 <a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">P</span><span class="p">;</span>
 <a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="nx">P</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n2</span><span class="p">;</span>
-<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="c1">// ノードPを削除</span>
+<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="c1">// ノード P を削除する</span>
 <a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n2</span><span class="p">;</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_tree.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* ノードの挿入と削除 */</span>
 <a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
-<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="c1">// n1とn2の間にノードPを挿入</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="c1">// n1 -&gt; n2 の間にノード P を挿入する</span>
 <a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="n">n1</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="p">;</span>
 <a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="n">P</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
-<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="c1">// ノードPを削除</span>
+<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="c1">// ノード P を削除する</span>
 <a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="n">n1</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_tree.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="kd">let</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
-<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="c1">// n1とn2の間にノードPを挿入</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="c1">// n1 -&gt; n2 の間にノード P を挿入する</span>
 <a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="n">n1</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">p</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
 <a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="n">p</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">n2</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
-<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="c1">// ノードPを削除</span>
+<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="c1">// ノード p を削除する</span>
 <a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="n">n1</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">n2</span><span class="p">);</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_tree.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* ノードの挿入と削除 */</span>
 <a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newTreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
-<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="c1">// n1とn2の間にノードPを挿入</span>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="c1">// n1 -&gt; n2 の間にノード P を挿入する</span>
 <a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="n">n1</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="p">;</span>
 <a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="n">P</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
-<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="c1">// ノードPを削除</span>
+<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="c1">// ノード P を削除する</span>
 <a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="n">n1</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="c1">// メモリを解放する</span>
+<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="n">free</span><span class="p">(</span><span class="n">P</span><span class="p">);</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_tree.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="kd">val</span><span class="w"> </span><span class="nv">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
-<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="c1">// n1とn2の間にノードPを挿入</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="c1">// n1 -&gt; n2 の間にノード P を挿入する</span>
 <a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="n">n1</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span>
 <a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="n">P</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span>
-<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="c1">// ノードPを削除</span>
+<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="c1">// ノード P を削除する</span>
 <a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="n">n1</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a>
+<div class="highlight"><span class="filename">binary_tree.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="c1"># ノードの挿入と削除</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="n">_p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="c1"># n1 -&gt; n2 の間にノード _p を挿入する</span>
+<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="n">n1</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_p</span>
+<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="n">_p</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span>
+<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="c1"># ノードを削除する</span>
+<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="n">n1</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>実行の可視化</summary>
+<p>https://pythontutor.com/render.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%8F%89%E6%A0%91%E8%8A%82%E7%82%B9%E7%B1%BB%22%22%22%0A%20%20%20%20def%20__init__%28self,%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E8%8A%82%E7%82%B9%E5%80%BC%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%23%20%E5%8F%B3%E5%AD%90%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E4%BA%8C%E5%8F%89%E6%A0%91%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E8%8A%82%E7%82%B9%0A%20%20%20%20n1%20%3D%20TreeNode%28val%3D1%29%0A%20%20%20%20n2%20%3D%20TreeNode%28val%3D2%29%0A%20%20%20%20n3%20%3D%20TreeNode%28val%3D3%29%0A%20%20%20%20n4%20%3D%20TreeNode%28val%3D4%29%0A%20%20%20%20n5%20%3D%20TreeNode%28val%3D5%29%0A%20%20%20%20%23%20%E6%9E%84%E5%BB%BA%E8%8A%82%E7%82%B9%E4%B9%8B%E9%97%B4%E7%9A%84%E5%BC%95%E7%94%A8%EF%BC%88%E6%8C%87%E9%92%88%EF%BC%89%0A%20%20%20%20n1.left%20%3D%20n2%0A%20%20%20%20n1.right%20%3D%20n3%0A%20%20%20%20n2.left%20%3D%20n4%0A%20%20%20%20n2.right%20%3D%20n5%0A%0A%20%20%20%20%23%20%E6%8F%92%E5%85%A5%E4%B8%8E%E5%88%A0%E9%99%A4%E8%8A%82%E7%82%B9%0A%20%20%20%20p%20%3D%20TreeNode%280%29%0A%20%20%20%20%23%20%E5%9C%A8%20n1%20-%3E%20n2%20%E4%B8%AD%E9%97%B4%E6%8F%92%E5%85%A5%E8%8A%82%E7%82%B9%20P%0A%20%20%20%20n1.left%20%3D%20p%0A%20%20%20%20p.left%20%3D%20n2%0A%20%20%20%20%23%20%E5%88%A0%E9%99%A4%E8%8A%82%E7%82%B9%20P%0A%20%20%20%20n1.left%20%3D%20n2&amp;cumulative=false&amp;curInstr=37&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>
+</details>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>ノードの挿入は二分木の元の論理構造を変更する可能性があり、ノードの削除は通常そのノードとそのすべての部分木を削除することになることに注意してください。したがって、二分木では、挿入と削除は通常一連の操作を通じて実行され、意味のある結果を得ます。</p>
+<p>注意すべき点として、ノードの挿入は二分木の元の論理構造を変える可能性があり、ノードの削除は通常、そのノードと配下のすべての部分木の削除を意味します。そのため、二分木における挿入と削除は、実際に意味のある操作を実現するために、通常は一連の操作を組み合わせて行います。</p>
 </div>
-<h2 id="713">7.1.3 &nbsp; 二分木の一般的な種類<a class="headerlink" href="#713" title="Permanent link">&para;</a></h2>
-<h3 id="1_1">1. &nbsp; 完全二分木<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
-<p>下図に示すように、<u>完全二分木</u>では、すべてのレベルがノードで完全に埋められています。完全二分木では、葉ノードの次数は<span class="arithmatex">\(0\)</span>で、他のすべてのノードの次数は<span class="arithmatex">\(2\)</span>です。ノードの総数は<span class="arithmatex">\(2^{h+1} - 1\)</span>として計算でき、ここで<span class="arithmatex">\(h\)</span>は木の高さです。これは標準的な指数関係を示し、自然界の細胞分裂の一般的な現象を反映しています。</p>
+<h2 id="713">7.1.3 &nbsp; 一般的な二分木の種類<a class="headerlink" href="#713" title="Permanent link">&para;</a></h2>
+<h3 id="1_1">1. &nbsp; 充足二分木<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
+<p>以下の図に示すように、<u>充足二分木（perfect binary tree）</u>ではすべてのレベルのノードが完全に埋まっています。充足二分木では、葉ノードの次数は <span class="arithmatex">\(0\)</span> で、それ以外のすべてのノードの次数は <span class="arithmatex">\(2\)</span> です。木の高さを <span class="arithmatex">\(h\)</span> とすると、ノード総数は <span class="arithmatex">\(2^{h+1} - 1\)</span> となり、標準的な指数関係を示して、自然界でよく見られる細胞分裂の現象を反映しています。</p>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>中国語圏では、完全二分木はしばしば<u>満二分木</u>と呼ばれることに注意してください。</p>
+<p>なお、中国語圏では充足二分木は<u>満二分木</u>と呼ばれることもあります。</p>
 </div>
-<p><img alt="完全二分木" class="animation-figure" src="../binary_tree.assets/perfect_binary_tree.png" /></p>
-<p align="center"> 図 7-4 &nbsp; 完全二分木 </p>
+<p><img alt="充足二分木" class="animation-figure" src="../binary_tree.assets/perfect_binary_tree.png" /></p>
+<p align="center"> 図 7-4 &nbsp; 充足二分木 </p>
 
-<h3 id="2_1">2. &nbsp; 完備二分木<a class="headerlink" href="#2_1" title="Permanent link">&para;</a></h3>
-<p>下図に示すように、<u>完備二分木</u>は、最下位レベルのみが完全に埋められていない可能性がある二分木で、最下位レベルのノードは左から右に連続して埋められる必要があります。完全二分木は完備二分木でもあることに注意してください。</p>
-<p><img alt="完備二分木" class="animation-figure" src="../binary_tree.assets/complete_binary_tree.png" /></p>
-<p align="center"> 図 7-5 &nbsp; 完備二分木 </p>
+<h3 id="2_1">2. &nbsp; 完全二分木<a class="headerlink" href="#2_1" title="Permanent link">&para;</a></h3>
+<p>以下の図に示すように、<u>完全二分木（complete binary tree）</u>では最下層のノードだけが完全に埋まっていなくてもよく、しかも最下層のノードは左から右へ連続して詰められていなければなりません。なお、充足二分木も完全二分木の一種です。</p>
+<p><img alt="完全二分木" class="animation-figure" src="../binary_tree.assets/complete_binary_tree.png" /></p>
+<p align="center"> 図 7-5 &nbsp; 完全二分木 </p>
 
-<h3 id="3">3. &nbsp; 満二分木<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
-<p>下図に示すように、<u>満二分木</u>では、葉ノードを除いて、他のすべてのノードが2つの子ノードを持ちます。</p>
-<p><img alt="満二分木" class="animation-figure" src="../binary_tree.assets/full_binary_tree.png" /></p>
-<p align="center"> 図 7-6 &nbsp; 満二分木 </p>
+<h3 id="3">3. &nbsp; 充満二分木<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
+<p>以下の図に示すように、<u>充満二分木（full binary tree）</u>では、葉ノードを除くすべてのノードが 2 つの子ノードを持ちます。</p>
+<p><img alt="充満二分木" class="animation-figure" src="../binary_tree.assets/full_binary_tree.png" /></p>
+<p align="center"> 図 7-6 &nbsp; 充満二分木 </p>
 
 <h3 id="4">4. &nbsp; 平衡二分木<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
-<p>下図に示すように、<u>平衡二分木</u>では、任意のノードの左と右の部分木の高さの絶対差が1を超えません。</p>
+<p>以下の図に示すように、<u>平衡二分木（balanced binary tree）</u>では、任意のノードについて左部分木と右部分木の高さの差の絶対値が 1 を超えません。</p>
 <p><img alt="平衡二分木" class="animation-figure" src="../binary_tree.assets/balanced_binary_tree.png" /></p>
 <p align="center"> 図 7-7 &nbsp; 平衡二分木 </p>
 
 <h2 id="714">7.1.4 &nbsp; 二分木の退化<a class="headerlink" href="#714" title="Permanent link">&para;</a></h2>
-<p>下図は、二分木の理想的な構造と退化した構造を示しています。二分木は、すべてのレベルが埋められているときに「完全二分木」になり、すべてのノードが一方に偏っているときに「連結リスト」に退化します。</p>
+<p>以下の図は、二分木の理想的な構造と退化した構造を示しています。二分木の各レベルのノードがすべて埋まっていると「充足二分木」となり、すべてのノードが片側に偏ると二分木は「連結リスト」へ退化します。</p>
 <ul>
-<li>完全二分木は、二分木の「分割統治法」の利点を十分に活用できる理想的なシナリオです。</li>
-<li>一方、連結リストは別の極端を表し、すべての操作が線形になり、時間計算量が<span class="arithmatex">\(O(n)\)</span>になります。</li>
+<li>充足二分木は理想的なケースであり、二分木の「分割統治」の利点を十分に発揮できます。</li>
+<li>連結リストはその対極にあり、各種操作はすべて線形操作となり、時間計算量は <span class="arithmatex">\(O(n)\)</span> まで退化します。</li>
 </ul>
-<p><img alt="二分木の最良と最悪の構造" class="animation-figure" src="../binary_tree.assets/binary_tree_best_worst_cases.png" /></p>
-<p align="center"> 図 7-8 &nbsp; 二分木の最良と最悪の構造 </p>
+<p><img alt="二分木の最良構造と最悪構造" class="animation-figure" src="../binary_tree.assets/binary_tree_best_worst_cases.png" /></p>
+<p align="center"> 図 7-8 &nbsp; 二分木の最良構造と最悪構造 </p>
 
-<p>下表に示すように、最良と最悪の構造では、二分木は葉ノード数、総ノード数、高さの最大値または最小値を達成します。</p>
-<p align="center"> 表 7-1 &nbsp; 二分木の最良と最悪の構造 </p>
+<p>以下の表に示すように、最良構造と最悪構造では、二分木の葉ノード数、ノード総数、高さなどが極大または極小になります。</p>
+<p align="center"> 表 7-1 &nbsp; 二分木の最良構造と最悪構造 </p>
 
 <div class="center-table">
 <table>
 <thead>
 <tr>
 <th></th>
-<th>完全二分木</th>
+<th>充足二分木</th>
 <th>連結リスト</th>
 </tr>
 </thead>
 <tbody>
 <tr>
-<td>レベル<span class="arithmatex">\(i\)</span>のノード数</td>
+<td>第 <span class="arithmatex">\(i\)</span> レベルのノード数</td>
 <td><span class="arithmatex">\(2^{i-1}\)</span></td>
 <td><span class="arithmatex">\(1\)</span></td>
 </tr>
 <tr>
-<td>高さ<span class="arithmatex">\(h\)</span>の木の葉ノード数</td>
+<td>高さ <span class="arithmatex">\(h\)</span> の木の葉ノード数</td>
 <td><span class="arithmatex">\(2^h\)</span></td>
 <td><span class="arithmatex">\(1\)</span></td>
 </tr>
 <tr>
-<td>高さ<span class="arithmatex">\(h\)</span>の木の総ノード数</td>
+<td>高さ <span class="arithmatex">\(h\)</span> の木のノード総数</td>
 <td><span class="arithmatex">\(2^{h+1} - 1\)</span></td>
 <td><span class="arithmatex">\(h + 1\)</span></td>
 </tr>
 <tr>
-<td>総ノード数<span class="arithmatex">\(n\)</span>の木の高さ</td>
+<td>ノード総数 <span class="arithmatex">\(n\)</span> の木の高さ</td>
 <td><span class="arithmatex">\(\log_2 (n+1) - 1\)</span></td>
 <td><span class="arithmatex">\(n - 1\)</span></td>
 </tr>
diff --git a/ja/chapter_tree/binary_tree_traversal/index.html b/ja/chapter_tree/binary_tree_traversal/index.html
index 100df82bd..dbbc59b36 100644
--- a/ja/chapter_tree/binary_tree_traversal/index.html
+++ b/ja/chapter_tree/binary_tree_traversal/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
     </svg>
-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1635,7 +1635,7 @@
   <span class="md-ellipsis">
     
   
-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
@@ -1929,7 +1929,7 @@
   <a href="#1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; コード実装
+        1. &nbsp; コードの実装
       
     </span>
   </a>
@@ -1940,7 +1940,7 @@
   <a href="#2" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2. &nbsp; 計算量分析
+        2. &nbsp; 計算量
       
     </span>
   </a>
@@ -1956,19 +1956,19 @@
   <a href="#722" class="md-nav__link">
     <span class="md-ellipsis">
       
-        7.2.2 &nbsp; 前順、中順、後順走査
+        7.2.2 &nbsp; 先行順・中間順・後行順走査
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="7.2.2 前順、中順、後順走査">
+    <nav class="md-nav" aria-label="7.2.2 先行順・中間順・後行順走査">
       <ul class="md-nav__list">
         
           <li class="md-nav__item">
   <a href="#1_1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; コード実装
+        1. &nbsp; コードの実装
       
     </span>
   </a>
@@ -1979,7 +1979,7 @@
   <a href="#2_1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2. &nbsp; 計算量分析
+        2. &nbsp; 計算量
       
     </span>
   </a>
@@ -2070,7 +2070,7 @@
   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2233,7 +2233,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2619,7 +2619,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2675,7 +2675,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2703,7 +2703,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3241,7 +3241,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3297,7 +3297,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3325,7 +3325,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3518,7 +3518,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3546,7 +3546,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3687,7 +3687,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3715,7 +3715,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3743,7 +3743,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3771,7 +3771,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3964,7 +3964,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4209,7 +4209,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4367,7 +4367,7 @@
   <a href="#1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; コード実装
+        1. &nbsp; コードの実装
       
     </span>
   </a>
@@ -4378,7 +4378,7 @@
   <a href="#2" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2. &nbsp; 計算量分析
+        2. &nbsp; 計算量
       
     </span>
   </a>
@@ -4394,19 +4394,19 @@
   <a href="#722" class="md-nav__link">
     <span class="md-ellipsis">
       
-        7.2.2 &nbsp; 前順、中順、後順走査
+        7.2.2 &nbsp; 先行順・中間順・後行順走査
       
     </span>
   </a>
   
-    <nav class="md-nav" aria-label="7.2.2 前順、中順、後順走査">
+    <nav class="md-nav" aria-label="7.2.2 先行順・中間順・後行順走査">
       <ul class="md-nav__list">
         
           <li class="md-nav__item">
   <a href="#1_1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; コード実装
+        1. &nbsp; コードの実装
       
     </span>
   </a>
@@ -4417,7 +4417,7 @@
   <a href="#2_1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        2. &nbsp; 計算量分析
+        2. &nbsp; 計算量
       
     </span>
   </a>
@@ -4467,52 +4467,52 @@
 
 <!-- Page content -->
 <h1 id="72">7.2 &nbsp; 二分木の走査<a class="headerlink" href="#72" title="Permanent link">&para;</a></h1>
-<p>物理的構造の観点から見ると、木は連結リストに基づくデータ構造です。したがって、その走査方法はポインタを通してノードに一つずつアクセスすることを含みます。しかし、木は非線形データ構造であるため、木の走査は連結リストの走査よりも複雑で、検索アルゴリズムの支援が必要です。</p>
-<p>二分木の一般的な走査方法には、レベル順走査、前順走査、中順走査、後順走査があります。</p>
+<p>物理構造の観点から見ると、木は連結リストを基盤としたデータ構造であり、その走査はポインタを通じてノードへ順にアクセスすることで行われます。しかし、木は非線形データ構造であるため、木の走査は連結リストの走査よりも複雑であり、検索アルゴリズムを用いて実現する必要があります。</p>
+<p>二分木の一般的な走査方法には、レベル順走査、先行順走査、中間順走査、後行順走査などがあります。</p>
 <h2 id="721">7.2.1 &nbsp; レベル順走査<a class="headerlink" href="#721" title="Permanent link">&para;</a></h2>
-<p>下図に示すように、<u>レベル順走査</u>は二分木を上から下へ、層ごとに走査します。各レベル内では、左から右へノードを訪問します。</p>
-<p>レベル順走査は本質的に<u>幅優先走査</u>の一種で、<u>幅優先探索（BFS）</u>とも呼ばれ、「周囲に向かって外向きに拡張する」層ごとの走査方法を体現しています。</p>
+<p>次の図に示すように、<u>レベル順走査（level-order traversal）</u>では、二分木を上から下へ層ごとに走査し、各層では左から右の順にノードへアクセスします。</p>
+<p>レベル順走査は本質的に<u>幅優先走査（breadth-first traversal）</u>に属し、<u>幅優先探索（breadth-first search, BFS）</u>とも呼ばれます。これは「同心円状に外側へ広がる」ような、層ごとの走査方法を表しています。</p>
 <p><img alt="二分木のレベル順走査" class="animation-figure" src="../binary_tree_traversal.assets/binary_tree_bfs.png" /></p>
 <p align="center"> 図 7-9 &nbsp; 二分木のレベル順走査 </p>
 
-<h3 id="1">1. &nbsp; コード実装<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>幅優先走査は通常「キュー」の助けを借りて実装されます。キューは「先入れ先出し」の規則に従い、幅優先走査は「層ごとの進行」規則に従います。両者の基本的な考え方は一致しています。実装コードは以下の通りです：</p>
+<h3 id="1">1. &nbsp; コードの実装<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>幅優先走査は通常「キュー」を用いて実装します。キューは「先入れ先出し」の規則に従い、幅優先走査は「層ごとに進む」という規則に従います。両者の背後にある考え方は一致しています。実装コードは次のとおりです：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_tree_bfs.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">level_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
 <a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;レベル順走査&quot;&quot;&quot;</span>
-<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># キューを初期化し、ルートノードを追加</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># キューを初期化し、ルートノードを追加する</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">queue</span><span class="p">:</span> <span class="n">deque</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]</span> <span class="o">=</span> <span class="n">deque</span><span class="p">()</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="n">queue</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
-<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 走査シーケンスを格納するリストを初期化</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 走査順序を保存するためのリストを初期化する</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="k">while</span> <span class="n">queue</span><span class="p">:</span>
-<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">=</span> <span class="n">queue</span><span class="o">.</span><span class="n">popleft</span><span class="p">()</span>  <span class="c1"># キューからデキュー</span>
-<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>  <span class="c1"># ノードの値を保存</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">=</span> <span class="n">queue</span><span class="o">.</span><span class="n">popleft</span><span class="p">()</span>  <span class="c1"># デキュー</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>  <span class="c1"># ノードの値を保存する</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="k">if</span> <span class="n">node</span><span class="o">.</span><span class="n">left</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>            <span class="n">queue</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>  <span class="c1"># 左の子ノードをエンキュー</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>            <span class="n">queue</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>  <span class="c1"># 左子ノードをキューに追加</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="k">if</span> <span class="n">node</span><span class="o">.</span><span class="n">right</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>            <span class="n">queue</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>  <span class="c1"># 右の子ノードをエンキュー</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>            <span class="n">queue</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>  <span class="c1"># 右子ノードをキューに追加</span>
 <a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="k">return</span> <span class="n">res</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_tree_bfs.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* レベル順走査 */</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">levelOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// キューを初期化、ルートノードを追加</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// キューを初期化し、ルートノードを追加する</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="n">queue</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">queue</span><span class="p">;</span>
 <a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="n">queue</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
-<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// 走査順序を保存するリストを初期化</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// 走査順序を保存するためのリストを初期化する</span>
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">vec</span><span class="p">;</span>
 <a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">queue</span><span class="p">.</span><span class="n">empty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">        </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">front</span><span class="p">();</span>
-<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="n">queue</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w">              </span><span class="c1">// キューからデキュー</span>
-<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="n">vec</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span><span class="w"> </span><span class="c1">// ノード値を保存</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="n">queue</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w">              </span><span class="c1">// デキュー</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="n">vec</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span><span class="w"> </span><span class="c1">// ノードの値を保存する</span>
 <a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
-<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">            </span><span class="n">queue</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">);</span><span class="w"> </span><span class="c1">// 左の子ノードをエンキュー</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">            </span><span class="n">queue</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">);</span><span class="w"> </span><span class="c1">// 左子ノードをキューに追加</span>
 <a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
-<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">            </span><span class="n">queue</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右の子ノードをエンキュー</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">            </span><span class="n">queue</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右子ノードをキューに追加</span>
 <a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">vec</span><span class="p">;</span>
 <a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="p">}</span>
@@ -4521,86 +4521,278 @@
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_tree_bfs.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* レベル順走査 */</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">levelOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// キューを初期化し、根ノードを追加</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// キューを初期化し、ルートノードを追加する</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="n">Queue</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">LinkedList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="n">queue</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
-<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// 走査順序を格納するリストを初期化</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// 走査順序を保存するためのリストを初期化する</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">list</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">queue</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">        </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// キューのデキュー</span>
-<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="n">list</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">);</span><span class="w">           </span><span class="c1">// ノードの値を保存</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">        </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// デキュー</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="n">list</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">);</span><span class="w">           </span><span class="c1">// ノードの値を保存する</span>
 <a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
-<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">            </span><span class="n">queue</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">);</span><span class="w">   </span><span class="c1">// 左の子ノードをエンキュー</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">            </span><span class="n">queue</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">);</span><span class="w">   </span><span class="c1">// 左子ノードをキューに追加</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
-<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">            </span><span class="n">queue</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">);</span><span class="w">  </span><span class="c1">// 右の子ノードをエンキュー</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">            </span><span class="n">queue</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">);</span><span class="w">  </span><span class="c1">// 右子ノードをキューに追加</span>
 <a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">list</span><span class="p">;</span>
 <a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree_bfs.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_tree_bfs</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">LevelOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_tree_bfs.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* レベル順走査 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">LevelOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="c1">// キューを初期化し、ルートノードを追加する</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="n">Queue</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">();</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="n">queue</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="c1">// 走査順序を保存するためのリストを初期化する</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">list</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">queue</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">        </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w"> </span><span class="c1">// デキュー</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">        </span><span class="n">list</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="o">!</span><span class="p">.</span><span class="n">Value</span><span class="p">);</span><span class="w">       </span><span class="c1">// ノードの値を保存する</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="p">)</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">            </span><span class="n">queue</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">);</span><span class="w">    </span><span class="c1">// 左子ノードをキューに追加</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="p">)</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">            </span><span class="n">queue</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">);</span><span class="w">   </span><span class="c1">// 右子ノードをキューに追加</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">list</span><span class="p">;</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree_bfs.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">levelOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_tree_bfs.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* レベル順走査 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">levelOrder</span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// キューを初期化し、ルートノードを追加する</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">queue</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">list</span><span class="p">.</span><span class="nx">New</span><span class="p">()</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="nx">queue</span><span class="p">.</span><span class="nx">PushBack</span><span class="p">(</span><span class="nx">root</span><span class="p">)</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="c1">// 走査順を保存するためのスライスを初期化する</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="nx">nums</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">any</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">queue</span><span class="p">.</span><span class="nx">Len</span><span class="p">()</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">        </span><span class="c1">// デキュー</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">        </span><span class="nx">node</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">queue</span><span class="p">.</span><span class="nx">Remove</span><span class="p">(</span><span class="nx">queue</span><span class="p">.</span><span class="nx">Front</span><span class="p">()).(</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">        </span><span class="c1">// ノードの値を保存する</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">        </span><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Val</span><span class="p">)</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">            </span><span class="c1">// 左子ノードをキューに追加</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">            </span><span class="nx">queue</span><span class="p">.</span><span class="nx">PushBack</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span><span class="p">)</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w">            </span><span class="c1">// 右子ノードをキューに追加</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w">            </span><span class="nx">queue</span><span class="p">.</span><span class="nx">PushBack</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="p">)</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">nums</span>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree_bfs.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">levelOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_tree_bfs.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* レベル順走査 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">levelOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// キューを初期化し、ルートノードを追加する</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">queue</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="n">root</span><span class="p">]</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="c1">// 走査順序を保存するためのリストを初期化する</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">list</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">queue</span><span class="p">.</span><span class="bp">isEmpty</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">removeFirst</span><span class="p">()</span><span class="w"> </span><span class="c1">// デキュー</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">        </span><span class="n">list</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="c1">// ノードの値を保存する</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="kr">left</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">            </span><span class="n">queue</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="kr">left</span><span class="p">)</span><span class="w"> </span><span class="c1">// 左子ノードをキューに追加</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="kr">right</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">            </span><span class="n">queue</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="kr">right</span><span class="p">)</span><span class="w"> </span><span class="c1">// 右子ノードをキューに追加</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">list</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree_bfs.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">levelOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_tree_bfs.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* レベル順走査 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">levelOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="c1">// キューを初期化し、ルートノードを追加する</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">root</span><span class="p">];</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="c1">// 走査順序を保存するためのリストを初期化する</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">list</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">queue</span><span class="p">.</span><span class="nx">length</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">queue</span><span class="p">.</span><span class="nx">shift</span><span class="p">();</span><span class="w"> </span><span class="c1">// デキュー</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">        </span><span class="nx">list</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span><span class="w"> </span><span class="c1">// ノードの値を保存する</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="p">)</span><span class="w"> </span><span class="nx">queue</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="p">);</span><span class="w"> </span><span class="c1">// 左子ノードをキューに追加</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="nx">queue</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右子ノードをキューに追加</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">list</span><span class="p">;</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree_bfs.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">levelOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_tree_bfs.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* レベル順走査 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">levelOrder</span><span class="p">(</span><span class="nx">root</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="c1">// キューを初期化し、ルートノードを追加する</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">root</span><span class="p">];</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="c1">// 走査順序を保存するためのリストを初期化する</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">list</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">queue</span><span class="p">.</span><span class="nx">length</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">queue</span><span class="p">.</span><span class="nx">shift</span><span class="p">()</span><span class="w"> </span><span class="kr">as</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">;</span><span class="w"> </span><span class="c1">// デキュー</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">        </span><span class="nx">list</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span><span class="w"> </span><span class="c1">// ノードの値を保存する</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">            </span><span class="nx">queue</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="p">);</span><span class="w"> </span><span class="c1">// 左子ノードをキューに追加</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">            </span><span class="nx">queue</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右子ノードをキューに追加</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">list</span><span class="p">;</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree_bfs.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">levelOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_tree_bfs.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* レベル順走査 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">levelOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="c1">// キューを初期化し、ルートノードを追加する</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="n">Queue</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">?&gt;</span><span class="w"> </span><span class="n">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Queue</span><span class="p">();</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="n">queue</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="c1">// 走査順序を保存するためのリストを初期化する</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">queue</span><span class="p">.</span><span class="n">isNotEmpty</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">    </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">removeFirst</span><span class="p">();</span><span class="w"> </span><span class="c1">// デキュー</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">node</span><span class="o">!</span><span class="p">.</span><span class="n">val</span><span class="p">);</span><span class="w"> </span><span class="c1">// ノードの値を保存する</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">);</span><span class="w"> </span><span class="c1">// 左子ノードをキューに追加</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右子ノードをキューに追加</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree_bfs.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">level_order</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_tree_bfs.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* レベル順走査 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">level_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="c1">// キューを初期化し、ルートノードを追加する</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">que</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">VecDeque</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="n">que</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="c1">// 走査順序を保存するためのリストを初期化する</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">vec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="n">pop_front</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">        </span><span class="c1">// デキュー</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">        </span><span class="n">vec</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">);</span><span class="w"> </span><span class="c1">// ノードの値を保存する</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">            </span><span class="n">que</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span><span class="w"> </span><span class="c1">// 左子ノードをキューに追加</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">            </span><span class="n">que</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span><span class="w"> </span><span class="c1">// 右子ノードをキューに追加</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">        </span><span class="p">};</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">    </span><span class="n">vec</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree_bfs.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">levelOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_tree_bfs.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* レベル順走査 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="nf">levelOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="cm">/* 補助キュー */</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">front</span><span class="p">,</span><span class="w"> </span><span class="n">rear</span><span class="p">;</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">arr</span><span class="p">;</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">**</span><span class="n">queue</span><span class="p">;</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">    </span><span class="cm">/* 補助キュー */</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="n">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">**</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">);</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="c1">// キューへのポインタ</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">    </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">    </span><span class="c1">// 根ノードを追加する</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">    </span><span class="n">queue</span><span class="p">[</span><span class="n">rear</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">    </span><span class="c1">// 走査順序を保存するためのリストを初期化する</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">    </span><span class="cm">/* 補助配列 */</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">    </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">);</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">    </span><span class="c1">// 配列ポインタ</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w">    </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">rear</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="w">        </span><span class="c1">// デキュー</span>
+<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w">        </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">[</span><span class="n">front</span><span class="o">++</span><span class="p">];</span>
+<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w">        </span><span class="c1">// ノードの値を保存する</span>
+<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="w">        </span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="w">            </span><span class="c1">// 左子ノードをキューに追加</span>
+<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="w">            </span><span class="n">queue</span><span class="p">[</span><span class="n">rear</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="w">            </span><span class="c1">// 右子ノードをキューに追加</span>
+<a id="__codelineno-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></a><span class="w">            </span><span class="n">queue</span><span class="p">[</span><span class="n">rear</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-10-32" name="__codelineno-10-32" href="#__codelineno-10-32"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-10-33" name="__codelineno-10-33" href="#__codelineno-10-33"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-34" name="__codelineno-10-34" href="#__codelineno-10-34"></a><span class="w">    </span><span class="c1">// 配列長の値を更新</span>
+<a id="__codelineno-10-35" name="__codelineno-10-35" href="#__codelineno-10-35"></a><span class="w">    </span><span class="o">*</span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
+<a id="__codelineno-10-36" name="__codelineno-10-36" href="#__codelineno-10-36"></a><span class="w">    </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">realloc</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="n">size</span><span class="p">));</span>
+<a id="__codelineno-10-37" name="__codelineno-10-37" href="#__codelineno-10-37"></a>
+<a id="__codelineno-10-38" name="__codelineno-10-38" href="#__codelineno-10-38"></a><span class="w">    </span><span class="c1">// 補助配列の領域を解放する</span>
+<a id="__codelineno-10-39" name="__codelineno-10-39" href="#__codelineno-10-39"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">queue</span><span class="p">);</span>
+<a id="__codelineno-10-40" name="__codelineno-10-40" href="#__codelineno-10-40"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">arr</span><span class="p">;</span>
+<a id="__codelineno-10-41" name="__codelineno-10-41" href="#__codelineno-10-41"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree_bfs.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">levelOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_tree_bfs.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* レベル順走査 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">levelOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="c1">// キューを初期化し、ルートノードを追加する</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">LinkedList</span><span class="o">&lt;</span><span class="n">TreeNode?&gt;</span><span class="p">()</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="n">queue</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="c1">// 走査順序を保存するためのリストを初期化する</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">list</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">queue</span><span class="p">.</span><span class="na">isNotEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">        </span><span class="kd">val</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="na">poll</span><span class="p">()</span><span class="w">      </span><span class="c1">// デキュー</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">        </span><span class="n">list</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">node</span><span class="o">?.</span><span class="na">_val</span><span class="o">!!</span><span class="p">)</span><span class="w">       </span><span class="c1">// ノードの値を保存する</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">            </span><span class="n">queue</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">)</span><span class="w">   </span><span class="c1">// 左子ノードをキューに追加</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">            </span><span class="n">queue</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">)</span><span class="w">  </span><span class="c1">// 右子ノードをキューに追加</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">list</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree_bfs.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">level_order</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_tree_bfs.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### レベル順走査 ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">level_order</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># キューを初期化し、ルートノードを追加する</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="n">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">root</span><span class="o">]</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="c1"># 走査順序を保存するためのリストを初期化する</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">queue</span><span class="o">.</span><span class="n">empty?</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">.</span><span class="n">shift</span><span class="w"> </span><span class="c1"># デキュー</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">    </span><span class="n">res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="c1"># ノードの値を保存する</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">    </span><span class="n">queue</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="o">.</span><span class="n">nil?</span><span class="w"> </span><span class="c1"># 左子ノードをキューに追加</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">    </span><span class="n">queue</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="o">.</span><span class="n">nil?</span><span class="w"> </span><span class="c1"># 右子ノードをキューに追加</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">  </span><span class="n">res</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
-<h3 id="2">2. &nbsp; 計算量分析<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=from%20collections%20import%20deque%0A%0Aclass%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E5%80%A4%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%23%20%E5%8F%B3%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%0Adef%20list_to_tree_dfs%28arr%3A%20list%5Bint%5D%2C%20i%3A%20int%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E4%BA%8C%E5%88%86%E6%9C%A8%E3%81%AB%E3%83%87%E3%82%B7%E3%83%AA%E3%82%A2%E3%83%A9%E3%82%A4%E3%82%BA%E3%81%99%E3%82%8B%3A%20%E5%86%8D%E5%B8%B0%22%22%22%0A%20%20%20%20%23%20%E6%B7%BB%E5%AD%97%E3%81%8C%E9%85%8D%E5%88%97%E9%95%B7%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%8B%E3%80%81%E5%AF%BE%E5%BF%9C%E3%81%99%E3%82%8B%E8%A6%81%E7%B4%A0%E3%81%8C%20None%20%E3%81%AA%E3%82%89%E3%80%81None%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20if%20i%20%3C%200%20or%20i%20%3E%3D%20len%28arr%29%20or%20arr%5Bi%5D%20is%20None%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%23%20%E7%8F%BE%E5%9C%A8%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20root%20%3D%20TreeNode%28arr%5Bi%5D%29%0A%20%20%20%20%23%20%E5%B7%A6%E5%8F%B3%E3%81%AE%E9%83%A8%E5%88%86%E6%9C%A8%E3%82%92%E5%86%8D%E5%B8%B0%E7%9A%84%E3%81%AB%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20root.left%20%3D%20list_to_tree_dfs%28arr%2C%202%20%2A%20i%20%2B%201%29%0A%20%20%20%20root.right%20%3D%20list_to_tree_dfs%28arr%2C%202%20%2A%20i%20%2B%202%29%0A%20%20%20%20return%20root%0A%0Adef%20list_to_tree%28arr%3A%20list%5Bint%5D%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E4%BA%8C%E5%88%86%E6%9C%A8%E3%81%AB%E3%83%87%E3%82%B7%E3%83%AA%E3%82%A2%E3%83%A9%E3%82%A4%E3%82%BA%E3%81%99%E3%82%8B%22%22%22%0A%20%20%20%20return%20list_to_tree_dfs%28arr%2C%200%29%0A%0A%0Adef%20level_order%28root%3A%20TreeNode%20%7C%20None%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%22%22%22%E3%83%AC%E3%83%99%E3%83%AB%E9%A0%86%E8%B5%B0%E6%9F%BB%22%22%22%0A%20%20%20%20%23%20%E3%82%AD%E3%83%A5%E3%83%BC%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%97%E3%80%81%E3%83%AB%E3%83%BC%E3%83%88%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E8%BF%BD%E5%8A%A0%E3%81%99%E3%82%8B%0A%20%20%20%20queue%3A%20deque%5BTreeNode%5D%20%3D%20deque%28%29%0A%20%20%20%20queue.append%28root%29%0A%20%20%20%20%23%20%E8%B5%B0%E6%9F%BB%E9%A0%86%E5%BA%8F%E3%82%92%E4%BF%9D%E5%AD%98%E3%81%99%E3%82%8B%E3%81%9F%E3%82%81%E3%81%AE%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20res%20%3D%20%5B%5D%0A%20%20%20%20while%20queue%3A%0A%20%20%20%20%20%20%20%20node%3A%20TreeNode%20%3D%20queue.popleft%28%29%20%20%23%20%E3%83%87%E3%82%AD%E3%83%A5%E3%83%BC%0A%20%20%20%20%20%20%20%20res.append%28node.val%29%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AE%E5%80%A4%E3%82%92%E4%BF%9D%E5%AD%98%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20if%20node.left%20is%20not%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20queue.append%28node.left%29%20%20%23%20%E5%B7%A6%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E3%82%AD%E3%83%A5%E3%83%BC%E3%81%AB%E8%BF%BD%E5%8A%A0%0A%20%20%20%20%20%20%20%20if%20node.right%20is%20not%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20queue.append%28node.right%29%20%20%23%20%E5%8F%B3%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E3%82%AD%E3%83%A5%E3%83%BC%E3%81%AB%E8%BF%BD%E5%8A%A0%0A%20%20%20%20return%20res%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E4%BA%8C%E5%88%86%E6%9C%A8%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20%23%20%E3%81%93%E3%81%93%E3%81%A7%E3%81%AF%E3%80%81%E9%85%8D%E5%88%97%E3%81%8B%E3%82%89%E7%9B%B4%E6%8E%A5%E4%BA%8C%E5%88%86%E6%9C%A8%E3%82%92%E7%94%9F%E6%88%90%E3%81%99%E3%82%8B%E9%96%A2%E6%95%B0%E3%82%92%E5%88%A9%E7%94%A8%E3%81%99%E3%82%8B%0A%20%20%20%20root%20%3D%20list_to_tree%28arr%3D%5B1%2C%202%2C%203%2C%204%2C%205%2C%206%2C%207%5D%29%0A%0A%20%20%20%20%23%20%E3%83%AC%E3%83%99%E3%83%AB%E9%A0%86%E8%B5%B0%E6%9F%BB%0A%20%20%20%20res%20%3D%20level_order%28root%29%0A%20%20%20%20print%28%22%5Cn%E3%83%AC%E3%83%99%E3%83%AB%E9%A0%86%E8%B5%B0%E6%9F%BB%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E5%87%BA%E5%8A%9B%E3%82%B7%E3%83%BC%E3%82%B1%E3%83%B3%E3%82%B9%20%3D%20%22%2C%20res%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=127&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=from%20collections%20import%20deque%0A%0Aclass%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E5%80%A4%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%23%20%E5%8F%B3%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%0Adef%20list_to_tree_dfs%28arr%3A%20list%5Bint%5D%2C%20i%3A%20int%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E4%BA%8C%E5%88%86%E6%9C%A8%E3%81%AB%E3%83%87%E3%82%B7%E3%83%AA%E3%82%A2%E3%83%A9%E3%82%A4%E3%82%BA%E3%81%99%E3%82%8B%3A%20%E5%86%8D%E5%B8%B0%22%22%22%0A%20%20%20%20%23%20%E6%B7%BB%E5%AD%97%E3%81%8C%E9%85%8D%E5%88%97%E9%95%B7%E3%82%92%E8%B6%85%E3%81%88%E3%82%8B%E3%81%8B%E3%80%81%E5%AF%BE%E5%BF%9C%E3%81%99%E3%82%8B%E8%A6%81%E7%B4%A0%E3%81%8C%20None%20%E3%81%AA%E3%82%89%E3%80%81None%20%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20if%20i%20%3C%200%20or%20i%20%3E%3D%20len%28arr%29%20or%20arr%5Bi%5D%20is%20None%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%23%20%E7%8F%BE%E5%9C%A8%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20root%20%3D%20TreeNode%28arr%5Bi%5D%29%0A%20%20%20%20%23%20%E5%B7%A6%E5%8F%B3%E3%81%AE%E9%83%A8%E5%88%86%E6%9C%A8%E3%82%92%E5%86%8D%E5%B8%B0%E7%9A%84%E3%81%AB%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20root.left%20%3D%20list_to_tree_dfs%28arr%2C%202%20%2A%20i%20%2B%201%29%0A%20%20%20%20root.right%20%3D%20list_to_tree_dfs%28arr%2C%202%20%2A%20i%20%2B%202%29%0A%20%20%20%20return%20root%0A%0Adef%20list_to_tree%28arr%3A%20list%5Bint%5D%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E4%BA%8C%E5%88%86%E6%9C%A8%E3%81%AB%E3%83%87%E3%82%B7%E3%83%AA%E3%82%A2%E3%83%A9%E3%82%A4%E3%82%BA%E3%81%99%E3%82%8B%22%22%22%0A%20%20%20%20return%20list_to_tree_dfs%28arr%2C%200%29%0A%0A%0Adef%20level_order%28root%3A%20TreeNode%20%7C%20None%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%22%22%22%E3%83%AC%E3%83%99%E3%83%AB%E9%A0%86%E8%B5%B0%E6%9F%BB%22%22%22%0A%20%20%20%20%23%20%E3%82%AD%E3%83%A5%E3%83%BC%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%97%E3%80%81%E3%83%AB%E3%83%BC%E3%83%88%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E8%BF%BD%E5%8A%A0%E3%81%99%E3%82%8B%0A%20%20%20%20queue%3A%20deque%5BTreeNode%5D%20%3D%20deque%28%29%0A%20%20%20%20queue.append%28root%29%0A%20%20%20%20%23%20%E8%B5%B0%E6%9F%BB%E9%A0%86%E5%BA%8F%E3%82%92%E4%BF%9D%E5%AD%98%E3%81%99%E3%82%8B%E3%81%9F%E3%82%81%E3%81%AE%E3%83%AA%E3%82%B9%E3%83%88%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20res%20%3D%20%5B%5D%0A%20%20%20%20while%20queue%3A%0A%20%20%20%20%20%20%20%20node%3A%20TreeNode%20%3D%20queue.popleft%28%29%20%20%23%20%E3%83%87%E3%82%AD%E3%83%A5%E3%83%BC%0A%20%20%20%20%20%20%20%20res.append%28node.val%29%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E3%81%AE%E5%80%A4%E3%82%92%E4%BF%9D%E5%AD%98%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20if%20node.left%20is%20not%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20queue.append%28node.left%29%20%20%23%20%E5%B7%A6%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E3%82%AD%E3%83%A5%E3%83%BC%E3%81%AB%E8%BF%BD%E5%8A%A0%0A%20%20%20%20%20%20%20%20if%20node.right%20is%20not%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20queue.append%28node.right%29%20%20%23%20%E5%8F%B3%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E3%82%AD%E3%83%A5%E3%83%BC%E3%81%AB%E8%BF%BD%E5%8A%A0%0A%20%20%20%20return%20res%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E4%BA%8C%E5%88%86%E6%9C%A8%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%0A%20%20%20%20%23%20%E3%81%93%E3%81%93%E3%81%A7%E3%81%AF%E3%80%81%E9%85%8D%E5%88%97%E3%81%8B%E3%82%89%E7%9B%B4%E6%8E%A5%E4%BA%8C%E5%88%86%E6%9C%A8%E3%82%92%E7%94%9F%E6%88%90%E3%81%99%E3%82%8B%E9%96%A2%E6%95%B0%E3%82%92%E5%88%A9%E7%94%A8%E3%81%99%E3%82%8B%0A%20%20%20%20root%20%3D%20list_to_tree%28arr%3D%5B1%2C%202%2C%203%2C%204%2C%205%2C%206%2C%207%5D%29%0A%0A%20%20%20%20%23%20%E3%83%AC%E3%83%99%E3%83%AB%E9%A0%86%E8%B5%B0%E6%9F%BB%0A%20%20%20%20res%20%3D%20level_order%28root%29%0A%20%20%20%20print%28%22%5Cn%E3%83%AC%E3%83%99%E3%83%AB%E9%A0%86%E8%B5%B0%E6%9F%BB%E3%81%AE%E3%83%8E%E3%83%BC%E3%83%89%E5%87%BA%E5%8A%9B%E3%82%B7%E3%83%BC%E3%82%B1%E3%83%B3%E3%82%B9%20%3D%20%22%2C%20res%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=127&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
+<h3 id="2">2. &nbsp; 計算量<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
 <ul>
-<li><strong>時間計算量は<span class="arithmatex">\(O(n)\)</span></strong>: すべてのノードが一度ずつ訪問され、<span class="arithmatex">\(O(n)\)</span>の時間がかかります。ここで<span class="arithmatex">\(n\)</span>はノード数です。</li>
-<li><strong>空間計算量は<span class="arithmatex">\(O(n)\)</span></strong>: 最悪の場合、つまり完全二分木の場合、最下位レベルに走査する前に、キューは最大<span class="arithmatex">\((n + 1) / 2\)</span>個のノードを同時に含むことができ、<span class="arithmatex">\(O(n)\)</span>の空間を占有します。</li>
+<li><strong>時間計算量は <span class="arithmatex">\(O(n)\)</span></strong> ：すべてのノードを1回ずつ訪問するため、計算量は <span class="arithmatex">\(O(n)\)</span> です。ここで、<span class="arithmatex">\(n\)</span> はノード数です。</li>
+<li><strong>空間計算量は <span class="arithmatex">\(O(n)\)</span></strong> ：最悪の場合、すなわち完全二分木では、最下層に到達する前に、キュー内には最大で同時に <span class="arithmatex">\((n + 1) / 2\)</span> 個のノードが存在し、<span class="arithmatex">\(O(n)\)</span> の空間を使用します。</li>
 </ul>
-<h2 id="722">7.2.2 &nbsp; 前順、中順、後順走査<a class="headerlink" href="#722" title="Permanent link">&para;</a></h2>
-<p>対応して、前順、中順、後順走査はすべて<u>深度優先走査</u>に属し、<u>深度優先探索（DFS）</u>とも呼ばれ、「まず最後まで進み、その後バックトラックして続行する」走査方法を体現しています。</p>
-<p>下図は二分木に対して深度優先走査を実行する動作原理を示しています。<strong>深度優先走査は二分木全体を「歩き回る」ようなもので</strong>、各ノードで3つの位置に遭遇し、それらは前順、中順、後順走査に対応しています。</p>
-<p><img alt="二分探索木の前順、中順、後順走査" class="animation-figure" src="../binary_tree_traversal.assets/binary_tree_dfs.png" /></p>
-<p align="center"> 図 7-10 &nbsp; 二分探索木の前順、中順、後順走査 </p>
+<h2 id="722">7.2.2 &nbsp; 先行順・中間順・後行順走査<a class="headerlink" href="#722" title="Permanent link">&para;</a></h2>
+<p>同様に、先行順・中間順・後行順走査はいずれも<u>深度優先走査（depth-first traversal）</u>に属し、<u>深度優先探索（depth-first search, DFS）</u>とも呼ばれます。これは「まず行き止まりまで進み、その後で戻って続ける」という走査方法を表しています。</p>
+<p>次の図は、二分木に対して深度優先走査を行う仕組みを示しています。<strong>深度優先走査は、二分木全体の外周をぐるりと「一周する」ようなものです</strong>。各ノードでは3つの位置に出会い、それぞれが先行順走査・中間順走査・後行順走査に対応します。</p>
+<p><img alt="二分探索木の先行順・中間順・後行順走査" class="animation-figure" src="../binary_tree_traversal.assets/binary_tree_dfs.png" /></p>
+<p align="center"> 図 7-10 &nbsp; 二分探索木の先行順・中間順・後行順走査 </p>
 
-<h3 id="1_1">1. &nbsp; コード実装<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
-<p>深度優先探索は通常再帰に基づいて実装されます：</p>
+<h3 id="1_1">1. &nbsp; コードの実装<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
+<p>深度優先探索は通常、再帰に基づいて実装されます：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_tree_dfs.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">):</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;前順走査&quot;&quot;&quot;</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;先行順走査&quot;&quot;&quot;</span>
 <a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="k">if</span> <span class="n">root</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>        <span class="k">return</span>
-<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># 訪問順序: ルートノード -&gt; 左部分木 -&gt; 右部分木</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木</span>
 <a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>    <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
 <a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>    <span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">=</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
 <a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>    <span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">=</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
@@ -4609,7 +4801,7 @@
 <a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;中順走査&quot;&quot;&quot;</span>
 <a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>    <span class="k">if</span> <span class="n">root</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a>        <span class="k">return</span>
-<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>    <span class="c1"># 訪問順序: 左部分木 -&gt; ルートノード -&gt; 右部分木</span>
+<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>    <span class="c1"># 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木</span>
 <a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a>    <span class="n">in_order</span><span class="p">(</span><span class="n">root</span><span class="o">=</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
 <a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a>    <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
 <a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>    <span class="n">in_order</span><span class="p">(</span><span class="n">root</span><span class="o">=</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
@@ -4618,18 +4810,18 @@
 <a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;後順走査&quot;&quot;&quot;</span>
 <a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a>    <span class="k">if</span> <span class="n">root</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a>        <span class="k">return</span>
-<a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a>    <span class="c1"># 訪問順序: 左部分木 -&gt; 右部分木 -&gt; ルートノード</span>
+<a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a>    <span class="c1"># 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード</span>
 <a id="__codelineno-13-24" name="__codelineno-13-24" href="#__codelineno-13-24"></a>    <span class="n">post_order</span><span class="p">(</span><span class="n">root</span><span class="o">=</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
 <a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a>    <span class="n">post_order</span><span class="p">(</span><span class="n">root</span><span class="o">=</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
 <a id="__codelineno-13-26" name="__codelineno-13-26" href="#__codelineno-13-26"></a>    <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree_dfs.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 前順走査 */</span>
+<div class="highlight"><span class="filename">binary_tree_dfs.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 先行順走査 */</span>
 <a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
 <a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="c1">// 訪問優先度：ルートノード -&gt; 左部分木 -&gt; 右部分木</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="c1">// 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木</span>
 <a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="n">vec</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
 <a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">);</span>
 <a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
@@ -4639,7 +4831,7 @@
 <a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">inOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
 <a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">    </span><span class="c1">// 訪問優先度：左部分木 -&gt; ルートノード -&gt; 右部分木</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">    </span><span class="c1">// 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木</span>
 <a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">    </span><span class="n">inOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">);</span>
 <a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w">    </span><span class="n">vec</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
 <a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w">    </span><span class="n">inOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
@@ -4649,7 +4841,7 @@
 <a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a><span class="kt">void</span><span class="w"> </span><span class="nf">postOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
 <a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a><span class="w">    </span><span class="c1">// 訪問優先度：左部分木 -&gt; 右部分木 -&gt; ルートノード</span>
+<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a><span class="w">    </span><span class="c1">// 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード</span>
 <a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a><span class="w">    </span><span class="n">postOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">);</span>
 <a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a><span class="w">    </span><span class="n">postOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
 <a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a><span class="w">    </span><span class="n">vec</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
@@ -4657,11 +4849,11 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree_dfs.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 前順走査 */</span>
+<div class="highlight"><span class="filename">binary_tree_dfs.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 先行順走査 */</span>
 <a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
 <a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="c1">// 訪問優先度: 根ノード -&gt; 左部分木 -&gt; 右部分木</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="c1">// 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木</span>
 <a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="n">list</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
 <a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">);</span>
 <a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">);</span>
@@ -4671,7 +4863,7 @@
 <a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">inOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
 <a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="c1">// 訪問優先度: 左部分木 -&gt; 根ノード -&gt; 右部分木</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="c1">// 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木</span>
 <a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">    </span><span class="n">inOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">);</span>
 <a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">    </span><span class="n">list</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
 <a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">    </span><span class="n">inOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">);</span>
@@ -4681,7 +4873,7 @@
 <a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="kt">void</span><span class="w"> </span><span class="nf">postOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
 <a id="__codelineno-15-24" name="__codelineno-15-24" href="#__codelineno-15-24"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
-<a id="__codelineno-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></a><span class="w">    </span><span class="c1">// 訪問優先度: 左部分木 -&gt; 右部分木 -&gt; 根ノード</span>
+<a id="__codelineno-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></a><span class="w">    </span><span class="c1">// 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード</span>
 <a id="__codelineno-15-26" name="__codelineno-15-26" href="#__codelineno-15-26"></a><span class="w">    </span><span class="n">postOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">);</span>
 <a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></a><span class="w">    </span><span class="n">postOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">);</span>
 <a id="__codelineno-15-28" name="__codelineno-15-28" href="#__codelineno-15-28"></a><span class="w">    </span><span class="n">list</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
@@ -4689,100 +4881,367 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree_dfs.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_tree_dfs</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">PreOrder</span><span class="p">}</span>
-<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a>
-<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_tree_dfs</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">InOrder</span><span class="p">}</span>
-<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a>
-<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_tree_dfs</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">PostOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_tree_dfs.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 先行順走査 */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">PreOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="c1">// 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="n">list</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="o">!</span><span class="p">.</span><span class="n">Value</span><span class="p">);</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="n">PreOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">left</span><span class="p">);</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="n">PreOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="p">}</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="cm">/* 中順走査 */</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="k">void</span><span class="w"> </span><span class="nf">InOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">    </span><span class="c1">// 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">    </span><span class="n">InOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">left</span><span class="p">);</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">    </span><span class="n">list</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="o">!</span><span class="p">.</span><span class="n">Value</span><span class="p">);</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">    </span><span class="n">InOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="p">}</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="cm">/* 後順走査 */</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="k">void</span><span class="w"> </span><span class="nf">PostOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="w">    </span><span class="c1">// 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード</span>
+<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="w">    </span><span class="n">PostOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">left</span><span class="p">);</span>
+<a id="__codelineno-16-24" name="__codelineno-16-24" href="#__codelineno-16-24"></a><span class="w">    </span><span class="n">PostOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-16-25" name="__codelineno-16-25" href="#__codelineno-16-25"></a><span class="w">    </span><span class="n">list</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="o">!</span><span class="p">.</span><span class="n">Value</span><span class="p">);</span>
+<a id="__codelineno-16-26" name="__codelineno-16-26" href="#__codelineno-16-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree_dfs.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">preOrder</span><span class="p">}</span>
-<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a>
-<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">inOrder</span><span class="p">}</span>
-<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a>
-<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">postOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_tree_dfs.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 先行順走査 */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">    </span><span class="c1">// 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">    </span><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Val</span><span class="p">)</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">    </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span><span class="p">)</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">    </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="p">)</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="p">}</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="cm">/* 中順走査 */</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="kd">func</span><span class="w"> </span><span class="nx">inOrder</span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="w">    </span><span class="c1">// 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木</span>
+<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="w">    </span><span class="nx">inOrder</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span><span class="p">)</span>
+<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="w">    </span><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Val</span><span class="p">)</span>
+<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a><span class="w">    </span><span class="nx">inOrder</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="p">)</span>
+<a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></a><span class="p">}</span>
+<a id="__codelineno-17-22" name="__codelineno-17-22" href="#__codelineno-17-22"></a>
+<a id="__codelineno-17-23" name="__codelineno-17-23" href="#__codelineno-17-23"></a><span class="cm">/* 後順走査 */</span>
+<a id="__codelineno-17-24" name="__codelineno-17-24" href="#__codelineno-17-24"></a><span class="kd">func</span><span class="w"> </span><span class="nx">postOrder</span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-25" name="__codelineno-17-25" href="#__codelineno-17-25"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-26" name="__codelineno-17-26" href="#__codelineno-17-26"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-17-27" name="__codelineno-17-27" href="#__codelineno-17-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-28" name="__codelineno-17-28" href="#__codelineno-17-28"></a><span class="w">    </span><span class="c1">// 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード</span>
+<a id="__codelineno-17-29" name="__codelineno-17-29" href="#__codelineno-17-29"></a><span class="w">    </span><span class="nx">postOrder</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span><span class="p">)</span>
+<a id="__codelineno-17-30" name="__codelineno-17-30" href="#__codelineno-17-30"></a><span class="w">    </span><span class="nx">postOrder</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="p">)</span>
+<a id="__codelineno-17-31" name="__codelineno-17-31" href="#__codelineno-17-31"></a><span class="w">    </span><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Val</span><span class="p">)</span>
+<a id="__codelineno-17-32" name="__codelineno-17-32" href="#__codelineno-17-32"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree_dfs.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
-<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a>
-<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">inOrder</span><span class="p">}</span>
-<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a>
-<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">postOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_tree_dfs.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 先行順走査 */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="k">guard</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">root</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">    </span><span class="c1">// 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w">    </span><span class="n">list</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="kr">left</span><span class="p">)</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="kr">right</span><span class="p">)</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="p">}</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="cm">/* 中順走査 */</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="kd">func</span><span class="w"> </span><span class="nf">inOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="w">    </span><span class="k">guard</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">root</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="w">    </span><span class="c1">// 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木</span>
+<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="w">    </span><span class="n">inOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="kr">left</span><span class="p">)</span>
+<a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a><span class="w">    </span><span class="n">list</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a><span class="w">    </span><span class="n">inOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="kr">right</span><span class="p">)</span>
+<a id="__codelineno-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></a><span class="p">}</span>
+<a id="__codelineno-18-22" name="__codelineno-18-22" href="#__codelineno-18-22"></a>
+<a id="__codelineno-18-23" name="__codelineno-18-23" href="#__codelineno-18-23"></a><span class="cm">/* 後順走査 */</span>
+<a id="__codelineno-18-24" name="__codelineno-18-24" href="#__codelineno-18-24"></a><span class="kd">func</span><span class="w"> </span><span class="nf">postOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-25" name="__codelineno-18-25" href="#__codelineno-18-25"></a><span class="w">    </span><span class="k">guard</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">root</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-26" name="__codelineno-18-26" href="#__codelineno-18-26"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-18-27" name="__codelineno-18-27" href="#__codelineno-18-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-28" name="__codelineno-18-28" href="#__codelineno-18-28"></a><span class="w">    </span><span class="c1">// 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード</span>
+<a id="__codelineno-18-29" name="__codelineno-18-29" href="#__codelineno-18-29"></a><span class="w">    </span><span class="n">postOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="kr">left</span><span class="p">)</span>
+<a id="__codelineno-18-30" name="__codelineno-18-30" href="#__codelineno-18-30"></a><span class="w">    </span><span class="n">postOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="kr">right</span><span class="p">)</span>
+<a id="__codelineno-18-31" name="__codelineno-18-31" href="#__codelineno-18-31"></a><span class="w">    </span><span class="n">list</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-18-32" name="__codelineno-18-32" href="#__codelineno-18-32"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree_dfs.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">preOrder</span><span class="p">}</span>
-<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a>
-<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">inOrder</span><span class="p">}</span>
-<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a>
-<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">postOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_tree_dfs.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 先行順走査 */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="c1">// 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">    </span><span class="nx">list</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">    </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">left</span><span class="p">);</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">    </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">right</span><span class="p">);</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="p">}</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="cm">/* 中順走査 */</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="kd">function</span><span class="w"> </span><span class="nx">inOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w">    </span><span class="c1">// 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木</span>
+<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w">    </span><span class="nx">inOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">left</span><span class="p">);</span>
+<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w">    </span><span class="nx">list</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a><span class="w">    </span><span class="nx">inOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">right</span><span class="p">);</span>
+<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="p">}</span>
+<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a>
+<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a><span class="cm">/* 後順走査 */</span>
+<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a><span class="kd">function</span><span class="w"> </span><span class="nx">postOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-19-22" name="__codelineno-19-22" href="#__codelineno-19-22"></a><span class="w">    </span><span class="c1">// 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード</span>
+<a id="__codelineno-19-23" name="__codelineno-19-23" href="#__codelineno-19-23"></a><span class="w">    </span><span class="nx">postOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">left</span><span class="p">);</span>
+<a id="__codelineno-19-24" name="__codelineno-19-24" href="#__codelineno-19-24"></a><span class="w">    </span><span class="nx">postOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">right</span><span class="p">);</span>
+<a id="__codelineno-19-25" name="__codelineno-19-25" href="#__codelineno-19-25"></a><span class="w">    </span><span class="nx">list</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-19-26" name="__codelineno-19-26" href="#__codelineno-19-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree_dfs.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">preOrder</span><span class="p">}</span>
-<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a>
-<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">inOrder</span><span class="p">}</span>
-<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a>
-<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">postOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_tree_dfs.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 先行順走査 */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">    </span><span class="c1">// 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">    </span><span class="nx">list</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">    </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">left</span><span class="p">);</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">    </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">right</span><span class="p">);</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="p">}</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="cm">/* 中順走査 */</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="kd">function</span><span class="w"> </span><span class="nx">inOrder</span><span class="p">(</span><span class="nx">root</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-17" name="__codelineno-20-17" href="#__codelineno-20-17"></a><span class="w">    </span><span class="c1">// 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木</span>
+<a id="__codelineno-20-18" name="__codelineno-20-18" href="#__codelineno-20-18"></a><span class="w">    </span><span class="nx">inOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">left</span><span class="p">);</span>
+<a id="__codelineno-20-19" name="__codelineno-20-19" href="#__codelineno-20-19"></a><span class="w">    </span><span class="nx">list</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-20-20" name="__codelineno-20-20" href="#__codelineno-20-20"></a><span class="w">    </span><span class="nx">inOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">right</span><span class="p">);</span>
+<a id="__codelineno-20-21" name="__codelineno-20-21" href="#__codelineno-20-21"></a><span class="p">}</span>
+<a id="__codelineno-20-22" name="__codelineno-20-22" href="#__codelineno-20-22"></a>
+<a id="__codelineno-20-23" name="__codelineno-20-23" href="#__codelineno-20-23"></a><span class="cm">/* 後順走査 */</span>
+<a id="__codelineno-20-24" name="__codelineno-20-24" href="#__codelineno-20-24"></a><span class="kd">function</span><span class="w"> </span><span class="nx">postOrder</span><span class="p">(</span><span class="nx">root</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-25" name="__codelineno-20-25" href="#__codelineno-20-25"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-26" name="__codelineno-20-26" href="#__codelineno-20-26"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-20-27" name="__codelineno-20-27" href="#__codelineno-20-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-28" name="__codelineno-20-28" href="#__codelineno-20-28"></a><span class="w">    </span><span class="c1">// 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード</span>
+<a id="__codelineno-20-29" name="__codelineno-20-29" href="#__codelineno-20-29"></a><span class="w">    </span><span class="nx">postOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">left</span><span class="p">);</span>
+<a id="__codelineno-20-30" name="__codelineno-20-30" href="#__codelineno-20-30"></a><span class="w">    </span><span class="nx">postOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">right</span><span class="p">);</span>
+<a id="__codelineno-20-31" name="__codelineno-20-31" href="#__codelineno-20-31"></a><span class="w">    </span><span class="nx">list</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span>
+<a id="__codelineno-20-32" name="__codelineno-20-32" href="#__codelineno-20-32"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree_dfs.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
-<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a>
-<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">inOrder</span><span class="p">}</span>
-<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a>
-<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">postOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_tree_dfs.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 先行順走査 */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="c1">// 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">  </span><span class="n">list</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">  </span><span class="n">preOrder</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">);</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">  </span><span class="n">preOrder</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="p">}</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="cm">/* 中順走査 */</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="kt">void</span><span class="w"> </span><span class="n">inOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">  </span><span class="c1">// 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w">  </span><span class="n">inOrder</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">);</span>
+<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w">  </span><span class="n">list</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="w">  </span><span class="n">inOrder</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-21-17" name="__codelineno-21-17" href="#__codelineno-21-17"></a><span class="p">}</span>
+<a id="__codelineno-21-18" name="__codelineno-21-18" href="#__codelineno-21-18"></a>
+<a id="__codelineno-21-19" name="__codelineno-21-19" href="#__codelineno-21-19"></a><span class="cm">/* 後順走査 */</span>
+<a id="__codelineno-21-20" name="__codelineno-21-20" href="#__codelineno-21-20"></a><span class="kt">void</span><span class="w"> </span><span class="n">postOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-21" name="__codelineno-21-21" href="#__codelineno-21-21"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-21-22" name="__codelineno-21-22" href="#__codelineno-21-22"></a><span class="w">  </span><span class="c1">// 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード</span>
+<a id="__codelineno-21-23" name="__codelineno-21-23" href="#__codelineno-21-23"></a><span class="w">  </span><span class="n">postOrder</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">);</span>
+<a id="__codelineno-21-24" name="__codelineno-21-24" href="#__codelineno-21-24"></a><span class="w">  </span><span class="n">postOrder</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-21-25" name="__codelineno-21-25" href="#__codelineno-21-25"></a><span class="w">  </span><span class="n">list</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-21-26" name="__codelineno-21-26" href="#__codelineno-21-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree_dfs.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">pre_order</span><span class="p">}</span>
-<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a>
-<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">in_order</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_tree_dfs.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 先行順走査 */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">result</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span>
 <a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a>
-<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">post_order</span><span class="p">}</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">            </span><span class="c1">// 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">();</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w">            </span><span class="n">dfs</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">(),</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w">            </span><span class="n">dfs</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">(),</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">result</span><span class="p">);</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a>
+<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="w">    </span><span class="n">result</span>
+<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="p">}</span>
+<a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a>
+<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="cm">/* 中順走査 */</span>
+<a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a><span class="k">fn</span><span class="w"> </span><span class="nf">in_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-21" name="__codelineno-22-21" href="#__codelineno-22-21"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">result</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span>
+<a id="__codelineno-22-22" name="__codelineno-22-22" href="#__codelineno-22-22"></a>
+<a id="__codelineno-22-23" name="__codelineno-22-23" href="#__codelineno-22-23"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-24" name="__codelineno-22-24" href="#__codelineno-22-24"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-25" name="__codelineno-22-25" href="#__codelineno-22-25"></a><span class="w">            </span><span class="c1">// 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木</span>
+<a id="__codelineno-22-26" name="__codelineno-22-26" href="#__codelineno-22-26"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">();</span>
+<a id="__codelineno-22-27" name="__codelineno-22-27" href="#__codelineno-22-27"></a><span class="w">            </span><span class="n">dfs</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">(),</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-22-28" name="__codelineno-22-28" href="#__codelineno-22-28"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-22-29" name="__codelineno-22-29" href="#__codelineno-22-29"></a><span class="w">            </span><span class="n">dfs</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">(),</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-22-30" name="__codelineno-22-30" href="#__codelineno-22-30"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-31" name="__codelineno-22-31" href="#__codelineno-22-31"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-32" name="__codelineno-22-32" href="#__codelineno-22-32"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">result</span><span class="p">);</span>
+<a id="__codelineno-22-33" name="__codelineno-22-33" href="#__codelineno-22-33"></a>
+<a id="__codelineno-22-34" name="__codelineno-22-34" href="#__codelineno-22-34"></a><span class="w">    </span><span class="n">result</span>
+<a id="__codelineno-22-35" name="__codelineno-22-35" href="#__codelineno-22-35"></a><span class="p">}</span>
+<a id="__codelineno-22-36" name="__codelineno-22-36" href="#__codelineno-22-36"></a>
+<a id="__codelineno-22-37" name="__codelineno-22-37" href="#__codelineno-22-37"></a><span class="cm">/* 後順走査 */</span>
+<a id="__codelineno-22-38" name="__codelineno-22-38" href="#__codelineno-22-38"></a><span class="k">fn</span><span class="w"> </span><span class="nf">post_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-39" name="__codelineno-22-39" href="#__codelineno-22-39"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">result</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span>
+<a id="__codelineno-22-40" name="__codelineno-22-40" href="#__codelineno-22-40"></a>
+<a id="__codelineno-22-41" name="__codelineno-22-41" href="#__codelineno-22-41"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-42" name="__codelineno-22-42" href="#__codelineno-22-42"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-43" name="__codelineno-22-43" href="#__codelineno-22-43"></a><span class="w">            </span><span class="c1">// 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード</span>
+<a id="__codelineno-22-44" name="__codelineno-22-44" href="#__codelineno-22-44"></a><span class="w">            </span><span class="kd">let</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">();</span>
+<a id="__codelineno-22-45" name="__codelineno-22-45" href="#__codelineno-22-45"></a><span class="w">            </span><span class="n">dfs</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">(),</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-22-46" name="__codelineno-22-46" href="#__codelineno-22-46"></a><span class="w">            </span><span class="n">dfs</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">(),</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-22-47" name="__codelineno-22-47" href="#__codelineno-22-47"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-22-48" name="__codelineno-22-48" href="#__codelineno-22-48"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-22-49" name="__codelineno-22-49" href="#__codelineno-22-49"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-50" name="__codelineno-22-50" href="#__codelineno-22-50"></a>
+<a id="__codelineno-22-51" name="__codelineno-22-51" href="#__codelineno-22-51"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">result</span><span class="p">);</span>
+<a id="__codelineno-22-52" name="__codelineno-22-52" href="#__codelineno-22-52"></a>
+<a id="__codelineno-22-53" name="__codelineno-22-53" href="#__codelineno-22-53"></a><span class="w">    </span><span class="n">result</span>
+<a id="__codelineno-22-54" name="__codelineno-22-54" href="#__codelineno-22-54"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree_dfs.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
-<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a>
-<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">inOrder</span><span class="p">}</span>
-<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a>
-<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">postOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_tree_dfs.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 先行順走査 */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">    </span><span class="c1">// 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w">    </span><span class="n">arr</span><span class="p">[(</span><span class="o">*</span><span class="n">size</span><span class="p">)</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">);</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">);</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="p">}</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="cm">/* 中順走査 */</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">inOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="w">    </span><span class="c1">// 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木</span>
+<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="w">    </span><span class="n">inOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">);</span>
+<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="w">    </span><span class="n">arr</span><span class="p">[(</span><span class="o">*</span><span class="n">size</span><span class="p">)</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="w">    </span><span class="n">inOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">);</span>
+<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="p">}</span>
+<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a>
+<a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a><span class="cm">/* 後順走査 */</span>
+<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a><span class="kt">void</span><span class="w"> </span><span class="nf">postOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-23" name="__codelineno-23-23" href="#__codelineno-23-23"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span>
+<a id="__codelineno-23-24" name="__codelineno-23-24" href="#__codelineno-23-24"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-23-25" name="__codelineno-23-25" href="#__codelineno-23-25"></a><span class="w">    </span><span class="c1">// 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード</span>
+<a id="__codelineno-23-26" name="__codelineno-23-26" href="#__codelineno-23-26"></a><span class="w">    </span><span class="n">postOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">);</span>
+<a id="__codelineno-23-27" name="__codelineno-23-27" href="#__codelineno-23-27"></a><span class="w">    </span><span class="n">postOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">);</span>
+<a id="__codelineno-23-28" name="__codelineno-23-28" href="#__codelineno-23-28"></a><span class="w">    </span><span class="n">arr</span><span class="p">[(</span><span class="o">*</span><span class="n">size</span><span class="p">)</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-23-29" name="__codelineno-23-29" href="#__codelineno-23-29"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree_dfs.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">preOrder</span><span class="p">}</span>
-<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a>
-<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">inOrder</span><span class="p">}</span>
-<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a>
-<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">postOrder</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_tree_dfs.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 先行順走査 */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">    </span><span class="c1">// 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">    </span><span class="n">list</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">_val</span><span class="p">)</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">)</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">)</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="p">}</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="cm">/* 中順走査 */</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">inOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w">    </span><span class="c1">// 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木</span>
+<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w">    </span><span class="n">inOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">)</span>
+<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="w">    </span><span class="n">list</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">_val</span><span class="p">)</span>
+<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="w">    </span><span class="n">inOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">)</span>
+<a id="__codelineno-24-17" name="__codelineno-24-17" href="#__codelineno-24-17"></a><span class="p">}</span>
+<a id="__codelineno-24-18" name="__codelineno-24-18" href="#__codelineno-24-18"></a>
+<a id="__codelineno-24-19" name="__codelineno-24-19" href="#__codelineno-24-19"></a><span class="cm">/* 後順走査 */</span>
+<a id="__codelineno-24-20" name="__codelineno-24-20" href="#__codelineno-24-20"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">postOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-21" name="__codelineno-24-21" href="#__codelineno-24-21"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span>
+<a id="__codelineno-24-22" name="__codelineno-24-22" href="#__codelineno-24-22"></a><span class="w">    </span><span class="c1">// 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード</span>
+<a id="__codelineno-24-23" name="__codelineno-24-23" href="#__codelineno-24-23"></a><span class="w">    </span><span class="n">postOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">)</span>
+<a id="__codelineno-24-24" name="__codelineno-24-24" href="#__codelineno-24-24"></a><span class="w">    </span><span class="n">postOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">)</span>
+<a id="__codelineno-24-25" name="__codelineno-24-25" href="#__codelineno-24-25"></a><span class="w">    </span><span class="n">list</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">_val</span><span class="p">)</span>
+<a id="__codelineno-24-26" name="__codelineno-24-26" href="#__codelineno-24-26"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">binary_tree_dfs.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">pre_order</span><span class="p">}</span>
-<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a>
-<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">in_order</span><span class="p">}</span>
+<div class="highlight"><span class="filename">binary_tree_dfs.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### 前順走査 ###</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">nil?</span>
 <a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a>
-<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">post_order</span><span class="p">}</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">  </span><span class="c1"># 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">  </span><span class="vg">$res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">  </span><span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w">  </span><span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="k">end</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="c1">### 中順走査 ###</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="k">def</span><span class="w"> </span><span class="nf">in_order</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a>
+<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w">  </span><span class="c1"># 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木</span>
+<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w">  </span><span class="n">in_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
+<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="w">  </span><span class="vg">$res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a><span class="w">  </span><span class="n">in_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="k">end</span>
+<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a>
+<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="c1">### 後順走査 ###</span>
+<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a><span class="k">def</span><span class="w"> </span><span class="nf">post_order</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
+<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">nil?</span>
+<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a>
+<a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a><span class="w">  </span><span class="c1"># 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード</span>
+<a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></a><span class="w">  </span><span class="n">post_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
+<a id="__codelineno-25-27" name="__codelineno-25-27" href="#__codelineno-25-27"></a><span class="w">  </span><span class="n">post_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-25-28" name="__codelineno-25-28" href="#__codelineno-25-28"></a><span class="w">  </span><span class="vg">$res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-25-29" name="__codelineno-25-29" href="#__codelineno-25-29"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 </div>
 </div>
+<details class="pythontutor">
+<summary>コードの可視化</summary>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" 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target="_blank" rel="noopener noreferrer">全画面で見る &gt;</a></div></p>
+</details>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>深度優先探索は反復に基づいても実装できます。興味のある読者は自分で学習してください。</p>
+<p>深度優先探索は反復によって実装することもできます。興味のある読者は自身で調べてみてください。</p>
 </div>
-<p>下図は二分木の前順走査の再帰プロセスを示しており、これは「再帰」と「復帰」という2つの反対の部分に分けることができます。</p>
+<p>次の図は、二分木の先行順走査における再帰の過程を示しており、「行き」と「帰り」という2つの逆向きの部分に分けられます。</p>
 <ol>
-<li>「再帰」は新しいメソッドを開始することを意味し、プログラムはこのプロセスで次のノードにアクセスします。</li>
-<li>「復帰」は関数が戻ることを意味し、現在のノードが完全にアクセスされたことを示します。</li>
+<li>「行き」は新しいメソッドの開始を表し、この過程でプログラムは次のノードにアクセスします。</li>
+<li>「帰り」は関数の復帰を表し、現在のノードへのアクセスが完了したことを意味します。</li>
 </ol>
 <div class="tabbed-set tabbed-alternate" data-tabs="3:11"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">&lt;1&gt;</label><label for="__tabbed_3_2">&lt;2&gt;</label><label for="__tabbed_3_3">&lt;3&gt;</label><label for="__tabbed_3_4">&lt;4&gt;</label><label for="__tabbed_3_5">&lt;5&gt;</label><label for="__tabbed_3_6">&lt;6&gt;</label><label for="__tabbed_3_7">&lt;7&gt;</label><label for="__tabbed_3_8">&lt;8&gt;</label><label for="__tabbed_3_9">&lt;9&gt;</label><label for="__tabbed_3_10">&lt;10&gt;</label><label for="__tabbed_3_11">&lt;11&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<p><img alt="前順走査の再帰プロセス" class="animation-figure" src="../binary_tree_traversal.assets/preorder_step1.png" /></p>
+<p><img alt="先行順走査の再帰過程" class="animation-figure" src="../binary_tree_traversal.assets/preorder_step1.png" /></p>
 </div>
 <div class="tabbed-block">
 <p><img alt="preorder_step2" class="animation-figure" src="../binary_tree_traversal.assets/preorder_step2.png" /></p>
@@ -4816,12 +5275,12 @@
 </div>
 </div>
 </div>
-<p align="center"> 図 7-11 &nbsp; 前順走査の再帰プロセス </p>
+<p align="center"> 図 7-11 &nbsp; 先行順走査の再帰過程 </p>
 
-<h3 id="2_1">2. &nbsp; 計算量分析<a class="headerlink" href="#2_1" title="Permanent link">&para;</a></h3>
+<h3 id="2_1">2. &nbsp; 計算量<a class="headerlink" href="#2_1" title="Permanent link">&para;</a></h3>
 <ul>
-<li><strong>時間計算量は<span class="arithmatex">\(O(n)\)</span></strong>: すべてのノードが一度ずつ訪問され、<span class="arithmatex">\(O(n)\)</span>の時間を使用します。</li>
-<li><strong>空間計算量は<span class="arithmatex">\(O(n)\)</span></strong>: 最悪の場合、つまり木が連結リストに退化した場合、再帰の深さは<span class="arithmatex">\(n\)</span>に達し、システムは<span class="arithmatex">\(O(n)\)</span>のスタックフレーム空間を占有します。</li>
+<li><strong>時間計算量は <span class="arithmatex">\(O(n)\)</span></strong> ：すべてのノードを1回ずつ訪問するため、計算量は <span class="arithmatex">\(O(n)\)</span> です。</li>
+<li><strong>空間計算量は <span class="arithmatex">\(O(n)\)</span></strong> ：最悪の場合、すなわち木が連結リストに退化したとき、再帰の深さは <span class="arithmatex">\(n\)</span> に達し、システムは <span class="arithmatex">\(O(n)\)</span> のスタックフレーム空間を使用します。</li>
 </ul>
 
 <!-- Source file information -->
diff --git a/ja/chapter_tree/index.html b/ja/chapter_tree/index.html
index 64a508cf5..6f81c03dd 100644
--- a/ja/chapter_tree/index.html
+++ b/ja/chapter_tree/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
         <path
             d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
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+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
@@ -358,7 +358,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1635,7 +1635,7 @@
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-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
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   <span class="md-ellipsis">
     
   
-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2107,7 +2107,7 @@
   <span class="md-ellipsis">
     
   
-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2493,7 +2493,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
@@ -2549,7 +2549,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 &nbsp; ハッシュ最適化戦略
+    10.4 &nbsp; ハッシュによる最適化戦略
   
 
     
@@ -2577,7 +2577,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 &nbsp; 探索アルゴリズムの再認識
+    10.5 &nbsp; 探索アルゴリズム再考
   
 
     
@@ -3115,7 +3115,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 &nbsp; 分割統治アルゴリズム
+    12.1 &nbsp; 分割統治法
   
 
     
@@ -3171,7 +3171,7 @@
   <span class="md-ellipsis">
     
   
-    12.3 &nbsp; 木の構築問題
+    12.3 &nbsp; 二分木の構築問題
   
 
     
@@ -3199,7 +3199,7 @@
   <span class="md-ellipsis">
     
   
-    12.4 &nbsp; ハノイの塔問題
+    12.4 &nbsp; ハノイの塔の問題
   
 
     
@@ -3392,7 +3392,7 @@
   <span class="md-ellipsis">
     
   
-    13.3 &nbsp; 部分集合和問題
+    13.3 &nbsp; 部分和問題
   
 
     
@@ -3420,7 +3420,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 &nbsp; Nクイーン問題
+    13.4 &nbsp; n クイーン問題
   
 
     
@@ -3561,7 +3561,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 &nbsp; 動的計画法の初歩
+    14.1 &nbsp; 動的計画法入門
   
 
     
@@ -3589,7 +3589,7 @@
   <span class="md-ellipsis">
     
   
-    14.2 &nbsp; DP 問題の特性
+    14.2 &nbsp; 動的計画法の問題特性
   
 
     
@@ -3617,7 +3617,7 @@
   <span class="md-ellipsis">
     
   
-    14.3 &nbsp; DP の解法の考え方
+    14.3 &nbsp; 動的計画法の問題解決の考え方
   
 
     
@@ -3645,7 +3645,7 @@
   <span class="md-ellipsis">
     
   
-    14.4 &nbsp; 0-1ナップサック問題
+    14.4 &nbsp; 0-1 ナップサック問題
   
 
     
@@ -3838,7 +3838,7 @@
   <span class="md-ellipsis">
     
   
-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4083,7 +4083,7 @@
   <span class="md-ellipsis">
     
   
-    16.2 &nbsp; 一緒に創作に参加する
+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4277,8 +4277,8 @@
 <p><img alt="木" class="cover-image" src="../assets/covers/chapter_tree.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>そびえ立つ木は活力に満ちた本質を放ち、深い根と豊かな葉を誇りながらも、その枝は疎らに散らばり、幽玄な雰囲気を醸し出しています。</p>
-<p>それはデータにおける分割統治の鮮やかな形を私たちに示しています。</p>
+<p>大樹は生命力に満ち、根は深く葉は生い茂り、枝は豊かに広がる。</p>
+<p>それはデータ分割統治の生き生きとした姿を私たちに示してくれる。</p>
 </div>
 <h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
@@ -4286,7 +4286,7 @@
 <li><a href="binary_tree_traversal/">7.2 &nbsp; 二分木の走査</a></li>
 <li><a href="array_representation_of_tree/">7.3 &nbsp; 二分木の配列表現</a></li>
 <li><a href="binary_search_tree/">7.4 &nbsp; 二分探索木</a></li>
-<li><a href="avl_tree/">7.5 &nbsp; AVL木 *</a></li>
+<li><a href="avl_tree/">7.5 &nbsp; AVL 木 *</a></li>
 <li><a href="summary/">7.6 &nbsp; まとめ</a></li>
 </ul>
 
diff --git a/ja/chapter_tree/summary/index.html b/ja/chapter_tree/summary/index.html
index 916bdd6d6..670d32e1b 100644
--- a/ja/chapter_tree/summary/index.html
+++ b/ja/chapter_tree/summary/index.html
@@ -6,7 +6,7 @@
       <meta charset="utf-8">
       <meta name="viewport" content="width=device-width,initial-scale=1">
       
-        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
+        <meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
       
       
         <meta name="author" content="krahets">
@@ -117,7 +117,7 @@
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-    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+    <span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
 </div>
 
           </div>
@@ -341,7 +341,7 @@
   <span class="md-ellipsis">
     
   
-    序
+    はじめに
   
 
     
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-    序
+    はじめに
   
 
           </label>
@@ -618,7 +618,7 @@
   <span class="md-ellipsis">
     
   
-    1.1 &nbsp; アルゴリズムはどこにでもある
+    1.1 &nbsp; アルゴリズムは至るところにある
   
 
     
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 &nbsp; アルゴリズムとは何か
+    1.2 &nbsp; アルゴリズムとは
   
 
     
@@ -783,7 +783,7 @@
   <span class="md-ellipsis">
     
   
-    2.1 &nbsp; アルゴリズムの効率評価
+    2.1 &nbsp; アルゴリズム効率の評価
   
 
     
@@ -1060,7 +1060,7 @@
   <span class="md-ellipsis">
     
   
-    3.3 &nbsp; 数値の符号化 *
+    3.3 &nbsp; 数値エンコーディング *
   
 
     
@@ -1088,7 +1088,7 @@
   <span class="md-ellipsis">
     
   
-    3.4 &nbsp; 文字の符号化 *
+    3.4 &nbsp; 文字エンコーディング *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    第 6 章 &nbsp; ハッシュ表
+    第 6 章 &nbsp; ハッシュテーブル
   
 
           </label>
@@ -1635,7 +1635,7 @@
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-    6.1 &nbsp; ハッシュ表
+    6.1 &nbsp; ハッシュテーブル
   
 
     
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-    7.5 &nbsp; AVL木 *
+    7.5 &nbsp; AVL 木 *
   
 
     
@@ -2029,7 +2029,7 @@
   <a href="#1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; 重要なポイント
+        1. &nbsp; 要点の振り返り
       
     </span>
   </a>
@@ -2177,7 +2177,7 @@
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-    8.2 &nbsp; ヒープ構築操作
+    8.2 &nbsp; ヒープ構築
   
 
     
@@ -2563,7 +2563,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 &nbsp; 二分探索の挿入点
+    10.2 &nbsp; 二分探索の挿入位置
   
 
     
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-    14.4 &nbsp; 0-1ナップサック問題
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-    15.1 &nbsp; 貪欲アルゴリズム
+    15.1 &nbsp; 貪欲法
   
 
     
@@ -4153,7 +4153,7 @@
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+    16.2 &nbsp; 一緒に制作に参加しましょう
   
 
     
@@ -4299,7 +4299,7 @@
   <a href="#1" class="md-nav__link">
     <span class="md-ellipsis">
       
-        1. &nbsp; 重要なポイント
+        1. &nbsp; 要点の振り返り
       
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 <!-- Page content -->
 <h1 id="76">7.6 &nbsp; まとめ<a class="headerlink" href="#76" title="Permanent link">&para;</a></h1>
-<h3 id="1">1. &nbsp; 重要なポイント<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<h3 id="1">1. &nbsp; 要点の振り返り<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
-<li>二分木は非線形データ構造で、「一つを二つに分ける」分割統治のロジックを反映しています。各二分木ノードには値と2つのポインタが含まれ、それぞれ左と右の子ノードを指します。</li>
-<li>二分木のノードについて、その左（右）子ノードとその下に形成される木は、まとめてそのノードの左（右）部分木と呼ばれます。</li>
-<li>二分木に関連する用語には、根ノード、葉ノード、レベル、次数、エッジ、高さ、深さがあります。</li>
-<li>二分木の初期化、ノードの挿入、ノードの削除の操作は、連結リストの操作と似ています。</li>
-<li>一般的な二分木の種類には、完全二分木、完備二分木、満二分木、平衡二分木があります。完全二分木は理想的な状態を表し、連結リストは退化後の最悪の状態です。</li>
-<li>二分木は、ノード値と空きスロットをレベル順走査シーケンスで配置し、親ノードと子ノード間のインデックスマッピング関係に基づいてポインタを実装することで、配列を使用して表現できます。</li>
-<li>二分木のレベル順走査は幅優先探索手法で、「円を拡大しながら」の層ごとの走査方式を反映しています。通常はキューを使用して実装されます。</li>
-<li>前順、中順、後順走査はすべて深度優先探索手法で、「まず最後まで行き、その後バックトラックして続行する」走査方式を反映しています。通常は再帰を使用して実装されます。</li>
-<li>二分探索木は要素検索のための効率的なデータ構造で、検索、挿入、削除操作の時間計算量はすべて<span class="arithmatex">\(O(\log n)\)</span>です。二分探索木が連結リストに退化すると、これらの時間計算量は<span class="arithmatex">\(O(n)\)</span>に悪化します。</li>
-<li>AVL木は平衡二分探索木とも呼ばれ、回転操作を通して継続的なノード挿入と削除後も木が平衡を保つことを保証します。</li>
-<li>AVL木の回転操作には、右回転、左回転、右左回転、左右回転があります。ノードの挿入または削除後、AVL木はボトムアップ方式でこれらの回転を実行して自己平衡を取ります。</li>
+<li>二分木は非線形データ構造の一種であり、「二分する」分割統治の考え方を体現している。各二分木ノードは 1 つの値と 2 本のポインタを持ち、それぞれ左子ノードと右子ノードを指す。</li>
+<li>二分木のあるノードについて、その左（右）子ノードおよびその配下から構成される木を、そのノードの左（右）部分木と呼ぶ。</li>
+<li>二分木に関する用語には、根ノード、葉ノード、レベル、次数、辺、高さ、深さなどがある。</li>
+<li>二分木の初期化、ノードの挿入、ノードの削除は、連結リストの操作方法と似ている。</li>
+<li>一般的な二分木の種類には、perfect 二分木、complete 二分木、full 二分木、平衡二分木がある。perfect 二分木が最も理想的な状態であり、連結リストは退化後の最悪の状態である。</li>
+<li>二分木は配列で表現できる。方法としては、ノード値と空き位置をレベル順走査の順に並べ、親ノードと子ノードのインデックス対応関係に基づいてポインタを実現する。</li>
+<li>二分木のレベル順走査は幅優先探索の一種であり、「同心円状に外へ広がる」ような逐次的な走査方式を表しており、通常はキューによって実装される。</li>
+<li>前順、中順、後順走査はいずれも深さ優先探索に属し、「まず末端まで進み、その後バックトラックして続ける」という走査方式を体現しており、通常は再帰で実装される。</li>
+<li>二分探索木は効率的な要素探索データ構造であり、探索、挿入、削除の時間計算量はいずれも <span class="arithmatex">\(O(\log n)\)</span> である。二分探索木が連結リストへ退化すると、各操作の時間計算量は <span class="arithmatex">\(O(n)\)</span> まで悪化する。</li>
+<li>AVL 木は平衡二分探索木とも呼ばれ、回転操作によって、ノードの挿入と削除を繰り返した後も木が平衡を保つようにしている。</li>
+<li>AVL 木の回転操作には、右回転、左回転、右回転してから左回転、左回転してから右回転がある。ノードの挿入または削除の後、AVL 木は下から上へ回転操作を行い、木を再び平衡状態に戻す。</li>
 </ul>
 <h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
-<p><strong>Q</strong>: 一つのノードのみを持つ二分木について、木の高さと根ノードの深さの両方が<span class="arithmatex">\(0\)</span>ですか？</p>
-<p>はい、高さと深さは通常「通過したエッジの数」として定義されるためです。</p>
-<p><strong>Q</strong>: 二分木における挿入と削除は一般的に一連の操作によって達成されます。ここでの「一連の操作」とは何を指しますか？子ノードのリソースを解放することを意味しますか？</p>
-<p>二分探索木を例に取ると、ノードを削除する操作は3つの異なるシナリオで処理する必要があり、それぞれ複数ステップのノード操作が必要です。</p>
-<p><strong>Q</strong>: 二分木のDFS走査で前順、中順、後順の3つのシーケンスがあるのはなぜですか？その用途は何ですか？</p>
-<p>配列の順次および逆順走査と同様に、前順、中順、後順走査は二分木を走査する3つの方法であり、特定の順序で走査結果を取得できます。例えば、二分探索木では、ノードサイズが「左子ノード値 &lt; 根ノード値 &lt; 右子ノード値」を満たすため、「左 <span class="arithmatex">\(\rightarrow\)</span> 根 <span class="arithmatex">\(\rightarrow\)</span> 右」の優先順位で木を走査することで、順序付けられたノードシーケンスを取得できます。</p>
-<p><strong>Q</strong>: 不平衡ノード<code>node</code>、<code>child</code>、<code>grand_child</code>間の関係を処理する右回転操作において、右回転後に<code>node</code>とその親ノード間の接続と<code>node</code>の元のリンクが失われるのではありませんか？</p>
-<p>この問題を再帰的な観点から見る必要があります。<code>right_rotate(root)</code>操作は部分木の根ノードを渡し、最終的に<code>return child</code>で回転された部分木の根ノードを返します。部分木の根ノードとその親ノード間の接続は、この関数が戻った後に確立され、これは右回転操作の保守範囲外です。</p>
-<p><strong>Q</strong>: C++では、関数は<code>private</code>と<code>public</code>セクションに分かれています。これにはどのような考慮事項がありますか？なぜ<code>height()</code>関数と<code>updateHeight()</code>関数がそれぞれ<code>public</code>と<code>private</code>に配置されているのですか？</p>
-<p>これはメソッドの使用範囲によります。メソッドがクラス内でのみ使用される場合、<code>private</code>に設計されます。例えば、ユーザーが独自に<code>updateHeight()</code>を呼び出すことは意味がありません。これは挿入または削除操作の一ステップに過ぎないからです。しかし、<code>height()</code>はノードの高さにアクセスするためのもので、<code>vector.size()</code>と同様であるため、使用のために<code>public</code>に設定されています。</p>
-<p><strong>Q</strong>: 入力データのセットから二分探索木をどのように構築しますか？根ノードの選択は非常に重要ですか？</p>
-<p>はい、木を構築する方法は二分探索木コードの<code>build_tree()</code>メソッドで提供されています。根ノードの選択については、通常入力データをソートし、中央の要素を根ノードとして選択し、再帰的に左と右の部分木を構築します。このアプローチは木の平衡を最大化します。</p>
-<p><strong>Q</strong>: Javaでは、文字列比較に常に<code>equals()</code>メソッドを使用する必要がありますか？</p>
-<p>Javaでは、プリミティブデータ型の場合、<code>==</code>は2つの変数の値が等しいかどうかを比較するために使用されます。参照型の場合、2つのシンボルの動作原理は異なります。</p>
+<p><strong>Q</strong>：ノードが 1 つしかない二分木では、木の高さと根ノードの深さはどちらも <span class="arithmatex">\(0\)</span> ですか？</p>
+<p>はい。高さと深さは通常「通過した辺の本数」として定義されるからです。</p>
+<p><strong>Q</strong>：二分木における挿入と削除は通常一連の操作を組み合わせて完了しますが、ここでいう「一連の操作」とは何を指すのでしょうか？リソースの子ノードに対するリソース解放と理解できますか？</p>
+<p>二分探索木を例にすると、ノード削除は 3 つのケースに分けて処理する必要があり、各ケースで複数段階のノード操作が必要になります。</p>
+<p><strong>Q</strong>：なぜ DFS による二分木走査には前順・中順・後順の 3 種類があり、それぞれどのような用途があるのですか？</p>
+<p>配列の順方向走査と逆方向走査に似て、前順・中順・後順走査は二分木の 3 つの走査方法であり、特定の順序で走査結果を得るために使えます。たとえば二分探索木では、ノードの大小関係が <code>左子ノードの値 &lt; 根ノードの値 &lt; 右子ノードの値</code> を満たすため、「左 <span class="arithmatex">\(\rightarrow\)</span> 根 <span class="arithmatex">\(\rightarrow\)</span> 右」の優先順で木を走査すれば、整列済みのノード列を得られます。</p>
+<p><strong>Q</strong>：右回転操作は不平衡ノード <code>node</code>、<code>child</code>、<code>grand_child</code> の関係を処理するものですが、<code>node</code> の親ノードと <code>node</code> の元の接続は維持しなくてよいのですか？右回転後に切れてしまいませんか？</p>
+<p>この問題は再帰の視点から考える必要があります。右回転操作 <code>right_rotate(root)</code> に渡されるのは部分木の根ノードであり、最終的に <code>return child</code> によって回転後の部分木の根ノードを返します。部分木の根ノードとその親ノードの接続は、この関数の返却後に行われるため、右回転操作自身が管理する範囲には含まれません。</p>
+<p><strong>Q</strong>：C++ では関数を <code>private</code> と <code>public</code> に分けますが、この設計にはどのような考えがありますか？なぜ <code>height()</code> 関数と <code>updateHeight()</code> 関数をそれぞれ <code>public</code> と <code>private</code> に置くのですか？</p>
+<p>主に、そのメソッドの利用範囲を見て決めます。メソッドがクラス内部でしか使われないなら、<code>private</code> に設計します。たとえば、利用者が <code>updateHeight()</code> を単独で呼び出しても意味はなく、これは挿入や削除の途中の 1 ステップにすぎません。一方で <code>height()</code> はノードの高さにアクセスするためのもので、<code>vector.size()</code> に似た役割を持つため、使いやすいように <code>public</code> に設定します。</p>
+<p><strong>Q</strong>：入力データの集合から二分探索木をどのように構築しますか？根ノードの選び方は重要ですか？</p>
+<p>はい。木の構築方法は、二分探索木のコード中の <code>build_tree()</code> メソッドですでに示されています。根ノードの選択については、通常は入力データをソートし、その中央の要素を根ノードにしてから、左右の部分木を再帰的に構築します。こうすることで、木の平衡性を最大限に保てます。</p>
+<p><strong>Q</strong>：Java では、文字列比較には必ず <code>equals()</code> メソッドを使うべきですか？</p>
+<p>Java では、基本データ型については <code>==</code> を使って 2 つの変数の値が等しいかどうかを比較します。参照型については、この 2 つの記法の働き方は異なります。</p>
 <ul>
-<li><code>==</code>: 2つの変数が同じオブジェクトを指しているかどうか、つまりメモリ内の位置が同じかどうかを比較するために使用されます。</li>
-<li><code>equals()</code>: 2つのオブジェクトの値が等しいかどうかを比較するために使用されます。</li>
+<li><code>==</code> ：2 つの変数が同じオブジェクトを指しているか、つまりメモリ上の位置が同じかどうかを比較するために使います。</li>
+<li><code>equals()</code>：2 つのオブジェクトの値が等しいかどうかを比較するために使います。</li>
 </ul>
-<p>したがって、値を比較するには<code>equals()</code>を使用すべきです。ただし、<code>String a = "hi"; String b = "hi";</code>で初期化された文字列は文字列定数プールに格納され、同じオブジェクトを指すため、<code>a == b</code>も2つの文字列の内容を比較するために使用できます。</p>
-<p><strong>Q</strong>: 最下位レベルに到達する前に、幅優先走査でキュー内のノード数は<span class="arithmatex">\(2^h\)</span>ですか？</p>
-<p>はい、例えば高さ<span class="arithmatex">\(h = 2\)</span>の満二分木は合計<span class="arithmatex">\(n = 7\)</span>個のノードを持ち、最下位レベルには<span class="arithmatex">\(4 = 2^h = (n + 1) / 2\)</span>個のノードがあります。</p>
+<p>したがって、値を比較したい場合は <code>equals()</code> を使うべきです。ただし、<code>String a = "hi"; String b = "hi";</code> によって初期化された文字列は文字列定数プールに格納され、同じオブジェクトを指すため、<code>a == b</code> でも 2 つの文字列の内容を比較できます。</p>
+<p><strong>Q</strong>：幅優先走査で最下層に到達する前、キュー内のノード数は <span class="arithmatex">\(2^h\)</span> ですか？</p>
+<p>はい。たとえば高さ <span class="arithmatex">\(h = 2\)</span> の充足二分木では、ノード総数は <span class="arithmatex">\(n = 7\)</span> であり、最下層のノード数は <span class="arithmatex">\(4 = 2^h = (n + 1) / 2\)</span> です。</p>
 
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+    <meta content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書" name="description"/>
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                             <a class="md-nav__link" href="./chapter_searching/replace_linear_by_hashing/">
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-                                10.4   ハッシュ最適化戦略
+                                10.4   ハッシュによる最適化戦略
                               </span>
                             </a>
                           </li>
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_searching/searching_algorithm_revisited/">
                               <span class="md-ellipsis">
-                                10.5   探索アルゴリズムの再認識
+                                10.5   探索アルゴリズム再考
                               </span>
                             </a>
                           </li>
@@ -1461,7 +1461,7 @@
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_divide_and_conquer/divide_and_conquer/">
                               <span class="md-ellipsis">
-                                12.1   分割統治アルゴリズム
+                                12.1   分割統治法
                               </span>
                             </a>
                           </li>
@@ -1475,14 +1475,14 @@
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_divide_and_conquer/build_binary_tree_problem/">
                               <span class="md-ellipsis">
-                                12.3   木の構築問題
+                                12.3   二分木の構築問題
                               </span>
                             </a>
                           </li>
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_divide_and_conquer/hanota_problem/">
                               <span class="md-ellipsis">
-                                12.4   ハノイの塔問題
+                                12.4   ハノイの塔の問題
                               </span>
                             </a>
                           </li>
@@ -1537,14 +1537,14 @@
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_backtracking/subset_sum_problem/">
                               <span class="md-ellipsis">
-                                13.3   部分集合和問題
+                                13.3   部分和問題
                               </span>
                             </a>
                           </li>
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_backtracking/n_queens_problem/">
                               <span class="md-ellipsis">
-                                13.4   Nクイーン問題
+                                13.4   n クイーン問題
                               </span>
                             </a>
                           </li>
@@ -1585,28 +1585,28 @@
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_dynamic_programming/intro_to_dynamic_programming/">
                               <span class="md-ellipsis">
-                                14.1   動的計画法の初歩
+                                14.1   動的計画法入門
                               </span>
                             </a>
                           </li>
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_dynamic_programming/dp_problem_features/">
                               <span class="md-ellipsis">
-                                14.2   DP 問題の特性
+                                14.2   動的計画法の問題特性
                               </span>
                             </a>
                           </li>
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_dynamic_programming/dp_solution_pipeline/">
                               <span class="md-ellipsis">
-                                14.3   DP の解法の考え方
+                                14.3   動的計画法の問題解決の考え方
                               </span>
                             </a>
                           </li>
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_dynamic_programming/knapsack_problem/">
                               <span class="md-ellipsis">
-                                14.4   0-1ナップサック問題
+                                14.4   0-1 ナップサック問題
                               </span>
                             </a>
                           </li>
@@ -1661,7 +1661,7 @@
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_greedy/greedy_algorithm/">
                               <span class="md-ellipsis">
-                                15.1   貪欲アルゴリズム
+                                15.1   貪欲法
                               </span>
                             </a>
                           </li>
@@ -1730,7 +1730,7 @@
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_appendix/contribution/">
                               <span class="md-ellipsis">
-                                16.2   一緒に創作に参加する
+                                16.2   一緒に制作に参加しましょう
                               </span>
                             </a>
                           </li>
diff --git a/ja/javascripts/katex.js b/ja/javascripts/katex.js
index 9c3d34a8e..a2883ff16 100644
--- a/ja/javascripts/katex.js
+++ b/ja/javascripts/katex.js
@@ -8,4 +8,4 @@ document$.subscribe(({ body }) => {
     ],
   });
 });
-/*! update cache: 20260329054750 */
+/*! update cache: 20260330081613 */
diff --git a/ja/javascripts/mathjax.js b/ja/javascripts/mathjax.js
index 0bc404c9a..33b49f89f 100644
--- a/ja/javascripts/mathjax.js
+++ b/ja/javascripts/mathjax.js
@@ -15,4 +15,4 @@ window.MathJax = {
 document$.subscribe(() => {
   MathJax.typesetPromise();
 });
-/*! update cache: 20260329054750 */
+/*! update cache: 20260330081613 */
diff --git a/ja/javascripts/starfield.js b/ja/javascripts/starfield.js
index 9c89e82da..9c80a47d6 100644
--- a/ja/javascripts/starfield.js
+++ b/ja/javascripts/starfield.js
@@ -469,4 +469,4 @@
 
   return Starfield;
 });
-/*! update cache: 20260329054750 */
+/*! update cache: 20260330081613 */
diff --git a/ja/search.json b/ja/search.json
index 777308654..8a9462800 100644
--- a/ja/search.json
+++ b/ja/search.json
@@ -1 +1 @@
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付録","16.1 &nbsp; インストール"],"tags":[]},{"location":"chapter_appendix/installation/#2-cc","level":3,"title":"2.   C/C++環境","text":"<ol> <li>WindowsシステムではMinGWをインストールする必要があります（設定チュートリアル）。MacOSにはClangが付属しているため、インストールは不要です。</li> <li>VS Code拡張機能マーケットプレイスで<code>c++</code>を検索し、C/C++ Extension Packをインストールします。</li> <li>（オプション）設定ページを開き、<code>Clang_format_fallback Style</code>コードフォーマッティングオプションを検索し、<code>{ BasedOnStyle: Microsoft, BreakBeforeBraces: Attach }</code>に設定します。</li> </ol>","path":["第 16 章 &nbsp; 付録","16.1 &nbsp; インストール"],"tags":[]},{"location":"chapter_appendix/installation/#3-java","level":3,"title":"3.   Java環境","text":"<ol> <li>OpenJDKをダウンロードしてインストールします（バージョンはJDK 9より新しい必要があります）。</li> <li>VS Code拡張機能マーケットプレイスで<code>java</code>を検索し、Extension Pack for Javaをインストールします。</li> </ol>","path":["第 16 章 &nbsp; 付録","16.1 &nbsp; インストール"],"tags":[]},{"location":"chapter_appendix/installation/#4-c","level":3,"title":"4.   C#環境","text":"<ol> <li>.Net 8.0をダウンロードしてインストールします。</li> <li>VS Code拡張機能マーケットプレイスで<code>C# Dev Kit</code>を検索し、C# Dev Kitをインストールします（設定チュートリアル）。</li> <li>Visual Studioを使用することもできます（インストールチュートリアル）。</li> </ol>","path":["第 16 章 &nbsp; 付録","16.1 &nbsp; インストール"],"tags":[]},{"location":"chapter_appendix/installation/#5-go","level":3,"title":"5.   Go環境","text":"<ol> <li>goをダウンロードしてインストールします。</li> <li>VS Code拡張機能マーケットプレイスで<code>go</code>を検索し、Goをインストールします。</li> <li><code>Ctrl + Shift + P</code>を押してコマンドバーを呼び出し、goと入力し、<code>Go: Install/Update Tools</code>を選択し、すべてを選択してインストールします。</li> </ol>","path":["第 16 章 &nbsp; 付録","16.1 &nbsp; インストール"],"tags":[]},{"location":"chapter_appendix/installation/#6-swift","level":3,"title":"6.   Swift環境","text":"<ol> <li>Swiftをダウンロードしてインストールします。</li> <li>VS Code拡張機能マーケットプレイスで<code>swift</code>を検索し、Swift for Visual Studio Codeをインストールします。</li> </ol>","path":["第 16 章 &nbsp; 付録","16.1 &nbsp; インストール"],"tags":[]},{"location":"chapter_appendix/installation/#7-javascript","level":3,"title":"7.   JavaScript環境","text":"<ol> <li>Node.jsをダウンロードしてインストールします。</li> <li>（オプション）VS Code拡張機能マーケットプレイスで<code>Prettier</code>を検索し、コードフォーマッティングツールをインストールします。</li> </ol>","path":["第 16 章 &nbsp; 付録","16.1 &nbsp; インストール"],"tags":[]},{"location":"chapter_appendix/installation/#8-typescript","level":3,"title":"8.   TypeScript環境","text":"<ol> <li>JavaScript環境と同じインストール手順に従います。</li> <li>TypeScript Execute (tsx)をインストールします。</li> <li>VS Code拡張機能マーケットプレイスで<code>typescript</code>を検索し、Pretty TypeScript Errorsをインストールします。</li> </ol>","path":["第 16 章 &nbsp; 付録","16.1 &nbsp; インストール"],"tags":[]},{"location":"chapter_appendix/installation/#9-dart","level":3,"title":"9.   Dart環境","text":"<ol> <li>Dartをダウンロードしてインストールします。</li> <li>VS Code拡張機能マーケットプレイスで<code>dart</code>を検索し、Dartをインストールします。</li> </ol>","path":["第 16 章 &nbsp; 付録","16.1 &nbsp; インストール"],"tags":[]},{"location":"chapter_appendix/installation/#10-rust","level":3,"title":"10.   Rust環境","text":"<ol> <li>Rustをダウンロードしてインストールします。</li> <li>VS Code拡張機能マーケットプレイスで<code>rust</code>を検索し、rust-analyzerをインストールします。</li> </ol>","path":["第 16 章 &nbsp; 付録","16.1 &nbsp; インストール"],"tags":[]},{"location":"chapter_appendix/terminology/","level":1,"title":"16.3   用語集","text":"<p>下の表は本書に登場する重要な用語をリストアップしており、以下の点に注意する価値があります。</p> <ul> <li>英語文献を読みやすくするため、用語の英語名を覚えることをお勧めします。</li> <li>一部の用語は簡体字中国語と繁体字中国語で異なる名前を持ちます。</li> </ul> <p> 表 16-1   データ構造とアルゴリズムの重要用語 </p> English 日本語 简体中文 繁体中文 algorithm アルゴリズム 算法 演算法 data structure データ構造 数据结构 資料結構 code コード 代码 程式碼 file ファイル 文件 檔案 function 関数 函数 函式 method メソッド 方法 方法 variable 変数 变量 變數 asymptotic complexity analysis 漸近計算量解析 渐近复杂度分析 漸近複雜度分析 time complexity 時間計算量 时间复杂度 時間複雜度 space complexity 空間計算量 空间复杂度 空間複雜度 loop ループ 循环 迴圈 iteration 反復 迭代 迭代 recursion 再帰 递归 遞迴 tail recursion 末尾再帰 尾递归 尾遞迴 recursion tree 再帰木 递归树 遞迴樹 big-\\(O\\) notation ビッグO記法 大 \\(O\\) 记号 大 \\(O\\) 記號 asymptotic upper bound 漸近上界 渐近上界 漸近上界 sign-magnitude 符号と絶対値 原码 原碼 1's complement 1の補数 反码 一補數 2's complement 2の補数 补码 二補數 array 配列 数组 陣列 index インデックス 索引 索引 linked list 連結リスト 链表 鏈結串列 linked list node, list node 連結リストノード 链表节点 鏈結串列節點 head node 先頭ノード 头节点 頭節點 tail node 末尾ノード 尾节点 尾節點 list リスト 列表 串列 dynamic array 動的配列 动态数组 動態陣列 hard disk ハードディスク 硬盘 硬碟 random-access memory (RAM) メモリ 内存 記憶體 cache memory キャッシュメモリ 缓存 快取 cache miss キャッシュミス 缓存未命中 快取未命中 cache hit rate キャッシュヒット率 缓存命中率 快取命中率 stack スタック 栈 堆疊 top of the stack スタックトップ 栈顶 堆疊頂 bottom of the stack スタックボトム 栈底 堆疊底 queue キュー 队列 佇列 double-ended queue 両端キュー 双向队列 雙向佇列 front of the queue キューの先頭 队首 佇列首 rear of the queue キューの末尾 队尾 佇列尾 hash table ハッシュテーブル 哈希表 雜湊表 hash set ハッシュセット 哈希集合 雜湊集合 bucket バケット 桶 桶 hash function ハッシュ関数 哈希函数 雜湊函式 hash collision ハッシュ衝突 哈希冲突 雜湊衝突 load factor 負荷率 负载因子 負載因子 separate chaining チェイン法 链式地址 鏈結位址 open addressing オープンアドレス法 开放寻址 開放定址 linear probing 線形プローブ法 线性探测 線性探查 lazy deletion 遅延削除 懒删除 懶刪除 binary tree 二分木 二叉树 二元樹 tree node 木のノード 树节点 樹節點 left-child node 左の子ノード 左子节点 左子節點 right-child node 右の子ノード 右子节点 右子節點 parent node 親ノード 父节点 父節點 left subtree 左の部分木 左子树 左子樹 right subtree 右の部分木 右子树 右子樹 root node ルートノード 根节点 根節點 leaf node 葉ノード 叶节点 葉節點 edge エッジ 边 邊 level レベル 层 層 degree 次数 度 度 height 高さ 高度 高度 depth 深さ 深度 深度 perfect binary tree 完全二分木 完美二叉树 完美二元樹 complete binary tree 完全二分木 完全二叉树 完全二元樹 full binary tree 満二分木 完满二叉树 完滿二元樹 balanced binary tree 平衡二分木 平衡二叉树 平衡二元樹 binary search tree 二分探索木 二叉搜索树 二元搜尋樹 AVL tree AVL木 AVL 树 AVL 樹 red-black tree 赤黒木 红黑树 紅黑樹 level-order traversal レベル順走査 层序遍历 層序走訪 breadth-first traversal 幅優先走査 广度优先遍历 廣度優先走訪 depth-first traversal 深さ優先走査 深度优先遍历 深度優先走訪 binary search tree 二分探索木 二叉搜索树 二元搜尋樹 balanced binary search tree 平衡二分探索木 平衡二叉搜索树 平衡二元搜尋樹 balance factor 平衡因子 平衡因子 平衡因子 heap ヒープ 堆 堆積 max heap 最大ヒープ 大顶堆 大頂堆積 min heap 最小ヒープ 小顶堆 小頂堆積 priority queue 優先度キュー 优先队列 優先佇列 heapify ヒープ化 堆化 堆積化 top-\\(k\\) problem Top-\\(k\\) 問題 Top-\\(k\\) 问题 Top-\\(k\\) 問題 graph グラフ 图 圖 vertex 頂点 顶点 頂點 undirected graph 無向グラフ 无向图 無向圖 directed graph 有向グラフ 有向图 有向圖 connected graph 連結グラフ 连通图 連通圖 disconnected graph 非連結グラフ 非连通图 非連通圖 weighted graph 重み付きグラフ 有权图 有權圖 adjacency 隣接 邻接 鄰接 path パス 路径 路徑 in-degree 入次数 入度 入度 out-degree 出次数 出度 出度 adjacency matrix 隣接行列 邻接矩阵 鄰接矩陣 adjacency list 隣接リスト 邻接表 鄰接表 breadth-first search 幅優先探索 广度优先搜索 廣度優先搜尋 depth-first search 深さ優先探索 深度优先搜索 深度優先搜尋 binary search 二分探索 二分查找 二分搜尋 searching algorithm 探索アルゴリズム 搜索算法 搜尋演算法 sorting algorithm ソートアルゴリズム 排序算法 排序演算法 selection sort 選択ソート 选择排序 選擇排序 bubble sort バブルソート 冒泡排序 泡沫排序 insertion sort 挿入ソート 插入排序 插入排序 quick sort クイックソート 快速排序 快速排序 merge sort マージソート 归并排序 合併排序 heap sort ヒープソート 堆排序 堆積排序 bucket sort バケットソート 桶排序 桶排序 counting sort 計数ソート 计数排序 計數排序 radix sort 基数ソート 基数排序 基數排序 divide and conquer 分割統治法 分治 分治 hanota problem ハノイの塔問題 汉诺塔问题 河內塔問題 backtracking algorithm バックトラッキング 回溯算法 回溯演算法 constraint 制約 约束 約束 solution 解 解 解 state 状態 状态 狀態 pruning 枝刈り 剪枝 剪枝 permutations problem 順列問題 全排列问题 全排列問題 subset-sum problem 部分集合和問題 子集和问题 子集合問題 \\(n\\)-queens problem \\(n\\) クイーン問題 \\(n\\) 皇后问题 \\(n\\) 皇后問題 dynamic programming 動的プログラミング 动态规划 動態規劃 initial state 初期状態 初始状态 初始狀態 state-transition equation 状態遷移方程式 状态转移方程 狀態轉移方程 knapsack problem ナップサック問題 背包问题 背包問題 edit distance problem 編集距離問題 编辑距离问题 編輯距離問題 greedy algorithm 貪欲アルゴリズム 贪心算法 貪婪演算法","path":["第 16 章 &nbsp; 付録","16.3 &nbsp; 用語集"],"tags":[]},{"location":"chapter_array_and_linkedlist/","level":1,"title":"第 4 章   配列と連結リスト","text":"<p>Abstract</p> <p>データ構造の世界は頑丈なレンガの壁に似ています。</p> <p>配列では、レンガがぴったりと整列し、それぞれが次のものと継ぎ目なく隣り合って、統一された形成を作っている姿を想像してください。一方、連結リストでは、これらのレンガが自由に散らばり、それらの間を優雅に編み込む蔦に抱かれています。</p>","path":["第 4 章 &nbsp; 配列と連結リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/#_1","level":2,"title":"章の内容","text":"<ul> <li>4.1   配列</li> <li>4.2   連結リスト</li> <li>4.3   リスト</li> <li>4.4   メモリとキャッシュ *</li> <li>4.5   まとめ</li> </ul>","path":["第 4 章 &nbsp; 配列と連結リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/","level":1,"title":"4.1   配列","text":"<p>配列は線形データ構造で、同じような項目が並んでいるようなもので、コンピュータのメモリ内の連続した空間に一緒に格納されます。これは整理された格納を維持するシーケンスのようなものです。この並びの各項目には、インデックスとして知られる独自の「位置」があります。以下の図を参照して、配列の動作を観察し、これらの重要な用語を理解してください。</p> <p></p> <p> 図 4-1   配列の定義と格納方法 </p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.1 &nbsp; 配列"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#411","level":2,"title":"4.1.1   配列の一般的な操作","text":"","path":["第 4 章 &nbsp; 配列と連結リスト","4.1 &nbsp; 配列"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#1","level":3,"title":"1.   配列の初期化","text":"<p>配列は必要に応じて2つの方法で初期化できます：初期値なしまたは指定された初期値付きです。初期値が指定されていない場合、ほとんどのプログラミング言語は配列要素を\\(0\\)に設定します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlin array.py<pre><code># 配列を初期化\narr: list[int] = [0] * 5  # [ 0, 0, 0, 0, 0 ]\nnums: list[int] = [1, 3, 2, 5, 4]\n</code></pre> array.cpp<pre><code>/* 配列を初期化 */\n// スタックに格納\nint arr[5];\nint nums[5] = { 1, 3, 2, 5, 4 };\n// ヒープに格納（手動でのメモリ解放が必要）\nint* arr1 = new int[5];\nint* nums1 = new int[5] { 1, 3, 2, 5, 4 };\n</code></pre> array.java<pre><code>/* 配列を初期化 */\nint[] arr = new int[5]; // { 0, 0, 0, 0, 0 }\nint[] nums = { 1, 3, 2, 5, 4 };\n</code></pre> array.cs<pre><code>/* 配列を初期化 */\nint[] arr = new int[5]; // [ 0, 0, 0, 0, 0 ]\nint[] nums = [1, 3, 2, 5, 4];\n</code></pre> array.go<pre><code>/* 配列を初期化 */\nvar arr [5]int\n// Goでは、長さを指定（[5]int）すると配列を示し、指定しない（[]int）とスライスを示します。\n// Goの配列はコンパイル時に固定長を持つよう設計されているため、長さの指定には定数のみ使用できます。\n// extend()メソッドの実装の便宜上、ここではSliceを配列として扱います。\nnums := []int{1, 3, 2, 5, 4}\n</code></pre> array.swift<pre><code>/* 配列を初期化 */\nlet arr = Array(repeating: 0, count: 5) // [0, 0, 0, 0, 0]\nlet nums = [1, 3, 2, 5, 4]\n</code></pre> array.js<pre><code>/* 配列を初期化 */\nvar arr = new Array(5).fill(0);\nvar nums = [1, 3, 2, 5, 4];\n</code></pre> array.ts<pre><code>/* 配列を初期化 */\nlet arr: number[] = new Array(5).fill(0);\nlet nums: number[] = [1, 3, 2, 5, 4];\n</code></pre> array.dart<pre><code>/* 配列を初期化 */\nList&lt;int&gt; arr = List.filled(5, 0); // [0, 0, 0, 0, 0]\nList&lt;int&gt; nums = [1, 3, 2, 5, 4];\n</code></pre> array.rs<pre><code>/* 配列を初期化 */\nlet arr: [i32; 5] = [0; 5]; // [0, 0, 0, 0, 0]\nlet slice: &amp;[i32] = &amp;[0; 5];\n// Rustでは、長さを指定（[i32; 5]）すると配列を示し、指定しない（&amp;[i32]）とスライスを示します。\n// Rustの配列はコンパイル時に固定長を持つよう設計されているため、長さの指定には定数のみ使用できます。\n// 一般的にRustでは動的配列としてVectorが使用されます。\n// extend()メソッドの実装の便宜上、ここではベクターを配列として扱います。\nlet nums: Vec&lt;i32&gt; = vec![1, 3, 2, 5, 4];\n</code></pre> array.c<pre><code>/* 配列を初期化 */\nint arr[5] = { 0 }; // { 0, 0, 0, 0, 0 }\nint nums[5] = { 1, 3, 2, 5, 4 };\n</code></pre> array.kt<pre><code>\n</code></pre>","path":["第 4 章 &nbsp; 配列と連結リスト","4.1 &nbsp; 配列"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#2","level":3,"title":"2.   要素へのアクセス","text":"<p>配列内の要素は連続したメモリ空間に格納されるため、各要素のメモリアドレスを計算することが簡単になります。以下の図に示されている公式は、配列のメモリアドレス（特に、最初の要素のアドレス）と要素のインデックスを利用して、要素のメモリアドレスを決定するのに役立ちます。この計算により、目的の要素への直接アクセスが合理化されます。</p> <p></p> <p> 図 4-2   配列要素のメモリアドレス計算 </p> <p>上の図で観察されるように、配列のインデックスは慣例的に\\(0\\)から始まります。これは直感に反するように見えるかもしれません。数を数えるのは通常\\(1\\)から始まるためですが、アドレス計算公式内では、**インデックスは本質的にメモリアドレスからのオフセット**です。最初の要素のアドレスでは、このオフセットは\\(0\\)で、そのインデックスが\\(0\\)であることを検証しています。</p> <p>配列内の要素へのアクセスは非常に効率的で、\\(O(1)\\)時間で任意の要素にランダムアクセスできます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code>def random_access(nums: list[int]) -&gt; int:\n    \"\"\"要素へのランダムアクセス\"\"\"\n    # 区間 [0, len(nums)-1] から数値をランダムに選択\n    random_index = random.randint(0, len(nums) - 1)\n    # ランダムな要素を取得して返す\n    random_num = nums[random_index]\n    return random_num\n</code></pre> array.cpp<pre><code>/* 要素への乱数アクセス */\nint randomAccess(int *nums, int size) {\n    // [0, size)の範囲で乱数を選択\n    int randomIndex = rand() % size;\n    // 乱数要素を取得して返却\n    int randomNum = nums[randomIndex];\n    return randomNum;\n}\n</code></pre> array.java<pre><code>/* 要素へのランダムアクセス */\nint randomAccess(int[] nums) {\n    // 区間 [0, nums.length) からランダムに数を選択\n    int randomIndex = ThreadLocalRandom.current().nextInt(0, nums.length);\n    // ランダム要素を取得して返す\n    int randomNum = nums[randomIndex];\n    return randomNum;\n}\n</code></pre> array.cs<pre><code>[class]{array}-[func]{RandomAccess}\n</code></pre> array.go<pre><code>[class]{}-[func]{randomAccess}\n</code></pre> array.swift<pre><code>[class]{}-[func]{randomAccess}\n</code></pre> array.js<pre><code>[class]{}-[func]{randomAccess}\n</code></pre> array.ts<pre><code>[class]{}-[func]{randomAccess}\n</code></pre> array.dart<pre><code>[class]{}-[func]{randomAccess}\n</code></pre> array.rs<pre><code>[class]{}-[func]{random_access}\n</code></pre> array.c<pre><code>[class]{}-[func]{randomAccess}\n</code></pre> array.kt<pre><code>[class]{}-[func]{randomAccess}\n</code></pre> array.rb<pre><code>[class]{}-[func]{random_access}\n</code></pre>","path":["第 4 章 &nbsp; 配列と連結リスト","4.1 &nbsp; 配列"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#3","level":3,"title":"3.   要素の挿入","text":"<p>配列要素はメモリ内で密に詰まっており、それらの間に追加データを収容するための空間はありません。以下の図に示すように、配列の中央に要素を挿入するには、後続のすべての要素を1つずつ後ろにシフトして、新しい要素のための空間を作る必要があります。</p> <p></p> <p> 図 4-3   配列要素挿入の例 </p> <p>配列の長さが固定されているため、要素を挿入すると必然的に配列の最後の要素が失われることに注意することが重要です。この問題を解決する方法は「リスト」の章で探求されます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code>def insert(nums: list[int], num: int, index: int):\n    \"\"\"インデックス index に要素 num を挿入\"\"\"\n    # インデックス index より後のすべての要素を1つ後ろに移動\n    for i in range(len(nums) - 1, index, -1):\n        nums[i] = nums[i - 1]\n    # num を index の位置の要素に代入\n    nums[index] = num\n</code></pre> array.cpp<pre><code>/* `index`に要素numを挿入 */\nvoid insert(int *nums, int size, int num, int index) {\n    // `index`より後のすべての要素を1つ後ろに移動\n    for (int i = size - 1; i &gt; index; i--) {\n        nums[i] = nums[i - 1];\n    }\n    // indexの位置にnumを代入\n    nums[index] = num;\n}\n</code></pre> array.java<pre><code>/* `index` に要素 num を挿入 */\nvoid insert(int[] nums, int num, int index) {\n    // `index` より後のすべての要素を1つ後ろに移動\n    for (int i = nums.length - 1; i &gt; index; i--) {\n        nums[i] = nums[i - 1];\n    }\n    // index の要素に num を代入\n    nums[index] = num;\n}\n</code></pre> array.cs<pre><code>[class]{array}-[func]{Insert}\n</code></pre> array.go<pre><code>[class]{}-[func]{insert}\n</code></pre> array.swift<pre><code>[class]{}-[func]{insert}\n</code></pre> array.js<pre><code>[class]{}-[func]{insert}\n</code></pre> array.ts<pre><code>[class]{}-[func]{insert}\n</code></pre> array.dart<pre><code>[class]{}-[func]{insert}\n</code></pre> array.rs<pre><code>[class]{}-[func]{insert}\n</code></pre> array.c<pre><code>[class]{}-[func]{insert}\n</code></pre> array.kt<pre><code>[class]{}-[func]{insert}\n</code></pre> array.rb<pre><code>[class]{}-[func]{insert}\n</code></pre>","path":["第 4 章 &nbsp; 配列と連結リスト","4.1 &nbsp; 配列"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#4","level":3,"title":"4.   要素の削除","text":"<p>同様に、以下の図に示すように、インデックス\\(i\\)の要素を削除するには、インデックス\\(i\\)に続くすべての要素を1つずつ前に移動する必要があります。</p> <p></p> <p> 図 4-4   配列要素削除の例 </p> <p>削除後、元の最後の要素は「意味がない」ものになるため、特定の修正は必要ないことに注意してください。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code>def remove(nums: list[int], index: int):\n    \"\"\"インデックス index の要素を削除\"\"\"\n    # インデックス index より後のすべての要素を1つ前に移動\n    for i in range(index, len(nums) - 1):\n        nums[i] = nums[i + 1]\n</code></pre> array.cpp<pre><code>/* `index`の要素を削除 */\nvoid remove(int *nums, int size, int index) {\n    // `index`より後のすべての要素を1つ前に移動\n    for (int i = index; i &lt; size - 1; i++) {\n        nums[i] = nums[i + 1];\n    }\n}\n</code></pre> array.java<pre><code>/* `index` の要素を削除 */\nvoid remove(int[] nums, int index) {\n    // `index` より後のすべての要素を1つ前に移動\n    for (int i = index; i &lt; nums.length - 1; i++) {\n        nums[i] = nums[i + 1];\n    }\n}\n</code></pre> array.cs<pre><code>[class]{array}-[func]{Remove}\n</code></pre> array.go<pre><code>[class]{}-[func]{remove}\n</code></pre> array.swift<pre><code>[class]{}-[func]{remove}\n</code></pre> array.js<pre><code>[class]{}-[func]{remove}\n</code></pre> array.ts<pre><code>[class]{}-[func]{remove}\n</code></pre> array.dart<pre><code>[class]{}-[func]{remove}\n</code></pre> array.rs<pre><code>[class]{}-[func]{remove}\n</code></pre> array.c<pre><code>[class]{}-[func]{removeItem}\n</code></pre> array.kt<pre><code>[class]{}-[func]{remove}\n</code></pre> array.rb<pre><code>[class]{}-[func]{remove}\n</code></pre> <p>要約すると、配列の挿入と削除操作には以下の欠点があります：</p> <ul> <li>高い時間計算量：配列の挿入と削除の両方の平均時間計算量は\\(O(n)\\)で、ここで\\(n\\)は配列の長さです。</li> <li>要素の損失：配列の長さが固定されているため、挿入時に配列の容量を超える要素は失われます。</li> <li>メモリの無駄：より長い配列を初期化して前部分のみを利用すると、挿入時に「意味のない」末尾要素が生じ、メモリ空間の無駄につながります。</li> </ul>","path":["第 4 章 &nbsp; 配列と連結リスト","4.1 &nbsp; 配列"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#5","level":3,"title":"5.   配列の走査","text":"<p>ほとんどのプログラミング言語では、インデックスを使用するか、各要素を直接反復することで配列を走査できます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code>def traverse(nums: list[int]):\n    \"\"\"配列の走査\"\"\"\n    count = 0\n    # インデックスによる配列の走査\n    for i in range(len(nums)):\n        count += nums[i]\n    # 配列要素の走査\n    for num in nums:\n        count += num\n    # データのインデックスと要素の両方を走査\n    for i, num in enumerate(nums):\n        count += nums[i]\n        count += num\n</code></pre> array.cpp<pre><code>/* 配列の走査 */\nvoid traverse(int *nums, int size) {\n    int count = 0;\n    // インデックスによる配列の走査\n    for (int i = 0; i &lt; size; i++) {\n        count += nums[i];\n    }\n}\n</code></pre> array.java<pre><code>/* 配列を走査 */\nvoid traverse(int[] nums) {\n    int count = 0;\n    // インデックスによる配列の走査\n    for (int i = 0; i &lt; nums.length; i++) {\n        count += nums[i];\n    }\n    // 配列要素の走査\n    for (int num : nums) {\n        count += num;\n    }\n}\n</code></pre> array.cs<pre><code>[class]{array}-[func]{Traverse}\n</code></pre> array.go<pre><code>[class]{}-[func]{traverse}\n</code></pre> array.swift<pre><code>[class]{}-[func]{traverse}\n</code></pre> array.js<pre><code>[class]{}-[func]{traverse}\n</code></pre> array.ts<pre><code>[class]{}-[func]{traverse}\n</code></pre> array.dart<pre><code>[class]{}-[func]{traverse}\n</code></pre> array.rs<pre><code>[class]{}-[func]{traverse}\n</code></pre> array.c<pre><code>[class]{}-[func]{traverse}\n</code></pre> array.kt<pre><code>[class]{}-[func]{traverse}\n</code></pre> array.rb<pre><code>[class]{}-[func]{traverse}\n</code></pre>","path":["第 4 章 &nbsp; 配列と連結リスト","4.1 &nbsp; 配列"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#6","level":3,"title":"6.   要素の検索","text":"<p>配列内の特定の要素を見つけることは、配列を反復し、各要素をチェックして目的の値と一致するかどうかを決定することを含みます。</p> <p>配列は線形データ構造であるため、この操作は一般的に「線形探索」と呼ばれます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code>def find(nums: list[int], target: int) -&gt; int:\n    \"\"\"配列内の指定された要素を検索\"\"\"\n    for i in range(len(nums)):\n        if nums[i] == target:\n            return i\n    return -1\n</code></pre> array.cpp<pre><code>/* 配列内の指定要素を検索 */\nint find(int *nums, int size, int target) {\n    for (int i = 0; i &lt; size; i++) {\n        if (nums[i] == target)\n            return i;\n    }\n    return -1;\n}\n</code></pre> array.java<pre><code>/* 配列内で指定された要素を検索 */\nint find(int[] nums, int target) {\n    for (int i = 0; i &lt; nums.length; i++) {\n        if (nums[i] == target)\n            return i;\n    }\n    return -1;\n}\n</code></pre> array.cs<pre><code>[class]{array}-[func]{Find}\n</code></pre> array.go<pre><code>[class]{}-[func]{find}\n</code></pre> array.swift<pre><code>[class]{}-[func]{find}\n</code></pre> array.js<pre><code>[class]{}-[func]{find}\n</code></pre> array.ts<pre><code>[class]{}-[func]{find}\n</code></pre> array.dart<pre><code>[class]{}-[func]{find}\n</code></pre> array.rs<pre><code>[class]{}-[func]{find}\n</code></pre> array.c<pre><code>[class]{}-[func]{find}\n</code></pre> array.kt<pre><code>[class]{}-[func]{find}\n</code></pre> array.rb<pre><code>[class]{}-[func]{find}\n</code></pre>","path":["第 4 章 &nbsp; 配列と連結リスト","4.1 &nbsp; 配列"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#7","level":3,"title":"7.   配列の拡張","text":"<p>複雑なシステム環境では、安全な容量拡張のために配列の後にメモリ空間の可用性を確保することが困難になります。その結果、ほとんどのプログラミング言語では、**配列の長さは不変**です。</p> <p>配列を拡張するには、より大きな配列を作成し、元の配列から要素をコピーする必要があります。この操作の時間計算量は\\(O(n)\\)で、大きな配列では時間がかかる可能性があります。コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code>def extend(nums: list[int], enlarge: int) -&gt; list[int]:\n    \"\"\"配列の長さを拡張\"\"\"\n    # 拡張された長さの配列を初期化\n    res = [0] * (len(nums) + enlarge)\n    # 元の配列のすべての要素を新しい配列にコピー\n    for i in range(len(nums)):\n        res[i] = nums[i]\n    # 拡張後の新しい配列を返す\n    return res\n</code></pre> array.cpp<pre><code>/* 配列長の拡張 */\nint *extend(int *nums, int size, int enlarge) {\n    // 拡張された長さの配列を初期化\n    int *res = new int[size + enlarge];\n    // 元の配列の全要素を新しい配列にコピー\n    for (int i = 0; i &lt; size; i++) {\n        res[i] = nums[i];\n    }\n    // メモリを解放\n    delete[] nums;\n    // 拡張後の新しい配列を返却\n    return res;\n}\n</code></pre> array.java<pre><code>/* 配列長の拡張 */\nint[] extend(int[] nums, int enlarge) {\n    // 拡張された長さの配列を初期化\n    int[] res = new int[nums.length + enlarge];\n    // 元の配列のすべての要素を新しい配列にコピー\n    for (int i = 0; i &lt; nums.length; i++) {\n        res[i] = nums[i];\n    }\n    // 拡張後の新しい配列を返す\n    return res;\n}\n</code></pre> array.cs<pre><code>[class]{array}-[func]{Extend}\n</code></pre> array.go<pre><code>[class]{}-[func]{extend}\n</code></pre> array.swift<pre><code>[class]{}-[func]{extend}\n</code></pre> array.js<pre><code>[class]{}-[func]{extend}\n</code></pre> array.ts<pre><code>[class]{}-[func]{extend}\n</code></pre> array.dart<pre><code>[class]{}-[func]{extend}\n</code></pre> array.rs<pre><code>[class]{}-[func]{extend}\n</code></pre> array.c<pre><code>[class]{}-[func]{extend}\n</code></pre> array.kt<pre><code>[class]{}-[func]{extend}\n</code></pre> array.rb<pre><code>[class]{}-[func]{extend}\n</code></pre>","path":["第 4 章 &nbsp; 配列と連結リスト","4.1 &nbsp; 配列"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#412","level":2,"title":"4.1.2   配列の利点と制限","text":"<p>配列は連続したメモリ空間に格納され、同じ型の要素で構成されます。このアプローチは、システムがデータ構造操作の効率を最適化するために活用できる実質的な事前情報を提供します。</p> <ul> <li>高い空間効率：配列はデータのための連続したメモリブロックを割り当て、追加の構造的オーバーヘッドの必要性を排除します。</li> <li>ランダムアクセスのサポート：配列は任意の要素への\\(O(1)\\)時間アクセスを可能にします。</li> <li>キャッシュ局所性：配列要素にアクセスするとき、コンピュータはそれらを読み込むだけでなく、周囲のデータもキャッシュし、高速キャッシュを利用して後続の操作速度を向上させます。</li> </ul> <p>しかし、連続空間格納は諸刃の剣で、以下の制限があります：</p> <ul> <li>挿入と削除の効率が低い：配列に多くの要素が蓄積されると、要素の挿入や削除には大量の要素をシフトする必要があります。</li> <li>固定長：配列の長さは初期化後に固定されます。配列を拡張するには、すべてのデータを新しい配列にコピーする必要があり、大きなコストがかかります。</li> <li>空間の無駄：割り当てられた配列サイズが必要以上に大きい場合、余分な空間が無駄になります。</li> </ul>","path":["第 4 章 &nbsp; 配列と連結リスト","4.1 &nbsp; 配列"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#413","level":2,"title":"4.1.3   配列の典型的な応用","text":"<p>配列は基本的で広く使用されるデータ構造です。様々なアルゴリズムで頻繁に応用され、複雑なデータ構造の実装に役立ちます。</p> <ul> <li>ランダムアクセス：配列はランダムサンプリングが必要なときのデータ格納に理想的です。インデックスに基づいてランダムシーケンスを生成することで、効率的にランダムサンプリングを実現できます。</li> <li>ソートと検索：配列はソートと検索アルゴリズムで最も一般的に使用されるデータ構造です。クイックソート、マージソート、二分探索などの技術は主に配列で動作します。</li> <li>ルックアップテーブル：配列は迅速な要素や関係の取得のための効率的なルックアップテーブルとして機能します。例えば、文字をASCIIコードにマッピングすることは、ASCIIコード値をインデックスとして使用し、対応する要素を配列に格納することで簡単になります。</li> <li>機械学習：ニューラルネットワークの領域では、配列はベクトル、行列、テンソルを含む重要な線形代数演算の実行において重要な役割を果たします。配列はニューラルネットワークプログラミングにおいて主要かつ最も広範囲に使用されるデータ構造として機能します。</li> <li>データ構造の実装：配列は、スタック、キュー、ハッシュ表、ヒープ、グラフなど、様々なデータ構造を実装するための構成要素として機能します。例えば、グラフの隣接行列表現は本質的に二次元配列です。</li> </ul>","path":["第 4 章 &nbsp; 配列と連結リスト","4.1 &nbsp; 配列"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/","level":1,"title":"4.2   連結リスト","text":"<p>メモリ空間は、すべてのプログラム間で共有されるリソースです。複雑なシステム環境では、使用可能なメモリがメモリ空間全体に分散している可能性があります。配列に割り当てられるメモリは連続している必要があることを理解していますが、非常に大きな配列の場合、十分な大きさの連続メモリ空間を見つけるのは困難な場合があります。ここで、連結リストの柔軟な利点が明らかになります。</p> <p>連結リストは線形データ構造であり、各要素はノードオブジェクトで、ノードは「参照」を通じて相互接続されています。これらの参照は後続ノードのメモリアドレスを保持し、1つのノードから次のノードへのナビゲーションを可能にします。</p> <p>連結リストの設計では、ノードを連続するメモリアドレスを必要とせずに、メモリ位置全体に分散配置することができます。</p> <p></p> <p> 図 4-5   連結リストの定義と格納方法 </p> <p>上図に示すように、連結リストの基本的な構成要素はノードオブジェクトです。各ノードは2つの主要なコンポーネントで構成されています：ノードの「値」と次のノードへの「参照」です。</p> <ul> <li>連結リストの最初のノードは「ヘッドノード」、最後のノードは「テールノード」です。</li> <li>テールノードは「null」を指し、Javaでは<code>null</code>、C++では<code>nullptr</code>、Pythonでは<code>None</code>として指定されます。</li> <li>C、C++、Go、Rustなどのポインタをサポートする言語では、この「参照」は通常「ポインタ」として実装されます。</li> </ul> <p>以下のコードが示すように、連結リストの<code>ListNode</code>は値を保持するだけでなく、追加の参照（またはポインタ）も維持する必要があります。したがって、連結リストは同じ量のデータを格納する場合、配列よりも多くのメモリ空間を占有します。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlin <pre><code>class ListNode:\n    \"\"\"連結リストノードクラス\"\"\"\n    def __init__(self, val: int):\n        self.val: int = val               # ノード値\n        self.next: ListNode | None = None # 次のノードへの参照\n</code></pre> <pre><code>/* 連結リストノード構造体 */\nstruct ListNode {\n    int val;         // ノード値\n    ListNode *next;  // 次のノードへのポインタ\n    ListNode(int x) : val(x), next(nullptr) {}  // コンストラクタ\n};\n</code></pre> <pre><code>/* 連結リストノードクラス */\nclass ListNode {\n    int val;        // ノード値\n    ListNode next;  // 次のノードへの参照\n    ListNode(int x) { val = x; }  // コンストラクタ\n}\n</code></pre> <pre><code>/* 連結リストノードクラス */\nclass ListNode(int x) {  // コンストラクタ\n    int val = x;         // ノード値\n    ListNode? next;      // 次のノードへの参照\n}\n</code></pre> <pre><code>/* 連結リストノード構造体 */\ntype ListNode struct {\n    Val  int       // ノード値\n    Next *ListNode // 次のノードへのポインタ\n}\n\n// NewListNode コンストラクタ、新しい連結リストを作成\nfunc NewListNode(val int) *ListNode {\n    return &amp;ListNode{\n        Val:  val,\n        Next: nil,\n    }\n}\n</code></pre> <pre><code>/* 連結リストノードクラス */\nclass ListNode {\n    var val: Int // ノード値\n    var next: ListNode? // 次のノードへの参照\n\n    init(x: Int) { // コンストラクタ\n        val = x\n    }\n}\n</code></pre> <pre><code>/* 連結リストノードクラス */\nclass ListNode {\n    constructor(val, next) {\n        this.val = (val === undefined ? 0 : val);       // ノード値\n        this.next = (next === undefined ? null : next); // 次のノードへの参照\n    }\n}\n</code></pre> <pre><code>/* 連結リストノードクラス */\nclass ListNode {\n    val: number;\n    next: ListNode | null;\n    constructor(val?: number, next?: ListNode | null) {\n        this.val = val === undefined ? 0 : val;        // ノード値\n        this.next = next === undefined ? null : next;  // 次のノードへの参照\n    }\n}\n</code></pre> <pre><code>/* 連結リストノードクラス */\nclass ListNode {\n  int val; // ノード値\n  ListNode? next; // 次のノードへの参照\n  ListNode(this.val, [this.next]); // コンストラクタ\n}\n</code></pre> <pre><code>use std::rc::Rc;\nuse std::cell::RefCell;\n/* 連結リストノードクラス */\n#[derive(Debug)]\nstruct ListNode {\n    val: i32, // ノード値\n    next: Option&lt;Rc&lt;RefCell&lt;ListNode&gt;&gt;&gt;, // 次のノードへのポインタ\n}\n</code></pre> <pre><code>/* 連結リストノード構造体 */\ntypedef struct ListNode {\n    int val;               // ノード値\n    struct ListNode *next; // 次のノードへのポインタ\n} ListNode;\n\n/* コンストラクタ */\nListNode *newListNode(int val) {\n    ListNode *node;\n    node = (ListNode *) malloc(sizeof(ListNode));\n    node-&gt;val = val;\n    node-&gt;next = NULL;\n    return node;\n}\n</code></pre> <pre><code>\n</code></pre>","path":["第 4 章 &nbsp; 配列と連結リスト","4.2 &nbsp; 連結リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#421","level":2,"title":"4.2.1   連結リストの一般的な操作","text":"","path":["第 4 章 &nbsp; 配列と連結リスト","4.2 &nbsp; 連結リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#1","level":3,"title":"1.   連結リストの初期化","text":"<p>連結リストの構築は2段階のプロセスです：まず各ノードオブジェクトを初期化し、次にノード間の参照リンクを形成します。初期化後、ヘッドノードから<code>next</code>参照をたどってすべてのノードを順次巡回できます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlin linked_list.py<pre><code># 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4\n# 各ノードを初期化\nn0 = ListNode(1)\nn1 = ListNode(3)\nn2 = ListNode(2)\nn3 = ListNode(5)\nn4 = ListNode(4)\n# ノード間の参照を構築\nn0.next = n1\nn1.next = n2\nn2.next = n3\nn3.next = n4\n</code></pre> linked_list.cpp<pre><code>/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// 各ノードを初期化\nListNode* n0 = new ListNode(1);\nListNode* n1 = new ListNode(3);\nListNode* n2 = new ListNode(2);\nListNode* n3 = new ListNode(5);\nListNode* n4 = new ListNode(4);\n// ノード間の参照を構築\nn0-&gt;next = n1;\nn1-&gt;next = n2;\nn2-&gt;next = n3;\nn3-&gt;next = n4;\n</code></pre> linked_list.java<pre><code>/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// 各ノードを初期化\nListNode n0 = new ListNode(1);\nListNode n1 = new ListNode(3);\nListNode n2 = new ListNode(2);\nListNode n3 = new ListNode(5);\nListNode n4 = new ListNode(4);\n// ノード間の参照を構築\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.cs<pre><code>/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// 各ノードを初期化\nListNode n0 = new(1);\nListNode n1 = new(3);\nListNode n2 = new(2);\nListNode n3 = new(5);\nListNode n4 = new(4);\n// ノード間の参照を構築\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.go<pre><code>/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// 各ノードを初期化\nn0 := NewListNode(1)\nn1 := NewListNode(3)\nn2 := NewListNode(2)\nn3 := NewListNode(5)\nn4 := NewListNode(4)\n// ノード間の参照を構築\nn0.Next = n1\nn1.Next = n2\nn2.Next = n3\nn3.Next = n4\n</code></pre> linked_list.swift<pre><code>/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// 各ノードを初期化\nlet n0 = ListNode(x: 1)\nlet n1 = ListNode(x: 3)\nlet n2 = ListNode(x: 2)\nlet n3 = ListNode(x: 5)\nlet n4 = ListNode(x: 4)\n// ノード間の参照を構築\nn0.next = n1\nn1.next = n2\nn2.next = n3\nn3.next = n4\n</code></pre> linked_list.js<pre><code>/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// 各ノードを初期化\nconst n0 = new ListNode(1);\nconst n1 = new ListNode(3);\nconst n2 = new ListNode(2);\nconst n3 = new ListNode(5);\nconst n4 = new ListNode(4);\n// ノード間の参照を構築\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.ts<pre><code>/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// 各ノードを初期化\nconst n0 = new ListNode(1);\nconst n1 = new ListNode(3);\nconst n2 = new ListNode(2);\nconst n3 = new ListNode(5);\nconst n4 = new ListNode(4);\n// ノード間の参照を構築\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.dart<pre><code>/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// 各ノードを初期化\nListNode n0 = ListNode(1);\nListNode n1 = ListNode(3);\nListNode n2 = ListNode(2);\nListNode n3 = ListNode(5);\nListNode n4 = ListNode(4);\n// ノード間の参照を構築\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.rs<pre><code>/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// 各ノードを初期化\nlet n0 = Rc::new(RefCell::new(ListNode { val: 1, next: None }));\nlet n1 = Rc::new(RefCell::new(ListNode { val: 3, next: None }));\nlet n2 = Rc::new(RefCell::new(ListNode { val: 2, next: None }));\nlet n3 = Rc::new(RefCell::new(ListNode { val: 5, next: None }));\nlet n4 = Rc::new(RefCell::new(ListNode { val: 4, next: None }));\n\n// ノード間の参照を構築\nn0.borrow_mut().next = Some(n1.clone());\nn1.borrow_mut().next = Some(n2.clone());\nn2.borrow_mut().next = Some(n3.clone());\nn3.borrow_mut().next = Some(n4.clone());\n</code></pre> linked_list.c<pre><code>/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// 各ノードを初期化\nListNode* n0 = newListNode(1);\nListNode* n1 = newListNode(3);\nListNode* n2 = newListNode(2);\nListNode* n3 = newListNode(5);\nListNode* n4 = newListNode(4);\n// ノード間の参照を構築\nn0-&gt;next = n1;\nn1-&gt;next = n2;\nn2-&gt;next = n3;\nn3-&gt;next = n4;\n</code></pre> linked_list.kt<pre><code>\n</code></pre> <p>配列全体は1つの変数です。例えば、配列<code>nums</code>には<code>nums[0]</code>、<code>nums[1]</code>などの要素が含まれますが、連結リストは複数の異なるノードオブジェクトで構成されています。通常、連結リストはそのヘッドノードで参照されます。例えば、前のコードスニペットの連結リストは<code>n0</code>として参照されます。</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.2 &nbsp; 連結リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#2","level":3,"title":"2.   ノードの挿入","text":"<p>連結リストにノードを挿入するのは非常に簡単です。下図に示すように、隣接する2つのノード<code>n0</code>と<code>n1</code>の間に新しいノード<code>P</code>を挿入することを目指すとします。これは2つのノード参照（ポインタ）を変更するだけで実現でき、時間計算量は\\(O(1)\\)です。</p> <p>比較すると、配列に要素を挿入する時間計算量は\\(O(n)\\)であり、大量のデータを扱う場合には効率が悪くなります。</p> <p></p> <p> 図 4-6   連結リストノード挿入の例 </p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linked_list.py<pre><code>def insert(n0: ListNode, P: ListNode):\n    \"\"\"連結リストのノード n0 の後にノード P を挿入\"\"\"\n    n1 = n0.next\n    P.next = n1\n    n0.next = P\n</code></pre> linked_list.cpp<pre><code>/* 連結リストのノードn0の後にノードPを挿入 */\nvoid insert(ListNode *n0, ListNode *P) {\n    ListNode *n1 = n0-&gt;next;\n    P-&gt;next = n1;\n    n0-&gt;next = P;\n}\n</code></pre> linked_list.java<pre><code>/* 連結リストでノード n0 の後にノード P を挿入 */\nvoid insert(ListNode n0, ListNode P) {\n    ListNode n1 = n0.next;\n    P.next = n1;\n    n0.next = P;\n}\n</code></pre> linked_list.cs<pre><code>[class]{linked_list}-[func]{Insert}\n</code></pre> linked_list.go<pre><code>[class]{}-[func]{insertNode}\n</code></pre> linked_list.swift<pre><code>[class]{}-[func]{insert}\n</code></pre> linked_list.js<pre><code>[class]{}-[func]{insert}\n</code></pre> linked_list.ts<pre><code>[class]{}-[func]{insert}\n</code></pre> linked_list.dart<pre><code>[class]{}-[func]{insert}\n</code></pre> linked_list.rs<pre><code>[class]{}-[func]{insert}\n</code></pre> linked_list.c<pre><code>[class]{}-[func]{insert}\n</code></pre> linked_list.kt<pre><code>[class]{}-[func]{insert}\n</code></pre> linked_list.rb<pre><code>[class]{}-[func]{insert}\n</code></pre>","path":["第 4 章 &nbsp; 配列と連結リスト","4.2 &nbsp; 連結リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#3","level":3,"title":"3.   ノードの削除","text":"<p>下図に示すように、連結リストからノードを削除することも非常に簡単で、1つのノードの参照（ポインタ）を変更するだけです。</p> <p>重要な点は、ノード<code>P</code>が削除された後も<code>n1</code>を指し続けていることですが、連結リストの巡回中にはアクセスできなくなることです。これは事実上、<code>P</code>が連結リストの一部ではなくなったことを意味します。</p> <p></p> <p> 図 4-7   連結リストノードの削除 </p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linked_list.py<pre><code>def remove(n0: ListNode):\n    \"\"\"連結リストのノード n0 の後の最初のノードを削除\"\"\"\n    if not n0.next:\n        return\n    # n0 -&gt; P -&gt; n1\n    P = n0.next\n    n1 = P.next\n    n0.next = n1\n</code></pre> linked_list.cpp<pre><code>/* 連結リストのノードn0の後の最初のノードを削除 */\nvoid remove(ListNode *n0) {\n    if (n0-&gt;next == nullptr)\n        return;\n    // n0 -&gt; P -&gt; n1\n    ListNode *P = n0-&gt;next;\n    ListNode *n1 = P-&gt;next;\n    n0-&gt;next = n1;\n    // メモリを解放\n    delete P;\n}\n</code></pre> linked_list.java<pre><code>/* 連結リストでノード n0 の後の最初のノードを削除 */\nvoid remove(ListNode n0) {\n    if (n0.next == null)\n        return;\n    // n0 -&gt; P -&gt; n1\n    ListNode P = n0.next;\n    ListNode n1 = P.next;\n    n0.next = n1;\n}\n</code></pre> linked_list.cs<pre><code>[class]{linked_list}-[func]{Remove}\n</code></pre> linked_list.go<pre><code>[class]{}-[func]{removeItem}\n</code></pre> linked_list.swift<pre><code>[class]{}-[func]{remove}\n</code></pre> linked_list.js<pre><code>[class]{}-[func]{remove}\n</code></pre> linked_list.ts<pre><code>[class]{}-[func]{remove}\n</code></pre> linked_list.dart<pre><code>[class]{}-[func]{remove}\n</code></pre> linked_list.rs<pre><code>[class]{}-[func]{remove}\n</code></pre> linked_list.c<pre><code>[class]{}-[func]{removeItem}\n</code></pre> linked_list.kt<pre><code>[class]{}-[func]{remove}\n</code></pre> linked_list.rb<pre><code>[class]{}-[func]{remove}\n</code></pre>","path":["第 4 章 &nbsp; 配列と連結リスト","4.2 &nbsp; 連結リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#4","level":3,"title":"4.   ノードへのアクセス","text":"<p>連結リストでのノードへのアクセスは効率が悪いです。前述したように、配列の任意の要素には\\(O(1)\\)時間でアクセスできます。対照的に、連結リストでは、プログラムはヘッドノードから開始して目的のノードが見つかるまで順次ノードを巡回する必要があります。つまり、連結リストの\\(i\\)番目のノードにアクセスするには、プログラムは\\(i - 1\\)個のノードを反復処理する必要があり、時間計算量は\\(O(n)\\)になります。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linked_list.py<pre><code>def access(head: ListNode, index: int) -&gt; ListNode | None:\n    \"\"\"連結リストのインデックス index のノードにアクセス\"\"\"\n    for _ in range(index):\n        if not head:\n            return None\n        head = head.next\n    return head\n</code></pre> linked_list.cpp<pre><code>/* 連結リストの`index`番目のノードにアクセス */\nListNode *access(ListNode *head, int index) {\n    for (int i = 0; i &lt; index; i++) {\n        if (head == nullptr)\n            return nullptr;\n        head = head-&gt;next;\n    }\n    return head;\n}\n</code></pre> linked_list.java<pre><code>/* 連結リストの `index` のノードにアクセス */\nListNode access(ListNode head, int index) {\n    for (int i = 0; i &lt; index; i++) {\n        if (head == null)\n            return null;\n        head = head.next;\n    }\n    return head;\n}\n</code></pre> linked_list.cs<pre><code>[class]{linked_list}-[func]{Access}\n</code></pre> linked_list.go<pre><code>[class]{}-[func]{access}\n</code></pre> linked_list.swift<pre><code>[class]{}-[func]{access}\n</code></pre> linked_list.js<pre><code>[class]{}-[func]{access}\n</code></pre> linked_list.ts<pre><code>[class]{}-[func]{access}\n</code></pre> linked_list.dart<pre><code>[class]{}-[func]{access}\n</code></pre> linked_list.rs<pre><code>[class]{}-[func]{access}\n</code></pre> linked_list.c<pre><code>[class]{}-[func]{access}\n</code></pre> linked_list.kt<pre><code>[class]{}-[func]{access}\n</code></pre> linked_list.rb<pre><code>[class]{}-[func]{access}\n</code></pre>","path":["第 4 章 &nbsp; 配列と連結リスト","4.2 &nbsp; 連結リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#5","level":3,"title":"5.   ノードの検索","text":"<p>連結リストを巡回して、値が<code>target</code>に一致するノードを見つけ、連結リスト内でのそのノードのインデックスを出力します。この手順も線形検索の例です。対応するコードは以下のとおりです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linked_list.py<pre><code>def find(head: ListNode, target: int) -&gt; int:\n    \"\"\"連結リストで値 target を持つ最初のノードを検索\"\"\"\n    index = 0\n    while head:\n        if head.val == target:\n            return index\n        head = head.next\n        index += 1\n    return -1\n</code></pre> linked_list.cpp<pre><code>/* 連結リストで値がtargetの最初のノードを検索 */\nint find(ListNode *head, int target) {\n    int index = 0;\n    while (head != nullptr) {\n        if (head-&gt;val == target)\n            return index;\n        head = head-&gt;next;\n        index++;\n    }\n    return -1;\n}\n</code></pre> linked_list.java<pre><code>/* 連結リストで値 target を持つ最初のノードを検索 */\nint find(ListNode head, int target) {\n    int index = 0;\n    while (head != null) {\n        if (head.val == target)\n            return index;\n        head = head.next;\n        index++;\n    }\n    return -1;\n}\n</code></pre> linked_list.cs<pre><code>[class]{linked_list}-[func]{Find}\n</code></pre> linked_list.go<pre><code>[class]{}-[func]{findNode}\n</code></pre> linked_list.swift<pre><code>[class]{}-[func]{find}\n</code></pre> linked_list.js<pre><code>[class]{}-[func]{find}\n</code></pre> linked_list.ts<pre><code>[class]{}-[func]{find}\n</code></pre> linked_list.dart<pre><code>[class]{}-[func]{find}\n</code></pre> linked_list.rs<pre><code>[class]{}-[func]{find}\n</code></pre> linked_list.c<pre><code>[class]{}-[func]{find}\n</code></pre> linked_list.kt<pre><code>[class]{}-[func]{find}\n</code></pre> linked_list.rb<pre><code>[class]{}-[func]{find}\n</code></pre>","path":["第 4 章 &nbsp; 配列と連結リスト","4.2 &nbsp; 連結リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#422-vs","level":2,"title":"4.2.2   配列 vs. 連結リスト","text":"<p>下表は配列と連結リストの特性をまとめ、様々な操作における効率も比較しています。それぞれが対照的な格納戦略を使用するため、それぞれの特性と操作効率は明確に対比されています。</p> <p> 表 4-1   配列と連結リストの効率比較 </p> 配列 連結リスト 格納方式 連続メモリ空間 分散メモリ空間 容量拡張 固定長 柔軟な拡張 メモリ効率 要素あたりのメモリ少、潜在的な空間の無駄 要素あたりのメモリ多 要素へのアクセス \\(O(1)\\) \\(O(n)\\) 要素の追加 \\(O(n)\\) \\(O(1)\\) 要素の削除 \\(O(n)\\) \\(O(1)\\)","path":["第 4 章 &nbsp; 配列と連結リスト","4.2 &nbsp; 連結リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#423","level":2,"title":"4.2.3   連結リストの一般的な種類","text":"<p>下図に示すように、連結リストには3つの一般的な種類があります。</p> <ul> <li>単方向連結リスト：これは前述した標準的な連結リストです。単方向連結リストのノードには値と次のノードへの参照が含まれます。最初のノードはヘッドノードと呼ばれ、null（<code>None</code>）を指す最後のノードはテールノードです。</li> <li>循環連結リスト：これは単方向連結リストのテールノードがヘッドノードを指してループを作ることで形成されます。循環連結リストでは、任意のノードがヘッドノードとして機能できます。</li> <li>双方向連結リスト：単方向連結リストとは対照的に、双方向連結リストは2つの方向で参照を維持します。各ノードには後続者（次のノード）と前任者（前のノード）の両方への参照（ポインタ）が含まれます。双方向連結リストはどちらの方向にも巡回できるより多くの柔軟性を提供しますが、より多くのメモリ空間も消費します。</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlin <pre><code>class ListNode:\n    \"\"\"双方向連結リストノードクラス\"\"\"\n    def __init__(self, val: int):\n        self.val: int = val                # ノード値\n        self.next: ListNode | None = None  # 後続ノードへの参照\n        self.prev: ListNode | None = None  # 前任ノードへの参照\n</code></pre> <pre><code>/* 双方向連結リストノード構造体 */\nstruct ListNode {\n    int val;         // ノード値\n    ListNode *next;  // 後続ノードへのポインタ\n    ListNode *prev;  // 前任ノードへのポインタ\n    ListNode(int x) : val(x), next(nullptr), prev(nullptr) {}  // コンストラクタ\n};\n</code></pre> <pre><code>/* 双方向連結リストノードクラス */\nclass ListNode {\n    int val;        // ノード値\n    ListNode next;  // 次のノードへの参照\n    ListNode prev;  // 前任ノードへの参照\n    ListNode(int x) { val = x; }  // コンストラクタ\n}\n</code></pre> <pre><code>/* 双方向連結リストノードクラス */\nclass ListNode(int x) {  // コンストラクタ\n    int val = x;    // ノード値\n    ListNode next;  // 次のノードへの参照\n    ListNode prev;  // 前任ノードへの参照\n}\n</code></pre> <pre><code>/* 双方向連結リストノード構造体 */\ntype DoublyListNode struct {\n    Val  int             // ノード値\n    Next *DoublyListNode // 後続ノードへのポインタ\n    Prev *DoublyListNode // 前任ノードへのポインタ\n}\n\n// NewDoublyListNode 初期化\nfunc NewDoublyListNode(val int) *DoublyListNode {\n    return &amp;DoublyListNode{\n        Val:  val,\n        Next: nil,\n        Prev: nil,\n    }\n}\n</code></pre> <pre><code>/* 双方向連結リストノードクラス */\nclass ListNode {\n    var val: Int // ノード値\n    var next: ListNode? // 次のノードへの参照\n    var prev: ListNode? // 前任ノードへの参照\n\n    init(x: Int) { // コンストラクタ\n        val = x\n    }\n}\n</code></pre> <pre><code>/* 双方向連結リストノードクラス */\nclass ListNode {\n    constructor(val, next, prev) {\n        this.val = val  ===  undefined ? 0 : val;        // ノード値\n        this.next = next  ===  undefined ? null : next;  // 後続ノードへの参照\n        this.prev = prev  ===  undefined ? null : prev;  // 前任ノードへの参照\n    }\n}\n</code></pre> <pre><code>/* 双方向連結リストノードクラス */\nclass ListNode {\n    val: number;\n    next: ListNode | null;\n    prev: ListNode | null;\n    constructor(val?: number, next?: ListNode | null, prev?: ListNode | null) {\n        this.val = val  ===  undefined ? 0 : val;        // ノード値\n        this.next = next  ===  undefined ? null : next;  // 後続ノードへの参照\n        this.prev = prev  ===  undefined ? null : prev;  // 前任ノードへの参照\n    }\n}\n</code></pre> <pre><code>/* 双方向連結リストノードクラス */\nclass ListNode {\n    int val;        // ノード値\n    ListNode next;  // 次のノードへの参照\n    ListNode prev;  // 前任ノードへの参照\n    ListNode(this.val, [this.next, this.prev]);  // コンストラクタ\n}\n</code></pre> <pre><code>use std::rc::Rc;\nuse std::cell::RefCell;\n\n/* 双方向連結リストノード型 */\n#[derive(Debug)]\nstruct ListNode {\n    val: i32, // ノード値\n    next: Option&lt;Rc&lt;RefCell&lt;ListNode&gt;&gt;&gt;, // 後続ノードへのポインタ\n    prev: Option&lt;Rc&lt;RefCell&lt;ListNode&gt;&gt;&gt;, // 前任ノードへのポインタ\n}\n\n/* コンストラクタ */\nimpl ListNode {\n    fn new(val: i32) -&gt; Self {\n        ListNode {\n            val,\n            next: None,\n            prev: None,\n        }\n    }\n}\n</code></pre> <pre><code>/* 双方向連結リストノード構造体 */\ntypedef struct ListNode {\n    int val;               // ノード値\n    struct ListNode *next; // 後続ノードへのポインタ\n    struct ListNode *prev; // 前任ノードへのポインタ\n} ListNode;\n\n/* コンストラクタ */\nListNode *newListNode(int val) {\n    ListNode *node, *next;\n    node = (ListNode *) malloc(sizeof(ListNode));\n    node-&gt;val = val;\n    node-&gt;next = NULL;\n    node-&gt;prev = NULL;\n    return node;\n}\n</code></pre> <pre><code>\n</code></pre> <p></p> <p> 図 4-8   連結リストの一般的な種類 </p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.2 &nbsp; 連結リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#424","level":2,"title":"4.2.4   連結リストの典型的な応用","text":"<p>単方向連結リストは、スタック、キュー、ハッシュ表、グラフの実装によく使用されます。</p> <ul> <li>スタックとキュー：単方向連結リストで、挿入と削除が同じ端で行われる場合、スタック（後入先出）のように動作します。逆に、挿入が一方の端で、削除がもう一方の端で行われる場合、キュー（先入先出）のように機能します。</li> <li>ハッシュ表：連結リストは、ハッシュ衝突を解決する人気の方法である連鎖法で使用されます。ここでは、すべての衝突した要素が連結リストにグループ化されます。</li> <li>グラフ：グラフ表現の標準的な方法である隣接リストは、各グラフ頂点を連結リストに関連付けます。このリストには、対応する頂点に接続された頂点を表す要素が含まれます。</li> </ul> <p>双方向連結リストは、前後の要素への高速アクセスが必要なシナリオに最適です。</p> <ul> <li>高度なデータ構造：赤黒木やB木などの構造では、ノードの親へのアクセスが重要です。これは各ノードに親ノードへの参照を組み込むことで実現され、双方向連結リストに似ています。</li> <li>ブラウザ履歴：Webブラウザでは、双方向連結リストにより、ユーザーが前進または後退ボタンをクリックしたときの訪問ページの履歴ナビゲーションが容易になります。</li> <li>LRUアルゴリズム：双方向連結リストは、最近最少使用（LRU）キャッシュ削除アルゴリズムに適しており、最近最少使用データの迅速な識別と、高速なノード追加・削除を可能にします。</li> </ul> <p>循環連結リストは、オペレーティングシステムでのリソーススケジューリングなど、周期的な操作が必要なアプリケーションに最適です。</p> <ul> <li>ラウンドロビンスケジューリングアルゴリズム：オペレーティングシステムでは、ラウンドロビンスケジューリングアルゴリズムは一般的なCPUスケジューリング方法であり、プロセスのグループを循環する必要があります。各プロセスにはタイムスライスが割り当てられ、期限切れになるとCPUは次のプロセスに回転します。この循環操作は循環連結リストを使用して効率的に実現でき、すべてのプロセス間で公平かつ時分割システムを可能にします。</li> <li>データバッファ：循環連結リストは、オーディオやビデオプレーヤーなどのデータバッファでも使用され、データストリームが複数のバッファブロックに分割され、シームレスな再生のために循環方式で配置されます。</li> </ul>","path":["第 4 章 &nbsp; 配列と連結リスト","4.2 &nbsp; 連結リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/","level":1,"title":"4.3   リスト","text":"<p>リストは、要素へのアクセス、変更、追加、削除、走査などの操作をサポートする、順序付けられた要素のコレクションを表す抽象的なデータ構造の概念であり、ユーザーが容量制限を考慮する必要がありません。リストは連結リストまたは配列に基づいて実装できます。</p> <ul> <li>連結リストは本質的にリストとして機能し、要素の追加、削除、検索、変更の操作をサポートし、サイズを動的に調整する柔軟性があります。</li> <li>配列もこれらの操作をサポートしますが、長さが不変であるため、長さ制限のあるリストと考えることができます。</li> </ul> <p>配列を使用してリストを実装する場合、長さの不変性によりリストの実用性が低下します。これは、事前に格納するデータ量を予測することが困難な場合が多く、適切なリスト長を選択することが困難であるためです。長さが小さすぎると要件を満たさない可能性があり、大きすぎるとメモリ空間を無駄にする可能性があります。</p> <p>この問題を解決するために、動的配列を使用してリストを実装できます。これは配列の利点を継承し、プログラム実行中に動的に拡張できます。</p> <p>実際、多くのプログラミング言語の標準ライブラリは動的配列を使用してリストを実装しています。例えば、Pythonの<code>list</code>、Javaの<code>ArrayList</code>、C++の<code>vector</code>、C#の<code>List</code>などです。以下の議論では、「リスト」と「動的配列」を同義の概念として扱います。</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.3 &nbsp; リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#431","level":2,"title":"4.3.1   リストの一般的な操作","text":"","path":["第 4 章 &nbsp; 配列と連結リスト","4.3 &nbsp; リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#1","level":3,"title":"1.   リストの初期化","text":"<p>通常、「初期値なし」と「初期値あり」の2つの初期化方法を使用します。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlin list.py<pre><code># リストを初期化\n# 初期値なし\nnums1: list[int] = []\n# 初期値あり\nnums: list[int] = [1, 3, 2, 5, 4]\n</code></pre> list.cpp<pre><code>/* リストを初期化 */\n// 注意: C++では、vectorがここで説明されているnumsに相当します\n// 初期値なし\nvector&lt;int&gt; nums1;\n// 初期値あり\nvector&lt;int&gt; nums = { 1, 3, 2, 5, 4 };\n</code></pre> list.java<pre><code>/* リストを初期化 */\n// 初期値なし\nList&lt;Integer&gt; nums1 = new ArrayList&lt;&gt;();\n// 初期値あり（要素型はint[]のラッパークラスInteger[]である必要があります）\nInteger[] numbers = new Integer[] { 1, 3, 2, 5, 4 };\nList&lt;Integer&gt; nums = new ArrayList&lt;&gt;(Arrays.asList(numbers));\n</code></pre> list.cs<pre><code>/* リストを初期化 */\n// 初期値なし\nList&lt;int&gt; nums1 = [];\n// 初期値あり\nint[] numbers = [1, 3, 2, 5, 4];\nList&lt;int&gt; nums = [.. numbers];\n</code></pre> list_test.go<pre><code>/* リストを初期化 */\n// 初期値なし\nnums1 := []int{}\n// 初期値あり\nnums := []int{1, 3, 2, 5, 4}\n</code></pre> list.swift<pre><code>/* リストを初期化 */\n// 初期値なし\nlet nums1: [Int] = []\n// 初期値あり\nvar nums = [1, 3, 2, 5, 4]\n</code></pre> list.js<pre><code>/* リストを初期化 */\n// 初期値なし\nconst nums1 = [];\n// 初期値あり\nconst nums = [1, 3, 2, 5, 4];\n</code></pre> list.ts<pre><code>/* リストを初期化 */\n// 初期値なし\nconst nums1: number[] = [];\n// 初期値あり\nconst nums: number[] = [1, 3, 2, 5, 4];\n</code></pre> list.dart<pre><code>/* リストを初期化 */\n// 初期値なし\nList&lt;int&gt; nums1 = [];\n// 初期値あり\nList&lt;int&gt; nums = [1, 3, 2, 5, 4];\n</code></pre> list.rs<pre><code>/* リストを初期化 */\n// 初期値なし\nlet nums1: Vec&lt;i32&gt; = Vec::new();\n// 初期値あり\nlet nums: Vec&lt;i32&gt; = vec![1, 3, 2, 5, 4];\n</code></pre> list.c<pre><code>// Cは組み込みの動的配列を提供していません\n</code></pre> list.kt<pre><code>\n</code></pre>","path":["第 4 章 &nbsp; 配列と連結リスト","4.3 &nbsp; リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#2","level":3,"title":"2.   要素へのアクセス","text":"<p>リストは本質的に配列であるため、\\(O(1)\\)時間で要素にアクセスし更新することができ、非常に効率的です。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlin list.py<pre><code># 要素にアクセス\nnum: int = nums[1]  # インデックス1の要素にアクセス\n\n# 要素を更新\nnums[1] = 0    # インデックス1の要素を0に更新\n</code></pre> list.cpp<pre><code>/* 要素にアクセス */\nint num = nums[1];  // インデックス1の要素にアクセス\n\n/* 要素を更新 */\nnums[1] = 0;  // インデックス1の要素を0に更新\n</code></pre> list.java<pre><code>/* 要素にアクセス */\nint num = nums.get(1);  // インデックス1の要素にアクセス\n\n/* 要素を更新 */\nnums.set(1, 0);  // インデックス1の要素を0に更新\n</code></pre> list.cs<pre><code>/* 要素にアクセス */\nint num = nums[1];  // インデックス1の要素にアクセス\n\n/* 要素を更新 */\nnums[1] = 0;  // インデックス1の要素を0に更新\n</code></pre> list_test.go<pre><code>/* 要素にアクセス */\nnum := nums[1]  // インデックス1の要素にアクセス\n\n/* 要素を更新 */\nnums[1] = 0     // インデックス1の要素を0に更新\n</code></pre> list.swift<pre><code>/* 要素にアクセス */\nlet num = nums[1] // インデックス1の要素にアクセス\n\n/* 要素を更新 */\nnums[1] = 0 // インデックス1の要素を0に更新\n</code></pre> list.js<pre><code>/* 要素にアクセス */\nconst num = nums[1];  // インデックス1の要素にアクセス\n\n/* 要素を更新 */\nnums[1] = 0;  // インデックス1の要素を0に更新\n</code></pre> list.ts<pre><code>/* 要素にアクセス */\nconst num: number = nums[1];  // インデックス1の要素にアクセス\n\n/* 要素を更新 */\nnums[1] = 0;  // インデックス1の要素を0に更新\n</code></pre> list.dart<pre><code>/* 要素にアクセス */\nint num = nums[1];  // インデックス1の要素にアクセス\n\n/* 要素を更新 */\nnums[1] = 0;  // インデックス1の要素を0に更新\n</code></pre> list.rs<pre><code>/* 要素にアクセス */\nlet num: i32 = nums[1];  // インデックス1の要素にアクセス\n/* 要素を更新 */\nnums[1] = 0;             // インデックス1の要素を0に更新\n</code></pre> list.c<pre><code>// Cは組み込みの動的配列を提供していません\n</code></pre> list.kt<pre><code>\n</code></pre>","path":["第 4 章 &nbsp; 配列と連結リスト","4.3 &nbsp; リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#3","level":3,"title":"3.   要素の挿入と削除","text":"<p>配列と比較して、リストは要素の追加と削除においてより柔軟性を提供します。リストの末尾への要素追加は\\(O(1)\\)操作ですが、リストの他の場所での要素の挿入と削除の効率は配列と同じままで、時間計算量は\\(O(n)\\)です。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlin list.py<pre><code># リストをクリア\nnums.clear()\n\n# 末尾に要素を追加\nnums.append(1)\nnums.append(3)\nnums.append(2)\nnums.append(5)\nnums.append(4)\n\n# 中間に要素を挿入\nnums.insert(3, 6)  # インデックス3に数値6を挿入\n\n# 要素を削除\nnums.pop(3)        # インデックス3の要素を削除\n</code></pre> list.cpp<pre><code>/* リストをクリア */\nnums.clear();\n\n/* 末尾に要素を追加 */\nnums.push_back(1);\nnums.push_back(3);\nnums.push_back(2);\nnums.push_back(5);\nnums.push_back(4);\n\n/* 中間に要素を挿入 */\nnums.insert(nums.begin() + 3, 6);  // インデックス3に数値6を挿入\n\n/* 要素を削除 */\nnums.erase(nums.begin() + 3);      // インデックス3の要素を削除\n</code></pre> list.java<pre><code>/* リストをクリア */\nnums.clear();\n\n/* 末尾に要素を追加 */\nnums.add(1);\nnums.add(3);\nnums.add(2);\nnums.add(5);\nnums.add(4);\n\n/* 中間に要素を挿入 */\nnums.add(3, 6);  // インデックス3に数値6を挿入\n\n/* 要素を削除 */\nnums.remove(3);  // インデックス3の要素を削除\n</code></pre> list.cs<pre><code>/* リストをクリア */\nnums.Clear();\n\n/* 末尾に要素を追加 */\nnums.Add(1);\nnums.Add(3);\nnums.Add(2);\nnums.Add(5);\nnums.Add(4);\n\n/* 中間に要素を挿入 */\nnums.Insert(3, 6);\n\n/* 要素を削除 */\nnums.RemoveAt(3);\n</code></pre> list_test.go<pre><code>/* リストをクリア */\nnums = nil\n\n/* 末尾に要素を追加 */\nnums = append(nums, 1)\nnums = append(nums, 3)\nnums = append(nums, 2)\nnums = append(nums, 5)\nnums = append(nums, 4)\n\n/* 中間に要素を挿入 */\nnums = append(nums[:3], append([]int{6}, nums[3:]...)...) // インデックス3に数値6を挿入\n\n/* 要素を削除 */\nnums = append(nums[:3], nums[4:]...) // インデックス3の要素を削除\n</code></pre> list.swift<pre><code>/* リストをクリア */\nnums.removeAll()\n\n/* 末尾に要素を追加 */\nnums.append(1)\nnums.append(3)\nnums.append(2)\nnums.append(5)\nnums.append(4)\n\n/* 中間に要素を挿入 */\nnums.insert(6, at: 3) // インデックス3に数値6を挿入\n\n/* 要素を削除 */\nnums.remove(at: 3) // インデックス3の要素を削除\n</code></pre> list.js<pre><code>/* リストをクリア */\nnums.length = 0;\n\n/* 末尾に要素を追加 */\nnums.push(1);\nnums.push(3);\nnums.push(2);\nnums.push(5);\nnums.push(4);\n\n/* 中間に要素を挿入 */\nnums.splice(3, 0, 6);\n\n/* 要素を削除 */\nnums.splice(3, 1);\n</code></pre> list.ts<pre><code>/* リストをクリア */\nnums.length = 0;\n\n/* 末尾に要素を追加 */\nnums.push(1);\nnums.push(3);\nnums.push(2);\nnums.push(5);\nnums.push(4);\n\n/* 中間に要素を挿入 */\nnums.splice(3, 0, 6);\n\n/* 要素を削除 */\nnums.splice(3, 1);\n</code></pre> list.dart<pre><code>/* リストをクリア */\nnums.clear();\n\n/* 末尾に要素を追加 */\nnums.add(1);\nnums.add(3);\nnums.add(2);\nnums.add(5);\nnums.add(4);\n\n/* 中間に要素を挿入 */\nnums.insert(3, 6); // インデックス3に数値6を挿入\n\n/* 要素を削除 */\nnums.removeAt(3); // インデックス3の要素を削除\n</code></pre> list.rs<pre><code>/* リストをクリア */\nnums.clear();\n\n/* 末尾に要素を追加 */\nnums.push(1);\nnums.push(3);\nnums.push(2);\nnums.push(5);\nnums.push(4);\n\n/* 中間に要素を挿入 */\nnums.insert(3, 6);  // インデックス3に数値6を挿入\n\n/* 要素を削除 */\nnums.remove(3);    // インデックス3の要素を削除\n</code></pre> list.c<pre><code>// Cは組み込みの動的配列を提供していません\n</code></pre> list.kt<pre><code>\n</code></pre>","path":["第 4 章 &nbsp; 配列と連結リスト","4.3 &nbsp; リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#4","level":3,"title":"4.   リストの反復","text":"<p>配列と同様に、リストはインデックスを使用して反復することも、各要素を直接反復することもできます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlin list.py<pre><code># インデックスでリストを反復\ncount = 0\nfor i in range(len(nums)):\n    count += nums[i]\n\n# リスト要素を直接反復\nfor num in nums:\n    count += num\n</code></pre> list.cpp<pre><code>/* インデックスでリストを反復 */\nint count = 0;\nfor (int i = 0; i &lt; nums.size(); i++) {\n    count += nums[i];\n}\n\n/* リスト要素を直接反復 */\ncount = 0;\nfor (int num : nums) {\n    count += num;\n}\n</code></pre> list.java<pre><code>/* インデックスでリストを反復 */\nint count = 0;\nfor (int i = 0; i &lt; nums.size(); i++) {\n    count += nums.get(i);\n}\n\n/* リスト要素を直接反復 */\nfor (int num : nums) {\n    count += num;\n}\n</code></pre> list.cs<pre><code>/* インデックスでリストを反復 */\nint count = 0;\nfor (int i = 0; i &lt; nums.Count; i++) {\n    count += nums[i];\n}\n\n/* リスト要素を直接反復 */\ncount = 0;\nforeach (int num in nums) {\n    count += num;\n}\n</code></pre> list_test.go<pre><code>/* インデックスでリストを反復 */\ncount := 0\nfor i := 0; i &lt; len(nums); i++ {\n    count += nums[i]\n}\n\n/* リスト要素を直接反復 */\ncount = 0\nfor _, num := range nums {\n    count += num\n}\n</code></pre> list.swift<pre><code>/* インデックスでリストを反復 */\nvar count = 0\nfor i in nums.indices {\n    count += nums[i]\n}\n\n/* リスト要素を直接反復 */\ncount = 0\nfor num in nums {\n    count += num\n}\n</code></pre> list.js<pre><code>/* インデックスでリストを反復 */\nlet count = 0;\nfor (let i = 0; i &lt; nums.length; i++) {\n    count += nums[i];\n}\n\n/* リスト要素を直接反復 */\ncount = 0;\nfor (const num of nums) {\n    count += num;\n}\n</code></pre> list.ts<pre><code>/* インデックスでリストを反復 */\nlet count = 0;\nfor (let i = 0; i &lt; nums.length; i++) {\n    count += nums[i];\n}\n\n/* リスト要素を直接反復 */\ncount = 0;\nfor (const num of nums) {\n    count += num;\n}\n</code></pre> list.dart<pre><code>/* インデックスでリストを反復 */\nint count = 0;\nfor (var i = 0; i &lt; nums.length; i++) {\n    count += nums[i];\n}\n\n/* リスト要素を直接反復 */\ncount = 0;\nfor (var num in nums) {\n    count += num;\n}\n</code></pre> list.rs<pre><code>// インデックスでリストを反復\nlet mut _count = 0;\nfor i in 0..nums.len() {\n    _count += nums[i];\n}\n\n// リスト要素を直接反復\n_count = 0;\nfor num in &amp;nums {\n    _count += num;\n}\n</code></pre> list.c<pre><code>// Cは組み込みの動的配列を提供していません\n</code></pre> list.kt<pre><code>\n</code></pre>","path":["第 4 章 &nbsp; 配列と連結リスト","4.3 &nbsp; リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#5","level":3,"title":"5.   リストの連結","text":"<p>新しいリスト<code>nums1</code>が与えられたとき、それを元のリストの末尾に追加できます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlin list.py<pre><code># 2つのリストを連結\nnums1: list[int] = [6, 8, 7, 10, 9]\nnums += nums1  # nums1をnumsの末尾に連結\n</code></pre> list.cpp<pre><code>/* 2つのリストを連結 */\nvector&lt;int&gt; nums1 = { 6, 8, 7, 10, 9 };\n// nums1をnumsの末尾に連結\nnums.insert(nums.end(), nums1.begin(), nums1.end());\n</code></pre> list.java<pre><code>/* 2つのリストを連結 */\nList&lt;Integer&gt; nums1 = new ArrayList&lt;&gt;(Arrays.asList(new Integer[] { 6, 8, 7, 10, 9 }));\nnums.addAll(nums1);  // nums1をnumsの末尾に連結\n</code></pre> list.cs<pre><code>/* 2つのリストを連結 */\nList&lt;int&gt; nums1 = [6, 8, 7, 10, 9];\nnums.AddRange(nums1);  // nums1をnumsの末尾に連結\n</code></pre> list_test.go<pre><code>/* 2つのリストを連結 */\nnums1 := []int{6, 8, 7, 10, 9}\nnums = append(nums, nums1...)  // nums1をnumsの末尾に連結\n</code></pre> list.swift<pre><code>/* 2つのリストを連結 */\nlet nums1 = [6, 8, 7, 10, 9]\nnums.append(contentsOf: nums1) // nums1をnumsの末尾に連結\n</code></pre> list.js<pre><code>/* 2つのリストを連結 */\nconst nums1 = [6, 8, 7, 10, 9];\nnums.push(...nums1);  // nums1をnumsの末尾に連結\n</code></pre> list.ts<pre><code>/* 2つのリストを連結 */\nconst nums1: number[] = [6, 8, 7, 10, 9];\nnums.push(...nums1);  // nums1をnumsの末尾に連結\n</code></pre> list.dart<pre><code>/* 2つのリストを連結 */\nList&lt;int&gt; nums1 = [6, 8, 7, 10, 9];\nnums.addAll(nums1);  // nums1をnumsの末尾に連結\n</code></pre> list.rs<pre><code>/* 2つのリストを連結 */\nlet nums1: Vec&lt;i32&gt; = vec![6, 8, 7, 10, 9];\nnums.extend(nums1);\n</code></pre> list.c<pre><code>// Cは組み込みの動的配列を提供していません\n</code></pre> list.kt<pre><code>\n</code></pre>","path":["第 4 章 &nbsp; 配列と連結リスト","4.3 &nbsp; リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#6","level":3,"title":"6.   リストのソート","text":"<p>リストがソートされると、「二分探索」や「双ポインタ」アルゴリズムなど、配列関連のアルゴリズム問題でよく使用されるアルゴリズムを使用できます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlin list.py<pre><code># リストをソート\nnums.sort()  # ソート後、リスト要素は昇順になります\n</code></pre> list.cpp<pre><code>/* リストをソート */\nsort(nums.begin(), nums.end());  // ソート後、リスト要素は昇順になります\n</code></pre> list.java<pre><code>/* リストをソート */\nCollections.sort(nums);  // ソート後、リスト要素は昇順になります\n</code></pre> list.cs<pre><code>/* リストをソート */\nnums.Sort(); // ソート後、リスト要素は昇順になります\n</code></pre> list_test.go<pre><code>/* リストをソート */\nsort.Ints(nums)  // ソート後、リスト要素は昇順になります\n</code></pre> list.swift<pre><code>/* リストをソート */\nnums.sort() // ソート後、リスト要素は昇順になります\n</code></pre> list.js<pre><code>/* リストをソート */\nnums.sort((a, b) =&gt; a - b);  // ソート後、リスト要素は昇順になります\n</code></pre> list.ts<pre><code>/* リストをソート */\nnums.sort((a, b) =&gt; a - b);  // ソート後、リスト要素は昇順になります\n</code></pre> list.dart<pre><code>/* リストをソート */\nnums.sort(); // ソート後、リスト要素は昇順になります\n</code></pre> list.rs<pre><code>/* リストをソート */\nnums.sort(); // ソート後、リスト要素は昇順になります\n</code></pre> list.c<pre><code>// Cは組み込みの動的配列を提供していません\n</code></pre> list.kt<pre><code>\n</code></pre>","path":["第 4 章 &nbsp; 配列と連結リスト","4.3 &nbsp; リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#432","level":2,"title":"4.3.2   リストの実装","text":"<p>多くのプログラミング言語には、Java、C++、Pythonなどを含む組み込みリストが付属しています。それらの実装は、初期容量や拡張係数などの様々なパラメータを慎重に考慮した設定で、複雑になりがちです。興味のある読者は、さらなる学習のためにソースコードを調べることができます。</p> <p>リストがどのように動作するかの理解を深めるために、3つの重要な設計側面に焦点を当てて、簡略化されたリストの実装を試みます：</p> <ul> <li>初期容量：配列に合理的な初期容量を選択します。この例では、初期容量として10を選択します。</li> <li>サイズ記録：リスト内の現在の要素数を記録する変数<code>size</code>を宣言し、要素の挿入と削除でリアルタイムに更新します。この変数により、リストの末尾を特定し、拡張が必要かどうかを判断できます。</li> <li>拡張メカニズム：要素挿入時にリストが満杯に達した場合、拡張プロセスが必要です。これには拡張係数に基づいてより大きな配列を作成し、現在の配列からすべての要素を新しい配列に転送することが含まれます。この例では、拡張のたびに配列サイズを2倍にすることを規定します。</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby my_list.py<pre><code>class MyList:\n    \"\"\"リストクラス\"\"\"\n\n    def __init__(self):\n        \"\"\"コンストラクタ\"\"\"\n        self._capacity: int = 10  # リストの容量\n        self._arr: list[int] = [0] * self._capacity  # 配列（リスト要素を格納）\n        self._size: int = 0  # リストの長さ（現在の要素数）\n        self._extend_ratio: int = 2  # 各リスト拡張の倍数\n\n    def size(self) -&gt; int:\n        \"\"\"リストの長さ（現在の要素数）を取得\"\"\"\n        return self._size\n\n    def capacity(self) -&gt; int:\n        \"\"\"リストの容量を取得\"\"\"\n        return self._capacity\n\n    def get(self, index: int) -&gt; int:\n        \"\"\"要素にアクセス\"\"\"\n        # インデックスが範囲外の場合、以下のように例外をスロー\n        if index &lt; 0 or index &gt;= self._size:\n            raise IndexError(\"Index out of bounds\")\n        return self._arr[index]\n\n    def set(self, num: int, index: int):\n        \"\"\"要素を更新\"\"\"\n        if index &lt; 0 or index &gt;= self._size:\n            raise IndexError(\"Index out of bounds\")\n        self._arr[index] = num\n\n    def add(self, num: int):\n        \"\"\"末尾に要素を追加\"\"\"\n        # 要素数が容量を超える場合、拡張メカニズムをトリガー\n        if self.size() == self.capacity():\n            self.extend_capacity()\n        self._arr[self._size] = num\n        self._size += 1\n\n    def insert(self, num: int, index: int):\n        \"\"\"中間に要素を挿入\"\"\"\n        if index &lt; 0 or index &gt;= self._size:\n            raise IndexError(\"Index out of bounds\")\n        # 要素数が容量を超える場合、拡張メカニズムをトリガー\n        if self._size == self.capacity():\n            self.extend_capacity()\n        # インデックス index より後のすべての要素を1つ後ろに移動\n        for j in range(self._size - 1, index - 1, -1):\n            self._arr[j + 1] = self._arr[j]\n        self._arr[index] = num\n        # 要素数を更新\n        self._size += 1\n\n    def remove(self, index: int) -&gt; int:\n        \"\"\"要素を削除\"\"\"\n        if index &lt; 0 or index &gt;= self._size:\n            raise IndexError(\"Index out of bounds\")\n        num = self._arr[index]\n        # インデックス index より後のすべての要素を1つ前に移動\n        for j in range(index, self._size - 1):\n            self._arr[j] = self._arr[j + 1]\n        # 要素数を更新\n        self._size -= 1\n        # 削除された要素を返す\n        return num\n\n    def extend_capacity(self):\n        \"\"\"リストを拡張\"\"\"\n        # 元の配列の _extend_ratio 倍の長さの新しい配列を作成し、元の配列を新しい配列にコピー\n        self._arr = self._arr + [0] * self.capacity() * (self._extend_ratio - 1)\n        # リストの容量を更新\n        self._capacity = len(self._arr)\n\n    def to_array(self) -&gt; list[int]:\n        \"\"\"有効な長さのリストを返す\"\"\"\n        return self._arr[: self._size]\n</code></pre> my_list.cpp<pre><code>/* リストクラス */\nclass MyList {\n  private:\n    int *arr;             // 配列（リスト要素を格納）\n    int arrCapacity = 10; // リストの容量\n    int arrSize = 0;      // リストの長さ（現在の要素数）\n    int extendRatio = 2;   // リスト拡張時の倍率\n\n  public:\n    /* コンストラクタ */\n    MyList() {\n        arr = new int[arrCapacity];\n    }\n\n    /* デストラクタ */\n    ~MyList() {\n        delete[] arr;\n    }\n\n    /* リストの長さを取得（現在の要素数）*/\n    int size() {\n        return arrSize;\n    }\n\n    /* リストの容量を取得 */\n    int capacity() {\n        return arrCapacity;\n    }\n\n    /* 要素にアクセス */\n    int get(int index) {\n        // インデックスが範囲外の場合、例外をスロー（以下同様）\n        if (index &lt; 0 || index &gt;= size())\n            throw out_of_range(\"Index out of bounds\");\n        return arr[index];\n    }\n\n    /* 要素を更新 */\n    void set(int index, int num) {\n        if (index &lt; 0 || index &gt;= size())\n            throw out_of_range(\"Index out of bounds\");\n        arr[index] = num;\n    }\n\n    /* 末尾に要素を追加 */\n    void add(int num) {\n        // 要素数が容量を超えた場合、拡張メカニズムをトリガー\n        if (size() == capacity())\n            extendCapacity();\n        arr[size()] = num;\n        // 要素数を更新\n        arrSize++;\n    }\n\n    /* 中間に要素を挿入 */\n    void insert(int index, int num) {\n        if (index &lt; 0 || index &gt;= size())\n            throw out_of_range(\"Index out of bounds\");\n        // 要素数が容量を超えた場合、拡張メカニズムをトリガー\n        if (size() == capacity())\n            extendCapacity();\n        // `index`より後のすべての要素を1つ後ろに移動\n        for (int j = size() - 1; j &gt;= index; j--) {\n            arr[j + 1] = arr[j];\n        }\n        arr[index] = num;\n        // 要素数を更新\n        arrSize++;\n    }\n\n    /* 要素を削除 */\n    int remove(int index) {\n        if (index &lt; 0 || index &gt;= size())\n            throw out_of_range(\"Index out of bounds\");\n        int num = arr[index];\n        // `index`より後のすべての要素を1つ前に移動\n        for (int j = index; j &lt; size() - 1; j++) {\n            arr[j] = arr[j + 1];\n        }\n        // 要素数を更新\n        arrSize--;\n        // 削除された要素を返却\n        return num;\n    }\n\n    /* リストを拡張 */\n    void extendCapacity() {\n        // 元の配列のextendRatio倍の長さで新しい配列を作成\n        int newCapacity = capacity() * extendRatio;\n        int *tmp = arr;\n        arr = new int[newCapacity];\n        // 元の配列のすべての要素を新しい配列にコピー\n        for (int i = 0; i &lt; size(); i++) {\n            arr[i] = tmp[i];\n        }\n        // メモリを解放\n        delete[] tmp;\n        arrCapacity = newCapacity;\n    }\n\n    /* リストをVectorに変換して印刷用に使用 */\n    vector&lt;int&gt; toVector() {\n        // 有効な長さ範囲内の要素のみを変換\n        vector&lt;int&gt; vec(size());\n        for (int i = 0; i &lt; size(); i++) {\n            vec[i] = arr[i];\n        }\n        return vec;\n    }\n};\n</code></pre> my_list.java<pre><code>/* リストクラス */\nclass MyList {\n    private int[] arr; // 配列（リスト要素を格納）\n    private int capacity = 10; // リスト容量\n    private int size = 0; // リスト長（現在の要素数）\n    private int extendRatio = 2; // リストの各拡張倍率\n\n    /* コンストラクタ */\n    public MyList() {\n        arr = new int[capacity];\n    }\n\n    /* リスト長を取得（現在の要素数） */\n    public int size() {\n        return size;\n    }\n\n    /* リスト容量を取得 */\n    public int capacity() {\n        return capacity;\n    }\n\n    /* 要素へのアクセス */\n    public int get(int index) {\n        // インデックスが範囲外の場合、以下のように例外をスロー\n        if (index &lt; 0 || index &gt;= size)\n            throw new IndexOutOfBoundsException(\"インデックスが範囲外です\");\n        return arr[index];\n    }\n\n    /* 要素の更新 */\n    public void set(int index, int num) {\n        if (index &lt; 0 || index &gt;= size)\n            throw new IndexOutOfBoundsException(\"インデックスが範囲外です\");\n        arr[index] = num;\n    }\n\n    /* 末尾に要素を追加 */\n    public void add(int num) {\n        // 要素数が容量を超える場合、拡張メカニズムを実行\n        if (size == capacity())\n            extendCapacity();\n        arr[size] = num;\n        // 要素数を更新\n        size++;\n    }\n\n    /* 中間に要素を挿入 */\n    public void insert(int index, int num) {\n        if (index &lt; 0 || index &gt;= size)\n            throw new IndexOutOfBoundsException(\"インデックスが範囲外です\");\n        // 要素数が容量を超える場合、拡張メカニズムを実行\n        if (size == capacity())\n            extendCapacity();\n        // `index` より後のすべての要素を1つ後ろに移動\n        for (int j = size - 1; j &gt;= index; j--) {\n            arr[j + 1] = arr[j];\n        }\n        arr[index] = num;\n        // 要素数を更新\n        size++;\n    }\n\n    /* 要素の削除 */\n    public int remove(int index) {\n        if (index &lt; 0 || index &gt;= size)\n            throw new IndexOutOfBoundsException(\"インデックスが範囲外です\");\n        int num = arr[index];\n        // `index` より後のすべての要素を1つ前に移動\n        for (int j = index; j &lt; size - 1; j++) {\n            arr[j] = arr[j + 1];\n        }\n        // 要素数を更新\n        size--;\n        // 削除された要素を返す\n        return num;\n    }\n\n    /* リストを拡張 */\n    public void extendCapacity() {\n        // 元の配列の長さを extendRatio 倍した新しい配列を作成し、元の配列を新しい配列にコピー\n        arr = Arrays.copyOf(arr, capacity() * extendRatio);\n        // リスト容量を更新\n        capacity = arr.length;\n    }\n\n    /* リストを配列に変換 */\n    public int[] toArray() {\n        int size = size();\n        // 有効な長さ範囲内の要素のみを変換\n        int[] arr = new int[size];\n        for (int i = 0; i &lt; size; i++) {\n            arr[i] = get(i);\n        }\n        return arr;\n    }\n}\n</code></pre> my_list.cs<pre><code>[class]{MyList}-[func]{}\n</code></pre> my_list.go<pre><code>[class]{myList}-[func]{}\n</code></pre> my_list.swift<pre><code>[class]{MyList}-[func]{}\n</code></pre> my_list.js<pre><code>[class]{MyList}-[func]{}\n</code></pre> my_list.ts<pre><code>[class]{MyList}-[func]{}\n</code></pre> my_list.dart<pre><code>[class]{MyList}-[func]{}\n</code></pre> my_list.rs<pre><code>[class]{MyList}-[func]{}\n</code></pre> my_list.c<pre><code>[class]{MyList}-[func]{}\n</code></pre> my_list.kt<pre><code>[class]{MyList}-[func]{}\n</code></pre> my_list.rb<pre><code>[class]{MyList}-[func]{}\n</code></pre>","path":["第 4 章 &nbsp; 配列と連結リスト","4.3 &nbsp; リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/ram_and_cache/","level":1,"title":"4.4   メモリとキャッシュ *","text":"<p>この章の最初の2つのセクションでは、「連続格納」と「分散格納」をそれぞれ表現する2つの基本的なデータ構造である配列と連結リストを探究しました。</p> <p>実際、物理構造はプログラムがメモリとキャッシュをどの程度効率的に利用するかを大きく決定し、これがアルゴリズムの全体的なパフォーマンスに影響を与えます。</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.4 &nbsp; メモリとキャッシュ *"],"tags":[]},{"location":"chapter_array_and_linkedlist/ram_and_cache/#441","level":2,"title":"4.4.1   コンピュータ記憶装置","text":"<p>コンピュータには3種類の記憶装置があります：ハードディスク、ランダムアクセスメモリ（RAM）、およびキャッシュメモリです。以下の表は、コンピュータシステムにおけるそれぞれの役割とパフォーマンス特性を示しています。</p> <p> 表 4-2   コンピュータ記憶装置 </p> ハードディスク メモリ キャッシュ 用途 OS、プログラム、ファイルなどのデータの長期保存 現在実行中のプログラムと処理中のデータの一時保存 頻繁にアクセスされるデータと命令を保存し、CPUのメモリへのアクセス数を削減 揮発性 電源オフ後もデータは失われない 電源オフ後にデータは失われる 電源オフ後にデータは失われる 容量 より大きい、TBレベル より小さい、GBレベル 非常に小さい、MBレベル 速度 より遅い、数百から数千MB/s より高速、数十GB/s 非常に高速、数十から数百GB/s 価格（USD） より安価、数セント/GB より高価、数ドル/GB 非常に高価、CPUと一緒に価格設定 <p>コンピュータ記憶システムは、下図に示すようにピラミッドとして視覚化できます。ピラミッドの上部にある記憶装置ほど高速で、容量が小さく、より高価です。このマルチレベル設計は偶然ではなく、コンピュータ科学者とエンジニアによる慎重な検討の結果です。</p> <ul> <li>ハードディスクをメモリに置き換えるのは困難です。第一に、メモリ内のデータは電源オフ後に失われるため、長期データ保存には適していません。第二に、メモリはハードディスクよりも大幅に高価で、消費者市場での広範囲な使用の実現可能性を制限しています。</li> <li>キャッシュは大容量と高速のトレードオフに直面しています。L1、L2、L3キャッシュの容量が増加するにつれて、その物理サイズが大きくなり、CPUコアからの距離が増加します。これによりデータ転送時間が長くなり、アクセス遅延が高くなります。現在の技術では、マルチレベルキャッシュ構造が容量、速度、コストの間の最適なバランスを提供します。</li> </ul> <p></p> <p> 図 4-9   コンピュータ記憶システム </p> <p>Tip</p> <p>コンピュータの記憶階層は、速度、容量、コストの間の慎重なバランスを反映しています。このタイプのトレードオフは様々な業界で一般的であり、利益と制限の間の最適なバランスを見つけることが重要です。</p> <p>全体的に、ハードディスクは大量のデータの長期保存を提供し、メモリはプログラム実行中に処理されるデータの一時保存として機能し、キャッシュは頻繁にアクセスされるデータと命令を保存して実行効率を向上させます。それらは一緒になってコンピュータシステムの効率的な動作を保証します。</p> <p>下図に示すように、プログラム実行中、データはハードディスクからメモリに読み込まれ、CPU計算が行われます。CPUの拡張として機能するキャッシュは、**メモリからインテリジェントにデータを先読み**し、CPUのより高速なデータアクセスを可能にします。これによりプログラム実行効率が大幅に向上し、低速なメモリへの依存が減少します。</p> <p></p> <p> 図 4-10   ハードディスク、メモリ、キャッシュ間のデータフロー </p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.4 &nbsp; メモリとキャッシュ *"],"tags":[]},{"location":"chapter_array_and_linkedlist/ram_and_cache/#442","level":2,"title":"4.4.2   データ構造のメモリ効率","text":"<p>メモリ空間利用の観点から、配列と連結リストにはそれぞれ利点と制限があります。</p> <p>一方で、**メモリは限られており、複数のプログラム間で共有できない**ため、データ構造での空間使用の最適化は重要です。配列は要素が密接にパックされており、連結リストのように参照（ポインタ）のための追加メモリを必要としないため、空間効率的です。しかし、配列は連続したメモリブロックを事前に割り当てる必要があり、割り当てられた空間が実際の必要量を超える場合、無駄につながる可能性があります。配列の拡張も追加の時間と空間のオーバーヘッドを伴います。対照的に、連結リストは各ノードに対してメモリを動的に割り当て・解放し、ポインタのための追加メモリのコストでより大きな柔軟性を提供します。</p> <p>一方で、プログラム実行中、繰り返されるメモリの割り当てと解放はメモリの断片化を増加させ、メモリ利用効率を低下させます。配列は連続記憶方式により、メモリ断片化を引き起こす可能性が比較的低いです。対照的に、連結リストは要素を非連続の場所に保存し、頻繁な挿入と削除はメモリ断片化を悪化させる可能性があります。</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.4 &nbsp; メモリとキャッシュ *"],"tags":[]},{"location":"chapter_array_and_linkedlist/ram_and_cache/#443","level":2,"title":"4.4.3   データ構造のキャッシュ効率","text":"<p>キャッシュはメモリよりも空間容量がはるかに小さいですが、はるかに高速で、プログラム実行速度において重要な役割を果たします。限られた容量のため、キャッシュは頻繁にアクセスされるデータのサブセットのみを保存できます。CPUがキャッシュに存在しないデータにアクセスしようとすると、キャッシュミスが発生し、CPUは低速なメモリから必要なデータを取得する必要があり、パフォーマンスに影響を与える可能性があります。</p> <p>明らかに、キャッシュミスが少ないほど、CPUのデータ読み書き効率が高く、プログラムパフォーマンスが向上します。CPUがキャッシュからデータを正常に取得する割合はキャッシュヒット率と呼ばれ、キャッシュ効率を測定するためによく使用される指標です。</p> <p>より高い効率を達成するために、キャッシュは以下のデータロードメカニズムを採用します。</p> <ul> <li>キャッシュライン：キャッシュは個々のバイトではなく、キャッシュラインと呼ばれる単位でデータを保存・ロードして動作します。このアプローチは、一度により大きなデータブロックを転送することで効率を向上させます。</li> <li>先読みメカニズム：プロセッサはデータアクセスパターン（例：連続または固定ストライドアクセス）を予測し、これらのパターンに基づいてデータをキャッシュに先読みして、キャッシュヒット率を向上させます。</li> <li>空間的局所性：特定のデータがアクセスされると、近くのデータもまもなくアクセスされる可能性があります。これを活用するために、キャッシュは要求されたデータと一緒に隣接するデータをロードし、ヒット率を向上させます。</li> <li>時間的局所性：データがアクセスされた場合、近い将来に再びアクセスされる可能性があります。キャッシュはこの原理を使用して、最近アクセスされたデータを保持してヒット率を向上させます。</li> </ul> <p>実際、配列と連結リストは異なるキャッシュ利用効率を持ち、これは主に以下の側面に反映されます。</p> <ul> <li>占有空間：連結リスト要素は配列要素よりも多くの空間を占有するため、キャッシュに保持される有効データが少なくなります。</li> <li>キャッシュライン：連結リストデータはメモリ全体に散在し、キャッシュは「行単位でロード」されるため、ロードされる無効データの割合が高くなります。</li> <li>先読みメカニズム：配列のデータアクセスパターンは連結リストよりも「予測可能」で、つまりシステムがこれからロードされるデータを推測しやすいです。</li> <li>空間的局所性：配列は連続したメモリ空間に保存されるため、ロードされているデータの近くのデータがまもなくアクセスされる可能性が高くなります。</li> </ul> <p>全体的に、配列はより高いキャッシュヒット率を持ち、一般的に連結リストよりも操作効率が高いです。これにより、配列に基づくデータ構造はアルゴリズム問題の解決において人気があります。</p> <p>**高いキャッシュ効率が配列が常に連結リストより優れているという意味ではない**ことに注意すべきです。データ構造の選択は特定のアプリケーション要件に依存すべきです。例えば、配列と連結リストの両方が「スタック」データ構造を実装できますが（次章で詳細説明）、それらは異なるシナリオに適しています。</p> <ul> <li>アルゴリズム問題では、より高い操作効率とランダムアクセス機能を提供するため、配列に基づくスタックを選択する傾向があります。唯一のコストは配列に対して一定量のメモリ空間を事前に割り当てる必要があることです。</li> <li>データ量が非常に大きく、高度に動的で、スタックの予想サイズを推定するのが困難な場合、連結リストに基づくスタックがより良い選択です。連結リストは大量のデータをメモリの異なる部分に分散でき、配列拡張の追加オーバーヘッドを回避できます。</li> </ul>","path":["第 4 章 &nbsp; 配列と連結リスト","4.4 &nbsp; メモリとキャッシュ *"],"tags":[]},{"location":"chapter_array_and_linkedlist/summary/","level":1,"title":"4.5   まとめ","text":"","path":["第 4 章 &nbsp; 配列と連結リスト","4.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_array_and_linkedlist/summary/#1","level":3,"title":"1.   重要な復習","text":"<ul> <li>配列と連結リストは2つの基本的なデータ構造であり、コンピュータメモリにおける2つの格納方法を表しています：連続空間格納と非連続空間格納です。それらの特性は互いに補完し合います。</li> <li>配列はランダムアクセスをサポートし、使用するメモリが少ない一方で、要素の挿入と削除は非効率的で、初期化後の長さが固定されています。</li> <li>連結リストは参照（ポインタ）の変更によって効率的なノードの挿入と削除を実装し、長さを柔軟に調整できますが、ノードアクセス効率が低く、より多くのメモリを消費します。</li> <li>連結リストの一般的な種類には、単方向連結リスト、循環連結リスト、双方向連結リストがあり、それぞれに独自の応用シナリオがあります。</li> <li>リストは要素の順序付けられたコレクションで、追加、削除、変更をサポートし、通常は動的配列に基づいて実装され、配列の利点を保持しながら柔軟な長さ調整を可能にします。</li> <li>リストの出現により配列の実用性が大幅に向上しましたが、一部のメモリ空間の無駄につながる可能性があります。</li> <li>プログラム実行中、データは主にメモリに格納されます。配列はより高いメモリ空間効率を提供し、連結リストはメモリ使用においてより柔軟です。</li> <li>キャッシュは、キャッシュライン、先読み、空間的局所性、時間的局所性などのメカニズムを通じてCPUに高速データアクセスを提供し、プログラム実行効率を大幅に向上させます。</li> <li>より高いキャッシュヒット率により、配列は一般的に連結リストよりも効率的です。データ構造を選択する際は、特定のニーズとシナリオに基づいて適切な選択をすべきです。</li> </ul>","path":["第 4 章 &nbsp; 配列と連結リスト","4.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_array_and_linkedlist/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q：配列をスタックに格納するかヒープに格納するかは、時間と空間効率に影響しますか？</p> <p>スタックとヒープの両方に格納される配列は連続したメモリ空間に格納され、データ操作効率は本質的に同じです。しかし、スタックとヒープには独自の特性があり、以下の違いが生じます。</p> <ol> <li>割り当てと解放効率：スタックはより小さなメモリブロックで、コンパイラによって自動的に割り当てられます。ヒープメモリは比較的大きく、コードで動的に割り当てることができ、断片化しやすいです。したがって、ヒープでの割り当てと解放操作は一般的にスタックよりも遅くなります。</li> <li>サイズ制限：スタックメモリは比較的小さく、ヒープサイズは一般的に利用可能なメモリによって制限されます。したがって、ヒープは大きな配列の格納により適しています。</li> <li>柔軟性：スタック上の配列のサイズはコンパイル時に決定される必要がありますが、ヒープ上の配列のサイズは実行時に動的に決定できます。</li> </ol> <p>Q：なぜ配列は同じ型の要素を必要とし、連結リストは同じ型の要素を強調しないのですか？</p> <p>連結リストは参照（ポインタ）によって接続されたノードで構成され、各ノードはint、double、string、objectなど、異なる型のデータを格納できます。</p> <p>対照的に、配列要素は同じ型である必要があり、これにより対応する要素位置にアクセスするためのオフセットを計算できます。例えば、intとlong型の両方を含む配列で、単一要素がそれぞれ4バイトと8バイトを占有する場合、配列に2つの異なる長さの要素が含まれているため、以下の式を使用してオフセットを計算できません。</p> <pre><code># 要素メモリアドレス = 配列メモリアドレス + 要素長 * 要素インデックス\n</code></pre> <p>Q：ノードを削除した後、<code>P.next</code>を<code>None</code>に設定する必要がありますか？</p> <p><code>P.next</code>を変更しなくても問題ありません。連結リストの観点から、ヘッドノードからテールノードまでの巡回で<code>P</code>に遭遇することはもうありません。これは、ノード<code>P</code>がリストから効果的に削除されたことを意味し、<code>P</code>が指す場所はもはやリストに影響しません。</p> <p>ガベージコレクションの観点から、Java、Python、Goなどの自動ガベージコレクションメカニズムを持つ言語では、ノード<code>P</code>が収集されるかどうかは、それを指す参照がまだあるかどうかに依存し、<code>P.next</code>の値には依存しません。CやC++などの言語では、ノードのメモリを手動で解放する必要があります。</p> <p>Q：連結リストでは、挿入と削除操作の時間計算量は<code>O(1)</code>です。しかし、挿入や削除前の要素検索には<code>O(n)</code>時間がかかるので、なぜ時間計算量は<code>O(n)</code>ではないのですか？</p> <p>要素を最初に検索してから削除する場合、時間計算量は確かに<code>O(n)</code>です。しかし、連結リストの挿入と削除における<code>O(1)</code>の利点は他のアプリケーションで実現できます。例えば、連結リストを使用した両端キューの実装では、常にヘッドとテールノードを指すポインタを維持し、各挿入と削除操作を<code>O(1)</code>にします。</p> <p>Q：「連結リストの定義と格納方法」の図で、薄青色の格納ノードは単一のメモリアドレスを占有しますか、それともノード値と半分を共有しますか？</p> <p>図は単なる定性的な表現であり、定量的分析は特定の状況に依存します。</p> <ul> <li>異なる型のノード値は異なる量の空間を占有します。例えば、int、long、double、オブジェクトインスタンスです。</li> <li>ポインタ変数によって占有されるメモリ空間は、使用されるオペレーティングシステムとコンパイル環境に依存し、通常8バイトまたは4バイトです。</li> </ul> <p>Q：リストの末尾への要素追加は常に<code>O(1)</code>ですか？</p> <p>要素を追加することでリスト長を超える場合、リストは最初に拡張される必要があります。システムは新しいメモリブロックを要求し、元のリストのすべての要素を移動するため、この場合の時間計算量は<code>O(n)</code>になります。</p> <p>Q：「リストの出現により配列の実用性が大幅に向上しましたが、一部のメモリ空間の無駄につながる可能性があります」という文は、容量、長さ、拡張係数などの追加変数によって占有されるメモリを指していますか？</p> <p>ここでの空間の無駄は主に2つの側面を指します：一方で、リストは初期長で設定されますが、常に必要とは限りません。他方で、頻繁な拡張を防ぐため、拡張は通常\\(\\times 1.5\\)などの係数で乗算されます。これにより多くの空きスロットが生まれ、通常は完全に埋めることができません。</p> <p>Q：Pythonで<code>n = [1, 2, 3]</code>を初期化した後、これら3つの要素のアドレスは連続していますが、<code>m = [2, 1, 3]</code>を初期化すると、各要素の<code>id</code>は連続していないが<code>n</code>のものと同一です。これらの要素のアドレスが連続していない場合、<code>m</code>はまだ配列ですか？</p> <p>リスト要素を連結リストノード<code>n = [n1, n2, n3, n4, n5]</code>に置き換える場合、これら5つのノードオブジェクトも通常メモリ全体に分散しています。しかし、リストインデックスが与えられれば、<code>O(1)</code>時間でノードのメモリアドレスにアクセスでき、対応するノードにアクセスできます。これは、配列がノード自体ではなく、ノードへの参照を格納するためです。</p> <p>多くの言語とは異なり、Pythonでは数値もオブジェクトとしてラップされ、リストは数値自体ではなく、これらの数値への参照を格納します。したがって、2つの配列の同じ数値が同じ<code>id</code>を持ち、これらの数値のメモリアドレスは連続である必要がないことがわかります。</p> <p>Q：C++ STLの<code>std::list</code>はすでに双方向連結リストを実装していますが、一部のアルゴリズム書籍では直接使用していないようです。何か制限がありますか？</p> <p>一方で、アルゴリズムを実装する際は配列を使用することを好み、必要な場合のみ連結リストを使用します。主に2つの理由があります。</p> <ul> <li>空間オーバーヘッド：各要素に2つの追加ポインタ（前の要素用と次の要素用）が必要なため、<code>std::list</code>は通常<code>std::vector</code>よりも多くの空間を占有します。</li> <li>キャッシュ非友好的：データが連続して格納されていないため、<code>std::list</code>はキャッシュ利用率が低くなります。一般的に、<code>std::vector</code>の方がパフォーマンスが優れています。</li> </ul> <p>他方で、連結リストは主に二分木とグラフに必要です。スタックとキューは、連結リストではなく、プログラミング言語の<code>stack</code>と<code>queue</code>クラスを使用して実装されることが多いです。</p> <p>Q：リスト<code>res = [0] * self.size()</code>を初期化すると、<code>res</code>の各要素は同じアドレスを参照しますか？</p> <p>いいえ。しかし、この問題は二次元配列で発生します。例えば、二次元リスト<code>res = [[0]] * self.size()</code>を初期化すると、同じリスト<code>[0]</code>を複数回参照することになります。</p> <p>Q：ノードを削除する際、その後続ノードへの参照を断つ必要がありますか？</p> <p>データ構造とアルゴリズム（問題解決）の観点から、プログラムのロジックが正しい限り、リンクを断たなくても問題ありません。標準ライブラリの観点から、リンクを断つ方が安全で論理的に明確です。リンクを断たず、削除されたノードが適切にリサイクルされない場合、後続ノードのメモリのリサイクルに影響を与える可能性があります。</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_backtracking/","level":1,"title":"第 13 章   バックトラッキング","text":"<p>Abstract</p> <p>迷路の探検家のように、私たちは前進する道で障害に遭遇することがあります。</p> <p>バックトラッキングの力は、私たちに新しく始めること、試し続けること、そして最終的に光への出口を見つけることを可能にします。</p>","path":["第 13 章 &nbsp; バックトラッキング"],"tags":[]},{"location":"chapter_backtracking/#_1","level":2,"title":"章の内容","text":"<ul> <li>13.1   バックトラッキングアルゴリズム</li> <li>13.2   全順列問題</li> <li>13.3   部分集合和問題</li> <li>13.4   Nクイーン問題</li> <li>13.5   まとめ</li> </ul>","path":["第 13 章 &nbsp; バックトラッキング"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/","level":1,"title":"13.1   バックトラッキングアルゴリズム","text":"<p>バックトラッキングアルゴリズムは全数探索によって問題を解決する方法です。その核心概念は、初期状態から開始してすべての可能な解を総当たりで探索することです。アルゴリズムは正しいものを記録し、解が見つかるか、すべての可能な解が試されたが解が見つからないまで続けます。</p> <p>バックトラッキングは通常「深さ優先探索」を使用して解空間を走査します。「二分木」の章で、前順、中順、後順走査はすべて深さ優先探索であることを述べました。次に、前順走査を使用してバックトラッキング問題を解決し、アルゴリズムの動作を段階的に理解していきます。</p> <p>例1</p> <p>二分木が与えられた場合、値が \\(7\\) のすべてのノードを検索して記録し、リストで返してください。</p> <p>この問題を解決するために、この木を前順で走査し、現在のノードの値が \\(7\\) かどうかを確認します。そうであれば、ノードの値を結果リスト <code>res</code> に追加します。プロセスは以下の図に示されています：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby preorder_traversal_i_compact.py<pre><code>def pre_order(root: TreeNode):\n    \"\"\"前順走査：例一\"\"\"\n    if root is None:\n        return\n    if root.val == 7:\n        # 解を記録\n        res.append(root)\n    pre_order(root.left)\n    pre_order(root.right)\n</code></pre> preorder_traversal_i_compact.cpp<pre><code>/* 前順走査：例１ */\nvoid preOrder(TreeNode *root) {\n    if (root == nullptr) {\n        return;\n    }\n    if (root-&gt;val == 7) {\n        // 解を記録\n        res.push_back(root);\n    }\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n}\n</code></pre> preorder_traversal_i_compact.java<pre><code>/* 前順走査：例１ */\nvoid preOrder(TreeNode root) {\n    if (root == null) {\n        return;\n    }\n    if (root.val == 7) {\n        // 解を記録\n        res.add(root);\n    }\n    preOrder(root.left);\n    preOrder(root.right);\n}\n</code></pre> preorder_traversal_i_compact.cs<pre><code>[class]{preorder_traversal_i_compact}-[func]{PreOrder}\n</code></pre> preorder_traversal_i_compact.go<pre><code>[class]{}-[func]{preOrderI}\n</code></pre> preorder_traversal_i_compact.swift<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_i_compact.js<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_i_compact.ts<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_i_compact.dart<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_i_compact.rs<pre><code>[class]{}-[func]{pre_order}\n</code></pre> preorder_traversal_i_compact.c<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_i_compact.kt<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_i_compact.rb<pre><code>[class]{}-[func]{pre_order}\n</code></pre> <p></p> <p> 図 13-1   前順走査でのノード検索 </p>","path":["第 13 章 &nbsp; バックトラッキング","13.1 &nbsp; バックトラッキングアルゴリズム"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/#1311","level":2,"title":"13.1.1   試行と後退","text":"<p>解空間を探索する際に「試行」と「後退」戦略を使用するため、バックトラッキングアルゴリズムと呼ばれます。探索中、満足のいく解を得るためにもはや進めない状態に遭遇するたびに、前の選択を取り消して前の状態に戻り、次の試行のために他の可能な選択を選択できるようにします。</p> <p>例1では、各ノードの訪問が「試行」を開始します。そして葉ノードを通過するか、<code>return</code> 文で親ノードに戻ることが「後退」を示唆します。</p> <p>後退は単に関数の戻り値ではないことに注意してください。例1の問題を少し拡張して、それが何を意味するかを説明します。</p> <p>例2</p> <p>二分木で、値が \\(7\\) のすべてのノードを検索し、すべてのマッチングノードについて、ルートノードからそのノードまでのパスを返してください。</p> <p>例1のコードに基づいて、訪問したノードパスを記録するために <code>path</code> というリストを使用する必要があります。値が \\(7\\) のノードに到達すると、<code>path</code> をコピーして結果リスト <code>res</code> に追加します。走査後、<code>res</code> にはすべての解が保持されます。コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby preorder_traversal_ii_compact.py<pre><code>def pre_order(root: TreeNode):\n    \"\"\"前順走査：例二\"\"\"\n    if root is None:\n        return\n    # 試行\n    path.append(root)\n    if root.val == 7:\n        # 解を記録\n        res.append(list(path))\n    pre_order(root.left)\n    pre_order(root.right)\n    # 撤回\n    path.pop()\n</code></pre> preorder_traversal_ii_compact.cpp<pre><code>/* 前順走査：例２ */\nvoid preOrder(TreeNode *root) {\n    if (root == nullptr) {\n        return;\n    }\n    // 試行\n    path.push_back(root);\n    if (root-&gt;val == 7) {\n        // 解を記録\n        res.push_back(path);\n    }\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n    // 回退\n    path.pop_back();\n}\n</code></pre> preorder_traversal_ii_compact.java<pre><code>/* 前順走査：例２ */\nvoid preOrder(TreeNode root) {\n    if (root == null) {\n        return;\n    }\n    // 試行\n    path.add(root);\n    if (root.val == 7) {\n        // 解を記録\n        res.add(new ArrayList&lt;&gt;(path));\n    }\n    preOrder(root.left);\n    preOrder(root.right);\n    // 回退\n    path.remove(path.size() - 1);\n}\n</code></pre> preorder_traversal_ii_compact.cs<pre><code>[class]{preorder_traversal_ii_compact}-[func]{PreOrder}\n</code></pre> preorder_traversal_ii_compact.go<pre><code>[class]{}-[func]{preOrderII}\n</code></pre> preorder_traversal_ii_compact.swift<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_ii_compact.js<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_ii_compact.ts<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_ii_compact.dart<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_ii_compact.rs<pre><code>[class]{}-[func]{pre_order}\n</code></pre> preorder_traversal_ii_compact.c<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_ii_compact.kt<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_ii_compact.rb<pre><code>[class]{}-[func]{pre_order}\n</code></pre> <p>各「試行」で、現在のノードを <code>path</code> に追加することでパスを記録します。「後退」が必要なときはいつでも、<code>path</code> からノードをポップして**この失敗した試行前の状態を復元します**。</p> <p>以下の図に示すプロセスを観察することで、試行は「前進」のようで、後退は「元に戻す」のようです。後者のペアは、対応するものに対する逆操作と見なすことができます。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 13-2   試行と後退 </p>","path":["第 13 章 &nbsp; バックトラッキング","13.1 &nbsp; バックトラッキングアルゴリズム"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/#1312","level":2,"title":"13.1.2   剪定","text":"<p>複雑なバックトラッキング問題は通常1つ以上の制約を含み、これらは「剪定」によく使用されます。</p> <p>例3</p> <p>二分木で、値が \\(7\\) のすべてのノードを検索し、ルートからこれらのノードまでのパスを返してください。ただし、パスには値が \\(3\\) のノードを含まないという制限があります。</p> <p>上記の制約を満たすために、剪定操作を追加する必要があります：検索プロセス中に、値が \\(3\\) のノードに遭遇した場合、そのパスを通じてさらに検索することを即座に中止します。コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby preorder_traversal_iii_compact.py<pre><code>def pre_order(root: TreeNode):\n    \"\"\"前順走査：例三\"\"\"\n    # 枝刈り\n    if root is None or root.val == 3:\n        return\n    # 試行\n    path.append(root)\n    if root.val == 7:\n        # 解を記録\n        res.append(list(path))\n    pre_order(root.left)\n    pre_order(root.right)\n    # 撤回\n    path.pop()\n</code></pre> preorder_traversal_iii_compact.cpp<pre><code>/* 前順走査：例３ */\nvoid preOrder(TreeNode *root) {\n    // 剪定\n    if (root == nullptr || root-&gt;val == 3) {\n        return;\n    }\n    // 試行\n    path.push_back(root);\n    if (root-&gt;val == 7) {\n        // 解を記録\n        res.push_back(path);\n    }\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n    // 回退\n    path.pop_back();\n}\n</code></pre> preorder_traversal_iii_compact.java<pre><code>/* 前順走査：例３ */\nvoid preOrder(TreeNode root) {\n    // 剪定\n    if (root == null || root.val == 3) {\n        return;\n    }\n    // 試行\n    path.add(root);\n    if (root.val == 7) {\n        // 解を記録\n        res.add(new ArrayList&lt;&gt;(path));\n    }\n    preOrder(root.left);\n    preOrder(root.right);\n    // 回退\n    path.remove(path.size() - 1);\n}\n</code></pre> preorder_traversal_iii_compact.cs<pre><code>[class]{preorder_traversal_iii_compact}-[func]{PreOrder}\n</code></pre> preorder_traversal_iii_compact.go<pre><code>[class]{}-[func]{preOrderIII}\n</code></pre> preorder_traversal_iii_compact.swift<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_iii_compact.js<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_iii_compact.ts<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_iii_compact.dart<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_iii_compact.rs<pre><code>[class]{}-[func]{pre_order}\n</code></pre> preorder_traversal_iii_compact.c<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_iii_compact.kt<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_iii_compact.rb<pre><code>[class]{}-[func]{pre_order}\n</code></pre> <p>「剪定」は非常に生き生きとした名詞です。以下の図に示すように、検索プロセスで、制約を満たさない検索分岐を「切り取り」ます。さらなる不要な試行を避け、検索効率を向上させます。</p> <p></p> <p> 図 13-3   制約に基づく剪定 </p>","path":["第 13 章 &nbsp; バックトラッキング","13.1 &nbsp; バックトラッキングアルゴリズム"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/#1313","level":2,"title":"13.1.3   フレームワークコード","text":"<p>今度は、バックトラッキングから「試行、後退、剪定」の主要なフレームワークを抽出して、コードの汎用性を向上させてみましょう。</p> <p>以下のフレームワークコードでは、<code>state</code> は問題の現在の状態を表し、<code>choices</code> は現在の状態で利用可能な選択肢を表します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>def backtrack(state: State, choices: list[choice], res: list[state]):\n    \"\"\"バックトラッキングアルゴリズムフレームワーク\"\"\"\n    # 解かどうかを確認\n    if is_solution(state):\n        # 解を記録\n        record_solution(state, res)\n        # 検索を停止\n        return\n    # すべての選択肢を反復\n    for choice in choices:\n        # 剪定：選択肢が有効かどうかを確認\n        if is_valid(state, choice):\n            # 試行：選択を行い、状態を更新\n            make_choice(state, choice)\n            backtrack(state, choices, res)\n            # 後退：選択を取り消し、前の状態に戻す\n            undo_choice(state, choice)\n</code></pre> <pre><code>/* バックトラッキングアルゴリズムフレームワーク */\nvoid backtrack(State *state, vector&lt;Choice *&gt; &amp;choices, vector&lt;State *&gt; &amp;res) {\n    // 解かどうかを確認\n    if (isSolution(state)) {\n        // 解を記録\n        recordSolution(state, res);\n        // 検索を停止\n        return;\n    }\n    // すべての選択肢を反復\n    for (Choice choice : choices) {\n        // 剪定：選択肢が有効かどうかを確認\n        if (isValid(state, choice)) {\n            // 試行：選択を行い、状態を更新\n            makeChoice(state, choice);\n            backtrack(state, choices, res);\n            // 後退：選択を取り消し、前の状態に戻す\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* バックトラッキングアルゴリズムフレームワーク */\nvoid backtrack(State state, List&lt;Choice&gt; choices, List&lt;State&gt; res) {\n    // 解かどうかを確認\n    if (isSolution(state)) {\n        // 解を記録\n        recordSolution(state, res);\n        // 検索を停止\n        return;\n    }\n    // すべての選択肢を反復\n    for (Choice choice : choices) {\n        // 剪定：選択肢が有効かどうかを確認\n        if (isValid(state, choice)) {\n            // 試行：選択を行い、状態を更新\n            makeChoice(state, choice);\n            backtrack(state, choices, res);\n            // 後退：選択を取り消し、前の状態に戻す\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* バックトラッキングアルゴリズムフレームワーク */\nvoid Backtrack(State state, List&lt;Choice&gt; choices, List&lt;State&gt; res) {\n    // 解かどうかを確認\n    if (IsSolution(state)) {\n        // 解を記録\n        RecordSolution(state, res);\n        // 検索を停止\n        return;\n    }\n    // すべての選択肢を反復\n    foreach (Choice choice in choices) {\n        // 剪定：選択肢が有効かどうかを確認\n        if (IsValid(state, choice)) {\n            // 試行：選択を行い、状態を更新\n            MakeChoice(state, choice);\n            Backtrack(state, choices, res);\n            // 後退：選択を取り消し、前の状態に戻す\n            UndoChoice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* バックトラッキングアルゴリズムフレームワーク */\nfunc backtrack(state *State, choices []Choice, res *[]State) {\n    // 解かどうかを確認\n    if isSolution(state) {\n        // 解を記録\n        recordSolution(state, res)\n        // 検索を停止\n        return\n    }\n    // すべての選択肢を反復\n    for _, choice := range choices {\n        // 剪定：選択肢が有効かどうかを確認\n        if isValid(state, choice) {\n            // 試行：選択を行い、状態を更新\n            makeChoice(state, choice)\n            backtrack(state, choices, res)\n            // 後退：選択を取り消し、前の状態に戻す\n            undoChoice(state, choice)\n        }\n    }\n}\n</code></pre> <pre><code>/* バックトラッキングアルゴリズムフレームワーク */\nfunc backtrack(state: inout State, choices: [Choice], res: inout [State]) {\n    // 解かどうかを確認\n    if isSolution(state: state) {\n        // 解を記録\n        recordSolution(state: state, res: &amp;res)\n        // 検索を停止\n        return\n    }\n    // すべての選択肢を反復\n    for choice in choices {\n        // 剪定：選択肢が有効かどうかを確認\n        if isValid(state: state, choice: choice) {\n            // 試行：選択を行い、状態を更新\n            makeChoice(state: &amp;state, choice: choice)\n            backtrack(state: &amp;state, choices: choices, res: &amp;res)\n            // 後退：選択を取り消し、前の状態に戻す\n            undoChoice(state: &amp;state, choice: choice)\n        }\n    }\n}\n</code></pre> <pre><code>/* バックトラッキングアルゴリズムフレームワーク */\nfunction backtrack(state, choices, res) {\n    // 解かどうかを確認\n    if (isSolution(state)) {\n        // 解を記録\n        recordSolution(state, res);\n        // 検索を停止\n        return;\n    }\n    // すべての選択肢を反復\n    for (let choice of choices) {\n        // 剪定：選択肢が有効かどうかを確認\n        if (isValid(state, choice)) {\n            // 試行：選択を行い、状態を更新\n            makeChoice(state, choice);\n            backtrack(state, choices, res);\n            // 後退：選択を取り消し、前の状態に戻す\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* バックトラッキングアルゴリズムフレームワーク */\nfunction backtrack(state: State, choices: Choice[], res: State[]): void {\n    // 解かどうかを確認\n    if (isSolution(state)) {\n        // 解を記録\n        recordSolution(state, res);\n        // 検索を停止\n        return;\n    }\n    // すべての選択肢を反復\n    for (let choice of choices) {\n        // 剪定：選択肢が有効かどうかを確認\n        if (isValid(state, choice)) {\n            // 試行：選択を行い、状態を更新\n            makeChoice(state, choice);\n            backtrack(state, choices, res);\n            // 後退：選択を取り消し、前の状態に戻す\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* バックトラッキングアルゴリズムフレームワーク */\nvoid backtrack(State state, List&lt;Choice&gt;, List&lt;State&gt; res) {\n  // 解かどうかを確認\n  if (isSolution(state)) {\n    // 解を記録\n    recordSolution(state, res);\n    // 検索を停止\n    return;\n  }\n  // すべての選択肢を反復\n  for (Choice choice in choices) {\n    // 剪定：選択肢が有効かどうかを確認\n    if (isValid(state, choice)) {\n      // 試行：選択を行い、状態を更新\n      makeChoice(state, choice);\n      backtrack(state, choices, res);\n      // 後退：選択を取り消し、前の状態に戻す\n      undoChoice(state, choice);\n    }\n  }\n}\n</code></pre> <pre><code>/* バックトラッキングアルゴリズムフレームワーク */\nfn backtrack(state: &amp;mut State, choices: &amp;Vec&lt;Choice&gt;, res: &amp;mut Vec&lt;State&gt;) {\n    // 解かどうかを確認\n    if is_solution(state) {\n        // 解を記録\n        record_solution(state, res);\n        // 検索を停止\n        return;\n    }\n    // すべての選択肢を反復\n    for choice in choices {\n        // 剪定：選択肢が有効かどうかを確認\n        if is_valid(state, choice) {\n            // 試行：選択を行い、状態を更新\n            make_choice(state, choice);\n            backtrack(state, choices, res);\n            // 後退：選択を取り消し、前の状態に戻す\n            undo_choice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* バックトラッキングアルゴリズムフレームワーク */\nvoid backtrack(State *state, Choice *choices, int numChoices, State *res, int numRes) {\n    // 解かどうかを確認\n    if (isSolution(state)) {\n        // 解を記録\n        recordSolution(state, res, numRes);\n        // 検索を停止\n        return;\n    }\n    // すべての選択肢を反復\n    for (int i = 0; i &lt; numChoices; i++) {\n        // 剪定：選択肢が有効かどうかを確認\n        if (isValid(state, &amp;choices[i])) {\n            // 試行：選択を行い、状態を更新\n            makeChoice(state, &amp;choices[i]);\n            backtrack(state, choices, numChoices, res, numRes);\n            // 後退：選択を取り消し、前の状態に戻す\n            undoChoice(state, &amp;choices[i]);\n        }\n    }\n}\n</code></pre> <pre><code>/* バックトラッキングアルゴリズムフレームワーク */\nfun backtrack(state: State?, choices: List&lt;Choice?&gt;, res: List&lt;State?&gt;?) {\n    // 解かどうかを確認\n    if (isSolution(state)) {\n        // 解を記録\n        recordSolution(state, res)\n        // 検索を停止\n        return\n    }\n    // すべての選択肢を反復\n    for (choice in choices) {\n        // 剪定：選択肢が有効かどうかを確認\n        if (isValid(state, choice)) {\n            // 試行：選択を行い、状態を更新\n            makeChoice(state, choice)\n            backtrack(state, choices, res)\n            // 後退：選択を取り消し、前の状態に戻す\n            undoChoice(state, choice)\n        }\n    }\n}\n</code></pre> <pre><code>### バックトラッキングアルゴリズムフレームワーク ###\ndef backtrack(state, choices, res)\n    # 解かどうかを確認\n    if is_solution?(state)\n        # 解を記録\n        record_solution(state, res)\n        return\n    end\n\n    # すべての選択肢を反復\n    for choice in choices\n        # 剪定：選択肢が有効かどうかを確認\n        if is_valid?(state, choice)\n            # 試行：選択を行い、状態を更新\n            make_choice(state, choice)\n            backtrack(state, choices, res)\n            # 後退：選択を取り消し、前の状態に戻す\n            undo_choice(state, choice)\n        end\n    end\nend\n</code></pre> <p>次に、フレームワークコードに基づいて例題 3 を解きます。状態 <code>state</code> はノードの走査経路を表し、選択肢 <code>choices</code> は現在ノードの左子ノードと右子ノード、結果 <code>res</code> は経路リストです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby preorder_traversal_iii_template.py<pre><code>def is_solution(state: list[TreeNode]) -&gt; bool:\n    \"\"\"現在の状態が解かどうかを判定\"\"\"\n    return state and state[-1].val == 7\n\ndef record_solution(state: list[TreeNode], res: list[list[TreeNode]]):\n    \"\"\"解を記録\"\"\"\n    res.append(list(state))\n\ndef is_valid(state: list[TreeNode], choice: TreeNode) -&gt; bool:\n    \"\"\"現在の状態下で選択が合法かどうかを判定\"\"\"\n    return choice is not None and choice.val != 3\n\ndef make_choice(state: list[TreeNode], choice: TreeNode):\n    \"\"\"状態を更新\"\"\"\n    state.append(choice)\n\ndef undo_choice(state: list[TreeNode], choice: TreeNode):\n    \"\"\"状態を復元\"\"\"\n    state.pop()\n\ndef backtrack(\n    state: list[TreeNode], choices: list[TreeNode], res: list[list[TreeNode]]\n):\n    \"\"\"バックトラッキングアルゴリズム：例三\"\"\"\n    # 解かどうかをチェック\n    if is_solution(state):\n        # 解を記録\n        record_solution(state, res)\n    # すべての選択肢を走査\n    for choice in choices:\n        # 枝刈り：選択が合法かどうかをチェック\n        if is_valid(state, choice):\n            # 試行：選択を行い、状態を更新\n            make_choice(state, choice)\n            # 次の選択ラウンドに進む\n            backtrack(state, [choice.left, choice.right], res)\n            # 撤回：選択を取り消し、前の状態に復元\n            undo_choice(state, choice)\n</code></pre> preorder_traversal_iii_template.cpp<pre><code>/* 現在の状態が解かどうかを判定 */\nbool isSolution(vector&lt;TreeNode *&gt; &amp;state) {\n    return !state.empty() &amp;&amp; state.back()-&gt;val == 7;\n}\n\n/* 解を記録 */\nvoid recordSolution(vector&lt;TreeNode *&gt; &amp;state, vector&lt;vector&lt;TreeNode *&gt;&gt; &amp;res) {\n    res.push_back(state);\n}\n\n/* 現在の状態下で選択が合法かどうかを判定 */\nbool isValid(vector&lt;TreeNode *&gt; &amp;state, TreeNode *choice) {\n    return choice != nullptr &amp;&amp; choice-&gt;val != 3;\n}\n\n/* 状態を更新 */\nvoid makeChoice(vector&lt;TreeNode *&gt; &amp;state, TreeNode *choice) {\n    state.push_back(choice);\n}\n\n/* 状態を復元 */\nvoid undoChoice(vector&lt;TreeNode *&gt; &amp;state, TreeNode *choice) {\n    state.pop_back();\n}\n\n/* バックトラッキングアルゴリズム：例３ */\nvoid backtrack(vector&lt;TreeNode *&gt; &amp;state, vector&lt;TreeNode *&gt; &amp;choices, vector&lt;vector&lt;TreeNode *&gt;&gt; &amp;res) {\n    // 解かどうかをチェック\n    if (isSolution(state)) {\n        // 解を記録\n        recordSolution(state, res);\n    }\n    // すべての選択肢を走査\n    for (TreeNode *choice : choices) {\n        // 剪定：選択が合法かどうかをチェック\n        if (isValid(state, choice)) {\n            // 試行：選択を行い、状態を更新\n            makeChoice(state, choice);\n            // 次のラウンドの選択に進む\n            vector&lt;TreeNode *&gt; nextChoices{choice-&gt;left, choice-&gt;right};\n            backtrack(state, nextChoices, res);\n            // 回退：選択を取り消し、前の状態に復元\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.java<pre><code>/* 現在の状態が解かどうかを判定 */\nboolean isSolution(List&lt;TreeNode&gt; state) {\n    return !state.isEmpty() &amp;&amp; state.get(state.size() - 1).val == 7;\n}\n\n/* 解を記録 */\nvoid recordSolution(List&lt;TreeNode&gt; state, List&lt;List&lt;TreeNode&gt;&gt; res) {\n    res.add(new ArrayList&lt;&gt;(state));\n}\n\n/* 現在の状態下で選択が合法かどうかを判定 */\nboolean isValid(List&lt;TreeNode&gt; state, TreeNode choice) {\n    return choice != null &amp;&amp; choice.val != 3;\n}\n\n/* 状態を更新 */\nvoid makeChoice(List&lt;TreeNode&gt; state, TreeNode choice) {\n    state.add(choice);\n}\n\n/* 状態を復元 */\nvoid undoChoice(List&lt;TreeNode&gt; state, TreeNode choice) {\n    state.remove(state.size() - 1);\n}\n\n/* バックトラッキングアルゴリズム：例３ */\nvoid backtrack(List&lt;TreeNode&gt; state, List&lt;TreeNode&gt; choices, List&lt;List&lt;TreeNode&gt;&gt; res) {\n    // 解かどうかをチェック\n    if (isSolution(state)) {\n        // 解を記録\n        recordSolution(state, res);\n    }\n    // すべての選択肢を走査\n    for (TreeNode choice : choices) {\n        // 剪定：選択が合法かどうかをチェック\n        if (isValid(state, choice)) {\n            // 試行：選択を行い、状態を更新\n            makeChoice(state, choice);\n            // 次のラウンドの選択に進む\n            backtrack(state, Arrays.asList(choice.left, choice.right), res);\n            // 回退：選択を取り消し、前の状態に復元\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.cs<pre><code>[class]{preorder_traversal_iii_template}-[func]{IsSolution}\n\n[class]{preorder_traversal_iii_template}-[func]{RecordSolution}\n\n[class]{preorder_traversal_iii_template}-[func]{IsValid}\n\n[class]{preorder_traversal_iii_template}-[func]{MakeChoice}\n\n[class]{preorder_traversal_iii_template}-[func]{UndoChoice}\n\n[class]{preorder_traversal_iii_template}-[func]{Backtrack}\n</code></pre> preorder_traversal_iii_template.go<pre><code>[class]{}-[func]{isSolution}\n\n[class]{}-[func]{recordSolution}\n\n[class]{}-[func]{isValid}\n\n[class]{}-[func]{makeChoice}\n\n[class]{}-[func]{undoChoice}\n\n[class]{}-[func]{backtrackIII}\n</code></pre> preorder_traversal_iii_template.swift<pre><code>[class]{}-[func]{isSolution}\n\n[class]{}-[func]{recordSolution}\n\n[class]{}-[func]{isValid}\n\n[class]{}-[func]{makeChoice}\n\n[class]{}-[func]{undoChoice}\n\n[class]{}-[func]{backtrack}\n</code></pre> preorder_traversal_iii_template.js<pre><code>[class]{}-[func]{isSolution}\n\n[class]{}-[func]{recordSolution}\n\n[class]{}-[func]{isValid}\n\n[class]{}-[func]{makeChoice}\n\n[class]{}-[func]{undoChoice}\n\n[class]{}-[func]{backtrack}\n</code></pre> preorder_traversal_iii_template.ts<pre><code>[class]{}-[func]{isSolution}\n\n[class]{}-[func]{recordSolution}\n\n[class]{}-[func]{isValid}\n\n[class]{}-[func]{makeChoice}\n\n[class]{}-[func]{undoChoice}\n\n[class]{}-[func]{backtrack}\n</code></pre> preorder_traversal_iii_template.dart<pre><code>[class]{}-[func]{isSolution}\n\n[class]{}-[func]{recordSolution}\n\n[class]{}-[func]{isValid}\n\n[class]{}-[func]{makeChoice}\n\n[class]{}-[func]{undoChoice}\n\n[class]{}-[func]{backtrack}\n</code></pre> preorder_traversal_iii_template.rs<pre><code>[class]{}-[func]{is_solution}\n\n[class]{}-[func]{record_solution}\n\n[class]{}-[func]{is_valid}\n\n[class]{}-[func]{make_choice}\n\n[class]{}-[func]{undo_choice}\n\n[class]{}-[func]{backtrack}\n</code></pre> preorder_traversal_iii_template.c<pre><code>[class]{}-[func]{isSolution}\n\n[class]{}-[func]{recordSolution}\n\n[class]{}-[func]{isValid}\n\n[class]{}-[func]{makeChoice}\n\n[class]{}-[func]{undoChoice}\n\n[class]{}-[func]{backtrack}\n</code></pre> preorder_traversal_iii_template.kt<pre><code>[class]{}-[func]{isSolution}\n\n[class]{}-[func]{recordSolution}\n\n[class]{}-[func]{isValid}\n\n[class]{}-[func]{makeChoice}\n\n[class]{}-[func]{undoChoice}\n\n[class]{}-[func]{backtrack}\n</code></pre> preorder_traversal_iii_template.rb<pre><code>[class]{}-[func]{is_solution}\n\n[class]{}-[func]{record_solution}\n\n[class]{}-[func]{is_valid}\n\n[class]{}-[func]{make_choice}\n\n[class]{}-[func]{undo_choice}\n\n[class]{}-[func]{backtrack}\n</code></pre> <p>問題文の意味に従い、値が \\(7\\) のノードを見つけた後も探索を続ける必要があります。したがって、解を記録した後の <code>return</code> 文を削除する必要があります。次の図は、<code>return</code> 文を保持する場合と削除する場合の探索過程の比較です。</p> <p></p> <p> 図 13-4   returnを保持する場合と削除する場合の探索過程の比較 </p> <p>前順走査に基づくコード実装と比べると、バックトラッキングアルゴリズムのフレームワークに基づく実装はやや冗長に見えますが、汎用性はより高いです。実際、多くのバックトラッキング問題はこのフレームワークの下で解くことができます。具体的な問題に応じて <code>state</code> と <code>choices</code> を定義し、フレームワーク内の各メソッドを実装すればよいのです。</p>","path":["第 13 章 &nbsp; バックトラッキング","13.1 &nbsp; バックトラッキングアルゴリズム"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/#1314","level":2,"title":"13.1.4   よく使われる用語","text":"<p>アルゴリズム問題をより明確に分析するために、バックトラッキングアルゴリズムでよく使われる用語の意味をまとめ、例題 3 の対応例を以下の表に示します。</p> <p> 表 13-1   バックトラッキングアルゴリズムでよく使われる用語 </p> 名称 定義 例題 3 解（solution） 解は問題の特定条件を満たす答えであり、1 つまたは複数存在する可能性がある 根ノードからノード \\(7\\) までの制約条件を満たすすべての経路 制約条件（constraint） 制約条件は、解の実現可能性を制限する条件であり、通常は枝刈りに使用される 経路にノード \\(3\\) を含まない 状態（state） 状態は、ある時点での問題の状況を表し、これまでに行った選択を含む 現在訪問したノード経路、すなわち <code>path</code> ノードリスト 試行（attempt） 試行は、利用可能な選択肢に基づいて解空間を探索する過程であり、選択を行い、状態を更新し、解かどうかを確認する 左（右）子ノードを再帰的に訪問し、ノードを <code>path</code> に追加し、ノードの値が \\(7\\) かを確認する バックトラック（backtracking） 制約条件を満たさない状態に遭遇した場合、以前の選択を取り消して前の状態に戻ること 葉ノードを越えたとき、探索終了、値が \\(3\\) のノードに遭遇したとき探索を終了し、関数が戻る 枝刈り（pruning） 問題の特性や制約条件に基づき、無意味な探索経路を避ける方法であり、探索効率を向上させる 値が \\(3\\) のノードに遭遇した場合、それ以上探索しない <p>Tip</p> <p>問題、解、状態などの概念は一般的なものであり、分割統治、バックトラッキング、動的計画法、貪欲法などのアルゴリズムにも関係します。</p>","path":["第 13 章 &nbsp; バックトラッキング","13.1 &nbsp; バックトラッキングアルゴリズム"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/#1315","level":2,"title":"13.1.5   長所と限界","text":"<p>バックトラッキングアルゴリズムは本質的に深さ優先探索（DFS）アルゴリズムの一種であり、条件を満たす解を見つけるまであらゆる可能な解を試みます。この方法の利点は、すべての可能な解を見つけられる点であり、適切な枝刈りを行えば効率が高いことです。</p> <p>しかし、大規模または複雑な問題を扱う場合、バックトラッキングアルゴリズムの実行効率は許容できないほど低下する可能性があります。</p> <ul> <li>時間：バックトラッキングアルゴリズムは通常、状態空間のすべての可能性を探索する必要があり、時間計算量は指数オーダーまたは階乗オーダーに達する可能性があります。</li> <li>空間：再帰呼び出し中に現在の状態（例：経路、枝刈り用の補助変数など）を保存する必要があり、深さが大きい場合、空間の使用量が増加します。</li> </ul> <p>それでもなお、バックトラッキングアルゴリズムは特定の探索問題や制約満足問題の最良の解法であることが多いです。これらの問題では、どの選択が有効な解を生成するかを予測できないため、すべての可能な選択を試す必要があります。このような場合、**効率の最適化が鍵**となります。一般的な最適化手法は次の 2 つです。</p> <ul> <li>枝刈り：解を生成しないことが確実な経路を避けることで、時間と空間を節約します。</li> <li>ヒューリスティック探索：探索中に戦略や評価値を導入し、有効な解を生成する可能性が高い経路を優先的に探索します。</li> </ul>","path":["第 13 章 &nbsp; バックトラッキング","13.1 &nbsp; バックトラッキングアルゴリズム"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/#1316","level":2,"title":"13.1.6   バックトラッキングの典型的な例題","text":"<p>バックトラッキングアルゴリズムは、多くの探索問題、制約満足問題、組合せ最適化問題を解くのに使用できます。</p> <p>探索問題：この種の問題の目標は、特定の条件を満たす解を見つけることです。</p> <ul> <li>全順列問題：与えられた集合のすべての可能な順列を求める。</li> <li>部分和問題：与えられた集合と目標和に対して、和が目標値になるすべての部分集合を求める。</li> <li>ハノイの塔：3 本の柱と異なるサイズの円盤があり、すべての円盤を 1 本の柱から別の柱に移す。1 回に 1 枚しか動かせず、大きな円盤を小さい円盤の上に置くことはできない。</li> </ul> <p>制約満足問題：この種の問題の目標は、すべての制約条件を満たす解を見つけることです。</p> <ul> <li>\\(n\\) クイーン問題：\\(n imes n\\) のチェス盤に \\(n\\) 個のクイーンを配置し、互いに攻撃しないようにする。</li> <li>数独：\\(9 imes 9\\) のグリッドに数字 \\(1\\) ~ \\(9\\) を入力し、各行、列、\\(3 imes 3\\) のサブグリッドに重複がないようにする。</li> <li>グラフ彩色問題：与えられた無向グラフに対し、隣接頂点が異なる色になるように最小限の色で彩色する。</li> </ul> <p>組合せ最適化問題：この種の問題の目標は、組合せ空間内で特定の条件を満たす最適解を見つけることです。</p> <ul> <li>0-1 ナップサック問題：与えられた物品群とバックパックがあり、各物品には価値と重さが設定されている。バックパックの容量制限内で、総価値を最大化する物品の選択を求める。</li> <li>旅行セールスマン問題：グラフ上で、1 つの点から出発し、すべての他の点を 1 回ずつ訪問して出発点に戻る最短経路を求める。</li> <li>最大クリーク問題：与えられた無向グラフの中で、任意の 2 頂点間に辺が存在する最大の完全部分グラフを見つける。</li> </ul> <p>注意すべきは、多くの組合せ最適化問題に対して、バックトラッキングが最適解法ではないということです。</p> <ul> <li>0-1 ナップサック問題は、時間効率を高めるために動的計画法がよく使用されます。</li> <li>旅行セールスマン問題は有名な NP-Hard 問題であり、遺伝的アルゴリズムやアントコロニーアルゴリズムなどの手法がよく使われます。</li> <li>最大クリーク問題はグラフ理論の古典的な問題であり、貪欲法などのヒューリスティックアルゴリズムで解くことができます。</li> </ul>","path":["第 13 章 &nbsp; バックトラッキング","13.1 &nbsp; バックトラッキングアルゴリズム"],"tags":[]},{"location":"chapter_backtracking/n_queens_problem/","level":1,"title":"13.4   Nクイーン問題","text":"<p>Question</p> <p>チェスのルールによると、クイーンは同じ行、列、または対角線上の駒を攻撃できます。\\(n\\) 個のクイーンと \\(n \\times n\\) のチェスボードが与えられた場合、2つのクイーンが互いに攻撃できない配置を見つけてください。</p> <p>以下の図に示すように、\\(n = 4\\) の場合、2つの解があります。バックトラッキングアルゴリズムの観点から、\\(n \\times n\\) のチェスボードには \\(n^2\\) 個のマスがあり、すべての可能な選択肢 <code>choices</code> を示しています。チェスボードの状態 <code>state</code> は、各クイーンが配置されるにつれて継続的に変化します。</p> <p></p> <p> 図 13-15   4クイーン問題の解 </p> <p>以下の図は、この問題の3つの制約を示しています：複数のクイーンは同じ行、列、または対角線を占有できません。対角線は主対角線 <code>\\</code> と副対角線 <code>/</code> に分かれることに注意することが重要です。</p> <p></p> <p> 図 13-16   Nクイーン問題の制約 </p>","path":["第 13 章 &nbsp; バックトラッキング","13.4 &nbsp; Nクイーン問題"],"tags":[]},{"location":"chapter_backtracking/n_queens_problem/#1","level":3,"title":"1.   行ごとの配置戦略","text":"<p>クイーンの数がチェスボードの行数と等しく、どちらも \\(n\\) であるため、**チェスボードの各行には1つのクイーンのみが配置できることが**容易に結論付けられます。</p> <p>これは、行ごとの配置戦略を採用できることを意味します：最初の行から開始して、最後の行に到達するまで行ごとに1つのクイーンを配置します。</p> <p>以下の図は、4クイーン問題の行ごとの配置プロセスを示しています。スペースの制限により、図は最初の行の1つの検索分岐のみを展開し、列と対角線の制約を満たさない配置を剪定します。</p> <p></p> <p> 図 13-17   行ごとの配置戦略 </p> <p>本質的に、行ごとの配置戦略は剪定関数として機能し、同じ行に複数のクイーンを配置するすべての検索分岐を除去します。</p>","path":["第 13 章 &nbsp; バックトラッキング","13.4 &nbsp; Nクイーン問題"],"tags":[]},{"location":"chapter_backtracking/n_queens_problem/#2","level":3,"title":"2.   列と対角線の剪定","text":"<p>列の制約を満たすために、長さ \\(n\\) のブール配列 <code>cols</code> を使用して、各列にクイーンが占有されているかどうかを追跡できます。各配置決定の前に、<code>cols</code> を使用してすでにクイーンがある列を剪定し、バックトラッキング中に動的に更新されます。</p> <p>Tip</p> <p>行列の原点は左上隅にあり、行インデックスは上から下に増加し、列インデックスは左から右に増加することに注意してください。</p> <p>対角線の制約はどうでしょうか？チェスボード上の特定のセルの行と列のインデックスを \\((row, col)\\) とします。特定の主対角線を選択することで、その対角線上のすべてのセルで差 \\(row - col\\) が同じであることに気付きます。つまり、\\(row - col\\) は主対角線上で定数値です。</p> <p>言い換えると、2つのセルが \\(row_1 - col_1 = row_2 - col_2\\) を満たす場合、それらは確実に同じ主対角線上にあります。このパターンを使用して、以下の図に示す配列 <code>diags1</code> を利用して、クイーンが主対角線上にあるかどうかを追跡できます。</p> <p>同様に、\\(row + col\\) の和は副対角線上のすべてのセルで定数値です。配列 <code>diags2</code> を使用して副対角線の制約も処理できます。</p> <p></p> <p> 図 13-18   列と対角線の制約の処理 </p>","path":["第 13 章 &nbsp; バックトラッキング","13.4 &nbsp; Nクイーン問題"],"tags":[]},{"location":"chapter_backtracking/n_queens_problem/#3","level":3,"title":"3.   コード実装","text":"<p>\\(n\\) 次元の正方行列では、\\(row - col\\) の範囲は \\([-n + 1, n - 1]\\) で、\\(row + col\\) の範囲は \\([0, 2n - 2]\\) であることに注意してください。したがって、主対角線と副対角線の数はどちらも \\(2n - 1\\) で、配列 <code>diags1</code> と <code>diags2</code> の長さは \\(2n - 1\\) です。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby n_queens.py<pre><code>def backtrack(\n    row: int,\n    n: int,\n    state: list[list[str]],\n    res: list[list[list[str]]],\n    cols: list[bool],\n    diags1: list[bool],\n    diags2: list[bool],\n):\n    \"\"\"バックトラッキングアルゴリズム：n クイーン\"\"\"\n    # すべての行が配置されたら、解を記録\n    if row == n:\n        res.append([list(row) for row in state])\n        return\n    # すべての列を走査\n    for col in range(n):\n        # セルに対応する主対角線と副対角線を計算\n        diag1 = row - col + n - 1\n        diag2 = row + col\n        # 枝刈り：セルの列、主対角線、副対角線にクイーンを配置しない\n        if not cols[col] and not diags1[diag1] and not diags2[diag2]:\n            # 試行：セルにクイーンを配置\n            state[row][col] = \"Q\"\n            cols[col] = diags1[diag1] = diags2[diag2] = True\n            # 次の行を配置\n            backtrack(row + 1, n, state, res, cols, diags1, diags2)\n            # 撤回：セルを空のスポットに復元\n            state[row][col] = \"#\"\n            cols[col] = diags1[diag1] = diags2[diag2] = False\n\ndef n_queens(n: int) -&gt; list[list[list[str]]]:\n    \"\"\"n クイーンを解く\"\"\"\n    # n*n サイズのチェスボードを初期化、'Q' はクイーンを表し、'#' は空のスポットを表す\n    state = [[\"#\" for _ in range(n)] for _ in range(n)]\n    cols = [False] * n  # クイーンがある列を記録\n    diags1 = [False] * (2 * n - 1)  # クイーンがある主対角線を記録\n    diags2 = [False] * (2 * n - 1)  # クイーンがある副対角線を記録\n    res = []\n    backtrack(0, n, state, res, cols, diags1, diags2)\n\n    return res\n</code></pre> n_queens.cpp<pre><code>/* バックトラッキングアルゴリズム：n クイーン */\nvoid backtrack(int row, int n, vector&lt;vector&lt;string&gt;&gt; &amp;state, vector&lt;vector&lt;vector&lt;string&gt;&gt;&gt; &amp;res, vector&lt;bool&gt; &amp;cols,\n               vector&lt;bool&gt; &amp;diags1, vector&lt;bool&gt; &amp;diags2) {\n    // すべての行が配置されたら、解を記録\n    if (row == n) {\n        res.push_back(state);\n        return;\n    }\n    // すべての列を走査\n    for (int col = 0; col &lt; n; col++) {\n        // セルに対応する主対角線と副対角線を計算\n        int diag1 = row - col + n - 1;\n        int diag2 = row + col;\n        // 剪定：セルの列、主対角線、副対角線にクイーンを配置することを許可しない\n        if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n            // 試行：セルにクイーンを配置\n            state[row][col] = \"Q\";\n            cols[col] = diags1[diag1] = diags2[diag2] = true;\n            // 次の行を配置\n            backtrack(row + 1, n, state, res, cols, diags1, diags2);\n            // 回退：セルを空のスポットに復元\n            state[row][col] = \"#\";\n            cols[col] = diags1[diag1] = diags2[diag2] = false;\n        }\n    }\n}\n\n/* n クイーンを解く */\nvector&lt;vector&lt;vector&lt;string&gt;&gt;&gt; nQueens(int n) {\n    // n*n サイズのチェスボードを初期化、'Q' はクイーンを表し、'#' は空のスポットを表す\n    vector&lt;vector&lt;string&gt;&gt; state(n, vector&lt;string&gt;(n, \"#\"));\n    vector&lt;bool&gt; cols(n, false);           // クイーンのある列を記録\n    vector&lt;bool&gt; diags1(2 * n - 1, false); // クイーンのある主対角線を記録\n    vector&lt;bool&gt; diags2(2 * n - 1, false); // クイーンのある副対角線を記録\n    vector&lt;vector&lt;vector&lt;string&gt;&gt;&gt; res;\n\n    backtrack(0, n, state, res, cols, diags1, diags2);\n\n    return res;\n}\n</code></pre> n_queens.java<pre><code>/* バックトラッキングアルゴリズム：n クイーン */\nvoid backtrack(int row, int n, List&lt;List&lt;String&gt;&gt; state, List&lt;List&lt;List&lt;String&gt;&gt;&gt; res,\n        boolean[] cols, boolean[] diags1, boolean[] diags2) {\n    // すべての行が配置されたら、解を記録\n    if (row == n) {\n        List&lt;List&lt;String&gt;&gt; copyState = new ArrayList&lt;&gt;();\n        for (List&lt;String&gt; sRow : state) {\n            copyState.add(new ArrayList&lt;&gt;(sRow));\n        }\n        res.add(copyState);\n        return;\n    }\n    // すべての列を走査\n    for (int col = 0; col &lt; n; col++) {\n        // セルに対応する主対角線と副対角線を計算\n        int diag1 = row - col + n - 1;\n        int diag2 = row + col;\n        // 剪定：セルの列、主対角線、副対角線にクイーンを配置することを許可しない\n        if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n            // 試行：セルにクイーンを配置\n            state.get(row).set(col, \"Q\");\n            cols[col] = diags1[diag1] = diags2[diag2] = true;\n            // 次の行を配置\n            backtrack(row + 1, n, state, res, cols, diags1, diags2);\n            // 回退：セルを空のスポットに復元\n            state.get(row).set(col, \"#\");\n            cols[col] = diags1[diag1] = diags2[diag2] = false;\n        }\n    }\n}\n\n/* n クイーンを解く */\nList&lt;List&lt;List&lt;String&gt;&gt;&gt; nQueens(int n) {\n    // n*n サイズのチェスボードを初期化、'Q' はクイーンを表し、'#' は空のスポットを表す\n    List&lt;List&lt;String&gt;&gt; state = new ArrayList&lt;&gt;();\n    for (int i = 0; i &lt; n; i++) {\n        List&lt;String&gt; row = new ArrayList&lt;&gt;();\n        for (int j = 0; j &lt; n; j++) {\n            row.add(\"#\");\n        }\n        state.add(row);\n    }\n    boolean[] cols = new boolean[n]; // クイーンのある列を記録\n    boolean[] diags1 = new boolean[2 * n - 1]; // クイーンのある主対角線を記録\n    boolean[] diags2 = new boolean[2 * n - 1]; // クイーンのある副対角線を記録\n    List&lt;List&lt;List&lt;String&gt;&gt;&gt; res = new ArrayList&lt;&gt;();\n\n    backtrack(0, n, state, res, cols, diags1, diags2);\n\n    return res;\n}\n</code></pre> n_queens.cs<pre><code>[class]{n_queens}-[func]{Backtrack}\n\n[class]{n_queens}-[func]{NQueens}\n</code></pre> n_queens.go<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{nQueens}\n</code></pre> n_queens.swift<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{nQueens}\n</code></pre> n_queens.js<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{nQueens}\n</code></pre> n_queens.ts<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{nQueens}\n</code></pre> n_queens.dart<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{nQueens}\n</code></pre> n_queens.rs<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{n_queens}\n</code></pre> n_queens.c<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{nQueens}\n</code></pre> n_queens.kt<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{nQueens}\n</code></pre> n_queens.rb<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{n_queens}\n</code></pre> <p>\\(n\\) 個のクイーンを行ごとに配置し、列の制約を考慮して、最初の行から最後の行まで、\\(n\\)、\\(n-1\\)、\\(\\dots\\)、\\(2\\)、\\(1\\) の選択肢があり、\\(O(n!)\\) 時間を使用します。解を記録する際、行列 <code>state</code> をコピーして <code>res</code> に追加する必要があり、コピー操作は \\(O(n^2)\\) 時間を使用します。したがって、全体の時間計算量は \\(O(n! \\cdot n^2)\\) です。実際には、対角線制約に基づく剪定により検索空間を大幅に削減できるため、多くの場合、検索効率は上記の時間計算量よりも優れています。</p> <p>配列 <code>state</code> は \\(O(n^2)\\) 空間を使用し、配列 <code>cols</code>、<code>diags1</code>、<code>diags2</code> はそれぞれ \\(O(n)\\) 空間を使用します。最大再帰深度は \\(n\\) で、\\(O(n)\\) のスタックフレーム空間を使用します。したがって、空間計算量は \\(O(n^2)\\) です。</p>","path":["第 13 章 &nbsp; バックトラッキング","13.4 &nbsp; Nクイーン問題"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/","level":1,"title":"13.2   順列問題","text":"<p>順列問題は、バックトラッキングアルゴリズムの典型的な応用です。これは、配列や文字列などの与えられた集合から要素のすべての可能な配置（順列）を見つけることを含みます。</p> <p>以下の表は、入力配列とその対応する順列を含むいくつかの例を示しています。</p> <p> 表 13-2   順列の例 </p> 入力配列 順列 \\([1]\\) \\([1]\\) \\([1, 2]\\) \\([1, 2], [2, 1]\\) \\([1, 2, 3]\\) \\([1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]\\)","path":["第 13 章 &nbsp; バックトラッキング","13.2 &nbsp; 順列問題"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#1321","level":2,"title":"13.2.1   重複要素がない場合","text":"<p>Question</p> <p>重複要素のない整数配列が与えられた場合、すべての可能な順列を返してください。</p> <p>バックトラッキングの観点から、順列を生成するプロセスを一連の選択として見ることができます。 入力配列が \\([1, 2, 3]\\) だとします。最初に \\(1\\) を選択し、次に \\(3\\)、最後に \\(2\\) を選択すると、順列 \\([1, 3, 2]\\) が得られます。「バックトラッキング」は前の選択を取り消して、代替オプションを探索することを意味します。</p> <p>コーディングの観点から、候補集合 <code>choices</code> は入力配列のすべての要素で構成され、<code>state</code> はこれまでに選択された要素を保持します。各要素は一度だけ選択できるため、<code>state</code> のすべての要素は一意である必要があります。</p> <p>以下の図に示すように、検索プロセスを再帰木に展開できます。各ノードは現在の <code>state</code> を表します。ルートノードから開始して、3回の選択の後、葉ノードに到達します—それぞれが順列に対応します。</p> <p></p> <p> 図 13-5   順列の再帰木 </p>","path":["第 13 章 &nbsp; バックトラッキング","13.2 &nbsp; 順列問題"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#1","level":3,"title":"1.   重複選択の剪定","text":"<p>各要素が一度だけ選択されることを保証するために、ブール配列 <code>selected</code> を導入します。ここで <code>selected[i]</code> は <code>choices[i]</code> が選択されたかどうかを示します。次に、この配列に基づいて剪定ステップを実行します：</p> <ul> <li><code>choice[i]</code> を選択した後、<code>selected[i]</code> を \\(\\text{True}\\) に設定して選択されたとマークします。</li> <li><code>choices</code> を反復処理する際、選択されたとマークされたすべての要素をスキップします（つまり、それらの分岐を剪定します）。</li> </ul> <p>以下の図に示すように、最初のラウンドで1を選択し、2番目のラウンドで3を選択し、最後のラウンドで2を選択するとします。2番目のラウンドで要素1の分岐と、3番目のラウンドで要素1と3の分岐を剪定する必要があります。</p> <p></p> <p> 図 13-6   順列の剪定例 </p> <p>図から、この剪定プロセスが検索空間を \\(O(n^n)\\) から \\(O(n!)\\) に削減することがわかります。</p>","path":["第 13 章 &nbsp; バックトラッキング","13.2 &nbsp; 順列問題"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#2","level":3,"title":"2.   コード実装","text":"<p>この理解により、フレームワークコードの「空欄を埋める」ことができます。全体のコードを簡潔に保つため、フレームワークの各部分を個別に実装せず、代わりに <code>backtrack()</code> 関数ですべてを展開します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby permutations_i.py<pre><code>def backtrack(\n    state: list[int], choices: list[int], selected: list[bool], res: list[list[int]]\n):\n    \"\"\"バックトラッキングアルゴリズム：順列 I\"\"\"\n    # 状態の長さが要素数と等しいとき、解を記録\n    if len(state) == len(choices):\n        res.append(list(state))\n        return\n    # すべての選択肢を走査\n    for i, choice in enumerate(choices):\n        # 枝刈り：要素の重複選択を許可しない\n        if not selected[i]:\n            # 試行：選択を行い、状態を更新\n            selected[i] = True\n            state.append(choice)\n            # 次の選択ラウンドに進む\n            backtrack(state, choices, selected, res)\n            # 撤回：選択を取り消し、前の状態に復元\n            selected[i] = False\n            state.pop()\n\ndef permutations_i(nums: list[int]) -&gt; list[list[int]]:\n    \"\"\"順列 I\"\"\"\n    res = []\n    backtrack(state=[], choices=nums, selected=[False] * len(nums), res=res)\n    return res\n</code></pre> permutations_i.cpp<pre><code>/* バックトラッキングアルゴリズム：順列 I */\nvoid backtrack(vector&lt;int&gt; &amp;state, const vector&lt;int&gt; &amp;choices, vector&lt;bool&gt; &amp;selected, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n    // 状態の長さが要素数と等しくなったら、解を記録\n    if (state.size() == choices.size()) {\n        res.push_back(state);\n        return;\n    }\n    // すべての選択肢を走査\n    for (int i = 0; i &lt; choices.size(); i++) {\n        int choice = choices[i];\n        // 剪定：要素の重複選択を許可しない\n        if (!selected[i]) {\n            // 試行：選択を行い、状態を更新\n            selected[i] = true;\n            state.push_back(choice);\n            // 次のラウンドの選択に進む\n            backtrack(state, choices, selected, res);\n            // 回退：選択を取り消し、前の状態に復元\n            selected[i] = false;\n            state.pop_back();\n        }\n    }\n}\n\n/* 順列 I */\nvector&lt;vector&lt;int&gt;&gt; permutationsI(vector&lt;int&gt; nums) {\n    vector&lt;int&gt; state;\n    vector&lt;bool&gt; selected(nums.size(), false);\n    vector&lt;vector&lt;int&gt;&gt; res;\n    backtrack(state, nums, selected, res);\n    return res;\n}\n</code></pre> permutations_i.java<pre><code>/* バックトラッキングアルゴリズム：順列 I */\nvoid backtrack(List&lt;Integer&gt; state, int[] choices, boolean[] selected, List&lt;List&lt;Integer&gt;&gt; res) {\n    // 状態の長さが要素数と等しくなったら、解を記録\n    if (state.size() == choices.length) {\n        res.add(new ArrayList&lt;Integer&gt;(state));\n        return;\n    }\n    // すべての選択肢を走査\n    for (int i = 0; i &lt; choices.length; i++) {\n        int choice = choices[i];\n        // 剪定：要素の重複選択を許可しない\n        if (!selected[i]) {\n            // 試行：選択を行い、状態を更新\n            selected[i] = true;\n            state.add(choice);\n            // 次のラウンドの選択に進む\n            backtrack(state, choices, selected, res);\n            // 回退：選択を取り消し、前の状態に復元\n            selected[i] = false;\n            state.remove(state.size() - 1);\n        }\n    }\n}\n\n/* 順列 I */\nList&lt;List&lt;Integer&gt;&gt; permutationsI(int[] nums) {\n    List&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;List&lt;Integer&gt;&gt;();\n    backtrack(new ArrayList&lt;Integer&gt;(), nums, new boolean[nums.length], res);\n    return res;\n}\n</code></pre> permutations_i.cs<pre><code>[class]{permutations_i}-[func]{Backtrack}\n\n[class]{permutations_i}-[func]{PermutationsI}\n</code></pre> permutations_i.go<pre><code>[class]{}-[func]{backtrackI}\n\n[class]{}-[func]{permutationsI}\n</code></pre> permutations_i.swift<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsI}\n</code></pre> permutations_i.js<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsI}\n</code></pre> permutations_i.ts<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsI}\n</code></pre> permutations_i.dart<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsI}\n</code></pre> permutations_i.rs<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutations_i}\n</code></pre> permutations_i.c<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsI}\n</code></pre> permutations_i.kt<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsI}\n</code></pre> permutations_i.rb<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutations_i}\n</code></pre>","path":["第 13 章 &nbsp; バックトラッキング","13.2 &nbsp; 順列問題"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#1322","level":2,"title":"13.2.2   重複要素を考慮する場合","text":"<p>Question</p> <p>**重複要素を含む可能性のある**整数配列が与えられた場合、すべての一意の順列を返してください。</p> <p>入力配列が \\([1, 1, 2]\\) だとします。2つの同一要素 \\(1\\) を区別するために、2番目を \\(\\hat{1}\\) とラベル付けします。</p> <p>以下の図に示すように、この方法で生成される順列の半分は重複です：</p> <p></p> <p> 図 13-7   重複順列 </p> <p>では、これらの重複順列をどのように除去できるでしょうか？一つの直接的なアプローチは、すべての順列を生成した後にハッシュセットを使用して重複を除去することです。しかし、これはあまり優雅ではありません。重複を生成する分岐は本来不要であり、事前に剪定されるべきだからです、これによりアルゴリズムの効率が向上します。</p>","path":["第 13 章 &nbsp; バックトラッキング","13.2 &nbsp; 順列問題"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#1_1","level":3,"title":"1.   等値要素の剪定","text":"<p>以下の図を見ると、最初のラウンドで \\(1\\) または \\(\\hat{1}\\) を選択すると同じ順列につながるため、\\(\\hat{1}\\) を剪定します。</p> <p>同様に、最初のラウンドで \\(2\\) を選択した後、2番目のラウンドで \\(1\\) または \\(\\hat{1}\\) を選択しても重複分岐につながるため、その時も \\(\\hat{1}\\) を剪定します。</p> <p>本質的に、私たちの目標は、複数の同一要素が選択の各ラウンドで一度だけ選択されることを保証することです。</p> <p></p> <p> 図 13-8   重複順列の剪定 </p>","path":["第 13 章 &nbsp; バックトラッキング","13.2 &nbsp; 順列問題"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#2_1","level":3,"title":"2.   コード実装","text":"<p>前の問題のコードに基づいて、各ラウンドでハッシュセット <code>duplicated</code> を導入します。このセットは、すでに試行した要素を追跡し、重複を剪定できるようにします：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby permutations_ii.py<pre><code>def backtrack(\n    state: list[int], choices: list[int], selected: list[bool], res: list[list[int]]\n):\n    \"\"\"バックトラッキングアルゴリズム：順列 II\"\"\"\n    # 状態の長さが要素数と等しいとき、解を記録\n    if len(state) == len(choices):\n        res.append(list(state))\n        return\n    # すべての選択肢を走査\n    duplicated = set[int]()\n    for i, choice in enumerate(choices):\n        # 枝刈り：要素の重複選択を許可せず、等しい要素の重複選択も許可しない\n        if not selected[i] and choice not in duplicated:\n            # 試行：選択を行い、状態を更新\n            duplicated.add(choice)  # 選択された要素値を記録\n            selected[i] = True\n            state.append(choice)\n            # 次の選択ラウンドに進む\n            backtrack(state, choices, selected, res)\n            # 撤回：選択を取り消し、前の状態に復元\n            selected[i] = False\n            state.pop()\n\ndef permutations_ii(nums: list[int]) -&gt; list[list[int]]:\n    \"\"\"順列 II\"\"\"\n    res = []\n    backtrack(state=[], choices=nums, selected=[False] * len(nums), res=res)\n    return res\n</code></pre> permutations_ii.cpp<pre><code>/* バックトラッキングアルゴリズム：順列 II */\nvoid backtrack(vector&lt;int&gt; &amp;state, const vector&lt;int&gt; &amp;choices, vector&lt;bool&gt; &amp;selected, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n    // 状態の長さが要素数と等しくなったら、解を記録\n    if (state.size() == choices.size()) {\n        res.push_back(state);\n        return;\n    }\n    // すべての選択肢を走査\n    unordered_set&lt;int&gt; duplicated;\n    for (int i = 0; i &lt; choices.size(); i++) {\n        int choice = choices[i];\n        // 剪定：要素の重複選択を許可せず、等しい要素の重複選択も許可しない\n        if (!selected[i] &amp;&amp; duplicated.find(choice) == duplicated.end()) {\n            // 試行：選択を行い、状態を更新\n            duplicated.emplace(choice); // 選択された要素値を記録\n            selected[i] = true;\n            state.push_back(choice);\n            // 次のラウンドの選択に進む\n            backtrack(state, choices, selected, res);\n            // 回退：選択を取り消し、前の状態に復元\n            selected[i] = false;\n            state.pop_back();\n        }\n    }\n}\n\n/* 順列 II */\nvector&lt;vector&lt;int&gt;&gt; permutationsII(vector&lt;int&gt; nums) {\n    vector&lt;int&gt; state;\n    vector&lt;bool&gt; selected(nums.size(), false);\n    vector&lt;vector&lt;int&gt;&gt; res;\n    backtrack(state, nums, selected, res);\n    return res;\n}\n</code></pre> permutations_ii.java<pre><code>/* バックトラッキングアルゴリズム：順列 II */\nvoid backtrack(List&lt;Integer&gt; state, int[] choices, boolean[] selected, List&lt;List&lt;Integer&gt;&gt; res) {\n    // 状態の長さが要素数と等しくなったら、解を記録\n    if (state.size() == choices.length) {\n        res.add(new ArrayList&lt;Integer&gt;(state));\n        return;\n    }\n    // すべての選択肢を走査\n    Set&lt;Integer&gt; duplicated = new HashSet&lt;Integer&gt;();\n    for (int i = 0; i &lt; choices.length; i++) {\n        int choice = choices[i];\n        // 剪定：要素の重複選択を許可せず、等しい要素の重複選択も許可しない\n        if (!selected[i] &amp;&amp; !duplicated.contains(choice)) {\n            // 試行：選択を行い、状態を更新\n            duplicated.add(choice); // 選択された要素値を記録\n            selected[i] = true;\n            state.add(choice);\n            // 次のラウンドの選択に進む\n            backtrack(state, choices, selected, res);\n            // 回退：選択を取り消し、前の状態に復元\n            selected[i] = false;\n            state.remove(state.size() - 1);\n        }\n    }\n}\n\n/* 順列 II */\nList&lt;List&lt;Integer&gt;&gt; permutationsII(int[] nums) {\n    List&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;List&lt;Integer&gt;&gt;();\n    backtrack(new ArrayList&lt;Integer&gt;(), nums, new boolean[nums.length], res);\n    return res;\n}\n</code></pre> permutations_ii.cs<pre><code>[class]{permutations_ii}-[func]{Backtrack}\n\n[class]{permutations_ii}-[func]{PermutationsII}\n</code></pre> permutations_ii.go<pre><code>[class]{}-[func]{backtrackII}\n\n[class]{}-[func]{permutationsII}\n</code></pre> permutations_ii.swift<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsII}\n</code></pre> permutations_ii.js<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsII}\n</code></pre> permutations_ii.ts<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsII}\n</code></pre> permutations_ii.dart<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsII}\n</code></pre> permutations_ii.rs<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutations_ii}\n</code></pre> permutations_ii.c<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsII}\n</code></pre> permutations_ii.kt<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsII}\n</code></pre> permutations_ii.rb<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutations_ii}\n</code></pre> <p>すべての要素が異なると仮定すると、\\(n\\) 個の要素の順列は \\(n!\\) （階乗）個あります。各結果を記録するには長さ \\(n\\) のリストをコピーする必要があり、これには \\(O(n)\\) 時間がかかります。したがって、総時間計算量は \\(O(n!n)\\) です。</p> <p>最大再帰深度は \\(n\\) で、\\(O(n)\\) のスタック空間を使用します。<code>selected</code> 配列も \\(O(n)\\) 空間が必要です。一度に最大 \\(n\\) 個の個別の <code>duplicated</code> セットが存在する可能性があるため、それらは集合的に \\(O(n^2)\\) 空間を占有します。したがって、空間計算量は \\(O(n^2)\\) です。</p>","path":["第 13 章 &nbsp; バックトラッキング","13.2 &nbsp; 順列問題"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#3-2","level":3,"title":"3.   2つの剪定方法の比較","text":"<p><code>selected</code> と <code>duplicated</code> はどちらも剪定メカニズムとして機能しますが、異なる問題をターゲットにしています：</p> <ul> <li>重複選択の剪定（<code>selected</code> 経由）：検索全体に単一の <code>selected</code> 配列があり、現在の状態にすでにある要素を示します。これにより、同じ要素が <code>state</code> に複数回現れることを防ぎます。</li> <li>等値要素の剪定（<code>duplicated</code> 経由）：<code>backtrack</code> 関数の各呼び出しは独自の <code>duplicated</code> セットを使用し、その特定の反復（<code>for</code> ループ）ですでに選択された要素を記録します。これにより、等しい要素が選択の各ラウンドで一度だけ選択されることを保証します。</li> </ul> <p>以下の図は、これら2つの剪定戦略の範囲を示しています。木の各ノードは選択を表します。ルートから任意の葉への経路は、1つの完全な順列に対応します。</p> <p></p> <p> 図 13-9   2つの剪定条件の範囲 </p>","path":["第 13 章 &nbsp; バックトラッキング","13.2 &nbsp; 順列問題"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/","level":1,"title":"13.3   部分集合和問題","text":"","path":["第 13 章 &nbsp; バックトラッキング","13.3 &nbsp; 部分集合和問題"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#1331","level":2,"title":"13.3.1   重複要素がない場合","text":"<p>Question</p> <p>正の整数の配列 <code>nums</code> とターゲット正整数 <code>target</code> が与えられた場合、組み合わせ内の要素の和が <code>target</code> に等しくなるようなすべての可能な組み合わせを見つけてください。与えられた配列には重複要素がなく、各要素は複数回選択できます。これらの組み合わせを重複する組み合わせを含まないリストとして返してください。</p> <p>例えば、入力集合 \\(\\{3, 4, 5\\}\\) とターゲット整数 \\(9\\) の場合、解は \\(\\{3, 3, 3\\}, \\{4, 5\\}\\) です。以下の2点に注意してください。</p> <ul> <li>入力集合の要素は無制限に選択できます。</li> <li>部分集合は要素の順序を区別しません。例えば \\(\\{4, 5\\}\\) と \\(\\{5, 4\\}\\) は同じ部分集合です。</li> </ul>","path":["第 13 章 &nbsp; バックトラッキング","13.3 &nbsp; 部分集合和問題"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#1","level":3,"title":"1.   順列解法の参考","text":"<p>順列問題と同様に、部分集合の生成を一連の選択として想像でき、選択プロセス中に「要素和」をリアルタイムで更新できます。要素和が <code>target</code> に等しくなったとき、部分集合を結果リストに記録します。</p> <p>順列問題とは異なり、この問題では要素は無制限に選択できるため、要素が選択されたかどうかを記録するための <code>selected</code> ブール配列を使用する必要がありません。順列コードに軽微な修正を加えて、最初に問題を解決できます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby subset_sum_i_naive.py<pre><code>def backtrack(\n    state: list[int],\n    target: int,\n    total: int,\n    choices: list[int],\n    res: list[list[int]],\n):\n    \"\"\"バックトラッキングアルゴリズム：部分集合の和 I\"\"\"\n    # 部分集合の和が target と等しいとき、解を記録\n    if total == target:\n        res.append(list(state))\n        return\n    # すべての選択肢を走査\n    for i in range(len(choices)):\n        # 枝刈り：部分集合の和が target を超える場合、その選択をスキップ\n        if total + choices[i] &gt; target:\n            continue\n        # 試行：選択を行い、要素と total を更新\n        state.append(choices[i])\n        # 次の選択ラウンドに進む\n        backtrack(state, target, total + choices[i], choices, res)\n        # 撤回：選択を取り消し、前の状態に復元\n        state.pop()\n\ndef subset_sum_i_naive(nums: list[int], target: int) -&gt; list[list[int]]:\n    \"\"\"部分集合の和 I を解く（重複する部分集合を含む）\"\"\"\n    state = []  # 状態（部分集合）\n    total = 0  # 部分集合の和\n    res = []  # 結果リスト（部分集合リスト）\n    backtrack(state, target, total, nums, res)\n    return res\n</code></pre> subset_sum_i_naive.cpp<pre><code>/* バックトラッキングアルゴリズム：部分集合和 I */\nvoid backtrack(vector&lt;int&gt; &amp;state, int target, int total, vector&lt;int&gt; &amp;choices, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n    // 部分集合の和がtargetと等しいとき、解を記録\n    if (total == target) {\n        res.push_back(state);\n        return;\n    }\n    // すべての選択肢を走査\n    for (int i = 0; i &lt; choices.size(); i++) {\n        // 剪定：部分集合の和がtargetを超えた場合、その選択をスキップ\n        if (total + choices[i] &gt; target) {\n            continue;\n        }\n        // 試行：選択を行い、要素とtotalを更新\n        state.push_back(choices[i]);\n        // 次のラウンドの選択に進む\n        backtrack(state, target, total + choices[i], choices, res);\n        // 回退：選択を取り消し、前の状態に復元\n        state.pop_back();\n    }\n}\n\n/* 部分集合和 I を解く（重複する部分集合を含む） */\nvector&lt;vector&lt;int&gt;&gt; subsetSumINaive(vector&lt;int&gt; nums, int target) {\n    vector&lt;int&gt; state;       // 状態（部分集合）\n    int total = 0;           // 部分集合の和\n    vector&lt;vector&lt;int&gt;&gt; res; // 結果リスト（部分集合リスト）\n    backtrack(state, target, total, nums, res);\n    return res;\n}\n</code></pre> subset_sum_i_naive.java<pre><code>/* バックトラッキングアルゴリズム：部分集合和 I */\nvoid backtrack(List&lt;Integer&gt; state, int target, int total, int[] choices, List&lt;List&lt;Integer&gt;&gt; res) {\n    // 部分集合の和がtargetと等しいとき、解を記録\n    if (total == target) {\n        res.add(new ArrayList&lt;&gt;(state));\n        return;\n    }\n    // すべての選択肢を走査\n    for (int i = 0; i &lt; choices.length; i++) {\n        // 剪定：部分集合の和がtargetを超えた場合、その選択をスキップ\n        if (total + choices[i] &gt; target) {\n            continue;\n        }\n        // 試行：選択を行い、要素とtotalを更新\n        state.add(choices[i]);\n        // 次のラウンドの選択に進む\n        backtrack(state, target, total + choices[i], choices, res);\n        // 回退：選択を取り消し、前の状態に復元\n        state.remove(state.size() - 1);\n    }\n}\n\n/* 部分集合和 I を解く（重複する部分集合を含む） */\nList&lt;List&lt;Integer&gt;&gt; subsetSumINaive(int[] nums, int target) {\n    List&lt;Integer&gt; state = new ArrayList&lt;&gt;(); // 状態（部分集合）\n    int total = 0; // 部分集合の和\n    List&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;&gt;(); // 結果リスト（部分集合リスト）\n    backtrack(state, target, total, nums, res);\n    return res;\n}\n</code></pre> subset_sum_i_naive.cs<pre><code>[class]{subset_sum_i_naive}-[func]{Backtrack}\n\n[class]{subset_sum_i_naive}-[func]{SubsetSumINaive}\n</code></pre> subset_sum_i_naive.go<pre><code>[class]{}-[func]{backtrackSubsetSumINaive}\n\n[class]{}-[func]{subsetSumINaive}\n</code></pre> subset_sum_i_naive.swift<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumINaive}\n</code></pre> subset_sum_i_naive.js<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumINaive}\n</code></pre> subset_sum_i_naive.ts<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumINaive}\n</code></pre> subset_sum_i_naive.dart<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumINaive}\n</code></pre> subset_sum_i_naive.rs<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subset_sum_i_naive}\n</code></pre> subset_sum_i_naive.c<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumINaive}\n</code></pre> subset_sum_i_naive.kt<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumINaive}\n</code></pre> subset_sum_i_naive.rb<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subset_sum_i_naive}\n</code></pre> <p>配列 \\([3, 4, 5]\\) とターゲット要素 \\(9\\) を上記のコードに入力すると、結果 \\([3, 3, 3], [4, 5], [5, 4]\\) が得られます。和が \\(9\\) のすべての部分集合を正常に見つけましたが、重複する部分集合 \\([4, 5]\\) と \\([5, 4]\\) が含まれています。</p> <p>これは、検索プロセスが選択の順序を区別するためですが、部分集合は選択順序を区別しません。以下の図に示すように、\\(5\\) の前に \\(4\\) を選択することと \\(4\\) の前に \\(5\\) を選択することは異なる分岐ですが、同じ部分集合に対応します。</p> <p></p> <p> 図 13-10   部分集合の検索と境界外の剪定 </p> <p>重複する部分集合を除去するために、直接的なアイデアは結果リストを重複除去することです。しかし、この方法は2つの理由で非常に非効率的です。</p> <ul> <li>配列要素が多い場合、特に <code>target</code> が大きい場合、検索プロセスで大量の重複する部分集合が生成されます。</li> <li>部分集合（配列）の差異を比較することは非常に時間がかかり、まず配列をソートし、次に配列の各要素の差異を比較する必要があります。</li> </ul>","path":["第 13 章 &nbsp; バックトラッキング","13.3 &nbsp; 部分集合和問題"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#2","level":3,"title":"2.   重複部分集合の剪定","text":"<p>剪定を通じて検索プロセス中に重複除去を検討します。以下の図を観察すると、異なる順序で配列要素を選択するときに重複する部分集合が生成されます。例えば、以下の状況です。</p> <ol> <li>最初のラウンドで \\(3\\) を選択し、2番目のラウンドで \\(4\\) を選択すると、これら2つの要素を含むすべての部分集合が生成され、\\([3, 4, \\dots]\\) と表記されます。</li> <li>後で、最初のラウンドで \\(4\\) が選択されたとき、2番目のラウンドは \\(3\\) をスキップすべきです。この選択によって生成される部分集合 \\([4, 3, \\dots]\\) はステップ <code>1.</code> の部分集合と完全に重複するからです。</li> </ol> <p>検索プロセスでは、各層の選択が左から右に一つずつ試行されるため、右側の分岐ほどより多く剪定されます。</p> <ol> <li>最初の2ラウンドで \\(3\\) と \\(5\\) を選択し、部分集合 \\([3, 5, \\dots]\\) を生成します。</li> <li>最初の2ラウンドで \\(4\\) と \\(5\\) を選択し、部分集合 \\([4, 5, \\dots]\\) を生成します。</li> <li>最初のラウンドで \\(5\\) が選択された場合、2番目のラウンドは \\(3\\) と \\(4\\) をスキップすべきです。部分集合 \\([5, 3, \\dots]\\) と \\([5, 4, \\dots]\\) はステップ <code>1.</code> と <code>2.</code> で記述された部分集合と完全に重複するからです。</li> </ol> <p></p> <p> 図 13-11   異なる選択順序による重複部分集合 </p> <p>要約すると、入力配列 \\([x_1, x_2, \\dots, x_n]\\) が与えられた場合、検索プロセスでの選択シーケンスは \\([x_{i_1}, x_{i_2}, \\dots, x_{i_m}]\\) であるべきで、\\(i_1 \\leq i_2 \\leq \\dots \\leq i_m\\) を満たす必要があります。この条件を満たさない選択シーケンスは重複を引き起こし、剪定されるべきです。</p>","path":["第 13 章 &nbsp; バックトラッキング","13.3 &nbsp; 部分集合和問題"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#3","level":3,"title":"3.   コード実装","text":"<p>この剪定を実装するために、変数 <code>start</code> を初期化し、これは走査の開始点を示します。選択 \\(x_{i}\\) を行った後、次のラウンドをインデックス \\(i\\) から開始するように設定します。これにより、選択シーケンスが \\(i_1 \\leq i_2 \\leq \\dots \\leq i_m\\) を満たすことが保証され、部分集合の一意性が保証されます。</p> <p>さらに、コードに以下の2つの最適化を行いました。</p> <ul> <li>検索を開始する前に、配列 <code>nums</code> をソートします。すべての選択の走査で、部分集合和が <code>target</code> を超えたときにループを直接終了します。後続の要素はより大きく、それらの部分集合和は確実に <code>target</code> を超えるからです。</li> <li>要素和変数 <code>total</code> を除去し、<code>target</code> に対して減算を実行して要素和をカウントします。<code>target</code> が \\(0\\) に等しくなったとき、解を記録します。</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby subset_sum_i.py<pre><code>def backtrack(\n    state: list[int], target: int, choices: list[int], start: int, res: list[list[int]]\n):\n    \"\"\"バックトラッキングアルゴリズム：部分集合の和 I\"\"\"\n    # 部分集合の和が target と等しいとき、解を記録\n    if target == 0:\n        res.append(list(state))\n        return\n    # すべての選択肢を走査\n    # 枝刈り二：start から走査を開始して重複する部分集合の生成を避ける\n    for i in range(start, len(choices)):\n        # 枝刈り一：部分集合の和が target を超える場合、直ちにループを終了\n        # これは配列がソートされており、後の要素がより大きいため、部分集合の和は必ず target を超えるため\n        if target - choices[i] &lt; 0:\n            break\n        # 試行：選択を行い、target、start を更新\n        state.append(choices[i])\n        # 次の選択ラウンドに進む\n        backtrack(state, target - choices[i], choices, i, res)\n        # 撤回：選択を取り消し、前の状態に復元\n        state.pop()\n\ndef subset_sum_i(nums: list[int], target: int) -&gt; list[list[int]]:\n    \"\"\"部分集合の和 I を解く\"\"\"\n    state = []  # 状態（部分集合）\n    nums.sort()  # nums をソート\n    start = 0  # 走査の開始点\n    res = []  # 結果リスト（部分集合リスト）\n    backtrack(state, target, nums, start, res)\n    return res\n</code></pre> subset_sum_i.cpp<pre><code>/* バックトラッキングアルゴリズム：部分集合和 I */\nvoid backtrack(vector&lt;int&gt; &amp;state, int target, vector&lt;int&gt; &amp;choices, int start, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n    // 部分集合の和がtargetと等しいとき、解を記録\n    if (target == 0) {\n        res.push_back(state);\n        return;\n    }\n    // すべての選択肢を走査\n    // 剪定二：startから走査を開始し、重複する部分集合の生成を回避\n    for (int i = start; i &lt; choices.size(); i++) {\n        // 剪定一：部分集合の和がtargetを超えた場合、即座にループを終了\n        // 配列がソートされているため、後の要素はさらに大きく、部分集合の和は必ずtargetを超える\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // 試行：選択を行い、target、startを更新\n        state.push_back(choices[i]);\n        // 次のラウンドの選択に進む\n        backtrack(state, target - choices[i], choices, i, res);\n        // 回退：選択を取り消し、前の状態に復元\n        state.pop_back();\n    }\n}\n\n/* 部分集合和 I を解く */\nvector&lt;vector&lt;int&gt;&gt; subsetSumI(vector&lt;int&gt; nums, int target) {\n    vector&lt;int&gt; state;              // 状態（部分集合）\n    sort(nums.begin(), nums.end()); // nums をソート\n    int start = 0;                  // 走査の開始点\n    vector&lt;vector&lt;int&gt;&gt; res;        // 結果リスト（部分集合リスト）\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_i.java<pre><code>/* バックトラッキングアルゴリズム：部分集合和 I */\nvoid backtrack(List&lt;Integer&gt; state, int target, int[] choices, int start, List&lt;List&lt;Integer&gt;&gt; res) {\n    // 部分集合の和がtargetと等しいとき、解を記録\n    if (target == 0) {\n        res.add(new ArrayList&lt;&gt;(state));\n        return;\n    }\n    // すべての選択肢を走査\n    // 剪定二：startから走査を開始し、重複する部分集合の生成を回避\n    for (int i = start; i &lt; choices.length; i++) {\n        // 剪定一：部分集合の和がtargetを超えた場合、即座にループを終了\n        // 配列がソートされているため、後の要素はさらに大きく、部分集合の和は必ずtargetを超える\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // 試行：選択を行い、target、startを更新\n        state.add(choices[i]);\n        // 次のラウンドの選択に進む\n        backtrack(state, target - choices[i], choices, i, res);\n        // 回退：選択を取り消し、前の状態に復元\n        state.remove(state.size() - 1);\n    }\n}\n\n/* 部分集合和 I を解く */\nList&lt;List&lt;Integer&gt;&gt; subsetSumI(int[] nums, int target) {\n    List&lt;Integer&gt; state = new ArrayList&lt;&gt;(); // 状態（部分集合）\n    Arrays.sort(nums); // nums をソート\n    int start = 0; // 走査の開始点\n    List&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;&gt;(); // 結果リスト（部分集合リスト）\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_i.cs<pre><code>[class]{subset_sum_i}-[func]{Backtrack}\n\n[class]{subset_sum_i}-[func]{SubsetSumI}\n</code></pre> subset_sum_i.go<pre><code>[class]{}-[func]{backtrackSubsetSumI}\n\n[class]{}-[func]{subsetSumI}\n</code></pre> subset_sum_i.swift<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumI}\n</code></pre> subset_sum_i.js<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumI}\n</code></pre> subset_sum_i.ts<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumI}\n</code></pre> subset_sum_i.dart<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumI}\n</code></pre> subset_sum_i.rs<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subset_sum_i}\n</code></pre> subset_sum_i.c<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumI}\n</code></pre> subset_sum_i.kt<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumI}\n</code></pre> subset_sum_i.rb<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subset_sum_i}\n</code></pre> <p>以下の図は、配列 \\([3, 4, 5]\\) とターゲット要素 \\(9\\) を上記のコードに入力した後の全体的なバックトラッキングプロセスを示しています。</p> <p></p> <p> 図 13-12   部分集合和 I のバックトラッキングプロセス </p>","path":["第 13 章 &nbsp; バックトラッキング","13.3 &nbsp; 部分集合和問題"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#1332","level":2,"title":"13.3.2   重複要素がある場合を考慮","text":"<p>Question</p> <p>正の整数の配列 <code>nums</code> とターゲット正整数 <code>target</code> が与えられた場合、組み合わせ内の要素の和が <code>target</code> に等しくなるようなすべての可能な組み合わせを見つけてください。与えられた配列には重複要素が含まれる可能性があり、各要素は一度だけ選択できます。これらの組み合わせを重複する組み合わせを含まないリストとして返してください。</p> <p>前の問題と比較して、この問題の入力配列には重複要素が含まれる可能性があり、新しい問題が導入されます。例えば、配列 \\([4, \\hat{4}, 5]\\) とターゲット要素 \\(9\\) が与えられた場合、既存のコードの出力結果は \\([4, 5], [\\hat{4}, 5]\\) となり、重複する部分集合が生成されます。</p> <p>この重複の理由は、特定のラウンドで等しい要素が複数回選択されることです。以下の図では、最初のラウンドに3つの選択肢があり、そのうち2つが \\(4\\) であり、2つの重複する検索分岐を生成し、重複する部分集合を出力します。同様に、2番目のラウンドの2つの \\(4\\) も重複する部分集合を生成します。</p> <p></p> <p> 図 13-13   等しい要素による重複部分集合 </p>","path":["第 13 章 &nbsp; バックトラッキング","13.3 &nbsp; 部分集合和問題"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#1_1","level":3,"title":"1.   等値要素の剪定","text":"<p>この問題を解決するために、等しい要素がラウンドごとに一度だけ選択されるように制限する必要があります。実装は非常に巧妙です：配列がソートされているため、等しい要素は隣接しています。これは、特定のラウンドの選択で、現在の要素がその左側の要素と等しい場合、それはすでに選択されていることを意味するため、現在の要素を直接スキップします。</p> <p>同時に、この問題では各配列要素は一度だけ選択できると規定されています。幸い、変数 <code>start</code> を使用してこの制約も満たすことができます：選択 \\(x_{i}\\) を行った後、次のラウンドをインデックス \\(i + 1\\) から前方に開始するように設定します。これにより、重複する部分集合が除去されるだけでなく、要素の重複選択も回避されます。</p>","path":["第 13 章 &nbsp; バックトラッキング","13.3 &nbsp; 部分集合和問題"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#2_1","level":3,"title":"2.   コード実装","text":"PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby subset_sum_ii.py<pre><code>def backtrack(\n    state: list[int], target: int, choices: list[int], start: int, res: list[list[int]]\n):\n    \"\"\"バックトラッキングアルゴリズム：部分集合の和 II\"\"\"\n    # 部分集合の和が target と等しいとき、解を記録\n    if target == 0:\n        res.append(list(state))\n        return\n    # すべての選択肢を走査\n    # 枝刈り二：start から走査を開始して重複する部分集合の生成を避ける\n    # 枝刈り三：start から走査を開始して同じ要素の重複選択を避ける\n    for i in range(start, len(choices)):\n        # 枝刈り一：部分集合の和が target を超える場合、直ちにループを終了\n        # これは配列がソートされており、後の要素がより大きいため、部分集合の和は必ず target を超えるため\n        if target - choices[i] &lt; 0:\n            break\n        # 枝刈り四：要素が左の要素と等しい場合、検索分岐が重複していることを示すため、スキップ\n        if i &gt; start and choices[i] == choices[i - 1]:\n            continue\n        # 試行：選択を行い、target、start を更新\n        state.append(choices[i])\n        # 次の選択ラウンドに進む\n        backtrack(state, target - choices[i], choices, i + 1, res)\n        # 撤回：選択を取り消し、前の状態に復元\n        state.pop()\n\ndef subset_sum_ii(nums: list[int], target: int) -&gt; list[list[int]]:\n    \"\"\"部分集合の和 II を解く\"\"\"\n    state = []  # 状態（部分集合）\n    nums.sort()  # nums をソート\n    start = 0  # 走査の開始点\n    res = []  # 結果リスト（部分集合リスト）\n    backtrack(state, target, nums, start, res)\n    return res\n</code></pre> subset_sum_ii.cpp<pre><code>/* バックトラッキングアルゴリズム：部分集合和 II */\nvoid backtrack(vector&lt;int&gt; &amp;state, int target, vector&lt;int&gt; &amp;choices, int start, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n    // 部分集合の和がtargetと等しいとき、解を記録\n    if (target == 0) {\n        res.push_back(state);\n        return;\n    }\n    // すべての選択肢を走査\n    // 剪定二：startから走査を開始し、重複する部分集合の生成を回避\n    // 剪定三：startから走査を開始し、同じ要素の繰り返し選択を回避\n    for (int i = start; i &lt; choices.size(); i++) {\n        // 剪定一：部分集合の和がtargetを超えた場合、即座にループを終了\n        // 配列がソートされているため、後の要素はさらに大きく、部分集合の和は必ずtargetを超える\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // 剪定四：要素が左の要素と等しい場合、検索ブランチの重複を示すのでスキップ\n        if (i &gt; start &amp;&amp; choices[i] == choices[i - 1]) {\n            continue;\n        }\n        // 試行：選択を行い、target、startを更新\n        state.push_back(choices[i]);\n        // 次のラウンドの選択に進む\n        backtrack(state, target - choices[i], choices, i + 1, res);\n        // 回退：選択を取り消し、前の状態に復元\n        state.pop_back();\n    }\n}\n\n/* 部分集合和 II を解く */\nvector&lt;vector&lt;int&gt;&gt; subsetSumII(vector&lt;int&gt; nums, int target) {\n    vector&lt;int&gt; state;              // 状態（部分集合）\n    sort(nums.begin(), nums.end()); // nums をソート\n    int start = 0;                  // 走査の開始点\n    vector&lt;vector&lt;int&gt;&gt; res;        // 結果リスト（部分集合リスト）\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_ii.java<pre><code>/* バックトラッキングアルゴリズム：部分集合和 II */\nvoid backtrack(List&lt;Integer&gt; state, int target, int[] choices, int start, List&lt;List&lt;Integer&gt;&gt; res) {\n    // 部分集合の和がtargetと等しいとき、解を記録\n    if (target == 0) {\n        res.add(new ArrayList&lt;&gt;(state));\n        return;\n    }\n    // すべての選択肢を走査\n    // 剪定二：startから走査を開始し、重複する部分集合の生成を回避\n    // 剪定三：startから走査を開始し、同じ要素の繰り返し選択を回避\n    for (int i = start; i &lt; choices.length; i++) {\n        // 剪定一：部分集合の和がtargetを超えた場合、即座にループを終了\n        // 配列がソートされているため、後の要素はさらに大きく、部分集合の和は必ずtargetを超える\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // 剪定四：要素が左の要素と等しい場合、検索ブランチの重複を示すのでスキップ\n        if (i &gt; start &amp;&amp; choices[i] == choices[i - 1]) {\n            continue;\n        }\n        // 試行：選択を行い、target、startを更新\n        state.add(choices[i]);\n        // 次のラウンドの選択に進む\n        backtrack(state, target - choices[i], choices, i + 1, res);\n        // 回退：選択を取り消し、前の状態に復元\n        state.remove(state.size() - 1);\n    }\n}\n\n/* 部分集合和 II を解く */\nList&lt;List&lt;Integer&gt;&gt; subsetSumII(int[] nums, int target) {\n    List&lt;Integer&gt; state = new ArrayList&lt;&gt;(); // 状態（部分集合）\n    Arrays.sort(nums); // nums をソート\n    int start = 0; // 走査の開始点\n    List&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;&gt;(); // 結果リスト（部分集合リスト）\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_ii.cs<pre><code>[class]{subset_sum_ii}-[func]{Backtrack}\n\n[class]{subset_sum_ii}-[func]{SubsetSumII}\n</code></pre> subset_sum_ii.go<pre><code>[class]{}-[func]{backtrackSubsetSumII}\n\n[class]{}-[func]{subsetSumII}\n</code></pre> subset_sum_ii.swift<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumII}\n</code></pre> subset_sum_ii.js<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumII}\n</code></pre> subset_sum_ii.ts<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumII}\n</code></pre> subset_sum_ii.dart<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumII}\n</code></pre> subset_sum_ii.rs<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subset_sum_ii}\n</code></pre> subset_sum_ii.c<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumII}\n</code></pre> subset_sum_ii.kt<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumII}\n</code></pre> subset_sum_ii.rb<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subset_sum_ii}\n</code></pre> <p>以下の図は、配列 \\([4, 4, 5]\\) とターゲット要素 \\(9\\) のバックトラッキングプロセスを示し、4種類の剪定操作が含まれています。図とコードのコメントを組み合わせて、検索プロセス全体と各種類の剪定操作の動作を理解してください。</p> <p></p> <p> 図 13-14   部分集合和 II のバックトラッキングプロセス </p>","path":["第 13 章 &nbsp; バックトラッキング","13.3 &nbsp; 部分集合和問題"],"tags":[]},{"location":"chapter_backtracking/summary/","level":1,"title":"13.5   まとめ","text":"","path":["第 13 章 &nbsp; バックトラッキング","13.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_backtracking/summary/#1","level":3,"title":"1.   重要な復習","text":"<ul> <li>バックトラッキングアルゴリズムの本質は全数探索です。解空間の深さ優先走査を実行することで条件を満たす解を求めます。検索中に満足のいく解が見つかった場合、それを記録し、すべての解が見つかるか走査が完了するまで続けます。</li> <li>バックトラッキングアルゴリズムの検索プロセスには試行と後退が含まれます。深さ優先探索を使用して様々な選択を探索し、選択が制約を満たさない場合、前の選択を取り消します。そして前の状態に戻って他のオプションを試し続けます。試行と後退は反対方向の操作です。</li> <li>バックトラッキング問題には通常複数の制約が含まれます。これらの制約は剪定操作を実行するために使用できます。剪定は不要な検索分岐を事前に終了し、検索効率を大幅に向上させることができます。</li> <li>バックトラッキングアルゴリズムは主に検索問題と制約満足問題を解決するために使用されます。組み合わせ最適化問題はバックトラッキングを使用して解決できますが、多くの場合、より効率的または効果的な解決方法が利用可能です。</li> <li>順列問題は、与えられた集合の要素のすべての可能な順列を検索することを目的とします。各要素が選択されたかどうかを記録するために配列を使用し、同じ要素の重複選択を避けます。これにより、各要素が一度だけ選択されることが保証されます。</li> <li>順列問題では、集合に重複要素が含まれている場合、最終結果に重複順列が含まれます。同一要素が各ラウンドで一度だけ選択できるように制限する必要があり、これは通常ハッシュセットを使用して実装されます。</li> <li>部分集合和問題は、与えられた集合でターゲット値に合計する全ての部分集合を見つけることを目的とします。集合は要素の順序を区別しませんが、検索プロセスでは重複する部分集合が生成される可能性があります。これは、アルゴリズムが異なる要素順序を独特のパスとして探索するために発生します。バックトラッキングの前に、データをソートし、各ラウンドの走査の開始点を示す変数を設定します。これにより、重複する部分集合を生成する検索分岐を剪定できます。</li> <li>部分集合和問題では、配列内の等しい要素は重複集合を生成する可能性があります。配列がすでにソートされているという前提条件を使用して、隣接する要素が等しいかどうかを判定することで剪定を行います。これにより、等しい要素がラウンドごとに一度だけ選択されることが保証されます。</li> <li>\\(n\\) クイーン問題は、2つのクイーンが互いに攻撃できないように \\(n \\times n\\) のチェスボードに \\(n\\) 個のクイーンを配置する方案を見つけることを目的とします。問題の制約には行制約、列制約、および主対角線と副対角線の制約が含まれます。行制約を満たすために、行ごとに1つのクイーンを配置する戦略を採用し、各行に1つのクイーンが配置されることを保証します。</li> <li>列制約と対角線制約の処理は似ています。列制約については、各列にクイーンがあるかどうかを記録する配列を使用し、選択されたセルが合法かどうかを示します。対角線制約については、2つの配列を使用して主対角線と副対角線にそれぞれクイーンの存在を記録します。課題は、同じ主対角線または副対角線上のセルの行と列のインデックス間の関係を決定することです。</li> </ul>","path":["第 13 章 &nbsp; バックトラッキング","13.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_backtracking/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: バックトラッキングと再帰の関係をどのように理解すればよいですか？</p> <p>全体的に、バックトラッキングは「アルゴリズム戦略」であり、再帰はより「ツール」です。</p> <ul> <li>バックトラッキングアルゴリズムは通常再帰に基づいています。しかし、バックトラッキングは再帰の応用シナリオの一つであり、特に検索問題においてです。</li> <li>再帰の構造は「部分問題分解」の問題解決パラダイムを反映します。分割統治、バックトラッキング、動的プログラミング（メモ化再帰）を含む問題の解決でよく使用されます。</li> </ul>","path":["第 13 章 &nbsp; バックトラッキング","13.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_computational_complexity/","level":1,"title":"第 2 章   複雑度解析","text":"<p>Abstract</p> <p>複雑度解析は、アルゴリズムの広大な宇宙における時空のナビゲーターのようなものです。</p> <p>時間と空間の次元をより深く探求し、より優雅な解決策を求めるためのガイドとなります。</p>","path":["第 2 章 &nbsp; 計算量解析","第 2 章 &nbsp; 複雑度解析"],"tags":[]},{"location":"chapter_computational_complexity/#_1","level":2,"title":"章の内容","text":"<ul> <li>2.1   アルゴリズムの効率評価</li> <li>2.2   反復と再帰</li> <li>2.3   時間計算量</li> <li>2.4   空間計算量</li> <li>2.5   まとめ</li> </ul>","path":["第 2 章 &nbsp; 計算量解析","第 2 章 &nbsp; 複雑度解析"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/","level":1,"title":"2.2   反復と再帰","text":"<p>アルゴリズムにおいて、タスクの繰り返し実行は非常に一般的であり、複雑度の分析と密接に関係しています。したがって、時間計算量と空間計算量の概念を詳しく学ぶ前に、まずプログラミングで繰り返しタスクを実装する方法を探究しましょう。これには、2つの基本的なプログラミング制御構造である反復と再帰の理解が含まれます。</p>","path":["第 2 章 &nbsp; 計算量解析","2.2 &nbsp; 反復と再帰"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#221","level":2,"title":"2.2.1   反復","text":"<p>反復は、タスクを繰り返し実行するための制御構造です。反復では、プログラムは特定の条件が満たされている限りコードブロックを繰り返し実行し、この条件が満たされなくなるまで続けます。</p>","path":["第 2 章 &nbsp; 計算量解析","2.2 &nbsp; 反復と再帰"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#1-for","level":3,"title":"1.   forループ","text":"<p><code>for</code>ループは反復の最も一般的な形式の1つであり、反復回数が事前に分かっている場合に特に適しています。</p> <p>以下の関数は<code>for</code>ループを使用して\\(1 + 2 + \\dots + n\\)の合計を実行し、合計を変数<code>res</code>に格納します。Pythonでは、<code>range(a, b)</code>は<code>a</code>を含み<code>b</code>を除く区間を作成することに注意してください。つまり、\\(a\\)から\\(b−1\\)までの範囲で反復します。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby iteration.py<pre><code>def for_loop(n: int) -&gt; int:\n    \"\"\"forループ\"\"\"\n    res = 0\n    # 1, 2, ..., n-1, n の合計をループ\n    for i in range(1, n + 1):\n        res += i\n    return res\n</code></pre> iteration.cpp<pre><code>/* for ループ */\nint forLoop(int n) {\n    int res = 0;\n    // 1, 2, ..., n-1, n の合計をループ計算\n    for (int i = 1; i &lt;= n; ++i) {\n        res += i;\n    }\n    return res;\n}\n</code></pre> iteration.java<pre><code>/* for ループ */\nint forLoop(int n) {\n    int res = 0;\n    // 1, 2, ..., n-1, n の合計をループ計算\n    for (int i = 1; i &lt;= n; i++) {\n        res += i;\n    }\n    return res;\n}\n</code></pre> iteration.cs<pre><code>[class]{iteration}-[func]{ForLoop}\n</code></pre> iteration.go<pre><code>[class]{}-[func]{forLoop}\n</code></pre> iteration.swift<pre><code>[class]{}-[func]{forLoop}\n</code></pre> iteration.js<pre><code>[class]{}-[func]{forLoop}\n</code></pre> iteration.ts<pre><code>[class]{}-[func]{forLoop}\n</code></pre> iteration.dart<pre><code>[class]{}-[func]{forLoop}\n</code></pre> iteration.rs<pre><code>[class]{}-[func]{for_loop}\n</code></pre> iteration.c<pre><code>[class]{}-[func]{forLoop}\n</code></pre> iteration.kt<pre><code>[class]{}-[func]{forLoop}\n</code></pre> iteration.rb<pre><code>[class]{}-[func]{for_loop}\n</code></pre> <p>以下の図はこの合計関数を表しています。</p> <p></p> <p> 図 2-1   Flowchart of the sum function </p> <p>この合計関数での操作数は入力データのサイズ\\(n\\)に比例する、つまり線形関係があります。この「線形関係」こそが時間計算量が記述するものです。このトピックについては次のセクションで詳しく説明します。</p>","path":["第 2 章 &nbsp; 計算量解析","2.2 &nbsp; 反復と再帰"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#2-while","level":3,"title":"2.   whileループ","text":"<p><code>for</code>ループと同様に、<code>while</code>ループは反復を実装するためのもう1つのアプローチです。<code>while</code>ループでは、プログラムは各反復の開始時に条件をチェックし、条件が真の場合は実行を継続し、そうでなければループを終了します。</p> <p>以下では<code>while</code>ループを使用して合計\\(1 + 2 + \\dots + n\\)を実装します。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby iteration.py<pre><code>def while_loop(n: int) -&gt; int:\n    \"\"\"whileループ\"\"\"\n    res = 0\n    i = 1  # 条件変数を初期化\n    # 1, 2, ..., n-1, n の合計をループ\n    while i &lt;= n:\n        res += i\n        i += 1  # 条件変数を更新\n    return res\n</code></pre> iteration.cpp<pre><code>/* while ループ */\nint whileLoop(int n) {\n    int res = 0;\n    int i = 1; // 条件変数を初期化\n    // 1, 2, ..., n-1, n の合計をループ計算\n    while (i &lt;= n) {\n        res += i;\n        i++; // 条件変数を更新\n    }\n    return res;\n}\n</code></pre> iteration.java<pre><code>/* while ループ */\nint whileLoop(int n) {\n    int res = 0;\n    int i = 1; // 条件変数を初期化\n    // 1, 2, ..., n-1, n の合計をループ計算\n    while (i &lt;= n) {\n        res += i;\n        i++; // 条件変数を更新\n    }\n    return res;\n}\n</code></pre> iteration.cs<pre><code>[class]{iteration}-[func]{WhileLoop}\n</code></pre> iteration.go<pre><code>[class]{}-[func]{whileLoop}\n</code></pre> iteration.swift<pre><code>[class]{}-[func]{whileLoop}\n</code></pre> iteration.js<pre><code>[class]{}-[func]{whileLoop}\n</code></pre> iteration.ts<pre><code>[class]{}-[func]{whileLoop}\n</code></pre> iteration.dart<pre><code>[class]{}-[func]{whileLoop}\n</code></pre> iteration.rs<pre><code>[class]{}-[func]{while_loop}\n</code></pre> iteration.c<pre><code>[class]{}-[func]{whileLoop}\n</code></pre> iteration.kt<pre><code>[class]{}-[func]{whileLoop}\n</code></pre> iteration.rb<pre><code>[class]{}-[func]{while_loop}\n</code></pre> <p><code>while</code>ループは<code>for</code>ループよりも柔軟性を提供します。特に、条件変数のカスタム初期化と各ステップでの変更が可能です。</p> <p>例えば、以下のコードでは、条件変数\\(i\\)が各ラウンドで2回更新されますが、これは<code>for</code>ループでは実装が不便です。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby iteration.py<pre><code>def while_loop_ii(n: int) -&gt; int:\n    \"\"\"whileループ（2つの更新）\"\"\"\n    res = 0\n    i = 1  # 条件変数を初期化\n    # 1, 4, 10, ... の合計をループ\n    while i &lt;= n:\n        res += i\n        # 条件変数を更新\n        i += 1\n        i *= 2\n    return res\n</code></pre> iteration.cpp<pre><code>/* while ループ（2つの更新） */\nint whileLoopII(int n) {\n    int res = 0;\n    int i = 1; // 条件変数を初期化\n    // 1, 4, 10, ... の合計をループ計算\n    while (i &lt;= n) {\n        res += i;\n        // 条件変数を更新\n        i++;\n        i *= 2;\n    }\n    return res;\n}\n</code></pre> iteration.java<pre><code>/* while ループ（2つの更新） */\nint whileLoopII(int n) {\n    int res = 0;\n    int i = 1; // 条件変数を初期化\n    // 1, 4, 10, ... の合計をループ計算\n    while (i &lt;= n) {\n        res += i;\n        // 条件変数を更新\n        i++;\n        i *= 2;\n    }\n    return res;\n}\n</code></pre> iteration.cs<pre><code>[class]{iteration}-[func]{WhileLoopII}\n</code></pre> iteration.go<pre><code>[class]{}-[func]{whileLoopII}\n</code></pre> iteration.swift<pre><code>[class]{}-[func]{whileLoopII}\n</code></pre> iteration.js<pre><code>[class]{}-[func]{whileLoopII}\n</code></pre> iteration.ts<pre><code>[class]{}-[func]{whileLoopII}\n</code></pre> iteration.dart<pre><code>[class]{}-[func]{whileLoopII}\n</code></pre> iteration.rs<pre><code>[class]{}-[func]{while_loop_ii}\n</code></pre> iteration.c<pre><code>[class]{}-[func]{whileLoopII}\n</code></pre> iteration.kt<pre><code>[class]{}-[func]{whileLoopII}\n</code></pre> iteration.rb<pre><code>[class]{}-[func]{while_loop_ii}\n</code></pre> <p>全体的に、<code>for</code>ループはより簡潔で、<code>while</code>ループはより柔軟です。どちらも反復構造を実装できます。どちらを使用するかは、問題の具体的な要件に基づいて決定する必要があります。</p>","path":["第 2 章 &nbsp; 計算量解析","2.2 &nbsp; 反復と再帰"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#3","level":3,"title":"3.   ネストしたループ","text":"<p>1つのループ構造を別のループ構造内にネストできます。以下は<code>for</code>ループを使用した例です：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby iteration.py<pre><code>def nested_for_loop(n: int) -&gt; str:\n    \"\"\"二重forループ\"\"\"\n    res = \"\"\n    # i = 1, 2, ..., n-1, n をループ\n    for i in range(1, n + 1):\n        # j = 1, 2, ..., n-1, n をループ\n        for j in range(1, n + 1):\n            res += f\"({i}, {j}), \"\n    return res\n</code></pre> iteration.cpp<pre><code>/* 2重 for ループ */\nstring nestedForLoop(int n) {\n    ostringstream res;\n    // ループ i = 1, 2, ..., n-1, n\n    for (int i = 1; i &lt;= n; ++i) {\n        // ループ j = 1, 2, ..., n-1, n\n        for (int j = 1; j &lt;= n; ++j) {\n            res &lt;&lt; \"(\" &lt;&lt; i &lt;&lt; \", \" &lt;&lt; j &lt;&lt; \"), \";\n        }\n    }\n    return res.str();\n}\n</code></pre> iteration.java<pre><code>/* 2重 for ループ */\nString nestedForLoop(int n) {\n    StringBuilder res = new StringBuilder();\n    // ループ i = 1, 2, ..., n-1, n\n    for (int i = 1; i &lt;= n; i++) {\n        // ループ j = 1, 2, ..., n-1, n\n        for (int j = 1; j &lt;= n; j++) {\n            res.append(\"(\" + i + \", \" + j + \"), \");\n        }\n    }\n    return res.toString();\n}\n</code></pre> iteration.cs<pre><code>[class]{iteration}-[func]{NestedForLoop}\n</code></pre> iteration.go<pre><code>[class]{}-[func]{nestedForLoop}\n</code></pre> iteration.swift<pre><code>[class]{}-[func]{nestedForLoop}\n</code></pre> iteration.js<pre><code>[class]{}-[func]{nestedForLoop}\n</code></pre> iteration.ts<pre><code>[class]{}-[func]{nestedForLoop}\n</code></pre> iteration.dart<pre><code>[class]{}-[func]{nestedForLoop}\n</code></pre> iteration.rs<pre><code>[class]{}-[func]{nested_for_loop}\n</code></pre> iteration.c<pre><code>[class]{}-[func]{nestedForLoop}\n</code></pre> iteration.kt<pre><code>[class]{}-[func]{nestedForLoop}\n</code></pre> iteration.rb<pre><code>[class]{}-[func]{nested_for_loop}\n</code></pre> <p>以下の図はこのネストしたループを表しています。</p> <p></p> <p> 図 2-2   Flowchart of the nested loop </p> <p>このような場合、関数の操作数は\\(n^2\\)に比例します。つまり、アルゴリズムの実行時間と入力データのサイズ\\(n\\)には「二次関係」があります。</p> <p>さらにネストしたループを追加することで複雑度を高めることができ、各レベルのネストは事実上「次元を増加」させ、時間計算量を「三次」、「四次」などに引き上げます。</p>","path":["第 2 章 &nbsp; 計算量解析","2.2 &nbsp; 反復と再帰"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#222","level":2,"title":"2.2.2   再帰","text":"<p>再帰は、関数が自分自身を呼び出すことで問題を解決するアルゴリズム戦略です。主に2つのフェーズが含まれます：</p> <ol> <li>呼び出し: プログラムが自分自身を繰り返し呼び出し、しばしばより小さいまたはより単純な引数で、「終了条件」に向かって進みます。</li> <li>返却: 「終了条件」がトリガーされると、プログラムは最も深い再帰関数から返り始め、各レイヤーの結果を集約します。</li> </ol> <p>実装の観点から、再帰コードは主に3つの要素を含みます。</p> <ol> <li>終了条件: 「呼び出し」から「返却」にいつ切り替えるかを決定します。</li> <li>再帰呼び出し: 「呼び出し」に対応し、関数が自分自身を呼び出し、通常はより小さいまたはより単純化されたパラメータで行います。</li> <li>結果の返却: 「返却」に対応し、現在の再帰レベルの結果が前のレイヤーに返されます。</li> </ol> <p>以下のコードを観察してください。単純に関数<code>recur(n)</code>を呼び出すだけで\\(1 + 2 + \\dots + n\\)の合計を計算できます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby recursion.py<pre><code>def recur(n: int) -&gt; int:\n    \"\"\"再帰\"\"\"\n    # 終了条件\n    if n == 1:\n        return 1\n    # 再帰：再帰呼び出し\n    res = recur(n - 1)\n    # 復帰：結果を返す\n    return n + res\n</code></pre> recursion.cpp<pre><code>/* 再帰 */\nint recur(int n) {\n    // 終了条件\n    if (n == 1)\n        return 1;\n    // 再帰：再帰呼び出し\n    int res = recur(n - 1);\n    // 戻り値：結果を返す\n    return n + res;\n}\n</code></pre> recursion.java<pre><code>/* 再帰 */\nint recur(int n) {\n    // 終了条件\n    if (n == 1)\n        return 1;\n    // 再帰：再帰呼び出し\n    int res = recur(n - 1);\n    // 戻り値：結果を返す\n    return n + res;\n}\n</code></pre> recursion.cs<pre><code>[class]{recursion}-[func]{Recur}\n</code></pre> recursion.go<pre><code>[class]{}-[func]{recur}\n</code></pre> recursion.swift<pre><code>[class]{}-[func]{recur}\n</code></pre> recursion.js<pre><code>[class]{}-[func]{recur}\n</code></pre> recursion.ts<pre><code>[class]{}-[func]{recur}\n</code></pre> recursion.dart<pre><code>[class]{}-[func]{recur}\n</code></pre> recursion.rs<pre><code>[class]{}-[func]{recur}\n</code></pre> recursion.c<pre><code>[class]{}-[func]{recur}\n</code></pre> recursion.kt<pre><code>[class]{}-[func]{recur}\n</code></pre> recursion.rb<pre><code>[class]{}-[func]{recur}\n</code></pre> <p>以下の図はこの関数の再帰プロセスを示しています。</p> <p></p> <p> 図 2-3   Recursive process of the sum function </p> <p>反復と再帰は計算の観点から同じ結果を達成できますが、それらは思考と問題解決の全く異なるパラダイムを表します。</p> <ul> <li>反復: 「ボトムアップ」で問題を解決します。最も基本的なステップから始まり、タスクが完了するまでこれらのステップを繰り返し追加または累積します。</li> <li>再帰: 「トップダウン」で問題を解決します。元の問題をより小さなサブ問題に分解し、各サブ問題は元の問題と同じ形式を持ちます。これらのサブ問題は、解が分かっているベースケースで停止するまで、さらに小さなサブ問題に分解されます。</li> </ul> <p>先ほどの合計関数の例を取ってみましょう。\\(f(n) = 1 + 2 + \\dots + n\\)として定義されます。</p> <ul> <li>反復: このアプローチでは、ループ内で合計プロセスをシミュレートします。\\(1\\)から始まり\\(n\\)まで横断し、各反復で合計操作を実行して最終的に\\(f(n)\\)を計算します。</li> <li>再帰: ここでは、問題はサブ問題に分解されます：\\(f(n) = n + f(n-1)\\)。この分解は、ベースケースの\\(f(1) = 1\\)に到達するまで再帰的に続き、そこで再帰が終了します。</li> </ul>","path":["第 2 章 &nbsp; 計算量解析","2.2 &nbsp; 反復と再帰"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#1","level":3,"title":"1.   呼び出しスタック","text":"<p>再帰関数が自分自身を呼び出すたびに、システムは新しく開始された関数にメモリを割り当てて、ローカル変数、戻りアドレス、その他の関連情報を格納します。これは2つの主要な結果をもたらします。</p> <ul> <li>関数のコンテキストデータは「スタックフレーム空間」と呼ばれるメモリ領域に格納され、関数が返された後にのみ解放されます。したがって、再帰は一般的に反復よりも多くのメモリ空間を消費します。</li> <li>再帰呼び出しは追加のオーバーヘッドを導入します。したがって、再帰は通常ループよりも時間効率が劣ります。</li> </ul> <p>以下の図に示されているように、終了条件がトリガーされる前に\\(n\\)個の未返却の再帰関数があり、再帰の深さが\\(n\\)であることを示しています。</p> <p></p> <p> 図 2-4   Recursion call depth </p> <p>実際には、プログラミング言語で許可される再帰の深さは通常制限されており、過度に深い再帰はスタックオーバーフローエラーを引き起こす可能性があります。</p>","path":["第 2 章 &nbsp; 計算量解析","2.2 &nbsp; 反復と再帰"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#2","level":3,"title":"2.   末尾再帰","text":"<p>興味深いことに、関数が返す直前の最後のステップとして再帰呼び出しを実行する場合、コンパイラまたはインタープリターによって反復と同じ空間効率になるように最適化できます。このシナリオは末尾再帰として知られています。</p> <ul> <li>通常の再帰: 標準的な再帰では、関数が前のレベルに戻ったとき、さらにコードを実行し続けるため、システムは前の呼び出しのコンテキストを保存する必要があります。</li> <li>末尾再帰: ここでは、再帰呼び出しは関数が返す前の最終操作です。これは、前のレベルに戻った際に、さらなるアクションが必要ないことを意味するため、システムは前のレベルのコンテキストを保存する必要がありません。</li> </ul> <p>例えば、\\(1 + 2 + \\dots + n\\)の計算では、結果変数<code>res</code>を関数のパラメータにすることで、末尾再帰を実現できます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby recursion.py<pre><code>def tail_recur(n, res):\n    \"\"\"末尾再帰\"\"\"\n    # 終了条件\n    if n == 0:\n        return res\n    # 末尾再帰呼び出し\n    return tail_recur(n - 1, res + n)\n</code></pre> recursion.cpp<pre><code>/* 末尾再帰 */\nint tailRecur(int n, int res) {\n    // 終了条件\n    if (n == 0)\n        return res;\n    // 末尾再帰呼び出し\n    return tailRecur(n - 1, res + n);\n}\n</code></pre> recursion.java<pre><code>/* 末尾再帰 */\nint tailRecur(int n, int res) {\n    // 終了条件\n    if (n == 0)\n        return res;\n    // 末尾再帰呼び出し\n    return tailRecur(n - 1, res + n);\n}\n</code></pre> recursion.cs<pre><code>[class]{recursion}-[func]{TailRecur}\n</code></pre> recursion.go<pre><code>[class]{}-[func]{tailRecur}\n</code></pre> recursion.swift<pre><code>[class]{}-[func]{tailRecur}\n</code></pre> recursion.js<pre><code>[class]{}-[func]{tailRecur}\n</code></pre> recursion.ts<pre><code>[class]{}-[func]{tailRecur}\n</code></pre> recursion.dart<pre><code>[class]{}-[func]{tailRecur}\n</code></pre> recursion.rs<pre><code>[class]{}-[func]{tail_recur}\n</code></pre> recursion.c<pre><code>[class]{}-[func]{tailRecur}\n</code></pre> recursion.kt<pre><code>[class]{}-[func]{tailRecur}\n</code></pre> recursion.rb<pre><code>[class]{}-[func]{tail_recur}\n</code></pre> <p>末尾再帰の実行プロセスは以下の図に示されています。通常の再帰と末尾再帰を比較すると、合計操作のポイントが異なります。</p> <ul> <li>通常の再帰: 合計操作は「返却」フェーズで発生し、各レイヤーが返った後にもう一度合計が必要です。</li> <li>末尾再帰: 合計操作は「呼び出し」フェーズで発生し、「返却」フェーズは各レイヤーを通じて返すだけです。</li> </ul> <p></p> <p> 図 2-5   Tail recursion process </p> <p>Tip</p> <p>多くのコンパイラやインタープリターは末尾再帰最適化をサポートしていないことに注意してください。例えば、Pythonはデフォルトで末尾再帰最適化をサポートしていないため、関数が末尾再帰の形式であっても、スタックオーバーフローの問題に遭遇する可能性があります。</p>","path":["第 2 章 &nbsp; 計算量解析","2.2 &nbsp; 反復と再帰"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#3_1","level":3,"title":"3.   再帰木","text":"<p>「分割統治」に関連するアルゴリズムを扱う際、再帰は反復よりもしばしばより直感的なアプローチとより読みやすいコードを提供します。「フィボナッチ数列」を例に取ってみましょう。</p> <p>Question</p> <p>フィボナッチ数列\\(0, 1, 1, 2, 3, 5, 8, 13, \\dots\\)が与えられた場合、数列の\\(n\\)番目の数を求めなさい。</p> <p>フィボナッチ数列の\\(n\\)番目の数を\\(f(n)\\)とすると、2つの結論を簡単に導き出せます：</p> <ul> <li>数列の最初の2つの数は\\(f(1) = 0\\)と\\(f(2) = 1\\)です。</li> <li>数列の各数は前の2つの数の合計です。つまり、\\(f(n) = f(n - 1) + f(n - 2)\\)です。</li> </ul> <p>再帰関係を使用し、最初の2つの数を終了条件として考慮すると、再帰コードを書けます。<code>fib(n)</code>を呼び出すとフィボナッチ数列の\\(n\\)番目の数が得られます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby recursion.py<pre><code>def fib(n: int) -&gt; int:\n    \"\"\"フィボナッチ数列：再帰\"\"\"\n    # 終了条件 f(1) = 0, f(2) = 1\n    if n == 1 or n == 2:\n        return n - 1\n    # 再帰呼び出し f(n) = f(n-1) + f(n-2)\n    res = fib(n - 1) + fib(n - 2)\n    # 結果 f(n) を返す\n    return res\n</code></pre> recursion.cpp<pre><code>/* フィボナッチ数列：再帰 */\nint fib(int n) {\n    // 終了条件 f(1) = 0, f(2) = 1\n    if (n == 1 || n == 2)\n        return n - 1;\n    // 再帰呼び出し f(n) = f(n-1) + f(n-2)\n    int res = fib(n - 1) + fib(n - 2);\n    // 結果 f(n) を返す\n    return res;\n}\n</code></pre> recursion.java<pre><code>/* フィボナッチ数列：再帰 */\nint fib(int n) {\n    // 終了条件 f(1) = 0, f(2) = 1\n    if (n == 1 || n == 2)\n        return n - 1;\n    // 再帰呼び出し f(n) = f(n-1) + f(n-2)\n    int res = fib(n - 1) + fib(n - 2);\n    // 結果 f(n) を返す\n    return res;\n}\n</code></pre> recursion.cs<pre><code>[class]{recursion}-[func]{Fib}\n</code></pre> recursion.go<pre><code>[class]{}-[func]{fib}\n</code></pre> recursion.swift<pre><code>[class]{}-[func]{fib}\n</code></pre> recursion.js<pre><code>[class]{}-[func]{fib}\n</code></pre> recursion.ts<pre><code>[class]{}-[func]{fib}\n</code></pre> recursion.dart<pre><code>[class]{}-[func]{fib}\n</code></pre> recursion.rs<pre><code>[class]{}-[func]{fib}\n</code></pre> recursion.c<pre><code>[class]{}-[func]{fib}\n</code></pre> recursion.kt<pre><code>[class]{}-[func]{fib}\n</code></pre> recursion.rb<pre><code>[class]{}-[func]{fib}\n</code></pre> <p>上記のコードを観察すると、それ自体の中で2つの関数を再帰的に呼び出していることがわかります。つまり、1回の呼び出しで2つの分岐呼び出しが生成されます。以下の図に示されているように、この継続的な再帰呼び出しは最終的に深さ\\(n\\)の再帰木を作成します。</p> <p></p> <p> 図 2-6   Fibonacci sequence recursion tree </p> <p>基本的に、再帰は「問題をより小さなサブ問題に分解する」パラダイムを体現しています。この分割統治戦略は重要です。</p> <ul> <li>アルゴリズムの観点から、探索、ソート、バックトラッキング、分割統治、動的プログラミングなどの多くの重要な戦略は、直接的または間接的にこの思考方法を使用しています。</li> <li>データ構造の観点から、再帰は連結リスト、木、グラフを扱うのに自然に適しており、これらは分割統治アプローチを使用した分析に適しているためです。</li> </ul>","path":["第 2 章 &nbsp; 計算量解析","2.2 &nbsp; 反復と再帰"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#223","level":2,"title":"2.2.3   比較","text":"<p>上記の内容をまとめると、以下の表は実装、性能、適用性の観点から反復と再帰の違いを示しています。</p> <p> 表: 反復と再帰の特性の比較 </p> 反復 再帰 アプローチ ループ構造 関数が自分自身を呼び出す 時間効率 一般的により高い効率、関数呼び出しのオーバーヘッドなし 各関数呼び出しがオーバーヘッドを生成 メモリ使用量 通常は固定サイズのメモリ空間を使用 累積的な関数呼び出しが大量のスタックフレーム空間を使用する可能性 適用可能な問題 単純なループタスクに適している、直感的で読みやすいコード 問題の分解に適している（木、グラフ、分割統治、バックトラッキングなど）、簡潔で明確なコード構造 <p>Tip</p> <p>以下の内容が理解しにくい場合は、「スタック」の章を読んだ後に再び訪れることを検討してください。</p> <p>それでは、反復と再帰の本質的な関連は何でしょうか？上記の再帰関数を例に取ると、合計操作は再帰の「返却」フェーズで発生します。これは、最初に呼び出された関数が最後に合計操作を完了することを意味し、スタックの「後入れ先出し」原理を反映しています。</p> <p>「呼び出しスタック」や「スタックフレーム空間」などの再帰用語は、再帰とスタックの密接な関係を示しています。</p> <ol> <li>呼び出し: 関数が呼び出されると、システムは「呼び出しスタック」上にその関数用の新しいスタックフレームを割り当て、ローカル変数、パラメータ、戻りアドレス、その他のデータを格納します。</li> <li>返却: 関数が実行を完了して返ると、対応するスタックフレームが「呼び出しスタック」から削除され、前の関数の実行環境が復元されます。</li> </ol> <p>したがって、明示的なスタックを使用して呼び出しスタックの動作をシミュレートできます。これにより再帰を反復形式に変換できます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby recursion.py<pre><code>def for_loop_recur(n: int) -&gt; int:\n    \"\"\"反復で再帰をシミュレート\"\"\"\n    # 明示的なスタックを使用してシステムコールスタックをシミュレート\n    stack = []\n    res = 0\n    # 再帰：再帰呼び出し\n    for i in range(n, 0, -1):\n        # 「スタックへのプッシュ」で「再帰」をシミュレート\n        stack.append(i)\n    # 復帰：結果を返す\n    while stack:\n        # 「スタックからのポップ」で「復帰」をシミュレート\n        res += stack.pop()\n    # res = 1+2+3+...+n\n    return res\n</code></pre> recursion.cpp<pre><code>/* 反復で再帰をシミュレート */\nint forLoopRecur(int n) {\n    // 明示的なスタックを使用してシステムコールスタックをシミュレート\n    stack&lt;int&gt; stack;\n    int res = 0;\n    // 再帰：再帰呼び出し\n    for (int i = n; i &gt; 0; i--) {\n        // 「スタックへのプッシュ」で「再帰」をシミュレート\n        stack.push(i);\n    }\n    // 戻り値：結果を返す\n    while (!stack.empty()) {\n        // 「スタックからのポップ」で「戻り値」をシミュレート\n        res += stack.top();\n        stack.pop();\n    }\n    // res = 1+2+3+...+n\n    return res;\n}\n</code></pre> recursion.java<pre><code>/* 反復で再帰をシミュレート */\nint forLoopRecur(int n) {\n    // 明示的なスタックを使用してシステムコールスタックをシミュレート\n    Stack&lt;Integer&gt; stack = new Stack&lt;&gt;();\n    int res = 0;\n    // 再帰：再帰呼び出し\n    for (int i = n; i &gt; 0; i--) {\n        // 「スタックへのプッシュ」で「再帰」をシミュレート\n        stack.push(i);\n    }\n    // 戻り値：結果を返す\n    while (!stack.isEmpty()) {\n        // 「スタックからのポップ」で「戻り値」をシミュレート\n        res += stack.pop();\n    }\n    // res = 1+2+3+...+n\n    return res;\n}\n</code></pre> recursion.cs<pre><code>[class]{recursion}-[func]{ForLoopRecur}\n</code></pre> recursion.go<pre><code>[class]{}-[func]{forLoopRecur}\n</code></pre> recursion.swift<pre><code>[class]{}-[func]{forLoopRecur}\n</code></pre> recursion.js<pre><code>[class]{}-[func]{forLoopRecur}\n</code></pre> recursion.ts<pre><code>[class]{}-[func]{forLoopRecur}\n</code></pre> recursion.dart<pre><code>[class]{}-[func]{forLoopRecur}\n</code></pre> recursion.rs<pre><code>[class]{}-[func]{for_loop_recur}\n</code></pre> recursion.c<pre><code>[class]{}-[func]{forLoopRecur}\n</code></pre> recursion.kt<pre><code>[class]{}-[func]{forLoopRecur}\n</code></pre> recursion.rb<pre><code>[class]{}-[func]{for_loop_recur}\n</code></pre> <p>上記のコードを観察すると、再帰が反復に変換されたとき、コードはより複雑になります。反復と再帰はしばしば相互に変換できますが、2つの理由でそうすることが常に推奨されるわけではありません：</p> <ul> <li>変換されたコードは理解がより困難になり、読みにくくなる可能性があります。</li> <li>一部の複雑な問題では、システムの呼び出しスタックの動作をシミュレートすることは非常に困難です。</li> </ul> <p>結論として、反復または再帰を選択するかは問題の具体的な性質によります。プログラミングの実践では、両方の長所と短所を比較検討し、手元の状況に最も適したアプローチを選択することが重要です。</p>","path":["第 2 章 &nbsp; 計算量解析","2.2 &nbsp; 反復と再帰"],"tags":[]},{"location":"chapter_computational_complexity/performance_evaluation/","level":1,"title":"2.1   アルゴリズムの効率評価","text":"<p>アルゴリズム設計において、私たちは順序に従って以下の2つの目標を追求します。</p> <ol> <li>問題の解決策を見つける: アルゴリズムは、指定された入力範囲内で確実に正しい解を見つけることができるべきです。</li> <li>最適解を求める: 同じ問題に対して複数の解決策が存在する場合があり、私たちは可能な限り最も効率的なアルゴリズムを見つけることを目指します。</li> </ol> <p>つまり、問題を解決できることを前提として、アルゴリズムの効率がアルゴリズムを評価する主要な基準となっており、これには以下の2つの次元が含まれます。</p> <ul> <li>時間効率: アルゴリズムが実行される速度。</li> <li>空間効率: アルゴリズムが占有するメモリ空間のサイズ。</li> </ul> <p>要するに、私たちの目標は、高速でメモリ効率の良いデータ構造とアルゴリズムを設計することです。アルゴリズムの効率を効果的に評価することは重要です。なぜなら、そうすることで初めて様々なアルゴリズムを比較し、アルゴリズムの設計と最適化プロセスを導くことができるからです。</p> <p>効率評価には主に2つの方法があります：実際のテストと理論的推定です。</p>","path":["第 2 章 &nbsp; 計算量解析","2.1 &nbsp; アルゴリズムの効率評価"],"tags":[]},{"location":"chapter_computational_complexity/performance_evaluation/#211","level":2,"title":"2.1.1   実際のテスト","text":"<p>アルゴリズム<code>A</code>と<code>B</code>があり、どちらも同じ問題を解決でき、それらの効率を比較する必要があるとします。最も直接的な方法は、コンピュータを使用してこれら2つのアルゴリズムを実行し、実行時間とメモリ使用量を監視・記録することです。この評価方法は実際の状況を反映しますが、大きな制限があります。</p> <p>一方で、テスト環境からの干渉を排除することは困難です。ハードウェア構成はアルゴリズムの性能に影響を与える可能性があります。例えば、並列度の高いアルゴリズムはマルチコアCPUでの実行により適していますし、集約的なメモリ操作を含むアルゴリズムは高性能メモリでより良い性能を発揮します。アルゴリズムのテスト結果は、異なるマシン間で変わる可能性があります。これは、平均効率を計算するために複数のマシンでテストすることが実用的でないことを意味します。</p> <p>一方で、完全なテストを実施することは非常にリソース集約的です。アルゴリズムの効率は入力データサイズによって変わります。例えば、データ量が少ない場合はアルゴリズム<code>A</code>が<code>B</code>より速く実行される可能性がありますが、データ量が多い場合はテスト結果が逆になる可能性があります。したがって、説得力のある結論を導くためには、幅広い入力データサイズをテストする必要があり、これには過度な計算リソースが必要になります。</p>","path":["第 2 章 &nbsp; 計算量解析","2.1 &nbsp; アルゴリズムの効率評価"],"tags":[]},{"location":"chapter_computational_complexity/performance_evaluation/#212","level":2,"title":"2.1.2   理論的推定","text":"<p>実際のテストの大きな制限により、計算のみでアルゴリズムの効率を評価することを検討できます。この推定方法は漸近的複雑度解析、または単に複雑度解析として知られています。</p> <p>複雑度解析は、アルゴリズムの実行に必要な時間と空間リソースと入力データのサイズとの関係を反映します。これは、入力データのサイズが増加するにつれて、アルゴリズムに必要な時間と空間の増加傾向を記述します。この定義は複雑に聞こえるかもしれませんが、より良く理解するために3つの重要なポイントに分解できます。</p> <ul> <li>「時間と空間リソース」は、それぞれ時間計算量と空間計算量に対応します。</li> <li>「入力データのサイズが増加するにつれて」は、複雑度がアルゴリズムの効率と入力データ量との関係を反映することを意味します。</li> <li>「時間と空間の増加傾向」は、複雑度解析が実行時間や占有空間の具体的な値ではなく、時間や空間が増加する「率」に焦点を当てることを示します。</li> </ul> <p>複雑度解析は実際のテスト方法の欠点を克服します。これは以下の側面で反映されます：</p> <ul> <li>実際にコードを実行する必要がないため、より環境に優しく、エネルギー効率が良いです。</li> <li>テスト環境に依存せず、すべての動作プラットフォームに適用できます。</li> <li>異なるデータ量でのアルゴリズムの効率を反映でき、特に大量データでのアルゴリズムの性能を示します。</li> </ul> <p>Tip</p> <p>複雑度の概念についてまだ混乱している場合でも、心配しないでください。以降の章で詳しく取り上げます。</p> <p>複雑度解析は、アルゴリズムの効率を評価する「ものさし」を提供し、実行に必要な時間と空間リソースを測定し、異なるアルゴリズムの効率を比較することを可能にします。</p> <p>複雑度は数学的概念であり、初心者には抽象的で困難かもしれません。この観点から、複雑度解析は最初に紹介するのに最も適したトピックではないかもしれません。しかし、特定のデータ構造やアルゴリズムの特性について議論するとき、その速度と空間使用量を分析することを避けるのは困難です。</p> <p>要約すると、データ構造とアルゴリズムに深く入る前に複雑度解析の基本的な理解を身につけることをお勧めします。これにより、簡単なアルゴリズムで複雑度解析を実行できるようになります。</p>","path":["第 2 章 &nbsp; 計算量解析","2.1 &nbsp; アルゴリズムの効率評価"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/","level":1,"title":"2.4   空間計算量","text":"<p>空間計算量は、データ量が増加するにつれてアルゴリズムが占有するメモリ空間の増加傾向を測定するために使用されます。この概念は時間計算量と非常に似ていますが、「実行時間」が「占有メモリ空間」に置き換えられています。</p>","path":["第 2 章 &nbsp; 計算量解析","2.4 &nbsp; 空間計算量"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#241","level":2,"title":"2.4.1   アルゴリズムに関連する空間","text":"<p>アルゴリズムが実行中に使用するメモリ空間には、主に以下の種類があります。</p> <ul> <li>入力空間: アルゴリズムの入力データを格納するために使用されます。</li> <li>一時空間: アルゴリズムの実行中に変数、オブジェクト、関数コンテキスト、その他のデータを格納するために使用されます。</li> <li>出力空間: アルゴリズムの出力データを格納するために使用されます。</li> </ul> <p>一般的に、空間計算量の統計範囲には「一時空間」と「出力空間」の両方が含まれます。</p> <p>一時空間はさらに3つの部分に分けることができます。</p> <ul> <li>一時データ: アルゴリズムの実行中に様々な定数、変数、オブジェクトなどを保存するために使用されます。</li> <li>スタックフレーム空間: 呼び出された関数のコンテキストデータを保存するために使用されます。システムは関数が呼び出されるたびにスタックの頂上にスタックフレームを作成し、関数が返された後にスタックフレーム空間を解放します。</li> <li>命令空間: コンパイル済みプログラム命令を格納するために使用され、実際の統計では通常無視できます。</li> </ul> <p>プログラムの空間計算量を分析する際、通常は一時データ、スタックフレーム空間、出力データをカウントします。以下の図に示されています。</p> <p></p> <p> 図 2-15   Space types used in algorithms </p> <p>関連するコードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlin <pre><code>class Node:\n    \"\"\"クラス\"\"\"\n    def __init__(self, x: int):\n        self.val: int = x               # ノード値\n        self.next: Node | None = None   # 次のノードへの参照\n\ndef function() -&gt; int:\n    \"\"\"関数\"\"\"\n    # 特定の操作を実行...\n    return 0\n\ndef algorithm(n) -&gt; int:    # 入力データ\n    A = 0                   # 一時データ（定数、通常大文字）\n    b = 0                   # 一時データ（変数）\n    node = Node(0)          # 一時データ（オブジェクト）\n    c = function()          # スタックフレーム空間（関数呼び出し）\n    return A + b + c        # 出力データ\n</code></pre> <pre><code>/* 構造体 */\nstruct Node {\n    int val;\n    Node *next;\n    Node(int x) : val(x), next(nullptr) {}\n};\n\n/* 関数 */\nint func() {\n    // 特定の操作を実行...\n    return 0;\n}\n\nint algorithm(int n) {          // 入力データ\n    const int a = 0;            // 一時データ（定数）\n    int b = 0;                  // 一時データ（変数）\n    Node* node = new Node(0);   // 一時データ（オブジェクト）\n    int c = func();             // スタックフレーム空間（関数呼び出し）\n    return a + b + c;           // 出力データ\n}\n</code></pre> <pre><code>/* クラス */\nclass Node {\n    int val;\n    Node next;\n    Node(int x) { val = x; }\n}\n\n/* 関数 */\nint function() {\n    // 特定の操作を実行...\n    return 0;\n}\n\nint algorithm(int n) {          // 入力データ\n    final int a = 0;            // 一時データ（定数）\n    int b = 0;                  // 一時データ（変数）\n    Node node = new Node(0);    // 一時データ（オブジェクト）\n    int c = function();         // スタックフレーム空間（関数呼び出し）\n    return a + b + c;           // 出力データ\n}\n</code></pre> <pre><code>/* クラス */\nclass Node {\n    int val;\n    Node next;\n    Node(int x) { val = x; }\n}\n\n/* 関数 */\nint Function() {\n    // 特定の操作を実行...\n    return 0;\n}\n\nint Algorithm(int n) {  // 入力データ\n    const int a = 0;    // 一時データ（定数）\n    int b = 0;          // 一時データ（変数）\n    Node node = new(0); // 一時データ（オブジェクト）\n    int c = Function(); // スタックフレーム空間（関数呼び出し）\n    return a + b + c;   // 出力データ\n}\n</code></pre> <pre><code>/* 構造体 */\ntype node struct {\n    val  int\n    next *node\n}\n\n/* ノード構造体を作成 */\nfunc newNode(val int) *node {\n    return &amp;node{val: val}\n}\n\n/* 関数 */\nfunc function() int {\n    // 特定の操作を実行...\n    return 0\n}\n\nfunc algorithm(n int) int { // 入力データ\n    const a = 0             // 一時データ（定数）\n    b := 0                  // 一時データ（変数）\n    newNode(0)              // 一時データ（オブジェクト）\n    c := function()         // スタックフレーム空間（関数呼び出し）\n    return a + b + c        // 出力データ\n}\n</code></pre> <pre><code>/* クラス */\nclass Node {\n    var val: Int\n    var next: Node?\n\n    init(x: Int) {\n        val = x\n    }\n}\n\n/* 関数 */\nfunc function() -&gt; Int {\n    // 特定の操作を実行...\n    return 0\n}\n\nfunc algorithm(n: Int) -&gt; Int { // 入力データ\n    let a = 0                   // 一時データ（定数）\n    var b = 0                   // 一時データ（変数）\n    let node = Node(x: 0)       // 一時データ（オブジェクト）\n    let c = function()          // スタックフレーム空間（関数呼び出し）\n    return a + b + c            // 出力データ\n}\n</code></pre> <pre><code>/* クラス */\nclass Node {\n    val;\n    next;\n    constructor(val) {\n        this.val = val === undefined ? 0 : val; // ノード値\n        this.next = null;                       // 次のノードへの参照\n    }\n}\n\n/* 関数 */\nfunction constFunc() {\n    // 特定の操作を実行\n    return 0;\n}\n\nfunction algorithm(n) {         // 入力データ\n    const a = 0;                // 一時データ（定数）\n    let b = 0;                  // 一時データ（変数）\n    const node = new Node(0);   // 一時データ（オブジェクト）\n    const c = constFunc();      // スタックフレーム空間（関数呼び出し）\n    return a + b + c;           // 出力データ\n}\n</code></pre> <pre><code>/* クラス */\nclass Node {\n    val: number;\n    next: Node | null;\n    constructor(val?: number) {\n        this.val = val === undefined ? 0 : val; // ノード値\n        this.next = null;                       // 次のノードへの参照\n    }\n}\n\n/* 関数 */\nfunction constFunc(): number {\n    // 特定の操作を実行\n    return 0;\n}\n\nfunction algorithm(n: number): number { // 入力データ\n    const a = 0;                        // 一時データ（定数）\n    let b = 0;                          // 一時データ（変数）\n    const node = new Node(0);           // 一時データ（オブジェクト）\n    const c = constFunc();              // スタックフレーム空間（関数呼び出し）\n    return a + b + c;                   // 出力データ\n}\n</code></pre> <pre><code>/* クラス */\nclass Node {\n  int val;\n  Node next;\n  Node(this.val, [this.next]);\n}\n\n/* 関数 */\nint function() {\n  // 特定の操作を実行...\n  return 0;\n}\n\nint algorithm(int n) {  // 入力データ\n  const int a = 0;      // 一時データ（定数）\n  int b = 0;            // 一時データ（変数）\n  Node node = Node(0);  // 一時データ（オブジェクト）\n  int c = function();   // スタックフレーム空間（関数呼び出し）\n  return a + b + c;     // 出力データ\n}\n</code></pre> <pre><code>use std::rc::Rc;\nuse std::cell::RefCell;\n\n/* 構造体 */\nstruct Node {\n    val: i32,\n    next: Option&lt;Rc&lt;RefCell&lt;Node&gt;&gt;&gt;,\n}\n\n/* コンストラクタ */\nimpl Node {\n    fn new(val: i32) -&gt; Self {\n        Self { val: val, next: None }\n    }\n}\n\n/* 関数 */\nfn function() -&gt; i32 {\n    // 特定の操作を実行...\n    return 0;\n}\n\nfn algorithm(n: i32) -&gt; i32 {   // 入力データ\n    const a: i32 = 0;           // 一時データ（定数）\n    let mut b = 0;              // 一時データ（変数）\n    let node = Node::new(0);    // 一時データ（オブジェクト）\n    let c = function();         // スタックフレーム空間（関数呼び出し）\n    return a + b + c;           // 出力データ\n}\n</code></pre> <pre><code>/* 関数 */\nint func() {\n    // 特定の操作を実行...\n    return 0;\n}\n\nint algorithm(int n) {  // 入力データ\n    const int a = 0;    // 一時データ（定数）\n    int b = 0;          // 一時データ（変数）\n    int c = func();     // スタックフレーム空間（関数呼び出し）\n    return a + b + c;   // 出力データ\n}\n</code></pre> <pre><code>\n</code></pre>","path":["第 2 章 &nbsp; 計算量解析","2.4 &nbsp; 空間計算量"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#242","level":2,"title":"2.4.2   計算方法","text":"<p>空間計算量を計算する方法は時間計算量とほぼ同様で、統計対象を「操作数」から「使用空間のサイズ」に変更するだけです。</p> <p>しかし、時間計算量とは異なり、通常は最悪ケース空間計算量のみに焦点を当てます。これは、メモリ空間がハード要件であり、すべての入力データの下で十分なメモリ空間が確保されていることを保証する必要があるためです。</p> <p>以下のコードを考えてみましょう。最悪ケース空間計算量の「最悪ケース」という用語には2つの意味があります。</p> <ol> <li>最悪の入力データに基づく: \\(n &lt; 10\\)の場合、空間計算量は\\(O(1)\\)ですが、\\(n &gt; 10\\)の場合、初期化された配列<code>nums</code>が\\(O(n)\\)の空間を占有するため、最悪ケース空間計算量は\\(O(n)\\)です。</li> <li>アルゴリズムの実行中に使用されるピークメモリに基づく: 例えば、最後の行を実行する前、プログラムは\\(O(1)\\)の空間を占有します。配列<code>nums</code>を初期化する際、プログラムは\\(O(n)\\)の空間を占有するため、最悪ケース空間計算量は\\(O(n)\\)です。</li> </ol> PythonC++JavaC#GoSwiftJSTSDartRustCKotlin <pre><code>def algorithm(n: int):\n    a = 0               # O(1)\n    b = [0] * 10000     # O(1)\n    if n &gt; 10:\n        nums = [0] * n  # O(n)\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 0;               // O(1)\n    vector&lt;int&gt; b(10000);    // O(1)\n    if (n &gt; 10)\n        vector&lt;int&gt; nums(n); // O(n)\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 0;                   // O(1)\n    int[] b = new int[10000];    // O(1)\n    if (n &gt; 10)\n        int[] nums = new int[n]; // O(n)\n}\n</code></pre> <pre><code>void Algorithm(int n) {\n    int a = 0;                   // O(1)\n    int[] b = new int[10000];    // O(1)\n    if (n &gt; 10) {\n        int[] nums = new int[n]; // O(n)\n    }\n}\n</code></pre> <pre><code>func algorithm(n int) {\n    a := 0                      // O(1)\n    b := make([]int, 10000)     // O(1)\n    var nums []int\n    if n &gt; 10 {\n        nums := make([]int, n)  // O(n)\n    }\n    fmt.Println(a, b, nums)\n}\n</code></pre> <pre><code>func algorithm(n: Int) {\n    let a = 0 // O(1)\n    let b = Array(repeating: 0, count: 10000) // O(1)\n    if n &gt; 10 {\n        let nums = Array(repeating: 0, count: n) // O(n)\n    }\n}\n</code></pre> <pre><code>function algorithm(n) {\n    const a = 0;                   // O(1)\n    const b = new Array(10000);    // O(1)\n    if (n &gt; 10) {\n        const nums = new Array(n); // O(n)\n    }\n}\n</code></pre> <pre><code>function algorithm(n: number): void {\n    const a = 0;                   // O(1)\n    const b = new Array(10000);    // O(1)\n    if (n &gt; 10) {\n        const nums = new Array(n); // O(n)\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n  int a = 0;                            // O(1)\n  List&lt;int&gt; b = List.filled(10000, 0);  // O(1)\n  if (n &gt; 10) {\n    List&lt;int&gt; nums = List.filled(n, 0); // O(n)\n  }\n}\n</code></pre> <pre><code>fn algorithm(n: i32) {\n    let a = 0;                           // O(1)\n    let b = [0; 10000];                  // O(1)\n    if n &gt; 10 {\n        let nums = vec![0; n as usize];  // O(n)\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 0;               // O(1)\n    int b[10000];            // O(1)\n    if (n &gt; 10)\n        int nums[n] = {0};   // O(n)\n}\n</code></pre> <pre><code>\n</code></pre> <p>再帰関数では、スタックフレーム空間を考慮に入れる必要があります。以下のコードを考えてみましょう：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlin <pre><code>def function() -&gt; int:\n    # 特定の操作を実行\n    return 0\n\ndef loop(n: int):\n    \"\"\"ループ O(1)\"\"\"\n    for _ in range(n):\n        function()\n\ndef recur(n: int):\n    \"\"\"再帰 O(n)\"\"\"\n    if n == 1:\n        return\n    return recur(n - 1)\n</code></pre> <pre><code>int func() {\n    // 特定の操作を実行\n    return 0;\n}\n/* サイクル O(1) */\nvoid loop(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        func();\n    }\n}\n/* 再帰 O(n) */\nvoid recur(int n) {\n    if (n == 1) return;\n    recur(n - 1);\n}\n</code></pre> <pre><code>int function() {\n    // 特定の操作を実行\n    return 0;\n}\n/* サイクル O(1) */\nvoid loop(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        function();\n    }\n}\n/* 再帰 O(n) */\nvoid recur(int n) {\n    if (n == 1) return;\n    recur(n - 1);\n}\n</code></pre> <pre><code>int Function() {\n    // 特定の操作を実行\n    return 0;\n}\n/* サイクル O(1) */\nvoid Loop(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        Function();\n    }\n}\n/* 再帰 O(n) */\nint Recur(int n) {\n    if (n == 1) return 1;\n    return Recur(n - 1);\n}\n</code></pre> <pre><code>func function() int {\n    // 特定の操作を実行\n    return 0\n}\n\n/* サイクル O(1) */\nfunc loop(n int) {\n    for i := 0; i &lt; n; i++ {\n        function()\n    }\n}\n\n/* 再帰 O(n) */\nfunc recur(n int) {\n    if n == 1 {\n        return\n    }\n    recur(n - 1)\n}\n</code></pre> <pre><code>@discardableResult\nfunc function() -&gt; Int {\n    // 特定の操作を実行\n    return 0\n}\n\n/* サイクル O(1) */\nfunc loop(n: Int) {\n    for _ in 0 ..&lt; n {\n        function()\n    }\n}\n\n/* 再帰 O(n) */\nfunc recur(n: Int) {\n    if n == 1 {\n        return\n    }\n    recur(n: n - 1)\n}\n</code></pre> <pre><code>function constFunc() {\n    // 特定の操作を実行\n    return 0;\n}\n/* サイクル O(1) */\nfunction loop(n) {\n    for (let i = 0; i &lt; n; i++) {\n        constFunc();\n    }\n}\n/* 再帰 O(n) */\nfunction recur(n) {\n    if (n === 1) return;\n    return recur(n - 1);\n}\n</code></pre> <pre><code>function constFunc(): number {\n    // 特定の操作を実行\n    return 0;\n}\n/* サイクル O(1) */\nfunction loop(n: number): void {\n    for (let i = 0; i &lt; n; i++) {\n        constFunc();\n    }\n}\n/* 再帰 O(n) */\nfunction recur(n: number): void {\n    if (n === 1) return;\n    return recur(n - 1);\n}\n</code></pre> <pre><code>int function() {\n  // 特定の操作を実行\n  return 0;\n}\n/* サイクル O(1) */\nvoid loop(int n) {\n  for (int i = 0; i &lt; n; i++) {\n    function();\n  }\n}\n/* 再帰 O(n) */\nvoid recur(int n) {\n  if (n == 1) return;\n  recur(n - 1);\n}\n</code></pre> <pre><code>fn function() -&gt; i32 {\n    // 特定の操作を実行\n    return 0;\n}\n/* サイクル O(1) */\nfn loop(n: i32) {\n    for i in 0..n {\n        function();\n    }\n}\n/* 再帰 O(n) */\nvoid recur(n: i32) {\n    if n == 1 {\n        return;\n    }\n    recur(n - 1);\n}\n</code></pre> <pre><code>int func() {\n    // 特定の操作を実行\n    return 0;\n}\n/* サイクル O(1) */\nvoid loop(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        func();\n    }\n}\n/* 再帰 O(n) */\nvoid recur(int n) {\n    if (n == 1) return;\n    recur(n - 1);\n}\n</code></pre> <pre><code>\n</code></pre> <p><code>loop()</code>関数と<code>recur()</code>関数の時間計算量は両方とも\\(O(n)\\)ですが、それらの空間計算量は異なります。</p> <ul> <li><code>loop()</code>関数はループ内で<code>function()</code>を\\(n\\)回呼び出し、各反復の<code>function()</code>は返ってそのスタックフレーム空間を解放するため、空間計算量は\\(O(1)\\)のままです。</li> <li>再帰関数<code>recur()</code>は実行中に\\(n\\)個の未返却の<code>recur()</code>インスタンスが同時に存在するため、\\(O(n)\\)のスタックフレーム空間を占有します。</li> </ul>","path":["第 2 章 &nbsp; 計算量解析","2.4 &nbsp; 空間計算量"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#243","level":2,"title":"2.4.3   一般的な種類","text":"<p>入力データのサイズを\\(n\\)とすると、下図は一般的な空間計算量の種類を示しています（低いものから高いものへと並べられています）。</p> \\[ \\begin{aligned} &amp; O(1) &lt; O(\\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \\newline &amp; \\text{定数} &lt; \\text{対数} &lt; \\text{線形} &lt; \\text{二次} &lt; \\text{指数} \\end{aligned} \\] <p></p> <p> 図 2-16   Common types of space complexity </p>","path":["第 2 章 &nbsp; 計算量解析","2.4 &nbsp; 空間計算量"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#1-o1","level":3,"title":"1.   定数オーダー \\(O(1)\\)","text":"<p>定数オーダーは、入力データサイズ\\(n\\)とは無関係な定数、変数、オブジェクトで一般的です。</p> <p>ループで変数を初期化したり関数を呼び出したりするために占有されるメモリは、次のサイクルに入る際に解放され、空間上で累積されないため、空間計算量は\\(O(1)\\)のままです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby space_complexity.py<pre><code>def function() -&gt; int:\n    \"\"\"関数\"\"\"\n    # 何らかの操作を実行\n    return 0\n\ndef constant(n: int):\n    \"\"\"定数複雑度\"\"\"\n    # 定数、変数、オブジェクトは O(1) のスペースを占有\n    a = 0\n    nums = [0] * 10000\n    node = ListNode(0)\n    # ループ内の変数は O(1) のスペースを占有\n    for _ in range(n):\n        c = 0\n    # ループ内の関数は O(1) のスペースを占有\n    for _ in range(n):\n        function()\n</code></pre> space_complexity.cpp<pre><code>/* 関数 */\nint func() {\n    // 何らかの操作を実行\n    return 0;\n}\n\n/* 定数計算量 */\nvoid constant(int n) {\n    // 定数、変数、オブジェクトは O(1) 空間を占める\n    const int a = 0;\n    int b = 0;\n    vector&lt;int&gt; nums(10000);\n    ListNode node(0);\n    // ループ内の変数は O(1) 空間を占める\n    for (int i = 0; i &lt; n; i++) {\n        int c = 0;\n    }\n    // ループ内の関数は O(1) 空間を占める\n    for (int i = 0; i &lt; n; i++) {\n        func();\n    }\n}\n</code></pre> space_complexity.java<pre><code>/* 関数 */\nint function() {\n    // 何らかの操作を実行\n    return 0;\n}\n\n/* 定数計算量 */\nvoid constant(int n) {\n    // 定数、変数、オブジェクトは O(1) 空間を占める\n    final int a = 0;\n    int b = 0;\n    int[] nums = new int[10000];\n    ListNode node = new ListNode(0);\n    // ループ内の変数は O(1) 空間を占める\n    for (int i = 0; i &lt; n; i++) {\n        int c = 0;\n    }\n    // ループ内の関数は O(1) 空間を占める\n    for (int i = 0; i &lt; n; i++) {\n        function();\n    }\n}\n</code></pre> space_complexity.cs<pre><code>[class]{space_complexity}-[func]{Function}\n\n[class]{space_complexity}-[func]{Constant}\n</code></pre> space_complexity.go<pre><code>[class]{}-[func]{function}\n\n[class]{}-[func]{spaceConstant}\n</code></pre> space_complexity.swift<pre><code>[class]{}-[func]{function}\n\n[class]{}-[func]{constant}\n</code></pre> space_complexity.js<pre><code>[class]{}-[func]{constFunc}\n\n[class]{}-[func]{constant}\n</code></pre> space_complexity.ts<pre><code>[class]{}-[func]{constFunc}\n\n[class]{}-[func]{constant}\n</code></pre> space_complexity.dart<pre><code>[class]{}-[func]{function}\n\n[class]{}-[func]{constant}\n</code></pre> space_complexity.rs<pre><code>[class]{}-[func]{function}\n\n[class]{}-[func]{constant}\n</code></pre> space_complexity.c<pre><code>[class]{}-[func]{func}\n\n[class]{}-[func]{constant}\n</code></pre> space_complexity.kt<pre><code>[class]{}-[func]{function}\n\n[class]{}-[func]{constant}\n</code></pre> space_complexity.rb<pre><code>[class]{}-[func]{function}\n\n[class]{}-[func]{constant}\n</code></pre>","path":["第 2 章 &nbsp; 計算量解析","2.4 &nbsp; 空間計算量"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#2-on","level":3,"title":"2.   線形オーダー \\(O(n)\\)","text":"<p>線形オーダーは配列、連結リスト、スタック、キューなどで一般的で、要素数は\\(n\\)に比例します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby space_complexity.py<pre><code>def linear(n: int):\n    \"\"\"線形複雑度\"\"\"\n    # 長さ n のリストは O(n) のスペースを占有\n    nums = [0] * n\n    # 長さ n のハッシュマップは O(n) のスペースを占有\n    hmap = dict[int, str]()\n    for i in range(n):\n        hmap[i] = str(i)\n</code></pre> space_complexity.cpp<pre><code>/* 線形計算量 */\nvoid linear(int n) {\n    // 長さ n の配列は O(n) 空間を占める\n    vector&lt;int&gt; nums(n);\n    // 長さ n のリストは O(n) 空間を占める\n    vector&lt;ListNode&gt; nodes;\n    for (int i = 0; i &lt; n; i++) {\n        nodes.push_back(ListNode(i));\n    }\n    // 長さ n のハッシュテーブルは O(n) 空間を占める\n    unordered_map&lt;int, string&gt; map;\n    for (int i = 0; i &lt; n; i++) {\n        map[i] = to_string(i);\n    }\n}\n</code></pre> space_complexity.java<pre><code>/* 線形計算量 */\nvoid linear(int n) {\n    // 長さ n の配列は O(n) 空間を占める\n    int[] nums = new int[n];\n    // 長さ n のリストは O(n) 空間を占める\n    List&lt;ListNode&gt; nodes = new ArrayList&lt;&gt;();\n    for (int i = 0; i &lt; n; i++) {\n        nodes.add(new ListNode(i));\n    }\n    // 長さ n のハッシュテーブルは O(n) 空間を占める\n    Map&lt;Integer, String&gt; map = new HashMap&lt;&gt;();\n    for (int i = 0; i &lt; n; i++) {\n        map.put(i, String.valueOf(i));\n    }\n}\n</code></pre> space_complexity.cs<pre><code>[class]{space_complexity}-[func]{Linear}\n</code></pre> space_complexity.go<pre><code>[class]{}-[func]{spaceLinear}\n</code></pre> space_complexity.swift<pre><code>[class]{}-[func]{linear}\n</code></pre> space_complexity.js<pre><code>[class]{}-[func]{linear}\n</code></pre> space_complexity.ts<pre><code>[class]{}-[func]{linear}\n</code></pre> space_complexity.dart<pre><code>[class]{}-[func]{linear}\n</code></pre> space_complexity.rs<pre><code>[class]{}-[func]{linear}\n</code></pre> space_complexity.c<pre><code>[class]{HashTable}-[func]{}\n\n[class]{}-[func]{linear}\n</code></pre> space_complexity.kt<pre><code>[class]{}-[func]{linear}\n</code></pre> space_complexity.rb<pre><code>[class]{}-[func]{linear}\n</code></pre> <p>下図に示されているように、この関数の再帰深度は\\(n\\)で、\\(n\\)個の未返却の<code>linear_recur()</code>関数インスタンスがあり、\\(O(n)\\)サイズのスタックフレーム空間を使用します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby space_complexity.py<pre><code>def linear_recur(n: int):\n    \"\"\"線形複雑度（再帰実装）\"\"\"\n    print(\"再帰 n =\", n)\n    if n == 1:\n        return\n    linear_recur(n - 1)\n</code></pre> space_complexity.cpp<pre><code>/* 線形計算量（再帰実装） */\nvoid linearRecur(int n) {\n    cout &lt;&lt; \"再帰 n = \" &lt;&lt; n &lt;&lt; endl;\n    if (n == 1)\n        return;\n    linearRecur(n - 1);\n}\n</code></pre> space_complexity.java<pre><code>/* 線形計算量（再帰実装） */\nvoid linearRecur(int n) {\n    System.out.println(\"再帰 n = \" + n);\n    if (n == 1)\n        return;\n    linearRecur(n - 1);\n}\n</code></pre> space_complexity.cs<pre><code>[class]{space_complexity}-[func]{LinearRecur}\n</code></pre> space_complexity.go<pre><code>[class]{}-[func]{spaceLinearRecur}\n</code></pre> space_complexity.swift<pre><code>[class]{}-[func]{linearRecur}\n</code></pre> space_complexity.js<pre><code>[class]{}-[func]{linearRecur}\n</code></pre> space_complexity.ts<pre><code>[class]{}-[func]{linearRecur}\n</code></pre> space_complexity.dart<pre><code>[class]{}-[func]{linearRecur}\n</code></pre> space_complexity.rs<pre><code>[class]{}-[func]{linear_recur}\n</code></pre> space_complexity.c<pre><code>[class]{}-[func]{linearRecur}\n</code></pre> space_complexity.kt<pre><code>[class]{}-[func]{linearRecur}\n</code></pre> space_complexity.rb<pre><code>[class]{}-[func]{linear_recur}\n</code></pre> <p></p> <p> 図 2-17   Recursive function generating linear order space complexity </p>","path":["第 2 章 &nbsp; 計算量解析","2.4 &nbsp; 空間計算量"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#3-on2","level":3,"title":"3.   二次オーダー \\(O(n^2)\\)","text":"<p>二次オーダーは行列やグラフで一般的で、要素数は\\(n\\)の二乗に比例します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby space_complexity.py<pre><code>def quadratic(n: int):\n    \"\"\"平方複雑度\"\"\"\n    # 二次元リストは O(n^2) のスペースを占有\n    num_matrix = [[0] * n for _ in range(n)]\n</code></pre> space_complexity.cpp<pre><code>/* 二次計算量 */\nvoid quadratic(int n) {\n    // 二次元リストは O(n^2) 空間を占める\n    vector&lt;vector&lt;int&gt;&gt; numMatrix;\n    for (int i = 0; i &lt; n; i++) {\n        vector&lt;int&gt; tmp;\n        for (int j = 0; j &lt; n; j++) {\n            tmp.push_back(0);\n        }\n        numMatrix.push_back(tmp);\n    }\n}\n</code></pre> space_complexity.java<pre><code>/* 二次計算量 */\nvoid quadratic(int n) {\n    // 行列は O(n^2) 空間を占める\n    int[][] numMatrix = new int[n][n];\n    // 二次元リストは O(n^2) 空間を占める\n    List&lt;List&lt;Integer&gt;&gt; numList = new ArrayList&lt;&gt;();\n    for (int i = 0; i &lt; n; i++) {\n        List&lt;Integer&gt; tmp = new ArrayList&lt;&gt;();\n        for (int j = 0; j &lt; n; j++) {\n            tmp.add(0);\n        }\n        numList.add(tmp);\n    }\n}\n</code></pre> space_complexity.cs<pre><code>[class]{space_complexity}-[func]{Quadratic}\n</code></pre> space_complexity.go<pre><code>[class]{}-[func]{spaceQuadratic}\n</code></pre> space_complexity.swift<pre><code>[class]{}-[func]{quadratic}\n</code></pre> space_complexity.js<pre><code>[class]{}-[func]{quadratic}\n</code></pre> space_complexity.ts<pre><code>[class]{}-[func]{quadratic}\n</code></pre> space_complexity.dart<pre><code>[class]{}-[func]{quadratic}\n</code></pre> space_complexity.rs<pre><code>[class]{}-[func]{quadratic}\n</code></pre> space_complexity.c<pre><code>[class]{}-[func]{quadratic}\n</code></pre> space_complexity.kt<pre><code>[class]{}-[func]{quadratic}\n</code></pre> space_complexity.rb<pre><code>[class]{}-[func]{quadratic}\n</code></pre> <p>下図に示されているように、この関数の再帰深度は\\(n\\)で、各再帰呼び出しで長さ\\(n\\)、\\(n-1\\)、\\(\\dots\\)、\\(2\\)、\\(1\\)の配列が初期化され、平均\\(n/2\\)となり、全体として\\(O(n^2)\\)の空間を占有します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby space_complexity.py<pre><code>def quadratic_recur(n: int) -&gt; int:\n    \"\"\"平方複雑度（再帰実装）\"\"\"\n    if n &lt;= 0:\n        return 0\n    nums = [0] * n\n    print(f\"再帰 n = {n} の中で配列の長さ = {len(nums)}\")\n    return quadratic_recur(n - 1)\n</code></pre> space_complexity.cpp<pre><code>/* 二次計算量（再帰実装） */\nint quadraticRecur(int n) {\n    if (n &lt;= 0)\n        return 0;\n    vector&lt;int&gt; nums(n);\n    cout &lt;&lt; \"再帰 n = \" &lt;&lt; n &lt;&lt; \", nums の長さ = \" &lt;&lt; nums.size() &lt;&lt; endl;\n    return quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.java<pre><code>/* 二次計算量（再帰実装） */\nint quadraticRecur(int n) {\n    if (n &lt;= 0)\n        return 0;\n    // 配列 nums の長さ = n, n-1, ..., 2, 1\n    int[] nums = new int[n];\n    System.out.println(\"再帰 n = \" + n + \" の nums の長さ = \" + nums.length);\n    return quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.cs<pre><code>[class]{space_complexity}-[func]{QuadraticRecur}\n</code></pre> space_complexity.go<pre><code>[class]{}-[func]{spaceQuadraticRecur}\n</code></pre> space_complexity.swift<pre><code>[class]{}-[func]{quadraticRecur}\n</code></pre> space_complexity.js<pre><code>[class]{}-[func]{quadraticRecur}\n</code></pre> space_complexity.ts<pre><code>[class]{}-[func]{quadraticRecur}\n</code></pre> space_complexity.dart<pre><code>[class]{}-[func]{quadraticRecur}\n</code></pre> space_complexity.rs<pre><code>[class]{}-[func]{quadratic_recur}\n</code></pre> space_complexity.c<pre><code>[class]{}-[func]{quadraticRecur}\n</code></pre> space_complexity.kt<pre><code>[class]{}-[func]{quadraticRecur}\n</code></pre> space_complexity.rb<pre><code>[class]{}-[func]{quadratic_recur}\n</code></pre> <p></p> <p> 図 2-18   Recursive function generating quadratic order space complexity </p>","path":["第 2 章 &nbsp; 計算量解析","2.4 &nbsp; 空間計算量"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#4-o2n","level":3,"title":"4.   指数オーダー \\(O(2^n)\\)","text":"<p>指数オーダーは二分木で一般的です。下図を観察すると、\\(n\\)レベルの「完全二分木」は\\(2^n - 1\\)個のノードを持ち、\\(O(2^n)\\)の空間を占有します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby space_complexity.py<pre><code>def build_tree(n: int) -&gt; TreeNode | None:\n    \"\"\"指数複雑度（完全二分木の構築）\"\"\"\n    if n == 0:\n        return None\n    root = TreeNode(0)\n    root.left = build_tree(n - 1)\n    root.right = build_tree(n - 1)\n    return root\n</code></pre> space_complexity.cpp<pre><code>/* 指数計算量（完全二分木の構築） */\nTreeNode *buildTree(int n) {\n    if (n == 0)\n        return nullptr;\n    TreeNode *root = new TreeNode(0);\n    root-&gt;left = buildTree(n - 1);\n    root-&gt;right = buildTree(n - 1);\n    return root;\n}\n</code></pre> space_complexity.java<pre><code>/* 指数計算量（完全二分木の構築） */\nTreeNode buildTree(int n) {\n    if (n == 0)\n        return null;\n    TreeNode root = new TreeNode(0);\n    root.left = buildTree(n - 1);\n    root.right = buildTree(n - 1);\n    return root;\n}\n</code></pre> space_complexity.cs<pre><code>[class]{space_complexity}-[func]{BuildTree}\n</code></pre> space_complexity.go<pre><code>[class]{}-[func]{buildTree}\n</code></pre> space_complexity.swift<pre><code>[class]{}-[func]{buildTree}\n</code></pre> space_complexity.js<pre><code>[class]{}-[func]{buildTree}\n</code></pre> space_complexity.ts<pre><code>[class]{}-[func]{buildTree}\n</code></pre> space_complexity.dart<pre><code>[class]{}-[func]{buildTree}\n</code></pre> space_complexity.rs<pre><code>[class]{}-[func]{build_tree}\n</code></pre> space_complexity.c<pre><code>[class]{}-[func]{buildTree}\n</code></pre> space_complexity.kt<pre><code>[class]{}-[func]{buildTree}\n</code></pre> space_complexity.rb<pre><code>[class]{}-[func]{build_tree}\n</code></pre> <p></p> <p> 図 2-19   Full binary tree generating exponential order space complexity </p>","path":["第 2 章 &nbsp; 計算量解析","2.4 &nbsp; 空間計算量"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#5-olog-n","level":3,"title":"5.   対数オーダー \\(O(\\log n)\\)","text":"<p>対数オーダーは分割統治アルゴリズムで一般的です。例えば、マージソートでは、長さ\\(n\\)の配列が各ラウンドで再帰的に半分に分割され、高さ\\(\\log n\\)の再帰木を形成し、\\(O(\\log n)\\)のスタックフレーム空間を使用します。</p> <p>別の例は、数値を文字列に変換することです。正の整数\\(n\\)が与えられた場合、その桁数は\\(\\log_{10} n + 1\\)で、文字列の長さに対応するため、空間計算量は\\(O(\\log_{10} n + 1) = O(\\log n)\\)です。</p>","path":["第 2 章 &nbsp; 計算量解析","2.4 &nbsp; 空間計算量"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#244","level":2,"title":"2.4.4   時間と空間のバランス","text":"<p>理想的には、時間計算量と空間計算量の両方が最適であることを目指します。しかし、実際には両方を同時に最適化することはしばしば困難です。</p> <p>時間計算量を下げることは通常、空間計算量の増加を代償とし、その逆も同様です。アルゴリズムの速度を向上させるためにメモリ空間を犠牲にするアプローチは「時空トレードオフ」として知られ、その逆は「空時トレードオフ」として知られています。</p> <p>選択は、どちらの側面をより重視するかに依存します。ほとんどの場合、時間は空間よりも貴重であるため、「時空トレードオフ」がより一般的な戦略です。もちろん、大量のデータを扱う際は空間計算量を制御することも非常に重要です。</p>","path":["第 2 章 &nbsp; 計算量解析","2.4 &nbsp; 空間計算量"],"tags":[]},{"location":"chapter_computational_complexity/summary/","level":1,"title":"2.5   まとめ","text":"","path":["第 2 章 &nbsp; 計算量解析","2.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_computational_complexity/summary/#1","level":3,"title":"1.   重要なレビュー","text":"<p>アルゴリズム効率評価</p> <ul> <li>時間効率と空間効率は、アルゴリズムの優劣を評価する2つの主要な基準です。</li> <li>実際のテストによってアルゴリズムの効率を評価できますが、テスト環境の影響を排除することは困難で、大量の計算リソースを消費します。</li> <li>複雑度分析は実際のテストの欠点を克服できます。その結果はすべての動作プラットフォームに適用でき、異なるデータスケールでのアルゴリズムの効率を明らかにできます。</li> </ul> <p>時間計算量</p> <ul> <li>時間計算量は、データ量の増加に伴うアルゴリズムの実行時間の傾向を測定し、アルゴリズムの効率を効果的に評価します。しかし、入力データ量が少ない場合や時間計算量が同じ場合など、特定のケースでは失敗することがあり、アルゴリズムの効率を正確に比較することが困難になります。</li> <li>最悪ケース時間計算量はビッグ\\(O\\)記法を使用して表記され、漸近上限を表し、\\(n\\)が無限大に近づくにつれての操作数\\(T(n)\\)の増加レベルを反映します。</li> <li>時間計算量の計算には2つのステップが含まれます：まず操作数をカウントし、次に漸近上限を決定します。</li> <li>一般的な時間計算量は、低いものから高いものへと並べると、\\(O(1)\\)、\\(O(\\log n)\\)、\\(O(n)\\)、\\(O(n \\log n)\\)、\\(O(n^2)\\)、\\(O(2^n)\\)、\\(O(n!)\\)などが含まれます。</li> <li>一部のアルゴリズムの時間計算量は固定されておらず、入力データの分布に依存します。時間計算量は最悪、最良、平均のケースに分けられます。最良ケースは、入力データが最良ケースを達成するために厳格な条件を満たす必要があるため、ほとんど使用されません。</li> <li>平均時間計算量は、ランダムデータ入力下でのアルゴリズムの効率を反映し、実際のアプリケーションでのアルゴリズムの性能に密接に類似しています。平均時間計算量の計算には、入力データの分布とその後の数学的期待値を考慮する必要があります。</li> </ul> <p>空間計算量</p> <ul> <li>空間計算量は、時間計算量と同様に、データ量の増加に伴うアルゴリズムが占有するメモリ空間の傾向を測定します。</li> <li>アルゴリズムの実行中に使用される関連メモリ空間は、入力空間、一時空間、出力空間に分けることができます。一般的に、入力空間は空間計算量の計算に含まれません。一時空間は一時データ、スタックフレーム空間、命令空間に分けることができ、スタックフレーム空間は通常、再帰関数でのみ空間計算量に影響します。</li> <li>通常は最悪ケース空間計算量のみに焦点を当てます。これは、最悪の入力データと操作の最悪の瞬間でのアルゴリズムの空間計算量を計算することを意味します。</li> <li>一般的な空間計算量は、低いものから高いものへと並べると、\\(O(1)\\)、\\(O(\\log n)\\)、\\(O(n)\\)、\\(O(n^2)\\)、\\(O(2^n)\\)などが含まれます。</li> </ul>","path":["第 2 章 &nbsp; 計算量解析","2.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_computational_complexity/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: 末尾再帰の空間計算量は\\(O(1)\\)ですか？</p> <p>理論的には、末尾再帰関数の空間計算量は\\(O(1)\\)に最適化できます。しかし、ほとんどのプログラミング言語（Java、Python、C++、Go、C#など）は末尾再帰の自動最適化をサポートしていないため、一般的に空間計算量は\\(O(n)\\)と考えられています。</p> <p>Q: 「関数」と「メソッド」という用語の違いは何ですか？</p> <p>関数は独立して実行でき、すべてのパラメータが明示的に渡されます。メソッドはオブジェクトに関連付けられ、それを呼び出すオブジェクトに暗黙的に渡され、クラスのインスタンス内に含まれるデータを操作できます。</p> <p>一般的なプログラミング言語からの例をいくつか示します：</p> <ul> <li>Cは手続き型プログラミング言語で、オブジェクト指向の概念がないため、関数のみがあります。しかし、構造体（struct）を作成することでオブジェクト指向プログラミングをシミュレートでき、これらの構造体に関連付けられた関数は他のプログラミング言語のメソッドと同等です。</li> <li>JavaとC#はオブジェクト指向プログラミング言語で、コードブロック（メソッド）は通常クラスの一部です。静的メソッドはクラスにバインドされ、特定のインスタンス変数にアクセスできないため、関数のように動作します。</li> <li>C++とPythonは手続き型プログラミング（関数）とオブジェクト指向プログラミング（メソッド）の両方をサポートしています。</li> </ul> <p>Q: 「空間計算量の一般的な種類」の図は、占有空間の絶対サイズを反映していますか？</p> <p>いいえ、図は空間計算量を示しており、これは増加傾向を反映するものであり、占有空間の絶対サイズではありません。</p> <p>\\(n = 8\\)を取ると、各曲線の値がその関数に対応していないことに気づくかもしれません。これは、各曲線に定数項が含まれているためで、値の範囲を視覚的に快適な範囲に圧縮することを意図しています。</p> <p>実際には、通常は各メソッドの「定数項」複雑度を知らないため、複雑度のみに基づいて\\(n = 8\\)の最良ソリューションを選択することは一般的に不可能です。しかし、\\(n = 8^5\\)の場合、増加傾向が支配的になるため、選択がはるかに容易になります。</p>","path":["第 2 章 &nbsp; 計算量解析","2.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/","level":1,"title":"2.3   時間計算量","text":"<p>実行時間は、アルゴリズムの効率を直感的に評価できます。アルゴリズムの実行時間を正確に推定するにはどうすればよいでしょうか？</p> <ol> <li>実行プラットフォームの決定: これには、ハードウェア構成、プログラミング言語、システム環境などが含まれ、これらすべてがコードの実行効率に影響する可能性があります。</li> <li>様々な計算操作の実行時間の評価: 例えば、加算操作<code>+</code>は1 ns、乗算操作<code>*</code>は10 ns、印刷操作<code>print()</code>は5 nsなどかかる可能性があります。</li> <li>コード内のすべての計算操作をカウント: これらすべての操作の実行時間を合計すると、総実行時間が得られます。</li> </ol> <p>例えば、入力サイズが\\(n\\)の以下のコードを考えてみましょう：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlin <pre><code># 特定の操作プラットフォーム下で\ndef algorithm(n: int):\n    a = 2      # 1 ns\n    a = a + 1  # 1 ns\n    a = a * 2  # 10 ns\n    # n回ループ\n    for _ in range(n):  # 1 ns\n        print(0)        # 5 ns\n</code></pre> <pre><code>// 特定の操作プラットフォーム下で\nvoid algorithm(int n) {\n    int a = 2;  // 1 ns\n    a = a + 1;  // 1 ns\n    a = a * 2;  // 10 ns\n    // n回ループ\n    for (int i = 0; i &lt; n; i++) {  // 1 ns, 毎回i++が実行される\n        cout &lt;&lt; 0 &lt;&lt; endl;         // 5 ns\n    }\n}\n</code></pre> <pre><code>// 特定の操作プラットフォーム下で\nvoid algorithm(int n) {\n    int a = 2;  // 1 ns\n    a = a + 1;  // 1 ns\n    a = a * 2;  // 10 ns\n    // n回ループ\n    for (int i = 0; i &lt; n; i++) {  // 1 ns, 毎回i++が実行される\n        System.out.println(0);     // 5 ns\n    }\n}\n</code></pre> <pre><code>// 特定の操作プラットフォーム下で\nvoid Algorithm(int n) {\n    int a = 2;  // 1 ns\n    a = a + 1;  // 1 ns\n    a = a * 2;  // 10 ns\n    // n回ループ\n    for (int i = 0; i &lt; n; i++) {  // 1 ns, 毎回i++が実行される\n        Console.WriteLine(0);      // 5 ns\n    }\n}\n</code></pre> <pre><code>// 特定の操作プラットフォーム下で\nfunc algorithm(n int) {\n    a := 2     // 1 ns\n    a = a + 1  // 1 ns\n    a = a * 2  // 10 ns\n    // n回ループ\n    for i := 0; i &lt; n; i++ {  // 1 ns\n        fmt.Println(a)        // 5 ns\n    }\n}\n</code></pre> <pre><code>// 特定の操作プラットフォーム下で\nfunc algorithm(n: Int) {\n    var a = 2 // 1 ns\n    a = a + 1 // 1 ns\n    a = a * 2 // 10 ns\n    // n回ループ\n    for _ in 0 ..&lt; n { // 1 ns\n        print(0) // 5 ns\n    }\n}\n</code></pre> <pre><code>// 特定の操作プラットフォーム下で\nfunction algorithm(n) {\n    var a = 2; // 1 ns\n    a = a + 1; // 1 ns\n    a = a * 2; // 10 ns\n    // n回ループ\n    for(let i = 0; i &lt; n; i++) { // 1 ns, 毎回i++が実行される\n        console.log(0); // 5 ns\n    }\n}\n</code></pre> <pre><code>// 特定の操作プラットフォーム下で\nfunction algorithm(n: number): void {\n    var a: number = 2; // 1 ns\n    a = a + 1; // 1 ns\n    a = a * 2; // 10 ns\n    // n回ループ\n    for(let i = 0; i &lt; n; i++) { // 1 ns, 毎回i++が実行される\n        console.log(0); // 5 ns\n    }\n}\n</code></pre> <pre><code>// 特定の操作プラットフォーム下で\nvoid algorithm(int n) {\n  int a = 2; // 1 ns\n  a = a + 1; // 1 ns\n  a = a * 2; // 10 ns\n  // n回ループ\n  for (int i = 0; i &lt; n; i++) { // 1 ns, 毎回i++が実行される\n    print(0); // 5 ns\n  }\n}\n</code></pre> <pre><code>// 特定の操作プラットフォーム下で\nfn algorithm(n: i32) {\n    let mut a = 2;      // 1 ns\n    a = a + 1;          // 1 ns\n    a = a * 2;          // 10 ns\n    // n回ループ\n    for _ in 0..n {     // 毎回i++で1 ns\n        println!(\"{}\", 0);  // 5 ns\n    }\n}\n</code></pre> <pre><code>// 特定の操作プラットフォーム下で\nvoid algorithm(int n) {\n    int a = 2;  // 1 ns\n    a = a + 1;  // 1 ns\n    a = a * 2;  // 10 ns\n    // n回ループ\n    for (int i = 0; i &lt; n; i++) {   // 1 ns, 毎回i++が実行される\n        printf(\"%d\", 0);            // 5 ns\n    }\n}\n</code></pre> <pre><code>\n</code></pre> <p>上記の方法を使用すると、アルゴリズムの実行時間は\\((6n + 12)\\) nsとして計算できます：</p> \\[ 1 + 1 + 10 + (1 + 5) \\times n = 6n + 12 \\] <p>しかし、実際には、アルゴリズムの実行時間をカウントすることは実用的でも合理的でもありません。第一に、推定時間を実行プラットフォームに結び付けたくありません。アルゴリズムは様々なプラットフォームで実行される必要があるからです。第二に、各種操作の実行時間を知ることは困難であり、推定プロセスを難しくします。</p>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#231","level":2,"title":"2.3.1   時間増加傾向の評価","text":"<p>時間計算量分析は、アルゴリズムの実行時間をカウントするのではなく、**データ量が増加するにつれての実行時間の増加傾向**を分析します。</p> <p>この「時間増加傾向」の概念を例で理解しましょう。入力データサイズを\\(n\\)とし、3つのアルゴリズム<code>A</code>、<code>B</code>、<code>C</code>を考えてみます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlin <pre><code># アルゴリズムAの時間計算量：定数オーダー\ndef algorithm_A(n: int):\n    print(0)\n# アルゴリズムBの時間計算量：線形オーダー\ndef algorithm_B(n: int):\n    for _ in range(n):\n        print(0)\n# アルゴリズムCの時間計算量：定数オーダー\ndef algorithm_C(n: int):\n    for _ in range(1000000):\n        print(0)\n</code></pre> <pre><code>// アルゴリズムAの時間計算量：定数オーダー\nvoid algorithm_A(int n) {\n    cout &lt;&lt; 0 &lt;&lt; endl;\n}\n// アルゴリズムBの時間計算量：線形オーダー\nvoid algorithm_B(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        cout &lt;&lt; 0 &lt;&lt; endl;\n    }\n}\n// アルゴリズムCの時間計算量：定数オーダー\nvoid algorithm_C(int n) {\n    for (int i = 0; i &lt; 1000000; i++) {\n        cout &lt;&lt; 0 &lt;&lt; endl;\n    }\n}\n</code></pre> <pre><code>// アルゴリズムAの時間計算量：定数オーダー\nvoid algorithm_A(int n) {\n    System.out.println(0);\n}\n// アルゴリズムBの時間計算量：線形オーダー\nvoid algorithm_B(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        System.out.println(0);\n    }\n}\n// アルゴリズムCの時間計算量：定数オーダー\nvoid algorithm_C(int n) {\n    for (int i = 0; i &lt; 1000000; i++) {\n        System.out.println(0);\n    }\n}\n</code></pre> <pre><code>// アルゴリズムAの時間計算量：定数オーダー\nvoid AlgorithmA(int n) {\n    Console.WriteLine(0);\n}\n// アルゴリズムBの時間計算量：線形オーダー\nvoid AlgorithmB(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        Console.WriteLine(0);\n    }\n}\n// アルゴリズムCの時間計算量：定数オーダー\nvoid AlgorithmC(int n) {\n    for (int i = 0; i &lt; 1000000; i++) {\n        Console.WriteLine(0);\n    }\n}\n</code></pre> <pre><code>// アルゴリズムAの時間計算量：定数オーダー\nfunc algorithm_A(n int) {\n    fmt.Println(0)\n}\n// アルゴリズムBの時間計算量：線形オーダー\nfunc algorithm_B(n int) {\n    for i := 0; i &lt; n; i++ {\n        fmt.Println(0)\n    }\n}\n// アルゴリズムCの時間計算量：定数オーダー\nfunc algorithm_C(n int) {\n    for i := 0; i &lt; 1000000; i++ {\n        fmt.Println(0)\n    }\n}\n</code></pre> <pre><code>// アルゴリズムAの時間計算量：定数オーダー\nfunc algorithmA(n: Int) {\n    print(0)\n}\n\n// アルゴリズムBの時間計算量：線形オーダー\nfunc algorithmB(n: Int) {\n    for _ in 0 ..&lt; n {\n        print(0)\n    }\n}\n\n// アルゴリズムCの時間計算量：定数オーダー\nfunc algorithmC(n: Int) {\n    for _ in 0 ..&lt; 1_000_000 {\n        print(0)\n    }\n}\n</code></pre> <pre><code>// アルゴリズムAの時間計算量：定数オーダー\nfunction algorithm_A(n) {\n    console.log(0);\n}\n// アルゴリズムBの時間計算量：線形オーダー\nfunction algorithm_B(n) {\n    for (let i = 0; i &lt; n; i++) {\n        console.log(0);\n    }\n}\n// アルゴリズムCの時間計算量：定数オーダー\nfunction algorithm_C(n) {\n    for (let i = 0; i &lt; 1000000; i++) {\n        console.log(0);\n    }\n}\n</code></pre> <pre><code>// アルゴリズムAの時間計算量：定数オーダー\nfunction algorithm_A(n: number): void {\n    console.log(0);\n}\n// アルゴリズムBの時間計算量：線形オーダー\nfunction algorithm_B(n: number): void {\n    for (let i = 0; i &lt; n; i++) {\n        console.log(0);\n    }\n}\n// アルゴリズムCの時間計算量：定数オーダー\nfunction algorithm_C(n: number): void {\n    for (let i = 0; i &lt; 1000000; i++) {\n        console.log(0);\n    }\n}\n</code></pre> <pre><code>// アルゴリズムAの時間計算量：定数オーダー\nvoid algorithmA(int n) {\n  print(0);\n}\n// アルゴリズムBの時間計算量：線形オーダー\nvoid algorithmB(int n) {\n  for (int i = 0; i &lt; n; i++) {\n    print(0);\n  }\n}\n// アルゴリズムCの時間計算量：定数オーダー\nvoid algorithmC(int n) {\n  for (int i = 0; i &lt; 1000000; i++) {\n    print(0);\n  }\n}\n</code></pre> <pre><code>// アルゴリズムAの時間計算量：定数オーダー\nfn algorithm_A(n: i32) {\n    println!(\"{}\", 0);\n}\n// アルゴリズムBの時間計算量：線形オーダー\nfn algorithm_B(n: i32) {\n    for _ in 0..n {\n        println!(\"{}\", 0);\n    }\n}\n// アルゴリズムCの時間計算量：定数オーダー\nfn algorithm_C(n: i32) {\n    for _ in 0..1000000 {\n        println!(\"{}\", 0);\n    }\n}\n</code></pre> <pre><code>// アルゴリズムAの時間計算量：定数オーダー\nvoid algorithm_A(int n) {\n    printf(\"%d\", 0);\n}\n// アルゴリズムBの時間計算量：線形オーダー\nvoid algorithm_B(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        printf(\"%d\", 0);\n    }\n}\n// アルゴリズムCの時間計算量：定数オーダー\nvoid algorithm_C(int n) {\n    for (int i = 0; i &lt; 1000000; i++) {\n        printf(\"%d\", 0);\n    }\n}\n</code></pre> <pre><code>\n</code></pre> <p>下図はこれら3つのアルゴリズムの時間計算量を示しています。</p> <ul> <li>アルゴリズム<code>A</code>には1つの印刷操作のみがあり、その実行時間は\\(n\\)とともに増加しません。その時間計算量は「定数オーダー」と考えられます。</li> <li>アルゴリズム<code>B</code>には\\(n\\)回ループする印刷操作があり、その実行時間は\\(n\\)と線形に増加します。その時間計算量は「線形オーダー」です。</li> <li>アルゴリズム<code>C</code>には1,000,000回ループする印刷操作があります。時間はかかりますが、入力データサイズ\\(n\\)とは無関係です。したがって、<code>C</code>の時間計算量は<code>A</code>と同じ「定数オーダー」です。</li> </ul> <p></p> <p> 図 2-7   Time growth trend of algorithms a, b, and c </p> <p>アルゴリズムの実行時間を直接カウントすることと比較して、時間計算量分析の特徴は何でしょうか？</p> <ul> <li>時間計算量はアルゴリズムの効率を効果的に評価します。例えば、アルゴリズム<code>B</code>は線形に増加する実行時間を持ち、\\(n &gt; 1\\)の時はアルゴリズム<code>A</code>より遅く、\\(n &gt; 1,000,000\\)の時は<code>C</code>より遅くなります。実際、入力データサイズ\\(n\\)が十分に大きい限り、「定数オーダー」複雑度アルゴリズムは常に「線形オーダー」よりも優れており、時間増加傾向の本質を示しています。</li> <li>時間計算量分析はより直感的です。明らかに、実行プラットフォームと計算操作の種類は実行時間増加の傾向とは無関係です。したがって、時間計算量分析では、すべての計算操作の実行時間を同じ「単位時間」として扱うことができ、「計算操作実行時間カウント」を「計算操作カウント」に単純化できます。これにより推定の複雑さが大幅に軽減されます。</li> <li>時間計算量には制限があります。例えば、アルゴリズム<code>A</code>と<code>C</code>は同じ時間計算量を持ちますが、実際の実行時間は大きく異なる場合があります。同様に、アルゴリズム<code>B</code>は<code>C</code>よりも高い時間計算量を持ちますが、入力データサイズ\\(n\\)が小さい場合は明らかに優れています。これらの場合、時間計算量のみに基づいてアルゴリズムの効率を判断することは困難です。しかし、これらの問題にもかかわらず、複雑度分析はアルゴリズムの効率を評価するための最も効果的で一般的に使用される方法です。</li> </ul>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#232","level":2,"title":"2.3.2   漸近上限","text":"<p>入力サイズが\\(n\\)の関数を考えてみましょう：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlin <pre><code>def algorithm(n: int):\n    a = 1      # +1\n    a = a + 1  # +1\n    a = a * 2  # +1\n    # n回ループ\n    for i in range(n):  # +1\n        print(0)        # +1\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +1\n    a = a + 1;  // +1\n    a = a * 2;  // +1\n    // n回ループ\n    for (int i = 0; i &lt; n; i++) { // +1 (毎回i++が実行される)\n        cout &lt;&lt; 0 &lt;&lt; endl;    // +1\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +1\n    a = a + 1;  // +1\n    a = a * 2;  // +1\n    // n回ループ\n    for (int i = 0; i &lt; n; i++) { // +1 (毎回i++が実行される)\n        System.out.println(0);    // +1\n    }\n}\n</code></pre> <pre><code>void Algorithm(int n) {\n    int a = 1;  // +1\n    a = a + 1;  // +1\n    a = a * 2;  // +1\n    // n回ループ\n    for (int i = 0; i &lt; n; i++) {   // +1 (毎回i++が実行される)\n        Console.WriteLine(0);   // +1\n    }\n}\n</code></pre> <pre><code>func algorithm(n int) {\n    a := 1      // +1\n    a = a + 1   // +1\n    a = a * 2   // +1\n    // n回ループ\n    for i := 0; i &lt; n; i++ {   // +1\n        fmt.Println(a)         // +1\n    }\n}\n</code></pre> <pre><code>func algorithm(n: Int) {\n    var a = 1 // +1\n    a = a + 1 // +1\n    a = a * 2 // +1\n    // n回ループ\n    for _ in 0 ..&lt; n { // +1\n        print(0) // +1\n    }\n}\n</code></pre> <pre><code>function algorithm(n) {\n    var a = 1; // +1\n    a += 1; // +1\n    a *= 2; // +1\n    // n回ループ\n    for(let i = 0; i &lt; n; i++){ // +1 (毎回i++が実行される)\n        console.log(0); // +1\n    }\n}\n</code></pre> <pre><code>function algorithm(n: number): void{\n    var a: number = 1; // +1\n    a += 1; // +1\n    a *= 2; // +1\n    // n回ループ\n    for(let i = 0; i &lt; n; i++){ // +1 (毎回i++が実行される)\n        console.log(0); // +1\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n  int a = 1; // +1\n  a = a + 1; // +1\n  a = a * 2; // +1\n  // n回ループ\n  for (int i = 0; i &lt; n; i++) { // +1 (毎回i++が実行される)\n    print(0); // +1\n  }\n}\n</code></pre> <pre><code>fn algorithm(n: i32) {\n    let mut a = 1;   // +1\n    a = a + 1;      // +1\n    a = a * 2;      // +1\n\n    // n回ループ\n    for _ in 0..n { // +1 (毎回i++が実行される)\n        println!(\"{}\", 0); // +1\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +1\n    a = a + 1;  // +1\n    a = a * 2;  // +1\n    // n回ループ\n    for (int i = 0; i &lt; n; i++) {   // +1 (毎回i++が実行される)\n        printf(\"%d\", 0);            // +1\n    }\n}\n</code></pre> <pre><code>\n</code></pre> <p>アルゴリズムの操作数を入力サイズ\\(n\\)の関数として表す関数を\\(T(n)\\)とすると、以下の例を考えてみましょう：</p> \\[ T(n) = 3 + 2n \\] <p>\\(T(n)\\)は線形関数であるため、その増加傾向は線形であり、したがって、その時間計算量は線形オーダーで、\\(O(n)\\)と表記されます。この数学記法はビッグO記法として知られ、関数\\(T(n)\\)の漸近上限を表します。</p> <p>本質的に、時間計算量分析は「操作数\\(T(n)\\)」の漸近上限を見つけることです。それには正確な数学的定義があります。</p> <p>漸近上限</p> <p>すべての\\(n &gt; n_0\\)に対して\\(T(n) \\leq c \\cdot f(n)\\)となるような正の実数\\(c\\)と\\(n_0\\)が存在する場合、\\(f(n)\\)は\\(T(n)\\)の漸近上限とみなされ、\\(T(n) = O(f(n))\\)と表記されます。</p> <p>下図に示されているように、漸近上限の計算では、\\(n\\)が無限大に近づくにつれて、\\(T(n)\\)と\\(f(n)\\)が同じ増加オーダーを持ち、定数因子\\(c\\)のみが異なるような関数\\(f(n)\\)を見つけることが含まれます。</p> <p></p> <p> 図 2-8   Asymptotic upper bound of a function </p>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#233","level":2,"title":"2.3.3   計算方法","text":"<p>漸近上限の概念は数学的に濃密に見えるかもしれませんが、今すぐ完全に理解する必要はありません。まず計算方法を理解し、時間をかけて練習し理解しましょう。</p> <p>\\(f(n)\\)が決まれば、時間計算量\\(O(f(n))\\)が得られます。しかし、漸近上限\\(f(n)\\)をどのように決定するのでしょうか？このプロセスには一般的に2つのステップが含まれます：操作数のカウントと漸近上限の決定です。</p>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#1-1","level":3,"title":"1.   ステップ1: 操作数のカウント","text":"<p>このステップでは、コードを行ごとに確認します。しかし、\\(c \\cdot f(n)\\)の定数\\(c\\)の存在により、\\(T(n)\\)のすべての係数と定数項は無視できます。この原理により、操作をカウントする際の簡略化技法が可能になります。</p> <ol> <li>\\(T(n)\\)の定数項を無視します。これらは\\(n\\)とは無関係であるため、時間計算量に影響しません。</li> <li>すべての係数を省略します。例えば、\\(2n\\)、\\(5n + 1\\)回などのループは、\\(n\\)の前の係数が時間計算量に影響しないため、\\(n\\)回に簡略化できます。</li> <li>ネストしたループには乗算を使用します。総操作数は各ループの操作数の積であり、ポイント1と2の簡略化技法を各ループレベルに適用します。</li> </ol> <p>関数が与えられた場合、これらの技法を使用して操作をカウントできます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlin <pre><code>def algorithm(n: int):\n    a = 1      # +0 (技法1)\n    a = a + n  # +0 (技法1)\n    # +n (技法2)\n    for i in range(5 * n + 1):\n        print(0)\n    # +n*n (技法3)\n    for i in range(2 * n):\n        for j in range(n + 1):\n            print(0)\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +0 (技法1)\n    a = a + n;  // +0 (技法1)\n    // +n (技法2)\n    for (int i = 0; i &lt; 5 * n + 1; i++) {\n        cout &lt;&lt; 0 &lt;&lt; endl;\n    }\n    // +n*n (技法3)\n    for (int i = 0; i &lt; 2 * n; i++) {\n        for (int j = 0; j &lt; n + 1; j++) {\n            cout &lt;&lt; 0 &lt;&lt; endl;\n        }\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +0 (技法1)\n    a = a + n;  // +0 (技法1)\n    // +n (技法2)\n    for (int i = 0; i &lt; 5 * n + 1; i++) {\n        System.out.println(0);\n    }\n    // +n*n (技法3)\n    for (int i = 0; i &lt; 2 * n; i++) {\n        for (int j = 0; j &lt; n + 1; j++) {\n            System.out.println(0);\n        }\n    }\n}\n</code></pre> <pre><code>void Algorithm(int n) {\n    int a = 1;  // +0 (技法1)\n    a = a + n;  // +0 (技法1)\n    // +n (技法2)\n    for (int i = 0; i &lt; 5 * n + 1; i++) {\n        Console.WriteLine(0);\n    }\n    // +n*n (技法3)\n    for (int i = 0; i &lt; 2 * n; i++) {\n        for (int j = 0; j &lt; n + 1; j++) {\n            Console.WriteLine(0);\n        }\n    }\n}\n</code></pre> <pre><code>func algorithm(n int) {\n    a := 1     // +0 (技法1)\n    a = a + n  // +0 (技法1)\n    // +n (技法2)\n    for i := 0; i &lt; 5 * n + 1; i++ {\n        fmt.Println(0)\n    }\n    // +n*n (技法3)\n    for i := 0; i &lt; 2 * n; i++ {\n        for j := 0; j &lt; n + 1; j++ {\n            fmt.Println(0)\n        }\n    }\n}\n</code></pre> <pre><code>func algorithm(n: Int) {\n    var a = 1 // +0 (技法1)\n    a = a + n // +0 (技法1)\n    // +n (技法2)\n    for _ in 0 ..&lt; (5 * n + 1) {\n        print(0)\n    }\n    // +n*n (技法3)\n    for _ in 0 ..&lt; (2 * n) {\n        for _ in 0 ..&lt; (n + 1) {\n            print(0)\n        }\n    }\n}\n</code></pre> <pre><code>function algorithm(n) {\n    let a = 1;  // +0 (技法1)\n    a = a + n;  // +0 (技法1)\n    // +n (技法2)\n    for (let i = 0; i &lt; 5 * n + 1; i++) {\n        console.log(0);\n    }\n    // +n*n (技法3)\n    for (let i = 0; i &lt; 2 * n; i++) {\n        for (let j = 0; j &lt; n + 1; j++) {\n            console.log(0);\n        }\n    }\n}\n</code></pre> <pre><code>function algorithm(n: number): void {\n    let a = 1;  // +0 (技法1)\n    a = a + n;  // +0 (技法1)\n    // +n (技法2)\n    for (let i = 0; i &lt; 5 * n + 1; i++) {\n        console.log(0);\n    }\n    // +n*n (技法3)\n    for (let i = 0; i &lt; 2 * n; i++) {\n        for (let j = 0; j &lt; n + 1; j++) {\n            console.log(0);\n        }\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n  int a = 1; // +0 (技法1)\n  a = a + n; // +0 (技法1)\n  // +n (技法2)\n  for (int i = 0; i &lt; 5 * n + 1; i++) {\n    print(0);\n  }\n  // +n*n (技法3)\n  for (int i = 0; i &lt; 2 * n; i++) {\n    for (int j = 0; j &lt; n + 1; j++) {\n      print(0);\n    }\n  }\n}\n</code></pre> <pre><code>fn algorithm(n: i32) {\n    let mut a = 1;     // +0 (技法1)\n    a = a + n;        // +0 (技法1)\n\n    // +n (技法2)\n    for i in 0..(5 * n + 1) {\n        println!(\"{}\", 0);\n    }\n\n    // +n*n (技法3)\n    for i in 0..(2 * n) {\n        for j in 0..(n + 1) {\n            println!(\"{}\", 0);\n        }\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +0 (技法1)\n    a = a + n;  // +0 (技法1)\n    // +n (技法2)\n    for (int i = 0; i &lt; 5 * n + 1; i++) {\n        printf(\"%d\", 0);\n    }\n    // +n*n (技法3)\n    for (int i = 0; i &lt; 2 * n; i++) {\n        for (int j = 0; j &lt; n + 1; j++) {\n            printf(\"%d\", 0);\n        }\n    }\n}\n</code></pre> <pre><code>\n</code></pre> <p>以下の式は、簡略化前後のカウント結果を示しており、どちらも\\(O(n^2)\\)の時間計算量に導きます：</p> \\[ \\begin{aligned} T(n) &amp; = 2n(n + 1) + (5n + 1) + 2 &amp; \\text{完全カウント (-.-|||)} \\newline &amp; = 2n^2 + 7n + 3 \\newline T(n) &amp; = n^2 + n &amp; \\text{簡略化カウント (o.O)} \\end{aligned} \\]","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#2-2","level":3,"title":"2.   ステップ2: 漸近上限の決定","text":"<p>時間計算量は\\(T(n)\\)の最高次項によって決定されます。これは、\\(n\\)が無限大に近づくにつれて、最高次項が支配的になり、他の項の影響は無視できるようになるためです。</p> <p>以下の表は、異なる操作カウントとそれに対応する時間計算量の例を示しています。係数が増加オーダーを変更できないことを強調するために、誇張された値が使用されています。\\(n\\)が非常に大きくなると、これらの定数は重要でなくなります。</p> <p> 表: 異なる操作カウントに対する時間計算量 </p> 操作カウント \\(T(n)\\) 時間計算量 \\(O(f(n))\\) \\(100000\\) \\(O(1)\\) \\(3n + 2\\) \\(O(n)\\) \\(2n^2 + 3n + 2\\) \\(O(n^2)\\) \\(n^3 + 10000n^2\\) \\(O(n^3)\\) \\(2^n + 10000n^{10000}\\) \\(O(2^n)\\)","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#234","level":2,"title":"2.3.4   一般的な時間計算量の種類","text":"<p>入力データサイズを\\(n\\)としましょう。一般的な時間計算量の種類を下図に示し、低いものから高いものへと並べています：</p> \\[ \\begin{aligned} &amp; O(1) &lt; O(\\log n) &lt; O(n) &lt; O(n \\log n) &lt; O(n^2) &lt; O(2^n) &lt; O(n!) \\newline &amp; \\text{定数} &lt; \\text{対数} &lt; \\text{線形} &lt; \\text{線形対数} &lt; \\text{二次} &lt; \\text{指数} &lt; \\text{階乗} \\end{aligned} \\] <p></p> <p> 図 2-9   Common types of time complexity </p>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#1-o1","level":3,"title":"1.   定数オーダー \\(O(1)\\)","text":"<p>定数オーダーは、操作数が入力データサイズ\\(n\\)とは無関係であることを意味します。以下の関数では、操作数<code>size</code>が大きい場合でも、\\(n\\)とは無関係であるため、時間計算量は\\(O(1)\\)のままです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def constant(n: int) -&gt; int:\n    \"\"\"定数複雑度\"\"\"\n    count = 0\n    size = 100000\n    for _ in range(size):\n        count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* 定数計算量 */\nint constant(int n) {\n    int count = 0;\n    int size = 100000;\n    for (int i = 0; i &lt; size; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* 定数計算量 */\nint constant(int n) {\n    int count = 0;\n    int size = 100000;\n    for (int i = 0; i &lt; size; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>[class]{time_complexity}-[func]{Constant}\n</code></pre> time_complexity.go<pre><code>[class]{}-[func]{constant}\n</code></pre> time_complexity.swift<pre><code>[class]{}-[func]{constant}\n</code></pre> time_complexity.js<pre><code>[class]{}-[func]{constant}\n</code></pre> time_complexity.ts<pre><code>[class]{}-[func]{constant}\n</code></pre> time_complexity.dart<pre><code>[class]{}-[func]{constant}\n</code></pre> time_complexity.rs<pre><code>[class]{}-[func]{constant}\n</code></pre> time_complexity.c<pre><code>[class]{}-[func]{constant}\n</code></pre> time_complexity.kt<pre><code>[class]{}-[func]{constant}\n</code></pre> time_complexity.rb<pre><code>[class]{}-[func]{constant}\n</code></pre>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#2-on","level":3,"title":"2.   線形オーダー \\(O(n)\\)","text":"<p>線形オーダーは、操作数が入力データサイズ\\(n\\)と線形に増加することを示します。線形オーダーは一般的に単一ループ構造で現れます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def linear(n: int) -&gt; int:\n    \"\"\"線形複雑度\"\"\"\n    count = 0\n    for _ in range(n):\n        count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* 線形計算量 */\nint linear(int n) {\n    int count = 0;\n    for (int i = 0; i &lt; n; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* 線形計算量 */\nint linear(int n) {\n    int count = 0;\n    for (int i = 0; i &lt; n; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>[class]{time_complexity}-[func]{Linear}\n</code></pre> time_complexity.go<pre><code>[class]{}-[func]{linear}\n</code></pre> time_complexity.swift<pre><code>[class]{}-[func]{linear}\n</code></pre> time_complexity.js<pre><code>[class]{}-[func]{linear}\n</code></pre> time_complexity.ts<pre><code>[class]{}-[func]{linear}\n</code></pre> time_complexity.dart<pre><code>[class]{}-[func]{linear}\n</code></pre> time_complexity.rs<pre><code>[class]{}-[func]{linear}\n</code></pre> time_complexity.c<pre><code>[class]{}-[func]{linear}\n</code></pre> time_complexity.kt<pre><code>[class]{}-[func]{linear}\n</code></pre> time_complexity.rb<pre><code>[class]{}-[func]{linear}\n</code></pre> <p>配列の走査や連結リストの走査などの操作は時間計算量が\\(O(n)\\)で、\\(n\\)は配列またはリストの長さです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def array_traversal(nums: list[int]) -&gt; int:\n    \"\"\"線形複雑度（配列の走査）\"\"\"\n    count = 0\n    # ループ回数は配列の長さに比例する\n    for num in nums:\n        count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* 線形計算量（配列の走査） */\nint arrayTraversal(vector&lt;int&gt; &amp;nums) {\n    int count = 0;\n    // ループ回数は配列の長さに比例\n    for (int num : nums) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* 線形計算量（配列の走査） */\nint arrayTraversal(int[] nums) {\n    int count = 0;\n    // ループ回数は配列の長さに比例\n    for (int num : nums) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>[class]{time_complexity}-[func]{ArrayTraversal}\n</code></pre> time_complexity.go<pre><code>[class]{}-[func]{arrayTraversal}\n</code></pre> time_complexity.swift<pre><code>[class]{}-[func]{arrayTraversal}\n</code></pre> time_complexity.js<pre><code>[class]{}-[func]{arrayTraversal}\n</code></pre> time_complexity.ts<pre><code>[class]{}-[func]{arrayTraversal}\n</code></pre> time_complexity.dart<pre><code>[class]{}-[func]{arrayTraversal}\n</code></pre> time_complexity.rs<pre><code>[class]{}-[func]{array_traversal}\n</code></pre> time_complexity.c<pre><code>[class]{}-[func]{arrayTraversal}\n</code></pre> time_complexity.kt<pre><code>[class]{}-[func]{arrayTraversal}\n</code></pre> time_complexity.rb<pre><code>[class]{}-[func]{array_traversal}\n</code></pre> <p>入力データサイズ\\(n\\)は入力データの種類に基づいて決定する必要があります。例えば、最初の例では、\\(n\\)は入力データサイズを表し、2番目の例では、配列の長さ\\(n\\)がデータサイズです。</p>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#3-on2","level":3,"title":"3.   二次オーダー \\(O(n^2)\\)","text":"<p>二次オーダーは、操作数が入力データサイズ\\(n\\)の二乗に比例して増加することを意味します。二次オーダーは通常ネストしたループで現れ、外側と内側のループの両方が時間計算量\\(O(n)\\)を持ち、全体の複雑度は\\(O(n^2)\\)になります：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def quadratic(n: int) -&gt; int:\n    \"\"\"二次複雑度\"\"\"\n    count = 0\n    # ループ回数はデータサイズnの二乗に比例する\n    for i in range(n):\n        for j in range(n):\n            count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* 二次計算量 */\nint quadratic(int n) {\n    int count = 0;\n    // ループ回数はデータサイズ n の二乗に比例\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; n; j++) {\n            count++;\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* 二次計算量 */\nint quadratic(int n) {\n    int count = 0;\n    // ループ回数はデータサイズ n の二乗に比例\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; n; j++) {\n            count++;\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>[class]{time_complexity}-[func]{Quadratic}\n</code></pre> time_complexity.go<pre><code>[class]{}-[func]{quadratic}\n</code></pre> time_complexity.swift<pre><code>[class]{}-[func]{quadratic}\n</code></pre> time_complexity.js<pre><code>[class]{}-[func]{quadratic}\n</code></pre> time_complexity.ts<pre><code>[class]{}-[func]{quadratic}\n</code></pre> time_complexity.dart<pre><code>[class]{}-[func]{quadratic}\n</code></pre> time_complexity.rs<pre><code>[class]{}-[func]{quadratic}\n</code></pre> time_complexity.c<pre><code>[class]{}-[func]{quadratic}\n</code></pre> time_complexity.kt<pre><code>[class]{}-[func]{quadratic}\n</code></pre> time_complexity.rb<pre><code>[class]{}-[func]{quadratic}\n</code></pre> <p>下図は定数オーダー、線形オーダー、二次オーダーの時間計算量を比較しています。</p> <p></p> <p> 図 2-10   Constant, linear, and quadratic order time complexities </p> <p>例えば、バブルソートでは、外側のループが\\(n - 1\\)回実行され、内側のループが\\(n-1\\)、\\(n-2\\)、...、\\(2\\)、\\(1\\)回実行され、平均\\(n / 2\\)回となり、時間計算量は\\(O((n - 1) n / 2) = O(n^2)\\)になります：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def bubble_sort(nums: list[int]) -&gt; int:\n    \"\"\"二次複雑度（バブルソート）\"\"\"\n    count = 0  # カウンタ\n    # 外側のループ: 未ソート範囲は [0, i]\n    for i in range(len(nums) - 1, 0, -1):\n        # 内側のループ: 未ソート範囲 [0, i] の最大要素を右端にスワップ\n        for j in range(i):\n            if nums[j] &gt; nums[j + 1]:\n                # nums[j] と nums[j + 1] をスワップ\n                tmp: int = nums[j]\n                nums[j] = nums[j + 1]\n                nums[j + 1] = tmp\n                count += 3  # 要素のスワップは3つの個別操作を含む\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* 二次計算量（バブルソート） */\nint bubbleSort(vector&lt;int&gt; &amp;nums) {\n    int count = 0; // カウンター\n    // 外側ループ：未ソート範囲は [0, i]\n    for (int i = nums.size() - 1; i &gt; 0; i--) {\n        // 内側ループ：未ソート範囲 [0, i] の最大要素を範囲の右端にスワップ\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] と nums[j + 1] をスワップ\n                int tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                count += 3; // 要素のスワップには3つの個別操作が含まれる\n            }\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* 二次計算量（バブルソート） */\nint bubbleSort(int[] nums) {\n    int count = 0; // カウンター\n    // 外側ループ：未ソート範囲は [0, i]\n    for (int i = nums.length - 1; i &gt; 0; i--) {\n        // 内側ループ：未ソート範囲 [0, i] の最大要素を範囲の右端にスワップ\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] と nums[j + 1] をスワップ\n                int tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                count += 3; // 要素のスワップには3つの個別操作が含まれる\n            }\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>[class]{time_complexity}-[func]{BubbleSort}\n</code></pre> time_complexity.go<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> time_complexity.swift<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> time_complexity.js<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> time_complexity.ts<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> time_complexity.dart<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> time_complexity.rs<pre><code>[class]{}-[func]{bubble_sort}\n</code></pre> time_complexity.c<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> time_complexity.kt<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> time_complexity.rb<pre><code>[class]{}-[func]{bubble_sort}\n</code></pre>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#4-o2n","level":3,"title":"4.   指数オーダー \\(O(2^n)\\)","text":"<p>生物学的「細胞分裂」は指数オーダー増加の典型例です：1つの細胞から始まり、1回の分裂後に2つ、2回の分裂後に4つとなり、\\(n\\)回の分裂後に\\(2^n\\)個の細胞になります。</p> <p>下図とコードは細胞分裂プロセスをシミュレートし、時間計算量は\\(O(2^n)\\)です：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def exponential(n: int) -&gt; int:\n    \"\"\"指数複雑度（ループ実装）\"\"\"\n    count = 0\n    base = 1\n    # セルは毎回2つに分裂し、1, 2, 4, 8, ..., 2^(n-1) の数列を形成する\n    for _ in range(n):\n        for _ in range(base):\n            count += 1\n        base *= 2\n    # count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* 指数計算量（ループ実装） */\nint exponential(int n) {\n    int count = 0, base = 1;\n    // セルは毎ラウンド2つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; base; j++) {\n            count++;\n        }\n        base *= 2;\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* 指数計算量（ループ実装） */\nint exponential(int n) {\n    int count = 0, base = 1;\n    // セルは毎ラウンド2つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; base; j++) {\n            count++;\n        }\n        base *= 2;\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>[class]{time_complexity}-[func]{Exponential}\n</code></pre> time_complexity.go<pre><code>[class]{}-[func]{exponential}\n</code></pre> time_complexity.swift<pre><code>[class]{}-[func]{exponential}\n</code></pre> time_complexity.js<pre><code>[class]{}-[func]{exponential}\n</code></pre> time_complexity.ts<pre><code>[class]{}-[func]{exponential}\n</code></pre> time_complexity.dart<pre><code>[class]{}-[func]{exponential}\n</code></pre> time_complexity.rs<pre><code>[class]{}-[func]{exponential}\n</code></pre> time_complexity.c<pre><code>[class]{}-[func]{exponential}\n</code></pre> time_complexity.kt<pre><code>[class]{}-[func]{exponential}\n</code></pre> time_complexity.rb<pre><code>[class]{}-[func]{exponential}\n</code></pre> <p></p> <p> 図 2-11   Exponential order time complexity </p> <p>実際には、指数オーダーは再帰関数でよく現れます。例えば、以下のコードでは、再帰的に2つの半分に分割し、\\(n\\)回の分割後に停止します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def exp_recur(n: int) -&gt; int:\n    \"\"\"指数複雑度（再帰実装）\"\"\"\n    if n == 1:\n        return 1\n    return exp_recur(n - 1) + exp_recur(n - 1) + 1\n</code></pre> time_complexity.cpp<pre><code>/* 指数計算量（再帰実装） */\nint expRecur(int n) {\n    if (n == 1)\n        return 1;\n    return expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.java<pre><code>/* 指数計算量（再帰実装） */\nint expRecur(int n) {\n    if (n == 1)\n        return 1;\n    return expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.cs<pre><code>[class]{time_complexity}-[func]{ExpRecur}\n</code></pre> time_complexity.go<pre><code>[class]{}-[func]{expRecur}\n</code></pre> time_complexity.swift<pre><code>[class]{}-[func]{expRecur}\n</code></pre> time_complexity.js<pre><code>[class]{}-[func]{expRecur}\n</code></pre> time_complexity.ts<pre><code>[class]{}-[func]{expRecur}\n</code></pre> time_complexity.dart<pre><code>[class]{}-[func]{expRecur}\n</code></pre> time_complexity.rs<pre><code>[class]{}-[func]{exp_recur}\n</code></pre> time_complexity.c<pre><code>[class]{}-[func]{expRecur}\n</code></pre> time_complexity.kt<pre><code>[class]{}-[func]{expRecur}\n</code></pre> time_complexity.rb<pre><code>[class]{}-[func]{exp_recur}\n</code></pre> <p>指数オーダーの増加は極めて急速で、全数探索法（ブルートフォース、バックトラッキングなど）でよく見られます。大規模問題では、指数オーダーは受け入れられず、しばしば動的プログラミングや貪欲アルゴリズムが解決策として必要になります。</p>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#5-olog-n","level":3,"title":"5.   対数オーダー \\(O(\\log n)\\)","text":"<p>指数オーダーとは対照的に、対数オーダーは「各ラウンドでサイズが半分になる」状況を反映します。入力データサイズが\\(n\\)の場合、各ラウンドでサイズが半分になるため、反復回数は\\(\\log_2 n\\)で、これは\\(2^n\\)の逆関数です。</p> <p>下図とコードは「各ラウンドで半分にする」プロセスをシミュレートし、時間計算量は\\(O(\\log_2 n)\\)で、一般的に\\(O(\\log n)\\)と省略されます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def logarithmic(n: int) -&gt; int:\n    \"\"\"対数複雑度（ループ実装）\"\"\"\n    count = 0\n    while n &gt; 1:\n        n = n / 2\n        count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* 対数計算量（ループ実装） */\nint logarithmic(int n) {\n    int count = 0;\n    while (n &gt; 1) {\n        n = n / 2;\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* 対数計算量（ループ実装） */\nint logarithmic(int n) {\n    int count = 0;\n    while (n &gt; 1) {\n        n = n / 2;\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>[class]{time_complexity}-[func]{Logarithmic}\n</code></pre> time_complexity.go<pre><code>[class]{}-[func]{logarithmic}\n</code></pre> time_complexity.swift<pre><code>[class]{}-[func]{logarithmic}\n</code></pre> time_complexity.js<pre><code>[class]{}-[func]{logarithmic}\n</code></pre> time_complexity.ts<pre><code>[class]{}-[func]{logarithmic}\n</code></pre> time_complexity.dart<pre><code>[class]{}-[func]{logarithmic}\n</code></pre> time_complexity.rs<pre><code>[class]{}-[func]{logarithmic}\n</code></pre> time_complexity.c<pre><code>[class]{}-[func]{logarithmic}\n</code></pre> time_complexity.kt<pre><code>[class]{}-[func]{logarithmic}\n</code></pre> time_complexity.rb<pre><code>[class]{}-[func]{logarithmic}\n</code></pre> <p></p> <p> 図 2-12   Logarithmic order time complexity </p> <p>指数オーダーと同様に、対数オーダーも再帰関数で頻繁に現れます。以下のコードは高さ\\(\\log_2 n\\)の再帰木を形成します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def log_recur(n: int) -&gt; int:\n    \"\"\"対数複雑度（再帰実装）\"\"\"\n    if n &lt;= 1:\n        return 0\n    return log_recur(n / 2) + 1\n</code></pre> time_complexity.cpp<pre><code>/* 対数計算量（再帰実装） */\nint logRecur(int n) {\n    if (n &lt;= 1)\n        return 0;\n    return logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.java<pre><code>/* 対数計算量（再帰実装） */\nint logRecur(int n) {\n    if (n &lt;= 1)\n        return 0;\n    return logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.cs<pre><code>[class]{time_complexity}-[func]{LogRecur}\n</code></pre> time_complexity.go<pre><code>[class]{}-[func]{logRecur}\n</code></pre> time_complexity.swift<pre><code>[class]{}-[func]{logRecur}\n</code></pre> time_complexity.js<pre><code>[class]{}-[func]{logRecur}\n</code></pre> time_complexity.ts<pre><code>[class]{}-[func]{logRecur}\n</code></pre> time_complexity.dart<pre><code>[class]{}-[func]{logRecur}\n</code></pre> time_complexity.rs<pre><code>[class]{}-[func]{log_recur}\n</code></pre> time_complexity.c<pre><code>[class]{}-[func]{logRecur}\n</code></pre> time_complexity.kt<pre><code>[class]{}-[func]{logRecur}\n</code></pre> time_complexity.rb<pre><code>[class]{}-[func]{log_recur}\n</code></pre> <p>対数オーダーは分割統治戦略に基づくアルゴリズムの典型で、「多くに分割」と「複雑な問題を単純化」するアプローチを体現しています。増加が遅く、定数オーダーの次に最も理想的な時間計算量です。</p> <p>\\(O(\\log n)\\)の底は何ですか？</p> <p>技術的には、「\\(m\\)に分割」は時間計算量\\(O(\\log_m n)\\)に対応します。対数の底変更公式を使用すると、異なる対数複雑度を等価にできます：</p> \\[ O(\\log_m n) = O(\\log_k n / \\log_k m) = O(\\log_k n) \\] <p>これは、底\\(m\\)を複雑度に影響を与えることなく変更できることを意味します。したがって、しばしば底\\(m\\)を省略し、単に対数オーダーを\\(O(\\log n)\\)と表記します。</p>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#6-on-log-n","level":3,"title":"6.   線形対数オーダー \\(O(n \\log n)\\)","text":"<p>線形対数オーダーはネストしたループでよく現れ、2つのループの複雑度がそれぞれ\\(O(\\log n)\\)と\\(O(n)\\)です。関連するコードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def linear_log_recur(n: int) -&gt; int:\n    \"\"\"線形対数複雑度\"\"\"\n    if n &lt;= 1:\n        return 1\n    count: int = linear_log_recur(n // 2) + linear_log_recur(n // 2)\n    for _ in range(n):\n        count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* 線形対数計算量 */\nint linearLogRecur(int n) {\n    if (n &lt;= 1)\n        return 1;\n    int count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\n    for (int i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* 線形対数計算量 */\nint linearLogRecur(int n) {\n    if (n &lt;= 1)\n        return 1;\n    int count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\n    for (int i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>[class]{time_complexity}-[func]{LinearLogRecur}\n</code></pre> time_complexity.go<pre><code>[class]{}-[func]{linearLogRecur}\n</code></pre> time_complexity.swift<pre><code>[class]{}-[func]{linearLogRecur}\n</code></pre> time_complexity.js<pre><code>[class]{}-[func]{linearLogRecur}\n</code></pre> time_complexity.ts<pre><code>[class]{}-[func]{linearLogRecur}\n</code></pre> time_complexity.dart<pre><code>[class]{}-[func]{linearLogRecur}\n</code></pre> time_complexity.rs<pre><code>[class]{}-[func]{linear_log_recur}\n</code></pre> time_complexity.c<pre><code>[class]{}-[func]{linearLogRecur}\n</code></pre> time_complexity.kt<pre><code>[class]{}-[func]{linearLogRecur}\n</code></pre> time_complexity.rb<pre><code>[class]{}-[func]{linear_log_recur}\n</code></pre> <p>下図は線形対数オーダーがどのように生成されるかを示しています。二分木の各レベルには\\(n\\)個の操作があり、木には\\(\\log_2 n + 1\\)レベルがあり、時間計算量は\\(O(n \\log n)\\)になります。</p> <p></p> <p> 図 2-13   Linear-logarithmic order time complexity </p> <p>主流のソートアルゴリズムは通常\\(O(n \\log n)\\)の時間計算量を持ち、クイックソート、マージソート、ヒープソートなどがあります。</p>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#7-on","level":3,"title":"7.   階乗オーダー \\(O(n!)\\)","text":"<p>階乗オーダーは「全順列」の数学問題に対応します。\\(n\\)個の異なる要素が与えられた場合、可能な順列の総数は：</p> \\[ n! = n \\times (n - 1) \\times (n - 2) \\times \\dots \\times 2 \\times 1 \\] <p>階乗は通常再帰を使用して実装されます。以下のコードと図に示されているように、第1レベルは\\(n\\)個の分岐に分割され、第2レベルは\\(n - 1\\)個の分岐に分割され、第\\(n\\)レベル後に停止します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def factorial_recur(n: int) -&gt; int:\n    \"\"\"階乗複雑度（再帰実装）\"\"\"\n    if n == 0:\n        return 1\n    count = 0\n    # 1つからnに分岐\n    for _ in range(n):\n        count += factorial_recur(n - 1)\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* 階乗計算量（再帰実装） */\nint factorialRecur(int n) {\n    if (n == 0)\n        return 1;\n    int count = 0;\n    // 1から n に分裂\n    for (int i = 0; i &lt; n; i++) {\n        count += factorialRecur(n - 1);\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* 階乗計算量（再帰実装） */\nint factorialRecur(int n) {\n    if (n == 0)\n        return 1;\n    int count = 0;\n    // 1から n に分裂\n    for (int i = 0; i &lt; n; i++) {\n        count += factorialRecur(n - 1);\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>[class]{time_complexity}-[func]{FactorialRecur}\n</code></pre> time_complexity.go<pre><code>[class]{}-[func]{factorialRecur}\n</code></pre> time_complexity.swift<pre><code>[class]{}-[func]{factorialRecur}\n</code></pre> time_complexity.js<pre><code>[class]{}-[func]{factorialRecur}\n</code></pre> time_complexity.ts<pre><code>[class]{}-[func]{factorialRecur}\n</code></pre> time_complexity.dart<pre><code>[class]{}-[func]{factorialRecur}\n</code></pre> time_complexity.rs<pre><code>[class]{}-[func]{factorial_recur}\n</code></pre> time_complexity.c<pre><code>[class]{}-[func]{factorialRecur}\n</code></pre> time_complexity.kt<pre><code>[class]{}-[func]{factorialRecur}\n</code></pre> time_complexity.rb<pre><code>[class]{}-[func]{factorial_recur}\n</code></pre> <p></p> <p> 図 2-14   Factorial order time complexity </p> <p>階乗オーダーは指数オーダーよりもさらに速く増加することに注意してください。より大きな\\(n\\)値では受け入れられません。</p>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#235","level":2,"title":"2.3.5   最悪、最良、平均時間計算量","text":"<p>アルゴリズムの時間効率は固定されていないことが多く、入力データの分布に依存します。長さ\\(n\\)の配列<code>nums</code>があり、\\(1\\)から\\(n\\)までの数で構成され、それぞれが一度だけ現れますが、ランダムにシャッフルされた順序であるとします。タスクは要素\\(1\\)のインデックスを返すことです。以下の結論を導けます：</p> <ul> <li><code>nums = [?, ?, ..., 1]</code>の場合、つまり最後の要素が\\(1\\)の場合、配列の完全な走査が必要で、最悪ケース時間計算量\\(O(n)\\)を達成します。</li> <li><code>nums = [1, ?, ?, ...]</code>の場合、つまり最初の要素が\\(1\\)の場合、配列の長さに関係なく、さらなる走査は不要で、最良ケース時間計算量\\(\\Omega(1)\\)を達成します。</li> </ul> <p>「最悪ケース時間計算量」は漸近上限に対応し、大きな\\(O\\)記法で表されます。対応して、「最良ケース時間計算量」は漸近下限に対応し、\\(\\Omega\\)で表されます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby worst_best_time_complexity.py<pre><code>def random_numbers(n: int) -&gt; list[int]:\n    \"\"\"要素 1, 2, ..., n を含む配列を生成、順序はシャッフル\"\"\"\n    # 配列 nums = 1, 2, 3, ..., n を生成\n    nums = [i for i in range(1, n + 1)]\n    # 配列要素をランダムにシャッフル\n    random.shuffle(nums)\n    return nums\n\ndef find_one(nums: list[int]) -&gt; int:\n    \"\"\"配列 nums で数値 1 のインデックスを検索\"\"\"\n    for i in range(len(nums)):\n        # 要素 1 が配列の最初にある場合、最良時間計算量 O(1) を達成\n        # 要素 1 が配列の最後にある場合、最悪時間計算量 O(n) を達成\n        if nums[i] == 1:\n            return i\n    return -1\n</code></pre> worst_best_time_complexity.cpp<pre><code>/* 要素 {1, 2, ..., n} をランダムにシャッフルした配列を生成 */\nvector&lt;int&gt; randomNumbers(int n) {\n    vector&lt;int&gt; nums(n);\n    // 配列 nums = { 1, 2, 3, ..., n } を生成\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = i + 1;\n    }\n    // システム時刻を使用してランダムシードを生成\n    unsigned seed = chrono::system_clock::now().time_since_epoch().count();\n    // 配列要素をランダムにシャッフル\n    shuffle(nums.begin(), nums.end(), default_random_engine(seed));\n    return nums;\n}\n\n/* 配列 nums で数値1のインデックスを見つける */\nint findOne(vector&lt;int&gt; &amp;nums) {\n    for (int i = 0; i &lt; nums.size(); i++) {\n        // 要素1が配列の先頭にある場合、最良時間計算量 O(1) を達成\n        // 要素1が配列の末尾にある場合、最悪時間計算量 O(n) を達成\n        if (nums[i] == 1)\n            return i;\n    }\n    return -1;\n}\n</code></pre> worst_best_time_complexity.java<pre><code>/* 要素 {1, 2, ..., n} をランダムにシャッフルした配列を生成 */\nint[] randomNumbers(int n) {\n    Integer[] nums = new Integer[n];\n    // 配列 nums = { 1, 2, 3, ..., n } を生成\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = i + 1;\n    }\n    // 配列要素をランダムにシャッフル\n    Collections.shuffle(Arrays.asList(nums));\n    // Integer[] -&gt; int[]\n    int[] res = new int[n];\n    for (int i = 0; i &lt; n; i++) {\n        res[i] = nums[i];\n    }\n    return res;\n}\n\n/* 配列 nums で数値1のインデックスを見つける */\nint findOne(int[] nums) {\n    for (int i = 0; i &lt; nums.length; i++) {\n        // 要素1が配列の先頭にある場合、最良時間計算量 O(1) を達成\n        // 要素1が配列の末尾にある場合、最悪時間計算量 O(n) を達成\n        if (nums[i] == 1)\n            return i;\n    }\n    return -1;\n}\n</code></pre> worst_best_time_complexity.cs<pre><code>[class]{worst_best_time_complexity}-[func]{RandomNumbers}\n\n[class]{worst_best_time_complexity}-[func]{FindOne}\n</code></pre> worst_best_time_complexity.go<pre><code>[class]{}-[func]{randomNumbers}\n\n[class]{}-[func]{findOne}\n</code></pre> worst_best_time_complexity.swift<pre><code>[class]{}-[func]{randomNumbers}\n\n[class]{}-[func]{findOne}\n</code></pre> worst_best_time_complexity.js<pre><code>[class]{}-[func]{randomNumbers}\n\n[class]{}-[func]{findOne}\n</code></pre> worst_best_time_complexity.ts<pre><code>[class]{}-[func]{randomNumbers}\n\n[class]{}-[func]{findOne}\n</code></pre> worst_best_time_complexity.dart<pre><code>[class]{}-[func]{randomNumbers}\n\n[class]{}-[func]{findOne}\n</code></pre> worst_best_time_complexity.rs<pre><code>[class]{}-[func]{random_numbers}\n\n[class]{}-[func]{find_one}\n</code></pre> worst_best_time_complexity.c<pre><code>[class]{}-[func]{randomNumbers}\n\n[class]{}-[func]{findOne}\n</code></pre> worst_best_time_complexity.kt<pre><code>[class]{}-[func]{randomNumbers}\n\n[class]{}-[func]{findOne}\n</code></pre> worst_best_time_complexity.rb<pre><code>[class]{}-[func]{random_numbers}\n\n[class]{}-[func]{find_one}\n</code></pre> <p>最良ケース時間計算量は実際にはほとんど使用されないことに注意してください。通常は非常に低い確率でのみ達成可能で、誤解を招く可能性があるからです。最悪ケース時間計算量はより実用的で、効率の安全値を提供し、アルゴリズムを自信を持って使用できるようにします。</p> <p>上記の例から、最悪ケースと最良ケースの時間計算量は両方とも「特殊なデータ分布」下でのみ発生し、発生確率が小さく、アルゴリズムの実行効率を正確に反映しない可能性があることが明らかです。対照的に、平均時間計算量はランダム入力データ下でのアルゴリズムの効率を反映でき、\\(\\Theta\\)記法で表されます。</p> <p>一部のアルゴリズムでは、ランダムデータ分布下での平均ケースを簡単に推定できます。例えば、前述の例では、入力配列がシャッフルされているため、要素\\(1\\)が任意のインデックスに現れる確率は等しいです。したがって、アルゴリズムの平均ループ数は配列長さの半分\\(n / 2\\)で、平均時間計算量は\\(\\Theta(n / 2) = \\Theta(n)\\)です。</p> <p>しかし、より複雑なアルゴリズムの平均時間計算量を計算することは非常に困難です。データ分布下での全体的な数学的期待値を分析することが困難だからです。そのような場合、通常はアルゴリズムの効率を判断する基準として最悪ケース時間計算量を使用します。</p> <p>\\(\\Theta\\)記号はなぜほとんど見られないのですか？</p> <p>おそらく\\(O\\)記法がより一般的に話されるため、平均時間計算量を表すためによく使用されます。しかし、厳密に言えば、この実践は正確ではありません。この本や他の資料で「平均時間計算量\\(O(n)\\)」のような表現に遭遇した場合は、直接\\(\\Theta(n)\\)として理解してください。</p>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_data_structure/","level":1,"title":"第 3 章   データ構造","text":"<p>Abstract</p> <p>データ構造は堅牢で多様なフレームワークとして機能します。</p> <p>データの整然とした組織化のための設計図を提供し、その上でアルゴリズムが生き生きと動き出します。</p>","path":["第 3 章 &nbsp; データ構造"],"tags":[]},{"location":"chapter_data_structure/#_1","level":2,"title":"章の内容","text":"<ul> <li>3.1   データ構造の分類</li> <li>3.2   基本データ型</li> <li>3.3   数値の符号化 *</li> <li>3.4   文字の符号化 *</li> <li>3.5   まとめ</li> </ul>","path":["第 3 章 &nbsp; データ構造"],"tags":[]},{"location":"chapter_data_structure/basic_data_types/","level":1,"title":"3.2   基本データ型","text":"<p>コンピュータ内のデータについて考える際、テキスト、画像、動画、音声、3Dモデルなど、様々な形式が思い浮かびます。これらの組織的な形式は異なりますが、すべて様々な基本データ型から構成されています。</p> <p>**基本データ型とは、CPUが直接操作できるもの**であり、アルゴリズムで直接使用されます。主に以下が含まれます。</p> <ul> <li>整数型：<code>byte</code>、<code>short</code>、<code>int</code>、<code>long</code></li> <li>浮動小数点型：<code>float</code>、<code>double</code>、小数を表現するために使用</li> <li>文字型：<code>char</code>、様々な言語の文字、句読点、さらには絵文字を表現するために使用</li> <li>ブール型：<code>bool</code>、「はい」または「いいえ」の判断を表現するために使用</li> </ul> <p>基本データ型は、コンピュータ内で二進形式で格納されます。1つの二進桁は1ビットです。ほとんどの現代的なオペレーティングシステムでは、1バイトは8ビットで構成されています。</p> <p>基本データ型の値の範囲は、それらが占める空間のサイズに依存します。以下では、Javaを例に説明します。</p> <ul> <li>整数型<code>byte</code>は1バイト = 8ビットを占め、\\(2^8\\)個の数値を表現できます。</li> <li>整数型<code>int</code>は4バイト = 32ビットを占め、\\(2^{32}\\)個の数値を表現できます。</li> </ul> <p>以下の表は、Javaにおける様々な基本データ型が占める空間、値の範囲、デフォルト値を示しています。この表を暗記する必要はありませんが、一般的な理解を持ち、必要時に参照することをお勧めします。</p> <p> 表 3-1   基本データ型が占める空間と値の範囲 </p> 型 シンボル 占有空間 最小値 最大値 デフォルト値 整数 <code>byte</code> 1バイト \\(-2^7\\) (\\(-128\\)) \\(2^7 - 1\\) (\\(127\\)) 0 <code>short</code> 2バイト \\(-2^{15}\\) \\(2^{15} - 1\\) 0 <code>int</code> 4バイト \\(-2^{31}\\) \\(2^{31} - 1\\) 0 <code>long</code> 8バイト \\(-2^{63}\\) \\(2^{63} - 1\\) 0 浮動小数点 <code>float</code> 4バイト \\(1.175 \\times 10^{-38}\\) \\(3.403 \\times 10^{38}\\) \\(0.0\\text{f}\\) <code>double</code> 8バイト \\(2.225 \\times 10^{-308}\\) \\(1.798 \\times 10^{308}\\) 0.0 文字 <code>char</code> 2バイト 0 \\(2^{16} - 1\\) 0 ブール <code>bool</code> 1バイト \\(\\text{false}\\) \\(\\text{true}\\) \\(\\text{false}\\) <p>上記の表はJavaの基本データ型に特有であることにご注意ください。すべてのプログラミング言語には独自のデータ型定義があり、占有空間、値の範囲、デフォルト値が異なる場合があります。</p> <ul> <li>Pythonでは、整数型<code>int</code>は任意のサイズになることができ、利用可能なメモリによってのみ制限されます。浮動小数点<code>float</code>は倍精度64ビットです。<code>char</code>型は存在せず、単一文字は実際には長さ1の文字列<code>str</code>です。</li> <li>CおよびC++では基本データ型のサイズが指定されておらず、実装とプラットフォームによって異なります。上記の表はLP64データモデルに従っており、LinuxやmacOSを含むUnix 64ビットオペレーティングシステムで使用されています。</li> <li>CおよびC++における<code>char</code>のサイズは1バイトですが、ほとんどのプログラミング言語では、特定の文字エンコーディング方法に依存し、詳細は「文字エンコーディング」の章で説明されています。</li> <li>ブール値の表現には1ビット（0または1）のみが必要ですが、通常はメモリ内に1バイトとして格納されます。これは、現代のコンピュータCPUが通常1バイトを最小のアドレス可能なメモリ単位として使用するためです。</li> </ul> <p>では、基本データ型とデータ構造の関係は何でしょうか？データ構造とは、コンピュータ内でデータを組織化し格納する方法であることを知っています。ここでの焦点は「データ」ではなく「構造」です。</p> <p>「数値の列」を表現したい場合、自然に配列の使用を考えます。これは、配列の線形構造が数値の隣接性と順序性を表現できるためですが、格納される内容が整数<code>int</code>、小数<code>float</code>、文字<code>char</code>のいずれであっても、「データ構造」とは無関係です。</p> <p>言い換えると、基本データ型はデータの「内容型」を提供し、データ構造はデータの「組織化方法」を提供します。例えば、以下のコードでは、同じデータ構造（配列）を使用して、<code>int</code>、<code>float</code>、<code>char</code>、<code>bool</code>などの異なる基本データ型を格納し表現しています。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlin <pre><code># 様々な基本データ型を使用して配列を初期化\nnumbers: list[int] = [0] * 5\ndecimals: list[float] = [0.0] * 5\n# Pythonの文字は実際には長さ1の文字列\ncharacters: list[str] = ['0'] * 5\nbools: list[bool] = [False] * 5\n# Pythonのリストは様々な基本データ型とオブジェクト参照を自由に格納可能\ndata = [0, 0.0, 'a', False, ListNode(0)]\n</code></pre> <pre><code>// 様々な基本データ型を使用して配列を初期化\nint numbers[5];\nfloat decimals[5];\nchar characters[5];\nbool bools[5];\n</code></pre> <pre><code>// 様々な基本データ型を使用して配列を初期化\nint[] numbers = new int[5];\nfloat[] decimals = new float[5];\nchar[] characters = new char[5];\nboolean[] bools = new boolean[5];\n</code></pre> <pre><code>// 様々な基本データ型を使用して配列を初期化\nint[] numbers = new int[5];\nfloat[] decimals = new float[5];\nchar[] characters = new char[5];\nbool[] bools = new bool[5];\n</code></pre> <pre><code>// 様々な基本データ型を使用して配列を初期化\nvar numbers = [5]int{}\nvar decimals = [5]float64{}\nvar characters = [5]byte{}\nvar bools = [5]bool{}\n</code></pre> <pre><code>// 様々な基本データ型を使用して配列を初期化\nlet numbers = Array(repeating: 0, count: 5)\nlet decimals = Array(repeating: 0.0, count: 5)\nlet characters: [Character] = Array(repeating: \"a\", count: 5)\nlet bools = Array(repeating: false, count: 5)\n</code></pre> <pre><code>// JavaScriptの配列は様々な基本データ型とオブジェクトを自由に格納可能\nconst array = [0, 0.0, 'a', false];\n</code></pre> <pre><code>// 様々な基本データ型を使用して配列を初期化\nconst numbers: number[] = [];\nconst characters: string[] = [];\nconst bools: boolean[] = [];\n</code></pre> <pre><code>// 様々な基本データ型を使用して配列を初期化\nList&lt;int&gt; numbers = List.filled(5, 0);\nList&lt;double&gt; decimals = List.filled(5, 0.0);\nList&lt;String&gt; characters = List.filled(5, 'a');\nList&lt;bool&gt; bools = List.filled(5, false);\n</code></pre> <pre><code>// 様々な基本データ型を使用して配列を初期化\nlet numbers: Vec&lt;i32&gt; = vec![0; 5];\nlet decimals: Vec&lt;f32&gt; = vec![0.0, 5];\nlet characters: Vec&lt;char&gt; = vec!['0'; 5];\nlet bools: Vec&lt;bool&gt; = vec![false; 5];\n</code></pre> <pre><code>// 様々な基本データ型を使用して配列を初期化\nint numbers[10];\nfloat decimals[10];\nchar characters[10];\nbool bools[10];\n</code></pre> <pre><code>\n</code></pre>","path":["第 3 章 &nbsp; データ構造","3.2 &nbsp; 基本データ型"],"tags":[]},{"location":"chapter_data_structure/character_encoding/","level":1,"title":"3.4   文字エンコーディング *","text":"<p>コンピュータシステムでは、すべてのデータが二進形式で格納され、<code>char</code>も例外ではありません。文字を表現するために、各文字と二進数の一対一のマッピングを定義する「文字セット」を開発する必要があります。文字セットがあれば、コンピュータは表を参照して二進数を文字に変換できます。</p>","path":["第 3 章 &nbsp; データ構造","3.4 &nbsp; 文字エンコーディング *"],"tags":[]},{"location":"chapter_data_structure/character_encoding/#341-ascii","level":2,"title":"3.4.1   ASCII文字セット","text":"<p>ASCIIコードは最も初期の文字セットの一つで、正式にはAmerican Standard Code for Information Interchangeとして知られています。7つの二進桁（1バイトの下位7ビット）を使用して文字を表現し、最大128種類の異なる文字を表現できます。以下の図に示すように、ASCIIには英語の大文字と小文字、0〜9の数字、様々な句読点、特定の制御文字（改行やタブなど）が含まれています。</p> <p></p> <p> 図 3-6   ASCIIコード </p> <p>しかし、ASCIIは英語の文字のみを表現できます。コンピュータのグローバル化に伴い、より多くの言語を表現するためにEASCIIと呼ばれる文字セットが開発されました。ASCIIの7ビット構造から8ビットに拡張し、256文字の表現を可能にしました。</p> <p>世界的に、様々な地域固有のEASCII文字セットが導入されました。これらのセットの最初の128文字はASCIIと一致していますが、残りの128文字は異なる言語の要件に対応するために異なって定義されています。</p>","path":["第 3 章 &nbsp; データ構造","3.4 &nbsp; 文字エンコーディング *"],"tags":[]},{"location":"chapter_data_structure/character_encoding/#342-gbk","level":2,"title":"3.4.2   GBK文字セット","text":"<p>後に、**EASCIIでも多くの言語の文字要件を満たすことができない**ことが判明しました。例えば、中国語には約10万の漢字があり、そのうち数千が定期的に使用されています。1980年、中国標準化委員会は6763の中国語文字を含むGB2312文字セットを発表し、中国語のコンピュータ処理ニーズを本質的に満たしました。</p> <p>しかし、GB2312は一部の稀少文字や繁体字を処理できませんでした。GBK文字セットはGB2312を拡張し、21886の中国語文字を含んでいます。GBKエンコーディングスキームでは、ASCII文字は1バイトで表現され、中国語文字は2バイトを使用します。</p>","path":["第 3 章 &nbsp; データ構造","3.4 &nbsp; 文字エンコーディング *"],"tags":[]},{"location":"chapter_data_structure/character_encoding/#343-unicode","level":2,"title":"3.4.3   Unicode文字セット","text":"<p>コンピュータ技術の急速な発展と多数の文字セットおよびエンコーディング標準により、数多くの問題が発生しました。一方では、これらの文字セットは一般的に特定の言語の文字のみを定義し、多言語環境では適切に機能できませんでした。他方では、同じ言語に対する複数の文字セット標準の存在により、異なるエンコーディング標準を使用するコンピュータ間で情報交換を行う際に文字化けが発生しました。</p> <p>当時の研究者たちは考えました：世界のすべての言語と記号を含む包括的な文字セットが開発されれば、言語横断環境と文字化けに関連する問題を解決できるのではないでしょうか？ このアイデアにインスパイアされて、広範囲な文字セットであるUnicodeが誕生しました。</p> <p>Unicodeは中国語で「统一码」（統一コード）と呼ばれ、理論的に100万文字以上を収容できます。世界中のすべての文字を単一のセットに組み込み、様々な言語の処理と表示のための汎用文字セットを提供し、異なるエンコーディング標準による文字化けの問題を減らすことを目指しています。</p> <p>1991年のリリース以来、Unicodeは新しい言語と文字を含むよう継続的に拡張されています。2022年9月現在、Unicodeには149,186文字が含まれており、様々な言語の文字、記号、さらには絵文字も含まれています。広大なUnicode文字セットでは、一般的に使用される文字は2バイトを占有し、一部の稀少な文字は3バイトまたは4バイトを占有する場合があります。</p> <p>Unicodeは各文字に数値（「コードポイント」と呼ばれる）を割り当てる汎用文字セットですが、これらの文字コードポイントがコンピュータシステムにどのように格納されるべきかは指定していません。疑問が生じるかもしれません：システムはテキスト内の異なる長さのUnicodeコードポイントをどのように解釈するのでしょうか？例えば、2バイトのコードが与えられた場合、システムはそれが単一の2バイト文字を表すのか、2つの1バイト文字を表すのかをどのように判断するのでしょうか？</p> <p>この問題に対する簡単な解決策は、すべての文字を等長エンコーディングとして格納することです。以下の図に示すように、「Hello」の各文字は1バイトを占有し、「算法」（アルゴリズム）の各文字は2バイトを占有します。上位ビットをゼロで埋めることで、「Hello 算法」のすべての文字を2バイトとしてエンコードできます。この方法により、システムは2バイトごとに文字を解釈し、フレーズの内容を復元できます。</p> <p></p> <p> 図 3-7   Unicodeエンコーディング例 </p> <p>しかし、ASCIIが示したように、英語のエンコーディングには1バイトのみが必要です。上記のアプローチを使用すると、英語テキストが占有する空間がASCIIエンコーディングと比較して2倍になり、メモリ空間の無駄になります。したがって、より効率的なUnicodeエンコーディング方法が必要です。</p>","path":["第 3 章 &nbsp; データ構造","3.4 &nbsp; 文字エンコーディング *"],"tags":[]},{"location":"chapter_data_structure/character_encoding/#344-utf-8","level":2,"title":"3.4.4   UTF-8エンコーディング","text":"<p>現在、UTF-8は国際的に最も広く使用されているUnicodeエンコーディング方法になっています。**これは可変長エンコーディング**で、文字の複雑さに応じて1〜4バイトを使用して文字を表現します。ASCII文字は1バイトのみが必要で、ラテン文字とギリシャ文字は2バイト、一般的に使用される中国語文字は3バイト、その他の稀少な文字は4バイトが必要です。</p> <p>UTF-8のエンコーディング規則は複雑ではなく、2つのケースに分けることができます：</p> <ul> <li>1バイト文字の場合、最上位ビットを\\(0\\)に設定し、残りの7ビットをUnicodeコードポイントに設定します。注目すべきは、ASCII文字がUnicodeセットの最初の128コードポイントを占有することです。これは**UTF-8エンコーディングがASCIIと後方互換性がある**ことを意味します。これは、UTF-8を使用して古いASCIIテキストを解析できることを意味します。</li> <li>長さ\\(n\\)バイトの文字（\\(n &gt; 1\\)）の場合、最初のバイトの最上位\\(n\\)ビットを\\(1\\)に設定し、\\((n + 1)^{\\text{th}}\\)ビットを\\(0\\)に設定します。2番目のバイトから、各バイトの最上位2ビットを\\(10\\)に設定します。残りのビットはUnicodeコードポイントを埋めるために使用されます。</li> </ul> <p>以下の図は「Hello算法」のUTF-8エンコーディングを示しています。最上位\\(n\\)ビットが\\(1\\)に設定されているため、システムは最上位ビットで\\(1\\)に設定されたビット数を数えることで文字の長さを\\(n\\)として決定できることが観察できます。</p> <p>しかし、なぜ残りのバイトの最上位2ビットを\\(10\\)に設定するのでしょうか？実際、この\\(10\\)は一種のチェックサムとして機能します。システムが間違ったバイトからテキストの解析を開始した場合、バイトの先頭の\\(10\\)によりシステムは異常を迅速に検出できます。</p> <p>\\(10\\)をチェックサムとして使用する理由は、UTF-8エンコーディング規則の下では、文字の最上位2ビットが\\(10\\)になることは不可能だからです。これは矛盾により証明できます：文字の最上位2ビットが\\(10\\)の場合、文字の長さが\\(1\\)であることを示し、これはASCIIに対応します。しかし、ASCII文字の最上位ビットは\\(0\\)であるべきで、これは仮定と矛盾します。</p> <p></p> <p> 図 3-8   UTF-8エンコーディング例 </p> <p>UTF-8以外にも、他の一般的なエンコーディング方法には以下があります：</p> <ul> <li>UTF-16エンコーディング：2または4バイトを使用して文字を表現します。すべてのASCII文字と一般的に使用される非英語文字は2バイトで表現され、少数の文字は4バイトが必要です。2バイト文字の場合、UTF-16エンコーディングはUnicodeコードポイントと等しくなります。</li> <li>UTF-32エンコーディング：すべての文字が4バイトを使用します。これは、UTF-32がUTF-8やUTF-16よりも多くの空間を占有することを意味し、特にASCII文字の割合が高いテキストでは顕著です。</li> </ul> <p>ストレージ空間の観点から、UTF-8を使用して英語文字を表現することは1バイトのみが必要なため非常に効率的です。UTF-16を使用して一部の非英語文字（中国語など）をエンコードすることは、2バイトのみが必要なためより効率的になる場合があります。一方、UTF-8では3バイトが必要になる場合があります。</p> <p>互換性の観点から、UTF-8は最も汎用性があり、多くのツールとライブラリがUTF-8を優先的にサポートしています。</p>","path":["第 3 章 &nbsp; データ構造","3.4 &nbsp; 文字エンコーディング *"],"tags":[]},{"location":"chapter_data_structure/character_encoding/#345","level":2,"title":"3.4.5   プログラミング言語における文字エンコーディング","text":"<p>歴史的に、多くのプログラミング言語はプログラム実行中の文字列処理にUTF-16やUTF-32などの固定長エンコーディングを利用していました。これにより文字列を配列として処理でき、いくつかの利点があります：</p> <ul> <li>ランダムアクセス：UTF-16でエンコードされた文字列は簡単にランダムアクセスできます。可変長エンコーディングであるUTF-8の場合、\\(i^{th}\\)文字の位置を特定するには文字列の開始から\\(i^{th}\\)位置まで走査する必要があり、\\(O(n)\\)時間がかかります。</li> <li>文字数カウント：ランダムアクセスと同様に、UTF-16でエンコードされた文字列の文字数をカウントすることは\\(O(1)\\)操作です。しかし、UTF-8でエンコードされた文字列の文字数をカウントするには文字列全体を走査する必要があります。</li> <li>文字列操作：分割、連結、挿入、削除などの多くの文字列操作は、UTF-16でエンコードされた文字列で簡単です。これらの操作は一般的に、UTF-8エンコーディングの有効性を確保するためにUTF-8でエンコードされた文字列で追加の計算が必要です。</li> </ul> <p>プログラミング言語における文字エンコーディングスキームの設計は、様々な要因を含む興味深いトピックです：</p> <ul> <li>Javaの<code>String</code>型はUTF-16エンコーディングを使用し、各文字が2バイトを占有します。これは、16ビットがすべての可能な文字を表現するのに十分であるという初期の信念に基づいており、後に間違いであることが証明されました。Unicode標準が16ビットを超えて拡張されると、Javaの文字は「サロゲートペア」として知られる16ビット値のペアで表現される場合があります。</li> <li>JavaScriptとTypeScriptは、Javaと同様の理由でUTF-16エンコーディングを使用します。JavaScriptが1995年にNetscapeによって最初に導入されたとき、Unicodeはまだ初期段階にあり、16ビットエンコーディングはすべてのUnicode文字を表現するのに十分でした。</li> <li>C#はUTF-16エンコーディングを使用し、これは主にMicrosoftによって設計された.NETプラットフォーム、および多くのMicrosoft技術（Windowsオペレーティングシステムを含む）がUTF-16エンコーディングを広範囲に使用しているためです。</li> </ul> <p>文字数の過小評価により、これらの言語は16ビットを超えるUnicode文字を表現するために「サロゲートペア」を使用する必要がありました。このアプローチには欠点があります：サロゲートペアを含む文字列は2バイトまたは4バイトを占有する文字を持つ場合があり、固定長エンコーディングの利点を失います。さらに、サロゲートペアの処理はプログラミングに複雑さとデバッグの困難さを追加します。</p> <p>これらの課題に対処するため、一部の言語は代替エンコーディング戦略を採用しています：</p> <ul> <li>Pythonの<code>str</code>型は、文字のストレージ長が文字列内の最大のUnicodeコードポイントに依存する柔軟な表現でUnicodeエンコーディングを使用します。すべての文字がASCIIの場合、各文字は1バイトを占有し、基本多言語面（BMP）内の文字は2バイト、BMPを超える文字は4バイトを占有します。</li> <li>Goの<code>string</code>型は内部的にUTF-8エンコーディングを使用します。Goは個別のUnicodeコードポイントを表現するための<code>rune</code>型も提供します。</li> <li>Rustの<code>str</code>と<code>String</code>型は内部的にUTF-8エンコーディングを使用します。Rustは個別のUnicodeコードポイント用の<code>char</code>型も提供します。</li> </ul> <p>上記の議論は、プログラミング言語での文字列の格納方法に関するものであり、**ファイルでの文字列の格納方法やネットワーク上での送信方法とは異なる**ことに注意することが重要です。ファイルストレージやネットワーク送信では、文字列は通常、最適な互換性と空間効率のためにUTF-8形式でエンコードされます。</p>","path":["第 3 章 &nbsp; データ構造","3.4 &nbsp; 文字エンコーディング *"],"tags":[]},{"location":"chapter_data_structure/classification_of_data_structure/","level":1,"title":"3.1   データ構造の分類","text":"<p>一般的なデータ構造には、配列、連結リスト、スタック、キュー、ハッシュ表、木、ヒープ、グラフがあります。これらは「論理構造」と「物理構造」に分類できます。</p>","path":["第 3 章 &nbsp; データ構造","3.1 &nbsp; データ構造の分類"],"tags":[]},{"location":"chapter_data_structure/classification_of_data_structure/#311","level":2,"title":"3.1.1   論理構造：線形と非線形","text":"<p>論理構造はデータ要素間の論理的関係を明らかにします。配列と連結リストでは、データは特定の順序で配置され、データ間の線形関係を示しています。一方、木では、データは上から下へ階層的に配置され、「祖先」と「子孫」間の派生関係を示しています。そして、グラフはノードとエッジから構成され、複雑なネットワーク関係を反映しています。</p> <p>下図に示されているように、論理構造は「線形」と「非線形」の2つの主要カテゴリに分けることができます。線形構造はより直感的で、データが論理関係において線形に配置されていることを示しています。非線形構造は、逆に非線形に配置されています。</p> <ul> <li>線形データ構造：配列、連結リスト、スタック、キュー、ハッシュ表。要素が一対一の順次関係を持ちます。</li> <li>非線形データ構造：木、ヒープ、グラフ、ハッシュ表。</li> </ul> <p>非線形データ構造は、さらに木構造とネットワーク構造に分けることができます。</p> <ul> <li>木構造：木、ヒープ、ハッシュ表。要素が一対多の関係を持ちます。</li> <li>ネットワーク構造：グラフ。要素が多対多の関係を持ちます。</li> </ul> <p></p> <p> 図 3-1   Linear and non-linear data structures </p>","path":["第 3 章 &nbsp; データ構造","3.1 &nbsp; データ構造の分類"],"tags":[]},{"location":"chapter_data_structure/classification_of_data_structure/#312","level":2,"title":"3.1.2   物理構造：連続と分散","text":"<p>アルゴリズムの実行中、処理されるデータはメモリに格納されます。下図はコンピュータのメモリスティックを示しており、各黒い正方形は物理メモリ空間です。メモリを巨大なExcelスプレッドシートと考えることができ、各セルは一定量のデータを格納できます。</p> <p>システムはメモリアドレスによって目標位置のデータにアクセスします。下図に示されているように、コンピュータは特定のルールに従って表の各セルに一意の識別子を割り当て、各メモリ空間が一意のメモリアドレスを持つことを保証します。これらのアドレスにより、プログラムはメモリに格納されたデータにアクセスできます。</p> <p></p> <p> 図 3-2   Memory stick, memory spaces, memory addresses </p> <p>Tip</p> <p>メモリをExcelスプレッドシートに比較することは簡略化された類推であることに注意してください。メモリの実際の動作メカニズムはより複雑で、アドレス空間、メモリ管理、キャッシュメカニズム、仮想メモリ、物理メモリなどの概念が関係しています。</p> <p>メモリはすべてのプログラムの共有リソースです。あるメモリブロックが1つのプログラムによって占有されると、他のプログラムが同時に使用することはできません。したがって、メモリリソースはデータ構造とアルゴリズムの設計における重要な考慮事項です。例えば、アルゴリズムのピークメモリ使用量は、システムの残り空きメモリを超えてはいけません。連続したメモリブロックが不足している場合は、非連続メモリブロックに格納できるデータ構造を選択する必要があります。</p> <p>下図に示されているように、物理構造はコンピュータメモリにおけるデータの格納方法を反映し、連続空間格納（配列）と非連続空間格納（連結リスト）に分けることができます。2つのタイプの物理構造は、時間効率と空間効率の観点で補完的な特性を示します。</p> <p></p> <p> 図 3-3   Contiguous space storage and dispersed space storage </p> <p>すべてのデータ構造は配列、連結リスト、またはその組み合わせに基づいて実装されていることに注意してください。例えば、スタックとキューは配列または連結リストのどちらでも実装できます。ハッシュ表の実装には配列と連結リストの両方が関係する場合があります。</p> <ul> <li>配列ベースの実装：スタック、キュー、ハッシュ表、木、ヒープ、グラフ、行列、テンソル（次元\\(\\geq 3\\)の配列）。</li> <li>連結リストベースの実装：スタック、キュー、ハッシュ表、木、ヒープ、グラフなど。</li> </ul> <p>配列に基づいて実装されたデータ構造は「静的データ構造」とも呼ばれ、初期化後に長さを変更できないことを意味します。逆に、連結リストに基づいたものは「動的データ構造」と呼ばれ、プログラム実行中にサイズを調整できます。</p> <p>Tip</p> <p>物理構造を理解するのが困難な場合は、次の章「配列と連結リスト」を読んでから、この節に戻ることをお勧めします。</p>","path":["第 3 章 &nbsp; データ構造","3.1 &nbsp; データ構造の分類"],"tags":[]},{"location":"chapter_data_structure/number_encoding/","level":1,"title":"3.3   数値エンコーディング *","text":"<p>Tip</p> <p>本書では、アスタリスク「*」が付いた章は任意読書です。時間が不足している場合や難しいと感じる場合は、最初はこれらをスキップして、必須の章を完了した後に戻ることができます。</p>","path":["第 3 章 &nbsp; データ構造","3.3 &nbsp; 数値エンコーディング *"],"tags":[]},{"location":"chapter_data_structure/number_encoding/#331","level":2,"title":"3.3.1   整数エンコーディング","text":"<p>前の節の表で、すべての整数型は正の数よりも1つ多い負の数を表現できることを観察しました。例えば、<code>byte</code>の範囲は\\([-128, 127]\\)です。この現象は直感に反するように見え、その根本的な理由には符号絶対値、1の補数、2の補数エンコーディングの知識が関与しています。</p> <p>まず重要なことは、**数値はコンピュータ内で2の補数形式で格納される**ということです。なぜそうなのかを分析する前に、これら3つのエンコーディング方法を定義しましょう：</p> <ul> <li>符号絶対値：数値の二進表現の最上位ビットを符号ビットとし、\\(0\\)は正の数、\\(1\\)は負の数を表します。残りのビットは数値の値を表します。</li> <li>1の補数：正の数の1の補数は符号絶対値と同じです。負の数の場合、符号ビット以外のすべてのビットを反転して得られます。</li> <li>2の補数：正の数の2の補数は符号絶対値と同じです。負の数の場合、その1の補数に\\(1\\)を加えて得られます。</li> </ul> <p>以下の図は、符号絶対値、1の補数、2の補数間の変換を示しています：</p> <p></p> <p> 図 3-4   符号絶対値、1の補数、2の補数間の変換 </p> <p>符号絶対値は最も直感的ですが、制限があります。一つには、符号絶対値の負の数は計算で直接使用できません。例えば、符号絶対値で\\(1 + (-2)\\)を計算すると\\(-3\\)になり、これは正しくありません。</p> \\[ \\begin{aligned} &amp; 1 + (-2) \\newline &amp; \\rightarrow 0000 \\; 0001 + 1000 \\; 0010 \\newline &amp; = 1000 \\; 0011 \\newline &amp; \\rightarrow -3 \\end{aligned} \\] <p>この問題に対処するため、コンピュータは1の補数を導入しました。1の補数に変換して\\(1 + (-2)\\)を計算し、結果を符号絶対値に戻すと、正しい結果\\(-1\\)が得られます。</p> \\[ \\begin{aligned} &amp; 1 + (-2) \\newline &amp; \\rightarrow 0000 \\; 0001 \\; \\text{(符号絶対値)} + 1000 \\; 0010 \\; \\text{(符号絶対値)} \\newline &amp; = 0000 \\; 0001 \\; \\text{(1の補数)} + 1111 \\; 1101 \\; \\text{(1の補数)} \\newline &amp; = 1111 \\; 1110 \\; \\text{(1の補数)} \\newline &amp; = 1000 \\; 0001 \\; \\text{(符号絶対値)} \\newline &amp; \\rightarrow -1 \\end{aligned} \\] <p>また、符号絶対値では0に2つの表現があります：\\(+0\\)と\\(-0\\)です。これは0に対して2つの異なる二進エンコーディングがあることを意味し、曖昧さを引き起こす可能性があります。例えば、条件チェックで正と負の0を区別しないと、正しくない結果になる可能性があります。この曖昧さに対処するには追加のチェックが必要で、計算効率が低下する可能性があります。</p> \\[ \\begin{aligned} +0 &amp; \\rightarrow 0000 \\; 0000 \\newline -0 &amp; \\rightarrow 1000 \\; 0000 \\end{aligned} \\] <p>符号絶対値と同様に、1の補数も正と負の0の曖昧さに悩まされます。そのため、コンピュータはさらに2の補数を導入しました。符号絶対値、1の補数、2の補数における負の0の変換過程を観察してみましょう：</p> \\[ \\begin{aligned} -0 \\rightarrow \\; &amp; 1000 \\; 0000 \\; \\text{(符号絶対値)} \\newline = \\; &amp; 1111 \\; 1111 \\; \\text{(1の補数)} \\newline = 1 \\; &amp; 0000 \\; 0000 \\; \\text{(2の補数)} \\newline \\end{aligned} \\] <p>負の0の1の補数に\\(1\\)を加えると桁上がりが発生しますが、<code>byte</code>の長さは8ビットのみのため、9番目のビットへの桁上がり\\(1\\)は破棄されます。したがって、**負の0の2の補数は\\(0000 \\; 0000\\)**で、正の0と同じになり、曖昧さが解決されます。</p> <p>最後の謎は、<code>byte</code>の\\([-128, 127]\\)の範囲で、追加の負の数\\(-128\\)があることです。\\([-127, +127]\\)の区間では、すべての整数に対応する符号絶対値、1の補数、2の補数があり、相互変換が可能であることを観察します。</p> <p>しかし、2の補数\\(1000 \\; 0000\\)は対応する符号絶対値を持たない例外です。変換方法によると、その符号絶対値は\\(0000 \\; 0000\\)で、0を示します。これは矛盾を示しています。なぜなら、その2の補数は自分自身を表すべきだからです。コンピュータは、この特別な2の補数\\(1000 \\; 0000\\)を\\(-128\\)を表すものとして指定しています。実際、2の補数での\\((-1) + (-127)\\)の計算結果は\\(-128\\)になります。</p> \\[ \\begin{aligned} &amp; (-127) + (-1) \\newline &amp; \\rightarrow 1111 \\; 1111 \\; \\text{(符号絶対値)} + 1000 \\; 0001 \\; \\text{(符号絶対値)} \\newline &amp; = 1000 \\; 0000 \\; \\text{(1の補数)} + 1111 \\; 1110 \\; \\text{(1の補数)} \\newline &amp; = 1000 \\; 0001 \\; \\text{(2の補数)} + 1111 \\; 1111 \\; \\text{(2の補数)} \\newline &amp; = 1000 \\; 0000 \\; \\text{(2の補数)} \\newline &amp; \\rightarrow -128 \\end{aligned} \\] <p>お気づきかもしれませんが、これらの計算はすべて加算であり、重要な事実を示唆しています：コンピュータの内部ハードウェア回路は主に加算演算を中心に設計されています。これは、加算が乗算、除算、減算などの他の演算と比較してハードウェアで実装しやすく、並列化が容易で高速計算が可能だからです。</p> <p>これはコンピュータが加算のみを実行できることを意味するものではありません。加算と基本的な論理演算を組み合わせることで、コンピュータは様々な他の数学演算を実行できます。例えば、減算\\(a - b\\)は\\(a + (-b)\\)に変換でき、乗算と除算は複数の加算または減算に変換できます。</p> <p>コンピュータで2の補数を使用する理由をまとめることができます：2の補数表現により、コンピュータは同じ回路と演算を使用して正と負の数の加算を処理でき、減算用の特別なハードウェア回路の必要性を排除し、正と負の0の曖昧さを回避できます。これによりハードウェア設計が大幅に簡素化され、計算効率が向上します。</p> <p>2の補数の設計は非常に巧妙で、スペースの制約により、ここで停止します。興味のある読者はさらに探求することを奨励します。</p>","path":["第 3 章 &nbsp; データ構造","3.3 &nbsp; 数値エンコーディング *"],"tags":[]},{"location":"chapter_data_structure/number_encoding/#332","level":2,"title":"3.3.2   浮動小数点数エンコーディング","text":"<p>興味深いことに気づいたかもしれません：同じ4バイトの長さにもかかわらず、なぜ<code>float</code>は<code>int</code>と比較してはるかに大きい値の範囲を持つのでしょうか？これは直感に反するように見えます。<code>float</code>は分数を表現する必要があるため、範囲が縮小すると予想されるからです。</p> <p>実際、これは浮動小数点数（<code>float</code>）で使用される異なる表現方法によるものです。32ビットの二進数を次のように考えてみましょう：</p> \\[ b_{31} b_{30} b_{29} \\ldots b_2 b_1 b_0 \\] <p>IEEE 754標準によると、32ビットの<code>float</code>は次の3つの部分で構成されます：</p> <ul> <li>符号ビット\\(\\mathrm{S}\\)：1ビットを占有し、\\(b_{31}\\)に対応します。</li> <li>指数ビット\\(\\mathrm{E}\\)：8ビットを占有し、\\(b_{30} b_{29} \\ldots b_{23}\\)に対応します。</li> <li>仮数ビット\\(\\mathrm{N}\\)：23ビットを占有し、\\(b_{22} b_{21} \\ldots b_0\\)に対応します。</li> </ul> <p>二進<code>float</code>数の値は次のように計算されます：</p> \\[ \\text{val} = (-1)^{b_{31}} \\times 2^{\\left(b_{30} b_{29} \\ldots b_{23}\\right)_2 - 127} \\times \\left(1 . b_{22} b_{21} \\ldots b_0\\right)_2 \\] <p>十進公式に変換すると、次のようになります：</p> \\[ \\text{val} = (-1)^{\\mathrm{S}} \\times 2^{\\mathrm{E} - 127} \\times (1 + \\mathrm{N}) \\] <p>各成分の範囲は：</p> \\[ \\begin{aligned} \\mathrm{S} \\in &amp; \\{ 0, 1\\}, \\quad \\mathrm{E} \\in \\{ 1, 2, \\dots, 254 \\} \\newline (1 + \\mathrm{N}) = &amp; (1 + \\sum_{i=1}^{23} b_{23-i} \\times 2^{-i}) \\subset [1, 2 - 2^{-23}] \\end{aligned} \\] <p></p> <p> 図 3-5   IEEE 754標準での浮動小数点数の計算例 </p> <p>上の図を観察すると、例のデータ\\(\\mathrm{S} = 0\\)、\\(\\mathrm{E} = 124\\)、\\(\\mathrm{N} = 2^{-2} + 2^{-3} = 0.375\\)が与えられた場合：</p> \\[ \\text{val} = (-1)^0 \\times 2^{124 - 127} \\times (1 + 0.375) = 0.171875 \\] <p>これで最初の質問に答えることができます：<code>float</code>の表現には指数ビットが含まれているため、<code>int</code>よりもはるかに大きい範囲を持ちます。上記の計算に基づくと、<code>float</code>で表現可能な最大正の数は約\\(2^{254 - 127} \\times (2 - 2^{-23}) \\approx 3.4 \\times 10^{38}\\)で、最小負の数は符号ビットを切り替えることで得られます。</p> <p>しかし、<code>float</code>の拡張された範囲のトレードオフは精度の犠牲です。整数型<code>int</code>は32ビットすべてを数値表現に使用し、値は均等に分布していますが、指数ビットのため、<code>float</code>の値が大きいほど、隣接する数値間の差が大きくなります。</p> <p>以下の表に示すように、指数ビット\\(\\mathrm{E} = 0\\)と\\(\\mathrm{E} = 255\\)は特別な意味を持ち、0、無限大、\\(\\mathrm{NaN}\\)などを表現するために使用されます。</p> <p> 表 3-2   指数ビットの意味 </p> 指数ビットE 仮数ビット\\(\\mathrm{N} = 0\\) 仮数ビット\\(\\mathrm{N} \\ne 0\\) 計算公式 \\(0\\) \\(\\pm 0\\) 非正規化数 \\((-1)^{\\mathrm{S}} \\times 2^{-126} \\times (0.\\mathrm{N})\\) \\(1, 2, \\dots, 254\\) 正規化数 正規化数 \\((-1)^{\\mathrm{S}} \\times 2^{(\\mathrm{E} -127)} \\times (1.\\mathrm{N})\\) \\(255\\) \\(\\pm \\infty\\) \\(\\mathrm{NaN}\\) <p>非正規化数は浮動小数点数の精度を大幅に向上させることは注目に値します。最小の正の正規化数は\\(2^{-126}\\)で、最小の正の非正規化数は\\(2^{-126} \\times 2^{-23}\\)です。</p> <p>倍精度<code>double</code>も<code>float</code>と同様の表現方法を使用しますが、簡潔さのためここでは詳述しません。</p>","path":["第 3 章 &nbsp; データ構造","3.3 &nbsp; 数値エンコーディング *"],"tags":[]},{"location":"chapter_data_structure/summary/","level":1,"title":"3.5   まとめ","text":"","path":["第 3 章 &nbsp; データ構造","3.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_data_structure/summary/#1","level":3,"title":"1.   重要なポイント","text":"<ul> <li>データ構造は論理構造と物理構造の2つの観点から分類できます。論理構造はデータ間の論理的関係を記述し、物理構造はデータがメモリにどのように格納されるかを記述します。</li> <li>よく使用される論理構造には、線形構造、木、ネットワークがあります。通常、論理構造に基づいてデータ構造を線形（配列、連結リスト、スタック、キュー）と非線形（木、グラフ、ヒープ）に分けます。ハッシュ表の実装は線形と非線形の両方のデータ構造を含む場合があります。</li> <li>プログラムが実行中の際、データはメモリに格納されます。各メモリ空間には対応するアドレスがあり、プログラムはこれらのアドレスを通じてデータにアクセスします。</li> <li>物理構造は連続空間格納（配列）と離散空間格納（連結リスト）に分けることができます。すべてのデータ構造は配列、連結リスト、またはその両方の組み合わせを使用して実装されます。</li> <li>コンピュータの基本データ型には、整数（<code>byte</code>、<code>short</code>、<code>int</code>、<code>long</code>）、浮動小数点数（<code>float</code>、<code>double</code>）、文字（<code>char</code>）、ブール値（<code>bool</code>）が含まれます。データ型の値の範囲は、そのサイズと表現に依存します。</li> <li>符号絶対値、1の補数、2の補数は、コンピュータで整数をエンコードする3つの方法であり、相互に変換することができます。符号絶対値の最上位ビットは符号ビットで、残りのビットは数値の値を表します。</li> <li>整数はコンピュータで2の補数によってエンコードされます。この表現の利点には、(i)コンピュータが正と負の整数の加算を統一できる、(ii)減算用の特別なハードウェア回路を設計する必要がない、(iii)正と負の0の曖昧さがない、があります。</li> <li>浮動小数点数のエンコーディングは、1つの符号ビット、8つの指数ビット、23の仮数ビットで構成されます。指数ビットのため、浮動小数点数の範囲は整数よりもはるかに大きくなりますが、精度を犠牲にします。</li> <li>ASCIIは最初期の英語文字セットで、1バイトの長さで計127文字です。GBKは人気のある中国語文字セットで、2万文字以上の中国語文字を含みます。Unicodeは世界の様々な言語の文字を含む完全な文字セット標準を提供することを目的とし、文字エンコーディング方法の不一致による文字化け問題を解決します。</li> <li>UTF-8は最も人気があり一般的なUnicodeエンコーディング方法です。これは可変長エンコーディング方法で、優れた拡張性と空間効率を持ちます。UTF-16とUTF-32は固定長エンコーディング方法です。中国語文字をエンコードする際、UTF-16はUTF-8よりも少ない空間を使用します。JavaやC#などのプログラミング言語はデフォルトでUTF-16エンコーディングを使用します。</li> </ul>","path":["第 3 章 &nbsp; データ構造","3.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_data_structure/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: なぜハッシュ表は線形と非線形の両方のデータ構造を含むのですか？</p> <p>ハッシュ表の基礎構造は配列です。ハッシュ衝突を解決するために、「チェイン法」を使用する場合があります（後の節「ハッシュ衝突」で説明）：配列の各バケットは連結リストを指し、その長さが特定の閾値より大きくなると木（通常は赤黒木）に変換される可能性があります。 格納の観点から、ハッシュ表の基礎構造は配列で、各バケットには値、連結リスト、または木が含まれる場合があります。したがって、ハッシュ表は線形データ構造（配列、連結リスト）と非線形データ構造（木）の両方を含む場合があります。</p> <p>Q: <code>char</code>型の長さは1バイトですか？</p> <p><code>char</code>型の長さは、プログラミング言語のエンコーディング方法によって決まります。例えば、Java、JavaScript、TypeScript、C#はすべてUTF-16エンコーディング（Unicodeコードポイントを保存するため）を使用するため、<code>char</code>型の長さは2バイトです。</p> <p>Q: 配列ベースのデータ構造を「静的データ構造」と呼ぶことに曖昧さはありませんか？スタックもプッシュやポップなどの「動的」操作を実行できます。</p> <p>スタックは動的なデータ操作を実装できますが、データ構造は依然として「静的」です（長さが固定）。配列ベースのデータ構造は動的に要素を追加または削除できますが、その容量は固定されています。スタックサイズが事前に割り当てられたサイズを超える場合、古い配列は新しく作成されたより大きな配列にコピーされます。</p> <p>Q: スタック（キュー）を構築する際、そのサイズが指定されていないのに、なぜ「静的データ構造」なのですか？</p> <p>高級プログラミング言語では、スタック（キュー）の初期容量を手動で指定する必要はありません。このタスクはクラス内で自動的に完了されます。例えば、Javaの<code>ArrayList</code>の初期容量は通常10です。さらに、拡張操作も自動的に完了されます。詳細については、後続の「リスト」の章を参照してください。</p> <p>Q: 符号絶対値を2の補数に変換する方法は「最初に否定してから1を加える」ですので、2の補数を符号絶対値に変換することはその逆操作「最初に1を減算してから否定する」であるべきです。 しかし、2の補数も「最初に否定してから1を加える」を通じて符号絶対値に変換できます。なぜですか？</p> <p>A: これは、符号絶対値と2の補数間の相互変換が「補数」の計算と等価だからです。まず補数を定義します：\\(a + b = c\\)と仮定すると、\\(a\\)は\\(b\\)の\\(c\\)に対する補数と言い、逆に\\(b\\)は\\(a\\)の\\(c\\)に対する補数と言います。</p> <p>長さ\\(n = 4\\)の二進数\\(0010\\)が与えられた場合、この数が符号絶対値（符号ビットを無視）の場合、その2の補数は「最初に否定してから1を加える」ことで得られます：</p> \\[ 0010 \\rightarrow 1101 \\rightarrow 1110 \\] <p>符号絶対値と2の補数の和が\\(0010 + 1110 = 10000\\)であることを観察します。つまり、2の補数\\(1110\\)は符号絶対値\\(0010\\)の\\(10000\\)に対する「補数」です。これは、上記の「最初に否定してから1を加える」が\\(10000\\)に対する補数の計算と等価であることを意味します。</p> <p>では、\\(1110\\)の\\(10000\\)に対する「補数」は何でしょうか？「最初に否定してから1を加える」ことで計算できます：</p> \\[ 1110 \\rightarrow 0001 \\rightarrow 0010 \\] <p>言い換えると、符号絶対値と2の補数は互いに\\(10000\\)に対する「補数」であるため、「符号絶対値から2の補数」と「2の補数から符号絶対値」は同じ操作（最初に否定してから1を加える）で実装できます。</p> <p>もちろん、「最初に否定してから1を加える」の逆操作を使用して2の補数\\(1110\\)の符号絶対値を求めることもできます。つまり、「最初に1を減算してから否定する」：</p> \\[ 1110 \\rightarrow 1101 \\rightarrow 0010 \\] <p>要約すると、「最初に否定してから1を加える」と「最初に1を減算してから否定する」は両方とも\\(10000\\)に対する補数を計算しており、等価です。</p> <p>本質的に、「否定」操作は実際には\\(1111\\)に対する補数を求めることです（<code>符号絶対値 + 1の補数 = 1111</code>が常に成り立つため）。そして1の補数に1を加えることは\\(10000\\)に対する2の補数と等しくなります。</p> <p>上記では\\(n = 4\\)を例に取りましたが、任意の桁数の任意の二進数に一般化できます。</p>","path":["第 3 章 &nbsp; データ構造","3.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_divide_and_conquer/","level":1,"title":"第 12 章   分割統治","text":"<p>Abstract</p> <p>困難な問題は層を重ねて分解され、各分解によってより単純になります。</p> <p>分割統治は深い真理を明らかにします：単純さから始めれば、複雑さは解決される。</p>","path":["第 12 章 &nbsp; 分割統治"],"tags":[]},{"location":"chapter_divide_and_conquer/#_1","level":2,"title":"章の内容","text":"<ul> <li>12.1   分割統治アルゴリズム</li> <li>12.2   分割統治探索戦略</li> <li>12.3   木の構築問題</li> <li>12.4   ハノイの塔問題</li> <li>12.5   まとめ</li> </ul>","path":["第 12 章 &nbsp; 分割統治"],"tags":[]},{"location":"chapter_divide_and_conquer/binary_search_recur/","level":1,"title":"12.2   分割統治検索戦略","text":"<p>私たちは検索アルゴリズムが主に2つのカテゴリに分類されることを学びました。</p> <ul> <li>総当たり検索：データ構造を走査することで実装され、時間計算量は \\(O(n)\\) です。</li> <li>適応検索：独特なデータ組織形式や事前情報を利用し、時間計算量は \\(O(\\log n)\\) または \\(O(1)\\) に達することができます。</li> </ul> <p>実際、時間計算量が \\(O(\\log n)\\) の検索アルゴリズムは通常分割統治戦略に基づいています。例えば、二分探索や木などです。</p> <ul> <li>二分探索の各ステップは、問題（配列内でターゲット要素を検索する）をより小さな問題（配列の半分でターゲット要素を検索する）に分割し、配列が空になるかターゲット要素が見つかるまで続けます。</li> <li>木は分割統治のアイデアを表現し、二分探索木、AVL木、ヒープなどのデータ構造では、様々な操作の時間計算量は \\(O(\\log n)\\) です。</li> </ul> <p>二分探索の分割統治戦略は以下の通りです。</p> <ul> <li>問題を分割できる：二分探索は元の問題（配列内での検索）を部分問題（配列の半分での検索）に再帰的に分割し、中間要素とターゲット要素を比較することで実現されます。</li> <li>部分問題は独立している：二分探索では、各ラウンドで一つの部分問題を処理し、他の部分問題に影響されません。</li> <li>部分問題の解をマージする必要がない：二分探索は特定の要素を見つけることを目的としているため、部分問題の解をマージする必要がありません。部分問題が解決されると、元の問題も解決されます。</li> </ul> <p>分割統治は検索効率を向上させることができます。なぜなら、総当たり検索はラウンドごとに1つの選択肢しか除去できませんが、分割統治は選択肢の半分を除去できるからです。</p>","path":["第 12 章 &nbsp; 分割統治","12.2 &nbsp; 分割統治検索戦略"],"tags":[]},{"location":"chapter_divide_and_conquer/binary_search_recur/#1","level":3,"title":"1.   分割統治に基づく二分探索の実装","text":"<p>前の章では、二分探索は反復に基づいて実装されました。今度は、分割統治（再帰）に基づいて実装します。</p> <p>Question</p> <p>長さ \\(n\\) の順序付けられた配列 <code>nums</code> が与えられ、すべての要素が一意である場合、要素 <code>target</code> を見つけてください。</p> <p>分割統治の観点から、検索区間 \\([i, j]\\) に対応する部分問題を \\(f(i, j)\\) と表します。</p> <p>元の問題 \\(f(0, n-1)\\) から開始して、以下のステップで二分探索を実行します。</p> <ol> <li>検索区間 \\([i, j]\\) の中点 \\(m\\) を計算し、それを使用して検索区間の半分を除去します。</li> <li>半分のサイズに縮小された部分問題を再帰的に解決します。これは \\(f(i, m-1)\\) または \\(f(m+1, j)\\) になる可能性があります。</li> <li><code>target</code> が見つかるか区間が空になってリターンするまで、ステップ <code>1.</code> と <code>2.</code> を繰り返します。</li> </ol> <p>以下の図は、配列内で要素 \\(6\\) を探す二分探索の分割統治過程を示しています。</p> <p></p> <p> 図 12-4   二分探索の分割統治過程 </p> <p>実装コードでは、問題 \\(f(i, j)\\) を解決するために再帰関数 <code>dfs()</code> を宣言します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_recur.py<pre><code>def dfs(nums: list[int], target: int, i: int, j: int) -&gt; int:\n    \"\"\"二分探索：問題 f(i, j)\"\"\"\n    # 区間が空の場合、対象要素がないことを示すため、-1 を返す\n    if i &gt; j:\n        return -1\n    # 中点インデックス m を計算\n    m = (i + j) // 2\n    if nums[m] &lt; target:\n        # 再帰部分問題 f(m+1, j)\n        return dfs(nums, target, m + 1, j)\n    elif nums[m] &gt; target:\n        # 再帰部分問題 f(i, m-1)\n        return dfs(nums, target, i, m - 1)\n    else:\n        # 対象要素を発見したため、そのインデックスを返す\n        return m\n\ndef binary_search(nums: list[int], target: int) -&gt; int:\n    \"\"\"二分探索\"\"\"\n    n = len(nums)\n    # 問題 f(0, n-1) を解く\n    return dfs(nums, target, 0, n - 1)\n</code></pre> binary_search_recur.cpp<pre><code>/* 二分探索：問題 f(i, j) */\nint dfs(vector&lt;int&gt; &amp;nums, int target, int i, int j) {\n    // 区間が空の場合、対象要素が存在しないことを示すため、-1 を返す\n    if (i &gt; j) {\n        return -1;\n    }\n    // 中点インデックス m を計算\n    int m = i + (j - i) / 2;\n    if (nums[m] &lt; target) {\n        // 再帰的な部分問題 f(m+1, j)\n        return dfs(nums, target, m + 1, j);\n    } else if (nums[m] &gt; target) {\n        // 再帰的な部分問題 f(i, m-1)\n        return dfs(nums, target, i, m - 1);\n    } else {\n        // 対象要素が見つかったため、そのインデックスを返す\n        return m;\n    }\n}\n\n/* 二分探索 */\nint binarySearch(vector&lt;int&gt; &amp;nums, int target) {\n    int n = nums.size();\n    // 問題 f(0, n-1) を解く\n    return dfs(nums, target, 0, n - 1);\n}\n</code></pre> binary_search_recur.java<pre><code>/* 二分探索：問題 f(i, j) */\nint dfs(int[] nums, int target, int i, int j) {\n    // 区間が空の場合、対象要素が存在しないことを示すため、-1 を返す\n    if (i &gt; j) {\n        return -1;\n    }\n    // 中点インデックス m を計算\n    int m = i + (j - i) / 2;\n    if (nums[m] &lt; target) {\n        // 再帰的な部分問題 f(m+1, j)\n        return dfs(nums, target, m + 1, j);\n    } else if (nums[m] &gt; target) {\n        // 再帰的な部分問題 f(i, m-1)\n        return dfs(nums, target, i, m - 1);\n    } else {\n        // 対象要素が見つかったため、そのインデックスを返す\n        return m;\n    }\n}\n\n/* 二分探索 */\nint binarySearch(int[] nums, int target) {\n    int n = nums.length;\n    // 問題 f(0, n-1) を解く\n    return dfs(nums, target, 0, n - 1);\n}\n</code></pre> binary_search_recur.cs<pre><code>[class]{binary_search_recur}-[func]{DFS}\n\n[class]{binary_search_recur}-[func]{BinarySearch}\n</code></pre> binary_search_recur.go<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{binarySearch}\n</code></pre> binary_search_recur.swift<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{binarySearch}\n</code></pre> binary_search_recur.js<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{binarySearch}\n</code></pre> binary_search_recur.ts<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{binarySearch}\n</code></pre> binary_search_recur.dart<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{binarySearch}\n</code></pre> binary_search_recur.rs<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{binary_search}\n</code></pre> binary_search_recur.c<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{binarySearch}\n</code></pre> binary_search_recur.kt<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{binarySearch}\n</code></pre> binary_search_recur.rb<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{binary_search}\n</code></pre>","path":["第 12 章 &nbsp; 分割統治","12.2 &nbsp; 分割統治検索戦略"],"tags":[]},{"location":"chapter_divide_and_conquer/build_binary_tree_problem/","level":1,"title":"12.3   二分木構築問題","text":"<p>Question</p> <p>二分木の前順走査 <code>preorder</code> シーケンスと中順走査 <code>inorder</code> シーケンスが与えられた場合、二分木を構築してそのルートノードを返してください。二分木に重複するノード値がないと仮定します（以下の図に示すように）。</p> <p></p> <p> 図 12-5   二分木構築のサンプルデータ </p>","path":["第 12 章 &nbsp; 分割統治","12.3 &nbsp; 二分木構築問題"],"tags":[]},{"location":"chapter_divide_and_conquer/build_binary_tree_problem/#1","level":3,"title":"1.   分割統治問題かどうかの判定","text":"<p><code>preorder</code> と <code>inorder</code> シーケンスから二分木を構築する元の問題は、典型的な分割統治問題です。</p> <ul> <li>問題を分解できる：分割統治の観点から、元の問題を2つの部分問題（左の部分木の構築と右の部分木の構築）とルートノードの初期化という1つの操作に分割できます。各部分木（部分問題）について、同じアプローチを継続的に適用し、より小さな部分木（部分問題）に分割し、最小の部分問題（空の部分木）に到達するまで続けます。</li> <li>部分問題は独立している：左と右の部分木は重複しません。左の部分木を構築する際、左の部分木に対応する中順走査と前順走査のセグメントのみが必要です。右の部分木にも同じアプローチが適用されます。</li> <li>部分問題の解を組み合わせることができる：左と右の部分木（部分問題の解）を構築したら、それらをルートノードに接続して元の問題の解を取得できます。</li> </ul>","path":["第 12 章 &nbsp; 分割統治","12.3 &nbsp; 二分木構築問題"],"tags":[]},{"location":"chapter_divide_and_conquer/build_binary_tree_problem/#2","level":3,"title":"2.   部分木の分割方法","text":"<p>上記の分析に基づいて、この問題は分割統治を使用して解決できます。しかし、前順走査 <code>preorder</code> シーケンスと中順走査 <code>inorder</code> シーケンスを使用して左と右の部分木をどのように分割すればよいでしょうか？</p> <p>定義により、<code>preorder</code> と <code>inorder</code> シーケンスの両方を3つの部分に分割できます：</p> <ul> <li>前順走査：<code>[ ルート | 左の部分木 | 右の部分木 ]</code>。例えば、図では、木は <code>[ 3 | 9 | 2 1 7 ]</code> に対応します。</li> <li>中順走査：<code>[ 左の部分木 | ルート | 右の部分木 ]</code>。例えば、図では、木は <code>[ 9 | 3 | 1 2 7 ]</code> に対応します。</li> </ul> <p>前の図のデータを使用して、次の図に示すステップに従って分割結果を取得できます：</p> <ol> <li>前順走査の最初の要素3がルートノードの値です。</li> <li><code>inorder</code> シーケンス内でルートノード3のインデックスを見つけ、このインデックスを使用して <code>inorder</code> を <code>[ 9 | 3 ｜ 1 2 7 ]</code> に分割します。</li> <li><code>inorder</code> シーケンスの分割に従って、左と右の部分木がそれぞれ1個と3個のノードを含むことが簡単に決定できるため、<code>preorder</code> シーケンスを <code>[ 3 | 9 | 2 1 7 ]</code> に対応して分割できます。</li> </ol> <p></p> <p> 図 12-6   前順走査と中順走査での部分木の分割 </p>","path":["第 12 章 &nbsp; 分割統治","12.3 &nbsp; 二分木構築問題"],"tags":[]},{"location":"chapter_divide_and_conquer/build_binary_tree_problem/#3","level":3,"title":"3.   変数に基づく部分木範囲の記述","text":"<p>上記の分割方法に基づいて、<code>preorder</code> と <code>inorder</code> シーケンスにおけるルート、左の部分木、右の部分木のインデックス範囲を取得しました。これらのインデックス範囲を記述するために、いくつかのポインタ変数を使用します。</p> <ul> <li>現在の木のルートノードの <code>preorder</code> シーケンスでのインデックスを \\(i\\) とします。</li> <li>現在の木のルートノードの <code>inorder</code> シーケンスでのインデックスを \\(m\\) とします。</li> <li>現在の木の <code>inorder</code> シーケンスでのインデックス範囲を \\([l, r]\\) とします。</li> </ul> <p>以下の表に示すように、これらの変数は <code>preorder</code> シーケンスでのルートノードのインデックスと <code>inorder</code> シーケンスでの部分木のインデックス範囲を表します。</p> <p> 表 12-1   前順走査と中順走査でのルートノードと部分木のインデックス </p> <code>preorder</code> でのルートノードインデックス <code>inorder</code> での部分木インデックス範囲 現在の木 \\(i\\) \\([l, r]\\) 左の部分木 \\(i + 1\\) \\([l, m-1]\\) 右の部分木 \\(i + 1 + (m - l)\\) \\([m+1, r]\\) <p>右の部分木のルートインデックスの \\((m-l)\\) は「左の部分木のノード数」を表すことに注意してください。より明確な理解のために、以下の図を参照することが役立つ場合があります。</p> <p></p> <p> 図 12-7   ルートノードと左右の部分木のインデックス </p>","path":["第 12 章 &nbsp; 分割統治","12.3 &nbsp; 二分木構築問題"],"tags":[]},{"location":"chapter_divide_and_conquer/build_binary_tree_problem/#4","level":3,"title":"4.   コード実装","text":"<p>\\(m\\) の問い合わせの効率を向上させるために、ハッシュテーブル <code>hmap</code> を使用して <code>inorder</code> シーケンスの要素からそのインデックスへのマッピングを格納します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby build_tree.py<pre><code>def dfs(\n    preorder: list[int],\n    inorder_map: dict[int, int],\n    i: int,\n    l: int,\n    r: int,\n) -&gt; TreeNode | None:\n    \"\"\"二分木の構築：分割統治\"\"\"\n    # 部分木の区間が空のとき終了\n    if r - l &lt; 0:\n        return None\n    # ルートノードを初期化\n    root = TreeNode(preorder[i])\n    # m をクエリして左部分木と右部分木を分割\n    m = inorder_map[preorder[i]]\n    # 部分問題：左部分木を構築\n    root.left = dfs(preorder, inorder_map, i + 1, l, m - 1)\n    # 部分問題：右部分木を構築\n    root.right = dfs(preorder, inorder_map, i + 1 + m - l, m + 1, r)\n    # ルートノードを返す\n    return root\n\ndef build_tree(preorder: list[int], inorder: list[int]) -&gt; TreeNode | None:\n    \"\"\"二分木を構築\"\"\"\n    # ハッシュテーブルを初期化、中順走査の要素からインデックスへのマッピングを保存\n    inorder_map = {val: i for i, val in enumerate(inorder)}\n    root = dfs(preorder, inorder_map, 0, 0, len(inorder) - 1)\n    return root\n</code></pre> build_tree.cpp<pre><code>/* 二分木の構築：分割統治 */\nTreeNode *dfs(vector&lt;int&gt; &amp;preorder, unordered_map&lt;int, int&gt; &amp;inorderMap, int i, int l, int r) {\n    // 部分木の区間が空の場合に終了\n    if (r - l &lt; 0)\n        return NULL;\n    // ルートノードを初期化\n    TreeNode *root = new TreeNode(preorder[i]);\n    // m を問い合わせて左右の部分木を分割\n    int m = inorderMap[preorder[i]];\n    // 部分問題：左の部分木を構築\n    root-&gt;left = dfs(preorder, inorderMap, i + 1, l, m - 1);\n    // 部分問題：右の部分木を構築\n    root-&gt;right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r);\n    // ルートノードを返す\n    return root;\n}\n\n/* 二分木の構築 */\nTreeNode *buildTree(vector&lt;int&gt; &amp;preorder, vector&lt;int&gt; &amp;inorder) {\n    // ハッシュテーブルを初期化し、中間順序の要素からインデックスへのマッピングを格納\n    unordered_map&lt;int, int&gt; inorderMap;\n    for (int i = 0; i &lt; inorder.size(); i++) {\n        inorderMap[inorder[i]] = i;\n    }\n    TreeNode *root = dfs(preorder, inorderMap, 0, 0, inorder.size() - 1);\n    return root;\n}\n</code></pre> build_tree.java<pre><code>/* 二分木の構築：分割統治 */\nTreeNode dfs(int[] preorder, Map&lt;Integer, Integer&gt; inorderMap, int i, int l, int r) {\n    // 部分木の区間が空の場合に終了\n    if (r - l &lt; 0)\n        return null;\n    // ルートノードを初期化\n    TreeNode root = new TreeNode(preorder[i]);\n    // m を問い合わせて左右の部分木を分割\n    int m = inorderMap.get(preorder[i]);\n    // 部分問題：左の部分木を構築\n    root.left = dfs(preorder, inorderMap, i + 1, l, m - 1);\n    // 部分問題：右の部分木を構築\n    root.right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r);\n    // ルートノードを返す\n    return root;\n}\n\n/* 二分木の構築 */\nTreeNode buildTree(int[] preorder, int[] inorder) {\n    // ハッシュテーブルを初期化し、中間順序の要素からインデックスへのマッピングを格納\n    Map&lt;Integer, Integer&gt; inorderMap = new HashMap&lt;&gt;();\n    for (int i = 0; i &lt; inorder.length; i++) {\n        inorderMap.put(inorder[i], i);\n    }\n    TreeNode root = dfs(preorder, inorderMap, 0, 0, inorder.length - 1);\n    return root;\n}\n</code></pre> build_tree.cs<pre><code>[class]{build_tree}-[func]{DFS}\n\n[class]{build_tree}-[func]{BuildTree}\n</code></pre> build_tree.go<pre><code>[class]{}-[func]{dfsBuildTree}\n\n[class]{}-[func]{buildTree}\n</code></pre> build_tree.swift<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{buildTree}\n</code></pre> build_tree.js<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{buildTree}\n</code></pre> build_tree.ts<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{buildTree}\n</code></pre> build_tree.dart<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{buildTree}\n</code></pre> build_tree.rs<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{build_tree}\n</code></pre> build_tree.c<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{buildTree}\n</code></pre> build_tree.kt<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{buildTree}\n</code></pre> build_tree.rb<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{build_tree}\n</code></pre> <p>以下の図は、二分木を構築する再帰過程を示しています。各ノードは再帰の「下降」段階で作成され、各エッジ（参照）は「上昇」段階で形成されます。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 12-8   二分木構築の再帰過程 </p> <p>各再帰関数の <code>preorder</code> と <code>inorder</code> シーケンスの分割は以下の図に示されています。</p> <p></p> <p> 図 12-9   各再帰関数での分割 </p> <p>二分木が \\(n\\) 個のノードを持つと仮定すると、各ノードの初期化（再帰関数 <code>dfs()</code> の呼び出し）には \\(O(1)\\) 時間がかかります。したがって、全体の時間計算量は \\(O(n)\\) です。</p> <p>ハッシュテーブルは <code>inorder</code> 要素からそのインデックスへのマッピングを格納するため、\\(O(n)\\) スペースが必要です。最悪の場合、二分木が連結リストに退化すると、再帰の深さは \\(n\\) に達し、\\(O(n)\\) のスタックスペースを消費する可能性があります。したがって、全体の空間計算量は \\(O(n)\\) です。</p>","path":["第 12 章 &nbsp; 分割統治","12.3 &nbsp; 二分木構築問題"],"tags":[]},{"location":"chapter_divide_and_conquer/divide_and_conquer/","level":1,"title":"12.1   分割統治アルゴリズム","text":"<p>分割統治は重要で人気のあるアルゴリズム戦略です。名前が示すように、アルゴリズムは通常再帰的に実装され、「分割」と「統治」の2つのステップから構成されます。</p> <ol> <li>分割（分割段階）：元の問題を再帰的に2つ以上の小さな部分問題に分解し、最小の部分問題に到達するまで続けます。</li> <li>統治（マージ段階）：解決方法が既知の最小の部分問題から開始し、部分問題の解をボトムアップ方式でマージして元の問題の解を構築します。</li> </ol> <p>以下の図に示すように、「マージソート」は分割統治戦略の典型的な応用の一つです。</p> <ol> <li>分割：元の配列（元の問題）を再帰的に2つの副配列（部分問題）に分割し、副配列が1つの要素のみになるまで（最小の部分問題）続けます。</li> <li>統治：順序付けられた副配列（部分問題の解）をボトムアップでマージして、順序付けられた元の配列（元の問題の解）を取得します。</li> </ol> <p></p> <p> 図 12-1   マージソートの分割統治戦略 </p>","path":["第 12 章 &nbsp; 分割統治","12.1 &nbsp; 分割統治アルゴリズム"],"tags":[]},{"location":"chapter_divide_and_conquer/divide_and_conquer/#1211","level":2,"title":"12.1.1   分割統治問題を特定する方法","text":"<p>問題が分割統治解決に適しているかどうかは、通常以下の基準に基づいて決定できます。</p> <ol> <li>問題をより小さなものに分解できる：元の問題をより小さく類似した部分問題に分割でき、そのような過程を同じ方法で再帰的に実行できます。</li> <li>部分問題は独立している：部分問題間に重複がなく、独立しており、個別に解決できます。</li> <li>部分問題の解をマージできる：元の問題の解は、部分問題の解を組み合わせることで導出されます。</li> </ol> <p>明らかに、マージソートはこれら3つの基準を満たしています。</p> <ol> <li>問題をより小さなものに分解できる：配列（元の問題）を再帰的に2つの副配列（部分問題）に分割します。</li> <li>部分問題は独立している：各副配列は独立してソートできます（部分問題は独立して解決できます）。</li> <li>部分問題の解をマージできる：2つの順序付けられた副配列（部分問題の解）を1つの順序付けられた配列（元の問題の解）にマージできます。</li> </ol>","path":["第 12 章 &nbsp; 分割統治","12.1 &nbsp; 分割統治アルゴリズム"],"tags":[]},{"location":"chapter_divide_and_conquer/divide_and_conquer/#1212","level":2,"title":"12.1.2   分割統治による効率の向上","text":"<p>分割統治戦略はアルゴリズム問題を効果的に解決するだけでなく、しばしば効率を向上させます。ソートアルゴリズムでは、クイックソート、マージソート、ヒープソートは、分割統治戦略を適用しているため、選択ソート、バブルソート、挿入ソートよりも高速です。</p> <p>私たちの心には疑問があるかもしれません：なぜ分割統治はアルゴリズムの効率を向上させることができ、その根本的な論理は何ですか？ つまり、問題を部分問題に分解し、それらを解決し、それらの解を組み合わせて元の問題に対処することが、元の問題を直接解決するよりも効率的である理由は何ですか？この質問は2つの側面から分析できます：操作数と並列計算。</p>","path":["第 12 章 &nbsp; 分割統治","12.1 &nbsp; 分割統治アルゴリズム"],"tags":[]},{"location":"chapter_divide_and_conquer/divide_and_conquer/#1","level":3,"title":"1.   操作数の最適化","text":"<p>「バブルソート」を例にとると、長さ \\(n\\) の配列を処理するのに \\(O(n^2)\\) 時間が必要です。以下の図に示すように、配列を中点から2つの副配列に分割するとします。そのような分割には \\(O(n)\\) 時間が必要です。各副配列のソートには \\(O((n / 2)^2)\\) 時間が必要です。そして2つの副配列のマージには \\(O(n)\\) 時間が必要です。したがって、全体の時間計算量は：</p> \\[ O(n + (\\frac{n}{2})^2 \\times 2 + n) = O(\\frac{n^2}{2} + 2n) \\] <p></p> <p> 図 12-2   配列分割前後のバブルソート </p> <p>以下の不等式を計算してみましょう。左側は分割前の総操作数を表し、右側は分割後の総操作数をそれぞれ表します：</p> \\[ \\begin{aligned} n^2 &amp; &gt; \\frac{n^2}{2} + 2n \\newline n^2 - \\frac{n^2}{2} - 2n &amp; &gt; 0 \\newline n(n - 4) &amp; &gt; 0 \\end{aligned} \\] <p>これは \\(n &gt; 4\\) の場合、分割後の操作数が少なく、より良いパフォーマンスにつながることを意味します。分割後の時間計算量は依然として二次 \\(O(n^2)\\) ですが、計算量の定数係数が減少していることに注意してください。</p> <p>さらに進むことができます。副配列をその中点からさらに2つの副配列に分割し続けて、副配列が1つの要素のみになるまで続けたらどうでしょうか？ このアイデアは実際には「マージソート」で、時間計算量は \\(O(n \\log n)\\) です。</p> <p>少し違うことを試してみましょう。2つではなく、より多くの分割に分割したらどうでしょうか？ 例えば、元の配列を \\(k\\) 個の副配列に均等に分割しますか？このアプローチは「バケットソート」と非常に似ており、大量のデータのソートに非常に適しています。理論的には、時間計算量は \\(O(n + k)\\) に達することができます。</p>","path":["第 12 章 &nbsp; 分割統治","12.1 &nbsp; 分割統治アルゴリズム"],"tags":[]},{"location":"chapter_divide_and_conquer/divide_and_conquer/#2","level":3,"title":"2.   並列計算による最適化","text":"<p>分割統治によって生成される部分問題は互いに独立していることが分かっています。これは、それらを並列で解決できることを意味します。 その結果、分割統治はアルゴリズムの時間計算量を減らすだけでなく、現代のオペレーティングシステムによる並列最適化も促進します。</p> <p>並列最適化は、複数のコアやプロセッサを持つ環境で特に効果的です。システムが複数の部分問題を同時に処理できるため、計算リソースを完全に活用し、全体的な実行時間が大幅に短縮されます。</p> <p>例えば、以下の図に示す「バケットソート」では、大量のデータを様々なバケットに均等に分解します。各バケットのソート作業は、利用可能な計算ユニットに割り当てることができます。すべての作業が完了すると、すべてのソートされたバケットがマージされて最終結果が生成されます。</p> <p></p> <p> 図 12-3   バケットソートの並列計算 </p>","path":["第 12 章 &nbsp; 分割統治","12.1 &nbsp; 分割統治アルゴリズム"],"tags":[]},{"location":"chapter_divide_and_conquer/divide_and_conquer/#1213","level":2,"title":"12.1.3   分割統治の一般的な応用","text":"<p>分割統治は多くの古典的なアルゴリズム問題を解決するために使用できます。</p> <ul> <li>最近点対の発見：このアルゴリズムは点の集合を2つの半分に分割することで動作します。そして各半分で再帰的に最近点対を見つけます。最後に、2つの半分にまたがるペアを考慮して、全体の最近点対を見つけます。</li> <li>大整数の乗算：一つのアルゴリズムはKaratsubaと呼ばれます。大整数の乗算をいくつかの小さな整数の乗算と加算に分解します。</li> <li>行列の乗算：一例はStrassenアルゴリズムです。大きな行列の乗算を複数の小さな行列の乗算と加算に分解します。</li> <li>ハノイの塔問題：ハノイの塔問題は再帰的に解決でき、分割統治戦略の典型的な応用です。</li> <li>転倒対の解決：シーケンスで、前の数が後の数より大きい場合、これら2つの数は転倒対を構成します。転倒対問題の解決は、マージソートの助けを借りて、分割統治のアイデアを利用できます。</li> </ul> <p>分割統治はアルゴリズムとデータ構造の設計にも広く応用されています。</p> <ul> <li>二分探索：二分探索は、ソート済み配列を中点インデックスから2つの半分に分割します。そして、ターゲット値と中間要素値の比較結果に基づいて、一方の半分が破棄されます。同じプロセスで残りの半分で検索が続行され、ターゲットが見つかるか残りの要素がなくなるまで続きます。</li> <li>マージソート：この節の冒頭ですでに紹介したため、さらなる詳述は不要です。</li> <li>クイックソート：クイックソートはピボット値を選択して配列を2つの副配列に分割し、一方はピボットより小さい要素、もう一方はピボットより大きい要素を持ちます。このプロセスは、これら2つの副配列のそれぞれに対して、1つの要素のみを保持するまで続きます。</li> <li>バケットソート：バケットソートの基本的なアイデアは、データを複数のバケットに分散させることです。各バケット内の要素をソートした後、バケットから順序よく要素を取得して順序付けられた配列を取得します。</li> <li>木：例えば、二分探索木、AVL木、赤黒木、B木、B+木など。その操作（検索、挿入、削除）はすべて分割統治戦略の応用と見なすことができます。</li> <li>ヒープ：ヒープは特別なタイプの完全二分木です。その様々な操作（挿入、削除、ヒープ化）は、実際に分割統治のアイデアを含意しています。</li> <li>ハッシュテーブル：ハッシュテーブルは直接分割統治を適用しませんが、一部のハッシュ衝突解決ソリューションは間接的にこの戦略を適用します。例えば、チェイン法の長いリストは、クエリ効率を向上させるために赤黒木に変換される場合があります。</li> </ul> <p>**分割統治は巧妙に浸透するアルゴリズムアイデア**であり、様々なアルゴリズムとデータ構造に組み込まれていることが分かります。</p>","path":["第 12 章 &nbsp; 分割統治","12.1 &nbsp; 分割統治アルゴリズム"],"tags":[]},{"location":"chapter_divide_and_conquer/hanota_problem/","level":1,"title":"12.4   ハノイの塔問題","text":"<p>マージソートと二分木構築の両方で、元の問題を2つの部分問題に分解し、それぞれが元の問題のサイズの半分でした。しかし、ハノイの塔では、異なる分解戦略を採用します。</p> <p>Question</p> <p>3つの柱があり、それぞれ <code>A</code>、<code>B</code>、<code>C</code> と表記されます。最初、柱 <code>A</code> には \\(n\\) 枚の円盤があり、上から下に向かって昇順のサイズで配置されています。私たちのタスクは、これらの \\(n\\) 枚の円盤を柱 <code>C</code> に移動し、元の順序を維持することです（以下の図に示すように）。移動中には以下のルールが適用されます：</p> <ol> <li>円盤は柱の上部からのみ取り除くことができ、別の柱の上部に置く必要があります。</li> <li>一度に移動できるのは1枚の円盤のみです。</li> <li>小さい円盤は常に大きい円盤の上にある必要があります。</li> </ol> <p></p> <p> 図 12-10   ハノイの塔の例 </p> <p>サイズ \\(i\\) のハノイの塔問題を \\(f(i)\\) と表記します。例えば、\\(f(3)\\) は3枚の円盤を柱 <code>A</code> から柱 <code>C</code> に移動することを表します。</p>","path":["第 12 章 &nbsp; 分割統治","12.4 &nbsp; ハノイの塔問題"],"tags":[]},{"location":"chapter_divide_and_conquer/hanota_problem/#1","level":3,"title":"1.   基本ケースを考える","text":"<p>以下の図に示すように、問題 \\(f(1)\\)（円盤が1枚のみ）については、<code>A</code> から <code>C</code> に直接移動できます。</p> &lt;1&gt;&lt;2&gt; <p></p> <p></p> <p> 図 12-11   サイズ1の問題の解 </p> <p>\\(f(2)\\)（円盤が2枚）については、**柱 <code>B</code> の助けを借りて小さい円盤を大きい円盤の上に保つ**必要があります。以下の図に示すように：</p> <ol> <li>まず、小さい円盤を <code>A</code> から <code>B</code> に移動します。</li> <li>次に、大きい円盤を <code>A</code> から <code>C</code> に移動します。</li> <li>最後に、小さい円盤を <code>B</code> から <code>C</code> に移動します。</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p> 図 12-12   サイズ2の問題の解 </p> <p>\\(f(2)\\) を解決する過程は次のように要約できます：<code>B</code> の助けを借りて2枚の円盤を <code>A</code> から <code>C</code> に移動する。ここで、<code>C</code> をターゲット柱、<code>B</code> をバッファ柱と呼びます。</p>","path":["第 12 章 &nbsp; 分割統治","12.4 &nbsp; ハノイの塔問題"],"tags":[]},{"location":"chapter_divide_and_conquer/hanota_problem/#2","level":3,"title":"2.   部分問題の分解","text":"<p>問題 \\(f(3)\\)（つまり、円盤が3枚の場合）については、状況がやや複雑になります。</p> <p>すでに \\(f(1)\\) と \\(f(2)\\) の解が分かっているので、分割統治の観点を採用し、<code>A</code> の上の2枚の円盤を1つの単位として扱い、以下の図に示すステップを実行できます。これにより、3枚の円盤を <code>A</code> から <code>C</code> に正常に移動できます。</p> <ol> <li><code>B</code> をターゲット柱、<code>C</code> をバッファ柱として、2枚の円盤を <code>A</code> から <code>B</code> に移動します。</li> <li>残りの円盤を <code>A</code> から直接 <code>C</code> に移動します。</li> <li><code>C</code> をターゲット柱、<code>A</code> をバッファ柱として、2枚の円盤を <code>B</code> から <code>C</code> に移動します。</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p> 図 12-13   サイズ3の問題の解 </p> <p>本質的に、\\(f(3)\\) を2つの \\(f(2)\\) 部分問題と1つの \\(f(1)\\) 部分問題に分解します。これら3つの部分問題を順次解決することで、元の問題が解決され、部分問題が独立しており、それらの解をマージできることを示しています。</p> <p>ここから、以下の図に示すハノイの塔の分割統治戦略を要約できます。元の問題 \\(f(n)\\) を2つの部分問題 \\(f(n-1)\\) と1つの部分問題 \\(f(1)\\) に分割し、以下の順序でこれら3つの部分問題を解決します：</p> <ol> <li><code>C</code> をバッファとして使用し、\\(n-1\\) 枚の円盤を <code>A</code> から <code>B</code> に移動します。</li> <li>残りの円盤を <code>A</code> から直接 <code>C</code> に移動します。</li> <li><code>A</code> をバッファとして使用し、\\(n-1\\) 枚の円盤を <code>B</code> から <code>C</code> に移動します。</li> </ol> <p>各 \\(f(n-1)\\) 部分問題について、同じ再帰分割を適用でき、最小の部分問題 \\(f(1)\\) に到達するまで続けます。\\(f(1)\\) は単一の移動のみが必要であることがすでに分かっているため、解決するのは簡単です。</p> <p></p> <p> 図 12-14   ハノイの塔を解決するための分割統治戦略 </p>","path":["第 12 章 &nbsp; 分割統治","12.4 &nbsp; ハノイの塔問題"],"tags":[]},{"location":"chapter_divide_and_conquer/hanota_problem/#3","level":3,"title":"3.   コード実装","text":"<p>コードでは、再帰関数 <code>dfs(i, src, buf, tar)</code> を定義します。これは柱 <code>src</code> から上の \\(i\\) 枚の円盤を柱 <code>tar</code> に移動し、柱 <code>buf</code> をバッファとして使用します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby hanota.py<pre><code>def move(src: list[int], tar: list[int]):\n    \"\"\"円盤を移動\"\"\"\n    # src の上から円盤を取り出す\n    pan = src.pop()\n    # 円盤を tar の上に置く\n    tar.append(pan)\n\ndef dfs(i: int, src: list[int], buf: list[int], tar: list[int]):\n    \"\"\"ハノイの塔問題 f(i) を解く\"\"\"\n    # src に円盤が 1 つだけ残っている場合、それを tar に移動\n    if i == 1:\n        move(src, tar)\n        return\n    # 部分問題 f(i-1)：tar の助けを借りて src の上の i-1 個の円盤を buf に移動\n    dfs(i - 1, src, tar, buf)\n    # 部分問題 f(1)：残りの 1 個の円盤を src から tar に移動\n    move(src, tar)\n    # 部分問題 f(i-1)：src の助けを借りて buf の上の i-1 個の円盤を tar に移動\n    dfs(i - 1, buf, src, tar)\n\ndef solve_hanota(A: list[int], B: list[int], C: list[int]):\n    \"\"\"ハノイの塔問題を解く\"\"\"\n    n = len(A)\n    # B の助けを借りて A の上の n 個の円盤を C に移動\n    dfs(n, A, B, C)\n</code></pre> hanota.cpp<pre><code>/* 円盤を移動 */\nvoid move(vector&lt;int&gt; &amp;src, vector&lt;int&gt; &amp;tar) {\n    // src の最上部から円盤を取り出す\n    int pan = src.back();\n    src.pop_back();\n    // 円盤を tar の最上部に配置\n    tar.push_back(pan);\n}\n\n/* ハノイの塔問題 f(i) を解く */\nvoid dfs(int i, vector&lt;int&gt; &amp;src, vector&lt;int&gt; &amp;buf, vector&lt;int&gt; &amp;tar) {\n    // src に円盤が1つだけ残っている場合、それを tar に移動\n    if (i == 1) {\n        move(src, tar);\n        return;\n    }\n    // 部分問題 f(i-1)：tar の助けを借りて、上位 i-1 個の円盤を src から buf に移動\n    dfs(i - 1, src, tar, buf);\n    // 部分問題 f(1)：残りの1つの円盤を src から tar に移動\n    move(src, tar);\n    // 部分問題 f(i-1)：src の助けを借りて、上位 i-1 個の円盤を buf から tar に移動\n    dfs(i - 1, buf, src, tar);\n}\n\n/* ハノイの塔問題を解く */\nvoid solveHanota(vector&lt;int&gt; &amp;A, vector&lt;int&gt; &amp;B, vector&lt;int&gt; &amp;C) {\n    int n = A.size();\n    // B の助けを借りて、上位 n 個の円盤を A から C に移動\n    dfs(n, A, B, C);\n}\n</code></pre> hanota.java<pre><code>/* 円盤を移動 */\nvoid move(List&lt;Integer&gt; src, List&lt;Integer&gt; tar) {\n    // src の最上部から円盤を取り出す\n    Integer pan = src.remove(src.size() - 1);\n    // 円盤を tar の最上部に配置\n    tar.add(pan);\n}\n\n/* ハノイの塔問題 f(i) を解く */\nvoid dfs(int i, List&lt;Integer&gt; src, List&lt;Integer&gt; buf, List&lt;Integer&gt; tar) {\n    // src に円盤が1つだけ残っている場合、それを tar に移動\n    if (i == 1) {\n        move(src, tar);\n        return;\n    }\n    // 部分問題 f(i-1)：tar の助けを借りて、上位 i-1 個の円盤を src から buf に移動\n    dfs(i - 1, src, tar, buf);\n    // 部分問題 f(1)：残りの1つの円盤を src から tar に移動\n    move(src, tar);\n    // 部分問題 f(i-1)：src の助けを借りて、上位 i-1 個の円盤を buf から tar に移動\n    dfs(i - 1, buf, src, tar);\n}\n\n/* ハノイの塔問題を解く */\nvoid solveHanota(List&lt;Integer&gt; A, List&lt;Integer&gt; B, List&lt;Integer&gt; C) {\n    int n = A.size();\n    // B の助けを借りて、上位 n 個の円盤を A から C に移動\n    dfs(n, A, B, C);\n}\n</code></pre> hanota.cs<pre><code>[class]{hanota}-[func]{Move}\n\n[class]{hanota}-[func]{DFS}\n\n[class]{hanota}-[func]{SolveHanota}\n</code></pre> hanota.go<pre><code>[class]{}-[func]{move}\n\n[class]{}-[func]{dfsHanota}\n\n[class]{}-[func]{solveHanota}\n</code></pre> hanota.swift<pre><code>[class]{}-[func]{move}\n\n[class]{}-[func]{dfs}\n\n[class]{}-[func]{solveHanota}\n</code></pre> hanota.js<pre><code>[class]{}-[func]{move}\n\n[class]{}-[func]{dfs}\n\n[class]{}-[func]{solveHanota}\n</code></pre> hanota.ts<pre><code>[class]{}-[func]{move}\n\n[class]{}-[func]{dfs}\n\n[class]{}-[func]{solveHanota}\n</code></pre> hanota.dart<pre><code>[class]{}-[func]{move}\n\n[class]{}-[func]{dfs}\n\n[class]{}-[func]{solveHanota}\n</code></pre> hanota.rs<pre><code>[class]{}-[func]{move_pan}\n\n[class]{}-[func]{dfs}\n\n[class]{}-[func]{solve_hanota}\n</code></pre> hanota.c<pre><code>[class]{}-[func]{move}\n\n[class]{}-[func]{dfs}\n\n[class]{}-[func]{solveHanota}\n</code></pre> hanota.kt<pre><code>[class]{}-[func]{move}\n\n[class]{}-[func]{dfs}\n\n[class]{}-[func]{solveHanota}\n</code></pre> hanota.rb<pre><code>[class]{}-[func]{move}\n\n[class]{}-[func]{dfs}\n\n[class]{}-[func]{solve_hanota}\n</code></pre> <p>以下の図に示すように、ハノイの塔問題は高さ \\(n\\) の再帰木として視覚化できます。各ノードは部分問題を表し、<code>dfs()</code> の呼び出しに対応します。したがって、時間計算量は \\(O(2^n)\\)、空間計算量は \\(O(n)\\) です。</p> <p></p> <p> 図 12-15   ハノイの塔の再帰木 </p> <p>Quote</p> <p>ハノイの塔は古代の伝説に由来します。古代インドの寺院で、僧侶たちは3本の高いダイヤモンドの柱と、異なるサイズの \\(64\\) 枚の金の円盤を持っていました。彼らは、最後の円盤が正しく置かれたとき、世界が終わると信じていました。</p> <p>しかし、僧侶たちが1秒に1枚の円盤を移動したとしても、約 \\(2^{64} \\approx 1.84×10^{19}\\) —約5850億年—かかり、宇宙の年齢の現在の推定をはるかに超えています。したがって、この伝説が真実であれば、世界の終わりについて心配する必要はおそらくないでしょう。</p>","path":["第 12 章 &nbsp; 分割統治","12.4 &nbsp; ハノイの塔問題"],"tags":[]},{"location":"chapter_divide_and_conquer/summary/","level":1,"title":"12.5   まとめ","text":"<ul> <li>分割統治は一般的なアルゴリズム設計戦略で、分割（分割）と統治（マージ）の2つの段階から構成され、一般的に再帰を使用して実装されます。</li> <li>問題が分割統治アプローチに適しているかどうかを判断するために、問題が分解可能かどうか、部分問題が独立しているかどうか、部分問題をマージできるかどうかを確認します。</li> <li>マージソートは分割統治戦略の典型的な例です。配列を再帰的に2つの等しい長さの副配列に分割し、1つの要素のみが残るまで続け、次にこれらの副配列を層ごとにマージしてソートを完了します。</li> <li>分割統治戦略の導入は、しばしばアルゴリズムの効率を向上させます。一方では操作数を減らし、他方では分割後のシステムの並列最適化を促進します。</li> <li>分割統治は多数のアルゴリズム問題に適用でき、データ構造とアルゴリズム設計で広く使用され、多くのシナリオに現れます。</li> <li>総当たり検索と比較して、適応検索はより効率的です。時間計算量が \\(O(\\log n)\\) の検索アルゴリズムは、通常分割統治戦略に基づいています。</li> <li>二分探索は分割統治戦略のもう一つの古典的な応用です。部分問題の解のマージを含まず、再帰的な分割統治アプローチで実装できます。</li> <li>二分木構築問題では、木の構築（元の問題）を左の部分木と右の部分木の構築（部分問題）に分割できます。これは前順走査と中順走査のインデックス範囲を分割することで実現できます。</li> <li>ハノイの塔問題では、サイズ \\(n\\) の問題をサイズ \\(n-1\\) の2つの部分問題とサイズ \\(1\\) の1つの部分問題に分解できます。これら3つの部分問題を順次解決することで、元の問題が解決されます。</li> </ul>","path":["第 12 章 &nbsp; 分割統治","12.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_dynamic_programming/","level":1,"title":"第 14 章   動的プログラミング","text":"<p>Abstract</p> <p>川が流れて海に注ぐように、</p> <p>動的プログラミングは小さな問題の解を織り合わせて、より大きな問題の解へと導きます。一歩一歩進んで、最終的な答えが待つ彼岸へと向かいます。</p>","path":["第 14 章 &nbsp; 動的計画法","第 14 章 &nbsp; 動的プログラミング"],"tags":[]},{"location":"chapter_dynamic_programming/#_1","level":2,"title":"章の内容","text":"<ul> <li>14.1   動的計画法の初歩</li> <li>14.2   DP 問題の特性</li> <li>14.3   DP の解法の考え方</li> <li>14.4   0-1ナップサック問題</li> <li>14.5   完全ナップサック問題</li> <li>14.6   編集距離問題</li> <li>14.7   まとめ</li> </ul>","path":["第 14 章 &nbsp; 動的計画法","第 14 章 &nbsp; 動的プログラミング"],"tags":[]},{"location":"chapter_dynamic_programming/dp_problem_features/","level":1,"title":"14.2   動的プログラミング問題の特徴","text":"<p>前のセクションでは、動的プログラミングが問題を部分問題に分解することで元の問題を解決する方法を学びました。実際、部分問題の分解は一般的なアルゴリズムアプローチであり、分割統治法、動的プログラミング、バックトラッキングでは異なる重点があります。</p> <ul> <li>分割統治法アルゴリズムは元の問題を複数の独立した部分問題に再帰的に分割し、最小の部分問題に到達するまで続け、バックトラッキング時に部分問題の解を組み合わせて最終的に元の問題の解を得ます。</li> <li>動的プログラミングも問題を再帰的に分解しますが、分割統治法アルゴリズムとの主な違いは、動的プログラミングの部分問題が相互依存的であり、分解プロセス中に多くの重複する部分問題が現れることです。</li> <li>バックトラッキングアルゴリズムは試行錯誤によってすべての可能な解を網羅し、枝刈りによって不必要な探索分岐を避けます。元の問題の解は一連の決定ステップから構成され、各決定ステップ前の各部分シーケンスを部分問題として考えることができます。</li> </ul> <p>実際、動的プログラミングは最適化問題を解決するためによく使用され、これらは重複する部分問題を含むだけでなく、他に2つの主要な特徴があります：最適部分構造と無記憶性です。</p>","path":["第 14 章 &nbsp; 動的計画法","14.2 &nbsp; 動的プログラミング問題の特徴"],"tags":[]},{"location":"chapter_dynamic_programming/dp_problem_features/#1421","level":2,"title":"14.2.1   最適部分構造","text":"<p>階段登り問題を少し修正して、最適部分構造の概念を実証するのにより適したものにします。</p> <p>階段登りの最小コスト</p> <p>階段があり、一度に1段または2段上ることができ、階段の各段にはその段で支払う必要があるコストを表す非負の整数があります。非負の整数配列 \\(cost\\) が与えられ、\\(cost[i]\\) は \\(i\\) 段目で支払う必要があるコストを表し、\\(cost[0]\\) は地面（開始点）です。頂上に到達するために必要な最小コストは何ですか？</p> <p>下の図に示すように、1段目、2段目、3段目のコストがそれぞれ \\(1\\)、\\(10\\)、\\(1\\) の場合、地面から3段目に登る最小コストは \\(2\\) です。</p> <p></p> <p> 図 14-6   3段目に登る最小コスト </p> <p>\\(dp[i]\\) を \\(i\\) 段目に登る累積コストとします。\\(i\\) 段目は \\(i-1\\) 段目または \\(i-2\\) 段目からのみ来ることができるため、\\(dp[i]\\) は \\(dp[i-1] + cost[i]\\) または \\(dp[i-2] + cost[i]\\) のいずれかしかありえません。コストを最小化するために、2つのうち小さい方を選択すべきです：</p> \\[ dp[i] = \\min(dp[i-1], dp[i-2]) + cost[i] \\] <p>これにより最適部分構造の意味がわかります：元の問題の最適解は部分問題の最適解から構築される。</p> <p>この問題は明らかに最適部分構造を持っています：2つの部分問題 \\(dp[i-1]\\) と \\(dp[i-2]\\) の最適解からより良い方を選択し、それを使用して元の問題 \\(dp[i]\\) の最適解を構築します。</p> <p>では、前のセクションの階段登り問題は最適部分構造を持っているでしょうか？その目標は解の数を求めることで、これは数え上げ問題のようですが、別の方法で尋ねてみましょう：「解の最大数を求める」。驚くことに、**問題が変わったにもかかわらず、最適部分構造が現れた**ことがわかります：\\(n\\) 段目での解の最大数は、\\(n-1\\) 段目と \\(n-2\\) 段目での解の最大数の和に等しいです。したがって、最適部分構造の解釈は非常に柔軟で、異なる問題では異なる意味を持ちます。</p> <p>状態遷移方程式と初期状態 \\(dp[1] = cost[1]\\) および \\(dp[2] = cost[2]\\) に従って、動的プログラミングコードを得ることができます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby min_cost_climbing_stairs_dp.py<pre><code>def min_cost_climbing_stairs_dp(cost: list[int]) -&gt; int:\n    \"\"\"最小コスト階段登り：動的プログラミング\"\"\"\n    n = len(cost) - 1\n    if n == 1 or n == 2:\n        return cost[n]\n    # dp テーブルを初期化、部分問題の解を格納するために使用\n    dp = [0] * (n + 1)\n    # 初期状態：最小の部分問題の解を事前設定\n    dp[1], dp[2] = cost[1], cost[2]\n    # 状態遷移：小さい部分問題から大きい部分問題を段階的に解く\n    for i in range(3, n + 1):\n        dp[i] = min(dp[i - 1], dp[i - 2]) + cost[i]\n    return dp[n]\n</code></pre> min_cost_climbing_stairs_dp.cpp<pre><code>/* 最小コスト階段登り：動的プログラミング */\nint minCostClimbingStairsDP(vector&lt;int&gt; &amp;cost) {\n    int n = cost.size() - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    // DPテーブルを初期化し、部分問題の解を格納するために使用\n    vector&lt;int&gt; dp(n + 1);\n    // 初期状態：最小の部分問題の解を事前設定\n    dp[1] = cost[1];\n    dp[2] = cost[2];\n    // 状態遷移：小さな問題から大きな部分問題を段階的に解く\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = min(dp[i - 1], dp[i - 2]) + cost[i];\n    }\n    return dp[n];\n}\n</code></pre> min_cost_climbing_stairs_dp.java<pre><code>/* 最小コスト階段登り：動的プログラミング */\nint minCostClimbingStairsDP(int[] cost) {\n    int n = cost.length - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    // DPテーブルを初期化し、部分問題の解を格納するために使用\n    int[] dp = new int[n + 1];\n    // 初期状態：最小の部分問題の解を事前設定\n    dp[1] = cost[1];\n    dp[2] = cost[2];\n    // 状態遷移：小さな問題から大きな部分問題を段階的に解く\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = Math.min(dp[i - 1], dp[i - 2]) + cost[i];\n    }\n    return dp[n];\n}\n</code></pre> min_cost_climbing_stairs_dp.cs<pre><code>[class]{min_cost_climbing_stairs_dp}-[func]{MinCostClimbingStairsDP}\n</code></pre> min_cost_climbing_stairs_dp.go<pre><code>[class]{}-[func]{minCostClimbingStairsDP}\n</code></pre> min_cost_climbing_stairs_dp.swift<pre><code>[class]{}-[func]{minCostClimbingStairsDP}\n</code></pre> min_cost_climbing_stairs_dp.js<pre><code>[class]{}-[func]{minCostClimbingStairsDP}\n</code></pre> min_cost_climbing_stairs_dp.ts<pre><code>[class]{}-[func]{minCostClimbingStairsDP}\n</code></pre> min_cost_climbing_stairs_dp.dart<pre><code>[class]{}-[func]{minCostClimbingStairsDP}\n</code></pre> min_cost_climbing_stairs_dp.rs<pre><code>[class]{}-[func]{min_cost_climbing_stairs_dp}\n</code></pre> min_cost_climbing_stairs_dp.c<pre><code>[class]{}-[func]{minCostClimbingStairsDP}\n</code></pre> min_cost_climbing_stairs_dp.kt<pre><code>[class]{}-[func]{minCostClimbingStairsDP}\n</code></pre> min_cost_climbing_stairs_dp.rb<pre><code>[class]{}-[func]{min_cost_climbing_stairs_dp}\n</code></pre> <p>下の図は上記コードの動的プログラミングプロセスを示しています。</p> <p></p> <p> 図 14-7   階段登りの最小コストの動的プログラミングプロセス </p> <p>この問題も空間最適化が可能で、1次元を0に圧縮し、空間計算量を \\(O(n)\\) から \\(O(1)\\) に削減できます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby min_cost_climbing_stairs_dp.py<pre><code>def min_cost_climbing_stairs_dp_comp(cost: list[int]) -&gt; int:\n    \"\"\"最小コスト階段登り：空間最適化動的プログラミング\"\"\"\n    n = len(cost) - 1\n    if n == 1 or n == 2:\n        return cost[n]\n    a, b = cost[1], cost[2]\n    for i in range(3, n + 1):\n        a, b = b, min(a, b) + cost[i]\n    return b\n</code></pre> min_cost_climbing_stairs_dp.cpp<pre><code>/* 最小コスト階段登り：空間最適化動的プログラミング */\nint minCostClimbingStairsDPComp(vector&lt;int&gt; &amp;cost) {\n    int n = cost.size() - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    int a = cost[1], b = cost[2];\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = min(a, tmp) + cost[i];\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> min_cost_climbing_stairs_dp.java<pre><code>/* 最小コスト階段登り：空間最適化動的プログラミング */\nint minCostClimbingStairsDPComp(int[] cost) {\n    int n = cost.length - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    int a = cost[1], b = cost[2];\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = Math.min(a, tmp) + cost[i];\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> min_cost_climbing_stairs_dp.cs<pre><code>[class]{min_cost_climbing_stairs_dp}-[func]{MinCostClimbingStairsDPComp}\n</code></pre> min_cost_climbing_stairs_dp.go<pre><code>[class]{}-[func]{minCostClimbingStairsDPComp}\n</code></pre> min_cost_climbing_stairs_dp.swift<pre><code>[class]{}-[func]{minCostClimbingStairsDPComp}\n</code></pre> min_cost_climbing_stairs_dp.js<pre><code>[class]{}-[func]{minCostClimbingStairsDPComp}\n</code></pre> min_cost_climbing_stairs_dp.ts<pre><code>[class]{}-[func]{minCostClimbingStairsDPComp}\n</code></pre> min_cost_climbing_stairs_dp.dart<pre><code>[class]{}-[func]{minCostClimbingStairsDPComp}\n</code></pre> min_cost_climbing_stairs_dp.rs<pre><code>[class]{}-[func]{min_cost_climbing_stairs_dp_comp}\n</code></pre> min_cost_climbing_stairs_dp.c<pre><code>[class]{}-[func]{minCostClimbingStairsDPComp}\n</code></pre> min_cost_climbing_stairs_dp.kt<pre><code>[class]{}-[func]{minCostClimbingStairsDPComp}\n</code></pre> min_cost_climbing_stairs_dp.rb<pre><code>[class]{}-[func]{min_cost_climbing_stairs_dp_comp}\n</code></pre>","path":["第 14 章 &nbsp; 動的計画法","14.2 &nbsp; 動的プログラミング問題の特徴"],"tags":[]},{"location":"chapter_dynamic_programming/dp_problem_features/#1422","level":2,"title":"14.2.2   無記憶性","text":"<p>無記憶性は動的プログラミングが問題解決に効果的であることを可能にする重要な特徴の1つです。その定義は：特定の状態が与えられたとき、その将来の発展は現在の状態のみに関連し、過去に経験したすべての状態とは無関係である。</p> <p>階段登り問題を例に取ると、状態 \\(i\\) が与えられたとき、それは状態 \\(i+1\\) と \\(i+2\\) に発展し、それぞれ1段ジャンプと2段ジャンプに対応します。これら2つの選択をするとき、状態 \\(i\\) より前の状態を考慮する必要はありません。なぜなら、それらは状態 \\(i\\) の将来に影響しないからです。</p> <p>しかし、階段登り問題に制約を追加すると、状況が変わります。</p> <p>制約付き階段登り</p> <p>\\(n\\) 段の階段があり、毎回1段または2段上ることができますが、1段を2回連続でジャンプすることはできません。頂上に登る方法は何通りありますか？</p> <p>下の図に示すように、3段目に登る実行可能な選択肢は2つだけで、1段を3回連続でジャンプする選択肢は制約条件を満たさないため破棄されます。</p> <p></p> <p> 図 14-8   制約付きで3段目に登る実行可能な選択肢の数 </p> <p>この問題では、前回が1段ジャンプだった場合、次回は必ず2段ジャンプでなければなりません。これは**次のステップの選択が現在の状態（現在の階段段数）だけでは独立して決定できず、前の状態（前回の階段段数）にも依存する**ことを意味します。</p> <p>この問題がもはや無記憶性を満たさず、状態遷移方程式 \\(dp[i] = dp[i-1] + dp[i-2]\\) も失敗することは容易にわかります。なぜなら \\(dp[i-1]\\) は今回の1段ジャンプを表しますが、多くの「前回が1段ジャンプだった」選択肢を含んでおり、制約を満たすためにはこれらを直接 \\(dp[i]\\) に含めることはできません。</p> <p>このため、状態定義を拡張する必要があります：状態 \\([i, j]\\) は \\(i\\) 段目にいて、前回が \\(j\\) 段ジャンプだったことを表す。ここで \\(j \\in \\{1, 2\\}\\) です。この状態定義は前回が1段ジャンプだったか2段ジャンプだったかを効果的に区別し、現在の状態がどこから来たかを適切に判断できます。</p> <ul> <li>前回が1段ジャンプだった場合、前々回は必ず2段ジャンプを選択していたはずです。つまり、\\(dp[i, 1]\\) は \\(dp[i-1, 2]\\) からのみ遷移できます。</li> <li>前回が2段ジャンプだった場合、前々回は1段ジャンプまたは2段ジャンプを選択できました。つまり、\\(dp[i, 2]\\) は \\(dp[i-2, 1]\\) または \\(dp[i-2, 2]\\) から遷移できます。</li> </ul> <p>下の図に示すように、\\(dp[i, j]\\) は状態 \\([i, j]\\) の解の数を表します。この時点で、状態遷移方程式は次のようになります：</p> \\[ \\begin{cases} dp[i, 1] = dp[i-1, 2] \\\\ dp[i, 2] = dp[i-2, 1] + dp[i-2, 2] \\end{cases} \\] <p></p> <p> 図 14-9   制約を考慮した再帰関係 </p> <p>最終的に、\\(dp[n, 1] + dp[n, 2]\\) を返せばよく、この2つの合計が \\(n\\) 段目に登る解の総数を表します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby climbing_stairs_constraint_dp.py<pre><code>def climbing_stairs_constraint_dp(n: int) -&gt; int:\n    \"\"\"制約付き階段登り：動的プログラミング\"\"\"\n    if n == 1 or n == 2:\n        return 1\n    # dp テーブルを初期化、部分問題の解を格納するために使用\n    dp = [[0] * 3 for _ in range(n + 1)]\n    # 初期状態：最小の部分問題の解を事前設定\n    dp[1][1], dp[1][2] = 1, 0\n    dp[2][1], dp[2][2] = 0, 1\n    # 状態遷移：小さい部分問題から大きい部分問題を段階的に解く\n    for i in range(3, n + 1):\n        dp[i][1] = dp[i - 1][2]\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2]\n    return dp[n][1] + dp[n][2]\n</code></pre> climbing_stairs_constraint_dp.cpp<pre><code>/* 制約付き階段登り：動的プログラミング */\nint climbingStairsConstraintDP(int n) {\n    if (n == 1 || n == 2) {\n        return 1;\n    }\n    // DPテーブルを初期化し、部分問題の解を格納するために使用\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(3, 0));\n    // 初期状態：最小の部分問題の解を事前設定\n    dp[1][1] = 1;\n    dp[1][2] = 0;\n    dp[2][1] = 0;\n    dp[2][2] = 1;\n    // 状態遷移：小さな問題から大きな部分問題を段階的に解く\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i][1] = dp[i - 1][2];\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2];\n    }\n    return dp[n][1] + dp[n][2];\n}\n</code></pre> climbing_stairs_constraint_dp.java<pre><code>/* 制約付き階段登り：動的プログラミング */\nint climbingStairsConstraintDP(int n) {\n    if (n == 1 || n == 2) {\n        return 1;\n    }\n    // DPテーブルを初期化し、部分問題の解を格納するために使用\n    int[][] dp = new int[n + 1][3];\n    // 初期状態：最小の部分問題の解を事前設定\n    dp[1][1] = 1;\n    dp[1][2] = 0;\n    dp[2][1] = 0;\n    dp[2][2] = 1;\n    // 状態遷移：小さな問題から大きな部分問題を段階的に解く\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i][1] = dp[i - 1][2];\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2];\n    }\n    return dp[n][1] + dp[n][2];\n}\n</code></pre> climbing_stairs_constraint_dp.cs<pre><code>[class]{climbing_stairs_constraint_dp}-[func]{ClimbingStairsConstraintDP}\n</code></pre> climbing_stairs_constraint_dp.go<pre><code>[class]{}-[func]{climbingStairsConstraintDP}\n</code></pre> climbing_stairs_constraint_dp.swift<pre><code>[class]{}-[func]{climbingStairsConstraintDP}\n</code></pre> climbing_stairs_constraint_dp.js<pre><code>[class]{}-[func]{climbingStairsConstraintDP}\n</code></pre> climbing_stairs_constraint_dp.ts<pre><code>[class]{}-[func]{climbingStairsConstraintDP}\n</code></pre> climbing_stairs_constraint_dp.dart<pre><code>[class]{}-[func]{climbingStairsConstraintDP}\n</code></pre> climbing_stairs_constraint_dp.rs<pre><code>[class]{}-[func]{climbing_stairs_constraint_dp}\n</code></pre> climbing_stairs_constraint_dp.c<pre><code>[class]{}-[func]{climbingStairsConstraintDP}\n</code></pre> climbing_stairs_constraint_dp.kt<pre><code>[class]{}-[func]{climbingStairsConstraintDP}\n</code></pre> climbing_stairs_constraint_dp.rb<pre><code>[class]{}-[func]{climbing_stairs_constraint_dp}\n</code></pre> <p>上記のケースでは、前の状態のみを考慮すればよいため、状態定義を拡張することで依然として無記憶性を満たすことができます。しかし、一部の問題では非常に深刻な「状態効果」があります。</p> <p>障害物生成付き階段登り</p> <p>\\(n\\) 段の階段があり、毎回1段または2段上ることができます。**\\(i\\) 段目に登ったとき、システムが自動的に \\(2i\\) 段目に障害物を置き、その後のすべてのラウンドで \\(2i\\) 段目にジャンプすることが禁止される**と規定されています。例えば、最初の2ラウンドで2段目と3段目にジャンプした場合、その後は4段目と6段目にジャンプできません。頂上に登る方法は何通りありますか？</p> <p>この問題では、次のジャンプはすべての過去の状態に依存します。各ジャンプがより高い段に障害物を置き、将来のジャンプに影響するからです。このような問題では、動的プログラミングはしばしば解決に苦労します。</p> <p>実際、多くの複雑な組み合わせ最適化問題（巡回セールスマン問題など）は無記憶性を満たしません。このような問題に対しては、通常、ヒューリスティック探索、遺伝的アルゴリズム、強化学習などの他の方法を選択して、限られた時間内に使用可能な局所最適解を得ます。</p>","path":["第 14 章 &nbsp; 動的計画法","14.2 &nbsp; 動的プログラミング問題の特徴"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/","level":1,"title":"14.3   動的プログラミング問題解決アプローチ","text":"<p>前の2つのセクションでは、動的プログラミング問題の主要な特徴を紹介しました。次に、より実用的な2つの問題を一緒に探索しましょう。</p> <ol> <li>問題が動的プログラミング問題かどうかをどのように判断するか？</li> <li>動的プログラミング問題を解決する完全なステップは何か？</li> </ol>","path":["第 14 章 &nbsp; 動的計画法","14.3 &nbsp; 動的プログラミング問題解決アプローチ"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#1431","level":2,"title":"14.3.1   問題の判定","text":"<p>一般的に言えば、問題が重複する部分問題、最適部分構造を含み、無記憶性を示す場合、通常動的プログラミング解法に適しています。しかし、問題の説明から直接これらの特徴を抽出することはしばしば困難です。したがって、通常は条件を緩和し、**まず問題がバックトラッキング（全探索）を使用した解決に適しているかどうかを観察**します。</p> <p>**バックトラッキングに適した問題は通常「決定木モデル」に適合**し、これは木構造を使用して記述でき、各ノードは決定を表し、各パスは決定のシーケンスを表します。</p> <p>言い換えると、問題が明示的な決定概念を含み、解が一連の決定を通じて生成される場合、それは決定木モデルに適合し、通常バックトラッキングを使用して解決できます。</p> <p>この基礎の上で、動的プログラミング問題を判定するための「ボーナスポイント」があります。</p> <ul> <li>問題に最大化（最小化）または最も（最も少ない）最適な解を見つけるという記述が含まれている。</li> <li>問題の状態がリスト、多次元行列、または木を使用して表現でき、状態がその周囲の状態と再帰関係を持っている。</li> </ul> <p>対応して、「ペナルティポイント」もあります。</p> <ul> <li>問題の目標は最適解だけでなく、すべての可能な解を見つけることである。</li> <li>問題の説明に順列と組み合わせの明らかな特徴があり、特定の複数の解を返す必要がある。</li> </ul> <p>問題が決定木モデルに適合し、比較的明らかな「ボーナスポイント」を持つ場合、それが動的プログラミング問題であると仮定し、解決プロセス中に検証できます。</p>","path":["第 14 章 &nbsp; 動的計画法","14.3 &nbsp; 動的プログラミング問題解決アプローチ"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#1432","level":2,"title":"14.3.2   問題解決ステップ","text":"<p>動的プログラミング問題解決プロセスは問題の性質と難易度によって異なりますが、一般的に次のステップに従います：決定の記述、状態の定義、\\(dp\\) テーブルの確立、状態遷移方程式の導出、境界条件の決定など。</p> <p>問題解決ステップをより具体的に説明するために、古典的な問題「最小経路和」を例として使用します。</p> <p>Question</p> <p>\\(n \\times m\\) の二次元グリッド <code>grid</code> が与えられ、グリッドの各セルには負でない整数が含まれ、そのセルのコストを表します。ロボットは左上のセルから始まり、各ステップで下または右にのみ移動でき、右下のセルに到達するまで続けます。左上から右下への最小経路和を返してください。</p> <p>下の図は例を示しており、与えられたグリッドの最小経路和は \\(13\\) です。</p> <p></p> <p> 図 14-10   最小経路和の例データ </p> <p>第1ステップ：各ラウンドの決定を考え、状態を定義し、それにより \\(dp\\) テーブルを得る</p> <p>この問題の各ラウンドの決定は、現在のセルから下または右に1ステップ移動することです。現在のセルの行と列のインデックスが \\([i, j]\\) であると仮定すると、下または右に移動した後、インデックスは \\([i+1, j]\\) または \\([i, j+1]\\) になります。したがって、状態には2つの変数が含まれるべきです：行インデックスと列インデックス、\\([i, j]\\) と表記されます。</p> <p>状態 \\([i, j]\\) は部分問題に対応します：開始点 \\([0, 0]\\) から \\([i, j]\\) への最小経路和、\\(dp[i, j]\\) と表記されます。</p> <p>このようにして、下の図に示す二次元 \\(dp\\) 行列を得ます。そのサイズは入力グリッド \\(grid\\) と同じです。</p> <p></p> <p> 図 14-11   状態定義とDPテーブル </p> <p>Note</p> <p>動的プログラミングとバックトラッキングは決定のシーケンスとして記述でき、状態はすべての決定変数から構成されます。問題解決の進行を記述するすべての変数を含むべきで、次の状態を導出するのに十分な情報を含んでいる必要があります。</p> <p>各状態は部分問題に対応し、すべての部分問題の解を保存するための \\(dp\\) テーブルを定義します。状態の各独立変数は \\(dp\\) テーブルの次元です。本質的に、\\(dp\\) テーブルは状態と部分問題の解の間のマッピングです。</p> <p>第2ステップ：最適部分構造を特定し、状態遷移方程式を導出する</p> <p>状態 \\([i, j]\\) について、それは上のセル \\([i-1, j]\\) または左のセル \\([i, j-1]\\) からのみ導出できます。したがって、最適部分構造は：\\([i, j]\\) に到達する最小経路和は、\\([i, j-1]\\) と \\([i-1, j]\\) の最小経路和の小さい方によって決定されます。</p> <p>上記の分析に基づいて、下の図に示す状態遷移方程式を導出できます：</p> \\[ dp[i, j] = \\min(dp[i-1, j], dp[i, j-1]) + grid[i, j] \\] <p></p> <p> 図 14-12   最適部分構造と状態遷移方程式 </p> <p>Note</p> <p>定義された \\(dp\\) テーブルに基づいて、元の問題と部分問題の関係を考え、部分問題の最適解から元の問題の最適解をどのように構築するか、つまり最適部分構造を見つけます。</p> <p>最適部分構造を特定したら、それを使用して状態遷移方程式を構築できます。</p> <p>第3ステップ：境界条件と状態遷移順序を決定する</p> <p>この問題では、最初の行の状態は左の状態からのみ来ることができ、最初の列の状態は上の状態からのみ来ることができるため、最初の行 \\(i = 0\\) と最初の列 \\(j = 0\\) が境界条件です。</p> <p>下の図に示すように、各セルは左のセルと上のセルから導出されるため、ループを使用して行列を走査し、外側のループは行を反復し、内側のループは列を反復します。</p> <p></p> <p> 図 14-13   境界条件と状態遷移順序 </p> <p>Note</p> <p>境界条件は動的プログラミングで \\(dp\\) テーブルを初期化するために使用され、探索では枝刈りに使用されます。</p> <p>状態遷移順序の核心は、現在の問題の解を計算するとき、それが依存するすべての小さな部分問題が既に正しく計算されていることを確保することです。</p> <p>上記の分析に基づいて、動的プログラミングコードを直接書くことができます。しかし、部分問題の分解はトップダウンアプローチであるため、「力任せ探索 → メモ化探索 → 動的プログラミング」の順序で実装することが習慣的な思考により適合します。</p>","path":["第 14 章 &nbsp; 動的計画法","14.3 &nbsp; 動的プログラミング問題解決アプローチ"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#1-1","level":3,"title":"1.   方法1：力任せ探索","text":"<p>状態 \\([i, j]\\) から探索を開始し、それを常により小さな状態 \\([i-1, j]\\) と \\([i, j-1]\\) に分解します。再帰関数には以下の要素が含まれます。</p> <ul> <li>再帰パラメータ：状態 \\([i, j]\\)。</li> <li>戻り値：\\([0, 0]\\) から \\([i, j]\\) への最小経路和 \\(dp[i, j]\\)。</li> <li>終了条件：\\(i = 0\\) かつ \\(j = 0\\) のとき、コスト \\(grid[0, 0]\\) を返す。</li> <li>枝刈り：\\(i &lt; 0\\) または \\(j &lt; 0\\) でインデックスが範囲外のとき、コスト \\(+\\infty\\) を返し、実行不可能性を表す。</li> </ul> <p>実装コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby min_path_sum.py<pre><code>def min_path_sum_dfs(grid: list[list[int]], i: int, j: int) -&gt; int:\n    \"\"\"最小パス和：ブルートフォース探索\"\"\"\n    # 左上のセルの場合、探索を終了\n    if i == 0 and j == 0:\n        return grid[0][0]\n    # 行または列のインデックスが範囲外の場合、+∞ コストを返す\n    if i &lt; 0 or j &lt; 0:\n        return inf\n    # 左上から (i-1, j) と (i, j-1) への最小パスコストを計算\n    up = min_path_sum_dfs(grid, i - 1, j)\n    left = min_path_sum_dfs(grid, i, j - 1)\n    # 左上から (i, j) への最小パスコストを返す\n    return min(left, up) + grid[i][j]\n</code></pre> min_path_sum.cpp<pre><code>/* 最小パス和：ブルートフォース探索 */\nint minPathSumDFS(vector&lt;vector&lt;int&gt;&gt; &amp;grid, int i, int j) {\n    // 左上のセルの場合、探索を終了\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // 行または列のインデックスが範囲外の場合、+∞ のコストを返す\n    if (i &lt; 0 || j &lt; 0) {\n        return INT_MAX;\n    }\n    // 左上から (i-1, j) と (i, j-1) への最小パスコストを計算\n    int up = minPathSumDFS(grid, i - 1, j);\n    int left = minPathSumDFS(grid, i, j - 1);\n    // 左上から (i, j) への最小パスコストを返す\n    return min(left, up) + grid[i][j];\n}\n</code></pre> min_path_sum.java<pre><code>/* 最小パス和：ブルートフォース探索 */\nint minPathSumDFS(int[][] grid, int i, int j) {\n    // 左上のセルの場合、探索を終了\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // 行または列のインデックスが範囲外の場合、+∞ のコストを返す\n    if (i &lt; 0 || j &lt; 0) {\n        return Integer.MAX_VALUE;\n    }\n    // 左上から (i-1, j) と (i, j-1) への最小パスコストを計算\n    int up = minPathSumDFS(grid, i - 1, j);\n    int left = minPathSumDFS(grid, i, j - 1);\n    // 左上から (i, j) への最小パスコストを返す\n    return Math.min(left, up) + grid[i][j];\n}\n</code></pre> min_path_sum.cs<pre><code>[class]{min_path_sum}-[func]{MinPathSumDFS}\n</code></pre> min_path_sum.go<pre><code>[class]{}-[func]{minPathSumDFS}\n</code></pre> min_path_sum.swift<pre><code>[class]{}-[func]{minPathSumDFS}\n</code></pre> min_path_sum.js<pre><code>[class]{}-[func]{minPathSumDFS}\n</code></pre> min_path_sum.ts<pre><code>[class]{}-[func]{minPathSumDFS}\n</code></pre> min_path_sum.dart<pre><code>[class]{}-[func]{minPathSumDFS}\n</code></pre> min_path_sum.rs<pre><code>[class]{}-[func]{min_path_sum_dfs}\n</code></pre> min_path_sum.c<pre><code>[class]{}-[func]{minPathSumDFS}\n</code></pre> min_path_sum.kt<pre><code>[class]{}-[func]{minPathSumDFS}\n</code></pre> min_path_sum.rb<pre><code>[class]{}-[func]{min_path_sum_dfs}\n</code></pre> <p>下の図は \\(dp[2, 1]\\) を根とする再帰木を示しており、いくつかの重複する部分問題を含み、その数はグリッド <code>grid</code> のサイズが増加すると急激に増加します。</p> <p>本質的に、重複する部分問題の理由は：**左上隅から特定のセルに到達する複数のパスが存在する**ことです。</p> <p></p> <p> 図 14-14   力任せ探索の再帰木 </p> <p>各状態には下と右の2つの選択があるため、左上隅から右下隅までの総ステップ数は \\(m + n - 2\\) で、最悪時間計算量は \\(O(2^{m + n})\\) です。この計算方法はグリッドエッジ近くの状況を考慮していないことに注意してください。ネットワークエッジに到達したとき、選択肢が1つしか残らないため、実際のパス数はより少なくなります。</p>","path":["第 14 章 &nbsp; 動的計画法","14.3 &nbsp; 動的プログラミング問題解決アプローチ"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#2-2","level":3,"title":"2.   方法2：メモ化探索","text":"<p>グリッド <code>grid</code> と同じサイズのメモリスト <code>mem</code> を導入し、様々な部分問題の解を記録し、重複する部分問題を枝刈りします：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby min_path_sum.py<pre><code>def min_path_sum_dfs_mem(\n    grid: list[list[int]], mem: list[list[int]], i: int, j: int\n) -&gt; int:\n    \"\"\"最小パス和：記憶化探索\"\"\"\n    # 左上のセルの場合、探索を終了\n    if i == 0 and j == 0:\n        return grid[0][0]\n    # 行または列のインデックスが範囲外の場合、+∞ コストを返す\n    if i &lt; 0 or j &lt; 0:\n        return inf\n    # 記録がある場合、それを返す\n    if mem[i][j] != -1:\n        return mem[i][j]\n    # 左と上のセルからの最小パスコスト\n    up = min_path_sum_dfs_mem(grid, mem, i - 1, j)\n    left = min_path_sum_dfs_mem(grid, mem, i, j - 1)\n    # 左上から (i, j) への最小パスコストを記録して返す\n    mem[i][j] = min(left, up) + grid[i][j]\n    return mem[i][j]\n</code></pre> min_path_sum.cpp<pre><code>[class]{}-[func]{minPathSumDFSMem}\n</code></pre> min_path_sum.java<pre><code>/* 最小パス和：メモ化探索 */\nint minPathSumDFSMem(int[][] grid, int[][] mem, int i, int j) {\n    // 左上のセルの場合、探索を終了\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // 行または列のインデックスが範囲外の場合、+∞ のコストを返す\n    if (i &lt; 0 || j &lt; 0) {\n        return Integer.MAX_VALUE;\n    }\n    // 記録がある場合、それを返す\n    if (mem[i][j] != -1) {\n        return mem[i][j];\n    }\n    // 左と上のセルからの最小パスコスト\n    int up = minPathSumDFSMem(grid, mem, i - 1, j);\n    int left = minPathSumDFSMem(grid, mem, i, j - 1);\n    // 左上から (i, j) への最小パスコストを記録して返す\n    mem[i][j] = Math.min(left, up) + grid[i][j];\n    return mem[i][j];\n}\n</code></pre> min_path_sum.cs<pre><code>[class]{min_path_sum}-[func]{MinPathSumDFSMem}\n</code></pre> min_path_sum.go<pre><code>[class]{}-[func]{minPathSumDFSMem}\n</code></pre> min_path_sum.swift<pre><code>[class]{}-[func]{minPathSumDFSMem}\n</code></pre> min_path_sum.js<pre><code>[class]{}-[func]{minPathSumDFSMem}\n</code></pre> min_path_sum.ts<pre><code>[class]{}-[func]{minPathSumDFSMem}\n</code></pre> min_path_sum.dart<pre><code>[class]{}-[func]{minPathSumDFSMem}\n</code></pre> min_path_sum.rs<pre><code>[class]{}-[func]{min_path_sum_dfs_mem}\n</code></pre> min_path_sum.c<pre><code>[class]{}-[func]{minPathSumDFSMem}\n</code></pre> min_path_sum.kt<pre><code>[class]{}-[func]{minPathSumDFSMem}\n</code></pre> min_path_sum.rb<pre><code>[class]{}-[func]{min_path_sum_dfs_mem}\n</code></pre> <p>下の図に示すように、メモ化を導入した後、すべての部分問題の解は一度だけ計算される必要があるため、時間計算量は状態の総数、つまりグリッドサイズ \\(O(nm)\\) に依存します。</p> <p></p> <p> 図 14-15   メモ化探索の再帰木 </p>","path":["第 14 章 &nbsp; 動的計画法","14.3 &nbsp; 動的プログラミング問題解決アプローチ"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#3-3","level":3,"title":"3.   方法3：動的プログラミング","text":"<p>動的プログラミング解法を反復的に実装します。コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby min_path_sum.py<pre><code>def min_path_sum_dp(grid: list[list[int]]) -&gt; int:\n    \"\"\"最小パス和：動的プログラミング\"\"\"\n    n, m = len(grid), len(grid[0])\n    # dp テーブルを初期化\n    dp = [[0] * m for _ in range(n)]\n    dp[0][0] = grid[0][0]\n    # 状態遷移：最初の行\n    for j in range(1, m):\n        dp[0][j] = dp[0][j - 1] + grid[0][j]\n    # 状態遷移：最初の列\n    for i in range(1, n):\n        dp[i][0] = dp[i - 1][0] + grid[i][0]\n    # 状態遷移：残りの行と列\n    for i in range(1, n):\n        for j in range(1, m):\n            dp[i][j] = min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j]\n    return dp[n - 1][m - 1]\n</code></pre> min_path_sum.cpp<pre><code>/* 最小パス和：動的プログラミング */\nint minPathSumDP(vector&lt;vector&lt;int&gt;&gt; &amp;grid) {\n    int n = grid.size(), m = grid[0].size();\n    // DPテーブルを初期化\n    vector&lt;vector&lt;int&gt;&gt; dp(n, vector&lt;int&gt;(m));\n    dp[0][0] = grid[0][0];\n    // 状態遷移：最初の行\n    for (int j = 1; j &lt; m; j++) {\n        dp[0][j] = dp[0][j - 1] + grid[0][j];\n    }\n    // 状態遷移：最初の列\n    for (int i = 1; i &lt; n; i++) {\n        dp[i][0] = dp[i - 1][0] + grid[i][0];\n    }\n    // 状態遷移：残りの行と列\n    for (int i = 1; i &lt; n; i++) {\n        for (int j = 1; j &lt; m; j++) {\n            dp[i][j] = min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];\n        }\n    }\n    return dp[n - 1][m - 1];\n}\n</code></pre> min_path_sum.java<pre><code>/* 最小パス和：動的プログラミング */\nint minPathSumDP(int[][] grid) {\n    int n = grid.length, m = grid[0].length;\n    // DPテーブルを初期化\n    int[][] dp = new int[n][m];\n    dp[0][0] = grid[0][0];\n    // 状態遷移：最初の行\n    for (int j = 1; j &lt; m; j++) {\n        dp[0][j] = dp[0][j - 1] + grid[0][j];\n    }\n    // 状態遷移：最初の列\n    for (int i = 1; i &lt; n; i++) {\n        dp[i][0] = dp[i - 1][0] + grid[i][0];\n    }\n    // 状態遷移：残りの行と列\n    for (int i = 1; i &lt; n; i++) {\n        for (int j = 1; j &lt; m; j++) {\n            dp[i][j] = Math.min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];\n        }\n    }\n    return dp[n - 1][m - 1];\n}\n</code></pre> min_path_sum.cs<pre><code>[class]{min_path_sum}-[func]{MinPathSumDP}\n</code></pre> min_path_sum.go<pre><code>[class]{}-[func]{minPathSumDP}\n</code></pre> min_path_sum.swift<pre><code>[class]{}-[func]{minPathSumDP}\n</code></pre> min_path_sum.js<pre><code>[class]{}-[func]{minPathSumDP}\n</code></pre> min_path_sum.ts<pre><code>[class]{}-[func]{minPathSumDP}\n</code></pre> min_path_sum.dart<pre><code>[class]{}-[func]{minPathSumDP}\n</code></pre> min_path_sum.rs<pre><code>[class]{}-[func]{min_path_sum_dp}\n</code></pre> min_path_sum.c<pre><code>[class]{}-[func]{minPathSumDP}\n</code></pre> min_path_sum.kt<pre><code>[class]{}-[func]{minPathSumDP}\n</code></pre> min_path_sum.rb<pre><code>[class]{}-[func]{min_path_sum_dp}\n</code></pre> <p>下の図は最小経路和の状態遷移プロセスを示し、グリッド全体を走査するため、時間計算量は \\(O(nm)\\) です。</p> <p>配列 <code>dp</code> のサイズは \\(n \\times m\\) であるため、空間計算量は \\(O(nm)\\) です。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 14-16   最小経路和の動的プログラミングプロセス </p>","path":["第 14 章 &nbsp; 動的計画法","14.3 &nbsp; 動的プログラミング問題解決アプローチ"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#4","level":3,"title":"4.   空間最適化","text":"<p>各セルは左と上のセルのみに関連するため、単一行配列を使用して \\(dp\\) テーブルを実装できます。</p> <p>配列 <code>dp</code> は1行の状態のみを表現できるため、最初の列の状態を事前に初期化できず、各行を走査するときに更新することに注意してください：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby min_path_sum.py<pre><code>def min_path_sum_dp_comp(grid: list[list[int]]) -&gt; int:\n    \"\"\"最小パス和：空間最適化動的プログラミング\"\"\"\n    n, m = len(grid), len(grid[0])\n    # dp テーブルを初期化\n    dp = [0] * m\n    # 状態遷移：最初の行\n    dp[0] = grid[0][0]\n    for j in range(1, m):\n        dp[j] = dp[j - 1] + grid[0][j]\n    # 状態遷移：残りの行\n    for i in range(1, n):\n        # 状態遷移：最初の列\n        dp[0] = dp[0] + grid[i][0]\n        # 状態遷移：残りの列\n        for j in range(1, m):\n            dp[j] = min(dp[j - 1], dp[j]) + grid[i][j]\n    return dp[m - 1]\n</code></pre> min_path_sum.cpp<pre><code>[class]{}-[func]{minPathSumDPComp}\n</code></pre> min_path_sum.java<pre><code>/* 最小パス和：空間最適化動的プログラミング */\nint minPathSumDPComp(int[][] grid) {\n    int n = grid.length, m = grid[0].length;\n    // DPテーブルを初期化\n    int[] dp = new int[m];\n    // 状態遷移：最初の行\n    dp[0] = grid[0][0];\n    for (int j = 1; j &lt; m; j++) {\n        dp[j] = dp[j - 1] + grid[0][j];\n    }\n    // 状態遷移：残りの行\n    for (int i = 1; i &lt; n; i++) {\n        // 状態遷移：最初の列\n        dp[0] = dp[0] + grid[i][0];\n        // 状態遷移：残りの列\n        for (int j = 1; j &lt; m; j++) {\n            dp[j] = Math.min(dp[j - 1], dp[j]) + grid[i][j];\n        }\n    }\n    return dp[m - 1];\n}\n</code></pre> min_path_sum.cs<pre><code>[class]{min_path_sum}-[func]{MinPathSumDPComp}\n</code></pre> min_path_sum.go<pre><code>[class]{}-[func]{minPathSumDPComp}\n</code></pre> min_path_sum.swift<pre><code>[class]{}-[func]{minPathSumDPComp}\n</code></pre> min_path_sum.js<pre><code>[class]{}-[func]{minPathSumDPComp}\n</code></pre> min_path_sum.ts<pre><code>[class]{}-[func]{minPathSumDPComp}\n</code></pre> min_path_sum.dart<pre><code>[class]{}-[func]{minPathSumDPComp}\n</code></pre> min_path_sum.rs<pre><code>[class]{}-[func]{min_path_sum_dp_comp}\n</code></pre> min_path_sum.c<pre><code>[class]{}-[func]{minPathSumDPComp}\n</code></pre> min_path_sum.kt<pre><code>[class]{}-[func]{minPathSumDPComp}\n</code></pre> min_path_sum.rb<pre><code>[class]{}-[func]{min_path_sum_dp_comp}\n</code></pre>","path":["第 14 章 &nbsp; 動的計画法","14.3 &nbsp; 動的プログラミング問題解決アプローチ"],"tags":[]},{"location":"chapter_dynamic_programming/edit_distance_problem/","level":1,"title":"14.6   編集距離問題","text":"<p>編集距離は、レーベンシュタイン距離とも呼ばれ、一つの文字列を別の文字列に変換するために必要な最小修正回数を指し、情報検索や自然言語処理で2つのシーケンス間の類似度を測定するためによく使用されます。</p> <p>Question</p> <p>2つの文字列 \\(s\\) と \\(t\\) が与えられたとき、\\(s\\) を \\(t\\) に変換するために必要な最小編集回数を返してください。</p> <p>文字列に対して3種類の編集を実行できます：文字の挿入、文字の削除、または文字を他の任意の文字に置換。</p> <p>下の図に示すように、<code>kitten</code> を <code>sitting</code> に変換するには3回の編集が必要で、2回の置換と1回の挿入を含みます。<code>hello</code> を <code>algo</code> に変換するには3ステップが必要で、2回の置換と1回の削除を含みます。</p> <p></p> <p> 図 14-27   編集距離の例データ </p> <p>編集距離問題は決定木モデルで自然に説明できます。文字列は木のノードに対応し、1ラウンドの決定（編集操作）は木のエッジに対応します。</p> <p>下の図に示すように、操作に制限がない場合、各ノードは多くのエッジを導出でき、それぞれが1つの操作に対応するため、<code>hello</code> を <code>algo</code> に変換する可能な経路は多数あります。</p> <p>決定木の観点から、この問題の目標は、ノード <code>hello</code> とノード <code>algo</code> の間の最短経路を見つけることです。</p> <p></p> <p> 図 14-28   決定木モデルに基づいて表現された編集距離問題 </p>","path":["第 14 章 &nbsp; 動的計画法","14.6 &nbsp; 編集距離問題"],"tags":[]},{"location":"chapter_dynamic_programming/edit_distance_problem/#1","level":3,"title":"1.   動的プログラミングアプローチ","text":"<p>ステップ1：各ラウンドの決定を考え、状態を定義し、それにより \\(dp\\) テーブルを得る</p> <p>各ラウンドの決定は、文字列 \\(s\\) に対して1つの編集操作を実行することを含みます。</p> <p>編集プロセス中に問題のサイズを段階的に縮小することを目指し、これにより部分問題を構築できます。文字列 \\(s\\) と \\(t\\) の長さをそれぞれ \\(n\\) と \\(m\\) とします。まず、両方の文字列の末尾文字 \\(s[n-1]\\) と \\(t[m-1]\\) を考慮します。</p> <ul> <li>\\(s[n-1]\\) と \\(t[m-1]\\) が同じ場合、それらをスキップして直接 \\(s[n-2]\\) と \\(t[m-2]\\) を考慮できます。</li> <li>\\(s[n-1]\\) と \\(t[m-1]\\) が異なる場合、\\(s\\) に対して1つの編集（挿入、削除、置換）を実行して、2つの文字列の末尾文字を一致させ、それらをスキップしてより小規模な問題を考慮できるようにする必要があります。</li> </ul> <p>したがって、文字列 \\(s\\) での各ラウンドの決定（編集操作）は、\\(s\\) と \\(t\\) でマッチされる残りの文字を変更します。したがって、状態は \\(s\\) と \\(t\\) で現在考慮されている \\(i\\) 番目と \\(j\\) 番目の文字であり、\\([i, j]\\) と表記されます。</p> <p>状態 \\([i, j]\\) は部分問題に対応します：\\(s\\) の最初の \\(i\\) 文字を \\(t\\) の最初の \\(j\\) 文字に変更するために必要な最小編集回数。</p> <p>これから、サイズ \\((i+1) \\times (j+1)\\) の二次元 \\(dp\\) テーブルを得ます。</p> <p>ステップ2：最適部分構造を特定し、状態遷移方程式を導出する</p> <p>部分問題 \\(dp[i, j]\\) を考慮すると、これに対応する2つの文字列の末尾文字は \\(s[i-1]\\) と \\(t[j-1]\\) であり、下の図に示すように3つのシナリオに分けることができます。</p> <ol> <li>\\(s[i-1]\\) の後に \\(t[j-1]\\) を追加すると、残りの部分問題は \\(dp[i, j-1]\\) です。</li> <li>\\(s[i-1]\\) を削除すると、残りの部分問題は \\(dp[i-1, j]\\) です。</li> <li>\\(s[i-1]\\) を \\(t[j-1]\\) に置換すると、残りの部分問題は \\(dp[i-1, j-1]\\) です。</li> </ol> <p></p> <p> 図 14-29   編集距離の状態遷移 </p> <p>上記の分析に基づいて、最適部分構造を決定できます：\\(dp[i, j]\\) の最小編集回数は、\\(dp[i, j-1]\\)、\\(dp[i-1, j]\\)、\\(dp[i-1, j-1]\\) の中の最小値に編集ステップ \\(1\\) を加えたものです。対応する状態遷移方程式は：</p> \\[ dp[i, j] = \\min(dp[i, j-1], dp[i-1, j], dp[i-1, j-1]) + 1 \\] <p>注意してください。\\(s[i-1]\\) と \\(t[j-1]\\) が同じ場合、現在の文字に対して編集は必要ありません。この場合、状態遷移方程式は：</p> \\[ dp[i, j] = dp[i-1, j-1] \\] <p>ステップ3：境界条件と状態遷移の順序を決定する</p> <p>両方の文字列が空の場合、編集回数は \\(0\\) です。つまり、\\(dp[0, 0] = 0\\) です。\\(s\\) が空で \\(t\\) が空でない場合、最小編集回数は \\(t\\) の長さに等しく、つまり最初の行 \\(dp[0, j] = j\\) です。\\(s\\) が空でなく \\(t\\) が空の場合、最小編集回数は \\(s\\) の長さに等しく、つまり最初の列 \\(dp[i, 0] = i\\) です。</p> <p>状態遷移方程式を観察すると、\\(dp[i, j]\\) の解決は左、上、左上の解に依存するため、二重ループを使用して正しい順序で \\(dp\\) テーブル全体を走査できます。</p>","path":["第 14 章 &nbsp; 動的計画法","14.6 &nbsp; 編集距離問題"],"tags":[]},{"location":"chapter_dynamic_programming/edit_distance_problem/#2","level":3,"title":"2.   コード実装","text":"PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby edit_distance.py<pre><code>def edit_distance_dp(s: str, t: str) -&gt; int:\n    \"\"\"編集距離：動的プログラミング\"\"\"\n    n, m = len(s), len(t)\n    dp = [[0] * (m + 1) for _ in range(n + 1)]\n    # 状態遷移：最初の行と最初の列\n    for i in range(1, n + 1):\n        dp[i][0] = i\n    for j in range(1, m + 1):\n        dp[0][j] = j\n    # 状態遷移：残りの行と列\n    for i in range(1, n + 1):\n        for j in range(1, m + 1):\n            if s[i - 1] == t[j - 1]:\n                # 2 つの文字が等しい場合、これら 2 つの文字をスキップ\n                dp[i][j] = dp[i - 1][j - 1]\n            else:\n                # 最小編集数 = 3 つの操作（挿入、削除、置換）からの最小編集数 + 1\n                dp[i][j] = min(dp[i][j - 1], dp[i - 1][j], dp[i - 1][j - 1]) + 1\n    return dp[n][m]\n</code></pre> edit_distance.cpp<pre><code>/* 編集距離：動的プログラミング */\nint editDistanceDP(string s, string t) {\n    int n = s.length(), m = t.length();\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(m + 1, 0));\n    // 状態遷移：最初の行と最初の列\n    for (int i = 1; i &lt;= n; i++) {\n        dp[i][0] = i;\n    }\n    for (int j = 1; j &lt;= m; j++) {\n        dp[0][j] = j;\n    }\n    // 状態遷移：残りの行と列\n    for (int i = 1; i &lt;= n; i++) {\n        for (int j = 1; j &lt;= m; j++) {\n            if (s[i - 1] == t[j - 1]) {\n                // 2つの文字が等しい場合、これら2つの文字をスキップ\n                dp[i][j] = dp[i - 1][j - 1];\n            } else {\n                // 最小編集数 = 3つの操作（挿入、削除、置換）からの最小編集数 + 1\n                dp[i][j] = min(min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;\n            }\n        }\n    }\n    return dp[n][m];\n}\n</code></pre> edit_distance.java<pre><code>/* 編集距離：動的プログラミング */\nint editDistanceDP(String s, String t) {\n    int n = s.length(), m = t.length();\n    int[][] dp = new int[n + 1][m + 1];\n    // 状態遷移：最初の行と最初の列\n    for (int i = 1; i &lt;= n; i++) {\n        dp[i][0] = i;\n    }\n    for (int j = 1; j &lt;= m; j++) {\n        dp[0][j] = j;\n    }\n    // 状態遷移：残りの行と列\n    for (int i = 1; i &lt;= n; i++) {\n        for (int j = 1; j &lt;= m; j++) {\n            if (s.charAt(i - 1) == t.charAt(j - 1)) {\n                // 2つの文字が等しい場合、これら2つの文字をスキップ\n                dp[i][j] = dp[i - 1][j - 1];\n            } else {\n                // 最小編集数 = 3つの操作（挿入、削除、置換）からの最小編集数 + 1\n                dp[i][j] = Math.min(Math.min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;\n            }\n        }\n    }\n    return dp[n][m];\n}\n</code></pre> edit_distance.cs<pre><code>[class]{edit_distance}-[func]{EditDistanceDP}\n</code></pre> edit_distance.go<pre><code>[class]{}-[func]{editDistanceDP}\n</code></pre> edit_distance.swift<pre><code>[class]{}-[func]{editDistanceDP}\n</code></pre> edit_distance.js<pre><code>[class]{}-[func]{editDistanceDP}\n</code></pre> edit_distance.ts<pre><code>[class]{}-[func]{editDistanceDP}\n</code></pre> edit_distance.dart<pre><code>[class]{}-[func]{editDistanceDP}\n</code></pre> edit_distance.rs<pre><code>[class]{}-[func]{edit_distance_dp}\n</code></pre> edit_distance.c<pre><code>[class]{}-[func]{editDistanceDP}\n</code></pre> edit_distance.kt<pre><code>[class]{}-[func]{editDistanceDP}\n</code></pre> edit_distance.rb<pre><code>[class]{}-[func]{edit_distance_dp}\n</code></pre> <p>下の図に示すように、編集距離問題の状態遷移プロセスはナップサック問題と非常に似ており、二次元グリッドを埋めることと見なすことができます。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt;&lt;13&gt;&lt;14&gt;&lt;15&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 14-30   編集距離の動的プログラミングプロセス </p>","path":["第 14 章 &nbsp; 動的計画法","14.6 &nbsp; 編集距離問題"],"tags":[]},{"location":"chapter_dynamic_programming/edit_distance_problem/#3","level":3,"title":"3.   空間最適化","text":"<p>\\(dp[i, j]\\) は上の \\(dp[i-1, j]\\)、左の \\(dp[i, j-1]\\)、左上の \\(dp[i-1, j-1]\\) の解から導出され、直接走査では左上の解 \\(dp[i-1, j-1]\\) が失われ、逆走査では事前に \\(dp[i, j-1]\\) を構築できないため、どちらの走査順序も実行可能ではありません。</p> <p>この理由で、変数 <code>leftup</code> を使用して左上の \\(dp[i-1, j-1]\\) からの解を一時的に保存し、左と上の解のみを考慮すればよくなります。この状況は無制限ナップサック問題と似ており、直接走査が可能です。コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby edit_distance.py<pre><code>def edit_distance_dp_comp(s: str, t: str) -&gt; int:\n    \"\"\"編集距離：空間最適化動的プログラミング\"\"\"\n    n, m = len(s), len(t)\n    dp = [0] * (m + 1)\n    # 状態遷移：最初の行\n    for j in range(1, m + 1):\n        dp[j] = j\n    # 状態遷移：残りの行\n    for i in range(1, n + 1):\n        # 状態遷移：最初の列\n        leftup = dp[0]  # dp[i-1, j-1] を一時的に保存\n        dp[0] += 1\n        # 状態遷移：残りの列\n        for j in range(1, m + 1):\n            temp = dp[j]\n            if s[i - 1] == t[j - 1]:\n                # 2 つの文字が等しい場合、これら 2 つの文字をスキップ\n                dp[j] = leftup\n            else:\n                # 最小編集数 = 3 つの操作（挿入、削除、置換）からの最小編集数 + 1\n                dp[j] = min(dp[j - 1], dp[j], leftup) + 1\n            leftup = temp  # 次の dp[i-1, j-1] のために更新\n    return dp[m]\n</code></pre> edit_distance.cpp<pre><code>[class]{}-[func]{editDistanceDPComp}\n</code></pre> edit_distance.java<pre><code>/* 編集距離：空間最適化動的プログラミング */\nint editDistanceDPComp(String s, String t) {\n    int n = s.length(), m = t.length();\n    int[] dp = new int[m + 1];\n    // 状態遷移：最初の行\n    for (int j = 1; j &lt;= m; j++) {\n        dp[j] = j;\n    }\n    // 状態遷移：残りの行\n    for (int i = 1; i &lt;= n; i++) {\n        // 状態遷移：最初の列\n        int leftup = dp[0]; // dp[i-1, j-1] を一時的に格納\n        dp[0] = i;\n        // 状態遷移：残りの列\n        for (int j = 1; j &lt;= m; j++) {\n            int temp = dp[j];\n            if (s.charAt(i - 1) == t.charAt(j - 1)) {\n                // 2つの文字が等しい場合、これら2つの文字をスキップ\n                dp[j] = leftup;\n            } else {\n                // 最小編集数 = 3つの操作（挿入、削除、置換）からの最小編集数 + 1\n                dp[j] = Math.min(Math.min(dp[j - 1], dp[j]), leftup) + 1;\n            }\n            leftup = temp; // 次のラウンドの dp[i-1, j-1] のために更新\n        }\n    }\n    return dp[m];\n}\n</code></pre> edit_distance.cs<pre><code>[class]{edit_distance}-[func]{EditDistanceDPComp}\n</code></pre> edit_distance.go<pre><code>[class]{}-[func]{editDistanceDPComp}\n</code></pre> edit_distance.swift<pre><code>[class]{}-[func]{editDistanceDPComp}\n</code></pre> edit_distance.js<pre><code>[class]{}-[func]{editDistanceDPComp}\n</code></pre> edit_distance.ts<pre><code>[class]{}-[func]{editDistanceDPComp}\n</code></pre> edit_distance.dart<pre><code>[class]{}-[func]{editDistanceDPComp}\n</code></pre> edit_distance.rs<pre><code>[class]{}-[func]{edit_distance_dp_comp}\n</code></pre> edit_distance.c<pre><code>[class]{}-[func]{editDistanceDPComp}\n</code></pre> edit_distance.kt<pre><code>[class]{}-[func]{editDistanceDPComp}\n</code></pre> edit_distance.rb<pre><code>[class]{}-[func]{edit_distance_dp_comp}\n</code></pre>","path":["第 14 章 &nbsp; 動的計画法","14.6 &nbsp; 編集距離問題"],"tags":[]},{"location":"chapter_dynamic_programming/intro_to_dynamic_programming/","level":1,"title":"14.1   動的プログラミングの紹介","text":"<p>動的プログラミングは重要なアルゴリズムパラダイムであり、問題を一連の小さな部分問題に分解し、これらの部分問題の解を保存することで冗長な計算を避け、時間効率を大幅に向上させます。</p> <p>このセクションでは、古典的な問題から始めて、まず力任せの探索法による解法を提示し、重複する部分問題を特定してから、より効率的な動的プログラミング解法を段階的に導出します。</p> <p>階段登り</p> <p>\\(n\\) 段の階段があり、一度に \\(1\\) 段または \\(2\\) 段上ることができます。頂上に到達する方法は何通りありますか？</p> <p>下の図に示すように、\\(3\\) 段の階段の頂上に到達する方法は \\(3\\) 通りあります。</p> <p></p> <p> 図 14-1   3段目に到達する方法の数 </p> <p>この問題は**バックトラッキングを用いてすべての可能性を網羅**することで方法の数を計算することを目的としています。具体的には、階段登りの問題を多段階選択プロセスとして考えます：地面から始めて、毎回 \\(1\\) 段または \\(2\\) 段上るかを選択し、階段の頂上に到達したら方法の数をカウントし、頂上を超えた場合はプルーニング（枝刈り）を行います。コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby climbing_stairs_backtrack.py<pre><code>def backtrack(choices: list[int], state: int, n: int, res: list[int]) -&gt; int:\n    \"\"\"バックトラッキング\"\"\"\n    # n 段目に登ったとき、解の数に 1 を加える\n    if state == n:\n        res[0] += 1\n    # すべての選択肢を走査\n    for choice in choices:\n        # 枝刈り：n 段を超えて登ることを許可しない\n        if state + choice &gt; n:\n            continue\n        # 試行：選択を行い、状態を更新\n        backtrack(choices, state + choice, n, res)\n        # 撤回\n\ndef climbing_stairs_backtrack(n: int) -&gt; int:\n    \"\"\"階段登り：バックトラッキング\"\"\"\n    choices = [1, 2]  # 1 段または 2 段登ることを選択可能\n    state = 0  # 0 段目から登り始める\n    res = [0]  # res[0] を使用して解の数を記録\n    backtrack(choices, state, n, res)\n    return res[0]\n</code></pre> climbing_stairs_backtrack.cpp<pre><code>/* バックトラッキング */\nvoid backtrack(vector&lt;int&gt; &amp;choices, int state, int n, vector&lt;int&gt; &amp;res) {\n    // n段目に到達したとき、解の数に1を加える\n    if (state == n)\n        res[0]++;\n    // すべての選択肢を走査\n    for (auto &amp;choice : choices) {\n        // 剪定：n段を超えて登ることを許可しない\n        if (state + choice &gt; n)\n            continue;\n        // 試行：選択を行い、状態を更新\n        backtrack(choices, state + choice, n, res);\n        // 撤回\n    }\n}\n\n/* 階段登り：バックトラッキング */\nint climbingStairsBacktrack(int n) {\n    vector&lt;int&gt; choices = {1, 2}; // 1段または2段登ることを選択可能\n    int state = 0;                // 0段目から登り始める\n    vector&lt;int&gt; res = {0};        // res[0] を使用して解の数を記録\n    backtrack(choices, state, n, res);\n    return res[0];\n}\n</code></pre> climbing_stairs_backtrack.java<pre><code>/* バックトラッキング */\nvoid backtrack(List&lt;Integer&gt; choices, int state, int n, List&lt;Integer&gt; res) {\n    // n段目に到達したとき、解の数に1を加える\n    if (state == n)\n        res.set(0, res.get(0) + 1);\n    // すべての選択肢を走査\n    for (Integer choice : choices) {\n        // 剪定：n段を超えて登ることを許可しない\n        if (state + choice &gt; n)\n            continue;\n        // 試行：選択を行い、状態を更新\n        backtrack(choices, state + choice, n, res);\n        // 撤回\n    }\n}\n\n/* 階段登り：バックトラッキング */\nint climbingStairsBacktrack(int n) {\n    List&lt;Integer&gt; choices = Arrays.asList(1, 2); // 1段または2段登ることを選択可能\n    int state = 0; // 0段目から登り始める\n    List&lt;Integer&gt; res = new ArrayList&lt;&gt;();\n    res.add(0); // res[0] を使用して解の数を記録\n    backtrack(choices, state, n, res);\n    return res.get(0);\n}\n</code></pre> climbing_stairs_backtrack.cs<pre><code>[class]{climbing_stairs_backtrack}-[func]{Backtrack}\n\n[class]{climbing_stairs_backtrack}-[func]{ClimbingStairsBacktrack}\n</code></pre> climbing_stairs_backtrack.go<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{climbingStairsBacktrack}\n</code></pre> climbing_stairs_backtrack.swift<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{climbingStairsBacktrack}\n</code></pre> climbing_stairs_backtrack.js<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{climbingStairsBacktrack}\n</code></pre> climbing_stairs_backtrack.ts<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{climbingStairsBacktrack}\n</code></pre> climbing_stairs_backtrack.dart<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{climbingStairsBacktrack}\n</code></pre> climbing_stairs_backtrack.rs<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{climbing_stairs_backtrack}\n</code></pre> climbing_stairs_backtrack.c<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{climbingStairsBacktrack}\n</code></pre> climbing_stairs_backtrack.kt<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{climbingStairsBacktrack}\n</code></pre> climbing_stairs_backtrack.rb<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{climbing_stairs_backtrack}\n</code></pre>","path":["第 14 章 &nbsp; 動的計画法","14.1 &nbsp; 動的プログラミングの紹介"],"tags":[]},{"location":"chapter_dynamic_programming/intro_to_dynamic_programming/#1411-1","level":2,"title":"14.1.1   方法1：力任せ探索","text":"<p>バックトラッキングアルゴリズムは問題を明示的に部分問題に分解しません。代わりに、問題を一連の決定ステップとして扱い、試行と枝刈りを通じてすべての可能性を探索します。</p> <p>この問題を分解アプローチを使って分析できます。\\(dp[i]\\) を \\(i\\) 段目に到達する方法の数とします。この場合、\\(dp[i]\\) が元の問題であり、その部分問題は次のようになります：</p> \\[ dp[i-1], dp[i-2], \\dots, dp[2], dp[1] \\] <p>各移動は \\(1\\) 段または \\(2\\) 段しか進めないため、\\(i\\) 段目に立っているとき、前のステップは \\(i-1\\) 段目または \\(i-2\\) 段目のいずれかにいたはずです。つまり、\\(i\\) 段目には \\(i-1\\) 段目または \\(i-2\\) 段目からしか到達できません。</p> <p>これにより重要な結論が得られます：\\(i-1\\) 段目に到達する方法の数に \\(i-2\\) 段目に到達する方法の数を加えたものが、\\(i\\) 段目に到達する方法の数に等しい。式は以下の通りです：</p> \\[ dp[i] = dp[i-1] + dp[i-2] \\] <p>これは、階段登り問題において部分問題間に再帰関係があることを意味し、元の問題の解は部分問題の解から構築できます。下の図はこの再帰関係を示しています。</p> <p></p> <p> 図 14-2   解の数の再帰関係 </p> <p>再帰式に従って力任せ探索解法を得ることができます。\\(dp[n]\\) から始めて、**より大きな問題を再帰的に2つの小さな部分問題の和に分解**し、解が既知の最小の部分問題 \\(dp[1]\\) と \\(dp[2]\\) に到達するまで続けます。\\(dp[1] = 1\\) と \\(dp[2] = 2\\) で、それぞれ1段目と2段目に登る方法が \\(1\\) 通りと \\(2\\) 通りあることを表します。</p> <p>以下のコードを観察すると、標準的なバックトラッキングコードと同様に深さ優先探索に属しますが、より簡潔です：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby climbing_stairs_dfs.py<pre><code>def dfs(i: int) -&gt; int:\n    \"\"\"探索\"\"\"\n    # 既知の dp[1] と dp[2] は、それらを返す\n    if i == 1 or i == 2:\n        return i\n    # dp[i] = dp[i-1] + dp[i-2]\n    count = dfs(i - 1) + dfs(i - 2)\n    return count\n\ndef climbing_stairs_dfs(n: int) -&gt; int:\n    \"\"\"階段登り：探索\"\"\"\n    return dfs(n)\n</code></pre> climbing_stairs_dfs.cpp<pre><code>/* 探索 */\nint dfs(int i) {\n    // 既知の dp[1] と dp[2] を返す\n    if (i == 1 || i == 2)\n        return i;\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1) + dfs(i - 2);\n    return count;\n}\n\n/* 階段登り：探索 */\nint climbingStairsDFS(int n) {\n    return dfs(n);\n}\n</code></pre> climbing_stairs_dfs.java<pre><code>/* 探索 */\nint dfs(int i) {\n    // 既知の dp[1] と dp[2] を返す\n    if (i == 1 || i == 2)\n        return i;\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1) + dfs(i - 2);\n    return count;\n}\n\n/* 階段登り：探索 */\nint climbingStairsDFS(int n) {\n    return dfs(n);\n}\n</code></pre> climbing_stairs_dfs.cs<pre><code>[class]{climbing_stairs_dfs}-[func]{DFS}\n\n[class]{climbing_stairs_dfs}-[func]{ClimbingStairsDFS}\n</code></pre> climbing_stairs_dfs.go<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFS}\n</code></pre> climbing_stairs_dfs.swift<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFS}\n</code></pre> climbing_stairs_dfs.js<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFS}\n</code></pre> climbing_stairs_dfs.ts<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFS}\n</code></pre> climbing_stairs_dfs.dart<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFS}\n</code></pre> climbing_stairs_dfs.rs<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbing_stairs_dfs}\n</code></pre> climbing_stairs_dfs.c<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFS}\n</code></pre> climbing_stairs_dfs.kt<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFS}\n</code></pre> climbing_stairs_dfs.rb<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbing_stairs_dfs}\n</code></pre> <p>下の図は力任せ探索によって形成される再帰木を示しています。問題 \\(dp[n]\\) について、その再帰木の深さは \\(n\\) で、時間計算量は \\(O(2^n)\\) です。この指数的増加により、\\(n\\) が大きいとプログラムの実行がはるかに遅くなり、長い待機時間が生じます。</p> <p></p> <p> 図 14-3   階段登りの再帰木 </p> <p>上の図を観察すると、**指数時間計算量は「重複する部分問題」によって引き起こされる**ことがわかります。例えば、\\(dp[9]\\) は \\(dp[8]\\) と \\(dp[7]\\) に分解され、\\(dp[8]\\) はさらに \\(dp[7]\\) と \\(dp[6]\\) に分解され、両方とも部分問題 \\(dp[7]\\) を含んでいます。</p> <p>このように、部分問題にはさらに小さな重複する部分問題が含まれ、これは無限に続きます。計算リソースの大部分がこれらの重複する部分問題に浪費されています。</p>","path":["第 14 章 &nbsp; 動的計画法","14.1 &nbsp; 動的プログラミングの紹介"],"tags":[]},{"location":"chapter_dynamic_programming/intro_to_dynamic_programming/#1412-2","level":2,"title":"14.1.2   方法2：メモ化探索","text":"<p>アルゴリズムの効率を向上させるため、**すべての重複する部分問題を一度だけ計算したい**と考えます。この目的のため、各部分問題の解を記録する配列 <code>mem</code> を宣言し、探索プロセス中に重複する部分問題を枝刈りします。</p> <ol> <li>\\(dp[i]\\) が初めて計算されるとき、後で使用するために <code>mem[i]</code> に記録します。</li> <li>\\(dp[i]\\) を再度計算する必要があるとき、<code>mem[i]</code> から直接結果を取得でき、その部分問題の冗長な計算を避けられます。</li> </ol> <p>コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby climbing_stairs_dfs_mem.py<pre><code>def dfs(i: int, mem: list[int]) -&gt; int:\n    \"\"\"記憶化探索\"\"\"\n    # 既知の dp[1] と dp[2] は、それらを返す\n    if i == 1 or i == 2:\n        return i\n    # dp[i] の記録がある場合、それを返す\n    if mem[i] != -1:\n        return mem[i]\n    # dp[i] = dp[i-1] + dp[i-2]\n    count = dfs(i - 1, mem) + dfs(i - 2, mem)\n    # dp[i] を記録\n    mem[i] = count\n    return count\n\ndef climbing_stairs_dfs_mem(n: int) -&gt; int:\n    \"\"\"階段登り：記憶化探索\"\"\"\n    # mem[i] は i 段目に登る解の総数を記録、-1 は記録なしを意味する\n    mem = [-1] * (n + 1)\n    return dfs(n, mem)\n</code></pre> climbing_stairs_dfs_mem.cpp<pre><code>/* メモ化探索 */\nint dfs(int i, vector&lt;int&gt; &amp;mem) {\n    // 既知の dp[1] と dp[2] を返す\n    if (i == 1 || i == 2)\n        return i;\n    // dp[i] の記録がある場合、それを返す\n    if (mem[i] != -1)\n        return mem[i];\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1, mem) + dfs(i - 2, mem);\n    // dp[i] を記録\n    mem[i] = count;\n    return count;\n}\n\n/* 階段登り：メモ化探索 */\nint climbingStairsDFSMem(int n) {\n    // mem[i] は i 段目に登る総解数を記録、-1 は記録なしを意味する\n    vector&lt;int&gt; mem(n + 1, -1);\n    return dfs(n, mem);\n}\n</code></pre> climbing_stairs_dfs_mem.java<pre><code>/* メモ化探索 */\nint dfs(int i, int[] mem) {\n    // 既知の dp[1] と dp[2] を返す\n    if (i == 1 || i == 2)\n        return i;\n    // dp[i] の記録がある場合、それを返す\n    if (mem[i] != -1)\n        return mem[i];\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1, mem) + dfs(i - 2, mem);\n    // dp[i] を記録\n    mem[i] = count;\n    return count;\n}\n\n/* 階段登り：メモ化探索 */\nint climbingStairsDFSMem(int n) {\n    // mem[i] は i 段目に登る総解数を記録、-1 は記録なしを意味する\n    int[] mem = new int[n + 1];\n    Arrays.fill(mem, -1);\n    return dfs(n, mem);\n}\n</code></pre> climbing_stairs_dfs_mem.cs<pre><code>[class]{climbing_stairs_dfs_mem}-[func]{DFS}\n\n[class]{climbing_stairs_dfs_mem}-[func]{ClimbingStairsDFSMem}\n</code></pre> climbing_stairs_dfs_mem.go<pre><code>[class]{}-[func]{dfsMem}\n\n[class]{}-[func]{climbingStairsDFSMem}\n</code></pre> climbing_stairs_dfs_mem.swift<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFSMem}\n</code></pre> climbing_stairs_dfs_mem.js<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFSMem}\n</code></pre> climbing_stairs_dfs_mem.ts<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFSMem}\n</code></pre> climbing_stairs_dfs_mem.dart<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFSMem}\n</code></pre> climbing_stairs_dfs_mem.rs<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbing_stairs_dfs_mem}\n</code></pre> climbing_stairs_dfs_mem.c<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFSMem}\n</code></pre> climbing_stairs_dfs_mem.kt<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFSMem}\n</code></pre> climbing_stairs_dfs_mem.rb<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbing_stairs_dfs_mem}\n</code></pre> <p>下の図を観察すると、**メモ化後、すべての重複する部分問題は一度だけ計算される必要があり、時間計算量を \\(O(n)\\) に最適化**します。これは大幅な改善です。</p> <p></p> <p> 図 14-4   メモ化探索による再帰木 </p>","path":["第 14 章 &nbsp; 動的計画法","14.1 &nbsp; 動的プログラミングの紹介"],"tags":[]},{"location":"chapter_dynamic_programming/intro_to_dynamic_programming/#1413-3","level":2,"title":"14.1.3   方法3：動的プログラミング","text":"<p>**メモ化探索は「トップダウン」方式**です：元の問題（根ノード）から始めて、より大きな部分問題をより小さなものに再帰的に分解し、最小の既知の部分問題（葉ノード）の解に到達するまで続けます。その後、バックトラッキングにより部分問題の解を収集し、元の問題の解を構築します。</p> <p>一方、**動的プログラミングは「ボトムアップ」方式**です：最小の部分問題の解から始めて、元の問題が解決されるまで、より大きな部分問題の解を反復的に構築します。</p> <p>動的プログラミングはバックトラッキングを必要としないため、ループを使った反復のみが必要で、再帰は不要です。以下のコードでは、配列 <code>dp</code> を初期化して部分問題の解を保存し、メモ化探索の配列 <code>mem</code> と同じ記録機能を果たします：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby climbing_stairs_dp.py<pre><code>def climbing_stairs_dp(n: int) -&gt; int:\n    \"\"\"階段登り：動的プログラミング\"\"\"\n    if n == 1 or n == 2:\n        return n\n    # dp テーブルを初期化、部分問題の解を格納するため使用\n    dp = [0] * (n + 1)\n    # 初期状態：最小の部分問題の解を事前設定\n    dp[1], dp[2] = 1, 2\n    # 状態遷移：小さい部分問題から大きい部分問題を段階的に解く\n    for i in range(3, n + 1):\n        dp[i] = dp[i - 1] + dp[i - 2]\n    return dp[n]\n</code></pre> climbing_stairs_dp.cpp<pre><code>/* 階段登り：動的プログラミング */\nint climbingStairsDP(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    // DPテーブルを初期化し、部分問題の解を格納するために使用\n    vector&lt;int&gt; dp(n + 1);\n    // 初期状態：最小の部分問題の解を事前設定\n    dp[1] = 1;\n    dp[2] = 2;\n    // 状態遷移：小さな問題から大きな部分問題を段階的に解く\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    return dp[n];\n}\n</code></pre> climbing_stairs_dp.java<pre><code>/* 階段登り：動的プログラミング */\nint climbingStairsDP(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    // DPテーブルを初期化し、部分問題の解を格納するために使用\n    int[] dp = new int[n + 1];\n    // 初期状態：最小の部分問題の解を事前設定\n    dp[1] = 1;\n    dp[2] = 2;\n    // 状態遷移：小さな問題から大きな部分問題を段階的に解く\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    return dp[n];\n}\n</code></pre> climbing_stairs_dp.cs<pre><code>[class]{climbing_stairs_dp}-[func]{ClimbingStairsDP}\n</code></pre> climbing_stairs_dp.go<pre><code>[class]{}-[func]{climbingStairsDP}\n</code></pre> climbing_stairs_dp.swift<pre><code>[class]{}-[func]{climbingStairsDP}\n</code></pre> climbing_stairs_dp.js<pre><code>[class]{}-[func]{climbingStairsDP}\n</code></pre> climbing_stairs_dp.ts<pre><code>[class]{}-[func]{climbingStairsDP}\n</code></pre> climbing_stairs_dp.dart<pre><code>[class]{}-[func]{climbingStairsDP}\n</code></pre> climbing_stairs_dp.rs<pre><code>[class]{}-[func]{climbing_stairs_dp}\n</code></pre> climbing_stairs_dp.c<pre><code>[class]{}-[func]{climbingStairsDP}\n</code></pre> climbing_stairs_dp.kt<pre><code>[class]{}-[func]{climbingStairsDP}\n</code></pre> climbing_stairs_dp.rb<pre><code>[class]{}-[func]{climbing_stairs_dp}\n</code></pre> <p>下の図は上記コードの実行プロセスをシミュレートしています。</p> <p></p> <p> 図 14-5   階段登りの動的プログラミングプロセス </p> <p>バックトラッキングアルゴリズムと同様に、動的プログラミングも「状態」の概念を使用して問題解決の特定の段階を表現し、各状態は部分問題とその局所最適解に対応します。例えば、階段登り問題の状態は現在のステップ番号 \\(i\\) として定義されます。</p> <p>上記の内容に基づいて、動的プログラミングでよく使用される用語をまとめることができます。</p> <ul> <li>配列 <code>dp</code> はDPテーブルと呼ばれ、\\(dp[i]\\) は状態 \\(i\\) に対応する部分問題の解を表します。</li> <li>最小の部分問題（ステップ \\(1\\) と \\(2\\)）に対応する状態は初期状態と呼ばれます。</li> <li>再帰式 \\(dp[i] = dp[i-1] + dp[i-2]\\) は状態遷移方程式と呼ばれます。</li> </ul>","path":["第 14 章 &nbsp; 動的計画法","14.1 &nbsp; 動的プログラミングの紹介"],"tags":[]},{"location":"chapter_dynamic_programming/intro_to_dynamic_programming/#1414","level":2,"title":"14.1.4   空間最適化","text":"<p>注意深い読者は**\\(dp[i]\\) は \\(dp[i-1]\\) と \\(dp[i-2]\\) のみに関連するため、すべての部分問題の解を保存するために配列 <code>dp</code> を使用する必要がない**ことに気づくでしょう。単に2つの変数を使って反復的に進めることができます。コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby climbing_stairs_dp.py<pre><code>def climbing_stairs_dp_comp(n: int) -&gt; int:\n    \"\"\"階段登り：空間最適化動的プログラミング\"\"\"\n    if n == 1 or n == 2:\n        return n\n    a, b = 1, 2\n    for _ in range(3, n + 1):\n        a, b = b, a + b\n    return b\n</code></pre> climbing_stairs_dp.cpp<pre><code>/* 階段登り：空間最適化動的プログラミング */\nint climbingStairsDPComp(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    int a = 1, b = 2;\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = a + b;\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> climbing_stairs_dp.java<pre><code>/* 階段登り：空間最適化動的プログラミング */\nint climbingStairsDPComp(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    int a = 1, b = 2;\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = a + b;\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> climbing_stairs_dp.cs<pre><code>[class]{climbing_stairs_dp}-[func]{ClimbingStairsDPComp}\n</code></pre> climbing_stairs_dp.go<pre><code>[class]{}-[func]{climbingStairsDPComp}\n</code></pre> climbing_stairs_dp.swift<pre><code>[class]{}-[func]{climbingStairsDPComp}\n</code></pre> climbing_stairs_dp.js<pre><code>[class]{}-[func]{climbingStairsDPComp}\n</code></pre> climbing_stairs_dp.ts<pre><code>[class]{}-[func]{climbingStairsDPComp}\n</code></pre> climbing_stairs_dp.dart<pre><code>[class]{}-[func]{climbingStairsDPComp}\n</code></pre> climbing_stairs_dp.rs<pre><code>[class]{}-[func]{climbing_stairs_dp_comp}\n</code></pre> climbing_stairs_dp.c<pre><code>[class]{}-[func]{climbingStairsDPComp}\n</code></pre> climbing_stairs_dp.kt<pre><code>[class]{}-[func]{climbingStairsDPComp}\n</code></pre> climbing_stairs_dp.rb<pre><code>[class]{}-[func]{climbing_stairs_dp_comp}\n</code></pre> <p>上記のコードを観察すると、配列 <code>dp</code> が占有していた空間が削除されるため、空間計算量は \\(O(n)\\) から \\(O(1)\\) に削減されます。</p> <p>多くの動的プログラミング問題では、現在の状態は限られた数の前の状態のみに依存するため、必要な状態のみを保持し、「次元削減」によってメモリ空間を節約できます。この空間最適化技術は「ローリング変数」または「ローリング配列」として知られています。</p>","path":["第 14 章 &nbsp; 動的計画法","14.1 &nbsp; 動的プログラミングの紹介"],"tags":[]},{"location":"chapter_dynamic_programming/knapsack_problem/","level":1,"title":"14.4   0-1ナップサック問題","text":"<p>ナップサック問題は動的プログラミングの優れた入門問題であり、動的プログラミングで最も一般的な問題タイプです。0-1ナップサック問題、無制限ナップサック問題、複数ナップサック問題など、多くの変種があります。</p> <p>このセクションでは、まず最も一般的な0-1ナップサック問題を解決します。</p> <p>Question</p> <p>\\(n\\) 個のアイテムが与えられ、\\(i\\) 番目のアイテムの重量は \\(wgt[i-1]\\) で値は \\(val[i-1]\\) です。容量が \\(cap\\) のナップサックがあります。各アイテムは1回のみ選択できます。容量制限下でナップサックに入れることができるアイテムの最大値は何ですか？</p> <p>下の図を観察すると、アイテム番号 \\(i\\) は1から数え始め、配列インデックスは0から始まるため、アイテム \\(i\\) の重量は \\(wgt[i-1]\\) に対応し、値は \\(val[i-1]\\) に対応します。</p> <p></p> <p> 図 14-17   0-1ナップサックの例データ </p> <p>0-1ナップサック問題を \\(n\\) ラウンドの決定から構成されるプロセスとして考えることができます。各アイテムについて入れない、または入れるという2つの決定があり、したがって問題は決定木モデルに適合します。</p> <p>この問題の目的は「限られた容量の下でナップサックに入れることができるアイテムの値を最大化する」ことであり、動的プログラミング問題である可能性が高いです。</p> <p>第1ステップ：各ラウンドの決定を考え、状態を定義し、それにより \\(dp\\) テーブルを得る</p> <p>各アイテムについて、ナップサックに入れなければ容量は変わらず、入れれば容量は減少します。これから状態定義を得ることができます：現在のアイテム番号 \\(i\\) とナップサック容量 \\(c\\)、\\([i, c]\\) と表記されます。</p> <p>状態 \\([i, c]\\) は部分問題に対応します：容量 \\(c\\) のナップサックでの最初の \\(i\\) 個のアイテムの最大値、\\(dp[i, c]\\) と表記されます。</p> <p>探している解は \\(dp[n, cap]\\) であるため、サイズ \\((n+1) \\times (cap+1)\\) の二次元 \\(dp\\) テーブルが必要です。</p> <p>第2ステップ：最適部分構造を特定し、状態遷移方程式を導出する</p> <p>アイテム \\(i\\) の決定を行った後、残るのは最初の \\(i-1\\) 個のアイテムの決定の部分問題であり、これは2つのケースに分けることができます。</p> <ul> <li>アイテム \\(i\\) を入れない：ナップサック容量は変わらず、状態は \\([i-1, c]\\) に変わります。</li> <li>アイテム \\(i\\) を入れる：ナップサック容量は \\(wgt[i-1]\\) だけ減少し、値は \\(val[i-1]\\) だけ増加し、状態は \\([i-1, c-wgt[i-1]]\\) に変わります。</li> </ul> <p>上記の分析により、この問題の最適部分構造が明らかになります：最大値 \\(dp[i, c]\\) は、アイテム \\(i\\) を入れない方案とアイテム \\(i\\) を入れる方案の2つのうち、より大きな値に等しい。これから状態遷移方程式を導出できます：</p> \\[ dp[i, c] = \\max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1]) \\] <p>現在のアイテムの重量 \\(wgt[i - 1]\\) が残りのナップサック容量 \\(c\\) を超える場合、唯一の選択肢はナップサックに入れないことであることに注意することが重要です。</p> <p>第3ステップ：境界条件と状態遷移の順序を決定する</p> <p>アイテムがない場合またはナップサック容量が \\(0\\) の場合、最大値は \\(0\\) です。つまり、最初の列 \\(dp[i, 0]\\) と最初の行 \\(dp[0, c]\\) はどちらも \\(0\\) に等しいです。</p> <p>現在の状態 \\([i, c]\\) は直接上の状態 \\([i-1, c]\\) と左上の状態 \\([i-1, c-wgt[i-1]]\\) から遷移するため、2層のループを通じて \\(dp\\) テーブル全体を順序通りに走査します。</p> <p>上記の分析に従って、次に力任せ探索、メモ化探索、動的プログラミングの順序で解法を実装します。</p>","path":["第 14 章 &nbsp; 動的計画法","14.4 &nbsp; 0-1ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/knapsack_problem/#1-1","level":3,"title":"1.   方法1：力任せ探索","text":"<p>探索コードには以下の要素が含まれます。</p> <ul> <li>再帰パラメータ：状態 \\([i, c]\\)。</li> <li>戻り値：部分問題 \\(dp[i, c]\\) の解。</li> <li>終了条件：アイテム番号が範囲外 \\(i = 0\\) またはナップサックの残り容量が \\(0\\) のとき、再帰を終了し値 \\(0\\) を返す。</li> <li>枝刈り：現在のアイテムの重量がナップサックの残り容量を超える場合、唯一の選択肢はナップサックに入れないことです。</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby knapsack.py<pre><code>def knapsack_dfs(wgt: list[int], val: list[int], i: int, c: int) -&gt; int:\n    \"\"\"0-1 ナップサック：ブルートフォース探索\"\"\"\n    # すべてのアイテムが選択されたかナップサックに残り容量がない場合、値 0 を返す\n    if i == 0 or c == 0:\n        return 0\n    # ナップサック容量を超える場合、ナップサックに入れないことしか選択できない\n    if wgt[i - 1] &gt; c:\n        return knapsack_dfs(wgt, val, i - 1, c)\n    # アイテム i を入れないのと入れるのとの最大値を計算\n    no = knapsack_dfs(wgt, val, i - 1, c)\n    yes = knapsack_dfs(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1]\n    # 2 つの選択肢のうち大きい値を返す\n    return max(no, yes)\n</code></pre> knapsack.cpp<pre><code>/* 0-1 ナップサック：ブルートフォース探索 */\nint knapsackDFS(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int i, int c) {\n    // すべてのアイテムが選択されたか、ナップサックに残り容量がない場合、値 0 を返す\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // ナップサックの容量を超える場合、ナップサックに入れないことしか選択できない\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFS(wgt, val, i - 1, c);\n    }\n    // アイテム i を入れない場合と入れる場合の最大値を計算\n    int no = knapsackDFS(wgt, val, i - 1, c);\n    int yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // 2つの選択肢のより大きい値を返す\n    return max(no, yes);\n}\n</code></pre> knapsack.java<pre><code>/* 0-1 ナップサック：ブルートフォース探索 */\nint knapsackDFS(int[] wgt, int[] val, int i, int c) {\n    // すべてのアイテムが選択されたか、ナップサックに残り容量がない場合、値 0 を返す\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // ナップサックの容量を超える場合、ナップサックに入れないことしか選択できない\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFS(wgt, val, i - 1, c);\n    }\n    // アイテム i を入れない場合と入れる場合の最大値を計算\n    int no = knapsackDFS(wgt, val, i - 1, c);\n    int yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // 2つの選択肢のより大きい値を返す\n    return Math.max(no, yes);\n}\n</code></pre> knapsack.cs<pre><code>[class]{knapsack}-[func]{KnapsackDFS}\n</code></pre> knapsack.go<pre><code>[class]{}-[func]{knapsackDFS}\n</code></pre> knapsack.swift<pre><code>[class]{}-[func]{knapsackDFS}\n</code></pre> knapsack.js<pre><code>[class]{}-[func]{knapsackDFS}\n</code></pre> knapsack.ts<pre><code>[class]{}-[func]{knapsackDFS}\n</code></pre> knapsack.dart<pre><code>[class]{}-[func]{knapsackDFS}\n</code></pre> knapsack.rs<pre><code>[class]{}-[func]{knapsack_dfs}\n</code></pre> knapsack.c<pre><code>[class]{}-[func]{knapsackDFS}\n</code></pre> knapsack.kt<pre><code>[class]{}-[func]{knapsackDFS}\n</code></pre> knapsack.rb<pre><code>[class]{}-[func]{knapsack_dfs}\n</code></pre> <p>下の図に示すように、各アイテムは選択しないと選択するという2つの探索分岐を生成するため、時間計算量は \\(O(2^n)\\) です。</p> <p>再帰木を観察すると、\\(dp[1, 10]\\) などの重複する部分問題があることが容易にわかります。アイテムが多く、ナップサック容量が大きい場合、特に同じ重量のアイテムが多い場合、重複する部分問題の数は大幅に増加します。</p> <p></p> <p> 図 14-18   0-1ナップサック問題の力任せ探索再帰木 </p>","path":["第 14 章 &nbsp; 動的計画法","14.4 &nbsp; 0-1ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/knapsack_problem/#2-2","level":3,"title":"2.   方法2：メモ化探索","text":"<p>重複する部分問題が一度だけ計算されることを確保するために、部分問題の解を記録するメモ化リスト <code>mem</code> を使用します。ここで <code>mem[i][c]</code> は \\(dp[i, c]\\) に対応します。</p> <p>メモ化を導入した後、**時間計算量は部分問題の数に依存**し、\\(O(n \\times cap)\\) になります。実装コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby knapsack.py<pre><code>def knapsack_dfs_mem(\n    wgt: list[int], val: list[int], mem: list[list[int]], i: int, c: int\n) -&gt; int:\n    \"\"\"0-1 ナップサック：記憶化探索\"\"\"\n    # すべてのアイテムが選択されたかナップサックに残り容量がない場合、値 0 を返す\n    if i == 0 or c == 0:\n        return 0\n    # 記録がある場合、それを返す\n    if mem[i][c] != -1:\n        return mem[i][c]\n    # ナップサック容量を超える場合、ナップサックに入れないことしか選択できない\n    if wgt[i - 1] &gt; c:\n        return knapsack_dfs_mem(wgt, val, mem, i - 1, c)\n    # アイテム i を入れないのと入れるのとの最大値を計算\n    no = knapsack_dfs_mem(wgt, val, mem, i - 1, c)\n    yes = knapsack_dfs_mem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1]\n    # 2 つの選択肢のうち大きい値を記録して返す\n    mem[i][c] = max(no, yes)\n    return mem[i][c]\n</code></pre> knapsack.cpp<pre><code>[class]{}-[func]{knapsackDFSMem}\n</code></pre> knapsack.java<pre><code>/* 0-1 ナップサック：メモ化探索 */\nint knapsackDFSMem(int[] wgt, int[] val, int[][] mem, int i, int c) {\n    // すべてのアイテムが選択されたか、ナップサックに残り容量がない場合、値 0 を返す\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // 記録がある場合、それを返す\n    if (mem[i][c] != -1) {\n        return mem[i][c];\n    }\n    // ナップサックの容量を超える場合、ナップサックに入れないことしか選択できない\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFSMem(wgt, val, mem, i - 1, c);\n    }\n    // アイテム i を入れない場合と入れる場合の最大値を計算\n    int no = knapsackDFSMem(wgt, val, mem, i - 1, c);\n    int yes = knapsackDFSMem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // 2つの選択肢のより大きい値を記録して返す\n    mem[i][c] = Math.max(no, yes);\n    return mem[i][c];\n}\n</code></pre> knapsack.cs<pre><code>[class]{knapsack}-[func]{KnapsackDFSMem}\n</code></pre> knapsack.go<pre><code>[class]{}-[func]{knapsackDFSMem}\n</code></pre> knapsack.swift<pre><code>[class]{}-[func]{knapsackDFSMem}\n</code></pre> knapsack.js<pre><code>[class]{}-[func]{knapsackDFSMem}\n</code></pre> knapsack.ts<pre><code>[class]{}-[func]{knapsackDFSMem}\n</code></pre> knapsack.dart<pre><code>[class]{}-[func]{knapsackDFSMem}\n</code></pre> knapsack.rs<pre><code>[class]{}-[func]{knapsack_dfs_mem}\n</code></pre> knapsack.c<pre><code>[class]{}-[func]{knapsackDFSMem}\n</code></pre> knapsack.kt<pre><code>[class]{}-[func]{knapsackDFSMem}\n</code></pre> knapsack.rb<pre><code>[class]{}-[func]{knapsack_dfs_mem}\n</code></pre> <p>下の図はメモ化探索で枝刈りされる探索分岐を示しています。</p> <p></p> <p> 図 14-19   0-1ナップサック問題のメモ化探索再帰木 </p>","path":["第 14 章 &nbsp; 動的計画法","14.4 &nbsp; 0-1ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/knapsack_problem/#3-3","level":3,"title":"3.   方法3：動的プログラミング","text":"<p>動的プログラミングは本質的に状態遷移中に \\(dp\\) テーブルを埋めることを含みます。コードは下の図に示されています：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby knapsack.py<pre><code>def knapsack_dp(wgt: list[int], val: list[int], cap: int) -&gt; int:\n    \"\"\"0-1 ナップサック：動的プログラミング\"\"\"\n    n = len(wgt)\n    # dp テーブルを初期化\n    dp = [[0] * (cap + 1) for _ in range(n + 1)]\n    # 状態遷移\n    for i in range(1, n + 1):\n        for c in range(1, cap + 1):\n            if wgt[i - 1] &gt; c:\n                # ナップサック容量を超える場合、アイテム i を選択しない\n                dp[i][c] = dp[i - 1][c]\n            else:\n                # アイテム i を選択しないのと選択するのとで大きい値\n                dp[i][c] = max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1])\n    return dp[n][cap]\n</code></pre> knapsack.cpp<pre><code>/* 0-1 ナップサック：動的プログラミング */\nint knapsackDP(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int cap) {\n    int n = wgt.size();\n    // DPテーブルを初期化\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(cap + 1, 0));\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサックの容量を超える場合、アイテム i を選択しない\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // 選択しない場合とアイテム i を選択する場合のより大きい値\n                dp[i][c] = max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> knapsack.java<pre><code>/* 0-1 ナップサック：動的プログラミング */\nint knapsackDP(int[] wgt, int[] val, int cap) {\n    int n = wgt.length;\n    // DPテーブルを初期化\n    int[][] dp = new int[n + 1][cap + 1];\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサックの容量を超える場合、アイテム i を選択しない\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // 選択しない場合とアイテム i を選択する場合のより大きい値\n                dp[i][c] = Math.max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> knapsack.cs<pre><code>[class]{knapsack}-[func]{KnapsackDP}\n</code></pre> knapsack.go<pre><code>[class]{}-[func]{knapsackDP}\n</code></pre> knapsack.swift<pre><code>[class]{}-[func]{knapsackDP}\n</code></pre> knapsack.js<pre><code>[class]{}-[func]{knapsackDP}\n</code></pre> knapsack.ts<pre><code>[class]{}-[func]{knapsackDP}\n</code></pre> knapsack.dart<pre><code>[class]{}-[func]{knapsackDP}\n</code></pre> knapsack.rs<pre><code>[class]{}-[func]{knapsack_dp}\n</code></pre> knapsack.c<pre><code>[class]{}-[func]{knapsackDP}\n</code></pre> knapsack.kt<pre><code>[class]{}-[func]{knapsackDP}\n</code></pre> knapsack.rb<pre><code>[class]{}-[func]{knapsack_dp}\n</code></pre> <p>下の図に示すように、時間計算量と空間計算量の両方が配列 <code>dp</code> のサイズ、つまり \\(O(n \\times cap)\\) によって決定されます。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt;&lt;13&gt;&lt;14&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 14-20   0-1ナップサック問題の動的プログラミングプロセス </p>","path":["第 14 章 &nbsp; 動的計画法","14.4 &nbsp; 0-1ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/knapsack_problem/#4","level":3,"title":"4.   空間最適化","text":"<p>各状態は上の行の状態のみに関連するため、2つの配列を使用してローリング前進させ、空間計算量を \\(O(n^2)\\) から \\(O(n)\\) に削減できます。</p> <p>さらに考えてみると、1つの配列だけで空間最適化を達成できるでしょうか？各状態が直接上のセルまたは左上のセルから遷移することが観察できます。配列が1つしかない場合、\\(i\\) 行目の走査を開始するとき、その配列はまだ \\(i-1\\) 行目の状態を保存しています。</p> <ul> <li>通常の順序で走査する場合、\\(dp[i, j]\\) に走査したとき、左上の \\(dp[i-1, 1]\\) ～ \\(dp[i-1, j-1]\\) の値がすでに上書きされている可能性があり、正しい状態遷移結果を得ることができません。</li> <li>逆順で走査する場合、上書き問題はなく、状態遷移を正しく実行できます。</li> </ul> <p>下の図は単一配列での \\(i = 1\\) 行目から \\(i = 2\\) 行目への遷移プロセスを示しています。通常順序走査と逆順走査の違いについて考えてみてください。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 14-21   0-1ナップサックの空間最適化動的プログラミングプロセス </p> <p>コード実装では、配列 <code>dp</code> の最初の次元 \\(i\\) を削除し、内側のループを逆走査に変更するだけです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby knapsack.py<pre><code>def knapsack_dp_comp(wgt: list[int], val: list[int], cap: int) -&gt; int:\n    \"\"\"0-1 ナップサック：空間最適化動的プログラミング\"\"\"\n    n = len(wgt)\n    # dp テーブルを初期化\n    dp = [0] * (cap + 1)\n    # 状態遷移\n    for i in range(1, n + 1):\n        # 逆順で走査\n        for c in range(cap, 0, -1):\n            if wgt[i - 1] &gt; c:\n                # ナップサック容量を超える場合、アイテム i を選択しない\n                dp[c] = dp[c]\n            else:\n                # アイテム i を選択しないのと選択するのとで大きい値\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1])\n    return dp[cap]\n</code></pre> knapsack.cpp<pre><code>/* 0-1 ナップサック：空間最適化動的プログラミング */\nint knapsackDPComp(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int cap) {\n    int n = wgt.size();\n    // DPテーブルを初期化\n    vector&lt;int&gt; dp(cap + 1, 0);\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        // 逆順で走査\n        for (int c = cap; c &gt;= 1; c--) {\n            if (wgt[i - 1] &lt;= c) {\n                // 選択しない場合とアイテム i を選択する場合のより大きい値\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> knapsack.java<pre><code>/* 0-1 ナップサック：空間最適化動的プログラミング */\nint knapsackDPComp(int[] wgt, int[] val, int cap) {\n    int n = wgt.length;\n    // DPテーブルを初期化\n    int[] dp = new int[cap + 1];\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        // 逆順で走査\n        for (int c = cap; c &gt;= 1; c--) {\n            if (wgt[i - 1] &lt;= c) {\n                // 選択しない場合とアイテム i を選択する場合のより大きい値\n                dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> knapsack.cs<pre><code>[class]{knapsack}-[func]{KnapsackDPComp}\n</code></pre> knapsack.go<pre><code>[class]{}-[func]{knapsackDPComp}\n</code></pre> knapsack.swift<pre><code>[class]{}-[func]{knapsackDPComp}\n</code></pre> knapsack.js<pre><code>[class]{}-[func]{knapsackDPComp}\n</code></pre> knapsack.ts<pre><code>[class]{}-[func]{knapsackDPComp}\n</code></pre> knapsack.dart<pre><code>[class]{}-[func]{knapsackDPComp}\n</code></pre> knapsack.rs<pre><code>[class]{}-[func]{knapsack_dp_comp}\n</code></pre> knapsack.c<pre><code>[class]{}-[func]{knapsackDPComp}\n</code></pre> knapsack.kt<pre><code>[class]{}-[func]{knapsackDPComp}\n</code></pre> knapsack.rb<pre><code>[class]{}-[func]{knapsack_dp_comp}\n</code></pre>","path":["第 14 章 &nbsp; 動的計画法","14.4 &nbsp; 0-1ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/summary/","level":1,"title":"14.7   まとめ","text":"<ul> <li>動的プログラミングは問題を分解し、部分問題の解を保存することで冗長な計算を避け、計算効率を向上させます。</li> <li>時間を考慮しなければ、すべての動的プログラミング問題はバックトラッキング（力任せ探索）を使用して解決できますが、再帰木には多くの重複する部分問題があり、効率が非常に低くなります。記憶化リストを導入することで、計算されたすべての部分問題の解を保存し、重複する部分問題が一度だけ計算されることを保証できます。</li> <li>記憶化探索はトップダウンの再帰解法であり、動的プログラミングはボトムアップの反復アプローチに対応し、「表を埋める」ことに似ています。現在の状態は特定の局所状態のみに依存するため、dpテーブルの1次元を削除して空間計算量を削減できます。</li> <li>部分問題の分解は汎用的なアルゴリズムアプローチであり、分割統治法、動的プログラミング、バックトラッキングで特徴が異なります。</li> <li>動的プログラミング問題には3つの主要な特徴があります：重複する部分問題、最適部分構造、無記憶性。</li> <li>元の問題の最適解がその部分問題の最適解から構築できる場合、最適部分構造を持ちます。</li> <li>無記憶性とは、状態の将来の発展が現在の状態のみに依存し、過去に経験したすべての状態に依存しないことを意味します。多くの組み合わせ最適化問題にはこの特性がなく、動的プログラミングを使用して迅速に解決することはできません。</li> </ul> <p>ナップサック問題</p> <ul> <li>ナップサック問題は最も典型的な動的プログラミング問題の1つで、0-1ナップサック、無制限ナップサック、複数ナップサックなどの変種があります。</li> <li>0-1ナップサックの状態定義は、最初の \\(i\\) 個のアイテムを含む容量 \\(c\\) のナップサックでの最大値です。アイテムをナップサックに入れないまたは入れるという決定に基づいて、最適部分構造を特定し、状態遷移方程式を構築できます。空間最適化では、各状態が直接上と左上の状態に依存するため、左上の状態の上書きを避けるためにリストを逆順で走査する必要があります。</li> <li>無制限ナップサック問題では、各種類のアイテムを選択できる数に制限がないため、アイテムを含める状態遷移は0-1ナップサックと異なります。状態が直接上と左の状態に依存するため、空間最適化では前方走査を含める必要があります。</li> <li>コイン交換問題は無制限ナップサック問題の変種で、「最大」値を求めることから「最小」コイン数を求めることに変わり、状態遷移方程式は \\(\\max()\\) を \\(\\min()\\) に変更する必要があります。ナップサックの容量を「超えない」ことを追求することから、正確に目標金額を求めることに変わり、「目標金額を構成できない」無効解を表すために \\(amt + 1\\) を使用します。</li> <li>コイン交換問題IIは「最小コイン数」を求めることから「コインの組み合わせ数」を求めることに変わり、状態遷移方程式を \\(\\min()\\) から和算演算子に変更します。</li> </ul> <p>編集距離問題</p> <ul> <li>編集距離（レーベンシュタイン距離）は2つの文字列間の類似度を測定し、一つの文字列を別の文字列に変更するために必要な最小編集ステップ数として定義され、編集操作には追加、削除、置換が含まれます。</li> <li>編集距離問題の状態定義は、\\(s\\) の最初の \\(i\\) 文字を \\(t\\) の最初の \\(j\\) 文字に変更するために必要な最小編集ステップ数です。\\(s[i] \\ne t[j]\\) の場合、追加、削除、置換の3つの決定があり、それぞれに対応する残余部分問題があります。これから最適部分構造を特定し、状態遷移方程式を構築できます。\\(s[i] = t[j]\\) の場合、現在の文字の編集は必要ありません。</li> <li>編集距離では、状態が直接上、左、左上の状態に依存します。したがって、空間最適化後、前方走査も逆走査も正しく状態遷移を実行できません。これに対処するため、変数を使用して左上の状態を一時的に保存し、無制限ナップサック問題の状況と同等にし、空間最適化後に前方走査を可能にします。</li> </ul>","path":["第 14 章 &nbsp; 動的計画法","14.7 &nbsp; まとめ"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/","level":1,"title":"14.5   無制限ナップサック問題","text":"<p>このセクションでは、まず別の一般的なナップサック問題である無制限ナップサックを解決し、次にその特殊ケースであるコイン交換問題を探索します。</p>","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 無制限ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1451","level":2,"title":"14.5.1   無制限ナップサック問題","text":"<p>Question</p> <p>\\(n\\) 個のアイテムが与えられ、\\(i\\) 番目のアイテムの重量は \\(wgt[i-1]\\) で値は \\(val[i-1]\\) です。容量が \\(cap\\) のバックパックがあります。各アイテムは複数回選択できます。容量を超えることなくバックパックに入れることができるアイテムの最大値は何ですか？以下の例を参照してください。</p> <p></p> <p> 図 14-22   無制限ナップサック問題の例データ </p>","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 無制限ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1","level":3,"title":"1.   動的プログラミングアプローチ","text":"<p>無制限ナップサック問題は0-1ナップサック問題と非常に似ており、唯一の違いはアイテムを選択できる回数に制限がないことです。</p> <ul> <li>0-1ナップサック問題では、各アイテムは1つしかないため、アイテム \\(i\\) をバックパックに入れた後は、前の \\(i-1\\) 個のアイテムからのみ選択できます。</li> <li>無制限ナップサック問題では、各アイテムの数量は無制限であるため、アイテム \\(i\\) をバックパックに入れた後も、前の \\(i\\) 個のアイテムから引き続き選択できます。</li> </ul> <p>無制限ナップサック問題のルールの下で、状態 \\([i, c]\\) は2つの方法で変化できます。</p> <ul> <li>アイテム \\(i\\) を入れない：0-1ナップサック問題と同様に、\\([i-1, c]\\) に遷移します。</li> <li>アイテム \\(i\\) を入れる：0-1ナップサック問題とは異なり、\\([i, c-wgt[i-1]]\\) に遷移します。</li> </ul> <p>したがって、状態遷移方程式は次のようになります：</p> \\[ dp[i, c] = \\max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1]) \\]","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 無制限ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#2","level":3,"title":"2.   コード実装","text":"<p>2つの問題のコードを比較すると、状態遷移が \\(i-1\\) から \\(i\\) に変わり、残りは完全に同一です：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby unbounded_knapsack.py<pre><code>def unbounded_knapsack_dp(wgt: list[int], val: list[int], cap: int) -&gt; int:\n    \"\"\"完全ナップサック：動的プログラミング\"\"\"\n    n = len(wgt)\n    # dp テーブルを初期化\n    dp = [[0] * (cap + 1) for _ in range(n + 1)]\n    # 状態遷移\n    for i in range(1, n + 1):\n        for c in range(1, cap + 1):\n            if wgt[i - 1] &gt; c:\n                # ナップサック容量を超える場合、アイテム i を選択しない\n                dp[i][c] = dp[i - 1][c]\n            else:\n                # アイテム i を選択しないのと選択するのとで大きい値\n                dp[i][c] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1])\n    return dp[n][cap]\n</code></pre> unbounded_knapsack.cpp<pre><code>/* 完全ナップサック：動的プログラミング */\nint unboundedKnapsackDP(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int cap) {\n    int n = wgt.size();\n    // DPテーブルを初期化\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(cap + 1, 0));\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサックの容量を超える場合、アイテム i を選択しない\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // 選択しない場合とアイテム i を選択する場合のより大きい値\n                dp[i][c] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> unbounded_knapsack.java<pre><code>/* 完全ナップサック：動的プログラミング */\nint unboundedKnapsackDP(int[] wgt, int[] val, int cap) {\n    int n = wgt.length;\n    // DPテーブルを初期化\n    int[][] dp = new int[n + 1][cap + 1];\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサックの容量を超える場合、アイテム i を選択しない\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // 選択しない場合とアイテム i を選択する場合のより大きい値\n                dp[i][c] = Math.max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> unbounded_knapsack.cs<pre><code>[class]{unbounded_knapsack}-[func]{UnboundedKnapsackDP}\n</code></pre> unbounded_knapsack.go<pre><code>[class]{}-[func]{unboundedKnapsackDP}\n</code></pre> unbounded_knapsack.swift<pre><code>[class]{}-[func]{unboundedKnapsackDP}\n</code></pre> unbounded_knapsack.js<pre><code>[class]{}-[func]{unboundedKnapsackDP}\n</code></pre> unbounded_knapsack.ts<pre><code>[class]{}-[func]{unboundedKnapsackDP}\n</code></pre> unbounded_knapsack.dart<pre><code>[class]{}-[func]{unboundedKnapsackDP}\n</code></pre> unbounded_knapsack.rs<pre><code>[class]{}-[func]{unbounded_knapsack_dp}\n</code></pre> unbounded_knapsack.c<pre><code>[class]{}-[func]{unboundedKnapsackDP}\n</code></pre> unbounded_knapsack.kt<pre><code>[class]{}-[func]{unboundedKnapsackDP}\n</code></pre> unbounded_knapsack.rb<pre><code>[class]{}-[func]{unbounded_knapsack_dp}\n</code></pre>","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 無制限ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#3","level":3,"title":"3.   空間最適化","text":"<p>現在の状態は左と上の状態から来るため、空間最適化解法は \\(dp\\) テーブルの各行に対して前方走査を実行する必要があります。</p> <p>この走査順序は0-1ナップサックの場合とは逆です。違いを理解するために下の図を参照してください。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 14-23   空間最適化後の無制限ナップサック問題の動的プログラミングプロセス </p> <p>コード実装は非常に簡単で、配列 <code>dp</code> の最初の次元を削除するだけです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby unbounded_knapsack.py<pre><code>def unbounded_knapsack_dp_comp(wgt: list[int], val: list[int], cap: int) -&gt; int:\n    \"\"\"完全ナップサック：空間最適化動的プログラミング\"\"\"\n    n = len(wgt)\n    # dp テーブルを初期化\n    dp = [0] * (cap + 1)\n    # 状態遷移\n    for i in range(1, n + 1):\n        # 順序で走査\n        for c in range(1, cap + 1):\n            if wgt[i - 1] &gt; c:\n                # ナップサック容量を超える場合、アイテム i を選択しない\n                dp[c] = dp[c]\n            else:\n                # アイテム i を選択しないのと選択するのとで大きい値\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1])\n    return dp[cap]\n</code></pre> unbounded_knapsack.cpp<pre><code>/* 完全ナップサック：空間最適化動的プログラミング */\nint unboundedKnapsackDPComp(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int cap) {\n    int n = wgt.size();\n    // DPテーブルを初期化\n    vector&lt;int&gt; dp(cap + 1, 0);\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサックの容量を超える場合、アイテム i を選択しない\n                dp[c] = dp[c];\n            } else {\n                // 選択しない場合とアイテム i を選択する場合のより大きい値\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> unbounded_knapsack.java<pre><code>/* 完全ナップサック：空間最適化動的プログラミング */\nint unboundedKnapsackDPComp(int[] wgt, int[] val, int cap) {\n    int n = wgt.length;\n    // DPテーブルを初期化\n    int[] dp = new int[cap + 1];\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサックの容量を超える場合、アイテム i を選択しない\n                dp[c] = dp[c];\n            } else {\n                // 選択しない場合とアイテム i を選択する場合のより大きい値\n                dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> unbounded_knapsack.cs<pre><code>[class]{unbounded_knapsack}-[func]{UnboundedKnapsackDPComp}\n</code></pre> unbounded_knapsack.go<pre><code>[class]{}-[func]{unboundedKnapsackDPComp}\n</code></pre> unbounded_knapsack.swift<pre><code>[class]{}-[func]{unboundedKnapsackDPComp}\n</code></pre> unbounded_knapsack.js<pre><code>[class]{}-[func]{unboundedKnapsackDPComp}\n</code></pre> unbounded_knapsack.ts<pre><code>[class]{}-[func]{unboundedKnapsackDPComp}\n</code></pre> unbounded_knapsack.dart<pre><code>[class]{}-[func]{unboundedKnapsackDPComp}\n</code></pre> unbounded_knapsack.rs<pre><code>[class]{}-[func]{unbounded_knapsack_dp_comp}\n</code></pre> unbounded_knapsack.c<pre><code>[class]{}-[func]{unboundedKnapsackDPComp}\n</code></pre> unbounded_knapsack.kt<pre><code>[class]{}-[func]{unboundedKnapsackDPComp}\n</code></pre> unbounded_knapsack.rb<pre><code>[class]{}-[func]{unbounded_knapsack_dp_comp}\n</code></pre>","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 無制限ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1452","level":2,"title":"14.5.2   コイン交換問題","text":"<p>ナップサック問題は動的プログラミング問題の大きなクラスの代表であり、コイン交換問題など多くの変種があります。</p> <p>Question</p> <p>\\(n\\) 種類のコインが与えられ、\\(i\\) 番目の種類のコインの額面は \\(coins[i - 1]\\) で、目標金額は \\(amt\\) です。各種類のコインは複数回選択できます。目標金額を構成するのに必要な最小コイン数は何ですか？目標金額を構成できない場合は \\(-1\\) を返してください。以下の例を参照してください。</p> <p></p> <p> 図 14-24   コイン交換問題の例データ </p>","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 無制限ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1_1","level":3,"title":"1.   動的プログラミングアプローチ","text":"<p>コイン交換は無制限ナップサック問題の特殊ケースと見なすことができ、以下の類似点と相違点を共有しています。</p> <ul> <li>2つの問題は互いに変換できます：「アイテム」は「コイン」に対応し、「アイテムの重量」は「コインの額面」に対応し、「バックパックの容量」は「目標金額」に対応します。</li> <li>最適化目標は逆です：無制限ナップサック問題はアイテムの値を最大化することを目的とし、コイン交換問題はコインの数を最小化することを目的とします。</li> <li>無制限ナップサック問題はバックパック容量を「超えない」解を求め、コイン交換は目標金額を「正確に」構成する解を求めます。</li> </ul> <p>第1ステップ：各ラウンドの意思決定を考え、状態を定義し、それにより \\(dp\\) テーブルを導出する</p> <p>状態 \\([i, a]\\) は部分問題に対応します：最初の \\(i\\) 種類のコインを使用して金額 \\(a\\) を構成できる最小コイン数、\\(dp[i, a]\\) と表記されます。</p> <p>二次元 \\(dp\\) テーブルのサイズは \\((n+1) \\times (amt+1)\\) です。</p> <p>第2ステップ：最適部分構造を特定し、状態遷移方程式を導出する</p> <p>この問題は状態遷移方程式の2つの側面で無制限ナップサック問題と異なります。</p> <ul> <li>この問題は最小値を求めるため、演算子 \\(\\max()\\) を \\(\\min()\\) に変更する必要があります。</li> <li>最適化はコインの数に焦点を当てているため、コインが選択されたときに単純に \\(+1\\) を追加します。</li> </ul> \\[ dp[i, a] = \\min(dp[i-1, a], dp[i, a - coins[i-1]] + 1) \\] <p>第3ステップ：境界条件と状態遷移順序を定義する</p> <p>目標金額が \\(0\\) の場合、それを構成するのに必要な最小コイン数は \\(0\\) であるため、最初の列のすべての \\(dp[i, 0]\\) は \\(0\\) です。</p> <p>コインがない場合、**任意の金額 &gt;0 を構成することは不可能**であり、これは無効な解です。状態遷移方程式の \\(\\min()\\) 関数が無効な解を認識してフィルタリングできるように、\\(+\\infty\\) を使用してそれらを表現することを検討し、つまり最初の行のすべての \\(dp[0, a]\\) を \\(+\\infty\\) に設定します。</p>","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 無制限ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#2_1","level":3,"title":"2.   コード実装","text":"<p>ほとんどのプログラミング言語は \\(+\\infty\\) 変数を提供しておらず、整数 <code>int</code> の最大値のみを代替として使用できます。これによりオーバーフローが発生する可能性があります：状態遷移方程式の \\(+1\\) 演算がオーバーフローする可能性があります。</p> <p>この理由で、数値 \\(amt + 1\\) を使用して無効な解を表します。なぜなら、\\(amt\\) を構成するのに必要な最大コイン数は最大でも \\(amt\\) だからです。結果を返す前に、\\(dp[n, amt]\\) が \\(amt + 1\\) に等しいかどうかを確認し、そうであれば \\(-1\\) を返し、目標金額を構成できないことを示します。コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby coin_change.py<pre><code>def coin_change_dp(coins: list[int], amt: int) -&gt; int:\n    \"\"\"硬貨交換：動的プログラミング\"\"\"\n    n = len(coins)\n    MAX = amt + 1\n    # dp テーブルを初期化\n    dp = [[0] * (amt + 1) for _ in range(n + 1)]\n    # 状態遷移：最初の行と最初の列\n    for a in range(1, amt + 1):\n        dp[0][a] = MAX\n    # 状態遷移：残りの行と列\n    for i in range(1, n + 1):\n        for a in range(1, amt + 1):\n            if coins[i - 1] &gt; a:\n                # 目標金額を超える場合、硬貨 i を選択しない\n                dp[i][a] = dp[i - 1][a]\n            else:\n                # 硬貨 i を選択しないのと選択するのとで小さい値\n                dp[i][a] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1)\n    return dp[n][amt] if dp[n][amt] != MAX else -1\n</code></pre> coin_change.cpp<pre><code>/* 硬貨両替：動的プログラミング */\nint coinChangeDP(vector&lt;int&gt; &amp;coins, int amt) {\n    int n = coins.size();\n    int MAX = amt + 1;\n    // DPテーブルを初期化\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(amt + 1, 0));\n    // 状態遷移：最初の行と最初の列\n    for (int a = 1; a &lt;= amt; a++) {\n        dp[0][a] = MAX;\n    }\n    // 状態遷移：残りの行と列\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超える場合、硬貨 i を選択しない\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // 選択しない場合と硬貨 i を選択する場合のより小さい値\n                dp[i][a] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[n][amt] != MAX ? dp[n][amt] : -1;\n}\n</code></pre> coin_change.java<pre><code>/* 硬貨両替：動的プログラミング */\nint coinChangeDP(int[] coins, int amt) {\n    int n = coins.length;\n    int MAX = amt + 1;\n    // DPテーブルを初期化\n    int[][] dp = new int[n + 1][amt + 1];\n    // 状態遷移：最初の行と最初の列\n    for (int a = 1; a &lt;= amt; a++) {\n        dp[0][a] = MAX;\n    }\n    // 状態遷移：残りの行と列\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超える場合、硬貨 i を選択しない\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // 選択しない場合と硬貨 i を選択する場合のより小さい値\n                dp[i][a] = Math.min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[n][amt] != MAX ? dp[n][amt] : -1;\n}\n</code></pre> coin_change.cs<pre><code>[class]{coin_change}-[func]{CoinChangeDP}\n</code></pre> coin_change.go<pre><code>[class]{}-[func]{coinChangeDP}\n</code></pre> coin_change.swift<pre><code>[class]{}-[func]{coinChangeDP}\n</code></pre> coin_change.js<pre><code>[class]{}-[func]{coinChangeDP}\n</code></pre> coin_change.ts<pre><code>[class]{}-[func]{coinChangeDP}\n</code></pre> coin_change.dart<pre><code>[class]{}-[func]{coinChangeDP}\n</code></pre> coin_change.rs<pre><code>[class]{}-[func]{coin_change_dp}\n</code></pre> coin_change.c<pre><code>[class]{}-[func]{coinChangeDP}\n</code></pre> coin_change.kt<pre><code>[class]{}-[func]{coinChangeDP}\n</code></pre> coin_change.rb<pre><code>[class]{}-[func]{coin_change_dp}\n</code></pre> <p>下の図はコイン交換問題の動的プログラミングプロセスを示しており、無制限ナップサック問題と非常に似ています。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt;&lt;13&gt;&lt;14&gt;&lt;15&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 14-25   コイン交換問題の動的プログラミングプロセス </p>","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 無制限ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#3_1","level":3,"title":"3.   空間最適化","text":"<p>コイン交換問題の空間最適化は無制限ナップサック問題と同じ方法で処理されます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby coin_change.py<pre><code>def coin_change_dp_comp(coins: list[int], amt: int) -&gt; int:\n    \"\"\"硬貨交換：空間最適化動的プログラミング\"\"\"\n    n = len(coins)\n    MAX = amt + 1\n    # dp テーブルを初期化\n    dp = [MAX] * (amt + 1)\n    dp[0] = 0\n    # 状態遷移\n    for i in range(1, n + 1):\n        # 順序で走査\n        for a in range(1, amt + 1):\n            if coins[i - 1] &gt; a:\n                # 目標金額を超える場合、硬貨 i を選択しない\n                dp[a] = dp[a]\n            else:\n                # 硬貨 i を選択しないのと選択するのとで小さい値\n                dp[a] = min(dp[a], dp[a - coins[i - 1]] + 1)\n    return dp[amt] if dp[amt] != MAX else -1\n</code></pre> coin_change.cpp<pre><code>/* 硬貨両替：空間最適化動的プログラミング */\nint coinChangeDPComp(vector&lt;int&gt; &amp;coins, int amt) {\n    int n = coins.size();\n    int MAX = amt + 1;\n    // DPテーブルを初期化\n    vector&lt;int&gt; dp(amt + 1, MAX);\n    dp[0] = 0;\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超える場合、硬貨 i を選択しない\n                dp[a] = dp[a];\n            } else {\n                // 選択しない場合と硬貨 i を選択する場合のより小さい値\n                dp[a] = min(dp[a], dp[a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[amt] != MAX ? dp[amt] : -1;\n}\n</code></pre> coin_change.java<pre><code>/* 硬貨両替：空間最適化動的プログラミング */\nint coinChangeDPComp(int[] coins, int amt) {\n    int n = coins.length;\n    int MAX = amt + 1;\n    // DPテーブルを初期化\n    int[] dp = new int[amt + 1];\n    Arrays.fill(dp, MAX);\n    dp[0] = 0;\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超える場合、硬貨 i を選択しない\n                dp[a] = dp[a];\n            } else {\n                // 選択しない場合と硬貨 i を選択する場合のより小さい値\n                dp[a] = Math.min(dp[a], dp[a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[amt] != MAX ? dp[amt] : -1;\n}\n</code></pre> coin_change.cs<pre><code>[class]{coin_change}-[func]{CoinChangeDPComp}\n</code></pre> coin_change.go<pre><code>[class]{}-[func]{coinChangeDPComp}\n</code></pre> coin_change.swift<pre><code>[class]{}-[func]{coinChangeDPComp}\n</code></pre> coin_change.js<pre><code>[class]{}-[func]{coinChangeDPComp}\n</code></pre> coin_change.ts<pre><code>[class]{}-[func]{coinChangeDPComp}\n</code></pre> coin_change.dart<pre><code>[class]{}-[func]{coinChangeDPComp}\n</code></pre> coin_change.rs<pre><code>[class]{}-[func]{coin_change_dp_comp}\n</code></pre> coin_change.c<pre><code>[class]{}-[func]{coinChangeDPComp}\n</code></pre> coin_change.kt<pre><code>[class]{}-[func]{coinChangeDPComp}\n</code></pre> coin_change.rb<pre><code>[class]{}-[func]{coin_change_dp_comp}\n</code></pre>","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 無制限ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1453-ii","level":2,"title":"14.5.3   コイン交換問題II","text":"<p>Question</p> <p>\\(n\\) 種類のコインが与えられ、\\(i\\) 番目の種類のコインの額面は \\(coins[i - 1]\\) で、目標金額は \\(amt\\) です。各種類のコインは複数回選択でき、目標金額を構成できるコインの組み合わせは何通りありますか。以下の例を参照してください。</p> <p></p> <p> 図 14-26   コイン交換問題IIの例データ </p>","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 無制限ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1_2","level":3,"title":"1.   動的プログラミングアプローチ","text":"<p>前の問題と比較して、この問題の目標は組み合わせの数を決定することであるため、部分問題は次のようになります：最初の \\(i\\) 種類のコインを使用して金額 \\(a\\) を構成できる組み合わせの数。\\(dp\\) テーブルはサイズ \\((n+1) \\times (amt + 1)\\) の二次元行列のまま残ります。</p> <p>現在の状態の組み合わせ数は、現在のコインを選択しない組み合わせと現在のコインを選択する組み合わせの合計です。状態遷移方程式は：</p> \\[ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]] \\] <p>目標金額が \\(0\\) の場合、目標金額を構成するのにコインは必要ないため、最初の列のすべての \\(dp[i, 0]\\) は \\(1\\) に初期化されるべきです。コインがない場合、任意の金額 &gt;0 を構成することは不可能であるため、最初の行のすべての \\(dp[0, a]\\) は \\(0\\) に設定されるべきです。</p>","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 無制限ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#2_2","level":3,"title":"2.   コード実装","text":"PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby coin_change_ii.py<pre><code>def coin_change_ii_dp(coins: list[int], amt: int) -&gt; int:\n    \"\"\"硬貨交換 II：動的プログラミング\"\"\"\n    n = len(coins)\n    # dp テーブルを初期化\n    dp = [[0] * (amt + 1) for _ in range(n + 1)]\n    # 最初の列を初期化\n    for i in range(n + 1):\n        dp[i][0] = 1\n    # 状態遷移\n    for i in range(1, n + 1):\n        for a in range(1, amt + 1):\n            if coins[i - 1] &gt; a:\n                # 目標金額を超える場合、硬貨 i を選択しない\n                dp[i][a] = dp[i - 1][a]\n            else:\n                # 硬貨 i を選択しないのと選択するのとの両方の選択肢の和\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]]\n    return dp[n][amt]\n</code></pre> coin_change_ii.cpp<pre><code>/* 硬貨両替 II：動的プログラミング */\nint coinChangeIIDP(vector&lt;int&gt; &amp;coins, int amt) {\n    int n = coins.size();\n    // DPテーブルを初期化\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(amt + 1, 0));\n    // 最初の列を初期化\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i][0] = 1;\n    }\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超える場合、硬貨 i を選択しない\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // 選択しない場合と硬貨 i を選択する場合の2つの選択肢の合計\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[n][amt];\n}\n</code></pre> coin_change_ii.java<pre><code>/* 硬貨両替 II：動的プログラミング */\nint coinChangeIIDP(int[] coins, int amt) {\n    int n = coins.length;\n    // DPテーブルを初期化\n    int[][] dp = new int[n + 1][amt + 1];\n    // 最初の列を初期化\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i][0] = 1;\n    }\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超える場合、硬貨 i を選択しない\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // 選択しない場合と硬貨 i を選択する場合の2つの選択肢の合計\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[n][amt];\n}\n</code></pre> coin_change_ii.cs<pre><code>[class]{coin_change_ii}-[func]{CoinChangeIIDP}\n</code></pre> coin_change_ii.go<pre><code>[class]{}-[func]{coinChangeIIDP}\n</code></pre> coin_change_ii.swift<pre><code>[class]{}-[func]{coinChangeIIDP}\n</code></pre> coin_change_ii.js<pre><code>[class]{}-[func]{coinChangeIIDP}\n</code></pre> coin_change_ii.ts<pre><code>[class]{}-[func]{coinChangeIIDP}\n</code></pre> coin_change_ii.dart<pre><code>[class]{}-[func]{coinChangeIIDP}\n</code></pre> coin_change_ii.rs<pre><code>[class]{}-[func]{coin_change_ii_dp}\n</code></pre> coin_change_ii.c<pre><code>[class]{}-[func]{coinChangeIIDP}\n</code></pre> coin_change_ii.kt<pre><code>[class]{}-[func]{coinChangeIIDP}\n</code></pre> coin_change_ii.rb<pre><code>[class]{}-[func]{coin_change_ii_dp}\n</code></pre>","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 無制限ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#3_2","level":3,"title":"3.   空間最適化","text":"<p>空間最適化アプローチは同じで、コインの次元を削除するだけです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby coin_change_ii.py<pre><code>def coin_change_ii_dp_comp(coins: list[int], amt: int) -&gt; int:\n    \"\"\"硬貨交換 II：空間最適化動的プログラミング\"\"\"\n    n = len(coins)\n    # dp テーブルを初期化\n    dp = [0] * (amt + 1)\n    dp[0] = 1\n    # 状態遷移\n    for i in range(1, n + 1):\n        # 順序で走査\n        for a in range(1, amt + 1):\n            if coins[i - 1] &gt; a:\n                # 目標金額を超える場合、硬貨 i を選択しない\n                dp[a] = dp[a]\n            else:\n                # 硬貨 i を選択しないのと選択するのとの両方の選択肢の和\n                dp[a] = dp[a] + dp[a - coins[i - 1]]\n    return dp[amt]\n</code></pre> coin_change_ii.cpp<pre><code>/* 硬貨両替 II：空間最適化動的プログラミング */\nint coinChangeIIDPComp(vector&lt;int&gt; &amp;coins, int amt) {\n    int n = coins.size();\n    // DPテーブルを初期化\n    vector&lt;int&gt; dp(amt + 1, 0);\n    dp[0] = 1;\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超える場合、硬貨 i を選択しない\n                dp[a] = dp[a];\n            } else {\n                // 選択しない場合と硬貨 i を選択する場合の2つの選択肢の合計\n                dp[a] = dp[a] + dp[a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[amt];\n}\n</code></pre> coin_change_ii.java<pre><code>/* 硬貨両替 II：空間最適化動的プログラミング */\nint coinChangeIIDPComp(int[] coins, int amt) {\n    int n = coins.length;\n    // DPテーブルを初期化\n    int[] dp = new int[amt + 1];\n    dp[0] = 1;\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超える場合、硬貨 i を選択しない\n                dp[a] = dp[a];\n            } else {\n                // 選択しない場合と硬貨 i を選択する場合の2つの選択肢の合計\n                dp[a] = dp[a] + dp[a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[amt];\n}\n</code></pre> coin_change_ii.cs<pre><code>[class]{coin_change_ii}-[func]{CoinChangeIIDPComp}\n</code></pre> coin_change_ii.go<pre><code>[class]{}-[func]{coinChangeIIDPComp}\n</code></pre> coin_change_ii.swift<pre><code>[class]{}-[func]{coinChangeIIDPComp}\n</code></pre> coin_change_ii.js<pre><code>[class]{}-[func]{coinChangeIIDPComp}\n</code></pre> coin_change_ii.ts<pre><code>[class]{}-[func]{coinChangeIIDPComp}\n</code></pre> coin_change_ii.dart<pre><code>[class]{}-[func]{coinChangeIIDPComp}\n</code></pre> coin_change_ii.rs<pre><code>[class]{}-[func]{coin_change_ii_dp_comp}\n</code></pre> coin_change_ii.c<pre><code>[class]{}-[func]{coinChangeIIDPComp}\n</code></pre> coin_change_ii.kt<pre><code>[class]{}-[func]{coinChangeIIDPComp}\n</code></pre> coin_change_ii.rb<pre><code>[class]{}-[func]{coin_change_ii_dp_comp}\n</code></pre>","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 無制限ナップサック問題"],"tags":[]},{"location":"chapter_graph/","level":1,"title":"第 9 章   グラフ","text":"<p>Abstract</p> <p>人生の旅路において、私たちの一人一人はノードであり、無数の見えない辺で結ばれています。</p> <p>一つ一つの出会いと別れが、この広大な人生のグラフに独特の印を残していきます。</p>","path":["第 9 章 &nbsp; グラフ"],"tags":[]},{"location":"chapter_graph/#_1","level":2,"title":"章の内容","text":"<ul> <li>9.1   グラフ</li> <li>9.2   グラフの基本操作</li> <li>9.3   グラフの走査</li> <li>9.4   まとめ</li> </ul>","path":["第 9 章 &nbsp; グラフ"],"tags":[]},{"location":"chapter_graph/graph/","level":1,"title":"9.1   グラフ","text":"<p>グラフは非線形データ構造の一種で、頂点と辺で構成されます。グラフ\\(G\\)は、頂点の集合\\(V\\)と辺の集合\\(E\\)の組み合わせとして抽象的に表現できます。以下の例は、5つの頂点と7つの辺を含むグラフを示しています。</p> \\[ \\begin{aligned} V &amp; = \\{ 1, 2, 3, 4, 5 \\} \\newline E &amp; = \\{ (1,2), (1,3), (1,5), (2,3), (2,4), (2,5), (4,5) \\} \\newline G &amp; = \\{ V, E \\} \\newline \\end{aligned} \\] <p>頂点をノード、辺をノードを接続する参照（ポインタ）と見なすと、グラフは連結リストから拡張されたデータ構造として見ることができます。下図に示すように、線形関係（連結リスト）や分割統治関係（木）と比較して、ネットワーク関係（グラフ）は自由度が高いため、より複雑です。</p> <p></p> <p> 図 9-1   連結リスト、木、グラフの関係 </p>","path":["第 9 章 &nbsp; グラフ","9.1 &nbsp; グラフ"],"tags":[]},{"location":"chapter_graph/graph/#911","level":2,"title":"9.1.1   グラフの一般的な種類と用語","text":"<p>グラフは、辺に方向があるかどうかによって無向グラフと有向グラフに分けることができます（下図参照）。</p> <ul> <li>無向グラフでは、辺は2つの頂点間の「双方向」接続を表します。例えば、Facebookの「友達」関係です。</li> <li>有向グラフでは、辺に方向性があります。つまり、辺\\(A \\rightarrow B\\)と\\(A \\leftarrow B\\)は互いに独立しています。例えば、InstagramやTikTokの「フォロー」と「フォロワー」の関係です。</li> </ul> <p></p> <p> 図 9-2   有向グラフと無向グラフ </p> <p>すべての頂点が接続されているかどうかによって、グラフは連結グラフと非連結グラフに分けることができます（下図参照）。</p> <ul> <li>連結グラフでは、任意の頂点から開始して他の任意の頂点に到達することが可能です。</li> <li>非連結グラフでは、任意の開始頂点から到達できない頂点が少なくとも1つ存在します。</li> </ul> <p></p> <p> 図 9-3   連結グラフと非連結グラフ </p> <p>辺に重み変数を追加することもでき、その結果として重み付きグラフが生まれます（下図参照）。例えば、Instagramでは、システムがあなたと他のユーザーとの間の相互作用レベル（いいね、閲覧、コメントなど）によってフォロワーとフォロー中のリストをソートします。このような相互作用ネットワークは重み付きグラフで表現できます。</p> <p></p> <p> 図 9-4   重み付きグラフと重みなしグラフ </p> <p>グラフデータ構造には、以下のような一般的に使用される用語があります。</p> <ul> <li>隣接：2つの頂点を接続する辺がある場合、これら2つの頂点は「隣接」していると言われます。上図では、頂点1の隣接頂点は頂点2、3、5です。</li> <li>パス：頂点Aから頂点Bまでに通過する辺のシーケンスを、AからBへのパスと呼びます。上図では、辺のシーケンス1-5-2-4は頂点1から頂点4へのパスです。</li> <li>次数：頂点が持つ辺の数です。有向グラフの場合、入次数はその頂点を指す辺の数、出次数はその頂点から出る辺の数を指します。</li> </ul>","path":["第 9 章 &nbsp; グラフ","9.1 &nbsp; グラフ"],"tags":[]},{"location":"chapter_graph/graph/#912","level":2,"title":"9.1.2   グラフの表現","text":"<p>グラフの一般的な表現には「隣接行列」と「隣接リスト」があります。以下の例では無向グラフを使用します。</p>","path":["第 9 章 &nbsp; グラフ","9.1 &nbsp; グラフ"],"tags":[]},{"location":"chapter_graph/graph/#1","level":3,"title":"1.   隣接行列","text":"<p>グラフの頂点数を\\(n\\)とすると、隣接行列は\\(n \\times n\\)の行列を使用してグラフを表現します。各行（列）は頂点を表し、行列要素は辺を表し、2つの頂点間に辺があるかどうかを\\(1\\)または\\(0\\)で示します。</p> <p>下図に示すように、隣接行列を\\(M\\)、頂点のリストを\\(V\\)とすると、行列要素\\(M[i, j] = 1\\)は頂点\\(V[i]\\)と頂点\\(V[j]\\)の間に辺があることを示し、逆に\\(M[i, j] = 0\\)は2つの頂点間に辺がないことを示します。</p> <p></p> <p> 図 9-5   隣接行列によるグラフの表現 </p> <p>隣接行列には以下の特性があります。</p> <ul> <li>頂点は自分自身に接続することはできないため、隣接行列の主対角線上の要素は意味がありません。</li> <li>無向グラフの場合、両方向の辺は等価であるため、隣接行列は主対角線に関して対称です。</li> <li>隣接行列の要素を\\(1\\)と\\(0\\)から重みに置き換えることで、重み付きグラフを表現できます。</li> </ul> <p>隣接行列でグラフを表現する場合、行列要素に直接アクセスして辺を取得できるため、追加、削除、検索、変更の操作が効率的で、すべて時間計算量\\(O(1)\\)です。ただし、行列の空間計算量は\\(O(n^2)\\)で、より多くのメモリを消費します。</p>","path":["第 9 章 &nbsp; グラフ","9.1 &nbsp; グラフ"],"tags":[]},{"location":"chapter_graph/graph/#2","level":3,"title":"2.   隣接リスト","text":"<p>隣接リストは\\(n\\)個の連結リストを使用してグラフを表現し、各連結リストノードは頂点を表します。\\(i\\)番目の連結リストは頂点\\(i\\)に対応し、すべての隣接頂点（その頂点に接続された頂点）を含みます。下図は隣接リストを使用して格納されたグラフの例を示しています。</p> <p></p> <p> 図 9-6   隣接リストによるグラフの表現 </p> <p>隣接リストは実際の辺のみを格納し、辺の総数は\\(n^2\\)よりもはるかに少ないことが多く、より空間効率的です。ただし、隣接リストで辺を見つけるには連結リストを走査する必要があるため、その時間効率は隣接行列ほど良くありません。</p> <p>上図を観察すると、隣接リストの構造はハッシュテーブルの「チェイン法」と非常に似ているため、同様の方法を使用して効率を最適化できます。例えば、連結リストが長い場合、それをAVL木や赤黒木に変換して、時間効率を\\(O(n)\\)から\\(O(\\log n)\\)に最適化できます。連結リストをハッシュテーブルに変換することで、時間計算量を\\(O(1)\\)に削減することもできます。</p>","path":["第 9 章 &nbsp; グラフ","9.1 &nbsp; グラフ"],"tags":[]},{"location":"chapter_graph/graph/#913","level":2,"title":"9.1.3   グラフの一般的な応用","text":"<p>下表に示すように、多くの現実世界のシステムはグラフでモデル化でき、対応する問題はグラフ計算問題に削減できます。</p> <p> 表 9-1   現実生活の一般的なグラフ </p> 頂点 辺 グラフ計算問題 ソーシャルネットワーク ユーザー フォロー / フォロワー関係 潜在的フォロー推薦 地下鉄路線 駅 駅間の接続性 最短ルート推薦 太陽系 天体 天体間の重力 惑星軌道計算","path":["第 9 章 &nbsp; グラフ","9.1 &nbsp; グラフ"],"tags":[]},{"location":"chapter_graph/graph_operations/","level":1,"title":"9.2   グラフの基本操作","text":"<p>グラフの基本操作は「辺」に対する操作と「頂点」に対する操作に分けることができます。「隣接行列」と「隣接リスト」の2つの表現方法の下では、実装が異なります。</p>","path":["第 9 章 &nbsp; グラフ","9.2 &nbsp; グラフの基本操作"],"tags":[]},{"location":"chapter_graph/graph_operations/#921","level":2,"title":"9.2.1   隣接行列に基づく実装","text":"<p>\\(n\\)個の頂点を持つ無向グラフが与えられた場合、さまざまな操作は下図のように実装されます。</p> <ul> <li>辺の追加または削除：隣接行列内の指定された辺を直接変更し、\\(O(1)\\)時間を使用します。無向グラフであるため、両方向の辺を同時に更新する必要があります。</li> <li>頂点の追加：隣接行列の末尾に行と列を追加し、すべて\\(0\\)で埋めます。\\(O(n)\\)時間を使用します。</li> <li>頂点の削除：隣接行列内の行と列を削除します。最悪の場合は最初の行と列が削除されるときで、\\((n-1)^2\\)個の要素を「上と左に移動」する必要があり、\\(O(n^2)\\)時間を使用します。</li> <li>初期化：\\(n\\)個の頂点を渡し、長さ\\(n\\)の頂点リスト<code>vertices</code>を初期化し、\\(O(n)\\)時間を使用します。\\(n \\times n\\)サイズの隣接行列<code>adjMat</code>を初期化し、\\(O(n^2)\\)時間を使用します。</li> </ul> 隣接行列の初期化辺の追加辺の削除頂点の追加頂点の削除 <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 9-7   隣接行列での初期化、辺の追加と削除、頂点の追加と削除 </p> <p>以下は隣接行列を使用して表現されたグラフの実装コードです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby graph_adjacency_matrix.py<pre><code>class GraphAdjMat:\n    \"\"\"隣接行列に基づく無向グラフクラス\"\"\"\n\n    def __init__(self, vertices: list[int], edges: list[list[int]]):\n        \"\"\"コンストラクタ\"\"\"\n        # 頂点リスト、要素は「頂点値」を表し、インデックスは「頂点インデックス」を表す\n        self.vertices: list[int] = []\n        # 隣接行列、行と列のインデックスは「頂点インデックス」に対応\n        self.adj_mat: list[list[int]] = []\n        # 頂点を追加\n        for val in vertices:\n            self.add_vertex(val)\n        # 辺を追加\n        # edges要素は頂点インデックスを表す\n        for e in edges:\n            self.add_edge(e[0], e[1])\n\n    def size(self) -&gt; int:\n        \"\"\"頂点数を取得\"\"\"\n        return len(self.vertices)\n\n    def add_vertex(self, val: int):\n        \"\"\"頂点を追加\"\"\"\n        n = self.size()\n        # 頂点リストに新しい頂点値を追加\n        self.vertices.append(val)\n        # 隣接行列に行を追加\n        new_row = [0] * n\n        self.adj_mat.append(new_row)\n        # 隣接行列に列を追加\n        for row in self.adj_mat:\n            row.append(0)\n\n    def remove_vertex(self, index: int):\n        \"\"\"頂点を削除\"\"\"\n        if index &gt;= self.size():\n            raise IndexError()\n        # 頂点リストから`index`の頂点を削除\n        self.vertices.pop(index)\n        # 隣接行列から`index`の行を削除\n        self.adj_mat.pop(index)\n        # 隣接行列から`index`の列を削除\n        for row in self.adj_mat:\n            row.pop(index)\n\n    def add_edge(self, i: int, j: int):\n        \"\"\"辺を追加\"\"\"\n        # パラメータi、jは頂点要素のインデックスに対応\n        # インデックスの範囲外と等価性を処理\n        if i &lt; 0 or j &lt; 0 or i &gt;= self.size() or j &gt;= self.size() or i == j:\n            raise IndexError()\n        # 無向グラフでは、隣接行列は主対角線について対称、すなわち (i, j) == (j, i) を満たす\n        self.adj_mat[i][j] = 1\n        self.adj_mat[j][i] = 1\n\n    def remove_edge(self, i: int, j: int):\n        \"\"\"辺を削除\"\"\"\n        # パラメータi、jは頂点要素のインデックスに対応\n        # インデックスの範囲外と等価性を処理\n        if i &lt; 0 or j &lt; 0 or i &gt;= self.size() or j &gt;= self.size() or i == j:\n            raise IndexError()\n        self.adj_mat[i][j] = 0\n        self.adj_mat[j][i] = 0\n\n    def print(self):\n        \"\"\"隣接行列を出力\"\"\"\n        print(\"頂点リスト =\", self.vertices)\n        print(\"隣接行列 =\")\n        print_matrix(self.adj_mat)\n</code></pre> graph_adjacency_matrix.cpp<pre><code>/* 隣接行列に基づく無向グラフクラス */\nclass GraphAdjMat {\n    vector&lt;int&gt; vertices;       // 頂点リスト、要素は「頂点値」を表し、インデックスは「頂点インデックス」を表す\n    vector&lt;vector&lt;int&gt;&gt; adjMat; // 隣接行列、行と列のインデックスは「頂点インデックス」に対応\n\n  public:\n    /* コンストラクタ */\n    GraphAdjMat(const vector&lt;int&gt; &amp;vertices, const vector&lt;vector&lt;int&gt;&gt; &amp;edges) {\n        // 頂点を追加\n        for (int val : vertices) {\n            addVertex(val);\n        }\n        // 辺を追加\n        // 辺の要素は頂点インデックスを表す\n        for (const vector&lt;int&gt; &amp;edge : edges) {\n            addEdge(edge[0], edge[1]);\n        }\n    }\n\n    /* 頂点数を取得 */\n    int size() const {\n        return vertices.size();\n    }\n\n    /* 頂点を追加 */\n    void addVertex(int val) {\n        int n = size();\n        // 頂点リストに新しい頂点値を追加\n        vertices.push_back(val);\n        // 隣接行列に行を追加\n        adjMat.emplace_back(vector&lt;int&gt;(n, 0));\n        // 隣接行列に列を追加\n        for (vector&lt;int&gt; &amp;row : adjMat) {\n            row.push_back(0);\n        }\n    }\n\n    /* 頂点を削除 */\n    void removeVertex(int index) {\n        if (index &gt;= size()) {\n            throw out_of_range(\"Vertex does not exist\");\n        }\n        // 頂点リストから`index`の頂点を削除\n        vertices.erase(vertices.begin() + index);\n        // 隣接行列から`index`の行を削除\n        adjMat.erase(adjMat.begin() + index);\n        // 隣接行列から`index`の列を削除\n        for (vector&lt;int&gt; &amp;row : adjMat) {\n            row.erase(row.begin() + index);\n        }\n    }\n\n    /* 辺を追加 */\n    // パラメータi、jは頂点要素のインデックスに対応\n    void addEdge(int i, int j) {\n        // インデックス範囲外と等価性を処理\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j) {\n            throw out_of_range(\"Vertex does not exist\");\n        }\n        // 無向グラフでは、隣接行列は主対角線について対称、即ち(i, j) == (j, i)を満たす\n        adjMat[i][j] = 1;\n        adjMat[j][i] = 1;\n    }\n\n    /* 辺を削除 */\n    // パラメータi、jは頂点要素のインデックスに対応\n    void removeEdge(int i, int j) {\n        // インデックス範囲外と等価性を処理\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j) {\n            throw out_of_range(\"Vertex does not exist\");\n        }\n        adjMat[i][j] = 0;\n        adjMat[j][i] = 0;\n    }\n\n    /* 隣接行列を印刷 */\n    void print() {\n        cout &lt;&lt; \"頂点リスト = \";\n        printVector(vertices);\n        cout &lt;&lt; \"隣接行列 =\" &lt;&lt; endl;\n        printVectorMatrix(adjMat);\n    }\n};\n</code></pre> graph_adjacency_matrix.java<pre><code>/* 隣接行列に基づく無向グラフクラス */\nclass GraphAdjMat {\n    List&lt;Integer&gt; vertices; // 頂点リスト、要素は「頂点値」を表し、インデックスは「頂点インデックス」を表す\n    List&lt;List&lt;Integer&gt;&gt; adjMat; // 隣接行列、行と列のインデックスは「頂点インデックス」に対応\n\n    /* コンストラクタ */\n    public GraphAdjMat(int[] vertices, int[][] edges) {\n        this.vertices = new ArrayList&lt;&gt;();\n        this.adjMat = new ArrayList&lt;&gt;();\n        // 頂点を追加\n        for (int val : vertices) {\n            addVertex(val);\n        }\n        // 辺を追加\n        // 辺の要素は頂点インデックスを表す\n        for (int[] e : edges) {\n            addEdge(e[0], e[1]);\n        }\n    }\n\n    /* 頂点数を取得 */\n    public int size() {\n        return vertices.size();\n    }\n\n    /* 頂点を追加 */\n    public void addVertex(int val) {\n        int n = size();\n        // 頂点リストに新しい頂点値を追加\n        vertices.add(val);\n        // 隣接行列に行を追加\n        List&lt;Integer&gt; newRow = new ArrayList&lt;&gt;(n);\n        for (int j = 0; j &lt; n; j++) {\n            newRow.add(0);\n        }\n        adjMat.add(newRow);\n        // 隣接行列に列を追加\n        for (List&lt;Integer&gt; row : adjMat) {\n            row.add(0);\n        }\n    }\n\n    /* 頂点を削除 */\n    public void removeVertex(int index) {\n        if (index &gt;= size())\n            throw new IndexOutOfBoundsException();\n        // 頂点リストから `index` の頂点を削除\n        vertices.remove(index);\n        // 隣接行列から `index` の行を削除\n        adjMat.remove(index);\n        // 隣接行列から `index` の列を削除\n        for (List&lt;Integer&gt; row : adjMat) {\n            row.remove(index);\n        }\n    }\n\n    /* 辺を追加 */\n    // パラメータ i、j は頂点要素のインデックスに対応\n    public void addEdge(int i, int j) {\n        // インデックスの範囲外と等価性を処理\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j)\n            throw new IndexOutOfBoundsException();\n        // 無向グラフでは、隣接行列は主対角線について対称、すなわち (i, j) == (j, i) を満たす\n        adjMat.get(i).set(j, 1);\n        adjMat.get(j).set(i, 1);\n    }\n\n    /* 辺を削除 */\n    // パラメータ i、j は頂点要素のインデックスに対応\n    public void removeEdge(int i, int j) {\n        // インデックスの範囲外と等価性を処理\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j)\n            throw new IndexOutOfBoundsException();\n        adjMat.get(i).set(j, 0);\n        adjMat.get(j).set(i, 0);\n    }\n\n    /* 隣接行列を出力 */\n    public void print() {\n        System.out.print(\"頂点リスト = \");\n        System.out.println(vertices);\n        System.out.println(\"隣接行列 =\");\n        PrintUtil.printMatrix(adjMat);\n    }\n}\n</code></pre> graph_adjacency_matrix.cs<pre><code>[class]{GraphAdjMat}-[func]{}\n</code></pre> graph_adjacency_matrix.go<pre><code>[class]{graphAdjMat}-[func]{}\n</code></pre> graph_adjacency_matrix.swift<pre><code>[class]{GraphAdjMat}-[func]{}\n</code></pre> graph_adjacency_matrix.js<pre><code>[class]{GraphAdjMat}-[func]{}\n</code></pre> graph_adjacency_matrix.ts<pre><code>[class]{GraphAdjMat}-[func]{}\n</code></pre> graph_adjacency_matrix.dart<pre><code>[class]{GraphAdjMat}-[func]{}\n</code></pre> graph_adjacency_matrix.rs<pre><code>[class]{GraphAdjMat}-[func]{}\n</code></pre> graph_adjacency_matrix.c<pre><code>[class]{GraphAdjMat}-[func]{}\n</code></pre> graph_adjacency_matrix.kt<pre><code>[class]{GraphAdjMat}-[func]{}\n</code></pre> graph_adjacency_matrix.rb<pre><code>[class]{GraphAdjMat}-[func]{}\n</code></pre>","path":["第 9 章 &nbsp; グラフ","9.2 &nbsp; グラフの基本操作"],"tags":[]},{"location":"chapter_graph/graph_operations/#922","level":2,"title":"9.2.2   隣接リストに基づく実装","text":"<p>総計\\(n\\)個の頂点と\\(m\\)個の辺を持つ無向グラフが与えられた場合、さまざまな操作は下図のように実装できます。</p> <ul> <li>辺の追加：対応する頂点の連結リストの末尾に辺を追加するだけで、\\(O(1)\\)時間を使用します。無向グラフであるため、両方向に同時に辺を追加する必要があります。</li> <li>辺の削除：対応する頂点の連結リスト内で指定された辺を見つけて削除し、\\(O(m)\\)時間を使用します。無向グラフでは、両方向の辺を同時に削除する必要があります。</li> <li>頂点の追加：隣接リストに連結リストを追加し、新しい頂点をリストのヘッドノードにし、\\(O(1)\\)時間を使用します。</li> <li>頂点の削除：隣接リスト全体を走査し、指定された頂点を含むすべての辺を削除する必要があり、\\(O(n + m)\\)時間を使用します。</li> <li>初期化：隣接リストに\\(n\\)個の頂点と\\(2m\\)個の辺を作成し、\\(O(n + m)\\)時間を使用します。</li> </ul> 隣接リストの初期化辺の追加辺の削除頂点の追加頂点の削除 <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 9-8   隣接リストでの初期化、辺の追加と削除、頂点の追加と削除 </p> <p>以下は隣接リストのコード実装です。上図と比較して、実際のコードには以下の違いがあります。</p> <ul> <li>頂点の追加と削除の便宜、およびコードの簡素化のため、連結リストの代わりにリスト（動的配列）を使用します。</li> <li>ハッシュテーブルを使用して隣接リストを格納し、<code>key</code>が頂点インスタンス、<code>value</code>がその頂点の隣接頂点のリスト（連結リスト）です。</li> </ul> <p>さらに、隣接リストで頂点を表現するために<code>Vertex</code>クラスを使用します。その理由は：隣接行列のようにリストインデックスを使用して異なる頂点を区別する場合、インデックス\\(i\\)の頂点を削除したい場合、隣接リスト全体を走査し、\\(i\\)より大きいすべてのインデックスを1つずつ減少させる必要があり、これは非常に非効率的です。しかし、各頂点が一意の<code>Vertex</code>インスタンスである場合、頂点を削除しても他の頂点に変更を加える必要がありません。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby graph_adjacency_list.py<pre><code>class GraphAdjList:\n    \"\"\"隣接リストに基づく無向グラフクラス\"\"\"\n\n    def __init__(self, edges: list[list[Vertex]]):\n        \"\"\"コンストラクタ\"\"\"\n        # 隣接リスト、キー: 頂点、値: その頂点の隣接する全頂点\n        self.adj_list = dict[Vertex, list[Vertex]]()\n        # すべての頂点と辺を追加\n        for edge in edges:\n            self.add_vertex(edge[0])\n            self.add_vertex(edge[1])\n            self.add_edge(edge[0], edge[1])\n\n    def size(self) -&gt; int:\n        \"\"\"頂点数を取得\"\"\"\n        return len(self.adj_list)\n\n    def add_edge(self, vet1: Vertex, vet2: Vertex):\n        \"\"\"辺を追加\"\"\"\n        if vet1 not in self.adj_list or vet2 not in self.adj_list or vet1 == vet2:\n            raise ValueError()\n        # 辺 vet1 - vet2 を追加\n        self.adj_list[vet1].append(vet2)\n        self.adj_list[vet2].append(vet1)\n\n    def remove_edge(self, vet1: Vertex, vet2: Vertex):\n        \"\"\"辺を削除\"\"\"\n        if vet1 not in self.adj_list or vet2 not in self.adj_list or vet1 == vet2:\n            raise ValueError()\n        # 辺 vet1 - vet2 を削除\n        self.adj_list[vet1].remove(vet2)\n        self.adj_list[vet2].remove(vet1)\n\n    def add_vertex(self, vet: Vertex):\n        \"\"\"頂点を追加\"\"\"\n        if vet in self.adj_list:\n            return\n        # 隣接リストに新しい連結リストを追加\n        self.adj_list[vet] = []\n\n    def remove_vertex(self, vet: Vertex):\n        \"\"\"頂点を削除\"\"\"\n        if vet not in self.adj_list:\n            raise ValueError()\n        # 隣接リストから頂点vetに対応する連結リストを削除\n        self.adj_list.pop(vet)\n        # 他の頂点の連結リストを走査し、vetを含むすべての辺を削除\n        for vertex in self.adj_list:\n            if vet in self.adj_list[vertex]:\n                self.adj_list[vertex].remove(vet)\n\n    def print(self):\n        \"\"\"隣接リストを出力\"\"\"\n        print(\"隣接リスト =\")\n        for vertex in self.adj_list:\n            tmp = [v.val for v in self.adj_list[vertex]]\n            print(f\"{vertex.val}: {tmp},\")\n</code></pre> graph_adjacency_list.cpp<pre><code>/* 隣接リストに基づく無向グラフクラス */\nclass GraphAdjList {\n  public:\n    // 隣接リスト、キー：頂点、値：その頂点のすべての隣接頂点\n    unordered_map&lt;Vertex *, vector&lt;Vertex *&gt;&gt; adjList;\n\n    /* ベクターから指定されたノードを削除 */\n    void remove(vector&lt;Vertex *&gt; &amp;vec, Vertex *vet) {\n        for (int i = 0; i &lt; vec.size(); i++) {\n            if (vec[i] == vet) {\n                vec.erase(vec.begin() + i);\n                break;\n            }\n        }\n    }\n\n    /* コンストラクタ */\n    GraphAdjList(const vector&lt;vector&lt;Vertex *&gt;&gt; &amp;edges) {\n        // すべての頂点と辺を追加\n        for (const vector&lt;Vertex *&gt; &amp;edge : edges) {\n            addVertex(edge[0]);\n            addVertex(edge[1]);\n            addEdge(edge[0], edge[1]);\n        }\n    }\n\n    /* 頂点数を取得 */\n    int size() {\n        return adjList.size();\n    }\n\n    /* 辺を追加 */\n    void addEdge(Vertex *vet1, Vertex *vet2) {\n        if (!adjList.count(vet1) || !adjList.count(vet2) || vet1 == vet2)\n            throw invalid_argument(\"Vertex does not exist\");\n        // 辺 vet1 - vet2 を追加\n        adjList[vet1].push_back(vet2);\n        adjList[vet2].push_back(vet1);\n    }\n\n    /* 辺を削除 */\n    void removeEdge(Vertex *vet1, Vertex *vet2) {\n        if (!adjList.count(vet1) || !adjList.count(vet2) || vet1 == vet2)\n            throw invalid_argument(\"Vertex does not exist\");\n        // 辺 vet1 - vet2 を削除\n        remove(adjList[vet1], vet2);\n        remove(adjList[vet2], vet1);\n    }\n\n    /* 頂点を追加 */\n    void addVertex(Vertex *vet) {\n        if (adjList.count(vet))\n            return;\n        // 隣接リストに新しい連結リストを追加\n        adjList[vet] = vector&lt;Vertex *&gt;();\n    }\n\n    /* 頂点を削除 */\n    void removeVertex(Vertex *vet) {\n        if (!adjList.count(vet))\n            throw invalid_argument(\"Vertex does not exist\");\n        // 隣接リストから頂点vetに対応する連結リストを削除\n        adjList.erase(vet);\n        // 他の頂点の連結リストを走査し、vetを含むすべての辺を削除\n        for (auto &amp;adj : adjList) {\n            remove(adj.second, vet);\n        }\n    }\n\n    /* 隣接リストを印刷 */\n    void print() {\n        cout &lt;&lt; \"隣接リスト =\" &lt;&lt; endl;\n        for (auto &amp;adj : adjList) {\n            const auto &amp;key = adj.first;\n            const auto &amp;vec = adj.second;\n            cout &lt;&lt; key-&gt;val &lt;&lt; \": \";\n            printVector(vetsToVals(vec));\n        }\n    }\n};\n</code></pre> graph_adjacency_list.java<pre><code>/* 隣接リストに基づく無向グラフクラス */\nclass GraphAdjList {\n    // 隣接リスト、キー: 頂点、値: その頂点のすべての隣接頂点\n    Map&lt;Vertex, List&lt;Vertex&gt;&gt; adjList;\n\n    /* コンストラクタ */\n    public GraphAdjList(Vertex[][] edges) {\n        this.adjList = new HashMap&lt;&gt;();\n        // すべての頂点と辺を追加\n        for (Vertex[] edge : edges) {\n            addVertex(edge[0]);\n            addVertex(edge[1]);\n            addEdge(edge[0], edge[1]);\n        }\n    }\n\n    /* 頂点数を取得 */\n    public int size() {\n        return adjList.size();\n    }\n\n    /* 辺を追加 */\n    public void addEdge(Vertex vet1, Vertex vet2) {\n        if (!adjList.containsKey(vet1) || !adjList.containsKey(vet2) || vet1 == vet2)\n            throw new IllegalArgumentException();\n        // 辺 vet1 - vet2 を追加\n        adjList.get(vet1).add(vet2);\n        adjList.get(vet2).add(vet1);\n    }\n\n    /* 辺を削除 */\n    public void removeEdge(Vertex vet1, Vertex vet2) {\n        if (!adjList.containsKey(vet1) || !adjList.containsKey(vet2) || vet1 == vet2)\n            throw new IllegalArgumentException();\n        // 辺 vet1 - vet2 を削除\n        adjList.get(vet1).remove(vet2);\n        adjList.get(vet2).remove(vet1);\n    }\n\n    /* 頂点を追加 */\n    public void addVertex(Vertex vet) {\n        if (adjList.containsKey(vet))\n            return;\n        // 隣接リストに新しい連結リストを追加\n        adjList.put(vet, new ArrayList&lt;&gt;());\n    }\n\n    /* 頂点を削除 */\n    public void removeVertex(Vertex vet) {\n        if (!adjList.containsKey(vet))\n            throw new IllegalArgumentException();\n        // 隣接リストから頂点 vet に対応する連結リストを削除\n        adjList.remove(vet);\n        // 他の頂点の連結リストを走査し、vet を含むすべての辺を削除\n        for (List&lt;Vertex&gt; list : adjList.values()) {\n            list.remove(vet);\n        }\n    }\n\n    /* 隣接リストを出力 */\n    public void print() {\n        System.out.println(\"隣接リスト =\");\n        for (Map.Entry&lt;Vertex, List&lt;Vertex&gt;&gt; pair : adjList.entrySet()) {\n            List&lt;Integer&gt; tmp = new ArrayList&lt;&gt;();\n            for (Vertex vertex : pair.getValue())\n                tmp.add(vertex.val);\n            System.out.println(pair.getKey().val + \": \" + tmp + \",\");\n        }\n    }\n}\n</code></pre> graph_adjacency_list.cs<pre><code>[class]{GraphAdjList}-[func]{}\n</code></pre> graph_adjacency_list.go<pre><code>[class]{graphAdjList}-[func]{}\n</code></pre> graph_adjacency_list.swift<pre><code>[class]{GraphAdjList}-[func]{}\n</code></pre> graph_adjacency_list.js<pre><code>[class]{GraphAdjList}-[func]{}\n</code></pre> graph_adjacency_list.ts<pre><code>[class]{GraphAdjList}-[func]{}\n</code></pre> graph_adjacency_list.dart<pre><code>[class]{GraphAdjList}-[func]{}\n</code></pre> graph_adjacency_list.rs<pre><code>[class]{GraphAdjList}-[func]{}\n</code></pre> graph_adjacency_list.c<pre><code>[class]{AdjListNode}-[func]{}\n\n[class]{GraphAdjList}-[func]{}\n</code></pre> graph_adjacency_list.kt<pre><code>[class]{GraphAdjList}-[func]{}\n</code></pre> graph_adjacency_list.rb<pre><code>[class]{GraphAdjList}-[func]{}\n</code></pre>","path":["第 9 章 &nbsp; グラフ","9.2 &nbsp; グラフの基本操作"],"tags":[]},{"location":"chapter_graph/graph_operations/#923","level":2,"title":"9.2.3   効率の比較","text":"<p>グラフに\\(n\\)個の頂点と\\(m\\)個の辺があると仮定すると、下表は隣接行列と隣接リストの時間効率と空間効率を比較しています。</p> <p> 表 9-2   隣接行列と隣接リストの比較 </p> 隣接行列 隣接リスト（連結リスト） 隣接リスト（ハッシュテーブル） 隣接性の判定 \\(O(1)\\) \\(O(m)\\) \\(O(1)\\) 辺の追加 \\(O(1)\\) \\(O(1)\\) \\(O(1)\\) 辺の削除 \\(O(1)\\) \\(O(m)\\) \\(O(1)\\) 頂点の追加 \\(O(n)\\) \\(O(1)\\) \\(O(1)\\) 頂点の削除 \\(O(n^2)\\) \\(O(n + m)\\) \\(O(n)\\) メモリ空間使用量 \\(O(n^2)\\) \\(O(n + m)\\) \\(O(n + m)\\) <p>上表を観察すると、隣接リスト（ハッシュテーブル）が最高の時間効率と空間効率を持っているように見えます。しかし、実際には、隣接行列での辺に対する操作がより効率的で、単一の配列アクセスまたは代入操作のみが必要です。全体的に、隣接行列は「空間と時間のトレードオフ」の原則を例示し、隣接リストは「時間と空間のトレードオフ」を例示しています。</p>","path":["第 9 章 &nbsp; グラフ","9.2 &nbsp; グラフの基本操作"],"tags":[]},{"location":"chapter_graph/graph_traversal/","level":1,"title":"9.3   グラフ走査","text":"<p>木は「一対多」の関係を表現し、グラフはより高い自由度を持ち、任意の「多対多」の関係を表現できます。したがって、木をグラフの特別なケースと見なすことができます。明らかに、木の走査操作もグラフ走査操作の特別なケースです。</p> <p>グラフと木の両方で、走査操作を実装するために探索アルゴリズムの応用が必要です。グラフ走査は2つのタイプに分けることができます：幅優先探索（BFS）と深さ優先探索（DFS）です。</p>","path":["第 9 章 &nbsp; グラフ","9.3 &nbsp; グラフ走査"],"tags":[]},{"location":"chapter_graph/graph_traversal/#931","level":2,"title":"9.3.1   幅優先探索","text":"<p>幅優先探索は近くから遠くへの走査方法で、ある頂点から開始し、常に最も近い頂点を優先的に訪問し、層ごとに外側に展開していきます。下図に示すように、左上の頂点から開始し、まずその頂点のすべての隣接頂点を走査し、次に次の頂点のすべての隣接頂点を走査し、以下同様に、すべての頂点が訪問されるまで続けます。</p> <p></p> <p> 図 9-9   グラフの幅優先走査 </p>","path":["第 9 章 &nbsp; グラフ","9.3 &nbsp; グラフ走査"],"tags":[]},{"location":"chapter_graph/graph_traversal/#1","level":3,"title":"1.   アルゴリズムの実装","text":"<p>BFSは通常キューの助けを借りて実装されます（下記のコード参照）。キューは「先入先出」で、これは「近くから遠くへ」走査するBFSの考え方と一致します。</p> <ol> <li>開始頂点<code>startVet</code>をキューに追加し、ループを開始します。</li> <li>ループの各反復で、キューの先頭の頂点をポップし、それを訪問済みとして記録し、次にその頂点のすべての隣接頂点をキューの末尾に追加します。</li> <li>すべての頂点が訪問されるまで手順<code>2.</code>を繰り返します。</li> </ol> <p>頂点の再訪問を防ぐために、ハッシュセット<code>visited</code>を使用してどのノードが訪問されたかを記録します。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby graph_bfs.py<pre><code>def graph_bfs(graph: GraphAdjList, start_vet: Vertex) -&gt; list[Vertex]:\n    \"\"\"幅優先走査\"\"\"\n    # 隣接リストを使用してグラフを表現し、指定された頂点のすべての隣接頂点を取得\n    # 頂点走査シーケンス\n    res = []\n    # ハッシュセット、訪問済み頂点を記録するために使用\n    visited = set[Vertex]([start_vet])\n    # BFSを実装するために使用されるキュー\n    que = deque[Vertex]([start_vet])\n    # 頂点vetから開始し、すべての頂点が訪問されるまでループ\n    while len(que) &gt; 0:\n        vet = que.popleft()  # キューの先頭の頂点をデキュー\n        res.append(vet)  # 訪問済み頂点を記録\n        # その頂点のすべての隣接頂点を走査\n        for adj_vet in graph.adj_list[vet]:\n            if adj_vet in visited:\n                continue  # 既に訪問済みの頂点をスキップ\n            que.append(adj_vet)  # 未訪問の頂点のみをエンキュー\n            visited.add(adj_vet)  # 頂点を訪問済みとしてマーク\n    # 頂点走査シーケンスを返す\n    return res\n</code></pre> graph_bfs.cpp<pre><code>/* 幅優先走査 */\n// 隣接リストを使用してグラフを表現し、指定された頂点のすべての隣接頂点を取得\nvector&lt;Vertex *&gt; graphBFS(GraphAdjList &amp;graph, Vertex *startVet) {\n    // 頂点走査順序\n    vector&lt;Vertex *&gt; res;\n    // ハッシュセット、訪問済み頂点を記録するために使用\n    unordered_set&lt;Vertex *&gt; visited = {startVet};\n    // BFSを実装するために使用されるキュー\n    queue&lt;Vertex *&gt; que;\n    que.push(startVet);\n    // 頂点vetから開始し、すべての頂点が訪問されるまでループ\n    while (!que.empty()) {\n        Vertex *vet = que.front();\n        que.pop();          // キューの先頭の頂点をデキュー\n        res.push_back(vet); // 訪問済み頂点を記録\n        // その頂点のすべての隣接頂点を走査\n        for (auto adjVet : graph.adjList[vet]) {\n            if (visited.count(adjVet))\n                continue;            // すでに訪問済みの頂点をスキップ\n            que.push(adjVet);        // 未訪問の頂点のみをエンキュー\n            visited.emplace(adjVet); // 頂点を訪問済みとしてマーク\n        }\n    }\n    // 頂点走査順序を返す\n    return res;\n}\n</code></pre> graph_bfs.java<pre><code>/* 幅優先走査 */\n// 隣接リストを使用してグラフを表現し、指定した頂点のすべての隣接頂点を取得\nList&lt;Vertex&gt; graphBFS(GraphAdjList graph, Vertex startVet) {\n    // 頂点走査順序\n    List&lt;Vertex&gt; res = new ArrayList&lt;&gt;();\n    // ハッシュセット、訪問済みの頂点を記録するために使用\n    Set&lt;Vertex&gt; visited = new HashSet&lt;&gt;();\n    visited.add(startVet);\n    // BFS を実装するために使用するキュー\n    Queue&lt;Vertex&gt; que = new LinkedList&lt;&gt;();\n    que.offer(startVet);\n    // 頂点 vet から開始し、すべての頂点が訪問されるまでループ\n    while (!que.isEmpty()) {\n        Vertex vet = que.poll(); // キューの先頭の頂点をデキュー\n        res.add(vet);            // 訪問した頂点を記録\n        // その頂点のすべての隣接頂点を走査\n        for (Vertex adjVet : graph.adjList.get(vet)) {\n            if (visited.contains(adjVet))\n                continue;        // すでに訪問済みの頂点をスキップ\n            que.offer(adjVet);   // 未訪問の頂点のみをエンキュー\n            visited.add(adjVet); // 頂点を訪問済みとしてマーク\n        }\n    }\n    // 頂点走査順序を返す\n    return res;\n}\n</code></pre> graph_bfs.cs<pre><code>[class]{graph_bfs}-[func]{GraphBFS}\n</code></pre> graph_bfs.go<pre><code>[class]{}-[func]{graphBFS}\n</code></pre> graph_bfs.swift<pre><code>[class]{}-[func]{graphBFS}\n</code></pre> graph_bfs.js<pre><code>[class]{}-[func]{graphBFS}\n</code></pre> graph_bfs.ts<pre><code>[class]{}-[func]{graphBFS}\n</code></pre> graph_bfs.dart<pre><code>[class]{}-[func]{graphBFS}\n</code></pre> graph_bfs.rs<pre><code>[class]{}-[func]{graph_bfs}\n</code></pre> graph_bfs.c<pre><code>[class]{Queue}-[func]{}\n\n[class]{}-[func]{isVisited}\n\n[class]{}-[func]{graphBFS}\n</code></pre> graph_bfs.kt<pre><code>[class]{}-[func]{graphBFS}\n</code></pre> graph_bfs.rb<pre><code>[class]{}-[func]{graph_bfs}\n</code></pre> <p>コードは比較的抽象的ですが、下図と比較することでより良く理解できます。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 9-10   グラフの幅優先探索の手順 </p> <p>幅優先走査のシーケンスは一意ですか？</p> <p>一意ではありません。幅優先走査は「近くから遠く」の順序で走査することのみを要求し、同じ距離の頂点の走査順序は任意にできます。例えば、上図では、頂点\\(1\\)と\\(3\\)の訪問順序を交換できますし、頂点\\(2\\)、\\(4\\)、\\(6\\)の順序も同様です。</p>","path":["第 9 章 &nbsp; グラフ","9.3 &nbsp; グラフ走査"],"tags":[]},{"location":"chapter_graph/graph_traversal/#2","level":3,"title":"2.   計算量分析","text":"<p>時間計算量：すべての頂点が一度ずつエンキューおよびデキューされ、\\(O(|V|)\\)時間を使用します。隣接頂点を走査する過程で、無向グラフであるため、すべての辺が\\(2\\)回訪問され、\\(O(2|E|)\\)時間を使用します。全体で\\(O(|V| + |E|)\\)時間を使用します。</p> <p>空間計算量：リスト<code>res</code>、ハッシュセット<code>visited</code>、キュー<code>que</code>の最大頂点数は\\(|V|\\)で、\\(O(|V|)\\)空間を使用します。</p>","path":["第 9 章 &nbsp; グラフ","9.3 &nbsp; グラフ走査"],"tags":[]},{"location":"chapter_graph/graph_traversal/#932","level":2,"title":"9.3.2   深さ優先探索","text":"<p>深さ優先探索は可能な限り遠くまで行き、それ以上のパスがない場合にバックトラックする走査方法です。下図に示すように、左上の頂点から開始し、それ以上のパスがなくなるまで現在の頂点のいずれかの隣接頂点を訪問し、次に戻って続行し、すべての頂点が走査されるまで続けます。</p> <p></p> <p> 図 9-11   グラフの深さ優先走査 </p>","path":["第 9 章 &nbsp; グラフ","9.3 &nbsp; グラフ走査"],"tags":[]},{"location":"chapter_graph/graph_traversal/#1_1","level":3,"title":"1.   アルゴリズムの実装","text":"<p>この「可能な限り遠くまで行ってから戻る」アルゴリズムパラダイムは通常再帰に基づいて実装されます。幅優先探索と同様に、深さ優先探索でも、再訪問を避けるために訪問済み頂点を記録するハッシュセット<code>visited</code>の助けが必要です。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby graph_dfs.py<pre><code>def dfs(graph: GraphAdjList, visited: set[Vertex], res: list[Vertex], vet: Vertex):\n    \"\"\"深さ優先走査のヘルパー関数\"\"\"\n    res.append(vet)  # 訪問済み頂点を記録\n    visited.add(vet)  # 頂点を訪問済みとしてマーク\n    # その頂点のすべての隣接頂点を走査\n    for adjVet in graph.adj_list[vet]:\n        if adjVet in visited:\n            continue  # 既に訪問済みの頂点をスキップ\n        # 隣接頂点を再帰的に訪問\n        dfs(graph, visited, res, adjVet)\n\ndef graph_dfs(graph: GraphAdjList, start_vet: Vertex) -&gt; list[Vertex]:\n    \"\"\"深さ優先走査\"\"\"\n    # 隣接リストを使用してグラフを表現し、指定された頂点のすべての隣接頂点を取得\n    # 頂点走査シーケンス\n    res = []\n    # ハッシュセット、訪問済み頂点を記録するために使用\n    visited = set[Vertex]()\n    dfs(graph, visited, res, start_vet)\n    return res\n</code></pre> graph_dfs.cpp<pre><code>/* 深さ優先走査ヘルパー関数 */\nvoid dfs(GraphAdjList &amp;graph, unordered_set&lt;Vertex *&gt; &amp;visited, vector&lt;Vertex *&gt; &amp;res, Vertex *vet) {\n    res.push_back(vet);   // 訪問済み頂点を記録\n    visited.emplace(vet); // 頂点を訪問済みとしてマーク\n    // その頂点のすべての隣接頂点を走査\n    for (Vertex *adjVet : graph.adjList[vet]) {\n        if (visited.count(adjVet))\n            continue; // すでに訪問済みの頂点をスキップ\n        // 隣接頂点を再帰的に訪問\n        dfs(graph, visited, res, adjVet);\n    }\n}\n\n/* 深さ優先走査 */\n// 隣接リストを使用してグラフを表現し、指定された頂点のすべての隣接頂点を取得\nvector&lt;Vertex *&gt; graphDFS(GraphAdjList &amp;graph, Vertex *startVet) {\n    // 頂点走査順序\n    vector&lt;Vertex *&gt; res;\n    // ハッシュセット、訪問済み頂点を記録するために使用\n    unordered_set&lt;Vertex *&gt; visited;\n    dfs(graph, visited, res, startVet);\n    return res;\n}\n</code></pre> graph_dfs.java<pre><code>/* 深さ優先走査の補助関数 */\nvoid dfs(GraphAdjList graph, Set&lt;Vertex&gt; visited, List&lt;Vertex&gt; res, Vertex vet) {\n    res.add(vet);     // 訪問した頂点を記録\n    visited.add(vet); // 頂点を訪問済みとしてマーク\n    // その頂点のすべての隣接頂点を走査\n    for (Vertex adjVet : graph.adjList.get(vet)) {\n        if (visited.contains(adjVet))\n            continue; // すでに訪問済みの頂点をスキップ\n        // 隣接頂点を再帰的に訪問\n        dfs(graph, visited, res, adjVet);\n    }\n}\n\n/* 深さ優先走査 */\n// 隣接リストを使用してグラフを表現し、指定した頂点のすべての隣接頂点を取得\nList&lt;Vertex&gt; graphDFS(GraphAdjList graph, Vertex startVet) {\n    // 頂点走査順序\n    List&lt;Vertex&gt; res = new ArrayList&lt;&gt;();\n    // ハッシュセット、訪問済みの頂点を記録するために使用\n    Set&lt;Vertex&gt; visited = new HashSet&lt;&gt;();\n    dfs(graph, visited, res, startVet);\n    return res;\n}\n</code></pre> graph_dfs.cs<pre><code>[class]{graph_dfs}-[func]{DFS}\n\n[class]{graph_dfs}-[func]{GraphDFS}\n</code></pre> graph_dfs.go<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{graphDFS}\n</code></pre> graph_dfs.swift<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{graphDFS}\n</code></pre> graph_dfs.js<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{graphDFS}\n</code></pre> graph_dfs.ts<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{graphDFS}\n</code></pre> graph_dfs.dart<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{graphDFS}\n</code></pre> graph_dfs.rs<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{graph_dfs}\n</code></pre> graph_dfs.c<pre><code>[class]{}-[func]{isVisited}\n\n[class]{}-[func]{dfs}\n\n[class]{}-[func]{graphDFS}\n</code></pre> graph_dfs.kt<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{graphDFS}\n</code></pre> graph_dfs.rb<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{graph_dfs}\n</code></pre> <p>深さ優先探索のアルゴリズムプロセスを下図に示します。</p> <ul> <li>破線は下向きの再帰を表し、新しい頂点を訪問するために新しい再帰メソッドが開始されたことを示します。</li> <li>曲線の破線は上向きのバックトラックを表し、この再帰メソッドがこのメソッドが開始された位置に戻ったことを示します。</li> </ul> <p>理解を深めるため、下図とコードを組み合わせて、DFSプロセス全体を頭の中でシミュレート（または描画）することをお勧めします。各再帰メソッドがいつ開始され、いつ戻るかを含めてです。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 9-12   グラフの深さ優先探索の手順 </p> <p>深さ優先走査のシーケンスは一意ですか？</p> <p>幅優先走査と同様に、深さ優先走査シーケンスの順序も一意ではありません。ある頂点が与えられた場合、どの方向を最初に探索することも可能です。つまり、隣接頂点の順序は任意にシャッフルできますが、すべて深さ優先走査の一部です。</p> <p>木の走査を例に取ると、「根 \\(\\rightarrow\\) 左 \\(\\rightarrow\\) 右」、「左 \\(\\rightarrow\\) 根 \\(\\rightarrow\\) 右」、「左 \\(\\rightarrow\\) 右 \\(\\rightarrow\\) 根」は、それぞれ前順、中順、後順走査に対応します。これらは3つの異なる走査優先度を示していますが、3つすべてが深さ優先走査と見なされます。</p>","path":["第 9 章 &nbsp; グラフ","9.3 &nbsp; グラフ走査"],"tags":[]},{"location":"chapter_graph/graph_traversal/#2_1","level":3,"title":"2.   計算量分析","text":"<p>時間計算量：すべての頂点が一度訪問され、\\(O(|V|)\\)時間を使用します。すべての辺が2回訪問され、\\(O(2|E|)\\)時間を使用します。全体で\\(O(|V| + |E|)\\)時間を使用します。</p> <p>空間計算量：リスト<code>res</code>、ハッシュセット<code>visited</code>の最大頂点数は\\(|V|\\)で、最大再帰深度は\\(|V|\\)です。したがって、\\(O(|V|)\\)空間を使用します。</p>","path":["第 9 章 &nbsp; グラフ","9.3 &nbsp; グラフ走査"],"tags":[]},{"location":"chapter_graph/summary/","level":1,"title":"9.4   まとめ","text":"","path":["第 9 章 &nbsp; グラフ","9.4 &nbsp; まとめ"],"tags":[]},{"location":"chapter_graph/summary/#1","level":3,"title":"1.   重要な復習","text":"<ul> <li>グラフは頂点と辺で構成されます。頂点の集合と辺の集合として記述できます。</li> <li>線形関係（連結リストなど）や階層関係（木など）と比較して、ネットワーク関係（グラフ）はより大きな柔軟性を提供し、より複雑になります。</li> <li>有向グラフでは、辺に方向があります。連結グラフでは、任意の頂点から他の任意の頂点に到達できます。重み付きグラフでは、各辺に関連する重み変数があります。</li> <li>隣接行列は、行列（2次元配列）を使用してグラフを表現する方法です。行と列は頂点を表します。行列要素の値は、2つの頂点間に辺があるかどうかを示し、辺がある場合は\\(1\\)、ない場合は\\(0\\)を使用します。隣接行列は辺の追加、削除、チェックなどの操作に非常に効率的ですが、より多くのスペースが必要です。</li> <li>隣接リストは、連結リストの集合を使用してグラフを表現するもう一つの一般的な方法です。グラフ内の各頂点には、その隣接するすべての頂点を含むリストがあります。\\(i\\)番目のリストは頂点\\(i\\)を表します。隣接リストは隣接行列と比較してより少ないスペースを使用します。ただし、辺を見つけるためにリストを走査する必要があるため、時間効率は低くなります。</li> <li>隣接リストの連結リストが十分に長くなったとき、ルックアップ効率を向上させるために赤黒木やハッシュテーブルに変換できます。</li> <li>アルゴリズム設計の観点から、隣接行列は「空間と時間のトレードオフ」の概念を反映し、隣接リストは「時間と空間のトレードオフ」を反映します。</li> <li>グラフは、ソーシャルネットワークや地下鉄路線など、さまざまな現実世界のシステムをモデル化するために使用できます。</li> <li>木はグラフの特別なケースであり、木の走査もグラフ走査の特別なケースです。</li> <li>グラフの幅優先走査は、近くから遠くへと層ごとに拡張する探索方法で、通常キューを使用します。</li> <li>グラフの深さ優先走査は、それ以上のパスがない場合にバックトラックする前に、まず終端に到達することを優先する探索方法です。しばしば再帰を使用して実装されます。</li> </ul>","path":["第 9 章 &nbsp; グラフ","9.4 &nbsp; まとめ"],"tags":[]},{"location":"chapter_graph/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: パスは頂点のシーケンスとして定義されますか、それとも辺のシーケンスとして定義されますか？</p> <p>グラフ理論では、グラフ内のパスは頂点のシーケンスを結ぶ有限または無限の辺のシーケンスです。</p> <p>この文書では、パスは頂点のシーケンスではなく、辺のシーケンスと考えられます。これは、2つの頂点を結ぶ複数の辺がある可能性があり、その場合各辺がパスに対応するためです。</p> <p>Q: 非連結グラフでは、走査できない点がありますか？</p> <p>非連結グラフでは、特定の点から到達できない頂点が少なくとも1つあります。非連結グラフを走査するには、グラフのすべての連結成分を走査するために複数の開始点を設定する必要があります。</p> <p>Q: 隣接リストで、「その頂点に接続されたすべての頂点」の順序は重要ですか？</p> <p>任意の順序で構いません。ただし、実際のアプリケーションでは、頂点が追加された順序や頂点値の順序など、特定のルールに従ってそれらをソートする必要がある場合があります。これにより、特定の極値を持つ頂点を素早く見つけることができます。</p>","path":["第 9 章 &nbsp; グラフ","9.4 &nbsp; まとめ"],"tags":[]},{"location":"chapter_greedy/","level":1,"title":"第 15 章   貪欲法","text":"<p>Abstract</p> <p>ひまわりは太陽の方を向き、常に自分にとって最大の成長を求めます。</p> <p>貪欲な戦略は、一連の単純な選択を通じて、段階的に最良の答えへと導きます。</p>","path":["第 15 章 &nbsp; 貪欲法"],"tags":[]},{"location":"chapter_greedy/#_1","level":2,"title":"章の内容","text":"<ul> <li>15.1   貪欲アルゴリズム</li> <li>15.2   分数ナップサック問題</li> <li>15.3   最大容量問題</li> <li>15.4   最大積分割問題</li> <li>15.5   まとめ</li> </ul>","path":["第 15 章 &nbsp; 貪欲法"],"tags":[]},{"location":"chapter_greedy/fractional_knapsack_problem/","level":1,"title":"15.2   分数ナップサック問題","text":"<p>Question</p> <p>\\(n\\) 個のアイテムが与えられ、\\(i\\) 番目のアイテムの重量は \\(wgt[i-1]\\) で値は \\(val[i-1]\\) です。容量が \\(cap\\) のナップサックがあります。各アイテムは1回のみ選択できますが、アイテムの一部を選択することができ、その値は選択された重量の割合に基づいて計算されます。限られた容量の下でナップサック内のアイテムの最大値は何ですか？例を下の図に示します。</p> <p></p> <p> 図 15-3   分数ナップサック問題の例データ </p> <p>分数ナップサック問題は全体的に0-1ナップサック問題と非常に似ており、現在のアイテム \\(i\\) と容量 \\(c\\) を含み、ナップサックの限られた容量内で値を最大化することを目的としています。</p> <p>違いは、この問題ではアイテムの一部のみを選択できることです。下の図に示すように、アイテムを任意に分割し、重量の割合に基づいて対応する値を計算できます。</p> <ol> <li>アイテム \\(i\\) について、その単位重量あたりの値は \\(val[i-1] / wgt[i-1]\\) で、単位値と呼ばれます。</li> <li>重量 \\(w\\) のアイテム \\(i\\) の一部をナップサックに入れるとすると、ナップサックに追加される値は \\(w \\times val[i-1] / wgt[i-1]\\) です。</li> </ol> <p></p> <p> 図 15-4   アイテムの単位重量あたりの値 </p>","path":["第 15 章 &nbsp; 貪欲法","15.2 &nbsp; 分数ナップサック問題"],"tags":[]},{"location":"chapter_greedy/fractional_knapsack_problem/#1","level":3,"title":"1.   貪欲戦略の決定","text":"<p>ナップサック内のアイテムの総値を最大化することは、本質的に単位重量あたりの値を最大化することを意味します。これから、下の図に示す貪欲戦略を導出できます。</p> <ol> <li>アイテムを単位値の高い順から低い順にソートします。</li> <li>すべてのアイテムを反復し、**各ラウンドで最も高い単位値を持つアイテムを貪欲に選択**します。</li> <li>ナップサックの残り容量が不十分な場合、現在のアイテムの一部を使用してナップサックを満たします。</li> </ol> <p></p> <p> 図 15-5   分数ナップサック問題の貪欲戦略 </p>","path":["第 15 章 &nbsp; 貪欲法","15.2 &nbsp; 分数ナップサック問題"],"tags":[]},{"location":"chapter_greedy/fractional_knapsack_problem/#2","level":3,"title":"2.   コード実装","text":"<p>アイテムを単位値でソートするために <code>Item</code> クラスを作成しました。ナップサックが満たされるまでループして貪欲な選択を行い、その後終了して解を返します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby fractional_knapsack.py<pre><code>class Item:\n    \"\"\"アイテム\"\"\"\n\n    def __init__(self, w: int, v: int):\n        self.w = w  # アイテムの重量\n        self.v = v  # アイテムの価値\n\ndef fractional_knapsack(wgt: list[int], val: list[int], cap: int) -&gt; int:\n    \"\"\"分数ナップサック：貪欲法\"\"\"\n    # アイテムリストを作成、2 つの属性を含む：重量、価値\n    items = [Item(w, v) for w, v in zip(wgt, val)]\n    # 単位価値 item.v / item.w で高い順にソート\n    items.sort(key=lambda item: item.v / item.w, reverse=True)\n    # 貪欲選択をループ\n    res = 0\n    for item in items:\n        if item.w &lt;= cap:\n            # 残り容量が十分な場合、アイテム全体をナップサックに入れる\n            res += item.v\n            cap -= item.w\n        else:\n            # 残り容量が不十分な場合、アイテムの一部をナップサックに入れる\n            res += (item.v / item.w) * cap\n            # 残り容量がなくなったため、ループを中断\n            break\n    return res\n</code></pre> fractional_knapsack.cpp<pre><code>/* アイテム */\nclass Item {\n  public:\n    int w; // アイテムの重量\n    int v; // アイテムの価値\n\n    Item(int w, int v) : w(w), v(v) {\n    }\n};\n\n/* 分数ナップサック：貪欲法 */\ndouble fractionalKnapsack(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int cap) {\n    // アイテムリストを作成、2つの属性を含む：重量、価値\n    vector&lt;Item&gt; items;\n    for (int i = 0; i &lt; wgt.size(); i++) {\n        items.push_back(Item(wgt[i], val[i]));\n    }\n    // 単位価値 item.v / item.w で高い順にソート\n    sort(items.begin(), items.end(), [](Item &amp;a, Item &amp;b) { return (double)a.v / a.w &gt; (double)b.v / b.w; });\n    // 貪欲選択をループ\n    double res = 0;\n    for (auto &amp;item : items) {\n        if (item.w &lt;= cap) {\n            // 残り容量が十分な場合、アイテム全体をナップサックに入れる\n            res += item.v;\n            cap -= item.w;\n        } else {\n            // 残り容量が不十分な場合、アイテムの一部をナップサックに入れる\n            res += (double)item.v / item.w * cap;\n            // 残り容量がなくなったため、ループを中断\n            break;\n        }\n    }\n    return res;\n}\n</code></pre> fractional_knapsack.java<pre><code>/* アイテム */\nclass Item {\n    int w; // アイテムの重量\n    int v; // アイテムの価値\n\n    public Item(int w, int v) {\n        this.w = w;\n        this.v = v;\n    }\n}\n\n/* 分数ナップサック：貪欲法 */\ndouble fractionalKnapsack(int[] wgt, int[] val, int cap) {\n    // アイテムリストを作成、2つの属性を含む：重量、価値\n    Item[] items = new Item[wgt.length];\n    for (int i = 0; i &lt; wgt.length; i++) {\n        items[i] = new Item(wgt[i], val[i]);\n    }\n    // 単位価値 item.v / item.w で高い順にソート\n    Arrays.sort(items, Comparator.comparingDouble(item -&gt; -((double) item.v / item.w)));\n    // 貪欲選択をループ\n    double res = 0;\n    for (Item item : items) {\n        if (item.w &lt;= cap) {\n            // 残り容量が十分な場合、アイテム全体をナップサックに入れる\n            res += item.v;\n            cap -= item.w;\n        } else {\n            // 残り容量が不十分な場合、アイテムの一部をナップサックに入れる\n            res += (double) item.v / item.w * cap;\n            // 残り容量がなくなったため、ループを中断\n            break;\n        }\n    }\n    return res;\n}\n</code></pre> fractional_knapsack.cs<pre><code>[class]{Item}-[func]{}\n\n[class]{fractional_knapsack}-[func]{FractionalKnapsack}\n</code></pre> fractional_knapsack.go<pre><code>[class]{Item}-[func]{}\n\n[class]{}-[func]{fractionalKnapsack}\n</code></pre> fractional_knapsack.swift<pre><code>[class]{Item}-[func]{}\n\n[class]{}-[func]{fractionalKnapsack}\n</code></pre> fractional_knapsack.js<pre><code>[class]{Item}-[func]{}\n\n[class]{}-[func]{fractionalKnapsack}\n</code></pre> fractional_knapsack.ts<pre><code>[class]{Item}-[func]{}\n\n[class]{}-[func]{fractionalKnapsack}\n</code></pre> fractional_knapsack.dart<pre><code>[class]{Item}-[func]{}\n\n[class]{}-[func]{fractionalKnapsack}\n</code></pre> fractional_knapsack.rs<pre><code>[class]{Item}-[func]{}\n\n[class]{}-[func]{fractional_knapsack}\n</code></pre> fractional_knapsack.c<pre><code>[class]{Item}-[func]{}\n\n[class]{}-[func]{fractionalKnapsack}\n</code></pre> fractional_knapsack.kt<pre><code>[class]{Item}-[func]{}\n\n[class]{}-[func]{fractionalKnapsack}\n</code></pre> fractional_knapsack.rb<pre><code>[class]{Item}-[func]{}\n\n[class]{}-[func]{fractional_knapsack}\n</code></pre> <p>ソート以外に、最悪の場合、アイテムのリスト全体を走査する必要があるため、時間計算量は \\(O(n)\\) です。ここで \\(n\\) はアイテムの数です。</p> <p><code>Item</code> オブジェクトリストが初期化されるため、空間計算量は \\(O(n)\\) です。</p>","path":["第 15 章 &nbsp; 貪欲法","15.2 &nbsp; 分数ナップサック問題"],"tags":[]},{"location":"chapter_greedy/fractional_knapsack_problem/#3","level":3,"title":"3.   正しさの証明","text":"<p>背理法を使用します。アイテム \\(x\\) が最高の単位値を持ち、あるアルゴリズムが最大値 <code>res</code> を生成するが、解にアイテム \\(x\\) が含まれていないと仮定します。</p> <p>今、ナップサックから任意のアイテムの単位重量を取り除き、アイテム \\(x\\) の単位重量で置き換えます。アイテム \\(x\\) の単位値が最高であるため、置き換え後の総値は確実に <code>res</code> より大きくなります。これは <code>res</code> が最適解であるという仮定と矛盾し、最適解には必ずアイテム \\(x\\) が含まれることを証明します。</p> <p>この解の他のアイテムについても、上記の矛盾を構築できます。全体的に、**単位値がより大きいアイテムは常により良い選択**であり、貪欲戦略が効果的であることを証明します。</p> <p>下の図に示すように、アイテムの重量と単位値をそれぞれ二次元チャートの横軸と縦軸と見なすと、分数ナップサック問題は「限られた横軸範囲内で囲まれる最大面積を求める」ことに変換できます。この類推は、幾何学的観点から貪欲戦略の効果を理解するのに役立ちます。</p> <p></p> <p> 図 15-6   分数ナップサック問題の幾何学的表現 </p>","path":["第 15 章 &nbsp; 貪欲法","15.2 &nbsp; 分数ナップサック問題"],"tags":[]},{"location":"chapter_greedy/greedy_algorithm/","level":1,"title":"15.1   貪欲アルゴリズム","text":"<p>貪欲アルゴリズムは最適化問題を解決するための一般的なアルゴリズムで、基本的に問題の各意思決定段階で最も良い選択をすること、つまり局所的に最適な決定を貪欲に行い、グローバルに最適な解を見つけることを望みます。貪欲アルゴリズムは簡潔で効率的であり、多くの実用的な問題で広く使用されています。</p> <p>貪欲アルゴリズムと動的プログラミングは、どちらも最適化問題を解決するためによく使用されます。両者は最適部分構造の性質に依存するなど、いくつかの類似点を共有していますが、動作方法が異なります。</p> <ul> <li>動的プログラミングは現在の決定段階ですべての以前の決定を考慮し、過去の部分問題の解を使用して現在の部分問題の解を構築します。</li> <li>貪欲アルゴリズムは過去の決定を考慮せず、代わりに貪欲な選択を続け、問題が解決されるまで問題の範囲を継続的に狭めます。</li> </ul> <p>まず、「完全ナップサック問題」の章で紹介された「コイン交換」の例を通じて貪欲アルゴリズムの動作原理を理解しましょう。すでによく知っていると思います。</p> <p>Question</p> <p>\\(n\\) 種類のコインが与えられ、\\(i\\) 番目の種類のコインの額面は \\(coins[i - 1]\\) で、目標金額は \\(amt\\) です。各種類のコインは無制限に利用可能で、目標金額を構成するのに必要な最小コイン数は何ですか？目標金額を構成できない場合は \\(-1\\) を返してください。</p> <p>この問題で採用される貪欲戦略を下の図に示します。目標金額が与えられたとき、**それに最も近く、それを超えないコインを貪欲に選択**し、目標金額が満たされるまでこのステップを繰り返します。</p> <p></p> <p> 図 15-1   コイン交換の貪欲戦略 </p> <p>実装コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby coin_change_greedy.py<pre><code>def coin_change_greedy(coins: list[int], amt: int) -&gt; int:\n    \"\"\"硬貨交換：貪欲法\"\"\"\n    # coins リストがソートされていると仮定\n    i = len(coins) - 1\n    count = 0\n    # 残り金額がなくなるまで貪欲選択をループ\n    while amt &gt; 0:\n        # 残り金額に最も近く、それより小さい硬貨を見つける\n        while i &gt; 0 and coins[i] &gt; amt:\n            i -= 1\n        # coins[i] を選択\n        amt -= coins[i]\n        count += 1\n    # 実行可能な解が見つからない場合、-1 を返す\n    return count if amt == 0 else -1\n</code></pre> coin_change_greedy.cpp<pre><code>/* 硬貨両替：貪欲法 */\nint coinChangeGreedy(vector&lt;int&gt; &amp;coins, int amt) {\n    // 硬貨リストが順序付けされていると仮定\n    int i = coins.size() - 1;\n    int count = 0;\n    // 残り金額がなくなるまで貪欲選択をループ\n    while (amt &gt; 0) {\n        // 残り金額に近く、それ以下の最小硬貨を見つける\n        while (i &gt; 0 &amp;&amp; coins[i] &gt; amt) {\n            i--;\n        }\n        // coins[i] を選択\n        amt -= coins[i];\n        count++;\n    }\n    // 実行可能な解が見つからない場合、-1 を返す\n    return amt == 0 ? count : -1;\n}\n</code></pre> coin_change_greedy.java<pre><code>/* 硬貨両替：貪欲法 */\nint coinChangeGreedy(int[] coins, int amt) {\n    // 硬貨リストが順序付けされていると仮定\n    int i = coins.length - 1;\n    int count = 0;\n    // 残り金額がなくなるまで貪欲選択をループ\n    while (amt &gt; 0) {\n        // 残り金額に近く、それ以下の最小硬貨を見つける\n        while (i &gt; 0 &amp;&amp; coins[i] &gt; amt) {\n            i--;\n        }\n        // coins[i] を選択\n        amt -= coins[i];\n        count++;\n    }\n    // 実行可能な解が見つからない場合、-1 を返す\n    return amt == 0 ? count : -1;\n}\n</code></pre> coin_change_greedy.cs<pre><code>[class]{coin_change_greedy}-[func]{CoinChangeGreedy}\n</code></pre> coin_change_greedy.go<pre><code>[class]{}-[func]{coinChangeGreedy}\n</code></pre> coin_change_greedy.swift<pre><code>[class]{}-[func]{coinChangeGreedy}\n</code></pre> coin_change_greedy.js<pre><code>[class]{}-[func]{coinChangeGreedy}\n</code></pre> coin_change_greedy.ts<pre><code>[class]{}-[func]{coinChangeGreedy}\n</code></pre> coin_change_greedy.dart<pre><code>[class]{}-[func]{coinChangeGreedy}\n</code></pre> coin_change_greedy.rs<pre><code>[class]{}-[func]{coin_change_greedy}\n</code></pre> coin_change_greedy.c<pre><code>[class]{}-[func]{coinChangeGreedy}\n</code></pre> coin_change_greedy.kt<pre><code>[class]{}-[func]{coinChangeGreedy}\n</code></pre> coin_change_greedy.rb<pre><code>[class]{}-[func]{coin_change_greedy}\n</code></pre> <p>感嘆するかもしれません：なんて簡潔なんだ！貪欲アルゴリズムは約10行のコードでコイン交換問題を解決します。</p>","path":["第 15 章 &nbsp; 貪欲法","15.1 &nbsp; 貪欲アルゴリズム"],"tags":[]},{"location":"chapter_greedy/greedy_algorithm/#1511","level":2,"title":"15.1.1   貪欲アルゴリズムの利点と制限","text":"<p>貪欲アルゴリズムは直接的で実装が簡単であるだけでなく、通常非常に効率的でもあります。上記のコードで、最小のコイン額面を \\(\\min(coins)\\) とすると、貪欲な選択ループは最大 \\(amt / \\min(coins)\\) 回実行され、時間計算量は \\(O(amt / \\min(coins))\\) になります。これは動的プログラミング解法の時間計算量 \\(O(n \\times amt)\\) よりも一桁小さいです。</p> <p>しかし、一部のコイン額面の組み合わせでは、貪欲アルゴリズムは最適解を見つけることができません。下の図は2つの例を示しています。</p> <ul> <li>正の例 \\(coins = [1, 5, 10, 20, 50, 100]\\)：このコインの組み合わせでは、任意の \\(amt\\) に対して、貪欲アルゴリズムは最適解を見つけることができます。</li> <li>負の例 \\(coins = [1, 20, 50]\\)：\\(amt = 60\\) とすると、貪欲アルゴリズムは組み合わせ \\(50 + 1 \\times 10\\) しか見つけられず、合計11枚のコインですが、動的プログラミングは最適解 \\(20 + 20 + 20\\) を見つけることができ、3枚のコインのみが必要です。</li> <li>負の例 \\(coins = [1, 49, 50]\\)：\\(amt = 98\\) とすると、貪欲アルゴリズムは組み合わせ \\(50 + 1 \\times 48\\) しか見つけられず、合計49枚のコインですが、動的プログラミングは最適解 \\(49 + 49\\) を見つけることができ、2枚のコインのみが必要です。</li> </ul> <p></p> <p> 図 15-2   貪欲アルゴリズムが最適解を見つけられない例 </p> <p>これは、コイン交換問題において、貪欲アルゴリズムがグローバルに最適な解を見つけることを保証できず、非常に悪い解を見つける可能性があることを意味します。動的プログラミングの方が適しています。</p> <p>一般的に、貪欲アルゴリズムの適用性は2つのカテゴリに分類されます。</p> <ol> <li>最適解を見つけることが保証される：これらの場合、貪欲アルゴリズムはしばしば最良の選択で、バックトラッキングや動的プログラミングよりも効率的である傾向があります。</li> <li>準最適解を見つけることができる：貪欲アルゴリズムはここでも適用可能です。多くの複雑な問題では、グローバル最適解を見つけることは非常に困難であり、高効率の準最適解を見つけることも非常に価値があります。</li> </ol>","path":["第 15 章 &nbsp; 貪欲法","15.1 &nbsp; 貪欲アルゴリズム"],"tags":[]},{"location":"chapter_greedy/greedy_algorithm/#1512","level":2,"title":"15.1.2   貪欲アルゴリズムの特徴","text":"<p>それでは、どのような問題が貪欲アルゴリズムで解決するのに適しているのでしょうか？言い換えれば、どのような条件下で貪欲アルゴリズムは最適解を見つけることを保証できるのでしょうか？</p> <p>動的プログラミングと比較して、貪欲アルゴリズムはより厳しい使用条件を持ち、主に問題の2つの性質に焦点を当てています。</p> <ul> <li>貪欲選択性：局所的に最適な選択が常にグローバルに最適な解に導くことができる場合のみ、貪欲アルゴリズムは最適解を得ることを保証できます。</li> <li>最適部分構造：元の問題の最適解はその部分問題の最適解を含みます。</li> </ul> <p>最適部分構造は「動的プログラミング」の章ですでに紹介されているため、ここではこれ以上議論しません。一部の問題には明らかな最適部分構造がありませんが、それでも貪欲アルゴリズムを使用して解決できることに注意することが重要です。</p> <p>主に貪欲選択性を決定する方法を探索します。その記述は単純に見えますが、実際には、多くの問題の貪欲選択性を証明することは容易ではありません。</p> <p>例えば、コイン交換問題では、貪欲選択性を反証するために反例を簡単に挙げることができますが、それを証明することははるかに困難です。**コインの組み合わせが貪欲アルゴリズムを使用して解決できるためには、どのような条件を満たす必要があるか**と尋ねられた場合、厳密な数学的証明を提供することが困難であるため、しばしば直感や例に頼って曖昧な答えを提供しなければなりません。</p> <p>Quote</p> <p>ある論文では、コインの組み合わせが任意の金額に対して貪欲アルゴリズムを使用して最適解を見つけることができるかどうかを判定するための時間計算量 \\(O(n^3)\\) のアルゴリズムが提示されています。</p> <p>Pearson, D. A polynomial-time algorithm for the change-making problem[J]. Operations Research Letters, 2005, 33(3): 231-234.</p>","path":["第 15 章 &nbsp; 貪欲法","15.1 &nbsp; 貪欲アルゴリズム"],"tags":[]},{"location":"chapter_greedy/greedy_algorithm/#1513","level":2,"title":"15.1.3   貪欲アルゴリズムによる問題解決のステップ","text":"<p>貪欲問題の問題解決プロセスは、一般的に以下の3つのステップに分けることができます。</p> <ol> <li>問題分析：問題の特徴を整理し理解する。状態定義、最適化目標、制約などを含みます。このステップはバックトラッキングや動的プログラミングでも関与します。</li> <li>貪欲戦略の決定：各ステップで貪欲な選択をする方法を決定する。この戦略は各ステップで問題の規模を縮小し、最終的に問題全体を解決できます。</li> <li>正確性の証明：通常、問題が貪欲選択性と最適部分構造の両方を持つことを証明する必要があります。このステップには、帰納法や背理法などの数学的証明が必要な場合があります。</li> </ol> <p>貪欲戦略の決定は問題解決の核心ステップですが、実装は容易ではない場合があります。主な理由は以下の通りです。</p> <ul> <li>異なる問題間で貪欲戦略は大きく異なる。多くの問題では、貪欲戦略はかなり直接的で、一般的な思考と試行を通じて思いつくことができます。しかし、一部の複雑な問題では、貪欲戦略は非常に見つけにくく、これは個人の問題解決経験とアルゴリズム能力の真のテストです。</li> <li>一部の貪欲戦略は非常に誤解を招く。自信を持って貪欲戦略を設計し、コードを書いてテストに提出したとき、一部のテストケースが通らない可能性が高いです。これは設計された貪欲戦略が「部分的に正しい」だけであるためで、上記のコイン交換の例で説明した通りです。</li> </ul> <p>正確性を確保するために、貪欲戦略に対して厳密な数学的証明を提供すべきで、通常は背理法や数学的帰納法を含みます。</p> <p>しかし、正確性を証明することは容易な作業ではない場合があります。途方に暮れた場合、通常はテストケースに基づいてコードをデバッグし、貪欲戦略を段階的に修正し検証することを選択します。</p>","path":["第 15 章 &nbsp; 貪欲法","15.1 &nbsp; 貪欲アルゴリズム"],"tags":[]},{"location":"chapter_greedy/greedy_algorithm/#1514","level":2,"title":"15.1.4   貪欲アルゴリズムで解決される典型的な問題","text":"<p>貪欲アルゴリズムは、貪欲選択と最適部分構造の性質を満たす最適化問題によく適用されます。以下は典型的な貪欲アルゴリズム問題のいくつかです。</p> <ul> <li>コイン交換問題：一部のコインの組み合わせでは、貪欲アルゴリズムは常に最適解を提供します。</li> <li>区間スケジューリング問題：いくつかのタスクがあり、それぞれが一定期間にわたって行われるとします。目標はできるだけ多くのタスクを完了することです。常に最も早く終了するタスクを選択すると、貪欲アルゴリズムは最適解を達成できます。</li> <li>分数ナップサック問題：アイテムのセットと運搬容量が与えられ、目標は総重量が運搬容量を超えず、総価値が最大化されるようなアイテムのセットを選択することです。常に最高の価値対重量比（価値/重量）のアイテムを選択すると、貪欲アルゴリズムは一部のケースで最適解を達成できます。</li> <li>株式取引問題：株価の履歴のセットが与えられ、複数回の取引を行うことができますが、すでに株式を所有している場合は売却後でないと再度購入できません。目標は最大利益を達成することです。</li> <li>ハフマン符号化：ハフマン符号化は無損失データ圧縮に使用される貪欲アルゴリズムです。ハフマン木を構築することにより、常に最低頻度の2つのノードを統合し、最小重み付きパス長（符号化長）のハフマン木を生成します。</li> <li>ダイクストラのアルゴリズム：これは与えられたソース頂点から他のすべての頂点への最短経路問題を解決するための貪欲アルゴリズムです。</li> </ul>","path":["第 15 章 &nbsp; 貪欲法","15.1 &nbsp; 貪欲アルゴリズム"],"tags":[]},{"location":"chapter_greedy/max_capacity_problem/","level":1,"title":"15.3   最大容量問題","text":"<p>Question</p> <p>配列 \\(ht\\) を入力します。各要素は垂直仕切りの高さを表します。配列内の任意の2つの仕切りと、それらの間のスペースによってコンテナを形成できます。</p> <p>コンテナの容量は高さと幅の積（面積）で、高さは短い方の仕切りによって決定され、幅は2つの仕切りの配列インデックスの差です。</p> <p>コンテナの容量を最大化する2つの仕切りを配列から選択し、この最大容量を返してください。例を下の図に示します。</p> <p></p> <p> 図 15-7   最大容量問題の例データ </p> <p>コンテナは任意の2つの仕切りによって形成されるため、この問題の状態は2つの仕切りのインデックスで表現され、\\([i, j]\\) と表記されます。</p> <p>問題の記述によれば、容量は高さと幅の積に等しく、高さは短い方の仕切りによって決定され、幅は2つの仕切りの配列インデックスの差です。容量 \\(cap[i, j]\\) の式は：</p> \\[ cap[i, j] = \\min(ht[i], ht[j]) \\times (j - i) \\] <p>配列の長さを \\(n\\) と仮定すると、2つの仕切りの組み合わせ数（状態の総数）は \\(C_n^2 = \\frac{n(n - 1)}{2}\\) です。最も直接的なアプローチは**すべての可能な状態を列挙する**ことで、時間計算量は \\(O(n^2)\\) になります。</p>","path":["第 15 章 &nbsp; 貪欲法","15.3 &nbsp; 最大容量問題"],"tags":[]},{"location":"chapter_greedy/max_capacity_problem/#1","level":3,"title":"1.   貪欲戦略の決定","text":"<p>この問題にはより効率的な解法があります。下の図に示すように、インデックス \\(i &lt; j\\) かつ高さ \\(ht[i] &lt; ht[j]\\) の状態 \\([i, j]\\) を選択します。つまり、\\(i\\) は短い仕切り、\\(j\\) は高い仕切りです。</p> <p></p> <p> 図 15-8   初期状態 </p> <p>下の図に示すように、高い仕切り \\(j\\) を短い仕切り \\(i\\) に近づけて移動すると、容量は確実に減少します。</p> <p>これは、高い仕切り \\(j\\) を移動すると、幅 \\(j-i\\) が確実に減少するためです。高さは短い仕切りによって決定されるため、高さは同じまま（\\(i\\) が短い仕切りのまま）か減少（移動した \\(j\\) が短い仕切りになる）しかありません。</p> <p></p> <p> 図 15-9   高い仕切りを内側に移動した後の状態 </p> <p>逆に、短い仕切り \\(i\\) を内側に移動することによってのみ容量を増加させることが可能です。幅は確実に減少しますが、高さが増加する可能性があります（移動した短い仕切り \\(i\\) が高くなる場合）。例えば、下の図では、短い仕切りを移動した後に面積が増加しています。</p> <p></p> <p> 図 15-10   短い仕切りを内側に移動した後の状態 </p> <p>これにより、この問題の貪欲戦略が導かれます：コンテナの両端に2つのポインタを初期化し、各ラウンドで短い仕切りに対応するポインタを内側に移動し、2つのポインタが出会うまで続けます。</p> <p>下の図は貪欲戦略の実行を示しています。</p> <ol> <li>最初に、ポインタ \\(i\\) と \\(j\\) が配列の両端に配置されます。</li> <li>現在の状態の容量 \\(cap[i, j]\\) を計算し、最大容量を更新します。</li> <li>仕切り \\(i\\) と \\(j\\) の高さを比較し、短い仕切りを1ステップ内側に移動します。</li> <li>\\(i\\) と \\(j\\) が出会うまでステップ <code>2.</code> と <code>3.</code> を繰り返します。</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 15-11   最大容量問題の貪欲プロセス </p>","path":["第 15 章 &nbsp; 貪欲法","15.3 &nbsp; 最大容量問題"],"tags":[]},{"location":"chapter_greedy/max_capacity_problem/#2","level":3,"title":"2.   実装","text":"<p>コードは最大 \\(n\\) 回ループするため、時間計算量は \\(O(n)\\) です。</p> <p>変数 \\(i\\)、\\(j\\)、\\(res\\) は一定量の追加スペースを使用するため、空間計算量は \\(O(1)\\) です。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby max_capacity.py<pre><code>def max_capacity(ht: list[int]) -&gt; int:\n    \"\"\"最大容量：貪欲法\"\"\"\n    # i、j を初期化、配列の両端で分割させる\n    i, j = 0, len(ht) - 1\n    # 初期最大容量は 0\n    res = 0\n    # 2 つの板が出会うまで貪欲選択をループ\n    while i &lt; j:\n        # 最大容量を更新\n        cap = min(ht[i], ht[j]) * (j - i)\n        res = max(res, cap)\n        # 短い板を内側に移動\n        if ht[i] &lt; ht[j]:\n            i += 1\n        else:\n            j -= 1\n    return res\n</code></pre> max_capacity.cpp<pre><code>/* 最大容量：貪欲法 */\nint maxCapacity(vector&lt;int&gt; &amp;ht) {\n    // i、j を初期化し、配列の両端で分割させる\n    int i = 0, j = ht.size() - 1;\n    // 初期最大容量は 0\n    int res = 0;\n    // 2つの板が出会うまで貪欲選択をループ\n    while (i &lt; j) {\n        // 最大容量を更新\n        int cap = min(ht[i], ht[j]) * (j - i);\n        res = max(res, cap);\n        // より短い板を内側に移動\n        if (ht[i] &lt; ht[j]) {\n            i++;\n        } else {\n            j--;\n        }\n    }\n    return res;\n}\n</code></pre> max_capacity.java<pre><code>/* 最大容量：貪欲法 */\nint maxCapacity(int[] ht) {\n    // i、j を初期化し、配列の両端で分割させる\n    int i = 0, j = ht.length - 1;\n    // 初期最大容量は 0\n    int res = 0;\n    // 2つの板が出会うまで貪欲選択をループ\n    while (i &lt; j) {\n        // 最大容量を更新\n        int cap = Math.min(ht[i], ht[j]) * (j - i);\n        res = Math.max(res, cap);\n        // より短い板を内側に移動\n        if (ht[i] &lt; ht[j]) {\n            i++;\n        } else {\n            j--;\n        }\n    }\n    return res;\n}\n</code></pre> max_capacity.cs<pre><code>[class]{max_capacity}-[func]{MaxCapacity}\n</code></pre> max_capacity.go<pre><code>[class]{}-[func]{maxCapacity}\n</code></pre> max_capacity.swift<pre><code>[class]{}-[func]{maxCapacity}\n</code></pre> max_capacity.js<pre><code>[class]{}-[func]{maxCapacity}\n</code></pre> max_capacity.ts<pre><code>[class]{}-[func]{maxCapacity}\n</code></pre> max_capacity.dart<pre><code>[class]{}-[func]{maxCapacity}\n</code></pre> max_capacity.rs<pre><code>[class]{}-[func]{max_capacity}\n</code></pre> max_capacity.c<pre><code>[class]{}-[func]{maxCapacity}\n</code></pre> max_capacity.kt<pre><code>[class]{}-[func]{maxCapacity}\n</code></pre> max_capacity.rb<pre><code>[class]{}-[func]{max_capacity}\n</code></pre>","path":["第 15 章 &nbsp; 貪欲法","15.3 &nbsp; 最大容量問題"],"tags":[]},{"location":"chapter_greedy/max_capacity_problem/#3","level":3,"title":"3.   正しさの証明","text":"<p>貪欲法が列挙よりも高速である理由は、各ラウンドの貪欲選択が一部の状態を「スキップ」するからです。</p> <p>例えば、\\(i\\) が短い仕切りで \\(j\\) が高い仕切りである状態 \\(cap[i, j]\\) の下で、短い仕切り \\(i\\) を貪欲に1ステップ内側に移動すると、下の図に示す「スキップされた」状態につながります。これは、これらの状態の容量を後で検証できないことを意味します。</p> \\[ cap[i, i+1], cap[i, i+2], \\dots, cap[i, j-2], cap[i, j-1] \\] <p></p> <p> 図 15-12   短い仕切りの移動によってスキップされる状態 </p> <p>観察すると、これらのスキップされた状態は実際には高い仕切り \\(j\\) が内側に移動したすべての状態**です。高い仕切りを内側に移動すると容量が確実に減少することをすでに証明しました。したがって、スキップされた状態は最適解である可能性がなく、**それらをスキップしても最適解を見逃すことはありません。</p> <p>分析により、短い仕切りを移動する操作は「安全」であり、貪欲戦略が効果的であることが示されます。</p>","path":["第 15 章 &nbsp; 貪欲法","15.3 &nbsp; 最大容量問題"],"tags":[]},{"location":"chapter_greedy/max_product_cutting_problem/","level":1,"title":"15.4   最大積切断問題","text":"<p>Question</p> <p>正の整数 \\(n\\) が与えられたとき、それを合計が \\(n\\) になる少なくとも2つの正の整数に分割し、これらの整数の最大積を求めてください。下の図に示すとおりです。</p> <p></p> <p> 図 15-13   最大積切断問題の定義 </p> <p>\\(n\\) を \\(m\\) 個の整数因子に分割すると仮定し、\\(i\\) 番目の因子を \\(n_i\\) と表記すると、</p> \\[ n = \\sum_{i=1}^{m}n_i \\] <p>この問題の目標は、すべての整数因子の最大積を見つけることです。すなわち、</p> \\[ \\max(\\prod_{i=1}^{m}n_i) \\] <p>考慮すべき点：分割数 \\(m\\) はどの程度大きくすべきか、各 \\(n_i\\) は何であるべきか？</p>","path":["第 15 章 &nbsp; 貪欲法","15.4 &nbsp; 最大積切断問題"],"tags":[]},{"location":"chapter_greedy/max_product_cutting_problem/#1","level":3,"title":"1.   貪欲戦略の決定","text":"<p>経験的に、2つの整数の積は多くの場合その和よりも大きくなります。\\(n\\) から因子 \\(2\\) を分割すると仮定すると、その積は \\(2(n-2)\\) です。この積を \\(n\\) と比較します：</p> \\[ \\begin{aligned} 2(n-2) &amp; \\geq n \\newline 2n - n - 4 &amp; \\geq 0 \\newline n &amp; \\geq 4 \\end{aligned} \\] <p>下の図に示すように、\\(n \\geq 4\\) のとき、\\(2\\) を分割すると積が増加します。これは4以上の整数を分割すべきであることを示しています。</p> <p>貪欲戦略1：分割スキームが \\(\\geq 4\\) の因子を含む場合、それらはさらに分割されるべきです。最終的な分割は因子 \\(1\\)、\\(2\\)、\\(3\\) のみを含むべきです。</p> <p></p> <p> 図 15-14   分割による積の増加 </p> <p>次に、どの因子が最適かを考慮します。因子 \\(1\\)、\\(2\\)、\\(3\\) の中で、明らかに \\(1\\) が最悪です。\\(1 \\times (n-1) &lt; n\\) が常に成り立つため、\\(1\\) を分割すると実際に積が減少します。</p> <p>下の図に示すように、\\(n = 6\\) のとき、\\(3 \\times 3 &gt; 2 \\times 2 \\times 2\\) です。これは \\(3\\) を分割する方が \\(2\\) を分割するよりも良いことを意味します。</p> <p>貪欲戦略2：分割スキームには最大で2つの \\(2\\) があるべきです。3つの \\(2\\) は常に2つの \\(3\\) に置き換えてより高い積を得ることができるからです。</p> <p></p> <p> 図 15-15   最適な分割因子 </p> <p>上記から、以下の貪欲戦略を導出できます。</p> <ol> <li>入力整数 \\(n\\) について、余りが \\(0\\)、\\(1\\)、または \\(2\\) になるまで因子 \\(3\\) を継続的に分割します。</li> <li>余りが \\(0\\) の場合、\\(n\\) が \\(3\\) の倍数であることを意味するため、それ以上の行動は取りません。</li> <li>余りが \\(2\\) の場合、さらに分割を続けず、そのまま保持します。</li> <li>余りが \\(1\\) の場合、\\(2 \\times 2 &gt; 1 \\times 3\\) であるため、最後の \\(3\\) を \\(2\\) に置き換えるべきです。</li> </ol>","path":["第 15 章 &nbsp; 貪欲法","15.4 &nbsp; 最大積切断問題"],"tags":[]},{"location":"chapter_greedy/max_product_cutting_problem/#2","level":3,"title":"2.   コード実装","text":"<p>下の図に示すように、整数を分割するためにループを使用する必要はなく、床除算演算を使用して \\(3\\) の数 \\(a\\) を取得し、剰余演算を使用して余り \\(b\\) を取得できます。したがって：</p> \\[ n = 3a + b \\] <p>\\(n \\leq 3\\) の境界ケースでは、\\(1\\) を分割する必要があり、積は \\(1 \\times (n - 1)\\) であることに注意してください。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby max_product_cutting.py<pre><code>def max_product_cutting(n: int) -&gt; int:\n    \"\"\"切断の最大積：貪欲法\"\"\"\n    # n &lt;= 3 の場合、1 を切り出す必要がある\n    if n &lt;= 3:\n        return 1 * (n - 1)\n    # 貪欲的に 3 を切り出す、a は 3 の個数、b は余り\n    a, b = n // 3, n % 3\n    if b == 1:\n        # 余りが 1 の場合、1 * 3 のペアを 2 * 2 に変換\n        return int(math.pow(3, a - 1)) * 2 * 2\n    if b == 2:\n        # 余りが 2 の場合、何もしない\n        return int(math.pow(3, a)) * 2\n    # 余りが 0 の場合、何もしない\n    return int(math.pow(3, a))\n</code></pre> max_product_cutting.cpp<pre><code>/* 最大積切断：貪欲法 */\nint maxProductCutting(int n) {\n    // n &lt;= 3 の場合、1 を切り出す必要がある\n    if (n &lt;= 3) {\n        return 1 * (n - 1);\n    }\n    // 貪欲に 3 を切り出す。a は 3 の個数、b は余り\n    int a = n / 3;\n    int b = n % 3;\n    if (b == 1) {\n        // 余りが 1 の場合、1 * 3 のペアを 2 * 2 に変換\n        return (int)pow(3, a - 1) * 2 * 2;\n    }\n    if (b == 2) {\n        // 余りが 2 の場合、何もしない\n        return (int)pow(3, a) * 2;\n    }\n    // 余りが 0 の場合、何もしない\n    return (int)pow(3, a);\n}\n</code></pre> max_product_cutting.java<pre><code>/* 最大積切断：貪欲法 */\nint maxProductCutting(int n) {\n    // n &lt;= 3 の場合、1 を切り出す必要がある\n    if (n &lt;= 3) {\n        return 1 * (n - 1);\n    }\n    // 貪欲に 3 を切り出す。a は 3 の個数、b は余り\n    int a = n / 3;\n    int b = n % 3;\n    if (b == 1) {\n        // 余りが 1 の場合、1 * 3 のペアを 2 * 2 に変換\n        return (int) Math.pow(3, a - 1) * 2 * 2;\n    }\n    if (b == 2) {\n        // 余りが 2 の場合、何もしない\n        return (int) Math.pow(3, a) * 2;\n    }\n    // 余りが 0 の場合、何もしない\n    return (int) Math.pow(3, a);\n}\n</code></pre> max_product_cutting.cs<pre><code>[class]{max_product_cutting}-[func]{MaxProductCutting}\n</code></pre> max_product_cutting.go<pre><code>[class]{}-[func]{maxProductCutting}\n</code></pre> max_product_cutting.swift<pre><code>[class]{}-[func]{maxProductCutting}\n</code></pre> max_product_cutting.js<pre><code>[class]{}-[func]{maxProductCutting}\n</code></pre> max_product_cutting.ts<pre><code>[class]{}-[func]{maxProductCutting}\n</code></pre> max_product_cutting.dart<pre><code>[class]{}-[func]{maxProductCutting}\n</code></pre> max_product_cutting.rs<pre><code>[class]{}-[func]{max_product_cutting}\n</code></pre> max_product_cutting.c<pre><code>[class]{}-[func]{maxProductCutting}\n</code></pre> max_product_cutting.kt<pre><code>[class]{}-[func]{maxProductCutting}\n</code></pre> max_product_cutting.rb<pre><code>[class]{}-[func]{max_product_cutting}\n</code></pre> <p></p> <p> 図 15-16   切断後の最大積の計算方法 </p> <p>時間計算量はプログラミング言語のべき乗演算の実装に依存します。Pythonでは、よく使用されるべき乗計算関数は3種類あります：</p> <ul> <li>演算子 <code>**</code> と関数 <code>pow()</code> の両方の時間計算量は \\(O(\\log⁡ a)\\) です。</li> <li><code>math.pow()</code> 関数は内部でC言語ライブラリの <code>pow()</code> 関数を呼び出し、浮動小数点べき乗を実行し、時間計算量は \\(O(1)\\) です。</li> </ul> <p>変数 \\(a\\) と \\(b\\) は一定サイズの追加スペースを使用するため、空間計算量は \\(O(1)\\) です。</p>","path":["第 15 章 &nbsp; 貪欲法","15.4 &nbsp; 最大積切断問題"],"tags":[]},{"location":"chapter_greedy/max_product_cutting_problem/#3","level":3,"title":"3.   正しさの証明","text":"<p>背理法を使用し、\\(n \\geq 3\\) のケースのみを分析します。</p> <ol> <li>すべての因子 \\(\\leq 3\\)：最適分割スキームが因子 \\(x \\geq 4\\) を含むと仮定すると、それを確実に \\(2(x-2)\\) にさらに分割でき、より大きな積を得られます。これは仮定と矛盾します。</li> <li>分割スキームに \\(1\\) が含まれない：最適分割スキームが因子 \\(1\\) を含むと仮定すると、それを確実に別の因子と結合してより大きな積を得られます。これは仮定と矛盾します。</li> <li>分割スキームには最大で2つの \\(2\\) が含まれる：最適分割スキームが3つの \\(2\\) を含むと仮定すると、それらを確実に2つの \\(3\\) に置き換えて、より高い積を達成できます。これは仮定と矛盾します。</li> </ol>","path":["第 15 章 &nbsp; 貪欲法","15.4 &nbsp; 最大積切断問題"],"tags":[]},{"location":"chapter_greedy/summary/","level":1,"title":"15.5   まとめ","text":"<ul> <li>貪欲アルゴリズムは最適化問題を解決するためによく使用され、原理は各決定段階で局所的に最適な決定を行い、グローバルに最適な解を達成することです。</li> <li>貪欲アルゴリズムは貪欲な選択を次々と反復的に行い、各ラウンドで問題をより小さな部分問題に変換し、問題が解決されるまで続けます。</li> <li>貪欲アルゴリズムは実装が簡単なだけでなく、問題解決効率も高いです。動的プログラミングと比較して、貪欲アルゴリズムは一般的により低い時間計算量を持ちます。</li> <li>コイン交換問題において、貪欲アルゴリズムは特定のコインの組み合わせに対して最適解を保証できますが、他の組み合わせでは貪欲アルゴリズムが非常に悪い解を見つける可能性があります。</li> <li>貪欲アルゴリズム解法に適した問題は2つの主要な性質を持ちます：貪欲選択性と最適部分構造。貪欲選択性は貪欲戦略の効果を表します。</li> <li>一部の複雑な問題では、貪欲選択性を証明することは簡単ではありません。逆に、無効性を証明することはしばしばより容易で、コイン交換問題などがその例です。</li> <li>貪欲問題の解決は主に3つのステップから構成されます：問題分析、貪欲戦略の決定、正しさの証明。このうち、貪欲戦略の決定が重要なステップであり、正しさの証明がしばしば挑戦となります。</li> <li>分数ナップサック問題は0-1ナップサック問題に基づいてアイテムの一部の選択を可能にし、したがって貪欲アルゴリズムを使用して解決できます。貪欲戦略の正しさは背理法によって証明できます。</li> <li>最大容量問題は全探索法で解決でき、時間計算量は \\(O(n^2)\\) です。貪欲戦略を設計することで、各ラウンドで短い板を内側に移動し、時間計算量を \\(O(n)\\) に最適化します。</li> <li>切断後の最大積問題において、2つの貪欲戦略を導出します：\\(\\geq 4\\) の整数は継続的に切断されるべきで、最適な切断因子は \\(3\\) です。コードにはべき乗演算が含まれ、時間計算量はべき乗演算の実装方法に依存し、一般的に \\(O(1)\\) または \\(O(\\log n)\\) です。</li> </ul>","path":["第 15 章 &nbsp; 貪欲法","15.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_hashing/","level":1,"title":"第 6 章   ハッシュ表","text":"<p>Abstract</p> <p>コンピューティングの世界において、ハッシュ表は賢い司書のようなものです。</p> <p>インデックス番号の計算方法を理解し、目的の本を迅速に取得することを可能にします。</p>","path":["第 6 章 &nbsp; ハッシュ表"],"tags":[]},{"location":"chapter_hashing/#_1","level":2,"title":"章の内容","text":"<ul> <li>6.1   ハッシュ表</li> <li>6.2   ハッシュ衝突</li> <li>6.3   ハッシュアルゴリズム</li> <li>6.4   まとめ</li> </ul>","path":["第 6 章 &nbsp; ハッシュ表"],"tags":[]},{"location":"chapter_hashing/hash_algorithm/","level":1,"title":"6.3   ハッシュアルゴリズム","text":"<p>前の2つの節では、ハッシュ表の動作原理とハッシュ衝突を処理する方法を紹介しました。しかし、オープンアドレス法と連鎖法はどちらも**衝突が発生した際にハッシュ表が正常に機能することのみを保証でき、ハッシュ衝突の発生頻度を減らすことはできません**。</p> <p>ハッシュ衝突があまりにも頻繁に発生すると、ハッシュ表の性能は劇的に悪化します。下図に示すように、連鎖法ハッシュ表では、理想的なケースではキー値ペアがバケット間に均等に分散され、最適なクエリ効率を実現します。最悪のケースでは、すべてのキー値ペアが同じバケットに格納され、時間計算量が\\(O(n)\\)に悪化します。</p> <p></p> <p> 図 6-8   ハッシュ衝突の理想的および最悪のケース </p> <p>キー値ペアの分布はハッシュ関数によって決定されます。ハッシュ関数の計算ステップを思い出すと、まずハッシュ値を計算し、次に配列長で剰余を取ります：</p> <pre><code>index = hash(key) % capacity\n</code></pre> <p>上記の式を観察すると、ハッシュ表の容量<code>capacity</code>が固定されている場合、ハッシュアルゴリズム<code>hash()</code>が出力値を決定し、それによってハッシュ表におけるキー値ペアの分布を決定します。</p> <p>これは、ハッシュ衝突の確率を減らすために、ハッシュアルゴリズム<code>hash()</code>の設計に焦点を当てるべきであることを意味します。</p>","path":["第 6 章 &nbsp; ハッシュ表","6.3 &nbsp; ハッシュアルゴリズム"],"tags":[]},{"location":"chapter_hashing/hash_algorithm/#631","level":2,"title":"6.3.1   ハッシュアルゴリズムの目標","text":"<p>「高速で安定した」ハッシュ表データ構造を実現するために、ハッシュアルゴリズムは以下の特性を持つべきです：</p> <ul> <li>決定性: 同じ入力に対して、ハッシュアルゴリズムは常に同じ出力を生成するべきです。そうでなければハッシュ表は信頼できません。</li> <li>高効率: ハッシュ値を計算するプロセスは十分に高速である必要があります。計算オーバーヘッドが小さいほど、ハッシュ表はより実用的になります。</li> <li>均等分散: ハッシュアルゴリズムはキー値ペアがハッシュ表に均等に分散されることを保証するべきです。分散が均等であるほど、ハッシュ衝突の確率は低くなります。</li> </ul> <p>実際、ハッシュアルゴリズムはハッシュ表の実装だけでなく、他の分野でも広く応用されています。</p> <ul> <li>パスワード保存: ユーザーパスワードのセキュリティを保護するために、システムは通常平文パスワードを保存せず、パスワードのハッシュ値を保存します。ユーザーがパスワードを入力すると、システムは入力のハッシュ値を計算し、保存されているハッシュ値と比較します。一致すれば、パスワードは正しいと見なされます。</li> <li>データ整合性チェック: データ送信者はデータのハッシュ値を計算して一緒に送信できます。受信者は受信したデータのハッシュ値を再計算し、受信したハッシュ値と比較できます。一致すれば、データは完全であると見なされます。</li> </ul> <p>暗号化アプリケーションでは、ハッシュ値から元のパスワードを推測するなどの逆行分析を防ぐために、ハッシュアルゴリズムはより高いレベルのセキュリティ機能が必要です。</p> <ul> <li>一方向性: ハッシュ値から入力データに関する情報を推測することは不可能であるべきです。</li> <li>衝突耐性: 同じハッシュ値を生成する2つの異なる入力を見つけることは極めて困難であるべきです。</li> <li>雪崩効果: 入力の小さな変更は、出力に大きく予測不可能な変化をもたらすべきです。</li> </ul> <p>**「均等分散」と「衝突耐性」は2つの別々の概念**であることに注意してください。均等分散を満たしても、必ずしも衝突耐性があるとは限りません。例えば、ランダムな入力<code>key</code>の下で、ハッシュ関数<code>key % 100</code>は均等に分散された出力を生成できます。しかし、このハッシュアルゴリズムは過度にシンプルで、下二桁が同じすべての<code>key</code>は同じ出力を持つため、ハッシュ値から使用可能な<code>key</code>を簡単に推測でき、パスワードを破ることができます。</p>","path":["第 6 章 &nbsp; ハッシュ表","6.3 &nbsp; ハッシュアルゴリズム"],"tags":[]},{"location":"chapter_hashing/hash_algorithm/#632","level":2,"title":"6.3.2   ハッシュアルゴリズムの設計","text":"<p>ハッシュアルゴリズムの設計は多くの要因を考慮する必要がある複雑な問題です。しかし、要求が少ない一部のシナリオでは、いくつかの簡単なハッシュアルゴリズムを設計することもできます。</p> <ul> <li>加算ハッシュ: 入力の各文字のASCIIコードを合計し、合計をハッシュ値として使用します。</li> <li>乗算ハッシュ: 乗算の非相関性を利用し、各ラウンドで定数を乗算し、各文字のASCIIコードをハッシュ値に累積します。</li> <li>XORハッシュ: 入力データの各要素をXORすることでハッシュ値を累積します。</li> <li>回転ハッシュ: 各文字のASCIIコードをハッシュ値に累積し、各累積前にハッシュ値に回転操作を実行します。</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby simple_hash.py<pre><code>def add_hash(key: str) -&gt; int:\n    \"\"\"加法ハッシュ\"\"\"\n    hash = 0\n    modulus = 1000000007\n    for c in key:\n        hash += ord(c)\n    return hash % modulus\n\ndef mul_hash(key: str) -&gt; int:\n    \"\"\"乗法ハッシュ\"\"\"\n    hash = 0\n    modulus = 1000000007\n    for c in key:\n        hash = 31 * hash + ord(c)\n    return hash % modulus\n\ndef xor_hash(key: str) -&gt; int:\n    \"\"\"XORハッシュ\"\"\"\n    hash = 0\n    modulus = 1000000007\n    for c in key:\n        hash ^= ord(c)\n    return hash % modulus\n\ndef rot_hash(key: str) -&gt; int:\n    \"\"\"回転ハッシュ\"\"\"\n    hash = 0\n    modulus = 1000000007\n    for c in key:\n        hash = (hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ ord(c)\n    return hash % modulus\n</code></pre> simple_hash.cpp<pre><code>/* 加算ハッシュ */\nint addHash(string key) {\n    long long hash = 0;\n    const int MODULUS = 1000000007;\n    for (unsigned char c : key) {\n        hash = (hash + (int)c) % MODULUS;\n    }\n    return (int)hash;\n}\n\n/* 乗算ハッシュ */\nint mulHash(string key) {\n    long long hash = 0;\n    const int MODULUS = 1000000007;\n    for (unsigned char c : key) {\n        hash = (31 * hash + (int)c) % MODULUS;\n    }\n    return (int)hash;\n}\n\n/* XORハッシュ */\nint xorHash(string key) {\n    int hash = 0;\n    const int MODULUS = 1000000007;\n    for (unsigned char c : key) {\n        hash ^= (int)c;\n    }\n    return hash &amp; MODULUS;\n}\n\n/* 回転ハッシュ */\nint rotHash(string key) {\n    long long hash = 0;\n    const int MODULUS = 1000000007;\n    for (unsigned char c : key) {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ (int)c) % MODULUS;\n    }\n    return (int)hash;\n}\n</code></pre> simple_hash.java<pre><code>/* 加算ハッシュ */\nint addHash(String key) {\n    long hash = 0;\n    final int MODULUS = 1000000007;\n    for (char c : key.toCharArray()) {\n        hash = (hash + (int) c) % MODULUS;\n    }\n    return (int) hash;\n}\n\n/* 乗算ハッシュ */\nint mulHash(String key) {\n    long hash = 0;\n    final int MODULUS = 1000000007;\n    for (char c : key.toCharArray()) {\n        hash = (31 * hash + (int) c) % MODULUS;\n    }\n    return (int) hash;\n}\n\n/* XORハッシュ */\nint xorHash(String key) {\n    int hash = 0;\n    final int MODULUS = 1000000007;\n    for (char c : key.toCharArray()) {\n        hash ^= (int) c;\n    }\n    return hash &amp; MODULUS;\n}\n\n/* 回転ハッシュ */\nint rotHash(String key) {\n    long hash = 0;\n    final int MODULUS = 1000000007;\n    for (char c : key.toCharArray()) {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ (int) c) % MODULUS;\n    }\n    return (int) hash;\n}\n</code></pre> simple_hash.cs<pre><code>[class]{simple_hash}-[func]{AddHash}\n\n[class]{simple_hash}-[func]{MulHash}\n\n[class]{simple_hash}-[func]{XorHash}\n\n[class]{simple_hash}-[func]{RotHash}\n</code></pre> simple_hash.go<pre><code>[class]{}-[func]{addHash}\n\n[class]{}-[func]{mulHash}\n\n[class]{}-[func]{xorHash}\n\n[class]{}-[func]{rotHash}\n</code></pre> simple_hash.swift<pre><code>[class]{}-[func]{addHash}\n\n[class]{}-[func]{mulHash}\n\n[class]{}-[func]{xorHash}\n\n[class]{}-[func]{rotHash}\n</code></pre> simple_hash.js<pre><code>[class]{}-[func]{addHash}\n\n[class]{}-[func]{mulHash}\n\n[class]{}-[func]{xorHash}\n\n[class]{}-[func]{rotHash}\n</code></pre> simple_hash.ts<pre><code>[class]{}-[func]{addHash}\n\n[class]{}-[func]{mulHash}\n\n[class]{}-[func]{xorHash}\n\n[class]{}-[func]{rotHash}\n</code></pre> simple_hash.dart<pre><code>[class]{}-[func]{addHash}\n\n[class]{}-[func]{mulHash}\n\n[class]{}-[func]{xorHash}\n\n[class]{}-[func]{rotHash}\n</code></pre> simple_hash.rs<pre><code>[class]{}-[func]{add_hash}\n\n[class]{}-[func]{mul_hash}\n\n[class]{}-[func]{xor_hash}\n\n[class]{}-[func]{rot_hash}\n</code></pre> simple_hash.c<pre><code>[class]{}-[func]{addHash}\n\n[class]{}-[func]{mulHash}\n\n[class]{}-[func]{xorHash}\n\n[class]{}-[func]{rotHash}\n</code></pre> simple_hash.kt<pre><code>[class]{}-[func]{addHash}\n\n[class]{}-[func]{mulHash}\n\n[class]{}-[func]{xorHash}\n\n[class]{}-[func]{rotHash}\n</code></pre> simple_hash.rb<pre><code>[class]{}-[func]{add_hash}\n\n[class]{}-[func]{mul_hash}\n\n[class]{}-[func]{xor_hash}\n\n[class]{}-[func]{rot_hash}\n</code></pre> <p>各ハッシュアルゴリズムの最後のステップが大きな素数\\(1000000007\\)の剰余を取ることで、ハッシュ値が適切な範囲内にあることを保証していることが観察されます。なぜ素数の剰余を取ることが強調されるのか、または合成数の剰余を取ることの欠点は何かを考える価値があります。これは興味深い質問です。</p> <p>結論として：大きな素数を剰余として使用することで、ハッシュ値の均等分散を最大化できます。素数は他の数と共通因子を持たないため、剰余演算によって引き起こされる周期的パターンを減らし、ハッシュ衝突を回避できます。</p> <p>例えば、合成数\\(9\\)を剰余として選択するとします。これは\\(3\\)で割り切れるため、\\(3\\)で割り切れるすべての<code>key</code>はハッシュ値\\(0\\)、\\(3\\)、\\(6\\)にマッピングされます。</p> \\[ \\begin{aligned} \\text{modulus} &amp; = 9 \\newline \\text{key} &amp; = \\{ 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, \\dots \\} \\newline \\text{hash} &amp; = \\{ 0, 3, 6, 0, 3, 6, 0, 3, 6, 0, 3, 6,\\dots \\} \\end{aligned} \\] <p>入力<code>key</code>がたまたまこの種の等差数列分布を持つ場合、ハッシュ値がクラスターし、ハッシュ衝突を悪化させます。今度は<code>modulus</code>を素数\\(13\\)に置き換えるとします。<code>key</code>と<code>modulus</code>の間に共通因子がないため、出力ハッシュ値の均等性が大幅に改善されます。</p> \\[ \\begin{aligned} \\text{modulus} &amp; = 13 \\newline \\text{key} &amp; = \\{ 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, \\dots \\} \\newline \\text{hash} &amp; = \\{ 0, 3, 6, 9, 12, 2, 5, 8, 11, 1, 4, 7, \\dots \\} \\end{aligned} \\] <p><code>key</code>がランダムで均等に分散されることが保証されている場合、剰余として素数または合成数を選択しても、両方とも均等に分散されたハッシュ値を生成できることは注目に値します。しかし、<code>key</code>の分布にある種の周期性がある場合、合成数の剰余はクラスタリングを引き起こしやすくなります。</p> <p>要約すると、通常は素数を剰余として選択し、この素数は周期的パターンを可能な限り排除し、ハッシュアルゴリズムの堅牢性を向上させるために十分大きくある必要があります。</p>","path":["第 6 章 &nbsp; ハッシュ表","6.3 &nbsp; ハッシュアルゴリズム"],"tags":[]},{"location":"chapter_hashing/hash_algorithm/#633","level":2,"title":"6.3.3   一般的なハッシュアルゴリズム","text":"<p>上記で言及した簡単なハッシュアルゴリズムはかなり「脆弱」で、ハッシュアルゴリズムの設計目標から程遠いことは難しくありません。例えば、加算とXORは交換法則に従うため、加算ハッシュとXORハッシュは同じ内容だが順序が異なる文字列を区別できず、ハッシュ衝突を悪化させ、セキュリティ問題を引き起こす可能性があります。</p> <p>実際には、通常MD5、SHA-1、SHA-2、SHA-3などの標準ハッシュアルゴリズムを使用します。これらは任意の長さの入力データを固定長のハッシュ値にマッピングできます。</p> <p>過去1世紀にわたって、ハッシュアルゴリズムは継続的なアップグレードと最適化のプロセスにありました。一部の研究者はハッシュアルゴリズムの性能向上に努め、ハッカーを含む他の人々はハッシュアルゴリズムのセキュリティ問題を見つけることに専念しています。以下の表は、実用的なアプリケーションで一般的に使用されるハッシュアルゴリズムを示しています。</p> <ul> <li>MD5とSHA-1は複数回攻撃に成功しており、さまざまなセキュリティアプリケーションで放棄されています。</li> <li>SHA-2シリーズ、特にSHA-256は、現在最も安全なハッシュアルゴリズムの1つで、成功した攻撃は報告されておらず、さまざまなセキュリティアプリケーションとプロトコルで一般的に使用されています。</li> <li>SHA-3はSHA-2と比較して実装コストが低く、計算効率が高いですが、現在の使用範囲はSHA-2シリーズほど広範囲ではありません。</li> </ul> <p> 表 6-2   一般的なハッシュアルゴリズム </p> MD5 SHA-1 SHA-2 SHA-3 リリース年 1992 1995 2002 2008 出力長 128 bit 160 bit 256/512 bit 224/256/384/512 bit ハッシュ衝突 頻繁 頻繁 まれ まれ セキュリティレベル 低、攻撃に成功している 低、攻撃に成功している 高 高 アプリケーション 放棄、データ整合性チェックにまだ使用 放棄 暗号通貨取引検証、デジタル署名など SHA-2の代替として使用可能","path":["第 6 章 &nbsp; ハッシュ表","6.3 &nbsp; ハッシュアルゴリズム"],"tags":[]},{"location":"chapter_hashing/hash_algorithm/#_1","level":1,"title":"データ構造におけるハッシュ値","text":"<p>ハッシュ表のキーは整数、小数、文字列などのさまざまなデータ型にできることを知っています。プログラミング言語は通常、これらのデータ型に対して組み込みのハッシュアルゴリズムを提供し、ハッシュ表のバケットインデックスを計算します。Pythonを例に取ると、<code>hash()</code>関数を使用してさまざまなデータ型のハッシュ値を計算できます。</p> <ul> <li>整数とブール値のハッシュ値は、それら自身の値です。</li> <li>浮動小数点数と文字列のハッシュ値の計算はより複雑で、興味のある読者は自分で研究することをお勧めします。</li> <li>タプルのハッシュ値は、その各要素のハッシュ値の組み合わせで、単一のハッシュ値になります。</li> <li>オブジェクトのハッシュ値は、そのメモリアドレスに基づいて生成されます。オブジェクトのハッシュメソッドをオーバーライドすることで、内容に基づいてハッシュ値を生成できます。</li> </ul> <p>Tip</p> <p>異なるプログラミング言語における組み込みハッシュ値計算関数の定義と方法は異なることに注意してください。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlin built_in_hash.py<pre><code>num = 3\nhash_num = hash(num)\n# 整数3のハッシュ値は3\n\nbol = True\nhash_bol = hash(bol)\n# ブール値Trueのハッシュ値は1\n\ndec = 3.14159\nhash_dec = hash(dec)\n# 小数3.14159のハッシュ値は326484311674566659\n\nstr = \"Hello 算法\"\nhash_str = hash(str)\n# 文字列\"Hello 算法\"のハッシュ値は4617003410720528961\n\ntup = (12836, \"小哈\")\nhash_tup = hash(tup)\n# タプル(12836, '小哈')のハッシュ値は1029005403108185979\n\nobj = ListNode(0)\nhash_obj = hash(obj)\n# ListNodeオブジェクト0x1058fd810のハッシュ値は274267521\n</code></pre> built_in_hash.cpp<pre><code>int num = 3;\nsize_t hashNum = hash&lt;int&gt;()(num);\n// 整数3のハッシュ値は3\n\nbool bol = true;\nsize_t hashBol = hash&lt;bool&gt;()(bol);\n// ブール値1のハッシュ値は1\n\ndouble dec = 3.14159;\nsize_t hashDec = hash&lt;double&gt;()(dec);\n// 小数3.14159のハッシュ値は4614256650576692846\n\nstring str = \"Hello 算法\";\nsize_t hashStr = hash&lt;string&gt;()(str);\n// 文字列\"Hello 算法\"のハッシュ値は15466937326284535026\n\n// C++では、組み込みstd::hash()は基本データ型のハッシュ値のみを提供\n// 配列とオブジェクトのハッシュ値は別途実装が必要\n</code></pre> built_in_hash.java<pre><code>int num = 3;\nint hashNum = Integer.hashCode(num);\n// 整数3のハッシュ値は3\n\nboolean bol = true;\nint hashBol = Boolean.hashCode(bol);\n// ブール値trueのハッシュ値は1231\n\ndouble dec = 3.14159;\nint hashDec = Double.hashCode(dec);\n// 小数3.14159のハッシュ値は-1340954729\n\nString str = \"Hello 算法\";\nint hashStr = str.hashCode();\n// 文字列\"Hello 算法\"のハッシュ値は-727081396\n\nObject[] arr = { 12836, \"小哈\" };\nint hashTup = Arrays.hashCode(arr);\n// 配列[12836, 小哈]のハッシュ値は1151158\n\nListNode obj = new ListNode(0);\nint hashObj = obj.hashCode();\n// ListNodeオブジェクトutils.ListNode@7dc5e7b4のハッシュ値は2110121908\n</code></pre> built_in_hash.cs<pre><code>int num = 3;\nint hashNum = num.GetHashCode();\n// 整数3のハッシュ値は3;\n\nbool bol = true;\nint hashBol = bol.GetHashCode();\n// ブール値trueのハッシュ値は1;\n\ndouble dec = 3.14159;\nint hashDec = dec.GetHashCode();\n// 小数3.14159のハッシュ値は-1340954729;\n\nstring str = \"Hello 算法\";\nint hashStr = str.GetHashCode();\n// 文字列\"Hello 算法\"のハッシュ値は-586107568;\n\nobject[] arr = [12836, \"小哈\"];\nint hashTup = arr.GetHashCode();\n// 配列[12836, 小哈]のハッシュ値は42931033;\n\nListNode obj = new(0);\nint hashObj = obj.GetHashCode();\n// ListNodeオブジェクト0のハッシュ値は39053774;\n</code></pre> built_in_hash.go<pre><code>// Goには組み込みのハッシュコード関数が提供されていません\n</code></pre> built_in_hash.swift<pre><code>let num = 3\nlet hashNum = num.hashValue\n// 整数3のハッシュ値は9047044699613009734\n\nlet bol = true\nlet hashBol = bol.hashValue\n// ブール値trueのハッシュ値は-4431640247352757451\n\nlet dec = 3.14159\nlet hashDec = dec.hashValue\n// 小数3.14159のハッシュ値は-2465384235396674631\n\nlet str = \"Hello 算法\"\nlet hashStr = str.hashValue\n// 文字列\"Hello 算法\"のハッシュ値は-7850626797806988787\n\nlet arr = [AnyHashable(12836), AnyHashable(\"小哈\")]\nlet hashTup = arr.hashValue\n// 配列[AnyHashable(12836), AnyHashable(\"小哈\")]のハッシュ値は-2308633508154532996\n\nlet obj = ListNode(x: 0)\nlet hashObj = obj.hashValue\n// ListNodeオブジェクトutils.ListNodeのハッシュ値は-2434780518035996159\n</code></pre> built_in_hash.js<pre><code>// JavaScriptには組み込みのハッシュコード関数が提供されていません\n</code></pre> built_in_hash.ts<pre><code>// TypeScriptには組み込みのハッシュコード関数が提供されていません\n</code></pre> built_in_hash.dart<pre><code>int num = 3;\nint hashNum = num.hashCode;\n// 整数3のハッシュ値は34803\n\nbool bol = true;\nint hashBol = bol.hashCode;\n// ブール値trueのハッシュ値は1231\n\ndouble dec = 3.14159;\nint hashDec = dec.hashCode;\n// 小数3.14159のハッシュ値は2570631074981783\n\nString str = \"Hello 算法\";\nint hashStr = str.hashCode;\n// 文字列\"Hello 算法\"のハッシュ値は468167534\n\nList arr = [12836, \"小哈\"];\nint hashArr = arr.hashCode;\n// 配列[12836, 小哈]のハッシュ値は976512528\n\nListNode obj = new ListNode(0);\nint hashObj = obj.hashCode;\n// ListNodeオブジェクトInstance of 'ListNode'のハッシュ値は1033450432\n</code></pre> built_in_hash.rs<pre><code>use std::collections::hash_map::DefaultHasher;\nuse std::hash::{Hash, Hasher};\n\nlet num = 3;\nlet mut num_hasher = DefaultHasher::new();\nnum.hash(&amp;mut num_hasher);\nlet hash_num = num_hasher.finish();\n// 整数3のハッシュ値は568126464209439262\n\nlet bol = true;\nlet mut bol_hasher = DefaultHasher::new();\nbol.hash(&amp;mut bol_hasher);\nlet hash_bol = bol_hasher.finish();\n// ブール値trueのハッシュ値は4952851536318644461\n\nlet dec: f32 = 3.14159;\nlet mut dec_hasher = DefaultHasher::new();\ndec.to_bits().hash(&amp;mut dec_hasher);\nlet hash_dec = dec_hasher.finish();\n// 小数3.14159のハッシュ値は2566941990314602357\n\nlet str = \"Hello 算法\";\nlet mut str_hasher = DefaultHasher::new();\nstr.hash(&amp;mut str_hasher);\nlet hash_str = str_hasher.finish();\n// 文字列\"Hello 算法\"のハッシュ値は16092673739211250988\n\nlet arr = (&amp;12836, &amp;\"小哈\");\nlet mut tup_hasher = DefaultHasher::new();\narr.hash(&amp;mut tup_hasher);\nlet hash_tup = tup_hasher.finish();\n// タプル(12836, \"小哈\")のハッシュ値は1885128010422702749\n\nlet node = ListNode::new(42);\nlet mut hasher = DefaultHasher::new();\nnode.borrow().val.hash(&amp;mut hasher);\nlet hash = hasher.finish();\n// ListNodeオブジェクトRefCell { value: ListNode { val: 42, next: None } }のハッシュ値は15387811073369036852\n</code></pre> built_in_hash.c<pre><code>// Cには組み込みのハッシュコード関数が提供されていません\n</code></pre> built_in_hash.kt<pre><code>\n</code></pre> <p>多くのプログラミング言語では、不変オブジェクトのみがハッシュ表の<code>key</code>として機能できます。リスト（動的配列）を<code>key</code>として使用する場合、リストの内容が変更されると、そのハッシュ値も変更され、ハッシュ表で元の<code>value</code>を見つけることができなくなります。</p> <p>カスタムオブジェクト（連結リストノードなど）のメンバー変数は可変ですが、ハッシュ可能です。これは、オブジェクトのハッシュ値が通常そのメモリアドレスに基づいて生成されるためです。オブジェクトの内容が変更されても、メモリアドレスは同じままなので、ハッシュ値は変更されません。</p> <p>異なるコンソールで出力されるハッシュ値が異なることに気づいたかもしれません。これは、Pythonインタープリターが起動するたびに文字列ハッシュ関数にランダムソルトを追加するためです。このアプローチはHashDoS攻撃を効果的に防ぎ、ハッシュアルゴリズムのセキュリティを向上させます。</p>","path":["第 6 章 &nbsp; ハッシュ表","6.3 &nbsp; ハッシュアルゴリズム"],"tags":[]},{"location":"chapter_hashing/hash_collision/","level":1,"title":"6.2   ハッシュ衝突","text":"<p>前節で述べたように、**ほとんどの場合、ハッシュ関数の入力空間は出力空間よりもはるかに大きい**ため、理論的にはハッシュ衝突は避けられません。例えば、入力空間がすべての整数で、出力空間が配列容量のサイズの場合、複数の整数が必然的に同じバケットインデックスにマッピングされます。</p> <p>ハッシュ衝突は誤ったクエリ結果につながり、ハッシュ表の使いやすさに深刻な影響を与える可能性があります。この問題に対処するために、ハッシュ衝突が発生するたびに、衝突が消えるまでハッシュ表のリサイズを実行します。このアプローチは非常にシンプルで直接的であり、うまく機能します。しかし、テーブルの拡張には大量のデータ移行とハッシュコードの再計算が含まれ、これらは高コストであるため、非常に非効率的に見えます。効率を向上させるために、以下の戦略を採用できます：</p> <ol> <li>**ハッシュ衝突が発生した場合でも、ターゲット要素の検索が適切に機能する**ようにハッシュ表のデータ構造を改善する。</li> <li>深刻な衝突が観察され、必要になる前に、拡張は最後の手段とする。</li> </ol> <p>ハッシュ表の構造を改善する主な方法は2つあります：「連鎖法」と「オープンアドレス法」です。</p>","path":["第 6 章 &nbsp; ハッシュ表","6.2 &nbsp; ハッシュ衝突"],"tags":[]},{"location":"chapter_hashing/hash_collision/#621","level":2,"title":"6.2.1   連鎖法","text":"<p>元のハッシュ表では、各バケットは1つのキー値ペアのみを格納できます。連鎖法は単一の要素を連結リストに変換し、キー値ペアをリストノードとして扱い、衝突するすべてのキー値ペアを同じ連結リストに格納します。下図は連鎖法を使用したハッシュ表の例を示しています。</p> <p></p> <p> 図 6-5   連鎖法ハッシュ表 </p> <p>連鎖法で実装されたハッシュ表の操作は以下のように変更されます：</p> <ul> <li>要素のクエリ: <code>key</code>を入力し、ハッシュ関数を通してバケットインデックスを取得し、連結リストのヘッドノードにアクセスします。連結リストを走査してキーを比較し、ターゲットキー値ペアを見つけます。</li> <li>要素の追加: ハッシュ関数を通して連結リストのヘッドノードにアクセスし、ノード（キー値ペア）をリストに追加します。</li> <li>要素の削除: ハッシュ関数の結果に基づいて連結リストのヘッドにアクセスし、連結リストを走査してターゲットノードを見つけて削除します。</li> </ul> <p>連鎖法には以下の制限があります：</p> <ul> <li>空間使用量の増加: 連結リストにはノードポインタが含まれており、配列よりも多くのメモリ空間を消費します。</li> <li>クエリ効率の低下: 対応する要素を見つけるために連結リストの線形走査が必要になるためです。</li> </ul> <p>以下のコードは連鎖法ハッシュ表の簡単な実装を提供し、注意すべき2つの点があります：</p> <ul> <li>簡単にするために、連結リストの代わりにリスト（動的配列）を使用します。この設定では、ハッシュ表（配列）は複数のバケットを含み、各バケットはリストです。</li> <li>この実装にはハッシュ表のリサイズメソッドが含まれています。負荷率が\\(\\frac{2}{3}\\)を超えると、ハッシュ表を元のサイズの2倍に拡張します。</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby hash_map_chaining.py<pre><code>class HashMapChaining:\n    \"\"\"チェーンアドレス法ハッシュテーブル\"\"\"\n\n    def __init__(self):\n        \"\"\"コンストラクタ\"\"\"\n        self.size = 0  # キー値ペアの数\n        self.capacity = 4  # ハッシュテーブルの容量\n        self.load_thres = 2.0 / 3.0  # 拡張をトリガーする負荷率の閾値\n        self.extend_ratio = 2  # 拡張の倍数\n        self.buckets = [[] for _ in range(self.capacity)]  # バケット配列\n\n    def hash_func(self, key: int) -&gt; int:\n        \"\"\"ハッシュ関数\"\"\"\n        return key % self.capacity\n\n    def load_factor(self) -&gt; float:\n        \"\"\"負荷率\"\"\"\n        return self.size / self.capacity\n\n    def get(self, key: int) -&gt; str | None:\n        \"\"\"照会操作\"\"\"\n        index = self.hash_func(key)\n        bucket = self.buckets[index]\n        # バケットを走査し、キーが見つかれば対応する val を返す\n        for pair in bucket:\n            if pair.key == key:\n                return pair.val\n        # キーが見つからない場合、None を返す\n        return None\n\n    def put(self, key: int, val: str):\n        \"\"\"追加操作\"\"\"\n        # 負荷率が閾値を超えた場合、拡張を実行\n        if self.load_factor() &gt; self.load_thres:\n            self.extend()\n        index = self.hash_func(key)\n        bucket = self.buckets[index]\n        # バケットを走査し、指定されたキーに遭遇した場合、対応する val を更新して返す\n        for pair in bucket:\n            if pair.key == key:\n                pair.val = val\n                return\n        # キーが見つからない場合、キー値ペアを末尾に追加\n        pair = Pair(key, val)\n        bucket.append(pair)\n        self.size += 1\n\n    def remove(self, key: int):\n        \"\"\"削除操作\"\"\"\n        index = self.hash_func(key)\n        bucket = self.buckets[index]\n        # バケットを走査し、その中からキー値ペアを削除\n        for pair in bucket:\n            if pair.key == key:\n                bucket.remove(pair)\n                self.size -= 1\n                break\n\n    def extend(self):\n        \"\"\"ハッシュテーブルを拡張\"\"\"\n        # 元のハッシュテーブルを一時的に保存\n        buckets = self.buckets\n        # 拡張された新しいハッシュテーブルを初期化\n        self.capacity *= self.extend_ratio\n        self.buckets = [[] for _ in range(self.capacity)]\n        self.size = 0\n        # 元のハッシュテーブルから新しいハッシュテーブルにキー値ペアを移動\n        for bucket in buckets:\n            for pair in bucket:\n                self.put(pair.key, pair.val)\n\n    def print(self):\n        \"\"\"ハッシュテーブルを出力\"\"\"\n        for bucket in self.buckets:\n            res = []\n            for pair in bucket:\n                res.append(str(pair.key) + \" -&gt; \" + pair.val)\n            print(res)\n</code></pre> hash_map_chaining.cpp<pre><code>/* チェイン法ハッシュテーブル */\nclass HashMapChaining {\n  private:\n    int size;                       // キー値ペアの数\n    int capacity;                   // ハッシュテーブルの容量\n    double loadThres;               // 拡張をトリガーする負荷率の閾値\n    int extendRatio;                // 拡張倍率\n    vector&lt;vector&lt;Pair *&gt;&gt; buckets; // バケット配列\n\n  public:\n    /* コンストラクタ */\n    HashMapChaining() : size(0), capacity(4), loadThres(2.0 / 3.0), extendRatio(2) {\n        buckets.resize(capacity);\n    }\n\n    /* デストラクタ */\n    ~HashMapChaining() {\n        for (auto &amp;bucket : buckets) {\n            for (Pair *pair : bucket) {\n                // メモリを解放\n                delete pair;\n            }\n        }\n    }\n\n    /* ハッシュ関数 */\n    int hashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* 負荷率 */\n    double loadFactor() {\n        return (double)size / (double)capacity;\n    }\n\n    /* クエリ操作 */\n    string get(int key) {\n        int index = hashFunc(key);\n        // バケットを走査、キーが見つかった場合、対応するvalを返却\n        for (Pair *pair : buckets[index]) {\n            if (pair-&gt;key == key) {\n                return pair-&gt;val;\n            }\n        }\n        // キーが見つからない場合、空文字列を返却\n        return \"\";\n    }\n\n    /* 追加操作 */\n    void put(int key, string val) {\n        // 負荷率が閾値を超えた場合、拡張を実行\n        if (loadFactor() &gt; loadThres) {\n            extend();\n        }\n        int index = hashFunc(key);\n        // バケットを走査、指定キーに遭遇した場合、対応するvalを更新して返却\n        for (Pair *pair : buckets[index]) {\n            if (pair-&gt;key == key) {\n                pair-&gt;val = val;\n                return;\n            }\n        }\n        // キーが見つからない場合、キー値ペアを末尾に追加\n        buckets[index].push_back(new Pair(key, val));\n        size++;\n    }\n\n    /* 削除操作 */\n    void remove(int key) {\n        int index = hashFunc(key);\n        auto &amp;bucket = buckets[index];\n        // バケットを走査、キー値ペアを削除\n        for (int i = 0; i &lt; bucket.size(); i++) {\n            if (bucket[i]-&gt;key == key) {\n                Pair *tmp = bucket[i];\n                bucket.erase(bucket.begin() + i); // キー値ペアを削除\n                delete tmp;                       // メモリを解放\n                size--;\n                return;\n            }\n        }\n    }\n\n    /* ハッシュテーブルを拡張 */\n    void extend() {\n        // 元のハッシュテーブルを一時保存\n        vector&lt;vector&lt;Pair *&gt;&gt; bucketsTmp = buckets;\n        // 拡張された新しいハッシュテーブルを初期化\n        capacity *= extendRatio;\n        buckets.clear();\n        buckets.resize(capacity);\n        size = 0;\n        // 元のハッシュテーブルから新しいハッシュテーブルにキー値ペアを移動\n        for (auto &amp;bucket : bucketsTmp) {\n            for (Pair *pair : bucket) {\n                put(pair-&gt;key, pair-&gt;val);\n                // メモリを解放\n                delete pair;\n            }\n        }\n    }\n\n    /* ハッシュテーブルを印刷 */\n    void print() {\n        for (auto &amp;bucket : buckets) {\n            cout &lt;&lt; \"[\";\n            for (Pair *pair : bucket) {\n                cout &lt;&lt; pair-&gt;key &lt;&lt; \" -&gt; \" &lt;&lt; pair-&gt;val &lt;&lt; \", \";\n            }\n            cout &lt;&lt; \"]\\n\";\n        }\n    }\n};\n</code></pre> hash_map_chaining.java<pre><code>/* チェイン法ハッシュテーブル */\nclass HashMapChaining {\n    int size; // キー値ペアの数\n    int capacity; // ハッシュテーブルの容量\n    double loadThres; // 拡張をトリガーする負荷率の閾値\n    int extendRatio; // 拡張倍率\n    List&lt;List&lt;Pair&gt;&gt; buckets; // バケット配列\n\n    /* コンストラクタ */\n    public HashMapChaining() {\n        size = 0;\n        capacity = 4;\n        loadThres = 2.0 / 3.0;\n        extendRatio = 2;\n        buckets = new ArrayList&lt;&gt;(capacity);\n        for (int i = 0; i &lt; capacity; i++) {\n            buckets.add(new ArrayList&lt;&gt;());\n        }\n    }\n\n    /* ハッシュ関数 */\n    int hashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* 負荷率 */\n    double loadFactor() {\n        return (double) size / capacity;\n    }\n\n    /* クエリ操作 */\n    String get(int key) {\n        int index = hashFunc(key);\n        List&lt;Pair&gt; bucket = buckets.get(index);\n        // バケットを走査、キーが見つかった場合対応するvalを返す\n        for (Pair pair : bucket) {\n            if (pair.key == key) {\n                return pair.val;\n            }\n        }\n        // キーが見つからない場合、nullを返す\n        return null;\n    }\n\n    /* 追加操作 */\n    void put(int key, String val) {\n        // 負荷率が閾値を超えた場合、拡張を実行\n        if (loadFactor() &gt; loadThres) {\n            extend();\n        }\n        int index = hashFunc(key);\n        List&lt;Pair&gt; bucket = buckets.get(index);\n        // バケットを走査、指定したキーに遭遇した場合、対応するvalを更新して戻る\n        for (Pair pair : bucket) {\n            if (pair.key == key) {\n                pair.val = val;\n                return;\n            }\n        }\n        // キーが見つからない場合、キー値ペアを末尾に追加\n        Pair pair = new Pair(key, val);\n        bucket.add(pair);\n        size++;\n    }\n\n    /* 削除操作 */\n    void remove(int key) {\n        int index = hashFunc(key);\n        List&lt;Pair&gt; bucket = buckets.get(index);\n        // バケットを走査、その中からキー値ペアを削除\n        for (Pair pair : bucket) {\n            if (pair.key == key) {\n                bucket.remove(pair);\n                size--;\n                break;\n            }\n        }\n    }\n\n    /* ハッシュテーブルを拡張 */\n    void extend() {\n        // 元のハッシュテーブルを一時的に保存\n        List&lt;List&lt;Pair&gt;&gt; bucketsTmp = buckets;\n        // 拡張された新しいハッシュテーブルを初期化\n        capacity *= extendRatio;\n        buckets = new ArrayList&lt;&gt;(capacity);\n        for (int i = 0; i &lt; capacity; i++) {\n            buckets.add(new ArrayList&lt;&gt;());\n        }\n        size = 0;\n        // 元のハッシュテーブルから新しいハッシュテーブルにキー値ペアを移動\n        for (List&lt;Pair&gt; bucket : bucketsTmp) {\n            for (Pair pair : bucket) {\n                put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* ハッシュテーブルを印刷 */\n    void print() {\n        for (List&lt;Pair&gt; bucket : buckets) {\n            List&lt;String&gt; res = new ArrayList&lt;&gt;();\n            for (Pair pair : bucket) {\n                res.add(pair.key + \" -&gt; \" + pair.val);\n            }\n            System.out.println(res);\n        }\n    }\n}\n</code></pre> hash_map_chaining.cs<pre><code>[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.go<pre><code>[class]{hashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.swift<pre><code>[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.js<pre><code>[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.ts<pre><code>[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.dart<pre><code>[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.rs<pre><code>[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.c<pre><code>[class]{Node}-[func]{}\n\n[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.kt<pre><code>[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.rb<pre><code>[class]{HashMapChaining}-[func]{}\n</code></pre> <p>連結リストが非常に長い場合、クエリ効率\\(O(n)\\)が悪いことは注目に値します。この場合、リストを「AVL木」または「赤黒木」に変換して、クエリ操作の時間計算量を\\(O(\\log n)\\)に最適化できます。</p>","path":["第 6 章 &nbsp; ハッシュ表","6.2 &nbsp; ハッシュ衝突"],"tags":[]},{"location":"chapter_hashing/hash_collision/#622","level":2,"title":"6.2.2   オープンアドレス法","text":"<p>オープンアドレス法は追加のデータ構造を導入せず、代わりに「複数回プローブ」を通してハッシュ衝突を処理します。プローブ方法には主に線形プローブ、二次プローブ、二重ハッシュがあります。</p> <p>線形プローブを例にして、オープンアドレス法ハッシュ表のメカニズムを紹介しましょう。</p>","path":["第 6 章 &nbsp; ハッシュ表","6.2 &nbsp; ハッシュ衝突"],"tags":[]},{"location":"chapter_hashing/hash_collision/#1","level":3,"title":"1.   線形プローブ","text":"<p>線形プローブは固定ステップの線形検索をプローブに使用し、通常のハッシュ表とは異なります。</p> <ul> <li>要素の挿入: ハッシュ関数を使用してバケットインデックスを計算します。バケットに既に要素が含まれている場合、衝突位置から線形に前方に走査し（通常ステップサイズは\\(1\\)）、空のバケットが見つかるまで進み、要素を挿入します。</li> <li>要素の検索: ハッシュ衝突に遭遇した場合、同じステップサイズを使用して線形に前方に走査し、対応する要素が見つかったら<code>value</code>を返します。空のバケットに遭遇した場合、ターゲット要素がハッシュ表にないことを意味するため、<code>None</code>を返します。</li> </ul> <p>下図はオープンアドレス法（線形プローブ）ハッシュ表におけるキー値ペアの分布を示しています。このハッシュ関数によると、下二桁が同じキーは同じバケットにマッピングされます。線形プローブを通して、それらはそのバケットとその下のバケットに順次格納されます。</p> <p></p> <p> 図 6-6   オープンアドレス法（線形プローブ）ハッシュ表におけるキー値ペアの分布 </p> <p>しかし、線形プローブは「クラスタリング」を作りやすい傾向があります。具体的には、配列内の連続的に占有された位置が長いほど、これらの連続した位置でハッシュ衝突が発生する確率が高くなり、その位置でのクラスタリングの成長をさらに促進し、悪循環を形成し、最終的に挿入、削除、クエリ、更新操作の効率低下につながります。</p> <p>**オープンアドレス法ハッシュ表では要素を直接削除できない**ことに注意することが重要です。要素を削除すると、配列に空のバケット<code>None</code>が作成されます。要素を検索する際、線形プローブがこの空のバケットに遭遇すると戻ってしまい、このバケットの下の要素にアクセスできなくなります。プログラムはこれらの要素が存在しないと誤って仮定する可能性があります。下図に示すとおりです。</p> <p></p> <p> 図 6-7   オープンアドレス法での削除によるクエリ問題 </p> <p>この問題を解決するために、遅延削除メカニズムを採用できます：ハッシュ表から要素を直接削除する代わりに、定数<code>TOMBSTONE</code>を使用してバケットをマークします。このメカニズムでは、<code>None</code>と<code>TOMBSTONE</code>の両方が空のバケットを表し、キー値ペアを保持できます。ただし、線形プローブが<code>TOMBSTONE</code>に遭遇した場合、その下にまだキー値ペアがある可能性があるため、走査を続ける必要があります。</p> <p>しかし、遅延削除はハッシュ表の性能劣化を加速する可能性があります。削除操作のたびに削除マークが生成され、<code>TOMBSTONE</code>が増加すると、線形プローブがターゲット要素を見つけるために複数の<code>TOMBSTONE</code>をスキップする必要がある可能性があるため、検索時間も増加します。</p> <p>これに対処するために、線形プローブ中に最初に遭遇した<code>TOMBSTONE</code>のインデックスを記録し、検索されたターゲット要素とその<code>TOMBSTONE</code>の位置を交換することを検討してください。これを行う利点は、要素がクエリまたは追加されるたびに、要素がその理想的な位置（プローブの開始点）により近いバケットに移動され、クエリ効率が最適化されることです。</p> <p>以下のコードは、遅延削除を使用したオープンアドレス法（線形プローブ）ハッシュ表を実装しています。ハッシュ表の空間をより有効に活用するために、ハッシュ表を「循環配列」として扱います。配列の終わりを超えると、最初に戻って走査を続けます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby hash_map_open_addressing.py<pre><code>class HashMapOpenAddressing:\n    \"\"\"オープンアドレス法ハッシュテーブル\"\"\"\n\n    def __init__(self):\n        \"\"\"コンストラクタ\"\"\"\n        self.size = 0  # キー値ペアの数\n        self.capacity = 4  # ハッシュテーブルの容量\n        self.load_thres = 2.0 / 3.0  # 拡張をトリガーする負荷率の閾値\n        self.extend_ratio = 2  # 拡張の倍数\n        self.buckets: list[Pair | None] = [None] * self.capacity  # バケット配列\n        self.TOMBSTONE = Pair(-1, \"-1\")  # 削除マーク\n\n    def hash_func(self, key: int) -&gt; int:\n        \"\"\"ハッシュ関数\"\"\"\n        return key % self.capacity\n\n    def load_factor(self) -&gt; float:\n        \"\"\"負荷率\"\"\"\n        return self.size / self.capacity\n\n    def find_bucket(self, key: int) -&gt; int:\n        \"\"\"key に対応するバケットインデックスを検索\"\"\"\n        index = self.hash_func(key)\n        first_tombstone = -1\n        # 線形探査、空のバケットに遭遇したらブレーク\n        while self.buckets[index] is not None:\n            # キーに遭遇した場合、対応するバケットインデックスを返す\n            if self.buckets[index].key == key:\n                # 削除マークが以前に遭遇していた場合、キー値ペアをそのインデックスに移動\n                if first_tombstone != -1:\n                    self.buckets[first_tombstone] = self.buckets[index]\n                    self.buckets[index] = self.TOMBSTONE\n                    return first_tombstone  # 移動されたバケットインデックスを返す\n                return index  # バケットインデックスを返す\n            # 最初に遭遇した削除マークを記録\n            if first_tombstone == -1 and self.buckets[index] is self.TOMBSTONE:\n                first_tombstone = index\n            # バケットインデックスを計算、末尾を超えた場合は先頭に戻る\n            index = (index + 1) % self.capacity\n        # キーが存在しない場合、挿入ポイントのインデックスを返す\n        return index if first_tombstone == -1 else first_tombstone\n\n    def get(self, key: int) -&gt; str:\n        \"\"\"照会操作\"\"\"\n        # key に対応するバケットインデックスを検索\n        index = self.find_bucket(key)\n        # キー値ペアが見つかれば、対応する val を返す\n        if self.buckets[index] not in [None, self.TOMBSTONE]:\n            return self.buckets[index].val\n        # キー値ペアが存在しない場合、None を返す\n        return None\n\n    def put(self, key: int, val: str):\n        \"\"\"追加操作\"\"\"\n        # 負荷率が閾値を超えた場合、拡張を実行\n        if self.load_factor() &gt; self.load_thres:\n            self.extend()\n        # key に対応するバケットインデックスを検索\n        index = self.find_bucket(key)\n        # キー値ペアが見つかれば、val を上書きして返す\n        if self.buckets[index] not in [None, self.TOMBSTONE]:\n            self.buckets[index].val = val\n            return\n        # キー値ペアが存在しない場合、キー値ペアを追加\n        self.buckets[index] = Pair(key, val)\n        self.size += 1\n\n    def remove(self, key: int):\n        \"\"\"削除操作\"\"\"\n        # key に対応するバケットインデックスを検索\n        index = self.find_bucket(key)\n        # キー値ペアが見つかれば、削除マークで覆う\n        if self.buckets[index] not in [None, self.TOMBSTONE]:\n            self.buckets[index] = self.TOMBSTONE\n            self.size -= 1\n\n    def extend(self):\n        \"\"\"ハッシュテーブルを拡張\"\"\"\n        # 元のハッシュテーブルを一時的に保存\n        buckets_tmp = self.buckets\n        # 拡張された新しいハッシュテーブルを初期化\n        self.capacity *= self.extend_ratio\n        self.buckets = [None] * self.capacity\n        self.size = 0\n        # 元のハッシュテーブルから新しいハッシュテーブルにキー値ペアを移動\n        for pair in buckets_tmp:\n            if pair not in [None, self.TOMBSTONE]:\n                self.put(pair.key, pair.val)\n\n    def print(self):\n        \"\"\"ハッシュテーブルを出力\"\"\"\n        for pair in self.buckets:\n            if pair is None:\n                print(\"None\")\n            elif pair is self.TOMBSTONE:\n                print(\"TOMBSTONE\")\n            else:\n                print(pair.key, \"-&gt;\", pair.val)\n</code></pre> hash_map_open_addressing.cpp<pre><code>/* オープンアドレス法ハッシュテーブル */\nclass HashMapOpenAddressing {\n  private:\n    int size;                             // キー値ペアの数\n    int capacity = 4;                     // ハッシュテーブルの容量\n    const double loadThres = 2.0 / 3.0;     // 拡張をトリガーする負荷率の閾値\n    const int extendRatio = 2;            // 拡張倍率\n    vector&lt;Pair *&gt; buckets;               // バケット配列\n    Pair *TOMBSTONE = new Pair(-1, \"-1\"); // 削除マーク\n\n  public:\n    /* コンストラクタ */\n    HashMapOpenAddressing() : size(0), buckets(capacity, nullptr) {\n    }\n\n    /* デストラクタ */\n    ~HashMapOpenAddressing() {\n        for (Pair *pair : buckets) {\n            if (pair != nullptr &amp;&amp; pair != TOMBSTONE) {\n                delete pair;\n            }\n        }\n        delete TOMBSTONE;\n    }\n\n    /* ハッシュ関数 */\n    int hashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* 負荷率 */\n    double loadFactor() {\n        return (double)size / capacity;\n    }\n\n    /* keyに対応するバケットインデックスを検索 */\n    int findBucket(int key) {\n        int index = hashFunc(key);\n        int firstTombstone = -1;\n        // 線形探査、空のバケットに遭遇したら中断\n        while (buckets[index] != nullptr) {\n            // keyに遭遇した場合、対応するバケットインデックスを返却\n            if (buckets[index]-&gt;key == key) {\n                // 以前に削除マークに遭遇していた場合、キー値ペアをそのインデックスに移動\n                if (firstTombstone != -1) {\n                    buckets[firstTombstone] = buckets[index];\n                    buckets[index] = TOMBSTONE;\n                    return firstTombstone; // 移動されたバケットインデックスを返却\n                }\n                return index; // バケットインデックスを返却\n            }\n            // 最初に遭遇した削除マークを記録\n            if (firstTombstone == -1 &amp;&amp; buckets[index] == TOMBSTONE) {\n                firstTombstone = index;\n            }\n            // バケットインデックスを計算、末尾を超えた場合は先頭に戻る\n            index = (index + 1) % capacity;\n        }\n        // keyが存在しない場合、挿入ポイントのインデックスを返却\n        return firstTombstone == -1 ? index : firstTombstone;\n    }\n\n    /* クエリ操作 */\n    string get(int key) {\n        // keyに対応するバケットインデックスを検索\n        int index = findBucket(key);\n        // キー値ペアが見つかった場合、対応するvalを返却\n        if (buckets[index] != nullptr &amp;&amp; buckets[index] != TOMBSTONE) {\n            return buckets[index]-&gt;val;\n        }\n        // キー値ペアが存在しない場合、空文字列を返却\n        return \"\";\n    }\n\n    /* 追加操作 */\n    void put(int key, string val) {\n        // 負荷率が閾値を超えた場合、拡張を実行\n        if (loadFactor() &gt; loadThres) {\n            extend();\n        }\n        // keyに対応するバケットインデックスを検索\n        int index = findBucket(key);\n        // キー値ペアが見つかった場合、valを上書きして返却\n        if (buckets[index] != nullptr &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index]-&gt;val = val;\n            return;\n        }\n        // キー値ペアが存在しない場合、キー値ペアを追加\n        buckets[index] = new Pair(key, val);\n        size++;\n    }\n\n    /* 削除操作 */\n    void remove(int key) {\n        // keyに対応するバケットインデックスを検索\n        int index = findBucket(key);\n        // キー値ペアが見つかった場合、削除マークで覆う\n        if (buckets[index] != nullptr &amp;&amp; buckets[index] != TOMBSTONE) {\n            delete buckets[index];\n            buckets[index] = TOMBSTONE;\n            size--;\n        }\n    }\n\n    /* ハッシュテーブルを拡張 */\n    void extend() {\n        // 元のハッシュテーブルを一時保存\n        vector&lt;Pair *&gt; bucketsTmp = buckets;\n        // 拡張された新しいハッシュテーブルを初期化\n        capacity *= extendRatio;\n        buckets = vector&lt;Pair *&gt;(capacity, nullptr);\n        size = 0;\n        // 元のハッシュテーブルから新しいハッシュテーブルにキー値ペアを移動\n        for (Pair *pair : bucketsTmp) {\n            if (pair != nullptr &amp;&amp; pair != TOMBSTONE) {\n                put(pair-&gt;key, pair-&gt;val);\n                delete pair;\n            }\n        }\n    }\n\n    /* ハッシュテーブルを印刷 */\n    void print() {\n        for (Pair *pair : buckets) {\n            if (pair == nullptr) {\n                cout &lt;&lt; \"nullptr\" &lt;&lt; endl;\n            } else if (pair == TOMBSTONE) {\n                cout &lt;&lt; \"TOMBSTONE\" &lt;&lt; endl;\n            } else {\n                cout &lt;&lt; pair-&gt;key &lt;&lt; \" -&gt; \" &lt;&lt; pair-&gt;val &lt;&lt; endl;\n            }\n        }\n    }\n};\n</code></pre> hash_map_open_addressing.java<pre><code>/* オープンアドレス法ハッシュテーブル */\nclass HashMapOpenAddressing {\n    private int size; // キー値ペアの数\n    private int capacity = 4; // ハッシュテーブルの容量\n    private final double loadThres = 2.0 / 3.0; // 拡張をトリガーする負荷率の閾値\n    private final int extendRatio = 2; // 拡張倍率\n    private Pair[] buckets; // バケット配列\n    private final Pair TOMBSTONE = new Pair(-1, \"-1\"); // 削除マーク\n\n    /* コンストラクタ */\n    public HashMapOpenAddressing() {\n        size = 0;\n        buckets = new Pair[capacity];\n    }\n\n    /* ハッシュ関数 */\n    private int hashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* 負荷率 */\n    private double loadFactor() {\n        return (double) size / capacity;\n    }\n\n    /* keyに対応するバケットインデックスを検索 */\n    private int findBucket(int key) {\n        int index = hashFunc(key);\n        int firstTombstone = -1;\n        // 線形探査、空のバケットに遭遇したら終了\n        while (buckets[index] != null) {\n            // keyに遭遇した場合、対応するバケットインデックスを返す\n            if (buckets[index].key == key) {\n                // 以前に削除マークに遭遇していた場合、キー値ペアをそのインデックスに移動\n                if (firstTombstone != -1) {\n                    buckets[firstTombstone] = buckets[index];\n                    buckets[index] = TOMBSTONE;\n                    return firstTombstone; // 移動後のバケットインデックスを返す\n                }\n                return index; // バケットインデックスを返す\n            }\n            // 最初に遭遇した削除マークを記録\n            if (firstTombstone == -1 &amp;&amp; buckets[index] == TOMBSTONE) {\n                firstTombstone = index;\n            }\n            // バケットインデックスを計算、末尾を超えた場合は先頭に戻る\n            index = (index + 1) % capacity;\n        }\n        // keyが存在しない場合、挿入ポイントのインデックスを返す\n        return firstTombstone == -1 ? index : firstTombstone;\n    }\n\n    /* クエリ操作 */\n    public String get(int key) {\n        // keyに対応するバケットインデックスを検索\n        int index = findBucket(key);\n        // キー値ペアが見つかった場合、対応するvalを返す\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            return buckets[index].val;\n        }\n        // キー値ペアが存在しない場合、nullを返す\n        return null;\n    }\n\n    /* 追加操作 */\n    public void put(int key, String val) {\n        // 負荷率が閾値を超えた場合、拡張を実行\n        if (loadFactor() &gt; loadThres) {\n            extend();\n        }\n        // keyに対応するバケットインデックスを検索\n        int index = findBucket(key);\n        // キー値ペアが見つかった場合、valを上書きして戻る\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index].val = val;\n            return;\n        }\n        // キー値ペアが存在しない場合、キー値ペアを追加\n        buckets[index] = new Pair(key, val);\n        size++;\n    }\n\n    /* 削除操作 */\n    public void remove(int key) {\n        // keyに対応するバケットインデックスを検索\n        int index = findBucket(key);\n        // キー値ペアが見つかった場合、削除マークで覆う\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index] = TOMBSTONE;\n            size--;\n        }\n    }\n\n    /* ハッシュテーブルを拡張 */\n    private void extend() {\n        // 元のハッシュテーブルを一時的に保存\n        Pair[] bucketsTmp = buckets;\n        // 拡張された新しいハッシュテーブルを初期化\n        capacity *= extendRatio;\n        buckets = new Pair[capacity];\n        size = 0;\n        // 元のハッシュテーブルから新しいハッシュテーブルにキー値ペアを移動\n        for (Pair pair : bucketsTmp) {\n            if (pair != null &amp;&amp; pair != TOMBSTONE) {\n                put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* ハッシュテーブルを印刷 */\n    public void print() {\n        for (Pair pair : buckets) {\n            if (pair == null) {\n                System.out.println(\"null\");\n            } else if (pair == TOMBSTONE) {\n                System.out.println(\"TOMBSTONE\");\n            } else {\n                System.out.println(pair.key + \" -&gt; \" + pair.val);\n            }\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.cs<pre><code>[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.go<pre><code>[class]{hashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.swift<pre><code>[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.js<pre><code>[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.ts<pre><code>[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.dart<pre><code>[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.rs<pre><code>[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.c<pre><code>[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.kt<pre><code>[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.rb<pre><code>[class]{HashMapOpenAddressing}-[func]{}\n</code></pre>","path":["第 6 章 &nbsp; ハッシュ表","6.2 &nbsp; ハッシュ衝突"],"tags":[]},{"location":"chapter_hashing/hash_collision/#2","level":3,"title":"2.   二次プローブ","text":"<p>二次プローブは線形プローブに似ており、オープンアドレス法の一般的な戦略の1つです。衝突が発生した場合、二次プローブは単純に固定ステップ数をスキップするのではなく、「プローブ回数の二乗」に等しいステップ数、つまり\\(1, 4, 9, \\dots\\)ステップをスキップします。</p> <p>二次プローブには以下の利点があります：</p> <ul> <li>二次プローブは、プローブ回数の二乗の距離をスキップすることで、線形プローブのクラスタリング効果を軽減しようとします。</li> <li>二次プローブはより大きな距離をスキップして空の位置を見つけ、データをより均等に分散するのに役立ちます。</li> </ul> <p>しかし、二次プローブは完璧ではありません：</p> <ul> <li>クラスタリングは依然として存在し、つまり一部の位置は他の位置よりも占有される可能性が高いです。</li> <li>二乗の成長により、二次プローブはハッシュ表全体をプローブできない可能性があり、ハッシュ表に空のバケットがあっても、二次プローブがアクセスできない可能性があります。</li> </ul>","path":["第 6 章 &nbsp; ハッシュ表","6.2 &nbsp; ハッシュ衝突"],"tags":[]},{"location":"chapter_hashing/hash_collision/#3","level":3,"title":"3.   二重ハッシュ","text":"<p>名前が示すように、二重ハッシュ法は複数のハッシュ関数\\(f_1(x)\\)、\\(f_2(x)\\)、\\(f_3(x)\\)、\\(\\dots\\)をプローブに使用します。</p> <ul> <li>要素の挿入: ハッシュ関数\\(f_1(x)\\)が衝突に遭遇した場合、\\(f_2(x)\\)を試し、以下同様に、空の位置が見つかって要素が挿入されるまで続けます。</li> <li>要素の検索: 同じハッシュ関数の順序で検索し、ターゲット要素が見つかって返されるまで、または空の位置に遭遇するかすべてのハッシュ関数が試されるまで続け、要素がハッシュ表にないことを示し、<code>None</code>を返します。</li> </ul> <p>線形プローブと比較して、二重ハッシュ法はクラスタリングが起こりにくいですが、複数のハッシュ関数は追加の計算オーバーヘッドを導入します。</p> <p>Tip</p> <p>オープンアドレス法（線形プローブ、二次プローブ、二重ハッシュ）ハッシュ表はすべて「要素を直接削除できない」という問題があることに注意してください。</p>","path":["第 6 章 &nbsp; ハッシュ表","6.2 &nbsp; ハッシュ衝突"],"tags":[]},{"location":"chapter_hashing/hash_collision/#623","level":2,"title":"6.2.3   プログラミング言語の選択","text":"<p>異なるプログラミング言語は異なるハッシュ表実装戦略を採用しています。以下にいくつかの例を示します：</p> <ul> <li>Pythonはオープンアドレス法を使用します。<code>dict</code>辞書はプローブに疑似乱数を使用します。</li> <li>Javaは連鎖法を使用します。JDK 1.8以降、<code>HashMap</code>の配列長が64に達し、連結リストの長さが8に達すると、連結リストは検索性能を向上させるために赤黒木に変換されます。</li> <li>Goは連鎖法を使用します。Goは各バケットが最大8つのキー値ペアを格納できることを規定し、容量を超えた場合はオーバーフローバケットが連結されます。オーバーフローバケットが多すぎる場合、性能を確保するために特別な等容量リサイズ操作が実行されます。</li> </ul>","path":["第 6 章 &nbsp; ハッシュ表","6.2 &nbsp; ハッシュ衝突"],"tags":[]},{"location":"chapter_hashing/hash_map/","level":1,"title":"6.1   ハッシュ表","text":"<p>ハッシュ表はハッシュマップとも呼ばれ、キーと値の間のマッピングを確立し、効率的な要素の取得を可能にするデータ構造です。具体的には、ハッシュ表に<code>key</code>を入力すると、\\(O(1)\\)の時間計算量で対応する<code>value</code>を取得できます。</p> <p>下図に示すように、\\(n\\)人の学生がいて、各学生には「名前」と「学籍番号」の2つのデータフィールドがあるとします。学籍番号を入力として対応する名前を返すクエリ機能を実装したい場合、下図に示すハッシュ表を使用できます。</p> <p></p> <p> 図 6-1   ハッシュ表の抽象的な表現 </p> <p>ハッシュ表に加えて、配列や連結リストもクエリ機能の実装に使用できますが、時間計算量が異なります。効率は以下の表で比較されています：</p> <ul> <li>要素の挿入: 配列（または連結リスト）の末尾に要素を追加するだけです。この操作の時間計算量は\\(O(1)\\)です。</li> <li>要素の検索: 配列（または連結リスト）がソートされていないため、要素を検索するにはすべての要素を走査する必要があります。この操作の時間計算量は\\(O(n)\\)です。</li> <li>要素の削除: 要素を削除するには、まずその要素を見つけてから、配列（または連結リスト）から削除します。この操作の時間計算量は\\(O(n)\\)です。</li> </ul> <p> 表 6-1   一般的な操作の時間効率の比較 </p> 配列 連結リスト ハッシュ表 要素の検索 \\(O(n)\\) \\(O(n)\\) \\(O(1)\\) 要素の挿入 \\(O(1)\\) \\(O(1)\\) \\(O(1)\\) 要素の削除 \\(O(n)\\) \\(O(n)\\) \\(O(1)\\) <p>観察されるように、**ハッシュ表における操作（挿入、削除、検索、変更）の時間計算量は\\(O(1)\\)**で、非常に効率的です。</p>","path":["第 6 章 &nbsp; ハッシュ表","6.1 &nbsp; ハッシュ表"],"tags":[]},{"location":"chapter_hashing/hash_map/#611","level":2,"title":"6.1.1   ハッシュ表の一般的な操作","text":"<p>ハッシュ表の一般的な操作には、初期化、クエリ、キー値ペアの追加、キー値ペアの削除があります。以下はコード例です：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlin hash_map.py<pre><code># ハッシュ表を初期化\nhmap: dict = {}\n\n# 追加操作\n# ハッシュ表にキー値ペア (key, value) を追加\nhmap[12836] = \"小哈\"\nhmap[15937] = \"小啰\"\nhmap[16750] = \"小算\"\nhmap[13276] = \"小法\"\nhmap[10583] = \"小鸭\"\n\n# クエリ操作\n# ハッシュ表にキーを入力し、値を取得\nname: str = hmap[15937]\n\n# 削除操作\n# ハッシュ表からキー値ペア (key, value) を削除\nhmap.pop(10583)\n</code></pre> hash_map.cpp<pre><code>/* ハッシュ表を初期化 */\nunordered_map&lt;int, string&gt; map;\n\n/* 追加操作 */\n// ハッシュ表にキー値ペア (key, value) を追加\nmap[12836] = \"小哈\";\nmap[15937] = \"小啰\";\nmap[16750] = \"小算\";\nmap[13276] = \"小法\";\nmap[10583] = \"小鸭\";\n\n/* クエリ操作 */\n// ハッシュ表にキーを入力し、値を取得\nstring name = map[15937];\n\n/* 削除操作 */\n// ハッシュ表からキー値ペア (key, value) を削除\nmap.erase(10583);\n</code></pre> hash_map.java<pre><code>/* ハッシュ表を初期化 */\nMap&lt;Integer, String&gt; map = new HashMap&lt;&gt;();\n\n/* 追加操作 */\n// ハッシュ表にキー値ペア (key, value) を追加\nmap.put(12836, \"小哈\");\nmap.put(15937, \"小啰\");\nmap.put(16750, \"小算\");\nmap.put(13276, \"小法\");\nmap.put(10583, \"小鸭\");\n\n/* クエリ操作 */\n// ハッシュ表にキーを入力し、値を取得\nString name = map.get(15937);\n\n/* 削除操作 */\n// ハッシュ表からキー値ペア (key, value) を削除\nmap.remove(10583);\n</code></pre> hash_map.cs<pre><code>/* ハッシュ表を初期化 */\nDictionary&lt;int, string&gt; map = new() {\n    /* 追加操作 */\n    // ハッシュ表にキー値ペア (key, value) を追加\n    { 12836, \"小哈\" },\n    { 15937, \"小啰\" },\n    { 16750, \"小算\" },\n    { 13276, \"小法\" },\n    { 10583, \"小鸭\" }\n};\n\n/* クエリ操作 */\n// ハッシュ表にキーを入力し、値を取得\nstring name = map[15937];\n\n/* 削除操作 */\n// ハッシュ表からキー値ペア (key, value) を削除\nmap.Remove(10583);\n</code></pre> hash_map_test.go<pre><code>/* ハッシュ表を初期化 */\nhmap := make(map[int]string)\n\n/* 追加操作 */\n// ハッシュ表にキー値ペア (key, value) を追加\nhmap[12836] = \"小哈\"\nhmap[15937] = \"小啰\"\nhmap[16750] = \"小算\"\nhmap[13276] = \"小法\"\nhmap[10583] = \"小鸭\"\n\n/* クエリ操作 */\n// ハッシュ表にキーを入力し、値を取得\nname := hmap[15937]\n\n/* 削除操作 */\n// ハッシュ表からキー値ペア (key, value) を削除\ndelete(hmap, 10583)\n</code></pre> hash_map.swift<pre><code>/* ハッシュ表を初期化 */\nvar map: [Int: String] = [:]\n\n/* 追加操作 */\n// ハッシュ表にキー値ペア (key, value) を追加\nmap[12836] = \"小哈\"\nmap[15937] = \"小啰\"\nmap[16750] = \"小算\"\nmap[13276] = \"小法\"\nmap[10583] = \"小鸭\"\n\n/* クエリ操作 */\n// ハッシュ表にキーを入力し、値を取得\nlet name = map[15937]!\n\n/* 削除操作 */\n// ハッシュ表からキー値ペア (key, value) を削除\nmap.removeValue(forKey: 10583)\n</code></pre> hash_map.js<pre><code>/* ハッシュ表を初期化 */\nconst map = new Map();\n/* 追加操作 */\n// ハッシュ表にキー値ペア (key, value) を追加\nmap.set(12836, '小哈');\nmap.set(15937, '小啰');\nmap.set(16750, '小算');\nmap.set(13276, '小法');\nmap.set(10583, '小鸭');\n\n/* クエリ操作 */\n// ハッシュ表にキーを入力し、値を取得\nlet name = map.get(15937);\n\n/* 削除操作 */\n// ハッシュ表からキー値ペア (key, value) を削除\nmap.delete(10583);\n</code></pre> hash_map.ts<pre><code>/* ハッシュ表を初期化 */\nconst map = new Map&lt;number, string&gt;();\n/* 追加操作 */\n// ハッシュ表にキー値ペア (key, value) を追加\nmap.set(12836, '小哈');\nmap.set(15937, '小啰');\nmap.set(16750, '小算');\nmap.set(13276, '小法');\nmap.set(10583, '小鸭');\nconsole.info('\\n追加後、ハッシュ表は\\nKey -&gt; Value');\nconsole.info(map);\n\n/* クエリ操作 */\n// ハッシュ表にキーを入力し、値を取得\nlet name = map.get(15937);\nconsole.info('\\n学籍番号15937を入力、名前を問い合わせ ' + name);\n\n/* 削除操作 */\n// ハッシュ表からキー値ペア (key, value) を削除\nmap.delete(10583);\nconsole.info('\\n10583を削除後、ハッシュ表は\\nKey -&gt; Value');\nconsole.info(map);\n</code></pre> hash_map.dart<pre><code>/* ハッシュ表を初期化 */\nMap&lt;int, String&gt; map = {};\n\n/* 追加操作 */\n// ハッシュ表にキー値ペア (key, value) を追加\nmap[12836] = \"小哈\";\nmap[15937] = \"小啰\";\nmap[16750] = \"小算\";\nmap[13276] = \"小法\";\nmap[10583] = \"小鸭\";\n\n/* クエリ操作 */\n// ハッシュ表にキーを入力し、値を取得\nString name = map[15937];\n\n/* 削除操作 */\n// ハッシュ表からキー値ペア (key, value) を削除\nmap.remove(10583);\n</code></pre> hash_map.rs<pre><code>use std::collections::HashMap;\n\n/* ハッシュ表を初期化 */\nlet mut map: HashMap&lt;i32, String&gt; = HashMap::new();\n\n/* 追加操作 */\n// ハッシュ表にキー値ペア (key, value) を追加\nmap.insert(12836, \"小哈\".to_string());\nmap.insert(15937, \"小啰\".to_string());\nmap.insert(16750, \"小算\".to_string());\nmap.insert(13279, \"小法\".to_string());\nmap.insert(10583, \"小鸭\".to_string());\n\n/* クエリ操作 */\n// ハッシュ表にキーを入力し、値を取得\nlet _name: Option&lt;&amp;String&gt; = map.get(&amp;15937);\n\n/* 削除操作 */\n// ハッシュ表からキー値ペア (key, value) を削除\nlet _removed_value: Option&lt;String&gt; = map.remove(&amp;10583);\n</code></pre> hash_map.c<pre><code>// Cには組み込みのハッシュ表が提供されていません\n</code></pre> hash_map.kt<pre><code>\n</code></pre> <p>ハッシュ表を走査する一般的な方法は3つあります：キー値ペアの走査、キーの走査、値の走査。以下はコード例です：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlin hash_map.py<pre><code># ハッシュ表を走査\n# キー値ペア key-&gt;value を走査\nfor key, value in hmap.items():\n    print(key, \"-&gt;\", value)\n# キーのみを走査\nfor key in hmap.keys():\n    print(key)\n# 値のみを走査\nfor value in hmap.values():\n    print(value)\n</code></pre> hash_map.cpp<pre><code>/* ハッシュ表を走査 */\n// キー値ペア key-&gt;value を走査\nfor (auto kv: map) {\n    cout &lt;&lt; kv.first &lt;&lt; \" -&gt; \" &lt;&lt; kv.second &lt;&lt; endl;\n}\n// イテレータを使用してキー値ペア key-&gt;value を走査\nfor (auto iter = map.begin(); iter != map.end(); iter++) {\n    cout &lt;&lt; iter-&gt;first &lt;&lt; \"-&gt;\" &lt;&lt; iter-&gt;second &lt;&lt; endl;\n}\n</code></pre> hash_map.java<pre><code>/* ハッシュ表を走査 */\n// キー値ペア key-&gt;value を走査\nfor (Map.Entry&lt;Integer, String&gt; kv: map.entrySet()) {\n    System.out.println(kv.getKey() + \" -&gt; \" + kv.getValue());\n}\n// キーのみを走査\nfor (int key: map.keySet()) {\n    System.out.println(key);\n}\n// 値のみを走査\nfor (String val: map.values()) {\n    System.out.println(val);\n}\n</code></pre> hash_map.cs<pre><code>/* ハッシュ表を走査 */\n// キー値ペア Key-&gt;Value を走査\nforeach (var kv in map) {\n    Console.WriteLine(kv.Key + \" -&gt; \" + kv.Value);\n}\n// キーのみを走査\nforeach (int key in map.Keys) {\n    Console.WriteLine(key);\n}\n// 値のみを走査\nforeach (string val in map.Values) {\n    Console.WriteLine(val);\n}\n</code></pre> hash_map_test.go<pre><code>/* ハッシュ表を走査 */\n// キー値ペア key-&gt;value を走査\nfor key, value := range hmap {\n    fmt.Println(key, \"-&gt;\", value)\n}\n// キーのみを走査\nfor key := range hmap {\n    fmt.Println(key)\n}\n// 値のみを走査\nfor _, value := range hmap {\n    fmt.Println(value)\n}\n</code></pre> hash_map.swift<pre><code>/* ハッシュ表を走査 */\n// キー値ペア Key-&gt;Value を走査\nfor (key, value) in map {\n    print(\"\\(key) -&gt; \\(value)\")\n}\n// キーのみを走査\nfor key in map.keys {\n    print(key)\n}\n// 値のみを走査\nfor value in map.values {\n    print(value)\n}\n</code></pre> hash_map.js<pre><code>/* ハッシュ表を走査 */\nconsole.info('\\nキー値ペア Key-&gt;Value を走査');\nfor (const [k, v] of map.entries()) {\n    console.info(k + ' -&gt; ' + v);\n}\nconsole.info('\\nキーのみを走査 Key');\nfor (const k of map.keys()) {\n    console.info(k);\n}\nconsole.info('\\n値のみを走査 Value');\nfor (const v of map.values()) {\n    console.info(v);\n}\n</code></pre> hash_map.ts<pre><code>/* ハッシュ表を走査 */\nconsole.info('\\nキー値ペア Key-&gt;Value を走査');\nfor (const [k, v] of map.entries()) {\n    console.info(k + ' -&gt; ' + v);\n}\nconsole.info('\\nキーのみを走査 Key');\nfor (const k of map.keys()) {\n    console.info(k);\n}\nconsole.info('\\n値のみを走査 Value');\nfor (const v of map.values()) {\n    console.info(v);\n}\n</code></pre> hash_map.dart<pre><code>/* ハッシュ表を走査 */\n// キー値ペア Key-&gt;Value を走査\nmap.forEach((key, value) {\nprint('$key -&gt; $value');\n});\n\n// キーのみを走査 Key\nmap.keys.forEach((key) {\nprint(key);\n});\n\n// 値のみを走査 Value\nmap.values.forEach((value) {\nprint(value);\n});\n</code></pre> hash_map.rs<pre><code>/* ハッシュ表を走査 */\n// キー値ペア Key-&gt;Value を走査\nfor (key, value) in &amp;map {\n    println!(\"{key} -&gt; {value}\");\n}\n\n// キーのみを走査 Key\nfor key in map.keys() {\n    println!(\"{key}\");\n}\n\n// 値のみを走査 Value\nfor value in map.values() {\n    println!(\"{value}\");\n}\n</code></pre> hash_map.c<pre><code>// Cには組み込みのハッシュ表が提供されていません\n</code></pre> hash_map.kt<pre><code>\n</code></pre>","path":["第 6 章 &nbsp; ハッシュ表","6.1 &nbsp; ハッシュ表"],"tags":[]},{"location":"chapter_hashing/hash_map/#612","level":2,"title":"6.1.2   ハッシュ表の簡単な実装","text":"<p>まず、最も簡単なケースを考えてみましょう：配列のみを使ってハッシュ表を実装すること。ハッシュ表において、配列の各空きスロットはバケットと呼ばれ、各バケットはキー値ペアを格納できます。したがって、クエリ操作は<code>key</code>に対応するバケットを見つけ、そこから<code>value</code>を取得することになります。</p> <p>では、<code>key</code>に基づいて対応するバケットをどのように特定するのでしょうか？これはハッシュ関数によって実現されます。ハッシュ関数の役割は、より大きな入力空間をより小さな出力空間にマッピングすることです。ハッシュ表では、入力空間はすべてのキーで構成され、出力空間はすべてのバケット（配列インデックス）で構成されます。つまり、<code>key</code>が与えられた場合、ハッシュ関数を使用して対応するキー値ペアの配列内の格納位置を決定できます。</p> <p>与えられた<code>key</code>に対して、ハッシュ関数の計算は2つのステップで構成されます：</p> <ol> <li>特定のハッシュアルゴリズム<code>hash()</code>を使用してハッシュ値を計算します。</li> <li>ハッシュ値をバケット数（配列長）<code>capacity</code>で剰余を取り、キーに対応する配列<code>index</code>を取得します。</li> </ol> <pre><code>index = hash(key) % capacity\n</code></pre> <p>その後、<code>index</code>を使用してハッシュ表内の対応するバケットにアクセスし、<code>value</code>を取得できます。</p> <p>配列長が<code>capacity = 100</code>で、ハッシュアルゴリズムが<code>hash(key) = key</code>として定義されているとします。したがって、ハッシュ関数は<code>key % 100</code>として表現できます。以下の図は、<code>key</code>を学籍番号、<code>value</code>を名前として、ハッシュ関数の動作原理を示しています。</p> <p></p> <p> 図 6-2   ハッシュ関数の動作原理 </p> <p>以下のコードは簡単なハッシュ表を実装しています。ここでは、<code>key</code>と<code>value</code>を<code>Pair</code>クラスにカプセル化してキー値ペアを表現しています。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array_hash_map.py<pre><code>class Pair:\n    \"\"\"キー値ペア\"\"\"\n\n    def __init__(self, key: int, val: str):\n        self.key = key\n        self.val = val\n\nclass ArrayHashMap:\n    \"\"\"配列実装に基づくハッシュテーブル\"\"\"\n\n    def __init__(self):\n        \"\"\"コンストラクタ\"\"\"\n        # 100個のバケットを含む配列を初期化\n        self.buckets: list[Pair | None] = [None] * 100\n\n    def hash_func(self, key: int) -&gt; int:\n        \"\"\"ハッシュ関数\"\"\"\n        index = key % 100\n        return index\n\n    def get(self, key: int) -&gt; str:\n        \"\"\"照会操作\"\"\"\n        index: int = self.hash_func(key)\n        pair: Pair = self.buckets[index]\n        if pair is None:\n            return None\n        return pair.val\n\n    def put(self, key: int, val: str):\n        \"\"\"追加操作\"\"\"\n        pair = Pair(key, val)\n        index: int = self.hash_func(key)\n        self.buckets[index] = pair\n\n    def remove(self, key: int):\n        \"\"\"削除操作\"\"\"\n        index: int = self.hash_func(key)\n        # None に設定し、削除を表現\n        self.buckets[index] = None\n\n    def entry_set(self) -&gt; list[Pair]:\n        \"\"\"すべてのキー値ペアを取得\"\"\"\n        result: list[Pair] = []\n        for pair in self.buckets:\n            if pair is not None:\n                result.append(pair)\n        return result\n\n    def key_set(self) -&gt; list[int]:\n        \"\"\"すべてのキーを取得\"\"\"\n        result = []\n        for pair in self.buckets:\n            if pair is not None:\n                result.append(pair.key)\n        return result\n\n    def value_set(self) -&gt; list[str]:\n        \"\"\"すべての値を取得\"\"\"\n        result = []\n        for pair in self.buckets:\n            if pair is not None:\n                result.append(pair.val)\n        return result\n\n    def print(self):\n        \"\"\"ハッシュテーブルを出力\"\"\"\n        for pair in self.buckets:\n            if pair is not None:\n                print(pair.key, \"-&gt;\", pair.val)\n</code></pre> array_hash_map.cpp<pre><code>/* キー値ペア */\nstruct Pair {\n  public:\n    int key;\n    string val;\n    Pair(int key, string val) {\n        this-&gt;key = key;\n        this-&gt;val = val;\n    }\n};\n\n/* 配列実装に基づくハッシュテーブル */\nclass ArrayHashMap {\n  private:\n    vector&lt;Pair *&gt; buckets;\n\n  public:\n    ArrayHashMap() {\n        // 配列を初期化、100個のバケットを含む\n        buckets = vector&lt;Pair *&gt;(100);\n    }\n\n    ~ArrayHashMap() {\n        // メモリを解放\n        for (const auto &amp;bucket : buckets) {\n            delete bucket;\n        }\n        buckets.clear();\n    }\n\n    /* ハッシュ関数 */\n    int hashFunc(int key) {\n        int index = key % 100;\n        return index;\n    }\n\n    /* クエリ操作 */\n    string get(int key) {\n        int index = hashFunc(key);\n        Pair *pair = buckets[index];\n        if (pair == nullptr)\n            return \"\";\n        return pair-&gt;val;\n    }\n\n    /* 追加操作 */\n    void put(int key, string val) {\n        Pair *pair = new Pair(key, val);\n        int index = hashFunc(key);\n        buckets[index] = pair;\n    }\n\n    /* 削除操作 */\n    void remove(int key) {\n        int index = hashFunc(key);\n        // メモリを解放してnullptrに設定\n        delete buckets[index];\n        buckets[index] = nullptr;\n    }\n\n    /* すべてのキー値ペアを取得 */\n    vector&lt;Pair *&gt; pairSet() {\n        vector&lt;Pair *&gt; pairSet;\n        for (Pair *pair : buckets) {\n            if (pair != nullptr) {\n                pairSet.push_back(pair);\n            }\n        }\n        return pairSet;\n    }\n\n    /* すべてのキーを取得 */\n    vector&lt;int&gt; keySet() {\n        vector&lt;int&gt; keySet;\n        for (Pair *pair : buckets) {\n            if (pair != nullptr) {\n                keySet.push_back(pair-&gt;key);\n            }\n        }\n        return keySet;\n    }\n\n    /* すべての値を取得 */\n    vector&lt;string&gt; valueSet() {\n        vector&lt;string&gt; valueSet;\n        for (Pair *pair : buckets) {\n            if (pair != nullptr) {\n                valueSet.push_back(pair-&gt;val);\n            }\n        }\n        return valueSet;\n    }\n\n    /* ハッシュテーブルを印刷 */\n    void print() {\n        for (Pair *kv : pairSet()) {\n            cout &lt;&lt; kv-&gt;key &lt;&lt; \" -&gt; \" &lt;&lt; kv-&gt;val &lt;&lt; endl;\n        }\n    }\n};\n</code></pre> array_hash_map.java<pre><code>/* キー値ペア */\nclass Pair {\n    public int key;\n    public String val;\n\n    public Pair(int key, String val) {\n        this.key = key;\n        this.val = val;\n    }\n}\n\n/* 配列実装に基づくハッシュテーブル */\nclass ArrayHashMap {\n    private List&lt;Pair&gt; buckets;\n\n    public ArrayHashMap() {\n        // 100個のバケットを含む配列を初期化\n        buckets = new ArrayList&lt;&gt;();\n        for (int i = 0; i &lt; 100; i++) {\n            buckets.add(null);\n        }\n    }\n\n    /* ハッシュ関数 */\n    private int hashFunc(int key) {\n        int index = key % 100;\n        return index;\n    }\n\n    /* クエリ操作 */\n    public String get(int key) {\n        int index = hashFunc(key);\n        Pair pair = buckets.get(index);\n        if (pair == null)\n            return null;\n        return pair.val;\n    }\n\n    /* 追加操作 */\n    public void put(int key, String val) {\n        Pair pair = new Pair(key, val);\n        int index = hashFunc(key);\n        buckets.set(index, pair);\n    }\n\n    /* 削除操作 */\n    public void remove(int key) {\n        int index = hashFunc(key);\n        // nullに設定して削除を示す\n        buckets.set(index, null);\n    }\n\n    /* すべてのキー値ペアを取得 */\n    public List&lt;Pair&gt; pairSet() {\n        List&lt;Pair&gt; pairSet = new ArrayList&lt;&gt;();\n        for (Pair pair : buckets) {\n            if (pair != null)\n                pairSet.add(pair);\n        }\n        return pairSet;\n    }\n\n    /* すべてのキーを取得 */\n    public List&lt;Integer&gt; keySet() {\n        List&lt;Integer&gt; keySet = new ArrayList&lt;&gt;();\n        for (Pair pair : buckets) {\n            if (pair != null)\n                keySet.add(pair.key);\n        }\n        return keySet;\n    }\n\n    /* すべての値を取得 */\n    public List&lt;String&gt; valueSet() {\n        List&lt;String&gt; valueSet = new ArrayList&lt;&gt;();\n        for (Pair pair : buckets) {\n            if (pair != null)\n                valueSet.add(pair.val);\n        }\n        return valueSet;\n    }\n\n    /* ハッシュテーブルを印刷 */\n    public void print() {\n        for (Pair kv : pairSet()) {\n            System.out.println(kv.key + \" -&gt; \" + kv.val);\n        }\n    }\n}\n</code></pre> array_hash_map.cs<pre><code>[class]{Pair}-[func]{}\n\n[class]{ArrayHashMap}-[func]{}\n</code></pre> array_hash_map.go<pre><code>[class]{pair}-[func]{}\n\n[class]{arrayHashMap}-[func]{}\n</code></pre> array_hash_map.swift<pre><code>[file]{utils/pair.swift}-[class]{Pair}-[func]{}\n\n[class]{ArrayHashMap}-[func]{}\n</code></pre> array_hash_map.js<pre><code>[class]{Pair}-[func]{}\n\n[class]{ArrayHashMap}-[func]{}\n</code></pre> array_hash_map.ts<pre><code>[class]{Pair}-[func]{}\n\n[class]{ArrayHashMap}-[func]{}\n</code></pre> array_hash_map.dart<pre><code>[class]{Pair}-[func]{}\n\n[class]{ArrayHashMap}-[func]{}\n</code></pre> array_hash_map.rs<pre><code>[class]{Pair}-[func]{}\n\n[class]{ArrayHashMap}-[func]{}\n</code></pre> array_hash_map.c<pre><code>[class]{Pair}-[func]{}\n\n[class]{ArrayHashMap}-[func]{}\n</code></pre> array_hash_map.kt<pre><code>[class]{Pair}-[func]{}\n\n[class]{ArrayHashMap}-[func]{}\n</code></pre> array_hash_map.rb<pre><code>[class]{Pair}-[func]{}\n\n[class]{ArrayHashMap}-[func]{}\n</code></pre>","path":["第 6 章 &nbsp; ハッシュ表","6.1 &nbsp; ハッシュ表"],"tags":[]},{"location":"chapter_hashing/hash_map/#613","level":2,"title":"6.1.3   ハッシュ衝突とリサイズ","text":"<p>本質的に、ハッシュ関数の役割は、すべてのキーの入力空間全体を、すべての配列インデックスの出力空間にマッピングすることです。しかし、入力空間は出力空間よりもはるかに大きいことがよくあります。したがって、理論的には、「複数の入力が同じ出力に対応する」ケースが常に存在します。</p> <p>上記の例では、与えられたハッシュ関数で、入力<code>key</code>の下二桁が同じ場合、ハッシュ関数は同じ出力を生成します。例えば、学籍番号12836と20336の2人の学生をクエリすると、以下のことがわかります：</p> <pre><code>12836 % 100 = 36\n20336 % 100 = 36\n</code></pre> <p>下図に示すように、両方の学籍番号が同じ名前を指しており、これは明らかに間違っています。この複数の入力が同じ出力に対応する状況をハッシュ衝突と呼びます。</p> <p></p> <p> 図 6-3   ハッシュ衝突の例 </p> <p>ハッシュ表の容量\\(n\\)が増加するにつれて、複数のキーが同じバケットに割り当てられる確率が減少し、衝突が少なくなることは理解しやすいです。したがって、ハッシュ表をリサイズすることでハッシュ衝突を減らすことができます。</p> <p>下図に示すように、リサイズ前は、キー値ペア<code>(136, A)</code>と<code>(236, D)</code>が衝突していました。しかし、リサイズ後は衝突が解決されています。</p> <p></p> <p> 図 6-4   ハッシュ表のリサイズ </p> <p>配列の拡張と同様に、ハッシュ表のリサイズにはすべてのキー値ペアを元のハッシュ表から新しいものに移行する必要があり、時間がかかります。さらに、ハッシュ表の<code>capacity</code>が変更されるため、ハッシュ関数を使用してすべてのキー値ペアの格納位置を再計算する必要があり、リサイズプロセスの計算オーバーヘッドがさらに増加します。したがって、プログラミング言語は頻繁なリサイズを防ぐために、ハッシュ表に十分大きな容量を割り当てることがよくあります。</p> <p>負荷率はハッシュ表の重要な概念です。ハッシュ表内の要素数とバケット数の比率として定義されます。ハッシュ衝突の深刻度を測定するために使用され、しばしばハッシュ表のリサイズのトリガーとしても機能します。例えば、Javaでは、負荷率が\\(0.75\\)を超えると、システムはハッシュ表を元のサイズの2倍にリサイズします。</p>","path":["第 6 章 &nbsp; ハッシュ表","6.1 &nbsp; ハッシュ表"],"tags":[]},{"location":"chapter_hashing/summary/","level":1,"title":"6.4   まとめ","text":"","path":["第 6 章 &nbsp; ハッシュ表","6.4 &nbsp; まとめ"],"tags":[]},{"location":"chapter_hashing/summary/#1","level":3,"title":"1.   重要なポイント","text":"<ul> <li>入力<code>key</code>が与えられると、ハッシュ表は\\(O(1)\\)の時間で対応する<code>value</code>を取得でき、非常に効率的です。</li> <li>一般的なハッシュ表の操作には、クエリ、キー値ペアの追加、キー値ペアの削除、ハッシュ表の走査があります。</li> <li>ハッシュ関数は<code>key</code>を配列インデックスにマッピングし、対応するバケットにアクセスして<code>value</code>を取得できるようにします。</li> <li>2つの異なるキーがハッシュ化後に同じ配列インデックスになる場合があり、誤ったクエリ結果につながります。この現象はハッシュ衝突として知られています。</li> <li>ハッシュ表の容量が大きいほど、ハッシュ衝突の確率は低くなります。したがって、ハッシュ表のリサイズはハッシュ衝突を緩和できます。配列のリサイズと同様に、ハッシュ表のリサイズはコストが高いです。</li> <li>要素数をバケット数で割った負荷率は、ハッシュ衝突の深刻度を反映し、しばしばハッシュ表リサイズのトリガー条件として使用されます。</li> <li>連鎖法は各要素を連結リストに変換し、衝突するすべての要素を同じリストに格納することでハッシュ衝突に対処します。ただし、過度に長いリストはクエリ効率を低下させる可能性があり、リストを赤黒木に変換することで改善できます。</li> <li>オープンアドレス法は複数回のプローブを通してハッシュ衝突を処理します。線形プローブは固定ステップサイズを使用しますが、要素を削除できず、クラスタリングを起こしやすい傾向があります。多重ハッシュはプローブに複数のハッシュ関数を使用し、線形プローブと比較してクラスタリングを減らしますが、計算オーバーヘッドが増加します。</li> <li>異なるプログラミング言語はさまざまなハッシュ表実装を採用しています。例えば、Javaの<code>HashMap</code>は連鎖法を使用し、Pythonの<code>dict</code>はオープンアドレス法を採用しています。</li> <li>ハッシュ表では、決定性、高効率、均等分散を持つハッシュアルゴリズムが望まれます。暗号化では、ハッシュアルゴリズムは衝突耐性と雪崩効果も持つべきです。</li> <li>ハッシュアルゴリズムは通常、ハッシュ値の均等分散を保証し、ハッシュ衝突を減らすために、大きな素数を剰余として使用します。</li> <li>一般的なハッシュアルゴリズムには、MD5、SHA-1、SHA-2、SHA-3があります。MD5はファイル整合性チェックによく使用され、SHA-2は安全なアプリケーションとプロトコルで一般的に使用されます。</li> <li>プログラミング言語は通常、ハッシュ表のバケットインデックスを計算するために、データ型に対して組み込みのハッシュアルゴリズムを提供します。一般的に、不変オブジェクトのみがハッシュ可能です。</li> </ul>","path":["第 6 章 &nbsp; ハッシュ表","6.4 &nbsp; まとめ"],"tags":[]},{"location":"chapter_hashing/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: ハッシュ表の時間計算量が\\(O(n)\\)に悪化するのはいつですか？</p> <p>ハッシュ表の時間計算量は、ハッシュ衝突が深刻な場合に\\(O(n)\\)に悪化する可能性があります。ハッシュ関数が適切に設計され、容量が適切に設定され、衝突が均等に分散されている場合、時間計算量は\\(O(1)\\)です。プログラミング言語の組み込みハッシュ表を使用する場合、通常は時間計算量を\\(O(1)\\)と考えます。</p> <p>Q: なぜハッシュ関数\\(f(x) = x\\)を使用しないのですか？これなら衝突を排除できます。</p> <p>ハッシュ関数\\(f(x) = x\\)では、各要素が一意のバケットインデックスに対応し、これは配列と同等です。しかし、入力空間は通常出力空間（配列長）よりもはるかに大きいため、ハッシュ関数の最後のステップは配列長の剰余を取ることがよくあります。言い換えると、ハッシュ表の目標は、\\(O(1)\\)のクエリ効率を提供しながら、より大きな状態空間をより小さなものにマッピングすることです。</p> <p>Q: ハッシュ表がこれらの構造を使って実装されているにもかかわらず、なぜ配列、連結リスト、二分木よりも効率的になれるのですか？</p> <p>まず、ハッシュ表は時間効率が高いですが、空間効率は低いです。ハッシュ表のメモリの大部分は未使用のままです。</p> <p>次に、ハッシュ表は特定のユースケースでのみ時間効率が高いです。配列や連結リストを使用して同じ時間計算量で機能を実装できる場合、通常はハッシュ表を使用するよりも高速です。これは、ハッシュ関数の計算がオーバーヘッドを発生させ、時間計算量の定数因子が大きくなるためです。</p> <p>最後に、ハッシュ表の時間計算量は悪化する可能性があります。例えば、連鎖法では、連結リストや赤黒木で検索操作を実行し、これは依然として\\(O(n)\\)時間に悪化するリスクがあります。</p> <p>Q: 多重ハッシュにも要素を直接削除できないという欠陥がありますか？削除としてマークされた空間は再利用できますか？</p> <p>多重ハッシュはオープンアドレス法の一形態であり、すべてのオープンアドレス法には要素を直接削除できないという欠点があります。要素を削除済みとしてマークする必要があります。マークされた空間は再利用できます。ハッシュ表に新しい要素を挿入する際、ハッシュ関数が削除済みとしてマークされた位置を指している場合、その位置は新しい要素によって使用できます。これにより、ハッシュ表のプローブシーケンスを維持しながら、空間の効率的な使用が保証されます。</p> <p>Q: なぜ線形プローブの検索プロセス中にハッシュ衝突が発生するのですか？</p> <p>検索プロセス中、ハッシュ関数は対応するバケットとキー値ペアを指します。<code>key</code>が一致しない場合、ハッシュ衝突を示します。したがって、線形プローブは正しいキー値ペアが見つかるか検索が失敗するまで、事前に決められたステップサイズで下方向に検索します。</p> <p>Q: なぜハッシュ表のリサイズがハッシュ衝突を緩和できるのですか？</p> <p>ハッシュ関数の最後のステップは、出力を配列インデックス範囲内に保つために、配列長\\(n\\)の剰余を取ることがよくあります。リサイズ時、配列長\\(n\\)が変化し、キーに対応するインデックスも変化する可能性があります。以前に同じバケットにマッピングされていたキーが、リサイズ後に複数のバケットに分散される可能性があり、それによってハッシュ衝突が緩和されます。</p>","path":["第 6 章 &nbsp; ハッシュ表","6.4 &nbsp; まとめ"],"tags":[]},{"location":"chapter_heap/","level":1,"title":"第 8 章   ヒープ","text":"<p>Abstract</p> <p>ヒープは山とその険しい峰のように、層をなして起伏し、それぞれが独特の形を持っています。</p> <p>各山の頂は散らばった高さで上下しますが、最も高いものが常に最初に注目を集めます。</p>","path":["第 8 章 &nbsp; ヒープ"],"tags":[]},{"location":"chapter_heap/#_1","level":2,"title":"章の内容","text":"<ul> <li>8.1   ヒープ</li> <li>8.2   ヒープ構築操作</li> <li>8.3   Top-k 問題</li> <li>8.4   まとめ</li> </ul>","path":["第 8 章 &nbsp; ヒープ"],"tags":[]},{"location":"chapter_heap/build_heap/","level":1,"title":"8.2   ヒープ構築操作","text":"<p>場合によっては、リストのすべての要素を使用してヒープを構築したいことがあり、このプロセスは「ヒープ構築操作」として知られています。</p>","path":["第 8 章 &nbsp; ヒープ","8.2 &nbsp; ヒープ構築操作"],"tags":[]},{"location":"chapter_heap/build_heap/#821","level":2,"title":"8.2.1   ヒープ挿入操作による実装","text":"<p>まず、空のヒープを作成し、次にリストを反復処理して、各要素に対して順番に「ヒープ挿入操作」を実行します。これは、要素をヒープの末尾に追加し、次に下から上に「ヒープ化」することを意味します。</p> <p>ヒープに要素が追加されるたびに、ヒープの長さは1つずつ増加します。ノードは二分木に上から下に追加されるため、ヒープは「上から下に」構築されます。</p> <p>要素数を\\(n\\)とすると、各要素の挿入操作は\\(O(\\log{n})\\)時間かかるため、このヒープ構築方法の時間計算量は\\(O(n \\log n)\\)です。</p>","path":["第 8 章 &nbsp; ヒープ","8.2 &nbsp; ヒープ構築操作"],"tags":[]},{"location":"chapter_heap/build_heap/#822","level":2,"title":"8.2.2   走査によるヒープ化の実装","text":"<p>実際には、2つのステップでより効率的なヒープ構築方法を実装できます。</p> <ol> <li>リストのすべての要素をそのままヒープに追加します。この時点では、ヒープの性質はまだ満たされていません。</li> <li>ヒープを逆順（レベル順走査の逆）で走査し、各非葉ノードに対して「上から下のヒープ化」を実行します。</li> </ol> <p>ノードをヒープ化した後、そのノードを根とする部分木は有効な部分ヒープになります。走査が逆順であるため、ヒープは「下から上に」構築されます。</p> <p>逆走査を選択する理由は、現在のノードの下の部分木がすでに有効な部分ヒープであることを保証し、現在のノードのヒープ化を効果的にするためです。</p> <p>言及する価値があるのは、**葉ノードは子を持たないため、自然に有効な部分ヒープを形成し、ヒープ化する必要がない**ということです。以下のコードに示すように、最後の非葉ノードは最後のノードの親です。そこから開始して逆順に走査してヒープ化を実行します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby my_heap.py<pre><code>def __init__(self, nums: list[int]):\n    \"\"\"コンストラクタ、入力リストに基づいてヒープを構築\"\"\"\n    # すべてのリスト要素をヒープに追加\n    self.max_heap = nums\n    # 葉以外のすべてのノードをヒープ化\n    for i in range(self.parent(self.size() - 1), -1, -1):\n        self.sift_down(i)\n</code></pre> my_heap.cpp<pre><code>/* コンストラクタ、入力リストに基づいてヒープを構築 */\nMaxHeap(vector&lt;int&gt; nums) {\n    // すべてのリスト要素をヒープに追加\n    maxHeap = nums;\n    // 葉以外のすべてのノードをヒープ化\n    for (int i = parent(size() - 1); i &gt;= 0; i--) {\n        siftDown(i);\n    }\n}\n</code></pre> my_heap.java<pre><code>/* コンストラクタ、入力リストに基づいてヒープを構築 */\nMaxHeap(List&lt;Integer&gt; nums) {\n    // すべてのリスト要素をヒープに追加\n    maxHeap = new ArrayList&lt;&gt;(nums);\n    // 葉を除くすべてのノードをヒープ化\n    for (int i = parent(size() - 1); i &gt;= 0; i--) {\n        siftDown(i);\n    }\n}\n</code></pre> my_heap.cs<pre><code>[class]{MaxHeap}-[func]{MaxHeap}\n</code></pre> my_heap.go<pre><code>[class]{maxHeap}-[func]{newMaxHeap}\n</code></pre> my_heap.swift<pre><code>[class]{MaxHeap}-[func]{init}\n</code></pre> my_heap.js<pre><code>[class]{MaxHeap}-[func]{constructor}\n</code></pre> my_heap.ts<pre><code>[class]{MaxHeap}-[func]{constructor}\n</code></pre> my_heap.dart<pre><code>[class]{MaxHeap}-[func]{MaxHeap}\n</code></pre> my_heap.rs<pre><code>[class]{MaxHeap}-[func]{new}\n</code></pre> my_heap.c<pre><code>[class]{MaxHeap}-[func]{newMaxHeap}\n</code></pre> my_heap.kt<pre><code>[class]{MaxHeap}-[func]{}\n</code></pre> my_heap.rb<pre><code>[class]{MaxHeap}-[func]{initialize}\n</code></pre>","path":["第 8 章 &nbsp; ヒープ","8.2 &nbsp; ヒープ構築操作"],"tags":[]},{"location":"chapter_heap/build_heap/#823","level":2,"title":"8.2.3   計算量分析","text":"<p>次に、この第2のヒープ構築方法の時間計算量を計算してみましょう。</p> <ul> <li>完備二分木のノード数を\\(n\\)と仮定すると、葉ノードの数は\\((n + 1) / 2\\)です。ここで\\(/\\) は整数除算です。したがって、ヒープ化が必要なノードの数は\\((n - 1) / 2\\)です。</li> <li>「上から下のヒープ化」のプロセスでは、各ノードは最大で葉ノードまでヒープ化されるため、最大反復回数は二分木の高さ\\(\\log n\\)です。</li> </ul> <p>この2つを掛け合わせると、ヒープ構築プロセスの時間計算量は\\(O(n \\log n)\\)となります。しかし、この推定は正確ではありません。二分木の下位レベルには上位よりもはるかに多くのノードがあるという性質を考慮していないからです。</p> <p>より正確な計算を行いましょう。計算を簡素化するため、\\(n\\)個のノードと高さ\\(h\\)を持つ「完全二分木」を仮定します。この仮定は結果の正確性に影響しません。</p> <p></p> <p> 図 8-5   完全二分木の各レベルのノード数 </p> <p>上図に示すように、ノードが「上から下にヒープ化される」最大反復回数は、そのノードから葉ノードまでの距離と等しく、これは正確に「ノードの高さ」です。したがって、各レベルで「ノード数×ノードの高さ」を合計して、**すべてのノードの総ヒープ化反復回数を得る**ことができます。</p> \\[ T(h) = 2^0h + 2^1(h-1) + 2^2(h-2) + \\dots + 2^{(h-1)}\\times1 \\] <p>上記の方程式を簡素化するために、高校の数列の知識を使用する必要があります。まず\\(T(h)\\)に\\(2\\)を掛けて以下を得ます：</p> \\[ \\begin{aligned} T(h) &amp; = 2^0h + 2^1(h-1) + 2^2(h-2) + \\dots + 2^{h-1}\\times1 \\newline 2T(h) &amp; = 2^1h + 2^2(h-1) + 2^3(h-2) + \\dots + 2^h\\times1 \\newline \\end{aligned} \\] <p>変位法を使用して\\(2T(h)\\)から\\(T(h)\\)を減算すると、以下を得ます：</p> \\[ 2T(h) - T(h) = T(h) = -2^0h + 2^1 + 2^2 + \\dots + 2^{h-1} + 2^h \\] <p>方程式を観察すると、\\(T(h)\\)は等比数列であり、和の公式を使用して直接計算でき、時間計算量は以下になります：</p> \\[ \\begin{aligned} T(h) &amp; = 2 \\frac{1 - 2^h}{1 - 2} - h \\newline &amp; = 2^{h+1} - h - 2 \\newline &amp; = O(2^h) \\end{aligned} \\] <p>さらに、高さ\\(h\\)の完全二分木は\\(n = 2^{h+1} - 1\\)個のノードを持つため、計算量は\\(O(2^h) = O(n)\\)です。この計算は、**リストを入力してヒープを構築する時間計算量が\\(O(n)\\)であり、非常に効率的である**ことを示しています。</p>","path":["第 8 章 &nbsp; ヒープ","8.2 &nbsp; ヒープ構築操作"],"tags":[]},{"location":"chapter_heap/heap/","level":1,"title":"8.1   ヒープ","text":"<p>ヒープは特定の条件を満たす完備二分木で、主に次の2つのタイプに分類されます（下図参照）。</p> <ul> <li>最小ヒープ：任意のノードの値 \\(\\leq\\) その子ノードの値。</li> <li>最大ヒープ：任意のノードの値 \\(\\geq\\) その子ノードの値。</li> </ul> <p></p> <p> 図 8-1   最小ヒープと最大ヒープ </p> <p>完備二分木の特別なケースとして、ヒープには以下の特性があります：</p> <ul> <li>最下位層のノードは左から右に埋められ、他の層のノードは完全に埋められています。</li> <li>二分木の根ノードをヒープの「先頭」と呼び、最も右下のノードをヒープの「末尾」と呼びます。</li> <li>最大ヒープ（最小ヒープ）の場合、先頭要素（根）の値はすべての要素の中で最大（最小）です。</li> </ul>","path":["第 8 章 &nbsp; ヒープ","8.1 &nbsp; ヒープ"],"tags":[]},{"location":"chapter_heap/heap/#811","level":2,"title":"8.1.1   ヒープの一般的な操作","text":"<p>多くのプログラミング言語が優先度キューを提供していることに注意してください。これは優先度付きソートを持つキューとして定義される抽象データ構造です。</p> <p>実際には、ヒープは優先度キューを実装するためによく使用されます。最大ヒープは、要素が降順でデキューされる優先度キューに対応します。使用の観点から、「優先度キュー」と「ヒープ」を同等のデータ構造と考えることができます。したがって、この本では両者を特別に区別せず、統一して「ヒープ」と呼びます。</p> <p>ヒープの一般的な操作を下表に示します。メソッド名はプログラミング言語によって異なる場合があります。</p> <p> 表 8-1   ヒープ操作の効率 </p> メソッド名 説明 時間計算量 <code>push()</code> ヒープに要素を追加 \\(O(\\log n)\\) <code>pop()</code> ヒープから先頭要素を削除 \\(O(\\log n)\\) <code>peek()</code> 先頭要素にアクセス（最大/最小ヒープの場合、最大/最小値） \\(O(1)\\) <code>size()</code> ヒープ内の要素数を取得 \\(O(1)\\) <code>isEmpty()</code> ヒープが空かどうかをチェック \\(O(1)\\) <p>実際には、プログラミング言語によって提供されるヒープクラス（または優先度キュークラス）を直接使用できます。</p> <p>ソートアルゴリズムで「昇順」と「降順」があるように、<code>flag</code>を設定するか<code>Comparator</code>を変更することで「最小ヒープ」と「最大ヒープ」を切り替えることができます。コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby heap.py<pre><code># 最小ヒープの初期化\nmin_heap, flag = [], 1\n# 最大ヒープの初期化\nmax_heap, flag = [], -1\n\n# Pythonのheapqモジュールはデフォルトで最小ヒープを実装\n# 要素をヒープにプッシュする前に負の値にすることで、順序を反転させ、最大ヒープを実装\n# この例では、flag = 1は最小ヒープに対応し、flag = -1は最大ヒープに対応\n\n# ヒープに要素をプッシュ\nheapq.heappush(max_heap, flag * 1)\nheapq.heappush(max_heap, flag * 3)\nheapq.heappush(max_heap, flag * 2)\nheapq.heappush(max_heap, flag * 5)\nheapq.heappush(max_heap, flag * 4)\n\n# ヒープの先頭要素を取得\npeek: int = flag * max_heap[0] # 5\n\n# ヒープの先頭要素をポップ\n# ポップされた要素は降順のシーケンスを形成\nval = flag * heapq.heappop(max_heap) # 5\nval = flag * heapq.heappop(max_heap) # 4\nval = flag * heapq.heappop(max_heap) # 3\nval = flag * heapq.heappop(max_heap) # 2\nval = flag * heapq.heappop(max_heap) # 1\n\n# ヒープのサイズを取得\nsize: int = len(max_heap)\n\n# ヒープが空かどうかをチェック\nis_empty: bool = not max_heap\n\n# リストからヒープを作成\nmin_heap: list[int] = [1, 3, 2, 5, 4]\nheapq.heapify(min_heap)\n</code></pre> heap.cpp<pre><code>/* ヒープの初期化 */\n// 最小ヒープの初期化\npriority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; minHeap;\n// 最大ヒープの初期化\npriority_queue&lt;int, vector&lt;int&gt;, less&lt;int&gt;&gt; maxHeap;\n\n/* ヒープに要素をプッシュ */\nmaxHeap.push(1);\nmaxHeap.push(3);\nmaxHeap.push(2);\nmaxHeap.push(5);\nmaxHeap.push(4);\n\n/* ヒープの先頭要素を取得 */\nint peek = maxHeap.top(); // 5\n\n/* ヒープの先頭要素をポップ */\n// ポップされた要素は降順のシーケンスを形成\nmaxHeap.pop(); // 5\nmaxHeap.pop(); // 4\nmaxHeap.pop(); // 3\nmaxHeap.pop(); // 2\nmaxHeap.pop(); // 1\n\n/* ヒープのサイズを取得 */\nint size = maxHeap.size();\n\n/* ヒープが空かどうかをチェック */\nbool isEmpty = maxHeap.empty();\n\n/* リストからヒープを作成 */\nvector&lt;int&gt; input{1, 3, 2, 5, 4};\npriority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; minHeap(input.begin(), input.end());\n</code></pre> heap.java<pre><code>/* ヒープの初期化 */\n// 最小ヒープの初期化\nQueue&lt;Integer&gt; minHeap = new PriorityQueue&lt;&gt;();\n// 最大ヒープの初期化（ラムダ式でComparatorを変更するだけ）\nQueue&lt;Integer&gt; maxHeap = new PriorityQueue&lt;&gt;((a, b) -&gt; b - a);\n\n/* ヒープに要素をプッシュ */\nmaxHeap.offer(1);\nmaxHeap.offer(3);\nmaxHeap.offer(2);\nmaxHeap.offer(5);\nmaxHeap.offer(4);\n\n/* ヒープの先頭要素を取得 */\nint peek = maxHeap.peek(); // 5\n\n/* ヒープの先頭要素をポップ */\n// ポップされた要素は降順のシーケンスを形成\npeek = maxHeap.poll(); // 5\npeek = maxHeap.poll(); // 4\npeek = maxHeap.poll(); // 3\npeek = maxHeap.poll(); // 2\npeek = maxHeap.poll(); // 1\n\n/* ヒープのサイズを取得 */\nint size = maxHeap.size();\n\n/* ヒープが空かどうかをチェック */\nboolean isEmpty = maxHeap.isEmpty();\n\n/* リストからヒープを作成 */\nminHeap = new PriorityQueue&lt;&gt;(Arrays.asList(1, 3, 2, 5, 4));\n</code></pre> heap.cs<pre><code>/* ヒープの初期化 */\n// 最小ヒープの初期化\nPriorityQueue&lt;int, int&gt; minHeap = new();\n// 最大ヒープの初期化（ラムダ式でComparatorを変更するだけ）\nPriorityQueue&lt;int, int&gt; maxHeap = new(Comparer&lt;int&gt;.Create((x, y) =&gt; y - x));\n\n/* ヒープに要素をプッシュ */\nmaxHeap.Enqueue(1, 1);\nmaxHeap.Enqueue(3, 3);\nmaxHeap.Enqueue(2, 2);\nmaxHeap.Enqueue(5, 5);\nmaxHeap.Enqueue(4, 4);\n\n/* ヒープの先頭要素を取得 */\nint peek = maxHeap.Peek();//5\n\n/* ヒープの先頭要素をポップ */\n// ポップされた要素は降順のシーケンスを形成\npeek = maxHeap.Dequeue();  // 5\npeek = maxHeap.Dequeue();  // 4\npeek = maxHeap.Dequeue();  // 3\npeek = maxHeap.Dequeue();  // 2\npeek = maxHeap.Dequeue();  // 1\n\n/* ヒープのサイズを取得 */\nint size = maxHeap.Count;\n\n/* ヒープが空かどうかをチェック */\nbool isEmpty = maxHeap.Count == 0;\n\n/* リストからヒープを作成 */\nminHeap = new PriorityQueue&lt;int, int&gt;([(1, 1), (3, 3), (2, 2), (5, 5), (4, 4)]);\n</code></pre> heap.go<pre><code>// Goでは、heap.Interfaceを実装することで整数の最大ヒープを構築できます\n// heap.Interfaceを実装するには、sort.Interfaceも実装する必要があります\ntype intHeap []any\n\n// heap.InterfaceのPushメソッド、要素をヒープにプッシュ\nfunc (h *intHeap) Push(x any) {\n    // PushとPopの両方でポインタレシーバーを使用\n    // スライスの要素を調整するだけでなく、その長さも変更するため\n    *h = append(*h, x.(int))\n}\n\n// heap.InterfaceのPopメソッド、ヒープの先頭要素を削除\nfunc (h *intHeap) Pop() any {\n    // ヒープからポップする要素は末尾に格納\n    last := (*h)[len(*h)-1]\n    *h = (*h)[:len(*h)-1]\n    return last\n}\n\n// sort.InterfaceのLenメソッド\nfunc (h *intHeap) Len() int {\n    return len(*h)\n}\n\n// sort.InterfaceのLessメソッド\nfunc (h *intHeap) Less(i, j int) bool {\n    // 最小ヒープを実装したい場合は、これを小なり比較に変更\n    return (*h)[i].(int) &gt; (*h)[j].(int)\n}\n\n// sort.InterfaceのSwapメソッド\nfunc (h *intHeap) Swap(i, j int) {\n    (*h)[i], (*h)[j] = (*h)[j], (*h)[i]\n}\n\n// Top ヒープの先頭要素を取得\nfunc (h *intHeap) Top() any {\n    return (*h)[0]\n}\n\n/* ドライバーコード */\nfunc TestHeap(t *testing.T) {\n    /* ヒープの初期化 */\n    // 最大ヒープの初期化\n    maxHeap := &amp;intHeap{}\n    heap.Init(maxHeap)\n    /* ヒープに要素をプッシュ */\n    // heap.Interfaceのメソッドを呼び出して要素を追加\n    heap.Push(maxHeap, 1)\n    heap.Push(maxHeap, 3)\n    heap.Push(maxHeap, 2)\n    heap.Push(maxHeap, 4)\n    heap.Push(maxHeap, 5)\n\n    /* ヒープの先頭要素を取得 */\n    top := maxHeap.Top()\n    fmt.Printf(\"ヒープの先頭要素は %d\\n\", top)\n\n    /* ヒープの先頭要素をポップ */\n    // heap.Interfaceのメソッドを呼び出して要素を削除\n    heap.Pop(maxHeap) // 5\n    heap.Pop(maxHeap) // 4\n    heap.Pop(maxHeap) // 3\n    heap.Pop(maxHeap) // 2\n    heap.Pop(maxHeap) // 1\n\n    /* ヒープのサイズを取得 */\n    size := len(*maxHeap)\n    fmt.Printf(\"ヒープ内の要素数は %d\\n\", size)\n\n    /* ヒープが空かどうかをチェック */\n    isEmpty := len(*maxHeap) == 0\n    fmt.Printf(\"ヒープは空ですか？ %t\\n\", isEmpty)\n}\n</code></pre> heap.swift<pre><code>/* ヒープの初期化 */\n// SwiftのHeap型は最大ヒープと最小ヒープの両方をサポートし、swift-collectionsライブラリが必要\nvar heap = Heap&lt;Int&gt;()\n\n/* ヒープに要素をプッシュ */\nheap.insert(1)\nheap.insert(3)\nheap.insert(2)\nheap.insert(5)\nheap.insert(4)\n\n/* ヒープの先頭要素を取得 */\nvar peek = heap.max()!\n\n/* ヒープの先頭要素をポップ */\npeek = heap.removeMax() // 5\npeek = heap.removeMax() // 4\npeek = heap.removeMax() // 3\npeek = heap.removeMax() // 2\npeek = heap.removeMax() // 1\n\n/* ヒープのサイズを取得 */\nlet size = heap.count\n\n/* ヒープが空かどうかをチェック */\nlet isEmpty = heap.isEmpty\n\n/* リストからヒープを作成 */\nlet heap2 = Heap([1, 3, 2, 5, 4])\n</code></pre> heap.js<pre><code>// JavaScriptは組み込みのHeapクラスを提供していません\n</code></pre> heap.ts<pre><code>// TypeScriptは組み込みのHeapクラスを提供していません\n</code></pre> heap.dart<pre><code>// Dartは組み込みのHeapクラスを提供していません\n</code></pre> heap.rs<pre><code>use std::collections::BinaryHeap;\nuse std::cmp::Reverse;\n\n/* ヒープの初期化 */\n// 最小ヒープの初期化\nlet mut min_heap = BinaryHeap::&lt;Reverse&lt;i32&gt;&gt;::new();\n// 最大ヒープの初期化\nlet mut max_heap = BinaryHeap::new();\n\n/* ヒープに要素をプッシュ */\nmax_heap.push(1);\nmax_heap.push(3);\nmax_heap.push(2);\nmax_heap.push(5);\nmax_heap.push(4);\n\n/* ヒープの先頭要素を取得 */\nlet peek = max_heap.peek().unwrap();  // 5\n\n/* ヒープの先頭要素をポップ */\n// ポップされた要素は降順のシーケンスを形成\nlet peek = max_heap.pop().unwrap();   // 5\nlet peek = max_heap.pop().unwrap();   // 4\nlet peek = max_heap.pop().unwrap();   // 3\nlet peek = max_heap.pop().unwrap();   // 2\nlet peek = max_heap.pop().unwrap();   // 1\n\n/* ヒープのサイズを取得 */\nlet size = max_heap.len();\n\n/* ヒープが空かどうかをチェック */\nlet is_empty = max_heap.is_empty();\n\n/* リストからヒープを作成 */\nlet min_heap = BinaryHeap::from(vec![Reverse(1), Reverse(3), Reverse(2), Reverse(5), Reverse(4)]);\n</code></pre> heap.c<pre><code>// Cは組み込みのHeapクラスを提供していません\n</code></pre> heap.kt<pre><code>/* ヒープの初期化 */\n// 最小ヒープの初期化\nvar minHeap = PriorityQueue&lt;Int&gt;()\n// 最大ヒープの初期化（ラムダ式でComparatorを変更するだけ）\nval maxHeap = PriorityQueue { a: Int, b: Int -&gt; b - a }\n\n/* ヒープに要素をプッシュ */\nmaxHeap.offer(1)\nmaxHeap.offer(3)\nmaxHeap.offer(2)\nmaxHeap.offer(5)\nmaxHeap.offer(4)\n\n/* ヒープの先頭要素を取得 */\nvar peek = maxHeap.peek() // 5\n\n/* ヒープの先頭要素をポップ */\n// ポップされた要素は降順のシーケンスを形成\npeek = maxHeap.poll() // 5\npeek = maxHeap.poll() // 4\npeek = maxHeap.poll() // 3\npeek = maxHeap.poll() // 2\npeek = maxHeap.poll() // 1\n\n/* ヒープのサイズを取得 */\nval size = maxHeap.size\n\n/* ヒープが空かどうかをチェック */\nval isEmpty = maxHeap.isEmpty()\n\n/* リストからヒープを作成 */\nminHeap = PriorityQueue(mutableListOf(1, 3, 2, 5, 4))\n</code></pre> heap.rb<pre><code>\n</code></pre>","path":["第 8 章 &nbsp; ヒープ","8.1 &nbsp; ヒープ"],"tags":[]},{"location":"chapter_heap/heap/#812","level":2,"title":"8.1.2   ヒープの実装","text":"<p>以下の実装は最大ヒープです。最小ヒープに変換するには、すべてのサイズ論理比較を反転させるだけです（例えば、\\(\\geq\\)を\\(\\leq\\)に置き換える）。興味のある読者は自分で実装することをお勧めします。</p>","path":["第 8 章 &nbsp; ヒープ","8.1 &nbsp; ヒープ"],"tags":[]},{"location":"chapter_heap/heap/#1","level":3,"title":"1.   ヒープの格納と表現","text":"<p>「二分木」の節で述べたように、完備二分木は配列表現に非常に適しています。ヒープは完備二分木の一種なので、配列を使用してヒープを格納します。</p> <p>配列を使用して二分木を表現する場合、要素はノード値を表し、インデックスは二分木内のノード位置を表します。ノードポインタはインデックスマッピング公式を通じて実装されます。</p> <p>下図に示すように、インデックス\\(i\\)が与えられた場合、その左の子のインデックスは\\(2i + 1\\)、右の子のインデックスは\\(2i + 2\\)、親のインデックスは\\((i - 1) / 2\\)（床除算）です。インデックスが範囲外の場合、nullノードまたはノードが存在しないことを意味します。</p> <p></p> <p> 図 8-2   ヒープの表現と格納 </p> <p>後で便利に使用するため、インデックスマッピング公式を関数にカプセル化できます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby my_heap.py<pre><code>def left(self, i: int) -&gt; int:\n    \"\"\"左の子ノードのインデックスを取得\"\"\"\n    return 2 * i + 1\n\ndef right(self, i: int) -&gt; int:\n    \"\"\"右の子ノードのインデックスを取得\"\"\"\n    return 2 * i + 2\n\ndef parent(self, i: int) -&gt; int:\n    \"\"\"親ノードのインデックスを取得\"\"\"\n    return (i - 1) // 2  # 整数除算で切り下げ\n</code></pre> my_heap.cpp<pre><code>/* 左の子ノードのインデックスを取得 */\nint left(int i) {\n    return 2 * i + 1;\n}\n\n/* 右の子ノードのインデックスを取得 */\nint right(int i) {\n    return 2 * i + 2;\n}\n\n/* 親ノードのインデックスを取得 */\nint parent(int i) {\n    return (i - 1) / 2; // 整数除算で切り下げ\n}\n</code></pre> my_heap.java<pre><code>/* 左の子ノードのインデックスを取得 */\nint left(int i) {\n    return 2 * i + 1;\n}\n\n/* 右の子ノードのインデックスを取得 */\nint right(int i) {\n    return 2 * i + 2;\n}\n\n/* 親ノードのインデックスを取得 */\nint parent(int i) {\n    return (i - 1) / 2; // 整数除算で切り下げ\n}\n</code></pre> my_heap.cs<pre><code>[class]{MaxHeap}-[func]{Left}\n\n[class]{MaxHeap}-[func]{Right}\n\n[class]{MaxHeap}-[func]{Parent}\n</code></pre> my_heap.go<pre><code>[class]{maxHeap}-[func]{left}\n\n[class]{maxHeap}-[func]{right}\n\n[class]{maxHeap}-[func]{parent}\n</code></pre> my_heap.swift<pre><code>[class]{MaxHeap}-[func]{left}\n\n[class]{MaxHeap}-[func]{right}\n\n[class]{MaxHeap}-[func]{parent}\n</code></pre> my_heap.js<pre><code>[class]{MaxHeap}-[func]{left}\n\n[class]{MaxHeap}-[func]{right}\n\n[class]{MaxHeap}-[func]{parent}\n</code></pre> my_heap.ts<pre><code>[class]{MaxHeap}-[func]{left}\n\n[class]{MaxHeap}-[func]{right}\n\n[class]{MaxHeap}-[func]{parent}\n</code></pre> my_heap.dart<pre><code>[class]{MaxHeap}-[func]{_left}\n\n[class]{MaxHeap}-[func]{_right}\n\n[class]{MaxHeap}-[func]{_parent}\n</code></pre> my_heap.rs<pre><code>[class]{MaxHeap}-[func]{left}\n\n[class]{MaxHeap}-[func]{right}\n\n[class]{MaxHeap}-[func]{parent}\n</code></pre> my_heap.c<pre><code>[class]{MaxHeap}-[func]{left}\n\n[class]{MaxHeap}-[func]{right}\n\n[class]{MaxHeap}-[func]{parent}\n</code></pre> my_heap.kt<pre><code>[class]{MaxHeap}-[func]{left}\n\n[class]{MaxHeap}-[func]{right}\n\n[class]{MaxHeap}-[func]{parent}\n</code></pre> my_heap.rb<pre><code>[class]{MaxHeap}-[func]{left}\n\n[class]{MaxHeap}-[func]{right}\n\n[class]{MaxHeap}-[func]{parent}\n</code></pre>","path":["第 8 章 &nbsp; ヒープ","8.1 &nbsp; ヒープ"],"tags":[]},{"location":"chapter_heap/heap/#2","level":3,"title":"2.   ヒープの先頭要素へのアクセス","text":"<p>ヒープの先頭要素は二分木の根ノードで、リストの最初の要素でもあります：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby my_heap.py<pre><code>def peek(self) -&gt; int:\n    \"\"\"ヒープの先頭要素にアクセス\"\"\"\n    return self.max_heap[0]\n</code></pre> my_heap.cpp<pre><code>/* ヒープの先頭要素にアクセス */\nint peek() {\n    return maxHeap[0];\n}\n</code></pre> my_heap.java<pre><code>/* ヒープの先頭要素にアクセス */\nint peek() {\n    return maxHeap.get(0);\n}\n</code></pre> my_heap.cs<pre><code>[class]{MaxHeap}-[func]{Peek}\n</code></pre> my_heap.go<pre><code>[class]{maxHeap}-[func]{peek}\n</code></pre> my_heap.swift<pre><code>[class]{MaxHeap}-[func]{peek}\n</code></pre> my_heap.js<pre><code>[class]{MaxHeap}-[func]{peek}\n</code></pre> my_heap.ts<pre><code>[class]{MaxHeap}-[func]{peek}\n</code></pre> my_heap.dart<pre><code>[class]{MaxHeap}-[func]{peek}\n</code></pre> my_heap.rs<pre><code>[class]{MaxHeap}-[func]{peek}\n</code></pre> my_heap.c<pre><code>[class]{MaxHeap}-[func]{peek}\n</code></pre> my_heap.kt<pre><code>[class]{MaxHeap}-[func]{peek}\n</code></pre> my_heap.rb<pre><code>[class]{MaxHeap}-[func]{peek}\n</code></pre>","path":["第 8 章 &nbsp; ヒープ","8.1 &nbsp; ヒープ"],"tags":[]},{"location":"chapter_heap/heap/#3","level":3,"title":"3.   ヒープへの要素挿入","text":"<p>要素<code>val</code>が与えられた場合、まずそれをヒープの底に追加します。追加後、<code>val</code>がヒープ内の他の要素より大きい可能性があるため、ヒープの完全性が損なわれる可能性があります。したがって、挿入されたノードから根ノードまでのパスを修復する必要があります。この操作はヒープ化と呼ばれます。</p> <p>挿入されたノードから開始して、下から上にヒープ化を実行します。下図に示すように、挿入されたノードの値をその親ノードと比較し、挿入されたノードが大きい場合はそれらを交換します。次にこの操作を続行し、根に到達するか、交換が不要なノードに遭遇するまで、下から上にヒープ内の各ノードを修復します。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 8-3   ヒープへの要素挿入の手順 </p> <p>総ノード数を\\(n\\)とすると、木の高さは\\(O(\\log n)\\)です。したがって、ヒープ化操作のループ反復回数は最大\\(O(\\log n)\\)で、要素挿入操作の時間計算量は\\(O(\\log n)\\)になります。コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby my_heap.py<pre><code>def push(self, val: int):\n    \"\"\"ヒープに要素をプッシュ\"\"\"\n    # ノードを追加\n    self.max_heap.append(val)\n    # 下から上へヒープ化\n    self.sift_up(self.size() - 1)\n\ndef sift_up(self, i: int):\n    \"\"\"ノードiから開始して、下から上へヒープ化\"\"\"\n    while True:\n        # ノードiの親ノードを取得\n        p = self.parent(i)\n        # 「ルートノードを越える」または「ノードが修復不要」の場合、ヒープ化を終了\n        if p &lt; 0 or self.max_heap[i] &lt;= self.max_heap[p]:\n            break\n        # 2つのノードを交換\n        self.swap(i, p)\n        # 上向きのループヒープ化\n        i = p\n</code></pre> my_heap.cpp<pre><code>/* ヒープに要素をプッシュ */\nvoid push(int val) {\n    // ノードを追加\n    maxHeap.push_back(val);\n    // 下から上へヒープ化\n    siftUp(size() - 1);\n}\n\n/* ノードiから上向きにヒープ化を開始 */\nvoid siftUp(int i) {\n    while (true) {\n        // ノードiの親ノードを取得\n        int p = parent(i);\n        // 「ルートノードを超える」または「ノードが修復不要」の場合、ヒープ化を終了\n        if (p &lt; 0 || maxHeap[i] &lt;= maxHeap[p])\n            break;\n        // 2つのノードを交換\n        swap(maxHeap[i], maxHeap[p]);\n        // 上向きにループしてヒープ化\n        i = p;\n    }\n}\n</code></pre> my_heap.java<pre><code>/* 要素をヒープにプッシュ */\nvoid push(int val) {\n    // ノードを追加\n    maxHeap.add(val);\n    // 下から上へヒープ化\n    siftUp(size() - 1);\n}\n\n/* ノード i から上向きにヒープ化を開始 */\nvoid siftUp(int i) {\n    while (true) {\n        // ノード i の親ノードを取得\n        int p = parent(i);\n        // 「根ノードを越える」または「ノードが修復不要」の場合、ヒープ化を終了\n        if (p &lt; 0 || maxHeap.get(i) &lt;= maxHeap.get(p))\n            break;\n        // 2つのノードを交換\n        swap(i, p);\n        // 上向きにヒープ化をループ\n        i = p;\n    }\n}\n</code></pre> my_heap.cs<pre><code>[class]{MaxHeap}-[func]{Push}\n\n[class]{MaxHeap}-[func]{SiftUp}\n</code></pre> my_heap.go<pre><code>[class]{maxHeap}-[func]{push}\n\n[class]{maxHeap}-[func]{siftUp}\n</code></pre> my_heap.swift<pre><code>[class]{MaxHeap}-[func]{push}\n\n[class]{MaxHeap}-[func]{siftUp}\n</code></pre> my_heap.js<pre><code>[class]{MaxHeap}-[func]{push}\n\n[class]{MaxHeap}-[func]{siftUp}\n</code></pre> my_heap.ts<pre><code>[class]{MaxHeap}-[func]{push}\n\n[class]{MaxHeap}-[func]{siftUp}\n</code></pre> my_heap.dart<pre><code>[class]{MaxHeap}-[func]{push}\n\n[class]{MaxHeap}-[func]{siftUp}\n</code></pre> my_heap.rs<pre><code>[class]{MaxHeap}-[func]{push}\n\n[class]{MaxHeap}-[func]{sift_up}\n</code></pre> my_heap.c<pre><code>[class]{MaxHeap}-[func]{push}\n\n[class]{MaxHeap}-[func]{siftUp}\n</code></pre> my_heap.kt<pre><code>[class]{MaxHeap}-[func]{push}\n\n[class]{MaxHeap}-[func]{siftUp}\n</code></pre> my_heap.rb<pre><code>[class]{MaxHeap}-[func]{push}\n\n[class]{MaxHeap}-[func]{sift_up}\n</code></pre>","path":["第 8 章 &nbsp; ヒープ","8.1 &nbsp; ヒープ"],"tags":[]},{"location":"chapter_heap/heap/#4","level":3,"title":"4.   ヒープからの先頭要素削除","text":"<p>ヒープの先頭要素は二分木の根ノード、つまりリストの最初の要素です。リストから最初の要素を直接削除すると、二分木内のすべてのノードインデックスが変更され、後続の修復にヒープ化を使用することが困難になります。要素インデックスの変更を最小限に抑えるため、次の手順を使用します。</p> <ol> <li>ヒープの先頭要素と底の要素を交換します（根ノードと最も右の葉ノードを交換）。</li> <li>交換後、リストからヒープの底を削除します（交換されているため、実際には元の先頭要素が削除される）。</li> <li>根ノードから開始して、上から下にヒープ化を実行します。</li> </ol> <p>下図に示すように、「上から下のヒープ化」の方向は「下から上のヒープ化」と反対です。根ノードの値をその2つの子と比較し、最大の子と交換します。次に、葉ノードに到達するか、交換が不要なノードに遭遇するまで、この操作を繰り返します。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 8-4   ヒープからの先頭要素削除の手順 </p> <p>要素挿入操作と同様に、先頭要素削除操作の時間計算量も\\(O(\\log n)\\)です。コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby my_heap.py<pre><code>def pop(self) -&gt; int:\n    \"\"\"要素をヒープから出す\"\"\"\n    # 空の処理\n    if self.is_empty():\n        raise IndexError(\"Heap is empty\")\n    # ルートノードと最右端の葉ノードを交換（最初の要素と最後の要素を交換）\n    self.swap(0, self.size() - 1)\n    # ノードを削除\n    val = self.max_heap.pop()\n    # 上から下へヒープ化\n    self.sift_down(0)\n    # ヒープの先頭要素を返す\n    return val\n\ndef sift_down(self, i: int):\n    \"\"\"ノードiから開始して、上から下へヒープ化\"\"\"\n    while True:\n        # i、l、rの中で最大のノードを決定し、maとする\n        l, r, ma = self.left(i), self.right(i), i\n        if l &lt; self.size() and self.max_heap[l] &gt; self.max_heap[ma]:\n            ma = l\n        if r &lt; self.size() and self.max_heap[r] &gt; self.max_heap[ma]:\n            ma = r\n        # ノードiが最大またはインデックスl、rが範囲外の場合、さらなるヒープ化は不要、ブレーク\n        if ma == i:\n            break\n        # 2つのノードを交換\n        self.swap(i, ma)\n        # 下向きのループヒープ化\n        i = ma\n</code></pre> my_heap.cpp<pre><code>/* 要素がヒープから退出 */\nvoid pop() {\n    // 空の処理\n    if (isEmpty()) {\n        throw out_of_range(\"Heap is empty\");\n    }\n    // ルートノードを最も右の葉ノードと交換（最初の要素と最後の要素を交換）\n    swap(maxHeap[0], maxHeap[size() - 1]);\n    // ノードを削除\n    maxHeap.pop_back();\n    // 上から下へヒープ化\n    siftDown(0);\n}\n\n/* ノードiから下向きにヒープ化を開始 */\nvoid siftDown(int i) {\n    while (true) {\n        // i、l、rの中で最大のノードを決定し、maとして記録\n        int l = left(i), r = right(i), ma = i;\n        if (l &lt; size() &amp;&amp; maxHeap[l] &gt; maxHeap[ma])\n            ma = l;\n        if (r &lt; size() &amp;&amp; maxHeap[r] &gt; maxHeap[ma])\n            ma = r;\n        // ノードiが最大、またはインデックスl、rが範囲外の場合、これ以上のヒープ化は不要、ブレーク\n        if (ma == i)\n            break;\n        swap(maxHeap[i], maxHeap[ma]);\n        // 下向きにループしてヒープ化\n        i = ma;\n    }\n}\n</code></pre> my_heap.java<pre><code>/* 要素がヒープから退出 */\nint pop() {\n    // 空の処理\n    if (isEmpty())\n        throw new IndexOutOfBoundsException();\n    // 根ノードを最も右の葉ノードと交換（最初の要素を最後の要素と交換）\n    swap(0, size() - 1);\n    // ノードを削除\n    int val = maxHeap.remove(size() - 1);\n    // 上から下へヒープ化\n    siftDown(0);\n    // ヒープの先頭要素を返す\n    return val;\n}\n\n/* ノード i から下向きにヒープ化を開始 */\nvoid siftDown(int i) {\n    while (true) {\n        // i、l、r の中で最大のノードを決定し、ma とする\n        int l = left(i), r = right(i), ma = i;\n        if (l &lt; size() &amp;&amp; maxHeap.get(l) &gt; maxHeap.get(ma))\n            ma = l;\n        if (r &lt; size() &amp;&amp; maxHeap.get(r) &gt; maxHeap.get(ma))\n            ma = r;\n        // ノード i が最大の場合、またはインデックス l、r が範囲外の場合、さらなるヒープ化は不要、終了\n        if (ma == i)\n            break;\n        // 2つのノードを交換\n        swap(i, ma);\n        // 下向きにヒープ化をループ\n        i = ma;\n    }\n}\n</code></pre> my_heap.cs<pre><code>[class]{MaxHeap}-[func]{Pop}\n\n[class]{MaxHeap}-[func]{SiftDown}\n</code></pre> my_heap.go<pre><code>[class]{maxHeap}-[func]{pop}\n\n[class]{maxHeap}-[func]{siftDown}\n</code></pre> my_heap.swift<pre><code>[class]{MaxHeap}-[func]{pop}\n\n[class]{MaxHeap}-[func]{siftDown}\n</code></pre> my_heap.js<pre><code>[class]{MaxHeap}-[func]{pop}\n\n[class]{MaxHeap}-[func]{siftDown}\n</code></pre> my_heap.ts<pre><code>[class]{MaxHeap}-[func]{pop}\n\n[class]{MaxHeap}-[func]{siftDown}\n</code></pre> my_heap.dart<pre><code>[class]{MaxHeap}-[func]{pop}\n\n[class]{MaxHeap}-[func]{siftDown}\n</code></pre> my_heap.rs<pre><code>[class]{MaxHeap}-[func]{pop}\n\n[class]{MaxHeap}-[func]{sift_down}\n</code></pre> my_heap.c<pre><code>[class]{MaxHeap}-[func]{pop}\n\n[class]{MaxHeap}-[func]{siftDown}\n</code></pre> my_heap.kt<pre><code>[class]{MaxHeap}-[func]{pop}\n\n[class]{MaxHeap}-[func]{siftDown}\n</code></pre> my_heap.rb<pre><code>[class]{MaxHeap}-[func]{pop}\n\n[class]{MaxHeap}-[func]{sift_down}\n</code></pre>","path":["第 8 章 &nbsp; ヒープ","8.1 &nbsp; ヒープ"],"tags":[]},{"location":"chapter_heap/heap/#813","level":2,"title":"8.1.3   ヒープの一般的な応用","text":"<ul> <li>優先度キュー：ヒープは優先度キューを実装するための好ましいデータ構造で、エンキュー操作とデキュー操作の両方の時間計算量が\\(O(\\log n)\\)、キュー構築の時間計算量が\\(O(n)\\)で、すべて非常に効率的です。</li> <li>ヒープソート：データセットが与えられた場合、それらからヒープを作成し、次に要素削除操作を継続的に実行して順序付けされたデータを取得できます。ただし、ヒープソートを実装するより洗練された方法があり、「ヒープソート」の章で説明されています。</li> <li>最大\\(k\\)個の要素の発見：これは古典的なアルゴリズム問題であり、一般的な使用例でもあります。Weiboホット検索のトップ10ホットニュースの選択や、トップ10の売れ筋商品の選択などです。</li> </ul>","path":["第 8 章 &nbsp; ヒープ","8.1 &nbsp; ヒープ"],"tags":[]},{"location":"chapter_heap/summary/","level":1,"title":"8.4   まとめ","text":"","path":["第 8 章 &nbsp; ヒープ","8.4 &nbsp; まとめ"],"tags":[]},{"location":"chapter_heap/summary/#1","level":3,"title":"1.   重要な復習","text":"<ul> <li>ヒープは完備二分木で、その構築性質に基づいて最大ヒープまたは最小ヒープに分類できます。最大ヒープの先頭要素は最大で、最小ヒープの先頭要素は最小です。</li> <li>優先度キューは、デキューの優先度を持つキューとして定義され、通常ヒープを使用して実装されます。</li> <li>ヒープの一般的な操作とそれに対応する時間計算量には以下があります：ヒープへの要素挿入\\(O(\\log n)\\)、ヒープからの先頭要素削除\\(O(\\log n)\\)、ヒープの先頭要素へのアクセス\\(O(1)\\)。</li> <li>完備二分木は配列で表現するのに適しているため、ヒープは一般的に配列を使用して格納されます。</li> <li>ヒープ化操作はヒープの性質を維持するために使用され、ヒープの挿入操作と削除操作の両方で使用されます。</li> <li>\\(n\\)個の要素が入力として与えられた場合のヒープ構築の時間計算量は\\(O(n)\\)に最適化でき、これは非常に効率的です。</li> <li>Top-kは古典的なアルゴリズム問題で、ヒープデータ構造を使用して効率的に解決でき、時間計算量は\\(O(n \\log k)\\)です。</li> </ul>","path":["第 8 章 &nbsp; ヒープ","8.4 &nbsp; まとめ"],"tags":[]},{"location":"chapter_heap/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: データ構造の「ヒープ」とメモリ管理の「ヒープ」は同じ概念ですか？</p> <p>この2つは、どちらも「ヒープ」と呼ばれますが、同じ概念ではありません。コンピュータシステムメモリのヒープは動的メモリ割り当ての一部で、プログラムが実行中にデータを格納するために使用できます。プログラムは、オブジェクトや配列などの複雑な構造を格納するために、一定量のヒープメモリを要求できます。割り当てられたデータが不要になったときは、メモリリークを防ぐためにプログラムがこのメモリを解放する必要があります。スタックメモリと比較して、ヒープメモリの管理と使用にはより多くの注意が必要で、不適切な使用はメモリリークやダングリングポインタにつながる可能性があります。</p>","path":["第 8 章 &nbsp; ヒープ","8.4 &nbsp; まとめ"],"tags":[]},{"location":"chapter_heap/top_k/","level":1,"title":"8.3   Top-k問題","text":"<p>Question</p> <p>長さ\\(n\\)の順序付けられていない配列<code>nums</code>が与えられたとき、配列内の最大\\(k\\)個の要素を返してください。</p> <p>この問題について、まず2つの直接的な解法を紹介し、次により効率的なヒープベースの方法を説明します。</p>","path":["第 8 章 &nbsp; ヒープ","8.3 &nbsp; Top-k問題"],"tags":[]},{"location":"chapter_heap/top_k/#831-1","level":2,"title":"8.3.1   方法1：反復選択","text":"<p>下図に示すように、\\(k\\)回の反復を実行し、各回で\\(1\\)番目、\\(2\\)番目、\\(\\dots\\)、\\(k\\)番目に大きい要素を抽出できます。時間計算量は\\(O(nk)\\)です。</p> <p>この方法は\\(k \\ll n\\)の場合にのみ適しています。\\(k\\)が\\(n\\)に近い場合、時間計算量は\\(O(n^2)\\)に近づき、非常に時間がかかります。</p> <p></p> <p> 図 8-6   最大k個の要素を反復的に見つける </p> <p>Tip</p> <p>\\(k = n\\)の場合、完全に順序付けられたシーケンスを得ることができ、これは「選択ソート」アルゴリズムと同等です。</p>","path":["第 8 章 &nbsp; ヒープ","8.3 &nbsp; Top-k問題"],"tags":[]},{"location":"chapter_heap/top_k/#832-2","level":2,"title":"8.3.2   方法2：ソート","text":"<p>下図に示すように、まず配列<code>nums</code>をソートし、次に最後の\\(k\\)個の要素を返すことができます。時間計算量は\\(O(n \\log n)\\)です。</p> <p>明らかに、この方法はタスクを「やりすぎ」ています。最大\\(k\\)個の要素を見つけるだけでよく、他の要素をソートする必要はありません。</p> <p></p> <p> 図 8-7   ソートによる最大k個の要素の発見 </p>","path":["第 8 章 &nbsp; ヒープ","8.3 &nbsp; Top-k問題"],"tags":[]},{"location":"chapter_heap/top_k/#833-3","level":2,"title":"8.3.3   方法3：ヒープ","text":"<p>以下のプロセスに示すように、ヒープに基づいてTop-k問題をより効率的に解決できます。</p> <ol> <li>最小ヒープを初期化します。先頭要素が最小になります。</li> <li>まず、配列の最初の\\(k\\)個の要素をヒープに挿入します。</li> <li>\\(k + 1\\)番目の要素から開始し、現在の要素がヒープの先頭要素より大きい場合、ヒープの先頭要素を削除し、現在の要素をヒープに挿入します。</li> <li>走査を完了した後、ヒープには最大\\(k\\)個の要素が含まれています。</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 8-8   ヒープに基づく最大k個の要素の発見 </p> <p>サンプルコードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby top_k.py<pre><code>def top_k_heap(nums: list[int], k: int) -&gt; list[int]:\n    \"\"\"ヒープを使用して配列内の最大k個の要素を見つける\"\"\"\n    # 最小ヒープを初期化\n    heap = []\n    # 配列の最初のk個の要素をヒープに入力\n    for i in range(k):\n        heapq.heappush(heap, nums[i])\n    # k+1番目の要素から、ヒープの長さをkに保つ\n    for i in range(k, len(nums)):\n        # 現在の要素がヒープの先頭要素より大きい場合、ヒープの先頭要素を削除し、現在の要素をヒープに入力\n        if nums[i] &gt; heap[0]:\n            heapq.heappop(heap)\n            heapq.heappush(heap, nums[i])\n    return heap\n</code></pre> top_k.cpp<pre><code>/* ヒープを使用して配列内の最大k個の要素を見つける */\npriority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; topKHeap(vector&lt;int&gt; &amp;nums, int k) {\n    // 最小ヒープを初期化\n    priority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; heap;\n    // 配列の最初のk個の要素をヒープに入力\n    for (int i = 0; i &lt; k; i++) {\n        heap.push(nums[i]);\n    }\n    // k+1番目の要素から、ヒープの長さをkに保つ\n    for (int i = k; i &lt; nums.size(); i++) {\n        // 現在の要素がヒープの先頭要素より大きい場合、ヒープの先頭要素を削除し、現在の要素をヒープに入力\n        if (nums[i] &gt; heap.top()) {\n            heap.pop();\n            heap.push(nums[i]);\n        }\n    }\n    return heap;\n}\n</code></pre> top_k.java<pre><code>/* ヒープを使用して配列内の最大 k 個の要素を検索 */\nQueue&lt;Integer&gt; topKHeap(int[] nums, int k) {\n    // 最小ヒープを初期化\n    Queue&lt;Integer&gt; heap = new PriorityQueue&lt;Integer&gt;();\n    // 配列の最初の k 個の要素をヒープに入力\n    for (int i = 0; i &lt; k; i++) {\n        heap.offer(nums[i]);\n    }\n    // k+1 番目の要素から、ヒープの長さを k に保つ\n    for (int i = k; i &lt; nums.length; i++) {\n        // 現在の要素がヒープの先頭要素より大きい場合、ヒープの先頭要素を削除し、現在の要素をヒープに入力\n        if (nums[i] &gt; heap.peek()) {\n            heap.poll();\n            heap.offer(nums[i]);\n        }\n    }\n    return heap;\n}\n</code></pre> top_k.cs<pre><code>[class]{top_k}-[func]{TopKHeap}\n</code></pre> top_k.go<pre><code>[class]{}-[func]{topKHeap}\n</code></pre> top_k.swift<pre><code>[class]{}-[func]{topKHeap}\n</code></pre> top_k.js<pre><code>[class]{}-[func]{pushMinHeap}\n\n[class]{}-[func]{popMinHeap}\n\n[class]{}-[func]{peekMinHeap}\n\n[class]{}-[func]{getMinHeap}\n\n[class]{}-[func]{topKHeap}\n</code></pre> top_k.ts<pre><code>[class]{}-[func]{pushMinHeap}\n\n[class]{}-[func]{popMinHeap}\n\n[class]{}-[func]{peekMinHeap}\n\n[class]{}-[func]{getMinHeap}\n\n[class]{}-[func]{topKHeap}\n</code></pre> top_k.dart<pre><code>[class]{}-[func]{topKHeap}\n</code></pre> top_k.rs<pre><code>[class]{}-[func]{top_k_heap}\n</code></pre> top_k.c<pre><code>[class]{}-[func]{pushMinHeap}\n\n[class]{}-[func]{popMinHeap}\n\n[class]{}-[func]{peekMinHeap}\n\n[class]{}-[func]{getMinHeap}\n\n[class]{}-[func]{topKHeap}\n</code></pre> top_k.kt<pre><code>[class]{}-[func]{topKHeap}\n</code></pre> top_k.rb<pre><code>[class]{}-[func]{top_k_heap}\n</code></pre> <p>合計\\(n\\)回のヒープ挿入と削除が実行され、最大ヒープサイズが\\(k\\)であるため、時間計算量は\\(O(n \\log k)\\)です。この方法は非常に効率的で、\\(k\\)が小さい場合、時間計算量は\\(O(n)\\)に近づき、\\(k\\)が大きい場合でも、時間計算量は\\(O(n \\log n)\\)を超えません。</p> <p>さらに、この方法は動的データストリームのシナリオに適しています。データを継続的に追加することで、ヒープ内の要素を維持し、最大\\(k\\)個の要素の動的更新を実現できます。</p>","path":["第 8 章 &nbsp; ヒープ","8.3 &nbsp; Top-k問題"],"tags":[]},{"location":"chapter_hello_algo/","level":1,"title":"はじめに","text":"<p>数年前、私はLeetCodeで「剣指Offer」の問題解答を共有し、多くの読者から励ましとサポートを受けました。読者とのやり取りの中で、最もよく聞かれた質問は「アルゴリズムの勉強をどう始めたらよいか」でした。次第に、私はこの質問に強い関心を抱くようになりました。</p> <p>問題を直接解くことが最も人気のある方法のようです。これはシンプルで直接的で効果的です。しかし、問題解決はマインスイーパーをプレイするようなものです。自学自習の能力が高い人は、地雷を一つずつ回避していくことができますが、しっかりとした基礎がない人は、何度もつまずいて挫折しながら後退することになるかもしれません。教科書を読むことも一般的な方法ですが、就職活動中の人にとって、卒業論文の執筆、履歴書の提出、筆記試験や面接の準備が既にエネルギーの大部分を消費しており、分厚い本を読むことはしばしば困難な挑戦となります。</p> <p>もしあなたが同様の悩みを抱えているなら、この本があなたを見つけることができて幸運です。この本は、この質問に対する私の答えです。これが最良の解決策ではないかもしれませんが、少なくとも積極的な試みです。この本があなたに直接内定をもたらすことはできませんが、データ構造とアルゴリズムの「知識地図」を探索する手引きとなり、さまざまな「地雷」の形、大きさ、位置を理解し、さまざまな「地雷除去方法」をマスターできるようお手伝いします。これらのスキルがあれば、より快適に問題を解き、文献を読むことができ、徐々に知識体系を構築できると信じています。</p> <p>私は、ファインマン教授の言葉に深く同感します。「知識は無料ではありません。注意を払わなければならないのです。」この意味で、この本は完全に「無料」ではありません。この本に対するあなたの貴重な「注意」に応えるために、私は最善を尽くし、最大の「注意」を払ってこの本を書きます。</p> <p>自分の限界を認識しており、この本の内容が時間をかけて洗練されたにもかかわらず、間違いは確実に残っていることを理解しています。先生方や学生の皆様からの批評と訂正を心から歓迎いたします。</p> <p></p> Hello, Algo! <p>コンピュータの出現は世界に大きな変化をもたらしました。高速な計算能力と優れたプログラム可能性により、コンピュータはアルゴリズムを実行しデータを処理するための理想的な媒体となりました。ビデオゲームのリアルなグラフィックス、自動運転の知的な判断、AlphaGoの見事な囲碁ゲーム、ChatGPTの自然な対話など、これらのアプリケーションはすべて、コンピュータ上で動作するアルゴリズムの精巧な実演です。</p> <p>実際、コンピュータの出現以前から、アルゴリズムとデータ構造は世界の至る所に存在していました。初期のアルゴリズムは比較的シンプルで、古代の計数方法や道具作りの手順などがありました。文明が進歩するにつれて、アルゴリズムはより洗練され複雑になりました。職人の精巧な技術から、生産力を解放する工業製品、宇宙を支配する科学法則まで、ほぼすべての平凡または驚異的なことの背後には、アルゴリズムの巧妙な思考があります。</p> <p>同様に、データ構造は至る所にあります。ソーシャルネットワークから地下鉄路線まで、多くのシステムは「グラフ」としてモデル化できます。国から家族まで、社会組織の主要な形態は「木」の特徴を示します。冬服は「スタック」のようで、最初に着たものが最後に脱がれます。バドミントンのシャトル筒は「キュー」に似ており、一方の端で挿入し、もう一方の端で取り出します。辞書は「ハッシュテーブル」のようで、目標エントリを素早く検索できます。</p> <p>この本は、明確で理解しやすいアニメーション図解と実行可能なコード例を通じて、読者がアルゴリズムとデータ構造の核心概念を理解し、プログラミングを通じてそれらを実装できるようになることを目指しています。この基盤の上で、この本は複雑な世界におけるアルゴリズムの生き生きとした現れを明らかにし、アルゴリズムの美しさを示すことに努めています。この本があなたのお役に立てることを願っています！</p>","path":["序","はじめに"],"tags":[]},{"location":"chapter_introduction/","level":1,"title":"第 1 章   アルゴリズムとの出会い","text":"<p>Abstract</p> <p>優雅な乙女が踊ります。データと絡み合い、アルゴリズムのメロディーに合わせてスカートをなびかせながら。</p> <p>彼女があなたをダンスに誘います。彼女のステップに従って、論理と美に満ちたアルゴリズムの世界に入りましょう。</p>","path":["第 1 章 &nbsp; アルゴリズムを知る","第 1 章 &nbsp; アルゴリズムとの出会い"],"tags":[]},{"location":"chapter_introduction/#_1","level":2,"title":"章の内容","text":"<ul> <li>1.1   アルゴリズムはどこにでもある</li> <li>1.2   アルゴリズムとは何か</li> <li>1.3   まとめ</li> </ul>","path":["第 1 章 &nbsp; アルゴリズムを知る","第 1 章 &nbsp; アルゴリズムとの出会い"],"tags":[]},{"location":"chapter_introduction/algorithms_are_everywhere/","level":1,"title":"1.1   アルゴリズムは至る所にある","text":"<p>「アルゴリズム」という言葉を聞くと、自然に数学を思い浮かべます。しかし、多くのアルゴリズムは複雑な数学を含まず、基本的な論理により多く依存しており、これは私たちの日常生活の至る所で見ることができます。</p> <p>アルゴリズムについて正式に議論を始める前に、興味深い事実を共有する価値があります。あなたは無意識のうちに多くのアルゴリズムを学び、日常生活でそれらを応用することに慣れています。ここで、この点を証明するためにいくつかの具体的な例を挙げます。</p> <p>例1：辞書の引き方。英語の辞書では、単語がアルファベット順に並んでいます。\\(r\\)で始まる単語を探していると仮定すると、通常は以下の方法で行います：</p> <ol> <li>辞書を大体半分ぐらいのところで開き、そのページの最初の語彙を確認します。例えば\\(m\\)で始まる文字だとしましょう。</li> <li>\\(r\\)はアルファベットで\\(m\\)の後に来るので、前半を無視して、探索空間を後半に絞ります。</li> <li>\\(r\\)で始まる単語を見つけるまで、ステップ<code>1.</code>と<code>2.</code>を繰り返します。</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 1-1   辞書を引く過程 </p> <p>辞書を引くことは、小学生にとって必須のスキルですが、実際には有名な「二分探索」アルゴリズムです。データ構造の観点から、辞書をソートされた「配列」と考えることができます。アルゴリズムの観点から、辞書で単語を探すために取られる一連の行動は、「二分探索」アルゴリズムと見なすことができます。</p> <p>例2：トランプの整理。トランプをプレイするとき、手札を昇順に並べる必要があります。以下の過程で示されます。</p> <ol> <li>トランプを「整列済み」と「未整列」のセクションに分けます。最初は一番左のカードが既に整列していると仮定します。</li> <li>未整列セクションからカードを1枚取り出し、整列済みセクションの正しい位置に挿入します。この後、左端の2枚のカードが整列します。</li> <li>すべてのカードが整列するまで、ステップ<code>2</code>を繰り返します。</li> </ol> <p></p> <p> 図 1-2   トランプの整理過程 </p> <p>上記のトランプを整理する方法は、実質的に「挿入ソート」アルゴリズムであり、小さなデータセットに対して非常に効率的です。多くのプログラミング言語のソート関数には挿入ソートが含まれています。</p> <p>例3：お釣りの計算。スーパーマーケットで\\(69\\)の買い物をしたと仮定します。レジ係に\\(100\\)を渡すと、\\(31\\)のお釣りを提供する必要があります。この過程は以下の図で明確に理解できます。</p> <ol> <li>選択肢は\\(31\\)以下の価値のある通貨で、\\(1\\)、\\(5\\)、\\(10\\)、\\(20\\)が含まれます。</li> <li>選択肢から最大の\\(20\\)を取り出し、\\(31 - 20 = 11\\)が残ります。</li> <li>残りの選択肢から最大の\\(10\\)を取り出し、\\(11 - 10 = 1\\)が残ります。</li> <li>残りの選択肢から最大の\\(1\\)を取り出し、\\(1 - 1 = 0\\)が残ります。</li> <li>お釣りの計算が完了し、解答は\\(20 + 10 + 1 = 31\\)です。</li> </ol> <p></p> <p> 図 1-3   お釣りの計算過程 </p> <p>記述されたステップでは、利用可能な最大の額面を使用して各段階で最良の選択肢を選ぶことで、効果的なお釣り計算戦略につながります。データ構造とアルゴリズムの観点から、このアプローチは「貪欲」アルゴリズムとして知られています。</p> <p>料理の準備から宇宙旅行まで、ほぼすべての問題解決にはアルゴリズムが関わっています。コンピュータの出現により、メモリにデータ構造を格納し、CPUとGPUを呼び出してアルゴリズムを実行するコードを書くことができるようになりました。このようにして、現実世界の問題をコンピュータに移し、より効率的な方法でさまざまな複雑な問題を解決できます。</p> <p>Tip</p> <p>データ構造、アルゴリズム、配列、二分探索などの概念についてまだ混乱している場合は、読み続けることをお勧めします。この本は、データ構造とアルゴリズムの理解の領域へと優しく導いてくれるでしょう。</p>","path":["第 1 章 &nbsp; アルゴリズムを知る","1.1 &nbsp; アルゴリズムは至る所にある"],"tags":[]},{"location":"chapter_introduction/summary/","level":1,"title":"1.3   まとめ","text":"<ul> <li>アルゴリズムは日常生活にありふれており、思っているほどアクセスしにくく複雑なものではありません。実際、私たちは既に無意識のうちに多くのアルゴリズムを学び、生活の様々な問題を解決するために使用しています。</li> <li>辞書で単語を引く原理は二分探索アルゴリズムと一致しています。二分探索アルゴリズムは分割統治という重要なアルゴリズム概念を体現しています。</li> <li>トランプを整理する過程は挿入ソートアルゴリズムと非常に似ています。挿入ソートアルゴリズムは小さなデータセットのソートに適しています。</li> <li>通貨でお釣りを計算するステップは本質的に貪欲アルゴリズムに従っており、各ステップでその時点での最良の選択をします。</li> <li>アルゴリズムは有限時間内で特定の問題を解決するための段階的な指示のセットですが、データ構造はコンピュータでのデータの組織化と保存方法を定義します。</li> <li>データ構造とアルゴリズムは密接に関連しています。データ構造はアルゴリズムの基礎であり、アルゴリズムはデータ構造の機能を活用するステージです。</li> <li>データ構造とアルゴリズムをブロックの組み立てに例えることができます。ブロックはデータを表し、ブロックの形状と接続方法はデータ構造を表し、ブロックを組み立てるステップはアルゴリズムに対応します。</li> </ul>","path":["第 1 章 &nbsp; アルゴリズムを知る","1.3 &nbsp; まとめ"],"tags":[]},{"location":"chapter_introduction/summary/#1-q-a","level":3,"title":"1.   Q &amp; A","text":"<p>Q：プログラマーとして、日常の仕事でアルゴリズムを手動で実装する必要があることはめったにありません。最も一般的に使用されるアルゴリズムは、既にプログラミング言語とライブラリに組み込まれており、すぐに使用できます。これは、私たちが仕事で遭遇する問題が、カスタムアルゴリズム設計を必要とする複雑さのレベルにまだ達していないことを示唆していますか？</p> <p>特定の仕事スキルが武術の「技」のようなものだとすれば、基礎科目は「内功」のようなものです。</p> <p>アルゴリズム（およびその他の基礎科目）を学ぶ意義は、必ずしも仕事でそれらを一から実装することではなく、概念の確固たる理解に基づいて、より専門的な意思決定と問題解決を可能にし、それによって仕事の全体的な質を向上させることだと私は信じています。例えば、すべてのプログラミング言語には組み込みのソート関数があります：</p> <ul> <li>データ構造とアルゴリズムを学んでいない場合、どんなデータが与えられても、このソート関数に渡すだけかもしれません。スムーズに動作し、良いパフォーマンスを示し、問題がないように見えます。</li> <li>しかし、アルゴリズムを学んだことがあれば、組み込みのソート関数の時間複雑度は通常\\(O(n \\log n)\\)であることを理解しています。さらに、データが固定桁数の整数（学生IDなど）で構成されている場合、基数ソートのようなより効率的なアプローチを適用でき、時間複雑度をO(nk)に削減できます。ここでkは桁数です。大量のデータを処理する際、節約された時間は重要な価値に変わります — コストの削減、ユーザーエクスペリエンスの向上、システムパフォーマンスの向上。</li> </ul> <p>エンジニアリングでは、多くの問題を最適に解決することは困難です。ほとんどは「準最適」解決策で対処されます。問題の難しさは、その固有の複雑さだけでなく、それに取り組む人の知識と経験にも依存します。専門知識と経験が深いほど、分析がより徹底的になり、問題をより優雅に解決できます。</p>","path":["第 1 章 &nbsp; アルゴリズムを知る","1.3 &nbsp; まとめ"],"tags":[]},{"location":"chapter_introduction/what_is_dsa/","level":1,"title":"1.2   アルゴリズムとは何か","text":"","path":["第 1 章 &nbsp; アルゴリズムを知る","1.2 &nbsp; アルゴリズムとは何か"],"tags":[]},{"location":"chapter_introduction/what_is_dsa/#121","level":2,"title":"1.2.1   アルゴリズムの定義","text":"<p>アルゴリズムは、有限時間内で特定の問題を解決するための一連の指示またはステップです。以下の特徴があります：</p> <ul> <li>問題が明確に定義されており、入力と出力の明確な定義が含まれています。</li> <li>アルゴリズムは実行可能で、有限の回数のステップ、時間、メモリ空間内で完了できることを意味します。</li> <li>各ステップには明確な意味があります。同じ入力と条件の下で出力は一貫して同じです。</li> </ul>","path":["第 1 章 &nbsp; アルゴリズムを知る","1.2 &nbsp; アルゴリズムとは何か"],"tags":[]},{"location":"chapter_introduction/what_is_dsa/#122","level":2,"title":"1.2.2   データ構造の定義","text":"<p>データ構造は、コンピュータ内でデータを組織し保存する方法で、以下の設計目標があります：</p> <ul> <li>コンピュータのメモリを節約するために空間占有を最小化する。</li> <li>データ操作を可能な限り高速にし、データのアクセス、追加、削除、更新などをカバーする。</li> <li>効率的なアルゴリズム実行を可能にするために、簡潔なデータ表現と論理情報を提供する。</li> </ul> <p>データ構造の設計はバランスを取る行為であり、しばしばトレードオフが必要です。一つの側面を改善したい場合、しばしば別の側面で妥協する必要があります。以下は2つの例です：</p> <ul> <li>配列と比較して、連結リストはデータの追加と削除においてより便利ですが、データアクセス速度を犠牲にします。</li> <li>連結リストと比較して、グラフはより豊富な論理情報を提供しますが、より多くのメモリ空間が必要です。</li> </ul>","path":["第 1 章 &nbsp; アルゴリズムを知る","1.2 &nbsp; アルゴリズムとは何か"],"tags":[]},{"location":"chapter_introduction/what_is_dsa/#123","level":2,"title":"1.2.3   データ構造とアルゴリズムの関係","text":"<p>以下の図に示すように、データ構造とアルゴリズムは高度に関連し、密接に統合されており、具体的には以下の3つの側面があります：</p> <ul> <li>データ構造はアルゴリズムの基礎です。構造化されたデータ保存とアルゴリズムのためのデータ操作方法を提供します。</li> <li>アルゴリズムはデータ構造に活力を注入します。データ構造だけではデータ情報を保存するだけです。アルゴリズムの応用によって、特定の問題を解決できます。</li> <li>アルゴリズムは異なるデータ構造に基づいて実装できることが多いですが、実行効率は大きく異なることがあります。適切なデータ構造を選択することが鍵です。</li> </ul> <p></p> <p> 図 1-4   データ構造とアルゴリズムの関係 </p> <p>データ構造とアルゴリズムは、以下の図に示すように、ブロックのセットに例えることができます。ブロックセットには多数のピースが含まれ、詳細な組み立て説明書が付いています。これらの説明書に段階的に従うことで、複雑なブロックモデルを構築できます。</p> <p></p> <p> 図 1-5   ブロックの組み立て </p> <p>両者の詳細な対応関係は以下の表に示されています。</p> <p> 表 1-1   データ構造とアルゴリズムをブロックと比較 </p> データ構造とアルゴリズム ブロック 入力データ 未組み立てのブロック データ構造 ブロックの組織、形状、サイズ、接続などを含む アルゴリズム ブロックを望ましい形状に組み立てる一連のステップ 出力データ 完成したブロックモデル <p>データ構造とアルゴリズムはプログラミング言語から独立していることは注目に値します。この理由により、この本は複数のプログラミング言語での実装を提供できます。</p> <p>慣習的な略語</p> <p>実生活の議論では、「データ構造とアルゴリズム」を単純に「アルゴリズム」と呼ぶことがよくあります。例えば、よく知られたLeetCodeアルゴリズム問題は、実際にはデータ構造とアルゴリズムの両方の知識をテストしています。</p>","path":["第 1 章 &nbsp; アルゴリズムを知る","1.2 &nbsp; アルゴリズムとは何か"],"tags":[]},{"location":"chapter_preface/","level":1,"title":"第 0 章   序文","text":"<p>Abstract</p> <p>アルゴリズムは美しい交響曲のようで、コードの一行一行がリズムのように流れています。</p> <p>この本があなたの心の中で静かに響き、独特で深い旋律を残すことを願っています。</p>","path":["第 0 章 &nbsp; 前書き","第 0 章 &nbsp; 序文"],"tags":[]},{"location":"chapter_preface/#_1","level":2,"title":"章の内容","text":"<ul> <li>0.1   本書について</li> <li>0.2   本書の使い方</li> <li>0.3   まとめ</li> </ul>","path":["第 0 章 &nbsp; 前書き","第 0 章 &nbsp; 序文"],"tags":[]},{"location":"chapter_preface/about_the_book/","level":1,"title":"0.1   この本について","text":"<p>このオープンソースプロジェクトは、データ構造とアルゴリズムに関する無料で初心者にやさしいクラッシュコースの作成を目指しています。</p> <ul> <li>アニメーション付きの図解、理解しやすい内容、滑らかな学習曲線により、初心者がデータ構造とアルゴリズムの「知識マップ」を探索するのに役立ちます。</li> <li>ワンクリックでコードを実行できるため、読者のプログラミングスキルの向上と、アルゴリズムの動作原理およびデータ構造の基礎実装の理解に役立ちます。</li> <li>教えることによる学習を促進し、質問や洞察の共有を自由に行ってください。議論を通じて一緒に成長しましょう。</li> </ul>","path":["第 0 章 &nbsp; 前書き","0.1 &nbsp; この本について"],"tags":[]},{"location":"chapter_preface/about_the_book/#011","level":2,"title":"0.1.1   対象読者","text":"<p>もしあなたがアルゴリズムに触れたばかりで経験が限られている場合、またはアルゴリズムである程度の経験を積んでいても、データ構造とアルゴリズムについて曖昧な理解しかなく、常に「分かった」と「うーん」の間を行き来している場合、この本はあなたのためのものです！</p> <p>すでにある程度の問題解決経験を積んでおり、ほとんどのタイプの問題に精通している場合、この本はアルゴリズムの知識体系を復習し整理するのに役立ちます。リポジトリのソースコードは「問題解決ツールキット」や「アルゴリズムチートシート」として使用できます。</p> <p>もしあなたがアルゴリズムの専門家であれば、貴重な提案をいただくか、参加して協力していただければと思います。</p> <p>前提条件</p> <p>少なくとも一つのプログラミング言語で簡単なコードを書いて読むことができる必要があります。</p>","path":["第 0 章 &nbsp; 前書き","0.1 &nbsp; この本について"],"tags":[]},{"location":"chapter_preface/about_the_book/#012","level":2,"title":"0.1.2   内容構成","text":"<p>本書の主な内容を下図に示します。</p> <ul> <li>計算量解析: データ構造とアルゴリズムを評価する側面と方法を探求します。時間計算量と空間計算量を導出する方法、および一般的なタイプと例を扱います。</li> <li>データ構造: 基本的なデータ型、分類方法、定義、長所と短所、一般的な操作、タイプ、応用、および配列、連結リスト、スタック、キュー、ハッシュテーブル、木、ヒープ、グラフなどのデータ構造の実装方法に焦点を当てます。</li> <li>アルゴリズム: アルゴリズムを定義し、その長所と短所、効率性、応用シナリオ、問題解決ステップについて議論し、検索、ソート、分割統治、バックトラッキング、動的プログラミング、貪欲アルゴリズムなど、さまざまなアルゴリズムのサンプル問題を含みます。</li> </ul> <p></p> <p> 図 0-1   本書の主な内容 </p>","path":["第 0 章 &nbsp; 前書き","0.1 &nbsp; この本について"],"tags":[]},{"location":"chapter_preface/about_the_book/#013","level":2,"title":"0.1.3   謝辞","text":"<p>本書は、オープンソースコミュニティの多数の貢献者による共同の努力のもと、継続的に改善されています。時間と労力を注いで執筆に携わってくださったすべての方々に感謝します。貢献者は以下のとおりです（GitHub により自動生成された順序）：krahets、coderonion、Gonglja、nuomi1、Reanon、justin-tse、hpstory、danielsss、curtishd、night-cruise、S-N-O-R-L-A-X、rongyi、msk397、gvenusleo、khoaxuantu、rivertwilight、K3v123、gyt95、zhuoqinyue、yuelinxin、Zuoxun、mingXta、Phoenix0415、FangYuan33、GN-Yu、longsizhuo、IsChristina、xBLACKICEx、guowei-gong、Cathay-Chen、pengchzn、QiLOL、magentaqin、hello-ikun、JoseHung、qualifier1024、thomasq0、sunshinesDL、L-Super、Guanngxu、Transmigration-zhou、WSL0809、Slone123c、lhxsm、yuan0221、what-is-me、Shyam-Chen、theNefelibatas、longranger2、codeberg-user、xiongsp、JeffersonHuang、prinpal、seven1240、Wonderdch、malone6、xiaomiusa87、gaofer、bluebean-cloud、a16su、SamJin98、hongyun-robot、nanlei、XiaChuerwu、yd-j、iron-irax、mgisr、steventimes、junminhong、heshuyue、danny900714、MolDuM、Nigh、Dr-XYZ、XC-Zero、reeswell、PXG-XPG、NI-SW、Horbin-Magician、Enlightenus、YangXuanyi、beatrix-chan、DullSword、xjr7670、jiaxianhua、qq909244296、iStig、boloboloda、hts0000、gledfish、wenjianmin、keshida、kilikilikid、lclc6、lwbaptx、linyejoe2、liuxjerry、llql1211、fbigm、echo1937、szu17dmy、dshlstarr、Yucao-cy、coderlef、czruby、bongbongbakudan、beintentional、ZongYangL、ZhongYuuu、ZhongGuanbin、hezhizhen、linzeyan、ZJKung、luluxia、xb534、ztkuaikuai、yw-1021、ElaBosak233、baagod、zhouLion、yishangzhang、yi427、yanedie、yabo083、weibk、wangwang105、th1nk3r-ing、tao363、4yDX3906、syd168、sslmj2020、smilelsb、siqyka、selear、sdshaoda、Xi-Row、popozhu、nuquist19、noobcodemaker、XiaoK29、chadyi、lyl625760、lucaswangdev、0130w、shanghai-Jerry、EJackYang、Javesun99、eltociear、lipusheng、KNChiu、BlindTerran、ShiMaRing、lovelock、FreddieLi、FloranceYeh、fanchenggang、gltianwen、goerll、nedchu、curly210102、CuB3y0nd、KraHsu、CarrotDLaw、youshaoXG、bubble9um、Asashishi、Asa0oo0o0o、fanenr、eagleanurag、akshiterate、52coder、foursevenlove、KorsChen、GaochaoZhu、hopkings2008、yang-le、realwujing、Evilrabbit520、Umer-Jahangir、Turing-1024-Lee、Suremotoo、paoxiaomooo、Chieko-Seren、Allen-Scai、ymmmas、Risuntsy、Richard-Zhang1019、RafaelCaso、qingpeng9802、primexiao、Urbaner3、zhongfq、nidhoggfgg、MwumLi、CreatorMetaSky、martinx、ZnYang2018、hugtyftg、logan-qiu、psychelzh、Keynman、KeiichiKasai、KawaiiAsh。</p> <p>この本のコードレビュー作業は、coderonion, Gonglja, gvenusleo, hpstory, justin‐tse, khoaxuantu, krahets, night-cruise, nuomi1, Reanon and rongyi（アルファベット順）によって完了されました。彼らの時間と努力に感謝し、様々な言語でのコードの標準化と統一性を確保してくださいました。</p> <p>本書の繁体字中国語版は Shyam-Chen および Dr-XYZ によってレビューされ、英語版は yuelinxin、K3v123、QiLOL、Phoenix0415、SamJin98、yanedie、RafaelCaso、pengchzn、thomasq0、magentaqin によってレビューされ、日本語版は eltociear によってレビューされました。彼らの継続的な貢献のおかげで、本書はより幅広い読者層に提供することができています。ここに深く感謝いたします。</p> <p>この本の制作過程において、多くの方々から貴重な支援をいただきました。これらに限定されませんが：</p> <ul> <li>会社でのメンター、李熙博士に感謝します。ある会話で「早く行動しろ」と励ましていただき、この本を書く決意を固めることができました。</li> <li>ガールフレンドのBubbleに感謝します。この本の最初の読者として、アルゴリズム初心者の視点から多くの貴重な提案をいただき、この本を初心者により適したものにしてくださいました。</li> <li>Tengbao、Qibao、Feibaoに感謝します。この本のクリエイティブな名前を考えてくださり、みんなが初めて「Hello World!」を書いた時の素晴らしい思い出を呼び起こしてくれました。</li> <li>Xiaoquanに感謝します。知的財産に関する専門的な支援を提供してくださり、このオープンソース本の開発において重要な役割を果たしてくださいました。</li> <li>Sutongに感謝します。この本の美しいカバーとロゴをデザインしてくださり、私の要求で何度も修正を辛抱強く行ってくださいました。</li> <li>@squidfunk に感謝します。執筆と組版の提案、および彼が開発したオープンソースドキュメントテーマ Material-for-MkDocs を提供してくださいました。</li> </ul> <p>執筆の過程で、データ構造とアルゴリズムに関する多数の教科書や記事を深く研究しました。これらの作品は模範的なモデルとして機能し、この本の内容の正確性と品質を確保してくださいました。先人の方々の貴重な貢献に感謝いたします！</p> <p>この本は、理論と実践を組み合わせた学習を提唱しており、この点で \"Dive into Deep Learning\" からインスピレーションを受けています。この優れた本をすべての読者に強くお勧めします。</p> <p>継続的な支援と励ましにより、この興味深い仕事をすることを可能にしてくださった両親に心から感謝いたします。</p>","path":["第 0 章 &nbsp; 前書き","0.1 &nbsp; この本について"],"tags":[]},{"location":"chapter_preface/suggestions/","level":1,"title":"0.2   読み方","text":"<p>Tip</p> <p>最良の読書体験のために、このセクションを通読することをお勧めします。</p>","path":["第 0 章 &nbsp; 前書き","0.2 &nbsp; 読み方"],"tags":[]},{"location":"chapter_preface/suggestions/#021","level":2,"title":"0.2.1   記述規則","text":"<ul> <li>タイトルの後に「*」が付いた章は任意であり、比較的難易度の高い内容が含まれています。時間に制約がある場合は、これらをスキップすることをお勧めします。</li> <li>技術用語は太字（印刷版およびPDF版）または下線（Web版）で表示されます。例えば、配列などです。技術文書をより良く理解するために、これらに慣れることをお勧めします。</li> <li>**太字のテキスト**は重要な内容や要約文を示し、特別な注意を払う価値があります。</li> <li>特定の意味を持つ単語や句は「引用符」で示され、曖昧さを避けます。</li> <li>プログラミング言語間で一致しない用語については、この本はPythonに従います。例えば、<code>null</code>を意味するために<code>None</code>を使用します。</li> <li>この本は、よりコンパクトなコンテンツレイアウトと引き換えに、プログラミング言語のコメント規約を部分的に無視しています。コメントは主に3つのタイプで構成されています：タイトルコメント、内容コメント、複数行コメント。</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlin <pre><code>\"\"\"関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント\"\"\"\n\n# 詳細を説明するためのコメント\n\n\"\"\"\n複数行\nコメント\n\"\"\"\n</code></pre> <pre><code>/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */\n\n// 詳細を説明するためのコメント\n\n/**\n * 複数行\n * コメント\n */\n</code></pre> <pre><code>/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */\n\n// 詳細を説明するためのコメント\n\n/**\n * 複数行\n * コメント\n */\n</code></pre> <pre><code>/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */\n\n// 詳細を説明するためのコメント\n\n/**\n * 複数行\n * コメント\n */\n</code></pre> <pre><code>/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */\n\n// 詳細を説明するためのコメント\n\n/**\n * 複数行\n * コメント\n */\n</code></pre> <pre><code>/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */\n\n// 詳細を説明するためのコメント\n\n/**\n * 複数行\n * コメント\n */\n</code></pre> <pre><code>/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */\n\n// 詳細を説明するためのコメント\n\n/**\n * 複数行\n * コメント\n */\n</code></pre> <pre><code>/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */\n\n// 詳細を説明するためのコメント\n\n/**\n * 複数行\n * コメント\n */\n</code></pre> <pre><code>/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */\n\n// 詳細を説明するためのコメント\n\n/**\n * 複数行\n * コメント\n */\n</code></pre> <pre><code>/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */\n\n// 詳細を説明するためのコメント\n\n/**\n * 複数行\n * コメント\n */\n</code></pre> <pre><code>/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */\n\n// 詳細を説明するためのコメント\n\n/**\n * 複数行\n * コメント\n */\n</code></pre> <pre><code>/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */\n\n// 詳細を説明するためのコメント\n\n/**\n * 複数行\n * コメント\n */\n</code></pre>","path":["第 0 章 &nbsp; 前書き","0.2 &nbsp; 読み方"],"tags":[]},{"location":"chapter_preface/suggestions/#022","level":2,"title":"0.2.2   アニメーション図解による効率的学習","text":"<p>テキストと比較して、動画や画像は情報密度が高く、より構造化されており、理解しやすくなっています。この本では、重要で難しい概念は主にアニメーションと図解を通じて提示され、テキストは説明と補足として機能します。</p> <p>下図に示すようなアニメーションや図解のある内容に遭遇した場合、図の理解を優先し、テキストを補足として、両方を統合して包括的な理解を得てください。</p> <p></p> <p> 図 0-2   アニメーション図解の例 </p>","path":["第 0 章 &nbsp; 前書き","0.2 &nbsp; 読み方"],"tags":[]},{"location":"chapter_preface/suggestions/#023","level":2,"title":"0.2.3   コーディング実践による理解の深化","text":"<p>この本のソースコードはGitHubリポジトリでホストされています。下図に示すように、ソースコードにはテスト例が付属しており、ワンクリックで実行できます。</p> <p>時間に余裕がある場合は、自分でコードをタイプすることをお勧めします。時間がない場合は、少なくともすべてのコードを読んで実行してください。</p> <p>コードを読むだけと比較して、コードを書くことは多くの場合、より多くの学習をもたらします。実践による学習こそが真の学習方法です。</p> <p></p> <p> 図 0-3   コード実行例 </p> <p>コードを実行するための設定には、主に3つのステップが含まれます。</p> <p>ステップ1：ローカルプログラミング環境をインストール。付録のチュートリアルに従ってインストールするか、すでにインストールされている場合はこのステップをスキップしてください。</p> <p>ステップ2：コードリポジトリをクローンまたはダウンロード。GitHubリポジトリを訪問してください。</p> <p>Gitがインストールされている場合は、次のコマンドを使用してリポジトリをクローンします：</p> <pre><code>git clone https://github.com/krahets/hello-algo.git\n</code></pre> <p>または、下図に示す場所にある「Download ZIP」ボタンをクリックして、コードを圧縮ZIPファイルとして直接ダウンロードすることもできます。その後、ローカルで展開するだけです。</p> <p></p> <p> 図 0-4   リポジトリのクローンとコードのダウンロード </p> <p>ステップ3：ソースコードを実行。下図に示すように、上部にファイル名が記載されたコードブロックについては、リポジトリの<code>codes</code>フォルダで対応するソースコードファイルを見つけることができます。これらのファイルはワンクリックで実行でき、不要なデバッグ時間を節約し、学習に集中できます。</p> <p></p> <p> 図 0-5   コードブロックと対応するソースコードファイル </p>","path":["第 0 章 &nbsp; 前書き","0.2 &nbsp; 読み方"],"tags":[]},{"location":"chapter_preface/suggestions/#024","level":2,"title":"0.2.4   議論による共同学習","text":"<p>この本を読んでいる間、学べなかった点を飛ばさないでください。コメントセクションで気軽に質問してください。喜んでお答えし、通常2日以内に回答できます。</p> <p>下図に示すように、各章の下部にコメントセクションがあります。これらのコメントに注意を払うことをお勧めします。他の人が遭遇した問題を知ることで、知識のギャップを特定し、より深い思索を促すだけでなく、仲間の読者の質問に答えたり、洞察を共有したり、相互の向上を促進したりすることで寛大に貢献することも招待します。</p> <p></p> <p> 図 0-6   コメントセクションの例 </p>","path":["第 0 章 &nbsp; 前書き","0.2 &nbsp; 読み方"],"tags":[]},{"location":"chapter_preface/suggestions/#025","level":2,"title":"0.2.5   アルゴリズム学習パス","text":"<p>全体的に、データ構造とアルゴリズムをマスターする旅は3つの段階に分けることができます：</p> <ol> <li>段階1：アルゴリズムの入門。さまざまなデータ構造の特性と使用法に慣れ、異なるアルゴリズムの原理、プロセス、用途、効率について学ぶ必要があります。</li> <li>段階2：アルゴリズム問題の練習。Sword for OfferやLeetCode Hot 100などの人気のある問題から始めることをお勧めし、少なくとも100問を蓄積して主流のアルゴリズム問題に慣れることです。練習を始めると忘却が課題になる可能性がありますが、これは正常なことですのでご安心ください。「エビングハウスの忘却曲線」に従って問題を復習することができ、通常3〜5回の反復の後、それらを覚えることができるでしょう。</li> <li>段階3：知識体系の構築。学習の面では、アルゴリズムコラム記事、解法フレームワーク、アルゴリズム教科書を読んで知識体系を継続的に豊かにすることができます。練習の面では、トピック別分類、一つの問題に対する複数の解法、複数の問題に対する一つの解法など、高度な戦略を試すことができます。これらの戦略に関する洞察は、さまざまなコミュニティで見つけることができます。</li> </ol> <p>下図に示すように、この本は主に「段階1」をカバーしており、段階2と3により効率的に取り組むのに役立つことを目的としています。</p> <p></p> <p> 図 0-7   アルゴリズム学習パス </p>","path":["第 0 章 &nbsp; 前書き","0.2 &nbsp; 読み方"],"tags":[]},{"location":"chapter_preface/summary/","level":1,"title":"0.3   まとめ","text":"<ul> <li>この本の主な読者はアルゴリズムの初心者です。すでに基本的な知識をお持ちの場合、この本はアルゴリズムの知識を体系的に復習するのに役立ち、この本のソースコードは「コーディングツールキット」としても使用できます。</li> <li>この本は3つの主要なセクション、計算量解析、データ構造、アルゴリズムで構成されており、この分野のほとんどのトピックをカバーしています。</li> <li>アルゴリズムの初心者にとって、多くの回り道や一般的な落とし穴を避けるために、初期段階で入門書を読むことが重要です。</li> <li>本書内のアニメーションと図は通常、重要なポイントと難しい知識を紹介するために使用されます。本を読む際にはこれらにより多くの注意を払う必要があります。</li> <li>実践はプログラミングを学ぶ最良の方法です。ソースコードを実行し、自分でコードをタイプすることを強くお勧めします。</li> <li>この本のWeb版の各章には議論セクションがあり、いつでも質問や洞察を共有することを歓迎します。</li> </ul>","path":["第 0 章 &nbsp; 前書き","0.3 &nbsp; まとめ"],"tags":[]},{"location":"chapter_reference/","level":1,"title":"参考文献","text":"<p>[1] Thomas H. Cormen, et al. Introduction to Algorithms (3<sup>rd</sup> Edition).</p> <p>[2] Aditya Bhargava. Grokking Algorithms: An Illustrated Guide for Programmers and Other Curious People (1<sup>st</sup> Edition).</p> <p>[3] Robert Sedgewick, et al. Algorithms (4<sup>th</sup> Edition).</p> <p>[4] Yan Weimin. Data Structures (C Language Version).</p> <p>[5] Deng Junhui. Data Structures (C++ Language Version, Third Edition).</p> <p>[6] Mark Allen Weiss, translated by Chen Yue. Data Structures and Algorithm Analysis in Java (Third Edition).</p> <p>[7] Cheng Jie. Speaking of Data Structures.</p> <p>[8] Wang Zheng. The Beauty of Data Structures and Algorithms.</p> <p>[9] Gayle Laakmann McDowell. Cracking the Coding Interview: 189 Programming Questions and Solutions (6<sup>th</sup> Edition).</p> <p>[10] Aston Zhang, et al. Dive into Deep Learning.</p>","path":["参考文献"],"tags":[]},{"location":"chapter_searching/","level":1,"title":"第 10 章   探索","text":"<p>Abstract</p> <p>探索は未知への冒険です。神秘的な空間の隅々まで巡る必要があるかもしれませんし、あるいはすぐに目標を見つけることができるかもしれません。</p> <p>この発見の旅において、それぞれの探査は予期しない答えで終わるかもしれません。</p>","path":["第 10 章 &nbsp; 探索"],"tags":[]},{"location":"chapter_searching/#_1","level":2,"title":"章の内容","text":"<ul> <li>10.1   二分探索</li> <li>10.2   二分探索の挿入点</li> <li>10.3   二分探索の境界</li> <li>10.4   ハッシュ最適化戦略</li> <li>10.5   探索アルゴリズムの再認識</li> <li>10.6   まとめ</li> </ul>","path":["第 10 章 &nbsp; 探索"],"tags":[]},{"location":"chapter_searching/binary_search/","level":1,"title":"10.1   二分探索","text":"<p>二分探索は分割統治戦略を用いる効率的な探索アルゴリズムです。配列内の要素の整列順序を利用し、各反復で探索区間を半分に減らしながら、目標要素が見つかるか探索区間が空になるまで続行します。</p> <p>Question</p> <p>長さ\\(n\\)の配列<code>nums</code>が与えられ、要素は重複なしで昇順に配列されています。この配列内の要素<code>target</code>のインデックスを見つけて返してください。配列に要素が含まれていない場合は\\(-1\\)を返してください。例を下図に示します。</p> <p></p> <p> 図 10-1   Binary search example data </p> <p>下図に示すように、まず\\(i = 0\\)と\\(j = n - 1\\)でポインタを初期化し、それぞれ配列の最初と最後の要素を指します。これらはまた全体の探索区間\\([0, n - 1]\\)を表します。角括弧は閉区間を示し、境界値自身も含むことに注意してください。</p> <p>そして、以下の2つのステップをループで実行する可能性があります。</p> <ol> <li>中点インデックス\\(m = \\lfloor {(i + j) / 2} \\rfloor\\)を計算します。ここで\\(\\lfloor \\: \\rfloor\\)は床関数を表します。</li> <li><code>nums[m]</code>と<code>target</code>の比較に基づいて、以下の3つのケースのうち1つを選択して実行します。<ol> <li><code>nums[m] &lt; target</code>の場合、<code>target</code>は区間\\([m + 1, j]\\)にあることを示すため、\\(i = m + 1\\)とします。</li> <li><code>nums[m] &gt; target</code>の場合、<code>target</code>は区間\\([i, m - 1]\\)にあることを示すため、\\(j = m - 1\\)とします。</li> <li><code>nums[m] = target</code>の場合、<code>target</code>が見つかったことを示すため、インデックス\\(m\\)を返します。</li> </ol> </li> </ol> <p>配列に目標要素が含まれていない場合、探索区間は最終的に空になり、\\(-1\\)を返して終了します。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 10-2   Binary search process </p> <p>\\(i\\)と\\(j\\)が両方とも<code>int</code>型であるため、**\\(i + j\\)は<code>int</code>型の範囲を超える可能性がある**ことは注目に値します。大きな数のオーバーフローを避けるため、通常は式\\(m = \\lfloor {i + (j - i) / 2} \\rfloor\\)を使用して中点を計算します。</p> <p>コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search.py<pre><code>def binary_search(nums: list[int], target: int) -&gt; int:\n    \"\"\"二分探索（両端閉区間）\"\"\"\n    # 両端閉区間 [0, n-1] を初期化、すなわち i, j はそれぞれ配列の最初の要素と最後の要素を指す\n    i, j = 0, len(nums) - 1\n    # 検索区間が空になるまでループ（i &gt; j のとき空）\n    while i &lt;= j:\n        # 理論的には、Pythonの数値は無限に大きくなることができる（メモリサイズに依存）ため、大きな数のオーバーフローを考慮する必要はない\n        m = i + (j - i) // 2  # 中点インデックス m を計算\n        if nums[m] &lt; target:\n            i = m + 1  # この場合、target は区間 [m+1, j] にあることを示す\n        elif nums[m] &gt; target:\n            j = m - 1  # この場合、target は区間 [i, m-1] にあることを示す\n        else:\n            return m  # ターゲット要素が見つかったため、そのインデックスを返す\n    return -1  # ターゲット要素が見つからなかったため、-1 を返す\n</code></pre> binary_search.cpp<pre><code>/* 二分探索（両端閉区間） */\nint binarySearch(vector&lt;int&gt; &amp;nums, int target) {\n    // 両端閉区間[0, n-1]を初期化、すなわちi、jはそれぞれ配列の最初の要素と最後の要素を指す\n    int i = 0, j = nums.size() - 1;\n    // 探索区間が空になるまでループ（i &gt; jの時空になる）\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // 中点インデックスmを計算\n        if (nums[m] &lt; target)    // この状況はtargetが区間[m+1, j]にあることを示す\n            i = m + 1;\n        else if (nums[m] &gt; target) // この状況はtargetが区間[i, m-1]にあることを示す\n            j = m - 1;\n        else // ターゲット要素が見つかったため、そのインデックスを返す\n            return m;\n    }\n    // ターゲット要素が見つからなかったため、-1を返す\n    return -1;\n}\n</code></pre> binary_search.java<pre><code>/* 二分探索（両端閉区間） */\nint binarySearch(int[] nums, int target) {\n    // 両端閉区間 [0, n-1] を初期化、すなわち i, j はそれぞれ配列の最初の要素と最後の要素を指す\n    int i = 0, j = nums.length - 1;\n    // 探索区間が空になるまでループ（i &gt; j のとき空）\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // 中点インデックス m を計算\n        if (nums[m] &lt; target) // この状況は target が区間 [m+1, j] にあることを示す\n            i = m + 1;\n        else if (nums[m] &gt; target) // この状況は target が区間 [i, m-1] にあることを示す\n            j = m - 1;\n        else // 目標要素を見つけたので、そのインデックスを返す\n            return m;\n    }\n    // 目標要素を見つけられなかったので、-1 を返す\n    return -1;\n}\n</code></pre> binary_search.cs<pre><code>[class]{binary_search}-[func]{BinarySearch}\n</code></pre> binary_search.go<pre><code>[class]{}-[func]{binarySearch}\n</code></pre> binary_search.swift<pre><code>[class]{}-[func]{binarySearch}\n</code></pre> binary_search.js<pre><code>[class]{}-[func]{binarySearch}\n</code></pre> binary_search.ts<pre><code>[class]{}-[func]{binarySearch}\n</code></pre> binary_search.dart<pre><code>[class]{}-[func]{binarySearch}\n</code></pre> binary_search.rs<pre><code>[class]{}-[func]{binary_search}\n</code></pre> binary_search.c<pre><code>[class]{}-[func]{binarySearch}\n</code></pre> binary_search.kt<pre><code>[class]{}-[func]{binarySearch}\n</code></pre> binary_search.rb<pre><code>[class]{}-[func]{binary_search}\n</code></pre> <p>時間計算量は\\(O(\\log n)\\)です：二分ループにおいて、区間は各ラウンドで半分に減少するため、反復回数は\\(\\log_2 n\\)となります。</p> <p>空間計算量は\\(O(1)\\)です：ポインタ\\(i\\)と\\(j\\)は定数サイズの空間を占有します。</p>","path":["第 10 章 &nbsp; 探索","10.1 &nbsp; 二分探索"],"tags":[]},{"location":"chapter_searching/binary_search/#1011","level":2,"title":"10.1.1   区間表現方法","text":"<p>上記の閉区間の他に、もう一つの一般的な区間表現は「左閉右開」区間で、\\([0, n)\\)として定義され、左境界は自身を含み、右境界は含みません。この表現では、\\(i = j\\)のとき区間\\([i, j)\\)は空になります。</p> <p>この表現に基づいて同じ機能を持つ二分探索アルゴリズムを実装できます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search.py<pre><code>def binary_search_lcro(nums: list[int], target: int) -&gt; int:\n    \"\"\"二分探索（左閉右開区間）\"\"\"\n    # 左閉右開区間 [0, n) を初期化、すなわち i, j はそれぞれ配列の最初の要素と最後の要素+1を指す\n    i, j = 0, len(nums)\n    # 検索区間が空になるまでループ（i = j のとき空）\n    while i &lt; j:\n        m = i + (j - i) // 2  # 中点インデックス m を計算\n        if nums[m] &lt; target:\n            i = m + 1  # この場合、target は区間 [m+1, j) にあることを示す\n        elif nums[m] &gt; target:\n            j = m  # この場合、target は区間 [i, m) にあることを示す\n        else:\n            return m  # ターゲット要素が見つかったため、そのインデックスを返す\n    return -1  # ターゲット要素が見つからなかったため、-1 を返す\n</code></pre> binary_search.cpp<pre><code>/* 二分探索（左閉右開区間） */\nint binarySearchLCRO(vector&lt;int&gt; &amp;nums, int target) {\n    // 左閉右開区間[0, n)を初期化、すなわちi、jはそれぞれ配列の最初の要素と最後の要素+1を指す\n    int i = 0, j = nums.size();\n    // 探索区間が空になるまでループ（i = jの時空になる）\n    while (i &lt; j) {\n        int m = i + (j - i) / 2; // 中点インデックスmを計算\n        if (nums[m] &lt; target)    // この状況はtargetが区間[m+1, j)にあることを示す\n            i = m + 1;\n        else if (nums[m] &gt; target) // この状況はtargetが区間[i, m)にあることを示す\n            j = m;\n        else // ターゲット要素が見つかったため、そのインデックスを返す\n            return m;\n    }\n    // ターゲット要素が見つからなかったため、-1を返す\n    return -1;\n}\n</code></pre> binary_search.java<pre><code>/* 二分探索（左閉右開区間） */\nint binarySearchLCRO(int[] nums, int target) {\n    // 左閉右開区間 [0, n) を初期化、すなわち i, j はそれぞれ配列の最初の要素と最後の要素+1を指す\n    int i = 0, j = nums.length;\n    // 探索区間が空になるまでループ（i = j のとき空）\n    while (i &lt; j) {\n        int m = i + (j - i) / 2; // 中点インデックス m を計算\n        if (nums[m] &lt; target) // この状況は target が区間 [m+1, j) にあることを示す\n            i = m + 1;\n        else if (nums[m] &gt; target) // この状況は target が区間 [i, m) にあることを示す\n            j = m;\n        else // 目標要素を見つけたので、そのインデックスを返す\n            return m;\n    }\n    // 目標要素を見つけられなかったので、-1 を返す\n    return -1;\n}\n</code></pre> binary_search.cs<pre><code>[class]{binary_search}-[func]{BinarySearchLCRO}\n</code></pre> binary_search.go<pre><code>[class]{}-[func]{binarySearchLCRO}\n</code></pre> binary_search.swift<pre><code>[class]{}-[func]{binarySearchLCRO}\n</code></pre> binary_search.js<pre><code>[class]{}-[func]{binarySearchLCRO}\n</code></pre> binary_search.ts<pre><code>[class]{}-[func]{binarySearchLCRO}\n</code></pre> binary_search.dart<pre><code>[class]{}-[func]{binarySearchLCRO}\n</code></pre> binary_search.rs<pre><code>[class]{}-[func]{binary_search_lcro}\n</code></pre> binary_search.c<pre><code>[class]{}-[func]{binarySearchLCRO}\n</code></pre> binary_search.kt<pre><code>[class]{}-[func]{binarySearchLCRO}\n</code></pre> binary_search.rb<pre><code>[class]{}-[func]{binary_search_lcro}\n</code></pre> <p>下図に示すように、2つの区間表現タイプにおいて、二分探索アルゴリズムの初期化、ループ条件、区間縮小操作が異なります。</p> <p>「閉区間」表現では両方の境界が包含的であるため、ポインタ\\(i\\)と\\(j\\)による区間縮小操作も対称的です。これによりエラーが発生しにくくなるため、一般的に「閉区間」アプローチの使用が推奨されます。</p> <p></p> <p> 図 10-3   Two types of interval definitions </p>","path":["第 10 章 &nbsp; 探索","10.1 &nbsp; 二分探索"],"tags":[]},{"location":"chapter_searching/binary_search/#1012","level":2,"title":"10.1.2   利点と制限","text":"<p>二分探索は時間と空間の両方の面で良好な性能を示します。</p> <ul> <li>二分探索は時間効率が良いです。大きなデータセットでは、対数時間計算量が大きな利点を提供します。例えば、サイズ\\(n = 2^{20}\\)のデータセットが与えられた場合、線形探索は\\(2^{20} = 1048576\\)回の反復が必要ですが、二分探索は\\(\\log_2 2^{20} = 20\\)回のループのみで済みます。</li> <li>二分探索には追加の空間が必要ありません。追加の空間に依存する探索アルゴリズム（ハッシュ探索など）と比較して、二分探索はより空間効率的です。</li> </ul> <p>しかし、二分探索は以下の懸念により、すべてのシナリオに適しているとは限りません。</p> <ul> <li>二分探索はソート済みデータにのみ適用できます。未ソートのデータは二分探索を適用する前にソートする必要があり、ソートアルゴリズムは通常\\(O(n \\log n)\\)の時間計算量を持つため、これは価値がないかもしれません。このコストは線形探索よりも高く、二分探索自体は言うまでもありません。頻繁な挿入があるシナリオでは、配列を順序に保つコストは非常に高く、特定の位置に新しい要素を挿入する時間計算量は\\(O(n)\\)です。</li> <li>二分探索は配列のみを使用できます。二分探索には非連続（ジャンプ）要素アクセスが必要で、これは連結リストでは非効率的です。そのため、連結リストや連結リストに基づくデータ構造はこのアルゴリズムに適していない可能性があります。</li> <li>線形探索は小さなデータセットでより良い性能を示します。線形探索では各反復で1つの判定操作のみが必要ですが、二分探索では1つの加算、1つの除算、1つから3つの判定操作、1つの加算（減算）を含み、合計4つから6つの操作が必要です。そのため、データサイズ\\(n\\)が小さい場合、線形探索は二分探索よりも高速です。</li> </ul>","path":["第 10 章 &nbsp; 探索","10.1 &nbsp; 二分探索"],"tags":[]},{"location":"chapter_searching/binary_search_edge/","level":1,"title":"10.3   二分探索の境界","text":"","path":["第 10 章 &nbsp; 探索","10.3 &nbsp; 二分探索の境界"],"tags":[]},{"location":"chapter_searching/binary_search_edge/#1031","level":2,"title":"10.3.1   左境界を見つける","text":"<p>Question</p> <p>重複要素を含む可能性がある長さ\\(n\\)のソート済み配列<code>nums</code>が与えられ、最も左の要素<code>target</code>のインデックスを返してください。要素が配列に存在しない場合は、\\(-1\\)を返してください。</p> <p>挿入位置の二分探索方法を思い出すと、探索完了後、インデックス\\(i\\)は<code>target</code>の最も左の出現を指します。したがって、挿入位置の探索は本質的に最も左の<code>target</code>のインデックスを見つけることと同じです。</p> <p>挿入位置を見つける関数を使用して<code>target</code>の左境界を見つけることができます。配列に<code>target</code>が含まれていない可能性があることに注意してください。これは以下の2つの結果につながる可能性があります：</p> <ul> <li>挿入位置のインデックス\\(i\\)が範囲外です。</li> <li>要素<code>nums[i]</code>が<code>target</code>と等しくありません。</li> </ul> <p>これらの場合、単に\\(-1\\)を返します。コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_edge.py<pre><code>def binary_search_left_edge(nums: list[int], target: int) -&gt; int:\n    \"\"\"最左端のターゲットの二分探索\"\"\"\n    # ターゲットの挿入位置を見つけることと同等\n    i = binary_search_insertion(nums, target)\n    # ターゲットが見つからなかった場合、-1 を返す\n    if i == len(nums) or nums[i] != target:\n        return -1\n    # ターゲットが見つかった場合、インデックス i を返す\n    return i\n</code></pre> binary_search_edge.cpp<pre><code>/* 最左のターゲットの二分探索 */\nint binarySearchLeftEdge(vector&lt;int&gt; &amp;nums, int target) {\n    // targetの挿入ポイントを見つけることと等価\n    int i = binarySearchInsertion(nums, target);\n    // targetが見つからなかったため、-1を返す\n    if (i == nums.size() || nums[i] != target) {\n        return -1;\n    }\n    // targetが見つかったため、インデックスiを返す\n    return i;\n}\n</code></pre> binary_search_edge.java<pre><code>/* 最も左の target を二分探索 */\nint binarySearchLeftEdge(int[] nums, int target) {\n    // target の挿入点を見つけることと等価\n    int i = binary_search_insertion.binarySearchInsertion(nums, target);\n    // target を見つけられなかったので、-1 を返す\n    if (i == nums.length || nums[i] != target) {\n        return -1;\n    }\n    // target を見つけたので、インデックス i を返す\n    return i;\n}\n</code></pre> binary_search_edge.cs<pre><code>[class]{binary_search_edge}-[func]{BinarySearchLeftEdge}\n</code></pre> binary_search_edge.go<pre><code>[class]{}-[func]{binarySearchLeftEdge}\n</code></pre> binary_search_edge.swift<pre><code>[class]{}-[func]{binarySearchLeftEdge}\n</code></pre> binary_search_edge.js<pre><code>[class]{}-[func]{binarySearchLeftEdge}\n</code></pre> binary_search_edge.ts<pre><code>[class]{}-[func]{binarySearchLeftEdge}\n</code></pre> binary_search_edge.dart<pre><code>[class]{}-[func]{binarySearchLeftEdge}\n</code></pre> binary_search_edge.rs<pre><code>[class]{}-[func]{binary_search_left_edge}\n</code></pre> binary_search_edge.c<pre><code>[class]{}-[func]{binarySearchLeftEdge}\n</code></pre> binary_search_edge.kt<pre><code>[class]{}-[func]{binarySearchLeftEdge}\n</code></pre> binary_search_edge.rb<pre><code>[class]{}-[func]{binary_search_left_edge}\n</code></pre>","path":["第 10 章 &nbsp; 探索","10.3 &nbsp; 二分探索の境界"],"tags":[]},{"location":"chapter_searching/binary_search_edge/#1032","level":2,"title":"10.3.2   右境界を見つける","text":"<p><code>target</code>の最も右の出現をどのように見つけるでしょうか？最も直接的な方法は、<code>nums[m] == target</code>の場合に探索境界を調整する方法を変更して、従来の二分探索ロジックを修正することです。コードはここでは省略されています。興味がある場合は、自分でコードを実装してみてください。</p> <p>以下では、さらに2つの巧妙な方法を紹介します。</p>","path":["第 10 章 &nbsp; 探索","10.3 &nbsp; 二分探索の境界"],"tags":[]},{"location":"chapter_searching/binary_search_edge/#1","level":3,"title":"1.   左境界探索を再利用する","text":"<p><code>target</code>の最も右の出現を見つけるには、最も左の<code>target</code>を見つけるために使用された関数を再利用できます。具体的には、最も右のターゲットの探索を最も左のターゲット + 1の探索に変換します。</p> <p>下図に示すように、探索完了後、ポインタ\\(i\\)は最も左の<code>target + 1</code>（存在する場合）を指し、ポインタ\\(j\\)は<code>target</code>の最も右の出現を指します。したがって、\\(j\\)を返すことで右境界が得られます。</p> <p></p> <p> 図 10-7   Transforming the search for the right boundary into the search for the left boundary </p> <p>返される挿入位置は\\(i\\)であることに注意してください。したがって、\\(j\\)を得るためには1を引く必要があります：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_edge.py<pre><code>def binary_search_right_edge(nums: list[int], target: int) -&gt; int:\n    \"\"\"最右端のターゲットの二分探索\"\"\"\n    # 最左端のターゲット + 1 を見つけることに変換\n    i = binary_search_insertion(nums, target + 1)\n    # j は最右端のターゲットを指し、i はターゲットより大きい最初の要素を指す\n    j = i - 1\n    # ターゲットが見つからなかった場合、-1 を返す\n    if j == -1 or nums[j] != target:\n        return -1\n    # ターゲットが見つかった場合、インデックス j を返す\n    return j\n</code></pre> binary_search_edge.cpp<pre><code>/* 最右のターゲットの二分探索 */\nint binarySearchRightEdge(vector&lt;int&gt; &amp;nums, int target) {\n    // 最左のtarget + 1を見つけることに変換\n    int i = binarySearchInsertion(nums, target + 1);\n    // jは最右のターゲットを指し、iはtargetより大きい最初の要素を指す\n    int j = i - 1;\n    // targetが見つからなかったため、-1を返す\n    if (j == -1 || nums[j] != target) {\n        return -1;\n    }\n    // targetが見つかったため、インデックスjを返す\n    return j;\n}\n</code></pre> binary_search_edge.java<pre><code>/* 最も右の target を二分探索 */\nint binarySearchRightEdge(int[] nums, int target) {\n    // 最も左の target + 1 を見つけることに変換\n    int i = binary_search_insertion.binarySearchInsertion(nums, target + 1);\n    // j は最も右の target を指し、i は target より大きい最初の要素を指す\n    int j = i - 1;\n    // target を見つけられなかったので、-1 を返す\n    if (j == -1 || nums[j] != target) {\n        return -1;\n    }\n    // target を見つけたので、インデックス j を返す\n    return j;\n}\n</code></pre> binary_search_edge.cs<pre><code>[class]{binary_search_edge}-[func]{BinarySearchRightEdge}\n</code></pre> binary_search_edge.go<pre><code>[class]{}-[func]{binarySearchRightEdge}\n</code></pre> binary_search_edge.swift<pre><code>[class]{}-[func]{binarySearchRightEdge}\n</code></pre> binary_search_edge.js<pre><code>[class]{}-[func]{binarySearchRightEdge}\n</code></pre> binary_search_edge.ts<pre><code>[class]{}-[func]{binarySearchRightEdge}\n</code></pre> binary_search_edge.dart<pre><code>[class]{}-[func]{binarySearchRightEdge}\n</code></pre> binary_search_edge.rs<pre><code>[class]{}-[func]{binary_search_right_edge}\n</code></pre> binary_search_edge.c<pre><code>[class]{}-[func]{binarySearchRightEdge}\n</code></pre> binary_search_edge.kt<pre><code>[class]{}-[func]{binarySearchRightEdge}\n</code></pre> binary_search_edge.rb<pre><code>[class]{}-[func]{binary_search_right_edge}\n</code></pre>","path":["第 10 章 &nbsp; 探索","10.3 &nbsp; 二分探索の境界"],"tags":[]},{"location":"chapter_searching/binary_search_edge/#2","level":3,"title":"2.   要素探索に変換する","text":"<p>配列に<code>target</code>が含まれていない場合、\\(i\\)と\\(j\\)は最終的に<code>target</code>より大きい最初の要素と小さい最初の要素をそれぞれ指します。</p> <p>したがって、下図に示すように、配列に存在しない要素を構築して、左と右の境界を探索できます。</p> <ul> <li>最も左の<code>target</code>を見つけるには：<code>target - 0.5</code>を探索することに変換でき、ポインタ\\(i\\)を返します。</li> <li>最も右の<code>target</code>を見つけるには：<code>target + 0.5</code>を探索することに変換でき、ポインタ\\(j\\)を返します。</li> </ul> <p></p> <p> 図 10-8   Transforming the search for boundaries into the search for an element </p> <p>コードはここでは省略されていますが、このアプローチについて注意すべき2つの重要な点があります。</p> <ul> <li>与えられた配列<code>nums</code>には小数が含まれていないため、等しい場合の処理は心配ありません。</li> <li>ただし、このアプローチで小数を導入するには、<code>target</code>変数を浮動小数点型に変更する必要があります（Pythonでは変更は不要です）。</li> </ul>","path":["第 10 章 &nbsp; 探索","10.3 &nbsp; 二分探索の境界"],"tags":[]},{"location":"chapter_searching/binary_search_insertion/","level":1,"title":"10.2   二分探索による挿入","text":"<p>二分探索は目標要素を探索するだけでなく、目標要素の挿入位置を探索するなど、多くの変種問題を解決するためにも使用されます。</p>","path":["第 10 章 &nbsp; 探索","10.2 &nbsp; 二分探索による挿入"],"tags":[]},{"location":"chapter_searching/binary_search_insertion/#1021","level":2,"title":"10.2.1   重複要素がない場合","text":"<p>Question</p> <p>一意の要素を持つ長さ\\(n\\)のソート済み配列<code>nums</code>と要素<code>target</code>が与えられ、ソート順を維持しながら<code>target</code>を<code>nums</code>に挿入します。<code>target</code>が配列にすでに存在する場合は、既存の要素の左側に挿入します。挿入後の配列における<code>target</code>のインデックスを返してください。下図に示す例を参照してください。</p> <p></p> <p> 図 10-4   Example data for binary search insertion point </p> <p>前のセクションの二分探索コードを再利用したい場合、以下の2つの質問に答える必要があります。</p> <p>質問1：配列にすでに<code>target</code>が含まれている場合、挿入位置は既存要素のインデックスになりますか？</p> <p><code>target</code>を等しい要素の左側に挿入するという要件は、新しく挿入される<code>target</code>が元の<code>target</code>の位置を置き換えることを意味します。つまり、配列に<code>target</code>が含まれている場合、挿入位置は確かにその<code>target</code>のインデックスです。</p> <p>質問2：配列に<code>target</code>が含まれていない場合、どのインデックスに挿入されますか？</p> <p>二分探索プロセスをさらに考えてみましょう：<code>nums[m] &lt; target</code>のとき、ポインタ\\(i\\)が移動します。これは、ポインタ\\(i\\)が<code>target</code>以上の要素に近づいていることを意味します。同様に、ポインタ\\(j\\)は常に<code>target</code>以下の要素に近づいています。</p> <p>したがって、二分の終了時には確実に：\\(i\\)は<code>target</code>より大きい最初の要素を指し、\\(j\\)は<code>target</code>より小さい最初の要素を指します。配列に<code>target</code>が含まれていない場合、挿入位置は\\(i\\)であることは明らかです。コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_insertion.py<pre><code>def binary_search_insertion_simple(nums: list[int], target: int) -&gt; int:\n    \"\"\"挿入位置の二分探索（重複要素なし）\"\"\"\n    i, j = 0, len(nums) - 1  # 両端閉区間 [0, n-1] を初期化\n    while i &lt;= j:\n        m = i + (j - i) // 2  # 中点インデックス m を計算\n        if nums[m] &lt; target:\n            i = m + 1  # ターゲットは区間 [m+1, j] にある\n        elif nums[m] &gt; target:\n            j = m - 1  # ターゲットは区間 [i, m-1] にある\n        else:\n            return m  # ターゲットが見つかった場合、挿入位置 m を返す\n    # ターゲットが見つからなかった場合、挿入位置 i を返す\n    return i\n</code></pre> binary_search_insertion.cpp<pre><code>/* 挿入ポイントの二分探索（重複要素なし） */\nint binarySearchInsertionSimple(vector&lt;int&gt; &amp;nums, int target) {\n    int i = 0, j = nums.size() - 1; // 両端閉区間[0, n-1]を初期化\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // 中点インデックスmを計算\n        if (nums[m] &lt; target) {\n            i = m + 1; // ターゲットは区間[m+1, j]にある\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // ターゲットは区間[i, m-1]にある\n        } else {\n            return m; // ターゲットが見つかったため、挿入ポイントmを返す\n        }\n    }\n    // ターゲットが見つからなかったため、挿入ポイントiを返す\n    return i;\n}\n</code></pre> binary_search_insertion.java<pre><code>/* 挿入点の二分探索（重複要素なし） */\nint binarySearchInsertionSimple(int[] nums, int target) {\n    int i = 0, j = nums.length - 1; // 両端閉区間 [0, n-1] を初期化\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // 中点インデックス m を計算\n        if (nums[m] &lt; target) {\n            i = m + 1; // target は区間 [m+1, j] にある\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target は区間 [i, m-1] にある\n        } else {\n            return m; // target を見つけたので、挿入点 m を返す\n        }\n    }\n    // target を見つけられなかったので、挿入点 i を返す\n    return i;\n}\n</code></pre> binary_search_insertion.cs<pre><code>[class]{binary_search_insertion}-[func]{BinarySearchInsertionSimple}\n</code></pre> binary_search_insertion.go<pre><code>[class]{}-[func]{binarySearchInsertionSimple}\n</code></pre> binary_search_insertion.swift<pre><code>[class]{}-[func]{binarySearchInsertionSimple}\n</code></pre> binary_search_insertion.js<pre><code>[class]{}-[func]{binarySearchInsertionSimple}\n</code></pre> binary_search_insertion.ts<pre><code>[class]{}-[func]{binarySearchInsertionSimple}\n</code></pre> binary_search_insertion.dart<pre><code>[class]{}-[func]{binarySearchInsertionSimple}\n</code></pre> binary_search_insertion.rs<pre><code>[class]{}-[func]{binary_search_insertion_simple}\n</code></pre> binary_search_insertion.c<pre><code>[class]{}-[func]{binarySearchInsertionSimple}\n</code></pre> binary_search_insertion.kt<pre><code>[class]{}-[func]{binarySearchInsertionSimple}\n</code></pre> binary_search_insertion.rb<pre><code>[class]{}-[func]{binary_search_insertion_simple}\n</code></pre>","path":["第 10 章 &nbsp; 探索","10.2 &nbsp; 二分探索による挿入"],"tags":[]},{"location":"chapter_searching/binary_search_insertion/#1022","level":2,"title":"10.2.2   重複要素がある場合","text":"<p>Question</p> <p>前の質問に基づいて、配列に重複要素が含まれている可能性があると仮定し、他はすべて同じとします。</p> <p>配列に<code>target</code>の複数の出現がある場合、通常の二分探索は<code>target</code>の1つの出現のインデックスのみを返すことができ、その位置の左右に<code>target</code>の出現がいくつあるかを特定することはできません。</p> <p>問題では目標要素を最も左の位置に挿入することが要求されているため、配列内の最も左の<code>target</code>のインデックスを見つける必要があります。最初に下図に示すステップを通してこれを実装することを考えてみましょう。</p> <ol> <li>二分探索を実行して<code>target</code>の任意のインデックス、例えば\\(k\\)を見つけます。</li> <li>インデックス\\(k\\)から開始して、最も左の<code>target</code>の出現が見つかるまで左に線形探索を行い、このインデックスを返します。</li> </ol> <p></p> <p> 図 10-5   Linear search for the insertion point of duplicate elements </p> <p>この方法は実現可能ですが、線形探索を含むため、時間計算量は\\(O(n)\\)です。この方法は、配列に多くの重複する<code>target</code>が含まれている場合に非効率です。</p> <p>今度は二分探索コードを拡張することを考えてみましょう。下図に示すように、全体的なプロセスは同じままです。各ラウンドで、まず中間インデックス\\(m\\)を計算し、次に<code>target</code>と<code>nums[m]</code>の値を比較して、以下のケースになります。</p> <ul> <li><code>nums[m] &lt; target</code>または<code>nums[m] &gt; target</code>のとき、これは<code>target</code>がまだ見つかっていないことを意味するため、通常の二分探索を使用して探索範囲を狭め、ポインタ\\(i\\)と\\(j\\)を<code>target</code>に近づけます。</li> <li><code>nums[m] == target</code>のとき、これは<code>target</code>より小さい要素が範囲\\([i, m - 1]\\)にあることを示すため、\\(j = m - 1\\)を使用して範囲を狭め、ポインタ\\(j\\)を<code>target</code>より小さい要素に近づけます。</li> </ul> <p>ループ後、\\(i\\)は最も左の<code>target</code>を指し、\\(j\\)は<code>target</code>より小さい最初の要素を指すため、インデックス\\(i\\)が挿入位置です。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 10-6   Steps for binary search insertion point of duplicate elements </p> <p>以下のコードを観察してください。分岐<code>nums[m] &gt; target</code>と<code>nums[m] == target</code>の操作は同じであるため、これら2つの分岐をマージできます。</p> <p>それでも、ロジックがより明確になり、可読性が向上するため、条件を展開したままにしておくことができます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_insertion.py<pre><code>def binary_search_insertion(nums: list[int], target: int) -&gt; int:\n    \"\"\"挿入位置の二分探索（重複要素あり）\"\"\"\n    i, j = 0, len(nums) - 1  # 両端閉区間 [0, n-1] を初期化\n    while i &lt;= j:\n        m = i + (j - i) // 2  # 中点インデックス m を計算\n        if nums[m] &lt; target:\n            i = m + 1  # ターゲットは区間 [m+1, j] にある\n        elif nums[m] &gt; target:\n            j = m - 1  # ターゲットは区間 [i, m-1] にある\n        else:\n            j = m - 1  # ターゲット未満の最初の要素は区間 [i, m-1] にある\n    # 挿入位置 i を返す\n    return i\n</code></pre> binary_search_insertion.cpp<pre><code>/* 挿入ポイントの二分探索（重複要素あり） */\nint binarySearchInsertion(vector&lt;int&gt; &amp;nums, int target) {\n    int i = 0, j = nums.size() - 1; // 両端閉区間[0, n-1]を初期化\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // 中点インデックスmを計算\n        if (nums[m] &lt; target) {\n            i = m + 1; // ターゲットは区間[m+1, j]にある\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // ターゲットは区間[i, m-1]にある\n        } else {\n            j = m - 1; // ターゲット未満の最初の要素は区間[i, m-1]にある\n        }\n    }\n    // 挿入ポイントiを返す\n    return i;\n}\n</code></pre> binary_search_insertion.java<pre><code>/* 挿入点の二分探索（重複要素あり） */\nint binarySearchInsertion(int[] nums, int target) {\n    int i = 0, j = nums.length - 1; // 両端閉区間 [0, n-1] を初期化\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // 中点インデックス m を計算\n        if (nums[m] &lt; target) {\n            i = m + 1; // target は区間 [m+1, j] にある\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target は区間 [i, m-1] にある\n        } else {\n            j = m - 1; // target より小さい最初の要素は区間 [i, m-1] にある\n        }\n    }\n    // 挿入点 i を返す\n    return i;\n}\n</code></pre> binary_search_insertion.cs<pre><code>[class]{binary_search_insertion}-[func]{BinarySearchInsertion}\n</code></pre> binary_search_insertion.go<pre><code>[class]{}-[func]{binarySearchInsertion}\n</code></pre> binary_search_insertion.swift<pre><code>[class]{}-[func]{binarySearchInsertion}\n</code></pre> binary_search_insertion.js<pre><code>[class]{}-[func]{binarySearchInsertion}\n</code></pre> binary_search_insertion.ts<pre><code>[class]{}-[func]{binarySearchInsertion}\n</code></pre> binary_search_insertion.dart<pre><code>[class]{}-[func]{binarySearchInsertion}\n</code></pre> binary_search_insertion.rs<pre><code>[class]{}-[func]{binary_search_insertion}\n</code></pre> binary_search_insertion.c<pre><code>[class]{}-[func]{binarySearchInsertion}\n</code></pre> binary_search_insertion.kt<pre><code>[class]{}-[func]{binarySearchInsertion}\n</code></pre> binary_search_insertion.rb<pre><code>[class]{}-[func]{binary_search_insertion}\n</code></pre> <p>Tip</p> <p>このセクションのコードは「閉区間」を使用しています。「左閉右開」に興味がある場合は、自分でコードを実装してみてください。</p> <p>要約すると、二分探索は本質的にポインタ\\(i\\)と\\(j\\)の探索目標を設定することです。これらの目標は特定の要素（<code>target</code>など）または要素の範囲（<code>target</code>より小さいものなど）である可能性があります。</p> <p>二分探索の連続ループにおいて、ポインタ\\(i\\)と\\(j\\)は段階的に事前定義された目標に近づきます。最終的に、それらは答えを見つけるか、境界を越えた後に停止します。</p>","path":["第 10 章 &nbsp; 探索","10.2 &nbsp; 二分探索による挿入"],"tags":[]},{"location":"chapter_searching/replace_linear_by_hashing/","level":1,"title":"10.4   ハッシュ最適化戦略","text":"<p>アルゴリズム問題において、線形探索をハッシュベースの探索に置き換えることで、アルゴリズムの時間計算量を削減することがよくあります。アルゴリズム問題を使用して理解を深めましょう。</p> <p>Question</p> <p>整数配列<code>nums</code>と目標要素<code>target</code>が与えられ、配列内で「和」が<code>target</code>に等しい2つの要素を探索し、それらの配列インデックスを返してください。任意の解が受け入れられます。</p>","path":["第 10 章 &nbsp; 探索","10.4 &nbsp; ハッシュ最適化戦略"],"tags":[]},{"location":"chapter_searching/replace_linear_by_hashing/#1041","level":2,"title":"10.4.1   線形探索：時間を空間と交換","text":"<p>すべての可能な組み合わせを直接横断することを考えてみます。下図に示すように、ネストしたループを開始し、各反復で2つの整数の和が<code>target</code>に等しいかどうかを判断します。そうであれば、それらのインデックスを返します。</p> <p></p> <p> 図 10-9   Linear search solution for two-sum problem </p> <p>コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby two_sum.py<pre><code>def two_sum_brute_force(nums: list[int], target: int) -&gt; list[int]:\n    \"\"\"方法一：ブルートフォース列挙\"\"\"\n    # 二重ループ、時間計算量は O(n^2)\n    for i in range(len(nums) - 1):\n        for j in range(i + 1, len(nums)):\n            if nums[i] + nums[j] == target:\n                return [i, j]\n    return []\n</code></pre> two_sum.cpp<pre><code>/* 方法一：ブルートフォース列挙 */\nvector&lt;int&gt; twoSumBruteForce(vector&lt;int&gt; &amp;nums, int target) {\n    int size = nums.size();\n    // 二重ループ、時間計算量はO(n^2)\n    for (int i = 0; i &lt; size - 1; i++) {\n        for (int j = i + 1; j &lt; size; j++) {\n            if (nums[i] + nums[j] == target)\n                return {i, j};\n        }\n    }\n    return {};\n}\n</code></pre> two_sum.java<pre><code>/* 方法一: 暴力列挙 */\nint[] twoSumBruteForce(int[] nums, int target) {\n    int size = nums.length;\n    // 二重ループ、時間計算量は O(n^2)\n    for (int i = 0; i &lt; size - 1; i++) {\n        for (int j = i + 1; j &lt; size; j++) {\n            if (nums[i] + nums[j] == target)\n                return new int[] { i, j };\n        }\n    }\n    return new int[0];\n}\n</code></pre> two_sum.cs<pre><code>[class]{two_sum}-[func]{TwoSumBruteForce}\n</code></pre> two_sum.go<pre><code>[class]{}-[func]{twoSumBruteForce}\n</code></pre> two_sum.swift<pre><code>[class]{}-[func]{twoSumBruteForce}\n</code></pre> two_sum.js<pre><code>[class]{}-[func]{twoSumBruteForce}\n</code></pre> two_sum.ts<pre><code>[class]{}-[func]{twoSumBruteForce}\n</code></pre> two_sum.dart<pre><code>[class]{}-[func]{twoSumBruteForce}\n</code></pre> two_sum.rs<pre><code>[class]{}-[func]{two_sum_brute_force}\n</code></pre> two_sum.c<pre><code>[class]{}-[func]{twoSumBruteForce}\n</code></pre> two_sum.kt<pre><code>[class]{}-[func]{twoSumBruteForce}\n</code></pre> two_sum.rb<pre><code>[class]{}-[func]{two_sum_brute_force}\n</code></pre> <p>この方法の時間計算量は\\(O(n^2)\\)、空間計算量は\\(O(1)\\)で、大容量データでは非常に時間がかかる可能性があります。</p>","path":["第 10 章 &nbsp; 探索","10.4 &nbsp; ハッシュ最適化戦略"],"tags":[]},{"location":"chapter_searching/replace_linear_by_hashing/#1042","level":2,"title":"10.4.2   ハッシュ探索：空間を時間と交換","text":"<p>ハッシュテーブルの使用を考えてみましょう。キーと値のペアはそれぞれ配列要素とそのインデックスです。配列をループし、各反復中に下図に示すステップを実行します。</p> <ol> <li>数値<code>target - nums[i]</code>がハッシュテーブルにあるかどうかを確認します。ある場合は、これら2つの要素のインデックスを直接返します。</li> <li>キーと値のペア<code>nums[i]</code>とインデックス<code>i</code>をハッシュテーブルに追加します。</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt; <p></p> <p></p> <p></p> <p> 図 10-10   Help hash table solve two-sum </p> <p>実装コードは以下に示され、単一のループのみが必要です：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby two_sum.py<pre><code>def two_sum_hash_table(nums: list[int], target: int) -&gt; list[int]:\n    \"\"\"方法二：補助ハッシュテーブル\"\"\"\n    # 補助ハッシュテーブル、空間計算量は O(n)\n    dic = {}\n    # 単一ループ、時間計算量は O(n)\n    for i in range(len(nums)):\n        if target - nums[i] in dic:\n            return [dic[target - nums[i]], i]\n        dic[nums[i]] = i\n    return []\n</code></pre> two_sum.cpp<pre><code>/* 方法二：補助ハッシュテーブル */\nvector&lt;int&gt; twoSumHashTable(vector&lt;int&gt; &amp;nums, int target) {\n    int size = nums.size();\n    // 補助ハッシュテーブル、空間計算量はO(n)\n    unordered_map&lt;int, int&gt; dic;\n    // 単層ループ、時間計算量はO(n)\n    for (int i = 0; i &lt; size; i++) {\n        if (dic.find(target - nums[i]) != dic.end()) {\n            return {dic[target - nums[i]], i};\n        }\n        dic.emplace(nums[i], i);\n    }\n    return {};\n}\n</code></pre> two_sum.java<pre><code>/* 方法二: 補助ハッシュテーブル */\nint[] twoSumHashTable(int[] nums, int target) {\n    int size = nums.length;\n    // 補助ハッシュテーブル、空間計算量は O(n)\n    Map&lt;Integer, Integer&gt; dic = new HashMap&lt;&gt;();\n    // 単一層ループ、時間計算量は O(n)\n    for (int i = 0; i &lt; size; i++) {\n        if (dic.containsKey(target - nums[i])) {\n            return new int[] { dic.get(target - nums[i]), i };\n        }\n        dic.put(nums[i], i);\n    }\n    return new int[0];\n}\n</code></pre> two_sum.cs<pre><code>[class]{two_sum}-[func]{TwoSumHashTable}\n</code></pre> two_sum.go<pre><code>[class]{}-[func]{twoSumHashTable}\n</code></pre> two_sum.swift<pre><code>[class]{}-[func]{twoSumHashTable}\n</code></pre> two_sum.js<pre><code>[class]{}-[func]{twoSumHashTable}\n</code></pre> two_sum.ts<pre><code>[class]{}-[func]{twoSumHashTable}\n</code></pre> two_sum.dart<pre><code>[class]{}-[func]{twoSumHashTable}\n</code></pre> two_sum.rs<pre><code>[class]{}-[func]{two_sum_hash_table}\n</code></pre> two_sum.c<pre><code>[class]{HashTable}-[func]{}\n\n[class]{}-[func]{twoSumHashTable}\n</code></pre> two_sum.kt<pre><code>[class]{}-[func]{twoSumHashTable}\n</code></pre> two_sum.rb<pre><code>[class]{}-[func]{two_sum_hash_table}\n</code></pre> <p>この方法は、ハッシュ探索を使用することで時間計算量を\\(O(n^2)\\)から\\(O(n)\\)に削減し、実行時効率を大幅に向上させます。</p> <p>追加のハッシュテーブルを維持する必要があるため、空間計算量は\\(O(n)\\)です。それにもかかわらず、この方法は全体的により均衡のとれた時空間効率を持ち、この問題の最適解となります。</p>","path":["第 10 章 &nbsp; 探索","10.4 &nbsp; ハッシュ最適化戦略"],"tags":[]},{"location":"chapter_searching/searching_algorithm_revisited/","level":1,"title":"10.5   探索アルゴリズムの再検討","text":"<p>探索アルゴリズム（検索アルゴリズム）は、配列、連結リスト、木、グラフなどのデータ構造内で特定の基準を満たす1つ以上の要素を取得するために使用されます。</p> <p>探索アルゴリズムは、そのアプローチに基づいて以下の2つのカテゴリに分けることができます。</p> <ul> <li>データ構造を横断することで目標要素を特定する：配列、連結リスト、木、グラフの横断など。</li> <li>データの組織構造や既存のデータを使用して効率的な要素探索を実現する：二分探索、ハッシュ探索、二分探索木探索など。</li> </ul> <p>これらのトピックは前の章で紹介されたため、私たちには馴染みのないものではありません。このセクションでは、より体系的な観点から探索アルゴリズムを再検討します。</p>","path":["第 10 章 &nbsp; 探索","10.5 &nbsp; 探索アルゴリズムの再検討"],"tags":[]},{"location":"chapter_searching/searching_algorithm_revisited/#1051","level":2,"title":"10.5.1   総当たり探索","text":"<p>総当たり探索は、データ構造のすべての要素を横断することで目標要素を特定します。</p> <ul> <li>「線形探索」は配列や連結リストなどの線形データ構造に適しています。データ構造の一端から開始し、目標要素が見つかるか、目標要素を見つけることなく他端に到達するまで、各要素に一つずつアクセスします。</li> <li>「幅優先探索」と「深さ優先探索」は、グラフと木の2つの横断戦略です。幅優先探索は初期ノードから開始し、層ごと（左から右へ）に探索し、近くから遠くのノードにアクセスします。深さ優先探索は初期ノードから開始し、パスの終端（上から下へ）まで追跡し、その後バックトラックして他のパスを試し、データ構造全体が横断されるまで続行します。</li> </ul> <p>総当たり探索の利点は、その単純さと汎用性であり、**データの前処理や追加のデータ構造の助けが不要**です。</p> <p>ただし、**このタイプのアルゴリズムの時間計算量は\\(O(n)\\)**で、\\(n\\)は要素数であるため、大規模なデータセットでは性能が悪くなります。</p>","path":["第 10 章 &nbsp; 探索","10.5 &nbsp; 探索アルゴリズムの再検討"],"tags":[]},{"location":"chapter_searching/searching_algorithm_revisited/#1052","level":2,"title":"10.5.2   適応的探索","text":"<p>適応的探索は、データの固有の性質（順序など）を使用して探索プロセスを最適化し、それにより目標要素をより効率的に特定します。</p> <ul> <li>「二分探索」はデータの整列性を使用して効率的な探索を実現し、配列にのみ適用可能です。</li> <li>「ハッシュ探索」はハッシュテーブルを使用して探索データと目標データの間にキーと値のマッピングを確立し、それによりクエリ操作を実装します。</li> <li>特定の木構造（二分探索木など）での「木探索」は、ノード値の比較に基づいてノードを迅速に除外し、それにより目標要素を特定します。</li> </ul> <p>これらのアルゴリズムの利点は高効率であり、時間計算量が\\(O(\\log n)\\)または\\(O(1)\\)にまで達します。</p> <p>ただし、これらのアルゴリズムを使用するには、多くの場合データの前処理が必要です。例えば、二分探索では事前に配列をソートする必要があり、ハッシュ探索と木探索の両方で追加のデータ構造の助けが必要です。これらの構造を維持することも、時間と空間の面でより多くのオーバーヘッドが必要です。</p> <p>Tip</p> <p>適応的探索アルゴリズムは、多くの場合探索アルゴリズムと呼ばれ、主に特定のデータ構造内で目標要素を迅速に取得するために使用されます。</p>","path":["第 10 章 &nbsp; 探索","10.5 &nbsp; 探索アルゴリズムの再検討"],"tags":[]},{"location":"chapter_searching/searching_algorithm_revisited/#1053","level":2,"title":"10.5.3   探索方法の選択","text":"<p>サイズ\\(n\\)のデータセットが与えられた場合、線形探索、二分探索、木探索、ハッシュ探索、またはその他の方法を使用して目標要素を取得できます。これらの方法の動作原理を下図に示します。</p> <p></p> <p> 図 10-11   Various search strategies </p> <p>前述の方法の特性と操作効率を以下の表に示します。</p> <p> 表 10-1   探索アルゴリズム効率の比較 </p> 線形探索 二分探索 木探索 ハッシュ探索 要素探索 \\(O(n)\\) \\(O(\\log n)\\) \\(O(\\log n)\\) \\(O(1)\\) 要素挿入 \\(O(1)\\) \\(O(n)\\) \\(O(\\log n)\\) \\(O(1)\\) 要素削除 \\(O(n)\\) \\(O(n)\\) \\(O(\\log n)\\) \\(O(1)\\) 追加空間 \\(O(1)\\) \\(O(1)\\) \\(O(n)\\) \\(O(n)\\) データ前処理 / ソート \\(O(n \\log n)\\) 木構築 \\(O(n \\log n)\\) ハッシュテーブル構築 \\(O(n)\\) データ順序性 無順序 順序 順序 無順序 <p>探索アルゴリズムの選択は、データ量、探索性能要件、データクエリと更新の頻度などにも依存します。</p> <p>線形探索</p> <ul> <li>汎用性が良く、データ前処理操作が不要です。データを一度だけクエリする必要がある場合、他の3つの方法のデータ前処理時間は線形探索の時間よりも長くなります。</li> <li>小容量のデータに適しており、時間計算量が効率に与える影響は小さいです。</li> <li>データ更新が非常に頻繁なシナリオに適しています。この方法はデータの追加メンテナンスを必要としないためです。</li> </ul> <p>二分探索</p> <ul> <li>より大きなデータ量に適しており、安定した性能と最悪ケースの時間計算量\\(O(\\log n)\\)を持ちます。</li> <li>ただし、データ量が大きすぎることはできません。配列の保存には連続したメモリ空間が必要だからです。</li> <li>頻繁な追加と削除があるシナリオには適していません。順序付き配列の維持に多くのオーバーヘッドが発生するためです。</li> </ul> <p>ハッシュ探索</p> <ul> <li>高速クエリ性能が不可欠なシナリオに適しており、平均時間計算量は\\(O(1)\\)です。</li> <li>順序付きデータや範囲探索が必要なシナリオには適していません。ハッシュテーブルはデータの順序性を維持できないためです。</li> <li>ハッシュ関数とハッシュ衝突処理戦略への依存度が高く、性能劣化のリスクが大きいです。</li> <li>過度に大容量のデータには適していません。ハッシュテーブルは衝突を最小化し、良好なクエリ性能を提供するために追加の空間が必要だからです。</li> </ul> <p>木探索</p> <ul> <li>大容量データに適しています。木ノードはメモリ内に分散して保存されるためです。</li> <li>順序付きデータの維持や範囲探索に適しています。</li> <li>ノードの継続的な追加と削除により、二分探索木は偏る可能性があり、時間計算量が\\(O(n)\\)に劣化する可能性があります。</li> <li>AVL木や赤黒木を使用する場合、操作は\\(O(\\log n)\\)効率で安定して実行できますが、木のバランスを維持する操作により追加のオーバーヘッドが追加されます。</li> </ul>","path":["第 10 章 &nbsp; 探索","10.5 &nbsp; 探索アルゴリズムの再検討"],"tags":[]},{"location":"chapter_searching/summary/","level":1,"title":"10.6   まとめ","text":"<ul> <li>二分探索はデータの順序に依存し、探索区間を反復的に半分にすることで探索を実行します。入力データがソート済みである必要があり、配列または配列ベースのデータ構造にのみ適用可能です。</li> <li>無順序データセット内のエントリを見つけるには、総当たり探索が必要な場合があります。データ構造に基づいて異なる探索アルゴリズムを適用できます：線形探索は配列と連結リストに適しており、幅優先探索（BFS）と深さ優先探索（DFS）はグラフと木に適しています。これらのアルゴリズムは非常に汎用性が高く、データの前処理が不要ですが、\\(O(n)\\)という高い時間計算量を持ちます。</li> <li>ハッシュ探索、木探索、二分探索は効率的な探索方法で、特定のデータ構造内で目標要素を迅速に特定できます。これらのアルゴリズムは非常に効率的で、時間計算量が\\(O(\\log n)\\)または\\(O(1)\\)にまで達しますが、通常は追加のデータ構造を収容するために追加の空間が必要です。</li> <li>実際には、データ量、探索性能要件、データクエリと更新頻度などの要因を分析して、適切な探索方法を選択する必要があります。</li> <li>線形探索は小さなデータや頻繁に更新される（変動性の高い）データに理想的です。二分探索は大きくてソート済みのデータに適しています。ハッシュ探索は高いクエリ効率が必要で範囲クエリが不要なデータに適しています。木探索は順序を維持し、範囲クエリをサポートする必要がある大きな動的データに最も適しています。</li> <li>線形探索をハッシュ探索に置き換えることは、実行時性能を最適化する一般的な戦略で、時間計算量を\\(O(n)\\)から\\(O(1)\\)に削減します。</li> </ul>","path":["第 10 章 &nbsp; 探索","10.6 &nbsp; まとめ"],"tags":[]},{"location":"chapter_sorting/","level":1,"title":"第 11 章   ソート","text":"<p>Abstract</p> <p>ソートは混沌を秩序に変える魔法の鍵のようなもので、データをより効率的に理解し処理することを可能にします。</p> <p>単純な昇順であろうと複雑なカテゴリ配列であろうと、ソートはデータの調和美を明らかにします。</p>","path":["第 11 章 &nbsp; ソート"],"tags":[]},{"location":"chapter_sorting/#_1","level":2,"title":"章の内容","text":"<ul> <li>11.1   ソートアルゴリズム</li> <li>11.2   選択ソート</li> <li>11.3   バブルソート</li> <li>11.4   挿入ソート</li> <li>11.5   クイックソート</li> <li>11.6   マージソート</li> <li>11.7   ヒープソート</li> <li>11.8   バケットソート</li> <li>11.9   計数ソート</li> <li>11.10   基数ソート</li> <li>11.11   まとめ</li> </ul>","path":["第 11 章 &nbsp; ソート"],"tags":[]},{"location":"chapter_sorting/bubble_sort/","level":1,"title":"11.3   バブルソート","text":"<p>バブルソートは、隣接する要素を継続的に比較し交換することで動作します。このプロセスは泡が底から上に上昇するようなものなので、「バブルソート」と名付けられました。</p> <p>下図に示すように、バブリングプロセスは要素交換を使用してシミュレートできます：配列の左端から開始して右に移動し、隣接する要素の各ペアを比較します。左の要素が右の要素より大きい場合は、それらを交換します。横断後、最大要素は配列の右端にバブルアップします。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 11-4   Simulating bubble process using element swap </p>","path":["第 11 章 &nbsp; ソート","11.3 &nbsp; バブルソート"],"tags":[]},{"location":"chapter_sorting/bubble_sort/#1131","level":2,"title":"11.3.1   アルゴリズムプロセス","text":"<p>配列の長さを\\(n\\)とします。バブルソートのステップは下図に示されます：</p> <ol> <li>まず、\\(n\\)個の要素に対して1回の「バブル」パスを実行し、最大要素を正しい位置に交換します。</li> <li>次に、残りの\\(n - 1\\)個の要素に対して「バブル」パスを実行し、2番目に大きい要素を正しい位置に交換します。</li> <li>この方法で続行します；\\(n - 1\\)回のパスの後、最大\\(n - 1\\)個の要素が正しい位置に移動されます。</li> <li>残りの唯一の要素は**必ず**最小であるため、**さらなる**ソートは必要ありません。この時点で、配列はソートされます。</li> </ol> <p></p> <p> 図 11-5   Bubble sort process </p> <p>コード例は以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby bubble_sort.py<pre><code>def bubble_sort(nums: list[int]):\n    \"\"\"バブルソート\"\"\"\n    n = len(nums)\n    # 外側のループ：未ソート範囲は [0, i]\n    for i in range(n - 1, 0, -1):\n        # 内側のループ：未ソート範囲 [0, i] の最大要素を範囲の右端に移動\n        for j in range(i):\n            if nums[j] &gt; nums[j + 1]:\n                # nums[j] と nums[j + 1] を交換\n                nums[j], nums[j + 1] = nums[j + 1], nums[j]\n</code></pre> bubble_sort.cpp<pre><code>/* バブルソート */\nvoid bubbleSort(vector&lt;int&gt; &amp;nums) {\n    // 外側ループ：未ソート範囲は[0, i]\n    for (int i = nums.size() - 1; i &gt; 0; i--) {\n        // 内側ループ：未ソート範囲[0, i]内の最大要素を範囲の右端に交換\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j]とnums[j + 1]を交換\n                // ここではstdのswapを使用\n                swap(nums[j], nums[j + 1]);\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.java<pre><code>/* バブルソート */\nvoid bubbleSort(int[] nums) {\n    // 外側ループ: 未ソート範囲は [0, i]\n    for (int i = nums.length - 1; i &gt; 0; i--) {\n        // 内側ループ: 未ソート範囲 [0, i] の最大要素を範囲の右端に交換\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] と nums[j + 1] を交換\n                int tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.cs<pre><code>[class]{bubble_sort}-[func]{BubbleSort}\n</code></pre> bubble_sort.go<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> bubble_sort.swift<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> bubble_sort.js<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> bubble_sort.ts<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> bubble_sort.dart<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> bubble_sort.rs<pre><code>[class]{}-[func]{bubble_sort}\n</code></pre> bubble_sort.c<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> bubble_sort.kt<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> bubble_sort.rb<pre><code>[class]{}-[func]{bubble_sort}\n</code></pre>","path":["第 11 章 &nbsp; ソート","11.3 &nbsp; バブルソート"],"tags":[]},{"location":"chapter_sorting/bubble_sort/#1132","level":2,"title":"11.3.2   効率の最適化","text":"<p>「バブリング」のラウンド中に交換が発生しない場合、配列はすでにソートされているため、すぐに戻ることができます。これを検出するために、<code>flag</code>変数を追加できます；パスで交換が行われない場合は、フラグを設定して早期に戻ります。</p> <p>この最適化があっても、バブルソートの最悪時間計算量と平均時間計算量は\\(O(n^2)\\)のままです。ただし、入力配列がすでにソートされている場合、最良ケース時間計算量は\\(O(n)\\)まで低くなる可能性があります。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby bubble_sort.py<pre><code>def bubble_sort_with_flag(nums: list[int]):\n    \"\"\"バブルソート（フラグによる最適化）\"\"\"\n    n = len(nums)\n    # 外側のループ：未ソート範囲は [0, i]\n    for i in range(n - 1, 0, -1):\n        flag = False  # フラグを初期化\n        # 内側のループ：未ソート範囲 [0, i] の最大要素を範囲の右端に移動\n        for j in range(i):\n            if nums[j] &gt; nums[j + 1]:\n                # nums[j] と nums[j + 1] を交換\n                nums[j], nums[j + 1] = nums[j + 1], nums[j]\n                flag = True  # 要素を交換したことを記録\n        if not flag:\n            break  # この回の「バブリング」で要素が交換されなかった場合、終了\n</code></pre> bubble_sort.cpp<pre><code>/* バブルソート（フラグ最適化版）*/\nvoid bubbleSortWithFlag(vector&lt;int&gt; &amp;nums) {\n    // 外側ループ：未ソート範囲は[0, i]\n    for (int i = nums.size() - 1; i &gt; 0; i--) {\n        bool flag = false; // フラグを初期化\n        // 内側ループ：未ソート範囲[0, i]内の最大要素を範囲の右端に交換\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j]とnums[j + 1]を交換\n                // ここではstdのswapを使用\n                swap(nums[j], nums[j + 1]);\n                flag = true; // 交換された要素を記録\n            }\n        }\n        if (!flag)\n            break; // この回の「バブリング」で要素が交換されなかった場合、終了\n    }\n}\n</code></pre> bubble_sort.java<pre><code>/* バブルソート（フラグによる最適化） */\nvoid bubbleSortWithFlag(int[] nums) {\n    // 外側ループ: 未ソート範囲は [0, i]\n    for (int i = nums.length - 1; i &gt; 0; i--) {\n        boolean flag = false; // フラグを初期化\n        // 内側ループ: 未ソート範囲 [0, i] の最大要素を範囲の右端に交換\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] と nums[j + 1] を交換\n                int tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                flag = true; // 交換された要素を記録\n            }\n        }\n        if (!flag)\n            break; // この「バブリング」ラウンドで要素が交換されなかった場合、終了\n    }\n}\n</code></pre> bubble_sort.cs<pre><code>[class]{bubble_sort}-[func]{BubbleSortWithFlag}\n</code></pre> bubble_sort.go<pre><code>[class]{}-[func]{bubbleSortWithFlag}\n</code></pre> bubble_sort.swift<pre><code>[class]{}-[func]{bubbleSortWithFlag}\n</code></pre> bubble_sort.js<pre><code>[class]{}-[func]{bubbleSortWithFlag}\n</code></pre> bubble_sort.ts<pre><code>[class]{}-[func]{bubbleSortWithFlag}\n</code></pre> bubble_sort.dart<pre><code>[class]{}-[func]{bubbleSortWithFlag}\n</code></pre> bubble_sort.rs<pre><code>[class]{}-[func]{bubble_sort_with_flag}\n</code></pre> bubble_sort.c<pre><code>[class]{}-[func]{bubbleSortWithFlag}\n</code></pre> bubble_sort.kt<pre><code>[class]{}-[func]{bubbleSortWithFlag}\n</code></pre> bubble_sort.rb<pre><code>[class]{}-[func]{bubble_sort_with_flag}\n</code></pre>","path":["第 11 章 &nbsp; ソート","11.3 &nbsp; バブルソート"],"tags":[]},{"location":"chapter_sorting/bubble_sort/#1133","level":2,"title":"11.3.3   アルゴリズムの特性","text":"<ul> <li>\\(O(n^2)\\)の時間計算量、適応ソート。 各「バブリング」ラウンドは長さ\\(n - 1\\)、\\(n - 2\\)、\\(\\dots\\)、\\(2\\)、\\(1\\)の配列セグメントを横断し、合計は\\((n - 1) n / 2\\)となります。<code>flag</code>最適化により、配列がすでにソートされている場合、最良ケース時間計算量は\\(O(n)\\)に達する可能性があります。</li> <li>\\(O(1)\\)の空間計算量、インプレースソート。 ポインタ\\(i\\)と\\(j\\)によって定数量の追加空間のみが使用されます。</li> <li>安定ソート。 等しい要素は「バブリング」中に交換されないため、元の順序が保持され、これは安定ソートになります。</li> </ul>","path":["第 11 章 &nbsp; ソート","11.3 &nbsp; バブルソート"],"tags":[]},{"location":"chapter_sorting/bucket_sort/","level":1,"title":"11.8   バケットソート","text":"<p>前述のソートアルゴリズムはすべて「比較ベースのソートアルゴリズム」で、値を比較することで要素をソートします。このようなソートアルゴリズムは \\(O(n \\log n)\\) より良い時間計算量を持つことはできません。次に、線形時間計算量を達成できるいくつかの「非比較ソートアルゴリズム」について議論します。</p> <p>バケットソートは分割統治戦略の典型的な応用です。一連の順序付けられたバケットを設定し、各バケットがデータの範囲を含み、入力データをこれらのバケットに均等に分散させることで動作します。そして、各バケット内のデータを個別にソートします。最後に、すべてのバケットからのソート済みデータを順次マージして最終結果を生成します。</p>","path":["第 11 章 &nbsp; ソート","11.8 &nbsp; バケットソート"],"tags":[]},{"location":"chapter_sorting/bucket_sort/#1181","level":2,"title":"11.8.1   アルゴリズムの過程","text":"<p>長さ \\(n\\) の配列で、\\([0, 1)\\) の範囲の浮動小数点数を考えてみます。バケットソートの過程は以下の図に示されています。</p> <ol> <li>\\(k\\) 個のバケットを初期化し、\\(n\\) 個の要素をこれらの \\(k\\) 個のバケットに分散させます。</li> <li>各バケットを個別にソートします（プログラミング言語の組み込みソート関数を使用）。</li> <li>最小から最大のバケットの順序で結果をマージします。</li> </ol> <p></p> <p> 図 11-13   バケットソートアルゴリズムの過程 </p> <p>コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby bucket_sort.py<pre><code>def bucket_sort(nums: list[float]):\n    \"\"\"バケットソート\"\"\"\n    # k = n/2 個のバケットを初期化、各バケットに平均2個の要素を配置することを期待\n    k = len(nums) // 2\n    buckets = [[] for _ in range(k)]\n    # 1. 配列要素を各バケットに分散\n    for num in nums:\n        # 入力データ範囲は [0, 1)、num * k を使用してインデックス範囲 [0, k-1] にマッピング\n        i = int(num * k)\n        # num をバケット i に追加\n        buckets[i].append(num)\n    # 2. 各バケットをソート\n    for bucket in buckets:\n        # 組み込みソート関数を使用、他のソートアルゴリズムに置き換えることも可能\n        bucket.sort()\n    # 3. バケットを走査して結果をマージ\n    i = 0\n    for bucket in buckets:\n        for num in bucket:\n            nums[i] = num\n            i += 1\n</code></pre> bucket_sort.cpp<pre><code>/* バケットソート */\nvoid bucketSort(vector&lt;float&gt; &amp;nums) {\n    // k = n/2個のバケットを初期化、各バケットに2つの要素を割り当てることを期待\n    int k = nums.size() / 2;\n    vector&lt;vector&lt;float&gt;&gt; buckets(k);\n    // 1. 配列要素を各バケットに分配\n    for (float num : nums) {\n        // 入力データ範囲は[0, 1)、num * kを使用してインデックス範囲[0, k-1]にマップ\n        int i = num * k;\n        // bucket_idxバケットに数値を追加\n        buckets[i].push_back(num);\n    }\n    // 2. 各バケットをソート\n    for (vector&lt;float&gt; &amp;bucket : buckets) {\n        // 組み込みソート関数を使用、他のソートアルゴリズムに置き換えることも可能\n        sort(bucket.begin(), bucket.end());\n    }\n    // 3. バケットを走査して結果をマージ\n    int i = 0;\n    for (vector&lt;float&gt; &amp;bucket : buckets) {\n        for (float num : bucket) {\n            nums[i++] = num;\n        }\n    }\n}\n</code></pre> bucket_sort.java<pre><code>/* バケットソート */\nvoid bucketSort(float[] nums) {\n    // k = n/2 個のバケットを初期化、各バケットに期待される要素数は 2 個\n    int k = nums.length / 2;\n    List&lt;List&lt;Float&gt;&gt; buckets = new ArrayList&lt;&gt;();\n    for (int i = 0; i &lt; k; i++) {\n        buckets.add(new ArrayList&lt;&gt;());\n    }\n    // 1. 配列要素を各バケットに分散\n    for (float num : nums) {\n        // 入力データ範囲は [0, 1)、num * k を使ってインデックス範囲 [0, k-1] にマッピング\n        int i = (int) (num * k);\n        // num をバケット i に追加\n        buckets.get(i).add(num);\n    }\n    // 2. 各バケットをソート\n    for (List&lt;Float&gt; bucket : buckets) {\n        // 組み込みソート関数を使用、他のソートアルゴリズムに置き換えることも可能\n        Collections.sort(bucket);\n    }\n    // 3. バケットを走査して結果をマージ\n    int i = 0;\n    for (List&lt;Float&gt; bucket : buckets) {\n        for (float num : bucket) {\n            nums[i++] = num;\n        }\n    }\n}\n</code></pre> bucket_sort.cs<pre><code>[class]{bucket_sort}-[func]{BucketSort}\n</code></pre> bucket_sort.go<pre><code>[class]{}-[func]{bucketSort}\n</code></pre> bucket_sort.swift<pre><code>[class]{}-[func]{bucketSort}\n</code></pre> bucket_sort.js<pre><code>[class]{}-[func]{bucketSort}\n</code></pre> bucket_sort.ts<pre><code>[class]{}-[func]{bucketSort}\n</code></pre> bucket_sort.dart<pre><code>[class]{}-[func]{bucketSort}\n</code></pre> bucket_sort.rs<pre><code>[class]{}-[func]{bucket_sort}\n</code></pre> bucket_sort.c<pre><code>[class]{}-[func]{bucketSort}\n</code></pre> bucket_sort.kt<pre><code>[class]{}-[func]{bucketSort}\n</code></pre> bucket_sort.rb<pre><code>[class]{}-[func]{bucket_sort}\n</code></pre>","path":["第 11 章 &nbsp; ソート","11.8 &nbsp; バケットソート"],"tags":[]},{"location":"chapter_sorting/bucket_sort/#1182","level":2,"title":"11.8.2   アルゴリズムの特徴","text":"<p>バケットソートは非常に大きなデータセットの処理に適しています。例えば、入力データに100万個の要素が含まれ、システムメモリの制限によりすべてのデータを同時にロードできない場合、データを1,000個のバケットに分割し、各バケットを個別にソートしてから結果をマージできます。</p> <ul> <li>時間計算量は \\(O(n + k)\\)：要素がバケット間で均等に分散されていると仮定すると、各バケット内の要素数は \\(n/k\\) です。単一のバケットのソートに \\(O(n/k \\log(n/k))\\) 時間がかかると仮定すると、すべてのバケットのソートに \\(O(n \\log(n/k))\\) 時間がかかります。バケット数 \\(k\\) が比較的大きいとき、時間計算量は \\(O(n)\\) に近づきます。結果のマージには、すべてのバケットと要素を走査する必要があり、\\(O(n + k)\\) 時間がかかります。最悪の場合、すべてのデータが単一のバケットに分散され、そのバケットのソートには \\(O(n^2)\\) 時間がかかります。</li> <li>空間計算量は \\(O(n + k)\\)、非インプレースソート：\\(k\\) 個のバケットと合計 \\(n\\) 個の要素のための追加スペースが必要です。</li> <li>バケットソートが安定かどうかは、各バケット内で使用されるソートアルゴリズムが安定かどうかに依存します。</li> </ul>","path":["第 11 章 &nbsp; ソート","11.8 &nbsp; バケットソート"],"tags":[]},{"location":"chapter_sorting/bucket_sort/#1183","level":2,"title":"11.8.3   均等分散を達成する方法","text":"<p>バケットソートの理論的時間計算量は \\(O(n)\\) に達することができます。重要なことは、すべてのバケットに要素を均等に分散させることです。実世界のデータはしばしば均一に分散されていないからです。例えば、eBayのすべての商品を価格範囲で10個のバケットに均等に分散させたいとします。しかし、商品価格の分散は均等でない可能性があり、100ドル未満の商品が多く、500ドル以上の商品が少ないかもしれません。価格範囲を均等に10分割すると、各バケットの商品数の差が大きくなります。</p> <p>均等分散を達成するために、最初におおよその境界を設定して、データを3つのバケットに大まかに分割できます。分散が完了した後、より多くのアイテムを持つバケットをさらに3つのバケットに分割し、すべてのバケットの要素数がほぼ等しくなるまで続けます。</p> <p>以下の図に示すように、この方法は本質的に再帰木を構築し、葉ノードの要素数ができるだけ均等になることを目指します。もちろん、各ラウンドでデータを3つのバケットに分割する必要はありません - 分割戦略はデータの独特な特性に適応的に調整できます。</p> <p></p> <p> 図 11-14   バケットの再帰的分割 </p> <p>商品価格の確率分布を事前に知っている場合、データの確率分布に基づいて各バケットの価格境界を設定できます。データ分布を具体的に計算する必要は必ずしもなく、代わりに確率モデルを使用してデータ特性に基づいて近似できることに注意してください。</p> <p>以下の図に示すように、商品価格が正規分布に従うと仮定すると、バケット間でアイテムの分散のバランスを取るために合理的な価格区間を定義できます。</p> <p></p> <p> 図 11-15   確率分布に基づくバケット分割 </p>","path":["第 11 章 &nbsp; ソート","11.8 &nbsp; バケットソート"],"tags":[]},{"location":"chapter_sorting/counting_sort/","level":1,"title":"11.9   計数ソート","text":"<p>計数ソートは要素の数をカウントすることでソートを実現し、通常は整数配列に適用されます。</p>","path":["第 11 章 &nbsp; ソート","11.9 &nbsp; 計数ソート"],"tags":[]},{"location":"chapter_sorting/counting_sort/#1191","level":2,"title":"11.9.1   簡単な実装","text":"<p>簡単な例から始めましょう。長さ \\(n\\) の配列 <code>nums</code> が与えられ、すべての要素が「非負整数」である場合、計数ソートの全体的な過程は以下の図に示されています。</p> <ol> <li>配列を走査して最大数を見つけ、それを \\(m\\) とし、長さ \\(m + 1\\) の補助配列 <code>counter</code> を作成します。</li> <li><code>counter</code> を使用して <code>nums</code> 内の各数の出現回数をカウントします。ここで <code>counter[num]</code> は数 <code>num</code> の出現回数に対応します。カウント方法は簡単で、<code>nums</code> を走査し（現在の数を <code>num</code> とする）、各ラウンドで <code>counter[num]</code> を \\(1\\) 増やします。</li> <li><code>counter</code> のインデックスは自然に順序付けられているため、すべての数は本質的にすでにソートされています。次に、<code>counter</code> を走査し、出現順に <code>nums</code> を昇順で埋めます。</li> </ol> <p></p> <p> 図 11-16   計数ソートの過程 </p> <p>コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby counting_sort.py<pre><code>def counting_sort_naive(nums: list[int]):\n    \"\"\"計数ソート\"\"\"\n    # シンプルな実装、オブジェクトのソートには使用できない\n    # 1. 配列内の最大要素 m を統計\n    m = 0\n    for num in nums:\n        m = max(m, num)\n    # 2. 各数字の出現回数を統計\n    # counter[num] は num の出現回数を表す\n    counter = [0] * (m + 1)\n    for num in nums:\n        counter[num] += 1\n    # 3. counter を走査し、各要素を元の配列 nums に埋め戻し\n    i = 0\n    for num in range(m + 1):\n        for _ in range(counter[num]):\n            nums[i] = num\n            i += 1\n</code></pre> counting_sort.cpp<pre><code>/* カウントソート */\n// 簡単な実装、オブジェクトのソートには使用できない\nvoid countingSortNaive(vector&lt;int&gt; &amp;nums) {\n    // 1. 配列の最大要素mを統計\n    int m = 0;\n    for (int num : nums) {\n        m = max(m, num);\n    }\n    // 2. 各数字の出現回数を統計\n    // counter[num]はnumの出現回数を表す\n    vector&lt;int&gt; counter(m + 1, 0);\n    for (int num : nums) {\n        counter[num]++;\n    }\n    // 3. counterを走査し、各要素を元の配列numsに戻す\n    int i = 0;\n    for (int num = 0; num &lt; m + 1; num++) {\n        for (int j = 0; j &lt; counter[num]; j++, i++) {\n            nums[i] = num;\n        }\n    }\n}\n</code></pre> counting_sort.java<pre><code>/* 計数ソート */\n// 簡単な実装、オブジェクトのソートには使用できない\nvoid countingSortNaive(int[] nums) {\n    // 1. 配列の最大要素 m を統計\n    int m = 0;\n    for (int num : nums) {\n        m = Math.max(m, num);\n    }\n    // 2. 各数字の出現回数を統計\n    // counter[num] は num の出現回数を表す\n    int[] counter = new int[m + 1];\n    for (int num : nums) {\n        counter[num]++;\n    }\n    // 3. counter を走査し、各要素を元の配列 nums に戻す\n    int i = 0;\n    for (int num = 0; num &lt; m + 1; num++) {\n        for (int j = 0; j &lt; counter[num]; j++, i++) {\n            nums[i] = num;\n        }\n    }\n}\n</code></pre> counting_sort.cs<pre><code>[class]{counting_sort}-[func]{CountingSortNaive}\n</code></pre> counting_sort.go<pre><code>[class]{}-[func]{countingSortNaive}\n</code></pre> counting_sort.swift<pre><code>[class]{}-[func]{countingSortNaive}\n</code></pre> counting_sort.js<pre><code>[class]{}-[func]{countingSortNaive}\n</code></pre> counting_sort.ts<pre><code>[class]{}-[func]{countingSortNaive}\n</code></pre> counting_sort.dart<pre><code>[class]{}-[func]{countingSortNaive}\n</code></pre> counting_sort.rs<pre><code>[class]{}-[func]{counting_sort_naive}\n</code></pre> counting_sort.c<pre><code>[class]{}-[func]{countingSortNaive}\n</code></pre> counting_sort.kt<pre><code>[class]{}-[func]{countingSortNaive}\n</code></pre> counting_sort.rb<pre><code>[class]{}-[func]{counting_sort_naive}\n</code></pre> <p>計数ソートとバケットソートの関係</p> <p>バケットソートの観点から、計数ソートにおける計数配列 <code>counter</code> の各インデックスをバケットと考え、カウントの過程を要素を対応するバケットに分散させることと考えることができます。本質的に、計数ソートは整数データのためのバケットソートの特別なケースです。</p>","path":["第 11 章 &nbsp; ソート","11.9 &nbsp; 計数ソート"],"tags":[]},{"location":"chapter_sorting/counting_sort/#1192","level":2,"title":"11.9.2   完全な実装","text":"<p>注意深い読者は気付くかもしれませんが、入力データがオブジェクトの場合、上記の手順 <code>3.</code> は無効です。入力データが商品オブジェクトで、価格（クラスメンバ変数）で商品をソートしたいとします。しかし、上記のアルゴリズムは結果としてソート済みの価格のみを提供できます。</p> <p>では、元のデータのソート結果をどのように取得できるでしょうか？まず、<code>counter</code> の「前置和」を計算します。名前が示すように、インデックス <code>i</code> での前置和 <code>prefix[i]</code> は、配列の最初の <code>i</code> 個の要素の和に等しいです：</p> \\[ \\text{prefix}[i] = \\sum_{j=0}^i \\text{counter[j]} \\] <p>前置和には明確な意味があります。<code>prefix[num] - 1</code> は結果配列 <code>res</code> における要素 <code>num</code> の最後の出現のインデックスを表します。この情報は重要で、各要素が結果配列のどこに現れるべきかを教えてくれます。次に、元の配列 <code>nums</code> の各要素 <code>num</code> を逆順で走査し、各反復で以下の2つの手順を実行します。</p> <ol> <li>インデックス <code>prefix[num] - 1</code> で配列 <code>res</code> に <code>num</code> を埋めます。</li> <li>前置和 <code>prefix[num]</code> を \\(1\\) 減らして、<code>num</code> を配置する次のインデックスを取得します。</li> </ol> <p>走査後、配列 <code>res</code> にはソートされた結果が含まれ、最後に <code>res</code> が元の配列 <code>nums</code> を置き換えます。完全な計数ソートの過程は以下の図に示されています。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 11-17   計数ソートの過程 </p> <p>計数ソートの実装コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby counting_sort.py<pre><code>def counting_sort(nums: list[int]):\n    \"\"\"計数ソート\"\"\"\n    # 完全な実装、オブジェクトのソートが可能で、安定ソート\n    # 1. 配列内の最大要素 m を統計\n    m = max(nums)\n    # 2. 各数字の出現回数を統計\n    # counter[num] は num の出現回数を表す\n    counter = [0] * (m + 1)\n    for num in nums:\n        counter[num] += 1\n    # 3. counter の前置和を計算し、「出現回数」を「末尾インデックス」に変換\n    # counter[num]-1 は res において num が最後に出現するインデックス\n    for i in range(m):\n        counter[i + 1] += counter[i]\n    # 4. nums を逆順に走査し、各要素を結果配列 res に配置\n    # 結果を記録するための配列 res を初期化\n    n = len(nums)\n    res = [0] * n\n    for i in range(n - 1, -1, -1):\n        num = nums[i]\n        res[counter[num] - 1] = num  # num を対応するインデックスに配置\n        counter[num] -= 1  # 前置和を1減らし、num を配置する次のインデックスを取得\n    # 結果配列 res を使用して元の配列 nums を上書き\n    for i in range(n):\n        nums[i] = res[i]\n</code></pre> counting_sort.cpp<pre><code>/* カウントソート */\n// 完全な実装、オブジェクトのソートが可能で安定ソート\nvoid countingSort(vector&lt;int&gt; &amp;nums) {\n    // 1. 配列の最大要素mを統計\n    int m = 0;\n    for (int num : nums) {\n        m = max(m, num);\n    }\n    // 2. 各数字の出現回数を統計\n    // counter[num]はnumの出現回数を表す\n    vector&lt;int&gt; counter(m + 1, 0);\n    for (int num : nums) {\n        counter[num]++;\n    }\n    // 3. counterの前缀和を計算し、「出現回数」を「末尾インデックス」に変換\n    // counter[num]-1はnumがresで現れる最後のインデックス\n    for (int i = 0; i &lt; m; i++) {\n        counter[i + 1] += counter[i];\n    }\n    // 4. numsを逆順で走査し、各要素を結果配列resに配置\n    // 結果を記録する配列resを初期化\n    int n = nums.size();\n    vector&lt;int&gt; res(n);\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int num = nums[i];\n        res[counter[num] - 1] = num; // numを対応するインデックスに配置\n        counter[num]--;              // 前缀和を1減らし、numを配置する次のインデックスを取得\n    }\n    // 結果配列resで元の配列numsを上書き\n    nums = res;\n}\n</code></pre> counting_sort.java<pre><code>/* 計数ソート */\n// 完全な実装、オブジェクトをソートでき、安定ソート\nvoid countingSort(int[] nums) {\n    // 1. 配列の最大要素 m を統計\n    int m = 0;\n    for (int num : nums) {\n        m = Math.max(m, num);\n    }\n    // 2. 各数字の出現回数を統計\n    // counter[num] は num の出現回数を表す\n    int[] counter = new int[m + 1];\n    for (int num : nums) {\n        counter[num]++;\n    }\n    // 3. counter の累積和を計算し、「出現回数」を「尻尾インデックス」に変換\n    // counter[num]-1 は res 内で num が出現する最後のインデックス\n    for (int i = 0; i &lt; m; i++) {\n        counter[i + 1] += counter[i];\n    }\n    // 4. nums を逆順に走査し、各要素を結果配列 res に配置\n    // 結果を記録する配列 res を初期化\n    int n = nums.length;\n    int[] res = new int[n];\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int num = nums[i];\n        res[counter[num] - 1] = num; // num を対応するインデックスに配置\n        counter[num]--; // 累積和を 1 減算し、num を配置する次のインデックスを取得\n    }\n    // 結果配列 res を使って元の配列 nums を上書き\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = res[i];\n    }\n}\n</code></pre> counting_sort.cs<pre><code>[class]{counting_sort}-[func]{CountingSort}\n</code></pre> counting_sort.go<pre><code>[class]{}-[func]{countingSort}\n</code></pre> counting_sort.swift<pre><code>[class]{}-[func]{countingSort}\n</code></pre> counting_sort.js<pre><code>[class]{}-[func]{countingSort}\n</code></pre> counting_sort.ts<pre><code>[class]{}-[func]{countingSort}\n</code></pre> counting_sort.dart<pre><code>[class]{}-[func]{countingSort}\n</code></pre> counting_sort.rs<pre><code>[class]{}-[func]{counting_sort}\n</code></pre> counting_sort.c<pre><code>[class]{}-[func]{countingSort}\n</code></pre> counting_sort.kt<pre><code>[class]{}-[func]{countingSort}\n</code></pre> counting_sort.rb<pre><code>[class]{}-[func]{counting_sort}\n</code></pre>","path":["第 11 章 &nbsp; ソート","11.9 &nbsp; 計数ソート"],"tags":[]},{"location":"chapter_sorting/counting_sort/#1193","level":2,"title":"11.9.3   アルゴリズムの特徴","text":"<ul> <li>時間計算量は \\(O(n + m)\\)、非適応ソート：<code>nums</code> と <code>counter</code> の走査が含まれ、どちらも線形時間を使用します。一般的に、\\(n \\gg m\\) であり、時間計算量は \\(O(n)\\) に近づきます。</li> <li>空間計算量は \\(O(n + m)\\)、非インプレースソート：長さ \\(n\\) の配列 <code>res</code> と長さ \\(m\\) の配列 <code>counter</code> をそれぞれ使用します。</li> <li>安定ソート：要素が「右から左」の順序で <code>res</code> に埋められるため、<code>nums</code> の走査を逆順にすることで、等しい要素間の相対位置の変化を防ぎ、安定したソートを実現できます。実際、<code>nums</code> を順番に走査しても正しいソート結果を生成できますが、結果は不安定です。</li> </ul>","path":["第 11 章 &nbsp; ソート","11.9 &nbsp; 計数ソート"],"tags":[]},{"location":"chapter_sorting/counting_sort/#1194","level":2,"title":"11.9.4   制限事項","text":"<p>今までに、計数ソートは非常に巧妙だと感じるかもしれません。単に量をカウントするだけで効率的なソートを実現できるからです。しかし、計数ソートを使用するための前提条件は比較的厳しいです。</p> <p>計数ソートは非負整数にのみ適用できます。他のタイプのデータに適用したい場合、これらのデータが要素の元の順序を変更することなく非負整数に変換できることを保証する必要があります。例えば、負の整数を含む配列の場合、最初にすべての数に定数を加えて、すべてを正の数に変換し、ソート完了後に元に戻すことができます。</p> <p>計数ソートは値の範囲が小さい大きなデータセットに適しています。例えば、上記の例では、\\(m\\) は大きすぎるべきではありません。そうでなければ、あまりにも多くのスペースを占有してしまいます。そして \\(n \\ll m\\) の場合、計数ソートは \\(O(m)\\) 時間を使用し、\\(O(n \\log n)\\) ソートアルゴリズムより遅い可能性があります。</p>","path":["第 11 章 &nbsp; ソート","11.9 &nbsp; 計数ソート"],"tags":[]},{"location":"chapter_sorting/heap_sort/","level":1,"title":"11.7   ヒープソート","text":"<p>Tip</p> <p>この節を読む前に、「ヒープ」の章を必ず完了させてください。</p> <p>ヒープソートは、ヒープデータ構造に基づく効率的なソートアルゴリズムです。すでに学習した「ヒープの構築」と「要素の抽出」操作を使用してヒープソートを実装できます。</p> <ol> <li>配列を入力し、最小ヒープを構築します。ここで、最小要素がヒープの頂上に位置します。</li> <li>継続的に抽出操作を実行し、抽出された要素を順次記録して、最小から最大までのソート済みリストを取得します。</li> </ol> <p>上記の方法は実現可能ですが、ポップされた要素を格納するための追加の配列が必要で、やや空間を消費します。実際には、通常、より優雅な実装を使用します。</p>","path":["第 11 章 &nbsp; ソート","11.7 &nbsp; ヒープソート"],"tags":[]},{"location":"chapter_sorting/heap_sort/#1171","level":2,"title":"11.7.1   アルゴリズムの流れ","text":"<p>配列の長さを \\(n\\) とすると、ヒープソートの過程は以下の通りです。</p> <ol> <li>配列を入力し、最大ヒープを構築します。この手順の後、最大要素がヒープの頂上に位置します。</li> <li>ヒープの頂上要素（最初の要素）とヒープの底部要素（最後の要素）を交換します。この交換の後、ヒープの長さを \\(1\\) 減らし、ソート済み要素の数を \\(1\\) 増やします。</li> <li>ヒープの頂上から開始して、上から下へのsift-down操作を実行します。sift-downの後、ヒープの性質が復元されます。</li> <li>手順 <code>2.</code> と <code>3.</code> を繰り返します。\\(n - 1\\) ラウンドループして、配列のソートを完了します。</li> </ol> <p>Tip</p> <p>実際、要素抽出操作も手順 <code>2.</code> と <code>3.</code> を含み、抽出された要素をヒープから削除する追加の手順があります。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 11-12   ヒープソートの過程 </p> <p>コードの実装では、「ヒープ」の章からのsift-down関数 <code>sift_down()</code> を使用しました。最大要素が抽出されるにつれてヒープの長さが減少するため、<code>sift_down()</code> 関数に長さパラメータ \\(n\\) を追加して、ヒープの現在の有効長を指定する必要があることに注意することが重要です。コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby heap_sort.py<pre><code>def sift_down(nums: list[int], n: int, i: int):\n    \"\"\"ヒープの長さが n、ノード i から上から下へヒープ化を開始\"\"\"\n    while True:\n        # i、l、r の中で最大のノードを判定し、ma とする\n        l = 2 * i + 1\n        r = 2 * i + 2\n        ma = i\n        if l &lt; n and nums[l] &gt; nums[ma]:\n            ma = l\n        if r &lt; n and nums[r] &gt; nums[ma]:\n            ma = r\n        # ノード i が最大または l、r のインデックスが範囲外の場合、さらなるヒープ化は不要、ループを抜ける\n        if ma == i:\n            break\n        # 2つのノードを交換\n        nums[i], nums[ma] = nums[ma], nums[i]\n        # 下向きにヒープ化をループ\n        i = ma\n\ndef heap_sort(nums: list[int]):\n    \"\"\"ヒープソート\"\"\"\n    # ヒープ構築操作：葉ノード以外のすべてのノードをヒープ化\n    for i in range(len(nums) // 2 - 1, -1, -1):\n        sift_down(nums, len(nums), i)\n    # ヒープから最大要素を抽出し、n-1 回繰り返す\n    for i in range(len(nums) - 1, 0, -1):\n        # ルートノードと最も右の葉ノードを交換（最初の要素と最後の要素を交換）\n        nums[0], nums[i] = nums[i], nums[0]\n        # ルートノードから上から下へヒープ化を開始\n        sift_down(nums, i, 0)\n</code></pre> heap_sort.cpp<pre><code>/* ヒープの長さはn、ノードiから上から下へヒープ化を開始 */\nvoid siftDown(vector&lt;int&gt; &amp;nums, int n, int i) {\n    while (true) {\n        // i、l、r の中で最大のノードを決定し、maとして記録\n        int l = 2 * i + 1;\n        int r = 2 * i + 2;\n        int ma = i;\n        if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma])\n            ma = l;\n        if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma])\n            ma = r;\n        // ノードiが最大か、インデックスl、rが境界外の場合、それ以上のヒープ化は不要で終了\n        if (ma == i) {\n            break;\n        }\n        // 二つのノードを交換\n        swap(nums[i], nums[ma]);\n        // 下向きにヒープ化をループ\n        i = ma;\n    }\n}\n\n/* ヒープソート */\nvoid heapSort(vector&lt;int&gt; &amp;nums) {\n    // ヒープ構築操作：葉以外のすべてのノードをヒープ化\n    for (int i = nums.size() / 2 - 1; i &gt;= 0; --i) {\n        siftDown(nums, nums.size(), i);\n    }\n    // ヒープから最大要素を抽出し、n-1回繰り返す\n    for (int i = nums.size() - 1; i &gt; 0; --i) {\n        // ルートノードを最右葉ノードと交換（最初の要素を最後の要素と交換）\n        swap(nums[0], nums[i]);\n        // ルートノードから上から下へヒープ化を開始\n        siftDown(nums, i, 0);\n    }\n}\n</code></pre> heap_sort.java<pre><code>/* ヒープの長さは n、ノード i から上から下へヒープ化開始 */\nvoid siftDown(int[] nums, int n, int i) {\n    while (true) {\n        // i, l, r の中で最大のノードを判定し、ma とする\n        int l = 2 * i + 1;\n        int r = 2 * i + 2;\n        int ma = i;\n        if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma])\n            ma = l;\n        if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma])\n            ma = r;\n        // ノード i が最大、またはインデックス l, r が範囲外の場合、さらなるヒープ化は不要、ブレーク\n        if (ma == i)\n            break;\n        // 2つのノードを交換\n        int temp = nums[i];\n        nums[i] = nums[ma];\n        nums[ma] = temp;\n        // 下向きにヒープ化をループ\n        i = ma;\n    }\n}\n\n/* ヒープソート */\nvoid heapSort(int[] nums) {\n    // ヒープ構築操作: 葉ノード以外のすべてのノードをヒープ化\n    for (int i = nums.length / 2 - 1; i &gt;= 0; i--) {\n        siftDown(nums, nums.length, i);\n    }\n    // ヒープから最大要素を抽出し、n-1 回繰り返し\n    for (int i = nums.length - 1; i &gt; 0; i--) {\n        // ルートノードと最も右の葉ノードを交換（最初の要素と最後の要素を交換）\n        int tmp = nums[0];\n        nums[0] = nums[i];\n        nums[i] = tmp;\n        // ルートノードから上から下へヒープ化開始\n        siftDown(nums, i, 0);\n    }\n}\n</code></pre> heap_sort.cs<pre><code>[class]{heap_sort}-[func]{SiftDown}\n\n[class]{heap_sort}-[func]{HeapSort}\n</code></pre> heap_sort.go<pre><code>[class]{}-[func]{siftDown}\n\n[class]{}-[func]{heapSort}\n</code></pre> heap_sort.swift<pre><code>[class]{}-[func]{siftDown}\n\n[class]{}-[func]{heapSort}\n</code></pre> heap_sort.js<pre><code>[class]{}-[func]{siftDown}\n\n[class]{}-[func]{heapSort}\n</code></pre> heap_sort.ts<pre><code>[class]{}-[func]{siftDown}\n\n[class]{}-[func]{heapSort}\n</code></pre> heap_sort.dart<pre><code>[class]{}-[func]{siftDown}\n\n[class]{}-[func]{heapSort}\n</code></pre> heap_sort.rs<pre><code>[class]{}-[func]{sift_down}\n\n[class]{}-[func]{heap_sort}\n</code></pre> heap_sort.c<pre><code>[class]{}-[func]{siftDown}\n\n[class]{}-[func]{heapSort}\n</code></pre> heap_sort.kt<pre><code>[class]{}-[func]{siftDown}\n\n[class]{}-[func]{heapSort}\n</code></pre> heap_sort.rb<pre><code>[class]{}-[func]{sift_down}\n\n[class]{}-[func]{heap_sort}\n</code></pre>","path":["第 11 章 &nbsp; ソート","11.7 &nbsp; ヒープソート"],"tags":[]},{"location":"chapter_sorting/heap_sort/#1172","level":2,"title":"11.7.2   アルゴリズムの特徴","text":"<ul> <li>時間計算量は \\(O(n \\log n)\\)、非適応ソート：ヒープの構築は \\(O(n)\\) 時間を使用します。ヒープから最大要素を抽出するには \\(O(\\log n)\\) 時間がかかり、\\(n - 1\\) ラウンドループします。</li> <li>空間計算量は \\(O(1)\\)、インプレースソート：いくつかのポインタ変数が \\(O(1)\\) 空間を使用します。要素の交換とヒープ化操作は元の配列で実行されます。</li> <li>非安定ソート：ヒープの頂上と底部要素の交換中に、等しい要素の相対位置が変わる可能性があります。</li> </ul>","path":["第 11 章 &nbsp; ソート","11.7 &nbsp; ヒープソート"],"tags":[]},{"location":"chapter_sorting/insertion_sort/","level":1,"title":"11.4   挿入ソート","text":"<p>挿入ソートは、トランプのデッキを手動でソートするプロセスによく似た動作をするシンプルなソートアルゴリズムです。</p> <p>具体的には、未ソート区間からベース要素を選択し、その左側のソート済み区間の要素と比較して、要素を正しい位置に挿入します。</p> <p>下図は、要素が配列に挿入される方法を示しています。ベース要素を<code>base</code>とすると、ターゲットインデックスから<code>base</code>までのすべての要素を右に1つずつシフトし、その後<code>base</code>をターゲットインデックスに割り当てる必要があります。</p> <p></p> <p> 図 11-6   Single insertion operation </p>","path":["第 11 章 &nbsp; ソート","11.4 &nbsp; 挿入ソート"],"tags":[]},{"location":"chapter_sorting/insertion_sort/#1141","level":2,"title":"11.4.1   アルゴリズムプロセス","text":"<p>挿入ソートの全体的なプロセスは下図に示されます。</p> <ol> <li>配列の最初の要素をソート済みとみなします。</li> <li>2番目の要素を<code>base</code>として選択し、正しい位置に挿入して、最初の2つの要素をソート済みにします。</li> <li>3番目の要素を<code>base</code>として選択し、正しい位置に挿入して、最初の3つの要素をソート済みにします。</li> <li>この方法で続行し、最後の反復では、最後の要素を<code>base</code>として取り、正しい位置に挿入した後、すべての要素がソートされます。</li> </ol> <p></p> <p> 図 11-7   Insertion sort process </p> <p>コード例は以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby insertion_sort.py<pre><code>def insertion_sort(nums: list[int]):\n    \"\"\"挿入ソート\"\"\"\n    # 外側のループ：ソート済み範囲は [0, i-1]\n    for i in range(1, len(nums)):\n        base = nums[i]\n        j = i - 1\n        # 内側のループ：base をソート済み範囲 [0, i-1] の正しい位置に挿入\n        while j &gt;= 0 and nums[j] &gt; base:\n            nums[j + 1] = nums[j]  # nums[j] を右に1つ移動\n            j -= 1\n        nums[j + 1] = base  # base を正しい位置に代入\n</code></pre> insertion_sort.cpp<pre><code>/* 挿入ソート */\nvoid insertionSort(vector&lt;int&gt; &amp;nums) {\n    // 外側ループ：ソート済み範囲は[0, i-1]\n    for (int i = 1; i &lt; nums.size(); i++) {\n        int base = nums[i], j = i - 1;\n        // 内側ループ：baseをソート済み範囲[0, i-1]内の正しい位置に挿入\n        while (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n            nums[j + 1] = nums[j]; // nums[j]を一つ右に移動\n            j--;\n        }\n        nums[j + 1] = base; // baseを正しい位置に代入\n    }\n}\n</code></pre> insertion_sort.java<pre><code>/* 挿入ソート */\nvoid insertionSort(int[] nums) {\n    // 外側ループ: ソート済み範囲は [0, i-1]\n    for (int i = 1; i &lt; nums.length; i++) {\n        int base = nums[i], j = i - 1;\n        // 内側ループ: base をソート済み範囲 [0, i-1] の正しい位置に挿入\n        while (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n            nums[j + 1] = nums[j]; // nums[j] を右に1つ移動\n            j--;\n        }\n        nums[j + 1] = base;        // base を正しい位置に代入\n    }\n}\n</code></pre> insertion_sort.cs<pre><code>[class]{insertion_sort}-[func]{InsertionSort}\n</code></pre> insertion_sort.go<pre><code>[class]{}-[func]{insertionSort}\n</code></pre> insertion_sort.swift<pre><code>[class]{}-[func]{insertionSort}\n</code></pre> insertion_sort.js<pre><code>[class]{}-[func]{insertionSort}\n</code></pre> insertion_sort.ts<pre><code>[class]{}-[func]{insertionSort}\n</code></pre> insertion_sort.dart<pre><code>[class]{}-[func]{insertionSort}\n</code></pre> insertion_sort.rs<pre><code>[class]{}-[func]{insertion_sort}\n</code></pre> insertion_sort.c<pre><code>[class]{}-[func]{insertionSort}\n</code></pre> insertion_sort.kt<pre><code>[class]{}-[func]{insertionSort}\n</code></pre> insertion_sort.rb<pre><code>[class]{}-[func]{insertion_sort}\n</code></pre>","path":["第 11 章 &nbsp; ソート","11.4 &nbsp; 挿入ソート"],"tags":[]},{"location":"chapter_sorting/insertion_sort/#1142","level":2,"title":"11.4.2   アルゴリズムの特性","text":"<ul> <li>時間計算量は\\(O(n^2)\\)、適応ソート：最悪の場合、各挿入操作には\\(n - 1\\)、\\(n-2\\)、...、\\(2\\)、\\(1\\)のループが必要で、合計は\\((n - 1) n / 2\\)となり、時間計算量は\\(O(n^2)\\)です。順序付きデータの場合、挿入操作は早期に終了します。入力配列が完全に順序付けられている場合、挿入ソートは最良時間計算量\\(O(n)\\)を実現します。</li> <li>空間計算量は\\(O(1)\\)、インプレースソート：ポインタ\\(i\\)と\\(j\\)は定数量の追加空間を使用します。</li> <li>安定ソート：挿入操作中、等しい要素の右側に要素を挿入し、順序を変更しません。</li> </ul>","path":["第 11 章 &nbsp; ソート","11.4 &nbsp; 挿入ソート"],"tags":[]},{"location":"chapter_sorting/insertion_sort/#1143","level":2,"title":"11.4.3   挿入ソートの利点","text":"<p>挿入ソートの時間計算量は\\(O(n^2)\\)で、次に学習するクイックソートの時間計算量は\\(O(n \\log n)\\)です。挿入ソートはより高い時間計算量を持ちますが、小さな入力サイズでは通常より高速です。</p> <p>この結論は線形探索と二分探索の結論と似ています。時間計算量が\\(O(n \\log n)\\)で分割統治戦略に基づくクイックソートなどのアルゴリズムは、多くの場合より多くの単位操作を含みます。小さな入力サイズでは、\\(n^2\\)と\\(n \\log n\\)の数値は近く、計算量が支配的でなく、ラウンドあたりの単位操作数が決定的な役割を果たします。</p> <p>実際、多くのプログラミング言語（Javaなど）は、組み込みソート関数内で挿入ソートを使用しています。一般的なアプローチは：長い配列に対しては、クイックソートなどの分割統治戦略に基づくソートアルゴリズムを使用し、短い配列に対しては挿入ソートを直接使用します。</p> <p>バブルソート、選択ソート、挿入ソートはすべて時間計算量\\(O(n^2)\\)を持ちますが、実際には、挿入ソートはバブルソートや選択ソートよりも一般的に使用されます。主な理由は以下の通りです。</p> <ul> <li>バブルソートは要素交換に基づき、一時変数の使用が必要で、3つの単位操作を含みます；挿入ソートは要素代入に基づき、1つの単位操作のみが必要です。したがって、バブルソートの計算オーバーヘッドは一般的に挿入ソートよりも高くなります。</li> <li>選択ソートの時間計算量は常に\\(O(n^2)\\)です。部分的に順序付けられたデータのセットが与えられた場合、挿入ソートは通常選択ソートよりも効率的です。</li> <li>選択ソートは不安定で、マルチレベルソートに適用できません。</li> </ul>","path":["第 11 章 &nbsp; ソート","11.4 &nbsp; 挿入ソート"],"tags":[]},{"location":"chapter_sorting/merge_sort/","level":1,"title":"11.6   マージソート","text":"<p>マージソートは分割統治戦略に基づくソートアルゴリズムで、下図に示す「分割」と「マージ」フェーズを含みます。</p> <ol> <li>分割フェーズ：中点から配列を再帰的に分割し、長い配列のソート問題をより短い配列に変換します。</li> <li>マージフェーズ：サブ配列の長さが1になったときに分割を停止し、その後マージを開始します。2つの短いソート済み配列を連続的により長いソート済み配列にマージし、プロセスが完了するまで続行します。</li> </ol> <p></p> <p> 図 11-10   The divide and merge phases of merge sort </p>","path":["第 11 章 &nbsp; ソート","11.6 &nbsp; マージソート"],"tags":[]},{"location":"chapter_sorting/merge_sort/#1161","level":2,"title":"11.6.1   アルゴリズムワークフロー","text":"<p>下図に示すように、「分割フェーズ」は中点から配列を上から下に2つのサブ配列に再帰的に分割します。</p> <ol> <li>中点<code>mid</code>を計算し、左サブ配列（区間<code>[left, mid]</code>）と右サブ配列（区間<code>[mid + 1, right]</code>）を再帰的に分割します。</li> <li>サブ配列の長さが1になるまでステップ<code>1.</code>を再帰的に続行し、その後停止します。</li> </ol> <p>「マージフェーズ」は左と右のサブ配列を下から上にソート済み配列に結合します。重要なのは、マージが長さ1のサブ配列から開始され、マージフェーズ中に各サブ配列がソートされることです。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 11-11   Merge sort process </p> <p>マージソートの再帰順序は二分木の後順横断と一致することが観察できます。</p> <ul> <li>後順横断：まず左のサブツリーを再帰的に横断し、次に右のサブツリーを横断し、最後にルートノードを処理します。</li> <li>マージソート：まず左のサブ配列を再帰的に処理し、次に右のサブ配列を処理し、最後にマージを実行します。</li> </ul> <p>マージソートの実装は以下のコードに示されます。<code>nums</code>でマージされる区間は<code>[left, right]</code>で、<code>tmp</code>の対応する区間は<code>[0, right - left]</code>であることに注意してください。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby merge_sort.py<pre><code>def merge(nums: list[int], left: int, mid: int, right: int):\n    \"\"\"左サブ配列と右サブ配列をマージ\"\"\"\n    # 左サブ配列区間は [left, mid]、右サブ配列区間は [mid+1, right]\n    # 一時配列 tmp を作成してマージ結果を格納\n    tmp = [0] * (right - left + 1)\n    # 左右サブ配列の開始インデックスを初期化\n    i, j, k = left, mid + 1, 0\n    # 両方のサブ配列に要素が残っている間、より小さい要素を一時配列にコピー\n    while i &lt;= mid and j &lt;= right:\n        if nums[i] &lt;= nums[j]:\n            tmp[k] = nums[i]\n            i += 1\n        else:\n            tmp[k] = nums[j]\n            j += 1\n        k += 1\n    # 残った左右サブ配列の要素を一時配列にコピー\n    while i &lt;= mid:\n        tmp[k] = nums[i]\n        i += 1\n        k += 1\n    while j &lt;= right:\n        tmp[k] = nums[j]\n        j += 1\n        k += 1\n    # 一時配列 tmp の要素を元の配列 nums の対応する区間にコピーバック\n    for k in range(0, len(tmp)):\n        nums[left + k] = tmp[k]\n\ndef merge_sort(nums: list[int], left: int, right: int):\n    \"\"\"マージソート\"\"\"\n    # 終了条件\n    if left &gt;= right:\n        return  # サブ配列の長さが1のときに再帰を終了\n    # 分割段階\n    mid = left + (right - left) // 2  # 中点を計算\n    merge_sort(nums, left, mid)  # 左サブ配列を再帰的に処理\n    merge_sort(nums, mid + 1, right)  # 右サブ配列を再帰的に処理\n    # マージ段階\n    merge(nums, left, mid, right)\n</code></pre> merge_sort.cpp<pre><code>/* 左サブ配列と右サブ配列をマージ */\nvoid merge(vector&lt;int&gt; &amp;nums, int left, int mid, int right) {\n    // 左サブ配列の区間は[left, mid]、右サブ配列の区間は[mid+1, right]\n    // マージ結果を保存する一時配列tmpを作成\n    vector&lt;int&gt; tmp(right - left + 1);\n    // 左右サブ配列の開始インデックスを初期化\n    int i = left, j = mid + 1, k = 0;\n    // 両サブ配列に要素がある間、小さい方の要素を一時配列にコピー\n    while (i &lt;= mid &amp;&amp; j &lt;= right) {\n        if (nums[i] &lt;= nums[j])\n            tmp[k++] = nums[i++];\n        else\n            tmp[k++] = nums[j++];\n    }\n    // 左右サブ配列の残りの要素を一時配列にコピー\n    while (i &lt;= mid) {\n        tmp[k++] = nums[i++];\n    }\n    while (j &lt;= right) {\n        tmp[k++] = nums[j++];\n    }\n    // 一時配列tmpの要素を元の配列numsの対応する区間にコピー\n    for (k = 0; k &lt; tmp.size(); k++) {\n        nums[left + k] = tmp[k];\n    }\n}\n\n/* マージソート */\nvoid mergeSort(vector&lt;int&gt; &amp;nums, int left, int right) {\n    // 終了条件\n    if (left &gt;= right)\n        return; // サブ配列の長さが1の時、再帰を終了\n    // 分割段階\n    int mid = left + (right - left) / 2;    // 中点を計算\n    mergeSort(nums, left, mid);      // 左サブ配列を再帰的に処理\n    mergeSort(nums, mid + 1, right); // 右サブ配列を再帰的に処理\n    // マージ段階\n    merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.java<pre><code>/* 左部分配列と右部分配列をマージ */\nvoid merge(int[] nums, int left, int mid, int right) {\n    // 左部分配列区間は [left, mid]、右部分配列区間は [mid+1, right]\n    // 一時配列 tmp を作成してマージ結果を格納\n    int[] tmp = new int[right - left + 1];\n    // 左右部分配列の開始インデックスを初期化\n    int i = left, j = mid + 1, k = 0;\n    // 両部分配列にまだ要素がある間、比較してより小さい要素を一時配列にコピー\n    while (i &lt;= mid &amp;&amp; j &lt;= right) {\n        if (nums[i] &lt;= nums[j])\n            tmp[k++] = nums[i++];\n        else\n            tmp[k++] = nums[j++];\n    }\n    // 左右部分配列の残りの要素を一時配列にコピー\n    while (i &lt;= mid) {\n        tmp[k++] = nums[i++];\n    }\n    while (j &lt;= right) {\n        tmp[k++] = nums[j++];\n    }\n    // 一時配列 tmp の要素を元の配列 nums の対応する区間にコピーバック\n    for (k = 0; k &lt; tmp.length; k++) {\n        nums[left + k] = tmp[k];\n    }\n}\n\n/* マージソート */\nvoid mergeSort(int[] nums, int left, int right) {\n    // 終了条件\n    if (left &gt;= right)\n        return; // 部分配列の長さが 1 のとき再帰を終了\n    // 分割段階\n    int mid = left + (right - left) / 2; // 中点を計算\n    mergeSort(nums, left, mid); // 左部分配列を再帰的に処理\n    mergeSort(nums, mid + 1, right); // 右部分配列を再帰的に処理\n    // マージ段階\n    merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.cs<pre><code>[class]{merge_sort}-[func]{Merge}\n\n[class]{merge_sort}-[func]{MergeSort}\n</code></pre> merge_sort.go<pre><code>[class]{}-[func]{merge}\n\n[class]{}-[func]{mergeSort}\n</code></pre> merge_sort.swift<pre><code>[class]{}-[func]{merge}\n\n[class]{}-[func]{mergeSort}\n</code></pre> merge_sort.js<pre><code>[class]{}-[func]{merge}\n\n[class]{}-[func]{mergeSort}\n</code></pre> merge_sort.ts<pre><code>[class]{}-[func]{merge}\n\n[class]{}-[func]{mergeSort}\n</code></pre> merge_sort.dart<pre><code>[class]{}-[func]{merge}\n\n[class]{}-[func]{mergeSort}\n</code></pre> merge_sort.rs<pre><code>[class]{}-[func]{merge}\n\n[class]{}-[func]{merge_sort}\n</code></pre> merge_sort.c<pre><code>[class]{}-[func]{merge}\n\n[class]{}-[func]{mergeSort}\n</code></pre> merge_sort.kt<pre><code>[class]{}-[func]{merge}\n\n[class]{}-[func]{mergeSort}\n</code></pre> merge_sort.rb<pre><code>[class]{}-[func]{merge}\n\n[class]{}-[func]{merge_sort}\n</code></pre>","path":["第 11 章 &nbsp; ソート","11.6 &nbsp; マージソート"],"tags":[]},{"location":"chapter_sorting/merge_sort/#1162","level":2,"title":"11.6.2   アルゴリズムの特性","text":"<ul> <li>\\(O(n \\log n)\\)の時間計算量、非適応ソート：分割により高さ\\(\\log n\\)の再帰ツリーが作成され、各層で合計\\(n\\)回の操作をマージし、全体的な時間計算量は\\(O(n \\log n)\\)となります。</li> <li>\\(O(n)\\)の空間計算量、非インプレースソート：再帰深度は\\(\\log n\\)で、\\(O(\\log n)\\)のスタックフレーム空間を使用します。マージ操作には補助配列が必要で、追加の\\(O(n)\\)空間を使用します。</li> <li>安定ソート：マージプロセス中、等しい要素の順序は変更されません。</li> </ul>","path":["第 11 章 &nbsp; ソート","11.6 &nbsp; マージソート"],"tags":[]},{"location":"chapter_sorting/merge_sort/#1163","level":2,"title":"11.6.3   連結リストのソート","text":"<p>連結リストの場合、マージソートは他のソートアルゴリズムよりも大きな利点があります。連結リストソートタスクの空間計算量を\\(O(1)\\)に最適化できます。</p> <ul> <li>分割フェーズ：「再帰」の代わりに「反復」を使用して連結リスト分割作業を実行できるため、再帰で使用されるスタックフレーム空間を節約できます。</li> <li>マージフェーズ：連結リストでは、ノードの挿入と削除操作は参照（ポインタ）を変更することで実現できるため、マージフェーズ（2つの短い順序付きリストを1つの長い順序付きリストに結合）中に追加のリストを作成する必要がありません。</li> </ul> <p>実装の詳細は比較的複雑で、興味のある読者は関連資料を参照して学習してください。</p>","path":["第 11 章 &nbsp; ソート","11.6 &nbsp; マージソート"],"tags":[]},{"location":"chapter_sorting/quick_sort/","level":1,"title":"11.5   クイックソート","text":"<p>クイックソートは分割統治戦略に基づくソートアルゴリズムで、その効率性と幅広い応用で知られています。</p> <p>クイックソートのコア操作は「ピボット分割」で、配列から要素を「ピボット」として選択し、ピボットより小さいすべての要素をその左側に移動し、ピボットより大きいすべての要素をその右側に移動することを目的としています。具体的に、ピボット分割のプロセスは下図に示されます。</p> <ol> <li>配列の最も左の要素をピボットとして選択し、2つのポインタ<code>i</code>と<code>j</code>を初期化して配列の両端をそれぞれ指すようにします。</li> <li>各ラウンドで<code>i</code>（<code>j</code>）を使用してピボットより大きい（小さい）最初の要素を探索し、次にこれら2つの要素を交換するループを設定します。</li> <li><code>i</code>と<code>j</code>が出会うまでステップ<code>2.</code>を繰り返し、最後にピボットを2つのサブ配列の境界に交換します。</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 11-8   Pivot division process </p> <p>ピボット分割後、元の配列は3つの部分に分割されます：左サブ配列、ピボット、右サブ配列で、「左サブ配列の任意の要素 \\(\\leq\\) ピボット \\(\\leq\\) 右サブ配列の任意の要素」を満たします。したがって、これら2つのサブ配列のみをソートすればよいのです。</p> <p>クイックソートの分割統治戦略</p> <p>ピボット分割の本質は、より長い配列のソート問題をより短い2つの配列に簡素化することです。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby quick_sort.py<pre><code>def partition(self, nums: list[int], left: int, right: int) -&gt; int:\n    \"\"\"分割\"\"\"\n    # nums[left] をピボットとして使用\n    i, j = left, right\n    while i &lt; j:\n        while i &lt; j and nums[j] &gt;= nums[left]:\n            j -= 1  # 右から左へピボットより小さい最初の要素を探す\n        while i &lt; j and nums[i] &lt;= nums[left]:\n            i += 1  # 左から右へピボットより大きい最初の要素を探す\n        # 要素を交換\n        nums[i], nums[j] = nums[j], nums[i]\n    # ピボットを2つのサブ配列の境界に交換\n    nums[i], nums[left] = nums[left], nums[i]\n    return i  # ピボットのインデックスを返す\n</code></pre> quick_sort.cpp<pre><code>/* 分割 */\nint partition(vector&lt;int&gt; &amp;nums, int left, int right) {\n    // nums[left]をピボットとして使用\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--; // 右から左へピボットより小さい最初の要素を検索\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;          // 左から右へピボットより大きい最初の要素を検索\n        swap(nums, i, j); // これら二つの要素を交換\n    }\n    swap(nums, i, left); // ピボットを二つのサブ配列の境界に交換\n    return i;            // ピボットのインデックスを返す\n}\n</code></pre> quick_sort.java<pre><code>/* 要素を交換 */\nvoid swap(int[] nums, int i, int j) {\n    int tmp = nums[i];\n    nums[i] = nums[j];\n    nums[j] = tmp;\n}\n\n/* 分割 */\nint partition(int[] nums, int left, int right) {\n    // nums[left] を基準値として使用\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--;          // 右から左へ、基準値より小さい最初の要素を検索\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;          // 左から右へ、基準値より大きい最初の要素を検索\n        swap(nums, i, j); // これら2つの要素を交換\n    }\n    swap(nums, i, left);  // 基準値を2つの部分配列の境界に交換\n    return i;             // 基準値のインデックスを返す\n}\n</code></pre> quick_sort.cs<pre><code>[class]{quickSort}-[func]{Swap}\n\n[class]{quickSort}-[func]{Partition}\n</code></pre> quick_sort.go<pre><code>[class]{quickSort}-[func]{partition}\n</code></pre> quick_sort.swift<pre><code>[class]{}-[func]{partition}\n</code></pre> quick_sort.js<pre><code>[class]{QuickSort}-[func]{swap}\n\n[class]{QuickSort}-[func]{partition}\n</code></pre> quick_sort.ts<pre><code>[class]{QuickSort}-[func]{swap}\n\n[class]{QuickSort}-[func]{partition}\n</code></pre> quick_sort.dart<pre><code>[class]{QuickSort}-[func]{_swap}\n\n[class]{QuickSort}-[func]{_partition}\n</code></pre> quick_sort.rs<pre><code>[class]{QuickSort}-[func]{partition}\n</code></pre> quick_sort.c<pre><code>[class]{}-[func]{swap}\n\n[class]{}-[func]{partition}\n</code></pre> quick_sort.kt<pre><code>[class]{}-[func]{swap}\n\n[class]{}-[func]{partition}\n</code></pre> quick_sort.rb<pre><code>[class]{QuickSort}-[func]{partition}\n</code></pre>","path":["第 11 章 &nbsp; ソート","11.5 &nbsp; クイックソート"],"tags":[]},{"location":"chapter_sorting/quick_sort/#1151","level":2,"title":"11.5.1   アルゴリズムプロセス","text":"<p>クイックソートの全体的なプロセスは下図に示されます。</p> <ol> <li>まず、元の配列に対して「ピボット分割」を実行し、未ソートの左と右のサブ配列を取得します。</li> <li>次に、左と右のサブ配列に対してそれぞれ再帰的に「ピボット分割」を実行します。</li> <li>サブ配列の長さが1になるまで再帰を続け、配列全体のソートを完了します。</li> </ol> <p></p> <p> 図 11-9   Quick sort process </p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby quick_sort.py<pre><code>def quick_sort(self, nums: list[int], left: int, right: int):\n    \"\"\"クイックソート\"\"\"\n    # サブ配列の長さが1のときに再帰を終了\n    if left &gt;= right:\n        return\n    # 分割\n    pivot = self.partition(nums, left, right)\n    # 左サブ配列と右サブ配列を再帰的に処理\n    self.quick_sort(nums, left, pivot - 1)\n    self.quick_sort(nums, pivot + 1, right)\n</code></pre> quick_sort.cpp<pre><code>/* クイックソート */\nvoid quickSort(vector&lt;int&gt; &amp;nums, int left, int right) {\n    // サブ配列の長さが1の時、再帰を終了\n    if (left &gt;= right)\n        return;\n    // 分割\n    int pivot = partition(nums, left, right);\n    // 左サブ配列と右サブ配列を再帰的に処理\n    quickSort(nums, left, pivot - 1);\n    quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.java<pre><code>/* クイックソート */\nvoid quickSort(int[] nums, int left, int right) {\n    // 部分配列の長さが 1 のとき再帰を終了\n    if (left &gt;= right)\n        return;\n    // 分割\n    int pivot = partition(nums, left, right);\n    // 左部分配列と右部分配列を再帰的に処理\n    quickSort(nums, left, pivot - 1);\n    quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.cs<pre><code>[class]{quickSort}-[func]{QuickSort}\n</code></pre> quick_sort.go<pre><code>[class]{quickSort}-[func]{quickSort}\n</code></pre> quick_sort.swift<pre><code>[class]{}-[func]{quickSort}\n</code></pre> quick_sort.js<pre><code>[class]{QuickSort}-[func]{quickSort}\n</code></pre> quick_sort.ts<pre><code>[class]{QuickSort}-[func]{quickSort}\n</code></pre> quick_sort.dart<pre><code>[class]{QuickSort}-[func]{quickSort}\n</code></pre> quick_sort.rs<pre><code>[class]{QuickSort}-[func]{quick_sort}\n</code></pre> quick_sort.c<pre><code>[class]{}-[func]{quickSort}\n</code></pre> quick_sort.kt<pre><code>[class]{}-[func]{quickSort}\n</code></pre> quick_sort.rb<pre><code>[class]{QuickSort}-[func]{quick_sort}\n</code></pre>","path":["第 11 章 &nbsp; ソート","11.5 &nbsp; クイックソート"],"tags":[]},{"location":"chapter_sorting/quick_sort/#1152","level":2,"title":"11.5.2   アルゴリズムの特徴","text":"<ul> <li>\\(O(n \\log n)\\)の時間計算量、非適応ソート：平均的なケースでは、ピボット分割の再帰レベルは\\(\\log n\\)で、レベルあたりのループの総数は\\(n\\)であり、全体で\\(O(n \\log n)\\)の時間を使用します。最悪の場合、各ラウンドのピボット分割は長さ\\(n\\)の配列を長さ\\(0\\)と\\(n - 1\\)の2つのサブ配列に分割し、再帰レベル数が\\(n\\)に達すると、各レベルのループ数は\\(n\\)で、使用される総時間は\\(O(n^2)\\)です。</li> <li>\\(O(n)\\)の空間計算量、インプレースソート：入力配列が完全に逆順の場合、最悪の再帰深度は\\(n\\)に達し、\\(O(n)\\)のスタックフレーム空間を使用します。ソート操作は追加の配列の助けなしに元の配列で実行されます。</li> <li>非安定ソート：ピボット分割の最終ステップで、ピボットは等しい要素の右側に交換される可能性があります。</li> </ul>","path":["第 11 章 &nbsp; ソート","11.5 &nbsp; クイックソート"],"tags":[]},{"location":"chapter_sorting/quick_sort/#1153","level":2,"title":"11.5.3   なぜクイックソートは高速なのか","text":"<p>名前が示すように、クイックソートは効率性の面で一定の利点を持つべきです。クイックソートの平均時間計算量は「マージソート」や「ヒープソート」と同じですが、以下の理由で一般的により効率的です。</p> <ul> <li>最悪ケースシナリオの低い確率：クイックソートの最悪時間計算量は\\(O(n^2)\\)で、マージソートほど安定していませんが、ほとんどの場合、クイックソートは\\(O(n \\log n)\\)の時間計算量で動作できます。</li> <li>高いキャッシュ利用率：ピボット分割操作中、システムはサブ配列全体をキャッシュにロードできるため、要素により効率的にアクセスできます。対照的に、「ヒープソート」などのアルゴリズムは要素にジャンプ方式でアクセスする必要があり、この特徴を欠いています。</li> <li>計算量の小さな定数係数：上記3つのアルゴリズムの中で、クイックソートは比較、代入、交換などの操作の総数が最も少ないです。これは「挿入ソート」が「バブルソート」よりも高速な理由と似ています。</li> </ul>","path":["第 11 章 &nbsp; ソート","11.5 &nbsp; クイックソート"],"tags":[]},{"location":"chapter_sorting/quick_sort/#1154","level":2,"title":"11.5.4   ピボット最適化","text":"<p>クイックソートの時間効率は特定の入力で劣化する可能性があります。例えば、入力配列が完全に逆順の場合、最も左の要素をピボットとして選択するため、ピボット分割後、ピボットは配列の右端に交換され、左サブ配列の長さが\\(n - 1\\)、右サブ配列の長さが\\(0\\)になります。この方法を続けると、各ラウンドのピボット分割でサブ配列の長さが\\(0\\)になり、分割統治戦略が失敗し、クイックソートは「バブルソート」に似た形に劣化します。</p> <p>この状況を避けるため、ピボット分割でピボット選択戦略を最適化できます。例えば、要素をランダムに選択してピボットとすることができます。ただし、運が悪く、一貫して最適でないピボットを選択した場合、効率はまだ満足できません。</p> <p>プログラミング言語は通常「疑似乱数」を生成することに注意することが重要です。疑似乱数シーケンスに対して特定のテストケースを構築すると、クイックソートの効率はまだ劣化する可能性があります。</p> <p>さらなる改善のため、3つの候補要素（通常は配列の最初、最後、中点の要素）を選択し、**これら3つの候補要素の中央値をピボットとして使用**できます。この方法で、ピボットが「小さすぎず大きすぎない」確率が大幅に増加します。もちろん、さらに多くの候補要素を選択してアルゴリズムの堅牢性をさらに向上させることもできます。この方法により、時間計算量が\\(O(n^2)\\)に劣化する確率が大幅に削減されます。</p> <p>サンプルコードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby quick_sort.py<pre><code>def median_three(self, nums: list[int], left: int, mid: int, right: int) -&gt; int:\n    \"\"\"3つの候補要素の中央値を選択\"\"\"\n    l, m, r = nums[left], nums[mid], nums[right]\n    if (l &lt;= m &lt;= r) or (r &lt;= m &lt;= l):\n        return mid  # m は l と r の間\n    if (m &lt;= l &lt;= r) or (r &lt;= l &lt;= m):\n        return left  # l は m と r の間\n    return right\n\ndef partition(self, nums: list[int], left: int, right: int) -&gt; int:\n    \"\"\"分割（三点中央値）\"\"\"\n    # nums[left] をピボットとして使用\n    med = self.median_three(nums, left, (left + right) // 2, right)\n    # 中央値を配列の最左端に交換\n    nums[left], nums[med] = nums[med], nums[left]\n    # nums[left] をピボットとして使用\n    i, j = left, right\n    while i &lt; j:\n        while i &lt; j and nums[j] &gt;= nums[left]:\n            j -= 1  # 右から左へピボットより小さい最初の要素を探す\n        while i &lt; j and nums[i] &lt;= nums[left]:\n            i += 1  # 左から右へピボットより大きい最初の要素を探す\n        # 要素を交換\n        nums[i], nums[j] = nums[j], nums[i]\n    # ピボットを2つのサブ配列の境界に交換\n    nums[i], nums[left] = nums[left], nums[i]\n    return i  # ピボットのインデックスを返す\n</code></pre> quick_sort.cpp<pre><code>/* 三つの候補要素の中央値を選択 */\nint medianThree(vector&lt;int&gt; &amp;nums, int left, int mid, int right) {\n    int l = nums[left], m = nums[mid], r = nums[right];\n    if ((l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l))\n        return mid; // mはlとrの間\n    if ((m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m))\n        return left; // lはmとrの間\n    return right;\n}\n\n/* 分割（三つの中央値） */\nint partition(vector&lt;int&gt; &amp;nums, int left, int right) {\n    // 三つの候補要素の中央値を選択\n    int med = medianThree(nums, left, (left + right) / 2, right);\n    // 中央値を配列の最左位置に交換\n    swap(nums, left, med);\n    // nums[left]をピボットとして使用\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--; // 右から左へピボットより小さい最初の要素を検索\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;          // 左から右へピボットより大きい最初の要素を検索\n        swap(nums, i, j); // これら二つの要素を交換\n    }\n    swap(nums, i, left); // ピボットを二つのサブ配列の境界に交換\n    return i;            // ピボットのインデックスを返す\n}\n</code></pre> quick_sort.java<pre><code>/* 3つの候補要素の中央値を選択 */\nint medianThree(int[] nums, int left, int mid, int right) {\n    int l = nums[left], m = nums[mid], r = nums[right];\n    if ((l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l))\n        return mid; // m は l と r の間\n    if ((m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m))\n        return left; // l は m と r の間\n    return right;\n}\n\n/* 分割（3つの中央値） */\nint partition(int[] nums, int left, int right) {\n    // 3つの候補要素の中央値を選択\n    int med = medianThree(nums, left, (left + right) / 2, right);\n    // 中央値を配列の最左端の位置に交換\n    swap(nums, left, med);\n    // nums[left] を基準値として使用\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--;          // 右から左へ、基準値より小さい最初の要素を検索\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;          // 左から右へ、基準値より大きい最初の要素を検索\n        swap(nums, i, j); // これら2つの要素を交換\n    }\n    swap(nums, i, left);  // 基準値を2つの部分配列の境界に交換\n    return i;             // 基準値のインデックスを返す\n}\n</code></pre> quick_sort.cs<pre><code>[class]{QuickSortMedian}-[func]{MedianThree}\n\n[class]{QuickSortMedian}-[func]{Partition}\n</code></pre> quick_sort.go<pre><code>[class]{quickSortMedian}-[func]{medianThree}\n\n[class]{quickSortMedian}-[func]{partition}\n</code></pre> quick_sort.swift<pre><code>[class]{}-[func]{medianThree}\n\n[class]{}-[func]{partitionMedian}\n</code></pre> quick_sort.js<pre><code>[class]{QuickSortMedian}-[func]{medianThree}\n\n[class]{QuickSortMedian}-[func]{partition}\n</code></pre> quick_sort.ts<pre><code>[class]{QuickSortMedian}-[func]{medianThree}\n\n[class]{QuickSortMedian}-[func]{partition}\n</code></pre> quick_sort.dart<pre><code>[class]{QuickSortMedian}-[func]{_medianThree}\n\n[class]{QuickSortMedian}-[func]{_partition}\n</code></pre> quick_sort.rs<pre><code>[class]{QuickSortMedian}-[func]{median_three}\n\n[class]{QuickSortMedian}-[func]{partition}\n</code></pre> quick_sort.c<pre><code>[class]{}-[func]{medianThree}\n\n[class]{}-[func]{partitionMedian}\n</code></pre> quick_sort.kt<pre><code>[class]{}-[func]{medianThree}\n\n[class]{}-[func]{partitionMedian}\n</code></pre> quick_sort.rb<pre><code>[class]{QuickSortMedian}-[func]{median_three}\n\n[class]{QuickSortMedian}-[func]{partition}\n</code></pre>","path":["第 11 章 &nbsp; ソート","11.5 &nbsp; クイックソート"],"tags":[]},{"location":"chapter_sorting/quick_sort/#1155","level":2,"title":"11.5.5   末尾再帰最適化","text":"<p>特定の入力では、クイックソートはより多くの空間を占有する可能性があります。例えば、完全に順序付けられた入力配列を考えてみましょう。再帰でのサブ配列の長さを\\(m\\)とします。各ラウンドのピボット分割で、長さ\\(0\\)の左サブ配列と長さ\\(m - 1\\)の右サブ配列が生成されます。これは、再帰呼び出しごとに問題サイズが1つの要素のみ減少することを意味し、各レベルの再帰での削減が非常に小さくなります。 結果として、再帰ツリーの高さは\\(n − 1\\)に達する可能性があり、これには\\(O(n)\\)のスタックフレーム空間が必要です。</p> <p>スタックフレーム空間の蓄積を防ぐため、各ラウンドのピボットソート後に2つのサブ配列の長さを比較し、**より短いサブ配列のみを再帰的にソート**できます。より短いサブ配列の長さは\\(n / 2\\)を超えないため、この方法は再帰深度が\\(\\log n\\)を超えないことを保証し、最悪空間計算量を\\(O(\\log n)\\)に最適化します。コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby quick_sort.py<pre><code>def quick_sort(self, nums: list[int], left: int, right: int):\n    \"\"\"クイックソート（末尾再帰最適化）\"\"\"\n    # サブ配列の長さが1のときに終了\n    while left &lt; right:\n        # 分割操作\n        pivot = self.partition(nums, left, right)\n        # 2つのサブ配列のうち短い方に対してクイックソートを実行\n        if pivot - left &lt; right - pivot:\n            self.quick_sort(nums, left, pivot - 1)  # 左サブ配列を再帰的にソート\n            left = pivot + 1  # 残りの未ソート区間は [pivot + 1, right]\n        else:\n            self.quick_sort(nums, pivot + 1, right)  # 右サブ配列を再帰的にソート\n            right = pivot - 1  # 残りの未ソート区間は [left, pivot - 1]\n</code></pre> quick_sort.cpp<pre><code>/* クイックソート（末尾再帰最適化） */\nvoid quickSort(vector&lt;int&gt; &amp;nums, int left, int right) {\n    // サブ配列の長さが1の時終了\n    while (left &lt; right) {\n        // 分割操作\n        int pivot = partition(nums, left, right);\n        // 二つのサブ配列のうち短い方でクイックソートを実行\n        if (pivot - left &lt; right - pivot) {\n            quickSort(nums, left, pivot - 1); // 左サブ配列を再帰的にソート\n            left = pivot + 1;                 // 残りの未ソート区間は[pivot + 1, right]\n        } else {\n            quickSort(nums, pivot + 1, right); // 右サブ配列を再帰的にソート\n            right = pivot - 1;                 // 残りの未ソート区間は[left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.java<pre><code>/* クイックソート（末尾再帰最適化） */\nvoid quickSort(int[] nums, int left, int right) {\n    // 部分配列の長さが 1 のとき終了\n    while (left &lt; right) {\n        // 分割操作\n        int pivot = partition(nums, left, right);\n        // 2つの部分配列のうち短い方にクイックソートを実行\n        if (pivot - left &lt; right - pivot) {\n            quickSort(nums, left, pivot - 1); // 左部分配列を再帰的にソート\n            left = pivot + 1; // 残りの未ソート区間は [pivot + 1, right]\n        } else {\n            quickSort(nums, pivot + 1, right); // 右部分配列を再帰的にソート\n            right = pivot - 1; // 残りの未ソート区間は [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.cs<pre><code>[class]{QuickSortTailCall}-[func]{QuickSort}\n</code></pre> quick_sort.go<pre><code>[class]{quickSortTailCall}-[func]{quickSort}\n</code></pre> quick_sort.swift<pre><code>[class]{}-[func]{quickSortTailCall}\n</code></pre> quick_sort.js<pre><code>[class]{QuickSortTailCall}-[func]{quickSort}\n</code></pre> quick_sort.ts<pre><code>[class]{QuickSortTailCall}-[func]{quickSort}\n</code></pre> quick_sort.dart<pre><code>[class]{QuickSortTailCall}-[func]{quickSort}\n</code></pre> quick_sort.rs<pre><code>[class]{QuickSortTailCall}-[func]{quick_sort}\n</code></pre> quick_sort.c<pre><code>[class]{}-[func]{quickSortTailCall}\n</code></pre> quick_sort.kt<pre><code>[class]{}-[func]{quickSortTailCall}\n</code></pre> quick_sort.rb<pre><code>[class]{QuickSortTailCall}-[func]{quick_sort}\n</code></pre>","path":["第 11 章 &nbsp; ソート","11.5 &nbsp; クイックソート"],"tags":[]},{"location":"chapter_sorting/radix_sort/","level":1,"title":"11.10   基数ソート","text":"<p>前の節では計数ソートを紹介しました。これは、データサイズ \\(n\\) が大きいがデータ範囲 \\(m\\) が小さいシナリオに適しています。\\(n = 10^6\\) の学生IDをソートする必要があり、各IDが \\(8\\) 桁の数字であるとします。これは、データ範囲 \\(m = 10^8\\) が非常に大きいことを意味します。この場合、計数ソートを使用すると、大量のメモリスペースが必要になります。基数ソートはこの状況を回避できます。</p> <p>基数ソートは計数ソートと同じ核心概念を共有し、要素の頻度をカウントすることでソートします。同時に、基数ソートは数字の桁間の漸進的関係を利用してこれを基盤としています。桁を一度に一つずつ処理してソートし、最終的なソート順序を達成します。</p>","path":["第 11 章 &nbsp; ソート","11.10 &nbsp; 基数ソート"],"tags":[]},{"location":"chapter_sorting/radix_sort/#11101","level":2,"title":"11.10.1   アルゴリズムの過程","text":"<p>学生IDデータを例として、最下位桁を \\(1\\) 番目、最上位桁を \\(8\\) 番目とすると、基数ソートの過程は以下の図に示されています。</p> <ol> <li>桁 \\(k = 1\\) を初期化します。</li> <li>学生IDの \\(k\\) 番目の桁に対して「計数ソート」を実行します。完了後、データは \\(k\\) 番目の桁に基づいて最小から最大までソートされます。</li> <li>\\(k\\) を \\(1\\) 増やし、手順 <code>2.</code> に戻って反復を続け、すべての桁がソートされるまで続けます。この時点で過程が終了します。</li> </ol> <p></p> <p> 図 11-18   基数ソートアルゴリズムの過程 </p> <p>以下、コード実装を詳しく見てみます。基数 \\(d\\) での数 \\(x\\) に対して、その \\(k\\) 番目の桁 \\(x_k\\) を取得するには、以下の計算式を使用できます：</p> \\[ x_k = \\lfloor\\frac{x}{d^{k-1}}\\rfloor \\bmod d \\] <p>ここで \\(\\lfloor a \\rfloor\\) は浮動小数点数 \\(a\\) の切り捨てを表し、\\(\\bmod \\: d\\) は \\(d\\) による剰余を表します。学生IDデータの場合、\\(d = 10\\) で \\(k \\in [1, 8]\\) です。</p> <p>さらに、\\(k\\) 番目の桁に基づいてソートできるように、計数ソートのコードを少し修正する必要があります：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby radix_sort.py<pre><code>def digit(num: int, exp: int) -&gt; int:\n    \"\"\"要素 num の k 番目の桁を取得、exp = 10^(k-1)\"\"\"\n    # k の代わりに exp を渡すことで、ここでコストの高い累乗計算を避けることができる\n    return (num // exp) % 10\n\ndef counting_sort_digit(nums: list[int], exp: int):\n    \"\"\"計数ソート（nums の k 番目の桁に基づく）\"\"\"\n    # 10進数の桁の範囲は 0~9、したがって長さ10のバケット配列が必要\n    counter = [0] * 10\n    n = len(nums)\n    # 数字 0~9 の出現回数を統計\n    for i in range(n):\n        d = digit(nums[i], exp)  # nums[i] の k 番目の桁を取得、d とする\n        counter[d] += 1  # 数字 d の出現回数を統計\n    # 前置和を計算し、「出現回数」を「配列インデックス」に変換\n    for i in range(1, 10):\n        counter[i] += counter[i - 1]\n    # 逆順に走査し、バケット統計に基づいて各要素を res に配置\n    res = [0] * n\n    for i in range(n - 1, -1, -1):\n        d = digit(nums[i], exp)\n        j = counter[d] - 1  # 配列内の d のインデックス j を取得\n        res[j] = nums[i]  # 現在の要素をインデックス j に配置\n        counter[d] -= 1  # d の数を1減らす\n    # 結果を使用して元の配列 nums を上書き\n    for i in range(n):\n        nums[i] = res[i]\n\ndef radix_sort(nums: list[int]):\n    \"\"\"基数ソート\"\"\"\n    # 配列の最大要素を取得し、最大桁数を判定するために使用\n    m = max(nums)\n    # 最下位桁から最上位桁まで走査\n    exp = 1\n    while exp &lt;= m:\n        # 配列要素の k 番目の桁に対して計数ソートを実行\n        # k = 1 -&gt; exp = 1\n        # k = 2 -&gt; exp = 10\n        # つまり、exp = 10^(k-1)\n        counting_sort_digit(nums, exp)\n        exp *= 10\n</code></pre> radix_sort.cpp<pre><code>/* 要素numのk番目の桁を取得、exp = 10^(k-1) */\nint digit(int num, int exp) {\n    // kの代わりにexpを渡すことで、ここで繰り返される高価な冪乗計算を避けることができる\n    return (num / exp) % 10;\n}\n\n/* カウントソート（numsのk番目の桁に基づく） */\nvoid countingSortDigit(vector&lt;int&gt; &amp;nums, int exp) {\n    // 10進数の桁範囲は0~9なので、長さ10のバケット配列が必要\n    vector&lt;int&gt; counter(10, 0);\n    int n = nums.size();\n    // 数字0~9の出現回数を統計\n    for (int i = 0; i &lt; n; i++) {\n        int d = digit(nums[i], exp); // nums[i]のk番目の桁を取得、dとして記録\n        counter[d]++;                // 数字dの出現回数を統計\n    }\n    // 前缀和を計算し、「出現回数」を「配列インデックス」に変換\n    for (int i = 1; i &lt; 10; i++) {\n        counter[i] += counter[i - 1];\n    }\n    // 逆順で走査し、バケット統計に基づいて各要素をresに配置\n    vector&lt;int&gt; res(n, 0);\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int d = digit(nums[i], exp);\n        int j = counter[d] - 1; // dが配列内にあるインデックスjを取得\n        res[j] = nums[i];       // 現在の要素をインデックスjに配置\n        counter[d]--;           // dのカウントを1減らす\n    }\n    // 結果で元の配列numsを上書き\n    for (int i = 0; i &lt; n; i++)\n        nums[i] = res[i];\n}\n\n/* 基数ソート */\nvoid radixSort(vector&lt;int&gt; &amp;nums) {\n    // 配列の最大要素を取得、最大桁数を判定するために使用\n    int m = *max_element(nums.begin(), nums.end());\n    // 最下位桁から最上位桁まで走査\n    for (int exp = 1; exp &lt;= m; exp *= 10)\n        // 配列要素のk番目の桁でカウントソートを実行\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // つまり、exp = 10^(k-1)\n        countingSortDigit(nums, exp);\n}\n</code></pre> radix_sort.java<pre><code>/* 要素 num の k 番目の桁を取得、exp = 10^(k-1) */\nint digit(int num, int exp) {\n    // k の代わりに exp を渡すことで、ここでコストの高い累乗計算の繰り返しを避けることができる\n    return (num / exp) % 10;\n}\n\n/* 計数ソート（nums の k 番目の桁に基づく） */\nvoid countingSortDigit(int[] nums, int exp) {\n    // 10進数の桁の範囲は 0~9、したがって長さ 10 のバケット配列が必要\n    int[] counter = new int[10];\n    int n = nums.length;\n    // 桁 0~9 の出現回数を統計\n    for (int i = 0; i &lt; n; i++) {\n        int d = digit(nums[i], exp); // nums[i] の k 番目の桁を取得、d とする\n        counter[d]++;                // 桁 d の出現回数を統計\n    }\n    // 累積和を計算し、「出現回数」を「配列インデックス」に変換\n    for (int i = 1; i &lt; 10; i++) {\n        counter[i] += counter[i - 1];\n    }\n    // 逆順に走査し、バケット統計に基づいて各要素を res に配置\n    int[] res = new int[n];\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int d = digit(nums[i], exp);\n        int j = counter[d] - 1; // 配列内での d のインデックス j を取得\n        res[j] = nums[i];       // 現在の要素をインデックス j に配置\n        counter[d]--;           // d のカウントを 1 減らす\n    }\n    // 結果で元の配列 nums を上書き\n    for (int i = 0; i &lt; n; i++)\n        nums[i] = res[i];\n}\n\n/* 基数ソート */\nvoid radixSort(int[] nums) {\n    // 配列の最大要素を取得し、最大桁数を判定するために使用\n    int m = Integer.MIN_VALUE;\n    for (int num : nums)\n        if (num &gt; m)\n            m = num;\n    // 最下位桁から最上位桁まで走査\n    for (int exp = 1; exp &lt;= m; exp *= 10) {\n        // 配列要素の k 番目の桁に対して計数ソートを実行\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // すなわち exp = 10^(k-1)\n        countingSortDigit(nums, exp);\n    }\n}\n</code></pre> radix_sort.cs<pre><code>[class]{radix_sort}-[func]{Digit}\n\n[class]{radix_sort}-[func]{CountingSortDigit}\n\n[class]{radix_sort}-[func]{RadixSort}\n</code></pre> radix_sort.go<pre><code>[class]{}-[func]{digit}\n\n[class]{}-[func]{countingSortDigit}\n\n[class]{}-[func]{radixSort}\n</code></pre> radix_sort.swift<pre><code>[class]{}-[func]{digit}\n\n[class]{}-[func]{countingSortDigit}\n\n[class]{}-[func]{radixSort}\n</code></pre> radix_sort.js<pre><code>[class]{}-[func]{digit}\n\n[class]{}-[func]{countingSortDigit}\n\n[class]{}-[func]{radixSort}\n</code></pre> radix_sort.ts<pre><code>[class]{}-[func]{digit}\n\n[class]{}-[func]{countingSortDigit}\n\n[class]{}-[func]{radixSort}\n</code></pre> radix_sort.dart<pre><code>[class]{}-[func]{digit}\n\n[class]{}-[func]{countingSortDigit}\n\n[class]{}-[func]{radixSort}\n</code></pre> radix_sort.rs<pre><code>[class]{}-[func]{digit}\n\n[class]{}-[func]{counting_sort_digit}\n\n[class]{}-[func]{radix_sort}\n</code></pre> radix_sort.c<pre><code>[class]{}-[func]{digit}\n\n[class]{}-[func]{countingSortDigit}\n\n[class]{}-[func]{radixSort}\n</code></pre> radix_sort.kt<pre><code>[class]{}-[func]{digit}\n\n[class]{}-[func]{countingSortDigit}\n\n[class]{}-[func]{radixSort}\n</code></pre> radix_sort.rb<pre><code>[class]{}-[func]{digit}\n\n[class]{}-[func]{counting_sort_digit}\n\n[class]{}-[func]{radix_sort}\n</code></pre> <p>なぜ最下位桁から開始するのか？</p> <p>連続するソートラウンドでは、後のラウンドの結果が前のラウンドの結果を上書きします。例えば、最初のラウンドの結果が \\(a &lt; b\\) で、2番目のラウンドが \\(a &gt; b\\) の場合、2番目のラウンドの結果が最初のラウンドの結果を置き換えます。上位桁は下位桁より優先されるため、上位桁の前に下位桁をソートすることが理にかなっています。</p>","path":["第 11 章 &nbsp; ソート","11.10 &nbsp; 基数ソート"],"tags":[]},{"location":"chapter_sorting/radix_sort/#11102","level":2,"title":"11.10.2   アルゴリズムの特徴","text":"<p>計数ソートと比較して、基数ソートはより大きな数値範囲に適していますが、データが固定桁数で表現でき、桁数があまり大きくないことを前提としています。例えば、浮動小数点数は桁数 \\(k\\) が大きい可能性があり、時間計算量 \\(O(nk) \\gg O(n^2)\\) につながる可能性があるため、基数ソートには適していません。</p> <ul> <li>時間計算量は \\(O(nk)\\)、非適応ソート：データサイズを \\(n\\)、データが基数 \\(d\\)、最大桁数を \\(k\\) とすると、単一桁のソートには \\(O(n + d)\\) 時間がかかり、すべての \\(k\\) 桁のソートには \\(O((n + d)k)\\) 時間がかかります。一般的に、\\(d\\) と \\(k\\) はどちらも比較的小さく、時間計算量は \\(O(n)\\) に近づきます。</li> <li>空間計算量は \\(O(n + d)\\)、非インプレースソート：計数ソートと同様に、基数ソートは長さ \\(n\\) と \\(d\\) の配列 <code>res</code> と <code>counter</code> にそれぞれ依存します。</li> <li>安定ソート：計数ソートが安定な場合、基数ソートも安定です。計数ソートが不安定な場合、基数ソートは正しいソート順序を保証できません。</li> </ul>","path":["第 11 章 &nbsp; ソート","11.10 &nbsp; 基数ソート"],"tags":[]},{"location":"chapter_sorting/selection_sort/","level":1,"title":"11.2   選択ソート","text":"<p>選択ソートは非常にシンプルな原理で動作します：各反復で未ソート区間から最小要素を選択し、ソート済みセクションの末尾に移動するループを使用します。</p> <p>配列の長さを\\(n\\)とすると、選択ソートのステップは下図に示されます。</p> <ol> <li>最初に、すべての要素は未ソートで、つまり未ソート（インデックス）区間は\\([0, n-1]\\)です。</li> <li>区間\\([0, n-1]\\)の最小要素を選択し、インデックス\\(0\\)の要素と交換します。この後、配列の最初の要素がソートされます。</li> <li>区間\\([1, n-1]\\)の最小要素を選択し、インデックス\\(1\\)の要素と交換します。この後、配列の最初の2つの要素がソートされます。</li> <li>この方法で続行します。\\(n - 1\\)ラウンドの選択と交換の後、最初の\\(n - 1\\)個の要素がソートされます。</li> <li>残りの唯一の要素は結果的に最大要素であり、ソートする必要がないため、配列はソートされます。</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 11-2   Selection sort process </p> <p>コードでは、\\(k\\)を使用して未ソート区間内の最小要素を記録します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby selection_sort.py<pre><code>def selection_sort(nums: list[int]):\n    \"\"\"選択ソート\"\"\"\n    n = len(nums)\n    # 外側のループ：未ソート範囲は [i, n-1]\n    for i in range(n - 1):\n        # 内側のループ：未ソート範囲内で最小要素を見つける\n        k = i\n        for j in range(i + 1, n):\n            if nums[j] &lt; nums[k]:\n                k = j  # 最小要素のインデックスを記録\n        # 最小要素を未ソート範囲の先頭要素と交換\n        nums[i], nums[k] = nums[k], nums[i]\n</code></pre> selection_sort.cpp<pre><code>/* 選択ソート */\nvoid selectionSort(vector&lt;int&gt; &amp;nums) {\n    int n = nums.size();\n    // 外側ループ：未ソート範囲は[i, n-1]\n    for (int i = 0; i &lt; n - 1; i++) {\n        // 内側ループ：未ソート範囲内で最小要素を見つける\n        int k = i;\n        for (int j = i + 1; j &lt; n; j++) {\n            if (nums[j] &lt; nums[k])\n                k = j; // 最小要素のインデックスを記録\n        }\n        // 最小要素を未ソート範囲の最初の要素と交換\n        swap(nums[i], nums[k]);\n    }\n}\n</code></pre> selection_sort.java<pre><code>/* 選択ソート */\nvoid selectionSort(int[] nums) {\n    int n = nums.length;\n    // 外側ループ: 未ソート範囲は [i, n-1]\n    for (int i = 0; i &lt; n - 1; i++) {\n        // 内側ループ: 未ソート範囲内で最小要素を見つける\n        int k = i;\n        for (int j = i + 1; j &lt; n; j++) {\n            if (nums[j] &lt; nums[k])\n                k = j; // 最小要素のインデックスを記録\n        }\n        // 最小要素と未ソート範囲の最初の要素を交換\n        int temp = nums[i];\n        nums[i] = nums[k];\n        nums[k] = temp;\n    }\n}\n</code></pre> selection_sort.cs<pre><code>[class]{selection_sort}-[func]{SelectionSort}\n</code></pre> selection_sort.go<pre><code>[class]{}-[func]{selectionSort}\n</code></pre> selection_sort.swift<pre><code>[class]{}-[func]{selectionSort}\n</code></pre> selection_sort.js<pre><code>[class]{}-[func]{selectionSort}\n</code></pre> selection_sort.ts<pre><code>[class]{}-[func]{selectionSort}\n</code></pre> selection_sort.dart<pre><code>[class]{}-[func]{selectionSort}\n</code></pre> selection_sort.rs<pre><code>[class]{}-[func]{selection_sort}\n</code></pre> selection_sort.c<pre><code>[class]{}-[func]{selectionSort}\n</code></pre> selection_sort.kt<pre><code>[class]{}-[func]{selectionSort}\n</code></pre> selection_sort.rb<pre><code>[class]{}-[func]{selection_sort}\n</code></pre>","path":["第 11 章 &nbsp; ソート","11.2 &nbsp; 選択ソート"],"tags":[]},{"location":"chapter_sorting/selection_sort/#1121","level":2,"title":"11.2.1   アルゴリズムの特性","text":"<ul> <li>\\(O(n^2)\\)の時間計算量、非適応ソート：外側ループに\\(n - 1\\)回の反復があり、未ソートセクションの長さは最初の反復で\\(n\\)から始まり、最後の反復で\\(2\\)まで減少します。つまり、各外側ループ反復にはそれぞれ\\(n\\)、\\(n - 1\\)、\\(\\dots\\)、\\(3\\)、\\(2\\)回の内側ループ反復が含まれ、合計は\\(\\frac{(n - 1)(n + 2)}{2}\\)となります。</li> <li>\\(O(1)\\)の空間計算量、インプレースソート：ポインタ\\(i\\)と\\(j\\)で定数の追加空間を使用します。</li> <li>非安定ソート：下図に示すように、要素<code>nums[i]</code>は等しい要素の右側に交換される可能性があり、相対順序が変わる原因となります。</li> </ul> <p> 図 11-3   Selection sort instability example </p>","path":["第 11 章 &nbsp; ソート","11.2 &nbsp; 選択ソート"],"tags":[]},{"location":"chapter_sorting/sorting_algorithm/","level":1,"title":"11.1   ソートアルゴリズム","text":"<p>ソートアルゴリズムは、データセットを特定の順序で配列するために使用されます。ソートアルゴリズムは、順序付けられたデータは通常、より効率的に探索、分析、処理できるため、幅広い応用があります。</p> <p>下図に示すように、ソートアルゴリズムのデータ型は整数、浮動小数点数、文字、文字列などです。ソート基準は、数値サイズ、文字ASCII順序、またはカスタム基準など、必要に応じて設定できます。</p> <p></p> <p> 図 11-1   Data types and comparator examples </p>","path":["第 11 章 &nbsp; ソート","11.1 &nbsp; ソートアルゴリズム"],"tags":[]},{"location":"chapter_sorting/sorting_algorithm/#1111","level":2,"title":"11.1.1   評価次元","text":"<p>実行効率：ソートアルゴリズムの時間計算量ができるだけ低いことを期待し、全体的な操作数も少ないこと（時間計算量の定数項を下げる）を望みます。大容量データでは、実行効率が特に重要です。</p> <p>インプレース性：名前が示すとおり、インプレースソートは元の配列を直接操作することで実現され、追加のヘルパー配列が不要であるため、メモリを節約します。一般的に、インプレースソートはデータ移動操作が少なく、高速です。</p> <p>安定性：安定ソートは、ソート後に配列内の等しい要素の相対順序が変わらないことを保証します。</p> <p>安定ソートは、マルチキーソートシナリオにおいて必要条件です。学生情報を格納するテーブルがあり、第1列と第2列がそれぞれ名前と年齢であるとします。この場合、不安定ソートは入力データの順序を失う可能性があります：</p> <pre><code># 入力データは名前でソート済み\n# (名前, 年齢)\n  ('A', 19)\n  ('B', 18)\n  ('C', 21)\n  ('D', 19)\n  ('E', 23)\n\n# 不安定ソートアルゴリズムを使用してリストを年齢でソートすると仮定すると、\n# 結果は('D', 19)と('A', 19)の相対位置を変更し、\n# 入力データが名前でソート済みであるという性質が失われる\n  ('B', 18)\n  ('D', 19)\n  ('A', 19)\n  ('C', 21)\n  ('E', 23)\n</code></pre> <p>適応性：適応ソートは入力データ内の既存の順序情報を活用して計算負荷を削減し、より最適な時間効率を実現します。適応ソートアルゴリズムの最良ケース時間計算量は、通常平均ケース時間計算量よりも優れています。</p> <p>比較ベースまたは非比較ベース：比較ベースソートは比較演算子（\\(&lt;\\)、\\(=\\)、\\(&gt;\\)）に依存して要素の相対順序を決定し、配列全体をソートします。理論的最適時間計算量は\\(O(n \\log n)\\)です。一方、非比較ソートは比較演算子を使用せず、\\(O(n)\\)の時間計算量を実現できますが、汎用性は比較的劣ります。</p>","path":["第 11 章 &nbsp; ソート","11.1 &nbsp; ソートアルゴリズム"],"tags":[]},{"location":"chapter_sorting/sorting_algorithm/#1112","level":2,"title":"11.1.2   理想的なソートアルゴリズム","text":"<p>高速実行、インプレース、安定、適応、汎用。明らかに、これらのすべての特徴を組み合わせたソートアルゴリズムは今日まで見つかっていません。したがって、ソートアルゴリズムを選択する際は、データの特定の特徴と問題の要件に基づいて決定する必要があります。</p> <p>次に、さまざまなソートアルゴリズムを一緒に学び、上記の評価次元に基づいてそれぞれの利点と欠点を分析します。</p>","path":["第 11 章 &nbsp; ソート","11.1 &nbsp; ソートアルゴリズム"],"tags":[]},{"location":"chapter_sorting/summary/","level":1,"title":"11.11   まとめ","text":"","path":["第 11 章 &nbsp; ソート","11.11 &nbsp; まとめ"],"tags":[]},{"location":"chapter_sorting/summary/#1","level":3,"title":"1.   重要な復習","text":"<ul> <li>バブルソートは隣接する要素を交換することで動作します。フラグを追加して早期リターンを可能にすることで、バブルソートの最良ケースの時間計算量を \\(O(n)\\) に最適化できます。</li> <li>挿入ソートは、未ソート区間から要素を取り出してソート済み区間の正しい位置に挿入することで各ラウンドをソートします。挿入ソートの時間計算量は \\(O(n^2)\\) ですが、単位あたりの操作が比較的少ないため、少量のデータのソートでは非常に人気があります。</li> <li>クイックソートは歩哨分割操作に基づいています。歩哨分割では、常に最悪のピボットを選ぶ可能性があり、時間計算量が \\(O(n^2)\\) に劣化する可能性があります。中央値やランダムピボットを導入することで、そのような劣化の確率を減らすことができます。末尾再帰は再帰の深さを効果的に減らし、空間計算量を \\(O(\\log n)\\) に最適化します。</li> <li>マージソートには分割とマージの2つの段階があり、通常分割統治戦略を体現しています。マージソートでは、配列のソートには補助配列の作成が必要で、空間計算量は \\(O(n)\\) になります。しかし、リストのソートの空間計算量は \\(O(1)\\) に最適化できます。</li> <li>バケットソートは3つの手順から構成されます：データをバケットに分散、各バケット内でのソート、バケット順での結果のマージ。これも分割統治戦略を体現し、非常に大きなデータセットに適しています。バケットソートの鍵はデータの均等分散です。</li> <li>計数ソートはバケットソートの変形で、各データポイントの出現回数をカウントすることでソートします。計数ソートは限られた範囲のデータを持つ大きなデータセットに適しており、データを正の整数に変換する必要があります。</li> <li>基数ソートは桁ごとにソートすることでデータを処理し、データが固定長の数値として表現される必要があります。</li> <li>全体的に、私たちは高効率、安定性、インプレース操作、適応性を持つソートアルゴリズムを求めています。しかし、他のデータ構造やアルゴリズムと同様に、これらすべての条件を同時に満たすソートアルゴリズムは存在しません。実際の応用では、データの特性に基づいて適切なソートアルゴリズムを選択する必要があります。</li> <li>以下の図は、効率性、安定性、インプレース性、適応性の観点から主流のソートアルゴリズムを比較しています。</li> </ul> <p> 図 11-19   ソートアルゴリズムの比較 </p>","path":["第 11 章 &nbsp; ソート","11.11 &nbsp; まとめ"],"tags":[]},{"location":"chapter_sorting/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: ソートアルゴリズムの安定性はいつ必要ですか？</p> <p>実際には、オブジェクトの一つの属性に基づいてソートする場合があります。例えば、学生は名前と身長の属性を持ち、多段階ソートを実装することを目指します：最初に名前で <code>(A, 180) (B, 185) (C, 170) (D, 170)</code> を取得し、次に身長で。ソートアルゴリズムが不安定なため、<code>(D, 170) (C, 170) (A, 180) (B, 185)</code> になってしまう可能性があります。</p> <p>学生DとCの位置が交換され、名前の順序性が破られているのが分かります。これは望ましくありません。</p> <p>Q: 歩哨分割での「右から左への検索」と「左から右への検索」の順序を交換できますか？</p> <p>いいえ、最左要素をピボットとして使用する場合、最初に「右から左への検索」を行い、次に「左から右への検索」を行う必要があります。この結論はやや直観に反するので、理由を分析してみましょう。</p> <p>歩哨分割 <code>partition()</code> の最後のステップは <code>nums[left]</code> と <code>nums[i]</code> を交換することです。交換後、ピボットの左側の要素はすべてピボット以下になります。これには最後の交換前に <code>nums[left] &gt;= nums[i]</code> が成り立つ必要があります。「左から右への検索」を最初に行い、ピボットより大きい要素が見つからない場合、<code>i == j</code> でループを終了し、<code>nums[j] == nums[i] &gt; nums[left]</code> となる可能性があります。つまり、最終交換操作はピボットより大きい要素を配列の左端に交換し、歩哨分割を失敗させます。</p> <p>例えば、配列 <code>[0, 0, 0, 0, 1]</code> が与えられた場合、最初に「左から右への検索」を行うと、歩哨分割後の配列は <code>[1, 0, 0, 0, 0]</code> となり、これは正しくありません。</p> <p>さらに考えると、<code>nums[right]</code> をピボットとして選択する場合、まったく逆で、最初に「左から右への検索」を行う必要があります。</p> <p>Q: 末尾再帰最適化について、短い配列を選択することで再帰の深さが \\(\\log n\\) を超えないことを保証するのはなぜですか？</p> <p>再帰の深さは現在リターンしていない再帰メソッドの数です。歩哨分割の各ラウンドは元の配列を2つの副配列に分割します。末尾再帰最適化により、再帰的に続行する副配列の長さは最大でも元の配列長の半分です。最悪の場合常に長さを半分にすると仮定すると、最終的な再帰の深さは \\(\\log n\\) になります。</p> <p>元のクイックソートを見直すと、より大きな配列を継続的に再帰処理する可能性があり、最悪の場合 \\(n\\)、\\(n - 1\\)、...、\\(2\\)、\\(1\\) で、再帰の深さは \\(n\\) になります。末尾再帰最適化はこのシナリオを回避できます。</p> <p>Q: 配列のすべての要素が等しい場合、クイックソートの時間計算量は \\(O(n^2)\\) ですか？この劣化ケースをどう処理すべきですか？</p> <p>はい。この状況については、歩哨分割を使用して配列をピボットより小さい、等しい、大きいの3つの部分に分割することを検討してください。小さい部分と大きい部分のみを再帰的に進めます。この方法では、すべての入力要素が等しい配列を1ラウンドの歩哨分割だけでソートできます。</p> <p>Q: なぜバケットソートの最悪ケース時間計算量は \\(O(n^2)\\) ですか？</p> <p>最悪の場合、すべての要素が同じバケットに配置されます。これらの要素をソートするために \\(O(n^2)\\) アルゴリズムを使用する場合、時間計算量は \\(O(n^2)\\) になります。</p>","path":["第 11 章 &nbsp; ソート","11.11 &nbsp; まとめ"],"tags":[]},{"location":"chapter_stack_and_queue/","level":1,"title":"第 5 章   スタックとキュー","text":"<p>Abstract</p> <p>スタックは積み重ねられた猫のようなもので、キューは一列に並んだ猫のようなものです。</p> <p>それらはそれぞれ、後入先出（LIFO）と先入先出（FIFO）の論理関係を表しています。</p>","path":["第 5 章 &nbsp; スタックとキュー"],"tags":[]},{"location":"chapter_stack_and_queue/#_1","level":2,"title":"章の内容","text":"<ul> <li>5.1   スタック</li> <li>5.2   キュー</li> <li>5.3   両端キュー</li> <li>5.4   まとめ</li> </ul>","path":["第 5 章 &nbsp; スタックとキュー"],"tags":[]},{"location":"chapter_stack_and_queue/deque/","level":1,"title":"5.3   両端キュー","text":"<p>キューでは、先頭からの要素の削除や末尾への要素の追加のみが可能です。下図に示すように、両端キュー（deque）はより柔軟性を提供し、先頭と末尾の両方で要素の追加や削除を可能にします。</p> <p></p> <p> 図 5-7   両端キューの操作 </p>","path":["第 5 章 &nbsp; スタックとキュー","5.3 &nbsp; 両端キュー"],"tags":[]},{"location":"chapter_stack_and_queue/deque/#531","level":2,"title":"5.3.1   両端キューの一般的な操作","text":"<p>両端キューの一般的な操作は以下の通りです。具体的なメソッド名は使用するプログラミング言語によって異なります。</p> <p> 表 5-3   両端キューの操作効率 </p> メソッド名 説明 時間計算量 <code>pushFirst()</code> 先頭に要素を追加 \\(O(1)\\) <code>pushLast()</code> 末尾に要素を追加 \\(O(1)\\) <code>popFirst()</code> 先頭要素を削除 \\(O(1)\\) <code>popLast()</code> 末尾要素を削除 \\(O(1)\\) <code>peekFirst()</code> 先頭要素にアクセス \\(O(1)\\) <code>peekLast()</code> 末尾要素にアクセス \\(O(1)\\) <p>同様に、プログラミング言語で実装された両端キュークラスを直接使用することができます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlin deque.py<pre><code>from collections import deque\n\n# 両端キューを初期化\ndeq: deque[int] = deque()\n\n# 要素をエンキュー\ndeq.append(2)      # 末尾に追加\ndeq.append(5)\ndeq.append(4)\ndeq.appendleft(3)  # 先頭に追加\ndeq.appendleft(1)\n\n# 要素にアクセス\nfront: int = deq[0]  # 先頭要素\nrear: int = deq[-1]  # 末尾要素\n\n# 要素をデキュー\npop_front: int = deq.popleft()  # 先頭要素をデキュー\npop_rear: int = deq.pop()       # 末尾要素をデキュー\n\n# 両端キューの長さを取得\nsize: int = len(deq)\n\n# 両端キューが空かどうかを確認\nis_empty: bool = len(deq) == 0\n</code></pre> deque.cpp<pre><code>/* 両端キューを初期化 */\ndeque&lt;int&gt; deque;\n\n/* 要素をエンキュー */\ndeque.push_back(2);   // 末尾に追加\ndeque.push_back(5);\ndeque.push_back(4);\ndeque.push_front(3);  // 先頭に追加\ndeque.push_front(1);\n\n/* 要素にアクセス */\nint front = deque.front(); // 先頭要素\nint back = deque.back();   // 末尾要素\n\n/* 要素をデキュー */\ndeque.pop_front();  // 先頭要素をデキュー\ndeque.pop_back();   // 末尾要素をデキュー\n\n/* 両端キューの長さを取得 */\nint size = deque.size();\n\n/* 両端キューが空かどうかを確認 */\nbool empty = deque.empty();\n</code></pre> deque.java<pre><code>/* 両端キューを初期化 */\nDeque&lt;Integer&gt; deque = new LinkedList&lt;&gt;();\n\n/* 要素をエンキュー */\ndeque.offerLast(2);   // 末尾に追加\ndeque.offerLast(5);\ndeque.offerLast(4);\ndeque.offerFirst(3);  // 先頭に追加\ndeque.offerFirst(1);\n\n/* 要素にアクセス */\nint peekFirst = deque.peekFirst();  // 先頭要素\nint peekLast = deque.peekLast();    // 末尾要素\n\n/* 要素をデキュー */\nint popFirst = deque.pollFirst();  // 先頭要素をデキュー\nint popLast = deque.pollLast();    // 末尾要素をデキュー\n\n/* 両端キューの長さを取得 */\nint size = deque.size();\n\n/* 両端キューが空かどうかを確認 */\nboolean isEmpty = deque.isEmpty();\n</code></pre> deque.cs<pre><code>/* 両端キューを初期化 */\n// C#では、LinkedListを両端キューとして使用\nLinkedList&lt;int&gt; deque = new();\n\n/* 要素をエンキュー */\ndeque.AddLast(2);   // 末尾に追加\ndeque.AddLast(5);\ndeque.AddLast(4);\ndeque.AddFirst(3);  // 先頭に追加\ndeque.AddFirst(1);\n\n/* 要素にアクセス */\nint peekFirst = deque.First.Value;  // 先頭要素\nint peekLast = deque.Last.Value;    // 末尾要素\n\n/* 要素をデキュー */\ndeque.RemoveFirst();  // 先頭要素をデキュー\ndeque.RemoveLast();   // 末尾要素をデキュー\n\n/* 両端キューの長さを取得 */\nint size = deque.Count;\n\n/* 両端キューが空かどうかを確認 */\nbool isEmpty = deque.Count == 0;\n</code></pre> deque_test.go<pre><code>/* 両端キューを初期化 */\n// Goでは、listを両端キューとして使用\ndeque := list.New()\n\n/* 要素をエンキュー */\ndeque.PushBack(2)      // 末尾に追加\ndeque.PushBack(5)\ndeque.PushBack(4)\ndeque.PushFront(3)     // 先頭に追加\ndeque.PushFront(1)\n\n/* 要素にアクセス */\nfront := deque.Front() // 先頭要素\nrear := deque.Back()   // 末尾要素\n\n/* 要素をデキュー */\ndeque.Remove(front)    // 先頭要素をデキュー\ndeque.Remove(rear)     // 末尾要素をデキュー\n\n/* 両端キューの長さを取得 */\nsize := deque.Len()\n\n/* 両端キューが空かどうかを確認 */\nisEmpty := deque.Len() == 0\n</code></pre> deque.swift<pre><code>/* 両端キューを初期化 */\n// Swiftには組み込みの両端キュークラスがないため、Arrayを両端キューとして使用\nvar deque: [Int] = []\n\n/* 要素をエンキュー */\ndeque.append(2) // 末尾に追加\ndeque.append(5)\ndeque.append(4)\ndeque.insert(3, at: 0) // 先頭に追加\ndeque.insert(1, at: 0)\n\n/* 要素にアクセス */\nlet peekFirst = deque.first! // 先頭要素\nlet peekLast = deque.last!   // 末尾要素\n\n/* 要素をデキュー */\n// Arrayを使用する場合、popFirstの計算量はO(n)\nlet popFirst = deque.removeFirst() // 先頭要素をデキュー\nlet popLast = deque.removeLast()   // 末尾要素をデキュー\n\n/* 両端キューの長さを取得 */\nlet size = deque.count\n\n/* 両端キューが空かどうかを確認 */\nlet isEmpty = deque.isEmpty\n</code></pre> deque.js<pre><code>/* 両端キューを初期化 */\n// JavaScriptには組み込みの両端キューがないため、Arrayを両端キューとして使用\nconst deque = [];\n\n/* 要素をエンキュー */\ndeque.push(2);\ndeque.push(5);\ndeque.push(4);\n// 注意：unshift()は配列のため時間計算量がO(n)\ndeque.unshift(3);\ndeque.unshift(1);\n\n/* 要素にアクセス */\nconst peekFirst = deque[0]; // 先頭要素\nconst peekLast = deque[deque.length - 1]; // 末尾要素\n\n/* 要素をデキュー */\n// 注意：shift()は配列のため時間計算量がO(n)\nconst popFront = deque.shift(); // 先頭要素をデキュー\nconst popBack = deque.pop();    // 末尾要素をデキュー\n\n/* 両端キューの長さを取得 */\nconst size = deque.length;\n\n/* 両端キューが空かどうかを確認 */\nconst isEmpty = size === 0;\n</code></pre> deque.ts<pre><code>/* 両端キューを初期化 */\n// TypeScriptには組み込みの両端キューがないため、Arrayを両端キューとして使用\nconst deque: number[] = [];\n\n/* 要素をエンキュー */\ndeque.push(2);\ndeque.push(5);\ndeque.push(4);\n// 注意：unshift()は配列のため時間計算量がO(n)\ndeque.unshift(3);\ndeque.unshift(1);\n\n/* 要素にアクセス */\nconst peekFirst: number = deque[0]; // 先頭要素\nconst peekLast: number = deque[deque.length - 1]; // 末尾要素\n\n/* 要素をデキュー */\n// 注意：shift()は配列のため時間計算量がO(n)\nconst popFront: number = deque.shift() as number; // 先頭要素をデキュー\nconst popBack: number = deque.pop() as number;    // 末尾要素をデキュー\n\n/* 両端キューの長さを取得 */\nconst size: number = deque.length;\n\n/* 両端キューが空かどうかを確認 */\nconst isEmpty: boolean = size === 0;\n</code></pre> deque.dart<pre><code>/* 両端キューを初期化 */\n// Dartでは、Queueが両端キューとして定義される\nQueue&lt;int&gt; deque = Queue&lt;int&gt;();\n\n/* 要素をエンキュー */\ndeque.addLast(2);  // 末尾に追加\ndeque.addLast(5);\ndeque.addLast(4);\ndeque.addFirst(3); // 先頭に追加\ndeque.addFirst(1);\n\n/* 要素にアクセス */\nint peekFirst = deque.first; // 先頭要素\nint peekLast = deque.last;   // 末尾要素\n\n/* 要素をデキュー */\nint popFirst = deque.removeFirst(); // 先頭要素をデキュー\nint popLast = deque.removeLast();   // 末尾要素をデキュー\n\n/* 両端キューの長さを取得 */\nint size = deque.length;\n\n/* 両端キューが空かどうかを確認 */\nbool isEmpty = deque.isEmpty;\n</code></pre> deque.rs<pre><code>/* 両端キューを初期化 */\nlet mut deque: VecDeque&lt;u32&gt; = VecDeque::new();\n\n/* 要素をエンキュー */\ndeque.push_back(2);  // 末尾に追加\ndeque.push_back(5);\ndeque.push_back(4);\ndeque.push_front(3); // 先頭に追加\ndeque.push_front(1);\n\n/* 要素にアクセス */\nif let Some(front) = deque.front() { // 先頭要素\n}\nif let Some(rear) = deque.back() {   // 末尾要素\n}\n\n/* 要素をデキュー */\nif let Some(pop_front) = deque.pop_front() { // 先頭要素をデキュー\n}\nif let Some(pop_rear) = deque.pop_back() {   // 末尾要素をデキュー\n}\n\n/* 両端キューの長さを取得 */\nlet size = deque.len();\n\n/* 両端キューが空かどうかを確認 */\nlet is_empty = deque.is_empty();\n</code></pre> deque.c<pre><code>// Cには組み込みの両端キューが提供されていません\n</code></pre> deque.kt<pre><code>\n</code></pre>","path":["第 5 章 &nbsp; スタックとキュー","5.3 &nbsp; 両端キュー"],"tags":[]},{"location":"chapter_stack_and_queue/deque/#532","level":2,"title":"5.3.2   両端キューの実装 *","text":"<p>両端キューの実装は通常のキューの実装と似ており、連結リストまたは配列を基盤となるデータ構造として使用できます。</p>","path":["第 5 章 &nbsp; スタックとキュー","5.3 &nbsp; 両端キュー"],"tags":[]},{"location":"chapter_stack_and_queue/deque/#1","level":3,"title":"1.   双方向連結リストに基づく実装","text":"<p>前節で、通常の単一連結リストを使ってキューを実装したことを思い出してください。これは先頭からの削除（デキュー操作に対応）と末尾への新しい要素の追加（エンキュー操作に対応）を便利に行えるためでした。</p> <p>両端キューでは、先頭と末尾の両方でエンキューとデキュー操作を実行できます。つまり、両端キューは逆方向の操作も実装する必要があります。このため、両端キューの基盤となるデータ構造として「双方向連結リスト」を使用します。</p> <p>下図に示すように、双方向連結リストの先頭ノードと末尾ノードをそれぞれ両端キューの前端と後端として扱い、両端でのノードの追加と削除機能を実装します。</p> LinkedListDequepushLast()pushFirst()popLast()popFirst() <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 5-8   双方向連結リストによる両端キューのエンキューとデキュー操作の実装 </p> <p>実装コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linkedlist_deque.py<pre><code>class ListNode:\n    \"\"\"双方向連結リストノード\"\"\"\n\n    def __init__(self, val: int):\n        \"\"\"コンストラクタ\"\"\"\n        self.val: int = val\n        self.next: ListNode | None = None  # 後続ノードへの参照\n        self.prev: ListNode | None = None  # 前駆ノードへの参照\n\nclass LinkedListDeque:\n    \"\"\"双方向連結リストベースの双端キュークラス\"\"\"\n\n    def __init__(self):\n        \"\"\"コンストラクタ\"\"\"\n        self._front: ListNode | None = None  # ヘッドノード front\n        self._rear: ListNode | None = None  # テールノード rear\n        self._size: int = 0  # 双端キューの長さ\n\n    def size(self) -&gt; int:\n        \"\"\"双端キューの長さを取得\"\"\"\n        return self._size\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"双端キューが空かどうかを判定\"\"\"\n        return self._size == 0\n\n    def push(self, num: int, is_front: bool):\n        \"\"\"エンキュー操作\"\"\"\n        node = ListNode(num)\n        # リストが空の場合、front と rear の両方を node に向ける\n        if self.is_empty():\n            self._front = self._rear = node\n        # 前端エンキュー操作\n        elif is_front:\n            # ノードをリストの先頭に追加\n            self._front.prev = node\n            node.next = self._front\n            self._front = node  # ヘッドノードを更新\n        # 後端エンキュー操作\n        else:\n            # ノードをリストの末尾に追加\n            self._rear.next = node\n            node.prev = self._rear\n            self._rear = node  # テールノードを更新\n        self._size += 1  # キューの長さを更新\n\n    def push_first(self, num: int):\n        \"\"\"前端エンキュー\"\"\"\n        self.push(num, True)\n\n    def push_last(self, num: int):\n        \"\"\"後端エンキュー\"\"\"\n        self.push(num, False)\n\n    def pop(self, is_front: bool) -&gt; int:\n        \"\"\"デキュー操作\"\"\"\n        if self.is_empty():\n            raise IndexError(\"Double-ended queue is empty\")\n        # 前端デキュー操作\n        if is_front:\n            val: int = self._front.val  # ヘッドノードの値を一時的に保存\n            # ヘッドノードを削除\n            fnext: ListNode | None = self._front.next\n            if fnext is not None:\n                fnext.prev = None\n                self._front.next = None\n            self._front = fnext  # ヘッドノードを更新\n        # 後端デキュー操作\n        else:\n            val: int = self._rear.val  # テールノードの値を一時的に保存\n            # テールノードを削除\n            rprev: ListNode | None = self._rear.prev\n            if rprev is not None:\n                rprev.next = None\n                self._rear.prev = None\n            self._rear = rprev  # テールノードを更新\n        self._size -= 1  # キューの長さを更新\n        return val\n\n    def pop_first(self) -&gt; int:\n        \"\"\"前端デキュー\"\"\"\n        return self.pop(True)\n\n    def pop_last(self) -&gt; int:\n        \"\"\"後端デキュー\"\"\"\n        return self.pop(False)\n\n    def peek_first(self) -&gt; int:\n        \"\"\"前端要素にアクセス\"\"\"\n        if self.is_empty():\n            raise IndexError(\"Double-ended queue is empty\")\n        return self._front.val\n\n    def peek_last(self) -&gt; int:\n        \"\"\"後端要素にアクセス\"\"\"\n        if self.is_empty():\n            raise IndexError(\"Double-ended queue is empty\")\n        return self._rear.val\n\n    def to_array(self) -&gt; list[int]:\n        \"\"\"出力用の配列を返す\"\"\"\n        node = self._front\n        res = [0] * self.size()\n        for i in range(self.size()):\n            res[i] = node.val\n            node = node.next\n        return res\n</code></pre> linkedlist_deque.cpp<pre><code>/* 双方向連結リストノード */\nstruct DoublyListNode {\n    int val;              // ノードの値\n    DoublyListNode *next; // 後続ノードへのポインタ\n    DoublyListNode *prev; // 前続ノードへのポインタ\n    DoublyListNode(int val) : val(val), prev(nullptr), next(nullptr) {\n    }\n};\n\n/* 双方向連結リストに基づく両端キュークラス */\nclass LinkedListDeque {\n  private:\n    DoublyListNode *front, *rear; // 先頭ノードfront、末尾ノードrear\n    int queSize = 0;              // 両端キューの長さ\n\n  public:\n    /* コンストラクタ */\n    LinkedListDeque() : front(nullptr), rear(nullptr) {\n    }\n\n    /* デストラクタ */\n    ~LinkedListDeque() {\n        // 連結リストを走査、ノードを削除、メモリを解放\n        DoublyListNode *pre, *cur = front;\n        while (cur != nullptr) {\n            pre = cur;\n            cur = cur-&gt;next;\n            delete pre;\n        }\n    }\n\n    /* 両端キューの長さを取得 */\n    int size() {\n        return queSize;\n    }\n\n    /* 両端キューが空かどうかを判定 */\n    bool isEmpty() {\n        return size() == 0;\n    }\n\n    /* エンキュー操作 */\n    void push(int num, bool isFront) {\n        DoublyListNode *node = new DoublyListNode(num);\n        // リストが空の場合、frontとrearの両方をnodeに向ける\n        if (isEmpty())\n            front = rear = node;\n        // 先頭エンキュー操作\n        else if (isFront) {\n            // ノードをリストの先頭に追加\n            front-&gt;prev = node;\n            node-&gt;next = front;\n            front = node; // 先頭ノードを更新\n        // 末尾エンキュー操作\n        } else {\n            // ノードをリストの末尾に追加\n            rear-&gt;next = node;\n            node-&gt;prev = rear;\n            rear = node; // 末尾ノードを更新\n        }\n        queSize++; // キュー長を更新\n    }\n\n    /* 先頭エンキュー */\n    void pushFirst(int num) {\n        push(num, true);\n    }\n\n    /* 末尾エンキュー */\n    void pushLast(int num) {\n        push(num, false);\n    }\n\n    /* デキュー操作 */\n    int pop(bool isFront) {\n        if (isEmpty())\n            throw out_of_range(\"Queue is empty\");\n        int val;\n        // 先頭デキュー操作\n        if (isFront) {\n            val = front-&gt;val; // 先頭ノードの値を一時保存\n            // 先頭ノードを削除\n            DoublyListNode *fNext = front-&gt;next;\n            if (fNext != nullptr) {\n                fNext-&gt;prev = nullptr;\n                front-&gt;next = nullptr;\n            }\n            delete front;\n            front = fNext; // 先頭ノードを更新\n        // 末尾デキュー操作\n        } else {\n            val = rear-&gt;val; // 末尾ノードの値を一時保存\n            // 末尾ノードを削除\n            DoublyListNode *rPrev = rear-&gt;prev;\n            if (rPrev != nullptr) {\n                rPrev-&gt;next = nullptr;\n                rear-&gt;prev = nullptr;\n            }\n            delete rear;\n            rear = rPrev; // 末尾ノードを更新\n        }\n        queSize--; // キュー長を更新\n        return val;\n    }\n\n    /* 先頭デキュー */\n    int popFirst() {\n        return pop(true);\n    }\n\n    /* 末尾デキュー */\n    int popLast() {\n        return pop(false);\n    }\n\n    /* 先頭要素にアクセス */\n    int peekFirst() {\n        if (isEmpty())\n            throw out_of_range(\"Double-ended queue is empty\");\n        return front-&gt;val;\n    }\n\n    /* 末尾要素にアクセス */\n    int peekLast() {\n        if (isEmpty())\n            throw out_of_range(\"Double-ended queue is empty\");\n        return rear-&gt;val;\n    }\n\n    /* 印刷用に配列を返却 */\n    vector&lt;int&gt; toVector() {\n        DoublyListNode *node = front;\n        vector&lt;int&gt; res(size());\n        for (int i = 0; i &lt; res.size(); i++) {\n            res[i] = node-&gt;val;\n            node = node-&gt;next;\n        }\n        return res;\n    }\n};\n</code></pre> linkedlist_deque.java<pre><code>/* 双方向連結リストノード */\nclass ListNode {\n    int val; // ノード値\n    ListNode next; // 後続ノードへの参照\n    ListNode prev; // 前任ノードへの参照\n\n    ListNode(int val) {\n        this.val = val;\n        prev = next = null;\n    }\n}\n\n/* 双方向連結リストに基づく両端キュークラス */\nclass LinkedListDeque {\n    private ListNode front, rear; // 先頭ノード front、末尾ノード rear\n    private int queSize = 0; // 両端キューの長さ\n\n    public LinkedListDeque() {\n        front = rear = null;\n    }\n\n    /* 両端キューの長さを取得 */\n    public int size() {\n        return queSize;\n    }\n\n    /* 両端キューが空かどうかを判定 */\n    public boolean isEmpty() {\n        return size() == 0;\n    }\n\n    /* エンキュー操作 */\n    private void push(int num, boolean isFront) {\n        ListNode node = new ListNode(num);\n        // リストが空の場合、front と rear の両方を node に指す\n        if (isEmpty())\n            front = rear = node;\n        // 先頭エンキュー操作\n        else if (isFront) {\n            // node をリストの先頭に追加\n            front.prev = node;\n            node.next = front;\n            front = node; // front を更新\n        // 末尾エンキュー操作\n        } else {\n            // node をリストの末尾に追加\n            rear.next = node;\n            node.prev = rear;\n            rear = node; // rear を更新\n        }\n        queSize++; // 長さを更新\n    }\n\n    /* 先頭エンキュー */\n    public void pushFirst(int num) {\n        push(num, true);\n    }\n\n    /* 末尾エンキュー */\n    public void pushLast(int num) {\n        push(num, false);\n    }\n\n    /* デキュー操作 */\n    private int pop(boolean isFront) {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        int val;\n        // 先頭デキュー操作\n        if (isFront) {\n            val = front.val; // 一時的に先頭ノード値を保存\n            // 次のノードを削除\n            ListNode fNext = front.next;\n            if (fNext != null) {\n                fNext.prev = null;\n                front.next = null;\n            }\n            front = fNext; // front を更新\n        // 末尾デキュー操作\n        } else {\n            val = rear.val; // 一時的に末尾ノード値を保存\n            // 前のノードを削除\n            ListNode rPrev = rear.prev;\n            if (rPrev != null) {\n                rPrev.next = null;\n                rear.prev = null;\n            }\n            rear = rPrev; // rear を更新\n        }\n        queSize--; // 長さを更新\n        return val;\n    }\n\n    /* 先頭デキュー */\n    public int popFirst() {\n        return pop(true);\n    }\n\n    /* 末尾デキュー */\n    public int popLast() {\n        return pop(false);\n    }\n\n    /* 先頭要素にアクセス */\n    public int peekFirst() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return front.val;\n    }\n\n    /* 末尾要素にアクセス */\n    public int peekLast() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return rear.val;\n    }\n\n    /* 配列を返す */\n    public int[] toArray() {\n        ListNode node = front;\n        int[] res = new int[size()];\n        for (int i = 0; i &lt; res.length; i++) {\n            res[i] = node.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_deque.cs<pre><code>[class]{ListNode}-[func]{}\n\n[class]{LinkedListDeque}-[func]{}\n</code></pre> linkedlist_deque.go<pre><code>[class]{linkedListDeque}-[func]{}\n</code></pre> linkedlist_deque.swift<pre><code>[class]{ListNode}-[func]{}\n\n[class]{LinkedListDeque}-[func]{}\n</code></pre> linkedlist_deque.js<pre><code>[class]{ListNode}-[func]{}\n\n[class]{LinkedListDeque}-[func]{}\n</code></pre> linkedlist_deque.ts<pre><code>[class]{ListNode}-[func]{}\n\n[class]{LinkedListDeque}-[func]{}\n</code></pre> linkedlist_deque.dart<pre><code>[class]{ListNode}-[func]{}\n\n[class]{LinkedListDeque}-[func]{}\n</code></pre> linkedlist_deque.rs<pre><code>[class]{ListNode}-[func]{}\n\n[class]{LinkedListDeque}-[func]{}\n</code></pre> linkedlist_deque.c<pre><code>[class]{DoublyListNode}-[func]{}\n\n[class]{LinkedListDeque}-[func]{}\n</code></pre> linkedlist_deque.kt<pre><code>[class]{ListNode}-[func]{}\n\n[class]{LinkedListDeque}-[func]{}\n</code></pre> linkedlist_deque.rb<pre><code>[class]{ListNode}-[func]{}\n\n[class]{LinkedListDeque}-[func]{}\n</code></pre>","path":["第 5 章 &nbsp; スタックとキュー","5.3 &nbsp; 両端キュー"],"tags":[]},{"location":"chapter_stack_and_queue/deque/#2","level":3,"title":"2.   配列に基づく実装","text":"<p>下図に示すように、配列でキューを実装するのと同様に、循環配列を使って両端キューを実装することもできます。</p> ArrayDequepushLast()pushFirst()popLast()popFirst() <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 5-9   配列による両端キューのエンキューとデキュー操作の実装 </p> <p>実装では「前端エンキュー」と「後端デキュー」のメソッドを追加するだけです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array_deque.py<pre><code>class ArrayDeque:\n    \"\"\"循環配列ベースの双端キュークラス\"\"\"\n\n    def __init__(self, capacity: int):\n        \"\"\"コンストラクタ\"\"\"\n        self._nums: list[int] = [0] * capacity\n        self._front: int = 0\n        self._size: int = 0\n\n    def capacity(self) -&gt; int:\n        \"\"\"双端キューの容量を取得\"\"\"\n        return len(self._nums)\n\n    def size(self) -&gt; int:\n        \"\"\"双端キューの長さを取得\"\"\"\n        return self._size\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"双端キューが空かどうかを判定\"\"\"\n        return self._size == 0\n\n    def index(self, i: int) -&gt; int:\n        \"\"\"循環配列のインデックスを計算\"\"\"\n        # モジュロ演算によって循環配列を実装\n        # i が配列の末尾を超えた場合、先頭に戻る\n        # i が配列の先頭を超えた場合、末尾に戻る\n        return (i + self.capacity()) % self.capacity()\n\n    def push_first(self, num: int):\n        \"\"\"前端エンキュー\"\"\"\n        if self._size == self.capacity():\n            print(\"双端キューが満杯です\")\n            return\n        # フロントポインタを左に1つ移動\n        # モジュロ演算によってフロントが配列の先頭を超えて末尾に戻ることを実装\n        self._front = self.index(self._front - 1)\n        # num を前端に追加\n        self._nums[self._front] = num\n        self._size += 1\n\n    def push_last(self, num: int):\n        \"\"\"後端エンキュー\"\"\"\n        if self._size == self.capacity():\n            print(\"双端キューが満杯です\")\n            return\n        # リアポインタを計算、リアインデックス + 1 を指す\n        rear = self.index(self._front + self._size)\n        # num を後端に追加\n        self._nums[rear] = num\n        self._size += 1\n\n    def pop_first(self) -&gt; int:\n        \"\"\"前端デキュー\"\"\"\n        num = self.peek_first()\n        # フロントポインタを1つ後ろに移動\n        self._front = self.index(self._front + 1)\n        self._size -= 1\n        return num\n\n    def pop_last(self) -&gt; int:\n        \"\"\"後端デキュー\"\"\"\n        num = self.peek_last()\n        self._size -= 1\n        return num\n\n    def peek_first(self) -&gt; int:\n        \"\"\"前端要素にアクセス\"\"\"\n        if self.is_empty():\n            raise IndexError(\"Double-ended queue is empty\")\n        return self._nums[self._front]\n\n    def peek_last(self) -&gt; int:\n        \"\"\"後端要素にアクセス\"\"\"\n        if self.is_empty():\n            raise IndexError(\"Double-ended queue is empty\")\n        # 後端要素のインデックスを計算\n        last = self.index(self._front + self._size - 1)\n        return self._nums[last]\n\n    def to_array(self) -&gt; list[int]:\n        \"\"\"出力用の配列を返す\"\"\"\n        # 有効な長さ範囲内の要素のみを変換\n        res = []\n        for i in range(self._size):\n            res.append(self._nums[self.index(self._front + i)])\n        return res\n</code></pre> array_deque.cpp<pre><code>/* 循環配列に基づく両端キュークラス */\nclass ArrayDeque {\n  private:\n    vector&lt;int&gt; nums; // 両端キューの要素を格納する配列\n    int front;        // 先頭ポインタ、先頭要素を指す\n    int queSize;      // 両端キューの長さ\n\n  public:\n    /* コンストラクタ */\n    ArrayDeque(int capacity) {\n        nums.resize(capacity);\n        front = queSize = 0;\n    }\n\n    /* 両端キューの容量を取得 */\n    int capacity() {\n        return nums.size();\n    }\n\n    /* 両端キューの長さを取得 */\n    int size() {\n        return queSize;\n    }\n\n    /* 両端キューが空かどうかを判定 */\n    bool isEmpty() {\n        return queSize == 0;\n    }\n\n    /* 循環配列のインデックスを計算 */\n    int index(int i) {\n        // 剰余演算で循環配列を実現\n        // iが配列の末尾を超えた場合、先頭に戻る\n        // iが配列の先頭を超えた場合、末尾に戻る\n        return (i + capacity()) % capacity();\n    }\n\n    /* 先頭エンキュー */\n    void pushFirst(int num) {\n        if (queSize == capacity()) {\n            cout &lt;&lt; \"Double-ended queue is full\" &lt;&lt; endl;\n            return;\n        }\n        // 先頭ポインタを1つ左に移動\n        // 剰余演算でfrontが配列の先頭を越えて末尾に戻ることを実現\n        front = index(front - 1);\n        // numを先頭に追加\n        nums[front] = num;\n        queSize++;\n    }\n\n    /* 末尾エンキュー */\n    void pushLast(int num) {\n        if (queSize == capacity()) {\n            cout &lt;&lt; \"Double-ended queue is full\" &lt;&lt; endl;\n            return;\n        }\n        // 末尾ポインタを計算、末尾インデックス + 1を指す\n        int rear = index(front + queSize);\n        // numを末尾に追加\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* 先頭デキュー */\n    int popFirst() {\n        int num = peekFirst();\n        // 先頭ポインタを1つ後ろに移動\n        front = index(front + 1);\n        queSize--;\n        return num;\n    }\n\n    /* 末尾デキュー */\n    int popLast() {\n        int num = peekLast();\n        queSize--;\n        return num;\n    }\n\n    /* 先頭要素にアクセス */\n    int peekFirst() {\n        if (isEmpty())\n            throw out_of_range(\"Double-ended queue is empty\");\n        return nums[front];\n    }\n\n    /* 末尾要素にアクセス */\n    int peekLast() {\n        if (isEmpty())\n            throw out_of_range(\"Double-ended queue is empty\");\n        // 末尾要素のインデックスを計算\n        int last = index(front + queSize - 1);\n        return nums[last];\n    }\n\n    /* 印刷用に配列を返却 */\n    vector&lt;int&gt; toVector() {\n        // 有効な長さ範囲内の要素のみを変換\n        vector&lt;int&gt; res(queSize);\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            res[i] = nums[index(j)];\n        }\n        return res;\n    }\n};\n</code></pre> array_deque.java<pre><code>/* 循環配列に基づく両端キュークラス */\nclass ArrayDeque {\n    private int[] nums; // 両端キューの要素を格納する配列\n    private int front; // 先頭ポインタ、先頭要素を指す\n    private int queSize; // 両端キューの長さ\n\n    /* コンストラクタ */\n    public ArrayDeque(int capacity) {\n        this.nums = new int[capacity];\n        front = queSize = 0;\n    }\n\n    /* 両端キューの容量を取得 */\n    public int capacity() {\n        return nums.length;\n    }\n\n    /* 両端キューの長さを取得 */\n    public int size() {\n        return queSize;\n    }\n\n    /* 両端キューが空かどうかを判定 */\n    public boolean isEmpty() {\n        return queSize == 0;\n    }\n\n    /* 循環配列インデックスを計算 */\n    private int index(int i) {\n        // モジュロ演算により循環配列を実装\n        // i が配列の末尾を超える場合、先頭に戻る\n        // i が配列の先頭を超える場合、末尾に戻る\n        return (i + capacity()) % capacity();\n    }\n\n    /* 先頭エンキュー */\n    public void pushFirst(int num) {\n        if (queSize == capacity()) {\n            System.out.println(\"両端キューが満杯です\");\n            return;\n        }\n        // 先頭ポインタを左に移動し、境界を越える場合は配列の末尾に回る\n        front = index(front - 1);\n        // 先頭に num を追加\n        nums[front] = num;\n        queSize++;\n    }\n\n    /* 末尾エンキュー */\n    public void pushLast(int num) {\n        if (queSize == capacity()) {\n            System.out.println(\"両端キューが満杯です\");\n            return;\n        }\n        // 末尾ポインタを計算し、末尾に要素を追加\n        int rear = index(front + queSize);\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* 先頭デキュー */\n    public int popFirst() {\n        int num = peekFirst();\n        // 先頭ポインタを右に移動\n        front = index(front + 1);\n        queSize--;\n        return num;\n    }\n\n    /* 末尾デキュー */\n    public int popLast() {\n        int num = peekLast();\n        queSize--;\n        return num;\n    }\n\n    /* 先頭要素にアクセス */\n    public int peekFirst() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return nums[front];\n    }\n\n    /* 末尾要素にアクセス */\n    public int peekLast() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        // 末尾要素のインデックスを計算\n        int last = index(front + queSize - 1);\n        return nums[last];\n    }\n\n    /* 配列を返す */\n    public int[] toArray() {\n        // front から開始して queSize 個の要素のみをコピー\n        int[] res = new int[queSize];\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            res[i] = nums[index(j)];\n        }\n        return res;\n    }\n}\n</code></pre> array_deque.cs<pre><code>[class]{ArrayDeque}-[func]{}\n</code></pre> array_deque.go<pre><code>[class]{arrayDeque}-[func]{}\n</code></pre> array_deque.swift<pre><code>[class]{ArrayDeque}-[func]{}\n</code></pre> array_deque.js<pre><code>[class]{ArrayDeque}-[func]{}\n</code></pre> array_deque.ts<pre><code>[class]{ArrayDeque}-[func]{}\n</code></pre> array_deque.dart<pre><code>[class]{ArrayDeque}-[func]{}\n</code></pre> array_deque.rs<pre><code>[class]{ArrayDeque}-[func]{}\n</code></pre> array_deque.c<pre><code>[class]{ArrayDeque}-[func]{}\n</code></pre> array_deque.kt<pre><code>[class]{ArrayDeque}-[func]{}\n</code></pre> array_deque.rb<pre><code>[class]{ArrayDeque}-[func]{}\n</code></pre>","path":["第 5 章 &nbsp; スタックとキュー","5.3 &nbsp; 両端キュー"],"tags":[]},{"location":"chapter_stack_and_queue/deque/#533","level":2,"title":"5.3.3   両端キューの応用","text":"<p>両端キューはスタックとキューの両方のロジックを組み合わせているため、それぞれのすべてのユースケースを実装でき、より大きな柔軟性を提供します。</p> <p>ソフトウェアの「元に戻す」機能は通常スタックを使って実装されることを知っています：システムは各変更操作をスタックに<code>push</code>し、次に<code>pop</code>して元に戻すことを実装します。しかし、システムリソースの制限を考慮して、ソフトウェアは元に戻すステップの数を制限することがよくあります（例えば、最後の50ステップのみを許可）。スタックの長さが50を超えた場合、ソフトウェアはスタックの底部（キューの前端）で削除操作を実行する必要があります。しかし、通常のスタックではこの機能を実行できないため、両端キューが必要になります。「元に戻す」のコアロジックは依然としてスタックの後入れ先出し原則に従いますが、両端キューはより柔軟にいくつかの追加ロジックを実装できることに注意してください。</p>","path":["第 5 章 &nbsp; スタックとキュー","5.3 &nbsp; 両端キュー"],"tags":[]},{"location":"chapter_stack_and_queue/queue/","level":1,"title":"5.2   キュー","text":"<p>キューは、先入先出（FIFO）ルールに従う線形データ構造です。名前が示すように、キューは行列の現象をシミュレートし、新参者は列の後ろに並び、前の人が最初に列を離れます。</p> <p>下図に示すように、キューの前面を「ヘッド」、後面を「テール」と呼びます。キューの後ろに要素を追加する操作を「エンキュー」、前から要素を削除する操作を「デキュー」と呼びます。</p> <p></p> <p> 図 5-4   キューの先入先出ルール </p>","path":["第 5 章 &nbsp; スタックとキュー","5.2 &nbsp; キュー"],"tags":[]},{"location":"chapter_stack_and_queue/queue/#521","level":2,"title":"5.2.1   キューの一般的な操作","text":"<p>キューの一般的な操作を下表に示します。メソッド名はプログラミング言語によって異なる場合があることに注意してください。ここでは、スタックで使用したのと同じ命名規則を使用します。</p> <p> 表 5-2   キュー操作の効率 </p> メソッド名 説明 時間計算量 <code>push()</code> 要素をエンキュー、テールに追加 \\(O(1)\\) <code>pop()</code> ヘッド要素をデキュー \\(O(1)\\) <code>peek()</code> ヘッド要素にアクセス \\(O(1)\\) <p>プログラミング言語で用意されているキュークラスを直接使用できます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlin queue.py<pre><code>from collections import deque\n\n# キューを初期化\n# Pythonでは、一般的にdequeクラスをキューとして使用します\n# queue.Queue()は純粋なキュークラスですが、使いにくいため推奨されません\nque: deque[int] = deque()\n\n# 要素をエンキュー\nque.append(1)\nque.append(3)\nque.append(2)\nque.append(5)\nque.append(4)\n\n# 最初の要素にアクセス\nfront: int = que[0]\n\n# 要素をデキュー\npop: int = que.popleft()\n\n# キューの長さを取得\nsize: int = len(que)\n\n# キューが空かどうかチェック\nis_empty: bool = len(que) == 0\n</code></pre> queue.cpp<pre><code>/* キューを初期化 */\nqueue&lt;int&gt; queue;\n\n/* 要素をエンキュー */\nqueue.push(1);\nqueue.push(3);\nqueue.push(2);\nqueue.push(5);\nqueue.push(4);\n\n/* 最初の要素にアクセス */\nint front = queue.front();\n\n/* 要素をデキュー */\nqueue.pop();\n\n/* キューの長さを取得 */\nint size = queue.size();\n\n/* キューが空かどうかチェック */\nbool empty = queue.empty();\n</code></pre> queue.java<pre><code>/* キューを初期化 */\nQueue&lt;Integer&gt; queue = new LinkedList&lt;&gt;();\n\n/* 要素をエンキュー */\nqueue.offer(1);\nqueue.offer(3);\nqueue.offer(2);\nqueue.offer(5);\nqueue.offer(4);\n\n/* 最初の要素にアクセス */\nint peek = queue.peek();\n\n/* 要素をデキュー */\nint pop = queue.poll();\n\n/* キューの長さを取得 */\nint size = queue.size();\n\n/* キューが空かどうかチェック */\nboolean isEmpty = queue.isEmpty();\n</code></pre> queue.cs<pre><code>/* キューを初期化 */\nQueue&lt;int&gt; queue = new();\n\n/* 要素をエンキュー */\nqueue.Enqueue(1);\nqueue.Enqueue(3);\nqueue.Enqueue(2);\nqueue.Enqueue(5);\nqueue.Enqueue(4);\n\n/* 最初の要素にアクセス */\nint peek = queue.Peek();\n\n/* 要素をデキュー */\nint pop = queue.Dequeue();\n\n/* キューの長さを取得 */\nint size = queue.Count;\n\n/* キューが空かどうかチェック */\nbool isEmpty = queue.Count == 0;\n</code></pre> queue_test.go<pre><code>/* キューを初期化 */\n// Goでは、listをキューとして使用\nqueue := list.New()\n\n/* 要素をエンキュー */\nqueue.PushBack(1)\nqueue.PushBack(3)\nqueue.PushBack(2)\nqueue.PushBack(5)\nqueue.PushBack(4)\n\n/* 最初の要素にアクセス */\npeek := queue.Front()\n\n/* 要素をデキュー */\npop := queue.Front()\nqueue.Remove(pop)\n\n/* キューの長さを取得 */\nsize := queue.Len()\n\n/* キューが空かどうかチェック */\nisEmpty := queue.Len() == 0\n</code></pre> queue.swift<pre><code>/* キューを初期化 */\n// Swiftには組み込みのキュークラスがないため、Arrayをキューとして使用\nvar queue: [Int] = []\n\n/* 要素をエンキュー */\nqueue.append(1)\nqueue.append(3)\nqueue.append(2)\nqueue.append(5)\nqueue.append(4)\n\n/* 最初の要素にアクセス */\nlet peek = queue.first!\n\n/* 要素をデキュー */\n// 配列なので、removeFirstの計算量はO(n)\nlet pool = queue.removeFirst()\n\n/* キューの長さを取得 */\nlet size = queue.count\n\n/* キューが空かどうかチェック */\nlet isEmpty = queue.isEmpty\n</code></pre> queue.js<pre><code>/* キューを初期化 */\n// JavaScriptには組み込みのキューがないため、Arrayをキューとして使用\nconst queue = [];\n\n/* 要素をエンキュー */\nqueue.push(1);\nqueue.push(3);\nqueue.push(2);\nqueue.push(5);\nqueue.push(4);\n\n/* 最初の要素にアクセス */\nconst peek = queue[0];\n\n/* 要素をデキュー */\n// 基礎構造が配列なので、shift()メソッドの時間計算量はO(n)\nconst pop = queue.shift();\n\n/* キューの長さを取得 */\nconst size = queue.length;\n\n/* キューが空かどうかチェック */\nconst empty = queue.length === 0;\n</code></pre> queue.ts<pre><code>/* キューを初期化 */\n// TypeScriptには組み込みのキューがないため、Arrayをキューとして使用\nconst queue: number[] = [];\n\n/* 要素をエンキュー */\nqueue.push(1);\nqueue.push(3);\nqueue.push(2);\nqueue.push(5);\nqueue.push(4);\n\n/* 最初の要素にアクセス */\nconst peek = queue[0];\n\n/* 要素をデキュー */\n// 基礎構造が配列なので、shift()メソッドの時間計算量はO(n)\nconst pop = queue.shift();\n\n/* キューの長さを取得 */\nconst size = queue.length;\n\n/* キューが空かどうかチェック */\nconst empty = queue.length === 0;\n</code></pre> queue.dart<pre><code>/* キューを初期化 */\n// DartのQueueクラスは双方向キューですが、キューとして使用できます\nQueue&lt;int&gt; queue = Queue();\n\n/* 要素をエンキュー */\nqueue.add(1);\nqueue.add(3);\nqueue.add(2);\nqueue.add(5);\nqueue.add(4);\n\n/* 最初の要素にアクセス */\nint peek = queue.first;\n\n/* 要素をデキュー */\nint pop = queue.removeFirst();\n\n/* キューの長さを取得 */\nint size = queue.length;\n\n/* キューが空かどうかチェック */\nbool isEmpty = queue.isEmpty;\n</code></pre> queue.rs<pre><code>/* 双方向キューを初期化 */\n// Rustでは、双方向キューを通常のキューとして使用\nlet mut deque: VecDeque&lt;u32&gt; = VecDeque::new();\n\n/* 要素をエンキュー */\ndeque.push_back(1);\ndeque.push_back(3);\ndeque.push_back(2);\ndeque.push_back(5);\ndeque.push_back(4);\n\n/* 最初の要素にアクセス */\nif let Some(front) = deque.front() {\n}\n\n/* 要素をデキュー */\nif let Some(pop) = deque.pop_front() {\n}\n\n/* キューの長さを取得 */\nlet size = deque.len();\n\n/* キューが空かどうかチェック */\nlet is_empty = deque.is_empty();\n</code></pre> queue.c<pre><code>// Cは組み込みのキューを提供していません\n</code></pre> queue.kt<pre><code>\n</code></pre>","path":["第 5 章 &nbsp; スタックとキュー","5.2 &nbsp; キュー"],"tags":[]},{"location":"chapter_stack_and_queue/queue/#522","level":2,"title":"5.2.2   キューの実装","text":"<p>キューを実装するには、一方の端で要素を追加し、もう一方の端で要素を削除できるデータ構造が必要です。連結リストと配列の両方がこの要件を満たします。</p>","path":["第 5 章 &nbsp; スタックとキュー","5.2 &nbsp; キュー"],"tags":[]},{"location":"chapter_stack_and_queue/queue/#1","level":3,"title":"1.   連結リストベースの実装","text":"<p>下図に示すように、連結リストの「ヘッドノード」と「テールノード」をそれぞれキューの「フロント」と「リア」と考えることができます。ノードは後ろでのみ追加でき、前でのみ削除できるように規定されています。</p> LinkedListQueuepush()pop() <p></p> <p></p> <p></p> <p> 図 5-5   連結リストによるキュー実装のエンキューとデキュー操作 </p> <p>以下は、連結リストを使用してキューを実装するコードです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linkedlist_queue.py<pre><code>class LinkedListQueue:\n    \"\"\"連結リストベースのキュークラス\"\"\"\n\n    def __init__(self):\n        \"\"\"コンストラクタ\"\"\"\n        self._front: ListNode | None = None  # ヘッドノード front\n        self._rear: ListNode | None = None  # テールノード rear\n        self._size: int = 0\n\n    def size(self) -&gt; int:\n        \"\"\"キューの長さを取得\"\"\"\n        return self._size\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"キューが空かどうかを判定\"\"\"\n        return self._size == 0\n\n    def push(self, num: int):\n        \"\"\"エンキュー\"\"\"\n        # テールノードの後ろに num を追加\n        node = ListNode(num)\n        # キューが空の場合、ヘッドとテールノードの両方をそのノードに向ける\n        if self._front is None:\n            self._front = node\n            self._rear = node\n        # キューが空でない場合、そのノードをテールノードの後ろに追加\n        else:\n            self._rear.next = node\n            self._rear = node\n        self._size += 1\n\n    def pop(self) -&gt; int:\n        \"\"\"デキュー\"\"\"\n        num = self.peek()\n        # ヘッドノードを削除\n        self._front = self._front.next\n        self._size -= 1\n        return num\n\n    def peek(self) -&gt; int:\n        \"\"\"フロント要素にアクセス\"\"\"\n        if self.is_empty():\n            raise IndexError(\"Queue is empty\")\n        return self._front.val\n\n    def to_list(self) -&gt; list[int]:\n        \"\"\"出力用のリストに変換\"\"\"\n        queue = []\n        temp = self._front\n        while temp:\n            queue.append(temp.val)\n            temp = temp.next\n        return queue\n</code></pre> linkedlist_queue.cpp<pre><code>/* 連結リストに基づくキュークラス */\nclass LinkedListQueue {\n  private:\n    ListNode *front, *rear; // 先頭ノードfront、末尾ノードrear\n    int queSize;\n\n  public:\n    LinkedListQueue() {\n        front = nullptr;\n        rear = nullptr;\n        queSize = 0;\n    }\n\n    ~LinkedListQueue() {\n        // 連結リストを走査、ノードを削除、メモリを解放\n        freeMemoryLinkedList(front);\n    }\n\n    /* キューの長さを取得 */\n    int size() {\n        return queSize;\n    }\n\n    /* キューが空かどうかを判定 */\n    bool isEmpty() {\n        return queSize == 0;\n    }\n\n    /* エンキュー */\n    void push(int num) {\n        // 末尾ノードの後ろにnumを追加\n        ListNode *node = new ListNode(num);\n        // キューが空の場合、先頭と末尾ノードの両方をそのノードに向ける\n        if (front == nullptr) {\n            front = node;\n            rear = node;\n        }\n        // キューが空でない場合、そのノードを末尾ノードの後ろに追加\n        else {\n            rear-&gt;next = node;\n            rear = node;\n        }\n        queSize++;\n    }\n\n    /* デキュー */\n    int pop() {\n        int num = peek();\n        // 先頭ノードを削除\n        ListNode *tmp = front;\n        front = front-&gt;next;\n        // メモリを解放\n        delete tmp;\n        queSize--;\n        return num;\n    }\n\n    /* 先頭要素にアクセス */\n    int peek() {\n        if (size() == 0)\n            throw out_of_range(\"Queue is empty\");\n        return front-&gt;val;\n    }\n\n    /* 連結リストをVectorに変換して返却 */\n    vector&lt;int&gt; toVector() {\n        ListNode *node = front;\n        vector&lt;int&gt; res(size());\n        for (int i = 0; i &lt; res.size(); i++) {\n            res[i] = node-&gt;val;\n            node = node-&gt;next;\n        }\n        return res;\n    }\n};\n</code></pre> linkedlist_queue.java<pre><code>/* 連結リストに基づくキュークラス */\nclass LinkedListQueue {\n    private ListNode front, rear; // 先頭ノード front、末尾ノード rear\n    private int queSize = 0;\n\n    public LinkedListQueue() {\n        front = null;\n        rear = null;\n    }\n\n    /* キューの長さを取得 */\n    public int size() {\n        return queSize;\n    }\n\n    /* キューが空かどうかを判定 */\n    public boolean isEmpty() {\n        return size() == 0;\n    }\n\n    /* エンキュー */\n    public void push(int num) {\n        // 末尾ノードの後ろに num を追加\n        ListNode node = new ListNode(num);\n        // キューが空の場合、先頭と末尾ノードの両方をそのノードにポイント\n        if (front == null) {\n            front = node;\n            rear = node;\n        // キューが空でない場合、そのノードを末尾ノードの後ろに追加\n        } else {\n            rear.next = node;\n            rear = node;\n        }\n        queSize++;\n    }\n\n    /* デキュー */\n    public int pop() {\n        int num = peek();\n        // 先頭ノードを削除\n        front = front.next;\n        queSize--;\n        return num;\n    }\n\n    /* 先頭要素にアクセス */\n    public int peek() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return front.val;\n    }\n\n    /* 連結リストを配列に変換して返す */\n    public int[] toArray() {\n        ListNode node = front;\n        int[] res = new int[size()];\n        for (int i = 0; i &lt; res.length; i++) {\n            res[i] = node.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_queue.cs<pre><code>[class]{LinkedListQueue}-[func]{}\n</code></pre> linkedlist_queue.go<pre><code>[class]{linkedListQueue}-[func]{}\n</code></pre> linkedlist_queue.swift<pre><code>[class]{LinkedListQueue}-[func]{}\n</code></pre> linkedlist_queue.js<pre><code>[class]{LinkedListQueue}-[func]{}\n</code></pre> linkedlist_queue.ts<pre><code>[class]{LinkedListQueue}-[func]{}\n</code></pre> linkedlist_queue.dart<pre><code>[class]{LinkedListQueue}-[func]{}\n</code></pre> linkedlist_queue.rs<pre><code>[class]{LinkedListQueue}-[func]{}\n</code></pre> linkedlist_queue.c<pre><code>[class]{LinkedListQueue}-[func]{}\n</code></pre> linkedlist_queue.kt<pre><code>[class]{LinkedListQueue}-[func]{}\n</code></pre> linkedlist_queue.rb<pre><code>[class]{LinkedListQueue}-[func]{}\n</code></pre>","path":["第 5 章 &nbsp; スタックとキュー","5.2 &nbsp; キュー"],"tags":[]},{"location":"chapter_stack_and_queue/queue/#2","level":3,"title":"2.   配列ベースの実装","text":"<p>配列の最初の要素を削除する時間計算量は\\(O(n)\\)で、デキュー操作が非効率になります。しかし、この問題は以下のように巧妙に回避できます。</p> <p>変数<code>front</code>を使用してフロント要素のインデックスを示し、変数<code>size</code>を維持してキューの長さを記録します。<code>rear = front + size</code>を定義し、これはテール要素の直後の位置を指します。</p> <p>この設計により、配列内の要素の有効な間隔は<code>[front, rear - 1]</code>です。各操作の実装方法を下図に示します。</p> <ul> <li>エンキュー操作：入力要素を<code>rear</code>インデックスに割り当て、<code>size</code>を1増加させます。</li> <li>デキュー操作：単に<code>front</code>を1増加させ、<code>size</code>を1減少させます。</li> </ul> <p>エンキューとデキュー操作は両方とも単一の操作のみを必要とし、それぞれの時間計算量は\\(O(1)\\)です。</p> ArrayQueuepush()pop() <p></p> <p></p> <p></p> <p> 図 5-6   配列によるキュー実装のエンキューとデキュー操作 </p> <p>問題に気づくかもしれません：エンキューとデキュー操作が継続的に実行されると、<code>front</code>と<code>rear</code>の両方が右に移動し、最終的に配列の末尾に到達してそれ以上移動できなくなります。これを解決するために、配列を「循環配列」として扱い、配列の末尾を先頭に接続します。</p> <p>循環配列では、<code>front</code>または<code>rear</code>が末尾に到達すると、配列の先頭にループバックする必要があります。この循環パターンは、以下のコードに示すように「剰余演算」で実現できます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array_queue.py<pre><code>class ArrayQueue:\n    \"\"\"循環配列ベースのキュークラス\"\"\"\n\n    def __init__(self, size: int):\n        \"\"\"コンストラクタ\"\"\"\n        self._nums: list[int] = [0] * size  # キュー要素を格納する配列\n        self._front: int = 0  # フロントポインタ、フロント要素を指す\n        self._size: int = 0  # キューの長さ\n\n    def capacity(self) -&gt; int:\n        \"\"\"キューの容量を取得\"\"\"\n        return len(self._nums)\n\n    def size(self) -&gt; int:\n        \"\"\"キューの長さを取得\"\"\"\n        return self._size\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"キューが空かどうかを判定\"\"\"\n        return self._size == 0\n\n    def push(self, num: int):\n        \"\"\"エンキュー\"\"\"\n        if self._size == self.capacity():\n            raise IndexError(\"Queue is full\")\n        # リアポインタを計算、リアインデックス + 1 を指す\n        # モジュロ演算を使用してリアポインタを配列の末尾から先頭に戻す\n        rear: int = (self._front + self._size) % self.capacity()\n        # num をリアに追加\n        self._nums[rear] = num\n        self._size += 1\n\n    def pop(self) -&gt; int:\n        \"\"\"デキュー\"\"\"\n        num: int = self.peek()\n        # フロントポインタを1つ後ろに移動、末尾を超えた場合は配列の先頭に戻る\n        self._front = (self._front + 1) % self.capacity()\n        self._size -= 1\n        return num\n\n    def peek(self) -&gt; int:\n        \"\"\"フロント要素にアクセス\"\"\"\n        if self.is_empty():\n            raise IndexError(\"Queue is empty\")\n        return self._nums[self._front]\n\n    def to_list(self) -&gt; list[int]:\n        \"\"\"出力用の配列を返す\"\"\"\n        res = [0] * self.size()\n        j: int = self._front\n        for i in range(self.size()):\n            res[i] = self._nums[(j % self.capacity())]\n            j += 1\n        return res\n</code></pre> array_queue.cpp<pre><code>/* 循環配列に基づくキュークラス */\nclass ArrayQueue {\n  private:\n    int *nums;       // キュー要素を格納する配列\n    int front;       // 先頭ポインタ、先頭要素を指す\n    int queSize;     // キューの長さ\n    int queCapacity; // キューの容量\n\n  public:\n    ArrayQueue(int capacity) {\n        // 配列を初期化\n        nums = new int[capacity];\n        queCapacity = capacity;\n        front = queSize = 0;\n    }\n\n    ~ArrayQueue() {\n        delete[] nums;\n    }\n\n    /* キューの容量を取得 */\n    int capacity() {\n        return queCapacity;\n    }\n\n    /* キューの長さを取得 */\n    int size() {\n        return queSize;\n    }\n\n    /* キューが空かどうかを判定 */\n    bool isEmpty() {\n        return size() == 0;\n    }\n\n    /* エンキュー */\n    void push(int num) {\n        if (queSize == queCapacity) {\n            cout &lt;&lt; \"Queue is full\" &lt;&lt; endl;\n            return;\n        }\n        // 末尾ポインタを計算、末尾インデックス + 1を指す\n        // 剰余演算を使用して末尾ポインタが配列の末尾から先頭に戻るようにラップ\n        int rear = (front + queSize) % queCapacity;\n        // numを末尾に追加\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* デキュー */\n    int pop() {\n        int num = peek();\n        // 先頭ポインタを1つ後ろに移動、末尾を超えた場合は配列の先頭に戻る\n        front = (front + 1) % queCapacity;\n        queSize--;\n        return num;\n    }\n\n    /* 先頭要素にアクセス */\n    int peek() {\n        if (isEmpty())\n            throw out_of_range(\"Queue is empty\");\n        return nums[front];\n    }\n\n    /* 配列をVectorに変換して返却 */\n    vector&lt;int&gt; toVector() {\n        // 有効な長さ範囲内の要素のみを変換\n        vector&lt;int&gt; arr(queSize);\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            arr[i] = nums[j % queCapacity];\n        }\n        return arr;\n    }\n};\n</code></pre> array_queue.java<pre><code>/* 配列に基づくキュークラス */\nclass ArrayQueue {\n    private int[] nums; // 要素を格納する配列\n    private int front; // キューヘッドポインタ、最初の要素を指す\n    private int queSize; // キューの長さ\n\n    public ArrayQueue(int capacity) {\n        nums = new int[capacity];\n        front = queSize = 0;\n    }\n\n    /* キューの容量を取得 */\n    public int capacity() {\n        return nums.length;\n    }\n\n    /* キューの長さを取得 */\n    public int size() {\n        return queSize;\n    }\n\n    /* キューが空かどうかを判定 */\n    public boolean isEmpty() {\n        return queSize == 0;\n    }\n\n    /* エンキュー */\n    public void push(int num) {\n        if (queSize == capacity()) {\n            System.out.println(\"キューが満杯です\");\n            return;\n        }\n        // リアポインタを計算：front + queSize\n        // モジュロ操作により rear が配列の長さを超えることを回避\n        int rear = (front + queSize) % capacity();\n        // 要素をキューリアに追加\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* デキュー */\n    public int pop() {\n        int num = peek();\n        // キューヘッドポインタを後ろに1つ移動、モジュロ操作により範囲を超えることを回避\n        front = (front + 1) % capacity();\n        queSize--;\n        return num;\n    }\n\n    /* キューヘッド要素にアクセス */\n    public int peek() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return nums[front];\n    }\n\n    /* 配列を返す */\n    public int[] toArray() {\n        // front から開始して queSize 個の要素のみをコピー\n        int[] res = new int[queSize];\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            res[i] = nums[j % capacity()];\n        }\n        return res;\n    }\n}\n</code></pre> array_queue.cs<pre><code>[class]{ArrayQueue}-[func]{}\n</code></pre> array_queue.go<pre><code>[class]{arrayQueue}-[func]{}\n</code></pre> array_queue.swift<pre><code>[class]{ArrayQueue}-[func]{}\n</code></pre> array_queue.js<pre><code>[class]{ArrayQueue}-[func]{}\n</code></pre> array_queue.ts<pre><code>[class]{ArrayQueue}-[func]{}\n</code></pre> array_queue.dart<pre><code>[class]{ArrayQueue}-[func]{}\n</code></pre> array_queue.rs<pre><code>[class]{ArrayQueue}-[func]{}\n</code></pre> array_queue.c<pre><code>[class]{ArrayQueue}-[func]{}\n</code></pre> array_queue.kt<pre><code>[class]{ArrayQueue}-[func]{}\n</code></pre> array_queue.rb<pre><code>[class]{ArrayQueue}-[func]{}\n</code></pre> <p>上記のキュー実装にはまだ制限があります：長さが固定されています。しかし、この問題は解決が困難ではありません。配列を必要に応じて自動拡張できる動的配列に置き換えることができます。興味のある読者は自分で実装してみてください。</p> <p>2つの実装の比較はスタックの場合と一貫しており、ここでは繰り返しません。</p>","path":["第 5 章 &nbsp; スタックとキュー","5.2 &nbsp; キュー"],"tags":[]},{"location":"chapter_stack_and_queue/queue/#523","level":2,"title":"5.2.3   キューの典型的な応用","text":"<ul> <li>Amazonの注文：買い物客が注文を行った後、これらの注文はキューに参加し、システムは順番に処理します。独身の日などのイベント中は、短時間で大量の注文が生成され、高い同時実行性がエンジニアにとって重要な課題となります。</li> <li>様々なToDoリスト：「先着順」機能が必要なシナリオ、例えばプリンターのタスクキューやレストランの配達キューなど、キューで処理順序を効果的に維持できます。</li> </ul>","path":["第 5 章 &nbsp; スタックとキュー","5.2 &nbsp; キュー"],"tags":[]},{"location":"chapter_stack_and_queue/stack/","level":1,"title":"5.1   スタック","text":"<p>スタックは、後入先出（LIFO）の原則に従う線形データ構造です。</p> <p>スタックをテーブル上の皿の山に例えることができます。底の皿にアクセスするには、まず上の皿を取り除く必要があります。皿を様々な種類の要素（整数、文字、オブジェクトなど）に置き換えることで、スタックと呼ばれるデータ構造を得ることができます。</p> <p>下図に示すように、要素の山の上部を「スタックのトップ」、下部を「スタックのボトム」と呼びます。スタックのトップに要素を追加する操作を「プッシュ」、トップ要素を削除する操作を「ポップ」と呼びます。</p> <p></p> <p> 図 5-1   スタックの後入先出ルール </p>","path":["第 5 章 &nbsp; スタックとキュー","5.1 &nbsp; スタック"],"tags":[]},{"location":"chapter_stack_and_queue/stack/#511","level":2,"title":"5.1.1   スタックの一般的な操作","text":"<p>スタックの一般的な操作を下表に示します。具体的なメソッド名は使用するプログラミング言語によって異なります。ここでは、例として<code>push()</code>、<code>pop()</code>、<code>peek()</code>を使用します。</p> <p> 表 5-1   スタック操作の効率 </p> メソッド 説明 時間計算量 <code>push()</code> 要素をスタックにプッシュ（トップに追加） \\(O(1)\\) <code>pop()</code> スタックからトップ要素をポップ \\(O(1)\\) <code>peek()</code> スタックのトップ要素にアクセス \\(O(1)\\) <p>通常、プログラミング言語に組み込まれているスタッククラスを直接使用できます。ただし、一部の言語では具体的にスタッククラスを提供していない場合があります。これらの場合、言語の「配列」または「連結リスト」をスタックとして使用し、プログラムでスタックロジックに関連しない操作を無視できます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlin stack.py<pre><code># スタックを初期化\n# Pythonには組み込みのスタッククラスがないため、listをスタックとして使用\nstack: list[int] = []\n\n# 要素をスタックにプッシュ\nstack.append(1)\nstack.append(3)\nstack.append(2)\nstack.append(5)\nstack.append(4)\n\n# スタックのトップ要素にアクセス\npeek: int = stack[-1]\n\n# スタックから要素をポップ\npop: int = stack.pop()\n\n# スタックの長さを取得\nsize: int = len(stack)\n\n# スタックが空かどうかチェック\nis_empty: bool = len(stack) == 0\n</code></pre> stack.cpp<pre><code>/* スタックを初期化 */\nstack&lt;int&gt; stack;\n\n/* 要素をスタックにプッシュ */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n\n/* スタックのトップ要素にアクセス */\nint top = stack.top();\n\n/* スタックから要素をポップ */\nstack.pop(); // 戻り値なし\n\n/* スタックの長さを取得 */\nint size = stack.size();\n\n/* スタックが空かどうかチェック */\nbool empty = stack.empty();\n</code></pre> stack.java<pre><code>/* スタックを初期化 */\nStack&lt;Integer&gt; stack = new Stack&lt;&gt;();\n\n/* 要素をスタックにプッシュ */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n\n/* スタックのトップ要素にアクセス */\nint peek = stack.peek();\n\n/* スタックから要素をポップ */\nint pop = stack.pop();\n\n/* スタックの長さを取得 */\nint size = stack.size();\n\n/* スタックが空かどうかチェック */\nboolean isEmpty = stack.isEmpty();\n</code></pre> stack.cs<pre><code>/* スタックを初期化 */\nStack&lt;int&gt; stack = new();\n\n/* 要素をスタックにプッシュ */\nstack.Push(1);\nstack.Push(3);\nstack.Push(2);\nstack.Push(5);\nstack.Push(4);\n\n/* スタックのトップ要素にアクセス */\nint peek = stack.Peek();\n\n/* スタックから要素をポップ */\nint pop = stack.Pop();\n\n/* スタックの長さを取得 */\nint size = stack.Count;\n\n/* スタックが空かどうかチェック */\nbool isEmpty = stack.Count == 0;\n</code></pre> stack_test.go<pre><code>/* スタックを初期化 */\n// Goでは、Sliceをスタックとして使用することが推奨されます\nvar stack []int\n\n/* 要素をスタックにプッシュ */\nstack = append(stack, 1)\nstack = append(stack, 3)\nstack = append(stack, 2)\nstack = append(stack, 5)\nstack = append(stack, 4)\n\n/* スタックのトップ要素にアクセス */\npeek := stack[len(stack)-1]\n\n/* スタックから要素をポップ */\npop := stack[len(stack)-1]\nstack = stack[:len(stack)-1]\n\n/* スタックの長さを取得 */\nsize := len(stack)\n\n/* スタックが空かどうかチェック */\nisEmpty := len(stack) == 0\n</code></pre> stack.swift<pre><code>/* スタックを初期化 */\n// Swiftには組み込みのスタッククラスがないため、Arrayをスタックとして使用\nvar stack: [Int] = []\n\n/* 要素をスタックにプッシュ */\nstack.append(1)\nstack.append(3)\nstack.append(2)\nstack.append(5)\nstack.append(4)\n\n/* スタックのトップ要素にアクセス */\nlet peek = stack.last!\n\n/* スタックから要素をポップ */\nlet pop = stack.removeLast()\n\n/* スタックの長さを取得 */\nlet size = stack.count\n\n/* スタックが空かどうかチェック */\nlet isEmpty = stack.isEmpty\n</code></pre> stack.js<pre><code>/* スタックを初期化 */\n// JavaScriptには組み込みのスタッククラスがないため、Arrayをスタックとして使用\nconst stack = [];\n\n/* 要素をスタックにプッシュ */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n\n/* スタックのトップ要素にアクセス */\nconst peek = stack[stack.length-1];\n\n/* スタックから要素をポップ */\nconst pop = stack.pop();\n\n/* スタックの長さを取得 */\nconst size = stack.length;\n\n/* スタックが空かどうかチェック */\nconst is_empty = stack.length === 0;\n</code></pre> stack.ts<pre><code>/* スタックを初期化 */\n// TypeScriptには組み込みのスタッククラスがないため、Arrayをスタックとして使用\nconst stack: number[] = [];\n\n/* 要素をスタックにプッシュ */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n\n/* スタックのトップ要素にアクセス */\nconst peek = stack[stack.length - 1];\n\n/* スタックから要素をポップ */\nconst pop = stack.pop();\n\n/* スタックの長さを取得 */\nconst size = stack.length;\n\n/* スタックが空かどうかチェック */\nconst is_empty = stack.length === 0;\n</code></pre> stack.dart<pre><code>/* スタックを初期化 */\n// Dartには組み込みのスタッククラスがないため、Listをスタックとして使用\nList&lt;int&gt; stack = [];\n\n/* 要素をスタックにプッシュ */\nstack.add(1);\nstack.add(3);\nstack.add(2);\nstack.add(5);\nstack.add(4);\n\n/* スタックのトップ要素にアクセス */\nint peek = stack.last;\n\n/* スタックから要素をポップ */\nint pop = stack.removeLast();\n\n/* スタックの長さを取得 */\nint size = stack.length;\n\n/* スタックが空かどうかチェック */\nbool isEmpty = stack.isEmpty;\n</code></pre> stack.rs<pre><code>/* スタックを初期化 */\n// Vecをスタックとして使用\nlet mut stack: Vec&lt;i32&gt; = Vec::new();\n\n/* 要素をスタックにプッシュ */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n\n/* スタックのトップ要素にアクセス */\nlet top = stack.last().unwrap();\n\n/* スタックから要素をポップ */\nlet pop = stack.pop().unwrap();\n\n/* スタックの長さを取得 */\nlet size = stack.len();\n\n/* スタックが空かどうかチェック */\nlet is_empty = stack.is_empty();\n</code></pre> stack.c<pre><code>// Cは組み込みのスタックを提供していません\n</code></pre> stack.kt<pre><code>\n</code></pre>","path":["第 5 章 &nbsp; スタックとキュー","5.1 &nbsp; スタック"],"tags":[]},{"location":"chapter_stack_and_queue/stack/#512","level":2,"title":"5.1.2   スタックの実装","text":"<p>スタックがどのように動作するかをより深く理解するために、自分でスタッククラスを実装してみましょう。</p> <p>スタックは後入先出の原則に従うため、スタックのトップでのみ要素を追加または削除できます。しかし、配列と連結リストの両方は任意の位置で要素を追加・削除できるため、スタックは制限された配列または連結リストと見なすことができます。言い換えれば、配列や連結リストの特定の無関係な操作を「遮蔽」して、外部の動作をスタックの特性に合わせることができます。</p>","path":["第 5 章 &nbsp; スタックとキュー","5.1 &nbsp; スタック"],"tags":[]},{"location":"chapter_stack_and_queue/stack/#1","level":3,"title":"1.   連結リストベースの実装","text":"<p>連結リストを使用してスタックを実装する場合、リストのヘッドノードをスタックのトップ、テールノードをスタックのボトムと考えることができます。</p> <p>下図に示すように、プッシュ操作では、単に連結リストのヘッドに要素を挿入します。このノード挿入方法は「ヘッド挿入」として知られています。ポップ操作では、リストからヘッドノードを削除するだけです。</p> LinkedListStackpush()pop() <p></p> <p></p> <p></p> <p> 図 5-2   連結リストによるスタック実装のプッシュとポップ操作 </p> <p>以下は、連結リストに基づくスタック実装のサンプルコードです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linkedlist_stack.py<pre><code>class LinkedListStack:\n    \"\"\"連結リストベースのスタッククラス\"\"\"\n\n    def __init__(self):\n        \"\"\"コンストラクタ\"\"\"\n        self._peek: ListNode | None = None\n        self._size: int = 0\n\n    def size(self) -&gt; int:\n        \"\"\"スタックの長さを取得\"\"\"\n        return self._size\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"スタックが空かどうかを判定\"\"\"\n        return self._size == 0\n\n    def push(self, val: int):\n        \"\"\"プッシュ\"\"\"\n        node = ListNode(val)\n        node.next = self._peek\n        self._peek = node\n        self._size += 1\n\n    def pop(self) -&gt; int:\n        \"\"\"ポップ\"\"\"\n        num = self.peek()\n        self._peek = self._peek.next\n        self._size -= 1\n        return num\n\n    def peek(self) -&gt; int:\n        \"\"\"スタックトップ要素にアクセス\"\"\"\n        if self.is_empty():\n            raise IndexError(\"Stack is empty\")\n        return self._peek.val\n\n    def to_list(self) -&gt; list[int]:\n        \"\"\"出力用のリストに変換\"\"\"\n        arr = []\n        node = self._peek\n        while node:\n            arr.append(node.val)\n            node = node.next\n        arr.reverse()\n        return arr\n</code></pre> linkedlist_stack.cpp<pre><code>/* 連結リストに基づくスタッククラス */\nclass LinkedListStack {\n  private:\n    ListNode *stackTop; // 先頭ノードをスタックトップとして使用\n    int stkSize;        // スタックの長さ\n\n  public:\n    LinkedListStack() {\n        stackTop = nullptr;\n        stkSize = 0;\n    }\n\n    ~LinkedListStack() {\n        // 連結リストを走査、ノードを削除、メモリを解放\n        freeMemoryLinkedList(stackTop);\n    }\n\n    /* スタックの長さを取得 */\n    int size() {\n        return stkSize;\n    }\n\n    /* スタックが空かどうかを判定 */\n    bool isEmpty() {\n        return size() == 0;\n    }\n\n    /* プッシュ */\n    void push(int num) {\n        ListNode *node = new ListNode(num);\n        node-&gt;next = stackTop;\n        stackTop = node;\n        stkSize++;\n    }\n\n    /* ポップ */\n    int pop() {\n        int num = top();\n        ListNode *tmp = stackTop;\n        stackTop = stackTop-&gt;next;\n        // メモリを解放\n        delete tmp;\n        stkSize--;\n        return num;\n    }\n\n    /* スタックトップ要素にアクセス */\n    int top() {\n        if (isEmpty())\n            throw out_of_range(\"Stack is empty\");\n        return stackTop-&gt;val;\n    }\n\n    /* リストを配列に変換して返却 */\n    vector&lt;int&gt; toVector() {\n        ListNode *node = stackTop;\n        vector&lt;int&gt; res(size());\n        for (int i = res.size() - 1; i &gt;= 0; i--) {\n            res[i] = node-&gt;val;\n            node = node-&gt;next;\n        }\n        return res;\n    }\n};\n</code></pre> linkedlist_stack.java<pre><code>/* 連結リストに基づくスタッククラス */\nclass LinkedListStack {\n    private ListNode stackPeek; // ヘッドノードをスタックトップとして使用\n    private int stkSize = 0; // スタックの長さ\n\n    public LinkedListStack() {\n        stackPeek = null;\n    }\n\n    /* スタックの長さを取得 */\n    public int size() {\n        return stkSize;\n    }\n\n    /* スタックが空かどうかを判定 */\n    public boolean isEmpty() {\n        return size() == 0;\n    }\n\n    /* プッシュ */\n    public void push(int num) {\n        ListNode node = new ListNode(num);\n        node.next = stackPeek;\n        stackPeek = node;\n        stkSize++;\n    }\n\n    /* ポップ */\n    public int pop() {\n        int num = peek();\n        stackPeek = stackPeek.next;\n        stkSize--;\n        return num;\n    }\n\n    /* スタックトップ要素にアクセス */\n    public int peek() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return stackPeek.val;\n    }\n\n    /* List を Array に変換して返す */\n    public int[] toArray() {\n        ListNode node = stackPeek;\n        int[] res = new int[size()];\n        for (int i = res.length - 1; i &gt;= 0; i--) {\n            res[i] = node.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_stack.cs<pre><code>[class]{LinkedListStack}-[func]{}\n</code></pre> linkedlist_stack.go<pre><code>[class]{linkedListStack}-[func]{}\n</code></pre> linkedlist_stack.swift<pre><code>[class]{LinkedListStack}-[func]{}\n</code></pre> linkedlist_stack.js<pre><code>[class]{LinkedListStack}-[func]{}\n</code></pre> linkedlist_stack.ts<pre><code>[class]{LinkedListStack}-[func]{}\n</code></pre> linkedlist_stack.dart<pre><code>[class]{LinkedListStack}-[func]{}\n</code></pre> linkedlist_stack.rs<pre><code>[class]{LinkedListStack}-[func]{}\n</code></pre> linkedlist_stack.c<pre><code>[class]{LinkedListStack}-[func]{}\n</code></pre> linkedlist_stack.kt<pre><code>[class]{LinkedListStack}-[func]{}\n</code></pre> linkedlist_stack.rb<pre><code>[class]{LinkedListStack}-[func]{}\n</code></pre>","path":["第 5 章 &nbsp; スタックとキュー","5.1 &nbsp; スタック"],"tags":[]},{"location":"chapter_stack_and_queue/stack/#2","level":3,"title":"2.   配列ベースの実装","text":"<p>配列を使用してスタックを実装する場合、配列の末尾をスタックのトップと考えることができます。下図に示すように、プッシュとポップ操作は、それぞれ配列の末尾での要素の追加と削除に対応し、どちらも時間計算量\\(O(1)\\)です。</p> ArrayStackpush()pop() <p></p> <p></p> <p></p> <p> 図 5-3   配列によるスタック実装のプッシュとポップ操作 </p> <p>スタックにプッシュされる要素が継続的に増加する可能性があるため、動的配列を使用でき、配列拡張を自分で処理する必要がありません。以下はサンプルコードです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array_stack.py<pre><code>class ArrayStack:\n    \"\"\"配列ベースのスタッククラス\"\"\"\n\n    def __init__(self):\n        \"\"\"コンストラクタ\"\"\"\n        self._stack: list[int] = []\n\n    def size(self) -&gt; int:\n        \"\"\"スタックの長さを取得\"\"\"\n        return len(self._stack)\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"スタックが空かどうかを判定\"\"\"\n        return self.size() == 0\n\n    def push(self, item: int):\n        \"\"\"プッシュ\"\"\"\n        self._stack.append(item)\n\n    def pop(self) -&gt; int:\n        \"\"\"ポップ\"\"\"\n        if self.is_empty():\n            raise IndexError(\"Stack is empty\")\n        return self._stack.pop()\n\n    def peek(self) -&gt; int:\n        \"\"\"スタックトップ要素にアクセス\"\"\"\n        if self.is_empty():\n            raise IndexError(\"Stack is empty\")\n        return self._stack[-1]\n\n    def to_list(self) -&gt; list[int]:\n        \"\"\"出力用の配列を返す\"\"\"\n        return self._stack\n</code></pre> array_stack.cpp<pre><code>/* 配列に基づくスタッククラス */\nclass ArrayStack {\n  private:\n    vector&lt;int&gt; stack;\n\n  public:\n    /* スタックの長さを取得 */\n    int size() {\n        return stack.size();\n    }\n\n    /* スタックが空かどうかを判定 */\n    bool isEmpty() {\n        return stack.size() == 0;\n    }\n\n    /* プッシュ */\n    void push(int num) {\n        stack.push_back(num);\n    }\n\n    /* ポップ */\n    int pop() {\n        int num = top();\n        stack.pop_back();\n        return num;\n    }\n\n    /* スタックトップ要素にアクセス */\n    int top() {\n        if (isEmpty())\n            throw out_of_range(\"Stack is empty\");\n        return stack.back();\n    }\n\n    /* Vectorを返却 */\n    vector&lt;int&gt; toVector() {\n        return stack;\n    }\n};\n</code></pre> array_stack.java<pre><code>/* 配列に基づくスタッククラス */\nclass ArrayStack {\n    private ArrayList&lt;Integer&gt; stack;\n\n    public ArrayStack() {\n        // リスト（動的配列）を初期化\n        stack = new ArrayList&lt;&gt;();\n    }\n\n    /* スタックの長さを取得 */\n    public int size() {\n        return stack.size();\n    }\n\n    /* スタックが空かどうかを判定 */\n    public boolean isEmpty() {\n        return size() == 0;\n    }\n\n    /* プッシュ */\n    public void push(int num) {\n        stack.add(num);\n    }\n\n    /* ポップ */\n    public int pop() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return stack.remove(size() - 1);\n    }\n\n    /* スタックトップ要素にアクセス */\n    public int peek() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return stack.get(size() - 1);\n    }\n\n    /* List を Array に変換して返す */\n    public Object[] toArray() {\n        return stack.toArray();\n    }\n}\n</code></pre> array_stack.cs<pre><code>[class]{ArrayStack}-[func]{}\n</code></pre> array_stack.go<pre><code>[class]{arrayStack}-[func]{}\n</code></pre> array_stack.swift<pre><code>[class]{ArrayStack}-[func]{}\n</code></pre> array_stack.js<pre><code>[class]{ArrayStack}-[func]{}\n</code></pre> array_stack.ts<pre><code>[class]{ArrayStack}-[func]{}\n</code></pre> array_stack.dart<pre><code>[class]{ArrayStack}-[func]{}\n</code></pre> array_stack.rs<pre><code>[class]{ArrayStack}-[func]{}\n</code></pre> array_stack.c<pre><code>[class]{ArrayStack}-[func]{}\n</code></pre> array_stack.kt<pre><code>[class]{ArrayStack}-[func]{}\n</code></pre> array_stack.rb<pre><code>[class]{ArrayStack}-[func]{}\n</code></pre>","path":["第 5 章 &nbsp; スタックとキュー","5.1 &nbsp; スタック"],"tags":[]},{"location":"chapter_stack_and_queue/stack/#513-2","level":2,"title":"5.1.3   2つの実装の比較","text":"<p>サポートされる操作</p> <p>両方の実装は、スタックで定義されたすべての操作をサポートします。配列実装はさらにランダムアクセスをサポートしますが、これはスタック定義の範囲を超えており、一般的には使用されません。</p> <p>時間効率</p> <p>配列ベースの実装では、プッシュとポップ操作の両方が事前に割り当てられた連続メモリで発生し、良好なキャッシュ局所性があるため効率が高くなります。しかし、プッシュ操作が配列容量を超える場合、リサイズメカニズムがトリガーされ、そのプッシュ操作の時間計算量は\\(O(n)\\)になります。</p> <p>連結リスト実装では、リスト拡張は非常に柔軟で、配列拡張のような効率低下の問題はありません。しかし、プッシュ操作にはノードオブジェクトの初期化とポインタの変更が必要なため、効率は比較的低くなります。プッシュされる要素がすでにノードオブジェクトの場合、初期化ステップをスキップでき、効率が向上します。</p> <p>したがって、プッシュとポップ操作の要素が<code>int</code>や<code>double</code>などの基本データ型の場合、以下の結論を導くことができます：</p> <ul> <li>配列ベースのスタック実装は拡張時に効率が低下しますが、拡張は低頻度操作であるため、平均効率は高くなります。</li> <li>連結リストベースのスタック実装はより安定した効率パフォーマンスを提供します。</li> </ul> <p>空間効率</p> <p>リストを初期化する際、システムは「初期容量」を割り当てますが、これは実際の必要量を超える可能性があります。さらに、拡張メカニズムは通常、特定の係数（2倍など）で容量を増加させ、これも実際の必要量を超える可能性があります。したがって、配列ベースのスタックは一部の空間を無駄にする可能性があります。</p> <p>しかし、連結リストノードはポインタを格納するための追加空間が必要なため、連結リストノードが占有する空間は比較的大きくなります。</p> <p>まとめると、どちらの実装がよりメモリ効率的かを単純に判断することはできません。特定の状況に基づく分析が必要です。</p>","path":["第 5 章 &nbsp; スタックとキュー","5.1 &nbsp; スタック"],"tags":[]},{"location":"chapter_stack_and_queue/stack/#514","level":2,"title":"5.1.4   スタックの典型的な応用","text":"<ul> <li>ブラウザの戻ると進む、ソフトウェアの元に戻すとやり直し。新しいWebページを開くたびに、ブラウザは前のページをスタックにプッシュし、戻る操作（本質的にはポップ操作）を通じて前のページに戻ることができます。戻ると進むの両方をサポートするには、2つのスタックが連携して動作する必要があります。</li> <li>プログラムのメモリ管理。関数が呼び出されるたびに、システムはスタックのトップにスタックフレームを追加して関数のコンテキスト情報を記録します。再帰関数では、下方向の再帰フェーズはスタックへのプッシュを続け、上方向のバックトラッキングフェーズはスタックからのポップを続けます。</li> </ul>","path":["第 5 章 &nbsp; スタックとキュー","5.1 &nbsp; スタック"],"tags":[]},{"location":"chapter_stack_and_queue/summary/","level":1,"title":"5.4   まとめ","text":"","path":["第 5 章 &nbsp; スタックとキュー","5.4 &nbsp; まとめ"],"tags":[]},{"location":"chapter_stack_and_queue/summary/#1","level":3,"title":"1.   重要なポイント","text":"<ul> <li>スタックは後入れ先出し（LIFO）の原則に従うデータ構造で、配列または連結リストを使って実装できます。</li> <li>時間効率の観点では、スタックの配列実装の方が平均的な効率が高いです。ただし、拡張時には単一のプッシュ操作の時間計算量が\\(O(n)\\)に悪化する可能性があります。対照的に、スタックの連結リスト実装はより安定した効率を提供します。</li> <li>空間効率に関しては、スタックの配列実装は一定程度の空間の無駄につながる可能性があります。ただし、連結リストのノードが占有するメモリ空間は一般的に配列の要素よりも大きいことに注意することが重要です。</li> <li>キューは先入れ先出し（FIFO）の原則に従うデータ構造で、同様に配列または連結リストを使って実装できます。キューの時間と空間効率に関する結論は、スタックと似ています。</li> <li>両端キュー（deque）はより柔軟なキューの種類で、両端での要素の追加と削除を可能にします。</li> </ul>","path":["第 5 章 &nbsp; スタックとキュー","5.4 &nbsp; まとめ"],"tags":[]},{"location":"chapter_stack_and_queue/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: ブラウザの進む・戻る機能は双方向連結リストで実装されているのですか？</p> <p>ブラウザの進む・戻るナビゲーションは本質的に「スタック」概念の現れです。ユーザーが新しいページを訪問すると、そのページがスタックの先頭に追加されます。戻るボタンをクリックすると、ページがスタックの先頭からポップされます。両端キュー（deque）は、「両端キュー」の章で述べたように、いくつかの追加操作を便利に実装できます。</p> <p>Q: スタックからポップした後、ポップされたノードのメモリを解放する必要がありますか？</p> <p>ポップされたノードが後で使用される場合は、そのメモリを解放する必要はありません。自動ガベージコレクションを持つJavaやPythonなどの言語では、手動のメモリ解放は必要ありません。CやC++では、手動のメモリ解放が必要です。</p> <p>Q: 両端キューは2つのスタックを結合したもののように見えます。その用途は何ですか？</p> <p>両端キューは、スタックとキューの組み合わせまたは2つのスタックを結合したもので、スタックとキューの両方のロジックを示します。したがって、スタックとキューのすべてのアプリケーションを実装でき、より大きな柔軟性を提供します。</p> <p>Q: 元に戻すとやり直しは具体的にどのように実装されるのですか？</p> <p>元に戻すとやり直しの操作は2つのスタックを使って実装されます：元に戻す用のスタック<code>A</code>とやり直し用のスタック<code>B</code>です。</p> <ol> <li>ユーザーが操作を実行するたびに、それがスタック<code>A</code>にプッシュされ、スタック<code>B</code>がクリアされます。</li> <li>ユーザーが「元に戻す」を実行すると、最新の操作がスタック<code>A</code>からポップされ、スタック<code>B</code>にプッシュされます。</li> <li>ユーザーが「やり直し」を実行すると、最新の操作がスタック<code>B</code>からポップされ、スタック<code>A</code>に戻されます。</li> </ol>","path":["第 5 章 &nbsp; スタックとキュー","5.4 &nbsp; まとめ"],"tags":[]},{"location":"chapter_tree/","level":1,"title":"第 7 章   木","text":"<p>Abstract</p> <p>そびえ立つ木は活力に満ちた本質を放ち、深い根と豊かな葉を誇りながらも、その枝は疎らに散らばり、幽玄な雰囲気を醸し出しています。</p> <p>それはデータにおける分割統治の鮮やかな形を私たちに示しています。</p>","path":["第 7 章 &nbsp; 木"],"tags":[]},{"location":"chapter_tree/#_1","level":2,"title":"章の内容","text":"<ul> <li>7.1   二分木</li> <li>7.2   二分木の走査</li> <li>7.3   二分木の配列表現</li> <li>7.4   二分探索木</li> <li>7.5   AVL木 *</li> <li>7.6   まとめ</li> </ul>","path":["第 7 章 &nbsp; 木"],"tags":[]},{"location":"chapter_tree/array_representation_of_tree/","level":1,"title":"7.3   二分木の配列表現","text":"<p>連結リスト表現では、二分木の格納単位はノード<code>TreeNode</code>であり、ノードはポインタによって接続されます。連結リスト表現での二分木の基本操作については前の節で紹介しました。</p> <p>では、配列を使って二分木を表現することはできるでしょうか？答えはイエスです。</p>","path":["第 7 章 &nbsp; 木","7.3 &nbsp; 二分木の配列表現"],"tags":[]},{"location":"chapter_tree/array_representation_of_tree/#731","level":2,"title":"7.3.1   完全二分木の表現","text":"<p>まず簡単なケースから分析してみましょう。完全二分木が与えられたとき、レベル順探索の順序に従ってすべてのノードを配列に格納し、各ノードは一意の配列インデックスに対応します。</p> <p>レベル順探索の特性に基づいて、親ノードのインデックスとその子ノードの間の「マッピング公式」を導き出すことができます：ノードのインデックスが\\(i\\)の場合、その左の子のインデックスは\\(2i + 1\\)、右の子のインデックスは\\(2i + 2\\)です。下図は、さまざまなノードのインデックス間のマッピング関係を示しています。</p> <p></p> <p> 図 7-12   完全二分木の配列表現 </p> <p>マッピング公式は、連結リストのノード参照（ポインタ）と同様の役割を果たします。配列内の任意のノードが与えられたとき、マッピング公式を使用してその左（右）の子ノードにアクセスできます。</p>","path":["第 7 章 &nbsp; 木","7.3 &nbsp; 二分木の配列表現"],"tags":[]},{"location":"chapter_tree/array_representation_of_tree/#732","level":2,"title":"7.3.2   任意の二分木の表現","text":"<p>完全二分木は特別なケースです。二分木の中間レベルには多くの<code>None</code>値が存在することがよくあります。レベル順探索のシーケンスにはこれらの<code>None</code>値が含まれないため、このシーケンスだけに依存して<code>None</code>値の数と分布を推測することはできません。つまり、複数の二分木構造が同じレベル順探索シーケンスと一致する可能性があります。</p> <p>下図に示すように、完全でない二分木が与えられた場合、上記の配列表現方法は失敗します。</p> <p></p> <p> 図 7-13   レベル順探索シーケンスが複数の二分木の可能性に対応 </p> <p>この問題を解決するために、レベル順探索シーケンスですべての<code>None</code>値を明示的に書き出すことを検討できます。下図に示すように、この処理後、レベル順探索シーケンスは二分木を一意に表現できます。サンプルコードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code># 二分木の配列表現\n# Noneを使用して空のスロットを表現\ntree = [1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, None, None, 15]\n</code></pre> <pre><code>/* 二分木の配列表現 */\n// 最大整数値INT_MAXを使用して空のスロットをマーク\nvector&lt;int&gt; tree = {1, 2, 3, 4, INT_MAX, 6, 7, 8, 9, INT_MAX, INT_MAX, 12, INT_MAX, INT_MAX, 15};\n</code></pre> <pre><code>/* 二分木の配列表現 */\n// Integerラッパークラスを使用してnullで空のスロットをマーク\nInteger[] tree = { 1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15 };\n</code></pre> <pre><code>/* 二分木の配列表現 */\n// nullable int (int?)を使用してnullで空のスロットをマーク\nint?[] tree = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <pre><code>/* 二分木の配列表現 */\n// any型スライスを使用してnilで空のスロットをマーク\ntree := []any{1, 2, 3, 4, nil, 6, 7, 8, 9, nil, nil, 12, nil, nil, 15}\n</code></pre> <pre><code>/* 二分木の配列表現 */\n// optional Int (Int?)を使用してnilで空のスロットをマーク\nlet tree: [Int?] = [1, 2, 3, 4, nil, 6, 7, 8, 9, nil, nil, 12, nil, nil, 15]\n</code></pre> <pre><code>/* 二分木の配列表現 */\n// nullを使用して空のスロットを表現\nlet tree = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <pre><code>/* 二分木の配列表現 */\n// nullを使用して空のスロットを表現\nlet tree: (number | null)[] = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <pre><code>/* 二分木の配列表現 */\n// nullable int (int?)を使用してnullで空のスロットをマーク\nList&lt;int?&gt; tree = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <pre><code>/* 二分木の配列表現 */\n// Noneを使用して空のスロットをマーク\nlet tree = [Some(1), Some(2), Some(3), Some(4), None, Some(6), Some(7), Some(8), Some(9), None, None, Some(12), None, None, Some(15)];\n</code></pre> <pre><code>/* 二分木の配列表現 */\n// 最大int値を使用して空のスロットをマーク、したがってノード値はINT_MAXであってはならない\nint tree[] = {1, 2, 3, 4, INT_MAX, 6, 7, 8, 9, INT_MAX, INT_MAX, 12, INT_MAX, INT_MAX, 15};\n</code></pre> <pre><code>/* 二分木の配列表現 */\n// nullを使用して空のスロットを表現\nval tree = mutableListOf( 1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15 )\n</code></pre> <pre><code>\n</code></pre> <p></p> <p> 図 7-14   任意の種類の二分木の配列表現 </p> <p>注目すべきは、完備二分木は配列表現に非常に適している**ということです。完備二分木の定義を思い出すと、<code>None</code>は最下位レベルでのみ、かつ右側に向かって現れます。**つまり、すべての<code>None</code>値は確実にレベル順探索シーケンスの最後に現れます。</p> <p>これは、配列を使用して完備二分木を表現する際、すべての<code>None</code>値の格納を省略できることを意味し、非常に便利です。下図に例を示します。</p> <p></p> <p> 図 7-15   完備二分木の配列表現 </p> <p>以下のコードは、配列表現に基づく二分木を実装し、次の操作を含みます：</p> <ul> <li>ノードが与えられたとき、その値、左（右）の子ノード、および親ノードを取得する。</li> <li>前順、中順、後順、およびレベル順探索シーケンスを取得する。</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array_binary_tree.py<pre><code>class ArrayBinaryTree:\n    \"\"\"配列ベースの二分木クラス\"\"\"\n\n    def __init__(self, arr: list[int | None]):\n        \"\"\"コンストラクタ\"\"\"\n        self._tree = list(arr)\n\n    def size(self):\n        \"\"\"リストの容量\"\"\"\n        return len(self._tree)\n\n    def val(self, i: int) -&gt; int | None:\n        \"\"\"インデックスiのノードの値を取得\"\"\"\n        # インデックスが範囲外の場合、Noneを返し、空席を表す\n        if i &lt; 0 or i &gt;= self.size():\n            return None\n        return self._tree[i]\n\n    def left(self, i: int) -&gt; int | None:\n        \"\"\"インデックスiのノードの左の子のインデックスを取得\"\"\"\n        return 2 * i + 1\n\n    def right(self, i: int) -&gt; int | None:\n        \"\"\"インデックスiのノードの右の子のインデックスを取得\"\"\"\n        return 2 * i + 2\n\n    def parent(self, i: int) -&gt; int | None:\n        \"\"\"インデックスiのノードの親のインデックスを取得\"\"\"\n        return (i - 1) // 2\n\n    def level_order(self) -&gt; list[int]:\n        \"\"\"レベル順走査\"\"\"\n        self.res = []\n        # 配列を走査\n        for i in range(self.size()):\n            if self.val(i) is not None:\n                self.res.append(self.val(i))\n        return self.res\n\n    def dfs(self, i: int, order: str):\n        \"\"\"深さ優先走査\"\"\"\n        if self.val(i) is None:\n            return\n        # 前順走査\n        if order == \"pre\":\n            self.res.append(self.val(i))\n        self.dfs(self.left(i), order)\n        # 中順走査\n        if order == \"in\":\n            self.res.append(self.val(i))\n        self.dfs(self.right(i), order)\n        # 後順走査\n        if order == \"post\":\n            self.res.append(self.val(i))\n\n    def pre_order(self) -&gt; list[int]:\n        \"\"\"前順走査\"\"\"\n        self.res = []\n        self.dfs(0, order=\"pre\")\n        return self.res\n\n    def in_order(self) -&gt; list[int]:\n        \"\"\"中順走査\"\"\"\n        self.res = []\n        self.dfs(0, order=\"in\")\n        return self.res\n\n    def post_order(self) -&gt; list[int]:\n        \"\"\"後順走査\"\"\"\n        self.res = []\n        self.dfs(0, order=\"post\")\n        return self.res\n</code></pre> array_binary_tree.cpp<pre><code>/* 配列ベースの二分木クラス */\nclass ArrayBinaryTree {\n  public:\n    /* コンストラクタ */\n    ArrayBinaryTree(vector&lt;int&gt; arr) {\n        tree = arr;\n    }\n\n    /* リストの容量 */\n    int size() {\n        return tree.size();\n    }\n\n    /* インデックス i のノードの値を取得 */\n    int val(int i) {\n        // インデックスが範囲外の場合、INT_MAX を返す（null を表す）\n        if (i &lt; 0 || i &gt;= size())\n            return INT_MAX;\n        return tree[i];\n    }\n\n    /* インデックス i のノードの左の子のインデックスを取得 */\n    int left(int i) {\n        return 2 * i + 1;\n    }\n\n    /* インデックス i のノードの右の子のインデックスを取得 */\n    int right(int i) {\n        return 2 * i + 2;\n    }\n\n    /* インデックス i のノードの親のインデックスを取得 */\n    int parent(int i) {\n        return (i - 1) / 2;\n    }\n\n    /* レベル順走査 */\n    vector&lt;int&gt; levelOrder() {\n        vector&lt;int&gt; res;\n        // 配列を走査\n        for (int i = 0; i &lt; size(); i++) {\n            if (val(i) != INT_MAX)\n                res.push_back(val(i));\n        }\n        return res;\n    }\n\n    /* 前順走査 */\n    vector&lt;int&gt; preOrder() {\n        vector&lt;int&gt; res;\n        dfs(0, \"pre\", res);\n        return res;\n    }\n\n    /* 中順走査 */\n    vector&lt;int&gt; inOrder() {\n        vector&lt;int&gt; res;\n        dfs(0, \"in\", res);\n        return res;\n    }\n\n    /* 後順走査 */\n    vector&lt;int&gt; postOrder() {\n        vector&lt;int&gt; res;\n        dfs(0, \"post\", res);\n        return res;\n    }\n\n  private:\n    vector&lt;int&gt; tree;\n\n    /* 深さ優先走査 */\n    void dfs(int i, string order, vector&lt;int&gt; &amp;res) {\n        // 空の位置の場合、戻る\n        if (val(i) == INT_MAX)\n            return;\n        // 前順走査\n        if (order == \"pre\")\n            res.push_back(val(i));\n        dfs(left(i), order, res);\n        // 中順走査\n        if (order == \"in\")\n            res.push_back(val(i));\n        dfs(right(i), order, res);\n        // 後順走査\n        if (order == \"post\")\n            res.push_back(val(i));\n    }\n};\n</code></pre> array_binary_tree.java<pre><code>/* 配列ベースの二分木クラス */\nclass ArrayBinaryTree {\n    private List&lt;Integer&gt; tree;\n\n    /* コンストラクタ */\n    public ArrayBinaryTree(List&lt;Integer&gt; arr) {\n        tree = new ArrayList&lt;&gt;(arr);\n    }\n\n    /* リストの容量 */\n    public int size() {\n        return tree.size();\n    }\n\n    /* インデックス i のノードの値を取得 */\n    public Integer val(int i) {\n        // インデックスが範囲外の場合、null を返す（空の位置を表す）\n        if (i &lt; 0 || i &gt;= size())\n            return null;\n        return tree.get(i);\n    }\n\n    /* インデックス i のノードの左の子のインデックスを取得 */\n    public Integer left(int i) {\n        return 2 * i + 1;\n    }\n\n    /* インデックス i のノードの右の子のインデックスを取得 */\n    public Integer right(int i) {\n        return 2 * i + 2;\n    }\n\n    /* インデックス i のノードの親のインデックスを取得 */\n    public Integer parent(int i) {\n        return (i - 1) / 2;\n    }\n\n    /* レベル順走査 */\n    public List&lt;Integer&gt; levelOrder() {\n        List&lt;Integer&gt; res = new ArrayList&lt;&gt;();\n        // 配列を走査\n        for (int i = 0; i &lt; size(); i++) {\n            if (val(i) != null)\n                res.add(val(i));\n        }\n        return res;\n    }\n\n    /* 深さ優先走査 */\n    private void dfs(Integer i, String order, List&lt;Integer&gt; res) {\n        // 空の位置の場合、戻る\n        if (val(i) == null)\n            return;\n        // 前順走査\n        if (\"pre\".equals(order))\n            res.add(val(i));\n        dfs(left(i), order, res);\n        // 中順走査\n        if (\"in\".equals(order))\n            res.add(val(i));\n        dfs(right(i), order, res);\n        // 後順走査\n        if (\"post\".equals(order))\n            res.add(val(i));\n    }\n\n    /* 前順走査 */\n    public List&lt;Integer&gt; preOrder() {\n        List&lt;Integer&gt; res = new ArrayList&lt;&gt;();\n        dfs(0, \"pre\", res);\n        return res;\n    }\n\n    /* 中順走査 */\n    public List&lt;Integer&gt; inOrder() {\n        List&lt;Integer&gt; res = new ArrayList&lt;&gt;();\n        dfs(0, \"in\", res);\n        return res;\n    }\n\n    /* 後順走査 */\n    public List&lt;Integer&gt; postOrder() {\n        List&lt;Integer&gt; res = new ArrayList&lt;&gt;();\n        dfs(0, \"post\", res);\n        return res;\n    }\n}\n</code></pre> array_binary_tree.cs<pre><code>[class]{ArrayBinaryTree}-[func]{}\n</code></pre> array_binary_tree.go<pre><code>[class]{arrayBinaryTree}-[func]{}\n</code></pre> array_binary_tree.swift<pre><code>[class]{ArrayBinaryTree}-[func]{}\n</code></pre> array_binary_tree.js<pre><code>[class]{ArrayBinaryTree}-[func]{}\n</code></pre> array_binary_tree.ts<pre><code>[class]{ArrayBinaryTree}-[func]{}\n</code></pre> array_binary_tree.dart<pre><code>[class]{ArrayBinaryTree}-[func]{}\n</code></pre> array_binary_tree.rs<pre><code>[class]{ArrayBinaryTree}-[func]{}\n</code></pre> array_binary_tree.c<pre><code>[class]{ArrayBinaryTree}-[func]{}\n</code></pre> array_binary_tree.kt<pre><code>[class]{ArrayBinaryTree}-[func]{}\n</code></pre> array_binary_tree.rb<pre><code>[class]{ArrayBinaryTree}-[func]{}\n</code></pre>","path":["第 7 章 &nbsp; 木","7.3 &nbsp; 二分木の配列表現"],"tags":[]},{"location":"chapter_tree/array_representation_of_tree/#733","level":2,"title":"7.3.3   利点と制限","text":"<p>二分木の配列表現には以下の利点があります：</p> <ul> <li>配列は連続したメモリ空間に格納されるため、キャッシュフレンドリーで、より高速なアクセスと探索が可能です。</li> <li>ポインタを格納する必要がないため、スペースを節約できます。</li> <li>ノードへのランダムアクセスが可能です。</li> </ul> <p>しかし、配列表現にはいくつかの制限もあります：</p> <ul> <li>配列格納には連続したメモリ空間が必要なため、大量のデータを持つ木の格納には適していません。</li> <li>ノードの追加や削除には配列の挿入や削除操作が必要で、効率が低くなります。</li> <li>二分木に多くの<code>None</code>値がある場合、配列に含まれるノードデータの割合が低くなり、空間利用率が低下します。</li> </ul>","path":["第 7 章 &nbsp; 木","7.3 &nbsp; 二分木の配列表現"],"tags":[]},{"location":"chapter_tree/avl_tree/","level":1,"title":"7.5   AVL木 *","text":"<p>「二分探索木」の節では、複数の挿入と削除の後、二分探索木が連結リストに退化する可能性があることを述べました。このような場合、すべての操作の時間計算量が\\(O(\\log n)\\)から\\(O(n)\\)に悪化します。</p> <p>下図に示すように、2つのノード削除操作の後、この二分探索木は連結リストに退化します。</p> <p></p> <p> 図 7-24   ノード削除後のAVL木の退化 </p> <p>例えば、下図に示す完全二分木では、2つのノードを挿入した後、木が左に大きく傾き、検索操作の時間計算量も悪化します。</p> <p></p> <p> 図 7-25   ノード挿入後のAVL木の退化 </p> <p>1962年、G. M. Adelson-VelskyとE. M. Landisが論文「An algorithm for the organization of information」でAVL木を提案しました。この論文では、ノードの継続的な追加と削除の後もAVL木が退化しないことを保証する一連の操作について詳述し、さまざまな操作の時間計算量を\\(O(\\log n)\\)レベルに維持しました。つまり、頻繁な追加、削除、検索、変更が必要なシナリオで、AVL木は常に効率的なデータ操作性能を維持でき、大きな応用価値があります。</p>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#751-avl","level":2,"title":"7.5.1   AVL木の一般的な用語","text":"<p>AVL木は二分探索木でありかつ平衡二分木でもあり、これら2つの種類の二分木のすべての性質を満たしているため、平衡二分探索木です。</p>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#1","level":3,"title":"1.   ノードの高さ","text":"<p>AVL木に関連する操作ではノードの高さを取得する必要があるため、ノードクラスに<code>height</code>変数を追加する必要があります：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>class TreeNode:\n    \"\"\"AVL木ノード\"\"\"\n    def __init__(self, val: int):\n        self.val: int = val                 # ノード値\n        self.height: int = 0                # ノードの高さ\n        self.left: TreeNode | None = None   # 左の子への参照\n        self.right: TreeNode | None = None  # 右の子への参照\n</code></pre> <pre><code>/* AVL木ノード */\nstruct TreeNode {\n    int val{};          // ノード値\n    int height = 0;     // ノードの高さ\n    TreeNode *left{};   // 左の子\n    TreeNode *right{};  // 右の子\n    TreeNode() = default;\n    explicit TreeNode(int x) : val(x){}\n};\n</code></pre> <pre><code>/* AVL木ノード */\nclass TreeNode {\n    public int val;        // ノード値\n    public int height;     // ノードの高さ\n    public TreeNode left;  // 左の子\n    public TreeNode right; // 右の子\n    public TreeNode(int x) { val = x; }\n}\n</code></pre> <pre><code>/* AVL木ノード */\nclass TreeNode(int? x) {\n    public int? val = x;    // ノード値\n    public int height;      // ノードの高さ\n    public TreeNode? left;  // 左の子への参照\n    public TreeNode? right; // 右の子への参照\n}\n</code></pre> <pre><code>/* AVL木ノード */\ntype TreeNode struct {\n    Val    int       // ノード値\n    Height int       // ノードの高さ\n    Left   *TreeNode // 左の子への参照\n    Right  *TreeNode // 右の子への参照\n}\n</code></pre> <pre><code>/* AVL木ノード */\nclass TreeNode {\n    var val: Int // ノード値\n    var height: Int // ノードの高さ\n    var left: TreeNode? // 左の子\n    var right: TreeNode? // 右の子\n\n    init(x: Int) {\n        val = x\n        height = 0\n    }\n}\n</code></pre> <pre><code>/* AVL木ノード */\nclass TreeNode {\n    val; // ノード値\n    height; // ノードの高さ\n    left; // 左の子ポインタ\n    right; // 右の子ポインタ\n    constructor(val, left, right, height) {\n        this.val = val === undefined ? 0 : val;\n        this.height = height === undefined ? 0 : height;\n        this.left = left === undefined ? null : left;\n        this.right = right === undefined ? null : right;\n    }\n}\n</code></pre> <pre><code>/* AVL木ノード */\nclass TreeNode {\n    val: number;            // ノード値\n    height: number;         // ノードの高さ\n    left: TreeNode | null;  // 左の子ポインタ\n    right: TreeNode | null; // 右の子ポインタ\n    constructor(val?: number, height?: number, left?: TreeNode | null, right?: TreeNode | null) {\n        this.val = val === undefined ? 0 : val;\n        this.height = height === undefined ? 0 : height;\n        this.left = left === undefined ? null : left;\n        this.right = right === undefined ? null : right;\n    }\n}\n</code></pre> <pre><code>/* AVL木ノード */\nclass TreeNode {\n  int val;         // ノード値\n  int height;      // ノードの高さ\n  TreeNode? left;  // 左の子\n  TreeNode? right; // 右の子\n  TreeNode(this.val, [this.height = 0, this.left, this.right]);\n}\n</code></pre> <pre><code>use std::rc::Rc;\nuse std::cell::RefCell;\n\n/* AVL木ノード */\nstruct TreeNode {\n    val: i32,                               // ノード値\n    height: i32,                            // ノードの高さ\n    left: Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,    // 左の子\n    right: Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,   // 右の子\n}\n\nimpl TreeNode {\n    /* コンストラクタ */\n    fn new(val: i32) -&gt; Rc&lt;RefCell&lt;Self&gt;&gt; {\n        Rc::new(RefCell::new(Self {\n            val,\n            height: 0,\n            left: None,\n            right: None\n        }))\n    }\n}\n</code></pre> <pre><code>/* AVL木ノード */\nTreeNode struct TreeNode {\n    int val;\n    int height;\n    struct TreeNode *left;\n    struct TreeNode *right;\n} TreeNode;\n\n/* コンストラクタ */\nTreeNode *newTreeNode(int val) {\n    TreeNode *node;\n\n    node = (TreeNode *)malloc(sizeof(TreeNode));\n    node-&gt;val = val;\n    node-&gt;height = 0;\n    node-&gt;left = NULL;\n    node-&gt;right = NULL;\n    return node;\n}\n</code></pre> <pre><code>/* AVL木ノード */\nclass TreeNode(val _val: Int) {  // ノード値\n    val height: Int = 0          // ノードの高さ\n    val left: TreeNode? = null   // 左の子\n    val right: TreeNode? = null  // 右の子\n}\n</code></pre> <pre><code>\n</code></pre> <p>「ノードの高さ」とは、そのノードから最も遠い葉ノードまでの距離、つまり通過する「辺」の数を指します。重要なのは、葉ノードの高さは\\(0\\)で、nullノードの高さは\\(-1\\)であることです。ノードの高さを取得し、更新するための2つのユーティリティ関数を作成します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def height(self, node: TreeNode | None) -&gt; int:\n    \"\"\"ノードの高さを取得\"\"\"\n    # 空ノードの高さは-1、葉ノードの高さは0\n    if node is not None:\n        return node.height\n    return -1\n\ndef update_height(self, node: TreeNode | None):\n    \"\"\"ノードの高さを更新\"\"\"\n    # ノードの高さ = 最も高い部分木の高さ + 1\n    node.height = max([self.height(node.left), self.height(node.right)]) + 1\n</code></pre> avl_tree.cpp<pre><code>/* ノードの高さを取得 */\nint height(TreeNode *node) {\n    // 空ノードの高さは-1、葉ノードの高さは0\n    return node == nullptr ? -1 : node-&gt;height;\n}\n\n/* ノードの高さを更新 */\nvoid updateHeight(TreeNode *node) {\n    // ノードの高さ = 最も高い部分木の高さ + 1\n    node-&gt;height = max(height(node-&gt;left), height(node-&gt;right)) + 1;\n}\n</code></pre> avl_tree.java<pre><code>/* ノードの高さを取得 */\nint height(TreeNode node) {\n    // 空ノードの高さは -1、葉ノードの高さは 0\n    return node == null ? -1 : node.height;\n}\n\n/* ノードの高さを更新 */\nvoid updateHeight(TreeNode node) {\n    // ノードの高さは最も高い部分木の高さ + 1\n    node.height = Math.max(height(node.left), height(node.right)) + 1;\n}\n</code></pre> avl_tree.cs<pre><code>[class]{AVLTree}-[func]{Height}\n\n[class]{AVLTree}-[func]{UpdateHeight}\n</code></pre> avl_tree.go<pre><code>[class]{aVLTree}-[func]{height}\n\n[class]{aVLTree}-[func]{updateHeight}\n</code></pre> avl_tree.swift<pre><code>[class]{AVLTree}-[func]{height}\n\n[class]{AVLTree}-[func]{updateHeight}\n</code></pre> avl_tree.js<pre><code>[class]{AVLTree}-[func]{height}\n\n[class]{AVLTree}-[func]{updateHeight}\n</code></pre> avl_tree.ts<pre><code>[class]{AVLTree}-[func]{height}\n\n[class]{AVLTree}-[func]{updateHeight}\n</code></pre> avl_tree.dart<pre><code>[class]{AVLTree}-[func]{height}\n\n[class]{AVLTree}-[func]{updateHeight}\n</code></pre> avl_tree.rs<pre><code>[class]{AVLTree}-[func]{height}\n\n[class]{AVLTree}-[func]{update_height}\n</code></pre> avl_tree.c<pre><code>[class]{}-[func]{height}\n\n[class]{}-[func]{updateHeight}\n</code></pre> avl_tree.kt<pre><code>[class]{AVLTree}-[func]{height}\n\n[class]{AVLTree}-[func]{updateHeight}\n</code></pre> avl_tree.rb<pre><code>[class]{AVLTree}-[func]{height}\n\n[class]{AVLTree}-[func]{update_height}\n</code></pre>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#2","level":3,"title":"2.   ノードの平衡因子","text":"<p>ノードの平衡因子は、そのノードの左部分木の高さから右部分木の高さを引いた値として定義され、nullノードの平衡因子は\\(0\\)として定義されます。後で使いやすくするため、ノードの平衡因子を取得する機能も関数にカプセル化します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def balance_factor(self, node: TreeNode | None) -&gt; int:\n    \"\"\"バランス因子を取得\"\"\"\n    # 空ノードのバランス因子は0\n    if node is None:\n        return 0\n    # ノードのバランス因子 = 左部分木の高さ - 右部分木の高さ\n    return self.height(node.left) - self.height(node.right)\n</code></pre> avl_tree.cpp<pre><code>/* 平衡因子を取得 */\nint balanceFactor(TreeNode *node) {\n    // 空ノードの平衡因子は0\n    if (node == nullptr)\n        return 0;\n    // ノードの平衡因子 = 左部分木の高さ - 右部分木の高さ\n    return height(node-&gt;left) - height(node-&gt;right);\n}\n</code></pre> avl_tree.java<pre><code>/* 平衡因子を取得 */\nint balanceFactor(TreeNode node) {\n    // 空ノードの平衡因子は 0\n    if (node == null)\n        return 0;\n    // ノードの平衡因子 = 左部分木の高さ - 右部分木の高さ\n    return height(node.left) - height(node.right);\n}\n</code></pre> avl_tree.cs<pre><code>[class]{AVLTree}-[func]{BalanceFactor}\n</code></pre> avl_tree.go<pre><code>[class]{aVLTree}-[func]{balanceFactor}\n</code></pre> avl_tree.swift<pre><code>[class]{AVLTree}-[func]{balanceFactor}\n</code></pre> avl_tree.js<pre><code>[class]{AVLTree}-[func]{balanceFactor}\n</code></pre> avl_tree.ts<pre><code>[class]{AVLTree}-[func]{balanceFactor}\n</code></pre> avl_tree.dart<pre><code>[class]{AVLTree}-[func]{balanceFactor}\n</code></pre> avl_tree.rs<pre><code>[class]{AVLTree}-[func]{balance_factor}\n</code></pre> avl_tree.c<pre><code>[class]{}-[func]{balanceFactor}\n</code></pre> avl_tree.kt<pre><code>[class]{AVLTree}-[func]{balanceFactor}\n</code></pre> avl_tree.rb<pre><code>[class]{AVLTree}-[func]{balance_factor}\n</code></pre> <p>Tip</p> <p>平衡因子を\\(f\\)とすると、AVL木の任意のノードの平衡因子は\\(-1 \\le f \\le 1\\)を満たします。</p>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#752-avl","level":2,"title":"7.5.2   AVL木の回転","text":"<p>AVL木の特徴的な機能は「回転」操作で、これは二分木の中順探索シーケンスに影響を与えることなく、不平衡なノードのバランスを回復できます。つまり、回転操作は「二分探索木」の性質を維持しながら、木を「平衡二分木」に戻すことができます。</p> <p>絶対平衡因子が\\(&gt; 1\\)のノードを「不平衡ノード」と呼びます。不平衡のタイプに応じて、4種類の回転があります：右回転、左回転、右左回転、左右回転です。以下、これらの回転操作について詳しく説明します。</p>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#1_1","level":3,"title":"1.   右回転","text":"<p>下図に示すように、二分木で下から上への最初の不平衡ノードは「ノード3」です。この不平衡ノードを根とする部分木に焦点を当て、これを<code>node</code>とし、その左の子を<code>child</code>として、「右回転」を実行します。右回転後、部分木は再びバランスが取れ、同時に二分探索木の性質も維持されます。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p> 図 7-26   右回転の手順 </p> <p>下図に示すように、<code>child</code>ノードに右の子（<code>grand_child</code>と表記）がある場合、右回転で手順を追加する必要があります：<code>grand_child</code>を<code>node</code>の左の子に設定します。</p> <p></p> <p> 図 7-27   grand_childがある右回転 </p> <p>「右回転」は比喩的な用語で、実際にはノードポインタを変更することで実現されます。以下のコードで示されます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def right_rotate(self, node: TreeNode | None) -&gt; TreeNode | None:\n    \"\"\"右回転操作\"\"\"\n    child = node.left\n    grand_child = child.right\n    # childを中心にnodeを右に回転\n    child.right = node\n    node.left = grand_child\n    # ノードの高さを更新\n    self.update_height(node)\n    self.update_height(child)\n    # 回転後の部分木のルートを返す\n    return child\n</code></pre> avl_tree.cpp<pre><code>/* 右回転操作 */\nTreeNode *rightRotate(TreeNode *node) {\n    TreeNode *child = node-&gt;left;\n    TreeNode *grandChild = child-&gt;right;\n    // childを中心にnodeを右に回転\n    child-&gt;right = node;\n    node-&gt;left = grandChild;\n    // ノードの高さを更新\n    updateHeight(node);\n    updateHeight(child);\n    // 回転後の部分木のルートを返す\n    return child;\n}\n</code></pre> avl_tree.java<pre><code>/* 右回転操作 */\nTreeNode rightRotate(TreeNode node) {\n    TreeNode child = node.left;\n    TreeNode grandChild = child.right;\n    // child を軸として node を右に回転\n    child.right = node;\n    node.left = grandChild;\n    // ノードの高さを更新\n    updateHeight(node);\n    updateHeight(child);\n    // 回転後の部分木の根を返す\n    return child;\n}\n</code></pre> avl_tree.cs<pre><code>[class]{AVLTree}-[func]{RightRotate}\n</code></pre> avl_tree.go<pre><code>[class]{aVLTree}-[func]{rightRotate}\n</code></pre> avl_tree.swift<pre><code>[class]{AVLTree}-[func]{rightRotate}\n</code></pre> avl_tree.js<pre><code>[class]{AVLTree}-[func]{rightRotate}\n</code></pre> avl_tree.ts<pre><code>[class]{AVLTree}-[func]{rightRotate}\n</code></pre> avl_tree.dart<pre><code>[class]{AVLTree}-[func]{rightRotate}\n</code></pre> avl_tree.rs<pre><code>[class]{AVLTree}-[func]{right_rotate}\n</code></pre> avl_tree.c<pre><code>[class]{}-[func]{rightRotate}\n</code></pre> avl_tree.kt<pre><code>[class]{AVLTree}-[func]{rightRotate}\n</code></pre> avl_tree.rb<pre><code>[class]{AVLTree}-[func]{right_rotate}\n</code></pre>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#2_1","level":3,"title":"2.   左回転","text":"<p>対応して、上記の不平衡二分木の「鏡像」を考慮すると、下図に示す「左回転」操作を実行する必要があります。</p> <p></p> <p> 図 7-28   左回転操作 </p> <p>同様に、下図に示すように、<code>child</code>ノードに左の子（<code>grand_child</code>と表記）がある場合、左回転で手順を追加する必要があります：<code>grand_child</code>を<code>node</code>の右の子に設定します。</p> <p></p> <p> 図 7-29   grand_childがある左回転 </p> <p>**右回転と左回転の操作は論理的に対称であり、2つの対称的な不平衡タイプを解決します**ことが観察できます。対称性に基づいて、右回転の実装コードですべての<code>left</code>を<code>right</code>に、すべての<code>right</code>を<code>left</code>に置き換えることで、左回転の実装コードを得ることができます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def left_rotate(self, node: TreeNode | None) -&gt; TreeNode | None:\n    \"\"\"左回転操作\"\"\"\n    child = node.right\n    grand_child = child.left\n    # childを中心にnodeを左に回転\n    child.left = node\n    node.right = grand_child\n    # ノードの高さを更新\n    self.update_height(node)\n    self.update_height(child)\n    # 回転後の部分木のルートを返す\n    return child\n</code></pre> avl_tree.cpp<pre><code>/* 左回転操作 */\nTreeNode *leftRotate(TreeNode *node) {\n    TreeNode *child = node-&gt;right;\n    TreeNode *grandChild = child-&gt;left;\n    // childを中心にnodeを左に回転\n    child-&gt;left = node;\n    node-&gt;right = grandChild;\n    // ノードの高さを更新\n    updateHeight(node);\n    updateHeight(child);\n    // 回転後の部分木のルートを返す\n    return child;\n}\n</code></pre> avl_tree.java<pre><code>/* 左回転操作 */\nTreeNode leftRotate(TreeNode node) {\n    TreeNode child = node.right;\n    TreeNode grandChild = child.left;\n    // child を軸として node を左に回転\n    child.left = node;\n    node.right = grandChild;\n    // ノードの高さを更新\n    updateHeight(node);\n    updateHeight(child);\n    // 回転後の部分木の根を返す\n    return child;\n}\n</code></pre> avl_tree.cs<pre><code>[class]{AVLTree}-[func]{LeftRotate}\n</code></pre> avl_tree.go<pre><code>[class]{aVLTree}-[func]{leftRotate}\n</code></pre> avl_tree.swift<pre><code>[class]{AVLTree}-[func]{leftRotate}\n</code></pre> avl_tree.js<pre><code>[class]{AVLTree}-[func]{leftRotate}\n</code></pre> avl_tree.ts<pre><code>[class]{AVLTree}-[func]{leftRotate}\n</code></pre> avl_tree.dart<pre><code>[class]{AVLTree}-[func]{leftRotate}\n</code></pre> avl_tree.rs<pre><code>[class]{AVLTree}-[func]{left_rotate}\n</code></pre> avl_tree.c<pre><code>[class]{}-[func]{leftRotate}\n</code></pre> avl_tree.kt<pre><code>[class]{AVLTree}-[func]{leftRotate}\n</code></pre> avl_tree.rb<pre><code>[class]{AVLTree}-[func]{left_rotate}\n</code></pre>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#3","level":3,"title":"3.   左右回転","text":"<p>下図に示す不平衡ノード3の場合、左回転または右回転のいずれかだけでは部分木のバランスを回復できません。この場合、まず<code>child</code>に対して「左回転」を実行し、次に<code>node</code>に対して「右回転」を実行する必要があります。</p> <p></p> <p> 図 7-30   左右回転 </p>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#4","level":3,"title":"4.   右左回転","text":"<p>下図に示すように、上記の不平衡二分木の鏡像ケースでは、まず<code>child</code>に対して「右回転」を実行し、次に<code>node</code>に対して「左回転」を実行する必要があります。</p> <p></p> <p> 図 7-31   右左回転 </p>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#5","level":3,"title":"5.   回転の選択","text":"<p>下図に示す4種類の不平衡は、それぞれ上記で説明したケースに対応し、右回転、左右回転、右左回転、左回転が必要です。</p> <p></p> <p> 図 7-32   AVL木の4つの回転ケース </p> <p>下表に示すように、不平衡ノードの平衡因子とその高い側の子の平衡因子の符号を判断することで、不平衡ノードが上記のどのケースに属するかを決定します。</p> <p> 表 7-3   4つの回転ケースの選択条件 </p> 不平衡ノードの平衡因子 子ノードの平衡因子 使用する回転方法 \\(&gt; 1\\)（左に傾いた木） \\(\\geq 0\\) 右回転 \\(&gt; 1\\)（左に傾いた木） \\(&lt;0\\) 左回転してから右回転 \\(&lt; -1\\)（右に傾いた木） \\(\\leq 0\\) 左回転 \\(&lt; -1\\)（右に傾いた木） \\(&gt;0\\) 右回転してから左回転 <p>便宜上、回転操作を関数にカプセル化します。この関数により、さまざまな種類の不平衡に対して回転を実行し、不平衡ノードのバランスを回復できます。コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def rotate(self, node: TreeNode | None) -&gt; TreeNode | None:\n    \"\"\"回転操作を実行して部分木のバランスを復元\"\"\"\n    # nodeのバランス因子を取得\n    balance_factor = self.balance_factor(node)\n    # 左偏り木\n    if balance_factor &gt; 1:\n        if self.balance_factor(node.left) &gt;= 0:\n            # 右回転\n            return self.right_rotate(node)\n        else:\n            # 左回転してから右回転\n            node.left = self.left_rotate(node.left)\n            return self.right_rotate(node)\n    # 右偏り木\n    elif balance_factor &lt; -1:\n        if self.balance_factor(node.right) &lt;= 0:\n            # 左回転\n            return self.left_rotate(node)\n        else:\n            # 右回転してから左回転\n            node.right = self.right_rotate(node.right)\n            return self.left_rotate(node)\n    # バランスの取れた木、回転不要、戻る\n    return node\n</code></pre> avl_tree.cpp<pre><code>/* 回転操作を実行して部分木の平衡を回復 */\nTreeNode *rotate(TreeNode *node) {\n    // nodeの平衡因子を取得\n    int _balanceFactor = balanceFactor(node);\n    // 左に傾いた木\n    if (_balanceFactor &gt; 1) {\n        if (balanceFactor(node-&gt;left) &gt;= 0) {\n            // 右回転\n            return rightRotate(node);\n        } else {\n            // 先に左回転、その後右回転\n            node-&gt;left = leftRotate(node-&gt;left);\n            return rightRotate(node);\n        }\n    }\n    // 右に傾いた木\n    if (_balanceFactor &lt; -1) {\n        if (balanceFactor(node-&gt;right) &lt;= 0) {\n            // 左回転\n            return leftRotate(node);\n        } else {\n            // 先に右回転、その後左回転\n            node-&gt;right = rightRotate(node-&gt;right);\n            return leftRotate(node);\n        }\n    }\n    // 平衡な木、回転不要、そのまま戻る\n    return node;\n}\n</code></pre> avl_tree.java<pre><code>/* 回転操作を実行して部分木の平衡を回復 */\nTreeNode rotate(TreeNode node) {\n    // node の平衡因子を取得\n    int balanceFactor = balanceFactor(node);\n    // 左傾斜の木\n    if (balanceFactor &gt; 1) {\n        if (balanceFactor(node.left) &gt;= 0) {\n            // 右回転\n            return rightRotate(node);\n        } else {\n            // 先に左回転、その後右回転\n            node.left = leftRotate(node.left);\n            return rightRotate(node);\n        }\n    }\n    // 右傾斜の木\n    if (balanceFactor &lt; -1) {\n        if (balanceFactor(node.right) &lt;= 0) {\n            // 左回転\n            return leftRotate(node);\n        } else {\n            // 先に右回転、その後左回転\n            node.right = rightRotate(node.right);\n            return leftRotate(node);\n        }\n    }\n    // 平衡木、回転は不要、戻る\n    return node;\n}\n</code></pre> avl_tree.cs<pre><code>[class]{AVLTree}-[func]{Rotate}\n</code></pre> avl_tree.go<pre><code>[class]{aVLTree}-[func]{rotate}\n</code></pre> avl_tree.swift<pre><code>[class]{AVLTree}-[func]{rotate}\n</code></pre> avl_tree.js<pre><code>[class]{AVLTree}-[func]{rotate}\n</code></pre> avl_tree.ts<pre><code>[class]{AVLTree}-[func]{rotate}\n</code></pre> avl_tree.dart<pre><code>[class]{AVLTree}-[func]{rotate}\n</code></pre> avl_tree.rs<pre><code>[class]{AVLTree}-[func]{rotate}\n</code></pre> avl_tree.c<pre><code>[class]{}-[func]{rotate}\n</code></pre> avl_tree.kt<pre><code>[class]{AVLTree}-[func]{rotate}\n</code></pre> avl_tree.rb<pre><code>[class]{AVLTree}-[func]{rotate}\n</code></pre>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#753-avl","level":2,"title":"7.5.3   AVL木の一般的な操作","text":"","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#1_2","level":3,"title":"1.   ノードの挿入","text":"<p>AVL木のノード挿入操作は二分探索木のそれと似ています。唯一の違いは、AVL木でノードを挿入した後、そのノードから根ノードまでのパス上に一連の不平衡ノードが現れる可能性があることです。したがって、このノードから始めて上向きに回転操作を実行し、すべての不平衡ノードのバランスを回復する必要があります。コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def insert(self, val):\n    \"\"\"ノードを挿入\"\"\"\n    self._root = self.insert_helper(self._root, val)\n\ndef insert_helper(self, node: TreeNode | None, val: int) -&gt; TreeNode:\n    \"\"\"再帰的にノードを挿入（ヘルパーメソッド）\"\"\"\n    if node is None:\n        return TreeNode(val)\n    # 1. 挿入位置を見つけてノードを挿入\n    if val &lt; node.val:\n        node.left = self.insert_helper(node.left, val)\n    elif val &gt; node.val:\n        node.right = self.insert_helper(node.right, val)\n    else:\n        # 重複ノードは挿入しない、戻る\n        return node\n    # ノードの高さを更新\n    self.update_height(node)\n    # 2. 回転操作を実行して部分木のバランスを復元\n    return self.rotate(node)\n</code></pre> avl_tree.cpp<pre><code>/* ノードを挿入 */\nvoid insert(int val) {\n    root = insertHelper(root, val);\n}\n\n/* ノードを再帰的に挿入（ヘルパーメソッド） */\nTreeNode *insertHelper(TreeNode *node, int val) {\n    if (node == nullptr)\n        return new TreeNode(val);\n    /* 1. 挿入位置を見つけてノードを挿入 */\n    if (val &lt; node-&gt;val)\n        node-&gt;left = insertHelper(node-&gt;left, val);\n    else if (val &gt; node-&gt;val)\n        node-&gt;right = insertHelper(node-&gt;right, val);\n    else\n        return node;    // 重複ノードは挿入しない、そのまま戻る\n    updateHeight(node); // ノードの高さを更新\n    /* 2. 回転操作を実行して部分木の平衡を回復 */\n    node = rotate(node);\n    // 部分木のルートノードを返す\n    return node;\n}\n</code></pre> avl_tree.java<pre><code>/* ノードを挿入 */\nvoid insert(int val) {\n    root = insertHelper(root, val);\n}\n\n/* 再帰的にノードを挿入（補助メソッド） */\nTreeNode insertHelper(TreeNode node, int val) {\n    if (node == null)\n        return new TreeNode(val);\n    /* 1. 挿入位置を見つけてノードを挿入 */\n    if (val &lt; node.val)\n        node.left = insertHelper(node.left, val);\n    else if (val &gt; node.val)\n        node.right = insertHelper(node.right, val);\n    else\n        return node; // 重複ノードは挿入しない、戻る\n    updateHeight(node); // ノードの高さを更新\n    /* 2. 回転操作を実行して部分木の平衡を回復 */\n    node = rotate(node);\n    // 部分木の根ノードを返す\n    return node;\n}\n</code></pre> avl_tree.cs<pre><code>[class]{AVLTree}-[func]{Insert}\n\n[class]{AVLTree}-[func]{InsertHelper}\n</code></pre> avl_tree.go<pre><code>[class]{aVLTree}-[func]{insert}\n\n[class]{aVLTree}-[func]{insertHelper}\n</code></pre> avl_tree.swift<pre><code>[class]{AVLTree}-[func]{insert}\n\n[class]{AVLTree}-[func]{insertHelper}\n</code></pre> avl_tree.js<pre><code>[class]{AVLTree}-[func]{insert}\n\n[class]{AVLTree}-[func]{insertHelper}\n</code></pre> avl_tree.ts<pre><code>[class]{AVLTree}-[func]{insert}\n\n[class]{AVLTree}-[func]{insertHelper}\n</code></pre> avl_tree.dart<pre><code>[class]{AVLTree}-[func]{insert}\n\n[class]{AVLTree}-[func]{insertHelper}\n</code></pre> avl_tree.rs<pre><code>[class]{AVLTree}-[func]{insert}\n\n[class]{AVLTree}-[func]{insert_helper}\n</code></pre> avl_tree.c<pre><code>[class]{AVLTree}-[func]{insert}\n\n[class]{}-[func]{insertHelper}\n</code></pre> avl_tree.kt<pre><code>[class]{AVLTree}-[func]{insert}\n\n[class]{AVLTree}-[func]{insertHelper}\n</code></pre> avl_tree.rb<pre><code>[class]{AVLTree}-[func]{insert}\n\n[class]{AVLTree}-[func]{insert_helper}\n</code></pre>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#2_2","level":3,"title":"2.   ノードの削除","text":"<p>同様に、二分探索木でのノード削除方法に基づいて、下から上へ回転操作を実行してすべての不平衡ノードのバランスを回復する必要があります。コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def remove(self, val: int):\n    \"\"\"ノードを削除\"\"\"\n    self._root = self.remove_helper(self._root, val)\n\ndef remove_helper(self, node: TreeNode | None, val: int) -&gt; TreeNode | None:\n    \"\"\"再帰的にノードを削除（ヘルパーメソッド）\"\"\"\n    if node is None:\n        return None\n    # 1. ノードを見つけて削除\n    if val &lt; node.val:\n        node.left = self.remove_helper(node.left, val)\n    elif val &gt; node.val:\n        node.right = self.remove_helper(node.right, val)\n    else:\n        if node.left is None or node.right is None:\n            child = node.left or node.right\n            # 子ノード数 = 0、ノードを削除して戻る\n            if child is None:\n                return None\n            # 子ノード数 = 1、ノードを削除\n            else:\n                node = child\n        else:\n            # 子ノード数 = 2、中順走査の次のノードを削除し、それで現在のノードを置き換え\n            temp = node.right\n            while temp.left is not None:\n                temp = temp.left\n            node.right = self.remove_helper(node.right, temp.val)\n            node.val = temp.val\n    # ノードの高さを更新\n    self.update_height(node)\n    # 2. 回転操作を実行して部分木のバランスを復元\n    return self.rotate(node)\n</code></pre> avl_tree.cpp<pre><code>/* ノードを削除 */\nvoid remove(int val) {\n    root = removeHelper(root, val);\n}\n\n/* ノードを再帰的に削除（ヘルパーメソッド） */\nTreeNode *removeHelper(TreeNode *node, int val) {\n    if (node == nullptr)\n        return nullptr;\n    /* 1. ノードを見つけて削除 */\n    if (val &lt; node-&gt;val)\n        node-&gt;left = removeHelper(node-&gt;left, val);\n    else if (val &gt; node-&gt;val)\n        node-&gt;right = removeHelper(node-&gt;right, val);\n    else {\n        if (node-&gt;left == nullptr || node-&gt;right == nullptr) {\n            TreeNode *child = node-&gt;left != nullptr ? node-&gt;left : node-&gt;right;\n            // 子ノード数 = 0、ノードを削除して戻る\n            if (child == nullptr) {\n                delete node;\n                return nullptr;\n            }\n            // 子ノード数 = 1、ノードを削除\n            else {\n                delete node;\n                node = child;\n            }\n        } else {\n            // 子ノード数 = 2、中順走査の次のノードを削除し、現在のノードと置き換える\n            TreeNode *temp = node-&gt;right;\n            while (temp-&gt;left != nullptr) {\n                temp = temp-&gt;left;\n            }\n            int tempVal = temp-&gt;val;\n            node-&gt;right = removeHelper(node-&gt;right, temp-&gt;val);\n            node-&gt;val = tempVal;\n        }\n    }\n    updateHeight(node); // ノードの高さを更新\n    /* 2. 回転操作を実行して部分木の平衡を回復 */\n    node = rotate(node);\n    // 部分木のルートノードを返す\n    return node;\n}\n</code></pre> avl_tree.java<pre><code>/* ノードを削除 */\nvoid remove(int val) {\n    root = removeHelper(root, val);\n}\n\n/* 再帰的にノードを削除（補助メソッド） */\nTreeNode removeHelper(TreeNode node, int val) {\n    if (node == null)\n        return null;\n    /* 1. ノードを見つけて削除 */\n    if (val &lt; node.val)\n        node.left = removeHelper(node.left, val);\n    else if (val &gt; node.val)\n        node.right = removeHelper(node.right, val);\n    else {\n        if (node.left == null || node.right == null) {\n            TreeNode child = node.left != null ? node.left : node.right;\n            // 子ノード数 = 0、ノードを削除して戻る\n            if (child == null)\n                return null;\n            // 子ノード数 = 1、ノードを削除\n            else\n                node = child;\n        } else {\n            // 子ノード数 = 2、中順走査の次のノードを削除し、現在のノードをそれで置き換える\n            TreeNode temp = node.right;\n            while (temp.left != null) {\n                temp = temp.left;\n            }\n            node.right = removeHelper(node.right, temp.val);\n            node.val = temp.val;\n        }\n    }\n    updateHeight(node); // ノードの高さを更新\n    /* 2. 回転操作を実行して部分木の平衡を回復 */\n    node = rotate(node);\n    // 部分木の根ノードを返す\n    return node;\n}\n</code></pre> avl_tree.cs<pre><code>[class]{AVLTree}-[func]{Remove}\n\n[class]{AVLTree}-[func]{RemoveHelper}\n</code></pre> avl_tree.go<pre><code>[class]{aVLTree}-[func]{remove}\n\n[class]{aVLTree}-[func]{removeHelper}\n</code></pre> avl_tree.swift<pre><code>[class]{AVLTree}-[func]{remove}\n\n[class]{AVLTree}-[func]{removeHelper}\n</code></pre> avl_tree.js<pre><code>[class]{AVLTree}-[func]{remove}\n\n[class]{AVLTree}-[func]{removeHelper}\n</code></pre> avl_tree.ts<pre><code>[class]{AVLTree}-[func]{remove}\n\n[class]{AVLTree}-[func]{removeHelper}\n</code></pre> avl_tree.dart<pre><code>[class]{AVLTree}-[func]{remove}\n\n[class]{AVLTree}-[func]{removeHelper}\n</code></pre> avl_tree.rs<pre><code>[class]{AVLTree}-[func]{remove}\n\n[class]{AVLTree}-[func]{remove_helper}\n</code></pre> avl_tree.c<pre><code>[class]{AVLTree}-[func]{removeItem}\n\n[class]{}-[func]{removeHelper}\n</code></pre> avl_tree.kt<pre><code>[class]{AVLTree}-[func]{remove}\n\n[class]{AVLTree}-[func]{removeHelper}\n</code></pre> avl_tree.rb<pre><code>[class]{AVLTree}-[func]{remove}\n\n[class]{AVLTree}-[func]{remove_helper}\n</code></pre>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#3_1","level":3,"title":"3.   ノードの検索","text":"<p>AVL木でのノード検索操作は二分探索木のそれと一致しており、ここでは詳述しません。</p>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#754-avl","level":2,"title":"7.5.4   AVL木の典型的な応用","text":"<ul> <li>大量のデータの整理と格納に使用され、検索頻度が高く、挿入と削除の頻度が低いシナリオに適しています。</li> <li>データベースのインデックスシステムの構築に使用されます。</li> <li>赤黒木も一般的な平衡二分探索木の一種です。AVL木と比較して、赤黒木はより緩い平衡条件を持ち、ノードの挿入と削除にかかる回転数が少なく、ノードの追加と削除操作の平均効率が高くなります。</li> </ul>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL木 *"],"tags":[]},{"location":"chapter_tree/binary_search_tree/","level":1,"title":"7.4   二分探索木","text":"<p>下図に示すように、二分探索木は以下の条件を満たします。</p> <ol> <li>根ノードについて、左部分木のすべてのノードの値 \\(&lt;\\) 根ノードの値 \\(&lt;\\) 右部分木のすべてのノードの値。</li> <li>任意のノードの左と右の部分木も二分探索木です。つまり、条件<code>1.</code>も満たします。</li> </ol> <p></p> <p> 図 7-16   二分探索木 </p>","path":["第 7 章 &nbsp; 木","7.4 &nbsp; 二分探索木"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#741","level":2,"title":"7.4.1   二分探索木の操作","text":"<p>二分探索木をクラス<code>BinarySearchTree</code>としてカプセル化し、木の根ノードを指すメンバー変数<code>root</code>を宣言します。</p>","path":["第 7 章 &nbsp; 木","7.4 &nbsp; 二分探索木"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#1","level":3,"title":"1.   ノードの検索","text":"<p>ターゲットノード値<code>num</code>が与えられた場合、二分探索木の性質に従って検索できます。下図に示すように、ノード<code>cur</code>を宣言し、二分木の根ノード<code>root</code>から開始し、ノード値<code>cur.val</code>と<code>num</code>のサイズを比較するループを行います。</p> <ul> <li><code>cur.val &lt; num</code>の場合、ターゲットノードは<code>cur</code>の右部分木にあることを意味するため、<code>cur = cur.right</code>を実行します。</li> <li><code>cur.val &gt; num</code>の場合、ターゲットノードは<code>cur</code>の左部分木にあることを意味するため、<code>cur = cur.left</code>を実行します。</li> <li><code>cur.val = num</code>の場合、ターゲットノードが見つかったことを意味するため、ループを終了してノードを返します。</li> </ul> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p> 図 7-17   二分探索木でのノード検索例 </p> <p>二分探索木での検索操作は二分探索アルゴリズムと同じ原理で動作し、各ラウンドでケースの半分を排除します。ループ数は最大で二分木の高さです。二分木が平衡している場合、\\(O(\\log n)\\)の時間を使用します。コード例は以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_tree.py<pre><code>def search(self, num: int) -&gt; TreeNode | None:\n    \"\"\"ノードを探索\"\"\"\n    cur = self._root\n    # ループで探索、葉ノードを通過した後にブレーク\n    while cur is not None:\n        # ターゲットノードはcurの右部分木にある\n        if cur.val &lt; num:\n            cur = cur.right\n        # ターゲットノードはcurの左部分木にある\n        elif cur.val &gt; num:\n            cur = cur.left\n        # ターゲットノードを発見、ループをブレーク\n        else:\n            break\n    return cur\n</code></pre> binary_search_tree.cpp<pre><code>/* ノードを検索 */\nTreeNode *search(int num) {\n    TreeNode *cur = root;\n    // ループで検索、葉ノードを通り過ぎたら終了\n    while (cur != nullptr) {\n        // 目標ノードはcurの右部分木にある\n        if (cur-&gt;val &lt; num)\n            cur = cur-&gt;right;\n        // 目標ノードはcurの左部分木にある\n        else if (cur-&gt;val &gt; num)\n            cur = cur-&gt;left;\n        // 目標ノードを見つけた、ループを抜ける\n        else\n            break;\n    }\n    // 目標ノードを返す\n    return cur;\n}\n</code></pre> binary_search_tree.java<pre><code>/* ノードを検索 */\nTreeNode search(int num) {\n    TreeNode cur = root;\n    // ループで検索、葉ノードを通過後に終了\n    while (cur != null) {\n        // 対象ノードは cur の右部分木にある\n        if (cur.val &lt; num)\n            cur = cur.right;\n        // 対象ノードは cur の左部分木にある\n        else if (cur.val &gt; num)\n            cur = cur.left;\n        // 対象ノードを見つけた、ループを終了\n        else\n            break;\n    }\n    // 対象ノードを返す\n    return cur;\n}\n</code></pre> binary_search_tree.cs<pre><code>[class]{BinarySearchTree}-[func]{Search}\n</code></pre> binary_search_tree.go<pre><code>[class]{binarySearchTree}-[func]{search}\n</code></pre> binary_search_tree.swift<pre><code>[class]{BinarySearchTree}-[func]{search}\n</code></pre> binary_search_tree.js<pre><code>[class]{BinarySearchTree}-[func]{search}\n</code></pre> binary_search_tree.ts<pre><code>[class]{BinarySearchTree}-[func]{search}\n</code></pre> binary_search_tree.dart<pre><code>[class]{BinarySearchTree}-[func]{search}\n</code></pre> binary_search_tree.rs<pre><code>[class]{BinarySearchTree}-[func]{search}\n</code></pre> binary_search_tree.c<pre><code>[class]{BinarySearchTree}-[func]{search}\n</code></pre> binary_search_tree.kt<pre><code>[class]{BinarySearchTree}-[func]{search}\n</code></pre> binary_search_tree.rb<pre><code>[class]{BinarySearchTree}-[func]{search}\n</code></pre>","path":["第 7 章 &nbsp; 木","7.4 &nbsp; 二分探索木"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#2","level":3,"title":"2.   ノードの挿入","text":"<p>挿入する要素<code>num</code>が与えられた場合、二分探索木の性質「左部分木 &lt; 根ノード &lt; 右部分木」を維持するため、挿入操作は下図に示すように進行します。</p> <ol> <li>挿入位置を見つける: 検索操作と同様に、根ノードから開始し、現在のノード値と<code>num</code>のサイズ関係に従って下向きにループし、葉ノードを通過（<code>None</code>に走査）するまで、ループを終了します。</li> <li>この位置にノードを挿入: ノード<code>num</code>を初期化し、<code>None</code>があった場所に配置します。</li> </ol> <p></p> <p> 図 7-18   二分探索木へのノード挿入 </p> <p>コード実装では、以下の2点に注意してください。</p> <ul> <li>二分探索木は重複ノードの存在を許可しません。そうでなければ、その定義に違反します。したがって、挿入するノードが既に木に存在する場合、挿入は実行されず、ノードは直接戻ります。</li> <li>挿入操作を実行するには、前のループからのノードを保存するためにノード<code>pre</code>を使用する必要があります。このようにして、<code>None</code>に走査したときに、その親ノードを取得でき、ノード挿入操作を完了できます。</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_tree.py<pre><code>def insert(self, num: int):\n    \"\"\"ノードを挿入\"\"\"\n    # 木が空の場合、ルートノードを初期化\n    if self._root is None:\n        self._root = TreeNode(num)\n        return\n    # ループで探索、葉ノードを通過した後にブレーク\n    cur, pre = self._root, None\n    while cur is not None:\n        # 重複ノードを発見したため、戻る\n        if cur.val == num:\n            return\n        pre = cur\n        # 挿入位置はcurの右部分木にある\n        if cur.val &lt; num:\n            cur = cur.right\n        # 挿入位置はcurの左部分木にある\n        else:\n            cur = cur.left\n    # ノードを挿入\n    node = TreeNode(num)\n    if pre.val &lt; num:\n        pre.right = node\n    else:\n        pre.left = node\n</code></pre> binary_search_tree.cpp<pre><code>/* ノードを挿入 */\nvoid insert(int num) {\n    // 木が空の場合、ルートノードを初期化\n    if (root == nullptr) {\n        root = new TreeNode(num);\n        return;\n    }\n    TreeNode *cur = root, *pre = nullptr;\n    // ループで検索、葉ノードを通り過ぎたら終了\n    while (cur != nullptr) {\n        // 重複ノードを見つけた場合、戻る\n        if (cur-&gt;val == num)\n            return;\n        pre = cur;\n        // 挿入位置はcurの右部分木にある\n        if (cur-&gt;val &lt; num)\n            cur = cur-&gt;right;\n        // 挿入位置はcurの左部分木にある\n        else\n            cur = cur-&gt;left;\n    }\n    // ノードを挿入\n    TreeNode *node = new TreeNode(num);\n    if (pre-&gt;val &lt; num)\n        pre-&gt;right = node;\n    else\n        pre-&gt;left = node;\n}\n</code></pre> binary_search_tree.java<pre><code>/* ノードを挿入 */\nvoid insert(int num) {\n    // 木が空の場合、根ノードを初期化\n    if (root == null) {\n        root = new TreeNode(num);\n        return;\n    }\n    TreeNode cur = root, pre = null;\n    // ループで検索、葉ノードを通過後に終了\n    while (cur != null) {\n        // 重複ノードを見つけた場合、戻る\n        if (cur.val == num)\n            return;\n        pre = cur;\n        // 挿入位置は cur の右部分木にある\n        if (cur.val &lt; num)\n            cur = cur.right;\n        // 挿入位置は cur の左部分木にある\n        else\n            cur = cur.left;\n    }\n    // ノードを挿入\n    TreeNode node = new TreeNode(num);\n    if (pre.val &lt; num)\n        pre.right = node;\n    else\n        pre.left = node;\n}\n</code></pre> binary_search_tree.cs<pre><code>[class]{BinarySearchTree}-[func]{Insert}\n</code></pre> binary_search_tree.go<pre><code>[class]{binarySearchTree}-[func]{insert}\n</code></pre> binary_search_tree.swift<pre><code>[class]{BinarySearchTree}-[func]{insert}\n</code></pre> binary_search_tree.js<pre><code>[class]{BinarySearchTree}-[func]{insert}\n</code></pre> binary_search_tree.ts<pre><code>[class]{BinarySearchTree}-[func]{insert}\n</code></pre> binary_search_tree.dart<pre><code>[class]{BinarySearchTree}-[func]{insert}\n</code></pre> binary_search_tree.rs<pre><code>[class]{BinarySearchTree}-[func]{insert}\n</code></pre> binary_search_tree.c<pre><code>[class]{BinarySearchTree}-[func]{insert}\n</code></pre> binary_search_tree.kt<pre><code>[class]{BinarySearchTree}-[func]{insert}\n</code></pre> binary_search_tree.rb<pre><code>[class]{BinarySearchTree}-[func]{insert}\n</code></pre> <p>ノードの検索と同様に、ノードの挿入には\\(O(\\log n)\\)の時間を使用します。</p>","path":["第 7 章 &nbsp; 木","7.4 &nbsp; 二分探索木"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#3","level":3,"title":"3.   ノードの削除","text":"<p>まず、二分木でターゲットノードを見つけ、それを削除します。ノードの挿入と同様に、削除操作が完了した後も、二分探索木の性質「左部分木 &lt; 根ノード &lt; 右部分木」が満たされることを保証する必要があります。したがって、ターゲットノードの子ノード数に基づいて、0、1、2の3つのケースに分け、対応するノード削除操作を実行します。</p> <p>下図に示すように、削除するノードの次数が\\(0\\)の場合、そのノードは葉ノードであることを意味し、直接削除できます。</p> <p></p> <p> 図 7-19   二分探索木でのノード削除（次数0） </p> <p>下図に示すように、削除するノードの次数が\\(1\\)の場合、削除するノードをその子ノードで置き換えるだけで十分です。</p> <p></p> <p> 図 7-20   二分探索木でのノード削除（次数1） </p> <p>削除するノードの次数が\\(2\\)の場合、直接削除することはできませんが、ノードを使用して置き換える必要があります。二分探索木の性質「左部分木 \\(&lt;\\) 根ノード \\(&lt;\\) 右部分木」を維持するため、このノードは右部分木の最小ノードまたは左部分木の最大ノードのいずれかです。</p> <p>右部分木の最小ノード（中順走査での次のノード）を選択すると仮定すると、削除操作は下図に示すように進行します。</p> <ol> <li>削除するノードの「中順走査シーケンス」での次のノードを見つけ、<code>tmp</code>として示します。</li> <li>削除するノードの値を<code>tmp</code>の値で置き換え、木内でノード<code>tmp</code>を再帰的に削除します。</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p> 図 7-21   二分探索木でのノード削除（次数2） </p> <p>ノードを削除する操作も\\(O(\\log n)\\)の時間を使用します。削除するノードを見つけるのに\\(O(\\log n)\\)の時間が必要で、中順走査の後継ノードを取得するのに\\(O(\\log n)\\)の時間が必要です。コード例は以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_tree.py<pre><code>def remove(self, num: int):\n    \"\"\"ノードを削除\"\"\"\n    # 木が空の場合、戻る\n    if self._root is None:\n        return\n    # ループで探索、葉ノードを通過した後にブレーク\n    cur, pre = self._root, None\n    while cur is not None:\n        # 削除するノードを発見、ループをブレーク\n        if cur.val == num:\n            break\n        pre = cur\n        # 削除するノードはcurの右部分木にある\n        if cur.val &lt; num:\n            cur = cur.right\n        # 削除するノードはcurの左部分木にある\n        else:\n            cur = cur.left\n    # 削除するノードが存在しない場合、戻る\n    if cur is None:\n        return\n\n    # 子ノード数 = 0 または 1\n    if cur.left is None or cur.right is None:\n        # 子ノード数 = 0/1の場合、child = null/その子ノード\n        child = cur.left or cur.right\n        # ノードcurを削除\n        if cur != self._root:\n            if pre.left == cur:\n                pre.left = child\n            else:\n                pre.right = child\n        else:\n            # 削除されるノードがルートの場合、ルートを再割り当て\n            self._root = child\n    # 子ノード数 = 2\n    else:\n        # curの中順走査の次のノードを取得\n        tmp: TreeNode = cur.right\n        while tmp.left is not None:\n            tmp = tmp.left\n        # 再帰的にノードtmpを削除\n        self.remove(tmp.val)\n        # curをtmpで置き換え\n        cur.val = tmp.val\n</code></pre> binary_search_tree.cpp<pre><code>/* ノードを削除 */\nvoid remove(int num) {\n    // 木が空の場合、戻る\n    if (root == nullptr)\n        return;\n    TreeNode *cur = root, *pre = nullptr;\n    // ループで検索、葉ノードを通り過ぎたら終了\n    while (cur != nullptr) {\n        // 削除するノードを見つけた、ループを抜ける\n        if (cur-&gt;val == num)\n            break;\n        pre = cur;\n        // 削除するノードはcurの右部分木にある\n        if (cur-&gt;val &lt; num)\n            cur = cur-&gt;right;\n        // 削除するノードはcurの左部分木にある\n        else\n            cur = cur-&gt;left;\n    }\n    // 削除するノードがない場合、戻る\n    if (cur == nullptr)\n        return;\n    // 子ノード数 = 0 または 1\n    if (cur-&gt;left == nullptr || cur-&gt;right == nullptr) {\n        // 子ノード数 = 0 / 1の場合、child = nullptr / その子ノード\n        TreeNode *child = cur-&gt;left != nullptr ? cur-&gt;left : cur-&gt;right;\n        // ノードcurを削除\n        if (cur != root) {\n            if (pre-&gt;left == cur)\n                pre-&gt;left = child;\n            else\n                pre-&gt;right = child;\n        } else {\n            // 削除されるノードがルートの場合、ルートを再割り当て\n            root = child;\n        }\n        // メモリを解放\n        delete cur;\n    }\n    // 子ノード数 = 2\n    else {\n        // curの中順走査の次のノードを取得\n        TreeNode *tmp = cur-&gt;right;\n        while (tmp-&gt;left != nullptr) {\n            tmp = tmp-&gt;left;\n        }\n        int tmpVal = tmp-&gt;val;\n        // ノードtmpを再帰的に削除\n        remove(tmp-&gt;val);\n        // curをtmpで置き換え\n        cur-&gt;val = tmpVal;\n    }\n}\n</code></pre> binary_search_tree.java<pre><code>/* ノードを削除 */\nvoid remove(int num) {\n    // 木が空の場合、戻る\n    if (root == null)\n        return;\n    TreeNode cur = root, pre = null;\n    // ループで検索、葉ノードを通過後に終了\n    while (cur != null) {\n        // 削除するノードを見つけた、ループを終了\n        if (cur.val == num)\n            break;\n        pre = cur;\n        // 削除するノードは cur の右部分木にある\n        if (cur.val &lt; num)\n            cur = cur.right;\n        // 削除するノードは cur の左部分木にある\n        else\n            cur = cur.left;\n    }\n    // 削除するノードがない場合、戻る\n    if (cur == null)\n        return;\n    // 子ノード数 = 0 または 1\n    if (cur.left == null || cur.right == null) {\n        // 子ノード数 = 0/1 の場合、child = null/その子ノード\n        TreeNode child = cur.left != null ? cur.left : cur.right;\n        // ノード cur を削除\n        if (cur != root) {\n            if (pre.left == cur)\n                pre.left = child;\n            else\n                pre.right = child;\n        } else {\n            // 削除されるノードが根の場合、根を再割り当て\n            root = child;\n        }\n    }\n    // 子ノード数 = 2\n    else {\n        // cur の中順走査の次のノードを取得\n        TreeNode tmp = cur.right;\n        while (tmp.left != null) {\n            tmp = tmp.left;\n        }\n        // 再帰的にノード tmp を削除\n        remove(tmp.val);\n        // cur を tmp で置き換える\n        cur.val = tmp.val;\n    }\n}\n</code></pre> binary_search_tree.cs<pre><code>[class]{BinarySearchTree}-[func]{Remove}\n</code></pre> binary_search_tree.go<pre><code>[class]{binarySearchTree}-[func]{remove}\n</code></pre> binary_search_tree.swift<pre><code>[class]{BinarySearchTree}-[func]{remove}\n</code></pre> binary_search_tree.js<pre><code>[class]{BinarySearchTree}-[func]{remove}\n</code></pre> binary_search_tree.ts<pre><code>[class]{BinarySearchTree}-[func]{remove}\n</code></pre> binary_search_tree.dart<pre><code>[class]{BinarySearchTree}-[func]{remove}\n</code></pre> binary_search_tree.rs<pre><code>[class]{BinarySearchTree}-[func]{remove}\n</code></pre> binary_search_tree.c<pre><code>[class]{BinarySearchTree}-[func]{removeItem}\n</code></pre> binary_search_tree.kt<pre><code>[class]{BinarySearchTree}-[func]{remove}\n</code></pre> binary_search_tree.rb<pre><code>[class]{BinarySearchTree}-[func]{remove}\n</code></pre>","path":["第 7 章 &nbsp; 木","7.4 &nbsp; 二分探索木"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#4","level":3,"title":"4.   中順走査は順序付けされている","text":"<p>下図に示すように、二分木の中順走査は「左 \\(\\rightarrow\\) 根 \\(\\rightarrow\\) 右」の走査順序に従い、二分探索木は「左子ノード \\(&lt;\\) 根ノード \\(&lt;\\) 右子ノード」のサイズ関係を満たします。</p> <p>これは、二分探索木で中順走査を実行するときに、常に次に小さいノードが最初に走査されることを意味し、重要な性質につながります：二分探索木の中順走査のシーケンスは昇順です。</p> <p>中順走査の昇順性質を使用して、二分探索木で順序付けされたデータを取得するには\\(O(n)\\)の時間のみが必要で、追加のソート操作は不要であり、非常に効率的です。</p> <p></p> <p> 図 7-22   二分探索木の中順走査シーケンス </p>","path":["第 7 章 &nbsp; 木","7.4 &nbsp; 二分探索木"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#742","level":2,"title":"7.4.2   二分探索木の効率","text":"<p>データのセットが与えられた場合、配列または二分探索木を使用して格納することを検討します。下の表を観察すると、二分探索木のすべての操作は対数時間計算量を持ち、安定して効率的です。配列は、頻繁な追加と検索や削除の頻度が少ないシナリオでのみ、二分探索木よりも効率的です。</p> <p> 表 7-2   配列と探索木の効率比較 </p> 未ソート配列 二分探索木 要素の検索 \\(O(n)\\) \\(O(\\log n)\\) 要素の挿入 \\(O(1)\\) \\(O(\\log n)\\) 要素の削除 \\(O(n)\\) \\(O(\\log n)\\) <p>理想的には、二分探索木は「平衡」しており、任意のノードを\\(\\log n\\)ループ内で見つけることができます。</p> <p>しかし、二分探索木で継続的にノードを挿入および削除すると、下図に示すように連結リストに退化する可能性があり、さまざまな操作の時間計算量も\\(O(n)\\)に悪化します。</p> <p></p> <p> 図 7-23   二分探索木の退化 </p>","path":["第 7 章 &nbsp; 木","7.4 &nbsp; 二分探索木"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#743","level":2,"title":"7.4.3   二分探索木の一般的な応用","text":"<ul> <li>システムでの多レベルインデックスとして使用され、効率的な検索、挿入、削除操作を実装します。</li> <li>特定の検索アルゴリズムの基盤となるデータ構造として機能します。</li> <li>データストリームを格納して、その順序付けされた状態を維持するために使用されます。</li> </ul>","path":["第 7 章 &nbsp; 木","7.4 &nbsp; 二分探索木"],"tags":[]},{"location":"chapter_tree/binary_tree/","level":1,"title":"7.1   二分木","text":"<p>二分木は、祖先と子孫の間の階層関係を表現し、「二つに分割する」分割統治法の論理を体現する非線形データ構造です。連結リストと同様に、二分木の基本単位はノードであり、各ノードは値、左の子ノードへの参照、右の子ノードへの参照を含みます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>class TreeNode:\n    \"\"\"二分木ノード\"\"\"\n    def __init__(self, val: int):\n        self.val: int = val                # ノード値\n        self.left: TreeNode | None = None  # 左の子ノードへの参照\n        self.right: TreeNode | None = None # 右の子ノードへの参照\n</code></pre> <pre><code>/* 二分木ノード */\nstruct TreeNode {\n    int val;          // ノード値\n    TreeNode *left;   // 左の子ノードへのポインタ\n    TreeNode *right;  // 右の子ノードへのポインタ\n    TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}\n};\n</code></pre> <pre><code>/* 二分木ノード */\nclass TreeNode {\n    int val;         // ノード値\n    TreeNode left;   // 左の子ノードへの参照\n    TreeNode right;  // 右の子ノードへの参照\n    TreeNode(int x) { val = x; }\n}\n</code></pre> <pre><code>/* 二分木ノード */\nclass TreeNode(int? x) {\n    public int? val = x;    // ノード値\n    public TreeNode? left;  // 左の子ノードへの参照\n    public TreeNode? right; // 右の子ノードへの参照\n}\n</code></pre> <pre><code>/* 二分木ノード */\ntype TreeNode struct {\n    Val   int\n    Left  *TreeNode\n    Right *TreeNode\n}\n/* コンストラクタ */\nfunc NewTreeNode(v int) *TreeNode {\n    return &amp;TreeNode{\n        Left:  nil, // 左の子ノードへのポインタ\n        Right: nil, // 右の子ノードへのポインタ\n        Val:   v,   // ノード値\n    }\n}\n</code></pre> <pre><code>/* 二分木ノード */\nclass TreeNode {\n    var val: Int // ノード値\n    var left: TreeNode? // 左の子ノードへの参照\n    var right: TreeNode? // 右の子ノードへの参照\n\n    init(x: Int) {\n        val = x\n    }\n}\n</code></pre> <pre><code>/* 二分木ノード */\nclass TreeNode {\n    val; // ノード値\n    left; // 左の子ノードへのポインタ\n    right; // 右の子ノードへのポインタ\n    constructor(val, left, right) {\n        this.val = val === undefined ? 0 : val;\n        this.left = left === undefined ? null : left;\n        this.right = right === undefined ? null : right;\n    }\n}\n</code></pre> <pre><code>/* 二分木ノード */\nclass TreeNode {\n    val: number;\n    left: TreeNode | null;\n    right: TreeNode | null;\n\n    constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {\n        this.val = val === undefined ? 0 : val; // ノード値\n        this.left = left === undefined ? null : left; // 左の子ノードへの参照\n        this.right = right === undefined ? null : right; // 右の子ノードへの参照\n    }\n}\n</code></pre> <pre><code>/* 二分木ノード */\nclass TreeNode {\n  int val;         // ノード値\n  TreeNode? left;  // 左の子ノードへの参照\n  TreeNode? right; // 右の子ノードへの参照\n  TreeNode(this.val, [this.left, this.right]);\n}\n</code></pre> <pre><code>use std::rc::Rc;\nuse std::cell::RefCell;\n\n/* 二分木ノード */\nstruct TreeNode {\n    val: i32,                               // ノード値\n    left: Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,    // 左の子ノードへの参照\n    right: Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,   // 右の子ノードへの参照\n}\n\nimpl TreeNode {\n    /* コンストラクタ */\n    fn new(val: i32) -&gt; Rc&lt;RefCell&lt;Self&gt;&gt; {\n        Rc::new(RefCell::new(Self {\n            val,\n            left: None,\n            right: None\n        }))\n    }\n}\n</code></pre> <pre><code>/* 二分木ノード */\ntypedef struct TreeNode {\n    int val;                // ノード値\n    int height;             // ノードの高さ\n    struct TreeNode *left;  // 左の子ノードへのポインタ\n    struct TreeNode *right; // 右の子ノードへのポインタ\n} TreeNode;\n\n/* コンストラクタ */\nTreeNode *newTreeNode(int val) {\n    TreeNode *node;\n\n    node = (TreeNode *)malloc(sizeof(TreeNode));\n    node-&gt;val = val;\n    node-&gt;height = 0;\n    node-&gt;left = NULL;\n    node-&gt;right = NULL;\n    return node;\n}\n</code></pre> <pre><code>/* 二分木ノード */\nclass TreeNode(val _val: Int) {  // ノード値\n    val left: TreeNode? = null   // 左の子ノードへの参照\n    val right: TreeNode? = null  // 右の子ノードへの参照\n}\n</code></pre> <pre><code>\n</code></pre> <p>各ノードは2つの参照（ポインタ）を持ち、それぞれ左の子ノードと右の子ノードを指しています。このノードは、これら2つの子ノードの親ノードと呼ばれます。二分木のノードが与えられたとき、このノードの左の子とその下にあるすべてのノードで形成される木を、このノードの左部分木と呼びます。同様に、右部分木も定義できます。</p> <p>二分木では、葉ノードを除いて、他のすべてのノードは子ノードと空でない部分木を含みます。 下図に示すように、「ノード2」を親ノードとして見ると、その左と右の子ノードはそれぞれ「ノード4」と「ノード5」です。左部分木は「ノード4」とその下にあるすべてのノードで形成され、右部分木は「ノード5」とその下にあるすべてのノードで形成されます。</p> <p></p> <p> 図 7-1   親ノード、子ノード、部分木 </p>","path":["第 7 章 &nbsp; 木","7.1 &nbsp; 二分木"],"tags":[]},{"location":"chapter_tree/binary_tree/#711","level":2,"title":"7.1.1   二分木の一般的な用語","text":"<p>二分木でよく使用される用語を下図に示します。</p> <ul> <li>根ノード：二分木の最上位レベルにあるノードで、親ノードを持ちません。</li> <li>葉ノード：子ノードを持たないノードで、両方のポインタが<code>None</code>を指しています。</li> <li>辺：2つのノードを結ぶ線分で、ノード間の参照（ポインタ）を表現します。</li> <li>ノードのレベル：上から下に向かって増加し、根ノードがレベル1です。</li> <li>ノードの次数：ノードが持つ子ノードの数です。二分木では、次数は0、1、または2になります。</li> <li>二分木の高さ：根ノードから最も遠い葉ノードまでの辺の数です。</li> <li>ノードの深さ：根ノードからそのノードまでの辺の数です。</li> <li>ノードの高さ：最も遠い葉ノードからそのノードまでの辺の数です。</li> </ul> <p></p> <p> 図 7-2   二分木の一般的な用語 </p> <p>Tip</p> <p>「高さ」と「深さ」は通常「通過する辺の数」として定義しますが、一部の問題や教科書では「通過するノードの数」として定義されることがあります。この場合、高さと深さの両方を1だけ増やす必要があります。</p>","path":["第 7 章 &nbsp; 木","7.1 &nbsp; 二分木"],"tags":[]},{"location":"chapter_tree/binary_tree/#712","level":2,"title":"7.1.2   二分木の基本操作","text":"","path":["第 7 章 &nbsp; 木","7.1 &nbsp; 二分木"],"tags":[]},{"location":"chapter_tree/binary_tree/#1","level":3,"title":"1.   二分木の初期化","text":"<p>連結リストと同様に、二分木の初期化では、まずノードを作成し、次にそれらの間の参照（ポインタ）を確立します。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_tree.py<pre><code># 二分木の初期化\n# ノードの初期化\nn1 = TreeNode(val=1)\nn2 = TreeNode(val=2)\nn3 = TreeNode(val=3)\nn4 = TreeNode(val=4)\nn5 = TreeNode(val=5)\n# ノード間の参照（ポインタ）を結ぶ\nn1.left = n2\nn1.right = n3\nn2.left = n4\nn2.right = n5\n</code></pre> binary_tree.cpp<pre><code>/* 二分木の初期化 */\n// ノードの初期化\nTreeNode* n1 = new TreeNode(1);\nTreeNode* n2 = new TreeNode(2);\nTreeNode* n3 = new TreeNode(3);\nTreeNode* n4 = new TreeNode(4);\nTreeNode* n5 = new TreeNode(5);\n// ノード間の参照（ポインタ）を結ぶ\nn1-&gt;left = n2;\nn1-&gt;right = n3;\nn2-&gt;left = n4;\nn2-&gt;right = n5;\n</code></pre> binary_tree.java<pre><code>// ノードの初期化\nTreeNode n1 = new TreeNode(1);\nTreeNode n2 = new TreeNode(2);\nTreeNode n3 = new TreeNode(3);\nTreeNode n4 = new TreeNode(4);\nTreeNode n5 = new TreeNode(5);\n// ノード間の参照（ポインタ）を結ぶ\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.cs<pre><code>/* 二分木の初期化 */\n// ノードの初期化\nTreeNode n1 = new(1);\nTreeNode n2 = new(2);\nTreeNode n3 = new(3);\nTreeNode n4 = new(4);\nTreeNode n5 = new(5);\n// ノード間の参照（ポインタ）を結ぶ\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.go<pre><code>/* 二分木の初期化 */\n// ノードの初期化\nn1 := NewTreeNode(1)\nn2 := NewTreeNode(2)\nn3 := NewTreeNode(3)\nn4 := NewTreeNode(4)\nn5 := NewTreeNode(5)\n// ノード間の参照（ポインタ）を結ぶ\nn1.Left = n2\nn1.Right = n3\nn2.Left = n4\nn2.Right = n5\n</code></pre> binary_tree.swift<pre><code>// ノードの初期化\nlet n1 = TreeNode(x: 1)\nlet n2 = TreeNode(x: 2)\nlet n3 = TreeNode(x: 3)\nlet n4 = TreeNode(x: 4)\nlet n5 = TreeNode(x: 5)\n// ノード間の参照（ポインタ）を結ぶ\nn1.left = n2\nn1.right = n3\nn2.left = n4\nn2.right = n5\n</code></pre> binary_tree.js<pre><code>/* 二分木の初期化 */\n// ノードの初期化\nlet n1 = new TreeNode(1),\n    n2 = new TreeNode(2),\n    n3 = new TreeNode(3),\n    n4 = new TreeNode(4),\n    n5 = new TreeNode(5);\n// ノード間の参照（ポインタ）を結ぶ\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.ts<pre><code>/* 二分木の初期化 */\n// ノードの初期化\nlet n1 = new TreeNode(1),\n    n2 = new TreeNode(2),\n    n3 = new TreeNode(3),\n    n4 = new TreeNode(4),\n    n5 = new TreeNode(5);\n// ノード間の参照（ポインタ）を結ぶ\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.dart<pre><code>/* 二分木の初期化 */\n// ノードの初期化\nTreeNode n1 = new TreeNode(1);\nTreeNode n2 = new TreeNode(2);\nTreeNode n3 = new TreeNode(3);\nTreeNode n4 = new TreeNode(4);\nTreeNode n5 = new TreeNode(5);\n// ノード間の参照（ポインタ）を結ぶ\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.rs<pre><code>// ノードの初期化\nlet n1 = TreeNode::new(1);\nlet n2 = TreeNode::new(2);\nlet n3 = TreeNode::new(3);\nlet n4 = TreeNode::new(4);\nlet n5 = TreeNode::new(5);\n// ノード間の参照（ポインタ）を結ぶ\nn1.borrow_mut().left = Some(n2.clone());\nn1.borrow_mut().right = Some(n3);\nn2.borrow_mut().left = Some(n4);\nn2.borrow_mut().right = Some(n5);\n</code></pre> binary_tree.c<pre><code>/* 二分木の初期化 */\n// ノードの初期化\nTreeNode *n1 = newTreeNode(1);\nTreeNode *n2 = newTreeNode(2);\nTreeNode *n3 = newTreeNode(3);\nTreeNode *n4 = newTreeNode(4);\nTreeNode *n5 = newTreeNode(5);\n// ノード間の参照（ポインタ）を結ぶ\nn1-&gt;left = n2;\nn1-&gt;right = n3;\nn2-&gt;left = n4;\nn2-&gt;right = n5;\n</code></pre> binary_tree.kt<pre><code>// ノードの初期化\nval n1 = TreeNode(1)\nval n2 = TreeNode(2)\nval n3 = TreeNode(3)\nval n4 = TreeNode(4)\nval n5 = TreeNode(5)\n// ノード間の参照（ポインタ）を結ぶ\nn1.left = n2\nn1.right = n3\nn2.left = n4\nn2.right = n5\n</code></pre> binary_tree.rb<pre><code>\n</code></pre>","path":["第 7 章 &nbsp; 木","7.1 &nbsp; 二分木"],"tags":[]},{"location":"chapter_tree/binary_tree/#2","level":3,"title":"2.   ノードの挿入と削除","text":"<p>連結リストと同様に、二分木でのノードの挿入と削除はポインタを変更することで実現できます。下図に例を示します。</p> <p></p> <p> 図 7-3   二分木でのノードの挿入と削除 </p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_tree.py<pre><code># ノードの挿入と削除\np = TreeNode(0)\n# n1 -&gt; n2の間にノードPを挿入\nn1.left = p\np.left = n2\n# ノードPを削除\nn1.left = n2\n</code></pre> binary_tree.cpp<pre><code>/* ノードの挿入と削除 */\nTreeNode* P = new TreeNode(0);\n// n1とn2の間にノードPを挿入\nn1-&gt;left = P;\nP-&gt;left = n2;\n// ノードPを削除\nn1-&gt;left = n2;\n</code></pre> binary_tree.java<pre><code>TreeNode P = new TreeNode(0);\n// n1とn2の間にノードPを挿入\nn1.left = P;\nP.left = n2;\n// ノードPを削除\nn1.left = n2;\n</code></pre> binary_tree.cs<pre><code>/* ノードの挿入と削除 */\nTreeNode P = new(0);\n// n1とn2の間にノードPを挿入\nn1.left = P;\nP.left = n2;\n// ノードPを削除\nn1.left = n2;\n</code></pre> binary_tree.go<pre><code>/* ノードの挿入と削除 */\n// n1とn2の間にノードPを挿入\np := NewTreeNode(0)\nn1.Left = p\np.Left = n2\n// ノードPを削除\nn1.Left = n2\n</code></pre> binary_tree.swift<pre><code>let P = TreeNode(x: 0)\n// n1とn2の間にノードPを挿入\nn1.left = P\nP.left = n2\n// ノードPを削除\nn1.left = n2\n</code></pre> binary_tree.js<pre><code>/* ノードの挿入と削除 */\nlet P = new TreeNode(0);\n// n1とn2の間にノードPを挿入\nn1.left = P;\nP.left = n2;\n// ノードPを削除\nn1.left = n2;\n</code></pre> binary_tree.ts<pre><code>/* ノードの挿入と削除 */\nconst P = new TreeNode(0);\n// n1とn2の間にノードPを挿入\nn1.left = P;\nP.left = n2;\n// ノードPを削除\nn1.left = n2;\n</code></pre> binary_tree.dart<pre><code>/* ノードの挿入と削除 */\nTreeNode P = new TreeNode(0);\n// n1とn2の間にノードPを挿入\nn1.left = P;\nP.left = n2;\n// ノードPを削除\nn1.left = n2;\n</code></pre> binary_tree.rs<pre><code>let p = TreeNode::new(0);\n// n1とn2の間にノードPを挿入\nn1.borrow_mut().left = Some(p.clone());\np.borrow_mut().left = Some(n2.clone());\n// ノードPを削除\nn1.borrow_mut().left = Some(n2);\n</code></pre> binary_tree.c<pre><code>/* ノードの挿入と削除 */\nTreeNode *P = newTreeNode(0);\n// n1とn2の間にノードPを挿入\nn1-&gt;left = P;\nP-&gt;left = n2;\n// ノードPを削除\nn1-&gt;left = n2;\n</code></pre> binary_tree.kt<pre><code>val P = TreeNode(0)\n// n1とn2の間にノードPを挿入\nn1.left = P\nP.left = n2\n// ノードPを削除\nn1.left = n2\n</code></pre> binary_tree.rb<pre><code>\n</code></pre> <p>Tip</p> <p>ノードの挿入は二分木の元の論理構造を変更する可能性があり、ノードの削除は通常そのノードとそのすべての部分木を削除することになることに注意してください。したがって、二分木では、挿入と削除は通常一連の操作を通じて実行され、意味のある結果を得ます。</p>","path":["第 7 章 &nbsp; 木","7.1 &nbsp; 二分木"],"tags":[]},{"location":"chapter_tree/binary_tree/#713","level":2,"title":"7.1.3   二分木の一般的な種類","text":"","path":["第 7 章 &nbsp; 木","7.1 &nbsp; 二分木"],"tags":[]},{"location":"chapter_tree/binary_tree/#1_1","level":3,"title":"1.   完全二分木","text":"<p>下図に示すように、完全二分木では、すべてのレベルがノードで完全に埋められています。完全二分木では、葉ノードの次数は\\(0\\)で、他のすべてのノードの次数は\\(2\\)です。ノードの総数は\\(2^{h+1} - 1\\)として計算でき、ここで\\(h\\)は木の高さです。これは標準的な指数関係を示し、自然界の細胞分裂の一般的な現象を反映しています。</p> <p>Tip</p> <p>中国語圏では、完全二分木はしばしば満二分木と呼ばれることに注意してください。</p> <p></p> <p> 図 7-4   完全二分木 </p>","path":["第 7 章 &nbsp; 木","7.1 &nbsp; 二分木"],"tags":[]},{"location":"chapter_tree/binary_tree/#2_1","level":3,"title":"2.   完備二分木","text":"<p>下図に示すように、完備二分木は、最下位レベルのみが完全に埋められていない可能性がある二分木で、最下位レベルのノードは左から右に連続して埋められる必要があります。完全二分木は完備二分木でもあることに注意してください。</p> <p></p> <p> 図 7-5   完備二分木 </p>","path":["第 7 章 &nbsp; 木","7.1 &nbsp; 二分木"],"tags":[]},{"location":"chapter_tree/binary_tree/#3","level":3,"title":"3.   満二分木","text":"<p>下図に示すように、満二分木では、葉ノードを除いて、他のすべてのノードが2つの子ノードを持ちます。</p> <p></p> <p> 図 7-6   満二分木 </p>","path":["第 7 章 &nbsp; 木","7.1 &nbsp; 二分木"],"tags":[]},{"location":"chapter_tree/binary_tree/#4","level":3,"title":"4.   平衡二分木","text":"<p>下図に示すように、平衡二分木では、任意のノードの左と右の部分木の高さの絶対差が1を超えません。</p> <p></p> <p> 図 7-7   平衡二分木 </p>","path":["第 7 章 &nbsp; 木","7.1 &nbsp; 二分木"],"tags":[]},{"location":"chapter_tree/binary_tree/#714","level":2,"title":"7.1.4   二分木の退化","text":"<p>下図は、二分木の理想的な構造と退化した構造を示しています。二分木は、すべてのレベルが埋められているときに「完全二分木」になり、すべてのノードが一方に偏っているときに「連結リスト」に退化します。</p> <ul> <li>完全二分木は、二分木の「分割統治法」の利点を十分に活用できる理想的なシナリオです。</li> <li>一方、連結リストは別の極端を表し、すべての操作が線形になり、時間計算量が\\(O(n)\\)になります。</li> </ul> <p></p> <p> 図 7-8   二分木の最良と最悪の構造 </p> <p>下表に示すように、最良と最悪の構造では、二分木は葉ノード数、総ノード数、高さの最大値または最小値を達成します。</p> <p> 表 7-1   二分木の最良と最悪の構造 </p> 完全二分木 連結リスト レベル\\(i\\)のノード数 \\(2^{i-1}\\) \\(1\\) 高さ\\(h\\)の木の葉ノード数 \\(2^h\\) \\(1\\) 高さ\\(h\\)の木の総ノード数 \\(2^{h+1} - 1\\) \\(h + 1\\) 総ノード数\\(n\\)の木の高さ \\(\\log_2 (n+1) - 1\\) \\(n - 1\\)","path":["第 7 章 &nbsp; 木","7.1 &nbsp; 二分木"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/","level":1,"title":"7.2   二分木の走査","text":"<p>物理的構造の観点から見ると、木は連結リストに基づくデータ構造です。したがって、その走査方法はポインタを通してノードに一つずつアクセスすることを含みます。しかし、木は非線形データ構造であるため、木の走査は連結リストの走査よりも複雑で、検索アルゴリズムの支援が必要です。</p> <p>二分木の一般的な走査方法には、レベル順走査、前順走査、中順走査、後順走査があります。</p>","path":["第 7 章 &nbsp; 木","7.2 &nbsp; 二分木の走査"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/#721","level":2,"title":"7.2.1   レベル順走査","text":"<p>下図に示すように、レベル順走査は二分木を上から下へ、層ごとに走査します。各レベル内では、左から右へノードを訪問します。</p> <p>レベル順走査は本質的に幅優先走査の一種で、幅優先探索（BFS）とも呼ばれ、「周囲に向かって外向きに拡張する」層ごとの走査方法を体現しています。</p> <p></p> <p> 図 7-9   二分木のレベル順走査 </p>","path":["第 7 章 &nbsp; 木","7.2 &nbsp; 二分木の走査"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/#1","level":3,"title":"1.   コード実装","text":"<p>幅優先走査は通常「キュー」の助けを借りて実装されます。キューは「先入れ先出し」の規則に従い、幅優先走査は「層ごとの進行」規則に従います。両者の基本的な考え方は一致しています。実装コードは以下の通りです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_tree_bfs.py<pre><code>def level_order(root: TreeNode | None) -&gt; list[int]:\n    \"\"\"レベル順走査\"\"\"\n    # キューを初期化し、ルートノードを追加\n    queue: deque[TreeNode] = deque()\n    queue.append(root)\n    # 走査シーケンスを格納するリストを初期化\n    res = []\n    while queue:\n        node: TreeNode = queue.popleft()  # キューからデキュー\n        res.append(node.val)  # ノードの値を保存\n        if node.left is not None:\n            queue.append(node.left)  # 左の子ノードをエンキュー\n        if node.right is not None:\n            queue.append(node.right)  # 右の子ノードをエンキュー\n    return res\n</code></pre> binary_tree_bfs.cpp<pre><code>/* レベル順走査 */\nvector&lt;int&gt; levelOrder(TreeNode *root) {\n    // キューを初期化、ルートノードを追加\n    queue&lt;TreeNode *&gt; queue;\n    queue.push(root);\n    // 走査順序を保存するリストを初期化\n    vector&lt;int&gt; vec;\n    while (!queue.empty()) {\n        TreeNode *node = queue.front();\n        queue.pop();              // キューからデキュー\n        vec.push_back(node-&gt;val); // ノード値を保存\n        if (node-&gt;left != nullptr)\n            queue.push(node-&gt;left); // 左の子ノードをエンキュー\n        if (node-&gt;right != nullptr)\n            queue.push(node-&gt;right); // 右の子ノードをエンキュー\n    }\n    return vec;\n}\n</code></pre> binary_tree_bfs.java<pre><code>/* レベル順走査 */\nList&lt;Integer&gt; levelOrder(TreeNode root) {\n    // キューを初期化し、根ノードを追加\n    Queue&lt;TreeNode&gt; queue = new LinkedList&lt;&gt;();\n    queue.add(root);\n    // 走査順序を格納するリストを初期化\n    List&lt;Integer&gt; list = new ArrayList&lt;&gt;();\n    while (!queue.isEmpty()) {\n        TreeNode node = queue.poll(); // キューのデキュー\n        list.add(node.val);           // ノードの値を保存\n        if (node.left != null)\n            queue.offer(node.left);   // 左の子ノードをエンキュー\n        if (node.right != null)\n            queue.offer(node.right);  // 右の子ノードをエンキュー\n    }\n    return list;\n}\n</code></pre> binary_tree_bfs.cs<pre><code>[class]{binary_tree_bfs}-[func]{LevelOrder}\n</code></pre> binary_tree_bfs.go<pre><code>[class]{}-[func]{levelOrder}\n</code></pre> binary_tree_bfs.swift<pre><code>[class]{}-[func]{levelOrder}\n</code></pre> binary_tree_bfs.js<pre><code>[class]{}-[func]{levelOrder}\n</code></pre> binary_tree_bfs.ts<pre><code>[class]{}-[func]{levelOrder}\n</code></pre> binary_tree_bfs.dart<pre><code>[class]{}-[func]{levelOrder}\n</code></pre> binary_tree_bfs.rs<pre><code>[class]{}-[func]{level_order}\n</code></pre> binary_tree_bfs.c<pre><code>[class]{}-[func]{levelOrder}\n</code></pre> binary_tree_bfs.kt<pre><code>[class]{}-[func]{levelOrder}\n</code></pre> binary_tree_bfs.rb<pre><code>[class]{}-[func]{level_order}\n</code></pre>","path":["第 7 章 &nbsp; 木","7.2 &nbsp; 二分木の走査"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/#2","level":3,"title":"2.   計算量分析","text":"<ul> <li>時間計算量は\\(O(n)\\): すべてのノードが一度ずつ訪問され、\\(O(n)\\)の時間がかかります。ここで\\(n\\)はノード数です。</li> <li>空間計算量は\\(O(n)\\): 最悪の場合、つまり完全二分木の場合、最下位レベルに走査する前に、キューは最大\\((n + 1) / 2\\)個のノードを同時に含むことができ、\\(O(n)\\)の空間を占有します。</li> </ul>","path":["第 7 章 &nbsp; 木","7.2 &nbsp; 二分木の走査"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/#722","level":2,"title":"7.2.2   前順、中順、後順走査","text":"<p>対応して、前順、中順、後順走査はすべて深度優先走査に属し、深度優先探索（DFS）とも呼ばれ、「まず最後まで進み、その後バックトラックして続行する」走査方法を体現しています。</p> <p>下図は二分木に対して深度優先走査を実行する動作原理を示しています。深度優先走査は二分木全体を「歩き回る」ようなもので、各ノードで3つの位置に遭遇し、それらは前順、中順、後順走査に対応しています。</p> <p></p> <p> 図 7-10   二分探索木の前順、中順、後順走査 </p>","path":["第 7 章 &nbsp; 木","7.2 &nbsp; 二分木の走査"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/#1_1","level":3,"title":"1.   コード実装","text":"<p>深度優先探索は通常再帰に基づいて実装されます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_tree_dfs.py<pre><code>def pre_order(root: TreeNode | None):\n    \"\"\"前順走査\"\"\"\n    if root is None:\n        return\n    # 訪問順序: ルートノード -&gt; 左部分木 -&gt; 右部分木\n    res.append(root.val)\n    pre_order(root=root.left)\n    pre_order(root=root.right)\n\ndef in_order(root: TreeNode | None):\n    \"\"\"中順走査\"\"\"\n    if root is None:\n        return\n    # 訪問順序: 左部分木 -&gt; ルートノード -&gt; 右部分木\n    in_order(root=root.left)\n    res.append(root.val)\n    in_order(root=root.right)\n\ndef post_order(root: TreeNode | None):\n    \"\"\"後順走査\"\"\"\n    if root is None:\n        return\n    # 訪問順序: 左部分木 -&gt; 右部分木 -&gt; ルートノード\n    post_order(root=root.left)\n    post_order(root=root.right)\n    res.append(root.val)\n</code></pre> binary_tree_dfs.cpp<pre><code>/* 前順走査 */\nvoid preOrder(TreeNode *root) {\n    if (root == nullptr)\n        return;\n    // 訪問優先度：ルートノード -&gt; 左部分木 -&gt; 右部分木\n    vec.push_back(root-&gt;val);\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n}\n\n/* 中順走査 */\nvoid inOrder(TreeNode *root) {\n    if (root == nullptr)\n        return;\n    // 訪問優先度：左部分木 -&gt; ルートノード -&gt; 右部分木\n    inOrder(root-&gt;left);\n    vec.push_back(root-&gt;val);\n    inOrder(root-&gt;right);\n}\n\n/* 後順走査 */\nvoid postOrder(TreeNode *root) {\n    if (root == nullptr)\n        return;\n    // 訪問優先度：左部分木 -&gt; 右部分木 -&gt; ルートノード\n    postOrder(root-&gt;left);\n    postOrder(root-&gt;right);\n    vec.push_back(root-&gt;val);\n}\n</code></pre> binary_tree_dfs.java<pre><code>/* 前順走査 */\nvoid preOrder(TreeNode root) {\n    if (root == null)\n        return;\n    // 訪問優先度: 根ノード -&gt; 左部分木 -&gt; 右部分木\n    list.add(root.val);\n    preOrder(root.left);\n    preOrder(root.right);\n}\n\n/* 中順走査 */\nvoid inOrder(TreeNode root) {\n    if (root == null)\n        return;\n    // 訪問優先度: 左部分木 -&gt; 根ノード -&gt; 右部分木\n    inOrder(root.left);\n    list.add(root.val);\n    inOrder(root.right);\n}\n\n/* 後順走査 */\nvoid postOrder(TreeNode root) {\n    if (root == null)\n        return;\n    // 訪問優先度: 左部分木 -&gt; 右部分木 -&gt; 根ノード\n    postOrder(root.left);\n    postOrder(root.right);\n    list.add(root.val);\n}\n</code></pre> binary_tree_dfs.cs<pre><code>[class]{binary_tree_dfs}-[func]{PreOrder}\n\n[class]{binary_tree_dfs}-[func]{InOrder}\n\n[class]{binary_tree_dfs}-[func]{PostOrder}\n</code></pre> binary_tree_dfs.go<pre><code>[class]{}-[func]{preOrder}\n\n[class]{}-[func]{inOrder}\n\n[class]{}-[func]{postOrder}\n</code></pre> binary_tree_dfs.swift<pre><code>[class]{}-[func]{preOrder}\n\n[class]{}-[func]{inOrder}\n\n[class]{}-[func]{postOrder}\n</code></pre> binary_tree_dfs.js<pre><code>[class]{}-[func]{preOrder}\n\n[class]{}-[func]{inOrder}\n\n[class]{}-[func]{postOrder}\n</code></pre> binary_tree_dfs.ts<pre><code>[class]{}-[func]{preOrder}\n\n[class]{}-[func]{inOrder}\n\n[class]{}-[func]{postOrder}\n</code></pre> binary_tree_dfs.dart<pre><code>[class]{}-[func]{preOrder}\n\n[class]{}-[func]{inOrder}\n\n[class]{}-[func]{postOrder}\n</code></pre> binary_tree_dfs.rs<pre><code>[class]{}-[func]{pre_order}\n\n[class]{}-[func]{in_order}\n\n[class]{}-[func]{post_order}\n</code></pre> binary_tree_dfs.c<pre><code>[class]{}-[func]{preOrder}\n\n[class]{}-[func]{inOrder}\n\n[class]{}-[func]{postOrder}\n</code></pre> binary_tree_dfs.kt<pre><code>[class]{}-[func]{preOrder}\n\n[class]{}-[func]{inOrder}\n\n[class]{}-[func]{postOrder}\n</code></pre> binary_tree_dfs.rb<pre><code>[class]{}-[func]{pre_order}\n\n[class]{}-[func]{in_order}\n\n[class]{}-[func]{post_order}\n</code></pre> <p>Tip</p> <p>深度優先探索は反復に基づいても実装できます。興味のある読者は自分で学習してください。</p> <p>下図は二分木の前順走査の再帰プロセスを示しており、これは「再帰」と「復帰」という2つの反対の部分に分けることができます。</p> <ol> <li>「再帰」は新しいメソッドを開始することを意味し、プログラムはこのプロセスで次のノードにアクセスします。</li> <li>「復帰」は関数が戻ることを意味し、現在のノードが完全にアクセスされたことを示します。</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 7-11   前順走査の再帰プロセス </p>","path":["第 7 章 &nbsp; 木","7.2 &nbsp; 二分木の走査"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/#2_1","level":3,"title":"2.   計算量分析","text":"<ul> <li>時間計算量は\\(O(n)\\): すべてのノードが一度ずつ訪問され、\\(O(n)\\)の時間を使用します。</li> <li>空間計算量は\\(O(n)\\): 最悪の場合、つまり木が連結リストに退化した場合、再帰の深さは\\(n\\)に達し、システムは\\(O(n)\\)のスタックフレーム空間を占有します。</li> </ul>","path":["第 7 章 &nbsp; 木","7.2 &nbsp; 二分木の走査"],"tags":[]},{"location":"chapter_tree/summary/","level":1,"title":"7.6   まとめ","text":"","path":["第 7 章 &nbsp; 木","7.6 &nbsp; まとめ"],"tags":[]},{"location":"chapter_tree/summary/#1","level":3,"title":"1.   重要なポイント","text":"<ul> <li>二分木は非線形データ構造で、「一つを二つに分ける」分割統治のロジックを反映しています。各二分木ノードには値と2つのポインタが含まれ、それぞれ左と右の子ノードを指します。</li> <li>二分木のノードについて、その左（右）子ノードとその下に形成される木は、まとめてそのノードの左（右）部分木と呼ばれます。</li> <li>二分木に関連する用語には、根ノード、葉ノード、レベル、次数、エッジ、高さ、深さがあります。</li> <li>二分木の初期化、ノードの挿入、ノードの削除の操作は、連結リストの操作と似ています。</li> <li>一般的な二分木の種類には、完全二分木、完備二分木、満二分木、平衡二分木があります。完全二分木は理想的な状態を表し、連結リストは退化後の最悪の状態です。</li> <li>二分木は、ノード値と空きスロットをレベル順走査シーケンスで配置し、親ノードと子ノード間のインデックスマッピング関係に基づいてポインタを実装することで、配列を使用して表現できます。</li> <li>二分木のレベル順走査は幅優先探索手法で、「円を拡大しながら」の層ごとの走査方式を反映しています。通常はキューを使用して実装されます。</li> <li>前順、中順、後順走査はすべて深度優先探索手法で、「まず最後まで行き、その後バックトラックして続行する」走査方式を反映しています。通常は再帰を使用して実装されます。</li> <li>二分探索木は要素検索のための効率的なデータ構造で、検索、挿入、削除操作の時間計算量はすべて\\(O(\\log n)\\)です。二分探索木が連結リストに退化すると、これらの時間計算量は\\(O(n)\\)に悪化します。</li> <li>AVL木は平衡二分探索木とも呼ばれ、回転操作を通して継続的なノード挿入と削除後も木が平衡を保つことを保証します。</li> <li>AVL木の回転操作には、右回転、左回転、右左回転、左右回転があります。ノードの挿入または削除後、AVL木はボトムアップ方式でこれらの回転を実行して自己平衡を取ります。</li> </ul>","path":["第 7 章 &nbsp; 木","7.6 &nbsp; まとめ"],"tags":[]},{"location":"chapter_tree/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: 一つのノードのみを持つ二分木について、木の高さと根ノードの深さの両方が\\(0\\)ですか？</p> <p>はい、高さと深さは通常「通過したエッジの数」として定義されるためです。</p> <p>Q: 二分木における挿入と削除は一般的に一連の操作によって達成されます。ここでの「一連の操作」とは何を指しますか？子ノードのリソースを解放することを意味しますか？</p> <p>二分探索木を例に取ると、ノードを削除する操作は3つの異なるシナリオで処理する必要があり、それぞれ複数ステップのノード操作が必要です。</p> <p>Q: 二分木のDFS走査で前順、中順、後順の3つのシーケンスがあるのはなぜですか？その用途は何ですか？</p> <p>配列の順次および逆順走査と同様に、前順、中順、後順走査は二分木を走査する3つの方法であり、特定の順序で走査結果を取得できます。例えば、二分探索木では、ノードサイズが「左子ノード値 &lt; 根ノード値 &lt; 右子ノード値」を満たすため、「左 \\(\\rightarrow\\) 根 \\(\\rightarrow\\) 右」の優先順位で木を走査することで、順序付けられたノードシーケンスを取得できます。</p> <p>Q: 不平衡ノード<code>node</code>、<code>child</code>、<code>grand_child</code>間の関係を処理する右回転操作において、右回転後に<code>node</code>とその親ノード間の接続と<code>node</code>の元のリンクが失われるのではありませんか？</p> <p>この問題を再帰的な観点から見る必要があります。<code>right_rotate(root)</code>操作は部分木の根ノードを渡し、最終的に<code>return child</code>で回転された部分木の根ノードを返します。部分木の根ノードとその親ノード間の接続は、この関数が戻った後に確立され、これは右回転操作の保守範囲外です。</p> <p>Q: C++では、関数は<code>private</code>と<code>public</code>セクションに分かれています。これにはどのような考慮事項がありますか？なぜ<code>height()</code>関数と<code>updateHeight()</code>関数がそれぞれ<code>public</code>と<code>private</code>に配置されているのですか？</p> <p>これはメソッドの使用範囲によります。メソッドがクラス内でのみ使用される場合、<code>private</code>に設計されます。例えば、ユーザーが独自に<code>updateHeight()</code>を呼び出すことは意味がありません。これは挿入または削除操作の一ステップに過ぎないからです。しかし、<code>height()</code>はノードの高さにアクセスするためのもので、<code>vector.size()</code>と同様であるため、使用のために<code>public</code>に設定されています。</p> <p>Q: 入力データのセットから二分探索木をどのように構築しますか？根ノードの選択は非常に重要ですか？</p> <p>はい、木を構築する方法は二分探索木コードの<code>build_tree()</code>メソッドで提供されています。根ノードの選択については、通常入力データをソートし、中央の要素を根ノードとして選択し、再帰的に左と右の部分木を構築します。このアプローチは木の平衡を最大化します。</p> <p>Q: Javaでは、文字列比較に常に<code>equals()</code>メソッドを使用する必要がありますか？</p> <p>Javaでは、プリミティブデータ型の場合、<code>==</code>は2つの変数の値が等しいかどうかを比較するために使用されます。参照型の場合、2つのシンボルの動作原理は異なります。</p> <ul> <li><code>==</code>: 2つの変数が同じオブジェクトを指しているかどうか、つまりメモリ内の位置が同じかどうかを比較するために使用されます。</li> <li><code>equals()</code>: 2つのオブジェクトの値が等しいかどうかを比較するために使用されます。</li> </ul> <p>したがって、値を比較するには<code>equals()</code>を使用すべきです。ただし、<code>String a = \"hi\"; String b = \"hi\";</code>で初期化された文字列は文字列定数プールに格納され、同じオブジェクトを指すため、<code>a == b</code>も2つの文字列の内容を比較するために使用できます。</p> <p>Q: 最下位レベルに到達する前に、幅優先走査でキュー内のノード数は\\(2^h\\)ですか？</p> <p>はい、例えば高さ\\(h = 2\\)の満二分木は合計\\(n = 7\\)個のノードを持ち、最下位レベルには\\(4 = 2^h = (n + 1) / 2\\)個のノードがあります。</p>","path":["第 7 章 &nbsp; 木","7.6 &nbsp; まとめ"],"tags":[]}]}
\ No newline at end of file
+{"config":{"separator":"[\\s\\-_,:!=\\[\\]()\\\\\"`/]+|\\.(?!\\d)"},"items":[{"location":"chapter_appendix/","level":1,"title":"第 16 章   付録","text":"","path":["第 16 章 &nbsp; 付録"],"tags":[]},{"location":"chapter_appendix/#_1","level":2,"title":"章の内容","text":"<ul> <li>16.1   プログラミング環境のインストール</li> <li>16.2   一緒に制作に参加しましょう</li> <li>16.3   用語集</li> </ul>","path":["第 16 章 &nbsp; 付録"],"tags":[]},{"location":"chapter_appendix/contribution/","level":1,"title":"16.2   一緒に制作に参加しましょう","text":"<p>著者の力には限りがあるため、本書にはどうしても一部の漏れや誤りが含まれる可能性があります。ご了承ください。誤字、リンク切れ、内容の欠落、表現の曖昧さ、説明の不明瞭さ、文章構成の不適切さなどの問題を見つけた場合は、ぜひ修正にご協力ください。読者により良い学習リソースを提供できます。</p> <p>すべての寄稿者の GitHub ID は、本書のリポジトリ、Web 版、PDF 版のホームページに掲載され、オープンソースコミュニティへの惜しみない貢献に感謝を表します。</p> <p>オープンソースの魅力</p> <p>紙の書籍では、2 回の増刷の間隔が長くなりがちで、内容更新は非常に不便です。</p> <p>一方、このオープンソース書籍では、内容更新のサイクルは数日、場合によっては数時間にまで短縮されています。</p>","path":["第 16 章 &nbsp; 付録","16.2 &nbsp; 一緒に制作に参加しましょう"],"tags":[]},{"location":"chapter_appendix/contribution/#1","level":3,"title":"1.   内容の微調整","text":"<p>以下の図のように、各ページの右上には「編集アイコン」があります。次の手順で本文やコードを修正できます。</p> <ol> <li>「編集アイコン」をクリックし、「このリポジトリを Fork する必要があります」と表示された場合は、その操作を承認してください。</li> <li>Markdown のソースファイルを修正し、内容が正しいことを確認したうえで、できるだけ書式の統一を保ってください。</li> <li>ページ下部に修正内容の説明を入力し、その後「Propose file change」ボタンをクリックします。ページ遷移後、「Create pull request」ボタンをクリックするとプルリクエストを作成できます。</li> </ol> <p></p> <p> 図 16-3   ページ編集ボタン </p> <p>画像は直接修正できないため、新しい Issue を作成するかコメントで問題を説明してください。できるだけ早く描き直して差し替えます。</p>","path":["第 16 章 &nbsp; 付録","16.2 &nbsp; 一緒に制作に参加しましょう"],"tags":[]},{"location":"chapter_appendix/contribution/#2","level":3,"title":"2.   コンテンツ制作","text":"<p>コードを他のプログラミング言語へ翻訳することや、記事内容を拡充することなど、このオープンソースプロジェクトへの参加に興味がある場合は、以下の Pull Request ワークフローに従ってください。</p> <ol> <li>GitHub にログインし、本書のコードリポジトリを個人アカウントに Fork します。</li> <li>Fork したリポジトリのページに入り、<code>git clone</code> コマンドを使ってリポジトリをローカルにクローンします。</li> <li>ローカルでコンテンツを作成し、完全なテストを行ってコードの正しさを確認します。</li> <li>ローカルで行った変更を Commit し、その後リモートリポジトリへ Push します。</li> <li>リポジトリのページを更新し、「Create pull request」ボタンをクリックするとプルリクエストを作成できます。</li> </ol>","path":["第 16 章 &nbsp; 付録","16.2 &nbsp; 一緒に制作に参加しましょう"],"tags":[]},{"location":"chapter_appendix/contribution/#3-docker","level":3,"title":"3.   Docker デプロイ","text":"<p><code>hello-algo</code> のルートディレクトリで以下の Docker スクリプトを実行すると、<code>http://localhost:8000</code> で本プロジェクトにアクセスできます。</p> <pre><code>docker-compose up -d\n</code></pre> <p>以下のコマンドでデプロイを削除できます。</p> <pre><code>docker-compose down\n</code></pre>","path":["第 16 章 &nbsp; 付録","16.2 &nbsp; 一緒に制作に参加しましょう"],"tags":[]},{"location":"chapter_appendix/installation/","level":1,"title":"16.1   プログラミング環境のインストール","text":"","path":["第 16 章 &nbsp; 付録","16.1 &nbsp; プログラミング環境のインストール"],"tags":[]},{"location":"chapter_appendix/installation/#1611-ide","level":2,"title":"16.1.1   IDE のインストール","text":"<p>オープンソースで軽量な VS Code をローカルの統合開発環境（IDE）として使用することを推奨します。VS Code 公式サイト にアクセスし、使用している OS に応じたバージョンの VS Code をダウンロードしてインストールしてください。</p> <p></p> <p> 図 16-1   公式サイトから VS Code をダウンロード </p> <p>VS Code には強力な拡張機能のエコシステムがあり、ほとんどのプログラミング言語の実行とデバッグをサポートしています。Python を例にすると、「Python Extension Pack」拡張機能をインストールした後、Python コードをデバッグできるようになります。インストール手順を以下に示します。</p> <p></p> <p> 図 16-2   VS Code 拡張機能のインストール </p>","path":["第 16 章 &nbsp; 付録","16.1 &nbsp; プログラミング環境のインストール"],"tags":[]},{"location":"chapter_appendix/installation/#1612","level":2,"title":"16.1.2   言語環境のインストール","text":"","path":["第 16 章 &nbsp; 付録","16.1 &nbsp; プログラミング環境のインストール"],"tags":[]},{"location":"chapter_appendix/installation/#1-python","level":3,"title":"1.   Python 環境","text":"<ol> <li>Miniconda3 をダウンロードしてインストールします。Python 3.10 以降が必要です。</li> <li>VS Code の拡張機能マーケットプレイスで <code>python</code> を検索し、Python Extension Pack をインストールします。</li> <li>（任意）コマンドラインで <code>pip install black</code> を入力し、コード整形ツールをインストールします。</li> </ol>","path":["第 16 章 &nbsp; 付録","16.1 &nbsp; プログラミング環境のインストール"],"tags":[]},{"location":"chapter_appendix/installation/#2-cc","level":3,"title":"2.   C/C++ 環境","text":"<ol> <li>Windows システムでは MinGW をインストールする必要があります（設定チュートリアル）。MacOS には Clang が標準搭載されているため、追加インストールは不要です。</li> <li>VS Code の拡張機能マーケットプレイスで <code>c++</code> を検索し、C/C++ Extension Pack をインストールします。</li> <li>（任意）Settings ページを開き、コード整形オプション <code>Clang_format_fallback Style</code> を検索して、<code>{ BasedOnStyle: Microsoft, BreakBeforeBraces: Attach }</code> に設定します。</li> </ol>","path":["第 16 章 &nbsp; 付録","16.1 &nbsp; プログラミング環境のインストール"],"tags":[]},{"location":"chapter_appendix/installation/#3-java","level":3,"title":"3.   Java 環境","text":"<ol> <li>OpenJDK をダウンロードしてインストールします（バージョンは JDK 9 より新しい必要があります）。</li> <li>VS Code の拡張機能マーケットプレイスで <code>java</code> を検索し、Extension Pack for Java をインストールします。</li> </ol>","path":["第 16 章 &nbsp; 付録","16.1 &nbsp; プログラミング環境のインストール"],"tags":[]},{"location":"chapter_appendix/installation/#4-c","level":3,"title":"4.   C# 環境","text":"<ol> <li>.Net 8.0 をダウンロードしてインストールします。</li> <li>VS Code の拡張機能マーケットプレイスで <code>C# Dev Kit</code> を検索し、C# Dev Kit をインストールします（設定チュートリアル）。</li> <li>Visual Studio を使用することもできます（インストール手順）。</li> </ol>","path":["第 16 章 &nbsp; 付録","16.1 &nbsp; プログラミング環境のインストール"],"tags":[]},{"location":"chapter_appendix/installation/#5-go","level":3,"title":"5.   Go 環境","text":"<ol> <li>go をダウンロードしてインストールします。</li> <li>VS Code の拡張機能マーケットプレイスで <code>go</code> を検索し、Go をインストールします。</li> <li>ショートカットキー <code>Ctrl + Shift + P</code> を押してコマンドパレットを開き、go と入力して <code>Go: Install/Update Tools</code> を選択し、すべてにチェックを入れてインストールします。</li> </ol>","path":["第 16 章 &nbsp; 付録","16.1 &nbsp; プログラミング環境のインストール"],"tags":[]},{"location":"chapter_appendix/installation/#6-swift","level":3,"title":"6.   Swift 環境","text":"<ol> <li>Swift をダウンロードしてインストールします。</li> <li>VS Code の拡張機能マーケットプレイスで <code>swift</code> を検索し、Swift for Visual Studio Code をインストールします。</li> </ol>","path":["第 16 章 &nbsp; 付録","16.1 &nbsp; プログラミング環境のインストール"],"tags":[]},{"location":"chapter_appendix/installation/#7-javascript","level":3,"title":"7.   JavaScript 環境","text":"<ol> <li>Node.js をダウンロードしてインストールします。</li> <li>（任意）VS Code の拡張機能マーケットプレイスで <code>Prettier</code> を検索し、コード整形ツールをインストールします。</li> </ol>","path":["第 16 章 &nbsp; 付録","16.1 &nbsp; プログラミング環境のインストール"],"tags":[]},{"location":"chapter_appendix/installation/#8-typescript","level":3,"title":"8.   TypeScript 環境","text":"<ol> <li>JavaScript 環境と同じ手順でインストールします。</li> <li>TypeScript Execute (tsx) をインストールします。</li> <li>VS Code の拡張機能マーケットプレイスで <code>typescript</code> を検索し、Pretty TypeScript Errors をインストールします。</li> </ol>","path":["第 16 章 &nbsp; 付録","16.1 &nbsp; プログラミング環境のインストール"],"tags":[]},{"location":"chapter_appendix/installation/#9-dart","level":3,"title":"9.   Dart 環境","text":"<ol> <li>Dart をダウンロードしてインストールします。</li> <li>VS Code の拡張機能マーケットプレイスで <code>dart</code> を検索し、Dart をインストールします。</li> </ol>","path":["第 16 章 &nbsp; 付録","16.1 &nbsp; プログラミング環境のインストール"],"tags":[]},{"location":"chapter_appendix/installation/#10-rust","level":3,"title":"10.   Rust 環境","text":"<ol> <li>Rust をダウンロードしてインストールします。</li> <li>VS Code の拡張機能マーケットプレイスで <code>rust</code> を検索し、rust-analyzer をインストールします。</li> </ol>","path":["第 16 章 &nbsp; 付録","16.1 &nbsp; プログラミング環境のインストール"],"tags":[]},{"location":"chapter_appendix/terminology/","level":1,"title":"16.3   用語集","text":"<p>以下の表は、本書に登場する重要な用語を一覧にしたものです。特に次の点に注意してください。</p> <ul> <li>名詞の英語表現も覚えておくと、英語文献を読む際に役立ちます。</li> <li>一部の名詞は、簡体字中国語と繁体字中国語で呼び方が異なります。</li> </ul> <p> 表 16-1   データ構造とアルゴリズムの重要用語 </p> English 日本語 日本語 algorithm アルゴリズム アルゴリズム data structure データ構造 データ構造 code コード コード file ファイル ファイル function 関数 関数 method メソッド メソッド variable 変数 変数 asymptotic complexity analysis 漸近計算量解析 漸近計算量解析 time complexity 時間計算量 時間計算量 space complexity 空間計算量 空間計算量 loop ループ ループ iteration 反復 反復 recursion 再帰 再帰 tail recursion 末尾再帰 末尾再帰 recursion tree 再帰木 再帰木 big-\\(O\\) notation ビッグオー記法 ビッグオー記法 asymptotic upper bound 漸近上界 漸近上界 sign-magnitude 符号絶対値表現 符号絶対値表現 1’s complement 1の補数 1の補数 2’s complement 2の補数 2の補数 array 配列 配列 index インデックス インデックス linked list 連結リスト 連結リスト linked list node, list node 連結リストノード 連結リストノード head node 先頭ノード 先頭ノード tail node 末尾ノード 末尾ノード list リスト リスト dynamic array 動的配列 動的配列 hard disk ハードディスク ハードディスク random-access memory (RAM) メモリ メモリ cache memory キャッシュ キャッシュ cache miss キャッシュミス キャッシュミス cache hit rate キャッシュヒット率 キャッシュヒット率 stack スタック スタック top of the stack スタックトップ スタックトップ bottom of the stack スタックボトム スタックボトム queue キュー キュー double-ended queue 両端キュー 両端キュー front of the queue キュー先頭 キュー先頭 rear of the queue キュー末尾 キュー末尾 hash table ハッシュテーブル ハッシュテーブル hash set ハッシュ集合 ハッシュ集合 bucket バケット バケット hash function ハッシュ関数 ハッシュ関数 hash collision ハッシュ衝突 ハッシュ衝突 load factor 負荷率 負荷率 separate chaining 連鎖アドレス法 連鎖アドレス法 open addressing オープンアドレス法 オープンアドレス法 linear probing 線形探索 線形探索 lazy deletion 遅延削除 遅延削除 binary tree 二分木 二分木 tree node ノード ノード left-child node 左子ノード 左子ノード right-child node 右子ノード 右子ノード parent node 親ノード 親ノード left subtree 左部分木 左部分木 right subtree 右部分木 右部分木 root node 根ノード 根ノード leaf node 葉ノード 葉ノード edge 辺 辺 level レベル レベル degree 次数 次数 height 高さ 高さ depth 深さ 深さ perfect binary tree 完備二分木 完備二分木 complete binary tree 完全二分木 完全二分木 full binary tree 満二分木 満二分木 balanced binary tree 平衡二分木 平衡二分木 binary search tree 二分探索木 二分探索木 AVL tree AVL 木 AVL 木 red-black tree 赤黒木 赤黒木 level-order traversal レベル順走査 レベル順走査 breadth-first traversal 幅優先走査 幅優先走査 depth-first traversal 深さ優先走査 深さ優先走査 binary search tree 二分探索木 二分探索木 balanced binary search tree 平衡二分探索木 平衡二分探索木 balance factor 平衡係数 平衡係数 heap ヒープ ヒープ max heap 最大ヒープ 最大ヒープ min heap 最小ヒープ 最小ヒープ priority queue 優先度付きキュー 優先度付きキュー heapify ヒープ化 ヒープ化 top-\\(k\\) problem Top-\\(k\\) 問題 Top-\\(k\\) 問題 graph グラフ グラフ vertex 頂点 頂点 undirected graph 無向グラフ 無向グラフ directed graph 有向グラフ 有向グラフ connected graph 連結グラフ 連結グラフ disconnected graph 非連結グラフ 非連結グラフ weighted graph 重み付きグラフ 重み付きグラフ adjacency 隣接 隣接 path 経路 経路 in-degree 入次数 入次数 out-degree 出次数 出次数 adjacency matrix 隣接行列 隣接行列 adjacency list 隣接リスト 隣接リスト breadth-first search 幅優先探索 幅優先探索 depth-first search 深さ優先探索 深さ優先探索 binary search 二分探索 二分探索 searching algorithm 探索アルゴリズム 探索アルゴリズム sorting algorithm ソートアルゴリズム ソートアルゴリズム selection sort 選択ソート 選択ソート bubble sort バブルソート バブルソート insertion sort 挿入ソート 挿入ソート quick sort クイックソート クイックソート merge sort マージソート マージソート heap sort ヒープソート ヒープソート bucket sort バケットソート バケットソート counting sort 計数ソート 計数ソート radix sort 基数ソート 基数ソート divide and conquer 分割統治 分割統治 hanota problem ハノイの塔問題 ハノイの塔問題 backtracking algorithm バックトラッキングアルゴリズム バックトラッキングアルゴリズム constraint 制約 制約 solution 解 解 state 状態 状態 pruning 枝刈り 枝刈り permutations problem 全順列問題 全順列問題 subset-sum problem 部分和問題 部分和問題 \\(n\\)-queens problem \\(n\\) クイーン問題 \\(n\\) クイーン問題 dynamic programming 動的計画法 動的計画法 initial state 初期状態 初期状態 state-transition equation 状態遷移方程式 状態遷移方程式 knapsack problem ナップサック問題 ナップサック問題 edit distance problem 編集距離問題 編集距離問題 greedy algorithm 貪欲法 貪欲法","path":["第 16 章 &nbsp; 付録","16.3 &nbsp; 用語集"],"tags":[]},{"location":"chapter_array_and_linkedlist/","level":1,"title":"第 4 章   配列と連結リスト","text":"<p>Abstract</p> <p>データ構造の世界は、まるで重厚なれんがの壁のようです。</p> <p>配列のれんがは整然と並び、一つひとつがぴったりと接しています。連結リストのれんがはあちこちに分散し、それらをつなぐつるがれんがのすき間を自由に行き交います。</p>","path":["第 4 章 &nbsp; 配列と連結リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/#_1","level":2,"title":"章の内容","text":"<ul> <li>4.1   配列</li> <li>4.2   連結リスト</li> <li>4.3   リスト</li> <li>4.4   メモリとキャッシュ *</li> <li>4.5   まとめ</li> </ul>","path":["第 4 章 &nbsp; 配列と連結リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/","level":1,"title":"4.1   配列","text":"<p>配列（array）は線形データ構造の一種であり、同じ型の要素を連続したメモリ領域に格納します。要素が配列内にある位置を、その要素のインデックス（index）と呼びます。下図は、配列の主要な概念と格納方式を示しています。</p> <p></p> <p> 図 4-1   配列の定義と格納方式 </p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.1 &nbsp; 配列"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#411","level":2,"title":"4.1.1   配列の一般的な操作","text":"","path":["第 4 章 &nbsp; 配列と連結リスト","4.1 &nbsp; 配列"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#1","level":3,"title":"1.   配列の初期化","text":"<p>必要に応じて、配列の初期化方法として初期値なしと初期値ありの 2 種類を使い分けられます。初期値を指定しない場合、多くのプログラミング言語では配列要素は \\(0\\) に初期化されます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code># 配列を初期化する\narr: list[int] = [0] * 5  # [ 0, 0, 0, 0, 0 ]\nnums: list[int] = [1, 3, 2, 5, 4]\n</code></pre> array.cpp<pre><code>/* 配列を初期化する */\n// スタック上に格納\nint arr[5];\nint nums[5] = { 1, 3, 2, 5, 4 };\n// ヒープ上に格納（手動で領域を解放する必要がある）\nint* arr1 = new int[5];\nint* nums1 = new int[5] { 1, 3, 2, 5, 4 };\n</code></pre> array.java<pre><code>/* 配列を初期化する */\nint[] arr = new int[5]; // { 0, 0, 0, 0, 0 }\nint[] nums = { 1, 3, 2, 5, 4 };\n</code></pre> array.cs<pre><code>/* 配列を初期化する */\nint[] arr = new int[5]; // [ 0, 0, 0, 0, 0 ]\nint[] nums = [1, 3, 2, 5, 4];\n</code></pre> array.go<pre><code>/* 配列を初期化する */\nvar arr [5]int\n// Go では、長さを指定する場合（[5]int）は配列であり、長さを指定しない場合（[]int）はスライス\n// Go の配列はコンパイル時に長さが確定するよう設計されているため、長さの指定には定数しか使用できない\n// 拡張 extend() メソッドを実装しやすくするため、以下ではスライス（Slice）を配列（Array）として扱う\nnums := []int{1, 3, 2, 5, 4}\n</code></pre> array.swift<pre><code>/* 配列を初期化する */\nlet arr = Array(repeating: 0, count: 5) // [0, 0, 0, 0, 0]\nlet nums = [1, 3, 2, 5, 4]\n</code></pre> array.js<pre><code>/* 配列を初期化する */\nvar arr = new Array(5).fill(0);\nvar nums = [1, 3, 2, 5, 4];\n</code></pre> array.ts<pre><code>/* 配列を初期化する */\nlet arr: number[] = new Array(5).fill(0);\nlet nums: number[] = [1, 3, 2, 5, 4];\n</code></pre> array.dart<pre><code>/* 配列を初期化する */\nList&lt;int&gt; arr = List.filled(5, 0); // [0, 0, 0, 0, 0]\nList&lt;int&gt; nums = [1, 3, 2, 5, 4];\n</code></pre> array.rs<pre><code>/* 配列を初期化する */\nlet arr: [i32; 5] = [0; 5]; // [0, 0, 0, 0, 0]\nlet slice: &amp;[i32] = &amp;[0; 5];\n// Rust では、長さを指定する場合（[i32; 5]）は配列であり、長さを指定しない場合（&amp;[i32]）はスライス\n// Rust の配列はコンパイル時に長さが確定するよう設計されているため、長さの指定には定数しか使用できない\n// Vector は Rust で一般に動的配列として使われる型\n// 拡張 extend() メソッドを実装しやすくするため、以下では vector を配列（array）として扱う\nlet nums: Vec&lt;i32&gt; = vec![1, 3, 2, 5, 4];\n</code></pre> array.c<pre><code>/* 配列を初期化する */\nint arr[5] = { 0 }; // { 0, 0, 0, 0, 0 }\nint nums[5] = { 1, 3, 2, 5, 4 };\n</code></pre> array.kt<pre><code>/* 配列を初期化する */\nvar arr = IntArray(5) // { 0, 0, 0, 0, 0 }\nvar nums = intArrayOf(1, 3, 2, 5, 4)\n</code></pre> array.rb<pre><code># 配列を初期化する\narr = Array.new(5, 0)\nnums = [1, 3, 2, 5, 4]\n</code></pre> 実行の可視化 <p>https://pythontutor.com/render.html#code=%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E6%95%B0%E7%BB%84%0Aarr%20%3D%20%5B0%5D%20*%205%20%20%23%20%5B%200,%200,%200,%200,%200%20%5D%0Anums%20%3D%20%5B1,%203,%202,%205,%204%5D&amp;cumulative=false&amp;curInstr=0&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.1 &nbsp; 配列"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#2","level":3,"title":"2.   要素へのアクセス","text":"<p>配列要素は連続したメモリ領域に格納されるため、要素のメモリアドレスの計算は非常に容易です。配列のメモリアドレス（先頭要素のメモリアドレス）とある要素のインデックスが与えられれば、下図の式を使ってその要素のメモリアドレスを計算でき、直接その要素にアクセスできます。</p> <p></p> <p> 図 4-2   配列要素のメモリアドレスの計算 </p> <p>上図を見ると、配列の最初の要素のインデックスは \\(0\\) であり、これは少し直感に反するように思えます。というのも、\\(1\\) から数え始めるほうが自然だからです。しかし、アドレス計算式の観点では、**インデックスの本質はメモリアドレスのオフセット**です。先頭要素のアドレスのオフセットは \\(0\\) であるため、そのインデックスが \\(0\\) なのは妥当です。</p> <p>配列では要素へのアクセスは非常に効率的であり、\\(O(1)\\) 時間で任意の要素にランダムアクセスできます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code>def random_access(nums: list[int]) -&gt; int:\n    \"\"\"要素へランダムアクセス\"\"\"\n    # 区間 [0, len(nums)-1] からランダムに数字を 1 つ選ぶ\n    random_index = random.randint(0, len(nums) - 1)\n    # ランダムな要素を取得して返す\n    random_num = nums[random_index]\n    return random_num\n</code></pre> array.cpp<pre><code>/* 要素へランダムアクセス */\nint randomAccess(int *nums, int size) {\n    // 区間 [0, size) からランダムに 1 つの数を選ぶ\n    int randomIndex = rand() % size;\n    // ランダムな要素を取得して返す\n    int randomNum = nums[randomIndex];\n    return randomNum;\n}\n</code></pre> array.java<pre><code>/* 要素へランダムアクセス */\nint randomAccess(int[] nums) {\n    // 区間 [0, nums.length) からランダムに 1 つの数を選ぶ\n    int randomIndex = ThreadLocalRandom.current().nextInt(0, nums.length);\n    // ランダムな要素を取得して返す\n    int randomNum = nums[randomIndex];\n    return randomNum;\n}\n</code></pre> array.cs<pre><code>/* 要素へランダムアクセス */\nint RandomAccess(int[] nums) {\n    Random random = new();\n    // 区間 [0, nums.Length) からランダムに数字を 1 つ選ぶ\n    int randomIndex = random.Next(nums.Length);\n    // ランダムな要素を取得して返す\n    int randomNum = nums[randomIndex];\n    return randomNum;\n}\n</code></pre> array.go<pre><code>/* 要素へランダムアクセス */\nfunc randomAccess(nums []int) (randomNum int) {\n    // 区間 [0, nums.length) からランダムに 1 つの数を選ぶ\n    randomIndex := rand.Intn(len(nums))\n    // ランダムな要素を取得して返す\n    randomNum = nums[randomIndex]\n    return\n}\n</code></pre> array.swift<pre><code>/* 要素へランダムアクセス */\nfunc randomAccess(nums: [Int]) -&gt; Int {\n    // 区間 [0, nums.count) からランダムに数字を 1 つ選ぶ\n    let randomIndex = nums.indices.randomElement()!\n    // ランダムな要素を取得して返す\n    let randomNum = nums[randomIndex]\n    return randomNum\n}\n</code></pre> array.js<pre><code>/* 要素へランダムアクセス */\nfunction randomAccess(nums) {\n    // 区間 [0, nums.length) からランダムに 1 つの数を選ぶ\n    const random_index = Math.floor(Math.random() * nums.length);\n    // ランダムな要素を取得して返す\n    const random_num = nums[random_index];\n    return random_num;\n}\n</code></pre> array.ts<pre><code>/* 要素へランダムアクセス */\nfunction randomAccess(nums: number[]): number {\n    // 区間 [0, nums.length) からランダムに 1 つの数を選ぶ\n    const random_index = Math.floor(Math.random() * nums.length);\n    // ランダムな要素を取得して返す\n    const random_num = nums[random_index];\n    return random_num;\n}\n</code></pre> array.dart<pre><code>/* 要素へランダムアクセス */\nint randomAccess(List&lt;int&gt; nums) {\n  // 区間 [0, nums.length) からランダムに 1 つの数を選ぶ\n  int randomIndex = Random().nextInt(nums.length);\n  // ランダムな要素を取得して返す\n  int randomNum = nums[randomIndex];\n  return randomNum;\n}\n</code></pre> array.rs<pre><code>/* 要素へランダムアクセス */\nfn random_access(nums: &amp;[i32]) -&gt; i32 {\n    // 区間 [0, nums.len()) からランダムに数字を 1 つ選ぶ\n    let random_index = rand::thread_rng().gen_range(0..nums.len());\n    // ランダムな要素を取得して返す\n    let random_num = nums[random_index];\n    random_num\n}\n</code></pre> array.c<pre><code>/* 要素へランダムアクセス */\nint randomAccess(int *nums, int size) {\n    // 区間 [0, size) からランダムに 1 つの数を選ぶ\n    int randomIndex = rand() % size;\n    // ランダムな要素を取得して返す\n    int randomNum = nums[randomIndex];\n    return randomNum;\n}\n</code></pre> array.kt<pre><code>/* 要素へランダムアクセス */\nfun randomAccess(nums: IntArray): Int {\n    // 区間 [0, nums.size) からランダムに数字を 1 つ選ぶ\n    val randomIndex = ThreadLocalRandom.current().nextInt(0, nums.size)\n    // ランダムな要素を取得して返す\n    val randomNum = nums[randomIndex]\n    return randomNum\n}\n</code></pre> array.rb<pre><code>### 要素にランダムアクセス ###\ndef random_access(nums)\n  # 区間 [0, nums.length) からランダムに 1 つの数を選ぶ\n  random_index = Random.rand(0...nums.length)\n\n  # ランダムな要素を取得して返す\n  nums[random_index]\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.1 &nbsp; 配列"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#3","level":3,"title":"3.   要素の挿入","text":"<p>配列要素はメモリ内で「ぴったり隣接して」おり、その間にほかのデータを格納する余地はありません。下図のように、配列の途中に要素を挿入したい場合は、その要素より後ろにあるすべての要素を 1 つずつ後ろへずらし、その後でそのインデックスに要素を代入する必要があります。</p> <p></p> <p> 図 4-3   配列への要素挿入の例 </p> <p>注意すべき点として、配列の長さは固定であるため、要素を 1 つ挿入すると配列末尾の要素が必ず「失われ」ます。この問題の解決策は「リスト」の章で扱います。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code>def insert(nums: list[int], num: int, index: int):\n    \"\"\"配列の index 番目に要素 num を挿入\"\"\"\n    # インデックス index 以降の全要素を 1 つ後ろへ移動する\n    for i in range(len(nums) - 1, index, -1):\n        nums[i] = nums[i - 1]\n    # index の要素に num を代入する\n    nums[index] = num\n</code></pre> array.cpp<pre><code>/* 配列の index 番目に要素 num を挿入 */\nvoid insert(int *nums, int size, int num, int index) {\n    // インデックス index 以降の全要素を 1 つ後ろへ移動する\n    for (int i = size - 1; i &gt; index; i--) {\n        nums[i] = nums[i - 1];\n    }\n    // index の要素に num を代入する\n    nums[index] = num;\n}\n</code></pre> array.java<pre><code>/* 配列の index 番目に要素 num を挿入 */\nvoid insert(int[] nums, int num, int index) {\n    // インデックス index 以降の全要素を 1 つ後ろへ移動する\n    for (int i = nums.length - 1; i &gt; index; i--) {\n        nums[i] = nums[i - 1];\n    }\n    // index の要素に num を代入する\n    nums[index] = num;\n}\n</code></pre> array.cs<pre><code>/* 配列の index 番目に要素 num を挿入 */\nvoid Insert(int[] nums, int num, int index) {\n    // インデックス index 以降の全要素を 1 つ後ろへ移動する\n    for (int i = nums.Length - 1; i &gt; index; i--) {\n        nums[i] = nums[i - 1];\n    }\n    // index の要素に num を代入する\n    nums[index] = num;\n}\n</code></pre> array.go<pre><code>/* 配列の index 番目に要素 num を挿入 */\nfunc insert(nums []int, num int, index int) {\n    // インデックス index 以降の全要素を 1 つ後ろへ移動する\n    for i := len(nums) - 1; i &gt; index; i-- {\n        nums[i] = nums[i-1]\n    }\n    // index の要素に num を代入する\n    nums[index] = num\n}\n</code></pre> array.swift<pre><code>/* 配列の index 番目に要素 num を挿入 */\nfunc insert(nums: inout [Int], num: Int, index: Int) {\n    // インデックス index 以降の全要素を 1 つ後ろへ移動する\n    for i in nums.indices.dropFirst(index).reversed() {\n        nums[i] = nums[i - 1]\n    }\n    // index の要素に num を代入する\n    nums[index] = num\n}\n</code></pre> array.js<pre><code>/* 配列の index 番目に要素 num を挿入 */\nfunction insert(nums, num, index) {\n    // インデックス index 以降の全要素を 1 つ後ろへ移動する\n    for (let i = nums.length - 1; i &gt; index; i--) {\n        nums[i] = nums[i - 1];\n    }\n    // index の要素に num を代入する\n    nums[index] = num;\n}\n</code></pre> array.ts<pre><code>/* 配列の index 番目に要素 num を挿入 */\nfunction insert(nums: number[], num: number, index: number): void {\n    // インデックス index 以降の全要素を 1 つ後ろへ移動する\n    for (let i = nums.length - 1; i &gt; index; i--) {\n        nums[i] = nums[i - 1];\n    }\n    // index の要素に num を代入する\n    nums[index] = num;\n}\n</code></pre> array.dart<pre><code>/* 配列の添字 index に要素 _num を挿入 */\nvoid insert(List&lt;int&gt; nums, int _num, int index) {\n  // インデックス index 以降の全要素を 1 つ後ろへ移動する\n  for (var i = nums.length - 1; i &gt; index; i--) {\n    nums[i] = nums[i - 1];\n  }\n  // _num を index の位置の要素に代入\n  nums[index] = _num;\n}\n</code></pre> array.rs<pre><code>/* 配列の index 番目に要素 num を挿入 */\nfn insert(nums: &amp;mut [i32], num: i32, index: usize) {\n    // インデックス index 以降の全要素を 1 つ後ろへ移動する\n    for i in (index + 1..nums.len()).rev() {\n        nums[i] = nums[i - 1];\n    }\n    // index の要素に num を代入する\n    nums[index] = num;\n}\n</code></pre> array.c<pre><code>/* 配列の index 番目に要素 num を挿入 */\nvoid insert(int *nums, int size, int num, int index) {\n    // インデックス index 以降の全要素を 1 つ後ろへ移動する\n    for (int i = size - 1; i &gt; index; i--) {\n        nums[i] = nums[i - 1];\n    }\n    // index の要素に num を代入する\n    nums[index] = num;\n}\n</code></pre> array.kt<pre><code>/* 配列の index 番目に要素 num を挿入 */\nfun insert(nums: IntArray, num: Int, index: Int) {\n    // インデックス index 以降の全要素を 1 つ後ろへ移動する\n    for (i in nums.size - 1 downTo index + 1) {\n        nums[i] = nums[i - 1]\n    }\n    // index の要素に num を代入する\n    nums[index] = num\n}\n</code></pre> array.rb<pre><code>### 配列のインデックス index に要素 num を挿入 ###\ndef insert(nums, num, index)\n  # インデックス index 以降の全要素を 1 つ後ろへ移動する\n  for i in (nums.length - 1).downto(index + 1)\n    nums[i] = nums[i - 1]\n  end\n\n  # index の要素に num を代入する\n  nums[index] = num\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.1 &nbsp; 配列"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#4","level":3,"title":"4.   要素の削除","text":"<p>同様に、下図のように、インデックス \\(i\\) の要素を削除したい場合は、インデックス \\(i\\) より後ろの要素をすべて 1 つずつ前へずらす必要があります。</p> <p></p> <p> 図 4-4   配列からの要素削除の例 </p> <p>注意してください。要素の削除が完了すると、もともとの末尾要素は「意味を持たない」状態になるため、わざわざ変更する必要はありません。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code>def remove(nums: list[int], index: int):\n    \"\"\"index の要素を削除する\"\"\"\n    # インデックス index より後ろの全要素を 1 つ前へ移動する\n    for i in range(index, len(nums) - 1):\n        nums[i] = nums[i + 1]\n</code></pre> array.cpp<pre><code>/* index の要素を削除する */\nvoid remove(int *nums, int size, int index) {\n    // インデックス index より後ろの全要素を 1 つ前へ移動する\n    for (int i = index; i &lt; size - 1; i++) {\n        nums[i] = nums[i + 1];\n    }\n}\n</code></pre> array.java<pre><code>/* index の要素を削除する */\nvoid remove(int[] nums, int index) {\n    // インデックス index より後ろの全要素を 1 つ前へ移動する\n    for (int i = index; i &lt; nums.length - 1; i++) {\n        nums[i] = nums[i + 1];\n    }\n}\n</code></pre> array.cs<pre><code>/* index の要素を削除する */\nvoid Remove(int[] nums, int index) {\n    // インデックス index より後ろの全要素を 1 つ前へ移動する\n    for (int i = index; i &lt; nums.Length - 1; i++) {\n        nums[i] = nums[i + 1];\n    }\n}\n</code></pre> array.go<pre><code>/* index の要素を削除する */\nfunc remove(nums []int, index int) {\n    // インデックス index より後ろの全要素を 1 つ前へ移動する\n    for i := index; i &lt; len(nums)-1; i++ {\n        nums[i] = nums[i+1]\n    }\n}\n</code></pre> array.swift<pre><code>/* index の要素を削除する */\nfunc remove(nums: inout [Int], index: Int) {\n    // インデックス index より後ろの全要素を 1 つ前へ移動する\n    for i in nums.indices.dropFirst(index).dropLast() {\n        nums[i] = nums[i + 1]\n    }\n}\n</code></pre> array.js<pre><code>/* index の要素を削除する */\nfunction remove(nums, index) {\n    // インデックス index より後ろの全要素を 1 つ前へ移動する\n    for (let i = index; i &lt; nums.length - 1; i++) {\n        nums[i] = nums[i + 1];\n    }\n}\n</code></pre> array.ts<pre><code>/* index の要素を削除する */\nfunction remove(nums: number[], index: number): void {\n    // インデックス index より後ろの全要素を 1 つ前へ移動する\n    for (let i = index; i &lt; nums.length - 1; i++) {\n        nums[i] = nums[i + 1];\n    }\n}\n</code></pre> array.dart<pre><code>/* index の要素を削除する */\nvoid remove(List&lt;int&gt; nums, int index) {\n  // インデックス index より後ろの全要素を 1 つ前へ移動する\n  for (var i = index; i &lt; nums.length - 1; i++) {\n    nums[i] = nums[i + 1];\n  }\n}\n</code></pre> array.rs<pre><code>/* index の要素を削除する */\nfn remove(nums: &amp;mut [i32], index: usize) {\n    // インデックス index より後ろの全要素を 1 つ前へ移動する\n    for i in index..nums.len() - 1 {\n        nums[i] = nums[i + 1];\n    }\n}\n</code></pre> array.c<pre><code>/* index の要素を削除する */\n// 注意: stdio.h が remove 識別子を使用している\nvoid removeItem(int *nums, int size, int index) {\n    // インデックス index より後ろの全要素を 1 つ前へ移動する\n    for (int i = index; i &lt; size - 1; i++) {\n        nums[i] = nums[i + 1];\n    }\n}\n</code></pre> array.kt<pre><code>/* index の要素を削除する */\nfun remove(nums: IntArray, index: Int) {\n    // インデックス index より後ろの全要素を 1 つ前へ移動する\n    for (i in index..&lt;nums.size - 1) {\n        nums[i] = nums[i + 1]\n    }\n}\n</code></pre> array.rb<pre><code>### インデックス index の要素を削除 ###\ndef remove(nums, index)\n  # インデックス index より後ろの全要素を 1 つ前へ移動する\n  for i in index...(nums.length - 1)\n    nums[i] = nums[i + 1]\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>全体として見ると、配列の挿入と削除には次の欠点があります。</p> <ul> <li>時間計算量が高い：配列の挿入と削除の平均時間計算量はいずれも \\(O(n)\\) であり、ここで \\(n\\) は配列長です。</li> <li>要素が失われる：配列の長さは不変であるため、要素を挿入すると配列長の範囲を超えた要素は失われます。</li> <li>メモリの浪費：やや長めの配列を初期化して先頭部分だけを使うこともでき、この場合データ挿入時に失われる末尾要素はすべて「無意味」ですが、その代わり一部のメモリ領域が無駄になります。</li> </ul>","path":["第 4 章 &nbsp; 配列と連結リスト","4.1 &nbsp; 配列"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#5","level":3,"title":"5.   配列の走査","text":"<p>ほとんどのプログラミング言語では、インデックスを使って配列を走査することも、各要素を直接取り出しながら走査することもできます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code>def traverse(nums: list[int]):\n    \"\"\"配列を走査\"\"\"\n    count = 0\n    # インデックスで配列を走査\n    for i in range(len(nums)):\n        count += nums[i]\n    # 配列要素を直接走査\n    for num in nums:\n        count += num\n    # データのインデックスと要素を同時に走査する\n    for i, num in enumerate(nums):\n        count += nums[i]\n        count += num\n</code></pre> array.cpp<pre><code>/* 配列を走査 */\nvoid traverse(int *nums, int size) {\n    int count = 0;\n    // インデックスで配列を走査\n    for (int i = 0; i &lt; size; i++) {\n        count += nums[i];\n    }\n}\n</code></pre> array.java<pre><code>/* 配列を走査 */\nvoid traverse(int[] nums) {\n    int count = 0;\n    // インデックスで配列を走査\n    for (int i = 0; i &lt; nums.length; i++) {\n        count += nums[i];\n    }\n    // 配列要素を直接走査\n    for (int num : nums) {\n        count += num;\n    }\n}\n</code></pre> array.cs<pre><code>/* 配列を走査 */\nvoid Traverse(int[] nums) {\n    int count = 0;\n    // インデックスで配列を走査\n    for (int i = 0; i &lt; nums.Length; i++) {\n        count += nums[i];\n    }\n    // 配列要素を直接走査\n    foreach (int num in nums) {\n        count += num;\n    }\n}\n</code></pre> array.go<pre><code>/* 配列を走査 */\nfunc traverse(nums []int) {\n    count := 0\n    // インデックスで配列を走査\n    for i := 0; i &lt; len(nums); i++ {\n        count += nums[i]\n    }\n    count = 0\n    // 配列要素を直接走査\n    for _, num := range nums {\n        count += num\n    }\n    // データのインデックスと要素を同時に走査する\n    for i, num := range nums {\n        count += nums[i]\n        count += num\n    }\n}\n</code></pre> array.swift<pre><code>/* 配列を走査 */\nfunc traverse(nums: [Int]) {\n    var count = 0\n    // インデックスで配列を走査\n    for i in nums.indices {\n        count += nums[i]\n    }\n    // 配列要素を直接走査\n    for num in nums {\n        count += num\n    }\n    // データのインデックスと要素を同時に走査する\n    for (i, num) in nums.enumerated() {\n        count += nums[i]\n        count += num\n    }\n}\n</code></pre> array.js<pre><code>/* 配列を走査 */\nfunction traverse(nums) {\n    let count = 0;\n    // インデックスで配列を走査\n    for (let i = 0; i &lt; nums.length; i++) {\n        count += nums[i];\n    }\n    // 配列要素を直接走査\n    for (const num of nums) {\n        count += num;\n    }\n}\n</code></pre> array.ts<pre><code>/* 配列を走査 */\nfunction traverse(nums: number[]): void {\n    let count = 0;\n    // インデックスで配列を走査\n    for (let i = 0; i &lt; nums.length; i++) {\n        count += nums[i];\n    }\n    // 配列要素を直接走査\n    for (const num of nums) {\n        count += num;\n    }\n}\n</code></pre> array.dart<pre><code>/* 配列要素を走査する */\nvoid traverse(List&lt;int&gt; nums) {\n  int count = 0;\n  // インデックスで配列を走査\n  for (var i = 0; i &lt; nums.length; i++) {\n    count += nums[i];\n  }\n  // 配列要素を直接走査\n  for (int _num in nums) {\n    count += _num;\n  }\n  // forEach メソッドで配列を走査する\n  nums.forEach((_num) {\n    count += _num;\n  });\n}\n</code></pre> array.rs<pre><code>/* 配列を走査 */\nfn traverse(nums: &amp;[i32]) {\n    let mut _count = 0;\n    // インデックスで配列を走査\n    for i in 0..nums.len() {\n        _count += nums[i];\n    }\n    // 配列要素を直接走査\n    _count = 0;\n    for &amp;num in nums {\n        _count += num;\n    }\n}\n</code></pre> array.c<pre><code>/* 配列を走査 */\nvoid traverse(int *nums, int size) {\n    int count = 0;\n    // インデックスで配列を走査\n    for (int i = 0; i &lt; size; i++) {\n        count += nums[i];\n    }\n}\n</code></pre> array.kt<pre><code>/* 配列を走査 */\nfun traverse(nums: IntArray) {\n    var count = 0\n    // インデックスで配列を走査\n    for (i in nums.indices) {\n        count += nums[i]\n    }\n    // 配列要素を直接走査\n    for (j in nums) {\n        count += j\n    }\n}\n</code></pre> array.rb<pre><code>### 配列を走査 ###\ndef traverse(nums)\n  count = 0\n\n  # インデックスで配列を走査\n  for i in 0...nums.length\n    count += nums[i]\n  end\n\n  # 配列要素を直接走査\n  for num in nums\n    count += num\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.1 &nbsp; 配列"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#6","level":3,"title":"6.   要素の検索","text":"<p>配列内で指定した要素を探すには、配列を走査し、各反復で要素値が一致するかを判定し、一致したら対応するインデックスを出力します。</p> <p>配列は線形データ構造であるため、上記の検索操作は「線形探索」と呼ばれます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code>def find(nums: list[int], target: int) -&gt; int:\n    \"\"\"配列内で指定要素を探す\"\"\"\n    for i in range(len(nums)):\n        if nums[i] == target:\n            return i\n    return -1\n</code></pre> array.cpp<pre><code>/* 配列内で指定要素を探す */\nint find(int *nums, int size, int target) {\n    for (int i = 0; i &lt; size; i++) {\n        if (nums[i] == target)\n            return i;\n    }\n    return -1;\n}\n</code></pre> array.java<pre><code>/* 配列内で指定要素を探す */\nint find(int[] nums, int target) {\n    for (int i = 0; i &lt; nums.length; i++) {\n        if (nums[i] == target)\n            return i;\n    }\n    return -1;\n}\n</code></pre> array.cs<pre><code>/* 配列内で指定要素を探す */\nint Find(int[] nums, int target) {\n    for (int i = 0; i &lt; nums.Length; i++) {\n        if (nums[i] == target)\n            return i;\n    }\n    return -1;\n}\n</code></pre> array.go<pre><code>/* 配列内で指定要素を探す */\nfunc find(nums []int, target int) (index int) {\n    index = -1\n    for i := 0; i &lt; len(nums); i++ {\n        if nums[i] == target {\n            index = i\n            break\n        }\n    }\n    return\n}\n</code></pre> array.swift<pre><code>/* 配列内で指定要素を探す */\nfunc find(nums: [Int], target: Int) -&gt; Int {\n    for i in nums.indices {\n        if nums[i] == target {\n            return i\n        }\n    }\n    return -1\n}\n</code></pre> array.js<pre><code>/* 配列内で指定要素を探す */\nfunction find(nums, target) {\n    for (let i = 0; i &lt; nums.length; i++) {\n        if (nums[i] === target) return i;\n    }\n    return -1;\n}\n</code></pre> array.ts<pre><code>/* 配列内で指定要素を探す */\nfunction find(nums: number[], target: number): number {\n    for (let i = 0; i &lt; nums.length; i++) {\n        if (nums[i] === target) {\n            return i;\n        }\n    }\n    return -1;\n}\n</code></pre> array.dart<pre><code>/* 配列内で指定要素を探す */\nint find(List&lt;int&gt; nums, int target) {\n  for (var i = 0; i &lt; nums.length; i++) {\n    if (nums[i] == target) return i;\n  }\n  return -1;\n}\n</code></pre> array.rs<pre><code>/* 配列内で指定要素を探す */\nfn find(nums: &amp;[i32], target: i32) -&gt; Option&lt;usize&gt; {\n    for i in 0..nums.len() {\n        if nums[i] == target {\n            return Some(i);\n        }\n    }\n    None\n}\n</code></pre> array.c<pre><code>/* 配列内で指定要素を探す */\nint find(int *nums, int size, int target) {\n    for (int i = 0; i &lt; size; i++) {\n        if (nums[i] == target)\n            return i;\n    }\n    return -1;\n}\n</code></pre> array.kt<pre><code>/* 配列内で指定要素を探す */\nfun find(nums: IntArray, target: Int): Int {\n    for (i in nums.indices) {\n        if (nums[i] == target)\n            return i\n    }\n    return -1\n}\n</code></pre> array.rb<pre><code>### 配列内の指定要素を検索 ###\ndef find(nums, target)\n  for i in 0...nums.length\n    return i if nums[i] == target\n  end\n\n  -1\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.1 &nbsp; 配列"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#7","level":3,"title":"7.   配列の拡張","text":"<p>複雑なシステム環境では、配列の後方にあるメモリ領域が利用可能であることをプログラム側で保証できず、そのため安全に配列容量を拡張できません。したがって、ほとんどのプログラミング言語では、配列の長さは不変です。</p> <p>配列を拡張したい場合は、より大きな新しい配列を作り、元の配列の要素を順に新配列へコピーする必要があります。これは \\(O(n)\\) の操作であり、配列が大きい場合は非常に時間がかかります。コードは次のとおりです。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code>def extend(nums: list[int], enlarge: int) -&gt; list[int]:\n    \"\"\"配列長を拡張する\"\"\"\n    # 拡張後の長さを持つ配列を初期化する\n    res = [0] * (len(nums) + enlarge)\n    # 元の配列の全要素を新しい配列にコピー\n    for i in range(len(nums)):\n        res[i] = nums[i]\n    # 拡張後の新しい配列を返す\n    return res\n</code></pre> array.cpp<pre><code>/* 配列長を拡張する */\nint *extend(int *nums, int size, int enlarge) {\n    // 拡張後の長さを持つ配列を初期化する\n    int *res = new int[size + enlarge];\n    // 元の配列の全要素を新しい配列にコピー\n    for (int i = 0; i &lt; size; i++) {\n        res[i] = nums[i];\n    }\n    // メモリを解放する\n    delete[] nums;\n    // 拡張後の新しい配列を返す\n    return res;\n}\n</code></pre> array.java<pre><code>/* 配列長を拡張する */\nint[] extend(int[] nums, int enlarge) {\n    // 拡張後の長さを持つ配列を初期化する\n    int[] res = new int[nums.length + enlarge];\n    // 元の配列の全要素を新しい配列にコピー\n    for (int i = 0; i &lt; nums.length; i++) {\n        res[i] = nums[i];\n    }\n    // 拡張後の新しい配列を返す\n    return res;\n}\n</code></pre> array.cs<pre><code>/* 配列長を拡張する */\nint[] Extend(int[] nums, int enlarge) {\n    // 拡張後の長さを持つ配列を初期化する\n    int[] res = new int[nums.Length + enlarge];\n    // 元の配列の全要素を新しい配列にコピー\n    for (int i = 0; i &lt; nums.Length; i++) {\n        res[i] = nums[i];\n    }\n    // 拡張後の新しい配列を返す\n    return res;\n}\n</code></pre> array.go<pre><code>/* 配列長を拡張する */\nfunc extend(nums []int, enlarge int) []int {\n    // 拡張後の長さを持つ配列を初期化する\n    res := make([]int, len(nums)+enlarge)\n    // 元の配列の全要素を新しい配列にコピー\n    for i, num := range nums {\n        res[i] = num\n    }\n    // 拡張後の新しい配列を返す\n    return res\n}\n</code></pre> array.swift<pre><code>/* 配列長を拡張する */\nfunc extend(nums: [Int], enlarge: Int) -&gt; [Int] {\n    // 拡張後の長さを持つ配列を初期化する\n    var res = Array(repeating: 0, count: nums.count + enlarge)\n    // 元の配列の全要素を新しい配列にコピー\n    for i in nums.indices {\n        res[i] = nums[i]\n    }\n    // 拡張後の新しい配列を返す\n    return res\n}\n</code></pre> array.js<pre><code>/* 配列長を拡張する */\n// JavaScript の Array は動的配列であり、直接拡張できます\n// 学習しやすいよう、本関数では Array を長さ不変の配列として扱います\nfunction extend(nums, enlarge) {\n    // 拡張後の長さを持つ配列を初期化する\n    const res = new Array(nums.length + enlarge).fill(0);\n    // 元の配列の全要素を新しい配列にコピー\n    for (let i = 0; i &lt; nums.length; i++) {\n        res[i] = nums[i];\n    }\n    // 拡張後の新しい配列を返す\n    return res;\n}\n</code></pre> array.ts<pre><code>/* 配列長を拡張する */\n// TypeScript の Array は動的配列であり、直接拡張できます\n// 学習しやすいよう、本関数では Array を長さ不変の配列として扱います\nfunction extend(nums: number[], enlarge: number): number[] {\n    // 拡張後の長さを持つ配列を初期化する\n    const res = new Array(nums.length + enlarge).fill(0);\n    // 元の配列の全要素を新しい配列にコピー\n    for (let i = 0; i &lt; nums.length; i++) {\n        res[i] = nums[i];\n    }\n    // 拡張後の新しい配列を返す\n    return res;\n}\n</code></pre> array.dart<pre><code>/* 配列長を拡張する */\nList&lt;int&gt; extend(List&lt;int&gt; nums, int enlarge) {\n  // 拡張後の長さを持つ配列を初期化する\n  List&lt;int&gt; res = List.filled(nums.length + enlarge, 0);\n  // 元の配列の全要素を新しい配列にコピー\n  for (var i = 0; i &lt; nums.length; i++) {\n    res[i] = nums[i];\n  }\n  // 拡張後の新しい配列を返す\n  return res;\n}\n</code></pre> array.rs<pre><code>/* 配列長を拡張する */\nfn extend(nums: &amp;[i32], enlarge: usize) -&gt; Vec&lt;i32&gt; {\n    // 拡張後の長さを持つ配列を初期化する\n    let mut res: Vec&lt;i32&gt; = vec![0; nums.len() + enlarge];\n    // 元の配列の全要素を新しい配列にコピー\n    res[0..nums.len()].copy_from_slice(nums);\n\n    // 拡張後の新しい配列を返す\n    res\n}\n</code></pre> array.c<pre><code>/* 配列長を拡張する */\nint *extend(int *nums, int size, int enlarge) {\n    // 拡張後の長さを持つ配列を初期化する\n    int *res = (int *)malloc(sizeof(int) * (size + enlarge));\n    // 元の配列の全要素を新しい配列にコピー\n    for (int i = 0; i &lt; size; i++) {\n        res[i] = nums[i];\n    }\n    // 拡張後の領域を初期化する\n    for (int i = size; i &lt; size + enlarge; i++) {\n        res[i] = 0;\n    }\n    // 拡張後の新しい配列を返す\n    return res;\n}\n</code></pre> array.kt<pre><code>/* 配列長を拡張する */\nfun extend(nums: IntArray, enlarge: Int): IntArray {\n    // 拡張後の長さを持つ配列を初期化する\n    val res = IntArray(nums.size + enlarge)\n    // 元の配列の全要素を新しい配列にコピー\n    for (i in nums.indices) {\n        res[i] = nums[i]\n    }\n    // 拡張後の新しい配列を返す\n    return res\n}\n</code></pre> array.rb<pre><code>### 配列長を拡張 ###\n# Ruby の Array は動的配列であり、直接拡張できます\n# 学習しやすいよう、本関数では Array を長さ不変の配列として扱います\ndef extend(nums, enlarge)\n  # 拡張後の長さを持つ配列を初期化する\n  res = Array.new(nums.length + enlarge, 0)\n\n  # 元の配列の全要素を新しい配列にコピー\n  for i in 0...nums.length\n    res[i] = nums[i]\n  end\n\n  # 拡張後の新しい配列を返す\n  res\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.1 &nbsp; 配列"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#412","level":2,"title":"4.1.2   配列の利点と限界","text":"<p>配列は連続したメモリ領域に格納され、要素の型も同一です。この方法には豊富な事前情報が含まれており、システムはそれらを利用してデータ構造の操作効率を最適化できます。</p> <ul> <li>空間効率が高い：配列はデータに連続したメモリブロックを割り当てるため、追加の構造オーバーヘッドが不要です。</li> <li>ランダムアクセスをサポートする：配列では任意の要素に \\(O(1)\\) 時間でアクセスできます。</li> <li>キャッシュ局所性：配列要素にアクセスする際、コンピュータはその要素だけでなく周囲のデータもキャッシュするため、高速キャッシュを利用して後続操作の実行速度を高められます。</li> </ul> <p>連続領域への格納は諸刃の剣であり、次のような制約があります。</p> <ul> <li>挿入と削除の効率が低い：配列内の要素が多い場合、挿入や削除では大量の要素を移動する必要があります。</li> <li>長さが不変：配列は初期化後に長さが固定され、拡張するにはすべてのデータを新しい配列へコピーする必要があり、コストが大きくなります。</li> <li>空間の浪費：配列に割り当てたサイズが実際の必要量を上回る場合、余分な領域は無駄になります。</li> </ul>","path":["第 4 章 &nbsp; 配列と連結リスト","4.1 &nbsp; 配列"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#413","level":2,"title":"4.1.3   配列の典型的な応用","text":"<p>配列は基礎的で一般的なデータ構造であり、さまざまなアルゴリズムで頻繁に使われるだけでなく、多様な複雑データ構造の実装にも利用できます。</p> <ul> <li>ランダムアクセス：いくつかのサンプルをランダムに抽出したい場合、配列に格納してランダムな系列を生成し、インデックスに基づいてランダムサンプリングを行えます。</li> <li>ソートと探索：配列はソートアルゴリズムと探索アルゴリズムで最もよく使われるデータ構造です。クイックソート、マージソート、二分探索などは主に配列上で行われます。</li> <li>ルックアップテーブル：ある要素やその対応関係を高速に調べる必要がある場合、配列をルックアップテーブルとして使えます。たとえば文字から ASCII コードへの対応を実装したいなら、文字の ASCII コード値をインデックスとし、対応する要素を配列の対応位置に格納できます。</li> <li>機械学習：ニューラルネットワークでは、ベクトル、行列、テンソル間の線形代数演算が大量に使われ、これらのデータはいずれも配列の形で構築されます。配列はニューラルネットワークプログラミングで最もよく使われるデータ構造です。</li> <li>データ構造の実装：配列はスタック、キュー、ハッシュテーブル、ヒープ、グラフなどのデータ構造の実装に利用できます。たとえば、グラフの隣接行列表現は実際には 2 次元配列です。</li> </ul>","path":["第 4 章 &nbsp; 配列と連結リスト","4.1 &nbsp; 配列"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/","level":1,"title":"4.2   連結リスト","text":"<p>メモリ空間はすべてのプログラムに共通の資源であり、複雑なシステム実行環境では、空きメモリがメモリの各所に散在している可能性があります。配列を格納するメモリ空間は連続していなければなりませんが、配列が非常に大きい場合、メモリはそのような大きな連続領域を提供できないことがあります。このとき、連結リストの柔軟性という利点が現れます。</p> <p>連結リスト（linked list）は線形データ構造の一種であり、各要素はノードオブジェクトです。各ノードは「参照」によって接続されます。参照には次のノードのメモリアドレスが記録されており、これによって現在のノードから次のノードへアクセスできます。</p> <p>連結リストの設計では、各ノードをメモリの各所に分散して格納でき、それらのメモリアドレスは連続している必要がありません。</p> <p></p> <p> 図 4-5   連結リストの定義と格納方式 </p> <p>上図を見ると、連結リストの構成単位はノード（node）オブジェクトです。各ノードは 2 つのデータ、すなわちノードの「値」と次のノードを指す「参照」を含みます。</p> <ul> <li>連結リストの最初のノードを「先頭ノード」、最後のノードを「末尾ノード」と呼びます。</li> <li>末尾ノードが指す先は「空」であり、Java、C++、Python ではそれぞれ <code>null</code>、<code>nullptr</code>、<code>None</code> と表記します。</li> <li>C、C++、Go、Rust などポインタをサポートする言語では、上記の「参照」は「ポインタ」に置き換えるべきです。</li> </ul> <p>以下のコードが示すように、連結リストノード <code>ListNode</code> は値のほかに、追加で 1 つの参照（ポインタ）を保持する必要があります。そのため、同じデータ量であれば、連結リストは配列より多くのメモリ空間を消費します。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>class ListNode:\n    \"\"\"連結リストノードクラス\"\"\"\n    def __init__(self, val: int):\n        self.val: int = val               # ノードの値\n        self.next: ListNode | None = None # 次のノードへの参照\n</code></pre> <pre><code>/* 連結リストノード構造体 */\nstruct ListNode {\n    int val;         // ノードの値\n    ListNode *next;  // 次のノードへのポインタ\n    ListNode(int x) : val(x), next(nullptr) {}  // コンストラクタ\n};\n</code></pre> <pre><code>/* 連結リストノードクラス */\nclass ListNode {\n    int val;        // ノードの値\n    ListNode next;  // 次のノードへの参照\n    ListNode(int x) { val = x; }  // コンストラクタ\n}\n</code></pre> <pre><code>/* 連結リストノードクラス */\nclass ListNode(int x) {  //コンストラクタ\n    int val = x;         // ノードの値\n    ListNode? next;      // 次のノードへの参照\n}\n</code></pre> <pre><code>/* 連結リストノード構造体 */\ntype ListNode struct {\n    Val  int       // ノードの値\n    Next *ListNode // 次のノードへのポインタ\n}\n\n// NewListNode コンストラクタ。新しい連結リストを作成する\nfunc NewListNode(val int) *ListNode {\n    return &amp;ListNode{\n        Val:  val,\n        Next: nil,\n    }\n}\n</code></pre> <pre><code>/* 連結リストノードクラス */\nclass ListNode {\n    var val: Int // ノードの値\n    var next: ListNode? // 次のノードへの参照\n\n    init(x: Int) { // コンストラクタ\n        val = x\n    }\n}\n</code></pre> <pre><code>/* 連結リストノードクラス */\nclass ListNode {\n    constructor(val, next) {\n        this.val = (val === undefined ? 0 : val);       // ノードの値\n        this.next = (next === undefined ? null : next); // 次のノードへの参照\n    }\n}\n</code></pre> <pre><code>/* 連結リストノードクラス */\nclass ListNode {\n    val: number;\n    next: ListNode | null;\n    constructor(val?: number, next?: ListNode | null) {\n        this.val = val === undefined ? 0 : val;        // ノードの値\n        this.next = next === undefined ? null : next;  // 次のノードへの参照\n    }\n}\n</code></pre> <pre><code>/* 連結リストノードクラス */\nclass ListNode {\n  int val; // ノードの値\n  ListNode? next; // 次のノードへの参照\n  ListNode(this.val, [this.next]); // コンストラクタ\n}\n</code></pre> <pre><code>use std::rc::Rc;\nuse std::cell::RefCell;\n/* 連結リストノードクラス */\n#[derive(Debug)]\nstruct ListNode {\n    val: i32, // ノードの値\n    next: Option&lt;Rc&lt;RefCell&lt;ListNode&gt;&gt;&gt;, // 次のノードへのポインタ\n}\n</code></pre> <pre><code>/* 連結リストノード構造体 */\ntypedef struct ListNode {\n    int val;               // ノードの値\n    struct ListNode *next; // 次のノードへのポインタ\n} ListNode;\n\n/* コンストラクタ */\nListNode *newListNode(int val) {\n    ListNode *node;\n    node = (ListNode *) malloc(sizeof(ListNode));\n    node-&gt;val = val;\n    node-&gt;next = NULL;\n    return node;\n}\n</code></pre> <pre><code>/* 連結リストノードクラス */\n// コンストラクタ\nclass ListNode(x: Int) {\n    val _val: Int = x          // ノードの値\n    val next: ListNode? = null // 次のノードへの参照\n}\n</code></pre> <pre><code># 連結リストノードクラス\nclass ListNode\n  attr_accessor :val  # ノードの値\n  attr_accessor :next # 次のノードへの参照\n\n  def initialize(val=0, next_node=nil)\n    @val = val\n    @next = next_node\n  end\nend\n</code></pre>","path":["第 4 章 &nbsp; 配列と連結リスト","4.2 &nbsp; 連結リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#421","level":2,"title":"4.2.1   連結リストの基本操作","text":"","path":["第 4 章 &nbsp; 配列と連結リスト","4.2 &nbsp; 連結リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#1","level":3,"title":"1.   連結リストの初期化","text":"<p>連結リストの構築は 2 つの手順に分かれます。第 1 に各ノードオブジェクトを初期化し、第 2 にノード間の参照関係を構築します。初期化が完了したら、連結リストの先頭ノードから出発し、参照で <code>next</code> をたどってすべてのノードに順にアクセスできます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linked_list.py<pre><code># 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化\n# 各ノードを初期化\nn0 = ListNode(1)\nn1 = ListNode(3)\nn2 = ListNode(2)\nn3 = ListNode(5)\nn4 = ListNode(4)\n# ノード間の参照を構築\nn0.next = n1\nn1.next = n2\nn2.next = n3\nn3.next = n4\n</code></pre> linked_list.cpp<pre><code>/* 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化 */\n// 各ノードを初期化\nListNode* n0 = new ListNode(1);\nListNode* n1 = new ListNode(3);\nListNode* n2 = new ListNode(2);\nListNode* n3 = new ListNode(5);\nListNode* n4 = new ListNode(4);\n// ノード間の参照を構築\nn0-&gt;next = n1;\nn1-&gt;next = n2;\nn2-&gt;next = n3;\nn3-&gt;next = n4;\n</code></pre> linked_list.java<pre><code>/* 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化 */\n// 各ノードを初期化\nListNode n0 = new ListNode(1);\nListNode n1 = new ListNode(3);\nListNode n2 = new ListNode(2);\nListNode n3 = new ListNode(5);\nListNode n4 = new ListNode(4);\n// ノード間の参照を構築\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.cs<pre><code>/* 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化 */\n// 各ノードを初期化\nListNode n0 = new(1);\nListNode n1 = new(3);\nListNode n2 = new(2);\nListNode n3 = new(5);\nListNode n4 = new(4);\n// ノード間の参照を構築\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.go<pre><code>/* 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化 */\n// 各ノードを初期化\nn0 := NewListNode(1)\nn1 := NewListNode(3)\nn2 := NewListNode(2)\nn3 := NewListNode(5)\nn4 := NewListNode(4)\n// ノード間の参照を構築\nn0.Next = n1\nn1.Next = n2\nn2.Next = n3\nn3.Next = n4\n</code></pre> linked_list.swift<pre><code>/* 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化 */\n// 各ノードを初期化\nlet n0 = ListNode(x: 1)\nlet n1 = ListNode(x: 3)\nlet n2 = ListNode(x: 2)\nlet n3 = ListNode(x: 5)\nlet n4 = ListNode(x: 4)\n// ノード間の参照を構築\nn0.next = n1\nn1.next = n2\nn2.next = n3\nn3.next = n4\n</code></pre> linked_list.js<pre><code>/* 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化 */\n// 各ノードを初期化\nconst n0 = new ListNode(1);\nconst n1 = new ListNode(3);\nconst n2 = new ListNode(2);\nconst n3 = new ListNode(5);\nconst n4 = new ListNode(4);\n// ノード間の参照を構築\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.ts<pre><code>/* 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化 */\n// 各ノードを初期化\nconst n0 = new ListNode(1);\nconst n1 = new ListNode(3);\nconst n2 = new ListNode(2);\nconst n3 = new ListNode(5);\nconst n4 = new ListNode(4);\n// ノード間の参照を構築\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.dart<pre><code>/* 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化 */\\\n// 各ノードを初期化\nListNode n0 = ListNode(1);\nListNode n1 = ListNode(3);\nListNode n2 = ListNode(2);\nListNode n3 = ListNode(5);\nListNode n4 = ListNode(4);\n// ノード間の参照を構築\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.rs<pre><code>/* 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化 */\n// 各ノードを初期化\nlet n0 = Rc::new(RefCell::new(ListNode { val: 1, next: None }));\nlet n1 = Rc::new(RefCell::new(ListNode { val: 3, next: None }));\nlet n2 = Rc::new(RefCell::new(ListNode { val: 2, next: None }));\nlet n3 = Rc::new(RefCell::new(ListNode { val: 5, next: None }));\nlet n4 = Rc::new(RefCell::new(ListNode { val: 4, next: None }));\n\n// ノード間の参照を構築\nn0.borrow_mut().next = Some(n1.clone());\nn1.borrow_mut().next = Some(n2.clone());\nn2.borrow_mut().next = Some(n3.clone());\nn3.borrow_mut().next = Some(n4.clone());\n</code></pre> linked_list.c<pre><code>/* 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化 */\n// 各ノードを初期化\nListNode* n0 = newListNode(1);\nListNode* n1 = newListNode(3);\nListNode* n2 = newListNode(2);\nListNode* n3 = newListNode(5);\nListNode* n4 = newListNode(4);\n// ノード間の参照を構築\nn0-&gt;next = n1;\nn1-&gt;next = n2;\nn2-&gt;next = n3;\nn3-&gt;next = n4;\n</code></pre> linked_list.kt<pre><code>/* 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化 */\n// 各ノードを初期化\nval n0 = ListNode(1)\nval n1 = ListNode(3)\nval n2 = ListNode(2)\nval n3 = ListNode(5)\nval n4 = ListNode(4)\n// ノード間の参照を構築\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.rb<pre><code># 連結リスト 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 を初期化\n# 各ノードを初期化\nn0 = ListNode.new(1)\nn1 = ListNode.new(3)\nn2 = ListNode.new(2)\nn3 = ListNode.new(5)\nn4 = ListNode.new(4)\n# ノード間の参照を構築\nn0.next = n1\nn1.next = n2\nn2.next = n3\nn3.next = n4\n</code></pre> 可視化実行 <p>https://pythontutor.com/render.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%E9%93%BE%E8%A1%A8%E8%8A%82%E7%82%B9%E7%B1%BB%22%22%22%0A%20%20%20%20def%20__init__%28self,%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E8%8A%82%E7%82%B9%E5%80%BC%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%90%8E%E7%BB%A7%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E9%93%BE%E8%A1%A8%201%20-%3E%203%20-%3E%202%20-%3E%205%20-%3E%204%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%90%84%E4%B8%AA%E8%8A%82%E7%82%B9%0A%20%20%20%20n0%20%3D%20ListNode%281%29%0A%20%20%20%20n1%20%3D%20ListNode%283%29%0A%20%20%20%20n2%20%3D%20ListNode%282%29%0A%20%20%20%20n3%20%3D%20ListNode%285%29%0A%20%20%20%20n4%20%3D%20ListNode%284%29%0A%20%20%20%20%23%20%E6%9E%84%E5%BB%BA%E8%8A%82%E7%82%B9%E4%B9%8B%E9%97%B4%E7%9A%84%E5%BC%95%E7%94%A8%0A%20%20%20%20n0.next%20%3D%20n1%0A%20%20%20%20n1.next%20%3D%20n2%0A%20%20%20%20n2.next%20%3D%20n3%0A%20%20%20%20n3.next%20%3D%20n4&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p> <p>配列全体は 1 つの変数であり、たとえば配列 <code>nums</code> には <code>nums[0]</code> や <code>nums[1]</code> などの要素が含まれます。一方、連結リストは複数の独立したノードオブジェクトで構成されます。通常、先頭ノードを連結リストの代名詞として扱います。たとえば上記のコードの連結リストは <code>n0</code> と表せます。</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.2 &nbsp; 連結リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#2","level":3,"title":"2.   ノードの挿入","text":"<p>連結リストへのノード挿入は非常に簡単です。下図に示すように、隣り合う 2 つのノード <code>n0</code> と <code>n1</code> の間に新しいノード <code>P</code> を挿入したいとします。このとき 2 つのノードの参照（ポインタ）を変更するだけでよく、時間計算量は \\(O(1)\\) です。</p> <p>これに対して、配列に要素を挿入する時間計算量は \\(O(n)\\) であり、データ量が大きい場合の効率は低くなります。</p> <p></p> <p> 図 4-6   連結リストへのノード挿入例 </p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linked_list.py<pre><code>def insert(n0: ListNode, P: ListNode):\n    \"\"\"連結リストでノード n0 の後ろにノード P を挿入する\"\"\"\n    n1 = n0.next\n    P.next = n1\n    n0.next = P\n</code></pre> linked_list.cpp<pre><code>/* 連結リストでノード n0 の後ろにノード P を挿入する */\nvoid insert(ListNode *n0, ListNode *P) {\n    ListNode *n1 = n0-&gt;next;\n    P-&gt;next = n1;\n    n0-&gt;next = P;\n}\n</code></pre> linked_list.java<pre><code>/* 連結リストでノード n0 の後ろにノード P を挿入する */\nvoid insert(ListNode n0, ListNode P) {\n    ListNode n1 = n0.next;\n    P.next = n1;\n    n0.next = P;\n}\n</code></pre> linked_list.cs<pre><code>/* 連結リストでノード n0 の後ろにノード P を挿入する */\nvoid Insert(ListNode n0, ListNode P) {\n    ListNode? n1 = n0.next;\n    P.next = n1;\n    n0.next = P;\n}\n</code></pre> linked_list.go<pre><code>/* 連結リストでノード n0 の後ろにノード P を挿入する */\nfunc insertNode(n0 *ListNode, P *ListNode) {\n    n1 := n0.Next\n    P.Next = n1\n    n0.Next = P\n}\n</code></pre> linked_list.swift<pre><code>/* 連結リストでノード n0 の後ろにノード P を挿入する */\nfunc insert(n0: ListNode, P: ListNode) {\n    let n1 = n0.next\n    P.next = n1\n    n0.next = P\n}\n</code></pre> linked_list.js<pre><code>/* 連結リストでノード n0 の後ろにノード P を挿入する */\nfunction insert(n0, P) {\n    const n1 = n0.next;\n    P.next = n1;\n    n0.next = P;\n}\n</code></pre> linked_list.ts<pre><code>/* 連結リストでノード n0 の後ろにノード P を挿入する */\nfunction insert(n0: ListNode, P: ListNode): void {\n    const n1 = n0.next;\n    P.next = n1;\n    n0.next = P;\n}\n</code></pre> linked_list.dart<pre><code>/* 連結リストでノード n0 の後ろにノード P を挿入する */\nvoid insert(ListNode n0, ListNode P) {\n  ListNode? n1 = n0.next;\n  P.next = n1;\n  n0.next = P;\n}\n</code></pre> linked_list.rs<pre><code>/* 連結リストでノード n0 の後ろにノード P を挿入する */\n#[allow(non_snake_case)]\npub fn insert&lt;T&gt;(n0: &amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;, P: Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;) {\n    let n1 = n0.borrow_mut().next.take();\n    P.borrow_mut().next = n1;\n    n0.borrow_mut().next = Some(P);\n}\n</code></pre> linked_list.c<pre><code>/* 連結リストでノード n0 の後ろにノード P を挿入する */\nvoid insert(ListNode *n0, ListNode *P) {\n    ListNode *n1 = n0-&gt;next;\n    P-&gt;next = n1;\n    n0-&gt;next = P;\n}\n</code></pre> linked_list.kt<pre><code>/* 連結リストでノード n0 の後ろにノード P を挿入する */\nfun insert(n0: ListNode?, p: ListNode?) {\n    val n1 = n0?.next\n    p?.next = n1\n    n0?.next = p\n}\n</code></pre> linked_list.rb<pre><code>### 連結リストのノード n0 の後にノード _p を挿入 ###\n# Ruby の `p` は組み込み関数で、`P` は定数なので、代わりに `_p` を使える\ndef insert(n0, _p)\n  n1 = n0.next\n  _p.next = n1\n  n0.next = _p\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.2 &nbsp; 連結リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#3","level":3,"title":"3.   ノードの削除","text":"<p>下図に示すように、連結リストでのノード削除も非常に簡単で、1 つのノードの参照（ポインタ）を変更するだけで済みます。</p> <p>なお、削除操作が完了した後もノード <code>P</code> は依然として <code>n1</code> を指していますが、実際にはこの連結リストをたどっても <code>P</code> へはアクセスできません。つまり、<code>P</code> はすでにこの連結リストには属していません。</p> <p></p> <p> 図 4-7   連結リストのノード削除 </p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linked_list.py<pre><code>def remove(n0: ListNode):\n    \"\"\"連結リストでノード n0 の直後のノードを削除する\"\"\"\n    if not n0.next:\n        return\n    # n0 -&gt; P -&gt; n1\n    P = n0.next\n    n1 = P.next\n    n0.next = n1\n</code></pre> linked_list.cpp<pre><code>/* 連結リストでノード n0 の直後のノードを削除する */\nvoid remove(ListNode *n0) {\n    if (n0-&gt;next == nullptr)\n        return;\n    // n0 -&gt; P -&gt; n1\n    ListNode *P = n0-&gt;next;\n    ListNode *n1 = P-&gt;next;\n    n0-&gt;next = n1;\n    // メモリを解放する\n    delete P;\n}\n</code></pre> linked_list.java<pre><code>/* 連結リストでノード n0 の直後のノードを削除する */\nvoid remove(ListNode n0) {\n    if (n0.next == null)\n        return;\n    // n0 -&gt; P -&gt; n1\n    ListNode P = n0.next;\n    ListNode n1 = P.next;\n    n0.next = n1;\n}\n</code></pre> linked_list.cs<pre><code>/* 連結リストでノード n0 の直後のノードを削除する */\nvoid Remove(ListNode n0) {\n    if (n0.next == null)\n        return;\n    // n0 -&gt; P -&gt; n1\n    ListNode P = n0.next;\n    ListNode? n1 = P.next;\n    n0.next = n1;\n}\n</code></pre> linked_list.go<pre><code>/* 連結リストでノード n0 の直後のノードを削除する */\nfunc removeItem(n0 *ListNode) {\n    if n0.Next == nil {\n        return\n    }\n    // n0 -&gt; P -&gt; n1\n    P := n0.Next\n    n1 := P.Next\n    n0.Next = n1\n}\n</code></pre> linked_list.swift<pre><code>/* 連結リストでノード n0 の直後のノードを削除する */\nfunc remove(n0: ListNode) {\n    if n0.next == nil {\n        return\n    }\n    // n0 -&gt; P -&gt; n1\n    let P = n0.next\n    let n1 = P?.next\n    n0.next = n1\n}\n</code></pre> linked_list.js<pre><code>/* 連結リストでノード n0 の直後のノードを削除する */\nfunction remove(n0) {\n    if (!n0.next) return;\n    // n0 -&gt; P -&gt; n1\n    const P = n0.next;\n    const n1 = P.next;\n    n0.next = n1;\n}\n</code></pre> linked_list.ts<pre><code>/* 連結リストでノード n0 の直後のノードを削除する */\nfunction remove(n0: ListNode): void {\n    if (!n0.next) {\n        return;\n    }\n    // n0 -&gt; P -&gt; n1\n    const P = n0.next;\n    const n1 = P.next;\n    n0.next = n1;\n}\n</code></pre> linked_list.dart<pre><code>/* 連結リストでノード n0 の直後のノードを削除する */\nvoid remove(ListNode n0) {\n  if (n0.next == null) return;\n  // n0 -&gt; P -&gt; n1\n  ListNode P = n0.next!;\n  ListNode? n1 = P.next;\n  n0.next = n1;\n}\n</code></pre> linked_list.rs<pre><code>/* 連結リストでノード n0 の直後のノードを削除する */\n#[allow(non_snake_case)]\npub fn remove&lt;T&gt;(n0: &amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;) {\n    // n0 -&gt; P -&gt; n1\n    let P = n0.borrow_mut().next.take();\n    if let Some(node) = P {\n        let n1 = node.borrow_mut().next.take();\n        n0.borrow_mut().next = n1;\n    }\n}\n</code></pre> linked_list.c<pre><code>/* 連結リストでノード n0 の直後のノードを削除する */\n// 注意: stdio.h が remove 識別子を使用している\nvoid removeItem(ListNode *n0) {\n    if (!n0-&gt;next)\n        return;\n    // n0 -&gt; P -&gt; n1\n    ListNode *P = n0-&gt;next;\n    ListNode *n1 = P-&gt;next;\n    n0-&gt;next = n1;\n    // メモリを解放する\n    free(P);\n}\n</code></pre> linked_list.kt<pre><code>/* 連結リストでノード n0 の直後のノードを削除する */\nfun remove(n0: ListNode?) {\n    if (n0?.next == null)\n        return\n    // n0 -&gt; P -&gt; n1\n    val p = n0.next\n    val n1 = p?.next\n    n0.next = n1\n}\n</code></pre> linked_list.rb<pre><code>### 連結リストのノード n0 の直後のノードを削除 ###\ndef remove(n0)\n  return if n0.next.nil?\n\n  # n0 -&gt; remove_node -&gt; n1\n  remove_node = n0.next\n  n1 = remove_node.next\n  n0.next = n1\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.2 &nbsp; 連結リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#4","level":3,"title":"4.   ノードへのアクセス","text":"<p>**連結リストでノードにアクセスする効率は低い**です。前節で述べたように、配列では任意の要素へ \\(O(1)\\) 時間でアクセスできます。これに対して連結リストでは、プログラムは先頭ノードから出発し、1 つずつ後ろへたどって目的のノードを見つける必要があります。つまり、連結リストの第 \\(i\\) ノードにアクセスするには \\(i - 1\\) 回のループが必要であり、時間計算量は \\(O(n)\\) です。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linked_list.py<pre><code>def access(head: ListNode, index: int) -&gt; ListNode | None:\n    \"\"\"連結リスト内で index 番目のノードにアクセス\"\"\"\n    for _ in range(index):\n        if not head:\n            return None\n        head = head.next\n    return head\n</code></pre> linked_list.cpp<pre><code>/* 連結リスト内で index 番目のノードにアクセス */\nListNode *access(ListNode *head, int index) {\n    for (int i = 0; i &lt; index; i++) {\n        if (head == nullptr)\n            return nullptr;\n        head = head-&gt;next;\n    }\n    return head;\n}\n</code></pre> linked_list.java<pre><code>/* 連結リスト内で index 番目のノードにアクセス */\nListNode access(ListNode head, int index) {\n    for (int i = 0; i &lt; index; i++) {\n        if (head == null)\n            return null;\n        head = head.next;\n    }\n    return head;\n}\n</code></pre> linked_list.cs<pre><code>/* 連結リスト内で index 番目のノードにアクセス */\nListNode? Access(ListNode? head, int index) {\n    for (int i = 0; i &lt; index; i++) {\n        if (head == null)\n            return null;\n        head = head.next;\n    }\n    return head;\n}\n</code></pre> linked_list.go<pre><code>/* 連結リスト内で index 番目のノードにアクセス */\nfunc access(head *ListNode, index int) *ListNode {\n    for i := 0; i &lt; index; i++ {\n        if head == nil {\n            return nil\n        }\n        head = head.Next\n    }\n    return head\n}\n</code></pre> linked_list.swift<pre><code>/* 連結リスト内で index 番目のノードにアクセス */\nfunc access(head: ListNode, index: Int) -&gt; ListNode? {\n    var head: ListNode? = head\n    for _ in 0 ..&lt; index {\n        if head == nil {\n            return nil\n        }\n        head = head?.next\n    }\n    return head\n}\n</code></pre> linked_list.js<pre><code>/* 連結リスト内で index 番目のノードにアクセス */\nfunction access(head, index) {\n    for (let i = 0; i &lt; index; i++) {\n        if (!head) {\n            return null;\n        }\n        head = head.next;\n    }\n    return head;\n}\n</code></pre> linked_list.ts<pre><code>/* 連結リスト内で index 番目のノードにアクセス */\nfunction access(head: ListNode | null, index: number): ListNode | null {\n    for (let i = 0; i &lt; index; i++) {\n        if (!head) {\n            return null;\n        }\n        head = head.next;\n    }\n    return head;\n}\n</code></pre> linked_list.dart<pre><code>/* 連結リスト内で index 番目のノードにアクセス */\nListNode? access(ListNode? head, int index) {\n  for (var i = 0; i &lt; index; i++) {\n    if (head == null) return null;\n    head = head.next;\n  }\n  return head;\n}\n</code></pre> linked_list.rs<pre><code>/* 連結リスト内で index 番目のノードにアクセス */\npub fn access&lt;T&gt;(head: Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;, index: i32) -&gt; Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt; {\n    fn dfs&lt;T&gt;(\n        head: Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;,\n        index: i32,\n    ) -&gt; Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt; {\n        if index &lt;= 0 {\n            return head.cloned();\n        }\n\n        if let Some(node) = head {\n            dfs(node.borrow().next.as_ref(), index - 1)\n        } else {\n            None\n        }\n    }\n\n    dfs(Some(head).as_ref(), index)\n}\n</code></pre> linked_list.c<pre><code>/* 連結リスト内で index 番目のノードにアクセス */\nListNode *access(ListNode *head, int index) {\n    for (int i = 0; i &lt; index; i++) {\n        if (head == NULL)\n            return NULL;\n        head = head-&gt;next;\n    }\n    return head;\n}\n</code></pre> linked_list.kt<pre><code>/* 連結リスト内で index 番目のノードにアクセス */\nfun access(head: ListNode?, index: Int): ListNode? {\n    var h = head\n    for (i in 0..&lt;index) {\n        if (h == null)\n            return null\n        h = h.next\n    }\n    return h\n}\n</code></pre> linked_list.rb<pre><code>### 連結リスト内の index 番目のノードにアクセス ###\ndef access(head, index)\n  for i in 0...index\n    return nil if head.nil?\n    head = head.next\n  end\n\n  head\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.2 &nbsp; 連結リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#5","level":3,"title":"5.   ノードの探索","text":"<p>連結リストを走査し、その中から値が <code>target</code> のノードを探し、そのノードの連結リスト内でのインデックスを出力します。この処理も線形探索に属します。コードは次のとおりです。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linked_list.py<pre><code>def find(head: ListNode, target: int) -&gt; int:\n    \"\"\"連結リストで値が target の最初のノードを探す\"\"\"\n    index = 0\n    while head:\n        if head.val == target:\n            return index\n        head = head.next\n        index += 1\n    return -1\n</code></pre> linked_list.cpp<pre><code>/* 連結リストで値が target の最初のノードを探す */\nint find(ListNode *head, int target) {\n    int index = 0;\n    while (head != nullptr) {\n        if (head-&gt;val == target)\n            return index;\n        head = head-&gt;next;\n        index++;\n    }\n    return -1;\n}\n</code></pre> linked_list.java<pre><code>/* 連結リストで値が target の最初のノードを探す */\nint find(ListNode head, int target) {\n    int index = 0;\n    while (head != null) {\n        if (head.val == target)\n            return index;\n        head = head.next;\n        index++;\n    }\n    return -1;\n}\n</code></pre> linked_list.cs<pre><code>/* 連結リストで値が target の最初のノードを探す */\nint Find(ListNode? head, int target) {\n    int index = 0;\n    while (head != null) {\n        if (head.val == target)\n            return index;\n        head = head.next;\n        index++;\n    }\n    return -1;\n}\n</code></pre> linked_list.go<pre><code>/* 連結リストで値が target の最初のノードを探す */\nfunc findNode(head *ListNode, target int) int {\n    index := 0\n    for head != nil {\n        if head.Val == target {\n            return index\n        }\n        head = head.Next\n        index++\n    }\n    return -1\n}\n</code></pre> linked_list.swift<pre><code>/* 連結リストで値が target の最初のノードを探す */\nfunc find(head: ListNode, target: Int) -&gt; Int {\n    var head: ListNode? = head\n    var index = 0\n    while head != nil {\n        if head?.val == target {\n            return index\n        }\n        head = head?.next\n        index += 1\n    }\n    return -1\n}\n</code></pre> linked_list.js<pre><code>/* 連結リストで値が target の最初のノードを探す */\nfunction find(head, target) {\n    let index = 0;\n    while (head !== null) {\n        if (head.val === target) {\n            return index;\n        }\n        head = head.next;\n        index += 1;\n    }\n    return -1;\n}\n</code></pre> linked_list.ts<pre><code>/* 連結リストで値が target の最初のノードを探す */\nfunction find(head: ListNode | null, target: number): number {\n    let index = 0;\n    while (head !== null) {\n        if (head.val === target) {\n            return index;\n        }\n        head = head.next;\n        index += 1;\n    }\n    return -1;\n}\n</code></pre> linked_list.dart<pre><code>/* 連結リストで値が target の最初のノードを探す */\nint find(ListNode? head, int target) {\n  int index = 0;\n  while (head != null) {\n    if (head.val == target) {\n      return index;\n    }\n    head = head.next;\n    index++;\n  }\n  return -1;\n}\n</code></pre> linked_list.rs<pre><code>/* 連結リストで値が target の最初のノードを探す */\npub fn find&lt;T: PartialEq&gt;(head: Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;, target: T) -&gt; i32 {\n    fn find&lt;T: PartialEq&gt;(head: Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;, target: T, idx: i32) -&gt; i32 {\n        if let Some(node) = head {\n            if node.borrow().val == target {\n                return idx;\n            }\n            return find(node.borrow().next.as_ref(), target, idx + 1);\n        } else {\n            -1\n        }\n    }\n\n    find(Some(head).as_ref(), target, 0)\n}\n</code></pre> linked_list.c<pre><code>/* 連結リストで値が target の最初のノードを探す */\nint find(ListNode *head, int target) {\n    int index = 0;\n    while (head) {\n        if (head-&gt;val == target)\n            return index;\n        head = head-&gt;next;\n        index++;\n    }\n    return -1;\n}\n</code></pre> linked_list.kt<pre><code>/* 連結リストで値が target の最初のノードを探す */\nfun find(head: ListNode?, target: Int): Int {\n    var index = 0\n    var h = head\n    while (h != null) {\n        if (h._val == target)\n            return index\n        h = h.next\n        index++\n    }\n    return -1\n}\n</code></pre> linked_list.rb<pre><code>### 連結リストで値が target の最初のノードを探す ###\ndef find(head, target)\n  index = 0\n  while head\n    return index if head.val == target\n    head = head.next\n    index += 1\n  end\n\n  -1\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.2 &nbsp; 連結リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#422-vs","level":2,"title":"4.2.2   配列 vs. 連結リスト","text":"<p>次の表は、配列と連結リストの各種特徴と操作効率をまとめたものです。両者は互いに逆の格納戦略を採用しているため、各種性質や操作効率にも対照的な特徴が現れます。</p> <p> 表 4-1   配列と連結リストの効率比較 </p> 配列 連結リスト 格納方式 連続したメモリ空間 分散したメモリ空間 容量拡張 長さは不変 柔軟に拡張可能 メモリ効率 要素のメモリ消費は少ないが、空間を無駄にする可能性がある 要素のメモリ消費が多い 要素へのアクセス \\(O(1)\\) \\(O(n)\\) 要素の追加 \\(O(n)\\) \\(O(1)\\) 要素の削除 \\(O(n)\\) \\(O(1)\\)","path":["第 4 章 &nbsp; 配列と連結リスト","4.2 &nbsp; 連結リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#423","level":2,"title":"4.2.3   一般的な連結リストの種類","text":"<p>下図に示すように、一般的な連結リストの種類は 3 つあります。</p> <ul> <li>単方向連結リスト：前述した通常の連結リストのことです。単方向連結リストのノードは、値と次のノードを指す参照の 2 つのデータを含みます。最初のノードを先頭ノード、最後のノードを末尾ノードと呼び、末尾ノードは空 <code>None</code> を指します。</li> <li>循環連結リスト：単方向連結リストの末尾ノードを先頭ノードへ向けると（先頭と末尾をつなぐと）、循環連結リストが得られます。循環連結リストでは、任意のノードを先頭ノードとみなせます。</li> <li>双方向連結リスト：単方向連結リストと比べて、双方向連結リストは 2 方向の参照を記録します。双方向連結リストのノード定義には、後続ノード（次のノード）と前駆ノード（前のノード）を指す参照（ポインタ）が含まれます。単方向連結リストより柔軟で、2 方向に連結リストを走査できますが、そのぶん多くのメモリ空間を必要とします。</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>class ListNode:\n    \"\"\"双方向連結リストノードクラス\"\"\"\n    def __init__(self, val: int):\n        self.val: int = val                # ノードの値\n        self.next: ListNode | None = None  # 後続ノードへの参照\n        self.prev: ListNode | None = None  # 前駆ノードへの参照\n</code></pre> <pre><code>/* 双方向連結リストノード構造体 */\nstruct ListNode {\n    int val;         // ノードの値\n    ListNode *next;  // 後続ノードへのポインタ\n    ListNode *prev;  // 前駆ノードへのポインタ\n    ListNode(int x) : val(x), next(nullptr), prev(nullptr) {}  // コンストラクタ\n};\n</code></pre> <pre><code>/* 双方向連結リストノードクラス */\nclass ListNode {\n    int val;        // ノードの値\n    ListNode next;  // 後続ノードへの参照\n    ListNode prev;  // 前駆ノードへの参照\n    ListNode(int x) { val = x; }  // コンストラクタ\n}\n</code></pre> <pre><code>/* 双方向連結リストノードクラス */\nclass ListNode(int x) {  // コンストラクタ\n    int val = x;    // ノードの値\n    ListNode next;  // 後続ノードへの参照\n    ListNode prev;  // 前駆ノードへの参照\n}\n</code></pre> <pre><code>/* 双方向連結リストノード構造体 */\ntype DoublyListNode struct {\n    Val  int             // ノードの値\n    Next *DoublyListNode // 後続ノードへのポインタ\n    Prev *DoublyListNode // 前駆ノードへのポインタ\n}\n\n// NewDoublyListNode の初期化\nfunc NewDoublyListNode(val int) *DoublyListNode {\n    return &amp;DoublyListNode{\n        Val:  val,\n        Next: nil,\n        Prev: nil,\n    }\n}\n</code></pre> <pre><code>/* 双方向連結リストノードクラス */\nclass ListNode {\n    var val: Int // ノードの値\n    var next: ListNode? // 後続ノードへの参照\n    var prev: ListNode? // 前駆ノードへの参照\n\n    init(x: Int) { // コンストラクタ\n        val = x\n    }\n}\n</code></pre> <pre><code>/* 双方向連結リストノードクラス */\nclass ListNode {\n    constructor(val, next, prev) {\n        this.val = val  ===  undefined ? 0 : val;        // ノードの値\n        this.next = next  ===  undefined ? null : next;  // 後続ノードへの参照\n        this.prev = prev  ===  undefined ? null : prev;  // 前駆ノードへの参照\n    }\n}\n</code></pre> <pre><code>/* 双方向連結リストノードクラス */\nclass ListNode {\n    val: number;\n    next: ListNode | null;\n    prev: ListNode | null;\n    constructor(val?: number, next?: ListNode | null, prev?: ListNode | null) {\n        this.val = val  ===  undefined ? 0 : val;        // ノードの値\n        this.next = next  ===  undefined ? null : next;  // 後続ノードへの参照\n        this.prev = prev  ===  undefined ? null : prev;  // 前駆ノードへの参照\n    }\n}\n</code></pre> <pre><code>/* 双方向連結リストノードクラス */\nclass ListNode {\n    int val;        // ノードの値\n    ListNode? next;  // 後続ノードへの参照\n    ListNode? prev;  // 前駆ノードへの参照\n    ListNode(this.val, [this.next, this.prev]);  // コンストラクタ\n}\n</code></pre> <pre><code>use std::rc::Rc;\nuse std::cell::RefCell;\n\n/* 双方向連結リストノード型 */\n#[derive(Debug)]\nstruct ListNode {\n    val: i32, // ノードの値\n    next: Option&lt;Rc&lt;RefCell&lt;ListNode&gt;&gt;&gt;, // 後続ノードへのポインタ\n    prev: Option&lt;Rc&lt;RefCell&lt;ListNode&gt;&gt;&gt;, // 前駆ノードへのポインタ\n}\n\n/* コンストラクタ */\nimpl ListNode {\n    fn new(val: i32) -&gt; Self {\n        ListNode {\n            val,\n            next: None,\n            prev: None,\n        }\n    }\n}\n</code></pre> <pre><code>/* 双方向連結リストノード構造体 */\ntypedef struct ListNode {\n    int val;               // ノードの値\n    struct ListNode *next; // 後続ノードへのポインタ\n    struct ListNode *prev; // 前駆ノードへのポインタ\n} ListNode;\n\n/* コンストラクタ */\nListNode *newListNode(int val) {\n    ListNode *node;\n    node = (ListNode *) malloc(sizeof(ListNode));\n    node-&gt;val = val;\n    node-&gt;next = NULL;\n    node-&gt;prev = NULL;\n    return node;\n}\n</code></pre> <pre><code>/* 双方向連結リストノードクラス */\n// コンストラクタ\nclass ListNode(x: Int) {\n    val _val: Int = x           // ノードの値\n    val next: ListNode? = null  // 後続ノードへの参照\n    val prev: ListNode? = null  // 前駆ノードへの参照\n}\n</code></pre> <pre><code># 双方向連結リストノードクラス\nclass ListNode\n  attr_accessor :val    # ノードの値\n  attr_accessor :next   # 後続ノードへの参照\n  attr_accessor :prev   # 前駆ノードへの参照\n\n  def initialize(val=0, next_node=nil, prev_node=nil)\n    @val = val\n    @next = next_node\n    @prev = prev_node\n  end\nend\n</code></pre> <p></p> <p> 図 4-8   一般的な連結リストの種類 </p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.2 &nbsp; 連結リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#424","level":2,"title":"4.2.4   連結リストの典型的な応用","text":"<p>単方向連結リストは、スタック、キュー、ハッシュテーブル、グラフなどのデータ構造の実装によく用いられます。</p> <ul> <li>スタックとキュー：挿入と削除の両方の操作を連結リストの一端で行うと、その性質は後入れ先出しとなり、スタックに対応します。挿入を連結リストの一端で行い、削除をもう一端で行うと、その性質は先入れ先出しとなり、キューに対応します。</li> <li>ハッシュテーブル：連鎖アドレス法はハッシュ衝突を解決する主流の方式の 1 つであり、この方式では、衝突したすべての要素が 1 つの連結リストに格納されます。</li> <li>グラフ：隣接リストはグラフを表現する一般的な方法の 1 つであり、グラフの各頂点は 1 つの連結リストに関連付けられます。連結リスト内の各要素は、その頂点に接続されたほかの頂点を表します。</li> </ul> <p>双方向連結リストは、前後の要素をすばやく見つける必要がある場面でよく用いられます。</p> <ul> <li>高度なデータ構造：たとえば赤黒木や B 木では、ノードの親ノードへアクセスする必要があります。これは、ノード内に親ノードを指す参照を保持することで実現でき、双方向連結リストに似ています。</li> <li>ブラウザ履歴：Web ブラウザでユーザーが進むボタンや戻るボタンをクリックしたとき、ブラウザはユーザーが訪れた前後のページを知る必要があります。双方向連結リストの性質によって、この操作は簡単になります。</li> <li>LRU アルゴリズム：キャッシュ淘汰（LRU）アルゴリズムでは、最近最も使用されていないデータをすばやく見つける必要があり、さらにノードの高速な追加と削除も必要です。そのため、双方向連結リストが非常に適しています。</li> </ul> <p>循環連結リストは、オペレーティングシステムのリソーススケジューリングのように、周期的な操作が必要な場面でよく用いられます。</p> <ul> <li>ラウンドロビン時間片スケジューリングアルゴリズム：オペレーティングシステムにおいて、ラウンドロビン時間片スケジューリングは一般的な CPU スケジューリングアルゴリズムであり、一連のプロセスを循環的に処理する必要があります。各プロセスには 1 つの時間片が割り当てられ、その時間片を使い切ると、CPU は次のプロセスへ切り替わります。この循環操作は、循環連結リストで実現できます。</li> <li>データバッファ：一部のデータバッファ実装でも、循環連結リストが使われることがあります。たとえば音声・動画プレーヤーでは、データストリームを複数のバッファブロックに分割して循環連結リストへ格納し、シームレス再生を実現できます。</li> </ul>","path":["第 4 章 &nbsp; 配列と連結リスト","4.2 &nbsp; 連結リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/","level":1,"title":"4.3   リスト","text":"<p>リスト（list）は抽象的なデータ構造の概念であり、要素の順序付き集合を表す。要素のアクセス、更新、追加、削除、走査などの操作をサポートし、利用者は容量制限の問題を考慮する必要がない。リストは連結リストまたは配列に基づいて実装できる。</p> <ul> <li>連結リストは本質的にリストと見なすことができ、要素の追加・削除・参照・更新をサポートし、柔軟に動的拡張できる。</li> <li>配列も要素の追加・削除・参照・更新をサポートするが、長さが不変であるため、長さ制限のあるリストとしか見なせない。</li> </ul> <p>配列でリストを実装する場合、長さが不変である性質によってリストの実用性が低下する。これは、通常は事前にどれだけのデータを格納する必要があるかを決められず、適切なリスト長を選びにくいためである。長さが小さすぎると利用要件を満たせない可能性が高く、大きすぎるとメモリ空間の浪費を招く。</p> <p>この問題を解決するために、動的配列（dynamic array）を用いてリストを実装できる。これは配列の各種利点を引き継ぎつつ、プログラム実行中に動的な拡張を行える。</p> <p>実際には、多くのプログラミング言語の標準ライブラリが提供するリストは動的配列に基づいて実装されている。たとえば、Python の <code>list</code> 、Java の <code>ArrayList</code> 、C++ の <code>vector</code> 、C# の <code>List</code> などである。以降の議論では、「リスト」と「動的配列」を同じ概念として扱う。</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.3 &nbsp; リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#431","level":2,"title":"4.3.1   リストの基本操作","text":"","path":["第 4 章 &nbsp; 配列と連結リスト","4.3 &nbsp; リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#1","level":3,"title":"1.   リストの初期化","text":"<p>通常は「初期値なし」と「初期値あり」の 2 つの初期化方法を用いる。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby list.py<pre><code># リストを初期化\n# 初期値なし\nnums1: list[int] = []\n# 初期値あり\nnums: list[int] = [1, 3, 2, 5, 4]\n</code></pre> list.cpp<pre><code>/* リストを初期化 */\n// なお、C++ では vector が本稿でいう nums に相当する\n// 初期値なし\nvector&lt;int&gt; nums1;\n// 初期値あり\nvector&lt;int&gt; nums = { 1, 3, 2, 5, 4 };\n</code></pre> list.java<pre><code>/* リストを初期化 */\n// 初期値なし\nList&lt;Integer&gt; nums1 = new ArrayList&lt;&gt;();\n// 初期値あり（配列の要素型は int[] のラッパークラスである Integer[] である必要があることに注意）\nInteger[] numbers = new Integer[] { 1, 3, 2, 5, 4 };\nList&lt;Integer&gt; nums = new ArrayList&lt;&gt;(Arrays.asList(numbers));\n</code></pre> list.cs<pre><code>/* リストを初期化 */\n// 初期値なし\nList&lt;int&gt; nums1 = [];\n// 初期値あり\nint[] numbers = [1, 3, 2, 5, 4];\nList&lt;int&gt; nums = [.. numbers];\n</code></pre> list_test.go<pre><code>/* リストを初期化 */\n// 初期値なし\nnums1 := []int{}\n// 初期値あり\nnums := []int{1, 3, 2, 5, 4}\n</code></pre> list.swift<pre><code>/* リストを初期化 */\n// 初期値なし\nlet nums1: [Int] = []\n// 初期値あり\nvar nums = [1, 3, 2, 5, 4]\n</code></pre> list.js<pre><code>/* リストを初期化 */\n// 初期値なし\nconst nums1 = [];\n// 初期値あり\nconst nums = [1, 3, 2, 5, 4];\n</code></pre> list.ts<pre><code>/* リストを初期化 */\n// 初期値なし\nconst nums1: number[] = [];\n// 初期値あり\nconst nums: number[] = [1, 3, 2, 5, 4];\n</code></pre> list.dart<pre><code>/* リストを初期化 */\n// 初期値なし\nList&lt;int&gt; nums1 = [];\n// 初期値あり\nList&lt;int&gt; nums = [1, 3, 2, 5, 4];\n</code></pre> list.rs<pre><code>/* リストを初期化 */\n// 初期値なし\nlet nums1: Vec&lt;i32&gt; = Vec::new();\n// 初期値あり\nlet nums: Vec&lt;i32&gt; = vec![1, 3, 2, 5, 4];\n</code></pre> list.c<pre><code>// C には組み込みの動的配列がない\n</code></pre> list.kt<pre><code>/* リストを初期化 */\n// 初期値なし\nvar nums1 = listOf&lt;Int&gt;()\n// 初期値あり\nvar numbers = arrayOf(1, 3, 2, 5, 4)\nvar nums = numbers.toMutableList()\n</code></pre> list.rb<pre><code># リストを初期化\n# 初期値なし\nnums1 = []\n# 初期値あり\nnums = [1, 3, 2, 5, 4]\n</code></pre> 可視化実行 <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%88%97%E8%A1%A8%0A%20%20%20%20%23%20%E6%97%A0%E5%88%9D%E5%A7%8B%E5%80%BC%0A%20%20%20%20nums1%20%3D%20%5B%5D%0A%20%20%20%20%23%20%E6%9C%89%E5%88%9D%E5%A7%8B%E5%80%BC%0A%20%20%20%20nums%20%3D%20%5B1,%203,%202,%205,%204%5D&amp;cumulative=false&amp;curInstr=4&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.3 &nbsp; リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#2","level":3,"title":"2.   要素へのアクセス","text":"<p>リストの本質は配列であるため、要素へのアクセスと更新は \\(O(1)\\) 時間で行え、効率が高い。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby list.py<pre><code># 要素にアクセス\nnum: int = nums[1]  # インデックス 1 の要素にアクセス\n\n# 要素を更新\nnums[1] = 0    # インデックス 1 の要素を 0 に更新\n</code></pre> list.cpp<pre><code>/* 要素にアクセス */\nint num = nums[1];  // インデックス 1 の要素にアクセス\n\n/* 要素を更新 */\nnums[1] = 0;  // インデックス 1 の要素を 0 に更新\n</code></pre> list.java<pre><code>/* 要素にアクセス */\nint num = nums.get(1);  // インデックス 1 の要素にアクセス\n\n/* 要素を更新 */\nnums.set(1, 0);  // インデックス 1 の要素を 0 に更新\n</code></pre> list.cs<pre><code>/* 要素にアクセス */\nint num = nums[1];  // インデックス 1 の要素にアクセス\n\n/* 要素を更新 */\nnums[1] = 0;  // インデックス 1 の要素を 0 に更新\n</code></pre> list_test.go<pre><code>/* 要素にアクセス */\nnum := nums[1]  // インデックス 1 の要素にアクセス\n\n/* 要素を更新 */\nnums[1] = 0     // インデックス 1 の要素を 0 に更新\n</code></pre> list.swift<pre><code>/* 要素にアクセス */\nlet num = nums[1] // インデックス 1 の要素にアクセス\n\n/* 要素を更新 */\nnums[1] = 0 // インデックス 1 の要素を 0 に更新\n</code></pre> list.js<pre><code>/* 要素にアクセス */\nconst num = nums[1];  // インデックス 1 の要素にアクセス\n\n/* 要素を更新 */\nnums[1] = 0;  // インデックス 1 の要素を 0 に更新\n</code></pre> list.ts<pre><code>/* 要素にアクセス */\nconst num: number = nums[1];  // インデックス 1 の要素にアクセス\n\n/* 要素を更新 */\nnums[1] = 0;  // インデックス 1 の要素を 0 に更新\n</code></pre> list.dart<pre><code>/* 要素にアクセス */\nint num = nums[1];  // インデックス 1 の要素にアクセス\n\n/* 要素を更新 */\nnums[1] = 0;  // インデックス 1 の要素を 0 に更新\n</code></pre> list.rs<pre><code>/* 要素にアクセス */\nlet num: i32 = nums[1];  // インデックス 1 の要素にアクセス\n/* 要素を更新 */\nnums[1] = 0;             // インデックス 1 の要素を 0 に更新\n</code></pre> list.c<pre><code>// C には組み込みの動的配列がない\n</code></pre> list.kt<pre><code>/* 要素にアクセス */\nval num = nums[1]       // インデックス 1 の要素にアクセス\n/* 要素を更新 */\nnums[1] = 0             // インデックス 1 の要素を 0 に更新\n</code></pre> list.rb<pre><code># 要素にアクセス\nnum = nums[1] # インデックス 1 の要素にアクセス\n# 要素を更新\nnums[1] = 0 # インデックス 1 の要素を 0 に更新\n</code></pre> 可視化実行 <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%88%97%E8%A1%A8%0A%20%20%20%20nums%20%3D%20%5B1,%203,%202,%205,%204%5D%0A%0A%20%20%20%20%23%20%E8%AE%BF%E9%97%AE%E5%85%83%E7%B4%A0%0A%20%20%20%20num%20%3D%20nums%5B1%5D%20%20%23%20%E8%AE%BF%E9%97%AE%E7%B4%A2%E5%BC%95%201%20%E5%A4%84%E7%9A%84%E5%85%83%E7%B4%A0%0A%0A%20%20%20%20%23%20%E6%9B%B4%E6%96%B0%E5%85%83%E7%B4%A0%0A%20%20%20%20nums%5B1%5D%20%3D%200%20%20%20%20%23%20%E5%B0%86%E7%B4%A2%E5%BC%95%201%20%E5%A4%84%E7%9A%84%E5%85%83%E7%B4%A0%E6%9B%B4%E6%96%B0%E4%B8%BA%200&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.3 &nbsp; リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#3","level":3,"title":"3.   要素の挿入と削除","text":"<p>配列と比べて、リストでは要素を自由に追加・削除できる。リスト末尾への要素追加の時間計算量は \\(O(1)\\) だが、要素の挿入と削除の効率は依然として配列と同じで、時間計算量は \\(O(n)\\) である。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby list.py<pre><code># リストをクリア\nnums.clear()\n\n# 末尾に要素を追加\nnums.append(1)\nnums.append(3)\nnums.append(2)\nnums.append(5)\nnums.append(4)\n\n# 途中に要素を挿入\nnums.insert(3, 6)  # インデックス 3 に数値 6 を挿入\n\n# 要素を削除\nnums.pop(3)        # インデックス 3 の要素を削除\n</code></pre> list.cpp<pre><code>/* リストをクリア */\nnums.clear();\n\n/* 末尾に要素を追加 */\nnums.push_back(1);\nnums.push_back(3);\nnums.push_back(2);\nnums.push_back(5);\nnums.push_back(4);\n\n/* 途中に要素を挿入 */\nnums.insert(nums.begin() + 3, 6);  // インデックス 3 に数値 6 を挿入\n\n/* 要素を削除 */\nnums.erase(nums.begin() + 3);      // インデックス 3 の要素を削除\n</code></pre> list.java<pre><code>/* リストをクリア */\nnums.clear();\n\n/* 末尾に要素を追加 */\nnums.add(1);\nnums.add(3);\nnums.add(2);\nnums.add(5);\nnums.add(4);\n\n/* 途中に要素を挿入 */\nnums.add(3, 6);  // インデックス 3 に数値 6 を挿入\n\n/* 要素を削除 */\nnums.remove(3);  // インデックス 3 の要素を削除\n</code></pre> list.cs<pre><code>/* リストをクリア */\nnums.Clear();\n\n/* 末尾に要素を追加 */\nnums.Add(1);\nnums.Add(3);\nnums.Add(2);\nnums.Add(5);\nnums.Add(4);\n\n/* 途中に要素を挿入 */\nnums.Insert(3, 6);  // インデックス 3 に数値 6 を挿入\n\n/* 要素を削除 */\nnums.RemoveAt(3);  // インデックス 3 の要素を削除\n</code></pre> list_test.go<pre><code>/* リストをクリア */\nnums = nil\n\n/* 末尾に要素を追加 */\nnums = append(nums, 1)\nnums = append(nums, 3)\nnums = append(nums, 2)\nnums = append(nums, 5)\nnums = append(nums, 4)\n\n/* 途中に要素を挿入 */\nnums = append(nums[:3], append([]int{6}, nums[3:]...)...) // インデックス 3 に数値 6 を挿入\n\n/* 要素を削除 */\nnums = append(nums[:3], nums[4:]...) // インデックス 3 の要素を削除\n</code></pre> list.swift<pre><code>/* リストをクリア */\nnums.removeAll()\n\n/* 末尾に要素を追加 */\nnums.append(1)\nnums.append(3)\nnums.append(2)\nnums.append(5)\nnums.append(4)\n\n/* 途中に要素を挿入 */\nnums.insert(6, at: 3) // インデックス 3 に数値 6 を挿入\n\n/* 要素を削除 */\nnums.remove(at: 3) // インデックス 3 の要素を削除\n</code></pre> list.js<pre><code>/* リストをクリア */\nnums.length = 0;\n\n/* 末尾に要素を追加 */\nnums.push(1);\nnums.push(3);\nnums.push(2);\nnums.push(5);\nnums.push(4);\n\n/* 途中に要素を挿入 */\nnums.splice(3, 0, 6); // インデックス 3 に数値 6 を挿入\n\n/* 要素を削除 */\nnums.splice(3, 1);  // インデックス 3 の要素を削除\n</code></pre> list.ts<pre><code>/* リストをクリア */\nnums.length = 0;\n\n/* 末尾に要素を追加 */\nnums.push(1);\nnums.push(3);\nnums.push(2);\nnums.push(5);\nnums.push(4);\n\n/* 途中に要素を挿入 */\nnums.splice(3, 0, 6); // インデックス 3 に数値 6 を挿入\n\n/* 要素を削除 */\nnums.splice(3, 1);  // インデックス 3 の要素を削除\n</code></pre> list.dart<pre><code>/* リストをクリア */\nnums.clear();\n\n/* 末尾に要素を追加 */\nnums.add(1);\nnums.add(3);\nnums.add(2);\nnums.add(5);\nnums.add(4);\n\n/* 途中に要素を挿入 */\nnums.insert(3, 6); // インデックス 3 に数値 6 を挿入\n\n/* 要素を削除 */\nnums.removeAt(3); // インデックス 3 の要素を削除\n</code></pre> list.rs<pre><code>/* リストをクリア */\nnums.clear();\n\n/* 末尾に要素を追加 */\nnums.push(1);\nnums.push(3);\nnums.push(2);\nnums.push(5);\nnums.push(4);\n\n/* 途中に要素を挿入 */\nnums.insert(3, 6);  // インデックス 3 に数値 6 を挿入\n\n/* 要素を削除 */\nnums.remove(3);    // インデックス 3 の要素を削除\n</code></pre> list.c<pre><code>// C には組み込みの動的配列がない\n</code></pre> list.kt<pre><code>/* リストをクリア */\nnums.clear();\n\n/* 末尾に要素を追加 */\nnums.add(1);\nnums.add(3);\nnums.add(2);\nnums.add(5);\nnums.add(4);\n\n/* 途中に要素を挿入 */\nnums.add(3, 6);  // インデックス 3 に数値 6 を挿入\n\n/* 要素を削除 */\nnums.remove(3);  // インデックス 3 の要素を削除\n</code></pre> list.rb<pre><code># リストをクリア\nnums.clear\n\n# 末尾に要素を追加\nnums &lt;&lt; 1\nnums &lt;&lt; 3\nnums &lt;&lt; 2\nnums &lt;&lt; 5\nnums &lt;&lt; 4\n\n# 途中に要素を挿入\nnums.insert(3, 6) # インデックス 3 に数値 6 を挿入\n\n# 要素を削除\nnums.delete_at(3) # インデックス 3 の要素を削除\n</code></pre> 可視化実行 <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E6%9C%89%E5%88%9D%E5%A7%8B%E5%80%BC%0A%20%20%20%20nums%20%3D%20%5B1,%203,%202,%205,%204%5D%0A%20%20%20%20%0A%20%20%20%20%23%20%E6%B8%85%E7%A9%BA%E5%88%97%E8%A1%A8%0A%20%20%20%20nums.clear%28%29%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%9C%A8%E5%B0%BE%E9%83%A8%E6%B7%BB%E5%8A%A0%E5%85%83%E7%B4%A0%0A%20%20%20%20nums.append%281%29%0A%20%20%20%20nums.append%283%29%0A%20%20%20%20nums.append%282%29%0A%20%20%20%20nums.append%285%29%0A%20%20%20%20nums.append%284%29%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%9C%A8%E4%B8%AD%E9%97%B4%E6%8F%92%E5%85%A5%E5%85%83%E7%B4%A0%0A%20%20%20%20nums.insert%283,%206%29%20%20%23%20%E5%9C%A8%E7%B4%A2%E5%BC%95%203%20%E5%A4%84%E6%8F%92%E5%85%A5%E6%95%B0%E5%AD%97%206%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%88%A0%E9%99%A4%E5%85%83%E7%B4%A0%0A%20%20%20%20nums.pop%283%29%20%20%20%20%20%20%20%20%23%20%E5%88%A0%E9%99%A4%E7%B4%A2%E5%BC%95%203%20%E5%A4%84%E7%9A%84%E5%85%83%E7%B4%A0&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.3 &nbsp; リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#4","level":3,"title":"4.   リストの走査","text":"<p>配列と同様に、リストもインデックスに基づいて走査することも、各要素を直接走査することもできる。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby list.py<pre><code># インデックスでリストを走査\ncount = 0\nfor i in range(len(nums)):\n    count += nums[i]\n\n# リストの要素を直接走査\nfor num in nums:\n    count += num\n</code></pre> list.cpp<pre><code>/* インデックスでリストを走査 */\nint count = 0;\nfor (int i = 0; i &lt; nums.size(); i++) {\n    count += nums[i];\n}\n\n/* リストの要素を直接走査 */\ncount = 0;\nfor (int num : nums) {\n    count += num;\n}\n</code></pre> list.java<pre><code>/* インデックスでリストを走査 */\nint count = 0;\nfor (int i = 0; i &lt; nums.size(); i++) {\n    count += nums.get(i);\n}\n\n/* リストの要素を直接走査 */\nfor (int num : nums) {\n    count += num;\n}\n</code></pre> list.cs<pre><code>/* インデックスでリストを走査 */\nint count = 0;\nfor (int i = 0; i &lt; nums.Count; i++) {\n    count += nums[i];\n}\n\n/* リストの要素を直接走査 */\ncount = 0;\nforeach (int num in nums) {\n    count += num;\n}\n</code></pre> list_test.go<pre><code>/* インデックスでリストを走査 */\ncount := 0\nfor i := 0; i &lt; len(nums); i++ {\n    count += nums[i]\n}\n\n/* リストの要素を直接走査 */\ncount = 0\nfor _, num := range nums {\n    count += num\n}\n</code></pre> list.swift<pre><code>/* インデックスでリストを走査 */\nvar count = 0\nfor i in nums.indices {\n    count += nums[i]\n}\n\n/* リストの要素を直接走査 */\ncount = 0\nfor num in nums {\n    count += num\n}\n</code></pre> list.js<pre><code>/* インデックスでリストを走査 */\nlet count = 0;\nfor (let i = 0; i &lt; nums.length; i++) {\n    count += nums[i];\n}\n\n/* リストの要素を直接走査 */\ncount = 0;\nfor (const num of nums) {\n    count += num;\n}\n</code></pre> list.ts<pre><code>/* インデックスでリストを走査 */\nlet count = 0;\nfor (let i = 0; i &lt; nums.length; i++) {\n    count += nums[i];\n}\n\n/* リストの要素を直接走査 */\ncount = 0;\nfor (const num of nums) {\n    count += num;\n}\n</code></pre> list.dart<pre><code>/* インデックスでリストを走査 */\nint count = 0;\nfor (var i = 0; i &lt; nums.length; i++) {\n    count += nums[i];\n}\n\n/* リストの要素を直接走査 */\ncount = 0;\nfor (var num in nums) {\n    count += num;\n}\n</code></pre> list.rs<pre><code>// インデックスでリストを走査\nlet mut _count = 0;\nfor i in 0..nums.len() {\n    _count += nums[i];\n}\n\n// リストの要素を直接走査\n_count = 0;\nfor num in &amp;nums {\n    _count += num;\n}\n</code></pre> list.c<pre><code>// C には組み込みの動的配列がない\n</code></pre> list.kt<pre><code>/* インデックスでリストを走査 */\nvar count = 0\nfor (i in nums.indices) {\n    count += nums[i]\n}\n\n/* リストの要素を直接走査 */\nfor (num in nums) {\n    count += num\n}\n</code></pre> list.rb<pre><code># インデックスでリストを走査\ncount = 0\nfor i in 0...nums.length\n    count += nums[i]\nend\n\n# リストの要素を直接走査\ncount = 0\nfor num in nums\n    count += num\nend\n</code></pre> 可視化実行 <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%88%97%E8%A1%A8%0A%20%20%20%20nums%20%3D%20%5B1,%203,%202,%205,%204%5D%0A%20%20%20%20%0A%20%20%20%20%23%20%E9%80%9A%E8%BF%87%E7%B4%A2%E5%BC%95%E9%81%8D%E5%8E%86%E5%88%97%E8%A1%A8%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20for%20i%20in%20range%28len%28nums%29%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%20nums%5Bi%5D%0A%0A%20%20%20%20%23%20%E7%9B%B4%E6%8E%A5%E9%81%8D%E5%8E%86%E5%88%97%E8%A1%A8%E5%85%83%E7%B4%A0%0A%20%20%20%20for%20num%20in%20nums%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%20num&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.3 &nbsp; リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#5","level":3,"title":"5.   リストの連結","text":"<p>新しいリスト <code>nums1</code> が与えられたとき、それを元のリストの末尾に連結できる。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby list.py<pre><code># 2 つのリストを連結\nnums1: list[int] = [6, 8, 7, 10, 9]\nnums += nums1  # リスト nums1 を nums の後ろに連結\n</code></pre> list.cpp<pre><code>/* 2 つのリストを連結 */\nvector&lt;int&gt; nums1 = { 6, 8, 7, 10, 9 };\n// リスト nums1 を nums の後ろに連結\nnums.insert(nums.end(), nums1.begin(), nums1.end());\n</code></pre> list.java<pre><code>/* 2 つのリストを連結 */\nList&lt;Integer&gt; nums1 = new ArrayList&lt;&gt;(Arrays.asList(new Integer[] { 6, 8, 7, 10, 9 }));\nnums.addAll(nums1);  // リスト nums1 を nums の後ろに連結\n</code></pre> list.cs<pre><code>/* 2 つのリストを連結 */\nList&lt;int&gt; nums1 = [6, 8, 7, 10, 9];\nnums.AddRange(nums1);  // リスト nums1 を nums の後ろに連結\n</code></pre> list_test.go<pre><code>/* 2 つのリストを連結 */\nnums1 := []int{6, 8, 7, 10, 9}\nnums = append(nums, nums1...)  // リスト nums1 を nums の後ろに連結\n</code></pre> list.swift<pre><code>/* 2 つのリストを連結 */\nlet nums1 = [6, 8, 7, 10, 9]\nnums.append(contentsOf: nums1) // リスト nums1 を nums の後ろに連結\n</code></pre> list.js<pre><code>/* 2 つのリストを連結 */\nconst nums1 = [6, 8, 7, 10, 9];\nnums.push(...nums1);  // リスト nums1 を nums の後ろに連結\n</code></pre> list.ts<pre><code>/* 2 つのリストを連結 */\nconst nums1: number[] = [6, 8, 7, 10, 9];\nnums.push(...nums1);  // リスト nums1 を nums の後ろに連結\n</code></pre> list.dart<pre><code>/* 2 つのリストを連結 */\nList&lt;int&gt; nums1 = [6, 8, 7, 10, 9];\nnums.addAll(nums1);  // リスト nums1 を nums の後ろに連結\n</code></pre> list.rs<pre><code>/* 2 つのリストを連結 */\nlet nums1: Vec&lt;i32&gt; = vec![6, 8, 7, 10, 9];\nnums.extend(nums1);\n</code></pre> list.c<pre><code>// C には組み込みの動的配列がない\n</code></pre> list.kt<pre><code>/* 2 つのリストを連結 */\nval nums1 = intArrayOf(6, 8, 7, 10, 9).toMutableList()\nnums.addAll(nums1)  // リスト nums1 を nums の後ろに連結\n</code></pre> list.rb<pre><code># 2 つのリストを連結\nnums1 = [6, 8, 7, 10, 9]\nnums += nums1\n</code></pre> 可視化実行 <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%88%97%E8%A1%A8%0A%20%20%20%20nums%20%3D%20%5B1,%203,%202,%205,%204%5D%0A%20%20%20%20%0A%20%20%20%20%23%20%E6%8B%BC%E6%8E%A5%E4%B8%A4%E4%B8%AA%E5%88%97%E8%A1%A8%0A%20%20%20%20nums1%20%3D%20%5B6,%208,%207,%2010,%209%5D%0A%20%20%20%20nums%20%2B%3D%20nums1%20%20%23%20%E5%B0%86%E5%88%97%E8%A1%A8%20nums1%20%E6%8B%BC%E6%8E%A5%E5%88%B0%20nums%20%E4%B9%8B%E5%90%8E&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.3 &nbsp; リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#6","level":3,"title":"6.   リストをソート","text":"<p>リストのソートが完了すると、配列系アルゴリズム問題でよく問われる「二分探索」や「両ポインタ」アルゴリズムを使えるようになる。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby list.py<pre><code># リストをソート\nnums.sort()  # ソート後、リスト要素は小さい順に並ぶ\n</code></pre> list.cpp<pre><code>/* リストをソート */\nsort(nums.begin(), nums.end());  // ソート後、リスト要素は小さい順に並ぶ\n</code></pre> list.java<pre><code>/* リストをソート */\nCollections.sort(nums);  // ソート後、リスト要素は小さい順に並ぶ\n</code></pre> list.cs<pre><code>/* リストをソート */\nnums.Sort(); // ソート後、リスト要素は小さい順に並ぶ\n</code></pre> list_test.go<pre><code>/* リストをソート */\nsort.Ints(nums)  // ソート後、リスト要素は小さい順に並ぶ\n</code></pre> list.swift<pre><code>/* リストをソート */\nnums.sort() // ソート後、リスト要素は小さい順に並ぶ\n</code></pre> list.js<pre><code>/* リストをソート */\nnums.sort((a, b) =&gt; a - b);  // ソート後、リスト要素は小さい順に並ぶ\n</code></pre> list.ts<pre><code>/* リストをソート */\nnums.sort((a, b) =&gt; a - b);  // ソート後、リスト要素は小さい順に並ぶ\n</code></pre> list.dart<pre><code>/* リストをソート */\nnums.sort(); // ソート後、リスト要素は小さい順に並ぶ\n</code></pre> list.rs<pre><code>/* リストをソート */\nnums.sort(); // ソート後、リスト要素は小さい順に並ぶ\n</code></pre> list.c<pre><code>// C には組み込みの動的配列がない\n</code></pre> list.kt<pre><code>/* リストをソート */\nnums.sort() // ソート後、リスト要素は小さい順に並ぶ\n</code></pre> list.rb<pre><code># リストをソート\nnums = nums.sort { |a, b| a &lt;=&gt; b } # ソート後、リスト要素は小さい順に並ぶ\n</code></pre> 可視化実行 <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%88%97%E8%A1%A8%0A%20%20%20%20nums%20%3D%20%5B1,%203,%202,%205,%204%5D%0A%20%20%20%20%0A%20%20%20%20%23%20%E6%8E%92%E5%BA%8F%E5%88%97%E8%A1%A8%0A%20%20%20%20nums.sort%28%29%20%20%23%20%E6%8E%92%E5%BA%8F%E5%90%8E%EF%BC%8C%E5%88%97%E8%A1%A8%E5%85%83%E7%B4%A0%E4%BB%8E%E5%B0%8F%E5%88%B0%E5%A4%A7%E6%8E%92%E5%88%97&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.3 &nbsp; リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#432","level":2,"title":"4.3.2   リストの実装","text":"<p>多くのプログラミング言語にはリストが組み込まれており、たとえば Java、C++、Python などがある。それらの実装は比較的複雑で、初期容量や拡張倍率など各種パラメータの設定もよく考えられている。興味があればソースコードを参照して学べる。</p> <p>リストの動作原理への理解を深めるため、ここでは簡易版のリストを実装し、以下の 3 つの設計ポイントを含める。</p> <ul> <li>初期容量：妥当な配列の初期容量を選ぶ。この例では 10 を初期容量として選ぶ。</li> <li>要素数の記録：<code>size</code> という変数を宣言して、現在のリスト要素数を記録し、要素の挿入と削除に応じてリアルタイムに更新する。この変数により、リスト末尾の位置を特定し、拡張が必要かどうかを判断できる。</li> <li>拡張機構：要素を挿入する時点でリスト容量がいっぱいなら、拡張が必要になる。まず拡張倍率に応じてより大きな配列を作成し、次に現在の配列の全要素を順に新しい配列へ移す。この例では、配列を毎回以前の 2 倍に拡張する。</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby my_list.py<pre><code>class MyList:\n    \"\"\"リストクラス\"\"\"\n\n    def __init__(self):\n        \"\"\"コンストラクタ\"\"\"\n        self._capacity: int = 10  # リスト容量\n        self._arr: list[int] = [0] * self._capacity  # 配列（リスト要素を格納）\n        self._size: int = 0  # リストの長さ（現在の要素数）\n        self._extend_ratio: int = 2  # リスト拡張時の増加倍率\n\n    def size(self) -&gt; int:\n        \"\"\"リストの長さを取得（現在の要素数）\"\"\"\n        return self._size\n\n    def capacity(self) -&gt; int:\n        \"\"\"リスト容量を取得する\"\"\"\n        return self._capacity\n\n    def get(self, index: int) -&gt; int:\n        \"\"\"要素にアクセス\"\"\"\n        # インデックスが範囲外なら例外を送出する。以下同様\n        if index &lt; 0 or index &gt;= self._size:\n            raise IndexError(\"インデックスが範囲外です\")\n        return self._arr[index]\n\n    def set(self, num: int, index: int):\n        \"\"\"要素を更新\"\"\"\n        if index &lt; 0 or index &gt;= self._size:\n            raise IndexError(\"インデックスが範囲外です\")\n        self._arr[index] = num\n\n    def add(self, num: int):\n        \"\"\"末尾に要素を追加\"\"\"\n        # 要素数が容量を超えると、拡張機構が発動する\n        if self.size() == self.capacity():\n            self.extend_capacity()\n        self._arr[self._size] = num\n        self._size += 1\n\n    def insert(self, num: int, index: int):\n        \"\"\"中間に要素を挿入\"\"\"\n        if index &lt; 0 or index &gt;= self._size:\n            raise IndexError(\"インデックスが範囲外です\")\n        # 要素数が容量を超えると、拡張機構が発動する\n        if self._size == self.capacity():\n            self.extend_capacity()\n        # index 以降の要素をすべて 1 つ後ろへずらす\n        for j in range(self._size - 1, index - 1, -1):\n            self._arr[j + 1] = self._arr[j]\n        self._arr[index] = num\n        # 要素数を更新\n        self._size += 1\n\n    def remove(self, index: int) -&gt; int:\n        \"\"\"要素を削除\"\"\"\n        if index &lt; 0 or index &gt;= self._size:\n            raise IndexError(\"インデックスが範囲外です\")\n        num = self._arr[index]\n        # インデックス index より後の要素をすべて 1 つ前に移動する\n        for j in range(index, self._size - 1):\n            self._arr[j] = self._arr[j + 1]\n        # 要素数を更新\n        self._size -= 1\n        # 削除された要素を返す\n        return num\n\n    def extend_capacity(self):\n        \"\"\"リストの拡張\"\"\"\n        # 元の配列の `_extend_ratio` 倍の長さを持つ新しい配列を作成し、元の配列を新しい配列にコピーする\n        self._arr = self._arr + [0] * self.capacity() * (self._extend_ratio - 1)\n        # リストの容量を更新\n        self._capacity = len(self._arr)\n\n    def to_array(self) -&gt; list[int]:\n        \"\"\"有効長のリストを返す\"\"\"\n        return self._arr[: self._size]\n</code></pre> my_list.cpp<pre><code>/* リストクラス */\nclass MyList {\n  private:\n    int *arr;             // 配列（リスト要素を格納）\n    int arrCapacity = 10; // リスト容量\n    int arrSize = 0;      // リストの長さ（現在の要素数）\n    int extendRatio = 2;   // リスト拡張時の増加倍率\n\n  public:\n    /* コンストラクタ */\n    MyList() {\n        arr = new int[arrCapacity];\n    }\n\n    /* デストラクタメソッド */\n    ~MyList() {\n        delete[] arr;\n    }\n\n    /* リストの長さを取得（現在の要素数） */\n    int size() {\n        return arrSize;\n    }\n\n    /* リスト容量を取得する */\n    int capacity() {\n        return arrCapacity;\n    }\n\n    /* 要素にアクセス */\n    int get(int index) {\n        // インデックスが範囲外なら例外を送出する。以下同様\n        if (index &lt; 0 || index &gt;= size())\n            throw out_of_range(\"インデックスが範囲外\");\n        return arr[index];\n    }\n\n    /* 要素を更新 */\n    void set(int index, int num) {\n        if (index &lt; 0 || index &gt;= size())\n            throw out_of_range(\"インデックスが範囲外\");\n        arr[index] = num;\n    }\n\n    /* 末尾に要素を追加 */\n    void add(int num) {\n        // 要素数が容量を超えると、拡張機構が発動する\n        if (size() == capacity())\n            extendCapacity();\n        arr[size()] = num;\n        // 要素数を更新\n        arrSize++;\n    }\n\n    /* 中間に要素を挿入 */\n    void insert(int index, int num) {\n        if (index &lt; 0 || index &gt;= size())\n            throw out_of_range(\"インデックスが範囲外\");\n        // 要素数が容量を超えると、拡張機構が発動する\n        if (size() == capacity())\n            extendCapacity();\n        // index 以降の要素をすべて 1 つ後ろへずらす\n        for (int j = size() - 1; j &gt;= index; j--) {\n            arr[j + 1] = arr[j];\n        }\n        arr[index] = num;\n        // 要素数を更新\n        arrSize++;\n    }\n\n    /* 要素を削除 */\n    int remove(int index) {\n        if (index &lt; 0 || index &gt;= size())\n            throw out_of_range(\"インデックスが範囲外\");\n        int num = arr[index];\n        // インデックス index より後の要素をすべて 1 つ前に移動する\n        for (int j = index; j &lt; size() - 1; j++) {\n            arr[j] = arr[j + 1];\n        }\n        // 要素数を更新\n        arrSize--;\n        // 削除された要素を返す\n        return num;\n    }\n\n    /* リストの拡張 */\n    void extendCapacity() {\n        // 元の配列の `extendRatio` 倍の長さを持つ新しい配列を作成する\n        int newCapacity = capacity() * extendRatio;\n        int *tmp = arr;\n        arr = new int[newCapacity];\n        // 元の配列の全要素を新しい配列にコピー\n        for (int i = 0; i &lt; size(); i++) {\n            arr[i] = tmp[i];\n        }\n        // メモリを解放する\n        delete[] tmp;\n        arrCapacity = newCapacity;\n    }\n\n    /* 出力用にリストを Vector に変換 */\n    vector&lt;int&gt; toVector() {\n        // 有効長の範囲内のリスト要素のみを変換\n        vector&lt;int&gt; vec(size());\n        for (int i = 0; i &lt; size(); i++) {\n            vec[i] = arr[i];\n        }\n        return vec;\n    }\n};\n</code></pre> my_list.java<pre><code>/* リストクラス */\nclass MyList {\n    private int[] arr; // 配列（リスト要素を格納）\n    private int capacity = 10; // リスト容量\n    private int size = 0; // リストの長さ（現在の要素数）\n    private int extendRatio = 2; // リスト拡張時の増加倍率\n\n    /* コンストラクタ */\n    public MyList() {\n        arr = new int[capacity];\n    }\n\n    /* リストの長さを取得（現在の要素数） */\n    public int size() {\n        return size;\n    }\n\n    /* リスト容量を取得する */\n    public int capacity() {\n        return capacity;\n    }\n\n    /* 要素にアクセス */\n    public int get(int index) {\n        // インデックスが範囲外なら例外を送出する。以下同様\n        if (index &lt; 0 || index &gt;= size)\n            throw new IndexOutOfBoundsException(\"インデックスが範囲外です\");\n        return arr[index];\n    }\n\n    /* 要素を更新 */\n    public void set(int index, int num) {\n        if (index &lt; 0 || index &gt;= size)\n            throw new IndexOutOfBoundsException(\"インデックスが範囲外です\");\n        arr[index] = num;\n    }\n\n    /* 末尾に要素を追加 */\n    public void add(int num) {\n        // 要素数が容量を超えると、拡張機構が発動する\n        if (size == capacity())\n            extendCapacity();\n        arr[size] = num;\n        // 要素数を更新\n        size++;\n    }\n\n    /* 中間に要素を挿入 */\n    public void insert(int index, int num) {\n        if (index &lt; 0 || index &gt;= size)\n            throw new IndexOutOfBoundsException(\"インデックスが範囲外です\");\n        // 要素数が容量を超えると、拡張機構が発動する\n        if (size == capacity())\n            extendCapacity();\n        // index 以降の要素をすべて 1 つ後ろへずらす\n        for (int j = size - 1; j &gt;= index; j--) {\n            arr[j + 1] = arr[j];\n        }\n        arr[index] = num;\n        // 要素数を更新\n        size++;\n    }\n\n    /* 要素を削除 */\n    public int remove(int index) {\n        if (index &lt; 0 || index &gt;= size)\n            throw new IndexOutOfBoundsException(\"インデックスが範囲外です\");\n        int num = arr[index];\n        // インデックス index より後の要素をすべて 1 つ前に移動する\n        for (int j = index; j &lt; size - 1; j++) {\n            arr[j] = arr[j + 1];\n        }\n        // 要素数を更新\n        size--;\n        // 削除された要素を返す\n        return num;\n    }\n\n    /* リストの拡張 */\n    public void extendCapacity() {\n        // 元の配列の extendRatio 倍の長さを持つ新しい配列を作成し、元の配列をコピーする\n        arr = Arrays.copyOf(arr, capacity() * extendRatio);\n        // リストの容量を更新\n        capacity = arr.length;\n    }\n\n    /* リストを配列に変換する */\n    public int[] toArray() {\n        int size = size();\n        // 有効長の範囲内のリスト要素のみを変換\n        int[] arr = new int[size];\n        for (int i = 0; i &lt; size; i++) {\n            arr[i] = get(i);\n        }\n        return arr;\n    }\n}\n</code></pre> my_list.cs<pre><code>/* リストクラス */\nclass MyList {\n    private int[] arr;           // 配列（リスト要素を格納）\n    private int arrCapacity = 10;    // リスト容量\n    private int arrSize = 0;         // リストの長さ（現在の要素数）\n    private readonly int extendRatio = 2;  // リスト拡張時の増加倍率\n\n    /* コンストラクタ */\n    public MyList() {\n        arr = new int[arrCapacity];\n    }\n\n    /* リストの長さを取得（現在の要素数） */\n    public int Size() {\n        return arrSize;\n    }\n\n    /* リスト容量を取得する */\n    public int Capacity() {\n        return arrCapacity;\n    }\n\n    /* 要素にアクセス */\n    public int Get(int index) {\n        // インデックスが範囲外なら例外を送出する。以下同様\n        if (index &lt; 0 || index &gt;= arrSize)\n            throw new IndexOutOfRangeException(\"インデックスが範囲外です\");\n        return arr[index];\n    }\n\n    /* 要素を更新 */\n    public void Set(int index, int num) {\n        if (index &lt; 0 || index &gt;= arrSize)\n            throw new IndexOutOfRangeException(\"インデックスが範囲外です\");\n        arr[index] = num;\n    }\n\n    /* 末尾に要素を追加 */\n    public void Add(int num) {\n        // 要素数が容量を超えると、拡張機構が発動する\n        if (arrSize == arrCapacity)\n            ExtendCapacity();\n        arr[arrSize] = num;\n        // 要素数を更新\n        arrSize++;\n    }\n\n    /* 中間に要素を挿入 */\n    public void Insert(int index, int num) {\n        if (index &lt; 0 || index &gt;= arrSize)\n            throw new IndexOutOfRangeException(\"インデックスが範囲外です\");\n        // 要素数が容量を超えると、拡張機構が発動する\n        if (arrSize == arrCapacity)\n            ExtendCapacity();\n        // index 以降の要素をすべて 1 つ後ろへずらす\n        for (int j = arrSize - 1; j &gt;= index; j--) {\n            arr[j + 1] = arr[j];\n        }\n        arr[index] = num;\n        // 要素数を更新\n        arrSize++;\n    }\n\n    /* 要素を削除 */\n    public int Remove(int index) {\n        if (index &lt; 0 || index &gt;= arrSize)\n            throw new IndexOutOfRangeException(\"インデックスが範囲外です\");\n        int num = arr[index];\n        // インデックス index より後の要素をすべて 1 つ前に移動する\n        for (int j = index; j &lt; arrSize - 1; j++) {\n            arr[j] = arr[j + 1];\n        }\n        // 要素数を更新\n        arrSize--;\n        // 削除された要素を返す\n        return num;\n    }\n\n    /* リストの拡張 */\n    public void ExtendCapacity() {\n        // `arrCapacity * extendRatio` の長さを持つ配列を新規作成し、元の配列を新しい配列にコピーする\n        Array.Resize(ref arr, arrCapacity * extendRatio);\n        // リストの容量を更新\n        arrCapacity = arr.Length;\n    }\n\n    /* リストを配列に変換する */\n    public int[] ToArray() {\n        // 有効長の範囲内のリスト要素のみを変換\n        int[] arr = new int[arrSize];\n        for (int i = 0; i &lt; arrSize; i++) {\n            arr[i] = Get(i);\n        }\n        return arr;\n    }\n}\n</code></pre> my_list.go<pre><code>/* リストクラス */\ntype myList struct {\n    arrCapacity int\n    arr         []int\n    arrSize     int\n    extendRatio int\n}\n\n/* コンストラクタ */\nfunc newMyList() *myList {\n    return &amp;myList{\n        arrCapacity: 10,              // リスト容量\n        arr:         make([]int, 10), // 配列（リスト要素を格納）\n        arrSize:     0,               // リストの長さ（現在の要素数）\n        extendRatio: 2,               // リスト拡張時の増加倍率\n    }\n}\n\n/* リストの長さを取得（現在の要素数） */\nfunc (l *myList) size() int {\n    return l.arrSize\n}\n\n/* リスト容量を取得する */\nfunc (l *myList) capacity() int {\n    return l.arrCapacity\n}\n\n/* 要素にアクセス */\nfunc (l *myList) get(index int) int {\n    // インデックスが範囲外なら例外を送出する。以下同様\n    if index &lt; 0 || index &gt;= l.arrSize {\n        panic(\"インデックスが範囲外です\")\n    }\n    return l.arr[index]\n}\n\n/* 要素を更新 */\nfunc (l *myList) set(num, index int) {\n    if index &lt; 0 || index &gt;= l.arrSize {\n        panic(\"インデックスが範囲外です\")\n    }\n    l.arr[index] = num\n}\n\n/* 末尾に要素を追加 */\nfunc (l *myList) add(num int) {\n    // 要素数が容量を超えると、拡張機構が発動する\n    if l.arrSize == l.arrCapacity {\n        l.extendCapacity()\n    }\n    l.arr[l.arrSize] = num\n    // 要素数を更新\n    l.arrSize++\n}\n\n/* 中間に要素を挿入 */\nfunc (l *myList) insert(num, index int) {\n    if index &lt; 0 || index &gt;= l.arrSize {\n        panic(\"インデックスが範囲外です\")\n    }\n    // 要素数が容量を超えると、拡張機構が発動する\n    if l.arrSize == l.arrCapacity {\n        l.extendCapacity()\n    }\n    // index 以降の要素をすべて 1 つ後ろへずらす\n    for j := l.arrSize - 1; j &gt;= index; j-- {\n        l.arr[j+1] = l.arr[j]\n    }\n    l.arr[index] = num\n    // 要素数を更新\n    l.arrSize++\n}\n\n/* 要素を削除 */\nfunc (l *myList) remove(index int) int {\n    if index &lt; 0 || index &gt;= l.arrSize {\n        panic(\"インデックスが範囲外です\")\n    }\n    num := l.arr[index]\n    // インデックス index より後の要素をすべて 1 つ前に移動する\n    for j := index; j &lt; l.arrSize-1; j++ {\n        l.arr[j] = l.arr[j+1]\n    }\n    // 要素数を更新\n    l.arrSize--\n    // 削除された要素を返す\n    return num\n}\n\n/* リストの拡張 */\nfunc (l *myList) extendCapacity() {\n    // 元の配列の extendRatio 倍の長さを持つ新しい配列を作成し、元の配列をコピーする\n    l.arr = append(l.arr, make([]int, l.arrCapacity*(l.extendRatio-1))...)\n    // リストの容量を更新\n    l.arrCapacity = len(l.arr)\n}\n\n/* 有効長のリストを返す */\nfunc (l *myList) toArray() []int {\n    // 有効長の範囲内のリスト要素のみを変換\n    return l.arr[:l.arrSize]\n}\n</code></pre> my_list.swift<pre><code>/* リストクラス */\nclass MyList {\n    private var arr: [Int] // 配列（リスト要素を格納）\n    private var _capacity: Int // リスト容量\n    private var _size: Int // リストの長さ（現在の要素数）\n    private let extendRatio: Int // リスト拡張時の増加倍率\n\n    /* コンストラクタ */\n    init() {\n        _capacity = 10\n        _size = 0\n        extendRatio = 2\n        arr = Array(repeating: 0, count: _capacity)\n    }\n\n    /* リストの長さを取得（現在の要素数） */\n    func size() -&gt; Int {\n        _size\n    }\n\n    /* リスト容量を取得する */\n    func capacity() -&gt; Int {\n        _capacity\n    }\n\n    /* 要素にアクセス */\n    func get(index: Int) -&gt; Int {\n        // インデックスが範囲外ならエラーを投げる。以下同様\n        if index &lt; 0 || index &gt;= size() {\n            fatalError(\"インデックスが範囲外\")\n        }\n        return arr[index]\n    }\n\n    /* 要素を更新 */\n    func set(index: Int, num: Int) {\n        if index &lt; 0 || index &gt;= size() {\n            fatalError(\"インデックスが範囲外\")\n        }\n        arr[index] = num\n    }\n\n    /* 末尾に要素を追加 */\n    func add(num: Int) {\n        // 要素数が容量を超えると、拡張機構が発動する\n        if size() == capacity() {\n            extendCapacity()\n        }\n        arr[size()] = num\n        // 要素数を更新\n        _size += 1\n    }\n\n    /* 中間に要素を挿入 */\n    func insert(index: Int, num: Int) {\n        if index &lt; 0 || index &gt;= size() {\n            fatalError(\"インデックスが範囲外\")\n        }\n        // 要素数が容量を超えると、拡張機構が発動する\n        if size() == capacity() {\n            extendCapacity()\n        }\n        // index 以降の要素をすべて 1 つ後ろへずらす\n        for j in (index ..&lt; size()).reversed() {\n            arr[j + 1] = arr[j]\n        }\n        arr[index] = num\n        // 要素数を更新\n        _size += 1\n    }\n\n    /* 要素を削除 */\n    @discardableResult\n    func remove(index: Int) -&gt; Int {\n        if index &lt; 0 || index &gt;= size() {\n            fatalError(\"インデックスが範囲外\")\n        }\n        let num = arr[index]\n        // インデックス index より後の要素をすべて 1 つ前に移動する\n        for j in index ..&lt; (size() - 1) {\n            arr[j] = arr[j + 1]\n        }\n        // 要素数を更新\n        _size -= 1\n        // 削除された要素を返す\n        return num\n    }\n\n    /* リストの拡張 */\n    func extendCapacity() {\n        // 元の配列の extendRatio 倍の長さを持つ新しい配列を作成し、元の配列をコピーする\n        arr = arr + Array(repeating: 0, count: capacity() * (extendRatio - 1))\n        // リストの容量を更新\n        _capacity = arr.count\n    }\n\n    /* リストを配列に変換する */\n    func toArray() -&gt; [Int] {\n        Array(arr.prefix(size()))\n    }\n}\n</code></pre> my_list.js<pre><code>/* リストクラス */\nclass MyList {\n    #arr = new Array(); // 配列（リスト要素を格納）\n    #capacity = 10; // リスト容量\n    #size = 0; // リストの長さ（現在の要素数）\n    #extendRatio = 2; // リスト拡張時の増加倍率\n\n    /* コンストラクタ */\n    constructor() {\n        this.#arr = new Array(this.#capacity);\n    }\n\n    /* リストの長さを取得（現在の要素数） */\n    size() {\n        return this.#size;\n    }\n\n    /* リスト容量を取得する */\n    capacity() {\n        return this.#capacity;\n    }\n\n    /* 要素にアクセス */\n    get(index) {\n        // インデックスが範囲外なら例外を送出する。以下同様\n        if (index &lt; 0 || index &gt;= this.#size) throw new Error('インデックスが範囲外です');\n        return this.#arr[index];\n    }\n\n    /* 要素を更新 */\n    set(index, num) {\n        if (index &lt; 0 || index &gt;= this.#size) throw new Error('インデックスが範囲外です');\n        this.#arr[index] = num;\n    }\n\n    /* 末尾に要素を追加 */\n    add(num) {\n        // 長さが容量に等しい場合は拡張が必要\n        if (this.#size === this.#capacity) {\n            this.extendCapacity();\n        }\n        // 新しい要素をリストの末尾に追加する\n        this.#arr[this.#size] = num;\n        this.#size++;\n    }\n\n    /* 中間に要素を挿入 */\n    insert(index, num) {\n        if (index &lt; 0 || index &gt;= this.#size) throw new Error('インデックスが範囲外です');\n        // 要素数が容量を超えると、拡張機構が発動する\n        if (this.#size === this.#capacity) {\n            this.extendCapacity();\n        }\n        // index 以降の要素をすべて 1 つ後ろへずらす\n        for (let j = this.#size - 1; j &gt;= index; j--) {\n            this.#arr[j + 1] = this.#arr[j];\n        }\n        // 要素数を更新\n        this.#arr[index] = num;\n        this.#size++;\n    }\n\n    /* 要素を削除 */\n    remove(index) {\n        if (index &lt; 0 || index &gt;= this.#size) throw new Error('インデックスが範囲外です');\n        let num = this.#arr[index];\n        // インデックス index より後の要素をすべて 1 つ前に移動する\n        for (let j = index; j &lt; this.#size - 1; j++) {\n            this.#arr[j] = this.#arr[j + 1];\n        }\n        // 要素数を更新\n        this.#size--;\n        // 削除された要素を返す\n        return num;\n    }\n\n    /* リストの拡張 */\n    extendCapacity() {\n        // 元の配列の extendRatio 倍の長さを持つ新しい配列を作成し、元の配列をコピーする\n        this.#arr = this.#arr.concat(\n            new Array(this.capacity() * (this.#extendRatio - 1))\n        );\n        // リストの容量を更新\n        this.#capacity = this.#arr.length;\n    }\n\n    /* リストを配列に変換する */\n    toArray() {\n        let size = this.size();\n        // 有効長の範囲内のリスト要素のみを変換\n        const arr = new Array(size);\n        for (let i = 0; i &lt; size; i++) {\n            arr[i] = this.get(i);\n        }\n        return arr;\n    }\n}\n</code></pre> my_list.ts<pre><code>/* リストクラス */\nclass MyList {\n    private arr: Array&lt;number&gt;; // 配列（リスト要素を格納）\n    private _capacity: number = 10; // リスト容量\n    private _size: number = 0; // リストの長さ（現在の要素数）\n    private extendRatio: number = 2; // リスト拡張時の増加倍率\n\n    /* コンストラクタ */\n    constructor() {\n        this.arr = new Array(this._capacity);\n    }\n\n    /* リストの長さを取得（現在の要素数） */\n    public size(): number {\n        return this._size;\n    }\n\n    /* リスト容量を取得する */\n    public capacity(): number {\n        return this._capacity;\n    }\n\n    /* 要素にアクセス */\n    public get(index: number): number {\n        // インデックスが範囲外なら例外を送出する。以下同様\n        if (index &lt; 0 || index &gt;= this._size) throw new Error('インデックスが範囲外です');\n        return this.arr[index];\n    }\n\n    /* 要素を更新 */\n    public set(index: number, num: number): void {\n        if (index &lt; 0 || index &gt;= this._size) throw new Error('インデックスが範囲外です');\n        this.arr[index] = num;\n    }\n\n    /* 末尾に要素を追加 */\n    public add(num: number): void {\n        // 長さが容量に等しい場合は拡張が必要\n        if (this._size === this._capacity) this.extendCapacity();\n        // 新しい要素をリストの末尾に追加する\n        this.arr[this._size] = num;\n        this._size++;\n    }\n\n    /* 中間に要素を挿入 */\n    public insert(index: number, num: number): void {\n        if (index &lt; 0 || index &gt;= this._size) throw new Error('インデックスが範囲外です');\n        // 要素数が容量を超えると、拡張機構が発動する\n        if (this._size === this._capacity) {\n            this.extendCapacity();\n        }\n        // index 以降の要素をすべて 1 つ後ろへずらす\n        for (let j = this._size - 1; j &gt;= index; j--) {\n            this.arr[j + 1] = this.arr[j];\n        }\n        // 要素数を更新\n        this.arr[index] = num;\n        this._size++;\n    }\n\n    /* 要素を削除 */\n    public remove(index: number): number {\n        if (index &lt; 0 || index &gt;= this._size) throw new Error('インデックスが範囲外です');\n        let num = this.arr[index];\n        // インデックス index より後の要素をすべて 1 つ前に移動する\n        for (let j = index; j &lt; this._size - 1; j++) {\n            this.arr[j] = this.arr[j + 1];\n        }\n        // 要素数を更新\n        this._size--;\n        // 削除された要素を返す\n        return num;\n    }\n\n    /* リストの拡張 */\n    public extendCapacity(): void {\n        // `size` の長さを持つ配列を新規作成し、元の配列を新しい配列にコピーする\n        this.arr = this.arr.concat(\n            new Array(this.capacity() * (this.extendRatio - 1))\n        );\n        // リストの容量を更新\n        this._capacity = this.arr.length;\n    }\n\n    /* リストを配列に変換する */\n    public toArray(): number[] {\n        let size = this.size();\n        // 有効長の範囲内のリスト要素のみを変換\n        const arr = new Array(size);\n        for (let i = 0; i &lt; size; i++) {\n            arr[i] = this.get(i);\n        }\n        return arr;\n    }\n}\n</code></pre> my_list.dart<pre><code>/* リストクラス */\nclass MyList {\n  late List&lt;int&gt; _arr; // 配列（リスト要素を格納）\n  int _capacity = 10; // リスト容量\n  int _size = 0; // リストの長さ（現在の要素数）\n  int _extendRatio = 2; // リスト拡張時の増加倍率\n\n  /* コンストラクタ */\n  MyList() {\n    _arr = List.filled(_capacity, 0);\n  }\n\n  /* リストの長さを取得（現在の要素数） */\n  int size() =&gt; _size;\n\n  /* リスト容量を取得する */\n  int capacity() =&gt; _capacity;\n\n  /* 要素にアクセス */\n  int get(int index) {\n    if (index &gt;= _size) throw RangeError('インデックスが範囲外です');\n    return _arr[index];\n  }\n\n  /* 要素を更新 */\n  void set(int index, int _num) {\n    if (index &gt;= _size) throw RangeError('インデックスが範囲外です');\n    _arr[index] = _num;\n  }\n\n  /* 末尾に要素を追加 */\n  void add(int _num) {\n    // 要素数が容量を超えると、拡張機構が発動する\n    if (_size == _capacity) extendCapacity();\n    _arr[_size] = _num;\n    // 要素数を更新\n    _size++;\n  }\n\n  /* 中間に要素を挿入 */\n  void insert(int index, int _num) {\n    if (index &gt;= _size) throw RangeError('インデックスが範囲外です');\n    // 要素数が容量を超えると、拡張機構が発動する\n    if (_size == _capacity) extendCapacity();\n    // index 以降の要素をすべて 1 つ後ろへずらす\n    for (var j = _size - 1; j &gt;= index; j--) {\n      _arr[j + 1] = _arr[j];\n    }\n    _arr[index] = _num;\n    // 要素数を更新\n    _size++;\n  }\n\n  /* 要素を削除 */\n  int remove(int index) {\n    if (index &gt;= _size) throw RangeError('インデックスが範囲外です');\n    int _num = _arr[index];\n    // インデックス index より後の要素をすべて 1 つ前に移動する\n    for (var j = index; j &lt; _size - 1; j++) {\n      _arr[j] = _arr[j + 1];\n    }\n    // 要素数を更新\n    _size--;\n    // 削除された要素を返す\n    return _num;\n  }\n\n  /* リストの拡張 */\n  void extendCapacity() {\n    // 元の配列の `_extendRatio` 倍の長さを持つ新しい配列を作成する\n    final _newNums = List.filled(_capacity * _extendRatio, 0);\n    // 元の配列を新しい配列にコピー\n    List.copyRange(_newNums, 0, _arr);\n    // `_arr` の参照を更新\n    _arr = _newNums;\n    // リストの容量を更新\n    _capacity = _arr.length;\n  }\n\n  /* リストを配列に変換する */\n  List&lt;int&gt; toArray() {\n    List&lt;int&gt; arr = [];\n    for (var i = 0; i &lt; _size; i++) {\n      arr.add(get(i));\n    }\n    return arr;\n  }\n}\n</code></pre> my_list.rs<pre><code>/* リストクラス */\n#[allow(dead_code)]\nstruct MyList {\n    arr: Vec&lt;i32&gt;,       // 配列（リスト要素を格納）\n    capacity: usize,     // リスト容量\n    size: usize,         // リストの長さ（現在の要素数）\n    extend_ratio: usize, // リスト拡張時の増加倍率\n}\n\n#[allow(unused, unused_comparisons)]\nimpl MyList {\n    /* コンストラクタ */\n    pub fn new(capacity: usize) -&gt; Self {\n        let mut vec = vec![0; capacity];\n        Self {\n            arr: vec,\n            capacity,\n            size: 0,\n            extend_ratio: 2,\n        }\n    }\n\n    /* リストの長さを取得（現在の要素数） */\n    pub fn size(&amp;self) -&gt; usize {\n        return self.size;\n    }\n\n    /* リスト容量を取得する */\n    pub fn capacity(&amp;self) -&gt; usize {\n        return self.capacity;\n    }\n\n    /* 要素にアクセス */\n    pub fn get(&amp;self, index: usize) -&gt; i32 {\n        // インデックスが範囲外なら例外を送出する。以下同様\n        if index &gt;= self.size {\n            panic!(\"インデックスが範囲外です\")\n        };\n        return self.arr[index];\n    }\n\n    /* 要素を更新 */\n    pub fn set(&amp;mut self, index: usize, num: i32) {\n        if index &gt;= self.size {\n            panic!(\"インデックスが範囲外です\")\n        };\n        self.arr[index] = num;\n    }\n\n    /* 末尾に要素を追加 */\n    pub fn add(&amp;mut self, num: i32) {\n        // 要素数が容量を超えると、拡張機構が発動する\n        if self.size == self.capacity() {\n            self.extend_capacity();\n        }\n        self.arr[self.size] = num;\n        // 要素数を更新\n        self.size += 1;\n    }\n\n    /* 中間に要素を挿入 */\n    pub fn insert(&amp;mut self, index: usize, num: i32) {\n        if index &gt;= self.size() {\n            panic!(\"インデックスが範囲外です\")\n        };\n        // 要素数が容量を超えると、拡張機構が発動する\n        if self.size == self.capacity() {\n            self.extend_capacity();\n        }\n        // index 以降の要素をすべて 1 つ後ろへずらす\n        for j in (index..self.size).rev() {\n            self.arr[j + 1] = self.arr[j];\n        }\n        self.arr[index] = num;\n        // 要素数を更新\n        self.size += 1;\n    }\n\n    /* 要素を削除 */\n    pub fn remove(&amp;mut self, index: usize) -&gt; i32 {\n        if index &gt;= self.size() {\n            panic!(\"インデックスが範囲外です\")\n        };\n        let num = self.arr[index];\n        // インデックス index より後の要素をすべて 1 つ前に移動する\n        for j in index..self.size - 1 {\n            self.arr[j] = self.arr[j + 1];\n        }\n        // 要素数を更新\n        self.size -= 1;\n        // 削除された要素を返す\n        return num;\n    }\n\n    /* リストの拡張 */\n    pub fn extend_capacity(&amp;mut self) {\n        // 元の配列の extend_ratio 倍の長さを持つ新しい配列を作成し、元の配列をコピーする\n        let new_capacity = self.capacity * self.extend_ratio;\n        self.arr.resize(new_capacity, 0);\n        // リストの容量を更新\n        self.capacity = new_capacity;\n    }\n\n    /* リストを配列に変換する */\n    pub fn to_array(&amp;self) -&gt; Vec&lt;i32&gt; {\n        // 有効長の範囲内のリスト要素のみを変換\n        let mut arr = Vec::new();\n        for i in 0..self.size {\n            arr.push(self.get(i));\n        }\n        arr\n    }\n}\n</code></pre> my_list.c<pre><code>/* リストクラス */\ntypedef struct {\n    int *arr;        // 配列（リスト要素を格納）\n    int capacity;    // リスト容量\n    int size;        // リストのサイズ\n    int extendRatio; // リストが拡張されるたびの倍率\n} MyList;\n\n/* コンストラクタ */\nMyList *newMyList() {\n    MyList *nums = malloc(sizeof(MyList));\n    nums-&gt;capacity = 10;\n    nums-&gt;arr = malloc(sizeof(int) * nums-&gt;capacity);\n    nums-&gt;size = 0;\n    nums-&gt;extendRatio = 2;\n    return nums;\n}\n\n/* デストラクタ */\nvoid delMyList(MyList *nums) {\n    free(nums-&gt;arr);\n    free(nums);\n}\n\n/* リストの長さを取得 */\nint size(MyList *nums) {\n    return nums-&gt;size;\n}\n\n/* リスト容量を取得する */\nint capacity(MyList *nums) {\n    return nums-&gt;capacity;\n}\n\n/* 要素にアクセス */\nint get(MyList *nums, int index) {\n    assert(index &gt;= 0 &amp;&amp; index &lt; nums-&gt;size);\n    return nums-&gt;arr[index];\n}\n\n/* 要素を更新 */\nvoid set(MyList *nums, int index, int num) {\n    assert(index &gt;= 0 &amp;&amp; index &lt; nums-&gt;size);\n    nums-&gt;arr[index] = num;\n}\n\n/* 末尾に要素を追加 */\nvoid add(MyList *nums, int num) {\n    if (size(nums) == capacity(nums)) {\n        extendCapacity(nums); // 容量を拡張\n    }\n    nums-&gt;arr[size(nums)] = num;\n    nums-&gt;size++;\n}\n\n/* 中間に要素を挿入 */\nvoid insert(MyList *nums, int index, int num) {\n    assert(index &gt;= 0 &amp;&amp; index &lt; size(nums));\n    // 要素数が容量を超えると、拡張機構が発動する\n    if (size(nums) == capacity(nums)) {\n        extendCapacity(nums); // 容量を拡張\n    }\n    for (int i = size(nums); i &gt; index; --i) {\n        nums-&gt;arr[i] = nums-&gt;arr[i - 1];\n    }\n    nums-&gt;arr[index] = num;\n    nums-&gt;size++;\n}\n\n/* 要素を削除 */\n// 注意: stdio.h が remove 識別子を使用している\nint removeItem(MyList *nums, int index) {\n    assert(index &gt;= 0 &amp;&amp; index &lt; size(nums));\n    int num = nums-&gt;arr[index];\n    for (int i = index; i &lt; size(nums) - 1; i++) {\n        nums-&gt;arr[i] = nums-&gt;arr[i + 1];\n    }\n    nums-&gt;size--;\n    return num;\n}\n\n/* リストの拡張 */\nvoid extendCapacity(MyList *nums) {\n    // 先に領域を確保する\n    int newCapacity = capacity(nums) * nums-&gt;extendRatio;\n    int *extend = (int *)malloc(sizeof(int) * newCapacity);\n    int *temp = nums-&gt;arr;\n\n    // 古いデータを新しいデータにコピー\n    for (int i = 0; i &lt; size(nums); i++)\n        extend[i] = nums-&gt;arr[i];\n\n    // 古いデータを解放する\n    free(temp);\n\n    // 新しいデータに更新\n    nums-&gt;arr = extend;\n    nums-&gt;capacity = newCapacity;\n}\n\n/* 出力用にリストを Array に変換 */\nint *toArray(MyList *nums) {\n    return nums-&gt;arr;\n}\n</code></pre> my_list.kt<pre><code>/* リストクラス */\nclass MyList {\n    private var arr: IntArray = intArrayOf() // 配列（リスト要素を格納）\n    private var capacity: Int = 10 // リスト容量\n    private var size: Int = 0 // リストの長さ（現在の要素数）\n    private var extendRatio: Int = 2 // リスト拡張時の増加倍率\n\n    /* コンストラクタ */\n    init {\n        arr = IntArray(capacity)\n    }\n\n    /* リストの長さを取得（現在の要素数） */\n    fun size(): Int {\n        return size\n    }\n\n    /* リスト容量を取得する */\n    fun capacity(): Int {\n        return capacity\n    }\n\n    /* 要素にアクセス */\n    fun get(index: Int): Int {\n        // インデックスが範囲外なら例外を送出する。以下同様\n        if (index &lt; 0 || index &gt;= size)\n            throw IndexOutOfBoundsException(\"インデックスが範囲外\")\n        return arr[index]\n    }\n\n    /* 要素を更新 */\n    fun set(index: Int, num: Int) {\n        if (index &lt; 0 || index &gt;= size)\n            throw IndexOutOfBoundsException(\"インデックスが範囲外\")\n        arr[index] = num\n    }\n\n    /* 末尾に要素を追加 */\n    fun add(num: Int) {\n        // 要素数が容量を超えると、拡張機構が発動する\n        if (size == capacity())\n            extendCapacity()\n        arr[size] = num\n        // 要素数を更新\n        size++\n    }\n\n    /* 中間に要素を挿入 */\n    fun insert(index: Int, num: Int) {\n        if (index &lt; 0 || index &gt;= size)\n            throw IndexOutOfBoundsException(\"インデックスが範囲外\")\n        // 要素数が容量を超えると、拡張機構が発動する\n        if (size == capacity())\n            extendCapacity()\n        // index 以降の要素をすべて 1 つ後ろへずらす\n        for (j in size - 1 downTo index)\n            arr[j + 1] = arr[j]\n        arr[index] = num\n        // 要素数を更新\n        size++\n    }\n\n    /* 要素を削除 */\n    fun remove(index: Int): Int {\n        if (index &lt; 0 || index &gt;= size)\n            throw IndexOutOfBoundsException(\"インデックスが範囲外\")\n        val num = arr[index]\n        // インデックス index より後の要素をすべて 1 つ前に移動する\n        for (j in index..&lt;size - 1)\n            arr[j] = arr[j + 1]\n        // 要素数を更新\n        size--\n        // 削除された要素を返す\n        return num\n    }\n\n    /* リストの拡張 */\n    fun extendCapacity() {\n        // 元の配列の extendRatio 倍の長さを持つ新しい配列を作成し、元の配列をコピーする\n        arr = arr.copyOf(capacity() * extendRatio)\n        // リストの容量を更新\n        capacity = arr.size\n    }\n\n    /* リストを配列に変換する */\n    fun toArray(): IntArray {\n        val size = size()\n        // 有効長の範囲内のリスト要素のみを変換\n        val arr = IntArray(size)\n        for (i in 0..&lt;size) {\n            arr[i] = get(i)\n        }\n        return arr\n    }\n}\n</code></pre> my_list.rb<pre><code>### リストクラス ###\nclass MyList\n  attr_reader :size       # リストの長さを取得（現在の要素数）\n  attr_reader :capacity   # リスト容量を取得する\n\n  ### コンストラクタ ###\n  def initialize\n    @capacity = 10\n    @size = 0\n    @extend_ratio = 2\n    @arr = Array.new(capacity)\n  end\n\n  ### 要素にアクセス ###\n  def get(index)\n    # インデックスが範囲外なら例外を送出する。以下同様\n    raise IndexError, \"インデックスが範囲外です\" if index &lt; 0 || index &gt;= size\n    @arr[index]\n  end\n\n  ### 要素にアクセス ###\n  def set(index, num)\n    raise IndexError, \"インデックスが範囲外です\" if index &lt; 0 || index &gt;= size\n    @arr[index] = num\n  end\n\n  ### 末尾に要素を追加 ###\n  def add(num)\n    # 要素数が容量を超えると、拡張機構が発動する\n    extend_capacity if size == capacity\n    @arr[size] = num\n\n    # 要素数を更新\n    @size += 1\n  end\n\n  ### 途中に要素を挿入 ###\n  def insert(index, num)\n    raise IndexError, \"インデックスが範囲外です\" if index &lt; 0 || index &gt;= size\n\n    # 要素数が容量を超えると、拡張機構が発動する\n    extend_capacity if size == capacity\n\n    # index 以降の要素をすべて 1 つ後ろへずらす\n    for j in (size - 1).downto(index)\n      @arr[j + 1] = @arr[j]\n    end\n    @arr[index] = num\n\n    # 要素数を更新\n    @size += 1\n  end\n\n  ### 要素の削除 ###\n  def remove(index)\n    raise IndexError, \"インデックスが範囲外です\" if index &lt; 0 || index &gt;= size\n    num = @arr[index]\n\n    # インデックス index より後の要素をすべて 1 つ前に移動する\n    for j in index...size\n      @arr[j] = @arr[j + 1]\n    end\n\n    # 要素数を更新\n    @size -= 1\n\n    # 削除された要素を返す\n    num\n  end\n\n  ### リストの容量拡張 ###\n  def extend_capacity\n    # 元の配列の extend_ratio 倍の長さを持つ新しい配列を作成し、元の配列をコピーする\n    arr = @arr.dup + Array.new(capacity * (@extend_ratio - 1))\n    # リストの容量を更新\n    @capacity = arr.length\n  end\n\n  ### リストを配列に変換 ###\n  def to_array\n    sz = size\n    # 有効長の範囲内のリスト要素のみを変換\n    arr = Array.new(sz)\n    for i in 0...sz\n      arr[i] = get(i)\n    end\n    arr\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.3 &nbsp; リスト"],"tags":[]},{"location":"chapter_array_and_linkedlist/ram_and_cache/","level":1,"title":"4.4   メモリとキャッシュ *","text":"<p>本章の前二節では、配列と連結リストという二つの基礎的かつ重要なデータ構造を扱いました。これらはそれぞれ「連続格納」と「分散格納」という二つの物理構造を表しています。</p> <p>実際には、物理構造はプログラムにおけるメモリとキャッシュの利用効率を大きく左右し、ひいてはアルゴリズムプログラム全体の性能に影響します。</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.4 &nbsp; メモリとキャッシュ *"],"tags":[]},{"location":"chapter_array_and_linkedlist/ram_and_cache/#441","level":2,"title":"4.4.1   コンピュータの記憶装置","text":"<p>コンピュータには三種類の記憶装置があります。ハードディスク（hard disk）、メモリ（random-access memory, RAM）、キャッシュ（cache memory）です。以下の表は、これらがコンピュータシステムで担う役割と性能上の特徴を示しています。</p> <p> 表 4-2   コンピュータの記憶装置 </p> ハードディスク メモリ キャッシュ 用途 OS、プログラム、ファイルなどを長期保存 実行中のプログラムや処理中のデータを一時保存 頻繁にアクセスされるデータや命令を保存し、CPU のメモリアクセス回数を減らす 揮発性 電源断後もデータは失われない 電源断後にデータは失われる 電源断後にデータは失われる 容量 大きい、TB 級 小さい、GB 級 非常に小さい、MB 級 速度 遅い、数百〜数千 MB/s 速い、数十 GB/s 非常に速い、数十〜数百 GB/s 価格（人民元） 比較的安価、数角〜数元 / GB 比較的高価、数十〜数百元 / GB 非常に高価、CPU と一体で価格設定される <p>コンピュータの記憶システムは、下図のようなピラミッド構造として捉えられます。ピラミッドの頂点に近い記憶装置ほど速度は速く、容量は小さく、コストは高くなります。この多層構造は偶然ではなく、コンピュータ科学者やエンジニアによる熟慮の末の設計です。</p> <ul> <li>ハードディスクはメモリで置き換えにくい。まず、メモリ内のデータは電源断後に失われるため、長期保存には向きません。次に、メモリのコストはハードディスクの数十倍であり、消費者市場で広く普及しにくいという問題があります。</li> <li>キャッシュは大容量と高速性を両立しにくい。L1、L2、L3 キャッシュの容量が段階的に増えるにつれて、物理サイズは大きくなり、CPU コアとの物理的距離も遠くなります。その結果、データ転送時間が増え、要素アクセスの遅延も大きくなります。現在の技術では、多層キャッシュ構造が容量、速度、コストの最適なバランスです。</li> </ul> <p></p> <p> 図 4-9   コンピュータの記憶システム </p> <p>Tip</p> <p>コンピュータの記憶階層は、速度、容量、コストの三者間にある巧妙なバランスを体現しています。実際、このようなトレードオフはあらゆる工業分野に広く存在しており、異なる利点と制約のあいだで最適な均衡点を見つけることが求められます。</p> <p>要するに、ハードディスクは大量データの長期保存に、メモリはプログラム実行中に処理しているデータの一時保存に、キャッシュは頻繁にアクセスされるデータや命令の保存に用いられ、プログラム実行効率を高めます。三者は協調して動作し、コンピュータシステムの高効率な運用を支えています。</p> <p>次の図に示すように、プログラム実行時にはデータがハードディスクからメモリへ読み込まれ、CPU の計算に使われます。キャッシュは CPU の一部と見なせ、メモリからデータを賢く読み込むことで、CPU に高速なデータ読み出しを提供し、プログラムの実行効率を大きく高め、低速なメモリへの依存を減らします。</p> <p></p> <p> 図 4-10   ハードディスク、メモリ、キャッシュ間のデータの流れ </p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.4 &nbsp; メモリとキャッシュ *"],"tags":[]},{"location":"chapter_array_and_linkedlist/ram_and_cache/#442","level":2,"title":"4.4.2   データ構造のメモリ効率","text":"<p>メモリ空間の利用という観点では、配列と連結リストにはそれぞれ利点と制約があります。</p> <p>一方で、メモリは有限であり、同じメモリ領域を複数のプログラムで共有することはできません。そのため、データ構造にはできるだけ効率よく空間を使うことが求められます。配列の要素は密に並んでおり、連結リストのノード間参照（ポインタ）を保持する追加領域が不要なため、空間効率は高くなります。しかし、配列は十分な連続メモリを一度に確保する必要があり、メモリ浪費を招くことがありますし、拡張時にも追加の時間と空間コストがかかります。これに対して連結リストは「ノード」単位で動的にメモリを割り当て・解放でき、より高い柔軟性を備えています。</p> <p>他方で、プログラムの実行中には、メモリの確保と解放を繰り返すにつれて、空きメモリの断片化はますます進み、メモリ利用効率の低下を招きます。配列は連続した格納方式を取るため、比較的メモリ断片化を起こしにくい構造です。反対に、連結リストの要素は分散して格納されるため、頻繁な挿入や削除を行うと、より断片化を招きやすくなります。</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.4 &nbsp; メモリとキャッシュ *"],"tags":[]},{"location":"chapter_array_and_linkedlist/ram_and_cache/#443","level":2,"title":"4.4.3   データ構造のキャッシュ効率","text":"<p>キャッシュは容量こそメモリよりはるかに小さいものの、速度はメモリよりずっと速く、プログラム実行速度において極めて重要な役割を果たします。キャッシュ容量には限りがあり、頻繁にアクセスされる一部のデータしか保持できません。そのため、CPU がアクセスしようとするデータがキャッシュ内に存在しない場合、キャッシュミス（cache miss）が発生し、CPU は低速なメモリから必要なデータを読み込まなければなりません。</p> <p>当然ながら、「キャッシュミス」が少ないほど、CPU のデータ読み書き効率は高くなり、プログラム性能も向上します。CPU がキャッシュからデータを正常に取得できた割合をキャッシュヒット率（cache hit rate）と呼び、この指標は通常、キャッシュ効率の評価に用いられます。</p> <p>できるだけ高い効率を実現するため、キャッシュは次のようなデータ読み込みの仕組みを採用しています。</p> <ul> <li>キャッシュライン：キャッシュはデータを 1 バイト単位で保存・読み込みするのではなく、キャッシュライン単位で扱います。1 バイト単位の転送と比べて、キャッシュライン単位のほうが効率的です。</li> <li>プリフェッチ機構：プロセッサはデータアクセスのパターン（たとえば順次アクセス、一定ステップ幅のスキップアクセスなど）を予測し、そのパターンに応じてデータをキャッシュへ読み込むことで、ヒット率を高めます。</li> <li>空間的局所性：あるデータがアクセスされた場合、その近傍のデータも近いうちにアクセスされる可能性があります。そのため、キャッシュはあるデータを読み込む際に、その周辺のデータもあわせて読み込み、ヒット率を高めます。</li> <li>時間的局所性：あるデータがアクセスされた場合、そのデータは近い将来に再びアクセスされる可能性が高いです。キャッシュはこの性質を利用し、最近アクセスしたデータを保持することでヒット率を高めます。</li> </ul> <p>実際には、配列と連結リストではキャッシュの利用効率が異なり、主に次の点に表れます。</p> <ul> <li>使用空間：連結リストの要素は配列要素より多くの空間を占めるため、キャッシュに収まる有効データ量は少なくなります。</li> <li>キャッシュライン：連結リストのデータはメモリの各所に分散しており、キャッシュは「ライン単位で読み込む」ため、無効データまで読み込む割合が高くなります。</li> <li>プリフェッチ機構：配列のほうが連結リストよりもデータアクセスのパターンを「予測しやすく」、システムが次に読み込まれるデータを推測しやすくなります。</li> <li>空間的局所性：配列はまとまったメモリ空間に格納されるため、読み込まれたデータの近くにあるデータも、まもなくアクセスされる可能性が高くなります。</li> </ul> <p>全体として、配列はより高いキャッシュヒット率を持つため、操作効率では通常、連結リストより優れています。このため、アルゴリズム問題を解く際には、配列ベースで実装されたデータ構造のほうが好まれることが多くなります。</p> <p>注意すべきなのは、**キャッシュ効率が高いからといって、配列があらゆる状況で連結リストより優れているとは限らない**という点です。実際にどのデータ構造を選ぶかは、具体的な要件に応じて決めるべきです。たとえば、配列と連結リストはいずれも「スタック」データ構造を実装できますが（次章で詳しく説明します）、適した場面は異なります。</p> <ul> <li>アルゴリズム問題に取り組むときは、一般に配列ベースのスタックを選ぶ傾向があります。より高い操作効率とランダムアクセス能力を備えており、その代償は配列用に一定量のメモリを事前確保することだけです。</li> <li>データ量が非常に大きく、動的性が高く、スタックの想定サイズを見積もりにくい場合は、連結リストベースのスタックのほうが適しています。連結リストなら大量のデータをメモリの異なる場所に分散して保存でき、配列拡張による追加コストも回避できます。</li> </ul>","path":["第 4 章 &nbsp; 配列と連結リスト","4.4 &nbsp; メモリとキャッシュ *"],"tags":[]},{"location":"chapter_array_and_linkedlist/summary/","level":1,"title":"4.5   まとめ","text":"","path":["第 4 章 &nbsp; 配列と連結リスト","4.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_array_and_linkedlist/summary/#1","level":3,"title":"1.   要点の振り返り","text":"<ul> <li>配列と連結リストは 2 種類の基本的なデータ構造であり、それぞれコンピュータメモリにおけるデータの 2 つの格納方式、すなわち連続領域への格納と分散領域への格納を表す。両者の特徴は相互補完的である。</li> <li>配列はランダムアクセスをサポートし、使用メモリも少ない。一方で、要素の挿入と削除の効率は低く、初期化後に長さを変更できない。</li> <li>連結リストは参照（ポインタ）を変更することでノードの挿入と削除を効率的に行え、長さも柔軟に調整できる。一方で、ノードへのアクセス効率は低く、メモリ使用量も多い。一般的な連結リストには単方向連結リスト、循環連結リスト、双方向連結リストがある。</li> <li>リストは、追加・削除・検索・更新をサポートする順序付き要素集合であり、通常は動的配列に基づいて実装される。配列の利点を保ちながら、長さを柔軟に調整できる。</li> <li>リストの登場により配列の実用性は大幅に高まったが、一部のメモリ領域が無駄になる可能性がある。</li> <li>プログラムの実行時、データは主にメモリに格納される。配列はより高いメモリ空間効率を提供でき、連結リストはメモリ利用の面でより柔軟である。</li> <li>キャッシュは、キャッシュライン、プリフェッチ機構、空間局所性と時間局所性といったデータ読み込み機構を通じて CPU に高速なデータアクセスを提供し、プログラムの実行効率を大きく向上させる。</li> <li>配列はキャッシュヒット率が高いため、通常は連結リストよりも高効率である。データ構造を選択する際は、具体的な要件や場面に応じて適切に選ぶべきである。</li> </ul>","path":["第 4 章 &nbsp; 配列と連結リスト","4.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_array_and_linkedlist/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q：配列をスタックに格納する場合とヒープに格納する場合では、時間効率と空間効率に影響がありますか？</p> <p>スタック上とヒープ上の配列はいずれも連続したメモリ領域に格納されるため、データ操作の効率は基本的に同じである。ただし、スタックとヒープにはそれぞれ特徴があり、以下の違いが生じる。</p> <ol> <li>確保と解放の効率：スタックは比較的小さなメモリ領域で、確保はコンパイラによって自動的に行われる。一方、ヒープメモリは相対的に大きく、コード内で動的に確保できる反面、断片化しやすい。そのため、ヒープ上での確保と解放は通常スタック上より遅い。</li> <li>サイズ制限：スタックメモリは比較的小さく、ヒープのサイズは一般に利用可能メモリに制限される。そのため、ヒープは大きな配列の格納により適している。</li> <li>柔軟性：スタック上の配列サイズはコンパイル時に確定している必要があるが、ヒープ上の配列サイズは実行時に動的に決定できる。</li> </ol> <p>Q：なぜ配列では同じ型の要素が求められるのに、連結リストでは同じ型であることが強調されないのですか？</p> <p>連結リストはノードで構成され、ノード同士は参照（ポインタ）で接続されている。各ノードには <code>int</code>、<code>double</code>、<code>string</code>、<code>object</code> など、異なる型のデータを格納できる。</p> <p>これに対して、配列要素は同じ型でなければならない。そうでなければ、オフセットを計算して対応する要素位置を取得できないからである。たとえば、配列に <code>int</code> と <code>long</code> の 2 種類が同時に含まれていて、各要素がそれぞれ 4 バイトと 8 バイトを占める場合、配列内に 2 種類の「要素長」が存在するため、次の式ではオフセットを計算できない。</p> <pre><code># 要素のメモリアドレス = 配列のメモリアドレス（先頭要素のメモリアドレス） + 要素長 * 要素インデックス\n</code></pre> <p>Q：ノード <code>P</code> を削除した後、<code>P.next</code> を <code>None</code> に設定する必要はありますか？</p> <p><code>P.next</code> を変更しなくてもよい。この連結リストの観点では、先頭ノードから末尾ノードまでたどっても、もはや <code>P</code> に出会うことはない。つまり、ノード <code>P</code> はすでに連結リストから削除されており、この時点で <code>P</code> がどこを指していても、この連結リストには影響しない。</p> <p>データ構造とアルゴリズム（問題を解くとき）の観点では、切り離さなくても問題はなく、プログラムのロジックが正しいことを保証すればよい。標準ライブラリの観点では、切り離したほうがより安全で、ロジックも明確である。切り離さない場合、削除されたノードが適切に回収されなかったとすると、後続ノードのメモリ回収に影響する可能性がある。</p> <p>Q：連結リストでの挿入と削除の時間計算量は \\(O(1)\\) です。しかし、追加や削除の前には要素を探すのに \\(O(n)\\) の時間が必要です。では、なぜ時間計算量は \\(O(n)\\) ではないのですか？</p> <p>要素を先に探してから削除するのであれば、時間計算量が \\(O(n)\\) であるのは確かである。しかし、連結リストの \\(O(1)\\) での追加・削除という利点は、ほかの用途で生かせる。たとえば、両端キューは連結リストで実装するのに適しており、先頭ノードと末尾ノードを常に指すポインタ変数を維持すれば、各挿入・削除操作はどれも \\(O(1)\\) になる。</p> <p>Q：図「連結リストの定義と格納方式」で、薄青色のノードポインタ部分は 1 つのメモリアドレスを占めているのですか？ それともノード値と半分ずつなのでしょうか？</p> <p>この模式図は定性的な表現にすぎず、定量的な表現は具体的な状況に応じて分析する必要がある。</p> <ul> <li>ノード値が占める領域は型によって異なり、たとえば <code>int</code>、<code>long</code>、<code>double</code>、インスタンスオブジェクトなどがある。</li> <li>ポインタ変数が占めるメモリ空間の大きさは、使用する OS やコンパイル環境によって異なり、多くは 8 バイトまたは 4 バイトである。</li> </ul> <p>Q：リストの末尾への要素追加は常に \\(O(1)\\) ですか？</p> <p>要素を追加する際にリスト長を超える場合は、先にリストを拡張してから追加する必要がある。システムは新しいメモリ領域を確保し、元のリストの全要素をそこへ移動するため、このとき時間計算量は \\(O(n)\\) になる。</p> <p>Q：「リストの登場により配列の実用性は大きく向上したが、一部のメモリ空間が無駄になる可能性がある」というのは、容量、長さ、拡張倍率のような追加変数が占めるメモリのことですか？</p> <p>ここでいう空間の無駄には主に 2 つの意味がある。一方では、リストには初期長が設定されるが、必ずしもそれだけ必要とは限らない。もう一方では、頻繁な拡張を防ぐため、拡張時には通常ある係数、たとえば \\(\\times 1.5\\) を掛ける。このため、多くの空きスロットが生じ、通常それらを完全に埋めることはできない。</p> <p>Q：Python で <code>n = [1, 2, 3]</code> を初期化した後、この 3 つの要素のアドレスは連続しています。しかし <code>m = [2, 1, 3]</code> を初期化すると、各要素の id は連続しておらず、それぞれ <code>n</code> 内の同じ値と一致していることがわかります。これらの要素のアドレスが連続していないなら、<code>m</code> も配列なのですか？</p> <p>仮にリスト要素を連結リストのノード <code>n = [n1, n2, n3, n4, n5]</code> に置き換えたとしても、通常この 5 つのノードオブジェクトもメモリ上の各所に分散して格納される。それでも、与えられたリストインデックスに対して、私たちは依然として \\(O(1)\\) 時間でノードのメモリアドレスを取得し、対応するノードにアクセスできる。これは、配列に格納されているのがノードそのものではなく、ノードへの参照だからである。</p> <p>多くの言語と異なり、Python では数値もオブジェクトとしてラップされており、リストに格納されているのは数値そのものではなく、数値への参照である。そのため、2 つの配列内の同じ数値が同一の id を持つことがあり、しかもそれらの数値のメモリアドレスは連続している必要がない。</p> <p>Q：C++ STL の <code>std::list</code> はすでに双方向連結リストを実装していますが、アルゴリズム本ではあまり直接使われないようです。何か制約があるのでしょうか？</p> <p>一方では、私たちは多くの場合、アルゴリズムの実装に配列を好み、必要なときにだけ連結リストを使う。その主な理由は 2 つある。</p> <ul> <li>空間オーバーヘッド：各要素には 2 つの追加ポインタ（前の要素用と次の要素用）が必要なため、<code>std::list</code> は通常 <code>std::vector</code> より多くの空間を消費する。</li> <li>キャッシュ非効率：データが連続して格納されていないため、<code>std::list</code> はキャッシュの利用効率が低い。一般には、<code>std::vector</code> のほうが性能がよい。</li> </ul> <p>もう一方では、連結リストを使う必要がある代表的な場面は主に二分木とグラフである。スタックやキューについては、連結リストではなく、たいてい言語が提供する <code>stack</code> と <code>queue</code> を使う。</p> <p>Q：<code>res = [[0]] * n</code> という操作で 2 次元リストを生成した場合、それぞれの <code>[0]</code> は独立していますか？</p> <p>独立していない。この 2 次元リストでは、すべての <code>[0]</code> は実際には同一オブジェクトへの参照である。そのうちの 1 つを変更すると、対応するすべての要素が一緒に変化することがわかる。</p> <p>2 次元リスト内の各 <code>[0]</code> を独立させたい場合は、<code>res = [[0] for _ in range(n)]</code> を使って実現できる。この方式の原理は、独立した <code>[0]</code> リストオブジェクトを \\(n\\) 個初期化していることにある。</p> <p>Q：<code>res = [0] * n</code> という操作で生成されたリストでは、それぞれの整数 0 は独立していますか？</p> <p>このリストでは、すべての整数 0 が同一オブジェクトへの参照である。これは、Python が小さな整数（通常は -5 から 256）に対してキャッシュプール機構を採用し、オブジェクトの再利用を最大化して性能を向上させているためである。</p> <p>それらは同じオブジェクトを指しているが、それでもリスト内の各要素は独立して変更できる。これは、Python の整数が「イミュータブルオブジェクト」だからである。ある要素を変更するとき、実際には別のオブジェクトへの参照に切り替わるのであって、元のオブジェクトそのものを変更しているわけではない。</p> <p>しかし、リスト要素が「ミュータブルオブジェクト」（たとえばリスト、辞書、クラスインスタンスなど）である場合は、ある要素を変更するとそのオブジェクト自体が直接変更され、そのオブジェクトを参照しているすべての要素に同じ変化が生じる。</p>","path":["第 4 章 &nbsp; 配列と連結リスト","4.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_backtracking/","level":1,"title":"第 13 章   バックトラッキング","text":"<p>Abstract</p> <p>私たちは迷宮の探検者のように、前へ進む道で困難に出会うことがあります。</p> <p>バックトラッキングの力によってやり直しができ、試行を重ね、最後には光へ通じる出口を見つけられます。</p>","path":["第 13 章 &nbsp; バックトラッキング"],"tags":[]},{"location":"chapter_backtracking/#_1","level":2,"title":"章の内容","text":"<ul> <li>13.1   バックトラッキングアルゴリズム</li> <li>13.2   全順列問題</li> <li>13.3   部分和問題</li> <li>13.4   n クイーン問題</li> <li>13.5   まとめ</li> </ul>","path":["第 13 章 &nbsp; バックトラッキング"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/","level":1,"title":"13.1   バックトラッキングアルゴリズム","text":"<p>バックトラッキングアルゴリズム（backtracking algorithm）は、総当たりによって問題を解く手法です。その中核となる考え方は、初期状態から出発し、あり得るすべての解を力任せに探索し、正しい解に到達したらそれを記録し、解を見つけるか、考えられるすべての選択を試しても解が見つからなくなるまで続ける、というものです。</p> <p>バックトラッキングアルゴリズムでは、通常「深さ優先探索」を用いて解空間をたどります。「二分木」の章で述べたように、前順・中順・後順走査はいずれも深さ優先探索に属します。ここでは前順走査を使ってバックトラッキング問題を構成し、その仕組みを段階的に理解していきます。</p> <p>例題1</p> <p>1 本の二分木が与えられたとき、値が \\(7\\) のノードをすべて探索して記録し、そのノードのリストを返してください。</p> <p>この問題では、この木を前順走査し、現在のノードの値が \\(7\\) かどうかを判定します。該当する場合は、そのノードの値を結果リスト <code>res</code> に追加します。関連する処理は下図と次のコードのとおりです。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby preorder_traversal_i_compact.py<pre><code>def pre_order(root: TreeNode):\n    \"\"\"前順走査：例題 1\"\"\"\n    if root is None:\n        return\n    if root.val == 7:\n        # 解を記録\n        res.append(root)\n    pre_order(root.left)\n    pre_order(root.right)\n</code></pre> preorder_traversal_i_compact.cpp<pre><code>/* 前順走査：例題 1 */\nvoid preOrder(TreeNode *root) {\n    if (root == nullptr) {\n        return;\n    }\n    if (root-&gt;val == 7) {\n        // 解を記録\n        res.push_back(root);\n    }\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n}\n</code></pre> preorder_traversal_i_compact.java<pre><code>/* 前順走査：例題 1 */\nvoid preOrder(TreeNode root) {\n    if (root == null) {\n        return;\n    }\n    if (root.val == 7) {\n        // 解を記録\n        res.add(root);\n    }\n    preOrder(root.left);\n    preOrder(root.right);\n}\n</code></pre> preorder_traversal_i_compact.cs<pre><code>/* 前順走査：例題 1 */\nvoid PreOrder(TreeNode? root) {\n    if (root == null) {\n        return;\n    }\n    if (root.val == 7) {\n        // 解を記録\n        res.Add(root);\n    }\n    PreOrder(root.left);\n    PreOrder(root.right);\n}\n</code></pre> preorder_traversal_i_compact.go<pre><code>/* 前順走査：例題 1 */\nfunc preOrderI(root *TreeNode, res *[]*TreeNode) {\n    if root == nil {\n        return\n    }\n    if (root.Val).(int) == 7 {\n        // 解を記録\n        *res = append(*res, root)\n    }\n    preOrderI(root.Left, res)\n    preOrderI(root.Right, res)\n}\n</code></pre> preorder_traversal_i_compact.swift<pre><code>/* 前順走査：例題 1 */\nfunc preOrder(root: TreeNode?) {\n    guard let root = root else {\n        return\n    }\n    if root.val == 7 {\n        // 解を記録\n        res.append(root)\n    }\n    preOrder(root: root.left)\n    preOrder(root: root.right)\n}\n</code></pre> preorder_traversal_i_compact.js<pre><code>/* 前順走査：例題 1 */\nfunction preOrder(root, res) {\n    if (root === null) {\n        return;\n    }\n    if (root.val === 7) {\n        // 解を記録\n        res.push(root);\n    }\n    preOrder(root.left, res);\n    preOrder(root.right, res);\n}\n</code></pre> preorder_traversal_i_compact.ts<pre><code>/* 前順走査：例題 1 */\nfunction preOrder(root: TreeNode | null, res: TreeNode[]): void {\n    if (root === null) {\n        return;\n    }\n    if (root.val === 7) {\n        // 解を記録\n        res.push(root);\n    }\n    preOrder(root.left, res);\n    preOrder(root.right, res);\n}\n</code></pre> preorder_traversal_i_compact.dart<pre><code>/* 前順走査：例題 1 */\nvoid preOrder(TreeNode? root, List&lt;TreeNode&gt; res) {\n  if (root == null) {\n    return;\n  }\n  if (root.val == 7) {\n    // 解を記録\n    res.add(root);\n  }\n  preOrder(root.left, res);\n  preOrder(root.right, res);\n}\n</code></pre> preorder_traversal_i_compact.rs<pre><code>/* 前順走査：例題 1 */\nfn pre_order(res: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;, root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;) {\n    if root.is_none() {\n        return;\n    }\n    if let Some(node) = root {\n        if node.borrow().val == 7 {\n            // 解を記録\n            res.push(node.clone());\n        }\n        pre_order(res, node.borrow().left.as_ref());\n        pre_order(res, node.borrow().right.as_ref());\n    }\n}\n</code></pre> preorder_traversal_i_compact.c<pre><code>/* 前順走査：例題 1 */\nvoid preOrder(TreeNode *root) {\n    if (root == NULL) {\n        return;\n    }\n    if (root-&gt;val == 7) {\n        // 解を記録\n        res[resSize++] = root;\n    }\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n}\n</code></pre> preorder_traversal_i_compact.kt<pre><code>/* 前順走査：例題 1 */\nfun preOrder(root: TreeNode?) {\n    if (root == null) {\n        return\n    }\n    if (root._val == 7) {\n        // 解を記録\n        res!!.add(root)\n    }\n    preOrder(root.left)\n    preOrder(root.right)\n}\n</code></pre> preorder_traversal_i_compact.rb<pre><code>### 前順走査：例題1 ###\ndef pre_order(root)\n  return unless root\n\n  # 解を記録\n  $res &lt;&lt; root if root.val == 7\n\n  pre_order(root.left)\n  pre_order(root.right)\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p></p> <p> 図 13-1   前順走査でノードを探索する </p>","path":["第 13 章 &nbsp; バックトラッキング","13.1 &nbsp; バックトラッキングアルゴリズム"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/#1311","level":2,"title":"13.1.1   試行と戻る","text":"<p>バックトラッキングアルゴリズムと呼ばれるのは、解空間を探索する際に「試行」と「戻る」という戦略を取るためです。探索中に、ある状態から先へ進めない、または条件を満たす解を得られないと分かった場合、アルゴリズムは直前の選択を取り消して前の状態へ戻り、別の選択肢を試します。</p> <p>例題1では、各ノードへの訪問が 1 回の「試行」に対応し、葉ノードを越えるか親ノードへ戻る <code>return</code> は「戻る」を表します。</p> <p>ここで強調しておきたいのは、**戻るとは関数の return だけを指すわけではない**という点です。これを説明するために、例題1を少し拡張します。</p> <p>例題2</p> <p>二分木の中で値が \\(7\\) のノードをすべて探索し、根ノードからそれらのノードまでの経路を返してください。</p> <p>例題1のコードを土台に、訪問済みノードの経路を記録するためのリスト <code>path</code> を導入します。値が \\(7\\) のノードに到達したら、<code>path</code> をコピーして結果リスト <code>res</code> に追加します。走査が完了すると、<code>res</code> にはすべての解が保存されています。コードは次のとおりです。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby preorder_traversal_ii_compact.py<pre><code>def pre_order(root: TreeNode):\n    \"\"\"前順走査：例題 2\"\"\"\n    if root is None:\n        return\n    # 試す\n    path.append(root)\n    if root.val == 7:\n        # 解を記録\n        res.append(list(path))\n    pre_order(root.left)\n    pre_order(root.right)\n    # バックトラック\n    path.pop()\n</code></pre> preorder_traversal_ii_compact.cpp<pre><code>/* 前順走査：例題 2 */\nvoid preOrder(TreeNode *root) {\n    if (root == nullptr) {\n        return;\n    }\n    // 試す\n    path.push_back(root);\n    if (root-&gt;val == 7) {\n        // 解を記録\n        res.push_back(path);\n    }\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n    // バックトラック\n    path.pop_back();\n}\n</code></pre> preorder_traversal_ii_compact.java<pre><code>/* 前順走査：例題 2 */\nvoid preOrder(TreeNode root) {\n    if (root == null) {\n        return;\n    }\n    // 試す\n    path.add(root);\n    if (root.val == 7) {\n        // 解を記録\n        res.add(new ArrayList&lt;&gt;(path));\n    }\n    preOrder(root.left);\n    preOrder(root.right);\n    // バックトラック\n    path.remove(path.size() - 1);\n}\n</code></pre> preorder_traversal_ii_compact.cs<pre><code>/* 前順走査：例題 2 */\nvoid PreOrder(TreeNode? root) {\n    if (root == null) {\n        return;\n    }\n    // 試す\n    path.Add(root);\n    if (root.val == 7) {\n        // 解を記録\n        res.Add(new List&lt;TreeNode&gt;(path));\n    }\n    PreOrder(root.left);\n    PreOrder(root.right);\n    // バックトラック\n    path.RemoveAt(path.Count - 1);\n}\n</code></pre> preorder_traversal_ii_compact.go<pre><code>/* 前順走査：例題 2 */\nfunc preOrderII(root *TreeNode, res *[][]*TreeNode, path *[]*TreeNode) {\n    if root == nil {\n        return\n    }\n    // 試す\n    *path = append(*path, root)\n    if root.Val.(int) == 7 {\n        // 解を記録\n        *res = append(*res, append([]*TreeNode{}, *path...))\n    }\n    preOrderII(root.Left, res, path)\n    preOrderII(root.Right, res, path)\n    // バックトラック\n    *path = (*path)[:len(*path)-1]\n}\n</code></pre> preorder_traversal_ii_compact.swift<pre><code>/* 前順走査：例題 2 */\nfunc preOrder(root: TreeNode?) {\n    guard let root = root else {\n        return\n    }\n    // 試す\n    path.append(root)\n    if root.val == 7 {\n        // 解を記録\n        res.append(path)\n    }\n    preOrder(root: root.left)\n    preOrder(root: root.right)\n    // バックトラック\n    path.removeLast()\n}\n</code></pre> preorder_traversal_ii_compact.js<pre><code>/* 前順走査：例題 2 */\nfunction preOrder(root, path, res) {\n    if (root === null) {\n        return;\n    }\n    // 試す\n    path.push(root);\n    if (root.val === 7) {\n        // 解を記録\n        res.push([...path]);\n    }\n    preOrder(root.left, path, res);\n    preOrder(root.right, path, res);\n    // バックトラック\n    path.pop();\n}\n</code></pre> preorder_traversal_ii_compact.ts<pre><code>/* 前順走査：例題 2 */\nfunction preOrder(\n    root: TreeNode | null,\n    path: TreeNode[],\n    res: TreeNode[][]\n): void {\n    if (root === null) {\n        return;\n    }\n    // 試す\n    path.push(root);\n    if (root.val === 7) {\n        // 解を記録\n        res.push([...path]);\n    }\n    preOrder(root.left, path, res);\n    preOrder(root.right, path, res);\n    // バックトラック\n    path.pop();\n}\n</code></pre> preorder_traversal_ii_compact.dart<pre><code>/* 前順走査：例題 2 */\nvoid preOrder(\n  TreeNode? root,\n  List&lt;TreeNode&gt; path,\n  List&lt;List&lt;TreeNode&gt;&gt; res,\n) {\n  if (root == null) {\n    return;\n  }\n\n  // 試す\n  path.add(root);\n  if (root.val == 7) {\n    // 解を記録\n    res.add(List.from(path));\n  }\n  preOrder(root.left, path, res);\n  preOrder(root.right, path, res);\n  // バックトラック\n  path.removeLast();\n}\n</code></pre> preorder_traversal_ii_compact.rs<pre><code>/* 前順走査：例題 2 */\nfn pre_order(\n    res: &amp;mut Vec&lt;Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;&gt;,\n    path: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,\n    root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,\n) {\n    if root.is_none() {\n        return;\n    }\n    if let Some(node) = root {\n        // 試す\n        path.push(node.clone());\n        if node.borrow().val == 7 {\n            // 解を記録\n            res.push(path.clone());\n        }\n        pre_order(res, path, node.borrow().left.as_ref());\n        pre_order(res, path, node.borrow().right.as_ref());\n        // バックトラック\n        path.pop();\n    }\n}\n</code></pre> preorder_traversal_ii_compact.c<pre><code>/* 前順走査：例題 2 */\nvoid preOrder(TreeNode *root) {\n    if (root == NULL) {\n        return;\n    }\n    // 試す\n    path[pathSize++] = root;\n    if (root-&gt;val == 7) {\n        // 解を記録\n        for (int i = 0; i &lt; pathSize; ++i) {\n            res[resSize][i] = path[i];\n        }\n        resSize++;\n    }\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n    // バックトラック\n    pathSize--;\n}\n</code></pre> preorder_traversal_ii_compact.kt<pre><code>/* 前順走査：例題 2 */\nfun preOrder(root: TreeNode?) {\n    if (root == null) {\n        return\n    }\n    // 試す\n    path!!.add(root)\n    if (root._val == 7) {\n        // 解を記録\n        res!!.add(path!!.toMutableList())\n    }\n    preOrder(root.left)\n    preOrder(root.right)\n    // バックトラック\n    path!!.removeAt(path!!.size - 1)\n}\n</code></pre> preorder_traversal_ii_compact.rb<pre><code>### 前順走査：例題2 ###\ndef pre_order(root)\n  return unless root\n\n  # 試す\n  $path &lt;&lt; root\n\n  # 解を記録\n  $res &lt;&lt; $path.dup if root.val == 7\n\n  pre_order(root.left)\n  pre_order(root.right)\n\n  # バックトラック\n  $path.pop\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>各「試行」で現在のノードを <code>path</code> に追加して経路を記録し、「戻る」前にはそのノードを <code>path</code> から取り除き、**今回の試行前の状態を復元する**必要があります。</p> <p>次の図に示す過程を見ると、試行と戻るは「前進」と「取り消し」として理解できます。この 2 つの操作は互いに逆向きです。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 13-2   試行と戻る </p>","path":["第 13 章 &nbsp; バックトラッキング","13.1 &nbsp; バックトラッキングアルゴリズム"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/#1312","level":2,"title":"13.1.2   枝刈り","text":"<p>複雑なバックトラッキング問題には、通常 1 つ以上の制約条件が含まれます。制約条件は多くの場合「枝刈り」に利用できます。</p> <p>例題3</p> <p>二分木の中で値が \\(7\\) のノードをすべて探索し、根ノードからそれらのノードまでの経路を返してください。ただし、経路には値が \\(3\\) のノードを含めてはいけません。</p> <p>上の制約条件を満たすために、枝刈り操作を追加する必要があります。探索中に値が \\(3\\) のノードに出会った場合は、そこで早めに return し、それ以上探索を続けません。コードは次のとおりです。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby preorder_traversal_iii_compact.py<pre><code>def pre_order(root: TreeNode):\n    \"\"\"前順走査：例題 3\"\"\"\n    # 枝刈り\n    if root is None or root.val == 3:\n        return\n    # 試す\n    path.append(root)\n    if root.val == 7:\n        # 解を記録\n        res.append(list(path))\n    pre_order(root.left)\n    pre_order(root.right)\n    # バックトラック\n    path.pop()\n</code></pre> preorder_traversal_iii_compact.cpp<pre><code>/* 前順走査：例題 3 */\nvoid preOrder(TreeNode *root) {\n    // 枝刈り\n    if (root == nullptr || root-&gt;val == 3) {\n        return;\n    }\n    // 試す\n    path.push_back(root);\n    if (root-&gt;val == 7) {\n        // 解を記録\n        res.push_back(path);\n    }\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n    // バックトラック\n    path.pop_back();\n}\n</code></pre> preorder_traversal_iii_compact.java<pre><code>/* 前順走査：例題 3 */\nvoid preOrder(TreeNode root) {\n    // 枝刈り\n    if (root == null || root.val == 3) {\n        return;\n    }\n    // 試す\n    path.add(root);\n    if (root.val == 7) {\n        // 解を記録\n        res.add(new ArrayList&lt;&gt;(path));\n    }\n    preOrder(root.left);\n    preOrder(root.right);\n    // バックトラック\n    path.remove(path.size() - 1);\n}\n</code></pre> preorder_traversal_iii_compact.cs<pre><code>/* 前順走査：例題 3 */\nvoid PreOrder(TreeNode? root) {\n    // 枝刈り\n    if (root == null || root.val == 3) {\n        return;\n    }\n    // 試す\n    path.Add(root);\n    if (root.val == 7) {\n        // 解を記録\n        res.Add(new List&lt;TreeNode&gt;(path));\n    }\n    PreOrder(root.left);\n    PreOrder(root.right);\n    // バックトラック\n    path.RemoveAt(path.Count - 1);\n}\n</code></pre> preorder_traversal_iii_compact.go<pre><code>/* 前順走査：例題 3 */\nfunc preOrderIII(root *TreeNode, res *[][]*TreeNode, path *[]*TreeNode) {\n    // 枝刈り\n    if root == nil || root.Val == 3 {\n        return\n    }\n    // 試す\n    *path = append(*path, root)\n    if root.Val.(int) == 7 {\n        // 解を記録\n        *res = append(*res, append([]*TreeNode{}, *path...))\n    }\n    preOrderIII(root.Left, res, path)\n    preOrderIII(root.Right, res, path)\n    // バックトラック\n    *path = (*path)[:len(*path)-1]\n}\n</code></pre> preorder_traversal_iii_compact.swift<pre><code>/* 前順走査：例題 3 */\nfunc preOrder(root: TreeNode?) {\n    // 枝刈り\n    guard let root = root, root.val != 3 else {\n        return\n    }\n    // 試す\n    path.append(root)\n    if root.val == 7 {\n        // 解を記録\n        res.append(path)\n    }\n    preOrder(root: root.left)\n    preOrder(root: root.right)\n    // バックトラック\n    path.removeLast()\n}\n</code></pre> preorder_traversal_iii_compact.js<pre><code>/* 前順走査：例題 3 */\nfunction preOrder(root, path, res) {\n    // 枝刈り\n    if (root === null || root.val === 3) {\n        return;\n    }\n    // 試す\n    path.push(root);\n    if (root.val === 7) {\n        // 解を記録\n        res.push([...path]);\n    }\n    preOrder(root.left, path, res);\n    preOrder(root.right, path, res);\n    // バックトラック\n    path.pop();\n}\n</code></pre> preorder_traversal_iii_compact.ts<pre><code>/* 前順走査：例題 3 */\nfunction preOrder(\n    root: TreeNode | null,\n    path: TreeNode[],\n    res: TreeNode[][]\n): void {\n    // 枝刈り\n    if (root === null || root.val === 3) {\n        return;\n    }\n    // 試す\n    path.push(root);\n    if (root.val === 7) {\n        // 解を記録\n        res.push([...path]);\n    }\n    preOrder(root.left, path, res);\n    preOrder(root.right, path, res);\n    // バックトラック\n    path.pop();\n}\n</code></pre> preorder_traversal_iii_compact.dart<pre><code>/* 前順走査：例題 3 */\nvoid preOrder(\n  TreeNode? root,\n  List&lt;TreeNode&gt; path,\n  List&lt;List&lt;TreeNode&gt;&gt; res,\n) {\n  if (root == null || root.val == 3) {\n    return;\n  }\n\n  // 試す\n  path.add(root);\n  if (root.val == 7) {\n    // 解を記録\n    res.add(List.from(path));\n  }\n  preOrder(root.left, path, res);\n  preOrder(root.right, path, res);\n  // バックトラック\n  path.removeLast();\n}\n</code></pre> preorder_traversal_iii_compact.rs<pre><code>/* 前順走査：例題 3 */\nfn pre_order(\n    res: &amp;mut Vec&lt;Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;&gt;,\n    path: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,\n    root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,\n) {\n    // 枝刈り\n    if root.is_none() || root.as_ref().unwrap().borrow().val == 3 {\n        return;\n    }\n    if let Some(node) = root {\n        // 試す\n        path.push(node.clone());\n        if node.borrow().val == 7 {\n            // 解を記録\n            res.push(path.clone());\n        }\n        pre_order(res, path, node.borrow().left.as_ref());\n        pre_order(res, path, node.borrow().right.as_ref());\n        // バックトラック\n        path.pop();\n    }\n}\n</code></pre> preorder_traversal_iii_compact.c<pre><code>/* 前順走査：例題 3 */\nvoid preOrder(TreeNode *root) {\n    // 枝刈り\n    if (root == NULL || root-&gt;val == 3) {\n        return;\n    }\n    // 試す\n    path[pathSize++] = root;\n    if (root-&gt;val == 7) {\n        // 解を記録\n        for (int i = 0; i &lt; pathSize; i++) {\n            res[resSize][i] = path[i];\n        }\n        resSize++;\n    }\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n    // バックトラック\n    pathSize--;\n}\n</code></pre> preorder_traversal_iii_compact.kt<pre><code>/* 前順走査：例題 3 */\nfun preOrder(root: TreeNode?) {\n    // 枝刈り\n    if (root == null || root._val == 3) {\n        return\n    }\n    // 試す\n    path!!.add(root)\n    if (root._val == 7) {\n        // 解を記録\n        res!!.add(path!!.toMutableList())\n    }\n    preOrder(root.left)\n    preOrder(root.right)\n    // バックトラック\n    path!!.removeAt(path!!.size - 1)\n}\n</code></pre> preorder_traversal_iii_compact.rb<pre><code>### 前順走査：例題3 ###\ndef pre_order(root)\n  # 枝刈り\n  return if !root || root.val == 3\n\n  # 試す\n  $path.append(root)\n\n  # 解を記録\n  $res &lt;&lt; $path.dup if root.val == 7\n\n  pre_order(root.left)\n  pre_order(root.right)\n\n  # バックトラック\n  $path.pop\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>「枝刈り」は非常にイメージしやすい名称です。次の図のように、探索中に**制約条件を満たさない探索分岐を切り落とす**ことで、多くの無意味な試行を避け、探索効率を高められます。</p> <p></p> <p> 図 13-3   制約条件にもとづく枝刈り </p>","path":["第 13 章 &nbsp; バックトラッキング","13.1 &nbsp; バックトラッキングアルゴリズム"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/#1313","level":2,"title":"13.1.3   フレームワークコード","text":"<p>次に、バックトラッキングにおける「試行・戻る・枝刈り」の本体部分を抽出し、汎用性の高いコードフレームワークへまとめてみます。</p> <p>以下のフレームワークコードでは、<code>state</code> は問題の現在状態、<code>choices</code> はその状態で取り得る選択肢を表します。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>def backtrack(state: State, choices: list[choice], res: list[state]):\n    \"\"\"バックトラッキングアルゴリズムのフレームワーク\"\"\"\n    # 解かどうかを判定\n    if is_solution(state):\n        # 解を記録\n        record_solution(state, res)\n        # これ以上探索しない\n        return\n    # すべての選択肢を走査\n    for choice in choices:\n        # 枝刈り: 選択が妥当かを判定\n        if is_valid(state, choice):\n            # 試行: 選択を行い、状態を更新\n            make_choice(state, choice)\n            backtrack(state, choices, res)\n            # 戻る: 選択を取り消し、前の状態に戻す\n            undo_choice(state, choice)\n</code></pre> <pre><code>/* バックトラッキングアルゴリズムのフレームワーク */\nvoid backtrack(State *state, vector&lt;Choice *&gt; &amp;choices, vector&lt;State *&gt; &amp;res) {\n    // 解かどうかを判定\n    if (isSolution(state)) {\n        // 解を記録\n        recordSolution(state, res);\n        // これ以上探索しない\n        return;\n    }\n    // すべての選択肢を走査\n    for (Choice choice : choices) {\n        // 枝刈り: 選択が妥当かを判定\n        if (isValid(state, choice)) {\n            // 試行: 選択を行い、状態を更新\n            makeChoice(state, choice);\n            backtrack(state, choices, res);\n            // 戻る: 選択を取り消し、前の状態に戻す\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* バックトラッキングアルゴリズムのフレームワーク */\nvoid backtrack(State state, List&lt;Choice&gt; choices, List&lt;State&gt; res) {\n    // 解かどうかを判定\n    if (isSolution(state)) {\n        // 解を記録\n        recordSolution(state, res);\n        // これ以上探索しない\n        return;\n    }\n    // すべての選択肢を走査\n    for (Choice choice : choices) {\n        // 枝刈り: 選択が妥当かを判定\n        if (isValid(state, choice)) {\n            // 試行: 選択を行い、状態を更新\n            makeChoice(state, choice);\n            backtrack(state, choices, res);\n            // 戻る: 選択を取り消し、前の状態に戻す\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* バックトラッキングアルゴリズムのフレームワーク */\nvoid Backtrack(State state, List&lt;Choice&gt; choices, List&lt;State&gt; res) {\n    // 解かどうかを判定\n    if (IsSolution(state)) {\n        // 解を記録\n        RecordSolution(state, res);\n        // これ以上探索しない\n        return;\n    }\n    // すべての選択肢を走査\n    foreach (Choice choice in choices) {\n        // 枝刈り: 選択が妥当かを判定\n        if (IsValid(state, choice)) {\n            // 試行: 選択を行い、状態を更新\n            MakeChoice(state, choice);\n            Backtrack(state, choices, res);\n            // 戻る: 選択を取り消し、前の状態に戻す\n            UndoChoice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* バックトラッキングアルゴリズムのフレームワーク */\nfunc backtrack(state *State, choices []Choice, res *[]State) {\n    // 解かどうかを判定\n    if isSolution(state) {\n        // 解を記録\n        recordSolution(state, res)\n        // これ以上探索しない\n        return\n    }\n    // すべての選択肢を走査\n    for _, choice := range choices {\n        // 枝刈り: 選択が妥当かを判定\n        if isValid(state, choice) {\n            // 試行: 選択を行い、状態を更新\n            makeChoice(state, choice)\n            backtrack(state, choices, res)\n            // 戻る: 選択を取り消し、前の状態に戻す\n            undoChoice(state, choice)\n        }\n    }\n}\n</code></pre> <pre><code>/* バックトラッキングアルゴリズムのフレームワーク */\nfunc backtrack(state: inout State, choices: [Choice], res: inout [State]) {\n    // 解かどうかを判定\n    if isSolution(state: state) {\n        // 解を記録\n        recordSolution(state: state, res: &amp;res)\n        // これ以上探索しない\n        return\n    }\n    // すべての選択肢を走査\n    for choice in choices {\n        // 枝刈り: 選択が妥当かを判定\n        if isValid(state: state, choice: choice) {\n            // 試行: 選択を行い、状態を更新\n            makeChoice(state: &amp;state, choice: choice)\n            backtrack(state: &amp;state, choices: choices, res: &amp;res)\n            // 戻る: 選択を取り消し、前の状態に戻す\n            undoChoice(state: &amp;state, choice: choice)\n        }\n    }\n}\n</code></pre> <pre><code>/* バックトラッキングアルゴリズムのフレームワーク */\nfunction backtrack(state, choices, res) {\n    // 解かどうかを判定\n    if (isSolution(state)) {\n        // 解を記録\n        recordSolution(state, res);\n        // これ以上探索しない\n        return;\n    }\n    // すべての選択肢を走査\n    for (let choice of choices) {\n        // 枝刈り: 選択が妥当かを判定\n        if (isValid(state, choice)) {\n            // 試行: 選択を行い、状態を更新\n            makeChoice(state, choice);\n            backtrack(state, choices, res);\n            // 戻る: 選択を取り消し、前の状態に戻す\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* バックトラッキングアルゴリズムのフレームワーク */\nfunction backtrack(state: State, choices: Choice[], res: State[]): void {\n    // 解かどうかを判定\n    if (isSolution(state)) {\n        // 解を記録\n        recordSolution(state, res);\n        // これ以上探索しない\n        return;\n    }\n    // すべての選択肢を走査\n    for (let choice of choices) {\n        // 枝刈り: 選択が妥当かを判定\n        if (isValid(state, choice)) {\n            // 試行: 選択を行い、状態を更新\n            makeChoice(state, choice);\n            backtrack(state, choices, res);\n            // 戻る: 選択を取り消し、前の状態に戻す\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* バックトラッキングアルゴリズムのフレームワーク */\nvoid backtrack(State state, List&lt;Choice&gt;, List&lt;State&gt; res) {\n  // 解かどうかを判定\n  if (isSolution(state)) {\n    // 解を記録\n    recordSolution(state, res);\n    // これ以上探索しない\n    return;\n  }\n  // すべての選択肢を走査\n  for (Choice choice in choices) {\n    // 枝刈り: 選択が妥当かを判定\n    if (isValid(state, choice)) {\n      // 試行: 選択を行い、状態を更新\n      makeChoice(state, choice);\n      backtrack(state, choices, res);\n      // 戻る: 選択を取り消し、前の状態に戻す\n      undoChoice(state, choice);\n    }\n  }\n}\n</code></pre> <pre><code>/* バックトラッキングアルゴリズムのフレームワーク */\nfn backtrack(state: &amp;mut State, choices: &amp;Vec&lt;Choice&gt;, res: &amp;mut Vec&lt;State&gt;) {\n    // 解かどうかを判定\n    if is_solution(state) {\n        // 解を記録\n        record_solution(state, res);\n        // これ以上探索しない\n        return;\n    }\n    // すべての選択肢を走査\n    for choice in choices {\n        // 枝刈り: 選択が妥当かを判定\n        if is_valid(state, choice) {\n            // 試行: 選択を行い、状態を更新\n            make_choice(state, choice);\n            backtrack(state, choices, res);\n            // 戻る: 選択を取り消し、前の状態に戻す\n            undo_choice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* バックトラッキングアルゴリズムのフレームワーク */\nvoid backtrack(State *state, Choice *choices, int numChoices, State *res, int numRes) {\n    // 解かどうかを判定\n    if (isSolution(state)) {\n        // 解を記録\n        recordSolution(state, res, numRes);\n        // これ以上探索しない\n        return;\n    }\n    // すべての選択肢を走査\n    for (int i = 0; i &lt; numChoices; i++) {\n        // 枝刈り: 選択が妥当かを判定\n        if (isValid(state, &amp;choices[i])) {\n            // 試行: 選択を行い、状態を更新\n            makeChoice(state, &amp;choices[i]);\n            backtrack(state, choices, numChoices, res, numRes);\n            // 戻る: 選択を取り消し、前の状態に戻す\n            undoChoice(state, &amp;choices[i]);\n        }\n    }\n}\n</code></pre> <pre><code>/* バックトラッキングアルゴリズムのフレームワーク */\nfun backtrack(state: State?, choices: List&lt;Choice?&gt;, res: List&lt;State?&gt;?) {\n    // 解かどうかを判定\n    if (isSolution(state)) {\n        // 解を記録\n        recordSolution(state, res)\n        // これ以上探索しない\n        return\n    }\n    // すべての選択肢を走査\n    for (choice in choices) {\n        // 枝刈り: 選択が妥当かを判定\n        if (isValid(state, choice)) {\n            // 試行: 選択を行い、状態を更新\n            makeChoice(state, choice)\n            backtrack(state, choices, res)\n            // 戻る: 選択を取り消し、前の状態に戻す\n            undoChoice(state, choice)\n        }\n    }\n}\n</code></pre> <pre><code>### バックトラッキングアルゴリズムのフレームワーク ###\ndef backtrack(state, choices, res)\n    # 解かどうかを判定\n    if is_solution?(state)\n        # 解を記録\n        record_solution(state, res)\n        return\n    end\n\n    # すべての選択肢を走査\n    for choice in choices\n        # 枝刈り: 選択が妥当かを判定\n        if is_valid?(state, choice)\n            # 試行: 選択を行い、状態を更新\n            make_choice(state, choice)\n            backtrack(state, choices, res)\n            # 戻る: 選択を取り消し、前の状態に戻す\n            undo_choice(state, choice)\n        end\n    end\nend\n</code></pre> <p>次に、このフレームワークコードを用いて例題3を解きます。状態 <code>state</code> はノードの走査経路、選択肢 <code>choices</code> は現在のノードの左子ノードと右子ノード、結果 <code>res</code> は経路のリストです。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby preorder_traversal_iii_template.py<pre><code>def is_solution(state: list[TreeNode]) -&gt; bool:\n    \"\"\"現在の状態が解かどうかを判定\"\"\"\n    return state and state[-1].val == 7\n\ndef record_solution(state: list[TreeNode], res: list[list[TreeNode]]):\n    \"\"\"解を記録\"\"\"\n    res.append(list(state))\n\ndef is_valid(state: list[TreeNode], choice: TreeNode) -&gt; bool:\n    \"\"\"現在の状態で、この選択が有効かどうかを判定\"\"\"\n    return choice is not None and choice.val != 3\n\ndef make_choice(state: list[TreeNode], choice: TreeNode):\n    \"\"\"状態を更新\"\"\"\n    state.append(choice)\n\ndef undo_choice(state: list[TreeNode], choice: TreeNode):\n    \"\"\"状態を元に戻す\"\"\"\n    state.pop()\n\ndef backtrack(\n    state: list[TreeNode], choices: list[TreeNode], res: list[list[TreeNode]]\n):\n    \"\"\"バックトラッキング：例題 3\"\"\"\n    # 解かどうかを確認\n    if is_solution(state):\n        # 解を記録\n        record_solution(state, res)\n    # すべての選択肢を走査\n    for choice in choices:\n        # 枝刈り：選択が妥当かを確認する\n        if is_valid(state, choice):\n            # 試行: 選択を行い、状態を更新\n            make_choice(state, choice)\n            # 次の選択へ進む\n            backtrack(state, [choice.left, choice.right], res)\n            # バックトラック：選択を取り消し、前の状態に戻す\n            undo_choice(state, choice)\n</code></pre> preorder_traversal_iii_template.cpp<pre><code>/* 現在の状態が解かどうかを判定 */\nbool isSolution(vector&lt;TreeNode *&gt; &amp;state) {\n    return !state.empty() &amp;&amp; state.back()-&gt;val == 7;\n}\n\n/* 解を記録 */\nvoid recordSolution(vector&lt;TreeNode *&gt; &amp;state, vector&lt;vector&lt;TreeNode *&gt;&gt; &amp;res) {\n    res.push_back(state);\n}\n\n/* 現在の状態で、この選択が有効かどうかを判定 */\nbool isValid(vector&lt;TreeNode *&gt; &amp;state, TreeNode *choice) {\n    return choice != nullptr &amp;&amp; choice-&gt;val != 3;\n}\n\n/* 状態を更新 */\nvoid makeChoice(vector&lt;TreeNode *&gt; &amp;state, TreeNode *choice) {\n    state.push_back(choice);\n}\n\n/* 状態を元に戻す */\nvoid undoChoice(vector&lt;TreeNode *&gt; &amp;state, TreeNode *choice) {\n    state.pop_back();\n}\n\n/* バックトラッキング：例題 3 */\nvoid backtrack(vector&lt;TreeNode *&gt; &amp;state, vector&lt;TreeNode *&gt; &amp;choices, vector&lt;vector&lt;TreeNode *&gt;&gt; &amp;res) {\n    // 解かどうかを確認\n    if (isSolution(state)) {\n        // 解を記録\n        recordSolution(state, res);\n    }\n    // すべての選択肢を走査\n    for (TreeNode *choice : choices) {\n        // 枝刈り：選択が妥当かを確認する\n        if (isValid(state, choice)) {\n            // 試行: 選択を行い、状態を更新\n            makeChoice(state, choice);\n            // 次の選択へ進む\n            vector&lt;TreeNode *&gt; nextChoices{choice-&gt;left, choice-&gt;right};\n            backtrack(state, nextChoices, res);\n            // バックトラック：選択を取り消し、前の状態に戻す\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.java<pre><code>/* 現在の状態が解かどうかを判定 */\nboolean isSolution(List&lt;TreeNode&gt; state) {\n    return !state.isEmpty() &amp;&amp; state.get(state.size() - 1).val == 7;\n}\n\n/* 解を記録 */\nvoid recordSolution(List&lt;TreeNode&gt; state, List&lt;List&lt;TreeNode&gt;&gt; res) {\n    res.add(new ArrayList&lt;&gt;(state));\n}\n\n/* 現在の状態で、この選択が有効かどうかを判定 */\nboolean isValid(List&lt;TreeNode&gt; state, TreeNode choice) {\n    return choice != null &amp;&amp; choice.val != 3;\n}\n\n/* 状態を更新 */\nvoid makeChoice(List&lt;TreeNode&gt; state, TreeNode choice) {\n    state.add(choice);\n}\n\n/* 状態を元に戻す */\nvoid undoChoice(List&lt;TreeNode&gt; state, TreeNode choice) {\n    state.remove(state.size() - 1);\n}\n\n/* バックトラッキング：例題 3 */\nvoid backtrack(List&lt;TreeNode&gt; state, List&lt;TreeNode&gt; choices, List&lt;List&lt;TreeNode&gt;&gt; res) {\n    // 解かどうかを確認\n    if (isSolution(state)) {\n        // 解を記録\n        recordSolution(state, res);\n    }\n    // すべての選択肢を走査\n    for (TreeNode choice : choices) {\n        // 枝刈り：選択が妥当かを確認する\n        if (isValid(state, choice)) {\n            // 試行: 選択を行い、状態を更新\n            makeChoice(state, choice);\n            // 次の選択へ進む\n            backtrack(state, Arrays.asList(choice.left, choice.right), res);\n            // バックトラック：選択を取り消し、前の状態に戻す\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.cs<pre><code>/* 現在の状態が解かどうかを判定 */\nbool IsSolution(List&lt;TreeNode&gt; state) {\n    return state.Count != 0 &amp;&amp; state[^1].val == 7;\n}\n\n/* 解を記録 */\nvoid RecordSolution(List&lt;TreeNode&gt; state, List&lt;List&lt;TreeNode&gt;&gt; res) {\n    res.Add(new List&lt;TreeNode&gt;(state));\n}\n\n/* 現在の状態で、この選択が有効かどうかを判定 */\nbool IsValid(List&lt;TreeNode&gt; state, TreeNode choice) {\n    return choice != null &amp;&amp; choice.val != 3;\n}\n\n/* 状態を更新 */\nvoid MakeChoice(List&lt;TreeNode&gt; state, TreeNode choice) {\n    state.Add(choice);\n}\n\n/* 状態を元に戻す */\nvoid UndoChoice(List&lt;TreeNode&gt; state, TreeNode choice) {\n    state.RemoveAt(state.Count - 1);\n}\n\n/* バックトラッキング：例題 3 */\nvoid Backtrack(List&lt;TreeNode&gt; state, List&lt;TreeNode&gt; choices, List&lt;List&lt;TreeNode&gt;&gt; res) {\n    // 解かどうかを確認\n    if (IsSolution(state)) {\n        // 解を記録\n        RecordSolution(state, res);\n    }\n    // すべての選択肢を走査\n    foreach (TreeNode choice in choices) {\n        // 枝刈り：選択が妥当かを確認する\n        if (IsValid(state, choice)) {\n            // 試行: 選択を行い、状態を更新\n            MakeChoice(state, choice);\n            // 次の選択へ進む\n            Backtrack(state, [choice.left!, choice.right!], res);\n            // バックトラック：選択を取り消し、前の状態に戻す\n            UndoChoice(state, choice);\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.go<pre><code>/* 現在の状態が解かどうかを判定 */\nfunc isSolution(state *[]*TreeNode) bool {\n    return len(*state) != 0 &amp;&amp; (*state)[len(*state)-1].Val == 7\n}\n\n/* 解を記録 */\nfunc recordSolution(state *[]*TreeNode, res *[][]*TreeNode) {\n    *res = append(*res, append([]*TreeNode{}, *state...))\n}\n\n/* 現在の状態で、この選択が有効かどうかを判定 */\nfunc isValid(state *[]*TreeNode, choice *TreeNode) bool {\n    return choice != nil &amp;&amp; choice.Val != 3\n}\n\n/* 状態を更新 */\nfunc makeChoice(state *[]*TreeNode, choice *TreeNode) {\n    *state = append(*state, choice)\n}\n\n/* 状態を元に戻す */\nfunc undoChoice(state *[]*TreeNode, choice *TreeNode) {\n    *state = (*state)[:len(*state)-1]\n}\n\n/* バックトラッキング：例題 3 */\nfunc backtrackIII(state *[]*TreeNode, choices *[]*TreeNode, res *[][]*TreeNode) {\n    // 解かどうかを確認\n    if isSolution(state) {\n        // 解を記録\n        recordSolution(state, res)\n    }\n    // すべての選択肢を走査\n    for _, choice := range *choices {\n        // 枝刈り：選択が妥当かを確認する\n        if isValid(state, choice) {\n            // 試行: 選択を行い、状態を更新\n            makeChoice(state, choice)\n            // 次の選択へ進む\n            temp := make([]*TreeNode, 0)\n            temp = append(temp, choice.Left, choice.Right)\n            backtrackIII(state, &amp;temp, res)\n            // バックトラック：選択を取り消し、前の状態に戻す\n            undoChoice(state, choice)\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.swift<pre><code>/* 現在の状態が解かどうかを判定 */\nfunc isSolution(state: [TreeNode]) -&gt; Bool {\n    !state.isEmpty &amp;&amp; state.last!.val == 7\n}\n\n/* 解を記録 */\nfunc recordSolution(state: [TreeNode], res: inout [[TreeNode]]) {\n    res.append(state)\n}\n\n/* 現在の状態で、この選択が有効かどうかを判定 */\nfunc isValid(state: [TreeNode], choice: TreeNode?) -&gt; Bool {\n    choice != nil &amp;&amp; choice!.val != 3\n}\n\n/* 状態を更新 */\nfunc makeChoice(state: inout [TreeNode], choice: TreeNode) {\n    state.append(choice)\n}\n\n/* 状態を元に戻す */\nfunc undoChoice(state: inout [TreeNode], choice: TreeNode) {\n    state.removeLast()\n}\n\n/* バックトラッキング：例題 3 */\nfunc backtrack(state: inout [TreeNode], choices: [TreeNode], res: inout [[TreeNode]]) {\n    // 解かどうかを確認\n    if isSolution(state: state) {\n        recordSolution(state: state, res: &amp;res)\n    }\n    // すべての選択肢を走査\n    for choice in choices {\n        // 枝刈り：選択が妥当かを確認する\n        if isValid(state: state, choice: choice) {\n            // 試行: 選択を行い、状態を更新\n            makeChoice(state: &amp;state, choice: choice)\n            // 次の選択へ進む\n            backtrack(state: &amp;state, choices: [choice.left, choice.right].compactMap { $0 }, res: &amp;res)\n            // バックトラック：選択を取り消し、前の状態に戻す\n            undoChoice(state: &amp;state, choice: choice)\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.js<pre><code>/* 現在の状態が解かどうかを判定 */\nfunction isSolution(state) {\n    return state &amp;&amp; state[state.length - 1]?.val === 7;\n}\n\n/* 解を記録 */\nfunction recordSolution(state, res) {\n    res.push([...state]);\n}\n\n/* 現在の状態で、この選択が有効かどうかを判定 */\nfunction isValid(state, choice) {\n    return choice !== null &amp;&amp; choice.val !== 3;\n}\n\n/* 状態を更新 */\nfunction makeChoice(state, choice) {\n    state.push(choice);\n}\n\n/* 状態を元に戻す */\nfunction undoChoice(state) {\n    state.pop();\n}\n\n/* バックトラッキング：例題 3 */\nfunction backtrack(state, choices, res) {\n    // 解かどうかを確認\n    if (isSolution(state)) {\n        // 解を記録\n        recordSolution(state, res);\n    }\n    // すべての選択肢を走査\n    for (const choice of choices) {\n        // 枝刈り：選択が妥当かを確認する\n        if (isValid(state, choice)) {\n            // 試行: 選択を行い、状態を更新\n            makeChoice(state, choice);\n            // 次の選択へ進む\n            backtrack(state, [choice.left, choice.right], res);\n            // バックトラック：選択を取り消し、前の状態に戻す\n            undoChoice(state);\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.ts<pre><code>/* 現在の状態が解かどうかを判定 */\nfunction isSolution(state: TreeNode[]): boolean {\n    return state &amp;&amp; state[state.length - 1]?.val === 7;\n}\n\n/* 解を記録 */\nfunction recordSolution(state: TreeNode[], res: TreeNode[][]): void {\n    res.push([...state]);\n}\n\n/* 現在の状態で、この選択が有効かどうかを判定 */\nfunction isValid(state: TreeNode[], choice: TreeNode): boolean {\n    return choice !== null &amp;&amp; choice.val !== 3;\n}\n\n/* 状態を更新 */\nfunction makeChoice(state: TreeNode[], choice: TreeNode): void {\n    state.push(choice);\n}\n\n/* 状態を元に戻す */\nfunction undoChoice(state: TreeNode[]): void {\n    state.pop();\n}\n\n/* バックトラッキング：例題 3 */\nfunction backtrack(\n    state: TreeNode[],\n    choices: TreeNode[],\n    res: TreeNode[][]\n): void {\n    // 解かどうかを確認\n    if (isSolution(state)) {\n        // 解を記録\n        recordSolution(state, res);\n    }\n    // すべての選択肢を走査\n    for (const choice of choices) {\n        // 枝刈り：選択が妥当かを確認する\n        if (isValid(state, choice)) {\n            // 試行: 選択を行い、状態を更新\n            makeChoice(state, choice);\n            // 次の選択へ進む\n            backtrack(state, [choice.left, choice.right], res);\n            // バックトラック：選択を取り消し、前の状態に戻す\n            undoChoice(state);\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.dart<pre><code>/* 現在の状態が解かどうかを判定 */\nbool isSolution(List&lt;TreeNode&gt; state) {\n  return state.isNotEmpty &amp;&amp; state.last.val == 7;\n}\n\n/* 解を記録 */\nvoid recordSolution(List&lt;TreeNode&gt; state, List&lt;List&lt;TreeNode&gt;&gt; res) {\n  res.add(List.from(state));\n}\n\n/* 現在の状態で、この選択が有効かどうかを判定 */\nbool isValid(List&lt;TreeNode&gt; state, TreeNode? choice) {\n  return choice != null &amp;&amp; choice.val != 3;\n}\n\n/* 状態を更新 */\nvoid makeChoice(List&lt;TreeNode&gt; state, TreeNode? choice) {\n  state.add(choice!);\n}\n\n/* 状態を元に戻す */\nvoid undoChoice(List&lt;TreeNode&gt; state, TreeNode? choice) {\n  state.removeLast();\n}\n\n/* バックトラッキング：例題 3 */\nvoid backtrack(\n  List&lt;TreeNode&gt; state,\n  List&lt;TreeNode?&gt; choices,\n  List&lt;List&lt;TreeNode&gt;&gt; res,\n) {\n  // 解かどうかを確認\n  if (isSolution(state)) {\n    // 解を記録\n    recordSolution(state, res);\n  }\n  // すべての選択肢を走査\n  for (TreeNode? choice in choices) {\n    // 枝刈り：選択が妥当かを確認する\n    if (isValid(state, choice)) {\n      // 試行: 選択を行い、状態を更新\n      makeChoice(state, choice);\n      // 次の選択へ進む\n      backtrack(state, [choice!.left, choice.right], res);\n      // バックトラック：選択を取り消し、前の状態に戻す\n      undoChoice(state, choice);\n    }\n  }\n}\n</code></pre> preorder_traversal_iii_template.rs<pre><code>/* 現在の状態が解かどうかを判定 */\nfn is_solution(state: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;) -&gt; bool {\n    return !state.is_empty() &amp;&amp; state.last().unwrap().borrow().val == 7;\n}\n\n/* 解を記録 */\nfn record_solution(\n    state: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,\n    res: &amp;mut Vec&lt;Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;&gt;,\n) {\n    res.push(state.clone());\n}\n\n/* 現在の状態で、この選択が有効かどうかを判定 */\nfn is_valid(_: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;, choice: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;) -&gt; bool {\n    return choice.is_some() &amp;&amp; choice.unwrap().borrow().val != 3;\n}\n\n/* 状態を更新 */\nfn make_choice(state: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;, choice: Rc&lt;RefCell&lt;TreeNode&gt;&gt;) {\n    state.push(choice);\n}\n\n/* 状態を元に戻す */\nfn undo_choice(state: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;, _: Rc&lt;RefCell&lt;TreeNode&gt;&gt;) {\n    state.pop();\n}\n\n/* バックトラッキング：例題 3 */\nfn backtrack(\n    state: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,\n    choices: &amp;Vec&lt;Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;&gt;,\n    res: &amp;mut Vec&lt;Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;&gt;,\n) {\n    // 解かどうかを確認\n    if is_solution(state) {\n        // 解を記録\n        record_solution(state, res);\n    }\n    // すべての選択肢を走査\n    for &amp;choice in choices.iter() {\n        // 枝刈り：選択が妥当かを確認する\n        if is_valid(state, choice) {\n            // 試行: 選択を行い、状態を更新\n            make_choice(state, choice.unwrap().clone());\n            // 次の選択へ進む\n            backtrack(\n                state,\n                &amp;vec![\n                    choice.unwrap().borrow().left.as_ref(),\n                    choice.unwrap().borrow().right.as_ref(),\n                ],\n                res,\n            );\n            // バックトラック：選択を取り消し、前の状態に戻す\n            undo_choice(state, choice.unwrap().clone());\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.c<pre><code>/* 現在の状態が解かどうかを判定 */\nbool isSolution(void) {\n    return pathSize &gt; 0 &amp;&amp; path[pathSize - 1]-&gt;val == 7;\n}\n\n/* 解を記録 */\nvoid recordSolution(void) {\n    for (int i = 0; i &lt; pathSize; i++) {\n        res[resSize][i] = path[i];\n    }\n    resSize++;\n}\n\n/* 現在の状態で、この選択が有効かどうかを判定 */\nbool isValid(TreeNode *choice) {\n    return choice != NULL &amp;&amp; choice-&gt;val != 3;\n}\n\n/* 状態を更新 */\nvoid makeChoice(TreeNode *choice) {\n    path[pathSize++] = choice;\n}\n\n/* 状態を元に戻す */\nvoid undoChoice(void) {\n    pathSize--;\n}\n\n/* バックトラッキング：例題 3 */\nvoid backtrack(TreeNode *choices[2]) {\n    // 解かどうかを確認\n    if (isSolution()) {\n        // 解を記録\n        recordSolution();\n    }\n    // すべての選択肢を走査\n    for (int i = 0; i &lt; 2; i++) {\n        TreeNode *choice = choices[i];\n        // 枝刈り：選択が妥当かを確認する\n        if (isValid(choice)) {\n            // 試行: 選択を行い、状態を更新\n            makeChoice(choice);\n            // 次の選択へ進む\n            TreeNode *nextChoices[2] = {choice-&gt;left, choice-&gt;right};\n            backtrack(nextChoices);\n            // バックトラック：選択を取り消し、前の状態に戻す\n            undoChoice();\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.kt<pre><code>/* 現在の状態が解かどうかを判定 */\nfun isSolution(state: MutableList&lt;TreeNode?&gt;): Boolean {\n    return state.isNotEmpty() &amp;&amp; state[state.size - 1]?._val == 7\n}\n\n/* 解を記録 */\nfun recordSolution(state: MutableList&lt;TreeNode?&gt;?, res: MutableList&lt;MutableList&lt;TreeNode?&gt;?&gt;) {\n    res.add(state!!.toMutableList())\n}\n\n/* 現在の状態で、この選択が有効かどうかを判定 */\nfun isValid(state: MutableList&lt;TreeNode?&gt;?, choice: TreeNode?): Boolean {\n    return choice != null &amp;&amp; choice._val != 3\n}\n\n/* 状態を更新 */\nfun makeChoice(state: MutableList&lt;TreeNode?&gt;, choice: TreeNode?) {\n    state.add(choice)\n}\n\n/* 状態を元に戻す */\nfun undoChoice(state: MutableList&lt;TreeNode?&gt;, choice: TreeNode?) {\n    state.removeLast()\n}\n\n/* バックトラッキング：例題 3 */\nfun backtrack(\n    state: MutableList&lt;TreeNode?&gt;,\n    choices: MutableList&lt;TreeNode?&gt;,\n    res: MutableList&lt;MutableList&lt;TreeNode?&gt;?&gt;\n) {\n    // 解かどうかを確認\n    if (isSolution(state)) {\n        // 解を記録\n        recordSolution(state, res)\n    }\n    // すべての選択肢を走査\n    for (choice in choices) {\n        // 枝刈り：選択が妥当かを確認する\n        if (isValid(state, choice)) {\n            // 試行: 選択を行い、状態を更新\n            makeChoice(state, choice)\n            // 次の選択へ進む\n            backtrack(state, mutableListOf(choice!!.left, choice.right), res)\n            // バックトラック：選択を取り消し、前の状態に戻す\n            undoChoice(state, choice)\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.rb<pre><code>### 現在の状態が解かどうかを判定 ###\ndef is_solution?(state)\n  !state.empty? &amp;&amp; state.last.val == 7\nend\n\n### 解を記録 ###\ndef record_solution(state, res)\n  res &lt;&lt; state.dup\nend\n\n### 現在の状態で、この選択が妥当かを判定 ###\ndef is_valid?(state, choice)\n  choice &amp;&amp; choice.val != 3\nend\n\n### 状態を更新 ###\ndef make_choice(state, choice)\n  state &lt;&lt; choice\nend\n\n### 状態を復元 ###\ndef undo_choice(state, choice)\n  state.pop\nend\n\n### バックトラッキング法：例題3 ###\ndef backtrack(state, choices, res)\n  # 解かどうかを確認\n  record_solution(state, res) if is_solution?(state)\n\n  # すべての選択肢を走査\n  for choice in choices\n    # 枝刈り：選択が妥当かを確認する\n    if is_valid?(state, choice)\n      # 試行: 選択を行い、状態を更新\n      make_choice(state, choice)\n      # 次の選択へ進む\n      backtrack(state, [choice.left, choice.right], res)\n      # バックトラック：選択を取り消し、前の状態に戻す\n      undo_choice(state, choice)\n    end\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>問題の条件より、値が \\(7\\) のノードを見つけた後も探索を続ける必要があります。そのため、解を記録した後の <code>return</code> 文は削除しなければなりません。次の図は、<code>return</code> 文を残す場合と削除する場合の探索過程を比較したものです。</p> <p></p> <p> 図 13-4   return を残す場合と削除する場合の探索過程の比較 </p> <p>前順走査にもとづく実装と比べると、バックトラッキングアルゴリズムのフレームワークにもとづく実装はやや冗長に見えますが、汎用性に優れています。実際、多くのバックトラッキング問題はこのフレームワークで解けます。具体的な問題に応じて <code>state</code> と <code>choices</code> を定義し、各メソッドを実装すれば十分です。</p>","path":["第 13 章 &nbsp; バックトラッキング","13.1 &nbsp; バックトラッキングアルゴリズム"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/#1314","level":2,"title":"13.1.4   よく使われる用語","text":"<p>アルゴリズム問題をより明確に分析するために、バックトラッキングでよく使われる用語の意味を整理し、例題3に対応する例を次の表にまとめます。</p> <p> 表 13-1   よく使われるバックトラッキング用語 </p> 用語 定義 例題3 解（solution） 問題の特定の条件を満たす答えであり、1 つまたは複数存在し得る 根ノードからノード \\(7\\) までの、制約条件を満たすすべての経路 制約条件（constraint） 解の実現可能性を制限する条件であり、通常は枝刈りに用いられる 経路にノード \\(3\\) を含まないこと 状態（state） ある時点における問題の状況を表し、すでに行った選択を含む 現在までに訪問したノードの経路、すなわち <code>path</code> ノードリスト 試行（attempt） 利用可能な選択肢にもとづいて解空間を探索する過程であり、選択、状態更新、解判定を含む 左右の子ノードを再帰的に訪問し、ノードを <code>path</code> に追加し、値が \\(7\\) か判定する 戻る（backtracking） 制約条件を満たさない状態に出会ったとき、それまでの選択を取り消して前の状態へ戻ること 葉ノードを越えたとき、ノード訪問を終えたとき、値が \\(3\\) のノードに出会ったときに探索を終了し、関数から戻る 枝刈り（pruning） 問題の性質や制約条件にもとづき、無意味な探索経路を避ける方法であり、探索効率を高める 値が \\(3\\) のノードに出会ったら、それ以上探索しない <p>Tip</p> <p>問題、解、状態などの概念は汎用的であり、分割統治、バックトラッキング、動的計画法、貪欲法などのアルゴリズムにも共通して現れます。</p>","path":["第 13 章 &nbsp; バックトラッキング","13.1 &nbsp; バックトラッキングアルゴリズム"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/#1315","level":2,"title":"13.1.5   利点と限界","text":"<p>バックトラッキングアルゴリズムの本質は深さ優先探索です。条件を満たす解を見つけるまで、あり得るすべての解を試します。この方法の利点は、考えられるすべての解を見つけられることであり、適切な枝刈りを行えば高い効率を発揮します。</p> <p>しかし、大規模または複雑な問題を扱う場合、バックトラッキングアルゴリズムの実行効率は受け入れがたいことがあります。</p> <ul> <li>時間：バックトラッキングアルゴリズムでは通常、状態空間のすべての可能性をたどる必要があり、時間計算量は指数時間や階乗時間に達することがあります。</li> <li>空間：再帰呼び出しの過程では現在の状態（たとえば経路や枝刈り用の補助変数など）を保持する必要があり、深さが大きいと空間使用量も大きくなります。</li> </ul> <p>それでもなお、バックトラッキングアルゴリズムは一部の探索問題や制約充足問題に対する最良の解法です。この種の問題では、どの選択が有効な解を生むかを事前に予測できないため、可能な選択肢をすべてたどる必要があります。このときの鍵は**いかに効率を最適化するか**であり、代表的な方法は 2 つあります。</p> <ul> <li>枝刈り：解が生じないことが確実な経路を探索しないことで、時間と空間を節約する。</li> <li>ヒューリスティック探索：探索中に何らかの戦略や推定値を導入し、有効な解を生みやすい経路を優先的に探索する。</li> </ul>","path":["第 13 章 &nbsp; バックトラッキング","13.1 &nbsp; バックトラッキングアルゴリズム"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/#1316","level":2,"title":"13.1.6   バックトラッキングの典型例題","text":"<p>バックトラッキングアルゴリズムは、多くの探索問題、制約充足問題、組合せ最適化問題の解決に利用できます。</p> <p>探索問題：この種の問題の目標は、特定の条件を満たす解を見つけることです。</p> <ul> <li>全順列問題：ある集合が与えられたとき、考えられるすべての順列を求める。</li> <li>部分和問題：ある集合と目標和が与えられたとき、和が目標値となるすべての部分集合を見つける。</li> <li>ハノイの塔問題：3 本の柱と大きさの異なる複数の円盤が与えられたとき、すべての円盤を 1 本の柱から別の柱へ移動する。ただし 1 回に 1 枚しか動かせず、大きい円盤を小さい円盤の上に置いてはならない。</li> </ul> <p>制約充足問題：この種の問題の目標は、すべての制約条件を満たす解を見つけることです。</p> <ul> <li>\\(n\\) クイーン問題：\\(n \\times n\\) の盤面に \\(n\\) 個のクイーンを配置し、互いに攻撃し合わないようにする。</li> <li>数独：\\(9 \\times 9\\) のグリッドに数字 \\(1\\) ~ \\(9\\) を入れ、各行・各列・各 \\(3 \\times 3\\) の小区画で数字が重複しないようにする。</li> <li>グラフ彩色問題：無向グラフが与えられたとき、隣接する頂点が同じ色にならないように、できるだけ少ない色で各頂点を彩色する。</li> </ul> <p>組合せ最適化問題：この種の問題の目標は、組合せ空間の中で条件を満たす最適解を見つけることです。</p> <ul> <li>0-1 ナップサック問題：複数の品物とナップサックが与えられ、各品物には価値と重さがある。ナップサック容量の範囲内で総価値が最大になるように品物を選ぶ。</li> <li>巡回セールスマン問題：グラフ内のある頂点から出発し、他のすべての頂点をちょうど 1 回ずつ訪れて出発点へ戻るときの最短経路を求める。</li> <li>最大クリーク問題：無向グラフが与えられたとき、任意の 2 頂点間に辺が存在する最大の完全部分グラフを見つける。</li> </ul> <p>多くの組合せ最適化問題では、バックトラッキングは最適な解法ではない点に注意してください。</p> <ul> <li>0-1 ナップサック問題は通常、より高い時間効率を得るために動的計画法で解く。</li> <li>巡回セールスマン問題は著名な NP-Hard 問題であり、よく用いられる解法には遺伝的アルゴリズムや蟻コロニー最適化などがある。</li> <li>最大クリーク問題はグラフ理論における古典的問題であり、貪欲法などのヒューリスティックで解ける。</li> </ul>","path":["第 13 章 &nbsp; バックトラッキング","13.1 &nbsp; バックトラッキングアルゴリズム"],"tags":[]},{"location":"chapter_backtracking/n_queens_problem/","level":1,"title":"13.4   n クイーン問題","text":"<p>Question</p> <p>チェスのルールによれば、クイーンは同じ行、同じ列、または同じ斜線上にある駒を攻撃できます。\\(n\\) 個のクイーンと \\(n \\times n\\) サイズの盤面が与えられたとき、すべてのクイーンが互いに攻撃し合わない配置を求めます。</p> <p>下図に示すように、\\(n = 4\\) のとき、2 つの解を見つけることができます。バックトラッキングの観点から見ると、\\(n \\times n\\) サイズの盤面には合計 \\(n^2\\) 個のマスがあり、これがすべての選択肢 <code>choices</code> を与えます。クイーンを 1 つずつ配置していく過程で、盤面の状態は絶えず変化し、その各時点の盤面が状態 <code>state</code> です。</p> <p></p> <p> 図 13-15   4 クイーン問題の解 </p> <p>下図は本問題の 3 つの制約条件を示しています。複数のクイーンは同じ行、同じ列、同じ対角線上に置けません。なお、対角線には主対角線 <code>\\</code> と副対角線 <code>/</code> の 2 種類があります。</p> <p></p> <p> 図 13-16   n クイーン問題の制約条件 </p>","path":["第 13 章 &nbsp; バックトラッキング","13.4 &nbsp; n クイーン問題"],"tags":[]},{"location":"chapter_backtracking/n_queens_problem/#1","level":3,"title":"1.   行ごとの配置戦略","text":"<p>クイーンの数と盤面の行数はいずれも \\(n\\) なので、次の推論を容易に得られます：盤面の各行にはクイーンを 1 つだけ配置できます。</p> <p>つまり、行ごとの配置戦略を採用できます：最初の行から始めて、各行に 1 つのクイーンを配置し、最後の行まで進みます。</p> <p>下図は 4 クイーン問題における行ごとの配置過程を示しています。図の大きさの都合上、下図では 1 行目における検索分岐の 1 つだけを展開し、列制約と対角線制約を満たさない案はすべて枝刈りしています。</p> <p></p> <p> 図 13-17   行ごとの配置戦略 </p> <p>本質的には、行ごとの配置戦略は枝刈りとして機能します。これにより、同じ行に複数のクイーンが現れるすべての探索分岐を回避できます。</p>","path":["第 13 章 &nbsp; バックトラッキング","13.4 &nbsp; n クイーン問題"],"tags":[]},{"location":"chapter_backtracking/n_queens_problem/#2","level":3,"title":"2.   列と対角線の枝刈り","text":"<p>列制約を満たすために、長さ \\(n\\) のブール配列 <code>cols</code> を用いて、各列にクイーンがあるかどうかを記録できます。配置を決めるたびに、<code>cols</code> を使って既存のクイーンがある列を枝刈りし、バックトラッキングの中で <code>cols</code> の状態を動的に更新します。</p> <p>Tip</p> <p>注意として、行列の原点は左上にあり、行インデックスは上から下へ、列インデックスは左から右へ増加します。</p> <p>では、対角線制約はどのように扱えばよいのでしょうか。盤面上のあるマスの行列インデックスを \\((row, col)\\) とし、行列内のある主対角線を選ぶと、その対角線上のすべてのマスで行インデックスから列インデックスを引いた値が等しいことが分かります。つまり、主対角線上のすべてのマスでは \\(row - col\\) が一定値になります。</p> <p>つまり、2 つのマスが \\(row_1 - col_1 = row_2 - col_2\\) を満たすなら、それらは必ず同じ主対角線上にあります。この性質を利用して、下図の配列 <code>diags1</code> により、各主対角線にクイーンがあるかどうかを記録できます。</p> <p>同様に、副対角線上のすべてのマスでは \\(row + col\\) が一定値です。副対角線制約も配列 <code>diags2</code> を使って処理できます。</p> <p></p> <p> 図 13-18   列制約と対角線制約の処理 </p>","path":["第 13 章 &nbsp; バックトラッキング","13.4 &nbsp; n クイーン問題"],"tags":[]},{"location":"chapter_backtracking/n_queens_problem/#3","level":3,"title":"3.   コード実装","text":"<p>注意として、\\(n\\) 次正方行列では \\(row - col\\) の範囲は \\([-n + 1, n - 1]\\) 、\\(row + col\\) の範囲は \\([0, 2n - 2]\\) です。したがって、主対角線と副対角線の本数はいずれも \\(2n - 1\\) であり、配列 <code>diags1</code> と <code>diags2</code> の長さもともに \\(2n - 1\\) です。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby n_queens.py<pre><code>def backtrack(\n    row: int,\n    n: int,\n    state: list[list[str]],\n    res: list[list[list[str]]],\n    cols: list[bool],\n    diags1: list[bool],\n    diags2: list[bool],\n):\n    \"\"\"バックトラッキング：N クイーン\"\"\"\n    # すべての行への配置が完了したら、解を記録する\n    if row == n:\n        res.append([list(row) for row in state])\n        return\n    # すべての列を走査\n    for col in range(n):\n        # このマスに対応する主対角線と副対角線を計算\n        diag1 = row - col + n - 1\n        diag2 = row + col\n        # 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない\n        if not cols[col] and not diags1[diag1] and not diags2[diag2]:\n            # 試行：そのマスにクイーンを置く\n            state[row][col] = \"Q\"\n            cols[col] = diags1[diag1] = diags2[diag2] = True\n            # 次の行に配置する\n            backtrack(row + 1, n, state, res, cols, diags1, diags2)\n            # 戻す：そのマスを空きマスに戻す\n            state[row][col] = \"#\"\n            cols[col] = diags1[diag1] = diags2[diag2] = False\n\ndef n_queens(n: int) -&gt; list[list[list[str]]]:\n    \"\"\"N クイーンを解く\"\"\"\n    # n*n の盤面を初期化する。'Q' はクイーン、'#' は空きマスを表す\n    state = [[\"#\" for _ in range(n)] for _ in range(n)]\n    cols = [False] * n  # 列にクイーンがあるか記録\n    diags1 = [False] * (2 * n - 1)  # 主対角線にクイーンがあるかを記録\n    diags2 = [False] * (2 * n - 1)  # 副対角線にクイーンがあるかを記録\n    res = []\n    backtrack(0, n, state, res, cols, diags1, diags2)\n\n    return res\n</code></pre> n_queens.cpp<pre><code>/* バックトラッキング：N クイーン */\nvoid backtrack(int row, int n, vector&lt;vector&lt;string&gt;&gt; &amp;state, vector&lt;vector&lt;vector&lt;string&gt;&gt;&gt; &amp;res, vector&lt;bool&gt; &amp;cols,\n               vector&lt;bool&gt; &amp;diags1, vector&lt;bool&gt; &amp;diags2) {\n    // すべての行への配置が完了したら、解を記録する\n    if (row == n) {\n        res.push_back(state);\n        return;\n    }\n    // すべての列を走査\n    for (int col = 0; col &lt; n; col++) {\n        // このマスに対応する主対角線と副対角線を計算\n        int diag1 = row - col + n - 1;\n        int diag2 = row + col;\n        // 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない\n        if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n            // 試行：そのマスにクイーンを置く\n            state[row][col] = \"Q\";\n            cols[col] = diags1[diag1] = diags2[diag2] = true;\n            // 次の行に配置する\n            backtrack(row + 1, n, state, res, cols, diags1, diags2);\n            // 戻す：そのマスを空きマスに戻す\n            state[row][col] = \"#\";\n            cols[col] = diags1[diag1] = diags2[diag2] = false;\n        }\n    }\n}\n\n/* N クイーンを解く */\nvector&lt;vector&lt;vector&lt;string&gt;&gt;&gt; nQueens(int n) {\n    // n*n の盤面を初期化する。'Q' はクイーン、'#' は空きマスを表す\n    vector&lt;vector&lt;string&gt;&gt; state(n, vector&lt;string&gt;(n, \"#\"));\n    vector&lt;bool&gt; cols(n, false);           // 列にクイーンがあるか記録\n    vector&lt;bool&gt; diags1(2 * n - 1, false); // 主対角線にクイーンがあるかを記録\n    vector&lt;bool&gt; diags2(2 * n - 1, false); // 副対角線にクイーンがあるかを記録\n    vector&lt;vector&lt;vector&lt;string&gt;&gt;&gt; res;\n\n    backtrack(0, n, state, res, cols, diags1, diags2);\n\n    return res;\n}\n</code></pre> n_queens.java<pre><code>/* バックトラッキング：N クイーン */\nvoid backtrack(int row, int n, List&lt;List&lt;String&gt;&gt; state, List&lt;List&lt;List&lt;String&gt;&gt;&gt; res,\n        boolean[] cols, boolean[] diags1, boolean[] diags2) {\n    // すべての行への配置が完了したら、解を記録する\n    if (row == n) {\n        List&lt;List&lt;String&gt;&gt; copyState = new ArrayList&lt;&gt;();\n        for (List&lt;String&gt; sRow : state) {\n            copyState.add(new ArrayList&lt;&gt;(sRow));\n        }\n        res.add(copyState);\n        return;\n    }\n    // すべての列を走査\n    for (int col = 0; col &lt; n; col++) {\n        // このマスに対応する主対角線と副対角線を計算\n        int diag1 = row - col + n - 1;\n        int diag2 = row + col;\n        // 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない\n        if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n            // 試行：そのマスにクイーンを置く\n            state.get(row).set(col, \"Q\");\n            cols[col] = diags1[diag1] = diags2[diag2] = true;\n            // 次の行に配置する\n            backtrack(row + 1, n, state, res, cols, diags1, diags2);\n            // 戻す：そのマスを空きマスに戻す\n            state.get(row).set(col, \"#\");\n            cols[col] = diags1[diag1] = diags2[diag2] = false;\n        }\n    }\n}\n\n/* N クイーンを解く */\nList&lt;List&lt;List&lt;String&gt;&gt;&gt; nQueens(int n) {\n    // n*n の盤面を初期化する。'Q' はクイーン、'#' は空きマスを表す\n    List&lt;List&lt;String&gt;&gt; state = new ArrayList&lt;&gt;();\n    for (int i = 0; i &lt; n; i++) {\n        List&lt;String&gt; row = new ArrayList&lt;&gt;();\n        for (int j = 0; j &lt; n; j++) {\n            row.add(\"#\");\n        }\n        state.add(row);\n    }\n    boolean[] cols = new boolean[n]; // 列にクイーンがあるか記録\n    boolean[] diags1 = new boolean[2 * n - 1]; // 主対角線にクイーンがあるかを記録\n    boolean[] diags2 = new boolean[2 * n - 1]; // 副対角線にクイーンがあるかを記録\n    List&lt;List&lt;List&lt;String&gt;&gt;&gt; res = new ArrayList&lt;&gt;();\n\n    backtrack(0, n, state, res, cols, diags1, diags2);\n\n    return res;\n}\n</code></pre> n_queens.cs<pre><code>/* バックトラッキング：N クイーン */\nvoid Backtrack(int row, int n, List&lt;List&lt;string&gt;&gt; state, List&lt;List&lt;List&lt;string&gt;&gt;&gt; res,\n        bool[] cols, bool[] diags1, bool[] diags2) {\n    // すべての行への配置が完了したら、解を記録する\n    if (row == n) {\n        List&lt;List&lt;string&gt;&gt; copyState = [];\n        foreach (List&lt;string&gt; sRow in state) {\n            copyState.Add(new List&lt;string&gt;(sRow));\n        }\n        res.Add(copyState);\n        return;\n    }\n    // すべての列を走査\n    for (int col = 0; col &lt; n; col++) {\n        // このマスに対応する主対角線と副対角線を計算\n        int diag1 = row - col + n - 1;\n        int diag2 = row + col;\n        // 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない\n        if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n            // 試行：そのマスにクイーンを置く\n            state[row][col] = \"Q\";\n            cols[col] = diags1[diag1] = diags2[diag2] = true;\n            // 次の行に配置する\n            Backtrack(row + 1, n, state, res, cols, diags1, diags2);\n            // 戻す：そのマスを空きマスに戻す\n            state[row][col] = \"#\";\n            cols[col] = diags1[diag1] = diags2[diag2] = false;\n        }\n    }\n}\n\n/* N クイーンを解く */\nList&lt;List&lt;List&lt;string&gt;&gt;&gt; NQueens(int n) {\n    // n*n の盤面を初期化する。'Q' はクイーン、'#' は空きマスを表す\n    List&lt;List&lt;string&gt;&gt; state = [];\n    for (int i = 0; i &lt; n; i++) {\n        List&lt;string&gt; row = [];\n        for (int j = 0; j &lt; n; j++) {\n            row.Add(\"#\");\n        }\n        state.Add(row);\n    }\n    bool[] cols = new bool[n]; // 列にクイーンがあるか記録\n    bool[] diags1 = new bool[2 * n - 1]; // 主対角線にクイーンがあるかを記録\n    bool[] diags2 = new bool[2 * n - 1]; // 副対角線にクイーンがあるかを記録\n    List&lt;List&lt;List&lt;string&gt;&gt;&gt; res = [];\n\n    Backtrack(0, n, state, res, cols, diags1, diags2);\n\n    return res;\n}\n</code></pre> n_queens.go<pre><code>/* バックトラッキング：N クイーン */\nfunc backtrack(row, n int, state *[][]string, res *[][][]string, cols, diags1, diags2 *[]bool) {\n    // すべての行への配置が完了したら、解を記録する\n    if row == n {\n        newState := make([][]string, len(*state))\n        for i, _ := range newState {\n            newState[i] = make([]string, len((*state)[0]))\n            copy(newState[i], (*state)[i])\n\n        }\n        *res = append(*res, newState)\n        return\n    }\n    // すべての列を走査\n    for col := 0; col &lt; n; col++ {\n        // このマスに対応する主対角線と副対角線を計算\n        diag1 := row - col + n - 1\n        diag2 := row + col\n        // 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない\n        if !(*cols)[col] &amp;&amp; !(*diags1)[diag1] &amp;&amp; !(*diags2)[diag2] {\n            // 試行：そのマスにクイーンを置く\n            (*state)[row][col] = \"Q\"\n            (*cols)[col], (*diags1)[diag1], (*diags2)[diag2] = true, true, true\n            // 次の行に配置する\n            backtrack(row+1, n, state, res, cols, diags1, diags2)\n            // 戻す：そのマスを空きマスに戻す\n            (*state)[row][col] = \"#\"\n            (*cols)[col], (*diags1)[diag1], (*diags2)[diag2] = false, false, false\n        }\n    }\n}\n\n/* N クイーンを解く */\nfunc nQueens(n int) [][][]string {\n    // n*n の盤面を初期化する。'Q' はクイーン、'#' は空きマスを表す\n    state := make([][]string, n)\n    for i := 0; i &lt; n; i++ {\n        row := make([]string, n)\n        for i := 0; i &lt; n; i++ {\n            row[i] = \"#\"\n        }\n        state[i] = row\n    }\n    // 列にクイーンがあるか記録\n    cols := make([]bool, n)\n    diags1 := make([]bool, 2*n-1)\n    diags2 := make([]bool, 2*n-1)\n    res := make([][][]string, 0)\n    backtrack(0, n, &amp;state, &amp;res, &amp;cols, &amp;diags1, &amp;diags2)\n    return res\n}\n</code></pre> n_queens.swift<pre><code>/* バックトラッキング：N クイーン */\nfunc backtrack(row: Int, n: Int, state: inout [[String]], res: inout [[[String]]], cols: inout [Bool], diags1: inout [Bool], diags2: inout [Bool]) {\n    // すべての行への配置が完了したら、解を記録する\n    if row == n {\n        res.append(state)\n        return\n    }\n    // すべての列を走査\n    for col in 0 ..&lt; n {\n        // このマスに対応する主対角線と副対角線を計算\n        let diag1 = row - col + n - 1\n        let diag2 = row + col\n        // 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない\n        if !cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2] {\n            // 試行：そのマスにクイーンを置く\n            state[row][col] = \"Q\"\n            cols[col] = true\n            diags1[diag1] = true\n            diags2[diag2] = true\n            // 次の行に配置する\n            backtrack(row: row + 1, n: n, state: &amp;state, res: &amp;res, cols: &amp;cols, diags1: &amp;diags1, diags2: &amp;diags2)\n            // 戻す：そのマスを空きマスに戻す\n            state[row][col] = \"#\"\n            cols[col] = false\n            diags1[diag1] = false\n            diags2[diag2] = false\n        }\n    }\n}\n\n/* N クイーンを解く */\nfunc nQueens(n: Int) -&gt; [[[String]]] {\n    // n*n の盤面を初期化する。'Q' はクイーン、'#' は空きマスを表す\n    var state = Array(repeating: Array(repeating: \"#\", count: n), count: n)\n    var cols = Array(repeating: false, count: n) // 列にクイーンがあるか記録\n    var diags1 = Array(repeating: false, count: 2 * n - 1) // 主対角線にクイーンがあるかを記録\n    var diags2 = Array(repeating: false, count: 2 * n - 1) // 副対角線にクイーンがあるかを記録\n    var res: [[[String]]] = []\n\n    backtrack(row: 0, n: n, state: &amp;state, res: &amp;res, cols: &amp;cols, diags1: &amp;diags1, diags2: &amp;diags2)\n\n    return res\n}\n</code></pre> n_queens.js<pre><code>/* バックトラッキング：N クイーン */\nfunction backtrack(row, n, state, res, cols, diags1, diags2) {\n    // すべての行への配置が完了したら、解を記録する\n    if (row === n) {\n        res.push(state.map((row) =&gt; row.slice()));\n        return;\n    }\n    // すべての列を走査\n    for (let col = 0; col &lt; n; col++) {\n        // このマスに対応する主対角線と副対角線を計算\n        const diag1 = row - col + n - 1;\n        const diag2 = row + col;\n        // 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない\n        if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n            // 試行：そのマスにクイーンを置く\n            state[row][col] = 'Q';\n            cols[col] = diags1[diag1] = diags2[diag2] = true;\n            // 次の行に配置する\n            backtrack(row + 1, n, state, res, cols, diags1, diags2);\n            // 戻す：そのマスを空きマスに戻す\n            state[row][col] = '#';\n            cols[col] = diags1[diag1] = diags2[diag2] = false;\n        }\n    }\n}\n\n/* N クイーンを解く */\nfunction nQueens(n) {\n    // n*n の盤面を初期化する。'Q' はクイーン、'#' は空きマスを表す\n    const state = Array.from({ length: n }, () =&gt; Array(n).fill('#'));\n    const cols = Array(n).fill(false); // 列にクイーンがあるか記録\n    const diags1 = Array(2 * n - 1).fill(false); // 主対角線にクイーンがあるかを記録\n    const diags2 = Array(2 * n - 1).fill(false); // 副対角線にクイーンがあるかを記録\n    const res = [];\n\n    backtrack(0, n, state, res, cols, diags1, diags2);\n    return res;\n}\n</code></pre> n_queens.ts<pre><code>/* バックトラッキング：N クイーン */\nfunction backtrack(\n    row: number,\n    n: number,\n    state: string[][],\n    res: string[][][],\n    cols: boolean[],\n    diags1: boolean[],\n    diags2: boolean[]\n): void {\n    // すべての行への配置が完了したら、解を記録する\n    if (row === n) {\n        res.push(state.map((row) =&gt; row.slice()));\n        return;\n    }\n    // すべての列を走査\n    for (let col = 0; col &lt; n; col++) {\n        // このマスに対応する主対角線と副対角線を計算\n        const diag1 = row - col + n - 1;\n        const diag2 = row + col;\n        // 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない\n        if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n            // 試行：そのマスにクイーンを置く\n            state[row][col] = 'Q';\n            cols[col] = diags1[diag1] = diags2[diag2] = true;\n            // 次の行に配置する\n            backtrack(row + 1, n, state, res, cols, diags1, diags2);\n            // 戻す：そのマスを空きマスに戻す\n            state[row][col] = '#';\n            cols[col] = diags1[diag1] = diags2[diag2] = false;\n        }\n    }\n}\n\n/* N クイーンを解く */\nfunction nQueens(n: number): string[][][] {\n    // n*n の盤面を初期化する。'Q' はクイーン、'#' は空きマスを表す\n    const state = Array.from({ length: n }, () =&gt; Array(n).fill('#'));\n    const cols = Array(n).fill(false); // 列にクイーンがあるか記録\n    const diags1 = Array(2 * n - 1).fill(false); // 主対角線にクイーンがあるかを記録\n    const diags2 = Array(2 * n - 1).fill(false); // 副対角線にクイーンがあるかを記録\n    const res: string[][][] = [];\n\n    backtrack(0, n, state, res, cols, diags1, diags2);\n    return res;\n}\n</code></pre> n_queens.dart<pre><code>/* バックトラッキング：N クイーン */\nvoid backtrack(\n  int row,\n  int n,\n  List&lt;List&lt;String&gt;&gt; state,\n  List&lt;List&lt;List&lt;String&gt;&gt;&gt; res,\n  List&lt;bool&gt; cols,\n  List&lt;bool&gt; diags1,\n  List&lt;bool&gt; diags2,\n) {\n  // すべての行への配置が完了したら、解を記録する\n  if (row == n) {\n    List&lt;List&lt;String&gt;&gt; copyState = [];\n    for (List&lt;String&gt; sRow in state) {\n      copyState.add(List.from(sRow));\n    }\n    res.add(copyState);\n    return;\n  }\n  // すべての列を走査\n  for (int col = 0; col &lt; n; col++) {\n    // このマスに対応する主対角線と副対角線を計算\n    int diag1 = row - col + n - 1;\n    int diag2 = row + col;\n    // 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない\n    if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n      // 試行：そのマスにクイーンを置く\n      state[row][col] = \"Q\";\n      cols[col] = true;\n      diags1[diag1] = true;\n      diags2[diag2] = true;\n      // 次の行に配置する\n      backtrack(row + 1, n, state, res, cols, diags1, diags2);\n      // 戻す：そのマスを空きマスに戻す\n      state[row][col] = \"#\";\n      cols[col] = false;\n      diags1[diag1] = false;\n      diags2[diag2] = false;\n    }\n  }\n}\n\n/* N クイーンを解く */\nList&lt;List&lt;List&lt;String&gt;&gt;&gt; nQueens(int n) {\n  // n*n の盤面を初期化する。'Q' はクイーン、'#' は空きマスを表す\n  List&lt;List&lt;String&gt;&gt; state = List.generate(n, (index) =&gt; List.filled(n, \"#\"));\n  List&lt;bool&gt; cols = List.filled(n, false); // 列にクイーンがあるか記録\n  List&lt;bool&gt; diags1 = List.filled(2 * n - 1, false); // 主対角線にクイーンがあるかを記録\n  List&lt;bool&gt; diags2 = List.filled(2 * n - 1, false); // 副対角線にクイーンがあるかを記録\n  List&lt;List&lt;List&lt;String&gt;&gt;&gt; res = [];\n\n  backtrack(0, n, state, res, cols, diags1, diags2);\n\n  return res;\n}\n</code></pre> n_queens.rs<pre><code>/* バックトラッキング：N クイーン */\nfn backtrack(\n    row: usize,\n    n: usize,\n    state: &amp;mut Vec&lt;Vec&lt;String&gt;&gt;,\n    res: &amp;mut Vec&lt;Vec&lt;Vec&lt;String&gt;&gt;&gt;,\n    cols: &amp;mut [bool],\n    diags1: &amp;mut [bool],\n    diags2: &amp;mut [bool],\n) {\n    // すべての行への配置が完了したら、解を記録する\n    if row == n {\n        res.push(state.clone());\n        return;\n    }\n    // すべての列を走査\n    for col in 0..n {\n        // このマスに対応する主対角線と副対角線を計算\n        let diag1 = row + n - 1 - col;\n        let diag2 = row + col;\n        // 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない\n        if !cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2] {\n            // 試行：そのマスにクイーンを置く\n            state[row][col] = \"Q\".into();\n            (cols[col], diags1[diag1], diags2[diag2]) = (true, true, true);\n            // 次の行に配置する\n            backtrack(row + 1, n, state, res, cols, diags1, diags2);\n            // 戻す：そのマスを空きマスに戻す\n            state[row][col] = \"#\".into();\n            (cols[col], diags1[diag1], diags2[diag2]) = (false, false, false);\n        }\n    }\n}\n\n/* N クイーンを解く */\nfn n_queens(n: usize) -&gt; Vec&lt;Vec&lt;Vec&lt;String&gt;&gt;&gt; {\n    // n*n の盤面を初期化する。'Q' はクイーン、'#' は空きマスを表す\n    let mut state: Vec&lt;Vec&lt;String&gt;&gt; = vec![vec![\"#\".to_string(); n]; n];\n    let mut cols = vec![false; n]; // 列にクイーンがあるか記録\n    let mut diags1 = vec![false; 2 * n - 1]; // 主対角線にクイーンがあるかを記録\n    let mut diags2 = vec![false; 2 * n - 1]; // 副対角線にクイーンがあるかを記録\n    let mut res: Vec&lt;Vec&lt;Vec&lt;String&gt;&gt;&gt; = Vec::new();\n\n    backtrack(\n        0,\n        n,\n        &amp;mut state,\n        &amp;mut res,\n        &amp;mut cols,\n        &amp;mut diags1,\n        &amp;mut diags2,\n    );\n\n    res\n}\n</code></pre> n_queens.c<pre><code>/* バックトラッキング：N クイーン */\nvoid backtrack(int row, int n, char state[MAX_SIZE][MAX_SIZE], char ***res, int *resSize, bool cols[MAX_SIZE],\n               bool diags1[2 * MAX_SIZE - 1], bool diags2[2 * MAX_SIZE - 1]) {\n    // すべての行への配置が完了したら、解を記録する\n    if (row == n) {\n        res[*resSize] = (char **)malloc(sizeof(char *) * n);\n        for (int i = 0; i &lt; n; ++i) {\n            res[*resSize][i] = (char *)malloc(sizeof(char) * (n + 1));\n            strcpy(res[*resSize][i], state[i]);\n        }\n        (*resSize)++;\n        return;\n    }\n    // すべての列を走査\n    for (int col = 0; col &lt; n; col++) {\n        // このマスに対応する主対角線と副対角線を計算\n        int diag1 = row - col + n - 1;\n        int diag2 = row + col;\n        // 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない\n        if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n            // 試行：そのマスにクイーンを置く\n            state[row][col] = 'Q';\n            cols[col] = diags1[diag1] = diags2[diag2] = true;\n            // 次の行に配置する\n            backtrack(row + 1, n, state, res, resSize, cols, diags1, diags2);\n            // 戻す：そのマスを空きマスに戻す\n            state[row][col] = '#';\n            cols[col] = diags1[diag1] = diags2[diag2] = false;\n        }\n    }\n}\n\n/* N クイーンを解く */\nchar ***nQueens(int n, int *returnSize) {\n    char state[MAX_SIZE][MAX_SIZE];\n    // n*n の盤面を初期化する。'Q' はクイーン、'#' は空きマスを表す\n    for (int i = 0; i &lt; n; ++i) {\n        for (int j = 0; j &lt; n; ++j) {\n            state[i][j] = '#';\n        }\n        state[i][n] = '\\0';\n    }\n    bool cols[MAX_SIZE] = {false};           // 列にクイーンがあるか記録\n    bool diags1[2 * MAX_SIZE - 1] = {false}; // 主対角線にクイーンがあるかを記録\n    bool diags2[2 * MAX_SIZE - 1] = {false}; // 副対角線にクイーンがあるかを記録\n\n    char ***res = (char ***)malloc(sizeof(char **) * MAX_SIZE);\n    *returnSize = 0;\n    backtrack(0, n, state, res, returnSize, cols, diags1, diags2);\n    return res;\n}\n</code></pre> n_queens.kt<pre><code>/* バックトラッキング：N クイーン */\nfun backtrack(\n    row: Int,\n    n: Int,\n    state: MutableList&lt;MutableList&lt;String&gt;&gt;,\n    res: MutableList&lt;MutableList&lt;MutableList&lt;String&gt;&gt;?&gt;,\n    cols: BooleanArray,\n    diags1: BooleanArray,\n    diags2: BooleanArray\n) {\n    // すべての行への配置が完了したら、解を記録する\n    if (row == n) {\n        val copyState = mutableListOf&lt;MutableList&lt;String&gt;&gt;()\n        for (sRow in state) {\n            copyState.add(sRow.toMutableList())\n        }\n        res.add(copyState)\n        return\n    }\n    // すべての列を走査\n    for (col in 0..&lt;n) {\n        // このマスに対応する主対角線と副対角線を計算\n        val diag1 = row - col + n - 1\n        val diag2 = row + col\n        // 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない\n        if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n            // 試行：そのマスにクイーンを置く\n            state[row][col] = \"Q\"\n            diags2[diag2] = true\n            diags1[diag1] = diags2[diag2]\n            cols[col] = diags1[diag1]\n            // 次の行に配置する\n            backtrack(row + 1, n, state, res, cols, diags1, diags2)\n            // 戻す：そのマスを空きマスに戻す\n            state[row][col] = \"#\"\n            diags2[diag2] = false\n            diags1[diag1] = diags2[diag2]\n            cols[col] = diags1[diag1]\n        }\n    }\n}\n\n/* N クイーンを解く */\nfun nQueens(n: Int): MutableList&lt;MutableList&lt;MutableList&lt;String&gt;&gt;?&gt; {\n    // n*n の盤面を初期化する。'Q' はクイーン、'#' は空きマスを表す\n    val state = mutableListOf&lt;MutableList&lt;String&gt;&gt;()\n    for (i in 0..&lt;n) {\n        val row = mutableListOf&lt;String&gt;()\n        for (j in 0..&lt;n) {\n            row.add(\"#\")\n        }\n        state.add(row)\n    }\n    val cols = BooleanArray(n) // 列にクイーンがあるか記録\n    val diags1 = BooleanArray(2 * n - 1) // 主対角線にクイーンがあるかを記録\n    val diags2 = BooleanArray(2 * n - 1) // 副対角線にクイーンがあるかを記録\n    val res = mutableListOf&lt;MutableList&lt;MutableList&lt;String&gt;&gt;?&gt;()\n\n    backtrack(0, n, state, res, cols, diags1, diags2)\n\n    return res\n}\n</code></pre> n_queens.rb<pre><code>### バックトラッキング法：Nクイーン ###\ndef backtrack(row, n, state, res, cols, diags1, diags2)\n  # すべての行への配置が完了したら、解を記録する\n  if row == n\n    res &lt;&lt; state.map { |row| row.dup }\n    return\n  end\n\n  # すべての列を走査\n  for col in 0...n\n    # このマスに対応する主対角線と副対角線を計算\n    diag1 = row - col + n - 1\n    diag2 = row + col\n    # 枝刈り：そのマスの列、主対角線、副対角線にクイーンがあってはならない\n    if !cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]\n      # 試行：そのマスにクイーンを置く\n      state[row][col] = \"Q\"\n      cols[col] = diags1[diag1] = diags2[diag2] = true\n      # 次の行に配置する\n      backtrack(row + 1, n, state, res, cols, diags1, diags2)\n      # 戻す：そのマスを空きマスに戻す\n      state[row][col] = \"#\"\n      cols[col] = diags1[diag1] = diags2[diag2] = false\n    end\n  end\nend\n\n### Nクイーンを解く ###\ndef n_queens(n)\n  # n*n の盤面を初期化する。'Q' はクイーン、'#' は空きマスを表す\n  state = Array.new(n) { Array.new(n, \"#\") }\n  cols = Array.new(n, false) # 列にクイーンがあるか記録\n  diags1 = Array.new(2 * n - 1, false) # 主対角線にクイーンがあるかを記録\n  diags2 = Array.new(2 * n - 1, false) # 副対角線にクイーンがあるかを記録\n  res = []\n  backtrack(0, n, state, res, cols, diags1, diags2)\n\n  res\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>行ごとに \\(n\\) 回配置し、列制約を考慮すると、1 行目から最終行までの選択肢はそれぞれ \\(n\\)、\\(n-1\\)、\\(\\dots\\)、\\(2\\)、\\(1\\) 個となるため、時間計算量は \\(O(n!)\\) です。解を記録する際には、行列 <code>state</code> をコピーして <code>res</code> に追加する必要があり、このコピー操作には \\(O(n^2)\\) 時間を要します。したがって、全体の時間計算量は \\(O(n! \\cdot n^2)\\) です。実際には、対角線制約による枝刈りも探索空間を大きく縮小できるため、探索効率はしばしば上記の時間計算量より良くなります。</p> <p>配列 <code>state</code> は \\(O(n^2)\\) の空間を使用し、配列 <code>cols</code>、<code>diags1</code>、<code>diags2</code> はいずれも \\(O(n)\\) の空間を使用します。最大再帰深さは \\(n\\) で、スタックフレーム空間として \\(O(n)\\) を使用します。したがって、空間計算量は \\(O(n^2)\\) です。</p>","path":["第 13 章 &nbsp; バックトラッキング","13.4 &nbsp; n クイーン問題"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/","level":1,"title":"13.2   全順列問題","text":"<p>全順列問題はバックトラッキングアルゴリズムの典型的な応用例です。これは、ある集合（配列や文字列など）が与えられたとき、その要素のあり得るすべての順列を求める問題です。</p> <p>下表に、入力配列とそれに対応するすべての順列から成る例をいくつか示します。</p> <p> 表 13-2   全順列の例 </p> 入力配列 すべての順列 \\([1]\\) \\([1]\\) \\([1, 2]\\) \\([1, 2], [2, 1]\\) \\([1, 2, 3]\\) \\([1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]\\)","path":["第 13 章 &nbsp; バックトラッキング","13.2 &nbsp; 全順列問題"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#1321","level":2,"title":"13.2.1   等しい要素がない場合","text":"<p>Question</p> <p>重複要素を含まない整数配列を入力として受け取り、あり得るすべての順列を返します。</p> <p>バックトラッキングアルゴリズムの観点から見ると、順列生成の過程は一連の選択の結果として捉えられます。入力配列が \\([1, 2, 3]\\) だとすると、最初に \\(1\\) を選び、次に \\(3\\) を選び、最後に \\(2\\) を選べば、順列 \\([1, 3, 2]\\) が得られます。戻る操作は 1 つの選択を取り消し、その後で別の選択を試し続けることを表します。</p> <p>バックトラッキングコードの観点では、候補集合 <code>choices</code> は入力配列中のすべての要素であり、状態 <code>state</code> は現時点までに選ばれた要素です。各要素は 1 回しか選べないことに注意してください。したがって <code>state</code> 内の要素はすべて一意でなければなりません。</p> <p>下図のように、探索過程は再帰木として展開できます。木の各ノードは現在の状態 <code>state</code> を表します。根ノードから始めて 3 ラウンドの選択を経て葉ノードに到達し、各葉ノードが 1 つの順列に対応します。</p> <p></p> <p> 図 13-5   全順列の再帰木 </p>","path":["第 13 章 &nbsp; バックトラッキング","13.2 &nbsp; 全順列問題"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#1","level":3,"title":"1.   重複選択の枝刈り","text":"<p>各要素が 1 回しか選ばれないようにするため、ブール配列 <code>selected</code> の導入を考えます。ここで <code>selected[i]</code> は <code>choices[i]</code> がすでに選ばれているかどうかを表し、これに基づいて次の枝刈りを行います。</p> <ul> <li>選択 <code>choice[i]</code> を行った後、<code>selected[i]</code> を \\(\\text{True}\\) に設定し、その要素が選択済みであることを表します。</li> <li>選択肢リスト <code>choices</code> を走査するとき、すでに選ばれたノードはすべてスキップします。これが枝刈りです。</li> </ul> <p>下図のように、1 回目に 1、2 回目に 3、3 回目に 2 を選ぶとします。このとき 2 回目では要素 1 の分岐を、3 回目では要素 1 と要素 3 の分岐を刈り取る必要があります。</p> <p></p> <p> 図 13-6   全順列の枝刈り例 </p> <p>上図から、この枝刈りにより探索空間の大きさは \\(O(n^n)\\) から \\(O(n!)\\) へ削減されることがわかります。</p>","path":["第 13 章 &nbsp; バックトラッキング","13.2 &nbsp; 全順列問題"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#2","level":3,"title":"2.   コード実装","text":"<p>以上を整理できれば、フレームワークコードの「穴埋め」を行えます。全体のコードを短くするため、フレームワークコード中の各関数を個別には実装せず、これらを <code>backtrack()</code> 関数内に展開します。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby permutations_i.py<pre><code>def backtrack(\n    state: list[int], choices: list[int], selected: list[bool], res: list[list[int]]\n):\n    \"\"\"バックトラッキング：順列 I\"\"\"\n    # 状態の長さが要素数に等しければ、解を記録\n    if len(state) == len(choices):\n        res.append(list(state))\n        return\n    # すべての選択肢を走査\n    for i, choice in enumerate(choices):\n        # 枝刈り：要素の重複選択を許可しない\n        if not selected[i]:\n            # 試行: 選択を行い、状態を更新\n            selected[i] = True\n            state.append(choice)\n            # 次の選択へ進む\n            backtrack(state, choices, selected, res)\n            # バックトラック：選択を取り消し、前の状態に戻す\n            selected[i] = False\n            state.pop()\n\ndef permutations_i(nums: list[int]) -&gt; list[list[int]]:\n    \"\"\"全順列 I\"\"\"\n    res = []\n    backtrack(state=[], choices=nums, selected=[False] * len(nums), res=res)\n    return res\n</code></pre> permutations_i.cpp<pre><code>/* バックトラッキング：順列 I */\nvoid backtrack(vector&lt;int&gt; &amp;state, const vector&lt;int&gt; &amp;choices, vector&lt;bool&gt; &amp;selected, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n    // 状態の長さが要素数に等しければ、解を記録\n    if (state.size() == choices.size()) {\n        res.push_back(state);\n        return;\n    }\n    // すべての選択肢を走査\n    for (int i = 0; i &lt; choices.size(); i++) {\n        int choice = choices[i];\n        // 枝刈り：要素の重複選択を許可しない\n        if (!selected[i]) {\n            // 試行: 選択を行い、状態を更新\n            selected[i] = true;\n            state.push_back(choice);\n            // 次の選択へ進む\n            backtrack(state, choices, selected, res);\n            // バックトラック：選択を取り消し、前の状態に戻す\n            selected[i] = false;\n            state.pop_back();\n        }\n    }\n}\n\n/* 全順列 I */\nvector&lt;vector&lt;int&gt;&gt; permutationsI(vector&lt;int&gt; nums) {\n    vector&lt;int&gt; state;\n    vector&lt;bool&gt; selected(nums.size(), false);\n    vector&lt;vector&lt;int&gt;&gt; res;\n    backtrack(state, nums, selected, res);\n    return res;\n}\n</code></pre> permutations_i.java<pre><code>/* バックトラッキング：順列 I */\nvoid backtrack(List&lt;Integer&gt; state, int[] choices, boolean[] selected, List&lt;List&lt;Integer&gt;&gt; res) {\n    // 状態の長さが要素数に等しければ、解を記録\n    if (state.size() == choices.length) {\n        res.add(new ArrayList&lt;Integer&gt;(state));\n        return;\n    }\n    // すべての選択肢を走査\n    for (int i = 0; i &lt; choices.length; i++) {\n        int choice = choices[i];\n        // 枝刈り：要素の重複選択を許可しない\n        if (!selected[i]) {\n            // 試行: 選択を行い、状態を更新\n            selected[i] = true;\n            state.add(choice);\n            // 次の選択へ進む\n            backtrack(state, choices, selected, res);\n            // バックトラック：選択を取り消し、前の状態に戻す\n            selected[i] = false;\n            state.remove(state.size() - 1);\n        }\n    }\n}\n\n/* 全順列 I */\nList&lt;List&lt;Integer&gt;&gt; permutationsI(int[] nums) {\n    List&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;List&lt;Integer&gt;&gt;();\n    backtrack(new ArrayList&lt;Integer&gt;(), nums, new boolean[nums.length], res);\n    return res;\n}\n</code></pre> permutations_i.cs<pre><code>/* バックトラッキング：順列 I */\nvoid Backtrack(List&lt;int&gt; state, int[] choices, bool[] selected, List&lt;List&lt;int&gt;&gt; res) {\n    // 状態の長さが要素数に等しければ、解を記録\n    if (state.Count == choices.Length) {\n        res.Add(new List&lt;int&gt;(state));\n        return;\n    }\n    // すべての選択肢を走査\n    for (int i = 0; i &lt; choices.Length; i++) {\n        int choice = choices[i];\n        // 枝刈り：要素の重複選択を許可しない\n        if (!selected[i]) {\n            // 試行: 選択を行い、状態を更新\n            selected[i] = true;\n            state.Add(choice);\n            // 次の選択へ進む\n            Backtrack(state, choices, selected, res);\n            // バックトラック：選択を取り消し、前の状態に戻す\n            selected[i] = false;\n            state.RemoveAt(state.Count - 1);\n        }\n    }\n}\n\n/* 全順列 I */\nList&lt;List&lt;int&gt;&gt; PermutationsI(int[] nums) {\n    List&lt;List&lt;int&gt;&gt; res = [];\n    Backtrack([], nums, new bool[nums.Length], res);\n    return res;\n}\n</code></pre> permutations_i.go<pre><code>/* バックトラッキング：順列 I */\nfunc backtrackI(state *[]int, choices *[]int, selected *[]bool, res *[][]int) {\n    // 状態の長さが要素数に等しければ、解を記録\n    if len(*state) == len(*choices) {\n        newState := append([]int{}, *state...)\n        *res = append(*res, newState)\n    }\n    // すべての選択肢を走査\n    for i := 0; i &lt; len(*choices); i++ {\n        choice := (*choices)[i]\n        // 枝刈り：要素の重複選択を許可しない\n        if !(*selected)[i] {\n            // 試行: 選択を行い、状態を更新\n            (*selected)[i] = true\n            *state = append(*state, choice)\n            // 次の選択へ進む\n            backtrackI(state, choices, selected, res)\n            // バックトラック：選択を取り消し、前の状態に戻す\n            (*selected)[i] = false\n            *state = (*state)[:len(*state)-1]\n        }\n    }\n}\n\n/* 全順列 I */\nfunc permutationsI(nums []int) [][]int {\n    res := make([][]int, 0)\n    state := make([]int, 0)\n    selected := make([]bool, len(nums))\n    backtrackI(&amp;state, &amp;nums, &amp;selected, &amp;res)\n    return res\n}\n</code></pre> permutations_i.swift<pre><code>/* バックトラッキング：順列 I */\nfunc backtrack(state: inout [Int], choices: [Int], selected: inout [Bool], res: inout [[Int]]) {\n    // 状態の長さが要素数に等しければ、解を記録\n    if state.count == choices.count {\n        res.append(state)\n        return\n    }\n    // すべての選択肢を走査\n    for (i, choice) in choices.enumerated() {\n        // 枝刈り：要素の重複選択を許可しない\n        if !selected[i] {\n            // 試行: 選択を行い、状態を更新\n            selected[i] = true\n            state.append(choice)\n            // 次の選択へ進む\n            backtrack(state: &amp;state, choices: choices, selected: &amp;selected, res: &amp;res)\n            // バックトラック：選択を取り消し、前の状態に戻す\n            selected[i] = false\n            state.removeLast()\n        }\n    }\n}\n\n/* 全順列 I */\nfunc permutationsI(nums: [Int]) -&gt; [[Int]] {\n    var state: [Int] = []\n    var selected = Array(repeating: false, count: nums.count)\n    var res: [[Int]] = []\n    backtrack(state: &amp;state, choices: nums, selected: &amp;selected, res: &amp;res)\n    return res\n}\n</code></pre> permutations_i.js<pre><code>/* バックトラッキング：順列 I */\nfunction backtrack(state, choices, selected, res) {\n    // 状態の長さが要素数に等しければ、解を記録\n    if (state.length === choices.length) {\n        res.push([...state]);\n        return;\n    }\n    // すべての選択肢を走査\n    choices.forEach((choice, i) =&gt; {\n        // 枝刈り：要素の重複選択を許可しない\n        if (!selected[i]) {\n            // 試行: 選択を行い、状態を更新\n            selected[i] = true;\n            state.push(choice);\n            // 次の選択へ進む\n            backtrack(state, choices, selected, res);\n            // バックトラック：選択を取り消し、前の状態に戻す\n            selected[i] = false;\n            state.pop();\n        }\n    });\n}\n\n/* 全順列 I */\nfunction permutationsI(nums) {\n    const res = [];\n    backtrack([], nums, Array(nums.length).fill(false), res);\n    return res;\n}\n</code></pre> permutations_i.ts<pre><code>/* バックトラッキング：順列 I */\nfunction backtrack(\n    state: number[],\n    choices: number[],\n    selected: boolean[],\n    res: number[][]\n): void {\n    // 状態の長さが要素数に等しければ、解を記録\n    if (state.length === choices.length) {\n        res.push([...state]);\n        return;\n    }\n    // すべての選択肢を走査\n    choices.forEach((choice, i) =&gt; {\n        // 枝刈り：要素の重複選択を許可しない\n        if (!selected[i]) {\n            // 試行: 選択を行い、状態を更新\n            selected[i] = true;\n            state.push(choice);\n            // 次の選択へ進む\n            backtrack(state, choices, selected, res);\n            // バックトラック：選択を取り消し、前の状態に戻す\n            selected[i] = false;\n            state.pop();\n        }\n    });\n}\n\n/* 全順列 I */\nfunction permutationsI(nums: number[]): number[][] {\n    const res: number[][] = [];\n    backtrack([], nums, Array(nums.length).fill(false), res);\n    return res;\n}\n</code></pre> permutations_i.dart<pre><code>/* バックトラッキング：順列 I */\nvoid backtrack(\n  List&lt;int&gt; state,\n  List&lt;int&gt; choices,\n  List&lt;bool&gt; selected,\n  List&lt;List&lt;int&gt;&gt; res,\n) {\n  // 状態の長さが要素数に等しければ、解を記録\n  if (state.length == choices.length) {\n    res.add(List.from(state));\n    return;\n  }\n  // すべての選択肢を走査\n  for (int i = 0; i &lt; choices.length; i++) {\n    int choice = choices[i];\n    // 枝刈り：要素の重複選択を許可しない\n    if (!selected[i]) {\n      // 試行: 選択を行い、状態を更新\n      selected[i] = true;\n      state.add(choice);\n      // 次の選択へ進む\n      backtrack(state, choices, selected, res);\n      // バックトラック：選択を取り消し、前の状態に戻す\n      selected[i] = false;\n      state.removeLast();\n    }\n  }\n}\n\n/* 全順列 I */\nList&lt;List&lt;int&gt;&gt; permutationsI(List&lt;int&gt; nums) {\n  List&lt;List&lt;int&gt;&gt; res = [];\n  backtrack([], nums, List.filled(nums.length, false), res);\n  return res;\n}\n</code></pre> permutations_i.rs<pre><code>/* バックトラッキング：順列 I */\nfn backtrack(mut state: Vec&lt;i32&gt;, choices: &amp;[i32], selected: &amp;mut [bool], res: &amp;mut Vec&lt;Vec&lt;i32&gt;&gt;) {\n    // 状態の長さが要素数に等しければ、解を記録\n    if state.len() == choices.len() {\n        res.push(state);\n        return;\n    }\n    // すべての選択肢を走査\n    for i in 0..choices.len() {\n        let choice = choices[i];\n        // 枝刈り：要素の重複選択を許可しない\n        if !selected[i] {\n            // 試行: 選択を行い、状態を更新\n            selected[i] = true;\n            state.push(choice);\n            // 次の選択へ進む\n            backtrack(state.clone(), choices, selected, res);\n            // バックトラック：選択を取り消し、前の状態に戻す\n            selected[i] = false;\n            state.pop();\n        }\n    }\n}\n\n/* 全順列 I */\nfn permutations_i(nums: &amp;mut [i32]) -&gt; Vec&lt;Vec&lt;i32&gt;&gt; {\n    let mut res = Vec::new(); // 状態（部分集合）\n    backtrack(Vec::new(), nums, &amp;mut vec![false; nums.len()], &amp;mut res);\n    res\n}\n</code></pre> permutations_i.c<pre><code>/* バックトラッキング：順列 I */\nvoid backtrack(int *state, int stateSize, int *choices, int choicesSize, bool *selected, int **res, int *resSize) {\n    // 状態の長さが要素数に等しければ、解を記録\n    if (stateSize == choicesSize) {\n        res[*resSize] = (int *)malloc(choicesSize * sizeof(int));\n        for (int i = 0; i &lt; choicesSize; i++) {\n            res[*resSize][i] = state[i];\n        }\n        (*resSize)++;\n        return;\n    }\n    // すべての選択肢を走査\n    for (int i = 0; i &lt; choicesSize; i++) {\n        int choice = choices[i];\n        // 枝刈り：要素の重複選択を許可しない\n        if (!selected[i]) {\n            // 試行: 選択を行い、状態を更新\n            selected[i] = true;\n            state[stateSize] = choice;\n            // 次の選択へ進む\n            backtrack(state, stateSize + 1, choices, choicesSize, selected, res, resSize);\n            // バックトラック：選択を取り消し、前の状態に戻す\n            selected[i] = false;\n        }\n    }\n}\n\n/* 全順列 I */\nint **permutationsI(int *nums, int numsSize, int *returnSize) {\n    int *state = (int *)malloc(numsSize * sizeof(int));\n    bool *selected = (bool *)malloc(numsSize * sizeof(bool));\n    for (int i = 0; i &lt; numsSize; i++) {\n        selected[i] = false;\n    }\n    int **res = (int **)malloc(MAX_SIZE * sizeof(int *));\n    *returnSize = 0;\n\n    backtrack(state, 0, nums, numsSize, selected, res, returnSize);\n\n    free(state);\n    free(selected);\n\n    return res;\n}\n</code></pre> permutations_i.kt<pre><code>/* バックトラッキング：順列 I */\nfun backtrack(\n    state: MutableList&lt;Int&gt;,\n    choices: IntArray,\n    selected: BooleanArray,\n    res: MutableList&lt;MutableList&lt;Int&gt;?&gt;\n) {\n    // 状態の長さが要素数に等しければ、解を記録\n    if (state.size == choices.size) {\n        res.add(state.toMutableList())\n        return\n    }\n    // すべての選択肢を走査\n    for (i in choices.indices) {\n        val choice = choices[i]\n        // 枝刈り：要素の重複選択を許可しない\n        if (!selected[i]) {\n            // 試行: 選択を行い、状態を更新\n            selected[i] = true\n            state.add(choice)\n            // 次の選択へ進む\n            backtrack(state, choices, selected, res)\n            // バックトラック：選択を取り消し、前の状態に戻す\n            selected[i] = false\n            state.removeAt(state.size - 1)\n        }\n    }\n}\n\n/* 全順列 I */\nfun permutationsI(nums: IntArray): MutableList&lt;MutableList&lt;Int&gt;?&gt; {\n    val res = mutableListOf&lt;MutableList&lt;Int&gt;?&gt;()\n    backtrack(mutableListOf(), nums, BooleanArray(nums.size), res)\n    return res\n}\n</code></pre> permutations_i.rb<pre><code>### バックトラッキング法：全順列 I ###\ndef backtrack(state, choices, selected, res)\n  # 状態の長さが要素数に等しければ、解を記録\n  if state.length == choices.length\n    res &lt;&lt; state.dup\n    return\n  end\n\n  # すべての選択肢を走査\n  choices.each_with_index do |choice, i|\n    # 枝刈り：要素の重複選択を許可しない\n    unless selected[i]\n      # 試行: 選択を行い、状態を更新\n      selected[i] = true\n      state &lt;&lt; choice\n      # 次の選択へ進む\n      backtrack(state, choices, selected, res)\n      # バックトラック：選択を取り消し、前の状態に戻す\n      selected[i] = false\n      state.pop\n    end\n  end\nend\n\n### 全順列 I ###\ndef permutations_i(nums)\n  res = []\n  backtrack([], nums, Array.new(nums.length, false), res)\n  res\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 13 章 &nbsp; バックトラッキング","13.2 &nbsp; 全順列問題"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#1322","level":2,"title":"13.2.2   等しい要素を考慮する場合","text":"<p>Question</p> <p>整数配列を入力として受け取り、配列には重複要素が含まれる場合があります。重複しない順列をすべて返します。</p> <p>入力配列が \\([1, 1, 2]\\) だと仮定します。2 つの重複する要素 \\(1\\) を区別しやすくするため、2 つ目の \\(1\\) を \\(\\hat{1}\\) と記します。</p> <p>下図のように、上述の方法で生成される順列の半分は重複しています。</p> <p></p> <p> 図 13-7   重複した順列 </p> <p>では、重複した順列をどのように取り除けばよいのでしょうか。最も直接的なのは、ハッシュ集合を用いて順列結果をそのまま重複排除する方法です。しかしこのやり方は十分に洗練されていません。なぜなら、重複順列を生成する探索分岐はそもそも不要であり、事前に見つけて枝刈りすべきだからです。そうすることで、アルゴリズム効率をさらに高められます。</p>","path":["第 13 章 &nbsp; バックトラッキング","13.2 &nbsp; 全順列問題"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#1_1","level":3,"title":"1.   等しい要素の枝刈り","text":"<p>下図を見ると、1 回目のラウンドでは \\(1\\) を選ぶことと \\(\\hat{1}\\) を選ぶことは等価であり、これら 2 つの選択の下で生成される順列はすべて重複します。したがって \\(\\hat{1}\\) を枝刈りすべきです。</p> <p>同様に、1 回目で \\(2\\) を選んだ後では、2 回目のラウンドにおける \\(1\\) と \\(\\hat{1}\\) も重複分岐を生むため、2 回目の \\(\\hat{1}\\) も枝刈りすべきです。</p> <p>本質的には、各ラウンドの選択において、等しい複数の要素が 1 回しか選ばれないようにすることが目標です。</p> <p></p> <p> 図 13-8   重複順列の枝刈り </p>","path":["第 13 章 &nbsp; バックトラッキング","13.2 &nbsp; 全順列問題"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#2_1","level":3,"title":"2.   コード実装","text":"<p>前問のコードを土台として、各ラウンドの選択でハッシュ集合 <code>duplicated</code> を 1 つ用意し、そのラウンドですでに試した要素を記録して、重複要素を枝刈りすることを考えます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby permutations_ii.py<pre><code>def backtrack(\n    state: list[int], choices: list[int], selected: list[bool], res: list[list[int]]\n):\n    \"\"\"バックトラッキング：順列 II\"\"\"\n    # 状態の長さが要素数に等しければ、解を記録\n    if len(state) == len(choices):\n        res.append(list(state))\n        return\n    # すべての選択肢を走査\n    duplicated = set[int]()\n    for i, choice in enumerate(choices):\n        # 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない\n        if not selected[i] and choice not in duplicated:\n            # 試行: 選択を行い、状態を更新\n            duplicated.add(choice)  # 選択済みの要素値を記録\n            selected[i] = True\n            state.append(choice)\n            # 次の選択へ進む\n            backtrack(state, choices, selected, res)\n            # バックトラック：選択を取り消し、前の状態に戻す\n            selected[i] = False\n            state.pop()\n\ndef permutations_ii(nums: list[int]) -&gt; list[list[int]]:\n    \"\"\"全順列 II\"\"\"\n    res = []\n    backtrack(state=[], choices=nums, selected=[False] * len(nums), res=res)\n    return res\n</code></pre> permutations_ii.cpp<pre><code>/* バックトラッキング：順列 II */\nvoid backtrack(vector&lt;int&gt; &amp;state, const vector&lt;int&gt; &amp;choices, vector&lt;bool&gt; &amp;selected, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n    // 状態の長さが要素数に等しければ、解を記録\n    if (state.size() == choices.size()) {\n        res.push_back(state);\n        return;\n    }\n    // すべての選択肢を走査\n    unordered_set&lt;int&gt; duplicated;\n    for (int i = 0; i &lt; choices.size(); i++) {\n        int choice = choices[i];\n        // 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない\n        if (!selected[i] &amp;&amp; duplicated.find(choice) == duplicated.end()) {\n            // 試行: 選択を行い、状態を更新\n            duplicated.emplace(choice); // 選択済みの要素値を記録\n            selected[i] = true;\n            state.push_back(choice);\n            // 次の選択へ進む\n            backtrack(state, choices, selected, res);\n            // バックトラック：選択を取り消し、前の状態に戻す\n            selected[i] = false;\n            state.pop_back();\n        }\n    }\n}\n\n/* 全順列 II */\nvector&lt;vector&lt;int&gt;&gt; permutationsII(vector&lt;int&gt; nums) {\n    vector&lt;int&gt; state;\n    vector&lt;bool&gt; selected(nums.size(), false);\n    vector&lt;vector&lt;int&gt;&gt; res;\n    backtrack(state, nums, selected, res);\n    return res;\n}\n</code></pre> permutations_ii.java<pre><code>/* バックトラッキング：順列 II */\nvoid backtrack(List&lt;Integer&gt; state, int[] choices, boolean[] selected, List&lt;List&lt;Integer&gt;&gt; res) {\n    // 状態の長さが要素数に等しければ、解を記録\n    if (state.size() == choices.length) {\n        res.add(new ArrayList&lt;Integer&gt;(state));\n        return;\n    }\n    // すべての選択肢を走査\n    Set&lt;Integer&gt; duplicated = new HashSet&lt;Integer&gt;();\n    for (int i = 0; i &lt; choices.length; i++) {\n        int choice = choices[i];\n        // 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない\n        if (!selected[i] &amp;&amp; !duplicated.contains(choice)) {\n            // 試行: 選択を行い、状態を更新\n            duplicated.add(choice); // 選択済みの要素値を記録\n            selected[i] = true;\n            state.add(choice);\n            // 次の選択へ進む\n            backtrack(state, choices, selected, res);\n            // バックトラック：選択を取り消し、前の状態に戻す\n            selected[i] = false;\n            state.remove(state.size() - 1);\n        }\n    }\n}\n\n/* 全順列 II */\nList&lt;List&lt;Integer&gt;&gt; permutationsII(int[] nums) {\n    List&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;List&lt;Integer&gt;&gt;();\n    backtrack(new ArrayList&lt;Integer&gt;(), nums, new boolean[nums.length], res);\n    return res;\n}\n</code></pre> permutations_ii.cs<pre><code>/* バックトラッキング：順列 II */\nvoid Backtrack(List&lt;int&gt; state, int[] choices, bool[] selected, List&lt;List&lt;int&gt;&gt; res) {\n    // 状態の長さが要素数に等しければ、解を記録\n    if (state.Count == choices.Length) {\n        res.Add(new List&lt;int&gt;(state));\n        return;\n    }\n    // すべての選択肢を走査\n    HashSet&lt;int&gt; duplicated = [];\n    for (int i = 0; i &lt; choices.Length; i++) {\n        int choice = choices[i];\n        // 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない\n        if (!selected[i] &amp;&amp; !duplicated.Contains(choice)) {\n            // 試行: 選択を行い、状態を更新\n            duplicated.Add(choice); // 選択済みの要素値を記録\n            selected[i] = true;\n            state.Add(choice);\n            // 次の選択へ進む\n            Backtrack(state, choices, selected, res);\n            // バックトラック：選択を取り消し、前の状態に戻す\n            selected[i] = false;\n            state.RemoveAt(state.Count - 1);\n        }\n    }\n}\n\n/* 全順列 II */\nList&lt;List&lt;int&gt;&gt; PermutationsII(int[] nums) {\n    List&lt;List&lt;int&gt;&gt; res = [];\n    Backtrack([], nums, new bool[nums.Length], res);\n    return res;\n}\n</code></pre> permutations_ii.go<pre><code>/* バックトラッキング：順列 II */\nfunc backtrackII(state *[]int, choices *[]int, selected *[]bool, res *[][]int) {\n    // 状態の長さが要素数に等しければ、解を記録\n    if len(*state) == len(*choices) {\n        newState := append([]int{}, *state...)\n        *res = append(*res, newState)\n    }\n    // すべての選択肢を走査\n    duplicated := make(map[int]struct{}, 0)\n    for i := 0; i &lt; len(*choices); i++ {\n        choice := (*choices)[i]\n        // 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない\n        if _, ok := duplicated[choice]; !ok &amp;&amp; !(*selected)[i] {\n            // 試す: 選択を行って状態を更新\n            // 選択済みの要素値を記録\n            duplicated[choice] = struct{}{}\n            (*selected)[i] = true\n            *state = append(*state, choice)\n            // 次の選択へ進む\n            backtrackII(state, choices, selected, res)\n            // バックトラック：選択を取り消し、前の状態に戻す\n            (*selected)[i] = false\n            *state = (*state)[:len(*state)-1]\n        }\n    }\n}\n\n/* 全順列 II */\nfunc permutationsII(nums []int) [][]int {\n    res := make([][]int, 0)\n    state := make([]int, 0)\n    selected := make([]bool, len(nums))\n    backtrackII(&amp;state, &amp;nums, &amp;selected, &amp;res)\n    return res\n}\n</code></pre> permutations_ii.swift<pre><code>/* バックトラッキング：順列 II */\nfunc backtrack(state: inout [Int], choices: [Int], selected: inout [Bool], res: inout [[Int]]) {\n    // 状態の長さが要素数に等しければ、解を記録\n    if state.count == choices.count {\n        res.append(state)\n        return\n    }\n    // すべての選択肢を走査\n    var duplicated: Set&lt;Int&gt; = []\n    for (i, choice) in choices.enumerated() {\n        // 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない\n        if !selected[i], !duplicated.contains(choice) {\n            // 試行: 選択を行い、状態を更新\n            duplicated.insert(choice) // 選択済みの要素値を記録\n            selected[i] = true\n            state.append(choice)\n            // 次の選択へ進む\n            backtrack(state: &amp;state, choices: choices, selected: &amp;selected, res: &amp;res)\n            // バックトラック：選択を取り消し、前の状態に戻す\n            selected[i] = false\n            state.removeLast()\n        }\n    }\n}\n\n/* 全順列 II */\nfunc permutationsII(nums: [Int]) -&gt; [[Int]] {\n    var state: [Int] = []\n    var selected = Array(repeating: false, count: nums.count)\n    var res: [[Int]] = []\n    backtrack(state: &amp;state, choices: nums, selected: &amp;selected, res: &amp;res)\n    return res\n}\n</code></pre> permutations_ii.js<pre><code>/* バックトラッキング：順列 II */\nfunction backtrack(state, choices, selected, res) {\n    // 状態の長さが要素数に等しければ、解を記録\n    if (state.length === choices.length) {\n        res.push([...state]);\n        return;\n    }\n    // すべての選択肢を走査\n    const duplicated = new Set();\n    choices.forEach((choice, i) =&gt; {\n        // 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない\n        if (!selected[i] &amp;&amp; !duplicated.has(choice)) {\n            // 試行: 選択を行い、状態を更新\n            duplicated.add(choice); // 選択済みの要素値を記録\n            selected[i] = true;\n            state.push(choice);\n            // 次の選択へ進む\n            backtrack(state, choices, selected, res);\n            // バックトラック：選択を取り消し、前の状態に戻す\n            selected[i] = false;\n            state.pop();\n        }\n    });\n}\n\n/* 全順列 II */\nfunction permutationsII(nums) {\n    const res = [];\n    backtrack([], nums, Array(nums.length).fill(false), res);\n    return res;\n}\n</code></pre> permutations_ii.ts<pre><code>/* バックトラッキング：順列 II */\nfunction backtrack(\n    state: number[],\n    choices: number[],\n    selected: boolean[],\n    res: number[][]\n): void {\n    // 状態の長さが要素数に等しければ、解を記録\n    if (state.length === choices.length) {\n        res.push([...state]);\n        return;\n    }\n    // すべての選択肢を走査\n    const duplicated = new Set();\n    choices.forEach((choice, i) =&gt; {\n        // 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない\n        if (!selected[i] &amp;&amp; !duplicated.has(choice)) {\n            // 試行: 選択を行い、状態を更新\n            duplicated.add(choice); // 選択済みの要素値を記録\n            selected[i] = true;\n            state.push(choice);\n            // 次の選択へ進む\n            backtrack(state, choices, selected, res);\n            // バックトラック：選択を取り消し、前の状態に戻す\n            selected[i] = false;\n            state.pop();\n        }\n    });\n}\n\n/* 全順列 II */\nfunction permutationsII(nums: number[]): number[][] {\n    const res: number[][] = [];\n    backtrack([], nums, Array(nums.length).fill(false), res);\n    return res;\n}\n</code></pre> permutations_ii.dart<pre><code>/* バックトラッキング：順列 II */\nvoid backtrack(\n  List&lt;int&gt; state,\n  List&lt;int&gt; choices,\n  List&lt;bool&gt; selected,\n  List&lt;List&lt;int&gt;&gt; res,\n) {\n  // 状態の長さが要素数に等しければ、解を記録\n  if (state.length == choices.length) {\n    res.add(List.from(state));\n    return;\n  }\n  // すべての選択肢を走査\n  Set&lt;int&gt; duplicated = {};\n  for (int i = 0; i &lt; choices.length; i++) {\n    int choice = choices[i];\n    // 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない\n    if (!selected[i] &amp;&amp; !duplicated.contains(choice)) {\n      // 試行: 選択を行い、状態を更新\n      duplicated.add(choice); // 選択済みの要素値を記録\n      selected[i] = true;\n      state.add(choice);\n      // 次の選択へ進む\n      backtrack(state, choices, selected, res);\n      // バックトラック：選択を取り消し、前の状態に戻す\n      selected[i] = false;\n      state.removeLast();\n    }\n  }\n}\n\n/* 全順列 II */\nList&lt;List&lt;int&gt;&gt; permutationsII(List&lt;int&gt; nums) {\n  List&lt;List&lt;int&gt;&gt; res = [];\n  backtrack([], nums, List.filled(nums.length, false), res);\n  return res;\n}\n</code></pre> permutations_ii.rs<pre><code>/* バックトラッキング：順列 II */\nfn backtrack(mut state: Vec&lt;i32&gt;, choices: &amp;[i32], selected: &amp;mut [bool], res: &amp;mut Vec&lt;Vec&lt;i32&gt;&gt;) {\n    // 状態の長さが要素数に等しければ、解を記録\n    if state.len() == choices.len() {\n        res.push(state);\n        return;\n    }\n    // すべての選択肢を走査\n    let mut duplicated = HashSet::&lt;i32&gt;::new();\n    for i in 0..choices.len() {\n        let choice = choices[i];\n        // 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない\n        if !selected[i] &amp;&amp; !duplicated.contains(&amp;choice) {\n            // 試行: 選択を行い、状態を更新\n            duplicated.insert(choice); // 選択済みの要素値を記録\n            selected[i] = true;\n            state.push(choice);\n            // 次の選択へ進む\n            backtrack(state.clone(), choices, selected, res);\n            // バックトラック：選択を取り消し、前の状態に戻す\n            selected[i] = false;\n            state.pop();\n        }\n    }\n}\n\n/* 全順列 II */\nfn permutations_ii(nums: &amp;mut [i32]) -&gt; Vec&lt;Vec&lt;i32&gt;&gt; {\n    let mut res = Vec::new();\n    backtrack(Vec::new(), nums, &amp;mut vec![false; nums.len()], &amp;mut res);\n    res\n}\n</code></pre> permutations_ii.c<pre><code>/* バックトラッキング：順列 II */\nvoid backtrack(int *state, int stateSize, int *choices, int choicesSize, bool *selected, int **res, int *resSize) {\n    // 状態の長さが要素数に等しければ、解を記録\n    if (stateSize == choicesSize) {\n        res[*resSize] = (int *)malloc(choicesSize * sizeof(int));\n        for (int i = 0; i &lt; choicesSize; i++) {\n            res[*resSize][i] = state[i];\n        }\n        (*resSize)++;\n        return;\n    }\n    // すべての選択肢を走査\n    bool duplicated[MAX_SIZE] = {false};\n    for (int i = 0; i &lt; choicesSize; i++) {\n        int choice = choices[i];\n        // 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない\n        if (!selected[i] &amp;&amp; !duplicated[choice]) {\n            // 試行: 選択を行い、状態を更新\n            duplicated[choice] = true; // 選択済みの要素値を記録\n            selected[i] = true;\n            state[stateSize] = choice;\n            // 次の選択へ進む\n            backtrack(state, stateSize + 1, choices, choicesSize, selected, res, resSize);\n            // バックトラック：選択を取り消し、前の状態に戻す\n            selected[i] = false;\n        }\n    }\n}\n\n/* 全順列 II */\nint **permutationsII(int *nums, int numsSize, int *returnSize) {\n    int *state = (int *)malloc(numsSize * sizeof(int));\n    bool *selected = (bool *)malloc(numsSize * sizeof(bool));\n    for (int i = 0; i &lt; numsSize; i++) {\n        selected[i] = false;\n    }\n    int **res = (int **)malloc(MAX_SIZE * sizeof(int *));\n    *returnSize = 0;\n\n    backtrack(state, 0, nums, numsSize, selected, res, returnSize);\n\n    free(state);\n    free(selected);\n\n    return res;\n}\n</code></pre> permutations_ii.kt<pre><code>/* バックトラッキング：順列 II */\nfun backtrack(\n    state: MutableList&lt;Int&gt;,\n    choices: IntArray,\n    selected: BooleanArray,\n    res: MutableList&lt;MutableList&lt;Int&gt;?&gt;\n) {\n    // 状態の長さが要素数に等しければ、解を記録\n    if (state.size == choices.size) {\n        res.add(state.toMutableList())\n        return\n    }\n    // すべての選択肢を走査\n    val duplicated = HashSet&lt;Int&gt;()\n    for (i in choices.indices) {\n        val choice = choices[i]\n        // 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない\n        if (!selected[i] &amp;&amp; !duplicated.contains(choice)) {\n            // 試行: 選択を行い、状態を更新\n            duplicated.add(choice) // 選択済みの要素値を記録\n            selected[i] = true\n            state.add(choice)\n            // 次の選択へ進む\n            backtrack(state, choices, selected, res)\n            // バックトラック：選択を取り消し、前の状態に戻す\n            selected[i] = false\n            state.removeAt(state.size - 1)\n        }\n    }\n}\n\n/* 全順列 II */\nfun permutationsII(nums: IntArray): MutableList&lt;MutableList&lt;Int&gt;?&gt; {\n    val res = mutableListOf&lt;MutableList&lt;Int&gt;?&gt;()\n    backtrack(mutableListOf(), nums, BooleanArray(nums.size), res)\n    return res\n}\n</code></pre> permutations_ii.rb<pre><code>### バックトラッキング法：全順列 II ###\ndef backtrack(state, choices, selected, res)\n  # 状態の長さが要素数に等しければ、解を記録\n  if state.length == choices.length\n    res &lt;&lt; state.dup\n    return\n  end\n\n  # すべての選択肢を走査\n  duplicated = Set.new\n  choices.each_with_index do |choice, i|\n    # 枝刈り：要素の重複選択を許可せず、同値要素の重複選択も許可しない\n    if !selected[i] &amp;&amp; !duplicated.include?(choice)\n      # 試行: 選択を行い、状態を更新\n      duplicated.add(choice)\n      selected[i] = true\n      state &lt;&lt; choice\n      # 次の選択へ進む\n      backtrack(state, choices, selected, res)\n      # バックトラック：選択を取り消し、前の状態に戻す\n      selected[i] = false\n      state.pop\n    end\n  end\nend\n\n### 全順列 II ###\ndef permutations_ii(nums)\n  res = []\n  backtrack([], nums, Array.new(nums.length, false), res)\n  res\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>要素どうしがすべて互いに異なると仮定すると、\\(n\\) 個の要素には全部で \\(n!\\)  通りの順列（階乗）があります。結果を記録する際には、長さ \\(n\\) のリストをコピーする必要があり、これに \\(O(n)\\) 時間を要します。したがって時間計算量は \\(O(n!n)\\) です。</p> <p>再帰の最大深さは \\(n\\) であり、\\(O(n)\\) のスタックフレーム空間を使います。<code>selected</code> は \\(O(n)\\) 空間を使用します。同時刻に存在する <code>duplicated</code> は最大で \\(n\\) 個であり、\\(O(n^2)\\) 空間を要します。したがって空間計算量は \\(O(n^2)\\) です。</p>","path":["第 13 章 &nbsp; バックトラッキング","13.2 &nbsp; 全順列問題"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#3-2","level":3,"title":"3.   2 種類の枝刈りの比較","text":"<p><code>selected</code> と <code>duplicated</code> はどちらも枝刈りに用いられますが、目的は異なる点に注意してください。</p> <ul> <li>重複選択の枝刈り：探索全体を通して <code>selected</code> は 1 つだけです。これは現在の状態にどの要素が含まれているかを記録し、ある要素が <code>state</code> に重複して現れるのを防ぎます。</li> <li>等しい要素の枝刈り：各ラウンドの選択、すなわち各回の <code>backtrack</code> 呼び出しには <code>duplicated</code> が含まれます。これはそのラウンドの走査（<code>for</code> ループ）でどの要素がすでに選ばれたかを記録し、等しい要素が 1 回しか選ばれないことを保証します。</li> </ul> <p>下図は、2 つの枝刈り条件が有効になる範囲を示しています。木の各ノードは 1 つの選択を表し、根ノードから葉ノードまでの経路上の各ノードが 1 つの順列を構成することに注意してください。</p> <p></p> <p> 図 13-9   2 種類の枝刈り条件の作用範囲 </p>","path":["第 13 章 &nbsp; バックトラッキング","13.2 &nbsp; 全順列問題"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/","level":1,"title":"13.3   部分和問題","text":"","path":["第 13 章 &nbsp; バックトラッキング","13.3 &nbsp; 部分和問題"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#1331","level":2,"title":"13.3.1   重複しない要素の場合","text":"<p>Question</p> <p>正整数配列 <code>nums</code> と目標の正整数 <code>target</code> が与えられたとき、要素の和が <code>target</code> に等しくなるすべての組合せを見つけてください。配列に重複要素はなく、各要素は複数回選択できます。これらの組合せをリスト形式で返してください。リストに重複する組合せを含めてはなりません。</p> <p>例えば、入力集合 \\(\\{3, 4, 5\\}\\) と目標整数 \\(9\\) に対する解は \\(\\{3, 3, 3\\}, \\{4, 5\\}\\) です。次の 2 点に注意してください。</p> <ul> <li>入力集合内の要素は何度でも繰り返し選択できます。</li> <li>部分集合では要素の順序を区別しません。例えば \\(\\{4, 5\\}\\) と \\(\\{5, 4\\}\\) は同じ部分集合です。</li> </ul>","path":["第 13 章 &nbsp; バックトラッキング","13.3 &nbsp; 部分和問題"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#1","level":3,"title":"1.   全順列の解法を参考にする","text":"<p>全順列問題と同様に、部分集合の生成過程を一連の選択結果として捉え、選択の過程で「要素の和」を逐次更新できます。そして要素の和が <code>target</code> に等しくなった時点で、その部分集合を結果リストに記録します。</p> <p>ただし全順列問題と異なるのは、**この問題では集合内の要素を無制限に選択できる**点です。そのため、要素がすでに選択されたかどうかを記録する <code>selected</code> ブール配列は不要です。全順列のコードに少し修正を加えると、まず次の解法コードが得られます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby subset_sum_i_naive.py<pre><code>def backtrack(\n    state: list[int],\n    target: int,\n    total: int,\n    choices: list[int],\n    res: list[list[int]],\n):\n    \"\"\"バックトラッキング：部分和 I\"\"\"\n    # 部分集合の和が target に等しければ、解を記録\n    if total == target:\n        res.append(list(state))\n        return\n    # すべての選択肢を走査\n    for i in range(len(choices)):\n        # 枝刈り：部分和が target を超える場合はその選択をスキップする\n        if total + choices[i] &gt; target:\n            continue\n        # 試行：選択を行い、要素と total を更新する\n        state.append(choices[i])\n        # 次の選択へ進む\n        backtrack(state, target, total + choices[i], choices, res)\n        # バックトラック：選択を取り消し、前の状態に戻す\n        state.pop()\n\ndef subset_sum_i_naive(nums: list[int], target: int) -&gt; list[list[int]]:\n    \"\"\"部分和 I を解く（重複部分集合を含む）\"\"\"\n    state = []  # 状態（部分集合）\n    total = 0  # 部分和\n    res = []  # 結果リスト（部分集合のリスト）\n    backtrack(state, target, total, nums, res)\n    return res\n</code></pre> subset_sum_i_naive.cpp<pre><code>/* バックトラッキング：部分和 I */\nvoid backtrack(vector&lt;int&gt; &amp;state, int target, int total, vector&lt;int&gt; &amp;choices, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n    // 部分集合の和が target に等しければ、解を記録\n    if (total == target) {\n        res.push_back(state);\n        return;\n    }\n    // すべての選択肢を走査\n    for (size_t i = 0; i &lt; choices.size(); i++) {\n        // 枝刈り：部分和が target を超える場合はその選択をスキップする\n        if (total + choices[i] &gt; target) {\n            continue;\n        }\n        // 試行：選択を行い、要素と total を更新する\n        state.push_back(choices[i]);\n        // 次の選択へ進む\n        backtrack(state, target, total + choices[i], choices, res);\n        // バックトラック：選択を取り消し、前の状態に戻す\n        state.pop_back();\n    }\n}\n\n/* 部分和 I を解く（重複部分集合を含む） */\nvector&lt;vector&lt;int&gt;&gt; subsetSumINaive(vector&lt;int&gt; &amp;nums, int target) {\n    vector&lt;int&gt; state;       // 状態（部分集合）\n    int total = 0;           // 部分和\n    vector&lt;vector&lt;int&gt;&gt; res; // 結果リスト（部分集合のリスト）\n    backtrack(state, target, total, nums, res);\n    return res;\n}\n</code></pre> subset_sum_i_naive.java<pre><code>/* バックトラッキング：部分和 I */\nvoid backtrack(List&lt;Integer&gt; state, int target, int total, int[] choices, List&lt;List&lt;Integer&gt;&gt; res) {\n    // 部分集合の和が target に等しければ、解を記録\n    if (total == target) {\n        res.add(new ArrayList&lt;&gt;(state));\n        return;\n    }\n    // すべての選択肢を走査\n    for (int i = 0; i &lt; choices.length; i++) {\n        // 枝刈り：部分和が target を超える場合はその選択をスキップする\n        if (total + choices[i] &gt; target) {\n            continue;\n        }\n        // 試行：選択を行い、要素と total を更新する\n        state.add(choices[i]);\n        // 次の選択へ進む\n        backtrack(state, target, total + choices[i], choices, res);\n        // バックトラック：選択を取り消し、前の状態に戻す\n        state.remove(state.size() - 1);\n    }\n}\n\n/* 部分和 I を解く（重複部分集合を含む） */\nList&lt;List&lt;Integer&gt;&gt; subsetSumINaive(int[] nums, int target) {\n    List&lt;Integer&gt; state = new ArrayList&lt;&gt;(); // 状態（部分集合）\n    int total = 0; // 部分和\n    List&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;&gt;(); // 結果リスト（部分集合のリスト）\n    backtrack(state, target, total, nums, res);\n    return res;\n}\n</code></pre> subset_sum_i_naive.cs<pre><code>/* バックトラッキング：部分和 I */\nvoid Backtrack(List&lt;int&gt; state, int target, int total, int[] choices, List&lt;List&lt;int&gt;&gt; res) {\n    // 部分集合の和が target に等しければ、解を記録\n    if (total == target) {\n        res.Add(new List&lt;int&gt;(state));\n        return;\n    }\n    // すべての選択肢を走査\n    for (int i = 0; i &lt; choices.Length; i++) {\n        // 枝刈り：部分和が target を超える場合はその選択をスキップする\n        if (total + choices[i] &gt; target) {\n            continue;\n        }\n        // 試行：選択を行い、要素と total を更新する\n        state.Add(choices[i]);\n        // 次の選択へ進む\n        Backtrack(state, target, total + choices[i], choices, res);\n        // バックトラック：選択を取り消し、前の状態に戻す\n        state.RemoveAt(state.Count - 1);\n    }\n}\n\n/* 部分和 I を解く（重複部分集合を含む） */\nList&lt;List&lt;int&gt;&gt; SubsetSumINaive(int[] nums, int target) {\n    List&lt;int&gt; state = []; // 状態（部分集合）\n    int total = 0; // 部分和\n    List&lt;List&lt;int&gt;&gt; res = []; // 結果リスト（部分集合のリスト）\n    Backtrack(state, target, total, nums, res);\n    return res;\n}\n</code></pre> subset_sum_i_naive.go<pre><code>/* バックトラッキング：部分和 I */\nfunc backtrackSubsetSumINaive(total, target int, state, choices *[]int, res *[][]int) {\n    // 部分集合の和が target に等しければ、解を記録\n    if target == total {\n        newState := append([]int{}, *state...)\n        *res = append(*res, newState)\n        return\n    }\n    // すべての選択肢を走査\n    for i := 0; i &lt; len(*choices); i++ {\n        // 枝刈り：部分和が target を超える場合はその選択をスキップする\n        if total+(*choices)[i] &gt; target {\n            continue\n        }\n        // 試行：選択を行い、要素と total を更新する\n        *state = append(*state, (*choices)[i])\n        // 次の選択へ進む\n        backtrackSubsetSumINaive(total+(*choices)[i], target, state, choices, res)\n        // バックトラック：選択を取り消し、前の状態に戻す\n        *state = (*state)[:len(*state)-1]\n    }\n}\n\n/* 部分和 I を解く（重複部分集合を含む） */\nfunc subsetSumINaive(nums []int, target int) [][]int {\n    state := make([]int, 0) // 状態（部分集合）\n    total := 0              // 部分和\n    res := make([][]int, 0) // 結果リスト（部分集合のリスト）\n    backtrackSubsetSumINaive(total, target, &amp;state, &amp;nums, &amp;res)\n    return res\n}\n</code></pre> subset_sum_i_naive.swift<pre><code>/* バックトラッキング：部分和 I */\nfunc backtrack(state: inout [Int], target: Int, total: Int, choices: [Int], res: inout [[Int]]) {\n    // 部分集合の和が target に等しければ、解を記録\n    if total == target {\n        res.append(state)\n        return\n    }\n    // すべての選択肢を走査\n    for i in choices.indices {\n        // 枝刈り：部分和が target を超える場合はその選択をスキップする\n        if total + choices[i] &gt; target {\n            continue\n        }\n        // 試行：選択を行い、要素と total を更新する\n        state.append(choices[i])\n        // 次の選択へ進む\n        backtrack(state: &amp;state, target: target, total: total + choices[i], choices: choices, res: &amp;res)\n        // バックトラック：選択を取り消し、前の状態に戻す\n        state.removeLast()\n    }\n}\n\n/* 部分和 I を解く（重複部分集合を含む） */\nfunc subsetSumINaive(nums: [Int], target: Int) -&gt; [[Int]] {\n    var state: [Int] = [] // 状態（部分集合）\n    let total = 0 // 部分和\n    var res: [[Int]] = [] // 結果リスト（部分集合のリスト）\n    backtrack(state: &amp;state, target: target, total: total, choices: nums, res: &amp;res)\n    return res\n}\n</code></pre> subset_sum_i_naive.js<pre><code>/* バックトラッキング：部分和 I */\nfunction backtrack(state, target, total, choices, res) {\n    // 部分集合の和が target に等しければ、解を記録\n    if (total === target) {\n        res.push([...state]);\n        return;\n    }\n    // すべての選択肢を走査\n    for (let i = 0; i &lt; choices.length; i++) {\n        // 枝刈り：部分和が target を超える場合はその選択をスキップする\n        if (total + choices[i] &gt; target) {\n            continue;\n        }\n        // 試行：選択を行い、要素と total を更新する\n        state.push(choices[i]);\n        // 次の選択へ進む\n        backtrack(state, target, total + choices[i], choices, res);\n        // バックトラック：選択を取り消し、前の状態に戻す\n        state.pop();\n    }\n}\n\n/* 部分和 I を解く（重複部分集合を含む） */\nfunction subsetSumINaive(nums, target) {\n    const state = []; // 状態（部分集合）\n    const total = 0; // 部分和\n    const res = []; // 結果リスト（部分集合のリスト）\n    backtrack(state, target, total, nums, res);\n    return res;\n}\n</code></pre> subset_sum_i_naive.ts<pre><code>/* バックトラッキング：部分和 I */\nfunction backtrack(\n    state: number[],\n    target: number,\n    total: number,\n    choices: number[],\n    res: number[][]\n): void {\n    // 部分集合の和が target に等しければ、解を記録\n    if (total === target) {\n        res.push([...state]);\n        return;\n    }\n    // すべての選択肢を走査\n    for (let i = 0; i &lt; choices.length; i++) {\n        // 枝刈り：部分和が target を超える場合はその選択をスキップする\n        if (total + choices[i] &gt; target) {\n            continue;\n        }\n        // 試行：選択を行い、要素と total を更新する\n        state.push(choices[i]);\n        // 次の選択へ進む\n        backtrack(state, target, total + choices[i], choices, res);\n        // バックトラック：選択を取り消し、前の状態に戻す\n        state.pop();\n    }\n}\n\n/* 部分和 I を解く（重複部分集合を含む） */\nfunction subsetSumINaive(nums: number[], target: number): number[][] {\n    const state = []; // 状態（部分集合）\n    const total = 0; // 部分和\n    const res = []; // 結果リスト（部分集合のリスト）\n    backtrack(state, target, total, nums, res);\n    return res;\n}\n</code></pre> subset_sum_i_naive.dart<pre><code>/* バックトラッキング：部分和 I */\nvoid backtrack(\n  List&lt;int&gt; state,\n  int target,\n  int total,\n  List&lt;int&gt; choices,\n  List&lt;List&lt;int&gt;&gt; res,\n) {\n  // 部分集合の和が target に等しければ、解を記録\n  if (total == target) {\n    res.add(List.from(state));\n    return;\n  }\n  // すべての選択肢を走査\n  for (int i = 0; i &lt; choices.length; i++) {\n    // 枝刈り：部分和が target を超える場合はその選択をスキップする\n    if (total + choices[i] &gt; target) {\n      continue;\n    }\n    // 試行：選択を行い、要素と total を更新する\n    state.add(choices[i]);\n    // 次の選択へ進む\n    backtrack(state, target, total + choices[i], choices, res);\n    // バックトラック：選択を取り消し、前の状態に戻す\n    state.removeLast();\n  }\n}\n\n/* 部分和 I を解く（重複部分集合を含む） */\nList&lt;List&lt;int&gt;&gt; subsetSumINaive(List&lt;int&gt; nums, int target) {\n  List&lt;int&gt; state = []; // 状態（部分集合）\n  int total = 0; // 要素の合計\n  List&lt;List&lt;int&gt;&gt; res = []; // 結果リスト（部分集合のリスト）\n  backtrack(state, target, total, nums, res);\n  return res;\n}\n</code></pre> subset_sum_i_naive.rs<pre><code>/* バックトラッキング：部分和 I */\nfn backtrack(\n    state: &amp;mut Vec&lt;i32&gt;,\n    target: i32,\n    total: i32,\n    choices: &amp;[i32],\n    res: &amp;mut Vec&lt;Vec&lt;i32&gt;&gt;,\n) {\n    // 部分集合の和が target に等しければ、解を記録\n    if total == target {\n        res.push(state.clone());\n        return;\n    }\n    // すべての選択肢を走査\n    for i in 0..choices.len() {\n        // 枝刈り：部分和が target を超える場合はその選択をスキップする\n        if total + choices[i] &gt; target {\n            continue;\n        }\n        // 試行：選択を行い、要素と total を更新する\n        state.push(choices[i]);\n        // 次の選択へ進む\n        backtrack(state, target, total + choices[i], choices, res);\n        // バックトラック：選択を取り消し、前の状態に戻す\n        state.pop();\n    }\n}\n\n/* 部分和 I を解く（重複部分集合を含む） */\nfn subset_sum_i_naive(nums: &amp;[i32], target: i32) -&gt; Vec&lt;Vec&lt;i32&gt;&gt; {\n    let mut state = Vec::new(); // 状態（部分集合）\n    let total = 0; // 部分和\n    let mut res = Vec::new(); // 結果リスト（部分集合のリスト）\n    backtrack(&amp;mut state, target, total, nums, &amp;mut res);\n    res\n}\n</code></pre> subset_sum_i_naive.c<pre><code>/* バックトラッキング：部分和 I */\nvoid backtrack(int target, int total, int *choices, int choicesSize) {\n    // 部分集合の和が target に等しければ、解を記録\n    if (total == target) {\n        for (int i = 0; i &lt; stateSize; i++) {\n            res[resSize][i] = state[i];\n        }\n        resColSizes[resSize++] = stateSize;\n        return;\n    }\n    // すべての選択肢を走査\n    for (int i = 0; i &lt; choicesSize; i++) {\n        // 枝刈り：部分和が target を超える場合はその選択をスキップする\n        if (total + choices[i] &gt; target) {\n            continue;\n        }\n        // 試行：選択を行い、要素と total を更新する\n        state[stateSize++] = choices[i];\n        // 次の選択へ進む\n        backtrack(target, total + choices[i], choices, choicesSize);\n        // バックトラック：選択を取り消し、前の状態に戻す\n        stateSize--;\n    }\n}\n\n/* 部分和 I を解く（重複部分集合を含む） */\nvoid subsetSumINaive(int *nums, int numsSize, int target) {\n    resSize = 0; // 解の個数を 0 に初期化する\n    backtrack(target, 0, nums, numsSize);\n}\n</code></pre> subset_sum_i_naive.kt<pre><code>/* バックトラッキング：部分和 I */\nfun backtrack(\n    state: MutableList&lt;Int&gt;,\n    target: Int,\n    total: Int,\n    choices: IntArray,\n    res: MutableList&lt;MutableList&lt;Int&gt;?&gt;\n) {\n    // 部分集合の和が target に等しければ、解を記録\n    if (total == target) {\n        res.add(state.toMutableList())\n        return\n    }\n    // すべての選択肢を走査\n    for (i in choices.indices) {\n        // 枝刈り：部分和が target を超える場合はその選択をスキップする\n        if (total + choices[i] &gt; target) {\n            continue\n        }\n        // 試行：選択を行い、要素と total を更新する\n        state.add(choices[i])\n        // 次の選択へ進む\n        backtrack(state, target, total + choices[i], choices, res)\n        // バックトラック：選択を取り消し、前の状態に戻す\n        state.removeAt(state.size - 1)\n    }\n}\n\n/* 部分和 I を解く（重複部分集合を含む） */\nfun subsetSumINaive(nums: IntArray, target: Int): MutableList&lt;MutableList&lt;Int&gt;?&gt; {\n    val state = mutableListOf&lt;Int&gt;() // 状態（部分集合）\n    val total = 0 // 部分和\n    val res = mutableListOf&lt;MutableList&lt;Int&gt;?&gt;() // 結果リスト（部分集合のリスト）\n    backtrack(state, target, total, nums, res)\n    return res\n}\n</code></pre> subset_sum_i_naive.rb<pre><code>### バックトラッキング: 部分和 I ###\ndef backtrack(state, target, total, choices, res)\n  # 部分集合の和が target に等しければ、解を記録\n  if total == target\n    res &lt;&lt; state.dup\n    return\n  end\n\n  # すべての選択肢を走査\n  for i in 0...choices.length\n    # 枝刈り：部分和が target を超える場合はその選択をスキップする\n    next if total + choices[i] &gt; target\n    # 試行：選択を行い、要素と total を更新する\n    state &lt;&lt; choices[i]\n    # 次の選択へ進む\n    backtrack(state, target, total + choices[i], choices, res)\n    # バックトラック：選択を取り消し、前の状態に戻す\n    state.pop\n  end\nend\n\n### バックトラッキング: 部分和 I ###\ndef backtrack(state, target, total, choices, res)\n  # 部分集合の和が target に等しければ、解を記録\n  if total == target\n    res &lt;&lt; state.dup\n    return\n  end\n\n  # すべての選択肢を走査\n  for i in 0...choices.length\n    # 枝刈り：部分和が target を超える場合はその選択をスキップする\n    next if total + choices[i] &gt; target\n    # 試行：選択を行い、要素と total を更新する\n    state &lt;&lt; choices[i]\n    # 次の選択へ進む\n    backtrack(state, target, total + choices[i], choices, res)\n    # バックトラック：選択を取り消し、前の状態に戻す\n    state.pop\n  end\nend\n\n# ## 部分和 I を解く（重複する部分集合を含む）###\ndef subset_sum_i_naive(nums, target)\n  state = [] # 状態（部分集合）\n  total = 0 # 部分和\n  res = [] # 結果リスト（部分集合のリスト）\n  backtrack(state, target, total, nums, res)\n  res\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>上のコードに配列 \\([3, 4, 5]\\) と目標値 \\(9\\) を入力すると、出力は \\([3, 3, 3], [4, 5], [5, 4]\\) となります。和が \\(9\\) となる部分集合はすべて見つかっていますが、重複する部分集合 \\([4, 5]\\) と \\([5, 4]\\) が含まれています。</p> <p>これは、探索過程では選択順を区別する一方で、部分集合では選択順を区別しないためです。次の図のように、先に \\(4\\) を選んでから \\(5\\) を選ぶ場合と、先に \\(5\\) を選んでから \\(4\\) を選ぶ場合は別の分岐ですが、対応する部分集合は同じです。</p> <p></p> <p> 図 13-10   部分集合探索と境界超過の枝刈り </p> <p>重複する部分集合を取り除くために、**直接的な方法として結果リストの重複を除去する**ことが考えられます。しかし、この方法は効率が低く、その理由は次の 2 点です。</p> <ul> <li>配列要素が多い場合、特に <code>target</code> が大きい場合には、探索過程で大量の重複部分集合が生成されます。</li> <li>部分集合（配列）同士の違いを比較するのは非常に時間がかかり、まず配列をソートし、その後に各要素を比較する必要があります。</li> </ul>","path":["第 13 章 &nbsp; バックトラッキング","13.3 &nbsp; 部分和問題"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#2","level":3,"title":"2.   重複部分集合の枝刈り","text":"<p>**探索過程で枝刈りを行って重複を除去する**ことを考えます。次の図を観察すると、重複部分集合は配列要素を異なる順序で選択したときに生じます。例えば次のような状況です。</p> <ol> <li>1 回目と 2 回目でそれぞれ \\(3\\) と \\(4\\) を選ぶと、これら 2 要素を含むすべての部分集合、すなわち \\([3, 4, \\dots]\\) が生成されます。</li> <li>その後、1 回目で \\(4\\) を選んだ場合、**2 回目では \\(3\\) をスキップすべき**です。というのも、この選択で生成される部分集合 \\([4, 3, \\dots]\\) は、手順 <code>1.</code> で生成された部分集合と完全に重複するからです。</li> </ol> <p>探索過程では、各階層の選択は左から右へ順に試されるため、右側にある分岐ほど多く枝刈りされます。</p> <ol> <li>最初の 2 回で \\(3\\) と \\(5\\) を選ぶと、部分集合 \\([3, 5, \\dots]\\) が生成されます。</li> <li>最初の 2 回で \\(4\\) と \\(5\\) を選ぶと、部分集合 \\([4, 5, \\dots]\\) が生成されます。</li> <li>もし 1 回目で \\(5\\) を選ぶなら、**2 回目では \\(3\\) と \\(4\\) をスキップすべき**です。なぜなら、部分集合 \\([5, 3, \\dots]\\) と \\([5, 4, \\dots]\\) は、手順 <code>1.</code> と手順 <code>2.</code> で述べた部分集合と完全に重複するからです。</li> </ol> <p></p> <p> 図 13-11   異なる選択順によって生じる重複部分集合 </p> <p>まとめると、入力配列 \\([x_1, x_2, \\dots, x_n]\\) が与えられ、探索過程における選択列を \\([x_{i_1}, x_{i_2}, \\dots, x_{i_m}]\\) とすると、この選択列は \\(i_1 \\leq i_2 \\leq \\dots \\leq i_m\\) を満たす必要があります。この条件を満たさない選択列は重複を生むため、枝刈りすべきです。</p>","path":["第 13 章 &nbsp; バックトラッキング","13.3 &nbsp; 部分和問題"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#3","level":3,"title":"3.   コード実装","text":"<p>この枝刈りを実現するために、走査の開始位置を示す変数 <code>start</code> を初期化します。**選択 \\(x_{i}\\) を行った後、次のラウンドはインデックス \\(i\\) から走査を開始する**ように設定します。これにより、選択列が \\(i_1 \\leq i_2 \\leq \\dots \\leq i_m\\) を満たし、部分集合の一意性が保証されます。</p> <p>これに加えて、コードには次の 2 つの最適化も施しています。</p> <ul> <li>探索を始める前に、まず配列 <code>nums</code> をソートします。すべての選択肢を走査するとき、**部分集合の和が <code>target</code> を超えたら直ちにループを終了**します。後続の要素はさらに大きいため、その和も必ず <code>target</code> を超えるからです。</li> <li>要素和を保持する変数 <code>total</code> は省略し、**<code>target</code> から減算することで要素和を管理**します。<code>target</code> が \\(0\\) になったときに解を記録します。</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby subset_sum_i.py<pre><code>def backtrack(\n    state: list[int], target: int, choices: list[int], start: int, res: list[list[int]]\n):\n    \"\"\"バックトラッキング：部分和 I\"\"\"\n    # 部分集合の和が target に等しければ、解を記録\n    if target == 0:\n        res.append(list(state))\n        return\n    # すべての選択肢を走査\n    # 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n    for i in range(start, len(choices)):\n        # 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する\n        # 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため\n        if target - choices[i] &lt; 0:\n            break\n        # 試す：選択を行い、target と start を更新\n        state.append(choices[i])\n        # 次の選択へ進む\n        backtrack(state, target - choices[i], choices, i, res)\n        # バックトラック：選択を取り消し、前の状態に戻す\n        state.pop()\n\ndef subset_sum_i(nums: list[int], target: int) -&gt; list[list[int]]:\n    \"\"\"部分和 I を解く\"\"\"\n    state = []  # 状態（部分集合）\n    nums.sort()  # nums をソート\n    start = 0  # 開始点を走査\n    res = []  # 結果リスト（部分集合のリスト）\n    backtrack(state, target, nums, start, res)\n    return res\n</code></pre> subset_sum_i.cpp<pre><code>/* バックトラッキング：部分和 I */\nvoid backtrack(vector&lt;int&gt; &amp;state, int target, vector&lt;int&gt; &amp;choices, int start, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n    // 部分集合の和が target に等しければ、解を記録\n    if (target == 0) {\n        res.push_back(state);\n        return;\n    }\n    // すべての選択肢を走査\n    // 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n    for (int i = start; i &lt; choices.size(); i++) {\n        // 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する\n        // 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // 試す：選択を行い、target と start を更新\n        state.push_back(choices[i]);\n        // 次の選択へ進む\n        backtrack(state, target - choices[i], choices, i, res);\n        // バックトラック：選択を取り消し、前の状態に戻す\n        state.pop_back();\n    }\n}\n\n/* 部分和 I を解く */\nvector&lt;vector&lt;int&gt;&gt; subsetSumI(vector&lt;int&gt; &amp;nums, int target) {\n    vector&lt;int&gt; state;              // 状態（部分集合）\n    sort(nums.begin(), nums.end()); // nums をソート\n    int start = 0;                  // 開始点を走査\n    vector&lt;vector&lt;int&gt;&gt; res;        // 結果リスト（部分集合のリスト）\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_i.java<pre><code>/* バックトラッキング：部分和 I */\nvoid backtrack(List&lt;Integer&gt; state, int target, int[] choices, int start, List&lt;List&lt;Integer&gt;&gt; res) {\n    // 部分集合の和が target に等しければ、解を記録\n    if (target == 0) {\n        res.add(new ArrayList&lt;&gt;(state));\n        return;\n    }\n    // すべての選択肢を走査\n    // 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n    for (int i = start; i &lt; choices.length; i++) {\n        // 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する\n        // 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // 試す：選択を行い、target と start を更新\n        state.add(choices[i]);\n        // 次の選択へ進む\n        backtrack(state, target - choices[i], choices, i, res);\n        // バックトラック：選択を取り消し、前の状態に戻す\n        state.remove(state.size() - 1);\n    }\n}\n\n/* 部分和 I を解く */\nList&lt;List&lt;Integer&gt;&gt; subsetSumI(int[] nums, int target) {\n    List&lt;Integer&gt; state = new ArrayList&lt;&gt;(); // 状態（部分集合）\n    Arrays.sort(nums); // nums をソート\n    int start = 0; // 開始点を走査\n    List&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;&gt;(); // 結果リスト（部分集合のリスト）\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_i.cs<pre><code>/* バックトラッキング：部分和 I */\nvoid Backtrack(List&lt;int&gt; state, int target, int[] choices, int start, List&lt;List&lt;int&gt;&gt; res) {\n    // 部分集合の和が target に等しければ、解を記録\n    if (target == 0) {\n        res.Add(new List&lt;int&gt;(state));\n        return;\n    }\n    // すべての選択肢を走査\n    // 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n    for (int i = start; i &lt; choices.Length; i++) {\n        // 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する\n        // 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // 試す：選択を行い、target と start を更新\n        state.Add(choices[i]);\n        // 次の選択へ進む\n        Backtrack(state, target - choices[i], choices, i, res);\n        // バックトラック：選択を取り消し、前の状態に戻す\n        state.RemoveAt(state.Count - 1);\n    }\n}\n\n/* 部分和 I を解く */\nList&lt;List&lt;int&gt;&gt; SubsetSumI(int[] nums, int target) {\n    List&lt;int&gt; state = []; // 状態（部分集合）\n    Array.Sort(nums); // nums をソート\n    int start = 0; // 開始点を走査\n    List&lt;List&lt;int&gt;&gt; res = []; // 結果リスト（部分集合のリスト）\n    Backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_i.go<pre><code>/* バックトラッキング：部分和 I */\nfunc backtrackSubsetSumI(start, target int, state, choices *[]int, res *[][]int) {\n    // 部分集合の和が target に等しければ、解を記録\n    if target == 0 {\n        newState := append([]int{}, *state...)\n        *res = append(*res, newState)\n        return\n    }\n    // すべての選択肢を走査\n    // 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n    for i := start; i &lt; len(*choices); i++ {\n        // 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する\n        // 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため\n        if target-(*choices)[i] &lt; 0 {\n            break\n        }\n        // 試す：選択を行い、target と start を更新\n        *state = append(*state, (*choices)[i])\n        // 次の選択へ進む\n        backtrackSubsetSumI(i, target-(*choices)[i], state, choices, res)\n        // バックトラック：選択を取り消し、前の状態に戻す\n        *state = (*state)[:len(*state)-1]\n    }\n}\n\n/* 部分和 I を解く */\nfunc subsetSumI(nums []int, target int) [][]int {\n    state := make([]int, 0) // 状態（部分集合）\n    sort.Ints(nums)         // nums をソート\n    start := 0              // 開始点を走査\n    res := make([][]int, 0) // 結果リスト（部分集合のリスト）\n    backtrackSubsetSumI(start, target, &amp;state, &amp;nums, &amp;res)\n    return res\n}\n</code></pre> subset_sum_i.swift<pre><code>/* バックトラッキング：部分和 I */\nfunc backtrack(state: inout [Int], target: Int, choices: [Int], start: Int, res: inout [[Int]]) {\n    // 部分集合の和が target に等しければ、解を記録\n    if target == 0 {\n        res.append(state)\n        return\n    }\n    // すべての選択肢を走査\n    // 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n    for i in choices.indices.dropFirst(start) {\n        // 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する\n        // 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため\n        if target - choices[i] &lt; 0 {\n            break\n        }\n        // 試す：選択を行い、target と start を更新\n        state.append(choices[i])\n        // 次の選択へ進む\n        backtrack(state: &amp;state, target: target - choices[i], choices: choices, start: i, res: &amp;res)\n        // バックトラック：選択を取り消し、前の状態に戻す\n        state.removeLast()\n    }\n}\n\n/* 部分和 I を解く */\nfunc subsetSumI(nums: [Int], target: Int) -&gt; [[Int]] {\n    var state: [Int] = [] // 状態（部分集合）\n    let nums = nums.sorted() // nums をソート\n    let start = 0 // 開始点を走査\n    var res: [[Int]] = [] // 結果リスト（部分集合のリスト）\n    backtrack(state: &amp;state, target: target, choices: nums, start: start, res: &amp;res)\n    return res\n}\n</code></pre> subset_sum_i.js<pre><code>/* バックトラッキング：部分和 I */\nfunction backtrack(state, target, choices, start, res) {\n    // 部分集合の和が target に等しければ、解を記録\n    if (target === 0) {\n        res.push([...state]);\n        return;\n    }\n    // すべての選択肢を走査\n    // 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n    for (let i = start; i &lt; choices.length; i++) {\n        // 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する\n        // 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // 試す：選択を行い、target と start を更新\n        state.push(choices[i]);\n        // 次の選択へ進む\n        backtrack(state, target - choices[i], choices, i, res);\n        // バックトラック：選択を取り消し、前の状態に戻す\n        state.pop();\n    }\n}\n\n/* 部分和 I を解く */\nfunction subsetSumI(nums, target) {\n    const state = []; // 状態（部分集合）\n    nums.sort((a, b) =&gt; a - b); // nums をソート\n    const start = 0; // 開始点を走査\n    const res = []; // 結果リスト（部分集合のリスト）\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_i.ts<pre><code>/* バックトラッキング：部分和 I */\nfunction backtrack(\n    state: number[],\n    target: number,\n    choices: number[],\n    start: number,\n    res: number[][]\n): void {\n    // 部分集合の和が target に等しければ、解を記録\n    if (target === 0) {\n        res.push([...state]);\n        return;\n    }\n    // すべての選択肢を走査\n    // 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n    for (let i = start; i &lt; choices.length; i++) {\n        // 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する\n        // 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // 試す：選択を行い、target と start を更新\n        state.push(choices[i]);\n        // 次の選択へ進む\n        backtrack(state, target - choices[i], choices, i, res);\n        // バックトラック：選択を取り消し、前の状態に戻す\n        state.pop();\n    }\n}\n\n/* 部分和 I を解く */\nfunction subsetSumI(nums: number[], target: number): number[][] {\n    const state = []; // 状態（部分集合）\n    nums.sort((a, b) =&gt; a - b); // nums をソート\n    const start = 0; // 開始点を走査\n    const res = []; // 結果リスト（部分集合のリスト）\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_i.dart<pre><code>/* バックトラッキング：部分和 I */\nvoid backtrack(\n  List&lt;int&gt; state,\n  int target,\n  List&lt;int&gt; choices,\n  int start,\n  List&lt;List&lt;int&gt;&gt; res,\n) {\n  // 部分集合の和が target に等しければ、解を記録\n  if (target == 0) {\n    res.add(List.from(state));\n    return;\n  }\n  // すべての選択肢を走査\n  // 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n  for (int i = start; i &lt; choices.length; i++) {\n    // 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する\n    // 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため\n    if (target - choices[i] &lt; 0) {\n      break;\n    }\n    // 試す：選択を行い、target と start を更新\n    state.add(choices[i]);\n    // 次の選択へ進む\n    backtrack(state, target - choices[i], choices, i, res);\n    // バックトラック：選択を取り消し、前の状態に戻す\n    state.removeLast();\n  }\n}\n\n/* 部分和 I を解く */\nList&lt;List&lt;int&gt;&gt; subsetSumI(List&lt;int&gt; nums, int target) {\n  List&lt;int&gt; state = []; // 状態（部分集合）\n  nums.sort(); // nums をソート\n  int start = 0; // 開始点を走査\n  List&lt;List&lt;int&gt;&gt; res = []; // 結果リスト（部分集合のリスト）\n  backtrack(state, target, nums, start, res);\n  return res;\n}\n</code></pre> subset_sum_i.rs<pre><code>/* バックトラッキング：部分和 I */\nfn backtrack(\n    state: &amp;mut Vec&lt;i32&gt;,\n    target: i32,\n    choices: &amp;[i32],\n    start: usize,\n    res: &amp;mut Vec&lt;Vec&lt;i32&gt;&gt;,\n) {\n    // 部分集合の和が target に等しければ、解を記録\n    if target == 0 {\n        res.push(state.clone());\n        return;\n    }\n    // すべての選択肢を走査\n    // 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n    for i in start..choices.len() {\n        // 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する\n        // 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため\n        if target - choices[i] &lt; 0 {\n            break;\n        }\n        // 試す：選択を行い、target と start を更新\n        state.push(choices[i]);\n        // 次の選択へ進む\n        backtrack(state, target - choices[i], choices, i, res);\n        // バックトラック：選択を取り消し、前の状態に戻す\n        state.pop();\n    }\n}\n\n/* 部分和 I を解く */\nfn subset_sum_i(nums: &amp;mut [i32], target: i32) -&gt; Vec&lt;Vec&lt;i32&gt;&gt; {\n    let mut state = Vec::new(); // 状態（部分集合）\n    nums.sort(); // nums をソート\n    let start = 0; // 開始点を走査\n    let mut res = Vec::new(); // 結果リスト（部分集合のリスト）\n    backtrack(&amp;mut state, target, nums, start, &amp;mut res);\n    res\n}\n</code></pre> subset_sum_i.c<pre><code>/* バックトラッキング：部分和 I */\nvoid backtrack(int target, int *choices, int choicesSize, int start) {\n    // 部分集合の和が target に等しければ、解を記録\n    if (target == 0) {\n        for (int i = 0; i &lt; stateSize; ++i) {\n            res[resSize][i] = state[i];\n        }\n        resColSizes[resSize++] = stateSize;\n        return;\n    }\n    // すべての選択肢を走査\n    // 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n    for (int i = start; i &lt; choicesSize; i++) {\n        // 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する\n        // 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // 試す：選択を行い、target と start を更新\n        state[stateSize] = choices[i];\n        stateSize++;\n        // 次の選択へ進む\n        backtrack(target - choices[i], choices, choicesSize, i);\n        // バックトラック：選択を取り消し、前の状態に戻す\n        stateSize--;\n    }\n}\n\n/* 部分和 I を解く */\nvoid subsetSumI(int *nums, int numsSize, int target) {\n    qsort(nums, numsSize, sizeof(int), cmp); // nums をソート\n    int start = 0;                           // 開始点を走査\n    backtrack(target, nums, numsSize, start);\n}\n</code></pre> subset_sum_i.kt<pre><code>/* バックトラッキング：部分和 I */\nfun backtrack(\n    state: MutableList&lt;Int&gt;,\n    target: Int,\n    choices: IntArray,\n    start: Int,\n    res: MutableList&lt;MutableList&lt;Int&gt;?&gt;\n) {\n    // 部分集合の和が target に等しければ、解を記録\n    if (target == 0) {\n        res.add(state.toMutableList())\n        return\n    }\n    // すべての選択肢を走査\n    // 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n    for (i in start..&lt;choices.size) {\n        // 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する\n        // 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため\n        if (target - choices[i] &lt; 0) {\n            break\n        }\n        // 試す：選択を行い、target と start を更新\n        state.add(choices[i])\n        // 次の選択へ進む\n        backtrack(state, target - choices[i], choices, i, res)\n        // バックトラック：選択を取り消し、前の状態に戻す\n        state.removeAt(state.size - 1)\n    }\n}\n\n/* 部分和 I を解く */\nfun subsetSumI(nums: IntArray, target: Int): MutableList&lt;MutableList&lt;Int&gt;?&gt; {\n    val state = mutableListOf&lt;Int&gt;() // 状態（部分集合）\n    nums.sort() // nums をソート\n    val start = 0 // 開始点を走査\n    val res = mutableListOf&lt;MutableList&lt;Int&gt;?&gt;() // 結果リスト（部分集合のリスト）\n    backtrack(state, target, nums, start, res)\n    return res\n}\n</code></pre> subset_sum_i.rb<pre><code>### バックトラッキング: 部分和 I ###\ndef backtrack(state, target, choices, start, res)\n  # 部分集合の和が target に等しければ、解を記録\n  if target.zero?\n    res &lt;&lt; state.dup\n    return\n  end\n  # すべての選択肢を走査\n  # 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n  for i in start...choices.length\n    # 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する\n    # 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため\n    break if target - choices[i] &lt; 0\n    # 試す：選択を行い、target と start を更新\n    state &lt;&lt; choices[i]\n    # 次の選択へ進む\n    backtrack(state, target - choices[i], choices, i, res)\n    # バックトラック：選択を取り消し、前の状態に戻す\n    state.pop\n  end\nend\n\n### 部分和 I を解く ###\ndef subset_sum_i(nums, target)\n  state = [] # 状態（部分集合）\n  nums.sort! # nums をソート\n  start = 0 # 開始点を走査\n  res = [] # 結果リスト（部分集合のリスト）\n  backtrack(state, target, nums, start, res)\n  res\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>次の図は、配列 \\([3, 4, 5]\\) と目標値 \\(9\\) を上のコードに入力したときの、全体のバックトラッキング過程を示しています。</p> <p></p> <p> 図 13-12   部分和 I のバックトラッキング過程 </p>","path":["第 13 章 &nbsp; バックトラッキング","13.3 &nbsp; 部分和問題"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#1332","level":2,"title":"13.3.2   重複要素を考慮する場合","text":"<p>Question</p> <p>正整数配列 <code>nums</code> と目標の正整数 <code>target</code> が与えられたとき、要素の和が <code>target</code> に等しくなるすべての組合せを見つけてください。与えられた配列には重複要素が含まれる可能性があり、各要素は 1 回しか選択できません。これらの組合せをリスト形式で返してください。リストに重複する組合せを含めてはなりません。</p> <p>前問と比べると、この問題の入力配列には重複要素が含まれる可能性があります。そのため、新たな問題が生じます。例えば、配列 \\([4, \\hat{4}, 5]\\) と目標値 \\(9\\) が与えられると、既存コードの出力は \\([4, 5], [\\hat{4}, 5]\\) となり、重複部分集合が現れます。</p> <p>この重複が生じる原因は、同じ値の要素があるラウンドで複数回選ばれてしまうことにあります。次の図では、1 回目には 3 つの選択肢があり、そのうち 2 つはどちらも \\(4\\) です。これにより 2 本の重複した探索分岐が生じ、重複部分集合が出力されます。同様に、2 回目の 2 つの \\(4\\) も重複部分集合を生みます。</p> <p></p> <p> 図 13-13   等しい要素によって生じる重複部分集合 </p>","path":["第 13 章 &nbsp; バックトラッキング","13.3 &nbsp; 部分和問題"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#1_1","level":3,"title":"1.   等しい要素の枝刈り","text":"<p>この問題を解決するには、各ラウンドで等しい要素が 1 回しか選ばれないように制限する必要があります。実装方法は巧妙です。配列はすでにソートされているため、等しい要素は必ず隣り合っています。したがって、あるラウンドの選択で現在の要素が左隣の要素と等しいなら、それはすでに選ばれたことを意味するので、その要素を直接スキップします。</p> <p>同時に、**この問題では各配列要素を 1 回しか選択できない**という制約もあります。幸い、この制約も変数 <code>start</code> を使って満たせます。すなわち、選択 \\(x_{i}\\) を行った後、次のラウンドはインデックス \\(i + 1\\) から後ろへ走査するよう設定します。これにより、重複部分集合を除去できるだけでなく、同じ要素を繰り返し選ぶことも防げます。</p>","path":["第 13 章 &nbsp; バックトラッキング","13.3 &nbsp; 部分和問題"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#2_1","level":3,"title":"2.   コード実装","text":"PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby subset_sum_ii.py<pre><code>def backtrack(\n    state: list[int], target: int, choices: list[int], start: int, res: list[list[int]]\n):\n    \"\"\"バックトラッキング：部分和 II\"\"\"\n    # 部分集合の和が target に等しければ、解を記録\n    if target == 0:\n        res.append(list(state))\n        return\n    # すべての選択肢を走査\n    # 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n    # 枝刈り 3: start から走査し、同じ要素の重複選択を避ける\n    for i in range(start, len(choices)):\n        # 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する\n        # 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため\n        if target - choices[i] &lt; 0:\n            break\n        # 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする\n        if i &gt; start and choices[i] == choices[i - 1]:\n            continue\n        # 試す：選択を行い、target と start を更新\n        state.append(choices[i])\n        # 次の選択へ進む\n        backtrack(state, target - choices[i], choices, i + 1, res)\n        # バックトラック：選択を取り消し、前の状態に戻す\n        state.pop()\n\ndef subset_sum_ii(nums: list[int], target: int) -&gt; list[list[int]]:\n    \"\"\"部分和 II を解く\"\"\"\n    state = []  # 状態（部分集合）\n    nums.sort()  # nums をソート\n    start = 0  # 開始点を走査\n    res = []  # 結果リスト（部分集合のリスト）\n    backtrack(state, target, nums, start, res)\n    return res\n</code></pre> subset_sum_ii.cpp<pre><code>/* バックトラッキング：部分和 II */\nvoid backtrack(vector&lt;int&gt; &amp;state, int target, vector&lt;int&gt; &amp;choices, int start, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n    // 部分集合の和が target に等しければ、解を記録\n    if (target == 0) {\n        res.push_back(state);\n        return;\n    }\n    // すべての選択肢を走査\n    // 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n    // 枝刈り 3: start から走査し、同じ要素の重複選択を避ける\n    for (int i = start; i &lt; choices.size(); i++) {\n        // 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する\n        // 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする\n        if (i &gt; start &amp;&amp; choices[i] == choices[i - 1]) {\n            continue;\n        }\n        // 試す：選択を行い、target と start を更新\n        state.push_back(choices[i]);\n        // 次の選択へ進む\n        backtrack(state, target - choices[i], choices, i + 1, res);\n        // バックトラック：選択を取り消し、前の状態に戻す\n        state.pop_back();\n    }\n}\n\n/* 部分和 II を解く */\nvector&lt;vector&lt;int&gt;&gt; subsetSumII(vector&lt;int&gt; &amp;nums, int target) {\n    vector&lt;int&gt; state;              // 状態（部分集合）\n    sort(nums.begin(), nums.end()); // nums をソート\n    int start = 0;                  // 開始点を走査\n    vector&lt;vector&lt;int&gt;&gt; res;        // 結果リスト（部分集合のリスト）\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_ii.java<pre><code>/* バックトラッキング：部分和 II */\nvoid backtrack(List&lt;Integer&gt; state, int target, int[] choices, int start, List&lt;List&lt;Integer&gt;&gt; res) {\n    // 部分集合の和が target に等しければ、解を記録\n    if (target == 0) {\n        res.add(new ArrayList&lt;&gt;(state));\n        return;\n    }\n    // すべての選択肢を走査\n    // 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n    // 枝刈り 3: start から走査し、同じ要素の重複選択を避ける\n    for (int i = start; i &lt; choices.length; i++) {\n        // 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する\n        // 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする\n        if (i &gt; start &amp;&amp; choices[i] == choices[i - 1]) {\n            continue;\n        }\n        // 試す：選択を行い、target と start を更新\n        state.add(choices[i]);\n        // 次の選択へ進む\n        backtrack(state, target - choices[i], choices, i + 1, res);\n        // バックトラック：選択を取り消し、前の状態に戻す\n        state.remove(state.size() - 1);\n    }\n}\n\n/* 部分和 II を解く */\nList&lt;List&lt;Integer&gt;&gt; subsetSumII(int[] nums, int target) {\n    List&lt;Integer&gt; state = new ArrayList&lt;&gt;(); // 状態（部分集合）\n    Arrays.sort(nums); // nums をソート\n    int start = 0; // 開始点を走査\n    List&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;&gt;(); // 結果リスト（部分集合のリスト）\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_ii.cs<pre><code>/* バックトラッキング：部分和 II */\nvoid Backtrack(List&lt;int&gt; state, int target, int[] choices, int start, List&lt;List&lt;int&gt;&gt; res) {\n    // 部分集合の和が target に等しければ、解を記録\n    if (target == 0) {\n        res.Add(new List&lt;int&gt;(state));\n        return;\n    }\n    // すべての選択肢を走査\n    // 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n    // 枝刈り 3: start から走査し、同じ要素の重複選択を避ける\n    for (int i = start; i &lt; choices.Length; i++) {\n        // 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する\n        // 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする\n        if (i &gt; start &amp;&amp; choices[i] == choices[i - 1]) {\n            continue;\n        }\n        // 試す：選択を行い、target と start を更新\n        state.Add(choices[i]);\n        // 次の選択へ進む\n        Backtrack(state, target - choices[i], choices, i + 1, res);\n        // バックトラック：選択を取り消し、前の状態に戻す\n        state.RemoveAt(state.Count - 1);\n    }\n}\n\n/* 部分和 II を解く */\nList&lt;List&lt;int&gt;&gt; SubsetSumII(int[] nums, int target) {\n    List&lt;int&gt; state = []; // 状態（部分集合）\n    Array.Sort(nums); // nums をソート\n    int start = 0; // 開始点を走査\n    List&lt;List&lt;int&gt;&gt; res = []; // 結果リスト（部分集合のリスト）\n    Backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_ii.go<pre><code>/* バックトラッキング：部分和 II */\nfunc backtrackSubsetSumII(start, target int, state, choices *[]int, res *[][]int) {\n    // 部分集合の和が target に等しければ、解を記録\n    if target == 0 {\n        newState := append([]int{}, *state...)\n        *res = append(*res, newState)\n        return\n    }\n    // すべての選択肢を走査\n    // 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n    // 枝刈り 3: start から走査し、同じ要素の重複選択を避ける\n    for i := start; i &lt; len(*choices); i++ {\n        // 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する\n        // 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため\n        if target-(*choices)[i] &lt; 0 {\n            break\n        }\n        // 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする\n        if i &gt; start &amp;&amp; (*choices)[i] == (*choices)[i-1] {\n            continue\n        }\n        // 試す：選択を行い、target と start を更新\n        *state = append(*state, (*choices)[i])\n        // 次の選択へ進む\n        backtrackSubsetSumII(i+1, target-(*choices)[i], state, choices, res)\n        // バックトラック：選択を取り消し、前の状態に戻す\n        *state = (*state)[:len(*state)-1]\n    }\n}\n\n/* 部分和 II を解く */\nfunc subsetSumII(nums []int, target int) [][]int {\n    state := make([]int, 0) // 状態（部分集合）\n    sort.Ints(nums)         // nums をソート\n    start := 0              // 開始点を走査\n    res := make([][]int, 0) // 結果リスト（部分集合のリスト）\n    backtrackSubsetSumII(start, target, &amp;state, &amp;nums, &amp;res)\n    return res\n}\n</code></pre> subset_sum_ii.swift<pre><code>/* バックトラッキング：部分和 II */\nfunc backtrack(state: inout [Int], target: Int, choices: [Int], start: Int, res: inout [[Int]]) {\n    // 部分集合の和が target に等しければ、解を記録\n    if target == 0 {\n        res.append(state)\n        return\n    }\n    // すべての選択肢を走査\n    // 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n    // 枝刈り 3: start から走査し、同じ要素の重複選択を避ける\n    for i in choices.indices.dropFirst(start) {\n        // 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する\n        // 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため\n        if target - choices[i] &lt; 0 {\n            break\n        }\n        // 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする\n        if i &gt; start, choices[i] == choices[i - 1] {\n            continue\n        }\n        // 試す：選択を行い、target と start を更新\n        state.append(choices[i])\n        // 次の選択へ進む\n        backtrack(state: &amp;state, target: target - choices[i], choices: choices, start: i + 1, res: &amp;res)\n        // バックトラック：選択を取り消し、前の状態に戻す\n        state.removeLast()\n    }\n}\n\n/* 部分和 II を解く */\nfunc subsetSumII(nums: [Int], target: Int) -&gt; [[Int]] {\n    var state: [Int] = [] // 状態（部分集合）\n    let nums = nums.sorted() // nums をソート\n    let start = 0 // 開始点を走査\n    var res: [[Int]] = [] // 結果リスト（部分集合のリスト）\n    backtrack(state: &amp;state, target: target, choices: nums, start: start, res: &amp;res)\n    return res\n}\n</code></pre> subset_sum_ii.js<pre><code>/* バックトラッキング：部分和 II */\nfunction backtrack(state, target, choices, start, res) {\n    // 部分集合の和が target に等しければ、解を記録\n    if (target === 0) {\n        res.push([...state]);\n        return;\n    }\n    // すべての選択肢を走査\n    // 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n    // 枝刈り 3: start から走査し、同じ要素の重複選択を避ける\n    for (let i = start; i &lt; choices.length; i++) {\n        // 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する\n        // 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする\n        if (i &gt; start &amp;&amp; choices[i] === choices[i - 1]) {\n            continue;\n        }\n        // 試す：選択を行い、target と start を更新\n        state.push(choices[i]);\n        // 次の選択へ進む\n        backtrack(state, target - choices[i], choices, i + 1, res);\n        // バックトラック：選択を取り消し、前の状態に戻す\n        state.pop();\n    }\n}\n\n/* 部分和 II を解く */\nfunction subsetSumII(nums, target) {\n    const state = []; // 状態（部分集合）\n    nums.sort((a, b) =&gt; a - b); // nums をソート\n    const start = 0; // 開始点を走査\n    const res = []; // 結果リスト（部分集合のリスト）\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_ii.ts<pre><code>/* バックトラッキング：部分和 II */\nfunction backtrack(\n    state: number[],\n    target: number,\n    choices: number[],\n    start: number,\n    res: number[][]\n): void {\n    // 部分集合の和が target に等しければ、解を記録\n    if (target === 0) {\n        res.push([...state]);\n        return;\n    }\n    // すべての選択肢を走査\n    // 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n    // 枝刈り 3: start から走査し、同じ要素の重複選択を避ける\n    for (let i = start; i &lt; choices.length; i++) {\n        // 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する\n        // 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする\n        if (i &gt; start &amp;&amp; choices[i] === choices[i - 1]) {\n            continue;\n        }\n        // 試す：選択を行い、target と start を更新\n        state.push(choices[i]);\n        // 次の選択へ進む\n        backtrack(state, target - choices[i], choices, i + 1, res);\n        // バックトラック：選択を取り消し、前の状態に戻す\n        state.pop();\n    }\n}\n\n/* 部分和 II を解く */\nfunction subsetSumII(nums: number[], target: number): number[][] {\n    const state = []; // 状態（部分集合）\n    nums.sort((a, b) =&gt; a - b); // nums をソート\n    const start = 0; // 開始点を走査\n    const res = []; // 結果リスト（部分集合のリスト）\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_ii.dart<pre><code>/* バックトラッキング：部分和 II */\nvoid backtrack(\n  List&lt;int&gt; state,\n  int target,\n  List&lt;int&gt; choices,\n  int start,\n  List&lt;List&lt;int&gt;&gt; res,\n) {\n  // 部分集合の和が target に等しければ、解を記録\n  if (target == 0) {\n    res.add(List.from(state));\n    return;\n  }\n  // すべての選択肢を走査\n  // 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n  // 枝刈り 3: start から走査し、同じ要素の重複選択を避ける\n  for (int i = start; i &lt; choices.length; i++) {\n    // 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する\n    // 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため\n    if (target - choices[i] &lt; 0) {\n      break;\n    }\n    // 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする\n    if (i &gt; start &amp;&amp; choices[i] == choices[i - 1]) {\n      continue;\n    }\n    // 試す：選択を行い、target と start を更新\n    state.add(choices[i]);\n    // 次の選択へ進む\n    backtrack(state, target - choices[i], choices, i + 1, res);\n    // バックトラック：選択を取り消し、前の状態に戻す\n    state.removeLast();\n  }\n}\n\n/* 部分和 II を解く */\nList&lt;List&lt;int&gt;&gt; subsetSumII(List&lt;int&gt; nums, int target) {\n  List&lt;int&gt; state = []; // 状態（部分集合）\n  nums.sort(); // nums をソート\n  int start = 0; // 開始点を走査\n  List&lt;List&lt;int&gt;&gt; res = []; // 結果リスト（部分集合のリスト）\n  backtrack(state, target, nums, start, res);\n  return res;\n}\n</code></pre> subset_sum_ii.rs<pre><code>/* バックトラッキング：部分和 II */\nfn backtrack(\n    state: &amp;mut Vec&lt;i32&gt;,\n    target: i32,\n    choices: &amp;[i32],\n    start: usize,\n    res: &amp;mut Vec&lt;Vec&lt;i32&gt;&gt;,\n) {\n    // 部分集合の和が target に等しければ、解を記録\n    if target == 0 {\n        res.push(state.clone());\n        return;\n    }\n    // すべての選択肢を走査\n    // 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n    // 枝刈り 3: start から走査し、同じ要素の重複選択を避ける\n    for i in start..choices.len() {\n        // 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する\n        // 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため\n        if target - choices[i] &lt; 0 {\n            break;\n        }\n        // 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする\n        if i &gt; start &amp;&amp; choices[i] == choices[i - 1] {\n            continue;\n        }\n        // 試す：選択を行い、target と start を更新\n        state.push(choices[i]);\n        // 次の選択へ進む\n        backtrack(state, target - choices[i], choices, i + 1, res);\n        // バックトラック：選択を取り消し、前の状態に戻す\n        state.pop();\n    }\n}\n\n/* 部分和 II を解く */\nfn subset_sum_ii(nums: &amp;mut [i32], target: i32) -&gt; Vec&lt;Vec&lt;i32&gt;&gt; {\n    let mut state = Vec::new(); // 状態（部分集合）\n    nums.sort(); // nums をソート\n    let start = 0; // 開始点を走査\n    let mut res = Vec::new(); // 結果リスト（部分集合のリスト）\n    backtrack(&amp;mut state, target, nums, start, &amp;mut res);\n    res\n}\n</code></pre> subset_sum_ii.c<pre><code>/* バックトラッキング：部分和 II */\nvoid backtrack(int target, int *choices, int choicesSize, int start) {\n    // 部分集合の和が target に等しければ、解を記録\n    if (target == 0) {\n        for (int i = 0; i &lt; stateSize; i++) {\n            res[resSize][i] = state[i];\n        }\n        resColSizes[resSize++] = stateSize;\n        return;\n    }\n    // すべての選択肢を走査\n    // 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n    // 枝刈り 3: start から走査し、同じ要素の重複選択を避ける\n    for (int i = start; i &lt; choicesSize; i++) {\n        // 枝刈り 1: 部分集合の和が target を超えたら、そのままスキップする\n        if (target - choices[i] &lt; 0) {\n            continue;\n        }\n        // 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする\n        if (i &gt; start &amp;&amp; choices[i] == choices[i - 1]) {\n            continue;\n        }\n        // 試す：選択を行い、target と start を更新\n        state[stateSize] = choices[i];\n        stateSize++;\n        // 次の選択へ進む\n        backtrack(target - choices[i], choices, choicesSize, i + 1);\n        // バックトラック：選択を取り消し、前の状態に戻す\n        stateSize--;\n    }\n}\n\n/* 部分和 II を解く */\nvoid subsetSumII(int *nums, int numsSize, int target) {\n    // nums をソート\n    qsort(nums, numsSize, sizeof(int), cmp);\n    // バックトラッキングを開始\n    backtrack(target, nums, numsSize, 0);\n}\n</code></pre> subset_sum_ii.kt<pre><code>/* バックトラッキング：部分和 II */\nfun backtrack(\n    state: MutableList&lt;Int&gt;,\n    target: Int,\n    choices: IntArray,\n    start: Int,\n    res: MutableList&lt;MutableList&lt;Int&gt;?&gt;\n) {\n    // 部分集合の和が target に等しければ、解を記録\n    if (target == 0) {\n        res.add(state.toMutableList())\n        return\n    }\n    // すべての選択肢を走査\n    // 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n    // 枝刈り 3: start から走査し、同じ要素の重複選択を避ける\n    for (i in start..&lt;choices.size) {\n        // 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する\n        // 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため\n        if (target - choices[i] &lt; 0) {\n            break\n        }\n        // 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする\n        if (i &gt; start &amp;&amp; choices[i] == choices[i - 1]) {\n            continue\n        }\n        // 試す：選択を行い、target と start を更新\n        state.add(choices[i])\n        // 次の選択へ進む\n        backtrack(state, target - choices[i], choices, i + 1, res)\n        // バックトラック：選択を取り消し、前の状態に戻す\n        state.removeAt(state.size - 1)\n    }\n}\n\n/* 部分和 II を解く */\nfun subsetSumII(nums: IntArray, target: Int): MutableList&lt;MutableList&lt;Int&gt;?&gt; {\n    val state = mutableListOf&lt;Int&gt;() // 状態（部分集合）\n    nums.sort() // nums をソート\n    val start = 0 // 開始点を走査\n    val res = mutableListOf&lt;MutableList&lt;Int&gt;?&gt;() // 結果リスト（部分集合のリスト）\n    backtrack(state, target, nums, start, res)\n    return res\n}\n</code></pre> subset_sum_ii.rb<pre><code>### バックトラッキング法：部分和 II ###\ndef backtrack(state, target, choices, start, res)\n  # 部分集合の和が target に等しければ、解を記録\n  if target.zero?\n    res &lt;&lt; state.dup\n    return\n  end\n\n  # すべての選択肢を走査\n  # 枝刈り 2: start から走査し、重複する部分集合の生成を避ける\n  # 枝刈り 3: start から走査し、同じ要素の重複選択を避ける\n  for i in start...choices.length\n    # 枝刈り1：部分集合の和が target を超えたら、直ちにループを終了する\n    # 配列はソート済みで後続要素のほうが大きく、部分集合の和は必ず target を超えるため\n    break if target - choices[i] &lt; 0\n    # 枝刈り4：この要素が左隣の要素と等しければ、その探索分岐は重複しているためスキップする\n    next if i &gt; start &amp;&amp; choices[i] == choices[i - 1]\n    # 試す：選択を行い、target と start を更新\n    state &lt;&lt; choices[i]\n    # 次の選択へ進む\n    backtrack(state, target - choices[i], choices, i + 1, res)\n    # バックトラック：選択を取り消し、前の状態に戻す\n    state.pop\n  end\nend\n\n### 部分和 II を解く ###\ndef subset_sum_ii(nums, target)\n  state = [] # 状態（部分集合）\n  nums.sort! # nums をソート\n  start = 0 # 開始点を走査\n  res = [] # 結果リスト（部分集合のリスト）\n  backtrack(state, target, nums, start, res)\n  res\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>次の図は、配列 \\([4, 4, 5]\\) と目標値 \\(9\\) に対するバックトラッキング過程を示しており、全部で 4 種類の枝刈り操作が含まれています。図とコードコメントを対応させながら、探索全体の流れと、各枝刈り操作がどのように機能するかを理解してください。</p> <p></p> <p> 図 13-14   部分和 II のバックトラッキング過程 </p>","path":["第 13 章 &nbsp; バックトラッキング","13.3 &nbsp; 部分和問題"],"tags":[]},{"location":"chapter_backtracking/summary/","level":1,"title":"13.5   まとめ","text":"","path":["第 13 章 &nbsp; バックトラッキング","13.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_backtracking/summary/#1","level":3,"title":"1.   重要なポイントの振り返り","text":"<ul> <li>バックトラッキングアルゴリズムの本質は全探索法であり、解空間を深さ優先で走査することで条件を満たす解を探索します。探索の過程で条件を満たす解に出会ったら記録し、すべての解を見つけるか探索が完了するまで続けます。</li> <li>バックトラッキングアルゴリズムの探索過程は、試行と戻るという 2 つの部分から成ります。深さ優先探索によってさまざまな選択を試し、制約条件を満たさない状況に遭遇した場合は直前の選択を取り消して前の状態に戻り、ほかの選択を引き続き試します。試行と戻るは互いに逆方向の操作です。</li> <li>バックトラッキング問題には通常複数の制約条件が含まれており、それらを枝刈りに利用できます。枝刈りによって不要な探索分岐を早期に打ち切り、探索効率を大幅に高められます。</li> <li>バックトラッキングアルゴリズムは主に探索問題と制約充足問題の解決に用いられます。組合せ最適化問題もバックトラッキングで解けますが、より高効率またはより適した解法が存在することが少なくありません。</li> <li>全順列問題の目的は、与えられた集合要素のすべての可能な並べ方を探索することです。各要素が選択済みかどうかを配列で記録し、同じ要素を重複して選ぶ探索分岐を刈り取ることで、各要素が 1 度だけ選ばれるようにします。</li> <li>全順列問題では、集合内に重複要素があると最終結果にも重複した順列が現れます。各ラウンドで等しい要素は 1 回しか選べないように制約する必要があり、通常はハッシュ集合を用いて実現します。</li> <li>部分和問題の目標は、与えられた集合の中から和が目標値となるすべての部分集合を見つけることです。集合では要素順序を区別しませんが、探索過程では順序違いの結果も出力されるため、重複部分集合が生じます。そこで、バックトラッキング前にデータをソートし、各ラウンドの走査開始位置を示す変数を設定することで、重複部分集合を生成する探索分岐を枝刈りします。</li> <li>部分和問題では、配列中の等しい要素が重複集合を生みます。配列がソート済みであるという前提を利用し、隣接要素が等しいかどうかを判定して枝刈りすることで、等しい要素が各ラウンドで 1 回しか選ばれないようにします。</li> <li>\\(n\\) クイーン問題の目的は、\\(n \\times n\\) の盤面に \\(n\\) 個のクイーンを配置する方法を見つけることであり、どの 2 つのクイーンも互いに攻撃できないことが条件です。この問題の制約には行制約、列制約、主対角線制約、副対角線制約があります。行制約を満たすため、行ごとに配置する戦略を採用し、各行に 1 個のクイーンを置くことを保証します。</li> <li>列制約と対角線制約の扱い方は似ています。列制約については、各列にクイーンが存在するかどうかを配列で記録し、選択したマスが有効かどうかを判定します。対角線制約については、主対角線と副対角線それぞれにクイーンが存在するかを 2 つの配列で記録します。難点は、同じ主対角線または副対角線上にあるマスが満たす行列インデックスの規則を見つけることにあります。</li> </ul>","path":["第 13 章 &nbsp; バックトラッキング","13.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_backtracking/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q：バックトラッキングと再帰の関係はどのように理解すればよいですか？</p> <p>全体として見ると、バックトラッキングは「アルゴリズム戦略」の一種であり、再帰はむしろ「道具」に近いものです。</p> <ul> <li>バックトラッキングアルゴリズムは通常、再帰に基づいて実装されます。ただし、バックトラッキングは再帰の応用場面の 1 つであり、探索問題における再帰の応用です。</li> <li>再帰の構造は「部分問題への分解」という問題解決パラダイムを表しており、分割統治、バックトラッキング、動的計画法（メモ化再帰）などの問題によく用いられます。</li> </ul>","path":["第 13 章 &nbsp; バックトラッキング","13.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_computational_complexity/","level":1,"title":"第 2 章   計算量解析","text":"<p>Abstract</p> <p>計算量解析は、広大なアルゴリズム宇宙における時空の案内人のようなものです。</p> <p>それは、時間と空間という二つの次元で私たちをより深く探求へ導き、より洗練された解決策を見つけ出します。</p>","path":["第 2 章 &nbsp; 計算量解析"],"tags":[]},{"location":"chapter_computational_complexity/#_1","level":2,"title":"章の内容","text":"<ul> <li>2.1   アルゴリズム効率の評価</li> <li>2.2   反復と再帰</li> <li>2.3   時間計算量</li> <li>2.4   空間計算量</li> <li>2.5   まとめ</li> </ul>","path":["第 2 章 &nbsp; 計算量解析"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/","level":1,"title":"2.2   反復と再帰","text":"<p>アルゴリズムでは、ある処理を繰り返し実行することがよくあり、これは複雑度解析と密接に関係しています。そのため、時間計算量と空間計算量を紹介する前に、まずプログラム内で反復実行を実現する方法、つまり 2 つの基本的な制御構造である反復と再帰について見ていきます。</p>","path":["第 2 章 &nbsp; 計算量解析","2.2 &nbsp; 反復と再帰"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#221","level":2,"title":"2.2.1   反復","text":"<p>反復（iteration）は、ある処理を繰り返し実行するための制御構造です。反復では、プログラムは一定の条件を満たす間、あるコード片を繰り返し実行し、その条件を満たさなくなるまで続けます。</p>","path":["第 2 章 &nbsp; 計算量解析","2.2 &nbsp; 反復と再帰"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#1-for","level":3,"title":"1.   for ループ","text":"<p><code>for</code> ループは最も一般的な反復形式の 1 つで、反復回数があらかじめ分かっている場合に適しています。</p> <p>次の関数は <code>for</code> ループを用いて \\(1 + 2 + \\dots + n\\) の総和を計算しており、その結果は変数 <code>res</code> に記録されます。なお、Python の <code>range(a, b)</code> に対応する区間は「左閉右開」であり、走査範囲は \\(a, a + 1, \\dots, b-1\\) です。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby iteration.py<pre><code>def for_loop(n: int) -&gt; int:\n    \"\"\"for ループ\"\"\"\n    res = 0\n    # 1, 2, ..., n-1, n を順に加算する\n    for i in range(1, n + 1):\n        res += i\n    return res\n</code></pre> iteration.cpp<pre><code>/* for ループ */\nint forLoop(int n) {\n    int res = 0;\n    // 1, 2, ..., n-1, n を順に加算する\n    for (int i = 1; i &lt;= n; ++i) {\n        res += i;\n    }\n    return res;\n}\n</code></pre> iteration.java<pre><code>/* for ループ */\nint forLoop(int n) {\n    int res = 0;\n    // 1, 2, ..., n-1, n を順に加算する\n    for (int i = 1; i &lt;= n; i++) {\n        res += i;\n    }\n    return res;\n}\n</code></pre> iteration.cs<pre><code>/* for ループ */\nint ForLoop(int n) {\n    int res = 0;\n    // 1, 2, ..., n-1, n を順に加算する\n    for (int i = 1; i &lt;= n; i++) {\n        res += i;\n    }\n    return res;\n}\n</code></pre> iteration.go<pre><code>/* for ループ */\nfunc forLoop(n int) int {\n    res := 0\n    // 1, 2, ..., n-1, n を順に加算する\n    for i := 1; i &lt;= n; i++ {\n        res += i\n    }\n    return res\n}\n</code></pre> iteration.swift<pre><code>/* for ループ */\nfunc forLoop(n: Int) -&gt; Int {\n    var res = 0\n    // 1, 2, ..., n-1, n を順に加算する\n    for i in 1 ... n {\n        res += i\n    }\n    return res\n}\n</code></pre> iteration.js<pre><code>/* for ループ */\nfunction forLoop(n) {\n    let res = 0;\n    // 1, 2, ..., n-1, n を順に加算する\n    for (let i = 1; i &lt;= n; i++) {\n        res += i;\n    }\n    return res;\n}\n</code></pre> iteration.ts<pre><code>/* for ループ */\nfunction forLoop(n: number): number {\n    let res = 0;\n    // 1, 2, ..., n-1, n を順に加算する\n    for (let i = 1; i &lt;= n; i++) {\n        res += i;\n    }\n    return res;\n}\n</code></pre> iteration.dart<pre><code>/* for ループ */\nint forLoop(int n) {\n  int res = 0;\n  // 1, 2, ..., n-1, n を順に加算する\n  for (int i = 1; i &lt;= n; i++) {\n    res += i;\n  }\n  return res;\n}\n</code></pre> iteration.rs<pre><code>/* for ループ */\nfn for_loop(n: i32) -&gt; i32 {\n    let mut res = 0;\n    // 1, 2, ..., n-1, n を順に加算する\n    for i in 1..=n {\n        res += i;\n    }\n    res\n}\n</code></pre> iteration.c<pre><code>/* for ループ */\nint forLoop(int n) {\n    int res = 0;\n    // 1, 2, ..., n-1, n を順に加算する\n    for (int i = 1; i &lt;= n; i++) {\n        res += i;\n    }\n    return res;\n}\n</code></pre> iteration.kt<pre><code>/* for ループ */\nfun forLoop(n: Int): Int {\n    var res = 0\n    // 1, 2, ..., n-1, n を順に加算する\n    for (i in 1..n) {\n        res += i\n    }\n    return res\n}\n</code></pre> iteration.rb<pre><code>### for ループ ###\ndef for_loop(n)\n  res = 0\n\n  # 1, 2, ..., n-1, n を順に加算する\n  for i in 1..n\n    res += i\n  end\n\n  res\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>次の図は、この総和関数のフローチャートです。</p> <p></p> <p> 図 2-1   総和関数のフローチャート </p> <p>この総和関数の操作回数は入力データサイズ \\(n\\) に比例し、言い換えれば「線形関係」にあります。実際、時間計算量が記述するのはこの「線形関係」そのものです。関連内容は次節で詳しく説明します。</p>","path":["第 2 章 &nbsp; 計算量解析","2.2 &nbsp; 反復と再帰"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#2-while","level":3,"title":"2.   while ループ","text":"<p><code>for</code> ループと同様に、<code>while</code> ループも反復を実現する方法の 1 つです。<code>while</code> ループでは、各反復のたびにまず条件を確認し、条件が真であれば実行を続け、そうでなければループを終了します。</p> <p>次に、<code>while</code> ループを使って \\(1 + 2 + \\dots + n\\) の総和を求めてみましょう。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby iteration.py<pre><code>def while_loop(n: int) -&gt; int:\n    \"\"\"while ループ\"\"\"\n    res = 0\n    i = 1  # 条件変数を初期化する\n    # 1, 2, ..., n-1, n を順に加算する\n    while i &lt;= n:\n        res += i\n        i += 1  # 条件変数を更新する\n    return res\n</code></pre> iteration.cpp<pre><code>/* while ループ */\nint whileLoop(int n) {\n    int res = 0;\n    int i = 1; // 条件変数を初期化する\n    // 1, 2, ..., n-1, n を順に加算する\n    while (i &lt;= n) {\n        res += i;\n        i++; // 条件変数を更新する\n    }\n    return res;\n}\n</code></pre> iteration.java<pre><code>/* while ループ */\nint whileLoop(int n) {\n    int res = 0;\n    int i = 1; // 条件変数を初期化する\n    // 1, 2, ..., n-1, n を順に加算する\n    while (i &lt;= n) {\n        res += i;\n        i++; // 条件変数を更新する\n    }\n    return res;\n}\n</code></pre> iteration.cs<pre><code>/* while ループ */\nint WhileLoop(int n) {\n    int res = 0;\n    int i = 1; // 条件変数を初期化する\n    // 1, 2, ..., n-1, n を順に加算する\n    while (i &lt;= n) {\n        res += i;\n        i += 1; // 条件変数を更新する\n    }\n    return res;\n}\n</code></pre> iteration.go<pre><code>/* while ループ */\nfunc whileLoop(n int) int {\n    res := 0\n    // 条件変数を初期化する\n    i := 1\n    // 1, 2, ..., n-1, n を順に加算する\n    for i &lt;= n {\n        res += i\n        // 条件変数を更新する\n        i++\n    }\n    return res\n}\n</code></pre> iteration.swift<pre><code>/* while ループ */\nfunc whileLoop(n: Int) -&gt; Int {\n    var res = 0\n    var i = 1 // 条件変数を初期化する\n    // 1, 2, ..., n-1, n を順に加算する\n    while i &lt;= n {\n        res += i\n        i += 1 // 条件変数を更新する\n    }\n    return res\n}\n</code></pre> iteration.js<pre><code>/* while ループ */\nfunction whileLoop(n) {\n    let res = 0;\n    let i = 1; // 条件変数を初期化する\n    // 1, 2, ..., n-1, n を順に加算する\n    while (i &lt;= n) {\n        res += i;\n        i++; // 条件変数を更新する\n    }\n    return res;\n}\n</code></pre> iteration.ts<pre><code>/* while ループ */\nfunction whileLoop(n: number): number {\n    let res = 0;\n    let i = 1; // 条件変数を初期化する\n    // 1, 2, ..., n-1, n を順に加算する\n    while (i &lt;= n) {\n        res += i;\n        i++; // 条件変数を更新する\n    }\n    return res;\n}\n</code></pre> iteration.dart<pre><code>/* while ループ */\nint whileLoop(int n) {\n  int res = 0;\n  int i = 1; // 条件変数を初期化する\n  // 1, 2, ..., n-1, n を順に加算する\n  while (i &lt;= n) {\n    res += i;\n    i++; // 条件変数を更新する\n  }\n  return res;\n}\n</code></pre> iteration.rs<pre><code>/* while ループ */\nfn while_loop(n: i32) -&gt; i32 {\n    let mut res = 0;\n    let mut i = 1; // 条件変数を初期化する\n\n    // 1, 2, ..., n-1, n を順に加算する\n    while i &lt;= n {\n        res += i;\n        i += 1; // 条件変数を更新する\n    }\n    res\n}\n</code></pre> iteration.c<pre><code>/* while ループ */\nint whileLoop(int n) {\n    int res = 0;\n    int i = 1; // 条件変数を初期化する\n    // 1, 2, ..., n-1, n を順に加算する\n    while (i &lt;= n) {\n        res += i;\n        i++; // 条件変数を更新する\n    }\n    return res;\n}\n</code></pre> iteration.kt<pre><code>/* while ループ */\nfun whileLoop(n: Int): Int {\n    var res = 0\n    var i = 1 // 条件変数を初期化する\n    // 1, 2, ..., n-1, n を順に加算する\n    while (i &lt;= n) {\n        res += i\n        i++ // 条件変数を更新する\n    }\n    return res\n}\n</code></pre> iteration.rb<pre><code>### while ループ ###\ndef while_loop(n)\n  res = 0\n  i = 1 # 条件変数を初期化する\n\n  # 1, 2, ..., n-1, n を順に加算する\n  while i &lt;= n\n    res += i\n    i += 1 # 条件変数を更新する\n  end\n\n  res\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>**<code>while</code> ループは <code>for</code> ループより自由度が高い**です。<code>while</code> ループでは、条件変数の初期化や更新手順を柔軟に設計できます。</p> <p>たとえば次のコードでは、条件変数 \\(i\\) が各反復で 2 回更新されており、このようなケースは <code>for</code> ループではあまり扱いやすくありません。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby iteration.py<pre><code>def while_loop_ii(n: int) -&gt; int:\n    \"\"\"while ループ（2回更新）\"\"\"\n    res = 0\n    i = 1  # 条件変数を初期化する\n    # 1, 4, 10, ... を順に加算する\n    while i &lt;= n:\n        res += i\n        # 条件変数を更新する\n        i += 1\n        i *= 2\n    return res\n</code></pre> iteration.cpp<pre><code>/* while ループ（2回更新） */\nint whileLoopII(int n) {\n    int res = 0;\n    int i = 1; // 条件変数を初期化する\n    // 1, 4, 10, ... を順に加算する\n    while (i &lt;= n) {\n        res += i;\n        // 条件変数を更新する\n        i++;\n        i *= 2;\n    }\n    return res;\n}\n</code></pre> iteration.java<pre><code>/* while ループ（2回更新） */\nint whileLoopII(int n) {\n    int res = 0;\n    int i = 1; // 条件変数を初期化する\n    // 1, 4, 10, ... を順に加算する\n    while (i &lt;= n) {\n        res += i;\n        // 条件変数を更新する\n        i++;\n        i *= 2;\n    }\n    return res;\n}\n</code></pre> iteration.cs<pre><code>/* while ループ（2回更新） */\nint WhileLoopII(int n) {\n    int res = 0;\n    int i = 1; // 条件変数を初期化する\n    // 1, 4, 10, ... を順に加算する\n    while (i &lt;= n) {\n        res += i;\n        // 条件変数を更新する\n        i += 1; \n        i *= 2;\n    }\n    return res;\n}\n</code></pre> iteration.go<pre><code>/* while ループ（2回更新） */\nfunc whileLoopII(n int) int {\n    res := 0\n    // 条件変数を初期化する\n    i := 1\n    // 1, 4, 10, ... を順に加算する\n    for i &lt;= n {\n        res += i\n        // 条件変数を更新する\n        i++\n        i *= 2\n    }\n    return res\n}\n</code></pre> iteration.swift<pre><code>/* while ループ（2回更新） */\nfunc whileLoopII(n: Int) -&gt; Int {\n    var res = 0\n    var i = 1 // 条件変数を初期化する\n    // 1, 4, 10, ... を順に加算する\n    while i &lt;= n {\n        res += i\n        // 条件変数を更新する\n        i += 1\n        i *= 2\n    }\n    return res\n}\n</code></pre> iteration.js<pre><code>/* while ループ（2回更新） */\nfunction whileLoopII(n) {\n    let res = 0;\n    let i = 1; // 条件変数を初期化する\n    // 1, 4, 10, ... を順に加算する\n    while (i &lt;= n) {\n        res += i;\n        // 条件変数を更新する\n        i++;\n        i *= 2;\n    }\n    return res;\n}\n</code></pre> iteration.ts<pre><code>/* while ループ（2回更新） */\nfunction whileLoopII(n: number): number {\n    let res = 0;\n    let i = 1; // 条件変数を初期化する\n    // 1, 4, 10, ... を順に加算する\n    while (i &lt;= n) {\n        res += i;\n        // 条件変数を更新する\n        i++;\n        i *= 2;\n    }\n    return res;\n}\n</code></pre> iteration.dart<pre><code>/* while ループ（2回更新） */\nint whileLoopII(int n) {\n  int res = 0;\n  int i = 1; // 条件変数を初期化する\n  // 1, 4, 10, ... を順に加算する\n  while (i &lt;= n) {\n    res += i;\n    // 条件変数を更新する\n    i++;\n    i *= 2;\n  }\n  return res;\n}\n</code></pre> iteration.rs<pre><code>/* while ループ（2回更新） */\nfn while_loop_ii(n: i32) -&gt; i32 {\n    let mut res = 0;\n    let mut i = 1; // 条件変数を初期化する\n\n    // 1, 4, 10, ... を順に加算する\n    while i &lt;= n {\n        res += i;\n        // 条件変数を更新する\n        i += 1;\n        i *= 2;\n    }\n    res\n}\n</code></pre> iteration.c<pre><code>/* while ループ（2回更新） */\nint whileLoopII(int n) {\n    int res = 0;\n    int i = 1; // 条件変数を初期化する\n    // 1, 4, 10, ... を順に加算する\n    while (i &lt;= n) {\n        res += i;\n        // 条件変数を更新する\n        i++;\n        i *= 2;\n    }\n    return res;\n}\n</code></pre> iteration.kt<pre><code>/* while ループ（2回更新） */\nfun whileLoopII(n: Int): Int {\n    var res = 0\n    var i = 1 // 条件変数を初期化する\n    // 1, 4, 10, ... を順に加算する\n    while (i &lt;= n) {\n        res += i\n        // 条件変数を更新する\n        i++\n        i *= 2\n    }\n    return res\n}\n</code></pre> iteration.rb<pre><code>### while ループ ###\ndef while_loop(n)\n  res = 0\n  i = 1 # 条件変数を初期化する\n\n  # 1, 2, ..., n-1, n を順に加算する\n  while i &lt;= n\n    res += i\n    i += 1 # 条件変数を更新する\n  end\n\n  res\nend\n\n# ## while ループ（2 回更新）###\ndef while_loop_ii(n)\n  res = 0\n  i = 1 # 条件変数を初期化する\n\n  # 1, 4, 10, ... を順に加算する\n  while i &lt;= n\n    res += i\n    # 条件変数を更新する\n    i += 1\n    i *= 2\n  end\n\n  res\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>総じて、**<code>for</code> ループのコードはより簡潔で、<code>while</code> ループはより柔軟**です。どちらも反復構造を実現できますが、どちらを使うかは問題ごとの要件に応じて決めるべきです。</p>","path":["第 2 章 &nbsp; 計算量解析","2.2 &nbsp; 反復と再帰"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#3","level":3,"title":"3.   ネストしたループ","text":"<p>1 つのループ構造の中に別のループ構造を入れ子にできます。以下では <code>for</code> ループを例にします。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby iteration.py<pre><code>def nested_for_loop(n: int) -&gt; str:\n    \"\"\"二重 for ループ\"\"\"\n    res = \"\"\n    # i = 1, 2, ..., n-1, n とループする\n    for i in range(1, n + 1):\n        # j = 1, 2, ..., n-1, n とループする\n        for j in range(1, n + 1):\n            res += f\"({i}, {j}), \"\n    return res\n</code></pre> iteration.cpp<pre><code>/* 二重 for ループ */\nstring nestedForLoop(int n) {\n    ostringstream res;\n    // i = 1, 2, ..., n-1, n とループする\n    for (int i = 1; i &lt;= n; ++i) {\n        // j = 1, 2, ..., n-1, n とループする\n        for (int j = 1; j &lt;= n; ++j) {\n            res &lt;&lt; \"(\" &lt;&lt; i &lt;&lt; \", \" &lt;&lt; j &lt;&lt; \"), \";\n        }\n    }\n    return res.str();\n}\n</code></pre> iteration.java<pre><code>/* 二重 for ループ */\nString nestedForLoop(int n) {\n    StringBuilder res = new StringBuilder();\n    // i = 1, 2, ..., n-1, n とループする\n    for (int i = 1; i &lt;= n; i++) {\n        // j = 1, 2, ..., n-1, n とループする\n        for (int j = 1; j &lt;= n; j++) {\n            res.append(\"(\" + i + \", \" + j + \"), \");\n        }\n    }\n    return res.toString();\n}\n</code></pre> iteration.cs<pre><code>/* 二重 for ループ */\nstring NestedForLoop(int n) {\n    StringBuilder res = new();\n    // i = 1, 2, ..., n-1, n とループする\n    for (int i = 1; i &lt;= n; i++) {\n        // j = 1, 2, ..., n-1, n とループする\n        for (int j = 1; j &lt;= n; j++) {\n            res.Append($\"({i}, {j}), \");\n        }\n    }\n    return res.ToString();\n}\n</code></pre> iteration.go<pre><code>/* 二重 for ループ */\nfunc nestedForLoop(n int) string {\n    res := \"\"\n    // i = 1, 2, ..., n-1, n とループする\n    for i := 1; i &lt;= n; i++ {\n        for j := 1; j &lt;= n; j++ {\n            // j = 1, 2, ..., n-1, n とループする\n            res += fmt.Sprintf(\"(%d, %d), \", i, j)\n        }\n    }\n    return res\n}\n</code></pre> iteration.swift<pre><code>/* 二重 for ループ */\nfunc nestedForLoop(n: Int) -&gt; String {\n    var res = \"\"\n    // i = 1, 2, ..., n-1, n とループする\n    for i in 1 ... n {\n        // j = 1, 2, ..., n-1, n とループする\n        for j in 1 ... n {\n            res.append(\"(\\(i), \\(j)), \")\n        }\n    }\n    return res\n}\n</code></pre> iteration.js<pre><code>/* 二重 for ループ */\nfunction nestedForLoop(n) {\n    let res = '';\n    // i = 1, 2, ..., n-1, n とループする\n    for (let i = 1; i &lt;= n; i++) {\n        // j = 1, 2, ..., n-1, n とループする\n        for (let j = 1; j &lt;= n; j++) {\n            res += `(${i}, ${j}), `;\n        }\n    }\n    return res;\n}\n</code></pre> iteration.ts<pre><code>/* 二重 for ループ */\nfunction nestedForLoop(n: number): string {\n    let res = '';\n    // i = 1, 2, ..., n-1, n とループする\n    for (let i = 1; i &lt;= n; i++) {\n        // j = 1, 2, ..., n-1, n とループする\n        for (let j = 1; j &lt;= n; j++) {\n            res += `(${i}, ${j}), `;\n        }\n    }\n    return res;\n}\n</code></pre> iteration.dart<pre><code>/* 二重 for ループ */\nString nestedForLoop(int n) {\n  String res = \"\";\n  // i = 1, 2, ..., n-1, n とループする\n  for (int i = 1; i &lt;= n; i++) {\n    // j = 1, 2, ..., n-1, n とループする\n    for (int j = 1; j &lt;= n; j++) {\n      res += \"($i, $j), \";\n    }\n  }\n  return res;\n}\n</code></pre> iteration.rs<pre><code>/* 二重 for ループ */\nfn nested_for_loop(n: i32) -&gt; String {\n    let mut res = vec![];\n    // i = 1, 2, ..., n-1, n とループする\n    for i in 1..=n {\n        // j = 1, 2, ..., n-1, n とループする\n        for j in 1..=n {\n            res.push(format!(\"({}, {}), \", i, j));\n        }\n    }\n    res.join(\"\")\n}\n</code></pre> iteration.c<pre><code>/* 二重 for ループ */\nchar *nestedForLoop(int n) {\n    // n * n は対応する点の個数であり、\"(i, j), \" に対応する文字列長の最大は 6+10*2 で、さらに末尾の空文字 \\0 のための追加領域が必要\n    int size = n * n * 26 + 1;\n    char *res = malloc(size * sizeof(char));\n    // i = 1, 2, ..., n-1, n とループする\n    for (int i = 1; i &lt;= n; i++) {\n        // j = 1, 2, ..., n-1, n とループする\n        for (int j = 1; j &lt;= n; j++) {\n            char tmp[26];\n            snprintf(tmp, sizeof(tmp), \"(%d, %d), \", i, j);\n            strncat(res, tmp, size - strlen(res) - 1);\n        }\n    }\n    return res;\n}\n</code></pre> iteration.kt<pre><code>/* 二重 for ループ */\nfun nestedForLoop(n: Int): String {\n    val res = StringBuilder()\n    // i = 1, 2, ..., n-1, n とループする\n    for (i in 1..n) {\n        // j = 1, 2, ..., n-1, n とループする\n        for (j in 1..n) {\n            res.append(\" ($i, $j), \")\n        }\n    }\n    return res.toString()\n}\n</code></pre> iteration.rb<pre><code>### 二重 for ループ ###\ndef nested_for_loop(n)\n  res = \"\"\n\n  # i = 1, 2, ..., n-1, n とループする\n  for i in 1..n\n    # j = 1, 2, ..., n-1, n とループする\n    for j in 1..n\n      res += \"(#{i}, #{j}), \"\n    end\n  end\n\n  res\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>次の図は、このネストしたループのフローチャートです。</p> <p></p> <p> 図 2-2   ネストしたループのフローチャート </p> <p>この場合、関数の操作回数は \\(n^2\\) に比例し、言い換えればアルゴリズムの実行時間は入力データサイズ \\(n\\) と「二次関係」にあります。</p> <p>さらにネストしたループを追加することもできます。ネストが 1 段増えるたびに「次元が 1 つ上がる」ことになり、時間計算量は「三次関係」「四次関係」へと高くなっていきます。</p>","path":["第 2 章 &nbsp; 計算量解析","2.2 &nbsp; 反復と再帰"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#222","level":2,"title":"2.2.2   再帰","text":"<p>再帰（recursion）は、関数が自分自身を呼び出すことで問題を解決するアルゴリズム戦略です。主に 2 つの段階から成ります。</p> <ol> <li>再帰呼び出し：プログラムは自分自身をより深く呼び出し続け、通常はより小さい、またはより単純化された引数を渡し、「終了条件」に達するまで進みます。</li> <li>復帰： 「終了条件」が満たされると、プログラムは最も深い再帰関数から 1 層ずつ戻り、各層の結果をまとめていきます。</li> </ol> <p>実装の観点から見ると、再帰コードは主に 3 つの要素から成ります。</p> <ol> <li>終了条件：いつ再帰呼び出しから復帰へ切り替わるかを決めます。</li> <li>再帰呼び出し：再帰呼び出しに対応し、関数が自分自身を呼び出します。通常はより小さい、またはより単純化された引数を入力します。</li> <li>結果の返却：復帰に対応し、現在の再帰レベルの結果を 1 つ上の層へ返します。</li> </ol> <p>次のコードを見ると、関数 <code>recur(n)</code> を呼び出すだけで \\(1 + 2 + \\dots + n\\) を計算できます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby recursion.py<pre><code>def recur(n: int) -&gt; int:\n    \"\"\"再帰\"\"\"\n    # 終了条件\n    if n == 1:\n        return 1\n    # 再帰：再帰呼び出し\n    res = recur(n - 1)\n    # 帰りがけ：結果を返す\n    return n + res\n</code></pre> recursion.cpp<pre><code>/* 再帰 */\nint recur(int n) {\n    // 終了条件\n    if (n == 1)\n        return 1;\n    // 再帰：再帰呼び出し\n    int res = recur(n - 1);\n    // 帰りがけ：結果を返す\n    return n + res;\n}\n</code></pre> recursion.java<pre><code>/* 再帰 */\nint recur(int n) {\n    // 終了条件\n    if (n == 1)\n        return 1;\n    // 再帰：再帰呼び出し\n    int res = recur(n - 1);\n    // 帰りがけ：結果を返す\n    return n + res;\n}\n</code></pre> recursion.cs<pre><code>/* 再帰 */\nint Recur(int n) {\n    // 終了条件\n    if (n == 1)\n        return 1;\n    // 再帰：再帰呼び出し\n    int res = Recur(n - 1);\n    // 帰りがけ：結果を返す\n    return n + res;\n}\n</code></pre> recursion.go<pre><code>/* 再帰 */\nfunc recur(n int) int {\n    // 終了条件\n    if n == 1 {\n        return 1\n    }\n    // 再帰：再帰呼び出し\n    res := recur(n - 1)\n    // 帰りがけ：結果を返す\n    return n + res\n}\n</code></pre> recursion.swift<pre><code>/* 再帰 */\nfunc recur(n: Int) -&gt; Int {\n    // 終了条件\n    if n == 1 {\n        return 1\n    }\n    // 再帰：再帰呼び出し\n    let res = recur(n: n - 1)\n    // 帰りがけ：結果を返す\n    return n + res\n}\n</code></pre> recursion.js<pre><code>/* 再帰 */\nfunction recur(n) {\n    // 終了条件\n    if (n === 1) return 1;\n    // 再帰：再帰呼び出し\n    const res = recur(n - 1);\n    // 帰りがけ：結果を返す\n    return n + res;\n}\n</code></pre> recursion.ts<pre><code>/* 再帰 */\nfunction recur(n: number): number {\n    // 終了条件\n    if (n === 1) return 1;\n    // 再帰：再帰呼び出し\n    const res = recur(n - 1);\n    // 帰りがけ：結果を返す\n    return n + res;\n}\n</code></pre> recursion.dart<pre><code>/* 再帰 */\nint recur(int n) {\n  // 終了条件\n  if (n == 1) return 1;\n  // 再帰：再帰呼び出し\n  int res = recur(n - 1);\n  // 帰りがけ：結果を返す\n  return n + res;\n}\n</code></pre> recursion.rs<pre><code>/* 再帰 */\nfn recur(n: i32) -&gt; i32 {\n    // 終了条件\n    if n == 1 {\n        return 1;\n    }\n    // 再帰：再帰呼び出し\n    let res = recur(n - 1);\n    // 帰りがけ：結果を返す\n    n + res\n}\n</code></pre> recursion.c<pre><code>/* 再帰 */\nint recur(int n) {\n    // 終了条件\n    if (n == 1)\n        return 1;\n    // 再帰：再帰呼び出し\n    int res = recur(n - 1);\n    // 帰りがけ：結果を返す\n    return n + res;\n}\n</code></pre> recursion.kt<pre><code>/* 再帰 */\nfun recur(n: Int): Int {\n    // 終了条件\n    if (n == 1)\n        return 1\n    // 再帰: 再帰呼び出し\n    val res = recur(n - 1)\n    // 戻る: 結果を返す\n    return n + res\n}\n</code></pre> recursion.rb<pre><code>### 再帰 ###\ndef recur(n)\n  # 終了条件\n  return 1 if n == 1\n  # 再帰：再帰呼び出し\n  res = recur(n - 1)\n  # 帰りがけ：結果を返す\n  n + res\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>次の図は、この関数の再帰過程を示しています。</p> <p></p> <p> 図 2-3   総和関数の再帰過程 </p> <p>計算の観点では、反復と再帰は同じ結果を得られますが、それらは問題を考え解決するためのまったく異なる 2 つのパラダイムを表しています。</p> <ul> <li>反復：「ボトムアップ」で問題を解決します。最も基本的な手順から始め、それらを繰り返したり積み上げたりして、処理が完了するまで進めます。</li> <li>再帰：「トップダウン」で問題を解決します。元の問題をより小さな部分問題に分解し、それらの部分問題は元の問題と同じ形を持ちます。さらに部分問題をより小さな部分問題へと分解し、基本ケースに達したところで停止します（基本ケースの解は既知です）。</li> </ul> <p>前述の総和関数を例に、問題を \\(f(n) = 1 + 2 + \\dots + n\\) とします。</p> <ul> <li>反復：ループ内で総和の過程を模擬し、\\(1\\) から \\(n\\) まで走査して、各反復で加算を行えば \\(f(n)\\) を求められます。</li> <li>再帰：問題を部分問題 \\(f(n) = n + f(n-1)\\) に分解し、これを再帰的に分解し続け、基本ケース \\(f(1) = 1\\) に達したところで終了します。</li> </ul>","path":["第 2 章 &nbsp; 計算量解析","2.2 &nbsp; 反復と再帰"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#1","level":3,"title":"1.   呼び出しスタック","text":"<p>再帰関数が自分自身を呼び出すたびに、システムは新たに開始された関数のためにメモリを割り当て、局所変数、呼び出し先アドレス、その他の情報を保存します。これにより 2 つの結果が生じます。</p> <ul> <li>関数のコンテキストデータは「スタックフレーム領域」と呼ばれるメモリ領域に保存され、関数が戻るまで解放されません。したがって、再帰は通常、反復より多くのメモリ空間を消費します。</li> <li>再帰による関数呼び出しには追加のオーバーヘッドが発生します。そのため再帰は通常、ループより時間効率が低くなります。</li> </ul> <p>次の図のように、終了条件が発動する前には、まだ戻っていない再帰関数が同時に \\(n\\) 個存在し、再帰の深さは \\(n\\) になります。</p> <p></p> <p> 図 2-4   再帰呼び出しの深さ </p> <p>実際には、プログラミング言語が許容する再帰の深さには通常上限があり、深すぎる再帰はスタックオーバーフローを引き起こす可能性があります。</p>","path":["第 2 章 &nbsp; 計算量解析","2.2 &nbsp; 反復と再帰"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#2","level":3,"title":"2.   末尾再帰","text":"<p>興味深いことに、関数が返る直前の最後の処理で再帰呼び出しを行う場合、その関数はコンパイラやインタプリタによって最適化され、空間効率が反復と同程度になることがあります。これを末尾再帰（tail recursion）と呼びます。</p> <ul> <li>通常の再帰：関数が 1 つ上の階層の関数へ戻った後も、引き続きコードを実行する必要があるため、システムは 1 つ上の呼び出しのコンテキストを保存しておく必要があります。</li> <li>末尾再帰：再帰呼び出しが関数の返却前の最後の操作であるため、1 つ上の階層へ戻った後に他の処理を続ける必要がなく、システムは 1 つ上の関数のコンテキストを保存する必要がありません。</li> </ul> <p>\\(1 + 2 + \\dots + n\\) の計算を例にすると、結果変数 <code>res</code> を関数の引数にすることで、末尾再帰を実現できます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby recursion.py<pre><code>def tail_recur(n, res):\n    \"\"\"末尾再帰\"\"\"\n    # 終了条件\n    if n == 0:\n        return res\n    # 末尾再帰呼び出し\n    return tail_recur(n - 1, res + n)\n</code></pre> recursion.cpp<pre><code>/* 末尾再帰 */\nint tailRecur(int n, int res) {\n    // 終了条件\n    if (n == 0)\n        return res;\n    // 末尾再帰呼び出し\n    return tailRecur(n - 1, res + n);\n}\n</code></pre> recursion.java<pre><code>/* 末尾再帰 */\nint tailRecur(int n, int res) {\n    // 終了条件\n    if (n == 0)\n        return res;\n    // 末尾再帰呼び出し\n    return tailRecur(n - 1, res + n);\n}\n</code></pre> recursion.cs<pre><code>/* 末尾再帰 */\nint TailRecur(int n, int res) {\n    // 終了条件\n    if (n == 0)\n        return res;\n    // 末尾再帰呼び出し\n    return TailRecur(n - 1, res + n);\n}\n</code></pre> recursion.go<pre><code>/* 末尾再帰 */\nfunc tailRecur(n int, res int) int {\n    // 終了条件\n    if n == 0 {\n        return res\n    }\n    // 末尾再帰呼び出し\n    return tailRecur(n-1, res+n)\n}\n</code></pre> recursion.swift<pre><code>/* 末尾再帰 */\nfunc tailRecur(n: Int, res: Int) -&gt; Int {\n    // 終了条件\n    if n == 0 {\n        return res\n    }\n    // 末尾再帰呼び出し\n    return tailRecur(n: n - 1, res: res + n)\n}\n</code></pre> recursion.js<pre><code>/* 末尾再帰 */\nfunction tailRecur(n, res) {\n    // 終了条件\n    if (n === 0) return res;\n    // 末尾再帰呼び出し\n    return tailRecur(n - 1, res + n);\n}\n</code></pre> recursion.ts<pre><code>/* 末尾再帰 */\nfunction tailRecur(n: number, res: number): number {\n    // 終了条件\n    if (n === 0) return res;\n    // 末尾再帰呼び出し\n    return tailRecur(n - 1, res + n);\n}\n</code></pre> recursion.dart<pre><code>/* 末尾再帰 */\nint tailRecur(int n, int res) {\n  // 終了条件\n  if (n == 0) return res;\n  // 末尾再帰呼び出し\n  return tailRecur(n - 1, res + n);\n}\n</code></pre> recursion.rs<pre><code>/* 末尾再帰 */\nfn tail_recur(n: i32, res: i32) -&gt; i32 {\n    // 終了条件\n    if n == 0 {\n        return res;\n    }\n    // 末尾再帰呼び出し\n    tail_recur(n - 1, res + n)\n}\n</code></pre> recursion.c<pre><code>/* 末尾再帰 */\nint tailRecur(int n, int res) {\n    // 終了条件\n    if (n == 0)\n        return res;\n    // 末尾再帰呼び出し\n    return tailRecur(n - 1, res + n);\n}\n</code></pre> recursion.kt<pre><code>/* 末尾再帰 */\ntailrec fun tailRecur(n: Int, res: Int): Int {\n    // `tailrec` キーワードを追加して末尾再帰最適化を有効にする\n    // 終了条件\n    if (n == 0)\n        return res\n    // 末尾再帰呼び出し\n    return tailRecur(n - 1, res + n)\n}\n</code></pre> recursion.rb<pre><code>### 末尾再帰 ###\ndef tail_recur(n, res)\n  # 終了条件\n  return res if n == 0\n  # 末尾再帰呼び出し\n  tail_recur(n - 1, res + n)\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>末尾再帰の実行過程を次の図に示します。通常の再帰と末尾再帰を比べると、加算処理が実行されるタイミングが異なります。</p> <ul> <li>通常の再帰：加算処理は復帰の過程で実行され、各層が戻るたびにもう一度加算を行います。</li> <li>末尾再帰：加算処理は再帰呼び出しの過程で実行され、復帰の過程では各層が戻るだけで済みます。</li> </ul> <p></p> <p> 図 2-5   末尾再帰の過程 </p> <p>Tip</p> <p>多くのコンパイラやインタプリタは末尾再帰最適化をサポートしていない点に注意してください。たとえば、Python はデフォルトで末尾再帰最適化をサポートしていないため、関数が末尾再帰の形であっても、スタックオーバーフローが発生する可能性があります。</p>","path":["第 2 章 &nbsp; 計算量解析","2.2 &nbsp; 反復と再帰"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#3_1","level":3,"title":"3.   再帰木","text":"<p>「分割統治」に関連するアルゴリズム問題を扱う際、再帰は反復よりも発想が直感的で、コードも読みやすいことがよくあります。「フィボナッチ数列」を例に見てみましょう。</p> <p>Question</p> <p>フィボナッチ数列 \\(0, 1, 1, 2, 3, 5, 8, 13, \\dots\\) が与えられたとき、この数列の第 \\(n\\) 項を求めてください。</p> <p>フィボナッチ数列の第 \\(n\\) 項を \\(f(n)\\) とすると、次の 2 つが容易に分かります。</p> <ul> <li>数列の最初の 2 項は \\(f(1) = 0\\) と \\(f(2) = 1\\) です。</li> <li>数列中の各項は直前の 2 項の和であり、すなわち \\(f(n) = f(n - 1) + f(n - 2)\\) です。</li> </ul> <p>漸化式に従って再帰呼び出しを行い、最初の 2 項を終了条件とすれば、再帰コードを書けます。<code>fib(n)</code> を呼び出すことでフィボナッチ数列の第 \\(n\\) 項を得られます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby recursion.py<pre><code>def fib(n: int) -&gt; int:\n    \"\"\"フィボナッチ数列：再帰\"\"\"\n    # 終了条件 f(1) = 0, f(2) = 1\n    if n == 1 or n == 2:\n        return n - 1\n    # f(n) = f(n-1) + f(n-2) を再帰的に呼び出す\n    res = fib(n - 1) + fib(n - 2)\n    # 結果 f(n) を返す\n    return res\n</code></pre> recursion.cpp<pre><code>/* フィボナッチ数列：再帰 */\nint fib(int n) {\n    // 終了条件 f(1) = 0, f(2) = 1\n    if (n == 1 || n == 2)\n        return n - 1;\n    // f(n) = f(n-1) + f(n-2) を再帰的に呼び出す\n    int res = fib(n - 1) + fib(n - 2);\n    // 結果 f(n) を返す\n    return res;\n}\n</code></pre> recursion.java<pre><code>/* フィボナッチ数列：再帰 */\nint fib(int n) {\n    // 終了条件 f(1) = 0, f(2) = 1\n    if (n == 1 || n == 2)\n        return n - 1;\n    // f(n) = f(n-1) + f(n-2) を再帰的に呼び出す\n    int res = fib(n - 1) + fib(n - 2);\n    // 結果 f(n) を返す\n    return res;\n}\n</code></pre> recursion.cs<pre><code>/* フィボナッチ数列：再帰 */\nint Fib(int n) {\n    // 終了条件 f(1) = 0, f(2) = 1\n    if (n == 1 || n == 2)\n        return n - 1;\n    // f(n) = f(n-1) + f(n-2) を再帰的に呼び出す\n    int res = Fib(n - 1) + Fib(n - 2);\n    // 結果 f(n) を返す\n    return res;\n}\n</code></pre> recursion.go<pre><code>/* フィボナッチ数列：再帰 */\nfunc fib(n int) int {\n    // 終了条件 f(1) = 0, f(2) = 1\n    if n == 1 || n == 2 {\n        return n - 1\n    }\n    // f(n) = f(n-1) + f(n-2) を再帰的に呼び出す\n    res := fib(n-1) + fib(n-2)\n    // 結果 f(n) を返す\n    return res\n}\n</code></pre> recursion.swift<pre><code>/* フィボナッチ数列：再帰 */\nfunc fib(n: Int) -&gt; Int {\n    // 終了条件 f(1) = 0, f(2) = 1\n    if n == 1 || n == 2 {\n        return n - 1\n    }\n    // f(n) = f(n-1) + f(n-2) を再帰的に呼び出す\n    let res = fib(n: n - 1) + fib(n: n - 2)\n    // 結果 f(n) を返す\n    return res\n}\n</code></pre> recursion.js<pre><code>/* フィボナッチ数列：再帰 */\nfunction fib(n) {\n    // 終了条件 f(1) = 0, f(2) = 1\n    if (n === 1 || n === 2) return n - 1;\n    // f(n) = f(n-1) + f(n-2) を再帰的に呼び出す\n    const res = fib(n - 1) + fib(n - 2);\n    // 結果 f(n) を返す\n    return res;\n}\n</code></pre> recursion.ts<pre><code>/* フィボナッチ数列：再帰 */\nfunction fib(n: number): number {\n    // 終了条件 f(1) = 0, f(2) = 1\n    if (n === 1 || n === 2) return n - 1;\n    // f(n) = f(n-1) + f(n-2) を再帰的に呼び出す\n    const res = fib(n - 1) + fib(n - 2);\n    // 結果 f(n) を返す\n    return res;\n}\n</code></pre> recursion.dart<pre><code>/* フィボナッチ数列：再帰 */\nint fib(int n) {\n  // 終了条件 f(1) = 0, f(2) = 1\n  if (n == 1 || n == 2) return n - 1;\n  // f(n) = f(n-1) + f(n-2) を再帰的に呼び出す\n  int res = fib(n - 1) + fib(n - 2);\n  // 結果 f(n) を返す\n  return res;\n}\n</code></pre> recursion.rs<pre><code>/* フィボナッチ数列：再帰 */\nfn fib(n: i32) -&gt; i32 {\n    // 終了条件 f(1) = 0, f(2) = 1\n    if n == 1 || n == 2 {\n        return n - 1;\n    }\n    // f(n) = f(n-1) + f(n-2) を再帰的に呼び出す\n    let res = fib(n - 1) + fib(n - 2);\n    // 結果を返す\n    res\n}\n</code></pre> recursion.c<pre><code>/* フィボナッチ数列：再帰 */\nint fib(int n) {\n    // 終了条件 f(1) = 0, f(2) = 1\n    if (n == 1 || n == 2)\n        return n - 1;\n    // f(n) = f(n-1) + f(n-2) を再帰的に呼び出す\n    int res = fib(n - 1) + fib(n - 2);\n    // 結果 f(n) を返す\n    return res;\n}\n</code></pre> recursion.kt<pre><code>/* フィボナッチ数列：再帰 */\nfun fib(n: Int): Int {\n    // 終了条件 f(1) = 0, f(2) = 1\n    if (n == 1 || n == 2)\n        return n - 1\n    // f(n) = f(n-1) + f(n-2) を再帰的に呼び出す\n    val res = fib(n - 1) + fib(n - 2)\n    // 結果 f(n) を返す\n    return res\n}\n</code></pre> recursion.rb<pre><code>### フィボナッチ数列：再帰 ###\ndef fib(n)\n  # 終了条件 f(1) = 0, f(2) = 1\n  return n - 1 if n == 1 || n == 2\n  # f(n) = f(n-1) + f(n-2) を再帰的に呼び出す\n  res = fib(n - 1) + fib(n - 2)\n  # 結果 f(n) を返す\n  res\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>上のコードを見ると、関数内で 2 回の再帰呼び出しを行っています。これは 1 回の呼び出しから 2 つの呼び出し分岐が生じることを意味します。次の図のように、この再帰呼び出しを繰り返していくと、最終的に深さ \\(n\\) の再帰木（recursion tree）が生成されます。</p> <p></p> <p> 図 2-6   フィボナッチ数列の再帰木 </p> <p>本質的に見ると、再帰は「問題をより小さな部分問題へ分解する」という思考パラダイムを体現しており、この分割統治の戦略は非常に重要です。</p> <ul> <li>アルゴリズムの観点では、探索、ソート、バックトラッキング、分割統治、動的計画法など、多くの重要な戦略が直接または間接にこの考え方を用いています。</li> <li>データ構造の観点では、再帰は連結リスト、木、グラフに関する問題の処理に本質的に適しており、これらは分割統治の考え方で分析しやすいからです。</li> </ul>","path":["第 2 章 &nbsp; 計算量解析","2.2 &nbsp; 反復と再帰"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#223","level":2,"title":"2.2.3   両者の比較","text":"<p>以上をまとめると、次の表のように、反復と再帰は実装、性能、適用性の面で違いがあります。</p> <p> 表 2-1   反復と再帰の特徴の比較 </p> 反復 再帰 実装方法 ループ構造 関数が自分自身を呼び出す 時間効率 通常は効率が高く、関数呼び出しの負荷がない 関数呼び出しのたびにオーバーヘッドが発生する メモリ使用 通常は固定サイズのメモリ空間を使う 関数呼び出しの蓄積により大量のスタックフレーム領域を使う可能性がある 適用対象 単純な反復処理に適し、コードが直感的で読みやすい 木、グラフ、分割統治、バックトラッキングなどの部分問題分解に適し、コード構造が簡潔で明快 <p>Tip</p> <p>以下の内容が難しいと感じる場合は、「スタック」の章を読み終えた後に改めて復習してください。</p> <p>では、反復と再帰にはどのような内在的な関係があるのでしょうか。前述の再帰関数を例にすると、加算処理は再帰の復帰段階で行われます。これは、最初に呼び出された関数が実際には最後に加算を完了することを意味しており、この動作の仕組みはスタックの「後入れ先出し」の原則とよく似ています。</p> <p>実際、「呼び出しスタック」や「スタックフレーム領域」といった再帰の用語自体が、再帰とスタックの密接な関係を示唆しています。</p> <ol> <li>再帰呼び出し：関数が呼び出されると、システムは「呼び出しスタック」上にその関数のための新しいスタックフレームを割り当て、局所変数、引数、返却先アドレスなどのデータを保存します。</li> <li>復帰：関数の実行が完了して戻ると、対応するスタックフレームは「呼び出しスタック」から取り除かれ、前の関数の実行環境が復元されます。</li> </ol> <p>したがって、明示的なスタックを使って呼び出しスタックの振る舞いを模擬することができ、その結果として再帰を反復形式へ変換できます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby recursion.py<pre><code>def for_loop_recur(n: int) -&gt; int:\n    \"\"\"反復で再帰を模擬する\"\"\"\n    # 明示的なスタックを使ってシステムコールスタックを模擬する\n    stack = []\n    res = 0\n    # 再帰：再帰呼び出し\n    for i in range(n, 0, -1):\n        # 「スタックへのプッシュ」で「再帰」を模擬する\n        stack.append(i)\n    # 帰りがけ：結果を返す\n    while stack:\n        # 「スタックから取り出す操作」で「帰り」をシミュレート\n        res += stack.pop()\n    # res = 1+2+3+...+n\n    return res\n</code></pre> recursion.cpp<pre><code>/* 反復で再帰を模擬する */\nint forLoopRecur(int n) {\n    // 明示的なスタックを使ってシステムコールスタックを模擬する\n    stack&lt;int&gt; stack;\n    int res = 0;\n    // 再帰：再帰呼び出し\n    for (int i = n; i &gt; 0; i--) {\n        // 「スタックへのプッシュ」で「再帰」を模擬する\n        stack.push(i);\n    }\n    // 帰りがけ：結果を返す\n    while (!stack.empty()) {\n        // 「スタックから取り出す操作」で「帰り」をシミュレート\n        res += stack.top();\n        stack.pop();\n    }\n    // res = 1+2+3+...+n\n    return res;\n}\n</code></pre> recursion.java<pre><code>/* 反復で再帰を模擬する */\nint forLoopRecur(int n) {\n    // 明示的なスタックを使ってシステムコールスタックを模擬する\n    Stack&lt;Integer&gt; stack = new Stack&lt;&gt;();\n    int res = 0;\n    // 再帰：再帰呼び出し\n    for (int i = n; i &gt; 0; i--) {\n        // 「スタックへのプッシュ」で「再帰」を模擬する\n        stack.push(i);\n    }\n    // 帰りがけ：結果を返す\n    while (!stack.isEmpty()) {\n        // 「スタックから取り出す操作」で「帰り」をシミュレート\n        res += stack.pop();\n    }\n    // res = 1+2+3+...+n\n    return res;\n}\n</code></pre> recursion.cs<pre><code>/* 反復で再帰を模擬する */\nint ForLoopRecur(int n) {\n    // 明示的なスタックを使ってシステムコールスタックを模擬する\n    Stack&lt;int&gt; stack = new();\n    int res = 0;\n    // 再帰：再帰呼び出し\n    for (int i = n; i &gt; 0; i--) {\n        // 「スタックへのプッシュ」で「再帰」を模擬する\n        stack.Push(i);\n    }\n    // 帰りがけ：結果を返す\n    while (stack.Count &gt; 0) {\n        // 「スタックから取り出す操作」で「帰り」をシミュレート\n        res += stack.Pop();\n    }\n    // res = 1+2+3+...+n\n    return res;\n}\n</code></pre> recursion.go<pre><code>/* 反復で再帰を模擬する */\nfunc forLoopRecur(n int) int {\n    // 明示的なスタックを使ってシステムコールスタックを模擬する\n    stack := list.New()\n    res := 0\n    // 再帰：再帰呼び出し\n    for i := n; i &gt; 0; i-- {\n        // 「スタックへのプッシュ」で「再帰」を模擬する\n        stack.PushBack(i)\n    }\n    // 帰りがけ：結果を返す\n    for stack.Len() != 0 {\n        // 「スタックから取り出す操作」で「帰り」をシミュレート\n        res += stack.Back().Value.(int)\n        stack.Remove(stack.Back())\n    }\n    // res = 1+2+3+...+n\n    return res\n}\n</code></pre> recursion.swift<pre><code>/* 反復で再帰を模擬する */\nfunc forLoopRecur(n: Int) -&gt; Int {\n    // 明示的なスタックを使ってシステムコールスタックを模擬する\n    var stack: [Int] = []\n    var res = 0\n    // 再帰：再帰呼び出し\n    for i in (1 ... n).reversed() {\n        // 「スタックへのプッシュ」で「再帰」を模擬する\n        stack.append(i)\n    }\n    // 帰りがけ：結果を返す\n    while !stack.isEmpty {\n        // 「スタックから取り出す操作」で「帰り」をシミュレート\n        res += stack.removeLast()\n    }\n    // res = 1+2+3+...+n\n    return res\n}\n</code></pre> recursion.js<pre><code>/* 反復で再帰を模擬する */\nfunction forLoopRecur(n) {\n    // 明示的なスタックを使ってシステムコールスタックを模擬する\n    const stack = [];\n    let res = 0;\n    // 再帰：再帰呼び出し\n    for (let i = n; i &gt; 0; i--) {\n        // 「スタックへのプッシュ」で「再帰」を模擬する\n        stack.push(i);\n    }\n    // 帰りがけ：結果を返す\n    while (stack.length) {\n        // 「スタックから取り出す操作」で「帰り」をシミュレート\n        res += stack.pop();\n    }\n    // res = 1+2+3+...+n\n    return res;\n}\n</code></pre> recursion.ts<pre><code>/* 反復で再帰を模擬する */\nfunction forLoopRecur(n: number): number {\n    // 明示的なスタックを使ってシステムコールスタックを模擬する\n    const stack: number[] = [];\n    let res: number = 0;\n    // 再帰：再帰呼び出し\n    for (let i = n; i &gt; 0; i--) {\n        // 「スタックへのプッシュ」で「再帰」を模擬する\n        stack.push(i);\n    }\n    // 帰りがけ：結果を返す\n    while (stack.length) {\n        // 「スタックから取り出す操作」で「帰り」をシミュレート\n        res += stack.pop();\n    }\n    // res = 1+2+3+...+n\n    return res;\n}\n</code></pre> recursion.dart<pre><code>/* 反復で再帰を模擬する */\nint forLoopRecur(int n) {\n  // 明示的なスタックを使ってシステムコールスタックを模擬する\n  List&lt;int&gt; stack = [];\n  int res = 0;\n  // 再帰：再帰呼び出し\n  for (int i = n; i &gt; 0; i--) {\n    // 「スタックへのプッシュ」で「再帰」を模擬する\n    stack.add(i);\n  }\n  // 帰りがけ：結果を返す\n  while (!stack.isEmpty) {\n    // 「スタックから取り出す操作」で「帰り」をシミュレート\n    res += stack.removeLast();\n  }\n  // res = 1+2+3+...+n\n  return res;\n}\n</code></pre> recursion.rs<pre><code>/* 反復で再帰を模擬する */\nfn for_loop_recur(n: i32) -&gt; i32 {\n    // 明示的なスタックを使ってシステムコールスタックを模擬する\n    let mut stack = Vec::new();\n    let mut res = 0;\n    // 再帰：再帰呼び出し\n    for i in (1..=n).rev() {\n        // 「スタックへのプッシュ」で「再帰」を模擬する\n        stack.push(i);\n    }\n    // 帰りがけ：結果を返す\n    while !stack.is_empty() {\n        // 「スタックから取り出す操作」で「帰り」をシミュレート\n        res += stack.pop().unwrap();\n    }\n    // res = 1+2+3+...+n\n    res\n}\n</code></pre> recursion.c<pre><code>/* 反復で再帰を模擬する */\nint forLoopRecur(int n) {\n    int stack[1000]; // 大きな配列を使ってスタックを実装する\n    int top = -1;    // スタックトップのインデックス\n    int res = 0;\n    // 再帰：再帰呼び出し\n    for (int i = n; i &gt; 0; i--) {\n        // 「スタックへのプッシュ」で「再帰」を模擬する\n        stack[1 + top++] = i;\n    }\n    // 帰りがけ：結果を返す\n    while (top &gt;= 0) {\n        // 「スタックから取り出す操作」で「帰り」をシミュレート\n        res += stack[top--];\n    }\n    // res = 1+2+3+...+n\n    return res;\n}\n</code></pre> recursion.kt<pre><code>/* 反復で再帰を模擬する */\nfun forLoopRecur(n: Int): Int {\n    // 明示的なスタックを使ってシステムコールスタックを模擬する\n    val stack = Stack&lt;Int&gt;()\n    var res = 0\n    // 再帰: 再帰呼び出し\n    for (i in n downTo 0) {\n        // 「スタックへのプッシュ」で「再帰」を模擬する\n        stack.push(i)\n    }\n    // 戻る: 結果を返す\n    while (stack.isNotEmpty()) {\n        // 「スタックから取り出す操作」で「帰り」をシミュレート\n        res += stack.pop()\n    }\n    // res = 1+2+3+...+n\n    return res\n}\n</code></pre> recursion.rb<pre><code>### 反復で再帰をシミュレート ###\ndef for_loop_recur(n)\n  # 明示的なスタックを使ってシステムコールスタックを模擬する\n  stack = []\n  res = 0\n\n  # 再帰：再帰呼び出し\n  for i in n.downto(0)\n    # 「スタックへのプッシュ」で「再帰」を模擬する\n    stack &lt;&lt; i\n  end\n  # 帰りがけ：結果を返す\n  while !stack.empty?\n    res += stack.pop\n  end\n\n  # res = 1+2+3+...+n\n  res\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>上のコードを見ると、再帰を反復へ変換すると、コードはより複雑になります。反復と再帰は多くの場合に相互変換できますが、常にそうする価値があるとは限りません。理由は次の 2 点です。</p> <ul> <li>変換後のコードは理解しにくくなり、可読性が下がる可能性があります。</li> <li>複雑な問題によっては、システムの呼び出しスタックの振る舞いを模擬すること自体が非常に難しい場合があります。</li> </ul> <p>要するに、反復を選ぶか再帰を選ぶかは、対象となる問題の性質によって決まります。実際のプログラミングでは、両者の長所と短所を見極め、状況に応じて適切な方法を選ぶことが重要です。</p>","path":["第 2 章 &nbsp; 計算量解析","2.2 &nbsp; 反復と再帰"],"tags":[]},{"location":"chapter_computational_complexity/performance_evaluation/","level":1,"title":"2.1   アルゴリズム効率の評価","text":"<p>アルゴリズム設計では、次の 2 つのレベルの目標を順に追求します。</p> <ol> <li>問題の解法を見つける：アルゴリズムは、定められた入力範囲内で問題の正しい解を確実に求められる必要があります。</li> <li>最適な解法を追求する：同じ問題に対して複数の解法が存在する場合があり、私たちはできるだけ効率的なアルゴリズムを見つけたいと考えます。</li> </ol> <p>つまり、問題を解けることを前提として、アルゴリズム効率はその良し悪しを測る主要な評価指標となっており、次の 2 つの観点を含みます。</p> <ul> <li>時間効率：アルゴリズムの実行時間の長さ。</li> <li>空間効率：アルゴリズムが使用するメモリ空間の大きさ。</li> </ul> <p>簡単に言えば、**私たちの目標は「高速で省メモリ」なデータ構造とアルゴリズムを設計すること**です。そして、アルゴリズム効率を効果的に評価することは非常に重要です。そうすることで初めて、さまざまなアルゴリズムを比較し、さらにアルゴリズム設計と最適化の過程を導けるからです。</p> <p>効率の評価方法は主に 2 種類に分けられます。実測と理論的な見積もりです。</p>","path":["第 2 章 &nbsp; 計算量解析","2.1 &nbsp; アルゴリズム効率の評価"],"tags":[]},{"location":"chapter_computational_complexity/performance_evaluation/#211","level":2,"title":"2.1.1   実測","text":"<p>いまアルゴリズム <code>A</code> とアルゴリズム <code>B</code> があり、どちらも同じ問題を解けるとします。この 2 つのアルゴリズムの効率を比較する必要がある場合、最も直接的な方法は 1 台のコンピュータで両者を実行し、その実行時間とメモリ使用量を監視して記録することです。この評価方法は実際の状況を反映できますが、大きな制約もあります。</p> <p>一方では、**テスト環境による干渉要因を排除しにくい**という問題があります。ハードウェア構成はアルゴリズムの性能に影響します。たとえば、並列度の高いアルゴリズムはマルチコア CPU での実行により適しており、メモリアクセスが集中的なアルゴリズムは高性能メモリ上でより良い性能を示します。つまり、異なるマシンでのテスト結果は一致しない可能性があります。これは、さまざまなマシンでテストして平均効率を統計的に求める必要があることを意味しますが、それは現実的ではありません。</p> <p>他方では、**完全なテストを実施するには非常に多くの資源が必要**です。入力データ量が変化すると、アルゴリズムは異なる効率を示します。たとえば、入力データ量が小さいときはアルゴリズム <code>A</code> の実行時間がアルゴリズム <code>B</code> より短くても、入力データ量が大きいときには結果がちょうど逆になるかもしれません。そのため、説得力のある結論を得るには、さまざまな規模の入力データでテストする必要があり、それには大量の計算資源を要します。</p>","path":["第 2 章 &nbsp; 計算量解析","2.1 &nbsp; アルゴリズム効率の評価"],"tags":[]},{"location":"chapter_computational_complexity/performance_evaluation/#212","level":2,"title":"2.1.2   理論的な見積もり","text":"<p>実測には大きな制約があるため、いくつかの計算だけによってアルゴリズムの効率を評価することを考えられます。この見積もり方法は漸近計算量解析（asymptotic complexity analysis）と呼ばれ、略して計算量解析といいます。</p> <p>計算量解析は、アルゴリズムの実行に必要な時間資源と空間資源が入力データ規模とどのような関係にあるかを表します。これは、入力データ規模が増加するにつれて、アルゴリズムの実行に必要な時間と空間がどのように増加するかという傾向を記述するものです。この定義はややわかりにくいので、次の 3 つのポイントに分けて理解できます。</p> <ul> <li>「時間資源と空間資源」は、それぞれ時間計算量（time complexity）と空間計算量（space complexity）に対応します。</li> <li>「入力データ規模が増加するにつれて」とは、計算量がアルゴリズムの実行効率と入力データ規模との関係を反映していることを意味します。</li> <li>「時間と空間の増加傾向」とは、計算量解析が注目するのは実行時間や使用空間の具体的な値ではなく、時間や空間の増加の「速さ」であることを示します。</li> </ul> <p>計算量解析は実測という方法の欠点を克服しています。その点は次のように表れます。</p> <ul> <li>実際にコードを動かす必要がなく、より環境にやさしく省エネルギーです。</li> <li>テスト環境から独立しており、解析結果はすべての実行プラットフォームに適用できます。</li> <li>異なるデータ量におけるアルゴリズム効率を表せ、とくに大規模データ量での性能を反映できます。</li> </ul> <p>Tip</p> <p>それでも計算量の概念がまだわかりにくくても、心配はいりません。後続の章で詳しく説明します。</p> <p>計算量解析は、アルゴリズム効率を評価するための「物差し」を私たちに与えてくれます。これにより、あるアルゴリズムの実行に必要な時間資源と空間資源を測り、異なるアルゴリズム同士の効率を比較できます。</p> <p>計算量は数学的な概念であり、初学者にとってはやや抽象的で、学習の難度も比較的高いかもしれません。この観点から見ると、計算量解析は最初に紹介する内容としてはあまり適していない可能性があります。しかし、あるデータ構造やアルゴリズムの特徴を議論する際には、その実行速度や空間使用状況の分析を避けることはできません。</p> <p>以上を踏まえると、データ構造とアルゴリズムを深く学ぶ前に、**まず計算量解析について初歩的な理解を持ち、簡単なアルゴリズムの計算量解析ができるようにしておくこと**を勧めます。</p>","path":["第 2 章 &nbsp; 計算量解析","2.1 &nbsp; アルゴリズム効率の評価"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/","level":1,"title":"2.4   空間計算量","text":"<p>空間計算量（space complexity）は、アルゴリズムが占有するメモリ空間がデータ量の増加に伴ってどのように増えるかを測る指標です。この概念は時間計算量と非常によく似ており、「実行時間」を「占有メモリ空間」に置き換えるだけです。</p>","path":["第 2 章 &nbsp; 計算量解析","2.4 &nbsp; 空間計算量"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#241","level":2,"title":"2.4.1   アルゴリズムに関連する空間","text":"<p>アルゴリズムが実行中に使用するメモリ空間には、主に次の種類があります。</p> <ul> <li>入力空間：アルゴリズムの入力データを格納するための空間。</li> <li>一時空間：アルゴリズムの実行中に使用する変数、オブジェクト、関数コンテキストなどのデータを格納するための空間。</li> <li>出力空間：アルゴリズムの出力データを格納するための空間。</li> </ul> <p>一般に、空間計算量の集計範囲は「一時空間」と「出力空間」を合わせたものです。</p> <p>一時空間はさらに三つに分けられます。</p> <ul> <li>一時データ：アルゴリズム実行中の各種定数、変数、オブジェクトなどを保存するための空間。</li> <li>スタックフレーム空間：呼び出された関数のコンテキストデータを保存するための空間。システムは関数を呼び出すたびにスタックの先頭にスタックフレームを作成し、関数が戻るとその空間を解放します。</li> <li>命令空間：コンパイル後のプログラム命令を保存するための空間で、実際の集計では通常無視されます。</li> </ul> <p>プログラムの空間計算量を分析する際には、通常、一時データ、スタックフレーム空間、出力データの三つを数えます。以下の図に示すとおりです。</p> <p></p> <p> 図 2-15   アルゴリズムで使用される関連空間 </p> <p>関連するコードを以下に示します。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>class Node:\n    \"\"\"クラス\"\"\"\n    def __init__(self, x: int):\n        self.val: int = x              # ノードの値\n        self.next: Node | None = None  # 次のノードへの参照\n\ndef function() -&gt; int:\n    \"\"\"関数\"\"\"\n    # いくつかの処理を実行...\n    return 0\n\ndef algorithm(n) -&gt; int:  # 入力データ\n    A = 0                 # 一時データ（定数。一般に大文字で表す）\n    b = 0                 # 一時データ（変数）\n    node = Node(0)        # 一時データ（オブジェクト）\n    c = function()        # スタックフレーム空間（関数呼び出し）\n    return A + b + c      # 出力データ\n</code></pre> <pre><code>/* 構造体 */\nstruct Node {\n    int val;\n    Node *next;\n    Node(int x) : val(x), next(nullptr) {}\n};\n\n/* 関数 */\nint func() {\n    // いくつかの処理を実行...\n    return 0;\n}\n\nint algorithm(int n) {        // 入力データ\n    const int a = 0;          // 一時データ（定数）\n    int b = 0;                // 一時データ（変数）\n    Node* node = new Node(0); // 一時データ（オブジェクト）\n    int c = func();           // スタックフレーム空間（関数呼び出し）\n    return a + b + c;         // 出力データ\n}\n</code></pre> <pre><code>/* クラス */\nclass Node {\n    int val;\n    Node next;\n    Node(int x) { val = x; }\n}\n\n/* 関数 */\nint function() {\n    // いくつかの処理を実行...\n    return 0;\n}\n\nint algorithm(int n) {        // 入力データ\n    final int a = 0;          // 一時データ（定数）\n    int b = 0;                // 一時データ（変数）\n    Node node = new Node(0);  // 一時データ（オブジェクト）\n    int c = function();       // スタックフレーム空間（関数呼び出し）\n    return a + b + c;         // 出力データ\n}\n</code></pre> <pre><code>/* クラス */\nclass Node(int x) {\n    int val = x;\n    Node next;\n}\n\n/* 関数 */\nint Function() {\n    // いくつかの処理を実行...\n    return 0;\n}\n\nint Algorithm(int n) {        // 入力データ\n    const int a = 0;          // 一時データ（定数）\n    int b = 0;                // 一時データ（変数）\n    Node node = new(0);       // 一時データ（オブジェクト）\n    int c = Function();       // スタックフレーム空間（関数呼び出し）\n    return a + b + c;         // 出力データ\n}\n</code></pre> <pre><code>/* 構造体 */\ntype node struct {\n    val  int\n    next *node\n}\n\n/* node 構造体を作成 */\nfunc newNode(val int) *node {\n    return &amp;node{val: val}\n}\n\n/* 関数 */\nfunc function() int {\n    // いくつかの処理を実行...\n    return 0\n}\n\nfunc algorithm(n int) int { // 入力データ\n    const a = 0             // 一時データ（定数）\n    b := 0                  // 一時データ（変数）\n    newNode(0)              // 一時データ（オブジェクト）\n    c := function()         // スタックフレーム空間（関数呼び出し）\n    return a + b + c        // 出力データ\n}\n</code></pre> <pre><code>/* クラス */\nclass Node {\n    var val: Int\n    var next: Node?\n\n    init(x: Int) {\n        val = x\n    }\n}\n\n/* 関数 */\nfunc function() -&gt; Int {\n    // いくつかの処理を実行...\n    return 0\n}\n\nfunc algorithm(n: Int) -&gt; Int { // 入力データ\n    let a = 0             // 一時データ（定数）\n    var b = 0             // 一時データ（変数）\n    let node = Node(x: 0) // 一時データ（オブジェクト）\n    let c = function()    // スタックフレーム空間（関数呼び出し）\n    return a + b + c      // 出力データ\n}\n</code></pre> <pre><code>/* クラス */\nclass Node {\n    val;\n    next;\n    constructor(val) {\n        this.val = val === undefined ? 0 : val; // ノードの値\n        this.next = null;                       // 次のノードへの参照\n    }\n}\n\n/* 関数 */\nfunction constFunc() {\n    // いくつかの処理を実行\n    return 0;\n}\n\nfunction algorithm(n) {       // 入力データ\n    const a = 0;              // 一時データ（定数）\n    let b = 0;                // 一時データ（変数）\n    const node = new Node(0); // 一時データ（オブジェクト）\n    const c = constFunc();    // スタックフレーム空間（関数呼び出し）\n    return a + b + c;         // 出力データ\n}\n</code></pre> <pre><code>/* クラス */\nclass Node {\n    val: number;\n    next: Node | null;\n    constructor(val?: number) {\n        this.val = val === undefined ? 0 : val; // ノードの値\n        this.next = null;                       // 次のノードへの参照\n    }\n}\n\n/* 関数 */\nfunction constFunc(): number {\n    // いくつかの処理を実行\n    return 0;\n}\n\nfunction algorithm(n: number): number { // 入力データ\n    const a = 0;                        // 一時データ（定数）\n    let b = 0;                          // 一時データ（変数）\n    const node = new Node(0);           // 一時データ（オブジェクト）\n    const c = constFunc();              // スタックフレーム空間（関数呼び出し）\n    return a + b + c;                   // 出力データ\n}\n</code></pre> <pre><code>/* クラス */\nclass Node {\n  int val;\n  Node next;\n  Node(this.val, [this.next]);\n}\n\n/* 関数 */\nint function() {\n  // いくつかの処理を実行...\n  return 0;\n}\n\nint algorithm(int n) {  // 入力データ\n  const int a = 0;      // 一時データ（定数）\n  int b = 0;            // 一時データ（変数）\n  Node node = Node(0);  // 一時データ（オブジェクト）\n  int c = function();   // スタックフレーム空間（関数呼び出し）\n  return a + b + c;     // 出力データ\n}\n</code></pre> <pre><code>use std::rc::Rc;\nuse std::cell::RefCell;\n\n/* 構造体 */\nstruct Node {\n    val: i32,\n    next: Option&lt;Rc&lt;RefCell&lt;Node&gt;&gt;&gt;,\n}\n\n/* Node 構造体を作成 */\nimpl Node {\n    fn new(val: i32) -&gt; Self {\n        Self { val: val, next: None }\n    }\n}\n\n/* 関数 */\nfn function() -&gt; i32 {      \n    // いくつかの処理を実行...\n    return 0;\n}\n\nfn algorithm(n: i32) -&gt; i32 {       // 入力データ\n    const a: i32 = 0;               // 一時データ（定数）\n    let mut b = 0;                  // 一時データ（変数）\n    let node = Node::new(0);        // 一時データ（オブジェクト）\n    let c = function();             // スタックフレーム空間（関数呼び出し）\n    return a + b + c;               // 出力データ\n}\n</code></pre> <pre><code>/* 関数 */\nint func() {\n    // いくつかの処理を実行...\n    return 0;\n}\n\nint algorithm(int n) { // 入力データ\n    const int a = 0;   // 一時データ（定数）\n    int b = 0;         // 一時データ（変数）\n    int c = func();    // スタックフレーム空間（関数呼び出し）\n    return a + b + c;  // 出力データ\n}\n</code></pre> <pre><code>/* クラス */\nclass Node(var _val: Int) {\n    var next: Node? = null\n}\n\n/* 関数 */\nfun function(): Int {\n    // いくつかの処理を実行...\n    return 0\n}\n\nfun algorithm(n: Int): Int { // 入力データ\n    val a = 0                // 一時データ（定数）\n    var b = 0                // 一時データ（変数）\n    val node = Node(0)       // 一時データ（オブジェクト）\n    val c = function()       // スタックフレーム空間（関数呼び出し）\n    return a + b + c         // 出力データ\n}\n</code></pre> <pre><code>### クラス ###\nclass Node\n    attr_accessor :val      # ノードの値\n    attr_accessor :next     # 次のノードへの参照\n\n    def initialize(x)\n        @val = x\n    end\nend\n\n### 関数 ###\ndef function\n    # いくつかの処理を実行...\n    0\nend\n\n### アルゴリズム ###\ndef algorithm(n)        # 入力データ\n    a = 0               # 一時データ（定数）\n    b = 0               # 一時データ（変数）\n    node = Node.new(0)  # 一時データ（オブジェクト）\n    c = function        # スタックフレーム空間（関数呼び出し）\n    a + b + c           # 出力データ\nend\n</code></pre>","path":["第 2 章 &nbsp; 計算量解析","2.4 &nbsp; 空間計算量"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#242","level":2,"title":"2.4.2   推定方法","text":"<p>空間計算量の推定方法は時間計算量とおおむね同じで、数える対象を「操作回数」から「使用空間の大きさ」に変えるだけです。</p> <p>ただし時間計算量と異なり、通常は最悪空間計算量だけに注目します。メモリ空間は厳格な要件であり、どの入力データに対しても十分なメモリを確保できることを保証しなければならないからです。</p> <p>以下のコードを見ると、最悪空間計算量における「最悪」には二つの意味があります。</p> <ol> <li>最悪の入力データを基準にする：\\(n &lt; 10\\) のとき空間計算量は \\(O(1)\\) ですが、\\(n &gt; 10\\) のとき初期化される配列 <code>nums</code> が \\(O(n)\\) の空間を占有するため、最悪空間計算量は \\(O(n)\\) です。</li> <li>アルゴリズム実行中のメモリ使用量のピークを基準にする：例えば、プログラムは最後の行を実行する前までは \\(O(1)\\) の空間しか使いませんが、配列 <code>nums</code> を初期化するときには \\(O(n)\\) の空間を占有するため、最悪空間計算量は \\(O(n)\\) です。</li> </ol> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>def algorithm(n: int):\n    a = 0               # O(1)\n    b = [0] * 10000     # O(1)\n    if n &gt; 10:\n        nums = [0] * n  # O(n)\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 0;               // O(1)\n    vector&lt;int&gt; b(10000);    // O(1)\n    if (n &gt; 10)\n        vector&lt;int&gt; nums(n); // O(n)\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 0;                   // O(1)\n    int[] b = new int[10000];    // O(1)\n    if (n &gt; 10)\n        int[] nums = new int[n]; // O(n)\n}\n</code></pre> <pre><code>void Algorithm(int n) {\n    int a = 0;                   // O(1)\n    int[] b = new int[10000];    // O(1)\n    if (n &gt; 10) {\n        int[] nums = new int[n]; // O(n)\n    }\n}\n</code></pre> <pre><code>func algorithm(n int) {\n    a := 0                      // O(1)\n    b := make([]int, 10000)     // O(1)\n    var nums []int\n    if n &gt; 10 {\n        nums := make([]int, n)  // O(n)\n    }\n    fmt.Println(a, b, nums)\n}\n</code></pre> <pre><code>func algorithm(n: Int) {\n    let a = 0 // O(1)\n    let b = Array(repeating: 0, count: 10000) // O(1)\n    if n &gt; 10 {\n        let nums = Array(repeating: 0, count: n) // O(n)\n    }\n}\n</code></pre> <pre><code>function algorithm(n) {\n    const a = 0;                   // O(1)\n    const b = new Array(10000);    // O(1)\n    if (n &gt; 10) {\n        const nums = new Array(n); // O(n)\n    }\n}\n</code></pre> <pre><code>function algorithm(n: number): void {\n    const a = 0;                   // O(1)\n    const b = new Array(10000);    // O(1)\n    if (n &gt; 10) {\n        const nums = new Array(n); // O(n)\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n  int a = 0;                            // O(1)\n  List&lt;int&gt; b = List.filled(10000, 0);  // O(1)\n  if (n &gt; 10) {\n    List&lt;int&gt; nums = List.filled(n, 0); // O(n)\n  }\n}\n</code></pre> <pre><code>fn algorithm(n: i32) {\n    let a = 0;                              // O(1)\n    let b = [0; 10000];                     // O(1)\n    if n &gt; 10 {\n        let nums = vec![0; n as usize];     // O(n)\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 0;               // O(1)\n    int b[10000];            // O(1)\n    if (n &gt; 10)\n        int nums[n] = {0};   // O(n)\n}\n</code></pre> <pre><code>fun algorithm(n: Int) {\n    val a = 0                    // O(1)\n    val b = IntArray(10000)      // O(1)\n    if (n &gt; 10) {\n        val nums = IntArray(n)   // O(n)\n    }\n}\n</code></pre> <pre><code>def algorithm(n)\n    a = 0                           # O(1)\n    b = Array.new(10000)            # O(1)\n    nums = Array.new(n) if n &gt; 10   # O(n)\nend\n</code></pre> <p>再帰関数では、スタックフレーム空間の集計に注意が必要です。以下のコードを見てみましょう。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>def function() -&gt; int:\n    # いくつかの処理を実行\n    return 0\n\ndef loop(n: int):\n    \"\"\"ループの空間計算量は O(1)\"\"\"\n    for _ in range(n):\n        function()\n\ndef recur(n: int):\n    \"\"\"再帰の空間計算量は O(n)\"\"\"\n    if n == 1:\n        return\n    return recur(n - 1)\n</code></pre> <pre><code>int func() {\n    // いくつかの処理を実行\n    return 0;\n}\n/* ループの空間計算量は O(1) */\nvoid loop(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        func();\n    }\n}\n/* 再帰の空間計算量は O(n) */\nvoid recur(int n) {\n    if (n == 1) return;\n    recur(n - 1);\n}\n</code></pre> <pre><code>int function() {\n    // いくつかの処理を実行\n    return 0;\n}\n/* ループの空間計算量は O(1) */\nvoid loop(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        function();\n    }\n}\n/* 再帰の空間計算量は O(n) */\nvoid recur(int n) {\n    if (n == 1) return;\n    recur(n - 1);\n}\n</code></pre> <pre><code>int Function() {\n    // いくつかの処理を実行\n    return 0;\n}\n/* ループの空間計算量は O(1) */\nvoid Loop(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        Function();\n    }\n}\n/* 再帰の空間計算量は O(n) */\nint Recur(int n) {\n    if (n == 1) return 1;\n    return Recur(n - 1);\n}\n</code></pre> <pre><code>func function() int {\n    // いくつかの処理を実行\n    return 0\n}\n\n/* ループの空間計算量は O(1) */\nfunc loop(n int) {\n    for i := 0; i &lt; n; i++ {\n        function()\n    }\n}\n\n/* 再帰の空間計算量は O(n) */\nfunc recur(n int) {\n    if n == 1 {\n        return\n    }\n    recur(n - 1)\n}\n</code></pre> <pre><code>@discardableResult\nfunc function() -&gt; Int {\n    // いくつかの処理を実行\n    return 0\n}\n\n/* ループの空間計算量は O(1) */\nfunc loop(n: Int) {\n    for _ in 0 ..&lt; n {\n        function()\n    }\n}\n\n/* 再帰の空間計算量は O(n) */\nfunc recur(n: Int) {\n    if n == 1 {\n        return\n    }\n    recur(n: n - 1)\n}\n</code></pre> <pre><code>function constFunc() {\n    // いくつかの処理を実行\n    return 0;\n}\n/* ループの空間計算量は O(1) */\nfunction loop(n) {\n    for (let i = 0; i &lt; n; i++) {\n        constFunc();\n    }\n}\n/* 再帰の空間計算量は O(n) */\nfunction recur(n) {\n    if (n === 1) return;\n    return recur(n - 1);\n}\n</code></pre> <pre><code>function constFunc(): number {\n    // いくつかの処理を実行\n    return 0;\n}\n/* ループの空間計算量は O(1) */\nfunction loop(n: number): void {\n    for (let i = 0; i &lt; n; i++) {\n        constFunc();\n    }\n}\n/* 再帰の空間計算量は O(n) */\nfunction recur(n: number): void {\n    if (n === 1) return;\n    return recur(n - 1);\n}\n</code></pre> <pre><code>int function() {\n  // いくつかの処理を実行\n  return 0;\n}\n/* ループの空間計算量は O(1) */\nvoid loop(int n) {\n  for (int i = 0; i &lt; n; i++) {\n    function();\n  }\n}\n/* 再帰の空間計算量は O(n) */\nvoid recur(int n) {\n  if (n == 1) return;\n  recur(n - 1);\n}\n</code></pre> <pre><code>fn function() -&gt; i32 {\n    // いくつかの処理を実行\n    return 0;\n}\n/* ループの空間計算量は O(1) */\nfn loop(n: i32) {\n    for i in 0..n {\n        function();\n    }\n}\n/* 再帰の空間計算量は O(n) */\nfn recur(n: i32) {\n    if n == 1 {\n        return;\n    }\n    recur(n - 1);\n}\n</code></pre> <pre><code>int func() {\n    // いくつかの処理を実行\n    return 0;\n}\n/* ループの空間計算量は O(1) */\nvoid loop(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        func();\n    }\n}\n/* 再帰の空間計算量は O(n) */\nvoid recur(int n) {\n    if (n == 1) return;\n    recur(n - 1);\n}\n</code></pre> <pre><code>fun function(): Int {\n    // いくつかの処理を実行\n    return 0\n}\n/* ループの空間計算量は O(1) */\nfun loop(n: Int) {\n    for (i in 0..&lt;n) {\n        function()\n    }\n}\n/* 再帰の空間計算量は O(n) */\nfun recur(n: Int) {\n    if (n == 1) return\n    return recur(n - 1)\n}\n</code></pre> <pre><code>def function\n    # いくつかの処理を実行\n    0\nend\n\n### ループの空間計算量は O(1) ###\ndef loop(n)\n    (0...n).each { function }\nend\n\n### 再帰の空間計算量は O(n) ###\ndef recur(n)\n    return if n == 1\n    recur(n - 1)\nend\n</code></pre> <p>関数 <code>loop()</code> と <code>recur()</code> はどちらも時間計算量は \\(O(n)\\) ですが、空間計算量は異なります。</p> <ul> <li>関数 <code>loop()</code> はループの中で <code>function()</code> を \\(n\\) 回呼び出しますが、各反復での <code>function()</code> は戻るたびにスタックフレーム空間が解放されるため、空間計算量は依然として \\(O(1)\\) です。</li> <li>再帰関数 <code>recur()</code> は実行中に未返却の <code>recur()</code> が同時に \\(n\\) 個存在するため、\\(O(n)\\) のスタックフレーム空間を占有します。</li> </ul>","path":["第 2 章 &nbsp; 計算量解析","2.4 &nbsp; 空間計算量"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#243","level":2,"title":"2.4.3   よくある型","text":"<p>入力データサイズを \\(n\\) とすると、以下の図はよくある空間計算量の型を低い順から高い順に示しています。</p> \\[ \\begin{aligned} O(1) &lt; O(\\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \\newline \\text{定数階} &lt; \\text{対数階} &lt; \\text{線形階} &lt; \\text{平方階} &lt; \\text{指数階} \\end{aligned} \\] <p></p> <p> 図 2-16   よくある空間計算量の型 </p>","path":["第 2 章 &nbsp; 計算量解析","2.4 &nbsp; 空間計算量"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#1-o1","level":3,"title":"1.   定数階 \\(O(1)\\)","text":"<p>定数階は、個数が入力データサイズ \\(n\\) に依存しない定数、変数、オブジェクトなどによく現れます。</p> <p>注意すべき点として、ループ内で変数を初期化したり関数を呼び出したりして使用されたメモリは、次の反復に入ると解放されるため、空間の占有は累積せず、空間計算量は依然として \\(O(1)\\) です。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby space_complexity.py<pre><code>def function() -&gt; int:\n    \"\"\"関数\"\"\"\n    # 何らかの処理を行う\n    return 0\n\ndef constant(n: int):\n    \"\"\"定数階\"\"\"\n    # 定数、変数、オブジェクトは O(1) の空間を占める\n    a = 0\n    nums = [0] * 10000\n    node = ListNode(0)\n    # ループ内の変数は O(1) の空間を占める\n    for _ in range(n):\n        c = 0\n    # ループ内の関数は O(1) の空間を占める\n    for _ in range(n):\n        function()\n</code></pre> space_complexity.cpp<pre><code>/* 関数 */\nint func() {\n    // 何らかの処理を行う\n    return 0;\n}\n\n/* 定数階 */\nvoid constant(int n) {\n    // 定数、変数、オブジェクトは O(1) の空間を占める\n    const int a = 0;\n    int b = 0;\n    vector&lt;int&gt; nums(10000);\n    ListNode node(0);\n    // ループ内の変数は O(1) の空間を占める\n    for (int i = 0; i &lt; n; i++) {\n        int c = 0;\n    }\n    // ループ内の関数は O(1) の空間を占める\n    for (int i = 0; i &lt; n; i++) {\n        func();\n    }\n}\n</code></pre> space_complexity.java<pre><code>/* 関数 */\nint function() {\n    // 何らかの処理を行う\n    return 0;\n}\n\n/* 定数階 */\nvoid constant(int n) {\n    // 定数、変数、オブジェクトは O(1) の空間を占める\n    final int a = 0;\n    int b = 0;\n    int[] nums = new int[10000];\n    ListNode node = new ListNode(0);\n    // ループ内の変数は O(1) の空間を占める\n    for (int i = 0; i &lt; n; i++) {\n        int c = 0;\n    }\n    // ループ内の関数は O(1) の空間を占める\n    for (int i = 0; i &lt; n; i++) {\n        function();\n    }\n}\n</code></pre> space_complexity.cs<pre><code>/* 関数 */\nint Function() {\n    // 何らかの処理を行う\n    return 0;\n}\n\n/* 定数階 */\nvoid Constant(int n) {\n    // 定数、変数、オブジェクトは O(1) の空間を占める\n    int a = 0;\n    int b = 0;\n    int[] nums = new int[10000];\n    ListNode node = new(0);\n    // ループ内の変数は O(1) の空間を占める\n    for (int i = 0; i &lt; n; i++) {\n        int c = 0;\n    }\n    // ループ内の関数は O(1) の空間を占める\n    for (int i = 0; i &lt; n; i++) {\n        Function();\n    }\n}\n</code></pre> space_complexity.go<pre><code>/* 関数 */\nfunc function() int {\n    // いくつかの操作を実行...\n    return 0\n}\n\n/* 定数階 */\nfunc spaceConstant(n int) {\n    // 定数、変数、オブジェクトは O(1) の空間を占める\n    const a = 0\n    b := 0\n    nums := make([]int, 10000)\n    node := newNode(0)\n    // ループ内の変数は O(1) の空間を占める\n    var c int\n    for i := 0; i &lt; n; i++ {\n        c = 0\n    }\n    // ループ内の関数は O(1) の空間を占める\n    for i := 0; i &lt; n; i++ {\n        function()\n    }\n    b += 0\n    c += 0\n    nums[0] = 0\n    node.val = 0\n}\n</code></pre> space_complexity.swift<pre><code>/* 関数 */\n@discardableResult\nfunc function() -&gt; Int {\n    // 何らかの処理を行う\n    return 0\n}\n\n/* 定数階 */\nfunc constant(n: Int) {\n    // 定数、変数、オブジェクトは O(1) の空間を占める\n    let a = 0\n    var b = 0\n    let nums = Array(repeating: 0, count: 10000)\n    let node = ListNode(x: 0)\n    // ループ内の変数は O(1) の空間を占める\n    for _ in 0 ..&lt; n {\n        let c = 0\n    }\n    // ループ内の関数は O(1) の空間を占める\n    for _ in 0 ..&lt; n {\n        function()\n    }\n}\n</code></pre> space_complexity.js<pre><code>/* 関数 */\nfunction constFunc() {\n    // 何らかの処理を行う\n    return 0;\n}\n\n/* 定数階 */\nfunction constant(n) {\n    // 定数、変数、オブジェクトは O(1) の空間を占める\n    const a = 0;\n    const b = 0;\n    const nums = new Array(10000);\n    const node = new ListNode(0);\n    // ループ内の変数は O(1) の空間を占める\n    for (let i = 0; i &lt; n; i++) {\n        const c = 0;\n    }\n    // ループ内の関数は O(1) の空間を占める\n    for (let i = 0; i &lt; n; i++) {\n        constFunc();\n    }\n}\n</code></pre> space_complexity.ts<pre><code>/* 関数 */\nfunction constFunc(): number {\n    // 何らかの処理を行う\n    return 0;\n}\n\n/* 定数階 */\nfunction constant(n: number): void {\n    // 定数、変数、オブジェクトは O(1) の空間を占める\n    const a = 0;\n    const b = 0;\n    const nums = new Array(10000);\n    const node = new ListNode(0);\n    // ループ内の変数は O(1) の空間を占める\n    for (let i = 0; i &lt; n; i++) {\n        const c = 0;\n    }\n    // ループ内の関数は O(1) の空間を占める\n    for (let i = 0; i &lt; n; i++) {\n        constFunc();\n    }\n}\n</code></pre> space_complexity.dart<pre><code>/* 関数 */\nint function() {\n  // 何らかの処理を行う\n  return 0;\n}\n\n/* 定数階 */\nvoid constant(int n) {\n  // 定数、変数、オブジェクトは O(1) の空間を占める\n  final int a = 0;\n  int b = 0;\n  List&lt;int&gt; nums = List.filled(10000, 0);\n  ListNode node = ListNode(0);\n  // ループ内の変数は O(1) の空間を占める\n  for (var i = 0; i &lt; n; i++) {\n    int c = 0;\n  }\n  // ループ内の関数は O(1) の空間を占める\n  for (var i = 0; i &lt; n; i++) {\n    function();\n  }\n}\n</code></pre> space_complexity.rs<pre><code>/* 関数 */\nfn function() -&gt; i32 {\n    // 何らかの処理を行う\n    return 0;\n}\n\n/* 定数階 */\n#[allow(unused)]\nfn constant(n: i32) {\n    // 定数、変数、オブジェクトは O(1) の空間を占める\n    const A: i32 = 0;\n    let b = 0;\n    let nums = vec![0; 10000];\n    let node = ListNode::new(0);\n    // ループ内の変数は O(1) の空間を占める\n    for i in 0..n {\n        let c = 0;\n    }\n    // ループ内の関数は O(1) の空間を占める\n    for i in 0..n {\n        function();\n    }\n}\n</code></pre> space_complexity.c<pre><code>/* 関数 */\nint func() {\n    // 何らかの処理を行う\n    return 0;\n}\n\n/* 定数階 */\nvoid constant(int n) {\n    // 定数、変数、オブジェクトは O(1) の空間を占める\n    const int a = 0;\n    int b = 0;\n    int nums[1000];\n    ListNode *node = newListNode(0);\n    free(node);\n    // ループ内の変数は O(1) の空間を占める\n    for (int i = 0; i &lt; n; i++) {\n        int c = 0;\n    }\n    // ループ内の関数は O(1) の空間を占める\n    for (int i = 0; i &lt; n; i++) {\n        func();\n    }\n}\n</code></pre> space_complexity.kt<pre><code>/* 関数 */\nfun function(): Int {\n    // 何らかの処理を行う\n    return 0\n}\n\n/* 定数階 */\nfun constant(n: Int) {\n    // 定数、変数、オブジェクトは O(1) の空間を占める\n    val a = 0\n    var b = 0\n    val nums = Array(10000) { 0 }\n    val node = ListNode(0)\n    // ループ内の変数は O(1) の空間を占める\n    for (i in 0..&lt;n) {\n        val c = 0\n    }\n    // ループ内の関数は O(1) の空間を占める\n    for (i in 0..&lt;n) {\n        function()\n    }\n}\n</code></pre> space_complexity.rb<pre><code>### 関数 ###\ndef function\n  # 何らかの処理を行う\n  0\nend\n\n### 定数階 ###\ndef constant(n)\n  # 定数、変数、オブジェクトは O(1) の空間を占める\n  a = 0\n  nums = [0] * 10000\n  node = ListNode.new\n\n  # ループ内の変数は O(1) の空間を占める\n  (0...n).each { c = 0 }\n  # ループ内の関数は O(1) の空間を占める\n  (0...n).each { function }\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 2 章 &nbsp; 計算量解析","2.4 &nbsp; 空間計算量"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#2-on","level":3,"title":"2.   線形階 \\(O(n)\\)","text":"<p>線形階は、要素数が \\(n\\) に比例する配列、連結リスト、スタック、キューなどによく現れます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby space_complexity.py<pre><code>def linear(n: int):\n    \"\"\"線形階\"\"\"\n    # 長さ n のリストは O(n) の空間を使用\n    nums = [0] * n\n    # 長さ n のハッシュテーブルは O(n) の空間を使用\n    hmap = dict[int, str]()\n    for i in range(n):\n        hmap[i] = str(i)\n</code></pre> space_complexity.cpp<pre><code>/* 線形階 */\nvoid linear(int n) {\n    // 長さ n の配列は O(n) の空間を使用\n    vector&lt;int&gt; nums(n);\n    // 長さ n のリストは O(n) の空間を使用\n    vector&lt;ListNode&gt; nodes;\n    for (int i = 0; i &lt; n; i++) {\n        nodes.push_back(ListNode(i));\n    }\n    // 長さ n のハッシュテーブルは O(n) の空間を使用\n    unordered_map&lt;int, string&gt; map;\n    for (int i = 0; i &lt; n; i++) {\n        map[i] = to_string(i);\n    }\n}\n</code></pre> space_complexity.java<pre><code>/* 線形階 */\nvoid linear(int n) {\n    // 長さ n の配列は O(n) の空間を使用\n    int[] nums = new int[n];\n    // 長さ n のリストは O(n) の空間を使用\n    List&lt;ListNode&gt; nodes = new ArrayList&lt;&gt;();\n    for (int i = 0; i &lt; n; i++) {\n        nodes.add(new ListNode(i));\n    }\n    // 長さ n のハッシュテーブルは O(n) の空間を使用\n    Map&lt;Integer, String&gt; map = new HashMap&lt;&gt;();\n    for (int i = 0; i &lt; n; i++) {\n        map.put(i, String.valueOf(i));\n    }\n}\n</code></pre> space_complexity.cs<pre><code>/* 線形階 */\nvoid Linear(int n) {\n    // 長さ n の配列は O(n) の空間を使用\n    int[] nums = new int[n];\n    // 長さ n のリストは O(n) の空間を使用\n    List&lt;ListNode&gt; nodes = [];\n    for (int i = 0; i &lt; n; i++) {\n        nodes.Add(new ListNode(i));\n    }\n    // 長さ n のハッシュテーブルは O(n) の空間を使用\n    Dictionary&lt;int, string&gt; map = [];\n    for (int i = 0; i &lt; n; i++) {\n        map.Add(i, i.ToString());\n    }\n}\n</code></pre> space_complexity.go<pre><code>/* 線形階 */\nfunc spaceLinear(n int) {\n    // 長さ n の配列は O(n) の空間を使用\n    _ = make([]int, n)\n    // 長さ n のリストは O(n) の空間を使用\n    var nodes []*node\n    for i := 0; i &lt; n; i++ {\n        nodes = append(nodes, newNode(i))\n    }\n    // 長さ n のハッシュテーブルは O(n) の空間を使用\n    m := make(map[int]string, n)\n    for i := 0; i &lt; n; i++ {\n        m[i] = strconv.Itoa(i)\n    }\n}\n</code></pre> space_complexity.swift<pre><code>/* 線形階 */\nfunc linear(n: Int) {\n    // 長さ n の配列は O(n) の空間を使用\n    let nums = Array(repeating: 0, count: n)\n    // 長さ n のリストは O(n) の空間を使用\n    let nodes = (0 ..&lt; n).map { ListNode(x: $0) }\n    // 長さ n のハッシュテーブルは O(n) の空間を使用\n    let map = Dictionary(uniqueKeysWithValues: (0 ..&lt; n).map { ($0, \"\\($0)\") })\n}\n</code></pre> space_complexity.js<pre><code>/* 線形階 */\nfunction linear(n) {\n    // 長さ n の配列は O(n) の空間を使用\n    const nums = new Array(n);\n    // 長さ n のリストは O(n) の空間を使用\n    const nodes = [];\n    for (let i = 0; i &lt; n; i++) {\n        nodes.push(new ListNode(i));\n    }\n    // 長さ n のハッシュテーブルは O(n) の空間を使用\n    const map = new Map();\n    for (let i = 0; i &lt; n; i++) {\n        map.set(i, i.toString());\n    }\n}\n</code></pre> space_complexity.ts<pre><code>/* 線形階 */\nfunction linear(n: number): void {\n    // 長さ n の配列は O(n) の空間を使用\n    const nums = new Array(n);\n    // 長さ n のリストは O(n) の空間を使用\n    const nodes: ListNode[] = [];\n    for (let i = 0; i &lt; n; i++) {\n        nodes.push(new ListNode(i));\n    }\n    // 長さ n のハッシュテーブルは O(n) の空間を使用\n    const map = new Map();\n    for (let i = 0; i &lt; n; i++) {\n        map.set(i, i.toString());\n    }\n}\n</code></pre> space_complexity.dart<pre><code>/* 線形階 */\nvoid linear(int n) {\n  // 長さ n の配列は O(n) の空間を使用\n  List&lt;int&gt; nums = List.filled(n, 0);\n  // 長さ n のリストは O(n) の空間を使用\n  List&lt;ListNode&gt; nodes = [];\n  for (var i = 0; i &lt; n; i++) {\n    nodes.add(ListNode(i));\n  }\n  // 長さ n のハッシュテーブルは O(n) の空間を使用\n  Map&lt;int, String&gt; map = HashMap();\n  for (var i = 0; i &lt; n; i++) {\n    map.putIfAbsent(i, () =&gt; i.toString());\n  }\n}\n</code></pre> space_complexity.rs<pre><code>/* 線形階 */\n#[allow(unused)]\nfn linear(n: i32) {\n    // 長さ n の配列は O(n) の空間を使用\n    let mut nums = vec![0; n as usize];\n    // 長さ n のリストは O(n) の空間を使用\n    let mut nodes = Vec::new();\n    for i in 0..n {\n        nodes.push(ListNode::new(i))\n    }\n    // 長さ n のハッシュテーブルは O(n) の空間を使用\n    let mut map = HashMap::new();\n    for i in 0..n {\n        map.insert(i, i.to_string());\n    }\n}\n</code></pre> space_complexity.c<pre><code>/* ハッシュテーブル */\ntypedef struct {\n    int key;\n    int val;\n    UT_hash_handle hh; // uthash.h を用いて実装\n} HashTable;\n\n/* 線形階 */\nvoid linear(int n) {\n    // 長さ n の配列は O(n) の空間を使用\n    int *nums = malloc(sizeof(int) * n);\n    free(nums);\n\n    // 長さ n のリストは O(n) の空間を使用\n    ListNode **nodes = malloc(sizeof(ListNode *) * n);\n    for (int i = 0; i &lt; n; i++) {\n        nodes[i] = newListNode(i);\n    }\n    // メモリを解放する\n    for (int i = 0; i &lt; n; i++) {\n        free(nodes[i]);\n    }\n    free(nodes);\n\n    // 長さ n のハッシュテーブルは O(n) の空間を使用\n    HashTable *h = NULL;\n    for (int i = 0; i &lt; n; i++) {\n        HashTable *tmp = malloc(sizeof(HashTable));\n        tmp-&gt;key = i;\n        tmp-&gt;val = i;\n        HASH_ADD_INT(h, key, tmp);\n    }\n\n    // メモリを解放する\n    HashTable *curr, *tmp;\n    HASH_ITER(hh, h, curr, tmp) {\n        HASH_DEL(h, curr);\n        free(curr);\n    }\n}\n</code></pre> space_complexity.kt<pre><code>/* 線形階 */\nfun linear(n: Int) {\n    // 長さ n の配列は O(n) の空間を使用\n    val nums = Array(n) { 0 }\n    // 長さ n のリストは O(n) の空間を使用\n    val nodes = mutableListOf&lt;ListNode&gt;()\n    for (i in 0..&lt;n) {\n        nodes.add(ListNode(i))\n    }\n    // 長さ n のハッシュテーブルは O(n) の空間を使用\n    val map = mutableMapOf&lt;Int, String&gt;()\n    for (i in 0..&lt;n) {\n        map[i] = i.toString()\n    }\n}\n</code></pre> space_complexity.rb<pre><code>### 線形階 ###\ndef linear(n)\n  # 長さ n のリストは O(n) の空間を使用\n  nums = Array.new(n, 0)\n\n  # 長さ n のハッシュテーブルは O(n) の空間を使用\n  hmap = {}\n  for i in 0...n\n    hmap[i] = i.to_s\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>以下の図に示すように、この関数の再帰の深さは \\(n\\) であり、同時に \\(n\\) 個の未返却 <code>linear_recur()</code> 関数が存在するため、\\(O(n)\\) のスタックフレーム空間を使用します。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby space_complexity.py<pre><code>def linear_recur(n: int):\n    \"\"\"線形時間（再帰実装）\"\"\"\n    print(\"再帰 n =\", n)\n    if n == 1:\n        return\n    linear_recur(n - 1)\n</code></pre> space_complexity.cpp<pre><code>/* 線形時間（再帰実装） */\nvoid linearRecur(int n) {\n    cout &lt;&lt; \"再帰 n = \" &lt;&lt; n &lt;&lt; endl;\n    if (n == 1)\n        return;\n    linearRecur(n - 1);\n}\n</code></pre> space_complexity.java<pre><code>/* 線形時間（再帰実装） */\nvoid linearRecur(int n) {\n    System.out.println(\"再帰 n = \" + n);\n    if (n == 1)\n        return;\n    linearRecur(n - 1);\n}\n</code></pre> space_complexity.cs<pre><code>/* 線形時間（再帰実装） */\nvoid LinearRecur(int n) {\n    Console.WriteLine(\"再帰 n = \" + n);\n    if (n == 1) return;\n    LinearRecur(n - 1);\n}\n</code></pre> space_complexity.go<pre><code>/* 線形時間（再帰実装） */\nfunc spaceLinearRecur(n int) {\n    fmt.Println(\"再帰 n =\", n)\n    if n == 1 {\n        return\n    }\n    spaceLinearRecur(n - 1)\n}\n</code></pre> space_complexity.swift<pre><code>/* 線形時間（再帰実装） */\nfunc linearRecur(n: Int) {\n    print(\"再帰 n = \\(n)\")\n    if n == 1 {\n        return\n    }\n    linearRecur(n: n - 1)\n}\n</code></pre> space_complexity.js<pre><code>/* 線形時間（再帰実装） */\nfunction linearRecur(n) {\n    console.log(`再帰 n = ${n}`);\n    if (n === 1) return;\n    linearRecur(n - 1);\n}\n</code></pre> space_complexity.ts<pre><code>/* 線形時間（再帰実装） */\nfunction linearRecur(n: number): void {\n    console.log(`再帰 n = ${n}`);\n    if (n === 1) return;\n    linearRecur(n - 1);\n}\n</code></pre> space_complexity.dart<pre><code>/* 線形時間（再帰実装） */\nvoid linearRecur(int n) {\n  print('再帰 n = $n');\n  if (n == 1) return;\n  linearRecur(n - 1);\n}\n</code></pre> space_complexity.rs<pre><code>/* 線形時間（再帰実装） */\nfn linear_recur(n: i32) {\n    println!(\"再帰 n = {}\", n);\n    if n == 1 {\n        return;\n    };\n    linear_recur(n - 1);\n}\n</code></pre> space_complexity.c<pre><code>/* 線形時間（再帰実装） */\nvoid linearRecur(int n) {\n    printf(\"再帰 n = %d\\r\\n\", n);\n    if (n == 1)\n        return;\n    linearRecur(n - 1);\n}\n</code></pre> space_complexity.kt<pre><code>/* 線形時間（再帰実装） */\nfun linearRecur(n: Int) {\n    println(\"再帰 n = $n\")\n    if (n == 1)\n        return\n    linearRecur(n - 1)\n}\n</code></pre> space_complexity.rb<pre><code>### 線形階 ###\ndef linear(n)\n  # 長さ n のリストは O(n) の空間を使用\n  nums = Array.new(n, 0)\n\n  # 長さ n のハッシュテーブルは O(n) の空間を使用\n  hmap = {}\n  for i in 0...n\n    hmap[i] = i.to_s\n  end\nend\n\n# ## 線形階（再帰実装）###\ndef linear_recur(n)\n  puts \"再帰 n = #{n}\"\n  return if n == 1\n  linear_recur(n - 1)\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p></p> <p> 図 2-17   再帰関数が生み出す線形階の空間計算量 </p>","path":["第 2 章 &nbsp; 計算量解析","2.4 &nbsp; 空間計算量"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#3-on2","level":3,"title":"3.   平方階 \\(O(n^2)\\)","text":"<p>平方階は、要素数が \\(n\\) の二乗に比例する行列やグラフによく現れます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby space_complexity.py<pre><code>def quadratic(n: int):\n    \"\"\"二乗階\"\"\"\n    # 二次元リストは O(n^2) の空間を使用\n    num_matrix = [[0] * n for _ in range(n)]\n</code></pre> space_complexity.cpp<pre><code>/* 二乗階 */\nvoid quadratic(int n) {\n    // 二次元リストは O(n^2) の空間を使用\n    vector&lt;vector&lt;int&gt;&gt; numMatrix;\n    for (int i = 0; i &lt; n; i++) {\n        vector&lt;int&gt; tmp;\n        for (int j = 0; j &lt; n; j++) {\n            tmp.push_back(0);\n        }\n        numMatrix.push_back(tmp);\n    }\n}\n</code></pre> space_complexity.java<pre><code>/* 二乗階 */\nvoid quadratic(int n) {\n    // 行列は O(n^2) の空間を使用する\n    int[][] numMatrix = new int[n][n];\n    // 二次元リストは O(n^2) の空間を使用\n    List&lt;List&lt;Integer&gt;&gt; numList = new ArrayList&lt;&gt;();\n    for (int i = 0; i &lt; n; i++) {\n        List&lt;Integer&gt; tmp = new ArrayList&lt;&gt;();\n        for (int j = 0; j &lt; n; j++) {\n            tmp.add(0);\n        }\n        numList.add(tmp);\n    }\n}\n</code></pre> space_complexity.cs<pre><code>/* 二乗階 */\nvoid Quadratic(int n) {\n    // 行列は O(n^2) の空間を使用する\n    int[,] numMatrix = new int[n, n];\n    // 二次元リストは O(n^2) の空間を使用\n    List&lt;List&lt;int&gt;&gt; numList = [];\n    for (int i = 0; i &lt; n; i++) {\n        List&lt;int&gt; tmp = [];\n        for (int j = 0; j &lt; n; j++) {\n            tmp.Add(0);\n        }\n        numList.Add(tmp);\n    }\n}\n</code></pre> space_complexity.go<pre><code>/* 二乗階 */\nfunc spaceQuadratic(n int) {\n    // 行列は O(n^2) の空間を使用する\n    numMatrix := make([][]int, n)\n    for i := 0; i &lt; n; i++ {\n        numMatrix[i] = make([]int, n)\n    }\n}\n</code></pre> space_complexity.swift<pre><code>/* 二乗階 */\nfunc quadratic(n: Int) {\n    // 二次元リストは O(n^2) の空間を使用\n    let numList = Array(repeating: Array(repeating: 0, count: n), count: n)\n}\n</code></pre> space_complexity.js<pre><code>/* 二乗階 */\nfunction quadratic(n) {\n    // 行列は O(n^2) の空間を使用する\n    const numMatrix = Array(n)\n        .fill(null)\n        .map(() =&gt; Array(n).fill(null));\n    // 二次元リストは O(n^2) の空間を使用\n    const numList = [];\n    for (let i = 0; i &lt; n; i++) {\n        const tmp = [];\n        for (let j = 0; j &lt; n; j++) {\n            tmp.push(0);\n        }\n        numList.push(tmp);\n    }\n}\n</code></pre> space_complexity.ts<pre><code>/* 二乗階 */\nfunction quadratic(n: number): void {\n    // 行列は O(n^2) の空間を使用する\n    const numMatrix = Array(n)\n        .fill(null)\n        .map(() =&gt; Array(n).fill(null));\n    // 二次元リストは O(n^2) の空間を使用\n    const numList = [];\n    for (let i = 0; i &lt; n; i++) {\n        const tmp = [];\n        for (let j = 0; j &lt; n; j++) {\n            tmp.push(0);\n        }\n        numList.push(tmp);\n    }\n}\n</code></pre> space_complexity.dart<pre><code>/* 二乗階 */\nvoid quadratic(int n) {\n  // 行列は O(n^2) の空間を使用する\n  List&lt;List&lt;int&gt;&gt; numMatrix = List.generate(n, (_) =&gt; List.filled(n, 0));\n  // 二次元リストは O(n^2) の空間を使用\n  List&lt;List&lt;int&gt;&gt; numList = [];\n  for (var i = 0; i &lt; n; i++) {\n    List&lt;int&gt; tmp = [];\n    for (int j = 0; j &lt; n; j++) {\n      tmp.add(0);\n    }\n    numList.add(tmp);\n  }\n}\n</code></pre> space_complexity.rs<pre><code>/* 二乗階 */\n#[allow(unused)]\nfn quadratic(n: i32) {\n    // 行列は O(n^2) の空間を使用する\n    let num_matrix = vec![vec![0; n as usize]; n as usize];\n    // 二次元リストは O(n^2) の空間を使用\n    let mut num_list = Vec::new();\n    for i in 0..n {\n        let mut tmp = Vec::new();\n        for j in 0..n {\n            tmp.push(0);\n        }\n        num_list.push(tmp);\n    }\n}\n</code></pre> space_complexity.c<pre><code>/* 二乗階 */\nvoid quadratic(int n) {\n    // 二次元リストは O(n^2) の空間を使用\n    int **numMatrix = malloc(sizeof(int *) * n);\n    for (int i = 0; i &lt; n; i++) {\n        int *tmp = malloc(sizeof(int) * n);\n        for (int j = 0; j &lt; n; j++) {\n            tmp[j] = 0;\n        }\n        numMatrix[i] = tmp;\n    }\n\n    // メモリを解放する\n    for (int i = 0; i &lt; n; i++) {\n        free(numMatrix[i]);\n    }\n    free(numMatrix);\n}\n</code></pre> space_complexity.kt<pre><code>/* 二乗階 */\nfun quadratic(n: Int) {\n    // 行列は O(n^2) の空間を使用する\n    val numMatrix = arrayOfNulls&lt;Array&lt;Int&gt;?&gt;(n)\n    // 二次元リストは O(n^2) の空間を使用\n    val numList = mutableListOf&lt;MutableList&lt;Int&gt;&gt;()\n    for (i in 0..&lt;n) {\n        val tmp = mutableListOf&lt;Int&gt;()\n        for (j in 0..&lt;n) {\n            tmp.add(0)\n        }\n        numList.add(tmp)\n    }\n}\n</code></pre> space_complexity.rb<pre><code>### 平方階 ###\ndef quadratic(n)\n  # 二次元リストは O(n^2) の空間を使用\n  Array.new(n) { Array.new(n, 0) }\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>以下の図に示すように、この関数の再帰の深さは \\(n\\) であり、各再帰関数の中で長さがそれぞれ \\(n\\)、\\(n-1\\)、\\(\\dots\\)、\\(2\\)、\\(1\\) の配列を初期化しています。平均長は \\(n / 2\\) なので、全体では \\(O(n^2)\\) の空間を占有します。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby space_complexity.py<pre><code>def quadratic_recur(n: int) -&gt; int:\n    \"\"\"二次時間（再帰実装）\"\"\"\n    if n &lt;= 0:\n        return 0\n    # 配列 nums の長さは n, n-1, ..., 2, 1\n    nums = [0] * n\n    return quadratic_recur(n - 1)\n</code></pre> space_complexity.cpp<pre><code>/* 二次時間（再帰実装） */\nint quadraticRecur(int n) {\n    if (n &lt;= 0)\n        return 0;\n    vector&lt;int&gt; nums(n);\n    cout &lt;&lt; \"再帰 n = \" &lt;&lt; n &lt;&lt; \" における nums の長さ = \" &lt;&lt; nums.size() &lt;&lt; endl;\n    return quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.java<pre><code>/* 二次時間（再帰実装） */\nint quadraticRecur(int n) {\n    if (n &lt;= 0)\n        return 0;\n    // 配列 nums の長さは n, n-1, ..., 2, 1\n    int[] nums = new int[n];\n    System.out.println(\"再帰 n = \" + n + \" における nums の長さ = \" + nums.length);\n    return quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.cs<pre><code>/* 二次時間（再帰実装） */\nint QuadraticRecur(int n) {\n    if (n &lt;= 0) return 0;\n    int[] nums = new int[n];\n    Console.WriteLine(\"再帰 n = \" + n + \" における nums の長さ = \" + nums.Length);\n    return QuadraticRecur(n - 1);\n}\n</code></pre> space_complexity.go<pre><code>/* 二次時間（再帰実装） */\nfunc spaceQuadraticRecur(n int) int {\n    if n &lt;= 0 {\n        return 0\n    }\n    nums := make([]int, n)\n    fmt.Printf(\"再帰 n = %d における nums の長さ = %d \\n\", n, len(nums))\n    return spaceQuadraticRecur(n - 1)\n}\n</code></pre> space_complexity.swift<pre><code>/* 二次時間（再帰実装） */\n@discardableResult\nfunc quadraticRecur(n: Int) -&gt; Int {\n    if n &lt;= 0 {\n        return 0\n    }\n    // 配列 nums の長さは n, n-1, ..., 2, 1\n    let nums = Array(repeating: 0, count: n)\n    print(\"再帰 n = \\(n) における nums の長さ = \\(nums.count)\")\n    return quadraticRecur(n: n - 1)\n}\n</code></pre> space_complexity.js<pre><code>/* 二次時間（再帰実装） */\nfunction quadraticRecur(n) {\n    if (n &lt;= 0) return 0;\n    const nums = new Array(n);\n    console.log(`再帰 n = ${n} における nums の長さ = ${nums.length}`);\n    return quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.ts<pre><code>/* 二次時間（再帰実装） */\nfunction quadraticRecur(n: number): number {\n    if (n &lt;= 0) return 0;\n    const nums = new Array(n);\n    console.log(`再帰 n = ${n} における nums の長さ = ${nums.length}`);\n    return quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.dart<pre><code>/* 二次時間（再帰実装） */\nint quadraticRecur(int n) {\n  if (n &lt;= 0) return 0;\n  List&lt;int&gt; nums = List.filled(n, 0);\n  print('再帰 n = $n における nums の長さ = ${nums.length}');\n  return quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.rs<pre><code>/* 二次時間（再帰実装） */\nfn quadratic_recur(n: i32) -&gt; i32 {\n    if n &lt;= 0 {\n        return 0;\n    };\n    // 配列 nums の長さは n, n-1, ..., 2, 1\n    let nums = vec![0; n as usize];\n    println!(\"再帰 n = {} における nums の長さ = {}\", n, nums.len());\n    return quadratic_recur(n - 1);\n}\n</code></pre> space_complexity.c<pre><code>/* 二次時間（再帰実装） */\nint quadraticRecur(int n) {\n    if (n &lt;= 0)\n        return 0;\n    int *nums = malloc(sizeof(int) * n);\n    printf(\"再帰 n = %d における nums の長さ = %d\\r\\n\", n, n);\n    int res = quadraticRecur(n - 1);\n    free(nums);\n    return res;\n}\n</code></pre> space_complexity.kt<pre><code>/* 二次時間（再帰実装） */\ntailrec fun quadraticRecur(n: Int): Int {\n    if (n &lt;= 0)\n        return 0\n    // 配列 nums の長さは n, n-1, ..., 2, 1\n    val nums = Array(n) { 0 }\n    println(\"再帰 n = $n における nums の長さ = ${nums.size}\")\n    return quadraticRecur(n - 1)\n}\n</code></pre> space_complexity.rb<pre><code>### 平方階 ###\ndef quadratic(n)\n  # 二次元リストは O(n^2) の空間を使用\n  Array.new(n) { Array.new(n, 0) }\nend\n\n# ## 平方階（再帰実装）###\ndef quadratic_recur(n)\n  return 0 unless n &gt; 0\n\n  # 配列 nums の長さは n, n-1, ..., 2, 1\n  nums = Array.new(n, 0)\n  quadratic_recur(n - 1)\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p></p> <p> 図 2-18   再帰関数が生み出す平方階の空間計算量 </p>","path":["第 2 章 &nbsp; 計算量解析","2.4 &nbsp; 空間計算量"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#4-o2n","level":3,"title":"4.   指数階 \\(O(2^n)\\)","text":"<p>指数階は二分木によく現れます。以下の図を見ると、高さが \\(n\\) の「満二分木」のノード数は \\(2^n - 1\\) であり、\\(O(2^n)\\) の空間を占有します。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby space_complexity.py<pre><code>def build_tree(n: int) -&gt; TreeNode | None:\n    \"\"\"指数時間（完全二分木の構築）\"\"\"\n    if n == 0:\n        return None\n    root = TreeNode(0)\n    root.left = build_tree(n - 1)\n    root.right = build_tree(n - 1)\n    return root\n</code></pre> space_complexity.cpp<pre><code>/* 指数時間（完全二分木の構築） */\nTreeNode *buildTree(int n) {\n    if (n == 0)\n        return nullptr;\n    TreeNode *root = new TreeNode(0);\n    root-&gt;left = buildTree(n - 1);\n    root-&gt;right = buildTree(n - 1);\n    return root;\n}\n</code></pre> space_complexity.java<pre><code>/* 指数時間（完全二分木の構築） */\nTreeNode buildTree(int n) {\n    if (n == 0)\n        return null;\n    TreeNode root = new TreeNode(0);\n    root.left = buildTree(n - 1);\n    root.right = buildTree(n - 1);\n    return root;\n}\n</code></pre> space_complexity.cs<pre><code>/* 指数時間（完全二分木の構築） */\nTreeNode? BuildTree(int n) {\n    if (n == 0) return null;\n    TreeNode root = new(0) {\n        left = BuildTree(n - 1),\n        right = BuildTree(n - 1)\n    };\n    return root;\n}\n</code></pre> space_complexity.go<pre><code>/* 指数時間（完全二分木の構築） */\nfunc buildTree(n int) *TreeNode {\n    if n == 0 {\n        return nil\n    }\n    root := NewTreeNode(0)\n    root.Left = buildTree(n - 1)\n    root.Right = buildTree(n - 1)\n    return root\n}\n</code></pre> space_complexity.swift<pre><code>/* 指数時間（完全二分木の構築） */\nfunc buildTree(n: Int) -&gt; TreeNode? {\n    if n == 0 {\n        return nil\n    }\n    let root = TreeNode(x: 0)\n    root.left = buildTree(n: n - 1)\n    root.right = buildTree(n: n - 1)\n    return root\n}\n</code></pre> space_complexity.js<pre><code>/* 指数時間（完全二分木の構築） */\nfunction buildTree(n) {\n    if (n === 0) return null;\n    const root = new TreeNode(0);\n    root.left = buildTree(n - 1);\n    root.right = buildTree(n - 1);\n    return root;\n}\n</code></pre> space_complexity.ts<pre><code>/* 指数時間（完全二分木の構築） */\nfunction buildTree(n: number): TreeNode | null {\n    if (n === 0) return null;\n    const root = new TreeNode(0);\n    root.left = buildTree(n - 1);\n    root.right = buildTree(n - 1);\n    return root;\n}\n</code></pre> space_complexity.dart<pre><code>/* 指数時間（完全二分木の構築） */\nTreeNode? buildTree(int n) {\n  if (n == 0) return null;\n  TreeNode root = TreeNode(0);\n  root.left = buildTree(n - 1);\n  root.right = buildTree(n - 1);\n  return root;\n}\n</code></pre> space_complexity.rs<pre><code>/* 指数時間（完全二分木の構築） */\nfn build_tree(n: i32) -&gt; Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt; {\n    if n == 0 {\n        return None;\n    };\n    let root = TreeNode::new(0);\n    root.borrow_mut().left = build_tree(n - 1);\n    root.borrow_mut().right = build_tree(n - 1);\n    return Some(root);\n}\n</code></pre> space_complexity.c<pre><code>/* 指数時間（完全二分木の構築） */\nTreeNode *buildTree(int n) {\n    if (n == 0)\n        return NULL;\n    TreeNode *root = newTreeNode(0);\n    root-&gt;left = buildTree(n - 1);\n    root-&gt;right = buildTree(n - 1);\n    return root;\n}\n</code></pre> space_complexity.kt<pre><code>/* 指数時間（完全二分木の構築） */\nfun buildTree(n: Int): TreeNode? {\n    if (n == 0)\n        return null\n    val root = TreeNode(0)\n    root.left = buildTree(n - 1)\n    root.right = buildTree(n - 1)\n    return root\n}\n</code></pre> space_complexity.rb<pre><code>### 平方階 ###\ndef quadratic(n)\n  # 二次元リストは O(n^2) の空間を使用\n  Array.new(n) { Array.new(n, 0) }\nend\n\n# ## 平方階（再帰実装）###\ndef quadratic_recur(n)\n  return 0 unless n &gt; 0\n\n  # 配列 nums の長さは n, n-1, ..., 2, 1\n  nums = Array.new(n, 0)\n  quadratic_recur(n - 1)\nend\n\n# ## 指数階（満二分木を構築）###\ndef build_tree(n)\n  return if n == 0\n\n  TreeNode.new.tap do |root|\n    root.left = build_tree(n - 1)\n    root.right = build_tree(n - 1)\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p></p> <p> 図 2-19   満二分木が生み出す指数階の空間計算量 </p>","path":["第 2 章 &nbsp; 計算量解析","2.4 &nbsp; 空間計算量"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#5-olog-n","level":3,"title":"5.   対数階 \\(O(\\log n)\\)","text":"<p>対数階は分割統治アルゴリズムによく現れます。例えばマージソートでは、長さ \\(n\\) の配列を入力として、各再帰で配列を中央から二つに分割するため、高さ \\(\\log n\\) の再帰木が形成され、\\(O(\\log n)\\) のスタックフレーム空間を使用します。</p> <p>また、数値を文字列に変換する場合を考えると、正の整数 \\(n\\) の桁数は \\(\\lfloor \\log_{10} n \\rfloor + 1\\) であり、対応する文字列長も \\(\\lfloor \\log_{10} n \\rfloor + 1\\) です。したがって空間計算量は \\(O(\\log_{10} n + 1) = O(\\log n)\\) となります。</p>","path":["第 2 章 &nbsp; 計算量解析","2.4 &nbsp; 空間計算量"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#244","level":2,"title":"2.4.4   時間と空間のトレードオフ","text":"<p>理想的には、アルゴリズムの時間計算量と空間計算量の両方を最適にしたいところです。しかし実際には、この二つを同時に最適化するのは通常きわめて困難です。</p> <p>時間計算量を下げるには、通常、空間計算量を増やす代償が必要であり、その逆も同様です。メモリ空間を犠牲にして実行速度を上げる考え方を「空間を時間と引き換えにする」と呼び、その逆を「時間を空間と引き換えにする」と呼びます。</p> <p>どちらの考え方を選ぶかは、何をより重視するかによって決まります。多くの場合、空間より時間のほうが貴重なので、「空間を時間と引き換えにする」戦略のほうが一般的です。もちろん、データ量が非常に大きい場合には、空間計算量を抑えることも同じくらい重要です。</p>","path":["第 2 章 &nbsp; 計算量解析","2.4 &nbsp; 空間計算量"],"tags":[]},{"location":"chapter_computational_complexity/summary/","level":1,"title":"2.5   まとめ","text":"","path":["第 2 章 &nbsp; 計算量解析","2.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_computational_complexity/summary/#1","level":3,"title":"1.   要点の振り返り","text":"<p>アルゴリズム効率の評価</p> <ul> <li>時間効率と空間効率は、アルゴリズムの良し悪しを測る二つの主要な評価指標です。</li> <li>実測によってアルゴリズム効率を評価できますが、テスト環境の影響を排除しにくく、多くの計算資源も消費します。</li> <li>複雑度分析は実測の欠点を補い、分析結果はすべての実行プラットフォームに適用でき、データ規模ごとの効率も明らかにできます。</li> </ul> <p>時間計算量</p> <ul> <li>時間計算量は、アルゴリズムの実行時間がデータ量の増加に伴ってどう変化するかを測るためのものであり、効率評価に有効です。ただし、入力データ量が小さい場合や時間計算量が同じ場合などには、効率の優劣を正確に比較できないことがあります。</li> <li>最悪時間計算量はビッグオー記法 \\(O\\) で表され、関数の漸近上界に対応し、\\(n\\) が正の無限大に近づくときの操作回数 \\(T(n)\\) の増加の度合いを表します。</li> <li>時間計算量の推定は二段階に分かれ、まず操作回数を数え、次に漸近上界を判断します。</li> <li>一般的な時間計算量を低い順から並べると、\\(O(1)\\)、\\(O(\\log n)\\)、\\(O(n)\\)、\\(O(n \\log n)\\)、\\(O(n^2)\\)、\\(O(2^n)\\)、\\(O(n!)\\) などがあります。</li> <li>一部のアルゴリズムの時間計算量は固定ではなく、入力データの分布に関係します。時間計算量には最悪、最良、平均時間計算量がありますが、最良時間計算量は入力データが厳しい条件を満たす必要があるため、ほとんど使われません。</li> <li>平均時間計算量は、ランダムな入力データに対するアルゴリズムの実行効率を表し、実運用時の性能に最も近い指標です。平均時間計算量を求めるには、入力データの分布と、それを踏まえた数学的期待値を統計する必要があります。</li> </ul> <p>空間計算量</p> <ul> <li>空間計算量の役割は時間計算量に似ており、アルゴリズムが使用するメモリ空間がデータ量の増加に伴ってどう変化するかを測ります。</li> <li>アルゴリズム実行中に関係するメモリ空間は、入力空間、一時空間、出力空間に分けられます。通常、入力空間は空間計算量の計算に含めません。一時空間は一時データ、スタックフレーム空間、命令空間に分けられ、このうちスタックフレーム空間は通常、再帰関数でのみ空間計算量に影響します。</li> <li>私たちは通常、最悪空間計算量のみに注目し、最悪の入力データと最悪の実行時点における空間計算量を数えます。</li> <li>一般的な空間計算量を低い順から並べると、\\(O(1)\\)、\\(O(\\log n)\\)、\\(O(n)\\)、\\(O(n^2)\\)、\\(O(2^n)\\) などがあります。</li> </ul>","path":["第 2 章 &nbsp; 計算量解析","2.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_computational_complexity/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q：尾再帰の空間計算量は \\(O(1)\\) ですか？</p> <p>理論上、尾再帰関数の空間計算量は \\(O(1)\\) まで最適化できます。ただし、ほとんどのプログラミング言語（Java、Python、C++、Go、C# など）は尾再帰の自動最適化をサポートしていないため、通常は空間計算量を \\(O(n)\\) と見なします。</p> <p>Q：関数とメソッドという二つの用語の違いは何ですか？</p> <p>関数（function）は独立して実行でき、すべての引数は明示的に渡されます。メソッド（method）はオブジェクトに関連付けられ、それを呼び出すオブジェクトが暗黙的に渡され、クラスのインスタンスに含まれるデータを操作できます。</p> <p>以下では、いくつかの一般的なプログラミング言語を例に説明します。</p> <ul> <li>C 言語は手続き型プログラミング言語であり、オブジェクト指向の概念がないため、関数しかありません。ただし、構造体（struct）を作成してオブジェクト指向プログラミングを模倣でき、構造体に関連付けられた関数は、他のプログラミング言語におけるメソッドに相当します。</li> <li>Java と C# はオブジェクト指向のプログラミング言語であり、コードブロック（メソッド）は通常あるクラスの一部です。静的メソッドの振る舞いは関数に似ており、クラスに束縛され、特定のインスタンス変数にはアクセスできません。</li> <li>C++ と Python は、手続き型プログラミング（関数）にもオブジェクト指向プログラミング（メソッド）にも対応しています。</li> </ul> <p>Q：「一般的な空間計算量の種類」の図が表しているのは、使用空間の絶対量ですか？</p> <p>いいえ。この図が示しているのは空間計算量であり、表しているのは増加傾向であって、使用空間の絶対量ではありません。</p> <p>\\(n = 8\\) と仮定すると、各曲線の値が対応する関数と一致していないように見えるかもしれません。これは、各曲線に定数項が含まれており、値の範囲を視覚的に見やすい範囲へ圧縮しているためです。</p> <p>実際には、各手法の「定数項」の複雑度がどれほどか通常は分からないため、一般に複雑度だけを根拠に \\(n = 8\\) 以下で最適解を選ぶことはできません。ただし、\\(n = 8^5\\) であれば選びやすく、このときは増加傾向がすでに支配的になっています。</p> <p>Q 実際の利用場面に応じて、時間（または空間）を犠牲にしてアルゴリズムを設計することはありますか？</p> <p>実際の応用では、多くの場合、空間を犠牲にして時間を得る選択をします。たとえばデータベースのインデックスでは、通常 B+ 木やハッシュインデックスを構築し、大量のメモリ空間を使う代わりに、\\(O(\\log n)\\) あるいは \\(O(1)\\) の高速な検索を実現します。</p> <p>空間資源が貴重な場面では、時間を犠牲にして空間を得ることもあります。たとえば組み込み開発では、デバイスのメモリが非常に貴重なため、エンジニアはハッシュテーブルの使用をやめ、配列による順次探索を選んでメモリ使用量を節約することがあります。その代償として探索は遅くなります。</p>","path":["第 2 章 &nbsp; 計算量解析","2.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/","level":1,"title":"2.3   時間計算量","text":"<p>実行時間はアルゴリズムの効率を直感的かつ正確に反映します。あるコードの実行時間を正確に見積もりたい場合、どのようにすればよいでしょうか？</p> <ol> <li>実行プラットフォームを特定する。ハードウェア構成、プログラミング言語、システム環境などが含まれ、これらの要因はいずれもコードの実行効率に影響します。</li> <li>各種計算操作に必要な実行時間を評価する。例えば加算 <code>+</code> には 1 ns 、乗算 <code>*</code> には 10 ns 、出力 <code>print()</code> には 5 ns などが必要です。</li> <li>コード中のすべての計算操作を数える。そして各操作の実行時間を合計することで、実行時間を得ます。</li> </ol> <p>例えば次のコードでは、入力データサイズを \\(n\\) とします：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code># ある実行プラットフォーム上で\ndef algorithm(n: int):\n    a = 2      # 1 ns\n    a = a + 1  # 1 ns\n    a = a * 2  # 10 ns\n    # n 回ループ\n    for _ in range(n):  # 1 ns\n        print(0)        # 5 ns\n</code></pre> <pre><code>// ある実行プラットフォーム上で\nvoid algorithm(int n) {\n    int a = 2;  // 1 ns\n    a = a + 1;  // 1 ns\n    a = a * 2;  // 10 ns\n    // n 回ループ\n    for (int i = 0; i &lt; n; i++) {  // 1 ns\n        cout &lt;&lt; 0 &lt;&lt; endl;         // 5 ns\n    }\n}\n</code></pre> <pre><code>// ある実行プラットフォーム上で\nvoid algorithm(int n) {\n    int a = 2;  // 1 ns\n    a = a + 1;  // 1 ns\n    a = a * 2;  // 10 ns\n    // n 回ループ\n    for (int i = 0; i &lt; n; i++) {  // 1 ns\n        System.out.println(0);     // 5 ns\n    }\n}\n</code></pre> <pre><code>// ある実行プラットフォーム上で\nvoid Algorithm(int n) {\n    int a = 2;  // 1 ns\n    a = a + 1;  // 1 ns\n    a = a * 2;  // 10 ns\n    // n 回ループ\n    for (int i = 0; i &lt; n; i++) {  // 1 ns\n        Console.WriteLine(0);      // 5 ns\n    }\n}\n</code></pre> <pre><code>// ある実行プラットフォーム上で\nfunc algorithm(n int) {\n    a := 2     // 1 ns\n    a = a + 1  // 1 ns\n    a = a * 2  // 10 ns\n    // n 回ループ\n    for i := 0; i &lt; n; i++ {  // 1 ns\n        fmt.Println(a)        // 5 ns\n    }\n}\n</code></pre> <pre><code>// ある実行プラットフォーム上で\nfunc algorithm(n: Int) {\n    var a = 2 // 1 ns\n    a = a + 1 // 1 ns\n    a = a * 2 // 10 ns\n    // n 回ループ\n    for _ in 0 ..&lt; n { // 1 ns\n        print(0) // 5 ns\n    }\n}\n</code></pre> <pre><code>// ある実行プラットフォーム上で\nfunction algorithm(n) {\n    var a = 2; // 1 ns\n    a = a + 1; // 1 ns\n    a = a * 2; // 10 ns\n    // n 回ループ\n    for(let i = 0; i &lt; n; i++) { // 1 ns\n        console.log(0); // 5 ns\n    }\n}\n</code></pre> <pre><code>// ある実行プラットフォーム上で\nfunction algorithm(n: number): void {\n    var a: number = 2; // 1 ns\n    a = a + 1; // 1 ns\n    a = a * 2; // 10 ns\n    // n 回ループ\n    for(let i = 0; i &lt; n; i++) { // 1 ns\n        console.log(0); // 5 ns\n    }\n}\n</code></pre> <pre><code>// ある実行プラットフォーム上で\nvoid algorithm(int n) {\n  int a = 2; // 1 ns\n  a = a + 1; // 1 ns\n  a = a * 2; // 10 ns\n  // n 回ループ\n  for (int i = 0; i &lt; n; i++) { // 1 ns\n    print(0); // 5 ns\n  }\n}\n</code></pre> <pre><code>// ある実行プラットフォーム上で\nfn algorithm(n: i32) {\n    let mut a = 2;      // 1 ns\n    a = a + 1;          // 1 ns\n    a = a * 2;          // 10 ns\n    // n 回ループ\n    for _ in 0..n {     // 1 ns\n        println!(\"{}\", 0);  // 5 ns\n    }\n}\n</code></pre> <pre><code>// ある実行プラットフォーム上で\nvoid algorithm(int n) {\n    int a = 2;  // 1 ns\n    a = a + 1;  // 1 ns\n    a = a * 2;  // 10 ns\n    // n 回ループ\n    for (int i = 0; i &lt; n; i++) {   // 1 ns\n        printf(\"%d\", 0);            // 5 ns\n    }\n}\n</code></pre> <pre><code>// ある実行プラットフォーム上で\nfun algorithm(n: Int) {\n    var a = 2 // 1 ns\n    a = a + 1 // 1 ns\n    a = a * 2 // 10 ns\n    // n 回ループ\n    for (i in 0..&lt;n) {  // 1 ns\n        println(0)      // 5 ns\n    }\n}\n</code></pre> <pre><code># ある実行プラットフォーム上で\ndef algorithm(n)\n    a = 2       # 1 ns\n    a = a + 1   # 1 ns\n    a = a * 2   # 10 ns\n    # n 回ループ\n    (0...n).each do # 1 ns\n        puts 0      # 5 ns\n    end\nend\n</code></pre> <p>上記の方法に基づくと、アルゴリズムの実行時間は \\((6n + 12)\\) ns になります：</p> \\[ 1 + 1 + 10 + (1 + 5) \\times n = 6n + 12 \\] <p>しかし実際には、アルゴリズムの実行時間を統計的に求めることは合理的でも現実的でもありません。まず、見積もり時間を実行プラットフォームに縛りたくありません。アルゴリズムはさまざまな異なるプラットフォームで動作する必要があるからです。次に、各種操作の実行時間を知ること自体が難しく、見積もりの難易度を大きく引き上げます。</p>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#231","level":2,"title":"2.3.1   実行時間の増加傾向を捉える","text":"<p>時間計算量の分析で扱うのはアルゴリズムの実行時間そのものではなく、**データ量が増えたときに実行時間がどう増加するかという傾向**です。</p> <p>「実行時間の増加傾向」という概念はやや抽象的なので、例を通して理解してみましょう。入力データサイズを \\(n\\) とし、3 つのアルゴリズム <code>A</code>、<code>B</code>、<code>C</code> を考えます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code># アルゴリズム A の時間計算量：定数階\ndef algorithm_A(n: int):\n    print(0)\n# アルゴリズム B の時間計算量：線形階\ndef algorithm_B(n: int):\n    for _ in range(n):\n        print(0)\n# アルゴリズム C の時間計算量：定数階\ndef algorithm_C(n: int):\n    for _ in range(1000000):\n        print(0)\n</code></pre> <pre><code>// アルゴリズム A の時間計算量：定数階\nvoid algorithm_A(int n) {\n    cout &lt;&lt; 0 &lt;&lt; endl;\n}\n// アルゴリズム B の時間計算量：線形階\nvoid algorithm_B(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        cout &lt;&lt; 0 &lt;&lt; endl;\n    }\n}\n// アルゴリズム C の時間計算量：定数階\nvoid algorithm_C(int n) {\n    for (int i = 0; i &lt; 1000000; i++) {\n        cout &lt;&lt; 0 &lt;&lt; endl;\n    }\n}\n</code></pre> <pre><code>// アルゴリズム A の時間計算量：定数階\nvoid algorithm_A(int n) {\n    System.out.println(0);\n}\n// アルゴリズム B の時間計算量：線形階\nvoid algorithm_B(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        System.out.println(0);\n    }\n}\n// アルゴリズム C の時間計算量：定数階\nvoid algorithm_C(int n) {\n    for (int i = 0; i &lt; 1000000; i++) {\n        System.out.println(0);\n    }\n}\n</code></pre> <pre><code>// アルゴリズム A の時間計算量：定数階\nvoid AlgorithmA(int n) {\n    Console.WriteLine(0);\n}\n// アルゴリズム B の時間計算量：線形階\nvoid AlgorithmB(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        Console.WriteLine(0);\n    }\n}\n// アルゴリズム C の時間計算量：定数階\nvoid AlgorithmC(int n) {\n    for (int i = 0; i &lt; 1000000; i++) {\n        Console.WriteLine(0);\n    }\n}\n</code></pre> <pre><code>// アルゴリズム A の時間計算量：定数階\nfunc algorithm_A(n int) {\n    fmt.Println(0)\n}\n// アルゴリズム B の時間計算量：線形階\nfunc algorithm_B(n int) {\n    for i := 0; i &lt; n; i++ {\n        fmt.Println(0)\n    }\n}\n// アルゴリズム C の時間計算量：定数階\nfunc algorithm_C(n int) {\n    for i := 0; i &lt; 1000000; i++ {\n        fmt.Println(0)\n    }\n}\n</code></pre> <pre><code>// アルゴリズム A の時間計算量：定数階\nfunc algorithmA(n: Int) {\n    print(0)\n}\n\n// アルゴリズム B の時間計算量：線形階\nfunc algorithmB(n: Int) {\n    for _ in 0 ..&lt; n {\n        print(0)\n    }\n}\n\n// アルゴリズム C の時間計算量：定数階\nfunc algorithmC(n: Int) {\n    for _ in 0 ..&lt; 1_000_000 {\n        print(0)\n    }\n}\n</code></pre> <pre><code>// アルゴリズム A の時間計算量：定数階\nfunction algorithm_A(n) {\n    console.log(0);\n}\n// アルゴリズム B の時間計算量：線形階\nfunction algorithm_B(n) {\n    for (let i = 0; i &lt; n; i++) {\n        console.log(0);\n    }\n}\n// アルゴリズム C の時間計算量：定数階\nfunction algorithm_C(n) {\n    for (let i = 0; i &lt; 1000000; i++) {\n        console.log(0);\n    }\n}\n</code></pre> <pre><code>// アルゴリズム A の時間計算量：定数階\nfunction algorithm_A(n: number): void {\n    console.log(0);\n}\n// アルゴリズム B の時間計算量：線形階\nfunction algorithm_B(n: number): void {\n    for (let i = 0; i &lt; n; i++) {\n        console.log(0);\n    }\n}\n// アルゴリズム C の時間計算量：定数階\nfunction algorithm_C(n: number): void {\n    for (let i = 0; i &lt; 1000000; i++) {\n        console.log(0);\n    }\n}\n</code></pre> <pre><code>// アルゴリズム A の時間計算量：定数階\nvoid algorithmA(int n) {\n  print(0);\n}\n// アルゴリズム B の時間計算量：線形階\nvoid algorithmB(int n) {\n  for (int i = 0; i &lt; n; i++) {\n    print(0);\n  }\n}\n// アルゴリズム C の時間計算量：定数階\nvoid algorithmC(int n) {\n  for (int i = 0; i &lt; 1000000; i++) {\n    print(0);\n  }\n}\n</code></pre> <pre><code>// アルゴリズム A の時間計算量：定数階\nfn algorithm_A(n: i32) {\n    println!(\"{}\", 0);\n}\n// アルゴリズム B の時間計算量：線形階\nfn algorithm_B(n: i32) {\n    for _ in 0..n {\n        println!(\"{}\", 0);\n    }\n}\n// アルゴリズム C の時間計算量：定数階\nfn algorithm_C(n: i32) {\n    for _ in 0..1000000 {\n        println!(\"{}\", 0);\n    }\n}\n</code></pre> <pre><code>// アルゴリズム A の時間計算量：定数階\nvoid algorithm_A(int n) {\n    printf(\"%d\", 0);\n}\n// アルゴリズム B の時間計算量：線形階\nvoid algorithm_B(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        printf(\"%d\", 0);\n    }\n}\n// アルゴリズム C の時間計算量：定数階\nvoid algorithm_C(int n) {\n    for (int i = 0; i &lt; 1000000; i++) {\n        printf(\"%d\", 0);\n    }\n}\n</code></pre> <pre><code>// アルゴリズム A の時間計算量：定数階\nfun algoritm_A(n: Int) {\n    println(0)\n}\n// アルゴリズム B の時間計算量：線形階\nfun algorithm_B(n: Int) {\n    for (i in 0..&lt;n){\n        println(0)\n    }\n}\n// アルゴリズム C の時間計算量：定数階\nfun algorithm_C(n: Int) {\n    for (i in 0..&lt;1000000) {\n        println(0)\n    }\n}\n</code></pre> <pre><code># アルゴリズム A の時間計算量：定数階\ndef algorithm_A(n)\n    puts 0\nend\n\n# アルゴリズム B の時間計算量：線形階\ndef algorithm_B(n)\n    (0...n).each { puts 0 }\nend\n\n# アルゴリズム C の時間計算量：定数階\ndef algorithm_C(n)\n    (0...1_000_000).each { puts 0 }\nend\n</code></pre> <p>以下の図は、上記 3 つのアルゴリズム関数の時間計算量を示しています。</p> <ul> <li>アルゴリズム <code>A</code> には出力操作が \\(1\\) 回しかなく、実行時間は \\(n\\) が大きくなっても増加しません。このアルゴリズムの時間計算量を「定数階」と呼びます。</li> <li>アルゴリズム <code>B</code> の出力操作は \\(n\\) 回ループする必要があり、実行時間は \\(n\\) の増加に対して線形に増加します。このアルゴリズムの時間計算量は「線形階」と呼ばれます。</li> <li>アルゴリズム <code>C</code> の出力操作は \\(1000000\\) 回ループする必要があり、実行時間は長いものの、入力データサイズ \\(n\\) とは無関係です。したがって <code>C</code> の時間計算量は <code>A</code> と同じく、依然として「定数階」です。</li> </ul> <p></p> <p> 図 2-7   アルゴリズム A、B、C の時間増加傾向 </p> <p>アルゴリズムの実行時間を直接数える方法と比べて、時間計算量分析にはどのような特徴があるでしょうか？</p> <ul> <li>時間計算量はアルゴリズム効率を有効に評価できます。例えばアルゴリズム <code>B</code> の実行時間は線形に増加するため、\\(n &gt; 1\\) ではアルゴリズム <code>A</code> より遅く、\\(n &gt; 1000000\\) ではアルゴリズム <code>C</code> より遅くなります。実際、入力データサイズ \\(n\\) が十分に大きければ、「定数階」のアルゴリズムは必ず「線形階」のアルゴリズムより優れます。これが実行時間の増加傾向の意味です。</li> <li>時間計算量の見積もり方法はより簡潔です。実行プラットフォームや計算操作の種類は、アルゴリズム実行時間の増加傾向とは無関係です。そのため時間計算量分析では、すべての計算操作の実行時間を同じ「単位時間」とみなしてよく、「計算操作の実行時間を数える」作業を「計算操作の個数を数える」作業へ簡略化できます。これにより見積もりの難易度は大きく下がります。</li> <li>時間計算量には一定の限界もあります。例えばアルゴリズム <code>A</code> と <code>C</code> の時間計算量は同じでも、実際の実行時間には大きな差があります。同様に、アルゴリズム <code>B</code> の時間計算量は <code>C</code> より高いものの、入力データサイズ \\(n\\) が小さい場合にはアルゴリズム <code>B</code> のほうが明らかに優れます。このような場合、時間計算量だけでアルゴリズム効率の高低を判断するのは難しいことがあります。もっとも、こうした問題があっても、複雑度分析は依然としてアルゴリズム効率を評価する最も有効で一般的な方法です。</li> </ul>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#232","level":2,"title":"2.3.2   関数の漸近上界","text":"<p>入力サイズが \\(n\\) の次の関数を考えます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>def algorithm(n: int):\n    a = 1      # +1\n    a = a + 1  # +1\n    a = a * 2  # +1\n    # n 回ループ\n    for i in range(n):  # +1\n        print(0)        # +1\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +1\n    a = a + 1;  // +1\n    a = a * 2;  // +1\n    // n 回ループ\n    for (int i = 0; i &lt; n; i++) { // +1（各反復で i ++ を実行）\n        cout &lt;&lt; 0 &lt;&lt; endl;    // +1\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +1\n    a = a + 1;  // +1\n    a = a * 2;  // +1\n    // n 回ループ\n    for (int i = 0; i &lt; n; i++) { // +1（各反復で i ++ を実行）\n        System.out.println(0);    // +1\n    }\n}\n</code></pre> <pre><code>void Algorithm(int n) {\n    int a = 1;  // +1\n    a = a + 1;  // +1\n    a = a * 2;  // +1\n    // n 回ループ\n    for (int i = 0; i &lt; n; i++) {   // +1（各反復で i ++ を実行）\n        Console.WriteLine(0);   // +1\n    }\n}\n</code></pre> <pre><code>func algorithm(n int) {\n    a := 1      // +1\n    a = a + 1   // +1\n    a = a * 2   // +1\n    // n 回ループ\n    for i := 0; i &lt; n; i++ {   // +1\n        fmt.Println(a)         // +1\n    }\n}\n</code></pre> <pre><code>func algorithm(n: Int) {\n    var a = 1 // +1\n    a = a + 1 // +1\n    a = a * 2 // +1\n    // n 回ループ\n    for _ in 0 ..&lt; n { // +1\n        print(0) // +1\n    }\n}\n</code></pre> <pre><code>function algorithm(n) {\n    var a = 1; // +1\n    a += 1; // +1\n    a *= 2; // +1\n    // n 回ループ\n    for(let i = 0; i &lt; n; i++){ // +1（各反復で i ++ を実行）\n        console.log(0); // +1\n    }\n}\n</code></pre> <pre><code>function algorithm(n: number): void{\n    var a: number = 1; // +1\n    a += 1; // +1\n    a *= 2; // +1\n    // n 回ループ\n    for(let i = 0; i &lt; n; i++){ // +1（各反復で i ++ を実行）\n        console.log(0); // +1\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n  int a = 1; // +1\n  a = a + 1; // +1\n  a = a * 2; // +1\n  // n 回ループ\n  for (int i = 0; i &lt; n; i++) { // +1（各反復で i ++ を実行）\n    print(0); // +1\n  }\n}\n</code></pre> <pre><code>fn algorithm(n: i32) {\n    let mut a = 1;   // +1\n    a = a + 1;      // +1\n    a = a * 2;      // +1\n\n    // n 回ループ\n    for _ in 0..n { // +1（各反復で i ++ を実行）\n        println!(\"{}\", 0); // +1\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +1\n    a = a + 1;  // +1\n    a = a * 2;  // +1\n    // n 回ループ\n    for (int i = 0; i &lt; n; i++) {   // +1（各反復で i ++ を実行）\n        printf(\"%d\", 0);            // +1\n    }\n}\n</code></pre> <pre><code>fun algorithm(n: Int) {\n    var a = 1 // +1\n    a = a + 1 // +1\n    a = a * 2 // +1\n    // n 回ループ\n    for (i in 0..&lt;n) { // +1（各反復で i ++ を実行）\n        println(0) // +1\n    }\n}\n</code></pre> <pre><code>def algorithm(n)\n    a = 1       # +1\n    a = a + 1   # +1\n    a = a * 2   # +1\n    # n 回ループ\n    (0...n).each do # +1\n        puts 0      # +1\n    end\nend\n</code></pre> <p>アルゴリズムの操作回数を入力データサイズ \\(n\\) の関数とし、\\(T(n)\\) と表すと、上の関数の操作回数は次のようになります：</p> \\[ T(n) = 3 + 2n \\] <p>\\(T(n)\\) は一次関数であり、実行時間の増加傾向が線形であることを示しています。したがってその時間計算量は線形階です。</p> <p>線形階の時間計算量を \\(O(n)\\) と表します。この数学記号はビッグ \\(O\\) 記法（big-\\(O\\) notation）と呼ばれ、関数 \\(T(n)\\) の漸近上界（asymptotic upper bound）を表します。</p> <p>時間計算量の分析は本質的に「操作回数 \\(T(n)\\)」の漸近上界を求めることであり、明確な数学的定義があります。</p> <p>関数の漸近上界</p> <p>正の実数 \\(c\\) と実数 \\(n_0\\) が存在し、すべての \\(n &gt; n_0\\) について \\(T(n) \\leq c \\cdot f(n)\\) が成り立つならば、\\(f(n)\\) は \\(T(n)\\) の漸近上界の 1 つであるとみなせます。これを \\(T(n) = O(f(n))\\) と記します。</p> <p>下図のように、漸近上界を求めるとは関数 \\(f(n)\\) を探すことであり、\\(n\\) が無限大へ近づくときに \\(T(n)\\) と \\(f(n)\\) が同じ増加オーダーにあり、定数係数 \\(c\\) だけが異なる状態を表します。</p> <p></p> <p> 図 2-8   関数の漸近上界 </p>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#233","level":2,"title":"2.3.3   求め方","text":"<p>漸近上界はやや数学色が強い概念ですが、完全に理解できていなくても心配はいりません。まずは求め方を押さえ、実践を重ねる中で徐々にその数学的意味をつかめば十分です。</p> <p>定義より、\\(f(n)\\) が定まれば時間計算量 \\(O(f(n))\\) が得られます。では、漸近上界 \\(f(n)\\) をどのように決めればよいのでしょうか。大きく 2 段階あります。まず操作回数を数え、その後で漸近上界を判断します。</p>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#1-1","level":3,"title":"1.   第 1 ステップ：操作回数を数える","text":"<p>コードについては、上から下へ 1 行ずつ数えれば十分です。しかし、前述の \\(c \\cdot f(n)\\) における定数係数 \\(c\\) は任意に大きく取れるため、操作回数 \\(T(n)\\) に含まれるさまざまな係数や定数項は無視できます。この原則から、次のような簡略化のコツが得られます。</p> <ol> <li>\\(T(n)\\) 中の定数を無視する。それらはすべて \\(n\\) と無関係なので、時間計算量には影響しません。</li> <li>すべての係数を省略する。例えば \\(2n\\) 回や \\(5n + 1\\) 回のループは、いずれも \\(n\\) 回と簡略化できます。\\(n\\) の前の係数は時間計算量に影響しないからです。</li> <li>ループが入れ子のときは乗算を使う。総操作回数は外側のループと内側のループの操作回数の積に等しく、各ループ層には引き続き <code>1.</code> と <code>2.</code> のコツをそれぞれ適用できます。</li> </ol> <p>次の関数では、上記のコツを使って操作回数を数えられます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>def algorithm(n: int):\n    a = 1      # +0（コツ 1）\n    a = a + n  # +0（コツ 1）\n    # +n（コツ 2）\n    for i in range(5 * n + 1):\n        print(0)\n    # +n*n（コツ 3）\n    for i in range(2 * n):\n        for j in range(n + 1):\n            print(0)\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +0（コツ 1）\n    a = a + n;  // +0（コツ 1）\n    // +n（コツ 2）\n    for (int i = 0; i &lt; 5 * n + 1; i++) {\n        cout &lt;&lt; 0 &lt;&lt; endl;\n    }\n    // +n*n（コツ 3）\n    for (int i = 0; i &lt; 2 * n; i++) {\n        for (int j = 0; j &lt; n + 1; j++) {\n            cout &lt;&lt; 0 &lt;&lt; endl;\n        }\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +0（コツ 1）\n    a = a + n;  // +0（コツ 1）\n    // +n（コツ 2）\n    for (int i = 0; i &lt; 5 * n + 1; i++) {\n        System.out.println(0);\n    }\n    // +n*n（コツ 3）\n    for (int i = 0; i &lt; 2 * n; i++) {\n        for (int j = 0; j &lt; n + 1; j++) {\n            System.out.println(0);\n        }\n    }\n}\n</code></pre> <pre><code>void Algorithm(int n) {\n    int a = 1;  // +0（コツ 1）\n    a = a + n;  // +0（コツ 1）\n    // +n（コツ 2）\n    for (int i = 0; i &lt; 5 * n + 1; i++) {\n        Console.WriteLine(0);\n    }\n    // +n*n（コツ 3）\n    for (int i = 0; i &lt; 2 * n; i++) {\n        for (int j = 0; j &lt; n + 1; j++) {\n            Console.WriteLine(0);\n        }\n    }\n}\n</code></pre> <pre><code>func algorithm(n int) {\n    a := 1     // +0（コツ 1）\n    a = a + n  // +0（コツ 1）\n    // +n（コツ 2）\n    for i := 0; i &lt; 5 * n + 1; i++ {\n        fmt.Println(0)\n    }\n    // +n*n（コツ 3）\n    for i := 0; i &lt; 2 * n; i++ {\n        for j := 0; j &lt; n + 1; j++ {\n            fmt.Println(0)\n        }\n    }\n}\n</code></pre> <pre><code>func algorithm(n: Int) {\n    var a = 1 // +0（コツ 1）\n    a = a + n // +0（コツ 1）\n    // +n（コツ 2）\n    for _ in 0 ..&lt; (5 * n + 1) {\n        print(0)\n    }\n    // +n*n（コツ 3）\n    for _ in 0 ..&lt; (2 * n) {\n        for _ in 0 ..&lt; (n + 1) {\n            print(0)\n        }\n    }\n}\n</code></pre> <pre><code>function algorithm(n) {\n    let a = 1;  // +0（コツ 1）\n    a = a + n;  // +0（コツ 1）\n    // +n（コツ 2）\n    for (let i = 0; i &lt; 5 * n + 1; i++) {\n        console.log(0);\n    }\n    // +n*n（コツ 3）\n    for (let i = 0; i &lt; 2 * n; i++) {\n        for (let j = 0; j &lt; n + 1; j++) {\n            console.log(0);\n        }\n    }\n}\n</code></pre> <pre><code>function algorithm(n: number): void {\n    let a = 1;  // +0（コツ 1）\n    a = a + n;  // +0（コツ 1）\n    // +n（コツ 2）\n    for (let i = 0; i &lt; 5 * n + 1; i++) {\n        console.log(0);\n    }\n    // +n*n（コツ 3）\n    for (let i = 0; i &lt; 2 * n; i++) {\n        for (let j = 0; j &lt; n + 1; j++) {\n            console.log(0);\n        }\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n  int a = 1; // +0（コツ 1）\n  a = a + n; // +0（コツ 1）\n  // +n（コツ 2）\n  for (int i = 0; i &lt; 5 * n + 1; i++) {\n    print(0);\n  }\n  // +n*n（コツ 3）\n  for (int i = 0; i &lt; 2 * n; i++) {\n    for (int j = 0; j &lt; n + 1; j++) {\n      print(0);\n    }\n  }\n}\n</code></pre> <pre><code>fn algorithm(n: i32) {\n    let mut a = 1;     // +0（コツ 1）\n    a = a + n;        // +0（コツ 1）\n\n    // +n（コツ 2）\n    for i in 0..(5 * n + 1) {\n        println!(\"{}\", 0);\n    }\n\n    // +n*n（コツ 3）\n    for i in 0..(2 * n) {\n        for j in 0..(n + 1) {\n            println!(\"{}\", 0);\n        }\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +0（コツ 1）\n    a = a + n;  // +0（コツ 1）\n    // +n（コツ 2）\n    for (int i = 0; i &lt; 5 * n + 1; i++) {\n        printf(\"%d\", 0);\n    }\n    // +n*n（コツ 3）\n    for (int i = 0; i &lt; 2 * n; i++) {\n        for (int j = 0; j &lt; n + 1; j++) {\n            printf(\"%d\", 0);\n        }\n    }\n}\n</code></pre> <pre><code>fun algorithm(n: Int) {\n    var a = 1   // +0（コツ 1）\n    a = a + n   // +0（コツ 1）\n    // +n（コツ 2）\n    for (i in 0..&lt;5 * n + 1) {\n        println(0)\n    }\n    // +n*n（コツ 3）\n    for (i in 0..&lt;2 * n) {\n        for (j in 0..&lt;n + 1) {\n            println(0)\n        }\n    }\n}\n</code></pre> <pre><code>def algorithm(n)\n    a = 1       # +0（コツ 1）\n    a = a + n   # +0（コツ 1）\n    # +n（コツ 2）\n    (0...(5 * n + 1)).each do { puts 0 }\n    # +n*n（コツ 3）\n    (0...(2 * n)).each do\n        (0...(n + 1)).each do { puts 0 }\n    end\nend\n</code></pre> <p>次の式は、上記のコツを使う前後の集計結果を示したもので、どちらから求めても時間計算量は \\(O(n^2)\\) です。</p> \\[ \\begin{aligned} T(n) &amp; = 2n(n + 1) + (5n + 1) + 2 &amp; \\text{厳密集計 (-.-|||)} \\newline &amp; = 2n^2 + 7n + 3 \\newline T(n) &amp; = n^2 + n &amp; \\text{手抜き集計 (o.O)} \\end{aligned} \\]","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#2-2","level":3,"title":"2.   第 2 ステップ：漸近上界を判断する","text":"<p>時間計算量は \\(T(n)\\) の最高次の項によって決まります。これは、\\(n\\) が無限大に近づくとき、最高次の項が支配的となり、他の項の影響は無視できるからです。</p> <p>以下の表はその例です。いくつか極端な値を入れているのは、「係数では次数は変わらない」という結論を強調するためです。\\(n\\) が無限大に近づくと、これらの定数は重要でなくなります。</p> <p> 表 2-2   異なる操作回数に対応する時間計算量 </p> 操作回数 \\(T(n)\\) 時間計算量 \\(O(f(n))\\) \\(100000\\) \\(O(1)\\) \\(3n + 2\\) \\(O(n)\\) \\(2n^2 + 3n + 2\\) \\(O(n^2)\\) \\(n^3 + 10000n^2\\) \\(O(n^3)\\) \\(2^n + 10000n^{10000}\\) \\(O(2^n)\\)","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#234","level":2,"title":"2.3.4   よくある種類","text":"<p>入力データサイズを \\(n\\) とすると、よくある時間計算量の種類は次図のとおりです（小さい順に並べています）。</p> \\[ \\begin{aligned} O(1) &lt; O(\\log n) &lt; O(n) &lt; O(n \\log n) &lt; O(n^2) &lt; O(2^n) &lt; O(n!) \\newline \\text{定数階} &lt; \\text{対数階} &lt; \\text{線形階} &lt; \\text{線形対数階} &lt; \\text{平方階} &lt; \\text{指数階} &lt; \\text{階乗階} \\end{aligned} \\] <p></p> <p> 図 2-9   よくある時間計算量の種類 </p>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#1-o1","level":3,"title":"1.   定数階 \\(O(1)\\)","text":"<p>定数階の操作回数は入力データサイズ \\(n\\) と無関係であり、\\(n\\) が変化しても増減しません。</p> <p>次の関数では、操作回数 <code>size</code> が大きい可能性はありますが、入力データサイズ \\(n\\) とは無関係なので、時間計算量は依然として \\(O(1)\\) です：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def constant(n: int) -&gt; int:\n    \"\"\"定数階\"\"\"\n    count = 0\n    size = 100000\n    for _ in range(size):\n        count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* 定数階 */\nint constant(int n) {\n    int count = 0;\n    int size = 100000;\n    for (int i = 0; i &lt; size; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* 定数階 */\nint constant(int n) {\n    int count = 0;\n    int size = 100000;\n    for (int i = 0; i &lt; size; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* 定数階 */\nint Constant(int n) {\n    int count = 0;\n    int size = 100000;\n    for (int i = 0; i &lt; size; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* 定数階 */\nfunc constant(n int) int {\n    count := 0\n    size := 100000\n    for i := 0; i &lt; size; i++ {\n        count++\n    }\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* 定数階 */\nfunc constant(n: Int) -&gt; Int {\n    var count = 0\n    let size = 100_000\n    for _ in 0 ..&lt; size {\n        count += 1\n    }\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* 定数階 */\nfunction constant(n) {\n    let count = 0;\n    const size = 100000;\n    for (let i = 0; i &lt; size; i++) count++;\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* 定数階 */\nfunction constant(n: number): number {\n    let count = 0;\n    const size = 100000;\n    for (let i = 0; i &lt; size; i++) count++;\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* 定数階 */\nint constant(int n) {\n  int count = 0;\n  int size = 100000;\n  for (var i = 0; i &lt; size; i++) {\n    count++;\n  }\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* 定数階 */\nfn constant(n: i32) -&gt; i32 {\n    _ = n;\n    let mut count = 0;\n    let size = 100_000;\n    for _ in 0..size {\n        count += 1;\n    }\n    count\n}\n</code></pre> time_complexity.c<pre><code>/* 定数階 */\nint constant(int n) {\n    int count = 0;\n    int size = 100000;\n    int i = 0;\n    for (int i = 0; i &lt; size; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* 定数階 */\nfun constant(n: Int): Int {\n    var count = 0\n    val size = 100000\n    for (i in 0..&lt;size)\n        count++\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### 定数階 ###\ndef constant(n)\n  count = 0\n  size = 100000\n\n  (0...size).each { count += 1 }\n\n  count\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#2-on","level":3,"title":"2.   線形階 \\(O(n)\\)","text":"<p>線形階の操作回数は入力データサイズ \\(n\\) に対して線形に増加します。線形階は通常、単一ループに現れます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def linear(n: int) -&gt; int:\n    \"\"\"線形階\"\"\"\n    count = 0\n    for _ in range(n):\n        count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* 線形階 */\nint linear(int n) {\n    int count = 0;\n    for (int i = 0; i &lt; n; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* 線形階 */\nint linear(int n) {\n    int count = 0;\n    for (int i = 0; i &lt; n; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* 線形階 */\nint Linear(int n) {\n    int count = 0;\n    for (int i = 0; i &lt; n; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* 線形階 */\nfunc linear(n int) int {\n    count := 0\n    for i := 0; i &lt; n; i++ {\n        count++\n    }\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* 線形階 */\nfunc linear(n: Int) -&gt; Int {\n    var count = 0\n    for _ in 0 ..&lt; n {\n        count += 1\n    }\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* 線形階 */\nfunction linear(n) {\n    let count = 0;\n    for (let i = 0; i &lt; n; i++) count++;\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* 線形階 */\nfunction linear(n: number): number {\n    let count = 0;\n    for (let i = 0; i &lt; n; i++) count++;\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* 線形階 */\nint linear(int n) {\n  int count = 0;\n  for (var i = 0; i &lt; n; i++) {\n    count++;\n  }\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* 線形階 */\nfn linear(n: i32) -&gt; i32 {\n    let mut count = 0;\n    for _ in 0..n {\n        count += 1;\n    }\n    count\n}\n</code></pre> time_complexity.c<pre><code>/* 線形階 */\nint linear(int n) {\n    int count = 0;\n    for (int i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* 線形階 */\nfun linear(n: Int): Int {\n    var count = 0\n    for (i in 0..&lt;n)\n        count++\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### 線形階 ###\ndef linear(n)\n  count = 0\n  (0...n).each { count += 1 }\n  count\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>配列走査や連結リスト走査などの操作の時間計算量はいずれも \\(O(n)\\) であり、ここでの \\(n\\) は配列または連結リストの長さです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def array_traversal(nums: list[int]) -&gt; int:\n    \"\"\"線形時間（配列を走査）\"\"\"\n    count = 0\n    # ループ回数は配列長に比例する\n    for num in nums:\n        count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* 線形時間（配列を走査） */\nint arrayTraversal(vector&lt;int&gt; &amp;nums) {\n    int count = 0;\n    // ループ回数は配列長に比例する\n    for (int num : nums) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* 線形時間（配列を走査） */\nint arrayTraversal(int[] nums) {\n    int count = 0;\n    // ループ回数は配列長に比例する\n    for (int num : nums) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* 線形時間（配列を走査） */\nint ArrayTraversal(int[] nums) {\n    int count = 0;\n    // ループ回数は配列長に比例する\n    foreach (int num in nums) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* 線形時間（配列を走査） */\nfunc arrayTraversal(nums []int) int {\n    count := 0\n    // ループ回数は配列長に比例する\n    for range nums {\n        count++\n    }\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* 線形時間（配列を走査） */\nfunc arrayTraversal(nums: [Int]) -&gt; Int {\n    var count = 0\n    // ループ回数は配列長に比例する\n    for _ in nums {\n        count += 1\n    }\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* 線形時間（配列を走査） */\nfunction arrayTraversal(nums) {\n    let count = 0;\n    // ループ回数は配列長に比例する\n    for (let i = 0; i &lt; nums.length; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* 線形時間（配列を走査） */\nfunction arrayTraversal(nums: number[]): number {\n    let count = 0;\n    // ループ回数は配列長に比例する\n    for (let i = 0; i &lt; nums.length; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* 線形時間（配列を走査） */\nint arrayTraversal(List&lt;int&gt; nums) {\n  int count = 0;\n  // ループ回数は配列長に比例する\n  for (var _num in nums) {\n    count++;\n  }\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* 線形時間（配列を走査） */\nfn array_traversal(nums: &amp;[i32]) -&gt; i32 {\n    let mut count = 0;\n    // ループ回数は配列長に比例する\n    for _ in nums {\n        count += 1;\n    }\n    count\n}\n</code></pre> time_complexity.c<pre><code>/* 線形時間（配列を走査） */\nint arrayTraversal(int *nums, int n) {\n    int count = 0;\n    // ループ回数は配列長に比例する\n    for (int i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* 線形時間（配列を走査） */\nfun arrayTraversal(nums: IntArray): Int {\n    var count = 0\n    // ループ回数は配列長に比例する\n    for (num in nums) {\n        count++\n    }\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### 線形階 ###\ndef linear(n)\n  count = 0\n  (0...n).each { count += 1 }\n  count\nend\n\n# ## 線形階（配列を走査）###\ndef array_traversal(nums)\n  count = 0\n\n  # ループ回数は配列長に比例する\n  for num in nums\n    count += 1\n  end\n\n  count\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>注意すべきなのは、**入力データサイズ \\(n\\) は入力データの型に応じて具体的に定める必要がある**ということです。例えば 1 つ目の例では変数 \\(n\\) が入力データサイズであり、2 つ目の例では配列長 \\(n\\) がデータサイズです。</p>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#3-on2","level":3,"title":"3.   平方階 \\(O(n^2)\\)","text":"<p>平方階の操作回数は入力データサイズ \\(n\\) に対して二乗のオーダーで増加します。平方階は通常、入れ子ループに現れ、外側のループと内側のループの時間計算量がともに \\(O(n)\\) であるため、全体の時間計算量は \\(O(n^2)\\) になります：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def quadratic(n: int) -&gt; int:\n    \"\"\"二乗階\"\"\"\n    count = 0\n    # ループ回数はデータサイズ n の二乗に比例する\n    for i in range(n):\n        for j in range(n):\n            count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* 二乗階 */\nint quadratic(int n) {\n    int count = 0;\n    // ループ回数はデータサイズ n の二乗に比例する\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; n; j++) {\n            count++;\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* 二乗階 */\nint quadratic(int n) {\n    int count = 0;\n    // ループ回数はデータサイズ n の二乗に比例する\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; n; j++) {\n            count++;\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* 二乗階 */\nint Quadratic(int n) {\n    int count = 0;\n    // ループ回数はデータサイズ n の二乗に比例する\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; n; j++) {\n            count++;\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* 二乗階 */\nfunc quadratic(n int) int {\n    count := 0\n    // ループ回数はデータサイズ n の二乗に比例する\n    for i := 0; i &lt; n; i++ {\n        for j := 0; j &lt; n; j++ {\n            count++\n        }\n    }\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* 二乗階 */\nfunc quadratic(n: Int) -&gt; Int {\n    var count = 0\n    // ループ回数はデータサイズ n の二乗に比例する\n    for _ in 0 ..&lt; n {\n        for _ in 0 ..&lt; n {\n            count += 1\n        }\n    }\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* 二乗階 */\nfunction quadratic(n) {\n    let count = 0;\n    // ループ回数はデータサイズ n の二乗に比例する\n    for (let i = 0; i &lt; n; i++) {\n        for (let j = 0; j &lt; n; j++) {\n            count++;\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* 二乗階 */\nfunction quadratic(n: number): number {\n    let count = 0;\n    // ループ回数はデータサイズ n の二乗に比例する\n    for (let i = 0; i &lt; n; i++) {\n        for (let j = 0; j &lt; n; j++) {\n            count++;\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* 二乗階 */\nint quadratic(int n) {\n  int count = 0;\n  // ループ回数はデータサイズ n の二乗に比例する\n  for (int i = 0; i &lt; n; i++) {\n    for (int j = 0; j &lt; n; j++) {\n      count++;\n    }\n  }\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* 二乗階 */\nfn quadratic(n: i32) -&gt; i32 {\n    let mut count = 0;\n    // ループ回数はデータサイズ n の二乗に比例する\n    for _ in 0..n {\n        for _ in 0..n {\n            count += 1;\n        }\n    }\n    count\n}\n</code></pre> time_complexity.c<pre><code>/* 二乗階 */\nint quadratic(int n) {\n    int count = 0;\n    // ループ回数はデータサイズ n の二乗に比例する\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; n; j++) {\n            count++;\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* 二乗階 */\nfun quadratic(n: Int): Int {\n    var count = 0\n    // ループ回数はデータサイズ n の二乗に比例する\n    for (i in 0..&lt;n) {\n        for (j in 0..&lt;n) {\n            count++\n        }\n    }\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### 平方階 ###\ndef quadratic(n)\n  count = 0\n\n  # ループ回数はデータサイズ n の二乗に比例する\n  for i in 0...n\n    for j in 0...n\n      count += 1\n    end\n  end\n\n  count\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>以下の図は、定数階・線形階・平方階の 3 種類の時間計算量を比較したものです。</p> <p></p> <p> 図 2-10   定数階、線形階、平方階の時間計算量 </p> <p>バブルソートを例にとると、外側のループは \\(n - 1\\) 回実行され、内側のループは \\(n-1\\)、\\(n-2\\)、\\(\\dots\\)、\\(2\\)、\\(1\\) 回実行され、平均すると \\(n / 2\\) 回です。したがって時間計算量は \\(O((n - 1) n / 2) = O(n^2)\\) となります：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def bubble_sort(nums: list[int]) -&gt; int:\n    \"\"\"二次時間（バブルソート）\"\"\"\n    count = 0  # カウンタ\n    # 外側のループ：未ソート区間は [0, i]\n    for i in range(len(nums) - 1, 0, -1):\n        # 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for j in range(i):\n            if nums[j] &gt; nums[j + 1]:\n                # nums[j] と nums[j + 1] を交換\n                tmp: int = nums[j]\n                nums[j] = nums[j + 1]\n                nums[j + 1] = tmp\n                count += 3  # 要素交換には 3 回の単位操作が含まれる\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* 二次時間（バブルソート） */\nint bubbleSort(vector&lt;int&gt; &amp;nums) {\n    int count = 0; // カウンタ\n    // 外側のループ：未ソート区間は [0, i]\n    for (int i = nums.size() - 1; i &gt; 0; i--) {\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] と nums[j + 1] を交換\n                int tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                count += 3; // 要素交換には 3 回の単位操作が含まれる\n            }\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* 二次時間（バブルソート） */\nint bubbleSort(int[] nums) {\n    int count = 0; // カウンタ\n    // 外側のループ：未ソート区間は [0, i]\n    for (int i = nums.length - 1; i &gt; 0; i--) {\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] と nums[j + 1] を交換\n                int tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                count += 3; // 要素交換には 3 回の単位操作が含まれる\n            }\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* 二次時間（バブルソート） */\nint BubbleSort(int[] nums) {\n    int count = 0;  // カウンタ\n    // 外側のループ：未ソート区間は [0, i]\n    for (int i = nums.Length - 1; i &gt; 0; i--) {\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] と nums[j + 1] を交換\n                (nums[j + 1], nums[j]) = (nums[j], nums[j + 1]);\n                count += 3;  // 要素交換には 3 回の単位操作が含まれる\n            }\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* 二次時間（バブルソート） */\nfunc bubbleSort(nums []int) int {\n    count := 0 // カウンタ\n    // 外側のループ：未ソート区間は [0, i]\n    for i := len(nums) - 1; i &gt; 0; i-- {\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for j := 0; j &lt; i; j++ {\n            if nums[j] &gt; nums[j+1] {\n                // nums[j] と nums[j + 1] を交換\n                tmp := nums[j]\n                nums[j] = nums[j+1]\n                nums[j+1] = tmp\n                count += 3 // 要素交換には 3 回の単位操作が含まれる\n            }\n        }\n    }\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* 二次時間（バブルソート） */\nfunc bubbleSort(nums: inout [Int]) -&gt; Int {\n    var count = 0 // カウンタ\n    // 外側のループ：未ソート区間は [0, i]\n    for i in nums.indices.dropFirst().reversed() {\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for j in 0 ..&lt; i {\n            if nums[j] &gt; nums[j + 1] {\n                // nums[j] と nums[j + 1] を交換\n                let tmp = nums[j]\n                nums[j] = nums[j + 1]\n                nums[j + 1] = tmp\n                count += 3 // 要素交換には 3 回の単位操作が含まれる\n            }\n        }\n    }\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* 二次時間（バブルソート） */\nfunction bubbleSort(nums) {\n    let count = 0; // カウンタ\n    // 外側のループ：未ソート区間は [0, i]\n    for (let i = nums.length - 1; i &gt; 0; i--) {\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for (let j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] と nums[j + 1] を交換\n                let tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                count += 3; // 要素交換には 3 回の単位操作が含まれる\n            }\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* 二次時間（バブルソート） */\nfunction bubbleSort(nums: number[]): number {\n    let count = 0; // カウンタ\n    // 外側のループ：未ソート区間は [0, i]\n    for (let i = nums.length - 1; i &gt; 0; i--) {\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for (let j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] と nums[j + 1] を交換\n                let tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                count += 3; // 要素交換には 3 回の単位操作が含まれる\n            }\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* 二次時間（バブルソート） */\nint bubbleSort(List&lt;int&gt; nums) {\n  int count = 0; // カウンタ\n  // 外側のループ：未ソート区間は [0, i]\n  for (var i = nums.length - 1; i &gt; 0; i--) {\n    // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n    for (var j = 0; j &lt; i; j++) {\n      if (nums[j] &gt; nums[j + 1]) {\n        // nums[j] と nums[j + 1] を交換\n        int tmp = nums[j];\n        nums[j] = nums[j + 1];\n        nums[j + 1] = tmp;\n        count += 3; // 要素交換には 3 回の単位操作が含まれる\n      }\n    }\n  }\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* 二次時間（バブルソート） */\nfn bubble_sort(nums: &amp;mut [i32]) -&gt; i32 {\n    let mut count = 0; // カウンタ\n\n    // 外側のループ：未ソート区間は [0, i]\n    for i in (1..nums.len()).rev() {\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for j in 0..i {\n            if nums[j] &gt; nums[j + 1] {\n                // nums[j] と nums[j + 1] を交換\n                let tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                count += 3; // 要素交換には 3 回の単位操作が含まれる\n            }\n        }\n    }\n    count\n}\n</code></pre> time_complexity.c<pre><code>/* 二次時間（バブルソート） */\nint bubbleSort(int *nums, int n) {\n    int count = 0; // カウンタ\n    // 外側のループ：未ソート区間は [0, i]\n    for (int i = n - 1; i &gt; 0; i--) {\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] と nums[j + 1] を交換\n                int tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                count += 3; // 要素交換には 3 回の単位操作が含まれる\n            }\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* 二次時間（バブルソート） */\nfun bubbleSort(nums: IntArray): Int {\n    var count = 0 // カウンタ\n    // 外側のループ：未ソート区間は [0, i]\n    for (i in nums.size - 1 downTo 1) {\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for (j in 0..&lt;i) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] と nums[j + 1] を交換\n                val temp = nums[j]\n                nums[j] = nums[j + 1]\n                nums[j + 1] = temp\n                count += 3 // 要素交換には 3 回の単位操作が含まれる\n            }\n        }\n    }\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### 平方階 ###\ndef quadratic(n)\n  count = 0\n\n  # ループ回数はデータサイズ n の二乗に比例する\n  for i in 0...n\n    for j in 0...n\n      count += 1\n    end\n  end\n\n  count\nend\n\n# ## 平方階（バブルソート）###\ndef bubble_sort(nums)\n  count = 0  # カウンタ\n\n  # 外側のループ：未ソート区間は [0, i]\n  for i in (nums.length - 1).downto(0)\n    # 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n    for j in 0...i\n      if nums[j] &gt; nums[j + 1]\n        # nums[j] と nums[j + 1] を交換\n        tmp = nums[j]\n        nums[j] = nums[j + 1]\n        nums[j + 1] = tmp\n        count += 3 # 要素交換には 3 回の単位操作が含まれる\n      end\n    end\n  end\n\n  count\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#4-o2n","level":3,"title":"4.   指数階 \\(O(2^n)\\)","text":"<p>生物学における「細胞分裂」は指数階増加の典型例です。初期状態では細胞が \\(1\\) 個あり、1 回分裂すると \\(2\\) 個、2 回分裂すると \\(4\\) 個となり、以下同様に、\\(n\\) 回分裂すると \\(2^n\\) 個の細胞になります。</p> <p>以下の図とコードは細胞分裂の過程を模擬したもので、時間計算量は \\(O(2^n)\\) です。なお、入力の \\(n\\) は分裂回数を表し、戻り値 <code>count</code> は総分裂回数を表します。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def exponential(n: int) -&gt; int:\n    \"\"\"指数時間（ループ実装）\"\"\"\n    count = 0\n    base = 1\n    # 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する\n    for _ in range(n):\n        for _ in range(base):\n            count += 1\n        base *= 2\n    # count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* 指数時間（ループ実装） */\nint exponential(int n) {\n    int count = 0, base = 1;\n    // 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; base; j++) {\n            count++;\n        }\n        base *= 2;\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* 指数時間（ループ実装） */\nint exponential(int n) {\n    int count = 0, base = 1;\n    // 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; base; j++) {\n            count++;\n        }\n        base *= 2;\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* 指数時間（ループ実装） */\nint Exponential(int n) {\n    int count = 0, bas = 1;\n    // 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; bas; j++) {\n            count++;\n        }\n        bas *= 2;\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* 指数時間（ループ実装） */\nfunc exponential(n int) int {\n    count, base := 0, 1\n    // 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する\n    for i := 0; i &lt; n; i++ {\n        for j := 0; j &lt; base; j++ {\n            count++\n        }\n        base *= 2\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* 指数時間（ループ実装） */\nfunc exponential(n: Int) -&gt; Int {\n    var count = 0\n    var base = 1\n    // 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する\n    for _ in 0 ..&lt; n {\n        for _ in 0 ..&lt; base {\n            count += 1\n        }\n        base *= 2\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* 指数時間（ループ実装） */\nfunction exponential(n) {\n    let count = 0,\n        base = 1;\n    // 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する\n    for (let i = 0; i &lt; n; i++) {\n        for (let j = 0; j &lt; base; j++) {\n            count++;\n        }\n        base *= 2;\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* 指数時間（ループ実装） */\nfunction exponential(n: number): number {\n    let count = 0,\n        base = 1;\n    // 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する\n    for (let i = 0; i &lt; n; i++) {\n        for (let j = 0; j &lt; base; j++) {\n            count++;\n        }\n        base *= 2;\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* 指数時間（ループ実装） */\nint exponential(int n) {\n  int count = 0, base = 1;\n  // 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する\n  for (var i = 0; i &lt; n; i++) {\n    for (var j = 0; j &lt; base; j++) {\n      count++;\n    }\n    base *= 2;\n  }\n  // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* 指数時間（ループ実装） */\nfn exponential(n: i32) -&gt; i32 {\n    let mut count = 0;\n    let mut base = 1;\n    // 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する\n    for _ in 0..n {\n        for _ in 0..base {\n            count += 1\n        }\n        base *= 2;\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    count\n}\n</code></pre> time_complexity.c<pre><code>/* 指数時間（ループ実装） */\nint exponential(int n) {\n    int count = 0;\n    int bas = 1;\n    // 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; bas; j++) {\n            count++;\n        }\n        bas *= 2;\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* 指数時間（ループ実装） */\nfun exponential(n: Int): Int {\n    var count = 0\n    var base = 1\n    // 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する\n    for (i in 0..&lt;n) {\n        for (j in 0..&lt;base) {\n            count++\n        }\n        base *= 2\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### 平方階 ###\ndef quadratic(n)\n  count = 0\n\n  # ループ回数はデータサイズ n の二乗に比例する\n  for i in 0...n\n    for j in 0...n\n      count += 1\n    end\n  end\n\n  count\nend\n\n# ## 平方階（バブルソート）###\ndef bubble_sort(nums)\n  count = 0  # カウンタ\n\n  # 外側のループ：未ソート区間は [0, i]\n  for i in (nums.length - 1).downto(0)\n    # 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n    for j in 0...i\n      if nums[j] &gt; nums[j + 1]\n        # nums[j] と nums[j + 1] を交換\n        tmp = nums[j]\n        nums[j] = nums[j + 1]\n        nums[j + 1] = tmp\n        count += 3 # 要素交換には 3 回の単位操作が含まれる\n      end\n    end\n  end\n\n  count\nend\n\n# ## 指数階（ループ実装）###\ndef exponential(n)\n  count, base = 0, 1\n\n  # 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する\n  (0...n).each do\n    (0...base).each { count += 1 }\n    base *= 2\n  end\n\n  # count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n  count\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p></p> <p> 図 2-11   指数階の時間計算量 </p> <p>実際のアルゴリズムでも、指数階は再帰関数によく現れます。例えば次のコードでは、再帰的に 2 つへ分岐し、\\(n\\) 回分裂した後に停止します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def exp_recur(n: int) -&gt; int:\n    \"\"\"指数時間（再帰実装）\"\"\"\n    if n == 1:\n        return 1\n    return exp_recur(n - 1) + exp_recur(n - 1) + 1\n</code></pre> time_complexity.cpp<pre><code>/* 指数時間（再帰実装） */\nint expRecur(int n) {\n    if (n == 1)\n        return 1;\n    return expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.java<pre><code>/* 指数時間（再帰実装） */\nint expRecur(int n) {\n    if (n == 1)\n        return 1;\n    return expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.cs<pre><code>/* 指数時間（再帰実装） */\nint ExpRecur(int n) {\n    if (n == 1) return 1;\n    return ExpRecur(n - 1) + ExpRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.go<pre><code>/* 指数時間（再帰実装） */\nfunc expRecur(n int) int {\n    if n == 1 {\n        return 1\n    }\n    return expRecur(n-1) + expRecur(n-1) + 1\n}\n</code></pre> time_complexity.swift<pre><code>/* 指数時間（再帰実装） */\nfunc expRecur(n: Int) -&gt; Int {\n    if n == 1 {\n        return 1\n    }\n    return expRecur(n: n - 1) + expRecur(n: n - 1) + 1\n}\n</code></pre> time_complexity.js<pre><code>/* 指数時間（再帰実装） */\nfunction expRecur(n) {\n    if (n === 1) return 1;\n    return expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.ts<pre><code>/* 指数時間（再帰実装） */\nfunction expRecur(n: number): number {\n    if (n === 1) return 1;\n    return expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.dart<pre><code>/* 指数時間（再帰実装） */\nint expRecur(int n) {\n  if (n == 1) return 1;\n  return expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.rs<pre><code>/* 指数時間（再帰実装） */\nfn exp_recur(n: i32) -&gt; i32 {\n    if n == 1 {\n        return 1;\n    }\n    exp_recur(n - 1) + exp_recur(n - 1) + 1\n}\n</code></pre> time_complexity.c<pre><code>/* 指数時間（再帰実装） */\nint expRecur(int n) {\n    if (n == 1)\n        return 1;\n    return expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.kt<pre><code>/* 指数時間（再帰実装） */\nfun expRecur(n: Int): Int {\n    if (n == 1) {\n        return 1\n    }\n    return expRecur(n - 1) + expRecur(n - 1) + 1\n}\n</code></pre> time_complexity.rb<pre><code>### 平方階 ###\ndef quadratic(n)\n  count = 0\n\n  # ループ回数はデータサイズ n の二乗に比例する\n  for i in 0...n\n    for j in 0...n\n      count += 1\n    end\n  end\n\n  count\nend\n\n# ## 平方階（バブルソート）###\ndef bubble_sort(nums)\n  count = 0  # カウンタ\n\n  # 外側のループ：未ソート区間は [0, i]\n  for i in (nums.length - 1).downto(0)\n    # 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n    for j in 0...i\n      if nums[j] &gt; nums[j + 1]\n        # nums[j] と nums[j + 1] を交換\n        tmp = nums[j]\n        nums[j] = nums[j + 1]\n        nums[j + 1] = tmp\n        count += 3 # 要素交換には 3 回の単位操作が含まれる\n      end\n    end\n  end\n\n  count\nend\n\n# ## 指数階（ループ実装）###\ndef exponential(n)\n  count, base = 0, 1\n\n  # 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する\n  (0...n).each do\n    (0...base).each { count += 1 }\n    base *= 2\n  end\n\n  # count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n  count\nend\n\n# ## 指数階（再帰実装）###\ndef exp_recur(n)\n  return 1 if n == 1\n  exp_recur(n - 1) + exp_recur(n - 1) + 1\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>指数階の増加は非常に速く、全探索法（ブルートフォース、バックトラッキングなど）によく見られます。データ規模が大きい問題では、指数階は受け入れられず、通常は動的計画法や貪欲法などを使って解く必要があります。</p>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#5-olog-n","level":3,"title":"5.   対数階 \\(O(\\log n)\\)","text":"<p>指数階とは逆に、対数階は「各ラウンドで半分になる」状況を表します。入力データサイズを \\(n\\) とすると、各ラウンドで半減するため、ループ回数は \\(\\log_2 n\\)、すなわち \\(2^n\\) の逆関数になります。</p> <p>以下の図とコードは、「各ラウンドで半分になる」過程を模擬したもので、時間計算量は \\(O(\\log_2 n)\\)、簡潔には \\(O(\\log n)\\) と書きます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def logarithmic(n: int) -&gt; int:\n    \"\"\"対数時間（ループ実装）\"\"\"\n    count = 0\n    while n &gt; 1:\n        n = n / 2\n        count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* 対数時間（ループ実装） */\nint logarithmic(int n) {\n    int count = 0;\n    while (n &gt; 1) {\n        n = n / 2;\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* 対数時間（ループ実装） */\nint logarithmic(int n) {\n    int count = 0;\n    while (n &gt; 1) {\n        n = n / 2;\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* 対数時間（ループ実装） */\nint Logarithmic(int n) {\n    int count = 0;\n    while (n &gt; 1) {\n        n /= 2;\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* 対数時間（ループ実装） */\nfunc logarithmic(n int) int {\n    count := 0\n    for n &gt; 1 {\n        n = n / 2\n        count++\n    }\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* 対数時間（ループ実装） */\nfunc logarithmic(n: Int) -&gt; Int {\n    var count = 0\n    var n = n\n    while n &gt; 1 {\n        n = n / 2\n        count += 1\n    }\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* 対数時間（ループ実装） */\nfunction logarithmic(n) {\n    let count = 0;\n    while (n &gt; 1) {\n        n = n / 2;\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* 対数時間（ループ実装） */\nfunction logarithmic(n: number): number {\n    let count = 0;\n    while (n &gt; 1) {\n        n = n / 2;\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* 対数時間（ループ実装） */\nint logarithmic(int n) {\n  int count = 0;\n  while (n &gt; 1) {\n    n = n ~/ 2;\n    count++;\n  }\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* 対数時間（ループ実装） */\nfn logarithmic(mut n: i32) -&gt; i32 {\n    let mut count = 0;\n    while n &gt; 1 {\n        n = n / 2;\n        count += 1;\n    }\n    count\n}\n</code></pre> time_complexity.c<pre><code>/* 対数時間（ループ実装） */\nint logarithmic(int n) {\n    int count = 0;\n    while (n &gt; 1) {\n        n = n / 2;\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* 対数時間（ループ実装） */\nfun logarithmic(n: Int): Int {\n    var n1 = n\n    var count = 0\n    while (n1 &gt; 1) {\n        n1 /= 2\n        count++\n    }\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### 平方階 ###\ndef quadratic(n)\n  count = 0\n\n  # ループ回数はデータサイズ n の二乗に比例する\n  for i in 0...n\n    for j in 0...n\n      count += 1\n    end\n  end\n\n  count\nend\n\n# ## 平方階（バブルソート）###\ndef bubble_sort(nums)\n  count = 0  # カウンタ\n\n  # 外側のループ：未ソート区間は [0, i]\n  for i in (nums.length - 1).downto(0)\n    # 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n    for j in 0...i\n      if nums[j] &gt; nums[j + 1]\n        # nums[j] と nums[j + 1] を交換\n        tmp = nums[j]\n        nums[j] = nums[j + 1]\n        nums[j + 1] = tmp\n        count += 3 # 要素交換には 3 回の単位操作が含まれる\n      end\n    end\n  end\n\n  count\nend\n\n# ## 指数階（ループ実装）###\ndef exponential(n)\n  count, base = 0, 1\n\n  # 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する\n  (0...n).each do\n    (0...base).each { count += 1 }\n    base *= 2\n  end\n\n  # count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n  count\nend\n\n# ## 指数階（再帰実装）###\ndef exp_recur(n)\n  return 1 if n == 1\n  exp_recur(n - 1) + exp_recur(n - 1) + 1\nend\n\n# ## 対数階（ループ実装）###\ndef logarithmic(n)\n  count = 0\n\n  while n &gt; 1\n    n /= 2\n    count += 1\n  end\n\n  count\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p></p> <p> 図 2-12   対数階の時間計算量 </p> <p>指数階と同様に、対数階も再帰関数によく現れます。次のコードは高さ \\(\\log_2 n\\) の再帰木を形成します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def log_recur(n: int) -&gt; int:\n    \"\"\"対数時間（再帰実装）\"\"\"\n    if n &lt;= 1:\n        return 0\n    return log_recur(n / 2) + 1\n</code></pre> time_complexity.cpp<pre><code>/* 対数時間（再帰実装） */\nint logRecur(int n) {\n    if (n &lt;= 1)\n        return 0;\n    return logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.java<pre><code>/* 対数時間（再帰実装） */\nint logRecur(int n) {\n    if (n &lt;= 1)\n        return 0;\n    return logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.cs<pre><code>/* 対数時間（再帰実装） */\nint LogRecur(int n) {\n    if (n &lt;= 1) return 0;\n    return LogRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.go<pre><code>/* 対数時間（再帰実装） */\nfunc logRecur(n int) int {\n    if n &lt;= 1 {\n        return 0\n    }\n    return logRecur(n/2) + 1\n}\n</code></pre> time_complexity.swift<pre><code>/* 対数時間（再帰実装） */\nfunc logRecur(n: Int) -&gt; Int {\n    if n &lt;= 1 {\n        return 0\n    }\n    return logRecur(n: n / 2) + 1\n}\n</code></pre> time_complexity.js<pre><code>/* 対数時間（再帰実装） */\nfunction logRecur(n) {\n    if (n &lt;= 1) return 0;\n    return logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.ts<pre><code>/* 対数時間（再帰実装） */\nfunction logRecur(n: number): number {\n    if (n &lt;= 1) return 0;\n    return logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.dart<pre><code>/* 対数時間（再帰実装） */\nint logRecur(int n) {\n  if (n &lt;= 1) return 0;\n  return logRecur(n ~/ 2) + 1;\n}\n</code></pre> time_complexity.rs<pre><code>/* 対数時間（再帰実装） */\nfn log_recur(n: i32) -&gt; i32 {\n    if n &lt;= 1 {\n        return 0;\n    }\n    log_recur(n / 2) + 1\n}\n</code></pre> time_complexity.c<pre><code>/* 対数時間（再帰実装） */\nint logRecur(int n) {\n    if (n &lt;= 1)\n        return 0;\n    return logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.kt<pre><code>/* 対数時間（再帰実装） */\nfun logRecur(n: Int): Int {\n    if (n &lt;= 1)\n        return 0\n    return logRecur(n / 2) + 1\n}\n</code></pre> time_complexity.rb<pre><code>### 平方階 ###\ndef quadratic(n)\n  count = 0\n\n  # ループ回数はデータサイズ n の二乗に比例する\n  for i in 0...n\n    for j in 0...n\n      count += 1\n    end\n  end\n\n  count\nend\n\n# ## 平方階（バブルソート）###\ndef bubble_sort(nums)\n  count = 0  # カウンタ\n\n  # 外側のループ：未ソート区間は [0, i]\n  for i in (nums.length - 1).downto(0)\n    # 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n    for j in 0...i\n      if nums[j] &gt; nums[j + 1]\n        # nums[j] と nums[j + 1] を交換\n        tmp = nums[j]\n        nums[j] = nums[j + 1]\n        nums[j + 1] = tmp\n        count += 3 # 要素交換には 3 回の単位操作が含まれる\n      end\n    end\n  end\n\n  count\nend\n\n# ## 指数階（ループ実装）###\ndef exponential(n)\n  count, base = 0, 1\n\n  # 細胞は各ラウンドで 2 つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成する\n  (0...n).each do\n    (0...base).each { count += 1 }\n    base *= 2\n  end\n\n  # count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n  count\nend\n\n# ## 指数階（再帰実装）###\ndef exp_recur(n)\n  return 1 if n == 1\n  exp_recur(n - 1) + exp_recur(n - 1) + 1\nend\n\n# ## 対数階（ループ実装）###\ndef logarithmic(n)\n  count = 0\n\n  while n &gt; 1\n    n /= 2\n    count += 1\n  end\n\n  count\nend\n\n# ## 対数階（再帰実装）###\ndef log_recur(n)\n  return 0 unless n &gt; 1\n  log_recur(n / 2) + 1\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>対数階は分割統治に基づくアルゴリズムによく現れ、「1 つを複数に分ける」「複雑なものを単純化する」という考え方を体現しています。増加は緩やかで、定数階に次いで理想的な時間計算量です。</p> <p>\\(O(\\log n)\\) の底は何か？</p> <p>正確には、「\\(m\\) 個に分ける」場合に対応する時間計算量は \\(O(\\log_m n)\\) です。そして対数の底の変換公式により、底が異なっても同値な時間計算量が得られます：</p> \\[ O(\\log_m n) = O(\\log_k n / \\log_k m) = O(\\log_k n) \\] <p>つまり、底 \\(m\\) は複雑度に影響を与えずに変換できます。そのため通常は底 \\(m\\) を省略し、対数階を単に \\(O(\\log n)\\) と記します。</p>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#6-on-log-n","level":3,"title":"6.   線形対数階 \\(O(n \\log n)\\)","text":"<p>線形対数階は入れ子ループによく現れ、2 層のループの時間計算量はそれぞれ \\(O(\\log n)\\) と \\(O(n)\\) です。関連するコードは次のとおりです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def linear_log_recur(n: int) -&gt; int:\n    \"\"\"線形対数時間\"\"\"\n    if n &lt;= 1:\n        return 1\n    # 二つに分割すると、部分問題の規模は半分になる\n    count = linear_log_recur(n // 2) + linear_log_recur(n // 2)\n    # 現在の部分問題には n 個の操作が含まれる\n    for _ in range(n):\n        count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* 線形対数時間 */\nint linearLogRecur(int n) {\n    if (n &lt;= 1)\n        return 1;\n    int count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\n    for (int i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* 線形対数時間 */\nint linearLogRecur(int n) {\n    if (n &lt;= 1)\n        return 1;\n    int count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\n    for (int i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* 線形対数時間 */\nint LinearLogRecur(int n) {\n    if (n &lt;= 1) return 1;\n    int count = LinearLogRecur(n / 2) + LinearLogRecur(n / 2);\n    for (int i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* 線形対数時間 */\nfunc linearLogRecur(n int) int {\n    if n &lt;= 1 {\n        return 1\n    }\n    count := linearLogRecur(n/2) + linearLogRecur(n/2)\n    for i := 0; i &lt; n; i++ {\n        count++\n    }\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* 線形対数時間 */\nfunc linearLogRecur(n: Int) -&gt; Int {\n    if n &lt;= 1 {\n        return 1\n    }\n    var count = linearLogRecur(n: n / 2) + linearLogRecur(n: n / 2)\n    for _ in stride(from: 0, to: n, by: 1) {\n        count += 1\n    }\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* 線形対数時間 */\nfunction linearLogRecur(n) {\n    if (n &lt;= 1) return 1;\n    let count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\n    for (let i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* 線形対数時間 */\nfunction linearLogRecur(n: number): number {\n    if (n &lt;= 1) return 1;\n    let count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\n    for (let i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* 線形対数時間 */\nint linearLogRecur(int n) {\n  if (n &lt;= 1) return 1;\n  int count = linearLogRecur(n ~/ 2) + linearLogRecur(n ~/ 2);\n  for (var i = 0; i &lt; n; i++) {\n    count++;\n  }\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* 線形対数時間 */\nfn linear_log_recur(n: i32) -&gt; i32 {\n    if n &lt;= 1 {\n        return 1;\n    }\n    let mut count = linear_log_recur(n / 2) + linear_log_recur(n / 2);\n    for _ in 0..n {\n        count += 1;\n    }\n    return count;\n}\n</code></pre> time_complexity.c<pre><code>/* 線形対数時間 */\nint linearLogRecur(int n) {\n    if (n &lt;= 1)\n        return 1;\n    int count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\n    for (int i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* 線形対数時間 */\nfun linearLogRecur(n: Int): Int {\n    if (n &lt;= 1)\n        return 1\n    var count = linearLogRecur(n / 2) + linearLogRecur(n / 2)\n    for (i in 0..&lt;n) {\n        count++\n    }\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### 線形対数時間 ###\ndef linear_log_recur(n)\n  return 1 unless n &gt; 1\n\n  count = linear_log_recur(n / 2) + linear_log_recur(n / 2)\n  (0...n).each { count += 1 }\n\n  count\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>下図は線形対数階がどのように生じるかを示しています。二分木の各層の操作総数はすべて \\(n\\) であり、木全体は \\(\\log_2 n + 1\\) 層あるため、時間計算量は \\(O(n \\log n)\\) です。</p> <p></p> <p> 図 2-13   線形対数階の時間計算量 </p> <p>主なソートアルゴリズムの時間計算量は通常 \\(O(n \\log n)\\) であり、例えばクイックソート、マージソート、ヒープソートなどがあります。</p>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#7-on","level":3,"title":"7.   階乗階 \\(O(n!)\\)","text":"<p>階乗階は、数学における「全順列」の問題に対応します。互いに重複しない \\(n\\) 個の要素が与えられたとき、そのすべての並べ方を求めると、通り数は次のようになります：</p> \\[ n! = n \\times (n - 1) \\times (n - 2) \\times \\dots \\times 2 \\times 1 \\] <p>階乗は通常、再帰で実装されます。以下の図とコードのように、第 1 層では \\(n\\) 個に分岐し、第 2 層では \\(n - 1\\) 個に分岐し、以下同様に、第 \\(n\\) 層で分岐が停止します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def factorial_recur(n: int) -&gt; int:\n    \"\"\"階乗時間（再帰実装）\"\"\"\n    if n == 0:\n        return 1\n    count = 0\n    # 1個から n 個に分裂\n    for _ in range(n):\n        count += factorial_recur(n - 1)\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* 階乗時間（再帰実装） */\nint factorialRecur(int n) {\n    if (n == 0)\n        return 1;\n    int count = 0;\n    // 1個から n 個に分裂\n    for (int i = 0; i &lt; n; i++) {\n        count += factorialRecur(n - 1);\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* 階乗時間（再帰実装） */\nint factorialRecur(int n) {\n    if (n == 0)\n        return 1;\n    int count = 0;\n    // 1個から n 個に分裂\n    for (int i = 0; i &lt; n; i++) {\n        count += factorialRecur(n - 1);\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* 階乗時間（再帰実装） */\nint FactorialRecur(int n) {\n    if (n == 0) return 1;\n    int count = 0;\n    // 1個から n 個に分裂\n    for (int i = 0; i &lt; n; i++) {\n        count += FactorialRecur(n - 1);\n    }\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* 階乗時間（再帰実装） */\nfunc factorialRecur(n int) int {\n    if n == 0 {\n        return 1\n    }\n    count := 0\n    // 1個から n 個に分裂\n    for i := 0; i &lt; n; i++ {\n        count += factorialRecur(n - 1)\n    }\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* 階乗時間（再帰実装） */\nfunc factorialRecur(n: Int) -&gt; Int {\n    if n == 0 {\n        return 1\n    }\n    var count = 0\n    // 1個から n 個に分裂\n    for _ in 0 ..&lt; n {\n        count += factorialRecur(n: n - 1)\n    }\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* 階乗時間（再帰実装） */\nfunction factorialRecur(n) {\n    if (n === 0) return 1;\n    let count = 0;\n    // 1個から n 個に分裂\n    for (let i = 0; i &lt; n; i++) {\n        count += factorialRecur(n - 1);\n    }\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* 階乗時間（再帰実装） */\nfunction factorialRecur(n: number): number {\n    if (n === 0) return 1;\n    let count = 0;\n    // 1個から n 個に分裂\n    for (let i = 0; i &lt; n; i++) {\n        count += factorialRecur(n - 1);\n    }\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* 階乗時間（再帰実装） */\nint factorialRecur(int n) {\n  if (n == 0) return 1;\n  int count = 0;\n  // 1個から n 個に分裂\n  for (var i = 0; i &lt; n; i++) {\n    count += factorialRecur(n - 1);\n  }\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* 階乗時間（再帰実装） */\nfn factorial_recur(n: i32) -&gt; i32 {\n    if n == 0 {\n        return 1;\n    }\n    let mut count = 0;\n    // 1個から n 個に分裂\n    for _ in 0..n {\n        count += factorial_recur(n - 1);\n    }\n    count\n}\n</code></pre> time_complexity.c<pre><code>/* 階乗時間（再帰実装） */\nint factorialRecur(int n) {\n    if (n == 0)\n        return 1;\n    int count = 0;\n    for (int i = 0; i &lt; n; i++) {\n        count += factorialRecur(n - 1);\n    }\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* 階乗時間（再帰実装） */\nfun factorialRecur(n: Int): Int {\n    if (n == 0)\n        return 1\n    var count = 0\n    // 1個から n 個に分裂\n    for (i in 0..&lt;n) {\n        count += factorialRecur(n - 1)\n    }\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### 線形対数時間 ###\ndef linear_log_recur(n)\n  return 1 unless n &gt; 1\n\n  count = linear_log_recur(n / 2) + linear_log_recur(n / 2)\n  (0...n).each { count += 1 }\n\n  count\nend\n\n# ## 階乗階（再帰実装）###\ndef factorial_recur(n)\n  return 1 if n == 0\n\n  count = 0\n  # 1個から n 個に分裂\n  (0...n).each { count += factorial_recur(n - 1) }\n\n  count\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p></p> <p> 図 2-14   階乗階の時間計算量 </p> <p>注意すべき点として、\\(n \\geq 4\\) なら常に \\(n! &gt; 2^n\\) なので、階乗階は指数階よりもさらに速く増加し、\\(n\\) が大きい場合にはやはり受け入れられません。</p>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#235","level":2,"title":"2.3.5   最悪・最良・平均時間計算量","text":"<p>アルゴリズムの時間効率は固定ではなく、入力データの分布に左右されることが多いです。長さ \\(n\\) の配列 <code>nums</code> を考えます。<code>nums</code> は \\(1\\) から \\(n\\) までの数字で構成され、各数字は 1 回だけ現れます。ただし要素の順序はランダムにシャッフルされており、目標は要素 \\(1\\) のインデックスを返すことです。ここから次の結論が得られます。</p> <ul> <li><code>nums = [?, ?, ..., 1]</code>、つまり末尾の要素が \\(1\\) の場合は、配列全体を最後まで走査する必要があり、最悪時間計算量 \\(O(n)\\) になります。</li> <li><code>nums = [1, ?, ?, ...]</code>、つまり先頭要素が \\(1\\) の場合は、配列がどれだけ長くてもそれ以上走査する必要がなく、最良時間計算量 \\(\\Omega(1)\\) になります。</li> </ul> <p>「最悪時間計算量」は関数の漸近上界に対応し、ビッグ \\(O\\) 記法で表します。同様に、「最良時間計算量」は関数の漸近下界に対応し、\\(\\Omega\\) 記法で表します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby worst_best_time_complexity.py<pre><code>def random_numbers(n: int) -&gt; list[int]:\n    \"\"\"要素が 1, 2, ..., n で順序がシャッフルされた配列を生成する\"\"\"\n    # 配列 nums =: 1, 2, 3, ..., n を生成する\n    nums = [i for i in range(1, n + 1)]\n    # 配列要素をランダムにシャッフル\n    random.shuffle(nums)\n    return nums\n\ndef find_one(nums: list[int]) -&gt; int:\n    \"\"\"配列 nums 内で数値 1 のインデックスを探す\"\"\"\n    for i in range(len(nums)):\n        # 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる\n        # 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる\n        if nums[i] == 1:\n            return i\n    return -1\n</code></pre> worst_best_time_complexity.cpp<pre><code>/* 要素が { 1, 2, ..., n } で、順序がシャッフルされた配列を生成 */\nvector&lt;int&gt; randomNumbers(int n) {\n    vector&lt;int&gt; nums(n);\n    // 配列 nums = { 1, 2, 3, ..., n } を生成\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = i + 1;\n    }\n    // システム時刻を使って乱数シードを生成する\n    unsigned seed = chrono::system_clock::now().time_since_epoch().count();\n    // 配列要素をランダムにシャッフル\n    shuffle(nums.begin(), nums.end(), default_random_engine(seed));\n    return nums;\n}\n\n/* 配列 nums 内で数値 1 のインデックスを探す */\nint findOne(vector&lt;int&gt; &amp;nums) {\n    for (int i = 0; i &lt; nums.size(); i++) {\n        // 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる\n        // 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる\n        if (nums[i] == 1)\n            return i;\n    }\n    return -1;\n}\n</code></pre> worst_best_time_complexity.java<pre><code>/* 要素が { 1, 2, ..., n } で、順序がシャッフルされた配列を生成 */\nint[] randomNumbers(int n) {\n    Integer[] nums = new Integer[n];\n    // 配列 nums = { 1, 2, 3, ..., n } を生成\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = i + 1;\n    }\n    // 配列要素をランダムにシャッフル\n    Collections.shuffle(Arrays.asList(nums));\n    // Integer[] -&gt; int[]\n    int[] res = new int[n];\n    for (int i = 0; i &lt; n; i++) {\n        res[i] = nums[i];\n    }\n    return res;\n}\n\n/* 配列 nums 内で数値 1 のインデックスを探す */\nint findOne(int[] nums) {\n    for (int i = 0; i &lt; nums.length; i++) {\n        // 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる\n        // 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる\n        if (nums[i] == 1)\n            return i;\n    }\n    return -1;\n}\n</code></pre> worst_best_time_complexity.cs<pre><code>/* 要素が { 1, 2, ..., n } で、順序がシャッフルされた配列を生成 */\nint[] RandomNumbers(int n) {\n    int[] nums = new int[n];\n    // 配列 nums = { 1, 2, 3, ..., n } を生成\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = i + 1;\n    }\n\n    // 配列要素をランダムにシャッフル\n    for (int i = 0; i &lt; nums.Length; i++) {\n        int index = new Random().Next(i, nums.Length);\n        (nums[i], nums[index]) = (nums[index], nums[i]);\n    }\n    return nums;\n}\n\n/* 配列 nums 内で数値 1 のインデックスを探す */\nint FindOne(int[] nums) {\n    for (int i = 0; i &lt; nums.Length; i++) {\n        // 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる\n        // 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる\n        if (nums[i] == 1)\n            return i;\n    }\n    return -1;\n}\n</code></pre> worst_best_time_complexity.go<pre><code>/* 要素が { 1, 2, ..., n } で、順序がシャッフルされた配列を生成 */\nfunc randomNumbers(n int) []int {\n    nums := make([]int, n)\n    // 配列 nums = { 1, 2, 3, ..., n } を生成\n    for i := 0; i &lt; n; i++ {\n        nums[i] = i + 1\n    }\n    // 配列要素をランダムにシャッフル\n    rand.Shuffle(len(nums), func(i, j int) {\n        nums[i], nums[j] = nums[j], nums[i]\n    })\n    return nums\n}\n\n/* 配列 nums 内で数値 1 のインデックスを探す */\nfunc findOne(nums []int) int {\n    for i := 0; i &lt; len(nums); i++ {\n        // 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる\n        // 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる\n        if nums[i] == 1 {\n            return i\n        }\n    }\n    return -1\n}\n</code></pre> worst_best_time_complexity.swift<pre><code>/* 要素が { 1, 2, ..., n } で、順序がシャッフルされた配列を生成 */\nfunc randomNumbers(n: Int) -&gt; [Int] {\n    // 配列 nums = { 1, 2, 3, ..., n } を生成\n    var nums = Array(1 ... n)\n    // 配列要素をランダムにシャッフル\n    nums.shuffle()\n    return nums\n}\n\n/* 配列 nums 内で数値 1 のインデックスを探す */\nfunc findOne(nums: [Int]) -&gt; Int {\n    for i in nums.indices {\n        // 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる\n        // 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる\n        if nums[i] == 1 {\n            return i\n        }\n    }\n    return -1\n}\n</code></pre> worst_best_time_complexity.js<pre><code>/* 要素が { 1, 2, ..., n } で、順序がシャッフルされた配列を生成 */\nfunction randomNumbers(n) {\n    const nums = Array(n);\n    // 配列 nums = { 1, 2, 3, ..., n } を生成\n    for (let i = 0; i &lt; n; i++) {\n        nums[i] = i + 1;\n    }\n    // 配列要素をランダムにシャッフル\n    for (let i = 0; i &lt; n; i++) {\n        const r = Math.floor(Math.random() * (i + 1));\n        const temp = nums[i];\n        nums[i] = nums[r];\n        nums[r] = temp;\n    }\n    return nums;\n}\n\n/* 配列 nums 内で数値 1 のインデックスを探す */\nfunction findOne(nums) {\n    for (let i = 0; i &lt; nums.length; i++) {\n        // 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる\n        // 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる\n        if (nums[i] === 1) {\n            return i;\n        }\n    }\n    return -1;\n}\n</code></pre> worst_best_time_complexity.ts<pre><code>/* 要素が { 1, 2, ..., n } で、順序がシャッフルされた配列を生成 */\nfunction randomNumbers(n: number): number[] {\n    const nums = Array(n);\n    // 配列 nums = { 1, 2, 3, ..., n } を生成\n    for (let i = 0; i &lt; n; i++) {\n        nums[i] = i + 1;\n    }\n    // 配列要素をランダムにシャッフル\n    for (let i = 0; i &lt; n; i++) {\n        const r = Math.floor(Math.random() * (i + 1));\n        const temp = nums[i];\n        nums[i] = nums[r];\n        nums[r] = temp;\n    }\n    return nums;\n}\n\n/* 配列 nums 内で数値 1 のインデックスを探す */\nfunction findOne(nums: number[]): number {\n    for (let i = 0; i &lt; nums.length; i++) {\n        // 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる\n        // 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる\n        if (nums[i] === 1) {\n            return i;\n        }\n    }\n    return -1;\n}\n</code></pre> worst_best_time_complexity.dart<pre><code>/* 要素が { 1, 2, ..., n } で、順序がシャッフルされた配列を生成 */\nList&lt;int&gt; randomNumbers(int n) {\n  final nums = List.filled(n, 0);\n  // 配列 nums = { 1, 2, 3, ..., n } を生成\n  for (var i = 0; i &lt; n; i++) {\n    nums[i] = i + 1;\n  }\n  // 配列要素をランダムにシャッフル\n  nums.shuffle();\n\n  return nums;\n}\n\n/* 配列 nums 内で数値 1 のインデックスを探す */\nint findOne(List&lt;int&gt; nums) {\n  for (var i = 0; i &lt; nums.length; i++) {\n    // 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる\n    // 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる\n    if (nums[i] == 1) return i;\n  }\n\n  return -1;\n}\n</code></pre> worst_best_time_complexity.rs<pre><code>/* 要素が { 1, 2, ..., n } で、順序がシャッフルされた配列を生成 */\nfn random_numbers(n: i32) -&gt; Vec&lt;i32&gt; {\n    // 配列 nums = { 1, 2, 3, ..., n } を生成\n    let mut nums = (1..=n).collect::&lt;Vec&lt;i32&gt;&gt;();\n    // 配列要素をランダムにシャッフル\n    nums.shuffle(&amp;mut thread_rng());\n    nums\n}\n\n/* 配列 nums 内で数値 1 のインデックスを探す */\nfn find_one(nums: &amp;[i32]) -&gt; Option&lt;usize&gt; {\n    for i in 0..nums.len() {\n        // 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる\n        // 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる\n        if nums[i] == 1 {\n            return Some(i);\n        }\n    }\n    None\n}\n</code></pre> worst_best_time_complexity.c<pre><code>/* 要素が { 1, 2, ..., n } で、順序がシャッフルされた配列を生成 */\nint *randomNumbers(int n) {\n    // ヒープ領域にメモリを確保する（要素数 n、要素型 int の一次元可変長配列を作成）\n    int *nums = (int *)malloc(n * sizeof(int));\n    // 配列 nums = { 1, 2, 3, ..., n } を生成\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = i + 1;\n    }\n    // 配列要素をランダムにシャッフル\n    for (int i = n - 1; i &gt; 0; i--) {\n        int j = rand() % (i + 1);\n        int temp = nums[i];\n        nums[i] = nums[j];\n        nums[j] = temp;\n    }\n    return nums;\n}\n\n/* 配列 nums 内で数値 1 のインデックスを探す */\nint findOne(int *nums, int n) {\n    for (int i = 0; i &lt; n; i++) {\n        // 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる\n        // 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる\n        if (nums[i] == 1)\n            return i;\n    }\n    return -1;\n}\n</code></pre> worst_best_time_complexity.kt<pre><code>/* 要素が { 1, 2, ..., n } で、順序がシャッフルされた配列を生成 */\nfun randomNumbers(n: Int): Array&lt;Int?&gt; {\n    val nums = IntArray(n)\n    // 配列 nums = { 1, 2, 3, ..., n } を生成\n    for (i in 0..&lt;n) {\n        nums[i] = i + 1\n    }\n    // 配列要素をランダムにシャッフル\n    nums.shuffle()\n    val res = arrayOfNulls&lt;Int&gt;(n)\n    for (i in 0..&lt;n) {\n        res[i] = nums[i]\n    }\n    return res\n}\n\n/* 配列 nums 内で数値 1 のインデックスを探す */\nfun findOne(nums: Array&lt;Int?&gt;): Int {\n    for (i in nums.indices) {\n        // 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる\n        // 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる\n        if (nums[i] == 1)\n            return i\n    }\n    return -1\n}\n</code></pre> worst_best_time_complexity.rb<pre><code>### 1, 2, ..., n を要素とする配列を生成し、順序をシャッフルする ###\ndef random_numbers(n)\n  # 配列 nums =: 1, 2, 3, ..., n を生成する\n  nums = Array.new(n) { |i| i + 1 }\n  # 配列要素をランダムにシャッフル\n  nums.shuffle!\nend\n\n### 配列 nums 内の数値 1 のインデックスを探す ###\ndef find_one(nums)\n  for i in 0...nums.length\n    # 要素 1 が配列の先頭にあるとき、最良時間計算量 O(1) となる\n    # 要素 1 が配列の末尾にあるとき、最悪時間計算量 O(n) となる\n    return i if nums[i] == 1\n  end\n\n  -1\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>実際には、最良時間計算量を使うことはあまりありません。通常それが実現する確率はごく低く、誤解を招く可能性があるからです。**一方で最悪時間計算量はより実用的で、効率の安全側の目安を与えてくれる**ため、安心してアルゴリズムを使えます。</p> <p>上の例から分かるように、最悪時間計算量と最良時間計算量は「特殊なデータ分布」でのみ現れ、その発生確率は低いことが多く、アルゴリズムの実行効率をそのまま正確に反映するわけではありません。それに対して、**平均時間計算量はランダム入力におけるアルゴリズムの実行効率を表せる**ため、\\(\\Theta\\) 記法で表します。</p> <p>一部のアルゴリズムでは、ランダムなデータ分布における平均的な状況を比較的簡単に求められます。例えば上の例では、入力配列はシャッフルされているため、要素 \\(1\\) が任意のインデックスに現れる確率は等しいです。したがってアルゴリズムの平均ループ回数は配列長の半分 \\(n / 2\\) となり、平均時間計算量は \\(\\Theta(n / 2) = \\Theta(n)\\) です。</p> <p>しかし、より複雑なアルゴリズムでは、平均時間計算量を計算するのはしばしば困難です。データ分布に対する全体の数学的期待値を分析するのが難しいからです。そのような場合、通常は最悪時間計算量をアルゴリズム効率の評価基準として用います。</p> <p>なぜ \\(\\Theta\\) 記号をあまり見かけないのか？</p> <p>おそらく \\(O\\) 記号のほうが口にしやすいため、平均時間計算量を表すのにもよく使われます。ただし厳密には、この用法は正確ではありません。本書や他の資料で「平均時間計算量 \\(O(n)\\)」のような表現を見かけた場合は、そのまま \\(\\Theta(n)\\) と理解してください。</p>","path":["第 2 章 &nbsp; 計算量解析","2.3 &nbsp; 時間計算量"],"tags":[]},{"location":"chapter_data_structure/","level":1,"title":"第 3 章   データ構造","text":"<p>Abstract</p> <p>データ構造は、堅固で多様な枠組みのようなものである。</p> <p>それはデータを秩序立てて組織するための青写真を示し、アルゴリズムはその上で生き生きと動き出す。</p>","path":["第 3 章 &nbsp; データ構造"],"tags":[]},{"location":"chapter_data_structure/#_1","level":2,"title":"章の内容","text":"<ul> <li>3.1   データ構造の分類</li> <li>3.2   基本データ型</li> <li>3.3   数値エンコーディング *</li> <li>3.4   文字エンコーディング *</li> <li>3.5   まとめ</li> </ul>","path":["第 3 章 &nbsp; データ構造"],"tags":[]},{"location":"chapter_data_structure/basic_data_types/","level":1,"title":"3.2   基本データ型","text":"<p>コンピュータ内のデータについて考えるとき、テキスト、画像、動画、音声、3D モデルなど、さまざまな形態を思い浮かべます。これらのデータの構成形式はそれぞれ異なりますが、いずれも各種の基本データ型によって成り立っています。</p> <p>**基本データ型は CPU が直接演算できる型**であり、アルゴリズムの中で直接使われます。主なものは次のとおりです。</p> <ul> <li>整数型 <code>byte</code>、<code>short</code>、<code>int</code>、<code>long</code> 。</li> <li>浮動小数点数型 <code>float</code>、<code>double</code> ，小数を表すために使います。</li> <li>文字型 <code>char</code> ，各言語の文字、句読点、さらには絵文字などを表すために使います。</li> <li>真偽値型 <code>bool</code> ，真か偽かの判定を表すために使います。</li> </ul> <p>基本データ型はコンピュータ内で 2 進数の形で格納されます。1 つの二進桁は \\(1\\) ビットです。現代のほとんどのオペレーティングシステムでは、\\(1\\) バイト（byte）は \\(8\\) ビット（bit）で構成されます。</p> <p>基本データ型の値域は、その型が占める領域の大きさによって決まります。以下では Java を例に取ります。</p> <ul> <li>整数型 <code>byte</code> は \\(1\\) バイト = \\(8\\) ビットを占め、\\(2^{8}\\) 個の数を表せます。</li> <li>整数型 <code>int</code> は \\(4\\) バイト = \\(32\\) ビットを占め、\\(2^{32}\\) 個の数を表せます。</li> </ul> <p>下表は、Java における各種基本データ型の使用領域、値域、デフォルト値を示したものです。この表を丸暗記する必要はなく、大まかに理解しておけば十分であり、必要になったときに参照すればかまいません。</p> <p> 表 3-1   基本データ型の使用領域と値域 </p> 型 記号 使用領域 最小値 最大値 デフォルト値 整数 <code>byte</code> 1 バイト \\(-2^7\\) (\\(-128\\)) \\(2^7 - 1\\) (\\(127\\)) \\(0\\) <code>short</code> 2 バイト \\(-2^{15}\\) \\(2^{15} - 1\\) \\(0\\) <code>int</code> 4 バイト \\(-2^{31}\\) \\(2^{31} - 1\\) \\(0\\) <code>long</code> 8 バイト \\(-2^{63}\\) \\(2^{63} - 1\\) \\(0\\) 浮動小数点数 <code>float</code> 4 バイト \\(1.175 \\times 10^{-38}\\) \\(3.403 \\times 10^{38}\\) \\(0.0\\text{f}\\) <code>double</code> 8 バイト \\(2.225 \\times 10^{-308}\\) \\(1.798 \\times 10^{308}\\) \\(0.0\\) 文字 <code>char</code> 2 バイト \\(0\\) \\(2^{16} - 1\\) \\(0\\) 真偽値 <code>bool</code> 1 バイト \\(\\text{false}\\) \\(\\text{true}\\) \\(\\text{false}\\) <p>注意してください。上表は Java の基本データ型に対するものです。各プログラミング言語にはそれぞれ独自のデータ型定義があり、使用領域、値域、デフォルト値は異なる場合があります。</p> <ul> <li>Python では、整数型 <code>int</code> は利用可能なメモリに制限されるだけで任意の大きさを取れます。浮動小数点数 <code>float</code> は倍精度 64 ビットです。<code>char</code> 型はなく、1 文字は実際には長さ 1 の文字列 <code>str</code> です。</li> <li>C と C++ では基本データ型の大きさは明確に規定されておらず、実装やプラットフォームによって異なります。上表は LP64 データモデル に従っており、Linux や macOS を含む Unix 系 64 ビット OS で用いられています。</li> <li><code>char</code> の大きさは C と C++ では 1 バイトですが、多くのプログラミング言語では採用する文字エンコーディング方式によって決まります。詳しくは「文字エンコーディング」の章を参照してください。</li> <li>真偽値を表すのに必要なのは 1 ビット（\\(0\\) または \\(1\\)）だけですが、メモリ上では通常 1 バイトとして格納されます。これは、現代のコンピュータ CPU が通常 1 バイトを最小のアドレス指定可能なメモリ単位としているためです。</li> </ul> <p>では、基本データ型とデータ構造の間にはどのような関係があるのでしょうか。データ構造とは、コンピュータ内でデータを組織し格納する方法のことです。この言葉で主役なのは「データ」ではなく「構造」です。</p> <p>「数字の並び」を表したいなら、自然に配列の使用を思い浮かべるでしょう。これは、配列の線形構造が数字どうしの隣接関係や順序関係を表せるからです。しかし、格納する内容が整数 <code>int</code> なのか、小数 <code>float</code> なのか、文字 <code>char</code> なのかは、「データ構造」とは関係ありません。</p> <p>言い換えると、基本データ型はデータの「内容の型」を提供し、データ構造はデータの「組織方法」を提供します。たとえば次のコードでは、同じデータ構造（配列）を使って <code>int</code>、<code>float</code>、<code>char</code>、<code>bool</code> など異なる基本データ型を格納・表現しています。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code># さまざまな基本データ型で配列を初期化する\nnumbers: list[int] = [0] * 5\ndecimals: list[float] = [0.0] * 5\n# Python の文字は実際には長さ 1 の文字列\ncharacters: list[str] = ['0'] * 5\nbools: list[bool] = [False] * 5\n# Python のリストはさまざまな基本データ型とオブジェクト参照を自由に格納できる\ndata = [0, 0.0, 'a', False, ListNode(0)]\n</code></pre> <pre><code>// さまざまな基本データ型で配列を初期化する\nint numbers[5];\nfloat decimals[5];\nchar characters[5];\nbool bools[5];\n</code></pre> <pre><code>// さまざまな基本データ型で配列を初期化する\nint[] numbers = new int[5];\nfloat[] decimals = new float[5];\nchar[] characters = new char[5];\nboolean[] bools = new boolean[5];\n</code></pre> <pre><code>// さまざまな基本データ型で配列を初期化する\nint[] numbers = new int[5];\nfloat[] decimals = new float[5];\nchar[] characters = new char[5];\nbool[] bools = new bool[5];\n</code></pre> <pre><code>// さまざまな基本データ型で配列を初期化する\nvar numbers = [5]int{}\nvar decimals = [5]float64{}\nvar characters = [5]byte{}\nvar bools = [5]bool{}\n</code></pre> <pre><code>// さまざまな基本データ型で配列を初期化する\nlet numbers = Array(repeating: 0, count: 5)\nlet decimals = Array(repeating: 0.0, count: 5)\nlet characters: [Character] = Array(repeating: \"a\", count: 5)\nlet bools = Array(repeating: false, count: 5)\n</code></pre> <pre><code>// JavaScript の配列はさまざまな基本データ型とオブジェクトを自由に格納できる\nconst array = [0, 0.0, 'a', false];\n</code></pre> <pre><code>// さまざまな基本データ型で配列を初期化する\nconst numbers: number[] = [];\nconst characters: string[] = [];\nconst bools: boolean[] = [];\n</code></pre> <pre><code>// さまざまな基本データ型で配列を初期化する\nList&lt;int&gt; numbers = List.filled(5, 0);\nList&lt;double&gt; decimals = List.filled(5, 0.0);\nList&lt;String&gt; characters = List.filled(5, 'a');\nList&lt;bool&gt; bools = List.filled(5, false);\n</code></pre> <pre><code>// さまざまな基本データ型で配列を初期化する\nlet numbers: Vec&lt;i32&gt; = vec![0; 5];\nlet decimals: Vec&lt;f32&gt; = vec![0.0; 5];\nlet characters: Vec&lt;char&gt; = vec!['0'; 5];\nlet bools: Vec&lt;bool&gt; = vec![false; 5];\n</code></pre> <pre><code>// さまざまな基本データ型で配列を初期化する\nint numbers[10];\nfloat decimals[10];\nchar characters[10];\nbool bools[10];\n</code></pre> <pre><code>// さまざまな基本データ型で配列を初期化する\nval numbers = IntArray(5)\nval decinals = FloatArray(5)\nval characters = CharArray(5)\nval bools = BooleanArray(5)\n</code></pre> <pre><code># Ruby のリストはさまざまな基本データ型とオブジェクト参照を自由に格納できる\ndata = [0, 0.0, 'a', false, ListNode(0)]\n</code></pre> 実行の可視化 <p>https://pythontutor.com/render.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%E9%93%BE%E8%A1%A8%E8%8A%82%E7%82%B9%E7%B1%BB%22%22%22%0A%20%20%20%20def%20__init__%28self,%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E8%8A%82%E7%82%B9%E5%80%BC%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%90%8E%E7%BB%A7%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E4%BD%BF%E7%94%A8%E5%A4%9A%E7%A7%8D%E5%9F%BA%E6%9C%AC%E6%95%B0%E6%8D%AE%E7%B1%BB%E5%9E%8B%E6%9D%A5%E5%88%9D%E5%A7%8B%E5%8C%96%E6%95%B0%E7%BB%84%0A%20%20%20%20numbers%20%3D%20%5B0%5D%20*%205%0A%20%20%20%20decimals%20%3D%20%5B0.0%5D%20*%205%0A%20%20%20%20%23%20Python%20%E7%9A%84%E5%AD%97%E7%AC%A6%E5%AE%9E%E9%99%85%E4%B8%8A%E6%98%AF%E9%95%BF%E5%BA%A6%E4%B8%BA%201%20%E7%9A%84%E5%AD%97%E7%AC%A6%E4%B8%B2%0A%20%20%20%20characters%20%3D%20%5B'0'%5D%20*%205%0A%20%20%20%20bools%20%3D%20%5BFalse%5D%20*%205%0A%20%20%20%20%23%20Python%20%E7%9A%84%E5%88%97%E8%A1%A8%E5%8F%AF%E4%BB%A5%E8%87%AA%E7%94%B1%E5%AD%98%E5%82%A8%E5%90%84%E7%A7%8D%E5%9F%BA%E6%9C%AC%E6%95%B0%E6%8D%AE%E7%B1%BB%E5%9E%8B%E5%92%8C%E5%AF%B9%E8%B1%A1%E5%BC%95%E7%94%A8%0A%20%20%20%20data%20%3D%20%5B0,%200.0,%20'a',%20False,%20ListNode%280%29%5D&amp;cumulative=false&amp;curInstr=12&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["第 3 章 &nbsp; データ構造","3.2 &nbsp; 基本データ型"],"tags":[]},{"location":"chapter_data_structure/character_encoding/","level":1,"title":"3.4   文字エンコーディング *","text":"<p>コンピュータでは、すべてのデータは二進数の形で保存されており、文字 <code>char</code> も例外ではありません。文字を表すためには、「文字セット」を定義し、各文字と二進数の間の一対一の対応関係を定める必要があります。文字セットがあれば、コンピュータは対応表を参照して二進数から文字への変換を行えます。</p>","path":["第 3 章 &nbsp; データ構造","3.4 &nbsp; 文字エンコーディング *"],"tags":[]},{"location":"chapter_data_structure/character_encoding/#341-ascii","level":2,"title":"3.4.1   ASCII 文字セット","text":"<p>ASCII コードは最も早く登場した文字セットで、その正式名称は American Standard Code for Information Interchange（米国標準情報交換コード）です。これは 7 ビットの二進数（1 バイトの下位 7 ビット）で 1 文字を表し、最大で 128 種類の異なる文字を表現できます。下図のように、ASCII コードには英字の大文字と小文字、数字 0 ~ 9、いくつかの句読点、そしていくつかの制御文字（改行やタブなど）が含まれます。</p> <p></p> <p> 図 3-6   ASCII コード </p> <p>しかし、ASCII コードで表現できるのは英語だけです。コンピュータのグローバル化に伴い、より多くの言語を表せる EASCII 文字セットが生まれました。これは ASCII の 7 ビットを 8 ビットへ拡張したもので、256 種類の異なる文字を表現できます。</p> <p>世界では、さまざまな地域に適した EASCII 文字セットが次々に登場しました。これらの文字セットでは、前半の 128 文字は ASCII コードで統一され、後半の 128 文字は各言語の要件に合わせて個別に定義されています。</p>","path":["第 3 章 &nbsp; データ構造","3.4 &nbsp; 文字エンコーディング *"],"tags":[]},{"location":"chapter_data_structure/character_encoding/#342-gbk","level":2,"title":"3.4.2   GBK 文字セット","text":"<p>その後、人々は**EASCII コードでも多くの言語に必要な文字数を満たせない**ことに気づきました。たとえば漢字は 10 万字近くあり、日常的に使うものだけでも数千字あります。中国国家標準総局は 1980 年に GB2312 文字セットを公開し、6763 字の漢字を収録して、漢字のコンピュータ処理の基本的な需要を満たしました。</p> <p>しかし、GB2312 では一部の珍しい字や繁体字を扱えません。GBK 文字セットは GB2312 を基に拡張されたもので、合計 21886 字の漢字を収録しています。GBK のエンコーディング方式では、ASCII 文字は 1 バイト、漢字は 2 バイトで表されます。</p>","path":["第 3 章 &nbsp; データ構造","3.4 &nbsp; 文字エンコーディング *"],"tags":[]},{"location":"chapter_data_structure/character_encoding/#343-unicode","level":2,"title":"3.4.3   Unicode 文字セット","text":"<p>コンピュータ技術が急速に発展するにつれて、文字セットと符号化規格は百花繚乱の状態となり、それに伴って多くの問題も生じました。一方では、これらの文字セットは通常、特定の言語の文字しか定義しておらず、多言語環境では正常に動作できませんでした。もう一方では、同じ言語にも複数の文字セット規格が存在し、2 台のコンピュータが異なる符号化規格を使っていると、情報伝達の際に文字化けが発生しました。</p> <p>当時の研究者たちはこう考えました。十分に完全な文字セットを打ち出して、世界中のあらゆる言語と記号をそこに収録すれば、多言語環境や文字化けの問題を解決できるのではないか。この発想に後押しされて、大規模で包括的な文字セット Unicode が誕生しました。</p> <p>Unicode の中国語名は「統一コード」であり、理論上は 100 万を超える文字を収容できます。Unicode は世界中の文字を 1 つの文字セットに統合することを目指し、さまざまな言語の文字を処理・表示できる汎用文字セットを提供することで、符号化規格の違いによる文字化けを減らそうとしています。</p> <p>1991 年の公開以来、Unicode は新しい言語と文字を継続的に拡充してきました。2022 年 9 月時点で、Unicode にはすでに 149186 文字が含まれており、各種言語の文字、記号、さらには絵文字まで収録されています。巨大な Unicode 文字セットでは、よく使われる文字は 2 バイトを占め、一部の珍しい文字は 3 バイト、さらには 4 バイトを占めます。</p> <p>Unicode は汎用文字セットであり、本質的には各文字に番号（「コードポイント」）を割り当てるものですが、それらのコードポイントをコンピュータ内でどのように保存するかまでは規定していません。ここで疑問が生じます。長さの異なる Unicode コードポイントが同じテキストに現れたとき、システムはどのように文字を解析するのでしょうか。たとえば長さ 2 バイトの符号が与えられたとき、それが 2 バイトの 1 文字なのか、1 バイトの 2 文字なのかをどう判定するのでしょうか。</p> <p>この問題に対して、**すべての文字を固定長の符号として保存する**という直接的な解決策があります。下図のように、「Hello」の各文字は 1 バイト、「アルゴリズム」の各文字は 2 バイトを占めます。上位ビットを 0 で埋めることで、「Hello アルゴリズム」のすべての文字を 2 バイト長にエンコードできます。こうすれば、システムは 2 バイトごとに 1 文字を解析して、この語句の内容を復元できます。</p> <p></p> <p> 図 3-7   Unicode エンコーディングの例 </p> <p>しかし ASCII コードはすでに、英語の符号化には 1 バイトで十分であることを示しています。上記の方式を採用すると、英語のテキストが占める空間は ASCII エンコーディング時の 2 倍になり、メモリ空間の浪費が大きくなります。そのため、より効率的な Unicode エンコーディング方式が必要です。</p>","path":["第 3 章 &nbsp; データ構造","3.4 &nbsp; 文字エンコーディング *"],"tags":[]},{"location":"chapter_data_structure/character_encoding/#344-utf-8","level":2,"title":"3.4.4   UTF-8 エンコーディング","text":"<p>現在、UTF-8 は国際的に最も広く使われている Unicode エンコーディング方式になっています。**これは可変長のエンコーディング**であり、1 文字を 1 〜 4 バイトで表し、文字の複雑さに応じて長さが変わります。ASCII 文字は 1 バイト、ラテン文字とギリシャ文字は 2 バイト、一般的な漢字は 3 バイト、そのほかの一部の珍しい文字は 4 バイト必要です。</p> <p>UTF-8 の符号化規則はそれほど複雑ではなく、次の 2 つのケースに分けられます。</p> <ul> <li>長さ 1 バイトの文字では、最上位ビットを \\(0\\) にし、残りの 7 ビットを Unicode コードポイントに設定します。ここで注意すべきなのは、ASCII 文字が Unicode 文字セットの先頭 128 個のコードポイントを占めていることです。つまり、UTF-8 エンコーディングは ASCII コードと下位互換性があります。このため、UTF-8 を使って古い ASCII コードのテキストを解析できます。</li> <li>長さ \\(n\\) バイトの文字（ただし \\(n &gt; 1\\)）では、先頭バイトの上位 \\(n\\) ビットをすべて \\(1\\) にし、第 \\(n + 1\\) ビットを \\(0\\) に設定します。2 バイト目以降では、各バイトの上位 2 ビットをいずれも \\(10\\) にし、残りのすべてのビットで文字の Unicode コードポイントを埋めます。</li> </ul> <p>下図は「Helloアルゴリズム」に対応する UTF-8 エンコーディングを示しています。観察すると、上位 \\(n\\) ビットがすべて \\(1\\) に設定されているため、システムは先頭から連続する \\(1\\) の個数を読むことで、その文字の長さが \\(n\\) であると解析できます。</p> <p>では、なぜ残りのすべてのバイトの上位 2 ビットを \\(10\\) にするのでしょうか。実は、この \\(10\\) は検査用の印として機能します。システムが誤ったバイト位置からテキストを解析し始めたとしても、バイト先頭の \\(10\\) によって異常を素早く判定できます。</p> <p>この \\(10\\) を検査用の印とする理由は、UTF-8 の符号化規則では上位 2 ビットが \\(10\\) になる文字は存在しないからです。この結論は背理法で証明できます。ある文字の上位 2 ビットが \\(10\\) だと仮定すると、その文字の長さは \\(1\\) であり、ASCII コードに対応することになります。しかし ASCII コードの最上位ビットは \\(0\\) であるはずなので、仮定と矛盾します。</p> <p></p> <p> 図 3-8   UTF-8 エンコーディングの例 </p> <p>UTF-8 以外にも、一般的なエンコーディング方式として次の 2 つがあります。</p> <ul> <li>UTF-16 エンコーディング：1 文字を 2 バイトまたは 4 バイトで表します。すべての ASCII 文字と一般的な非英語文字は 2 バイトで表し、一部の文字だけが 4 バイトを必要とします。2 バイトの文字については、UTF-16 エンコーディングは Unicode コードポイントと等しくなります。</li> <li>UTF-32 エンコーディング：各文字を必ず 4 バイトで表します。つまり UTF-32 は UTF-8 や UTF-16 よりも多くの領域を消費し、とくに ASCII 文字の比率が高いテキストでその傾向が顕著です。</li> </ul> <p>記憶領域の使用量という観点では、UTF-8 は英語文字の表現に非常に効率的で、必要なのは 1 バイトだけです。一方、UTF-16 は一部の非英語文字（たとえば中国語の文字）の符号化でより効率的になることがあり、必要なのは 2 バイトだけで、UTF-8 では 3 バイト必要になる場合があります。</p> <p>互換性という観点では、UTF-8 の汎用性が最も高く、多くのツールやライブラリが UTF-8 を優先的にサポートしています。</p>","path":["第 3 章 &nbsp; データ構造","3.4 &nbsp; 文字エンコーディング *"],"tags":[]},{"location":"chapter_data_structure/character_encoding/#345","level":2,"title":"3.4.5   プログラミング言語の文字エンコーディング","text":"<p>従来の多くのプログラミング言語では、実行中の文字列に UTF-16 や UTF-32 のような固定長エンコーディングが使われています。固定長エンコーディングでは、文字列を配列のように扱えるため、次のような利点があります。</p> <ul> <li>ランダムアクセス：UTF-16 で符号化された文字列はランダムアクセスが容易です。UTF-8 は可変長エンコーディングなので、第 \\(i\\) 文字を見つけるには文字列の先頭から第 \\(i\\) 文字まで走査する必要があり、\\(O(n)\\) の時間がかかります。</li> <li>文字数の計算：ランダムアクセスと同様に、UTF-16 で符号化された文字列の長さを計算するのも \\(O(1)\\) の操作です。しかし、UTF-8 で符号化された文字列の長さを計算するには、文字列全体を走査する必要があります。</li> <li>文字列操作：UTF-16 で符号化された文字列では、多くの文字列操作（分割、連結、挿入、削除など）をより簡単に行えます。UTF-8 で符号化された文字列では、これらの操作を行う際に、無効な UTF-8 エンコーディングを生じさせないための追加計算が通常必要になります。</li> </ul> <p>実際、プログラミング言語における文字エンコーディング方式の設計は、とても興味深い話題であり、多くの要因が関わっています。</p> <ul> <li>Java の <code>String</code> 型は UTF-16 エンコーディングを使用し、各文字は 2 バイトを占めます。これは Java 言語の設計当初、人々が 16 ビットあればあらゆる文字を表現するのに十分だと考えていたためです。しかし、これは誤った判断でした。その後 Unicode 規格は 16 ビットを超える範囲へ拡張されたため、現在の Java では 1 文字が 16 ビット値の組（「サロゲートペア」）で表されることがあります。</li> <li>JavaScript と TypeScript の文字列が UTF-16 エンコーディングを使う理由も Java と似ています。1995 年に Netscape 社が初めて JavaScript 言語を公開した当時、Unicode はまだ発展初期にあり、16 ビットの符号化で十分すべての Unicode 文字を表せると考えられていました。</li> <li>C# が UTF-16 エンコーディングを使う主な理由は、.NET プラットフォームが Microsoft によって設計され、Microsoft の多くの技術（Windows オペレーティングシステムを含む）で UTF-16 エンコーディングが広く使われているためです。</li> </ul> <p>以上のプログラミング言語は文字数を過小評価していたため、16 ビットを超える長さの Unicode 文字を表すために「サロゲートペア」を採用せざるを得ませんでした。これはやむを得ない妥協策です。一方では、サロゲートペアを含む文字列では、1 文字が 2 バイトまたは 4 バイトを占める可能性があり、固定長エンコーディングの利点が失われます。もう一方では、サロゲートペアの処理には追加のコードが必要となり、プログラミングの複雑さとデバッグの難しさが増します。</p> <p>こうした理由から、一部のプログラミング言語では別のエンコーディング方式が採用されました。</p> <ul> <li>Python の <code>str</code> は Unicode エンコーディングを使用し、柔軟な文字列表現を採用しています。保存される文字の長さは、その文字列中で最大の Unicode コードポイントに依存します。文字列がすべて ASCII 文字であれば各文字は 1 バイト、ASCII の範囲を超える文字があってもすべてが基本多言語面（BMP）内であれば各文字は 2 バイト、BMP を超える文字があれば各文字は 4 バイトを占めます。</li> <li>Go 言語の <code>string</code> 型は内部で UTF-8 エンコーディングを使用します。Go 言語には単一の Unicode コードポイントを表す <code>rune</code> 型も用意されています。</li> <li>Rust 言語の <code>str</code> と <code>String</code> 型は内部で UTF-8 エンコーディングを使用します。Rust にも単一の Unicode コードポイントを表す <code>char</code> 型があります。</li> </ul> <p>注意すべきなのは、ここまでの議論はすべて、プログラミング言語内での文字列の保存方法についてであり、**文字列をファイルに保存したりネットワークで転送したりする方法とは別の問題である**ということです。ファイル保存やネットワーク転送では、通常、互換性と空間効率を最適化するために文字列を UTF-8 形式にエンコードします。</p>","path":["第 3 章 &nbsp; データ構造","3.4 &nbsp; 文字エンコーディング *"],"tags":[]},{"location":"chapter_data_structure/classification_of_data_structure/","level":1,"title":"3.1   データ構造の分類","text":"<p>代表的なデータ構造には、配列、連結リスト、スタック、キュー、ハッシュテーブル、木、ヒープ、グラフがあり、これらは「論理構造」と「物理構造」の 2 つの観点から分類できます。</p>","path":["第 3 章 &nbsp; データ構造","3.1 &nbsp; データ構造の分類"],"tags":[]},{"location":"chapter_data_structure/classification_of_data_structure/#311","level":2,"title":"3.1.1   論理構造：線形と非線形","text":"<p>論理構造はデータ要素間の論理的な関係を示します。配列と連結リストでは、データは一定の順序で並び、データ間の線形関係を表します。一方、木ではデータは上から下へ階層的に並び、「祖先」と「子孫」の派生関係を示します。グラフはノードと辺で構成され、複雑なネットワーク関係を反映します。</p> <p>以下の図に示すように、論理構造は「線形」と「非線形」の 2 つに大別できます。線形構造は比較的直感的で、データが論理関係において線形に並ぶことを指します。非線形構造はその逆で、非線形に配置されます。</p> <ul> <li>線形データ構造：配列、連結リスト、スタック、キュー、ハッシュテーブルであり、要素間は 1 対 1 の順序関係です。</li> <li>非線形データ構造：木、ヒープ、グラフ、ハッシュテーブル。</li> </ul> <p>非線形データ構造は、さらに木構造と網状構造に分けられます。</p> <ul> <li>木構造：木、ヒープ、ハッシュテーブルであり、要素間は 1 対多の関係です。</li> <li>網状構造：グラフであり、要素間は多対多の関係です。</li> </ul> <p></p> <p> 図 3-1   線形データ構造と非線形データ構造 </p>","path":["第 3 章 &nbsp; データ構造","3.1 &nbsp; データ構造の分類"],"tags":[]},{"location":"chapter_data_structure/classification_of_data_structure/#312","level":2,"title":"3.1.2   物理構造：連続と分散","text":"<p>アルゴリズムのプログラムが実行されるとき、処理中のデータは主にメモリに格納されます。下図はコンピュータのメモリモジュールを示しており、各黒い四角はそれぞれ 1 つのメモリ空間を表しています。メモリは巨大な Excel の表のようなものだと考えることができ、各セルには一定量のデータを格納できます。</p> <p>システムはメモリアドレスを通じて目的の位置にあるデータへアクセスします。下図に示すように、コンピュータは特定の規則に従って表内の各セルに番号を割り当て、各メモリ空間が一意のメモリアドレスを持つようにします。これらのアドレスがあれば、プログラムはメモリ内のデータにアクセスできます。</p> <p></p> <p> 図 3-2   メモリモジュール、メモリ空間、メモリアドレス </p> <p>Tip</p> <p>補足すると、メモリを Excel の表にたとえるのは単純化した比喩であり、実際のメモリの動作機構はより複雑で、アドレス空間、メモリ管理、キャッシュ機構、仮想メモリ、物理メモリなどの概念が関わります。</p> <p>メモリはすべてのプログラムで共有される資源であり、あるメモリ領域が 1 つのプログラムに占有されると、通常は他のプログラムが同時に利用できません。したがって、データ構造とアルゴリズムの設計では、メモリ資源は重要な考慮要素です。たとえば、アルゴリズムが使用するメモリ使用量のピークは、システムに残っている空きメモリを超えてはなりません。大きな連続メモリ領域が不足している場合、選択するデータ構造は分散したメモリ空間に格納できる必要があります。</p> <p>下図に示すように、物理構造はデータがコンピュータメモリ内にどのように格納されるかを表します。これは連続空間への格納（配列）と分散空間への格納（連結リスト）に分けられます。物理構造は低レベルでデータのアクセス、更新、追加、削除などの操作方法を決定し、2 種類の物理構造は時間効率と空間効率の面で相補的な特徴を持ちます。</p> <p></p> <p> 図 3-3   連続空間格納と分散空間格納 </p> <p>補足すると、すべてのデータ構造は配列、連結リスト、またはその両者の組み合わせに基づいて実装されます。たとえば、スタックとキューは配列でも連結リストでも実装できます。一方、ハッシュテーブルの実装には配列と連結リストの両方が含まれる場合があります。</p> <ul> <li>配列に基づいて実装可能：スタック、キュー、ハッシュテーブル、木、ヒープ、グラフ、行列、テンソル（次元 \\(\\geq 3\\) の配列）など。</li> <li>連結リストに基づいて実装可能：スタック、キュー、ハッシュテーブル、木、ヒープ、グラフなど。</li> </ul> <p>連結リストは初期化後も、プログラムの実行中に長さを調整できるため、「動的データ構造」とも呼ばれます。配列は初期化後に長さを変更できないため、「静的データ構造」とも呼ばれます。なお、配列もメモリを再割り当てすることで長さを変更でき、ある程度の「動的性」を持たせることができます。</p> <p>Tip</p> <p>物理構造の理解が難しいと感じる場合は、先に次の章を読んでから本節を振り返ることを勧めます。</p>","path":["第 3 章 &nbsp; データ構造","3.1 &nbsp; データ構造の分類"],"tags":[]},{"location":"chapter_data_structure/number_encoding/","level":1,"title":"3.3   数値エンコーディング *","text":"<p>Tip</p> <p>本書では、タイトルに * 記号が付いている章は選読です。時間が限られている場合や理解が難しいと感じる場合は、いったん読み飛ばし、必読章を終えてから個別に取り組んでください。</p>","path":["第 3 章 &nbsp; データ構造","3.3 &nbsp; 数値エンコーディング *"],"tags":[]},{"location":"chapter_data_structure/number_encoding/#331-1-2","level":2,"title":"3.3.1   符号付き絶対値表現、1 の補数、2 の補数","text":"<p>前節の表を見ると、すべての整数型で表せる負数の個数は正数より 1 つ多く、たとえば <code>byte</code> の値域は \\([-128, 127]\\) です。この現象は直感に反するように見えますが、その背景には符号付き絶対値表現、1 の補数、2 の補数に関する知識があります。</p> <p>まず押さえておくべきなのは、**数値はコンピュータ内で「2 の補数」の形で保存される**ということです。その理由を説明する前に、まずはこの 3 つの定義を示します。</p> <ul> <li>符号付き絶対値表現：数値の二進表現の最上位ビットを符号ビットとみなし、\\(0\\) は正数、\\(1\\) は負数を表し、残りのビットが数値の値を表します。</li> <li>1 の補数：正数の 1 の補数は符号付き絶対値表現と同じで、負数の 1 の補数は符号ビットを除くすべてのビットを反転したものです。</li> <li>2 の補数：正数の 2 の補数は符号付き絶対値表現と同じで、負数の 2 の補数は 1 の補数に \\(1\\) を加えたものです。</li> </ul> <p>下図は、符号付き絶対値表現、1 の補数、2 の補数の変換方法を示しています。</p> <p></p> <p> 図 3-4   符号付き絶対値表現、1 の補数、2 の補数の相互変換 </p> <p>符号付き絶対値表現（sign-magnitude）は最も直感的ですが、いくつかの制約があります。まず、負数の符号付き絶対値表現はそのまま演算に使えません。たとえば符号付き絶対値表現で \\(1 + (-2)\\) を計算すると、結果は \\(-3\\) になってしまい、これは明らかに誤りです。</p> \\[ \\begin{aligned} &amp; 1 + (-2) \\newline &amp; \\rightarrow 0000 \\; 0001 + 1000 \\; 0010 \\newline &amp; = 1000 \\; 0011 \\newline &amp; \\rightarrow -3 \\end{aligned} \\] <p>この問題を解決するために、コンピュータには1 の補数（1's complement）が導入されました。まず符号付き絶対値表現を 1 の補数に変換し、1 の補数で \\(1 + (-2)\\) を計算してから、結果を 1 の補数から符号付き絶対値表現へ戻すと、正しい結果 \\(-1\\) が得られます。</p> \\[ \\begin{aligned} &amp; 1 + (-2) \\newline &amp; \\rightarrow 0000 \\; 0001 \\; \\text{(符号付き絶対値表現)} + 1000 \\; 0010 \\; \\text{(符号付き絶対値表現)} \\newline &amp; = 0000 \\; 0001 \\; \\text{(1 の補数)} + 1111  \\; 1101 \\; \\text{(1 の補数)} \\newline &amp; = 1111 \\; 1110 \\; \\text{(1 の補数)} \\newline &amp; = 1000 \\; 0001 \\; \\text{(符号付き絶対値表現)} \\newline &amp; \\rightarrow -1 \\end{aligned} \\] <p>一方、数値 0 の符号付き絶対値表現には \\(+0\\) と \\(-0\\) の 2 つの表し方があります。つまり、数値 0 に対して異なる 2 つの二進コードが対応しており、これは曖昧さの原因になります。たとえば条件判定で正のゼロと負のゼロを区別しないと、誤った判定結果になる可能性があります。また、この曖昧さを解消しようとすると追加の判定処理が必要になり、計算効率が下がるおそれがあります。</p> \\[ \\begin{aligned} +0 &amp; \\rightarrow 0000 \\; 0000 \\newline -0 &amp; \\rightarrow 1000 \\; 0000 \\end{aligned} \\] <p>符号付き絶対値表現と同様に、1 の補数にも正負のゼロの曖昧さがあります。そこでコンピュータはさらに2 の補数（2's complement）を導入しました。まずは負のゼロについて、符号付き絶対値表現、1 の補数、2 の補数の変換を見てみましょう。</p> \\[ \\begin{aligned} -0 \\rightarrow \\; &amp; 1000 \\; 0000 \\; \\text{(符号付き絶対値表現)} \\newline = \\; &amp; 1111 \\; 1111 \\; \\text{(1 の補数)} \\newline = 1 \\; &amp; 0000 \\; 0000 \\; \\text{(2 の補数)} \\newline \\end{aligned} \\] <p>負のゼロの 1 の補数に \\(1\\) を加えると桁上がりが発生しますが、<code>byte</code> 型の長さは 8 ビットしかないため、第 9 ビットへあふれた \\(1\\) は捨てられます。つまり、負のゼロの 2 の補数は \\(0000 \\; 0000\\) であり、正のゼロの 2 の補数と同じです。そのため、2 の補数表現ではゼロは 1 つしか存在せず、正負のゼロの曖昧さは解消されます。</p> <p>最後にもう 1 つ疑問が残ります。<code>byte</code> 型の値域は \\([-128, 127]\\) ですが、余分にある負数 \\(-128\\) はどのように得られるのでしょうか。区間 \\([-127, +127]\\) にあるすべての整数には、それぞれ対応する符号付き絶対値表現、1 の補数、2 の補数があり、符号付き絶対値表現と 2 の補数の間は相互に変換できます。</p> <p>しかし、2 の補数 \\(1000 \\; 0000\\) だけは例外で、対応する符号付き絶対値表現を持ちません。変換規則に従うと、この 2 の補数に対応する符号付き絶対値表現は \\(0000 \\; 0000\\) になります。これは明らかに矛盾しています。なぜなら、この符号付き絶対値表現は数値 \\(0\\) を表し、その 2 の補数は自分自身であるはずだからです。コンピュータでは、この特別な 2 の補数 \\(1000 \\; 0000\\) を \\(-128\\) と定めています。実際、2 の補数での \\((-1) + (-127)\\) の計算結果はちょうど \\(-128\\) になります。</p> \\[ \\begin{aligned} &amp; (-127) + (-1) \\newline &amp; \\rightarrow 1111 \\; 1111 \\; \\text{(符号付き絶対値表現)} + 1000 \\; 0001 \\; \\text{(符号付き絶対値表現)} \\newline &amp; = 1000 \\; 0000 \\; \\text{(1 の補数)} + 1111  \\; 1110 \\; \\text{(1 の補数)} \\newline &amp; = 1000 \\; 0001 \\; \\text{(2 の補数)} + 1111  \\; 1111 \\; \\text{(2 の補数)} \\newline &amp; = 1000 \\; 0000 \\; \\text{(2 の補数)} \\newline &amp; \\rightarrow -128 \\end{aligned} \\] <p>すでにお気づきかもしれませんが、上の計算はすべて加算です。これは重要な事実を示しています。**コンピュータ内部のハードウェア回路は、主として加算を基準に設計されている**のです。なぜなら、加算はほかの演算（乗算、除算、減算など）に比べてハードウェアで実装しやすく、並列化もしやすく、演算速度も速いからです。</p> <p>ただし、これはコンピュータが加算しかできないという意味ではありません。加算といくつかの基本的な論理演算を組み合わせることで、コンピュータはさまざまな数学演算を実現できます。たとえば減算 \\(a - b\\) は加算 \\(a + (-b)\\) に変換できますし、乗算や除算も繰り返しの加算または減算に変換できます。</p> <p>これで、コンピュータが 2 の補数を使う理由をまとめられます。2 の補数表現に基づけば、コンピュータは同じ回路と操作で正数と負数の加算を扱うことができ、減算専用の特別なハードウェア回路を設計する必要がなく、正負のゼロの曖昧さも特別に処理しなくて済みます。これにより、ハードウェア設計は大幅に簡略化され、演算効率も向上します。</p> <p>2 の補数の設計は非常に巧妙ですが、紙幅の都合上ここまでにします。興味のある読者は、さらに深く調べてみてください。</p>","path":["第 3 章 &nbsp; データ構造","3.3 &nbsp; 数値エンコーディング *"],"tags":[]},{"location":"chapter_data_structure/number_encoding/#332","level":2,"title":"3.3.2   浮動小数点数のエンコーディング","text":"<p>注意深い人なら気づくかもしれません。<code>int</code> と <code>float</code> はどちらも長さが 4 バイトで同じなのに、なぜ <code>float</code> の値域は <code>int</code> よりはるかに広いのでしょうか。これはかなり直感に反します。というのも、<code>float</code> は小数を表す必要があるので、本来なら値域は狭くなるはずだからです。</p> <p>実際には、これは浮動小数点数 <code>float</code> が異なる表現方法を採用しているためです。32 ビット長の二進数を次のように表します。</p> \\[ b_{31} b_{30} b_{29} \\ldots b_2 b_1 b_0 \\] <p>IEEE 754 標準によれば、32-bit 長の <code>float</code> は次の 3 つの部分から構成されます。</p> <ul> <li>符号部 \\(\\mathrm{S}\\) ：1 ビットを占め、\\(b_{31}\\) に対応します。</li> <li>指数部 \\(\\mathrm{E}\\) ：8 ビットを占め、\\(b_{30} b_{29} \\ldots b_{23}\\) に対応します。</li> <li>仮数部 \\(\\mathrm{N}\\) ：23 ビットを占め、\\(b_{22} b_{21} \\ldots b_0\\) に対応します。</li> </ul> <p>二進数 <code>float</code> に対応する値は次式で計算されます。</p> \\[ \\text {val} = (-1)^{b_{31}} \\times 2^{\\left(b_{30} b_{29} \\ldots b_{23}\\right)_2-127} \\times\\left(1 . b_{22} b_{21} \\ldots b_0\\right)_2 \\] <p>十進数に直すと、計算式は次のようになります。</p> \\[ \\text {val}=(-1)^{\\mathrm{S}} \\times 2^{\\mathrm{E} -127} \\times (1 + \\mathrm{N}) \\] <p>各項の取り得る範囲は次のとおりです。</p> \\[ \\begin{aligned} \\mathrm{S} \\in &amp; \\{ 0, 1\\}, \\quad \\mathrm{E} \\in \\{ 1, 2, \\dots, 254 \\} \\newline (1 + \\mathrm{N}) = &amp; (1 + \\sum_{i=1}^{23} b_{23-i} 2^{-i}) \\subset [1, 2 - 2^{-23}] \\end{aligned} \\] <p></p> <p> 図 3-5   IEEE 754 標準における float の計算例 </p> <p>上図を見ると、例として \\(\\mathrm{S} = 0\\) 、 \\(\\mathrm{E} = 124\\) 、\\(\\mathrm{N} = 2^{-2} + 2^{-3} = 0.375\\) が与えられた場合、次のようになります。</p> \\[ \\text { val } = (-1)^0 \\times 2^{124 - 127} \\times (1 + 0.375) = 0.171875 \\] <p>これで最初の疑問に答えられます。**<code>float</code> の表現方法には指数部が含まれているため、その値域は <code>int</code> よりはるかに広い**のです。上の計算より、<code>float</code> が表せる最大の正数は \\(2^{254 - 127} \\times (2 - 2^{-23}) \\approx 3.4 \\times 10^{38}\\) であり、符号ビットを切り替えれば最小の負数が得られます。</p> <p>浮動小数点数 <code>float</code> は値域を広げる一方で、その代償として精度を犠牲にしています。整数型 <code>int</code> は 32 ビットすべてを数値の表現に使うため、数値は一様に分布します。しかし指数部があるため、浮動小数点数 <code>float</code> は値が大きくなるほど、隣り合う 2 つの数の差も大きくなる傾向があります。</p> <p>次の表のとおり、指数部 \\(\\mathrm{E} = 0\\) と \\(\\mathrm{E} = 255\\) には特別な意味があり、ゼロ、無限大、\\(\\mathrm{NaN}\\) などを表すために使われます。</p> <p> 表 3-2   指数部の意味 </p> 指数部 E 仮数部 \\(\\mathrm{N} = 0\\) 仮数部 \\(\\mathrm{N} \\ne 0\\) 計算式 \\(0\\) \\(\\pm 0\\) 非正規化数 \\((-1)^{\\mathrm{S}} \\times 2^{-126} \\times (0.\\mathrm{N})\\) \\(1, 2, \\dots, 254\\) 正規化数 正規化数 \\((-1)^{\\mathrm{S}} \\times 2^{(\\mathrm{E} -127)} \\times (1.\\mathrm{N})\\) \\(255\\) \\(\\pm \\infty\\) \\(\\mathrm{NaN}\\) <p>なお、非正規化数によって浮動小数点数の精度は大きく向上します。最小の正の正規化数は \\(2^{-126}\\) であり、最小の正の非正規化数は \\(2^{-126} \\times 2^{-23}\\) です。</p> <p>倍精度 <code>double</code> も <code>float</code> と同様の表現方法を採用しているため、ここでは詳述しません。</p>","path":["第 3 章 &nbsp; データ構造","3.3 &nbsp; 数値エンコーディング *"],"tags":[]},{"location":"chapter_data_structure/summary/","level":1,"title":"3.5   まとめ","text":"","path":["第 3 章 &nbsp; データ構造","3.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_data_structure/summary/#1","level":3,"title":"1.   重要ポイントの振り返り","text":"<ul> <li>データ構造は、論理構造と物理構造という 2 つの観点から分類できます。論理構造はデータ要素間の論理的関係を記述し、物理構造はデータのコンピュータメモリ上での格納方法を記述します。</li> <li>代表的な論理構造には、線形、木構造、網状構造などがあります。通常、論理構造に基づいてデータ構造を線形（配列、連結リスト、スタック、キュー）と非線形（木、グラフ、ヒープ）の 2 種類に分類します。ハッシュテーブルの実装には、線形データ構造と非線形データ構造が同時に含まれる場合があります。</li> <li>プログラムの実行時、データはコンピュータメモリに格納されます。各メモリ空間には対応するメモリアドレスがあり、プログラムはそれらのメモリアドレスを通じてデータにアクセスします。</li> <li>物理構造は主に連続領域への格納（配列）と分散領域への格納（連結リスト）に分けられます。すべてのデータ構造は、配列、連結リスト、またはその両方の組み合わせによって実装されます。</li> <li>コンピュータにおける基本データ型には、整数 <code>byte</code>、<code>short</code>、<code>int</code>、<code>long</code>、浮動小数点数 <code>float</code>、<code>double</code>、文字 <code>char</code>、真偽値 <code>bool</code> があります。これらの値域は、使用する記憶領域の大きさと表現方式によって決まります。</li> <li>符号付き絶対値表現、1 の補数、2 の補数は、コンピュータで数値を符号化する 3 つの方法であり、相互に変換できます。整数の符号付き絶対値表現では最上位ビットが符号ビットで、残りのビットが数値の値です。</li> <li>整数はコンピュータ内では 2 の補数の形式で格納されます。2 の補数表現では、コンピュータは正数と負数の加算を同じように扱うことができ、減算のために特別なハードウェア回路を別途設計する必要がなく、さらに正負のゼロが重複する問題もありません。</li> <li>浮動小数点数の符号化は、1 ビットの符号部、8 ビットの指数部、23 ビットの仮数部で構成されます。指数部があるため、浮動小数点数の値域は整数よりはるかに広くなりますが、その代償として精度が犠牲になります。</li> <li>ASCII コードは最も早く登場した英字文字集合で、長さは 1 バイト、収録文字数は 127 です。GBK 文字集合はよく使われる中国語文字集合で、2 万字以上の漢字を収録しています。Unicode は完全な文字集合標準を提供することを目指しており、世界中のさまざまな言語の文字を収録することで、文字コード方式の不一致によって生じる文字化けの問題を解決します。</li> <li>UTF-8 は最も広く使われている Unicode の符号化方式で、汎用性が非常に高いです。可変長の符号化方式であり、拡張性に優れ、記憶領域の利用効率を効果的に高めます。UTF-16 と UTF-32 は固定長の符号化方式です。中国語を符号化する場合、UTF-16 は UTF-8 よりも使用領域が小さくなります。Java や C# などのプログラミング言語は、デフォルトで UTF-16 を使用します。</li> </ul>","path":["第 3 章 &nbsp; データ構造","3.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_data_structure/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q：なぜハッシュテーブルには線形データ構造と非線形データ構造が同時に含まれるのですか？</p> <p>ハッシュテーブルの基盤は配列であり、ハッシュ衝突を解決するために「チェイン法」（後続の「ハッシュ衝突」の章で説明します）を使うことがあります。配列内の各バケットは 1 つの連結リストを指し、その連結リストの長さがある閾値を超えると、木（通常は赤黒木）に変換されることもあります。</p> <p>格納の観点から見ると、ハッシュテーブルの基盤は配列であり、各バケットスロットには値が入ることもあれば、連結リストや木が入ることもあります。したがって、ハッシュテーブルには線形データ構造（配列、連結リスト）と非線形データ構造（木）が同時に含まれる場合があります。</p> <p>Q：<code>char</code> 型の長さは 1 バイトですか？</p> <p><code>char</code> 型の長さは、プログラミング言語が採用する符号化方式によって決まります。たとえば、Java、JavaScript、TypeScript、C# はいずれも UTF-16 符号化（Unicode コードポイントを保持）を採用しているため、<code>char</code> 型の長さは 2 バイトです。</p> <p>Q：配列ベースで実装されたデータ構造を「静的データ構造」と呼ぶのは曖昧ではありませんか？ スタックも push や pop などの操作ができ、これらの操作はどれも「動的」です。</p> <p>スタックは確かに動的なデータ操作を実現できますが、データ構造自体は依然として「静的」（長さが不変）です。配列ベースのデータ構造でも要素を動的に追加または削除できますが、その容量は固定です。データ量が事前に確保した大きさを超えた場合は、より大きな新しい配列を作成し、古い配列の内容を新しい配列にコピーする必要があります。</p> <p>Q：スタック（キュー）を構築するときにサイズを指定していないのに、なぜそれらは「静的データ構造」なのですか？</p> <p>高水準プログラミング言語では、スタック（キュー）の初期容量を人手で指定する必要はなく、この作業はクラス内部で自動的に行われます。たとえば、Java の <code>ArrayList</code> の初期容量は通常 10 です。また、容量拡張も自動的に実装されています。詳しくは後続の「リスト」の章を参照してください。</p> <p>Q：符号付き絶対値表現から 2 の補数への変換方法は「先にビット反転してから 1 を加える」ですが、2 の補数から符号付き絶対値表現への変換は逆演算である「先に 1 を引いてからビット反転する」べきなのに、同じく「先にビット反転してから 1 を加える」でも求められます。これはなぜですか？</p> <p>これは、符号付き絶対値表現と 2 の補数の相互変換が、実際には「補数」を計算する過程だからです。まず補数の定義を示します。\\(a + b = c\\) とすると、\\(a\\) を \\(b\\) から \\(c\\) への補数と呼び、逆に \\(b\\) も \\(a\\) から \\(c\\) への補数と呼びます。</p> <p>長さ \\(n = 4\\) ビットの 2 進数 \\(0010\\) が与えられたとします。この数を符号付き絶対値表現（符号ビットは考慮しない）とみなすと、その 2 の補数は「先にビット反転してから 1 を加える」ことで得られます。</p> \\[ 0010 \\rightarrow 1101 \\rightarrow 1110 \\] <p>ここで、符号付き絶対値表現と 2 の補数の和は \\(0010 + 1110 = 10000\\) となります。つまり、2 の補数 \\(1110\\) は符号付き絶対値表現 \\(0010\\) から \\(10000\\) への「補数」です。これは、上記の「先にビット反転してから 1 を加える」が、実際には \\(10000\\) への補数を計算する過程であることを意味します。</p> <p>では、2 の補数 \\(1110\\) から \\(10000\\) への「補数」はいくつでしょうか。これもやはり「先にビット反転してから 1 を加える」ことで求められます。</p> \\[ 1110 \\rightarrow 0001 \\rightarrow 0010 \\] <p>言い換えると、符号付き絶対値表現と 2 の補数は互いに相手から \\(10000\\) への「補数」なので、「符号付き絶対値表現から 2 の補数への変換」と「2 の補数から符号付き絶対値表現への変換」は同じ操作（先にビット反転してから 1 を加える）で実現できます。</p> <p>もちろん、逆演算を用いて 2 の補数 \\(1110\\) の符号付き絶対値表現を求めることもでき、その場合は「先に 1 を引いてからビット反転する」ことになります。</p> \\[ 1110 \\rightarrow 1101 \\rightarrow 0010 \\] <p>まとめると、「先にビット反転してから 1 を加える」と「先に 1 を引いてからビット反転する」の 2 つの演算は、どちらも \\(10000\\) への補数を計算しており、等価です。</p> <p>本質的には、「ビット反転」という操作は実際には \\(1111\\) への補数を求めています（常に <code>符号付き絶対値表現 + 1 の補数 = 1111</code> が成り立つため）。そして、1 の補数にさらに 1 を加えて得られる 2 の補数が、\\(10000\\) への補数です。</p> <p>上記では \\(n = 4\\) を例にしましたが、この考え方は任意のビット長の 2 進数に一般化できます。</p>","path":["第 3 章 &nbsp; データ構造","3.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_divide_and_conquer/","level":1,"title":"第 12 章   分割統治","text":"<p>Abstract</p> <p>難題は段階的に分解され、そのたびにより単純になっていく。</p> <p>分割統治は一つの重要な事実を示している。単純なことから始めれば、すべてはもはや複雑ではない。</p>","path":["第 12 章 &nbsp; 分割統治"],"tags":[]},{"location":"chapter_divide_and_conquer/#_1","level":2,"title":"章の内容","text":"<ul> <li>12.1   分割統治法</li> <li>12.2   分割統治探索戦略</li> <li>12.3   二分木の構築問題</li> <li>12.4   ハノイの塔の問題</li> <li>12.5   まとめ</li> </ul>","path":["第 12 章 &nbsp; 分割統治"],"tags":[]},{"location":"chapter_divide_and_conquer/binary_search_recur/","level":1,"title":"12.2   分割統治探索戦略","text":"<p>私たちはすでに学んだように、探索アルゴリズムは大きく二つに分けられる。</p> <ul> <li>力ずく探索：データ構造を走査することで実現され、時間計算量は \\(O(n)\\) である。</li> <li>適応的探索：固有のデータ構造や事前情報を利用し、時間計算量は \\(O(\\log n)\\) 、さらには \\(O(1)\\) に達しうる。</li> </ul> <p>実際、時間計算量が \\(O(\\log n)\\) の探索アルゴリズムは通常、分割統治戦略に基づいて実装される。たとえば二分探索や木構造である。</p> <ul> <li>二分探索の各ステップでは、問題（配列内で目標要素を探索すること）を小さな問題（配列の半分で目標要素を探索すること）に分解し、この過程は配列が空になるか目標要素が見つかるまで続く。</li> <li>木構造は分割統治の考え方を代表するものであり、二分探索木、AVL 木、ヒープなどのデータ構造では、さまざまな操作の時間計算量はいずれも \\(O(\\log n)\\) である。</li> </ul> <p>二分探索の分割統治戦略は以下のとおりである。</p> <ul> <li>問題は分解できる：二分探索は、元の問題（配列内で探索すること）を部分問題（配列の半分で探索すること）へ再帰的に分解する。これは中央要素と目標要素を比較することで実現される。</li> <li>部分問題は独立している：二分探索では、各ラウンドで一つの部分問題だけを処理し、ほかの部分問題の影響を受けない。</li> <li>部分問題の解を統合する必要はない：二分探索は特定の要素を探すことを目的としているため、部分問題の解を統合する必要がない。部分問題が解決されると、元の問題も同時に解決される。</li> </ul> <p>分割統治が探索効率を高められる本質的な理由は、力ずく探索では各ラウンドで一つの候補しか除外できないのに対し、**分割統治による探索では各ラウンドで候補の半分を除外できる**からである。</p>","path":["第 12 章 &nbsp; 分割統治","12.2 &nbsp; 分割統治探索戦略"],"tags":[]},{"location":"chapter_divide_and_conquer/binary_search_recur/#1","level":3,"title":"1.   分割統治に基づく二分探索","text":"<p>前の章では、二分探索を漸化式（反復）に基づいて実装した。ここでは分割統治（再帰）に基づいてこれを実装する。</p> <p>Question</p> <p>長さ \\(n\\) の昇順配列 <code>nums</code> が与えられ、そのすべての要素は一意である。要素 <code>target</code> を探索せよ。</p> <p>分割統治の観点から、探索区間 \\([i, j]\\) に対応する部分問題を \\(f(i, j)\\) と記す。</p> <p>元の問題 \\(f(0, n-1)\\) を出発点として、次の手順で二分探索を行う。</p> <ol> <li>探索区間 \\([i, j]\\) の中点 \\(m\\) を計算し、それに基づいて探索区間の半分を除外する。</li> <li>規模が半分に縮小された部分問題を再帰的に解く。候補は \\(f(i, m-1)\\) または \\(f(m+1, j)\\) である。</li> <li><code>1.</code> と <code>2.</code> の手順を繰り返し、<code>target</code> が見つかるか区間が空になったら返す。</li> </ol> <p>次の図は、配列内で要素 \\(6\\) を二分探索する分割統治の過程を示している。</p> <p></p> <p> 図 12-4   二分探索の分割統治の過程 </p> <p>実装コードでは、再帰関数 <code>dfs()</code> を宣言して問題 \\(f(i, j)\\) を解く。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_recur.py<pre><code>def dfs(nums: list[int], target: int, i: int, j: int) -&gt; int:\n    \"\"\"二分探索：問題 f(i, j)\"\"\"\n    # 区間が空なら対象要素は存在しないので -1 を返す\n    if i &gt; j:\n        return -1\n    # 中点インデックス m を計算\n    m = (i + j) // 2\n    if nums[m] &lt; target:\n        # 部分問題 f(m+1, j) を再帰的に解く\n        return dfs(nums, target, m + 1, j)\n    elif nums[m] &gt; target:\n        # 部分問題 f(i, m-1) を再帰的に解く\n        return dfs(nums, target, i, m - 1)\n    else:\n        # 目標要素が見つかったらそのインデックスを返す\n        return m\n\ndef binary_search(nums: list[int], target: int) -&gt; int:\n    \"\"\"二分探索\"\"\"\n    n = len(nums)\n    # 問題 f(0, n-1) を解く\n    return dfs(nums, target, 0, n - 1)\n</code></pre> binary_search_recur.cpp<pre><code>/* 二分探索：問題 f(i, j) */\nint dfs(vector&lt;int&gt; &amp;nums, int target, int i, int j) {\n    // 区間が空なら対象要素は存在しないので -1 を返す\n    if (i &gt; j) {\n        return -1;\n    }\n    // 中点インデックス m を計算\n    int m = (i + j) / 2;\n    if (nums[m] &lt; target) {\n        // 部分問題 f(m+1, j) を再帰的に解く\n        return dfs(nums, target, m + 1, j);\n    } else if (nums[m] &gt; target) {\n        // 部分問題 f(i, m-1) を再帰的に解く\n        return dfs(nums, target, i, m - 1);\n    } else {\n        // 目標要素が見つかったらそのインデックスを返す\n        return m;\n    }\n}\n\n/* 二分探索 */\nint binarySearch(vector&lt;int&gt; &amp;nums, int target) {\n    int n = nums.size();\n    // 問題 f(0, n-1) を解く\n    return dfs(nums, target, 0, n - 1);\n}\n</code></pre> binary_search_recur.java<pre><code>/* 二分探索：問題 f(i, j) */\nint dfs(int[] nums, int target, int i, int j) {\n    // 区間が空なら対象要素は存在しないので -1 を返す\n    if (i &gt; j) {\n        return -1;\n    }\n    // 中点インデックス m を計算\n    int m = (i + j) / 2;\n    if (nums[m] &lt; target) {\n        // 部分問題 f(m+1, j) を再帰的に解く\n        return dfs(nums, target, m + 1, j);\n    } else if (nums[m] &gt; target) {\n        // 部分問題 f(i, m-1) を再帰的に解く\n        return dfs(nums, target, i, m - 1);\n    } else {\n        // 目標要素が見つかったらそのインデックスを返す\n        return m;\n    }\n}\n\n/* 二分探索 */\nint binarySearch(int[] nums, int target) {\n    int n = nums.length;\n    // 問題 f(0, n-1) を解く\n    return dfs(nums, target, 0, n - 1);\n}\n</code></pre> binary_search_recur.cs<pre><code>/* 二分探索：問題 f(i, j) */\nint DFS(int[] nums, int target, int i, int j) {\n    // 区間が空なら対象要素は存在しないので -1 を返す\n    if (i &gt; j) {\n        return -1;\n    }\n    // 中点インデックス m を計算\n    int m = (i + j) / 2;\n    if (nums[m] &lt; target) {\n        // 部分問題 f(m+1, j) を再帰的に解く\n        return DFS(nums, target, m + 1, j);\n    } else if (nums[m] &gt; target) {\n        // 部分問題 f(i, m-1) を再帰的に解く\n        return DFS(nums, target, i, m - 1);\n    } else {\n        // 目標要素が見つかったらそのインデックスを返す\n        return m;\n    }\n}\n\n/* 二分探索 */\nint BinarySearch(int[] nums, int target) {\n    int n = nums.Length;\n    // 問題 f(0, n-1) を解く\n    return DFS(nums, target, 0, n - 1);\n}\n</code></pre> binary_search_recur.go<pre><code>/* 二分探索：問題 f(i, j) */\nfunc dfs(nums []int, target, i, j int) int {\n    // 区間が空なら対象要素は存在しないため、-1 を返す\n    if i &gt; j {\n        return -1\n    }\n    // 中点インデックスを計算する\n    m := i + ((j - i) &gt;&gt; 1)\n    // 中点の要素と目標要素の大小を判定する\n    if nums[m] &lt; target {\n        // 小さければ右半分の配列を再帰\n        // 部分問題 f(m+1, j) を解く\n        return dfs(nums, target, m+1, j)\n    } else if nums[m] &gt; target {\n        // 大きければ左半分の配列を再帰\n        // 部分問題 f(i, m-1) を解く\n        return dfs(nums, target, i, m-1)\n    } else {\n        // 目標要素が見つかったらそのインデックスを返す\n        return m\n    }\n}\n\n/* 二分探索 */\nfunc binarySearch(nums []int, target int) int {\n    n := len(nums)\n    return dfs(nums, target, 0, n-1)\n}\n</code></pre> binary_search_recur.swift<pre><code>/* 二分探索：問題 f(i, j) */\nfunc dfs(nums: [Int], target: Int, i: Int, j: Int) -&gt; Int {\n    // 区間が空なら対象要素は存在しないので -1 を返す\n    if i &gt; j {\n        return -1\n    }\n    // 中点インデックス m を計算\n    let m = (i + j) / 2\n    if nums[m] &lt; target {\n        // 部分問題 f(m+1, j) を再帰的に解く\n        return dfs(nums: nums, target: target, i: m + 1, j: j)\n    } else if nums[m] &gt; target {\n        // 部分問題 f(i, m-1) を再帰的に解く\n        return dfs(nums: nums, target: target, i: i, j: m - 1)\n    } else {\n        // 目標要素が見つかったらそのインデックスを返す\n        return m\n    }\n}\n\n/* 二分探索 */\nfunc binarySearch(nums: [Int], target: Int) -&gt; Int {\n    // 問題 f(0, n-1) を解く\n    dfs(nums: nums, target: target, i: nums.startIndex, j: nums.endIndex - 1)\n}\n</code></pre> binary_search_recur.js<pre><code>/* 二分探索：問題 f(i, j) */\nfunction dfs(nums, target, i, j) {\n    // 区間が空なら対象要素は存在しないので -1 を返す\n    if (i &gt; j) {\n        return -1;\n    }\n    // 中点インデックス m を計算\n    const m = i + ((j - i) &gt;&gt; 1);\n    if (nums[m] &lt; target) {\n        // 部分問題 f(m+1, j) を再帰的に解く\n        return dfs(nums, target, m + 1, j);\n    } else if (nums[m] &gt; target) {\n        // 部分問題 f(i, m-1) を再帰的に解く\n        return dfs(nums, target, i, m - 1);\n    } else {\n        // 目標要素が見つかったらそのインデックスを返す\n        return m;\n    }\n}\n\n/* 二分探索 */\nfunction binarySearch(nums, target) {\n    const n = nums.length;\n    // 問題 f(0, n-1) を解く\n    return dfs(nums, target, 0, n - 1);\n}\n</code></pre> binary_search_recur.ts<pre><code>/* 二分探索：問題 f(i, j) */\nfunction dfs(nums: number[], target: number, i: number, j: number): number {\n    // 区間が空なら対象要素は存在しないので -1 を返す\n    if (i &gt; j) {\n        return -1;\n    }\n    // 中点インデックス m を計算\n    const m = i + ((j - i) &gt;&gt; 1);\n    if (nums[m] &lt; target) {\n        // 部分問題 f(m+1, j) を再帰的に解く\n        return dfs(nums, target, m + 1, j);\n    } else if (nums[m] &gt; target) {\n        // 部分問題 f(i, m-1) を再帰的に解く\n        return dfs(nums, target, i, m - 1);\n    } else {\n        // 目標要素が見つかったらそのインデックスを返す\n        return m;\n    }\n}\n\n/* 二分探索 */\nfunction binarySearch(nums: number[], target: number): number {\n    const n = nums.length;\n    // 問題 f(0, n-1) を解く\n    return dfs(nums, target, 0, n - 1);\n}\n</code></pre> binary_search_recur.dart<pre><code>/* 二分探索：問題 f(i, j) */\nint dfs(List&lt;int&gt; nums, int target, int i, int j) {\n  // 区間が空なら対象要素は存在しないので -1 を返す\n  if (i &gt; j) {\n    return -1;\n  }\n  // 中点インデックス m を計算\n  int m = (i + j) ~/ 2;\n  if (nums[m] &lt; target) {\n    // 部分問題 f(m+1, j) を再帰的に解く\n    return dfs(nums, target, m + 1, j);\n  } else if (nums[m] &gt; target) {\n    // 部分問題 f(i, m-1) を再帰的に解く\n    return dfs(nums, target, i, m - 1);\n  } else {\n    // 目標要素が見つかったらそのインデックスを返す\n    return m;\n  }\n}\n\n/* 二分探索 */\nint binarySearch(List&lt;int&gt; nums, int target) {\n  int n = nums.length;\n  // 問題 f(0, n-1) を解く\n  return dfs(nums, target, 0, n - 1);\n}\n</code></pre> binary_search_recur.rs<pre><code>/* 二分探索：問題 f(i, j) */\nfn dfs(nums: &amp;[i32], target: i32, i: i32, j: i32) -&gt; i32 {\n    // 区間が空なら対象要素は存在しないので -1 を返す\n    if i &gt; j {\n        return -1;\n    }\n    let m: i32 = i + (j - i) / 2;\n    if nums[m as usize] &lt; target {\n        // 部分問題 f(m+1, j) を再帰的に解く\n        return dfs(nums, target, m + 1, j);\n    } else if nums[m as usize] &gt; target {\n        // 部分問題 f(i, m-1) を再帰的に解く\n        return dfs(nums, target, i, m - 1);\n    } else {\n        // 目標要素が見つかったらそのインデックスを返す\n        return m;\n    }\n}\n\n/* 二分探索 */\nfn binary_search(nums: &amp;[i32], target: i32) -&gt; i32 {\n    let n = nums.len() as i32;\n    // 問題 f(0, n-1) を解く\n    dfs(nums, target, 0, n - 1)\n}\n</code></pre> binary_search_recur.c<pre><code>/* 二分探索：問題 f(i, j) */\nint dfs(int nums[], int target, int i, int j) {\n    // 区間が空なら対象要素は存在しないので -1 を返す\n    if (i &gt; j) {\n        return -1;\n    }\n    // 中点インデックス m を計算\n    int m = (i + j) / 2;\n    if (nums[m] &lt; target) {\n        // 部分問題 f(m+1, j) を再帰的に解く\n        return dfs(nums, target, m + 1, j);\n    } else if (nums[m] &gt; target) {\n        // 部分問題 f(i, m-1) を再帰的に解く\n        return dfs(nums, target, i, m - 1);\n    } else {\n        // 目標要素が見つかったらそのインデックスを返す\n        return m;\n    }\n}\n\n/* 二分探索 */\nint binarySearch(int nums[], int target, int numsSize) {\n    int n = numsSize;\n    // 問題 f(0, n-1) を解く\n    return dfs(nums, target, 0, n - 1);\n}\n</code></pre> binary_search_recur.kt<pre><code>/* 二分探索：問題 f(i, j) */\nfun dfs(\n    nums: IntArray,\n    target: Int,\n    i: Int,\n    j: Int\n): Int {\n    // 区間が空なら対象要素は存在しないので -1 を返す\n    if (i &gt; j) {\n        return -1\n    }\n    // 中点インデックス m を計算\n    val m = (i + j) / 2\n    return if (nums[m] &lt; target) {\n        // 部分問題 f(m+1, j) を再帰的に解く\n        dfs(nums, target, m + 1, j)\n    } else if (nums[m] &gt; target) {\n        // 部分問題 f(i, m-1) を再帰的に解く\n        dfs(nums, target, i, m - 1)\n    } else {\n        // 目標要素が見つかったらそのインデックスを返す\n        m\n    }\n}\n\n/* 二分探索 */\nfun binarySearch(nums: IntArray, target: Int): Int {\n    val n = nums.size\n    // 問題 f(0, n-1) を解く\n    return dfs(nums, target, 0, n - 1)\n}\n</code></pre> binary_search_recur.rb<pre><code>### 二分探索: 問題 f(i, j) ###\ndef dfs(nums, target, i, j)\n  # 区間が空なら対象要素は存在しないので -1 を返す\n  return -1 if i &gt; j\n\n  # 中点インデックス m を計算\n  m = (i + j) / 2\n\n  if nums[m] &lt; target\n    # 部分問題 f(m+1, j) を再帰的に解く\n    return dfs(nums, target, m + 1, j)\n  elsif nums[m] &gt; target\n    # 部分問題 f(i, m-1) を再帰的に解く\n    return dfs(nums, target, i, m - 1)\n  else\n    # 目標要素が見つかったらそのインデックスを返す\n    return m\n  end\nend\n\n### 二分探索 ###\ndef binary_search(nums, target)\n  n = nums.length\n  # 問題 f(0, n-1) を解く\n  dfs(nums, target, 0, n - 1)\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 12 章 &nbsp; 分割統治","12.2 &nbsp; 分割統治探索戦略"],"tags":[]},{"location":"chapter_divide_and_conquer/build_binary_tree_problem/","level":1,"title":"12.3   二分木の構築問題","text":"<p>Question</p> <p>二分木の前順走査 <code>preorder</code> と中順走査 <code>inorder</code> が与えられたとき、これらから二分木を構築し、その根ノードを返してください。二分木には値が重複するノードが存在しないものとします（下図のとおり）。</p> <p></p> <p> 図 12-5   二分木を構築する例のデータ </p>","path":["第 12 章 &nbsp; 分割統治","12.3 &nbsp; 二分木の構築問題"],"tags":[]},{"location":"chapter_divide_and_conquer/build_binary_tree_problem/#1","level":3,"title":"1.   分割統治問題かどうかを判断する","text":"<p>元の問題は <code>preorder</code> と <code>inorder</code> から二分木を構築することであり、典型的な分割統治問題です。</p> <ul> <li>問題は分解できる：分割統治の観点から見ると、元の問題は 2 つの部分問題、すなわち左部分木の構築と右部分木の構築に分けられ、さらに根ノードを初期化する 1 ステップが加わります。各部分木（部分問題）に対しても、同じ分割方法を再利用してより小さな部分木（部分問題）へと分けていき、最小の部分問題（空部分木）に達した時点で終了します。</li> <li>部分問題は独立している：左部分木と右部分木は互いに独立しており、両者の間に重なりはありません。左部分木を構築するときは、中順走査と前順走査のうち左部分木に対応する部分だけを見れば十分です。右部分木も同様です。</li> <li>部分問題の解は統合できる：左部分木と右部分木（部分問題の解）が得られたら、それらを根ノードに接続することで元の問題の解を得られます。</li> </ul>","path":["第 12 章 &nbsp; 分割統治","12.3 &nbsp; 二分木の構築問題"],"tags":[]},{"location":"chapter_divide_and_conquer/build_binary_tree_problem/#2","level":3,"title":"2.   部分木をどのように分割するか","text":"<p>以上の分析より、この問題は分割統治で解けます。では、前順走査 <code>preorder</code> と中順走査 <code>inorder</code> を使って左部分木と右部分木をどのように分割すればよいのでしょうか？</p> <p>定義に従うと、<code>preorder</code> と <code>inorder</code> はいずれも 3 つの部分に分けられます。</p> <ul> <li>前順走査：<code>[ 根ノード | 左部分木 | 右部分木 ]</code> ，例えば上図の木は <code>[ 3 | 9 | 2 1 7 ]</code> に対応します。</li> <li>中順走査：<code>[ 左部分木 | 根ノード ｜ 右部分木 ]</code> ，例えば上図の木は <code>[ 9 | 3 | 1 2 7 ]</code> に対応します。</li> </ul> <p>上図のデータを例にすると、下図の手順によって分割結果を得られます。</p> <ol> <li>前順走査の先頭要素 3 が根ノードの値です。</li> <li>根ノード 3 の <code>inorder</code> におけるインデックスを探すと、そのインデックスを用いて <code>inorder</code> を <code>[ 9 | 3 ｜ 1 2 7 ]</code> に分割できます。</li> <li><code>inorder</code> の分割結果から、左部分木と右部分木のノード数はそれぞれ 1 と 3 であることがわかり、したがって <code>preorder</code> を <code>[ 3 | 9 | 2 1 7 ]</code> に分割できます。</li> </ol> <p></p> <p> 図 12-6   前順走査と中順走査で部分木を分割する </p>","path":["第 12 章 &nbsp; 分割統治","12.3 &nbsp; 二分木の構築問題"],"tags":[]},{"location":"chapter_divide_and_conquer/build_binary_tree_problem/#3","level":3,"title":"3.   変数を用いて部分木区間を記述する","text":"<p>以上の分割方法により、**根ノード、左部分木、右部分木が <code>preorder</code> と <code>inorder</code> の中で占めるインデックス区間**が得られました。これらのインデックス区間を表すために、いくつかのポインタ変数を導入します。</p> <ul> <li>現在の木の根ノードが <code>preorder</code> に現れるインデックスを \\(i\\) とします。</li> <li>現在の木の根ノードが <code>inorder</code> に現れるインデックスを \\(m\\) とします。</li> <li>現在の木が <code>inorder</code> において占めるインデックス区間を \\([l, r]\\) とします。</li> </ul> <p>次の表のように、これらの変数を用いれば根ノードの <code>preorder</code> におけるインデックスと、部分木の <code>inorder</code> におけるインデックス区間を表せます。</p> <p> 表 12-1   根ノードと部分木の前順走査・中順走査におけるインデックス </p> 根ノードの <code>preorder</code> におけるインデックス 部分木の <code>inorder</code> におけるインデックス区間 現在の木 \\(i\\) \\([l, r]\\) 左部分木 \\(i + 1\\) \\([l, m-1]\\) 右部分木 \\(i + 1 + (m - l)\\) \\([m+1, r]\\) <p>右部分木の根ノードのインデックスにある \\((m-l)\\) は「左部分木のノード数」を意味します。下図と合わせて理解することを勧めます。</p> <p></p> <p> 図 12-7   根ノードと左右部分木のインデックス区間の表し方 </p>","path":["第 12 章 &nbsp; 分割統治","12.3 &nbsp; 二分木の構築問題"],"tags":[]},{"location":"chapter_divide_and_conquer/build_binary_tree_problem/#4","level":3,"title":"4.   コードの実装","text":"<p>\\(m\\) の検索効率を高めるために、ハッシュテーブル <code>hmap</code> を用いて配列 <code>inorder</code> の要素からインデックスへの対応を保存します。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby build_tree.py<pre><code>def dfs(\n    preorder: list[int],\n    inorder_map: dict[int, int],\n    i: int,\n    l: int,\n    r: int,\n) -&gt; TreeNode | None:\n    \"\"\"二分木を構築：分割統治\"\"\"\n    # 部分木区間が空なら終了する\n    if r - l &lt; 0:\n        return None\n    # ルートノードを初期化する\n    root = TreeNode(preorder[i])\n    # m を求めて左右部分木を分割する\n    m = inorder_map[preorder[i]]\n    # 部分問題：左部分木を構築する\n    root.left = dfs(preorder, inorder_map, i + 1, l, m - 1)\n    # 部分問題：右部分木を構築する\n    root.right = dfs(preorder, inorder_map, i + 1 + m - l, m + 1, r)\n    # 根ノードを返す\n    return root\n\ndef build_tree(preorder: list[int], inorder: list[int]) -&gt; TreeNode | None:\n    \"\"\"二分木を構築\"\"\"\n    # inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する\n    inorder_map = {val: i for i, val in enumerate(inorder)}\n    root = dfs(preorder, inorder_map, 0, 0, len(inorder) - 1)\n    return root\n</code></pre> build_tree.cpp<pre><code>/* 二分木を構築：分割統治 */\nTreeNode *dfs(vector&lt;int&gt; &amp;preorder, unordered_map&lt;int, int&gt; &amp;inorderMap, int i, int l, int r) {\n    // 部分木区間が空なら終了する\n    if (r - l &lt; 0)\n        return NULL;\n    // ルートノードを初期化する\n    TreeNode *root = new TreeNode(preorder[i]);\n    // m を求めて左右部分木を分割する\n    int m = inorderMap[preorder[i]];\n    // 部分問題：左部分木を構築する\n    root-&gt;left = dfs(preorder, inorderMap, i + 1, l, m - 1);\n    // 部分問題：右部分木を構築する\n    root-&gt;right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r);\n    // 根ノードを返す\n    return root;\n}\n\n/* 二分木を構築 */\nTreeNode *buildTree(vector&lt;int&gt; &amp;preorder, vector&lt;int&gt; &amp;inorder) {\n    // inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する\n    unordered_map&lt;int, int&gt; inorderMap;\n    for (int i = 0; i &lt; inorder.size(); i++) {\n        inorderMap[inorder[i]] = i;\n    }\n    TreeNode *root = dfs(preorder, inorderMap, 0, 0, inorder.size() - 1);\n    return root;\n}\n</code></pre> build_tree.java<pre><code>/* 二分木を構築：分割統治 */\nTreeNode dfs(int[] preorder, Map&lt;Integer, Integer&gt; inorderMap, int i, int l, int r) {\n    // 部分木区間が空なら終了する\n    if (r - l &lt; 0)\n        return null;\n    // ルートノードを初期化する\n    TreeNode root = new TreeNode(preorder[i]);\n    // m を求めて左右部分木を分割する\n    int m = inorderMap.get(preorder[i]);\n    // 部分問題：左部分木を構築する\n    root.left = dfs(preorder, inorderMap, i + 1, l, m - 1);\n    // 部分問題：右部分木を構築する\n    root.right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r);\n    // 根ノードを返す\n    return root;\n}\n\n/* 二分木を構築 */\nTreeNode buildTree(int[] preorder, int[] inorder) {\n    // inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する\n    Map&lt;Integer, Integer&gt; inorderMap = new HashMap&lt;&gt;();\n    for (int i = 0; i &lt; inorder.length; i++) {\n        inorderMap.put(inorder[i], i);\n    }\n    TreeNode root = dfs(preorder, inorderMap, 0, 0, inorder.length - 1);\n    return root;\n}\n</code></pre> build_tree.cs<pre><code>/* 二分木を構築：分割統治 */\nTreeNode? DFS(int[] preorder, Dictionary&lt;int, int&gt; inorderMap, int i, int l, int r) {\n    // 部分木区間が空なら終了する\n    if (r - l &lt; 0)\n        return null;\n    // ルートノードを初期化する\n    TreeNode root = new(preorder[i]);\n    // m を求めて左右部分木を分割する\n    int m = inorderMap[preorder[i]];\n    // 部分問題：左部分木を構築する\n    root.left = DFS(preorder, inorderMap, i + 1, l, m - 1);\n    // 部分問題：右部分木を構築する\n    root.right = DFS(preorder, inorderMap, i + 1 + m - l, m + 1, r);\n    // 根ノードを返す\n    return root;\n}\n\n/* 二分木を構築 */\nTreeNode? BuildTree(int[] preorder, int[] inorder) {\n    // inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する\n    Dictionary&lt;int, int&gt; inorderMap = [];\n    for (int i = 0; i &lt; inorder.Length; i++) {\n        inorderMap.TryAdd(inorder[i], i);\n    }\n    TreeNode? root = DFS(preorder, inorderMap, 0, 0, inorder.Length - 1);\n    return root;\n}\n</code></pre> build_tree.go<pre><code>/* 二分木を構築：分割統治 */\nfunc dfsBuildTree(preorder []int, inorderMap map[int]int, i, l, r int) *TreeNode {\n    // 部分木区間が空なら終了する\n    if r-l &lt; 0 {\n        return nil\n    }\n    // ルートノードを初期化する\n    root := NewTreeNode(preorder[i])\n    // m を求めて左右部分木を分割する\n    m := inorderMap[preorder[i]]\n    // 部分問題：左部分木を構築する\n    root.Left = dfsBuildTree(preorder, inorderMap, i+1, l, m-1)\n    // 部分問題：右部分木を構築する\n    root.Right = dfsBuildTree(preorder, inorderMap, i+1+m-l, m+1, r)\n    // 根ノードを返す\n    return root\n}\n\n/* 二分木を構築 */\nfunc buildTree(preorder, inorder []int) *TreeNode {\n    // inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する\n    inorderMap := make(map[int]int, len(inorder))\n    for i := 0; i &lt; len(inorder); i++ {\n        inorderMap[inorder[i]] = i\n    }\n\n    root := dfsBuildTree(preorder, inorderMap, 0, 0, len(inorder)-1)\n    return root\n}\n</code></pre> build_tree.swift<pre><code>/* 二分木を構築：分割統治 */\nfunc dfs(preorder: [Int], inorderMap: [Int: Int], i: Int, l: Int, r: Int) -&gt; TreeNode? {\n    // 部分木区間が空なら終了する\n    if r - l &lt; 0 {\n        return nil\n    }\n    // ルートノードを初期化する\n    let root = TreeNode(x: preorder[i])\n    // m を求めて左右部分木を分割する\n    let m = inorderMap[preorder[i]]!\n    // 部分問題：左部分木を構築する\n    root.left = dfs(preorder: preorder, inorderMap: inorderMap, i: i + 1, l: l, r: m - 1)\n    // 部分問題：右部分木を構築する\n    root.right = dfs(preorder: preorder, inorderMap: inorderMap, i: i + 1 + m - l, l: m + 1, r: r)\n    // 根ノードを返す\n    return root\n}\n\n/* 二分木を構築 */\nfunc buildTree(preorder: [Int], inorder: [Int]) -&gt; TreeNode? {\n    // inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する\n    let inorderMap = inorder.enumerated().reduce(into: [:]) { $0[$1.element] = $1.offset }\n    return dfs(preorder: preorder, inorderMap: inorderMap, i: inorder.startIndex, l: inorder.startIndex, r: inorder.endIndex - 1)\n}\n</code></pre> build_tree.js<pre><code>/* 二分木を構築：分割統治 */\nfunction dfs(preorder, inorderMap, i, l, r) {\n    // 部分木区間が空なら終了する\n    if (r - l &lt; 0) return null;\n    // ルートノードを初期化する\n    const root = new TreeNode(preorder[i]);\n    // m を求めて左右部分木を分割する\n    const m = inorderMap.get(preorder[i]);\n    // 部分問題：左部分木を構築する\n    root.left = dfs(preorder, inorderMap, i + 1, l, m - 1);\n    // 部分問題：右部分木を構築する\n    root.right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r);\n    // 根ノードを返す\n    return root;\n}\n\n/* 二分木を構築 */\nfunction buildTree(preorder, inorder) {\n    // inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する\n    let inorderMap = new Map();\n    for (let i = 0; i &lt; inorder.length; i++) {\n        inorderMap.set(inorder[i], i);\n    }\n    const root = dfs(preorder, inorderMap, 0, 0, inorder.length - 1);\n    return root;\n}\n</code></pre> build_tree.ts<pre><code>/* 二分木を構築：分割統治 */\nfunction dfs(\n    preorder: number[],\n    inorderMap: Map&lt;number, number&gt;,\n    i: number,\n    l: number,\n    r: number\n): TreeNode | null {\n    // 部分木区間が空なら終了する\n    if (r - l &lt; 0) return null;\n    // ルートノードを初期化する\n    const root: TreeNode = new TreeNode(preorder[i]);\n    // m を求めて左右部分木を分割する\n    const m = inorderMap.get(preorder[i]);\n    // 部分問題：左部分木を構築する\n    root.left = dfs(preorder, inorderMap, i + 1, l, m - 1);\n    // 部分問題：右部分木を構築する\n    root.right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r);\n    // 根ノードを返す\n    return root;\n}\n\n/* 二分木を構築 */\nfunction buildTree(preorder: number[], inorder: number[]): TreeNode | null {\n    // inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する\n    let inorderMap = new Map&lt;number, number&gt;();\n    for (let i = 0; i &lt; inorder.length; i++) {\n        inorderMap.set(inorder[i], i);\n    }\n    const root = dfs(preorder, inorderMap, 0, 0, inorder.length - 1);\n    return root;\n}\n</code></pre> build_tree.dart<pre><code>/* 二分木を構築：分割統治 */\nTreeNode? dfs(\n  List&lt;int&gt; preorder,\n  Map&lt;int, int&gt; inorderMap,\n  int i,\n  int l,\n  int r,\n) {\n  // 部分木区間が空なら終了する\n  if (r - l &lt; 0) {\n    return null;\n  }\n  // ルートノードを初期化する\n  TreeNode? root = TreeNode(preorder[i]);\n  // m を求めて左右部分木を分割する\n  int m = inorderMap[preorder[i]]!;\n  // 部分問題：左部分木を構築する\n  root.left = dfs(preorder, inorderMap, i + 1, l, m - 1);\n  // 部分問題：右部分木を構築する\n  root.right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r);\n  // 根ノードを返す\n  return root;\n}\n\n/* 二分木を構築 */\nTreeNode? buildTree(List&lt;int&gt; preorder, List&lt;int&gt; inorder) {\n  // inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する\n  Map&lt;int, int&gt; inorderMap = {};\n  for (int i = 0; i &lt; inorder.length; i++) {\n    inorderMap[inorder[i]] = i;\n  }\n  TreeNode? root = dfs(preorder, inorderMap, 0, 0, inorder.length - 1);\n  return root;\n}\n</code></pre> build_tree.rs<pre><code>/* 二分木を構築：分割統治 */\nfn dfs(\n    preorder: &amp;[i32],\n    inorder_map: &amp;HashMap&lt;i32, i32&gt;,\n    i: i32,\n    l: i32,\n    r: i32,\n) -&gt; Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt; {\n    // 部分木区間が空なら終了する\n    if r - l &lt; 0 {\n        return None;\n    }\n    // ルートノードを初期化する\n    let root = TreeNode::new(preorder[i as usize]);\n    // m を求めて左右部分木を分割する\n    let m = inorder_map.get(&amp;preorder[i as usize]).unwrap();\n    // 部分問題：左部分木を構築する\n    root.borrow_mut().left = dfs(preorder, inorder_map, i + 1, l, m - 1);\n    // 部分問題：右部分木を構築する\n    root.borrow_mut().right = dfs(preorder, inorder_map, i + 1 + m - l, m + 1, r);\n    // 根ノードを返す\n    Some(root)\n}\n\n/* 二分木を構築 */\nfn build_tree(preorder: &amp;[i32], inorder: &amp;[i32]) -&gt; Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt; {\n    // inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する\n    let mut inorder_map: HashMap&lt;i32, i32&gt; = HashMap::new();\n    for i in 0..inorder.len() {\n        inorder_map.insert(inorder[i], i as i32);\n    }\n    let root = dfs(preorder, &amp;inorder_map, 0, 0, inorder.len() as i32 - 1);\n    root\n}\n</code></pre> build_tree.c<pre><code>/* 二分木を構築：分割統治 */\nTreeNode *dfs(int *preorder, int *inorderMap, int i, int l, int r, int size) {\n    // 部分木区間が空なら終了する\n    if (r - l &lt; 0)\n        return NULL;\n    // ルートノードを初期化する\n    TreeNode *root = (TreeNode *)malloc(sizeof(TreeNode));\n    root-&gt;val = preorder[i];\n    root-&gt;left = NULL;\n    root-&gt;right = NULL;\n    // m を求めて左右部分木を分割する\n    int m = inorderMap[preorder[i]];\n    // 部分問題：左部分木を構築する\n    root-&gt;left = dfs(preorder, inorderMap, i + 1, l, m - 1, size);\n    // 部分問題：右部分木を構築する\n    root-&gt;right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r, size);\n    // 根ノードを返す\n    return root;\n}\n\n/* 二分木を構築 */\nTreeNode *buildTree(int *preorder, int preorderSize, int *inorder, int inorderSize) {\n    // inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する\n    int *inorderMap = (int *)malloc(sizeof(int) * MAX_SIZE);\n    for (int i = 0; i &lt; inorderSize; i++) {\n        inorderMap[inorder[i]] = i;\n    }\n    TreeNode *root = dfs(preorder, inorderMap, 0, 0, inorderSize - 1, inorderSize);\n    free(inorderMap);\n    return root;\n}\n</code></pre> build_tree.kt<pre><code>/* 二分木を構築：分割統治 */\nfun dfs(\n    preorder: IntArray,\n    inorderMap: Map&lt;Int?, Int?&gt;,\n    i: Int,\n    l: Int,\n    r: Int\n): TreeNode? {\n    // 部分木区間が空なら終了する\n    if (r - l &lt; 0) return null\n    // ルートノードを初期化する\n    val root = TreeNode(preorder[i])\n    // m を求めて左右部分木を分割する\n    val m = inorderMap[preorder[i]]!!\n    // 部分問題：左部分木を構築する\n    root.left = dfs(preorder, inorderMap, i + 1, l, m - 1)\n    // 部分問題：右部分木を構築する\n    root.right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r)\n    // 根ノードを返す\n    return root\n}\n\n/* 二分木を構築 */\nfun buildTree(preorder: IntArray, inorder: IntArray): TreeNode? {\n    // inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する\n    val inorderMap = HashMap&lt;Int?, Int?&gt;()\n    for (i in inorder.indices) {\n        inorderMap[inorder[i]] = i\n    }\n    val root = dfs(preorder, inorderMap, 0, 0, inorder.size - 1)\n    return root\n}\n</code></pre> build_tree.rb<pre><code>### 二分木を構築：分割統治 ###\ndef dfs(preorder, inorder_map, i, l, r)\n  # 部分木区間が空なら終了する\n  return if r - l &lt; 0\n\n  # ルートノードを初期化する\n  root = TreeNode.new(preorder[i])\n  # m を求めて左右部分木を分割する\n  m = inorder_map[preorder[i]]\n  # 部分問題：左部分木を構築する\n  root.left = dfs(preorder, inorder_map, i + 1, l, m - 1)\n  # 部分問題：右部分木を構築する\n  root.right = dfs(preorder, inorder_map, i + 1 + m - l, m + 1, r)\n\n  # 根ノードを返す\n  root\nend\n\n### 二分木を構築 ###\ndef build_tree(preorder, inorder)\n  # inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する\n  inorder_map = {}\n  inorder.each_with_index { |val, i| inorder_map[val] = i }\n  dfs(preorder, inorder_map, 0, 0, inorder.length - 1)\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>下図は二分木を構築する再帰過程を示しています。各ノードは下向きに「再帰していく」過程で生成され、各辺（参照）は上向きに「戻る」過程で張られます。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 12-8   二分木を構築する再帰過程 </p> <p>各再帰関数における前順走査 <code>preorder</code> と中順走査 <code>inorder</code> の分割結果を下図に示します。</p> <p></p> <p> 図 12-9   各再帰関数での分割結果 </p> <p>木のノード数を \\(n\\) とすると、各ノードの初期化（再帰関数 <code>dfs()</code> の 1 回の実行）には \\(O(1)\\) 時間かかります。したがって、全体の時間計算量は \\(O(n)\\) です。</p> <p>ハッシュテーブルには <code>inorder</code> の要素からインデックスへの対応を保存するため、空間計算量は \\(O(n)\\) です。最悪の場合、すなわち二分木が連結リストに退化すると、再帰の深さは \\(n\\) に達し、\\(O(n)\\) のスタックフレーム空間を使用します。したがって、全体の空間計算量は \\(O(n)\\) です。</p>","path":["第 12 章 &nbsp; 分割統治","12.3 &nbsp; 二分木の構築問題"],"tags":[]},{"location":"chapter_divide_and_conquer/divide_and_conquer/","level":1,"title":"12.1   分割統治法","text":"<p>分割統治法（divide and conquer）は、問題を分けて統べるという意味であり、非常に重要で一般的なアルゴリズム戦略です。分割統治法は通常、再帰に基づいて実装され、「分」と「治」の 2 つのステップから構成されます。</p> <ol> <li>分（分割段階）：元の問題を 2 つ以上の部分問題へ再帰的に分解し、最小の部分問題に到達した時点で停止します。</li> <li>治（統合段階）：解が既知である最小の部分問題から始めて、部分問題の解を下から上へ統合し、元の問題の解を構築します。</li> </ol> <p>以下の図に示すように、「マージソート」は分割統治戦略の典型的な応用の一つです。</p> <ol> <li>分：元の配列（元の問題）を 2 つの部分配列（部分問題）へ再帰的に分割し、部分配列に要素が 1 つだけ残るまで続けます。</li> <li>治：整列済みの部分配列（部分問題の解）を下から上へ統合し、整列済みの元の配列（元の問題の解）を得ます。</li> </ol> <p></p> <p> 図 12-1   マージソートの分割統治戦略 </p>","path":["第 12 章 &nbsp; 分割統治","12.1 &nbsp; 分割統治法"],"tags":[]},{"location":"chapter_divide_and_conquer/divide_and_conquer/#1211","level":2,"title":"12.1.1   分割統治法の問題を見極めるには","text":"<p>ある問題が分割統治法で解くのに適しているかどうかは、通常、次の判断基準を参考にできます。</p> <ol> <li>問題は分解できる：元の問題は、より小さく類似した部分問題に分解でき、同じ方法で再帰的に分割できます。</li> <li>部分問題は独立している：部分問題同士に重複がなく、相互依存もないため、独立して解決できます。</li> <li>部分問題の解は統合できる：元の問題の解は、部分問題の解を統合することで得られます。</li> </ol> <p>明らかに、マージソートは以上の 3 つの判断基準を満たしています。</p> <ol> <li>問題は分解できる：配列（元の問題）を 2 つの部分配列（部分問題）へ再帰的に分割します。</li> <li>部分問題は独立している：各部分配列は独立にソートできます（部分問題は独立に解けます）。</li> <li>部分問題の解は統合できる：2 つの整列済み部分配列（部分問題の解）は、1 つの整列済み配列（元の問題の解）に統合できます。</li> </ol>","path":["第 12 章 &nbsp; 分割統治","12.1 &nbsp; 分割統治法"],"tags":[]},{"location":"chapter_divide_and_conquer/divide_and_conquer/#1212","level":2,"title":"12.1.2   分割統治法で効率を高める","text":"<p>分割統治法はアルゴリズムの問題を効果的に解けるだけでなく、多くの場合アルゴリズムの効率も高められます。ソートアルゴリズムでは、クイックソート、マージソート、ヒープソートが選択ソート、バブルソート、挿入ソートより高速ですが、これは分割統治戦略を適用しているためです。</p> <p>ここで次の疑問が生じます。なぜ分割統治法はアルゴリズム効率を高められるのでしょうか。その根本的な仕組みは何でしょうか？言い換えると、大きな問題を複数の部分問題に分解し、部分問題を解き、それらの解を統合して元の問題の解にするという手順は、なぜ元の問題を直接解くより効率的なのでしょうか。この問題は、操作回数と並列計算の 2 つの観点から議論できます。</p>","path":["第 12 章 &nbsp; 分割統治","12.1 &nbsp; 分割統治法"],"tags":[]},{"location":"chapter_divide_and_conquer/divide_and_conquer/#1","level":3,"title":"1.   操作回数の最適化","text":"<p>「バブルソート」を例に取ると、長さ \\(n\\) の配列を処理するのに \\(O(n^2)\\) の時間がかかります。以下の図のように、配列を中央で 2 つの部分配列に分けると仮定すると、分割には \\(O(n)\\) の時間、各部分配列のソートには \\(O((n / 2)^2)\\) の時間、2 つの部分配列の統合には \\(O(n)\\) の時間が必要で、全体の時間計算量は次のようになります：</p> \\[ O(n + (\\frac{n}{2})^2 \\times 2 + n) = O(\\frac{n^2}{2} + 2n) \\] <p></p> <p> 図 12-2   配列分割前後のバブルソート </p> <p>次に、以下の不等式を計算します。左辺と右辺はそれぞれ、分割前と分割後の操作総数です：</p> \\[ \\begin{aligned} n^2 &amp; &gt; \\frac{n^2}{2} + 2n \\newline n^2 - \\frac{n^2}{2} - 2n &amp; &gt; 0 \\newline n(n - 4) &amp; &gt; 0 \\end{aligned} \\] <p>これは、\\(n &gt; 4\\) のときに分割後の操作回数の方が少なくなり、ソート効率が高くなることを意味します。ただし、分割後の時間計算量は依然として 2 次の \\(O(n^2)\\) であり、計算量の定数項が小さくなっただけです。</p> <p>さらに考えると、部分配列を中央からさらに 2 つの部分配列へと分割し続け、部分配列に要素が 1 つだけ残るまで分割を止めないとしたらどうでしょうか。この考え方がまさに「マージソート」であり、時間計算量は \\(O(n \\log n)\\) です。</p> <p>さらに、分割点をいくつか増やして、元の配列を平均的に \\(k\\) 個の部分配列に分けるとしたらどうでしょうか。この状況は「バケットソート」と非常によく似ており、大量データのソートに非常に適しています。理論上の時間計算量は \\(O(n + k)\\) に達します。</p>","path":["第 12 章 &nbsp; 分割統治","12.1 &nbsp; 分割統治法"],"tags":[]},{"location":"chapter_divide_and_conquer/divide_and_conquer/#2","level":3,"title":"2.   並列計算の最適化","text":"<p>分割統治法で生成される部分問題は互いに独立しているため、通常は並列に解くことができます。つまり、分割統治法はアルゴリズムの時間計算量を下げられるだけでなく、オペレーティングシステムの並列最適化にも有利です。</p> <p>並列最適化は、マルチコアまたはマルチプロセッサ環境で特に有効です。システムが複数の部分問題を同時に処理でき、計算資源をより十分に活用できるため、全体の実行時間を大幅に短縮できます。</p> <p>たとえば、以下の図に示す「バケットソート」では、大量のデータを各バケットに均等に割り当てることで、すべてのバケットのソート処理を各計算ユニットに分散し、完了後に結果を統合できます。</p> <p></p> <p> 図 12-3   バケットソートの並列計算 </p>","path":["第 12 章 &nbsp; 分割統治","12.1 &nbsp; 分割統治法"],"tags":[]},{"location":"chapter_divide_and_conquer/divide_and_conquer/#1213","level":2,"title":"12.1.3   分割統治法の代表的な応用","text":"<p>一方では、分割統治法は多くの古典的なアルゴリズム問題を解くのに使えます。</p> <ul> <li>最近点対探索：このアルゴリズムは、まず点集合を 2 つに分け、それぞれの部分における最近点対を求め、最後に 2 つの部分をまたぐ最近点対を求めます。</li> <li>大整数乗算：たとえば Karatsuba 法では、大整数の乗算を、より小さな整数どうしのいくつかの乗算と加算に分解します。</li> <li>行列乗算：たとえば Strassen 法では、大きな行列の乗算を、複数の小さな行列の乗算と加算に分解します。</li> <li>ハノイの塔問題：ハノイの塔問題は再帰によって解くことができ、これは典型的な分割統治戦略の応用です。</li> <li>反転対の計算：ある数列で前の数が後ろの数より大きい場合、その 2 つの数は反転対を構成します。反転対の問題は、分割統治の考え方を利用し、マージソートを用いて解けます。</li> </ul> <p>他方で、分割統治法はアルゴリズムとデータ構造の設計にも非常に広く応用されています。</p> <ul> <li>二分探索：二分探索では、整列済み配列を中央のインデックスで 2 つに分け、目標値と中央要素の比較結果に基づいてどちらの半区間を除外するかを決め、残った区間で同じ二分操作を行います。</li> <li>マージソート：本節の冒頭で紹介したため、ここでは繰り返しません。</li> <li>クイックソート：クイックソートは基準値を 1 つ選び、配列を、基準値より小さい要素の部分配列と、基準値より大きい要素の部分配列に分け、その後それぞれに対して同じ分割操作を行い、部分配列に要素が 1 つだけ残るまで続けます。</li> <li>バケットソート：バケットソートの基本的な考え方は、データを複数のバケットに分散し、各バケット内の要素をソートしたうえで、各バケットの要素を順に取り出して整列済み配列を得ることです。</li> <li>木構造：たとえば二分探索木、AVL 木、赤黒木、B 木、B+ 木などでは、探索・挿入・削除などの操作をいずれも分割統治戦略の応用とみなせます。</li> <li>ヒープ：ヒープは特殊な完全二分木であり、挿入、削除、ヒープ化などの各種操作には、実際には分割統治の考え方が含まれています。</li> <li>ハッシュテーブル：ハッシュテーブル自体は分割統治を直接適用しているわけではありませんが、いくつかのハッシュ衝突解決法では間接的に分割統治戦略が使われています。たとえば、連鎖アドレス法における長い連結リストは、検索効率を高めるために赤黒木へ変換されます。</li> </ul> <p>このように、**分割統治法は「静かに物を潤す」ようなアルゴリズム思想**であり、さまざまなアルゴリズムやデータ構造の中に潜んでいます。</p>","path":["第 12 章 &nbsp; 分割統治","12.1 &nbsp; 分割統治法"],"tags":[]},{"location":"chapter_divide_and_conquer/hanota_problem/","level":1,"title":"12.4   ハノイの塔の問題","text":"<p>マージソートや二分木の構築では、いずれも元の問題を元問題の半分の規模をもつ 2 つの部分問題に分解していました。しかし、ハノイの塔の問題では、異なる分解戦略を採用します。</p> <p>Question</p> <p>3 本の柱があり、それぞれを <code>A</code>、<code>B</code>、<code>C</code> とします。初期状態では、柱 <code>A</code> に \\(n\\) 枚の円盤が通されており、上から下へ小さい順に並んでいます。私たちの課題は、この \\(n\\) 枚の円盤を柱 <code>C</code> に移し、元の順序を保つことです（以下の図のとおり）。円盤を移動する際には、次のルールに従う必要があります。</p> <ol> <li>円盤は 1 本の柱の頂上から取り出し、別の柱の頂上に置くことしかできません。</li> <li>1 回に移動できる円盤は 1 枚だけです。</li> <li>小さい円盤は常に大きい円盤の上になければなりません。</li> </ol> <p></p> <p> 図 12-10   ハノイの塔の問題の例 </p> <p>規模が \\(i\\) のハノイの塔の問題を \\(f(i)\\) と表します 。たとえば \\(f(3)\\) は、\\(3\\) 枚の円盤を <code>A</code> から <code>C</code> へ移動するハノイの塔の問題を表します。</p>","path":["第 12 章 &nbsp; 分割統治","12.4 &nbsp; ハノイの塔の問題"],"tags":[]},{"location":"chapter_divide_and_conquer/hanota_problem/#1","level":3,"title":"1.   基本ケースを考える","text":"<p>以下の図に示すように、問題 \\(f(1)\\) 、すなわち円盤が 1 枚だけの場合は、それを <code>A</code> から <code>C</code> へ直接移動すれば済みます。</p> &lt;1&gt;&lt;2&gt; <p></p> <p></p> <p> 図 12-11   規模 1 の問題の解 </p> <p>以下の図に示すように、問題 \\(f(2)\\) 、すなわち円盤が 2 枚ある場合は、小さい円盤が常に大きい円盤の上にある条件を満たすため、<code>B</code> を借りて移動を行う必要があります。</p> <ol> <li>まず上の小さい円盤を <code>A</code> から <code>B</code> へ移します。</li> <li>次に大きい円盤を <code>A</code> から <code>C</code> へ移します。</li> <li>最後に小さい円盤を <code>B</code> から <code>C</code> へ移します。</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p> 図 12-12   規模 2 の問題の解 </p> <p>問題 \\(f(2)\\) を解く過程は、**2 枚の円盤を <code>B</code> を介して <code>A</code> から <code>C</code> へ移す**と要約できます。このとき、<code>C</code> を目標の柱、<code>B</code> を補助の柱と呼びます。</p>","path":["第 12 章 &nbsp; 分割統治","12.4 &nbsp; ハノイの塔の問題"],"tags":[]},{"location":"chapter_divide_and_conquer/hanota_problem/#2","level":3,"title":"2.   部分問題への分解","text":"<p>問題 \\(f(3)\\) 、すなわち円盤が 3 枚ある場合になると、状況はやや複雑になります。</p> <p>\\(f(1)\\) と \\(f(2)\\) の解が既知なので、分割統治の観点から、<code>A</code> の上部にある 2 枚の円盤をひとまとまりとみなして、次の図の手順を実行できます。こうして 3 枚の円盤を <code>A</code> から <code>C</code> へ順調に移動できます。</p> <ol> <li><code>B</code> を目標の柱、<code>C</code> を補助の柱として、2 枚の円盤を <code>A</code> から <code>B</code> へ移します。</li> <li><code>A</code> に残った 1 枚の円盤を <code>A</code> から <code>C</code> へ直接移動します。</li> <li><code>C</code> を目標の柱、<code>A</code> を補助の柱として、2 枚の円盤を <code>B</code> から <code>C</code> へ移します。</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p> 図 12-13   規模 3 の問題の解 </p> <p>本質的には、問題 \\(f(3)\\) を 2 つの部分問題 \\(f(2)\\) と 1 つの部分問題 \\(f(1)\\) に分けています 。この 3 つの部分問題を順に解けば、元の問題も解決されます。これは、部分問題が独立しており、解を組み合わせられることを示しています。</p> <p>ここまでで、次の図に示すハノイの塔の問題を解く分割統治戦略をまとめられます。元の問題 \\(f(n)\\) を 2 つの部分問題 \\(f(n-1)\\) と 1 つの部分問題 \\(f(1)\\) に分け、次の順序でこの 3 つの部分問題を解きます。</p> <ol> <li>\\(n-1\\) 枚の円盤を <code>C</code> を介して <code>A</code> から <code>B</code> へ移します。</li> <li>残り \\(1\\) 枚の円盤を <code>A</code> から <code>C</code> へ直接移します。</li> <li>\\(n-1\\) 枚の円盤を <code>A</code> を介して <code>B</code> から <code>C</code> へ移します。</li> </ol> <p>この 2 つの部分問題 \\(f(n-1)\\) は、同じ方法で再帰的に分割できます。最小の部分問題 \\(f(1)\\) に到達するまでこれを続けます。一方、\\(f(1)\\) の解は既知であり、1 回の移動操作だけで済みます。</p> <p></p> <p> 図 12-14   ハノイの塔の問題を解く分割統治戦略 </p>","path":["第 12 章 &nbsp; 分割統治","12.4 &nbsp; ハノイの塔の問題"],"tags":[]},{"location":"chapter_divide_and_conquer/hanota_problem/#3","level":3,"title":"3.   コードの実装","text":"<p>コードでは、再帰関数 <code>dfs(i, src, buf, tar)</code> を定義します。その役割は、柱 <code>src</code> の上部にある \\(i\\) 枚の円盤を、補助の柱 <code>buf</code> を使って目標の柱 <code>tar</code> へ移動することです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby hanota.py<pre><code>def move(src: list[int], tar: list[int]):\n    \"\"\"円盤を 1 枚移動\"\"\"\n    # src の上から円盤を1枚取り出す\n    pan = src.pop()\n    # 円盤を tar の上に置く\n    tar.append(pan)\n\ndef dfs(i: int, src: list[int], buf: list[int], tar: list[int]):\n    \"\"\"ハノイの塔の問題 f(i) を解く\"\"\"\n    # src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す\n    if i == 1:\n        move(src, tar)\n        return\n    # 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す\n    dfs(i - 1, src, tar, buf)\n    # 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す\n    move(src, tar)\n    # 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す\n    dfs(i - 1, buf, src, tar)\n\ndef solve_hanota(A: list[int], B: list[int], C: list[int]):\n    \"\"\"ハノイの塔を解く\"\"\"\n    n = len(A)\n    # A の上から n 枚の円盤を B を介して C へ移す\n    dfs(n, A, B, C)\n</code></pre> hanota.cpp<pre><code>/* 円盤を 1 枚移動 */\nvoid move(vector&lt;int&gt; &amp;src, vector&lt;int&gt; &amp;tar) {\n    // src の上から円盤を1枚取り出す\n    int pan = src.back();\n    src.pop_back();\n    // 円盤を tar の上に置く\n    tar.push_back(pan);\n}\n\n/* ハノイの塔の問題 f(i) を解く */\nvoid dfs(int i, vector&lt;int&gt; &amp;src, vector&lt;int&gt; &amp;buf, vector&lt;int&gt; &amp;tar) {\n    // src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す\n    if (i == 1) {\n        move(src, tar);\n        return;\n    }\n    // 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す\n    dfs(i - 1, src, tar, buf);\n    // 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す\n    move(src, tar);\n    // 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す\n    dfs(i - 1, buf, src, tar);\n}\n\n/* ハノイの塔を解く */\nvoid solveHanota(vector&lt;int&gt; &amp;A, vector&lt;int&gt; &amp;B, vector&lt;int&gt; &amp;C) {\n    int n = A.size();\n    // A の上から n 枚の円盤を B を介して C へ移す\n    dfs(n, A, B, C);\n}\n</code></pre> hanota.java<pre><code>/* 円盤を 1 枚移動 */\nvoid move(List&lt;Integer&gt; src, List&lt;Integer&gt; tar) {\n    // src の上から円盤を1枚取り出す\n    Integer pan = src.remove(src.size() - 1);\n    // 円盤を tar の上に置く\n    tar.add(pan);\n}\n\n/* ハノイの塔の問題 f(i) を解く */\nvoid dfs(int i, List&lt;Integer&gt; src, List&lt;Integer&gt; buf, List&lt;Integer&gt; tar) {\n    // src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す\n    if (i == 1) {\n        move(src, tar);\n        return;\n    }\n    // 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す\n    dfs(i - 1, src, tar, buf);\n    // 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す\n    move(src, tar);\n    // 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す\n    dfs(i - 1, buf, src, tar);\n}\n\n/* ハノイの塔を解く */\nvoid solveHanota(List&lt;Integer&gt; A, List&lt;Integer&gt; B, List&lt;Integer&gt; C) {\n    int n = A.size();\n    // A の上から n 枚の円盤を B を介して C へ移す\n    dfs(n, A, B, C);\n}\n</code></pre> hanota.cs<pre><code>/* 円盤を 1 枚移動 */\nvoid Move(List&lt;int&gt; src, List&lt;int&gt; tar) {\n    // src の上から円盤を1枚取り出す\n    int pan = src[^1];\n    src.RemoveAt(src.Count - 1);\n    // 円盤を tar の上に置く\n    tar.Add(pan);\n}\n\n/* ハノイの塔の問題 f(i) を解く */\nvoid DFS(int i, List&lt;int&gt; src, List&lt;int&gt; buf, List&lt;int&gt; tar) {\n    // src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す\n    if (i == 1) {\n        Move(src, tar);\n        return;\n    }\n    // 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す\n    DFS(i - 1, src, tar, buf);\n    // 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す\n    Move(src, tar);\n    // 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す\n    DFS(i - 1, buf, src, tar);\n}\n\n/* ハノイの塔を解く */\nvoid SolveHanota(List&lt;int&gt; A, List&lt;int&gt; B, List&lt;int&gt; C) {\n    int n = A.Count;\n    // A の上から n 枚の円盤を B を介して C へ移す\n    DFS(n, A, B, C);\n}\n</code></pre> hanota.go<pre><code>/* 円盤を 1 枚移動 */\nfunc move(src, tar *list.List) {\n    // src の上から円盤を1枚取り出す\n    pan := src.Back()\n    // 円盤を tar の上に置く\n    tar.PushBack(pan.Value)\n    // `src` の最上部の円盤を取り外す\n    src.Remove(pan)\n}\n\n/* ハノイの塔の問題 f(i) を解く */\nfunc dfsHanota(i int, src, buf, tar *list.List) {\n    // src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す\n    if i == 1 {\n        move(src, tar)\n        return\n    }\n    // 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す\n    dfsHanota(i-1, src, tar, buf)\n    // 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す\n    move(src, tar)\n    // 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す\n    dfsHanota(i-1, buf, src, tar)\n}\n\n/* ハノイの塔を解く */\nfunc solveHanota(A, B, C *list.List) {\n    n := A.Len()\n    // A の上から n 枚の円盤を B を介して C へ移す\n    dfsHanota(n, A, B, C)\n}\n</code></pre> hanota.swift<pre><code>/* 円盤を 1 枚移動 */\nfunc move(src: inout [Int], tar: inout [Int]) {\n    // src の上から円盤を1枚取り出す\n    let pan = src.popLast()!\n    // 円盤を tar の上に置く\n    tar.append(pan)\n}\n\n/* ハノイの塔の問題 f(i) を解く */\nfunc dfs(i: Int, src: inout [Int], buf: inout [Int], tar: inout [Int]) {\n    // src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す\n    if i == 1 {\n        move(src: &amp;src, tar: &amp;tar)\n        return\n    }\n    // 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す\n    dfs(i: i - 1, src: &amp;src, buf: &amp;tar, tar: &amp;buf)\n    // 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す\n    move(src: &amp;src, tar: &amp;tar)\n    // 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す\n    dfs(i: i - 1, src: &amp;buf, buf: &amp;src, tar: &amp;tar)\n}\n\n/* ハノイの塔を解く */\nfunc solveHanota(A: inout [Int], B: inout [Int], C: inout [Int]) {\n    let n = A.count\n    // リストの末尾が柱の上端に対応する\n    // src の上から n 個の円盤を、B を介して C に移動する\n    dfs(i: n, src: &amp;A, buf: &amp;B, tar: &amp;C)\n}\n</code></pre> hanota.js<pre><code>/* 円盤を 1 枚移動 */\nfunction move(src, tar) {\n    // src の上から円盤を1枚取り出す\n    const pan = src.pop();\n    // 円盤を tar の上に置く\n    tar.push(pan);\n}\n\n/* ハノイの塔の問題 f(i) を解く */\nfunction dfs(i, src, buf, tar) {\n    // src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す\n    if (i === 1) {\n        move(src, tar);\n        return;\n    }\n    // 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す\n    dfs(i - 1, src, tar, buf);\n    // 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す\n    move(src, tar);\n    // 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す\n    dfs(i - 1, buf, src, tar);\n}\n\n/* ハノイの塔を解く */\nfunction solveHanota(A, B, C) {\n    const n = A.length;\n    // A の上から n 枚の円盤を B を介して C へ移す\n    dfs(n, A, B, C);\n}\n</code></pre> hanota.ts<pre><code>/* 円盤を 1 枚移動 */\nfunction move(src: number[], tar: number[]): void {\n    // src の上から円盤を1枚取り出す\n    const pan = src.pop();\n    // 円盤を tar の上に置く\n    tar.push(pan);\n}\n\n/* ハノイの塔の問題 f(i) を解く */\nfunction dfs(i: number, src: number[], buf: number[], tar: number[]): void {\n    // src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す\n    if (i === 1) {\n        move(src, tar);\n        return;\n    }\n    // 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す\n    dfs(i - 1, src, tar, buf);\n    // 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す\n    move(src, tar);\n    // 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す\n    dfs(i - 1, buf, src, tar);\n}\n\n/* ハノイの塔を解く */\nfunction solveHanota(A: number[], B: number[], C: number[]): void {\n    const n = A.length;\n    // A の上から n 枚の円盤を B を介して C へ移す\n    dfs(n, A, B, C);\n}\n</code></pre> hanota.dart<pre><code>/* 円盤を 1 枚移動 */\nvoid move(List&lt;int&gt; src, List&lt;int&gt; tar) {\n  // src の上から円盤を1枚取り出す\n  int pan = src.removeLast();\n  // 円盤を tar の上に置く\n  tar.add(pan);\n}\n\n/* ハノイの塔の問題 f(i) を解く */\nvoid dfs(int i, List&lt;int&gt; src, List&lt;int&gt; buf, List&lt;int&gt; tar) {\n  // src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す\n  if (i == 1) {\n    move(src, tar);\n    return;\n  }\n  // 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す\n  dfs(i - 1, src, tar, buf);\n  // 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す\n  move(src, tar);\n  // 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す\n  dfs(i - 1, buf, src, tar);\n}\n\n/* ハノイの塔を解く */\nvoid solveHanota(List&lt;int&gt; A, List&lt;int&gt; B, List&lt;int&gt; C) {\n  int n = A.length;\n  // A の上から n 枚の円盤を B を介して C へ移す\n  dfs(n, A, B, C);\n}\n</code></pre> hanota.rs<pre><code>/* 円盤を 1 枚移動 */\nfn move_pan(src: &amp;mut Vec&lt;i32&gt;, tar: &amp;mut Vec&lt;i32&gt;) {\n    // src の上から円盤を1枚取り出す\n    let pan = src.pop().unwrap();\n    // 円盤を tar の上に置く\n    tar.push(pan);\n}\n\n/* ハノイの塔の問題 f(i) を解く */\nfn dfs(i: i32, src: &amp;mut Vec&lt;i32&gt;, buf: &amp;mut Vec&lt;i32&gt;, tar: &amp;mut Vec&lt;i32&gt;) {\n    // src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す\n    if i == 1 {\n        move_pan(src, tar);\n        return;\n    }\n    // 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す\n    dfs(i - 1, src, tar, buf);\n    // 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す\n    move_pan(src, tar);\n    // 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す\n    dfs(i - 1, buf, src, tar);\n}\n\n/* ハノイの塔を解く */\nfn solve_hanota(A: &amp;mut Vec&lt;i32&gt;, B: &amp;mut Vec&lt;i32&gt;, C: &amp;mut Vec&lt;i32&gt;) {\n    let n = A.len() as i32;\n    // A の上から n 枚の円盤を B を介して C へ移す\n    dfs(n, A, B, C);\n}\n</code></pre> hanota.c<pre><code>/* 円盤を 1 枚移動 */\nvoid move(int *src, int *srcSize, int *tar, int *tarSize) {\n    // src の上から円盤を1枚取り出す\n    int pan = src[*srcSize - 1];\n    src[*srcSize - 1] = 0;\n    (*srcSize)--;\n    // 円盤を tar の上に置く\n    tar[*tarSize] = pan;\n    (*tarSize)++;\n}\n\n/* ハノイの塔の問題 f(i) を解く */\nvoid dfs(int i, int *src, int *srcSize, int *buf, int *bufSize, int *tar, int *tarSize) {\n    // src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す\n    if (i == 1) {\n        move(src, srcSize, tar, tarSize);\n        return;\n    }\n    // 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す\n    dfs(i - 1, src, srcSize, tar, tarSize, buf, bufSize);\n    // 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す\n    move(src, srcSize, tar, tarSize);\n    // 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す\n    dfs(i - 1, buf, bufSize, src, srcSize, tar, tarSize);\n}\n\n/* ハノイの塔を解く */\nvoid solveHanota(int *A, int *ASize, int *B, int *BSize, int *C, int *CSize) {\n    // A の上から n 枚の円盤を B を介して C へ移す\n    dfs(*ASize, A, ASize, B, BSize, C, CSize);\n}\n</code></pre> hanota.kt<pre><code>/* 円盤を 1 枚移動 */\nfun move(src: MutableList&lt;Int&gt;, tar: MutableList&lt;Int&gt;) {\n    // src の上から円盤を1枚取り出す\n    val pan = src.removeAt(src.size - 1)\n    // 円盤を tar の上に置く\n    tar.add(pan)\n}\n\n/* ハノイの塔の問題 f(i) を解く */\nfun dfs(i: Int, src: MutableList&lt;Int&gt;, buf: MutableList&lt;Int&gt;, tar: MutableList&lt;Int&gt;) {\n    // src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す\n    if (i == 1) {\n        move(src, tar)\n        return\n    }\n    // 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す\n    dfs(i - 1, src, tar, buf)\n    // 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す\n    move(src, tar)\n    // 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す\n    dfs(i - 1, buf, src, tar)\n}\n\n/* ハノイの塔を解く */\nfun solveHanota(A: MutableList&lt;Int&gt;, B: MutableList&lt;Int&gt;, C: MutableList&lt;Int&gt;) {\n    val n = A.size\n    // A の上から n 枚の円盤を B を介して C へ移す\n    dfs(n, A, B, C)\n}\n</code></pre> hanota.rb<pre><code>### 円盤を1枚移動 ###\ndef move(src, tar)\n  # src の上から円盤を1枚取り出す\n  pan = src.pop\n  # 円盤を tar の上に置く\n  tar &lt;&lt; pan\nend\n\n### ハノイの塔 f(i) を解く ###\ndef dfs(i, src, buf, tar)\n  # src に円盤が 1 枚だけ残っている場合は、そのまま tar へ移す\n  if i == 1\n    move(src, tar)\n    return\n  end\n\n  # 部分問題 f(i-1)：src の上部 i-1 枚の円盤を tar を補助にして buf へ移す\n  dfs(i - 1, src, tar, buf)\n  # 部分問題 f(1)：src に残る 1 枚の円盤を tar に移す\n  move(src, tar)\n  # 部分問題 f(i-1)：buf の上部 i-1 枚の円盤を src を補助にして tar へ移す\n  dfs(i - 1, buf, src, tar)\nend\n\n### ハノイの塔を解く ###\ndef solve_hanota(_A, _B, _C)\n  n = _A.length\n  # A の上から n 枚の円盤を B を介して C へ移す\n  dfs(n, _A, _B, _C)\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>以下の図に示すように、ハノイの塔の問題は高さ \\(n\\) の再帰木を形成し、各ノードは 1 つの部分問題、すなわち 1 つ起動された <code>dfs()</code> 関数に対応します。したがって時間計算量は \\(O(2^n)\\) 、空間計算量は \\(O(n)\\) です。</p> <p></p> <p> 図 12-15   ハノイの塔の問題の再帰木 </p> <p>Quote</p> <p>ハノイの塔の問題は古い伝説に由来します。古代インドのある寺院で、僧侶たちは 3 本の高いダイヤモンドの柱と、\\(64\\) 枚の大きさの異なる金の円盤を持っていました。僧侶たちは絶えず円盤を動かし、最後の 1 枚が正しく置かれた瞬間に世界が終わると信じていました。</p> <p>しかし、たとえ僧侶たちが 1 秒に 1 回移動するとしても、合計でおよそ \\(2^{64} \\approx 1.84×10^{19}\\) 秒、約 \\(5850\\) 億年が必要で、現在推定されている宇宙の年齢をはるかに上回ります。したがって、この伝説が本当だったとしても、世界の終わりを心配する必要はなさそうです。</p>","path":["第 12 章 &nbsp; 分割統治","12.4 &nbsp; ハノイの塔の問題"],"tags":[]},{"location":"chapter_divide_and_conquer/summary/","level":1,"title":"12.5   まとめ","text":"","path":["第 12 章 &nbsp; 分割統治","12.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_divide_and_conquer/summary/#1","level":3,"title":"1.   要点の振り返り","text":"<ul> <li>分割統治法は一般的なアルゴリズム設計戦略であり、分（分割）と治（統合）の 2 つの段階からなり、通常は再帰に基づいて実装されます。</li> <li>それが分割統治法の問題かどうかを判断する基準には、問題を分解できるか、部分問題が独立しているか、部分問題を統合できるかが含まれます。</li> <li>マージソートは分割統治法の典型的な応用であり、配列を再帰的に同じ長さの 2 つの部分配列に分割し、要素が 1 つだけになるまで続け、その後で各層を順に統合してソートを完了します。</li> <li>分割統治法を導入すると、多くの場合アルゴリズムの効率を高められます。一方では操作回数が減り、他方では分割後にシステムの並列最適化を行いやすくなります。</li> <li>分割統治法は多くのアルゴリズム問題を解決できるだけでなく、データ構造やアルゴリズム設計にも広く応用されており、至る所でその姿を見ることができます。</li> <li>総当たり探索と比べて、適応的な探索のほうが効率的です。時間計算量が \\(O(\\log n)\\) の探索アルゴリズムは、通常は分割統治法に基づいて実装されます。</li> <li>二分探索は分割統治法のもう 1 つの典型的な応用であり、部分問題の解を統合する手順を含みません。再帰的な分割統治によって二分探索を実現できます。</li> <li>二分木を構築する問題では、木の構築（元の問題）を左部分木と右部分木の構築（部分問題）に分けられます。これは、先行順序走査と中間順序走査のインデックス区間を分割することで実現できます。</li> <li>ハノイの塔の問題では、規模 \\(n\\) の問題を、規模 \\(n-1\\) の 2 つの部分問題と規模 \\(1\\) の 1 つの部分問題に分けられます。これら 3 つの部分問題を順に解くと、元の問題も解決されます。</li> </ul>","path":["第 12 章 &nbsp; 分割統治","12.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_dynamic_programming/","level":1,"title":"第 14 章   動的計画法","text":"<p>Abstract</p> <p>小川は川へと注ぎ、河川は大海へと注ぐ。</p> <p>動的計画法は小さな問題の解を集めて大きな問題の答えとし、一歩ずつ私たちを問題解決の彼岸へと導く。</p>","path":["第 14 章 &nbsp; 動的計画法"],"tags":[]},{"location":"chapter_dynamic_programming/#_1","level":2,"title":"章の内容","text":"<ul> <li>14.1   動的計画法入門</li> <li>14.2   動的計画法の問題特性</li> <li>14.3   動的計画法の問題解決の考え方</li> <li>14.4   0-1 ナップサック問題</li> <li>14.5   完全ナップサック問題</li> <li>14.6   編集距離問題</li> <li>14.7   まとめ</li> </ul>","path":["第 14 章 &nbsp; 動的計画法"],"tags":[]},{"location":"chapter_dynamic_programming/dp_problem_features/","level":1,"title":"14.2   動的計画法の問題特性","text":"<p>前節では、動的計画法が部分問題への分解によってどのように元の問題を解くのかを学びました。実際、部分問題への分解は汎用的なアルゴリズムの考え方であり、分割統治法、動的計画法、バックトラッキングでは重視点が異なります。</p> <ul> <li>分割統治法は、元の問題を再帰的に複数の互いに独立した部分問題へ分割し、最小の部分問題に至るまで分解したうえで、バックトラック時に部分問題の解を統合し、最終的に元の問題の解を得ます。</li> <li>動的計画法も問題を再帰的に分解しますが、分割統治法との主な違いは、動的計画法における部分問題が相互依存しており、分解の過程で多数の重複部分問題が現れることです。</li> <li>バックトラッキング法は、試行と巻き戻しの中ですべての可能な解を列挙し、枝刈りによって不要な探索分岐を避けます。元の問題の解は一連の意思決定ステップから構成されるため、各決定ステップ以前の部分系列を一つの部分問題と見なせます。</li> </ul> <p>実際、動的計画法は最適化問題を解くためによく用いられます。これらは重複部分問題を含むだけでなく、さらに二つの大きな特性、すなわち最適部分構造と無後効性を備えています。</p>","path":["第 14 章 &nbsp; 動的計画法","14.2 &nbsp; 動的計画法の問題特性"],"tags":[]},{"location":"chapter_dynamic_programming/dp_problem_features/#1421","level":2,"title":"14.2.1   最適部分構造","text":"<p>階段昇り問題を少し変更し、最適部分構造の概念をより示しやすくします。</p> <p>階段昇りの最小コスト</p> <p>階段が与えられ、各ステップで \\(1\\) 段または \\(2\\) 段上ることができます。各段には非負整数が貼られており、その段に到達するために支払う必要があるコストを表します。非負整数配列 \\(cost\\) が与えられ、\\(cost[i]\\) は第 \\(i\\) 段で支払うコストを表し、\\(cost[0]\\) は地面（開始地点）です。頂上に到達するために必要な最小コストを求めてください。</p> <p>下図に示すように、第 \\(1\\)、\\(2\\)、\\(3\\) 段のコストがそれぞれ \\(1\\)、\\(10\\)、\\(1\\) である場合、地面から第 \\(3\\) 段まで上る最小コストは \\(2\\) です。</p> <p></p> <p> 図 14-6   第 3 段まで上る最小コスト </p> <p>\\(dp[i]\\) を第 \\(i\\) 段まで上るのに累積して支払ったコストとします。第 \\(i\\) 段には \\(i - 1\\) 段または \\(i - 2\\) 段からしか到達できないため、\\(dp[i]\\) は \\(dp[i - 1] + cost[i]\\) または \\(dp[i - 2] + cost[i]\\) のいずれかになります。コストをできるだけ小さくするには、この二つのうち小さいほうを選べばよいです。</p> \\[ dp[i] = \\min(dp[i-1], dp[i-2]) + cost[i] \\] <p>ここから最適部分構造の意味を導けます。**元の問題の最適解は、部分問題の最適解から構築される**ということです。</p> <p>この問題が最適部分構造を持つことは明らかです。二つの部分問題の最適解 \\(dp[i-1]\\) と \\(dp[i-2]\\) からより良いほうを選び、それを用いて元の問題 \\(dp[i]\\) の最適解を構築しています。</p> <p>では、前節の階段昇り問題には最適部分構造があるのでしょうか。その目的は方法数を求めることで、一見すると計数問題です。しかし問い方を変えて「最大の方法数を求める」とすると、意外にも、問題の変更前後は等価であるにもかかわらず、最適部分構造が現れます。すなわち、第 \\(n\\) 段の最大方法数は第 \\(n-1\\) 段と第 \\(n-2\\) 段の最大方法数の和に等しいのです。このように、最適部分構造の解釈は比較的柔軟であり、問題によって意味合いが異なります。</p> <p>状態遷移方程式と初期状態 \\(dp[1] = cost[1]\\) および \\(dp[2] = cost[2]\\) に基づいて、次の動的計画法コードが得られます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby min_cost_climbing_stairs_dp.py<pre><code>def min_cost_climbing_stairs_dp(cost: list[int]) -&gt; int:\n    \"\"\"階段登りの最小コスト：動的計画法\"\"\"\n    n = len(cost) - 1\n    if n == 1 or n == 2:\n        return cost[n]\n    # 部分問題の解を保存するために dp テーブルを初期化\n    dp = [0] * (n + 1)\n    # 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1], dp[2] = cost[1], cost[2]\n    # 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for i in range(3, n + 1):\n        dp[i] = min(dp[i - 1], dp[i - 2]) + cost[i]\n    return dp[n]\n</code></pre> min_cost_climbing_stairs_dp.cpp<pre><code>/* 階段登りの最小コスト：動的計画法 */\nint minCostClimbingStairsDP(vector&lt;int&gt; &amp;cost) {\n    int n = cost.size() - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    // 部分問題の解を保存するために dp テーブルを初期化\n    vector&lt;int&gt; dp(n + 1);\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1] = cost[1];\n    dp[2] = cost[2];\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = min(dp[i - 1], dp[i - 2]) + cost[i];\n    }\n    return dp[n];\n}\n</code></pre> min_cost_climbing_stairs_dp.java<pre><code>/* 階段登りの最小コスト：動的計画法 */\nint minCostClimbingStairsDP(int[] cost) {\n    int n = cost.length - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    // 部分問題の解を保存するために dp テーブルを初期化\n    int[] dp = new int[n + 1];\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1] = cost[1];\n    dp[2] = cost[2];\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = Math.min(dp[i - 1], dp[i - 2]) + cost[i];\n    }\n    return dp[n];\n}\n</code></pre> min_cost_climbing_stairs_dp.cs<pre><code>/* 階段登りの最小コスト：動的計画法 */\nint MinCostClimbingStairsDP(int[] cost) {\n    int n = cost.Length - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    // 部分問題の解を保存するために dp テーブルを初期化\n    int[] dp = new int[n + 1];\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1] = cost[1];\n    dp[2] = cost[2];\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = Math.Min(dp[i - 1], dp[i - 2]) + cost[i];\n    }\n    return dp[n];\n}\n</code></pre> min_cost_climbing_stairs_dp.go<pre><code>/* 階段登りの最小コスト：動的計画法 */\nfunc minCostClimbingStairsDP(cost []int) int {\n    n := len(cost) - 1\n    if n == 1 || n == 2 {\n        return cost[n]\n    }\n    min := func(a, b int) int {\n        if a &lt; b {\n            return a\n        }\n        return b\n    }\n    // 部分問題の解を保存するために dp テーブルを初期化\n    dp := make([]int, n+1)\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1] = cost[1]\n    dp[2] = cost[2]\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for i := 3; i &lt;= n; i++ {\n        dp[i] = min(dp[i-1], dp[i-2]) + cost[i]\n    }\n    return dp[n]\n}\n</code></pre> min_cost_climbing_stairs_dp.swift<pre><code>/* 階段登りの最小コスト：動的計画法 */\nfunc minCostClimbingStairsDP(cost: [Int]) -&gt; Int {\n    let n = cost.count - 1\n    if n == 1 || n == 2 {\n        return cost[n]\n    }\n    // 部分問題の解を保存するために dp テーブルを初期化\n    var dp = Array(repeating: 0, count: n + 1)\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1] = cost[1]\n    dp[2] = cost[2]\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for i in 3 ... n {\n        dp[i] = min(dp[i - 1], dp[i - 2]) + cost[i]\n    }\n    return dp[n]\n}\n</code></pre> min_cost_climbing_stairs_dp.js<pre><code>/* 階段登りの最小コスト：動的計画法 */\nfunction minCostClimbingStairsDP(cost) {\n    const n = cost.length - 1;\n    if (n === 1 || n === 2) {\n        return cost[n];\n    }\n    // 部分問題の解を保存するために dp テーブルを初期化\n    const dp = new Array(n + 1);\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1] = cost[1];\n    dp[2] = cost[2];\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for (let i = 3; i &lt;= n; i++) {\n        dp[i] = Math.min(dp[i - 1], dp[i - 2]) + cost[i];\n    }\n    return dp[n];\n}\n</code></pre> min_cost_climbing_stairs_dp.ts<pre><code>/* 階段登りの最小コスト：動的計画法 */\nfunction minCostClimbingStairsDP(cost: Array&lt;number&gt;): number {\n    const n = cost.length - 1;\n    if (n === 1 || n === 2) {\n        return cost[n];\n    }\n    // 部分問題の解を保存するために dp テーブルを初期化\n    const dp = new Array(n + 1);\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1] = cost[1];\n    dp[2] = cost[2];\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for (let i = 3; i &lt;= n; i++) {\n        dp[i] = Math.min(dp[i - 1], dp[i - 2]) + cost[i];\n    }\n    return dp[n];\n}\n</code></pre> min_cost_climbing_stairs_dp.dart<pre><code>/* 階段登りの最小コスト：動的計画法 */\nint minCostClimbingStairsDP(List&lt;int&gt; cost) {\n  int n = cost.length - 1;\n  if (n == 1 || n == 2) return cost[n];\n  // 部分問題の解を保存するために dp テーブルを初期化\n  List&lt;int&gt; dp = List.filled(n + 1, 0);\n  // 初期状態：最小部分問題の解をあらかじめ設定\n  dp[1] = cost[1];\n  dp[2] = cost[2];\n  // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n  for (int i = 3; i &lt;= n; i++) {\n    dp[i] = min(dp[i - 1], dp[i - 2]) + cost[i];\n  }\n  return dp[n];\n}\n</code></pre> min_cost_climbing_stairs_dp.rs<pre><code>/* 階段登りの最小コスト：動的計画法 */\nfn min_cost_climbing_stairs_dp(cost: &amp;[i32]) -&gt; i32 {\n    let n = cost.len() - 1;\n    if n == 1 || n == 2 {\n        return cost[n];\n    }\n    // 部分問題の解を保存するために dp テーブルを初期化\n    let mut dp = vec![-1; n + 1];\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1] = cost[1];\n    dp[2] = cost[2];\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for i in 3..=n {\n        dp[i] = cmp::min(dp[i - 1], dp[i - 2]) + cost[i];\n    }\n    dp[n]\n}\n</code></pre> min_cost_climbing_stairs_dp.c<pre><code>/* 階段登りの最小コスト：動的計画法 */\nint minCostClimbingStairsDP(int cost[], int costSize) {\n    int n = costSize - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    // 部分問題の解を保存するために dp テーブルを初期化\n    int *dp = calloc(n + 1, sizeof(int));\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1] = cost[1];\n    dp[2] = cost[2];\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = myMin(dp[i - 1], dp[i - 2]) + cost[i];\n    }\n    int res = dp[n];\n    // メモリを解放する\n    free(dp);\n    return res;\n}\n</code></pre> min_cost_climbing_stairs_dp.kt<pre><code>/* 階段登りの最小コスト：動的計画法 */\nfun minCostClimbingStairsDP(cost: IntArray): Int {\n    val n = cost.size - 1\n    if (n == 1 || n == 2) return cost[n]\n    // 部分問題の解を保存するために dp テーブルを初期化\n    val dp = IntArray(n + 1)\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1] = cost[1]\n    dp[2] = cost[2]\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for (i in 3..n) {\n        dp[i] = min(dp[i - 1], dp[i - 2]) + cost[i]\n    }\n    return dp[n]\n}\n</code></pre> min_cost_climbing_stairs_dp.rb<pre><code>### 階段登りの最小コスト：動的計画法 ###\ndef min_cost_climbing_stairs_dp(cost)\n  n = cost.length - 1\n  return cost[n] if n == 1 || n == 2\n  # 部分問題の解を保存するために dp テーブルを初期化\n  dp = Array.new(n + 1, 0)\n  # 初期状態：最小部分問題の解をあらかじめ設定\n  dp[1], dp[2] = cost[1], cost[2]\n  # 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n  (3...(n + 1)).each { |i| dp[i] = [dp[i - 1], dp[i - 2]].min + cost[i] }\n  dp[n]\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>下図は上記コードの動的計画法の過程を示しています。</p> <p></p> <p> 図 14-7   階段昇り最小コストの動的計画法の過程 </p> <p>この問題では空間最適化も可能であり、一次元をゼロ次元まで圧縮することで、空間計算量を \\(O(n)\\) から \\(O(1)\\) に削減できます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby min_cost_climbing_stairs_dp.py<pre><code>def min_cost_climbing_stairs_dp_comp(cost: list[int]) -&gt; int:\n    \"\"\"階段昇りの最小コスト：空間最適化後の動的計画法\"\"\"\n    n = len(cost) - 1\n    if n == 1 or n == 2:\n        return cost[n]\n    a, b = cost[1], cost[2]\n    for i in range(3, n + 1):\n        a, b = b, min(a, b) + cost[i]\n    return b\n</code></pre> min_cost_climbing_stairs_dp.cpp<pre><code>/* 階段昇りの最小コスト：空間最適化後の動的計画法 */\nint minCostClimbingStairsDPComp(vector&lt;int&gt; &amp;cost) {\n    int n = cost.size() - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    int a = cost[1], b = cost[2];\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = min(a, tmp) + cost[i];\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> min_cost_climbing_stairs_dp.java<pre><code>/* 階段昇りの最小コスト：空間最適化後の動的計画法 */\nint minCostClimbingStairsDPComp(int[] cost) {\n    int n = cost.length - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    int a = cost[1], b = cost[2];\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = Math.min(a, tmp) + cost[i];\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> min_cost_climbing_stairs_dp.cs<pre><code>/* 階段昇りの最小コスト：空間最適化後の動的計画法 */\nint MinCostClimbingStairsDPComp(int[] cost) {\n    int n = cost.Length - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    int a = cost[1], b = cost[2];\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = Math.Min(a, tmp) + cost[i];\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> min_cost_climbing_stairs_dp.go<pre><code>/* 階段昇りの最小コスト：空間最適化後の動的計画法 */\nfunc minCostClimbingStairsDPComp(cost []int) int {\n    n := len(cost) - 1\n    if n == 1 || n == 2 {\n        return cost[n]\n    }\n    min := func(a, b int) int {\n        if a &lt; b {\n            return a\n        }\n        return b\n    }\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    a, b := cost[1], cost[2]\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for i := 3; i &lt;= n; i++ {\n        tmp := b\n        b = min(a, tmp) + cost[i]\n        a = tmp\n    }\n    return b\n}\n</code></pre> min_cost_climbing_stairs_dp.swift<pre><code>/* 階段昇りの最小コスト：空間最適化後の動的計画法 */\nfunc minCostClimbingStairsDPComp(cost: [Int]) -&gt; Int {\n    let n = cost.count - 1\n    if n == 1 || n == 2 {\n        return cost[n]\n    }\n    var (a, b) = (cost[1], cost[2])\n    for i in 3 ... n {\n        (a, b) = (b, min(a, b) + cost[i])\n    }\n    return b\n}\n</code></pre> min_cost_climbing_stairs_dp.js<pre><code>/* 階段昇りの最小コスト：空間最適化後の動的計画法 */\nfunction minCostClimbingStairsDPComp(cost) {\n    const n = cost.length - 1;\n    if (n === 1 || n === 2) {\n        return cost[n];\n    }\n    let a = cost[1],\n        b = cost[2];\n    for (let i = 3; i &lt;= n; i++) {\n        const tmp = b;\n        b = Math.min(a, tmp) + cost[i];\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> min_cost_climbing_stairs_dp.ts<pre><code>/* 階段昇りの最小コスト：空間最適化後の動的計画法 */\nfunction minCostClimbingStairsDPComp(cost: Array&lt;number&gt;): number {\n    const n = cost.length - 1;\n    if (n === 1 || n === 2) {\n        return cost[n];\n    }\n    let a = cost[1],\n        b = cost[2];\n    for (let i = 3; i &lt;= n; i++) {\n        const tmp = b;\n        b = Math.min(a, tmp) + cost[i];\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> min_cost_climbing_stairs_dp.dart<pre><code>/* 階段昇りの最小コスト：空間最適化後の動的計画法 */\nint minCostClimbingStairsDPComp(List&lt;int&gt; cost) {\n  int n = cost.length - 1;\n  if (n == 1 || n == 2) return cost[n];\n  int a = cost[1], b = cost[2];\n  for (int i = 3; i &lt;= n; i++) {\n    int tmp = b;\n    b = min(a, tmp) + cost[i];\n    a = tmp;\n  }\n  return b;\n}\n</code></pre> min_cost_climbing_stairs_dp.rs<pre><code>/* 階段昇りの最小コスト：空間最適化後の動的計画法 */\nfn min_cost_climbing_stairs_dp_comp(cost: &amp;[i32]) -&gt; i32 {\n    let n = cost.len() - 1;\n    if n == 1 || n == 2 {\n        return cost[n];\n    };\n    let (mut a, mut b) = (cost[1], cost[2]);\n    for i in 3..=n {\n        let tmp = b;\n        b = cmp::min(a, tmp) + cost[i];\n        a = tmp;\n    }\n    b\n}\n</code></pre> min_cost_climbing_stairs_dp.c<pre><code>/* 階段昇りの最小コスト：空間最適化後の動的計画法 */\nint minCostClimbingStairsDPComp(int cost[], int costSize) {\n    int n = costSize - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    int a = cost[1], b = cost[2];\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = myMin(a, tmp) + cost[i];\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> min_cost_climbing_stairs_dp.kt<pre><code>/* 階段昇りの最小コスト：空間最適化後の動的計画法 */\nfun minCostClimbingStairsDPComp(cost: IntArray): Int {\n    val n = cost.size - 1\n    if (n == 1 || n == 2) return cost[n]\n    var a = cost[1]\n    var b = cost[2]\n    for (i in 3..n) {\n        val tmp = b\n        b = min(a, tmp) + cost[i]\n        a = tmp\n    }\n    return b\n}\n</code></pre> min_cost_climbing_stairs_dp.rb<pre><code>### 階段登りの最小コスト：動的計画法 ###\ndef min_cost_climbing_stairs_dp(cost)\n  n = cost.length - 1\n  return cost[n] if n == 1 || n == 2\n  # 部分問題の解を保存するために dp テーブルを初期化\n  dp = Array.new(n + 1, 0)\n  # 初期状態：最小部分問題の解をあらかじめ設定\n  dp[1], dp[2] = cost[1], cost[2]\n  # 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n  (3...(n + 1)).each { |i| dp[i] = [dp[i - 1], dp[i - 2]].min + cost[i] }\n  dp[n]\nend\n\n# 階段昇りの最小コスト：空間最適化後の動的計画法\ndef min_cost_climbing_stairs_dp_comp(cost)\n  n = cost.length - 1\n  return cost[n] if n == 1 || n == 2\n  a, b = cost[1], cost[2]\n  (3...(n + 1)).each { |i| a, b = b, [a, b].min + cost[i] }\n  b\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 14 章 &nbsp; 動的計画法","14.2 &nbsp; 動的計画法の問題特性"],"tags":[]},{"location":"chapter_dynamic_programming/dp_problem_features/#1422","level":2,"title":"14.2.2   無後効性","text":"<p>無後効性は、動的計画法が問題を効率よく解ける重要な特性の一つであり、その定義は次のとおりです。ある確定した状態が与えられたとき、その後の発展は現在の状態のみに依存し、過去に経たすべての状態には依存しない。</p> <p>階段昇り問題を例にすると、状態 \\(i\\) が与えられたとき、そこから状態 \\(i+1\\) と状態 \\(i+2\\) へ発展し、それぞれ \\(1\\) 段進む場合と \\(2\\) 段進む場合に対応します。この二つの選択を行う際、状態 \\(i\\) より前の状態を考慮する必要はなく、それらは状態 \\(i\\) の将来に影響を与えません。</p> <p>しかし、階段昇り問題に制約を一つ追加すると、状況は変わります。</p> <p>制約付き階段昇り</p> <p>全部で \\(n\\) 段ある階段が与えられ、各ステップで \\(1\\) 段または \\(2\\) 段上ることができます。ただし、連続する 2 回で \\(1\\) 段ずつ上ることはできません。頂上まで上る方法は何通りあるでしょうか。</p> <p>下図に示すように、第 \\(3\\) 段まで上る実行可能な方法は \\(2\\) 通りしか残りません。そのうち、\\(1\\) 段ずつ 3 回連続で上る方法は制約を満たさないため除外されます。</p> <p></p> <p> 図 14-8   制約付きで第 3 段まで上る方法数 </p> <p>この問題では、前回が \\(1\\) 段上りだった場合、次回は必ず \\(2\\) 段上らなければなりません。これは、**次の一手が現在の状態（現在いる階段の段数）だけでは独立に決まらず、一つ前の状態（前回いた段数）にも関係する**ことを意味します。</p> <p>容易に分かるように、この問題はもはや無後効性を満たしておらず、状態遷移方程式 \\(dp[i] = dp[i-1] + dp[i-2]\\) も成立しません。というのも、\\(dp[i-1]\\) は今回 \\(1\\) 段上る場合を表しますが、その中には「前回も \\(1\\) 段上ってきた」方法が多数含まれており、制約を満たすためには \\(dp[i-1]\\) をそのまま \\(dp[i]\\) に加えることができないからです。</p> <p>このため、状態定義を拡張する必要があります。**状態 \\([i, j]\\) は、第 \\(i\\) 段にいて前回に \\(j\\) 段上ったことを表す**とし、ここで \\(j \\in \\{1, 2\\}\\) です。この状態定義により、前回が \\(1\\) 段上りか \\(2\\) 段上りかを有効に区別でき、現在の状態がどこから来たのかを判断できます。</p> <ul> <li>前回に \\(1\\) 段上った場合、その前の回は \\(2\\) 段上りしか選べないため、\\(dp[i, 1]\\) は \\(dp[i-1, 2]\\) からのみ遷移できます。</li> <li>前回に \\(2\\) 段上った場合、その前の回は \\(1\\) 段上りまたは \\(2\\) 段上りを選べるため、\\(dp[i, 2]\\) は \\(dp[i-2, 1]\\) または \\(dp[i-2, 2]\\) から遷移できます。</li> </ul> <p>下図に示すように、この定義のもとでは \\(dp[i, j]\\) は状態 \\([i, j]\\) に対応する方法数を表します。このとき状態遷移方程式は次のようになります。</p> \\[ \\begin{cases} dp[i, 1] = dp[i-1, 2] \\\\ dp[i, 2] = dp[i-2, 1] + dp[i-2, 2] \\end{cases} \\] <p></p> <p> 図 14-9   制約を考慮した漸化関係 </p> <p>最終的に、\\(dp[n, 1] + dp[n, 2]\\) を返せば十分であり、その和が第 \\(n\\) 段まで上る方法の総数を表します。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby climbing_stairs_constraint_dp.py<pre><code>def climbing_stairs_constraint_dp(n: int) -&gt; int:\n    \"\"\"制約付き階段登り：動的計画法\"\"\"\n    if n == 1 or n == 2:\n        return 1\n    # 部分問題の解を保存するために dp テーブルを初期化\n    dp = [[0] * 3 for _ in range(n + 1)]\n    # 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1][1], dp[1][2] = 1, 0\n    dp[2][1], dp[2][2] = 0, 1\n    # 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for i in range(3, n + 1):\n        dp[i][1] = dp[i - 1][2]\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2]\n    return dp[n][1] + dp[n][2]\n</code></pre> climbing_stairs_constraint_dp.cpp<pre><code>/* 制約付き階段登り：動的計画法 */\nint climbingStairsConstraintDP(int n) {\n    if (n == 1 || n == 2) {\n        return 1;\n    }\n    // 部分問題の解を保存するために dp テーブルを初期化\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(3, 0));\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1][1] = 1;\n    dp[1][2] = 0;\n    dp[2][1] = 0;\n    dp[2][2] = 1;\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i][1] = dp[i - 1][2];\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2];\n    }\n    return dp[n][1] + dp[n][2];\n}\n</code></pre> climbing_stairs_constraint_dp.java<pre><code>/* 制約付き階段登り：動的計画法 */\nint climbingStairsConstraintDP(int n) {\n    if (n == 1 || n == 2) {\n        return 1;\n    }\n    // 部分問題の解を保存するために dp テーブルを初期化\n    int[][] dp = new int[n + 1][3];\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1][1] = 1;\n    dp[1][2] = 0;\n    dp[2][1] = 0;\n    dp[2][2] = 1;\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i][1] = dp[i - 1][2];\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2];\n    }\n    return dp[n][1] + dp[n][2];\n}\n</code></pre> climbing_stairs_constraint_dp.cs<pre><code>/* 制約付き階段登り：動的計画法 */\nint ClimbingStairsConstraintDP(int n) {\n    if (n == 1 || n == 2) {\n        return 1;\n    }\n    // 部分問題の解を保存するために dp テーブルを初期化\n    int[,] dp = new int[n + 1, 3];\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1, 1] = 1;\n    dp[1, 2] = 0;\n    dp[2, 1] = 0;\n    dp[2, 2] = 1;\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i, 1] = dp[i - 1, 2];\n        dp[i, 2] = dp[i - 2, 1] + dp[i - 2, 2];\n    }\n    return dp[n, 1] + dp[n, 2];\n}\n</code></pre> climbing_stairs_constraint_dp.go<pre><code>/* 制約付き階段登り：動的計画法 */\nfunc climbingStairsConstraintDP(n int) int {\n    if n == 1 || n == 2 {\n        return 1\n    }\n    // 部分問題の解を保存するために dp テーブルを初期化\n    dp := make([][3]int, n+1)\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1][1] = 1\n    dp[1][2] = 0\n    dp[2][1] = 0\n    dp[2][2] = 1\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for i := 3; i &lt;= n; i++ {\n        dp[i][1] = dp[i-1][2]\n        dp[i][2] = dp[i-2][1] + dp[i-2][2]\n    }\n    return dp[n][1] + dp[n][2]\n}\n</code></pre> climbing_stairs_constraint_dp.swift<pre><code>/* 制約付き階段登り：動的計画法 */\nfunc climbingStairsConstraintDP(n: Int) -&gt; Int {\n    if n == 1 || n == 2 {\n        return 1\n    }\n    // 部分問題の解を保存するために dp テーブルを初期化\n    var dp = Array(repeating: Array(repeating: 0, count: 3), count: n + 1)\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1][1] = 1\n    dp[1][2] = 0\n    dp[2][1] = 0\n    dp[2][2] = 1\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for i in 3 ... n {\n        dp[i][1] = dp[i - 1][2]\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2]\n    }\n    return dp[n][1] + dp[n][2]\n}\n</code></pre> climbing_stairs_constraint_dp.js<pre><code>/* 制約付き階段登り：動的計画法 */\nfunction climbingStairsConstraintDP(n) {\n    if (n === 1 || n === 2) {\n        return 1;\n    }\n    // 部分問題の解を保存するために dp テーブルを初期化\n    const dp = Array.from(new Array(n + 1), () =&gt; new Array(3));\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1][1] = 1;\n    dp[1][2] = 0;\n    dp[2][1] = 0;\n    dp[2][2] = 1;\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for (let i = 3; i &lt;= n; i++) {\n        dp[i][1] = dp[i - 1][2];\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2];\n    }\n    return dp[n][1] + dp[n][2];\n}\n</code></pre> climbing_stairs_constraint_dp.ts<pre><code>/* 制約付き階段登り：動的計画法 */\nfunction climbingStairsConstraintDP(n: number): number {\n    if (n === 1 || n === 2) {\n        return 1;\n    }\n    // 部分問題の解を保存するために dp テーブルを初期化\n    const dp = Array.from({ length: n + 1 }, () =&gt; new Array(3));\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1][1] = 1;\n    dp[1][2] = 0;\n    dp[2][1] = 0;\n    dp[2][2] = 1;\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for (let i = 3; i &lt;= n; i++) {\n        dp[i][1] = dp[i - 1][2];\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2];\n    }\n    return dp[n][1] + dp[n][2];\n}\n</code></pre> climbing_stairs_constraint_dp.dart<pre><code>/* 制約付き階段登り：動的計画法 */\nint climbingStairsConstraintDP(int n) {\n  if (n == 1 || n == 2) {\n    return 1;\n  }\n  // 部分問題の解を保存するために dp テーブルを初期化\n  List&lt;List&lt;int&gt;&gt; dp = List.generate(n + 1, (index) =&gt; List.filled(3, 0));\n  // 初期状態：最小部分問題の解をあらかじめ設定\n  dp[1][1] = 1;\n  dp[1][2] = 0;\n  dp[2][1] = 0;\n  dp[2][2] = 1;\n  // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n  for (int i = 3; i &lt;= n; i++) {\n    dp[i][1] = dp[i - 1][2];\n    dp[i][2] = dp[i - 2][1] + dp[i - 2][2];\n  }\n  return dp[n][1] + dp[n][2];\n}\n</code></pre> climbing_stairs_constraint_dp.rs<pre><code>/* 制約付き階段登り：動的計画法 */\nfn climbing_stairs_constraint_dp(n: usize) -&gt; i32 {\n    if n == 1 || n == 2 {\n        return 1;\n    };\n    // 部分問題の解を保存するために dp テーブルを初期化\n    let mut dp = vec![vec![-1; 3]; n + 1];\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1][1] = 1;\n    dp[1][2] = 0;\n    dp[2][1] = 0;\n    dp[2][2] = 1;\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for i in 3..=n {\n        dp[i][1] = dp[i - 1][2];\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2];\n    }\n    dp[n][1] + dp[n][2]\n}\n</code></pre> climbing_stairs_constraint_dp.c<pre><code>/* 制約付き階段登り：動的計画法 */\nint climbingStairsConstraintDP(int n) {\n    if (n == 1 || n == 2) {\n        return 1;\n    }\n    // 部分問題の解を保存するために dp テーブルを初期化\n    int **dp = malloc((n + 1) * sizeof(int *));\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i] = calloc(3, sizeof(int));\n    }\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1][1] = 1;\n    dp[1][2] = 0;\n    dp[2][1] = 0;\n    dp[2][2] = 1;\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i][1] = dp[i - 1][2];\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2];\n    }\n    int res = dp[n][1] + dp[n][2];\n    // メモリを解放する\n    for (int i = 0; i &lt;= n; i++) {\n        free(dp[i]);\n    }\n    free(dp);\n    return res;\n}\n</code></pre> climbing_stairs_constraint_dp.kt<pre><code>/* 制約付き階段登り：動的計画法 */\nfun climbingStairsConstraintDP(n: Int): Int {\n    if (n == 1 || n == 2) {\n        return 1\n    }\n    // 部分問題の解を保存するために dp テーブルを初期化\n    val dp = Array(n + 1) { IntArray(3) }\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1][1] = 1\n    dp[1][2] = 0\n    dp[2][1] = 0\n    dp[2][2] = 1\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for (i in 3..n) {\n        dp[i][1] = dp[i - 1][2]\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2]\n    }\n    return dp[n][1] + dp[n][2]\n}\n</code></pre> climbing_stairs_constraint_dp.rb<pre><code>### 制約付き階段登り：動的計画法 ###\ndef climbing_stairs_constraint_dp(n)\n  return 1 if n == 1 || n == 2\n\n  # 部分問題の解を保存するために dp テーブルを初期化\n  dp = Array.new(n + 1) { Array.new(3, 0) }\n  # 初期状態：最小部分問題の解をあらかじめ設定\n  dp[1][1], dp[1][2] = 1, 0\n  dp[2][1], dp[2][2] = 0, 1\n  # 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n  for i in 3...(n + 1)\n    dp[i][1] = dp[i - 1][2]\n    dp[i][2] = dp[i - 2][1] + dp[i - 2][2]\n  end\n\n  dp[n][1] + dp[n][2]\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>上の例では、追加で考慮すべきなのは一つ前の状態だけであるため、状態定義を拡張することで問題を再び無後効性に適合させることができます。しかし、問題によっては非常に強い「後効性」があります。</p> <p>階段昇りと障害物生成</p> <p>全部で \\(n\\) 段ある階段が与えられ、各ステップで \\(1\\) 段または \\(2\\) 段上ることができます。**第 \\(i\\) 段に到達すると、システムは自動的に第 \\(2i\\) 段に障害物を置き、それ以降はどの回でも第 \\(2i\\) 段へ跳ぶことができない**とします。例えば、最初の 2 回でそれぞれ第 \\(2\\) 段、第 \\(3\\) 段に到達した場合、その後は第 \\(4\\) 段と第 \\(6\\) 段に跳ぶことはできません。頂上まで上る方法は何通りあるでしょうか。</p> <p>この問題では、次の跳躍が過去のすべての状態に依存します。なぜなら、各跳躍がより高い段に障害物を設置し、将来の跳躍に影響するからです。この種の問題は、動的計画法では解きにくいことが多いです。</p> <p>実際、多くの複雑な組合せ最適化問題（例えば巡回セールスマン問題）は無後効性を満たしません。このような問題に対しては、通常、ヒューリスティック探索、遺伝的アルゴリズム、強化学習などの他の方法を用いて、限られた時間内に実用的な局所最適解を得ます。</p>","path":["第 14 章 &nbsp; 動的計画法","14.2 &nbsp; 動的計画法の問題特性"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/","level":1,"title":"14.3   動的計画法の問題解決の考え方","text":"<p>前の 2 節では動的計画法の問題の主要な特徴を紹介しました。ここからは、さらに実用的な 2 つの問題を一緒に考えていきます。</p> <ol> <li>ある問題が動的計画法の問題かどうかを、どのように判断すればよいでしょうか？</li> <li>動的計画法の問題を解くには、どこから着手し、完全な手順はどのようなものでしょうか？</li> </ol>","path":["第 14 章 &nbsp; 動的計画法","14.3 &nbsp; 動的計画法の問題解決の考え方"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#1431","level":2,"title":"14.3.1   問題の判定","text":"<p>一般に、ある問題が重複部分問題と最適部分構造を含み、さらに無後效性を満たしているなら、通常は動的計画法で解くのに適しています。しかし、問題文からこれらの性質を直接読み取るのは簡単ではありません。そのため通常は条件を少し緩めて、**まずその問題がバックトラッキング（全探索）で解くのに適しているか**を観察します。</p> <p>バックトラッキングで解くのに適した問題は、通常「決定木モデル」を満たします。この種の問題は木構造で表現でき、各ノードは 1 つの決定を表し、各経路は 1 つの決定列を表します。</p> <p>言い換えると、問題に明確な決定の概念が含まれており、解が一連の決定によって生成されるなら、その問題は決定木モデルを満たし、通常はバックトラッキングで解くことができます。</p> <p>これに加えて、動的計画法の問題には判定のための「加点要素」もあります。</p> <ul> <li>問題文に最大（最小）や最多（最少）などの最適化に関する記述がある。</li> <li>問題の状態が配列、多次元行列、または木で表現でき、ある状態とその周辺の状態の間に漸化的な関係がある。</li> </ul> <p>反対に、「減点要素」もあります。</p> <ul> <li>問題の目的が最適解を求めることではなく、あり得るすべての解を列挙することである。</li> <li>問題文に明確な順列・組合せの特徴があり、具体的な複数の解を返す必要がある。</li> </ul> <p>ある問題が決定木モデルを満たし、さらに比較的明確な「加点要素」を備えているなら、その問題は動的計画法の問題であると仮定し、解く過程でそれを検証できます。</p>","path":["第 14 章 &nbsp; 動的計画法","14.3 &nbsp; 動的計画法の問題解決の考え方"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#1432","level":2,"title":"14.3.2   問題を解く手順","text":"<p>動的計画法の解法の流れは問題の性質や難易度によって異なりますが、通常は次の手順に従います。すなわち、決定を記述し、状態を定義し、\\(dp\\) テーブルを構築し、状態遷移方程式を導出し、境界条件を定めます。</p> <p>解法の手順をより具体的に示すために、ここでは古典的な問題である「最小経路和」を例にします。</p> <p>Question</p> <p>\\(n \\times m\\) の 2 次元グリッド <code>grid</code> が与えられます。グリッドの各セルには非負整数が格納されており、そのセルのコストを表します。ロボットは左上のセルを始点とし、毎回下または右に 1 マスだけ移動して、右下のセルまで進みます。左上から右下までの最小経路和を返してください。</p> <p>次の図は 1 つの例を示しており、このグリッドの最小経路和は \\(13\\) です。</p> <p></p> <p> 図 14-10   最小経路和のサンプルデータ </p> <p>ステップ 1：各ラウンドの決定を考え、状態を定義して、\\(dp\\) テーブルを得る</p> <p>この問題における各ラウンドの決定は、現在のマスから下または右へ 1 マス進むことです。現在のマスの行・列インデックスを \\([i, j]\\) とすると、下または右へ 1 マス進んだ後のインデックスは \\([i+1, j]\\) または \\([i, j+1]\\) になります。したがって、状態には行インデックスと列インデックスの 2 つの変数を含め、\\([i, j]\\) と表します。</p> <p>状態 \\([i, j]\\) に対応する部分問題は、始点 \\([0, 0]\\) から \\([i, j]\\) まで進む最小経路和であり、その解を \\(dp[i, j]\\) と記します。</p> <p>これで、次の図に示す 2 次元の \\(dp\\) 行列が得られます。そのサイズは入力グリッド \\(grid\\) と同じです。</p> <p></p> <p> 図 14-11   状態の定義と dp テーブル </p> <p>Note</p> <p>動的計画法とバックトラッキングの過程は、いずれも 1 つの決定列として記述できます。そして状態は、すべての決定変数から構成されます。状態には解法の進行状況を表すすべての変数が含まれているべきであり、次の状態を導くのに十分な情報を持っている必要があります。</p> <p>各状態は 1 つの部分問題に対応しており、すべての部分問題の解を保存するために \\(dp\\) テーブルを定義します。状態の各独立変数は、\\(dp\\) テーブルの 1 つの次元に対応します。本質的に、\\(dp\\) テーブルは状態と部分問題の解との対応関係です。</p> <p>ステップ 2：最適部分構造を見つけ、状態遷移方程式を導出する</p> <p>状態 \\([i, j]\\) は、上のマス \\([i-1, j]\\) または左のマス \\([i, j-1]\\) からしか遷移してきません。したがって最適部分構造は、\\([i, j]\\) に到達する最小経路和が、\\([i, j-1]\\) の最小経路和と \\([i-1, j]\\) の最小経路和のうち小さい方によって決まる、ということです。</p> <p>以上の分析から、次の図に示す状態遷移方程式を導くことができます。</p> \\[ dp[i, j] = \\min(dp[i-1, j], dp[i, j-1]) + grid[i, j] \\] <p></p> <p> 図 14-12   最適部分構造と状態遷移方程式 </p> <p>Note</p> <p>定義済みの \\(dp\\) テーブルに基づいて、元の問題と部分問題の関係を考え、部分問題の最適解から元の問題の最適解を構成する方法、すなわち最適部分構造を見つけます。</p> <p>ひとたび最適部分構造が見つかれば、それを使って状態遷移方程式を構築できます。</p> <p>ステップ 3：境界条件と状態遷移の順序を決める</p> <p>この問題では、先頭行にある状態は左の状態からしか得られず、先頭列にある状態は上の状態からしか得られません。したがって、先頭行 \\(i = 0\\) と先頭列 \\(j = 0\\) が境界条件になります。</p> <p>次の図に示すように、各マスは左のマスと上のマスから遷移してくるため、ループを用いて行列を走査します。外側のループで各行を、内側のループで各列を走査します。</p> <p></p> <p> 図 14-13   境界条件と状態遷移の順序 </p> <p>Note</p> <p>境界条件は、動的計画法では \\(dp\\) テーブルの初期化に使われ、探索では枝刈りに使われます。</p> <p>状態遷移の順序で重要なのは、現在の問題の解を計算するときに、それが依存するより小さな部分問題の解がすべてすでに正しく計算済みであることを保証する点です。</p> <p>以上の分析により、すでに動的計画法のコードを直接書くことができます。しかし、部分問題への分解はトップダウンの考え方であるため、「力任せ探索 \\(\\rightarrow\\) メモ化探索 \\(\\rightarrow\\) 動的計画法」の順に実装するほうが、思考の流れにはより自然です。</p>","path":["第 14 章 &nbsp; 動的計画法","14.3 &nbsp; 動的計画法の問題解決の考え方"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#1-1","level":3,"title":"1.   方法 1：力任せ探索","text":"<p>状態 \\([i, j]\\) から探索を開始し、より小さな状態 \\([i-1, j]\\) と \\([i, j-1]\\) へと分解していきます。再帰関数には次の要素が含まれます。</p> <ul> <li>再帰引数：状態 \\([i, j]\\) 。</li> <li>戻り値：\\([0, 0]\\) から \\([i, j]\\) までの最小経路和 \\(dp[i, j]\\) 。</li> <li>終了条件：\\(i = 0\\) かつ \\(j = 0\\) のとき、コスト \\(grid[0, 0]\\) を返す。</li> <li>枝刈り：\\(i &lt; 0\\) または \\(j &lt; 0\\) でインデックスが範囲外になった場合、コスト \\(+\\infty\\) を返し、実行不可能であることを表す。</li> </ul> <p>実装コードは次のとおりです。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby min_path_sum.py<pre><code>def min_path_sum_dfs(grid: list[list[int]], i: int, j: int) -&gt; int:\n    \"\"\"最小経路和：全探索\"\"\"\n    # 左上のセルなら探索を終了する\n    if i == 0 and j == 0:\n        return grid[0][0]\n    # 行または列のインデックスが範囲外なら、コスト +∞ を返す\n    if i &lt; 0 or j &lt; 0:\n        return inf\n    # 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する\n    up = min_path_sum_dfs(grid, i - 1, j)\n    left = min_path_sum_dfs(grid, i, j - 1)\n    # 左上隅から (i, j) までの最小経路コストを返す\n    return min(left, up) + grid[i][j]\n</code></pre> min_path_sum.cpp<pre><code>/* 最小経路和：全探索 */\nint minPathSumDFS(vector&lt;vector&lt;int&gt;&gt; &amp;grid, int i, int j) {\n    // 左上のセルなら探索を終了する\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // 行または列のインデックスが範囲外なら、コスト +∞ を返す\n    if (i &lt; 0 || j &lt; 0) {\n        return INT_MAX;\n    }\n    // 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する\n    int up = minPathSumDFS(grid, i - 1, j);\n    int left = minPathSumDFS(grid, i, j - 1);\n    // 左上隅から (i, j) までの最小経路コストを返す\n    return min(left, up) != INT_MAX ? min(left, up) + grid[i][j] : INT_MAX;\n}\n</code></pre> min_path_sum.java<pre><code>/* 最小経路和：全探索 */\nint minPathSumDFS(int[][] grid, int i, int j) {\n    // 左上のセルなら探索を終了する\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // 行または列のインデックスが範囲外なら、コスト +∞ を返す\n    if (i &lt; 0 || j &lt; 0) {\n        return Integer.MAX_VALUE;\n    }\n    // 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する\n    int up = minPathSumDFS(grid, i - 1, j);\n    int left = minPathSumDFS(grid, i, j - 1);\n    // 左上隅から (i, j) までの最小経路コストを返す\n    return Math.min(left, up) + grid[i][j];\n}\n</code></pre> min_path_sum.cs<pre><code>/* 最小経路和：全探索 */\nint MinPathSumDFS(int[][] grid, int i, int j) {\n    // 左上のセルなら探索を終了する\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // 行または列のインデックスが範囲外なら、コスト +∞ を返す\n    if (i &lt; 0 || j &lt; 0) {\n        return int.MaxValue;\n    }\n    // 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する\n    int up = MinPathSumDFS(grid, i - 1, j);\n    int left = MinPathSumDFS(grid, i, j - 1);\n    // 左上隅から (i, j) までの最小経路コストを返す\n    return Math.Min(left, up) + grid[i][j];\n}\n</code></pre> min_path_sum.go<pre><code>/* 最小経路和：全探索 */\nfunc minPathSumDFS(grid [][]int, i, j int) int {\n    // 左上のセルなら探索を終了する\n    if i == 0 &amp;&amp; j == 0 {\n        return grid[0][0]\n    }\n    // 行または列のインデックスが範囲外なら、コスト +∞ を返す\n    if i &lt; 0 || j &lt; 0 {\n        return math.MaxInt\n    }\n    // 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する\n    up := minPathSumDFS(grid, i-1, j)\n    left := minPathSumDFS(grid, i, j-1)\n    // 左上隅から (i, j) までの最小経路コストを返す\n    return int(math.Min(float64(left), float64(up))) + grid[i][j]\n}\n</code></pre> min_path_sum.swift<pre><code>/* 最小経路和：全探索 */\nfunc minPathSumDFS(grid: [[Int]], i: Int, j: Int) -&gt; Int {\n    // 左上のセルなら探索を終了する\n    if i == 0, j == 0 {\n        return grid[0][0]\n    }\n    // 行または列のインデックスが範囲外なら、コスト +∞ を返す\n    if i &lt; 0 || j &lt; 0 {\n        return .max\n    }\n    // 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する\n    let up = minPathSumDFS(grid: grid, i: i - 1, j: j)\n    let left = minPathSumDFS(grid: grid, i: i, j: j - 1)\n    // 左上隅から (i, j) までの最小経路コストを返す\n    return min(left, up) + grid[i][j]\n}\n</code></pre> min_path_sum.js<pre><code>/* 最小経路和：全探索 */\nfunction minPathSumDFS(grid, i, j) {\n    // 左上のセルなら探索を終了する\n    if (i === 0 &amp;&amp; j === 0) {\n        return grid[0][0];\n    }\n    // 行または列のインデックスが範囲外なら、コスト +∞ を返す\n    if (i &lt; 0 || j &lt; 0) {\n        return Infinity;\n    }\n    // 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する\n    const up = minPathSumDFS(grid, i - 1, j);\n    const left = minPathSumDFS(grid, i, j - 1);\n    // 左上隅から (i, j) までの最小経路コストを返す\n    return Math.min(left, up) + grid[i][j];\n}\n</code></pre> min_path_sum.ts<pre><code>/* 最小経路和：全探索 */\nfunction minPathSumDFS(\n    grid: Array&lt;Array&lt;number&gt;&gt;,\n    i: number,\n    j: number\n): number {\n    // 左上のセルなら探索を終了する\n    if (i === 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // 行または列のインデックスが範囲外なら、コスト +∞ を返す\n    if (i &lt; 0 || j &lt; 0) {\n        return Infinity;\n    }\n    // 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する\n    const up = minPathSumDFS(grid, i - 1, j);\n    const left = minPathSumDFS(grid, i, j - 1);\n    // 左上隅から (i, j) までの最小経路コストを返す\n    return Math.min(left, up) + grid[i][j];\n}\n</code></pre> min_path_sum.dart<pre><code>/* 最小経路和：全探索 */\nint minPathSumDFS(List&lt;List&lt;int&gt;&gt; grid, int i, int j) {\n  // 左上のセルなら探索を終了する\n  if (i == 0 &amp;&amp; j == 0) {\n    return grid[0][0];\n  }\n  // 行または列のインデックスが範囲外なら、コスト +∞ を返す\n  if (i &lt; 0 || j &lt; 0) {\n    // Dart では、int 型は固定範囲の整数であり、「無限大」を表す値は存在しない\n    return BigInt.from(2).pow(31).toInt();\n  }\n  // 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する\n  int up = minPathSumDFS(grid, i - 1, j);\n  int left = minPathSumDFS(grid, i, j - 1);\n  // 左上隅から (i, j) までの最小経路コストを返す\n  return min(left, up) + grid[i][j];\n}\n</code></pre> min_path_sum.rs<pre><code>/* 最小経路和：全探索 */\nfn min_path_sum_dfs(grid: &amp;Vec&lt;Vec&lt;i32&gt;&gt;, i: i32, j: i32) -&gt; i32 {\n    // 左上のセルなら探索を終了する\n    if i == 0 &amp;&amp; j == 0 {\n        return grid[0][0];\n    }\n    // 行または列のインデックスが範囲外なら、コスト +∞ を返す\n    if i &lt; 0 || j &lt; 0 {\n        return i32::MAX;\n    }\n    // 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する\n    let up = min_path_sum_dfs(grid, i - 1, j);\n    let left = min_path_sum_dfs(grid, i, j - 1);\n    // 左上隅から (i, j) までの最小経路コストを返す\n    std::cmp::min(left, up) + grid[i as usize][j as usize]\n}\n</code></pre> min_path_sum.c<pre><code>/* 最小経路和：全探索 */\nint minPathSumDFS(int grid[MAX_SIZE][MAX_SIZE], int i, int j) {\n    // 左上のセルなら探索を終了する\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // 行または列のインデックスが範囲外なら、コスト +∞ を返す\n    if (i &lt; 0 || j &lt; 0) {\n        return INT_MAX;\n    }\n    // 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する\n    int up = minPathSumDFS(grid, i - 1, j);\n    int left = minPathSumDFS(grid, i, j - 1);\n    // 左上隅から (i, j) までの最小経路コストを返す\n    return myMin(left, up) != INT_MAX ? myMin(left, up) + grid[i][j] : INT_MAX;\n}\n</code></pre> min_path_sum.kt<pre><code>/* 最小経路和：全探索 */\nfun minPathSumDFS(grid: Array&lt;IntArray&gt;, i: Int, j: Int): Int {\n    // 左上のセルなら探索を終了する\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0]\n    }\n    // 行または列のインデックスが範囲外なら、コスト +∞ を返す\n    if (i &lt; 0 || j &lt; 0) {\n        return Int.MAX_VALUE\n    }\n    // 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する\n    val up = minPathSumDFS(grid, i - 1, j)\n    val left = minPathSumDFS(grid, i, j - 1)\n    // 左上隅から (i, j) までの最小経路コストを返す\n    return min(left, up) + grid[i][j]\n}\n</code></pre> min_path_sum.rb<pre><code>### 最小経路和：全探索 ###\ndef min_path_sum_dfs(grid, i, j)\n  # 左上のセルなら探索を終了する\n  return grid[i][j] if i == 0 &amp;&amp; j == 0\n  # 行または列のインデックスが範囲外なら、コスト +∞ を返す\n  return Float::INFINITY if i &lt; 0 || j &lt; 0\n  # 左上から (i-1, j) および (i, j-1) までの最小経路コストを計算する\n  up = min_path_sum_dfs(grid, i - 1, j)\n  left = min_path_sum_dfs(grid, i, j - 1)\n  # 左上隅から (i, j) までの最小経路コストを返す\n  [left, up].min + grid[i][j]\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>次の図は、\\(dp[2, 1]\\) を根ノードとする再帰木を示しています。この中にはいくつかの重複部分問題が含まれており、その数はグリッド <code>grid</code> のサイズが大きくなるにつれて急激に増加します。</p> <p>本質的に、重複部分問題が生じる理由は、**左上からあるセルへ到達する経路が複数存在すること**にあります。</p> <p></p> <p> 図 14-14   力任せ探索の再帰木 </p> <p>各状態には下と右の 2 通りの選択肢があり、左上から右下まで進むには合計で \\(m + n - 2\\) 歩必要です。したがって最悪時間計算量は \\(O(2^{m + n})\\) です。ここで、\\(n\\) と \\(m\\) はそれぞれグリッドの行数と列数を表します。なお、この見積もりではグリッド境界付近の状況を考慮していません。境界に達すると選択肢は 1 つだけになるため、実際の経路数はこれより少なくなります。</p>","path":["第 14 章 &nbsp; 動的計画法","14.3 &nbsp; 動的計画法の問題解決の考え方"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#2-2","level":3,"title":"2.   方法 2：メモ化探索","text":"<p>グリッド <code>grid</code> と同じサイズのメモ配列 <code>mem</code> を導入し、各部分問題の解を記録して、重複部分問題を枝刈りします。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby min_path_sum.py<pre><code>def min_path_sum_dfs_mem(\n    grid: list[list[int]], mem: list[list[int]], i: int, j: int\n) -&gt; int:\n    \"\"\"最小経路和：メモ化探索\"\"\"\n    # 左上のセルなら探索を終了する\n    if i == 0 and j == 0:\n        return grid[0][0]\n    # 行または列のインデックスが範囲外なら、コスト +∞ を返す\n    if i &lt; 0 or j &lt; 0:\n        return inf\n    # 既に記録があればそのまま返す\n    if mem[i][j] != -1:\n        return mem[i][j]\n    # 左と上のセルからの最小経路コスト\n    up = min_path_sum_dfs_mem(grid, mem, i - 1, j)\n    left = min_path_sum_dfs_mem(grid, mem, i, j - 1)\n    # 左上から (i, j) までの最小経路コストを記録して返す\n    mem[i][j] = min(left, up) + grid[i][j]\n    return mem[i][j]\n</code></pre> min_path_sum.cpp<pre><code>/* 最小経路和：メモ化探索 */\nint minPathSumDFSMem(vector&lt;vector&lt;int&gt;&gt; &amp;grid, vector&lt;vector&lt;int&gt;&gt; &amp;mem, int i, int j) {\n    // 左上のセルなら探索を終了する\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // 行または列のインデックスが範囲外なら、コスト +∞ を返す\n    if (i &lt; 0 || j &lt; 0) {\n        return INT_MAX;\n    }\n    // 既に記録があればそのまま返す\n    if (mem[i][j] != -1) {\n        return mem[i][j];\n    }\n    // 左と上のセルからの最小経路コスト\n    int up = minPathSumDFSMem(grid, mem, i - 1, j);\n    int left = minPathSumDFSMem(grid, mem, i, j - 1);\n    // 左上から (i, j) までの最小経路コストを記録して返す\n    mem[i][j] = min(left, up) != INT_MAX ? min(left, up) + grid[i][j] : INT_MAX;\n    return mem[i][j];\n}\n</code></pre> min_path_sum.java<pre><code>/* 最小経路和：メモ化探索 */\nint minPathSumDFSMem(int[][] grid, int[][] mem, int i, int j) {\n    // 左上のセルなら探索を終了する\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // 行または列のインデックスが範囲外なら、コスト +∞ を返す\n    if (i &lt; 0 || j &lt; 0) {\n        return Integer.MAX_VALUE;\n    }\n    // 既に記録があればそのまま返す\n    if (mem[i][j] != -1) {\n        return mem[i][j];\n    }\n    // 左と上のセルからの最小経路コスト\n    int up = minPathSumDFSMem(grid, mem, i - 1, j);\n    int left = minPathSumDFSMem(grid, mem, i, j - 1);\n    // 左上から (i, j) までの最小経路コストを記録して返す\n    mem[i][j] = Math.min(left, up) + grid[i][j];\n    return mem[i][j];\n}\n</code></pre> min_path_sum.cs<pre><code>/* 最小経路和：メモ化探索 */\nint MinPathSumDFSMem(int[][] grid, int[][] mem, int i, int j) {\n    // 左上のセルなら探索を終了する\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // 行または列のインデックスが範囲外なら、コスト +∞ を返す\n    if (i &lt; 0 || j &lt; 0) {\n        return int.MaxValue;\n    }\n    // 既に記録があればそのまま返す\n    if (mem[i][j] != -1) {\n        return mem[i][j];\n    }\n    // 左と上のセルからの最小経路コスト\n    int up = MinPathSumDFSMem(grid, mem, i - 1, j);\n    int left = MinPathSumDFSMem(grid, mem, i, j - 1);\n    // 左上から (i, j) までの最小経路コストを記録して返す\n    mem[i][j] = Math.Min(left, up) + grid[i][j];\n    return mem[i][j];\n}\n</code></pre> min_path_sum.go<pre><code>/* 最小経路和：メモ化探索 */\nfunc minPathSumDFSMem(grid, mem [][]int, i, j int) int {\n    // 左上のセルなら探索を終了する\n    if i == 0 &amp;&amp; j == 0 {\n        return grid[0][0]\n    }\n    // 行または列のインデックスが範囲外なら、コスト +∞ を返す\n    if i &lt; 0 || j &lt; 0 {\n        return math.MaxInt\n    }\n    // 既に記録があればそのまま返す\n    if mem[i][j] != -1 {\n        return mem[i][j]\n    }\n    // 左と上のセルからの最小経路コスト\n    up := minPathSumDFSMem(grid, mem, i-1, j)\n    left := minPathSumDFSMem(grid, mem, i, j-1)\n    // 左上から (i, j) までの最小経路コストを記録して返す\n    mem[i][j] = int(math.Min(float64(left), float64(up))) + grid[i][j]\n    return mem[i][j]\n}\n</code></pre> min_path_sum.swift<pre><code>/* 最小経路和：メモ化探索 */\nfunc minPathSumDFSMem(grid: [[Int]], mem: inout [[Int]], i: Int, j: Int) -&gt; Int {\n    // 左上のセルなら探索を終了する\n    if i == 0, j == 0 {\n        return grid[0][0]\n    }\n    // 行または列のインデックスが範囲外なら、コスト +∞ を返す\n    if i &lt; 0 || j &lt; 0 {\n        return .max\n    }\n    // 既に記録があればそのまま返す\n    if mem[i][j] != -1 {\n        return mem[i][j]\n    }\n    // 左と上のセルからの最小経路コスト\n    let up = minPathSumDFSMem(grid: grid, mem: &amp;mem, i: i - 1, j: j)\n    let left = minPathSumDFSMem(grid: grid, mem: &amp;mem, i: i, j: j - 1)\n    // 左上から (i, j) までの最小経路コストを記録して返す\n    mem[i][j] = min(left, up) + grid[i][j]\n    return mem[i][j]\n}\n</code></pre> min_path_sum.js<pre><code>/* 最小経路和：メモ化探索 */\nfunction minPathSumDFSMem(grid, mem, i, j) {\n    // 左上のセルなら探索を終了する\n    if (i === 0 &amp;&amp; j === 0) {\n        return grid[0][0];\n    }\n    // 行または列のインデックスが範囲外なら、コスト +∞ を返す\n    if (i &lt; 0 || j &lt; 0) {\n        return Infinity;\n    }\n    // 既に記録があればそのまま返す\n    if (mem[i][j] !== -1) {\n        return mem[i][j];\n    }\n    // 左と上のセルからの最小経路コスト\n    const up = minPathSumDFSMem(grid, mem, i - 1, j);\n    const left = minPathSumDFSMem(grid, mem, i, j - 1);\n    // 左上から (i, j) までの最小経路コストを記録して返す\n    mem[i][j] = Math.min(left, up) + grid[i][j];\n    return mem[i][j];\n}\n</code></pre> min_path_sum.ts<pre><code>/* 最小経路和：メモ化探索 */\nfunction minPathSumDFSMem(\n    grid: Array&lt;Array&lt;number&gt;&gt;,\n    mem: Array&lt;Array&lt;number&gt;&gt;,\n    i: number,\n    j: number\n): number {\n    // 左上のセルなら探索を終了する\n    if (i === 0 &amp;&amp; j === 0) {\n        return grid[0][0];\n    }\n    // 行または列のインデックスが範囲外なら、コスト +∞ を返す\n    if (i &lt; 0 || j &lt; 0) {\n        return Infinity;\n    }\n    // 既に記録があればそのまま返す\n    if (mem[i][j] != -1) {\n        return mem[i][j];\n    }\n    // 左と上のセルからの最小経路コスト\n    const up = minPathSumDFSMem(grid, mem, i - 1, j);\n    const left = minPathSumDFSMem(grid, mem, i, j - 1);\n    // 左上から (i, j) までの最小経路コストを記録して返す\n    mem[i][j] = Math.min(left, up) + grid[i][j];\n    return mem[i][j];\n}\n</code></pre> min_path_sum.dart<pre><code>/* 最小経路和：メモ化探索 */\nint minPathSumDFSMem(List&lt;List&lt;int&gt;&gt; grid, List&lt;List&lt;int&gt;&gt; mem, int i, int j) {\n  // 左上のセルなら探索を終了する\n  if (i == 0 &amp;&amp; j == 0) {\n    return grid[0][0];\n  }\n  // 行または列のインデックスが範囲外なら、コスト +∞ を返す\n  if (i &lt; 0 || j &lt; 0) {\n    // Dart では、int 型は固定範囲の整数であり、「無限大」を表す値は存在しない\n    return BigInt.from(2).pow(31).toInt();\n  }\n  // 既に記録があればそのまま返す\n  if (mem[i][j] != -1) {\n    return mem[i][j];\n  }\n  // 左と上のセルからの最小経路コスト\n  int up = minPathSumDFSMem(grid, mem, i - 1, j);\n  int left = minPathSumDFSMem(grid, mem, i, j - 1);\n  // 左上から (i, j) までの最小経路コストを記録して返す\n  mem[i][j] = min(left, up) + grid[i][j];\n  return mem[i][j];\n}\n</code></pre> min_path_sum.rs<pre><code>/* 最小経路和：メモ化探索 */\nfn min_path_sum_dfs_mem(grid: &amp;Vec&lt;Vec&lt;i32&gt;&gt;, mem: &amp;mut Vec&lt;Vec&lt;i32&gt;&gt;, i: i32, j: i32) -&gt; i32 {\n    // 左上のセルなら探索を終了する\n    if i == 0 &amp;&amp; j == 0 {\n        return grid[0][0];\n    }\n    // 行または列のインデックスが範囲外なら、コスト +∞ を返す\n    if i &lt; 0 || j &lt; 0 {\n        return i32::MAX;\n    }\n    // 既に記録があればそのまま返す\n    if mem[i as usize][j as usize] != -1 {\n        return mem[i as usize][j as usize];\n    }\n    // 左と上のセルからの最小経路コスト\n    let up = min_path_sum_dfs_mem(grid, mem, i - 1, j);\n    let left = min_path_sum_dfs_mem(grid, mem, i, j - 1);\n    // 左上から (i, j) までの最小経路コストを記録して返す\n    mem[i as usize][j as usize] = std::cmp::min(left, up) + grid[i as usize][j as usize];\n    mem[i as usize][j as usize]\n}\n</code></pre> min_path_sum.c<pre><code>/* 最小経路和：メモ化探索 */\nint minPathSumDFSMem(int grid[MAX_SIZE][MAX_SIZE], int mem[MAX_SIZE][MAX_SIZE], int i, int j) {\n    // 左上のセルなら探索を終了する\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // 行または列のインデックスが範囲外なら、コスト +∞ を返す\n    if (i &lt; 0 || j &lt; 0) {\n        return INT_MAX;\n    }\n    // 既に記録があればそのまま返す\n    if (mem[i][j] != -1) {\n        return mem[i][j];\n    }\n    // 左と上のセルからの最小経路コスト\n    int up = minPathSumDFSMem(grid, mem, i - 1, j);\n    int left = minPathSumDFSMem(grid, mem, i, j - 1);\n    // 左上から (i, j) までの最小経路コストを記録して返す\n    mem[i][j] = myMin(left, up) != INT_MAX ? myMin(left, up) + grid[i][j] : INT_MAX;\n    return mem[i][j];\n}\n</code></pre> min_path_sum.kt<pre><code>/* 最小経路和：メモ化探索 */\nfun minPathSumDFSMem(\n    grid: Array&lt;IntArray&gt;,\n    mem: Array&lt;IntArray&gt;,\n    i: Int,\n    j: Int\n): Int {\n    // 左上のセルなら探索を終了する\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0]\n    }\n    // 行または列のインデックスが範囲外なら、コスト +∞ を返す\n    if (i &lt; 0 || j &lt; 0) {\n        return Int.MAX_VALUE\n    }\n    // 既に記録があればそのまま返す\n    if (mem[i][j] != -1) {\n        return mem[i][j]\n    }\n    // 左と上のセルからの最小経路コスト\n    val up = minPathSumDFSMem(grid, mem, i - 1, j)\n    val left = minPathSumDFSMem(grid, mem, i, j - 1)\n    // 左上から (i, j) までの最小経路コストを記録して返す\n    mem[i][j] = min(left, up) + grid[i][j]\n    return mem[i][j]\n}\n</code></pre> min_path_sum.rb<pre><code>### 最小経路和：メモ化探索 ###\ndef min_path_sum_dfs_mem(grid, mem, i, j)\n  # 左上のセルなら探索を終了する\n  return grid[0][0] if i == 0 &amp;&amp; j == 0\n  # 行または列のインデックスが範囲外なら、コスト +∞ を返す\n  return Float::INFINITY if i &lt; 0 || j &lt; 0\n  # 既に記録があればそのまま返す\n  return mem[i][j] if mem[i][j] != -1\n  # 左と上のセルからの最小経路コスト\n  up = min_path_sum_dfs_mem(grid, mem, i - 1, j)\n  left = min_path_sum_dfs_mem(grid, mem, i, j - 1)\n  # 左上から (i, j) までの最小経路コストを記録して返す\n  mem[i][j] = [left, up].min + grid[i][j]\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>次の図に示すように、メモ化を導入すると、すべての部分問題の解は 1 回だけ計算すればよくなります。したがって時間計算量は状態総数、すなわちグリッドサイズの \\(O(nm)\\) に依存します。</p> <p></p> <p> 図 14-15   メモ化探索の再帰木 </p>","path":["第 14 章 &nbsp; 動的計画法","14.3 &nbsp; 動的計画法の問題解決の考え方"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#3-3","level":3,"title":"3.   方法 3：動的計画法","text":"<p>反復に基づいて動的計画法の解法を実装すると、コードは次のようになります。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby min_path_sum.py<pre><code>def min_path_sum_dp(grid: list[list[int]]) -&gt; int:\n    \"\"\"最小経路和：動的計画法\"\"\"\n    n, m = len(grid), len(grid[0])\n    # dp テーブルを初期化\n    dp = [[0] * m for _ in range(n)]\n    dp[0][0] = grid[0][0]\n    # 状態遷移：先頭行\n    for j in range(1, m):\n        dp[0][j] = dp[0][j - 1] + grid[0][j]\n    # 状態遷移：先頭列\n    for i in range(1, n):\n        dp[i][0] = dp[i - 1][0] + grid[i][0]\n    # 状態遷移: 残りの行と列\n    for i in range(1, n):\n        for j in range(1, m):\n            dp[i][j] = min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j]\n    return dp[n - 1][m - 1]\n</code></pre> min_path_sum.cpp<pre><code>/* 最小経路和：動的計画法 */\nint minPathSumDP(vector&lt;vector&lt;int&gt;&gt; &amp;grid) {\n    int n = grid.size(), m = grid[0].size();\n    // dp テーブルを初期化\n    vector&lt;vector&lt;int&gt;&gt; dp(n, vector&lt;int&gt;(m));\n    dp[0][0] = grid[0][0];\n    // 状態遷移：先頭行\n    for (int j = 1; j &lt; m; j++) {\n        dp[0][j] = dp[0][j - 1] + grid[0][j];\n    }\n    // 状態遷移：先頭列\n    for (int i = 1; i &lt; n; i++) {\n        dp[i][0] = dp[i - 1][0] + grid[i][0];\n    }\n    // 状態遷移: 残りの行と列\n    for (int i = 1; i &lt; n; i++) {\n        for (int j = 1; j &lt; m; j++) {\n            dp[i][j] = min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];\n        }\n    }\n    return dp[n - 1][m - 1];\n}\n</code></pre> min_path_sum.java<pre><code>/* 最小経路和：動的計画法 */\nint minPathSumDP(int[][] grid) {\n    int n = grid.length, m = grid[0].length;\n    // dp テーブルを初期化\n    int[][] dp = new int[n][m];\n    dp[0][0] = grid[0][0];\n    // 状態遷移：先頭行\n    for (int j = 1; j &lt; m; j++) {\n        dp[0][j] = dp[0][j - 1] + grid[0][j];\n    }\n    // 状態遷移：先頭列\n    for (int i = 1; i &lt; n; i++) {\n        dp[i][0] = dp[i - 1][0] + grid[i][0];\n    }\n    // 状態遷移: 残りの行と列\n    for (int i = 1; i &lt; n; i++) {\n        for (int j = 1; j &lt; m; j++) {\n            dp[i][j] = Math.min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];\n        }\n    }\n    return dp[n - 1][m - 1];\n}\n</code></pre> min_path_sum.cs<pre><code>/* 最小経路和：動的計画法 */\nint MinPathSumDP(int[][] grid) {\n    int n = grid.Length, m = grid[0].Length;\n    // dp テーブルを初期化\n    int[,] dp = new int[n, m];\n    dp[0, 0] = grid[0][0];\n    // 状態遷移：先頭行\n    for (int j = 1; j &lt; m; j++) {\n        dp[0, j] = dp[0, j - 1] + grid[0][j];\n    }\n    // 状態遷移：先頭列\n    for (int i = 1; i &lt; n; i++) {\n        dp[i, 0] = dp[i - 1, 0] + grid[i][0];\n    }\n    // 状態遷移: 残りの行と列\n    for (int i = 1; i &lt; n; i++) {\n        for (int j = 1; j &lt; m; j++) {\n            dp[i, j] = Math.Min(dp[i, j - 1], dp[i - 1, j]) + grid[i][j];\n        }\n    }\n    return dp[n - 1, m - 1];\n}\n</code></pre> min_path_sum.go<pre><code>/* 最小経路和：動的計画法 */\nfunc minPathSumDP(grid [][]int) int {\n    n, m := len(grid), len(grid[0])\n    // dp テーブルを初期化\n    dp := make([][]int, n)\n    for i := 0; i &lt; n; i++ {\n        dp[i] = make([]int, m)\n    }\n    dp[0][0] = grid[0][0]\n    // 状態遷移：先頭行\n    for j := 1; j &lt; m; j++ {\n        dp[0][j] = dp[0][j-1] + grid[0][j]\n    }\n    // 状態遷移：先頭列\n    for i := 1; i &lt; n; i++ {\n        dp[i][0] = dp[i-1][0] + grid[i][0]\n    }\n    // 状態遷移: 残りの行と列\n    for i := 1; i &lt; n; i++ {\n        for j := 1; j &lt; m; j++ {\n            dp[i][j] = int(math.Min(float64(dp[i][j-1]), float64(dp[i-1][j]))) + grid[i][j]\n        }\n    }\n    return dp[n-1][m-1]\n}\n</code></pre> min_path_sum.swift<pre><code>/* 最小経路和：動的計画法 */\nfunc minPathSumDP(grid: [[Int]]) -&gt; Int {\n    let n = grid.count\n    let m = grid[0].count\n    // dp テーブルを初期化\n    var dp = Array(repeating: Array(repeating: 0, count: m), count: n)\n    dp[0][0] = grid[0][0]\n    // 状態遷移：先頭行\n    for j in 1 ..&lt; m {\n        dp[0][j] = dp[0][j - 1] + grid[0][j]\n    }\n    // 状態遷移：先頭列\n    for i in 1 ..&lt; n {\n        dp[i][0] = dp[i - 1][0] + grid[i][0]\n    }\n    // 状態遷移: 残りの行と列\n    for i in 1 ..&lt; n {\n        for j in 1 ..&lt; m {\n            dp[i][j] = min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j]\n        }\n    }\n    return dp[n - 1][m - 1]\n}\n</code></pre> min_path_sum.js<pre><code>/* 最小経路和：動的計画法 */\nfunction minPathSumDP(grid) {\n    const n = grid.length,\n        m = grid[0].length;\n    // dp テーブルを初期化\n    const dp = Array.from({ length: n }, () =&gt;\n        Array.from({ length: m }, () =&gt; 0)\n    );\n    dp[0][0] = grid[0][0];\n    // 状態遷移：先頭行\n    for (let j = 1; j &lt; m; j++) {\n        dp[0][j] = dp[0][j - 1] + grid[0][j];\n    }\n    // 状態遷移：先頭列\n    for (let i = 1; i &lt; n; i++) {\n        dp[i][0] = dp[i - 1][0] + grid[i][0];\n    }\n    // 状態遷移: 残りの行と列\n    for (let i = 1; i &lt; n; i++) {\n        for (let j = 1; j &lt; m; j++) {\n            dp[i][j] = Math.min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];\n        }\n    }\n    return dp[n - 1][m - 1];\n}\n</code></pre> min_path_sum.ts<pre><code>/* 最小経路和：動的計画法 */\nfunction minPathSumDP(grid: Array&lt;Array&lt;number&gt;&gt;): number {\n    const n = grid.length,\n        m = grid[0].length;\n    // dp テーブルを初期化\n    const dp = Array.from({ length: n }, () =&gt;\n        Array.from({ length: m }, () =&gt; 0)\n    );\n    dp[0][0] = grid[0][0];\n    // 状態遷移：先頭行\n    for (let j = 1; j &lt; m; j++) {\n        dp[0][j] = dp[0][j - 1] + grid[0][j];\n    }\n    // 状態遷移：先頭列\n    for (let i = 1; i &lt; n; i++) {\n        dp[i][0] = dp[i - 1][0] + grid[i][0];\n    }\n    // 状態遷移: 残りの行と列\n    for (let i = 1; i &lt; n; i++) {\n        for (let j: number = 1; j &lt; m; j++) {\n            dp[i][j] = Math.min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];\n        }\n    }\n    return dp[n - 1][m - 1];\n}\n</code></pre> min_path_sum.dart<pre><code>/* 最小経路和：動的計画法 */\nint minPathSumDP(List&lt;List&lt;int&gt;&gt; grid) {\n  int n = grid.length, m = grid[0].length;\n  // dp テーブルを初期化\n  List&lt;List&lt;int&gt;&gt; dp = List.generate(n, (i) =&gt; List.filled(m, 0));\n  dp[0][0] = grid[0][0];\n  // 状態遷移：先頭行\n  for (int j = 1; j &lt; m; j++) {\n    dp[0][j] = dp[0][j - 1] + grid[0][j];\n  }\n  // 状態遷移：先頭列\n  for (int i = 1; i &lt; n; i++) {\n    dp[i][0] = dp[i - 1][0] + grid[i][0];\n  }\n  // 状態遷移: 残りの行と列\n  for (int i = 1; i &lt; n; i++) {\n    for (int j = 1; j &lt; m; j++) {\n      dp[i][j] = min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];\n    }\n  }\n  return dp[n - 1][m - 1];\n}\n</code></pre> min_path_sum.rs<pre><code>/* 最小経路和：動的計画法 */\nfn min_path_sum_dp(grid: &amp;Vec&lt;Vec&lt;i32&gt;&gt;) -&gt; i32 {\n    let (n, m) = (grid.len(), grid[0].len());\n    // dp テーブルを初期化\n    let mut dp = vec![vec![0; m]; n];\n    dp[0][0] = grid[0][0];\n    // 状態遷移：先頭行\n    for j in 1..m {\n        dp[0][j] = dp[0][j - 1] + grid[0][j];\n    }\n    // 状態遷移：先頭列\n    for i in 1..n {\n        dp[i][0] = dp[i - 1][0] + grid[i][0];\n    }\n    // 状態遷移: 残りの行と列\n    for i in 1..n {\n        for j in 1..m {\n            dp[i][j] = std::cmp::min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];\n        }\n    }\n    dp[n - 1][m - 1]\n}\n</code></pre> min_path_sum.c<pre><code>/* 最小経路和：動的計画法 */\nint minPathSumDP(int grid[MAX_SIZE][MAX_SIZE], int n, int m) {\n    // dp テーブルを初期化\n    int **dp = malloc(n * sizeof(int *));\n    for (int i = 0; i &lt; n; i++) {\n        dp[i] = calloc(m, sizeof(int));\n    }\n    dp[0][0] = grid[0][0];\n    // 状態遷移：先頭行\n    for (int j = 1; j &lt; m; j++) {\n        dp[0][j] = dp[0][j - 1] + grid[0][j];\n    }\n    // 状態遷移：先頭列\n    for (int i = 1; i &lt; n; i++) {\n        dp[i][0] = dp[i - 1][0] + grid[i][0];\n    }\n    // 状態遷移: 残りの行と列\n    for (int i = 1; i &lt; n; i++) {\n        for (int j = 1; j &lt; m; j++) {\n            dp[i][j] = myMin(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];\n        }\n    }\n    int res = dp[n - 1][m - 1];\n    // メモリを解放する\n    for (int i = 0; i &lt; n; i++) {\n        free(dp[i]);\n    }\n    return res;\n}\n</code></pre> min_path_sum.kt<pre><code>/* 最小経路和：動的計画法 */\nfun minPathSumDP(grid: Array&lt;IntArray&gt;): Int {\n    val n = grid.size\n    val m = grid[0].size\n    // dp テーブルを初期化\n    val dp = Array(n) { IntArray(m) }\n    dp[0][0] = grid[0][0]\n    // 状態遷移：先頭行\n    for (j in 1..&lt;m) {\n        dp[0][j] = dp[0][j - 1] + grid[0][j]\n    }\n    // 状態遷移：先頭列\n    for (i in 1..&lt;n) {\n        dp[i][0] = dp[i - 1][0] + grid[i][0]\n    }\n    // 状態遷移: 残りの行と列\n    for (i in 1..&lt;n) {\n        for (j in 1..&lt;m) {\n            dp[i][j] = min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j]\n        }\n    }\n    return dp[n - 1][m - 1]\n}\n</code></pre> min_path_sum.rb<pre><code>### 最小経路和：動的計画法 ###\ndef min_path_sum_dp(grid)\n  n, m = grid.length, grid.first.length\n  # dp テーブルを初期化\n  dp = Array.new(n) { Array.new(m, 0) }\n  dp[0][0] = grid[0][0]\n  # 状態遷移：先頭行\n  (1...m).each { |j| dp[0][j] = dp[0][j - 1] + grid[0][j] }\n  # 状態遷移：先頭列\n  (1...n).each { |i| dp[i][0] = dp[i - 1][0] + grid[i][0] }\n  # 状態遷移: 残りの行と列\n  for i in 1...n\n    for j in 1...m\n      dp[i][j] = [dp[i][j - 1], dp[i - 1][j]].min + grid[i][j]\n    end\n  end\n  dp[n -1][m -1]\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>次の図は最小経路和の状態遷移の過程を示しています。グリッド全体を走査するため、時間計算量は \\(O(nm)\\) です。</p> <p>配列 <code>dp</code> のサイズは \\(n \\times m\\) であるため、空間計算量は \\(O(nm)\\) です。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 14-16   最小経路和の動的計画法の過程 </p>","path":["第 14 章 &nbsp; 動的計画法","14.3 &nbsp; 動的計画法の問題解決の考え方"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#4","level":3,"title":"4.   空間最適化","text":"<p>各マスは左のマスと上のマスにのみ関係するため、1 行の配列だけを使って \\(dp\\) テーブルを実装できます。</p> <p>ただし、配列 <code>dp</code> は 1 行分の状態しか表せないため、先頭列の状態を事前に初期化することはできず、各行を走査するときに更新する必要があります。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby min_path_sum.py<pre><code>def min_path_sum_dp_comp(grid: list[list[int]]) -&gt; int:\n    \"\"\"最小経路和：空間最適化後の動的計画法\"\"\"\n    n, m = len(grid), len(grid[0])\n    # dp テーブルを初期化\n    dp = [0] * m\n    # 状態遷移：先頭行\n    dp[0] = grid[0][0]\n    for j in range(1, m):\n        dp[j] = dp[j - 1] + grid[0][j]\n    # 状態遷移：残りの行\n    for i in range(1, n):\n        # 状態遷移：先頭列\n        dp[0] = dp[0] + grid[i][0]\n        # 状態遷移：残りの列\n        for j in range(1, m):\n            dp[j] = min(dp[j - 1], dp[j]) + grid[i][j]\n    return dp[m - 1]\n</code></pre> min_path_sum.cpp<pre><code>/* 最小経路和：空間最適化後の動的計画法 */\nint minPathSumDPComp(vector&lt;vector&lt;int&gt;&gt; &amp;grid) {\n    int n = grid.size(), m = grid[0].size();\n    // dp テーブルを初期化\n    vector&lt;int&gt; dp(m);\n    // 状態遷移：先頭行\n    dp[0] = grid[0][0];\n    for (int j = 1; j &lt; m; j++) {\n        dp[j] = dp[j - 1] + grid[0][j];\n    }\n    // 状態遷移：残りの行\n    for (int i = 1; i &lt; n; i++) {\n        // 状態遷移：先頭列\n        dp[0] = dp[0] + grid[i][0];\n        // 状態遷移：残りの列\n        for (int j = 1; j &lt; m; j++) {\n            dp[j] = min(dp[j - 1], dp[j]) + grid[i][j];\n        }\n    }\n    return dp[m - 1];\n}\n</code></pre> min_path_sum.java<pre><code>/* 最小経路和：空間最適化後の動的計画法 */\nint minPathSumDPComp(int[][] grid) {\n    int n = grid.length, m = grid[0].length;\n    // dp テーブルを初期化\n    int[] dp = new int[m];\n    // 状態遷移：先頭行\n    dp[0] = grid[0][0];\n    for (int j = 1; j &lt; m; j++) {\n        dp[j] = dp[j - 1] + grid[0][j];\n    }\n    // 状態遷移：残りの行\n    for (int i = 1; i &lt; n; i++) {\n        // 状態遷移：先頭列\n        dp[0] = dp[0] + grid[i][0];\n        // 状態遷移：残りの列\n        for (int j = 1; j &lt; m; j++) {\n            dp[j] = Math.min(dp[j - 1], dp[j]) + grid[i][j];\n        }\n    }\n    return dp[m - 1];\n}\n</code></pre> min_path_sum.cs<pre><code>/* 最小経路和：空間最適化後の動的計画法 */\nint MinPathSumDPComp(int[][] grid) {\n    int n = grid.Length, m = grid[0].Length;\n    // dp テーブルを初期化\n    int[] dp = new int[m];\n    dp[0] = grid[0][0];\n    // 状態遷移：先頭行\n    for (int j = 1; j &lt; m; j++) {\n        dp[j] = dp[j - 1] + grid[0][j];\n    }\n    // 状態遷移：残りの行\n    for (int i = 1; i &lt; n; i++) {\n        // 状態遷移：先頭列\n        dp[0] = dp[0] + grid[i][0];\n        // 状態遷移：残りの列\n        for (int j = 1; j &lt; m; j++) {\n            dp[j] = Math.Min(dp[j - 1], dp[j]) + grid[i][j];\n        }\n    }\n    return dp[m - 1];\n}\n</code></pre> min_path_sum.go<pre><code>/* 最小経路和：空間最適化後の動的計画法 */\nfunc minPathSumDPComp(grid [][]int) int {\n    n, m := len(grid), len(grid[0])\n    // dp テーブルを初期化\n    dp := make([]int, m)\n    // 状態遷移：先頭行\n    dp[0] = grid[0][0]\n    for j := 1; j &lt; m; j++ {\n        dp[j] = dp[j-1] + grid[0][j]\n    }\n    // 状態遷移: 残りの行と列\n    for i := 1; i &lt; n; i++ {\n        // 状態遷移：先頭列\n        dp[0] = dp[0] + grid[i][0]\n        // 状態遷移：残りの列\n        for j := 1; j &lt; m; j++ {\n            dp[j] = int(math.Min(float64(dp[j-1]), float64(dp[j]))) + grid[i][j]\n        }\n    }\n    return dp[m-1]\n}\n</code></pre> min_path_sum.swift<pre><code>/* 最小経路和：空間最適化後の動的計画法 */\nfunc minPathSumDPComp(grid: [[Int]]) -&gt; Int {\n    let n = grid.count\n    let m = grid[0].count\n    // dp テーブルを初期化\n    var dp = Array(repeating: 0, count: m)\n    // 状態遷移：先頭行\n    dp[0] = grid[0][0]\n    for j in 1 ..&lt; m {\n        dp[j] = dp[j - 1] + grid[0][j]\n    }\n    // 状態遷移：残りの行\n    for i in 1 ..&lt; n {\n        // 状態遷移：先頭列\n        dp[0] = dp[0] + grid[i][0]\n        // 状態遷移：残りの列\n        for j in 1 ..&lt; m {\n            dp[j] = min(dp[j - 1], dp[j]) + grid[i][j]\n        }\n    }\n    return dp[m - 1]\n}\n</code></pre> min_path_sum.js<pre><code>/* 最小経路和：空間最適化後の動的計画法 */\nfunction minPathSumDPComp(grid) {\n    const n = grid.length,\n        m = grid[0].length;\n    // dp テーブルを初期化\n    const dp = new Array(m);\n    // 状態遷移：先頭行\n    dp[0] = grid[0][0];\n    for (let j = 1; j &lt; m; j++) {\n        dp[j] = dp[j - 1] + grid[0][j];\n    }\n    // 状態遷移：残りの行\n    for (let i = 1; i &lt; n; i++) {\n        // 状態遷移：先頭列\n        dp[0] = dp[0] + grid[i][0];\n        // 状態遷移：残りの列\n        for (let j = 1; j &lt; m; j++) {\n            dp[j] = Math.min(dp[j - 1], dp[j]) + grid[i][j];\n        }\n    }\n    return dp[m - 1];\n}\n</code></pre> min_path_sum.ts<pre><code>/* 最小経路和：空間最適化後の動的計画法 */\nfunction minPathSumDPComp(grid: Array&lt;Array&lt;number&gt;&gt;): number {\n    const n = grid.length,\n        m = grid[0].length;\n    // dp テーブルを初期化\n    const dp = new Array(m);\n    // 状態遷移：先頭行\n    dp[0] = grid[0][0];\n    for (let j = 1; j &lt; m; j++) {\n        dp[j] = dp[j - 1] + grid[0][j];\n    }\n    // 状態遷移：残りの行\n    for (let i = 1; i &lt; n; i++) {\n        // 状態遷移：先頭列\n        dp[0] = dp[0] + grid[i][0];\n        // 状態遷移：残りの列\n        for (let j = 1; j &lt; m; j++) {\n            dp[j] = Math.min(dp[j - 1], dp[j]) + grid[i][j];\n        }\n    }\n    return dp[m - 1];\n}\n</code></pre> min_path_sum.dart<pre><code>/* 最小経路和：空間最適化後の動的計画法 */\nint minPathSumDPComp(List&lt;List&lt;int&gt;&gt; grid) {\n  int n = grid.length, m = grid[0].length;\n  // dp テーブルを初期化\n  List&lt;int&gt; dp = List.filled(m, 0);\n  dp[0] = grid[0][0];\n  for (int j = 1; j &lt; m; j++) {\n    dp[j] = dp[j - 1] + grid[0][j];\n  }\n  // 状態遷移：残りの行\n  for (int i = 1; i &lt; n; i++) {\n    // 状態遷移：先頭列\n    dp[0] = dp[0] + grid[i][0];\n    // 状態遷移：残りの列\n    for (int j = 1; j &lt; m; j++) {\n      dp[j] = min(dp[j - 1], dp[j]) + grid[i][j];\n    }\n  }\n  return dp[m - 1];\n}\n</code></pre> min_path_sum.rs<pre><code>/* 最小経路和：空間最適化後の動的計画法 */\nfn min_path_sum_dp_comp(grid: &amp;Vec&lt;Vec&lt;i32&gt;&gt;) -&gt; i32 {\n    let (n, m) = (grid.len(), grid[0].len());\n    // dp テーブルを初期化\n    let mut dp = vec![0; m];\n    // 状態遷移：先頭行\n    dp[0] = grid[0][0];\n    for j in 1..m {\n        dp[j] = dp[j - 1] + grid[0][j];\n    }\n    // 状態遷移：残りの行\n    for i in 1..n {\n        // 状態遷移：先頭列\n        dp[0] = dp[0] + grid[i][0];\n        // 状態遷移：残りの列\n        for j in 1..m {\n            dp[j] = std::cmp::min(dp[j - 1], dp[j]) + grid[i][j];\n        }\n    }\n    dp[m - 1]\n}\n</code></pre> min_path_sum.c<pre><code>/* 最小経路和：空間最適化後の動的計画法 */\nint minPathSumDPComp(int grid[MAX_SIZE][MAX_SIZE], int n, int m) {\n    // dp テーブルを初期化\n    int *dp = calloc(m, sizeof(int));\n    // 状態遷移：先頭行\n    dp[0] = grid[0][0];\n    for (int j = 1; j &lt; m; j++) {\n        dp[j] = dp[j - 1] + grid[0][j];\n    }\n    // 状態遷移：残りの行\n    for (int i = 1; i &lt; n; i++) {\n        // 状態遷移：先頭列\n        dp[0] = dp[0] + grid[i][0];\n        // 状態遷移：残りの列\n        for (int j = 1; j &lt; m; j++) {\n            dp[j] = myMin(dp[j - 1], dp[j]) + grid[i][j];\n        }\n    }\n    int res = dp[m - 1];\n    // メモリを解放する\n    free(dp);\n    return res;\n}\n</code></pre> min_path_sum.kt<pre><code>/* 最小経路和：空間最適化後の動的計画法 */\nfun minPathSumDPComp(grid: Array&lt;IntArray&gt;): Int {\n    val n = grid.size\n    val m = grid[0].size\n    // dp テーブルを初期化\n    val dp = IntArray(m)\n    // 状態遷移：先頭行\n    dp[0] = grid[0][0]\n    for (j in 1..&lt;m) {\n        dp[j] = dp[j - 1] + grid[0][j]\n    }\n    // 状態遷移：残りの行\n    for (i in 1..&lt;n) {\n        // 状態遷移：先頭列\n        dp[0] = dp[0] + grid[i][0]\n        // 状態遷移：残りの列\n        for (j in 1..&lt;m) {\n            dp[j] = min(dp[j - 1], dp[j]) + grid[i][j]\n        }\n    }\n    return dp[m - 1]\n}\n</code></pre> min_path_sum.rb<pre><code>### 最小経路和：空間最適化後の動的計画法 ###\ndef min_path_sum_dp_comp(grid)\n  n, m = grid.length, grid.first.length\n  # dp テーブルを初期化\n  dp = Array.new(m, 0)\n  # 状態遷移：先頭行\n  dp[0] = grid[0][0]\n  (1...m).each { |j| dp[j] = dp[j - 1] + grid[0][j] }\n  # 状態遷移：残りの行\n  for i in 1...n\n    # 状態遷移：先頭列\n    dp[0] = dp[0] + grid[i][0]\n    # 状態遷移：残りの列\n    (1...m).each { |j| dp[j] = [dp[j - 1], dp[j]].min + grid[i][j] }\n  end\n  dp[m - 1]\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 14 章 &nbsp; 動的計画法","14.3 &nbsp; 動的計画法の問題解決の考え方"],"tags":[]},{"location":"chapter_dynamic_programming/edit_distance_problem/","level":1,"title":"14.6   編集距離問題","text":"<p>編集距離は、Levenshtein 距離とも呼ばれ、2つの文字列の相互変換に必要な最小の編集回数を指し、通常は情報検索や自然言語処理において2つの系列の類似度を測るために用いられます。</p> <p>Question</p> <p>2つの文字列 \\(s\\) と \\(t\\) を入力し、\\(s\\) を \\(t\\) に変換するのに必要な最小編集回数を返してください。</p> <p>1つの文字列に対して3種類の編集操作を行えます。1文字の挿入、1文字の削除、任意の文字への置換です。</p> <p>下図に示すように、<code>kitten</code> を <code>sitting</code> に変換するには 3 回の編集が必要で、内訳は 2 回の置換と 1 回の挿入です。<code>hello</code> を <code>algo</code> に変換する場合も 3 回必要で、内訳は 2 回の置換と 1 回の削除です。</p> <p></p> <p> 図 14-27   編集距離のサンプルデータ </p> <p>編集距離問題は決定木モデルで自然に説明できます。文字列が木のノードに対応し、1回の決定（1回の編集操作）が木の1本の辺に対応します。</p> <p>下図に示すように、操作に制限がない場合、各ノードからは多くの辺を派生でき、それぞれの辺が1種類の操作に対応します。これは <code>hello</code> から <code>algo</code> への変換に多くの経路があり得ることを意味します。</p> <p>決定木の観点から見ると、本問の目標はノード <code>hello</code> とノード <code>algo</code> の間の最短経路を求めることです。</p> <p></p> <p> 図 14-28   決定木モデルに基づく編集距離問題の表現 </p>","path":["第 14 章 &nbsp; 動的計画法","14.6 &nbsp; 編集距離問題"],"tags":[]},{"location":"chapter_dynamic_programming/edit_distance_problem/#1","level":3,"title":"1.   動的計画法の考え方","text":"<p>第1ステップ：各ラウンドの決定を考え、状態を定義して、\\(dp\\) テーブルを得る</p> <p>各ラウンドの決定は、文字列 \\(s\\) に対して1回の編集操作を行うことです。</p> <p>編集操作の過程で問題の規模が徐々に小さくなることを期待します。そうして初めて部分問題を構築できます。文字列 \\(s\\) と \\(t\\) の長さをそれぞれ \\(n\\) と \\(m\\) とし、まず両文字列の末尾の文字 \\(s[n-1]\\) と \\(t[m-1]\\) を考えます。</p> <ul> <li>\\(s[n-1]\\) と \\(t[m-1]\\) が同じなら、それらをスキップして、直接 \\(s[n-2]\\) と \\(t[m-2]\\) を考えます。</li> <li>\\(s[n-1]\\) と \\(t[m-1]\\) が異なるなら、\\(s\\) に対して1回の編集（挿入、削除、置換）を行い、両文字列の末尾の文字を同じにします。そうすることでそれらをスキップし、より小さい問題を考えられます。</li> </ul> <p>つまり、文字列 \\(s\\) に対する各ラウンドの決定（編集操作）は、\\(s\\) と \\(t\\) における残りの未一致文字を変化させます。したがって、状態は現在 \\(s\\) と \\(t\\) で考えている第 \\(i\\) と第 \\(j\\) 文字とし、\\([i, j]\\) と記します。</p> <p>状態 \\([i, j]\\) に対応する部分問題は、**\\(s\\) の先頭 \\(i\\) 文字を \\(t\\) の先頭 \\(j\\) 文字に変換するのに必要な最小編集回数**です。</p> <p>これにより、サイズが \\((i+1) \\times (j+1)\\) の2次元 \\(dp\\) テーブルが得られます。</p> <p>第2ステップ：最適部分構造を見つけ、状態遷移方程式を導く</p> <p>部分問題 \\(dp[i, j]\\) を考えます。これに対応する2つの文字列の末尾文字は \\(s[i-1]\\) と \\(t[j-1]\\) であり、編集操作の違いに応じて下図の3つの場合に分けられます。</p> <ol> <li>\\(s[i-1]\\) の後ろに \\(t[j-1]\\) を追加する。このとき残る部分問題は \\(dp[i, j-1]\\) です。</li> <li>\\(s[i-1]\\) を削除する。このとき残る部分問題は \\(dp[i-1, j]\\) です。</li> <li>\\(s[i-1]\\) を \\(t[j-1]\\) に置き換える。このとき残る部分問題は \\(dp[i-1, j-1]\\) です。</li> </ol> <p></p> <p> 図 14-29   編集距離の状態遷移 </p> <p>以上の分析から、最適部分構造は次のように得られます。\\(dp[i, j]\\) の最小編集回数は、\\(dp[i, j-1]\\)、\\(dp[i-1, j]\\)、\\(dp[i-1, j-1]\\) の3つのうち最小の編集回数に、今回の編集回数 \\(1\\) を加えたものです。対応する状態遷移方程式は次のとおりです：</p> \\[ dp[i, j] = \\min(dp[i, j-1], dp[i-1, j], dp[i-1, j-1]) + 1 \\] <p>注意すべき点として、\\(s[i-1]\\) と \\(t[j-1]\\) が同じ場合、現在の文字を編集する必要はありません。この場合の状態遷移方程式は次のとおりです：</p> \\[ dp[i, j] = dp[i-1, j-1] \\] <p>第3ステップ：境界条件と状態遷移の順序を決める</p> <p>2つの文字列がともに空のとき、編集回数は \\(0\\)、すなわち \\(dp[0, 0] = 0\\) です。\\(s\\) が空で \\(t\\) が空でないとき、最小編集回数は \\(t\\) の長さに等しいため、先頭行は \\(dp[0, j] = j\\) です。\\(s\\) が空でなく \\(t\\) が空のとき、最小編集回数は \\(s\\) の長さに等しいため、先頭列は \\(dp[i, 0] = i\\) です。</p> <p>状態遷移方程式を観察すると、\\(dp[i, j]\\) の解は左、上、左上の解に依存します。そのため、2重ループで \\(dp\\) テーブル全体を順方向に走査すれば十分です。</p>","path":["第 14 章 &nbsp; 動的計画法","14.6 &nbsp; 編集距離問題"],"tags":[]},{"location":"chapter_dynamic_programming/edit_distance_problem/#2","level":3,"title":"2.   コードの実装","text":"PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby edit_distance.py<pre><code>def edit_distance_dp(s: str, t: str) -&gt; int:\n    \"\"\"編集距離：動的計画法\"\"\"\n    n, m = len(s), len(t)\n    dp = [[0] * (m + 1) for _ in range(n + 1)]\n    # 状態遷移：先頭行と先頭列\n    for i in range(1, n + 1):\n        dp[i][0] = i\n    for j in range(1, m + 1):\n        dp[0][j] = j\n    # 状態遷移: 残りの行と列\n    for i in range(1, n + 1):\n        for j in range(1, m + 1):\n            if s[i - 1] == t[j - 1]:\n                # 2 つの文字が等しければ、その 2 文字をそのままスキップする\n                dp[i][j] = dp[i - 1][j - 1]\n            else:\n                # 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n                dp[i][j] = min(dp[i][j - 1], dp[i - 1][j], dp[i - 1][j - 1]) + 1\n    return dp[n][m]\n</code></pre> edit_distance.cpp<pre><code>/* 編集距離：動的計画法 */\nint editDistanceDP(string s, string t) {\n    int n = s.length(), m = t.length();\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(m + 1, 0));\n    // 状態遷移：先頭行と先頭列\n    for (int i = 1; i &lt;= n; i++) {\n        dp[i][0] = i;\n    }\n    for (int j = 1; j &lt;= m; j++) {\n        dp[0][j] = j;\n    }\n    // 状態遷移: 残りの行と列\n    for (int i = 1; i &lt;= n; i++) {\n        for (int j = 1; j &lt;= m; j++) {\n            if (s[i - 1] == t[j - 1]) {\n                // 2 つの文字が等しければ、その 2 文字をそのままスキップする\n                dp[i][j] = dp[i - 1][j - 1];\n            } else {\n                // 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n                dp[i][j] = min(min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;\n            }\n        }\n    }\n    return dp[n][m];\n}\n</code></pre> edit_distance.java<pre><code>/* 編集距離：動的計画法 */\nint editDistanceDP(String s, String t) {\n    int n = s.length(), m = t.length();\n    int[][] dp = new int[n + 1][m + 1];\n    // 状態遷移：先頭行と先頭列\n    for (int i = 1; i &lt;= n; i++) {\n        dp[i][0] = i;\n    }\n    for (int j = 1; j &lt;= m; j++) {\n        dp[0][j] = j;\n    }\n    // 状態遷移: 残りの行と列\n    for (int i = 1; i &lt;= n; i++) {\n        for (int j = 1; j &lt;= m; j++) {\n            if (s.charAt(i - 1) == t.charAt(j - 1)) {\n                // 2 つの文字が等しければ、その 2 文字をそのままスキップする\n                dp[i][j] = dp[i - 1][j - 1];\n            } else {\n                // 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n                dp[i][j] = Math.min(Math.min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;\n            }\n        }\n    }\n    return dp[n][m];\n}\n</code></pre> edit_distance.cs<pre><code>/* 編集距離：動的計画法 */\nint EditDistanceDP(string s, string t) {\n    int n = s.Length, m = t.Length;\n    int[,] dp = new int[n + 1, m + 1];\n    // 状態遷移：先頭行と先頭列\n    for (int i = 1; i &lt;= n; i++) {\n        dp[i, 0] = i;\n    }\n    for (int j = 1; j &lt;= m; j++) {\n        dp[0, j] = j;\n    }\n    // 状態遷移: 残りの行と列\n    for (int i = 1; i &lt;= n; i++) {\n        for (int j = 1; j &lt;= m; j++) {\n            if (s[i - 1] == t[j - 1]) {\n                // 2 つの文字が等しければ、その 2 文字をそのままスキップする\n                dp[i, j] = dp[i - 1, j - 1];\n            } else {\n                // 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n                dp[i, j] = Math.Min(Math.Min(dp[i, j - 1], dp[i - 1, j]), dp[i - 1, j - 1]) + 1;\n            }\n        }\n    }\n    return dp[n, m];\n}\n</code></pre> edit_distance.go<pre><code>/* 編集距離：動的計画法 */\nfunc editDistanceDP(s string, t string) int {\n    n := len(s)\n    m := len(t)\n    dp := make([][]int, n+1)\n    for i := 0; i &lt;= n; i++ {\n        dp[i] = make([]int, m+1)\n    }\n    // 状態遷移：先頭行と先頭列\n    for i := 1; i &lt;= n; i++ {\n        dp[i][0] = i\n    }\n    for j := 1; j &lt;= m; j++ {\n        dp[0][j] = j\n    }\n    // 状態遷移: 残りの行と列\n    for i := 1; i &lt;= n; i++ {\n        for j := 1; j &lt;= m; j++ {\n            if s[i-1] == t[j-1] {\n                // 2 つの文字が等しければ、その 2 文字をそのままスキップする\n                dp[i][j] = dp[i-1][j-1]\n            } else {\n                // 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n                dp[i][j] = MinInt(MinInt(dp[i][j-1], dp[i-1][j]), dp[i-1][j-1]) + 1\n            }\n        }\n    }\n    return dp[n][m]\n}\n</code></pre> edit_distance.swift<pre><code>/* 編集距離：動的計画法 */\nfunc editDistanceDP(s: String, t: String) -&gt; Int {\n    let n = s.utf8CString.count\n    let m = t.utf8CString.count\n    var dp = Array(repeating: Array(repeating: 0, count: m + 1), count: n + 1)\n    // 状態遷移：先頭行と先頭列\n    for i in 1 ... n {\n        dp[i][0] = i\n    }\n    for j in 1 ... m {\n        dp[0][j] = j\n    }\n    // 状態遷移: 残りの行と列\n    for i in 1 ... n {\n        for j in 1 ... m {\n            if s.utf8CString[i - 1] == t.utf8CString[j - 1] {\n                // 2 つの文字が等しければ、その 2 文字をそのままスキップする\n                dp[i][j] = dp[i - 1][j - 1]\n            } else {\n                // 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n                dp[i][j] = min(min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1\n            }\n        }\n    }\n    return dp[n][m]\n}\n</code></pre> edit_distance.js<pre><code>/* 編集距離：動的計画法 */\nfunction editDistanceDP(s, t) {\n    const n = s.length,\n        m = t.length;\n    const dp = Array.from({ length: n + 1 }, () =&gt; new Array(m + 1).fill(0));\n    // 状態遷移：先頭行と先頭列\n    for (let i = 1; i &lt;= n; i++) {\n        dp[i][0] = i;\n    }\n    for (let j = 1; j &lt;= m; j++) {\n        dp[0][j] = j;\n    }\n    // 状態遷移: 残りの行と列\n    for (let i = 1; i &lt;= n; i++) {\n        for (let j = 1; j &lt;= m; j++) {\n            if (s.charAt(i - 1) === t.charAt(j - 1)) {\n                // 2 つの文字が等しければ、その 2 文字をそのままスキップする\n                dp[i][j] = dp[i - 1][j - 1];\n            } else {\n                // 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n                dp[i][j] =\n                    Math.min(dp[i][j - 1], dp[i - 1][j], dp[i - 1][j - 1]) + 1;\n            }\n        }\n    }\n    return dp[n][m];\n}\n</code></pre> edit_distance.ts<pre><code>/* 編集距離：動的計画法 */\nfunction editDistanceDP(s: string, t: string): number {\n    const n = s.length,\n        m = t.length;\n    const dp = Array.from({ length: n + 1 }, () =&gt;\n        Array.from({ length: m + 1 }, () =&gt; 0)\n    );\n    // 状態遷移：先頭行と先頭列\n    for (let i = 1; i &lt;= n; i++) {\n        dp[i][0] = i;\n    }\n    for (let j = 1; j &lt;= m; j++) {\n        dp[0][j] = j;\n    }\n    // 状態遷移: 残りの行と列\n    for (let i = 1; i &lt;= n; i++) {\n        for (let j = 1; j &lt;= m; j++) {\n            if (s.charAt(i - 1) === t.charAt(j - 1)) {\n                // 2 つの文字が等しければ、その 2 文字をそのままスキップする\n                dp[i][j] = dp[i - 1][j - 1];\n            } else {\n                // 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n                dp[i][j] =\n                    Math.min(dp[i][j - 1], dp[i - 1][j], dp[i - 1][j - 1]) + 1;\n            }\n        }\n    }\n    return dp[n][m];\n}\n</code></pre> edit_distance.dart<pre><code>/* 編集距離：動的計画法 */\nint editDistanceDP(String s, String t) {\n  int n = s.length, m = t.length;\n  List&lt;List&lt;int&gt;&gt; dp = List.generate(n + 1, (_) =&gt; List.filled(m + 1, 0));\n  // 状態遷移：先頭行と先頭列\n  for (int i = 1; i &lt;= n; i++) {\n    dp[i][0] = i;\n  }\n  for (int j = 1; j &lt;= m; j++) {\n    dp[0][j] = j;\n  }\n  // 状態遷移: 残りの行と列\n  for (int i = 1; i &lt;= n; i++) {\n    for (int j = 1; j &lt;= m; j++) {\n      if (s[i - 1] == t[j - 1]) {\n        // 2 つの文字が等しければ、その 2 文字をそのままスキップする\n        dp[i][j] = dp[i - 1][j - 1];\n      } else {\n        // 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n        dp[i][j] = min(min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;\n      }\n    }\n  }\n  return dp[n][m];\n}\n</code></pre> edit_distance.rs<pre><code>/* 編集距離：動的計画法 */\nfn edit_distance_dp(s: &amp;str, t: &amp;str) -&gt; i32 {\n    let (n, m) = (s.len(), t.len());\n    let mut dp = vec![vec![0; m + 1]; n + 1];\n    // 状態遷移：先頭行と先頭列\n    for i in 1..=n {\n        dp[i][0] = i as i32;\n    }\n    for j in 1..m {\n        dp[0][j] = j as i32;\n    }\n    // 状態遷移: 残りの行と列\n    for i in 1..=n {\n        for j in 1..=m {\n            if s.chars().nth(i - 1) == t.chars().nth(j - 1) {\n                // 2 つの文字が等しければ、その 2 文字をそのままスキップする\n                dp[i][j] = dp[i - 1][j - 1];\n            } else {\n                // 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n                dp[i][j] =\n                    std::cmp::min(std::cmp::min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;\n            }\n        }\n    }\n    dp[n][m]\n}\n</code></pre> edit_distance.c<pre><code>/* 編集距離：動的計画法 */\nint editDistanceDP(char *s, char *t, int n, int m) {\n    int **dp = malloc((n + 1) * sizeof(int *));\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i] = calloc(m + 1, sizeof(int));\n    }\n    // 状態遷移：先頭行と先頭列\n    for (int i = 1; i &lt;= n; i++) {\n        dp[i][0] = i;\n    }\n    for (int j = 1; j &lt;= m; j++) {\n        dp[0][j] = j;\n    }\n    // 状態遷移: 残りの行と列\n    for (int i = 1; i &lt;= n; i++) {\n        for (int j = 1; j &lt;= m; j++) {\n            if (s[i - 1] == t[j - 1]) {\n                // 2 つの文字が等しければ、その 2 文字をそのままスキップする\n                dp[i][j] = dp[i - 1][j - 1];\n            } else {\n                // 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n                dp[i][j] = myMin(myMin(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;\n            }\n        }\n    }\n    int res = dp[n][m];\n    // メモリを解放する\n    for (int i = 0; i &lt;= n; i++) {\n        free(dp[i]);\n    }\n    return res;\n}\n</code></pre> edit_distance.kt<pre><code>/* 編集距離：動的計画法 */\nfun editDistanceDP(s: String, t: String): Int {\n    val n = s.length\n    val m = t.length\n    val dp = Array(n + 1) { IntArray(m + 1) }\n    // 状態遷移：先頭行と先頭列\n    for (i in 1..n) {\n        dp[i][0] = i\n    }\n    for (j in 1..m) {\n        dp[0][j] = j\n    }\n    // 状態遷移: 残りの行と列\n    for (i in 1..n) {\n        for (j in 1..m) {\n            if (s[i - 1] == t[j - 1]) {\n                // 2 つの文字が等しければ、その 2 文字をそのままスキップする\n                dp[i][j] = dp[i - 1][j - 1]\n            } else {\n                // 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n                dp[i][j] = min(min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1\n            }\n        }\n    }\n    return dp[n][m]\n}\n</code></pre> edit_distance.rb<pre><code>### 編集距離：動的計画法 ###\ndef edit_distance_dp(s, t)\n  n, m = s.length, t.length\n  dp = Array.new(n + 1) { Array.new(m + 1, 0) }\n  # 状態遷移：先頭行と先頭列\n  (1...(n + 1)).each { |i| dp[i][0] = i }\n  (1...(m + 1)).each { |j| dp[0][j] = j }\n  # 状態遷移: 残りの行と列\n  for i in 1...(n + 1)\n    for j in 1...(m +1)\n      if s[i - 1] == t[j - 1]\n        # 2 つの文字が等しければ、その 2 文字をそのままスキップする\n        dp[i][j] = dp[i - 1][j - 1]\n      else\n        # 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n        dp[i][j] = [dp[i][j - 1], dp[i - 1][j], dp[i - 1][j - 1]].min + 1\n      end\n    end\n  end\n  dp[n][m]\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>下図に示すように、編集距離問題の状態遷移の過程はナップサック問題と非常によく似ており、どちらも2次元グリッドを埋めていく過程とみなせます。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt;&lt;13&gt;&lt;14&gt;&lt;15&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 14-30   編集距離の動的計画法の過程 </p>","path":["第 14 章 &nbsp; 動的計画法","14.6 &nbsp; 編集距離問題"],"tags":[]},{"location":"chapter_dynamic_programming/edit_distance_problem/#3","level":3,"title":"3.   空間最適化","text":"<p>\\(dp[i,j]\\) は上の \\(dp[i-1, j]\\)、左の \\(dp[i, j-1]\\)、左上の \\(dp[i-1, j-1]\\) から遷移されますが、順方向走査では左上の \\(dp[i-1, j-1]\\) を失い、逆方向走査では \\(dp[i, j-1]\\) を事前に構築できません。そのため、どちらの走査順序も適切ではありません。</p> <p>そのため、変数 <code>leftup</code> を用いて左上の解 \\(dp[i-1, j-1]\\) を一時保存し、左と上の解だけを考えればよくなります。このときの状況は完全ナップサック問題と同じであり、順方向走査を用いることができます。コードは次のとおりです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby edit_distance.py<pre><code>def edit_distance_dp_comp(s: str, t: str) -&gt; int:\n    \"\"\"編集距離：空間最適化した動的計画法\"\"\"\n    n, m = len(s), len(t)\n    dp = [0] * (m + 1)\n    # 状態遷移：先頭行\n    for j in range(1, m + 1):\n        dp[j] = j\n    # 状態遷移：残りの行\n    for i in range(1, n + 1):\n        # 状態遷移：先頭列\n        leftup = dp[0]  # dp[i-1, j-1] を一時保存する\n        dp[0] += 1\n        # 状態遷移：残りの列\n        for j in range(1, m + 1):\n            temp = dp[j]\n            if s[i - 1] == t[j - 1]:\n                # 2 つの文字が等しければ、その 2 文字をそのままスキップする\n                dp[j] = leftup\n            else:\n                # 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n                dp[j] = min(dp[j - 1], dp[j], leftup) + 1\n            leftup = temp  # 次の反復の dp[i-1, j-1] に更新する\n    return dp[m]\n</code></pre> edit_distance.cpp<pre><code>/* 編集距離：空間最適化した動的計画法 */\nint editDistanceDPComp(string s, string t) {\n    int n = s.length(), m = t.length();\n    vector&lt;int&gt; dp(m + 1, 0);\n    // 状態遷移：先頭行\n    for (int j = 1; j &lt;= m; j++) {\n        dp[j] = j;\n    }\n    // 状態遷移：残りの行\n    for (int i = 1; i &lt;= n; i++) {\n        // 状態遷移：先頭列\n        int leftup = dp[0]; // dp[i-1, j-1] を一時保存する\n        dp[0] = i;\n        // 状態遷移：残りの列\n        for (int j = 1; j &lt;= m; j++) {\n            int temp = dp[j];\n            if (s[i - 1] == t[j - 1]) {\n                // 2 つの文字が等しければ、その 2 文字をそのままスキップする\n                dp[j] = leftup;\n            } else {\n                // 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n                dp[j] = min(min(dp[j - 1], dp[j]), leftup) + 1;\n            }\n            leftup = temp; // 次の反復の dp[i-1, j-1] に更新する\n        }\n    }\n    return dp[m];\n}\n</code></pre> edit_distance.java<pre><code>/* 編集距離：空間最適化した動的計画法 */\nint editDistanceDPComp(String s, String t) {\n    int n = s.length(), m = t.length();\n    int[] dp = new int[m + 1];\n    // 状態遷移：先頭行\n    for (int j = 1; j &lt;= m; j++) {\n        dp[j] = j;\n    }\n    // 状態遷移：残りの行\n    for (int i = 1; i &lt;= n; i++) {\n        // 状態遷移：先頭列\n        int leftup = dp[0]; // dp[i-1, j-1] を一時保存する\n        dp[0] = i;\n        // 状態遷移：残りの列\n        for (int j = 1; j &lt;= m; j++) {\n            int temp = dp[j];\n            if (s.charAt(i - 1) == t.charAt(j - 1)) {\n                // 2 つの文字が等しければ、その 2 文字をそのままスキップする\n                dp[j] = leftup;\n            } else {\n                // 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n                dp[j] = Math.min(Math.min(dp[j - 1], dp[j]), leftup) + 1;\n            }\n            leftup = temp; // 次の反復の dp[i-1, j-1] に更新する\n        }\n    }\n    return dp[m];\n}\n</code></pre> edit_distance.cs<pre><code>/* 編集距離：空間最適化した動的計画法 */\nint EditDistanceDPComp(string s, string t) {\n    int n = s.Length, m = t.Length;\n    int[] dp = new int[m + 1];\n    // 状態遷移：先頭行\n    for (int j = 1; j &lt;= m; j++) {\n        dp[j] = j;\n    }\n    // 状態遷移：残りの行\n    for (int i = 1; i &lt;= n; i++) {\n        // 状態遷移：先頭列\n        int leftup = dp[0]; // dp[i-1, j-1] を一時保存する\n        dp[0] = i;\n        // 状態遷移：残りの列\n        for (int j = 1; j &lt;= m; j++) {\n            int temp = dp[j];\n            if (s[i - 1] == t[j - 1]) {\n                // 2 つの文字が等しければ、その 2 文字をそのままスキップする\n                dp[j] = leftup;\n            } else {\n                // 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n                dp[j] = Math.Min(Math.Min(dp[j - 1], dp[j]), leftup) + 1;\n            }\n            leftup = temp; // 次の反復の dp[i-1, j-1] に更新する\n        }\n    }\n    return dp[m];\n}\n</code></pre> edit_distance.go<pre><code>/* 編集距離：空間最適化した動的計画法 */\nfunc editDistanceDPComp(s string, t string) int {\n    n := len(s)\n    m := len(t)\n    dp := make([]int, m+1)\n    // 状態遷移：先頭行\n    for j := 1; j &lt;= m; j++ {\n        dp[j] = j\n    }\n    // 状態遷移：残りの行\n    for i := 1; i &lt;= n; i++ {\n        // 状態遷移：先頭列\n        leftUp := dp[0] // dp[i-1, j-1] を一時保存する\n        dp[0] = i\n        // 状態遷移：残りの列\n        for j := 1; j &lt;= m; j++ {\n            temp := dp[j]\n            if s[i-1] == t[j-1] {\n                // 2 つの文字が等しければ、その 2 文字をそのままスキップする\n                dp[j] = leftUp\n            } else {\n                // 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n                dp[j] = MinInt(MinInt(dp[j-1], dp[j]), leftUp) + 1\n            }\n            leftUp = temp // 次の反復の dp[i-1, j-1] に更新する\n        }\n    }\n    return dp[m]\n}\n</code></pre> edit_distance.swift<pre><code>/* 編集距離：空間最適化した動的計画法 */\nfunc editDistanceDPComp(s: String, t: String) -&gt; Int {\n    let n = s.utf8CString.count\n    let m = t.utf8CString.count\n    var dp = Array(repeating: 0, count: m + 1)\n    // 状態遷移：先頭行\n    for j in 1 ... m {\n        dp[j] = j\n    }\n    // 状態遷移：残りの行\n    for i in 1 ... n {\n        // 状態遷移：先頭列\n        var leftup = dp[0] // dp[i-1, j-1] を一時保存する\n        dp[0] = i\n        // 状態遷移：残りの列\n        for j in 1 ... m {\n            let temp = dp[j]\n            if s.utf8CString[i - 1] == t.utf8CString[j - 1] {\n                // 2 つの文字が等しければ、その 2 文字をそのままスキップする\n                dp[j] = leftup\n            } else {\n                // 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n                dp[j] = min(min(dp[j - 1], dp[j]), leftup) + 1\n            }\n            leftup = temp // 次の反復の dp[i-1, j-1] に更新する\n        }\n    }\n    return dp[m]\n}\n</code></pre> edit_distance.js<pre><code>/* 編集距離：空間最適化した動的計画法 */\nfunction editDistanceDPComp(s, t) {\n    const n = s.length,\n        m = t.length;\n    const dp = new Array(m + 1).fill(0);\n    // 状態遷移：先頭行\n    for (let j = 1; j &lt;= m; j++) {\n        dp[j] = j;\n    }\n    // 状態遷移：残りの行\n    for (let i = 1; i &lt;= n; i++) {\n        // 状態遷移：先頭列\n        let leftup = dp[0]; // dp[i-1, j-1] を一時保存する\n        dp[0] = i;\n        // 状態遷移：残りの列\n        for (let j = 1; j &lt;= m; j++) {\n            const temp = dp[j];\n            if (s.charAt(i - 1) === t.charAt(j - 1)) {\n                // 2 つの文字が等しければ、その 2 文字をそのままスキップする\n                dp[j] = leftup;\n            } else {\n                // 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n                dp[j] = Math.min(dp[j - 1], dp[j], leftup) + 1;\n            }\n            leftup = temp; // 次の反復の dp[i-1, j-1] に更新する\n        }\n    }\n    return dp[m];\n}\n</code></pre> edit_distance.ts<pre><code>/* 編集距離：空間最適化した動的計画法 */\nfunction editDistanceDPComp(s: string, t: string): number {\n    const n = s.length,\n        m = t.length;\n    const dp = new Array(m + 1).fill(0);\n    // 状態遷移：先頭行\n    for (let j = 1; j &lt;= m; j++) {\n        dp[j] = j;\n    }\n    // 状態遷移：残りの行\n    for (let i = 1; i &lt;= n; i++) {\n        // 状態遷移：先頭列\n        let leftup = dp[0]; // dp[i-1, j-1] を一時保存する\n        dp[0] = i;\n        // 状態遷移：残りの列\n        for (let j = 1; j &lt;= m; j++) {\n            const temp = dp[j];\n            if (s.charAt(i - 1) === t.charAt(j - 1)) {\n                // 2 つの文字が等しければ、その 2 文字をそのままスキップする\n                dp[j] = leftup;\n            } else {\n                // 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n                dp[j] = Math.min(dp[j - 1], dp[j], leftup) + 1;\n            }\n            leftup = temp; // 次の反復の dp[i-1, j-1] に更新する\n        }\n    }\n    return dp[m];\n}\n</code></pre> edit_distance.dart<pre><code>/* 編集距離：空間最適化した動的計画法 */\nint editDistanceDPComp(String s, String t) {\n  int n = s.length, m = t.length;\n  List&lt;int&gt; dp = List.filled(m + 1, 0);\n  // 状態遷移：先頭行\n  for (int j = 1; j &lt;= m; j++) {\n    dp[j] = j;\n  }\n  // 状態遷移：残りの行\n  for (int i = 1; i &lt;= n; i++) {\n    // 状態遷移：先頭列\n    int leftup = dp[0]; // dp[i-1, j-1] を一時保存する\n    dp[0] = i;\n    // 状態遷移：残りの列\n    for (int j = 1; j &lt;= m; j++) {\n      int temp = dp[j];\n      if (s[i - 1] == t[j - 1]) {\n        // 2 つの文字が等しければ、その 2 文字をそのままスキップする\n        dp[j] = leftup;\n      } else {\n        // 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n        dp[j] = min(min(dp[j - 1], dp[j]), leftup) + 1;\n      }\n      leftup = temp; // 次の反復の dp[i-1, j-1] に更新する\n    }\n  }\n  return dp[m];\n}\n</code></pre> edit_distance.rs<pre><code>/* 編集距離：空間最適化した動的計画法 */\nfn edit_distance_dp_comp(s: &amp;str, t: &amp;str) -&gt; i32 {\n    let (n, m) = (s.len(), t.len());\n    let mut dp = vec![0; m + 1];\n    // 状態遷移：先頭行\n    for j in 1..m {\n        dp[j] = j as i32;\n    }\n    // 状態遷移：残りの行\n    for i in 1..=n {\n        // 状態遷移：先頭列\n        let mut leftup = dp[0]; // dp[i-1, j-1] を一時保存する\n        dp[0] = i as i32;\n        // 状態遷移：残りの列\n        for j in 1..=m {\n            let temp = dp[j];\n            if s.chars().nth(i - 1) == t.chars().nth(j - 1) {\n                // 2 つの文字が等しければ、その 2 文字をそのままスキップする\n                dp[j] = leftup;\n            } else {\n                // 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n                dp[j] = std::cmp::min(std::cmp::min(dp[j - 1], dp[j]), leftup) + 1;\n            }\n            leftup = temp; // 次の反復の dp[i-1, j-1] に更新する\n        }\n    }\n    dp[m]\n}\n</code></pre> edit_distance.c<pre><code>/* 編集距離：空間最適化した動的計画法 */\nint editDistanceDPComp(char *s, char *t, int n, int m) {\n    int *dp = calloc(m + 1, sizeof(int));\n    // 状態遷移：先頭行\n    for (int j = 1; j &lt;= m; j++) {\n        dp[j] = j;\n    }\n    // 状態遷移：残りの行\n    for (int i = 1; i &lt;= n; i++) {\n        // 状態遷移：先頭列\n        int leftup = dp[0]; // dp[i-1, j-1] を一時保存する\n        dp[0] = i;\n        // 状態遷移：残りの列\n        for (int j = 1; j &lt;= m; j++) {\n            int temp = dp[j];\n            if (s[i - 1] == t[j - 1]) {\n                // 2 つの文字が等しければ、その 2 文字をそのままスキップする\n                dp[j] = leftup;\n            } else {\n                // 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n                dp[j] = myMin(myMin(dp[j - 1], dp[j]), leftup) + 1;\n            }\n            leftup = temp; // 次の反復の dp[i-1, j-1] に更新する\n        }\n    }\n    int res = dp[m];\n    // メモリを解放する\n    free(dp);\n    return res;\n}\n</code></pre> edit_distance.kt<pre><code>/* 編集距離：空間最適化した動的計画法 */\nfun editDistanceDPComp(s: String, t: String): Int {\n    val n = s.length\n    val m = t.length\n    val dp = IntArray(m + 1)\n    // 状態遷移：先頭行\n    for (j in 1..m) {\n        dp[j] = j\n    }\n    // 状態遷移：残りの行\n    for (i in 1..n) {\n        // 状態遷移：先頭列\n        var leftup = dp[0] // dp[i-1, j-1] を一時保存する\n        dp[0] = i\n        // 状態遷移：残りの列\n        for (j in 1..m) {\n            val temp = dp[j]\n            if (s[i - 1] == t[j - 1]) {\n                // 2 つの文字が等しければ、その 2 文字をそのままスキップする\n                dp[j] = leftup\n            } else {\n                // 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n                dp[j] = min(min(dp[j - 1], dp[j]), leftup) + 1\n            }\n            leftup = temp // 次の反復の dp[i-1, j-1] に更新する\n        }\n    }\n    return dp[m]\n}\n</code></pre> edit_distance.rb<pre><code>### 編集距離：空間最適化した動的計画法 ###\ndef edit_distance_dp_comp(s, t)\n  n, m = s.length, t.length\n  dp = Array.new(m + 1, 0)\n  # 状態遷移：先頭行\n  (1...(m + 1)).each { |j| dp[j] = j }\n  # 状態遷移：残りの行\n  for i in 1...(n + 1)\n    # 状態遷移：先頭列\n    leftup = dp.first # dp[i-1, j-1] を一時保存する\n    dp[0] += 1\n    # 状態遷移：残りの列\n    for j in 1...(m + 1)\n      temp = dp[j]\n      if s[i - 1] == t[j - 1]\n        # 2 つの文字が等しければ、その 2 文字をそのままスキップする\n        dp[j] = leftup\n      else\n        # 最小編集回数 = 挿入・削除・置換の 3 操作における最小編集回数 + 1\n        dp[j] = [dp[j - 1], dp[j], leftup].min + 1\n      end\n      leftup = temp # 次の反復の dp[i-1, j-1] に更新する\n    end\n  end\n  dp[m]\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 14 章 &nbsp; 動的計画法","14.6 &nbsp; 編集距離問題"],"tags":[]},{"location":"chapter_dynamic_programming/intro_to_dynamic_programming/","level":1,"title":"14.1   動的計画法入門","text":"<p>動的計画法（dynamic programming）は重要なアルゴリズムパラダイムであり、問題をより小さな部分問題の列に分解し、それらの解を保存して重複計算を避けることで、時間効率を大幅に向上させます。</p> <p>本節では、古典的な例題から始めて、まずその力任せのバックトラッキング解法を示し、そこに含まれる重複部分問題を観察したうえで、より効率的な動的計画法の解法を段階的に導きます。</p> <p>階段を上る</p> <p>全体で \\(n\\) 段ある階段が与えられ、各ステップで \\(1\\) 段または \\(2\\) 段上ることができます。頂上まで到達する方法は何通りあるでしょうか？</p> <p>次の図に示すように、\\(3\\) 段の階段では、頂上まで到達する方法は全部で \\(3\\) 通りあります。</p> <p></p> <p> 図 14-1   3 段の階段を上る方法の数 </p> <p>この問題の目的は方法の総数を求めることです。考えられるすべての可能性をバックトラッキングで総当たりすることができます。具体的には、階段を上ることを複数ラウンドの選択過程とみなし、地面から出発して各ラウンドで \\(1\\) 段または \\(2\\) 段上ります。階段の頂上に到達するたびに方法数を \\(1\\) 増やし、頂上を越えた場合は枝刈りします。コードは次のとおりです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby climbing_stairs_backtrack.py<pre><code>def backtrack(choices: list[int], state: int, n: int, res: list[int]) -&gt; int:\n    \"\"\"バックトラッキング\"\"\"\n    # 第 n 段に到達したら、方法数を 1 増やす\n    if state == n:\n        res[0] += 1\n    # すべての選択肢を走査\n    for choice in choices:\n        # 枝刈り: 第 n 段を超えないようにする\n        if state + choice &gt; n:\n            continue\n        # 試行: 選択を行い、状態を更新\n        backtrack(choices, state + choice, n, res)\n        # バックトラック\n\ndef climbing_stairs_backtrack(n: int) -&gt; int:\n    \"\"\"階段登り：バックトラッキング\"\"\"\n    choices = [1, 2]  # 1 段または 2 段上ることを選べる\n    state = 0  # 第 0 段から上り始める\n    res = [0]  # res[0] を使って方法数を記録する\n    backtrack(choices, state, n, res)\n    return res[0]\n</code></pre> climbing_stairs_backtrack.cpp<pre><code>/* バックトラッキング */\nvoid backtrack(vector&lt;int&gt; &amp;choices, int state, int n, vector&lt;int&gt; &amp;res) {\n    // 第 n 段に到達したら、方法数を 1 増やす\n    if (state == n)\n        res[0]++;\n    // すべての選択肢を走査\n    for (auto &amp;choice : choices) {\n        // 枝刈り: 第 n 段を超えないようにする\n        if (state + choice &gt; n)\n            continue;\n        // 試行: 選択を行い、状態を更新\n        backtrack(choices, state + choice, n, res);\n        // バックトラック\n    }\n}\n\n/* 階段登り：バックトラッキング */\nint climbingStairsBacktrack(int n) {\n    vector&lt;int&gt; choices = {1, 2}; // 1 段または 2 段上ることを選べる\n    int state = 0;                // 第 0 段から上り始める\n    vector&lt;int&gt; res = {0};        // res[0] を使って方法数を記録する\n    backtrack(choices, state, n, res);\n    return res[0];\n}\n</code></pre> climbing_stairs_backtrack.java<pre><code>/* バックトラッキング */\nvoid backtrack(List&lt;Integer&gt; choices, int state, int n, List&lt;Integer&gt; res) {\n    // 第 n 段に到達したら、方法数を 1 増やす\n    if (state == n)\n        res.set(0, res.get(0) + 1);\n    // すべての選択肢を走査\n    for (Integer choice : choices) {\n        // 枝刈り: 第 n 段を超えないようにする\n        if (state + choice &gt; n)\n            continue;\n        // 試行: 選択を行い、状態を更新\n        backtrack(choices, state + choice, n, res);\n        // バックトラック\n    }\n}\n\n/* 階段登り：バックトラッキング */\nint climbingStairsBacktrack(int n) {\n    List&lt;Integer&gt; choices = Arrays.asList(1, 2); // 1 段または 2 段上ることを選べる\n    int state = 0; // 第 0 段から上り始める\n    List&lt;Integer&gt; res = new ArrayList&lt;&gt;();\n    res.add(0); // res[0] を使って方法数を記録する\n    backtrack(choices, state, n, res);\n    return res.get(0);\n}\n</code></pre> climbing_stairs_backtrack.cs<pre><code>/* バックトラッキング */\nvoid Backtrack(List&lt;int&gt; choices, int state, int n, List&lt;int&gt; res) {\n    // 第 n 段に到達したら、方法数を 1 増やす\n    if (state == n)\n        res[0]++;\n    // すべての選択肢を走査\n    foreach (int choice in choices) {\n        // 枝刈り: 第 n 段を超えないようにする\n        if (state + choice &gt; n)\n            continue;\n        // 試行: 選択を行い、状態を更新\n        Backtrack(choices, state + choice, n, res);\n        // バックトラック\n    }\n}\n\n/* 階段登り：バックトラッキング */\nint ClimbingStairsBacktrack(int n) {\n    List&lt;int&gt; choices = [1, 2]; // 1 段または 2 段上ることを選べる\n    int state = 0; // 第 0 段から上り始める\n    List&lt;int&gt; res = [0]; // res[0] を使って方法数を記録する\n    Backtrack(choices, state, n, res);\n    return res[0];\n}\n</code></pre> climbing_stairs_backtrack.go<pre><code>/* バックトラッキング */\nfunc backtrack(choices []int, state, n int, res []int) {\n    // 第 n 段に到達したら、方法数を 1 増やす\n    if state == n {\n        res[0] = res[0] + 1\n    }\n    // すべての選択肢を走査\n    for _, choice := range choices {\n        // 枝刈り: 第 n 段を超えないようにする\n        if state+choice &gt; n {\n            continue\n        }\n        // 試行: 選択を行い、状態を更新\n        backtrack(choices, state+choice, n, res)\n        // バックトラック\n    }\n}\n\n/* 階段登り：バックトラッキング */\nfunc climbingStairsBacktrack(n int) int {\n    // 1 段または 2 段上ることを選べる\n    choices := []int{1, 2}\n    // 第 0 段から上り始める\n    state := 0\n    res := make([]int, 1)\n    // res[0] を使って方法数を記録する\n    res[0] = 0\n    backtrack(choices, state, n, res)\n    return res[0]\n}\n</code></pre> climbing_stairs_backtrack.swift<pre><code>/* バックトラッキング */\nfunc backtrack(choices: [Int], state: Int, n: Int, res: inout [Int]) {\n    // 第 n 段に到達したら、方法数を 1 増やす\n    if state == n {\n        res[0] += 1\n    }\n    // すべての選択肢を走査\n    for choice in choices {\n        // 枝刈り: 第 n 段を超えないようにする\n        if state + choice &gt; n {\n            continue\n        }\n        // 試行: 選択を行い、状態を更新\n        backtrack(choices: choices, state: state + choice, n: n, res: &amp;res)\n        // バックトラック\n    }\n}\n\n/* 階段登り：バックトラッキング */\nfunc climbingStairsBacktrack(n: Int) -&gt; Int {\n    let choices = [1, 2] // 1 段または 2 段上ることを選べる\n    let state = 0 // 第 0 段から上り始める\n    var res: [Int] = []\n    res.append(0) // res[0] を使って方法数を記録する\n    backtrack(choices: choices, state: state, n: n, res: &amp;res)\n    return res[0]\n}\n</code></pre> climbing_stairs_backtrack.js<pre><code>/* バックトラッキング */\nfunction backtrack(choices, state, n, res) {\n    // 第 n 段に到達したら、方法数を 1 増やす\n    if (state === n) res.set(0, res.get(0) + 1);\n    // すべての選択肢を走査\n    for (const choice of choices) {\n        // 枝刈り: 第 n 段を超えないようにする\n        if (state + choice &gt; n) continue;\n        // 試行: 選択を行い、状態を更新\n        backtrack(choices, state + choice, n, res);\n        // バックトラック\n    }\n}\n\n/* 階段登り：バックトラッキング */\nfunction climbingStairsBacktrack(n) {\n    const choices = [1, 2]; // 1 段または 2 段上ることを選べる\n    const state = 0; // 第 0 段から上り始める\n    const res = new Map();\n    res.set(0, 0); // res[0] を使って方法数を記録する\n    backtrack(choices, state, n, res);\n    return res.get(0);\n}\n</code></pre> climbing_stairs_backtrack.ts<pre><code>/* バックトラッキング */\nfunction backtrack(\n    choices: number[],\n    state: number,\n    n: number,\n    res: Map&lt;0, any&gt;\n): void {\n    // 第 n 段に到達したら、方法数を 1 増やす\n    if (state === n) res.set(0, res.get(0) + 1);\n    // すべての選択肢を走査\n    for (const choice of choices) {\n        // 枝刈り: 第 n 段を超えないようにする\n        if (state + choice &gt; n) continue;\n        // 試行: 選択を行い、状態を更新\n        backtrack(choices, state + choice, n, res);\n        // バックトラック\n    }\n}\n\n/* 階段登り：バックトラッキング */\nfunction climbingStairsBacktrack(n: number): number {\n    const choices = [1, 2]; // 1 段または 2 段上ることを選べる\n    const state = 0; // 第 0 段から上り始める\n    const res = new Map();\n    res.set(0, 0); // res[0] を使って方法数を記録する\n    backtrack(choices, state, n, res);\n    return res.get(0);\n}\n</code></pre> climbing_stairs_backtrack.dart<pre><code>/* バックトラッキング */\nvoid backtrack(List&lt;int&gt; choices, int state, int n, List&lt;int&gt; res) {\n  // 第 n 段に到達したら、方法数を 1 増やす\n  if (state == n) {\n    res[0]++;\n  }\n  // すべての選択肢を走査\n  for (int choice in choices) {\n    // 枝刈り: 第 n 段を超えないようにする\n    if (state + choice &gt; n) continue;\n    // 試行: 選択を行い、状態を更新\n    backtrack(choices, state + choice, n, res);\n    // バックトラック\n  }\n}\n\n/* 階段登り：バックトラッキング */\nint climbingStairsBacktrack(int n) {\n  List&lt;int&gt; choices = [1, 2]; // 1 段または 2 段上ることを選べる\n  int state = 0; // 第 0 段から上り始める\n  List&lt;int&gt; res = [];\n  res.add(0); // res[0] を使って方法数を記録する\n  backtrack(choices, state, n, res);\n  return res[0];\n}\n</code></pre> climbing_stairs_backtrack.rs<pre><code>/* バックトラッキング */\nfn backtrack(choices: &amp;[i32], state: i32, n: i32, res: &amp;mut [i32]) {\n    // 第 n 段に到達したら、方法数を 1 増やす\n    if state == n {\n        res[0] = res[0] + 1;\n    }\n    // すべての選択肢を走査\n    for &amp;choice in choices {\n        // 枝刈り: 第 n 段を超えないようにする\n        if state + choice &gt; n {\n            continue;\n        }\n        // 試行: 選択を行い、状態を更新\n        backtrack(choices, state + choice, n, res);\n        // バックトラック\n    }\n}\n\n/* 階段登り：バックトラッキング */\nfn climbing_stairs_backtrack(n: usize) -&gt; i32 {\n    let choices = vec![1, 2]; // 1 段または 2 段上ることを選べる\n    let state = 0; // 第 0 段から上り始める\n    let mut res = Vec::new();\n    res.push(0); // res[0] を使って方法数を記録する\n    backtrack(&amp;choices, state, n as i32, &amp;mut res);\n    res[0]\n}\n</code></pre> climbing_stairs_backtrack.c<pre><code>/* バックトラッキング */\nvoid backtrack(int *choices, int state, int n, int *res, int len) {\n    // 第 n 段に到達したら、方法数を 1 増やす\n    if (state == n)\n        res[0]++;\n    // すべての選択肢を走査\n    for (int i = 0; i &lt; len; i++) {\n        int choice = choices[i];\n        // 枝刈り: 第 n 段を超えないようにする\n        if (state + choice &gt; n)\n            continue;\n        // 試行: 選択を行い、状態を更新\n        backtrack(choices, state + choice, n, res, len);\n        // バックトラック\n    }\n}\n\n/* 階段登り：バックトラッキング */\nint climbingStairsBacktrack(int n) {\n    int choices[2] = {1, 2}; // 1 段または 2 段上ることを選べる\n    int state = 0;           // 第 0 段から上り始める\n    int *res = (int *)malloc(sizeof(int));\n    *res = 0; // res[0] を使って方法数を記録する\n    int len = sizeof(choices) / sizeof(int);\n    backtrack(choices, state, n, res, len);\n    int result = *res;\n    free(res);\n    return result;\n}\n</code></pre> climbing_stairs_backtrack.kt<pre><code>/* バックトラッキング */\nfun backtrack(\n    choices: MutableList&lt;Int&gt;,\n    state: Int,\n    n: Int,\n    res: MutableList&lt;Int&gt;\n) {\n    // 第 n 段に到達したら、方法数を 1 増やす\n    if (state == n)\n        res[0] = res[0] + 1\n    // すべての選択肢を走査\n    for (choice in choices) {\n        // 枝刈り: 第 n 段を超えないようにする\n        if (state + choice &gt; n) continue\n        // 試行: 選択を行い、状態を更新\n        backtrack(choices, state + choice, n, res)\n        // バックトラック\n    }\n}\n\n/* 階段登り：バックトラッキング */\nfun climbingStairsBacktrack(n: Int): Int {\n    val choices = mutableListOf(1, 2) // 1 段または 2 段上ることを選べる\n    val state = 0 // 第 0 段から上り始める\n    val res = mutableListOf&lt;Int&gt;()\n    res.add(0) // res[0] を使って方法数を記録する\n    backtrack(choices, state, n, res)\n    return res[0]\n}\n</code></pre> climbing_stairs_backtrack.rb<pre><code>### バックトラッキング ###\ndef backtrack(choices, state, n, res)\n  # 第 n 段に到達したら、方法数を 1 増やす\n  res[0] += 1 if state == n\n  # すべての選択肢を走査\n  for choice in choices\n    # 枝刈り: 第 n 段を超えないようにする\n    next if state + choice &gt; n\n\n    # 試行: 選択を行い、状態を更新\n    backtrack(choices, state + choice, n, res)\n  end\n  # バックトラック\nend\n\n### 階段登り：バックトラッキング ###\ndef climbing_stairs_backtrack(n)\n  choices = [1, 2] # 1 段または 2 段上ることを選べる\n  state = 0 # 第 0 段から上り始める\n  res = [0] # res[0] を使って方法数を記録する\n  backtrack(choices, state, n, res)\n  res.first\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 14 章 &nbsp; 動的計画法","14.1 &nbsp; 動的計画法入門"],"tags":[]},{"location":"chapter_dynamic_programming/intro_to_dynamic_programming/#1411-1","level":2,"title":"14.1.1   方法 1：総当たり探索","text":"<p>バックトラッキング法は通常、問題を明示的に分解するのではなく、問題解決を一連の意思決定ステップとみなし、試行と枝刈りによってあらゆる可能な解を探索します。</p> <p>この問題を問題分解の観点から分析してみましょう。\\(i\\) 段目まで上る方法が全部で \\(dp[i]\\) 通りあるとすると、\\(dp[i]\\) が元の問題であり、その部分問題には次が含まれます：</p> \\[ dp[i-1], dp[i-2], \\dots, dp[2], dp[1] \\] <p>各ラウンドでは \\(1\\) 段または \\(2\\) 段しか上れないため、\\(i\\) 段目の階段に立っているとき、直前のラウンドでは \\(i - 1\\) 段目または \\(i - 2\\) 段目にしか立てません。言い換えると、\\(i -1\\) 段目または \\(i - 2\\) 段目からしか \\(i\\) 段目へ進めません。</p> <p>ここから重要な帰結が得られます。**\\(i - 1\\) 段目まで上る方法数と \\(i - 2\\) 段目まで上る方法数の和が、\\(i\\) 段目まで上る方法数に等しい**のです。式は次のとおりです：</p> \\[ dp[i] = dp[i-1] + dp[i-2] \\] <p>これは、階段を上る問題では各部分問題の間に漸化関係があり、**元の問題の解は部分問題の解から構築できる**ことを意味します。次の図はこの漸化関係を示しています。</p> <p></p> <p> 図 14-2   方法数の漸化関係 </p> <p>漸化式に基づいて総当たり探索の解法を得ることができます。\\(dp[n]\\) を出発点とし、**より大きな問題を再帰的に 2 つのより小さな問題の和へ分解**していき、最小部分問題 \\(dp[1]\\) と \\(dp[2]\\) に到達したら返します。ここで最小部分問題の解は既知であり、\\(dp[1] = 1\\)、\\(dp[2] = 2\\) です。これは、第 \\(1\\) 段目と第 \\(2\\) 段目まで上る方法がそれぞれ \\(1\\) 通り、\\(2\\) 通りであることを表します。</p> <p>次のコードを見ると、標準的なバックトラッキングコードと同じく深さ優先探索に属しますが、より簡潔です：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby climbing_stairs_dfs.py<pre><code>def dfs(i: int) -&gt; int:\n    \"\"\"検索\"\"\"\n    # dp[1] と dp[2] は既知なので返す\n    if i == 1 or i == 2:\n        return i\n    # dp[i] = dp[i-1] + dp[i-2]\n    count = dfs(i - 1) + dfs(i - 2)\n    return count\n\ndef climbing_stairs_dfs(n: int) -&gt; int:\n    \"\"\"階段登り：探索\"\"\"\n    return dfs(n)\n</code></pre> climbing_stairs_dfs.cpp<pre><code>/* 検索 */\nint dfs(int i) {\n    // dp[1] と dp[2] は既知なので返す\n    if (i == 1 || i == 2)\n        return i;\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1) + dfs(i - 2);\n    return count;\n}\n\n/* 階段登り：探索 */\nint climbingStairsDFS(int n) {\n    return dfs(n);\n}\n</code></pre> climbing_stairs_dfs.java<pre><code>/* 検索 */\nint dfs(int i) {\n    // dp[1] と dp[2] は既知なので返す\n    if (i == 1 || i == 2)\n        return i;\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1) + dfs(i - 2);\n    return count;\n}\n\n/* 階段登り：探索 */\nint climbingStairsDFS(int n) {\n    return dfs(n);\n}\n</code></pre> climbing_stairs_dfs.cs<pre><code>/* 検索 */\nint DFS(int i) {\n    // dp[1] と dp[2] は既知なので返す\n    if (i == 1 || i == 2)\n        return i;\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = DFS(i - 1) + DFS(i - 2);\n    return count;\n}\n\n/* 階段登り：探索 */\nint ClimbingStairsDFS(int n) {\n    return DFS(n);\n}\n</code></pre> climbing_stairs_dfs.go<pre><code>/* 検索 */\nfunc dfs(i int) int {\n    // dp[1] と dp[2] は既知なので返す\n    if i == 1 || i == 2 {\n        return i\n    }\n    // dp[i] = dp[i-1] + dp[i-2]\n    count := dfs(i-1) + dfs(i-2)\n    return count\n}\n\n/* 階段登り：探索 */\nfunc climbingStairsDFS(n int) int {\n    return dfs(n)\n}\n</code></pre> climbing_stairs_dfs.swift<pre><code>/* 検索 */\nfunc dfs(i: Int) -&gt; Int {\n    // dp[1] と dp[2] は既知なので返す\n    if i == 1 || i == 2 {\n        return i\n    }\n    // dp[i] = dp[i-1] + dp[i-2]\n    let count = dfs(i: i - 1) + dfs(i: i - 2)\n    return count\n}\n\n/* 階段登り：探索 */\nfunc climbingStairsDFS(n: Int) -&gt; Int {\n    dfs(i: n)\n}\n</code></pre> climbing_stairs_dfs.js<pre><code>/* 検索 */\nfunction dfs(i) {\n    // dp[1] と dp[2] は既知なので返す\n    if (i === 1 || i === 2) return i;\n    // dp[i] = dp[i-1] + dp[i-2]\n    const count = dfs(i - 1) + dfs(i - 2);\n    return count;\n}\n\n/* 階段登り：探索 */\nfunction climbingStairsDFS(n) {\n    return dfs(n);\n}\n</code></pre> climbing_stairs_dfs.ts<pre><code>/* 検索 */\nfunction dfs(i: number): number {\n    // dp[1] と dp[2] は既知なので返す\n    if (i === 1 || i === 2) return i;\n    // dp[i] = dp[i-1] + dp[i-2]\n    const count = dfs(i - 1) + dfs(i - 2);\n    return count;\n}\n\n/* 階段登り：探索 */\nfunction climbingStairsDFS(n: number): number {\n    return dfs(n);\n}\n</code></pre> climbing_stairs_dfs.dart<pre><code>/* 検索 */\nint dfs(int i) {\n  // dp[1] と dp[2] は既知なので返す\n  if (i == 1 || i == 2) return i;\n  // dp[i] = dp[i-1] + dp[i-2]\n  int count = dfs(i - 1) + dfs(i - 2);\n  return count;\n}\n\n/* 階段登り：探索 */\nint climbingStairsDFS(int n) {\n  return dfs(n);\n}\n</code></pre> climbing_stairs_dfs.rs<pre><code>/* 検索 */\nfn dfs(i: usize) -&gt; i32 {\n    // dp[1] と dp[2] は既知なので返す\n    if i == 1 || i == 2 {\n        return i as i32;\n    }\n    // dp[i] = dp[i-1] + dp[i-2]\n    let count = dfs(i - 1) + dfs(i - 2);\n    count\n}\n\n/* 階段登り：探索 */\nfn climbing_stairs_dfs(n: usize) -&gt; i32 {\n    dfs(n)\n}\n</code></pre> climbing_stairs_dfs.c<pre><code>/* 検索 */\nint dfs(int i) {\n    // dp[1] と dp[2] は既知なので返す\n    if (i == 1 || i == 2)\n        return i;\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1) + dfs(i - 2);\n    return count;\n}\n\n/* 階段登り：探索 */\nint climbingStairsDFS(int n) {\n    return dfs(n);\n}\n</code></pre> climbing_stairs_dfs.kt<pre><code>/* 検索 */\nfun dfs(i: Int): Int {\n    // dp[1] と dp[2] は既知なので返す\n    if (i == 1 || i == 2) return i\n    // dp[i] = dp[i-1] + dp[i-2]\n    val count = dfs(i - 1) + dfs(i - 2)\n    return count\n}\n\n/* 階段登り：探索 */\nfun climbingStairsDFS(n: Int): Int {\n    return dfs(n)\n}\n</code></pre> climbing_stairs_dfs.rb<pre><code>### 探索 ###\ndef dfs(i)\n  # dp[1] と dp[2] は既知なので返す\n  return i if i == 1 || i == 2\n  # dp[i] = dp[i-1] + dp[i-2]\n  dfs(i - 1) + dfs(i - 2)\nend\n\n### 階段登り：探索 ###\ndef climbing_stairs_dfs(n)\n  dfs(n)\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>次の図は総当たり探索によって形成される再帰木を示しています。問題 \\(dp[n]\\) に対して、その再帰木の深さは \\(n\\)、時間計算量は \\(O(2^n)\\) です。指数オーダーは爆発的に増加するため、比較的大きな \\(n\\) を入力すると長時間待たされることになります。</p> <p></p> <p> 図 14-3   階段上りに対応する再帰木 </p> <p>上の図を見ると、指数オーダーの時間計算量は「重複部分問題」によって生じています。たとえば \\(dp[9]\\) は \\(dp[8]\\) と \\(dp[7]\\) に分解され、\\(dp[8]\\) は \\(dp[7]\\) と \\(dp[6]\\) に分解されるため、どちらにも部分問題 \\(dp[7]\\) が含まれています。</p> <p>このように、部分問題の中にはさらに小さな重複部分問題が含まれ、それが際限なく続いていきます。計算資源の大部分は、こうした重複部分問題に浪費されています。</p>","path":["第 14 章 &nbsp; 動的計画法","14.1 &nbsp; 動的計画法入門"],"tags":[]},{"location":"chapter_dynamic_programming/intro_to_dynamic_programming/#1412-2","level":2,"title":"14.1.2   方法 2：メモ化探索","text":"<p>アルゴリズム効率を高めるため、**すべての重複部分問題を 1 回だけ計算したい**と考えます。そのために、各部分問題の解を記録する配列 <code>mem</code> を宣言し、探索の過程で重複部分問題を枝刈りします。</p> <ol> <li>\\(dp[i]\\) を初めて計算したとき、その結果を <code>mem[i]</code> に記録して後で使えるようにします。</li> <li>再び \\(dp[i]\\) を計算する必要が生じたときは、<code>mem[i]</code> から直接結果を取得し、その部分問題の重複計算を避けます。</li> </ol> <p>コードは次のとおりです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby climbing_stairs_dfs_mem.py<pre><code>def dfs(i: int, mem: list[int]) -&gt; int:\n    \"\"\"メモ化探索\"\"\"\n    # dp[1] と dp[2] は既知なので返す\n    if i == 1 or i == 2:\n        return i\n    # dp[i] の記録があれば、それをそのまま返す\n    if mem[i] != -1:\n        return mem[i]\n    # dp[i] = dp[i-1] + dp[i-2]\n    count = dfs(i - 1, mem) + dfs(i - 2, mem)\n    # dp[i] を記録する\n    mem[i] = count\n    return count\n\ndef climbing_stairs_dfs_mem(n: int) -&gt; int:\n    \"\"\"階段登り：メモ化探索\"\"\"\n    # mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す\n    mem = [-1] * (n + 1)\n    return dfs(n, mem)\n</code></pre> climbing_stairs_dfs_mem.cpp<pre><code>/* メモ化探索 */\nint dfs(int i, vector&lt;int&gt; &amp;mem) {\n    // dp[1] と dp[2] は既知なので返す\n    if (i == 1 || i == 2)\n        return i;\n    // dp[i] の記録があれば、それをそのまま返す\n    if (mem[i] != -1)\n        return mem[i];\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1, mem) + dfs(i - 2, mem);\n    // dp[i] を記録する\n    mem[i] = count;\n    return count;\n}\n\n/* 階段登り：メモ化探索 */\nint climbingStairsDFSMem(int n) {\n    // mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す\n    vector&lt;int&gt; mem(n + 1, -1);\n    return dfs(n, mem);\n}\n</code></pre> climbing_stairs_dfs_mem.java<pre><code>/* メモ化探索 */\nint dfs(int i, int[] mem) {\n    // dp[1] と dp[2] は既知なので返す\n    if (i == 1 || i == 2)\n        return i;\n    // dp[i] の記録があれば、それをそのまま返す\n    if (mem[i] != -1)\n        return mem[i];\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1, mem) + dfs(i - 2, mem);\n    // dp[i] を記録する\n    mem[i] = count;\n    return count;\n}\n\n/* 階段登り：メモ化探索 */\nint climbingStairsDFSMem(int n) {\n    // mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す\n    int[] mem = new int[n + 1];\n    Arrays.fill(mem, -1);\n    return dfs(n, mem);\n}\n</code></pre> climbing_stairs_dfs_mem.cs<pre><code>/* メモ化探索 */\nint DFS(int i, int[] mem) {\n    // dp[1] と dp[2] は既知なので返す\n    if (i == 1 || i == 2)\n        return i;\n    // dp[i] の記録があれば、それをそのまま返す\n    if (mem[i] != -1)\n        return mem[i];\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = DFS(i - 1, mem) + DFS(i - 2, mem);\n    // dp[i] を記録する\n    mem[i] = count;\n    return count;\n}\n\n/* 階段登り：メモ化探索 */\nint ClimbingStairsDFSMem(int n) {\n    // mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す\n    int[] mem = new int[n + 1];\n    Array.Fill(mem, -1);\n    return DFS(n, mem);\n}\n</code></pre> climbing_stairs_dfs_mem.go<pre><code>/* メモ化探索 */\nfunc dfsMem(i int, mem []int) int {\n    // dp[1] と dp[2] は既知なので返す\n    if i == 1 || i == 2 {\n        return i\n    }\n    // dp[i] の記録があれば、それをそのまま返す\n    if mem[i] != -1 {\n        return mem[i]\n    }\n    // dp[i] = dp[i-1] + dp[i-2]\n    count := dfsMem(i-1, mem) + dfsMem(i-2, mem)\n    // dp[i] を記録する\n    mem[i] = count\n    return count\n}\n\n/* 階段登り：メモ化探索 */\nfunc climbingStairsDFSMem(n int) int {\n    // mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す\n    mem := make([]int, n+1)\n    for i := range mem {\n        mem[i] = -1\n    }\n    return dfsMem(n, mem)\n}\n</code></pre> climbing_stairs_dfs_mem.swift<pre><code>/* メモ化探索 */\nfunc dfs(i: Int, mem: inout [Int]) -&gt; Int {\n    // dp[1] と dp[2] は既知なので返す\n    if i == 1 || i == 2 {\n        return i\n    }\n    // dp[i] の記録があれば、それをそのまま返す\n    if mem[i] != -1 {\n        return mem[i]\n    }\n    // dp[i] = dp[i-1] + dp[i-2]\n    let count = dfs(i: i - 1, mem: &amp;mem) + dfs(i: i - 2, mem: &amp;mem)\n    // dp[i] を記録する\n    mem[i] = count\n    return count\n}\n\n/* 階段登り：メモ化探索 */\nfunc climbingStairsDFSMem(n: Int) -&gt; Int {\n    // mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す\n    var mem = Array(repeating: -1, count: n + 1)\n    return dfs(i: n, mem: &amp;mem)\n}\n</code></pre> climbing_stairs_dfs_mem.js<pre><code>/* メモ化探索 */\nfunction dfs(i, mem) {\n    // dp[1] と dp[2] は既知なので返す\n    if (i === 1 || i === 2) return i;\n    // dp[i] の記録があれば、それをそのまま返す\n    if (mem[i] != -1) return mem[i];\n    // dp[i] = dp[i-1] + dp[i-2]\n    const count = dfs(i - 1, mem) + dfs(i - 2, mem);\n    // dp[i] を記録する\n    mem[i] = count;\n    return count;\n}\n\n/* 階段登り：メモ化探索 */\nfunction climbingStairsDFSMem(n) {\n    // mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す\n    const mem = new Array(n + 1).fill(-1);\n    return dfs(n, mem);\n}\n</code></pre> climbing_stairs_dfs_mem.ts<pre><code>/* メモ化探索 */\nfunction dfs(i: number, mem: number[]): number {\n    // dp[1] と dp[2] は既知なので返す\n    if (i === 1 || i === 2) return i;\n    // dp[i] の記録があれば、それをそのまま返す\n    if (mem[i] != -1) return mem[i];\n    // dp[i] = dp[i-1] + dp[i-2]\n    const count = dfs(i - 1, mem) + dfs(i - 2, mem);\n    // dp[i] を記録する\n    mem[i] = count;\n    return count;\n}\n\n/* 階段登り：メモ化探索 */\nfunction climbingStairsDFSMem(n: number): number {\n    // mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す\n    const mem = new Array(n + 1).fill(-1);\n    return dfs(n, mem);\n}\n</code></pre> climbing_stairs_dfs_mem.dart<pre><code>/* メモ化探索 */\nint dfs(int i, List&lt;int&gt; mem) {\n  // dp[1] と dp[2] は既知なので返す\n  if (i == 1 || i == 2) return i;\n  // dp[i] の記録があれば、それをそのまま返す\n  if (mem[i] != -1) return mem[i];\n  // dp[i] = dp[i-1] + dp[i-2]\n  int count = dfs(i - 1, mem) + dfs(i - 2, mem);\n  // dp[i] を記録する\n  mem[i] = count;\n  return count;\n}\n\n/* 階段登り：メモ化探索 */\nint climbingStairsDFSMem(int n) {\n  // mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す\n  List&lt;int&gt; mem = List.filled(n + 1, -1);\n  return dfs(n, mem);\n}\n</code></pre> climbing_stairs_dfs_mem.rs<pre><code>/* メモ化探索 */\nfn dfs(i: usize, mem: &amp;mut [i32]) -&gt; i32 {\n    // dp[1] と dp[2] は既知なので返す\n    if i == 1 || i == 2 {\n        return i as i32;\n    }\n    // dp[i] の記録があれば、それをそのまま返す\n    if mem[i] != -1 {\n        return mem[i];\n    }\n    // dp[i] = dp[i-1] + dp[i-2]\n    let count = dfs(i - 1, mem) + dfs(i - 2, mem);\n    // dp[i] を記録する\n    mem[i] = count;\n    count\n}\n\n/* 階段登り：メモ化探索 */\nfn climbing_stairs_dfs_mem(n: usize) -&gt; i32 {\n    // mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す\n    let mut mem = vec![-1; n + 1];\n    dfs(n, &amp;mut mem)\n}\n</code></pre> climbing_stairs_dfs_mem.c<pre><code>/* メモ化探索 */\nint dfs(int i, int *mem) {\n    // dp[1] と dp[2] は既知なので返す\n    if (i == 1 || i == 2)\n        return i;\n    // dp[i] の記録があれば、それをそのまま返す\n    if (mem[i] != -1)\n        return mem[i];\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1, mem) + dfs(i - 2, mem);\n    // dp[i] を記録する\n    mem[i] = count;\n    return count;\n}\n\n/* 階段登り：メモ化探索 */\nint climbingStairsDFSMem(int n) {\n    // mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す\n    int *mem = (int *)malloc((n + 1) * sizeof(int));\n    for (int i = 0; i &lt;= n; i++) {\n        mem[i] = -1;\n    }\n    int result = dfs(n, mem);\n    free(mem);\n    return result;\n}\n</code></pre> climbing_stairs_dfs_mem.kt<pre><code>/* メモ化探索 */\nfun dfs(i: Int, mem: IntArray): Int {\n    // dp[1] と dp[2] は既知なので返す\n    if (i == 1 || i == 2) return i\n    // dp[i] の記録があれば、それをそのまま返す\n    if (mem[i] != -1) return mem[i]\n    // dp[i] = dp[i-1] + dp[i-2]\n    val count = dfs(i - 1, mem) + dfs(i - 2, mem)\n    // dp[i] を記録する\n    mem[i] = count\n    return count\n}\n\n/* 階段登り：メモ化探索 */\nfun climbingStairsDFSMem(n: Int): Int {\n    // mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す\n    val mem = IntArray(n + 1)\n    mem.fill(-1)\n    return dfs(n, mem)\n}\n</code></pre> climbing_stairs_dfs_mem.rb<pre><code>### メモ化探索 ###\ndef dfs(i, mem)\n  # dp[1] と dp[2] は既知なので返す\n  return i if i == 1 || i == 2\n  # dp[i] の記録があれば、それをそのまま返す\n  return mem[i] if mem[i] != -1\n\n  # dp[i] = dp[i-1] + dp[i-2]\n  count = dfs(i - 1, mem) + dfs(i - 2, mem)\n  # dp[i] を記録する\n  mem[i] = count\nend\n\n### 階段登り：メモ化探索 ###\ndef climbing_stairs_dfs_mem(n)\n  # mem[i] は第 i 段まで上る方法の総数を記録し、-1 は未記録を表す\n  mem = Array.new(n + 1, -1)\n  dfs(n, mem)\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>次の図を見ると、メモ化を行うことで、すべての重複部分問題は 1 回だけ計算すればよくなり、時間計算量は \\(O(n)\\) まで改善されます。これは大きな飛躍です。</p> <p></p> <p> 図 14-4   メモ化探索に対応する再帰木 </p>","path":["第 14 章 &nbsp; 動的計画法","14.1 &nbsp; 動的計画法入門"],"tags":[]},{"location":"chapter_dynamic_programming/intro_to_dynamic_programming/#1413-3","level":2,"title":"14.1.3   方法 3：動的計画法","text":"<p>**メモ化探索は「トップダウン」の方法**です。元の問題（根ノード）から始めて、より大きな部分問題を再帰的により小さな部分問題へ分解し、解が既知である最小部分問題（葉ノード）に至ります。その後、バックトラックしながら各層で部分問題の解を集め、元の問題の解を構築します。</p> <p>これとは対照的に、**動的計画法は「ボトムアップ」の方法**です。最小部分問題の解から始めて、より大きな部分問題の解を反復的に構築し、最終的に元の問題の解を得ます。</p> <p>動的計画法にはバックトラックの過程が含まれないため、再帰を使う必要はなく、ループによる反復だけで実装できます。次のコードでは、部分問題の解を保存する配列 <code>dp</code> を初期化しており、これはメモ化探索における配列 <code>mem</code> と同じ記録の役割を果たします：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby climbing_stairs_dp.py<pre><code>def climbing_stairs_dp(n: int) -&gt; int:\n    \"\"\"階段登り：動的計画法\"\"\"\n    if n == 1 or n == 2:\n        return n\n    # 部分問題の解を保存するために dp テーブルを初期化\n    dp = [0] * (n + 1)\n    # 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1], dp[2] = 1, 2\n    # 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for i in range(3, n + 1):\n        dp[i] = dp[i - 1] + dp[i - 2]\n    return dp[n]\n</code></pre> climbing_stairs_dp.cpp<pre><code>/* 階段登り：動的計画法 */\nint climbingStairsDP(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    // 部分問題の解を保存するために dp テーブルを初期化\n    vector&lt;int&gt; dp(n + 1);\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1] = 1;\n    dp[2] = 2;\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    return dp[n];\n}\n</code></pre> climbing_stairs_dp.java<pre><code>/* 階段登り：動的計画法 */\nint climbingStairsDP(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    // 部分問題の解を保存するために dp テーブルを初期化\n    int[] dp = new int[n + 1];\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1] = 1;\n    dp[2] = 2;\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    return dp[n];\n}\n</code></pre> climbing_stairs_dp.cs<pre><code>/* 階段登り：動的計画法 */\nint ClimbingStairsDP(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    // 部分問題の解を保存するために dp テーブルを初期化\n    int[] dp = new int[n + 1];\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1] = 1;\n    dp[2] = 2;\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    return dp[n];\n}\n</code></pre> climbing_stairs_dp.go<pre><code>/* 階段登り：動的計画法 */\nfunc climbingStairsDP(n int) int {\n    if n == 1 || n == 2 {\n        return n\n    }\n    // 部分問題の解を保存するために dp テーブルを初期化\n    dp := make([]int, n+1)\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1] = 1\n    dp[2] = 2\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for i := 3; i &lt;= n; i++ {\n        dp[i] = dp[i-1] + dp[i-2]\n    }\n    return dp[n]\n}\n</code></pre> climbing_stairs_dp.swift<pre><code>/* 階段登り：動的計画法 */\nfunc climbingStairsDP(n: Int) -&gt; Int {\n    if n == 1 || n == 2 {\n        return n\n    }\n    // 部分問題の解を保存するために dp テーブルを初期化\n    var dp = Array(repeating: 0, count: n + 1)\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1] = 1\n    dp[2] = 2\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for i in 3 ... n {\n        dp[i] = dp[i - 1] + dp[i - 2]\n    }\n    return dp[n]\n}\n</code></pre> climbing_stairs_dp.js<pre><code>/* 階段登り：動的計画法 */\nfunction climbingStairsDP(n) {\n    if (n === 1 || n === 2) return n;\n    // 部分問題の解を保存するために dp テーブルを初期化\n    const dp = new Array(n + 1).fill(-1);\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1] = 1;\n    dp[2] = 2;\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for (let i = 3; i &lt;= n; i++) {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    return dp[n];\n}\n</code></pre> climbing_stairs_dp.ts<pre><code>/* 階段登り：動的計画法 */\nfunction climbingStairsDP(n: number): number {\n    if (n === 1 || n === 2) return n;\n    // 部分問題の解を保存するために dp テーブルを初期化\n    const dp = new Array(n + 1).fill(-1);\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1] = 1;\n    dp[2] = 2;\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for (let i = 3; i &lt;= n; i++) {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    return dp[n];\n}\n</code></pre> climbing_stairs_dp.dart<pre><code>/* 階段登り：動的計画法 */\nint climbingStairsDP(int n) {\n  if (n == 1 || n == 2) return n;\n  // 部分問題の解を保存するために dp テーブルを初期化\n  List&lt;int&gt; dp = List.filled(n + 1, 0);\n  // 初期状態：最小部分問題の解をあらかじめ設定\n  dp[1] = 1;\n  dp[2] = 2;\n  // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n  for (int i = 3; i &lt;= n; i++) {\n    dp[i] = dp[i - 1] + dp[i - 2];\n  }\n  return dp[n];\n}\n</code></pre> climbing_stairs_dp.rs<pre><code>/* 階段登り：動的計画法 */\nfn climbing_stairs_dp(n: usize) -&gt; i32 {\n    // dp[1] と dp[2] は既知なので返す\n    if n == 1 || n == 2 {\n        return n as i32;\n    }\n    // 部分問題の解を保存するために dp テーブルを初期化\n    let mut dp = vec![-1; n + 1];\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1] = 1;\n    dp[2] = 2;\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for i in 3..=n {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    dp[n]\n}\n</code></pre> climbing_stairs_dp.c<pre><code>/* 階段登り：動的計画法 */\nint climbingStairsDP(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    // 部分問題の解を保存するために dp テーブルを初期化\n    int *dp = (int *)malloc((n + 1) * sizeof(int));\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1] = 1;\n    dp[2] = 2;\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    int result = dp[n];\n    free(dp);\n    return result;\n}\n</code></pre> climbing_stairs_dp.kt<pre><code>/* 階段登り：動的計画法 */\nfun climbingStairsDP(n: Int): Int {\n    if (n == 1 || n == 2) return n\n    // 部分問題の解を保存するために dp テーブルを初期化\n    val dp = IntArray(n + 1)\n    // 初期状態：最小部分問題の解をあらかじめ設定\n    dp[1] = 1\n    dp[2] = 2\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for (i in 3..n) {\n        dp[i] = dp[i - 1] + dp[i - 2]\n    }\n    return dp[n]\n}\n</code></pre> climbing_stairs_dp.rb<pre><code>### 階段登り：動的計画法 ###\ndef climbing_stairs_dp(n)\n  return n  if n == 1 || n == 2\n\n  # 部分問題の解を保存するために dp テーブルを初期化\n  dp = Array.new(n + 1, 0)\n  # 初期状態：最小部分問題の解をあらかじめ設定\n  dp[1], dp[2] = 1, 2\n  # 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n  (3...(n + 1)).each { |i| dp[i] = dp[i - 1] + dp[i - 2] }\n\n  dp[n]\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>次の図は、以上のコードの実行過程をシミュレートしたものです。</p> <p></p> <p> 図 14-5   階段上りの動的計画法の過程 </p> <p>バックトラッキング法と同様に、動的計画法でも問題解決の特定段階を表すために「状態」という概念を用います。各状態は 1 つの部分問題と、それに対応する局所最適解に対応します。たとえば、階段を上る問題では、状態は現在いる階段の段数 \\(i\\) と定義されます。</p> <p>以上を踏まえると、動的計画法のよく使われる用語を次のようにまとめられます。</p> <ul> <li>配列 <code>dp</code> を dp テーブル と呼び、\\(dp[i]\\) は状態 \\(i\\) に対応する部分問題の解を表します。</li> <li>最小部分問題に対応する状態（第 \\(1\\) 段目と第 \\(2\\) 段目の階段）を初期状態と呼びます。</li> <li>漸化式 \\(dp[i] = dp[i-1] + dp[i-2]\\) を状態遷移方程式と呼びます。</li> </ul>","path":["第 14 章 &nbsp; 動的計画法","14.1 &nbsp; 動的計画法入門"],"tags":[]},{"location":"chapter_dynamic_programming/intro_to_dynamic_programming/#1414","level":2,"title":"14.1.4   空間最適化","text":"<p>注意深い読者は気づいたかもしれません。\\(dp[i]\\) は \\(dp[i-1]\\) と \\(dp[i-2]\\) にしか依存しないため、すべての部分問題の解を保存するために配列 <code>dp</code> を使う必要はありません。2 つの変数を順に更新していくだけで十分です。コードは次のとおりです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby climbing_stairs_dp.py<pre><code>def climbing_stairs_dp_comp(n: int) -&gt; int:\n    \"\"\"階段登り：空間最適化した動的計画法\"\"\"\n    if n == 1 or n == 2:\n        return n\n    a, b = 1, 2\n    for _ in range(3, n + 1):\n        a, b = b, a + b\n    return b\n</code></pre> climbing_stairs_dp.cpp<pre><code>/* 階段登り：空間最適化した動的計画法 */\nint climbingStairsDPComp(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    int a = 1, b = 2;\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = a + b;\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> climbing_stairs_dp.java<pre><code>/* 階段登り：空間最適化した動的計画法 */\nint climbingStairsDPComp(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    int a = 1, b = 2;\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = a + b;\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> climbing_stairs_dp.cs<pre><code>/* 階段登り：空間最適化した動的計画法 */\nint ClimbingStairsDPComp(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    int a = 1, b = 2;\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = a + b;\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> climbing_stairs_dp.go<pre><code>/* 階段登り：空間最適化した動的計画法 */\nfunc climbingStairsDPComp(n int) int {\n    if n == 1 || n == 2 {\n        return n\n    }\n    a, b := 1, 2\n    // 状態遷移：小さい部分問題から大きい部分問題へ順に解く\n    for i := 3; i &lt;= n; i++ {\n        a, b = b, a+b\n    }\n    return b\n}\n</code></pre> climbing_stairs_dp.swift<pre><code>/* 階段登り：空間最適化した動的計画法 */\nfunc climbingStairsDPComp(n: Int) -&gt; Int {\n    if n == 1 || n == 2 {\n        return n\n    }\n    var a = 1\n    var b = 2\n    for _ in 3 ... n {\n        (a, b) = (b, a + b)\n    }\n    return b\n}\n</code></pre> climbing_stairs_dp.js<pre><code>/* 階段登り：空間最適化した動的計画法 */\nfunction climbingStairsDPComp(n) {\n    if (n === 1 || n === 2) return n;\n    let a = 1,\n        b = 2;\n    for (let i = 3; i &lt;= n; i++) {\n        const tmp = b;\n        b = a + b;\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> climbing_stairs_dp.ts<pre><code>/* 階段登り：空間最適化した動的計画法 */\nfunction climbingStairsDPComp(n: number): number {\n    if (n === 1 || n === 2) return n;\n    let a = 1,\n        b = 2;\n    for (let i = 3; i &lt;= n; i++) {\n        const tmp = b;\n        b = a + b;\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> climbing_stairs_dp.dart<pre><code>/* 階段登り：空間最適化した動的計画法 */\nint climbingStairsDPComp(int n) {\n  if (n == 1 || n == 2) return n;\n  int a = 1, b = 2;\n  for (int i = 3; i &lt;= n; i++) {\n    int tmp = b;\n    b = a + b;\n    a = tmp;\n  }\n  return b;\n}\n</code></pre> climbing_stairs_dp.rs<pre><code>/* 階段登り：空間最適化した動的計画法 */\nfn climbing_stairs_dp_comp(n: usize) -&gt; i32 {\n    if n == 1 || n == 2 {\n        return n as i32;\n    }\n    let (mut a, mut b) = (1, 2);\n    for _ in 3..=n {\n        let tmp = b;\n        b = a + b;\n        a = tmp;\n    }\n    b\n}\n</code></pre> climbing_stairs_dp.c<pre><code>/* 階段登り：空間最適化した動的計画法 */\nint climbingStairsDPComp(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    int a = 1, b = 2;\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = a + b;\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> climbing_stairs_dp.kt<pre><code>/* 階段登り：空間最適化した動的計画法 */\nfun climbingStairsDPComp(n: Int): Int {\n    if (n == 1 || n == 2) return n\n    var a = 1\n    var b = 2\n    for (i in 3..n) {\n        val temp = b\n        b += a\n        a = temp\n    }\n    return b\n}\n</code></pre> climbing_stairs_dp.rb<pre><code>### 階段登り：空間最適化後の動的計画法 ###\ndef climbing_stairs_dp_comp(n)\n  return n if n == 1 || n == 2\n\n  a, b = 1, 2\n  (3...(n + 1)).each { a, b = b, a + b }\n\n  b\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>上のコードを見ると、配列 <code>dp</code> が占めていた領域を省けるため、空間計算量は \\(O(n)\\) から \\(O(1)\\) へと下がります。</p> <p>動的計画法の問題では、現在の状態はしばしば直前の限られた個数の状態にしか関係しません。このような場合は、必要な状態だけを保持し、「次元削減」によってメモリ空間を節約できます。この空間最適化の技巧は「ローリング変数」または「ローリング配列」と呼ばれます。</p>","path":["第 14 章 &nbsp; 動的計画法","14.1 &nbsp; 動的計画法入門"],"tags":[]},{"location":"chapter_dynamic_programming/knapsack_problem/","level":1,"title":"14.4   0-1 ナップサック問題","text":"<p>ナップサック問題は、動的計画法の入門として非常に適した問題であり、動的計画法で最もよく見られる問題形式の1つです。これには 0-1 ナップサック問題、完全ナップサック問題、多重ナップサック問題など、多くの派生があります。</p> <p>本節では、まず最も一般的な 0-1 ナップサック問題を解いていきます。</p> <p>Question</p> <p>\\(n\\) 個の品物が与えられ、\\(i\\) 番目の品物の重さは \\(wgt[i-1]\\)、価値は \\(val[i-1]\\) であり、容量 \\(cap\\) のナップサックがあります。各品物は1回しか選べないとき、ナップサック容量の制約下で入れられる品物の最大価値を求めてください。</p> <p>以下の図を見てみましょう。品物番号 \\(i\\) は \\(1\\) から始まり、配列のインデックスは \\(0\\) から始まるため、品物 \\(i\\) は重さ \\(wgt[i-1]\\)、価値 \\(val[i-1]\\) に対応します。</p> <p></p> <p> 図 14-17   0-1 ナップサックのサンプルデータ </p> <p>0-1 ナップサック問題は、\\(n\\) 回の意思決定からなる過程とみなせます。各品物について「入れない」「入れる」という2つの選択肢があるため、この問題は決定木モデルを満たします。</p> <p>この問題の目的は「ナップサック容量の制約下で入れられる品物の最大価値」を求めることなので、動的計画法の問題である可能性が高いです。</p> <p>ステップ1：各ラウンドの選択を考え、状態を定義して、\\(dp\\) テーブルを得る</p> <p>各品物について、ナップサックに入れなければ容量は変わらず、入れれば容量は減少します。ここから状態を、現在の品物番号 \\(i\\) とナップサック容量 \\(c\\) として定義し、\\([i, c]\\) と表せます。</p> <p>状態 \\([i, c]\\) に対応する部分問題は、先頭 \\(i\\) 個の品物を容量 \\(c\\) のナップサックに入れるときの最大価値 であり、これを \\(dp[i, c]\\) と記します。</p> <p>求めるべきものは \\(dp[n, cap]\\) なので、サイズ \\((n+1) \\times (cap+1)\\) の2次元 \\(dp\\) テーブルが必要です。</p> <p>ステップ2：最適部分構造を見つけ、状態遷移方程式を導く</p> <p>品物 \\(i\\) に対する選択を行った後に残るのは、先頭 \\(i-1\\) 個の品物に対する部分問題であり、次の2つのケースに分けられます。</p> <ul> <li>品物 \\(i\\) を入れない ：ナップサック容量は変わらず、状態は \\([i-1, c]\\) に変化します。</li> <li>品物 \\(i\\) を入れる ：ナップサック容量は \\(wgt[i-1]\\) だけ減少し、価値は \\(val[i-1]\\) だけ増加して、状態は \\([i-1, c-wgt[i-1]]\\) に変化します。</li> </ul> <p>以上の分析から、この問題の最適部分構造が分かります。すなわち、最大価値 \\(dp[i, c]\\) は、品物 \\(i\\) を入れない場合と入れる場合のうち、より価値の大きい方に等しい ということです。これにより、次の状態遷移方程式を導けます。</p> \\[ dp[i, c] = \\max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1]) \\] <p>注意すべき点として、現在の品物の重さ \\(wgt[i - 1]\\) が残りのナップサック容量 \\(c\\) を超える場合は、入れない選択しかできません。</p> <p>ステップ3：境界条件と状態遷移の順序を決める</p> <p>品物がない場合、またはナップサック容量が \\(0\\) の場合、最大価値は \\(0\\) です。すなわち、先頭列 \\(dp[i, 0]\\) と先頭行 \\(dp[0, c]\\) はいずれも \\(0\\) になります。</p> <p>現在の状態 \\([i, c]\\) は、上側の状態 \\([i-1, c]\\) と左上の状態 \\([i-1, c-wgt[i-1]]\\) から遷移してくるため、2重ループで \\(dp\\) テーブル全体を順方向に走査すれば十分です。</p> <p>以上の分析に基づき、次に全探索、メモ化探索、動的計画法の順で実装していきます。</p>","path":["第 14 章 &nbsp; 動的計画法","14.4 &nbsp; 0-1 ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/knapsack_problem/#1-1","level":3,"title":"1.   方法1：全探索","text":"<p>探索コードには次の要素が含まれます。</p> <ul> <li>再帰引数：状態 \\([i, c]\\) です。</li> <li>戻り値：部分問題の解 \\(dp[i, c]\\) です。</li> <li>終了条件：品物番号が範囲外である \\(i = 0\\)、またはナップサックの残り容量が \\(0\\) のとき、再帰を終了して価値 \\(0\\) を返します。</li> <li>枝刈り：現在の品物の重さがナップサックの残り容量を超える場合、入れない選択しかできません。</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby knapsack.py<pre><code>def knapsack_dfs(wgt: list[int], val: list[int], i: int, c: int) -&gt; int:\n    \"\"\"0-1 ナップサック：総当たり探索\"\"\"\n    # すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n    if i == 0 or c == 0:\n        return 0\n    # ナップサック容量を超える場合は、入れない選択しかできない\n    if wgt[i - 1] &gt; c:\n        return knapsack_dfs(wgt, val, i - 1, c)\n    # 品物 i を入れない場合と入れる場合の最大価値を計算する\n    no = knapsack_dfs(wgt, val, i - 1, c)\n    yes = knapsack_dfs(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1]\n    # 2つの案のうち価値が大きいほうを返す\n    return max(no, yes)\n</code></pre> knapsack.cpp<pre><code>/* 0-1 ナップサック：総当たり探索 */\nint knapsackDFS(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int i, int c) {\n    // すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // ナップサック容量を超える場合は、入れない選択しかできない\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFS(wgt, val, i - 1, c);\n    }\n    // 品物 i を入れない場合と入れる場合の最大価値を計算する\n    int no = knapsackDFS(wgt, val, i - 1, c);\n    int yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // 2つの案のうち価値が大きいほうを返す\n    return max(no, yes);\n}\n</code></pre> knapsack.java<pre><code>/* 0-1 ナップサック：総当たり探索 */\nint knapsackDFS(int[] wgt, int[] val, int i, int c) {\n    // すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // ナップサック容量を超える場合は、入れない選択しかできない\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFS(wgt, val, i - 1, c);\n    }\n    // 品物 i を入れない場合と入れる場合の最大価値を計算する\n    int no = knapsackDFS(wgt, val, i - 1, c);\n    int yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // 2つの案のうち価値が大きいほうを返す\n    return Math.max(no, yes);\n}\n</code></pre> knapsack.cs<pre><code>/* 0-1 ナップサック：総当たり探索 */\nint KnapsackDFS(int[] weight, int[] val, int i, int c) {\n    // すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // ナップサック容量を超える場合は、入れない選択しかできない\n    if (weight[i - 1] &gt; c) {\n        return KnapsackDFS(weight, val, i - 1, c);\n    }\n    // 品物 i を入れない場合と入れる場合の最大価値を計算する\n    int no = KnapsackDFS(weight, val, i - 1, c);\n    int yes = KnapsackDFS(weight, val, i - 1, c - weight[i - 1]) + val[i - 1];\n    // 2つの案のうち価値が大きいほうを返す\n    return Math.Max(no, yes);\n}\n</code></pre> knapsack.go<pre><code>/* 0-1 ナップサック：総当たり探索 */\nfunc knapsackDFS(wgt, val []int, i, c int) int {\n    // すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n    if i == 0 || c == 0 {\n        return 0\n    }\n    // ナップサック容量を超える場合は、入れない選択しかできない\n    if wgt[i-1] &gt; c {\n        return knapsackDFS(wgt, val, i-1, c)\n    }\n    // 品物 i を入れない場合と入れる場合の最大価値を計算する\n    no := knapsackDFS(wgt, val, i-1, c)\n    yes := knapsackDFS(wgt, val, i-1, c-wgt[i-1]) + val[i-1]\n    // 2つの案のうち価値が大きいほうを返す\n    return int(math.Max(float64(no), float64(yes)))\n}\n</code></pre> knapsack.swift<pre><code>/* 0-1 ナップサック：総当たり探索 */\nfunc knapsackDFS(wgt: [Int], val: [Int], i: Int, c: Int) -&gt; Int {\n    // すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n    if i == 0 || c == 0 {\n        return 0\n    }\n    // ナップサック容量を超える場合は、入れない選択しかできない\n    if wgt[i - 1] &gt; c {\n        return knapsackDFS(wgt: wgt, val: val, i: i - 1, c: c)\n    }\n    // 品物 i を入れない場合と入れる場合の最大価値を計算する\n    let no = knapsackDFS(wgt: wgt, val: val, i: i - 1, c: c)\n    let yes = knapsackDFS(wgt: wgt, val: val, i: i - 1, c: c - wgt[i - 1]) + val[i - 1]\n    // 2つの案のうち価値が大きいほうを返す\n    return max(no, yes)\n}\n</code></pre> knapsack.js<pre><code>/* 0-1 ナップサック：総当たり探索 */\nfunction knapsackDFS(wgt, val, i, c) {\n    // すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n    if (i === 0 || c === 0) {\n        return 0;\n    }\n    // ナップサック容量を超える場合は、入れない選択しかできない\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFS(wgt, val, i - 1, c);\n    }\n    // 品物 i を入れない場合と入れる場合の最大価値を計算する\n    const no = knapsackDFS(wgt, val, i - 1, c);\n    const yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // 2つの案のうち価値が大きいほうを返す\n    return Math.max(no, yes);\n}\n</code></pre> knapsack.ts<pre><code>/* 0-1 ナップサック：総当たり探索 */\nfunction knapsackDFS(\n    wgt: Array&lt;number&gt;,\n    val: Array&lt;number&gt;,\n    i: number,\n    c: number\n): number {\n    // すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n    if (i === 0 || c === 0) {\n        return 0;\n    }\n    // ナップサック容量を超える場合は、入れない選択しかできない\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFS(wgt, val, i - 1, c);\n    }\n    // 品物 i を入れない場合と入れる場合の最大価値を計算する\n    const no = knapsackDFS(wgt, val, i - 1, c);\n    const yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // 2つの案のうち価値が大きいほうを返す\n    return Math.max(no, yes);\n}\n</code></pre> knapsack.dart<pre><code>/* 0-1 ナップサック：総当たり探索 */\nint knapsackDFS(List&lt;int&gt; wgt, List&lt;int&gt; val, int i, int c) {\n  // すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n  if (i == 0 || c == 0) {\n    return 0;\n  }\n  // ナップサック容量を超える場合は、入れない選択しかできない\n  if (wgt[i - 1] &gt; c) {\n    return knapsackDFS(wgt, val, i - 1, c);\n  }\n  // 品物 i を入れない場合と入れる場合の最大価値を計算する\n  int no = knapsackDFS(wgt, val, i - 1, c);\n  int yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];\n  // 2つの案のうち価値が大きいほうを返す\n  return max(no, yes);\n}\n</code></pre> knapsack.rs<pre><code>/* 0-1 ナップサック：総当たり探索 */\nfn knapsack_dfs(wgt: &amp;[i32], val: &amp;[i32], i: usize, c: usize) -&gt; i32 {\n    // すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n    if i == 0 || c == 0 {\n        return 0;\n    }\n    // ナップサック容量を超える場合は、入れない選択しかできない\n    if wgt[i - 1] &gt; c as i32 {\n        return knapsack_dfs(wgt, val, i - 1, c);\n    }\n    // 品物 i を入れない場合と入れる場合の最大価値を計算する\n    let no = knapsack_dfs(wgt, val, i - 1, c);\n    let yes = knapsack_dfs(wgt, val, i - 1, c - wgt[i - 1] as usize) + val[i - 1];\n    // 2つの案のうち価値が大きいほうを返す\n    std::cmp::max(no, yes)\n}\n</code></pre> knapsack.c<pre><code>/* 0-1 ナップサック：総当たり探索 */\nint knapsackDFS(int wgt[], int val[], int i, int c) {\n    // すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // ナップサック容量を超える場合は、入れない選択しかできない\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFS(wgt, val, i - 1, c);\n    }\n    // 品物 i を入れない場合と入れる場合の最大価値を計算する\n    int no = knapsackDFS(wgt, val, i - 1, c);\n    int yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // 2つの案のうち価値が大きいほうを返す\n    return myMax(no, yes);\n}\n</code></pre> knapsack.kt<pre><code>/* 0-1 ナップサック：総当たり探索 */\nfun knapsackDFS(\n    wgt: IntArray,\n    _val: IntArray,\n    i: Int,\n    c: Int\n): Int {\n    // すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n    if (i == 0 || c == 0) {\n        return 0\n    }\n    // ナップサック容量を超える場合は、入れない選択しかできない\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFS(wgt, _val, i - 1, c)\n    }\n    // 品物 i を入れない場合と入れる場合の最大価値を計算する\n    val no = knapsackDFS(wgt, _val, i - 1, c)\n    val yes = knapsackDFS(wgt, _val, i - 1, c - wgt[i - 1]) + _val[i - 1]\n    // 2つの案のうち価値が大きいほうを返す\n    return max(no, yes)\n}\n</code></pre> knapsack.rb<pre><code>### 0-1 ナップサック: 全探索 ###\ndef knapsack_dfs(wgt, val, i, c)\n  # すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n  return 0 if i == 0 || c == 0\n  # ナップサック容量を超える場合は、入れない選択しかできない\n  return knapsack_dfs(wgt, val, i - 1, c) if wgt[i - 1] &gt; c\n  # 品物 i を入れない場合と入れる場合の最大価値を計算する\n  no = knapsack_dfs(wgt, val, i - 1, c)\n  yes = knapsack_dfs(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1]\n  # 2つの案のうち価値が大きいほうを返す\n  [no, yes].max\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>以下の図のように、各品物ごとに「選ばない」「選ぶ」の2つの探索分岐が生じるため、時間計算量は \\(O(2^n)\\) です。</p> <p>再帰木を観察すると、\\(dp[1, 10]\\) などの重複部分問題が存在することが分かります。品物数が多く、ナップサック容量が大きく、特に同じ重さの品物が多い場合には、重複部分問題の数は大幅に増加します。</p> <p></p> <p> 図 14-18   0-1 ナップサック問題の全探索の再帰木 </p>","path":["第 14 章 &nbsp; 動的計画法","14.4 &nbsp; 0-1 ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/knapsack_problem/#2-2","level":3,"title":"2.   方法2：メモ化探索","text":"<p>重複部分問題が一度だけ計算されるようにするため、メモ配列 <code>mem</code> を用いて部分問題の解を記録します。ここで <code>mem[i][c]</code> は \\(dp[i, c]\\) に対応します。</p> <p>メモ化を導入すると、時間計算量は部分問題の数に依存し、すなわち \\(O(n \\times cap)\\) になります。実装コードは次のとおりです。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby knapsack.py<pre><code>def knapsack_dfs_mem(\n    wgt: list[int], val: list[int], mem: list[list[int]], i: int, c: int\n) -&gt; int:\n    \"\"\"0-1 ナップサック：メモ化探索\"\"\"\n    # すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n    if i == 0 or c == 0:\n        return 0\n    # 既に記録があればそのまま返す\n    if mem[i][c] != -1:\n        return mem[i][c]\n    # ナップサック容量を超える場合は、入れない選択しかできない\n    if wgt[i - 1] &gt; c:\n        return knapsack_dfs_mem(wgt, val, mem, i - 1, c)\n    # 品物 i を入れない場合と入れる場合の最大価値を計算する\n    no = knapsack_dfs_mem(wgt, val, mem, i - 1, c)\n    yes = knapsack_dfs_mem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1]\n    # 2 つの案のうち価値が大きい方を記録して返す\n    mem[i][c] = max(no, yes)\n    return mem[i][c]\n</code></pre> knapsack.cpp<pre><code>/* 0-1 ナップサック：メモ化探索 */\nint knapsackDFSMem(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, vector&lt;vector&lt;int&gt;&gt; &amp;mem, int i, int c) {\n    // すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // 既に記録があればそのまま返す\n    if (mem[i][c] != -1) {\n        return mem[i][c];\n    }\n    // ナップサック容量を超える場合は、入れない選択しかできない\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFSMem(wgt, val, mem, i - 1, c);\n    }\n    // 品物 i を入れない場合と入れる場合の最大価値を計算する\n    int no = knapsackDFSMem(wgt, val, mem, i - 1, c);\n    int yes = knapsackDFSMem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // 2 つの案のうち価値が大きい方を記録して返す\n    mem[i][c] = max(no, yes);\n    return mem[i][c];\n}\n</code></pre> knapsack.java<pre><code>/* 0-1 ナップサック：メモ化探索 */\nint knapsackDFSMem(int[] wgt, int[] val, int[][] mem, int i, int c) {\n    // すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // 既に記録があればそのまま返す\n    if (mem[i][c] != -1) {\n        return mem[i][c];\n    }\n    // ナップサック容量を超える場合は、入れない選択しかできない\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFSMem(wgt, val, mem, i - 1, c);\n    }\n    // 品物 i を入れない場合と入れる場合の最大価値を計算する\n    int no = knapsackDFSMem(wgt, val, mem, i - 1, c);\n    int yes = knapsackDFSMem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // 2 つの案のうち価値が大きい方を記録して返す\n    mem[i][c] = Math.max(no, yes);\n    return mem[i][c];\n}\n</code></pre> knapsack.cs<pre><code>/* 0-1 ナップサック：メモ化探索 */\nint KnapsackDFSMem(int[] weight, int[] val, int[][] mem, int i, int c) {\n    // すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // 既に記録があればそのまま返す\n    if (mem[i][c] != -1) {\n        return mem[i][c];\n    }\n    // ナップサック容量を超える場合は、入れない選択しかできない\n    if (weight[i - 1] &gt; c) {\n        return KnapsackDFSMem(weight, val, mem, i - 1, c);\n    }\n    // 品物 i を入れない場合と入れる場合の最大価値を計算する\n    int no = KnapsackDFSMem(weight, val, mem, i - 1, c);\n    int yes = KnapsackDFSMem(weight, val, mem, i - 1, c - weight[i - 1]) + val[i - 1];\n    // 2 つの案のうち価値が大きい方を記録して返す\n    mem[i][c] = Math.Max(no, yes);\n    return mem[i][c];\n}\n</code></pre> knapsack.go<pre><code>/* 0-1 ナップサック：メモ化探索 */\nfunc knapsackDFSMem(wgt, val []int, mem [][]int, i, c int) int {\n    // すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n    if i == 0 || c == 0 {\n        return 0\n    }\n    // 既に記録があればそのまま返す\n    if mem[i][c] != -1 {\n        return mem[i][c]\n    }\n    // ナップサック容量を超える場合は、入れない選択しかできない\n    if wgt[i-1] &gt; c {\n        return knapsackDFSMem(wgt, val, mem, i-1, c)\n    }\n    // 品物 i を入れない場合と入れる場合の最大価値を計算する\n    no := knapsackDFSMem(wgt, val, mem, i-1, c)\n    yes := knapsackDFSMem(wgt, val, mem, i-1, c-wgt[i-1]) + val[i-1]\n    // 2つの案のうち価値が大きいほうを返す\n    mem[i][c] = int(math.Max(float64(no), float64(yes)))\n    return mem[i][c]\n}\n</code></pre> knapsack.swift<pre><code>/* 0-1 ナップサック：メモ化探索 */\nfunc knapsackDFSMem(wgt: [Int], val: [Int], mem: inout [[Int]], i: Int, c: Int) -&gt; Int {\n    // すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n    if i == 0 || c == 0 {\n        return 0\n    }\n    // 既に記録があればそのまま返す\n    if mem[i][c] != -1 {\n        return mem[i][c]\n    }\n    // ナップサック容量を超える場合は、入れない選択しかできない\n    if wgt[i - 1] &gt; c {\n        return knapsackDFSMem(wgt: wgt, val: val, mem: &amp;mem, i: i - 1, c: c)\n    }\n    // 品物 i を入れない場合と入れる場合の最大価値を計算する\n    let no = knapsackDFSMem(wgt: wgt, val: val, mem: &amp;mem, i: i - 1, c: c)\n    let yes = knapsackDFSMem(wgt: wgt, val: val, mem: &amp;mem, i: i - 1, c: c - wgt[i - 1]) + val[i - 1]\n    // 2 つの案のうち価値が大きい方を記録して返す\n    mem[i][c] = max(no, yes)\n    return mem[i][c]\n}\n</code></pre> knapsack.js<pre><code>/* 0-1 ナップサック：メモ化探索 */\nfunction knapsackDFSMem(wgt, val, mem, i, c) {\n    // すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n    if (i === 0 || c === 0) {\n        return 0;\n    }\n    // 既に記録があればそのまま返す\n    if (mem[i][c] !== -1) {\n        return mem[i][c];\n    }\n    // ナップサック容量を超える場合は、入れない選択しかできない\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFSMem(wgt, val, mem, i - 1, c);\n    }\n    // 品物 i を入れない場合と入れる場合の最大価値を計算する\n    const no = knapsackDFSMem(wgt, val, mem, i - 1, c);\n    const yes =\n        knapsackDFSMem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // 2 つの案のうち価値が大きい方を記録して返す\n    mem[i][c] = Math.max(no, yes);\n    return mem[i][c];\n}\n</code></pre> knapsack.ts<pre><code>/* 0-1 ナップサック：メモ化探索 */\nfunction knapsackDFSMem(\n    wgt: Array&lt;number&gt;,\n    val: Array&lt;number&gt;,\n    mem: Array&lt;Array&lt;number&gt;&gt;,\n    i: number,\n    c: number\n): number {\n    // すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n    if (i === 0 || c === 0) {\n        return 0;\n    }\n    // 既に記録があればそのまま返す\n    if (mem[i][c] !== -1) {\n        return mem[i][c];\n    }\n    // ナップサック容量を超える場合は、入れない選択しかできない\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFSMem(wgt, val, mem, i - 1, c);\n    }\n    // 品物 i を入れない場合と入れる場合の最大価値を計算する\n    const no = knapsackDFSMem(wgt, val, mem, i - 1, c);\n    const yes =\n        knapsackDFSMem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // 2 つの案のうち価値が大きい方を記録して返す\n    mem[i][c] = Math.max(no, yes);\n    return mem[i][c];\n}\n</code></pre> knapsack.dart<pre><code>/* 0-1 ナップサック：メモ化探索 */\nint knapsackDFSMem(\n  List&lt;int&gt; wgt,\n  List&lt;int&gt; val,\n  List&lt;List&lt;int&gt;&gt; mem,\n  int i,\n  int c,\n) {\n  // すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n  if (i == 0 || c == 0) {\n    return 0;\n  }\n  // 既に記録があればそのまま返す\n  if (mem[i][c] != -1) {\n    return mem[i][c];\n  }\n  // ナップサック容量を超える場合は、入れない選択しかできない\n  if (wgt[i - 1] &gt; c) {\n    return knapsackDFSMem(wgt, val, mem, i - 1, c);\n  }\n  // 品物 i を入れない場合と入れる場合の最大価値を計算する\n  int no = knapsackDFSMem(wgt, val, mem, i - 1, c);\n  int yes = knapsackDFSMem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1];\n  // 2 つの案のうち価値が大きい方を記録して返す\n  mem[i][c] = max(no, yes);\n  return mem[i][c];\n}\n</code></pre> knapsack.rs<pre><code>/* 0-1 ナップサック：メモ化探索 */\nfn knapsack_dfs_mem(wgt: &amp;[i32], val: &amp;[i32], mem: &amp;mut Vec&lt;Vec&lt;i32&gt;&gt;, i: usize, c: usize) -&gt; i32 {\n    // すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n    if i == 0 || c == 0 {\n        return 0;\n    }\n    // 既に記録があればそのまま返す\n    if mem[i][c] != -1 {\n        return mem[i][c];\n    }\n    // ナップサック容量を超える場合は、入れない選択しかできない\n    if wgt[i - 1] &gt; c as i32 {\n        return knapsack_dfs_mem(wgt, val, mem, i - 1, c);\n    }\n    // 品物 i を入れない場合と入れる場合の最大価値を計算する\n    let no = knapsack_dfs_mem(wgt, val, mem, i - 1, c);\n    let yes = knapsack_dfs_mem(wgt, val, mem, i - 1, c - wgt[i - 1] as usize) + val[i - 1];\n    // 2 つの案のうち価値が大きい方を記録して返す\n    mem[i][c] = std::cmp::max(no, yes);\n    mem[i][c]\n}\n</code></pre> knapsack.c<pre><code>/* 0-1 ナップサック：メモ化探索 */\nint knapsackDFSMem(int wgt[], int val[], int memCols, int **mem, int i, int c) {\n    // すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // 既に記録があればそのまま返す\n    if (mem[i][c] != -1) {\n        return mem[i][c];\n    }\n    // ナップサック容量を超える場合は、入れない選択しかできない\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFSMem(wgt, val, memCols, mem, i - 1, c);\n    }\n    // 品物 i を入れない場合と入れる場合の最大価値を計算する\n    int no = knapsackDFSMem(wgt, val, memCols, mem, i - 1, c);\n    int yes = knapsackDFSMem(wgt, val, memCols, mem, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // 2 つの案のうち価値が大きい方を記録して返す\n    mem[i][c] = myMax(no, yes);\n    return mem[i][c];\n}\n</code></pre> knapsack.kt<pre><code>/* 0-1 ナップサック：メモ化探索 */\nfun knapsackDFSMem(\n    wgt: IntArray,\n    _val: IntArray,\n    mem: Array&lt;IntArray&gt;,\n    i: Int,\n    c: Int\n): Int {\n    // すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n    if (i == 0 || c == 0) {\n        return 0\n    }\n    // 既に記録があればそのまま返す\n    if (mem[i][c] != -1) {\n        return mem[i][c]\n    }\n    // ナップサック容量を超える場合は、入れない選択しかできない\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFSMem(wgt, _val, mem, i - 1, c)\n    }\n    // 品物 i を入れない場合と入れる場合の最大価値を計算する\n    val no = knapsackDFSMem(wgt, _val, mem, i - 1, c)\n    val yes = knapsackDFSMem(wgt, _val, mem, i - 1, c - wgt[i - 1]) + _val[i - 1]\n    // 2 つの案のうち価値が大きい方を記録して返す\n    mem[i][c] = max(no, yes)\n    return mem[i][c]\n}\n</code></pre> knapsack.rb<pre><code>### 0-1 ナップサック: メモ化探索 ###\ndef knapsack_dfs_mem(wgt, val, mem, i, c)\n  # すべての品物を選び終えたか、ナップサックに残り容量がなければ、価値 0 を返す\n  return 0 if i == 0 || c == 0\n  # 既に記録があればそのまま返す\n  return mem[i][c] if mem[i][c] != -1\n  # ナップサック容量を超える場合は、入れない選択しかできない\n  return knapsack_dfs_mem(wgt, val, mem, i - 1, c) if wgt[i - 1] &gt; c\n  # 品物 i を入れない場合と入れる場合の最大価値を計算する\n  no = knapsack_dfs_mem(wgt, val, mem, i - 1, c)\n  yes = knapsack_dfs_mem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1]\n  # 2 つの案のうち価値が大きい方を記録して返す\n  mem[i][c] = [no, yes].max\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>次の図は、メモ化探索で剪定された探索分岐を示しています。</p> <p></p> <p> 図 14-19   0-1 ナップサック問題のメモ化探索の再帰木 </p>","path":["第 14 章 &nbsp; 動的計画法","14.4 &nbsp; 0-1 ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/knapsack_problem/#3-3","level":3,"title":"3.   方法3：動的計画法","text":"<p>動的計画法の本質は、状態遷移に従って \\(dp\\) テーブルを埋めていく過程です。コードは次のようになります。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby knapsack.py<pre><code>def knapsack_dp(wgt: list[int], val: list[int], cap: int) -&gt; int:\n    \"\"\"0-1 ナップサック：動的計画法\"\"\"\n    n = len(wgt)\n    # dp テーブルを初期化\n    dp = [[0] * (cap + 1) for _ in range(n + 1)]\n    # 状態遷移\n    for i in range(1, n + 1):\n        for c in range(1, cap + 1):\n            if wgt[i - 1] &gt; c:\n                # ナップサック容量を超えるなら品物 i は選ばない\n                dp[i][c] = dp[i - 1][c]\n            else:\n                # 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[i][c] = max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1])\n    return dp[n][cap]\n</code></pre> knapsack.cpp<pre><code>/* 0-1 ナップサック：動的計画法 */\nint knapsackDP(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int cap) {\n    int n = wgt.size();\n    // dp テーブルを初期化\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(cap + 1, 0));\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[i][c] = max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> knapsack.java<pre><code>/* 0-1 ナップサック：動的計画法 */\nint knapsackDP(int[] wgt, int[] val, int cap) {\n    int n = wgt.length;\n    // dp テーブルを初期化\n    int[][] dp = new int[n + 1][cap + 1];\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[i][c] = Math.max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> knapsack.cs<pre><code>/* 0-1 ナップサック：動的計画法 */\nint KnapsackDP(int[] weight, int[] val, int cap) {\n    int n = weight.Length;\n    // dp テーブルを初期化\n    int[,] dp = new int[n + 1, cap + 1];\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (weight[i - 1] &gt; c) {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[i, c] = dp[i - 1, c];\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[i, c] = Math.Max(dp[i - 1, c - weight[i - 1]] + val[i - 1], dp[i - 1, c]);\n            }\n        }\n    }\n    return dp[n, cap];\n}\n</code></pre> knapsack.go<pre><code>/* 0-1 ナップサック：動的計画法 */\nfunc knapsackDP(wgt, val []int, cap int) int {\n    n := len(wgt)\n    // dp テーブルを初期化\n    dp := make([][]int, n+1)\n    for i := 0; i &lt;= n; i++ {\n        dp[i] = make([]int, cap+1)\n    }\n    // 状態遷移\n    for i := 1; i &lt;= n; i++ {\n        for c := 1; c &lt;= cap; c++ {\n            if wgt[i-1] &gt; c {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[i][c] = dp[i-1][c]\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[i][c] = int(math.Max(float64(dp[i-1][c]), float64(dp[i-1][c-wgt[i-1]]+val[i-1])))\n            }\n        }\n    }\n    return dp[n][cap]\n}\n</code></pre> knapsack.swift<pre><code>/* 0-1 ナップサック：動的計画法 */\nfunc knapsackDP(wgt: [Int], val: [Int], cap: Int) -&gt; Int {\n    let n = wgt.count\n    // dp テーブルを初期化\n    var dp = Array(repeating: Array(repeating: 0, count: cap + 1), count: n + 1)\n    // 状態遷移\n    for i in 1 ... n {\n        for c in 1 ... cap {\n            if wgt[i - 1] &gt; c {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[i][c] = dp[i - 1][c]\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[i][c] = max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1])\n            }\n        }\n    }\n    return dp[n][cap]\n}\n</code></pre> knapsack.js<pre><code>/* 0-1 ナップサック：動的計画法 */\nfunction knapsackDP(wgt, val, cap) {\n    const n = wgt.length;\n    // dp テーブルを初期化\n    const dp = Array(n + 1)\n        .fill(0)\n        .map(() =&gt; Array(cap + 1).fill(0));\n    // 状態遷移\n    for (let i = 1; i &lt;= n; i++) {\n        for (let c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[i][c] = Math.max(\n                    dp[i - 1][c],\n                    dp[i - 1][c - wgt[i - 1]] + val[i - 1]\n                );\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> knapsack.ts<pre><code>/* 0-1 ナップサック：動的計画法 */\nfunction knapsackDP(\n    wgt: Array&lt;number&gt;,\n    val: Array&lt;number&gt;,\n    cap: number\n): number {\n    const n = wgt.length;\n    // dp テーブルを初期化\n    const dp = Array.from({ length: n + 1 }, () =&gt;\n        Array.from({ length: cap + 1 }, () =&gt; 0)\n    );\n    // 状態遷移\n    for (let i = 1; i &lt;= n; i++) {\n        for (let c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[i][c] = Math.max(\n                    dp[i - 1][c],\n                    dp[i - 1][c - wgt[i - 1]] + val[i - 1]\n                );\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> knapsack.dart<pre><code>/* 0-1 ナップサック：動的計画法 */\nint knapsackDP(List&lt;int&gt; wgt, List&lt;int&gt; val, int cap) {\n  int n = wgt.length;\n  // dp テーブルを初期化\n  List&lt;List&lt;int&gt;&gt; dp = List.generate(n + 1, (index) =&gt; List.filled(cap + 1, 0));\n  // 状態遷移\n  for (int i = 1; i &lt;= n; i++) {\n    for (int c = 1; c &lt;= cap; c++) {\n      if (wgt[i - 1] &gt; c) {\n        // ナップサック容量を超えるなら品物 i は選ばない\n        dp[i][c] = dp[i - 1][c];\n      } else {\n        // 品物 i を選ばない場合と選ぶ場合の大きい方\n        dp[i][c] = max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1]);\n      }\n    }\n  }\n  return dp[n][cap];\n}\n</code></pre> knapsack.rs<pre><code>/* 0-1 ナップサック：動的計画法 */\nfn knapsack_dp(wgt: &amp;[i32], val: &amp;[i32], cap: usize) -&gt; i32 {\n    let n = wgt.len();\n    // dp テーブルを初期化\n    let mut dp = vec![vec![0; cap + 1]; n + 1];\n    // 状態遷移\n    for i in 1..=n {\n        for c in 1..=cap {\n            if wgt[i - 1] &gt; c as i32 {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[i][c] = std::cmp::max(\n                    dp[i - 1][c],\n                    dp[i - 1][c - wgt[i - 1] as usize] + val[i - 1],\n                );\n            }\n        }\n    }\n    dp[n][cap]\n}\n</code></pre> knapsack.c<pre><code>/* 0-1 ナップサック：動的計画法 */\nint knapsackDP(int wgt[], int val[], int cap, int wgtSize) {\n    int n = wgtSize;\n    // dp テーブルを初期化\n    int **dp = malloc((n + 1) * sizeof(int *));\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i] = calloc(cap + 1, sizeof(int));\n    }\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[i][c] = myMax(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    int res = dp[n][cap];\n    // メモリを解放する\n    for (int i = 0; i &lt;= n; i++) {\n        free(dp[i]);\n    }\n    return res;\n}\n</code></pre> knapsack.kt<pre><code>/* 0-1 ナップサック：動的計画法 */\nfun knapsackDP(wgt: IntArray, _val: IntArray, cap: Int): Int {\n    val n = wgt.size\n    // dp テーブルを初期化\n    val dp = Array(n + 1) { IntArray(cap + 1) }\n    // 状態遷移\n    for (i in 1..n) {\n        for (c in 1..cap) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[i][c] = dp[i - 1][c]\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[i][c] = max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + _val[i - 1])\n            }\n        }\n    }\n    return dp[n][cap]\n}\n</code></pre> knapsack.rb<pre><code>### 0-1 ナップサック: 動的計画法 ###\ndef knapsack_dp(wgt, val, cap)\n  n = wgt.length\n  # dp テーブルを初期化\n  dp = Array.new(n + 1) { Array.new(cap + 1, 0) }\n  # 状態遷移\n  for i in 1...(n + 1)\n    for c in 1...(cap + 1)\n      if wgt[i - 1] &gt; c\n        # ナップサック容量を超えるなら品物 i は選ばない\n        dp[i][c] = dp[i - 1][c]\n      else\n        # 品物 i を選ばない場合と選ぶ場合の大きい方\n        dp[i][c] = [dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1]].max\n      end\n    end\n  end\n  dp[n][cap]\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>以下の図のように、時間計算量と空間計算量はいずれも配列 <code>dp</code> のサイズによって決まり、\\(O(n \\times cap)\\) です。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt;&lt;13&gt;&lt;14&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 14-20   0-1 ナップサック問題の動的計画法の過程 </p>","path":["第 14 章 &nbsp; 動的計画法","14.4 &nbsp; 0-1 ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/knapsack_problem/#4","level":3,"title":"4.   空間最適化","text":"<p>各状態は直前の行の状態にしか依存しないため、2つの配列をローテーションして用いることで、空間計算量を \\(O(n^2)\\) から \\(O(n)\\) に削減できます。</p> <p>さらに考えると、1つの配列だけで空間最適化を実現できるでしょうか。観察すると、各状態は真上または左上のマスから遷移してきます。配列が1つしかないと仮定すると、\\(i\\) 行目の走査を開始した時点では、その配列にはまだ \\(i-1\\) 行目の状態が格納されています。</p> <ul> <li>順方向に走査すると、\\(dp[i, j]\\) に到達した時点で、左上にある \\(dp[i-1, 1]\\) ~ \\(dp[i-1, j-1]\\) の値がすでに上書きされている可能性があり、正しい状態遷移結果を得られません。</li> <li>逆方向に走査すれば、上書きの問題は発生せず、状態遷移を正しく行えます。</li> </ul> <p>次の図は、単一配列のもとで \\(i = 1\\) 行目から \\(i = 2\\) 行目へ変換する過程を示しています。順方向走査と逆方向走査の違いを考えてみてください。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 14-21   0-1 ナップサックの空間最適化後の動的計画法の過程 </p> <p>コード実装では、配列 <code>dp</code> の第1次元 \\(i\\) をそのまま削除し、内側のループを逆方向走査に変更するだけで済みます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby knapsack.py<pre><code>def knapsack_dp_comp(wgt: list[int], val: list[int], cap: int) -&gt; int:\n    \"\"\"0-1 ナップサック：空間最適化後の動的計画法\"\"\"\n    n = len(wgt)\n    # dp テーブルを初期化\n    dp = [0] * (cap + 1)\n    # 状態遷移\n    for i in range(1, n + 1):\n        # 逆順に走査する\n        for c in range(cap, 0, -1):\n            if wgt[i - 1] &gt; c:\n                # ナップサック容量を超えるなら品物 i は選ばない\n                dp[c] = dp[c]\n            else:\n                # 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1])\n    return dp[cap]\n</code></pre> knapsack.cpp<pre><code>/* 0-1 ナップサック：空間最適化後の動的計画法 */\nint knapsackDPComp(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int cap) {\n    int n = wgt.size();\n    // dp テーブルを初期化\n    vector&lt;int&gt; dp(cap + 1, 0);\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        // 逆順に走査する\n        for (int c = cap; c &gt;= 1; c--) {\n            if (wgt[i - 1] &lt;= c) {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> knapsack.java<pre><code>/* 0-1 ナップサック：空間最適化後の動的計画法 */\nint knapsackDPComp(int[] wgt, int[] val, int cap) {\n    int n = wgt.length;\n    // dp テーブルを初期化\n    int[] dp = new int[cap + 1];\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        // 逆順に走査する\n        for (int c = cap; c &gt;= 1; c--) {\n            if (wgt[i - 1] &lt;= c) {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> knapsack.cs<pre><code>/* 0-1 ナップサック：空間最適化後の動的計画法 */\nint KnapsackDPComp(int[] weight, int[] val, int cap) {\n    int n = weight.Length;\n    // dp テーブルを初期化\n    int[] dp = new int[cap + 1];\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        // 逆順に走査する\n        for (int c = cap; c &gt; 0; c--) {\n            if (weight[i - 1] &gt; c) {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[c] = dp[c];\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[c] = Math.Max(dp[c], dp[c - weight[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> knapsack.go<pre><code>/* 0-1 ナップサック：空間最適化後の動的計画法 */\nfunc knapsackDPComp(wgt, val []int, cap int) int {\n    n := len(wgt)\n    // dp テーブルを初期化\n    dp := make([]int, cap+1)\n    // 状態遷移\n    for i := 1; i &lt;= n; i++ {\n        // 逆順に走査する\n        for c := cap; c &gt;= 1; c-- {\n            if wgt[i-1] &lt;= c {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[c] = int(math.Max(float64(dp[c]), float64(dp[c-wgt[i-1]]+val[i-1])))\n            }\n        }\n    }\n    return dp[cap]\n}\n</code></pre> knapsack.swift<pre><code>/* 0-1 ナップサック：空間最適化後の動的計画法 */\nfunc knapsackDPComp(wgt: [Int], val: [Int], cap: Int) -&gt; Int {\n    let n = wgt.count\n    // dp テーブルを初期化\n    var dp = Array(repeating: 0, count: cap + 1)\n    // 状態遷移\n    for i in 1 ... n {\n        // 逆順に走査する\n        for c in (1 ... cap).reversed() {\n            if wgt[i - 1] &lt;= c {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1])\n            }\n        }\n    }\n    return dp[cap]\n}\n</code></pre> knapsack.js<pre><code>/* 0-1 ナップサック：空間最適化後の動的計画法 */\nfunction knapsackDPComp(wgt, val, cap) {\n    const n = wgt.length;\n    // dp テーブルを初期化\n    const dp = Array(cap + 1).fill(0);\n    // 状態遷移\n    for (let i = 1; i &lt;= n; i++) {\n        // 逆順に走査する\n        for (let c = cap; c &gt;= 1; c--) {\n            if (wgt[i - 1] &lt;= c) {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> knapsack.ts<pre><code>/* 0-1 ナップサック：空間最適化後の動的計画法 */\nfunction knapsackDPComp(\n    wgt: Array&lt;number&gt;,\n    val: Array&lt;number&gt;,\n    cap: number\n): number {\n    const n = wgt.length;\n    // dp テーブルを初期化\n    const dp = Array(cap + 1).fill(0);\n    // 状態遷移\n    for (let i = 1; i &lt;= n; i++) {\n        // 逆順に走査する\n        for (let c = cap; c &gt;= 1; c--) {\n            if (wgt[i - 1] &lt;= c) {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> knapsack.dart<pre><code>/* 0-1 ナップサック：空間最適化後の動的計画法 */\nint knapsackDPComp(List&lt;int&gt; wgt, List&lt;int&gt; val, int cap) {\n  int n = wgt.length;\n  // dp テーブルを初期化\n  List&lt;int&gt; dp = List.filled(cap + 1, 0);\n  // 状態遷移\n  for (int i = 1; i &lt;= n; i++) {\n    // 逆順に走査する\n    for (int c = cap; c &gt;= 1; c--) {\n      if (wgt[i - 1] &lt;= c) {\n        // 品物 i を選ばない場合と選ぶ場合の大きい方\n        dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n      }\n    }\n  }\n  return dp[cap];\n}\n</code></pre> knapsack.rs<pre><code>/* 0-1 ナップサック：空間最適化後の動的計画法 */\nfn knapsack_dp_comp(wgt: &amp;[i32], val: &amp;[i32], cap: usize) -&gt; i32 {\n    let n = wgt.len();\n    // dp テーブルを初期化\n    let mut dp = vec![0; cap + 1];\n    // 状態遷移\n    for i in 1..=n {\n        // 逆順に走査する\n        for c in (1..=cap).rev() {\n            if wgt[i - 1] &lt;= c as i32 {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[c] = std::cmp::max(dp[c], dp[c - wgt[i - 1] as usize] + val[i - 1]);\n            }\n        }\n    }\n    dp[cap]\n}\n</code></pre> knapsack.c<pre><code>/* 0-1 ナップサック：空間最適化後の動的計画法 */\nint knapsackDPComp(int wgt[], int val[], int cap, int wgtSize) {\n    int n = wgtSize;\n    // dp テーブルを初期化\n    int *dp = calloc(cap + 1, sizeof(int));\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        // 逆順に走査する\n        for (int c = cap; c &gt;= 1; c--) {\n            if (wgt[i - 1] &lt;= c) {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[c] = myMax(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    int res = dp[cap];\n    // メモリを解放する\n    free(dp);\n    return res;\n}\n</code></pre> knapsack.kt<pre><code>/* 0-1 ナップサック：空間最適化後の動的計画法 */\nfun knapsackDPComp(wgt: IntArray, _val: IntArray, cap: Int): Int {\n    val n = wgt.size\n    // dp テーブルを初期化\n    val dp = IntArray(cap + 1)\n    // 状態遷移\n    for (i in 1..n) {\n        // 逆順に走査する\n        for (c in cap downTo 1) {\n            if (wgt[i - 1] &lt;= c) {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + _val[i - 1])\n            }\n        }\n    }\n    return dp[cap]\n}\n</code></pre> knapsack.rb<pre><code>### 0-1 ナップサック: 空間最適化後の動的計画法 ###\ndef knapsack_dp_comp(wgt, val, cap)\n  n = wgt.length\n  # dp テーブルを初期化\n  dp = Array.new(cap + 1, 0)\n  # 状態遷移\n  for i in 1...(n + 1)\n    # 逆順に走査する\n    for c in cap.downto(1)\n      if wgt[i - 1] &gt; c\n        # ナップサック容量を超えるなら品物 i は選ばない\n        dp[c] = dp[c]\n      else\n        # 品物 i を選ばない場合と選ぶ場合の大きい方\n        dp[c] = [dp[c], dp[c - wgt[i - 1]] + val[i - 1]].max\n      end\n    end\n  end\n  dp[cap]\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 14 章 &nbsp; 動的計画法","14.4 &nbsp; 0-1 ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/summary/","level":1,"title":"14.7   まとめ","text":"","path":["第 14 章 &nbsp; 動的計画法","14.7 &nbsp; まとめ"],"tags":[]},{"location":"chapter_dynamic_programming/summary/#1","level":3,"title":"1.   要点の振り返り","text":"<ul> <li>動的計画法は問題を分解し、部分問題の解を保存することで重複計算を避け、計算効率を高めます。</li> <li>時間を考慮しなければ、すべての動的計画法の問題はバックトラッキング（総当たり探索）で解けますが、再帰木には大量の重複部分問題が存在するため、効率はきわめて低くなります。メモ化配列を導入すると、計算済みのすべての部分問題の解を保存でき、重複部分問題が 1 回だけ計算されることを保証できます。</li> <li>メモ化探索はトップダウンの再帰的解法であり、それに対応する動的計画法はボトムアップの漸化式による解法で、ちょうど「表を埋める」ようなものです。現在の状態は一部の局所状態にのみ依存するため、\\(dp\\) 表の 1 次元を削減して空間計算量を下げることができます。</li> <li>部分問題への分解は汎用的なアルゴリズムの考え方であり、分割統治、動的計画法、バックトラッキングではそれぞれ異なる性質を持ちます。</li> <li>動的計画法の問題には 3 つの大きな特徴があります。重複部分問題、最適部分構造、無後効性です。</li> <li>元の問題の最適解が部分問題の最適解から構築できるなら、その問題は最適部分構造を持ちます。</li> <li>無後効性とは、ある状態の将来の発展がその状態のみに関係し、過去に経たすべての状態とは無関係であることを指します。多くの組合せ最適化問題は無後効性を持たず、動的計画法で高速に解くことはできません。</li> </ul> <p>ナップサック問題</p> <ul> <li>ナップサック問題は最も典型的な動的計画法の問題の 1 つであり、0-1 ナップサック、完全ナップサック、多重ナップサックなどの派生があります。</li> <li>0-1 ナップサックの状態は、容量 \\(c\\) のナップサックに対して、前 \\(i\\) 個の品物で得られる最大価値として定義されます。ナップサックに入れない場合と入れる場合の 2 つの判断から最適部分構造を得て、状態遷移方程式を構築できます。空間最適化では、各状態が真上と左上の状態に依存するため、左上の状態が上書きされるのを避けるために配列を逆順に走査する必要があります。</li> <li>完全ナップサック問題では各品物の選択数に制限がないため、品物を入れる場合の状態遷移は 0-1 ナップサック問題とは異なります。状態は真上と真左の状態に依存するので、空間最適化では順方向に走査するべきです。</li> <li>コイン両替問題は完全ナップサック問題の変種です。「最大」価値を求める問題から「最小」の硬貨枚数を求める問題へ変わるため、状態遷移方程式の \\(\\max()\\) は \\(\\min()\\) に置き換える必要があります。また、ナップサック容量を「超えない」ことを目指すのではなく、目標金額を「ちょうど」作ることを目指すため、\\(amt + 1\\) を「目標金額を作れない」無効解の表現として用います。</li> <li>コイン両替問題 II では、「最少硬貨枚数」を求める問題から「硬貨の組合せ数」を求める問題へ変わるため、状態遷移方程式も \\(\\min()\\) から総和演算子へ対応して変わります。</li> </ul> <p>編集距離問題</p> <ul> <li>編集距離（Levenshtein 距離）は 2 つの文字列間の類似度を測るために用いられ、ある文字列を別の文字列へ変換するための最小編集回数として定義されます。編集操作には追加、削除、置換が含まれます。</li> <li>編集距離問題の状態は、\\(s\\) の前 \\(i\\) 文字を \\(t\\) の前 \\(j\\) 文字へ変更するのに必要な最小編集回数として定義されます。\\(s[i] \\ne t[j]\\) のときは、追加、削除、置換の 3 つの判断があり、それぞれに対応する残りの部分問題があります。これにより最適部分構造を見いだし、状態遷移方程式を構築できます。一方、\\(s[i] = t[j]\\) のときは現在の文字を編集する必要はありません。</li> <li>編集距離では、状態は真上、真左、左上の状態に依存します。そのため、空間最適化後は順方向でも逆方向でも正しく状態遷移できません。そこで、変数を 1 つ用いて左上の状態を一時保存し、完全ナップサック問題と等価な形へ変換することで、空間最適化後に順方向走査を行えるようにします。</li> </ul>","path":["第 14 章 &nbsp; 動的計画法","14.7 &nbsp; まとめ"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/","level":1,"title":"14.5   完全ナップサック問題","text":"<p>本節では、まずもう 1 つの代表的なナップサック問題である完全ナップサック問題を解き、その特殊例である硬貨交換問題について見ていきます。</p>","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 完全ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1451","level":2,"title":"14.5.1   完全ナップサック問題","text":"<p>Question</p> <p>\\(n\\) 個の品物が与えられ、\\(i\\) 番目の品物の重さは \\(wgt[i-1]\\)、価値は \\(val[i-1]\\) であり、容量 \\(cap\\) のナップサックがあります。各品物は繰り返し選択できます。ナップサック容量の制約下で入れられる品物の最大価値を求めてください。例を以下の図に示します。</p> <p></p> <p> 図 14-22   完全ナップサック問題のサンプルデータ </p>","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 完全ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1","level":3,"title":"1.   動的計画法の考え方","text":"<p>完全ナップサック問題は 0-1 ナップサック問題と非常によく似ています。違いは、品物の選択回数に制限がない点だけです。</p> <ul> <li>0-1 ナップサック問題では、各品物は 1 つしかないため、品物 \\(i\\) をナップサックに入れた後は先頭 \\(i-1\\) 個の品物からしか選べません。</li> <li>完全ナップサック問題では、各品物の数は無限であるため、品物 \\(i\\) をナップサックに入れた後も、引き続き先頭 \\(i\\) 個の品物から選べます。</li> </ul> <p>完全ナップサック問題では、状態 \\([i, c]\\) の変化は 2 つの場合に分けられます。</p> <ul> <li>品物 \\(i\\) を入れない ：0-1 ナップサック問題と同様に、\\([i-1, c]\\) へ遷移します。</li> <li>品物 \\(i\\) を入れる ：0-1 ナップサック問題とは異なり、\\([i, c-wgt[i-1]]\\) へ遷移します。</li> </ul> <p>したがって、状態遷移方程式は次のようになります。</p> \\[ dp[i, c] = \\max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1]) \\]","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 完全ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#2","level":3,"title":"2.   コード実装","text":"<p>2 つの問題のコードを比較すると、状態遷移の中で 1 か所だけ \\(i-1\\) が \\(i\\) に変わり、それ以外は完全に同じです。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby unbounded_knapsack.py<pre><code>def unbounded_knapsack_dp(wgt: list[int], val: list[int], cap: int) -&gt; int:\n    \"\"\"完全ナップサック問題：動的計画法\"\"\"\n    n = len(wgt)\n    # dp テーブルを初期化\n    dp = [[0] * (cap + 1) for _ in range(n + 1)]\n    # 状態遷移\n    for i in range(1, n + 1):\n        for c in range(1, cap + 1):\n            if wgt[i - 1] &gt; c:\n                # ナップサック容量を超えるなら品物 i は選ばない\n                dp[i][c] = dp[i - 1][c]\n            else:\n                # 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[i][c] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1])\n    return dp[n][cap]\n</code></pre> unbounded_knapsack.cpp<pre><code>/* 完全ナップサック問題：動的計画法 */\nint unboundedKnapsackDP(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int cap) {\n    int n = wgt.size();\n    // dp テーブルを初期化\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(cap + 1, 0));\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[i][c] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> unbounded_knapsack.java<pre><code>/* 完全ナップサック問題：動的計画法 */\nint unboundedKnapsackDP(int[] wgt, int[] val, int cap) {\n    int n = wgt.length;\n    // dp テーブルを初期化\n    int[][] dp = new int[n + 1][cap + 1];\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[i][c] = Math.max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> unbounded_knapsack.cs<pre><code>/* 完全ナップサック問題：動的計画法 */\nint UnboundedKnapsackDP(int[] wgt, int[] val, int cap) {\n    int n = wgt.Length;\n    // dp テーブルを初期化\n    int[,] dp = new int[n + 1, cap + 1];\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[i, c] = dp[i - 1, c];\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[i, c] = Math.Max(dp[i - 1, c], dp[i, c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n, cap];\n}\n</code></pre> unbounded_knapsack.go<pre><code>/* 完全ナップサック問題：動的計画法 */\nfunc unboundedKnapsackDP(wgt, val []int, cap int) int {\n    n := len(wgt)\n    // dp テーブルを初期化\n    dp := make([][]int, n+1)\n    for i := 0; i &lt;= n; i++ {\n        dp[i] = make([]int, cap+1)\n    }\n    // 状態遷移\n    for i := 1; i &lt;= n; i++ {\n        for c := 1; c &lt;= cap; c++ {\n            if wgt[i-1] &gt; c {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[i][c] = dp[i-1][c]\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[i][c] = int(math.Max(float64(dp[i-1][c]), float64(dp[i][c-wgt[i-1]]+val[i-1])))\n            }\n        }\n    }\n    return dp[n][cap]\n}\n</code></pre> unbounded_knapsack.swift<pre><code>/* 完全ナップサック問題：動的計画法 */\nfunc unboundedKnapsackDP(wgt: [Int], val: [Int], cap: Int) -&gt; Int {\n    let n = wgt.count\n    // dp テーブルを初期化\n    var dp = Array(repeating: Array(repeating: 0, count: cap + 1), count: n + 1)\n    // 状態遷移\n    for i in 1 ... n {\n        for c in 1 ... cap {\n            if wgt[i - 1] &gt; c {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[i][c] = dp[i - 1][c]\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[i][c] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1])\n            }\n        }\n    }\n    return dp[n][cap]\n}\n</code></pre> unbounded_knapsack.js<pre><code>/* 完全ナップサック問題：動的計画法 */\nfunction unboundedKnapsackDP(wgt, val, cap) {\n    const n = wgt.length;\n    // dp テーブルを初期化\n    const dp = Array.from({ length: n + 1 }, () =&gt;\n        Array.from({ length: cap + 1 }, () =&gt; 0)\n    );\n    // 状態遷移\n    for (let i = 1; i &lt;= n; i++) {\n        for (let c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[i][c] = Math.max(\n                    dp[i - 1][c],\n                    dp[i][c - wgt[i - 1]] + val[i - 1]\n                );\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> unbounded_knapsack.ts<pre><code>/* 完全ナップサック問題：動的計画法 */\nfunction unboundedKnapsackDP(\n    wgt: Array&lt;number&gt;,\n    val: Array&lt;number&gt;,\n    cap: number\n): number {\n    const n = wgt.length;\n    // dp テーブルを初期化\n    const dp = Array.from({ length: n + 1 }, () =&gt;\n        Array.from({ length: cap + 1 }, () =&gt; 0)\n    );\n    // 状態遷移\n    for (let i = 1; i &lt;= n; i++) {\n        for (let c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[i][c] = Math.max(\n                    dp[i - 1][c],\n                    dp[i][c - wgt[i - 1]] + val[i - 1]\n                );\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> unbounded_knapsack.dart<pre><code>/* 完全ナップサック問題：動的計画法 */\nint unboundedKnapsackDP(List&lt;int&gt; wgt, List&lt;int&gt; val, int cap) {\n  int n = wgt.length;\n  // dp テーブルを初期化\n  List&lt;List&lt;int&gt;&gt; dp = List.generate(n + 1, (index) =&gt; List.filled(cap + 1, 0));\n  // 状態遷移\n  for (int i = 1; i &lt;= n; i++) {\n    for (int c = 1; c &lt;= cap; c++) {\n      if (wgt[i - 1] &gt; c) {\n        // ナップサック容量を超えるなら品物 i は選ばない\n        dp[i][c] = dp[i - 1][c];\n      } else {\n        // 品物 i を選ばない場合と選ぶ場合の大きい方\n        dp[i][c] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]);\n      }\n    }\n  }\n  return dp[n][cap];\n}\n</code></pre> unbounded_knapsack.rs<pre><code>/* 完全ナップサック問題：動的計画法 */\nfn unbounded_knapsack_dp(wgt: &amp;[i32], val: &amp;[i32], cap: usize) -&gt; i32 {\n    let n = wgt.len();\n    // dp テーブルを初期化\n    let mut dp = vec![vec![0; cap + 1]; n + 1];\n    // 状態遷移\n    for i in 1..=n {\n        for c in 1..=cap {\n            if wgt[i - 1] &gt; c as i32 {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[i][c] = std::cmp::max(dp[i - 1][c], dp[i][c - wgt[i - 1] as usize] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> unbounded_knapsack.c<pre><code>/* 完全ナップサック問題：動的計画法 */\nint unboundedKnapsackDP(int wgt[], int val[], int cap, int wgtSize) {\n    int n = wgtSize;\n    // dp テーブルを初期化\n    int **dp = malloc((n + 1) * sizeof(int *));\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i] = calloc(cap + 1, sizeof(int));\n    }\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[i][c] = myMax(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    int res = dp[n][cap];\n    // メモリを解放する\n    for (int i = 0; i &lt;= n; i++) {\n        free(dp[i]);\n    }\n    return res;\n}\n</code></pre> unbounded_knapsack.kt<pre><code>/* 完全ナップサック問題：動的計画法 */\nfun unboundedKnapsackDP(wgt: IntArray, _val: IntArray, cap: Int): Int {\n    val n = wgt.size\n    // dp テーブルを初期化\n    val dp = Array(n + 1) { IntArray(cap + 1) }\n    // 状態遷移\n    for (i in 1..n) {\n        for (c in 1..cap) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[i][c] = dp[i - 1][c]\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[i][c] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + _val[i - 1])\n            }\n        }\n    }\n    return dp[n][cap]\n}\n</code></pre> unbounded_knapsack.rb<pre><code>### 完全ナップサック：動的計画法 ###\ndef unbounded_knapsack_dp(wgt, val, cap)\n  n = wgt.length\n  # dp テーブルを初期化\n  dp = Array.new(n + 1) { Array.new(cap + 1, 0) }\n  # 状態遷移\n  for i in 1...(n + 1)\n    for c in 1...(cap + 1)\n      if wgt[i - 1] &gt; c\n        # ナップサック容量を超えるなら品物 i は選ばない\n        dp[i][c] = dp[i - 1][c]\n      else\n        # 品物 i を選ばない場合と選ぶ場合の大きい方\n        dp[i][c] = [dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]].max\n      end\n    end\n  end\n  dp[n][cap]\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 完全ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#3","level":3,"title":"3.   空間最適化","text":"<p>現在の状態は左側と上側の状態から遷移してくるため、空間最適化後は \\(dp\\) テーブルの各行を順方向に走査する必要があります。</p> <p>この走査順序は 0-1 ナップサックとはちょうど逆です。両者の違いは次の図を用いて理解してください。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 14-23   完全ナップサック問題における空間最適化後の動的計画法の過程 </p> <p>コード実装は比較的簡単で、配列 <code>dp</code> の第 1 次元を削除するだけです。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby unbounded_knapsack.py<pre><code>def unbounded_knapsack_dp_comp(wgt: list[int], val: list[int], cap: int) -&gt; int:\n    \"\"\"完全ナップサック問題：空間最適化後の動的計画法\"\"\"\n    n = len(wgt)\n    # dp テーブルを初期化\n    dp = [0] * (cap + 1)\n    # 状態遷移\n    for i in range(1, n + 1):\n        # 順方向に走査する\n        for c in range(1, cap + 1):\n            if wgt[i - 1] &gt; c:\n                # ナップサック容量を超えるなら品物 i は選ばない\n                dp[c] = dp[c]\n            else:\n                # 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1])\n    return dp[cap]\n</code></pre> unbounded_knapsack.cpp<pre><code>/* 完全ナップサック問題：空間最適化後の動的計画法 */\nint unboundedKnapsackDPComp(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int cap) {\n    int n = wgt.size();\n    // dp テーブルを初期化\n    vector&lt;int&gt; dp(cap + 1, 0);\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[c] = dp[c];\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> unbounded_knapsack.java<pre><code>/* 完全ナップサック問題：空間最適化後の動的計画法 */\nint unboundedKnapsackDPComp(int[] wgt, int[] val, int cap) {\n    int n = wgt.length;\n    // dp テーブルを初期化\n    int[] dp = new int[cap + 1];\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[c] = dp[c];\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> unbounded_knapsack.cs<pre><code>/* 完全ナップサック問題：空間最適化後の動的計画法 */\nint UnboundedKnapsackDPComp(int[] wgt, int[] val, int cap) {\n    int n = wgt.Length;\n    // dp テーブルを初期化\n    int[] dp = new int[cap + 1];\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[c] = dp[c];\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[c] = Math.Max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> unbounded_knapsack.go<pre><code>/* 完全ナップサック問題：空間最適化後の動的計画法 */\nfunc unboundedKnapsackDPComp(wgt, val []int, cap int) int {\n    n := len(wgt)\n    // dp テーブルを初期化\n    dp := make([]int, cap+1)\n    // 状態遷移\n    for i := 1; i &lt;= n; i++ {\n        for c := 1; c &lt;= cap; c++ {\n            if wgt[i-1] &gt; c {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[c] = dp[c]\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[c] = int(math.Max(float64(dp[c]), float64(dp[c-wgt[i-1]]+val[i-1])))\n            }\n        }\n    }\n    return dp[cap]\n}\n</code></pre> unbounded_knapsack.swift<pre><code>/* 完全ナップサック問題：空間最適化後の動的計画法 */\nfunc unboundedKnapsackDPComp(wgt: [Int], val: [Int], cap: Int) -&gt; Int {\n    let n = wgt.count\n    // dp テーブルを初期化\n    var dp = Array(repeating: 0, count: cap + 1)\n    // 状態遷移\n    for i in 1 ... n {\n        for c in 1 ... cap {\n            if wgt[i - 1] &gt; c {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[c] = dp[c]\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1])\n            }\n        }\n    }\n    return dp[cap]\n}\n</code></pre> unbounded_knapsack.js<pre><code>/* 完全ナップサック問題：空間最適化後の動的計画法 */\nfunction unboundedKnapsackDPComp(wgt, val, cap) {\n    const n = wgt.length;\n    // dp テーブルを初期化\n    const dp = Array.from({ length: cap + 1 }, () =&gt; 0);\n    // 状態遷移\n    for (let i = 1; i &lt;= n; i++) {\n        for (let c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[c] = dp[c];\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> unbounded_knapsack.ts<pre><code>/* 完全ナップサック問題：空間最適化後の動的計画法 */\nfunction unboundedKnapsackDPComp(\n    wgt: Array&lt;number&gt;,\n    val: Array&lt;number&gt;,\n    cap: number\n): number {\n    const n = wgt.length;\n    // dp テーブルを初期化\n    const dp = Array.from({ length: cap + 1 }, () =&gt; 0);\n    // 状態遷移\n    for (let i = 1; i &lt;= n; i++) {\n        for (let c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[c] = dp[c];\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> unbounded_knapsack.dart<pre><code>/* 完全ナップサック問題：空間最適化後の動的計画法 */\nint unboundedKnapsackDPComp(List&lt;int&gt; wgt, List&lt;int&gt; val, int cap) {\n  int n = wgt.length;\n  // dp テーブルを初期化\n  List&lt;int&gt; dp = List.filled(cap + 1, 0);\n  // 状態遷移\n  for (int i = 1; i &lt;= n; i++) {\n    for (int c = 1; c &lt;= cap; c++) {\n      if (wgt[i - 1] &gt; c) {\n        // ナップサック容量を超えるなら品物 i は選ばない\n        dp[c] = dp[c];\n      } else {\n        // 品物 i を選ばない場合と選ぶ場合の大きい方\n        dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n      }\n    }\n  }\n  return dp[cap];\n}\n</code></pre> unbounded_knapsack.rs<pre><code>/* 完全ナップサック問題：空間最適化後の動的計画法 */\nfn unbounded_knapsack_dp_comp(wgt: &amp;[i32], val: &amp;[i32], cap: usize) -&gt; i32 {\n    let n = wgt.len();\n    // dp テーブルを初期化\n    let mut dp = vec![0; cap + 1];\n    // 状態遷移\n    for i in 1..=n {\n        for c in 1..=cap {\n            if wgt[i - 1] &gt; c as i32 {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[c] = dp[c];\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[c] = std::cmp::max(dp[c], dp[c - wgt[i - 1] as usize] + val[i - 1]);\n            }\n        }\n    }\n    dp[cap]\n}\n</code></pre> unbounded_knapsack.c<pre><code>/* 完全ナップサック問題：空間最適化後の動的計画法 */\nint unboundedKnapsackDPComp(int wgt[], int val[], int cap, int wgtSize) {\n    int n = wgtSize;\n    // dp テーブルを初期化\n    int *dp = calloc(cap + 1, sizeof(int));\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[c] = dp[c];\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[c] = myMax(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    int res = dp[cap];\n    // メモリを解放する\n    free(dp);\n    return res;\n}\n</code></pre> unbounded_knapsack.kt<pre><code>/* 完全ナップサック問題：空間最適化後の動的計画法 */\nfun unboundedKnapsackDPComp(\n    wgt: IntArray,\n    _val: IntArray,\n    cap: Int\n): Int {\n    val n = wgt.size\n    // dp テーブルを初期化\n    val dp = IntArray(cap + 1)\n    // 状態遷移\n    for (i in 1..n) {\n        for (c in 1..cap) {\n            if (wgt[i - 1] &gt; c) {\n                // ナップサック容量を超えるなら品物 i は選ばない\n                dp[c] = dp[c]\n            } else {\n                // 品物 i を選ばない場合と選ぶ場合の大きい方\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + _val[i - 1])\n            }\n        }\n    }\n    return dp[cap]\n}\n</code></pre> unbounded_knapsack.rb<pre><code>### 完全ナップサック：動的計画法 ###\ndef unbounded_knapsack_dp(wgt, val, cap)\n  n = wgt.length\n  # dp テーブルを初期化\n  dp = Array.new(n + 1) { Array.new(cap + 1, 0) }\n  # 状態遷移\n  for i in 1...(n + 1)\n    for c in 1...(cap + 1)\n      if wgt[i - 1] &gt; c\n        # ナップサック容量を超えるなら品物 i は選ばない\n        dp[i][c] = dp[i - 1][c]\n      else\n        # 品物 i を選ばない場合と選ぶ場合の大きい方\n        dp[i][c] = [dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]].max\n      end\n    end\n  end\n  dp[n][cap]\nend\n\n# ## 完全ナップサック: 空間最適化後の動的計画法 ##3\ndef unbounded_knapsack_dp_comp(wgt, val, cap)\n  n = wgt.length\n  # dp テーブルを初期化\n  dp = Array.new(cap + 1, 0)\n  # 状態遷移\n  for i in 1...(n + 1)\n    # 順方向に走査する\n    for c in 1...(cap + 1)\n      if wgt[i -1] &gt; c\n        # ナップサック容量を超えるなら品物 i は選ばない\n        dp[c] = dp[c]\n      else\n        # 品物 i を選ばない場合と選ぶ場合の大きい方\n        dp[c] = [dp[c], dp[c - wgt[i - 1]] + val[i - 1]].max\n      end\n    end\n  end\n  dp[cap]\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 完全ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1452","level":2,"title":"14.5.2   硬貨交換問題","text":"<p>ナップサック問題は動的計画法の代表的な問題群であり、多くの派生問題があります。硬貨交換問題もその 1 つです。</p> <p>Question</p> <p>\\(n\\) 種類の硬貨が与えられ、\\(i\\) 番目の硬貨の額面は \\(coins[i - 1]\\) 、目標金額は \\(amt\\) です。各硬貨は繰り返し選択できます。目標金額を作るために必要な最小の硬貨枚数を求めてください。目標金額を作れない場合は \\(-1\\) を返します。例を以下の図に示します。</p> <p></p> <p> 図 14-24   硬貨交換問題のサンプルデータ </p>","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 完全ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1_1","level":3,"title":"1.   動的計画法の考え方","text":"<p>硬貨交換は完全ナップサック問題の特殊なケースとみなせます。両者には次の対応関係と相違点があります。</p> <ul> <li>2 つの問題は相互に変換でき、「品物」は「硬貨」、「品物の重さ」は「硬貨の額面」、「ナップサック容量」は「目標金額」に対応します。</li> <li>最適化の目標は逆であり、完全ナップサック問題は品物価値の最大化、硬貨交換問題は硬貨枚数の最小化を目指します。</li> <li>完全ナップサック問題はナップサック容量を「超えない」解を求めますが、硬貨交換は目標金額に「ちょうど」一致する解を求めます。</li> </ul> <p>ステップ 1：各ラウンドの選択を考え、状態を定義して、\\(dp\\) テーブルを得る</p> <p>状態 \\([i, a]\\) に対応する部分問題は、**先頭 \\(i\\) 種類の硬貨で金額 \\(a\\) を作るための最小硬貨枚数**であり、これを \\(dp[i, a]\\) と表します。</p> <p>2 次元 \\(dp\\) テーブルのサイズは \\((n+1) \\times (amt+1)\\) です。</p> <p>ステップ 2：最適部分構造を見つけ、状態遷移方程式を導く</p> <p>本問の状態遷移方程式は、完全ナップサック問題と比べて次の 2 点が異なります。</p> <ul> <li>本問では最小値を求めるため、演算子 \\(\\max()\\) を \\(\\min()\\) に変更する必要があります。</li> <li>最適化の対象は品物価値ではなく硬貨枚数であるため、硬貨を選んだときは \\(+1\\) すれば十分です。</li> </ul> \\[ dp[i, a] = \\min(dp[i-1, a], dp[i, a - coins[i-1]] + 1) \\] <p>ステップ 3：境界条件と状態遷移順序を決める</p> <p>目標金額が \\(0\\) のとき、それを作るための最小硬貨枚数は \\(0\\) です。つまり、先頭列のすべての \\(dp[i, 0]\\) は \\(0\\) になります。</p> <p>硬貨が 1 枚もない場合、任意の \\(&gt; 0\\) の目標金額を作ることはできません。これは無効解です。状態遷移方程式内の \\(\\min()\\) 関数が無効解を識別して除外できるように、それらを \\(+ \\infty\\) で表すことを考えます。すなわち、先頭行のすべての \\(dp[0, a]\\) を \\(+ \\infty\\) とします。</p>","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 完全ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#2_1","level":3,"title":"2.   コード実装","text":"<p>多くのプログラミング言語には \\(+ \\infty\\) を表す変数が用意されていないため、通常は整数型 <code>int</code> の最大値で代用します。しかし、その場合は大きな数のオーバーフローが起こり得ます。状態遷移方程式中の \\(+ 1\\) 操作で桁あふれが発生する可能性があるためです。</p> <p>そのため、ここでは数値 \\(amt + 1\\) を無効解の表現として用います。金額 \\(amt\\) を作るための硬貨枚数は最大でも \\(amt\\) 枚だからです。最後に返す前に、\\(dp[n, amt]\\) が \\(amt + 1\\) に等しいかを判定し、等しければ \\(-1\\) を返して目標金額を作れないことを表します。コードは次のとおりです。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby coin_change.py<pre><code>def coin_change_dp(coins: list[int], amt: int) -&gt; int:\n    \"\"\"コイン両替：動的計画法\"\"\"\n    n = len(coins)\n    MAX = amt + 1\n    # dp テーブルを初期化\n    dp = [[0] * (amt + 1) for _ in range(n + 1)]\n    # 状態遷移：先頭行と先頭列\n    for a in range(1, amt + 1):\n        dp[0][a] = MAX\n    # 状態遷移: 残りの行と列\n    for i in range(1, n + 1):\n        for a in range(1, amt + 1):\n            if coins[i - 1] &gt; a:\n                # 目標金額を超えるなら硬貨 i は選ばない\n                dp[i][a] = dp[i - 1][a]\n            else:\n                # 硬貨 i を選ばない場合と選ぶ場合の小さい方\n                dp[i][a] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1)\n    return dp[n][amt] if dp[n][amt] != MAX else -1\n</code></pre> coin_change.cpp<pre><code>/* コイン両替：動的計画法 */\nint coinChangeDP(vector&lt;int&gt; &amp;coins, int amt) {\n    int n = coins.size();\n    int MAX = amt + 1;\n    // dp テーブルを初期化\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(amt + 1, 0));\n    // 状態遷移：先頭行と先頭列\n    for (int a = 1; a &lt;= amt; a++) {\n        dp[0][a] = MAX;\n    }\n    // 状態遷移: 残りの行と列\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // 硬貨 i を選ばない場合と選ぶ場合の小さい方\n                dp[i][a] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[n][amt] != MAX ? dp[n][amt] : -1;\n}\n</code></pre> coin_change.java<pre><code>/* コイン両替：動的計画法 */\nint coinChangeDP(int[] coins, int amt) {\n    int n = coins.length;\n    int MAX = amt + 1;\n    // dp テーブルを初期化\n    int[][] dp = new int[n + 1][amt + 1];\n    // 状態遷移：先頭行と先頭列\n    for (int a = 1; a &lt;= amt; a++) {\n        dp[0][a] = MAX;\n    }\n    // 状態遷移: 残りの行と列\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // 硬貨 i を選ばない場合と選ぶ場合の小さい方\n                dp[i][a] = Math.min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[n][amt] != MAX ? dp[n][amt] : -1;\n}\n</code></pre> coin_change.cs<pre><code>/* コイン両替：動的計画法 */\nint CoinChangeDP(int[] coins, int amt) {\n    int n = coins.Length;\n    int MAX = amt + 1;\n    // dp テーブルを初期化\n    int[,] dp = new int[n + 1, amt + 1];\n    // 状態遷移：先頭行と先頭列\n    for (int a = 1; a &lt;= amt; a++) {\n        dp[0, a] = MAX;\n    }\n    // 状態遷移: 残りの行と列\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[i, a] = dp[i - 1, a];\n            } else {\n                // 硬貨 i を選ばない場合と選ぶ場合の小さい方\n                dp[i, a] = Math.Min(dp[i - 1, a], dp[i, a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[n, amt] != MAX ? dp[n, amt] : -1;\n}\n</code></pre> coin_change.go<pre><code>/* コイン両替：動的計画法 */\nfunc coinChangeDP(coins []int, amt int) int {\n    n := len(coins)\n    max := amt + 1\n    // dp テーブルを初期化\n    dp := make([][]int, n+1)\n    for i := 0; i &lt;= n; i++ {\n        dp[i] = make([]int, amt+1)\n    }\n    // 状態遷移：先頭行と先頭列\n    for a := 1; a &lt;= amt; a++ {\n        dp[0][a] = max\n    }\n    // 状態遷移: 残りの行と列\n    for i := 1; i &lt;= n; i++ {\n        for a := 1; a &lt;= amt; a++ {\n            if coins[i-1] &gt; a {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[i][a] = dp[i-1][a]\n            } else {\n                // 硬貨 i を選ばない場合と選ぶ場合の小さい方\n                dp[i][a] = int(math.Min(float64(dp[i-1][a]), float64(dp[i][a-coins[i-1]]+1)))\n            }\n        }\n    }\n    if dp[n][amt] != max {\n        return dp[n][amt]\n    }\n    return -1\n}\n</code></pre> coin_change.swift<pre><code>/* コイン両替：動的計画法 */\nfunc coinChangeDP(coins: [Int], amt: Int) -&gt; Int {\n    let n = coins.count\n    let MAX = amt + 1\n    // dp テーブルを初期化\n    var dp = Array(repeating: Array(repeating: 0, count: amt + 1), count: n + 1)\n    // 状態遷移：先頭行と先頭列\n    for a in 1 ... amt {\n        dp[0][a] = MAX\n    }\n    // 状態遷移: 残りの行と列\n    for i in 1 ... n {\n        for a in 1 ... amt {\n            if coins[i - 1] &gt; a {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[i][a] = dp[i - 1][a]\n            } else {\n                // 硬貨 i を選ばない場合と選ぶ場合の小さい方\n                dp[i][a] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1)\n            }\n        }\n    }\n    return dp[n][amt] != MAX ? dp[n][amt] : -1\n}\n</code></pre> coin_change.js<pre><code>/* コイン両替：動的計画法 */\nfunction coinChangeDP(coins, amt) {\n    const n = coins.length;\n    const MAX = amt + 1;\n    // dp テーブルを初期化\n    const dp = Array.from({ length: n + 1 }, () =&gt;\n        Array.from({ length: amt + 1 }, () =&gt; 0)\n    );\n    // 状態遷移：先頭行と先頭列\n    for (let a = 1; a &lt;= amt; a++) {\n        dp[0][a] = MAX;\n    }\n    // 状態遷移: 残りの行と列\n    for (let i = 1; i &lt;= n; i++) {\n        for (let a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // 硬貨 i を選ばない場合と選ぶ場合の小さい方\n                dp[i][a] = Math.min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[n][amt] !== MAX ? dp[n][amt] : -1;\n}\n</code></pre> coin_change.ts<pre><code>/* コイン両替：動的計画法 */\nfunction coinChangeDP(coins: Array&lt;number&gt;, amt: number): number {\n    const n = coins.length;\n    const MAX = amt + 1;\n    // dp テーブルを初期化\n    const dp = Array.from({ length: n + 1 }, () =&gt;\n        Array.from({ length: amt + 1 }, () =&gt; 0)\n    );\n    // 状態遷移：先頭行と先頭列\n    for (let a = 1; a &lt;= amt; a++) {\n        dp[0][a] = MAX;\n    }\n    // 状態遷移: 残りの行と列\n    for (let i = 1; i &lt;= n; i++) {\n        for (let a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // 硬貨 i を選ばない場合と選ぶ場合の小さい方\n                dp[i][a] = Math.min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[n][amt] !== MAX ? dp[n][amt] : -1;\n}\n</code></pre> coin_change.dart<pre><code>/* コイン両替：動的計画法 */\nint coinChangeDP(List&lt;int&gt; coins, int amt) {\n  int n = coins.length;\n  int MAX = amt + 1;\n  // dp テーブルを初期化\n  List&lt;List&lt;int&gt;&gt; dp = List.generate(n + 1, (index) =&gt; List.filled(amt + 1, 0));\n  // 状態遷移：先頭行と先頭列\n  for (int a = 1; a &lt;= amt; a++) {\n    dp[0][a] = MAX;\n  }\n  // 状態遷移: 残りの行と列\n  for (int i = 1; i &lt;= n; i++) {\n    for (int a = 1; a &lt;= amt; a++) {\n      if (coins[i - 1] &gt; a) {\n        // 目標金額を超えるなら硬貨 i は選ばない\n        dp[i][a] = dp[i - 1][a];\n      } else {\n        // 硬貨 i を選ばない場合と選ぶ場合の小さい方\n        dp[i][a] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);\n      }\n    }\n  }\n  return dp[n][amt] != MAX ? dp[n][amt] : -1;\n}\n</code></pre> coin_change.rs<pre><code>/* コイン両替：動的計画法 */\nfn coin_change_dp(coins: &amp;[i32], amt: usize) -&gt; i32 {\n    let n = coins.len();\n    let max = amt + 1;\n    // dp テーブルを初期化\n    let mut dp = vec![vec![0; amt + 1]; n + 1];\n    // 状態遷移：先頭行と先頭列\n    for a in 1..=amt {\n        dp[0][a] = max;\n    }\n    // 状態遷移: 残りの行と列\n    for i in 1..=n {\n        for a in 1..=amt {\n            if coins[i - 1] &gt; a as i32 {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // 硬貨 i を選ばない場合と選ぶ場合の小さい方\n                dp[i][a] = std::cmp::min(dp[i - 1][a], dp[i][a - coins[i - 1] as usize] + 1);\n            }\n        }\n    }\n    if dp[n][amt] != max {\n        return dp[n][amt] as i32;\n    } else {\n        -1\n    }\n}\n</code></pre> coin_change.c<pre><code>/* コイン両替：動的計画法 */\nint coinChangeDP(int coins[], int amt, int coinsSize) {\n    int n = coinsSize;\n    int MAX = amt + 1;\n    // dp テーブルを初期化\n    int **dp = malloc((n + 1) * sizeof(int *));\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i] = calloc(amt + 1, sizeof(int));\n    }\n    // 状態遷移：先頭行と先頭列\n    for (int a = 1; a &lt;= amt; a++) {\n        dp[0][a] = MAX;\n    }\n    // 状態遷移: 残りの行と列\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // 硬貨 i を選ばない場合と選ぶ場合の小さい方\n                dp[i][a] = myMin(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    int res = dp[n][amt] != MAX ? dp[n][amt] : -1;\n    // メモリを解放する\n    for (int i = 0; i &lt;= n; i++) {\n        free(dp[i]);\n    }\n    free(dp);\n    return res;\n}\n</code></pre> coin_change.kt<pre><code>/* コイン両替：動的計画法 */\nfun coinChangeDP(coins: IntArray, amt: Int): Int {\n    val n = coins.size\n    val MAX = amt + 1\n    // dp テーブルを初期化\n    val dp = Array(n + 1) { IntArray(amt + 1) }\n    // 状態遷移：先頭行と先頭列\n    for (a in 1..amt) {\n        dp[0][a] = MAX\n    }\n    // 状態遷移: 残りの行と列\n    for (i in 1..n) {\n        for (a in 1..amt) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[i][a] = dp[i - 1][a]\n            } else {\n                // 硬貨 i を選ばない場合と選ぶ場合の小さい方\n                dp[i][a] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1)\n            }\n        }\n    }\n    return if (dp[n][amt] != MAX) dp[n][amt] else -1\n}\n</code></pre> coin_change.rb<pre><code>### コイン両替：動的計画法 ###\ndef coin_change_dp(coins, amt)\n  n = coins.length\n  _MAX = amt + 1\n  # dp テーブルを初期化\n  dp = Array.new(n + 1) { Array.new(amt + 1, 0) }\n  # 状態遷移：先頭行と先頭列\n  (1...(amt + 1)).each { |a| dp[0][a] = _MAX }\n  # 状態遷移: 残りの行と列\n  for i in 1...(n + 1)\n    for a in 1...(amt + 1)\n      if coins[i - 1] &gt; a\n        # 目標金額を超えるなら硬貨 i は選ばない\n        dp[i][a] = dp[i - 1][a]\n      else\n        # 硬貨 i を選ばない場合と選ぶ場合の小さい方\n        dp[i][a] = [dp[i - 1][a], dp[i][a - coins[i - 1]] + 1].min\n      end\n    end\n  end\n  dp[n][amt] != _MAX ? dp[n][amt] : -1\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>次の図は硬貨交換の動的計画法の過程を示しており、完全ナップサック問題と非常によく似ています。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt;&lt;13&gt;&lt;14&gt;&lt;15&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 14-25   硬貨交換問題の動的計画法の過程 </p>","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 完全ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#3_1","level":3,"title":"3.   空間最適化","text":"<p>硬貨交換の空間最適化の方法は、完全ナップサック問題と同じです。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby coin_change.py<pre><code>def coin_change_dp_comp(coins: list[int], amt: int) -&gt; int:\n    \"\"\"コイン交換：空間最適化後の動的計画法\"\"\"\n    n = len(coins)\n    MAX = amt + 1\n    # dp テーブルを初期化\n    dp = [MAX] * (amt + 1)\n    dp[0] = 0\n    # 状態遷移\n    for i in range(1, n + 1):\n        # 順方向に走査する\n        for a in range(1, amt + 1):\n            if coins[i - 1] &gt; a:\n                # 目標金額を超えるなら硬貨 i は選ばない\n                dp[a] = dp[a]\n            else:\n                # 硬貨 i を選ばない場合と選ぶ場合の小さい方\n                dp[a] = min(dp[a], dp[a - coins[i - 1]] + 1)\n    return dp[amt] if dp[amt] != MAX else -1\n</code></pre> coin_change.cpp<pre><code>/* コイン交換：空間最適化後の動的計画法 */\nint coinChangeDPComp(vector&lt;int&gt; &amp;coins, int amt) {\n    int n = coins.size();\n    int MAX = amt + 1;\n    // dp テーブルを初期化\n    vector&lt;int&gt; dp(amt + 1, MAX);\n    dp[0] = 0;\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[a] = dp[a];\n            } else {\n                // 硬貨 i を選ばない場合と選ぶ場合の小さい方\n                dp[a] = min(dp[a], dp[a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[amt] != MAX ? dp[amt] : -1;\n}\n</code></pre> coin_change.java<pre><code>/* コイン交換：空間最適化後の動的計画法 */\nint coinChangeDPComp(int[] coins, int amt) {\n    int n = coins.length;\n    int MAX = amt + 1;\n    // dp テーブルを初期化\n    int[] dp = new int[amt + 1];\n    Arrays.fill(dp, MAX);\n    dp[0] = 0;\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[a] = dp[a];\n            } else {\n                // 硬貨 i を選ばない場合と選ぶ場合の小さい方\n                dp[a] = Math.min(dp[a], dp[a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[amt] != MAX ? dp[amt] : -1;\n}\n</code></pre> coin_change.cs<pre><code>/* コイン交換：空間最適化後の動的計画法 */\nint CoinChangeDPComp(int[] coins, int amt) {\n    int n = coins.Length;\n    int MAX = amt + 1;\n    // dp テーブルを初期化\n    int[] dp = new int[amt + 1];\n    Array.Fill(dp, MAX);\n    dp[0] = 0;\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[a] = dp[a];\n            } else {\n                // 硬貨 i を選ばない場合と選ぶ場合の小さい方\n                dp[a] = Math.Min(dp[a], dp[a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[amt] != MAX ? dp[amt] : -1;\n}\n</code></pre> coin_change.go<pre><code>/* コイン両替：動的計画法 */\nfunc coinChangeDPComp(coins []int, amt int) int {\n    n := len(coins)\n    max := amt + 1\n    // dp テーブルを初期化\n    dp := make([]int, amt+1)\n    for i := 1; i &lt;= amt; i++ {\n        dp[i] = max\n    }\n    // 状態遷移\n    for i := 1; i &lt;= n; i++ {\n        // 順方向に走査する\n        for a := 1; a &lt;= amt; a++ {\n            if coins[i-1] &gt; a {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[a] = dp[a]\n            } else {\n                // 硬貨 i を選ばない場合と選ぶ場合の小さい方\n                dp[a] = int(math.Min(float64(dp[a]), float64(dp[a-coins[i-1]]+1)))\n            }\n        }\n    }\n    if dp[amt] != max {\n        return dp[amt]\n    }\n    return -1\n}\n</code></pre> coin_change.swift<pre><code>/* コイン交換：空間最適化後の動的計画法 */\nfunc coinChangeDPComp(coins: [Int], amt: Int) -&gt; Int {\n    let n = coins.count\n    let MAX = amt + 1\n    // dp テーブルを初期化\n    var dp = Array(repeating: MAX, count: amt + 1)\n    dp[0] = 0\n    // 状態遷移\n    for i in 1 ... n {\n        for a in 1 ... amt {\n            if coins[i - 1] &gt; a {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[a] = dp[a]\n            } else {\n                // 硬貨 i を選ばない場合と選ぶ場合の小さい方\n                dp[a] = min(dp[a], dp[a - coins[i - 1]] + 1)\n            }\n        }\n    }\n    return dp[amt] != MAX ? dp[amt] : -1\n}\n</code></pre> coin_change.js<pre><code>/* コイン交換：空間最適化後の動的計画法 */\nfunction coinChangeDPComp(coins, amt) {\n    const n = coins.length;\n    const MAX = amt + 1;\n    // dp テーブルを初期化\n    const dp = Array.from({ length: amt + 1 }, () =&gt; MAX);\n    dp[0] = 0;\n    // 状態遷移\n    for (let i = 1; i &lt;= n; i++) {\n        for (let a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[a] = dp[a];\n            } else {\n                // 硬貨 i を選ばない場合と選ぶ場合の小さい方\n                dp[a] = Math.min(dp[a], dp[a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[amt] !== MAX ? dp[amt] : -1;\n}\n</code></pre> coin_change.ts<pre><code>/* コイン交換：空間最適化後の動的計画法 */\nfunction coinChangeDPComp(coins: Array&lt;number&gt;, amt: number): number {\n    const n = coins.length;\n    const MAX = amt + 1;\n    // dp テーブルを初期化\n    const dp = Array.from({ length: amt + 1 }, () =&gt; MAX);\n    dp[0] = 0;\n    // 状態遷移\n    for (let i = 1; i &lt;= n; i++) {\n        for (let a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[a] = dp[a];\n            } else {\n                // 硬貨 i を選ばない場合と選ぶ場合の小さい方\n                dp[a] = Math.min(dp[a], dp[a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[amt] !== MAX ? dp[amt] : -1;\n}\n</code></pre> coin_change.dart<pre><code>/* コイン交換：空間最適化後の動的計画法 */\nint coinChangeDPComp(List&lt;int&gt; coins, int amt) {\n  int n = coins.length;\n  int MAX = amt + 1;\n  // dp テーブルを初期化\n  List&lt;int&gt; dp = List.filled(amt + 1, MAX);\n  dp[0] = 0;\n  // 状態遷移\n  for (int i = 1; i &lt;= n; i++) {\n    for (int a = 1; a &lt;= amt; a++) {\n      if (coins[i - 1] &gt; a) {\n        // 目標金額を超えるなら硬貨 i は選ばない\n        dp[a] = dp[a];\n      } else {\n        // 硬貨 i を選ばない場合と選ぶ場合の小さい方\n        dp[a] = min(dp[a], dp[a - coins[i - 1]] + 1);\n      }\n    }\n  }\n  return dp[amt] != MAX ? dp[amt] : -1;\n}\n</code></pre> coin_change.rs<pre><code>/* コイン交換：空間最適化後の動的計画法 */\nfn coin_change_dp_comp(coins: &amp;[i32], amt: usize) -&gt; i32 {\n    let n = coins.len();\n    let max = amt + 1;\n    // dp テーブルを初期化\n    let mut dp = vec![0; amt + 1];\n    dp.fill(max);\n    dp[0] = 0;\n    // 状態遷移\n    for i in 1..=n {\n        for a in 1..=amt {\n            if coins[i - 1] &gt; a as i32 {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[a] = dp[a];\n            } else {\n                // 硬貨 i を選ばない場合と選ぶ場合の小さい方\n                dp[a] = std::cmp::min(dp[a], dp[a - coins[i - 1] as usize] + 1);\n            }\n        }\n    }\n    if dp[amt] != max {\n        return dp[amt] as i32;\n    } else {\n        -1\n    }\n}\n</code></pre> coin_change.c<pre><code>/* コイン交換：空間最適化後の動的計画法 */\nint coinChangeDPComp(int coins[], int amt, int coinsSize) {\n    int n = coinsSize;\n    int MAX = amt + 1;\n    // dp テーブルを初期化\n    int *dp = malloc((amt + 1) * sizeof(int));\n    for (int j = 1; j &lt;= amt; j++) {\n        dp[j] = MAX;\n    } \n    dp[0] = 0;\n\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[a] = dp[a];\n            } else {\n                // 硬貨 i を選ばない場合と選ぶ場合の小さい方\n                dp[a] = myMin(dp[a], dp[a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    int res = dp[amt] != MAX ? dp[amt] : -1;\n    // メモリを解放する\n    free(dp);\n    return res;\n}\n</code></pre> coin_change.kt<pre><code>/* コイン交換：空間最適化後の動的計画法 */\nfun coinChangeDPComp(coins: IntArray, amt: Int): Int {\n    val n = coins.size\n    val MAX = amt + 1\n    // dp テーブルを初期化\n    val dp = IntArray(amt + 1)\n    dp.fill(MAX)\n    dp[0] = 0\n    // 状態遷移\n    for (i in 1..n) {\n        for (a in 1..amt) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[a] = dp[a]\n            } else {\n                // 硬貨 i を選ばない場合と選ぶ場合の小さい方\n                dp[a] = min(dp[a], dp[a - coins[i - 1]] + 1)\n            }\n        }\n    }\n    return if (dp[amt] != MAX) dp[amt] else -1\n}\n</code></pre> coin_change.rb<pre><code>### コイン両替：空間最適化した動的計画法 ###\ndef coin_change_dp_comp(coins, amt)\n  n = coins.length\n  _MAX = amt + 1\n  # dp テーブルを初期化\n  dp = Array.new(amt + 1, _MAX)\n  dp[0] = 0\n  # 状態遷移\n  for i in 1...(n + 1)\n    # 順方向に走査する\n    for a in 1...(amt + 1)\n      if coins[i - 1] &gt; a\n        # 目標金額を超えるなら硬貨 i は選ばない\n        dp[a] = dp[a]\n      else\n        # 硬貨 i を選ばない場合と選ぶ場合の小さい方\n        dp[a] = [dp[a], dp[a - coins[i - 1]] + 1].min\n      end\n    end\n  end\n  dp[amt] != _MAX ? dp[amt] : -1\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 完全ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1453-ii","level":2,"title":"14.5.3   硬貨交換問題 II","text":"<p>Question</p> <p>\\(n\\) 種類の硬貨が与えられ、\\(i\\) 番目の硬貨の額面は \\(coins[i - 1]\\) 、目標金額は \\(amt\\) です。各硬貨は繰り返し選択できるとして、**目標金額を作る硬貨の組合せ数**を求めてください。例を以下の図に示します。</p> <p></p> <p> 図 14-26   硬貨交換問題 II のサンプルデータ </p>","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 完全ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1_2","level":3,"title":"1.   動的計画法の考え方","text":"<p>前問と比べて、本問の目的は組合せ数を求めることです。そのため、部分問題は 先頭 \\(i\\) 種類の硬貨で金額 \\(a\\) を作れる組合せ数 になります。一方、\\(dp\\) テーブルは引き続きサイズ \\((n+1) \\times (amt + 1)\\) の 2 次元行列です。</p> <p>現在の状態における組合せ数は、現在の硬貨を選ばない場合と選ぶ場合の 2 つの選択肢の組合せ数の和に等しくなります。状態遷移方程式は次のとおりです。</p> \\[ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]] \\] <p>目標金額が \\(0\\) のときは、どの硬貨も選ばなくても目標金額を作れるため、先頭列のすべての \\(dp[i, 0]\\) を \\(1\\) に初期化します。硬貨がないときは、任意の \\(&gt;0\\) の目標金額を作れないため、先頭行のすべての \\(dp[0, a]\\) は \\(0\\) になります。</p>","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 完全ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#2_2","level":3,"title":"2.   コード実装","text":"PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby coin_change_ii.py<pre><code>def coin_change_ii_dp(coins: list[int], amt: int) -&gt; int:\n    \"\"\"コイン両替 II：動的計画法\"\"\"\n    n = len(coins)\n    # dp テーブルを初期化\n    dp = [[0] * (amt + 1) for _ in range(n + 1)]\n    # 先頭列を初期化する\n    for i in range(n + 1):\n        dp[i][0] = 1\n    # 状態遷移\n    for i in range(1, n + 1):\n        for a in range(1, amt + 1):\n            if coins[i - 1] &gt; a:\n                # 目標金額を超えるなら硬貨 i は選ばない\n                dp[i][a] = dp[i - 1][a]\n            else:\n                # コイン i を選ばない場合と選ぶ場合の和\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]]\n    return dp[n][amt]\n</code></pre> coin_change_ii.cpp<pre><code>/* コイン両替 II：動的計画法 */\nint coinChangeIIDP(vector&lt;int&gt; &amp;coins, int amt) {\n    int n = coins.size();\n    // dp テーブルを初期化\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(amt + 1, 0));\n    // 先頭列を初期化する\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i][0] = 1;\n    }\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // コイン i を選ばない場合と選ぶ場合の和\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[n][amt];\n}\n</code></pre> coin_change_ii.java<pre><code>/* コイン両替 II：動的計画法 */\nint coinChangeIIDP(int[] coins, int amt) {\n    int n = coins.length;\n    // dp テーブルを初期化\n    int[][] dp = new int[n + 1][amt + 1];\n    // 先頭列を初期化する\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i][0] = 1;\n    }\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // コイン i を選ばない場合と選ぶ場合の和\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[n][amt];\n}\n</code></pre> coin_change_ii.cs<pre><code>/* コイン両替 II：動的計画法 */\nint CoinChangeIIDP(int[] coins, int amt) {\n    int n = coins.Length;\n    // dp テーブルを初期化\n    int[,] dp = new int[n + 1, amt + 1];\n    // 先頭列を初期化する\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i, 0] = 1;\n    }\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[i, a] = dp[i - 1, a];\n            } else {\n                // コイン i を選ばない場合と選ぶ場合の和\n                dp[i, a] = dp[i - 1, a] + dp[i, a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[n, amt];\n}\n</code></pre> coin_change_ii.go<pre><code>/* コイン両替 II：動的計画法 */\nfunc coinChangeIIDP(coins []int, amt int) int {\n    n := len(coins)\n    // dp テーブルを初期化\n    dp := make([][]int, n+1)\n    for i := 0; i &lt;= n; i++ {\n        dp[i] = make([]int, amt+1)\n    }\n    // 先頭列を初期化する\n    for i := 0; i &lt;= n; i++ {\n        dp[i][0] = 1\n    }\n    // 状態遷移: 残りの行と列\n    for i := 1; i &lt;= n; i++ {\n        for a := 1; a &lt;= amt; a++ {\n            if coins[i-1] &gt; a {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[i][a] = dp[i-1][a]\n            } else {\n                // コイン i を選ばない場合と選ぶ場合の和\n                dp[i][a] = dp[i-1][a] + dp[i][a-coins[i-1]]\n            }\n        }\n    }\n    return dp[n][amt]\n}\n</code></pre> coin_change_ii.swift<pre><code>/* コイン両替 II：動的計画法 */\nfunc coinChangeIIDP(coins: [Int], amt: Int) -&gt; Int {\n    let n = coins.count\n    // dp テーブルを初期化\n    var dp = Array(repeating: Array(repeating: 0, count: amt + 1), count: n + 1)\n    // 先頭列を初期化する\n    for i in 0 ... n {\n        dp[i][0] = 1\n    }\n    // 状態遷移\n    for i in 1 ... n {\n        for a in 1 ... amt {\n            if coins[i - 1] &gt; a {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[i][a] = dp[i - 1][a]\n            } else {\n                // コイン i を選ばない場合と選ぶ場合の和\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]]\n            }\n        }\n    }\n    return dp[n][amt]\n}\n</code></pre> coin_change_ii.js<pre><code>/* コイン両替 II：動的計画法 */\nfunction coinChangeIIDP(coins, amt) {\n    const n = coins.length;\n    // dp テーブルを初期化\n    const dp = Array.from({ length: n + 1 }, () =&gt;\n        Array.from({ length: amt + 1 }, () =&gt; 0)\n    );\n    // 先頭列を初期化する\n    for (let i = 0; i &lt;= n; i++) {\n        dp[i][0] = 1;\n    }\n    // 状態遷移\n    for (let i = 1; i &lt;= n; i++) {\n        for (let a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // コイン i を選ばない場合と選ぶ場合の和\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[n][amt];\n}\n</code></pre> coin_change_ii.ts<pre><code>/* コイン両替 II：動的計画法 */\nfunction coinChangeIIDP(coins: Array&lt;number&gt;, amt: number): number {\n    const n = coins.length;\n    // dp テーブルを初期化\n    const dp = Array.from({ length: n + 1 }, () =&gt;\n        Array.from({ length: amt + 1 }, () =&gt; 0)\n    );\n    // 先頭列を初期化する\n    for (let i = 0; i &lt;= n; i++) {\n        dp[i][0] = 1;\n    }\n    // 状態遷移\n    for (let i = 1; i &lt;= n; i++) {\n        for (let a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // コイン i を選ばない場合と選ぶ場合の和\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[n][amt];\n}\n</code></pre> coin_change_ii.dart<pre><code>/* コイン両替 II：動的計画法 */\nint coinChangeIIDP(List&lt;int&gt; coins, int amt) {\n  int n = coins.length;\n  // dp テーブルを初期化\n  List&lt;List&lt;int&gt;&gt; dp = List.generate(n + 1, (index) =&gt; List.filled(amt + 1, 0));\n  // 先頭列を初期化する\n  for (int i = 0; i &lt;= n; i++) {\n    dp[i][0] = 1;\n  }\n  // 状態遷移\n  for (int i = 1; i &lt;= n; i++) {\n    for (int a = 1; a &lt;= amt; a++) {\n      if (coins[i - 1] &gt; a) {\n        // 目標金額を超えるなら硬貨 i は選ばない\n        dp[i][a] = dp[i - 1][a];\n      } else {\n        // コイン i を選ばない場合と選ぶ場合の和\n        dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];\n      }\n    }\n  }\n  return dp[n][amt];\n}\n</code></pre> coin_change_ii.rs<pre><code>/* コイン両替 II：動的計画法 */\nfn coin_change_ii_dp(coins: &amp;[i32], amt: usize) -&gt; i32 {\n    let n = coins.len();\n    // dp テーブルを初期化\n    let mut dp = vec![vec![0; amt + 1]; n + 1];\n    // 先頭列を初期化する\n    for i in 0..=n {\n        dp[i][0] = 1;\n    }\n    // 状態遷移\n    for i in 1..=n {\n        for a in 1..=amt {\n            if coins[i - 1] &gt; a as i32 {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // コイン i を選ばない場合と選ぶ場合の和\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1] as usize];\n            }\n        }\n    }\n    dp[n][amt]\n}\n</code></pre> coin_change_ii.c<pre><code>/* コイン両替 II：動的計画法 */\nint coinChangeIIDP(int coins[], int amt, int coinsSize) {\n    int n = coinsSize;\n    // dp テーブルを初期化\n    int **dp = malloc((n + 1) * sizeof(int *));\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i] = calloc(amt + 1, sizeof(int));\n    }\n    // 先頭列を初期化する\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i][0] = 1;\n    }\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // コイン i を選ばない場合と選ぶ場合の和\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];\n            }\n        }\n    }\n    int res = dp[n][amt];\n    // メモリを解放する\n    for (int i = 0; i &lt;= n; i++) {\n        free(dp[i]);\n    }\n    free(dp);\n    return res;\n}\n</code></pre> coin_change_ii.kt<pre><code>/* コイン両替 II：動的計画法 */\nfun coinChangeIIDP(coins: IntArray, amt: Int): Int {\n    val n = coins.size\n    // dp テーブルを初期化\n    val dp = Array(n + 1) { IntArray(amt + 1) }\n    // 先頭列を初期化する\n    for (i in 0..n) {\n        dp[i][0] = 1\n    }\n    // 状態遷移\n    for (i in 1..n) {\n        for (a in 1..amt) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[i][a] = dp[i - 1][a]\n            } else {\n                // コイン i を選ばない場合と選ぶ場合の和\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]]\n            }\n        }\n    }\n    return dp[n][amt]\n}\n</code></pre> coin_change_ii.rb<pre><code>### コイン両替 II：動的計画法 ###\ndef coin_change_ii_dp(coins, amt)\n  n = coins.length\n  # dp テーブルを初期化\n  dp = Array.new(n + 1) { Array.new(amt + 1, 0) }\n  # 先頭列を初期化する\n  (0...(n + 1)).each { |i| dp[i][0] = 1 }\n  # 状態遷移\n  for i in 1...(n + 1)\n    for a in 1...(amt + 1)\n      if coins[i - 1] &gt; a\n        # 目標金額を超えるなら硬貨 i は選ばない\n        dp[i][a] = dp[i - 1][a]\n      else\n        # コイン i を選ばない場合と選ぶ場合の和\n        dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]]\n      end\n    end\n  end\n  dp[n][amt]\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 完全ナップサック問題"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#3_2","level":3,"title":"3.   空間最適化","text":"<p>空間最適化の方法も同様で、硬貨の次元を削除するだけです。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby coin_change_ii.py<pre><code>def coin_change_ii_dp_comp(coins: list[int], amt: int) -&gt; int:\n    \"\"\"コイン両替 II：空間最適化した動的計画法\"\"\"\n    n = len(coins)\n    # dp テーブルを初期化\n    dp = [0] * (amt + 1)\n    dp[0] = 1\n    # 状態遷移\n    for i in range(1, n + 1):\n        # 順方向に走査する\n        for a in range(1, amt + 1):\n            if coins[i - 1] &gt; a:\n                # 目標金額を超えるなら硬貨 i は選ばない\n                dp[a] = dp[a]\n            else:\n                # コイン i を選ばない場合と選ぶ場合の和\n                dp[a] = dp[a] + dp[a - coins[i - 1]]\n    return dp[amt]\n</code></pre> coin_change_ii.cpp<pre><code>/* コイン両替 II：空間最適化した動的計画法 */\nint coinChangeIIDPComp(vector&lt;int&gt; &amp;coins, int amt) {\n    int n = coins.size();\n    // dp テーブルを初期化\n    vector&lt;int&gt; dp(amt + 1, 0);\n    dp[0] = 1;\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[a] = dp[a];\n            } else {\n                // コイン i を選ばない場合と選ぶ場合の和\n                dp[a] = dp[a] + dp[a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[amt];\n}\n</code></pre> coin_change_ii.java<pre><code>/* コイン両替 II：空間最適化した動的計画法 */\nint coinChangeIIDPComp(int[] coins, int amt) {\n    int n = coins.length;\n    // dp テーブルを初期化\n    int[] dp = new int[amt + 1];\n    dp[0] = 1;\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[a] = dp[a];\n            } else {\n                // コイン i を選ばない場合と選ぶ場合の和\n                dp[a] = dp[a] + dp[a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[amt];\n}\n</code></pre> coin_change_ii.cs<pre><code>/* コイン両替 II：空間最適化した動的計画法 */\nint CoinChangeIIDPComp(int[] coins, int amt) {\n    int n = coins.Length;\n    // dp テーブルを初期化\n    int[] dp = new int[amt + 1];\n    dp[0] = 1;\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[a] = dp[a];\n            } else {\n                // コイン i を選ばない場合と選ぶ場合の和\n                dp[a] = dp[a] + dp[a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[amt];\n}\n</code></pre> coin_change_ii.go<pre><code>/* コイン両替 II：空間最適化した動的計画法 */\nfunc coinChangeIIDPComp(coins []int, amt int) int {\n    n := len(coins)\n    // dp テーブルを初期化\n    dp := make([]int, amt+1)\n    dp[0] = 1\n    // 状態遷移\n    for i := 1; i &lt;= n; i++ {\n        // 順方向に走査する\n        for a := 1; a &lt;= amt; a++ {\n            if coins[i-1] &gt; a {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[a] = dp[a]\n            } else {\n                // コイン i を選ばない場合と選ぶ場合の和\n                dp[a] = dp[a] + dp[a-coins[i-1]]\n            }\n        }\n    }\n    return dp[amt]\n}\n</code></pre> coin_change_ii.swift<pre><code>/* コイン両替 II：空間最適化した動的計画法 */\nfunc coinChangeIIDPComp(coins: [Int], amt: Int) -&gt; Int {\n    let n = coins.count\n    // dp テーブルを初期化\n    var dp = Array(repeating: 0, count: amt + 1)\n    dp[0] = 1\n    // 状態遷移\n    for i in 1 ... n {\n        for a in 1 ... amt {\n            if coins[i - 1] &gt; a {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[a] = dp[a]\n            } else {\n                // コイン i を選ばない場合と選ぶ場合の和\n                dp[a] = dp[a] + dp[a - coins[i - 1]]\n            }\n        }\n    }\n    return dp[amt]\n}\n</code></pre> coin_change_ii.js<pre><code>/* コイン両替 II：空間最適化した動的計画法 */\nfunction coinChangeIIDPComp(coins, amt) {\n    const n = coins.length;\n    // dp テーブルを初期化\n    const dp = Array.from({ length: amt + 1 }, () =&gt; 0);\n    dp[0] = 1;\n    // 状態遷移\n    for (let i = 1; i &lt;= n; i++) {\n        for (let a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[a] = dp[a];\n            } else {\n                // コイン i を選ばない場合と選ぶ場合の和\n                dp[a] = dp[a] + dp[a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[amt];\n}\n</code></pre> coin_change_ii.ts<pre><code>/* コイン両替 II：空間最適化した動的計画法 */\nfunction coinChangeIIDPComp(coins: Array&lt;number&gt;, amt: number): number {\n    const n = coins.length;\n    // dp テーブルを初期化\n    const dp = Array.from({ length: amt + 1 }, () =&gt; 0);\n    dp[0] = 1;\n    // 状態遷移\n    for (let i = 1; i &lt;= n; i++) {\n        for (let a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[a] = dp[a];\n            } else {\n                // コイン i を選ばない場合と選ぶ場合の和\n                dp[a] = dp[a] + dp[a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[amt];\n}\n</code></pre> coin_change_ii.dart<pre><code>/* コイン両替 II：空間最適化した動的計画法 */\nint coinChangeIIDPComp(List&lt;int&gt; coins, int amt) {\n  int n = coins.length;\n  // dp テーブルを初期化\n  List&lt;int&gt; dp = List.filled(amt + 1, 0);\n  dp[0] = 1;\n  // 状態遷移\n  for (int i = 1; i &lt;= n; i++) {\n    for (int a = 1; a &lt;= amt; a++) {\n      if (coins[i - 1] &gt; a) {\n        // 目標金額を超えるなら硬貨 i は選ばない\n        dp[a] = dp[a];\n      } else {\n        // コイン i を選ばない場合と選ぶ場合の和\n        dp[a] = dp[a] + dp[a - coins[i - 1]];\n      }\n    }\n  }\n  return dp[amt];\n}\n</code></pre> coin_change_ii.rs<pre><code>/* コイン両替 II：空間最適化した動的計画法 */\nfn coin_change_ii_dp_comp(coins: &amp;[i32], amt: usize) -&gt; i32 {\n    let n = coins.len();\n    // dp テーブルを初期化\n    let mut dp = vec![0; amt + 1];\n    dp[0] = 1;\n    // 状態遷移\n    for i in 1..=n {\n        for a in 1..=amt {\n            if coins[i - 1] &gt; a as i32 {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[a] = dp[a];\n            } else {\n                // コイン i を選ばない場合と選ぶ場合の和\n                dp[a] = dp[a] + dp[a - coins[i - 1] as usize];\n            }\n        }\n    }\n    dp[amt]\n}\n</code></pre> coin_change_ii.c<pre><code>/* コイン両替 II：空間最適化した動的計画法 */\nint coinChangeIIDPComp(int coins[], int amt, int coinsSize) {\n    int n = coinsSize;\n    // dp テーブルを初期化\n    int *dp = calloc(amt + 1, sizeof(int));\n    dp[0] = 1;\n    // 状態遷移\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[a] = dp[a];\n            } else {\n                // コイン i を選ばない場合と選ぶ場合の和\n                dp[a] = dp[a] + dp[a - coins[i - 1]];\n            }\n        }\n    }\n    int res = dp[amt];\n    // メモリを解放する\n    free(dp);\n    return res;\n}\n</code></pre> coin_change_ii.kt<pre><code>/* コイン両替 II：空間最適化した動的計画法 */\nfun coinChangeIIDPComp(coins: IntArray, amt: Int): Int {\n    val n = coins.size\n    // dp テーブルを初期化\n    val dp = IntArray(amt + 1)\n    dp[0] = 1\n    // 状態遷移\n    for (i in 1..n) {\n        for (a in 1..amt) {\n            if (coins[i - 1] &gt; a) {\n                // 目標金額を超えるなら硬貨 i は選ばない\n                dp[a] = dp[a]\n            } else {\n                // コイン i を選ばない場合と選ぶ場合の和\n                dp[a] = dp[a] + dp[a - coins[i - 1]]\n            }\n        }\n    }\n    return dp[amt]\n}\n</code></pre> coin_change_ii.rb<pre><code>### コイン両替 II：空間最適化した動的計画法 ###\ndef coin_change_ii_dp_comp(coins, amt)\n  n = coins.length\n  # dp テーブルを初期化\n  dp = Array.new(amt + 1, 0)\n  dp[0] = 1\n  # 状態遷移\n  for i in 1...(n + 1)\n    # 順方向に走査する\n    for a in 1...(amt + 1)\n      if coins[i - 1] &gt; a\n        # 目標金額を超えるなら硬貨 i は選ばない\n        dp[a] = dp[a]\n      else\n        # コイン i を選ばない場合と選ぶ場合の和\n        dp[a] = dp[a] + dp[a - coins[i - 1]]\n      end\n    end\n  end\n  dp[amt]\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 14 章 &nbsp; 動的計画法","14.5 &nbsp; 完全ナップサック問題"],"tags":[]},{"location":"chapter_graph/","level":1,"title":"第 9 章   グラフ","text":"<p>Abstract</p> <p>人生の旅路において、私たちはそれぞれ一つひとつのノードのようなものであり、無数の見えない辺によって結ばれています。</p> <p>出会いと別れのたびに、この巨大なネットワークグラフの中に固有の足跡が刻まれます。</p>","path":["第 9 章 &nbsp; グラフ"],"tags":[]},{"location":"chapter_graph/#_1","level":2,"title":"章の内容","text":"<ul> <li>9.1   グラフ</li> <li>9.2   グラフの基本操作</li> <li>9.3   グラフの走査</li> <li>9.4   まとめ</li> </ul>","path":["第 9 章 &nbsp; グラフ"],"tags":[]},{"location":"chapter_graph/graph/","level":1,"title":"9.1   グラフ","text":"<p>グラフ（graph）は、頂点（vertex）と辺（edge）から構成される非線形データ構造です。グラフ \\(G\\) は、頂点集合 \\(V\\) と辺集合 \\(E\\) からなる集合として抽象的に表せます。以下の例は、5 個の頂点と 7 本の辺を含むグラフを示しています。</p> \\[ \\begin{aligned} V &amp; = \\{ 1, 2, 3, 4, 5 \\} \\newline E &amp; = \\{ (1,2), (1,3), (1,5), (2,3), (2,4), (2,5), (4,5) \\} \\newline G &amp; = \\{ V, E \\} \\newline \\end{aligned} \\] <p>頂点をノード、辺を各ノードをつなぐ参照（ポインタ）とみなせば、グラフは連結リストを拡張したデータ構造の一種と捉えられます。次の図に示すように、線形関係（連結リスト）や分治関係（木）と比べて、ネットワーク関係（グラフ）は自由度が高く、そのぶん複雑です。</p> <p></p> <p> 図 9-1   連結リスト、木、グラフの関係 </p>","path":["第 9 章 &nbsp; グラフ","9.1 &nbsp; グラフ"],"tags":[]},{"location":"chapter_graph/graph/#911","level":2,"title":"9.1.1   グラフの一般的な種類と用語","text":"<p>辺が方向性を持つかどうかに応じて、無向グラフ（undirected graph）と有向グラフ（directed graph）に分けられます。次の図のとおりです。</p> <ul> <li>無向グラフでは、辺は 2 つの頂点間の「双方向」の接続関係を表します。例えば WeChat や QQ における「友だち関係」です。</li> <li>有向グラフでは、辺は方向性を持ち、すなわち \\(A \\rightarrow B\\) と \\(A \\leftarrow B\\) の 2 方向の辺は互いに独立です。例えば Weibo や Douyin における「フォロー」と「フォロワー」の関係です。</li> </ul> <p></p> <p> 図 9-2   有向グラフと無向グラフ </p> <p>すべての頂点が連結しているかどうかに応じて、連結グラフ（connected graph）と非連結グラフ（disconnected graph）に分けられます。次の図のとおりです。</p> <ul> <li>連結グラフでは、ある頂点から出発すると、ほかの任意の頂点に到達できます。</li> <li>非連結グラフでは、ある頂点から出発すると、少なくとも 1 つの頂点には到達できません。</li> </ul> <p></p> <p> 図 9-3   連結グラフと非連結グラフ </p> <p>辺に「重み」の変数を追加すると、次の図に示すような重み付きグラフ（weighted graph）が得られます。例えば『Honor of Kings』のようなモバイルゲームでは、システムが共にプレイした時間に基づいてプレイヤー間の「親密度」を計算します。この親密度ネットワークは重み付きグラフで表せます。</p> <p></p> <p> 図 9-4   重み付きグラフと重みなしグラフ </p> <p>グラフというデータ構造には、次のような基本用語があります。</p> <ul> <li>隣接（adjacency）：2 つの頂点の間に辺が存在するとき、この 2 つの頂点は「隣接している」といいます。上図では、頂点 1 に隣接する頂点は 2、3、5 です。</li> <li>経路（path）：頂点 A から頂点 B までに通過する辺で構成された列を、A から B への「経路」と呼びます。上図では、辺の列 1-5-2-4 は頂点 1 から頂点 4 への 1 本の経路です。</li> <li>次数（degree）：ある頂点が持つ辺の本数です。有向グラフでは、入次数（in-degree）はその頂点に向かう辺の本数を表し、出次数（out-degree）はその頂点から出る辺の本数を表します。</li> </ul>","path":["第 9 章 &nbsp; グラフ","9.1 &nbsp; グラフ"],"tags":[]},{"location":"chapter_graph/graph/#912","level":2,"title":"9.1.2   グラフの表現","text":"<p>グラフの一般的な表現方法には「隣接行列」と「隣接リスト」があります。以下では無向グラフを例に説明します。</p>","path":["第 9 章 &nbsp; グラフ","9.1 &nbsp; グラフ"],"tags":[]},{"location":"chapter_graph/graph/#1","level":3,"title":"1.   隣接行列","text":"<p>グラフの頂点数を \\(n\\) とすると、隣接行列（adjacency matrix）は \\(n \\times n\\) の行列を用いてグラフを表します。各行（列）は 1 つの頂点を表し、行列要素は辺を表します。\\(1\\) または \\(0\\) を用いて、2 つの頂点の間に辺があるかどうかを示します。</p> <p>次の図のように、隣接行列を \\(M\\)、頂点リストを \\(V\\) とすると、行列要素 \\(M[i, j] = 1\\) は頂点 \\(V[i]\\) から頂点 \\(V[j]\\) への辺が存在することを表し、逆に \\(M[i, j] = 0\\) は 2 つの頂点の間に辺がないことを表します。</p> <p></p> <p> 図 9-5   グラフの隣接行列による表現 </p> <p>隣接行列には次の特徴があります。</p> <ul> <li>単純グラフでは、頂点は自分自身とは接続できないため、このとき隣接行列の主対角線上の要素には意味がありません。</li> <li>無向グラフでは、2 方向の辺は等価であるため、このとき隣接行列は主対角線に関して対称です。</li> <li>隣接行列の要素を \\(1\\) と \\(0\\) から重みに置き換えると、重み付きグラフを表せます。</li> </ul> <p>隣接行列でグラフを表す場合、行列要素に直接アクセスして辺を取得できるため、追加・削除・検索・更新の操作効率は高く、時間計算量はいずれも \\(O(1)\\) です。しかし、行列の空間計算量は \\(O(n^2)\\) であり、メモリ使用量は多くなります。</p>","path":["第 9 章 &nbsp; グラフ","9.1 &nbsp; グラフ"],"tags":[]},{"location":"chapter_graph/graph/#2","level":3,"title":"2.   隣接リスト","text":"<p>隣接リスト（adjacency list）は、\\(n\\) 本の連結リストを使ってグラフを表します。連結リストのノードは頂点を表します。第 \\(i\\) 本の連結リストは頂点 \\(i\\) に対応し、その頂点に隣接するすべての頂点（その頂点と接続された頂点）を格納します。次の図は、隣接リストで保存したグラフの例です。</p> <p></p> <p> 図 9-6   グラフの隣接リストによる表現 </p> <p>隣接リストは実際に存在する辺だけを格納し、辺の総数は通常 \\(n^2\\) よりはるかに小さいため、より省スペースです。しかし、隣接リストでは辺を見つけるために連結リストを走査する必要があるため、時間効率は隣接行列に及びません。</p> <p>上図を見ると、隣接リストの構造はハッシュテーブルにおける「連鎖アドレス法」と非常によく似ているため、同様の方法で効率を最適化できます。例えば、連結リストが長い場合は AVL 木や赤黒木に変換して時間効率を \\(O(n)\\) から \\(O(\\log n)\\) に改善できます。さらに、連結リストをハッシュテーブルに変換すれば、時間計算量を \\(O(1)\\) まで下げられます。</p>","path":["第 9 章 &nbsp; グラフ","9.1 &nbsp; グラフ"],"tags":[]},{"location":"chapter_graph/graph/#913","level":2,"title":"9.1.3   グラフの一般的な応用","text":"<p>次の表のように、多くの現実のシステムはグラフでモデル化でき、対応する問題もグラフ計算の問題に帰着できます。</p> <p> 表 9-1   現実世界でよく見られるグラフ </p> 頂点 辺 グラフ計算問題 ソーシャルネットワーク ユーザー 友だち関係 潜在的な友だちの推薦 地下鉄路線 駅 駅間の接続性 最短経路の推薦 太陽系 天体 天体間の万有引力作用 惑星軌道の計算","path":["第 9 章 &nbsp; グラフ","9.1 &nbsp; グラフ"],"tags":[]},{"location":"chapter_graph/graph_operations/","level":1,"title":"9.2   グラフの基本操作","text":"<p>グラフの基本操作は、「辺」に対する操作と「頂点」に対する操作に分けられます。「隣接行列」と「隣接リスト」の 2 つの表現方法では、実装方法が異なります。</p>","path":["第 9 章 &nbsp; グラフ","9.2 &nbsp; グラフの基本操作"],"tags":[]},{"location":"chapter_graph/graph_operations/#921","level":2,"title":"9.2.1   隣接行列に基づく実装","text":"<p>頂点数が \\(n\\) の無向グラフを与えると、各種操作の実装方法は次図のとおりです。</p> <ul> <li>辺の追加または削除：隣接行列で指定した辺を直接変更すればよく、\\(O(1)\\) 時間です。無向グラフであるため、2 方向の辺を同時に更新する必要があります。</li> <li>頂点の追加：隣接行列の末尾に 1 行 1 列を追加し、すべてを \\(0\\) で埋めればよく、\\(O(n)\\) 時間です。</li> <li>頂点の削除：隣接行列から 1 行 1 列を削除します。先頭行と先頭列を削除する場合が最悪で、\\((n-1)^2\\) 個の要素を「左上へ移動」させる必要があるため、\\(O(n^2)\\) 時間です。</li> <li>初期化：\\(n\\) 個の頂点を受け取り、長さ \\(n\\) の頂点リスト <code>vertices</code> を初期化するのに \\(O(n)\\) 時間、サイズ \\(n \\times n\\) の隣接行列 <code>adjMat</code> を初期化するのに \\(O(n^2)\\) 時間かかります。</li> </ul> 隣接行列の初期化辺の追加辺の削除頂点の追加頂点の削除 <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 9-7   隣接行列の初期化、辺の追加と削除、頂点の追加と削除 </p> <p>以下は、隣接行列でグラフを表した実装コードです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby graph_adjacency_matrix.py<pre><code>class GraphAdjMat:\n    \"\"\"隣接行列に基づく無向グラフクラス\"\"\"\n\n    def __init__(self, vertices: list[int], edges: list[list[int]]):\n        \"\"\"コンストラクタ\"\"\"\n        # 頂点リスト。要素は「頂点値」、インデックスは「頂点インデックス」を表す\n        self.vertices: list[int] = []\n        # 隣接行列。行・列のインデックスは「頂点インデックス」に対応\n        self.adj_mat: list[list[int]] = []\n        # 頂点を追加\n        for val in vertices:\n            self.add_vertex(val)\n        # 辺を追加\n        # 注意：edges の各要素は頂点インデックスを表し、vertices の要素インデックスに対応する\n        for e in edges:\n            self.add_edge(e[0], e[1])\n\n    def size(self) -&gt; int:\n        \"\"\"頂点数を取得\"\"\"\n        return len(self.vertices)\n\n    def add_vertex(self, val: int):\n        \"\"\"頂点を追加\"\"\"\n        n = self.size()\n        # 頂点リストに新しい頂点の値を追加\n        self.vertices.append(val)\n        # 隣接行列に 1 行追加\n        new_row = [0] * n\n        self.adj_mat.append(new_row)\n        # 隣接行列に 1 列追加\n        for row in self.adj_mat:\n            row.append(0)\n\n    def remove_vertex(self, index: int):\n        \"\"\"頂点を削除\"\"\"\n        if index &gt;= self.size():\n            raise IndexError()\n        # 頂点リストから index の頂点を削除する\n        self.vertices.pop(index)\n        # 隣接行列で index 行を削除する\n        self.adj_mat.pop(index)\n        # 隣接行列で index 列を削除する\n        for row in self.adj_mat:\n            row.pop(index)\n\n    def add_edge(self, i: int, j: int):\n        \"\"\"辺を追加\"\"\"\n        # パラメータ i, j は vertices の要素インデックスに対応する\n        # 範囲外と同値の場合の処理\n        if i &lt; 0 or j &lt; 0 or i &gt;= self.size() or j &gt;= self.size() or i == j:\n            raise IndexError()\n        # 無向グラフでは、隣接行列は主対角線に関して対称、すなわち (i, j) == (j, i) を満たす\n        self.adj_mat[i][j] = 1\n        self.adj_mat[j][i] = 1\n\n    def remove_edge(self, i: int, j: int):\n        \"\"\"辺を削除\"\"\"\n        # パラメータ i, j は vertices の要素インデックスに対応する\n        # 範囲外と同値の場合の処理\n        if i &lt; 0 or j &lt; 0 or i &gt;= self.size() or j &gt;= self.size() or i == j:\n            raise IndexError()\n        self.adj_mat[i][j] = 0\n        self.adj_mat[j][i] = 0\n\n    def print(self):\n        \"\"\"隣接行列を出力\"\"\"\n        print(\"頂点リスト =\", self.vertices)\n        print(\"隣接行列 =\")\n        print_matrix(self.adj_mat)\n</code></pre> graph_adjacency_matrix.cpp<pre><code>/* 隣接行列に基づく無向グラフクラス */\nclass GraphAdjMat {\n    vector&lt;int&gt; vertices;       // 頂点リスト。要素は「頂点値」、インデックスは「頂点インデックス」を表す\n    vector&lt;vector&lt;int&gt;&gt; adjMat; // 隣接行列。行・列のインデックスは「頂点インデックス」に対応\n\n  public:\n    /* コンストラクタ */\n    GraphAdjMat(const vector&lt;int&gt; &amp;vertices, const vector&lt;vector&lt;int&gt;&gt; &amp;edges) {\n        // 頂点を追加\n        for (int val : vertices) {\n            addVertex(val);\n        }\n        // 辺を追加\n        // 注意：edges の各要素は頂点インデックスを表し、vertices の要素インデックスに対応する\n        for (const vector&lt;int&gt; &amp;edge : edges) {\n            addEdge(edge[0], edge[1]);\n        }\n    }\n\n    /* 頂点数を取得 */\n    int size() const {\n        return vertices.size();\n    }\n\n    /* 頂点を追加 */\n    void addVertex(int val) {\n        int n = size();\n        // 頂点リストに新しい頂点の値を追加\n        vertices.push_back(val);\n        // 隣接行列に 1 行追加\n        adjMat.emplace_back(vector&lt;int&gt;(n, 0));\n        // 隣接行列に 1 列追加\n        for (vector&lt;int&gt; &amp;row : adjMat) {\n            row.push_back(0);\n        }\n    }\n\n    /* 頂点を削除 */\n    void removeVertex(int index) {\n        if (index &gt;= size()) {\n            throw out_of_range(\"頂点が存在しません\");\n        }\n        // 頂点リストから index の頂点を削除する\n        vertices.erase(vertices.begin() + index);\n        // 隣接行列で index 行を削除する\n        adjMat.erase(adjMat.begin() + index);\n        // 隣接行列で index 列を削除する\n        for (vector&lt;int&gt; &amp;row : adjMat) {\n            row.erase(row.begin() + index);\n        }\n    }\n\n    /* 辺を追加 */\n    // 引数 i, j は vertices の要素インデックスに対応する\n    void addEdge(int i, int j) {\n        // インデックスの範囲外と等値の処理\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j) {\n            throw out_of_range(\"頂点が存在しません\");\n        }\n        // 無向グラフでは、隣接行列は主対角線に関して対称、すなわち (i, j) == (j, i) を満たす\n        adjMat[i][j] = 1;\n        adjMat[j][i] = 1;\n    }\n\n    /* 辺を削除 */\n    // 引数 i, j は vertices の要素インデックスに対応する\n    void removeEdge(int i, int j) {\n        // インデックスの範囲外と等値の処理\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j) {\n            throw out_of_range(\"頂点が存在しません\");\n        }\n        adjMat[i][j] = 0;\n        adjMat[j][i] = 0;\n    }\n\n    /* 隣接行列を出力 */\n    void print() {\n        cout &lt;&lt; \"頂点リスト = \";\n        printVector(vertices);\n        cout &lt;&lt; \"隣接行列 =\" &lt;&lt; endl;\n        printVectorMatrix(adjMat);\n    }\n};\n</code></pre> graph_adjacency_matrix.java<pre><code>/* 隣接行列に基づく無向グラフクラス */\nclass GraphAdjMat {\n    List&lt;Integer&gt; vertices; // 頂点リスト。要素は「頂点値」、インデックスは「頂点インデックス」を表す\n    List&lt;List&lt;Integer&gt;&gt; adjMat; // 隣接行列。行・列のインデックスは「頂点インデックス」に対応\n\n    /* コンストラクタ */\n    public GraphAdjMat(int[] vertices, int[][] edges) {\n        this.vertices = new ArrayList&lt;&gt;();\n        this.adjMat = new ArrayList&lt;&gt;();\n        // 頂点を追加\n        for (int val : vertices) {\n            addVertex(val);\n        }\n        // 辺を追加\n        // 注意：edges の各要素は頂点インデックスを表し、vertices の要素インデックスに対応する\n        for (int[] e : edges) {\n            addEdge(e[0], e[1]);\n        }\n    }\n\n    /* 頂点数を取得 */\n    public int size() {\n        return vertices.size();\n    }\n\n    /* 頂点を追加 */\n    public void addVertex(int val) {\n        int n = size();\n        // 頂点リストに新しい頂点の値を追加\n        vertices.add(val);\n        // 隣接行列に 1 行追加\n        List&lt;Integer&gt; newRow = new ArrayList&lt;&gt;(n);\n        for (int j = 0; j &lt; n; j++) {\n            newRow.add(0);\n        }\n        adjMat.add(newRow);\n        // 隣接行列に 1 列追加\n        for (List&lt;Integer&gt; row : adjMat) {\n            row.add(0);\n        }\n    }\n\n    /* 頂点を削除 */\n    public void removeVertex(int index) {\n        if (index &gt;= size())\n            throw new IndexOutOfBoundsException();\n        // 頂点リストから index の頂点を削除する\n        vertices.remove(index);\n        // 隣接行列で index 行を削除する\n        adjMat.remove(index);\n        // 隣接行列で index 列を削除する\n        for (List&lt;Integer&gt; row : adjMat) {\n            row.remove(index);\n        }\n    }\n\n    /* 辺を追加 */\n    // 引数 i, j は vertices の要素インデックスに対応する\n    public void addEdge(int i, int j) {\n        // インデックスの範囲外と等値の処理\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j)\n            throw new IndexOutOfBoundsException();\n        // 無向グラフでは、隣接行列は主対角線に関して対称、すなわち (i, j) == (j, i) を満たす\n        adjMat.get(i).set(j, 1);\n        adjMat.get(j).set(i, 1);\n    }\n\n    /* 辺を削除 */\n    // 引数 i, j は vertices の要素インデックスに対応する\n    public void removeEdge(int i, int j) {\n        // インデックスの範囲外と等値の処理\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j)\n            throw new IndexOutOfBoundsException();\n        adjMat.get(i).set(j, 0);\n        adjMat.get(j).set(i, 0);\n    }\n\n    /* 隣接行列を出力 */\n    public void print() {\n        System.out.print(\"頂点リスト = \");\n        System.out.println(vertices);\n        System.out.println(\"隣接行列 =\");\n        PrintUtil.printMatrix(adjMat);\n    }\n}\n</code></pre> graph_adjacency_matrix.cs<pre><code>/* 隣接行列に基づく無向グラフクラス */\nclass GraphAdjMat {\n    List&lt;int&gt; vertices;     // 頂点リスト。要素は「頂点値」、インデックスは「頂点インデックス」を表す\n    List&lt;List&lt;int&gt;&gt; adjMat; // 隣接行列。行・列のインデックスは「頂点インデックス」に対応\n\n    /* コンストラクタ */\n    public GraphAdjMat(int[] vertices, int[][] edges) {\n        this.vertices = [];\n        this.adjMat = [];\n        // 頂点を追加\n        foreach (int val in vertices) {\n            AddVertex(val);\n        }\n        // 辺を追加\n        // 注意：edges の各要素は頂点インデックスを表し、vertices の要素インデックスに対応する\n        foreach (int[] e in edges) {\n            AddEdge(e[0], e[1]);\n        }\n    }\n\n    /* 頂点数を取得 */\n    int Size() {\n        return vertices.Count;\n    }\n\n    /* 頂点を追加 */\n    public void AddVertex(int val) {\n        int n = Size();\n        // 頂点リストに新しい頂点の値を追加\n        vertices.Add(val);\n        // 隣接行列に 1 行追加\n        List&lt;int&gt; newRow = new(n);\n        for (int j = 0; j &lt; n; j++) {\n            newRow.Add(0);\n        }\n        adjMat.Add(newRow);\n        // 隣接行列に 1 列追加\n        foreach (List&lt;int&gt; row in adjMat) {\n            row.Add(0);\n        }\n    }\n\n    /* 頂点を削除 */\n    public void RemoveVertex(int index) {\n        if (index &gt;= Size())\n            throw new IndexOutOfRangeException();\n        // 頂点リストから index の頂点を削除する\n        vertices.RemoveAt(index);\n        // 隣接行列で index 行を削除する\n        adjMat.RemoveAt(index);\n        // 隣接行列で index 列を削除する\n        foreach (List&lt;int&gt; row in adjMat) {\n            row.RemoveAt(index);\n        }\n    }\n\n    /* 辺を追加 */\n    // 引数 i, j は vertices の要素インデックスに対応する\n    public void AddEdge(int i, int j) {\n        // インデックスの範囲外と等値の処理\n        if (i &lt; 0 || j &lt; 0 || i &gt;= Size() || j &gt;= Size() || i == j)\n            throw new IndexOutOfRangeException();\n        // 無向グラフでは、隣接行列は主対角線に関して対称、すなわち (i, j) == (j, i) を満たす\n        adjMat[i][j] = 1;\n        adjMat[j][i] = 1;\n    }\n\n    /* 辺を削除 */\n    // 引数 i, j は vertices の要素インデックスに対応する\n    public void RemoveEdge(int i, int j) {\n        // インデックスの範囲外と等値の処理\n        if (i &lt; 0 || j &lt; 0 || i &gt;= Size() || j &gt;= Size() || i == j)\n            throw new IndexOutOfRangeException();\n        adjMat[i][j] = 0;\n        adjMat[j][i] = 0;\n    }\n\n    /* 隣接行列を出力 */\n    public void Print() {\n        Console.Write(\"頂点リスト = \");\n        PrintUtil.PrintList(vertices);\n        Console.WriteLine(\"隣接行列 =\");\n        PrintUtil.PrintMatrix(adjMat);\n    }\n}\n</code></pre> graph_adjacency_matrix.go<pre><code>/* 隣接行列に基づく無向グラフクラス */\ntype graphAdjMat struct {\n    // 頂点リスト。要素は「頂点値」、インデックスは「頂点インデックス」を表す\n    vertices []int\n    // 隣接行列。行・列のインデックスは「頂点インデックス」に対応\n    adjMat [][]int\n}\n\n/* コンストラクタ */\nfunc newGraphAdjMat(vertices []int, edges [][]int) *graphAdjMat {\n    // 頂点を追加\n    n := len(vertices)\n    adjMat := make([][]int, n)\n    for i := range adjMat {\n        adjMat[i] = make([]int, n)\n    }\n    // グラフを初期化する\n    g := &amp;graphAdjMat{\n        vertices: vertices,\n        adjMat:   adjMat,\n    }\n    // 辺を追加\n    // 注意：edges の各要素は頂点インデックスを表し、vertices の要素インデックスに対応する\n    for i := range edges {\n        g.addEdge(edges[i][0], edges[i][1])\n    }\n    return g\n}\n\n/* 頂点数を取得 */\nfunc (g *graphAdjMat) size() int {\n    return len(g.vertices)\n}\n\n/* 頂点を追加 */\nfunc (g *graphAdjMat) addVertex(val int) {\n    n := g.size()\n    // 頂点リストに新しい頂点の値を追加\n    g.vertices = append(g.vertices, val)\n    // 隣接行列に 1 行追加\n    newRow := make([]int, n)\n    g.adjMat = append(g.adjMat, newRow)\n    // 隣接行列に 1 列追加\n    for i := range g.adjMat {\n        g.adjMat[i] = append(g.adjMat[i], 0)\n    }\n}\n\n/* 頂点を削除 */\nfunc (g *graphAdjMat) removeVertex(index int) {\n    if index &gt;= g.size() {\n        return\n    }\n    // 頂点リストから index の頂点を削除する\n    g.vertices = append(g.vertices[:index], g.vertices[index+1:]...)\n    // 隣接行列で index 行を削除する\n    g.adjMat = append(g.adjMat[:index], g.adjMat[index+1:]...)\n    // 隣接行列で index 列を削除する\n    for i := range g.adjMat {\n        g.adjMat[i] = append(g.adjMat[i][:index], g.adjMat[i][index+1:]...)\n    }\n}\n\n/* 辺を追加 */\n// 引数 i, j は vertices の要素インデックスに対応する\nfunc (g *graphAdjMat) addEdge(i, j int) {\n    // インデックスの範囲外と等値の処理\n    if i &lt; 0 || j &lt; 0 || i &gt;= g.size() || j &gt;= g.size() || i == j {\n        fmt.Errorf(\"%s\", \"Index Out Of Bounds Exception\")\n    }\n    // 無向グラフでは、隣接行列は主対角線に関して対称、すなわち (i, j) == (j, i) を満たす\n    g.adjMat[i][j] = 1\n    g.adjMat[j][i] = 1\n}\n\n/* 辺を削除 */\n// 引数 i, j は vertices の要素インデックスに対応する\nfunc (g *graphAdjMat) removeEdge(i, j int) {\n    // インデックスの範囲外と等値の処理\n    if i &lt; 0 || j &lt; 0 || i &gt;= g.size() || j &gt;= g.size() || i == j {\n        fmt.Errorf(\"%s\", \"Index Out Of Bounds Exception\")\n    }\n    g.adjMat[i][j] = 0\n    g.adjMat[j][i] = 0\n}\n\n/* 隣接行列を出力 */\nfunc (g *graphAdjMat) print() {\n    fmt.Printf(\"\\t頂点リスト = %v\\n\", g.vertices)\n    fmt.Printf(\"\\t隣接行列 = \\n\")\n    for i := range g.adjMat {\n        fmt.Printf(\"\\t\\t\\t%v\\n\", g.adjMat[i])\n    }\n}\n</code></pre> graph_adjacency_matrix.swift<pre><code>/* 隣接行列に基づく無向グラフクラス */\nclass GraphAdjMat {\n    private var vertices: [Int] // 頂点リスト。要素は「頂点値」、インデックスは「頂点インデックス」を表す\n    private var adjMat: [[Int]] // 隣接行列。行・列のインデックスは「頂点インデックス」に対応\n\n    /* コンストラクタ */\n    init(vertices: [Int], edges: [[Int]]) {\n        self.vertices = []\n        adjMat = []\n        // 頂点を追加\n        for val in vertices {\n            addVertex(val: val)\n        }\n        // 辺を追加\n        // 注意：edges の各要素は頂点インデックスを表し、vertices の要素インデックスに対応する\n        for e in edges {\n            addEdge(i: e[0], j: e[1])\n        }\n    }\n\n    /* 頂点数を取得 */\n    func size() -&gt; Int {\n        vertices.count\n    }\n\n    /* 頂点を追加 */\n    func addVertex(val: Int) {\n        let n = size()\n        // 頂点リストに新しい頂点の値を追加\n        vertices.append(val)\n        // 隣接行列に 1 行追加\n        let newRow = Array(repeating: 0, count: n)\n        adjMat.append(newRow)\n        // 隣接行列に 1 列追加\n        for i in adjMat.indices {\n            adjMat[i].append(0)\n        }\n    }\n\n    /* 頂点を削除 */\n    func removeVertex(index: Int) {\n        if index &gt;= size() {\n            fatalError(\"範囲外\")\n        }\n        // 頂点リストから index の頂点を削除する\n        vertices.remove(at: index)\n        // 隣接行列で index 行を削除する\n        adjMat.remove(at: index)\n        // 隣接行列で index 列を削除する\n        for i in adjMat.indices {\n            adjMat[i].remove(at: index)\n        }\n    }\n\n    /* 辺を追加 */\n    // 引数 i, j は vertices の要素インデックスに対応する\n    func addEdge(i: Int, j: Int) {\n        // インデックスの範囲外と等値の処理\n        if i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j {\n            fatalError(\"範囲外\")\n        }\n        // 無向グラフでは、隣接行列は主対角線に関して対称、すなわち (i, j) == (j, i) を満たす\n        adjMat[i][j] = 1\n        adjMat[j][i] = 1\n    }\n\n    /* 辺を削除 */\n    // 引数 i, j は vertices の要素インデックスに対応する\n    func removeEdge(i: Int, j: Int) {\n        // インデックスの範囲外と等値の処理\n        if i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j {\n            fatalError(\"範囲外\")\n        }\n        adjMat[i][j] = 0\n        adjMat[j][i] = 0\n    }\n\n    /* 隣接行列を出力 */\n    func print() {\n        Swift.print(\"頂点リスト = \", terminator: \"\")\n        Swift.print(vertices)\n        Swift.print(\"隣接行列 =\")\n        PrintUtil.printMatrix(matrix: adjMat)\n    }\n}\n</code></pre> graph_adjacency_matrix.js<pre><code>/* 隣接行列に基づく無向グラフクラス */\nclass GraphAdjMat {\n    vertices; // 頂点リスト。要素は「頂点値」、インデックスは「頂点インデックス」を表す\n    adjMat; // 隣接行列。行・列のインデックスは「頂点インデックス」に対応\n\n    /* コンストラクタ */\n    constructor(vertices, edges) {\n        this.vertices = [];\n        this.adjMat = [];\n        // 頂点を追加\n        for (const val of vertices) {\n            this.addVertex(val);\n        }\n        // 辺を追加\n        // 注意：edges の各要素は頂点インデックスを表し、vertices の要素インデックスに対応する\n        for (const e of edges) {\n            this.addEdge(e[0], e[1]);\n        }\n    }\n\n    /* 頂点数を取得 */\n    size() {\n        return this.vertices.length;\n    }\n\n    /* 頂点を追加 */\n    addVertex(val) {\n        const n = this.size();\n        // 頂点リストに新しい頂点の値を追加\n        this.vertices.push(val);\n        // 隣接行列に 1 行追加\n        const newRow = [];\n        for (let j = 0; j &lt; n; j++) {\n            newRow.push(0);\n        }\n        this.adjMat.push(newRow);\n        // 隣接行列に 1 列追加\n        for (const row of this.adjMat) {\n            row.push(0);\n        }\n    }\n\n    /* 頂点を削除 */\n    removeVertex(index) {\n        if (index &gt;= this.size()) {\n            throw new RangeError('Index Out Of Bounds Exception');\n        }\n        // 頂点リストから index の頂点を削除する\n        this.vertices.splice(index, 1);\n\n        // 隣接行列で index 行を削除する\n        this.adjMat.splice(index, 1);\n        // 隣接行列で index 列を削除する\n        for (const row of this.adjMat) {\n            row.splice(index, 1);\n        }\n    }\n\n    /* 辺を追加 */\n    // 引数 i, j は vertices の要素インデックスに対応する\n    addEdge(i, j) {\n        // インデックスの範囲外と等値の処理\n        if (i &lt; 0 || j &lt; 0 || i &gt;= this.size() || j &gt;= this.size() || i === j) {\n            throw new RangeError('Index Out Of Bounds Exception');\n        }\n        // 無向グラフでは、隣接行列は主対角線に関して対称であり、(i, j) === (j, i) を満たす\n        this.adjMat[i][j] = 1;\n        this.adjMat[j][i] = 1;\n    }\n\n    /* 辺を削除 */\n    // 引数 i, j は vertices の要素インデックスに対応する\n    removeEdge(i, j) {\n        // インデックスの範囲外と等値の処理\n        if (i &lt; 0 || j &lt; 0 || i &gt;= this.size() || j &gt;= this.size() || i === j) {\n            throw new RangeError('Index Out Of Bounds Exception');\n        }\n        this.adjMat[i][j] = 0;\n        this.adjMat[j][i] = 0;\n    }\n\n    /* 隣接行列を出力 */\n    print() {\n        console.log('頂点リスト = ', this.vertices);\n        console.log('隣接行列 =', this.adjMat);\n    }\n}\n</code></pre> graph_adjacency_matrix.ts<pre><code>/* 隣接行列に基づく無向グラフクラス */\nclass GraphAdjMat {\n    vertices: number[]; // 頂点リスト。要素は「頂点値」、インデックスは「頂点インデックス」を表す\n    adjMat: number[][]; // 隣接行列。行・列のインデックスは「頂点インデックス」に対応\n\n    /* コンストラクタ */\n    constructor(vertices: number[], edges: number[][]) {\n        this.vertices = [];\n        this.adjMat = [];\n        // 頂点を追加\n        for (const val of vertices) {\n            this.addVertex(val);\n        }\n        // 辺を追加\n        // 注意：edges の各要素は頂点インデックスを表し、vertices の要素インデックスに対応する\n        for (const e of edges) {\n            this.addEdge(e[0], e[1]);\n        }\n    }\n\n    /* 頂点数を取得 */\n    size(): number {\n        return this.vertices.length;\n    }\n\n    /* 頂点を追加 */\n    addVertex(val: number): void {\n        const n: number = this.size();\n        // 頂点リストに新しい頂点の値を追加\n        this.vertices.push(val);\n        // 隣接行列に 1 行追加\n        const newRow: number[] = [];\n        for (let j: number = 0; j &lt; n; j++) {\n            newRow.push(0);\n        }\n        this.adjMat.push(newRow);\n        // 隣接行列に 1 列追加\n        for (const row of this.adjMat) {\n            row.push(0);\n        }\n    }\n\n    /* 頂点を削除 */\n    removeVertex(index: number): void {\n        if (index &gt;= this.size()) {\n            throw new RangeError('Index Out Of Bounds Exception');\n        }\n        // 頂点リストから index の頂点を削除する\n        this.vertices.splice(index, 1);\n\n        // 隣接行列で index 行を削除する\n        this.adjMat.splice(index, 1);\n        // 隣接行列で index 列を削除する\n        for (const row of this.adjMat) {\n            row.splice(index, 1);\n        }\n    }\n\n    /* 辺を追加 */\n    // 引数 i, j は vertices の要素インデックスに対応する\n    addEdge(i: number, j: number): void {\n        // インデックスの範囲外と等値の処理\n        if (i &lt; 0 || j &lt; 0 || i &gt;= this.size() || j &gt;= this.size() || i === j) {\n            throw new RangeError('Index Out Of Bounds Exception');\n        }\n        // 無向グラフでは、隣接行列は主対角線に関して対称であり、(i, j) === (j, i) を満たす\n        this.adjMat[i][j] = 1;\n        this.adjMat[j][i] = 1;\n    }\n\n    /* 辺を削除 */\n    // 引数 i, j は vertices の要素インデックスに対応する\n    removeEdge(i: number, j: number): void {\n        // インデックスの範囲外と等値の処理\n        if (i &lt; 0 || j &lt; 0 || i &gt;= this.size() || j &gt;= this.size() || i === j) {\n            throw new RangeError('Index Out Of Bounds Exception');\n        }\n        this.adjMat[i][j] = 0;\n        this.adjMat[j][i] = 0;\n    }\n\n    /* 隣接行列を出力 */\n    print(): void {\n        console.log('頂点リスト = ', this.vertices);\n        console.log('隣接行列 =', this.adjMat);\n    }\n}\n</code></pre> graph_adjacency_matrix.dart<pre><code>/* 隣接行列に基づく無向グラフクラス */\nclass GraphAdjMat {\n  List&lt;int&gt; vertices = []; // 頂点要素。要素は「頂点値」を表し、インデックスは「頂点インデックス」を表す\n  List&lt;List&lt;int&gt;&gt; adjMat = []; // 隣接行列。行・列のインデックスは「頂点インデックス」に対応\n\n  /* コンストラクタ */\n  GraphAdjMat(List&lt;int&gt; vertices, List&lt;List&lt;int&gt;&gt; edges) {\n    this.vertices = [];\n    this.adjMat = [];\n    // 頂点を追加\n    for (int val in vertices) {\n      addVertex(val);\n    }\n    // 辺を追加\n    // 注意：edges の各要素は頂点インデックスを表し、vertices の要素インデックスに対応する\n    for (List&lt;int&gt; e in edges) {\n      addEdge(e[0], e[1]);\n    }\n  }\n\n  /* 頂点数を取得 */\n  int size() {\n    return vertices.length;\n  }\n\n  /* 頂点を追加 */\n  void addVertex(int val) {\n    int n = size();\n    // 頂点リストに新しい頂点の値を追加\n    vertices.add(val);\n    // 隣接行列に 1 行追加\n    List&lt;int&gt; newRow = List.filled(n, 0, growable: true);\n    adjMat.add(newRow);\n    // 隣接行列に 1 列追加\n    for (List&lt;int&gt; row in adjMat) {\n      row.add(0);\n    }\n  }\n\n  /* 頂点を削除 */\n  void removeVertex(int index) {\n    if (index &gt;= size()) {\n      throw IndexError;\n    }\n    // 頂点リストから index の頂点を削除する\n    vertices.removeAt(index);\n    // 隣接行列で index 行を削除する\n    adjMat.removeAt(index);\n    // 隣接行列で index 列を削除する\n    for (List&lt;int&gt; row in adjMat) {\n      row.removeAt(index);\n    }\n  }\n\n  /* 辺を追加 */\n  // 引数 i, j は vertices の要素インデックスに対応する\n  void addEdge(int i, int j) {\n    // インデックスの範囲外と等値の処理\n    if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j) {\n      throw IndexError;\n    }\n    // 無向グラフでは、隣接行列は主対角線に関して対称、すなわち (i, j) == (j, i) を満たす\n    adjMat[i][j] = 1;\n    adjMat[j][i] = 1;\n  }\n\n  /* 辺を削除 */\n  // 引数 i, j は vertices の要素インデックスに対応する\n  void removeEdge(int i, int j) {\n    // インデックスの範囲外と等値の処理\n    if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j) {\n      throw IndexError;\n    }\n    adjMat[i][j] = 0;\n    adjMat[j][i] = 0;\n  }\n\n  /* 隣接行列を出力 */\n  void printAdjMat() {\n    print(\"頂点リスト = $vertices\");\n    print(\"隣接行列 = \");\n    printMatrix(adjMat);\n  }\n}\n</code></pre> graph_adjacency_matrix.rs<pre><code>/* 隣接行列に基づく無向グラフ型 */\npub struct GraphAdjMat {\n    // 頂点リスト。要素は「頂点値」、インデックスは「頂点インデックス」を表す\n    pub vertices: Vec&lt;i32&gt;,\n    // 隣接行列。行・列のインデックスは「頂点インデックス」に対応\n    pub adj_mat: Vec&lt;Vec&lt;i32&gt;&gt;,\n}\n\nimpl GraphAdjMat {\n    /* コンストラクタ */\n    pub fn new(vertices: Vec&lt;i32&gt;, edges: Vec&lt;[usize; 2]&gt;) -&gt; Self {\n        let mut graph = GraphAdjMat {\n            vertices: vec![],\n            adj_mat: vec![],\n        };\n        // 頂点を追加\n        for val in vertices {\n            graph.add_vertex(val);\n        }\n        // 辺を追加\n        // 注意：edges の各要素は頂点インデックスを表し、vertices の要素インデックスに対応する\n        for edge in edges {\n            graph.add_edge(edge[0], edge[1])\n        }\n\n        graph\n    }\n\n    /* 頂点数を取得 */\n    pub fn size(&amp;self) -&gt; usize {\n        self.vertices.len()\n    }\n\n    /* 頂点を追加 */\n    pub fn add_vertex(&amp;mut self, val: i32) {\n        let n = self.size();\n        // 頂点リストに新しい頂点の値を追加\n        self.vertices.push(val);\n        // 隣接行列に 1 行追加\n        self.adj_mat.push(vec![0; n]);\n        // 隣接行列に 1 列追加\n        for row in self.adj_mat.iter_mut() {\n            row.push(0);\n        }\n    }\n\n    /* 頂点を削除 */\n    pub fn remove_vertex(&amp;mut self, index: usize) {\n        if index &gt;= self.size() {\n            panic!(\"index error\")\n        }\n        // 頂点リストから index の頂点を削除する\n        self.vertices.remove(index);\n        // 隣接行列で index 行を削除する\n        self.adj_mat.remove(index);\n        // 隣接行列で index 列を削除する\n        for row in self.adj_mat.iter_mut() {\n            row.remove(index);\n        }\n    }\n\n    /* 辺を追加 */\n    pub fn add_edge(&amp;mut self, i: usize, j: usize) {\n        // パラメータ i, j は vertices の要素インデックスに対応する\n        // 範囲外と同値の場合の処理\n        if i &gt;= self.size() || j &gt;= self.size() || i == j {\n            panic!(\"index error\")\n        }\n        // 無向グラフでは、隣接行列は主対角線に関して対称、すなわち (i, j) == (j, i) を満たす\n        self.adj_mat[i][j] = 1;\n        self.adj_mat[j][i] = 1;\n    }\n\n    /* 辺を削除 */\n    // 引数 i, j は vertices の要素インデックスに対応する\n    pub fn remove_edge(&amp;mut self, i: usize, j: usize) {\n        // パラメータ i, j は vertices の要素インデックスに対応する\n        // 範囲外と同値の場合の処理\n        if i &gt;= self.size() || j &gt;= self.size() || i == j {\n            panic!(\"index error\")\n        }\n        self.adj_mat[i][j] = 0;\n        self.adj_mat[j][i] = 0;\n    }\n\n    /* 隣接行列を出力 */\n    pub fn print(&amp;self) {\n        println!(\"頂点リスト = {:?}\", self.vertices);\n        println!(\"隣接行列 =\");\n        println!(\"[\");\n        for row in &amp;self.adj_mat {\n            println!(\"  {:?},\", row);\n        }\n        println!(\"]\")\n    }\n}\n</code></pre> graph_adjacency_matrix.c<pre><code>/* 隣接行列に基づく無向グラフ構造体 */\ntypedef struct {\n    int vertices[MAX_SIZE];\n    int adjMat[MAX_SIZE][MAX_SIZE];\n    int size;\n} GraphAdjMat;\n\n/* コンストラクタ */\nGraphAdjMat *newGraphAdjMat() {\n    GraphAdjMat *graph = (GraphAdjMat *)malloc(sizeof(GraphAdjMat));\n    graph-&gt;size = 0;\n    for (int i = 0; i &lt; MAX_SIZE; i++) {\n        for (int j = 0; j &lt; MAX_SIZE; j++) {\n            graph-&gt;adjMat[i][j] = 0;\n        }\n    }\n    return graph;\n}\n\n/* デストラクタ */\nvoid delGraphAdjMat(GraphAdjMat *graph) {\n    free(graph);\n}\n\n/* 頂点を追加 */\nvoid addVertex(GraphAdjMat *graph, int val) {\n    if (graph-&gt;size == MAX_SIZE) {\n        fprintf(stderr, \"グラフの頂点数が最大値に達しました\\n\");\n        return;\n    }\n    // n 番目の頂点を追加し、n 行目と n 列目を 0 にする\n    int n = graph-&gt;size;\n    graph-&gt;vertices[n] = val;\n    for (int i = 0; i &lt;= n; i++) {\n        graph-&gt;adjMat[n][i] = graph-&gt;adjMat[i][n] = 0;\n    }\n    graph-&gt;size++;\n}\n\n/* 頂点を削除 */\nvoid removeVertex(GraphAdjMat *graph, int index) {\n    if (index &lt; 0 || index &gt;= graph-&gt;size) {\n        fprintf(stderr, \"頂点インデックスが範囲外です\\n\");\n        return;\n    }\n    // 頂点リストから index の頂点を削除する\n    for (int i = index; i &lt; graph-&gt;size - 1; i++) {\n        graph-&gt;vertices[i] = graph-&gt;vertices[i + 1];\n    }\n    // 隣接行列で index 行を削除する\n    for (int i = index; i &lt; graph-&gt;size - 1; i++) {\n        for (int j = 0; j &lt; graph-&gt;size; j++) {\n            graph-&gt;adjMat[i][j] = graph-&gt;adjMat[i + 1][j];\n        }\n    }\n    // 隣接行列で index 列を削除する\n    for (int i = 0; i &lt; graph-&gt;size; i++) {\n        for (int j = index; j &lt; graph-&gt;size - 1; j++) {\n            graph-&gt;adjMat[i][j] = graph-&gt;adjMat[i][j + 1];\n        }\n    }\n    graph-&gt;size--;\n}\n\n/* 辺を追加 */\n// 引数 i, j は vertices の要素インデックスに対応する\nvoid addEdge(GraphAdjMat *graph, int i, int j) {\n    if (i &lt; 0 || j &lt; 0 || i &gt;= graph-&gt;size || j &gt;= graph-&gt;size || i == j) {\n        fprintf(stderr, \"辺インデックスが範囲外であるか、同一です\\n\");\n        return;\n    }\n    graph-&gt;adjMat[i][j] = 1;\n    graph-&gt;adjMat[j][i] = 1;\n}\n\n/* 辺を削除 */\n// 引数 i, j は vertices の要素インデックスに対応する\nvoid removeEdge(GraphAdjMat *graph, int i, int j) {\n    if (i &lt; 0 || j &lt; 0 || i &gt;= graph-&gt;size || j &gt;= graph-&gt;size || i == j) {\n        fprintf(stderr, \"辺インデックスが範囲外であるか、同一です\\n\");\n        return;\n    }\n    graph-&gt;adjMat[i][j] = 0;\n    graph-&gt;adjMat[j][i] = 0;\n}\n\n/* 隣接行列を出力 */\nvoid printGraphAdjMat(GraphAdjMat *graph) {\n    printf(\"頂点リスト = \");\n    printArray(graph-&gt;vertices, graph-&gt;size);\n    printf(\"隣接行列 =\\n\");\n    for (int i = 0; i &lt; graph-&gt;size; i++) {\n        printArray(graph-&gt;adjMat[i], graph-&gt;size);\n    }\n}\n</code></pre> graph_adjacency_matrix.kt<pre><code>/* 隣接行列に基づく無向グラフクラス */\nclass GraphAdjMat(vertices: IntArray, edges: Array&lt;IntArray&gt;) {\n    val vertices = mutableListOf&lt;Int&gt;() // 頂点リスト。要素は「頂点値」、インデックスは「頂点インデックス」を表す\n    val adjMat = mutableListOf&lt;MutableList&lt;Int&gt;&gt;() // 隣接行列。行・列のインデックスは「頂点インデックス」に対応\n\n    /* コンストラクタ */\n    init {\n        // 頂点を追加\n        for (vertex in vertices) {\n            addVertex(vertex)\n        }\n        // 辺を追加\n        // 注意：edges の各要素は頂点インデックスを表し、vertices の要素インデックスに対応する\n        for (edge in edges) {\n            addEdge(edge[0], edge[1])\n        }\n    }\n\n    /* 頂点数を取得 */\n    fun size(): Int {\n        return vertices.size\n    }\n\n    /* 頂点を追加 */\n    fun addVertex(_val: Int) {\n        val n = size()\n        // 頂点リストに新しい頂点の値を追加\n        vertices.add(_val)\n        // 隣接行列に 1 行追加\n        val newRow = mutableListOf&lt;Int&gt;()\n        for (j in 0..&lt;n) {\n            newRow.add(0)\n        }\n        adjMat.add(newRow)\n        // 隣接行列に 1 列追加\n        for (row in adjMat) {\n            row.add(0)\n        }\n    }\n\n    /* 頂点を削除 */\n    fun removeVertex(index: Int) {\n        if (index &gt;= size())\n            throw IndexOutOfBoundsException()\n        // 頂点リストから index の頂点を削除する\n        vertices.removeAt(index)\n        // 隣接行列で index 行を削除する\n        adjMat.removeAt(index)\n        // 隣接行列で index 列を削除する\n        for (row in adjMat) {\n            row.removeAt(index)\n        }\n    }\n\n    /* 辺を追加 */\n    // 引数 i, j は vertices の要素インデックスに対応する\n    fun addEdge(i: Int, j: Int) {\n        // インデックスの範囲外と等値の処理\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j)\n            throw IndexOutOfBoundsException()\n        // 無向グラフでは、隣接行列は主対角線に関して対称、すなわち (i, j) == (j, i) を満たす\n        adjMat[i][j] = 1\n        adjMat[j][i] = 1\n    }\n\n    /* 辺を削除 */\n    // 引数 i, j は vertices の要素インデックスに対応する\n    fun removeEdge(i: Int, j: Int) {\n        // インデックスの範囲外と等値の処理\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j)\n            throw IndexOutOfBoundsException()\n        adjMat[i][j] = 0\n        adjMat[j][i] = 0\n    }\n\n    /* 隣接行列を出力 */\n    fun print() {\n        print(\"頂点リスト = \")\n        println(vertices)\n        println(\"隣接行列 =\")\n        printMatrix(adjMat)\n    }\n}\n</code></pre> graph_adjacency_matrix.rb<pre><code>### 隣接行列で実装した無向グラフクラス ###\nclass GraphAdjMat\n  def initialize(vertices, edges)\n    ### コンストラクタ ###\n    # 頂点リスト。要素は「頂点値」、インデックスは「頂点インデックス」を表す\n    @vertices = []\n    # 隣接行列。行・列のインデックスは「頂点インデックス」に対応\n    @adj_mat = []\n    # 頂点を追加\n    vertices.each { |val| add_vertex(val) }\n    # 辺を追加\n    # 注意：edges の各要素は頂点インデックスを表し、vertices の要素インデックスに対応する\n    edges.each { |e| add_edge(e[0], e[1]) }\n  end\n\n  ### 頂点数を取得 ###\n  def size\n    @vertices.length\n  end\n\n  ### 頂点を追加 ###\n  def add_vertex(val)\n    n = size\n    # 頂点リストに新しい頂点の値を追加\n    @vertices &lt;&lt; val\n    # 隣接行列に 1 行追加\n    new_row = Array.new(n, 0)\n    @adj_mat &lt;&lt; new_row\n    # 隣接行列に 1 列追加\n    @adj_mat.each { |row| row &lt;&lt; 0 }\n  end\n\n  ### 頂点を削除 ###\n  def remove_vertex(index)\n    raise IndexError if index &gt;= size\n\n    # 頂点リストから index の頂点を削除する\n    @vertices.delete_at(index)\n    # 隣接行列で index 行を削除する\n    @adj_mat.delete_at(index)\n    # 隣接行列で index 列を削除する\n    @adj_mat.each { |row| row.delete_at(index) }\n  end\n\n  ### 辺を追加 ###\n  def add_edge(i, j)\n    # パラメータ i, j は vertices の要素インデックスに対応する\n    # 範囲外と同値の場合の処理\n    if i &lt; 0 || j &lt; 0 || i &gt;= size || j &gt;= size || i == j\n      raise IndexError\n    end\n    # 無向グラフでは、隣接行列は主対角線に関して対称、すなわち (i, j) == (j, i) を満たす\n    @adj_mat[i][j] = 1\n    @adj_mat[j][i] = 1\n  end\n\n  ### 辺を削除 ###\n  def remove_edge(i, j)\n    # パラメータ i, j は vertices の要素インデックスに対応する\n    # 範囲外と同値の場合の処理\n    if i &lt; 0 || j &lt; 0 || i &gt;= size || j &gt;= size || i == j\n      raise IndexError\n    end\n    @adj_mat[i][j] = 0\n    @adj_mat[j][i] = 0\n  end\n\n  ### 隣接行列を出力 ###\n  def __print__\n    puts \"頂点リスト = #{@vertices}\"\n    puts '隣接行列 ='\n    print_matrix(@adj_mat)\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 9 章 &nbsp; グラフ","9.2 &nbsp; グラフの基本操作"],"tags":[]},{"location":"chapter_graph/graph_operations/#922","level":2,"title":"9.2.2   隣接リストに基づく実装","text":"<p>無向グラフの頂点総数を \\(n\\)、辺総数を \\(m\\) とすると、各種操作は次図の方法で実装できます。</p> <ul> <li>辺の追加：頂点に対応する連結リストの末尾に辺を追加すればよく、\\(O(1)\\) 時間です。無向グラフなので、2 方向の辺を同時に追加する必要があります。</li> <li>辺の削除：頂点に対応する連結リストから指定した辺を探して削除するため、\\(O(m)\\) 時間です。無向グラフでは、2 方向の辺を同時に削除する必要があります。</li> <li>頂点の追加：隣接リストに 1 つの連結リストを追加し、新しい頂点をその連結リストの先頭ノードとするため、\\(O(1)\\) 時間です。</li> <li>頂点の削除：隣接リスト全体を走査し、指定した頂点を含むすべての辺を削除する必要があるため、\\(O(n + m)\\) 時間です。</li> <li>初期化：隣接リストに \\(n\\) 個の頂点と \\(2m\\) 本の辺を作成するため、\\(O(n + m)\\) 時間です。</li> </ul> 隣接リストの初期化辺の追加辺の削除頂点の追加頂点の削除 <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 9-8   隣接リストの初期化、辺の追加と削除、頂点の追加と削除 </p> <p>以下は隣接リストのコード実装です。上図と比べると、実際のコードには次の違いがあります。</p> <ul> <li>頂点の追加と削除を容易にし、コードを簡潔にするため、連結リストの代わりにリスト（動的配列）を使用しています。</li> <li>ハッシュテーブルを用いて隣接リストを格納しており、<code>key</code> は頂点インスタンス、<code>value</code> はその頂点に隣接する頂点のリスト（連結リスト）です。</li> </ul> <p>また、隣接リストでは頂点を表すために <code>Vertex</code> クラスを使用しています。その理由は、もし隣接行列と同様にリストのインデックスで異なる頂点を区別すると、インデックス \\(i\\) の頂点を削除する場合、隣接リスト全体を走査して、\\(i\\) より大きいすべてのインデックスを \\(1\\) 減らす必要があり、効率が非常に低いためです。これに対して、各頂点が一意な <code>Vertex</code> インスタンスであれば、ある頂点を削除しても他の頂点を変更する必要はありません。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby graph_adjacency_list.py<pre><code>class GraphAdjList:\n    \"\"\"隣接リストに基づく無向グラフクラス\"\"\"\n\n    def __init__(self, edges: list[list[Vertex]]):\n        \"\"\"コンストラクタ\"\"\"\n        # 隣接リスト。key は頂点、value はその頂点に隣接する全頂点\n        self.adj_list = dict[Vertex, list[Vertex]]()\n        # すべての頂点と辺を追加\n        for edge in edges:\n            self.add_vertex(edge[0])\n            self.add_vertex(edge[1])\n            self.add_edge(edge[0], edge[1])\n\n    def size(self) -&gt; int:\n        \"\"\"頂点数を取得\"\"\"\n        return len(self.adj_list)\n\n    def add_edge(self, vet1: Vertex, vet2: Vertex):\n        \"\"\"辺を追加\"\"\"\n        if vet1 not in self.adj_list or vet2 not in self.adj_list or vet1 == vet2:\n            raise ValueError()\n        # 辺 vet1 - vet2 を追加\n        self.adj_list[vet1].append(vet2)\n        self.adj_list[vet2].append(vet1)\n\n    def remove_edge(self, vet1: Vertex, vet2: Vertex):\n        \"\"\"辺を削除\"\"\"\n        if vet1 not in self.adj_list or vet2 not in self.adj_list or vet1 == vet2:\n            raise ValueError()\n        # 辺 vet1 - vet2 を削除\n        self.adj_list[vet1].remove(vet2)\n        self.adj_list[vet2].remove(vet1)\n\n    def add_vertex(self, vet: Vertex):\n        \"\"\"頂点を追加\"\"\"\n        if vet in self.adj_list:\n            return\n        # 隣接リストに新しいリストを追加\n        self.adj_list[vet] = []\n\n    def remove_vertex(self, vet: Vertex):\n        \"\"\"頂点を削除\"\"\"\n        if vet not in self.adj_list:\n            raise ValueError()\n        # 隣接リストから頂点 vet に対応するリストを削除\n        self.adj_list.pop(vet)\n        # 他の頂点のリストを走査し、vet を含むすべての辺を削除\n        for vertex in self.adj_list:\n            if vet in self.adj_list[vertex]:\n                self.adj_list[vertex].remove(vet)\n\n    def print(self):\n        \"\"\"隣接リストを出力\"\"\"\n        print(\"隣接リスト =\")\n        for vertex in self.adj_list:\n            tmp = [v.val for v in self.adj_list[vertex]]\n            print(f\"{vertex.val}: {tmp},\")\n</code></pre> graph_adjacency_list.cpp<pre><code>/* 隣接リストに基づく無向グラフクラス */\nclass GraphAdjList {\n  public:\n    // 隣接リスト。key は頂点、value はその頂点に隣接する全頂点\n    unordered_map&lt;Vertex *, vector&lt;Vertex *&gt;&gt; adjList;\n\n    /* vector 内の指定ノードを削除 */\n    void remove(vector&lt;Vertex *&gt; &amp;vec, Vertex *vet) {\n        for (int i = 0; i &lt; vec.size(); i++) {\n            if (vec[i] == vet) {\n                vec.erase(vec.begin() + i);\n                break;\n            }\n        }\n    }\n\n    /* コンストラクタ */\n    GraphAdjList(const vector&lt;vector&lt;Vertex *&gt;&gt; &amp;edges) {\n        // すべての頂点と辺を追加\n        for (const vector&lt;Vertex *&gt; &amp;edge : edges) {\n            addVertex(edge[0]);\n            addVertex(edge[1]);\n            addEdge(edge[0], edge[1]);\n        }\n    }\n\n    /* 頂点数を取得 */\n    int size() {\n        return adjList.size();\n    }\n\n    /* 辺を追加 */\n    void addEdge(Vertex *vet1, Vertex *vet2) {\n        if (!adjList.count(vet1) || !adjList.count(vet2) || vet1 == vet2)\n            throw invalid_argument(\"頂点が存在しません\");\n        // 辺 vet1 - vet2 を追加\n        adjList[vet1].push_back(vet2);\n        adjList[vet2].push_back(vet1);\n    }\n\n    /* 辺を削除 */\n    void removeEdge(Vertex *vet1, Vertex *vet2) {\n        if (!adjList.count(vet1) || !adjList.count(vet2) || vet1 == vet2)\n            throw invalid_argument(\"頂点が存在しません\");\n        // 辺 vet1 - vet2 を削除\n        remove(adjList[vet1], vet2);\n        remove(adjList[vet2], vet1);\n    }\n\n    /* 頂点を追加 */\n    void addVertex(Vertex *vet) {\n        if (adjList.count(vet))\n            return;\n        // 隣接リストに新しいリストを追加\n        adjList[vet] = vector&lt;Vertex *&gt;();\n    }\n\n    /* 頂点を削除 */\n    void removeVertex(Vertex *vet) {\n        if (!adjList.count(vet))\n            throw invalid_argument(\"頂点が存在しません\");\n        // 隣接リストから頂点 vet に対応するリストを削除\n        adjList.erase(vet);\n        // 他の頂点のリストを走査し、vet を含むすべての辺を削除\n        for (auto &amp;adj : adjList) {\n            remove(adj.second, vet);\n        }\n    }\n\n    /* 隣接リストを出力 */\n    void print() {\n        cout &lt;&lt; \"隣接リスト =\" &lt;&lt; endl;\n        for (auto &amp;adj : adjList) {\n            const auto &amp;key = adj.first;\n            const auto &amp;vec = adj.second;\n            cout &lt;&lt; key-&gt;val &lt;&lt; \": \";\n            printVector(vetsToVals(vec));\n        }\n    }\n};\n</code></pre> graph_adjacency_list.java<pre><code>/* 隣接リストに基づく無向グラフクラス */\nclass GraphAdjList {\n    // 隣接リスト。key は頂点、value はその頂点に隣接する全頂点\n    Map&lt;Vertex, List&lt;Vertex&gt;&gt; adjList;\n\n    /* コンストラクタ */\n    public GraphAdjList(Vertex[][] edges) {\n        this.adjList = new HashMap&lt;&gt;();\n        // すべての頂点と辺を追加\n        for (Vertex[] edge : edges) {\n            addVertex(edge[0]);\n            addVertex(edge[1]);\n            addEdge(edge[0], edge[1]);\n        }\n    }\n\n    /* 頂点数を取得 */\n    public int size() {\n        return adjList.size();\n    }\n\n    /* 辺を追加 */\n    public void addEdge(Vertex vet1, Vertex vet2) {\n        if (!adjList.containsKey(vet1) || !adjList.containsKey(vet2) || vet1 == vet2)\n            throw new IllegalArgumentException();\n        // 辺 vet1 - vet2 を追加\n        adjList.get(vet1).add(vet2);\n        adjList.get(vet2).add(vet1);\n    }\n\n    /* 辺を削除 */\n    public void removeEdge(Vertex vet1, Vertex vet2) {\n        if (!adjList.containsKey(vet1) || !adjList.containsKey(vet2) || vet1 == vet2)\n            throw new IllegalArgumentException();\n        // 辺 vet1 - vet2 を削除\n        adjList.get(vet1).remove(vet2);\n        adjList.get(vet2).remove(vet1);\n    }\n\n    /* 頂点を追加 */\n    public void addVertex(Vertex vet) {\n        if (adjList.containsKey(vet))\n            return;\n        // 隣接リストに新しいリストを追加\n        adjList.put(vet, new ArrayList&lt;&gt;());\n    }\n\n    /* 頂点を削除 */\n    public void removeVertex(Vertex vet) {\n        if (!adjList.containsKey(vet))\n            throw new IllegalArgumentException();\n        // 隣接リストから頂点 vet に対応するリストを削除\n        adjList.remove(vet);\n        // 他の頂点のリストを走査し、vet を含むすべての辺を削除\n        for (List&lt;Vertex&gt; list : adjList.values()) {\n            list.remove(vet);\n        }\n    }\n\n    /* 隣接リストを出力 */\n    public void print() {\n        System.out.println(\"隣接リスト =\");\n        for (Map.Entry&lt;Vertex, List&lt;Vertex&gt;&gt; pair : adjList.entrySet()) {\n            List&lt;Integer&gt; tmp = new ArrayList&lt;&gt;();\n            for (Vertex vertex : pair.getValue())\n                tmp.add(vertex.val);\n            System.out.println(pair.getKey().val + \": \" + tmp + \",\");\n        }\n    }\n}\n</code></pre> graph_adjacency_list.cs<pre><code>/* 隣接リストに基づく無向グラフクラス */\nclass GraphAdjList {\n    // 隣接リスト。key は頂点、value はその頂点に隣接する全頂点\n    public Dictionary&lt;Vertex, List&lt;Vertex&gt;&gt; adjList;\n\n    /* コンストラクタ */\n    public GraphAdjList(Vertex[][] edges) {\n        adjList = [];\n        // すべての頂点と辺を追加\n        foreach (Vertex[] edge in edges) {\n            AddVertex(edge[0]);\n            AddVertex(edge[1]);\n            AddEdge(edge[0], edge[1]);\n        }\n    }\n\n    /* 頂点数を取得 */\n    int Size() {\n        return adjList.Count;\n    }\n\n    /* 辺を追加 */\n    public void AddEdge(Vertex vet1, Vertex vet2) {\n        if (!adjList.ContainsKey(vet1) || !adjList.ContainsKey(vet2) || vet1 == vet2)\n            throw new InvalidOperationException();\n        // 辺 vet1 - vet2 を追加\n        adjList[vet1].Add(vet2);\n        adjList[vet2].Add(vet1);\n    }\n\n    /* 辺を削除 */\n    public void RemoveEdge(Vertex vet1, Vertex vet2) {\n        if (!adjList.ContainsKey(vet1) || !adjList.ContainsKey(vet2) || vet1 == vet2)\n            throw new InvalidOperationException();\n        // 辺 vet1 - vet2 を削除\n        adjList[vet1].Remove(vet2);\n        adjList[vet2].Remove(vet1);\n    }\n\n    /* 頂点を追加 */\n    public void AddVertex(Vertex vet) {\n        if (adjList.ContainsKey(vet))\n            return;\n        // 隣接リストに新しいリストを追加\n        adjList.Add(vet, []);\n    }\n\n    /* 頂点を削除 */\n    public void RemoveVertex(Vertex vet) {\n        if (!adjList.ContainsKey(vet))\n            throw new InvalidOperationException();\n        // 隣接リストから頂点 vet に対応するリストを削除\n        adjList.Remove(vet);\n        // 他の頂点のリストを走査し、vet を含むすべての辺を削除\n        foreach (List&lt;Vertex&gt; list in adjList.Values) {\n            list.Remove(vet);\n        }\n    }\n\n    /* 隣接リストを出力 */\n    public void Print() {\n        Console.WriteLine(\"隣接リスト =\");\n        foreach (KeyValuePair&lt;Vertex, List&lt;Vertex&gt;&gt; pair in adjList) {\n            List&lt;int&gt; tmp = [];\n            foreach (Vertex vertex in pair.Value)\n                tmp.Add(vertex.val);\n            Console.WriteLine(pair.Key.val + \": [\" + string.Join(\", \", tmp) + \"],\");\n        }\n    }\n}\n</code></pre> graph_adjacency_list.go<pre><code>/* 隣接リストに基づく無向グラフクラス */\ntype graphAdjList struct {\n    // 隣接リスト。key は頂点、value はその頂点に隣接する全頂点\n    adjList map[Vertex][]Vertex\n}\n\n/* コンストラクタ */\nfunc newGraphAdjList(edges [][]Vertex) *graphAdjList {\n    g := &amp;graphAdjList{\n        adjList: make(map[Vertex][]Vertex),\n    }\n    // すべての頂点と辺を追加\n    for _, edge := range edges {\n        g.addVertex(edge[0])\n        g.addVertex(edge[1])\n        g.addEdge(edge[0], edge[1])\n    }\n    return g\n}\n\n/* 頂点数を取得 */\nfunc (g *graphAdjList) size() int {\n    return len(g.adjList)\n}\n\n/* 辺を追加 */\nfunc (g *graphAdjList) addEdge(vet1 Vertex, vet2 Vertex) {\n    _, ok1 := g.adjList[vet1]\n    _, ok2 := g.adjList[vet2]\n    if !ok1 || !ok2 || vet1 == vet2 {\n        panic(\"error\")\n    }\n    // 辺 `vet1 - vet2` を追加し、無名 `struct{}` を追加する\n    g.adjList[vet1] = append(g.adjList[vet1], vet2)\n    g.adjList[vet2] = append(g.adjList[vet2], vet1)\n}\n\n/* 辺を削除 */\nfunc (g *graphAdjList) removeEdge(vet1 Vertex, vet2 Vertex) {\n    _, ok1 := g.adjList[vet1]\n    _, ok2 := g.adjList[vet2]\n    if !ok1 || !ok2 || vet1 == vet2 {\n        panic(\"error\")\n    }\n    // 辺 vet1 - vet2 を削除\n    g.adjList[vet1] = DeleteSliceElms(g.adjList[vet1], vet2)\n    g.adjList[vet2] = DeleteSliceElms(g.adjList[vet2], vet1)\n}\n\n/* 頂点を追加 */\nfunc (g *graphAdjList) addVertex(vet Vertex) {\n    _, ok := g.adjList[vet]\n    if ok {\n        return\n    }\n    // 隣接リストに新しいリストを追加\n    g.adjList[vet] = make([]Vertex, 0)\n}\n\n/* 頂点を削除 */\nfunc (g *graphAdjList) removeVertex(vet Vertex) {\n    _, ok := g.adjList[vet]\n    if !ok {\n        panic(\"error\")\n    }\n    // 隣接リストから頂点 vet に対応するリストを削除\n    delete(g.adjList, vet)\n    // 他の頂点のリストを走査し、vet を含むすべての辺を削除\n    for v, list := range g.adjList {\n        g.adjList[v] = DeleteSliceElms(list, vet)\n    }\n}\n\n/* 隣接リストを出力 */\nfunc (g *graphAdjList) print() {\n    var builder strings.Builder\n    fmt.Printf(\"隣接リスト = \\n\")\n    for k, v := range g.adjList {\n        builder.WriteString(\"\\t\\t\" + strconv.Itoa(k.Val) + \": \")\n        for _, vet := range v {\n            builder.WriteString(strconv.Itoa(vet.Val) + \" \")\n        }\n        fmt.Println(builder.String())\n        builder.Reset()\n    }\n}\n</code></pre> graph_adjacency_list.swift<pre><code>/* 隣接リストに基づく無向グラフクラス */\nclass GraphAdjList {\n    // 隣接リスト。key は頂点、value はその頂点に隣接する全頂点\n    public private(set) var adjList: [Vertex: [Vertex]]\n\n    /* コンストラクタ */\n    public init(edges: [[Vertex]]) {\n        adjList = [:]\n        // すべての頂点と辺を追加\n        for edge in edges {\n            addVertex(vet: edge[0])\n            addVertex(vet: edge[1])\n            addEdge(vet1: edge[0], vet2: edge[1])\n        }\n    }\n\n    /* 頂点数を取得 */\n    public func size() -&gt; Int {\n        adjList.count\n    }\n\n    /* 辺を追加 */\n    public func addEdge(vet1: Vertex, vet2: Vertex) {\n        if adjList[vet1] == nil || adjList[vet2] == nil || vet1 == vet2 {\n            fatalError(\"引数エラー\")\n        }\n        // 辺 vet1 - vet2 を追加\n        adjList[vet1]?.append(vet2)\n        adjList[vet2]?.append(vet1)\n    }\n\n    /* 辺を削除 */\n    public func removeEdge(vet1: Vertex, vet2: Vertex) {\n        if adjList[vet1] == nil || adjList[vet2] == nil || vet1 == vet2 {\n            fatalError(\"引数エラー\")\n        }\n        // 辺 vet1 - vet2 を削除\n        adjList[vet1]?.removeAll { $0 == vet2 }\n        adjList[vet2]?.removeAll { $0 == vet1 }\n    }\n\n    /* 頂点を追加 */\n    public func addVertex(vet: Vertex) {\n        if adjList[vet] != nil {\n            return\n        }\n        // 隣接リストに新しいリストを追加\n        adjList[vet] = []\n    }\n\n    /* 頂点を削除 */\n    public func removeVertex(vet: Vertex) {\n        if adjList[vet] == nil {\n            fatalError(\"引数エラー\")\n        }\n        // 隣接リストから頂点 vet に対応するリストを削除\n        adjList.removeValue(forKey: vet)\n        // 他の頂点のリストを走査し、vet を含むすべての辺を削除\n        for key in adjList.keys {\n            adjList[key]?.removeAll { $0 == vet }\n        }\n    }\n\n    /* 隣接リストを出力 */\n    public func print() {\n        Swift.print(\"隣接リスト =\")\n        for (vertex, list) in adjList {\n            let list = list.map { $0.val }\n            Swift.print(\"\\(vertex.val): \\(list),\")\n        }\n    }\n}\n</code></pre> graph_adjacency_list.js<pre><code>/* 隣接リストに基づく無向グラフクラス */\nclass GraphAdjList {\n    // 隣接リスト。key は頂点、value はその頂点に隣接する全頂点\n    adjList;\n\n    /* コンストラクタ */\n    constructor(edges) {\n        this.adjList = new Map();\n        // すべての頂点と辺を追加\n        for (const edge of edges) {\n            this.addVertex(edge[0]);\n            this.addVertex(edge[1]);\n            this.addEdge(edge[0], edge[1]);\n        }\n    }\n\n    /* 頂点数を取得 */\n    size() {\n        return this.adjList.size;\n    }\n\n    /* 辺を追加 */\n    addEdge(vet1, vet2) {\n        if (\n            !this.adjList.has(vet1) ||\n            !this.adjList.has(vet2) ||\n            vet1 === vet2\n        ) {\n            throw new Error('Illegal Argument Exception');\n        }\n        // 辺 vet1 - vet2 を追加\n        this.adjList.get(vet1).push(vet2);\n        this.adjList.get(vet2).push(vet1);\n    }\n\n    /* 辺を削除 */\n    removeEdge(vet1, vet2) {\n        if (\n            !this.adjList.has(vet1) ||\n            !this.adjList.has(vet2) ||\n            vet1 === vet2 ||\n            this.adjList.get(vet1).indexOf(vet2) === -1\n        ) {\n            throw new Error('Illegal Argument Exception');\n        }\n        // 辺 vet1 - vet2 を削除\n        this.adjList.get(vet1).splice(this.adjList.get(vet1).indexOf(vet2), 1);\n        this.adjList.get(vet2).splice(this.adjList.get(vet2).indexOf(vet1), 1);\n    }\n\n    /* 頂点を追加 */\n    addVertex(vet) {\n        if (this.adjList.has(vet)) return;\n        // 隣接リストに新しいリストを追加\n        this.adjList.set(vet, []);\n    }\n\n    /* 頂点を削除 */\n    removeVertex(vet) {\n        if (!this.adjList.has(vet)) {\n            throw new Error('Illegal Argument Exception');\n        }\n        // 隣接リストから頂点 vet に対応するリストを削除\n        this.adjList.delete(vet);\n        // 他の頂点のリストを走査し、vet を含むすべての辺を削除\n        for (const set of this.adjList.values()) {\n            const index = set.indexOf(vet);\n            if (index &gt; -1) {\n                set.splice(index, 1);\n            }\n        }\n    }\n\n    /* 隣接リストを出力 */\n    print() {\n        console.log('隣接リスト =');\n        for (const [key, value] of this.adjList) {\n            const tmp = [];\n            for (const vertex of value) {\n                tmp.push(vertex.val);\n            }\n            console.log(key.val + ': ' + tmp.join());\n        }\n    }\n}\n</code></pre> graph_adjacency_list.ts<pre><code>/* 隣接リストに基づく無向グラフクラス */\nclass GraphAdjList {\n    // 隣接リスト。key は頂点、value はその頂点に隣接する全頂点\n    adjList: Map&lt;Vertex, Vertex[]&gt;;\n\n    /* コンストラクタ */\n    constructor(edges: Vertex[][]) {\n        this.adjList = new Map();\n        // すべての頂点と辺を追加\n        for (const edge of edges) {\n            this.addVertex(edge[0]);\n            this.addVertex(edge[1]);\n            this.addEdge(edge[0], edge[1]);\n        }\n    }\n\n    /* 頂点数を取得 */\n    size(): number {\n        return this.adjList.size;\n    }\n\n    /* 辺を追加 */\n    addEdge(vet1: Vertex, vet2: Vertex): void {\n        if (\n            !this.adjList.has(vet1) ||\n            !this.adjList.has(vet2) ||\n            vet1 === vet2\n        ) {\n            throw new Error('Illegal Argument Exception');\n        }\n        // 辺 vet1 - vet2 を追加\n        this.adjList.get(vet1).push(vet2);\n        this.adjList.get(vet2).push(vet1);\n    }\n\n    /* 辺を削除 */\n    removeEdge(vet1: Vertex, vet2: Vertex): void {\n        if (\n            !this.adjList.has(vet1) ||\n            !this.adjList.has(vet2) ||\n            vet1 === vet2 ||\n            this.adjList.get(vet1).indexOf(vet2) === -1\n        ) {\n            throw new Error('Illegal Argument Exception');\n        }\n        // 辺 vet1 - vet2 を削除\n        this.adjList.get(vet1).splice(this.adjList.get(vet1).indexOf(vet2), 1);\n        this.adjList.get(vet2).splice(this.adjList.get(vet2).indexOf(vet1), 1);\n    }\n\n    /* 頂点を追加 */\n    addVertex(vet: Vertex): void {\n        if (this.adjList.has(vet)) return;\n        // 隣接リストに新しいリストを追加\n        this.adjList.set(vet, []);\n    }\n\n    /* 頂点を削除 */\n    removeVertex(vet: Vertex): void {\n        if (!this.adjList.has(vet)) {\n            throw new Error('Illegal Argument Exception');\n        }\n        // 隣接リストから頂点 vet に対応するリストを削除\n        this.adjList.delete(vet);\n        // 他の頂点のリストを走査し、vet を含むすべての辺を削除\n        for (const set of this.adjList.values()) {\n            const index: number = set.indexOf(vet);\n            if (index &gt; -1) {\n                set.splice(index, 1);\n            }\n        }\n    }\n\n    /* 隣接リストを出力 */\n    print(): void {\n        console.log('隣接リスト =');\n        for (const [key, value] of this.adjList.entries()) {\n            const tmp = [];\n            for (const vertex of value) {\n                tmp.push(vertex.val);\n            }\n            console.log(key.val + ': ' + tmp.join());\n        }\n    }\n}\n</code></pre> graph_adjacency_list.dart<pre><code>/* 隣接リストに基づく無向グラフクラス */\nclass GraphAdjList {\n  // 隣接リスト。key は頂点、value はその頂点に隣接する全頂点\n  Map&lt;Vertex, List&lt;Vertex&gt;&gt; adjList = {};\n\n  /* コンストラクタ */\n  GraphAdjList(List&lt;List&lt;Vertex&gt;&gt; edges) {\n    for (List&lt;Vertex&gt; edge in edges) {\n      addVertex(edge[0]);\n      addVertex(edge[1]);\n      addEdge(edge[0], edge[1]);\n    }\n  }\n\n  /* 頂点数を取得 */\n  int size() {\n    return adjList.length;\n  }\n\n  /* 辺を追加 */\n  void addEdge(Vertex vet1, Vertex vet2) {\n    if (!adjList.containsKey(vet1) ||\n        !adjList.containsKey(vet2) ||\n        vet1 == vet2) {\n      throw ArgumentError;\n    }\n    // 辺 vet1 - vet2 を追加\n    adjList[vet1]!.add(vet2);\n    adjList[vet2]!.add(vet1);\n  }\n\n  /* 辺を削除 */\n  void removeEdge(Vertex vet1, Vertex vet2) {\n    if (!adjList.containsKey(vet1) ||\n        !adjList.containsKey(vet2) ||\n        vet1 == vet2) {\n      throw ArgumentError;\n    }\n    // 辺 vet1 - vet2 を削除\n    adjList[vet1]!.remove(vet2);\n    adjList[vet2]!.remove(vet1);\n  }\n\n  /* 頂点を追加 */\n  void addVertex(Vertex vet) {\n    if (adjList.containsKey(vet)) return;\n    // 隣接リストに新しいリストを追加\n    adjList[vet] = [];\n  }\n\n  /* 頂点を削除 */\n  void removeVertex(Vertex vet) {\n    if (!adjList.containsKey(vet)) {\n      throw ArgumentError;\n    }\n    // 隣接リストから頂点 vet に対応するリストを削除\n    adjList.remove(vet);\n    // 他の頂点のリストを走査し、vet を含むすべての辺を削除\n    adjList.forEach((key, value) {\n      value.remove(vet);\n    });\n  }\n\n  /* 隣接リストを出力 */\n  void printAdjList() {\n    print(\"隣接リスト =\");\n    adjList.forEach((key, value) {\n      List&lt;int&gt; tmp = [];\n      for (Vertex vertex in value) {\n        tmp.add(vertex.val);\n      }\n      print(\"${key.val}: $tmp,\");\n    });\n  }\n}\n</code></pre> graph_adjacency_list.rs<pre><code>/* 隣接リストに基づく無向グラフ型 */\npub struct GraphAdjList {\n    // 隣接リスト。key は頂点、value はその頂点に隣接する全頂点\n    pub adj_list: HashMap&lt;Vertex, Vec&lt;Vertex&gt;&gt;, // maybe HashSet&lt;Vertex&gt; for value part is better?\n}\n\nimpl GraphAdjList {\n    /* コンストラクタ */\n    pub fn new(edges: Vec&lt;[Vertex; 2]&gt;) -&gt; Self {\n        let mut graph = GraphAdjList {\n            adj_list: HashMap::new(),\n        };\n        // すべての頂点と辺を追加\n        for edge in edges {\n            graph.add_vertex(edge[0]);\n            graph.add_vertex(edge[1]);\n            graph.add_edge(edge[0], edge[1]);\n        }\n\n        graph\n    }\n\n    /* 頂点数を取得 */\n    #[allow(unused)]\n    pub fn size(&amp;self) -&gt; usize {\n        self.adj_list.len()\n    }\n\n    /* 辺を追加 */\n    pub fn add_edge(&amp;mut self, vet1: Vertex, vet2: Vertex) {\n        if vet1 == vet2 {\n            panic!(\"value error\");\n        }\n        // 辺 vet1 - vet2 を追加\n        self.adj_list.entry(vet1).or_default().push(vet2);\n        self.adj_list.entry(vet2).or_default().push(vet1);\n    }\n\n    /* 辺を削除 */\n    #[allow(unused)]\n    pub fn remove_edge(&amp;mut self, vet1: Vertex, vet2: Vertex) {\n        if vet1 == vet2 {\n            panic!(\"value error\");\n        }\n        // 辺 vet1 - vet2 を削除\n        self.adj_list\n            .entry(vet1)\n            .and_modify(|v| v.retain(|&amp;e| e != vet2));\n        self.adj_list\n            .entry(vet2)\n            .and_modify(|v| v.retain(|&amp;e| e != vet1));\n    }\n\n    /* 頂点を追加 */\n    pub fn add_vertex(&amp;mut self, vet: Vertex) {\n        if self.adj_list.contains_key(&amp;vet) {\n            return;\n        }\n        // 隣接リストに新しいリストを追加\n        self.adj_list.insert(vet, vec![]);\n    }\n\n    /* 頂点を削除 */\n    #[allow(unused)]\n    pub fn remove_vertex(&amp;mut self, vet: Vertex) {\n        // 隣接リストから頂点 vet に対応するリストを削除\n        self.adj_list.remove(&amp;vet);\n        // 他の頂点のリストを走査し、vet を含むすべての辺を削除\n        for list in self.adj_list.values_mut() {\n            list.retain(|&amp;v| v != vet);\n        }\n    }\n\n    /* 隣接リストを出力 */\n    pub fn print(&amp;self) {\n        println!(\"隣接リスト =\");\n        for (vertex, list) in &amp;self.adj_list {\n            let list = list.iter().map(|vertex| vertex.val).collect::&lt;Vec&lt;i32&gt;&gt;();\n            println!(\"{}: {:?},\", vertex.val, list);\n        }\n    }\n}\n</code></pre> graph_adjacency_list.c<pre><code>/* ノード構造体 */\ntypedef struct AdjListNode {\n    Vertex *vertex;           // 頂点\n    struct AdjListNode *next; // 後続ノード\n} AdjListNode;\n\n/* 頂点に対応するノードを検索 */\nAdjListNode *findNode(GraphAdjList *graph, Vertex *vet) {\n    for (int i = 0; i &lt; graph-&gt;size; i++) {\n        if (graph-&gt;heads[i]-&gt;vertex == vet) {\n            return graph-&gt;heads[i];\n        }\n    }\n    return NULL;\n}\n\n/* 辺を追加する補助関数 */\nvoid addEdgeHelper(AdjListNode *head, Vertex *vet) {\n    AdjListNode *node = (AdjListNode *)malloc(sizeof(AdjListNode));\n    node-&gt;vertex = vet;\n    // 先頭挿入法\n    node-&gt;next = head-&gt;next;\n    head-&gt;next = node;\n}\n\n/* 辺削除の補助関数 */\nvoid removeEdgeHelper(AdjListNode *head, Vertex *vet) {\n    AdjListNode *pre = head;\n    AdjListNode *cur = head-&gt;next;\n    // 連結リスト内で vet に対応するノードを探索\n    while (cur != NULL &amp;&amp; cur-&gt;vertex != vet) {\n        pre = cur;\n        cur = cur-&gt;next;\n    }\n    if (cur == NULL)\n        return;\n    // vet に対応するノードを連結リストから削除\n    pre-&gt;next = cur-&gt;next;\n    // メモリを解放する\n    free(cur);\n}\n\n/* 隣接リストに基づく無向グラフクラス */\ntypedef struct {\n    AdjListNode *heads[MAX_SIZE]; // ノード配列\n    int size;                     // ノード数\n} GraphAdjList;\n\n/* コンストラクタ */\nGraphAdjList *newGraphAdjList() {\n    GraphAdjList *graph = (GraphAdjList *)malloc(sizeof(GraphAdjList));\n    if (!graph) {\n        return NULL;\n    }\n    graph-&gt;size = 0;\n    for (int i = 0; i &lt; MAX_SIZE; i++) {\n        graph-&gt;heads[i] = NULL;\n    }\n    return graph;\n}\n\n/* デストラクタ */\nvoid delGraphAdjList(GraphAdjList *graph) {\n    for (int i = 0; i &lt; graph-&gt;size; i++) {\n        AdjListNode *cur = graph-&gt;heads[i];\n        while (cur != NULL) {\n            AdjListNode *next = cur-&gt;next;\n            if (cur != graph-&gt;heads[i]) {\n                free(cur);\n            }\n            cur = next;\n        }\n        free(graph-&gt;heads[i]-&gt;vertex);\n        free(graph-&gt;heads[i]);\n    }\n    free(graph);\n}\n\n/* 頂点に対応するノードを検索 */\nAdjListNode *findNode(GraphAdjList *graph, Vertex *vet) {\n    for (int i = 0; i &lt; graph-&gt;size; i++) {\n        if (graph-&gt;heads[i]-&gt;vertex == vet) {\n            return graph-&gt;heads[i];\n        }\n    }\n    return NULL;\n}\n\n/* 辺を追加 */\nvoid addEdge(GraphAdjList *graph, Vertex *vet1, Vertex *vet2) {\n    AdjListNode *head1 = findNode(graph, vet1);\n    AdjListNode *head2 = findNode(graph, vet2);\n    assert(head1 != NULL &amp;&amp; head2 != NULL &amp;&amp; head1 != head2);\n    // 辺 vet1 - vet2 を追加\n    addEdgeHelper(head1, vet2);\n    addEdgeHelper(head2, vet1);\n}\n\n/* 辺を削除 */\nvoid removeEdge(GraphAdjList *graph, Vertex *vet1, Vertex *vet2) {\n    AdjListNode *head1 = findNode(graph, vet1);\n    AdjListNode *head2 = findNode(graph, vet2);\n    assert(head1 != NULL &amp;&amp; head2 != NULL);\n    // 辺 vet1 - vet2 を削除\n    removeEdgeHelper(head1, head2-&gt;vertex);\n    removeEdgeHelper(head2, head1-&gt;vertex);\n}\n\n/* 頂点を追加 */\nvoid addVertex(GraphAdjList *graph, Vertex *vet) {\n    assert(graph != NULL &amp;&amp; graph-&gt;size &lt; MAX_SIZE);\n    AdjListNode *head = (AdjListNode *)malloc(sizeof(AdjListNode));\n    head-&gt;vertex = vet;\n    head-&gt;next = NULL;\n    // 隣接リストに新しいリストを追加\n    graph-&gt;heads[graph-&gt;size++] = head;\n}\n\n/* 頂点を削除 */\nvoid removeVertex(GraphAdjList *graph, Vertex *vet) {\n    AdjListNode *node = findNode(graph, vet);\n    assert(node != NULL);\n    // 隣接リストから頂点 vet に対応するリストを削除\n    AdjListNode *cur = node, *pre = NULL;\n    while (cur) {\n        pre = cur;\n        cur = cur-&gt;next;\n        free(pre);\n    }\n    // 他の頂点のリストを走査し、vet を含むすべての辺を削除\n    for (int i = 0; i &lt; graph-&gt;size; i++) {\n        cur = graph-&gt;heads[i];\n        pre = NULL;\n        while (cur) {\n            pre = cur;\n            cur = cur-&gt;next;\n            if (cur &amp;&amp; cur-&gt;vertex == vet) {\n                pre-&gt;next = cur-&gt;next;\n                free(cur);\n                break;\n            }\n        }\n    }\n    // この頂点より後ろの頂点を前に詰めて欠損を埋める\n    int i;\n    for (i = 0; i &lt; graph-&gt;size; i++) {\n        if (graph-&gt;heads[i] == node)\n            break;\n    }\n    for (int j = i; j &lt; graph-&gt;size - 1; j++) {\n        graph-&gt;heads[j] = graph-&gt;heads[j + 1];\n    }\n    graph-&gt;size--;\n    free(vet);\n}\n</code></pre> graph_adjacency_list.kt<pre><code>/* 隣接リストに基づく無向グラフクラス */\nclass GraphAdjList(edges: Array&lt;Array&lt;Vertex?&gt;&gt;) {\n    // 隣接リスト。key は頂点、value はその頂点に隣接する全頂点\n    val adjList = HashMap&lt;Vertex, MutableList&lt;Vertex&gt;&gt;()\n\n    /* コンストラクタ */\n    init {\n        // すべての頂点と辺を追加\n        for (edge in edges) {\n            addVertex(edge[0]!!)\n            addVertex(edge[1]!!)\n            addEdge(edge[0]!!, edge[1]!!)\n        }\n    }\n\n    /* 頂点数を取得 */\n    fun size(): Int {\n        return adjList.size\n    }\n\n    /* 辺を追加 */\n    fun addEdge(vet1: Vertex, vet2: Vertex) {\n        if (!adjList.containsKey(vet1) || !adjList.containsKey(vet2) || vet1 == vet2)\n            throw IllegalArgumentException()\n        // 辺 vet1 - vet2 を追加\n        adjList[vet1]?.add(vet2)\n        adjList[vet2]?.add(vet1)\n    }\n\n    /* 辺を削除 */\n    fun removeEdge(vet1: Vertex, vet2: Vertex) {\n        if (!adjList.containsKey(vet1) || !adjList.containsKey(vet2) || vet1 == vet2)\n            throw IllegalArgumentException()\n        // 辺 vet1 - vet2 を削除\n        adjList[vet1]?.remove(vet2)\n        adjList[vet2]?.remove(vet1)\n    }\n\n    /* 頂点を追加 */\n    fun addVertex(vet: Vertex) {\n        if (adjList.containsKey(vet))\n            return\n        // 隣接リストに新しいリストを追加\n        adjList[vet] = mutableListOf()\n    }\n\n    /* 頂点を削除 */\n    fun removeVertex(vet: Vertex) {\n        if (!adjList.containsKey(vet))\n            throw IllegalArgumentException()\n        // 隣接リストから頂点 vet に対応するリストを削除\n        adjList.remove(vet)\n        // 他の頂点のリストを走査し、vet を含むすべての辺を削除\n        for (list in adjList.values) {\n            list.remove(vet)\n        }\n    }\n\n    /* 隣接リストを出力 */\n    fun print() {\n        println(\"隣接リスト =\")\n        for (pair in adjList.entries) {\n            val tmp = mutableListOf&lt;Int&gt;()\n            for (vertex in pair.value) {\n                tmp.add(vertex._val)\n            }\n            println(\"${pair.key._val}: $tmp,\")\n        }\n    }\n}\n</code></pre> graph_adjacency_list.rb<pre><code>### 隣接リストで実装した無向グラフクラス ###\nclass GraphAdjList\n  attr_reader :adj_list\n\n  ### コンストラクタ ###\n  def initialize(edges)\n    # 隣接リスト。key は頂点、value はその頂点に隣接する全頂点\n    @adj_list = {}\n    # すべての頂点と辺を追加\n    for edge in edges\n      add_vertex(edge[0])\n      add_vertex(edge[1])\n      add_edge(edge[0], edge[1])\n    end\n  end\n\n  ### 頂点数を取得 ###\n  def size\n    @adj_list.length\n  end\n\n  ### 辺を追加 ###\n  def add_edge(vet1, vet2)\n    raise ArgumentError if !@adj_list.include?(vet1) || !@adj_list.include?(vet2)\n\n    @adj_list[vet1] &lt;&lt; vet2\n    @adj_list[vet2] &lt;&lt; vet1\n  end\n\n  ### 辺を削除 ###\n  def remove_edge(vet1, vet2)\n    raise ArgumentError if !@adj_list.include?(vet1) || !@adj_list.include?(vet2)\n\n    # 辺 vet1 - vet2 を削除\n    @adj_list[vet1].delete(vet2)\n    @adj_list[vet2].delete(vet1)\n  end\n\n  ### 頂点を追加 ###\n  def add_vertex(vet)\n    return if @adj_list.include?(vet)\n\n    # 隣接リストに新しいリストを追加\n    @adj_list[vet] = []\n  end\n\n  ### 頂点を削除 ###\n  def remove_vertex(vet)\n    raise ArgumentError unless @adj_list.include?(vet)\n\n    # 隣接リストから頂点 vet に対応するリストを削除\n    @adj_list.delete(vet)\n    # 他の頂点のリストを走査し、vet を含むすべての辺を削除\n    for vertex in @adj_list\n      @adj_list[vertex.first].delete(vet) if @adj_list[vertex.first].include?(vet)\n    end\n  end\n\n  ### 隣接リストを出力 ###\n  def __print__\n    puts '隣接リスト ='\n    for vertex in @adj_list\n      tmp = @adj_list[vertex.first].map { |v| v.val }\n      puts \"#{vertex.first.val}: #{tmp},\"\n    end\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 9 章 &nbsp; グラフ","9.2 &nbsp; グラフの基本操作"],"tags":[]},{"location":"chapter_graph/graph_operations/#923","level":2,"title":"9.2.3   効率の比較","text":"<p>グラフに \\(n\\) 個の頂点と \\(m\\) 本の辺があるとすると、次の表は隣接行列と隣接リストの時間効率および空間効率を比較したものです。なお、隣接リスト（連結リスト）は本記事の実装に対応し、隣接リスト（ハッシュテーブル）はすべての連結リストをハッシュテーブルに置き換えた実装を指します。</p> <p> 表 9-2   隣接行列と隣接リストの比較 </p> 隣接行列 隣接リスト（連結リスト） 隣接リスト（ハッシュテーブル） 隣接判定 \\(O(1)\\) \\(O(n)\\) \\(O(1)\\) 辺の追加 \\(O(1)\\) \\(O(1)\\) \\(O(1)\\) 辺の削除 \\(O(1)\\) \\(O(n)\\) \\(O(1)\\) 頂点の追加 \\(O(n)\\) \\(O(1)\\) \\(O(1)\\) 頂点の削除 \\(O(n^2)\\) \\(O(n + m)\\) \\(O(n)\\) メモリ使用量 \\(O(n^2)\\) \\(O(n + m)\\) \\(O(n + m)\\) <p>上表を見ると、隣接リスト（ハッシュテーブル）の時間効率と空間効率が最も優れているように見えます。しかし実際には、隣接行列のほうが辺の操作効率は高く、必要なのは 1 回の配列アクセスまたは代入だけです。総合的に見ると、隣接行列は「空間を時間と引き換えにする」原則を体現し、隣接リストは「時間を空間と引き換えにする」原則を体現しています。</p>","path":["第 9 章 &nbsp; グラフ","9.2 &nbsp; グラフの基本操作"],"tags":[]},{"location":"chapter_graph/graph_traversal/","level":1,"title":"9.3   グラフの走査","text":"<p>木は「一対多」の関係を表すのに対し、グラフはより高い自由度を持ち、任意の「多対多」の関係を表現できます。したがって、木はグラフの一種の特殊な場合とみなせます。明らかに、木の走査操作もグラフの走査操作の一種の特殊な場合です。</p> <p>グラフと木はいずれも、走査操作を実現するために探索アルゴリズムを用いる必要があります。グラフの走査方法も、幅優先走査と深さ優先走査の 2 種類に分けられます。</p>","path":["第 9 章 &nbsp; グラフ","9.3 &nbsp; グラフの走査"],"tags":[]},{"location":"chapter_graph/graph_traversal/#931","level":2,"title":"9.3.1   幅優先走査","text":"<p>幅優先走査は、近いところから遠いところへ向かう走査方法であり、ある頂点から出発して、常に最も近い頂点を優先して訪問し、層ごとに外側へ広がっていきます。以下の図に示すように、左上の頂点から出発し、まずその頂点のすべての隣接頂点を走査し、次に次の頂点のすべての隣接頂点を走査し、これを繰り返して、すべての頂点を訪問するまで続けます。</p> <p></p> <p> 図 9-9   グラフの幅優先走査 </p>","path":["第 9 章 &nbsp; グラフ","9.3 &nbsp; グラフの走査"],"tags":[]},{"location":"chapter_graph/graph_traversal/#1","level":3,"title":"1.   アルゴリズムの実装","text":"<p>BFS は通常キューを用いて実装され、コードは以下のとおりです。キューは「先入れ先出し」という性質を持ち、これは BFS の「近いところから遠いところへ」という考え方と本質的に一致しています。</p> <ol> <li>走査の開始頂点 <code>startVet</code> をキューに追加し、ループを開始します。</li> <li>ループの各反復で、キュー先頭の頂点を取り出して訪問を記録し、その後その頂点のすべての隣接頂点をキューの末尾に追加します。</li> <li>手順 <code>2.</code> を繰り返し、すべての頂点が訪問されると終了します。</li> </ol> <p>頂点の重複走査を防ぐために、どの頂点が訪問済みかを記録するハッシュ集合 <code>visited</code> を用います。</p> <p>Tip</p> <p>ハッシュ集合は、<code>value</code> を持たず <code>key</code> だけを格納するハッシュテーブルとみなせます。これは \\(O(1)\\) の時間計算量で <code>key</code> の追加・削除・検索・更新を行えます。<code>key</code> の一意性にもとづき、ハッシュ集合は通常、データの重複排除などの場面で用いられます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby graph_bfs.py<pre><code>def graph_bfs(graph: GraphAdjList, start_vet: Vertex) -&gt; list[Vertex]:\n    \"\"\"幅優先探索\"\"\"\n    # 指定した頂点の隣接頂点をすべて取得できるよう、隣接リストでグラフを表現する\n    # 頂点の走査順序\n    res = []\n    # 訪問済み頂点を記録するためのハッシュ集合\n    visited = set[Vertex]([start_vet])\n    # BFS の実装にキューを用いる\n    que = deque[Vertex]([start_vet])\n    # 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す\n    while len(que) &gt; 0:\n        vet = que.popleft()  # 先頭の頂点をデキュー\n        res.append(vet)  # 訪問した頂点を記録\n        # この頂点のすべての隣接頂点を走査\n        for adj_vet in graph.adj_list[vet]:\n            if adj_vet in visited:\n                continue  # 訪問済みの頂点をスキップ\n            que.append(adj_vet)  # 未訪問の頂点のみをキューに追加\n            visited.add(adj_vet)  # この頂点を訪問済みにする\n    # 頂点の走査順を返す\n    return res\n</code></pre> graph_bfs.cpp<pre><code>/* 幅優先探索 */\n// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする\nvector&lt;Vertex *&gt; graphBFS(GraphAdjList &amp;graph, Vertex *startVet) {\n    // 頂点の走査順序\n    vector&lt;Vertex *&gt; res;\n    // 訪問済み頂点を記録するためのハッシュ集合\n    unordered_set&lt;Vertex *&gt; visited = {startVet};\n    // BFS の実装にキューを用いる\n    queue&lt;Vertex *&gt; que;\n    que.push(startVet);\n    // 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す\n    while (!que.empty()) {\n        Vertex *vet = que.front();\n        que.pop();          // 先頭の頂点をデキュー\n        res.push_back(vet); // 訪問した頂点を記録\n        // この頂点のすべての隣接頂点を走査\n        for (auto adjVet : graph.adjList[vet]) {\n            if (visited.count(adjVet))\n                continue;            // 訪問済みの頂点をスキップ\n            que.push(adjVet);        // 未訪問の頂点のみをキューに追加\n            visited.emplace(adjVet); // この頂点を訪問済みにする\n        }\n    }\n    // 頂点の走査順を返す\n    return res;\n}\n</code></pre> graph_bfs.java<pre><code>/* 幅優先探索 */\n// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする\nList&lt;Vertex&gt; graphBFS(GraphAdjList graph, Vertex startVet) {\n    // 頂点の走査順序\n    List&lt;Vertex&gt; res = new ArrayList&lt;&gt;();\n    // 訪問済み頂点を記録するためのハッシュ集合\n    Set&lt;Vertex&gt; visited = new HashSet&lt;&gt;();\n    visited.add(startVet);\n    // BFS の実装にキューを用いる\n    Queue&lt;Vertex&gt; que = new LinkedList&lt;&gt;();\n    que.offer(startVet);\n    // 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す\n    while (!que.isEmpty()) {\n        Vertex vet = que.poll(); // 先頭の頂点をデキュー\n        res.add(vet);            // 訪問した頂点を記録\n        // この頂点のすべての隣接頂点を走査\n        for (Vertex adjVet : graph.adjList.get(vet)) {\n            if (visited.contains(adjVet))\n                continue;        // 訪問済みの頂点をスキップ\n            que.offer(adjVet);   // 未訪問の頂点のみをキューに追加\n            visited.add(adjVet); // この頂点を訪問済みにする\n        }\n    }\n    // 頂点の走査順を返す\n    return res;\n}\n</code></pre> graph_bfs.cs<pre><code>/* 幅優先探索 */\n// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする\nList&lt;Vertex&gt; GraphBFS(GraphAdjList graph, Vertex startVet) {\n    // 頂点の走査順序\n    List&lt;Vertex&gt; res = [];\n    // 訪問済み頂点を記録するためのハッシュ集合\n    HashSet&lt;Vertex&gt; visited = [startVet];\n    // BFS の実装にキューを用いる\n    Queue&lt;Vertex&gt; que = new();\n    que.Enqueue(startVet);\n    // 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す\n    while (que.Count &gt; 0) {\n        Vertex vet = que.Dequeue(); // 先頭の頂点をデキュー\n        res.Add(vet);               // 訪問した頂点を記録\n        foreach (Vertex adjVet in graph.adjList[vet]) {\n            if (visited.Contains(adjVet)) {\n                continue;          // 訪問済みの頂点をスキップ\n            }\n            que.Enqueue(adjVet);   // 未訪問の頂点のみをキューに追加\n            visited.Add(adjVet);   // この頂点を訪問済みにする\n        }\n    }\n\n    // 頂点の走査順を返す\n    return res;\n}\n</code></pre> graph_bfs.go<pre><code>/* 幅優先探索 */\n// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする\nfunc graphBFS(g *graphAdjList, startVet Vertex) []Vertex {\n    // 頂点の走査順序\n    res := make([]Vertex, 0)\n    // 訪問済み頂点を記録するためのハッシュ集合\n    visited := make(map[Vertex]struct{})\n    visited[startVet] = struct{}{}\n    // キューは BFS の実装に用い、スライスでキューをシミュレートする\n    queue := make([]Vertex, 0)\n    queue = append(queue, startVet)\n    // 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す\n    for len(queue) &gt; 0 {\n        // 先頭の頂点をデキュー\n        vet := queue[0]\n        queue = queue[1:]\n        // 訪問した頂点を記録\n        res = append(res, vet)\n        // この頂点のすべての隣接頂点を走査\n        for _, adjVet := range g.adjList[vet] {\n            _, isExist := visited[adjVet]\n            // 未訪問の頂点のみをキューに追加\n            if !isExist {\n                queue = append(queue, adjVet)\n                visited[adjVet] = struct{}{}\n            }\n        }\n    }\n    // 頂点の走査順を返す\n    return res\n}\n</code></pre> graph_bfs.swift<pre><code>/* 幅優先探索 */\n// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする\nfunc graphBFS(graph: GraphAdjList, startVet: Vertex) -&gt; [Vertex] {\n    // 頂点の走査順序\n    var res: [Vertex] = []\n    // 訪問済み頂点を記録するためのハッシュ集合\n    var visited: Set&lt;Vertex&gt; = [startVet]\n    // BFS の実装にキューを用いる\n    var que: [Vertex] = [startVet]\n    // 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す\n    while !que.isEmpty {\n        let vet = que.removeFirst() // 先頭の頂点をデキュー\n        res.append(vet) // 訪問した頂点を記録\n        // この頂点のすべての隣接頂点を走査\n        for adjVet in graph.adjList[vet] ?? [] {\n            if visited.contains(adjVet) {\n                continue // 訪問済みの頂点をスキップ\n            }\n            que.append(adjVet) // 未訪問の頂点のみをキューに追加\n            visited.insert(adjVet) // この頂点を訪問済みにする\n        }\n    }\n    // 頂点の走査順を返す\n    return res\n}\n</code></pre> graph_bfs.js<pre><code>/* 幅優先探索 */\n// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする\nfunction graphBFS(graph, startVet) {\n    // 頂点の走査順序\n    const res = [];\n    // 訪問済み頂点を記録するためのハッシュ集合\n    const visited = new Set();\n    visited.add(startVet);\n    // BFS の実装にキューを用いる\n    const que = [startVet];\n    // 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す\n    while (que.length) {\n        const vet = que.shift(); // 先頭の頂点をデキュー\n        res.push(vet); // 訪問した頂点を記録\n        // この頂点のすべての隣接頂点を走査\n        for (const adjVet of graph.adjList.get(vet) ?? []) {\n            if (visited.has(adjVet)) {\n                continue; // 訪問済みの頂点をスキップ\n            }\n            que.push(adjVet); // 未訪問の頂点のみをキューに追加\n            visited.add(adjVet); // この頂点を訪問済みにする\n        }\n    }\n    // 頂点の走査順を返す\n    return res;\n}\n</code></pre> graph_bfs.ts<pre><code>/* 幅優先探索 */\n// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする\nfunction graphBFS(graph: GraphAdjList, startVet: Vertex): Vertex[] {\n    // 頂点の走査順序\n    const res: Vertex[] = [];\n    // 訪問済み頂点を記録するためのハッシュ集合\n    const visited: Set&lt;Vertex&gt; = new Set();\n    visited.add(startVet);\n    // BFS の実装にキューを用いる\n    const que = [startVet];\n    // 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す\n    while (que.length) {\n        const vet = que.shift(); // 先頭の頂点をデキュー\n        res.push(vet); // 訪問した頂点を記録\n        // この頂点のすべての隣接頂点を走査\n        for (const adjVet of graph.adjList.get(vet) ?? []) {\n            if (visited.has(adjVet)) {\n                continue; // 訪問済みの頂点をスキップ\n            }\n            que.push(adjVet); // 未訪問のものだけをキューに入れる\n            visited.add(adjVet); // この頂点を訪問済みにする\n        }\n    }\n    // 頂点の走査順を返す\n    return res;\n}\n</code></pre> graph_bfs.dart<pre><code>/* 幅優先探索 */\nList&lt;Vertex&gt; graphBFS(GraphAdjList graph, Vertex startVet) {\n  // 指定した頂点の隣接頂点をすべて取得できるよう、隣接リストでグラフを表現する\n  // 頂点の走査順序\n  List&lt;Vertex&gt; res = [];\n  // 訪問済み頂点を記録するためのハッシュ集合\n  Set&lt;Vertex&gt; visited = {};\n  visited.add(startVet);\n  // BFS の実装にキューを用いる\n  Queue&lt;Vertex&gt; que = Queue();\n  que.add(startVet);\n  // 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す\n  while (que.isNotEmpty) {\n    Vertex vet = que.removeFirst(); // 先頭の頂点をデキュー\n    res.add(vet); // 訪問した頂点を記録\n    // この頂点のすべての隣接頂点を走査\n    for (Vertex adjVet in graph.adjList[vet]!) {\n      if (visited.contains(adjVet)) {\n        continue; // 訪問済みの頂点をスキップ\n      }\n      que.add(adjVet); // 未訪問の頂点のみをキューに追加\n      visited.add(adjVet); // この頂点を訪問済みにする\n    }\n  }\n  // 頂点の走査順を返す\n  return res;\n}\n</code></pre> graph_bfs.rs<pre><code>/* 幅優先探索 */\n// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする\nfn graph_bfs(graph: GraphAdjList, start_vet: Vertex) -&gt; Vec&lt;Vertex&gt; {\n    // 頂点の走査順序\n    let mut res = vec![];\n    // 訪問済み頂点を記録するためのハッシュ集合\n    let mut visited = HashSet::new();\n    visited.insert(start_vet);\n    // BFS の実装にキューを用いる\n    let mut que = VecDeque::new();\n    que.push_back(start_vet);\n    // 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す\n    while let Some(vet) = que.pop_front() {\n        res.push(vet); // 訪問した頂点を記録\n\n        // この頂点のすべての隣接頂点を走査\n        if let Some(adj_vets) = graph.adj_list.get(&amp;vet) {\n            for &amp;adj_vet in adj_vets {\n                if visited.contains(&amp;adj_vet) {\n                    continue; // 訪問済みの頂点をスキップ\n                }\n                que.push_back(adj_vet); // 未訪問の頂点のみをキューに追加\n                visited.insert(adj_vet); // この頂点を訪問済みにする\n            }\n        }\n    }\n    // 頂点の走査順を返す\n    res\n}\n</code></pre> graph_bfs.c<pre><code>/* ノードキュー構造体 */\ntypedef struct {\n    Vertex *vertices[MAX_SIZE];\n    int front, rear, size;\n} Queue;\n\n/* コンストラクタ */\nQueue *newQueue() {\n    Queue *q = (Queue *)malloc(sizeof(Queue));\n    q-&gt;front = q-&gt;rear = q-&gt;size = 0;\n    return q;\n}\n\n/* キューが空かどうかを判定 */\nint isEmpty(Queue *q) {\n    return q-&gt;size == 0;\n}\n\n/* エンキュー操作 */\nvoid enqueue(Queue *q, Vertex *vet) {\n    q-&gt;vertices[q-&gt;rear] = vet;\n    q-&gt;rear = (q-&gt;rear + 1) % MAX_SIZE;\n    q-&gt;size++;\n}\n\n/* デキュー操作 */\nVertex *dequeue(Queue *q) {\n    Vertex *vet = q-&gt;vertices[q-&gt;front];\n    q-&gt;front = (q-&gt;front + 1) % MAX_SIZE;\n    q-&gt;size--;\n    return vet;\n}\n\n/* 頂点が訪問済みかを確認 */\nint isVisited(Vertex **visited, int size, Vertex *vet) {\n    // 走査してノードを探すため、O(n) 時間を要する\n    for (int i = 0; i &lt; size; i++) {\n        if (visited[i] == vet)\n            return 1;\n    }\n    return 0;\n}\n\n/* 幅優先探索 */\n// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする\nvoid graphBFS(GraphAdjList *graph, Vertex *startVet, Vertex **res, int *resSize, Vertex **visited, int *visitedSize) {\n    // BFS の実装にキューを用いる\n    Queue *queue = newQueue();\n    enqueue(queue, startVet);\n    visited[(*visitedSize)++] = startVet;\n    // 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す\n    while (!isEmpty(queue)) {\n        Vertex *vet = dequeue(queue); // 先頭の頂点をデキュー\n        res[(*resSize)++] = vet;      // 訪問した頂点を記録\n        // この頂点のすべての隣接頂点を走査\n        AdjListNode *node = findNode(graph, vet);\n        while (node != NULL) {\n            // 訪問済みの頂点をスキップ\n            if (!isVisited(visited, *visitedSize, node-&gt;vertex)) {\n                enqueue(queue, node-&gt;vertex);             // 未訪問の頂点のみをキューに追加\n                visited[(*visitedSize)++] = node-&gt;vertex; // この頂点を訪問済みにする\n            }\n            node = node-&gt;next;\n        }\n    }\n    // メモリを解放する\n    free(queue);\n}\n</code></pre> graph_bfs.kt<pre><code>/* 幅優先探索 */\n// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする\nfun graphBFS(graph: GraphAdjList, startVet: Vertex): MutableList&lt;Vertex?&gt; {\n    // 頂点の走査順序\n    val res = mutableListOf&lt;Vertex?&gt;()\n    // 訪問済み頂点を記録するためのハッシュ集合\n    val visited = HashSet&lt;Vertex&gt;()\n    visited.add(startVet)\n    // BFS の実装にキューを用いる\n    val que = LinkedList&lt;Vertex&gt;()\n    que.offer(startVet)\n    // 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す\n    while (!que.isEmpty()) {\n        val vet = que.poll() // 先頭の頂点をデキュー\n        res.add(vet)         // 訪問した頂点を記録\n        // この頂点のすべての隣接頂点を走査\n        for (adjVet in graph.adjList[vet]!!) {\n            if (visited.contains(adjVet))\n                continue        // 訪問済みの頂点をスキップ\n            que.offer(adjVet)   // 未訪問の頂点のみをキューに追加\n            visited.add(adjVet) // この頂点を訪問済みにする\n        }\n    }\n    // 頂点の走査順を返す\n    return res\n}\n</code></pre> graph_bfs.rb<pre><code>### 幅優先探索 ###\ndef graph_bfs(graph, start_vet)\n  # 指定した頂点の隣接頂点をすべて取得できるよう、隣接リストでグラフを表現する\n  # 頂点の走査順序\n  res = []\n  # 訪問済み頂点を記録するためのハッシュ集合\n  visited = Set.new([start_vet])\n  # BFS の実装にキューを用いる\n  que = [start_vet]\n  # 頂点 vet を起点に、すべての頂点を訪問し終えるまで繰り返す\n  while que.length &gt; 0\n    vet = que.shift # 先頭の頂点をデキュー\n    res &lt;&lt; vet # 訪問した頂点を記録\n    # この頂点のすべての隣接頂点を走査\n    for adj_vet in graph.adj_list[vet]\n      next if visited.include?(adj_vet) # 訪問済みの頂点をスキップ\n      que &lt;&lt; adj_vet # 未訪問の頂点のみをキューに追加\n      visited.add(adj_vet) # この頂点を訪問済みにする\n    end\n  end\n  # 頂点の走査順を返す\n  res\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>コードはやや抽象的なので、以下の図と照らし合わせて理解を深めることを勧めます。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 9-10   グラフの幅優先走査の手順 </p> <p>幅優先走査の順序列は一意ですか？</p> <p>一意ではありません。幅優先走査は「近いところから遠いところへ」の順で走査することだけを要求し、同じ距離にある複数の頂点の走査順は任意に入れ替えて構いません。上図を例にすると、頂点 \\(1\\) と \\(3\\) の訪問順は交換でき、頂点 \\(2\\)、\\(4\\)、\\(6\\) の訪問順も任意に入れ替えられます。</p>","path":["第 9 章 &nbsp; グラフ","9.3 &nbsp; グラフの走査"],"tags":[]},{"location":"chapter_graph/graph_traversal/#2","level":3,"title":"2.   計算量の分析","text":"<p>時間計算量：すべての頂点は 1 回ずつキューに入り、1 回ずつキューから出るため、\\(O(|V|)\\) 時間です。隣接頂点を走査する過程では、無向グラフであるため、すべての辺が \\(2\\) 回訪問され、\\(O(2|E|)\\) 時間です。したがって全体では \\(O(|V| + |E|)\\) 時間です。</p> <p>空間計算量：リスト <code>res</code>、ハッシュ集合 <code>visited</code>、キュー <code>que</code> に含まれる頂点数は最大で \\(|V|\\) であるため、\\(O(|V|)\\) 空間です。</p>","path":["第 9 章 &nbsp; グラフ","9.3 &nbsp; グラフの走査"],"tags":[]},{"location":"chapter_graph/graph_traversal/#932","level":2,"title":"9.3.2   深さ優先走査","text":"<p>深さ優先走査は、まず行けるところまで進み、進めなくなったら戻る走査方法です。以下の図に示すように、左上の頂点から出発し、現在の頂点のある隣接頂点を訪問して、行き止まりに達するまで進んだら戻り、再び別の方向へ進んで行き止まりまで進んで戻る、ということを繰り返し、すべての頂点の走査が完了するまで続けます。</p> <p></p> <p> 図 9-11   グラフの深さ優先走査 </p>","path":["第 9 章 &nbsp; グラフ","9.3 &nbsp; グラフの走査"],"tags":[]},{"location":"chapter_graph/graph_traversal/#1_1","level":3,"title":"1.   アルゴリズムの実装","text":"<p>この「行き止まりまで進んでから戻る」アルゴリズムのパターンは、通常再帰にもとづいて実装されます。幅優先走査と同様に、深さ優先走査でも、頂点の重複訪問を避けるために、訪問済みの頂点を記録するハッシュ集合 <code>visited</code> を用います。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby graph_dfs.py<pre><code>def dfs(graph: GraphAdjList, visited: set[Vertex], res: list[Vertex], vet: Vertex):\n    \"\"\"深さ優先走査の補助関数\"\"\"\n    res.append(vet)  # 訪問した頂点を記録\n    visited.add(vet)  # この頂点を訪問済みにする\n    # この頂点のすべての隣接頂点を走査\n    for adjVet in graph.adj_list[vet]:\n        if adjVet in visited:\n            continue  # 訪問済みの頂点をスキップ\n        # 隣接頂点を再帰的に訪問\n        dfs(graph, visited, res, adjVet)\n\ndef graph_dfs(graph: GraphAdjList, start_vet: Vertex) -&gt; list[Vertex]:\n    \"\"\"深さ優先探索\"\"\"\n    # 指定した頂点の隣接頂点をすべて取得できるよう、隣接リストでグラフを表現する\n    # 頂点の走査順序\n    res = []\n    # 訪問済み頂点を記録するためのハッシュ集合\n    visited = set[Vertex]()\n    dfs(graph, visited, res, start_vet)\n    return res\n</code></pre> graph_dfs.cpp<pre><code>/* 深さ優先走査の補助関数 */\nvoid dfs(GraphAdjList &amp;graph, unordered_set&lt;Vertex *&gt; &amp;visited, vector&lt;Vertex *&gt; &amp;res, Vertex *vet) {\n    res.push_back(vet);   // 訪問した頂点を記録\n    visited.emplace(vet); // この頂点を訪問済みにする\n    // この頂点のすべての隣接頂点を走査\n    for (Vertex *adjVet : graph.adjList[vet]) {\n        if (visited.count(adjVet))\n            continue; // 訪問済みの頂点をスキップ\n        // 隣接頂点を再帰的に訪問\n        dfs(graph, visited, res, adjVet);\n    }\n}\n\n/* 深さ優先探索 */\n// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする\nvector&lt;Vertex *&gt; graphDFS(GraphAdjList &amp;graph, Vertex *startVet) {\n    // 頂点の走査順序\n    vector&lt;Vertex *&gt; res;\n    // 訪問済み頂点を記録するためのハッシュ集合\n    unordered_set&lt;Vertex *&gt; visited;\n    dfs(graph, visited, res, startVet);\n    return res;\n}\n</code></pre> graph_dfs.java<pre><code>/* 深さ優先走査の補助関数 */\nvoid dfs(GraphAdjList graph, Set&lt;Vertex&gt; visited, List&lt;Vertex&gt; res, Vertex vet) {\n    res.add(vet);     // 訪問した頂点を記録\n    visited.add(vet); // この頂点を訪問済みにする\n    // この頂点のすべての隣接頂点を走査\n    for (Vertex adjVet : graph.adjList.get(vet)) {\n        if (visited.contains(adjVet))\n            continue; // 訪問済みの頂点をスキップ\n        // 隣接頂点を再帰的に訪問\n        dfs(graph, visited, res, adjVet);\n    }\n}\n\n/* 深さ優先探索 */\n// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする\nList&lt;Vertex&gt; graphDFS(GraphAdjList graph, Vertex startVet) {\n    // 頂点の走査順序\n    List&lt;Vertex&gt; res = new ArrayList&lt;&gt;();\n    // 訪問済み頂点を記録するためのハッシュ集合\n    Set&lt;Vertex&gt; visited = new HashSet&lt;&gt;();\n    dfs(graph, visited, res, startVet);\n    return res;\n}\n</code></pre> graph_dfs.cs<pre><code>/* 深さ優先走査の補助関数 */\nvoid DFS(GraphAdjList graph, HashSet&lt;Vertex&gt; visited, List&lt;Vertex&gt; res, Vertex vet) {\n    res.Add(vet);     // 訪問した頂点を記録\n    visited.Add(vet); // この頂点を訪問済みにする\n    // この頂点のすべての隣接頂点を走査\n    foreach (Vertex adjVet in graph.adjList[vet]) {\n        if (visited.Contains(adjVet)) {\n            continue; // 訪問済みの頂点をスキップ\n        }\n        // 隣接頂点を再帰的に訪問\n        DFS(graph, visited, res, adjVet);\n    }\n}\n\n/* 深さ優先探索 */\n// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする\nList&lt;Vertex&gt; GraphDFS(GraphAdjList graph, Vertex startVet) {\n    // 頂点の走査順序\n    List&lt;Vertex&gt; res = [];\n    // 訪問済み頂点を記録するためのハッシュ集合\n    HashSet&lt;Vertex&gt; visited = [];\n    DFS(graph, visited, res, startVet);\n    return res;\n}\n</code></pre> graph_dfs.go<pre><code>/* 深さ優先走査の補助関数 */\nfunc dfs(g *graphAdjList, visited map[Vertex]struct{}, res *[]Vertex, vet Vertex) {\n    // append 操作は新しい参照を返すため、元の参照を新しい slice の参照で再代入する必要がある\n    *res = append(*res, vet)\n    visited[vet] = struct{}{}\n    // この頂点のすべての隣接頂点を走査\n    for _, adjVet := range g.adjList[vet] {\n        _, isExist := visited[adjVet]\n        // 隣接頂点を再帰的に訪問\n        if !isExist {\n            dfs(g, visited, res, adjVet)\n        }\n    }\n}\n\n/* 深さ優先探索 */\n// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする\nfunc graphDFS(g *graphAdjList, startVet Vertex) []Vertex {\n    // 頂点の走査順序\n    res := make([]Vertex, 0)\n    // 訪問済み頂点を記録するためのハッシュ集合\n    visited := make(map[Vertex]struct{})\n    dfs(g, visited, &amp;res, startVet)\n    // 頂点の走査順を返す\n    return res\n}\n</code></pre> graph_dfs.swift<pre><code>/* 深さ優先走査の補助関数 */\nfunc dfs(graph: GraphAdjList, visited: inout Set&lt;Vertex&gt;, res: inout [Vertex], vet: Vertex) {\n    res.append(vet) // 訪問した頂点を記録\n    visited.insert(vet) // この頂点を訪問済みにする\n    // この頂点のすべての隣接頂点を走査\n    for adjVet in graph.adjList[vet] ?? [] {\n        if visited.contains(adjVet) {\n            continue // 訪問済みの頂点をスキップ\n        }\n        // 隣接頂点を再帰的に訪問\n        dfs(graph: graph, visited: &amp;visited, res: &amp;res, vet: adjVet)\n    }\n}\n\n/* 深さ優先探索 */\n// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする\nfunc graphDFS(graph: GraphAdjList, startVet: Vertex) -&gt; [Vertex] {\n    // 頂点の走査順序\n    var res: [Vertex] = []\n    // 訪問済み頂点を記録するためのハッシュ集合\n    var visited: Set&lt;Vertex&gt; = []\n    dfs(graph: graph, visited: &amp;visited, res: &amp;res, vet: startVet)\n    return res\n}\n</code></pre> graph_dfs.js<pre><code>/* 深さ優先探索 */\n// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする\nfunction dfs(graph, visited, res, vet) {\n    res.push(vet); // 訪問した頂点を記録\n    visited.add(vet); // この頂点を訪問済みにする\n    // この頂点のすべての隣接頂点を走査\n    for (const adjVet of graph.adjList.get(vet)) {\n        if (visited.has(adjVet)) {\n            continue; // 訪問済みの頂点をスキップ\n        }\n        // 隣接頂点を再帰的に訪問\n        dfs(graph, visited, res, adjVet);\n    }\n}\n\n/* 深さ優先探索 */\n// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする\nfunction graphDFS(graph, startVet) {\n    // 頂点の走査順序\n    const res = [];\n    // 訪問済み頂点を記録するためのハッシュ集合\n    const visited = new Set();\n    dfs(graph, visited, res, startVet);\n    return res;\n}\n</code></pre> graph_dfs.ts<pre><code>/* 深さ優先走査の補助関数 */\nfunction dfs(\n    graph: GraphAdjList,\n    visited: Set&lt;Vertex&gt;,\n    res: Vertex[],\n    vet: Vertex\n): void {\n    res.push(vet); // 訪問した頂点を記録\n    visited.add(vet); // この頂点を訪問済みにする\n    // この頂点のすべての隣接頂点を走査\n    for (const adjVet of graph.adjList.get(vet)) {\n        if (visited.has(adjVet)) {\n            continue; // 訪問済みの頂点をスキップ\n        }\n        // 隣接頂点を再帰的に訪問\n        dfs(graph, visited, res, adjVet);\n    }\n}\n\n/* 深さ優先探索 */\n// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする\nfunction graphDFS(graph: GraphAdjList, startVet: Vertex): Vertex[] {\n    // 頂点の走査順序\n    const res: Vertex[] = [];\n    // 訪問済み頂点を記録するためのハッシュ集合\n    const visited: Set&lt;Vertex&gt; = new Set();\n    dfs(graph, visited, res, startVet);\n    return res;\n}\n</code></pre> graph_dfs.dart<pre><code>/* 深さ優先走査の補助関数 */\nvoid dfs(\n  GraphAdjList graph,\n  Set&lt;Vertex&gt; visited,\n  List&lt;Vertex&gt; res,\n  Vertex vet,\n) {\n  res.add(vet); // 訪問した頂点を記録\n  visited.add(vet); // この頂点を訪問済みにする\n  // この頂点のすべての隣接頂点を走査\n  for (Vertex adjVet in graph.adjList[vet]!) {\n    if (visited.contains(adjVet)) {\n      continue; // 訪問済みの頂点をスキップ\n    }\n    // 隣接頂点を再帰的に訪問\n    dfs(graph, visited, res, adjVet);\n  }\n}\n\n/* 深さ優先探索 */\nList&lt;Vertex&gt; graphDFS(GraphAdjList graph, Vertex startVet) {\n  // 頂点の走査順序\n  List&lt;Vertex&gt; res = [];\n  // 訪問済み頂点を記録するためのハッシュ集合\n  Set&lt;Vertex&gt; visited = {};\n  dfs(graph, visited, res, startVet);\n  return res;\n}\n</code></pre> graph_dfs.rs<pre><code>/* 深さ優先走査の補助関数 */\nfn dfs(graph: &amp;GraphAdjList, visited: &amp;mut HashSet&lt;Vertex&gt;, res: &amp;mut Vec&lt;Vertex&gt;, vet: Vertex) {\n    res.push(vet); // 訪問した頂点を記録\n    visited.insert(vet); // この頂点を訪問済みにする\n                         // この頂点のすべての隣接頂点を走査\n    if let Some(adj_vets) = graph.adj_list.get(&amp;vet) {\n        for &amp;adj_vet in adj_vets {\n            if visited.contains(&amp;adj_vet) {\n                continue; // 訪問済みの頂点をスキップ\n            }\n            // 隣接頂点を再帰的に訪問\n            dfs(graph, visited, res, adj_vet);\n        }\n    }\n}\n\n/* 深さ優先探索 */\n// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする\nfn graph_dfs(graph: GraphAdjList, start_vet: Vertex) -&gt; Vec&lt;Vertex&gt; {\n    // 頂点の走査順序\n    let mut res = vec![];\n    // 訪問済み頂点を記録するためのハッシュ集合\n    let mut visited = HashSet::new();\n    dfs(&amp;graph, &amp;mut visited, &amp;mut res, start_vet);\n\n    res\n}\n</code></pre> graph_dfs.c<pre><code>/* 頂点が訪問済みかを確認 */\nint isVisited(Vertex **res, int size, Vertex *vet) {\n    // 走査してノードを探すため、O(n) 時間を要する\n    for (int i = 0; i &lt; size; i++) {\n        if (res[i] == vet) {\n            return 1;\n        }\n    }\n    return 0;\n}\n\n/* 深さ優先走査の補助関数 */\nvoid dfs(GraphAdjList *graph, Vertex **res, int *resSize, Vertex *vet) {\n    // 訪問した頂点を記録\n    res[(*resSize)++] = vet;\n    // この頂点のすべての隣接頂点を走査\n    AdjListNode *node = findNode(graph, vet);\n    while (node != NULL) {\n        // 訪問済みの頂点をスキップ\n        if (!isVisited(res, *resSize, node-&gt;vertex)) {\n            // 隣接頂点を再帰的に訪問\n            dfs(graph, res, resSize, node-&gt;vertex);\n        }\n        node = node-&gt;next;\n    }\n}\n\n/* 深さ優先探索 */\n// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする\nvoid graphDFS(GraphAdjList *graph, Vertex *startVet, Vertex **res, int *resSize) {\n    dfs(graph, res, resSize, startVet);\n}\n</code></pre> graph_dfs.kt<pre><code>/* 深さ優先走査の補助関数 */\nfun dfs(\n    graph: GraphAdjList,\n    visited: MutableSet&lt;Vertex?&gt;,\n    res: MutableList&lt;Vertex?&gt;,\n    vet: Vertex?\n) {\n    res.add(vet)     // 訪問した頂点を記録\n    visited.add(vet) // この頂点を訪問済みにする\n    // この頂点のすべての隣接頂点を走査\n    for (adjVet in graph.adjList[vet]!!) {\n        if (visited.contains(adjVet))\n            continue  // 訪問済みの頂点をスキップ\n        // 隣接頂点を再帰的に訪問\n        dfs(graph, visited, res, adjVet)\n    }\n}\n\n/* 深さ優先探索 */\n// グラフを隣接リストで表し、指定した頂点の隣接頂点をすべて取得できるようにする\nfun graphDFS(graph: GraphAdjList, startVet: Vertex?): MutableList&lt;Vertex?&gt; {\n    // 頂点の走査順序\n    val res = mutableListOf&lt;Vertex?&gt;()\n    // 訪問済み頂点を記録するためのハッシュ集合\n    val visited = HashSet&lt;Vertex?&gt;()\n    dfs(graph, visited, res, startVet)\n    return res\n}\n</code></pre> graph_dfs.rb<pre><code>### 深さ優先探索の補助関数 ###\ndef dfs(graph, visited, res, vet)\n  res &lt;&lt; vet # 訪問した頂点を記録\n  visited.add(vet) # この頂点を訪問済みにする\n  # この頂点のすべての隣接頂点を走査\n  for adj_vet in graph.adj_list[vet]\n    next if visited.include?(adj_vet) # 訪問済みの頂点をスキップ\n    # 隣接頂点を再帰的に訪問\n    dfs(graph, visited, res, adj_vet)\n  end\nend\n\n### 深さ優先探索 ###\ndef graph_dfs(graph, start_vet)\n  # 指定した頂点の隣接頂点をすべて取得できるよう、隣接リストでグラフを表現する\n  # 頂点の走査順序\n  res = []\n  # 訪問済み頂点を記録するためのハッシュ集合\n  visited = Set.new\n  dfs(graph, visited, res, start_vet)\n  res\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>深さ優先走査のアルゴリズムの流れは以下の図のとおりです。</p> <ul> <li>**直線の破線は下向きの再帰呼び出し**を表し、新しい頂点を訪問するために新たな再帰メソッドが開始されたことを意味します。</li> <li>**曲線の破線は上向きのバックトラック**を表し、この再帰メソッドがすでに戻って、呼び出し元の位置までたどり着いたことを意味します。</li> </ul> <p>理解を深めるために、以下の図とコードを結びつけて、DFS 全体の過程を頭の中でシミュレーションする（あるいは紙に書き出す）ことを勧めます。各再帰メソッドがいつ開始し、いつ戻るかも含めて追ってみてください。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 9-12   グラフの深さ優先走査の手順 </p> <p>深さ優先走査の順序列は一意ですか？</p> <p>幅優先走査と同様に、深さ優先走査の順序列も一意ではありません。ある頂点が与えられたとき、どの方向を先に探索してもよく、つまり隣接頂点の順序は任意に入れ替えられ、それでも深さ優先走査になります。</p> <p>木の走査を例にすると、「根 \\(\\rightarrow\\) 左 \\(\\rightarrow\\) 右」「左 \\(\\rightarrow\\) 根 \\(\\rightarrow\\) 右」「左 \\(\\rightarrow\\) 右 \\(\\rightarrow\\) 根」は、それぞれ先行順、中間順、後行順走査に対応します。これらは 3 種類の走査優先順位を示していますが、いずれも深さ優先走査に属します。</p>","path":["第 9 章 &nbsp; グラフ","9.3 &nbsp; グラフの走査"],"tags":[]},{"location":"chapter_graph/graph_traversal/#2_1","level":3,"title":"2.   計算量の分析","text":"<p>時間計算量：すべての頂点は \\(1\\) 回ずつ訪問されるため、\\(O(|V|)\\) 時間です。すべての辺は \\(2\\) 回ずつ訪問されるため、\\(O(2|E|)\\) 時間です。したがって全体では \\(O(|V| + |E|)\\) 時間です。</p> <p>空間計算量：リスト <code>res</code> とハッシュ集合 <code>visited</code> に含まれる頂点数は最大で \\(|V|\\) であり、再帰の深さも最大で \\(|V|\\) であるため、\\(O(|V|)\\) 空間です。</p>","path":["第 9 章 &nbsp; グラフ","9.3 &nbsp; グラフの走査"],"tags":[]},{"location":"chapter_graph/summary/","level":1,"title":"9.4   まとめ","text":"","path":["第 9 章 &nbsp; グラフ","9.4 &nbsp; まとめ"],"tags":[]},{"location":"chapter_graph/summary/#1","level":3,"title":"1.   重要なポイントの振り返り","text":"<ul> <li>グラフは頂点と辺から構成され、一組の頂点と一組の辺からなる集合として表せます。</li> <li>線形関係（連結リスト）や分治関係（木）と比べて、ネットワーク関係（グラフ）は自由度が高く、そのぶん複雑です。</li> <li>有向グラフの辺は方向性を持ち、連結グラフでは任意の頂点に到達でき、重み付きグラフの各辺は重み変数を含みます。</li> <li>隣接行列は行列を用いてグラフを表し、各行（列）が 1 つの頂点を表し、行列要素が辺を表します。\\(1\\) または \\(0\\) を用いて、2 つの頂点の間に辺があるかないかを示します。隣接行列は追加・削除・検索・更新の操作効率が高い一方で、より多くの空間を消費します。</li> <li>隣接リストは複数の連結リストを使ってグラフを表し、第 \\(i\\) 個の連結リストが頂点 \\(i\\) に対応し、その頂点に隣接するすべての頂点を格納します。隣接リストは隣接行列よりも省スペースですが、辺を探すために連結リストを走査する必要があるため、時間効率は低くなります。</li> <li>隣接リスト内の連結リストが長くなりすぎた場合は、赤黒木やハッシュテーブルに変換することで、検索効率を高められます。</li> <li>アルゴリズムの考え方という観点では、隣接行列は「空間を時間と引き換えにする」ことを体現し、隣接リストは「時間を空間と引き換えにする」ことを体現します。</li> <li>グラフは、ソーシャルネットワークや地下鉄路線など、さまざまな現実のシステムをモデル化するために使えます。</li> <li>木はグラフの特殊な一例であり、木の走査もグラフ走査の特殊な一例です。</li> <li>グラフの幅優先探索は、近いところから遠いところへ、層ごとに広がっていく探索方法であり、通常はキューを使って実装します。</li> <li>グラフの深さ優先探索は、まず行けるところまで進み、進めなくなったらバックトラックする探索方法であり、通常は再帰に基づいて実装します。</li> </ul>","path":["第 9 章 &nbsp; グラフ","9.4 &nbsp; まとめ"],"tags":[]},{"location":"chapter_graph/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q：経路の定義は頂点列ですか、それとも辺列ですか？</p> <p>Wikipedia では言語版ごとに定義が一致していません。英語版では「経路は辺の列」であり、中国語版では「経路は頂点の列」です。以下は英語版の原文です：In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices.</p> <p>本書では、経路を頂点列ではなく辺列とみなします。これは、2 つの頂点の間に複数の辺が存在する可能性があり、その場合は各辺がそれぞれ 1 本の経路に対応するためです。</p> <p>Q：非連結グラフには到達できない頂点がありますか？</p> <p>非連結グラフでは、ある頂点から出発すると、少なくとも 1 つの頂点には到達できません。非連結グラフ全体を走査するには、グラフ内のすべての連結成分をたどれるように複数の始点を設定する必要があります。</p> <p>Q：隣接リストにおいて、「その頂点に接続されたすべての頂点」の順序に決まりはありますか？</p> <p>順序は任意でかまいません。ただし実際の応用では、頂点を追加した順序や頂点値の大小順など、特定の規則に従って並べ替える必要がある場合があります。そうすることで、「ある種の極値を持つ」頂点をすばやく見つけやすくなります。</p>","path":["第 9 章 &nbsp; グラフ","9.4 &nbsp; まとめ"],"tags":[]},{"location":"chapter_greedy/","level":1,"title":"第 15 章   貪欲法","text":"<p>Abstract</p> <p>ヒマワリは太陽に向かって回り、自らが最も大きく成長できる可能性を常に追い求める。</p> <p>貪欲戦略は、一回ごとの単純な選択を通じて、徐々に最適な答えへと導く。</p>","path":["第 15 章 &nbsp; 貪欲法"],"tags":[]},{"location":"chapter_greedy/#_1","level":2,"title":"章の内容","text":"<ul> <li>15.1   貪欲法</li> <li>15.2   分数ナップサック問題</li> <li>15.3   最大容量問題</li> <li>15.4   最大積分割問題</li> <li>15.5   まとめ</li> </ul>","path":["第 15 章 &nbsp; 貪欲法"],"tags":[]},{"location":"chapter_greedy/fractional_knapsack_problem/","level":1,"title":"15.2   分数ナップサック問題","text":"<p>Question</p> <p>\\(n\\) 個の品物が与えられ、第 \\(i\\) 個の品物の重さは \\(wgt[i-1]\\)、価値は \\(val[i-1]\\) であり、容量が \\(cap\\) のナップサックがある。各品物は 1 回だけ選択できるが、品物の一部を選ぶこともでき、価値は選択した重量の割合に応じて計算される。容量制限の下でナップサック内の品物の最大価値を求めよ。例を以下に示す。</p> <p></p> <p> 図 15-3   分数ナップサック問題の例データ </p> <p>分数ナップサック問題は 0-1 ナップサック問題と全体として非常によく似ており、状態には現在の品物 \\(i\\) と容量 \\(c\\) が含まれ、目標は容量制限下での最大価値を求めることである。</p> <p>異なる点は、本問では品物の一部だけを選べることである。以下に示すように、品物は任意に分割でき、対応する価値は重量の割合に応じて計算される。</p> <ol> <li>品物 \\(i\\) について、単位重量あたりの価値は \\(val[i-1] / wgt[i-1]\\) であり、これを単位価値と呼ぶ。</li> <li>品物 \\(i\\) の一部を重さ \\(w\\) だけ入れると、ナップサックに増える価値は \\(w \\times val[i-1] / wgt[i-1]\\) となる。</li> </ol> <p></p> <p> 図 15-4   品物の単位重量あたりの価値 </p>","path":["第 15 章 &nbsp; 貪欲法","15.2 &nbsp; 分数ナップサック問題"],"tags":[]},{"location":"chapter_greedy/fractional_knapsack_problem/#1","level":3,"title":"1.   貪欲戦略の決定","text":"<p>ナップサック内の品物の総価値を最大化することは、**本質的には単位重量あたりの品物価値を最大化すること**である。そこから、以下に示す貪欲戦略を導ける。</p> <ol> <li>品物を単位価値の高い順にソートする。</li> <li>すべての品物を走査し、各回で単位価値が最も高い品物を貪欲に選択する。</li> <li>残りのナップサック容量が足りない場合は、現在の品物の一部を使ってナップサックを満たす。</li> </ol> <p></p> <p> 図 15-5   分数ナップサック問題の貪欲戦略 </p>","path":["第 15 章 &nbsp; 貪欲法","15.2 &nbsp; 分数ナップサック問題"],"tags":[]},{"location":"chapter_greedy/fractional_knapsack_problem/#2","level":3,"title":"2.   コード実装","text":"<p>品物を単位価値でソートできるように、<code>Item</code> クラスを定義する。貪欲選択を繰り返し、ナップサックが満杯になったら終了して解を返す。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby fractional_knapsack.py<pre><code>class Item:\n    \"\"\"品物\"\"\"\n\n    def __init__(self, w: int, v: int):\n        self.w = w  # 品物の重さ\n        self.v = v  # 品物の価値\n\ndef fractional_knapsack(wgt: list[int], val: list[int], cap: int) -&gt; int:\n    \"\"\"分数ナップサック：貪欲法\"\"\"\n    # 重さと価値の 2 属性を持つ品物リストを作成\n    items = [Item(w, v) for w, v in zip(wgt, val)]\n    # 単位価値 item.v / item.w の高い順にソートする\n    items.sort(key=lambda item: item.v / item.w, reverse=True)\n    # 貪欲選択を繰り返す\n    res = 0\n    for item in items:\n        if item.w &lt;= cap:\n            # 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる\n            res += item.v\n            cap -= item.w\n        else:\n            # 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる\n            res += (item.v / item.w) * cap\n            # 残り容量がないため、ループを抜ける\n            break\n    return res\n</code></pre> fractional_knapsack.cpp<pre><code>/* 品物 */\nclass Item {\n  public:\n    int w; // 品物の重さ\n    int v; // 品物の価値\n\n    Item(int w, int v) : w(w), v(v) {\n    }\n};\n\n/* 分数ナップサック：貪欲法 */\ndouble fractionalKnapsack(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int cap) {\n    // 重さと価値の 2 属性を持つ品物リストを作成\n    vector&lt;Item&gt; items;\n    for (int i = 0; i &lt; wgt.size(); i++) {\n        items.push_back(Item(wgt[i], val[i]));\n    }\n    // 単位価値 item.v / item.w の高い順にソートする\n    sort(items.begin(), items.end(), [](Item &amp;a, Item &amp;b) { return (double)a.v / a.w &gt; (double)b.v / b.w; });\n    // 貪欲選択を繰り返す\n    double res = 0;\n    for (auto &amp;item : items) {\n        if (item.w &lt;= cap) {\n            // 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる\n            res += item.v;\n            cap -= item.w;\n        } else {\n            // 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる\n            res += (double)item.v / item.w * cap;\n            // 残り容量がないため、ループを抜ける\n            break;\n        }\n    }\n    return res;\n}\n</code></pre> fractional_knapsack.java<pre><code>/* 品物 */\nclass Item {\n    int w; // 品物の重さ\n    int v; // 品物の価値\n\n    public Item(int w, int v) {\n        this.w = w;\n        this.v = v;\n    }\n}\n\n/* 分数ナップサック：貪欲法 */\ndouble fractionalKnapsack(int[] wgt, int[] val, int cap) {\n    // 重さと価値の 2 属性を持つ品物リストを作成\n    Item[] items = new Item[wgt.length];\n    for (int i = 0; i &lt; wgt.length; i++) {\n        items[i] = new Item(wgt[i], val[i]);\n    }\n    // 単位価値 item.v / item.w の高い順にソートする\n    Arrays.sort(items, Comparator.comparingDouble(item -&gt; -((double) item.v / item.w)));\n    // 貪欲選択を繰り返す\n    double res = 0;\n    for (Item item : items) {\n        if (item.w &lt;= cap) {\n            // 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる\n            res += item.v;\n            cap -= item.w;\n        } else {\n            // 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる\n            res += (double) item.v / item.w * cap;\n            // 残り容量がないため、ループを抜ける\n            break;\n        }\n    }\n    return res;\n}\n</code></pre> fractional_knapsack.cs<pre><code>/* 品物 */\nclass Item(int w, int v) {\n    public int w = w; // 品物の重さ\n    public int v = v; // 品物の価値\n}\n\n/* 分数ナップサック：貪欲法 */\ndouble FractionalKnapsack(int[] wgt, int[] val, int cap) {\n    // 重さと価値の 2 属性を持つ品物リストを作成\n    Item[] items = new Item[wgt.Length];\n    for (int i = 0; i &lt; wgt.Length; i++) {\n        items[i] = new Item(wgt[i], val[i]);\n    }\n    // 単位価値 item.v / item.w の高い順にソートする\n    Array.Sort(items, (x, y) =&gt; (y.v / y.w).CompareTo(x.v / x.w));\n    // 貪欲選択を繰り返す\n    double res = 0;\n    foreach (Item item in items) {\n        if (item.w &lt;= cap) {\n            // 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる\n            res += item.v;\n            cap -= item.w;\n        } else {\n            // 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる\n            res += (double)item.v / item.w * cap;\n            // 残り容量がないため、ループを抜ける\n            break;\n        }\n    }\n    return res;\n}\n</code></pre> fractional_knapsack.go<pre><code>/* 品物 */\ntype Item struct {\n    w int // 品物の重さ\n    v int // 品物の価値\n}\n\n/* 分数ナップサック：貪欲法 */\nfunc fractionalKnapsack(wgt []int, val []int, cap int) float64 {\n    // 重さと価値の 2 属性を持つ品物リストを作成\n    items := make([]Item, len(wgt))\n    for i := 0; i &lt; len(wgt); i++ {\n        items[i] = Item{wgt[i], val[i]}\n    }\n    // 単位価値 item.v / item.w の高い順にソートする\n    sort.Slice(items, func(i, j int) bool {\n        return float64(items[i].v)/float64(items[i].w) &gt; float64(items[j].v)/float64(items[j].w)\n    })\n    // 貪欲選択を繰り返す\n    res := 0.0\n    for _, item := range items {\n        if item.w &lt;= cap {\n            // 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる\n            res += float64(item.v)\n            cap -= item.w\n        } else {\n            // 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる\n            res += float64(item.v) / float64(item.w) * float64(cap)\n            // 残り容量がないため、ループを抜ける\n            break\n        }\n    }\n    return res\n}\n</code></pre> fractional_knapsack.swift<pre><code>/* 品物 */\nclass Item {\n    var w: Int // 品物の重さ\n    var v: Int // 品物の価値\n\n    init(w: Int, v: Int) {\n        self.w = w\n        self.v = v\n    }\n}\n\n/* 分数ナップサック：貪欲法 */\nfunc fractionalKnapsack(wgt: [Int], val: [Int], cap: Int) -&gt; Double {\n    // 重さと価値の 2 属性を持つ品物リストを作成\n    var items = zip(wgt, val).map { Item(w: $0, v: $1) }\n    // 単位価値 item.v / item.w の高い順にソートする\n    items.sort { -(Double($0.v) / Double($0.w)) &lt; -(Double($1.v) / Double($1.w)) }\n    // 貪欲選択を繰り返す\n    var res = 0.0\n    var cap = cap\n    for item in items {\n        if item.w &lt;= cap {\n            // 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる\n            res += Double(item.v)\n            cap -= item.w\n        } else {\n            // 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる\n            res += Double(item.v) / Double(item.w) * Double(cap)\n            // 残り容量がないため、ループを抜ける\n            break\n        }\n    }\n    return res\n}\n</code></pre> fractional_knapsack.js<pre><code>/* 品物 */\nclass Item {\n    constructor(w, v) {\n        this.w = w; // 品物の重さ\n        this.v = v; // 品物の価値\n    }\n}\n\n/* 分数ナップサック：貪欲法 */\nfunction fractionalKnapsack(wgt, val, cap) {\n    // 重さと価値の 2 属性を持つ品物リストを作成\n    const items = wgt.map((w, i) =&gt; new Item(w, val[i]));\n    // 単位価値 item.v / item.w の高い順にソートする\n    items.sort((a, b) =&gt; b.v / b.w - a.v / a.w);\n    // 貪欲選択を繰り返す\n    let res = 0;\n    for (const item of items) {\n        if (item.w &lt;= cap) {\n            // 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる\n            res += item.v;\n            cap -= item.w;\n        } else {\n            // 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる\n            res += (item.v / item.w) * cap;\n            // 残り容量がないため、ループを抜ける\n            break;\n        }\n    }\n    return res;\n}\n</code></pre> fractional_knapsack.ts<pre><code>/* 品物 */\nclass Item {\n    w: number; // 品物の重さ\n    v: number; // 品物の価値\n\n    constructor(w: number, v: number) {\n        this.w = w;\n        this.v = v;\n    }\n}\n\n/* 分数ナップサック：貪欲法 */\nfunction fractionalKnapsack(wgt: number[], val: number[], cap: number): number {\n    // 重さと価値の 2 属性を持つ品物リストを作成\n    const items: Item[] = wgt.map((w, i) =&gt; new Item(w, val[i]));\n    // 単位価値 item.v / item.w の高い順にソートする\n    items.sort((a, b) =&gt; b.v / b.w - a.v / a.w);\n    // 貪欲選択を繰り返す\n    let res = 0;\n    for (const item of items) {\n        if (item.w &lt;= cap) {\n            // 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる\n            res += item.v;\n            cap -= item.w;\n        } else {\n            // 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる\n            res += (item.v / item.w) * cap;\n            // 残り容量がないため、ループを抜ける\n            break;\n        }\n    }\n    return res;\n}\n</code></pre> fractional_knapsack.dart<pre><code>/* 品物 */\nclass Item {\n  int w; // 品物の重さ\n  int v; // 品物の価値\n\n  Item(this.w, this.v);\n}\n\n/* 分数ナップサック：貪欲法 */\ndouble fractionalKnapsack(List&lt;int&gt; wgt, List&lt;int&gt; val, int cap) {\n  // 重さと価値の 2 属性を持つ品物リストを作成\n  List&lt;Item&gt; items = List.generate(wgt.length, (i) =&gt; Item(wgt[i], val[i]));\n  // 単位価値 item.v / item.w の高い順にソートする\n  items.sort((a, b) =&gt; (b.v / b.w).compareTo(a.v / a.w));\n  // 貪欲選択を繰り返す\n  double res = 0;\n  for (Item item in items) {\n    if (item.w &lt;= cap) {\n      // 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる\n      res += item.v;\n      cap -= item.w;\n    } else {\n      // 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる\n      res += item.v / item.w * cap;\n      // 残り容量がないため、ループを抜ける\n      break;\n    }\n  }\n  return res;\n}\n</code></pre> fractional_knapsack.rs<pre><code>/* 品物 */\nstruct Item {\n    w: i32, // 品物の重さ\n    v: i32, // 品物の価値\n}\n\nimpl Item {\n    fn new(w: i32, v: i32) -&gt; Self {\n        Self { w, v }\n    }\n}\n\n/* 分数ナップサック：貪欲法 */\nfn fractional_knapsack(wgt: &amp;[i32], val: &amp;[i32], mut cap: i32) -&gt; f64 {\n    // 重さと価値の 2 属性を持つ品物リストを作成\n    let mut items = wgt\n        .iter()\n        .zip(val.iter())\n        .map(|(&amp;w, &amp;v)| Item::new(w, v))\n        .collect::&lt;Vec&lt;Item&gt;&gt;();\n    // 単位価値 item.v / item.w の高い順にソートする\n    items.sort_by(|a, b| {\n        (b.v as f64 / b.w as f64)\n            .partial_cmp(&amp;(a.v as f64 / a.w as f64))\n            .unwrap()\n    });\n    // 貪欲選択を繰り返す\n    let mut res = 0.0;\n    for item in &amp;items {\n        if item.w &lt;= cap {\n            // 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる\n            res += item.v as f64;\n            cap -= item.w;\n        } else {\n            // 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる\n            res += item.v as f64 / item.w as f64 * cap as f64;\n            // 残り容量がないため、ループを抜ける\n            break;\n        }\n    }\n    res\n}\n</code></pre> fractional_knapsack.c<pre><code>/* 品物 */\ntypedef struct {\n    int w; // 品物の重さ\n    int v; // 品物の価値\n} Item;\n\n/* 分数ナップサック：貪欲法 */\nfloat fractionalKnapsack(int wgt[], int val[], int itemCount, int cap) {\n    // 重さと価値の 2 属性を持つ品物リストを作成\n    Item *items = malloc(sizeof(Item) * itemCount);\n    for (int i = 0; i &lt; itemCount; i++) {\n        items[i] = (Item){.w = wgt[i], .v = val[i]};\n    }\n    // 単位価値 item.v / item.w の高い順にソートする\n    qsort(items, (size_t)itemCount, sizeof(Item), sortByValueDensity);\n    // 貪欲選択を繰り返す\n    float res = 0.0;\n    for (int i = 0; i &lt; itemCount; i++) {\n        if (items[i].w &lt;= cap) {\n            // 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる\n            res += items[i].v;\n            cap -= items[i].w;\n        } else {\n            // 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる\n            res += (float)cap / items[i].w * items[i].v;\n            cap = 0;\n            break;\n        }\n    }\n    free(items);\n    return res;\n}\n</code></pre> fractional_knapsack.kt<pre><code>/* 品物 */\nclass Item(\n    val w: Int, // 品物\n    val v: Int  // 品物の価値\n)\n\n/* 分数ナップサック：貪欲法 */\nfun fractionalKnapsack(wgt: IntArray, _val: IntArray, c: Int): Double {\n    // 重さと価値の 2 属性を持つ品物リストを作成\n    var cap = c\n    val items = arrayOfNulls&lt;Item&gt;(wgt.size)\n    for (i in wgt.indices) {\n        items[i] = Item(wgt[i], _val[i])\n    }\n    // 単位価値 item.v / item.w の高い順にソートする\n    items.sortBy { item: Item? -&gt; -(item!!.v.toDouble() / item.w) }\n    // 貪欲選択を繰り返す\n    var res = 0.0\n    for (item in items) {\n        if (item!!.w &lt;= cap) {\n            // 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる\n            res += item.v\n            cap -= item.w\n        } else {\n            // 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる\n            res += item.v.toDouble() / item.w * cap\n            // 残り容量がないため、ループを抜ける\n            break\n        }\n    }\n    return res\n}\n</code></pre> fractional_knapsack.rb<pre><code>### アイテム ###\nclass Item\n  attr_accessor :w # 品物の重さ\n  attr_accessor :v # 品物の価値\n\n  def initialize(w, v)\n    @w = w\n    @v = v\n  end\nend\n\n### 分数ナップサック：貪欲法 ###\ndef fractional_knapsack(wgt, val, cap)\n  # 重さと価値の 2 属性を持つ品物リストを作成する\n  items = wgt.each_with_index.map { |w, i| Item.new(w, val[i]) }\n  # 単位価値 item.v / item.w の高い順にソートする\n  items.sort! { |a, b| (b.v.to_f / b.w) &lt;=&gt; (a.v.to_f / a.w) }\n  # 貪欲選択を繰り返す\n  res = 0\n  for item in items\n    if item.w &lt;= cap\n      # 残り容量が十分なら、現在の品物を丸ごとナップサックに入れる\n      res += item.v\n      cap -= item.w\n    else\n      # 残り容量が足りない場合は、現在の品物の一部だけをナップサックに入れる\n      res += (item.v.to_f / item.w) * cap\n      # 残り容量がないため、ループを抜ける\n      break\n    end\n  end\n  res\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>組み込みのソートアルゴリズムの時間計算量は通常 \\(O(\\log n)\\)、空間計算量は通常 \\(O(\\log n)\\) または \\(O(n)\\) であり、具体的な値はプログラミング言語の実装に依存する。</p> <p>ソートを除けば、最悪の場合は品物リスト全体を走査する必要があるため、時間計算量は \\(O(n)\\) であり、ここで \\(n\\) は品物数である。</p> <p><code>Item</code> オブジェクトのリストを初期化しているため、空間計算量は \\(O(n)\\) である。</p>","path":["第 15 章 &nbsp; 貪欲法","15.2 &nbsp; 分数ナップサック問題"],"tags":[]},{"location":"chapter_greedy/fractional_knapsack_problem/#3","level":3,"title":"3.   正しさの証明","text":"<p>背理法を用いる。品物 \\(x\\) が単位価値最大の品物であり、あるアルゴリズムで得られた最大価値を <code>res</code> とするが、その解には品物 \\(x\\) が含まれていないと仮定する。</p> <p>ここでナップサックから単位重量の任意の品物を取り出し、単位重量の品物 \\(x\\) に置き換える。品物 \\(x\\) の単位価値が最大であるため、置き換え後の総価値は必ず <code>res</code> より大きくなる。これは <code>res</code> が最適解であることに矛盾し、最適解には必ず品物 \\(x\\) が含まれなければならないことを示す。</p> <p>この解に含まれる他の品物についても、同様の矛盾を構成できる。要するに、単位価値がより大きい品物は常により良い選択である。これは貪欲戦略が有効であることを示している。</p> <p>以下に示すように、品物の重さと品物の単位価値をそれぞれ二次元グラフの横軸と縦軸とみなすと、分数ナップサック問題は「有限な横軸区間で囲まれる最大面積を求める問題」に変換できる。この類比は、幾何学的な観点から貪欲戦略の有効性を理解する助けになる。</p> <p></p> <p> 図 15-6   分数ナップサック問題の幾何学的表現 </p>","path":["第 15 章 &nbsp; 貪欲法","15.2 &nbsp; 分数ナップサック問題"],"tags":[]},{"location":"chapter_greedy/greedy_algorithm/","level":1,"title":"15.1   貪欲法","text":"<p>貪欲法（greedy algorithm）は、最適化問題を解くための一般的なアルゴリズムです。その基本的な考え方は、問題の各意思決定段階において、その時点で最善に見える選択を行い、すなわち貪欲に局所最適な決定を下すことで、大域最適解を得ようとするものです。貪欲法は簡潔で効率的であり、多くの実際の問題で広く用いられています。</p> <p>貪欲法と動的計画法は、どちらも最適化問題を解く際によく用いられます。両者には、最適部分構造に依存するなどの共通点がありますが、その動作原理は異なります。</p> <ul> <li>動的計画法は、前の段階までのすべての決定に基づいて現在の決定を考え、過去の部分問題の解を用いて現在の部分問題の解を構築します。</li> <li>貪欲法は過去の決定を考慮せず、ひたすら前に進みながら貪欲な選択を行い、問題の範囲を縮小し続けて、最終的に問題を解決します。</li> </ul> <p>まずは例題「コイン両替」を通して、貪欲法の仕組みを理解しましょう。この問題はすでに「完全ナップサック問題」の節で紹介しているので、見覚えがあるはずです。</p> <p>Question</p> <p>\\(n\\) 種類の硬貨が与えられ、\\(i\\) 番目の硬貨の額面は \\(coins[i - 1]\\) 、目標金額は \\(amt\\) です。各硬貨は何度でも選べるとき、目標金額を作るために必要な最小の硬貨枚数を求めてください。目標金額を作れない場合は \\(-1\\) を返します。</p> <p>この問題で採用する貪欲戦略は下図のとおりです。目標金額が与えられたら、それを超えず、かつ最も近い硬貨を貪欲に選択し、この手順を目標金額を作り切るまで繰り返します。</p> <p></p> <p> 図 15-1   コイン両替の貪欲戦略 </p> <p>実装コードは次のとおりです。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby coin_change_greedy.py<pre><code>def coin_change_greedy(coins: list[int], amt: int) -&gt; int:\n    \"\"\"コイン交換：貪欲法\"\"\"\n    # coins リストはソート済みと仮定する\n    i = len(coins) - 1\n    count = 0\n    # 残額がなくなるまで貪欲選択を繰り返す\n    while amt &gt; 0:\n        # 残額以下で最も近い硬貨を見つける\n        while i &gt; 0 and coins[i] &gt; amt:\n            i -= 1\n        # coins[i] を選択する\n        amt -= coins[i]\n        count += 1\n    # 実行可能な解が見つからなければ -1 を返す\n    return count if amt == 0 else -1\n</code></pre> coin_change_greedy.cpp<pre><code>/* コイン交換：貪欲法 */\nint coinChangeGreedy(vector&lt;int&gt; &amp;coins, int amt) {\n    // coins リストはソート済みと仮定する\n    int i = coins.size() - 1;\n    int count = 0;\n    // 残額がなくなるまで貪欲選択を繰り返す\n    while (amt &gt; 0) {\n        // 残額以下で最も近い硬貨を見つける\n        while (i &gt; 0 &amp;&amp; coins[i] &gt; amt) {\n            i--;\n        }\n        // coins[i] を選択する\n        amt -= coins[i];\n        count++;\n    }\n    // 実行可能な解が見つからなければ -1 を返す\n    return amt == 0 ? count : -1;\n}\n</code></pre> coin_change_greedy.java<pre><code>/* コイン交換：貪欲法 */\nint coinChangeGreedy(int[] coins, int amt) {\n    // coins リストはソート済みと仮定する\n    int i = coins.length - 1;\n    int count = 0;\n    // 残額がなくなるまで貪欲選択を繰り返す\n    while (amt &gt; 0) {\n        // 残額以下で最も近い硬貨を見つける\n        while (i &gt; 0 &amp;&amp; coins[i] &gt; amt) {\n            i--;\n        }\n        // coins[i] を選択する\n        amt -= coins[i];\n        count++;\n    }\n    // 実行可能な解が見つからなければ -1 を返す\n    return amt == 0 ? count : -1;\n}\n</code></pre> coin_change_greedy.cs<pre><code>/* コイン交換：貪欲法 */\nint CoinChangeGreedy(int[] coins, int amt) {\n    // coins リストはソート済みと仮定する\n    int i = coins.Length - 1;\n    int count = 0;\n    // 残額がなくなるまで貪欲選択を繰り返す\n    while (amt &gt; 0) {\n        // 残額以下で最も近い硬貨を見つける\n        while (i &gt; 0 &amp;&amp; coins[i] &gt; amt) {\n            i--;\n        }\n        // coins[i] を選択する\n        amt -= coins[i];\n        count++;\n    }\n    // 実行可能な解が見つからなければ -1 を返す\n    return amt == 0 ? count : -1;\n}\n</code></pre> coin_change_greedy.go<pre><code>/* コイン交換：貪欲法 */\nfunc coinChangeGreedy(coins []int, amt int) int {\n    // coins リストはソート済みと仮定する\n    i := len(coins) - 1\n    count := 0\n    // 残額がなくなるまで貪欲選択を繰り返す\n    for amt &gt; 0 {\n        // 残額以下で最も近い硬貨を見つける\n        for i &gt; 0 &amp;&amp; coins[i] &gt; amt {\n            i--\n        }\n        // coins[i] を選択する\n        amt -= coins[i]\n        count++\n    }\n    // 実行可能な解が見つからなければ -1 を返す\n    if amt != 0 {\n        return -1\n    }\n    return count\n}\n</code></pre> coin_change_greedy.swift<pre><code>/* コイン交換：貪欲法 */\nfunc coinChangeGreedy(coins: [Int], amt: Int) -&gt; Int {\n    // coins リストはソート済みと仮定する\n    var i = coins.count - 1\n    var count = 0\n    var amt = amt\n    // 残額がなくなるまで貪欲選択を繰り返す\n    while amt &gt; 0 {\n        // 残額以下で最も近い硬貨を見つける\n        while i &gt; 0 &amp;&amp; coins[i] &gt; amt {\n            i -= 1\n        }\n        // coins[i] を選択する\n        amt -= coins[i]\n        count += 1\n    }\n    // 実行可能な解が見つからなければ -1 を返す\n    return amt == 0 ? count : -1\n}\n</code></pre> coin_change_greedy.js<pre><code>/* コイン交換：貪欲法 */\nfunction coinChangeGreedy(coins, amt) {\n    // coins 配列はソート済みと仮定する\n    let i = coins.length - 1;\n    let count = 0;\n    // 残額がなくなるまで貪欲選択を繰り返す\n    while (amt &gt; 0) {\n        // 残額以下で最も近い硬貨を見つける\n        while (i &gt; 0 &amp;&amp; coins[i] &gt; amt) {\n            i--;\n        }\n        // coins[i] を選択する\n        amt -= coins[i];\n        count++;\n    }\n    // 実行可能な解が見つからなければ -1 を返す\n    return amt === 0 ? count : -1;\n}\n</code></pre> coin_change_greedy.ts<pre><code>/* コイン交換：貪欲法 */\nfunction coinChangeGreedy(coins: number[], amt: number): number {\n    // coins 配列はソート済みと仮定する\n    let i = coins.length - 1;\n    let count = 0;\n    // 残額がなくなるまで貪欲選択を繰り返す\n    while (amt &gt; 0) {\n        // 残額以下で最も近い硬貨を見つける\n        while (i &gt; 0 &amp;&amp; coins[i] &gt; amt) {\n            i--;\n        }\n        // coins[i] を選択する\n        amt -= coins[i];\n        count++;\n    }\n    // 実行可能な解が見つからなければ -1 を返す\n    return amt === 0 ? count : -1;\n}\n</code></pre> coin_change_greedy.dart<pre><code>/* コイン交換：貪欲法 */\nint coinChangeGreedy(List&lt;int&gt; coins, int amt) {\n  // coins リストはソート済みと仮定する\n  int i = coins.length - 1;\n  int count = 0;\n  // 残額がなくなるまで貪欲選択を繰り返す\n  while (amt &gt; 0) {\n    // 残額以下で最も近い硬貨を見つける\n    while (i &gt; 0 &amp;&amp; coins[i] &gt; amt) {\n      i--;\n    }\n    // coins[i] を選択する\n    amt -= coins[i];\n    count++;\n  }\n  // 実行可能な解が見つからなければ -1 を返す\n  return amt == 0 ? count : -1;\n}\n</code></pre> coin_change_greedy.rs<pre><code>/* コイン交換：貪欲法 */\nfn coin_change_greedy(coins: &amp;[i32], mut amt: i32) -&gt; i32 {\n    // coins リストはソート済みと仮定する\n    let mut i = coins.len() - 1;\n    let mut count = 0;\n    // 残額がなくなるまで貪欲選択を繰り返す\n    while amt &gt; 0 {\n        // 残額以下で最も近い硬貨を見つける\n        while i &gt; 0 &amp;&amp; coins[i] &gt; amt {\n            i -= 1;\n        }\n        // coins[i] を選択する\n        amt -= coins[i];\n        count += 1;\n    }\n    // 実行可能な解が見つからなければ -1 を返す\n    if amt == 0 {\n        count\n    } else {\n        -1\n    }\n}\n</code></pre> coin_change_greedy.c<pre><code>/* コイン交換：貪欲法 */\nint coinChangeGreedy(int *coins, int size, int amt) {\n    // coins リストはソート済みと仮定する\n    int i = size - 1;\n    int count = 0;\n    // 残額がなくなるまで貪欲選択を繰り返す\n    while (amt &gt; 0) {\n        // 残額以下で最も近い硬貨を見つける\n        while (i &gt; 0 &amp;&amp; coins[i] &gt; amt) {\n            i--;\n        }\n        // coins[i] を選択する\n        amt -= coins[i];\n        count++;\n    }\n    // 実行可能な解が見つからなければ -1 を返す\n    return amt == 0 ? count : -1;\n}\n</code></pre> coin_change_greedy.kt<pre><code>/* コイン交換：貪欲法 */\nfun coinChangeGreedy(coins: IntArray, amt: Int): Int {\n    // coins リストはソート済みと仮定する\n    var am = amt\n    var i = coins.size - 1\n    var count = 0\n    // 残額がなくなるまで貪欲選択を繰り返す\n    while (am &gt; 0) {\n        // 残額以下で最も近い硬貨を見つける\n        while (i &gt; 0 &amp;&amp; coins[i] &gt; am) {\n            i--\n        }\n        // coins[i] を選択する\n        am -= coins[i]\n        count++\n    }\n    // 実行可能な解が見つからなければ -1 を返す\n    return if (am == 0) count else -1\n}\n</code></pre> coin_change_greedy.rb<pre><code>### コイン両替：貪欲法 ###\ndef coin_change_greedy(coins, amt)\n  # coins リストはソート済みと仮定する\n  i = coins.length - 1\n  count = 0\n  # 残額がなくなるまで貪欲選択を繰り返す\n  while amt &gt; 0\n    # 残額以下で最も近い硬貨を見つける\n    while i &gt; 0 &amp;&amp; coins[i] &gt; amt\n      i -= 1\n    end\n    # coins[i] を選択する\n    amt -= coins[i]\n    count += 1\n  end\n  # 実行可能な解が見つからなければ `-1` を返す\n  amt == 0 ? count : -1\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>思わずこう言いたくなるかもしれません。So clean！貪欲法はわずか十行ほどのコードでコイン両替問題を解いてしまいます。</p>","path":["第 15 章 &nbsp; 貪欲法","15.1 &nbsp; 貪欲法"],"tags":[]},{"location":"chapter_greedy/greedy_algorithm/#1511","level":2,"title":"15.1.1   貪欲法の利点と限界","text":"<p>**貪欲法は操作が直接的で実装が簡単なだけでなく、通常は効率も高い**です。上のコードでは、硬貨の最小額面を \\(\\min(coins)\\) とすると、貪欲選択のループ回数は高々 \\(amt / \\min(coins)\\) 回であり、時間計算量は \\(O(amt / \\min(coins))\\) です。これは動的計画法による解法の時間計算量 \\(O(n \\times amt)\\) より 1 桁小さいオーダーです。</p> <p>しかし、硬貨の額面の組み合わせによっては、貪欲法では最適解を見つけられません。下図に 2 つの例を示します。</p> <ul> <li>正例 \\(coins = [1, 5, 10, 20, 50, 100]\\)：この硬貨の組み合わせでは、任意の \\(amt\\) に対して貪欲法で最適解を見つけられます。</li> <li>反例 \\(coins = [1, 20, 50]\\)：\\(amt = 60\\) とすると、貪欲法では \\(50 + 1 \\times 10\\) という両替しか見つからず、硬貨は合計 \\(11\\) 枚になります。しかし動的計画法なら最適解 \\(20 + 20 + 20\\) を見つけられ、必要なのはわずか \\(3\\) 枚です。</li> <li>反例 \\(coins = [1, 49, 50]\\)：\\(amt = 98\\) とすると、貪欲法では \\(50 + 1 \\times 48\\) という両替しか見つからず、硬貨は合計 \\(49\\) 枚になります。しかし動的計画法なら最適解 \\(49 + 49\\) を見つけられ、必要なのはわずか \\(2\\) 枚です。</li> </ul> <p></p> <p> 図 15-2   貪欲法では最適解を見つけられない例 </p> <p>つまり、コイン両替問題に対して、貪欲法は大域最適解を保証できず、非常に悪い解を見つけてしまうこともあります。この問題は動的計画法で解くほうが適しています。</p> <p>一般に、貪欲法が適用できる状況は次の 2 つに分けられます。</p> <ol> <li>最適解を保証できる場合：この場合、貪欲法はしばしば最良の選択です。多くの場合、バックトラッキングや動的計画法より効率的だからです。</li> <li>近似最適解を見つけられる場合：この場合も貪欲法は有効です。多くの複雑な問題では、大域最適解を求めること自体が非常に難しく、より高い効率で準最適解を得られるだけでも十分価値があります。</li> </ol>","path":["第 15 章 &nbsp; 貪欲法","15.1 &nbsp; 貪欲法"],"tags":[]},{"location":"chapter_greedy/greedy_algorithm/#1512","level":2,"title":"15.1.2   貪欲法の特性","text":"<p>では、どのような問題が貪欲法に適しているのでしょうか。言い換えると、貪欲法はどのような場合に最適解を保証できるのでしょうか。</p> <p>動的計画法と比べると、貪欲法の適用条件はより厳しく、主に次の 2 つの性質に注目します。</p> <ul> <li>貪欲選択性：局所最適な選択が常に大域最適解につながる場合にのみ、貪欲法は最適解を保証できます。</li> <li>最適部分構造：元の問題の最適解が、部分問題の最適解を含むことです。</li> </ul> <p>最適部分構造については「動的計画法」の節ですでに紹介したので、ここでは繰り返しません。なお、問題によっては最適部分構造が明確でなくても、貪欲法で解ける場合があります。</p> <p>ここでは主に、貪欲選択性をどのように判定するかを考えます。説明だけを見ると単純そうですが、実際には多くの問題で、貪欲選択性を証明するのは容易ではありません。</p> <p>たとえばコイン両替問題では、反例を挙げて貪欲選択性が成り立たないことを示すのは簡単ですが、成り立つことを証明するのは難しいです。もし、**どのような条件を満たす硬貨の組み合わせなら貪欲法で解けるのか**と問われると、直感や例示に頼った曖昧な答えしか出せず、厳密な数学的証明を与えるのは困難です。</p> <p>Quote</p> <p>ある論文では、ある硬貨の組み合わせについて、任意の金額に対する最適解を貪欲法で求められるかどうかを判定する、時間計算量 \\(O(n^3)\\) のアルゴリズムが示されています。</p> <p>Pearson, D. A polynomial-time algorithm for the change-making problem[J]. Operations Research Letters, 2005, 33(3): 231-234.</p>","path":["第 15 章 &nbsp; 貪欲法","15.1 &nbsp; 貪欲法"],"tags":[]},{"location":"chapter_greedy/greedy_algorithm/#1513","level":2,"title":"15.1.3   貪欲法の問題解決手順","text":"<p>貪欲法による問題解決の流れは、おおむね次の 3 段階に分けられます。</p> <ol> <li>問題分析：状態の定義、最適化目標、制約条件などを整理し、問題の性質を理解します。この段階はバックトラッキングや動的計画法でも共通して現れます。</li> <li>貪欲戦略の決定：各ステップでどのように貪欲選択を行うかを定めます。この戦略により各ステップで問題規模を縮小し、最終的に問題全体を解決します。</li> <li>正しさの証明：通常は、その問題が貪欲選択性と最適部分構造を持つことを示す必要があります。この段階では、帰納法や背理法などの数学的証明が必要になることがあります。</li> </ol> <p>貪欲戦略を定めることは問題解決の核心ですが、実際には簡単ではないことも多く、主な理由は次のとおりです。</p> <ul> <li>問題ごとに貪欲戦略の差が大きい。多くの問題では貪欲戦略は比較的わかりやすく、おおまかな考察や試行だけで見つけられます。しかし複雑な問題では、貪欲戦略が非常に見えにくいことがあり、その場合は解法経験やアルゴリズム力が大きく問われます。</li> <li>一見もっともらしい貪欲戦略もある。自信を持って貪欲戦略を設計し、コードを書いて提出しても、一部のテストケースを通過できないことがあります。これは、その貪欲戦略が「部分的にしか正しくない」ためであり、先ほどのコイン両替は典型例です。</li> </ul> <p>正しさを保証するためには、貪欲戦略に対して厳密な数学的証明を行うべきであり、通常は背理法や数学的帰納法が必要になります。</p> <p>しかし、正しさの証明もまた簡単とは限りません。手がかりがない場合には、テストケースを使ってコードをデバッグしながら、貪欲戦略を少しずつ修正して検証していくことがよくあります。</p>","path":["第 15 章 &nbsp; 貪欲法","15.1 &nbsp; 貪欲法"],"tags":[]},{"location":"chapter_greedy/greedy_algorithm/#1514","level":2,"title":"15.1.4   貪欲法の典型問題","text":"<p>貪欲法は、貪欲選択性と最適部分構造を満たす最適化問題によく用いられます。以下に典型的な貪欲法の問題をいくつか挙げます。</p> <ul> <li>硬貨のお釣り問題：ある種の硬貨の組み合わせでは、貪欲法で常に最適解が得られます。</li> <li>区間スケジューリング問題：いくつかのタスクがあり、それぞれがある時間区間で実行されるとします。できるだけ多くのタスクを完了することが目標で、毎回終了時刻が最も早いタスクを選ぶなら、貪欲法で最適解を得られます。</li> <li>分数ナップサック問題：一群の品物と積載容量が与えられたとき、総重量が容量を超えず、かつ総価値が最大になるように品物を選ぶ問題です。毎回、価値対重量比（価値 / 重量）が最も高い品物を選ぶなら、ある条件下で貪欲法は最適解を得られます。</li> <li>株式売買問題：株価の履歴が与えられ、複数回の売買が可能ですが、すでに株を保有している場合は売却前に再度購入することはできません。目標は最大利益を得ることです。</li> <li>ハフマン符号化：ハフマン符号化は、可逆データ圧縮に用いられる貪欲法です。ハフマン木を構築する際、毎回出現頻度が最も低い 2 つのノードを選んで併合すると、最終的に得られるハフマン木の重み付きパス長（符号長）は最小になります。</li> <li>Dijkstra アルゴリズム：与えられた始点から他の各頂点への最短経路問題を解く貪欲法です。</li> </ul>","path":["第 15 章 &nbsp; 貪欲法","15.1 &nbsp; 貪欲法"],"tags":[]},{"location":"chapter_greedy/max_capacity_problem/","level":1,"title":"15.3   最大容量問題","text":"<p>Question</p> <p>配列 \\(ht\\) が与えられ、各要素は垂直な仕切り板の高さを表します。配列内の任意の 2 枚の仕切り板と、その間の空間で容器を構成できます。</p> <p>容器の容量は高さと幅の積（面積）に等しく、高さは短い方の仕切り板で決まり、幅は 2 枚の仕切り板の配列インデックスの差です。</p> <p>配列から 2 枚の仕切り板を選び、構成される容器の容量が最大となるようにしてください。最大容量を返します。例を以下の図に示します。</p> <p></p> <p> 図 15-7   最大容量問題のサンプルデータ </p> <p>容器は任意の 2 枚の仕切り板で囲まれるため、本問の状態は 2 枚の仕切り板のインデックスで表され、\\([i, j]\\) と記します。</p> <p>問題の条件より、容量は高さと幅の積に等しく、高さは短い板で決まり、幅は 2 枚の仕切り板の配列インデックスの差です。容量を \\(cap[i, j]\\) とすると、計算式は次のようになります。</p> \\[ cap[i, j] = \\min(ht[i], ht[j]) \\times (j - i) \\] <p>配列の長さを \\(n\\) とすると、2 枚の仕切り板の組合せ数（状態総数）は \\(C_n^2 = \\frac{n(n - 1)}{2}\\) 個です。最も直接的には、すべての状態を総当たりできます。これにより最大容量を求められ、時間計算量は \\(O(n^2)\\) です。</p>","path":["第 15 章 &nbsp; 貪欲法","15.3 &nbsp; 最大容量問題"],"tags":[]},{"location":"chapter_greedy/max_capacity_problem/#1","level":3,"title":"1.   貪欲戦略の決定","text":"<p>この問題にはさらに効率的な解法があります。以下の図のように、状態 \\([i, j]\\) を 1 つ選び、インデックスが \\(i &lt; j\\) かつ高さが \\(ht[i] &lt; ht[j]\\) を満たすとします。つまり、\\(i\\) が短い板、\\(j\\) が長い板です。</p> <p></p> <p> 図 15-8   初期状態 </p> <p>以下の図のように、このとき長い板 \\(j\\) を短い板 \\(i\\) に近づけると、容量は必ず小さくなります。</p> <p>これは、長い板 \\(j\\) を動かした後は幅 \\(j-i\\) が必ず小さくなるためです。また、高さは短い板で決まるので、高さは変わらない（ \\(i\\) が依然として短い板）か、小さくなる（移動後の \\(j\\) が短い板になる）ことしかありません。</p> <p></p> <p> 図 15-9   長い板を内側へ動かした後の状態 </p> <p>逆に考えると、短い板 \\(i\\) を内側へ縮めた場合にのみ、容量が大きくなる可能性があります。幅は必ず小さくなりますが、**高さは大きくなる可能性がある**からです（移動後の短い板 \\(i\\) がより長くなる可能性があります）。たとえば次の図では、短い板を動かした後に面積が大きくなっています。</p> <p></p> <p> 図 15-10   短い板を内側へ動かした後の状態 </p> <p>以上から、本問の貪欲戦略を導けます。2 本のポインタを初期化して容器の両端に置き、各ラウンドで短い板に対応するポインタを内側へ縮め、2 本のポインタが出会うまで続けます。</p> <p>以下の図は、貪欲戦略の実行過程を示しています。</p> <ol> <li>初期状態では、ポインタ \\(i\\) と \\(j\\) は配列の両端にあります。</li> <li>現在の状態の容量 \\(cap[i, j]\\) を計算し、最大容量を更新します。</li> <li>板 \\(i\\) と板 \\(j\\) の高さを比較し、短い板を内側へ 1 マス移動します。</li> <li><code>2.</code> と <code>3.</code> を繰り返し実行し、\\(i\\) と \\(j\\) が出会ったら終了します。</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 15-11   最大容量問題の貪欲な過程 </p>","path":["第 15 章 &nbsp; 貪欲法","15.3 &nbsp; 最大容量問題"],"tags":[]},{"location":"chapter_greedy/max_capacity_problem/#2","level":3,"title":"2.   コード実装","text":"<p>コードのループ回数は最大でも \\(n\\) 回であるため、時間計算量は \\(O(n)\\) です。</p> <p>変数 \\(i\\)、\\(j\\)、\\(res\\) が使う追加領域は定数サイズなので、空間計算量は \\(O(1)\\) です。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby max_capacity.py<pre><code>def max_capacity(ht: list[int]) -&gt; int:\n    \"\"\"最大容量：貪欲法\"\"\"\n    # i, j を初期化し、それぞれ配列の両端に置く\n    i, j = 0, len(ht) - 1\n    # 初期の最大容量は 0\n    res = 0\n    # 2 枚の板が出会うまで貪欲選択を繰り返す\n    while i &lt; j:\n        # 最大容量を更新する\n        cap = min(ht[i], ht[j]) * (j - i)\n        res = max(res, cap)\n        # 短い方を内側へ動かす\n        if ht[i] &lt; ht[j]:\n            i += 1\n        else:\n            j -= 1\n    return res\n</code></pre> max_capacity.cpp<pre><code>/* 最大容量：貪欲法 */\nint maxCapacity(vector&lt;int&gt; &amp;ht) {\n    // i, j を初期化し、それぞれ配列の両端に置く\n    int i = 0, j = ht.size() - 1;\n    // 初期の最大容量は 0\n    int res = 0;\n    // 2 枚の板が出会うまで貪欲選択を繰り返す\n    while (i &lt; j) {\n        // 最大容量を更新する\n        int cap = min(ht[i], ht[j]) * (j - i);\n        res = max(res, cap);\n        // 短い方を内側へ動かす\n        if (ht[i] &lt; ht[j]) {\n            i++;\n        } else {\n            j--;\n        }\n    }\n    return res;\n}\n</code></pre> max_capacity.java<pre><code>/* 最大容量：貪欲法 */\nint maxCapacity(int[] ht) {\n    // i, j を初期化し、それぞれ配列の両端に置く\n    int i = 0, j = ht.length - 1;\n    // 初期の最大容量は 0\n    int res = 0;\n    // 2 枚の板が出会うまで貪欲選択を繰り返す\n    while (i &lt; j) {\n        // 最大容量を更新する\n        int cap = Math.min(ht[i], ht[j]) * (j - i);\n        res = Math.max(res, cap);\n        // 短い方を内側へ動かす\n        if (ht[i] &lt; ht[j]) {\n            i++;\n        } else {\n            j--;\n        }\n    }\n    return res;\n}\n</code></pre> max_capacity.cs<pre><code>/* 最大容量：貪欲法 */\nint MaxCapacity(int[] ht) {\n    // i, j を初期化し、それぞれ配列の両端に置く\n    int i = 0, j = ht.Length - 1;\n    // 初期の最大容量は 0\n    int res = 0;\n    // 2 枚の板が出会うまで貪欲選択を繰り返す\n    while (i &lt; j) {\n        // 最大容量を更新する\n        int cap = Math.Min(ht[i], ht[j]) * (j - i);\n        res = Math.Max(res, cap);\n        // 短い方を内側へ動かす\n        if (ht[i] &lt; ht[j]) {\n            i++;\n        } else {\n            j--;\n        }\n    }\n    return res;\n}\n</code></pre> max_capacity.go<pre><code>/* 最大容量：貪欲法 */\nfunc maxCapacity(ht []int) int {\n    // i, j を初期化し、それぞれ配列の両端に置く\n    i, j := 0, len(ht)-1\n    // 初期の最大容量は 0\n    res := 0\n    // 2 枚の板が出会うまで貪欲選択を繰り返す\n    for i &lt; j {\n        // 最大容量を更新する\n        capacity := int(math.Min(float64(ht[i]), float64(ht[j]))) * (j - i)\n        res = int(math.Max(float64(res), float64(capacity)))\n        // 短い方を内側へ動かす\n        if ht[i] &lt; ht[j] {\n            i++\n        } else {\n            j--\n        }\n    }\n    return res\n}\n</code></pre> max_capacity.swift<pre><code>/* 最大容量：貪欲法 */\nfunc maxCapacity(ht: [Int]) -&gt; Int {\n    // i, j を初期化し、それぞれ配列の両端に置く\n    var i = ht.startIndex, j = ht.endIndex - 1\n    // 初期の最大容量は 0\n    var res = 0\n    // 2 枚の板が出会うまで貪欲選択を繰り返す\n    while i &lt; j {\n        // 最大容量を更新する\n        let cap = min(ht[i], ht[j]) * (j - i)\n        res = max(res, cap)\n        // 短い方を内側へ動かす\n        if ht[i] &lt; ht[j] {\n            i += 1\n        } else {\n            j -= 1\n        }\n    }\n    return res\n}\n</code></pre> max_capacity.js<pre><code>/* 最大容量：貪欲法 */\nfunction maxCapacity(ht) {\n    // i, j を初期化し、それぞれ配列の両端に置く\n    let i = 0,\n        j = ht.length - 1;\n    // 初期の最大容量は 0\n    let res = 0;\n    // 2 枚の板が出会うまで貪欲選択を繰り返す\n    while (i &lt; j) {\n        // 最大容量を更新する\n        const cap = Math.min(ht[i], ht[j]) * (j - i);\n        res = Math.max(res, cap);\n        // 短い方を内側へ動かす\n        if (ht[i] &lt; ht[j]) {\n            i += 1;\n        } else {\n            j -= 1;\n        }\n    }\n    return res;\n}\n</code></pre> max_capacity.ts<pre><code>/* 最大容量：貪欲法 */\nfunction maxCapacity(ht: number[]): number {\n    // i, j を初期化し、それぞれ配列の両端に置く\n    let i = 0,\n        j = ht.length - 1;\n    // 初期の最大容量は 0\n    let res = 0;\n    // 2 枚の板が出会うまで貪欲選択を繰り返す\n    while (i &lt; j) {\n        // 最大容量を更新する\n        const cap: number = Math.min(ht[i], ht[j]) * (j - i);\n        res = Math.max(res, cap);\n        // 短い方を内側へ動かす\n        if (ht[i] &lt; ht[j]) {\n            i += 1;\n        } else {\n            j -= 1;\n        }\n    }\n    return res;\n}\n</code></pre> max_capacity.dart<pre><code>/* 最大容量：貪欲法 */\nint maxCapacity(List&lt;int&gt; ht) {\n  // i, j を初期化し、それぞれ配列の両端に置く\n  int i = 0, j = ht.length - 1;\n  // 初期の最大容量は 0\n  int res = 0;\n  // 2 枚の板が出会うまで貪欲選択を繰り返す\n  while (i &lt; j) {\n    // 最大容量を更新する\n    int cap = min(ht[i], ht[j]) * (j - i);\n    res = max(res, cap);\n    // 短い方を内側へ動かす\n    if (ht[i] &lt; ht[j]) {\n      i++;\n    } else {\n      j--;\n    }\n  }\n  return res;\n}\n</code></pre> max_capacity.rs<pre><code>/* 最大容量：貪欲法 */\nfn max_capacity(ht: &amp;[i32]) -&gt; i32 {\n    // i, j を初期化し、それぞれ配列の両端に置く\n    let mut i = 0;\n    let mut j = ht.len() - 1;\n    // 初期の最大容量は 0\n    let mut res = 0;\n    // 2 枚の板が出会うまで貪欲選択を繰り返す\n    while i &lt; j {\n        // 最大容量を更新する\n        let cap = std::cmp::min(ht[i], ht[j]) * (j - i) as i32;\n        res = std::cmp::max(res, cap);\n        // 短い方を内側へ動かす\n        if ht[i] &lt; ht[j] {\n            i += 1;\n        } else {\n            j -= 1;\n        }\n    }\n    res\n}\n</code></pre> max_capacity.c<pre><code>/* 最大容量：貪欲法 */\nint maxCapacity(int ht[], int htLength) {\n    // i, j を初期化し、それぞれ配列の両端に置く\n    int i = 0;\n    int j = htLength - 1;\n    // 初期の最大容量は 0\n    int res = 0;\n    // 2 枚の板が出会うまで貪欲選択を繰り返す\n    while (i &lt; j) {\n        // 最大容量を更新する\n        int capacity = myMin(ht[i], ht[j]) * (j - i);\n        res = myMax(res, capacity);\n        // 短い方を内側へ動かす\n        if (ht[i] &lt; ht[j]) {\n            i++;\n        } else {\n            j--;\n        }\n    }\n    return res;\n}\n</code></pre> max_capacity.kt<pre><code>/* 最大容量：貪欲法 */\nfun maxCapacity(ht: IntArray): Int {\n    // i, j を初期化し、それぞれ配列の両端に置く\n    var i = 0\n    var j = ht.size - 1\n    // 初期の最大容量は 0\n    var res = 0\n    // 2 枚の板が出会うまで貪欲選択を繰り返す\n    while (i &lt; j) {\n        // 最大容量を更新する\n        val cap = min(ht[i], ht[j]) * (j - i)\n        res = max(res, cap)\n        // 短い方を内側へ動かす\n        if (ht[i] &lt; ht[j]) {\n            i++\n        } else {\n            j--\n        }\n    }\n    return res\n}\n</code></pre> max_capacity.rb<pre><code>### 最大容量：貪欲法 ###\ndef max_capacity(ht)\n  # i, j を初期化し、それぞれ配列の両端に置く\n  i, j = 0, ht.length - 1\n  # 初期の最大容量は 0\n  res = 0\n\n  # 2 枚の板が出会うまで貪欲選択を繰り返す\n  while i &lt; j\n    # 最大容量を更新する\n    cap = [ht[i], ht[j]].min * (j - i)\n    res = [res, cap].max\n    # 短い方を内側へ動かす\n    if ht[i] &lt; ht[j]\n      i += 1\n    else\n      j -= 1\n    end\n  end\n\n  res\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 15 章 &nbsp; 貪欲法","15.3 &nbsp; 最大容量問題"],"tags":[]},{"location":"chapter_greedy/max_capacity_problem/#3","level":3,"title":"3.   正しさの証明","text":"<p>貪欲法が総当たりより速いのは、各ラウンドの貪欲な選択がいくつかの状態を「スキップ」するためです。</p> <p>たとえば状態 \\(cap[i, j]\\) において、\\(i\\) が短い板、\\(j\\) が長い板だとします。貪欲に短い板 \\(i\\) を内側へ 1 マス動かすと、次の図に示す状態が「スキップ」されます。これは、その後それらの状態の容量を検証できないことを意味します。</p> \\[ cap[i, i+1], cap[i, i+2], \\dots, cap[i, j-2], cap[i, j-1] \\] <p></p> <p> 図 15-12   短い板の移動によってスキップされる状態 </p> <p>観察すると、これらのスキップされた状態は、実際には長い板 \\(j\\) を内側へ動かしたすべての状態そのものです。前述のとおり、長い板を内側へ動かすと容量は必ず小さくなります。つまり、スキップされた状態はいずれも最適解にはなりえず、それらを飛ばしても最適解を逃すことはありません。</p> <p>以上の分析から、短い板を動かす操作は「安全」であり、貪欲戦略は有効であると分かります。</p>","path":["第 15 章 &nbsp; 貪欲法","15.3 &nbsp; 最大容量問題"],"tags":[]},{"location":"chapter_greedy/max_product_cutting_problem/","level":1,"title":"15.4   最大積分割問題","text":"<p>Question</p> <p>正整数 \\(n\\) が与えられたとき、それを少なくとも 2 つの正整数の和に分割し、分割後のすべての整数の積の最大値を求めよ。下図に示す。</p> <p></p> <p> 図 15-13   最大積分割問題の定義 </p> <p>仮に \\(n\\) を \\(m\\) 個の整数因子に分割し、そのうち第 \\(i\\) 個の因子を \\(n_i\\) と記すと、</p> \\[ n = \\sum_{i=1}^{m}n_i \\] <p>本問題の目的は、すべての整数因子の積の最大値を求めることであり、すなわち</p> \\[ \\max(\\prod_{i=1}^{m}n_i) \\] <p>考えるべきことは、分割数 \\(m\\) をいくつにすべきか、各 \\(n_i\\) をいくつにすべきかである。</p>","path":["第 15 章 &nbsp; 貪欲法","15.4 &nbsp; 最大積分割問題"],"tags":[]},{"location":"chapter_greedy/max_product_cutting_problem/#1","level":3,"title":"1.   貪欲戦略の決定","text":"<p>経験的に、2 つの整数の積はその和より大きくなることが多い。\\(n\\) から因子 \\(2\\) を 1 つ切り出すと、それらの積は \\(2(n-2)\\) となる。この積を \\(n\\) と比較すると、</p> \\[ \\begin{aligned} 2(n-2) &amp; \\geq n \\newline 2n - n - 4 &amp; \\geq 0 \\newline n &amp; \\geq 4 \\end{aligned} \\] <p>下図のように、\\(n \\geq 4\\) のとき、\\(2\\) を 1 つ切り出すと積は大きくなる。これは、\\(4\\) 以上の整数はすべて分割すべきことを意味する。</p> <p>貪欲戦略一：分割方法に \\(\\geq 4\\) の因子が含まれるなら、それはさらに分割すべきである。最終的な分割方法に現れる因子は \\(1\\)、\\(2\\)、\\(3\\) の 3 種類だけである。</p> <p></p> <p> 図 15-14   分割により積が大きくなる </p> <p>次に、どの因子が最適かを考える。\\(1\\)、\\(2\\)、\\(3\\) の 3 つの因子のうち、明らかに \\(1\\) が最も悪い。なぜなら \\(1 \\times (n-1) &lt; n\\) は常に成り立ち、\\(1\\) を切り出すとかえって積が小さくなるからである。</p> <p>下図のように、\\(n = 6\\) のとき、\\(3 \\times 3 &gt; 2 \\times 2 \\times 2\\) が成り立つ。これは、\\(2\\) を切り出すより \\(3\\) を切り出すほうが有利であることを意味する。</p> <p>貪欲戦略二：分割方法の中に存在してよい \\(2\\) は高々 2 つである。なぜなら、3 つの \\(2\\) は常に 2 つの \\(3\\) に置き換えられ、より大きな積を得られるからである。</p> <p></p> <p> 図 15-15   最適な分割因子 </p> <p>以上より、次の貪欲戦略が導かれる。</p> <ol> <li>整数 \\(n\\) を入力し、余りが \\(0\\)、\\(1\\)、\\(2\\) になるまで、そこから因子 \\(3\\) を繰り返し切り出す。</li> <li>余りが \\(0\\) のとき、\\(n\\) は \\(3\\) の倍数であることを表すため、何も処理しない。</li> <li>余りが \\(2\\) のときは、それ以上分割せず、そのまま残す。</li> <li>余りが \\(1\\) のとき、\\(2 \\times 2 &gt; 1 \\times 3\\) であるため、最後の \\(3\\) を \\(2\\) に置き換えるべきである。</li> </ol>","path":["第 15 章 &nbsp; 貪欲法","15.4 &nbsp; 最大積分割問題"],"tags":[]},{"location":"chapter_greedy/max_product_cutting_problem/#2","level":3,"title":"2.   コード実装","text":"<p>下図のように、ループで整数を分割する必要はなく、切り捨て除算によって \\(3\\) の個数 \\(a\\) を、剰余演算によって余り \\(b\\) を得られる。このとき、</p> \\[ n = 3 a + b \\] <p>なお、\\(n \\leq 3\\) の境界ケースでは、必ず \\(1\\) を 1 つ分割する必要があり、積は \\(1 \\times (n - 1)\\) となる。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby max_product_cutting.py<pre><code>def max_product_cutting(n: int) -&gt; int:\n    \"\"\"最大切断積：貪欲法\"\"\"\n    # n &lt;= 3 のときは、必ず 1 を切り出す\n    if n &lt;= 3:\n        return 1 * (n - 1)\n    # 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする\n    a, b = n // 3, n % 3\n    if b == 1:\n        # 余りが 1 のときは、1 * 3 を 2 * 2 に変える\n        return int(math.pow(3, a - 1)) * 2 * 2\n    if b == 2:\n        # 余りが 2 のときは、そのままにする\n        return int(math.pow(3, a)) * 2\n    # 余りが 0 のときは、そのままにする\n    return int(math.pow(3, a))\n</code></pre> max_product_cutting.cpp<pre><code>/* 最大切断積：貪欲法 */\nint maxProductCutting(int n) {\n    // n &lt;= 3 のときは、必ず 1 を切り出す\n    if (n &lt;= 3) {\n        return 1 * (n - 1);\n    }\n    // 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする\n    int a = n / 3;\n    int b = n % 3;\n    if (b == 1) {\n        // 余りが 1 のときは、1 * 3 を 2 * 2 に変える\n        return (int)pow(3, a - 1) * 2 * 2;\n    }\n    if (b == 2) {\n        // 余りが 2 のときは、そのままにする\n        return (int)pow(3, a) * 2;\n    }\n    // 余りが 0 のときは、そのままにする\n    return (int)pow(3, a);\n}\n</code></pre> max_product_cutting.java<pre><code>/* 最大切断積：貪欲法 */\nint maxProductCutting(int n) {\n    // n &lt;= 3 のときは、必ず 1 を切り出す\n    if (n &lt;= 3) {\n        return 1 * (n - 1);\n    }\n    // 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする\n    int a = n / 3;\n    int b = n % 3;\n    if (b == 1) {\n        // 余りが 1 のときは、1 * 3 を 2 * 2 に変える\n        return (int) Math.pow(3, a - 1) * 2 * 2;\n    }\n    if (b == 2) {\n        // 余りが 2 のときは、そのままにする\n        return (int) Math.pow(3, a) * 2;\n    }\n    // 余りが 0 のときは、そのままにする\n    return (int) Math.pow(3, a);\n}\n</code></pre> max_product_cutting.cs<pre><code>/* 最大切断積：貪欲法 */\nint MaxProductCutting(int n) {\n    // n &lt;= 3 のときは、必ず 1 を切り出す\n    if (n &lt;= 3) {\n        return 1 * (n - 1);\n    }\n    // 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする\n    int a = n / 3;\n    int b = n % 3;\n    if (b == 1) {\n        // 余りが 1 のときは、1 * 3 を 2 * 2 に変える\n        return (int)Math.Pow(3, a - 1) * 2 * 2;\n    }\n    if (b == 2) {\n        // 余りが 2 のときは、そのままにする\n        return (int)Math.Pow(3, a) * 2;\n    }\n    // 余りが 0 のときは、そのままにする\n    return (int)Math.Pow(3, a);\n}\n</code></pre> max_product_cutting.go<pre><code>/* 最大切断積：貪欲法 */\nfunc maxProductCutting(n int) int {\n    // n &lt;= 3 のときは、必ず 1 を切り出す\n    if n &lt;= 3 {\n        return 1 * (n - 1)\n    }\n    // 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする\n    a := n / 3\n    b := n % 3\n    if b == 1 {\n        // 余りが 1 のときは、1 * 3 を 2 * 2 に変える\n        return int(math.Pow(3, float64(a-1))) * 2 * 2\n    }\n    if b == 2 {\n        // 余りが 2 のときは、そのままにする\n        return int(math.Pow(3, float64(a))) * 2\n    }\n    // 余りが 0 のときは、そのままにする\n    return int(math.Pow(3, float64(a)))\n}\n</code></pre> max_product_cutting.swift<pre><code>/* 最大切断積：貪欲法 */\nfunc maxProductCutting(n: Int) -&gt; Int {\n    // n &lt;= 3 のときは、必ず 1 を切り出す\n    if n &lt;= 3 {\n        return 1 * (n - 1)\n    }\n    // 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする\n    let a = n / 3\n    let b = n % 3\n    if b == 1 {\n        // 余りが 1 のときは、1 * 3 を 2 * 2 に変える\n        return pow(3, a - 1) * 2 * 2\n    }\n    if b == 2 {\n        // 余りが 2 のときは、そのままにする\n        return pow(3, a) * 2\n    }\n    // 余りが 0 のときは、そのままにする\n    return pow(3, a)\n}\n</code></pre> max_product_cutting.js<pre><code>/* 最大切断積：貪欲法 */\nfunction maxProductCutting(n) {\n    // n &lt;= 3 のときは、必ず 1 を切り出す\n    if (n &lt;= 3) {\n        return 1 * (n - 1);\n    }\n    // 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする\n    let a = Math.floor(n / 3);\n    let b = n % 3;\n    if (b === 1) {\n        // 余りが 1 のときは、1 * 3 を 2 * 2 に変える\n        return Math.pow(3, a - 1) * 2 * 2;\n    }\n    if (b === 2) {\n        // 余りが 2 のときは、そのままにする\n        return Math.pow(3, a) * 2;\n    }\n    // 余りが 0 のときは、そのままにする\n    return Math.pow(3, a);\n}\n</code></pre> max_product_cutting.ts<pre><code>/* 最大切断積：貪欲法 */\nfunction maxProductCutting(n: number): number {\n    // n &lt;= 3 のときは、必ず 1 を切り出す\n    if (n &lt;= 3) {\n        return 1 * (n - 1);\n    }\n    // 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする\n    let a: number = Math.floor(n / 3);\n    let b: number = n % 3;\n    if (b === 1) {\n        // 余りが 1 のときは、1 * 3 を 2 * 2 に変える\n        return Math.pow(3, a - 1) * 2 * 2;\n    }\n    if (b === 2) {\n        // 余りが 2 のときは、そのままにする\n        return Math.pow(3, a) * 2;\n    }\n    // 余りが 0 のときは、そのままにする\n    return Math.pow(3, a);\n}\n</code></pre> max_product_cutting.dart<pre><code>/* 最大切断積：貪欲法 */\nint maxProductCutting(int n) {\n  // n &lt;= 3 のときは、必ず 1 を切り出す\n  if (n &lt;= 3) {\n    return 1 * (n - 1);\n  }\n  // 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする\n  int a = n ~/ 3;\n  int b = n % 3;\n  if (b == 1) {\n    // 余りが 1 のときは、1 * 3 を 2 * 2 に変える\n    return (pow(3, a - 1) * 2 * 2).toInt();\n  }\n  if (b == 2) {\n    // 余りが 2 のときは、そのままにする\n    return (pow(3, a) * 2).toInt();\n  }\n  // 余りが 0 のときは、そのままにする\n  return pow(3, a).toInt();\n}\n</code></pre> max_product_cutting.rs<pre><code>/* 最大切断積：貪欲法 */\nfn max_product_cutting(n: i32) -&gt; i32 {\n    // n &lt;= 3 のときは、必ず 1 を切り出す\n    if n &lt;= 3 {\n        return 1 * (n - 1);\n    }\n    // 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする\n    let a = n / 3;\n    let b = n % 3;\n    if b == 1 {\n        // 余りが 1 のときは、1 * 3 を 2 * 2 に変える\n        3_i32.pow(a as u32 - 1) * 2 * 2\n    } else if b == 2 {\n        // 余りが 2 のときは、そのままにする\n        3_i32.pow(a as u32) * 2\n    } else {\n        // 余りが 0 のときは、そのままにする\n        3_i32.pow(a as u32)\n    }\n}\n</code></pre> max_product_cutting.c<pre><code>/* 最大切断積：貪欲法 */\nint maxProductCutting(int n) {\n    // n &lt;= 3 のときは、必ず 1 を切り出す\n    if (n &lt;= 3) {\n        return 1 * (n - 1);\n    }\n    // 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする\n    int a = n / 3;\n    int b = n % 3;\n    if (b == 1) {\n        // 余りが 1 のときは、1 * 3 を 2 * 2 に変える\n        return pow(3, a - 1) * 2 * 2;\n    }\n    if (b == 2) {\n        // 余りが 2 のときは、そのままにする\n        return pow(3, a) * 2;\n    }\n    // 余りが 0 のときは、そのままにする\n    return pow(3, a);\n}\n</code></pre> max_product_cutting.kt<pre><code>/* 最大切断積：貪欲法 */\nfun maxProductCutting(n: Int): Int {\n    // n &lt;= 3 のときは、必ず 1 を切り出す\n    if (n &lt;= 3) {\n        return 1 * (n - 1)\n    }\n    // 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする\n    val a = n / 3\n    val b = n % 3\n    if (b == 1) {\n        // 余りが 1 のときは、1 * 3 を 2 * 2 に変える\n        return 3.0.pow((a - 1)).toInt() * 2 * 2\n    }\n    if (b == 2) {\n        // 余りが 2 のときは、そのままにする\n        return 3.0.pow(a).toInt() * 2 * 2\n    }\n    // 余りが 0 のときは、そのままにする\n    return 3.0.pow(a).toInt()\n}\n</code></pre> max_product_cutting.rb<pre><code>### 最大分割積：貪欲法 ###\ndef max_product_cutting(n)\n  # n &lt;= 3 のときは、必ず 1 を切り出す\n  return 1 * (n - 1) if n &lt;= 3\n  # 貪欲に 3 を切り出し、a を 3 の個数、b を余りとする\n  a, b = n / 3, n % 3\n  # 余りが 1 のときは、1 * 3 を 2 * 2 に変える\n  return (3.pow(a - 1) * 2 * 2).to_i if b == 1\n  # 余りが 2 のときは、そのままにする\n  return (3.pow(a) * 2).to_i if b == 2\n  # 余りが 0 のときは、そのままにする\n  3.pow(a).to_i\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p></p> <p> 図 15-16   最大積分割の計算方法 </p> <p>時間計算量は、プログラミング言語におけるべき乗演算の実装方法に依存する。Python を例に取ると、よく使われるべき乗計算関数は 3 種類ある。</p> <ul> <li>演算子 <code>**</code> と関数 <code>pow()</code> の時間計算量はいずれも \\(O(\\log⁡ a)\\) である。</li> <li>関数 <code>math.pow()</code> は内部で C 言語ライブラリの <code>pow()</code> 関数を呼び出し、浮動小数点のべき乗を実行するため、時間計算量は \\(O(1)\\) である。</li> </ul> <p>変数 \\(a\\) と \\(b\\) が使う追加領域は定数サイズであり、したがって空間計算量は \\(O(1)\\) である。</p>","path":["第 15 章 &nbsp; 貪欲法","15.4 &nbsp; 最大積分割問題"],"tags":[]},{"location":"chapter_greedy/max_product_cutting_problem/#3","level":3,"title":"3.   正しさの証明","text":"<p>背理法を用い、\\(n \\geq 4\\) の場合のみを考える。</p> <ol> <li>すべての因子は \\(\\leq 3\\) ：最適な分割方法に \\(\\geq 4\\) の因子 \\(x\\) が存在すると仮定すると、それは必ずさらに \\(2(x-2)\\) に分割でき、より大きい（または等しい）積が得られる。これは仮定に矛盾する。</li> <li>分割方法に \\(1\\) は含まれない ：最適な分割方法に因子 \\(1\\) が 1 つ存在すると仮定すると、それは必ず別の因子に併合でき、より大きい積を得られる。これは仮定に矛盾する。</li> <li>分割方法に含まれる \\(2\\) は高々 2 つ ：最適な分割方法に 3 つの \\(2\\) が含まれると仮定すると、それは必ず 2 つの \\(3\\) に置き換えられ、積はより大きくなる。これは仮定に矛盾する。</li> </ol>","path":["第 15 章 &nbsp; 貪欲法","15.4 &nbsp; 最大積分割問題"],"tags":[]},{"location":"chapter_greedy/summary/","level":1,"title":"15.5   まとめ","text":"","path":["第 15 章 &nbsp; 貪欲法","15.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_greedy/summary/#1","level":3,"title":"1.   重要な振り返り","text":"<ul> <li>貪欲法は通常、最適化問題を解くために用いられ、その原理は各意思決定段階で局所最適な決定を行い、全体最適解を得ることを目指すというものである。</li> <li>貪欲法は反復的に次々と貪欲な選択を行い、各ラウンドで問題をより小さな部分問題へと変換し、最終的に問題を解決する。</li> <li>貪欲法は実装が簡単であるだけでなく、問題を解く効率も高い。動的計画法と比べると、貪欲法の時間計算量は通常より低い。</li> <li>硬貨両替問題では、ある種の硬貨の組み合わせに対しては貪欲法で最適解を保証できるが、別の組み合わせではそうではなく、非常に悪い解を見つけてしまう可能性がある。</li> <li>貪欲法による解法に適した問題は、貪欲選択性と最適部分構造という 2 つの性質を備えている。貪欲選択性は、貪欲戦略の有効性を表している。</li> <li>一部の複雑な問題では、貪欲選択性を証明するのは容易ではない。相対的には、反例による否定のほうが簡単であり、硬貨両替問題がその一例である。</li> <li>貪欲法の問題を解く流れは主に 3 段階に分かれる。すなわち、問題分析、貪欲戦略の決定、正しさの証明である。このうち、貪欲戦略の決定が中核であり、正しさの証明はしばしば難所となる。</li> <li>分数ナップサック問題は 0-1 ナップサックを基に、品物の一部を選ぶことを許しているため、貪欲法で解くことができる。貪欲戦略の正しさは背理法で証明できる。</li> <li>最大容量問題は全探索で解くことができ、時間計算量は \\(O(n^2)\\) である。貪欲戦略を設計し、各ラウンドで短い板を内側へ動かすことで、時間計算量を \\(O(n)\\) に最適化できる。</li> <li>最大分割積問題では、2 つの貪欲戦略を順に導いた。すなわち、\\(\\geq 4\\) の整数はすべてさらに分割すべきであり、最適な分割因子は \\(3\\) である。コードにはべき乗演算が含まれており、時間計算量はその実装方法に依存し、通常は \\(O(1)\\) または \\(O(\\log n)\\) である。</li> </ul>","path":["第 15 章 &nbsp; 貪欲法","15.5 &nbsp; まとめ"],"tags":[]},{"location":"chapter_hashing/","level":1,"title":"第 6 章   ハッシュテーブル","text":"<p>Abstract</p> <p>コンピュータの世界では、ハッシュテーブルは聡明な図書館員のような存在です。</p> <p>彼は請求記号の計算方法を知っており、そのため目的の本を素早く見つけられます。</p>","path":["第 6 章 &nbsp; ハッシュテーブル"],"tags":[]},{"location":"chapter_hashing/#_1","level":2,"title":"章の内容","text":"<ul> <li>6.1   ハッシュテーブル</li> <li>6.2   ハッシュ衝突</li> <li>6.3   ハッシュアルゴリズム</li> <li>6.4   まとめ</li> </ul>","path":["第 6 章 &nbsp; ハッシュテーブル"],"tags":[]},{"location":"chapter_hashing/hash_algorithm/","level":1,"title":"6.3   ハッシュアルゴリズム","text":"<p>前の 2 節では、ハッシュテーブルの動作原理とハッシュ衝突の処理方法を紹介しました。しかし、オープンアドレス法であれ連鎖方式であれ、それらが保証できるのは衝突発生時でもハッシュテーブルが正常に動作することだけであり、ハッシュ衝突そのものを減らすことはできません。</p> <p>ハッシュ衝突があまりにも頻繁に発生すると、ハッシュテーブルの性能は急激に劣化します。下図のように、連鎖方式のハッシュテーブルでは、理想的な場合にはキーと値のペアが各バケットに均等に分布し、最良の検索効率を達成します。最悪の場合には、すべてのキーと値のペアが同じバケットに格納され、時間計算量は \\(O(n)\\) に劣化します。</p> <p></p> <p> 図 6-8   ハッシュ衝突の最良ケースと最悪ケース </p> <p>キーと値のペアの分布はハッシュ関数によって決まります。ハッシュ関数の計算手順を思い出すと、まずハッシュ値を計算し、その後で配列長に対して剰余を取ります。</p> <pre><code>index = hash(key) % capacity\n</code></pre> <p>上の式から分かるように、ハッシュテーブルの容量 <code>capacity</code> が固定されているとき、出力値を決めるのはハッシュアルゴリズム <code>hash()</code> です。したがって、それがキーと値のペアのハッシュテーブル内での分布も決定します。</p> <p>これは、ハッシュ衝突の発生確率を下げるには、ハッシュアルゴリズム <code>hash()</code> の設計に注目すべきだということを意味します。</p>","path":["第 6 章 &nbsp; ハッシュテーブル","6.3 &nbsp; ハッシュアルゴリズム"],"tags":[]},{"location":"chapter_hashing/hash_algorithm/#631","level":2,"title":"6.3.1   ハッシュアルゴリズムの目標","text":"<p>「高速かつ安定した」ハッシュテーブルというデータ構造を実現するために、ハッシュアルゴリズムは次の特徴を備える必要があります。</p> <ul> <li>決定性：同じ入力に対して、ハッシュアルゴリズムは常に同じ出力を生成しなければなりません。そうして初めて、ハッシュテーブルの信頼性が保たれます。</li> <li>高効率：ハッシュ値の計算過程は十分に高速であるべきです。計算コストが小さいほど、ハッシュテーブルの実用性は高くなります。</li> <li>均一分布：ハッシュアルゴリズムは、キーと値のペアがハッシュテーブル内に均等に分布するようにすべきです。分布が均一であるほど、ハッシュ衝突の確率は低くなります。</li> </ul> <p>実際には、ハッシュアルゴリズムはハッシュテーブルの実装だけでなく、ほかの多くの分野でも広く利用されています。</p> <ul> <li>パスワード保存：ユーザーのパスワードを保護するために、システムは通常、平文パスワードを直接保存せず、そのハッシュ値を保存します。ユーザーがパスワードを入力すると、システムは入力内容のハッシュ値を計算し、保存済みのハッシュ値と比較します。一致すれば、そのパスワードは正しいと見なされます。</li> <li>データ完全性検査：送信側はデータのハッシュ値を計算してデータと一緒に送信できます。受信側は受け取ったデータのハッシュ値を再計算し、受信したハッシュ値と比較できます。両者が一致すれば、そのデータは完全だと見なされます。</li> </ul> <p>暗号分野の応用では、ハッシュ値から元のパスワードを推測するといった逆解析を防ぐために、ハッシュアルゴリズムにはさらに高いレベルの安全性が求められます。</p> <ul> <li>一方向性：ハッシュ値から入力データに関するいかなる情報も逆算できないこと。</li> <li>耐衝突性：異なる 2 つの入力で同じハッシュ値になるものを見つけることが、極めて困難であること。</li> <li>アバランシェ効果：入力のわずかな変化が、出力の大きく予測不能な変化を引き起こすこと。</li> </ul> <p>注意してほしいのは、**「均一分布」と「耐衝突性」は独立した 2 つの概念である**という点です。均一分布を満たしていても、耐衝突性を満たすとは限りません。たとえば、入力 <code>key</code> がランダムである場合、ハッシュ関数 <code>key % 100</code> は均一に分布した出力を生成できます。しかし、このハッシュアルゴリズムはあまりにも単純で、下 2 桁が同じ <code>key</code> はすべて同じ出力になります。そのため、ハッシュ値から利用可能な <code>key</code> を容易に逆算でき、結果としてパスワードが破られてしまいます。</p>","path":["第 6 章 &nbsp; ハッシュテーブル","6.3 &nbsp; ハッシュアルゴリズム"],"tags":[]},{"location":"chapter_hashing/hash_algorithm/#632","level":2,"title":"6.3.2   ハッシュアルゴリズムの設計","text":"<p>ハッシュアルゴリズムの設計は、多くの要素を考慮しなければならない複雑な問題です。しかし、要求の高くない場面であれば、いくつかの単純なハッシュアルゴリズムを設計することもできます。</p> <ul> <li>加算ハッシュ：入力の各文字の ASCII コードを足し合わせ、その合計をハッシュ値とします。</li> <li>乗算ハッシュ：乗算の非相関性を利用し、各ラウンドで定数を掛けながら、各文字の ASCII コードをハッシュ値に累積します。</li> <li>XOR ハッシュ：入力データの各要素を XOR 演算で 1 つのハッシュ値に累積します。</li> <li>回転ハッシュ：各文字の ASCII コードを 1 つのハッシュ値に累積し、各回の累積前にハッシュ値を回転させます。</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby simple_hash.py<pre><code>def add_hash(key: str) -&gt; int:\n    \"\"\"加算ハッシュ\"\"\"\n    hash = 0\n    modulus = 1000000007\n    for c in key:\n        hash += ord(c)\n    return hash % modulus\n\ndef mul_hash(key: str) -&gt; int:\n    \"\"\"乗算ハッシュ\"\"\"\n    hash = 0\n    modulus = 1000000007\n    for c in key:\n        hash = 31 * hash + ord(c)\n    return hash % modulus\n\ndef xor_hash(key: str) -&gt; int:\n    \"\"\"XOR ハッシュ\"\"\"\n    hash = 0\n    modulus = 1000000007\n    for c in key:\n        hash ^= ord(c)\n    return hash % modulus\n\ndef rot_hash(key: str) -&gt; int:\n    \"\"\"回転ハッシュ\"\"\"\n    hash = 0\n    modulus = 1000000007\n    for c in key:\n        hash = (hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ ord(c)\n    return hash % modulus\n</code></pre> simple_hash.cpp<pre><code>/* 加算ハッシュ */\nint addHash(string key) {\n    long long hash = 0;\n    const int MODULUS = 1000000007;\n    for (unsigned char c : key) {\n        hash = (hash + (int)c) % MODULUS;\n    }\n    return (int)hash;\n}\n\n/* 乗算ハッシュ */\nint mulHash(string key) {\n    long long hash = 0;\n    const int MODULUS = 1000000007;\n    for (unsigned char c : key) {\n        hash = (31 * hash + (int)c) % MODULUS;\n    }\n    return (int)hash;\n}\n\n/* XOR ハッシュ */\nint xorHash(string key) {\n    int hash = 0;\n    const int MODULUS = 1000000007;\n    for (unsigned char c : key) {\n        hash ^= (int)c;\n    }\n    return hash &amp; MODULUS;\n}\n\n/* 回転ハッシュ */\nint rotHash(string key) {\n    long long hash = 0;\n    const int MODULUS = 1000000007;\n    for (unsigned char c : key) {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ (int)c) % MODULUS;\n    }\n    return (int)hash;\n}\n</code></pre> simple_hash.java<pre><code>/* 加算ハッシュ */\nint addHash(String key) {\n    long hash = 0;\n    final int MODULUS = 1000000007;\n    for (char c : key.toCharArray()) {\n        hash = (hash + (int) c) % MODULUS;\n    }\n    return (int) hash;\n}\n\n/* 乗算ハッシュ */\nint mulHash(String key) {\n    long hash = 0;\n    final int MODULUS = 1000000007;\n    for (char c : key.toCharArray()) {\n        hash = (31 * hash + (int) c) % MODULUS;\n    }\n    return (int) hash;\n}\n\n/* XOR ハッシュ */\nint xorHash(String key) {\n    int hash = 0;\n    final int MODULUS = 1000000007;\n    for (char c : key.toCharArray()) {\n        hash ^= (int) c;\n    }\n    return hash &amp; MODULUS;\n}\n\n/* 回転ハッシュ */\nint rotHash(String key) {\n    long hash = 0;\n    final int MODULUS = 1000000007;\n    for (char c : key.toCharArray()) {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ (int) c) % MODULUS;\n    }\n    return (int) hash;\n}\n</code></pre> simple_hash.cs<pre><code>/* 加算ハッシュ */\nint AddHash(string key) {\n    long hash = 0;\n    const int MODULUS = 1000000007;\n    foreach (char c in key) {\n        hash = (hash + c) % MODULUS;\n    }\n    return (int)hash;\n}\n\n/* 乗算ハッシュ */\nint MulHash(string key) {\n    long hash = 0;\n    const int MODULUS = 1000000007;\n    foreach (char c in key) {\n        hash = (31 * hash + c) % MODULUS;\n    }\n    return (int)hash;\n}\n\n/* XOR ハッシュ */\nint XorHash(string key) {\n    int hash = 0;\n    const int MODULUS = 1000000007;\n    foreach (char c in key) {\n        hash ^= c;\n    }\n    return hash &amp; MODULUS;\n}\n\n/* 回転ハッシュ */\nint RotHash(string key) {\n    long hash = 0;\n    const int MODULUS = 1000000007;\n    foreach (char c in key) {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ c) % MODULUS;\n    }\n    return (int)hash;\n}\n</code></pre> simple_hash.go<pre><code>/* 加算ハッシュ */\nfunc addHash(key string) int {\n    var hash int64\n    var modulus int64\n\n    modulus = 1000000007\n    for _, b := range []byte(key) {\n        hash = (hash + int64(b)) % modulus\n    }\n    return int(hash)\n}\n\n/* 乗算ハッシュ */\nfunc mulHash(key string) int {\n    var hash int64\n    var modulus int64\n\n    modulus = 1000000007\n    for _, b := range []byte(key) {\n        hash = (31*hash + int64(b)) % modulus\n    }\n    return int(hash)\n}\n\n/* XOR ハッシュ */\nfunc xorHash(key string) int {\n    hash := 0\n    modulus := 1000000007\n    for _, b := range []byte(key) {\n        fmt.Println(int(b))\n        hash ^= int(b)\n        hash = (31*hash + int(b)) % modulus\n    }\n    return hash &amp; modulus\n}\n\n/* 回転ハッシュ */\nfunc rotHash(key string) int {\n    var hash int64\n    var modulus int64\n\n    modulus = 1000000007\n    for _, b := range []byte(key) {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ int64(b)) % modulus\n    }\n    return int(hash)\n}\n</code></pre> simple_hash.swift<pre><code>/* 加算ハッシュ */\nfunc addHash(key: String) -&gt; Int {\n    var hash = 0\n    let MODULUS = 1_000_000_007\n    for c in key {\n        for scalar in c.unicodeScalars {\n            hash = (hash + Int(scalar.value)) % MODULUS\n        }\n    }\n    return hash\n}\n\n/* 乗算ハッシュ */\nfunc mulHash(key: String) -&gt; Int {\n    var hash = 0\n    let MODULUS = 1_000_000_007\n    for c in key {\n        for scalar in c.unicodeScalars {\n            hash = (31 * hash + Int(scalar.value)) % MODULUS\n        }\n    }\n    return hash\n}\n\n/* XOR ハッシュ */\nfunc xorHash(key: String) -&gt; Int {\n    var hash = 0\n    let MODULUS = 1_000_000_007\n    for c in key {\n        for scalar in c.unicodeScalars {\n            hash ^= Int(scalar.value)\n        }\n    }\n    return hash &amp; MODULUS\n}\n\n/* 回転ハッシュ */\nfunc rotHash(key: String) -&gt; Int {\n    var hash = 0\n    let MODULUS = 1_000_000_007\n    for c in key {\n        for scalar in c.unicodeScalars {\n            hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ Int(scalar.value)) % MODULUS\n        }\n    }\n    return hash\n}\n</code></pre> simple_hash.js<pre><code>/* 加算ハッシュ */\nfunction addHash(key) {\n    let hash = 0;\n    const MODULUS = 1000000007;\n    for (const c of key) {\n        hash = (hash + c.charCodeAt(0)) % MODULUS;\n    }\n    return hash;\n}\n\n/* 乗算ハッシュ */\nfunction mulHash(key) {\n    let hash = 0;\n    const MODULUS = 1000000007;\n    for (const c of key) {\n        hash = (31 * hash + c.charCodeAt(0)) % MODULUS;\n    }\n    return hash;\n}\n\n/* XOR ハッシュ */\nfunction xorHash(key) {\n    let hash = 0;\n    const MODULUS = 1000000007;\n    for (const c of key) {\n        hash ^= c.charCodeAt(0);\n    }\n    return hash % MODULUS;\n}\n\n/* 回転ハッシュ */\nfunction rotHash(key) {\n    let hash = 0;\n    const MODULUS = 1000000007;\n    for (const c of key) {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ c.charCodeAt(0)) % MODULUS;\n    }\n    return hash;\n}\n</code></pre> simple_hash.ts<pre><code>/* 加算ハッシュ */\nfunction addHash(key: string): number {\n    let hash = 0;\n    const MODULUS = 1000000007;\n    for (const c of key) {\n        hash = (hash + c.charCodeAt(0)) % MODULUS;\n    }\n    return hash;\n}\n\n/* 乗算ハッシュ */\nfunction mulHash(key: string): number {\n    let hash = 0;\n    const MODULUS = 1000000007;\n    for (const c of key) {\n        hash = (31 * hash + c.charCodeAt(0)) % MODULUS;\n    }\n    return hash;\n}\n\n/* XOR ハッシュ */\nfunction xorHash(key: string): number {\n    let hash = 0;\n    const MODULUS = 1000000007;\n    for (const c of key) {\n        hash ^= c.charCodeAt(0);\n    }\n    return hash % MODULUS;\n}\n\n/* 回転ハッシュ */\nfunction rotHash(key: string): number {\n    let hash = 0;\n    const MODULUS = 1000000007;\n    for (const c of key) {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ c.charCodeAt(0)) % MODULUS;\n    }\n    return hash;\n}\n</code></pre> simple_hash.dart<pre><code>/* 加算ハッシュ */\nint addHash(String key) {\n  int hash = 0;\n  final int MODULUS = 1000000007;\n  for (int i = 0; i &lt; key.length; i++) {\n    hash = (hash + key.codeUnitAt(i)) % MODULUS;\n  }\n  return hash;\n}\n\n/* 乗算ハッシュ */\nint mulHash(String key) {\n  int hash = 0;\n  final int MODULUS = 1000000007;\n  for (int i = 0; i &lt; key.length; i++) {\n    hash = (31 * hash + key.codeUnitAt(i)) % MODULUS;\n  }\n  return hash;\n}\n\n/* XOR ハッシュ */\nint xorHash(String key) {\n  int hash = 0;\n  final int MODULUS = 1000000007;\n  for (int i = 0; i &lt; key.length; i++) {\n    hash ^= key.codeUnitAt(i);\n  }\n  return hash &amp; MODULUS;\n}\n\n/* 回転ハッシュ */\nint rotHash(String key) {\n  int hash = 0;\n  final int MODULUS = 1000000007;\n  for (int i = 0; i &lt; key.length; i++) {\n    hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ key.codeUnitAt(i)) % MODULUS;\n  }\n  return hash;\n}\n</code></pre> simple_hash.rs<pre><code>/* 加算ハッシュ */\nfn add_hash(key: &amp;str) -&gt; i32 {\n    let mut hash = 0_i64;\n    const MODULUS: i64 = 1000000007;\n\n    for c in key.chars() {\n        hash = (hash + c as i64) % MODULUS;\n    }\n\n    hash as i32\n}\n\n/* 乗算ハッシュ */\nfn mul_hash(key: &amp;str) -&gt; i32 {\n    let mut hash = 0_i64;\n    const MODULUS: i64 = 1000000007;\n\n    for c in key.chars() {\n        hash = (31 * hash + c as i64) % MODULUS;\n    }\n\n    hash as i32\n}\n\n/* XOR ハッシュ */\nfn xor_hash(key: &amp;str) -&gt; i32 {\n    let mut hash = 0_i64;\n    const MODULUS: i64 = 1000000007;\n\n    for c in key.chars() {\n        hash ^= c as i64;\n    }\n\n    (hash &amp; MODULUS) as i32\n}\n\n/* 回転ハッシュ */\nfn rot_hash(key: &amp;str) -&gt; i32 {\n    let mut hash = 0_i64;\n    const MODULUS: i64 = 1000000007;\n\n    for c in key.chars() {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ c as i64) % MODULUS;\n    }\n\n    hash as i32\n}\n</code></pre> simple_hash.c<pre><code>/* 加算ハッシュ */\nint addHash(char *key) {\n    long long hash = 0;\n    const int MODULUS = 1000000007;\n    for (int i = 0; i &lt; strlen(key); i++) {\n        hash = (hash + (unsigned char)key[i]) % MODULUS;\n    }\n    return (int)hash;\n}\n\n/* 乗算ハッシュ */\nint mulHash(char *key) {\n    long long hash = 0;\n    const int MODULUS = 1000000007;\n    for (int i = 0; i &lt; strlen(key); i++) {\n        hash = (31 * hash + (unsigned char)key[i]) % MODULUS;\n    }\n    return (int)hash;\n}\n\n/* XOR ハッシュ */\nint xorHash(char *key) {\n    int hash = 0;\n    const int MODULUS = 1000000007;\n\n    for (int i = 0; i &lt; strlen(key); i++) {\n        hash ^= (unsigned char)key[i];\n    }\n    return hash &amp; MODULUS;\n}\n\n/* 回転ハッシュ */\nint rotHash(char *key) {\n    long long hash = 0;\n    const int MODULUS = 1000000007;\n    for (int i = 0; i &lt; strlen(key); i++) {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ (unsigned char)key[i]) % MODULUS;\n    }\n\n    return (int)hash;\n}\n</code></pre> simple_hash.kt<pre><code>/* 加算ハッシュ */\nfun addHash(key: String): Int {\n    var hash = 0L\n    val MODULUS = 1000000007\n    for (c in key.toCharArray()) {\n        hash = (hash + c.code) % MODULUS\n    }\n    return hash.toInt()\n}\n\n/* 乗算ハッシュ */\nfun mulHash(key: String): Int {\n    var hash = 0L\n    val MODULUS = 1000000007\n    for (c in key.toCharArray()) {\n        hash = (31 * hash + c.code) % MODULUS\n    }\n    return hash.toInt()\n}\n\n/* XOR ハッシュ */\nfun xorHash(key: String): Int {\n    var hash = 0\n    val MODULUS = 1000000007\n    for (c in key.toCharArray()) {\n        hash = hash xor c.code\n    }\n    return hash and MODULUS\n}\n\n/* 回転ハッシュ */\nfun rotHash(key: String): Int {\n    var hash = 0L\n    val MODULUS = 1000000007\n    for (c in key.toCharArray()) {\n        hash = ((hash shl 4) xor (hash shr 28) xor c.code.toLong()) % MODULUS\n    }\n    return hash.toInt()\n}\n</code></pre> simple_hash.rb<pre><code>### 加算ハッシュ ###\ndef add_hash(key)\n  hash = 0\n  modulus = 1_000_000_007\n\n  key.each_char { |c| hash += c.ord }\n\n  hash % modulus\nend\n\n### 乗算ハッシュ ###\ndef mul_hash(key)\n  hash = 0\n  modulus = 1_000_000_007\n\n  key.each_char { |c| hash = 31 * hash + c.ord }\n\n  hash % modulus\nend\n\n### XOR ハッシュ ###\ndef xor_hash(key)\n  hash = 0\n  modulus = 1_000_000_007\n\n  key.each_char { |c| hash ^= c.ord }\n\n  hash % modulus\nend\n\n### 回転ハッシュ ###\ndef rot_hash(key)\n  hash = 0\n  modulus = 1_000_000_007\n\n  key.each_char { |c| hash = (hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ c.ord }\n\n  hash % modulus\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>見て分かるように、各ハッシュアルゴリズムの最後のステップでは、大きな素数 \\(1000000007\\) で剰余を取り、ハッシュ値が適切な範囲に収まるようにしています。ここで考えてみる価値があるのは、なぜ素数での剰余を強調するのか、あるいは合成数で剰余を取ることにどんな欠点があるのか、という点です。これは興味深い問題です。</p> <p>先に結論を述べると、法として大きな素数を使うと、ハッシュ値が均一に分布することを最大限に保証できます。素数はほかの数と公約数を持たないため、剰余演算によって生じる周期的なパターンを減らし、ハッシュ衝突を避けやすくなります。</p> <p>たとえば、法として合成数 \\(9\\) を選ぶとします。これは \\(3\\) で割り切れるため、\\(3\\) で割り切れるすべての <code>key</code> は、\\(0\\)、\\(3\\)、\\(6\\) の 3 つのハッシュ値に写像されます。</p> \\[ \\begin{aligned} \\text{modulus} &amp; = 9 \\newline \\text{key} &amp; = \\{ 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, \\dots \\} \\newline \\text{hash} &amp; = \\{ 0, 3, 6, 0, 3, 6, 0, 3, 6, 0, 3, 6,\\dots \\} \\end{aligned} \\] <p>入力 <code>key</code> がたまたまこのような等差数列の分布をしていると、ハッシュ値に偏りが生じ、ハッシュ衝突がさらに深刻になります。そこで <code>modulus</code> を素数 \\(13\\) に置き換えると仮定すると、<code>key</code> と <code>modulus</code> の間に公約数が存在しないため、出力されるハッシュ値の均一性は明らかに向上します。</p> \\[ \\begin{aligned} \\text{modulus} &amp; = 13 \\newline \\text{key} &amp; = \\{ 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, \\dots \\} \\newline \\text{hash} &amp; = \\{ 0, 3, 6, 9, 12, 2, 5, 8, 11, 1, 4, 7, \\dots \\} \\end{aligned} \\] <p>補足すると、<code>key</code> がランダムかつ均一に分布していると保証できるなら、法に素数を選んでも合成数を選んでも構いません。どちらでも均一に分布したハッシュ値を出力できます。しかし、<code>key</code> の分布に何らかの周期性がある場合、合成数で剰余を取るほうが偏りが生じやすくなります。</p> <p>要するに、通常は法として素数を選び、その素数はできるだけ大きいほうが望ましいです。そうすることで周期的なパターンをできる限り取り除き、ハッシュアルゴリズムの堅牢性を高められます。</p>","path":["第 6 章 &nbsp; ハッシュテーブル","6.3 &nbsp; ハッシュアルゴリズム"],"tags":[]},{"location":"chapter_hashing/hash_algorithm/#633","level":2,"title":"6.3.3   一般的なハッシュアルゴリズム","text":"<p>上で紹介した単純なハッシュアルゴリズムは、どれも比較的「脆弱」であり、ハッシュアルゴリズムの設計目標にはほど遠いことが分かります。たとえば、加算と XOR は交換法則を満たすため、加算ハッシュと XOR ハッシュでは、内容が同じで順序だけ異なる文字列を区別できません。これはハッシュ衝突を悪化させ、一部の安全上の問題を引き起こす可能性があります。</p> <p>実際には、MD5、SHA-1、SHA-2、SHA-3 などの標準的なハッシュアルゴリズムを用いることが一般的です。これらは任意長の入力データを、固定長のハッシュ値へ写像できます。</p> <p>ここ 1 世紀近くの間、ハッシュアルゴリズムは継続的に改良と最適化が進められてきました。ある研究者たちは性能向上に取り組み、別の研究者やハッカーたちは安全性の弱点を探し続けてきました。次の表は、実際の応用でよく使われるハッシュアルゴリズムを示したものです。</p> <ul> <li>MD5 と SHA-1 は何度も攻撃に成功されているため、各種のセキュリティ用途では廃止されています。</li> <li>SHA-2 系列の SHA-256 は最も安全なハッシュアルゴリズムの 1 つであり、いまだに成功した攻撃例がないため、多くのセキュリティ用途やプロトコルで広く使われています。</li> <li>SHA-3 は SHA-2 と比べて実装コストが低く、計算効率も高い一方で、現時点での普及度は SHA-2 系列に及びません。</li> </ul> <p> 表 6-2   一般的なハッシュアルゴリズム </p> MD5 SHA-1 SHA-2 SHA-3 発表年 1992 1995 2002 2008 出力長 128 bit 160 bit 256/512 bit 224/256/384/512 bit ハッシュ衝突 多い 多い 非常に少ない 非常に少ない セキュリティレベル 低く、攻撃に成功されている 低く、攻撃に成功されている 高い 高い 用途 廃止済みだが、データ完全性検査には使われる 廃止済み 暗号資産の取引検証、デジタル署名など SHA-2 の代替に使える","path":["第 6 章 &nbsp; ハッシュテーブル","6.3 &nbsp; ハッシュアルゴリズム"],"tags":[]},{"location":"chapter_hashing/hash_algorithm/#634","level":2,"title":"6.3.4   データ構造のハッシュ値","text":"<p>ご存じのように、ハッシュテーブルの <code>key</code> には整数、小数、文字列などのデータ型を使えます。プログラミング言語は通常、これらのデータ型に対して組み込みのハッシュアルゴリズムを提供し、ハッシュテーブル内のバケットインデックス計算に利用します。Python を例にすると、<code>hash()</code> 関数を呼び出して各種データ型のハッシュ値を計算できます。</p> <ul> <li>整数と真理値のハッシュ値は、その値自身です。</li> <li>浮動小数点数と文字列のハッシュ値の計算はやや複雑なので、興味がある読者は自分で調べてみてください。</li> <li>タプルのハッシュ値は、各要素のハッシュ値を求めてから、それらを組み合わせて 1 つのハッシュ値にしたものです。</li> <li>オブジェクトのハッシュ値は、そのメモリアドレスに基づいて生成されます。オブジェクトのハッシュメソッドをオーバーライドすれば、内容に基づくハッシュ値を実装できます。</li> </ul> <p>Tip</p> <p>注意してください。組み込みのハッシュ値計算関数の定義や方法は、プログラミング言語ごとに異なります。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby built_in_hash.py<pre><code>num = 3\nhash_num = hash(num)\n# 整数 3 のハッシュ値は 3\n\nbol = True\nhash_bol = hash(bol)\n# 真理値 True のハッシュ値は 1\n\ndec = 3.14159\nhash_dec = hash(dec)\n# 小数 3.14159 のハッシュ値は 326484311674566659\n\nstr = \"Hello アルゴリズム\"\nhash_str = hash(str)\n# 文字列「Hello アルゴリズム」のハッシュ値は 4617003410720528961\n\ntup = (12836, \"シャオハ\")\nhash_tup = hash(tup)\n# タプル (12836, 'シャオハ') のハッシュ値は 1029005403108185979\n\nobj = ListNode(0)\nhash_obj = hash(obj)\n# ノードオブジェクト &lt;ListNode object at 0x1058fd810&gt; のハッシュ値は 274267521\n</code></pre> built_in_hash.cpp<pre><code>int num = 3;\nsize_t hashNum = hash&lt;int&gt;()(num);\n// 整数 3 のハッシュ値は 3\n\nbool bol = true;\nsize_t hashBol = hash&lt;bool&gt;()(bol);\n// 真理値 1 のハッシュ値は 1\n\ndouble dec = 3.14159;\nsize_t hashDec = hash&lt;double&gt;()(dec);\n// 小数 3.14159 のハッシュ値は 4614256650576692846\n\nstring str = \"Hello アルゴリズム\";\nsize_t hashStr = hash&lt;string&gt;()(str);\n// 文字列「Hello アルゴリズム」のハッシュ値は 15466937326284535026\n\n// C++ では、組み込みの std:hash() は基本データ型のハッシュ値計算のみを提供する\n// 配列やオブジェクトのハッシュ値計算は自分で実装する必要がある\n</code></pre> built_in_hash.java<pre><code>int num = 3;\nint hashNum = Integer.hashCode(num);\n// 整数 3 のハッシュ値は 3\n\nboolean bol = true;\nint hashBol = Boolean.hashCode(bol);\n// 真理値 true のハッシュ値は 1231\n\ndouble dec = 3.14159;\nint hashDec = Double.hashCode(dec);\n// 小数 3.14159 のハッシュ値は -1340954729\n\nString str = \"Hello アルゴリズム\";\nint hashStr = str.hashCode();\n// 文字列「Hello アルゴリズム」のハッシュ値は -727081396\n\nObject[] arr = { 12836, \"シャオハ\" };\nint hashTup = Arrays.hashCode(arr);\n// 配列 [12836, シャオハ] のハッシュ値は 1151158\n\nListNode obj = new ListNode(0);\nint hashObj = obj.hashCode();\n// ノードオブジェクト utils.ListNode@7dc5e7b4 のハッシュ値は 2110121908\n</code></pre> built_in_hash.cs<pre><code>int num = 3;\nint hashNum = num.GetHashCode();\n// 整数 3 のハッシュ値は 3;\n\nbool bol = true;\nint hashBol = bol.GetHashCode();\n// 真理値 true のハッシュ値は 1;\n\ndouble dec = 3.14159;\nint hashDec = dec.GetHashCode();\n// 小数 3.14159 のハッシュ値は -1340954729;\n\nstring str = \"Hello アルゴリズム\";\nint hashStr = str.GetHashCode();\n// 文字列「Hello アルゴリズム」のハッシュ値は -586107568;\n\nobject[] arr = [12836, \"シャオハ\"];\nint hashTup = arr.GetHashCode();\n// 配列 [12836, シャオハ] のハッシュ値は 42931033;\n\nListNode obj = new(0);\nint hashObj = obj.GetHashCode();\n// ノードオブジェクト 0 のハッシュ値は 39053774;\n</code></pre> built_in_hash.go<pre><code>// Go は組み込みの hash code 関数を提供していない\n</code></pre> built_in_hash.swift<pre><code>let num = 3\nlet hashNum = num.hashValue\n// 整数 3 のハッシュ値は 9047044699613009734\n\nlet bol = true\nlet hashBol = bol.hashValue\n// 真理値 true のハッシュ値は -4431640247352757451\n\nlet dec = 3.14159\nlet hashDec = dec.hashValue\n// 小数 3.14159 のハッシュ値は -2465384235396674631\n\nlet str = \"Hello アルゴリズム\"\nlet hashStr = str.hashValue\n// 文字列「Hello アルゴリズム」のハッシュ値は -7850626797806988787\n\nlet arr = [AnyHashable(12836), AnyHashable(\"シャオハ\")]\nlet hashTup = arr.hashValue\n// 配列 [AnyHashable(12836), AnyHashable(\"シャオハ\")] のハッシュ値は -2308633508154532996\n\nlet obj = ListNode(x: 0)\nlet hashObj = obj.hashValue\n// ノードオブジェクト utils.ListNode のハッシュ値は -2434780518035996159\n</code></pre> built_in_hash.js<pre><code>// JavaScript は組み込みの hash code 関数を提供していない\n</code></pre> built_in_hash.ts<pre><code>// TypeScript は組み込みの hash code 関数を提供していない\n</code></pre> built_in_hash.dart<pre><code>int num = 3;\nint hashNum = num.hashCode;\n// 整数 3 のハッシュ値は 34803\n\nbool bol = true;\nint hashBol = bol.hashCode;\n// 真理値 true のハッシュ値は 1231\n\ndouble dec = 3.14159;\nint hashDec = dec.hashCode;\n// 小数 3.14159 のハッシュ値は 2570631074981783\n\nString str = \"Hello アルゴリズム\";\nint hashStr = str.hashCode;\n// 文字列「Hello アルゴリズム」のハッシュ値は 468167534\n\nList arr = [12836, \"シャオハ\"];\nint hashArr = arr.hashCode;\n// 配列 [12836, シャオハ] のハッシュ値は 976512528\n\nListNode obj = new ListNode(0);\nint hashObj = obj.hashCode;\n// ノードオブジェクト Instance of 'ListNode' のハッシュ値は 1033450432\n</code></pre> built_in_hash.rs<pre><code>use std::collections::hash_map::DefaultHasher;\nuse std::hash::{Hash, Hasher};\n\nlet num = 3;\nlet mut num_hasher = DefaultHasher::new();\nnum.hash(&amp;mut num_hasher);\nlet hash_num = num_hasher.finish();\n// 整数 3 のハッシュ値は 568126464209439262\n\nlet bol = true;\nlet mut bol_hasher = DefaultHasher::new();\nbol.hash(&amp;mut bol_hasher);\nlet hash_bol = bol_hasher.finish();\n// 真理値 true のハッシュ値は 4952851536318644461\n\nlet dec: f32 = 3.14159;\nlet mut dec_hasher = DefaultHasher::new();\ndec.to_bits().hash(&amp;mut dec_hasher);\nlet hash_dec = dec_hasher.finish();\n// 小数 3.14159 のハッシュ値は 2566941990314602357\n\nlet str = \"Hello アルゴリズム\";\nlet mut str_hasher = DefaultHasher::new();\nstr.hash(&amp;mut str_hasher);\nlet hash_str = str_hasher.finish();\n// 文字列「Hello アルゴリズム」のハッシュ値は 16092673739211250988\n\nlet arr = (&amp;12836, &amp;\"シャオハ\");\nlet mut tup_hasher = DefaultHasher::new();\narr.hash(&amp;mut tup_hasher);\nlet hash_tup = tup_hasher.finish();\n// タプル (12836, \"シャオハ\") のハッシュ値は 1885128010422702749\n\nlet node = ListNode::new(42);\nlet mut hasher = DefaultHasher::new();\nnode.borrow().val.hash(&amp;mut hasher);\nlet hash = hasher.finish();\n// ノードオブジェクト RefCell { value: ListNode { val: 42, next: None } } のハッシュ値は15387811073369036852\n</code></pre> built_in_hash.c<pre><code>// C は組み込みの hash code 関数を提供していない\n</code></pre> built_in_hash.kt<pre><code>val num = 3\nval hashNum = num.hashCode()\n// 整数 3 のハッシュ値は 3\n\nval bol = true\nval hashBol = bol.hashCode()\n// 真理値 true のハッシュ値は 1231\n\nval dec = 3.14159\nval hashDec = dec.hashCode()\n// 小数 3.14159 のハッシュ値は -1340954729\n\nval str = \"Hello アルゴリズム\"\nval hashStr = str.hashCode()\n// 文字列「Hello アルゴリズム」のハッシュ値は -727081396\n\nval arr = arrayOf&lt;Any&gt;(12836, \"シャオハ\")\nval hashTup = arr.hashCode()\n// 配列 [12836, シャオハ] のハッシュ値は 189568618\n\nval obj = ListNode(0)\nval hashObj = obj.hashCode()\n// ノードオブジェクト utils.ListNode@1d81eb93 のハッシュ値は 495053715\n</code></pre> built_in_hash.rb<pre><code>num = 3\nhash_num = num.hash\n# 整数 3 のハッシュ値は -4385856518450339636\n\nbol = true\nhash_bol = bol.hash\n# 真理値 true のハッシュ値は -1617938112149317027\n\ndec = 3.14159\nhash_dec = dec.hash\n# 小数 3.14159 のハッシュ値は -1479186995943067893\n\nstr = \"Hello アルゴリズム\"\nhash_str = str.hash\n# 文字列「Hello アルゴリズム」のハッシュ値は -4075943250025831763\n\ntup = [12836, 'シャオハ']\nhash_tup = tup.hash\n# タプル (12836, 'シャオハ') のハッシュ値は 1999544809202288822\n\nobj = ListNode.new(0)\nhash_obj = obj.hash\n# ノードオブジェクト #&lt;ListNode:0x000078133140ab70&gt; のハッシュ値は 4302940560806366381\n</code></pre> 可視化実行 <p>https://pythontutor.com/render.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%E9%93%BE%E8%A1%A8%E8%8A%82%E7%82%B9%E7%B1%BB%22%22%22%0A%20%20%20%20def%20__init__%28self,%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E8%8A%82%E7%82%B9%E5%80%BC%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%90%8E%E7%BB%A7%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20num%20%3D%203%0A%20%20%20%20hash_num%20%3D%20hash%28num%29%0A%20%20%20%20%23%20%E6%95%B4%E6%95%B0%203%20%E7%9A%84%E5%93%88%E5%B8%8C%E5%80%BC%E4%B8%BA%203%0A%0A%20%20%20%20bol%20%3D%20True%0A%20%20%20%20hash_bol%20%3D%20hash%28bol%29%0A%20%20%20%20%23%20%E5%B8%83%E5%B0%94%E9%87%8F%20True%20%E7%9A%84%E5%93%88%E5%B8%8C%E5%80%BC%E4%B8%BA%201%0A%0A%20%20%20%20dec%20%3D%203.14159%0A%20%20%20%20hash_dec%20%3D%20hash%28dec%29%0A%20%20%20%20%23%20%E5%B0%8F%E6%95%B0%203.14159%20%E7%9A%84%E5%93%88%E5%B8%8C%E5%80%BC%E4%B8%BA%20326484311674566659%0A%0A%20%20%20%20str%20%3D%20%22Hello%20%E7%AE%97%E6%B3%95%22%0A%20%20%20%20hash_str%20%3D%20hash%28str%29%0A%20%20%20%20%23%20%E5%AD%97%E7%AC%A6%E4%B8%B2%E2%80%9CHello%20%E7%AE%97%E6%B3%95%E2%80%9D%E7%9A%84%E5%93%88%E5%B8%8C%E5%80%BC%E4%B8%BA%204617003410720528961%0A%0A%20%20%20%20tup%20%3D%20%2812836,%20%22%E5%B0%8F%E5%93%88%22%29%0A%20%20%20%20hash_tup%20%3D%20hash%28tup%29%0A%20%20%20%20%23%20%E5%85%83%E7%BB%84%20%2812836,%20'%E5%B0%8F%E5%93%88'%29%20%E7%9A%84%E5%93%88%E5%B8%8C%E5%80%BC%E4%B8%BA%201029005403108185979%0A%0A%20%20%20%20obj%20%3D%20ListNode%280%29%0A%20%20%20%20hash_obj%20%3D%20hash%28obj%29%0A%20%20%20%20%23%20%E8%8A%82%E7%82%B9%E5%AF%B9%E8%B1%A1%20%3CListNode%20object%20at%200x1058fd810%3E%20%E7%9A%84%E5%93%88%E5%B8%8C%E5%80%BC%E4%B8%BA%20274267521&amp;cumulative=false&amp;curInstr=19&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p> <p>多くのプログラミング言語では、不変オブジェクトだけがハッシュテーブルの <code>key</code> として使えます。仮にリスト（動的配列）を <code>key</code> とすると、その内容が変化したときにハッシュ値も変わってしまうため、もとの <code>value</code> をハッシュテーブルから検索できなくなります。</p> <p>カスタムオブジェクト（たとえば連結リストのノード）のメンバ変数は可変ですが、それでもハッシュ可能です。これは、オブジェクトのハッシュ値が通常はメモリアドレスに基づいて生成されるためです。オブジェクトの内容が変化しても、メモリアドレスが変わらなければ、ハッシュ値も変わりません。</p> <p>注意深い人なら、異なるコンソールでプログラムを実行したときに、出力されるハッシュ値が異なることに気づくかもしれません。これは、Python インタプリタが起動のたびに文字列ハッシュ関数へランダムな salt 値を追加しているためです。この方法によって HashDoS 攻撃を効果的に防ぎ、ハッシュアルゴリズムの安全性を高めています。</p>","path":["第 6 章 &nbsp; ハッシュテーブル","6.3 &nbsp; ハッシュアルゴリズム"],"tags":[]},{"location":"chapter_hashing/hash_collision/","level":1,"title":"6.2   ハッシュ衝突","text":"<p>前節で述べたように、**通常、ハッシュ関数の入力空間は出力空間よりもはるかに大きい**ため、理論上ハッシュ衝突は避けられません。例えば、入力空間がすべての整数で、出力空間が配列の容量サイズである場合、必然的に複数の整数が同じバケットインデックスに写像されます。</p> <p>ハッシュ衝突は検索結果の誤りを招き、ハッシュテーブルの利用可能性に深刻な影響を与えます。この問題を解決するために、ハッシュ衝突が発生するたびにハッシュテーブルを拡張し、衝突が消えるまで続けることが考えられます。この方法は単純で効果的ですが、効率が低すぎます。なぜなら、ハッシュテーブルの拡張には大量のデータ移動とハッシュ値の計算が必要だからです。効率を高めるために、次の戦略を採用できます。</p> <ol> <li>ハッシュテーブルのデータ構造を改良し、ハッシュ衝突が発生してもハッシュテーブルが正常に動作できるようにする。</li> <li>必要な場合、すなわちハッシュ衝突が比較的深刻なときにのみ、拡張操作を実行する。</li> </ol> <p>ハッシュテーブルの構造改善方法には、主に「チェイン法」と「オープンアドレッシング」があります。</p>","path":["第 6 章 &nbsp; ハッシュテーブル","6.2 &nbsp; ハッシュ衝突"],"tags":[]},{"location":"chapter_hashing/hash_collision/#621","level":2,"title":"6.2.1   チェイン法","text":"<p>元のハッシュテーブルでは、各バケットには 1 つのキーと値のペアしか格納できません。チェイン法（separate chaining）では、単一要素を連結リストに置き換え、キーと値のペアを連結リストのノードとして扱い、衝突したすべてのキーと値のペアを同じ連結リストに格納します。下図はチェイン法によるハッシュテーブルの例を示しています。</p> <p></p> <p> 図 6-5   チェイン法ハッシュテーブル </p> <p>チェイン法で実装されたハッシュテーブルでは、操作方法が次のように変わります。</p> <ul> <li>要素の検索：入力 <code>key</code> をハッシュ関数に通してバケットインデックスを得ると、連結リストの先頭ノードにアクセスできます。その後、連結リストを走査して <code>key</code> を比較し、目的のキーと値のペアを探します。</li> <li>要素の追加：まずハッシュ関数で連結リストの先頭ノードにアクセスし、その後ノード（キーと値のペア）を連結リストに追加します。</li> <li>要素の削除：ハッシュ関数の結果に基づいて連結リストの先頭にアクセスし、続いて連結リストを走査して対象ノードを探し、削除します。</li> </ul> <p>チェイン法には次の制約があります。</p> <ul> <li>使用メモリの増加：連結リストにはノードポインタが含まれるため、配列よりも多くのメモリを消費します。</li> <li>検索効率の低下：対応する要素を見つけるために連結リストを線形走査する必要があるためです。</li> </ul> <p>以下のコードはチェイン法ハッシュテーブルの簡単な実装を示しています。注意すべき点は 2 つあります。</p> <ul> <li>連結リストの代わりにリスト（動的配列）を使って、コードを簡潔にしています。この設定では、ハッシュテーブル（配列）は複数のバケットを含み、各バケットは 1 つのリストです。</li> <li>以下の実装にはハッシュテーブルの拡張メソッドが含まれています。負荷率が \\(\\frac{2}{3}\\) を超えたとき、ハッシュテーブルを元の \\(2\\) 倍に拡張します。</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby hash_map_chaining.py<pre><code>class HashMapChaining:\n    \"\"\"チェイン法ハッシュテーブル\"\"\"\n\n    def __init__(self):\n        \"\"\"コンストラクタ\"\"\"\n        self.size = 0  # キーと値のペア数\n        self.capacity = 4  # ハッシュテーブル容量\n        self.load_thres = 2.0 / 3.0  # リサイズを発動する負荷率のしきい値\n        self.extend_ratio = 2  # 拡張倍率\n        self.buckets = [[] for _ in range(self.capacity)]  # バケット配列\n\n    def hash_func(self, key: int) -&gt; int:\n        \"\"\"ハッシュ関数\"\"\"\n        return key % self.capacity\n\n    def load_factor(self) -&gt; float:\n        \"\"\"負荷率\"\"\"\n        return self.size / self.capacity\n\n    def get(self, key: int) -&gt; str | None:\n        \"\"\"検索操作\"\"\"\n        index = self.hash_func(key)\n        bucket = self.buckets[index]\n        # バケットを走査し、key が見つかれば対応する val を返す\n        for pair in bucket:\n            if pair.key == key:\n                return pair.val\n        # key が見つからない場合は None を返す\n        return None\n\n    def put(self, key: int, val: str):\n        \"\"\"追加操作\"\"\"\n        # 負荷率がしきい値を超えたら、リサイズを実行\n        if self.load_factor() &gt; self.load_thres:\n            self.extend()\n        index = self.hash_func(key)\n        bucket = self.buckets[index]\n        # バケットを走査し、指定した key が見つかれば対応する val を更新して返す\n        for pair in bucket:\n            if pair.key == key:\n                pair.val = val\n                return\n        # その key が存在しなければ、キーと値のペアを末尾に追加\n        pair = Pair(key, val)\n        bucket.append(pair)\n        self.size += 1\n\n    def remove(self, key: int):\n        \"\"\"削除操作\"\"\"\n        index = self.hash_func(key)\n        bucket = self.buckets[index]\n        # バケットを走査してキーと値のペアを削除\n        for pair in bucket:\n            if pair.key == key:\n                bucket.remove(pair)\n                self.size -= 1\n                break\n\n    def extend(self):\n        \"\"\"ハッシュテーブルを拡張\"\"\"\n        # 元のハッシュテーブルを一時保存\n        buckets = self.buckets\n        # リサイズ後の新しいハッシュテーブルを初期化\n        self.capacity *= self.extend_ratio\n        self.buckets = [[] for _ in range(self.capacity)]\n        self.size = 0\n        # キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n        for bucket in buckets:\n            for pair in bucket:\n                self.put(pair.key, pair.val)\n\n    def print(self):\n        \"\"\"ハッシュテーブルを出力\"\"\"\n        for bucket in self.buckets:\n            res = []\n            for pair in bucket:\n                res.append(str(pair.key) + \" -&gt; \" + pair.val)\n            print(res)\n</code></pre> hash_map_chaining.cpp<pre><code>/* チェイン法ハッシュテーブル */\nclass HashMapChaining {\n  private:\n    int size;                       // キーと値のペア数\n    int capacity;                   // ハッシュテーブル容量\n    double loadThres;               // リサイズを発動する負荷率のしきい値\n    int extendRatio;                // 拡張倍率\n    vector&lt;vector&lt;Pair *&gt;&gt; buckets; // バケット配列\n\n  public:\n    /* コンストラクタ */\n    HashMapChaining() : size(0), capacity(4), loadThres(2.0 / 3.0), extendRatio(2) {\n        buckets.resize(capacity);\n    }\n\n    /* デストラクタメソッド */\n    ~HashMapChaining() {\n        for (auto &amp;bucket : buckets) {\n            for (Pair *pair : bucket) {\n                // メモリを解放する\n                delete pair;\n            }\n        }\n    }\n\n    /* ハッシュ関数 */\n    int hashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* 負荷率 */\n    double loadFactor() {\n        return (double)size / (double)capacity;\n    }\n\n    /* 検索操作 */\n    string get(int key) {\n        int index = hashFunc(key);\n        // バケットを走査し、key が見つかれば対応する val を返す\n        for (Pair *pair : buckets[index]) {\n            if (pair-&gt;key == key) {\n                return pair-&gt;val;\n            }\n        }\n        // key が見つからない場合は空文字列を返す\n        return \"\";\n    }\n\n    /* 追加操作 */\n    void put(int key, string val) {\n        // 負荷率がしきい値を超えたら、リサイズを実行\n        if (loadFactor() &gt; loadThres) {\n            extend();\n        }\n        int index = hashFunc(key);\n        // バケットを走査し、指定した key が見つかれば対応する val を更新して返す\n        for (Pair *pair : buckets[index]) {\n            if (pair-&gt;key == key) {\n                pair-&gt;val = val;\n                return;\n            }\n        }\n        // その key が存在しなければ、キーと値のペアを末尾に追加\n        buckets[index].push_back(new Pair(key, val));\n        size++;\n    }\n\n    /* 削除操作 */\n    void remove(int key) {\n        int index = hashFunc(key);\n        auto &amp;bucket = buckets[index];\n        // バケットを走査してキーと値のペアを削除\n        for (int i = 0; i &lt; bucket.size(); i++) {\n            if (bucket[i]-&gt;key == key) {\n                Pair *tmp = bucket[i];\n                bucket.erase(bucket.begin() + i); // そこからキーと値の組を削除する\n                delete tmp;                       // メモリを解放する\n                size--;\n                return;\n            }\n        }\n    }\n\n    /* ハッシュテーブルを拡張 */\n    void extend() {\n        // 元のハッシュテーブルを一時保存\n        vector&lt;vector&lt;Pair *&gt;&gt; bucketsTmp = buckets;\n        // リサイズ後の新しいハッシュテーブルを初期化\n        capacity *= extendRatio;\n        buckets.clear();\n        buckets.resize(capacity);\n        size = 0;\n        // キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n        for (auto &amp;bucket : bucketsTmp) {\n            for (Pair *pair : bucket) {\n                put(pair-&gt;key, pair-&gt;val);\n                // メモリを解放する\n                delete pair;\n            }\n        }\n    }\n\n    /* ハッシュテーブルを出力 */\n    void print() {\n        for (auto &amp;bucket : buckets) {\n            cout &lt;&lt; \"[\";\n            for (Pair *pair : bucket) {\n                cout &lt;&lt; pair-&gt;key &lt;&lt; \" -&gt; \" &lt;&lt; pair-&gt;val &lt;&lt; \", \";\n            }\n            cout &lt;&lt; \"]\\n\";\n        }\n    }\n};\n</code></pre> hash_map_chaining.java<pre><code>/* チェイン法ハッシュテーブル */\nclass HashMapChaining {\n    int size; // キーと値のペア数\n    int capacity; // ハッシュテーブル容量\n    double loadThres; // リサイズを発動する負荷率のしきい値\n    int extendRatio; // 拡張倍率\n    List&lt;List&lt;Pair&gt;&gt; buckets; // バケット配列\n\n    /* コンストラクタ */\n    public HashMapChaining() {\n        size = 0;\n        capacity = 4;\n        loadThres = 2.0 / 3.0;\n        extendRatio = 2;\n        buckets = new ArrayList&lt;&gt;(capacity);\n        for (int i = 0; i &lt; capacity; i++) {\n            buckets.add(new ArrayList&lt;&gt;());\n        }\n    }\n\n    /* ハッシュ関数 */\n    int hashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* 負荷率 */\n    double loadFactor() {\n        return (double) size / capacity;\n    }\n\n    /* 検索操作 */\n    String get(int key) {\n        int index = hashFunc(key);\n        List&lt;Pair&gt; bucket = buckets.get(index);\n        // バケットを走査し、key が見つかれば対応する val を返す\n        for (Pair pair : bucket) {\n            if (pair.key == key) {\n                return pair.val;\n            }\n        }\n        // key が見つからない場合は null を返す\n        return null;\n    }\n\n    /* 追加操作 */\n    void put(int key, String val) {\n        // 負荷率がしきい値を超えたら、リサイズを実行\n        if (loadFactor() &gt; loadThres) {\n            extend();\n        }\n        int index = hashFunc(key);\n        List&lt;Pair&gt; bucket = buckets.get(index);\n        // バケットを走査し、指定した key が見つかれば対応する val を更新して返す\n        for (Pair pair : bucket) {\n            if (pair.key == key) {\n                pair.val = val;\n                return;\n            }\n        }\n        // その key が存在しなければ、キーと値のペアを末尾に追加\n        Pair pair = new Pair(key, val);\n        bucket.add(pair);\n        size++;\n    }\n\n    /* 削除操作 */\n    void remove(int key) {\n        int index = hashFunc(key);\n        List&lt;Pair&gt; bucket = buckets.get(index);\n        // バケットを走査してキーと値のペアを削除\n        for (Pair pair : bucket) {\n            if (pair.key == key) {\n                bucket.remove(pair);\n                size--;\n                break;\n            }\n        }\n    }\n\n    /* ハッシュテーブルを拡張 */\n    void extend() {\n        // 元のハッシュテーブルを一時保存\n        List&lt;List&lt;Pair&gt;&gt; bucketsTmp = buckets;\n        // リサイズ後の新しいハッシュテーブルを初期化\n        capacity *= extendRatio;\n        buckets = new ArrayList&lt;&gt;(capacity);\n        for (int i = 0; i &lt; capacity; i++) {\n            buckets.add(new ArrayList&lt;&gt;());\n        }\n        size = 0;\n        // キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n        for (List&lt;Pair&gt; bucket : bucketsTmp) {\n            for (Pair pair : bucket) {\n                put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* ハッシュテーブルを出力 */\n    void print() {\n        for (List&lt;Pair&gt; bucket : buckets) {\n            List&lt;String&gt; res = new ArrayList&lt;&gt;();\n            for (Pair pair : bucket) {\n                res.add(pair.key + \" -&gt; \" + pair.val);\n            }\n            System.out.println(res);\n        }\n    }\n}\n</code></pre> hash_map_chaining.cs<pre><code>/* チェイン法ハッシュテーブル */\nclass HashMapChaining {\n    int size; // キーと値のペア数\n    int capacity; // ハッシュテーブル容量\n    double loadThres; // リサイズを発動する負荷率のしきい値\n    int extendRatio; // 拡張倍率\n    List&lt;List&lt;Pair&gt;&gt; buckets; // バケット配列\n\n    /* コンストラクタ */\n    public HashMapChaining() {\n        size = 0;\n        capacity = 4;\n        loadThres = 2.0 / 3.0;\n        extendRatio = 2;\n        buckets = new List&lt;List&lt;Pair&gt;&gt;(capacity);\n        for (int i = 0; i &lt; capacity; i++) {\n            buckets.Add([]);\n        }\n    }\n\n    /* ハッシュ関数 */\n    int HashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* 負荷率 */\n    double LoadFactor() {\n        return (double)size / capacity;\n    }\n\n    /* 検索操作 */\n    public string? Get(int key) {\n        int index = HashFunc(key);\n        // バケットを走査し、key が見つかれば対応する val を返す\n        foreach (Pair pair in buckets[index]) {\n            if (pair.key == key) {\n                return pair.val;\n            }\n        }\n        // key が見つからない場合は null を返す\n        return null;\n    }\n\n    /* 追加操作 */\n    public void Put(int key, string val) {\n        // 負荷率がしきい値を超えたら、リサイズを実行\n        if (LoadFactor() &gt; loadThres) {\n            Extend();\n        }\n        int index = HashFunc(key);\n        // バケットを走査し、指定した key が見つかれば対応する val を更新して返す\n        foreach (Pair pair in buckets[index]) {\n            if (pair.key == key) {\n                pair.val = val;\n                return;\n            }\n        }\n        // その key が存在しなければ、キーと値のペアを末尾に追加\n        buckets[index].Add(new Pair(key, val));\n        size++;\n    }\n\n    /* 削除操作 */\n    public void Remove(int key) {\n        int index = HashFunc(key);\n        // バケットを走査してキーと値のペアを削除\n        foreach (Pair pair in buckets[index].ToList()) {\n            if (pair.key == key) {\n                buckets[index].Remove(pair);\n                size--;\n                break;\n            }\n        }\n    }\n\n    /* ハッシュテーブルを拡張 */\n    void Extend() {\n        // 元のハッシュテーブルを一時保存\n        List&lt;List&lt;Pair&gt;&gt; bucketsTmp = buckets;\n        // リサイズ後の新しいハッシュテーブルを初期化\n        capacity *= extendRatio;\n        buckets = new List&lt;List&lt;Pair&gt;&gt;(capacity);\n        for (int i = 0; i &lt; capacity; i++) {\n            buckets.Add([]);\n        }\n        size = 0;\n        // キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n        foreach (List&lt;Pair&gt; bucket in bucketsTmp) {\n            foreach (Pair pair in bucket) {\n                Put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* ハッシュテーブルを出力 */\n    public void Print() {\n        foreach (List&lt;Pair&gt; bucket in buckets) {\n            List&lt;string&gt; res = [];\n            foreach (Pair pair in bucket) {\n                res.Add(pair.key + \" -&gt; \" + pair.val);\n            }\n            foreach (string kv in res) {\n                Console.WriteLine(kv);\n            }\n        }\n    }\n}\n</code></pre> hash_map_chaining.go<pre><code>/* チェイン法ハッシュテーブル */\ntype hashMapChaining struct {\n    size        int      // キーと値のペア数\n    capacity    int      // ハッシュテーブル容量\n    loadThres   float64  // リサイズを発動する負荷率のしきい値\n    extendRatio int      // 拡張倍率\n    buckets     [][]pair // バケット配列\n}\n\n/* コンストラクタ */\nfunc newHashMapChaining() *hashMapChaining {\n    buckets := make([][]pair, 4)\n    for i := 0; i &lt; 4; i++ {\n        buckets[i] = make([]pair, 0)\n    }\n    return &amp;hashMapChaining{\n        size:        0,\n        capacity:    4,\n        loadThres:   2.0 / 3.0,\n        extendRatio: 2,\n        buckets:     buckets,\n    }\n}\n\n/* ハッシュ関数 */\nfunc (m *hashMapChaining) hashFunc(key int) int {\n    return key % m.capacity\n}\n\n/* 負荷率 */\nfunc (m *hashMapChaining) loadFactor() float64 {\n    return float64(m.size) / float64(m.capacity)\n}\n\n/* 検索操作 */\nfunc (m *hashMapChaining) get(key int) string {\n    idx := m.hashFunc(key)\n    bucket := m.buckets[idx]\n    // バケットを走査し、key が見つかれば対応する val を返す\n    for _, p := range bucket {\n        if p.key == key {\n            return p.val\n        }\n    }\n    // key が見つからない場合は空文字列を返す\n    return \"\"\n}\n\n/* 追加操作 */\nfunc (m *hashMapChaining) put(key int, val string) {\n    // 負荷率がしきい値を超えたら、リサイズを実行\n    if m.loadFactor() &gt; m.loadThres {\n        m.extend()\n    }\n    idx := m.hashFunc(key)\n    // バケットを走査し、指定した key が見つかれば対応する val を更新して返す\n    for i := range m.buckets[idx] {\n        if m.buckets[idx][i].key == key {\n            m.buckets[idx][i].val = val\n            return\n        }\n    }\n    // その key が存在しなければ、キーと値のペアを末尾に追加\n    p := pair{\n        key: key,\n        val: val,\n    }\n    m.buckets[idx] = append(m.buckets[idx], p)\n    m.size += 1\n}\n\n/* 削除操作 */\nfunc (m *hashMapChaining) remove(key int) {\n    idx := m.hashFunc(key)\n    // バケットを走査してキーと値のペアを削除\n    for i, p := range m.buckets[idx] {\n        if p.key == key {\n            // スライスから削除する\n            m.buckets[idx] = append(m.buckets[idx][:i], m.buckets[idx][i+1:]...)\n            m.size -= 1\n            break\n        }\n    }\n}\n\n/* ハッシュテーブルを拡張 */\nfunc (m *hashMapChaining) extend() {\n    // 元のハッシュテーブルを一時保存\n    tmpBuckets := make([][]pair, len(m.buckets))\n    for i := 0; i &lt; len(m.buckets); i++ {\n        tmpBuckets[i] = make([]pair, len(m.buckets[i]))\n        copy(tmpBuckets[i], m.buckets[i])\n    }\n    // リサイズ後の新しいハッシュテーブルを初期化\n    m.capacity *= m.extendRatio\n    m.buckets = make([][]pair, m.capacity)\n    for i := 0; i &lt; m.capacity; i++ {\n        m.buckets[i] = make([]pair, 0)\n    }\n    m.size = 0\n    // キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n    for _, bucket := range tmpBuckets {\n        for _, p := range bucket {\n            m.put(p.key, p.val)\n        }\n    }\n}\n\n/* ハッシュテーブルを出力 */\nfunc (m *hashMapChaining) print() {\n    var builder strings.Builder\n\n    for _, bucket := range m.buckets {\n        builder.WriteString(\"[\")\n        for _, p := range bucket {\n            builder.WriteString(strconv.Itoa(p.key) + \" -&gt; \" + p.val + \" \")\n        }\n        builder.WriteString(\"]\")\n        fmt.Println(builder.String())\n        builder.Reset()\n    }\n}\n</code></pre> hash_map_chaining.swift<pre><code>/* チェイン法ハッシュテーブル */\nclass HashMapChaining {\n    var size: Int // キーと値のペア数\n    var capacity: Int // ハッシュテーブル容量\n    var loadThres: Double // リサイズを発動する負荷率のしきい値\n    var extendRatio: Int // 拡張倍率\n    var buckets: [[Pair]] // バケット配列\n\n    /* コンストラクタ */\n    init() {\n        size = 0\n        capacity = 4\n        loadThres = 2.0 / 3.0\n        extendRatio = 2\n        buckets = Array(repeating: [], count: capacity)\n    }\n\n    /* ハッシュ関数 */\n    func hashFunc(key: Int) -&gt; Int {\n        key % capacity\n    }\n\n    /* 負荷率 */\n    func loadFactor() -&gt; Double {\n        Double(size) / Double(capacity)\n    }\n\n    /* 検索操作 */\n    func get(key: Int) -&gt; String? {\n        let index = hashFunc(key: key)\n        let bucket = buckets[index]\n        // バケットを走査し、key が見つかれば対応する val を返す\n        for pair in bucket {\n            if pair.key == key {\n                return pair.val\n            }\n        }\n        // `key` が見つからなければ `nil` を返す\n        return nil\n    }\n\n    /* 追加操作 */\n    func put(key: Int, val: String) {\n        // 負荷率がしきい値を超えたら、リサイズを実行\n        if loadFactor() &gt; loadThres {\n            extend()\n        }\n        let index = hashFunc(key: key)\n        let bucket = buckets[index]\n        // バケットを走査し、指定した key が見つかれば対応する val を更新して返す\n        for pair in bucket {\n            if pair.key == key {\n                pair.val = val\n                return\n            }\n        }\n        // その key が存在しなければ、キーと値のペアを末尾に追加\n        let pair = Pair(key: key, val: val)\n        buckets[index].append(pair)\n        size += 1\n    }\n\n    /* 削除操作 */\n    func remove(key: Int) {\n        let index = hashFunc(key: key)\n        let bucket = buckets[index]\n        // バケットを走査してキーと値のペアを削除\n        for (pairIndex, pair) in bucket.enumerated() {\n            if pair.key == key {\n                buckets[index].remove(at: pairIndex)\n                size -= 1\n                break\n            }\n        }\n    }\n\n    /* ハッシュテーブルを拡張 */\n    func extend() {\n        // 元のハッシュテーブルを一時保存\n        let bucketsTmp = buckets\n        // リサイズ後の新しいハッシュテーブルを初期化\n        capacity *= extendRatio\n        buckets = Array(repeating: [], count: capacity)\n        size = 0\n        // キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n        for bucket in bucketsTmp {\n            for pair in bucket {\n                put(key: pair.key, val: pair.val)\n            }\n        }\n    }\n\n    /* ハッシュテーブルを出力 */\n    func print() {\n        for bucket in buckets {\n            let res = bucket.map { \"\\($0.key) -&gt; \\($0.val)\" }\n            Swift.print(res)\n        }\n    }\n}\n</code></pre> hash_map_chaining.js<pre><code>/* チェイン法ハッシュテーブル */\nclass HashMapChaining {\n    #size; // キーと値のペア数\n    #capacity; // ハッシュテーブル容量\n    #loadThres; // リサイズを発動する負荷率のしきい値\n    #extendRatio; // 拡張倍率\n    #buckets; // バケット配列\n\n    /* コンストラクタ */\n    constructor() {\n        this.#size = 0;\n        this.#capacity = 4;\n        this.#loadThres = 2.0 / 3.0;\n        this.#extendRatio = 2;\n        this.#buckets = new Array(this.#capacity).fill(null).map((x) =&gt; []);\n    }\n\n    /* ハッシュ関数 */\n    #hashFunc(key) {\n        return key % this.#capacity;\n    }\n\n    /* 負荷率 */\n    #loadFactor() {\n        return this.#size / this.#capacity;\n    }\n\n    /* 検索操作 */\n    get(key) {\n        const index = this.#hashFunc(key);\n        const bucket = this.#buckets[index];\n        // バケットを走査し、key が見つかれば対応する val を返す\n        for (const pair of bucket) {\n            if (pair.key === key) {\n                return pair.val;\n            }\n        }\n        // key が見つからない場合は null を返す\n        return null;\n    }\n\n    /* 追加操作 */\n    put(key, val) {\n        // 負荷率がしきい値を超えたら、リサイズを実行\n        if (this.#loadFactor() &gt; this.#loadThres) {\n            this.#extend();\n        }\n        const index = this.#hashFunc(key);\n        const bucket = this.#buckets[index];\n        // バケットを走査し、指定した key が見つかれば対応する val を更新して返す\n        for (const pair of bucket) {\n            if (pair.key === key) {\n                pair.val = val;\n                return;\n            }\n        }\n        // その key が存在しなければ、キーと値のペアを末尾に追加\n        const pair = new Pair(key, val);\n        bucket.push(pair);\n        this.#size++;\n    }\n\n    /* 削除操作 */\n    remove(key) {\n        const index = this.#hashFunc(key);\n        let bucket = this.#buckets[index];\n        // バケットを走査してキーと値のペアを削除\n        for (let i = 0; i &lt; bucket.length; i++) {\n            if (bucket[i].key === key) {\n                bucket.splice(i, 1);\n                this.#size--;\n                break;\n            }\n        }\n    }\n\n    /* ハッシュテーブルを拡張 */\n    #extend() {\n        // 元のハッシュテーブルを一時保存\n        const bucketsTmp = this.#buckets;\n        // リサイズ後の新しいハッシュテーブルを初期化\n        this.#capacity *= this.#extendRatio;\n        this.#buckets = new Array(this.#capacity).fill(null).map((x) =&gt; []);\n        this.#size = 0;\n        // キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n        for (const bucket of bucketsTmp) {\n            for (const pair of bucket) {\n                this.put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* ハッシュテーブルを出力 */\n    print() {\n        for (const bucket of this.#buckets) {\n            let res = [];\n            for (const pair of bucket) {\n                res.push(pair.key + ' -&gt; ' + pair.val);\n            }\n            console.log(res);\n        }\n    }\n}\n</code></pre> hash_map_chaining.ts<pre><code>/* チェイン法ハッシュテーブル */\nclass HashMapChaining {\n    #size: number; // キーと値のペア数\n    #capacity: number; // ハッシュテーブル容量\n    #loadThres: number; // リサイズを発動する負荷率のしきい値\n    #extendRatio: number; // 拡張倍率\n    #buckets: Pair[][]; // バケット配列\n\n    /* コンストラクタ */\n    constructor() {\n        this.#size = 0;\n        this.#capacity = 4;\n        this.#loadThres = 2.0 / 3.0;\n        this.#extendRatio = 2;\n        this.#buckets = new Array(this.#capacity).fill(null).map((x) =&gt; []);\n    }\n\n    /* ハッシュ関数 */\n    #hashFunc(key: number): number {\n        return key % this.#capacity;\n    }\n\n    /* 負荷率 */\n    #loadFactor(): number {\n        return this.#size / this.#capacity;\n    }\n\n    /* 検索操作 */\n    get(key: number): string | null {\n        const index = this.#hashFunc(key);\n        const bucket = this.#buckets[index];\n        // バケットを走査し、key が見つかれば対応する val を返す\n        for (const pair of bucket) {\n            if (pair.key === key) {\n                return pair.val;\n            }\n        }\n        // key が見つからない場合は null を返す\n        return null;\n    }\n\n    /* 追加操作 */\n    put(key: number, val: string): void {\n        // 負荷率がしきい値を超えたら、リサイズを実行\n        if (this.#loadFactor() &gt; this.#loadThres) {\n            this.#extend();\n        }\n        const index = this.#hashFunc(key);\n        const bucket = this.#buckets[index];\n        // バケットを走査し、指定した key が見つかれば対応する val を更新して返す\n        for (const pair of bucket) {\n            if (pair.key === key) {\n                pair.val = val;\n                return;\n            }\n        }\n        // その key が存在しなければ、キーと値のペアを末尾に追加\n        const pair = new Pair(key, val);\n        bucket.push(pair);\n        this.#size++;\n    }\n\n    /* 削除操作 */\n    remove(key: number): void {\n        const index = this.#hashFunc(key);\n        let bucket = this.#buckets[index];\n        // バケットを走査してキーと値のペアを削除\n        for (let i = 0; i &lt; bucket.length; i++) {\n            if (bucket[i].key === key) {\n                bucket.splice(i, 1);\n                this.#size--;\n                break;\n            }\n        }\n    }\n\n    /* ハッシュテーブルを拡張 */\n    #extend(): void {\n        // 元のハッシュテーブルを一時保存\n        const bucketsTmp = this.#buckets;\n        // リサイズ後の新しいハッシュテーブルを初期化\n        this.#capacity *= this.#extendRatio;\n        this.#buckets = new Array(this.#capacity).fill(null).map((x) =&gt; []);\n        this.#size = 0;\n        // キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n        for (const bucket of bucketsTmp) {\n            for (const pair of bucket) {\n                this.put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* ハッシュテーブルを出力 */\n    print(): void {\n        for (const bucket of this.#buckets) {\n            let res = [];\n            for (const pair of bucket) {\n                res.push(pair.key + ' -&gt; ' + pair.val);\n            }\n            console.log(res);\n        }\n    }\n}\n</code></pre> hash_map_chaining.dart<pre><code>/* チェイン法ハッシュテーブル */\nclass HashMapChaining {\n  late int size; // キーと値のペア数\n  late int capacity; // ハッシュテーブル容量\n  late double loadThres; // リサイズを発動する負荷率のしきい値\n  late int extendRatio; // 拡張倍率\n  late List&lt;List&lt;Pair&gt;&gt; buckets; // バケット配列\n\n  /* コンストラクタ */\n  HashMapChaining() {\n    size = 0;\n    capacity = 4;\n    loadThres = 2.0 / 3.0;\n    extendRatio = 2;\n    buckets = List.generate(capacity, (_) =&gt; []);\n  }\n\n  /* ハッシュ関数 */\n  int hashFunc(int key) {\n    return key % capacity;\n  }\n\n  /* 負荷率 */\n  double loadFactor() {\n    return size / capacity;\n  }\n\n  /* 検索操作 */\n  String? get(int key) {\n    int index = hashFunc(key);\n    List&lt;Pair&gt; bucket = buckets[index];\n    // バケットを走査し、key が見つかれば対応する val を返す\n    for (Pair pair in bucket) {\n      if (pair.key == key) {\n        return pair.val;\n      }\n    }\n    // key が見つからない場合は null を返す\n    return null;\n  }\n\n  /* 追加操作 */\n  void put(int key, String val) {\n    // 負荷率がしきい値を超えたら、リサイズを実行\n    if (loadFactor() &gt; loadThres) {\n      extend();\n    }\n    int index = hashFunc(key);\n    List&lt;Pair&gt; bucket = buckets[index];\n    // バケットを走査し、指定した key が見つかれば対応する val を更新して返す\n    for (Pair pair in bucket) {\n      if (pair.key == key) {\n        pair.val = val;\n        return;\n      }\n    }\n    // その key が存在しなければ、キーと値のペアを末尾に追加\n    Pair pair = Pair(key, val);\n    bucket.add(pair);\n    size++;\n  }\n\n  /* 削除操作 */\n  void remove(int key) {\n    int index = hashFunc(key);\n    List&lt;Pair&gt; bucket = buckets[index];\n    // バケットを走査してキーと値のペアを削除\n    for (Pair pair in bucket) {\n      if (pair.key == key) {\n        bucket.remove(pair);\n        size--;\n        break;\n      }\n    }\n  }\n\n  /* ハッシュテーブルを拡張 */\n  void extend() {\n    // 元のハッシュテーブルを一時保存\n    List&lt;List&lt;Pair&gt;&gt; bucketsTmp = buckets;\n    // リサイズ後の新しいハッシュテーブルを初期化\n    capacity *= extendRatio;\n    buckets = List.generate(capacity, (_) =&gt; []);\n    size = 0;\n    // キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n    for (List&lt;Pair&gt; bucket in bucketsTmp) {\n      for (Pair pair in bucket) {\n        put(pair.key, pair.val);\n      }\n    }\n  }\n\n  /* ハッシュテーブルを出力 */\n  void printHashMap() {\n    for (List&lt;Pair&gt; bucket in buckets) {\n      List&lt;String&gt; res = [];\n      for (Pair pair in bucket) {\n        res.add(\"${pair.key} -&gt; ${pair.val}\");\n      }\n      print(res);\n    }\n  }\n}\n</code></pre> hash_map_chaining.rs<pre><code>/* チェイン法ハッシュテーブル */\nstruct HashMapChaining {\n    size: usize,\n    capacity: usize,\n    load_thres: f32,\n    extend_ratio: usize,\n    buckets: Vec&lt;Vec&lt;Pair&gt;&gt;,\n}\n\nimpl HashMapChaining {\n    /* コンストラクタ */\n    fn new() -&gt; Self {\n        Self {\n            size: 0,\n            capacity: 4,\n            load_thres: 2.0 / 3.0,\n            extend_ratio: 2,\n            buckets: vec![vec![]; 4],\n        }\n    }\n\n    /* ハッシュ関数 */\n    fn hash_func(&amp;self, key: i32) -&gt; usize {\n        key as usize % self.capacity\n    }\n\n    /* 負荷率 */\n    fn load_factor(&amp;self) -&gt; f32 {\n        self.size as f32 / self.capacity as f32\n    }\n\n    /* 削除操作 */\n    fn remove(&amp;mut self, key: i32) -&gt; Option&lt;String&gt; {\n        let index = self.hash_func(key);\n\n        // バケットを走査してキーと値のペアを削除\n        for (i, p) in self.buckets[index].iter_mut().enumerate() {\n            if p.key == key {\n                let pair = self.buckets[index].remove(i);\n                self.size -= 1;\n                return Some(pair.val);\n            }\n        }\n\n        // key が見つからない場合は None を返す\n        None\n    }\n\n    /* ハッシュテーブルを拡張 */\n    fn extend(&amp;mut self) {\n        // 元のハッシュテーブルを一時保存\n        let buckets_tmp = std::mem::take(&amp;mut self.buckets);\n\n        // リサイズ後の新しいハッシュテーブルを初期化\n        self.capacity *= self.extend_ratio;\n        self.buckets = vec![Vec::new(); self.capacity as usize];\n        self.size = 0;\n\n        // キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n        for bucket in buckets_tmp {\n            for pair in bucket {\n                self.put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* ハッシュテーブルを出力 */\n    fn print(&amp;self) {\n        for bucket in &amp;self.buckets {\n            let mut res = Vec::new();\n            for pair in bucket {\n                res.push(format!(\"{} -&gt; {}\", pair.key, pair.val));\n            }\n            println!(\"{:?}\", res);\n        }\n    }\n\n    /* 追加操作 */\n    fn put(&amp;mut self, key: i32, val: String) {\n        // 負荷率がしきい値を超えたら、リサイズを実行\n        if self.load_factor() &gt; self.load_thres {\n            self.extend();\n        }\n\n        let index = self.hash_func(key);\n\n        // バケットを走査し、指定した key が見つかれば対応する val を更新して返す\n        for pair in self.buckets[index].iter_mut() {\n            if pair.key == key {\n                pair.val = val;\n                return;\n            }\n        }\n\n        // その key が存在しなければ、キーと値のペアを末尾に追加\n        let pair = Pair { key, val };\n        self.buckets[index].push(pair);\n        self.size += 1;\n    }\n\n    /* 検索操作 */\n    fn get(&amp;self, key: i32) -&gt; Option&lt;&amp;str&gt; {\n        let index = self.hash_func(key);\n\n        // バケットを走査し、key が見つかれば対応する val を返す\n        for pair in self.buckets[index].iter() {\n            if pair.key == key {\n                return Some(&amp;pair.val);\n            }\n        }\n\n        // key が見つからない場合は None を返す\n        None\n    }\n}\n</code></pre> hash_map_chaining.c<pre><code>/* 連結リストノード */\ntypedef struct Node {\n    Pair *pair;\n    struct Node *next;\n} Node;\n\n/* チェイン法ハッシュテーブル */\ntypedef struct {\n    int size;         // キーと値のペア数\n    int capacity;     // ハッシュテーブル容量\n    double loadThres; // リサイズを発動する負荷率のしきい値\n    int extendRatio;  // 拡張倍率\n    Node **buckets;   // バケット配列\n} HashMapChaining;\n\n/* コンストラクタ */\nHashMapChaining *newHashMapChaining() {\n    HashMapChaining *hashMap = (HashMapChaining *)malloc(sizeof(HashMapChaining));\n    hashMap-&gt;size = 0;\n    hashMap-&gt;capacity = 4;\n    hashMap-&gt;loadThres = 2.0 / 3.0;\n    hashMap-&gt;extendRatio = 2;\n    hashMap-&gt;buckets = (Node **)malloc(hashMap-&gt;capacity * sizeof(Node *));\n    for (int i = 0; i &lt; hashMap-&gt;capacity; i++) {\n        hashMap-&gt;buckets[i] = NULL;\n    }\n    return hashMap;\n}\n\n/* デストラクタ */\nvoid delHashMapChaining(HashMapChaining *hashMap) {\n    for (int i = 0; i &lt; hashMap-&gt;capacity; i++) {\n        Node *cur = hashMap-&gt;buckets[i];\n        while (cur) {\n            Node *tmp = cur;\n            cur = cur-&gt;next;\n            free(tmp-&gt;pair);\n            free(tmp);\n        }\n    }\n    free(hashMap-&gt;buckets);\n    free(hashMap);\n}\n\n/* ハッシュ関数 */\nint hashFunc(HashMapChaining *hashMap, int key) {\n    return key % hashMap-&gt;capacity;\n}\n\n/* 負荷率 */\ndouble loadFactor(HashMapChaining *hashMap) {\n    return (double)hashMap-&gt;size / (double)hashMap-&gt;capacity;\n}\n\n/* 検索操作 */\nchar *get(HashMapChaining *hashMap, int key) {\n    int index = hashFunc(hashMap, key);\n    // バケットを走査し、key が見つかれば対応する val を返す\n    Node *cur = hashMap-&gt;buckets[index];\n    while (cur) {\n        if (cur-&gt;pair-&gt;key == key) {\n            return cur-&gt;pair-&gt;val;\n        }\n        cur = cur-&gt;next;\n    }\n    return \"\"; // key が見つからない場合は空文字列を返す\n}\n\n/* 追加操作 */\nvoid put(HashMapChaining *hashMap, int key, const char *val) {\n    // 負荷率がしきい値を超えたら、リサイズを実行\n    if (loadFactor(hashMap) &gt; hashMap-&gt;loadThres) {\n        extend(hashMap);\n    }\n    int index = hashFunc(hashMap, key);\n    // バケットを走査し、指定した key が見つかれば対応する val を更新して返す\n    Node *cur = hashMap-&gt;buckets[index];\n    while (cur) {\n        if (cur-&gt;pair-&gt;key == key) {\n            strcpy(cur-&gt;pair-&gt;val, val); // 指定した `key` に遭遇したら、対応する `val` を更新して返す\n            return;\n        }\n        cur = cur-&gt;next;\n    }\n    // 該当する `key` がなければ、キーと値のペアを連結リストの先頭に追加する\n    Pair *newPair = (Pair *)malloc(sizeof(Pair));\n    newPair-&gt;key = key;\n    strcpy(newPair-&gt;val, val);\n    Node *newNode = (Node *)malloc(sizeof(Node));\n    newNode-&gt;pair = newPair;\n    newNode-&gt;next = hashMap-&gt;buckets[index];\n    hashMap-&gt;buckets[index] = newNode;\n    hashMap-&gt;size++;\n}\n\n/* ハッシュテーブルを拡張 */\nvoid extend(HashMapChaining *hashMap) {\n    // 元のハッシュテーブルを一時保存\n    int oldCapacity = hashMap-&gt;capacity;\n    Node **oldBuckets = hashMap-&gt;buckets;\n    // リサイズ後の新しいハッシュテーブルを初期化\n    hashMap-&gt;capacity *= hashMap-&gt;extendRatio;\n    hashMap-&gt;buckets = (Node **)malloc(hashMap-&gt;capacity * sizeof(Node *));\n    for (int i = 0; i &lt; hashMap-&gt;capacity; i++) {\n        hashMap-&gt;buckets[i] = NULL;\n    }\n    hashMap-&gt;size = 0;\n    // キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n    for (int i = 0; i &lt; oldCapacity; i++) {\n        Node *cur = oldBuckets[i];\n        while (cur) {\n            put(hashMap, cur-&gt;pair-&gt;key, cur-&gt;pair-&gt;val);\n            Node *temp = cur;\n            cur = cur-&gt;next;\n            // メモリを解放する\n            free(temp-&gt;pair);\n            free(temp);\n        }\n    }\n\n    free(oldBuckets);\n}\n\n/* 削除操作 */\nvoid removeItem(HashMapChaining *hashMap, int key) {\n    int index = hashFunc(hashMap, key);\n    Node *cur = hashMap-&gt;buckets[index];\n    Node *pre = NULL;\n    while (cur) {\n        if (cur-&gt;pair-&gt;key == key) {\n            // そこからキーと値の組を削除する\n            if (pre) {\n                pre-&gt;next = cur-&gt;next;\n            } else {\n                hashMap-&gt;buckets[index] = cur-&gt;next;\n            }\n            // メモリを解放する\n            free(cur-&gt;pair);\n            free(cur);\n            hashMap-&gt;size--;\n            return;\n        }\n        pre = cur;\n        cur = cur-&gt;next;\n    }\n}\n\n/* ハッシュテーブルを出力 */\nvoid print(HashMapChaining *hashMap) {\n    for (int i = 0; i &lt; hashMap-&gt;capacity; i++) {\n        Node *cur = hashMap-&gt;buckets[i];\n        printf(\"[\");\n        while (cur) {\n            printf(\"%d -&gt; %s, \", cur-&gt;pair-&gt;key, cur-&gt;pair-&gt;val);\n            cur = cur-&gt;next;\n        }\n        printf(\"]\\n\");\n    }\n}\n</code></pre> hash_map_chaining.kt<pre><code>/* チェイン法ハッシュテーブル */\nclass HashMapChaining {\n    var size: Int // キーと値のペア数\n    var capacity: Int // ハッシュテーブル容量\n    val loadThres: Double // リサイズを発動する負荷率のしきい値\n    val extendRatio: Int // 拡張倍率\n    var buckets: MutableList&lt;MutableList&lt;Pair&gt;&gt; // バケット配列\n\n    /* コンストラクタ */\n    init {\n        size = 0\n        capacity = 4\n        loadThres = 2.0 / 3.0\n        extendRatio = 2\n        buckets = mutableListOf()\n        for (i in 0..&lt;capacity) {\n            buckets.add(mutableListOf())\n        }\n    }\n\n    /* ハッシュ関数 */\n    fun hashFunc(key: Int): Int {\n        return key % capacity\n    }\n\n    /* 負荷率 */\n    fun loadFactor(): Double {\n        return (size / capacity).toDouble()\n    }\n\n    /* 検索操作 */\n    fun get(key: Int): String? {\n        val index = hashFunc(key)\n        val bucket = buckets[index]\n        // バケットを走査し、key が見つかれば対応する val を返す\n        for (pair in bucket) {\n            if (pair.key == key) return pair._val\n        }\n        // key が見つからない場合は null を返す\n        return null\n    }\n\n    /* 追加操作 */\n    fun put(key: Int, _val: String) {\n        // 負荷率がしきい値を超えたら、リサイズを実行\n        if (loadFactor() &gt; loadThres) {\n            extend()\n        }\n        val index = hashFunc(key)\n        val bucket = buckets[index]\n        // バケットを走査し、指定した key が見つかれば対応する val を更新して返す\n        for (pair in bucket) {\n            if (pair.key == key) {\n                pair._val = _val\n                return\n            }\n        }\n        // その key が存在しなければ、キーと値のペアを末尾に追加\n        val pair = Pair(key, _val)\n        bucket.add(pair)\n        size++\n    }\n\n    /* 削除操作 */\n    fun remove(key: Int) {\n        val index = hashFunc(key)\n        val bucket = buckets[index]\n        // バケットを走査してキーと値のペアを削除\n        for (pair in bucket) {\n            if (pair.key == key) {\n                bucket.remove(pair)\n                size--\n                break\n            }\n        }\n    }\n\n    /* ハッシュテーブルを拡張 */\n    fun extend() {\n        // 元のハッシュテーブルを一時保存\n        val bucketsTmp = buckets\n        // リサイズ後の新しいハッシュテーブルを初期化\n        capacity *= extendRatio\n        // mutablelist には固定サイズがない\n        buckets = mutableListOf()\n        for (i in 0..&lt;capacity) {\n            buckets.add(mutableListOf())\n        }\n        size = 0\n        // キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n        for (bucket in bucketsTmp) {\n            for (pair in bucket) {\n                put(pair.key, pair._val)\n            }\n        }\n    }\n\n    /* ハッシュテーブルを出力 */\n    fun print() {\n        for (bucket in buckets) {\n            val res = mutableListOf&lt;String&gt;()\n            for (pair in bucket) {\n                val k = pair.key\n                val v = pair._val\n                res.add(\"$k -&gt; $v\")\n            }\n            println(res)\n        }\n    }\n}\n</code></pre> hash_map_chaining.rb<pre><code>### キーアドレス法ハッシュテーブル ###\nclass HashMapChaining\n  ### コンストラクタ ###\n  def initialize\n    @size = 0 # キーと値のペア数\n    @capacity = 4 # ハッシュテーブル容量\n    @load_thres = 2.0 / 3.0 # リサイズを発動する負荷率のしきい値\n    @extend_ratio = 2 # 拡張倍率\n    @buckets = Array.new(@capacity) { [] } # バケット配列\n  end\n\n  ### ハッシュ関数 ###\n  def hash_func(key)\n    key % @capacity\n  end\n\n  ### 負荷率 ###\n  def load_factor\n    @size / @capacity\n  end\n\n  ### 検索操作 ###\n  def get(key)\n    index = hash_func(key)\n    bucket = @buckets[index]\n    # バケットを走査し、key が見つかれば対応する val を返す\n    for pair in bucket\n      return pair.val if pair.key == key\n    end\n    # `key` が見つからなければ `nil` を返す\n    nil\n  end\n\n  ### 追加操作 ###\n  def put(key, val)\n    # 負荷率がしきい値を超えたら、リサイズを実行\n    extend if load_factor &gt; @load_thres\n    index = hash_func(key)\n    bucket = @buckets[index]\n    # バケットを走査し、指定した key が見つかれば対応する val を更新して返す\n    for pair in bucket\n      if pair.key == key\n        pair.val = val\n        return\n      end\n    end\n    # その key が存在しなければ、キーと値のペアを末尾に追加\n    pair = Pair.new(key, val)\n    bucket &lt;&lt; pair\n    @size += 1\n  end\n\n  ### 削除操作 ###\n  def remove(key)\n    index = hash_func(key)\n    bucket = @buckets[index]\n    # バケットを走査してキーと値のペアを削除\n    for pair in bucket\n      if pair.key == key\n        bucket.delete(pair)\n        @size -= 1\n        break\n      end\n    end\n  end\n\n  ### ハッシュテーブルを拡張 ###\n  def extend\n    # 元のハッシュテーブルを一時保存\n    buckets = @buckets\n    # リサイズ後の新しいハッシュテーブルを初期化\n    @capacity *= @extend_ratio\n    @buckets = Array.new(@capacity) { [] }\n    @size = 0\n    # キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n    for bucket in buckets\n      for pair in bucket\n        put(pair.key, pair.val)\n      end\n    end\n  end\n\n  ### ハッシュテーブルを出力 ###\n  def print\n    for bucket in @buckets\n      res = []\n      for pair in bucket\n        res &lt;&lt; \"#{pair.key} -&gt; #{pair.val}\"\n      end\n      pp res\n    end\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>注意すべきなのは、連結リストが長い場合、検索効率 \\(O(n)\\) は非常に低いことです。このとき、連結リストを「AVL 木」または「赤黒木」に変換することで、検索操作の時間計算量を \\(O(\\log n)\\) に最適化できます。</p>","path":["第 6 章 &nbsp; ハッシュテーブル","6.2 &nbsp; ハッシュ衝突"],"tags":[]},{"location":"chapter_hashing/hash_collision/#622","level":2,"title":"6.2.2   オープンアドレッシング","text":"<p>オープンアドレッシング（open addressing）では追加のデータ構造を導入せず、「複数回の探索」によってハッシュ衝突を処理します。探索方法には主に線形探索、二次探索、多重ハッシュなどがあります。</p> <p>以下では線形探索を例に、オープンアドレッシングハッシュテーブルの動作の仕組みを説明します。</p>","path":["第 6 章 &nbsp; ハッシュテーブル","6.2 &nbsp; ハッシュ衝突"],"tags":[]},{"location":"chapter_hashing/hash_collision/#1","level":3,"title":"1.   線形探索","text":"<p>線形探索では、固定ステップ長の線形探索によって探索を行います。その操作方法は通常のハッシュテーブルとは異なります。</p> <ul> <li>要素の挿入：ハッシュ関数によってバケットインデックスを計算し、バケット内にすでに要素がある場合は、衝突位置から後方へ線形に走査し（ステップ長は通常 \\(1\\) ）、空のバケットが見つかるまで進み、その中に要素を挿入します。</li> <li>要素の検索：ハッシュ衝突が見つかった場合は、同じステップ長で後方へ線形走査を行い、対応する要素が見つかるまで続け、 <code>value</code> を返します。空のバケットに遭遇した場合は、対象要素がハッシュテーブル内に存在しないことを意味するため、 <code>None</code> を返します。</li> </ul> <p>下図はオープンアドレッシング（線形探索）ハッシュテーブルにおけるキーと値のペアの分布を示しています。このハッシュ関数では、末尾 2 桁が同じ <code>key</code> はすべて同じバケットに写像されます。線形探索によって、それらはそのバケットとその後続のバケットに順に格納されます。</p> <p></p> <p> 図 6-6   オープンアドレッシング（線形探索）ハッシュテーブルにおけるキーと値のペアの分布 </p> <p>しかし、**線形探索では「クラスタリング現象」が起こりやすい**です。具体的には、配列内で連続して占有された位置が長いほど、それらの連続位置でハッシュ衝突が発生する可能性が高くなり、さらにその位置の集積成長を促して悪循環を生み、最終的には追加・削除・検索・更新操作の効率低下を招きます。</p> <p>注意すべきなのは、**オープンアドレッシングハッシュテーブルでは要素を直接削除できない**ことです。これは、要素を削除すると配列内に空バケット <code>None</code> が生じ、要素を検索するときに線形探索がその空バケットに到達した時点で返ってしまうため、その空バケットより後ろの要素には二度とアクセスできなくなるからです。結果として、プログラムがそれらの要素を存在しないと誤判定する可能性があります。下図のとおりです。</p> <p></p> <p> 図 6-7   オープンアドレッシングで要素を削除したことによる検索問題 </p> <p>この問題を解決するために、遅延削除（lazy deletion）の仕組みを採用できます。これは要素をハッシュテーブルから直接取り除かず、代わりに定数 <code>TOMBSTONE</code> を使ってこのバケットをマークします。この仕組みでは、<code>None</code> と <code>TOMBSTONE</code> はどちらも空バケットを表し、どちらにもキーと値のペアを配置できます。ただし異なるのは、線形探索が <code>TOMBSTONE</code> に到達した場合は、その先にキーと値のペアが存在する可能性があるため、探索を続けるべきだという点です。</p> <p>しかし、遅延削除はハッシュテーブルの性能劣化を加速させる可能性があります。これは、削除操作のたびに削除マークが 1 つ生成され、<code>TOMBSTONE</code> が増えるにつれて探索時間も増加するためです。線形探索では、対象要素を見つけるまでに複数の <code>TOMBSTONE</code> を飛び越える必要があるかもしれません。</p> <p>そのため、線形探索では、遭遇した最初の <code>TOMBSTONE</code> のインデックスを記録し、見つかった対象要素とその <code>TOMBSTONE</code> を交換することを考えます。こうする利点は、要素を検索または追加するたびに、要素が理想位置（探索開始点）により近いバケットへ移動し、検索効率が向上することです。</p> <p>以下のコードは、遅延削除を含むオープンアドレッシング（線形探索）ハッシュテーブルを実装したものです。ハッシュテーブルの空間をより十分に活用するために、ハッシュテーブルを「環状配列」とみなし、配列末尾を越えたら先頭に戻って探索を続けます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby hash_map_open_addressing.py<pre><code>class HashMapOpenAddressing:\n    \"\"\"オープンアドレス法ハッシュテーブル\"\"\"\n\n    def __init__(self):\n        \"\"\"コンストラクタ\"\"\"\n        self.size = 0  # キーと値のペア数\n        self.capacity = 4  # ハッシュテーブル容量\n        self.load_thres = 2.0 / 3.0  # リサイズを発動する負荷率のしきい値\n        self.extend_ratio = 2  # 拡張倍率\n        self.buckets: list[Pair | None] = [None] * self.capacity  # バケット配列\n        self.TOMBSTONE = Pair(-1, \"-1\")  # 削除済みマーク\n\n    def hash_func(self, key: int) -&gt; int:\n        \"\"\"ハッシュ関数\"\"\"\n        return key % self.capacity\n\n    def load_factor(self) -&gt; float:\n        \"\"\"負荷率\"\"\"\n        return self.size / self.capacity\n\n    def find_bucket(self, key: int) -&gt; int:\n        \"\"\"key に対応するバケットインデックスを探す\"\"\"\n        index = self.hash_func(key)\n        first_tombstone = -1\n        # 線形プロービングを行い、空バケットに達したら終了\n        while self.buckets[index] is not None:\n            # key が見つかったら、対応するバケットのインデックスを返す\n            if self.buckets[index].key == key:\n                # 以前に削除マークが見つかっていれば、そのインデックスへキーと値のペアを移動\n                if first_tombstone != -1:\n                    self.buckets[first_tombstone] = self.buckets[index]\n                    self.buckets[index] = self.TOMBSTONE\n                    return first_tombstone  # 移動後のバケットインデックスを返す\n                return index  # バケットのインデックスを返す\n            # 最初に見つかった削除マークを記録\n            if first_tombstone == -1 and self.buckets[index] is self.TOMBSTONE:\n                first_tombstone = index\n            # バケットのインデックスを計算し、末尾を越えたら先頭に戻る\n            index = (index + 1) % self.capacity\n        # key が存在しない場合は追加位置のインデックスを返す\n        return index if first_tombstone == -1 else first_tombstone\n\n    def get(self, key: int) -&gt; str:\n        \"\"\"検索操作\"\"\"\n        # key に対応するバケットインデックスを探す\n        index = self.find_bucket(key)\n        # キーと値の組が見つかったら、対応する val を返す\n        if self.buckets[index] not in [None, self.TOMBSTONE]:\n            return self.buckets[index].val\n        # キーと値のペアが存在しない場合は `None` を返す\n        return None\n\n    def put(self, key: int, val: str):\n        \"\"\"追加操作\"\"\"\n        # 負荷率がしきい値を超えたら、リサイズを実行\n        if self.load_factor() &gt; self.load_thres:\n            self.extend()\n        # key に対応するバケットインデックスを探す\n        index = self.find_bucket(key)\n        # キーと値の組が見つかったら、val を上書きして返す\n        if self.buckets[index] not in [None, self.TOMBSTONE]:\n            self.buckets[index].val = val\n            return\n        # キーと値の組が存在しない場合は、その組を追加する\n        self.buckets[index] = Pair(key, val)\n        self.size += 1\n\n    def remove(self, key: int):\n        \"\"\"削除操作\"\"\"\n        # key に対応するバケットインデックスを探す\n        index = self.find_bucket(key)\n        # キーと値の組が見つかったら、削除マーカーで上書きする\n        if self.buckets[index] not in [None, self.TOMBSTONE]:\n            self.buckets[index] = self.TOMBSTONE\n            self.size -= 1\n\n    def extend(self):\n        \"\"\"ハッシュテーブルを拡張\"\"\"\n        # 元のハッシュテーブルを一時保存\n        buckets_tmp = self.buckets\n        # リサイズ後の新しいハッシュテーブルを初期化\n        self.capacity *= self.extend_ratio\n        self.buckets = [None] * self.capacity\n        self.size = 0\n        # キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n        for pair in buckets_tmp:\n            if pair not in [None, self.TOMBSTONE]:\n                self.put(pair.key, pair.val)\n\n    def print(self):\n        \"\"\"ハッシュテーブルを出力\"\"\"\n        for pair in self.buckets:\n            if pair is None:\n                print(\"None\")\n            elif pair is self.TOMBSTONE:\n                print(\"TOMBSTONE\")\n            else:\n                print(pair.key, \"-&gt;\", pair.val)\n</code></pre> hash_map_open_addressing.cpp<pre><code>/* オープンアドレス法ハッシュテーブル */\nclass HashMapOpenAddressing {\n  private:\n    int size;                             // キーと値のペア数\n    int capacity = 4;                     // ハッシュテーブル容量\n    const double loadThres = 2.0 / 3.0;     // リサイズを発動する負荷率のしきい値\n    const int extendRatio = 2;            // 拡張倍率\n    vector&lt;Pair *&gt; buckets;               // バケット配列\n    Pair *TOMBSTONE = new Pair(-1, \"-1\"); // 削除済みマーク\n\n  public:\n    /* コンストラクタ */\n    HashMapOpenAddressing() : size(0), buckets(capacity, nullptr) {\n    }\n\n    /* デストラクタメソッド */\n    ~HashMapOpenAddressing() {\n        for (Pair *pair : buckets) {\n            if (pair != nullptr &amp;&amp; pair != TOMBSTONE) {\n                delete pair;\n            }\n        }\n        delete TOMBSTONE;\n    }\n\n    /* ハッシュ関数 */\n    int hashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* 負荷率 */\n    double loadFactor() {\n        return (double)size / capacity;\n    }\n\n    /* key に対応するバケットインデックスを探す */\n    int findBucket(int key) {\n        int index = hashFunc(key);\n        int firstTombstone = -1;\n        // 線形プロービングを行い、空バケットに達したら終了\n        while (buckets[index] != nullptr) {\n            // key が見つかったら、対応するバケットのインデックスを返す\n            if (buckets[index]-&gt;key == key) {\n                // 以前に削除マークが見つかっていれば、そのインデックスへキーと値のペアを移動\n                if (firstTombstone != -1) {\n                    buckets[firstTombstone] = buckets[index];\n                    buckets[index] = TOMBSTONE;\n                    return firstTombstone; // 移動後のバケットインデックスを返す\n                }\n                return index; // バケットのインデックスを返す\n            }\n            // 最初に見つかった削除マークを記録\n            if (firstTombstone == -1 &amp;&amp; buckets[index] == TOMBSTONE) {\n                firstTombstone = index;\n            }\n            // バケットのインデックスを計算し、末尾を越えたら先頭に戻る\n            index = (index + 1) % capacity;\n        }\n        // key が存在しない場合は追加位置のインデックスを返す\n        return firstTombstone == -1 ? index : firstTombstone;\n    }\n\n    /* 検索操作 */\n    string get(int key) {\n        // key に対応するバケットインデックスを探す\n        int index = findBucket(key);\n        // キーと値の組が見つかったら、対応する val を返す\n        if (buckets[index] != nullptr &amp;&amp; buckets[index] != TOMBSTONE) {\n            return buckets[index]-&gt;val;\n        }\n        // キーと値の組が存在しない場合は空文字列を返す\n        return \"\";\n    }\n\n    /* 追加操作 */\n    void put(int key, string val) {\n        // 負荷率がしきい値を超えたら、リサイズを実行\n        if (loadFactor() &gt; loadThres) {\n            extend();\n        }\n        // key に対応するバケットインデックスを探す\n        int index = findBucket(key);\n        // キーと値の組が見つかったら、val を上書きして返す\n        if (buckets[index] != nullptr &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index]-&gt;val = val;\n            return;\n        }\n        // キーと値の組が存在しない場合は、その組を追加する\n        buckets[index] = new Pair(key, val);\n        size++;\n    }\n\n    /* 削除操作 */\n    void remove(int key) {\n        // key に対応するバケットインデックスを探す\n        int index = findBucket(key);\n        // キーと値の組が見つかったら、削除マーカーで上書きする\n        if (buckets[index] != nullptr &amp;&amp; buckets[index] != TOMBSTONE) {\n            delete buckets[index];\n            buckets[index] = TOMBSTONE;\n            size--;\n        }\n    }\n\n    /* ハッシュテーブルを拡張 */\n    void extend() {\n        // 元のハッシュテーブルを一時保存\n        vector&lt;Pair *&gt; bucketsTmp = buckets;\n        // リサイズ後の新しいハッシュテーブルを初期化\n        capacity *= extendRatio;\n        buckets = vector&lt;Pair *&gt;(capacity, nullptr);\n        size = 0;\n        // キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n        for (Pair *pair : bucketsTmp) {\n            if (pair != nullptr &amp;&amp; pair != TOMBSTONE) {\n                put(pair-&gt;key, pair-&gt;val);\n                delete pair;\n            }\n        }\n    }\n\n    /* ハッシュテーブルを出力 */\n    void print() {\n        for (Pair *pair : buckets) {\n            if (pair == nullptr) {\n                cout &lt;&lt; \"nullptr\" &lt;&lt; endl;\n            } else if (pair == TOMBSTONE) {\n                cout &lt;&lt; \"TOMBSTONE\" &lt;&lt; endl;\n            } else {\n                cout &lt;&lt; pair-&gt;key &lt;&lt; \" -&gt; \" &lt;&lt; pair-&gt;val &lt;&lt; endl;\n            }\n        }\n    }\n};\n</code></pre> hash_map_open_addressing.java<pre><code>/* オープンアドレス法ハッシュテーブル */\nclass HashMapOpenAddressing {\n    private int size; // キーと値のペア数\n    private int capacity = 4; // ハッシュテーブル容量\n    private final double loadThres = 2.0 / 3.0; // リサイズを発動する負荷率のしきい値\n    private final int extendRatio = 2; // 拡張倍率\n    private Pair[] buckets; // バケット配列\n    private final Pair TOMBSTONE = new Pair(-1, \"-1\"); // 削除済みマーク\n\n    /* コンストラクタ */\n    public HashMapOpenAddressing() {\n        size = 0;\n        buckets = new Pair[capacity];\n    }\n\n    /* ハッシュ関数 */\n    private int hashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* 負荷率 */\n    private double loadFactor() {\n        return (double) size / capacity;\n    }\n\n    /* key に対応するバケットインデックスを探す */\n    private int findBucket(int key) {\n        int index = hashFunc(key);\n        int firstTombstone = -1;\n        // 線形プロービングを行い、空バケットに達したら終了\n        while (buckets[index] != null) {\n            // key が見つかったら、対応するバケットのインデックスを返す\n            if (buckets[index].key == key) {\n                // 以前に削除マークが見つかっていれば、そのインデックスへキーと値のペアを移動\n                if (firstTombstone != -1) {\n                    buckets[firstTombstone] = buckets[index];\n                    buckets[index] = TOMBSTONE;\n                    return firstTombstone; // 移動後のバケットインデックスを返す\n                }\n                return index; // バケットのインデックスを返す\n            }\n            // 最初に見つかった削除マークを記録\n            if (firstTombstone == -1 &amp;&amp; buckets[index] == TOMBSTONE) {\n                firstTombstone = index;\n            }\n            // バケットのインデックスを計算し、末尾を越えたら先頭に戻る\n            index = (index + 1) % capacity;\n        }\n        // key が存在しない場合は追加位置のインデックスを返す\n        return firstTombstone == -1 ? index : firstTombstone;\n    }\n\n    /* 検索操作 */\n    public String get(int key) {\n        // key に対応するバケットインデックスを探す\n        int index = findBucket(key);\n        // キーと値の組が見つかったら、対応する val を返す\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            return buckets[index].val;\n        }\n        // キーと値の組が存在しなければ null を返す\n        return null;\n    }\n\n    /* 追加操作 */\n    public void put(int key, String val) {\n        // 負荷率がしきい値を超えたら、リサイズを実行\n        if (loadFactor() &gt; loadThres) {\n            extend();\n        }\n        // key に対応するバケットインデックスを探す\n        int index = findBucket(key);\n        // キーと値の組が見つかったら、val を上書きして返す\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index].val = val;\n            return;\n        }\n        // キーと値の組が存在しない場合は、その組を追加する\n        buckets[index] = new Pair(key, val);\n        size++;\n    }\n\n    /* 削除操作 */\n    public void remove(int key) {\n        // key に対応するバケットインデックスを探す\n        int index = findBucket(key);\n        // キーと値の組が見つかったら、削除マーカーで上書きする\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index] = TOMBSTONE;\n            size--;\n        }\n    }\n\n    /* ハッシュテーブルを拡張 */\n    private void extend() {\n        // 元のハッシュテーブルを一時保存\n        Pair[] bucketsTmp = buckets;\n        // リサイズ後の新しいハッシュテーブルを初期化\n        capacity *= extendRatio;\n        buckets = new Pair[capacity];\n        size = 0;\n        // キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n        for (Pair pair : bucketsTmp) {\n            if (pair != null &amp;&amp; pair != TOMBSTONE) {\n                put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* ハッシュテーブルを出力 */\n    public void print() {\n        for (Pair pair : buckets) {\n            if (pair == null) {\n                System.out.println(\"null\");\n            } else if (pair == TOMBSTONE) {\n                System.out.println(\"TOMBSTONE\");\n            } else {\n                System.out.println(pair.key + \" -&gt; \" + pair.val);\n            }\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.cs<pre><code>/* オープンアドレス法ハッシュテーブル */\nclass HashMapOpenAddressing {\n    int size; // キーと値のペア数\n    int capacity = 4; // ハッシュテーブル容量\n    double loadThres = 2.0 / 3.0; // リサイズを発動する負荷率のしきい値\n    int extendRatio = 2; // 拡張倍率\n    Pair[] buckets; // バケット配列\n    Pair TOMBSTONE = new(-1, \"-1\"); // 削除済みマーク\n\n    /* コンストラクタ */\n    public HashMapOpenAddressing() {\n        size = 0;\n        buckets = new Pair[capacity];\n    }\n\n    /* ハッシュ関数 */\n    int HashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* 負荷率 */\n    double LoadFactor() {\n        return (double)size / capacity;\n    }\n\n    /* key に対応するバケットインデックスを探す */\n    int FindBucket(int key) {\n        int index = HashFunc(key);\n        int firstTombstone = -1;\n        // 線形プロービングを行い、空バケットに達したら終了\n        while (buckets[index] != null) {\n            // key が見つかったら、対応するバケットのインデックスを返す\n            if (buckets[index].key == key) {\n                // 以前に削除マークが見つかっていれば、そのインデックスへキーと値のペアを移動\n                if (firstTombstone != -1) {\n                    buckets[firstTombstone] = buckets[index];\n                    buckets[index] = TOMBSTONE;\n                    return firstTombstone; // 移動後のバケットインデックスを返す\n                }\n                return index; // バケットのインデックスを返す\n            }\n            // 最初に見つかった削除マークを記録\n            if (firstTombstone == -1 &amp;&amp; buckets[index] == TOMBSTONE) {\n                firstTombstone = index;\n            }\n            // バケットのインデックスを計算し、末尾を越えたら先頭に戻る\n            index = (index + 1) % capacity;\n        }\n        // key が存在しない場合は追加位置のインデックスを返す\n        return firstTombstone == -1 ? index : firstTombstone;\n    }\n\n    /* 検索操作 */\n    public string? Get(int key) {\n        // key に対応するバケットインデックスを探す\n        int index = FindBucket(key);\n        // キーと値の組が見つかったら、対応する val を返す\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            return buckets[index].val;\n        }\n        // キーと値の組が存在しなければ null を返す\n        return null;\n    }\n\n    /* 追加操作 */\n    public void Put(int key, string val) {\n        // 負荷率がしきい値を超えたら、リサイズを実行\n        if (LoadFactor() &gt; loadThres) {\n            Extend();\n        }\n        // key に対応するバケットインデックスを探す\n        int index = FindBucket(key);\n        // キーと値の組が見つかったら、val を上書きして返す\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index].val = val;\n            return;\n        }\n        // キーと値の組が存在しない場合は、その組を追加する\n        buckets[index] = new Pair(key, val);\n        size++;\n    }\n\n    /* 削除操作 */\n    public void Remove(int key) {\n        // key に対応するバケットインデックスを探す\n        int index = FindBucket(key);\n        // キーと値の組が見つかったら、削除マーカーで上書きする\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index] = TOMBSTONE;\n            size--;\n        }\n    }\n\n    /* ハッシュテーブルを拡張 */\n    void Extend() {\n        // 元のハッシュテーブルを一時保存\n        Pair[] bucketsTmp = buckets;\n        // リサイズ後の新しいハッシュテーブルを初期化\n        capacity *= extendRatio;\n        buckets = new Pair[capacity];\n        size = 0;\n        // キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n        foreach (Pair pair in bucketsTmp) {\n            if (pair != null &amp;&amp; pair != TOMBSTONE) {\n                Put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* ハッシュテーブルを出力 */\n    public void Print() {\n        foreach (Pair pair in buckets) {\n            if (pair == null) {\n                Console.WriteLine(\"null\");\n            } else if (pair == TOMBSTONE) {\n                Console.WriteLine(\"TOMBSTONE\");\n            } else {\n                Console.WriteLine(pair.key + \" -&gt; \" + pair.val);\n            }\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.go<pre><code>/* オープンアドレス法ハッシュテーブル */\ntype hashMapOpenAddressing struct {\n    size        int     // キーと値のペア数\n    capacity    int     // ハッシュテーブル容量\n    loadThres   float64 // リサイズを発動する負荷率のしきい値\n    extendRatio int     // 拡張倍率\n    buckets     []*pair // バケット配列\n    TOMBSTONE   *pair   // 削除済みマーク\n}\n\n/* コンストラクタ */\nfunc newHashMapOpenAddressing() *hashMapOpenAddressing {\n    return &amp;hashMapOpenAddressing{\n        size:        0,\n        capacity:    4,\n        loadThres:   2.0 / 3.0,\n        extendRatio: 2,\n        buckets:     make([]*pair, 4),\n        TOMBSTONE:   &amp;pair{-1, \"-1\"},\n    }\n}\n\n/* ハッシュ関数 */\nfunc (h *hashMapOpenAddressing) hashFunc(key int) int {\n    return key % h.capacity // キーに基づいてハッシュ値を計算\n}\n\n/* 負荷率 */\nfunc (h *hashMapOpenAddressing) loadFactor() float64 {\n    return float64(h.size) / float64(h.capacity) // 現在の負荷率を計算\n}\n\n/* key に対応するバケットインデックスを探す */\nfunc (h *hashMapOpenAddressing) findBucket(key int) int {\n    index := h.hashFunc(key) // 初期インデックスを取得\n    firstTombstone := -1     // 最初に遭遇した `TOMBSTONE` の位置を記録する\n    for h.buckets[index] != nil {\n        if h.buckets[index].key == key {\n            if firstTombstone != -1 {\n                // 以前に削除マークが見つかっていれば、そのインデックスへキーと値のペアを移動\n                h.buckets[firstTombstone] = h.buckets[index]\n                h.buckets[index] = h.TOMBSTONE\n                return firstTombstone // 移動後のバケットインデックスを返す\n            }\n            return index // 見つかったインデックスを返す\n        }\n        if firstTombstone == -1 &amp;&amp; h.buckets[index] == h.TOMBSTONE {\n            firstTombstone = index // 最初に遭遇した削除マークの位置を記録する\n        }\n        index = (index + 1) % h.capacity // 線形探索を行い、末尾を越えたら先頭に戻る\n    }\n    // key が存在しない場合は追加位置のインデックスを返す\n    if firstTombstone != -1 {\n        return firstTombstone\n    }\n    return index\n}\n\n/* 検索操作 */\nfunc (h *hashMapOpenAddressing) get(key int) string {\n    index := h.findBucket(key) // key に対応するバケットインデックスを探す\n    if h.buckets[index] != nil &amp;&amp; h.buckets[index] != h.TOMBSTONE {\n        return h.buckets[index].val // キーと値の組が見つかったら、対応する val を返す\n    }\n    return \"\" // キーと値のペアが存在しない場合は `\"\"` を返す\n}\n\n/* 追加操作 */\nfunc (h *hashMapOpenAddressing) put(key int, val string) {\n    if h.loadFactor() &gt; h.loadThres {\n        h.extend() // 負荷率がしきい値を超えたら、リサイズを実行\n    }\n    index := h.findBucket(key) // key に対応するバケットインデックスを探す\n    if h.buckets[index] == nil || h.buckets[index] == h.TOMBSTONE {\n        h.buckets[index] = &amp;pair{key, val} // キーと値の組が存在しない場合は、その組を追加する\n        h.size++\n    } else {\n        h.buckets[index].val = val // キーと値のペアが見つかった場合は、`val` を上書きする\n    }\n}\n\n/* 削除操作 */\nfunc (h *hashMapOpenAddressing) remove(key int) {\n    index := h.findBucket(key) // key に対応するバケットインデックスを探す\n    if h.buckets[index] != nil &amp;&amp; h.buckets[index] != h.TOMBSTONE {\n        h.buckets[index] = h.TOMBSTONE // キーと値の組が見つかったら、削除マーカーで上書きする\n        h.size--\n    }\n}\n\n/* ハッシュテーブルを拡張 */\nfunc (h *hashMapOpenAddressing) extend() {\n    oldBuckets := h.buckets               // 元のハッシュテーブルを一時保存\n    h.capacity *= h.extendRatio           // 容量を更新\n    h.buckets = make([]*pair, h.capacity) // リサイズ後の新しいハッシュテーブルを初期化\n    h.size = 0                            // サイズをリセットする\n    // キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n    for _, pair := range oldBuckets {\n        if pair != nil &amp;&amp; pair != h.TOMBSTONE {\n            h.put(pair.key, pair.val)\n        }\n    }\n}\n\n/* ハッシュテーブルを出力 */\nfunc (h *hashMapOpenAddressing) print() {\n    for _, pair := range h.buckets {\n        if pair == nil {\n            fmt.Println(\"nil\")\n        } else if pair == h.TOMBSTONE {\n            fmt.Println(\"TOMBSTONE\")\n        } else {\n            fmt.Printf(\"%d -&gt; %s\\n\", pair.key, pair.val)\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.swift<pre><code>/* オープンアドレス法ハッシュテーブル */\nclass HashMapOpenAddressing {\n    var size: Int // キーと値のペア数\n    var capacity: Int // ハッシュテーブル容量\n    var loadThres: Double // リサイズを発動する負荷率のしきい値\n    var extendRatio: Int // 拡張倍率\n    var buckets: [Pair?] // バケット配列\n    var TOMBSTONE: Pair // 削除済みマーク\n\n    /* コンストラクタ */\n    init() {\n        size = 0\n        capacity = 4\n        loadThres = 2.0 / 3.0\n        extendRatio = 2\n        buckets = Array(repeating: nil, count: capacity)\n        TOMBSTONE = Pair(key: -1, val: \"-1\")\n    }\n\n    /* ハッシュ関数 */\n    func hashFunc(key: Int) -&gt; Int {\n        key % capacity\n    }\n\n    /* 負荷率 */\n    func loadFactor() -&gt; Double {\n        Double(size) / Double(capacity)\n    }\n\n    /* key に対応するバケットインデックスを探す */\n    func findBucket(key: Int) -&gt; Int {\n        var index = hashFunc(key: key)\n        var firstTombstone = -1\n        // 線形プロービングを行い、空バケットに達したら終了\n        while buckets[index] != nil {\n            // key が見つかったら、対応するバケットのインデックスを返す\n            if buckets[index]!.key == key {\n                // 以前に削除マークが見つかっていれば、そのインデックスへキーと値のペアを移動\n                if firstTombstone != -1 {\n                    buckets[firstTombstone] = buckets[index]\n                    buckets[index] = TOMBSTONE\n                    return firstTombstone // 移動後のバケットインデックスを返す\n                }\n                return index // バケットのインデックスを返す\n            }\n            // 最初に見つかった削除マークを記録\n            if firstTombstone == -1 &amp;&amp; buckets[index] == TOMBSTONE {\n                firstTombstone = index\n            }\n            // バケットのインデックスを計算し、末尾を越えたら先頭に戻る\n            index = (index + 1) % capacity\n        }\n        // key が存在しない場合は追加位置のインデックスを返す\n        return firstTombstone == -1 ? index : firstTombstone\n    }\n\n    /* 検索操作 */\n    func get(key: Int) -&gt; String? {\n        // key に対応するバケットインデックスを探す\n        let index = findBucket(key: key)\n        // キーと値の組が見つかったら、対応する val を返す\n        if buckets[index] != nil, buckets[index] != TOMBSTONE {\n            return buckets[index]!.val\n        }\n        // キーと値の組が存在しなければ null を返す\n        return nil\n    }\n\n    /* 追加操作 */\n    func put(key: Int, val: String) {\n        // 負荷率がしきい値を超えたら、リサイズを実行\n        if loadFactor() &gt; loadThres {\n            extend()\n        }\n        // key に対応するバケットインデックスを探す\n        let index = findBucket(key: key)\n        // キーと値の組が見つかったら、val を上書きして返す\n        if buckets[index] != nil, buckets[index] != TOMBSTONE {\n            buckets[index]!.val = val\n            return\n        }\n        // キーと値の組が存在しない場合は、その組を追加する\n        buckets[index] = Pair(key: key, val: val)\n        size += 1\n    }\n\n    /* 削除操作 */\n    func remove(key: Int) {\n        // key に対応するバケットインデックスを探す\n        let index = findBucket(key: key)\n        // キーと値の組が見つかったら、削除マーカーで上書きする\n        if buckets[index] != nil, buckets[index] != TOMBSTONE {\n            buckets[index] = TOMBSTONE\n            size -= 1\n        }\n    }\n\n    /* ハッシュテーブルを拡張 */\n    func extend() {\n        // 元のハッシュテーブルを一時保存\n        let bucketsTmp = buckets\n        // リサイズ後の新しいハッシュテーブルを初期化\n        capacity *= extendRatio\n        buckets = Array(repeating: nil, count: capacity)\n        size = 0\n        // キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n        for pair in bucketsTmp {\n            if let pair, pair != TOMBSTONE {\n                put(key: pair.key, val: pair.val)\n            }\n        }\n    }\n\n    /* ハッシュテーブルを出力 */\n    func print() {\n        for pair in buckets {\n            if pair == nil {\n                Swift.print(\"null\")\n            } else if pair == TOMBSTONE {\n                Swift.print(\"TOMBSTONE\")\n            } else {\n                Swift.print(\"\\(pair!.key) -&gt; \\(pair!.val)\")\n            }\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.js<pre><code>/* オープンアドレス法ハッシュテーブル */\nclass HashMapOpenAddressing {\n    #size; // キーと値のペア数\n    #capacity; // ハッシュテーブル容量\n    #loadThres; // リサイズを発動する負荷率のしきい値\n    #extendRatio; // 拡張倍率\n    #buckets; // バケット配列\n    #TOMBSTONE; // 削除済みマーク\n\n    /* コンストラクタ */\n    constructor() {\n        this.#size = 0; // キーと値のペア数\n        this.#capacity = 4; // ハッシュテーブル容量\n        this.#loadThres = 2.0 / 3.0; // リサイズを発動する負荷率のしきい値\n        this.#extendRatio = 2; // 拡張倍率\n        this.#buckets = Array(this.#capacity).fill(null); // バケット配列\n        this.#TOMBSTONE = new Pair(-1, '-1'); // 削除済みマーク\n    }\n\n    /* ハッシュ関数 */\n    #hashFunc(key) {\n        return key % this.#capacity;\n    }\n\n    /* 負荷率 */\n    #loadFactor() {\n        return this.#size / this.#capacity;\n    }\n\n    /* key に対応するバケットインデックスを探す */\n    #findBucket(key) {\n        let index = this.#hashFunc(key);\n        let firstTombstone = -1;\n        // 線形プロービングを行い、空バケットに達したら終了\n        while (this.#buckets[index] !== null) {\n            // key が見つかったら、対応するバケットのインデックスを返す\n            if (this.#buckets[index].key === key) {\n                // 以前に削除マークが見つかっていれば、そのインデックスへキーと値のペアを移動\n                if (firstTombstone !== -1) {\n                    this.#buckets[firstTombstone] = this.#buckets[index];\n                    this.#buckets[index] = this.#TOMBSTONE;\n                    return firstTombstone; // 移動後のバケットインデックスを返す\n                }\n                return index; // バケットのインデックスを返す\n            }\n            // 最初に見つかった削除マークを記録\n            if (\n                firstTombstone === -1 &amp;&amp;\n                this.#buckets[index] === this.#TOMBSTONE\n            ) {\n                firstTombstone = index;\n            }\n            // バケットのインデックスを計算し、末尾を越えたら先頭に戻る\n            index = (index + 1) % this.#capacity;\n        }\n        // key が存在しない場合は追加位置のインデックスを返す\n        return firstTombstone === -1 ? index : firstTombstone;\n    }\n\n    /* 検索操作 */\n    get(key) {\n        // key に対応するバケットインデックスを探す\n        const index = this.#findBucket(key);\n        // キーと値の組が見つかったら、対応する val を返す\n        if (\n            this.#buckets[index] !== null &amp;&amp;\n            this.#buckets[index] !== this.#TOMBSTONE\n        ) {\n            return this.#buckets[index].val;\n        }\n        // キーと値の組が存在しなければ null を返す\n        return null;\n    }\n\n    /* 追加操作 */\n    put(key, val) {\n        // 負荷率がしきい値を超えたら、リサイズを実行\n        if (this.#loadFactor() &gt; this.#loadThres) {\n            this.#extend();\n        }\n        // key に対応するバケットインデックスを探す\n        const index = this.#findBucket(key);\n        // キーと値の組が見つかったら、val を上書きして返す\n        if (\n            this.#buckets[index] !== null &amp;&amp;\n            this.#buckets[index] !== this.#TOMBSTONE\n        ) {\n            this.#buckets[index].val = val;\n            return;\n        }\n        // キーと値の組が存在しない場合は、その組を追加する\n        this.#buckets[index] = new Pair(key, val);\n        this.#size++;\n    }\n\n    /* 削除操作 */\n    remove(key) {\n        // key に対応するバケットインデックスを探す\n        const index = this.#findBucket(key);\n        // キーと値の組が見つかったら、削除マーカーで上書きする\n        if (\n            this.#buckets[index] !== null &amp;&amp;\n            this.#buckets[index] !== this.#TOMBSTONE\n        ) {\n            this.#buckets[index] = this.#TOMBSTONE;\n            this.#size--;\n        }\n    }\n\n    /* ハッシュテーブルを拡張 */\n    #extend() {\n        // 元のハッシュテーブルを一時保存\n        const bucketsTmp = this.#buckets;\n        // リサイズ後の新しいハッシュテーブルを初期化\n        this.#capacity *= this.#extendRatio;\n        this.#buckets = Array(this.#capacity).fill(null);\n        this.#size = 0;\n        // キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n        for (const pair of bucketsTmp) {\n            if (pair !== null &amp;&amp; pair !== this.#TOMBSTONE) {\n                this.put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* ハッシュテーブルを出力 */\n    print() {\n        for (const pair of this.#buckets) {\n            if (pair === null) {\n                console.log('null');\n            } else if (pair === this.#TOMBSTONE) {\n                console.log('TOMBSTONE');\n            } else {\n                console.log(pair.key + ' -&gt; ' + pair.val);\n            }\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.ts<pre><code>/* オープンアドレス法ハッシュテーブル */\nclass HashMapOpenAddressing {\n    private size: number; // キーと値のペア数\n    private capacity: number; // ハッシュテーブル容量\n    private loadThres: number; // リサイズを発動する負荷率のしきい値\n    private extendRatio: number; // 拡張倍率\n    private buckets: Array&lt;Pair | null&gt;; // バケット配列\n    private TOMBSTONE: Pair; // 削除済みマーク\n\n    /* コンストラクタ */\n    constructor() {\n        this.size = 0; // キーと値のペア数\n        this.capacity = 4; // ハッシュテーブル容量\n        this.loadThres = 2.0 / 3.0; // リサイズを発動する負荷率のしきい値\n        this.extendRatio = 2; // 拡張倍率\n        this.buckets = Array(this.capacity).fill(null); // バケット配列\n        this.TOMBSTONE = new Pair(-1, '-1'); // 削除済みマーク\n    }\n\n    /* ハッシュ関数 */\n    private hashFunc(key: number): number {\n        return key % this.capacity;\n    }\n\n    /* 負荷率 */\n    private loadFactor(): number {\n        return this.size / this.capacity;\n    }\n\n    /* key に対応するバケットインデックスを探す */\n    private findBucket(key: number): number {\n        let index = this.hashFunc(key);\n        let firstTombstone = -1;\n        // 線形プロービングを行い、空バケットに達したら終了\n        while (this.buckets[index] !== null) {\n            // key が見つかったら、対応するバケットのインデックスを返す\n            if (this.buckets[index]!.key === key) {\n                // 以前に削除マークが見つかっていれば、そのインデックスへキーと値のペアを移動\n                if (firstTombstone !== -1) {\n                    this.buckets[firstTombstone] = this.buckets[index];\n                    this.buckets[index] = this.TOMBSTONE;\n                    return firstTombstone; // 移動後のバケットインデックスを返す\n                }\n                return index; // バケットのインデックスを返す\n            }\n            // 最初に見つかった削除マークを記録\n            if (\n                firstTombstone === -1 &amp;&amp;\n                this.buckets[index] === this.TOMBSTONE\n            ) {\n                firstTombstone = index;\n            }\n            // バケットのインデックスを計算し、末尾を越えたら先頭に戻る\n            index = (index + 1) % this.capacity;\n        }\n        // key が存在しない場合は追加位置のインデックスを返す\n        return firstTombstone === -1 ? index : firstTombstone;\n    }\n\n    /* 検索操作 */\n    get(key: number): string | null {\n        // key に対応するバケットインデックスを探す\n        const index = this.findBucket(key);\n        // キーと値の組が見つかったら、対応する val を返す\n        if (\n            this.buckets[index] !== null &amp;&amp;\n            this.buckets[index] !== this.TOMBSTONE\n        ) {\n            return this.buckets[index]!.val;\n        }\n        // キーと値の組が存在しなければ null を返す\n        return null;\n    }\n\n    /* 追加操作 */\n    put(key: number, val: string): void {\n        // 負荷率がしきい値を超えたら、リサイズを実行\n        if (this.loadFactor() &gt; this.loadThres) {\n            this.extend();\n        }\n        // key に対応するバケットインデックスを探す\n        const index = this.findBucket(key);\n        // キーと値の組が見つかったら、val を上書きして返す\n        if (\n            this.buckets[index] !== null &amp;&amp;\n            this.buckets[index] !== this.TOMBSTONE\n        ) {\n            this.buckets[index]!.val = val;\n            return;\n        }\n        // キーと値の組が存在しない場合は、その組を追加する\n        this.buckets[index] = new Pair(key, val);\n        this.size++;\n    }\n\n    /* 削除操作 */\n    remove(key: number): void {\n        // key に対応するバケットインデックスを探す\n        const index = this.findBucket(key);\n        // キーと値の組が見つかったら、削除マーカーで上書きする\n        if (\n            this.buckets[index] !== null &amp;&amp;\n            this.buckets[index] !== this.TOMBSTONE\n        ) {\n            this.buckets[index] = this.TOMBSTONE;\n            this.size--;\n        }\n    }\n\n    /* ハッシュテーブルを拡張 */\n    private extend(): void {\n        // 元のハッシュテーブルを一時保存\n        const bucketsTmp = this.buckets;\n        // リサイズ後の新しいハッシュテーブルを初期化\n        this.capacity *= this.extendRatio;\n        this.buckets = Array(this.capacity).fill(null);\n        this.size = 0;\n        // キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n        for (const pair of bucketsTmp) {\n            if (pair !== null &amp;&amp; pair !== this.TOMBSTONE) {\n                this.put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* ハッシュテーブルを出力 */\n    print(): void {\n        for (const pair of this.buckets) {\n            if (pair === null) {\n                console.log('null');\n            } else if (pair === this.TOMBSTONE) {\n                console.log('TOMBSTONE');\n            } else {\n                console.log(pair.key + ' -&gt; ' + pair.val);\n            }\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.dart<pre><code>/* オープンアドレス法ハッシュテーブル */\nclass HashMapOpenAddressing {\n  late int _size; // キーと値のペア数\n  int _capacity = 4; // ハッシュテーブル容量\n  double _loadThres = 2.0 / 3.0; // リサイズを発動する負荷率のしきい値\n  int _extendRatio = 2; // 拡張倍率\n  late List&lt;Pair?&gt; _buckets; // バケット配列\n  Pair _TOMBSTONE = Pair(-1, \"-1\"); // 削除済みマーク\n\n  /* コンストラクタ */\n  HashMapOpenAddressing() {\n    _size = 0;\n    _buckets = List.generate(_capacity, (index) =&gt; null);\n  }\n\n  /* ハッシュ関数 */\n  int hashFunc(int key) {\n    return key % _capacity;\n  }\n\n  /* 負荷率 */\n  double loadFactor() {\n    return _size / _capacity;\n  }\n\n  /* key に対応するバケットインデックスを探す */\n  int findBucket(int key) {\n    int index = hashFunc(key);\n    int firstTombstone = -1;\n    // 線形プロービングを行い、空バケットに達したら終了\n    while (_buckets[index] != null) {\n      // key が見つかったら、対応するバケットのインデックスを返す\n      if (_buckets[index]!.key == key) {\n        // 以前に削除マークが見つかっていれば、そのインデックスへキーと値のペアを移動\n        if (firstTombstone != -1) {\n          _buckets[firstTombstone] = _buckets[index];\n          _buckets[index] = _TOMBSTONE;\n          return firstTombstone; // 移動後のバケットインデックスを返す\n        }\n        return index; // バケットのインデックスを返す\n      }\n      // 最初に見つかった削除マークを記録\n      if (firstTombstone == -1 &amp;&amp; _buckets[index] == _TOMBSTONE) {\n        firstTombstone = index;\n      }\n      // バケットのインデックスを計算し、末尾を越えたら先頭に戻る\n      index = (index + 1) % _capacity;\n    }\n    // key が存在しない場合は追加位置のインデックスを返す\n    return firstTombstone == -1 ? index : firstTombstone;\n  }\n\n  /* 検索操作 */\n  String? get(int key) {\n    // key に対応するバケットインデックスを探す\n    int index = findBucket(key);\n    // キーと値の組が見つかったら、対応する val を返す\n    if (_buckets[index] != null &amp;&amp; _buckets[index] != _TOMBSTONE) {\n      return _buckets[index]!.val;\n    }\n    // キーと値の組が存在しなければ null を返す\n    return null;\n  }\n\n  /* 追加操作 */\n  void put(int key, String val) {\n    // 負荷率がしきい値を超えたら、リサイズを実行\n    if (loadFactor() &gt; _loadThres) {\n      extend();\n    }\n    // key に対応するバケットインデックスを探す\n    int index = findBucket(key);\n    // キーと値の組が見つかったら、val を上書きして返す\n    if (_buckets[index] != null &amp;&amp; _buckets[index] != _TOMBSTONE) {\n      _buckets[index]!.val = val;\n      return;\n    }\n    // キーと値の組が存在しない場合は、その組を追加する\n    _buckets[index] = new Pair(key, val);\n    _size++;\n  }\n\n  /* 削除操作 */\n  void remove(int key) {\n    // key に対応するバケットインデックスを探す\n    int index = findBucket(key);\n    // キーと値の組が見つかったら、削除マーカーで上書きする\n    if (_buckets[index] != null &amp;&amp; _buckets[index] != _TOMBSTONE) {\n      _buckets[index] = _TOMBSTONE;\n      _size--;\n    }\n  }\n\n  /* ハッシュテーブルを拡張 */\n  void extend() {\n    // 元のハッシュテーブルを一時保存\n    List&lt;Pair?&gt; bucketsTmp = _buckets;\n    // リサイズ後の新しいハッシュテーブルを初期化\n    _capacity *= _extendRatio;\n    _buckets = List.generate(_capacity, (index) =&gt; null);\n    _size = 0;\n    // キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n    for (Pair? pair in bucketsTmp) {\n      if (pair != null &amp;&amp; pair != _TOMBSTONE) {\n        put(pair.key, pair.val);\n      }\n    }\n  }\n\n  /* ハッシュテーブルを出力 */\n  void printHashMap() {\n    for (Pair? pair in _buckets) {\n      if (pair == null) {\n        print(\"null\");\n      } else if (pair == _TOMBSTONE) {\n        print(\"TOMBSTONE\");\n      } else {\n        print(\"${pair.key} -&gt; ${pair.val}\");\n      }\n    }\n  }\n}\n</code></pre> hash_map_open_addressing.rs<pre><code>/* オープンアドレス法ハッシュテーブル */\nstruct HashMapOpenAddressing {\n    size: usize,                // キーと値のペア数\n    capacity: usize,            // ハッシュテーブル容量\n    load_thres: f64,            // リサイズを発動する負荷率のしきい値\n    extend_ratio: usize,        // 拡張倍率\n    buckets: Vec&lt;Option&lt;Pair&gt;&gt;, // バケット配列\n    TOMBSTONE: Option&lt;Pair&gt;,    // 削除済みマーク\n}\n\nimpl HashMapOpenAddressing {\n    /* コンストラクタ */\n    fn new() -&gt; Self {\n        Self {\n            size: 0,\n            capacity: 4,\n            load_thres: 2.0 / 3.0,\n            extend_ratio: 2,\n            buckets: vec![None; 4],\n            TOMBSTONE: Some(Pair {\n                key: -1,\n                val: \"-1\".to_string(),\n            }),\n        }\n    }\n\n    /* ハッシュ関数 */\n    fn hash_func(&amp;self, key: i32) -&gt; usize {\n        (key % self.capacity as i32) as usize\n    }\n\n    /* 負荷率 */\n    fn load_factor(&amp;self) -&gt; f64 {\n        self.size as f64 / self.capacity as f64\n    }\n\n    /* key に対応するバケットインデックスを探す */\n    fn find_bucket(&amp;mut self, key: i32) -&gt; usize {\n        let mut index = self.hash_func(key);\n        let mut first_tombstone = -1;\n        // 線形プロービングを行い、空バケットに達したら終了\n        while self.buckets[index].is_some() {\n            // `key` に遭遇したら、対応するバケットのインデックスを返す\n            if self.buckets[index].as_ref().unwrap().key == key {\n                // 以前に削除マークに遭遇していた場合は、キーと値のペアをそのインデックスへ移動する\n                if first_tombstone != -1 {\n                    self.buckets[first_tombstone as usize] = self.buckets[index].take();\n                    self.buckets[index] = self.TOMBSTONE.clone();\n                    return first_tombstone as usize; // 移動後のバケットインデックスを返す\n                }\n                return index; // バケットのインデックスを返す\n            }\n            // 最初に見つかった削除マークを記録\n            if first_tombstone == -1 &amp;&amp; self.buckets[index] == self.TOMBSTONE {\n                first_tombstone = index as i32;\n            }\n            // バケットのインデックスを計算し、末尾を越えたら先頭に戻る\n            index = (index + 1) % self.capacity;\n        }\n        // key が存在しない場合は追加位置のインデックスを返す\n        if first_tombstone == -1 {\n            index\n        } else {\n            first_tombstone as usize\n        }\n    }\n\n    /* 検索操作 */\n    fn get(&amp;mut self, key: i32) -&gt; Option&lt;&amp;str&gt; {\n        // key に対応するバケットインデックスを探す\n        let index = self.find_bucket(key);\n        // キーと値の組が見つかったら、対応する val を返す\n        if self.buckets[index].is_some() &amp;&amp; self.buckets[index] != self.TOMBSTONE {\n            return self.buckets[index].as_ref().map(|pair| &amp;pair.val as &amp;str);\n        }\n        // キーと値の組が存在しなければ null を返す\n        None\n    }\n\n    /* 追加操作 */\n    fn put(&amp;mut self, key: i32, val: String) {\n        // 負荷率がしきい値を超えたら、リサイズを実行\n        if self.load_factor() &gt; self.load_thres {\n            self.extend();\n        }\n        // key に対応するバケットインデックスを探す\n        let index = self.find_bucket(key);\n        // キーと値の組が見つかったら、val を上書きして返す\n        if self.buckets[index].is_some() &amp;&amp; self.buckets[index] != self.TOMBSTONE {\n            self.buckets[index].as_mut().unwrap().val = val;\n            return;\n        }\n        // キーと値の組が存在しない場合は、その組を追加する\n        self.buckets[index] = Some(Pair { key, val });\n        self.size += 1;\n    }\n\n    /* 削除操作 */\n    fn remove(&amp;mut self, key: i32) {\n        // key に対応するバケットインデックスを探す\n        let index = self.find_bucket(key);\n        // キーと値の組が見つかったら、削除マーカーで上書きする\n        if self.buckets[index].is_some() &amp;&amp; self.buckets[index] != self.TOMBSTONE {\n            self.buckets[index] = self.TOMBSTONE.clone();\n            self.size -= 1;\n        }\n    }\n\n    /* ハッシュテーブルを拡張 */\n    fn extend(&amp;mut self) {\n        // 元のハッシュテーブルを一時保存\n        let buckets_tmp = self.buckets.clone();\n        // リサイズ後の新しいハッシュテーブルを初期化\n        self.capacity *= self.extend_ratio;\n        self.buckets = vec![None; self.capacity];\n        self.size = 0;\n\n        // キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n        for pair in buckets_tmp {\n            if pair.is_none() || pair == self.TOMBSTONE {\n                continue;\n            }\n            let pair = pair.unwrap();\n\n            self.put(pair.key, pair.val);\n        }\n    }\n    /* ハッシュテーブルを出力 */\n    fn print(&amp;self) {\n        for pair in &amp;self.buckets {\n            if pair.is_none() {\n                println!(\"null\");\n            } else if pair == &amp;self.TOMBSTONE {\n                println!(\"TOMBSTONE\");\n            } else {\n                let pair = pair.as_ref().unwrap();\n                println!(\"{} -&gt; {}\", pair.key, pair.val);\n            }\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.c<pre><code>/* オープンアドレス法ハッシュテーブル */\ntypedef struct {\n    int size;         // キーと値のペア数\n    int capacity;     // ハッシュテーブル容量\n    double loadThres; // リサイズを発動する負荷率のしきい値\n    int extendRatio;  // 拡張倍率\n    Pair **buckets;   // バケット配列\n    Pair *TOMBSTONE;  // 削除済みマーク\n} HashMapOpenAddressing;\n\n/* コンストラクタ */\nHashMapOpenAddressing *newHashMapOpenAddressing() {\n    HashMapOpenAddressing *hashMap = (HashMapOpenAddressing *)malloc(sizeof(HashMapOpenAddressing));\n    hashMap-&gt;size = 0;\n    hashMap-&gt;capacity = 4;\n    hashMap-&gt;loadThres = 2.0 / 3.0;\n    hashMap-&gt;extendRatio = 2;\n    hashMap-&gt;buckets = (Pair **)calloc(hashMap-&gt;capacity, sizeof(Pair *));\n    hashMap-&gt;TOMBSTONE = (Pair *)malloc(sizeof(Pair));\n    hashMap-&gt;TOMBSTONE-&gt;key = -1;\n    hashMap-&gt;TOMBSTONE-&gt;val = \"-1\";\n\n    return hashMap;\n}\n\n/* デストラクタ */\nvoid delHashMapOpenAddressing(HashMapOpenAddressing *hashMap) {\n    for (int i = 0; i &lt; hashMap-&gt;capacity; i++) {\n        Pair *pair = hashMap-&gt;buckets[i];\n        if (pair != NULL &amp;&amp; pair != hashMap-&gt;TOMBSTONE) {\n            free(pair-&gt;val);\n            free(pair);\n        }\n    }\n    free(hashMap-&gt;buckets);\n    free(hashMap-&gt;TOMBSTONE);\n    free(hashMap);\n}\n\n/* ハッシュ関数 */\nint hashFunc(HashMapOpenAddressing *hashMap, int key) {\n    return key % hashMap-&gt;capacity;\n}\n\n/* 負荷率 */\ndouble loadFactor(HashMapOpenAddressing *hashMap) {\n    return (double)hashMap-&gt;size / (double)hashMap-&gt;capacity;\n}\n\n/* key に対応するバケットインデックスを探す */\nint findBucket(HashMapOpenAddressing *hashMap, int key) {\n    int index = hashFunc(hashMap, key);\n    int firstTombstone = -1;\n    // 線形プロービングを行い、空バケットに達したら終了\n    while (hashMap-&gt;buckets[index] != NULL) {\n        // key が見つかったら、対応するバケットのインデックスを返す\n        if (hashMap-&gt;buckets[index]-&gt;key == key) {\n            // 以前に削除マークが見つかっていれば、そのインデックスへキーと値のペアを移動\n            if (firstTombstone != -1) {\n                hashMap-&gt;buckets[firstTombstone] = hashMap-&gt;buckets[index];\n                hashMap-&gt;buckets[index] = hashMap-&gt;TOMBSTONE;\n                return firstTombstone; // 移動後のバケットインデックスを返す\n            }\n            return index; // バケットのインデックスを返す\n        }\n        // 最初に見つかった削除マークを記録\n        if (firstTombstone == -1 &amp;&amp; hashMap-&gt;buckets[index] == hashMap-&gt;TOMBSTONE) {\n            firstTombstone = index;\n        }\n        // バケットのインデックスを計算し、末尾を越えたら先頭に戻る\n        index = (index + 1) % hashMap-&gt;capacity;\n    }\n    // key が存在しない場合は追加位置のインデックスを返す\n    return firstTombstone == -1 ? index : firstTombstone;\n}\n\n/* 検索操作 */\nchar *get(HashMapOpenAddressing *hashMap, int key) {\n    // key に対応するバケットインデックスを探す\n    int index = findBucket(hashMap, key);\n    // キーと値の組が見つかったら、対応する val を返す\n    if (hashMap-&gt;buckets[index] != NULL &amp;&amp; hashMap-&gt;buckets[index] != hashMap-&gt;TOMBSTONE) {\n        return hashMap-&gt;buckets[index]-&gt;val;\n    }\n    // キーと値の組が存在しない場合は空文字列を返す\n    return \"\";\n}\n\n/* 追加操作 */\nvoid put(HashMapOpenAddressing *hashMap, int key, char *val) {\n    // 負荷率がしきい値を超えたら、リサイズを実行\n    if (loadFactor(hashMap) &gt; hashMap-&gt;loadThres) {\n        extend(hashMap);\n    }\n    // key に対応するバケットインデックスを探す\n    int index = findBucket(hashMap, key);\n    // キーと値の組が見つかったら、val を上書きして返す\n    if (hashMap-&gt;buckets[index] != NULL &amp;&amp; hashMap-&gt;buckets[index] != hashMap-&gt;TOMBSTONE) {\n        free(hashMap-&gt;buckets[index]-&gt;val);\n        hashMap-&gt;buckets[index]-&gt;val = (char *)malloc(sizeof(strlen(val) + 1));\n        strcpy(hashMap-&gt;buckets[index]-&gt;val, val);\n        hashMap-&gt;buckets[index]-&gt;val[strlen(val)] = '\\0';\n        return;\n    }\n    // キーと値の組が存在しない場合は、その組を追加する\n    Pair *pair = (Pair *)malloc(sizeof(Pair));\n    pair-&gt;key = key;\n    pair-&gt;val = (char *)malloc(sizeof(strlen(val) + 1));\n    strcpy(pair-&gt;val, val);\n    pair-&gt;val[strlen(val)] = '\\0';\n\n    hashMap-&gt;buckets[index] = pair;\n    hashMap-&gt;size++;\n}\n\n/* 削除操作 */\nvoid removeItem(HashMapOpenAddressing *hashMap, int key) {\n    // key に対応するバケットインデックスを探す\n    int index = findBucket(hashMap, key);\n    // キーと値の組が見つかったら、削除マーカーで上書きする\n    if (hashMap-&gt;buckets[index] != NULL &amp;&amp; hashMap-&gt;buckets[index] != hashMap-&gt;TOMBSTONE) {\n        Pair *pair = hashMap-&gt;buckets[index];\n        free(pair-&gt;val);\n        free(pair);\n        hashMap-&gt;buckets[index] = hashMap-&gt;TOMBSTONE;\n        hashMap-&gt;size--;\n    }\n}\n\n/* ハッシュテーブルを拡張 */\nvoid extend(HashMapOpenAddressing *hashMap) {\n    // 元のハッシュテーブルを一時保存\n    Pair **bucketsTmp = hashMap-&gt;buckets;\n    int oldCapacity = hashMap-&gt;capacity;\n    // リサイズ後の新しいハッシュテーブルを初期化\n    hashMap-&gt;capacity *= hashMap-&gt;extendRatio;\n    hashMap-&gt;buckets = (Pair **)calloc(hashMap-&gt;capacity, sizeof(Pair *));\n    hashMap-&gt;size = 0;\n    // キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n    for (int i = 0; i &lt; oldCapacity; i++) {\n        Pair *pair = bucketsTmp[i];\n        if (pair != NULL &amp;&amp; pair != hashMap-&gt;TOMBSTONE) {\n            put(hashMap, pair-&gt;key, pair-&gt;val);\n            free(pair-&gt;val);\n            free(pair);\n        }\n    }\n    free(bucketsTmp);\n}\n\n/* ハッシュテーブルを出力 */\nvoid print(HashMapOpenAddressing *hashMap) {\n    for (int i = 0; i &lt; hashMap-&gt;capacity; i++) {\n        Pair *pair = hashMap-&gt;buckets[i];\n        if (pair == NULL) {\n            printf(\"NULL\\n\");\n        } else if (pair == hashMap-&gt;TOMBSTONE) {\n            printf(\"TOMBSTONE\\n\");\n        } else {\n            printf(\"%d -&gt; %s\\n\", pair-&gt;key, pair-&gt;val);\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.kt<pre><code>/* オープンアドレス法ハッシュテーブル */\nclass HashMapOpenAddressing {\n    private var size: Int               // キーと値のペア数\n    private var capacity: Int           // ハッシュテーブル容量\n    private val loadThres: Double       // リサイズを発動する負荷率のしきい値\n    private val extendRatio: Int        // 拡張倍率\n    private var buckets: Array&lt;Pair?&gt;   // バケット配列\n    private val TOMBSTONE: Pair         // 削除済みマーク\n\n    /* コンストラクタ */\n    init {\n        size = 0\n        capacity = 4\n        loadThres = 2.0 / 3.0\n        extendRatio = 2\n        buckets = arrayOfNulls(capacity)\n        TOMBSTONE = Pair(-1, \"-1\")\n    }\n\n    /* ハッシュ関数 */\n    fun hashFunc(key: Int): Int {\n        return key % capacity\n    }\n\n    /* 負荷率 */\n    fun loadFactor(): Double {\n        return (size / capacity).toDouble()\n    }\n\n    /* key に対応するバケットインデックスを探す */\n    fun findBucket(key: Int): Int {\n        var index = hashFunc(key)\n        var firstTombstone = -1\n        // 線形プロービングを行い、空バケットに達したら終了\n        while (buckets[index] != null) {\n            // key が見つかったら、対応するバケットのインデックスを返す\n            if (buckets[index]?.key == key) {\n                // 以前に削除マークが見つかっていれば、そのインデックスへキーと値のペアを移動\n                if (firstTombstone != -1) {\n                    buckets[firstTombstone] = buckets[index]\n                    buckets[index] = TOMBSTONE\n                    return firstTombstone // 移動後のバケットインデックスを返す\n                }\n                return index // バケットのインデックスを返す\n            }\n            // 最初に見つかった削除マークを記録\n            if (firstTombstone == -1 &amp;&amp; buckets[index] == TOMBSTONE) {\n                firstTombstone = index\n            }\n            // バケットのインデックスを計算し、末尾を越えたら先頭に戻る\n            index = (index + 1) % capacity\n        }\n        // key が存在しない場合は追加位置のインデックスを返す\n        return if (firstTombstone == -1) index else firstTombstone\n    }\n\n    /* 検索操作 */\n    fun get(key: Int): String? {\n        // key に対応するバケットインデックスを探す\n        val index = findBucket(key)\n        // キーと値の組が見つかったら、対応する val を返す\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            return buckets[index]?._val\n        }\n        // キーと値の組が存在しなければ null を返す\n        return null\n    }\n\n    /* 追加操作 */\n    fun put(key: Int, _val: String) {\n        // 負荷率がしきい値を超えたら、リサイズを実行\n        if (loadFactor() &gt; loadThres) {\n            extend()\n        }\n        // key に対応するバケットインデックスを探す\n        val index = findBucket(key)\n        // キーと値の組が見つかったら、val を上書きして返す\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index]!!._val = _val\n            return\n        }\n        // キーと値の組が存在しない場合は、その組を追加する\n        buckets[index] = Pair(key, _val)\n        size++\n    }\n\n    /* 削除操作 */\n    fun remove(key: Int) {\n        // key に対応するバケットインデックスを探す\n        val index = findBucket(key)\n        // キーと値の組が見つかったら、削除マーカーで上書きする\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index] = TOMBSTONE\n            size--\n        }\n    }\n\n    /* ハッシュテーブルを拡張 */\n    fun extend() {\n        // 元のハッシュテーブルを一時保存\n        val bucketsTmp = buckets\n        // リサイズ後の新しいハッシュテーブルを初期化\n        capacity *= extendRatio\n        buckets = arrayOfNulls(capacity)\n        size = 0\n        // キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n        for (pair in bucketsTmp) {\n            if (pair != null &amp;&amp; pair != TOMBSTONE) {\n                put(pair.key, pair._val)\n            }\n        }\n    }\n\n    /* ハッシュテーブルを出力 */\n    fun print() {\n        for (pair in buckets) {\n            if (pair == null) {\n                println(\"null\")\n            } else if (pair == TOMBSTONE) {\n                println(\"TOMESTOME\")\n            } else {\n                println(\"${pair.key} -&gt; ${pair._val}\")\n            }\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.rb<pre><code>### オープンアドレス法ハッシュテーブル ###\nclass HashMapOpenAddressing\n  TOMBSTONE = Pair.new(-1, '-1') # 削除済みマーク\n\n  ### コンストラクタ ###\n  def initialize\n    @size = 0 # キーと値のペア数\n    @capacity = 4 # ハッシュテーブル容量\n    @load_thres = 2.0 / 3.0 # リサイズを発動する負荷率のしきい値\n    @extend_ratio = 2 # 拡張倍率\n    @buckets = Array.new(@capacity) # バケット配列\n  end\n\n  ### ハッシュ関数 ###\n  def hash_func(key)\n    key % @capacity\n  end\n\n  ### 負荷率 ###\n  def load_factor\n    @size / @capacity\n  end\n\n  ### key に対応するバケットインデックスを検索 ###\n  def find_bucket(key)\n    index = hash_func(key)\n    first_tombstone = -1\n    # 線形プロービングを行い、空バケットに達したら終了\n    while !@buckets[index].nil?\n      # key が見つかったら、対応するバケットのインデックスを返す\n      if @buckets[index].key == key\n        # 以前に削除マークが見つかっていれば、そのインデックスへキーと値のペアを移動\n        if first_tombstone != -1\n          @buckets[first_tombstone] = @buckets[index]\n          @buckets[index] = TOMBSTONE\n          return first_tombstone # 移動後のバケットインデックスを返す\n        end\n        return index # バケットのインデックスを返す\n      end\n      # 最初に見つかった削除マークを記録\n      first_tombstone = index if first_tombstone == -1 &amp;&amp; @buckets[index] == TOMBSTONE\n      # バケットのインデックスを計算し、末尾を越えたら先頭に戻る\n      index = (index + 1) % @capacity\n    end\n    # key が存在しない場合は追加位置のインデックスを返す\n    first_tombstone == -1 ? index : first_tombstone\n  end\n\n  ### 検索操作 ###\n  def get(key)\n    # key に対応するバケットインデックスを探す\n    index = find_bucket(key)\n    # キーと値の組が見つかったら、対応する val を返す\n    return @buckets[index].val unless [nil, TOMBSTONE].include?(@buckets[index])\n    # キーと値のペアが存在しない場合は `nil` を返す\n    nil\n  end\n\n  ### 追加操作 ###\n  def put(key, val)\n    # 負荷率がしきい値を超えたら、リサイズを実行\n    extend if load_factor &gt; @load_thres\n    # key に対応するバケットインデックスを探す\n    index = find_bucket(key)\n    # キーと値のペアが見つかった場合は、`val` を上書きして返す\n    unless [nil, TOMBSTONE].include?(@buckets[index])\n      @buckets[index].val = val\n      return\n    end\n    # キーと値の組が存在しない場合は、その組を追加する\n    @buckets[index] = Pair.new(key, val)\n    @size += 1\n  end\n\n  ### 削除操作 ###\n  def remove(key)\n    # key に対応するバケットインデックスを探す\n    index = find_bucket(key)\n    # キーと値の組が見つかったら、削除マーカーで上書きする\n    unless [nil, TOMBSTONE].include?(@buckets[index])\n      @buckets[index] = TOMBSTONE\n      @size -= 1\n    end\n  end\n\n  ### ハッシュテーブルを拡張 ###\n  def extend\n    # 元のハッシュテーブルを一時保存\n    buckets_tmp = @buckets\n    # リサイズ後の新しいハッシュテーブルを初期化\n    @capacity *= @extend_ratio\n    @buckets = Array.new(@capacity)\n    @size = 0\n    # キーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移す\n    for pair in buckets_tmp\n      put(pair.key, pair.val) unless [nil, TOMBSTONE].include?(pair)\n    end\n  end\n\n  ### ハッシュテーブルを出力 ###\n  def print\n    for pair in @buckets\n      if pair.nil?\n        puts \"Nil\"\n      elsif pair == TOMBSTONE\n        puts \"TOMBSTONE\"\n      else\n        puts \"#{pair.key} -&gt; #{pair.val}\"\n      end\n    end\n  end\nend\n</code></pre>","path":["第 6 章 &nbsp; ハッシュテーブル","6.2 &nbsp; ハッシュ衝突"],"tags":[]},{"location":"chapter_hashing/hash_collision/#2","level":3,"title":"2.   二次探索","text":"<p>二次探索は線形探索に似ており、オープンアドレッシングの一般的な戦略の 1 つです。衝突が発生したとき、二次探索では単純に固定歩数を飛ばすのではなく、「探索回数の二乗」に相当する歩数、すなわち \\(1, 4, 9, \\dots\\) 歩を飛ばします。</p> <p>二次探索には主に次の利点があります。</p> <ul> <li>二次探索は、探索回数の二乗の距離を飛ばすことで、線形探索のクラスタリング効果を緩和しようとします。</li> <li>二次探索はより大きな距離を飛ばして空き位置を探すため、データ分布がより均一になるのに役立ちます。</li> </ul> <p>しかし、二次探索は完璧ではありません。</p> <ul> <li>依然としてクラスタリング現象は存在し、ある位置が他の位置より占有されやすいことがあります。</li> <li>二乗の増加により、二次探索はハッシュテーブル全体を探索できない可能性があります。これは、ハッシュテーブルに空バケットがあっても、二次探索ではそこに到達できないことがあることを意味します。</li> </ul>","path":["第 6 章 &nbsp; ハッシュテーブル","6.2 &nbsp; ハッシュ衝突"],"tags":[]},{"location":"chapter_hashing/hash_collision/#3","level":3,"title":"3.   多重ハッシュ","text":"<p>その名のとおり、多重ハッシュ法では複数のハッシュ関数 \\(f_1(x)\\)、\\(f_2(x)\\)、\\(f_3(x)\\)、\\(\\dots\\) を使って探索を行います。</p> <ul> <li>要素の挿入：ハッシュ関数 \\(f_1(x)\\) で衝突が発生した場合は、\\(f_2(x)\\) を試し、以下同様に、空き位置が見つかるまで続けてから要素を挿入します。</li> <li>要素の検索：同じハッシュ関数の順序で探索し、対象要素が見つかった時点で返します。空き位置に遭遇するか、すべてのハッシュ関数を試しても見つからない場合は、ハッシュテーブル内にその要素は存在しないため、 <code>None</code> を返します。</li> </ul> <p>線形探索と比べると、多重ハッシュ法はクラスタリングを起こしにくい一方で、複数のハッシュ関数により追加の計算量が発生します。</p> <p>Tip</p> <p>注意してください。オープンアドレッシング（線形探索、二次探索、多重ハッシュ）のハッシュテーブルには、いずれも「要素を直接削除できない」という問題があります。</p>","path":["第 6 章 &nbsp; ハッシュテーブル","6.2 &nbsp; ハッシュ衝突"],"tags":[]},{"location":"chapter_hashing/hash_collision/#623","level":2,"title":"6.2.3   プログラミング言語の選択","text":"<p>各種プログラミング言語は異なるハッシュテーブル実装戦略を採用しています。以下にいくつか例を挙げます。</p> <ul> <li>Python はオープンアドレッシングを採用しています。辞書 <code>dict</code> は疑似乱数を用いて探索します。</li> <li>Java はチェイン法を採用しています。JDK 1.8 以降、<code>HashMap</code> 内の配列長が 64 に達し、かつ連結リスト長が 8 に達すると、連結リストは検索性能を高めるため赤黒木に変換されます。</li> <li>Go はチェイン法を採用しています。Go では各バケットに最大 8 個のキーと値のペアを格納でき、容量を超えるとオーバーフローバケットを連結します。オーバーフローバケットが多すぎる場合は、性能を確保するために特殊な等量拡張操作を実行します。</li> </ul>","path":["第 6 章 &nbsp; ハッシュテーブル","6.2 &nbsp; ハッシュ衝突"],"tags":[]},{"location":"chapter_hashing/hash_map/","level":1,"title":"6.1   ハッシュテーブル","text":"<p>ハッシュテーブル（hash table）は、散列表とも呼ばれ、キー <code>key</code> と値 <code>value</code> の対応関係を構築することで、高効率な要素検索を実現します。具体的には、ハッシュテーブルにキー <code>key</code> を入力すると、対応する値 <code>value</code> を \\(O(1)\\) 時間で取得できます。</p> <p>以下の図に示すように、\\(n\\) 人の学生がいるとし、各学生は「名前」と「学籍番号」の 2 つの情報を持っています。もし「学籍番号を入力すると対応する名前を返す」という検索機能を実現したいなら、下図のようなハッシュテーブルを用いることができます。</p> <p></p> <p> 図 6-1   ハッシュテーブルの抽象表現 </p> <p>ハッシュテーブルのほかに、配列や連結リストでも検索機能を実現できます。それらの効率比較を次の表に示します。</p> <ul> <li>要素の追加：要素を配列（連結リスト）の末尾に追加するだけでよく、\\(O(1)\\) 時間です。</li> <li>要素の検索：配列（連結リスト）は無秩序なので、すべての要素を走査する必要があり、\\(O(n)\\) 時間かかります。</li> <li>要素の削除：先に要素を検索してから配列（連結リスト）から削除する必要があり、\\(O(n)\\) 時間かかります。</li> </ul> <p> 表 6-1   要素検索効率の比較 </p> 配列 連結リスト ハッシュテーブル 要素の検索 \\(O(n)\\) \\(O(n)\\) \\(O(1)\\) 要素の追加 \\(O(1)\\) \\(O(1)\\) \\(O(1)\\) 要素の削除 \\(O(n)\\) \\(O(n)\\) \\(O(1)\\) <p>以上から分かるように、ハッシュテーブルにおける追加・削除・検索・更新の時間計算量はいずれも \\(O(1)\\) であり、非常に高効率です。</p>","path":["第 6 章 &nbsp; ハッシュテーブル","6.1 &nbsp; ハッシュテーブル"],"tags":[]},{"location":"chapter_hashing/hash_map/#611","level":2,"title":"6.1.1   ハッシュテーブルの基本操作","text":"<p>ハッシュテーブルの一般的な操作には、初期化、検索、キーと値のペアの追加、キーと値のペアの削除などがあります。コード例は以下のとおりです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby hash_map.py<pre><code># ハッシュテーブルを初期化\nhmap: dict = {}\n\n# 追加操作\n# ハッシュテーブルにキーと値のペア (key, value) を追加\nhmap[12836] = \"シャオハ\"\nhmap[15937] = \"シャオルオ\"\nhmap[16750] = \"シャオスワン\"\nhmap[13276] = \"シャオファ\"\nhmap[10583] = \"シャオヤー\"\n\n# 検索操作\n# ハッシュテーブルにキー key を入力し、値 value を取得\nname: str = hmap[15937]\n\n# 削除操作\n# ハッシュテーブルからキーと値のペア (key, value) を削除\nhmap.pop(10583)\n</code></pre> hash_map.cpp<pre><code>/* ハッシュテーブルを初期化 */\nunordered_map&lt;int, string&gt; map;\n\n/* 追加操作 */\n// ハッシュテーブルにキーと値のペア (key, value) を追加\nmap[12836] = \"シャオハ\";\nmap[15937] = \"シャオルオ\";\nmap[16750] = \"シャオスワン\";\nmap[13276] = \"シャオファ\";\nmap[10583] = \"シャオヤー\";\n\n/* 検索操作 */\n// ハッシュテーブルにキー key を入力し、値 value を取得\nstring name = map[15937];\n\n/* 削除操作 */\n// ハッシュテーブルからキーと値のペア (key, value) を削除\nmap.erase(10583);\n</code></pre> hash_map.java<pre><code>/* ハッシュテーブルを初期化 */\nMap&lt;Integer, String&gt; map = new HashMap&lt;&gt;();\n\n/* 追加操作 */\n// ハッシュテーブルにキーと値のペア (key, value) を追加\nmap.put(12836, \"シャオハ\");\nmap.put(15937, \"シャオルオ\");\nmap.put(16750, \"シャオスワン\");\nmap.put(13276, \"シャオファ\");\nmap.put(10583, \"シャオヤー\");\n\n/* 検索操作 */\n// ハッシュテーブルにキー key を入力し、値 value を取得\nString name = map.get(15937);\n\n/* 削除操作 */\n// ハッシュテーブルからキーと値のペア (key, value) を削除\nmap.remove(10583);\n</code></pre> hash_map.cs<pre><code>/* ハッシュテーブルを初期化 */\nDictionary&lt;int, string&gt; map = new() {\n    /* 追加操作 */\n    // ハッシュテーブルにキーと値のペア (key, value) を追加\n    { 12836, \"シャオハ\" },\n    { 15937, \"シャオルオ\" },\n    { 16750, \"シャオスワン\" },\n    { 13276, \"シャオファ\" },\n    { 10583, \"シャオヤー\" }\n};\n\n/* 検索操作 */\n// ハッシュテーブルにキー key を入力し、値 value を取得\nstring name = map[15937];\n\n/* 削除操作 */\n// ハッシュテーブルからキーと値のペア (key, value) を削除\nmap.Remove(10583);\n</code></pre> hash_map_test.go<pre><code>/* ハッシュテーブルを初期化 */\nhmap := make(map[int]string)\n\n/* 追加操作 */\n// ハッシュテーブルにキーと値のペア (key, value) を追加\nhmap[12836] = \"シャオハ\"\nhmap[15937] = \"シャオルオ\"\nhmap[16750] = \"シャオスワン\"\nhmap[13276] = \"シャオファ\"\nhmap[10583] = \"シャオヤー\"\n\n/* 検索操作 */\n// ハッシュテーブルにキー key を入力し、値 value を取得\nname := hmap[15937]\n\n/* 削除操作 */\n// ハッシュテーブルからキーと値のペア (key, value) を削除\ndelete(hmap, 10583)\n</code></pre> hash_map.swift<pre><code>/* ハッシュテーブルを初期化 */\nvar map: [Int: String] = [:]\n\n/* 追加操作 */\n// ハッシュテーブルにキーと値のペア (key, value) を追加\nmap[12836] = \"シャオハ\"\nmap[15937] = \"シャオルオ\"\nmap[16750] = \"シャオスワン\"\nmap[13276] = \"シャオファ\"\nmap[10583] = \"シャオヤー\"\n\n/* 検索操作 */\n// ハッシュテーブルにキー key を入力し、値 value を取得\nlet name = map[15937]!\n\n/* 削除操作 */\n// ハッシュテーブルからキーと値のペア (key, value) を削除\nmap.removeValue(forKey: 10583)\n</code></pre> hash_map.js<pre><code>/* ハッシュテーブルを初期化 */\nconst map = new Map();\n/* 追加操作 */\n// ハッシュテーブルにキーと値のペア (key, value) を追加\nmap.set(12836, 'シャオハ');\nmap.set(15937, 'シャオルオ');\nmap.set(16750, 'シャオスワン');\nmap.set(13276, 'シャオファ');\nmap.set(10583, 'シャオヤー');\n\n/* 検索操作 */\n// ハッシュテーブルにキー key を入力し、値 value を取得\nlet name = map.get(15937);\n\n/* 削除操作 */\n// ハッシュテーブルからキーと値のペア (key, value) を削除\nmap.delete(10583);\n</code></pre> hash_map.ts<pre><code>/* ハッシュテーブルを初期化 */\nconst map = new Map&lt;number, string&gt;();\n/* 追加操作 */\n// ハッシュテーブルにキーと値のペア (key, value) を追加\nmap.set(12836, 'シャオハ');\nmap.set(15937, 'シャオルオ');\nmap.set(16750, 'シャオスワン');\nmap.set(13276, 'シャオファ');\nmap.set(10583, 'シャオヤー');\nconsole.info('\\n追加後のハッシュテーブルは次のとおりです\\nKey -&gt; Value');\nconsole.info(map);\n\n/* 検索操作 */\n// ハッシュテーブルにキー key を入力し、値 value を取得\nlet name = map.get(15937);\nconsole.info('\\n学籍番号 15937 を入力し、名前を検索: ' + name);\n\n/* 削除操作 */\n// ハッシュテーブルからキーと値のペア (key, value) を削除\nmap.delete(10583);\nconsole.info('\\n10583 を削除した後のハッシュテーブル\\nKey -&gt; Value');\nconsole.info(map);\n</code></pre> hash_map.dart<pre><code>/* ハッシュテーブルを初期化 */\nMap&lt;int, String&gt; map = {};\n\n/* 追加操作 */\n// ハッシュテーブルにキーと値のペア (key, value) を追加\nmap[12836] = \"シャオハ\";\nmap[15937] = \"シャオルオ\";\nmap[16750] = \"シャオスワン\";\nmap[13276] = \"シャオファ\";\nmap[10583] = \"シャオヤー\";\n\n/* 検索操作 */\n// ハッシュテーブルにキー key を入力し、値 value を取得\nString name = map[15937];\n\n/* 削除操作 */\n// ハッシュテーブルからキーと値のペア (key, value) を削除\nmap.remove(10583);\n</code></pre> hash_map.rs<pre><code>use std::collections::HashMap;\n\n/* ハッシュテーブルを初期化 */\nlet mut map: HashMap&lt;i32, String&gt; = HashMap::new();\n\n/* 追加操作 */\n// ハッシュテーブルにキーと値のペア (key, value) を追加\nmap.insert(12836, \"シャオハ\".to_string());\nmap.insert(15937, \"シャオルオ\".to_string());\nmap.insert(16750, \"シャオスワン\".to_string());\nmap.insert(13279, \"シャオファ\".to_string());\nmap.insert(10583, \"シャオヤー\".to_string());\n\n/* 検索操作 */\n// ハッシュテーブルにキー key を入力し、値 value を取得\nlet _name: Option&lt;&amp;String&gt; = map.get(&amp;15937);\n\n/* 削除操作 */\n// ハッシュテーブルからキーと値のペア (key, value) を削除\nlet _removed_value: Option&lt;String&gt; = map.remove(&amp;10583);\n</code></pre> hash_map.c<pre><code>// C には組み込みのハッシュテーブルはありません\n</code></pre> hash_map.kt<pre><code>/* ハッシュテーブルを初期化 */\nval map = HashMap&lt;Int,String&gt;()\n\n/* 追加操作 */\n// ハッシュテーブルにキーと値のペア (key, value) を追加\nmap[12836] = \"シャオハ\"\nmap[15937] = \"シャオルオ\"\nmap[16750] = \"シャオスワン\"\nmap[13276] = \"シャオファ\"\nmap[10583] = \"シャオヤー\"\n\n/* 検索操作 */\n// ハッシュテーブルにキー key を入力し、値 value を取得\nval name = map[15937]\n\n/* 削除操作 */\n// ハッシュテーブルからキーと値のペア (key, value) を削除\nmap.remove(10583)\n</code></pre> hash_map.rb<pre><code># ハッシュテーブルを初期化\nhmap = {}\n\n# 追加操作\n# ハッシュテーブルにキーと値のペア (key, value) を追加\nhmap[12836] = \"シャオハ\"\nhmap[15937] = \"シャオルオ\"\nhmap[16750] = \"シャオスワン\"\nhmap[13276] = \"シャオファ\"\nhmap[10583] = \"シャオヤー\"\n\n# 検索操作\n# ハッシュテーブルにキー key を入力し、値 value を取得\nname = hmap[15937]\n\n# 削除操作\n# ハッシュテーブルからキーと値のペア (key, value) を削除\nhmap.delete(10583)\n</code></pre> 可視化実行 <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%93%88%E5%B8%8C%E8%A1%A8%0A%20%20%20%20hmap%20%3D%20%7B%7D%0A%20%20%20%20%0A%20%20%20%20%23%20%E6%B7%BB%E5%8A%A0%E6%93%8D%E4%BD%9C%0A%20%20%20%20%23%20%E5%9C%A8%E5%93%88%E5%B8%8C%E8%A1%A8%E4%B8%AD%E6%B7%BB%E5%8A%A0%E9%94%AE%E5%80%BC%E5%AF%B9%20%28key,%20value%29%0A%20%20%20%20hmap%5B12836%5D%20%3D%20%22%E5%B0%8F%E5%93%88%22%0A%20%20%20%20hmap%5B15937%5D%20%3D%20%22%E5%B0%8F%E5%95%B0%22%0A%20%20%20%20hmap%5B16750%5D%20%3D%20%22%E5%B0%8F%E7%AE%97%22%0A%20%20%20%20hmap%5B13276%5D%20%3D%20%22%E5%B0%8F%E6%B3%95%22%0A%20%20%20%20hmap%5B10583%5D%20%3D%20%22%E5%B0%8F%E9%B8%AD%22%0A%20%20%20%20%0A%20%20%20%20%23%20%E6%9F%A5%E8%AF%A2%E6%93%8D%E4%BD%9C%0A%20%20%20%20%23%20%E5%90%91%E5%93%88%E5%B8%8C%E8%A1%A8%E4%B8%AD%E8%BE%93%E5%85%A5%E9%94%AE%20key%20%EF%BC%8C%E5%BE%97%E5%88%B0%E5%80%BC%20value%0A%20%20%20%20name%20%3D%20hmap%5B15937%5D%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%88%A0%E9%99%A4%E6%93%8D%E4%BD%9C%0A%20%20%20%20%23%20%E5%9C%A8%E5%93%88%E5%B8%8C%E8%A1%A8%E4%B8%AD%E5%88%A0%E9%99%A4%E9%94%AE%E5%80%BC%E5%AF%B9%20%28key,%20value%29%0A%20%20%20%20hmap.pop%2810583%29&amp;cumulative=false&amp;curInstr=2&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p> <p>ハッシュテーブルには、キーと値のペア、キー、値を走査する 3 つの一般的な方法があります。コード例は以下のとおりです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby hash_map.py<pre><code># ハッシュテーブルを走査\n# キーと値のペア key-&gt;value を走査\nfor key, value in hmap.items():\n    print(key, \"-&gt;\", value)\n# キー key のみを走査\nfor key in hmap.keys():\n    print(key)\n# 値 value のみを走査\nfor value in hmap.values():\n    print(value)\n</code></pre> hash_map.cpp<pre><code>/* ハッシュテーブルを走査 */\n// キーと値のペア key-&gt;value を走査\nfor (auto kv: map) {\n    cout &lt;&lt; kv.first &lt;&lt; \" -&gt; \" &lt;&lt; kv.second &lt;&lt; endl;\n}\n// イテレータを使って key-&gt;value を走査\nfor (auto iter = map.begin(); iter != map.end(); iter++) {\n    cout &lt;&lt; iter-&gt;first &lt;&lt; \"-&gt;\" &lt;&lt; iter-&gt;second &lt;&lt; endl;\n}\n</code></pre> hash_map.java<pre><code>/* ハッシュテーブルを走査 */\n// キーと値のペア key-&gt;value を走査\nfor (Map.Entry &lt;Integer, String&gt; kv: map.entrySet()) {\n    System.out.println(kv.getKey() + \" -&gt; \" + kv.getValue());\n}\n// キー key のみを走査\nfor (int key: map.keySet()) {\n    System.out.println(key);\n}\n// 値 value のみを走査\nfor (String val: map.values()) {\n    System.out.println(val);\n}\n</code></pre> hash_map.cs<pre><code>/* ハッシュテーブルを走査 */\n// キーと値のペア Key-&gt;Value を走査\nforeach (var kv in map) {\n    Console.WriteLine(kv.Key + \" -&gt; \" + kv.Value);\n}\n// キー key のみを走査\nforeach (int key in map.Keys) {\n    Console.WriteLine(key);\n}\n// 値 value のみを走査\nforeach (string val in map.Values) {\n    Console.WriteLine(val);\n}\n</code></pre> hash_map_test.go<pre><code>/* ハッシュテーブルを走査 */\n// キーと値のペア key-&gt;value を走査\nfor key, value := range hmap {\n    fmt.Println(key, \"-&gt;\", value)\n}\n// キー key のみを走査\nfor key := range hmap {\n    fmt.Println(key)\n}\n// 値 value のみを走査\nfor _, value := range hmap {\n    fmt.Println(value)\n}\n</code></pre> hash_map.swift<pre><code>/* ハッシュテーブルを走査 */\n// キーと値のペア Key-&gt;Value を走査\nfor (key, value) in map {\n    print(\"\\(key) -&gt; \\(value)\")\n}\n// キー Key のみを走査\nfor key in map.keys {\n    print(key)\n}\n// 値 Value のみを走査\nfor value in map.values {\n    print(value)\n}\n</code></pre> hash_map.js<pre><code>/* ハッシュテーブルを走査 */\nconsole.info('\\nキーと値のペア Key-&gt;Value を走査');\nfor (const [k, v] of map.entries()) {\n    console.info(k + ' -&gt; ' + v);\n}\nconsole.info('\\nキー Key のみを走査');\nfor (const k of map.keys()) {\n    console.info(k);\n}\nconsole.info('\\n値 Value のみを走査');\nfor (const v of map.values()) {\n    console.info(v);\n}\n</code></pre> hash_map.ts<pre><code>/* ハッシュテーブルを走査 */\nconsole.info('\\nキーと値のペア Key-&gt;Value を走査');\nfor (const [k, v] of map.entries()) {\n    console.info(k + ' -&gt; ' + v);\n}\nconsole.info('\\nキー Key のみを走査');\nfor (const k of map.keys()) {\n    console.info(k);\n}\nconsole.info('\\n値 Value のみを走査');\nfor (const v of map.values()) {\n    console.info(v);\n}\n</code></pre> hash_map.dart<pre><code>/* ハッシュテーブルを走査 */\n// キーと値のペア Key-&gt;Value を走査\nmap.forEach((key, value) {\n  print('$key -&gt; $value');\n});\n\n// キー Key のみを走査\nmap.keys.forEach((key) {\n  print(key);\n});\n\n// 値 Value のみを走査\nmap.values.forEach((value) {\n  print(value);\n});\n</code></pre> hash_map.rs<pre><code>/* ハッシュテーブルを走査 */\n// キーと値のペア Key-&gt;Value を走査\nfor (key, value) in &amp;map {\n    println!(\"{key} -&gt; {value}\");\n}\n\n// キー Key のみを走査\nfor key in map.keys() {\n    println!(\"{key}\");\n}\n\n// 値 Value のみを走査\nfor value in map.values() {\n    println!(\"{value}\");\n}\n</code></pre> hash_map.c<pre><code>// C には組み込みのハッシュテーブルはありません\n</code></pre> hash_map.kt<pre><code>/* ハッシュテーブルを走査 */\n// キーと値のペア key-&gt;value を走査\nfor ((key, value) in map) {\n    println(\"$key -&gt; $value\")\n}\n// キー key のみを走査\nfor (key in map.keys) {\n    println(key)\n}\n// 値 value のみを走査\nfor (_val in map.values) {\n    println(_val)\n}\n</code></pre> hash_map.rb<pre><code># ハッシュテーブルを走査\n# キーと値のペア key-&gt;value を走査\nhmap.entries.each { |key, value| puts \"#{key} -&gt; #{value}\" }\n\n# キー key のみを走査\nhmap.keys.each { |key| puts key }\n\n# 値 value のみを走査\nhmap.values.each { |val| puts val }\n</code></pre> 可視化実行 <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%93%88%E5%B8%8C%E8%A1%A8%0A%20%20%20%20hmap%20%3D%20%7B%7D%0A%20%20%20%20%0A%20%20%20%20%23%20%E6%B7%BB%E5%8A%A0%E6%93%8D%E4%BD%9C%0A%20%20%20%20%23%20%E5%9C%A8%E5%93%88%E5%B8%8C%E8%A1%A8%E4%B8%AD%E6%B7%BB%E5%8A%A0%E9%94%AE%E5%80%BC%E5%AF%B9%20%28key,%20value%29%0A%20%20%20%20hmap%5B12836%5D%20%3D%20%22%E5%B0%8F%E5%93%88%22%0A%20%20%20%20hmap%5B15937%5D%20%3D%20%22%E5%B0%8F%E5%95%B0%22%0A%20%20%20%20hmap%5B16750%5D%20%3D%20%22%E5%B0%8F%E7%AE%97%22%0A%20%20%20%20hmap%5B13276%5D%20%3D%20%22%E5%B0%8F%E6%B3%95%22%0A%20%20%20%20hmap%5B10583%5D%20%3D%20%22%E5%B0%8F%E9%B8%AD%22%0A%20%20%20%20%0A%20%20%20%20%23%20%E9%81%8D%E5%8E%86%E5%93%88%E5%B8%8C%E8%A1%A8%0A%20%20%20%20%23%20%E9%81%8D%E5%8E%86%E9%94%AE%E5%80%BC%E5%AF%B9%20key-%3Evalue%0A%20%20%20%20for%20key,%20value%20in%20hmap.items%28%29%3A%0A%20%20%20%20%20%20%20%20print%28key,%20%22-%3E%22,%20value%29%0A%20%20%20%20%23%20%E5%8D%95%E7%8B%AC%E9%81%8D%E5%8E%86%E9%94%AE%20key%0A%20%20%20%20for%20key%20in%20hmap.keys%28%29%3A%0A%20%20%20%20%20%20%20%20print%28key%29%0A%20%20%20%20%23%20%E5%8D%95%E7%8B%AC%E9%81%8D%E5%8E%86%E5%80%BC%20value%0A%20%20%20%20for%20value%20in%20hmap.values%28%29%3A%0A%20%20%20%20%20%20%20%20print%28value%29&amp;cumulative=false&amp;curInstr=8&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["第 6 章 &nbsp; ハッシュテーブル","6.1 &nbsp; ハッシュテーブル"],"tags":[]},{"location":"chapter_hashing/hash_map/#612","level":2,"title":"6.1.2   ハッシュテーブルの簡単な実装","text":"<p>まずは最も単純なケースとして、**1 つの配列だけでハッシュテーブルを実装する**ことを考えます。ハッシュテーブルでは、配列中の各空き位置をバケット（bucket）と呼び、各バケットには 1 つのキーと値のペアを格納できます。したがって、検索操作とは <code>key</code> に対応するバケットを見つけ、そのバケットから <code>value</code> を取得することです。</p> <p>では、<code>key</code> に基づいて対応するバケットをどのように特定するのでしょうか。これはハッシュ関数（hash function）によって実現されます。ハッシュ関数の役割は、大きな入力空間をより小さな出力空間に写像することです。ハッシュテーブルでは、入力空間はすべての <code>key</code> 、出力空間はすべてのバケット（配列インデックス）です。言い換えると、<code>key</code> を入力すると、ハッシュ関数によってその <code>key</code> に対応するキーと値のペアの配列内での格納位置を求められます。</p> <p><code>key</code> を入力したとき、ハッシュ関数の計算過程は次の 2 段階に分かれます。</p> <ol> <li>あるハッシュアルゴリズム <code>hash()</code> を用いてハッシュ値を計算します。</li> <li>ハッシュ値をバケット数（配列長）<code>capacity</code> で剰余し、その <code>key</code> に対応するバケット（配列インデックス）<code>index</code> を求めます。</li> </ol> <pre><code>index = hash(key) % capacity\n</code></pre> <p>その後、<code>index</code> を使ってハッシュテーブル内の対応するバケットにアクセスし、<code>value</code> を取得できます。</p> <p>配列長を <code>capacity = 100</code> 、ハッシュアルゴリズムを <code>hash(key) = key</code> とすると、ハッシュ関数は <code>key % 100</code> となります。次の図では、<code>key</code> を学籍番号、<code>value</code> を名前の例として、ハッシュ関数の動作原理を示します。</p> <p></p> <p> 図 6-2   ハッシュ関数の動作原理 </p> <p>以下のコードは、単純なハッシュテーブルを実装したものです。ここでは、キーと値のペアを表すために <code>key</code> と <code>value</code> をクラス <code>Pair</code> にまとめています。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array_hash_map.py<pre><code>class Pair:\n    \"\"\"キーと値の組\"\"\"\n\n    def __init__(self, key: int, val: str):\n        self.key = key\n        self.val = val\n\nclass ArrayHashMap:\n    \"\"\"配列ベースのハッシュテーブル\"\"\"\n\n    def __init__(self):\n        \"\"\"コンストラクタ\"\"\"\n        # 100 個のバケットを含む配列を初期化\n        self.buckets: list[Pair | None] = [None] * 100\n\n    def hash_func(self, key: int) -&gt; int:\n        \"\"\"ハッシュ関数\"\"\"\n        index = key % 100\n        return index\n\n    def get(self, key: int) -&gt; str | None:\n        \"\"\"検索操作\"\"\"\n        index: int = self.hash_func(key)\n        pair: Pair = self.buckets[index]\n        if pair is None:\n            return None\n        return pair.val\n\n    def put(self, key: int, val: str):\n        \"\"\"追加と更新の操作\"\"\"\n        pair = Pair(key, val)\n        index: int = self.hash_func(key)\n        self.buckets[index] = pair\n\n    def remove(self, key: int):\n        \"\"\"削除操作\"\"\"\n        index: int = self.hash_func(key)\n        # None に設定し、削除を表す\n        self.buckets[index] = None\n\n    def entry_set(self) -&gt; list[Pair]:\n        \"\"\"すべてのキーと値のペアを取得\"\"\"\n        result: list[Pair] = []\n        for pair in self.buckets:\n            if pair is not None:\n                result.append(pair)\n        return result\n\n    def key_set(self) -&gt; list[int]:\n        \"\"\"すべてのキーを取得\"\"\"\n        result = []\n        for pair in self.buckets:\n            if pair is not None:\n                result.append(pair.key)\n        return result\n\n    def value_set(self) -&gt; list[str]:\n        \"\"\"すべての値を取得\"\"\"\n        result = []\n        for pair in self.buckets:\n            if pair is not None:\n                result.append(pair.val)\n        return result\n\n    def print(self):\n        \"\"\"ハッシュテーブルを出力\"\"\"\n        for pair in self.buckets:\n            if pair is not None:\n                print(pair.key, \"-&gt;\", pair.val)\n</code></pre> array_hash_map.cpp<pre><code>/* キーと値の組 */\nstruct Pair {\n  public:\n    int key;\n    string val;\n    Pair(int key, string val) {\n        this-&gt;key = key;\n        this-&gt;val = val;\n    }\n};\n\n/* 配列ベースのハッシュテーブル */\nclass ArrayHashMap {\n  private:\n    vector&lt;Pair *&gt; buckets;\n\n  public:\n    ArrayHashMap() {\n        // 100 個のバケットを含む配列を初期化\n        buckets = vector&lt;Pair *&gt;(100);\n    }\n\n    ~ArrayHashMap() {\n        // メモリを解放する\n        for (const auto &amp;bucket : buckets) {\n            delete bucket;\n        }\n        buckets.clear();\n    }\n\n    /* ハッシュ関数 */\n    int hashFunc(int key) {\n        int index = key % 100;\n        return index;\n    }\n\n    /* 検索操作 */\n    string get(int key) {\n        int index = hashFunc(key);\n        Pair *pair = buckets[index];\n        if (pair == nullptr)\n            return \"\";\n        return pair-&gt;val;\n    }\n\n    /* 追加操作 */\n    void put(int key, string val) {\n        Pair *pair = new Pair(key, val);\n        int index = hashFunc(key);\n        buckets[index] = pair;\n    }\n\n    /* 削除操作 */\n    void remove(int key) {\n        int index = hashFunc(key);\n        // メモリを解放して nullptr に設定する\n        delete buckets[index];\n        buckets[index] = nullptr;\n    }\n\n    /* すべてのキーと値のペアを取得 */\n    vector&lt;Pair *&gt; pairSet() {\n        vector&lt;Pair *&gt; pairSet;\n        for (Pair *pair : buckets) {\n            if (pair != nullptr) {\n                pairSet.push_back(pair);\n            }\n        }\n        return pairSet;\n    }\n\n    /* すべてのキーを取得 */\n    vector&lt;int&gt; keySet() {\n        vector&lt;int&gt; keySet;\n        for (Pair *pair : buckets) {\n            if (pair != nullptr) {\n                keySet.push_back(pair-&gt;key);\n            }\n        }\n        return keySet;\n    }\n\n    /* すべての値を取得 */\n    vector&lt;string&gt; valueSet() {\n        vector&lt;string&gt; valueSet;\n        for (Pair *pair : buckets) {\n            if (pair != nullptr) {\n                valueSet.push_back(pair-&gt;val);\n            }\n        }\n        return valueSet;\n    }\n\n    /* ハッシュテーブルを出力 */\n    void print() {\n        for (Pair *kv : pairSet()) {\n            cout &lt;&lt; kv-&gt;key &lt;&lt; \" -&gt; \" &lt;&lt; kv-&gt;val &lt;&lt; endl;\n        }\n    }\n};\n</code></pre> array_hash_map.java<pre><code>/* キーと値の組 */\nclass Pair {\n    public int key;\n    public String val;\n\n    public Pair(int key, String val) {\n        this.key = key;\n        this.val = val;\n    }\n}\n\n/* 配列ベースのハッシュテーブル */\nclass ArrayHashMap {\n    private List&lt;Pair&gt; buckets;\n\n    public ArrayHashMap() {\n        // 100 個のバケットを含む配列を初期化\n        buckets = new ArrayList&lt;&gt;();\n        for (int i = 0; i &lt; 100; i++) {\n            buckets.add(null);\n        }\n    }\n\n    /* ハッシュ関数 */\n    private int hashFunc(int key) {\n        int index = key % 100;\n        return index;\n    }\n\n    /* 検索操作 */\n    public String get(int key) {\n        int index = hashFunc(key);\n        Pair pair = buckets.get(index);\n        if (pair == null)\n            return null;\n        return pair.val;\n    }\n\n    /* 追加操作 */\n    public void put(int key, String val) {\n        Pair pair = new Pair(key, val);\n        int index = hashFunc(key);\n        buckets.set(index, pair);\n    }\n\n    /* 削除操作 */\n    public void remove(int key) {\n        int index = hashFunc(key);\n        // null に設定し、削除を表す\n        buckets.set(index, null);\n    }\n\n    /* すべてのキーと値のペアを取得 */\n    public List&lt;Pair&gt; pairSet() {\n        List&lt;Pair&gt; pairSet = new ArrayList&lt;&gt;();\n        for (Pair pair : buckets) {\n            if (pair != null)\n                pairSet.add(pair);\n        }\n        return pairSet;\n    }\n\n    /* すべてのキーを取得 */\n    public List&lt;Integer&gt; keySet() {\n        List&lt;Integer&gt; keySet = new ArrayList&lt;&gt;();\n        for (Pair pair : buckets) {\n            if (pair != null)\n                keySet.add(pair.key);\n        }\n        return keySet;\n    }\n\n    /* すべての値を取得 */\n    public List&lt;String&gt; valueSet() {\n        List&lt;String&gt; valueSet = new ArrayList&lt;&gt;();\n        for (Pair pair : buckets) {\n            if (pair != null)\n                valueSet.add(pair.val);\n        }\n        return valueSet;\n    }\n\n    /* ハッシュテーブルを出力 */\n    public void print() {\n        for (Pair kv : pairSet()) {\n            System.out.println(kv.key + \" -&gt; \" + kv.val);\n        }\n    }\n}\n</code></pre> array_hash_map.cs<pre><code>/* キーと値の組 int-&gt;string */\nclass Pair(int key, string val) {\n    public int key = key;\n    public string val = val;\n}\n\n/* 配列ベースのハッシュテーブル */\nclass ArrayHashMap {\n    List&lt;Pair?&gt; buckets;\n    public ArrayHashMap() {\n        // 100 個のバケットを含む配列を初期化\n        buckets = [];\n        for (int i = 0; i &lt; 100; i++) {\n            buckets.Add(null);\n        }\n    }\n\n    /* ハッシュ関数 */\n    int HashFunc(int key) {\n        int index = key % 100;\n        return index;\n    }\n\n    /* 検索操作 */\n    public string? Get(int key) {\n        int index = HashFunc(key);\n        Pair? pair = buckets[index];\n        if (pair == null) return null;\n        return pair.val;\n    }\n\n    /* 追加操作 */\n    public void Put(int key, string val) {\n        Pair pair = new(key, val);\n        int index = HashFunc(key);\n        buckets[index] = pair;\n    }\n\n    /* 削除操作 */\n    public void Remove(int key) {\n        int index = HashFunc(key);\n        // null に設定し、削除を表す\n        buckets[index] = null;\n    }\n\n    /* すべてのキーと値のペアを取得 */\n    public List&lt;Pair&gt; PairSet() {\n        List&lt;Pair&gt; pairSet = [];\n        foreach (Pair? pair in buckets) {\n            if (pair != null)\n                pairSet.Add(pair);\n        }\n        return pairSet;\n    }\n\n    /* すべてのキーを取得 */\n    public List&lt;int&gt; KeySet() {\n        List&lt;int&gt; keySet = [];\n        foreach (Pair? pair in buckets) {\n            if (pair != null)\n                keySet.Add(pair.key);\n        }\n        return keySet;\n    }\n\n    /* すべての値を取得 */\n    public List&lt;string&gt; ValueSet() {\n        List&lt;string&gt; valueSet = [];\n        foreach (Pair? pair in buckets) {\n            if (pair != null)\n                valueSet.Add(pair.val);\n        }\n        return valueSet;\n    }\n\n    /* ハッシュテーブルを出力 */\n    public void Print() {\n        foreach (Pair kv in PairSet()) {\n            Console.WriteLine(kv.key + \" -&gt; \" + kv.val);\n        }\n    }\n}\n</code></pre> array_hash_map.go<pre><code>/* キーと値の組 */\ntype pair struct {\n    key int\n    val string\n}\n\n/* 配列ベースのハッシュテーブル */\ntype arrayHashMap struct {\n    buckets []*pair\n}\n\n/* ハッシュテーブルを初期化 */\nfunc newArrayHashMap() *arrayHashMap {\n    // 100 個のバケットを含む配列を初期化\n    buckets := make([]*pair, 100)\n    return &amp;arrayHashMap{buckets: buckets}\n}\n\n/* ハッシュ関数 */\nfunc (a *arrayHashMap) hashFunc(key int) int {\n    index := key % 100\n    return index\n}\n\n/* 検索操作 */\nfunc (a *arrayHashMap) get(key int) string {\n    index := a.hashFunc(key)\n    pair := a.buckets[index]\n    if pair == nil {\n        return \"Not Found\"\n    }\n    return pair.val\n}\n\n/* 追加操作 */\nfunc (a *arrayHashMap) put(key int, val string) {\n    pair := &amp;pair{key: key, val: val}\n    index := a.hashFunc(key)\n    a.buckets[index] = pair\n}\n\n/* 削除操作 */\nfunc (a *arrayHashMap) remove(key int) {\n    index := a.hashFunc(key)\n    // nil に設定し、削除を表す\n    a.buckets[index] = nil\n}\n\n/* すべてのキーのペアを取得する */\nfunc (a *arrayHashMap) pairSet() []*pair {\n    var pairs []*pair\n    for _, pair := range a.buckets {\n        if pair != nil {\n            pairs = append(pairs, pair)\n        }\n    }\n    return pairs\n}\n\n/* すべてのキーを取得 */\nfunc (a *arrayHashMap) keySet() []int {\n    var keys []int\n    for _, pair := range a.buckets {\n        if pair != nil {\n            keys = append(keys, pair.key)\n        }\n    }\n    return keys\n}\n\n/* すべての値を取得 */\nfunc (a *arrayHashMap) valueSet() []string {\n    var values []string\n    for _, pair := range a.buckets {\n        if pair != nil {\n            values = append(values, pair.val)\n        }\n    }\n    return values\n}\n\n/* ハッシュテーブルを出力 */\nfunc (a *arrayHashMap) print() {\n    for _, pair := range a.buckets {\n        if pair != nil {\n            fmt.Println(pair.key, \"-&gt;\", pair.val)\n        }\n    }\n}\n</code></pre> array_hash_map.swift<pre><code>/* キーと値の組 */\nclass Pair: Equatable {\n    public var key: Int\n    public var val: String\n\n    public init(key: Int, val: String) {\n        self.key = key\n        self.val = val\n    }\n\n    public static func == (lhs: Pair, rhs: Pair) -&gt; Bool {\n        lhs.key == rhs.key &amp;&amp; lhs.val == rhs.val\n    }\n}\n\n/* 配列ベースのハッシュテーブル */\nclass ArrayHashMap {\n    private var buckets: [Pair?]\n\n    init() {\n        // 100 個のバケットを含む配列を初期化\n        buckets = Array(repeating: nil, count: 100)\n    }\n\n    /* ハッシュ関数 */\n    private func hashFunc(key: Int) -&gt; Int {\n        let index = key % 100\n        return index\n    }\n\n    /* 検索操作 */\n    func get(key: Int) -&gt; String? {\n        let index = hashFunc(key: key)\n        let pair = buckets[index]\n        return pair?.val\n    }\n\n    /* 追加操作 */\n    func put(key: Int, val: String) {\n        let pair = Pair(key: key, val: val)\n        let index = hashFunc(key: key)\n        buckets[index] = pair\n    }\n\n    /* 削除操作 */\n    func remove(key: Int) {\n        let index = hashFunc(key: key)\n        // nil に設定し、削除を表す\n        buckets[index] = nil\n    }\n\n    /* すべてのキーと値のペアを取得 */\n    func pairSet() -&gt; [Pair] {\n        buckets.compactMap { $0 }\n    }\n\n    /* すべてのキーを取得 */\n    func keySet() -&gt; [Int] {\n        buckets.compactMap { $0?.key }\n    }\n\n    /* すべての値を取得 */\n    func valueSet() -&gt; [String] {\n        buckets.compactMap { $0?.val }\n    }\n\n    /* ハッシュテーブルを出力 */\n    func print() {\n        for pair in pairSet() {\n            Swift.print(\"\\(pair.key) -&gt; \\(pair.val)\")\n        }\n    }\n}\n</code></pre> array_hash_map.js<pre><code>/* キーと値の組 Number -&gt; String */\nclass Pair {\n    constructor(key, val) {\n        this.key = key;\n        this.val = val;\n    }\n}\n\n/* 配列ベースのハッシュテーブル */\nclass ArrayHashMap {\n    #buckets;\n    constructor() {\n        // 100 個のバケットを含む配列を初期化\n        this.#buckets = new Array(100).fill(null);\n    }\n\n    /* ハッシュ関数 */\n    #hashFunc(key) {\n        return key % 100;\n    }\n\n    /* 検索操作 */\n    get(key) {\n        let index = this.#hashFunc(key);\n        let pair = this.#buckets[index];\n        if (pair === null) return null;\n        return pair.val;\n    }\n\n    /* 追加操作 */\n    set(key, val) {\n        let index = this.#hashFunc(key);\n        this.#buckets[index] = new Pair(key, val);\n    }\n\n    /* 削除操作 */\n    delete(key) {\n        let index = this.#hashFunc(key);\n        // null に設定し、削除を表す\n        this.#buckets[index] = null;\n    }\n\n    /* すべてのキーと値のペアを取得 */\n    entries() {\n        let arr = [];\n        for (let i = 0; i &lt; this.#buckets.length; i++) {\n            if (this.#buckets[i]) {\n                arr.push(this.#buckets[i]);\n            }\n        }\n        return arr;\n    }\n\n    /* すべてのキーを取得 */\n    keys() {\n        let arr = [];\n        for (let i = 0; i &lt; this.#buckets.length; i++) {\n            if (this.#buckets[i]) {\n                arr.push(this.#buckets[i].key);\n            }\n        }\n        return arr;\n    }\n\n    /* すべての値を取得 */\n    values() {\n        let arr = [];\n        for (let i = 0; i &lt; this.#buckets.length; i++) {\n            if (this.#buckets[i]) {\n                arr.push(this.#buckets[i].val);\n            }\n        }\n        return arr;\n    }\n\n    /* ハッシュテーブルを出力 */\n    print() {\n        let pairSet = this.entries();\n        for (const pair of pairSet) {\n            console.info(`${pair.key} -&gt; ${pair.val}`);\n        }\n    }\n}\n</code></pre> array_hash_map.ts<pre><code>/* キーと値の組 Number -&gt; String */\nclass Pair {\n    public key: number;\n    public val: string;\n\n    constructor(key: number, val: string) {\n        this.key = key;\n        this.val = val;\n    }\n}\n\n/* 配列ベースのハッシュテーブル */\nclass ArrayHashMap {\n    private readonly buckets: (Pair | null)[];\n\n    constructor() {\n        // 100 個のバケットを含む配列を初期化\n        this.buckets = new Array(100).fill(null);\n    }\n\n    /* ハッシュ関数 */\n    private hashFunc(key: number): number {\n        return key % 100;\n    }\n\n    /* 検索操作 */\n    public get(key: number): string | null {\n        let index = this.hashFunc(key);\n        let pair = this.buckets[index];\n        if (pair === null) return null;\n        return pair.val;\n    }\n\n    /* 追加操作 */\n    public set(key: number, val: string) {\n        let index = this.hashFunc(key);\n        this.buckets[index] = new Pair(key, val);\n    }\n\n    /* 削除操作 */\n    public delete(key: number) {\n        let index = this.hashFunc(key);\n        // null に設定し、削除を表す\n        this.buckets[index] = null;\n    }\n\n    /* すべてのキーと値のペアを取得 */\n    public entries(): (Pair | null)[] {\n        let arr: (Pair | null)[] = [];\n        for (let i = 0; i &lt; this.buckets.length; i++) {\n            if (this.buckets[i]) {\n                arr.push(this.buckets[i]);\n            }\n        }\n        return arr;\n    }\n\n    /* すべてのキーを取得 */\n    public keys(): (number | undefined)[] {\n        let arr: (number | undefined)[] = [];\n        for (let i = 0; i &lt; this.buckets.length; i++) {\n            if (this.buckets[i]) {\n                arr.push(this.buckets[i].key);\n            }\n        }\n        return arr;\n    }\n\n    /* すべての値を取得 */\n    public values(): (string | undefined)[] {\n        let arr: (string | undefined)[] = [];\n        for (let i = 0; i &lt; this.buckets.length; i++) {\n            if (this.buckets[i]) {\n                arr.push(this.buckets[i].val);\n            }\n        }\n        return arr;\n    }\n\n    /* ハッシュテーブルを出力 */\n    public print() {\n        let pairSet = this.entries();\n        for (const pair of pairSet) {\n            console.info(`${pair.key} -&gt; ${pair.val}`);\n        }\n    }\n}\n</code></pre> array_hash_map.dart<pre><code>/* キーと値の組 */\nclass Pair {\n  int key;\n  String val;\n  Pair(this.key, this.val);\n}\n\n/* 配列ベースのハッシュテーブル */\nclass ArrayHashMap {\n  late List&lt;Pair?&gt; _buckets;\n\n  ArrayHashMap() {\n    // 100 個のバケットを含む配列を初期化\n    _buckets = List.filled(100, null);\n  }\n\n  /* ハッシュ関数 */\n  int _hashFunc(int key) {\n    final int index = key % 100;\n    return index;\n  }\n\n  /* 検索操作 */\n  String? get(int key) {\n    final int index = _hashFunc(key);\n    final Pair? pair = _buckets[index];\n    if (pair == null) {\n      return null;\n    }\n    return pair.val;\n  }\n\n  /* 追加操作 */\n  void put(int key, String val) {\n    final Pair pair = Pair(key, val);\n    final int index = _hashFunc(key);\n    _buckets[index] = pair;\n  }\n\n  /* 削除操作 */\n  void remove(int key) {\n    final int index = _hashFunc(key);\n    _buckets[index] = null;\n  }\n\n  /* すべてのキーと値のペアを取得 */\n  List&lt;Pair&gt; pairSet() {\n    List&lt;Pair&gt; pairSet = [];\n    for (final Pair? pair in _buckets) {\n      if (pair != null) {\n        pairSet.add(pair);\n      }\n    }\n    return pairSet;\n  }\n\n  /* すべてのキーを取得 */\n  List&lt;int&gt; keySet() {\n    List&lt;int&gt; keySet = [];\n    for (final Pair? pair in _buckets) {\n      if (pair != null) {\n        keySet.add(pair.key);\n      }\n    }\n    return keySet;\n  }\n\n  /* すべての値を取得 */\n  List&lt;String&gt; values() {\n    List&lt;String&gt; valueSet = [];\n    for (final Pair? pair in _buckets) {\n      if (pair != null) {\n        valueSet.add(pair.val);\n      }\n    }\n    return valueSet;\n  }\n\n  /* ハッシュテーブルを出力 */\n  void printHashMap() {\n    for (final Pair kv in pairSet()) {\n      print(\"${kv.key} -&gt; ${kv.val}\");\n    }\n  }\n}\n</code></pre> array_hash_map.rs<pre><code>/* キーと値の組 */\n#[derive(Debug, Clone, PartialEq)]\npub struct Pair {\n    pub key: i32,\n    pub val: String,\n}\n\n/* 配列ベースのハッシュテーブル */\npub struct ArrayHashMap {\n    buckets: Vec&lt;Option&lt;Pair&gt;&gt;,\n}\n\nimpl ArrayHashMap {\n    pub fn new() -&gt; ArrayHashMap {\n        // 100 個のバケットを含む配列を初期化\n        Self {\n            buckets: vec![None; 100],\n        }\n    }\n\n    /* ハッシュ関数 */\n    fn hash_func(&amp;self, key: i32) -&gt; usize {\n        key as usize % 100\n    }\n\n    /* 検索操作 */\n    pub fn get(&amp;self, key: i32) -&gt; Option&lt;&amp;String&gt; {\n        let index = self.hash_func(key);\n        self.buckets[index].as_ref().map(|pair| &amp;pair.val)\n    }\n\n    /* 追加操作 */\n    pub fn put(&amp;mut self, key: i32, val: &amp;str) {\n        let index = self.hash_func(key);\n        self.buckets[index] = Some(Pair {\n            key,\n            val: val.to_string(),\n        });\n    }\n\n    /* 削除操作 */\n    pub fn remove(&amp;mut self, key: i32) {\n        let index = self.hash_func(key);\n        // None に設定し、削除を表す\n        self.buckets[index] = None;\n    }\n\n    /* すべてのキーと値のペアを取得 */\n    pub fn entry_set(&amp;self) -&gt; Vec&lt;&amp;Pair&gt; {\n        self.buckets\n            .iter()\n            .filter_map(|pair| pair.as_ref())\n            .collect()\n    }\n\n    /* すべてのキーを取得 */\n    pub fn key_set(&amp;self) -&gt; Vec&lt;&amp;i32&gt; {\n        self.buckets\n            .iter()\n            .filter_map(|pair| pair.as_ref().map(|pair| &amp;pair.key))\n            .collect()\n    }\n\n    /* すべての値を取得 */\n    pub fn value_set(&amp;self) -&gt; Vec&lt;&amp;String&gt; {\n        self.buckets\n            .iter()\n            .filter_map(|pair| pair.as_ref().map(|pair| &amp;pair.val))\n            .collect()\n    }\n\n    /* ハッシュテーブルを出力 */\n    pub fn print(&amp;self) {\n        for pair in self.entry_set() {\n            println!(\"{} -&gt; {}\", pair.key, pair.val);\n        }\n    }\n}\n</code></pre> array_hash_map.c<pre><code>/* キーと値の組 int-&gt;string */\ntypedef struct {\n    int key;\n    char *val;\n} Pair;\n\n/* 配列ベースのハッシュテーブル */\ntypedef struct {\n    Pair *buckets[MAX_SIZE];\n} ArrayHashMap;\n\n/* コンストラクタ */\nArrayHashMap *newArrayHashMap() {\n    ArrayHashMap *hmap = malloc(sizeof(ArrayHashMap));\n    for (int i=0; i &lt; MAX_SIZE; i++) {\n        hmap-&gt;buckets[i] = NULL;\n    }\n    return hmap;\n}\n\n/* デストラクタ */\nvoid delArrayHashMap(ArrayHashMap *hmap) {\n    for (int i = 0; i &lt; MAX_SIZE; i++) {\n        if (hmap-&gt;buckets[i] != NULL) {\n            free(hmap-&gt;buckets[i]-&gt;val);\n            free(hmap-&gt;buckets[i]);\n        }\n    }\n    free(hmap);\n}\n\n/* 追加操作 */\nvoid put(ArrayHashMap *hmap, const int key, const char *val) {\n    Pair *Pair = malloc(sizeof(Pair));\n    Pair-&gt;key = key;\n    Pair-&gt;val = malloc(strlen(val) + 1);\n    strcpy(Pair-&gt;val, val);\n\n    int index = hashFunc(key);\n    hmap-&gt;buckets[index] = Pair;\n}\n\n/* 削除操作 */\nvoid removeItem(ArrayHashMap *hmap, const int key) {\n    int index = hashFunc(key);\n    free(hmap-&gt;buckets[index]-&gt;val);\n    free(hmap-&gt;buckets[index]);\n    hmap-&gt;buckets[index] = NULL;\n}\n\n/* すべてのキーと値のペアを取得 */\nvoid pairSet(ArrayHashMap *hmap, MapSet *set) {\n    Pair *entries;\n    int i = 0, index = 0;\n    int total = 0;\n    /* 有効なキーと値のペア数を集計 */\n    for (i = 0; i &lt; MAX_SIZE; i++) {\n        if (hmap-&gt;buckets[i] != NULL) {\n            total++;\n        }\n    }\n    entries = malloc(sizeof(Pair) * total);\n    for (i = 0; i &lt; MAX_SIZE; i++) {\n        if (hmap-&gt;buckets[i] != NULL) {\n            entries[index].key = hmap-&gt;buckets[i]-&gt;key;\n            entries[index].val = malloc(strlen(hmap-&gt;buckets[i]-&gt;val) + 1);\n            strcpy(entries[index].val, hmap-&gt;buckets[i]-&gt;val);\n            index++;\n        }\n    }\n    set-&gt;set = entries;\n    set-&gt;len = total;\n}\n\n/* すべてのキーを取得 */\nvoid keySet(ArrayHashMap *hmap, MapSet *set) {\n    int *keys;\n    int i = 0, index = 0;\n    int total = 0;\n    /* 有効なキーと値のペア数を集計 */\n    for (i = 0; i &lt; MAX_SIZE; i++) {\n        if (hmap-&gt;buckets[i] != NULL) {\n            total++;\n        }\n    }\n    keys = malloc(total * sizeof(int));\n    for (i = 0; i &lt; MAX_SIZE; i++) {\n        if (hmap-&gt;buckets[i] != NULL) {\n            keys[index] = hmap-&gt;buckets[i]-&gt;key;\n            index++;\n        }\n    }\n    set-&gt;set = keys;\n    set-&gt;len = total;\n}\n\n/* すべての値を取得 */\nvoid valueSet(ArrayHashMap *hmap, MapSet *set) {\n    char **vals;\n    int i = 0, index = 0;\n    int total = 0;\n    /* 有効なキーと値のペア数を集計 */\n    for (i = 0; i &lt; MAX_SIZE; i++) {\n        if (hmap-&gt;buckets[i] != NULL) {\n            total++;\n        }\n    }\n    vals = malloc(total * sizeof(char *));\n    for (i = 0; i &lt; MAX_SIZE; i++) {\n        if (hmap-&gt;buckets[i] != NULL) {\n            vals[index] = hmap-&gt;buckets[i]-&gt;val;\n            index++;\n        }\n    }\n    set-&gt;set = vals;\n    set-&gt;len = total;\n}\n\n/* ハッシュテーブルを出力 */\nvoid print(ArrayHashMap *hmap) {\n    int i;\n    MapSet set;\n    pairSet(hmap, &amp;set);\n    Pair *entries = (Pair *)set.set;\n    for (i = 0; i &lt; set.len; i++) {\n        printf(\"%d -&gt; %s\\n\", entries[i].key, entries[i].val);\n    }\n    free(set.set);\n}\n</code></pre> array_hash_map.kt<pre><code>/* キーと値の組 */\nclass Pair(\n    var key: Int,\n    var _val: String\n)\n\n/* 配列ベースのハッシュテーブル */\nclass ArrayHashMap {\n    // 100 個のバケットを含む配列を初期化\n    private val buckets = arrayOfNulls&lt;Pair&gt;(100)\n\n    /* ハッシュ関数 */\n    fun hashFunc(key: Int): Int {\n        val index = key % 100\n        return index\n    }\n\n    /* 検索操作 */\n    fun get(key: Int): String? {\n        val index = hashFunc(key)\n        val pair = buckets[index] ?: return null\n        return pair._val\n    }\n\n    /* 追加操作 */\n    fun put(key: Int, _val: String) {\n        val pair = Pair(key, _val)\n        val index = hashFunc(key)\n        buckets[index] = pair\n    }\n\n    /* 削除操作 */\n    fun remove(key: Int) {\n        val index = hashFunc(key)\n        // null に設定し、削除を表す\n        buckets[index] = null\n    }\n\n    /* すべてのキーと値のペアを取得 */\n    fun pairSet(): MutableList&lt;Pair&gt; {\n        val pairSet = mutableListOf&lt;Pair&gt;()\n        for (pair in buckets) {\n            if (pair != null)\n                pairSet.add(pair)\n        }\n        return pairSet\n    }\n\n    /* すべてのキーを取得 */\n    fun keySet(): MutableList&lt;Int&gt; {\n        val keySet = mutableListOf&lt;Int&gt;()\n        for (pair in buckets) {\n            if (pair != null)\n                keySet.add(pair.key)\n        }\n        return keySet\n    }\n\n    /* すべての値を取得 */\n    fun valueSet(): MutableList&lt;String&gt; {\n        val valueSet = mutableListOf&lt;String&gt;()\n        for (pair in buckets) {\n            if (pair != null)\n                valueSet.add(pair._val)\n        }\n        return valueSet\n    }\n\n    /* ハッシュテーブルを出力 */\n    fun print() {\n        for (kv in pairSet()) {\n            val key = kv.key\n            val _val = kv._val\n            println(\"$key -&gt; $_val\")\n        }\n    }\n}\n</code></pre> array_hash_map.rb<pre><code>### キーと値のペア ###\nclass Pair\n  attr_accessor :key, :val\n\n  def initialize(key, val)\n    @key = key\n    @val = val\n  end\nend\n\n### 配列で実装したハッシュテーブル ###\nclass ArrayHashMap\n  ### コンストラクタ ###\n  def initialize\n    # 100 個のバケットを含む配列を初期化\n    @buckets = Array.new(100)\n  end\n\n  ### ハッシュ関数 ###\n  def hash_func(key)\n    index = key % 100\n  end\n\n  ### 検索操作 ###\n  def get(key)\n    index = hash_func(key)\n    pair = @buckets[index]\n\n    return if pair.nil?\n    pair.val\n  end\n\n  ### 追加操作 ###\n  def put(key, val)\n    pair = Pair.new(key, val)\n    index = hash_func(key)\n    @buckets[index] = pair\n  end\n\n  ### 削除操作 ###\n  def remove(key)\n    index = hash_func(key)\n    # nil に設定し、削除を表す\n    @buckets[index] = nil\n  end\n\n  ### すべてのキーと値のペアを取得 ###\n  def entry_set\n    result = []\n    @buckets.each { |pair| result &lt;&lt; pair unless pair.nil? }\n    result\n  end\n\n  ### すべてのキーを取得 ###\n  def key_set\n    result = []\n    @buckets.each { |pair| result &lt;&lt; pair.key unless pair.nil? }\n    result\n  end\n\n  ### すべての値を取得 ###\n  def value_set\n    result = []\n    @buckets.each { |pair| result &lt;&lt; pair.val unless pair.nil? }\n    result\n  end\n\n  ### ハッシュテーブルを出力 ###\n  def print\n    @buckets.each { |pair| puts \"#{pair.key} -&gt; #{pair.val}\" unless pair.nil? }\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 6 章 &nbsp; ハッシュテーブル","6.1 &nbsp; ハッシュテーブル"],"tags":[]},{"location":"chapter_hashing/hash_map/#613","level":2,"title":"6.1.3   ハッシュ衝突と拡張","text":"<p>本質的には、ハッシュ関数の役割は、すべての <code>key</code> からなる入力空間を、配列のすべてのインデックスからなる出力空間に写像することです。しかし、入力空間は多くの場合、出力空間よりはるかに大きいため、理論上は必ず「複数の入力が同じ出力に対応する」状況が存在します。</p> <p>上の例のハッシュ関数では、入力 <code>key</code> の下 2 桁が同じであれば、出力結果も同じになります。たとえば、学籍番号 12836 と 20336 の 2 人の学生を検索すると、次の結果を得ます：</p> <pre><code>12836 % 100 = 36\n20336 % 100 = 36\n</code></pre> <p>次の図に示すように、2 つの学籍番号が同じ名前を指してしまっており、これは明らかに誤りです。このような、複数の入力が同じ出力に対応する状況をハッシュ衝突（hash collision）と呼びます。</p> <p></p> <p> 図 6-3   ハッシュ衝突の例 </p> <p>容易に分かるように、ハッシュテーブルの容量 \\(n\\) が大きいほど、複数の <code>key</code> が同じバケットに割り当てられる確率は低くなり、衝突も少なくなります。したがって、ハッシュテーブルを拡張することでハッシュ衝突を減らせます。</p> <p>次の図に示すように、拡張前はキーと値のペア <code>(136, A)</code> と <code>(236, D)</code> が衝突していますが、拡張後は衝突が解消されます。</p> <p></p> <p> 図 6-4   ハッシュテーブルの拡張 </p> <p>配列の拡張と同様に、ハッシュテーブルの拡張ではすべてのキーと値のペアを元のハッシュテーブルから新しいハッシュテーブルへ移し替える必要があり、非常に時間がかかります。また、ハッシュテーブルの容量 <code>capacity</code> が変わるため、ハッシュ関数を使ってすべてのキーと値のペアの格納位置を再計算しなければならず、これによって拡張過程の計算コストがさらに増加します。そのため、プログラミング言語では通常、頻繁な拡張を防ぐために十分大きなハッシュテーブル容量をあらかじめ確保します。</p> <p>負荷率（load factor）はハッシュテーブルにおける重要な概念であり、ハッシュテーブル内の要素数をバケット数で割ったものとして定義され、ハッシュ衝突の深刻さを測るために用いられます。また、ハッシュテーブル拡張の発動条件としてもよく使われます。例えば Java では、負荷率が \\(0.75\\) を超えると、システムはハッシュテーブルを元の \\(2\\) 倍に拡張します。</p>","path":["第 6 章 &nbsp; ハッシュテーブル","6.1 &nbsp; ハッシュテーブル"],"tags":[]},{"location":"chapter_hashing/summary/","level":1,"title":"6.4   まとめ","text":"","path":["第 6 章 &nbsp; ハッシュテーブル","6.4 &nbsp; まとめ"],"tags":[]},{"location":"chapter_hashing/summary/#1","level":3,"title":"1.   重要ポイントの振り返り","text":"<ul> <li><code>key</code> を入力すると、ハッシュテーブルは \\(O(1)\\) 時間で <code>value</code> を検索でき、非常に高効率である。</li> <li>一般的なハッシュテーブルの操作には、検索、キーと値のペアの追加、キーと値のペアの削除、ハッシュテーブルの走査などがある。</li> <li>ハッシュ関数は <code>key</code> を配列インデックスに写像し、それによって対応するバケットにアクセスして <code>value</code> を取得する。</li> <li>異なる 2 つの <code>key</code> が、ハッシュ関数を通した後に同じ配列インデックスになることがあり、検索結果の誤りを引き起こす。この現象をハッシュ衝突と呼ぶ。</li> <li>ハッシュテーブルの容量が大きいほど、ハッシュ衝突の確率は低くなる。そのため、ハッシュテーブルを拡張することでハッシュ衝突を緩和できる。配列の拡張と同様に、ハッシュテーブルの拡張操作のコストは大きい。</li> <li>負荷率は、ハッシュテーブル内の要素数をバケット数で割ったものと定義され、ハッシュ衝突の深刻さを反映する。ハッシュテーブル拡張を発動する条件としてよく用いられる。</li> <li>連鎖方式では、単一要素を連結リストに変換し、衝突したすべての要素を同じ連結リストに格納する。しかし、連結リストが長すぎると検索効率が低下するため、さらに連結リストを赤黒木に変換して効率を高めることができる。</li> <li>オープンアドレス法は複数回の探索によってハッシュ衝突を処理する。線形探索は固定のステップ幅を用いるが、要素を削除できず、クラスタリングが発生しやすいという欠点がある。二重ハッシュは複数のハッシュ関数を用いて探索するため、線形探索に比べてクラスタリングが起きにくいが、複数のハッシュ関数によって計算量が増える。</li> <li>プログラミング言語ごとに、異なるハッシュテーブル実装が採用されている。たとえば、Java の <code>HashMap</code> は連鎖方式を使用し、Python の <code>Dict</code> はオープンアドレス法を採用している。</li> <li>ハッシュテーブルでは、ハッシュアルゴリズムに決定性、高効率、均一分布という特徴が求められる。暗号学では、ハッシュアルゴリズムはさらに耐衝突性とアバランシェ効果も備えるべきである。</li> <li>ハッシュアルゴリズムは通常、大きな素数を法として用い、ハッシュ値の均一分布を最大限に保証してハッシュ衝突を減らす。</li> <li>一般的なハッシュアルゴリズムには MD5、SHA-1、SHA-2、SHA-3 などがある。MD5 はファイル完全性の検証によく用いられ、SHA-2 はセキュリティ用途やプロトコルでよく用いられる。</li> <li>プログラミング言語は通常、データ型に対して組み込みのハッシュアルゴリズムを提供し、ハッシュテーブル内のバケットインデックスの計算に用いる。通常、ハッシュ可能なのは不変オブジェクトだけである。</li> </ul>","path":["第 6 章 &nbsp; ハッシュテーブル","6.4 &nbsp; まとめ"],"tags":[]},{"location":"chapter_hashing/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q：ハッシュテーブルの時間計算量が \\(O(n)\\) になるのはどのような場合ですか？</p> <p>ハッシュ衝突が深刻な場合、ハッシュテーブルの時間計算量は \\(O(n)\\) に劣化する。ハッシュ関数の設計が適切で、容量設定が合理的で、衝突が比較的均等な場合、時間計算量は \\(O(1)\\) である。プログラミング言語組み込みのハッシュテーブルを使うとき、通常は時間計算量を \\(O(1)\\) とみなす。</p> <p>Q：なぜハッシュ関数 \\(f(x) = x\\) を使わないのですか？ そうすれば衝突は起きません。</p> <p>\\(f(x) = x\\) というハッシュ関数では、各要素は一意のバケットインデックスに対応し、これは配列と等価である。しかし、入力空間は通常、出力空間（配列長）よりはるかに大きいため、ハッシュ関数の最後のステップはたいてい配列長での剰余になる。言い換えると、ハッシュテーブルの目的は、大きな状態空間をより小さな空間に写像し、\\(O(1)\\) の検索効率を提供することである。</p> <p>Q：ハッシュテーブルの基礎実装は配列、連結リスト、二分木なのに、なぜそれらより高効率になり得るのですか？</p> <p>まず、ハッシュテーブルは時間効率が高くなる一方で、空間効率は低くなる。ハッシュテーブルには、かなりの部分で未使用のメモリが存在する。</p> <p>次に、時間効率が高くなるのは特定の利用場面に限られる。ある機能が同じ時間計算量で配列や連結リストによって実装できるなら、通常はハッシュテーブルより速い。これは、ハッシュ関数の計算にコストがかかり、時間計算量の定数項がより大きいからである。</p> <p>最後に、ハッシュテーブルの時間計算量は劣化する可能性がある。たとえば連鎖方式では、連結リストや赤黒木で検索操作を行うため、なお \\(O(n)\\) 時間に劣化するリスクがある。</p> <p>Q：二重ハッシュにも要素を直接削除できない欠点がありますか？ 削除済みとマークした領域は再利用できますか？</p> <p>二重ハッシュはオープンアドレス法の一種であり、オープンアドレス法はいずれも要素を直接削除できないという欠点があるため、削除のマーク付けが必要になる。削除済みとマークされた領域は再利用できる。新しい要素をハッシュテーブルに挿入し、ハッシュ関数によって削除済みとマークされた位置を見つけた場合、その位置は新しい要素に使用できる。こうすることで、ハッシュテーブルの探索系列を変えずに保ちつつ、空間利用率も確保できる。</p> <p>Q：なぜ線形探索では、要素を探すときにハッシュ衝突が発生するのですか？</p> <p>探索時には、ハッシュ関数で対応するバケットとキーと値のペアを見つけ、<code>key</code> が一致しないことが分かると、それはハッシュ衝突を意味する。そのため、線形探索法では事前に設定したステップ幅に従って順に探索し、正しいキーと値のペアを見つけるか、見つからずに終了するまで続ける。</p> <p>Q：なぜハッシュテーブルの拡張でハッシュ衝突を緩和できるのですか？</p> <p>ハッシュ関数の最後のステップは、たいてい配列長 \\(n\\) での剰余を取り、出力値を配列インデックスの範囲内に収めることである。拡張後は配列長 \\(n\\) が変化し、<code>key</code> に対応するインデックスも変化する可能性がある。もともと同じバケットに入っていた複数の <code>key</code> は、拡張後には複数のバケットに割り当てられる可能性があり、それによってハッシュ衝突が緩和される。</p> <p>Q：高効率な読み書きのためなら、配列を直接使えばよいのではないですか？</p> <p>データの <code>key</code> が連続した小範囲の整数であれば、配列を直接使えばよく、単純で高効率である。しかし <code>key</code> が別の型（たとえば文字列）の場合は、ハッシュ関数を用いて <code>key</code> を配列インデックスに写像し、さらにバケット配列を通じて要素を格納する必要がある。このような構造がハッシュテーブルである。</p>","path":["第 6 章 &nbsp; ハッシュテーブル","6.4 &nbsp; まとめ"],"tags":[]},{"location":"chapter_heap/","level":1,"title":"第 8 章   ヒープ","text":"<p>Abstract</p> <p>ヒープは連なる山々の峰のように、幾重にも重なり、さまざまな形をしている。</p> <p>いくつもの山の高さはまちまちだが、最も高い峰がいつも最初に目に入る。</p>","path":["第 8 章 &nbsp; ヒープ"],"tags":[]},{"location":"chapter_heap/#_1","level":2,"title":"章の内容","text":"<ul> <li>8.1   ヒープ</li> <li>8.2   ヒープ構築</li> <li>8.3   Top-k 問題</li> <li>8.4   まとめ</li> </ul>","path":["第 8 章 &nbsp; ヒープ"],"tags":[]},{"location":"chapter_heap/build_heap/","level":1,"title":"8.2   ヒープ構築","text":"<p>場合によっては、リスト内のすべての要素を使ってヒープを構築したいことがあります。この過程を「ヒープ構築」と呼びます。</p>","path":["第 8 章 &nbsp; ヒープ","8.2 &nbsp; ヒープ構築"],"tags":[]},{"location":"chapter_heap/build_heap/#821","level":2,"title":"8.2.1   ヒープへの挿入操作による実現","text":"<p>まず空のヒープを作成し、次にリストを走査して、各要素に対して順に「ヒープへの挿入操作」を実行します。つまり、要素をヒープの末尾に追加してから、その要素に対して「下から上へ」のヒープ化を行います。</p> <p>要素が1つヒープに挿入されるたびに、ヒープの長さは1増加します。ノードは上から下へ順に二分木へ追加されるため、ヒープは「上から下へ」構築されます。</p> <p>要素数を \\(n\\) とすると、各要素のヒープへの挿入操作には \\(O(\\log{n})\\) の時間がかかるため、このヒープ構築法の時間計算量は \\(O(n \\log n)\\) です。</p>","path":["第 8 章 &nbsp; ヒープ","8.2 &nbsp; ヒープ構築"],"tags":[]},{"location":"chapter_heap/build_heap/#822","level":2,"title":"8.2.2   走査によるヒープ化で実現","text":"<p>実際には、より効率的なヒープ構築法を実現でき、全体は2つの手順に分かれます。</p> <ol> <li>リストのすべての要素をそのままヒープに追加します。この時点では、ヒープの性質はまだ満たされていません。</li> <li>ヒープを逆順で走査し（レベル順走査の逆順）、各非葉ノードに対して順に「上から下へ」のヒープ化を実行します。</li> </ol> <p>あるノードをヒープ化するたびに、そのノードを根とする部分木は合法な部分ヒープになります。また、逆順で走査するため、ヒープは「下から上へ」構築されます。</p> <p>逆順走査を選ぶのは、この方法なら現在のノードの下にある部分木がすでに合法な部分ヒープであることを保証でき、そのうえで現在のノードをヒープ化してはじめて有効になるからです。</p> <p>なお、葉ノードには子ノードがないため、それ自体が自然に合法な部分ヒープであり、ヒープ化は不要です。以下のコードが示すように、最後の非葉ノードは最後のノードの親ノードであり、そこから逆順に走査してヒープ化を実行します。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby my_heap.py<pre><code>def __init__(self, nums: list[int]):\n    \"\"\"コンストラクタ。入力リストに基づいてヒープを構築する\"\"\"\n    # リスト要素をそのままヒープに追加\n    self.max_heap = nums\n    # 葉ノード以外のすべてのノードをヒープ化\n    for i in range(self.parent(self.size() - 1), -1, -1):\n        self.sift_down(i)\n</code></pre> my_heap.cpp<pre><code>/* コンストラクタ。入力リストに基づいてヒープを構築する */\nMaxHeap(vector&lt;int&gt; nums) {\n    // リスト要素をそのままヒープに追加\n    maxHeap = nums;\n    // 葉ノード以外のすべてのノードをヒープ化\n    for (int i = parent(size() - 1); i &gt;= 0; i--) {\n        siftDown(i);\n    }\n}\n</code></pre> my_heap.java<pre><code>/* コンストラクタ。入力リストに基づいてヒープを構築する */\nMaxHeap(List&lt;Integer&gt; nums) {\n    // リスト要素をそのままヒープに追加\n    maxHeap = new ArrayList&lt;&gt;(nums);\n    // 葉ノード以外のすべてのノードをヒープ化\n    for (int i = parent(size() - 1); i &gt;= 0; i--) {\n        siftDown(i);\n    }\n}\n</code></pre> my_heap.cs<pre><code>/* コンストラクタ。入力リストに基づいてヒープを構築 */\nMaxHeap(IEnumerable&lt;int&gt; nums) {\n    // リスト要素をそのままヒープに追加\n    maxHeap = new List&lt;int&gt;(nums);\n    // 葉ノード以外のすべてのノードをヒープ化\n    var size = Parent(this.Size() - 1);\n    for (int i = size; i &gt;= 0; i--) {\n        SiftDown(i);\n    }\n}\n</code></pre> my_heap.go<pre><code>/* コンストラクタ。スライスからヒープを構築する */\nfunc newMaxHeap(nums []any) *maxHeap {\n    // リスト要素をそのままヒープに追加\n    h := &amp;maxHeap{data: nums}\n    for i := h.parent(len(h.data) - 1); i &gt;= 0; i-- {\n        // 葉ノード以外のすべてのノードをヒープ化\n        h.siftDown(i)\n    }\n    return h\n}\n</code></pre> my_heap.swift<pre><code>/* コンストラクタ。入力リストに基づいてヒープを構築する */\ninit(nums: [Int]) {\n    // リスト要素をそのままヒープに追加\n    maxHeap = nums\n    // 葉ノード以外のすべてのノードをヒープ化\n    for i in (0 ... parent(i: size() - 1)).reversed() {\n        siftDown(i: i)\n    }\n}\n</code></pre> my_heap.js<pre><code>/* コンストラクタ。空のヒープを作成するか、入力リストからヒープを構築する */\nconstructor(nums) {\n    // リスト要素をそのままヒープに追加\n    this.#maxHeap = nums === undefined ? [] : [...nums];\n    // 葉ノード以外のすべてのノードをヒープ化\n    for (let i = this.#parent(this.size() - 1); i &gt;= 0; i--) {\n        this.#siftDown(i);\n    }\n}\n</code></pre> my_heap.ts<pre><code>/* コンストラクタ。空のヒープを作成するか、入力リストからヒープを構築する */\nconstructor(nums?: number[]) {\n    // リスト要素をそのままヒープに追加\n    this.maxHeap = nums === undefined ? [] : [...nums];\n    // 葉ノード以外のすべてのノードをヒープ化\n    for (let i = this.parent(this.size() - 1); i &gt;= 0; i--) {\n        this.siftDown(i);\n    }\n}\n</code></pre> my_heap.dart<pre><code>/* コンストラクタ。入力リストに基づいてヒープを構築する */\nMaxHeap(List&lt;int&gt; nums) {\n  // リスト要素をそのままヒープに追加\n  _maxHeap = nums;\n  // 葉ノード以外のすべてのノードをヒープ化\n  for (int i = _parent(size() - 1); i &gt;= 0; i--) {\n    siftDown(i);\n  }\n}\n</code></pre> my_heap.rs<pre><code>/* コンストラクタ。入力リストに基づいてヒープを構築する */\nfn new(nums: Vec&lt;i32&gt;) -&gt; Self {\n    // リスト要素をそのままヒープに追加\n    let mut heap = MaxHeap { max_heap: nums };\n    // 葉ノード以外のすべてのノードをヒープ化\n    for i in (0..=Self::parent(heap.size() - 1)).rev() {\n        heap.sift_down(i);\n    }\n    heap\n}\n</code></pre> my_heap.c<pre><code>/* コンストラクタ。スライスからヒープを構築する */\nMaxHeap *newMaxHeap(int nums[], int size) {\n    // すべての要素をヒープに入れる\n    MaxHeap *maxHeap = (MaxHeap *)malloc(sizeof(MaxHeap));\n    maxHeap-&gt;size = size;\n    memcpy(maxHeap-&gt;data, nums, size * sizeof(int));\n    for (int i = parent(maxHeap, size - 1); i &gt;= 0; i--) {\n        // 葉ノード以外のすべてのノードをヒープ化\n        siftDown(maxHeap, i);\n    }\n    return maxHeap;\n}\n</code></pre> my_heap.kt<pre><code>/* 最大ヒープ */\nclass MaxHeap(nums: MutableList&lt;Int&gt;?) {\n    // 配列ではなくリストを使うことで、拡張を考慮する必要がない\n    private val maxHeap = mutableListOf&lt;Int&gt;()\n\n    /* コンストラクタ。入力リストに基づいてヒープを構築する */\n    init {\n        // リスト要素をそのままヒープに追加\n        maxHeap.addAll(nums!!)\n        // 葉ノード以外のすべてのノードをヒープ化\n        for (i in parent(size() - 1) downTo 0) {\n            siftDown(i)\n        }\n    }\n\n    /* 左子ノードのインデックスを取得 */\n    private fun left(i: Int): Int {\n        return 2 * i + 1\n    }\n\n    /* 右子ノードのインデックスを取得 */\n    private fun right(i: Int): Int {\n        return 2 * i + 2\n    }\n\n    /* 親ノードのインデックスを取得 */\n    private fun parent(i: Int): Int {\n        return (i - 1) / 2 // 切り捨て除算\n    }\n\n    /* 要素を交換 */\n    private fun swap(i: Int, j: Int) {\n        val temp = maxHeap[i]\n        maxHeap[i] = maxHeap[j]\n        maxHeap[j] = temp\n    }\n\n    /* ヒープのサイズを取得 */\n    fun size(): Int {\n        return maxHeap.size\n    }\n\n    /* ヒープが空かどうかを判定 */\n    fun isEmpty(): Boolean {\n        /* ヒープが空かどうかを判定 */\n        return size() == 0\n    }\n\n    /* ヒープ先頭要素にアクセス */\n    fun peek(): Int {\n        return maxHeap[0]\n    }\n\n    /* 要素をヒープに追加 */\n    fun push(_val: Int) {\n        // ノードを追加\n        maxHeap.add(_val)\n        // 下から上へヒープ化\n        siftUp(size() - 1)\n    }\n\n    /* ノード i から始めて、下から上へヒープ化 */\n    private fun siftUp(it: Int) {\n        // Kotlin の関数引数は不変のため、一時変数を作成する\n        var i = it\n        while (true) {\n            // ノード i の親ノードを取得\n            val p = parent(i)\n            // 「根ノードを越えた」または「ノードの修復が不要」になったらヒープ化を終了\n            if (p &lt; 0 || maxHeap[i] &lt;= maxHeap[p]) break\n            // 2 つのノードを交換\n            swap(i, p)\n            // ループで下から上へヒープ化\n            i = p\n        }\n    }\n\n    /* 要素をヒープから取り出す */\n    fun pop(): Int {\n        // 空判定の処理\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        // 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n        swap(0, size() - 1)\n        // ノードを削除\n        val _val = maxHeap.removeAt(size() - 1)\n        // 上から下へヒープ化\n        siftDown(0)\n        // ヒープ先頭要素を返す\n        return _val\n    }\n\n    /* ノード i から始めて、上から下へヒープ化 */\n    private fun siftDown(it: Int) {\n        // Kotlin の関数引数は不変のため、一時変数を作成する\n        var i = it\n        while (true) {\n            // ノード i, l, r のうち値が最大のノードを ma とする\n            val l = left(i)\n            val r = right(i)\n            var ma = i\n            if (l &lt; size() &amp;&amp; maxHeap[l] &gt; maxHeap[ma]) ma = l\n            if (r &lt; size() &amp;&amp; maxHeap[r] &gt; maxHeap[ma]) ma = r\n            // ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n            if (ma == i) break\n            // 2 つのノードを交換\n            swap(i, ma)\n            // ループで上から下へヒープ化\n            i = ma\n        }\n    }\n\n    /* ヒープ（二分木）を出力 */\n    fun print() {\n        val queue = PriorityQueue { a: Int, b: Int -&gt; b - a }\n        queue.addAll(maxHeap)\n        printHeap(queue)\n    }\n}\n</code></pre> my_heap.rb<pre><code>### コンストラクタ。入力リストに基づいてヒープを構築 ###\ndef initialize(nums)\n  # リスト要素をそのままヒープに追加\n  @max_heap = nums\n  # 葉ノード以外のすべてのノードをヒープ化\n  parent(size - 1).downto(0) do |i|\n    sift_down(i)\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 8 章 &nbsp; ヒープ","8.2 &nbsp; ヒープ構築"],"tags":[]},{"location":"chapter_heap/build_heap/#823","level":2,"title":"8.2.3   計算量の分析","text":"<p>以下では、2つ目のヒープ構築法の時間計算量を求めてみましょう。</p> <ul> <li>完全二分木のノード数を \\(n\\) とすると、葉ノード数は \\((n + 1) / 2\\) です。ここで \\(/\\) は切り捨て除算を表します。したがって、ヒープ化が必要なノード数は \\((n - 1) / 2\\) です。</li> <li>上から下へのヒープ化の過程では、各ノードは最大で葉ノードまでヒープ化されるため、最大反復回数は二分木の高さ \\(\\log n\\) です。</li> </ul> <p>上の2つを掛け合わせると、ヒープ構築過程の時間計算量は \\(O(n \\log n)\\) となります。しかし、この見積もりは正確ではありません。二分木では下層のノード数が上層よりはるかに多いという性質を考慮していないためです。</p> <p>次に、より正確な計算を行います。計算を簡単にするため、ノード数が \\(n\\) 、高さが \\(h\\) の「満二分木」を仮定します。この仮定は計算結果の正しさに影響しません。</p> <p></p> <p> 図 8-5   満二分木の各層のノード数 </p> <p>上図に示すように、ノードを「上から下へヒープ化」する最大反復回数は、そのノードから葉ノードまでの距離に等しく、この距離こそが「ノードの高さ」です。したがって、各層の「ノード数 \\(\\times\\) ノードの高さ」を合計すれば、**すべてのノードのヒープ化反復回数の総和**が得られます。</p> \\[ T(h) = 2^0h + 2^1(h-1) + 2^2(h-2) + \\dots + 2^{(h-1)}\\times1 \\] <p>上式を簡約するには中学の数列の知識を用います。まず \\(T(h)\\) に \\(2\\) を掛けると、次のようになります。</p> \\[ \\begin{aligned} T(h) &amp; = 2^0h + 2^1(h-1) + 2^2(h-2) + \\dots + 2^{h-1}\\times1 \\newline 2 T(h) &amp; = 2^1h + 2^2(h-1) + 2^3(h-2) + \\dots + 2^{h}\\times1 \\newline \\end{aligned} \\] <p>ずらして引く方法を用い、下式の \\(2 T(h)\\) から上式の \\(T(h)\\) を引くと、次が得られます。</p> \\[ 2T(h) - T(h) = T(h) = -2^0h + 2^1 + 2^2 + \\dots + 2^{h-1} + 2^h \\] <p>上式を見ると、\\(T(h)\\) は等比数列であることがわかるため、和の公式を直接用いて、時間計算量は次のように求められます。</p> \\[ \\begin{aligned} T(h) &amp; = 2 \\frac{1 - 2^h}{1 - 2} - h \\newline &amp; = 2^{h+1} - h - 2 \\newline &amp; = O(2^h) \\end{aligned} \\] <p>さらに、高さ \\(h\\) の満二分木のノード数は \\(n = 2^{h+1} - 1\\) であるため、計算量は容易に \\(O(2^h) = O(n)\\) とわかります。以上の導出は、**入力リストからヒープを構築する時間計算量が \\(O(n)\\) であり、非常に効率的である**ことを示しています。</p>","path":["第 8 章 &nbsp; ヒープ","8.2 &nbsp; ヒープ構築"],"tags":[]},{"location":"chapter_heap/heap/","level":1,"title":"8.1   ヒープ","text":"<p>ヒープ（heap）は、特定の条件を満たす完全二分木であり、主に次の 2 種類に分けられます。</p> <ul> <li>最小ヒープ（min heap）：任意のノードの値 \\(\\leq\\) その子ノードの値。</li> <li>最大ヒープ（max heap）：任意のノードの値 \\(\\geq\\) その子ノードの値。</li> </ul> <p></p> <p> 図 8-1   最小ヒープと最大ヒープ </p> <p>ヒープは完全二分木の特殊な例であり、次の性質を持ちます。</p> <ul> <li>最下層のノードは左から順に埋められ、ほかの層のノードはすべて埋まっています。</li> <li>二分木の根ノードを「ヒープ頂点」、最下層で最も右にあるノードを「ヒープ底」と呼びます。</li> <li>最大ヒープ（最小ヒープ）では、ヒープ頂点の要素（根ノード）の値が最大（最小）です。</li> </ul>","path":["第 8 章 &nbsp; ヒープ","8.1 &nbsp; ヒープ"],"tags":[]},{"location":"chapter_heap/heap/#811","level":2,"title":"8.1.1   ヒープの基本操作","text":"<p>ここで注意したいのは、多くのプログラミング言語が提供しているのは優先度付きキュー（priority queue）であり、これは優先度順に並ぶキューとして定義される抽象データ構造だということです。</p> <p>実際には、ヒープは通常、優先度付きキューの実装に用いられ、最大ヒープは要素が大きい順に取り出される優先度付きキューに相当します。利用の観点では、「優先度付きキュー」と「ヒープ」は等価なデータ構造とみなせます。そのため、本書では両者を特に区別せず、まとめて「ヒープ」と呼びます。</p> <p>ヒープの基本操作を以下の表に示します。メソッド名はプログラミング言語によって異なります。</p> <p> 表 8-1   ヒープの操作効率 </p> メソッド名 説明 時間計算量 <code>push()</code> 要素をヒープに追加 \\(O(\\log n)\\) <code>pop()</code> ヒープ頂点の要素を取り出す \\(O(\\log n)\\) <code>peek()</code> ヒープ頂点の要素にアクセス（最大 / 最小ヒープではそれぞれ最大 / 最小値） \\(O(1)\\) <code>size()</code> ヒープ内の要素数を取得 \\(O(1)\\) <code>isEmpty()</code> ヒープが空かどうかを判定 \\(O(1)\\) <p>実際の応用では、プログラミング言語が提供するヒープクラス（または優先度付きキュークラス）をそのまま使えます。</p> <p>ソートアルゴリズムにおける「昇順」と「降順」と同様に、<code>flag</code> を設定したり <code>Comparator</code> を変更したりすることで、「最小ヒープ」と「最大ヒープ」を切り替えられます。コードは以下のとおりです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby heap.py<pre><code># 最小ヒープを初期化\nmin_heap, flag = [], 1\n# 最大ヒープを初期化\nmax_heap, flag = [], -1\n\n# Python の heapq モジュールはデフォルトで最小ヒープを実装している\n# 「要素を負にして」からヒープに追加すると、大小関係を反転させて最大ヒープを実現できる\n# この例では、flag = 1 のときは最小ヒープ、flag = -1 のときは最大ヒープに対応する\n\n# 要素をヒープに追加\nheapq.heappush(max_heap, flag * 1)\nheapq.heappush(max_heap, flag * 3)\nheapq.heappush(max_heap, flag * 2)\nheapq.heappush(max_heap, flag * 5)\nheapq.heappush(max_heap, flag * 4)\n\n# ヒープ頂点の要素を取得\npeek: int = flag * max_heap[0] # 5\n\n# ヒープ頂点の要素を取り出す\n# 取り出された要素は大きい順の列になる\nval = flag * heapq.heappop(max_heap) # 5\nval = flag * heapq.heappop(max_heap) # 4\nval = flag * heapq.heappop(max_heap) # 3\nval = flag * heapq.heappop(max_heap) # 2\nval = flag * heapq.heappop(max_heap) # 1\n\n# ヒープのサイズを取得\nsize: int = len(max_heap)\n\n# ヒープが空かどうかを判定\nis_empty: bool = not max_heap\n\n# 入力リストからヒープを構築\nmin_heap: list[int] = [1, 3, 2, 5, 4]\nheapq.heapify(min_heap)\n</code></pre> heap.cpp<pre><code>/* ヒープを初期化 */\n// 最小ヒープを初期化\npriority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; minHeap;\n// 最大ヒープを初期化\npriority_queue&lt;int, vector&lt;int&gt;, less&lt;int&gt;&gt; maxHeap;\n\n/* 要素をヒープに追加 */\nmaxHeap.push(1);\nmaxHeap.push(3);\nmaxHeap.push(2);\nmaxHeap.push(5);\nmaxHeap.push(4);\n\n/* ヒープ頂点の要素を取得 */\nint peek = maxHeap.top(); // 5\n\n/* ヒープ頂点の要素を取り出す */\n// 取り出された要素は大きい順の列になる\nmaxHeap.pop(); // 5\nmaxHeap.pop(); // 4\nmaxHeap.pop(); // 3\nmaxHeap.pop(); // 2\nmaxHeap.pop(); // 1\n\n/* ヒープのサイズを取得 */\nint size = maxHeap.size();\n\n/* ヒープが空かどうかを判定 */\nbool isEmpty = maxHeap.empty();\n\n/* 入力リストからヒープを構築 */\nvector&lt;int&gt; input{1, 3, 2, 5, 4};\npriority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; minHeap(input.begin(), input.end());\n</code></pre> heap.java<pre><code>/* ヒープを初期化 */\n// 最小ヒープを初期化\nQueue&lt;Integer&gt; minHeap = new PriorityQueue&lt;&gt;();\n// 最大ヒープを初期化（lambda 式で Comparator を変更すればよい）\nQueue&lt;Integer&gt; maxHeap = new PriorityQueue&lt;&gt;((a, b) -&gt; b - a);\n\n/* 要素をヒープに追加 */\nmaxHeap.offer(1);\nmaxHeap.offer(3);\nmaxHeap.offer(2);\nmaxHeap.offer(5);\nmaxHeap.offer(4);\n\n/* ヒープ頂点の要素を取得 */\nint peek = maxHeap.peek(); // 5\n\n/* ヒープ頂点の要素を取り出す */\n// 取り出された要素は大きい順の列になる\npeek = maxHeap.poll(); // 5\npeek = maxHeap.poll(); // 4\npeek = maxHeap.poll(); // 3\npeek = maxHeap.poll(); // 2\npeek = maxHeap.poll(); // 1\n\n/* ヒープのサイズを取得 */\nint size = maxHeap.size();\n\n/* ヒープが空かどうかを判定 */\nboolean isEmpty = maxHeap.isEmpty();\n\n/* 入力リストからヒープを構築 */\nminHeap = new PriorityQueue&lt;&gt;(Arrays.asList(1, 3, 2, 5, 4));\n</code></pre> heap.cs<pre><code>/* ヒープを初期化 */\n// 最小ヒープを初期化\nPriorityQueue&lt;int, int&gt; minHeap = new();\n// 最大ヒープを初期化（lambda 式で Comparer を変更すればよい）\nPriorityQueue&lt;int, int&gt; maxHeap = new(Comparer&lt;int&gt;.Create((x, y) =&gt; y.CompareTo(x)));\n\n/* 要素をヒープに追加 */\nmaxHeap.Enqueue(1, 1);\nmaxHeap.Enqueue(3, 3);\nmaxHeap.Enqueue(2, 2);\nmaxHeap.Enqueue(5, 5);\nmaxHeap.Enqueue(4, 4);\n\n/* ヒープ頂点の要素を取得 */\nint peek = maxHeap.Peek();//5\n\n/* ヒープ頂点の要素を取り出す */\n// 取り出された要素は大きい順の列になる\npeek = maxHeap.Dequeue();  // 5\npeek = maxHeap.Dequeue();  // 4\npeek = maxHeap.Dequeue();  // 3\npeek = maxHeap.Dequeue();  // 2\npeek = maxHeap.Dequeue();  // 1\n\n/* ヒープのサイズを取得 */\nint size = maxHeap.Count;\n\n/* ヒープが空かどうかを判定 */\nbool isEmpty = maxHeap.Count == 0;\n\n/* 入力リストからヒープを構築 */\nminHeap = new PriorityQueue&lt;int, int&gt;([(1, 1), (3, 3), (2, 2), (5, 5), (4, 4)]);\n</code></pre> heap.go<pre><code>// Go では、heap.Interface を実装することで整数の最大ヒープを構築できる\n// heap.Interface を実装するには、同時に sort.Interface も実装する必要がある\ntype intHeap []any\n\n// Push は heap.Interface のメソッドで、要素をヒープに追加する\nfunc (h *intHeap) Push(x any) {\n    // Push と Pop は pointer receiver を引数に取る\n    // スライスの内容を調整するだけでなく、スライスの長さも変更するため。\n    *h = append(*h, x.(int))\n}\n\n// Pop は heap.Interface のメソッドで、ヒープ頂点の要素を取り出す\nfunc (h *intHeap) Pop() any {\n    // 取り出す要素は末尾に格納されている\n    last := (*h)[len(*h)-1]\n    *h = (*h)[:len(*h)-1]\n    return last\n}\n\n// Len は sort.Interface のメソッド\nfunc (h *intHeap) Len() int {\n    return len(*h)\n}\n\n// Less は sort.Interface のメソッド\nfunc (h *intHeap) Less(i, j int) bool {\n    // 最小ヒープを実装する場合は、不等号を小なりに変更する\n    return (*h)[i].(int) &gt; (*h)[j].(int)\n}\n\n// Swap は sort.Interface のメソッド\nfunc (h *intHeap) Swap(i, j int) {\n    (*h)[i], (*h)[j] = (*h)[j], (*h)[i]\n}\n\n// Top はヒープ頂点の要素を取得\nfunc (h *intHeap) Top() any {\n    return (*h)[0]\n}\n\n/* Driver Code */\nfunc TestHeap(t *testing.T) {\n    /* ヒープを初期化 */\n    // 最大ヒープを初期化\n    maxHeap := &amp;intHeap{}\n    heap.Init(maxHeap)\n    /* 要素をヒープに追加 */\n    // heap.Interface のメソッドを呼び出して要素を追加する\n    heap.Push(maxHeap, 1)\n    heap.Push(maxHeap, 3)\n    heap.Push(maxHeap, 2)\n    heap.Push(maxHeap, 4)\n    heap.Push(maxHeap, 5)\n\n    /* ヒープ頂点の要素を取得 */\n    top := maxHeap.Top()\n    fmt.Printf(\"ヒープ頂点の要素は %d\\n\", top)\n\n    /* ヒープ頂点の要素を取り出す */\n    // heap.Interface のメソッドを呼び出して要素を削除する\n    heap.Pop(maxHeap) // 5\n    heap.Pop(maxHeap) // 4\n    heap.Pop(maxHeap) // 3\n    heap.Pop(maxHeap) // 2\n    heap.Pop(maxHeap) // 1\n\n    /* ヒープのサイズを取得 */\n    size := len(*maxHeap)\n    fmt.Printf(\"ヒープ内の要素数は %d\\n\", size)\n\n    /* ヒープが空かどうかを判定 */\n    isEmpty := len(*maxHeap) == 0\n    fmt.Printf(\"ヒープは空か %t\\n\", isEmpty)\n}\n</code></pre> heap.swift<pre><code>/* ヒープを初期化 */\n// Swift の Heap 型は最大ヒープと最小ヒープの両方をサポートしており、swift-collections の導入が必要\nvar heap = Heap&lt;Int&gt;()\n\n/* 要素をヒープに追加 */\nheap.insert(1)\nheap.insert(3)\nheap.insert(2)\nheap.insert(5)\nheap.insert(4)\n\n/* ヒープ頂点の要素を取得 */\nvar peek = heap.max()!\n\n/* ヒープ頂点の要素を取り出す */\npeek = heap.removeMax() // 5\npeek = heap.removeMax() // 4\npeek = heap.removeMax() // 3\npeek = heap.removeMax() // 2\npeek = heap.removeMax() // 1\n\n/* ヒープのサイズを取得 */\nlet size = heap.count\n\n/* ヒープが空かどうかを判定 */\nlet isEmpty = heap.isEmpty\n\n/* 入力リストからヒープを構築 */\nlet heap2 = Heap([1, 3, 2, 5, 4])\n</code></pre> heap.js<pre><code>// JavaScript には組み込みの Heap クラスがない\n</code></pre> heap.ts<pre><code>// TypeScript には組み込みの Heap クラスがない\n</code></pre> heap.dart<pre><code>// Dart には組み込みの Heap クラスがない\n</code></pre> heap.rs<pre><code>use std::collections::BinaryHeap;\nuse std::cmp::Reverse;\n\n/* ヒープを初期化 */\n// 最小ヒープを初期化\nlet mut min_heap = BinaryHeap::&lt;Reverse&lt;i32&gt;&gt;::new();\n// 最大ヒープを初期化\nlet mut max_heap = BinaryHeap::new();\n\n/* 要素をヒープに追加 */\nmax_heap.push(1);\nmax_heap.push(3);\nmax_heap.push(2);\nmax_heap.push(5);\nmax_heap.push(4);\n\n/* ヒープ頂点の要素を取得 */\nlet peek = max_heap.peek().unwrap();  // 5\n\n/* ヒープ頂点の要素を取り出す */\n// 取り出された要素は大きい順の列になる\nlet peek = max_heap.pop().unwrap();   // 5\nlet peek = max_heap.pop().unwrap();   // 4\nlet peek = max_heap.pop().unwrap();   // 3\nlet peek = max_heap.pop().unwrap();   // 2\nlet peek = max_heap.pop().unwrap();   // 1\n\n/* ヒープのサイズを取得 */\nlet size = max_heap.len();\n\n/* ヒープが空かどうかを判定 */\nlet is_empty = max_heap.is_empty();\n\n/* 入力リストからヒープを構築 */\nlet min_heap = BinaryHeap::from(vec![Reverse(1), Reverse(3), Reverse(2), Reverse(5), Reverse(4)]);\n</code></pre> heap.c<pre><code>// C には組み込みの Heap クラスがない\n</code></pre> heap.kt<pre><code>/* ヒープを初期化 */\n// 最小ヒープを初期化\nvar minHeap = PriorityQueue&lt;Int&gt;()\n// 最大ヒープを初期化（lambda 式で Comparator を変更すればよい）\nval maxHeap = PriorityQueue { a: Int, b: Int -&gt; b - a }\n\n/* 要素をヒープに追加 */\nmaxHeap.offer(1)\nmaxHeap.offer(3)\nmaxHeap.offer(2)\nmaxHeap.offer(5)\nmaxHeap.offer(4)\n\n/* ヒープ頂点の要素を取得 */\nvar peek = maxHeap.peek() // 5\n\n/* ヒープ頂点の要素を取り出す */\n// 取り出された要素は大きい順の列になる\npeek = maxHeap.poll() // 5\npeek = maxHeap.poll() // 4\npeek = maxHeap.poll() // 3\npeek = maxHeap.poll() // 2\npeek = maxHeap.poll() // 1\n\n/* ヒープのサイズを取得 */\nval size = maxHeap.size\n\n/* ヒープが空かどうかを判定 */\nval isEmpty = maxHeap.isEmpty()\n\n/* 入力リストからヒープを構築 */\nminHeap = PriorityQueue(mutableListOf(1, 3, 2, 5, 4))\n</code></pre> heap.rb<pre><code># Ruby には組み込みの Heap クラスがない\n</code></pre> 実行を可視化 <p>https://pythontutor.com/render.html#code=import%20heapq%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%B0%8F%E9%A1%B6%E5%A0%86%0A%20%20%20%20min_heap,%20flag%20%3D%20%5B%5D,%201%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20max_heap,%20flag%20%3D%20%5B%5D,%20-1%0A%20%20%20%20%0A%20%20%20%20%23%20Python%20%E7%9A%84%20heapq%20%E6%A8%A1%E5%9D%97%E9%BB%98%E8%AE%A4%E5%AE%9E%E7%8E%B0%E5%B0%8F%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E8%80%83%E8%99%91%E5%B0%86%E2%80%9C%E5%85%83%E7%B4%A0%E5%8F%96%E8%B4%9F%E2%80%9D%E5%90%8E%E5%86%8D%E5%85%A5%E5%A0%86%EF%BC%8C%E8%BF%99%E6%A0%B7%E5%B0%B1%E5%8F%AF%E4%BB%A5%E5%B0%86%E5%A4%A7%E5%B0%8F%E5%85%B3%E7%B3%BB%E9%A2%A0%E5%80%92%EF%BC%8C%E4%BB%8E%E8%80%8C%E5%AE%9E%E7%8E%B0%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E5%9C%A8%E6%9C%AC%E7%A4%BA%E4%BE%8B%E4%B8%AD%EF%BC%8Cflag%20%3D%201%20%E6%97%B6%E5%AF%B9%E5%BA%94%E5%B0%8F%E9%A1%B6%E5%A0%86%EF%BC%8Cflag%20%3D%20-1%20%E6%97%B6%E5%AF%B9%E5%BA%94%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%85%A5%E5%A0%86%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%201%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%203%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%202%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%205%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%204%29%0A%20%20%20%20%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%0A%20%20%20%20peek%20%3D%20flag%20*%20max_heap%5B0%5D%20%23%205%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%E5%87%BA%E5%A0%86%0A%20%20%20%20%23%20%E5%87%BA%E5%A0%86%E5%85%83%E7%B4%A0%E4%BC%9A%E5%BD%A2%E6%88%90%E4%B8%80%E4%B8%AA%E4%BB%8E%E5%A4%A7%E5%88%B0%E5%B0%8F%E7%9A%84%E5%BA%8F%E5%88%97%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%205%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%204%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%203%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%202%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%201%0A%20%20%20%20%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E5%A0%86%E5%A4%A7%E5%B0%8F%0A%20%20%20%20size%20%3D%20len%28max_heap%29%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%88%A4%E6%96%AD%E5%A0%86%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%0A%20%20%20%20is_empty%20%3D%20not%20max_heap%0A%20%20%20%20%0A%20%20%20%20%23%20%E8%BE%93%E5%85%A5%E5%88%97%E8%A1%A8%E5%B9%B6%E5%BB%BA%E5%A0%86%0A%20%20%20%20min_heap%20%3D%20%5B1,%203,%202,%205,%204%5D%0A%20%20%20%20heapq.heapify%28min_heap%29&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["第 8 章 &nbsp; ヒープ","8.1 &nbsp; ヒープ"],"tags":[]},{"location":"chapter_heap/heap/#812","level":2,"title":"8.1.2   ヒープの実装","text":"<p>以下では最大ヒープを実装します。最小ヒープに変換したい場合は、すべての大小比較ロジックを反転させるだけです（たとえば、\\(\\geq\\) を \\(\\leq\\) に置き換えます）。興味のある読者は自分で実装してみてください。</p>","path":["第 8 章 &nbsp; ヒープ","8.1 &nbsp; ヒープ"],"tags":[]},{"location":"chapter_heap/heap/#1","level":3,"title":"1.   ヒープの格納と表現","text":"<p>「二分木」の章で述べたように、完全二分木は配列で表現するのに非常に適しています。ヒープはまさに完全二分木の一種なので、ここでは配列を使ってヒープを格納します。</p> <p>配列で二分木を表す場合、要素はノードの値を表し、インデックスは二分木におけるノードの位置を表します。ノード間の参照関係はインデックスの対応式によって実現できます。</p> <p>次の図に示すように、インデックス \\(i\\) に対して、左子ノードのインデックスは \\(2i + 1\\) 、右子ノードのインデックスは \\(2i + 2\\) 、親ノードのインデックスは \\((i - 1) / 2\\)（切り捨て除算）です。インデックスが範囲外であれば、空ノードまたはノードが存在しないことを表します。</p> <p></p> <p> 図 8-2   ヒープの表現と格納 </p> <p>インデックスの対応式は関数にまとめておくと、後続で使いやすくなります：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby my_heap.py<pre><code>def left(self, i: int) -&gt; int:\n    \"\"\"左子ノードのインデックスを取得\"\"\"\n    return 2 * i + 1\n\ndef right(self, i: int) -&gt; int:\n    \"\"\"右子ノードのインデックスを取得\"\"\"\n    return 2 * i + 2\n\ndef parent(self, i: int) -&gt; int:\n    \"\"\"親ノードのインデックスを取得\"\"\"\n    return (i - 1) // 2  # 切り捨て除算\n</code></pre> my_heap.cpp<pre><code>/* 左子ノードのインデックスを取得 */\nint left(int i) {\n    return 2 * i + 1;\n}\n\n/* 右子ノードのインデックスを取得 */\nint right(int i) {\n    return 2 * i + 2;\n}\n\n/* 親ノードのインデックスを取得 */\nint parent(int i) {\n    return (i - 1) / 2; // 切り捨て除算\n}\n</code></pre> my_heap.java<pre><code>/* 左子ノードのインデックスを取得 */\nint left(int i) {\n    return 2 * i + 1;\n}\n\n/* 右子ノードのインデックスを取得 */\nint right(int i) {\n    return 2 * i + 2;\n}\n\n/* 親ノードのインデックスを取得 */\nint parent(int i) {\n    return (i - 1) / 2; // 切り捨て除算\n}\n</code></pre> my_heap.cs<pre><code>/* 左子ノードのインデックスを取得 */\nint Left(int i) {\n    return 2 * i + 1;\n}\n\n/* 右子ノードのインデックスを取得 */\nint Right(int i) {\n    return 2 * i + 2;\n}\n\n/* 親ノードのインデックスを取得 */\nint Parent(int i) {\n    return (i - 1) / 2; // 切り捨て除算\n}\n</code></pre> my_heap.go<pre><code>/* 左子ノードのインデックスを取得 */\nfunc (h *maxHeap) left(i int) int {\n    return 2*i + 1\n}\n\n/* 右子ノードのインデックスを取得 */\nfunc (h *maxHeap) right(i int) int {\n    return 2*i + 2\n}\n\n/* 親ノードのインデックスを取得 */\nfunc (h *maxHeap) parent(i int) int {\n    // 切り捨て除算\n    return (i - 1) / 2\n}\n</code></pre> my_heap.swift<pre><code>/* 左子ノードのインデックスを取得 */\nfunc left(i: Int) -&gt; Int {\n    2 * i + 1\n}\n\n/* 右子ノードのインデックスを取得 */\nfunc right(i: Int) -&gt; Int {\n    2 * i + 2\n}\n\n/* 親ノードのインデックスを取得 */\nfunc parent(i: Int) -&gt; Int {\n    (i - 1) / 2 // 切り捨て除算\n}\n</code></pre> my_heap.js<pre><code>/* 左子ノードのインデックスを取得 */\n#left(i) {\n    return 2 * i + 1;\n}\n\n/* 右子ノードのインデックスを取得 */\n#right(i) {\n    return 2 * i + 2;\n}\n\n/* 親ノードのインデックスを取得 */\n#parent(i) {\n    return Math.floor((i - 1) / 2); // 切り捨て除算\n}\n</code></pre> my_heap.ts<pre><code>/* 左子ノードのインデックスを取得 */\nleft(i: number): number {\n    return 2 * i + 1;\n}\n\n/* 右子ノードのインデックスを取得 */\nright(i: number): number {\n    return 2 * i + 2;\n}\n\n/* 親ノードのインデックスを取得 */\nparent(i: number): number {\n    return Math.floor((i - 1) / 2); // 切り捨て除算\n}\n</code></pre> my_heap.dart<pre><code>/* 左子ノードのインデックスを取得 */\nint _left(int i) {\n  return 2 * i + 1;\n}\n\n/* 右子ノードのインデックスを取得 */\nint _right(int i) {\n  return 2 * i + 2;\n}\n\n/* 親ノードのインデックスを取得 */\nint _parent(int i) {\n  return (i - 1) ~/ 2; // 切り捨て除算\n}\n</code></pre> my_heap.rs<pre><code>/* 左子ノードのインデックスを取得 */\nfn left(i: usize) -&gt; usize {\n    2 * i + 1\n}\n\n/* 右子ノードのインデックスを取得 */\nfn right(i: usize) -&gt; usize {\n    2 * i + 2\n}\n\n/* 親ノードのインデックスを取得 */\nfn parent(i: usize) -&gt; usize {\n    (i - 1) / 2 // 切り捨て除算\n}\n</code></pre> my_heap.c<pre><code>/* 左子ノードのインデックスを取得 */\nint left(MaxHeap *maxHeap, int i) {\n    return 2 * i + 1;\n}\n\n/* 右子ノードのインデックスを取得 */\nint right(MaxHeap *maxHeap, int i) {\n    return 2 * i + 2;\n}\n\n/* 親ノードのインデックスを取得 */\nint parent(MaxHeap *maxHeap, int i) {\n    return (i - 1) / 2; // 切り捨て\n}\n</code></pre> my_heap.kt<pre><code>/* 左子ノードのインデックスを取得 */\nfun left(i: Int): Int {\n    return 2 * i + 1\n}\n\n/* 右子ノードのインデックスを取得 */\nfun right(i: Int): Int {\n    return 2 * i + 2\n}\n\n/* 親ノードのインデックスを取得 */\nfun parent(i: Int): Int {\n    return (i - 1) / 2 // 切り捨て除算\n}\n</code></pre> my_heap.rb<pre><code>### 左子ノードのインデックスを取得 ###\ndef left(i)\n  2 * i + 1\nend\n\n### 右子ノードのインデックスを取得 ###\ndef right(i)\n  2 * i + 2\nend\n\n### 親ノードのインデックスを取得 ###\ndef parent(i)\n  (i - 1) / 2     # 切り捨て除算\nend\n</code></pre>","path":["第 8 章 &nbsp; ヒープ","8.1 &nbsp; ヒープ"],"tags":[]},{"location":"chapter_heap/heap/#2","level":3,"title":"2.   ヒープ頂点の要素にアクセス","text":"<p>ヒープ頂点の要素は二分木の根ノード、すなわちリストの先頭要素です：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby my_heap.py<pre><code>def peek(self) -&gt; int:\n    \"\"\"ヒープ先頭要素にアクセス\"\"\"\n    return self.max_heap[0]\n</code></pre> my_heap.cpp<pre><code>/* ヒープ先頭要素にアクセス */\nint peek() {\n    return maxHeap[0];\n}\n</code></pre> my_heap.java<pre><code>/* ヒープ先頭要素にアクセス */\nint peek() {\n    return maxHeap.get(0);\n}\n</code></pre> my_heap.cs<pre><code>/* ヒープ先頭要素にアクセス */\nint Peek() {\n    return maxHeap[0];\n}\n</code></pre> my_heap.go<pre><code>/* ヒープ先頭要素にアクセス */\nfunc (h *maxHeap) peek() any {\n    return h.data[0]\n}\n</code></pre> my_heap.swift<pre><code>/* ヒープ先頭要素にアクセス */\nfunc peek() -&gt; Int {\n    maxHeap[0]\n}\n</code></pre> my_heap.js<pre><code>/* ヒープ先頭要素にアクセス */\npeek() {\n    return this.#maxHeap[0];\n}\n</code></pre> my_heap.ts<pre><code>/* ヒープ先頭要素にアクセス */\npeek(): number {\n    return this.maxHeap[0];\n}\n</code></pre> my_heap.dart<pre><code>/* ヒープ先頭要素にアクセス */\nint peek() {\n  return _maxHeap[0];\n}\n</code></pre> my_heap.rs<pre><code>/* ヒープ先頭要素にアクセス */\nfn peek(&amp;self) -&gt; Option&lt;i32&gt; {\n    self.max_heap.first().copied()\n}\n</code></pre> my_heap.c<pre><code>/* ヒープ先頭要素にアクセス */\nint peek(MaxHeap *maxHeap) {\n    return maxHeap-&gt;data[0];\n}\n</code></pre> my_heap.kt<pre><code>/* ヒープ先頭要素にアクセス */\nfun peek(): Int {\n    return maxHeap[0]\n}\n</code></pre> my_heap.rb<pre><code>### ヒープ先頭要素を参照 ###\ndef peek\n  @max_heap[0]\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 8 章 &nbsp; ヒープ","8.1 &nbsp; ヒープ"],"tags":[]},{"location":"chapter_heap/heap/#3","level":3,"title":"3.   要素をヒープに追加","text":"<p>与えられた要素 <code>val</code> を、まずヒープの底に追加します。追加後、<code>val</code> がヒープ内のほかの要素より大きい可能性があるため、ヒープ条件が崩れているかもしれません。そのため、挿入ノードから根ノードまでの経路上にある各ノードを修復する必要があります。この操作をヒープ化（heapify）と呼びます。</p> <p>ヒープへ追加したノードから始めて、**下から上へヒープ化**を行います。次の図のように、挿入ノードとその親ノードの値を比較し、挿入ノードのほうが大きければそれらを交換します。その後もこの操作を繰り返し、下から上へ各ノードを修復して、根ノードを越えるか交換不要のノードに達した時点で終了します。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 8-3   要素をヒープに追加する手順 </p> <p>ノード総数を \\(n\\) とすると、木の高さは \\(O(\\log n)\\) です。したがって、ヒープ化操作のループ回数は高々 \\(O(\\log n)\\) であり、要素をヒープに追加する操作の時間計算量は \\(O(\\log n)\\) です。コードは以下のとおりです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby my_heap.py<pre><code>def push(self, val: int):\n    \"\"\"要素をヒープに追加\"\"\"\n    # ノードを追加\n    self.max_heap.append(val)\n    # 下から上へヒープ化\n    self.sift_up(self.size() - 1)\n\ndef sift_up(self, i: int):\n    \"\"\"ノード i から始めて、下から上へヒープ化\"\"\"\n    while True:\n        # ノード i の親ノードを取得\n        p = self.parent(i)\n        # 「根ノードを越えた」または「ノードの修復が不要」になったらヒープ化を終了\n        if p &lt; 0 or self.max_heap[i] &lt;= self.max_heap[p]:\n            break\n        # 2 つのノードを交換\n        self.swap(i, p)\n        # ループで下から上へヒープ化\n        i = p\n</code></pre> my_heap.cpp<pre><code>/* 要素をヒープに追加 */\nvoid push(int val) {\n    // ノードを追加\n    maxHeap.push_back(val);\n    // 下から上へヒープ化\n    siftUp(size() - 1);\n}\n\n/* ノード i から始めて、下から上へヒープ化 */\nvoid siftUp(int i) {\n    while (true) {\n        // ノード i の親ノードを取得\n        int p = parent(i);\n        // 「根ノードを越えた」または「ノードの修復が不要」になったらヒープ化を終了\n        if (p &lt; 0 || maxHeap[i] &lt;= maxHeap[p])\n            break;\n        // 2 つのノードを交換\n        swap(maxHeap[i], maxHeap[p]);\n        // ループで下から上へヒープ化\n        i = p;\n    }\n}\n</code></pre> my_heap.java<pre><code>/* 要素をヒープに追加 */\nvoid push(int val) {\n    // ノードを追加\n    maxHeap.add(val);\n    // 下から上へヒープ化\n    siftUp(size() - 1);\n}\n\n/* ノード i から始めて、下から上へヒープ化 */\nvoid siftUp(int i) {\n    while (true) {\n        // ノード i の親ノードを取得\n        int p = parent(i);\n        // 「根ノードを越えた」または「ノードの修復が不要」になったらヒープ化を終了\n        if (p &lt; 0 || maxHeap.get(i) &lt;= maxHeap.get(p))\n            break;\n        // 2 つのノードを交換\n        swap(i, p);\n        // ループで下から上へヒープ化\n        i = p;\n    }\n}\n</code></pre> my_heap.cs<pre><code>/* 要素をヒープに追加 */\nvoid Push(int val) {\n    // ノードを追加\n    maxHeap.Add(val);\n    // 下から上へヒープ化\n    SiftUp(Size() - 1);\n}\n\n/* ノード i から始めて、下から上へヒープ化 */\nvoid SiftUp(int i) {\n    while (true) {\n        // ノード i の親ノードを取得\n        int p = Parent(i);\n        // 「根ノードを越えた」または「ノードの修復が不要」な場合は、ヒープ化を終了する\n        if (p &lt; 0 || maxHeap[i] &lt;= maxHeap[p])\n            break;\n        // 2 つのノードを交換\n        Swap(i, p);\n        // ループで下から上へヒープ化\n        i = p;\n    }\n}\n</code></pre> my_heap.go<pre><code>/* 要素をヒープに追加 */\nfunc (h *maxHeap) push(val any) {\n    // ノードを追加\n    h.data = append(h.data, val)\n    // 下から上へヒープ化\n    h.siftUp(len(h.data) - 1)\n}\n\n/* ノード i から始めて、下から上へヒープ化 */\nfunc (h *maxHeap) siftUp(i int) {\n    for true {\n        // ノード i の親ノードを取得\n        p := h.parent(i)\n        // 「根ノードを越えた」または「ノードの修復が不要」になったらヒープ化を終了\n        if p &lt; 0 || h.data[i].(int) &lt;= h.data[p].(int) {\n            break\n        }\n        // 2 つのノードを交換\n        h.swap(i, p)\n        // ループで下から上へヒープ化\n        i = p\n    }\n}\n</code></pre> my_heap.swift<pre><code>/* 要素をヒープに追加 */\nfunc push(val: Int) {\n    // ノードを追加\n    maxHeap.append(val)\n    // 下から上へヒープ化\n    siftUp(i: size() - 1)\n}\n\n/* ノード i から始めて、下から上へヒープ化 */\nfunc siftUp(i: Int) {\n    var i = i\n    while true {\n        // ノード i の親ノードを取得\n        let p = parent(i: i)\n        // 「根ノードを越えた」または「ノードの修復が不要」になったらヒープ化を終了\n        if p &lt; 0 || maxHeap[i] &lt;= maxHeap[p] {\n            break\n        }\n        // 2 つのノードを交換\n        swap(i: i, j: p)\n        // ループで下から上へヒープ化\n        i = p\n    }\n}\n</code></pre> my_heap.js<pre><code>/* 要素をヒープに追加 */\npush(val) {\n    // ノードを追加\n    this.#maxHeap.push(val);\n    // 下から上へヒープ化\n    this.#siftUp(this.size() - 1);\n}\n\n/* ノード i から始めて、下から上へヒープ化 */\n#siftUp(i) {\n    while (true) {\n        // ノード i の親ノードを取得\n        const p = this.#parent(i);\n        // 「根ノードを越えた」または「ノードの修復が不要」になったらヒープ化を終了\n        if (p &lt; 0 || this.#maxHeap[i] &lt;= this.#maxHeap[p]) break;\n        // 2 つのノードを交換\n        this.#swap(i, p);\n        // ループで下から上へヒープ化\n        i = p;\n    }\n}\n</code></pre> my_heap.ts<pre><code>/* 要素をヒープに追加 */\npush(val: number): void {\n    // ノードを追加\n    this.maxHeap.push(val);\n    // 下から上へヒープ化\n    this.siftUp(this.size() - 1);\n}\n\n/* ノード i から始めて、下から上へヒープ化 */\nsiftUp(i: number): void {\n    while (true) {\n        // ノード i の親ノードを取得\n        const p = this.parent(i);\n        // 「根ノードを越えた」または「ノードの修復が不要」になったらヒープ化を終了\n        if (p &lt; 0 || this.maxHeap[i] &lt;= this.maxHeap[p]) break;\n        // 2 つのノードを交換\n        this.swap(i, p);\n        // ループで下から上へヒープ化\n        i = p;\n    }\n}\n</code></pre> my_heap.dart<pre><code>/* 要素をヒープに追加 */\nvoid push(int val) {\n  // ノードを追加\n  _maxHeap.add(val);\n  // 下から上へヒープ化\n  siftUp(size() - 1);\n}\n\n/* ノード i から始めて、下から上へヒープ化 */\nvoid siftUp(int i) {\n  while (true) {\n    // ノード i の親ノードを取得\n    int p = _parent(i);\n    // 「根ノードを越えた」または「ノードの修復が不要」になったらヒープ化を終了\n    if (p &lt; 0 || _maxHeap[i] &lt;= _maxHeap[p]) {\n      break;\n    }\n    // 2 つのノードを交換\n    _swap(i, p);\n    // ループで下から上へヒープ化\n    i = p;\n  }\n}\n</code></pre> my_heap.rs<pre><code>/* 要素をヒープに追加 */\nfn push(&amp;mut self, val: i32) {\n    // ノードを追加\n    self.max_heap.push(val);\n    // 下から上へヒープ化\n    self.sift_up(self.size() - 1);\n}\n\n/* ノード i から始めて、下から上へヒープ化 */\nfn sift_up(&amp;mut self, mut i: usize) {\n    loop {\n        // ノード i はすでにヒープの先頭ノードなので、ヒープ化を終了する\n        if i == 0 {\n            break;\n        }\n        // ノード i の親ノードを取得\n        let p = Self::parent(i);\n        // 「ノードの修復が不要」になったら、ヒープ化を終了\n        if self.max_heap[i] &lt;= self.max_heap[p] {\n            break;\n        }\n        // 2 つのノードを交換\n        self.swap(i, p);\n        // ループで下から上へヒープ化\n        i = p;\n    }\n}\n</code></pre> my_heap.c<pre><code>/* 要素をヒープに追加 */\nvoid push(MaxHeap *maxHeap, int val) {\n    // 通常は、これほど多くのノードを追加すべきではない\n    if (maxHeap-&gt;size == MAX_SIZE) {\n        printf(\"heap is full!\");\n        return;\n    }\n    // ノードを追加\n    maxHeap-&gt;data[maxHeap-&gt;size] = val;\n    maxHeap-&gt;size++;\n\n    // 下から上へヒープ化\n    siftUp(maxHeap, maxHeap-&gt;size - 1);\n}\n\n/* ノード i から始めて、下から上へヒープ化 */\nvoid siftUp(MaxHeap *maxHeap, int i) {\n    while (true) {\n        // ノード i の親ノードを取得\n        int p = parent(maxHeap, i);\n        // 「根ノードを越えた」または「ノードの修復が不要」になったらヒープ化を終了\n        if (p &lt; 0 || maxHeap-&gt;data[i] &lt;= maxHeap-&gt;data[p]) {\n            break;\n        }\n        // 2 つのノードを交換\n        swap(maxHeap, i, p);\n        // ループで下から上へヒープ化\n        i = p;\n    }\n}\n</code></pre> my_heap.kt<pre><code>/* 要素をヒープに追加 */\nfun push(_val: Int) {\n    // ノードを追加\n    maxHeap.add(_val)\n    // 下から上へヒープ化\n    siftUp(size() - 1)\n}\n\n/* ノード i から始めて、下から上へヒープ化 */\nfun siftUp(it: Int) {\n    // Kotlin の関数引数は不変のため、一時変数を作成する\n    var i = it\n    while (true) {\n        // ノード i の親ノードを取得\n        val p = parent(i)\n        // 「根ノードを越えた」または「ノードの修復が不要」になったらヒープ化を終了\n        if (p &lt; 0 || maxHeap[i] &lt;= maxHeap[p]) break\n        // 2 つのノードを交換\n        swap(i, p)\n        // ループで下から上へヒープ化\n        i = p\n    }\n}\n</code></pre> my_heap.rb<pre><code>### 要素をヒープに挿入 ###\ndef push(val)\n  # ノードを追加\n  @max_heap &lt;&lt; val\n  # 下から上へヒープ化\n  sift_up(size - 1)\nend\n\n### ノード i から下から上へヒープ化 ###\ndef sift_up(i)\n  loop do\n    # ノード i の親ノードを取得\n    p = parent(i)\n    # 「根ノードを越えた」または「ノードの修復が不要」になったらヒープ化を終了\n    break if p &lt; 0 || @max_heap[i] &lt;= @max_heap[p]\n    # 2 つのノードを交換\n    swap(i, p)\n    # ループで下から上へヒープ化\n    i = p\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 8 章 &nbsp; ヒープ","8.1 &nbsp; ヒープ"],"tags":[]},{"location":"chapter_heap/heap/#4","level":3,"title":"4.   ヒープ頂点の要素を取り出す","text":"<p>ヒープ頂点の要素は二分木の根ノード、すなわちリストの先頭要素です。もし先頭要素をそのまま削除すると、二分木内のすべてのノードのインデックスが変化してしまい、その後のヒープ化による修復が困難になります。要素インデックスの変動をできるだけ小さくするため、次の手順を取ります。</p> <ol> <li>ヒープ頂点の要素とヒープ底の要素を交換する（根ノードと最も右の葉ノードを交換する）。</li> <li>交換後、ヒープ底をリストから削除する（すでに交換済みであるため、実際に削除されるのは元のヒープ頂点の要素であることに注意）。</li> <li>根ノードから開始し、**上から下へヒープ化**を行う。</li> </ol> <p>次の図のように、**「上から下へのヒープ化」の方向は「下から上へのヒープ化」と逆**です。根ノードの値を 2 つの子ノードと比較し、最大の子ノードと根ノードを交換します。その後、この操作を繰り返し、葉ノードを越えるか交換不要のノードに達した時点で終了します。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 8-4   ヒープ頂点の要素を取り出す手順 </p> <p>要素をヒープに追加する操作と同様に、ヒープ頂点の要素を取り出す操作の時間計算量も \\(O(\\log n)\\) です。コードは以下のとおりです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby my_heap.py<pre><code>def pop(self) -&gt; int:\n    \"\"\"要素をヒープから取り出す\"\"\"\n    # 空判定の処理\n    if self.is_empty():\n        raise IndexError(\"ヒープが空です\")\n    # 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n    self.swap(0, self.size() - 1)\n    # ノードを削除\n    val = self.max_heap.pop()\n    # 上から下へヒープ化\n    self.sift_down(0)\n    # ヒープ先頭要素を返す\n    return val\n\ndef sift_down(self, i: int):\n    \"\"\"ノード i から始めて、上から下へヒープ化\"\"\"\n    while True:\n        # ノード i, l, r のうち値が最大のノードを ma とする\n        l, r, ma = self.left(i), self.right(i), i\n        if l &lt; self.size() and self.max_heap[l] &gt; self.max_heap[ma]:\n            ma = l\n        if r &lt; self.size() and self.max_heap[r] &gt; self.max_heap[ma]:\n            ma = r\n        # ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n        if ma == i:\n            break\n        # 2 つのノードを交換\n        self.swap(i, ma)\n        # ループで上から下へヒープ化\n        i = ma\n</code></pre> my_heap.cpp<pre><code>/* 要素をヒープから取り出す */\nvoid pop() {\n    // 空判定の処理\n    if (isEmpty()) {\n        throw out_of_range(\"ヒープが空です\");\n    }\n    // 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n    swap(maxHeap[0], maxHeap[size() - 1]);\n    // ノードを削除\n    maxHeap.pop_back();\n    // 上から下へヒープ化\n    siftDown(0);\n}\n\n/* ノード i から始めて、上から下へヒープ化 */\nvoid siftDown(int i) {\n    while (true) {\n        // ノード i, l, r のうち値が最大のノードを ma とする\n        int l = left(i), r = right(i), ma = i;\n        if (l &lt; size() &amp;&amp; maxHeap[l] &gt; maxHeap[ma])\n            ma = l;\n        if (r &lt; size() &amp;&amp; maxHeap[r] &gt; maxHeap[ma])\n            ma = r;\n        // ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n        if (ma == i)\n            break;\n        swap(maxHeap[i], maxHeap[ma]);\n        // ループで上から下へヒープ化\n        i = ma;\n    }\n}\n</code></pre> my_heap.java<pre><code>/* 要素をヒープから取り出す */\nint pop() {\n    // 空判定の処理\n    if (isEmpty())\n        throw new IndexOutOfBoundsException();\n    // 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n    swap(0, size() - 1);\n    // ノードを削除\n    int val = maxHeap.remove(size() - 1);\n    // 上から下へヒープ化\n    siftDown(0);\n    // ヒープ先頭要素を返す\n    return val;\n}\n\n/* ノード i から始めて、上から下へヒープ化 */\nvoid siftDown(int i) {\n    while (true) {\n        // ノード i, l, r のうち値が最大のノードを ma とする\n        int l = left(i), r = right(i), ma = i;\n        if (l &lt; size() &amp;&amp; maxHeap.get(l) &gt; maxHeap.get(ma))\n            ma = l;\n        if (r &lt; size() &amp;&amp; maxHeap.get(r) &gt; maxHeap.get(ma))\n            ma = r;\n        // ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n        if (ma == i)\n            break;\n        // 2 つのノードを交換\n        swap(i, ma);\n        // ループで上から下へヒープ化\n        i = ma;\n    }\n}\n</code></pre> my_heap.cs<pre><code>/* 要素をヒープから取り出す */\nint Pop() {\n    // 空判定の処理\n    if (IsEmpty())\n        throw new IndexOutOfRangeException();\n    // 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n    Swap(0, Size() - 1);\n    // ノードを削除\n    int val = maxHeap.Last();\n    maxHeap.RemoveAt(Size() - 1);\n    // 上から下へヒープ化\n    SiftDown(0);\n    // ヒープ先頭要素を返す\n    return val;\n}\n\n/* ノード i から始めて、上から下へヒープ化 */\nvoid SiftDown(int i) {\n    while (true) {\n        // ノード i, l, r のうち値が最大のノードを ma とする\n        int l = Left(i), r = Right(i), ma = i;\n        if (l &lt; Size() &amp;&amp; maxHeap[l] &gt; maxHeap[ma])\n            ma = l;\n        if (r &lt; Size() &amp;&amp; maxHeap[r] &gt; maxHeap[ma])\n            ma = r;\n        // 「ノード i が最大」または「葉ノードを越えた」場合は、ヒープ化を終了する\n        if (ma == i) break;\n        // 2 つのノードを交換\n        Swap(i, ma);\n        // ループで上から下へヒープ化\n        i = ma;\n    }\n}\n</code></pre> my_heap.go<pre><code>/* 要素をヒープから取り出す */\nfunc (h *maxHeap) pop() any {\n    // 空判定の処理\n    if h.isEmpty() {\n        fmt.Println(\"error\")\n        return nil\n    }\n    // 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n    h.swap(0, h.size()-1)\n    // ノードを削除\n    val := h.data[len(h.data)-1]\n    h.data = h.data[:len(h.data)-1]\n    // 上から下へヒープ化\n    h.siftDown(0)\n\n    // ヒープ先頭要素を返す\n    return val\n}\n\n/* ノード i から始めて、上から下へヒープ化 */\nfunc (h *maxHeap) siftDown(i int) {\n    for true {\n        // ノード i, l, r のうち値が最大のノードを max とする\n        l, r, max := h.left(i), h.right(i), i\n        if l &lt; h.size() &amp;&amp; h.data[l].(int) &gt; h.data[max].(int) {\n            max = l\n        }\n        if r &lt; h.size() &amp;&amp; h.data[r].(int) &gt; h.data[max].(int) {\n            max = r\n        }\n        // ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n        if max == i {\n            break\n        }\n        // 2 つのノードを交換\n        h.swap(i, max)\n        // ループで上から下へヒープ化\n        i = max\n    }\n}\n</code></pre> my_heap.swift<pre><code>/* 要素をヒープから取り出す */\nfunc pop() -&gt; Int {\n    // 空判定の処理\n    if isEmpty() {\n        fatalError(\"ヒープが空です\")\n    }\n    // 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n    swap(i: 0, j: size() - 1)\n    // ノードを削除\n    let val = maxHeap.remove(at: size() - 1)\n    // 上から下へヒープ化\n    siftDown(i: 0)\n    // ヒープ先頭要素を返す\n    return val\n}\n\n/* ノード i から始めて、上から下へヒープ化 */\nfunc siftDown(i: Int) {\n    var i = i\n    while true {\n        // ノード i, l, r のうち値が最大のノードを ma とする\n        let l = left(i: i)\n        let r = right(i: i)\n        var ma = i\n        if l &lt; size(), maxHeap[l] &gt; maxHeap[ma] {\n            ma = l\n        }\n        if r &lt; size(), maxHeap[r] &gt; maxHeap[ma] {\n            ma = r\n        }\n        // ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n        if ma == i {\n            break\n        }\n        // 2 つのノードを交換\n        swap(i: i, j: ma)\n        // ループで上から下へヒープ化\n        i = ma\n    }\n}\n</code></pre> my_heap.js<pre><code>/* 要素をヒープから取り出す */\npop() {\n    // 空判定の処理\n    if (this.isEmpty()) throw new Error('ヒープが空です');\n    // 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n    this.#swap(0, this.size() - 1);\n    // ノードを削除\n    const val = this.#maxHeap.pop();\n    // 上から下へヒープ化\n    this.#siftDown(0);\n    // ヒープ先頭要素を返す\n    return val;\n}\n\n/* ノード i から始めて、上から下へヒープ化 */\n#siftDown(i) {\n    while (true) {\n        // ノード i, l, r のうち値が最大のノードを ma とする\n        const l = this.#left(i),\n            r = this.#right(i);\n        let ma = i;\n        if (l &lt; this.size() &amp;&amp; this.#maxHeap[l] &gt; this.#maxHeap[ma]) ma = l;\n        if (r &lt; this.size() &amp;&amp; this.#maxHeap[r] &gt; this.#maxHeap[ma]) ma = r;\n        // ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n        if (ma === i) break;\n        // 2 つのノードを交換\n        this.#swap(i, ma);\n        // ループで上から下へヒープ化\n        i = ma;\n    }\n}\n</code></pre> my_heap.ts<pre><code>/* 要素をヒープから取り出す */\npop(): number {\n    // 空判定の処理\n    if (this.isEmpty()) throw new RangeError('Heap is empty.');\n    // 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n    this.swap(0, this.size() - 1);\n    // ノードを削除\n    const val = this.maxHeap.pop();\n    // 上から下へヒープ化\n    this.siftDown(0);\n    // ヒープ先頭要素を返す\n    return val;\n}\n\n/* ノード i から始めて、上から下へヒープ化 */\nsiftDown(i: number): void {\n    while (true) {\n        // ノード i, l, r のうち値が最大のノードを ma とする\n        const l = this.left(i),\n            r = this.right(i);\n        let ma = i;\n        if (l &lt; this.size() &amp;&amp; this.maxHeap[l] &gt; this.maxHeap[ma]) ma = l;\n        if (r &lt; this.size() &amp;&amp; this.maxHeap[r] &gt; this.maxHeap[ma]) ma = r;\n        // ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n        if (ma === i) break;\n        // 2 つのノードを交換\n        this.swap(i, ma);\n        // ループで上から下へヒープ化\n        i = ma;\n    }\n}\n</code></pre> my_heap.dart<pre><code>/* 要素をヒープから取り出す */\nint pop() {\n  // 空判定の処理\n  if (isEmpty()) throw Exception('ヒープが空です');\n  // 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n  _swap(0, size() - 1);\n  // ノードを削除\n  int val = _maxHeap.removeLast();\n  // 上から下へヒープ化\n  siftDown(0);\n  // ヒープ先頭要素を返す\n  return val;\n}\n\n/* ノード i から始めて、上から下へヒープ化 */\nvoid siftDown(int i) {\n  while (true) {\n    // ノード i, l, r のうち値が最大のノードを ma とする\n    int l = _left(i);\n    int r = _right(i);\n    int ma = i;\n    if (l &lt; size() &amp;&amp; _maxHeap[l] &gt; _maxHeap[ma]) ma = l;\n    if (r &lt; size() &amp;&amp; _maxHeap[r] &gt; _maxHeap[ma]) ma = r;\n    // ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n    if (ma == i) break;\n    // 2 つのノードを交換\n    _swap(i, ma);\n    // ループで上から下へヒープ化\n    i = ma;\n  }\n}\n</code></pre> my_heap.rs<pre><code>/* 要素をヒープから取り出す */\nfn pop(&amp;mut self) -&gt; i32 {\n    // 空判定の処理\n    if self.is_empty() {\n        panic!(\"index out of bounds\");\n    }\n    // 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n    self.swap(0, self.size() - 1);\n    // ノードを削除\n    let val = self.max_heap.pop().unwrap();\n    // 上から下へヒープ化\n    self.sift_down(0);\n    // ヒープ先頭要素を返す\n    val\n}\n\n/* ノード i から始めて、上から下へヒープ化 */\nfn sift_down(&amp;mut self, mut i: usize) {\n    loop {\n        // ノード i, l, r のうち値が最大のノードを ma とする\n        let (l, r, mut ma) = (Self::left(i), Self::right(i), i);\n        if l &lt; self.size() &amp;&amp; self.max_heap[l] &gt; self.max_heap[ma] {\n            ma = l;\n        }\n        if r &lt; self.size() &amp;&amp; self.max_heap[r] &gt; self.max_heap[ma] {\n            ma = r;\n        }\n        // ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n        if ma == i {\n            break;\n        }\n        // 2 つのノードを交換\n        self.swap(i, ma);\n        // ループで上から下へヒープ化\n        i = ma;\n    }\n}\n</code></pre> my_heap.c<pre><code>/* 要素をヒープから取り出す */\nint pop(MaxHeap *maxHeap) {\n    // 空判定の処理\n    if (isEmpty(maxHeap)) {\n        printf(\"heap is empty!\");\n        return INT_MAX;\n    }\n    // 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n    swap(maxHeap, 0, size(maxHeap) - 1);\n    // ノードを削除\n    int val = maxHeap-&gt;data[maxHeap-&gt;size - 1];\n    maxHeap-&gt;size--;\n    // 上から下へヒープ化\n    siftDown(maxHeap, 0);\n\n    // ヒープ先頭要素を返す\n    return val;\n}\n\n/* ノード i から始めて、上から下へヒープ化 */\nvoid siftDown(MaxHeap *maxHeap, int i) {\n    while (true) {\n        // ノード i, l, r のうち値が最大のノードを max とする\n        int l = left(maxHeap, i);\n        int r = right(maxHeap, i);\n        int max = i;\n        if (l &lt; size(maxHeap) &amp;&amp; maxHeap-&gt;data[l] &gt; maxHeap-&gt;data[max]) {\n            max = l;\n        }\n        if (r &lt; size(maxHeap) &amp;&amp; maxHeap-&gt;data[r] &gt; maxHeap-&gt;data[max]) {\n            max = r;\n        }\n        // ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n        if (max == i) {\n            break;\n        }\n        // 2 つのノードを交換\n        swap(maxHeap, i, max);\n        // ループで上から下へヒープ化\n        i = max;\n    }\n}\n</code></pre> my_heap.kt<pre><code>/* 要素をヒープから取り出す */\nfun pop(): Int {\n    // 空判定の処理\n    if (isEmpty()) throw IndexOutOfBoundsException()\n    // 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n    swap(0, size() - 1)\n    // ノードを削除\n    val _val = maxHeap.removeAt(size() - 1)\n    // 上から下へヒープ化\n    siftDown(0)\n    // ヒープ先頭要素を返す\n    return _val\n}\n\n/* ノード i から始めて、上から下へヒープ化 */\nfun siftDown(it: Int) {\n    // Kotlin の関数引数は不変のため、一時変数を作成する\n    var i = it\n    while (true) {\n        // ノード i, l, r のうち値が最大のノードを ma とする\n        val l = left(i)\n        val r = right(i)\n        var ma = i\n        if (l &lt; size() &amp;&amp; maxHeap[l] &gt; maxHeap[ma]) ma = l\n        if (r &lt; size() &amp;&amp; maxHeap[r] &gt; maxHeap[ma]) ma = r\n        // ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n        if (ma == i) break\n        // 2 つのノードを交換\n        swap(i, ma)\n        // ループで上から下へヒープ化\n        i = ma\n    }\n}\n</code></pre> my_heap.rb<pre><code>### 要素をヒープから取り出す ###\ndef pop\n  # 空判定の処理\n  raise IndexError, \"ヒープが空です\" if is_empty?\n  # 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n  swap(0, size - 1)\n  # ノードを削除\n  val = @max_heap.pop\n  # 上から下へヒープ化\n  sift_down(0)\n  # ヒープ先頭要素を返す\n  val\nend\n\n### ノード i から上から下へヒープ化 ###\ndef sift_down(i)\n  loop do\n    # ノード i, l, r のうち値が最大のノードを ma とする\n    l, r, ma = left(i), right(i), i\n    ma = l if l &lt; size &amp;&amp; @max_heap[l] &gt; @max_heap[ma]\n    ma = r if r &lt; size &amp;&amp; @max_heap[r] &gt; @max_heap[ma]\n\n    # ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n    break if ma == i\n\n    # 2 つのノードを交換\n    swap(i, ma)\n    # ループで上から下へヒープ化\n    i = ma\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 8 章 &nbsp; ヒープ","8.1 &nbsp; ヒープ"],"tags":[]},{"location":"chapter_heap/heap/#813","level":2,"title":"8.1.3   ヒープの代表的な応用","text":"<ul> <li>優先度付きキュー：ヒープは、優先度付きキューを実装するための代表的なデータ構造です。キューへの追加と取り出しの時間計算量はいずれも \\(O(\\log n)\\) で、ヒープ構築は \\(O(n)\\) であり、これらの操作はいずれも非常に効率的です。</li> <li>ヒープソート：与えられたデータ群からヒープを構築し、要素の取り出しを繰り返すことで整列済みデータを得られます。ただし、通常はより洗練された方法でヒープソートを実装します。詳しくは「ヒープソート」の章を参照してください。</li> <li>最大の \\(k\\) 個の要素を取得：これは古典的なアルゴリズム問題であると同時に、典型的な応用でもあります。たとえば、人気上位 10 件のニュースをホットトピックとして選んだり、売上上位 10 件の商品を選んだりする場面です。</li> </ul>","path":["第 8 章 &nbsp; ヒープ","8.1 &nbsp; ヒープ"],"tags":[]},{"location":"chapter_heap/summary/","level":1,"title":"8.4   まとめ","text":"","path":["第 8 章 &nbsp; ヒープ","8.4 &nbsp; まとめ"],"tags":[]},{"location":"chapter_heap/summary/#1","level":3,"title":"1.   重要なポイントの振り返り","text":"<ul> <li>ヒープは完全二分木であり、条件の違いによって最大ヒープと最小ヒープに分けられる。最大（最小）ヒープの根の要素は最大値（最小値）である。</li> <li>優先度付きキューとは、取り出し時に優先度が考慮されるキューであり、通常はヒープを用いて実装される。</li> <li>ヒープの代表的な操作とそれに対応する時間計算量には、要素の挿入 \\(O(\\log n)\\)、根の要素の削除 \\(O(\\log n)\\)、根の要素へのアクセス \\(O(1)\\) などがある。</li> <li>完全二分木は配列で表現するのに非常に適しているため、通常は配列を使ってヒープを格納する。</li> <li>ヒープ化操作はヒープの性質を保つために用いられ、挿入操作と削除操作の両方で使用される。</li> <li>\\(n\\) 個の要素を入力してヒープを構築する時間計算量は \\(O(n)\\) まで最適化でき、非常に効率的である。</li> <li>Top-k は古典的なアルゴリズム問題であり、ヒープ構造を用いることで効率的に解くことができ、時間計算量は \\(O(n \\log k)\\) である。</li> </ul>","path":["第 8 章 &nbsp; ヒープ","8.4 &nbsp; まとめ"],"tags":[]},{"location":"chapter_heap/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q：データ構造の「ヒープ」とメモリ管理の「ヒープ」は同じ概念ですか？</p> <p>両者は同じ概念ではなく、たまたまどちらも「ヒープ」と呼ばれているだけである。コンピュータシステムのメモリにおけるヒープは動的メモリ割り当ての一部であり、プログラムは実行時にこれを使ってデータを格納できる。プログラムは一定量のヒープメモリを要求し、オブジェクトや配列などの複雑な構造を保存できる。これらのデータが不要になったときは、メモリリークを防ぐためにそのメモリを解放する必要がある。スタックメモリと比べると、ヒープメモリの管理と使用にはより慎重さが求められ、不適切に扱うとメモリリークやダングリングポインタなどの問題を引き起こす可能性がある。</p>","path":["第 8 章 &nbsp; ヒープ","8.4 &nbsp; まとめ"],"tags":[]},{"location":"chapter_heap/top_k/","level":1,"title":"8.3   Top-k 問題","text":"<p>Question</p> <p>長さ \\(n\\) の未整列配列 <code>nums</code> が与えられたとき、配列内で最大の \\(k\\) 個の要素を返してください。</p> <p>この問題について、まずは発想が比較的直接的な 2 つの解法を紹介し、その後でより効率の高いヒープ解法を紹介します。</p>","path":["第 8 章 &nbsp; ヒープ","8.3 &nbsp; Top-k 問題"],"tags":[]},{"location":"chapter_heap/top_k/#831","level":2,"title":"8.3.1   方法一：走査による選択","text":"<p>以下の図に示すように \\(k\\) 回の走査を行い、各ラウンドでそれぞれ第 \\(1\\)、\\(2\\)、\\(\\dots\\)、\\(k\\) 位の要素を取り出すことができます。時間計算量は \\(O(nk)\\) です。</p> <p>この方法は \\(k \\ll n\\) の場合にしか適していません。\\(k\\) が \\(n\\) にかなり近いと、時間計算量は \\(O(n^2)\\) に近づき、非常に時間がかかるためです。</p> <p></p> <p> 図 8-6   走査によって最大の k 個の要素を探す </p> <p>Tip</p> <p>\\(k = n\\) のとき、完全な昇順列を得ることができ、この場合は「選択ソート」アルゴリズムと等価になります。</p>","path":["第 8 章 &nbsp; ヒープ","8.3 &nbsp; Top-k 問題"],"tags":[]},{"location":"chapter_heap/top_k/#832","level":2,"title":"8.3.2   方法二：ソート","text":"<p>以下の図に示すように、まず配列 <code>nums</code> をソートし、その後で右端の \\(k\\) 個の要素を返すことができます。時間計算量は \\(O(n \\log n)\\) です。</p> <p>明らかに、この方法は必要以上の処理を行っています。なぜなら、必要なのは最大の \\(k\\) 個の要素を見つけることだけであり、他の要素をソートする必要はないからです。</p> <p></p> <p> 図 8-7   ソートによって最大の k 個の要素を探す </p>","path":["第 8 章 &nbsp; ヒープ","8.3 &nbsp; Top-k 問題"],"tags":[]},{"location":"chapter_heap/top_k/#833","level":2,"title":"8.3.3   方法三：ヒープ","text":"<p>ヒープを用いることで、Top-k 問題をより効率的に解くことができます。手順は以下の図のとおりです。</p> <ol> <li>最小ヒープを初期化し、そのヒープ頂点の要素が最小となるようにします。</li> <li>まず配列の先頭 \\(k\\) 個の要素を順にヒープへ挿入します。</li> <li>\\(k + 1\\) 番目の要素から開始し、現在の要素がヒープ頂点の要素より大きければ、ヒープ頂点の要素を取り出し、現在の要素をヒープへ挿入します。</li> <li>走査が完了した後、ヒープに保持されているのが最大の \\(k\\) 個の要素です。</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 8-8   ヒープに基づいて最大の k 個の要素を探す </p> <p>サンプルコードは以下のとおりです。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby top_k.py<pre><code>def top_k_heap(nums: list[int], k: int) -&gt; list[int]:\n    \"\"\"ヒープに基づいて配列中の最大の k 個の要素を探す\"\"\"\n    # 最小ヒープを初期化\n    heap = []\n    # 配列の先頭 k 個の要素をヒープに追加\n    for i in range(k):\n        heapq.heappush(heap, nums[i])\n    # k+1 番目の要素から開始し、ヒープ長を k に保つ\n    for i in range(k, len(nums)):\n        # 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する\n        if nums[i] &gt; heap[0]:\n            heapq.heappop(heap)\n            heapq.heappush(heap, nums[i])\n    return heap\n</code></pre> top_k.cpp<pre><code>/* ヒープに基づいて配列中の最大の k 個の要素を探す */\npriority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; topKHeap(vector&lt;int&gt; &amp;nums, int k) {\n    // 最小ヒープを初期化\n    priority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; heap;\n    // 配列の先頭 k 個の要素をヒープに追加\n    for (int i = 0; i &lt; k; i++) {\n        heap.push(nums[i]);\n    }\n    // k+1 番目の要素から開始し、ヒープ長を k に保つ\n    for (int i = k; i &lt; nums.size(); i++) {\n        // 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する\n        if (nums[i] &gt; heap.top()) {\n            heap.pop();\n            heap.push(nums[i]);\n        }\n    }\n    return heap;\n}\n</code></pre> top_k.java<pre><code>/* ヒープに基づいて配列中の最大の k 個の要素を探す */\nQueue&lt;Integer&gt; topKHeap(int[] nums, int k) {\n    // 最小ヒープを初期化\n    Queue&lt;Integer&gt; heap = new PriorityQueue&lt;Integer&gt;();\n    // 配列の先頭 k 個の要素をヒープに追加\n    for (int i = 0; i &lt; k; i++) {\n        heap.offer(nums[i]);\n    }\n    // k+1 番目の要素から開始し、ヒープ長を k に保つ\n    for (int i = k; i &lt; nums.length; i++) {\n        // 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する\n        if (nums[i] &gt; heap.peek()) {\n            heap.poll();\n            heap.offer(nums[i]);\n        }\n    }\n    return heap;\n}\n</code></pre> top_k.cs<pre><code>/* ヒープに基づいて配列中の最大の k 個の要素を探す */\nPriorityQueue&lt;int, int&gt; TopKHeap(int[] nums, int k) {\n    // 最小ヒープを初期化\n    PriorityQueue&lt;int, int&gt; heap = new();\n    // 配列の先頭 k 個の要素をヒープに追加\n    for (int i = 0; i &lt; k; i++) {\n        heap.Enqueue(nums[i], nums[i]);\n    }\n    // k+1 番目の要素から開始し、ヒープ長を k に保つ\n    for (int i = k; i &lt; nums.Length; i++) {\n        // 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する\n        if (nums[i] &gt; heap.Peek()) {\n            heap.Dequeue();\n            heap.Enqueue(nums[i], nums[i]);\n        }\n    }\n    return heap;\n}\n</code></pre> top_k.go<pre><code>/* ヒープに基づいて配列中の最大の k 個の要素を探す */\nfunc topKHeap(nums []int, k int) *minHeap {\n    // 最小ヒープを初期化\n    h := &amp;minHeap{}\n    heap.Init(h)\n    // 配列の先頭 k 個の要素をヒープに追加\n    for i := 0; i &lt; k; i++ {\n        heap.Push(h, nums[i])\n    }\n    // k+1 番目の要素から開始し、ヒープ長を k に保つ\n    for i := k; i &lt; len(nums); i++ {\n        // 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する\n        if nums[i] &gt; h.Top().(int) {\n            heap.Pop(h)\n            heap.Push(h, nums[i])\n        }\n    }\n    return h\n}\n</code></pre> top_k.swift<pre><code>/* ヒープに基づいて配列中の最大の k 個の要素を探す */\nfunc topKHeap(nums: [Int], k: Int) -&gt; [Int] {\n    // 最小ヒープを初期化し、先頭 k 個の要素でヒープを構築する\n    var heap = Heap(nums.prefix(k))\n    // k+1 番目の要素から開始し、ヒープ長を k に保つ\n    for i in nums.indices.dropFirst(k) {\n        // 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する\n        if nums[i] &gt; heap.min()! {\n            _ = heap.removeMin()\n            heap.insert(nums[i])\n        }\n    }\n    return heap.unordered\n}\n</code></pre> top_k.js<pre><code>/* 要素をヒープに追加 */\nfunction pushMinHeap(maxHeap, val) {\n    // 要素を反転する\n    maxHeap.push(-val);\n}\n\n/* 要素をヒープから取り出す */\nfunction popMinHeap(maxHeap) {\n    // 要素を反転する\n    return -maxHeap.pop();\n}\n\n/* ヒープ先頭要素にアクセス */\nfunction peekMinHeap(maxHeap) {\n    // 要素を反転する\n    return -maxHeap.peek();\n}\n\n/* ヒープから要素を取り出す */\nfunction getMinHeap(maxHeap) {\n    // 要素を反転する\n    return maxHeap.getMaxHeap().map((num) =&gt; -num);\n}\n\n/* ヒープに基づいて配列中の最大の k 個の要素を探す */\nfunction topKHeap(nums, k) {\n    // 最小ヒープを初期化する\n    // 注意: ヒープ内の全要素を反転し、最大ヒープで最小ヒープをシミュレートする\n    const maxHeap = new MaxHeap([]);\n    // 配列の先頭 k 個の要素をヒープに追加\n    for (let i = 0; i &lt; k; i++) {\n        pushMinHeap(maxHeap, nums[i]);\n    }\n    // k+1 番目の要素から開始し、ヒープ長を k に保つ\n    for (let i = k; i &lt; nums.length; i++) {\n        // 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する\n        if (nums[i] &gt; peekMinHeap(maxHeap)) {\n            popMinHeap(maxHeap);\n            pushMinHeap(maxHeap, nums[i]);\n        }\n    }\n    // ヒープ内の要素を返す\n    return getMinHeap(maxHeap);\n}\n</code></pre> top_k.ts<pre><code>/* 要素をヒープに追加 */\nfunction pushMinHeap(maxHeap: MaxHeap, val: number): void {\n    // 要素を反転する\n    maxHeap.push(-val);\n}\n\n/* 要素をヒープから取り出す */\nfunction popMinHeap(maxHeap: MaxHeap): number {\n    // 要素を反転する\n    return -maxHeap.pop();\n}\n\n/* ヒープ先頭要素にアクセス */\nfunction peekMinHeap(maxHeap: MaxHeap): number {\n    // 要素を反転する\n    return -maxHeap.peek();\n}\n\n/* ヒープから要素を取り出す */\nfunction getMinHeap(maxHeap: MaxHeap): number[] {\n    // 要素を反転する\n    return maxHeap.getMaxHeap().map((num: number) =&gt; -num);\n}\n\n/* ヒープに基づいて配列中の最大の k 個の要素を探す */\nfunction topKHeap(nums: number[], k: number): number[] {\n    // 最小ヒープを初期化する\n    // 注意: ヒープ内の全要素を反転し、最大ヒープで最小ヒープをシミュレートする\n    const maxHeap = new MaxHeap([]);\n    // 配列の先頭 k 個の要素をヒープに追加\n    for (let i = 0; i &lt; k; i++) {\n        pushMinHeap(maxHeap, nums[i]);\n    }\n    // k+1 番目の要素から開始し、ヒープ長を k に保つ\n    for (let i = k; i &lt; nums.length; i++) {\n        // 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する\n        if (nums[i] &gt; peekMinHeap(maxHeap)) {\n            popMinHeap(maxHeap);\n            pushMinHeap(maxHeap, nums[i]);\n        }\n    }\n    // ヒープ内の要素を返す\n    return getMinHeap(maxHeap);\n}\n</code></pre> top_k.dart<pre><code>/* ヒープに基づいて配列中の最大の k 個の要素を探す */\nMinHeap topKHeap(List&lt;int&gt; nums, int k) {\n  // 最小ヒープを初期化し、配列の先頭 k 個の要素をヒープに入れる\n  MinHeap heap = MinHeap(nums.sublist(0, k));\n  // k+1 番目の要素から開始し、ヒープ長を k に保つ\n  for (int i = k; i &lt; nums.length; i++) {\n    // 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する\n    if (nums[i] &gt; heap.peek()) {\n      heap.pop();\n      heap.push(nums[i]);\n    }\n  }\n  return heap;\n}\n</code></pre> top_k.rs<pre><code>/* ヒープに基づいて配列中の最大の k 個の要素を探す */\nfn top_k_heap(nums: Vec&lt;i32&gt;, k: usize) -&gt; BinaryHeap&lt;Reverse&lt;i32&gt;&gt; {\n    // BinaryHeap は最大ヒープであり、Reverse で要素の順序を反転することで最小ヒープを実現する\n    let mut heap = BinaryHeap::&lt;Reverse&lt;i32&gt;&gt;::new();\n    // 配列の先頭 k 個の要素をヒープに追加\n    for &amp;num in nums.iter().take(k) {\n        heap.push(Reverse(num));\n    }\n    // k+1 番目の要素から開始し、ヒープ長を k に保つ\n    for &amp;num in nums.iter().skip(k) {\n        // 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する\n        if num &gt; heap.peek().unwrap().0 {\n            heap.pop();\n            heap.push(Reverse(num));\n        }\n    }\n    heap\n}\n</code></pre> top_k.c<pre><code>/* 要素をヒープに追加 */\nvoid pushMinHeap(MaxHeap *maxHeap, int val) {\n    // 要素を反転する\n    push(maxHeap, -val);\n}\n\n/* 要素をヒープから取り出す */\nint popMinHeap(MaxHeap *maxHeap) {\n    // 要素を反転する\n    return -pop(maxHeap);\n}\n\n/* ヒープ先頭要素にアクセス */\nint peekMinHeap(MaxHeap *maxHeap) {\n    // 要素を反転する\n    return -peek(maxHeap);\n}\n\n/* ヒープから要素を取り出す */\nint *getMinHeap(MaxHeap *maxHeap) {\n    // ヒープ内のすべての要素を反転して res 配列に格納\n    int *res = (int *)malloc(maxHeap-&gt;size * sizeof(int));\n    for (int i = 0; i &lt; maxHeap-&gt;size; i++) {\n        res[i] = -maxHeap-&gt;data[i];\n    }\n    return res;\n}\n\n/* ヒープから要素を取り出す */\nint *getMinHeap(MaxHeap *maxHeap) {\n    // ヒープ内のすべての要素を反転して res 配列に格納\n    int *res = (int *)malloc(maxHeap-&gt;size * sizeof(int));\n    for (int i = 0; i &lt; maxHeap-&gt;size; i++) {\n        res[i] = -maxHeap-&gt;data[i];\n    }\n    return res;\n}\n\n// ヒープに基づいて配列中の最大の k 個の要素を求める関数\nint *topKHeap(int *nums, int sizeNums, int k) {\n    // 最小ヒープを初期化する\n    // 注意: ヒープ内の全要素を反転し、最大ヒープで最小ヒープをシミュレートする\n    int *empty = (int *)malloc(0);\n    MaxHeap *maxHeap = newMaxHeap(empty, 0);\n    // 配列の先頭 k 個の要素をヒープに追加\n    for (int i = 0; i &lt; k; i++) {\n        pushMinHeap(maxHeap, nums[i]);\n    }\n    // k+1 番目の要素から開始し、ヒープ長を k に保つ\n    for (int i = k; i &lt; sizeNums; i++) {\n        // 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する\n        if (nums[i] &gt; peekMinHeap(maxHeap)) {\n            popMinHeap(maxHeap);\n            pushMinHeap(maxHeap, nums[i]);\n        }\n    }\n    int *res = getMinHeap(maxHeap);\n    // メモリを解放する\n    delMaxHeap(maxHeap);\n    return res;\n}\n</code></pre> top_k.kt<pre><code>/* ヒープに基づいて配列中の最大の k 個の要素を探す */\nfun topKHeap(nums: IntArray, k: Int): Queue&lt;Int&gt; {\n    // 最小ヒープを初期化\n    val heap = PriorityQueue&lt;Int&gt;()\n    // 配列の先頭 k 個の要素をヒープに追加\n    for (i in 0..&lt;k) {\n        heap.offer(nums[i])\n    }\n    // k+1 番目の要素から開始し、ヒープ長を k に保つ\n    for (i in k..&lt;nums.size) {\n        // 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する\n        if (nums[i] &gt; heap.peek()) {\n            heap.poll()\n            heap.offer(nums[i])\n        }\n    }\n    return heap\n}\n</code></pre> top_k.rb<pre><code>### ヒープに基づいて配列中の最大 k 個の要素を探す ###\ndef top_k_heap(nums, k)\n  # 最小ヒープを初期化する\n  # 注意: ヒープ内の全要素を反転し、最大ヒープで最小ヒープをシミュレートする\n  max_heap = MaxHeap.new([])\n\n  # 配列の先頭 k 個の要素をヒープに追加\n  for i in 0...k\n    push_min_heap(max_heap, nums[i])\n  end\n\n  # k+1 番目の要素から開始し、ヒープ長を k に保つ\n  for i in k...nums.length\n    # 現在の要素がヒープ先頭より大きければ、ヒープ先頭を取り出して現在の要素を追加する\n    if nums[i] &gt; peek_min_heap(max_heap)\n      pop_min_heap(max_heap)\n      push_min_heap(max_heap, nums[i])\n    end\n  end\n\n  get_min_heap(max_heap)\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>合計で \\(n\\) 回のヒープ挿入と取り出しを行い、ヒープの最大長は \\(k\\) であるため、時間計算量は \\(O(n \\log k)\\) です。この方法は非常に効率が高く、\\(k\\) が小さいときは時間計算量が \\(O(n)\\) に近づき、\\(k\\) が大きいときでも \\(O(n \\log n)\\) を超えることはありません。</p> <p>さらに、この方法は動的データストリームの利用シーンにも適しています。データが継続的に追加される場合でも、ヒープ内の要素を保ち続けることで、最大の \\(k\\) 個の要素を動的に更新できます。</p>","path":["第 8 章 &nbsp; ヒープ","8.3 &nbsp; Top-k 問題"],"tags":[]},{"location":"chapter_hello_algo/","level":1,"title":"はじめに","text":"<p>数年前、私は LeetCode 中国版で「剣指 Offer」シリーズの解説を共有し、多くの読者から励ましと支持をいただきました。読者との交流の中で、最もよく聞かれた質問の一つが「アルゴリズムをどう学び始めればよいか」でした。次第に、私はこの問題に強い関心を抱くようになりました。</p> <p>手探りでひたすら問題を解くことは、最も人気のある方法のようです。単純で、直接的で、しかも効果的です。しかし問題演習は「マインスイーパー」を遊ぶことに似ており、独学力の高い人は地雷を一つずつうまく取り除ける一方で、基礎が十分でない人は大きな痛手を受け、挫折の中で少しずつ後退してしまいがちです。教材を通読するのもよくある方法ですが、就職を目指す人にとっては、卒業論文、履歴書の提出、筆記試験や面接の準備ですでに大半の力を使い果たしており、分厚い本を読み込むことはしばしば困難な挑戦になってしまいます。</p> <p>もしあなたも同じような悩みを抱えているなら、この本があなたのもとに“たどり着いた”のは幸運なことです。本書は、この問いに対して私が示す答えです。たとえ最良の解ではなくても、少なくとも前向きな試みではあります。本書だけで直接内定を得られるわけではありませんが、データ構造とアルゴリズムの「知識地図」を探る手助けをし、さまざまな「地雷」の形や大きさ、分布を理解し、いろいろな「地雷除去の方法」を身につけられるよう導きます。こうした力があれば、問題演習や文献読解をより自在に進め、やがて完整な知識体系を築いていけると信じています。</p> <p>私はファインマン教授の言葉に深く賛同しています。「Knowledge isn't free. You have to pay attention.」この意味において、本書は完全に「無料」ではありません。本書のためにあなたが払ってくれる貴重な「注意」に応えるため、私はできる限りの力を尽くし、最大限の「注意」を注いで本書を書き上げます。</p> <p>私は自らの学識と力量の浅さをよく承知しています。本書の内容はある程度磨きをかけてきたものの、なお多くの誤りが残っているはずです。先生方、そして学習者の皆さまからのご批判とご指摘を心よりお願いいたします。</p> <p></p> Hello、アルゴリズム！ <p>コンピュータの登場は世界に大きな変革をもたらしました。高速な計算能力と優れたプログラム可能性によって、アルゴリズムの実行とデータ処理の理想的な媒体となったのです。ビデオゲームのリアルな映像、自動運転の知的な意思決定、AlphaGo の見事な対局、ChatGPT の自然な対話に至るまで、これらの応用はいずれもコンピュータ上でアルゴリズムが巧みに表現されたものです。</p> <p>実際には、コンピュータが誕生する以前から、アルゴリズムとデータ構造は世界のいたるところに存在していました。初期のアルゴリズムは比較的単純で、たとえば古代の数え方や道具作りの手順などがそれに当たります。文明の進歩とともに、アルゴリズムは次第により精緻で複雑なものになっていきました。匠の巧みな技から、生産力を解放する工業製品、さらには宇宙の運行を支配する科学法則に至るまで、ほとんどあらゆる平凡なもの、あるいは驚嘆すべきものの背後には、精妙なアルゴリズムの思想が潜んでいます。</p> <p>同様に、データ構造も至るところに存在します。社会ネットワークのような大きなものから地下鉄路線のような小さなものまで、多くのシステムは「グラフ」としてモデル化できます。国家のような大きな単位から家庭のような小さな単位まで、社会の主な組織形態には「木」の特徴があります。冬服は「スタック」のように、最初に着たものが最後に脱がれます。バドミントンシャトルの筒は「キュー」のように、一方から入れて他方から取り出します。辞書は「ハッシュテーブル」のようなもので、目的の見出し語を素早く探せます。</p> <p>本書は、わかりやすいアニメーション図解と実行可能なコード例を通じて、読者がアルゴリズムとデータ構造の核心概念を理解し、さらにプログラミングによってそれらを実装できるようになることを目指しています。そのうえで、本書は複雑な世界の中にあるアルゴリズムの生き生きとした現れを明らかにし、アルゴリズムの美しさを示そうとしています。本書があなたの助けになれば幸いです。</p>","path":["はじめに"],"tags":[]},{"location":"chapter_introduction/","level":1,"title":"第 1 章   アルゴリズム入門","text":"<p>Abstract</p> <p>一人の少女が軽やかに舞い、データと織り重なり合いながら、スカートの裾にはアルゴリズムの旋律がたなびいています。</p> <p>彼女はあなたをこの舞いへと誘います。その足取りに続いて、論理と美しさに満ちたアルゴリズムの世界へ踏み入りましょう。</p>","path":["第 1 章 &nbsp; アルゴリズムを知る","第 1 章 &nbsp; アルゴリズム入門"],"tags":[]},{"location":"chapter_introduction/#_1","level":2,"title":"章の内容","text":"<ul> <li>1.1   アルゴリズムは至るところにある</li> <li>1.2   アルゴリズムとは</li> <li>1.3   まとめ</li> </ul>","path":["第 1 章 &nbsp; アルゴリズムを知る","第 1 章 &nbsp; アルゴリズム入門"],"tags":[]},{"location":"chapter_introduction/algorithms_are_everywhere/","level":1,"title":"1.1   アルゴリズムは至るところにある","text":"<p>「アルゴリズム」という言葉を聞くと、自然に数学を思い浮かべます。しかし実際には、多くのアルゴリズムは複雑な数学を必要とせず、むしろ基本的な論理に依存しており、その論理は私たちの日常生活のいたるところで見られます。</p> <p>アルゴリズムを本格的に議論する前に、ひとつ面白い事実を共有しておきます。あなたはすでに知らず知らずのうちに多くのアルゴリズムを身につけ、それらを日常生活に応用することに慣れているのです。以下では、いくつかの具体例を挙げてこれを示します。</p> <p>例1：辞書を引く。辞書では、各漢字に対応するピンインがあり、辞書はピンインのアルファベット順に並んでいます。ピンインの先頭文字が \\(r\\) の字を探すと仮定すると、通常は次の図のような方法で行います。</p> <ol> <li>辞書をおよそ半分のところまで開き、そのページの先頭文字を確認し、先頭文字が \\(m\\) だとします。</li> <li>ピンインのアルファベット表では \\(r\\) は \\(m\\) の後にあるため、辞書の前半を除外し、探索範囲を後半に絞ります。</li> <li>ピンインの先頭文字が \\(r\\) のページを見つけるまで、手順 <code>1.</code> と手順 <code>2.</code> を繰り返します。</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 1-1   辞書を引く手順 </p> <p>辞書を引くという小学生の必須スキルは、実は有名な「二分探索」アルゴリズムそのものです。データ構造の観点では、辞書を整列済みの「配列」とみなせます。アルゴリズムの観点では、上記の一連の辞書引きの操作を「二分探索」とみなせます。</p> <p>例2：トランプを整理する。カードゲームをするとき、毎回手札のトランプを小さい順に並べ替える必要があります。その流れは次の図のとおりです。</p> <ol> <li>トランプを「整列済み」と「未整列」の2つの部分に分け、初期状態では一番左の1枚がすでに整列済みだとします。</li> <li>未整列部分から1枚のトランプを取り出し、整列済み部分の正しい位置に挿入します。完了すると、左端の2枚は整列済みになります。</li> <li>手順 <code>2.</code> を繰り返し、各ラウンドで未整列部分から1枚を整列済み部分へ挿入し、すべてのトランプが整列済みになるまで続けます。</li> </ol> <p></p> <p> 図 1-2   トランプを並べ替える手順 </p> <p>上記のトランプ整理の方法は、本質的には「挿入ソート」アルゴリズムです。これは小規模なデータ集合を処理する際に非常に効率的で、多くのプログラミング言語のソートライブラリ関数にも挿入ソートが使われています。</p> <p>例3：お釣りを出す。スーパーで \\(69\\) 元の商品を購入し、店員に \\(100\\) 元渡したとすると、店員は \\(31\\) 元のお釣りを返す必要があります。店員は自然に次の図のような考え方をします。</p> <ol> <li>選択肢は \\(31\\) 元より小さい額面の貨幣で、\\(1\\) 元、\\(5\\) 元、\\(10\\) 元、\\(20\\) 元があります。</li> <li>選択肢の中から最大の \\(20\\) 元を取り出すと、残りは \\(31 - 20 = 11\\) 元です。</li> <li>残りの選択肢の中から最大の \\(10\\) 元を取り出すと、残りは \\(11 - 10 = 1\\) 元です。</li> <li>残りの選択肢の中から最大の \\(1\\) 元を取り出すと、残りは \\(1 - 1 = 0\\) 元です。</li> <li>お釣りは完了し、内訳は \\(20 + 10 + 1 = 31\\) 元です。</li> </ol> <p></p> <p> 図 1-3   お釣りの過程 </p> <p>以上の手順では、各ステップでその時点で最善と思われる選択肢を取っています。つまり、できるだけ額面の大きい貨幣を使い、最終的に実行可能なお釣りの方案を得ています。データ構造とアルゴリズムの観点から見ると、この方法は本質的に「貪欲法」です。</p> <p>料理を一品作ることから星間航行に至るまで、ほとんどあらゆる問題の解決にアルゴリズムは欠かせません。コンピュータの登場によって、プログラミングを通じてデータ構造をメモリに格納し、さらにコードを書いて CPU や GPU にアルゴリズムを実行させることが可能になりました。こうして、生活の中の問題をコンピュータに移し、より効率的な方法でさまざまな複雑な問題を解決できるのです。</p> <p>Tip</p> <p>データ構造、アルゴリズム、配列、二分探索といった概念がまだ少し曖昧でも、そのまま読み進めてください。本書がデータ構造とアルゴリズムの知識の世界へと案内します。</p>","path":["第 1 章 &nbsp; アルゴリズムを知る","1.1 &nbsp; アルゴリズムは至るところにある"],"tags":[]},{"location":"chapter_introduction/summary/","level":1,"title":"1.3   まとめ","text":"","path":["第 1 章 &nbsp; アルゴリズムを知る","1.3 &nbsp; まとめ"],"tags":[]},{"location":"chapter_introduction/summary/#1","level":3,"title":"1.   要点の振り返り","text":"<ul> <li>アルゴリズムは日常生活の至る所にあり、決して手の届かない難解な知識ではありません。実際、私たちは気づかないうちに多くのアルゴリズムを身につけ、生活のさまざまな問題を解決しています。</li> <li>辞書を引く原理は二分探索アルゴリズムと一致しています。二分探索アルゴリズムは分割統治という重要なアルゴリズム思想を体現しています。</li> <li>トランプを整理する過程は挿入ソートアルゴリズムと非常によく似ています。挿入ソートアルゴリズムは小規模なデータ集合のソートに適しています。</li> <li>貨幣の釣り銭を求める手順の本質は貪欲アルゴリズムであり、各ステップでその時点で最善と思われる選択を取ります。</li> <li>アルゴリズムとは、限られた時間内に特定の問題を解決するための一連の命令または操作手順であり、データ構造とは、コンピュータ内でデータを組織し保存する方法です。</li> <li>データ構造とアルゴリズムは密接に結びついています。データ構造はアルゴリズムの土台であり、アルゴリズムはデータ構造に生命を吹き込みます。</li> <li>データ構造とアルゴリズムは積み木の組み立てにたとえることができます。積み木はデータを表し、積み木の形や接続方法などはデータ構造を表し、積み木を組み立てる手順がアルゴリズムに対応します。</li> </ul>","path":["第 1 章 &nbsp; アルゴリズムを知る","1.3 &nbsp; まとめ"],"tags":[]},{"location":"chapter_introduction/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q：プログラマーとして、私は日常業務でアルゴリズムを使って問題を解決したことがありません。よく使うアルゴリズムはプログラミング言語にすべてカプセル化されており、そのまま使えばよいです。これは、仕事上の問題がまだアルゴリズムを必要とする段階に達していないことを意味するのでしょうか？</p> <p>具体的な仕事のスキルを武術の「型」にたとえるなら、基礎科目はむしろ「内功」に近いものです。</p> <p>私は、アルゴリズム（およびその他の基礎科目）を学ぶ意義は、仕事でそれをゼロから実装することではなく、学んだ知識に基づいて問題解決の際に専門的な反応や判断を下せるようになり、その結果として仕事全体の品質を高めることにあると考えています。簡単な例を挙げると、どのプログラミング言語にもソート関数が組み込まれています。</p> <ul> <li>もしデータ構造とアルゴリズムを学んでいなければ、どんなデータが与えられても、そのソート関数に任せてしまうかもしれません。問題なく動き、性能も悪くなく、一見すると特に問題はありません。</li> <li>しかしアルゴリズムを学んでいれば、組み込みのソート関数の時間計算量が \\(O(n \\log n)\\) であることを知っています。さらに、与えられたデータが固定桁数の整数（例えば学籍番号）であれば、より効率の高い「基数ソート」を使って、時間計算量を \\(O(nk)\\) に下げることができます。ここで \\(k\\) は桁数です。データ量が非常に大きい場合、節約できた実行時間は大きな価値を生みます（コスト削減、体験向上など）。</li> </ul> <p>工学分野では、多くの問題で最適解に到達することは難しく、少なくない問題は「だいたい」解決されているにすぎません。問題の難しさは、一方では問題そのものの性質に依存し、他方ではそれを観測する人の知識の蓄積にも依存します。知識が充実し、経験が豊富であるほど、問題分析はより深くなり、問題はより洗練された形で解決できるようになります。</p>","path":["第 1 章 &nbsp; アルゴリズムを知る","1.3 &nbsp; まとめ"],"tags":[]},{"location":"chapter_introduction/what_is_dsa/","level":1,"title":"1.2   アルゴリズムとは","text":"","path":["第 1 章 &nbsp; アルゴリズムを知る","1.2 &nbsp; アルゴリズムとは"],"tags":[]},{"location":"chapter_introduction/what_is_dsa/#121","level":2,"title":"1.2.1   アルゴリズムの定義","text":"<p>アルゴリズム（algorithm）とは、限られた時間内に特定の問題を解決するための一連の命令または操作手順であり、次のような特徴を持ちます。</p> <ul> <li>問題が明確であり、入力と出力の定義がはっきりしています。</li> <li>実行可能であり、有限の手順、時間、メモリ空間で完了できます。</li> <li>各手順の意味が確定しており、同じ入力と実行条件では常に同じ出力になります。</li> </ul>","path":["第 1 章 &nbsp; アルゴリズムを知る","1.2 &nbsp; アルゴリズムとは"],"tags":[]},{"location":"chapter_introduction/what_is_dsa/#122","level":2,"title":"1.2.2   データ構造の定義","text":"<p>データ構造（data structure）とは、データを整理して保存する方式であり、データの内容、データ間の関係、データの操作方法を含み、次のような設計目標があります。</p> <ul> <li>使用する空間をできるだけ少なくし、コンピュータのメモリを節約します。</li> <li>データの操作をできるだけ高速にし、アクセス、追加、削除、更新などを含みます。</li> <li>簡潔なデータ表現と論理情報を提供し、アルゴリズムが効率よく動作できるようにします。</li> </ul> <p>データ構造の設計はトレードオフに満ちた過程です。ある面を改善したい場合、別の面で妥協が必要になることがよくあります。以下に 2 つの例を示します。</p> <ul> <li>連結リストは配列に比べてデータの追加や削除がしやすい一方で、データアクセス速度を犠牲にしています。</li> <li>グラフは連結リストに比べてより豊富な論理情報を提供しますが、より大きなメモリ空間を必要とします。</li> </ul>","path":["第 1 章 &nbsp; アルゴリズムを知る","1.2 &nbsp; アルゴリズムとは"],"tags":[]},{"location":"chapter_introduction/what_is_dsa/#123","level":2,"title":"1.2.3   データ構造とアルゴリズムの関係","text":"<p>以下の図のように、データ構造とアルゴリズムは高度に関連し、密接に結び付いており、具体的には次の 3 つの点に表れます。</p> <ul> <li>データ構造はアルゴリズムの土台です。データ構造はアルゴリズムに対して、構造化して格納されたデータと、そのデータを操作する方法を提供します。</li> <li>アルゴリズムはデータ構造に命を吹き込みます。データ構造そのものはデータ情報を保存するだけであり、アルゴリズムと組み合わせて初めて特定の問題を解決できます。</li> <li>アルゴリズムは通常、異なるデータ構造に基づいて実装できますが、実行効率が大きく異なる場合があり、適切なデータ構造を選ぶことが重要です。</li> </ul> <p></p> <p> 図 1-4   データ構造とアルゴリズムの関係 </p> <p>データ構造とアルゴリズムは、以下の図に示す組み立てブロックのようなものです。1 セットのブロックには多くの部品が含まれるだけでなく、詳しい組み立て説明書も付いています。説明書に従って一歩ずつ操作すれば、精巧なブロック模型を組み立てられます。</p> <p></p> <p> 図 1-5   組み立てブロック </p> <p>両者の詳細な対応関係を次の表に示します。</p> <p> 表 1-1   データ構造とアルゴリズムを組み立てブロックにたとえる </p> データ構造とアルゴリズム 組み立てブロック 入力データ まだ組み立てていないブロック データ構造 ブロックの構成形式。形状、大きさ、接続方法などを含む アルゴリズム ブロックを目標の形に組み上げる一連の操作手順 出力データ ブロック模型 <p>特筆すべき点として、データ構造とアルゴリズムはプログラミング言語から独立しています。だからこそ、本書では複数のプログラミング言語に基づく実装を提供できます。</p> <p>慣習的な略称</p> <p>実際の議論では、私たちは通常「データ構造とアルゴリズム」を略して「アルゴリズム」と呼びます。たとえば広く知られている LeetCode のアルゴリズム問題は、実際にはデータ構造とアルゴリズムの両方の知識を同時に問うています。</p>","path":["第 1 章 &nbsp; アルゴリズムを知る","1.2 &nbsp; アルゴリズムとは"],"tags":[]},{"location":"chapter_paperbook/","level":1,"title":"紙の書籍","text":"<p>長い時間をかけて磨き上げた『Hello アルゴリズム』の紙の書籍が、ついに発売されました！今の気持ちは、次の一節で表せます：</p> <p>風を追い月を追って立ち止まるな、草原の果てには春の山がある。</p> <p></p> <p>以下の動画では紙の書籍を紹介しており、私の考えもいくつか含まれています：</p> <ul> <li>データ構造とアルゴリズムを学ぶ重要性。</li> <li>なぜ紙の書籍で Python を選んだのか。</li> <li>知識共有に対する理解。</li> </ul> <p>新人 UP 主ですので、ぜひ応援と高評価・チャンネル登録をお願いします～ありがとうございます！</p> <p>紙の書籍のスナップショット：</p> <p></p> <p></p>","path":["紙の書籍"],"tags":[]},{"location":"chapter_paperbook/#_2","level":2,"title":"長所と短所","text":"<p>紙の書籍ならではの魅力を、簡単にまとめると次のとおりです：</p> <ul> <li>フルカラー印刷を採用し、本書の「アニメーション図解」の強みをそのまま活かせます。</li> <li>紙の素材にもこだわり、色彩を高い精度で再現しつつ、紙の書籍ならではの質感も残しています。</li> <li>紙の書籍版は Web 版よりも書式が整っており、たとえば図中の数式には斜体を用いています。</li> <li>価格を上げずに、マインドマップの折り込みページやしおりも付属します。</li> <li>紙の書籍、Web 版、PDF 版で内容は同期しており、自由に切り替えて読めます。</li> </ul> <p>Tip</p> <p>紙の書籍と Web 版を同期させるのは難しいため、細かな違いが生じる場合があります。ご了承ください！</p> <p>もちろん、購入前に検討しておくべき点もいくつかあります：</p> <ul> <li>Python 言語を使用しているため、あなたの主言語と合わない可能性があります（Python は疑似コードと捉え、考え方の理解を重視してください）。</li> <li>フルカラー印刷は図解やコードの読みやすさを大きく高める一方で、白黒印刷より価格はやや高くなります。</li> </ul> <p>Tip</p> <p>「印刷品質」と「価格」は、アルゴリズムにおける「時間効率」と「空間効率」のようなもので、両立は容易ではありません。そして私は、「印刷品質」は「時間効率」に当たるため、より重視すべきだと考えています。</p>","path":["紙の書籍"],"tags":[]},{"location":"chapter_paperbook/#_3","level":2,"title":"購入リンク","text":"<p>紙の書籍に興味があれば、ぜひ一冊ご検討ください。新刊の 5 割引を用意していただきましたので、こちらのリンクをご覧いただくか、以下の QR コードをスキャンしてください：</p> <p></p>","path":["紙の書籍"],"tags":[]},{"location":"chapter_paperbook/#_4","level":2,"title":"あとがき","text":"<p>当初、私は紙の書籍出版に必要な作業量を甘く見ていて、オープンソースプロジェクトをきちんと保守していれば、紙の書籍版も何らかの自動化手段で生成できると思っていました。実際には、紙の書籍の制作フローとオープンソースプロジェクトの更新の仕組みには大きな違いがあり、その間をつなぐには多くの追加作業が必要でした。</p> <p>一冊の本の初稿と出版基準を満たす完成稿との間には、なお大きな隔たりがあります。出版社（企画、編集、デザイン、マーケティングなど）と著者が力を合わせ、長い時間をかけて磨き上げていく必要があります。ここで、図霊の企画編集者である王軍花さん、そして人民郵電出版社と図霊コミュニティで本書の出版工程に携わってくださったすべての皆さまに感謝いたします！</p> <p>この本があなたの助けになれば幸いです！</p>","path":["紙の書籍"],"tags":[]},{"location":"chapter_preface/","level":1,"title":"第 0 章   はじめに","text":"<p>Abstract</p> <p>アルゴリズムは美しい交響曲のようであり、コードの一行一行が旋律のように流れていきます。</p> <p>この本があなたの心の中でそっと響き、独自で深い旋律を残してくれることを願っています。</p>","path":["第 0 章 &nbsp; 前書き","第 0 章 &nbsp; はじめに"],"tags":[]},{"location":"chapter_preface/#_1","level":2,"title":"章の内容","text":"<ul> <li>0.1   本書について</li> <li>0.2   本書の使い方</li> <li>0.3   まとめ</li> </ul>","path":["第 0 章 &nbsp; 前書き","第 0 章 &nbsp; はじめに"],"tags":[]},{"location":"chapter_preface/about_the_book/","level":1,"title":"0.1   本書について","text":"<p>本プロジェクトは、オープンソースで無料、かつ初心者にやさしいデータ構造とアルゴリズムの入門書を作ることを目的としています。</p> <ul> <li>全編でアニメーション付きの図解を採用し、内容は明快で理解しやすく、学習曲線もなだらかで、初心者がデータ構造とアルゴリズムの知識地図を探求できるよう導きます。</li> <li>ソースコードはワンクリックで実行でき、読者が演習を通じてプログラミング能力を高め、アルゴリズムの動作原理とデータ構造の内部実装を理解する助けとなります。</li> <li>読者どうしの助け合いによる学習を推奨しており、コメント欄で質問や見解を共有し、対話と議論を通じてともに成長していくことを歓迎します。</li> </ul>","path":["第 0 章 &nbsp; 前書き","0.1 &nbsp; 本書について"],"tags":[]},{"location":"chapter_preface/about_the_book/#011","level":2,"title":"0.1.1   対象読者","text":"<p>もしあなたがアルゴリズム初心者で、これまでアルゴリズムに触れたことがない、あるいはすでに多少の問題演習の経験はあるものの、データ構造とアルゴリズムについてはまだ曖昧な理解にとどまり、できるかできないかの間を行き来しているなら、本書はまさにあなたのために作られています！</p> <p>もしすでに一定量の問題演習を積み、ほとんどの問題パターンに慣れているなら、本書はアルゴリズム知識体系の復習と整理に役立ちます。リポジトリのソースコードは「問題演習ツール集」や「アルゴリズム辞典」として活用できます。</p> <p>もしあなたがアルゴリズムの「達人」なら、貴重なご提案をいただけることを楽しみにしています。あるいは一緒に執筆に参加してください。</p> <p>前提条件</p> <p>少なくともいずれか一つの言語でのプログラミング基礎があり、簡単なコードを読んだり書いたりできる必要があります。</p>","path":["第 0 章 &nbsp; 前書き","0.1 &nbsp; 本書について"],"tags":[]},{"location":"chapter_preface/about_the_book/#012","level":2,"title":"0.1.2   内容構成","text":"<p>本書の主な内容は以下の図のとおりです。</p> <ul> <li>計算量解析：データ構造とアルゴリズムを評価する観点と方法。時間計算量と空間計算量の求め方、代表的な種類、例など。</li> <li>データ構造：基本データ型とデータ構造の分類方法。配列、連結リスト、スタック、キュー、ハッシュテーブル、木、ヒープ、グラフなどのデータ構造の定義、長所と短所、基本操作、代表的な種類、典型的な応用、実装方法など。</li> <li>アルゴリズム：探索、ソート、分割統治、バックトラッキング、動的計画法、貪欲法などのアルゴリズムの定義、長所と短所、効率、適用場面、問題を解く手順、例題など。</li> </ul> <p></p> <p> 図 0-1   本書の主な内容 </p>","path":["第 0 章 &nbsp; 前書き","0.1 &nbsp; 本書について"],"tags":[]},{"location":"chapter_preface/about_the_book/#013","level":2,"title":"0.1.3   謝辞","text":"<p>本書は、オープンソースコミュニティの多くの貢献者による共同の努力のもとで、継続的に改善されています。時間と労力を注いでくださったすべての執筆者の皆さんに感謝します。お名前は次のとおりです（GitHub により自動生成された順序）：krahets、coderonion、Gonglja、nuomi1、Reanon、justin-tse、hpstory、danielsss、curtishd、night-cruise、S-N-O-R-L-A-X、rongyi、msk397、gvenusleo、khoaxuantu、rivertwilight、K3v123、gyt95、zhuoqinyue、yuelinxin、Zuoxun、mingXta、Phoenix0415、FangYuan33、GN-Yu、longsizhuo、IsChristina、xBLACKICEx、guowei-gong、Cathay-Chen、pengchzn、QiLOL、magentaqin、hello-ikun、JoseHung、qualifier1024、thomasq0、sunshinesDL、L-Super、Guanngxu、Transmigration-zhou、WSL0809、Slone123c、lhxsm、yuan0221、what-is-me、Shyam-Chen、theNefelibatas、longranger2、codeberg-user、xiongsp、JeffersonHuang、prinpal、seven1240、Wonderdch、malone6、xiaomiusa87、gaofer、bluebean-cloud、a16su、SamJin98、hongyun-robot、nanlei、XiaChuerwu、yd-j、iron-irax、mgisr、steventimes、junminhong、heshuyue、danny900714、MolDuM、Nigh、Dr-XYZ、XC-Zero、reeswell、PXG-XPG、NI-SW、Horbin-Magician、Enlightenus、YangXuanyi、beatrix-chan、DullSword、xjr7670、jiaxianhua、qq909244296、iStig、boloboloda、hts0000、gledfish、wenjianmin、keshida、kilikilikid、lclc6、lwbaptx、linyejoe2、liuxjerry、llql1211、fbigm、echo1937、szu17dmy、dshlstarr、Yucao-cy、coderlef、czruby、bongbongbakudan、beintentional、ZongYangL、ZhongYuuu、ZhongGuanbin、hezhizhen、linzeyan、ZJKung、luluxia、xb534、ztkuaikuai、yw-1021、ElaBosak233、baagod、zhouLion、yishangzhang、yi427、yanedie、yabo083、weibk、wangwang105、th1nk3r-ing、tao363、4yDX3906、syd168、sslmj2020、smilelsb、siqyka、selear、sdshaoda、Xi-Row、popozhu、nuquist19、noobcodemaker、XiaoK29、chadyi、lyl625760、lucaswangdev、0130w、shanghai-Jerry、EJackYang、Javesun99、eltociear、lipusheng、KNChiu、BlindTerran、ShiMaRing、lovelock、FreddieLi、FloranceYeh、fanchenggang、gltianwen、goerll、nedchu、curly210102、CuB3y0nd、KraHsu、CarrotDLaw、youshaoXG、bubble9um、Asashishi、Asa0oo0o0o、fanenr、eagleanurag、akshiterate、52coder、foursevenlove、KorsChen、GaochaoZhu、hopkings2008、yang-le、realwujing、Evilrabbit520、Umer-Jahangir、Turing-1024-Lee、Suremotoo、paoxiaomooo、Chieko-Seren、Allen-Scai、ymmmas、Risuntsy、Richard-Zhang1019、RafaelCaso、qingpeng9802、primexiao、Urbaner3、zhongfq、nidhoggfgg、MwumLi、CreatorMetaSky、martinx、ZnYang2018、hugtyftg、logan-qiu、psychelzh、Keynman、KeiichiKasai と KawaiiAsh。</p> <p>本書のコードレビューは coderonion、curtishd、Gonglja、gvenusleo、hpstory、justin-tse、khoaxuantu、krahets、night-cruise、nuomi1、Reanon と rongyi によって行われました（アルファベット順）。彼らが費やしてくれた時間と労力に感謝します。各言語のコードの規範性と統一性が保たれているのは、まさに彼らのおかげです。</p> <p>本書の繁体字中国語版は Shyam-Chen と Dr-XYZ がレビューし、英語版は yuelinxin、K3v123、QiLOL、Phoenix0415、SamJin98、yanedie、RafaelCaso、pengchzn、thomasq0 と magentaqin がレビューし、日本語版は eltociear がレビューしました。彼らの継続的な貢献があってこそ、本書はより幅広い読者に届けられています。感謝いたします。</p> <p>本書の ePub 電子書籍生成ツールは zhongfq によって開発されました。彼の貢献に感謝します。読者により自由な読書方法を提供してくれました。</p> <p>本書の執筆過程で、私は多くの方々の助けを得ました。</p> <ul> <li>会社での私の指導教員である李汐博士に感謝します。ある対話の中で「すぐに行動しよう」と励ましてくださり、この本を書く決意を固めることができました；</li> <li>私の恋人であり、本書の最初の読者でもある泡泡に感謝します。アルゴリズム初心者の視点から多くの貴重な提案をしてくれたおかげで、本書はより初心者に適したものになりました；</li> <li>腾宝、琦宝、飞宝が本書に創造性あふれる名前を付けてくれたことに感謝します。みんなが最初のコード行「Hello World!」を書いた美しい記憶を呼び起こしてくれました；</li> <li>校铨が知的財産の面で専門的な支援をしてくれたことに感謝します。これは本オープンソース書籍の改善に重要な役割を果たしました；</li> <li>苏潼が本書の美しい表紙と logo をデザインし、私の完璧主義につき合って何度も辛抱強く修正してくれたことに感謝します；</li> <li>@squidfunk が組版に関する助言を提供してくれたこと、そして彼が開発したオープンソースのドキュメントテーマ Material-for-MkDocs に感謝します。</li> </ul> <p>執筆の過程で、私はデータ構造とアルゴリズムに関する多くの教材や記事を読みました。これらの作品は本書に優れた手本を与え、本書の内容の正確性と品質を支えてくれました。ここに、すべての先生方と先人たちの卓越した貢献に感謝します！</p> <p>本書は手と頭を同時に使う学習方法を提唱しています。この点で私は『手を動かして学ぶ深層学習』から大きな啓発を受けました。ここで読者の皆さんにこの優れた著作を強くお勧めします。</p> <p>心から両親に感謝します。いつも支え励ましてくれたからこそ、私はこの興味深いことに取り組む機会を得ることができました。</p>","path":["第 0 章 &nbsp; 前書き","0.1 &nbsp; 本書について"],"tags":[]},{"location":"chapter_preface/suggestions/","level":1,"title":"0.2   本書の使い方","text":"<p>Tip</p> <p>最適な読書体験を得るために、本節の内容を一通り読むことをおすすめします。</p>","path":["第 0 章 &nbsp; 前書き","0.2 &nbsp; 本書の使い方"],"tags":[]},{"location":"chapter_preface/suggestions/#021","level":2,"title":"0.2.1   文章スタイルの約束","text":"<ul> <li>見出しの後に <code>*</code> が付いているのは選読章で、内容は比較的難しめです。時間が限られている場合は、先に読み飛ばしてもかまいません。</li> <li>専門用語は太字（紙書籍版と PDF 版）または下線付き（Web 版）で示します。たとえば配列（array）のようなものです。文献を読む際に役立つため、覚えておくことをおすすめします。</li> <li>重要な内容やまとめの文は 太字 で示します。これらの文章には特に注意してください。</li> <li>特定の意味を持つ語句には“引用符”を付け、曖昧さを避けます。</li> <li>プログラミング言語ごとに用語が一致しない場合、本書では Python を基準とします。たとえば、“空”を表すのに <code>None</code> を使います。</li> <li>本書では、よりコンパクトなレイアウトのために、言語ごとのコメント規約を一部省略しています。コメントは主に3種類あります。タイトルコメント、内容コメント、複数行コメントです。</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>\"\"\"タイトルコメント。関数、クラス、テストケースなどを示すために使います\"\"\"\n\n# 内容コメント。コードを詳しく説明するために使います\n\n\"\"\"\n複数行\nコメント\n\"\"\"\n</code></pre> <pre><code>/* タイトルコメント。関数、クラス、テストケースなどを示すために使います */\n\n// 内容コメント。コードを詳しく説明するために使います\n\n/**\n * 複数行\n * コメント\n */\n</code></pre> <pre><code>/* タイトルコメント。関数、クラス、テストケースなどを示すために使います */\n\n// 内容コメント。コードを詳しく説明するために使います\n\n/**\n * 複数行\n * コメント\n */\n</code></pre> <pre><code>/* タイトルコメント。関数、クラス、テストケースなどを示すために使います */\n\n// 内容コメント。コードを詳しく説明するために使います\n\n/**\n * 複数行\n * コメント\n */\n</code></pre> <pre><code>/* タイトルコメント。関数、クラス、テストケースなどを示すために使います */\n\n// 内容コメント。コードを詳しく説明するために使います\n\n/**\n * 複数行\n * コメント\n */\n</code></pre> <pre><code>/* タイトルコメント。関数、クラス、テストケースなどを示すために使います */\n\n// 内容コメント。コードを詳しく説明するために使います\n\n/**\n * 複数行\n * コメント\n */\n</code></pre> <pre><code>/* タイトルコメント。関数、クラス、テストケースなどを示すために使います */\n\n// 内容コメント。コードを詳しく説明するために使います\n\n/**\n * 複数行\n * コメント\n */\n</code></pre> <pre><code>/* タイトルコメント。関数、クラス、テストケースなどを示すために使います */\n\n// 内容コメント。コードを詳しく説明するために使います\n\n/**\n * 複数行\n * コメント\n */\n</code></pre> <pre><code>/* タイトルコメント。関数、クラス、テストケースなどを示すために使います */\n\n// 内容コメント。コードを詳しく説明するために使います\n\n/**\n * 複数行\n * コメント\n */\n</code></pre> <pre><code>/* タイトルコメント。関数、クラス、テストケースなどを示すために使います */\n\n// 内容コメント。コードを詳しく説明するために使います\n\n/**\n * 複数行\n * コメント\n */\n</code></pre> <pre><code>/* タイトルコメント。関数、クラス、テストケースなどを示すために使います */\n\n// 内容コメント。コードを詳しく説明するために使います\n\n/**\n * 複数行\n * コメント\n */\n</code></pre> <pre><code>/* タイトルコメント。関数、クラス、テストケースなどを示すために使います */\n\n// 内容コメント。コードを詳しく説明するために使います\n\n/**\n * 複数行\n * コメント\n */\n</code></pre> <pre><code>### タイトルコメント。関数、クラス、テストケースなどを示すために使います ###\n\n# 内容コメント。コードを詳しく説明するために使います\n\n# 複数行\n# コメント\n</code></pre>","path":["第 0 章 &nbsp; 前書き","0.2 &nbsp; 本書の使い方"],"tags":[]},{"location":"chapter_preface/suggestions/#022","level":2,"title":"0.2.2   アニメーション図解で効率よく学ぶ","text":"<p>文字と比べて、動画や画像は情報密度と構造化の度合いが高く、理解しやすいものです。本書では、重要かつ難解な知識は主にアニメーションによる図解で示し、文章は説明と補足を担います。</p> <p>本書を読んでいて、ある内容に以下の図のようなアニメーション図解がある場合は、図を主、文章を従として、両方を合わせて理解してください。</p> <p></p> <p> 図 0-2   アニメーション図解の例 </p>","path":["第 0 章 &nbsp; 前書き","0.2 &nbsp; 本書の使い方"],"tags":[]},{"location":"chapter_preface/suggestions/#023","level":2,"title":"0.2.3   コード実践で理解を深める","text":"<p>本書のサンプルコードは GitHub リポジトリ で管理されています。以下の図のように、ソースコードにはテストケースが付いており、ワンクリックで実行できます。</p> <p>時間に余裕があれば、コードを見ながら自分で一度書いてみることをおすすめします。学習時間が限られている場合でも、少なくともすべてのコードに目を通し、実行してください。</p> <p>コードを読むのに比べて、書く過程のほうが得られるものは多いものです。手を動かしてこそ、本当に学んだことになります。</p> <p></p> <p> 図 0-3   コード実行例 </p> <p>コードを実行する前準備は主に3ステップです。</p> <p>第1ステップ：ローカルのプログラミング環境をインストールする。付録のチュートリアルを参照してインストールしてください。すでにインストール済みであれば、この手順は省略できます。</p> <p>第2ステップ：コードリポジトリをクローンまたはダウンロードする。 GitHub リポジトリ にアクセスしてください。すでに Git をインストールしている場合は、次のコマンドでこのリポジトリをクローンできます：</p> <pre><code>git clone https://github.com/krahets/hello-algo.git\n</code></pre> <p>もちろん、以下の図に示す場所で“Download ZIP”ボタンをクリックし、コードの圧縮ファイルを直接ダウンロードしてローカルで展開することもできます。</p> <p></p> <p> 図 0-4   リポジトリのクローンとコードのダウンロード </p> <p>第3ステップ：ソースコードを実行する。以下の図のように、上部にファイル名が表示されているコードブロックについては、リポジトリの <code>codes</code> フォルダ内に対応するソースコードファイルがあります。ソースコードファイルはワンクリックで実行できるため、不要なデバッグ時間を減らし、学習内容に集中できます。</p> <p></p> <p> 図 0-5   コードブロックと対応するソースコードファイル </p> <p>ローカルでコードを実行するだけでなく、Web 版では Python コードの可視化実行にも対応しています（pythontutor を利用）。以下の図のように、コードブロックの下にある“可視化実行”をクリックすると表示を展開し、アルゴリズムコードの実行過程を観察できます。また、“全画面表示”をクリックすると、より見やすい閲覧体験が得られます。</p> <p></p> <p> 図 0-6   Python コードの可視化実行 </p>","path":["第 0 章 &nbsp; 前書き","0.2 &nbsp; 本書の使い方"],"tags":[]},{"location":"chapter_preface/suggestions/#024","level":2,"title":"0.2.4   質問と議論を通じてともに成長する","text":"<p>本書を読んでいて、理解できていない知識点を安易に読み飛ばさないでください。コメント欄で気軽に質問してください。私と仲間たちが誠意をもって回答し、通常は 2 日以内に返信します。</p> <p>以下の図のように、Web 版では各章の下部にコメント欄があります。ぜひコメント欄の内容にも目を通してください。一方では、みんなが直面した問題を知ることで知識の抜けを補い、より深い思考を促せます。もう一方では、ほかの仲間の質問にも積極的に答え、見解を共有し、互いの成長を助けてほしいと思います。</p> <p></p> <p> 図 0-7   コメント欄の例 </p>","path":["第 0 章 &nbsp; 前書き","0.2 &nbsp; 本書の使い方"],"tags":[]},{"location":"chapter_preface/suggestions/#025","level":2,"title":"0.2.5   アルゴリズム学習ロードマップ","text":"<p>全体として見ると、データ構造とアルゴリズムの学習過程は 3 つの段階に分けられます。</p> <ol> <li>第 1 段階：アルゴリズム入門。さまざまなデータ構造の特徴と使い方に慣れ、異なるアルゴリズムの原理、流れ、用途、効率などを学ぶ必要があります。</li> <li>第 2 段階：アルゴリズム問題を解く。まずは人気の高い問題から取り組み、少なくとも 100 問は蓄積して、主流のアルゴリズム問題に慣れることをおすすめします。最初のうちは、“知識の忘却”が課題になるかもしれませんが、心配はいりません。これはごく自然なことです。“エビングハウスの忘却曲線”に沿って問題を復習すれば、通常は 3～5 回繰り返すことでしっかり記憶に定着します。おすすめの問題リストと学習計画は、この GitHub リポジトリ を参照してください。</li> <li>第 3 段階：知識体系を構築する。学習面では、アルゴリズムの連載記事、解法フレームワーク、教材などを読むことで、知識体系を継続的に充実させられます。問題演習の面では、トピック別分類、1 問多解、1 解多題といった発展的な戦略も試せます。関連する学習ノウハウは各コミュニティで見つけられます。</li> </ol> <p>以下の図のように、本書の内容は主に“第 1 段階”を扱っており、第 2 段階と第 3 段階の学習をより効率的に進める助けとなることを目的としています。</p> <p></p> <p> 図 0-8   アルゴリズム学習ロードマップ </p>","path":["第 0 章 &nbsp; 前書き","0.2 &nbsp; 本書の使い方"],"tags":[]},{"location":"chapter_preface/summary/","level":1,"title":"0.3   まとめ","text":"","path":["第 0 章 &nbsp; 前書き","0.3 &nbsp; まとめ"],"tags":[]},{"location":"chapter_preface/summary/#1","level":3,"title":"1.   重要ポイントの振り返り","text":"<ul> <li>本書の主な対象読者はアルゴリズム初学者です。すでにある程度の基礎がある場合でも、本書はアルゴリズム知識を体系的に振り返る助けとなり、書中のソースコードは「問題演習用ツール集」としても利用できます。</li> <li>本書の内容は主に計算量解析、データ構造、アルゴリズムの三部からなり、この分野の大部分のテーマを網羅しています。</li> <li>アルゴリズム初心者にとって、学習初期の段階で入門書を読むことは非常に重要であり、多くの遠回りを避けられます。</li> <li>本書のアニメーション図解は通常、重要な知識や難しい知識を紹介するために用いられます。本書を読む際は、これらの内容により多く注意を払うべきです。</li> <li>実践はプログラミングを学ぶ最良の方法です。ソースコードを実行し、実際に自分でコードを書くことを強く勧めます。</li> <li>本書のWeb版の各章にはコメント欄が設けられており、疑問や見解をいつでも共有することを歓迎します。</li> </ul>","path":["第 0 章 &nbsp; 前書き","0.3 &nbsp; まとめ"],"tags":[]},{"location":"chapter_reference/","level":1,"title":"参考文献","text":"<p>[1] Thomas H. Cormen, et al. Introduction to Algorithms (3<sup>rd</sup> Edition).</p> <p>[2] Aditya Bhargava. Grokking Algorithms: An Illustrated Guide for Programmers and Other Curious People (1<sup>st</sup> Edition).</p> <p>[3] Robert Sedgewick, et al. Algorithms (4<sup>th</sup> Edition).</p> <p>[4] 严蔚敏. データ構造（C 言語版）.</p> <p>[5] 邓俊辉. データ構造（C++ 言語版、第3版）.</p> <p>[6] マーク・アレン・ワイス著，陈越訳. データ構造とアルゴリズム解析：Java言語による記述（第3版）.</p> <p>[7] 程杰. データ構造の話.</p> <p>[8] 王争. データ構造とアルゴリズムの美.</p> <p>[9] Gayle Laakmann McDowell. Cracking the Coding Interview: 189 Programming Questions and Solutions (6<sup>th</sup> Edition).</p> <p>[10] Aston Zhang, et al. Dive into Deep Learning.</p>","path":["参考文献"],"tags":[]},{"location":"chapter_searching/","level":1,"title":"第 10 章   探索","text":"<p>Abstract</p> <p>探索は未知の冒険であり、私たちは神秘的な空間の隅々まで歩き回る必要があるかもしれず、あるいは素早く目標を特定できるかもしれません。</p> <p>この探索の旅において、すべての探求が思いもよらなかった答えをもたらすかもしれません。</p>","path":["第 10 章 &nbsp; 探索"],"tags":[]},{"location":"chapter_searching/#_1","level":2,"title":"章の内容","text":"<ul> <li>10.1   二分探索</li> <li>10.2   二分探索の挿入位置</li> <li>10.3   二分探索の境界</li> <li>10.4   ハッシュによる最適化戦略</li> <li>10.5   探索アルゴリズム再考</li> <li>10.6   まとめ</li> </ul>","path":["第 10 章 &nbsp; 探索"],"tags":[]},{"location":"chapter_searching/binary_search/","level":1,"title":"10.1   二分探索","text":"<p>二分探索（binary search）は分割統治法に基づく効率的な探索アルゴリズムです。データが整列済みである性質を利用し、各ラウンドで探索範囲を半分に縮小し、目標要素を見つけるか探索区間が空になるまで続けます。</p> <p>Question</p> <p>長さ \\(n\\) の配列 <code>nums</code> が与えられます。要素は小さい順に並んでおり、重複しません。要素 <code>target</code> がこの配列内にある場合はそのインデックスを返し、含まれない場合は \\(-1\\) を返してください。例を次の図に示します。</p> <p></p> <p> 図 10-1   二分探索の例 </p> <p>次の図に示すように、まずポインタ \\(i = 0\\) と \\(j = n - 1\\) を初期化し、それぞれ配列の先頭要素と末尾要素を指すようにして、探索区間 \\([0, n - 1]\\) を表します。角括弧は閉区間を表し、境界値自体を含むことに注意してください。</p> <p>次に、以下の 2 つの手順を繰り返します。</p> <ol> <li>中央のインデックス \\(m = \\lfloor {(i + j) / 2} \\rfloor\\) を計算します。ここで \\(\\lfloor \\: \\rfloor\\) は切り捨てを表します。</li> <li><code>nums[m]</code> と <code>target</code> の大小関係を判定し、次の 3 つの場合に分かれます。<ol> <li><code>nums[m] &lt; target</code> のとき、<code>target</code> は区間 \\([m + 1, j]\\) にあるため、\\(i = m + 1\\) を実行します。</li> <li><code>nums[m] &gt; target</code> のとき、<code>target</code> は区間 \\([i, m - 1]\\) にあるため、\\(j = m - 1\\) を実行します。</li> <li><code>nums[m] = target</code> のとき、<code>target</code> が見つかったので、インデックス \\(m\\) を返します。</li> </ol> </li> </ol> <p>配列に目標要素が含まれない場合、探索区間は最終的に空まで縮小されます。このとき \\(-1\\) を返します。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 10-2   二分探索の流れ </p> <p>注意すべき点として、\\(i\\) と \\(j\\) はどちらも <code>int</code> 型であるため、\\(i + j\\) が <code>int</code> 型の範囲を超える可能性があります。大きな数によるオーバーフローを避けるため、通常は式 \\(m = \\lfloor {i + (j - i) / 2} \\rfloor\\) を用いて中点を計算します。</p> <p>コードは次のとおりです。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search.py<pre><code>def binary_search(nums: list[int], target: int) -&gt; int:\n    \"\"\"二分探索（両閉区間）\"\"\"\n    # 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す\n    i, j = 0, len(nums) - 1\n    # ループし、探索区間が空になったら終了する（i &gt; j で空）\n    while i &lt;= j:\n        # 理論上、Python の数値は無限に大きくできるため（メモリ容量に依存）、大きな数のオーバーフローを考慮する必要はない\n        m = (i + j) // 2  # 中点インデックス m を計算\n        if nums[m] &lt; target:\n            i = m + 1  # この場合、target は区間 [m+1, j] にある\n        elif nums[m] &gt; target:\n            j = m - 1  # この場合、target は区間 [i, m-1] にある\n        else:\n            return m  # 目標要素が見つかったらそのインデックスを返す\n    return -1  # 目標要素が見つからなければ -1 を返す\n</code></pre> binary_search.cpp<pre><code>/* 二分探索（両閉区間） */\nint binarySearch(vector&lt;int&gt; &amp;nums, int target) {\n    // 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す\n    int i = 0, j = nums.size() - 1;\n    // ループし、探索区間が空になったら終了する（i &gt; j で空）\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // 中点インデックス m を計算\n        if (nums[m] &lt; target)    // この場合、target は区間 [m+1, j] にある\n            i = m + 1;\n        else if (nums[m] &gt; target) // この場合、target は区間 [i, m-1] にある\n            j = m - 1;\n        else // 目標要素が見つかったらそのインデックスを返す\n            return m;\n    }\n    // 目標要素が見つからなければ -1 を返す\n    return -1;\n}\n</code></pre> binary_search.java<pre><code>/* 二分探索（両閉区間） */\nint binarySearch(int[] nums, int target) {\n    // 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す\n    int i = 0, j = nums.length - 1;\n    // ループし、探索区間が空になったら終了する（i &gt; j で空）\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // 中点インデックス m を計算\n        if (nums[m] &lt; target) // この場合、target は区間 [m+1, j] にある\n            i = m + 1;\n        else if (nums[m] &gt; target) // この場合、target は区間 [i, m-1] にある\n            j = m - 1;\n        else // 目標要素が見つかったらそのインデックスを返す\n            return m;\n    }\n    // 目標要素が見つからなければ -1 を返す\n    return -1;\n}\n</code></pre> binary_search.cs<pre><code>/* 二分探索（両閉区間） */\nint BinarySearch(int[] nums, int target) {\n    // 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す\n    int i = 0, j = nums.Length - 1;\n    // ループし、探索区間が空になったら終了する（i &gt; j で空）\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2;   // 中点インデックス m を計算\n        if (nums[m] &lt; target)      // この場合、target は区間 [m+1, j] にある\n            i = m + 1;\n        else if (nums[m] &gt; target) // この場合、target は区間 [i, m-1] にある\n            j = m - 1;\n        else                       // 目標要素が見つかったらそのインデックスを返す\n            return m;\n    }\n    // 目標要素が見つからなければ -1 を返す\n    return -1;\n}\n</code></pre> binary_search.go<pre><code>/* 二分探索（両閉区間） */\nfunc binarySearch(nums []int, target int) int {\n    // 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す\n    i, j := 0, len(nums)-1\n    // ループし、探索区間が空になったら終了する（i &gt; j で空）\n    for i &lt;= j {\n        m := i + (j-i)/2      // 中点インデックス m を計算\n        if nums[m] &lt; target { // この場合、target は区間 [m+1, j] にある\n            i = m + 1\n        } else if nums[m] &gt; target { // この場合、target は区間 [i, m-1] にある\n            j = m - 1\n        } else { // 目標要素が見つかったらそのインデックスを返す\n            return m\n        }\n    }\n    // 目標要素が見つからなければ -1 を返す\n    return -1\n}\n</code></pre> binary_search.swift<pre><code>/* 二分探索（両閉区間） */\nfunc binarySearch(nums: [Int], target: Int) -&gt; Int {\n    // 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す\n    var i = nums.startIndex\n    var j = nums.endIndex - 1\n    // ループし、探索区間が空になったら終了する（i &gt; j で空）\n    while i &lt;= j {\n        let m = i + (j - i) / 2 // 中点インデックス m を計算\n        if nums[m] &lt; target { // この場合、target は区間 [m+1, j] にある\n            i = m + 1\n        } else if nums[m] &gt; target { // この場合、target は区間 [i, m-1] にある\n            j = m - 1\n        } else { // 目標要素が見つかったらそのインデックスを返す\n            return m\n        }\n    }\n    // 目標要素が見つからなければ -1 を返す\n    return -1\n}\n</code></pre> binary_search.js<pre><code>/* 二分探索（両閉区間） */\nfunction binarySearch(nums, target) {\n    // 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す\n    let i = 0,\n        j = nums.length - 1;\n    // ループし、探索区間が空になったら終了する（i &gt; j で空）\n    while (i &lt;= j) {\n        // 中点インデックス `m` を計算し、`parseInt()` で切り捨てる\n        const m = parseInt(i + (j - i) / 2);\n        if (nums[m] &lt; target)\n            // この場合、target は区間 [m+1, j] にある\n            i = m + 1;\n        else if (nums[m] &gt; target)\n            // この場合、target は区間 [i, m-1] にある\n            j = m - 1;\n        else return m; // 目標要素が見つかったらそのインデックスを返す\n    }\n    // 目標要素が見つからなければ -1 を返す\n    return -1;\n}\n</code></pre> binary_search.ts<pre><code>/* 二分探索（両閉区間） */\nfunction binarySearch(nums: number[], target: number): number {\n    // 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す\n    let i = 0,\n        j = nums.length - 1;\n    // ループし、探索区間が空になったら終了する（i &gt; j で空）\n    while (i &lt;= j) {\n        // 中点インデックス m を計算\n        const m = Math.floor(i + (j - i) / 2);\n        if (nums[m] &lt; target) {\n            // この場合、target は区間 [m+1, j] にある\n            i = m + 1;\n        } else if (nums[m] &gt; target) {\n            // この場合、target は区間 [i, m-1] にある\n            j = m - 1;\n        } else {\n            // 目標要素が見つかったらそのインデックスを返す\n            return m;\n        }\n    }\n    return -1; // 目標要素が見つからなければ -1 を返す\n}\n</code></pre> binary_search.dart<pre><code>/* 二分探索（両閉区間） */\nint binarySearch(List&lt;int&gt; nums, int target) {\n  // 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す\n  int i = 0, j = nums.length - 1;\n  // ループし、探索区間が空になったら終了する（i &gt; j で空）\n  while (i &lt;= j) {\n    int m = i + (j - i) ~/ 2; // 中点インデックス m を計算\n    if (nums[m] &lt; target) {\n      // この場合、target は区間 [m+1, j] にある\n      i = m + 1;\n    } else if (nums[m] &gt; target) {\n      // この場合、target は区間 [i, m-1] にある\n      j = m - 1;\n    } else {\n      // 目標要素が見つかったらそのインデックスを返す\n      return m;\n    }\n  }\n  // 目標要素が見つからなければ -1 を返す\n  return -1;\n}\n</code></pre> binary_search.rs<pre><code>/* 二分探索（両閉区間） */\nfn binary_search(nums: &amp;[i32], target: i32) -&gt; i32 {\n    // 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す\n    let mut i = 0;\n    let mut j = nums.len() as i32 - 1;\n    // ループし、探索区間が空になったら終了する（i &gt; j で空）\n    while i &lt;= j {\n        let m = i + (j - i) / 2; // 中点インデックス m を計算\n        if nums[m as usize] &lt; target {\n            // この場合、target は区間 [m+1, j] にある\n            i = m + 1;\n        } else if nums[m as usize] &gt; target {\n            // この場合、target は区間 [i, m-1] にある\n            j = m - 1;\n        } else {\n            // 目標要素が見つかったらそのインデックスを返す\n            return m;\n        }\n    }\n    // 目標要素が見つからなければ -1 を返す\n    return -1;\n}\n</code></pre> binary_search.c<pre><code>/* 二分探索（両閉区間） */\nint binarySearch(int *nums, int len, int target) {\n    // 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す\n    int i = 0, j = len - 1;\n    // ループし、探索区間が空になったら終了する（i &gt; j で空）\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // 中点インデックス m を計算\n        if (nums[m] &lt; target)    // この場合、target は区間 [m+1, j] にある\n            i = m + 1;\n        else if (nums[m] &gt; target) // この場合、target は区間 [i, m-1] にある\n            j = m - 1;\n        else // 目標要素が見つかったらそのインデックスを返す\n            return m;\n    }\n    // 目標要素が見つからなければ -1 を返す\n    return -1;\n}\n</code></pre> binary_search.kt<pre><code>/* 二分探索（両閉区間） */\nfun binarySearch(nums: IntArray, target: Int): Int {\n    // 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す\n    var i = 0\n    var j = nums.size - 1\n    // ループし、探索区間が空になったら終了する（i &gt; j で空）\n    while (i &lt;= j) {\n        val m = i + (j - i) / 2 // 中点インデックス m を計算\n        if (nums[m] &lt; target) // この場合、target は区間 [m+1, j] にある\n            i = m + 1\n        else if (nums[m] &gt; target) // この場合、target は区間 [i, m-1] にある\n            j = m - 1\n        else  // 目標要素が見つかったらそのインデックスを返す\n            return m\n    }\n    // 目標要素が見つからなければ -1 を返す\n    return -1\n}\n</code></pre> binary_search.rb<pre><code>### 二分探索（両閉区間） ###\ndef binary_search(nums, target)\n  # 両閉区間 [0, n-1] を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素を指す\n  i, j = 0, nums.length - 1\n\n  # ループし、探索区間が空になったら終了する（i &gt; j で空）\n  while i &lt;= j\n    # 理論上、Ruby の数値は無限に大きくできるため（メモリ容量に依存）、大きな数のオーバーフローを考慮する必要はない\n    m = (i + j) / 2   # 中点インデックス m を計算\n\n    if nums[m] &lt; target\n      i = m + 1 # この場合、target は区間 [m+1, j] にある\n    elsif nums[m] &gt; target\n      j = m - 1 # この場合、target は区間 [i, m-1] にある\n    else\n      return m  # 目標要素が見つかったらそのインデックスを返す\n    end\n  end\n\n  -1  # 目標要素が見つからなければ -1 を返す\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>時間計算量は \\(O(\\log n)\\) ：二分探索のループでは各ラウンドで区間が半分になるため、ループ回数は \\(\\log_2 n\\) です。</p> <p>空間計算量は \\(O(1)\\) ：ポインタ \\(i\\) と \\(j\\) に必要なのは定数サイズの空間だけです。</p>","path":["第 10 章 &nbsp; 探索","10.1 &nbsp; 二分探索"],"tags":[]},{"location":"chapter_searching/binary_search/#1011","level":2,"title":"10.1.1   区間の表し方","text":"<p>上記の両閉区間のほかに、一般的な区間表現として「左閉右開」区間があり、\\([0, n)\\) と定義されます。つまり左端は含み、右端は含みません。この表現では、区間 \\([i, j)\\) は \\(i = j\\) のとき空です。</p> <p>この表現に基づいて、同じ機能を持つ二分探索アルゴリズムを実装できます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search.py<pre><code>def binary_search_lcro(nums: list[int], target: int) -&gt; int:\n    \"\"\"二分探索（左閉右開区間）\"\"\"\n    # 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す\n    i, j = 0, len(nums)\n    # ループし、探索区間が空になったら終了する（i = j で空）\n    while i &lt; j:\n        m = (i + j) // 2  # 中点インデックス m を計算\n        if nums[m] &lt; target:\n            i = m + 1  # この場合、target は区間 [m+1, j) にある\n        elif nums[m] &gt; target:\n            j = m  # この場合、target は区間 [i, m) にある\n        else:\n            return m  # 目標要素が見つかったらそのインデックスを返す\n    return -1  # 目標要素が見つからなければ -1 を返す\n</code></pre> binary_search.cpp<pre><code>/* 二分探索（左閉右開区間） */\nint binarySearchLCRO(vector&lt;int&gt; &amp;nums, int target) {\n    // 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す\n    int i = 0, j = nums.size();\n    // ループし、探索区間が空になったら終了する（i = j で空）\n    while (i &lt; j) {\n        int m = i + (j - i) / 2; // 中点インデックス m を計算\n        if (nums[m] &lt; target)    // この場合、target は区間 [m+1, j) にある\n            i = m + 1;\n        else if (nums[m] &gt; target) // この場合、target は区間 [i, m) にある\n            j = m;\n        else // 目標要素が見つかったらそのインデックスを返す\n            return m;\n    }\n    // 目標要素が見つからなければ -1 を返す\n    return -1;\n}\n</code></pre> binary_search.java<pre><code>/* 二分探索（左閉右開区間） */\nint binarySearchLCRO(int[] nums, int target) {\n    // 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す\n    int i = 0, j = nums.length;\n    // ループし、探索区間が空になったら終了する（i = j で空）\n    while (i &lt; j) {\n        int m = i + (j - i) / 2; // 中点インデックス m を計算\n        if (nums[m] &lt; target) // この場合、target は区間 [m+1, j) にある\n            i = m + 1;\n        else if (nums[m] &gt; target) // この場合、target は区間 [i, m) にある\n            j = m;\n        else // 目標要素が見つかったらそのインデックスを返す\n            return m;\n    }\n    // 目標要素が見つからなければ -1 を返す\n    return -1;\n}\n</code></pre> binary_search.cs<pre><code>/* 二分探索（左閉右開区間） */\nint BinarySearchLCRO(int[] nums, int target) {\n    // 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す\n    int i = 0, j = nums.Length;\n    // ループし、探索区間が空になったら終了する（i = j で空）\n    while (i &lt; j) {\n        int m = i + (j - i) / 2;   // 中点インデックス m を計算\n        if (nums[m] &lt; target)      // この場合、target は区間 [m+1, j) にある\n            i = m + 1;\n        else if (nums[m] &gt; target) // この場合、target は区間 [i, m) にある\n            j = m;\n        else                       // 目標要素が見つかったらそのインデックスを返す\n            return m;\n    }\n    // 目標要素が見つからなければ -1 を返す\n    return -1;\n}\n</code></pre> binary_search.go<pre><code>/* 二分探索（左閉右開区間） */\nfunc binarySearchLCRO(nums []int, target int) int {\n    // 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す\n    i, j := 0, len(nums)\n    // ループし、探索区間が空になったら終了する（i = j で空）\n    for i &lt; j {\n        m := i + (j-i)/2      // 中点インデックス m を計算\n        if nums[m] &lt; target { // この場合、target は区間 [m+1, j) にある\n            i = m + 1\n        } else if nums[m] &gt; target { // この場合、target は区間 [i, m) にある\n            j = m\n        } else { // 目標要素が見つかったらそのインデックスを返す\n            return m\n        }\n    }\n    // 目標要素が見つからなければ -1 を返す\n    return -1\n}\n</code></pre> binary_search.swift<pre><code>/* 二分探索（左閉右開区間） */\nfunc binarySearchLCRO(nums: [Int], target: Int) -&gt; Int {\n    // 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す\n    var i = nums.startIndex\n    var j = nums.endIndex\n    // ループし、探索区間が空になったら終了する（i = j で空）\n    while i &lt; j {\n        let m = i + (j - i) / 2 // 中点インデックス m を計算\n        if nums[m] &lt; target { // この場合、target は区間 [m+1, j) にある\n            i = m + 1\n        } else if nums[m] &gt; target { // この場合、target は区間 [i, m) にある\n            j = m\n        } else { // 目標要素が見つかったらそのインデックスを返す\n            return m\n        }\n    }\n    // 目標要素が見つからなければ -1 を返す\n    return -1\n}\n</code></pre> binary_search.js<pre><code>/* 二分探索（左閉右開区間） */\nfunction binarySearchLCRO(nums, target) {\n    // 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す\n    let i = 0,\n        j = nums.length;\n    // ループし、探索区間が空になったら終了する（i = j で空）\n    while (i &lt; j) {\n        // 中点インデックス `m` を計算し、`parseInt()` で切り捨てる\n        const m = parseInt(i + (j - i) / 2);\n        if (nums[m] &lt; target)\n            // この場合、target は区間 [m+1, j) にある\n            i = m + 1;\n        else if (nums[m] &gt; target)\n            // この場合、target は区間 [i, m) にある\n            j = m;\n        // 目標要素が見つかったらそのインデックスを返す\n        else return m;\n    }\n    // 目標要素が見つからなければ -1 を返す\n    return -1;\n}\n</code></pre> binary_search.ts<pre><code>/* 二分探索（左閉右開区間） */\nfunction binarySearchLCRO(nums: number[], target: number): number {\n    // 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す\n    let i = 0,\n        j = nums.length;\n    // ループし、探索区間が空になったら終了する（i = j で空）\n    while (i &lt; j) {\n        // 中点インデックス m を計算\n        const m = Math.floor(i + (j - i) / 2);\n        if (nums[m] &lt; target) {\n            // この場合、target は区間 [m+1, j) にある\n            i = m + 1;\n        } else if (nums[m] &gt; target) {\n            // この場合、target は区間 [i, m) にある\n            j = m;\n        } else {\n            // 目標要素が見つかったらそのインデックスを返す\n            return m;\n        }\n    }\n    return -1; // 目標要素が見つからなければ -1 を返す\n}\n</code></pre> binary_search.dart<pre><code>/* 二分探索（左閉右開区間） */\nint binarySearchLCRO(List&lt;int&gt; nums, int target) {\n  // 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す\n  int i = 0, j = nums.length;\n  // ループし、探索区間が空になったら終了する（i = j で空）\n  while (i &lt; j) {\n    int m = i + (j - i) ~/ 2; // 中点インデックス m を計算\n    if (nums[m] &lt; target) {\n      // この場合、target は区間 [m+1, j) にある\n      i = m + 1;\n    } else if (nums[m] &gt; target) {\n      // この場合、target は区間 [i, m) にある\n      j = m;\n    } else {\n      // 目標要素が見つかったらそのインデックスを返す\n      return m;\n    }\n  }\n  // 目標要素が見つからなければ -1 を返す\n  return -1;\n}\n</code></pre> binary_search.rs<pre><code>/* 二分探索（左閉右開区間） */\nfn binary_search_lcro(nums: &amp;[i32], target: i32) -&gt; i32 {\n    // 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す\n    let mut i = 0;\n    let mut j = nums.len() as i32;\n    // ループし、探索区間が空になったら終了する（i = j で空）\n    while i &lt; j {\n        let m = i + (j - i) / 2; // 中点インデックス m を計算\n        if nums[m as usize] &lt; target {\n            // この場合、target は区間 [m+1, j) にある\n            i = m + 1;\n        } else if nums[m as usize] &gt; target {\n            // この場合、target は区間 [i, m) にある\n            j = m;\n        } else {\n            // 目標要素が見つかったらそのインデックスを返す\n            return m;\n        }\n    }\n    // 目標要素が見つからなければ -1 を返す\n    return -1;\n}\n</code></pre> binary_search.c<pre><code>/* 二分探索（左閉右開区間） */\nint binarySearchLCRO(int *nums, int len, int target) {\n    // 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す\n    int i = 0, j = len;\n    // ループし、探索区間が空になったら終了する（i = j で空）\n    while (i &lt; j) {\n        int m = i + (j - i) / 2; // 中点インデックス m を計算\n        if (nums[m] &lt; target)    // この場合、target は区間 [m+1, j) にある\n            i = m + 1;\n        else if (nums[m] &gt; target) // この場合、target は区間 [i, m) にある\n            j = m;\n        else // 目標要素が見つかったらそのインデックスを返す\n            return m;\n    }\n    // 目標要素が見つからなければ -1 を返す\n    return -1;\n}\n</code></pre> binary_search.kt<pre><code>/* 二分探索（左閉右開区間） */\nfun binarySearchLCRO(nums: IntArray, target: Int): Int {\n    // 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す\n    var i = 0\n    var j = nums.size\n    // ループし、探索区間が空になったら終了する（i = j で空）\n    while (i &lt; j) {\n        val m = i + (j - i) / 2 // 中点インデックス m を計算\n        if (nums[m] &lt; target) // この場合、target は区間 [m+1, j) にある\n            i = m + 1\n        else if (nums[m] &gt; target) // この場合、target は区間 [i, m) にある\n            j = m\n        else  // 目標要素が見つかったらそのインデックスを返す\n            return m\n    }\n    // 目標要素が見つからなければ -1 を返す\n    return -1\n}\n</code></pre> binary_search.rb<pre><code>### 二分探索（左閉右開区間） ###\ndef binary_search_lcro(nums, target)\n  # 左閉右開区間 [0, n) を初期化する。つまり i, j はそれぞれ配列の先頭要素と末尾要素+1を指す\n  i, j = 0, nums.length\n\n  # ループし、探索区間が空になったら終了する（i = j で空）\n  while i &lt; j\n    # 中点インデックス m を計算\n    m = (i + j) / 2\n\n    if nums[m] &lt; target\n      i = m + 1 # この場合、target は区間 [m+1, j) にある\n    elsif nums[m] &gt; target\n      j = m - 1 # この場合、target は区間 [i, m) にある\n    else\n      return m  # 目標要素が見つかったらそのインデックスを返す\n    end\n  end\n\n  -1  # 目標要素が見つからなければ -1 を返す\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>次の図に示すように、2 種類の区間表現では、二分探索アルゴリズムの初期化、ループ条件、区間の縮小操作がそれぞれ異なります。</p> <p>「両閉区間」の表現では左右の境界がどちらも閉区間として定義されるため、ポインタ \\(i\\) とポインタ \\(j\\) による区間縮小の操作も対称になります。このほうがミスをしにくいため、一般には「両閉区間」の書き方を推奨します。</p> <p></p> <p> 図 10-3   2 種類の区間定義 </p>","path":["第 10 章 &nbsp; 探索","10.1 &nbsp; 二分探索"],"tags":[]},{"location":"chapter_searching/binary_search/#1012","level":2,"title":"10.1.2   利点と限界","text":"<p>二分探索は時間と空間の両面で優れた性能を持ちます。</p> <ul> <li>二分探索は時間効率が高いです。データ量が大きい場合、対数時間計算量は大きな優位性を持ちます。たとえば、データサイズ \\(n = 2^{20}\\) のとき、線形探索では \\(2^{20} = 1048576\\) 回のループが必要ですが、二分探索では \\(\\log_2 2^{20} = 20\\) 回で済みます。</li> <li>二分探索は追加の空間を必要としません。追加領域を要する探索アルゴリズム（たとえばハッシュ探索）と比べて、二分探索はより省メモリです。</li> </ul> <p>しかし、二分探索があらゆる状況に適しているわけではなく、主な理由は次のとおりです。</p> <ul> <li>二分探索は整列済みデータにしか適用できません。入力データが無秩序な場合、二分探索を使うためだけにソートするのは割に合いません。ソートアルゴリズムの時間計算量は通常 \\(O(n \\log n)\\) であり、線形探索や二分探索よりも高いからです。要素を頻繁に挿入する場面では、配列の整列性を保つために特定位置へ挿入する必要があり、その時間計算量は \\(O(n)\\) と高コストです。</li> <li>二分探索は配列にしか適していません。二分探索では要素へ飛び飛びにアクセスする必要がありますが、連結リストでそのようなアクセスを行う効率は低いため、連結リストやそれを基に実装されたデータ構造には向きません。</li> <li>データ量が小さい場合は線形探索のほうが高性能です。線形探索では各ラウンドで 1 回の比較だけで済みますが、二分探索では 1 回の加算、1 回の除算、1 ~ 3 回の比較、1 回の加算（減算）が必要で、合計 4 ~ 6 個の基本操作になります。したがって、データ量 \\(n\\) が小さいときは、線形探索のほうがかえって速くなります。</li> </ul>","path":["第 10 章 &nbsp; 探索","10.1 &nbsp; 二分探索"],"tags":[]},{"location":"chapter_searching/binary_search_edge/","level":1,"title":"10.3   二分探索の境界","text":"","path":["第 10 章 &nbsp; 探索","10.3 &nbsp; 二分探索の境界"],"tags":[]},{"location":"chapter_searching/binary_search_edge/#1031","level":2,"title":"10.3.1   左端境界を探す","text":"<p>Question</p> <p>長さ \\(n\\) のソート済み配列 <code>nums</code> が与えられ、その中には重複要素が含まれる可能性があります。配列内で最も左にある要素 <code>target</code> のインデックスを返してください。配列にこの要素が含まれない場合は、\\(-1\\) を返します。</p> <p>二分探索で挿入位置を求める方法を思い出すと、探索完了後に \\(i\\) は最も左にある <code>target</code> を指します。したがって、挿入位置を探すことの本質は、最も左にある <code>target</code> のインデックスを探すことです。</p> <p>挿入位置を探す関数を使って左端境界を求めることを考えます。なお、配列に <code>target</code> が含まれない場合があり、そのときは次の 2 つの結果が起こりえます。</p> <ul> <li>挿入位置のインデックス \\(i\\) が範囲外になる。</li> <li>要素 <code>nums[i]</code> が <code>target</code> と等しくない。</li> </ul> <p>上の 2 つの状況に当てはまる場合は、直接 \\(-1\\) を返せば十分です。コードは以下のとおりです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_edge.py<pre><code>def binary_search_left_edge(nums: list[int], target: int) -&gt; int:\n    \"\"\"最も左の target を二分探索\"\"\"\n    # target の挿入位置を探すのと等価\n    i = binary_search_insertion(nums, target)\n    # target が見つからなければ、-1 を返す\n    if i == len(nums) or nums[i] != target:\n        return -1\n    # target が見つかったら、インデックス i を返す\n    return i\n</code></pre> binary_search_edge.cpp<pre><code>/* 最も左の target を二分探索 */\nint binarySearchLeftEdge(vector&lt;int&gt; &amp;nums, int target) {\n    // target の挿入位置を探すのと等価\n    int i = binarySearchInsertion(nums, target);\n    // target が見つからなければ、-1 を返す\n    if (i == nums.size() || nums[i] != target) {\n        return -1;\n    }\n    // target が見つかったら、インデックス i を返す\n    return i;\n}\n</code></pre> binary_search_edge.java<pre><code>/* 最も左の target を二分探索 */\nint binarySearchLeftEdge(int[] nums, int target) {\n    // target の挿入位置を探すのと等価\n    int i = binary_search_insertion.binarySearchInsertion(nums, target);\n    // target が見つからなければ、-1 を返す\n    if (i == nums.length || nums[i] != target) {\n        return -1;\n    }\n    // target が見つかったら、インデックス i を返す\n    return i;\n}\n</code></pre> binary_search_edge.cs<pre><code>/* 最も左の target を二分探索 */\nint BinarySearchLeftEdge(int[] nums, int target) {\n    // target の挿入位置を探すのと等価\n    int i = binary_search_insertion.BinarySearchInsertion(nums, target);\n    // target が見つからなければ、-1 を返す\n    if (i == nums.Length || nums[i] != target) {\n        return -1;\n    }\n    // target が見つかったら、インデックス i を返す\n    return i;\n}\n</code></pre> binary_search_edge.go<pre><code>/* 最も左の target を二分探索 */\nfunc binarySearchLeftEdge(nums []int, target int) int {\n    // target の挿入位置を探すのと等価\n    i := binarySearchInsertion(nums, target)\n    // target が見つからなければ、-1 を返す\n    if i == len(nums) || nums[i] != target {\n        return -1\n    }\n    // target が見つかったら、インデックス i を返す\n    return i\n}\n</code></pre> binary_search_edge.swift<pre><code>/* 最も左の target を二分探索 */\nfunc binarySearchLeftEdge(nums: [Int], target: Int) -&gt; Int {\n    // target の挿入位置を探すのと等価\n    let i = binarySearchInsertion(nums: nums, target: target)\n    // target が見つからなければ、-1 を返す\n    if i == nums.endIndex || nums[i] != target {\n        return -1\n    }\n    // target が見つかったら、インデックス i を返す\n    return i\n}\n</code></pre> binary_search_edge.js<pre><code>/* 最も左の target を二分探索 */\nfunction binarySearchLeftEdge(nums, target) {\n    // target の挿入位置を探すのと等価\n    const i = binarySearchInsertion(nums, target);\n    // target が見つからなければ、-1 を返す\n    if (i === nums.length || nums[i] !== target) {\n        return -1;\n    }\n    // target が見つかったら、インデックス i を返す\n    return i;\n}\n</code></pre> binary_search_edge.ts<pre><code>/* 最も左の target を二分探索 */\nfunction binarySearchLeftEdge(nums: Array&lt;number&gt;, target: number): number {\n    // target の挿入位置を探すのと等価\n    const i = binarySearchInsertion(nums, target);\n    // target が見つからなければ、-1 を返す\n    if (i === nums.length || nums[i] !== target) {\n        return -1;\n    }\n    // target が見つかったら、インデックス i を返す\n    return i;\n}\n</code></pre> binary_search_edge.dart<pre><code>/* 最も左の target を二分探索 */\nint binarySearchLeftEdge(List&lt;int&gt; nums, int target) {\n  // target の挿入位置を探すのと等価\n  int i = binarySearchInsertion(nums, target);\n  // target が見つからなければ、-1 を返す\n  if (i == nums.length || nums[i] != target) {\n    return -1;\n  }\n  // target が見つかったら、インデックス i を返す\n  return i;\n}\n</code></pre> binary_search_edge.rs<pre><code>/* 最も左の target を二分探索 */\nfn binary_search_left_edge(nums: &amp;[i32], target: i32) -&gt; i32 {\n    // target の挿入位置を探すのと等価\n    let i = binary_search_insertion(nums, target);\n    // target が見つからなければ、-1 を返す\n    if i == nums.len() as i32 || nums[i as usize] != target {\n        return -1;\n    }\n    // target が見つかったら、インデックス i を返す\n    i\n}\n</code></pre> binary_search_edge.c<pre><code>/* 最も左の target を二分探索 */\nint binarySearchLeftEdge(int *nums, int numSize, int target) {\n    // target の挿入位置を探すのと等価\n    int i = binarySearchInsertion(nums, numSize, target);\n    // target が見つからなければ、-1 を返す\n    if (i == numSize || nums[i] != target) {\n        return -1;\n    }\n    // target が見つかったら、インデックス i を返す\n    return i;\n}\n</code></pre> binary_search_edge.kt<pre><code>/* 最も左の target を二分探索 */\nfun binarySearchLeftEdge(nums: IntArray, target: Int): Int {\n    // target の挿入位置を探すのと等価\n    val i = binarySearchInsertion(nums, target)\n    // target が見つからなければ、-1 を返す\n    if (i == nums.size || nums[i] != target) {\n        return -1\n    }\n    // target が見つかったら、インデックス i を返す\n    return i\n}\n</code></pre> binary_search_edge.rb<pre><code>### target の最左位置を二分探索 ###\ndef binary_search_left_edge(nums, target)\n  # target の挿入位置を探すのと等価\n  i = binary_search_insertion(nums, target)\n\n  # target が見つからなければ、-1 を返す\n  return -1 if i == nums.length || nums[i] != target\n\n  i # target が見つかったら、インデックス i を返す\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 10 章 &nbsp; 探索","10.3 &nbsp; 二分探索の境界"],"tags":[]},{"location":"chapter_searching/binary_search_edge/#1032","level":2,"title":"10.3.2   右端境界を探す","text":"<p>では、最も右にある <code>target</code> はどのように探せるでしょうか。最も直接的な方法はコードを修正し、<code>nums[m] == target</code> の場合のポインタの縮小操作を置き換えることです。ここではコードを省略するので、興味があれば自分で実装してみてください。</p> <p>ここでは、より巧妙な 2 つの方法を紹介します。</p>","path":["第 10 章 &nbsp; 探索","10.3 &nbsp; 二分探索の境界"],"tags":[]},{"location":"chapter_searching/binary_search_edge/#1","level":3,"title":"1.   左端境界探索を再利用する","text":"<p>実際には、最も左の要素を探す関数を利用して最も右の要素を探せます。具体的には、最も右にある <code>target</code> を探すことを、最も左にある <code>target + 1</code> を探すことに変換します。</p> <p>下図のように、探索完了後、ポインタ \\(i\\) は最も左にある <code>target + 1</code>（存在する場合）を指し、\\(j\\) は最も右にある <code>target</code> を指します。したがって \\(j\\) を返せばよいです。</p> <p></p> <p> 図 10-7   右端境界の探索を左端境界の探索に変換する </p> <p>返される挿入位置は \\(i\\) なので、そこから \\(1\\) を引いて \\(j\\) を得る必要があることに注意してください：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_edge.py<pre><code>def binary_search_right_edge(nums: list[int], target: int) -&gt; int:\n    \"\"\"最も右の target を二分探索\"\"\"\n    # 最左の target + 1 を探す問題に変換する\n    i = binary_search_insertion(nums, target + 1)\n    # j は最も右の target を指し、i は target より大きい最初の要素を指す\n    j = i - 1\n    # target が見つからなければ、-1 を返す\n    if j == -1 or nums[j] != target:\n        return -1\n    # target が見つかったら、インデックス j を返す\n    return j\n</code></pre> binary_search_edge.cpp<pre><code>/* 最も右の target を二分探索 */\nint binarySearchRightEdge(vector&lt;int&gt; &amp;nums, int target) {\n    // 最左の target + 1 を探す問題に変換する\n    int i = binarySearchInsertion(nums, target + 1);\n    // j は最も右の target を指し、i は target より大きい最初の要素を指す\n    int j = i - 1;\n    // target が見つからなければ、-1 を返す\n    if (j == -1 || nums[j] != target) {\n        return -1;\n    }\n    // target が見つかったら、インデックス j を返す\n    return j;\n}\n</code></pre> binary_search_edge.java<pre><code>/* 最も右の target を二分探索 */\nint binarySearchRightEdge(int[] nums, int target) {\n    // 最左の target + 1 を探す問題に変換する\n    int i = binary_search_insertion.binarySearchInsertion(nums, target + 1);\n    // j は最も右の target を指し、i は target より大きい最初の要素を指す\n    int j = i - 1;\n    // target が見つからなければ、-1 を返す\n    if (j == -1 || nums[j] != target) {\n        return -1;\n    }\n    // target が見つかったら、インデックス j を返す\n    return j;\n}\n</code></pre> binary_search_edge.cs<pre><code>/* 最も右の target を二分探索 */\nint BinarySearchRightEdge(int[] nums, int target) {\n    // 最左の target + 1 を探す問題に変換する\n    int i = binary_search_insertion.BinarySearchInsertion(nums, target + 1);\n    // j は最も右の target を指し、i は target より大きい最初の要素を指す\n    int j = i - 1;\n    // target が見つからなければ、-1 を返す\n    if (j == -1 || nums[j] != target) {\n        return -1;\n    }\n    // target が見つかったら、インデックス j を返す\n    return j;\n}\n</code></pre> binary_search_edge.go<pre><code>/* 最も右の target を二分探索 */\nfunc binarySearchRightEdge(nums []int, target int) int {\n    // 最左の target + 1 を探す問題に変換する\n    i := binarySearchInsertion(nums, target+1)\n    // j は最も右の target を指し、i は target より大きい最初の要素を指す\n    j := i - 1\n    // target が見つからなければ、-1 を返す\n    if j == -1 || nums[j] != target {\n        return -1\n    }\n    // target が見つかったら、インデックス j を返す\n    return j\n}\n</code></pre> binary_search_edge.swift<pre><code>/* 最も右の target を二分探索 */\nfunc binarySearchRightEdge(nums: [Int], target: Int) -&gt; Int {\n    // 最左の target + 1 を探す問題に変換する\n    let i = binarySearchInsertion(nums: nums, target: target + 1)\n    // j は最も右の target を指し、i は target より大きい最初の要素を指す\n    let j = i - 1\n    // target が見つからなければ、-1 を返す\n    if j == -1 || nums[j] != target {\n        return -1\n    }\n    // target が見つかったら、インデックス j を返す\n    return j\n}\n</code></pre> binary_search_edge.js<pre><code>/* 最も右の target を二分探索 */\nfunction binarySearchRightEdge(nums, target) {\n    // 最左の target + 1 を探す問題に変換する\n    const i = binarySearchInsertion(nums, target + 1);\n    // j は最も右の target を指し、i は target より大きい最初の要素を指す\n    const j = i - 1;\n    // target が見つからなければ、-1 を返す\n    if (j === -1 || nums[j] !== target) {\n        return -1;\n    }\n    // target が見つかったら、インデックス j を返す\n    return j;\n}\n</code></pre> binary_search_edge.ts<pre><code>/* 最も右の target を二分探索 */\nfunction binarySearchRightEdge(nums: Array&lt;number&gt;, target: number): number {\n    // 最左の target + 1 を探す問題に変換する\n    const i = binarySearchInsertion(nums, target + 1);\n    // j は最も右の target を指し、i は target より大きい最初の要素を指す\n    const j = i - 1;\n    // target が見つからなければ、-1 を返す\n    if (j === -1 || nums[j] !== target) {\n        return -1;\n    }\n    // target が見つかったら、インデックス j を返す\n    return j;\n}\n</code></pre> binary_search_edge.dart<pre><code>/* 最も右の target を二分探索 */\nint binarySearchRightEdge(List&lt;int&gt; nums, int target) {\n  // 最左の target + 1 を探す問題に変換する\n  int i = binarySearchInsertion(nums, target + 1);\n  // j は最も右の target を指し、i は target より大きい最初の要素を指す\n  int j = i - 1;\n  // target が見つからなければ、-1 を返す\n  if (j == -1 || nums[j] != target) {\n    return -1;\n  }\n  // target が見つかったら、インデックス j を返す\n  return j;\n}\n</code></pre> binary_search_edge.rs<pre><code>/* 最も右の target を二分探索 */\nfn binary_search_right_edge(nums: &amp;[i32], target: i32) -&gt; i32 {\n    // 最左の target + 1 を探す問題に変換する\n    let i = binary_search_insertion(nums, target + 1);\n    // j は最も右の target を指し、i は target より大きい最初の要素を指す\n    let j = i - 1;\n    // target が見つからなければ、-1 を返す\n    if j == -1 || nums[j as usize] != target {\n        return -1;\n    }\n    // target が見つかったら、インデックス j を返す\n    j\n}\n</code></pre> binary_search_edge.c<pre><code>/* 最も右の target を二分探索 */\nint binarySearchRightEdge(int *nums, int numSize, int target) {\n    // 最左の target + 1 を探す問題に変換する\n    int i = binarySearchInsertion(nums, numSize, target + 1);\n    // j は最も右の target を指し、i は target より大きい最初の要素を指す\n    int j = i - 1;\n    // target が見つからなければ、-1 を返す\n    if (j == -1 || nums[j] != target) {\n        return -1;\n    }\n    // target が見つかったら、インデックス j を返す\n    return j;\n}\n</code></pre> binary_search_edge.kt<pre><code>/* 最も右の target を二分探索 */\nfun binarySearchRightEdge(nums: IntArray, target: Int): Int {\n    // 最左の target + 1 を探す問題に変換する\n    val i = binarySearchInsertion(nums, target + 1)\n    // j は最も右の target を指し、i は target より大きい最初の要素を指す\n    val j = i - 1\n    // target が見つからなければ、-1 を返す\n    if (j == -1 || nums[j] != target) {\n        return -1\n    }\n    // target が見つかったら、インデックス j を返す\n    return j\n}\n</code></pre> binary_search_edge.rb<pre><code>### target の最右位置を二分探索 ###\ndef binary_search_right_edge(nums, target)\n  # 最左の target + 1 を探す問題に変換する\n  i = binary_search_insertion(nums, target + 1)\n\n  # j は最も右の target を指し、i は target より大きい最初の要素を指す\n  j = i - 1\n\n  # target が見つからなければ、-1 を返す\n  return -1 if j == -1 || nums[j] != target\n\n  j # target が見つかったら、インデックス j を返す\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 10 章 &nbsp; 探索","10.3 &nbsp; 二分探索の境界"],"tags":[]},{"location":"chapter_searching/binary_search_edge/#2","level":3,"title":"2.   要素探索に変換する","text":"<p>配列に <code>target</code> が含まれない場合、最終的に \\(i\\) と \\(j\\) はそれぞれ <code>target</code> より大きい最初の要素と、<code>target</code> より小さい最初の要素を指すことになります。</p> <p>したがって、下図のように、配列中に存在しない要素を構成して、それを使って左右の境界を探せます。</p> <ul> <li>最も左にある <code>target</code> の探索：<code>target - 0.5</code> を探すことに変換でき、ポインタ \\(i\\) を返します。</li> <li>最も右にある <code>target</code> の探索：<code>target + 0.5</code> を探すことに変換でき、ポインタ \\(j\\) を返します。</li> </ul> <p></p> <p> 図 10-8   境界の探索を要素の探索に変換する </p> <p>ここではコードを省略しますが、次の 2 点に注意が必要です。</p> <ul> <li>与えられた配列には小数が含まれないため、等しい場合をどう処理するかを気にする必要はありません。</li> <li>この方法では小数を導入するため、関数内の変数 <code>target</code> を浮動小数点数型に変更する必要があります（Python は変更不要です）。</li> </ul>","path":["第 10 章 &nbsp; 探索","10.3 &nbsp; 二分探索の境界"],"tags":[]},{"location":"chapter_searching/binary_search_insertion/","level":1,"title":"10.2   二分探索の挿入位置","text":"<p>二分探索は目標要素の検索だけでなく、目標要素の挿入位置を探すなど、多くの派生問題の解決にも利用できます。</p>","path":["第 10 章 &nbsp; 探索","10.2 &nbsp; 二分探索の挿入位置"],"tags":[]},{"location":"chapter_searching/binary_search_insertion/#1021","level":2,"title":"10.2.1   重複要素がない場合","text":"<p>Question</p> <p>長さ \\(n\\) の整列済み配列 <code>nums</code> と要素 <code>target</code> が与えられます。配列には重複要素は存在しません。ここで <code>target</code> を配列 <code>nums</code> に挿入し、その順序を保ちます。配列中にすでに要素 <code>target</code> が存在する場合は、その左側に挿入します。挿入後の配列における <code>target</code> のインデックスを返してください。例を以下の図に示します。</p> <p></p> <p> 図 10-4   二分探索の挿入位置の例データ </p> <p>前節の二分探索コードを再利用したい場合は、次の二つの問題に答える必要があります。</p> <p>問題 1：配列に <code>target</code> が含まれる場合、挿入位置のインデックスはその要素のインデックスですか？</p> <p>問題では <code>target</code> を等しい要素の左側に挿入するよう求めているため、新しく挿入された <code>target</code> は元の <code>target</code> の位置に入ります。つまり、配列に <code>target</code> が含まれる場合、挿入位置のインデックスはその <code>target</code> のインデックスです。</p> <p>問題 2：配列に <code>target</code> が存在しない場合、挿入位置はどの要素のインデックスですか？</p> <p>二分探索の過程をさらに考えると、<code>nums[m] &lt; target</code> のときは \\(i\\) が移動します。これは、ポインタ \\(i\\) が <code>target</code> 以上の要素へ近づいていることを意味します。同様に、ポインタ \\(j\\) は常に <code>target</code> 以下の要素へ近づいています。</p> <p>したがって二分探索の終了時には、\\(i\\) は最初の <code>target</code> より大きい要素を指し、\\(j\\) は最初の <code>target</code> より小さい要素を指します。よって、配列に <code>target</code> が含まれない場合、挿入インデックスは \\(i\\) です。コードは次のとおりです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_insertion.py<pre><code>def binary_search_insertion_simple(nums: list[int], target: int) -&gt; int:\n    \"\"\"二分探索で挿入位置を探す（重複要素なし）\"\"\"\n    i, j = 0, len(nums) - 1  # 両閉区間 [0, n-1] を初期化\n    while i &lt;= j:\n        m = (i + j) // 2  # 中点インデックス m を計算\n        if nums[m] &lt; target:\n            i = m + 1  # target は区間 [m+1, j] にある\n        elif nums[m] &gt; target:\n            j = m - 1  # target は区間 [i, m-1] にある\n        else:\n            return m  # target が見つかったら、挿入位置 m を返す\n    # target が見つからなければ、挿入位置 i を返す\n    return i\n</code></pre> binary_search_insertion.cpp<pre><code>/* 二分探索で挿入位置を探す（重複要素なし） */\nint binarySearchInsertionSimple(vector&lt;int&gt; &amp;nums, int target) {\n    int i = 0, j = nums.size() - 1; // 両閉区間 [0, n-1] を初期化\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // 中点インデックス m を計算\n        if (nums[m] &lt; target) {\n            i = m + 1; // target は区間 [m+1, j] にある\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target は区間 [i, m-1] にある\n        } else {\n            return m; // target が見つかったら、挿入位置 m を返す\n        }\n    }\n    // target が見つからなければ、挿入位置 i を返す\n    return i;\n}\n</code></pre> binary_search_insertion.java<pre><code>/* 二分探索で挿入位置を探す（重複要素なし） */\nint binarySearchInsertionSimple(int[] nums, int target) {\n    int i = 0, j = nums.length - 1; // 両閉区間 [0, n-1] を初期化\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // 中点インデックス m を計算\n        if (nums[m] &lt; target) {\n            i = m + 1; // target は区間 [m+1, j] にある\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target は区間 [i, m-1] にある\n        } else {\n            return m; // target が見つかったら、挿入位置 m を返す\n        }\n    }\n    // target が見つからなければ、挿入位置 i を返す\n    return i;\n}\n</code></pre> binary_search_insertion.cs<pre><code>/* 二分探索で挿入位置を探す（重複要素なし） */\nint BinarySearchInsertionSimple(int[] nums, int target) {\n    int i = 0, j = nums.Length - 1; // 両閉区間 [0, n-1] を初期化\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // 中点インデックス m を計算\n        if (nums[m] &lt; target) {\n            i = m + 1; // target は区間 [m+1, j] にある\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target は区間 [i, m-1] にある\n        } else {\n            return m; // target が見つかったら、挿入位置 m を返す\n        }\n    }\n    // target が見つからなければ、挿入位置 i を返す\n    return i;\n}\n</code></pre> binary_search_insertion.go<pre><code>/* 二分探索で挿入位置を探す（重複要素なし） */\nfunc binarySearchInsertionSimple(nums []int, target int) int {\n    // 両閉区間 [0, n-1] を初期化\n    i, j := 0, len(nums)-1\n    for i &lt;= j {\n        // 中点インデックス m を計算\n        m := i + (j-i)/2\n        if nums[m] &lt; target {\n            // target は区間 [m+1, j] にある\n            i = m + 1\n        } else if nums[m] &gt; target {\n            // target は区間 [i, m-1] にある\n            j = m - 1\n        } else {\n            // target が見つかったら、挿入位置 m を返す\n            return m\n        }\n    }\n    // target が見つからなければ、挿入位置 i を返す\n    return i\n}\n</code></pre> binary_search_insertion.swift<pre><code>/* 二分探索で挿入位置を探す（重複要素なし） */\nfunc binarySearchInsertionSimple(nums: [Int], target: Int) -&gt; Int {\n    // 両閉区間 [0, n-1] を初期化\n    var i = nums.startIndex\n    var j = nums.endIndex - 1\n    while i &lt;= j {\n        let m = i + (j - i) / 2 // 中点インデックス m を計算\n        if nums[m] &lt; target {\n            i = m + 1 // target は区間 [m+1, j] にある\n        } else if nums[m] &gt; target {\n            j = m - 1 // target は区間 [i, m-1] にある\n        } else {\n            return m // target が見つかったら、挿入位置 m を返す\n        }\n    }\n    // target が見つからなければ、挿入位置 i を返す\n    return i\n}\n</code></pre> binary_search_insertion.js<pre><code>/* 二分探索で挿入位置を探す（重複要素なし） */\nfunction binarySearchInsertionSimple(nums, target) {\n    let i = 0,\n        j = nums.length - 1; // 両閉区間 [0, n-1] を初期化\n    while (i &lt;= j) {\n        const m = Math.floor(i + (j - i) / 2); // 中点インデックス m を計算し、Math.floor() で切り捨てる\n        if (nums[m] &lt; target) {\n            i = m + 1; // target は区間 [m+1, j] にある\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target は区間 [i, m-1] にある\n        } else {\n            return m; // target が見つかったら、挿入位置 m を返す\n        }\n    }\n    // target が見つからなければ、挿入位置 i を返す\n    return i;\n}\n</code></pre> binary_search_insertion.ts<pre><code>/* 二分探索で挿入位置を探す（重複要素なし） */\nfunction binarySearchInsertionSimple(\n    nums: Array&lt;number&gt;,\n    target: number\n): number {\n    let i = 0,\n        j = nums.length - 1; // 両閉区間 [0, n-1] を初期化\n    while (i &lt;= j) {\n        const m = Math.floor(i + (j - i) / 2); // 中点インデックス m を計算し、Math.floor() で切り捨てる\n        if (nums[m] &lt; target) {\n            i = m + 1; // target は区間 [m+1, j] にある\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target は区間 [i, m-1] にある\n        } else {\n            return m; // target が見つかったら、挿入位置 m を返す\n        }\n    }\n    // target が見つからなければ、挿入位置 i を返す\n    return i;\n}\n</code></pre> binary_search_insertion.dart<pre><code>/* 二分探索で挿入位置を探す（重複要素なし） */\nint binarySearchInsertionSimple(List&lt;int&gt; nums, int target) {\n  int i = 0, j = nums.length - 1; // 両閉区間 [0, n-1] を初期化\n  while (i &lt;= j) {\n    int m = i + (j - i) ~/ 2; // 中点インデックス m を計算\n    if (nums[m] &lt; target) {\n      i = m + 1; // target は区間 [m+1, j] にある\n    } else if (nums[m] &gt; target) {\n      j = m - 1; // target は区間 [i, m-1] にある\n    } else {\n      return m; // target が見つかったら、挿入位置 m を返す\n    }\n  }\n  // target が見つからなければ、挿入位置 i を返す\n  return i;\n}\n</code></pre> binary_search_insertion.rs<pre><code>/* 二分探索で挿入位置を探す（重複要素なし） */\nfn binary_search_insertion_simple(nums: &amp;[i32], target: i32) -&gt; i32 {\n    let (mut i, mut j) = (0, nums.len() as i32 - 1); // 両閉区間 [0, n-1] を初期化\n    while i &lt;= j {\n        let m = i + (j - i) / 2; // 中点インデックス m を計算\n        if nums[m as usize] &lt; target {\n            i = m + 1; // target は区間 [m+1, j] にある\n        } else if nums[m as usize] &gt; target {\n            j = m - 1; // target は区間 [i, m-1] にある\n        } else {\n            return m;\n        }\n    }\n    // target が見つからなければ、挿入位置 i を返す\n    i\n}\n</code></pre> binary_search_insertion.c<pre><code>/* 二分探索で挿入位置を探す（重複要素なし） */\nint binarySearchInsertionSimple(int *nums, int numSize, int target) {\n    int i = 0, j = numSize - 1; // 両閉区間 [0, n-1] を初期化\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // 中点インデックス m を計算\n        if (nums[m] &lt; target) {\n            i = m + 1; // target は区間 [m+1, j] にある\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target は区間 [i, m-1] にある\n        } else {\n            return m; // target が見つかったら、挿入位置 m を返す\n        }\n    }\n    // target が見つからなければ、挿入位置 i を返す\n    return i;\n}\n</code></pre> binary_search_insertion.kt<pre><code>/* 二分探索で挿入位置を探す（重複要素なし） */\nfun binarySearchInsertionSimple(nums: IntArray, target: Int): Int {\n    var i = 0\n    var j = nums.size - 1 // 両閉区間 [0, n-1] を初期化\n    while (i &lt;= j) {\n        val m = i + (j - i) / 2 // 中点インデックス m を計算\n        if (nums[m] &lt; target) {\n            i = m + 1 // target は区間 [m+1, j] にある\n        } else if (nums[m] &gt; target) {\n            j = m - 1 // target は区間 [i, m-1] にある\n        } else {\n            return m // target が見つかったら、挿入位置 m を返す\n        }\n    }\n    // target が見つからなければ、挿入位置 i を返す\n    return i\n}\n</code></pre> binary_search_insertion.rb<pre><code>### 二分探索の挿入位置（重複要素なし） ###\ndef binary_search_insertion_simple(nums, target)\n  # 両閉区間 [0, n-1] を初期化\n  i, j = 0, nums.length - 1\n\n  while i &lt;= j\n    # 中点インデックス m を計算\n    m = (i + j) / 2\n\n    if nums[m] &lt; target\n      i = m + 1 # target は区間 [m+1, j] にある\n    elsif nums[m] &gt; target\n      j = m - 1 # target は区間 [i, m-1] にある\n    else\n      return m  # target が見つかったら、挿入位置 m を返す\n    end\n  end\n\n  i # target が見つからなければ、挿入位置 i を返す\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 10 章 &nbsp; 探索","10.2 &nbsp; 二分探索の挿入位置"],"tags":[]},{"location":"chapter_searching/binary_search_insertion/#1022","level":2,"title":"10.2.2   重複要素がある場合","text":"<p>Question</p> <p>前問を踏まえ、配列には重複要素が含まれる可能性があるものとし、それ以外の条件は変わりません。</p> <p>配列中に複数の <code>target</code> が存在する場合、通常の二分探索ではそのうち一つの <code>target</code> のインデックスしか返せず、その要素の左側と右側にあといくつ <code>target</code> があるかは分かりません。</p> <p>問題では目標要素を最も左に挿入する必要があるため、配列中で最も左にある <code>target</code> のインデックスを探す必要があります。まずは以下の図に示す手順で実現することを考えます。</p> <ol> <li>二分探索を実行し、任意の <code>target</code> のインデックスを得て、これを \\(k\\) とします。</li> <li>インデックス \\(k\\) から始めて左へ線形探索し、最も左の <code>target</code> を見つけたら返します。</li> </ol> <p></p> <p> 図 10-5   線形探索による重複要素の挿入位置 </p> <p>この方法は使用できますが、線形探索を含むため、時間計算量は \\(O(n)\\) です。配列中に重複した <code>target</code> が多い場合、この方法の効率は低くなります。</p> <p>次に、二分探索のコードを拡張することを考えます。以下の図に示すように、全体の流れは変えず、各反復でまず中点インデックス \\(m\\) を計算し、その後 <code>target</code> と <code>nums[m]</code> の大小関係を判定して、次のいくつかの状況に分けます。</p> <ul> <li><code>nums[m] &lt; target</code> または <code>nums[m] &gt; target</code> のときは、まだ <code>target</code> を見つけていないことを意味するため、通常の二分探索と同じ区間縮小を行い、ポインタ \\(i\\) と \\(j\\) を <code>target</code> に近づけます。</li> <li><code>nums[m] == target</code> のときは、<code>target</code> より小さい要素が区間 \\([i, m - 1]\\) にあることを意味するため、\\(j = m - 1\\) として区間を縮小し、ポインタ \\(j\\) を <code>target</code> より小さい要素に近づけます。</li> </ul> <p>ループ終了後、\\(i\\) は最も左の <code>target</code> を指し、\\(j\\) は最初の <code>target</code> より小さい要素を指すため、インデックス \\(i\\) が挿入位置です。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 10-6   重複要素に対する二分探索の挿入位置の手順 </p> <p>以下のコードを観察すると、分岐 <code>nums[m] &gt; target</code> と <code>nums[m] == target</code> の処理は同じであるため、両者はまとめることができます。</p> <p>それでも、判定条件を分けたままにしておくことは可能であり、そのほうがロジックがより明確で、可読性も高くなります。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_insertion.py<pre><code>def binary_search_insertion(nums: list[int], target: int) -&gt; int:\n    \"\"\"二分探索で挿入位置を探す（重複要素あり）\"\"\"\n    i, j = 0, len(nums) - 1  # 両閉区間 [0, n-1] を初期化\n    while i &lt;= j:\n        m = (i + j) // 2  # 中点インデックス m を計算\n        if nums[m] &lt; target:\n            i = m + 1  # target は区間 [m+1, j] にある\n        elif nums[m] &gt; target:\n            j = m - 1  # target は区間 [i, m-1] にある\n        else:\n            j = m - 1  # target より小さい最初の要素は区間 [i, m-1] にある\n    # 挿入位置 i を返す\n    return i\n</code></pre> binary_search_insertion.cpp<pre><code>/* 二分探索で挿入位置を探す（重複要素あり） */\nint binarySearchInsertion(vector&lt;int&gt; &amp;nums, int target) {\n    int i = 0, j = nums.size() - 1; // 両閉区間 [0, n-1] を初期化\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // 中点インデックス m を計算\n        if (nums[m] &lt; target) {\n            i = m + 1; // target は区間 [m+1, j] にある\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target は区間 [i, m-1] にある\n        } else {\n            j = m - 1; // target より小さい最初の要素は区間 [i, m-1] にある\n        }\n    }\n    // 挿入位置 i を返す\n    return i;\n}\n</code></pre> binary_search_insertion.java<pre><code>/* 二分探索で挿入位置を探す（重複要素あり） */\nint binarySearchInsertion(int[] nums, int target) {\n    int i = 0, j = nums.length - 1; // 両閉区間 [0, n-1] を初期化\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // 中点インデックス m を計算\n        if (nums[m] &lt; target) {\n            i = m + 1; // target は区間 [m+1, j] にある\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target は区間 [i, m-1] にある\n        } else {\n            j = m - 1; // target より小さい最初の要素は区間 [i, m-1] にある\n        }\n    }\n    // 挿入位置 i を返す\n    return i;\n}\n</code></pre> binary_search_insertion.cs<pre><code>/* 二分探索で挿入位置を探す（重複要素あり） */\nint BinarySearchInsertion(int[] nums, int target) {\n    int i = 0, j = nums.Length - 1; // 両閉区間 [0, n-1] を初期化\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // 中点インデックス m を計算\n        if (nums[m] &lt; target) {\n            i = m + 1; // target は区間 [m+1, j] にある\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target は区間 [i, m-1] にある\n        } else {\n            j = m - 1; // target より小さい最初の要素は区間 [i, m-1] にある\n        }\n    }\n    // 挿入位置 i を返す\n    return i;\n}\n</code></pre> binary_search_insertion.go<pre><code>/* 二分探索で挿入位置を探す（重複要素あり） */\nfunc binarySearchInsertion(nums []int, target int) int {\n    // 両閉区間 [0, n-1] を初期化\n    i, j := 0, len(nums)-1\n    for i &lt;= j {\n        // 中点インデックス m を計算\n        m := i + (j-i)/2\n        if nums[m] &lt; target {\n            // target は区間 [m+1, j] にある\n            i = m + 1\n        } else if nums[m] &gt; target {\n            // target は区間 [i, m-1] にある\n            j = m - 1\n        } else {\n            // target より小さい最初の要素は区間 [i, m-1] にある\n            j = m - 1\n        }\n    }\n    // 挿入位置 i を返す\n    return i\n}\n</code></pre> binary_search_insertion.swift<pre><code>/* 二分探索で挿入位置を探す（重複要素あり） */\nfunc binarySearchInsertion(nums: [Int], target: Int) -&gt; Int {\n    // 両閉区間 [0, n-1] を初期化\n    var i = nums.startIndex\n    var j = nums.endIndex - 1\n    while i &lt;= j {\n        let m = i + (j - i) / 2 // 中点インデックス m を計算\n        if nums[m] &lt; target {\n            i = m + 1 // target は区間 [m+1, j] にある\n        } else if nums[m] &gt; target {\n            j = m - 1 // target は区間 [i, m-1] にある\n        } else {\n            j = m - 1 // target より小さい最初の要素は区間 [i, m-1] にある\n        }\n    }\n    // 挿入位置 i を返す\n    return i\n}\n</code></pre> binary_search_insertion.js<pre><code>/* 二分探索で挿入位置を探す（重複要素あり） */\nfunction binarySearchInsertion(nums, target) {\n    let i = 0,\n        j = nums.length - 1; // 両閉区間 [0, n-1] を初期化\n    while (i &lt;= j) {\n        const m = Math.floor(i + (j - i) / 2); // 中点インデックス m を計算し、Math.floor() で切り捨てる\n        if (nums[m] &lt; target) {\n            i = m + 1; // target は区間 [m+1, j] にある\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target は区間 [i, m-1] にある\n        } else {\n            j = m - 1; // target より小さい最初の要素は区間 [i, m-1] にある\n        }\n    }\n    // 挿入位置 i を返す\n    return i;\n}\n</code></pre> binary_search_insertion.ts<pre><code>/* 二分探索で挿入位置を探す（重複要素あり） */\nfunction binarySearchInsertion(nums: Array&lt;number&gt;, target: number): number {\n    let i = 0,\n        j = nums.length - 1; // 両閉区間 [0, n-1] を初期化\n    while (i &lt;= j) {\n        const m = Math.floor(i + (j - i) / 2); // 中点インデックス m を計算し、Math.floor() で切り捨てる\n        if (nums[m] &lt; target) {\n            i = m + 1; // target は区間 [m+1, j] にある\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target は区間 [i, m-1] にある\n        } else {\n            j = m - 1; // target より小さい最初の要素は区間 [i, m-1] にある\n        }\n    }\n    // 挿入位置 i を返す\n    return i;\n}\n</code></pre> binary_search_insertion.dart<pre><code>/* 二分探索で挿入位置を探す（重複要素あり） */\nint binarySearchInsertion(List&lt;int&gt; nums, int target) {\n  int i = 0, j = nums.length - 1; // 両閉区間 [0, n-1] を初期化\n  while (i &lt;= j) {\n    int m = i + (j - i) ~/ 2; // 中点インデックス m を計算\n    if (nums[m] &lt; target) {\n      i = m + 1; // target は区間 [m+1, j] にある\n    } else if (nums[m] &gt; target) {\n      j = m - 1; // target は区間 [i, m-1] にある\n    } else {\n      j = m - 1; // target より小さい最初の要素は区間 [i, m-1] にある\n    }\n  }\n  // 挿入位置 i を返す\n  return i;\n}\n</code></pre> binary_search_insertion.rs<pre><code>/* 二分探索で挿入位置を探す（重複要素あり） */\npub fn binary_search_insertion(nums: &amp;[i32], target: i32) -&gt; i32 {\n    let (mut i, mut j) = (0, nums.len() as i32 - 1); // 両閉区間 [0, n-1] を初期化\n    while i &lt;= j {\n        let m = i + (j - i) / 2; // 中点インデックス m を計算\n        if nums[m as usize] &lt; target {\n            i = m + 1; // target は区間 [m+1, j] にある\n        } else if nums[m as usize] &gt; target {\n            j = m - 1; // target は区間 [i, m-1] にある\n        } else {\n            j = m - 1; // target より小さい最初の要素は区間 [i, m-1] にある\n        }\n    }\n    // 挿入位置 i を返す\n    i\n}\n</code></pre> binary_search_insertion.c<pre><code>/* 二分探索で挿入位置を探す（重複要素あり） */\nint binarySearchInsertion(int *nums, int numSize, int target) {\n    int i = 0, j = numSize - 1; // 両閉区間 [0, n-1] を初期化\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // 中点インデックス m を計算\n        if (nums[m] &lt; target) {\n            i = m + 1; // target は区間 [m+1, j] にある\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target は区間 [i, m-1] にある\n        } else {\n            j = m - 1; // target より小さい最初の要素は区間 [i, m-1] にある\n        }\n    }\n    // 挿入位置 i を返す\n    return i;\n}\n</code></pre> binary_search_insertion.kt<pre><code>/* 二分探索で挿入位置を探す（重複要素あり） */\nfun binarySearchInsertion(nums: IntArray, target: Int): Int {\n    var i = 0\n    var j = nums.size - 1 // 両閉区間 [0, n-1] を初期化\n    while (i &lt;= j) {\n        val m = i + (j - i) / 2 // 中点インデックス m を計算\n        if (nums[m] &lt; target) {\n            i = m + 1 // target は区間 [m+1, j] にある\n        } else if (nums[m] &gt; target) {\n            j = m - 1 // target は区間 [i, m-1] にある\n        } else {\n            j = m - 1 // target より小さい最初の要素は区間 [i, m-1] にある\n        }\n    }\n    // 挿入位置 i を返す\n    return i\n}\n</code></pre> binary_search_insertion.rb<pre><code>### 二分探索の挿入位置（重複要素あり） ###\ndef binary_search_insertion(nums, target)\n  # 両閉区間 [0, n-1] を初期化\n  i, j = 0, nums.length - 1\n\n  while i &lt;= j\n    # 中点インデックス m を計算\n    m = (i + j) / 2\n\n    if nums[m] &lt; target\n      i = m + 1 # target は区間 [m+1, j] にある\n    elsif nums[m] &gt; target\n      j = m - 1 # target は区間 [i, m-1] にある\n    else\n      j = m - 1 # target より小さい最初の要素は区間 [i, m-1] にある\n    end\n  end\n\n  i # 挿入位置 i を返す\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>Tip</p> <p>本節のコードはすべて「両閉区間」の書き方です。興味のある読者は「左閉右開」の書き方を自分で実装してみてください。</p> <p>要するに、二分探索とはポインタ \\(i\\) と \\(j\\) にそれぞれ探索目標を設定することにほかなりません。目標は具体的な要素（たとえば <code>target</code>）である場合もあれば、要素の範囲（たとえば <code>target</code> より小さい要素）である場合もあります。</p> <p>繰り返される二分のループの中で、ポインタ \\(i\\) と \\(j\\) はどちらも事前に定めた目標へ徐々に近づいていきます。最終的に、それらは答えを見つけるか、境界を越えたところで停止します。</p>","path":["第 10 章 &nbsp; 探索","10.2 &nbsp; 二分探索の挿入位置"],"tags":[]},{"location":"chapter_searching/replace_linear_by_hashing/","level":1,"title":"10.4   ハッシュによる最適化戦略","text":"<p>アルゴリズムの問題では，線形探索をハッシュ探索に置き換えることでアルゴリズムの時間計算量を下げることがよくあります。ここでは，あるアルゴリズム問題を通じて理解を深めましょう。</p> <p>Question</p> <p>整数配列 <code>nums</code> と目標要素 <code>target</code> が与えられたとき，配列内から和が <code>target</code> となる 2 つの要素を探索し，それらの配列インデックスを返してください。任意の 1 つの解を返せば十分です。</p>","path":["第 10 章 &nbsp; 探索","10.4 &nbsp; ハッシュによる最適化戦略"],"tags":[]},{"location":"chapter_searching/replace_linear_by_hashing/#1041","level":2,"title":"10.4.1   線形探索：時間と引き換えに空間を節約","text":"<p>考えられるすべての組み合わせを直接走査することを考えます。次の図に示すように，2 重ループを開始し，各ラウンドで 2 つの整数の和が <code>target</code> であるかを判定します。そうであれば，それらのインデックスを返します。</p> <p></p> <p> 図 10-9   線形探索で 2 数の和を求める </p> <p>コードは次のとおりです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby two_sum.py<pre><code>def two_sum_brute_force(nums: list[int], target: int) -&gt; list[int]:\n    \"\"\"方法 1：総当たり列挙\"\"\"\n    # 2重ループのため、時間計算量は O(n^2)\n    for i in range(len(nums) - 1):\n        for j in range(i + 1, len(nums)):\n            if nums[i] + nums[j] == target:\n                return [i, j]\n    return []\n</code></pre> two_sum.cpp<pre><code>/* 方法 1：総当たり列挙 */\nvector&lt;int&gt; twoSumBruteForce(vector&lt;int&gt; &amp;nums, int target) {\n    int size = nums.size();\n    // 2重ループのため、時間計算量は O(n^2)\n    for (int i = 0; i &lt; size - 1; i++) {\n        for (int j = i + 1; j &lt; size; j++) {\n            if (nums[i] + nums[j] == target)\n                return {i, j};\n        }\n    }\n    return {};\n}\n</code></pre> two_sum.java<pre><code>/* 方法 1：総当たり列挙 */\nint[] twoSumBruteForce(int[] nums, int target) {\n    int size = nums.length;\n    // 2重ループのため、時間計算量は O(n^2)\n    for (int i = 0; i &lt; size - 1; i++) {\n        for (int j = i + 1; j &lt; size; j++) {\n            if (nums[i] + nums[j] == target)\n                return new int[] { i, j };\n        }\n    }\n    return new int[0];\n}\n</code></pre> two_sum.cs<pre><code>/* 方法 1：総当たり列挙 */\nint[] TwoSumBruteForce(int[] nums, int target) {\n    int size = nums.Length;\n    // 2重ループのため、時間計算量は O(n^2)\n    for (int i = 0; i &lt; size - 1; i++) {\n        for (int j = i + 1; j &lt; size; j++) {\n            if (nums[i] + nums[j] == target)\n                return [i, j];\n        }\n    }\n    return [];\n}\n</code></pre> two_sum.go<pre><code>/* 方法 1：総当たり列挙 */\nfunc twoSumBruteForce(nums []int, target int) []int {\n    size := len(nums)\n    // 2重ループのため、時間計算量は O(n^2)\n    for i := 0; i &lt; size-1; i++ {\n        for j := i + 1; j &lt; size; j++ {\n            if nums[i]+nums[j] == target {\n                return []int{i, j}\n            }\n        }\n    }\n    return nil\n}\n</code></pre> two_sum.swift<pre><code>/* 方法 1：総当たり列挙 */\nfunc twoSumBruteForce(nums: [Int], target: Int) -&gt; [Int] {\n    // 2重ループのため、時間計算量は O(n^2)\n    for i in nums.indices.dropLast() {\n        for j in nums.indices.dropFirst(i + 1) {\n            if nums[i] + nums[j] == target {\n                return [i, j]\n            }\n        }\n    }\n    return [0]\n}\n</code></pre> two_sum.js<pre><code>/* 方法 1：総当たり列挙 */\nfunction twoSumBruteForce(nums, target) {\n    const n = nums.length;\n    // 2重ループのため、時間計算量は O(n^2)\n    for (let i = 0; i &lt; n; i++) {\n        for (let j = i + 1; j &lt; n; j++) {\n            if (nums[i] + nums[j] === target) {\n                return [i, j];\n            }\n        }\n    }\n    return [];\n}\n</code></pre> two_sum.ts<pre><code>/* 方法 1：総当たり列挙 */\nfunction twoSumBruteForce(nums: number[], target: number): number[] {\n    const n = nums.length;\n    // 2重ループのため、時間計算量は O(n^2)\n    for (let i = 0; i &lt; n; i++) {\n        for (let j = i + 1; j &lt; n; j++) {\n            if (nums[i] + nums[j] === target) {\n                return [i, j];\n            }\n        }\n    }\n    return [];\n}\n</code></pre> two_sum.dart<pre><code>/* 方法1: 総当たり列挙 */\nList&lt;int&gt; twoSumBruteForce(List&lt;int&gt; nums, int target) {\n  int size = nums.length;\n  // 2重ループのため、時間計算量は O(n^2)\n  for (var i = 0; i &lt; size - 1; i++) {\n    for (var j = i + 1; j &lt; size; j++) {\n      if (nums[i] + nums[j] == target) return [i, j];\n    }\n  }\n  return [0];\n}\n</code></pre> two_sum.rs<pre><code>/* 方法 1：総当たり列挙 */\npub fn two_sum_brute_force(nums: &amp;Vec&lt;i32&gt;, target: i32) -&gt; Option&lt;Vec&lt;i32&gt;&gt; {\n    let size = nums.len();\n    // 2重ループのため、時間計算量は O(n^2)\n    for i in 0..size - 1 {\n        for j in i + 1..size {\n            if nums[i] + nums[j] == target {\n                return Some(vec![i as i32, j as i32]);\n            }\n        }\n    }\n    None\n}\n</code></pre> two_sum.c<pre><code>/* 方法 1：総当たり列挙 */\nint *twoSumBruteForce(int *nums, int numsSize, int target, int *returnSize) {\n    for (int i = 0; i &lt; numsSize; ++i) {\n        for (int j = i + 1; j &lt; numsSize; ++j) {\n            if (nums[i] + nums[j] == target) {\n                int *res = malloc(sizeof(int) * 2);\n                res[0] = i, res[1] = j;\n                *returnSize = 2;\n                return res;\n            }\n        }\n    }\n    *returnSize = 0;\n    return NULL;\n}\n</code></pre> two_sum.kt<pre><code>/* 方法 1：総当たり列挙 */\nfun twoSumBruteForce(nums: IntArray, target: Int): IntArray {\n    val size = nums.size\n    // 2重ループのため、時間計算量は O(n^2)\n    for (i in 0..&lt;size - 1) {\n        for (j in i + 1..&lt;size) {\n            if (nums[i] + nums[j] == target) return intArrayOf(i, j)\n        }\n    }\n    return IntArray(0)\n}\n</code></pre> two_sum.rb<pre><code>### 方法1：総当たり列挙 ###\ndef two_sum_brute_force(nums, target)\n  # 2重ループのため、時間計算量は O(n^2)\n  for i in 0...(nums.length - 1)\n    for j in (i + 1)...nums.length\n      return [i, j] if nums[i] + nums[j] == target\n    end\n  end\n\n  []\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>この方法の時間計算量は \\(O(n^2)\\) ，空間計算量は \\(O(1)\\) であり，大規模データでは非常に時間がかかります。</p>","path":["第 10 章 &nbsp; 探索","10.4 &nbsp; ハッシュによる最適化戦略"],"tags":[]},{"location":"chapter_searching/replace_linear_by_hashing/#1042","level":2,"title":"10.4.2   ハッシュ探索：空間と引き換えに時間を節約","text":"<p>ハッシュテーブルを利用し，キーと値をそれぞれ配列要素と要素のインデックスにします。配列をループで走査し，各ラウンドで次の図に示す手順を実行します。</p> <ol> <li>数値 <code>target - nums[i]</code> がハッシュテーブル内にあるかを判定します。あれば，この 2 つの要素のインデックスを直接返します。</li> <li>キーと値の組 <code>nums[i]</code> とインデックス <code>i</code> をハッシュテーブルに追加します。</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt; <p></p> <p></p> <p></p> <p> 図 10-10   補助ハッシュテーブルで 2 数の和を求める </p> <p>実装コードは次のとおりで，単一ループだけで済みます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby two_sum.py<pre><code>def two_sum_hash_table(nums: list[int], target: int) -&gt; list[int]:\n    \"\"\"方法 2：補助ハッシュテーブル\"\"\"\n    # 補助ハッシュテーブルを使用し、空間計算量は O(n)\n    dic = {}\n    # 単一ループで、時間計算量は O(n)\n    for i in range(len(nums)):\n        if target - nums[i] in dic:\n            return [dic[target - nums[i]], i]\n        dic[nums[i]] = i\n    return []\n</code></pre> two_sum.cpp<pre><code>/* 方法 2：補助ハッシュテーブル */\nvector&lt;int&gt; twoSumHashTable(vector&lt;int&gt; &amp;nums, int target) {\n    int size = nums.size();\n    // 補助ハッシュテーブルを使用し、空間計算量は O(n)\n    unordered_map&lt;int, int&gt; dic;\n    // 単一ループで、時間計算量は O(n)\n    for (int i = 0; i &lt; size; i++) {\n        if (dic.find(target - nums[i]) != dic.end()) {\n            return {dic[target - nums[i]], i};\n        }\n        dic.emplace(nums[i], i);\n    }\n    return {};\n}\n</code></pre> two_sum.java<pre><code>/* 方法 2：補助ハッシュテーブル */\nint[] twoSumHashTable(int[] nums, int target) {\n    int size = nums.length;\n    // 補助ハッシュテーブルを使用し、空間計算量は O(n)\n    Map&lt;Integer, Integer&gt; dic = new HashMap&lt;&gt;();\n    // 単一ループで、時間計算量は O(n)\n    for (int i = 0; i &lt; size; i++) {\n        if (dic.containsKey(target - nums[i])) {\n            return new int[] { dic.get(target - nums[i]), i };\n        }\n        dic.put(nums[i], i);\n    }\n    return new int[0];\n}\n</code></pre> two_sum.cs<pre><code>/* 方法 2：補助ハッシュテーブル */\nint[] TwoSumHashTable(int[] nums, int target) {\n    int size = nums.Length;\n    // 補助ハッシュテーブルを使用し、空間計算量は O(n)\n    Dictionary&lt;int, int&gt; dic = [];\n    // 単一ループで、時間計算量は O(n)\n    for (int i = 0; i &lt; size; i++) {\n        if (dic.ContainsKey(target - nums[i])) {\n            return [dic[target - nums[i]], i];\n        }\n        dic.Add(nums[i], i);\n    }\n    return [];\n}\n</code></pre> two_sum.go<pre><code>/* 方法 2：補助ハッシュテーブル */\nfunc twoSumHashTable(nums []int, target int) []int {\n    // 補助ハッシュテーブルを使用し、空間計算量は O(n)\n    hashTable := map[int]int{}\n    // 単一ループで、時間計算量は O(n)\n    for idx, val := range nums {\n        if preIdx, ok := hashTable[target-val]; ok {\n            return []int{preIdx, idx}\n        }\n        hashTable[val] = idx\n    }\n    return nil\n}\n</code></pre> two_sum.swift<pre><code>/* 方法 2：補助ハッシュテーブル */\nfunc twoSumHashTable(nums: [Int], target: Int) -&gt; [Int] {\n    // 補助ハッシュテーブルを使用し、空間計算量は O(n)\n    var dic: [Int: Int] = [:]\n    // 単一ループで、時間計算量は O(n)\n    for i in nums.indices {\n        if let j = dic[target - nums[i]] {\n            return [j, i]\n        }\n        dic[nums[i]] = i\n    }\n    return [0]\n}\n</code></pre> two_sum.js<pre><code>/* 方法 2：補助ハッシュテーブル */\nfunction twoSumHashTable(nums, target) {\n    // 補助ハッシュテーブルを使用し、空間計算量は O(n)\n    let m = {};\n    // 単一ループで、時間計算量は O(n)\n    for (let i = 0; i &lt; nums.length; i++) {\n        if (m[target - nums[i]] !== undefined) {\n            return [m[target - nums[i]], i];\n        } else {\n            m[nums[i]] = i;\n        }\n    }\n    return [];\n}\n</code></pre> two_sum.ts<pre><code>/* 方法 2：補助ハッシュテーブル */\nfunction twoSumHashTable(nums: number[], target: number): number[] {\n    // 補助ハッシュテーブルを使用し、空間計算量は O(n)\n    let m: Map&lt;number, number&gt; = new Map();\n    // 単一ループで、時間計算量は O(n)\n    for (let i = 0; i &lt; nums.length; i++) {\n        let index = m.get(target - nums[i]);\n        if (index !== undefined) {\n            return [index, i];\n        } else {\n            m.set(nums[i], i);\n        }\n    }\n    return [];\n}\n</code></pre> two_sum.dart<pre><code>/* 方法2: 補助ハッシュテーブル */\nList&lt;int&gt; twoSumHashTable(List&lt;int&gt; nums, int target) {\n  int size = nums.length;\n  // 補助ハッシュテーブルを使用し、空間計算量は O(n)\n  Map&lt;int, int&gt; dic = HashMap();\n  // 単一ループで、時間計算量は O(n)\n  for (var i = 0; i &lt; size; i++) {\n    if (dic.containsKey(target - nums[i])) {\n      return [dic[target - nums[i]]!, i];\n    }\n    dic.putIfAbsent(nums[i], () =&gt; i);\n  }\n  return [0];\n}\n</code></pre> two_sum.rs<pre><code>/* 方法 2：補助ハッシュテーブル */\npub fn two_sum_hash_table(nums: &amp;Vec&lt;i32&gt;, target: i32) -&gt; Option&lt;Vec&lt;i32&gt;&gt; {\n    // 補助ハッシュテーブルを使用し、空間計算量は O(n)\n    let mut dic = HashMap::new();\n    // 単一ループで、時間計算量は O(n)\n    for (i, num) in nums.iter().enumerate() {\n        match dic.get(&amp;(target - num)) {\n            Some(v) =&gt; return Some(vec![*v as i32, i as i32]),\n            None =&gt; dic.insert(num, i as i32),\n        };\n    }\n    None\n}\n</code></pre> two_sum.c<pre><code>/* ハッシュテーブル */\ntypedef struct {\n    int key;\n    int val;\n    UT_hash_handle hh; // uthash.h を用いて実装\n} HashTable;\n\n/* ハッシュテーブルを検索する */\nHashTable *find(HashTable *h, int key) {\n    HashTable *tmp;\n    HASH_FIND_INT(h, &amp;key, tmp);\n    return tmp;\n}\n\n/* ハッシュテーブルに要素を挿入する */\nvoid insert(HashTable **h, int key, int val) {\n    HashTable *t = find(*h, key);\n    if (t == NULL) {\n        HashTable *tmp = malloc(sizeof(HashTable));\n        tmp-&gt;key = key, tmp-&gt;val = val;\n        HASH_ADD_INT(*h, key, tmp);\n    } else {\n        t-&gt;val = val;\n    }\n}\n\n/* 方法 2：補助ハッシュテーブル */\nint *twoSumHashTable(int *nums, int numsSize, int target, int *returnSize) {\n    HashTable *hashtable = NULL;\n    for (int i = 0; i &lt; numsSize; i++) {\n        HashTable *t = find(hashtable, target - nums[i]);\n        if (t != NULL) {\n            int *res = malloc(sizeof(int) * 2);\n            res[0] = t-&gt;val, res[1] = i;\n            *returnSize = 2;\n            return res;\n        }\n        insert(&amp;hashtable, nums[i], i);\n    }\n    *returnSize = 0;\n    return NULL;\n}\n</code></pre> two_sum.kt<pre><code>/* 方法 2：補助ハッシュテーブル */\nfun twoSumHashTable(nums: IntArray, target: Int): IntArray {\n    val size = nums.size\n    // 補助ハッシュテーブルを使用し、空間計算量は O(n)\n    val dic = HashMap&lt;Int, Int&gt;()\n    // 単一ループで、時間計算量は O(n)\n    for (i in 0..&lt;size) {\n        if (dic.containsKey(target - nums[i])) {\n            return intArrayOf(dic[target - nums[i]]!!, i)\n        }\n        dic[nums[i]] = i\n    }\n    return IntArray(0)\n}\n</code></pre> two_sum.rb<pre><code>### 方法2：補助ハッシュテーブル ###\ndef two_sum_hash_table(nums, target)\n  # 補助ハッシュテーブルを使用し、空間計算量は O(n)\n  dic = {}\n  # 単一ループで、時間計算量は O(n)\n  for i in 0...nums.length\n    return [dic[target - nums[i]], i] if dic.has_key?(target - nums[i])\n\n    dic[nums[i]] = i\n  end\n\n  []\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>この方法ではハッシュ探索によって時間計算量を \\(O(n^2)\\) から \\(O(n)\\) に下げ，実行効率を大幅に向上させます。</p> <p>追加のハッシュテーブルを維持する必要があるため，空間計算量は \\(O(n)\\) です。それでも，この方法は全体として時間と空間の効率のバランスがより良く，本問の最適解です。</p>","path":["第 10 章 &nbsp; 探索","10.4 &nbsp; ハッシュによる最適化戦略"],"tags":[]},{"location":"chapter_searching/searching_algorithm_revisited/","level":1,"title":"10.5   探索アルゴリズム再考","text":"<p>探索アルゴリズム（searching algorithm）は、データ構造（配列、連結リスト、木、グラフなど）の中から、特定の条件を満たす 1 つまたは複数の要素を探索するために用いられます。</p> <p>探索アルゴリズムは、実装の考え方に応じて次の 2 種類に分けられます。</p> <ul> <li>データ構造を走査して目標要素を特定する方法。配列、連結リスト、木、グラフの走査などがこれに当たります。</li> <li>データの構成やデータに含まれる事前情報を利用して、要素を効率よく探す方法。二分探索、ハッシュ探索、二分探索木による探索などがこれに当たります。</li> </ul> <p>これらのトピックはすでに前の章で扱っているため、探索アルゴリズムは私たちにとって見慣れたものです。本節では、より体系的な視点から探索アルゴリズムをあらためて見直します。</p>","path":["第 10 章 &nbsp; 探索","10.5 &nbsp; 探索アルゴリズム再考"],"tags":[]},{"location":"chapter_searching/searching_algorithm_revisited/#1051","level":2,"title":"10.5.1   総当たり探索","text":"<p>総当たり探索は、データ構造の各要素を順に調べて目標要素を特定します。</p> <ul> <li>“線形探索”は配列や連結リストなどの線形データ構造に適しています。データ構造の一端から始めて、要素を 1 つずつ調べ、目標要素が見つかるか、もう一方の端に達しても見つからないまで続けます。</li> <li>“幅優先探索”と“深さ優先探索”は、グラフと木における 2 つの走査戦略です。幅優先探索は初期ノードから始めて層ごとに探索し、近いところから遠いところへ各ノードを訪れます。深さ優先探索は初期ノードから始めて 1 本の経路を最後までたどり、その後でバックトラックしてほかの経路を試し、データ構造全体を走査し終えるまで続けます。</li> </ul> <p>総当たり探索の利点は、単純で汎用性が高く、**データの前処理や追加のデータ構造を必要としない**ことです。</p> <p>しかし、この種のアルゴリズムの時間計算量は \\(O(n)\\) です。ここで \\(n\\) は要素数であり、そのためデータ量が大きい場合は性能が低くなります。</p>","path":["第 10 章 &nbsp; 探索","10.5 &nbsp; 探索アルゴリズム再考"],"tags":[]},{"location":"chapter_searching/searching_algorithm_revisited/#1052","level":2,"title":"10.5.2   適応的な探索","text":"<p>適応的な探索は、データが持つ固有の性質（整列性など）を利用して探索過程を最適化し、目標要素をより効率よく特定します。</p> <ul> <li>“二分探索”は、データの順序性を利用して効率的な探索を行う方法で、配列にしか適用できません。</li> <li>“ハッシュ探索”は、ハッシュ表を用いて探索対象のデータと目標データをキーと値の対応にし、問い合わせ操作を実現します。</li> <li>“木探索”は、特定の木構造（たとえば二分探索木）の中で、ノード値の比較に基づいて不要なノードをすばやく除外し、目標要素を特定します。</li> </ul> <p>この種のアルゴリズムの利点は効率が高く、**時間計算量が \\(O(\\log n)\\) あるいは \\(O(1)\\) に達する**ことです。</p> <p>しかし、これらのアルゴリズムを使うには、たいていデータの前処理が必要です。たとえば、二分探索では事前に配列をソートする必要があり、ハッシュ探索と木探索では追加のデータ構造が必要です。これらのデータ構造を維持するにも、追加の時間と空間のコストがかかります。</p> <p>Tip</p> <p>適応的な探索アルゴリズムは、しばしば検索アルゴリズムとも呼ばれ、主に特定のデータ構造の中で目標要素を高速に取得するために用いられます。</p>","path":["第 10 章 &nbsp; 探索","10.5 &nbsp; 探索アルゴリズム再考"],"tags":[]},{"location":"chapter_searching/searching_algorithm_revisited/#1053","level":2,"title":"10.5.3   探索手法の選択","text":"<p>大きさ \\(n\\) のデータ集合が与えられたとき、線形探索、二分探索、木探索、ハッシュ探索など、さまざまな方法で目標要素を探索できます。各手法の動作原理を下図に示します。</p> <p></p> <p> 図 10-11   複数の探索戦略 </p> <p>上記のいくつかの手法について、操作効率と特性を次の表に示します。</p> <p> 表 10-1   探索アルゴリズムの効率比較 </p> 線形探索 二分探索 木探索 ハッシュ探索 要素探索 \\(O(n)\\) \\(O(\\log n)\\) \\(O(\\log n)\\) \\(O(1)\\) 要素挿入 \\(O(1)\\) \\(O(n)\\) \\(O(\\log n)\\) \\(O(1)\\) 要素削除 \\(O(n)\\) \\(O(n)\\) \\(O(\\log n)\\) \\(O(1)\\) 追加領域 \\(O(1)\\) \\(O(1)\\) \\(O(n)\\) \\(O(n)\\) データ前処理 / ソート \\(O(n \\log n)\\) 木構築 \\(O(n \\log n)\\) ハッシュ表構築 \\(O(n)\\) データの順序性 なし あり あり なし <p>探索アルゴリズムの選択は、規模、探索性能の要求、データの問い合わせ頻度や更新頻度などにも左右されます。</p> <p>線形探索</p> <ul> <li>汎用性が高く、データの前処理をまったく必要としません。データを 1 回だけ問い合わせればよい場合、ほか 3 つの手法では前処理にかかる時間のほうが、線形探索そのものより長くなることがあります。</li> <li>規模の小さいデータに適しています。この場合、時間計算量が効率に与える影響は比較的小さいです。</li> <li>データ更新頻度が高い場面に適しています。この手法では、データに対する追加の保守が不要だからです。</li> </ul> <p>二分探索</p> <ul> <li>大規模データに適しており、効率が安定しています。最悪時間計算量は \\(O(\\log n)\\) です。</li> <li>データ量が大きすぎる場合には向きません。配列の格納には連続したメモリ領域が必要だからです。</li> <li>頻繁な挿入・削除がある場面には向きません。整列配列を維持するコストが高いためです。</li> </ul> <p>ハッシュ探索</p> <ul> <li>問い合わせ性能への要求が高い場面に適しており、平均時間計算量は \\(O(1)\\) です。</li> <li>順序付きデータや範囲探索が必要な場面には向きません。ハッシュ表ではデータの順序性を維持できないからです。</li> <li>ハッシュ関数とハッシュ衝突処理戦略への依存度が高く、性能劣化のリスクが大きいです。</li> <li>データ量が大きすぎる場合には向きません。ハッシュ表は衝突をできるだけ減らして良好な問い合わせ性能を出すために、追加の空間を必要とするからです。</li> </ul> <p>木探索</p> <ul> <li>巨大データに適しています。木ノードはメモリ上に分散して格納されるためです。</li> <li>順序付きデータの維持や範囲探索が必要な場面に適しています。</li> <li>ノードの挿入・削除を続ける過程で、二分探索木は偏ることがあり、時間計算量は \\(O(n)\\) まで劣化する可能性があります。</li> <li>AVL 木や赤黒木を使えば、各種操作を \\(O(\\log n)\\) の効率で安定して実行できますが、木の平衡を保つ処理による追加コストが発生します。</li> </ul>","path":["第 10 章 &nbsp; 探索","10.5 &nbsp; 探索アルゴリズム再考"],"tags":[]},{"location":"chapter_searching/summary/","level":1,"title":"10.6   まとめ","text":"","path":["第 10 章 &nbsp; 探索","10.6 &nbsp; まとめ"],"tags":[]},{"location":"chapter_searching/summary/#1","level":3,"title":"1.   要点の振り返り","text":"<ul> <li>二分探索はデータの順序性に依存し、ループによって探索区間を半分ずつ縮小しながら探索を行う。入力データがソート済みであることを前提とし、配列または配列ベースで実装されたデータ構造にのみ適用できる。</li> <li>総当たり探索はデータ構造を走査してデータを特定する。線形探索は配列と連結リストに適しており、幅優先探索と深さ優先探索はグラフと木に適している。この種のアルゴリズムは汎用性が高く、データの前処理を必要としないが、時間計算量 \\(O(n)\\) は高い。</li> <li>ハッシュ探索、木探索、二分探索は高効率な探索手法であり、特定のデータ構造内で目的の要素を高速に特定できる。この種のアルゴリズムは効率が高く、時間計算量は \\(O(\\log n)\\) あるいは \\(O(1)\\) に達するが、通常は追加のデータ構造を必要とする。</li> <li>実際には、データ規模、探索性能の要件、データの問い合わせ頻度や更新頻度などの要因を具体的に分析し、そのうえで適切な探索手法を選択する必要がある。</li> <li>線形探索は小規模または頻繁に更新されるデータに適している。二分探索は大規模でソート済みのデータに適している。ハッシュ探索は問い合わせ効率への要求が高く、範囲検索を必要としないデータに適している。木探索は順序の維持と範囲検索のサポートが必要な大規模動的データに適している。</li> <li>ハッシュ探索で線形探索を置き換えることは、実行時間を最適化するための一般的な戦略であり、時間計算量を \\(O(n)\\) から \\(O(1)\\) へと下げられる。</li> </ul>","path":["第 10 章 &nbsp; 探索","10.6 &nbsp; まとめ"],"tags":[]},{"location":"chapter_sorting/","level":1,"title":"第 11 章   ソート","text":"<p>Abstract</p> <p>ソートは、混沌を秩序へと変える魔法の鍵のようなものであり、データをより効率的に理解し処理することを可能にします。</p> <p>単純な昇順であれ、複雑な分類配列であれ、ソートはデータの調和のとれた美しさを私たちに示してくれます。</p>","path":["第 11 章 &nbsp; ソート"],"tags":[]},{"location":"chapter_sorting/#_1","level":2,"title":"章の内容","text":"<ul> <li>11.1   ソートアルゴリズム</li> <li>11.2   選択ソート</li> <li>11.3   バブルソート</li> <li>11.4   挿入ソート</li> <li>11.5   クイックソート</li> <li>11.6   マージソート</li> <li>11.7   ヒープソート</li> <li>11.8   バケットソート</li> <li>11.9   計数ソート</li> <li>11.10   基数ソート</li> <li>11.11   まとめ</li> </ul>","path":["第 11 章 &nbsp; ソート"],"tags":[]},{"location":"chapter_sorting/bubble_sort/","level":1,"title":"11.3   バブルソート","text":"<p>バブルソート（bubble sort）は、隣接する要素を繰り返し比較して交換することで整列を行います。この過程が泡のように下から上へ浮かび上がることから、バブルソートと呼ばれます。</p> <p>次の図に示すように、バブル処理は要素の交換操作によってシミュレートできます。配列の最も左の端から右へ走査し、隣接する要素の大小を順に比較して、「左要素 &gt; 右要素」であれば両者を交換します。走査が終わると、最大の要素は配列の最も右端へ移動します。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 11-4   要素の交換操作でバブル処理をシミュレート </p>","path":["第 11 章 &nbsp; ソート","11.3 &nbsp; バブルソート"],"tags":[]},{"location":"chapter_sorting/bubble_sort/#1131","level":2,"title":"11.3.1   アルゴリズムの流れ","text":"<p>配列の長さを \\(n\\) とすると、バブルソートの手順は次の図のとおりです。</p> <ol> <li>まず、\\(n\\) 個の要素に対して「バブル処理」を行い、配列中の最大要素を正しい位置へ交換します。</li> <li>次に、残りの \\(n - 1\\) 個の要素に対して「バブル処理」を行い、2 番目に大きい要素を正しい位置へ交換します。</li> <li>このようにして、\\(n - 1\\) 回の「バブル処理」を終えると、大きいほうから \\(n - 1\\) 個の要素がすべて正しい位置へ交換されます。</li> <li>残った 1 つの要素は必ず最小要素なので、並べ替える必要はなく、これで配列のソートが完了します。</li> </ol> <p></p> <p> 図 11-5   バブルソートの流れ </p> <p>コード例は次のとおりです。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby bubble_sort.py<pre><code>def bubble_sort(nums: list[int]):\n    \"\"\"バブルソート\"\"\"\n    n = len(nums)\n    # 外側のループ：未ソート区間は [0, i]\n    for i in range(n - 1, 0, -1):\n        # 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for j in range(i):\n            if nums[j] &gt; nums[j + 1]:\n                # nums[j] と nums[j + 1] を交換\n                nums[j], nums[j + 1] = nums[j + 1], nums[j]\n</code></pre> bubble_sort.cpp<pre><code>/* バブルソート */\nvoid bubbleSort(vector&lt;int&gt; &amp;nums) {\n    // 外側のループ：未ソート区間は [0, i]\n    for (int i = nums.size() - 1; i &gt; 0; i--) {\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] と nums[j + 1] を交換する\n                // ここでは std::swap() 関数を使用する\n                swap(nums[j], nums[j + 1]);\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.java<pre><code>/* バブルソート */\nvoid bubbleSort(int[] nums) {\n    // 外側のループ：未ソート区間は [0, i]\n    for (int i = nums.length - 1; i &gt; 0; i--) {\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] と nums[j + 1] を交換\n                int tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.cs<pre><code>/* バブルソート */\nvoid BubbleSort(int[] nums) {\n    // 外側のループ：未ソート区間は [0, i]\n    for (int i = nums.Length - 1; i &gt; 0; i--) {\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] と nums[j + 1] を交換\n                (nums[j + 1], nums[j]) = (nums[j], nums[j + 1]);\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.go<pre><code>/* バブルソート */\nfunc bubbleSort(nums []int) {\n    // 外側のループ：未ソート区間は [0, i]\n    for i := len(nums) - 1; i &gt; 0; i-- {\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for j := 0; j &lt; i; j++ {\n            if nums[j] &gt; nums[j+1] {\n                // nums[j] と nums[j + 1] を交換\n                nums[j], nums[j+1] = nums[j+1], nums[j]\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.swift<pre><code>/* バブルソート */\nfunc bubbleSort(nums: inout [Int]) {\n    // 外側のループ：未ソート区間は [0, i]\n    for i in nums.indices.dropFirst().reversed() {\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for j in 0 ..&lt; i {\n            if nums[j] &gt; nums[j + 1] {\n                // nums[j] と nums[j + 1] を交換\n                nums.swapAt(j, j + 1)\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.js<pre><code>/* バブルソート */\nfunction bubbleSort(nums) {\n    // 外側のループ：未ソート区間は [0, i]\n    for (let i = nums.length - 1; i &gt; 0; i--) {\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for (let j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] と nums[j + 1] を交換\n                let tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.ts<pre><code>/* バブルソート */\nfunction bubbleSort(nums: number[]): void {\n    // 外側のループ：未ソート区間は [0, i]\n    for (let i = nums.length - 1; i &gt; 0; i--) {\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for (let j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] と nums[j + 1] を交換\n                let tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.dart<pre><code>/* バブルソート */\nvoid bubbleSort(List&lt;int&gt; nums) {\n  // 外側のループ：未ソート区間は [0, i]\n  for (int i = nums.length - 1; i &gt; 0; i--) {\n    // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n    for (int j = 0; j &lt; i; j++) {\n      if (nums[j] &gt; nums[j + 1]) {\n        // nums[j] と nums[j + 1] を交換\n        int tmp = nums[j];\n        nums[j] = nums[j + 1];\n        nums[j + 1] = tmp;\n      }\n    }\n  }\n}\n</code></pre> bubble_sort.rs<pre><code>/* バブルソート */\nfn bubble_sort(nums: &amp;mut [i32]) {\n    // 外側のループ：未ソート区間は [0, i]\n    for i in (1..nums.len()).rev() {\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for j in 0..i {\n            if nums[j] &gt; nums[j + 1] {\n                // nums[j] と nums[j + 1] を交換\n                nums.swap(j, j + 1);\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.c<pre><code>/* バブルソート */\nvoid bubbleSort(int nums[], int size) {\n    // 外側のループ：未ソート区間は [0, i]\n    for (int i = size - 1; i &gt; 0; i--) {\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                int temp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = temp;\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.kt<pre><code>/* バブルソート */\nfun bubbleSort(nums: IntArray) {\n    // 外側のループ：未ソート区間は [0, i]\n    for (i in nums.size - 1 downTo 1) {\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for (j in 0..&lt;i) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] と nums[j + 1] を交換\n                val temp = nums[j]\n                nums[j] = nums[j + 1]\n                nums[j + 1] = temp\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.rb<pre><code>### バブルソート ###\ndef bubble_sort(nums)\n  n = nums.length\n  # 外側のループ：未ソート区間は [0, i]\n  for i in (n - 1).downto(1)\n    # 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n    for j in 0...i\n      if nums[j] &gt; nums[j + 1]\n        # nums[j] と nums[j + 1] を交換\n        nums[j], nums[j + 1] = nums[j + 1], nums[j]\n      end\n    end\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 11 章 &nbsp; ソート","11.3 &nbsp; バブルソート"],"tags":[]},{"location":"chapter_sorting/bubble_sort/#1132","level":2,"title":"11.3.2   効率の最適化","text":"<p>ある回の「バブル処理」で交換操作が一度も行われなければ、配列はすでにソート済みであり、結果をそのまま返せることがわかります。したがって、この状況を検出するためのフラグ <code>flag</code> を追加し、発生した時点で直ちに返すようにできます。</p> <p>最適化後も、バブルソートの最悪時間計算量と平均時間計算量は依然として \\(O(n^2)\\) です。ただし、入力配列が完全に整列済みであれば、最良時間計算量は \\(O(n)\\) に達します。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby bubble_sort.py<pre><code>def bubble_sort_with_flag(nums: list[int]):\n    \"\"\"バブルソート（フラグ最適化）\"\"\"\n    n = len(nums)\n    # 外側のループ：未ソート区間は [0, i]\n    for i in range(n - 1, 0, -1):\n        flag = False  # フラグを初期化する\n        # 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for j in range(i):\n            if nums[j] &gt; nums[j + 1]:\n                # nums[j] と nums[j + 1] を交換\n                nums[j], nums[j + 1] = nums[j + 1], nums[j]\n                flag = True  # 交換する要素を記録\n        if not flag:\n            break  # このバブル処理で要素交換が一度もなければそのまま終了\n</code></pre> bubble_sort.cpp<pre><code>/* バブルソート（フラグ最適化） */\nvoid bubbleSortWithFlag(vector&lt;int&gt; &amp;nums) {\n    // 外側のループ：未ソート区間は [0, i]\n    for (int i = nums.size() - 1; i &gt; 0; i--) {\n        bool flag = false; // フラグを初期化する\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] と nums[j + 1] を交換する\n                // ここでは std::swap() 関数を使用する\n                swap(nums[j], nums[j + 1]);\n                flag = true; // 交換する要素を記録\n            }\n        }\n        if (!flag)\n            break; // このバブル処理で要素交換が一度もなければそのまま終了\n    }\n}\n</code></pre> bubble_sort.java<pre><code>/* バブルソート（フラグ最適化） */\nvoid bubbleSortWithFlag(int[] nums) {\n    // 外側のループ：未ソート区間は [0, i]\n    for (int i = nums.length - 1; i &gt; 0; i--) {\n        boolean flag = false; // フラグを初期化する\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] と nums[j + 1] を交換\n                int tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                flag = true; // 交換する要素を記録\n            }\n        }\n        if (!flag)\n            break; // このバブル処理で要素交換が一度もなければそのまま終了\n    }\n}\n</code></pre> bubble_sort.cs<pre><code>/* バブルソート（フラグ最適化） */\nvoid BubbleSortWithFlag(int[] nums) {\n    // 外側のループ：未ソート区間は [0, i]\n    for (int i = nums.Length - 1; i &gt; 0; i--) {\n        bool flag = false; // フラグを初期化する\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] と nums[j + 1] を交換\n                (nums[j + 1], nums[j]) = (nums[j], nums[j + 1]);\n                flag = true;  // 交換する要素を記録\n            }\n        }\n        if (!flag) break;     // このバブル処理で要素交換が一度もなければそのまま終了\n    }\n}\n</code></pre> bubble_sort.go<pre><code>/* バブルソート（フラグ最適化） */\nfunc bubbleSortWithFlag(nums []int) {\n    // 外側のループ：未ソート区間は [0, i]\n    for i := len(nums) - 1; i &gt; 0; i-- {\n        flag := false // フラグを初期化する\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for j := 0; j &lt; i; j++ {\n            if nums[j] &gt; nums[j+1] {\n                // nums[j] と nums[j + 1] を交換\n                nums[j], nums[j+1] = nums[j+1], nums[j]\n                flag = true // 交換する要素を記録\n            }\n        }\n        if flag == false { // このバブル処理で要素交換が一度もなければそのまま終了\n            break\n        }\n    }\n}\n</code></pre> bubble_sort.swift<pre><code>/* バブルソート（フラグ最適化） */\nfunc bubbleSortWithFlag(nums: inout [Int]) {\n    // 外側のループ：未ソート区間は [0, i]\n    for i in nums.indices.dropFirst().reversed() {\n        var flag = false // フラグを初期化する\n        for j in 0 ..&lt; i {\n            if nums[j] &gt; nums[j + 1] {\n                // nums[j] と nums[j + 1] を交換\n                nums.swapAt(j, j + 1)\n                flag = true // 交換する要素を記録\n            }\n        }\n        if !flag { // このバブル処理で要素交換が一度もなければそのまま終了\n            break\n        }\n    }\n}\n</code></pre> bubble_sort.js<pre><code>/* バブルソート（フラグ最適化） */\nfunction bubbleSortWithFlag(nums) {\n    // 外側のループ：未ソート区間は [0, i]\n    for (let i = nums.length - 1; i &gt; 0; i--) {\n        let flag = false; // フラグを初期化する\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for (let j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] と nums[j + 1] を交換\n                let tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                flag = true; // 交換する要素を記録\n            }\n        }\n        if (!flag) break; // このバブル処理で要素交換が一度もなければそのまま終了\n    }\n}\n</code></pre> bubble_sort.ts<pre><code>/* バブルソート（フラグ最適化） */\nfunction bubbleSortWithFlag(nums: number[]): void {\n    // 外側のループ：未ソート区間は [0, i]\n    for (let i = nums.length - 1; i &gt; 0; i--) {\n        let flag = false; // フラグを初期化する\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for (let j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] と nums[j + 1] を交換\n                let tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                flag = true; // 交換する要素を記録\n            }\n        }\n        if (!flag) break; // このバブル処理で要素交換が一度もなければそのまま終了\n    }\n}\n</code></pre> bubble_sort.dart<pre><code>/* バブルソート（フラグ最適化） */\nvoid bubbleSortWithFlag(List&lt;int&gt; nums) {\n  // 外側のループ：未ソート区間は [0, i]\n  for (int i = nums.length - 1; i &gt; 0; i--) {\n    bool flag = false; // フラグを初期化する\n    // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n    for (int j = 0; j &lt; i; j++) {\n      if (nums[j] &gt; nums[j + 1]) {\n        // nums[j] と nums[j + 1] を交換\n        int tmp = nums[j];\n        nums[j] = nums[j + 1];\n        nums[j + 1] = tmp;\n        flag = true; // 交換する要素を記録\n      }\n    }\n    if (!flag) break; // このバブル処理で要素交換が一度もなければそのまま終了\n  }\n}\n</code></pre> bubble_sort.rs<pre><code>/* バブルソート（フラグ最適化） */\nfn bubble_sort_with_flag(nums: &amp;mut [i32]) {\n    // 外側のループ：未ソート区間は [0, i]\n    for i in (1..nums.len()).rev() {\n        let mut flag = false; // フラグを初期化する\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for j in 0..i {\n            if nums[j] &gt; nums[j + 1] {\n                // nums[j] と nums[j + 1] を交換\n                nums.swap(j, j + 1);\n                flag = true; // 交換する要素を記録\n            }\n        }\n        if !flag {\n            break; // このバブル処理で要素交換が一度もなければそのまま終了\n        };\n    }\n}\n</code></pre> bubble_sort.c<pre><code>/* バブルソート（フラグ最適化） */\nvoid bubbleSortWithFlag(int nums[], int size) {\n    // 外側のループ：未ソート区間は [0, i]\n    for (int i = size - 1; i &gt; 0; i--) {\n        bool flag = false;\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                int temp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = temp;\n                flag = true;\n            }\n        }\n        if (!flag)\n            break;\n    }\n}\n</code></pre> bubble_sort.kt<pre><code>/* バブルソート（フラグ最適化） */\nfun bubbleSortWithFlag(nums: IntArray) {\n    // 外側のループ：未ソート区間は [0, i]\n    for (i in nums.size - 1 downTo 1) {\n        var flag = false // フラグを初期化する\n        // 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n        for (j in 0..&lt;i) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] と nums[j + 1] を交換\n                val temp = nums[j]\n                nums[j] = nums[j + 1]\n                nums[j + 1] = temp\n                flag = true // 交換する要素を記録\n            }\n        }\n        if (!flag) break // このバブル処理で要素交換が一度もなければそのまま終了\n    }\n}\n</code></pre> bubble_sort.rb<pre><code>### バブルソート ###\ndef bubble_sort(nums)\n  n = nums.length\n  # 外側のループ：未ソート区間は [0, i]\n  for i in (n - 1).downto(1)\n    # 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n    for j in 0...i\n      if nums[j] &gt; nums[j + 1]\n        # nums[j] と nums[j + 1] を交換\n        nums[j], nums[j + 1] = nums[j + 1], nums[j]\n      end\n    end\n  end\nend\n\n# ## バブルソート（フラグ最適化）###\ndef bubble_sort_with_flag(nums)\n  n = nums.length\n  # 外側のループ：未ソート区間は [0, i]\n  for i in (n - 1).downto(1)\n    flag = false # フラグを初期化する\n\n    # 内側のループ：未ソート区間 [0, i] の最大要素をその区間の最右端へ交換\n    for j in 0...i\n      if nums[j] &gt; nums[j + 1]\n        # nums[j] と nums[j + 1] を交換\n        nums[j], nums[j + 1] = nums[j + 1], nums[j]\n        flag = true # 交換する要素を記録\n      end\n    end\n\n    break unless flag # このバブル処理で要素交換が一度もなければそのまま終了\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 11 章 &nbsp; ソート","11.3 &nbsp; バブルソート"],"tags":[]},{"location":"chapter_sorting/bubble_sort/#1133","level":2,"title":"11.3.3   アルゴリズムの特徴","text":"<ul> <li>時間計算量は \\(O(n^2)\\)、適応的ソート：各回の「バブル処理」で走査する配列の長さは順に \\(n - 1\\)、\\(n - 2\\)、\\(\\dots\\)、\\(2\\)、\\(1\\) であり、その総和は \\((n - 1) n / 2\\) です。<code>flag</code> による最適化を導入すると、最良時間計算量は \\(O(n)\\) に達します。</li> <li>空間計算量は \\(O(1)\\)、インプレースソート：ポインタ \\(i\\) と \\(j\\) は定数サイズの追加領域しか使用しません。</li> <li>安定ソート：「バブル処理」では等しい要素に出会っても交換しないためです。</li> </ul>","path":["第 11 章 &nbsp; ソート","11.3 &nbsp; バブルソート"],"tags":[]},{"location":"chapter_sorting/bucket_sort/","level":1,"title":"11.8   バケットソート","text":"<p>前述のいくつかのソートアルゴリズムは、いずれも「比較ベースのソートアルゴリズム」に属し、要素間の大小を比較することで整列を実現します。この種のソートアルゴリズムの時間計算量は \\(O(n \\log n)\\) を超えられません。続いて、時間計算量が線形オーダーに達しうる「非比較ソートアルゴリズム」をいくつか見ていきます。</p> <p>バケットソート（bucket sort）は分割統治戦略の典型的な応用です。大小関係をもつ複数のバケットを用意し、各バケットがあるデータ範囲に対応するようにして、データを各バケットへ均等に分配します。その後、各バケット内でそれぞれソートを行い、最後にバケットの順序に従ってすべてのデータを結合します。</p>","path":["第 11 章 &nbsp; ソート","11.8 &nbsp; バケットソート"],"tags":[]},{"location":"chapter_sorting/bucket_sort/#1181","level":2,"title":"11.8.1   アルゴリズムの流れ","text":"<p>長さ \\(n\\) の配列を考え、その要素は範囲 \\([0, 1)\\) の浮動小数点数であるとします。バケットソートの流れを以下の図に示します。</p> <ol> <li>\\(k\\) 個のバケットを初期化し、\\(n\\) 個の要素を \\(k\\) 個のバケットに分配します。</li> <li>各バケットに対してそれぞれソートを実行します（ここではプログラミング言語の組み込みソート関数を用います）。</li> <li>バケットを小さい順にたどって結果を結合します。</li> </ol> <p></p> <p> 図 11-13   バケットソートの流れ </p> <p>コードは以下のとおりです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby bucket_sort.py<pre><code>def bucket_sort(nums: list[float]):\n    \"\"\"バケットソート\"\"\"\n    # k = n/2 個のバケットを初期化し、各バケットに 2 要素ずつ割り当てる想定とする\n    k = len(nums) // 2\n    buckets = [[] for _ in range(k)]\n    # 1. 配列要素を各バケットに振り分ける\n    for num in nums:\n        # 入力データの範囲は [0, 1) であり、num * k を用いてインデックス範囲 [0, k-1] に写像する\n        i = int(num * k)\n        # num をバケット i に追加\n        buckets[i].append(num)\n    # 2. 各バケットをソートする\n    for bucket in buckets:\n        # 組み込みのソート関数を使う。他のソートアルゴリズムに置き換えてもよい\n        bucket.sort()\n    # 3. バケットを走査して結果を結合\n    i = 0\n    for bucket in buckets:\n        for num in bucket:\n            nums[i] = num\n            i += 1\n</code></pre> bucket_sort.cpp<pre><code>/* バケットソート */\nvoid bucketSort(vector&lt;float&gt; &amp;nums) {\n    // k = n/2 個のバケットを初期化し、各バケットに 2 要素ずつ割り当てる想定とする\n    int k = nums.size() / 2;\n    vector&lt;vector&lt;float&gt;&gt; buckets(k);\n    // 1. 配列要素を各バケットに振り分ける\n    for (float num : nums) {\n        // 入力データの範囲は [0, 1) であり、num * k を用いてインデックス範囲 [0, k-1] に写像する\n        int i = num * k;\n        // num をバケット bucket_idx に追加\n        buckets[i].push_back(num);\n    }\n    // 2. 各バケットをソートする\n    for (vector&lt;float&gt; &amp;bucket : buckets) {\n        // 組み込みのソート関数を使う。他のソートアルゴリズムに置き換えてもよい\n        sort(bucket.begin(), bucket.end());\n    }\n    // 3. バケットを走査して結果を結合\n    int i = 0;\n    for (vector&lt;float&gt; &amp;bucket : buckets) {\n        for (float num : bucket) {\n            nums[i++] = num;\n        }\n    }\n}\n</code></pre> bucket_sort.java<pre><code>/* バケットソート */\nvoid bucketSort(float[] nums) {\n    // k = n/2 個のバケットを初期化し、各バケットに 2 要素ずつ割り当てる想定とする\n    int k = nums.length / 2;\n    List&lt;List&lt;Float&gt;&gt; buckets = new ArrayList&lt;&gt;();\n    for (int i = 0; i &lt; k; i++) {\n        buckets.add(new ArrayList&lt;&gt;());\n    }\n    // 1. 配列要素を各バケットに振り分ける\n    for (float num : nums) {\n        // 入力データの範囲は [0, 1) であり、num * k を用いてインデックス範囲 [0, k-1] に写像する\n        int i = (int) (num * k);\n        // num をバケット i に追加\n        buckets.get(i).add(num);\n    }\n    // 2. 各バケットをソートする\n    for (List&lt;Float&gt; bucket : buckets) {\n        // 組み込みのソート関数を使う。他のソートアルゴリズムに置き換えてもよい\n        Collections.sort(bucket);\n    }\n    // 3. バケットを走査して結果を結合\n    int i = 0;\n    for (List&lt;Float&gt; bucket : buckets) {\n        for (float num : bucket) {\n            nums[i++] = num;\n        }\n    }\n}\n</code></pre> bucket_sort.cs<pre><code>/* バケットソート */\nvoid BucketSort(float[] nums) {\n    // k = n/2 個のバケットを初期化し、各バケットに 2 要素ずつ割り当てる想定とする\n    int k = nums.Length / 2;\n    List&lt;List&lt;float&gt;&gt; buckets = [];\n    for (int i = 0; i &lt; k; i++) {\n        buckets.Add([]);\n    }\n    // 1. 配列要素を各バケットに振り分ける\n    foreach (float num in nums) {\n        // 入力データの範囲は [0, 1) であり、num * k を用いてインデックス範囲 [0, k-1] に写像する\n        int i = (int)(num * k);\n        // num をバケット i に追加\n        buckets[i].Add(num);\n    }\n    // 2. 各バケットをソートする\n    foreach (List&lt;float&gt; bucket in buckets) {\n        // 組み込みのソート関数を使う。他のソートアルゴリズムに置き換えてもよい\n        bucket.Sort();\n    }\n    // 3. バケットを走査して結果を結合\n    int j = 0;\n    foreach (List&lt;float&gt; bucket in buckets) {\n        foreach (float num in bucket) {\n            nums[j++] = num;\n        }\n    }\n}\n</code></pre> bucket_sort.go<pre><code>/* バケットソート */\nfunc bucketSort(nums []float64) {\n    // k = n/2 個のバケットを初期化し、各バケットに 2 要素ずつ割り当てる想定とする\n    k := len(nums) / 2\n    buckets := make([][]float64, k)\n    for i := 0; i &lt; k; i++ {\n        buckets[i] = make([]float64, 0)\n    }\n    // 1. 配列要素を各バケットに振り分ける\n    for _, num := range nums {\n        // 入力データの範囲は [0, 1) であり、num * k を用いてインデックス範囲 [0, k-1] に写像する\n        i := int(num * float64(k))\n        // num をバケット i に追加\n        buckets[i] = append(buckets[i], num)\n    }\n    // 2. 各バケットをソートする\n    for i := 0; i &lt; k; i++ {\n        // 組み込みのスライスソート関数を使う。ほかのソートアルゴリズムに置き換えてもよい\n        sort.Float64s(buckets[i])\n    }\n    // 3. バケットを走査して結果を結合\n    i := 0\n    for _, bucket := range buckets {\n        for _, num := range bucket {\n            nums[i] = num\n            i++\n        }\n    }\n}\n</code></pre> bucket_sort.swift<pre><code>/* バケットソート */\nfunc bucketSort(nums: inout [Double]) {\n    // k = n/2 個のバケットを初期化し、各バケットに 2 要素ずつ割り当てる想定とする\n    let k = nums.count / 2\n    var buckets = (0 ..&lt; k).map { _ in [Double]() }\n    // 1. 配列要素を各バケットに振り分ける\n    for num in nums {\n        // 入力データの範囲は [0, 1) であり、num * k を用いてインデックス範囲 [0, k-1] に写像する\n        let i = Int(num * Double(k))\n        // num をバケット i に追加\n        buckets[i].append(num)\n    }\n    // 2. 各バケットをソートする\n    for i in buckets.indices {\n        // 組み込みのソート関数を使う。他のソートアルゴリズムに置き換えてもよい\n        buckets[i].sort()\n    }\n    // 3. バケットを走査して結果を結合\n    var i = nums.startIndex\n    for bucket in buckets {\n        for num in bucket {\n            nums[i] = num\n            i += 1\n        }\n    }\n}\n</code></pre> bucket_sort.js<pre><code>/* バケットソート */\nfunction bucketSort(nums) {\n    // k = n/2 個のバケットを初期化し、各バケットに 2 要素ずつ割り当てる想定とする\n    const k = nums.length / 2;\n    const buckets = [];\n    for (let i = 0; i &lt; k; i++) {\n        buckets.push([]);\n    }\n    // 1. 配列要素を各バケットに振り分ける\n    for (const num of nums) {\n        // 入力データの範囲は [0, 1) であり、num * k を用いてインデックス範囲 [0, k-1] に写像する\n        const i = Math.floor(num * k);\n        // num をバケット i に追加\n        buckets[i].push(num);\n    }\n    // 2. 各バケットをソートする\n    for (const bucket of buckets) {\n        // 組み込みのソート関数を使う。他のソートアルゴリズムに置き換えてもよい\n        bucket.sort((a, b) =&gt; a - b);\n    }\n    // 3. バケットを走査して結果を結合\n    let i = 0;\n    for (const bucket of buckets) {\n        for (const num of bucket) {\n            nums[i++] = num;\n        }\n    }\n}\n</code></pre> bucket_sort.ts<pre><code>/* バケットソート */\nfunction bucketSort(nums: number[]): void {\n    // k = n/2 個のバケットを初期化し、各バケットに 2 要素ずつ割り当てる想定とする\n    const k = nums.length / 2;\n    const buckets: number[][] = [];\n    for (let i = 0; i &lt; k; i++) {\n        buckets.push([]);\n    }\n    // 1. 配列要素を各バケットに振り分ける\n    for (const num of nums) {\n        // 入力データの範囲は [0, 1) であり、num * k を用いてインデックス範囲 [0, k-1] に写像する\n        const i = Math.floor(num * k);\n        // num をバケット i に追加\n        buckets[i].push(num);\n    }\n    // 2. 各バケットをソートする\n    for (const bucket of buckets) {\n        // 組み込みのソート関数を使う。他のソートアルゴリズムに置き換えてもよい\n        bucket.sort((a, b) =&gt; a - b);\n    }\n    // 3. バケットを走査して結果を結合\n    let i = 0;\n    for (const bucket of buckets) {\n        for (const num of bucket) {\n            nums[i++] = num;\n        }\n    }\n}\n</code></pre> bucket_sort.dart<pre><code>/* バケットソート */\nvoid bucketSort(List&lt;double&gt; nums) {\n  // k = n/2 個のバケットを初期化し、各バケットに 2 要素ずつ割り当てる想定とする\n  int k = nums.length ~/ 2;\n  List&lt;List&lt;double&gt;&gt; buckets = List.generate(k, (index) =&gt; []);\n\n  // 1. 配列要素を各バケットに振り分ける\n  for (double _num in nums) {\n    // 入力データの範囲は [0, 1) であり、_num * k を用いてインデックス範囲 [0, k-1] に写像する\n    int i = (_num * k).toInt();\n    // _num をバケット bucket_idx に追加\n    buckets[i].add(_num);\n  }\n  // 2. 各バケットをソートする\n  for (List&lt;double&gt; bucket in buckets) {\n    bucket.sort();\n  }\n  // 3. バケットを走査して結果を結合\n  int i = 0;\n  for (List&lt;double&gt; bucket in buckets) {\n    for (double _num in bucket) {\n      nums[i++] = _num;\n    }\n  }\n}\n</code></pre> bucket_sort.rs<pre><code>/* バケットソート */\nfn bucket_sort(nums: &amp;mut [f64]) {\n    // k = n/2 個のバケットを初期化し、各バケットに 2 要素ずつ割り当てる想定とする\n    let k = nums.len() / 2;\n    let mut buckets = vec![vec![]; k];\n    // 1. 配列要素を各バケットに振り分ける\n    for &amp;num in nums.iter() {\n        // 入力データの範囲は [0, 1) であり、num * k を用いてインデックス範囲 [0, k-1] に写像する\n        let i = (num * k as f64) as usize;\n        // num をバケット i に追加\n        buckets[i].push(num);\n    }\n    // 2. 各バケットをソートする\n    for bucket in &amp;mut buckets {\n        // 組み込みのソート関数を使う。他のソートアルゴリズムに置き換えてもよい\n        bucket.sort_by(|a, b| a.partial_cmp(b).unwrap());\n    }\n    // 3. バケットを走査して結果を結合\n    let mut i = 0;\n    for bucket in buckets.iter() {\n        for &amp;num in bucket.iter() {\n            nums[i] = num;\n            i += 1;\n        }\n    }\n}\n</code></pre> bucket_sort.c<pre><code>/* バケットソート */\nvoid bucketSort(float nums[], int n) {\n    int k = n / 2;                                 // k = n/2 個のバケットを初期化する\n    int *sizes = malloc(k * sizeof(int));          // 各バケットのサイズを記録する\n    float **buckets = malloc(k * sizeof(float *)); // 動的配列の配列（バケット）\n    // 各バケットに十分な容量を事前確保する\n    for (int i = 0; i &lt; k; ++i) {\n        buckets[i] = (float *)malloc(n * sizeof(float));\n        sizes[i] = 0;\n    }\n    // 1. 配列要素を各バケットに振り分ける\n    for (int i = 0; i &lt; n; ++i) {\n        int idx = (int)(nums[i] * k);\n        buckets[idx][sizes[idx]++] = nums[i];\n    }\n    // 2. 各バケットをソートする\n    for (int i = 0; i &lt; k; ++i) {\n        qsort(buckets[i], sizes[i], sizeof(float), compare);\n    }\n    // 3. ソート済みのバケットを結合する\n    int idx = 0;\n    for (int i = 0; i &lt; k; ++i) {\n        for (int j = 0; j &lt; sizes[i]; ++j) {\n            nums[idx++] = buckets[i][j];\n        }\n        // メモリを解放する\n        free(buckets[i]);\n    }\n}\n</code></pre> bucket_sort.kt<pre><code>/* バケットソート */\nfun bucketSort(nums: FloatArray) {\n    // k = n/2 個のバケットを初期化し、各バケットに 2 要素ずつ割り当てる想定とする\n    val k = nums.size / 2\n    val buckets = mutableListOf&lt;MutableList&lt;Float&gt;&gt;()\n    for (i in 0..&lt;k) {\n        buckets.add(mutableListOf())\n    }\n    // 1. 配列要素を各バケットに振り分ける\n    for (num in nums) {\n        // 入力データの範囲は [0, 1) であり、num * k を用いてインデックス範囲 [0, k-1] に写像する\n        val i = (num * k).toInt()\n        // num をバケット i に追加\n        buckets[i].add(num)\n    }\n    // 2. 各バケットをソートする\n    for (bucket in buckets) {\n        // 組み込みのソート関数を使う。他のソートアルゴリズムに置き換えてもよい\n        bucket.sort()\n    }\n    // 3. バケットを走査して結果を結合\n    var i = 0\n    for (bucket in buckets) {\n        for (num in bucket) {\n            nums[i++] = num\n        }\n    }\n}\n</code></pre> bucket_sort.rb<pre><code>### バケットソート ###\ndef bucket_sort(nums)\n  # k = n/2 個のバケットを初期化し、各バケットに 2 要素ずつ割り当てる想定とする\n  k = nums.length / 2\n  buckets = Array.new(k) { [] }\n\n  # 1. 配列要素を各バケットに振り分ける\n  nums.each do |num|\n    # 入力データの範囲は [0, 1) であり、num * k を用いてインデックス範囲 [0, k-1] に写像する\n    i = (num * k).to_i\n    # num をバケット i に追加\n    buckets[i] &lt;&lt; num\n  end\n\n  # 2. 各バケットをソートする\n  buckets.each do |bucket|\n    # 組み込みのソート関数を使う。他のソートアルゴリズムに置き換えてもよい\n    bucket.sort!\n  end\n\n  # 3. バケットを走査して結果を結合\n  i = 0\n  buckets.each do |bucket|\n    bucket.each do |num|\n      nums[i] = num\n      i += 1\n    end\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 11 章 &nbsp; ソート","11.8 &nbsp; バケットソート"],"tags":[]},{"location":"chapter_sorting/bucket_sort/#1182","level":2,"title":"11.8.2   アルゴリズムの特性","text":"<p>バケットソートは、非常に大規模なデータの処理に適しています。たとえば、入力データに 100 万個の要素が含まれ、空間の制約によりシステムメモリへすべてのデータを一度に読み込めない場合です。このとき、データを 1000 個のバケットに分け、それぞれのバケットを個別にソートしてから、最後に結果を結合できます。</p> <ul> <li>時間計算量は \\(O(n + k)\\) ：要素が各バケット内に平均的に分布していると仮定すると、各バケット内の要素数は \\(\\frac{n}{k}\\) です。1 つのバケットをソートするのに \\(O(\\frac{n}{k} \\log\\frac{n}{k})\\) の時間がかかるなら、すべてのバケットのソートには \\(O(n \\log\\frac{n}{k})\\) の時間がかかります。バケット数 \\(k\\) が十分大きいとき、時間計算量は \\(O(n)\\) に近づきます。結果を結合する際には、すべてのバケットと要素を走査する必要があり、\\(O(n + k)\\) の時間を要します。最悪の場合、すべてのデータが 1 つのバケットに割り当てられ、そのバケットのソートに \\(O(n^2)\\) の時間がかかります。</li> <li>空間計算量は \\(O(n + k)\\)、非インプレースソート：\\(k\\) 個のバケットと合計 \\(n\\) 個の要素ぶんの追加領域が必要です。</li> <li>バケットソートが安定かどうかは、バケット内要素のソートに用いるアルゴリズムが安定かどうかに依存します。</li> </ul>","path":["第 11 章 &nbsp; ソート","11.8 &nbsp; バケットソート"],"tags":[]},{"location":"chapter_sorting/bucket_sort/#1183","level":2,"title":"11.8.3   均等な分配を実現するには","text":"<p>バケットソートの時間計算量は理論上 \\(O(n)\\) に達しますが、鍵は要素を各バケットへ均等に分配すること にあります。実際のデータは均一に分布していないことが多いからです。たとえば、Taobao 上のすべての商品を価格帯ごとに 10 個のバケットへ均等に分けたいとしても、商品の価格分布は偏っており、100 元未満は非常に多く、1000 元超は非常に少ないかもしれません。価格区間を単純に 10 等分すると、各バケットの商品数には大きな差が生じます。</p> <p>均等な分配を実現するために、まず大まかな境界線を設定し、データをひとまず 3 個のバケットに粗く振り分けます。分配後は、商品数の多いバケットをさらに 3 個のバケットに分割し、すべてのバケット内の要素数がおおむね等しくなるまでこれを続けます。</p> <p>以下の図に示すように、この方法の本質は再帰木を構築することにあり、目標は葉ノードの値をできるだけ均等にすることです。もちろん、毎回データを 3 個のバケットに分割する必要はなく、具体的な分け方はデータの特徴に応じて柔軟に選べます。</p> <p></p> <p> 図 11-14   再帰的にバケットを分割 </p> <p>商品価格の確率分布をあらかじめ把握しているなら、データの確率分布に基づいて各バケットの価格境界を設定できます。なお、データ分布は必ずしも特別に統計を取る必要はなく、データの特徴に応じて何らかの確率モデルで近似することもできます。</p> <p>以下の図に示すように、商品価格が正規分布に従うと仮定すれば、価格区間を合理的に設定でき、それによって商品を各バケットへ均等に分配できます。</p> <p></p> <p> 図 11-15   確率分布に基づいてバケットを分割 </p>","path":["第 11 章 &nbsp; ソート","11.8 &nbsp; バケットソート"],"tags":[]},{"location":"chapter_sorting/counting_sort/","level":1,"title":"11.9   計数ソート","text":"<p>計数ソート（counting sort）は要素数を集計することでソートを実現し、通常は整数配列に適用されます。</p>","path":["第 11 章 &nbsp; ソート","11.9 &nbsp; 計数ソート"],"tags":[]},{"location":"chapter_sorting/counting_sort/#1191","level":2,"title":"11.9.1   単純な実装","text":"<p>まず簡単な例を見てみましょう。長さ \\(n\\) の配列 <code>nums</code> が与えられ、その要素はすべて「非負整数」であるとします。計数ソートの全体的な流れを以下の図に示します。</p> <ol> <li>配列を走査し、その中の最大値を見つけて \\(m\\) とし、続いて長さ \\(m + 1\\) の補助配列 <code>counter</code> を作成します。</li> <li><code>counter</code> を用いて <code>nums</code> 内の各数値の出現回数を集計します。ここで <code>counter[num]</code> は数値 <code>num</code> の出現回数に対応します。集計方法は非常に簡単で、<code>nums</code> を走査し（現在の数値を <code>num</code> とする）、各回で <code>counter[num]</code> を \\(1\\) 増やせばよいです。</li> <li><code>counter</code> の各インデックスは自然に順序づけられているため、すべての数値はすでに整列された状態とみなせます。続いて <code>counter</code> を走査し、各数値の出現回数に応じて小さい順に <code>nums</code> へ書き戻せば完了です。</li> </ol> <p></p> <p> 図 11-16   計数ソートの流れ </p> <p>コードは以下のとおりです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby counting_sort.py<pre><code>def counting_sort_naive(nums: list[int]):\n    \"\"\"計数ソート\"\"\"\n    # 簡易版。オブジェクトのソートには使えない\n    # 1. 配列の最大要素 m を求める\n    m = max(nums)\n    # 2. 各数値の出現回数を数える\n    # counter[num] は num の出現回数を表す\n    counter = [0] * (m + 1)\n    for num in nums:\n        counter[num] += 1\n    # 3. counter を走査し、各要素を元の配列 nums に書き戻す\n    i = 0\n    for num in range(m + 1):\n        for _ in range(counter[num]):\n            nums[i] = num\n            i += 1\n</code></pre> counting_sort.cpp<pre><code>/* 計数ソート */\n// 簡易実装のため、オブジェクトのソートには使えない\nvoid countingSortNaive(vector&lt;int&gt; &amp;nums) {\n    // 1. 配列の最大要素 m を求める\n    int m = 0;\n    for (int num : nums) {\n        m = max(m, num);\n    }\n    // 2. 各数値の出現回数を数える\n    // counter[num] は num の出現回数を表す\n    vector&lt;int&gt; counter(m + 1, 0);\n    for (int num : nums) {\n        counter[num]++;\n    }\n    // 3. counter を走査し、各要素を元の配列 nums に書き戻す\n    int i = 0;\n    for (int num = 0; num &lt; m + 1; num++) {\n        for (int j = 0; j &lt; counter[num]; j++, i++) {\n            nums[i] = num;\n        }\n    }\n}\n</code></pre> counting_sort.java<pre><code>/* 計数ソート */\n// 簡易実装のため、オブジェクトのソートには使えない\nvoid countingSortNaive(int[] nums) {\n    // 1. 配列の最大要素 m を求める\n    int m = 0;\n    for (int num : nums) {\n        m = Math.max(m, num);\n    }\n    // 2. 各数値の出現回数を数える\n    // counter[num] は num の出現回数を表す\n    int[] counter = new int[m + 1];\n    for (int num : nums) {\n        counter[num]++;\n    }\n    // 3. counter を走査し、各要素を元の配列 nums に書き戻す\n    int i = 0;\n    for (int num = 0; num &lt; m + 1; num++) {\n        for (int j = 0; j &lt; counter[num]; j++, i++) {\n            nums[i] = num;\n        }\n    }\n}\n</code></pre> counting_sort.cs<pre><code>/* 計数ソート */\n// 簡易実装のため、オブジェクトのソートには使えない\nvoid CountingSortNaive(int[] nums) {\n    // 1. 配列の最大要素 m を求める\n    int m = 0;\n    foreach (int num in nums) {\n        m = Math.Max(m, num);\n    }\n    // 2. 各数値の出現回数を数える\n    // counter[num] は num の出現回数を表す\n    int[] counter = new int[m + 1];\n    foreach (int num in nums) {\n        counter[num]++;\n    }\n    // 3. counter を走査し、各要素を元の配列 nums に書き戻す\n    int i = 0;\n    for (int num = 0; num &lt; m + 1; num++) {\n        for (int j = 0; j &lt; counter[num]; j++, i++) {\n            nums[i] = num;\n        }\n    }\n}\n</code></pre> counting_sort.go<pre><code>/* 計数ソート */\n// 簡易実装のため、オブジェクトのソートには使えない\nfunc countingSortNaive(nums []int) {\n    // 1. 配列の最大要素 m を求める\n    m := 0\n    for _, num := range nums {\n        if num &gt; m {\n            m = num\n        }\n    }\n    // 2. 各数値の出現回数を数える\n    // counter[num] は num の出現回数を表す\n    counter := make([]int, m+1)\n    for _, num := range nums {\n        counter[num]++\n    }\n    // 3. counter を走査し、各要素を元の配列 nums に書き戻す\n    for i, num := 0, 0; num &lt; m+1; num++ {\n        for j := 0; j &lt; counter[num]; j++ {\n            nums[i] = num\n            i++\n        }\n    }\n}\n</code></pre> counting_sort.swift<pre><code>/* 計数ソート */\n// 簡易実装のため、オブジェクトのソートには使えない\nfunc countingSortNaive(nums: inout [Int]) {\n    // 1. 配列の最大要素 m を求める\n    let m = nums.max()!\n    // 2. 各数値の出現回数を数える\n    // counter[num] は num の出現回数を表す\n    var counter = Array(repeating: 0, count: m + 1)\n    for num in nums {\n        counter[num] += 1\n    }\n    // 3. counter を走査し、各要素を元の配列 nums に書き戻す\n    var i = 0\n    for num in 0 ..&lt; m + 1 {\n        for _ in 0 ..&lt; counter[num] {\n            nums[i] = num\n            i += 1\n        }\n    }\n}\n</code></pre> counting_sort.js<pre><code>/* 計数ソート */\n// 簡易実装のため、オブジェクトのソートには使えない\nfunction countingSortNaive(nums) {\n    // 1. 配列の最大要素 m を求める\n    let m = Math.max(...nums);\n    // 2. 各数値の出現回数を数える\n    // counter[num] は num の出現回数を表す\n    const counter = new Array(m + 1).fill(0);\n    for (const num of nums) {\n        counter[num]++;\n    }\n    // 3. counter を走査し、各要素を元の配列 nums に書き戻す\n    let i = 0;\n    for (let num = 0; num &lt; m + 1; num++) {\n        for (let j = 0; j &lt; counter[num]; j++, i++) {\n            nums[i] = num;\n        }\n    }\n}\n</code></pre> counting_sort.ts<pre><code>/* 計数ソート */\n// 簡易実装のため、オブジェクトのソートには使えない\nfunction countingSortNaive(nums: number[]): void {\n    // 1. 配列の最大要素 m を求める\n    let m: number = Math.max(...nums);\n    // 2. 各数値の出現回数を数える\n    // counter[num] は num の出現回数を表す\n    const counter: number[] = new Array&lt;number&gt;(m + 1).fill(0);\n    for (const num of nums) {\n        counter[num]++;\n    }\n    // 3. counter を走査し、各要素を元の配列 nums に書き戻す\n    let i = 0;\n    for (let num = 0; num &lt; m + 1; num++) {\n        for (let j = 0; j &lt; counter[num]; j++, i++) {\n            nums[i] = num;\n        }\n    }\n}\n</code></pre> counting_sort.dart<pre><code>/* 計数ソート */\n// 簡易実装のため、オブジェクトのソートには使えない\nvoid countingSortNaive(List&lt;int&gt; nums) {\n  // 1. 配列の最大要素 m を求める\n  int m = 0;\n  for (int _num in nums) {\n    m = max(m, _num);\n  }\n  // 2. 各数値の出現回数を数える\n  // counter[_num] は _num の出現回数を表す\n  List&lt;int&gt; counter = List.filled(m + 1, 0);\n  for (int _num in nums) {\n    counter[_num]++;\n  }\n  // 3. counter を走査し、各要素を元の配列 nums に書き戻す\n  int i = 0;\n  for (int _num = 0; _num &lt; m + 1; _num++) {\n    for (int j = 0; j &lt; counter[_num]; j++, i++) {\n      nums[i] = _num;\n    }\n  }\n}\n</code></pre> counting_sort.rs<pre><code>/* 計数ソート */\n// 簡易実装のため、オブジェクトのソートには使えない\nfn counting_sort_naive(nums: &amp;mut [i32]) {\n    // 1. 配列の最大要素 m を求める\n    let m = *nums.iter().max().unwrap();\n    // 2. 各数値の出現回数を数える\n    // counter[num] は num の出現回数を表す\n    let mut counter = vec![0; m as usize + 1];\n    for &amp;num in nums.iter() {\n        counter[num as usize] += 1;\n    }\n    // 3. counter を走査し、各要素を元の配列 nums に書き戻す\n    let mut i = 0;\n    for num in 0..m + 1 {\n        for _ in 0..counter[num as usize] {\n            nums[i] = num;\n            i += 1;\n        }\n    }\n}\n</code></pre> counting_sort.c<pre><code>/* 計数ソート */\n// 簡易実装のため、オブジェクトのソートには使えない\nvoid countingSortNaive(int nums[], int size) {\n    // 1. 配列の最大要素 m を求める\n    int m = 0;\n    for (int i = 0; i &lt; size; i++) {\n        if (nums[i] &gt; m) {\n            m = nums[i];\n        }\n    }\n    // 2. 各数値の出現回数を数える\n    // counter[num] は num の出現回数を表す\n    int *counter = calloc(m + 1, sizeof(int));\n    for (int i = 0; i &lt; size; i++) {\n        counter[nums[i]]++;\n    }\n    // 3. counter を走査し、各要素を元の配列 nums に書き戻す\n    int i = 0;\n    for (int num = 0; num &lt; m + 1; num++) {\n        for (int j = 0; j &lt; counter[num]; j++, i++) {\n            nums[i] = num;\n        }\n    }\n    // 4. メモリを解放する\n    free(counter);\n}\n</code></pre> counting_sort.kt<pre><code>/* 計数ソート */\n// 簡易実装のため、オブジェクトのソートには使えない\nfun countingSortNaive(nums: IntArray) {\n    // 1. 配列の最大要素 m を求める\n    var m = 0\n    for (num in nums) {\n        m = max(m, num)\n    }\n    // 2. 各数値の出現回数を数える\n    // counter[num] は num の出現回数を表す\n    val counter = IntArray(m + 1)\n    for (num in nums) {\n        counter[num]++\n    }\n    // 3. counter を走査し、各要素を元の配列 nums に書き戻す\n    var i = 0\n    for (num in 0..&lt;m + 1) {\n        var j = 0\n        while (j &lt; counter[num]) {\n            nums[i] = num\n            j++\n            i++\n        }\n    }\n}\n</code></pre> counting_sort.rb<pre><code>### 計数ソート ###\ndef counting_sort_naive(nums)\n  # 簡易版。オブジェクトのソートには使えない\n  # 1. 配列の最大要素 m を求める\n  m = 0\n  nums.each { |num| m = [m, num].max }\n  # 2. 各数値の出現回数を数える\n  # counter[num] は num の出現回数を表す\n  counter = Array.new(m + 1, 0)\n  nums.each { |num| counter[num] += 1 }\n  # 3. counter を走査し、各要素を元の配列 nums に書き戻す\n  i = 0\n  for num in 0...(m + 1)\n    (0...counter[num]).each do\n      nums[i] = num\n      i += 1\n    end\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>計数ソートとバケットソートの関係</p> <p>バケットソートの観点から見ると、計数ソートにおける計数配列 <code>counter</code> の各インデックスを 1 つのバケットとみなし、個数を数える過程を各要素を対応するバケットへ振り分ける操作とみなせます。本質的には、計数ソートは整数データにおけるバケットソートの特殊な一例です。</p>","path":["第 11 章 &nbsp; ソート","11.9 &nbsp; 計数ソート"],"tags":[]},{"location":"chapter_sorting/counting_sort/#1192","level":2,"title":"11.9.2   完全な実装","text":"<p>注意深い読者なら、**入力データがオブジェクトである場合、上記の手順 <code>3.</code> は機能しない**ことに気づくかもしれません。入力データが商品オブジェクトであり、商品価格（クラスのメンバ変数）に基づいて商品をソートしたいとします。しかし上記のアルゴリズムが返せるのは価格のソート結果だけです。</p> <p>では、元のデータのソート結果を得るにはどうすればよいのでしょうか。まず <code>counter</code> の「累積和」を計算します。名前のとおり、インデックス <code>i</code> における累積和 <code>prefix[i]</code> は、配列の先頭から <code>i</code> 番目までの要素の総和に等しくなります：</p> \\[ \\text{prefix}[i] = \\sum_{j=0}^i \\text{counter[j]} \\] <p>累積和には明確な意味があり、<code>prefix[num] - 1</code> は要素 <code>num</code> が結果配列 <code>res</code> に最後に現れるインデックスを表します。この情報は非常に重要で、各要素が結果配列のどの位置に現れるべきかを示してくれます。続いて元の配列 <code>nums</code> を逆順に走査し、各要素 <code>num</code> に対して各反復で次の 2 つの手順を行います。</p> <ol> <li><code>num</code> を配列 <code>res</code> のインデックス <code>prefix[num] - 1</code> に格納します。</li> <li>累積和 <code>prefix[num]</code> を \\(1\\) 減らし、次に <code>num</code> を配置するインデックスを得ます。</li> </ol> <p>走査が完了すると、配列 <code>res</code> にソート済みの結果が格納されます。最後に <code>res</code> で元の配列 <code>nums</code> を上書きすれば完了です。以下の図は完全な計数ソートの流れを示しています。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 11-17   計数ソートの手順 </p> <p>計数ソートの実装コードは以下のとおりです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby counting_sort.py<pre><code>def counting_sort(nums: list[int]):\n    \"\"\"計数ソート\"\"\"\n    # 完全版。オブジェクトをソートでき、かつ安定ソートである\n    # 1. 配列の最大要素 m を求める\n    m = max(nums)\n    # 2. 各数値の出現回数を数える\n    # counter[num] は num の出現回数を表す\n    counter = [0] * (m + 1)\n    for num in nums:\n        counter[num] += 1\n    # 3. counter の累積和を求めて、「出現回数」を「末尾インデックス」に変換する\n    # つまり counter[num]-1 は、num が res に最後に現れるインデックス\n    for i in range(m):\n        counter[i + 1] += counter[i]\n    # 4. nums を逆順に走査し、各要素を結果配列 res に格納する\n    # 結果を記録するための配列 res を初期化\n    n = len(nums)\n    res = [0] * n\n    for i in range(n - 1, -1, -1):\n        num = nums[i]\n        res[counter[num] - 1] = num  # num を対応するインデックスに配置\n        counter[num] -= 1  # 累積和を 1 減らして、次に num を配置するインデックスを得る\n    # 結果配列 res で元の配列 nums を上書きする\n    for i in range(n):\n        nums[i] = res[i]\n</code></pre> counting_sort.cpp<pre><code>/* 計数ソート */\n// 完全な実装で、オブジェクトをソートでき、かつ安定ソートである\nvoid countingSort(vector&lt;int&gt; &amp;nums) {\n    // 1. 配列の最大要素 m を求める\n    int m = 0;\n    for (int num : nums) {\n        m = max(m, num);\n    }\n    // 2. 各数値の出現回数を数える\n    // counter[num] は num の出現回数を表す\n    vector&lt;int&gt; counter(m + 1, 0);\n    for (int num : nums) {\n        counter[num]++;\n    }\n    // 3. counter の累積和を求めて、「出現回数」を「末尾インデックス」に変換する\n    // つまり counter[num]-1 は、num が res に最後に現れるインデックス\n    for (int i = 0; i &lt; m; i++) {\n        counter[i + 1] += counter[i];\n    }\n    // 4. nums を逆順に走査し、各要素を結果配列 res に格納する\n    // 結果を記録するための配列 res を初期化\n    int n = nums.size();\n    vector&lt;int&gt; res(n);\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int num = nums[i];\n        res[counter[num] - 1] = num; // num を対応するインデックスに配置\n        counter[num]--;              // 累積和を 1 減らして、次に num を配置するインデックスを得る\n    }\n    // 結果配列 res で元の配列 nums を上書きする\n    nums = res;\n}\n</code></pre> counting_sort.java<pre><code>/* 計数ソート */\n// 完全な実装で、オブジェクトをソートでき、かつ安定ソートである\nvoid countingSort(int[] nums) {\n    // 1. 配列の最大要素 m を求める\n    int m = 0;\n    for (int num : nums) {\n        m = Math.max(m, num);\n    }\n    // 2. 各数値の出現回数を数える\n    // counter[num] は num の出現回数を表す\n    int[] counter = new int[m + 1];\n    for (int num : nums) {\n        counter[num]++;\n    }\n    // 3. counter の累積和を求めて、「出現回数」を「末尾インデックス」に変換する\n    // つまり counter[num]-1 は、num が res に最後に現れるインデックス\n    for (int i = 0; i &lt; m; i++) {\n        counter[i + 1] += counter[i];\n    }\n    // 4. nums を逆順に走査し、各要素を結果配列 res に格納する\n    // 結果を記録するための配列 res を初期化\n    int n = nums.length;\n    int[] res = new int[n];\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int num = nums[i];\n        res[counter[num] - 1] = num; // num を対応するインデックスに配置\n        counter[num]--; // 累積和を 1 減らして、次に num を配置するインデックスを得る\n    }\n    // 結果配列 res で元の配列 nums を上書きする\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = res[i];\n    }\n}\n</code></pre> counting_sort.cs<pre><code>/* 計数ソート */\n// 完全な実装で、オブジェクトをソートでき、かつ安定ソートである\nvoid CountingSort(int[] nums) {\n    // 1. 配列の最大要素 m を求める\n    int m = 0;\n    foreach (int num in nums) {\n        m = Math.Max(m, num);\n    }\n    // 2. 各数値の出現回数を数える\n    // counter[num] は num の出現回数を表す\n    int[] counter = new int[m + 1];\n    foreach (int num in nums) {\n        counter[num]++;\n    }\n    // 3. counter の累積和を求めて、「出現回数」を「末尾インデックス」に変換する\n    // つまり counter[num]-1 は、num が res に最後に現れるインデックス\n    for (int i = 0; i &lt; m; i++) {\n        counter[i + 1] += counter[i];\n    }\n    // 4. nums を逆順に走査し、各要素を結果配列 res に格納する\n    // 結果を記録するための配列 res を初期化\n    int n = nums.Length;\n    int[] res = new int[n];\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int num = nums[i];\n        res[counter[num] - 1] = num; // num を対応するインデックスに配置\n        counter[num]--; // 累積和を 1 減らして、次に num を配置するインデックスを得る\n    }\n    // 結果配列 res で元の配列 nums を上書きする\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = res[i];\n    }\n}\n</code></pre> counting_sort.go<pre><code>/* 計数ソート */\n// 完全な実装で、オブジェクトをソートでき、かつ安定ソートである\nfunc countingSort(nums []int) {\n    // 1. 配列の最大要素 m を求める\n    m := 0\n    for _, num := range nums {\n        if num &gt; m {\n            m = num\n        }\n    }\n    // 2. 各数値の出現回数を数える\n    // counter[num] は num の出現回数を表す\n    counter := make([]int, m+1)\n    for _, num := range nums {\n        counter[num]++\n    }\n    // 3. counter の累積和を求めて、「出現回数」を「末尾インデックス」に変換する\n    // つまり counter[num]-1 は、num が res に最後に現れるインデックス\n    for i := 0; i &lt; m; i++ {\n        counter[i+1] += counter[i]\n    }\n    // 4. nums を逆順に走査し、各要素を結果配列 res に格納する\n    // 結果を記録するための配列 res を初期化\n    n := len(nums)\n    res := make([]int, n)\n    for i := n - 1; i &gt;= 0; i-- {\n        num := nums[i]\n        // num を対応するインデックスに配置\n        res[counter[num]-1] = num\n        // 累積和を 1 減らして、次に num を配置するインデックスを得る\n        counter[num]--\n    }\n    // 結果配列 res で元の配列 nums を上書きする\n    copy(nums, res)\n}\n</code></pre> counting_sort.swift<pre><code>/* 計数ソート */\n// 完全な実装で、オブジェクトをソートでき、かつ安定ソートである\nfunc countingSort(nums: inout [Int]) {\n    // 1. 配列の最大要素 m を求める\n    let m = nums.max()!\n    // 2. 各数値の出現回数を数える\n    // counter[num] は num の出現回数を表す\n    var counter = Array(repeating: 0, count: m + 1)\n    for num in nums {\n        counter[num] += 1\n    }\n    // 3. counter の累積和を求めて、「出現回数」を「末尾インデックス」に変換する\n    // つまり counter[num]-1 は、num が res に最後に現れるインデックス\n    for i in 0 ..&lt; m {\n        counter[i + 1] += counter[i]\n    }\n    // 4. nums を逆順に走査し、各要素を結果配列 res に格納する\n    // 結果を記録するための配列 res を初期化\n    var res = Array(repeating: 0, count: nums.count)\n    for i in nums.indices.reversed() {\n        let num = nums[i]\n        res[counter[num] - 1] = num // num を対応するインデックスに配置\n        counter[num] -= 1 // 累積和を 1 減らして、次に num を配置するインデックスを得る\n    }\n    // 結果配列 res で元の配列 nums を上書きする\n    for i in nums.indices {\n        nums[i] = res[i]\n    }\n}\n</code></pre> counting_sort.js<pre><code>/* 計数ソート */\n// 完全な実装で、オブジェクトをソートでき、かつ安定ソートである\nfunction countingSort(nums) {\n    // 1. 配列の最大要素 m を求める\n    let m = Math.max(...nums);\n    // 2. 各数値の出現回数を数える\n    // counter[num] は num の出現回数を表す\n    const counter = new Array(m + 1).fill(0);\n    for (const num of nums) {\n        counter[num]++;\n    }\n    // 3. counter の累積和を求めて、「出現回数」を「末尾インデックス」に変換する\n    // つまり counter[num]-1 は、num が res に最後に現れるインデックス\n    for (let i = 0; i &lt; m; i++) {\n        counter[i + 1] += counter[i];\n    }\n    // 4. nums を逆順に走査し、各要素を結果配列 res に格納する\n    // 結果を記録するための配列 res を初期化\n    const n = nums.length;\n    const res = new Array(n);\n    for (let i = n - 1; i &gt;= 0; i--) {\n        const num = nums[i];\n        res[counter[num] - 1] = num; // num を対応するインデックスに配置\n        counter[num]--; // 累積和を 1 減らして、次に num を配置するインデックスを得る\n    }\n    // 結果配列 res で元の配列 nums を上書きする\n    for (let i = 0; i &lt; n; i++) {\n        nums[i] = res[i];\n    }\n}\n</code></pre> counting_sort.ts<pre><code>/* 計数ソート */\n// 完全な実装で、オブジェクトをソートでき、かつ安定ソートである\nfunction countingSort(nums: number[]): void {\n    // 1. 配列の最大要素 m を求める\n    let m: number = Math.max(...nums);\n    // 2. 各数値の出現回数を数える\n    // counter[num] は num の出現回数を表す\n    const counter: number[] = new Array&lt;number&gt;(m + 1).fill(0);\n    for (const num of nums) {\n        counter[num]++;\n    }\n    // 3. counter の累積和を求めて、「出現回数」を「末尾インデックス」に変換する\n    // つまり counter[num]-1 は、num が res に最後に現れるインデックス\n    for (let i = 0; i &lt; m; i++) {\n        counter[i + 1] += counter[i];\n    }\n    // 4. nums を逆順に走査し、各要素を結果配列 res に格納する\n    // 結果を記録するための配列 res を初期化\n    const n = nums.length;\n    const res: number[] = new Array&lt;number&gt;(n);\n    for (let i = n - 1; i &gt;= 0; i--) {\n        const num = nums[i];\n        res[counter[num] - 1] = num; // num を対応するインデックスに配置\n        counter[num]--; // 累積和を 1 減らして、次に num を配置するインデックスを得る\n    }\n    // 結果配列 res で元の配列 nums を上書きする\n    for (let i = 0; i &lt; n; i++) {\n        nums[i] = res[i];\n    }\n}\n</code></pre> counting_sort.dart<pre><code>/* 計数ソート */\n// 完全な実装で、オブジェクトをソートでき、かつ安定ソートである\nvoid countingSort(List&lt;int&gt; nums) {\n  // 1. 配列の最大要素 m を求める\n  int m = 0;\n  for (int _num in nums) {\n    m = max(m, _num);\n  }\n  // 2. 各数値の出現回数を数える\n  // counter[_num] は _num の出現回数を表す\n  List&lt;int&gt; counter = List.filled(m + 1, 0);\n  for (int _num in nums) {\n    counter[_num]++;\n  }\n  // 3. counter の累積和を求め、「出現回数」を「末尾インデックス」に変換する\n  // つまり counter[_num]-1 は、res において _num が最後に出現する位置のインデックスである\n  for (int i = 0; i &lt; m; i++) {\n    counter[i + 1] += counter[i];\n  }\n  // 4. nums を逆順に走査し、各要素を結果配列 res に格納する\n  // 結果を記録するための配列 res を初期化\n  int n = nums.length;\n  List&lt;int&gt; res = List.filled(n, 0);\n  for (int i = n - 1; i &gt;= 0; i--) {\n    int _num = nums[i];\n    res[counter[_num] - 1] = _num; // _num を対応する添字に配置\n    counter[_num]--; // 累積和を 1 減らし、次に _num を配置するインデックスを得る\n  }\n  // 結果配列 res で元の配列 nums を上書きする\n  nums.setAll(0, res);\n}\n</code></pre> counting_sort.rs<pre><code>/* 計数ソート */\n// 完全な実装で、オブジェクトをソートでき、かつ安定ソートである\nfn counting_sort(nums: &amp;mut [i32]) {\n    // 1. 配列の最大要素 m を求める\n    let m = *nums.iter().max().unwrap() as usize;\n    // 2. 各数値の出現回数を数える\n    // counter[num] は num の出現回数を表す\n    let mut counter = vec![0; m + 1];\n    for &amp;num in nums.iter() {\n        counter[num as usize] += 1;\n    }\n    // 3. counter の累積和を求めて、「出現回数」を「末尾インデックス」に変換する\n    // つまり counter[num]-1 は、num が res に最後に現れるインデックス\n    for i in 0..m {\n        counter[i + 1] += counter[i];\n    }\n    // 4. nums を逆順に走査し、各要素を結果配列 res に格納する\n    // 結果を記録するための配列 res を初期化\n    let n = nums.len();\n    let mut res = vec![0; n];\n    for i in (0..n).rev() {\n        let num = nums[i];\n        res[counter[num as usize] - 1] = num; // num を対応するインデックスに配置\n        counter[num as usize] -= 1; // 累積和を 1 減らして、次に num を配置するインデックスを得る\n    }\n    // 結果配列 res で元の配列 nums を上書きする\n    nums.copy_from_slice(&amp;res)\n}\n</code></pre> counting_sort.c<pre><code>/* 計数ソート */\n// 完全な実装で、オブジェクトをソートでき、かつ安定ソートである\nvoid countingSort(int nums[], int size) {\n    // 1. 配列の最大要素 m を求める\n    int m = 0;\n    for (int i = 0; i &lt; size; i++) {\n        if (nums[i] &gt; m) {\n            m = nums[i];\n        }\n    }\n    // 2. 各数値の出現回数を数える\n    // counter[num] は num の出現回数を表す\n    int *counter = calloc(m, sizeof(int));\n    for (int i = 0; i &lt; size; i++) {\n        counter[nums[i]]++;\n    }\n    // 3. counter の累積和を求めて、「出現回数」を「末尾インデックス」に変換する\n    // つまり counter[num]-1 は、num が res に最後に現れるインデックス\n    for (int i = 0; i &lt; m; i++) {\n        counter[i + 1] += counter[i];\n    }\n    // 4. nums を逆順に走査し、各要素を結果配列 res に格納する\n    // 結果を記録するための配列 res を初期化\n    int *res = malloc(sizeof(int) * size);\n    for (int i = size - 1; i &gt;= 0; i--) {\n        int num = nums[i];\n        res[counter[num] - 1] = num; // num を対応するインデックスに配置\n        counter[num]--;              // 累積和を 1 減らして、次に num を配置するインデックスを得る\n    }\n    // 結果配列 res で元の配列 nums を上書きする\n    memcpy(nums, res, size * sizeof(int));\n    // 5. メモリを解放する\n    free(res);\n    free(counter);\n}\n</code></pre> counting_sort.kt<pre><code>/* 計数ソート */\n// 完全な実装で、オブジェクトをソートでき、かつ安定ソートである\nfun countingSort(nums: IntArray) {\n    // 1. 配列の最大要素 m を求める\n    var m = 0\n    for (num in nums) {\n        m = max(m, num)\n    }\n    // 2. 各数値の出現回数を数える\n    // counter[num] は num の出現回数を表す\n    val counter = IntArray(m + 1)\n    for (num in nums) {\n        counter[num]++\n    }\n    // 3. counter の累積和を求めて、「出現回数」を「末尾インデックス」に変換する\n    // つまり counter[num]-1 は、num が res に最後に現れるインデックス\n    for (i in 0..&lt;m) {\n        counter[i + 1] += counter[i]\n    }\n    // 4. nums を逆順に走査し、各要素を結果配列 res に格納する\n    // 結果を記録するための配列 res を初期化\n    val n = nums.size\n    val res = IntArray(n)\n    for (i in n - 1 downTo 0) {\n        val num = nums[i]\n        res[counter[num] - 1] = num // num を対応するインデックスに配置\n        counter[num]-- // 累積和を 1 減らして、次に num を配置するインデックスを得る\n    }\n    // 結果配列 res で元の配列 nums を上書きする\n    for (i in 0..&lt;n) {\n        nums[i] = res[i]\n    }\n}\n</code></pre> counting_sort.rb<pre><code>### 計数ソート ###\ndef counting_sort(nums)\n  # 完全版。オブジェクトをソートでき、かつ安定ソートである\n  # 1. 配列の最大要素 m を求める\n  m = nums.max\n  # 2. 各数値の出現回数を数える\n  # counter[num] は num の出現回数を表す\n  counter = Array.new(m + 1, 0)\n  nums.each { |num| counter[num] += 1 }\n  # 3. counter の累積和を求めて、「出現回数」を「末尾インデックス」に変換する\n  # つまり counter[num]-1 は、num が res に最後に現れるインデックス\n  (0...m).each { |i| counter[i + 1] += counter[i] }\n  # 4. nums を逆順に走査し、各要素を結果配列 res に格納する\n  # 結果を記録するための配列 res を初期化する\n  n = nums.length\n  res = Array.new(n, 0)\n  (n - 1).downto(0).each do |i|\n    num = nums[i]\n    res[counter[num] - 1] = num # num を対応するインデックスに配置\n    counter[num] -= 1 # 累積和を 1 減らして、次に num を配置するインデックスを得る\n  end\n  # 結果配列 res で元の配列 nums を上書きする\n  (0...n).each { |i| nums[i] = res[i] }\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 11 章 &nbsp; ソート","11.9 &nbsp; 計数ソート"],"tags":[]},{"location":"chapter_sorting/counting_sort/#1193","level":2,"title":"11.9.3   アルゴリズムの特性","text":"<ul> <li>時間計算量は \\(O(n + m)\\)、非適応ソート ：<code>nums</code> の走査と <code>counter</code> の走査が含まれ、いずれも線形時間です。一般には \\(n \\gg m\\) であり、時間計算量は \\(O(n)\\) に近づきます。</li> <li>空間計算量は \\(O(n + m)\\)、非インプレースソート：長さがそれぞれ \\(n\\) と \\(m\\) の配列 <code>res</code> と <code>counter</code> を利用します。</li> <li>安定ソート：<code>res</code> に要素を埋める順序が「右から左」であるため、<code>nums</code> を逆順に走査することで等しい要素どうしの相対位置が変化するのを防ぎ、安定ソートを実現できます。実際には、<code>nums</code> を順方向に走査しても正しいソート結果は得られますが、その結果は安定ではありません。</li> </ul>","path":["第 11 章 &nbsp; ソート","11.9 &nbsp; 計数ソート"],"tags":[]},{"location":"chapter_sorting/counting_sort/#1194","level":2,"title":"11.9.4   制約","text":"<p>ここまで読むと、計数ソートは非常に巧妙で、個数を数えるだけで効率的なソートを実現できると感じるかもしれません。しかし、計数ソートを利用するための前提条件は比較的厳格です。</p> <p>計数ソートは非負整数にしか適用できません。ほかの型のデータに適用したい場合は、それらのデータを非負整数に変換でき、かつ変換の過程で要素間の相対的な大小関係が変わらないことを保証する必要があります。たとえば、負数を含む整数配列に対しては、すべての数値に定数を加えて正数へ変換し、ソート後に元へ戻すことができます。</p> <p>計数ソートはデータ量が多く、値域が小さい場合に適しています。たとえば上記の例では \\(m\\) が大きすぎてはならず、そうでないと過剰な空間を消費します。また、\\(n \\ll m\\) のとき、計数ソートは \\(O(m)\\) 時間を要するため、\\(O(n \\log n)\\) のソートアルゴリズムより遅くなる可能性があります。</p>","path":["第 11 章 &nbsp; ソート","11.9 &nbsp; 計数ソート"],"tags":[]},{"location":"chapter_sorting/heap_sort/","level":1,"title":"11.7   ヒープソート","text":"<p>Tip</p> <p>本節を読む前に、「ヒープ」の章を学習済みであることを確認してください。</p> <p>ヒープソート（heap sort）は、ヒープデータ構造に基づいて実装される効率的なソートアルゴリズムです。すでに学んだ「ヒープ構築操作」と「要素の取り出し操作」を利用してヒープソートを実現できます。</p> <ol> <li>配列を入力して最小ヒープを構築すると、このとき最小要素はヒープの頂点にあります。</li> <li>取り出し操作を繰り返し実行し、取り出された要素を順に記録すれば、昇順に並んだ列が得られます。</li> </ol> <p>以上の方法でも実行できますが、取り出した要素を保存するために追加の配列が必要となり、空間をやや無駄にします。実際には、通常はより洗練された実装方法を用います。</p>","path":["第 11 章 &nbsp; ソート","11.7 &nbsp; ヒープソート"],"tags":[]},{"location":"chapter_sorting/heap_sort/#1171","level":2,"title":"11.7.1   アルゴリズムの流れ","text":"<p>配列の長さを \\(n\\) とすると、ヒープソートの流れは次図のとおりです。</p> <ol> <li>配列を入力して最大ヒープを構築します。完了後、最大要素はヒープの頂点にあります。</li> <li>ヒープ頂点の要素（最初の要素）とヒープ末尾の要素（最後の要素）を交換します。交換後、ヒープの長さは \\(1\\) 減少し、整列済み要素数は \\(1\\) 増加します。</li> <li>ヒープ頂点の要素から始めて、上から下へヒープ化操作（sift down）を実行します。ヒープ化が完了すると、ヒープの性質が回復します。</li> <li>第 <code>2.</code> ステップと第 <code>3.</code> ステップを繰り返し実行します。これを \\(n - 1\\) 回繰り返すと、配列の整列が完了します。</li> </ol> <p>Tip</p> <p>実際には、要素の取り出し操作にも第 <code>2.</code> ステップと第 <code>3.</code> ステップが含まれており、要素を取り出す処理が 1 つ加わるだけです。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 11-12   ヒープソートの手順 </p> <p>コード実装では、「ヒープ」の章と同じ上から下へのヒープ化 <code>sift_down()</code> 関数を使用します。注意すべき点として、ヒープの長さは最大要素を取り出すたびに短くなるため、<code>sift_down()</code> 関数に長さパラメータ \\(n\\) を追加し、ヒープの現在の有効な長さを指定する必要があります。コードは以下のとおりです。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby heap_sort.py<pre><code>def sift_down(nums: list[int], n: int, i: int):\n    \"\"\"ヒープの長さは n。ノード i から下方向にヒープ化\"\"\"\n    while True:\n        # ノード i, l, r のうち値が最大のノードを ma とする\n        l = 2 * i + 1\n        r = 2 * i + 2\n        ma = i\n        if l &lt; n and nums[l] &gt; nums[ma]:\n            ma = l\n        if r &lt; n and nums[r] &gt; nums[ma]:\n            ma = r\n        # ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n        if ma == i:\n            break\n        # 2 つのノードを交換\n        nums[i], nums[ma] = nums[ma], nums[i]\n        # ループで上から下へヒープ化\n        i = ma\n\ndef heap_sort(nums: list[int]):\n    \"\"\"ヒープソート\"\"\"\n    # ヒープ構築：葉ノード以外のすべてのノードをヒープ化する\n    for i in range(len(nums) // 2 - 1, -1, -1):\n        sift_down(nums, len(nums), i)\n    # ヒープから最大要素を取り出し、n-1 回繰り返す\n    for i in range(len(nums) - 1, 0, -1):\n        # 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n        nums[0], nums[i] = nums[i], nums[0]\n        # 根ノードを起点に、上から下へヒープ化\n        sift_down(nums, i, 0)\n</code></pre> heap_sort.cpp<pre><code>/* ヒープの長さは n。ノード i から下方向にヒープ化 */\nvoid siftDown(vector&lt;int&gt; &amp;nums, int n, int i) {\n    while (true) {\n        // ノード i, l, r のうち値が最大のノードを ma とする\n        int l = 2 * i + 1;\n        int r = 2 * i + 2;\n        int ma = i;\n        if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma])\n            ma = l;\n        if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma])\n            ma = r;\n        // ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n        if (ma == i) {\n            break;\n        }\n        // 2 つのノードを交換\n        swap(nums[i], nums[ma]);\n        // ループで上から下へヒープ化\n        i = ma;\n    }\n}\n\n/* ヒープソート */\nvoid heapSort(vector&lt;int&gt; &amp;nums) {\n    // ヒープ構築：葉ノード以外のすべてのノードをヒープ化する\n    for (int i = nums.size() / 2 - 1; i &gt;= 0; --i) {\n        siftDown(nums, nums.size(), i);\n    }\n    // ヒープから最大要素を取り出し、n-1 回繰り返す\n    for (int i = nums.size() - 1; i &gt; 0; --i) {\n        // 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n        swap(nums[0], nums[i]);\n        // 根ノードを起点に、上から下へヒープ化\n        siftDown(nums, i, 0);\n    }\n}\n</code></pre> heap_sort.java<pre><code>/* ヒープの長さは n。ノード i から下方向にヒープ化 */\nvoid siftDown(int[] nums, int n, int i) {\n    while (true) {\n        // ノード i, l, r のうち値が最大のノードを ma とする\n        int l = 2 * i + 1;\n        int r = 2 * i + 2;\n        int ma = i;\n        if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma])\n            ma = l;\n        if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma])\n            ma = r;\n        // ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n        if (ma == i)\n            break;\n        // 2 つのノードを交換\n        int temp = nums[i];\n        nums[i] = nums[ma];\n        nums[ma] = temp;\n        // ループで上から下へヒープ化\n        i = ma;\n    }\n}\n\n/* ヒープソート */\nvoid heapSort(int[] nums) {\n    // ヒープ構築：葉ノード以外のすべてのノードをヒープ化する\n    for (int i = nums.length / 2 - 1; i &gt;= 0; i--) {\n        siftDown(nums, nums.length, i);\n    }\n    // ヒープから最大要素を取り出し、n-1 回繰り返す\n    for (int i = nums.length - 1; i &gt; 0; i--) {\n        // 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n        int tmp = nums[0];\n        nums[0] = nums[i];\n        nums[i] = tmp;\n        // 根ノードを起点に、上から下へヒープ化\n        siftDown(nums, i, 0);\n    }\n}\n</code></pre> heap_sort.cs<pre><code>/* ヒープの長さは n。ノード i から下方向にヒープ化 */\nvoid SiftDown(int[] nums, int n, int i) {\n    while (true) {\n        // ノード i, l, r のうち値が最大のノードを ma とする\n        int l = 2 * i + 1;\n        int r = 2 * i + 2;\n        int ma = i;\n        if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma])\n            ma = l;\n        if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma])\n            ma = r;\n        // ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n        if (ma == i)\n            break;\n        // 2 つのノードを交換\n        (nums[ma], nums[i]) = (nums[i], nums[ma]);\n        // ループで上から下へヒープ化\n        i = ma;\n    }\n}\n\n/* ヒープソート */\nvoid HeapSort(int[] nums) {\n    // ヒープ構築：葉ノード以外のすべてのノードをヒープ化する\n    for (int i = nums.Length / 2 - 1; i &gt;= 0; i--) {\n        SiftDown(nums, nums.Length, i);\n    }\n    // ヒープから最大要素を取り出し、n-1 回繰り返す\n    for (int i = nums.Length - 1; i &gt; 0; i--) {\n        // 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n        (nums[i], nums[0]) = (nums[0], nums[i]);\n        // 根ノードを起点に、上から下へヒープ化\n        SiftDown(nums, i, 0);\n    }\n}\n</code></pre> heap_sort.go<pre><code>/* ヒープの長さは n。ノード i から下方向にヒープ化 */\nfunc siftDown(nums *[]int, n, i int) {\n    for true {\n        // ノード i, l, r のうち値が最大のノードを ma とする\n        l := 2*i + 1\n        r := 2*i + 2\n        ma := i\n        if l &lt; n &amp;&amp; (*nums)[l] &gt; (*nums)[ma] {\n            ma = l\n        }\n        if r &lt; n &amp;&amp; (*nums)[r] &gt; (*nums)[ma] {\n            ma = r\n        }\n        // ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n        if ma == i {\n            break\n        }\n        // 2 つのノードを交換\n        (*nums)[i], (*nums)[ma] = (*nums)[ma], (*nums)[i]\n        // ループで上から下へヒープ化\n        i = ma\n    }\n}\n\n/* ヒープソート */\nfunc heapSort(nums *[]int) {\n    // ヒープ構築：葉ノード以外のすべてのノードをヒープ化する\n    for i := len(*nums)/2 - 1; i &gt;= 0; i-- {\n        siftDown(nums, len(*nums), i)\n    }\n    // ヒープから最大要素を取り出し、n-1 回繰り返す\n    for i := len(*nums) - 1; i &gt; 0; i-- {\n        // 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n        (*nums)[0], (*nums)[i] = (*nums)[i], (*nums)[0]\n        // 根ノードを起点に、上から下へヒープ化\n        siftDown(nums, i, 0)\n    }\n}\n</code></pre> heap_sort.swift<pre><code>/* ヒープの長さは n。ノード i から下方向にヒープ化 */\nfunc siftDown(nums: inout [Int], n: Int, i: Int) {\n    var i = i\n    while true {\n        // ノード i, l, r のうち値が最大のノードを ma とする\n        let l = 2 * i + 1\n        let r = 2 * i + 2\n        var ma = i\n        if l &lt; n, nums[l] &gt; nums[ma] {\n            ma = l\n        }\n        if r &lt; n, nums[r] &gt; nums[ma] {\n            ma = r\n        }\n        // ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n        if ma == i {\n            break\n        }\n        // 2 つのノードを交換\n        nums.swapAt(i, ma)\n        // ループで上から下へヒープ化\n        i = ma\n    }\n}\n\n/* ヒープソート */\nfunc heapSort(nums: inout [Int]) {\n    // ヒープ構築：葉ノード以外のすべてのノードをヒープ化する\n    for i in stride(from: nums.count / 2 - 1, through: 0, by: -1) {\n        siftDown(nums: &amp;nums, n: nums.count, i: i)\n    }\n    // ヒープから最大要素を取り出し、n-1 回繰り返す\n    for i in nums.indices.dropFirst().reversed() {\n        // 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n        nums.swapAt(0, i)\n        // 根ノードを起点に、上から下へヒープ化\n        siftDown(nums: &amp;nums, n: i, i: 0)\n    }\n}\n</code></pre> heap_sort.js<pre><code>/* ヒープの長さは n。ノード i から下方向にヒープ化 */\nfunction siftDown(nums, n, i) {\n    while (true) {\n        // ノード i, l, r のうち値が最大のノードを ma とする\n        let l = 2 * i + 1;\n        let r = 2 * i + 2;\n        let ma = i;\n        if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma]) {\n            ma = l;\n        }\n        if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma]) {\n            ma = r;\n        }\n        // ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n        if (ma === i) {\n            break;\n        }\n        // 2 つのノードを交換\n        [nums[i], nums[ma]] = [nums[ma], nums[i]];\n        // ループで上から下へヒープ化\n        i = ma;\n    }\n}\n\n/* ヒープソート */\nfunction heapSort(nums) {\n    // ヒープ構築：葉ノード以外のすべてのノードをヒープ化する\n    for (let i = Math.floor(nums.length / 2) - 1; i &gt;= 0; i--) {\n        siftDown(nums, nums.length, i);\n    }\n    // ヒープから最大要素を取り出し、n-1 回繰り返す\n    for (let i = nums.length - 1; i &gt; 0; i--) {\n        // 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n        [nums[0], nums[i]] = [nums[i], nums[0]];\n        // 根ノードを起点に、上から下へヒープ化\n        siftDown(nums, i, 0);\n    }\n}\n</code></pre> heap_sort.ts<pre><code>/* ヒープの長さは n。ノード i から下方向にヒープ化 */\nfunction siftDown(nums: number[], n: number, i: number): void {\n    while (true) {\n        // ノード i, l, r のうち値が最大のノードを ma とする\n        let l = 2 * i + 1;\n        let r = 2 * i + 2;\n        let ma = i;\n        if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma]) {\n            ma = l;\n        }\n        if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma]) {\n            ma = r;\n        }\n        // ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n        if (ma === i) {\n            break;\n        }\n        // 2 つのノードを交換\n        [nums[i], nums[ma]] = [nums[ma], nums[i]];\n        // ループで上から下へヒープ化\n        i = ma;\n    }\n}\n\n/* ヒープソート */\nfunction heapSort(nums: number[]): void {\n    // ヒープ構築：葉ノード以外のすべてのノードをヒープ化する\n    for (let i = Math.floor(nums.length / 2) - 1; i &gt;= 0; i--) {\n        siftDown(nums, nums.length, i);\n    }\n    // ヒープから最大要素を取り出し、n-1 回繰り返す\n    for (let i = nums.length - 1; i &gt; 0; i--) {\n        // 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n        [nums[0], nums[i]] = [nums[i], nums[0]];\n        // 根ノードを起点に、上から下へヒープ化\n        siftDown(nums, i, 0);\n    }\n}\n</code></pre> heap_sort.dart<pre><code>/* ヒープの長さは n。ノード i から下方向にヒープ化 */\nvoid siftDown(List&lt;int&gt; nums, int n, int i) {\n  while (true) {\n    // ノード i, l, r のうち値が最大のノードを ma とする\n    int l = 2 * i + 1;\n    int r = 2 * i + 2;\n    int ma = i;\n    if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma]) ma = l;\n    if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma]) ma = r;\n    // ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n    if (ma == i) break;\n    // 2 つのノードを交換\n    int temp = nums[i];\n    nums[i] = nums[ma];\n    nums[ma] = temp;\n    // ループで上から下へヒープ化\n    i = ma;\n  }\n}\n\n/* ヒープソート */\nvoid heapSort(List&lt;int&gt; nums) {\n  // ヒープ構築：葉ノード以外のすべてのノードをヒープ化する\n  for (int i = nums.length ~/ 2 - 1; i &gt;= 0; i--) {\n    siftDown(nums, nums.length, i);\n  }\n  // ヒープから最大要素を取り出し、n-1 回繰り返す\n  for (int i = nums.length - 1; i &gt; 0; i--) {\n    // 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n    int tmp = nums[0];\n    nums[0] = nums[i];\n    nums[i] = tmp;\n    // 根ノードを起点に、上から下へヒープ化\n    siftDown(nums, i, 0);\n  }\n}\n</code></pre> heap_sort.rs<pre><code>/* ヒープの長さは n。ノード i から下方向にヒープ化 */\nfn sift_down(nums: &amp;mut [i32], n: usize, mut i: usize) {\n    loop {\n        // ノード i, l, r のうち値が最大のノードを ma とする\n        let l = 2 * i + 1;\n        let r = 2 * i + 2;\n        let mut ma = i;\n        if l &lt; n &amp;&amp; nums[l] &gt; nums[ma] {\n            ma = l;\n        }\n        if r &lt; n &amp;&amp; nums[r] &gt; nums[ma] {\n            ma = r;\n        }\n        // ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n        if ma == i {\n            break;\n        }\n        // 2 つのノードを交換\n        nums.swap(i, ma);\n        // ループで上から下へヒープ化\n        i = ma;\n    }\n}\n\n/* ヒープソート */\nfn heap_sort(nums: &amp;mut [i32]) {\n    // ヒープ構築：葉ノード以外のすべてのノードをヒープ化する\n    for i in (0..nums.len() / 2).rev() {\n        sift_down(nums, nums.len(), i);\n    }\n    // ヒープから最大要素を取り出し、n-1 回繰り返す\n    for i in (1..nums.len()).rev() {\n        // 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n        nums.swap(0, i);\n        // 根ノードを起点に、上から下へヒープ化\n        sift_down(nums, i, 0);\n    }\n}\n</code></pre> heap_sort.c<pre><code>/* ヒープの長さは n。ノード i から下方向にヒープ化 */\nvoid siftDown(int nums[], int n, int i) {\n    while (1) {\n        // ノード i, l, r のうち値が最大のノードを ma とする\n        int l = 2 * i + 1;\n        int r = 2 * i + 2;\n        int ma = i;\n        if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma])\n            ma = l;\n        if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma])\n            ma = r;\n        // ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n        if (ma == i) {\n            break;\n        }\n        // 2 つのノードを交換\n        int temp = nums[i];\n        nums[i] = nums[ma];\n        nums[ma] = temp;\n        // ループで上から下へヒープ化\n        i = ma;\n    }\n}\n\n/* ヒープソート */\nvoid heapSort(int nums[], int n) {\n    // ヒープ構築：葉ノード以外のすべてのノードをヒープ化する\n    for (int i = n / 2 - 1; i &gt;= 0; --i) {\n        siftDown(nums, n, i);\n    }\n    // ヒープから最大要素を取り出し、n-1 回繰り返す\n    for (int i = n - 1; i &gt; 0; --i) {\n        // 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n        int tmp = nums[0];\n        nums[0] = nums[i];\n        nums[i] = tmp;\n        // 根ノードを起点に、上から下へヒープ化\n        siftDown(nums, i, 0);\n    }\n}\n</code></pre> heap_sort.kt<pre><code>/* ヒープの長さは n。ノード i から下方向にヒープ化 */\nfun siftDown(nums: IntArray, n: Int, li: Int) {\n    var i = li\n    while (true) {\n        // ノード i, l, r のうち値が最大のノードを ma とする\n        val l = 2 * i + 1\n        val r = 2 * i + 2\n        var ma = i\n        if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma]) \n            ma = l\n        if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma]) \n            ma = r\n        // ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n        if (ma == i) \n            break\n        // 2 つのノードを交換\n        val temp = nums[i]\n        nums[i] = nums[ma]\n        nums[ma] = temp\n        // ループで上から下へヒープ化\n        i = ma\n    }\n}\n\n/* ヒープソート */\nfun heapSort(nums: IntArray) {\n    // ヒープ構築：葉ノード以外のすべてのノードをヒープ化する\n    for (i in nums.size / 2 - 1 downTo 0) {\n        siftDown(nums, nums.size, i)\n    }\n    // ヒープから最大要素を取り出し、n-1 回繰り返す\n    for (i in nums.size - 1 downTo 1) {\n        // 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n        val temp = nums[0]\n        nums[0] = nums[i]\n        nums[i] = temp\n        // 根ノードを起点に、上から下へヒープ化\n        siftDown(nums, i, 0)\n    }\n}\n</code></pre> heap_sort.rb<pre><code>### ヒープ長 n で、ノード i から上から下へヒープ化 ###\ndef sift_down(nums, n, i)\n  while true\n    # ノード i, l, r のうち値が最大のノードを ma とする\n    l = 2 * i + 1\n    r = 2 * i + 2\n    ma = i\n    ma = l if l &lt; n &amp;&amp; nums[l] &gt; nums[ma]\n    ma = r if r &lt; n &amp;&amp; nums[r] &gt; nums[ma]\n    # ノード i が最大、またはインデックス l, r が範囲外なら、ヒープ化は不要なので抜ける\n    break if ma == i\n    # 2 つのノードを交換\n    nums[i], nums[ma] = nums[ma], nums[i]\n    # ループで上から下へヒープ化\n    i = ma\n  end\nend\n\n### ヒープソート ###\ndef heap_sort(nums)\n  # ヒープ構築：葉ノード以外のすべてのノードをヒープ化する\n  (nums.length / 2 - 1).downto(0) do |i|\n    sift_down(nums, nums.length, i)\n  end\n  # ヒープから最大要素を取り出し、n-1 回繰り返す\n  (nums.length - 1).downto(1) do |i|\n    # 根ノードと最も右の葉ノードを交換（先頭要素と末尾要素を交換）\n    nums[0], nums[i] = nums[i], nums[0]\n    # 根ノードを起点に、上から下へヒープ化\n    sift_down(nums, i, 0)\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 11 章 &nbsp; ソート","11.7 &nbsp; ヒープソート"],"tags":[]},{"location":"chapter_sorting/heap_sort/#1172","level":2,"title":"11.7.2   アルゴリズムの特性","text":"<ul> <li>時間計算量は \\(O(n \\log n)\\)、非適応ソート：ヒープ構築操作には \\(O(n)\\) の時間がかかります。ヒープから最大要素を取り出す時間計算量は \\(O(\\log n)\\) であり、これを合計 \\(n - 1\\) 回繰り返します。</li> <li>空間計算量は \\(O(1)\\)、インプレースソート：いくつかのポインタ変数が使う空間は \\(O(1)\\) です。要素の交換とヒープ化操作はいずれも元の配列上で行われます。</li> <li>非安定ソート：ヒープ頂点の要素とヒープ末尾の要素を交換する際、等しい要素どうしの相対位置が変化する可能性があります。</li> </ul>","path":["第 11 章 &nbsp; ソート","11.7 &nbsp; ヒープソート"],"tags":[]},{"location":"chapter_sorting/insertion_sort/","level":1,"title":"11.4   挿入ソート","text":"<p>挿入ソート（insertion sort）は単純なソートアルゴリズムであり、その動作原理は手作業でトランプの山を整える過程と非常によく似ています。</p> <p>具体的には、未ソート区間から基準要素を 1 つ選び、その要素を左側の整列済み区間の要素と 1 つずつ比較し、正しい位置に挿入します。</p> <p>以下の図は、配列に要素を挿入する操作の流れを示しています。基準要素を <code>base</code> とすると、目的のインデックスから <code>base</code> までのすべての要素を 1 つずつ右に移動し、その後 <code>base</code> を目的のインデックスに代入する必要があります。</p> <p></p> <p> 図 11-6   1 回の挿入操作 </p>","path":["第 11 章 &nbsp; ソート","11.4 &nbsp; 挿入ソート"],"tags":[]},{"location":"chapter_sorting/insertion_sort/#1141","level":2,"title":"11.4.1   アルゴリズムの流れ","text":"<p>挿入ソート全体の流れを以下の図に示します。</p> <ol> <li>初期状態では、配列の 1 番目の要素はすでに整列済みです。</li> <li>配列の 2 番目の要素を <code>base</code> として選び、正しい位置に挿入すると、**配列の先頭 2 要素が整列済み**になります。</li> <li>3 番目の要素を <code>base</code> として選び、正しい位置に挿入すると、**配列の先頭 3 要素が整列済み**になります。</li> <li>このように繰り返し、最後のラウンドで最後の要素を <code>base</code> として選んで正しい位置に挿入すると、**すべての要素が整列済み**になります。</li> </ol> <p></p> <p> 図 11-7   挿入ソートの流れ </p> <p>コード例は以下のとおりです。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby insertion_sort.py<pre><code>def insertion_sort(nums: list[int]):\n    \"\"\"挿入ソート\"\"\"\n    # 外側ループ：整列済み区間は [0, i-1]\n    for i in range(1, len(nums)):\n        base = nums[i]\n        j = i - 1\n        # 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する\n        while j &gt;= 0 and nums[j] &gt; base:\n            nums[j + 1] = nums[j]  # nums[j] を 1 つ右へ移動する\n            j -= 1\n        nums[j + 1] = base  # base を正しい位置に配置する\n</code></pre> insertion_sort.cpp<pre><code>/* 挿入ソート */\nvoid insertionSort(vector&lt;int&gt; &amp;nums) {\n    // 外側ループ：整列済み区間は [0, i-1]\n    for (int i = 1; i &lt; nums.size(); i++) {\n        int base = nums[i], j = i - 1;\n        // 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する\n        while (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n            nums[j + 1] = nums[j]; // nums[j] を 1 つ右へ移動する\n            j--;\n        }\n        nums[j + 1] = base; // base を正しい位置に配置する\n    }\n}\n</code></pre> insertion_sort.java<pre><code>/* 挿入ソート */\nvoid insertionSort(int[] nums) {\n    // 外側ループ：整列済み区間は [0, i-1]\n    for (int i = 1; i &lt; nums.length; i++) {\n        int base = nums[i], j = i - 1;\n        // 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する\n        while (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n            nums[j + 1] = nums[j]; // nums[j] を 1 つ右へ移動する\n            j--;\n        }\n        nums[j + 1] = base;        // base を正しい位置に配置する\n    }\n}\n</code></pre> insertion_sort.cs<pre><code>/* 挿入ソート */\nvoid InsertionSort(int[] nums) {\n    // 外側ループ：整列済み区間は [0, i-1]\n    for (int i = 1; i &lt; nums.Length; i++) {\n        int bas = nums[i], j = i - 1;\n        // 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する\n        while (j &gt;= 0 &amp;&amp; nums[j] &gt; bas) {\n            nums[j + 1] = nums[j]; // nums[j] を 1 つ右へ移動する\n            j--;\n        }\n        nums[j + 1] = bas;         // base を正しい位置に配置する\n    }\n}\n</code></pre> insertion_sort.go<pre><code>/* 挿入ソート */\nfunc insertionSort(nums []int) {\n    // 外側ループ：整列済み区間は [0, i-1]\n    for i := 1; i &lt; len(nums); i++ {\n        base := nums[i]\n        j := i - 1\n        // 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する\n        for j &gt;= 0 &amp;&amp; nums[j] &gt; base {\n            nums[j+1] = nums[j] // nums[j] を 1 つ右へ移動する\n            j--\n        }\n        nums[j+1] = base // base を正しい位置に配置する\n    }\n}\n</code></pre> insertion_sort.swift<pre><code>/* 挿入ソート */\nfunc insertionSort(nums: inout [Int]) {\n    // 外側ループ：整列済み区間は [0, i-1]\n    for i in nums.indices.dropFirst() {\n        let base = nums[i]\n        var j = i - 1\n        // 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する\n        while j &gt;= 0, nums[j] &gt; base {\n            nums[j + 1] = nums[j] // nums[j] を 1 つ右へ移動する\n            j -= 1\n        }\n        nums[j + 1] = base // base を正しい位置に配置する\n    }\n}\n</code></pre> insertion_sort.js<pre><code>/* 挿入ソート */\nfunction insertionSort(nums) {\n    // 外側ループ：整列済み区間は [0, i-1]\n    for (let i = 1; i &lt; nums.length; i++) {\n        let base = nums[i],\n            j = i - 1;\n        // 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する\n        while (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n            nums[j + 1] = nums[j]; // nums[j] を 1 つ右へ移動する\n            j--;\n        }\n        nums[j + 1] = base; // base を正しい位置に配置する\n    }\n}\n</code></pre> insertion_sort.ts<pre><code>/* 挿入ソート */\nfunction insertionSort(nums: number[]): void {\n    // 外側ループ：整列済み区間は [0, i-1]\n    for (let i = 1; i &lt; nums.length; i++) {\n        const base = nums[i];\n        let j = i - 1;\n        // 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する\n        while (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n            nums[j + 1] = nums[j]; // nums[j] を 1 つ右へ移動する\n            j--;\n        }\n        nums[j + 1] = base; // base を正しい位置に配置する\n    }\n}\n</code></pre> insertion_sort.dart<pre><code>/* 挿入ソート */\nvoid insertionSort(List&lt;int&gt; nums) {\n  // 外側ループ：整列済み区間は [0, i-1]\n  for (int i = 1; i &lt; nums.length; i++) {\n    int base = nums[i], j = i - 1;\n    // 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する\n    while (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n      nums[j + 1] = nums[j]; // nums[j] を 1 つ右へ移動する\n      j--;\n    }\n    nums[j + 1] = base; // base を正しい位置に配置する\n  }\n}\n</code></pre> insertion_sort.rs<pre><code>/* 挿入ソート */\nfn insertion_sort(nums: &amp;mut [i32]) {\n    // 外側ループ：整列済み区間は [0, i-1]\n    for i in 1..nums.len() {\n        let (base, mut j) = (nums[i], (i - 1) as i32);\n        // 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する\n        while j &gt;= 0 &amp;&amp; nums[j as usize] &gt; base {\n            nums[(j + 1) as usize] = nums[j as usize]; // nums[j] を 1 つ右へ移動する\n            j -= 1;\n        }\n        nums[(j + 1) as usize] = base; // base を正しい位置に配置する\n    }\n}\n</code></pre> insertion_sort.c<pre><code>/* 挿入ソート */\nvoid insertionSort(int nums[], int size) {\n    // 外側ループ：整列済み区間は [0, i-1]\n    for (int i = 1; i &lt; size; i++) {\n        int base = nums[i], j = i - 1;\n        // 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する\n        while (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n            // nums[j] を 1 つ右へ移動する\n            nums[j + 1] = nums[j];\n            j--;\n        }\n        // base を正しい位置に配置する\n        nums[j + 1] = base;\n    }\n}\n</code></pre> insertion_sort.kt<pre><code>/* 挿入ソート */\nfun insertionSort(nums: IntArray) {\n    // 外側ループ: ソート済み要素は 1, 2, ..., n\n    for (i in nums.indices) {\n        val base = nums[i]\n        var j = i - 1\n        // 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する\n        while (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n            nums[j + 1] = nums[j] // nums[j] を 1 つ右へ移動する\n            j--\n        }\n        nums[j + 1] = base        // base を正しい位置に配置する\n    }\n}\n</code></pre> insertion_sort.rb<pre><code>### 挿入ソート ###\ndef insertion_sort(nums)\n  n = nums.length\n  # 外側ループ：整列済み区間は [0, i-1]\n  for i in 1...n\n    base = nums[i]\n    j = i - 1\n    # 内側ループ: base をソート済み区間 [0, i-1] の正しい位置に挿入する\n    while j &gt;= 0 &amp;&amp; nums[j] &gt; base\n      nums[j + 1] = nums[j] # nums[j] を 1 つ右へ移動する\n      j -= 1\n    end\n    nums[j + 1] = base # base を正しい位置に配置する\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 11 章 &nbsp; ソート","11.4 &nbsp; 挿入ソート"],"tags":[]},{"location":"chapter_sorting/insertion_sort/#1142","level":2,"title":"11.4.2   アルゴリズムの特徴","text":"<ul> <li>計算量は \\(O(n^2)\\)、適応的ソート：最悪の場合、各挿入操作ではそれぞれ \\(n - 1\\)、\\(n-2\\)、\\(\\dots\\)、\\(2\\)、\\(1\\) 回のループが必要であり、合計は \\((n - 1) n / 2\\) となるため、時間計算量は \\(O(n^2)\\) です。データが整列済みであれば、挿入操作は早期に終了します。入力配列が完全に整列済みである場合、挿入ソートは最良の時間計算量 \\(O(n)\\) に達します。</li> <li>空間計算量は \\(O(1)\\)、インプレースソート：ポインタ \\(i\\) と \\(j\\) は定数サイズの追加領域しか使用しません。</li> <li>安定ソート：挿入操作の過程では、要素を等しい要素の右側に挿入するため、それらの順序は変化しません。</li> </ul>","path":["第 11 章 &nbsp; ソート","11.4 &nbsp; 挿入ソート"],"tags":[]},{"location":"chapter_sorting/insertion_sort/#1143","level":2,"title":"11.4.3   挿入ソートの利点","text":"<p>挿入ソートの時間計算量は \\(O(n^2)\\) であり、これから学ぶクイックソートの時間計算量は \\(O(n \\log n)\\) です。挿入ソートの時間計算量のほうが大きいにもかかわらず、**データ量が小さい場合には、挿入ソートのほうが通常は高速**です。</p> <p>この結論は、線形探索と二分探索の適用条件に関する結論と似ています。クイックソートのような \\(O(n \\log n)\\) のアルゴリズムは分割統治法に基づくソートアルゴリズムであり、一般により多くの基本演算を含みます。一方、データ量が小さい場合は、\\(n^2\\) と \\(n \\log n\\) の値は比較的近く、計算量が支配的ではなくなり、各ラウンドにおける基本演算の回数が決定的な役割を果たします。</p> <p>実際、多くのプログラミング言語（たとえば Java）の組み込みソート関数では挿入ソートが採用されており、その大まかな考え方は次のとおりです。長い配列にはクイックソートなどの分割統治法に基づくソートアルゴリズムを使い、短い配列には直接挿入ソートを使います。</p> <p>バブルソート、選択ソート、挿入ソートはいずれも時間計算量が \\(O(n^2)\\) ですが、実際には、挿入ソートはバブルソートや選択ソートよりもはるかに高い頻度で使われます。主な理由は次のとおりです。</p> <ul> <li>バブルソートは要素の交換によって実装され、1 つの一時変数を必要とするため、合計で 3 回の基本演算が関わります。これに対して、挿入ソートは要素の代入に基づいており、必要な基本演算は 1 回だけです。したがって、バブルソートの計算コストは通常、挿入ソートより高くなります。</li> <li>選択ソートの時間計算量はどのような場合でも \\(O(n^2)\\) です。**部分的に整列されたデータが与えられた場合、挿入ソートは通常、選択ソートより効率的**です。</li> <li>選択ソートは安定ではないため、多段ソートには適用できません。</li> </ul>","path":["第 11 章 &nbsp; ソート","11.4 &nbsp; 挿入ソート"],"tags":[]},{"location":"chapter_sorting/merge_sort/","level":1,"title":"11.6   マージソート","text":"<p>マージソート（merge sort）は分割統治戦略に基づくソートアルゴリズムであり、以下の図に示す「分割」と「マージ」の段階から構成されます。</p> <ol> <li>分割段階：再帰によって配列を中点で繰り返し分割し、長い配列のソート問題を短い配列のソート問題へ変換します。</li> <li>マージ段階：部分配列の長さが 1 になったら分割を終了し、マージを開始して、左右 2 つの短いソート済み配列をより長いソート済み配列へと繰り返しマージしていきます。</li> </ol> <p></p> <p> 図 11-10   マージソートの分割とマージの段階 </p>","path":["第 11 章 &nbsp; ソート","11.6 &nbsp; マージソート"],"tags":[]},{"location":"chapter_sorting/merge_sort/#1161","level":2,"title":"11.6.1   アルゴリズムの流れ","text":"<p>以下の図に示すように、「分割段階」では配列を上から下へ再帰的に中点で 2 つの部分配列へ分割します。</p> <ol> <li>配列の中点 <code>mid</code> を計算し、左部分配列（区間 <code>[left, mid]</code> ）と右部分配列（区間 <code>[mid + 1, right]</code> ）を再帰的に分割します。</li> <li>手順 <code>1.</code> を再帰的に実行し、部分配列区間の長さが 1 になった時点で終了します。</li> </ol> <p>「マージ段階」では左部分配列と右部分配列を下から上へとマージし、1 つのソート済み配列にします。長さ 1 の部分配列からマージを始めるため、この段階の各部分配列はすでに整列されています。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 11-11   マージソートの手順 </p> <p>観察すると、マージソートの再帰順序は二分木の後順走査と一致していることがわかります。</p> <ul> <li>後順走査：まず左部分木を再帰し、次に右部分木を再帰し、最後に根ノードを処理します。</li> <li>マージソート：まず左部分配列を再帰し、次に右部分配列を再帰し、最後にマージを処理します。</li> </ul> <p>マージソートの実装を以下のコードに示します。注意として、<code>nums</code> のマージ対象区間は <code>[left, right]</code> であり、<code>tmp</code> の対応区間は <code>[0, right - left]</code> です。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby merge_sort.py<pre><code>def merge(nums: list[int], left: int, mid: int, right: int):\n    \"\"\"左部分配列と右部分配列をマージ\"\"\"\n    # 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]\n    # マージ結果を格納する一時配列 tmp を作成\n    tmp = [0] * (right - left + 1)\n    # 左右の部分配列の開始インデックスを初期化する\n    i, j, k = left, mid + 1, 0\n    # 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする\n    while i &lt;= mid and j &lt;= right:\n        if nums[i] &lt;= nums[j]:\n            tmp[k] = nums[i]\n            i += 1\n        else:\n            tmp[k] = nums[j]\n            j += 1\n        k += 1\n    # 左右の部分配列の残り要素を一時配列にコピーする\n    while i &lt;= mid:\n        tmp[k] = nums[i]\n        i += 1\n        k += 1\n    while j &lt;= right:\n        tmp[k] = nums[j]\n        j += 1\n        k += 1\n    # 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする\n    for k in range(0, len(tmp)):\n        nums[left + k] = tmp[k]\n\ndef merge_sort(nums: list[int], left: int, right: int):\n    \"\"\"マージソート\"\"\"\n    # 終了条件\n    if left &gt;= right:\n        return  # 部分配列の長さが 1 になったら再帰を終了\n    # 分割フェーズ\n    mid = (left + right) // 2 # 中点を計算\n    merge_sort(nums, left, mid)  # 左部分配列を再帰処理\n    merge_sort(nums, mid + 1, right)  # 右部分配列を再帰処理\n    # マージフェーズ\n    merge(nums, left, mid, right)\n</code></pre> merge_sort.cpp<pre><code>/* 左部分配列と右部分配列をマージ */\nvoid merge(vector&lt;int&gt; &amp;nums, int left, int mid, int right) {\n    // 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]\n    // マージ結果を格納する一時配列 tmp を作成\n    vector&lt;int&gt; tmp(right - left + 1);\n    // 左右の部分配列の開始インデックスを初期化する\n    int i = left, j = mid + 1, k = 0;\n    // 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする\n    while (i &lt;= mid &amp;&amp; j &lt;= right) {\n        if (nums[i] &lt;= nums[j])\n            tmp[k++] = nums[i++];\n        else\n            tmp[k++] = nums[j++];\n    }\n    // 左右の部分配列の残り要素を一時配列にコピーする\n    while (i &lt;= mid) {\n        tmp[k++] = nums[i++];\n    }\n    while (j &lt;= right) {\n        tmp[k++] = nums[j++];\n    }\n    // 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする\n    for (k = 0; k &lt; tmp.size(); k++) {\n        nums[left + k] = tmp[k];\n    }\n}\n\n/* マージソート */\nvoid mergeSort(vector&lt;int&gt; &amp;nums, int left, int right) {\n    // 終了条件\n    if (left &gt;= right)\n        return; // 部分配列の長さが 1 になったら再帰を終了\n    // 分割フェーズ\n    int mid = left + (right - left) / 2;    // 中点を計算\n    mergeSort(nums, left, mid);      // 左部分配列を再帰処理\n    mergeSort(nums, mid + 1, right); // 右部分配列を再帰処理\n    // マージフェーズ\n    merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.java<pre><code>/* 左部分配列と右部分配列をマージ */\nvoid merge(int[] nums, int left, int mid, int right) {\n    // 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]\n    // マージ結果を格納する一時配列 tmp を作成\n    int[] tmp = new int[right - left + 1];\n    // 左右の部分配列の開始インデックスを初期化する\n    int i = left, j = mid + 1, k = 0;\n    // 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする\n    while (i &lt;= mid &amp;&amp; j &lt;= right) {\n        if (nums[i] &lt;= nums[j])\n            tmp[k++] = nums[i++];\n        else\n            tmp[k++] = nums[j++];\n    }\n    // 左右の部分配列の残り要素を一時配列にコピーする\n    while (i &lt;= mid) {\n        tmp[k++] = nums[i++];\n    }\n    while (j &lt;= right) {\n        tmp[k++] = nums[j++];\n    }\n    // 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする\n    for (k = 0; k &lt; tmp.length; k++) {\n        nums[left + k] = tmp[k];\n    }\n}\n\n/* マージソート */\nvoid mergeSort(int[] nums, int left, int right) {\n    // 終了条件\n    if (left &gt;= right)\n        return; // 部分配列の長さが 1 になったら再帰を終了\n    // 分割フェーズ\n    int mid = left + (right - left) / 2; // 中点を計算\n    mergeSort(nums, left, mid); // 左部分配列を再帰処理\n    mergeSort(nums, mid + 1, right); // 右部分配列を再帰処理\n    // マージフェーズ\n    merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.cs<pre><code>/* 左部分配列と右部分配列をマージ */\nvoid Merge(int[] nums, int left, int mid, int right) {\n    // 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]\n    // マージ結果を格納する一時配列 tmp を作成\n    int[] tmp = new int[right - left + 1];\n    // 左右の部分配列の開始インデックスを初期化する\n    int i = left, j = mid + 1, k = 0;\n    // 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする\n    while (i &lt;= mid &amp;&amp; j &lt;= right) {\n        if (nums[i] &lt;= nums[j])\n            tmp[k++] = nums[i++];\n        else\n            tmp[k++] = nums[j++];\n    }\n    // 左右の部分配列の残り要素を一時配列にコピーする\n    while (i &lt;= mid) {\n        tmp[k++] = nums[i++];\n    }\n    while (j &lt;= right) {\n        tmp[k++] = nums[j++];\n    }\n    // 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする\n    for (k = 0; k &lt; tmp.Length; ++k) {\n        nums[left + k] = tmp[k];\n    }\n}\n\n/* マージソート */\nvoid MergeSort(int[] nums, int left, int right) {\n    // 終了条件\n    if (left &gt;= right) return;       // 部分配列の長さが 1 になったら再帰を終了\n    // 分割フェーズ\n    int mid = left + (right - left) / 2;    // 中点を計算\n    MergeSort(nums, left, mid);      // 左部分配列を再帰処理\n    MergeSort(nums, mid + 1, right); // 右部分配列を再帰処理\n    // マージフェーズ\n    Merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.go<pre><code>/* 左部分配列と右部分配列をマージ */\nfunc merge(nums []int, left, mid, right int) {\n    // 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]\n    // マージ結果を格納する一時配列 tmp を作成\n    tmp := make([]int, right-left+1)\n    // 左右の部分配列の開始インデックスを初期化する\n    i, j, k := left, mid+1, 0\n    // 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする\n    for i &lt;= mid &amp;&amp; j &lt;= right {\n        if nums[i] &lt;= nums[j] {\n            tmp[k] = nums[i]\n            i++\n        } else {\n            tmp[k] = nums[j]\n            j++\n        }\n        k++\n    }\n    // 左右の部分配列の残り要素を一時配列にコピーする\n    for i &lt;= mid {\n        tmp[k] = nums[i]\n        i++\n        k++\n    }\n    for j &lt;= right {\n        tmp[k] = nums[j]\n        j++\n        k++\n    }\n    // 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする\n    for k := 0; k &lt; len(tmp); k++ {\n        nums[left+k] = tmp[k]\n    }\n}\n\n/* マージソート */\nfunc mergeSort(nums []int, left, right int) {\n    // 終了条件\n    if left &gt;= right {\n        return\n    }\n    // 分割フェーズ\n    mid := left + (right - left) / 2\n    mergeSort(nums, left, mid)\n    mergeSort(nums, mid+1, right)\n    // マージフェーズ\n    merge(nums, left, mid, right)\n}\n</code></pre> merge_sort.swift<pre><code>/* 左部分配列と右部分配列をマージ */\nfunc merge(nums: inout [Int], left: Int, mid: Int, right: Int) {\n    // 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]\n    // マージ結果を格納する一時配列 tmp を作成\n    var tmp = Array(repeating: 0, count: right - left + 1)\n    // 左右の部分配列の開始インデックスを初期化する\n    var i = left, j = mid + 1, k = 0\n    // 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする\n    while i &lt;= mid, j &lt;= right {\n        if nums[i] &lt;= nums[j] {\n            tmp[k] = nums[i]\n            i += 1\n        } else {\n            tmp[k] = nums[j]\n            j += 1\n        }\n        k += 1\n    }\n    // 左右の部分配列の残り要素を一時配列にコピーする\n    while i &lt;= mid {\n        tmp[k] = nums[i]\n        i += 1\n        k += 1\n    }\n    while j &lt;= right {\n        tmp[k] = nums[j]\n        j += 1\n        k += 1\n    }\n    // 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする\n    for k in tmp.indices {\n        nums[left + k] = tmp[k]\n    }\n}\n\n/* マージソート */\nfunc mergeSort(nums: inout [Int], left: Int, right: Int) {\n    // 終了条件\n    if left &gt;= right { // 部分配列の長さが 1 になったら再帰を終了\n        return\n    }\n    // 分割フェーズ\n    let mid = left + (right - left) / 2 // 中点を計算\n    mergeSort(nums: &amp;nums, left: left, right: mid) // 左部分配列を再帰処理\n    mergeSort(nums: &amp;nums, left: mid + 1, right: right) // 右部分配列を再帰処理\n    // マージフェーズ\n    merge(nums: &amp;nums, left: left, mid: mid, right: right)\n}\n</code></pre> merge_sort.js<pre><code>/* 左部分配列と右部分配列をマージ */\nfunction merge(nums, left, mid, right) {\n    // 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]\n    // マージ結果を格納する一時配列 tmp を作成\n    const tmp = new Array(right - left + 1);\n    // 左右の部分配列の開始インデックスを初期化する\n    let i = left,\n        j = mid + 1,\n        k = 0;\n    // 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする\n    while (i &lt;= mid &amp;&amp; j &lt;= right) {\n        if (nums[i] &lt;= nums[j]) {\n            tmp[k++] = nums[i++];\n        } else {\n            tmp[k++] = nums[j++];\n        }\n    }\n    // 左右の部分配列の残り要素を一時配列にコピーする\n    while (i &lt;= mid) {\n        tmp[k++] = nums[i++];\n    }\n    while (j &lt;= right) {\n        tmp[k++] = nums[j++];\n    }\n    // 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする\n    for (k = 0; k &lt; tmp.length; k++) {\n        nums[left + k] = tmp[k];\n    }\n}\n\n/* マージソート */\nfunction mergeSort(nums, left, right) {\n    // 終了条件\n    if (left &gt;= right) return; // 部分配列の長さが 1 になったら再帰を終了\n    // 分割フェーズ\n    let mid = Math.floor(left + (right - left) / 2); // 中点を計算\n    mergeSort(nums, left, mid); // 左部分配列を再帰処理\n    mergeSort(nums, mid + 1, right); // 右部分配列を再帰処理\n    // マージフェーズ\n    merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.ts<pre><code>/* 左部分配列と右部分配列をマージ */\nfunction merge(nums: number[], left: number, mid: number, right: number): void {\n    // 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]\n    // マージ結果を格納する一時配列 tmp を作成\n    const tmp = new Array(right - left + 1);\n    // 左右の部分配列の開始インデックスを初期化する\n    let i = left,\n        j = mid + 1,\n        k = 0;\n    // 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする\n    while (i &lt;= mid &amp;&amp; j &lt;= right) {\n        if (nums[i] &lt;= nums[j]) {\n            tmp[k++] = nums[i++];\n        } else {\n            tmp[k++] = nums[j++];\n        }\n    }\n    // 左右の部分配列の残り要素を一時配列にコピーする\n    while (i &lt;= mid) {\n        tmp[k++] = nums[i++];\n    }\n    while (j &lt;= right) {\n        tmp[k++] = nums[j++];\n    }\n    // 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする\n    for (k = 0; k &lt; tmp.length; k++) {\n        nums[left + k] = tmp[k];\n    }\n}\n\n/* マージソート */\nfunction mergeSort(nums: number[], left: number, right: number): void {\n    // 終了条件\n    if (left &gt;= right) return; // 部分配列の長さが 1 になったら再帰を終了\n    // 分割フェーズ\n    let mid = Math.floor(left + (right - left) / 2); // 中点を計算\n    mergeSort(nums, left, mid); // 左部分配列を再帰処理\n    mergeSort(nums, mid + 1, right); // 右部分配列を再帰処理\n    // マージフェーズ\n    merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.dart<pre><code>/* 左部分配列と右部分配列をマージ */\nvoid merge(List&lt;int&gt; nums, int left, int mid, int right) {\n  // 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]\n  // マージ結果を格納する一時配列 tmp を作成\n  List&lt;int&gt; tmp = List.filled(right - left + 1, 0);\n  // 左右の部分配列の開始インデックスを初期化する\n  int i = left, j = mid + 1, k = 0;\n  // 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする\n  while (i &lt;= mid &amp;&amp; j &lt;= right) {\n    if (nums[i] &lt;= nums[j])\n      tmp[k++] = nums[i++];\n    else\n      tmp[k++] = nums[j++];\n  }\n  // 左右の部分配列の残り要素を一時配列にコピーする\n  while (i &lt;= mid) {\n    tmp[k++] = nums[i++];\n  }\n  while (j &lt;= right) {\n    tmp[k++] = nums[j++];\n  }\n  // 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする\n  for (k = 0; k &lt; tmp.length; k++) {\n    nums[left + k] = tmp[k];\n  }\n}\n\n/* マージソート */\nvoid mergeSort(List&lt;int&gt; nums, int left, int right) {\n  // 終了条件\n  if (left &gt;= right) return; // 部分配列の長さが 1 になったら再帰を終了\n  // 分割フェーズ\n  int mid = left + (right - left) ~/ 2; // 中点を計算\n  mergeSort(nums, left, mid); // 左部分配列を再帰処理\n  mergeSort(nums, mid + 1, right); // 右部分配列を再帰処理\n  // マージフェーズ\n  merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.rs<pre><code>/* 左部分配列と右部分配列をマージ */\nfn merge(nums: &amp;mut [i32], left: usize, mid: usize, right: usize) {\n    // 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]\n    // マージ結果を格納する一時配列 tmp を作成\n    let tmp_size = right - left + 1;\n    let mut tmp = vec![0; tmp_size];\n    // 左右の部分配列の開始インデックスを初期化する\n    let (mut i, mut j, mut k) = (left, mid + 1, 0);\n    // 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする\n    while i &lt;= mid &amp;&amp; j &lt;= right {\n        if nums[i] &lt;= nums[j] {\n            tmp[k] = nums[i];\n            i += 1;\n        } else {\n            tmp[k] = nums[j];\n            j += 1;\n        }\n        k += 1;\n    }\n    // 左右の部分配列の残り要素を一時配列にコピーする\n    while i &lt;= mid {\n        tmp[k] = nums[i];\n        k += 1;\n        i += 1;\n    }\n    while j &lt;= right {\n        tmp[k] = nums[j];\n        k += 1;\n        j += 1;\n    }\n    // 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする\n    for k in 0..tmp_size {\n        nums[left + k] = tmp[k];\n    }\n}\n\n/* マージソート */\nfn merge_sort(nums: &amp;mut [i32], left: usize, right: usize) {\n    // 終了条件\n    if left &gt;= right {\n        return; // 部分配列の長さが 1 になったら再帰を終了\n    }\n\n    // 分割フェーズ\n    let mid = left + (right - left) / 2; // 中点を計算\n    merge_sort(nums, left, mid); // 左部分配列を再帰処理\n    merge_sort(nums, mid + 1, right); // 右部分配列を再帰処理\n\n    // マージフェーズ\n    merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.c<pre><code>/* 左部分配列と右部分配列をマージ */\nvoid merge(int *nums, int left, int mid, int right) {\n    // 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]\n    // マージ結果を格納する一時配列 tmp を作成\n    int tmpSize = right - left + 1;\n    int *tmp = (int *)malloc(tmpSize * sizeof(int));\n    // 左右の部分配列の開始インデックスを初期化する\n    int i = left, j = mid + 1, k = 0;\n    // 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする\n    while (i &lt;= mid &amp;&amp; j &lt;= right) {\n        if (nums[i] &lt;= nums[j]) {\n            tmp[k++] = nums[i++];\n        } else {\n            tmp[k++] = nums[j++];\n        }\n    }\n    // 左右の部分配列の残り要素を一時配列にコピーする\n    while (i &lt;= mid) {\n        tmp[k++] = nums[i++];\n    }\n    while (j &lt;= right) {\n        tmp[k++] = nums[j++];\n    }\n    // 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする\n    for (k = 0; k &lt; tmpSize; ++k) {\n        nums[left + k] = tmp[k];\n    }\n    // メモリを解放する\n    free(tmp);\n}\n\n/* マージソート */\nvoid mergeSort(int *nums, int left, int right) {\n    // 終了条件\n    if (left &gt;= right)\n        return; // 部分配列の長さが 1 になったら再帰を終了\n    // 分割フェーズ\n    int mid = left + (right - left) / 2;    // 中点を計算\n    mergeSort(nums, left, mid);      // 左部分配列を再帰処理\n    mergeSort(nums, mid + 1, right); // 右部分配列を再帰処理\n    // マージフェーズ\n    merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.kt<pre><code>/* 左部分配列と右部分配列をマージ */\nfun merge(nums: IntArray, left: Int, mid: Int, right: Int) {\n    // 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]\n    // マージ結果を格納する一時配列 tmp を作成\n    val tmp = IntArray(right - left + 1)\n    // 左右の部分配列の開始インデックスを初期化する\n    var i = left\n    var j = mid + 1\n    var k = 0\n    // 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする\n    while (i &lt;= mid &amp;&amp; j &lt;= right) {\n        if (nums[i] &lt;= nums[j])\n            tmp[k++] = nums[i++]\n        else\n            tmp[k++] = nums[j++]\n    }\n    // 左右の部分配列の残り要素を一時配列にコピーする\n    while (i &lt;= mid) {\n        tmp[k++] = nums[i++]\n    }\n    while (j &lt;= right) {\n        tmp[k++] = nums[j++]\n    }\n    // 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする\n    for (l in tmp.indices) {\n        nums[left + l] = tmp[l]\n    }\n}\n\n/* マージソート */\nfun mergeSort(nums: IntArray, left: Int, right: Int) {\n    // 終了条件\n    if (left &gt;= right) return  // 部分配列の長さが 1 になったら再帰を終了\n    // 分割フェーズ\n    val mid = left + (right - left) / 2 // 中点を計算\n    mergeSort(nums, left, mid) // 左部分配列を再帰処理\n    mergeSort(nums, mid + 1, right) // 右部分配列を再帰処理\n    // マージフェーズ\n    merge(nums, left, mid, right)\n}\n</code></pre> merge_sort.rb<pre><code>### 左部分配列と右部分配列をマージ ###\ndef merge(nums, left, mid, right)\n  # 左部分配列の区間は [left, mid]、右部分配列の区間は [mid+1, right]\n  # マージ結果を格納する一時配列 tmp を作成\n  tmp = Array.new(right - left + 1, 0)\n  # 左右の部分配列の開始インデックスを初期化する\n  i, j, k = left, mid + 1, 0\n  # 左右の部分配列にまだ要素がある間は比較し、小さいほうを一時配列にコピーする\n  while i &lt;= mid &amp;&amp; j &lt;= right\n    if nums[i] &lt;= nums[j]\n      tmp[k] = nums[i]\n      i += 1\n    else\n      tmp[k] = nums[j]\n      j += 1\n    end\n    k += 1\n  end\n  # 左右の部分配列の残り要素を一時配列にコピーする\n  while i &lt;= mid\n    tmp[k] = nums[i]\n    i += 1\n    k += 1\n  end\n  while j &lt;= right\n    tmp[k] = nums[j]\n    j += 1\n    k += 1\n  end\n  # 一時配列 tmp の要素を元の配列 nums の対応区間にコピーする\n  (0...tmp.length).each do |k|\n    nums[left + k] = tmp[k]\n  end\nend\n\n### マージソート ###\ndef merge_sort(nums, left, right)\n  # 終了条件\n  # 部分配列の長さが 1 になったら再帰を終了する\n  return if left &gt;= right\n  # 分割フェーズ\n  mid = left + (right - left) / 2 # 中点を計算\n  merge_sort(nums, left, mid) # 左部分配列を再帰処理\n  merge_sort(nums, mid + 1, right) # 右部分配列を再帰処理\n  # マージフェーズ\n  merge(nums, left, mid, right)\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 11 章 &nbsp; ソート","11.6 &nbsp; マージソート"],"tags":[]},{"location":"chapter_sorting/merge_sort/#1162","level":2,"title":"11.6.2   アルゴリズムの特性","text":"<ul> <li>時間計算量は \\(O(n \\log n)\\)、非適応型ソート：分割によって高さ \\(\\log n\\) の再帰木が生成され、各層でのマージ操作の総数は \\(n\\) であるため、全体の時間計算量は \\(O(n \\log n)\\) です。</li> <li>空間計算量は \\(O(n)\\)、インプレースではないソート：再帰の深さは \\(\\log n\\) であり、サイズ \\(O(\\log n)\\) のスタックフレーム領域を使用します。マージ操作は補助配列を用いて実装する必要があり、サイズ \\(O(n)\\) の追加領域を使用します。</li> <li>安定ソート：マージの過程では、等しい要素の順序は変化しません。</li> </ul>","path":["第 11 章 &nbsp; ソート","11.6 &nbsp; マージソート"],"tags":[]},{"location":"chapter_sorting/merge_sort/#1163","level":2,"title":"11.6.3   連結リストのソート","text":"<p>連結リストに対しては、マージソートは他のソートアルゴリズムと比べて顕著な利点があり、連結リストのソート問題の空間計算量を \\(O(1)\\) まで最適化できます 。</p> <ul> <li>分割段階：連結リストの分割は「再帰」の代わりに「反復」で実装できるため、再帰で使用するスタックフレーム領域を省けます。</li> <li>マージ段階：連結リストでは、ノードの追加や削除は参照（ポインタ）を変更するだけで実現できるため、マージ段階（2 つの短いソート済み連結リストを 1 つの長いソート済み連結リストにマージすること）では追加の連結リストを作成する必要がありません。</li> </ul> <p>具体的な実装の詳細は比較的複雑なので、興味のある読者は関連資料を参照して学習してください。</p>","path":["第 11 章 &nbsp; ソート","11.6 &nbsp; マージソート"],"tags":[]},{"location":"chapter_sorting/quick_sort/","level":1,"title":"11.5   クイックソート","text":"<p>クイックソート（quick sort）は分割統治戦略に基づくソートアルゴリズムであり、実行効率が高く、広く利用されています。</p> <p>クイックソートの中核操作は「パーティション」であり、その目的は、配列内のある要素を「基準数」として選び、基準数より小さいすべての要素を左側へ、大きい要素を右側へ移動することです。具体的には、パーティションの流れを下図に示します。</p> <ol> <li>配列の最左端の要素を基準数として選び、2 つのポインタ <code>i</code> と <code>j</code> を初期化して、それぞれ配列の両端を指すようにします。</li> <li>ループを設定し、各ラウンドで <code>i</code>（<code>j</code>）を使ってそれぞれ基準数より大きい（小さい）最初の要素を探し、その後この 2 つの要素を交換します。</li> <li><code>i</code> と <code>j</code> が出会うまでステップ <code>2.</code> を繰り返し、最後に基準数を 2 つの部分配列の境界へ交換します。</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 11-8   パーティションの手順 </p> <p>パーティションが完了すると、元の配列は左部分配列、基準数、右部分配列の 3 つに分けられ、「左部分配列の任意の要素 \\(\\leq\\) 基準数 \\(\\leq\\) 右部分配列の任意の要素」を満たします。したがって、次はこの 2 つの部分配列だけをソートすれば済みます。</p> <p>クイックソートの分割統治戦略</p> <p>パーティションの本質は、長い配列のソート問題を 2 つの短い配列のソート問題へ簡略化することです。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby quick_sort.py<pre><code>def partition(self, nums: list[int], left: int, right: int) -&gt; int:\n    \"\"\"番兵分割\"\"\"\n    # nums[left] を基準値とする\n    i, j = left, right\n    while i &lt; j:\n        while i &lt; j and nums[j] &gt;= nums[left]:\n            j -= 1  # 右から左へ基準値未満の最初の要素を探す\n        while i &lt; j and nums[i] &lt;= nums[left]:\n            i += 1  # 左から右へ基準値より大きい最初の要素を探す\n        # 要素の交換\n        nums[i], nums[j] = nums[j], nums[i]\n    # 基準値を 2 つの部分配列の境界へ交換する\n    nums[i], nums[left] = nums[left], nums[i]\n    return i  # 基準値のインデックスを返す\n</code></pre> quick_sort.cpp<pre><code>/* 番兵分割 */\nint partition(vector&lt;int&gt; &amp;nums, int left, int right) {\n    // nums[left] を基準値とする\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--;                // 右から左へ基準値未満の最初の要素を探す\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;                // 左から右へ基準値より大きい最初の要素を探す\n        swap(nums[i], nums[j]); // この 2 つの要素を交換\n    }\n    swap(nums[i], nums[left]);  // 基準値を 2 つの部分配列の境界へ交換する\n    return i;                   // 基準値のインデックスを返す\n}\n</code></pre> quick_sort.java<pre><code>/* 要素の交換 */\nvoid swap(int[] nums, int i, int j) {\n    int tmp = nums[i];\n    nums[i] = nums[j];\n    nums[j] = tmp;\n}\n\n/* 番兵分割 */\nint partition(int[] nums, int left, int right) {\n    // nums[left] を基準値とする\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--;          // 右から左へ基準値未満の最初の要素を探す\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;          // 左から右へ基準値より大きい最初の要素を探す\n        swap(nums, i, j); // この 2 つの要素を交換\n    }\n    swap(nums, i, left);  // 基準値を 2 つの部分配列の境界へ交換する\n    return i;             // 基準値のインデックスを返す\n}\n</code></pre> quick_sort.cs<pre><code>/* 要素の交換 */\nvoid Swap(int[] nums, int i, int j) {\n    (nums[j], nums[i]) = (nums[i], nums[j]);\n}\n\n/* 番兵分割 */\nint Partition(int[] nums, int left, int right) {\n    // nums[left] を基準値とする\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--;          // 右から左へ基準値未満の最初の要素を探す\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;          // 左から右へ基準値より大きい最初の要素を探す\n        Swap(nums, i, j); // この 2 つの要素を交換\n    }\n    Swap(nums, i, left);  // 基準値を 2 つの部分配列の境界へ交換する\n    return i;             // 基準値のインデックスを返す\n}\n</code></pre> quick_sort.go<pre><code>/* 番兵分割 */\nfunc (q *quickSort) partition(nums []int, left, right int) int {\n    // nums[left] を基準値とする\n    i, j := left, right\n    for i &lt; j {\n        for i &lt; j &amp;&amp; nums[j] &gt;= nums[left] {\n            j-- // 右から左へ基準値未満の最初の要素を探す\n        }\n        for i &lt; j &amp;&amp; nums[i] &lt;= nums[left] {\n            i++ // 左から右へ基準値より大きい最初の要素を探す\n        }\n        // 要素の交換\n        nums[i], nums[j] = nums[j], nums[i]\n    }\n    // 基準値を 2 つの部分配列の境界へ交換する\n    nums[i], nums[left] = nums[left], nums[i]\n    return i // 基準値のインデックスを返す\n}\n</code></pre> quick_sort.swift<pre><code>/* 番兵分割 */\nfunc partition(nums: inout [Int], left: Int, right: Int) -&gt; Int {\n    // nums[left] を基準値とする\n    var i = left\n    var j = right\n    while i &lt; j {\n        while i &lt; j, nums[j] &gt;= nums[left] {\n            j -= 1 // 右から左へ基準値未満の最初の要素を探す\n        }\n        while i &lt; j, nums[i] &lt;= nums[left] {\n            i += 1 // 左から右へ基準値より大きい最初の要素を探す\n        }\n        nums.swapAt(i, j) // この 2 つの要素を交換\n    }\n    nums.swapAt(i, left) // 基準値を 2 つの部分配列の境界へ交換する\n    return i // 基準値のインデックスを返す\n}\n</code></pre> quick_sort.js<pre><code>/* 要素の交換 */\nswap(nums, i, j) {\n    let tmp = nums[i];\n    nums[i] = nums[j];\n    nums[j] = tmp;\n}\n\n/* 番兵分割 */\npartition(nums, left, right) {\n    // nums[left] を基準値とする\n    let i = left,\n        j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) {\n            j -= 1; // 右から左へ基準値未満の最初の要素を探す\n        }\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) {\n            i += 1; // 左から右へ基準値より大きい最初の要素を探す\n        }\n        // 要素の交換\n        this.swap(nums, i, j); // この 2 つの要素を交換\n    }\n    this.swap(nums, i, left); // 基準値を 2 つの部分配列の境界へ交換する\n    return i; // 基準値のインデックスを返す\n}\n</code></pre> quick_sort.ts<pre><code>/* 要素の交換 */\nswap(nums: number[], i: number, j: number): void {\n    let tmp = nums[i];\n    nums[i] = nums[j];\n    nums[j] = tmp;\n}\n\n/* 番兵分割 */\npartition(nums: number[], left: number, right: number): number {\n    // nums[left] を基準値とする\n    let i = left,\n        j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) {\n            j -= 1; // 右から左へ基準値未満の最初の要素を探す\n        }\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) {\n            i += 1; // 左から右へ基準値より大きい最初の要素を探す\n        }\n        // 要素の交換\n        this.swap(nums, i, j); // この 2 つの要素を交換\n    }\n    this.swap(nums, i, left); // 基準値を 2 つの部分配列の境界へ交換する\n    return i; // 基準値のインデックスを返す\n}\n</code></pre> quick_sort.dart<pre><code>/* 要素の交換 */\nvoid _swap(List&lt;int&gt; nums, int i, int j) {\n  int tmp = nums[i];\n  nums[i] = nums[j];\n  nums[j] = tmp;\n}\n\n/* 番兵分割 */\nint _partition(List&lt;int&gt; nums, int left, int right) {\n  // nums[left] を基準値とする\n  int i = left, j = right;\n  while (i &lt; j) {\n    while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) j--; // 右から左へ基準値未満の最初の要素を探す\n    while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) i++; // 左から右へ基準値より大きい最初の要素を探す\n    _swap(nums, i, j); // この 2 つの要素を交換\n  }\n  _swap(nums, i, left); // 基準値を 2 つの部分配列の境界へ交換する\n  return i; // 基準値のインデックスを返す\n}\n</code></pre> quick_sort.rs<pre><code>/* 番兵分割 */\nfn partition(nums: &amp;mut [i32], left: usize, right: usize) -&gt; usize {\n    // nums[left] を基準値とする\n    let (mut i, mut j) = (left, right);\n    while i &lt; j {\n        while i &lt; j &amp;&amp; nums[j] &gt;= nums[left] {\n            j -= 1; // 右から左へ基準値未満の最初の要素を探す\n        }\n        while i &lt; j &amp;&amp; nums[i] &lt;= nums[left] {\n            i += 1; // 左から右へ基準値より大きい最初の要素を探す\n        }\n        nums.swap(i, j); // この 2 つの要素を交換\n    }\n    nums.swap(i, left); // 基準値を 2 つの部分配列の境界へ交換する\n    i // 基準値のインデックスを返す\n}\n</code></pre> quick_sort.c<pre><code>/* 要素の交換 */\nvoid swap(int nums[], int i, int j) {\n    int tmp = nums[i];\n    nums[i] = nums[j];\n    nums[j] = tmp;\n}\n\n/* 番兵分割 */\nint partition(int nums[], int left, int right) {\n    // nums[left] を基準値とする\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) {\n            j--; // 右から左へ基準値未満の最初の要素を探す\n        }\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) {\n            i++; // 左から右へ基準値より大きい最初の要素を探す\n        }\n        // この 2 つの要素を交換\n        swap(nums, i, j);\n    }\n    // 基準値を 2 つの部分配列の境界へ交換する\n    swap(nums, i, left);\n    // 基準値のインデックスを返す\n    return i;\n}\n</code></pre> quick_sort.kt<pre><code>/* 要素の交換 */\nfun swap(nums: IntArray, i: Int, j: Int) {\n    val temp = nums[i]\n    nums[i] = nums[j]\n    nums[j] = temp\n}\n\n/* 番兵分割 */\nfun partition(nums: IntArray, left: Int, right: Int): Int {\n    // nums[left] を基準値とする\n    var i = left\n    var j = right\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--           // 右から左へ基準値未満の最初の要素を探す\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++           // 左から右へ基準値より大きい最初の要素を探す\n        swap(nums, i, j)  // この 2 つの要素を交換\n    }\n    swap(nums, i, left)   // 基準値を 2 つの部分配列の境界へ交換する\n    return i              // 基準値のインデックスを返す\n}\n</code></pre> quick_sort.rb<pre><code>### 番兵分割 ###\ndef partition(nums, left, right)\n  # nums[left] を基準値とする\n  i, j = left, right\n  while i &lt; j\n    while i &lt; j &amp;&amp; nums[j] &gt;= nums[left]\n      j -= 1 # 右から左へ基準値未満の最初の要素を探す\n    end\n    while i &lt; j &amp;&amp; nums[i] &lt;= nums[left]\n      i += 1 # 左から右へ基準値より大きい最初の要素を探す\n    end\n    # 要素の交換\n    nums[i], nums[j] = nums[j], nums[i]\n  end\n  # 基準値を 2 つの部分配列の境界へ交換する\n  nums[i], nums[left] = nums[left], nums[i]\n  i # 基準値のインデックスを返す\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 11 章 &nbsp; ソート","11.5 &nbsp; クイックソート"],"tags":[]},{"location":"chapter_sorting/quick_sort/#1151","level":2,"title":"11.5.1   アルゴリズムの流れ","text":"<p>クイックソート全体の流れを下図に示します。</p> <ol> <li>まず、元の配列に対して 1 回「パーティション」を実行し、未ソートの左部分配列と右部分配列を得ます。</li> <li>次に、左部分配列と右部分配列に対してそれぞれ再帰的に「パーティション」を実行します。</li> <li>部分配列の長さが 1 になるまで再帰を続け、配列全体のソートを完了します。</li> </ol> <p></p> <p> 図 11-9   クイックソートの流れ </p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby quick_sort.py<pre><code>def quick_sort(self, nums: list[int], left: int, right: int):\n    \"\"\"クイックソート\"\"\"\n    # 部分配列の長さが 1 なら再帰を終了する\n    if left &gt;= right:\n        return\n    # 番兵分割\n    pivot = self.partition(nums, left, right)\n    # 左右の部分配列を再帰処理\n    self.quick_sort(nums, left, pivot - 1)\n    self.quick_sort(nums, pivot + 1, right)\n</code></pre> quick_sort.cpp<pre><code>/* クイックソート */\nvoid quickSort(vector&lt;int&gt; &amp;nums, int left, int right) {\n    // 部分配列の長さが 1 なら再帰を終了する\n    if (left &gt;= right)\n        return;\n    // 番兵分割\n    int pivot = partition(nums, left, right);\n    // 左右の部分配列を再帰処理\n    quickSort(nums, left, pivot - 1);\n    quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.java<pre><code>/* クイックソート */\nvoid quickSort(int[] nums, int left, int right) {\n    // 部分配列の長さが 1 なら再帰を終了する\n    if (left &gt;= right)\n        return;\n    // 番兵分割\n    int pivot = partition(nums, left, right);\n    // 左右の部分配列を再帰処理\n    quickSort(nums, left, pivot - 1);\n    quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.cs<pre><code>/* クイックソート */\nvoid QuickSort(int[] nums, int left, int right) {\n    // 部分配列の長さが 1 なら再帰を終了する\n    if (left &gt;= right)\n        return;\n    // 番兵分割\n    int pivot = Partition(nums, left, right);\n    // 左右の部分配列を再帰処理\n    QuickSort(nums, left, pivot - 1);\n    QuickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.go<pre><code>/* クイックソート */\nfunc (q *quickSort) quickSort(nums []int, left, right int) {\n    // 部分配列の長さが 1 なら再帰を終了する\n    if left &gt;= right {\n        return\n    }\n    // 番兵分割\n    pivot := q.partition(nums, left, right)\n    // 左右の部分配列を再帰処理\n    q.quickSort(nums, left, pivot-1)\n    q.quickSort(nums, pivot+1, right)\n}\n</code></pre> quick_sort.swift<pre><code>/* クイックソート */\nfunc quickSort(nums: inout [Int], left: Int, right: Int) {\n    // 部分配列の長さが 1 なら再帰を終了する\n    if left &gt;= right {\n        return\n    }\n    // 番兵分割\n    let pivot = partition(nums: &amp;nums, left: left, right: right)\n    // 左右の部分配列を再帰処理\n    quickSort(nums: &amp;nums, left: left, right: pivot - 1)\n    quickSort(nums: &amp;nums, left: pivot + 1, right: right)\n}\n</code></pre> quick_sort.js<pre><code>/* クイックソート */\nquickSort(nums, left, right) {\n    // 部分配列の長さが 1 なら再帰を終了する\n    if (left &gt;= right) return;\n    // 番兵分割\n    const pivot = this.partition(nums, left, right);\n    // 左右の部分配列を再帰処理\n    this.quickSort(nums, left, pivot - 1);\n    this.quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.ts<pre><code>/* クイックソート */\nquickSort(nums: number[], left: number, right: number): void {\n    // 部分配列の長さが 1 なら再帰を終了する\n    if (left &gt;= right) {\n        return;\n    }\n    // 番兵分割\n    const pivot = this.partition(nums, left, right);\n    // 左右の部分配列を再帰処理\n    this.quickSort(nums, left, pivot - 1);\n    this.quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.dart<pre><code>/* クイックソート */\nvoid quickSort(List&lt;int&gt; nums, int left, int right) {\n  // 部分配列の長さが 1 なら再帰を終了する\n  if (left &gt;= right) return;\n  // 番兵分割\n  int pivot = _partition(nums, left, right);\n  // 左右の部分配列を再帰処理\n  quickSort(nums, left, pivot - 1);\n  quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.rs<pre><code>/* クイックソート */\npub fn quick_sort(left: i32, right: i32, nums: &amp;mut [i32]) {\n    // 部分配列の長さが 1 なら再帰を終了する\n    if left &gt;= right {\n        return;\n    }\n    // 番兵分割\n    let pivot = Self::partition(nums, left as usize, right as usize) as i32;\n    // 左右の部分配列を再帰処理\n    Self::quick_sort(left, pivot - 1, nums);\n    Self::quick_sort(pivot + 1, right, nums);\n}\n</code></pre> quick_sort.c<pre><code>/* クイックソート */\nvoid quickSort(int nums[], int left, int right) {\n    // 部分配列の長さが 1 なら再帰を終了する\n    if (left &gt;= right) {\n        return;\n    }\n    // 番兵分割\n    int pivot = partition(nums, left, right);\n    // 左右の部分配列を再帰処理\n    quickSort(nums, left, pivot - 1);\n    quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.kt<pre><code>/* クイックソート */\nfun quickSort(nums: IntArray, left: Int, right: Int) {\n    // 部分配列の長さが 1 なら再帰を終了する\n    if (left &gt;= right) return\n    // 番兵分割\n    val pivot = partition(nums, left, right)\n    // 左右の部分配列を再帰処理\n    quickSort(nums, left, pivot - 1)\n    quickSort(nums, pivot + 1, right)\n}\n</code></pre> quick_sort.rb<pre><code>### クイックソートクラス ###\ndef quick_sort(nums, left, right)\n  # 部分配列の長さが 1 でない場合は再帰する\n  if left &lt; right\n    # 番兵分割\n    pivot = partition(nums, left, right)\n    # 左右の部分配列を再帰処理\n    quick_sort(nums, left, pivot - 1)\n    quick_sort(nums, pivot + 1, right)\n  end\n  nums\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 11 章 &nbsp; ソート","11.5 &nbsp; クイックソート"],"tags":[]},{"location":"chapter_sorting/quick_sort/#1152","level":2,"title":"11.5.2   アルゴリズムの特性","text":"<ul> <li>時間計算量は \\(O(n \\log n)\\)、非適応型ソート：平均的な場合、パーティションの再帰の深さは \\(\\log n\\) で、各層の総ループ回数は \\(n\\) のため、全体で \\(O(n \\log n)\\) 時間を要します。最悪の場合、各回のパーティション操作で長さ \\(n\\) の配列が長さ \\(0\\) と \\(n - 1\\) の 2 つの部分配列に分割され、このとき再帰の深さは \\(n\\) に達し、各層のループ回数は \\(n\\) となるため、全体で \\(O(n^2)\\) 時間を要します。</li> <li>空間計算量は \\(O(n)\\)、インプレースソート：入力配列が完全な逆順の場合、最悪の再帰深さ \\(n\\) に達し、\\(O(n)\\) のスタックフレーム空間を使用します。ソート操作は元の配列上で行われ、追加の配列は用いません。</li> <li>非安定ソート：パーティションの最後のステップで、基準数が等しい要素の右側へ交換される可能性があります。</li> </ul>","path":["第 11 章 &nbsp; ソート","11.5 &nbsp; クイックソート"],"tags":[]},{"location":"chapter_sorting/quick_sort/#1153","level":2,"title":"11.5.3   クイックソートが速い理由","text":"<p>名前からも分かるように、クイックソートは効率面で一定の優位性を持っています。クイックソートの平均時間計算量は「マージソート」や「ヒープソート」と同じですが、通常はクイックソートのほうが高効率であり、主な理由は次のとおりです。</p> <ul> <li>最悪ケースが起こる確率が低い：クイックソートの最悪時間計算量は \\(O(n^2)\\) で、「マージソート」ほど安定ではありませんが、大半のケースでは \\(O(n \\log n)\\) の時間計算量で動作します。</li> <li>キャッシュ利用効率が高い：パーティション操作の実行時には、システムが部分配列全体をキャッシュに読み込めるため、要素アクセスの効率が高くなります。一方、「ヒープソート」のようなアルゴリズムは要素へ飛び飛びにアクセスする必要があり、この性質を持ちません。</li> <li>計算量の定数係数が小さい：上記 3 つのアルゴリズムの中で、クイックソートは比較、代入、交換などの操作総数が最も少なくなります。これは「挿入ソート」が「バブルソート」より速い理由と似ています。</li> </ul>","path":["第 11 章 &nbsp; ソート","11.5 &nbsp; クイックソート"],"tags":[]},{"location":"chapter_sorting/quick_sort/#1154","level":2,"title":"11.5.4   基準数の最適化","text":"<p>クイックソートは、入力によっては時間効率が低下する可能性があります。極端な例として、入力配列が完全な逆順であるとします。最左端の要素を基準数として選ぶため、パーティション完了後には基準数が配列の最右端へ交換され、左部分配列の長さが \\(n - 1\\)、右部分配列の長さが \\(0\\) になります。この再帰を続けると、各回のパーティション後に必ず一方の部分配列の長さが \\(0\\) となり、分割統治戦略が機能せず、クイックソートは「バブルソート」に近い形へ退化します。</p> <p>この状況をできるだけ避けるため、パーティションにおける基準数の選び方を最適化できます。たとえば、ランダムに 1 つの要素を選んで基準数にできます。しかし、運が悪く毎回望ましくない基準数を選んでしまうと、効率は依然として十分ではありません。</p> <p>注意すべき点として、プログラミング言語が通常生成するのは「疑似乱数」です。疑似乱数列に合わせて特定のテストケースを構築すると、クイックソートの効率はやはり劣化する可能性があります。</p> <p>さらに改善するために、配列から 3 つの候補要素（通常は先頭、末尾、中間の要素）を選び、**その 3 つの候補要素の中央値を基準数とする**ことができます。こうすると、基準数が「小さすぎず大きすぎもしない」確率が大幅に上がります。もちろん、候補要素をさらに増やして、アルゴリズムの頑健性をいっそう高めることも可能です。この方法を採用すると、時間計算量が \\(O(n^2)\\) まで劣化する確率は大きく下がります。</p> <p>コード例を以下に示します。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby quick_sort.py<pre><code>def median_three(self, nums: list[int], left: int, mid: int, right: int) -&gt; int:\n    \"\"\"3つの候補要素の中央値を選ぶ\"\"\"\n    l, m, r = nums[left], nums[mid], nums[right]\n    if (l &lt;= m &lt;= r) or (r &lt;= m &lt;= l):\n        return mid  # m は l と r の間\n    if (m &lt;= l &lt;= r) or (r &lt;= l &lt;= m):\n        return left  # l は m と r の間\n    return right\n\ndef partition(self, nums: list[int], left: int, right: int) -&gt; int:\n    \"\"\"番兵による分割処理（3 点中央値）\"\"\"\n    # nums[left] を基準値とする\n    med = self.median_three(nums, left, (left + right) // 2, right)\n    # 中央値を配列の最左端に交換する\n    nums[left], nums[med] = nums[med], nums[left]\n    # nums[left] を基準値とする\n    i, j = left, right\n    while i &lt; j:\n        while i &lt; j and nums[j] &gt;= nums[left]:\n            j -= 1  # 右から左へ基準値未満の最初の要素を探す\n        while i &lt; j and nums[i] &lt;= nums[left]:\n            i += 1  # 左から右へ基準値より大きい最初の要素を探す\n        # 要素の交換\n        nums[i], nums[j] = nums[j], nums[i]\n    # 基準値を 2 つの部分配列の境界へ交換する\n    nums[i], nums[left] = nums[left], nums[i]\n    return i  # 基準値のインデックスを返す\n</code></pre> quick_sort.cpp<pre><code>/* 3つの候補要素の中央値を選ぶ */\nint medianThree(vector&lt;int&gt; &amp;nums, int left, int mid, int right) {\n    int l = nums[left], m = nums[mid], r = nums[right];\n    if ((l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l))\n        return mid; // m は l と r の間\n    if ((m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m))\n        return left; // l は m と r の間\n    return right;\n}\n\n/* 番兵による分割処理（3 点中央値） */\nint partition(vector&lt;int&gt; &amp;nums, int left, int right) {\n    // 3つの候補要素の中央値を選ぶ\n    int med = medianThree(nums, left, (left + right) / 2, right);\n    // 中央値を配列の最左端に交換する\n    swap(nums[left], nums[med]);\n    // nums[left] を基準値とする\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--;                // 右から左へ基準値未満の最初の要素を探す\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;                // 左から右へ基準値より大きい最初の要素を探す\n        swap(nums[i], nums[j]); // この 2 つの要素を交換\n    }\n    swap(nums[i], nums[left]);  // 基準値を 2 つの部分配列の境界へ交換する\n    return i;                   // 基準値のインデックスを返す\n}\n</code></pre> quick_sort.java<pre><code>/* 3つの候補要素の中央値を選ぶ */\nint medianThree(int[] nums, int left, int mid, int right) {\n    int l = nums[left], m = nums[mid], r = nums[right];\n    if ((l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l))\n        return mid; // m は l と r の間\n    if ((m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m))\n        return left; // l は m と r の間\n    return right;\n}\n\n/* 番兵による分割処理（3 点中央値） */\nint partition(int[] nums, int left, int right) {\n    // 3つの候補要素の中央値を選ぶ\n    int med = medianThree(nums, left, (left + right) / 2, right);\n    // 中央値を配列の最左端に交換する\n    swap(nums, left, med);\n    // nums[left] を基準値とする\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--;          // 右から左へ基準値未満の最初の要素を探す\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;          // 左から右へ基準値より大きい最初の要素を探す\n        swap(nums, i, j); // この 2 つの要素を交換\n    }\n    swap(nums, i, left);  // 基準値を 2 つの部分配列の境界へ交換する\n    return i;             // 基準値のインデックスを返す\n}\n</code></pre> quick_sort.cs<pre><code>/* 3つの候補要素の中央値を選ぶ */\nint MedianThree(int[] nums, int left, int mid, int right) {\n    int l = nums[left], m = nums[mid], r = nums[right];\n    if ((l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l))\n        return mid; // m は l と r の間\n    if ((m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m))\n        return left; // l は m と r の間\n    return right;\n}\n\n/* 番兵による分割処理（3 点中央値） */\nint Partition(int[] nums, int left, int right) {\n    // 3つの候補要素の中央値を選ぶ\n    int med = MedianThree(nums, left, (left + right) / 2, right);\n    // 中央値を配列の最左端に交換する\n    Swap(nums, left, med);\n    // nums[left] を基準値とする\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--;          // 右から左へ基準値未満の最初の要素を探す\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;          // 左から右へ基準値より大きい最初の要素を探す\n        Swap(nums, i, j); // この 2 つの要素を交換\n    }\n    Swap(nums, i, left);  // 基準値を 2 つの部分配列の境界へ交換する\n    return i;             // 基準値のインデックスを返す\n}\n</code></pre> quick_sort.go<pre><code>/* 3つの候補要素の中央値を選ぶ */\nfunc (q *quickSortMedian) medianThree(nums []int, left, mid, right int) int {\n    l, m, r := nums[left], nums[mid], nums[right]\n    if (l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l) {\n        return mid // m は l と r の間\n    }\n    if (m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m) {\n        return left // l は m と r の間\n    }\n    return right\n}\n\n/* 番兵による分割処理（3 点中央値） */\nfunc (q *quickSortMedian) partition(nums []int, left, right int) int {\n    // nums[left] を基準値とする\n    med := q.medianThree(nums, left, (left+right)/2, right)\n    // 中央値を配列の最左端に交換する\n    nums[left], nums[med] = nums[med], nums[left]\n    // nums[left] を基準値とする\n    i, j := left, right\n    for i &lt; j {\n        for i &lt; j &amp;&amp; nums[j] &gt;= nums[left] {\n            j-- // 右から左へ基準値未満の最初の要素を探す\n        }\n        for i &lt; j &amp;&amp; nums[i] &lt;= nums[left] {\n            i++ // 左から右へ基準値より大きい最初の要素を探す\n        }\n        // 要素の交換\n        nums[i], nums[j] = nums[j], nums[i]\n    }\n    // 基準値を 2 つの部分配列の境界へ交換する\n    nums[i], nums[left] = nums[left], nums[i]\n    return i // 基準値のインデックスを返す\n}\n</code></pre> quick_sort.swift<pre><code>/* 3つの候補要素の中央値を選ぶ */\nfunc medianThree(nums: [Int], left: Int, mid: Int, right: Int) -&gt; Int {\n    let l = nums[left]\n    let m = nums[mid]\n    let r = nums[right]\n    if (l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l) {\n        return mid // m は l と r の間\n    }\n    if (m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m) {\n        return left // l は m と r の間\n    }\n    return right\n}\n\n/* 番兵による分割処理（3 点中央値） */\nfunc partitionMedian(nums: inout [Int], left: Int, right: Int) -&gt; Int {\n    // 3つの候補要素の中央値を選ぶ\n    let med = medianThree(nums: nums, left: left, mid: left + (right - left) / 2, right: right)\n    // 中央値を配列の最左端に交換する\n    nums.swapAt(left, med)\n    return partition(nums: &amp;nums, left: left, right: right)\n}\n</code></pre> quick_sort.js<pre><code>/* 3つの候補要素の中央値を選ぶ */\nmedianThree(nums, left, mid, right) {\n    let l = nums[left],\n        m = nums[mid],\n        r = nums[right];\n    // m は l と r の間\n    if ((l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l)) return mid;\n    // l は m と r の間\n    if ((m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m)) return left;\n    return right;\n}\n\n/* 番兵による分割処理（3 点中央値） */\npartition(nums, left, right) {\n    // 3つの候補要素の中央値を選ぶ\n    let med = this.medianThree(\n        nums,\n        left,\n        Math.floor((left + right) / 2),\n        right\n    );\n    // 中央値を配列の最左端に交換する\n    this.swap(nums, left, med);\n    // nums[left] を基準値とする\n    let i = left,\n        j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) j--; // 右から左へ基準値未満の最初の要素を探す\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) i++; // 左から右へ基準値より大きい最初の要素を探す\n        this.swap(nums, i, j); // この 2 つの要素を交換\n    }\n    this.swap(nums, i, left); // 基準値を 2 つの部分配列の境界へ交換する\n    return i; // 基準値のインデックスを返す\n}\n</code></pre> quick_sort.ts<pre><code>/* 3つの候補要素の中央値を選ぶ */\nmedianThree(\n    nums: number[],\n    left: number,\n    mid: number,\n    right: number\n): number {\n    let l = nums[left],\n        m = nums[mid],\n        r = nums[right];\n    // m は l と r の間\n    if ((l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l)) return mid;\n    // l は m と r の間\n    if ((m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m)) return left;\n    return right;\n}\n\n/* 番兵による分割処理（3 点中央値） */\npartition(nums: number[], left: number, right: number): number {\n    // 3つの候補要素の中央値を選ぶ\n    let med = this.medianThree(\n        nums,\n        left,\n        Math.floor((left + right) / 2),\n        right\n    );\n    // 中央値を配列の最左端に交換する\n    this.swap(nums, left, med);\n    // nums[left] を基準値とする\n    let i = left,\n        j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) {\n            j--; // 右から左へ基準値未満の最初の要素を探す\n        }\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) {\n            i++; // 左から右へ基準値より大きい最初の要素を探す\n        }\n        this.swap(nums, i, j); // この 2 つの要素を交換\n    }\n    this.swap(nums, i, left); // 基準値を 2 つの部分配列の境界へ交換する\n    return i; // 基準値のインデックスを返す\n}\n</code></pre> quick_sort.dart<pre><code>/* 3つの候補要素の中央値を選ぶ */\nint _medianThree(List&lt;int&gt; nums, int left, int mid, int right) {\n  int l = nums[left], m = nums[mid], r = nums[right];\n  if ((l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l))\n    return mid; // m は l と r の間\n  if ((m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m))\n    return left; // l は m と r の間\n  return right;\n}\n\n/* 番兵による分割処理（3 点中央値） */\nint _partition(List&lt;int&gt; nums, int left, int right) {\n  // 3つの候補要素の中央値を選ぶ\n  int med = _medianThree(nums, left, (left + right) ~/ 2, right);\n  // 中央値を配列の最左端に交換する\n  _swap(nums, left, med);\n  // nums[left] を基準値とする\n  int i = left, j = right;\n  while (i &lt; j) {\n    while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) j--; // 右から左へ基準値未満の最初の要素を探す\n    while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) i++; // 左から右へ基準値より大きい最初の要素を探す\n    _swap(nums, i, j); // この 2 つの要素を交換\n  }\n  _swap(nums, i, left); // 基準値を 2 つの部分配列の境界へ交換する\n  return i; // 基準値のインデックスを返す\n}\n</code></pre> quick_sort.rs<pre><code>/* 3つの候補要素の中央値を選ぶ */\nfn median_three(nums: &amp;mut [i32], left: usize, mid: usize, right: usize) -&gt; usize {\n    let (l, m, r) = (nums[left], nums[mid], nums[right]);\n    if (l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l) {\n        return mid; // m は l と r の間\n    }\n    if (m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m) {\n        return left; // l は m と r の間\n    }\n    right\n}\n\n/* 番兵による分割処理（3 点中央値） */\nfn partition(nums: &amp;mut [i32], left: usize, right: usize) -&gt; usize {\n    // 3つの候補要素の中央値を選ぶ\n    let med = Self::median_three(nums, left, (left + right) / 2, right);\n    // 中央値を配列の最左端に交換する\n    nums.swap(left, med);\n    // nums[left] を基準値とする\n    let (mut i, mut j) = (left, right);\n    while i &lt; j {\n        while i &lt; j &amp;&amp; nums[j] &gt;= nums[left] {\n            j -= 1; // 右から左へ基準値未満の最初の要素を探す\n        }\n        while i &lt; j &amp;&amp; nums[i] &lt;= nums[left] {\n            i += 1; // 左から右へ基準値より大きい最初の要素を探す\n        }\n        nums.swap(i, j); // この 2 つの要素を交換\n    }\n    nums.swap(i, left); // 基準値を 2 つの部分配列の境界へ交換する\n    i // 基準値のインデックスを返す\n}\n</code></pre> quick_sort.c<pre><code>/* 3つの候補要素の中央値を選ぶ */\nint medianThree(int nums[], int left, int mid, int right) {\n    int l = nums[left], m = nums[mid], r = nums[right];\n    if ((l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l))\n        return mid; // m は l と r の間\n    if ((m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m))\n        return left; // l は m と r の間\n    return right;\n}\n\n/* 番兵による分割処理（3 点中央値） */\nint partitionMedian(int nums[], int left, int right) {\n    // 3つの候補要素の中央値を選ぶ\n    int med = medianThree(nums, left, (left + right) / 2, right);\n    // 中央値を配列の最左端に交換する\n    swap(nums, left, med);\n    // nums[left] を基準値とする\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--; // 右から左へ基準値未満の最初の要素を探す\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;          // 左から右へ基準値より大きい最初の要素を探す\n        swap(nums, i, j); // この 2 つの要素を交換\n    }\n    swap(nums, i, left); // 基準値を 2 つの部分配列の境界へ交換する\n    return i;            // 基準値のインデックスを返す\n}\n</code></pre> quick_sort.kt<pre><code>/* 3つの候補要素の中央値を選ぶ */\nfun medianThree(nums: IntArray, left: Int, mid: Int, right: Int): Int {\n    val l = nums[left]\n    val m = nums[mid]\n    val r = nums[right]\n    if ((m in l..r) || (m in r..l))\n        return mid  // m は l と r の間\n    if ((l in m..r) || (l in r..m))\n        return left // l は m と r の間\n    return right\n}\n\n/* 番兵による分割処理（3 点中央値） */\nfun partitionMedian(nums: IntArray, left: Int, right: Int): Int {\n    // 3つの候補要素の中央値を選ぶ\n    val med = medianThree(nums, left, (left + right) / 2, right)\n    // 中央値を配列の最左端に交換する\n    swap(nums, left, med)\n    // nums[left] を基準値とする\n    var i = left\n    var j = right\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--                      // 右から左へ基準値未満の最初の要素を探す\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++                      // 左から右へ基準値より大きい最初の要素を探す\n        swap(nums, i, j)             // この 2 つの要素を交換\n    }\n    swap(nums, i, left)              // 基準値を 2 つの部分配列の境界へ交換する\n    return i                         // 基準値のインデックスを返す\n}\n</code></pre> quick_sort.rb<pre><code>### 3 つの候補要素の中央値を選ぶ ###\ndef median_three(nums, left, mid, right)\n  # 3つの候補要素の中央値を選ぶ\n  _l, _m, _r = nums[left], nums[mid], nums[right]\n  # m は l と r の間\n  return mid if (_l &lt;= _m &amp;&amp; _m &lt;= _r) || (_r &lt;= _m &amp;&amp; _m &lt;= _l)\n  # l は m と r の間\n  return left if (_m &lt;= _l &amp;&amp; _l &lt;= _r) || (_r &lt;= _l &amp;&amp; _l &lt;= _m)\n  return right\nend\n\n### 3 つの候補要素の中央値を選ぶ ###\ndef median_three(nums, left, mid, right)\n  # 3つの候補要素の中央値を選ぶ\n  _l, _m, _r = nums[left], nums[mid], nums[right]\n  # m は l と r の間\n  return mid if (_l &lt;= _m &amp;&amp; _m &lt;= _r) || (_r &lt;= _m &amp;&amp; _m &lt;= _l)\n  # l は m と r の間\n  return left if (_m &lt;= _l &amp;&amp; _l &lt;= _r) || (_r &lt;= _l &amp;&amp; _l &lt;= _m)\n  return right\nend\n\n# ## 番兵分割（三数中央値）###\ndef partition(nums, left, right)\n  # ## nums[left] を基準値とする\n  med = median_three(nums, left, (left + right) / 2, right)\n  # 中央値を配列の最左端に交換する\n  nums[left], nums[med] = nums[med], nums[left]\n  i, j = left, right\n  while i &lt; j\n    while i &lt; j &amp;&amp; nums[j] &gt;= nums[left]\n      j -= 1 # 右から左へ基準値未満の最初の要素を探す\n    end\n    while i &lt; j &amp;&amp; nums[i] &lt;= nums[left]\n      i += 1 # 左から右へ基準値より大きい最初の要素を探す\n    end\n    # 要素の交換\n    nums[i], nums[j] = nums[j], nums[i]\n  end\n  # 基準値を 2 つの部分配列の境界へ交換する\n  nums[i], nums[left] = nums[left], nums[i]\n  i # 基準値のインデックスを返す\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 11 章 &nbsp; ソート","11.5 &nbsp; クイックソート"],"tags":[]},{"location":"chapter_sorting/quick_sort/#1155","level":2,"title":"11.5.5   再帰の深さの最適化","text":"<p>一部の入力では、クイックソートは多くの空間を消費する可能性があります。完全に整列済みの入力配列を例にとり、再帰中の部分配列の長さを \\(m\\) とします。各回のパーティション操作では長さ \\(0\\) の左部分配列と長さ \\(m - 1\\) の右部分配列が生成されます。これは、各再帰呼び出しで減る問題サイズが非常に小さいこと（要素が 1 つ減るだけ）を意味し、再帰木の高さは \\(n - 1\\) に達するため、このとき \\(O(n)\\) のスタックフレーム空間を占有します。</p> <p>スタックフレーム空間の蓄積を防ぐために、各回のパーティション完了後に 2 つの部分配列の長さを比較し、**短いほうの部分配列に対してのみ再帰**を行えます。短い部分配列の長さは \\(n / 2\\) を超えないため、この方法なら再帰の深さを \\(\\log n\\) 以下に抑えられ、最悪時の空間計算量を \\(O(\\log n)\\) まで最適化できます。コードを以下に示します。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby quick_sort.py<pre><code>def quick_sort(self, nums: list[int], left: int, right: int):\n    \"\"\"クイックソート（再帰深度最適化）\"\"\"\n    # 部分配列の長さが 1 なら終了\n    while left &lt; right:\n        # 番兵による分割処理\n        pivot = self.partition(nums, left, right)\n        # 2 つの部分配列のうち短いほうにクイックソートを適用する\n        if pivot - left &lt; right - pivot:\n            self.quick_sort(nums, left, pivot - 1)  # 左部分配列を再帰的にソート\n            left = pivot + 1  # 未ソート区間の残りは [pivot + 1, right]\n        else:\n            self.quick_sort(nums, pivot + 1, right)  # 右部分配列を再帰的にソート\n            right = pivot - 1  # 未ソート区間の残りは [left, pivot - 1]\n</code></pre> quick_sort.cpp<pre><code>/* クイックソート（再帰深度最適化） */\nvoid quickSort(vector&lt;int&gt; &amp;nums, int left, int right) {\n    // 部分配列の長さが 1 なら終了\n    while (left &lt; right) {\n        // 番兵による分割処理\n        int pivot = partition(nums, left, right);\n        // 2 つの部分配列のうち短いほうにクイックソートを適用する\n        if (pivot - left &lt; right - pivot) {\n            quickSort(nums, left, pivot - 1); // 左部分配列を再帰的にソート\n            left = pivot + 1;                 // 未ソート区間の残りは [pivot + 1, right]\n        } else {\n            quickSort(nums, pivot + 1, right); // 右部分配列を再帰的にソート\n            right = pivot - 1;                 // 未ソート区間の残りは [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.java<pre><code>/* クイックソート（再帰深度最適化） */\nvoid quickSort(int[] nums, int left, int right) {\n    // 部分配列の長さが 1 なら終了\n    while (left &lt; right) {\n        // 番兵による分割処理\n        int pivot = partition(nums, left, right);\n        // 2 つの部分配列のうち短いほうにクイックソートを適用する\n        if (pivot - left &lt; right - pivot) {\n            quickSort(nums, left, pivot - 1); // 左部分配列を再帰的にソート\n            left = pivot + 1; // 未ソート区間の残りは [pivot + 1, right]\n        } else {\n            quickSort(nums, pivot + 1, right); // 右部分配列を再帰的にソート\n            right = pivot - 1; // 未ソート区間の残りは [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.cs<pre><code>/* クイックソート（再帰深度最適化） */\nvoid QuickSort(int[] nums, int left, int right) {\n    // 部分配列の長さが 1 なら終了\n    while (left &lt; right) {\n        // 番兵による分割処理\n        int pivot = Partition(nums, left, right);\n        // 2 つの部分配列のうち短いほうにクイックソートを適用する\n        if (pivot - left &lt; right - pivot) {\n            QuickSort(nums, left, pivot - 1);  // 左部分配列を再帰的にソート\n            left = pivot + 1;  // 未ソート区間の残りは [pivot + 1, right]\n        } else {\n            QuickSort(nums, pivot + 1, right); // 右部分配列を再帰的にソート\n            right = pivot - 1; // 未ソート区間の残りは [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.go<pre><code>/* クイックソート（再帰深度最適化） */\nfunc (q *quickSortTailCall) quickSort(nums []int, left, right int) {\n    // 部分配列の長さが 1 なら終了\n    for left &lt; right {\n        // 番兵による分割処理\n        pivot := q.partition(nums, left, right)\n        // 2 つの部分配列のうち短いほうにクイックソートを適用する\n        if pivot-left &lt; right-pivot {\n            q.quickSort(nums, left, pivot-1) // 左部分配列を再帰的にソート\n            left = pivot + 1                 // 未ソート区間の残りは [pivot + 1, right]\n        } else {\n            q.quickSort(nums, pivot+1, right) // 右部分配列を再帰的にソート\n            right = pivot - 1                 // 未ソート区間の残りは [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.swift<pre><code>/* クイックソート（再帰深度最適化） */\nfunc quickSortTailCall(nums: inout [Int], left: Int, right: Int) {\n    var left = left\n    var right = right\n    // 部分配列の長さが 1 なら終了\n    while left &lt; right {\n        // 番兵による分割処理\n        let pivot = partition(nums: &amp;nums, left: left, right: right)\n        // 2 つの部分配列のうち短いほうにクイックソートを適用する\n        if (pivot - left) &lt; (right - pivot) {\n            quickSortTailCall(nums: &amp;nums, left: left, right: pivot - 1) // 左部分配列を再帰的にソート\n            left = pivot + 1 // 未ソート区間の残りは [pivot + 1, right]\n        } else {\n            quickSortTailCall(nums: &amp;nums, left: pivot + 1, right: right) // 右部分配列を再帰的にソート\n            right = pivot - 1 // 未ソート区間の残りは [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.js<pre><code>/* クイックソート（再帰深度最適化） */\nquickSort(nums, left, right) {\n    // 部分配列の長さが 1 なら終了\n    while (left &lt; right) {\n        // 番兵による分割処理\n        let pivot = this.partition(nums, left, right);\n        // 2 つの部分配列のうち短いほうにクイックソートを適用する\n        if (pivot - left &lt; right - pivot) {\n            this.quickSort(nums, left, pivot - 1); // 左部分配列を再帰的にソート\n            left = pivot + 1; // 未ソート区間の残りは [pivot + 1, right]\n        } else {\n            this.quickSort(nums, pivot + 1, right); // 右部分配列を再帰的にソート\n            right = pivot - 1; // 未ソート区間の残りは [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.ts<pre><code>/* クイックソート（再帰深度最適化） */\nquickSort(nums: number[], left: number, right: number): void {\n    // 部分配列の長さが 1 なら終了\n    while (left &lt; right) {\n        // 番兵による分割処理\n        let pivot = this.partition(nums, left, right);\n        // 2 つの部分配列のうち短いほうにクイックソートを適用する\n        if (pivot - left &lt; right - pivot) {\n            this.quickSort(nums, left, pivot - 1); // 左部分配列を再帰的にソート\n            left = pivot + 1; // 未ソート区間の残りは [pivot + 1, right]\n        } else {\n            this.quickSort(nums, pivot + 1, right); // 右部分配列を再帰的にソート\n            right = pivot - 1; // 未ソート区間の残りは [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.dart<pre><code>/* クイックソート（再帰深度最適化） */\nvoid quickSort(List&lt;int&gt; nums, int left, int right) {\n  // 部分配列の長さが 1 なら終了\n  while (left &lt; right) {\n    // 番兵による分割処理\n    int pivot = _partition(nums, left, right);\n    // 2 つの部分配列のうち短いほうにクイックソートを適用する\n    if (pivot - left &lt; right - pivot) {\n      quickSort(nums, left, pivot - 1); // 左部分配列を再帰的にソート\n      left = pivot + 1; // 未ソート区間の残りは [pivot + 1, right]\n    } else {\n      quickSort(nums, pivot + 1, right); // 右部分配列を再帰的にソート\n      right = pivot - 1; // 未ソート区間の残りは [left, pivot - 1]\n    }\n  }\n}\n</code></pre> quick_sort.rs<pre><code>/* クイックソート（再帰深度最適化） */\npub fn quick_sort(mut left: i32, mut right: i32, nums: &amp;mut [i32]) {\n    // 部分配列の長さが 1 なら終了\n    while left &lt; right {\n        // 番兵による分割処理\n        let pivot = Self::partition(nums, left as usize, right as usize) as i32;\n        // 2 つの部分配列のうち短いほうにクイックソートを適用する\n        if pivot - left &lt; right - pivot {\n            Self::quick_sort(left, pivot - 1, nums); // 左部分配列を再帰的にソート\n            left = pivot + 1; // 未ソート区間の残りは [pivot + 1, right]\n        } else {\n            Self::quick_sort(pivot + 1, right, nums); // 右部分配列を再帰的にソート\n            right = pivot - 1; // 未ソート区間の残りは [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.c<pre><code>/* クイックソート（再帰深度最適化） */\nvoid quickSortTailCall(int nums[], int left, int right) {\n    // 部分配列の長さが 1 なら終了\n    while (left &lt; right) {\n        // 番兵による分割処理\n        int pivot = partition(nums, left, right);\n        // 2 つの部分配列のうち短いほうにクイックソートを適用する\n        if (pivot - left &lt; right - pivot) {\n            // 左部分配列を再帰的にソート\n            quickSortTailCall(nums, left, pivot - 1);\n            // 未ソート区間の残りは [pivot + 1, right]\n            left = pivot + 1;\n        } else {\n            // 右部分配列を再帰的にソート\n            quickSortTailCall(nums, pivot + 1, right);\n            // 未ソート区間の残りは [left, pivot - 1]\n            right = pivot - 1;\n        }\n    }\n}\n</code></pre> quick_sort.kt<pre><code>/* クイックソート（再帰深度最適化） */\nfun quickSortTailCall(nums: IntArray, left: Int, right: Int) {\n    // 部分配列の長さが 1 なら終了\n    var l = left\n    var r = right\n    while (l &lt; r) {\n        // 番兵による分割処理\n        val pivot = partition(nums, l, r)\n        // 2 つの部分配列のうち短いほうにクイックソートを適用する\n        if (pivot - l &lt; r - pivot) {\n            quickSort(nums, l, pivot - 1) // 左部分配列を再帰的にソート\n            l = pivot + 1 // 未ソート区間の残りは [pivot + 1, right]\n        } else {\n            quickSort(nums, pivot + 1, r) // 右部分配列を再帰的にソート\n            r = pivot - 1 // 未ソート区間の残りは [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.rb<pre><code>### 番兵分割 ###\ndef partition(nums, left, right)\n  # nums[left] を基準値とする\n  i = left\n  j = right\n  while i &lt; j\n    while i &lt; j &amp;&amp; nums[j] &gt;= nums[left]\n      j -= 1 # 右から左へ基準値未満の最初の要素を探す\n    end\n    while i &lt; j &amp;&amp; nums[i] &lt;= nums[left]\n      i += 1 # 左から右へ基準値より大きい最初の要素を探す\n    end\n    # 要素の交換\n    nums[i], nums[j] = nums[j], nums[i]\n  end\n  # 基準値を 2 つの部分配列の境界へ交換する\n  nums[i], nums[left] = nums[left], nums[i]\n  i # 基準値のインデックスを返す\nend\n\n# ## クイックソート（再帰深度最適化）###\ndef quick_sort(nums, left, right)\n  # 部分配列の長さが 1 でない場合は再帰する\n  while left &lt; right\n    # 番兵分割\n    pivot = partition(nums, left, right)\n    # 2 つの部分配列のうち短いほうにクイックソートを適用する\n    if pivot - left &lt; right - pivot\n      quick_sort(nums, left, pivot - 1)\n      left = pivot + 1 # 未ソート区間の残りは [pivot + 1, right]\n    else\n      quick_sort(nums, pivot + 1, right)\n      right = pivot - 1 # 未ソート区間の残りは [left, pivot - 1]\n    end\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 11 章 &nbsp; ソート","11.5 &nbsp; クイックソート"],"tags":[]},{"location":"chapter_sorting/radix_sort/","level":1,"title":"11.10   基数ソート","text":"<p>前節では計数ソートを紹介しました。これは、データ量 \\(n\\) が大きく、データ範囲 \\(m\\) が小さい場合に適しています。\\(n = 10^6\\) 個の学籍番号をソートすると仮定すると、学籍番号は \\(8\\) 桁の数字なので、データ範囲 \\(m = 10^8\\) は非常に大きくなります。計数ソートでは大量のメモリ空間を確保する必要がありますが、基数ソートではこの問題を回避できます。</p> <p>基数ソート（radix sort）の基本的な考え方は計数ソートと同じで、個数を数えることによってソートを実現します。そのうえで、基数ソートは各桁の段階的な関係を利用し、各桁を順にソートすることで、最終的なソート結果を得ます。</p>","path":["第 11 章 &nbsp; ソート","11.10 &nbsp; 基数ソート"],"tags":[]},{"location":"chapter_sorting/radix_sort/#11101","level":2,"title":"11.10.1   アルゴリズムの流れ","text":"<p>学籍番号データを例にすると、数字の最下位桁を第 \\(1\\) 位、最上位桁を第 \\(8\\) 位としたとき、基数ソートの流れは次図のようになります。</p> <ol> <li>桁番号 \\(k = 1\\) を初期化します。</li> <li>学籍番号の第 \\(k\\) 位に対して「計数ソート」を実行します。完了すると、データは第 \\(k\\) 位に従って昇順に並びます。</li> <li>\\(k\\) を \\(1\\) 増やし、手順 <code>2.</code> に戻って反復を続けます。すべての桁のソートが完了したら終了します。</li> </ol> <p></p> <p> 図 11-18   基数ソートのアルゴリズムの流れ </p> <p>以下ではコード実装を分解して見ていきます。\\(d\\) 進数の数値 \\(x\\) について、その第 \\(k\\) 位 \\(x_k\\) を取得するには、次の計算式を用います。</p> \\[ x_k = \\lfloor\\frac{x}{d^{k-1}}\\rfloor \\bmod d \\] <p>ここで、\\(\\lfloor a \\rfloor\\) は浮動小数点数 \\(a\\) の切り捨てを表し、\\(\\bmod \\: d\\) は \\(d\\) による剰余を表します。学籍番号データでは、\\(d = 10\\) かつ \\(k \\in [1, 8]\\) です。</p> <p>さらに、数字の第 \\(k\\) 位に基づいてソートできるように、計数ソートのコードを少し変更する必要があります。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby radix_sort.py<pre><code>def digit(num: int, exp: int) -&gt; int:\n    \"\"\"要素 num の下から k 桁目を取得（exp = 10^(k-1)）\"\"\"\n    # ここで高コストな累乗計算を繰り返さないよう、k ではなく exp を渡す\n    return (num // exp) % 10\n\ndef counting_sort_digit(nums: list[int], exp: int):\n    \"\"\"計数ソート（nums の k 桁目でソート）\"\"\"\n    # 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要\n    counter = [0] * 10\n    n = len(nums)\n    # 0~9 の各数字の出現回数を集計する\n    for i in range(n):\n        d = digit(nums[i], exp)  # nums[i] の第 k 位を取得し、d とする\n        counter[d] += 1  # 数字 d の出現回数を数える\n    # 累積和を求め、「出現回数」を「配列インデックス」に変換する\n    for i in range(1, 10):\n        counter[i] += counter[i - 1]\n    # 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する\n    res = [0] * n\n    for i in range(n - 1, -1, -1):\n        d = digit(nums[i], exp)\n        j = counter[d] - 1  # d の配列内インデックス j を取得する\n        res[j] = nums[i]  # 現在の要素をインデックス j に格納する\n        counter[d] -= 1  # d の個数を 1 減らす\n    # 結果で元の配列 nums を上書きする\n    for i in range(n):\n        nums[i] = res[i]\n\ndef radix_sort(nums: list[int]):\n    \"\"\"基数ソート\"\"\"\n    # 最大桁数の判定用に配列の最大要素を取得\n    m = max(nums)\n    # 下位桁から上位桁の順に走査する\n    exp = 1\n    while exp &lt;= m:\n        # 配列要素の k 桁目に対して計数ソートを行う\n        # k = 1 -&gt; exp = 1\n        # k = 2 -&gt; exp = 10\n        # つまり exp = 10^(k-1)\n        counting_sort_digit(nums, exp)\n        exp *= 10\n</code></pre> radix_sort.cpp<pre><code>/* 要素 num の下から k 桁目を取得（exp = 10^(k-1)） */\nint digit(int num, int exp) {\n    // ここで高コストな累乗計算を繰り返さないよう、k ではなく exp を渡す\n    return (num / exp) % 10;\n}\n\n/* 計数ソート（nums の k 桁目でソート） */\nvoid countingSortDigit(vector&lt;int&gt; &amp;nums, int exp) {\n    // 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要\n    vector&lt;int&gt; counter(10, 0);\n    int n = nums.size();\n    // 0~9 の各数字の出現回数を集計する\n    for (int i = 0; i &lt; n; i++) {\n        int d = digit(nums[i], exp); // nums[i] の第 k 位を取得し、d とする\n        counter[d]++;                // 数字 d の出現回数を数える\n    }\n    // 累積和を求め、「出現回数」を「配列インデックス」に変換する\n    for (int i = 1; i &lt; 10; i++) {\n        counter[i] += counter[i - 1];\n    }\n    // 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する\n    vector&lt;int&gt; res(n, 0);\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int d = digit(nums[i], exp);\n        int j = counter[d] - 1; // d の配列内インデックス j を取得する\n        res[j] = nums[i];       // 現在の要素をインデックス j に格納する\n        counter[d]--;           // d の個数を 1 減らす\n    }\n    // 結果で元の配列 nums を上書きする\n    for (int i = 0; i &lt; n; i++)\n        nums[i] = res[i];\n}\n\n/* 基数ソート */\nvoid radixSort(vector&lt;int&gt; &amp;nums) {\n    // 最大桁数の判定用に配列の最大要素を取得\n    int m = *max_element(nums.begin(), nums.end());\n    // 下位桁から上位桁の順に走査する\n    for (int exp = 1; exp &lt;= m; exp *= 10)\n        // 配列要素の k 桁目に対して計数ソートを行う\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // つまり exp = 10^(k-1)\n        countingSortDigit(nums, exp);\n}\n</code></pre> radix_sort.java<pre><code>/* 要素 num の下から k 桁目を取得（exp = 10^(k-1)） */\nint digit(int num, int exp) {\n    // ここで高コストな累乗計算を繰り返さないよう、k ではなく exp を渡す\n    return (num / exp) % 10;\n}\n\n/* 計数ソート（nums の k 桁目でソート） */\nvoid countingSortDigit(int[] nums, int exp) {\n    // 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要\n    int[] counter = new int[10];\n    int n = nums.length;\n    // 0~9 の各数字の出現回数を集計する\n    for (int i = 0; i &lt; n; i++) {\n        int d = digit(nums[i], exp); // nums[i] の第 k 位を取得し、d とする\n        counter[d]++;                // 数字 d の出現回数を数える\n    }\n    // 累積和を求め、「出現回数」を「配列インデックス」に変換する\n    for (int i = 1; i &lt; 10; i++) {\n        counter[i] += counter[i - 1];\n    }\n    // 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する\n    int[] res = new int[n];\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int d = digit(nums[i], exp);\n        int j = counter[d] - 1; // d の配列内インデックス j を取得する\n        res[j] = nums[i];       // 現在の要素をインデックス j に格納する\n        counter[d]--;           // d の個数を 1 減らす\n    }\n    // 結果で元の配列 nums を上書きする\n    for (int i = 0; i &lt; n; i++)\n        nums[i] = res[i];\n}\n\n/* 基数ソート */\nvoid radixSort(int[] nums) {\n    // 最大桁数の判定用に配列の最大要素を取得\n    int m = Integer.MIN_VALUE;\n    for (int num : nums)\n        if (num &gt; m)\n            m = num;\n    // 下位桁から上位桁の順に走査する\n    for (int exp = 1; exp &lt;= m; exp *= 10) {\n        // 配列要素の k 桁目に対して計数ソートを行う\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // つまり exp = 10^(k-1)\n        countingSortDigit(nums, exp);\n    }\n}\n</code></pre> radix_sort.cs<pre><code>/* 要素 num の下から k 桁目を取得（exp = 10^(k-1)） */\nint Digit(int num, int exp) {\n    // ここで高コストな累乗計算を繰り返さないよう、k ではなく exp を渡す\n    return (num / exp) % 10;\n}\n\n/* 計数ソート（nums の k 桁目でソート） */\nvoid CountingSortDigit(int[] nums, int exp) {\n    // 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要\n    int[] counter = new int[10];\n    int n = nums.Length;\n    // 0~9 の各数字の出現回数を集計する\n    for (int i = 0; i &lt; n; i++) {\n        int d = Digit(nums[i], exp); // nums[i] の第 k 位を取得し、d とする\n        counter[d]++;                // 数字 d の出現回数を数える\n    }\n    // 累積和を求め、「出現回数」を「配列インデックス」に変換する\n    for (int i = 1; i &lt; 10; i++) {\n        counter[i] += counter[i - 1];\n    }\n    // 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する\n    int[] res = new int[n];\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int d = Digit(nums[i], exp);\n        int j = counter[d] - 1; // d の配列内インデックス j を取得する\n        res[j] = nums[i];       // 現在の要素をインデックス j に格納する\n        counter[d]--;           // d の個数を 1 減らす\n    }\n    // 結果で元の配列 nums を上書きする\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = res[i];\n    }\n}\n\n/* 基数ソート */\nvoid RadixSort(int[] nums) {\n    // 最大桁数の判定用に配列の最大要素を取得\n    int m = int.MinValue;\n    foreach (int num in nums) {\n        if (num &gt; m) m = num;\n    }\n    // 下位桁から上位桁の順に走査する\n    for (int exp = 1; exp &lt;= m; exp *= 10) {\n        // 配列要素の k 桁目に対して計数ソートを行う\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // つまり exp = 10^(k-1)\n        CountingSortDigit(nums, exp);\n    }\n}\n</code></pre> radix_sort.go<pre><code>/* 要素 num の下から k 桁目を取得（exp = 10^(k-1)） */\nfunc digit(num, exp int) int {\n    // ここで高コストな累乗計算を繰り返さないよう、k ではなく exp を渡す\n    return (num / exp) % 10\n}\n\n/* 計数ソート（nums の k 桁目でソート） */\nfunc countingSortDigit(nums []int, exp int) {\n    // 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要\n    counter := make([]int, 10)\n    n := len(nums)\n    // 0~9 の各数字の出現回数を集計する\n    for i := 0; i &lt; n; i++ {\n        d := digit(nums[i], exp) // nums[i] の第 k 位を取得し、d とする\n        counter[d]++             // 数字 d の出現回数を数える\n    }\n    // 累積和を求め、「出現回数」を「配列インデックス」に変換する\n    for i := 1; i &lt; 10; i++ {\n        counter[i] += counter[i-1]\n    }\n    // 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する\n    res := make([]int, n)\n    for i := n - 1; i &gt;= 0; i-- {\n        d := digit(nums[i], exp)\n        j := counter[d] - 1 // d の配列内インデックス j を取得する\n        res[j] = nums[i]    // 現在の要素をインデックス j に格納する\n        counter[d]--        // d の個数を 1 減らす\n    }\n    // 結果で元の配列 nums を上書きする\n    for i := 0; i &lt; n; i++ {\n        nums[i] = res[i]\n    }\n}\n\n/* 基数ソート */\nfunc radixSort(nums []int) {\n    // 最大桁数の判定用に配列の最大要素を取得\n    max := math.MinInt\n    for _, num := range nums {\n        if num &gt; max {\n            max = num\n        }\n    }\n    // 下位桁から上位桁の順に走査する\n    for exp := 1; max &gt;= exp; exp *= 10 {\n        // 配列要素の k 桁目に対して計数ソートを行う\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // つまり exp = 10^(k-1)\n        countingSortDigit(nums, exp)\n    }\n}\n</code></pre> radix_sort.swift<pre><code>/* 要素 num の下から k 桁目を取得（exp = 10^(k-1)） */\nfunc digit(num: Int, exp: Int) -&gt; Int {\n    // ここで高コストな累乗計算を繰り返さないよう、k ではなく exp を渡す\n    (num / exp) % 10\n}\n\n/* 計数ソート（nums の k 桁目でソート） */\nfunc countingSortDigit(nums: inout [Int], exp: Int) {\n    // 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要\n    var counter = Array(repeating: 0, count: 10)\n    // 0~9 の各数字の出現回数を集計する\n    for i in nums.indices {\n        let d = digit(num: nums[i], exp: exp) // nums[i] の第 k 位を取得し、d とする\n        counter[d] += 1 // 数字 d の出現回数を数える\n    }\n    // 累積和を求め、「出現回数」を「配列インデックス」に変換する\n    for i in 1 ..&lt; 10 {\n        counter[i] += counter[i - 1]\n    }\n    // 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する\n    var res = Array(repeating: 0, count: nums.count)\n    for i in nums.indices.reversed() {\n        let d = digit(num: nums[i], exp: exp)\n        let j = counter[d] - 1 // d の配列内インデックス j を取得する\n        res[j] = nums[i] // 現在の要素をインデックス j に格納する\n        counter[d] -= 1 // d の個数を 1 減らす\n    }\n    // 結果で元の配列 nums を上書きする\n    for i in nums.indices {\n        nums[i] = res[i]\n    }\n}\n\n/* 基数ソート */\nfunc radixSort(nums: inout [Int]) {\n    // 最大桁数の判定用に配列の最大要素を取得\n    var m = Int.min\n    for num in nums {\n        if num &gt; m {\n            m = num\n        }\n    }\n    // 下位桁から上位桁の順に走査する\n    for exp in sequence(first: 1, next: { m &gt;= ($0 * 10) ? $0 * 10 : nil }) {\n        // 配列要素の k 桁目に対して計数ソートを行う\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // つまり exp = 10^(k-1)\n        countingSortDigit(nums: &amp;nums, exp: exp)\n    }\n}\n</code></pre> radix_sort.js<pre><code>/* 要素 num の下から k 桁目を取得（exp = 10^(k-1)） */\nfunction digit(num, exp) {\n    // ここで高コストな累乗計算を繰り返さないよう、k ではなく exp を渡す\n    return Math.floor(num / exp) % 10;\n}\n\n/* 計数ソート（nums の k 桁目でソート） */\nfunction countingSortDigit(nums, exp) {\n    // 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要\n    const counter = new Array(10).fill(0);\n    const n = nums.length;\n    // 0~9 の各数字の出現回数を集計する\n    for (let i = 0; i &lt; n; i++) {\n        const d = digit(nums[i], exp); // nums[i] の第 k 位を取得し、d とする\n        counter[d]++; // 数字 d の出現回数を数える\n    }\n    // 累積和を求め、「出現回数」を「配列インデックス」に変換する\n    for (let i = 1; i &lt; 10; i++) {\n        counter[i] += counter[i - 1];\n    }\n    // 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する\n    const res = new Array(n).fill(0);\n    for (let i = n - 1; i &gt;= 0; i--) {\n        const d = digit(nums[i], exp);\n        const j = counter[d] - 1; // d の配列内インデックス j を取得する\n        res[j] = nums[i]; // 現在の要素をインデックス j に格納する\n        counter[d]--; // d の個数を 1 減らす\n    }\n    // 結果で元の配列 nums を上書きする\n    for (let i = 0; i &lt; n; i++) {\n        nums[i] = res[i];\n    }\n}\n\n/* 基数ソート */\nfunction radixSort(nums) {\n    // 最大桁数の判定用に配列の最大要素を取得\n    let m = Math.max(... nums);\n    // 下位桁から上位桁の順に走査する\n    for (let exp = 1; exp &lt;= m; exp *= 10) {\n        // 配列要素の k 桁目に対して計数ソートを行う\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // つまり exp = 10^(k-1)\n        countingSortDigit(nums, exp);\n    }\n}\n</code></pre> radix_sort.ts<pre><code>/* 要素 num の下から k 桁目を取得（exp = 10^(k-1)） */\nfunction digit(num: number, exp: number): number {\n    // ここで高コストな累乗計算を繰り返さないよう、k ではなく exp を渡す\n    return Math.floor(num / exp) % 10;\n}\n\n/* 計数ソート（nums の k 桁目でソート） */\nfunction countingSortDigit(nums: number[], exp: number): void {\n    // 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要\n    const counter = new Array(10).fill(0);\n    const n = nums.length;\n    // 0~9 の各数字の出現回数を集計する\n    for (let i = 0; i &lt; n; i++) {\n        const d = digit(nums[i], exp); // nums[i] の第 k 位を取得し、d とする\n        counter[d]++; // 数字 d の出現回数を数える\n    }\n    // 累積和を求め、「出現回数」を「配列インデックス」に変換する\n    for (let i = 1; i &lt; 10; i++) {\n        counter[i] += counter[i - 1];\n    }\n    // 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する\n    const res = new Array(n).fill(0);\n    for (let i = n - 1; i &gt;= 0; i--) {\n        const d = digit(nums[i], exp);\n        const j = counter[d] - 1; // d の配列内インデックス j を取得する\n        res[j] = nums[i]; // 現在の要素をインデックス j に格納する\n        counter[d]--; // d の個数を 1 減らす\n    }\n    // 結果で元の配列 nums を上書きする\n    for (let i = 0; i &lt; n; i++) {\n        nums[i] = res[i];\n    }\n}\n\n/* 基数ソート */\nfunction radixSort(nums: number[]): void {\n    // 最大桁数の判定用に配列の最大要素を取得\n    let m: number = Math.max(... nums);\n    // 下位桁から上位桁の順に走査する\n    for (let exp = 1; exp &lt;= m; exp *= 10) {\n        // 配列要素の k 桁目に対して計数ソートを行う\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // つまり exp = 10^(k-1)\n        countingSortDigit(nums, exp);\n    }\n}\n</code></pre> radix_sort.dart<pre><code>/* 要素 `_num` の第 k 桁を取得する。ここで `exp = 10^(k-1)` */\nint digit(int _num, int exp) {\n  // ここで高コストな累乗計算を繰り返さないよう、k ではなく exp を渡す\n  return (_num ~/ exp) % 10;\n}\n\n/* 計数ソート（nums の k 桁目でソート） */\nvoid countingSortDigit(List&lt;int&gt; nums, int exp) {\n  // 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要\n  List&lt;int&gt; counter = List&lt;int&gt;.filled(10, 0);\n  int n = nums.length;\n  // 0~9 の各数字の出現回数を集計する\n  for (int i = 0; i &lt; n; i++) {\n    int d = digit(nums[i], exp); // nums[i] の第 k 位を取得し、d とする\n    counter[d]++; // 数字 d の出現回数を数える\n  }\n  // 累積和を求め、「出現回数」を「配列インデックス」に変換する\n  for (int i = 1; i &lt; 10; i++) {\n    counter[i] += counter[i - 1];\n  }\n  // 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する\n  List&lt;int&gt; res = List&lt;int&gt;.filled(n, 0);\n  for (int i = n - 1; i &gt;= 0; i--) {\n    int d = digit(nums[i], exp);\n    int j = counter[d] - 1; // d の配列内インデックス j を取得する\n    res[j] = nums[i]; // 現在の要素をインデックス j に格納する\n    counter[d]--; // d の個数を 1 減らす\n  }\n  // 結果で元の配列 nums を上書きする\n  for (int i = 0; i &lt; n; i++) nums[i] = res[i];\n}\n\n/* 基数ソート */\nvoid radixSort(List&lt;int&gt; nums) {\n  // 最大桁数の判定用に配列の最大要素を取得する\n  // dart の `int` の長さは 64 ビット\n  int m = -1 &lt;&lt; 63;\n  for (int _num in nums) if (_num &gt; m) m = _num;\n  // 下位桁から上位桁の順に走査する\n  for (int exp = 1; exp &lt;= m; exp *= 10)\n    // 配列要素の k 桁目に対して計数ソートを行う\n    // k = 1 -&gt; exp = 1\n    // k = 2 -&gt; exp = 10\n    // つまり exp = 10^(k-1)\n    countingSortDigit(nums, exp);\n}\n</code></pre> radix_sort.rs<pre><code>/* 要素 num の下から k 桁目を取得（exp = 10^(k-1)） */\nfn digit(num: i32, exp: i32) -&gt; usize {\n    // ここで高コストな累乗計算を繰り返さないよう、k ではなく exp を渡す\n    return ((num / exp) % 10) as usize;\n}\n\n/* 計数ソート（nums の k 桁目でソート） */\nfn counting_sort_digit(nums: &amp;mut [i32], exp: i32) {\n    // 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要\n    let mut counter = [0; 10];\n    let n = nums.len();\n    // 0~9 の各数字の出現回数を集計する\n    for i in 0..n {\n        let d = digit(nums[i], exp); // nums[i] の第 k 位を取得し、d とする\n        counter[d] += 1; // 数字 d の出現回数を数える\n    }\n    // 累積和を求め、「出現回数」を「配列インデックス」に変換する\n    for i in 1..10 {\n        counter[i] += counter[i - 1];\n    }\n    // 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する\n    let mut res = vec![0; n];\n    for i in (0..n).rev() {\n        let d = digit(nums[i], exp);\n        let j = counter[d] - 1; // d の配列内インデックス j を取得する\n        res[j] = nums[i]; // 現在の要素をインデックス j に格納する\n        counter[d] -= 1; // d の個数を 1 減らす\n    }\n    // 結果で元の配列 nums を上書きする\n    nums.copy_from_slice(&amp;res);\n}\n\n/* 基数ソート */\nfn radix_sort(nums: &amp;mut [i32]) {\n    // 最大桁数の判定用に配列の最大要素を取得\n    let m = *nums.into_iter().max().unwrap();\n    // 下位桁から上位桁の順に走査する\n    let mut exp = 1;\n    while exp &lt;= m {\n        counting_sort_digit(nums, exp);\n        exp *= 10;\n    }\n}\n</code></pre> radix_sort.c<pre><code>/* 要素 num の下から k 桁目を取得（exp = 10^(k-1)） */\nint digit(int num, int exp) {\n    // ここで高コストな累乗計算を繰り返さないよう、k ではなく exp を渡す\n    return (num / exp) % 10;\n}\n\n/* 計数ソート（nums の k 桁目でソート） */\nvoid countingSortDigit(int nums[], int size, int exp) {\n    // 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要\n    int *counter = (int *)malloc((sizeof(int) * 10));\n    memset(counter, 0, sizeof(int) * 10); // 後続のメモリ解放に備えて 0 で初期化する\n    // 0~9 の各数字の出現回数を集計する\n    for (int i = 0; i &lt; size; i++) {\n        // nums[i] の第 k 位を取得し、d とする\n        int d = digit(nums[i], exp);\n        // 数字 d の出現回数を数える\n        counter[d]++;\n    }\n    // 累積和を求め、「出現回数」を「配列インデックス」に変換する\n    for (int i = 1; i &lt; 10; i++) {\n        counter[i] += counter[i - 1];\n    }\n    // 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する\n    int *res = (int *)malloc(sizeof(int) * size);\n    for (int i = size - 1; i &gt;= 0; i--) {\n        int d = digit(nums[i], exp);\n        int j = counter[d] - 1; // d の配列内インデックス j を取得する\n        res[j] = nums[i];       // 現在の要素をインデックス j に格納する\n        counter[d]--;           // d の個数を 1 減らす\n    }\n    // 結果で元の配列 nums を上書きする\n    for (int i = 0; i &lt; size; i++) {\n        nums[i] = res[i];\n    }\n    // メモリを解放する\n    free(res);\n    free(counter);\n}\n\n/* 基数ソート */\nvoid radixSort(int nums[], int size) {\n    // 最大桁数の判定用に配列の最大要素を取得\n    int max = INT32_MIN;\n    for (int i = 0; i &lt; size; i++) {\n        if (nums[i] &gt; max) {\n            max = nums[i];\n        }\n    }\n    // 下位桁から上位桁の順に走査する\n    for (int exp = 1; max &gt;= exp; exp *= 10)\n        // 配列要素の k 桁目に対して計数ソートを行う\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // つまり exp = 10^(k-1)\n        countingSortDigit(nums, size, exp);\n}\n</code></pre> radix_sort.kt<pre><code>/* 要素 num の下から k 桁目を取得（exp = 10^(k-1)） */\nfun digit(num: Int, exp: Int): Int {\n    // ここで高コストな累乗計算を繰り返さないよう、k ではなく exp を渡す\n    return (num / exp) % 10\n}\n\n/* 計数ソート（nums の k 桁目でソート） */\nfun countingSortDigit(nums: IntArray, exp: Int) {\n    // 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要\n    val counter = IntArray(10)\n    val n = nums.size\n    // 0~9 の各数字の出現回数を集計する\n    for (i in 0..&lt;n) {\n        val d = digit(nums[i], exp) // nums[i] の第 k 位を取得し、d とする\n        counter[d]++                // 数字 d の出現回数を数える\n    }\n    // 累積和を求め、「出現回数」を「配列インデックス」に変換する\n    for (i in 1..9) {\n        counter[i] += counter[i - 1]\n    }\n    // 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する\n    val res = IntArray(n)\n    for (i in n - 1 downTo 0) {\n        val d = digit(nums[i], exp)\n        val j = counter[d] - 1 // d の配列内インデックス j を取得する\n        res[j] = nums[i]       // 現在の要素をインデックス j に格納する\n        counter[d]--           // d の個数を 1 減らす\n    }\n    // 結果で元の配列 nums を上書きする\n    for (i in 0..&lt;n)\n        nums[i] = res[i]\n}\n\n/* 基数ソート */\nfun radixSort(nums: IntArray) {\n    // 最大桁数の判定用に配列の最大要素を取得\n    var m = Int.MIN_VALUE\n    for (num in nums) if (num &gt; m) m = num\n    var exp = 1\n    // 下位桁から上位桁の順に走査する\n    while (exp &lt;= m) {\n        // 配列要素の k 桁目に対して計数ソートを行う\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // つまり exp = 10^(k-1)\n        countingSortDigit(nums, exp)\n        exp *= 10\n    }\n}\n</code></pre> radix_sort.rb<pre><code>### num の第 k 桁を取得する。ここで exp = 10^(k-1) ###\ndef digit(num, exp)\n  # k ではなく exp を渡すことで、ここで高コストな累乗計算を繰り返し実行するのを避けられる\n  (num / exp) % 10\nend\n\n### num の第 k 桁を取得する。ここで exp = 10^(k-1) ###\ndef digit(num, exp)\n  # k ではなく exp を渡すことで、ここで高コストな累乗計算を繰り返し実行するのを避けられる\n  (num / exp) % 10\nend\n\n# ## 計数ソート（nums の k 桁目でソート）###\ndef counting_sort_digit(nums, exp)\n  # 10 進数の各桁は 0~9 の範囲なので、長さ 10 のバケット配列が必要\n  counter = Array.new(10, 0)\n  n = nums.length\n  # 0~9 の各数字の出現回数を集計する\n  for i in 0...n\n    d = digit(nums[i], exp) # nums[i] の第 k 位を取得し、d とする\n    counter[d] += 1 # 数字 d の出現回数を数える\n  end\n  # 累積和を求め、「出現回数」を「配列インデックス」に変換する\n  (1...10).each { |i| counter[i] += counter[i - 1] }\n  # 逆順に走査し、バケット内の集計結果に従って各要素を res に格納する\n  res = Array.new(n, 0)\n  for i in (n - 1).downto(0)\n    d = digit(nums[i], exp)\n    j = counter[d] - 1 # d の配列内インデックス j を取得する\n    res[j] = nums[i] # 現在の要素をインデックス j に格納する\n    counter[d] -= 1 # d の個数を 1 減らす\n  end\n  # 結果で元の配列 nums を上書きする\n  (0...n).each { |i| nums[i] = res[i] }\nend\n\n### 基数ソート ###\ndef radix_sort(nums)\n  # 最大桁数の判定用に配列の最大要素を取得\n  m = nums.max\n  # 下位桁から上位桁の順に走査する\n  exp = 1\n  while exp &lt;= m\n    # 配列要素の k 桁目に対して計数ソートを行う\n    # k = 1 -&gt; exp = 1\n    # k = 2 -&gt; exp = 10\n    # つまり exp = 10^(k-1)\n    counting_sort_digit(nums, exp)\n    exp *= 10\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>なぜ最下位桁からソートするのですか？</p> <p>連続するソートの各ラウンドでは、後のラウンドの結果が前のラウンドの結果を上書きします。たとえば、第1ラウンドで \\(a &lt; b\\) となっていても、第2ラウンドで \\(a &gt; b\\) となれば、第2ラウンドの結果が優先されます。数字では高位の優先度が低位より高いため、先に低位をソートし、その後で高位をソートする必要があります。</p>","path":["第 11 章 &nbsp; ソート","11.10 &nbsp; 基数ソート"],"tags":[]},{"location":"chapter_sorting/radix_sort/#11102","level":2,"title":"11.10.2   アルゴリズムの特徴","text":"<p>計数ソートと比べると、基数ソートは値の範囲が大きい場合に適しています。ただし、データが固定桁数の形式で表せること、かつ桁数が大きすぎないことが前提です。たとえば、浮動小数点数は基数ソートに適していません。桁数 \\(k\\) が大きすぎて、時間計算量が \\(O(nk) \\gg O(n^2)\\) になる可能性があるためです。</p> <ul> <li>時間計算量は \\(O(nk)\\)、非適応ソート：データ量を \\(n\\)、データが \\(d\\) 進数、最大桁数を \\(k\\) とすると、ある1桁に対して計数ソートを実行する時間は \\(O(n + d)\\) であり、全 \\(k\\) 桁をソートする時間は \\(O((n + d)k)\\) です。通常、\\(d\\) と \\(k\\) はどちらも比較的小さいため、時間計算量は \\(O(n)\\) に近づきます。</li> <li>空間計算量は \\(O(n + d)\\)、非原地ソート：計数ソートと同様に、基数ソートでは長さ \\(n\\) と \\(d\\) の配列 <code>res</code> と <code>counter</code> を補助的に用います。</li> <li>安定ソート：計数ソートが安定であれば基数ソートも安定です。計数ソートが不安定な場合、基数ソートでは正しいソート結果を保証できません。</li> </ul>","path":["第 11 章 &nbsp; ソート","11.10 &nbsp; 基数ソート"],"tags":[]},{"location":"chapter_sorting/selection_sort/","level":1,"title":"11.2   選択ソート","text":"<p>選択ソート（selection sort）の仕組みは非常に単純です。ループを開始し、各ラウンドで未ソート区間から最小の要素を選び、整列済み区間の末尾に配置します。</p> <p>配列の長さを \\(n\\) とすると、選択ソートの手順は次の図のようになります。</p> <ol> <li>初期状態では、すべての要素が未ソートであり、未ソートな（インデックス）区間は \\([0, n-1]\\) です。</li> <li>区間 \\([0, n-1]\\) 内の最小要素を選び、インデックス \\(0\\) の要素と交換します。これにより、配列の先頭 1 要素が整列済みになります。</li> <li>区間 \\([1, n-1]\\) 内の最小要素を選び、インデックス \\(1\\) の要素と交換します。これにより、配列の先頭 2 要素が整列済みになります。</li> <li>これを繰り返します。\\(n - 1\\) 回の選択と交換を経ると、配列の先頭 \\(n - 1\\) 要素が整列済みになります。</li> <li>残った 1 つの要素は必ず最大要素なので、ソートは不要です。これで配列のソートは完了します。</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 11-2   選択ソートの手順 </p> <p>コードでは、\\(k\\) を用いて未ソート区間内の最小要素を記録します。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby selection_sort.py<pre><code>def selection_sort(nums: list[int]):\n    \"\"\"選択ソート\"\"\"\n    n = len(nums)\n    # 外側ループ：未整列区間は [i, n-1]\n    for i in range(n - 1):\n        # 内側のループ：未ソート区間の最小要素を見つける\n        k = i\n        for j in range(i + 1, n):\n            if nums[j] &lt; nums[k]:\n                k = j  # 最小要素のインデックスを記録\n        # その最小要素を未整列区間の先頭要素と交換する\n        nums[i], nums[k] = nums[k], nums[i]\n</code></pre> selection_sort.cpp<pre><code>/* 選択ソート */\nvoid selectionSort(vector&lt;int&gt; &amp;nums) {\n    int n = nums.size();\n    // 外側ループ：未整列区間は [i, n-1]\n    for (int i = 0; i &lt; n - 1; i++) {\n        // 内側のループ：未ソート区間の最小要素を見つける\n        int k = i;\n        for (int j = i + 1; j &lt; n; j++) {\n            if (nums[j] &lt; nums[k])\n                k = j; // 最小要素のインデックスを記録\n        }\n        // その最小要素を未整列区間の先頭要素と交換する\n        swap(nums[i], nums[k]);\n    }\n}\n</code></pre> selection_sort.java<pre><code>/* 選択ソート */\nvoid selectionSort(int[] nums) {\n    int n = nums.length;\n    // 外側ループ：未整列区間は [i, n-1]\n    for (int i = 0; i &lt; n - 1; i++) {\n        // 内側のループ：未ソート区間の最小要素を見つける\n        int k = i;\n        for (int j = i + 1; j &lt; n; j++) {\n            if (nums[j] &lt; nums[k])\n                k = j; // 最小要素のインデックスを記録\n        }\n        // その最小要素を未整列区間の先頭要素と交換する\n        int temp = nums[i];\n        nums[i] = nums[k];\n        nums[k] = temp;\n    }\n}\n</code></pre> selection_sort.cs<pre><code>/* 選択ソート */\nvoid SelectionSort(int[] nums) {\n    int n = nums.Length;\n    // 外側ループ：未整列区間は [i, n-1]\n    for (int i = 0; i &lt; n - 1; i++) {\n        // 内側のループ：未ソート区間の最小要素を見つける\n        int k = i;\n        for (int j = i + 1; j &lt; n; j++) {\n            if (nums[j] &lt; nums[k])\n                k = j; // 最小要素のインデックスを記録\n        }\n        // その最小要素を未整列区間の先頭要素と交換する\n        (nums[k], nums[i]) = (nums[i], nums[k]);\n    }\n}\n</code></pre> selection_sort.go<pre><code>/* 選択ソート */\nfunc selectionSort(nums []int) {\n    n := len(nums)\n    // 外側ループ：未整列区間は [i, n-1]\n    for i := 0; i &lt; n-1; i++ {\n        // 内側のループ：未ソート区間の最小要素を見つける\n        k := i\n        for j := i + 1; j &lt; n; j++ {\n            if nums[j] &lt; nums[k] {\n                // 最小要素のインデックスを記録\n                k = j\n            }\n        }\n        // その最小要素を未整列区間の先頭要素と交換する\n        nums[i], nums[k] = nums[k], nums[i]\n\n    }\n}\n</code></pre> selection_sort.swift<pre><code>/* 選択ソート */\nfunc selectionSort(nums: inout [Int]) {\n    // 外側ループ：未整列区間は [i, n-1]\n    for i in nums.indices.dropLast() {\n        // 内側のループ：未ソート区間の最小要素を見つける\n        var k = i\n        for j in nums.indices.dropFirst(i + 1) {\n            if nums[j] &lt; nums[k] {\n                k = j // 最小要素のインデックスを記録\n            }\n        }\n        // その最小要素を未整列区間の先頭要素と交換する\n        nums.swapAt(i, k)\n    }\n}\n</code></pre> selection_sort.js<pre><code>/* 選択ソート */\nfunction selectionSort(nums) {\n    let n = nums.length;\n    // 外側ループ：未整列区間は [i, n-1]\n    for (let i = 0; i &lt; n - 1; i++) {\n        // 内側のループ：未ソート区間の最小要素を見つける\n        let k = i;\n        for (let j = i + 1; j &lt; n; j++) {\n            if (nums[j] &lt; nums[k]) {\n                k = j; // 最小要素のインデックスを記録\n            }\n        }\n        // その最小要素を未整列区間の先頭要素と交換する\n        [nums[i], nums[k]] = [nums[k], nums[i]];\n    }\n}\n</code></pre> selection_sort.ts<pre><code>/* 選択ソート */\nfunction selectionSort(nums: number[]): void {\n    let n = nums.length;\n    // 外側ループ：未整列区間は [i, n-1]\n    for (let i = 0; i &lt; n - 1; i++) {\n        // 内側のループ：未ソート区間の最小要素を見つける\n        let k = i;\n        for (let j = i + 1; j &lt; n; j++) {\n            if (nums[j] &lt; nums[k]) {\n                k = j; // 最小要素のインデックスを記録\n            }\n        }\n        // その最小要素を未整列区間の先頭要素と交換する\n        [nums[i], nums[k]] = [nums[k], nums[i]];\n    }\n}\n</code></pre> selection_sort.dart<pre><code>/* 選択ソート */\nvoid selectionSort(List&lt;int&gt; nums) {\n  int n = nums.length;\n  // 外側ループ：未整列区間は [i, n-1]\n  for (int i = 0; i &lt; n - 1; i++) {\n    // 内側のループ：未ソート区間の最小要素を見つける\n    int k = i;\n    for (int j = i + 1; j &lt; n; j++) {\n      if (nums[j] &lt; nums[k]) k = j; // 最小要素のインデックスを記録\n    }\n    // その最小要素を未整列区間の先頭要素と交換する\n    int temp = nums[i];\n    nums[i] = nums[k];\n    nums[k] = temp;\n  }\n}\n</code></pre> selection_sort.rs<pre><code>/* 選択ソート */\nfn selection_sort(nums: &amp;mut [i32]) {\n    if nums.is_empty() {\n        return;\n    }\n    let n = nums.len();\n    // 外側ループ：未整列区間は [i, n-1]\n    for i in 0..n - 1 {\n        // 内側のループ：未ソート区間の最小要素を見つける\n        let mut k = i;\n        for j in i + 1..n {\n            if nums[j] &lt; nums[k] {\n                k = j; // 最小要素のインデックスを記録\n            }\n        }\n        // その最小要素を未整列区間の先頭要素と交換する\n        nums.swap(i, k);\n    }\n}\n</code></pre> selection_sort.c<pre><code>/* 選択ソート */\nvoid selectionSort(int nums[], int n) {\n    // 外側ループ：未整列区間は [i, n-1]\n    for (int i = 0; i &lt; n - 1; i++) {\n        // 内側のループ：未ソート区間の最小要素を見つける\n        int k = i;\n        for (int j = i + 1; j &lt; n; j++) {\n            if (nums[j] &lt; nums[k])\n                k = j; // 最小要素のインデックスを記録\n        }\n        // その最小要素を未整列区間の先頭要素と交換する\n        int temp = nums[i];\n        nums[i] = nums[k];\n        nums[k] = temp;\n    }\n}\n</code></pre> selection_sort.kt<pre><code>/* 選択ソート */\nfun selectionSort(nums: IntArray) {\n    val n = nums.size\n    // 外側ループ：未整列区間は [i, n-1]\n    for (i in 0..&lt;n - 1) {\n        var k = i\n        // 内側のループ：未ソート区間の最小要素を見つける\n        for (j in i + 1..&lt;n) {\n            if (nums[j] &lt; nums[k])\n                k = j // 最小要素のインデックスを記録\n        }\n        // その最小要素を未整列区間の先頭要素と交換する\n        val temp = nums[i]\n        nums[i] = nums[k]\n        nums[k] = temp\n    }\n}\n</code></pre> selection_sort.rb<pre><code>### 選択ソート ###\ndef selection_sort(nums)\n  n = nums.length\n  # 外側ループ：未整列区間は [i, n-1]\n  for i in 0...(n - 1)\n    # 内側のループ：未ソート区間の最小要素を見つける\n    k = i\n    for j in (i + 1)...n\n      if nums[j] &lt; nums[k]\n        k = j # 最小要素のインデックスを記録\n      end\n    end\n    # その最小要素を未整列区間の先頭要素と交換する\n    nums[i], nums[k] = nums[k], nums[i]\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 11 章 &nbsp; ソート","11.2 &nbsp; 選択ソート"],"tags":[]},{"location":"chapter_sorting/selection_sort/#1121","level":2,"title":"11.2.1   アルゴリズムの特徴","text":"<ul> <li>時間計算量は \\(O(n^2)\\)、非適応ソート：外側のループは合計 \\(n - 1\\) 回です。最初のラウンドの未ソート区間の長さは \\(n\\)、最後のラウンドでは \\(2\\) であり、各ラウンドの内側のループ回数はそれぞれ \\(n\\)、\\(n - 1\\)、\\(\\dots\\)、\\(3\\)、\\(2\\) となります。総和は \\(\\frac{(n - 1)(n + 2)}{2}\\) です。</li> <li>空間計算量は \\(O(1)\\)、インプレースソート：ポインタ \\(i\\) と \\(j\\) は定数サイズの追加領域しか使用しません。</li> <li>不安定ソート：次の図のように、要素 <code>nums[i]</code> がそれと等しい要素の右側へ交換され、両者の相対的な順序が変わる可能性があります。</li> </ul> <p> 図 11-3   選択ソートの不安定な例 </p>","path":["第 11 章 &nbsp; ソート","11.2 &nbsp; 選択ソート"],"tags":[]},{"location":"chapter_sorting/sorting_algorithm/","level":1,"title":"11.1   ソートアルゴリズム","text":"<p>ソートアルゴリズム（sorting algorithm）は、データの集合を特定の順序に従って並べ替えるために用いられます。ソートアルゴリズムは幅広く応用されており、整列済みデータは通常、より効率的に検索、分析、処理できるためです。</p> <p>下図に示すように、ソートアルゴリズムにおけるデータ型は整数、浮動小数点数、文字、文字列などです。ソートの判定規則は、数値の大小、文字の ASCII コード順、またはカスタムルールなど、要件に応じて設定できます。</p> <p></p> <p> 図 11-1   データ型と判定規則の例 </p>","path":["第 11 章 &nbsp; ソート","11.1 &nbsp; ソートアルゴリズム"],"tags":[]},{"location":"chapter_sorting/sorting_algorithm/#1111","level":2,"title":"11.1.1   評価軸","text":"<p>実行効率：ソートアルゴリズムの時間計算量はできるだけ低く、かつ全体の操作回数も少ないこと（時間計算量における定数項が小さいこと）が望まれます。大量データの場合、実行効率はとりわけ重要です。</p> <p>インプレース性：その名のとおり、インプレースソートは元の配列を直接操作して並べ替えを行うため、追加の補助配列を必要とせず、メモリを節約できます。通常、インプレースソートはデータの移動操作が少なく、実行速度もより高速です。</p> <p>安定性：安定ソートは、並べ替え完了後も、等しい要素の配列内での相対順序が変化しません。</p> <p>安定ソートは多段ソートの場面で必要条件となります。学生情報を保存した表があり、第 1 列と第 2 列がそれぞれ氏名と年齢であると仮定します。この場合、不安定ソートによって入力データの順序性が失われる可能性があります。</p> <pre><code># 入力データは氏名順にソートされている\n# (name, age)\n  ('A', 19)\n  ('B', 18)\n  ('C', 21)\n  ('D', 19)\n  ('E', 23)\n\n# 不安定ソートアルゴリズムで年齢順にリストを並べ替えると仮定すると、\n# 結果では ('D', 19) と ('A', 19) の相対位置が変わり、\n# 入力データが氏名順である性質が失われる\n  ('B', 18)\n  ('D', 19)\n  ('A', 19)\n  ('C', 21)\n  ('E', 23)\n</code></pre> <p>適応性：適応的ソートは、入力データに既に存在する順序情報を利用して計算量を減らし、より優れた時間効率を実現できます。適応的ソートアルゴリズムの最良時間計算量は、通常、平均時間計算量より優れています。</p> <p>比較ベースかどうか：比較ベースのソートは、比較演算子（\\(&lt;\\)、\\(=\\)、\\(&gt;\\)）に依存して要素の相対順序を判定し、それによって配列全体をソートします。理論上の最良時間計算量は \\(O(n \\log n)\\) です。一方、非比較ソートは比較演算子を使用せず、時間計算量は \\(O(n)\\) に達しますが、汎用性は相対的に低くなります。</p>","path":["第 11 章 &nbsp; ソート","11.1 &nbsp; ソートアルゴリズム"],"tags":[]},{"location":"chapter_sorting/sorting_algorithm/#1112","level":2,"title":"11.1.2   理想的なソートアルゴリズム","text":"<p>高速、インプレース、安定、適応的、高い汎用性。明らかに、これまでのところ、以上のすべての特性を兼ね備えたソートアルゴリズムはまだ見つかっていません。そのため、ソートアルゴリズムを選択する際には、具体的なデータの特徴と問題の要件に応じて判断する必要があります。</p> <p>次に、さまざまなソートアルゴリズムを一緒に学び、上記の評価軸に基づいて各ソートアルゴリズムの長所と短所を分析していきます。</p>","path":["第 11 章 &nbsp; ソート","11.1 &nbsp; ソートアルゴリズム"],"tags":[]},{"location":"chapter_sorting/summary/","level":1,"title":"11.11   まとめ","text":"","path":["第 11 章 &nbsp; ソート","11.11 &nbsp; まとめ"],"tags":[]},{"location":"chapter_sorting/summary/#1","level":3,"title":"1.   重要なポイントの振り返り","text":"<ul> <li>バブルソートは隣接する要素を交換することで整列を行います。フラグを追加して早期リターンを可能にすると、バブルソートの最良時間計算量を \\(O(n)\\) に最適化できます。</li> <li>挿入ソートは各ラウンドで未整列区間の要素を整列済み区間の正しい位置に挿入することで整列を完了します。挿入ソートの時間計算量は \\(O(n^2)\\) ですが、基本操作が比較的少ないため、小規模データのソート処理で非常に人気があります。</li> <li>クイックソートは番兵分割操作に基づいて整列を行います。番兵分割では毎回最悪の基準値を選んでしまう可能性があり、その結果、時間計算量は \\(O(n^2)\\) まで劣化することがあります。中央値の基準値やランダムな基準値を導入すると、この劣化の確率を下げられます。短い部分配列を優先して再帰すれば、再帰の深さを効果的に抑え、空間計算量を \\(O(\\log n)\\) に最適化できます。</li> <li>マージソートは分割とマージという 2 つの段階からなり、分割統治戦略を典型的に体現しています。マージソートでは配列を整列する際に補助配列の作成が必要で、空間計算量は \\(O(n)\\) です。一方、連結リストを整列する場合の空間計算量は \\(O(1)\\) まで最適化できます。</li> <li>バケットソートはデータのバケット分配、バケット内ソート、結果の結合という 3 つの手順を含みます。これも分割統治戦略を体現しており、データ量が非常に大きい場合に適しています。バケットソートの鍵は、データを平均的に分配することにあります。</li> <li>カウントソートはバケットソートの特例であり、データの出現回数を数えることで整列を行います。カウントソートはデータ量が大きく、かつデータ範囲が限られている場合に適しており、データを正の整数に変換できることが前提です。</li> <li>基数ソートは各桁ごとの整列によってデータを整列し、データが固定桁数の数値として表せることを前提とします。</li> <li>総じて言えば、私たちは高効率で、安定で、インプレースで、さらに適応的であるといった利点を備えたソートアルゴリズムを見つけたいと考えます。しかし、ほかのデータ構造やアルゴリズムと同様に、これらすべての条件を同時に満たせるソートアルゴリズムは存在しません。実際の応用では、データの特性に応じて適切なソートアルゴリズムを選ぶ必要があります。</li> <li>下図では、主流のソートアルゴリズムについて、効率、安定性、インプレース性、適応性などを比較しています。</li> </ul> <p> 図 11-19   ソートアルゴリズムの比較 </p>","path":["第 11 章 &nbsp; ソート","11.11 &nbsp; まとめ"],"tags":[]},{"location":"chapter_sorting/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q：ソートアルゴリズムの安定性は、どのような場合に必須ですか？</p> <p>現実には、オブジェクトのある属性に基づいて整列することがあります。たとえば、学生には氏名と身長という 2 つの属性があり、多段階のソートを行いたいとします。まず氏名で整列して <code>(A, 180) (B, 185) (C, 170) (D, 170)</code> を得て、その後に身長で整列します。ソートアルゴリズムが不安定である場合、結果は <code>(D, 170) (C, 170) (A, 180) (B, 185)</code> になる可能性があります。</p> <p>このように、学生 D と C の位置が入れ替わり、氏名に関する順序性が壊れてしまいます。これは望ましくありません。</p> <p>Q：番兵分割において、「右から左へ探索する」順序と「左から右へ探索する」順序は入れ替えられますか？</p> <p>できません。最も左端の要素を基準値とする場合は、必ず先に「右から左へ探索する」を行い、その後に「左から右へ探索する」を行う必要があります。この結論はやや直感に反するので、理由を分析してみましょう。</p> <p>番兵分割 <code>partition()</code> の最後の手順は、<code>nums[left]</code> と <code>nums[i]</code> を交換することです。交換が終わると、基準値の左側にある要素はすべて基準値 <code>&lt;=</code> になります。したがって、最後の交換の前に <code>nums[left] &gt;= nums[i]</code> が必ず成り立っていなければなりません。仮に先に「左から右へ探索する」を行うと、基準値より大きい要素が見つからない場合、<code>i == j</code> の時点でループを抜け、このとき <code>nums[j] == nums[i] &gt; nums[left]</code> となる可能性があります。つまり、この最後の交換によって、基準値より大きい要素が配列の最左端へ移されてしまい、番兵分割は失敗します。</p> <p>たとえば、配列 <code>[0, 0, 0, 0, 1]</code> が与えられたとき、先に「左から右へ探索する」を行うと、番兵分割後の配列は <code>[1, 0, 0, 0, 0]</code> になります。これは誤った結果です。</p> <p>さらに考えると、<code>nums[right]</code> を基準値に選ぶ場合はちょうど逆になり、必ず先に「左から右へ探索する」を行う必要があります。</p> <p>Q：クイックソートの再帰深度最適化について、短い配列を選ぶとなぜ再帰深度が \\(\\log n\\) を超えないと保証できるのですか？</p> <p>再帰深度とは、現在まだ戻っていない再帰呼び出しの数のことです。各ラウンドの番兵分割では、元の配列を 2 つの部分配列に分けます。再帰深度の最適化後は、下方向に再帰する部分配列の長さは最大でも元の配列長の半分です。最悪の場合でも毎回半分の長さになると仮定すれば、最終的な再帰深度は \\(\\log n\\) になります。</p> <p>元のクイックソートを振り返ると、長いほうの配列に対して連続して再帰してしまう可能性があり、最悪の場合は \\(n\\)、\\(n - 1\\)、\\(\\dots\\)、\\(2\\)、\\(1\\) と続き、再帰深度は \\(n\\) になります。再帰深度の最適化により、このような状況を避けられます。</p> <p>Q：配列内のすべての要素が等しい場合、クイックソートの時間計算量は \\(O(n^2)\\) になりますか？このような退化はどう処理すべきですか？</p> <p>はい。この場合は、番兵分割によって配列を「基準値より小さい」「基準値に等しい」「基準値より大きい」の 3 つの部分に分ける方法を検討できます。下方向に再帰するのは、小さい部分と大きい部分だけです。この方法では、入力要素がすべて等しい配列は、1 回の番兵分割だけで整列を完了できます。</p> <p>Q：バケットソートの最悪時間計算量が \\(O(n^2)\\) なのはなぜですか？</p> <p>最悪の場合、すべての要素が同じバケットに振り分けられます。その要素群を整列するのに \\(O(n^2)\\) のアルゴリズムを使えば、時間計算量は \\(O(n^2)\\) になります。</p>","path":["第 11 章 &nbsp; ソート","11.11 &nbsp; まとめ"],"tags":[]},{"location":"chapter_stack_and_queue/","level":1,"title":"第 5 章   スタックとキュー","text":"<p>Abstract</p> <p>スタックは猫を積み重ねるようなもので、キューは猫が列に並ぶようなものです。</p> <p>両者はそれぞれ、後入れ先出しと先入れ先出しの論理関係を表します。</p>","path":["第 5 章 &nbsp; スタックとキュー"],"tags":[]},{"location":"chapter_stack_and_queue/#_1","level":2,"title":"章の内容","text":"<ul> <li>5.1   スタック</li> <li>5.2   キュー</li> <li>5.3   両端キュー</li> <li>5.4   まとめ</li> </ul>","path":["第 5 章 &nbsp; スタックとキュー"],"tags":[]},{"location":"chapter_stack_and_queue/deque/","level":1,"title":"5.3   両端キュー","text":"<p>キューでは、先頭要素を削除するか末尾に要素を追加することしかできません。次の図に示すように、両端キュー（double-ended queue）はより高い柔軟性を備えており、先頭と末尾の両方で要素の追加や削除を行えます。</p> <p></p> <p> 図 5-7   両端キューの操作 </p>","path":["第 5 章 &nbsp; スタックとキュー","5.3 &nbsp; 両端キュー"],"tags":[]},{"location":"chapter_stack_and_queue/deque/#531","level":2,"title":"5.3.1   両端キューの基本操作","text":"<p>両端キューの基本操作を次の表に示します。具体的なメソッド名は、使用するプログラミング言語によって異なります。</p> <p> 表 5-3   両端キューの操作効率 </p> メソッド名 説明 時間計算量 <code>push_first()</code> 先頭に要素を追加 \\(O(1)\\) <code>push_last()</code> 末尾に要素を追加 \\(O(1)\\) <code>pop_first()</code> 先頭要素を削除 \\(O(1)\\) <code>pop_last()</code> 末尾要素を削除 \\(O(1)\\) <code>peek_first()</code> 先頭要素にアクセス \\(O(1)\\) <code>peek_last()</code> 末尾要素にアクセス \\(O(1)\\) <p>同様に、プログラミング言語に組み込み実装されている両端キューのクラスを直接使うこともできます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby deque.py<pre><code>from collections import deque\n\n# 両端キューを初期化\ndeq: deque[int] = deque()\n\n# 要素をエンキュー\ndeq.append(2)      # 末尾に追加\ndeq.append(5)\ndeq.append(4)\ndeq.appendleft(3)  # 先頭に追加\ndeq.appendleft(1)\n\n# 要素にアクセス\nfront: int = deq[0]  # 先頭要素\nrear: int = deq[-1]  # 末尾要素\n\n# 要素をデキュー\npop_front: int = deq.popleft()  # 先頭要素をデキュー\npop_rear: int = deq.pop()       # 末尾要素をデキュー\n\n# 両端キューの長さを取得\nsize: int = len(deq)\n\n# 両端キューが空かどうかを判定\nis_empty: bool = len(deq) == 0\n</code></pre> deque.cpp<pre><code>/* 両端キューを初期化 */\ndeque&lt;int&gt; deque;\n\n/* 要素をエンキュー */\ndeque.push_back(2);   // 末尾に追加\ndeque.push_back(5);\ndeque.push_back(4);\ndeque.push_front(3);  // 先頭に追加\ndeque.push_front(1);\n\n/* 要素にアクセス */\nint front = deque.front(); // 先頭要素\nint back = deque.back();   // 末尾要素\n\n/* 要素をデキュー */\ndeque.pop_front();  // 先頭要素をデキュー\ndeque.pop_back();   // 末尾要素をデキュー\n\n/* 両端キューの長さを取得 */\nint size = deque.size();\n\n/* 両端キューが空かどうかを判定 */\nbool empty = deque.empty();\n</code></pre> deque.java<pre><code>/* 両端キューを初期化 */\nDeque&lt;Integer&gt; deque = new LinkedList&lt;&gt;();\n\n/* 要素をエンキュー */\ndeque.offerLast(2);   // 末尾に追加\ndeque.offerLast(5);\ndeque.offerLast(4);\ndeque.offerFirst(3);  // 先頭に追加\ndeque.offerFirst(1);\n\n/* 要素にアクセス */\nint peekFirst = deque.peekFirst();  // 先頭要素\nint peekLast = deque.peekLast();    // 末尾要素\n\n/* 要素をデキュー */\nint popFirst = deque.pollFirst();  // 先頭要素をデキュー\nint popLast = deque.pollLast();    // 末尾要素をデキュー\n\n/* 両端キューの長さを取得 */\nint size = deque.size();\n\n/* 両端キューが空かどうかを判定 */\nboolean isEmpty = deque.isEmpty();\n</code></pre> deque.cs<pre><code>/* 両端キューを初期化 */\n// C# では、連結リスト LinkedList を両端キューとして使用する\nLinkedList&lt;int&gt; deque = new();\n\n/* 要素をエンキュー */\ndeque.AddLast(2);   // 末尾に追加\ndeque.AddLast(5);\ndeque.AddLast(4);\ndeque.AddFirst(3);  // 先頭に追加\ndeque.AddFirst(1);\n\n/* 要素にアクセス */\nint peekFirst = deque.First.Value;  // 先頭要素\nint peekLast = deque.Last.Value;    // 末尾要素\n\n/* 要素をデキュー */\ndeque.RemoveFirst();  // 先頭要素をデキュー\ndeque.RemoveLast();   // 末尾要素をデキュー\n\n/* 両端キューの長さを取得 */\nint size = deque.Count;\n\n/* 両端キューが空かどうかを判定 */\nbool isEmpty = deque.Count == 0;\n</code></pre> deque_test.go<pre><code>/* 両端キューを初期化 */\n// Go では、list を両端キューとして使用する\ndeque := list.New()\n\n/* 要素をエンキュー */\ndeque.PushBack(2)      // 末尾に追加\ndeque.PushBack(5)\ndeque.PushBack(4)\ndeque.PushFront(3)     // 先頭に追加\ndeque.PushFront(1)\n\n/* 要素にアクセス */\nfront := deque.Front() // 先頭要素\nrear := deque.Back()   // 末尾要素\n\n/* 要素をデキュー */\ndeque.Remove(front)    // 先頭要素をデキュー\ndeque.Remove(rear)     // 末尾要素をデキュー\n\n/* 両端キューの長さを取得 */\nsize := deque.Len()\n\n/* 両端キューが空かどうかを判定 */\nisEmpty := deque.Len() == 0\n</code></pre> deque.swift<pre><code>/* 両端キューを初期化 */\n// Swift には組み込みの両端キュークラスがないため、Array を両端キューとして使用する\nvar deque: [Int] = []\n\n/* 要素をエンキュー */\ndeque.append(2) // 末尾に追加\ndeque.append(5)\ndeque.append(4)\ndeque.insert(3, at: 0) // 先頭に追加\ndeque.insert(1, at: 0)\n\n/* 要素にアクセス */\nlet peekFirst = deque.first! // 先頭要素\nlet peekLast = deque.last! // 末尾要素\n\n/* 要素をデキュー */\n// Array で模擬する場合、popFirst の計算量は O(n)\nlet popFirst = deque.removeFirst() // 先頭要素をデキュー\nlet popLast = deque.removeLast() // 末尾要素をデキュー\n\n/* 両端キューの長さを取得 */\nlet size = deque.count\n\n/* 両端キューが空かどうかを判定 */\nlet isEmpty = deque.isEmpty\n</code></pre> deque.js<pre><code>/* 両端キューを初期化 */\n// JavaScript には組み込みの両端キューがないため、Array を両端キューとして使用するしかない\nconst deque = [];\n\n/* 要素をエンキュー */\ndeque.push(2);\ndeque.push(5);\ndeque.push(4);\n// 配列であるため、unshift() メソッドの時間計算量は O(n) です\ndeque.unshift(3);\ndeque.unshift(1);\n\n/* 要素にアクセス */\nconst peekFirst = deque[0];\nconst peekLast = deque[deque.length - 1];\n\n/* 要素をデキュー */\n// 配列であるため、shift() メソッドの時間計算量は O(n) です\nconst popFront = deque.shift();\nconst popBack = deque.pop();\n\n/* 両端キューの長さを取得 */\nconst size = deque.length;\n\n/* 両端キューが空かどうかを判定 */\nconst isEmpty = size === 0;\n</code></pre> deque.ts<pre><code>/* 両端キューを初期化 */\n// TypeScript には組み込みの両端キューがないため、Array を両端キューとして使用するしかない\nconst deque: number[] = [];\n\n/* 要素をエンキュー */\ndeque.push(2);\ndeque.push(5);\ndeque.push(4);\n// 配列であるため、unshift() メソッドの時間計算量は O(n) です\ndeque.unshift(3);\ndeque.unshift(1);\n\n/* 要素にアクセス */\nconst peekFirst: number = deque[0];\nconst peekLast: number = deque[deque.length - 1];\n\n/* 要素をデキュー */\n// 配列であるため、shift() メソッドの時間計算量は O(n) です\nconst popFront: number = deque.shift() as number;\nconst popBack: number = deque.pop() as number;\n\n/* 両端キューの長さを取得 */\nconst size: number = deque.length;\n\n/* 両端キューが空かどうかを判定 */\nconst isEmpty: boolean = size === 0;\n</code></pre> deque.dart<pre><code>/* 両端キューを初期化 */\n// Dart では、Queue は両端キューとして定義されています\nQueue&lt;int&gt; deque = Queue&lt;int&gt;();\n\n/* 要素をエンキュー */\ndeque.addLast(2);  // 末尾に追加\ndeque.addLast(5);\ndeque.addLast(4);\ndeque.addFirst(3); // 先頭に追加\ndeque.addFirst(1);\n\n/* 要素にアクセス */\nint peekFirst = deque.first; // 先頭要素\nint peekLast = deque.last;   // 末尾要素\n\n/* 要素をデキュー */\nint popFirst = deque.removeFirst(); // 先頭要素をデキュー\nint popLast = deque.removeLast();   // 末尾要素をデキュー\n\n/* 両端キューの長さを取得 */\nint size = deque.length;\n\n/* 両端キューが空かどうかを判定 */\nbool isEmpty = deque.isEmpty;\n</code></pre> deque.rs<pre><code>/* 両端キューを初期化 */\nlet mut deque: VecDeque&lt;u32&gt; = VecDeque::new();\n\n/* 要素をエンキュー */\ndeque.push_back(2);  // 末尾に追加\ndeque.push_back(5);\ndeque.push_back(4);\ndeque.push_front(3); // 先頭に追加\ndeque.push_front(1);\n\n/* 要素にアクセス */\nif let Some(front) = deque.front() { // 先頭要素\n}\nif let Some(rear) = deque.back() {   // 末尾要素\n}\n\n/* 要素をデキュー */\nif let Some(pop_front) = deque.pop_front() { // 先頭要素をデキュー\n}\nif let Some(pop_rear) = deque.pop_back() {   // 末尾要素をデキュー\n}\n\n/* 両端キューの長さを取得 */\nlet size = deque.len();\n\n/* 両端キューが空かどうかを判定 */\nlet is_empty = deque.is_empty();\n</code></pre> deque.c<pre><code>// C には組み込みの両端キューがありません\n</code></pre> deque.kt<pre><code>/* 両端キューを初期化 */\nval deque = LinkedList&lt;Int&gt;()\n\n/* 要素をエンキュー */\ndeque.offerLast(2)  // 末尾に追加\ndeque.offerLast(5)\ndeque.offerLast(4)\ndeque.offerFirst(3) // 先頭に追加\ndeque.offerFirst(1)\n\n/* 要素にアクセス */\nval peekFirst = deque.peekFirst() // 先頭要素\nval peekLast = deque.peekLast()   // 末尾要素\n\n/* 要素をデキュー */\nval popFirst = deque.pollFirst() // 先頭要素をデキュー\nval popLast = deque.pollLast()   // 末尾要素をデキュー\n\n/* 両端キューの長さを取得 */\nval size = deque.size\n\n/* 両端キューが空かどうかを判定 */\nval isEmpty = deque.isEmpty()\n</code></pre> deque.rb<pre><code># 両端キューを初期化\n# Ruby には組み込みの両端キューがないため、Array を両端キューとして使用するしかありません\ndeque = []\n\n# 要素をエンキュー\ndeque &lt;&lt; 2\ndeque &lt;&lt; 5\ndeque &lt;&lt; 4\n# 配列であるため、Array#unshift メソッドの時間計算量は O(n) です\ndeque.unshift(3)\ndeque.unshift(1)\n\n# 要素にアクセス\npeek_first = deque.first\npeek_last = deque.last\n\n# 要素をデキュー\n# 配列であるため、 Array#shift メソッドの時間計算量は O(n) です\npop_front = deque.shift\npop_back = deque.pop\n\n# 両端キューの長さを取得\nsize = deque.length\n\n# 両端キューが空かどうかを判定\nis_empty = size.zero?\n</code></pre> 実行の可視化 <p>https://pythontutor.com/render.html#code=from%20collections%20import%20deque%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%0A%20%20%20%20deq%20%3D%20deque%28%29%0A%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%85%A5%E9%98%9F%0A%20%20%20%20deq.append%282%29%20%20%23%20%E6%B7%BB%E5%8A%A0%E8%87%B3%E9%98%9F%E5%B0%BE%0A%20%20%20%20deq.append%285%29%0A%20%20%20%20deq.append%284%29%0A%20%20%20%20deq.appendleft%283%29%20%20%23%20%E6%B7%BB%E5%8A%A0%E8%87%B3%E9%98%9F%E9%A6%96%0A%20%20%20%20deq.appendleft%281%29%0A%20%20%20%20print%28%22%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%20deque%20%3D%22,%20deq%29%0A%0A%20%20%20%20%23%20%E8%AE%BF%E9%97%AE%E5%85%83%E7%B4%A0%0A%20%20%20%20front%20%3D%20deq%5B0%5D%20%20%23%20%E9%98%9F%E9%A6%96%E5%85%83%E7%B4%A0%0A%20%20%20%20print%28%22%E9%98%9F%E9%A6%96%E5%85%83%E7%B4%A0%20front%20%3D%22,%20front%29%0A%20%20%20%20rear%20%3D%20deq%5B-1%5D%20%20%23%20%E9%98%9F%E5%B0%BE%E5%85%83%E7%B4%A0%0A%20%20%20%20print%28%22%E9%98%9F%E5%B0%BE%E5%85%83%E7%B4%A0%20rear%20%3D%22,%20rear%29%0A%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%87%BA%E9%98%9F%0A%20%20%20%20pop_front%20%3D%20deq.popleft%28%29%20%20%23%20%E9%98%9F%E9%A6%96%E5%85%83%E7%B4%A0%E5%87%BA%E9%98%9F%0A%20%20%20%20print%28%22%E9%98%9F%E9%A6%96%E5%87%BA%E9%98%9F%E5%85%83%E7%B4%A0%20%20pop_front%20%3D%22,%20pop_front%29%0A%20%20%20%20print%28%22%E9%98%9F%E9%A6%96%E5%87%BA%E9%98%9F%E5%90%8E%20deque%20%3D%22,%20deq%29%0A%20%20%20%20pop_rear%20%3D%20deq.pop%28%29%20%20%23%20%E9%98%9F%E5%B0%BE%E5%85%83%E7%B4%A0%E5%87%BA%E9%98%9F%0A%20%20%20%20print%28%22%E9%98%9F%E5%B0%BE%E5%87%BA%E9%98%9F%E5%85%83%E7%B4%A0%20%20pop_rear%20%3D%22,%20pop_rear%29%0A%20%20%20%20print%28%22%E9%98%9F%E5%B0%BE%E5%87%BA%E9%98%9F%E5%90%8E%20deque%20%3D%22,%20deq%29%0A%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%E7%9A%84%E9%95%BF%E5%BA%A6%0A%20%20%20%20size%20%3D%20len%28deq%29%0A%20%20%20%20print%28%22%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%E9%95%BF%E5%BA%A6%20size%20%3D%22,%20size%29%0A%0A%20%20%20%20%23%20%E5%88%A4%E6%96%AD%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%0A%20%20%20%20is_empty%20%3D%20len%28deq%29%20%3D%3D%200%0A%20%20%20%20print%28%22%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%20%3D%22,%20is_empty%29&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["第 5 章 &nbsp; スタックとキュー","5.3 &nbsp; 両端キュー"],"tags":[]},{"location":"chapter_stack_and_queue/deque/#532","level":2,"title":"5.3.2   両端キューの実装 *","text":"<p>両端キューの実装はキューと似ており、連結リストまたは配列を基盤となるデータ構造として選べます。</p>","path":["第 5 章 &nbsp; スタックとキュー","5.3 &nbsp; 両端キュー"],"tags":[]},{"location":"chapter_stack_and_queue/deque/#1","level":3,"title":"1.   双方向連結リストに基づく実装","text":"<p>前節を振り返ると、通常の単方向連結リストを使ってキューを実装しました。これは、先頭ノードの削除（デキューに対応）と末尾ノードの後ろへの新規ノード追加（エンキューに対応）を容易に行えるためです。</p> <p>両端キューでは、先頭と末尾のどちらでもエンキューとデキューを行えます。言い換えると、両端キューではもう一方の対称方向の操作も実装する必要があります。そのため、両端キューの基盤データ構造として「双方向連結リスト」を採用します。</p> <p>次の図に示すように、双方向連結リストの先頭ノードと末尾ノードを両端キューの先頭と末尾と見なし、両端でノードを追加および削除する機能を実現します。</p> LinkedListDequepush_last()push_first()pop_last()pop_first() <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 5-8   連結リストによる両端キューのエンキューとデキュー </p> <p>実装コードは次のとおりです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linkedlist_deque.py<pre><code>class ListNode:\n    \"\"\"双方向連結リストノード\"\"\"\n\n    def __init__(self, val: int):\n        \"\"\"コンストラクタ\"\"\"\n        self.val: int = val\n        self.next: ListNode | None = None  # 後続ノードへの参照\n        self.prev: ListNode | None = None  # 前駆ノードへの参照\n\nclass LinkedListDeque:\n    \"\"\"双方向連結リストベースの両端キュー\"\"\"\n\n    def __init__(self):\n        \"\"\"コンストラクタ\"\"\"\n        self._front: ListNode | None = None  # 先頭ノード front\n        self._rear: ListNode | None = None  # 末尾ノード rear\n        self._size: int = 0  # 両端キューの長さ\n\n    def size(self) -&gt; int:\n        \"\"\"両端キューの長さを取得\"\"\"\n        return self._size\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"両端キューが空かどうかを判定\"\"\"\n        return self._size == 0\n\n    def push(self, num: int, is_front: bool):\n        \"\"\"エンキュー操作\"\"\"\n        node = ListNode(num)\n        # 連結リストが空なら、front と rear の両方を node に向ける\n        if self.is_empty():\n            self._front = self._rear = node\n        # 先頭へのエンキュー操作\n        elif is_front:\n            # node を連結リストの先頭に追加\n            self._front.prev = node\n            node.next = self._front\n            self._front = node  # 先頭ノードを更新する\n        # 末尾へのエンキュー操作\n        else:\n            # node を連結リストの末尾に追加\n            self._rear.next = node\n            node.prev = self._rear\n            self._rear = node  # 末尾ノードを更新する\n        self._size += 1  # キューの長さを更新\n\n    def push_first(self, num: int):\n        \"\"\"キュー先頭にエンキュー\"\"\"\n        self.push(num, True)\n\n    def push_last(self, num: int):\n        \"\"\"キュー末尾にエンキュー\"\"\"\n        self.push(num, False)\n\n    def pop(self, is_front: bool) -&gt; int:\n        \"\"\"デキュー操作\"\"\"\n        if self.is_empty():\n            raise IndexError(\"両端キューが空です\")\n        # キュー先頭からの取り出し\n        if is_front:\n            val: int = self._front.val  # 先頭ノードの値を一時保存\n            # 先頭ノードを削除\n            fnext: ListNode | None = self._front.next\n            if fnext is not None:\n                fnext.prev = None\n                self._front.next = None\n            self._front = fnext  # 先頭ノードを更新する\n        # キュー末尾からの取り出し\n        else:\n            val: int = self._rear.val  # 末尾ノードの値を一時保存\n            # 末尾ノードを削除\n            rprev: ListNode | None = self._rear.prev\n            if rprev is not None:\n                rprev.next = None\n                self._rear.prev = None\n            self._rear = rprev  # 末尾ノードを更新する\n        self._size -= 1  # キューの長さを更新\n        return val\n\n    def pop_first(self) -&gt; int:\n        \"\"\"キュー先頭からデキュー\"\"\"\n        return self.pop(True)\n\n    def pop_last(self) -&gt; int:\n        \"\"\"キュー末尾からデキュー\"\"\"\n        return self.pop(False)\n\n    def peek_first(self) -&gt; int:\n        \"\"\"キュー先頭の要素にアクセス\"\"\"\n        if self.is_empty():\n            raise IndexError(\"両端キューが空です\")\n        return self._front.val\n\n    def peek_last(self) -&gt; int:\n        \"\"\"キュー末尾の要素にアクセス\"\"\"\n        if self.is_empty():\n            raise IndexError(\"両端キューが空です\")\n        return self._rear.val\n\n    def to_array(self) -&gt; list[int]:\n        \"\"\"出力用の配列を返す\"\"\"\n        node = self._front\n        res = [0] * self.size()\n        for i in range(self.size()):\n            res[i] = node.val\n            node = node.next\n        return res\n</code></pre> linkedlist_deque.cpp<pre><code>/* 双方向連結リストノード */\nstruct DoublyListNode {\n    int val;              // ノード値\n    DoublyListNode *next; // 後継ノードへのポインタ\n    DoublyListNode *prev; // 前駆ノードへのポインタ\n    DoublyListNode(int val) : val(val), prev(nullptr), next(nullptr) {\n    }\n};\n\n/* 双方向連結リストベースの両端キュー */\nclass LinkedListDeque {\n  private:\n    DoublyListNode *front, *rear; // 先頭ノード front、末尾ノード rear\n    int queSize = 0;              // 両端キューの長さ\n\n  public:\n    /* コンストラクタ */\n    LinkedListDeque() : front(nullptr), rear(nullptr) {\n    }\n\n    /* デストラクタメソッド */\n    ~LinkedListDeque() {\n        // 連結リストを走査してノードを削除し、メモリを解放する\n        DoublyListNode *pre, *cur = front;\n        while (cur != nullptr) {\n            pre = cur;\n            cur = cur-&gt;next;\n            delete pre;\n        }\n    }\n\n    /* 両端キューの長さを取得 */\n    int size() {\n        return queSize;\n    }\n\n    /* 両端キューが空かどうかを判定 */\n    bool isEmpty() {\n        return size() == 0;\n    }\n\n    /* エンキュー操作 */\n    void push(int num, bool isFront) {\n        DoublyListNode *node = new DoublyListNode(num);\n        // 連結リストが空なら、front と rear の両方を node に向ける\n        if (isEmpty())\n            front = rear = node;\n        // 先頭へのエンキュー操作\n        else if (isFront) {\n            // node を連結リストの先頭に追加\n            front-&gt;prev = node;\n            node-&gt;next = front;\n            front = node; // 先頭ノードを更新する\n        // 末尾へのエンキュー操作\n        } else {\n            // node を連結リストの末尾に追加\n            rear-&gt;next = node;\n            node-&gt;prev = rear;\n            rear = node; // 末尾ノードを更新する\n        }\n        queSize++; // キューの長さを更新\n    }\n\n    /* キュー先頭にエンキュー */\n    void pushFirst(int num) {\n        push(num, true);\n    }\n\n    /* キュー末尾にエンキュー */\n    void pushLast(int num) {\n        push(num, false);\n    }\n\n    /* デキュー操作 */\n    int pop(bool isFront) {\n        if (isEmpty())\n            throw out_of_range(\"キューが空です\");\n        int val;\n        // キュー先頭からの取り出し\n        if (isFront) {\n            val = front-&gt;val; // 先頭ノードの値を一時保存\n            // 先頭ノードを削除\n            DoublyListNode *fNext = front-&gt;next;\n            if (fNext != nullptr) {\n                fNext-&gt;prev = nullptr;\n                front-&gt;next = nullptr;\n            }\n            delete front;\n            front = fNext; // 先頭ノードを更新する\n        // キュー末尾からの取り出し\n        } else {\n            val = rear-&gt;val; // 末尾ノードの値を一時保存\n            // 末尾ノードを削除\n            DoublyListNode *rPrev = rear-&gt;prev;\n            if (rPrev != nullptr) {\n                rPrev-&gt;next = nullptr;\n                rear-&gt;prev = nullptr;\n            }\n            delete rear;\n            rear = rPrev; // 末尾ノードを更新する\n        }\n        queSize--; // キューの長さを更新\n        return val;\n    }\n\n    /* キュー先頭からデキュー */\n    int popFirst() {\n        return pop(true);\n    }\n\n    /* キュー末尾からデキュー */\n    int popLast() {\n        return pop(false);\n    }\n\n    /* キュー先頭の要素にアクセス */\n    int peekFirst() {\n        if (isEmpty())\n            throw out_of_range(\"両端キューが空です\");\n        return front-&gt;val;\n    }\n\n    /* キュー末尾の要素にアクセス */\n    int peekLast() {\n        if (isEmpty())\n            throw out_of_range(\"両端キューが空です\");\n        return rear-&gt;val;\n    }\n\n    /* 出力用の配列を返す */\n    vector&lt;int&gt; toVector() {\n        DoublyListNode *node = front;\n        vector&lt;int&gt; res(size());\n        for (int i = 0; i &lt; res.size(); i++) {\n            res[i] = node-&gt;val;\n            node = node-&gt;next;\n        }\n        return res;\n    }\n};\n</code></pre> linkedlist_deque.java<pre><code>/* 双方向連結リストノード */\nclass ListNode {\n    int val; // ノード値\n    ListNode next; // 後続ノードへの参照\n    ListNode prev; // 前駆ノードへの参照\n\n    ListNode(int val) {\n        this.val = val;\n        prev = next = null;\n    }\n}\n\n/* 双方向連結リストベースの両端キュー */\nclass LinkedListDeque {\n    private ListNode front, rear; // 先頭ノード front、末尾ノード rear\n    private int queSize = 0; // 両端キューの長さ\n\n    public LinkedListDeque() {\n        front = rear = null;\n    }\n\n    /* 両端キューの長さを取得 */\n    public int size() {\n        return queSize;\n    }\n\n    /* 両端キューが空かどうかを判定 */\n    public boolean isEmpty() {\n        return size() == 0;\n    }\n\n    /* エンキュー操作 */\n    private void push(int num, boolean isFront) {\n        ListNode node = new ListNode(num);\n        // 連結リストが空なら、front と rear の両方を node に向ける\n        if (isEmpty())\n            front = rear = node;\n        // 先頭へのエンキュー操作\n        else if (isFront) {\n            // node を連結リストの先頭に追加\n            front.prev = node;\n            node.next = front;\n            front = node; // 先頭ノードを更新する\n        // 末尾へのエンキュー操作\n        } else {\n            // node を連結リストの末尾に追加\n            rear.next = node;\n            node.prev = rear;\n            rear = node; // 末尾ノードを更新する\n        }\n        queSize++; // キューの長さを更新\n    }\n\n    /* キュー先頭にエンキュー */\n    public void pushFirst(int num) {\n        push(num, true);\n    }\n\n    /* キュー末尾にエンキュー */\n    public void pushLast(int num) {\n        push(num, false);\n    }\n\n    /* デキュー操作 */\n    private int pop(boolean isFront) {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        int val;\n        // キュー先頭からの取り出し\n        if (isFront) {\n            val = front.val; // 先頭ノードの値を一時保存\n            // 先頭ノードを削除\n            ListNode fNext = front.next;\n            if (fNext != null) {\n                fNext.prev = null;\n                front.next = null;\n            }\n            front = fNext; // 先頭ノードを更新する\n        // キュー末尾からの取り出し\n        } else {\n            val = rear.val; // 末尾ノードの値を一時保存\n            // 末尾ノードを削除\n            ListNode rPrev = rear.prev;\n            if (rPrev != null) {\n                rPrev.next = null;\n                rear.prev = null;\n            }\n            rear = rPrev; // 末尾ノードを更新する\n        }\n        queSize--; // キューの長さを更新\n        return val;\n    }\n\n    /* キュー先頭からデキュー */\n    public int popFirst() {\n        return pop(true);\n    }\n\n    /* キュー末尾からデキュー */\n    public int popLast() {\n        return pop(false);\n    }\n\n    /* キュー先頭の要素にアクセス */\n    public int peekFirst() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return front.val;\n    }\n\n    /* キュー末尾の要素にアクセス */\n    public int peekLast() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return rear.val;\n    }\n\n    /* 出力用の配列を返す */\n    public int[] toArray() {\n        ListNode node = front;\n        int[] res = new int[size()];\n        for (int i = 0; i &lt; res.length; i++) {\n            res[i] = node.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_deque.cs<pre><code>/* 双方向連結リストノード */\nclass ListNode(int val) {\n    public int val = val;       // ノード値\n    public ListNode? next = null; // 後続ノードへの参照\n    public ListNode? prev = null; // 前駆ノードへの参照\n}\n\n/* 双方向連結リストベースの両端キュー */\nclass LinkedListDeque {\n    ListNode? front, rear; // 先頭ノード front、末尾ノード rear\n    int queSize = 0;      // 両端キューの長さ\n\n    public LinkedListDeque() {\n        front = null;\n        rear = null;\n    }\n\n    /* 両端キューの長さを取得 */\n    public int Size() {\n        return queSize;\n    }\n\n    /* 両端キューが空かどうかを判定 */\n    public bool IsEmpty() {\n        return Size() == 0;\n    }\n\n    /* エンキュー操作 */\n    void Push(int num, bool isFront) {\n        ListNode node = new(num);\n        // 連結リストが空なら、front と rear の両方を node に向ける\n        if (IsEmpty()) {\n            front = node;\n            rear = node;\n        }\n        // 先頭へのエンキュー操作\n        else if (isFront) {\n            // node を連結リストの先頭に追加\n            front!.prev = node;\n            node.next = front;\n            front = node; // 先頭ノードを更新する\n        }\n        // 末尾へのエンキュー操作\n        else {\n            // node を連結リストの末尾に追加\n            rear!.next = node;\n            node.prev = rear;\n            rear = node;  // 末尾ノードを更新する\n        }\n\n        queSize++; // キューの長さを更新\n    }\n\n    /* キュー先頭にエンキュー */\n    public void PushFirst(int num) {\n        Push(num, true);\n    }\n\n    /* キュー末尾にエンキュー */\n    public void PushLast(int num) {\n        Push(num, false);\n    }\n\n    /* デキュー操作 */\n    int? Pop(bool isFront) {\n        if (IsEmpty())\n            throw new Exception();\n        int? val;\n        // キュー先頭からの取り出し\n        if (isFront) {\n            val = front?.val; // 先頭ノードの値を一時保存\n            // 先頭ノードを削除\n            ListNode? fNext = front?.next;\n            if (fNext != null) {\n                fNext.prev = null;\n                front!.next = null;\n            }\n            front = fNext;   // 先頭ノードを更新する\n        }\n        // キュー末尾からの取り出し\n        else {\n            val = rear?.val;  // 末尾ノードの値を一時保存\n            // 末尾ノードを削除\n            ListNode? rPrev = rear?.prev;\n            if (rPrev != null) {\n                rPrev.next = null;\n                rear!.prev = null;\n            }\n            rear = rPrev;    // 末尾ノードを更新する\n        }\n\n        queSize--; // キューの長さを更新\n        return val;\n    }\n\n    /* キュー先頭からデキュー */\n    public int? PopFirst() {\n        return Pop(true);\n    }\n\n    /* キュー末尾からデキュー */\n    public int? PopLast() {\n        return Pop(false);\n    }\n\n    /* キュー先頭の要素にアクセス */\n    public int? PeekFirst() {\n        if (IsEmpty())\n            throw new Exception();\n        return front?.val;\n    }\n\n    /* キュー末尾の要素にアクセス */\n    public int? PeekLast() {\n        if (IsEmpty())\n            throw new Exception();\n        return rear?.val;\n    }\n\n    /* 出力用の配列を返す */\n    public int?[] ToArray() {\n        ListNode? node = front;\n        int?[] res = new int?[Size()];\n        for (int i = 0; i &lt; res.Length; i++) {\n            res[i] = node?.val;\n            node = node?.next;\n        }\n\n        return res;\n    }\n}\n</code></pre> linkedlist_deque.go<pre><code>/* 双方向連結リストベースの両端キュー */\ntype linkedListDeque struct {\n    // 組み込みパッケージ list を使う\n    data *list.List\n}\n\n/* 両端キューを初期化する */\nfunc newLinkedListDeque() *linkedListDeque {\n    return &amp;linkedListDeque{\n        data: list.New(),\n    }\n}\n\n/* キュー先頭に要素を追加する */\nfunc (s *linkedListDeque) pushFirst(value any) {\n    s.data.PushFront(value)\n}\n\n/* キュー末尾に要素を追加する */\nfunc (s *linkedListDeque) pushLast(value any) {\n    s.data.PushBack(value)\n}\n\n/* 先頭要素を取り出す */\nfunc (s *linkedListDeque) popFirst() any {\n    if s.isEmpty() {\n        return nil\n    }\n    e := s.data.Front()\n    s.data.Remove(e)\n    return e.Value\n}\n\n/* 末尾要素を取り出す */\nfunc (s *linkedListDeque) popLast() any {\n    if s.isEmpty() {\n        return nil\n    }\n    e := s.data.Back()\n    s.data.Remove(e)\n    return e.Value\n}\n\n/* キュー先頭の要素にアクセス */\nfunc (s *linkedListDeque) peekFirst() any {\n    if s.isEmpty() {\n        return nil\n    }\n    e := s.data.Front()\n    return e.Value\n}\n\n/* キュー末尾の要素にアクセス */\nfunc (s *linkedListDeque) peekLast() any {\n    if s.isEmpty() {\n        return nil\n    }\n    e := s.data.Back()\n    return e.Value\n}\n\n/* キューの長さを取得 */\nfunc (s *linkedListDeque) size() int {\n    return s.data.Len()\n}\n\n/* キューが空かどうかを判定 */\nfunc (s *linkedListDeque) isEmpty() bool {\n    return s.data.Len() == 0\n}\n\n/* 表示用に List を取得 */\nfunc (s *linkedListDeque) toList() *list.List {\n    return s.data\n}\n</code></pre> linkedlist_deque.swift<pre><code>/* 双方向連結リストノード */\nclass ListNode {\n    var val: Int // ノード値\n    var next: ListNode? // 後続ノードへの参照\n    weak var prev: ListNode? // 前駆ノードへの参照\n\n    init(val: Int) {\n        self.val = val\n    }\n}\n\n/* 双方向連結リストベースの両端キュー */\nclass LinkedListDeque {\n    private var front: ListNode? // 先頭ノード front\n    private var rear: ListNode? // 末尾ノード rear\n    private var _size: Int // 両端キューの長さ\n\n    init() {\n        _size = 0\n    }\n\n    /* 両端キューの長さを取得 */\n    func size() -&gt; Int {\n        _size\n    }\n\n    /* 両端キューが空かどうかを判定 */\n    func isEmpty() -&gt; Bool {\n        size() == 0\n    }\n\n    /* エンキュー操作 */\n    private func push(num: Int, isFront: Bool) {\n        let node = ListNode(val: num)\n        // 連結リストが空なら、front と rear の両方を node に向ける\n        if isEmpty() {\n            front = node\n            rear = node\n        }\n        // 先頭へのエンキュー操作\n        else if isFront {\n            // node を連結リストの先頭に追加\n            front?.prev = node\n            node.next = front\n            front = node // 先頭ノードを更新する\n        }\n        // 末尾へのエンキュー操作\n        else {\n            // node を連結リストの末尾に追加\n            rear?.next = node\n            node.prev = rear\n            rear = node // 末尾ノードを更新する\n        }\n        _size += 1 // キューの長さを更新\n    }\n\n    /* キュー先頭にエンキュー */\n    func pushFirst(num: Int) {\n        push(num: num, isFront: true)\n    }\n\n    /* キュー末尾にエンキュー */\n    func pushLast(num: Int) {\n        push(num: num, isFront: false)\n    }\n\n    /* デキュー操作 */\n    private func pop(isFront: Bool) -&gt; Int {\n        if isEmpty() {\n            fatalError(\"両端キューが空です\")\n        }\n        let val: Int\n        // キュー先頭からの取り出し\n        if isFront {\n            val = front!.val // 先頭ノードの値を一時保存\n            // 先頭ノードを削除\n            let fNext = front?.next\n            if fNext != nil {\n                fNext?.prev = nil\n                front?.next = nil\n            }\n            front = fNext // 先頭ノードを更新する\n        }\n        // キュー末尾からの取り出し\n        else {\n            val = rear!.val // 末尾ノードの値を一時保存\n            // 末尾ノードを削除\n            let rPrev = rear?.prev\n            if rPrev != nil {\n                rPrev?.next = nil\n                rear?.prev = nil\n            }\n            rear = rPrev // 末尾ノードを更新する\n        }\n        _size -= 1 // キューの長さを更新\n        return val\n    }\n\n    /* キュー先頭からデキュー */\n    func popFirst() -&gt; Int {\n        pop(isFront: true)\n    }\n\n    /* キュー末尾からデキュー */\n    func popLast() -&gt; Int {\n        pop(isFront: false)\n    }\n\n    /* キュー先頭の要素にアクセス */\n    func peekFirst() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"両端キューが空です\")\n        }\n        return front!.val\n    }\n\n    /* キュー末尾の要素にアクセス */\n    func peekLast() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"両端キューが空です\")\n        }\n        return rear!.val\n    }\n\n    /* 出力用の配列を返す */\n    func toArray() -&gt; [Int] {\n        var node = front\n        var res = Array(repeating: 0, count: size())\n        for i in res.indices {\n            res[i] = node!.val\n            node = node?.next\n        }\n        return res\n    }\n}\n</code></pre> linkedlist_deque.js<pre><code>/* 双方向連結リストノード */\nclass ListNode {\n    prev; // 前駆ノードへの参照（ポインタ）\n    next; // 後継ノードへの参照（ポインタ）\n    val; // ノード値\n\n    constructor(val) {\n        this.val = val;\n        this.next = null;\n        this.prev = null;\n    }\n}\n\n/* 双方向連結リストベースの両端キュー */\nclass LinkedListDeque {\n    #front; // 先頭ノード front\n    #rear; // 末尾ノード rear\n    #queSize; // 両端キューの長さ\n\n    constructor() {\n        this.#front = null;\n        this.#rear = null;\n        this.#queSize = 0;\n    }\n\n    /* 末尾へのエンキュー操作 */\n    pushLast(val) {\n        const node = new ListNode(val);\n        // 連結リストが空なら、front と rear の両方を node に向ける\n        if (this.#queSize === 0) {\n            this.#front = node;\n            this.#rear = node;\n        } else {\n            // node を連結リストの末尾に追加\n            this.#rear.next = node;\n            node.prev = this.#rear;\n            this.#rear = node; // 末尾ノードを更新する\n        }\n        this.#queSize++;\n    }\n\n    /* 先頭へのエンキュー操作 */\n    pushFirst(val) {\n        const node = new ListNode(val);\n        // 連結リストが空なら、front と rear の両方を node に向ける\n        if (this.#queSize === 0) {\n            this.#front = node;\n            this.#rear = node;\n        } else {\n            // node を連結リストの先頭に追加\n            this.#front.prev = node;\n            node.next = this.#front;\n            this.#front = node; // 先頭ノードを更新する\n        }\n        this.#queSize++;\n    }\n\n    /* キュー末尾からの取り出し */\n    popLast() {\n        if (this.#queSize === 0) {\n            return null;\n        }\n        const value = this.#rear.val; // 末尾ノードの値を保存する\n        // 末尾ノードを削除\n        let temp = this.#rear.prev;\n        if (temp !== null) {\n            temp.next = null;\n            this.#rear.prev = null;\n        }\n        this.#rear = temp; // 末尾ノードを更新する\n        this.#queSize--;\n        return value;\n    }\n\n    /* キュー先頭からの取り出し */\n    popFirst() {\n        if (this.#queSize === 0) {\n            return null;\n        }\n        const value = this.#front.val; // 末尾ノードの値を保存する\n        // 先頭ノードを削除\n        let temp = this.#front.next;\n        if (temp !== null) {\n            temp.prev = null;\n            this.#front.next = null;\n        }\n        this.#front = temp; // 先頭ノードを更新する\n        this.#queSize--;\n        return value;\n    }\n\n    /* キュー末尾の要素にアクセス */\n    peekLast() {\n        return this.#queSize === 0 ? null : this.#rear.val;\n    }\n\n    /* キュー先頭の要素にアクセス */\n    peekFirst() {\n        return this.#queSize === 0 ? null : this.#front.val;\n    }\n\n    /* 両端キューの長さを取得 */\n    size() {\n        return this.#queSize;\n    }\n\n    /* 両端キューが空かどうかを判定 */\n    isEmpty() {\n        return this.#queSize === 0;\n    }\n\n    /* 両端キューを出力する */\n    print() {\n        const arr = [];\n        let temp = this.#front;\n        while (temp !== null) {\n            arr.push(temp.val);\n            temp = temp.next;\n        }\n        console.log('[' + arr.join(', ') + ']');\n    }\n}\n</code></pre> linkedlist_deque.ts<pre><code>/* 双方向連結リストノード */\nclass ListNode {\n    prev: ListNode; // 前駆ノードへの参照（ポインタ）\n    next: ListNode; // 後継ノードへの参照（ポインタ）\n    val: number; // ノード値\n\n    constructor(val: number) {\n        this.val = val;\n        this.next = null;\n        this.prev = null;\n    }\n}\n\n/* 双方向連結リストベースの両端キュー */\nclass LinkedListDeque {\n    private front: ListNode; // 先頭ノード front\n    private rear: ListNode; // 末尾ノード rear\n    private queSize: number; // 両端キューの長さ\n\n    constructor() {\n        this.front = null;\n        this.rear = null;\n        this.queSize = 0;\n    }\n\n    /* 末尾へのエンキュー操作 */\n    pushLast(val: number): void {\n        const node: ListNode = new ListNode(val);\n        // 連結リストが空なら、front と rear の両方を node に向ける\n        if (this.queSize === 0) {\n            this.front = node;\n            this.rear = node;\n        } else {\n            // node を連結リストの末尾に追加\n            this.rear.next = node;\n            node.prev = this.rear;\n            this.rear = node; // 末尾ノードを更新する\n        }\n        this.queSize++;\n    }\n\n    /* 先頭へのエンキュー操作 */\n    pushFirst(val: number): void {\n        const node: ListNode = new ListNode(val);\n        // 連結リストが空なら、front と rear の両方を node に向ける\n        if (this.queSize === 0) {\n            this.front = node;\n            this.rear = node;\n        } else {\n            // node を連結リストの先頭に追加\n            this.front.prev = node;\n            node.next = this.front;\n            this.front = node; // 先頭ノードを更新する\n        }\n        this.queSize++;\n    }\n\n    /* キュー末尾からの取り出し */\n    popLast(): number {\n        if (this.queSize === 0) {\n            return null;\n        }\n        const value: number = this.rear.val; // 末尾ノードの値を保存する\n        // 末尾ノードを削除\n        let temp: ListNode = this.rear.prev;\n        if (temp !== null) {\n            temp.next = null;\n            this.rear.prev = null;\n        }\n        this.rear = temp; // 末尾ノードを更新する\n        this.queSize--;\n        return value;\n    }\n\n    /* キュー先頭からの取り出し */\n    popFirst(): number {\n        if (this.queSize === 0) {\n            return null;\n        }\n        const value: number = this.front.val; // 末尾ノードの値を保存する\n        // 先頭ノードを削除\n        let temp: ListNode = this.front.next;\n        if (temp !== null) {\n            temp.prev = null;\n            this.front.next = null;\n        }\n        this.front = temp; // 先頭ノードを更新する\n        this.queSize--;\n        return value;\n    }\n\n    /* キュー末尾の要素にアクセス */\n    peekLast(): number {\n        return this.queSize === 0 ? null : this.rear.val;\n    }\n\n    /* キュー先頭の要素にアクセス */\n    peekFirst(): number {\n        return this.queSize === 0 ? null : this.front.val;\n    }\n\n    /* 両端キューの長さを取得 */\n    size(): number {\n        return this.queSize;\n    }\n\n    /* 両端キューが空かどうかを判定 */\n    isEmpty(): boolean {\n        return this.queSize === 0;\n    }\n\n    /* 両端キューを出力する */\n    print(): void {\n        const arr: number[] = [];\n        let temp: ListNode = this.front;\n        while (temp !== null) {\n            arr.push(temp.val);\n            temp = temp.next;\n        }\n        console.log('[' + arr.join(', ') + ']');\n    }\n}\n</code></pre> linkedlist_deque.dart<pre><code>/* 双方向連結リストノード */\nclass ListNode {\n  int val; // ノード値\n  ListNode? next; // 後続ノードへの参照\n  ListNode? prev; // 前駆ノードへの参照\n\n  ListNode(this.val, {this.next, this.prev});\n}\n\n/* 双方向連結リストに基づく双方向キュー */\nclass LinkedListDeque {\n  late ListNode? _front; // 先頭ノード _front\n  late ListNode? _rear; // 末尾ノード _rear\n  int _queSize = 0; // 両端キューの長さ\n\n  LinkedListDeque() {\n    this._front = null;\n    this._rear = null;\n  }\n\n  /* 両端キューの長さを取得 */\n  int size() {\n    return this._queSize;\n  }\n\n  /* 両端キューが空かどうかを判定 */\n  bool isEmpty() {\n    return size() == 0;\n  }\n\n  /* エンキュー操作 */\n  void push(int _num, bool isFront) {\n    final ListNode node = ListNode(_num);\n    if (isEmpty()) {\n      // 連結リストが空なら、`_front` と `_rear` の両方を `node` に向ける\n      _front = _rear = node;\n    } else if (isFront) {\n      // 先頭へのエンキュー操作\n      // node を連結リストの先頭に追加する\n      _front!.prev = node;\n      node.next = _front;\n      _front = node; // 先頭ノードを更新する\n    } else {\n      // 末尾へのエンキュー操作\n      // node を連結リストの末尾に追加する\n      _rear!.next = node;\n      node.prev = _rear;\n      _rear = node; // 末尾ノードを更新する\n    }\n    _queSize++; // キューの長さを更新\n  }\n\n  /* キュー先頭にエンキュー */\n  void pushFirst(int _num) {\n    push(_num, true);\n  }\n\n  /* キュー末尾にエンキュー */\n  void pushLast(int _num) {\n    push(_num, false);\n  }\n\n  /* デキュー操作 */\n  int? pop(bool isFront) {\n    // キューが空なら、そのまま `null` を返す\n    if (isEmpty()) {\n      return null;\n    }\n    final int val;\n    if (isFront) {\n      // キュー先頭からの取り出し\n      val = _front!.val; // 先頭ノードの値を一時保存\n      // 先頭ノードを削除\n      ListNode? fNext = _front!.next;\n      if (fNext != null) {\n        fNext.prev = null;\n        _front!.next = null;\n      }\n      _front = fNext; // 先頭ノードを更新する\n    } else {\n      // キュー末尾からの取り出し\n      val = _rear!.val; // 末尾ノードの値を一時保存\n      // 末尾ノードを削除\n      ListNode? rPrev = _rear!.prev;\n      if (rPrev != null) {\n        rPrev.next = null;\n        _rear!.prev = null;\n      }\n      _rear = rPrev; // 末尾ノードを更新する\n    }\n    _queSize--; // キューの長さを更新\n    return val;\n  }\n\n  /* キュー先頭からデキュー */\n  int? popFirst() {\n    return pop(true);\n  }\n\n  /* キュー末尾からデキュー */\n  int? popLast() {\n    return pop(false);\n  }\n\n  /* キュー先頭の要素にアクセス */\n  int? peekFirst() {\n    return _front?.val;\n  }\n\n  /* キュー末尾の要素にアクセス */\n  int? peekLast() {\n    return _rear?.val;\n  }\n\n  /* 出力用の配列を返す */\n  List&lt;int&gt; toArray() {\n    ListNode? node = _front;\n    final List&lt;int&gt; res = [];\n    for (int i = 0; i &lt; _queSize; i++) {\n      res.add(node!.val);\n      node = node.next;\n    }\n    return res;\n  }\n}\n</code></pre> linkedlist_deque.rs<pre><code>/* 双方向連結リストノード */\npub struct ListNode&lt;T&gt; {\n    pub val: T,                                 // ノード値\n    pub next: Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;, // 後継ノードへのポインタ\n    pub prev: Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;, // 前駆ノードへのポインタ\n}\n\nimpl&lt;T&gt; ListNode&lt;T&gt; {\n    pub fn new(val: T) -&gt; Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt; {\n        Rc::new(RefCell::new(ListNode {\n            val,\n            next: None,\n            prev: None,\n        }))\n    }\n}\n\n/* 双方向連結リストベースの両端キュー */\n#[allow(dead_code)]\npub struct LinkedListDeque&lt;T&gt; {\n    front: Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;, // 先頭ノード front\n    rear: Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;,  // 末尾ノード rear\n    que_size: usize,                         // 両端キューの長さ\n}\n\nimpl&lt;T: Copy&gt; LinkedListDeque&lt;T&gt; {\n    pub fn new() -&gt; Self {\n        Self {\n            front: None,\n            rear: None,\n            que_size: 0,\n        }\n    }\n\n    /* 両端キューの長さを取得 */\n    pub fn size(&amp;self) -&gt; usize {\n        return self.que_size;\n    }\n\n    /* 両端キューが空かどうかを判定 */\n    pub fn is_empty(&amp;self) -&gt; bool {\n        return self.que_size == 0;\n    }\n\n    /* エンキュー操作 */\n    fn push(&amp;mut self, num: T, is_front: bool) {\n        let node = ListNode::new(num);\n        // 先頭へのエンキュー操作\n        if is_front {\n            match self.front.take() {\n                // 連結リストが空なら、front と rear の両方を node に向ける\n                None =&gt; {\n                    self.rear = Some(node.clone());\n                    self.front = Some(node);\n                }\n                // node を連結リストの先頭に追加\n                Some(old_front) =&gt; {\n                    old_front.borrow_mut().prev = Some(node.clone());\n                    node.borrow_mut().next = Some(old_front);\n                    self.front = Some(node); // 先頭ノードを更新する\n                }\n            }\n        }\n        // 末尾へのエンキュー操作\n        else {\n            match self.rear.take() {\n                // 連結リストが空なら、front と rear の両方を node に向ける\n                None =&gt; {\n                    self.front = Some(node.clone());\n                    self.rear = Some(node);\n                }\n                // node を連結リストの末尾に追加\n                Some(old_rear) =&gt; {\n                    old_rear.borrow_mut().next = Some(node.clone());\n                    node.borrow_mut().prev = Some(old_rear);\n                    self.rear = Some(node); // 末尾ノードを更新する\n                }\n            }\n        }\n        self.que_size += 1; // キューの長さを更新\n    }\n\n    /* キュー先頭にエンキュー */\n    pub fn push_first(&amp;mut self, num: T) {\n        self.push(num, true);\n    }\n\n    /* キュー末尾にエンキュー */\n    pub fn push_last(&amp;mut self, num: T) {\n        self.push(num, false);\n    }\n\n    /* デキュー操作 */\n    fn pop(&amp;mut self, is_front: bool) -&gt; Option&lt;T&gt; {\n        // キューが空なら、そのまま `None` を返す\n        if self.is_empty() {\n            return None;\n        };\n        // キュー先頭からの取り出し\n        if is_front {\n            self.front.take().map(|old_front| {\n                match old_front.borrow_mut().next.take() {\n                    Some(new_front) =&gt; {\n                        new_front.borrow_mut().prev.take();\n                        self.front = Some(new_front); // 先頭ノードを更新する\n                    }\n                    None =&gt; {\n                        self.rear.take();\n                    }\n                }\n                self.que_size -= 1; // キューの長さを更新\n                old_front.borrow().val\n            })\n        }\n        // キュー末尾からの取り出し\n        else {\n            self.rear.take().map(|old_rear| {\n                match old_rear.borrow_mut().prev.take() {\n                    Some(new_rear) =&gt; {\n                        new_rear.borrow_mut().next.take();\n                        self.rear = Some(new_rear); // 末尾ノードを更新する\n                    }\n                    None =&gt; {\n                        self.front.take();\n                    }\n                }\n                self.que_size -= 1; // キューの長さを更新\n                old_rear.borrow().val\n            })\n        }\n    }\n\n    /* キュー先頭からデキュー */\n    pub fn pop_first(&amp;mut self) -&gt; Option&lt;T&gt; {\n        return self.pop(true);\n    }\n\n    /* キュー末尾からデキュー */\n    pub fn pop_last(&amp;mut self) -&gt; Option&lt;T&gt; {\n        return self.pop(false);\n    }\n\n    /* キュー先頭の要素にアクセス */\n    pub fn peek_first(&amp;self) -&gt; Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt; {\n        self.front.as_ref()\n    }\n\n    /* キュー末尾の要素にアクセス */\n    pub fn peek_last(&amp;self) -&gt; Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt; {\n        self.rear.as_ref()\n    }\n\n    /* 出力用の配列を返す */\n    pub fn to_array(&amp;self, head: Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;) -&gt; Vec&lt;T&gt; {\n        let mut res: Vec&lt;T&gt; = Vec::new();\n        fn recur&lt;T: Copy&gt;(cur: Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;, res: &amp;mut Vec&lt;T&gt;) {\n            if let Some(cur) = cur {\n                res.push(cur.borrow().val);\n                recur(cur.borrow().next.as_ref(), res);\n            }\n        }\n\n        recur(head, &amp;mut res);\n        res\n    }\n}\n</code></pre> linkedlist_deque.c<pre><code>/* 双方向連結リストノード */\ntypedef struct DoublyListNode {\n    int val;                     // ノード値\n    struct DoublyListNode *next; // 後続ノード\n    struct DoublyListNode *prev; // 前駆ノード\n} DoublyListNode;\n\n/* コンストラクタ */\nDoublyListNode *newDoublyListNode(int num) {\n    DoublyListNode *new = (DoublyListNode *)malloc(sizeof(DoublyListNode));\n    new-&gt;val = num;\n    new-&gt;next = NULL;\n    new-&gt;prev = NULL;\n    return new;\n}\n\n/* デストラクタ */\nvoid delDoublyListNode(DoublyListNode *node) {\n    free(node);\n}\n\n/* 双方向連結リストベースの両端キュー */\ntypedef struct {\n    DoublyListNode *front, *rear; // 先頭ノード front、末尾ノード rear\n    int queSize;                  // 両端キューの長さ\n} LinkedListDeque;\n\n/* コンストラクタ */\nLinkedListDeque *newLinkedListDeque() {\n    LinkedListDeque *deque = (LinkedListDeque *)malloc(sizeof(LinkedListDeque));\n    deque-&gt;front = NULL;\n    deque-&gt;rear = NULL;\n    deque-&gt;queSize = 0;\n    return deque;\n}\n\n/* デストラクタ */\nvoid delLinkedListdeque(LinkedListDeque *deque) {\n    // すべてのノードを解放\n    for (int i = 0; i &lt; deque-&gt;queSize &amp;&amp; deque-&gt;front != NULL; i++) {\n        DoublyListNode *tmp = deque-&gt;front;\n        deque-&gt;front = deque-&gt;front-&gt;next;\n        free(tmp);\n    }\n    // deque 構造体を解放する\n    free(deque);\n}\n\n/* キューの長さを取得 */\nint size(LinkedListDeque *deque) {\n    return deque-&gt;queSize;\n}\n\n/* キューが空かどうかを判定 */\nbool empty(LinkedListDeque *deque) {\n    return (size(deque) == 0);\n}\n\n/* エンキュー */\nvoid push(LinkedListDeque *deque, int num, bool isFront) {\n    DoublyListNode *node = newDoublyListNode(num);\n    // 連結リストが空なら、`front` と `rear` の両方を `node` に向ける\n    if (empty(deque)) {\n        deque-&gt;front = deque-&gt;rear = node;\n    }\n    // 先頭へのエンキュー操作\n    else if (isFront) {\n        // node を連結リストの先頭に追加\n        deque-&gt;front-&gt;prev = node;\n        node-&gt;next = deque-&gt;front;\n        deque-&gt;front = node; // 先頭ノードを更新する\n    }\n    // 末尾へのエンキュー操作\n    else {\n        // node を連結リストの末尾に追加\n        deque-&gt;rear-&gt;next = node;\n        node-&gt;prev = deque-&gt;rear;\n        deque-&gt;rear = node;\n    }\n    deque-&gt;queSize++; // キューの長さを更新\n}\n\n/* キュー先頭にエンキュー */\nvoid pushFirst(LinkedListDeque *deque, int num) {\n    push(deque, num, true);\n}\n\n/* キュー末尾にエンキュー */\nvoid pushLast(LinkedListDeque *deque, int num) {\n    push(deque, num, false);\n}\n\n/* キュー先頭の要素にアクセス */\nint peekFirst(LinkedListDeque *deque) {\n    assert(size(deque) &amp;&amp; deque-&gt;front);\n    return deque-&gt;front-&gt;val;\n}\n\n/* キュー末尾の要素にアクセス */\nint peekLast(LinkedListDeque *deque) {\n    assert(size(deque) &amp;&amp; deque-&gt;rear);\n    return deque-&gt;rear-&gt;val;\n}\n\n/* デキュー */\nint pop(LinkedListDeque *deque, bool isFront) {\n    if (empty(deque))\n        return -1;\n    int val;\n    // キュー先頭からの取り出し\n    if (isFront) {\n        val = peekFirst(deque); // 先頭ノードの値を一時保存\n        DoublyListNode *fNext = deque-&gt;front-&gt;next;\n        if (fNext) {\n            fNext-&gt;prev = NULL;\n            deque-&gt;front-&gt;next = NULL;\n        }\n        delDoublyListNode(deque-&gt;front);\n        deque-&gt;front = fNext; // 先頭ノードを更新する\n    }\n    // キュー末尾からの取り出し\n    else {\n        val = peekLast(deque); // 末尾ノードの値を一時保存\n        DoublyListNode *rPrev = deque-&gt;rear-&gt;prev;\n        if (rPrev) {\n            rPrev-&gt;next = NULL;\n            deque-&gt;rear-&gt;prev = NULL;\n        }\n        delDoublyListNode(deque-&gt;rear);\n        deque-&gt;rear = rPrev; // 末尾ノードを更新する\n    }\n    deque-&gt;queSize--; // キューの長さを更新\n    return val;\n}\n\n/* キュー先頭からデキュー */\nint popFirst(LinkedListDeque *deque) {\n    return pop(deque, true);\n}\n\n/* キュー末尾からデキュー */\nint popLast(LinkedListDeque *deque) {\n    return pop(deque, false);\n}\n\n/* キューを出力する */\nvoid printLinkedListDeque(LinkedListDeque *deque) {\n    int *arr = malloc(sizeof(int) * deque-&gt;queSize);\n    // 連結リスト内のデータを配列にコピー\n    int i;\n    DoublyListNode *node;\n    for (i = 0, node = deque-&gt;front; i &lt; deque-&gt;queSize; i++) {\n        arr[i] = node-&gt;val;\n        node = node-&gt;next;\n    }\n    printArray(arr, deque-&gt;queSize);\n    free(arr);\n}\n</code></pre> linkedlist_deque.kt<pre><code>/* 双方向連結リストノード */\nclass ListNode(var _val: Int) {\n    // ノード値\n    var next: ListNode? = null // 後続ノードへの参照\n    var prev: ListNode? = null // 前駆ノードへの参照\n}\n\n/* 双方向連結リストベースの両端キュー */\nclass LinkedListDeque {\n    private var front: ListNode? = null // 先頭ノード front\n    private var rear: ListNode? = null // 末尾ノード rear\n    private var queSize: Int = 0 // 両端キューの長さ\n\n    /* 両端キューの長さを取得 */\n    fun size(): Int {\n        return queSize\n    }\n\n    /* 両端キューが空かどうかを判定 */\n    fun isEmpty(): Boolean {\n        return size() == 0\n    }\n\n    /* エンキュー操作 */\n    fun push(num: Int, isFront: Boolean) {\n        val node = ListNode(num)\n        // 連結リストが空なら、front と rear の両方を node に向ける\n        if (isEmpty()) {\n            rear = node\n            front = rear\n            // 先頭へのエンキュー操作\n        } else if (isFront) {\n            // node を連結リストの先頭に追加\n            front?.prev = node\n            node.next = front\n            front = node // 先頭ノードを更新する\n            // 末尾へのエンキュー操作\n        } else {\n            // node を連結リストの末尾に追加\n            rear?.next = node\n            node.prev = rear\n            rear = node // 末尾ノードを更新する\n        }\n        queSize++ // キューの長さを更新\n    }\n\n    /* キュー先頭にエンキュー */\n    fun pushFirst(num: Int) {\n        push(num, true)\n    }\n\n    /* キュー末尾にエンキュー */\n    fun pushLast(num: Int) {\n        push(num, false)\n    }\n\n    /* デキュー操作 */\n    fun pop(isFront: Boolean): Int {\n        if (isEmpty()) \n            throw IndexOutOfBoundsException()\n        val _val: Int\n        // キュー先頭からの取り出し\n        if (isFront) {\n            _val = front!!._val // 先頭ノードの値を一時保存\n            // 先頭ノードを削除\n            val fNext = front!!.next\n            if (fNext != null) {\n                fNext.prev = null\n                front!!.next = null\n            }\n            front = fNext // 先頭ノードを更新する\n            // キュー末尾からの取り出し\n        } else {\n            _val = rear!!._val // 末尾ノードの値を一時保存\n            // 末尾ノードを削除\n            val rPrev = rear!!.prev\n            if (rPrev != null) {\n                rPrev.next = null\n                rear!!.prev = null\n            }\n            rear = rPrev // 末尾ノードを更新する\n        }\n        queSize-- // キューの長さを更新\n        return _val\n    }\n\n    /* キュー先頭からデキュー */\n    fun popFirst(): Int {\n        return pop(true)\n    }\n\n    /* キュー末尾からデキュー */\n    fun popLast(): Int {\n        return pop(false)\n    }\n\n    /* キュー先頭の要素にアクセス */\n    fun peekFirst(): Int {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        return front!!._val\n    }\n\n    /* キュー末尾の要素にアクセス */\n    fun peekLast(): Int {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        return rear!!._val\n    }\n\n    /* 出力用の配列を返す */\n    fun toArray(): IntArray {\n        var node = front\n        val res = IntArray(size())\n        for (i in res.indices) {\n            res[i] = node!!._val\n            node = node.next\n        }\n        return res\n    }\n}\n</code></pre> linkedlist_deque.rb<pre><code>=begin\nFile: linkedlist_deque.rb\nCreated Time: 2024-04-06\nAuthor: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)\n=end\n\n# ## 双方向連結リストノード\nclass ListNode\n  attr_accessor :val\n  attr_accessor :next # 後続ノードへの参照\n  attr_accessor :prev # 前ノードへの参照\n\n  ### コンストラクタ ###\n  def initialize(val)\n    @val = val\n  end\nend\n\n### 双方向連結リストで実装した両端キュー ###\nclass LinkedListDeque\n  ### 両端キューの長さを取得 ###\n  attr_reader :size\n\n  ### コンストラクタ ###\n  def initialize\n    @front = nil  # 先頭ノード front\n    @rear = nil   # 末尾ノード rear\n    @size = 0     # 両端キューの長さ\n  end\n\n  ### 両端キューが空か判定 ###\n  def is_empty?\n    size.zero?\n  end\n\n  ### エンキュー操作 ###\n  def push(num, is_front)\n    node = ListNode.new(num)\n    # 連結リストが空なら、`front` と `rear` の両方を `node` に向ける\n    if is_empty?\n      @front = @rear = node\n    # 先頭へのエンキュー操作\n    elsif is_front\n      # node を連結リストの先頭に追加\n      @front.prev = node\n      node.next = @front\n      @front = node # 先頭ノードを更新する\n    # 末尾へのエンキュー操作\n    else\n      # node を連結リストの末尾に追加\n      @rear.next = node\n      node.prev = @rear\n      @rear = node # 末尾ノードを更新する\n    end\n    @size += 1 # キューの長さを更新\n  end\n\n  ### キュー先頭に追加 ###\n  def push_first(num)\n    push(num, true)\n  end\n\n  ### キュー末尾に追加 ###\n  def push_last(num)\n    push(num, false)\n  end\n\n  ### デキュー操作 ###\n  def pop(is_front)\n    raise IndexError, '両端キューは空です' if is_empty?\n\n    # キュー先頭からの取り出し\n    if is_front\n      val = @front.val # 先頭ノードの値を一時保存\n      # 先頭ノードを削除\n      fnext = @front.next\n      unless fnext.nil?\n        fnext.prev = nil\n        @front.next = nil\n      end\n      @front = fnext # 先頭ノードを更新する\n    # キュー末尾からの取り出し\n    else\n      val = @rear.val # 末尾ノードの値を一時保存\n      # 末尾ノードを削除\n      rprev = @rear.prev\n      unless rprev.nil?\n        rprev.next = nil\n        @rear.prev = nil\n      end\n      @rear = rprev # 末尾ノードを更新する\n    end\n    @size -= 1 # キューの長さを更新\n\n    val\n  end\n\n  ### キュー先頭から取り出す ###\n  def pop_first\n    pop(true)\n  end\n\n  ### キュー先頭から取り出す ###\n  def pop_last\n    pop(false)\n  end\n\n  ### 先頭要素にアクセス ###\n  def peek_first\n    raise IndexError, '両端キューは空です' if is_empty?\n\n    @front.val\n  end\n\n  ### キュー末尾要素を参照 ###\n  def peek_last\n    raise IndexError, '両端キューは空です' if is_empty?\n\n    @rear.val\n  end\n\n  ### 表示用の配列を返す ###\n  def to_array\n    node = @front\n    res = Array.new(size, 0)\n    for i in 0...size\n      res[i] = node.val\n      node = node.next\n    end\n    res\n  end\nend\n</code></pre>","path":["第 5 章 &nbsp; スタックとキュー","5.3 &nbsp; 両端キュー"],"tags":[]},{"location":"chapter_stack_and_queue/deque/#2","level":3,"title":"2.   配列に基づく実装","text":"<p>次の図に示すように、配列によるキュー実装と同様に、循環配列を使って両端キューを実装することもできます。</p> ArrayDequepush_last()push_first()pop_last()pop_first() <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 5-9   配列による両端キューのエンキューとデキュー </p> <p>キュー実装を土台として、「先頭へのエンキュー」と「末尾からのデキュー」のメソッドを追加するだけで済みます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array_deque.py<pre><code>class ArrayDeque:\n    \"\"\"循環配列ベースの両端キュー\"\"\"\n\n    def __init__(self, capacity: int):\n        \"\"\"コンストラクタ\"\"\"\n        self._nums: list[int] = [0] * capacity\n        self._front: int = 0\n        self._size: int = 0\n\n    def capacity(self) -&gt; int:\n        \"\"\"両端キューの容量を取得\"\"\"\n        return len(self._nums)\n\n    def size(self) -&gt; int:\n        \"\"\"両端キューの長さを取得\"\"\"\n        return self._size\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"両端キューが空かどうかを判定\"\"\"\n        return self._size == 0\n\n    def index(self, i: int) -&gt; int:\n        \"\"\"循環配列のインデックスを計算\"\"\"\n        # 剰余演算により配列の先頭と末尾をつなげる\n        # i が配列の末尾を越えたら先頭に戻る\n        # i が配列の先頭を越えて前に出たら末尾に戻る\n        return (i + self.capacity()) % self.capacity()\n\n    def push_first(self, num: int):\n        \"\"\"キュー先頭にエンキュー\"\"\"\n        if self._size == self.capacity():\n            print(\"両端キューがいっぱいです\")\n            return\n        # 先頭ポインタを左に 1 つ移動する\n        # 剰余演算により、front が配列先頭を越えた後に末尾へ戻るようにする\n        self._front = self.index(self._front - 1)\n        # num をキュー先頭に追加\n        self._nums[self._front] = num\n        self._size += 1\n\n    def push_last(self, num: int):\n        \"\"\"キュー末尾にエンキュー\"\"\"\n        if self._size == self.capacity():\n            print(\"両端キューがいっぱいです\")\n            return\n        # キュー末尾ポインタを計算し、末尾インデックス + 1 を指す\n        rear = self.index(self._front + self._size)\n        # num をキュー末尾に追加\n        self._nums[rear] = num\n        self._size += 1\n\n    def pop_first(self) -&gt; int:\n        \"\"\"キュー先頭からデキュー\"\"\"\n        num = self.peek_first()\n        # 先頭ポインタを 1 つ後ろへ進める\n        self._front = self.index(self._front + 1)\n        self._size -= 1\n        return num\n\n    def pop_last(self) -&gt; int:\n        \"\"\"キュー末尾からデキュー\"\"\"\n        num = self.peek_last()\n        self._size -= 1\n        return num\n\n    def peek_first(self) -&gt; int:\n        \"\"\"キュー先頭の要素にアクセス\"\"\"\n        if self.is_empty():\n            raise IndexError(\"両端キューが空です\")\n        return self._nums[self._front]\n\n    def peek_last(self) -&gt; int:\n        \"\"\"キュー末尾の要素にアクセス\"\"\"\n        if self.is_empty():\n            raise IndexError(\"両端キューが空です\")\n        # 末尾要素のインデックスを計算\n        last = self.index(self._front + self._size - 1)\n        return self._nums[last]\n\n    def to_array(self) -&gt; list[int]:\n        \"\"\"出力用の配列を返す\"\"\"\n        # 有効長の範囲内のリスト要素のみを変換\n        res = []\n        for i in range(self._size):\n            res.append(self._nums[self.index(self._front + i)])\n        return res\n</code></pre> array_deque.cpp<pre><code>/* 循環配列ベースの両端キュー */\nclass ArrayDeque {\n  private:\n    vector&lt;int&gt; nums; // 両端キューの要素を格納する配列\n    int front;        // 先頭ポインタ。先頭要素を指す\n    int queSize;      // 両端キューの長さ\n\n  public:\n    /* コンストラクタ */\n    ArrayDeque(int capacity) {\n        nums.resize(capacity);\n        front = queSize = 0;\n    }\n\n    /* 両端キューの容量を取得 */\n    int capacity() {\n        return nums.size();\n    }\n\n    /* 両端キューの長さを取得 */\n    int size() {\n        return queSize;\n    }\n\n    /* 両端キューが空かどうかを判定 */\n    bool isEmpty() {\n        return queSize == 0;\n    }\n\n    /* 循環配列のインデックスを計算 */\n    int index(int i) {\n        // 剰余演算により配列の先頭と末尾をつなげる\n        // i が配列の末尾を越えたら先頭に戻る\n        // i が配列の先頭を越えて前に出たら末尾に戻る\n        return (i + capacity()) % capacity();\n    }\n\n    /* キュー先頭にエンキュー */\n    void pushFirst(int num) {\n        if (queSize == capacity()) {\n            cout &lt;&lt; \"両端キューがいっぱいです\" &lt;&lt; endl;\n            return;\n        }\n        // 先頭ポインタを左に 1 つ移動する\n        // 剰余演算により、front が配列先頭を越えた後に末尾へ戻るようにする\n        front = index(front - 1);\n        // num をキュー先頭に追加\n        nums[front] = num;\n        queSize++;\n    }\n\n    /* キュー末尾にエンキュー */\n    void pushLast(int num) {\n        if (queSize == capacity()) {\n            cout &lt;&lt; \"両端キューがいっぱいです\" &lt;&lt; endl;\n            return;\n        }\n        // キュー末尾ポインタを計算し、末尾インデックス + 1 を指す\n        int rear = index(front + queSize);\n        // num をキュー末尾に追加\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* キュー先頭からデキュー */\n    int popFirst() {\n        int num = peekFirst();\n        // 先頭ポインタを 1 つ後ろへ進める\n        front = index(front + 1);\n        queSize--;\n        return num;\n    }\n\n    /* キュー末尾からデキュー */\n    int popLast() {\n        int num = peekLast();\n        queSize--;\n        return num;\n    }\n\n    /* キュー先頭の要素にアクセス */\n    int peekFirst() {\n        if (isEmpty())\n            throw out_of_range(\"両端キューが空です\");\n        return nums[front];\n    }\n\n    /* キュー末尾の要素にアクセス */\n    int peekLast() {\n        if (isEmpty())\n            throw out_of_range(\"両端キューが空です\");\n        // 末尾要素のインデックスを計算\n        int last = index(front + queSize - 1);\n        return nums[last];\n    }\n\n    /* 出力用の配列を返す */\n    vector&lt;int&gt; toVector() {\n        // 有効長の範囲内のリスト要素のみを変換\n        vector&lt;int&gt; res(queSize);\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            res[i] = nums[index(j)];\n        }\n        return res;\n    }\n};\n</code></pre> array_deque.java<pre><code>/* 循環配列ベースの両端キュー */\nclass ArrayDeque {\n    private int[] nums; // 両端キューの要素を格納する配列\n    private int front; // 先頭ポインタ。先頭要素を指す\n    private int queSize; // 両端キューの長さ\n\n    /* コンストラクタ */\n    public ArrayDeque(int capacity) {\n        this.nums = new int[capacity];\n        front = queSize = 0;\n    }\n\n    /* 両端キューの容量を取得 */\n    public int capacity() {\n        return nums.length;\n    }\n\n    /* 両端キューの長さを取得 */\n    public int size() {\n        return queSize;\n    }\n\n    /* 両端キューが空かどうかを判定 */\n    public boolean isEmpty() {\n        return queSize == 0;\n    }\n\n    /* 循環配列のインデックスを計算 */\n    private int index(int i) {\n        // 剰余演算により配列の先頭と末尾をつなげる\n        // i が配列の末尾を越えたら先頭に戻る\n        // i が配列の先頭を越えて前に出たら末尾に戻る\n        return (i + capacity()) % capacity();\n    }\n\n    /* キュー先頭にエンキュー */\n    public void pushFirst(int num) {\n        if (queSize == capacity()) {\n            System.out.println(\"双方向キューは満杯です\");\n            return;\n        }\n        // 先頭ポインタを左に 1 つ移動する\n        // 剰余演算により、front が配列先頭を越えた後に末尾へ戻るようにする\n        front = index(front - 1);\n        // num をキュー先頭に追加\n        nums[front] = num;\n        queSize++;\n    }\n\n    /* キュー末尾にエンキュー */\n    public void pushLast(int num) {\n        if (queSize == capacity()) {\n            System.out.println(\"双方向キューは満杯です\");\n            return;\n        }\n        // キュー末尾ポインタを計算し、末尾インデックス + 1 を指す\n        int rear = index(front + queSize);\n        // num をキュー末尾に追加\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* キュー先頭からデキュー */\n    public int popFirst() {\n        int num = peekFirst();\n        // 先頭ポインタを 1 つ後ろへ進める\n        front = index(front + 1);\n        queSize--;\n        return num;\n    }\n\n    /* キュー末尾からデキュー */\n    public int popLast() {\n        int num = peekLast();\n        queSize--;\n        return num;\n    }\n\n    /* キュー先頭の要素にアクセス */\n    public int peekFirst() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return nums[front];\n    }\n\n    /* キュー末尾の要素にアクセス */\n    public int peekLast() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        // 末尾要素のインデックスを計算\n        int last = index(front + queSize - 1);\n        return nums[last];\n    }\n\n    /* 出力用の配列を返す */\n    public int[] toArray() {\n        // 有効長の範囲内のリスト要素のみを変換\n        int[] res = new int[queSize];\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            res[i] = nums[index(j)];\n        }\n        return res;\n    }\n}\n</code></pre> array_deque.cs<pre><code>/* 循環配列ベースの両端キュー */\nclass ArrayDeque {\n    int[] nums;  // 両端キューの要素を格納する配列\n    int front;   // 先頭ポインタ。先頭要素を指す\n    int queSize; // 両端キューの長さ\n\n    /* コンストラクタ */\n    public ArrayDeque(int capacity) {\n        nums = new int[capacity];\n        front = queSize = 0;\n    }\n\n    /* 両端キューの容量を取得 */\n    int Capacity() {\n        return nums.Length;\n    }\n\n    /* 両端キューの長さを取得 */\n    public int Size() {\n        return queSize;\n    }\n\n    /* 両端キューが空かどうかを判定 */\n    public bool IsEmpty() {\n        return queSize == 0;\n    }\n\n    /* 循環配列のインデックスを計算 */\n    int Index(int i) {\n        // 剰余演算により配列の先頭と末尾をつなげる\n        // i が配列の末尾を越えたら先頭に戻る\n        // i が配列の先頭を越えて前に出たら末尾に戻る\n        return (i + Capacity()) % Capacity();\n    }\n\n    /* キュー先頭にエンキュー */\n    public void PushFirst(int num) {\n        if (queSize == Capacity()) {\n            Console.WriteLine(\"両端キューは満杯です\");\n            return;\n        }\n        // 先頭ポインタを左に 1 つ移動する\n        // 剰余演算により、front が配列先頭を越えた後に末尾へ戻るようにする\n        front = Index(front - 1);\n        // num をキュー先頭に追加\n        nums[front] = num;\n        queSize++;\n    }\n\n    /* キュー末尾にエンキュー */\n    public void PushLast(int num) {\n        if (queSize == Capacity()) {\n            Console.WriteLine(\"両端キューは満杯です\");\n            return;\n        }\n        // キュー末尾ポインタを計算し、末尾インデックス + 1 を指す\n        int rear = Index(front + queSize);\n        // num をキュー末尾に追加\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* キュー先頭からデキュー */\n    public int PopFirst() {\n        int num = PeekFirst();\n        // 先頭ポインタを 1 つ後ろへ進める\n        front = Index(front + 1);\n        queSize--;\n        return num;\n    }\n\n    /* キュー末尾からデキュー */\n    public int PopLast() {\n        int num = PeekLast();\n        queSize--;\n        return num;\n    }\n\n    /* キュー先頭の要素にアクセス */\n    public int PeekFirst() {\n        if (IsEmpty()) {\n            throw new InvalidOperationException();\n        }\n        return nums[front];\n    }\n\n    /* キュー末尾の要素にアクセス */\n    public int PeekLast() {\n        if (IsEmpty()) {\n            throw new InvalidOperationException();\n        }\n        // 末尾要素のインデックスを計算\n        int last = Index(front + queSize - 1);\n        return nums[last];\n    }\n\n    /* 出力用の配列を返す */\n    public int[] ToArray() {\n        // 有効長の範囲内のリスト要素のみを変換\n        int[] res = new int[queSize];\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            res[i] = nums[Index(j)];\n        }\n        return res;\n    }\n}\n</code></pre> array_deque.go<pre><code>/* 循環配列ベースの両端キュー */\ntype arrayDeque struct {\n    nums        []int // 両端キューの要素を格納する配列\n    front       int   // 先頭ポインタ。先頭要素を指す\n    queSize     int   // 両端キューの長さ\n    queCapacity int   // キュー容量（格納できる要素数の上限）\n}\n\n/* キューを初期化 */\nfunc newArrayDeque(queCapacity int) *arrayDeque {\n    return &amp;arrayDeque{\n        nums:        make([]int, queCapacity),\n        queCapacity: queCapacity,\n        front:       0,\n        queSize:     0,\n    }\n}\n\n/* 両端キューの長さを取得 */\nfunc (q *arrayDeque) size() int {\n    return q.queSize\n}\n\n/* 両端キューが空かどうかを判定 */\nfunc (q *arrayDeque) isEmpty() bool {\n    return q.queSize == 0\n}\n\n/* 循環配列のインデックスを計算 */\nfunc (q *arrayDeque) index(i int) int {\n    // 剰余演算により配列の先頭と末尾をつなげる\n    // i が配列の末尾を越えたら先頭に戻る\n    // i が配列の先頭を越えて前に出たら末尾に戻る\n    return (i + q.queCapacity) % q.queCapacity\n}\n\n/* キュー先頭にエンキュー */\nfunc (q *arrayDeque) pushFirst(num int) {\n    if q.queSize == q.queCapacity {\n        fmt.Println(\"両端キューは満杯です\")\n        return\n    }\n    // 先頭ポインタを左に 1 つ移動する\n    // 剰余演算により、front が配列先頭を越えた後に末尾へ戻るようにする\n    q.front = q.index(q.front - 1)\n    // num をキュー先頭に追加\n    q.nums[q.front] = num\n    q.queSize++\n}\n\n/* キュー末尾にエンキュー */\nfunc (q *arrayDeque) pushLast(num int) {\n    if q.queSize == q.queCapacity {\n        fmt.Println(\"両端キューは満杯です\")\n        return\n    }\n    // キュー末尾ポインタを計算し、末尾インデックス + 1 を指す\n    rear := q.index(q.front + q.queSize)\n    // num をキュー末尾に追加\n    q.nums[rear] = num\n    q.queSize++\n}\n\n/* キュー先頭からデキュー */\nfunc (q *arrayDeque) popFirst() any {\n    num := q.peekFirst()\n    if num == nil {\n        return nil\n    }\n    // 先頭ポインタを 1 つ後ろへ進める\n    q.front = q.index(q.front + 1)\n    q.queSize--\n    return num\n}\n\n/* キュー末尾からデキュー */\nfunc (q *arrayDeque) popLast() any {\n    num := q.peekLast()\n    if num == nil {\n        return nil\n    }\n    q.queSize--\n    return num\n}\n\n/* キュー先頭の要素にアクセス */\nfunc (q *arrayDeque) peekFirst() any {\n    if q.isEmpty() {\n        return nil\n    }\n    return q.nums[q.front]\n}\n\n/* キュー末尾の要素にアクセス */\nfunc (q *arrayDeque) peekLast() any {\n    if q.isEmpty() {\n        return nil\n    }\n    // 末尾要素のインデックスを計算\n    last := q.index(q.front + q.queSize - 1)\n    return q.nums[last]\n}\n\n/* 表示用に Slice を取得 */\nfunc (q *arrayDeque) toSlice() []int {\n    // 有効長の範囲内のリスト要素のみを変換\n    res := make([]int, q.queSize)\n    for i, j := 0, q.front; i &lt; q.queSize; i++ {\n        res[i] = q.nums[q.index(j)]\n        j++\n    }\n    return res\n}\n</code></pre> array_deque.swift<pre><code>/* 循環配列ベースの両端キュー */\nclass ArrayDeque {\n    private var nums: [Int] // 両端キューの要素を格納する配列\n    private var front: Int // 先頭ポインタ。先頭要素を指す\n    private var _size: Int // 両端キューの長さ\n\n    /* コンストラクタ */\n    init(capacity: Int) {\n        nums = Array(repeating: 0, count: capacity)\n        front = 0\n        _size = 0\n    }\n\n    /* 両端キューの容量を取得 */\n    func capacity() -&gt; Int {\n        nums.count\n    }\n\n    /* 両端キューの長さを取得 */\n    func size() -&gt; Int {\n        _size\n    }\n\n    /* 両端キューが空かどうかを判定 */\n    func isEmpty() -&gt; Bool {\n        size() == 0\n    }\n\n    /* 循環配列のインデックスを計算 */\n    private func index(i: Int) -&gt; Int {\n        // 剰余演算により配列の先頭と末尾をつなげる\n        // i が配列の末尾を越えたら先頭に戻る\n        // i が配列の先頭を越えて前に出たら末尾に戻る\n        (i + capacity()) % capacity()\n    }\n\n    /* キュー先頭にエンキュー */\n    func pushFirst(num: Int) {\n        if size() == capacity() {\n            print(\"両端キューがいっぱいです\")\n            return\n        }\n        // 先頭ポインタを左に 1 つ移動する\n        // 剰余演算により、front が配列先頭を越えた後に末尾へ戻るようにする\n        front = index(i: front - 1)\n        // num をキュー先頭に追加\n        nums[front] = num\n        _size += 1\n    }\n\n    /* キュー末尾にエンキュー */\n    func pushLast(num: Int) {\n        if size() == capacity() {\n            print(\"両端キューがいっぱいです\")\n            return\n        }\n        // キュー末尾ポインタを計算し、末尾インデックス + 1 を指す\n        let rear = index(i: front + size())\n        // num をキュー末尾に追加\n        nums[rear] = num\n        _size += 1\n    }\n\n    /* キュー先頭からデキュー */\n    func popFirst() -&gt; Int {\n        let num = peekFirst()\n        // 先頭ポインタを 1 つ後ろへ進める\n        front = index(i: front + 1)\n        _size -= 1\n        return num\n    }\n\n    /* キュー末尾からデキュー */\n    func popLast() -&gt; Int {\n        let num = peekLast()\n        _size -= 1\n        return num\n    }\n\n    /* キュー先頭の要素にアクセス */\n    func peekFirst() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"両端キューが空です\")\n        }\n        return nums[front]\n    }\n\n    /* キュー末尾の要素にアクセス */\n    func peekLast() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"両端キューが空です\")\n        }\n        // 末尾要素のインデックスを計算\n        let last = index(i: front + size() - 1)\n        return nums[last]\n    }\n\n    /* 出力用の配列を返す */\n    func toArray() -&gt; [Int] {\n        // 有効長の範囲内のリスト要素のみを変換\n        (front ..&lt; front + size()).map { nums[index(i: $0)] }\n    }\n}\n</code></pre> array_deque.js<pre><code>/* 循環配列ベースの両端キュー */\nclass ArrayDeque {\n    #nums; // 両端キューの要素を格納する配列\n    #front; // 先頭ポインタ。先頭要素を指す\n    #queSize; // 両端キューの長さ\n\n    /* コンストラクタ */\n    constructor(capacity) {\n        this.#nums = new Array(capacity);\n        this.#front = 0;\n        this.#queSize = 0;\n    }\n\n    /* 両端キューの容量を取得 */\n    capacity() {\n        return this.#nums.length;\n    }\n\n    /* 両端キューの長さを取得 */\n    size() {\n        return this.#queSize;\n    }\n\n    /* 両端キューが空かどうかを判定 */\n    isEmpty() {\n        return this.#queSize === 0;\n    }\n\n    /* 循環配列のインデックスを計算 */\n    index(i) {\n        // 剰余演算により配列の先頭と末尾をつなげる\n        // i が配列の末尾を越えたら先頭に戻る\n        // i が配列の先頭を越えて前に出たら末尾に戻る\n        return (i + this.capacity()) % this.capacity();\n    }\n\n    /* キュー先頭にエンキュー */\n    pushFirst(num) {\n        if (this.#queSize === this.capacity()) {\n            console.log('両端キューがいっぱいです');\n            return;\n        }\n        // 先頭ポインタを左に 1 つ移動する\n        // 剰余演算により、front が配列先頭を越えた後に末尾へ戻るようにする\n        this.#front = this.index(this.#front - 1);\n        // num をキュー先頭に追加\n        this.#nums[this.#front] = num;\n        this.#queSize++;\n    }\n\n    /* キュー末尾にエンキュー */\n    pushLast(num) {\n        if (this.#queSize === this.capacity()) {\n            console.log('両端キューがいっぱいです');\n            return;\n        }\n        // キュー末尾ポインタを計算し、末尾インデックス + 1 を指す\n        const rear = this.index(this.#front + this.#queSize);\n        // num をキュー末尾に追加\n        this.#nums[rear] = num;\n        this.#queSize++;\n    }\n\n    /* キュー先頭からデキュー */\n    popFirst() {\n        const num = this.peekFirst();\n        // 先頭ポインタを 1 つ後ろへ進める\n        this.#front = this.index(this.#front + 1);\n        this.#queSize--;\n        return num;\n    }\n\n    /* キュー末尾からデキュー */\n    popLast() {\n        const num = this.peekLast();\n        this.#queSize--;\n        return num;\n    }\n\n    /* キュー先頭の要素にアクセス */\n    peekFirst() {\n        if (this.isEmpty()) throw new Error('The Deque Is Empty.');\n        return this.#nums[this.#front];\n    }\n\n    /* キュー末尾の要素にアクセス */\n    peekLast() {\n        if (this.isEmpty()) throw new Error('The Deque Is Empty.');\n        // 末尾要素のインデックスを計算\n        const last = this.index(this.#front + this.#queSize - 1);\n        return this.#nums[last];\n    }\n\n    /* 出力用の配列を返す */\n    toArray() {\n        // 有効長の範囲内のリスト要素のみを変換\n        const res = [];\n        for (let i = 0, j = this.#front; i &lt; this.#queSize; i++, j++) {\n            res[i] = this.#nums[this.index(j)];\n        }\n        return res;\n    }\n}\n</code></pre> array_deque.ts<pre><code>/* 循環配列ベースの両端キュー */\nclass ArrayDeque {\n    private nums: number[]; // 両端キューの要素を格納する配列\n    private front: number; // 先頭ポインタ。先頭要素を指す\n    private queSize: number; // 両端キューの長さ\n\n    /* コンストラクタ */\n    constructor(capacity: number) {\n        this.nums = new Array(capacity);\n        this.front = 0;\n        this.queSize = 0;\n    }\n\n    /* 両端キューの容量を取得 */\n    capacity(): number {\n        return this.nums.length;\n    }\n\n    /* 両端キューの長さを取得 */\n    size(): number {\n        return this.queSize;\n    }\n\n    /* 両端キューが空かどうかを判定 */\n    isEmpty(): boolean {\n        return this.queSize === 0;\n    }\n\n    /* 循環配列のインデックスを計算 */\n    index(i: number): number {\n        // 剰余演算により配列の先頭と末尾をつなげる\n        // i が配列の末尾を越えたら先頭に戻る\n        // i が配列の先頭を越えて前に出たら末尾に戻る\n        return (i + this.capacity()) % this.capacity();\n    }\n\n    /* キュー先頭にエンキュー */\n    pushFirst(num: number): void {\n        if (this.queSize === this.capacity()) {\n            console.log('両端キューは満杯です');\n            return;\n        }\n        // 先頭ポインタを左に 1 つ移動する\n        // 剰余演算により、front が配列先頭を越えた後に末尾へ戻るようにする\n        this.front = this.index(this.front - 1);\n        // num をキュー先頭に追加\n        this.nums[this.front] = num;\n        this.queSize++;\n    }\n\n    /* キュー末尾にエンキュー */\n    pushLast(num: number): void {\n        if (this.queSize === this.capacity()) {\n            console.log('両端キューは満杯です');\n            return;\n        }\n        // キュー末尾ポインタを計算し、末尾インデックス + 1 を指す\n        const rear: number = this.index(this.front + this.queSize);\n        // num をキュー末尾に追加\n        this.nums[rear] = num;\n        this.queSize++;\n    }\n\n    /* キュー先頭からデキュー */\n    popFirst(): number {\n        const num: number = this.peekFirst();\n        // 先頭ポインタを 1 つ後ろへ進める\n        this.front = this.index(this.front + 1);\n        this.queSize--;\n        return num;\n    }\n\n    /* キュー末尾からデキュー */\n    popLast(): number {\n        const num: number = this.peekLast();\n        this.queSize--;\n        return num;\n    }\n\n    /* キュー先頭の要素にアクセス */\n    peekFirst(): number {\n        if (this.isEmpty()) throw new Error('The Deque Is Empty.');\n        return this.nums[this.front];\n    }\n\n    /* キュー末尾の要素にアクセス */\n    peekLast(): number {\n        if (this.isEmpty()) throw new Error('The Deque Is Empty.');\n        // 末尾要素のインデックスを計算\n        const last = this.index(this.front + this.queSize - 1);\n        return this.nums[last];\n    }\n\n    /* 出力用の配列を返す */\n    toArray(): number[] {\n        // 有効長の範囲内のリスト要素のみを変換\n        const res: number[] = [];\n        for (let i = 0, j = this.front; i &lt; this.queSize; i++, j++) {\n            res[i] = this.nums[this.index(j)];\n        }\n        return res;\n    }\n}\n</code></pre> array_deque.dart<pre><code>/* 循環配列ベースの両端キュー */\nclass ArrayDeque {\n  late List&lt;int&gt; _nums; // 両端キューの要素を格納する配列\n  late int _front; // 先頭ポインタ。先頭要素を指す\n  late int _queSize; // 両端キューの長さ\n\n  /* コンストラクタ */\n  ArrayDeque(int capacity) {\n    this._nums = List.filled(capacity, 0);\n    this._front = this._queSize = 0;\n  }\n\n  /* 両端キューの容量を取得 */\n  int capacity() {\n    return _nums.length;\n  }\n\n  /* 両端キューの長さを取得 */\n  int size() {\n    return _queSize;\n  }\n\n  /* 両端キューが空かどうかを判定 */\n  bool isEmpty() {\n    return _queSize == 0;\n  }\n\n  /* 循環配列のインデックスを計算 */\n  int index(int i) {\n    // 剰余演算により配列の先頭と末尾をつなげる\n    // i が配列の末尾を越えたら先頭に戻る\n    // i が配列の先頭を越えて前に出たら末尾に戻る\n    return (i + capacity()) % capacity();\n  }\n\n  /* キュー先頭にエンキュー */\n  void pushFirst(int _num) {\n    if (_queSize == capacity()) {\n      throw Exception(\"両端キューがいっぱいです\");\n    }\n    // 先頭ポインタを左に 1 つ移動する\n    // 剰余演算により _front が配列の先頭を越えたあと末尾に戻るようにする\n    _front = index(_front - 1);\n    // _num をキューの先頭に追加\n    _nums[_front] = _num;\n    _queSize++;\n  }\n\n  /* キュー末尾にエンキュー */\n  void pushLast(int _num) {\n    if (_queSize == capacity()) {\n      throw Exception(\"両端キューがいっぱいです\");\n    }\n    // キュー末尾ポインタを計算し、末尾インデックス + 1 を指す\n    int rear = index(_front + _queSize);\n    // _num をキュー末尾に追加\n    _nums[rear] = _num;\n    _queSize++;\n  }\n\n  /* キュー先頭からデキュー */\n  int popFirst() {\n    int _num = peekFirst();\n    // 先頭ポインタを右に 1 つ移動する\n    _front = index(_front + 1);\n    _queSize--;\n    return _num;\n  }\n\n  /* キュー末尾からデキュー */\n  int popLast() {\n    int _num = peekLast();\n    _queSize--;\n    return _num;\n  }\n\n  /* キュー先頭の要素にアクセス */\n  int peekFirst() {\n    if (isEmpty()) {\n      throw Exception(\"両端キューが空です\");\n    }\n    return _nums[_front];\n  }\n\n  /* キュー末尾の要素にアクセス */\n  int peekLast() {\n    if (isEmpty()) {\n      throw Exception(\"両端キューが空です\");\n    }\n    // 末尾要素のインデックスを計算\n    int last = index(_front + _queSize - 1);\n    return _nums[last];\n  }\n\n  /* 出力用の配列を返す */\n  List&lt;int&gt; toArray() {\n    // 有効長の範囲内のリスト要素のみを変換\n    List&lt;int&gt; res = List.filled(_queSize, 0);\n    for (int i = 0, j = _front; i &lt; _queSize; i++, j++) {\n      res[i] = _nums[index(j)];\n    }\n    return res;\n  }\n}\n</code></pre> array_deque.rs<pre><code>/* 循環配列ベースの両端キュー */\nstruct ArrayDeque&lt;T&gt; {\n    nums: Vec&lt;T&gt;,    // 両端キューの要素を格納する配列\n    front: usize,    // 先頭ポインタ。先頭要素を指す\n    que_size: usize, // 両端キューの長さ\n}\n\nimpl&lt;T: Copy + Default&gt; ArrayDeque&lt;T&gt; {\n    /* コンストラクタ */\n    pub fn new(capacity: usize) -&gt; Self {\n        Self {\n            nums: vec![T::default(); capacity],\n            front: 0,\n            que_size: 0,\n        }\n    }\n\n    /* 両端キューの容量を取得 */\n    pub fn capacity(&amp;self) -&gt; usize {\n        self.nums.len()\n    }\n\n    /* 両端キューの長さを取得 */\n    pub fn size(&amp;self) -&gt; usize {\n        self.que_size\n    }\n\n    /* 両端キューが空かどうかを判定 */\n    pub fn is_empty(&amp;self) -&gt; bool {\n        self.que_size == 0\n    }\n\n    /* 循環配列のインデックスを計算 */\n    fn index(&amp;self, i: i32) -&gt; usize {\n        // 剰余演算により配列の先頭と末尾をつなげる\n        // i が配列の末尾を越えたら先頭に戻る\n        // i が配列の先頭を越えて前に出たら末尾に戻る\n        ((i + self.capacity() as i32) % self.capacity() as i32) as usize\n    }\n\n    /* キュー先頭にエンキュー */\n    pub fn push_first(&amp;mut self, num: T) {\n        if self.que_size == self.capacity() {\n            println!(\"両端キューがいっぱいです\");\n            return;\n        }\n        // 先頭ポインタを左に 1 つ移動する\n        // 剰余演算により、front が配列先頭を越えた後に末尾へ戻るようにする\n        self.front = self.index(self.front as i32 - 1);\n        // num をキュー先頭に追加\n        self.nums[self.front] = num;\n        self.que_size += 1;\n    }\n\n    /* キュー末尾にエンキュー */\n    pub fn push_last(&amp;mut self, num: T) {\n        if self.que_size == self.capacity() {\n            println!(\"両端キューがいっぱいです\");\n            return;\n        }\n        // キュー末尾ポインタを計算し、末尾インデックス + 1 を指す\n        let rear = self.index(self.front as i32 + self.que_size as i32);\n        // num をキュー末尾に追加\n        self.nums[rear] = num;\n        self.que_size += 1;\n    }\n\n    /* キュー先頭からデキュー */\n    fn pop_first(&amp;mut self) -&gt; T {\n        let num = self.peek_first();\n        // 先頭ポインタを 1 つ後ろへ進める\n        self.front = self.index(self.front as i32 + 1);\n        self.que_size -= 1;\n        num\n    }\n\n    /* キュー末尾からデキュー */\n    fn pop_last(&amp;mut self) -&gt; T {\n        let num = self.peek_last();\n        self.que_size -= 1;\n        num\n    }\n\n    /* キュー先頭の要素にアクセス */\n    fn peek_first(&amp;self) -&gt; T {\n        if self.is_empty() {\n            panic!(\"両端キューが空です\")\n        };\n        self.nums[self.front]\n    }\n\n    /* キュー末尾の要素にアクセス */\n    fn peek_last(&amp;self) -&gt; T {\n        if self.is_empty() {\n            panic!(\"両端キューが空です\")\n        };\n        // 末尾要素のインデックスを計算\n        let last = self.index(self.front as i32 + self.que_size as i32 - 1);\n        self.nums[last]\n    }\n\n    /* 出力用の配列を返す */\n    fn to_array(&amp;self) -&gt; Vec&lt;T&gt; {\n        // 有効長の範囲内のリスト要素のみを変換\n        let mut res = vec![T::default(); self.que_size];\n        let mut j = self.front;\n        for i in 0..self.que_size {\n            res[i] = self.nums[self.index(j as i32)];\n            j += 1;\n        }\n        res\n    }\n}\n</code></pre> array_deque.c<pre><code>/* 循環配列ベースの両端キュー */\ntypedef struct {\n    int *nums;       // キュー要素を格納する配列\n    int front;       // 先頭ポインタ。先頭要素を指す\n    int queSize;     // 末尾ポインタ。キューの末尾 + 1 を指す\n    int queCapacity; // キューの容量\n} ArrayDeque;\n\n/* コンストラクタ */\nArrayDeque *newArrayDeque(int capacity) {\n    ArrayDeque *deque = (ArrayDeque *)malloc(sizeof(ArrayDeque));\n    // 配列を初期化\n    deque-&gt;queCapacity = capacity;\n    deque-&gt;nums = (int *)malloc(sizeof(int) * deque-&gt;queCapacity);\n    deque-&gt;front = deque-&gt;queSize = 0;\n    return deque;\n}\n\n/* デストラクタ */\nvoid delArrayDeque(ArrayDeque *deque) {\n    free(deque-&gt;nums);\n    free(deque);\n}\n\n/* 両端キューの容量を取得 */\nint capacity(ArrayDeque *deque) {\n    return deque-&gt;queCapacity;\n}\n\n/* 両端キューの長さを取得 */\nint size(ArrayDeque *deque) {\n    return deque-&gt;queSize;\n}\n\n/* 両端キューが空かどうかを判定 */\nbool empty(ArrayDeque *deque) {\n    return deque-&gt;queSize == 0;\n}\n\n/* 循環配列のインデックスを計算 */\nint dequeIndex(ArrayDeque *deque, int i) {\n    // 剰余演算により配列の先頭と末尾をつなげる\n    // i が配列の末尾を越えたら先頭に戻る\n    // i が配列の先頭を越えたら末尾に戻る\n    return ((i + capacity(deque)) % capacity(deque));\n}\n\n/* キュー先頭にエンキュー */\nvoid pushFirst(ArrayDeque *deque, int num) {\n    if (deque-&gt;queSize == capacity(deque)) {\n        printf(\"両端キューがいっぱいです\\r\\n\");\n        return;\n    }\n    // 先頭ポインタを左に 1 つ移動する\n    // 剰余演算により front が配列の先頭を越えたあと末尾に戻るようにする\n    deque-&gt;front = dequeIndex(deque, deque-&gt;front - 1);\n    // num をキューの先頭に追加\n    deque-&gt;nums[deque-&gt;front] = num;\n    deque-&gt;queSize++;\n}\n\n/* キュー末尾にエンキュー */\nvoid pushLast(ArrayDeque *deque, int num) {\n    if (deque-&gt;queSize == capacity(deque)) {\n        printf(\"両端キューがいっぱいです\\r\\n\");\n        return;\n    }\n    // キュー末尾ポインタを計算し、末尾インデックス + 1 を指す\n    int rear = dequeIndex(deque, deque-&gt;front + deque-&gt;queSize);\n    // num をキュー末尾に追加\n    deque-&gt;nums[rear] = num;\n    deque-&gt;queSize++;\n}\n\n/* キュー先頭の要素にアクセス */\nint peekFirst(ArrayDeque *deque) {\n    // アクセス例外：双方向キューが空です\n    assert(empty(deque) == 0);\n    return deque-&gt;nums[deque-&gt;front];\n}\n\n/* キュー末尾の要素にアクセス */\nint peekLast(ArrayDeque *deque) {\n    // アクセス例外：双方向キューが空です\n    assert(empty(deque) == 0);\n    int last = dequeIndex(deque, deque-&gt;front + deque-&gt;queSize - 1);\n    return deque-&gt;nums[last];\n}\n\n/* キュー先頭からデキュー */\nint popFirst(ArrayDeque *deque) {\n    int num = peekFirst(deque);\n    // 先頭ポインタを 1 つ後ろへ進める\n    deque-&gt;front = dequeIndex(deque, deque-&gt;front + 1);\n    deque-&gt;queSize--;\n    return num;\n}\n\n/* キュー末尾からデキュー */\nint popLast(ArrayDeque *deque) {\n    int num = peekLast(deque);\n    deque-&gt;queSize--;\n    return num;\n}\n\n/* 出力用の配列を返す */\nint *toArray(ArrayDeque *deque, int *queSize) {\n    *queSize = deque-&gt;queSize;\n    int *res = (int *)calloc(deque-&gt;queSize, sizeof(int));\n    int j = deque-&gt;front;\n    for (int i = 0; i &lt; deque-&gt;queSize; i++) {\n        res[i] = deque-&gt;nums[j % deque-&gt;queCapacity];\n        j++;\n    }\n    return res;\n}\n</code></pre> array_deque.kt<pre><code>/* コンストラクタ */\nclass ArrayDeque(capacity: Int) {\n    private var nums: IntArray = IntArray(capacity) // 両端キューの要素を格納する配列\n    private var front: Int = 0 // 先頭ポインタ。先頭要素を指す\n    private var queSize: Int = 0 // 両端キューの長さ\n\n    /* 両端キューの容量を取得 */\n    fun capacity(): Int {\n        return nums.size\n    }\n\n    /* 両端キューの長さを取得 */\n    fun size(): Int {\n        return queSize\n    }\n\n    /* 両端キューが空かどうかを判定 */\n    fun isEmpty(): Boolean {\n        return queSize == 0\n    }\n\n    /* 循環配列のインデックスを計算 */\n    private fun index(i: Int): Int {\n        // 剰余演算により配列の先頭と末尾をつなげる\n        // i が配列の末尾を越えたら先頭に戻る\n        // i が配列の先頭を越えて前に出たら末尾に戻る\n        return (i + capacity()) % capacity()\n    }\n\n    /* キュー先頭にエンキュー */\n    fun pushFirst(num: Int) {\n        if (queSize == capacity()) {\n            println(\"双方向キューは満杯です\")\n            return\n        }\n        // 先頭ポインタを左に 1 つ移動する\n        // 剰余演算により、front が配列先頭を越えた後に末尾へ戻るようにする\n        front = index(front - 1)\n        // num をキュー先頭に追加\n        nums[front] = num\n        queSize++\n    }\n\n    /* キュー末尾にエンキュー */\n    fun pushLast(num: Int) {\n        if (queSize == capacity()) {\n            println(\"双方向キューは満杯です\")\n            return\n        }\n        // キュー末尾ポインタを計算し、末尾インデックス + 1 を指す\n        val rear = index(front + queSize)\n        // num をキュー末尾に追加\n        nums[rear] = num\n        queSize++\n    }\n\n    /* キュー先頭からデキュー */\n    fun popFirst(): Int {\n        val num = peekFirst()\n        // 先頭ポインタを 1 つ後ろへ進める\n        front = index(front + 1)\n        queSize--\n        return num\n    }\n\n    /* キュー末尾からデキュー */\n    fun popLast(): Int {\n        val num = peekLast()\n        queSize--\n        return num\n    }\n\n    /* キュー先頭の要素にアクセス */\n    fun peekFirst(): Int {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        return nums[front]\n    }\n\n    /* キュー末尾の要素にアクセス */\n    fun peekLast(): Int {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        // 末尾要素のインデックスを計算\n        val last = index(front + queSize - 1)\n        return nums[last]\n    }\n\n    /* 出力用の配列を返す */\n    fun toArray(): IntArray {\n        // 有効長の範囲内のリスト要素のみを変換\n        val res = IntArray(queSize)\n        var i = 0\n        var j = front\n        while (i &lt; queSize) {\n            res[i] = nums[index(j)]\n            i++\n            j++\n        }\n        return res\n    }\n}\n</code></pre> array_deque.rb<pre><code>### 循環配列で実装した両端キュー ###\nclass ArrayDeque\n  ### 両端キューの長さを取得 ###\n  attr_reader :size\n\n  ### コンストラクタ ###\n  def initialize(capacity)\n    @nums = Array.new(capacity, 0)\n    @front = 0\n    @size = 0\n  end\n\n  ### 両端キューの容量を取得 ###\n  def capacity\n    @nums.length\n  end\n\n  ### 両端キューが空か判定 ###\n  def is_empty?\n    size.zero?\n  end\n\n  ### キュー先頭に追加 ###\n  def push_first(num)\n    if size == capacity\n      puts '両端キューがいっぱいです'\n      return\n    end\n\n    # 先頭ポインタを左に 1 つ移動する\n    # 剰余演算により、front が配列先頭を越えた後に末尾へ戻るようにする\n    @front = index(@front - 1)\n    # num をキュー先頭に追加\n    @nums[@front] = num\n    @size += 1\n  end\n\n  ### キュー末尾に追加 ###\n  def push_last(num)\n    if size == capacity\n      puts '両端キューがいっぱいです'\n      return\n    end\n\n    # キュー末尾ポインタを計算し、末尾インデックス + 1 を指す\n    rear = index(@front + size)\n    # num をキュー末尾に追加\n    @nums[rear] = num\n    @size += 1\n  end\n\n  ### キュー先頭から取り出す ###\n  def pop_first\n    num = peek_first\n    # 先頭ポインタを 1 つ後ろへ進める\n    @front = index(@front + 1)\n    @size -= 1\n    num\n  end\n\n  ### キューの末尾から取り出す ###\n  def pop_last\n    num = peek_last\n    @size -= 1\n    num\n  end\n\n  ### 先頭要素にアクセス ###\n  def peek_first\n    raise IndexError, '両端キューは空です' if is_empty?\n\n    @nums[@front]\n  end\n\n  ### キュー末尾要素を参照 ###\n  def peek_last\n    raise IndexError, '両端キューは空です' if is_empty?\n\n    # 末尾要素のインデックスを計算\n    last = index(@front + size - 1)\n    @nums[last]\n  end\n\n  ### 表示用の配列を返す ###\n  def to_array\n    # 有効長の範囲内のリスト要素のみを変換\n    res = []\n    for i in 0...size\n      res &lt;&lt; @nums[index(@front + i)]\n    end\n    res\n  end\n\n  private\n\n  ### 循環配列のインデックスを計算 ###\n  def index(i)\n    # 剰余演算により配列の先頭と末尾をつなげる\n    # i が配列の末尾を越えたら先頭に戻る\n    # i が配列の先頭を越えて前に出たら末尾に戻る\n    (i + capacity) % capacity\n  end\nend\n</code></pre>","path":["第 5 章 &nbsp; スタックとキュー","5.3 &nbsp; 両端キュー"],"tags":[]},{"location":"chapter_stack_and_queue/deque/#533","level":2,"title":"5.3.3   両端キューの応用","text":"<p>両端キューはスタックとキューの両方の論理を備えているため、これら 2 つのすべての応用場面を実現でき、さらに高い自由度を提供します。</p> <p>私たちが知っているように、ソフトウェアの「元に戻す」機能は通常スタックを使って実装されます。システムは変更操作を毎回スタックに <code>push</code> し、その後 <code>pop</code> によって取り消しを実現します。しかし、システム資源の制約を考慮すると、通常ソフトウェアは取り消し可能な手数を制限します（たとえば \\(50\\) 手まで保存可能）。スタックの長さが \\(50\\) を超えると、ソフトウェアはスタックの底部（先頭）で削除操作を行う必要があります。しかしスタックではこの機能を実現できないため、この場合はスタックの代わりに両端キューを使用する必要があります。なお、「元に戻す」の中核ロジック自体は依然としてスタックの後入れ先出し原則に従っており、両端キューは追加のロジックをより柔軟に実装できるだけです。</p>","path":["第 5 章 &nbsp; スタックとキュー","5.3 &nbsp; 両端キュー"],"tags":[]},{"location":"chapter_stack_and_queue/queue/","level":1,"title":"5.2   キュー","text":"<p>キュー（queue）は、先入れ先出しの規則に従う線形データ構造です。名前のとおり、キューは順番待ちの現象を模したもので、新しく来た人は絶えずキュー末尾に加わり、キュー先頭にいる人から順に離れていきます。</p> <p>下図のように、キューの先頭を「キュー先頭」、末尾を「キュー末尾」と呼びます。要素をキュー末尾に加える操作を「エンキュー」、キュー先頭の要素を削除する操作を「デキュー」と呼びます。</p> <p></p> <p> 図 5-4   キューの先入れ先出し規則 </p>","path":["第 5 章 &nbsp; スタックとキュー","5.2 &nbsp; キュー"],"tags":[]},{"location":"chapter_stack_and_queue/queue/#521","level":2,"title":"5.2.1   キューの基本操作","text":"<p>キューの基本操作を以下の表に示します。なお、メソッド名はプログラミング言語によって異なる場合があります。ここではスタックと同じ命名を採用します。</p> <p> 表 5-2   キュー操作の効率 </p> メソッド名 説明 時間計算量 <code>push()</code> 要素をエンキューし、キュー末尾に追加する \\(O(1)\\) <code>pop()</code> キュー先頭の要素をデキューする \\(O(1)\\) <code>peek()</code> キュー先頭の要素にアクセスする \\(O(1)\\) <p>プログラミング言語に用意された既存のキュークラスをそのまま利用できます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby queue.py<pre><code>from collections import deque\n\n# キューを初期化\n# Python では、通常は双方向キュークラス deque をキューとして使用する\n# queue.Queue() は純粋なキュークラスだが、やや使いにくいため非推奨\nque: deque[int] = deque()\n\n# 要素をエンキュー\nque.append(1)\nque.append(3)\nque.append(2)\nque.append(5)\nque.append(4)\n\n# キュー先頭の要素にアクセス\nfront: int = que[0]\n\n# 要素をデキュー\npop: int = que.popleft()\n\n# キューの長さを取得\nsize: int = len(que)\n\n# キューが空かどうかを判定\nis_empty: bool = len(que) == 0\n</code></pre> queue.cpp<pre><code>/* キューを初期化 */\nqueue&lt;int&gt; queue;\n\n/* 要素をエンキュー */\nqueue.push(1);\nqueue.push(3);\nqueue.push(2);\nqueue.push(5);\nqueue.push(4);\n\n/* キュー先頭の要素にアクセス */\nint front = queue.front();\n\n/* 要素をデキュー */\nqueue.pop();\n\n/* キューの長さを取得 */\nint size = queue.size();\n\n/* キューが空かどうかを判定 */\nbool empty = queue.empty();\n</code></pre> queue.java<pre><code>/* キューを初期化 */\nQueue&lt;Integer&gt; queue = new LinkedList&lt;&gt;();\n\n/* 要素をエンキュー */\nqueue.offer(1);\nqueue.offer(3);\nqueue.offer(2);\nqueue.offer(5);\nqueue.offer(4);\n\n/* キュー先頭の要素にアクセス */\nint peek = queue.peek();\n\n/* 要素をデキュー */\nint pop = queue.poll();\n\n/* キューの長さを取得 */\nint size = queue.size();\n\n/* キューが空かどうかを判定 */\nboolean isEmpty = queue.isEmpty();\n</code></pre> queue.cs<pre><code>/* キューを初期化 */\nQueue&lt;int&gt; queue = new();\n\n/* 要素をエンキュー */\nqueue.Enqueue(1);\nqueue.Enqueue(3);\nqueue.Enqueue(2);\nqueue.Enqueue(5);\nqueue.Enqueue(4);\n\n/* キュー先頭の要素にアクセス */\nint peek = queue.Peek();\n\n/* 要素をデキュー */\nint pop = queue.Dequeue();\n\n/* キューの長さを取得 */\nint size = queue.Count;\n\n/* キューが空かどうかを判定 */\nbool isEmpty = queue.Count == 0;\n</code></pre> queue_test.go<pre><code>/* キューを初期化 */\n// Go では、list をキューとして使用する\nqueue := list.New()\n\n/* 要素をエンキュー */\nqueue.PushBack(1)\nqueue.PushBack(3)\nqueue.PushBack(2)\nqueue.PushBack(5)\nqueue.PushBack(4)\n\n/* キュー先頭の要素にアクセス */\npeek := queue.Front()\n\n/* 要素をデキュー */\npop := queue.Front()\nqueue.Remove(pop)\n\n/* キューの長さを取得 */\nsize := queue.Len()\n\n/* キューが空かどうかを判定 */\nisEmpty := queue.Len() == 0\n</code></pre> queue.swift<pre><code>/* キューを初期化 */\n// Swift には組み込みのキュークラスがないため、Array をキューとして使える\nvar queue: [Int] = []\n\n/* 要素をエンキュー */\nqueue.append(1)\nqueue.append(3)\nqueue.append(2)\nqueue.append(5)\nqueue.append(4)\n\n/* キュー先頭の要素にアクセス */\nlet peek = queue.first!\n\n/* 要素をデキュー */\n// 配列であるため、removeFirst の計算量は O(n)\nlet pool = queue.removeFirst()\n\n/* キューの長さを取得 */\nlet size = queue.count\n\n/* キューが空かどうかを判定 */\nlet isEmpty = queue.isEmpty\n</code></pre> queue.js<pre><code>/* キューを初期化 */\n// JavaScript には組み込みのキューがないため、Array をキューとして使える\nconst queue = [];\n\n/* 要素をエンキュー */\nqueue.push(1);\nqueue.push(3);\nqueue.push(2);\nqueue.push(5);\nqueue.push(4);\n\n/* キュー先頭の要素にアクセス */\nconst peek = queue[0];\n\n/* 要素をデキュー */\n// 基盤は配列であるため、shift() メソッドの時間計算量は O(n)\nconst pop = queue.shift();\n\n/* キューの長さを取得 */\nconst size = queue.length;\n\n/* キューが空かどうかを判定 */\nconst empty = queue.length === 0;\n</code></pre> queue.ts<pre><code>/* キューを初期化 */\n// TypeScript には組み込みのキューがないため、Array をキューとして使える\nconst queue: number[] = [];\n\n/* 要素をエンキュー */\nqueue.push(1);\nqueue.push(3);\nqueue.push(2);\nqueue.push(5);\nqueue.push(4);\n\n/* キュー先頭の要素にアクセス */\nconst peek = queue[0];\n\n/* 要素をデキュー */\n// 基盤は配列であるため、shift() メソッドの時間計算量は O(n)\nconst pop = queue.shift();\n\n/* キューの長さを取得 */\nconst size = queue.length;\n\n/* キューが空かどうかを判定 */\nconst empty = queue.length === 0;\n</code></pre> queue.dart<pre><code>/* キューを初期化 */\n// Dart では、キュークラス Qeque は双方向キューであり、キューとしても使用できる\nQueue&lt;int&gt; queue = Queue();\n\n/* 要素をエンキュー */\nqueue.add(1);\nqueue.add(3);\nqueue.add(2);\nqueue.add(5);\nqueue.add(4);\n\n/* キュー先頭の要素にアクセス */\nint peek = queue.first;\n\n/* 要素をデキュー */\nint pop = queue.removeFirst();\n\n/* キューの長さを取得 */\nint size = queue.length;\n\n/* キューが空かどうかを判定 */\nbool isEmpty = queue.isEmpty;\n</code></pre> queue.rs<pre><code>/* 双方向キューを初期化 */\n// Rust では双方向キューを通常のキューとして使う\nlet mut deque: VecDeque&lt;u32&gt; = VecDeque::new();\n\n/* 要素をエンキュー */\ndeque.push_back(1);\ndeque.push_back(3);\ndeque.push_back(2);\ndeque.push_back(5);\ndeque.push_back(4);\n\n/* キュー先頭の要素にアクセス */\nif let Some(front) = deque.front() {\n}\n\n/* 要素をデキュー */\nif let Some(pop) = deque.pop_front() {\n}\n\n/* キューの長さを取得 */\nlet size = deque.len();\n\n/* キューが空かどうかを判定 */\nlet is_empty = deque.is_empty();\n</code></pre> queue.c<pre><code>// C には組み込みのキューがない\n</code></pre> queue.kt<pre><code>/* キューを初期化 */\nval queue = LinkedList&lt;Int&gt;()\n\n/* 要素をエンキュー */\nqueue.offer(1)\nqueue.offer(3)\nqueue.offer(2)\nqueue.offer(5)\nqueue.offer(4)\n\n/* キュー先頭の要素にアクセス */\nval peek = queue.peek()\n\n/* 要素をデキュー */\nval pop = queue.poll()\n\n/* キューの長さを取得 */\nval size = queue.size\n\n/* キューが空かどうかを判定 */\nval isEmpty = queue.isEmpty()\n</code></pre> queue.rb<pre><code># キューを初期化\n# Ruby 組み込みのキュー（Thread::Queue) には peek と走査メソッドがないため、Array をキューとして使える\nqueue = []\n\n# 要素をエンキュー\nqueue.push(1)\nqueue.push(3)\nqueue.push(2)\nqueue.push(5)\nqueue.push(4)\n\n# キュー先頭の要素にアクセス\npeek = queue.first\n\n# 要素をデキュー\n# 注意：配列であるため、Array#shift メソッドの時間計算量は O(n)\npop = queue.shift\n\n# キューの長さを取得\nsize = queue.length\n\n# キューが空かどうかを判定\nis_empty = queue.empty?\n</code></pre> 可視化実行 <p>https://pythontutor.com/render.html#code=from%20collections%20import%20deque%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E9%98%9F%E5%88%97%0A%20%20%20%20%23%20%E5%9C%A8%20Python%20%E4%B8%AD%EF%BC%8C%E6%88%91%E4%BB%AC%E4%B8%80%E8%88%AC%E5%B0%86%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%E7%B1%BB%20deque%20%E7%9C%8B%E4%BD%9C%E9%98%9F%E5%88%97%E4%BD%BF%E7%94%A8%0A%20%20%20%20%23%20%E8%99%BD%E7%84%B6%20queue.Queue%28%29%20%E6%98%AF%E7%BA%AF%E6%AD%A3%E7%9A%84%E9%98%9F%E5%88%97%E7%B1%BB%EF%BC%8C%E4%BD%86%E4%B8%8D%E5%A4%AA%E5%A5%BD%E7%94%A8%0A%20%20%20%20que%20%3D%20deque%28%29%0A%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%85%A5%E9%98%9F%0A%20%20%20%20que.append%281%29%0A%20%20%20%20que.append%283%29%0A%20%20%20%20que.append%282%29%0A%20%20%20%20que.append%285%29%0A%20%20%20%20que.append%284%29%0A%20%20%20%20print%28%22%E9%98%9F%E5%88%97%20que%20%3D%22,%20que%29%0A%0A%20%20%20%20%23%20%E8%AE%BF%E9%97%AE%E9%98%9F%E9%A6%96%E5%85%83%E7%B4%A0%0A%20%20%20%20front%20%3D%20que%5B0%5D%0A%20%20%20%20print%28%22%E9%98%9F%E9%A6%96%E5%85%83%E7%B4%A0%20front%20%3D%22,%20front%29%0A%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%87%BA%E9%98%9F%0A%20%20%20%20pop%20%3D%20que.popleft%28%29%0A%20%20%20%20print%28%22%E5%87%BA%E9%98%9F%E5%85%83%E7%B4%A0%20pop%20%3D%22,%20pop%29%0A%20%20%20%20print%28%22%E5%87%BA%E9%98%9F%E5%90%8E%20que%20%3D%22,%20que%29%0A%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E9%98%9F%E5%88%97%E7%9A%84%E9%95%BF%E5%BA%A6%0A%20%20%20%20size%20%3D%20len%28que%29%0A%20%20%20%20print%28%22%E9%98%9F%E5%88%97%E9%95%BF%E5%BA%A6%20size%20%3D%22,%20size%29%0A%0A%20%20%20%20%23%20%E5%88%A4%E6%96%AD%E9%98%9F%E5%88%97%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%0A%20%20%20%20is_empty%20%3D%20len%28que%29%20%3D%3D%200%0A%20%20%20%20print%28%22%E9%98%9F%E5%88%97%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%20%3D%22,%20is_empty%29&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["第 5 章 &nbsp; スタックとキュー","5.2 &nbsp; キュー"],"tags":[]},{"location":"chapter_stack_and_queue/queue/#522","level":2,"title":"5.2.2   キューの実装","text":"<p>キューを実装するには、一方の端で要素を追加し、もう一方の端で要素を削除できるデータ構造が必要です。連結リストと配列はいずれもこの条件を満たします。</p>","path":["第 5 章 &nbsp; スタックとキュー","5.2 &nbsp; キュー"],"tags":[]},{"location":"chapter_stack_and_queue/queue/#1","level":3,"title":"1.   連結リストに基づく実装","text":"<p>下図のように、連結リストの「先頭ノード」と「末尾ノード」をそれぞれ「キュー先頭」と「キュー末尾」とみなし、キュー末尾ではノードの追加のみ、キュー先頭ではノードの削除のみを行うようにします。</p> LinkedListQueuepush()pop() <p></p> <p></p> <p></p> <p> 図 5-5   連結リストでキューを実装したエンキューとデキュー操作 </p> <p>以下は連結リストでキューを実装するコードです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linkedlist_queue.py<pre><code>class LinkedListQueue:\n    \"\"\"連結リストベースのキュー\"\"\"\n\n    def __init__(self):\n        \"\"\"コンストラクタ\"\"\"\n        self._front: ListNode | None = None  # 先頭ノード front\n        self._rear: ListNode | None = None  # 末尾ノード rear\n        self._size: int = 0\n\n    def size(self) -&gt; int:\n        \"\"\"キューの長さを取得\"\"\"\n        return self._size\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"キューが空かどうかを判定\"\"\"\n        return self._size == 0\n\n    def push(self, num: int):\n        \"\"\"エンキュー\"\"\"\n        # 末尾ノードの後ろに num を追加\n        node = ListNode(num)\n        # キューが空なら、先頭・末尾ノードをともにそのノードに設定\n        if self._front is None:\n            self._front = node\n            self._rear = node\n        # キューが空でなければ、そのノードを末尾ノードの後ろに追加\n        else:\n            self._rear.next = node\n            self._rear = node\n        self._size += 1\n\n    def pop(self) -&gt; int:\n        \"\"\"デキュー\"\"\"\n        num = self.peek()\n        # 先頭ノードを削除\n        self._front = self._front.next\n        self._size -= 1\n        return num\n\n    def peek(self) -&gt; int:\n        \"\"\"キュー先頭の要素にアクセス\"\"\"\n        if self.is_empty():\n            raise IndexError(\"キューが空です\")\n        return self._front.val\n\n    def to_list(self) -&gt; list[int]:\n        \"\"\"表示用にリストへ変換\"\"\"\n        queue = []\n        temp = self._front\n        while temp:\n            queue.append(temp.val)\n            temp = temp.next\n        return queue\n</code></pre> linkedlist_queue.cpp<pre><code>/* 連結リストベースのキュー */\nclass LinkedListQueue {\n  private:\n    ListNode *front, *rear; // 先頭ノード front、末尾ノード rear\n    int queSize;\n\n  public:\n    LinkedListQueue() {\n        front = nullptr;\n        rear = nullptr;\n        queSize = 0;\n    }\n\n    ~LinkedListQueue() {\n        // 連結リストを走査してノードを削除し、メモリを解放する\n        freeMemoryLinkedList(front);\n    }\n\n    /* キューの長さを取得 */\n    int size() {\n        return queSize;\n    }\n\n    /* キューが空かどうかを判定 */\n    bool isEmpty() {\n        return queSize == 0;\n    }\n\n    /* エンキュー */\n    void push(int num) {\n        // 末尾ノードの後ろに num を追加\n        ListNode *node = new ListNode(num);\n        // キューが空なら、先頭・末尾ノードをともにそのノードに設定\n        if (front == nullptr) {\n            front = node;\n            rear = node;\n        }\n        // キューが空でなければ、そのノードを末尾ノードの後ろに追加\n        else {\n            rear-&gt;next = node;\n            rear = node;\n        }\n        queSize++;\n    }\n\n    /* デキュー */\n    int pop() {\n        int num = peek();\n        // 先頭ノードを削除\n        ListNode *tmp = front;\n        front = front-&gt;next;\n        // メモリを解放する\n        delete tmp;\n        queSize--;\n        return num;\n    }\n\n    /* キュー先頭の要素にアクセス */\n    int peek() {\n        if (size() == 0)\n            throw out_of_range(\"キューが空です\");\n        return front-&gt;val;\n    }\n\n    /* 連結リストを Vector に変換して返す */\n    vector&lt;int&gt; toVector() {\n        ListNode *node = front;\n        vector&lt;int&gt; res(size());\n        for (int i = 0; i &lt; res.size(); i++) {\n            res[i] = node-&gt;val;\n            node = node-&gt;next;\n        }\n        return res;\n    }\n};\n</code></pre> linkedlist_queue.java<pre><code>/* 連結リストベースのキュー */\nclass LinkedListQueue {\n    private ListNode front, rear; // 先頭ノード front、末尾ノード rear\n    private int queSize = 0;\n\n    public LinkedListQueue() {\n        front = null;\n        rear = null;\n    }\n\n    /* キューの長さを取得 */\n    public int size() {\n        return queSize;\n    }\n\n    /* キューが空かどうかを判定 */\n    public boolean isEmpty() {\n        return size() == 0;\n    }\n\n    /* エンキュー */\n    public void push(int num) {\n        // 末尾ノードの後ろに num を追加\n        ListNode node = new ListNode(num);\n        // キューが空なら、先頭・末尾ノードをともにそのノードに設定\n        if (front == null) {\n            front = node;\n            rear = node;\n        // キューが空でなければ、そのノードを末尾ノードの後ろに追加\n        } else {\n            rear.next = node;\n            rear = node;\n        }\n        queSize++;\n    }\n\n    /* デキュー */\n    public int pop() {\n        int num = peek();\n        // 先頭ノードを削除\n        front = front.next;\n        queSize--;\n        return num;\n    }\n\n    /* キュー先頭の要素にアクセス */\n    public int peek() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return front.val;\n    }\n\n    /* 連結リストを Array に変換して返す */\n    public int[] toArray() {\n        ListNode node = front;\n        int[] res = new int[size()];\n        for (int i = 0; i &lt; res.length; i++) {\n            res[i] = node.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_queue.cs<pre><code>/* 連結リストベースのキュー */\nclass LinkedListQueue {\n    ListNode? front, rear;  // 先頭ノード front、末尾ノード rear\n    int queSize = 0;\n\n    public LinkedListQueue() {\n        front = null;\n        rear = null;\n    }\n\n    /* キューの長さを取得 */\n    public int Size() {\n        return queSize;\n    }\n\n    /* キューが空かどうかを判定 */\n    public bool IsEmpty() {\n        return Size() == 0;\n    }\n\n    /* エンキュー */\n    public void Push(int num) {\n        // 末尾ノードの後ろに num を追加\n        ListNode node = new(num);\n        // キューが空なら、先頭・末尾ノードをともにそのノードに設定\n        if (front == null) {\n            front = node;\n            rear = node;\n            // キューが空でなければ、そのノードを末尾ノードの後ろに追加\n        } else if (rear != null) {\n            rear.next = node;\n            rear = node;\n        }\n        queSize++;\n    }\n\n    /* デキュー */\n    public int Pop() {\n        int num = Peek();\n        // 先頭ノードを削除\n        front = front?.next;\n        queSize--;\n        return num;\n    }\n\n    /* キュー先頭の要素にアクセス */\n    public int Peek() {\n        if (IsEmpty())\n            throw new Exception();\n        return front!.val;\n    }\n\n    /* 連結リストを Array に変換して返す */\n    public int[] ToArray() {\n        if (front == null)\n            return [];\n\n        ListNode? node = front;\n        int[] res = new int[Size()];\n        for (int i = 0; i &lt; res.Length; i++) {\n            res[i] = node!.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_queue.go<pre><code>/* 連結リストベースのキュー */\ntype linkedListQueue struct {\n    // 組み込みパッケージ list でキューを実装する\n    data *list.List\n}\n\n/* キューを初期化 */\nfunc newLinkedListQueue() *linkedListQueue {\n    return &amp;linkedListQueue{\n        data: list.New(),\n    }\n}\n\n/* エンキュー */\nfunc (s *linkedListQueue) push(value any) {\n    s.data.PushBack(value)\n}\n\n/* デキュー */\nfunc (s *linkedListQueue) pop() any {\n    if s.isEmpty() {\n        return nil\n    }\n    e := s.data.Front()\n    s.data.Remove(e)\n    return e.Value\n}\n\n/* キュー先頭の要素にアクセス */\nfunc (s *linkedListQueue) peek() any {\n    if s.isEmpty() {\n        return nil\n    }\n    e := s.data.Front()\n    return e.Value\n}\n\n/* キューの長さを取得 */\nfunc (s *linkedListQueue) size() int {\n    return s.data.Len()\n}\n\n/* キューが空かどうかを判定 */\nfunc (s *linkedListQueue) isEmpty() bool {\n    return s.data.Len() == 0\n}\n\n/* 表示用に List を取得 */\nfunc (s *linkedListQueue) toList() *list.List {\n    return s.data\n}\n</code></pre> linkedlist_queue.swift<pre><code>/* 連結リストベースのキュー */\nclass LinkedListQueue {\n    private var front: ListNode? // 先頭ノード\n    private var rear: ListNode? // 末尾ノード\n    private var _size: Int\n\n    init() {\n        _size = 0\n    }\n\n    /* キューの長さを取得 */\n    func size() -&gt; Int {\n        _size\n    }\n\n    /* キューが空かどうかを判定 */\n    func isEmpty() -&gt; Bool {\n        size() == 0\n    }\n\n    /* エンキュー */\n    func push(num: Int) {\n        // 末尾ノードの後ろに num を追加\n        let node = ListNode(x: num)\n        // キューが空なら、先頭・末尾ノードをともにそのノードに設定\n        if front == nil {\n            front = node\n            rear = node\n        }\n        // キューが空でなければ、そのノードを末尾ノードの後ろに追加\n        else {\n            rear?.next = node\n            rear = node\n        }\n        _size += 1\n    }\n\n    /* デキュー */\n    @discardableResult\n    func pop() -&gt; Int {\n        let num = peek()\n        // 先頭ノードを削除\n        front = front?.next\n        _size -= 1\n        return num\n    }\n\n    /* キュー先頭の要素にアクセス */\n    func peek() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"キューが空です\")\n        }\n        return front!.val\n    }\n\n    /* 連結リストを Array に変換して返す */\n    func toArray() -&gt; [Int] {\n        var node = front\n        var res = Array(repeating: 0, count: size())\n        for i in res.indices {\n            res[i] = node!.val\n            node = node?.next\n        }\n        return res\n    }\n}\n</code></pre> linkedlist_queue.js<pre><code>/* 連結リストベースのキュー */\nclass LinkedListQueue {\n    #front; // 先頭ノード #front\n    #rear; // 末尾ノード #rear\n    #queSize = 0;\n\n    constructor() {\n        this.#front = null;\n        this.#rear = null;\n    }\n\n    /* キューの長さを取得 */\n    get size() {\n        return this.#queSize;\n    }\n\n    /* キューが空かどうかを判定 */\n    isEmpty() {\n        return this.size === 0;\n    }\n\n    /* エンキュー */\n    push(num) {\n        // 末尾ノードの後ろに num を追加\n        const node = new ListNode(num);\n        // キューが空なら、先頭・末尾ノードをともにそのノードに設定\n        if (!this.#front) {\n            this.#front = node;\n            this.#rear = node;\n            // キューが空でなければ、そのノードを末尾ノードの後ろに追加\n        } else {\n            this.#rear.next = node;\n            this.#rear = node;\n        }\n        this.#queSize++;\n    }\n\n    /* デキュー */\n    pop() {\n        const num = this.peek();\n        // 先頭ノードを削除\n        this.#front = this.#front.next;\n        this.#queSize--;\n        return num;\n    }\n\n    /* キュー先頭の要素にアクセス */\n    peek() {\n        if (this.size === 0) throw new Error('キューが空');\n        return this.#front.val;\n    }\n\n    /* 連結リストを Array に変換して返す */\n    toArray() {\n        let node = this.#front;\n        const res = new Array(this.size);\n        for (let i = 0; i &lt; res.length; i++) {\n            res[i] = node.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_queue.ts<pre><code>/* 連結リストベースのキュー */\nclass LinkedListQueue {\n    private front: ListNode | null; // 先頭ノード front\n    private rear: ListNode | null; // 末尾ノード rear\n    private queSize: number = 0;\n\n    constructor() {\n        this.front = null;\n        this.rear = null;\n    }\n\n    /* キューの長さを取得 */\n    get size(): number {\n        return this.queSize;\n    }\n\n    /* キューが空かどうかを判定 */\n    isEmpty(): boolean {\n        return this.size === 0;\n    }\n\n    /* エンキュー */\n    push(num: number): void {\n        // 末尾ノードの後ろに num を追加\n        const node = new ListNode(num);\n        // キューが空なら、先頭・末尾ノードをともにそのノードに設定\n        if (!this.front) {\n            this.front = node;\n            this.rear = node;\n            // キューが空でなければ、そのノードを末尾ノードの後ろに追加\n        } else {\n            this.rear!.next = node;\n            this.rear = node;\n        }\n        this.queSize++;\n    }\n\n    /* デキュー */\n    pop(): number {\n        const num = this.peek();\n        if (!this.front) throw new Error('キューが空です');\n        // 先頭ノードを削除\n        this.front = this.front.next;\n        this.queSize--;\n        return num;\n    }\n\n    /* キュー先頭の要素にアクセス */\n    peek(): number {\n        if (this.size === 0) throw new Error('キューが空です');\n        return this.front!.val;\n    }\n\n    /* 連結リストを Array に変換して返す */\n    toArray(): number[] {\n        let node = this.front;\n        const res = new Array&lt;number&gt;(this.size);\n        for (let i = 0; i &lt; res.length; i++) {\n            res[i] = node!.val;\n            node = node!.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_queue.dart<pre><code>/* 連結リストベースのキュー */\nclass LinkedListQueue {\n  ListNode? _front; // 先頭ノード _front\n  ListNode? _rear; // 末尾ノード _rear\n  int _queSize = 0; // キューの長さ\n\n  LinkedListQueue() {\n    _front = null;\n    _rear = null;\n  }\n\n  /* キューの長さを取得 */\n  int size() {\n    return _queSize;\n  }\n\n  /* キューが空かどうかを判定 */\n  bool isEmpty() {\n    return _queSize == 0;\n  }\n\n  /* エンキュー */\n  void push(int _num) {\n    // 末尾ノードの後ろに _num を追加\n    final node = ListNode(_num);\n    // キューが空なら、先頭・末尾ノードをともにそのノードに設定\n    if (_front == null) {\n      _front = node;\n      _rear = node;\n    } else {\n      // キューが空でなければ、そのノードを末尾ノードの後ろに追加\n      _rear!.next = node;\n      _rear = node;\n    }\n    _queSize++;\n  }\n\n  /* デキュー */\n  int pop() {\n    final int _num = peek();\n    // 先頭ノードを削除\n    _front = _front!.next;\n    _queSize--;\n    return _num;\n  }\n\n  /* キュー先頭の要素にアクセス */\n  int peek() {\n    if (_queSize == 0) {\n      throw Exception('キューが空です');\n    }\n    return _front!.val;\n  }\n\n  /* 連結リストを Array に変換して返す */\n  List&lt;int&gt; toArray() {\n    ListNode? node = _front;\n    final List&lt;int&gt; queue = [];\n    while (node != null) {\n      queue.add(node.val);\n      node = node.next;\n    }\n    return queue;\n  }\n}\n</code></pre> linkedlist_queue.rs<pre><code>/* 連結リストベースのキュー */\n#[allow(dead_code)]\npub struct LinkedListQueue&lt;T&gt; {\n    front: Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;, // 先頭ノード front\n    rear: Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;,  // 末尾ノード rear\n    que_size: usize,                         // キューの長さ\n}\n\nimpl&lt;T: Copy&gt; LinkedListQueue&lt;T&gt; {\n    pub fn new() -&gt; Self {\n        Self {\n            front: None,\n            rear: None,\n            que_size: 0,\n        }\n    }\n\n    /* キューの長さを取得 */\n    pub fn size(&amp;self) -&gt; usize {\n        return self.que_size;\n    }\n\n    /* キューが空かどうかを判定 */\n    pub fn is_empty(&amp;self) -&gt; bool {\n        return self.que_size == 0;\n    }\n\n    /* エンキュー */\n    pub fn push(&amp;mut self, num: T) {\n        // 末尾ノードの後ろに num を追加\n        let new_rear = ListNode::new(num);\n        match self.rear.take() {\n            // キューが空でなければ、そのノードを末尾ノードの後ろに追加\n            Some(old_rear) =&gt; {\n                old_rear.borrow_mut().next = Some(new_rear.clone());\n                self.rear = Some(new_rear);\n            }\n            // キューが空なら、先頭・末尾ノードをともにそのノードに設定\n            None =&gt; {\n                self.front = Some(new_rear.clone());\n                self.rear = Some(new_rear);\n            }\n        }\n        self.que_size += 1;\n    }\n\n    /* デキュー */\n    pub fn pop(&amp;mut self) -&gt; Option&lt;T&gt; {\n        self.front.take().map(|old_front| {\n            match old_front.borrow_mut().next.take() {\n                Some(new_front) =&gt; {\n                    self.front = Some(new_front);\n                }\n                None =&gt; {\n                    self.rear.take();\n                }\n            }\n            self.que_size -= 1;\n            old_front.borrow().val\n        })\n    }\n\n    /* キュー先頭の要素にアクセス */\n    pub fn peek(&amp;self) -&gt; Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt; {\n        self.front.as_ref()\n    }\n\n    /* 連結リストを Array に変換して返す */\n    pub fn to_array(&amp;self, head: Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;) -&gt; Vec&lt;T&gt; {\n        let mut res: Vec&lt;T&gt; = Vec::new();\n\n        fn recur&lt;T: Copy&gt;(cur: Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;, res: &amp;mut Vec&lt;T&gt;) {\n            if let Some(cur) = cur {\n                res.push(cur.borrow().val);\n                recur(cur.borrow().next.as_ref(), res);\n            }\n        }\n\n        recur(head, &amp;mut res);\n\n        res\n    }\n}\n</code></pre> linkedlist_queue.c<pre><code>/* 連結リストベースのキュー */\ntypedef struct {\n    ListNode *front, *rear;\n    int queSize;\n} LinkedListQueue;\n\n/* コンストラクタ */\nLinkedListQueue *newLinkedListQueue() {\n    LinkedListQueue *queue = (LinkedListQueue *)malloc(sizeof(LinkedListQueue));\n    queue-&gt;front = NULL;\n    queue-&gt;rear = NULL;\n    queue-&gt;queSize = 0;\n    return queue;\n}\n\n/* デストラクタ */\nvoid delLinkedListQueue(LinkedListQueue *queue) {\n    // すべてのノードを解放\n    while (queue-&gt;front != NULL) {\n        ListNode *tmp = queue-&gt;front;\n        queue-&gt;front = queue-&gt;front-&gt;next;\n        free(tmp);\n    }\n    // queue 構造体を解放する\n    free(queue);\n}\n\n/* キューの長さを取得 */\nint size(LinkedListQueue *queue) {\n    return queue-&gt;queSize;\n}\n\n/* キューが空かどうかを判定 */\nbool empty(LinkedListQueue *queue) {\n    return (size(queue) == 0);\n}\n\n/* エンキュー */\nvoid push(LinkedListQueue *queue, int num) {\n    // 末尾ノードに node を追加\n    ListNode *node = newListNode(num);\n    // キューが空なら、先頭・末尾ノードをともにそのノードに設定\n    if (queue-&gt;front == NULL) {\n        queue-&gt;front = node;\n        queue-&gt;rear = node;\n    }\n    // キューが空でなければ、そのノードを末尾ノードの後ろに追加\n    else {\n        queue-&gt;rear-&gt;next = node;\n        queue-&gt;rear = node;\n    }\n    queue-&gt;queSize++;\n}\n\n/* キュー先頭の要素にアクセス */\nint peek(LinkedListQueue *queue) {\n    assert(size(queue) &amp;&amp; queue-&gt;front);\n    return queue-&gt;front-&gt;val;\n}\n\n/* デキュー */\nint pop(LinkedListQueue *queue) {\n    int num = peek(queue);\n    ListNode *tmp = queue-&gt;front;\n    queue-&gt;front = queue-&gt;front-&gt;next;\n    free(tmp);\n    queue-&gt;queSize--;\n    return num;\n}\n\n/* キューを出力する */\nvoid printLinkedListQueue(LinkedListQueue *queue) {\n    int *arr = malloc(sizeof(int) * queue-&gt;queSize);\n    // 連結リスト内のデータを配列にコピー\n    int i;\n    ListNode *node;\n    for (i = 0, node = queue-&gt;front; i &lt; queue-&gt;queSize; i++) {\n        arr[i] = node-&gt;val;\n        node = node-&gt;next;\n    }\n    printArray(arr, queue-&gt;queSize);\n    free(arr);\n}\n</code></pre> linkedlist_queue.kt<pre><code>/* 連結リストベースのキュー */\nclass LinkedListQueue(\n    // 先頭ノード front、末尾ノード rear\n    private var front: ListNode? = null,\n    private var rear: ListNode? = null,\n    private var queSize: Int = 0\n) {\n\n    /* キューの長さを取得 */\n    fun size(): Int {\n        return queSize\n    }\n\n    /* キューが空かどうかを判定 */\n    fun isEmpty(): Boolean {\n        return size() == 0\n    }\n\n    /* エンキュー */\n    fun push(num: Int) {\n        // 末尾ノードの後ろに num を追加\n        val node = ListNode(num)\n        // キューが空なら、先頭・末尾ノードをともにそのノードに設定\n        if (front == null) {\n            front = node\n            rear = node\n            // キューが空でなければ、そのノードを末尾ノードの後ろに追加\n        } else {\n            rear?.next = node\n            rear = node\n        }\n        queSize++\n    }\n\n    /* デキュー */\n    fun pop(): Int {\n        val num = peek()\n        // 先頭ノードを削除\n        front = front?.next\n        queSize--\n        return num\n    }\n\n    /* キュー先頭の要素にアクセス */\n    fun peek(): Int {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        return front!!._val\n    }\n\n    /* 連結リストを Array に変換して返す */\n    fun toArray(): IntArray {\n        var node = front\n        val res = IntArray(size())\n        for (i in res.indices) {\n            res[i] = node!!._val\n            node = node.next\n        }\n        return res\n    }\n}\n</code></pre> linkedlist_queue.rb<pre><code>### 連結リストで実装したキュー ###\nclass LinkedListQueue\n  ### キューの長さを取得 ###\n  attr_reader :size\n\n  ### コンストラクタ ###\n  def initialize\n    @front = nil  # 先頭ノード front\n    @rear = nil   # 末尾ノード rear\n    @size = 0\n  end\n\n  ### キューが空か判定 ###\n  def is_empty?\n    @front.nil?\n  end\n\n  ### エンキュー ###\n  def push(num)\n    # 末尾ノードの後ろに num を追加\n    node = ListNode.new(num)\n\n    # キューが空なら、先頭ノードと末尾ノードの両方をそのノードに向ける\n    if @front.nil?\n      @front = node\n      @rear = node\n    # キューが空でなければ、そのノードを末尾ノードの後ろに追加する\n    else\n      @rear.next = node\n      @rear = node\n    end\n\n    @size += 1\n  end\n\n  ### デキュー ###\n  def pop\n    num = peek\n    # 先頭ノードを削除\n    @front = @front.next\n    @size -= 1\n    num\n  end\n\n  ### 先頭要素にアクセス ###\n  def peek\n    raise IndexError, 'キューは空です' if is_empty?\n\n    @front.val\n  end\n\n  ### 連結リストを Array に変換して返す ###\n  def to_array\n    queue = []\n    temp = @front\n    while temp\n      queue &lt;&lt; temp.val\n      temp = temp.next\n    end\n    queue\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 5 章 &nbsp; スタックとキュー","5.2 &nbsp; キュー"],"tags":[]},{"location":"chapter_stack_and_queue/queue/#2","level":3,"title":"2.   配列に基づく実装","text":"<p>配列で先頭要素を削除する時間計算量は \\(O(n)\\) であり、そのままではデキュー操作の効率が低くなります。しかし、次の巧妙な方法によってこの問題を回避できます。</p> <p>変数 <code>front</code> を用いてキュー先頭要素のインデックスを指し、さらに変数 <code>size</code> でキューの長さを記録できます。<code>rear = front + size</code> と定義すると、この式で得られる <code>rear</code> はキュー末尾要素の次の位置を指します。</p> <p>この設計に基づくと、配列内で要素を含む有効区間は <code>[front, rear - 1]</code> となります。各種操作の実装方法を下図に示します。</p> <ul> <li>エンキュー操作：入力要素を <code>rear</code> の位置に代入し、<code>size</code> を 1 増やします。</li> <li>デキュー操作：<code>front</code> を 1 増やし、<code>size</code> を 1 減らすだけです。</li> </ul> <p>このように、エンキューとデキューはいずれも 1 回の操作だけで済み、時間計算量はともに \\(O(1)\\) です。</p> ArrayQueuepush()pop() <p></p> <p></p> <p></p> <p> 図 5-6   配列でキューを実装したエンキューとデキュー操作 </p> <p>ここで 1 つ問題があります。エンキューとデキューを繰り返すと、<code>front</code> と <code>rear</code> はどちらも右へ移動し続け、配列の末尾に達するとそれ以上進めなくなります。この問題を解決するために、配列を先頭と末尾がつながった「環状配列」とみなします。</p> <p>環状配列では、<code>front</code> または <code>rear</code> が配列末尾を越えたときに、直ちに配列先頭へ戻って走査を続けられるようにする必要があります。この周期的な規則は「剰余演算」によって実現できます。コードは次のとおりです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array_queue.py<pre><code>class ArrayQueue:\n    \"\"\"循環配列ベースのキュー\"\"\"\n\n    def __init__(self, size: int):\n        \"\"\"コンストラクタ\"\"\"\n        self._nums: list[int] = [0] * size  # キュー要素を格納する配列\n        self._front: int = 0  # 先頭ポインタ。先頭要素を指す\n        self._size: int = 0  # キューの長さ\n\n    def capacity(self) -&gt; int:\n        \"\"\"キューの容量を取得\"\"\"\n        return len(self._nums)\n\n    def size(self) -&gt; int:\n        \"\"\"キューの長さを取得\"\"\"\n        return self._size\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"キューが空かどうかを判定\"\"\"\n        return self._size == 0\n\n    def push(self, num: int):\n        \"\"\"エンキュー\"\"\"\n        if self._size == self.capacity():\n            raise IndexError(\"キューがいっぱいです\")\n        # 末尾ポインタを計算し、末尾インデックス + 1 を指す\n        # 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする\n        rear: int = (self._front + self._size) % self.capacity()\n        # num をキュー末尾に追加\n        self._nums[rear] = num\n        self._size += 1\n\n    def pop(self) -&gt; int:\n        \"\"\"デキュー\"\"\"\n        num: int = self.peek()\n        # 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す\n        self._front = (self._front + 1) % self.capacity()\n        self._size -= 1\n        return num\n\n    def peek(self) -&gt; int:\n        \"\"\"キュー先頭の要素にアクセス\"\"\"\n        if self.is_empty():\n            raise IndexError(\"キューが空です\")\n        return self._nums[self._front]\n\n    def to_list(self) -&gt; list[int]:\n        \"\"\"表示用のリストを返す\"\"\"\n        res = [0] * self.size()\n        j: int = self._front\n        for i in range(self.size()):\n            res[i] = self._nums[(j % self.capacity())]\n            j += 1\n        return res\n</code></pre> array_queue.cpp<pre><code>/* 循環配列ベースのキュー */\nclass ArrayQueue {\n  private:\n    int *nums;       // キュー要素を格納する配列\n    int front;       // 先頭ポインタ。先頭要素を指す\n    int queSize;     // キューの長さ\n    int queCapacity; // キューの容量\n\n  public:\n    ArrayQueue(int capacity) {\n        // 配列を初期化\n        nums = new int[capacity];\n        queCapacity = capacity;\n        front = queSize = 0;\n    }\n\n    ~ArrayQueue() {\n        delete[] nums;\n    }\n\n    /* キューの容量を取得 */\n    int capacity() {\n        return queCapacity;\n    }\n\n    /* キューの長さを取得 */\n    int size() {\n        return queSize;\n    }\n\n    /* キューが空かどうかを判定 */\n    bool isEmpty() {\n        return size() == 0;\n    }\n\n    /* エンキュー */\n    void push(int num) {\n        if (queSize == queCapacity) {\n            cout &lt;&lt; \"キューがいっぱいです\" &lt;&lt; endl;\n            return;\n        }\n        // 末尾ポインタを計算し、末尾インデックス + 1 を指す\n        // 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする\n        int rear = (front + queSize) % queCapacity;\n        // num をキュー末尾に追加\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* デキュー */\n    int pop() {\n        int num = peek();\n        // 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す\n        front = (front + 1) % queCapacity;\n        queSize--;\n        return num;\n    }\n\n    /* キュー先頭の要素にアクセス */\n    int peek() {\n        if (isEmpty())\n            throw out_of_range(\"キューが空です\");\n        return nums[front];\n    }\n\n    /* 配列を Vector に変換して返す */\n    vector&lt;int&gt; toVector() {\n        // 有効長の範囲内のリスト要素のみを変換\n        vector&lt;int&gt; arr(queSize);\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            arr[i] = nums[j % queCapacity];\n        }\n        return arr;\n    }\n};\n</code></pre> array_queue.java<pre><code>/* 循環配列ベースのキュー */\nclass ArrayQueue {\n    private int[] nums; // キュー要素を格納する配列\n    private int front; // 先頭ポインタ。先頭要素を指す\n    private int queSize; // キューの長さ\n\n    public ArrayQueue(int capacity) {\n        nums = new int[capacity];\n        front = queSize = 0;\n    }\n\n    /* キューの容量を取得 */\n    public int capacity() {\n        return nums.length;\n    }\n\n    /* キューの長さを取得 */\n    public int size() {\n        return queSize;\n    }\n\n    /* キューが空かどうかを判定 */\n    public boolean isEmpty() {\n        return queSize == 0;\n    }\n\n    /* エンキュー */\n    public void push(int num) {\n        if (queSize == capacity()) {\n            System.out.println(\"キューは満杯です\");\n            return;\n        }\n        // 末尾ポインタを計算し、末尾インデックス + 1 を指す\n        // 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする\n        int rear = (front + queSize) % capacity();\n        // num をキュー末尾に追加\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* デキュー */\n    public int pop() {\n        int num = peek();\n        // 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す\n        front = (front + 1) % capacity();\n        queSize--;\n        return num;\n    }\n\n    /* キュー先頭の要素にアクセス */\n    public int peek() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return nums[front];\n    }\n\n    /* 配列を返す */\n    public int[] toArray() {\n        // 有効長の範囲内のリスト要素のみを変換\n        int[] res = new int[queSize];\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            res[i] = nums[j % capacity()];\n        }\n        return res;\n    }\n}\n</code></pre> array_queue.cs<pre><code>/* 循環配列ベースのキュー */\nclass ArrayQueue {\n    int[] nums;  // キュー要素を格納する配列\n    int front;   // 先頭ポインタ。先頭要素を指す\n    int queSize; // キューの長さ\n\n    public ArrayQueue(int capacity) {\n        nums = new int[capacity];\n        front = queSize = 0;\n    }\n\n    /* キューの容量を取得 */\n    int Capacity() {\n        return nums.Length;\n    }\n\n    /* キューの長さを取得 */\n    public int Size() {\n        return queSize;\n    }\n\n    /* キューが空かどうかを判定 */\n    public bool IsEmpty() {\n        return queSize == 0;\n    }\n\n    /* エンキュー */\n    public void Push(int num) {\n        if (queSize == Capacity()) {\n            Console.WriteLine(\"キューは満杯です\");\n            return;\n        }\n        // 末尾ポインタを計算し、末尾インデックス + 1 を指す\n        // 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする\n        int rear = (front + queSize) % Capacity();\n        // num をキュー末尾に追加\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* デキュー */\n    public int Pop() {\n        int num = Peek();\n        // 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す\n        front = (front + 1) % Capacity();\n        queSize--;\n        return num;\n    }\n\n    /* キュー先頭の要素にアクセス */\n    public int Peek() {\n        if (IsEmpty())\n            throw new Exception();\n        return nums[front];\n    }\n\n    /* 配列を返す */\n    public int[] ToArray() {\n        // 有効長の範囲内のリスト要素のみを変換\n        int[] res = new int[queSize];\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            res[i] = nums[j % this.Capacity()];\n        }\n        return res;\n    }\n}\n</code></pre> array_queue.go<pre><code>/* 循環配列ベースのキュー */\ntype arrayQueue struct {\n    nums        []int // キュー要素を格納する配列\n    front       int   // 先頭ポインタ。先頭要素を指す\n    queSize     int   // キューの長さ\n    queCapacity int   // キュー容量（格納できる要素数の上限）\n}\n\n/* キューを初期化 */\nfunc newArrayQueue(queCapacity int) *arrayQueue {\n    return &amp;arrayQueue{\n        nums:        make([]int, queCapacity),\n        queCapacity: queCapacity,\n        front:       0,\n        queSize:     0,\n    }\n}\n\n/* キューの長さを取得 */\nfunc (q *arrayQueue) size() int {\n    return q.queSize\n}\n\n/* キューが空かどうかを判定 */\nfunc (q *arrayQueue) isEmpty() bool {\n    return q.queSize == 0\n}\n\n/* エンキュー */\nfunc (q *arrayQueue) push(num int) {\n    // rear == queCapacity のときキューは満杯\n    if q.queSize == q.queCapacity {\n        return\n    }\n    // 末尾ポインタを計算し、末尾インデックス + 1 を指す\n    // 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする\n    rear := (q.front + q.queSize) % q.queCapacity\n    // num をキュー末尾に追加\n    q.nums[rear] = num\n    q.queSize++\n}\n\n/* デキュー */\nfunc (q *arrayQueue) pop() any {\n    num := q.peek()\n    if num == nil {\n        return nil\n    }\n\n    // 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す\n    q.front = (q.front + 1) % q.queCapacity\n    q.queSize--\n    return num\n}\n\n/* キュー先頭の要素にアクセス */\nfunc (q *arrayQueue) peek() any {\n    if q.isEmpty() {\n        return nil\n    }\n    return q.nums[q.front]\n}\n\n/* 表示用に Slice を取得 */\nfunc (q *arrayQueue) toSlice() []int {\n    rear := (q.front + q.queSize)\n    if rear &gt;= q.queCapacity {\n        rear %= q.queCapacity\n        return append(q.nums[q.front:], q.nums[:rear]...)\n    }\n    return q.nums[q.front:rear]\n}\n</code></pre> array_queue.swift<pre><code>/* 循環配列ベースのキュー */\nclass ArrayQueue {\n    private var nums: [Int] // キュー要素を格納する配列\n    private var front: Int // 先頭ポインタ。先頭要素を指す\n    private var _size: Int // キューの長さ\n\n    init(capacity: Int) {\n        // 配列を初期化\n        nums = Array(repeating: 0, count: capacity)\n        front = 0\n        _size = 0\n    }\n\n    /* キューの容量を取得 */\n    func capacity() -&gt; Int {\n        nums.count\n    }\n\n    /* キューの長さを取得 */\n    func size() -&gt; Int {\n        _size\n    }\n\n    /* キューが空かどうかを判定 */\n    func isEmpty() -&gt; Bool {\n        size() == 0\n    }\n\n    /* エンキュー */\n    func push(num: Int) {\n        if size() == capacity() {\n            print(\"キューがいっぱいです\")\n            return\n        }\n        // 末尾ポインタを計算し、末尾インデックス + 1 を指す\n        // 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする\n        let rear = (front + size()) % capacity()\n        // num をキュー末尾に追加\n        nums[rear] = num\n        _size += 1\n    }\n\n    /* デキュー */\n    @discardableResult\n    func pop() -&gt; Int {\n        let num = peek()\n        // 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す\n        front = (front + 1) % capacity()\n        _size -= 1\n        return num\n    }\n\n    /* キュー先頭の要素にアクセス */\n    func peek() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"キューが空です\")\n        }\n        return nums[front]\n    }\n\n    /* 配列を返す */\n    func toArray() -&gt; [Int] {\n        // 有効長の範囲内のリスト要素のみを変換\n        (front ..&lt; front + size()).map { nums[$0 % capacity()] }\n    }\n}\n</code></pre> array_queue.js<pre><code>/* 循環配列ベースのキュー */\nclass ArrayQueue {\n    #nums; // キュー要素を格納する配列\n    #front = 0; // 先頭ポインタ。先頭要素を指す\n    #queSize = 0; // キューの長さ\n\n    constructor(capacity) {\n        this.#nums = new Array(capacity);\n    }\n\n    /* キューの容量を取得 */\n    get capacity() {\n        return this.#nums.length;\n    }\n\n    /* キューの長さを取得 */\n    get size() {\n        return this.#queSize;\n    }\n\n    /* キューが空かどうかを判定 */\n    isEmpty() {\n        return this.#queSize === 0;\n    }\n\n    /* エンキュー */\n    push(num) {\n        if (this.size === this.capacity) {\n            console.log('キューがいっぱいです');\n            return;\n        }\n        // 末尾ポインタを計算し、末尾インデックス + 1 を指す\n        // 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする\n        const rear = (this.#front + this.size) % this.capacity;\n        // num をキュー末尾に追加\n        this.#nums[rear] = num;\n        this.#queSize++;\n    }\n\n    /* デキュー */\n    pop() {\n        const num = this.peek();\n        // 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す\n        this.#front = (this.#front + 1) % this.capacity;\n        this.#queSize--;\n        return num;\n    }\n\n    /* キュー先頭の要素にアクセス */\n    peek() {\n        if (this.isEmpty()) throw new Error('キューが空です');\n        return this.#nums[this.#front];\n    }\n\n    /* Array を返す */\n    toArray() {\n        // 有効長の範囲内のリスト要素のみを変換\n        const arr = new Array(this.size);\n        for (let i = 0, j = this.#front; i &lt; this.size; i++, j++) {\n            arr[i] = this.#nums[j % this.capacity];\n        }\n        return arr;\n    }\n}\n</code></pre> array_queue.ts<pre><code>/* 循環配列ベースのキュー */\nclass ArrayQueue {\n    private nums: number[]; // キュー要素を格納する配列\n    private front: number; // 先頭ポインタ。先頭要素を指す\n    private queSize: number; // キューの長さ\n\n    constructor(capacity: number) {\n        this.nums = new Array(capacity);\n        this.front = this.queSize = 0;\n    }\n\n    /* キューの容量を取得 */\n    get capacity(): number {\n        return this.nums.length;\n    }\n\n    /* キューの長さを取得 */\n    get size(): number {\n        return this.queSize;\n    }\n\n    /* キューが空かどうかを判定 */\n    isEmpty(): boolean {\n        return this.queSize === 0;\n    }\n\n    /* エンキュー */\n    push(num: number): void {\n        if (this.size === this.capacity) {\n            console.log('キューは満杯です');\n            return;\n        }\n        // 末尾ポインタを計算し、末尾インデックス + 1 を指す\n        // 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする\n        const rear = (this.front + this.queSize) % this.capacity;\n        // num をキュー末尾に追加\n        this.nums[rear] = num;\n        this.queSize++;\n    }\n\n    /* デキュー */\n    pop(): number {\n        const num = this.peek();\n        // 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す\n        this.front = (this.front + 1) % this.capacity;\n        this.queSize--;\n        return num;\n    }\n\n    /* キュー先頭の要素にアクセス */\n    peek(): number {\n        if (this.isEmpty()) throw new Error('キューが空です');\n        return this.nums[this.front];\n    }\n\n    /* Array を返す */\n    toArray(): number[] {\n        // 有効長の範囲内のリスト要素のみを変換\n        const arr = new Array(this.size);\n        for (let i = 0, j = this.front; i &lt; this.size; i++, j++) {\n            arr[i] = this.nums[j % this.capacity];\n        }\n        return arr;\n    }\n}\n</code></pre> array_queue.dart<pre><code>/* 循環配列ベースのキュー */\nclass ArrayQueue {\n  late List&lt;int&gt; _nums; // キュー要素を格納する配列\n  late int _front; // 先頭ポインタ。先頭要素を指す\n  late int _queSize; // キューの長さ\n\n  ArrayQueue(int capacity) {\n    _nums = List.filled(capacity, 0);\n    _front = _queSize = 0;\n  }\n\n  /* キューの容量を取得 */\n  int capaCity() {\n    return _nums.length;\n  }\n\n  /* キューの長さを取得 */\n  int size() {\n    return _queSize;\n  }\n\n  /* キューが空かどうかを判定 */\n  bool isEmpty() {\n    return _queSize == 0;\n  }\n\n  /* エンキュー */\n  void push(int _num) {\n    if (_queSize == capaCity()) {\n      throw Exception(\"キューは満杯です\");\n    }\n    // 末尾ポインタを計算し、末尾インデックス + 1 を指す\n    // 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする\n    int rear = (_front + _queSize) % capaCity();\n    // _num をキュー末尾に追加\n    _nums[rear] = _num;\n    _queSize++;\n  }\n\n  /* デキュー */\n  int pop() {\n    int _num = peek();\n    // 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す\n    _front = (_front + 1) % capaCity();\n    _queSize--;\n    return _num;\n  }\n\n  /* キュー先頭の要素にアクセス */\n  int peek() {\n    if (isEmpty()) {\n      throw Exception(\"キューが空です\");\n    }\n    return _nums[_front];\n  }\n\n  /* Array を返す */\n  List&lt;int&gt; toArray() {\n    // 有効長の範囲内のリスト要素のみを変換\n    final List&lt;int&gt; res = List.filled(_queSize, 0);\n    for (int i = 0, j = _front; i &lt; _queSize; i++, j++) {\n      res[i] = _nums[j % capaCity()];\n    }\n    return res;\n  }\n}\n</code></pre> array_queue.rs<pre><code>/* 循環配列ベースのキュー */\nstruct ArrayQueue&lt;T&gt; {\n    nums: Vec&lt;T&gt;,      // キュー要素を格納する配列\n    front: i32,        // 先頭ポインタ。先頭要素を指す\n    que_size: i32,     // キューの長さ\n    que_capacity: i32, // キューの容量\n}\n\nimpl&lt;T: Copy + Default&gt; ArrayQueue&lt;T&gt; {\n    /* コンストラクタ */\n    fn new(capacity: i32) -&gt; ArrayQueue&lt;T&gt; {\n        ArrayQueue {\n            nums: vec![T::default(); capacity as usize],\n            front: 0,\n            que_size: 0,\n            que_capacity: capacity,\n        }\n    }\n\n    /* キューの容量を取得 */\n    fn capacity(&amp;self) -&gt; i32 {\n        self.que_capacity\n    }\n\n    /* キューの長さを取得 */\n    fn size(&amp;self) -&gt; i32 {\n        self.que_size\n    }\n\n    /* キューが空かどうかを判定 */\n    fn is_empty(&amp;self) -&gt; bool {\n        self.que_size == 0\n    }\n\n    /* エンキュー */\n    fn push(&amp;mut self, num: T) {\n        if self.que_size == self.capacity() {\n            println!(\"キューがいっぱいです\");\n            return;\n        }\n        // 末尾ポインタを計算し、末尾インデックス + 1 を指す\n        // 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする\n        let rear = (self.front + self.que_size) % self.que_capacity;\n        // num をキュー末尾に追加\n        self.nums[rear as usize] = num;\n        self.que_size += 1;\n    }\n\n    /* デキュー */\n    fn pop(&amp;mut self) -&gt; T {\n        let num = self.peek();\n        // 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す\n        self.front = (self.front + 1) % self.que_capacity;\n        self.que_size -= 1;\n        num\n    }\n\n    /* キュー先頭の要素にアクセス */\n    fn peek(&amp;self) -&gt; T {\n        if self.is_empty() {\n            panic!(\"index out of bounds\");\n        }\n        self.nums[self.front as usize]\n    }\n\n    /* 配列を返す */\n    fn to_vector(&amp;self) -&gt; Vec&lt;T&gt; {\n        let cap = self.que_capacity;\n        let mut j = self.front;\n        let mut arr = vec![T::default(); cap as usize];\n        for i in 0..self.que_size {\n            arr[i as usize] = self.nums[(j % cap) as usize];\n            j += 1;\n        }\n        arr\n    }\n}\n</code></pre> array_queue.c<pre><code>/* 循環配列ベースのキュー */\ntypedef struct {\n    int *nums;       // キュー要素を格納する配列\n    int front;       // 先頭ポインタ。先頭要素を指す\n    int queSize;     // 末尾ポインタ。キューの末尾 + 1 を指す\n    int queCapacity; // キューの容量\n} ArrayQueue;\n\n/* コンストラクタ */\nArrayQueue *newArrayQueue(int capacity) {\n    ArrayQueue *queue = (ArrayQueue *)malloc(sizeof(ArrayQueue));\n    // 配列を初期化\n    queue-&gt;queCapacity = capacity;\n    queue-&gt;nums = (int *)malloc(sizeof(int) * queue-&gt;queCapacity);\n    queue-&gt;front = queue-&gt;queSize = 0;\n    return queue;\n}\n\n/* デストラクタ */\nvoid delArrayQueue(ArrayQueue *queue) {\n    free(queue-&gt;nums);\n    free(queue);\n}\n\n/* キューの容量を取得 */\nint capacity(ArrayQueue *queue) {\n    return queue-&gt;queCapacity;\n}\n\n/* キューの長さを取得 */\nint size(ArrayQueue *queue) {\n    return queue-&gt;queSize;\n}\n\n/* キューが空かどうかを判定 */\nbool empty(ArrayQueue *queue) {\n    return queue-&gt;queSize == 0;\n}\n\n/* キュー先頭の要素にアクセス */\nint peek(ArrayQueue *queue) {\n    assert(size(queue) != 0);\n    return queue-&gt;nums[queue-&gt;front];\n}\n\n/* エンキュー */\nvoid push(ArrayQueue *queue, int num) {\n    if (size(queue) == capacity(queue)) {\n        printf(\"キューは満杯です\\r\\n\");\n        return;\n    }\n    // 末尾ポインタを計算し、末尾インデックス + 1 を指す\n    // 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする\n    int rear = (queue-&gt;front + queue-&gt;queSize) % queue-&gt;queCapacity;\n    // num をキュー末尾に追加\n    queue-&gt;nums[rear] = num;\n    queue-&gt;queSize++;\n}\n\n/* デキュー */\nint pop(ArrayQueue *queue) {\n    int num = peek(queue);\n    // 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す\n    queue-&gt;front = (queue-&gt;front + 1) % queue-&gt;queCapacity;\n    queue-&gt;queSize--;\n    return num;\n}\n\n/* 出力用の配列を返す */\nint *toArray(ArrayQueue *queue, int *queSize) {\n    *queSize = queue-&gt;queSize;\n    int *res = (int *)calloc(queue-&gt;queSize, sizeof(int));\n    int j = queue-&gt;front;\n    for (int i = 0; i &lt; queue-&gt;queSize; i++) {\n        res[i] = queue-&gt;nums[j % queue-&gt;queCapacity];\n        j++;\n    }\n    return res;\n}\n</code></pre> array_queue.kt<pre><code>/* 循環配列ベースのキュー */\nclass ArrayQueue(capacity: Int) {\n    private val nums: IntArray = IntArray(capacity) // キュー要素を格納する配列\n    private var front: Int = 0 // 先頭ポインタ。先頭要素を指す\n    private var queSize: Int = 0 // キューの長さ\n\n    /* キューの容量を取得 */\n    fun capacity(): Int {\n        return nums.size\n    }\n\n    /* キューの長さを取得 */\n    fun size(): Int {\n        return queSize\n    }\n\n    /* キューが空かどうかを判定 */\n    fun isEmpty(): Boolean {\n        return queSize == 0\n    }\n\n    /* エンキュー */\n    fun push(num: Int) {\n        if (queSize == capacity()) {\n            println(\"キューは満杯です\")\n            return\n        }\n        // 末尾ポインタを計算し、末尾インデックス + 1 を指す\n        // 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする\n        val rear = (front + queSize) % capacity()\n        // num をキュー末尾に追加\n        nums[rear] = num\n        queSize++\n    }\n\n    /* デキュー */\n    fun pop(): Int {\n        val num = peek()\n        // 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す\n        front = (front + 1) % capacity()\n        queSize--\n        return num\n    }\n\n    /* キュー先頭の要素にアクセス */\n    fun peek(): Int {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        return nums[front]\n    }\n\n    /* 配列を返す */\n    fun toArray(): IntArray {\n        // 有効長の範囲内のリスト要素のみを変換\n        val res = IntArray(queSize)\n        var i = 0\n        var j = front\n        while (i &lt; queSize) {\n            res[i] = nums[j % capacity()]\n            i++\n            j++\n        }\n        return res\n    }\n}\n</code></pre> array_queue.rb<pre><code>### 循環配列で実装したキュー ###\nclass ArrayQueue\n  ### キューの長さを取得 ###\n  attr_reader :size\n\n  ### コンストラクタ ###\n  def initialize(size)\n    @nums = Array.new(size, 0) # キュー要素を格納する配列\n    @front = 0 # 先頭ポインタ。先頭要素を指す\n    @size = 0 # キューの長さ\n  end\n\n  ### キューの容量を取得 ###\n  def capacity\n    @nums.length\n  end\n\n  ### キューが空か判定 ###\n  def is_empty?\n    size.zero?\n  end\n\n  ### エンキュー ###\n  def push(num)\n    raise IndexError, 'キューがいっぱいです' if size == capacity\n\n    # 末尾ポインタを計算し、末尾インデックス + 1 を指す\n    # 剰余演算により、rear が配列末尾を越えた後に先頭へ戻るようにする\n    rear = (@front + size) % capacity\n    # num をキュー末尾に追加\n    @nums[rear] = num\n    @size += 1\n  end\n\n  ### デキュー ###\n  def pop\n    num = peek\n    # 先頭ポインタを1つ後ろへ進め、末尾を越えたら配列先頭に戻す\n    @front = (@front + 1) % capacity\n    @size -= 1\n    num\n  end\n\n  ### 先頭要素にアクセス ###\n  def peek\n    raise IndexError, 'キューは空です' if is_empty?\n\n    @nums[@front]\n  end\n\n  ### 表示用のリストを返す ###\n  def to_array\n    res = Array.new(size, 0)\n    j = @front\n\n    for i in 0...size\n      res[i] = @nums[j % capacity]\n      j += 1\n    end\n\n    res\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>上記の実装によるキューにも制約があり、長さを可変にできません。しかし、この問題の解決は難しくなく、配列を動的配列に置き換えれば容量拡張の仕組みを導入できます。興味があれば自分で実装してみてください。</p> <p>2 つの実装の比較に関する結論はスタックの場合と同じなので、ここでは繰り返しません。</p>","path":["第 5 章 &nbsp; スタックとキュー","5.2 &nbsp; キュー"],"tags":[]},{"location":"chapter_stack_and_queue/queue/#523","level":2,"title":"5.2.3   キューの典型的な応用","text":"<ul> <li>淘宝の注文。購入者が注文すると、その注文はキューに追加され、システムは順番に従って注文を処理します。ダブルイレブンの期間には短時間で膨大な注文が発生するため、高並行性がエンジニアにとって重点的に解決すべき課題になります。</li> <li>各種の待機事項。先着順の機能を実現する必要があるあらゆる場面、たとえばプリンターのジョブキューや飲食店の配膳キューなどでは、キューによって処理順序を効果的に維持できます。</li> </ul>","path":["第 5 章 &nbsp; スタックとキュー","5.2 &nbsp; キュー"],"tags":[]},{"location":"chapter_stack_and_queue/stack/","level":1,"title":"5.1   スタック","text":"<p>スタック（stack）は、後入れ先出しの論理に従う線形データ構造です。</p> <p>スタックは机の上に積まれた皿の山にたとえられます。1回に1枚の皿しか動かせないとすると、いちばん下の皿を取り出すには、上にある皿を順番にどかす必要があります。この皿をさまざまな型の要素（整数、文字、オブジェクトなど）に置き換えたものが、スタックというデータ構造です。</p> <p>下図のように、積み重なった要素の上端を「スタックトップ」、下端を「スタックボトム」と呼びます。要素をスタックトップに追加する操作を「プッシュ」、スタックトップの要素を削除する操作を「ポップ」と呼びます。</p> <p></p> <p> 図 5-1   スタックの後入れ先出しの規則 </p>","path":["第 5 章 &nbsp; スタックとキュー","5.1 &nbsp; スタック"],"tags":[]},{"location":"chapter_stack_and_queue/stack/#511","level":2,"title":"5.1.1   スタックの基本操作","text":"<p>スタックの基本操作を以下の表に示します。具体的なメソッド名は使用するプログラミング言語によって異なります。ここでは、一般的な <code>push()</code>、<code>pop()</code>、<code>peek()</code> を例に挙げます。</p> <p> 表 5-1   スタックの操作効率 </p> メソッド 説明 時間計算量 <code>push()</code> 要素をプッシュする（スタックトップに追加） \\(O(1)\\) <code>pop()</code> スタックトップの要素をポップする \\(O(1)\\) <code>peek()</code> スタックトップの要素にアクセスする \\(O(1)\\) <p>通常は、プログラミング言語に組み込まれているスタッククラスをそのまま利用できます。ただし、専用のスタッククラスが用意されていない言語もあります。その場合は、その言語の「配列」や「連結リスト」をスタックとして用い、プログラムのロジック上でスタックに無関係な操作を無視します。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby stack.py<pre><code># スタックを初期化\n# Python には組み込みのスタッククラスがないため、list をスタックとして使用できる\nstack: list[int] = []\n\n# 要素をプッシュ\nstack.append(1)\nstack.append(3)\nstack.append(2)\nstack.append(5)\nstack.append(4)\n\n# スタックトップの要素にアクセス\npeek: int = stack[-1]\n\n# 要素をポップ\npop: int = stack.pop()\n\n# スタックの長さを取得\nsize: int = len(stack)\n\n# 空かどうかを判定\nis_empty: bool = len(stack) == 0\n</code></pre> stack.cpp<pre><code>/* スタックを初期化 */\nstack&lt;int&gt; stack;\n\n/* 要素をプッシュ */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n\n/* スタックトップの要素にアクセス */\nint top = stack.top();\n\n/* 要素をポップ */\nstack.pop(); // 戻り値なし\n\n/* スタックの長さを取得 */\nint size = stack.size();\n\n/* 空かどうかを判定 */\nbool empty = stack.empty();\n</code></pre> stack.java<pre><code>/* スタックを初期化 */\nStack&lt;Integer&gt; stack = new Stack&lt;&gt;();\n\n/* 要素をプッシュ */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n\n/* スタックトップの要素にアクセス */\nint peek = stack.peek();\n\n/* 要素をポップ */\nint pop = stack.pop();\n\n/* スタックの長さを取得 */\nint size = stack.size();\n\n/* 空かどうかを判定 */\nboolean isEmpty = stack.isEmpty();\n</code></pre> stack.cs<pre><code>/* スタックを初期化 */\nStack&lt;int&gt; stack = new();\n\n/* 要素をプッシュ */\nstack.Push(1);\nstack.Push(3);\nstack.Push(2);\nstack.Push(5);\nstack.Push(4);\n\n/* スタックトップの要素にアクセス */\nint peek = stack.Peek();\n\n/* 要素をポップ */\nint pop = stack.Pop();\n\n/* スタックの長さを取得 */\nint size = stack.Count;\n\n/* 空かどうかを判定 */\nbool isEmpty = stack.Count == 0;\n</code></pre> stack_test.go<pre><code>/* スタックを初期化 */\n// Go では、Slice をスタックとして使うのが一般的\nvar stack []int\n\n/* 要素をプッシュ */\nstack = append(stack, 1)\nstack = append(stack, 3)\nstack = append(stack, 2)\nstack = append(stack, 5)\nstack = append(stack, 4)\n\n/* スタックトップの要素にアクセス */\npeek := stack[len(stack)-1]\n\n/* 要素をポップ */\npop := stack[len(stack)-1]\nstack = stack[:len(stack)-1]\n\n/* スタックの長さを取得 */\nsize := len(stack)\n\n/* 空かどうかを判定 */\nisEmpty := len(stack) == 0\n</code></pre> stack.swift<pre><code>/* スタックを初期化 */\n// Swift には組み込みのスタッククラスがないため、Array をスタックとして使用できる\nvar stack: [Int] = []\n\n/* 要素をプッシュ */\nstack.append(1)\nstack.append(3)\nstack.append(2)\nstack.append(5)\nstack.append(4)\n\n/* スタックトップの要素にアクセス */\nlet peek = stack.last!\n\n/* 要素をポップ */\nlet pop = stack.removeLast()\n\n/* スタックの長さを取得 */\nlet size = stack.count\n\n/* 空かどうかを判定 */\nlet isEmpty = stack.isEmpty\n</code></pre> stack.js<pre><code>/* スタックを初期化 */\n// JavaScript には組み込みのスタッククラスがないため、Array をスタックとして使用できる\nconst stack = [];\n\n/* 要素をプッシュ */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n\n/* スタックトップの要素にアクセス */\nconst peek = stack[stack.length-1];\n\n/* 要素をポップ */\nconst pop = stack.pop();\n\n/* スタックの長さを取得 */\nconst size = stack.length;\n\n/* 空かどうかを判定 */\nconst is_empty = stack.length === 0;\n</code></pre> stack.ts<pre><code>/* スタックを初期化 */\n// TypeScript には組み込みのスタッククラスがないため、Array をスタックとして使用できる\nconst stack: number[] = [];\n\n/* 要素をプッシュ */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n\n/* スタックトップの要素にアクセス */\nconst peek = stack[stack.length - 1];\n\n/* 要素をポップ */\nconst pop = stack.pop();\n\n/* スタックの長さを取得 */\nconst size = stack.length;\n\n/* 空かどうかを判定 */\nconst is_empty = stack.length === 0;\n</code></pre> stack.dart<pre><code>/* スタックを初期化 */\n// Dart には組み込みのスタッククラスがないため、List をスタックとして使用できる\nList&lt;int&gt; stack = [];\n\n/* 要素をプッシュ */\nstack.add(1);\nstack.add(3);\nstack.add(2);\nstack.add(5);\nstack.add(4);\n\n/* スタックトップの要素にアクセス */\nint peek = stack.last;\n\n/* 要素をポップ */\nint pop = stack.removeLast();\n\n/* スタックの長さを取得 */\nint size = stack.length;\n\n/* 空かどうかを判定 */\nbool isEmpty = stack.isEmpty;\n</code></pre> stack.rs<pre><code>/* スタックを初期化 */\n// Vec をスタックとして使用する\nlet mut stack: Vec&lt;i32&gt; = Vec::new();\n\n/* 要素をプッシュ */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n\n/* スタックトップの要素にアクセス */\nlet top = stack.last().unwrap();\n\n/* 要素をポップ */\nlet pop = stack.pop().unwrap();\n\n/* スタックの長さを取得 */\nlet size = stack.len();\n\n/* 空かどうかを判定 */\nlet is_empty = stack.is_empty();\n</code></pre> stack.c<pre><code>// C には組み込みのスタックがない\n</code></pre> stack.kt<pre><code>/* スタックを初期化 */\nval stack = Stack&lt;Int&gt;()\n\n/* 要素をプッシュ */\nstack.push(1)\nstack.push(3)\nstack.push(2)\nstack.push(5)\nstack.push(4)\n\n/* スタックトップの要素にアクセス */\nval peek = stack.peek()\n\n/* 要素をポップ */\nval pop = stack.pop()\n\n/* スタックの長さを取得 */\nval size = stack.size\n\n/* 空かどうかを判定 */\nval isEmpty = stack.isEmpty()\n</code></pre> stack.rb<pre><code># スタックを初期化\n# Ruby には組み込みのスタッククラスがないため、Array をスタックとして使用できる\nstack = []\n\n# 要素をプッシュ\nstack &lt;&lt; 1\nstack &lt;&lt; 3\nstack &lt;&lt; 2\nstack &lt;&lt; 5\nstack &lt;&lt; 4\n\n# スタックトップの要素にアクセス\npeek = stack.last\n\n# 要素をポップ\npop = stack.pop\n\n# スタックの長さを取得\nsize = stack.length\n\n# 空かどうかを判定\nis_empty = stack.empty?\n</code></pre> 実行の可視化 <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E6%A0%88%0A%20%20%20%20%23%20Python%20%E6%B2%A1%E6%9C%89%E5%86%85%E7%BD%AE%E7%9A%84%E6%A0%88%E7%B1%BB%EF%BC%8C%E5%8F%AF%E4%BB%A5%E6%8A%8A%20list%20%E5%BD%93%E4%BD%9C%E6%A0%88%E6%9D%A5%E4%BD%BF%E7%94%A8%0A%20%20%20%20stack%20%3D%20%5B%5D%0A%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%85%A5%E6%A0%88%0A%20%20%20%20stack.append%281%29%0A%20%20%20%20stack.append%283%29%0A%20%20%20%20stack.append%282%29%0A%20%20%20%20stack.append%285%29%0A%20%20%20%20stack.append%284%29%0A%20%20%20%20print%28%22%E6%A0%88%20stack%20%3D%22,%20stack%29%0A%0A%20%20%20%20%23%20%E8%AE%BF%E9%97%AE%E6%A0%88%E9%A1%B6%E5%85%83%E7%B4%A0%0A%20%20%20%20peek%20%3D%20stack%5B-1%5D%0A%20%20%20%20print%28%22%E6%A0%88%E9%A1%B6%E5%85%83%E7%B4%A0%20peek%20%3D%22,%20peek%29%0A%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%87%BA%E6%A0%88%0A%20%20%20%20pop%20%3D%20stack.pop%28%29%0A%20%20%20%20print%28%22%E5%87%BA%E6%A0%88%E5%85%83%E7%B4%A0%20pop%20%3D%22,%20pop%29%0A%20%20%20%20print%28%22%E5%87%BA%E6%A0%88%E5%90%8E%20stack%20%3D%22,%20stack%29%0A%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E6%A0%88%E7%9A%84%E9%95%BF%E5%BA%A6%0A%20%20%20%20size%20%3D%20len%28stack%29%0A%20%20%20%20print%28%22%E6%A0%88%E7%9A%84%E9%95%BF%E5%BA%A6%20size%20%3D%22,%20size%29%0A%0A%20%20%20%20%23%20%E5%88%A4%E6%96%AD%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%0A%20%20%20%20is_empty%20%3D%20len%28stack%29%20%3D%3D%200%0A%20%20%20%20print%28%22%E6%A0%88%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%20%3D%22,%20is_empty%29&amp;cumulative=false&amp;curInstr=2&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["第 5 章 &nbsp; スタックとキュー","5.1 &nbsp; スタック"],"tags":[]},{"location":"chapter_stack_and_queue/stack/#512","level":2,"title":"5.1.2   スタックの実装","text":"<p>スタックの動作の仕組みをより深く理解するために、自分でスタッククラスを実装してみましょう。</p> <p>スタックは後入れ先出しの原則に従うため、要素の追加や削除はスタックトップでしか行えません。一方、配列や連結リストでは任意の位置で要素を追加・削除できます。つまり、スタックは制限付きの配列または連結リストとみなせます。 言い換えると、配列や連結リストのうち無関係な操作を「隠蔽」することで、外から見た振る舞いをスタックの特性に合わせられます。</p>","path":["第 5 章 &nbsp; スタックとキュー","5.1 &nbsp; スタック"],"tags":[]},{"location":"chapter_stack_and_queue/stack/#1","level":3,"title":"1.   連結リストによる実装","text":"<p>連結リストでスタックを実装する場合、連結リストの先頭ノードをスタックトップ、末尾ノードをスタックボトムとみなせます。</p> <p>下図のように、プッシュ操作では要素を連結リストの先頭に挿入するだけでよく、このノード挿入方法は「頭部挿入法」と呼ばれます。ポップ操作では、先頭ノードを連結リストから削除するだけです。</p> LinkedListStackpush()pop() <p></p> <p></p> <p></p> <p> 図 5-2   連結リストによるスタック実装のプッシュ・ポップ操作 </p> <p>以下は、連結リストによってスタックを実装したコード例です：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linkedlist_stack.py<pre><code>class LinkedListStack:\n    \"\"\"連結リストベースのスタック\"\"\"\n\n    def __init__(self):\n        \"\"\"コンストラクタ\"\"\"\n        self._peek: ListNode | None = None\n        self._size: int = 0\n\n    def size(self) -&gt; int:\n        \"\"\"スタックの長さを取得\"\"\"\n        return self._size\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"スタックが空かどうかを判定\"\"\"\n        return self._size == 0\n\n    def push(self, val: int):\n        \"\"\"プッシュ\"\"\"\n        node = ListNode(val)\n        node.next = self._peek\n        self._peek = node\n        self._size += 1\n\n    def pop(self) -&gt; int:\n        \"\"\"ポップ\"\"\"\n        num = self.peek()\n        self._peek = self._peek.next\n        self._size -= 1\n        return num\n\n    def peek(self) -&gt; int:\n        \"\"\"スタックトップの要素にアクセス\"\"\"\n        if self.is_empty():\n            raise IndexError(\"スタックが空です\")\n        return self._peek.val\n\n    def to_list(self) -&gt; list[int]:\n        \"\"\"表示用にリストへ変換\"\"\"\n        arr = []\n        node = self._peek\n        while node:\n            arr.append(node.val)\n            node = node.next\n        arr.reverse()\n        return arr\n</code></pre> linkedlist_stack.cpp<pre><code>/* 連結リストベースのスタック */\nclass LinkedListStack {\n  private:\n    ListNode *stackTop; // 先頭ノードをスタックトップとする\n    int stkSize;        // スタックの長さ\n\n  public:\n    LinkedListStack() {\n        stackTop = nullptr;\n        stkSize = 0;\n    }\n\n    ~LinkedListStack() {\n        // 連結リストを走査してノードを削除し、メモリを解放する\n        freeMemoryLinkedList(stackTop);\n    }\n\n    /* スタックの長さを取得 */\n    int size() {\n        return stkSize;\n    }\n\n    /* スタックが空かどうかを判定 */\n    bool isEmpty() {\n        return size() == 0;\n    }\n\n    /* プッシュ */\n    void push(int num) {\n        ListNode *node = new ListNode(num);\n        node-&gt;next = stackTop;\n        stackTop = node;\n        stkSize++;\n    }\n\n    /* ポップ */\n    int pop() {\n        int num = top();\n        ListNode *tmp = stackTop;\n        stackTop = stackTop-&gt;next;\n        // メモリを解放する\n        delete tmp;\n        stkSize--;\n        return num;\n    }\n\n    /* スタックトップの要素にアクセス */\n    int top() {\n        if (isEmpty())\n            throw out_of_range(\"スタックが空です\");\n        return stackTop-&gt;val;\n    }\n\n    /* List を Array に変換して返す */\n    vector&lt;int&gt; toVector() {\n        ListNode *node = stackTop;\n        vector&lt;int&gt; res(size());\n        for (int i = res.size() - 1; i &gt;= 0; i--) {\n            res[i] = node-&gt;val;\n            node = node-&gt;next;\n        }\n        return res;\n    }\n};\n</code></pre> linkedlist_stack.java<pre><code>/* 連結リストベースのスタック */\nclass LinkedListStack {\n    private ListNode stackPeek; // 先頭ノードをスタックトップとする\n    private int stkSize = 0; // スタックの長さ\n\n    public LinkedListStack() {\n        stackPeek = null;\n    }\n\n    /* スタックの長さを取得 */\n    public int size() {\n        return stkSize;\n    }\n\n    /* スタックが空かどうかを判定 */\n    public boolean isEmpty() {\n        return size() == 0;\n    }\n\n    /* プッシュ */\n    public void push(int num) {\n        ListNode node = new ListNode(num);\n        node.next = stackPeek;\n        stackPeek = node;\n        stkSize++;\n    }\n\n    /* ポップ */\n    public int pop() {\n        int num = peek();\n        stackPeek = stackPeek.next;\n        stkSize--;\n        return num;\n    }\n\n    /* スタックトップの要素にアクセス */\n    public int peek() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return stackPeek.val;\n    }\n\n    /* List を Array に変換して返す */\n    public int[] toArray() {\n        ListNode node = stackPeek;\n        int[] res = new int[size()];\n        for (int i = res.length - 1; i &gt;= 0; i--) {\n            res[i] = node.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_stack.cs<pre><code>/* 連結リストベースのスタック */\nclass LinkedListStack {\n    ListNode? stackPeek;  // 先頭ノードをスタックトップとする\n    int stkSize = 0;   // スタックの長さ\n\n    public LinkedListStack() {\n        stackPeek = null;\n    }\n\n    /* スタックの長さを取得 */\n    public int Size() {\n        return stkSize;\n    }\n\n    /* スタックが空かどうかを判定 */\n    public bool IsEmpty() {\n        return Size() == 0;\n    }\n\n    /* プッシュ */\n    public void Push(int num) {\n        ListNode node = new(num) {\n            next = stackPeek\n        };\n        stackPeek = node;\n        stkSize++;\n    }\n\n    /* ポップ */\n    public int Pop() {\n        int num = Peek();\n        stackPeek = stackPeek!.next;\n        stkSize--;\n        return num;\n    }\n\n    /* スタックトップの要素にアクセス */\n    public int Peek() {\n        if (IsEmpty())\n            throw new Exception();\n        return stackPeek!.val;\n    }\n\n    /* List を Array に変換して返す */\n    public int[] ToArray() {\n        if (stackPeek == null)\n            return [];\n\n        ListNode? node = stackPeek;\n        int[] res = new int[Size()];\n        for (int i = res.Length - 1; i &gt;= 0; i--) {\n            res[i] = node!.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_stack.go<pre><code>/* 連結リストベースのスタック */\ntype linkedListStack struct {\n    // 組み込みパッケージ list でスタックを実装する\n    data *list.List\n}\n\n/* スタックを初期化 */\nfunc newLinkedListStack() *linkedListStack {\n    return &amp;linkedListStack{\n        data: list.New(),\n    }\n}\n\n/* プッシュ */\nfunc (s *linkedListStack) push(value int) {\n    s.data.PushBack(value)\n}\n\n/* ポップ */\nfunc (s *linkedListStack) pop() any {\n    if s.isEmpty() {\n        return nil\n    }\n    e := s.data.Back()\n    s.data.Remove(e)\n    return e.Value\n}\n\n/* スタックトップの要素にアクセス */\nfunc (s *linkedListStack) peek() any {\n    if s.isEmpty() {\n        return nil\n    }\n    e := s.data.Back()\n    return e.Value\n}\n\n/* スタックの長さを取得 */\nfunc (s *linkedListStack) size() int {\n    return s.data.Len()\n}\n\n/* スタックが空かどうかを判定 */\nfunc (s *linkedListStack) isEmpty() bool {\n    return s.data.Len() == 0\n}\n\n/* 表示用に List を取得 */\nfunc (s *linkedListStack) toList() *list.List {\n    return s.data\n}\n</code></pre> linkedlist_stack.swift<pre><code>/* 連結リストベースのスタック */\nclass LinkedListStack {\n    private var _peek: ListNode? // 先頭ノードをスタックトップとする\n    private var _size: Int // スタックの長さ\n\n    init() {\n        _size = 0\n    }\n\n    /* スタックの長さを取得 */\n    func size() -&gt; Int {\n        _size\n    }\n\n    /* スタックが空かどうかを判定 */\n    func isEmpty() -&gt; Bool {\n        size() == 0\n    }\n\n    /* プッシュ */\n    func push(num: Int) {\n        let node = ListNode(x: num)\n        node.next = _peek\n        _peek = node\n        _size += 1\n    }\n\n    /* ポップ */\n    @discardableResult\n    func pop() -&gt; Int {\n        let num = peek()\n        _peek = _peek?.next\n        _size -= 1\n        return num\n    }\n\n    /* スタックトップの要素にアクセス */\n    func peek() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"スタックが空です\")\n        }\n        return _peek!.val\n    }\n\n    /* List を Array に変換して返す */\n    func toArray() -&gt; [Int] {\n        var node = _peek\n        var res = Array(repeating: 0, count: size())\n        for i in res.indices.reversed() {\n            res[i] = node!.val\n            node = node?.next\n        }\n        return res\n    }\n}\n</code></pre> linkedlist_stack.js<pre><code>/* 連結リストベースのスタック */\nclass LinkedListStack {\n    #stackPeek; // 先頭ノードをスタックトップとする\n    #stkSize = 0; // スタックの長さ\n\n    constructor() {\n        this.#stackPeek = null;\n    }\n\n    /* スタックの長さを取得 */\n    get size() {\n        return this.#stkSize;\n    }\n\n    /* スタックが空かどうかを判定 */\n    isEmpty() {\n        return this.size === 0;\n    }\n\n    /* プッシュ */\n    push(num) {\n        const node = new ListNode(num);\n        node.next = this.#stackPeek;\n        this.#stackPeek = node;\n        this.#stkSize++;\n    }\n\n    /* ポップ */\n    pop() {\n        const num = this.peek();\n        this.#stackPeek = this.#stackPeek.next;\n        this.#stkSize--;\n        return num;\n    }\n\n    /* スタックトップの要素にアクセス */\n    peek() {\n        if (!this.#stackPeek) throw new Error('スタックが空');\n        return this.#stackPeek.val;\n    }\n\n    /* 連結リストを Array に変換して返す */\n    toArray() {\n        let node = this.#stackPeek;\n        const res = new Array(this.size);\n        for (let i = res.length - 1; i &gt;= 0; i--) {\n            res[i] = node.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_stack.ts<pre><code>/* 連結リストベースのスタック */\nclass LinkedListStack {\n    private stackPeek: ListNode | null; // 先頭ノードをスタックトップとする\n    private stkSize: number = 0; // スタックの長さ\n\n    constructor() {\n        this.stackPeek = null;\n    }\n\n    /* スタックの長さを取得 */\n    get size(): number {\n        return this.stkSize;\n    }\n\n    /* スタックが空かどうかを判定 */\n    isEmpty(): boolean {\n        return this.size === 0;\n    }\n\n    /* プッシュ */\n    push(num: number): void {\n        const node = new ListNode(num);\n        node.next = this.stackPeek;\n        this.stackPeek = node;\n        this.stkSize++;\n    }\n\n    /* ポップ */\n    pop(): number {\n        const num = this.peek();\n        if (!this.stackPeek) throw new Error('スタックが空です');\n        this.stackPeek = this.stackPeek.next;\n        this.stkSize--;\n        return num;\n    }\n\n    /* スタックトップの要素にアクセス */\n    peek(): number {\n        if (!this.stackPeek) throw new Error('スタックが空です');\n        return this.stackPeek.val;\n    }\n\n    /* 連結リストを Array に変換して返す */\n    toArray(): number[] {\n        let node = this.stackPeek;\n        const res = new Array&lt;number&gt;(this.size);\n        for (let i = res.length - 1; i &gt;= 0; i--) {\n            res[i] = node!.val;\n            node = node!.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_stack.dart<pre><code>/* 連結リストクラスに基づくスタック */\nclass LinkedListStack {\n  ListNode? _stackPeek; // 先頭ノードをスタックトップとする\n  int _stkSize = 0; // スタックの長さ\n\n  LinkedListStack() {\n    _stackPeek = null;\n  }\n\n  /* スタックの長さを取得 */\n  int size() {\n    return _stkSize;\n  }\n\n  /* スタックが空かどうかを判定 */\n  bool isEmpty() {\n    return _stkSize == 0;\n  }\n\n  /* プッシュ */\n  void push(int _num) {\n    final ListNode node = ListNode(_num);\n    node.next = _stackPeek;\n    _stackPeek = node;\n    _stkSize++;\n  }\n\n  /* ポップ */\n  int pop() {\n    final int _num = peek();\n    _stackPeek = _stackPeek!.next;\n    _stkSize--;\n    return _num;\n  }\n\n  /* スタックトップの要素にアクセス */\n  int peek() {\n    if (_stackPeek == null) {\n      throw Exception(\"スタックが空です\");\n    }\n    return _stackPeek!.val;\n  }\n\n  /* 連結リストを List に変換して返す */\n  List&lt;int&gt; toList() {\n    ListNode? node = _stackPeek;\n    List&lt;int&gt; list = [];\n    while (node != null) {\n      list.add(node.val);\n      node = node.next;\n    }\n    list = list.reversed.toList();\n    return list;\n  }\n}\n</code></pre> linkedlist_stack.rs<pre><code>/* 連結リストベースのスタック */\n#[allow(dead_code)]\npub struct LinkedListStack&lt;T&gt; {\n    stack_peek: Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;, // 先頭ノードをスタックトップとする\n    stk_size: usize,                              // スタックの長さ\n}\n\nimpl&lt;T: Copy&gt; LinkedListStack&lt;T&gt; {\n    pub fn new() -&gt; Self {\n        Self {\n            stack_peek: None,\n            stk_size: 0,\n        }\n    }\n\n    /* スタックの長さを取得 */\n    pub fn size(&amp;self) -&gt; usize {\n        return self.stk_size;\n    }\n\n    /* スタックが空かどうかを判定 */\n    pub fn is_empty(&amp;self) -&gt; bool {\n        return self.size() == 0;\n    }\n\n    /* プッシュ */\n    pub fn push(&amp;mut self, num: T) {\n        let node = ListNode::new(num);\n        node.borrow_mut().next = self.stack_peek.take();\n        self.stack_peek = Some(node);\n        self.stk_size += 1;\n    }\n\n    /* ポップ */\n    pub fn pop(&amp;mut self) -&gt; Option&lt;T&gt; {\n        self.stack_peek.take().map(|old_head| {\n            self.stack_peek = old_head.borrow_mut().next.take();\n            self.stk_size -= 1;\n\n            old_head.borrow().val\n        })\n    }\n\n    /* スタックトップの要素にアクセス */\n    pub fn peek(&amp;self) -&gt; Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt; {\n        self.stack_peek.as_ref()\n    }\n\n    /* List を Array に変換して返す */\n    pub fn to_array(&amp;self) -&gt; Vec&lt;T&gt; {\n        fn _to_array&lt;T: Sized + Copy&gt;(head: Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;) -&gt; Vec&lt;T&gt; {\n            if let Some(node) = head {\n                let mut nums = _to_array(node.borrow().next.as_ref());\n                nums.push(node.borrow().val);\n                return nums;\n            }\n            return Vec::new();\n        }\n\n        _to_array(self.peek())\n    }\n}\n</code></pre> linkedlist_stack.c<pre><code>/* 連結リストベースのスタック */\ntypedef struct {\n    ListNode *top; // 先頭ノードをスタックトップとする\n    int size;      // スタックの長さ\n} LinkedListStack;\n\n/* コンストラクタ */\nLinkedListStack *newLinkedListStack() {\n    LinkedListStack *s = malloc(sizeof(LinkedListStack));\n    s-&gt;top = NULL;\n    s-&gt;size = 0;\n    return s;\n}\n\n/* デストラクタ */\nvoid delLinkedListStack(LinkedListStack *s) {\n    while (s-&gt;top) {\n        ListNode *n = s-&gt;top-&gt;next;\n        free(s-&gt;top);\n        s-&gt;top = n;\n    }\n    free(s);\n}\n\n/* スタックの長さを取得 */\nint size(LinkedListStack *s) {\n    return s-&gt;size;\n}\n\n/* スタックが空かどうかを判定 */\nbool isEmpty(LinkedListStack *s) {\n    return size(s) == 0;\n}\n\n/* プッシュ */\nvoid push(LinkedListStack *s, int num) {\n    ListNode *node = (ListNode *)malloc(sizeof(ListNode));\n    node-&gt;next = s-&gt;top; // 新しく追加したノードのポインタフィールドを更新\n    node-&gt;val = num;     // 新しく追加したノードのデータフィールドを更新\n    s-&gt;top = node;       // スタックトップを更新\n    s-&gt;size++;           // スタックサイズを更新\n}\n\n/* スタックトップの要素にアクセス */\nint peek(LinkedListStack *s) {\n    if (s-&gt;size == 0) {\n        printf(\"スタックは空です\\n\");\n        return INT_MAX;\n    }\n    return s-&gt;top-&gt;val;\n}\n\n/* ポップ */\nint pop(LinkedListStack *s) {\n    int val = peek(s);\n    ListNode *tmp = s-&gt;top;\n    s-&gt;top = s-&gt;top-&gt;next;\n    // メモリを解放する\n    free(tmp);\n    s-&gt;size--;\n    return val;\n}\n</code></pre> linkedlist_stack.kt<pre><code>/* 連結リストベースのスタック */\nclass LinkedListStack(\n    private var stackPeek: ListNode? = null, // 先頭ノードをスタックトップとする\n    private var stkSize: Int = 0 // スタックの長さ\n) {\n\n    /* スタックの長さを取得 */\n    fun size(): Int {\n        return stkSize\n    }\n\n    /* スタックが空かどうかを判定 */\n    fun isEmpty(): Boolean {\n        return size() == 0\n    }\n\n    /* プッシュ */\n    fun push(num: Int) {\n        val node = ListNode(num)\n        node.next = stackPeek\n        stackPeek = node\n        stkSize++\n    }\n\n    /* ポップ */\n    fun pop(): Int? {\n        val num = peek()\n        stackPeek = stackPeek?.next\n        stkSize--\n        return num\n    }\n\n    /* スタックトップの要素にアクセス */\n    fun peek(): Int? {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        return stackPeek?._val\n    }\n\n    /* List を Array に変換して返す */\n    fun toArray(): IntArray {\n        var node = stackPeek\n        val res = IntArray(size())\n        for (i in res.size - 1 downTo 0) {\n            res[i] = node?._val!!\n            node = node.next\n        }\n        return res\n    }\n}\n</code></pre> linkedlist_stack.rb<pre><code>### 連結リストで実装したスタック ###\nclass LinkedListStack\n  attr_reader :size\n\n  ### コンストラクタ ###\n  def initialize\n    @size = 0\n  end\n\n  ### スタックが空か判定 ###\n  def is_empty?\n    @peek.nil?\n  end\n\n  ### プッシュ ###\n  def push(val)\n    node = ListNode.new(val)\n    node.next = @peek\n    @peek = node\n    @size += 1\n  end\n\n  ### ポップ ###\n  def pop\n    num = peek\n    @peek = @peek.next\n    @size -= 1\n    num\n  end\n\n  ### スタックトップ要素を参照 ###\n  def peek\n    raise IndexError, 'スタックは空です' if is_empty?\n\n    @peek.val\n  end\n\n  ### 連結リストを Array に変換して返す ###\n  def to_array\n    arr = []\n    node = @peek\n    while node\n      arr &lt;&lt; node.val\n      node = node.next\n    end\n    arr.reverse\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 5 章 &nbsp; スタックとキュー","5.1 &nbsp; スタック"],"tags":[]},{"location":"chapter_stack_and_queue/stack/#2","level":3,"title":"2.   配列による実装","text":"<p>配列でスタックを実装する場合、配列の末尾をスタックトップとして扱えます。下図のように、プッシュとポップはそれぞれ配列末尾への要素追加と削除に対応し、どちらの時間計算量も \\(O(1)\\) です。</p> ArrayStackpush()pop() <p></p> <p></p> <p></p> <p> 図 5-3   配列によるスタック実装のプッシュ・ポップ操作 </p> <p>プッシュされる要素は際限なく増える可能性があるため、動的配列を使えば、配列の拡張を自前で処理する必要がありません。以下にコード例を示します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array_stack.py<pre><code>class ArrayStack:\n    \"\"\"配列ベースのスタック\"\"\"\n\n    def __init__(self):\n        \"\"\"コンストラクタ\"\"\"\n        self._stack: list[int] = []\n\n    def size(self) -&gt; int:\n        \"\"\"スタックの長さを取得\"\"\"\n        return len(self._stack)\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"スタックが空かどうかを判定\"\"\"\n        return self.size() == 0\n\n    def push(self, item: int):\n        \"\"\"プッシュ\"\"\"\n        self._stack.append(item)\n\n    def pop(self) -&gt; int:\n        \"\"\"ポップ\"\"\"\n        if self.is_empty():\n            raise IndexError(\"スタックが空です\")\n        return self._stack.pop()\n\n    def peek(self) -&gt; int:\n        \"\"\"スタックトップの要素にアクセス\"\"\"\n        if self.is_empty():\n            raise IndexError(\"スタックが空です\")\n        return self._stack[-1]\n\n    def to_list(self) -&gt; list[int]:\n        \"\"\"表示用のリストを返す\"\"\"\n        return self._stack\n</code></pre> array_stack.cpp<pre><code>/* 配列ベースのスタック */\nclass ArrayStack {\n  private:\n    vector&lt;int&gt; stack;\n\n  public:\n    /* スタックの長さを取得 */\n    int size() {\n        return stack.size();\n    }\n\n    /* スタックが空かどうかを判定 */\n    bool isEmpty() {\n        return stack.size() == 0;\n    }\n\n    /* プッシュ */\n    void push(int num) {\n        stack.push_back(num);\n    }\n\n    /* ポップ */\n    int pop() {\n        int num = top();\n        stack.pop_back();\n        return num;\n    }\n\n    /* スタックトップの要素にアクセス */\n    int top() {\n        if (isEmpty())\n            throw out_of_range(\"スタックが空です\");\n        return stack.back();\n    }\n\n    /* Vector を返す */\n    vector&lt;int&gt; toVector() {\n        return stack;\n    }\n};\n</code></pre> array_stack.java<pre><code>/* 配列ベースのスタック */\nclass ArrayStack {\n    private ArrayList&lt;Integer&gt; stack;\n\n    public ArrayStack() {\n        // リスト（動的配列）を初期化する\n        stack = new ArrayList&lt;&gt;();\n    }\n\n    /* スタックの長さを取得 */\n    public int size() {\n        return stack.size();\n    }\n\n    /* スタックが空かどうかを判定 */\n    public boolean isEmpty() {\n        return size() == 0;\n    }\n\n    /* プッシュ */\n    public void push(int num) {\n        stack.add(num);\n    }\n\n    /* ポップ */\n    public int pop() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return stack.remove(size() - 1);\n    }\n\n    /* スタックトップの要素にアクセス */\n    public int peek() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return stack.get(size() - 1);\n    }\n\n    /* List を Array に変換して返す */\n    public Object[] toArray() {\n        return stack.toArray();\n    }\n}\n</code></pre> array_stack.cs<pre><code>/* 配列ベースのスタック */\nclass ArrayStack {\n    List&lt;int&gt; stack;\n    public ArrayStack() {\n        // リスト（動的配列）を初期化する\n        stack = [];\n    }\n\n    /* スタックの長さを取得 */\n    public int Size() {\n        return stack.Count;\n    }\n\n    /* スタックが空かどうかを判定 */\n    public bool IsEmpty() {\n        return Size() == 0;\n    }\n\n    /* プッシュ */\n    public void Push(int num) {\n        stack.Add(num);\n    }\n\n    /* ポップ */\n    public int Pop() {\n        if (IsEmpty())\n            throw new Exception();\n        var val = Peek();\n        stack.RemoveAt(Size() - 1);\n        return val;\n    }\n\n    /* スタックトップの要素にアクセス */\n    public int Peek() {\n        if (IsEmpty())\n            throw new Exception();\n        return stack[Size() - 1];\n    }\n\n    /* List を Array に変換して返す */\n    public int[] ToArray() {\n        return [.. stack];\n    }\n}\n</code></pre> array_stack.go<pre><code>/* 配列ベースのスタック */\ntype arrayStack struct {\n    data []int // データ\n}\n\n/* スタックを初期化 */\nfunc newArrayStack() *arrayStack {\n    return &amp;arrayStack{\n        // スタックの長さを 0、容量を 16 に設定\n        data: make([]int, 0, 16),\n    }\n}\n\n/* スタックの長さ */\nfunc (s *arrayStack) size() int {\n    return len(s.data)\n}\n\n/* スタックが空かどうか */\nfunc (s *arrayStack) isEmpty() bool {\n    return s.size() == 0\n}\n\n/* プッシュ */\nfunc (s *arrayStack) push(v int) {\n    // スライスは自動で拡張される\n    s.data = append(s.data, v)\n}\n\n/* ポップ */\nfunc (s *arrayStack) pop() any {\n    val := s.peek()\n    s.data = s.data[:len(s.data)-1]\n    return val\n}\n\n/* スタックトップ要素を取得する */\nfunc (s *arrayStack) peek() any {\n    if s.isEmpty() {\n        return nil\n    }\n    val := s.data[len(s.data)-1]\n    return val\n}\n\n/* 表示用に Slice を取得 */\nfunc (s *arrayStack) toSlice() []int {\n    return s.data\n}\n</code></pre> array_stack.swift<pre><code>/* 配列ベースのスタック */\nclass ArrayStack {\n    private var stack: [Int]\n\n    init() {\n        // リスト（動的配列）を初期化する\n        stack = []\n    }\n\n    /* スタックの長さを取得 */\n    func size() -&gt; Int {\n        stack.count\n    }\n\n    /* スタックが空かどうかを判定 */\n    func isEmpty() -&gt; Bool {\n        stack.isEmpty\n    }\n\n    /* プッシュ */\n    func push(num: Int) {\n        stack.append(num)\n    }\n\n    /* ポップ */\n    @discardableResult\n    func pop() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"スタックが空です\")\n        }\n        return stack.removeLast()\n    }\n\n    /* スタックトップの要素にアクセス */\n    func peek() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"スタックが空です\")\n        }\n        return stack.last!\n    }\n\n    /* List を Array に変換して返す */\n    func toArray() -&gt; [Int] {\n        stack\n    }\n}\n</code></pre> array_stack.js<pre><code>/* 配列ベースのスタック */\nclass ArrayStack {\n    #stack;\n    constructor() {\n        this.#stack = [];\n    }\n\n    /* スタックの長さを取得 */\n    get size() {\n        return this.#stack.length;\n    }\n\n    /* スタックが空かどうかを判定 */\n    isEmpty() {\n        return this.#stack.length === 0;\n    }\n\n    /* プッシュ */\n    push(num) {\n        this.#stack.push(num);\n    }\n\n    /* ポップ */\n    pop() {\n        if (this.isEmpty()) throw new Error('スタックが空');\n        return this.#stack.pop();\n    }\n\n    /* スタックトップの要素にアクセス */\n    top() {\n        if (this.isEmpty()) throw new Error('スタックが空');\n        return this.#stack[this.#stack.length - 1];\n    }\n\n    /* Array を返す */\n    toArray() {\n        return this.#stack;\n    }\n}\n</code></pre> array_stack.ts<pre><code>/* 配列ベースのスタック */\nclass ArrayStack {\n    private stack: number[];\n    constructor() {\n        this.stack = [];\n    }\n\n    /* スタックの長さを取得 */\n    get size(): number {\n        return this.stack.length;\n    }\n\n    /* スタックが空かどうかを判定 */\n    isEmpty(): boolean {\n        return this.stack.length === 0;\n    }\n\n    /* プッシュ */\n    push(num: number): void {\n        this.stack.push(num);\n    }\n\n    /* ポップ */\n    pop(): number | undefined {\n        if (this.isEmpty()) throw new Error('スタックが空です');\n        return this.stack.pop();\n    }\n\n    /* スタックトップの要素にアクセス */\n    top(): number | undefined {\n        if (this.isEmpty()) throw new Error('スタックが空です');\n        return this.stack[this.stack.length - 1];\n    }\n\n    /* Array を返す */\n    toArray() {\n        return this.stack;\n    }\n}\n</code></pre> array_stack.dart<pre><code>/* 配列ベースのスタック */\nclass ArrayStack {\n  late List&lt;int&gt; _stack;\n  ArrayStack() {\n    _stack = [];\n  }\n\n  /* スタックの長さを取得 */\n  int size() {\n    return _stack.length;\n  }\n\n  /* スタックが空かどうかを判定 */\n  bool isEmpty() {\n    return _stack.isEmpty;\n  }\n\n  /* プッシュ */\n  void push(int _num) {\n    _stack.add(_num);\n  }\n\n  /* ポップ */\n  int pop() {\n    if (isEmpty()) {\n      throw Exception(\"スタックが空です\");\n    }\n    return _stack.removeLast();\n  }\n\n  /* スタックトップの要素にアクセス */\n  int peek() {\n    if (isEmpty()) {\n      throw Exception(\"スタックが空です\");\n    }\n    return _stack.last;\n  }\n\n  /* スタックを Array に変換して返す */\n  List&lt;int&gt; toArray() =&gt; _stack;\n}\n</code></pre> array_stack.rs<pre><code>/* 配列ベースのスタック */\nstruct ArrayStack&lt;T&gt; {\n    stack: Vec&lt;T&gt;,\n}\n\nimpl&lt;T&gt; ArrayStack&lt;T&gt; {\n    /* スタックを初期化 */\n    fn new() -&gt; ArrayStack&lt;T&gt; {\n        ArrayStack::&lt;T&gt; {\n            stack: Vec::&lt;T&gt;::new(),\n        }\n    }\n\n    /* スタックの長さを取得 */\n    fn size(&amp;self) -&gt; usize {\n        self.stack.len()\n    }\n\n    /* スタックが空かどうかを判定 */\n    fn is_empty(&amp;self) -&gt; bool {\n        self.size() == 0\n    }\n\n    /* プッシュ */\n    fn push(&amp;mut self, num: T) {\n        self.stack.push(num);\n    }\n\n    /* ポップ */\n    fn pop(&amp;mut self) -&gt; Option&lt;T&gt; {\n        self.stack.pop()\n    }\n\n    /* スタックトップの要素にアクセス */\n    fn peek(&amp;self) -&gt; Option&lt;&amp;T&gt; {\n        if self.is_empty() {\n            panic!(\"スタックが空です\")\n        };\n        self.stack.last()\n    }\n\n    /* &amp;Vec を返す */\n    fn to_array(&amp;self) -&gt; &amp;Vec&lt;T&gt; {\n        &amp;self.stack\n    }\n}\n</code></pre> array_stack.c<pre><code>/* 配列ベースのスタック */\ntypedef struct {\n    int *data;\n    int size;\n} ArrayStack;\n\n/* コンストラクタ */\nArrayStack *newArrayStack() {\n    ArrayStack *stack = malloc(sizeof(ArrayStack));\n    // 大きめの容量で初期化し、拡張を避ける\n    stack-&gt;data = malloc(sizeof(int) * MAX_SIZE);\n    stack-&gt;size = 0;\n    return stack;\n}\n\n/* デストラクタ */\nvoid delArrayStack(ArrayStack *stack) {\n    free(stack-&gt;data);\n    free(stack);\n}\n\n/* スタックの長さを取得 */\nint size(ArrayStack *stack) {\n    return stack-&gt;size;\n}\n\n/* スタックが空かどうかを判定 */\nbool isEmpty(ArrayStack *stack) {\n    return stack-&gt;size == 0;\n}\n\n/* プッシュ */\nvoid push(ArrayStack *stack, int num) {\n    if (stack-&gt;size == MAX_SIZE) {\n        printf(\"スタックは満杯です\\n\");\n        return;\n    }\n    stack-&gt;data[stack-&gt;size] = num;\n    stack-&gt;size++;\n}\n\n/* スタックトップの要素にアクセス */\nint peek(ArrayStack *stack) {\n    if (stack-&gt;size == 0) {\n        printf(\"スタックは空です\\n\");\n        return INT_MAX;\n    }\n    return stack-&gt;data[stack-&gt;size - 1];\n}\n\n/* ポップ */\nint pop(ArrayStack *stack) {\n    int val = peek(stack);\n    stack-&gt;size--;\n    return val;\n}\n</code></pre> array_stack.kt<pre><code>/* 配列ベースのスタック */\nclass ArrayStack {\n    // リスト（動的配列）を初期化する\n    private val stack = mutableListOf&lt;Int&gt;()\n\n    /* スタックの長さを取得 */\n    fun size(): Int {\n        return stack.size\n    }\n\n    /* スタックが空かどうかを判定 */\n    fun isEmpty(): Boolean {\n        return size() == 0\n    }\n\n    /* プッシュ */\n    fun push(num: Int) {\n        stack.add(num)\n    }\n\n    /* ポップ */\n    fun pop(): Int {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        return stack.removeAt(size() - 1)\n    }\n\n    /* スタックトップの要素にアクセス */\n    fun peek(): Int {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        return stack[size() - 1]\n    }\n\n    /* List を Array に変換して返す */\n    fun toArray(): Array&lt;Any&gt; {\n        return stack.toTypedArray()\n    }\n}\n</code></pre> array_stack.rb<pre><code>### 配列で実装したスタック ###\nclass ArrayStack\n  ### コンストラクタ ###\n  def initialize\n    @stack = []\n  end\n\n  ### スタックの長さを取得 ###\n  def size\n    @stack.length\n  end\n\n  ### スタックが空か判定 ###\n  def is_empty?\n    @stack.empty?\n  end\n\n  ### プッシュ ###\n  def push(item)\n    @stack &lt;&lt; item\n  end\n\n  ### ポップ ###\n  def pop\n    raise IndexError, 'スタックは空です' if is_empty?\n\n    @stack.pop\n  end\n\n  ### スタックトップ要素を参照 ###\n  def peek\n    raise IndexError, 'スタックは空です' if is_empty?\n\n    @stack.last\n  end\n\n  ### 表示用のリストを返す ###\n  def to_array\n    @stack\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 5 章 &nbsp; スタックとキュー","5.1 &nbsp; スタック"],"tags":[]},{"location":"chapter_stack_and_queue/stack/#513-2","level":2,"title":"5.1.3   2つの実装の比較","text":"<p>対応する操作</p> <p>どちらの実装も、スタックの定義に含まれる各種操作をサポートします。配列ベースの実装はランダムアクセスも可能ですが、これはスタックの定義範囲を超えているため、通常は利用しません。</p> <p>時間効率</p> <p>配列ベースの実装では、プッシュとポップの両方があらかじめ確保された連続メモリ上で行われるため、キャッシュ局所性が高く、効率に優れます。ただし、プッシュ時に配列容量を超えると拡張処理が発生し、その1回のプッシュの時間計算量は \\(O(n)\\) になります。</p> <p>連結リストベースの実装では、サイズ拡張が非常に柔軟であり、前述のような配列拡張による効率低下はありません。ただし、プッシュ時にはノードオブジェクトの初期化とポインタの更新が必要になるため、効率は相対的に低くなります。もっとも、プッシュする要素自体がノードオブジェクトであれば、初期化の手間を省けるため、効率を高められます。</p> <p>以上を踏まえると、プッシュおよびポップの対象が <code>int</code> や <code>double</code> のような基本データ型である場合、次の結論が得られます。</p> <ul> <li>配列ベースのスタックは拡張時に効率が低下しますが、拡張は低頻度の操作であるため、平均効率はより高くなります。</li> <li>連結リストベースのスタックは、より安定した効率を提供できます。</li> </ul> <p>空間効率</p> <p>リストを初期化するとき、システムは「初期容量」を割り当てますが、この容量は実際の必要量を上回ることがあります。また、拡張は通常、一定の倍率（たとえば2倍）で行われるため、拡張後の容量も実際の必要量を超える可能性があります。したがって、配列ベースのスタックは一定のメモリ浪費を招く可能性があります。</p> <p>一方で、連結リストのノードはポインタを追加で保持する必要があるため、連結リストノードは相対的に大きな領域を占有します。</p> <p>以上より、どちらの実装がより省メモリかを単純に断定することはできず、具体的な状況に応じて分析する必要があります。</p>","path":["第 5 章 &nbsp; スタックとキュー","5.1 &nbsp; スタック"],"tags":[]},{"location":"chapter_stack_and_queue/stack/#514","level":2,"title":"5.1.4   スタックの典型的な応用","text":"<ul> <li>ブラウザにおける戻ると進む、ソフトウェアにおける取り消しとやり直し。新しいWebページを開くたびに、ブラウザは直前のページをスタックにプッシュするため、戻る操作によって前のページに戻れます。戻る操作は実際にはポップに相当します。戻ると進むを同時にサポートするには、2つのスタックを組み合わせて実現する必要があります。</li> <li>プログラムのメモリ管理。関数を呼び出すたびに、システムはスタックトップにスタックフレームを追加し、関数のコンテキスト情報を記録します。再帰関数では、下向きに再帰していく段階でプッシュが繰り返され、上向きにバックトラックする段階でポップが繰り返されます。</li> </ul>","path":["第 5 章 &nbsp; スタックとキュー","5.1 &nbsp; スタック"],"tags":[]},{"location":"chapter_stack_and_queue/summary/","level":1,"title":"5.4   まとめ","text":"","path":["第 5 章 &nbsp; スタックとキュー","5.4 &nbsp; まとめ"],"tags":[]},{"location":"chapter_stack_and_queue/summary/#1","level":3,"title":"1.   要点の振り返り","text":"<ul> <li>スタックは後入れ先出しの原則に従うデータ構造であり、配列または連結リストで実装できます。</li> <li>時間効率の面では、スタックの配列実装は平均効率が高い一方、拡張時には 1 回のプッシュ操作の時間計算量が \\(O(n)\\) まで悪化します。これに対して、スタックの連結リスト実装はより安定した効率を示します。</li> <li>空間効率の面では、スタックの配列実装はある程度の領域の無駄を生む可能性があります。ただし、連結リストのノードが占有するメモリは配列要素よりも大きい点に注意が必要です。</li> <li>キューは先入れ先出しの原則に従うデータ構造であり、同様に配列または連結リストで実装できます。時間効率と空間効率の比較における結論は、前述のスタックの場合と似ています。</li> <li>両端キューはより高い自由度を持つキューであり、両端で要素の追加と削除を行えます。</li> </ul>","path":["第 5 章 &nbsp; スタックとキュー","5.4 &nbsp; まとめ"],"tags":[]},{"location":"chapter_stack_and_queue/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q：ブラウザの進む・戻るは双方向連結リストで実装されているのですか？</p> <p>ブラウザの進む・戻る機能の本質は「スタック」の表れです。ユーザーが新しいページにアクセスすると、そのページはスタックの先頭に追加されます。ユーザーが戻るボタンをクリックすると、そのページはスタックの先頭から取り出されます。両端キューを使うといくつかの追加操作を簡単に実装でき、この点は「両端キュー」の章で触れています。</p> <p>Q：ポップした後、そのノードのメモリを解放する必要はありますか？</p> <p>後で取り出したノードを引き続き使うのであれば、メモリを解放する必要はありません。以降そのノードを使わない場合でも、<code>Java</code> や <code>Python</code> などの言語には自動ガベージコレクション機構があるため、手動でメモリを解放する必要はありません。一方、<code>C</code> と <code>C++</code> では手動でメモリを解放する必要があります。</p> <p>Q：両端キューは 2 つのスタックをつなげたように見えますが、用途は何ですか？</p> <p>両端キューは、スタックとキューの組み合わせ、あるいは 2 つのスタックをつなげたもののような構造です。表しているのはスタック + キューのロジックなので、スタックとキューのすべての応用を実現でき、しかもより柔軟です。</p> <p>Q：取り消し（undo）とやり直し（redo）は具体的にどのように実装されますか？</p> <p>2 つのスタックを使い、スタック <code>A</code> を取り消し用、スタック <code>B</code> をやり直し用に使います。</p> <ol> <li>ユーザーが操作を 1 つ実行するたびに、その操作をスタック <code>A</code> にプッシュし、スタック <code>B</code> を空にします。</li> <li>ユーザーが「取り消し」を実行したときは、スタック <code>A</code> から直近の操作をポップし、それをスタック <code>B</code> にプッシュします。</li> <li>ユーザーが「やり直し」を実行したときは、スタック <code>B</code> から直近の操作をポップし、それをスタック <code>A</code> にプッシュします。</li> </ol>","path":["第 5 章 &nbsp; スタックとキュー","5.4 &nbsp; まとめ"],"tags":[]},{"location":"chapter_tree/","level":1,"title":"第 7 章   木","text":"<p>Abstract</p> <p>大樹は生命力に満ち、根は深く葉は生い茂り、枝は豊かに広がる。</p> <p>それはデータ分割統治の生き生きとした姿を私たちに示してくれる。</p>","path":["第 7 章 &nbsp; 木"],"tags":[]},{"location":"chapter_tree/#_1","level":2,"title":"章の内容","text":"<ul> <li>7.1   二分木</li> <li>7.2   二分木の走査</li> <li>7.3   二分木の配列表現</li> <li>7.4   二分探索木</li> <li>7.5   AVL 木 *</li> <li>7.6   まとめ</li> </ul>","path":["第 7 章 &nbsp; 木"],"tags":[]},{"location":"chapter_tree/array_representation_of_tree/","level":1,"title":"7.3   二分木の配列表現","text":"<p>連結リスト表現では、二分木の記憶単位はノード <code>TreeNode</code> であり、ノード同士はポインタによって接続されます。前節では、連結リスト表現における二分木の各種基本操作を紹介しました。</p> <p>では、配列で二分木を表現できるでしょうか？答えはもちろん可能です。</p>","path":["第 7 章 &nbsp; 木","7.3 &nbsp; 二分木の配列表現"],"tags":[]},{"location":"chapter_tree/array_representation_of_tree/#731","level":2,"title":"7.3.1   充足二分木を表現する","text":"<p>まずは簡単な例を考えます。与えられた 1 本の充足二分木について、すべてのノードをレベル順走査の順に配列へ格納すると、各ノードは一意な配列インデックスに対応します。</p> <p>レベル順走査の性質に基づくと、親ノードのインデックスと子ノードのインデックスの間にある「対応式」を導けます。あるノードのインデックスが \\(i\\) なら、その左子ノードのインデックスは \\(2i + 1\\) 、右子ノードのインデックスは \\(2i + 2\\) です。以下の図は、各ノードインデックス間の対応関係を示しています。</p> <p></p> <p> 図 7-12   充足二分木の配列表現 </p> <p>対応式は、連結リストにおけるノード参照（ポインタ）と同じ役割を果たします。与えられた配列内の任意のノードについて、この対応式を使えばその左（右）子ノードにアクセスできます。</p>","path":["第 7 章 &nbsp; 木","7.3 &nbsp; 二分木の配列表現"],"tags":[]},{"location":"chapter_tree/array_representation_of_tree/#732","level":2,"title":"7.3.2   任意の二分木を表現する","text":"<p>充足二分木は特殊なケースであり、一般の二分木では中間層に多数の <code>None</code> が存在することがよくあります。レベル順走査の列にはこれらの <code>None</code> が含まれないため、その列だけから <code>None</code> の数や分布位置を推定することはできません。つまり、このレベル順走査列に一致する二分木構造は複数存在し得ます。</p> <p>次の図のように、非充足二分木が与えられると、上記の配列表現はすでに成り立ちません。</p> <p></p> <p> 図 7-13   レベル順走査列に対応する複数の二分木の可能性 </p> <p>この問題を解決するために、**レベル順走査列にすべての <code>None</code> を明示的に書き込む**ことを考えられます。次の図のように、このように処理すればレベル順走査列で二分木を一意に表現できます。コード例は以下のとおりです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code># 二分木の配列表現\n# 空き位置を表すために None を使う\ntree = [1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, None, None, 15]\n</code></pre> <pre><code>/* 二分木の配列表現 */\n// int の最大値 INT_MAX を使って空き位置を示す\nvector&lt;int&gt; tree = {1, 2, 3, 4, INT_MAX, 6, 7, 8, 9, INT_MAX, INT_MAX, 12, INT_MAX, INT_MAX, 15};\n</code></pre> <pre><code>/* 二分木の配列表現 */\n// int のラッパークラス Integer を使えば、null で空き位置を示せる\nInteger[] tree = { 1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15 };\n</code></pre> <pre><code>/* 二分木の配列表現 */\n// nullable な int? 型を使えば、null で空き位置を示せる\nint?[] tree = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <pre><code>/* 二分木の配列表現 */\n// any 型のスライスを使えば、nil で空き位置を示せる\ntree := []any{1, 2, 3, 4, nil, 6, 7, 8, 9, nil, nil, 12, nil, nil, 15}\n</code></pre> <pre><code>/* 二分木の配列表現 */\n// nullable な Int? 型を使えば、nil で空き位置を示せる\nlet tree: [Int?] = [1, 2, 3, 4, nil, 6, 7, 8, 9, nil, nil, 12, nil, nil, 15]\n</code></pre> <pre><code>/* 二分木の配列表現 */\n// null を使って空き位置を表す\nlet tree = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <pre><code>/* 二分木の配列表現 */\n// null を使って空き位置を表す\nlet tree: (number | null)[] = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <pre><code>/* 二分木の配列表現 */\n// nullable な int? 型を使えば、null で空き位置を示せる\nList&lt;int?&gt; tree = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <pre><code>/* 二分木の配列表現 */\n// None を使って空き位置を示す\nlet tree = [Some(1), Some(2), Some(3), Some(4), None, Some(6), Some(7), Some(8), Some(9), None, None, Some(12), None, None, Some(15)];\n</code></pre> <pre><code>/* 二分木の配列表現 */\n// int の最大値で空き位置を示すため、ノード値は INT_MAX であってはならない\nint tree[] = {1, 2, 3, 4, INT_MAX, 6, 7, 8, 9, INT_MAX, INT_MAX, 12, INT_MAX, INT_MAX, 15};\n</code></pre> <pre><code>/* 二分木の配列表現 */\n// null を使って空き位置を表す\nval tree = arrayOf( 1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15 )\n</code></pre> <pre><code>### 二分木の配列表現 ###\n# nil を使って空き位置を表す\ntree = [1, 2, 3, 4, nil, 6, 7, 8, 9, nil, nil, 12, nil, nil, 15]\n</code></pre> <p></p> <p> 図 7-14   任意の二分木の配列表現 </p> <p>補足すると、完全二分木は配列による表現に非常に適しています。完全二分木の定義を振り返ると、<code>None</code> は最下層の右側にしか現れないため、すべての <code>None</code> は必ずレベル順走査列の末尾に現れます。</p> <p>つまり、完全二分木を配列で表す場合は、すべての <code>None</code> の格納を省略できるため、非常に便利です。次の図に例を示します。</p> <p></p> <p> 図 7-15   完全二分木の配列表現 </p> <p>以下のコードでは、配列ベースで表現した二分木を実装しており、次の操作を含みます。</p> <ul> <li>あるノードが与えられたとき、その値、左（右）子ノード、親ノードを取得する。</li> <li>前順走査、中順走査、後順走査、レベル順走査の列を取得する。</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array_binary_tree.py<pre><code>class ArrayBinaryTree:\n    \"\"\"配列表現による二分木クラス\"\"\"\n\n    def __init__(self, arr: list[int | None]):\n        \"\"\"コンストラクタ\"\"\"\n        self._tree = list(arr)\n\n    def size(self):\n        \"\"\"リスト容量\"\"\"\n        return len(self._tree)\n\n    def val(self, i: int) -&gt; int | None:\n        \"\"\"インデックス i のノードの値を取得\"\"\"\n        # インデックスが範囲外なら、空きを表す None を返す\n        if i &lt; 0 or i &gt;= self.size():\n            return None\n        return self._tree[i]\n\n    def left(self, i: int) -&gt; int | None:\n        \"\"\"インデックス i のノードの左子ノードのインデックスを取得\"\"\"\n        return 2 * i + 1\n\n    def right(self, i: int) -&gt; int | None:\n        \"\"\"インデックス i のノードの右子ノードのインデックスを取得\"\"\"\n        return 2 * i + 2\n\n    def parent(self, i: int) -&gt; int | None:\n        \"\"\"インデックス i のノードの親ノードのインデックスを取得\"\"\"\n        return (i - 1) // 2\n\n    def level_order(self) -&gt; list[int]:\n        \"\"\"レベル順走査\"\"\"\n        self.res = []\n        # 配列を直接走査する\n        for i in range(self.size()):\n            if self.val(i) is not None:\n                self.res.append(self.val(i))\n        return self.res\n\n    def dfs(self, i: int, order: str):\n        \"\"\"深さ優先探索\"\"\"\n        if self.val(i) is None:\n            return\n        # 先行順走査\n        if order == \"pre\":\n            self.res.append(self.val(i))\n        self.dfs(self.left(i), order)\n        # 中順走査\n        if order == \"in\":\n            self.res.append(self.val(i))\n        self.dfs(self.right(i), order)\n        # 後順走査\n        if order == \"post\":\n            self.res.append(self.val(i))\n\n    def pre_order(self) -&gt; list[int]:\n        \"\"\"先行順走査\"\"\"\n        self.res = []\n        self.dfs(0, order=\"pre\")\n        return self.res\n\n    def in_order(self) -&gt; list[int]:\n        \"\"\"中順走査\"\"\"\n        self.res = []\n        self.dfs(0, order=\"in\")\n        return self.res\n\n    def post_order(self) -&gt; list[int]:\n        \"\"\"後順走査\"\"\"\n        self.res = []\n        self.dfs(0, order=\"post\")\n        return self.res\n</code></pre> array_binary_tree.cpp<pre><code>/* 配列表現による二分木クラス */\nclass ArrayBinaryTree {\n  public:\n    /* コンストラクタ */\n    ArrayBinaryTree(vector&lt;int&gt; arr) {\n        tree = arr;\n    }\n\n    /* リスト容量 */\n    int size() {\n        return tree.size();\n    }\n\n    /* インデックス i のノードの値を取得 */\n    int val(int i) {\n        // インデックスが範囲外なら、空きを表す INT_MAX を返す\n        if (i &lt; 0 || i &gt;= size())\n            return INT_MAX;\n        return tree[i];\n    }\n\n    /* インデックス i のノードの左子ノードのインデックスを取得 */\n    int left(int i) {\n        return 2 * i + 1;\n    }\n\n    /* インデックス i のノードの右子ノードのインデックスを取得 */\n    int right(int i) {\n        return 2 * i + 2;\n    }\n\n    /* インデックス i のノードの親ノードのインデックスを取得 */\n    int parent(int i) {\n        return (i - 1) / 2;\n    }\n\n    /* レベル順走査 */\n    vector&lt;int&gt; levelOrder() {\n        vector&lt;int&gt; res;\n        // 配列を直接走査する\n        for (int i = 0; i &lt; size(); i++) {\n            if (val(i) != INT_MAX)\n                res.push_back(val(i));\n        }\n        return res;\n    }\n\n    /* 先行順走査 */\n    vector&lt;int&gt; preOrder() {\n        vector&lt;int&gt; res;\n        dfs(0, \"pre\", res);\n        return res;\n    }\n\n    /* 中順走査 */\n    vector&lt;int&gt; inOrder() {\n        vector&lt;int&gt; res;\n        dfs(0, \"in\", res);\n        return res;\n    }\n\n    /* 後順走査 */\n    vector&lt;int&gt; postOrder() {\n        vector&lt;int&gt; res;\n        dfs(0, \"post\", res);\n        return res;\n    }\n\n  private:\n    vector&lt;int&gt; tree;\n\n    /* 深さ優先探索 */\n    void dfs(int i, string order, vector&lt;int&gt; &amp;res) {\n        // 空きスロットなら返す\n        if (val(i) == INT_MAX)\n            return;\n        // 先行順走査\n        if (order == \"pre\")\n            res.push_back(val(i));\n        dfs(left(i), order, res);\n        // 中順走査\n        if (order == \"in\")\n            res.push_back(val(i));\n        dfs(right(i), order, res);\n        // 後順走査\n        if (order == \"post\")\n            res.push_back(val(i));\n    }\n};\n</code></pre> array_binary_tree.java<pre><code>/* 配列表現による二分木クラス */\nclass ArrayBinaryTree {\n    private List&lt;Integer&gt; tree;\n\n    /* コンストラクタ */\n    public ArrayBinaryTree(List&lt;Integer&gt; arr) {\n        tree = new ArrayList&lt;&gt;(arr);\n    }\n\n    /* リスト容量 */\n    public int size() {\n        return tree.size();\n    }\n\n    /* インデックス i のノードの値を取得 */\n    public Integer val(int i) {\n        // インデックスが範囲外なら、空きを表す null を返す\n        if (i &lt; 0 || i &gt;= size())\n            return null;\n        return tree.get(i);\n    }\n\n    /* インデックス i のノードの左子ノードのインデックスを取得 */\n    public Integer left(int i) {\n        return 2 * i + 1;\n    }\n\n    /* インデックス i のノードの右子ノードのインデックスを取得 */\n    public Integer right(int i) {\n        return 2 * i + 2;\n    }\n\n    /* インデックス i のノードの親ノードのインデックスを取得 */\n    public Integer parent(int i) {\n        return (i - 1) / 2;\n    }\n\n    /* レベル順走査 */\n    public List&lt;Integer&gt; levelOrder() {\n        List&lt;Integer&gt; res = new ArrayList&lt;&gt;();\n        // 配列を直接走査する\n        for (int i = 0; i &lt; size(); i++) {\n            if (val(i) != null)\n                res.add(val(i));\n        }\n        return res;\n    }\n\n    /* 深さ優先探索 */\n    private void dfs(Integer i, String order, List&lt;Integer&gt; res) {\n        // 空きスロットなら返す\n        if (val(i) == null)\n            return;\n        // 先行順走査\n        if (\"pre\".equals(order))\n            res.add(val(i));\n        dfs(left(i), order, res);\n        // 中順走査\n        if (\"in\".equals(order))\n            res.add(val(i));\n        dfs(right(i), order, res);\n        // 後順走査\n        if (\"post\".equals(order))\n            res.add(val(i));\n    }\n\n    /* 先行順走査 */\n    public List&lt;Integer&gt; preOrder() {\n        List&lt;Integer&gt; res = new ArrayList&lt;&gt;();\n        dfs(0, \"pre\", res);\n        return res;\n    }\n\n    /* 中順走査 */\n    public List&lt;Integer&gt; inOrder() {\n        List&lt;Integer&gt; res = new ArrayList&lt;&gt;();\n        dfs(0, \"in\", res);\n        return res;\n    }\n\n    /* 後順走査 */\n    public List&lt;Integer&gt; postOrder() {\n        List&lt;Integer&gt; res = new ArrayList&lt;&gt;();\n        dfs(0, \"post\", res);\n        return res;\n    }\n}\n</code></pre> array_binary_tree.cs<pre><code>/* 配列表現による二分木クラス */\nclass ArrayBinaryTree(List&lt;int?&gt; arr) {\n    List&lt;int?&gt; tree = new(arr);\n\n    /* リスト容量 */\n    public int Size() {\n        return tree.Count;\n    }\n\n    /* インデックス i のノードの値を取得 */\n    public int? Val(int i) {\n        // インデックスが範囲外なら、空きを表す null を返す\n        if (i &lt; 0 || i &gt;= Size())\n            return null;\n        return tree[i];\n    }\n\n    /* インデックス i のノードの左子ノードのインデックスを取得 */\n    public int Left(int i) {\n        return 2 * i + 1;\n    }\n\n    /* インデックス i のノードの右子ノードのインデックスを取得 */\n    public int Right(int i) {\n        return 2 * i + 2;\n    }\n\n    /* インデックス i のノードの親ノードのインデックスを取得 */\n    public int Parent(int i) {\n        return (i - 1) / 2;\n    }\n\n    /* レベル順走査 */\n    public List&lt;int&gt; LevelOrder() {\n        List&lt;int&gt; res = [];\n        // 配列を直接走査する\n        for (int i = 0; i &lt; Size(); i++) {\n            if (Val(i).HasValue)\n                res.Add(Val(i)!.Value);\n        }\n        return res;\n    }\n\n    /* 深さ優先探索 */\n    void DFS(int i, string order, List&lt;int&gt; res) {\n        // 空きスロットなら返す\n        if (!Val(i).HasValue)\n            return;\n        // 先行順走査\n        if (order == \"pre\")\n            res.Add(Val(i)!.Value);\n        DFS(Left(i), order, res);\n        // 中順走査\n        if (order == \"in\")\n            res.Add(Val(i)!.Value);\n        DFS(Right(i), order, res);\n        // 後順走査\n        if (order == \"post\")\n            res.Add(Val(i)!.Value);\n    }\n\n    /* 先行順走査 */\n    public List&lt;int&gt; PreOrder() {\n        List&lt;int&gt; res = [];\n        DFS(0, \"pre\", res);\n        return res;\n    }\n\n    /* 中順走査 */\n    public List&lt;int&gt; InOrder() {\n        List&lt;int&gt; res = [];\n        DFS(0, \"in\", res);\n        return res;\n    }\n\n    /* 後順走査 */\n    public List&lt;int&gt; PostOrder() {\n        List&lt;int&gt; res = [];\n        DFS(0, \"post\", res);\n        return res;\n    }\n}\n</code></pre> array_binary_tree.go<pre><code>/* 配列表現による二分木クラス */\ntype arrayBinaryTree struct {\n    tree []any\n}\n\n/* コンストラクタ */\nfunc newArrayBinaryTree(arr []any) *arrayBinaryTree {\n    return &amp;arrayBinaryTree{\n        tree: arr,\n    }\n}\n\n/* リスト容量 */\nfunc (abt *arrayBinaryTree) size() int {\n    return len(abt.tree)\n}\n\n/* インデックス i のノードの値を取得 */\nfunc (abt *arrayBinaryTree) val(i int) any {\n    // インデックスが範囲外なら、空きを表す null を返す\n    if i &lt; 0 || i &gt;= abt.size() {\n        return nil\n    }\n    return abt.tree[i]\n}\n\n/* インデックス i のノードの左子ノードのインデックスを取得 */\nfunc (abt *arrayBinaryTree) left(i int) int {\n    return 2*i + 1\n}\n\n/* インデックス i のノードの右子ノードのインデックスを取得 */\nfunc (abt *arrayBinaryTree) right(i int) int {\n    return 2*i + 2\n}\n\n/* インデックス i のノードの親ノードのインデックスを取得 */\nfunc (abt *arrayBinaryTree) parent(i int) int {\n    return (i - 1) / 2\n}\n\n/* レベル順走査 */\nfunc (abt *arrayBinaryTree) levelOrder() []any {\n    var res []any\n    // 配列を直接走査する\n    for i := 0; i &lt; abt.size(); i++ {\n        if abt.val(i) != nil {\n            res = append(res, abt.val(i))\n        }\n    }\n    return res\n}\n\n/* 深さ優先探索 */\nfunc (abt *arrayBinaryTree) dfs(i int, order string, res *[]any) {\n    // 空きスロットなら返す\n    if abt.val(i) == nil {\n        return\n    }\n    // 先行順走査\n    if order == \"pre\" {\n        *res = append(*res, abt.val(i))\n    }\n    abt.dfs(abt.left(i), order, res)\n    // 中順走査\n    if order == \"in\" {\n        *res = append(*res, abt.val(i))\n    }\n    abt.dfs(abt.right(i), order, res)\n    // 後順走査\n    if order == \"post\" {\n        *res = append(*res, abt.val(i))\n    }\n}\n\n/* 先行順走査 */\nfunc (abt *arrayBinaryTree) preOrder() []any {\n    var res []any\n    abt.dfs(0, \"pre\", &amp;res)\n    return res\n}\n\n/* 中順走査 */\nfunc (abt *arrayBinaryTree) inOrder() []any {\n    var res []any\n    abt.dfs(0, \"in\", &amp;res)\n    return res\n}\n\n/* 後順走査 */\nfunc (abt *arrayBinaryTree) postOrder() []any {\n    var res []any\n    abt.dfs(0, \"post\", &amp;res)\n    return res\n}\n</code></pre> array_binary_tree.swift<pre><code>/* 配列表現による二分木クラス */\nclass ArrayBinaryTree {\n    private var tree: [Int?]\n\n    /* コンストラクタ */\n    init(arr: [Int?]) {\n        tree = arr\n    }\n\n    /* リスト容量 */\n    func size() -&gt; Int {\n        tree.count\n    }\n\n    /* インデックス i のノードの値を取得 */\n    func val(i: Int) -&gt; Int? {\n        // インデックスが範囲外なら、空きを表す null を返す\n        if i &lt; 0 || i &gt;= size() {\n            return nil\n        }\n        return tree[i]\n    }\n\n    /* インデックス i のノードの左子ノードのインデックスを取得 */\n    func left(i: Int) -&gt; Int {\n        2 * i + 1\n    }\n\n    /* インデックス i のノードの右子ノードのインデックスを取得 */\n    func right(i: Int) -&gt; Int {\n        2 * i + 2\n    }\n\n    /* インデックス i のノードの親ノードのインデックスを取得 */\n    func parent(i: Int) -&gt; Int {\n        (i - 1) / 2\n    }\n\n    /* レベル順走査 */\n    func levelOrder() -&gt; [Int] {\n        var res: [Int] = []\n        // 配列を直接走査する\n        for i in 0 ..&lt; size() {\n            if let val = val(i: i) {\n                res.append(val)\n            }\n        }\n        return res\n    }\n\n    /* 深さ優先探索 */\n    private func dfs(i: Int, order: String, res: inout [Int]) {\n        // 空きスロットなら返す\n        guard let val = val(i: i) else {\n            return\n        }\n        // 先行順走査\n        if order == \"pre\" {\n            res.append(val)\n        }\n        dfs(i: left(i: i), order: order, res: &amp;res)\n        // 中順走査\n        if order == \"in\" {\n            res.append(val)\n        }\n        dfs(i: right(i: i), order: order, res: &amp;res)\n        // 後順走査\n        if order == \"post\" {\n            res.append(val)\n        }\n    }\n\n    /* 先行順走査 */\n    func preOrder() -&gt; [Int] {\n        var res: [Int] = []\n        dfs(i: 0, order: \"pre\", res: &amp;res)\n        return res\n    }\n\n    /* 中順走査 */\n    func inOrder() -&gt; [Int] {\n        var res: [Int] = []\n        dfs(i: 0, order: \"in\", res: &amp;res)\n        return res\n    }\n\n    /* 後順走査 */\n    func postOrder() -&gt; [Int] {\n        var res: [Int] = []\n        dfs(i: 0, order: \"post\", res: &amp;res)\n        return res\n    }\n}\n</code></pre> array_binary_tree.js<pre><code>/* 配列表現による二分木クラス */\nclass ArrayBinaryTree {\n    #tree;\n\n    /* コンストラクタ */\n    constructor(arr) {\n        this.#tree = arr;\n    }\n\n    /* リスト容量 */\n    size() {\n        return this.#tree.length;\n    }\n\n    /* インデックス i のノードの値を取得 */\n    val(i) {\n        // インデックスが範囲外なら、空きを表す null を返す\n        if (i &lt; 0 || i &gt;= this.size()) return null;\n        return this.#tree[i];\n    }\n\n    /* インデックス i のノードの左子ノードのインデックスを取得 */\n    left(i) {\n        return 2 * i + 1;\n    }\n\n    /* インデックス i のノードの右子ノードのインデックスを取得 */\n    right(i) {\n        return 2 * i + 2;\n    }\n\n    /* インデックス i のノードの親ノードのインデックスを取得 */\n    parent(i) {\n        return Math.floor((i - 1) / 2); // 切り捨て除算\n    }\n\n    /* レベル順走査 */\n    levelOrder() {\n        let res = [];\n        // 配列を直接走査する\n        for (let i = 0; i &lt; this.size(); i++) {\n            if (this.val(i) !== null) res.push(this.val(i));\n        }\n        return res;\n    }\n\n    /* 深さ優先探索 */\n    #dfs(i, order, res) {\n        // 空きスロットなら返す\n        if (this.val(i) === null) return;\n        // 先行順走査\n        if (order === 'pre') res.push(this.val(i));\n        this.#dfs(this.left(i), order, res);\n        // 中順走査\n        if (order === 'in') res.push(this.val(i));\n        this.#dfs(this.right(i), order, res);\n        // 後順走査\n        if (order === 'post') res.push(this.val(i));\n    }\n\n    /* 先行順走査 */\n    preOrder() {\n        const res = [];\n        this.#dfs(0, 'pre', res);\n        return res;\n    }\n\n    /* 中順走査 */\n    inOrder() {\n        const res = [];\n        this.#dfs(0, 'in', res);\n        return res;\n    }\n\n    /* 後順走査 */\n    postOrder() {\n        const res = [];\n        this.#dfs(0, 'post', res);\n        return res;\n    }\n}\n</code></pre> array_binary_tree.ts<pre><code>/* 配列表現による二分木クラス */\nclass ArrayBinaryTree {\n    #tree: (number | null)[];\n\n    /* コンストラクタ */\n    constructor(arr: (number | null)[]) {\n        this.#tree = arr;\n    }\n\n    /* リスト容量 */\n    size(): number {\n        return this.#tree.length;\n    }\n\n    /* インデックス i のノードの値を取得 */\n    val(i: number): number | null {\n        // インデックスが範囲外なら、空きを表す null を返す\n        if (i &lt; 0 || i &gt;= this.size()) return null;\n        return this.#tree[i];\n    }\n\n    /* インデックス i のノードの左子ノードのインデックスを取得 */\n    left(i: number): number {\n        return 2 * i + 1;\n    }\n\n    /* インデックス i のノードの右子ノードのインデックスを取得 */\n    right(i: number): number {\n        return 2 * i + 2;\n    }\n\n    /* インデックス i のノードの親ノードのインデックスを取得 */\n    parent(i: number): number {\n        return Math.floor((i - 1) / 2); // 切り捨て除算\n    }\n\n    /* レベル順走査 */\n    levelOrder(): number[] {\n        let res = [];\n        // 配列を直接走査する\n        for (let i = 0; i &lt; this.size(); i++) {\n            if (this.val(i) !== null) res.push(this.val(i));\n        }\n        return res;\n    }\n\n    /* 深さ優先探索 */\n    #dfs(i: number, order: Order, res: (number | null)[]): void {\n        // 空きスロットなら返す\n        if (this.val(i) === null) return;\n        // 先行順走査\n        if (order === 'pre') res.push(this.val(i));\n        this.#dfs(this.left(i), order, res);\n        // 中順走査\n        if (order === 'in') res.push(this.val(i));\n        this.#dfs(this.right(i), order, res);\n        // 後順走査\n        if (order === 'post') res.push(this.val(i));\n    }\n\n    /* 先行順走査 */\n    preOrder(): (number | null)[] {\n        const res = [];\n        this.#dfs(0, 'pre', res);\n        return res;\n    }\n\n    /* 中順走査 */\n    inOrder(): (number | null)[] {\n        const res = [];\n        this.#dfs(0, 'in', res);\n        return res;\n    }\n\n    /* 後順走査 */\n    postOrder(): (number | null)[] {\n        const res = [];\n        this.#dfs(0, 'post', res);\n        return res;\n    }\n}\n</code></pre> array_binary_tree.dart<pre><code>/* 配列表現による二分木クラス */\nclass ArrayBinaryTree {\n  late List&lt;int?&gt; _tree;\n\n  /* コンストラクタ */\n  ArrayBinaryTree(this._tree);\n\n  /* リスト容量 */\n  int size() {\n    return _tree.length;\n  }\n\n  /* インデックス i のノードの値を取得 */\n  int? val(int i) {\n    // インデックスが範囲外なら、空きを表す null を返す\n    if (i &lt; 0 || i &gt;= size()) {\n      return null;\n    }\n    return _tree[i];\n  }\n\n  /* インデックス i のノードの左子ノードのインデックスを取得 */\n  int? left(int i) {\n    return 2 * i + 1;\n  }\n\n  /* インデックス i のノードの右子ノードのインデックスを取得 */\n  int? right(int i) {\n    return 2 * i + 2;\n  }\n\n  /* インデックス i のノードの親ノードのインデックスを取得 */\n  int? parent(int i) {\n    return (i - 1) ~/ 2;\n  }\n\n  /* レベル順走査 */\n  List&lt;int&gt; levelOrder() {\n    List&lt;int&gt; res = [];\n    for (int i = 0; i &lt; size(); i++) {\n      if (val(i) != null) {\n        res.add(val(i)!);\n      }\n    }\n    return res;\n  }\n\n  /* 深さ優先探索 */\n  void dfs(int i, String order, List&lt;int?&gt; res) {\n    // 空きスロットなら返す\n    if (val(i) == null) {\n      return;\n    }\n    // 先行順走査\n    if (order == 'pre') {\n      res.add(val(i));\n    }\n    dfs(left(i)!, order, res);\n    // 中順走査\n    if (order == 'in') {\n      res.add(val(i));\n    }\n    dfs(right(i)!, order, res);\n    // 後順走査\n    if (order == 'post') {\n      res.add(val(i));\n    }\n  }\n\n  /* 先行順走査 */\n  List&lt;int?&gt; preOrder() {\n    List&lt;int?&gt; res = [];\n    dfs(0, 'pre', res);\n    return res;\n  }\n\n  /* 中順走査 */\n  List&lt;int?&gt; inOrder() {\n    List&lt;int?&gt; res = [];\n    dfs(0, 'in', res);\n    return res;\n  }\n\n  /* 後順走査 */\n  List&lt;int?&gt; postOrder() {\n    List&lt;int?&gt; res = [];\n    dfs(0, 'post', res);\n    return res;\n  }\n}\n</code></pre> array_binary_tree.rs<pre><code>/* 配列表現による二分木クラス */\nstruct ArrayBinaryTree {\n    tree: Vec&lt;Option&lt;i32&gt;&gt;,\n}\n\nimpl ArrayBinaryTree {\n    /* コンストラクタ */\n    fn new(arr: Vec&lt;Option&lt;i32&gt;&gt;) -&gt; Self {\n        Self { tree: arr }\n    }\n\n    /* リスト容量 */\n    fn size(&amp;self) -&gt; i32 {\n        self.tree.len() as i32\n    }\n\n    /* インデックス i のノードの値を取得 */\n    fn val(&amp;self, i: i32) -&gt; Option&lt;i32&gt; {\n        // インデックスが範囲外なら、空きを表す None を返す\n        if i &lt; 0 || i &gt;= self.size() {\n            None\n        } else {\n            self.tree[i as usize]\n        }\n    }\n\n    /* インデックス i のノードの左子ノードのインデックスを取得 */\n    fn left(&amp;self, i: i32) -&gt; i32 {\n        2 * i + 1\n    }\n\n    /* インデックス i のノードの右子ノードのインデックスを取得 */\n    fn right(&amp;self, i: i32) -&gt; i32 {\n        2 * i + 2\n    }\n\n    /* インデックス i のノードの親ノードのインデックスを取得 */\n    fn parent(&amp;self, i: i32) -&gt; i32 {\n        (i - 1) / 2\n    }\n\n    /* レベル順走査 */\n    fn level_order(&amp;self) -&gt; Vec&lt;i32&gt; {\n        self.tree.iter().filter_map(|&amp;x| x).collect()\n    }\n\n    /* 深さ優先探索 */\n    fn dfs(&amp;self, i: i32, order: &amp;'static str, res: &amp;mut Vec&lt;i32&gt;) {\n        if self.val(i).is_none() {\n            return;\n        }\n        let val = self.val(i).unwrap();\n        // 先行順走査\n        if order == \"pre\" {\n            res.push(val);\n        }\n        self.dfs(self.left(i), order, res);\n        // 中順走査\n        if order == \"in\" {\n            res.push(val);\n        }\n        self.dfs(self.right(i), order, res);\n        // 後順走査\n        if order == \"post\" {\n            res.push(val);\n        }\n    }\n\n    /* 先行順走査 */\n    fn pre_order(&amp;self) -&gt; Vec&lt;i32&gt; {\n        let mut res = vec![];\n        self.dfs(0, \"pre\", &amp;mut res);\n        res\n    }\n\n    /* 中順走査 */\n    fn in_order(&amp;self) -&gt; Vec&lt;i32&gt; {\n        let mut res = vec![];\n        self.dfs(0, \"in\", &amp;mut res);\n        res\n    }\n\n    /* 後順走査 */\n    fn post_order(&amp;self) -&gt; Vec&lt;i32&gt; {\n        let mut res = vec![];\n        self.dfs(0, \"post\", &amp;mut res);\n        res\n    }\n}\n</code></pre> array_binary_tree.c<pre><code>/* 配列表現による二分木の構造体 */\ntypedef struct {\n    int *tree;\n    int size;\n} ArrayBinaryTree;\n\n/* コンストラクタ */\nArrayBinaryTree *newArrayBinaryTree(int *arr, int arrSize) {\n    ArrayBinaryTree *abt = (ArrayBinaryTree *)malloc(sizeof(ArrayBinaryTree));\n    abt-&gt;tree = malloc(sizeof(int) * arrSize);\n    memcpy(abt-&gt;tree, arr, sizeof(int) * arrSize);\n    abt-&gt;size = arrSize;\n    return abt;\n}\n\n/* デストラクタ */\nvoid delArrayBinaryTree(ArrayBinaryTree *abt) {\n    free(abt-&gt;tree);\n    free(abt);\n}\n\n/* リスト容量 */\nint size(ArrayBinaryTree *abt) {\n    return abt-&gt;size;\n}\n\n/* インデックス i のノードの値を取得 */\nint val(ArrayBinaryTree *abt, int i) {\n    // インデックスが範囲外なら、空きを表す INT_MAX を返す\n    if (i &lt; 0 || i &gt;= size(abt))\n        return INT_MAX;\n    return abt-&gt;tree[i];\n}\n\n/* レベル順走査 */\nint *levelOrder(ArrayBinaryTree *abt, int *returnSize) {\n    int *res = (int *)malloc(sizeof(int) * size(abt));\n    int index = 0;\n    // 配列を直接走査する\n    for (int i = 0; i &lt; size(abt); i++) {\n        if (val(abt, i) != INT_MAX)\n            res[index++] = val(abt, i);\n    }\n    *returnSize = index;\n    return res;\n}\n\n/* 深さ優先探索 */\nvoid dfs(ArrayBinaryTree *abt, int i, char *order, int *res, int *index) {\n    // 空きスロットなら返す\n    if (val(abt, i) == INT_MAX)\n        return;\n    // 先行順走査\n    if (strcmp(order, \"pre\") == 0)\n        res[(*index)++] = val(abt, i);\n    dfs(abt, left(i), order, res, index);\n    // 中順走査\n    if (strcmp(order, \"in\") == 0)\n        res[(*index)++] = val(abt, i);\n    dfs(abt, right(i), order, res, index);\n    // 後順走査\n    if (strcmp(order, \"post\") == 0)\n        res[(*index)++] = val(abt, i);\n}\n\n/* 先行順走査 */\nint *preOrder(ArrayBinaryTree *abt, int *returnSize) {\n    int *res = (int *)malloc(sizeof(int) * size(abt));\n    int index = 0;\n    dfs(abt, 0, \"pre\", res, &amp;index);\n    *returnSize = index;\n    return res;\n}\n\n/* 中順走査 */\nint *inOrder(ArrayBinaryTree *abt, int *returnSize) {\n    int *res = (int *)malloc(sizeof(int) * size(abt));\n    int index = 0;\n    dfs(abt, 0, \"in\", res, &amp;index);\n    *returnSize = index;\n    return res;\n}\n\n/* 後順走査 */\nint *postOrder(ArrayBinaryTree *abt, int *returnSize) {\n    int *res = (int *)malloc(sizeof(int) * size(abt));\n    int index = 0;\n    dfs(abt, 0, \"post\", res, &amp;index);\n    *returnSize = index;\n    return res;\n}\n</code></pre> array_binary_tree.kt<pre><code>/* 配列表現による二分木クラス */\nclass ArrayBinaryTree(val tree: MutableList&lt;Int?&gt;) {\n    /* リスト容量 */\n    fun size(): Int {\n        return tree.size\n    }\n\n    /* インデックス i のノードの値を取得 */\n    fun _val(i: Int): Int? {\n        // インデックスが範囲外なら、空きを表す null を返す\n        if (i &lt; 0 || i &gt;= size()) return null\n        return tree[i]\n    }\n\n    /* インデックス i のノードの左子ノードのインデックスを取得 */\n    fun left(i: Int): Int {\n        return 2 * i + 1\n    }\n\n    /* インデックス i のノードの右子ノードのインデックスを取得 */\n    fun right(i: Int): Int {\n        return 2 * i + 2\n    }\n\n    /* インデックス i のノードの親ノードのインデックスを取得 */\n    fun parent(i: Int): Int {\n        return (i - 1) / 2\n    }\n\n    /* レベル順走査 */\n    fun levelOrder(): MutableList&lt;Int?&gt; {\n        val res = mutableListOf&lt;Int?&gt;()\n        // 配列を直接走査する\n        for (i in 0..&lt;size()) {\n            if (_val(i) != null)\n                res.add(_val(i))\n        }\n        return res\n    }\n\n    /* 深さ優先探索 */\n    fun dfs(i: Int, order: String, res: MutableList&lt;Int?&gt;) {\n        // 空きスロットなら返す\n        if (_val(i) == null)\n            return\n        // 先行順走査\n        if (\"pre\" == order)\n            res.add(_val(i))\n        dfs(left(i), order, res)\n        // 中順走査\n        if (\"in\" == order)\n            res.add(_val(i))\n        dfs(right(i), order, res)\n        // 後順走査\n        if (\"post\" == order)\n            res.add(_val(i))\n    }\n\n    /* 先行順走査 */\n    fun preOrder(): MutableList&lt;Int?&gt; {\n        val res = mutableListOf&lt;Int?&gt;()\n        dfs(0, \"pre\", res)\n        return res\n    }\n\n    /* 中順走査 */\n    fun inOrder(): MutableList&lt;Int?&gt; {\n        val res = mutableListOf&lt;Int?&gt;()\n        dfs(0, \"in\", res)\n        return res\n    }\n\n    /* 後順走査 */\n    fun postOrder(): MutableList&lt;Int?&gt; {\n        val res = mutableListOf&lt;Int?&gt;()\n        dfs(0, \"post\", res)\n        return res\n    }\n}\n</code></pre> array_binary_tree.rb<pre><code>### 配列表現の二分木クラス ###\nclass ArrayBinaryTree\n  ### コンストラクタ ###\n  def initialize(arr)\n    @tree = arr.to_a\n  end\n\n  ### リスト容量 ###\n  def size\n    @tree.length\n  end\n\n  ### インデックス i のノードの値を取得 ###\n  def val(i)\n    # インデックスが範囲外なら `nil` を返し、空きスロットを表す\n    return if i &lt; 0 || i &gt;= size\n\n    @tree[i]\n  end\n\n  ### インデックス i のノードの左子ノードのインデックスを取得 ###\n  def left(i)\n    2 * i + 1\n  end\n\n  ### インデックス i のノードの右子ノードのインデックスを取得 ###\n  def right(i)\n    2 * i + 2\n  end\n\n  ### インデックス i のノードの親ノードのインデックスを取得 ###\n  def parent(i)\n    (i - 1) / 2\n  end\n\n  ### レベル順走査 ###\n  def level_order\n    @res = []\n\n    # 配列を直接走査する\n    for i in 0...size\n      @res &lt;&lt; val(i) unless val(i).nil?\n    end\n\n    @res\n  end\n\n  ### 深さ優先探索 ###\n  def dfs(i, order)\n    return if val(i).nil?\n    # 先行順走査\n    @res &lt;&lt; val(i) if order == :pre\n    dfs(left(i), order)\n    # 中順走査\n    @res &lt;&lt; val(i) if order == :in\n    dfs(right(i), order)\n    # 後順走査\n    @res &lt;&lt; val(i) if order == :post\n  end\n\n  ### 前順走査 ###\n  def pre_order\n    @res = []\n    dfs(0, :pre)\n    @res\n  end\n\n  ### 中順走査 ###\n  def in_order\n    @res = []\n    dfs(0, :in)\n    @res\n  end\n\n  ### 後順走査 ###\n  def post_order\n    @res = []\n    dfs(0, :post)\n    @res\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 7 章 &nbsp; 木","7.3 &nbsp; 二分木の配列表現"],"tags":[]},{"location":"chapter_tree/array_representation_of_tree/#733","level":2,"title":"7.3.3   利点と制約","text":"<p>二分木の配列表現には主に次の利点があります。</p> <ul> <li>配列は連続したメモリ空間に格納されるため、キャッシュ効率が高く、アクセスと走査が速い。</li> <li>ポインタを格納する必要がなく、比較的省スペースである。</li> <li>ノードへのランダムアクセスが可能である。</li> </ul> <p>ただし、配列表現にはいくつかの制約もあります。</p> <ul> <li>配列による格納には連続したメモリ空間が必要なため、データ量が大きすぎる木の格納には向かない。</li> <li>ノードの追加と削除は配列の挿入・削除操作で実現する必要があり、効率は低い。</li> <li>二分木に大量の <code>None</code> が存在すると、配列に占める実ノードデータの比率が低くなり、空間利用率も低下する。</li> </ul>","path":["第 7 章 &nbsp; 木","7.3 &nbsp; 二分木の配列表現"],"tags":[]},{"location":"chapter_tree/avl_tree/","level":1,"title":"7.5   AVL 木 *","text":"<p>「二分探索木」章で述べたように、挿入と削除を何度も繰り返すと、二分探索木は連結リストへ退化する可能性があります。この場合、すべての操作の時間計算量は \\(O(\\log n)\\) から \\(O(n)\\) へ劣化します。</p> <p>以下の図に示すように、ノード削除を 2 回行うと、この二分探索木は連結リストへ退化します。</p> <p></p> <p> 図 7-24   AVL 木がノード削除後に退化する </p> <p>別の例として、以下の図に示す完全二分木に 2 つのノードを挿入すると、木は大きく左に傾き、探索操作の時間計算量もそれに伴って劣化します。</p> <p></p> <p> 図 7-25   AVL 木がノード挿入後に退化する </p> <p>1962 年、G. M. Adelson-Velsky と E. M. Landis は論文“An algorithm for the organization of information”の中で AVL 木 を提案しました。論文では一連の操作が詳しく説明されており、ノードの追加と削除を続けても AVL 木が退化しないようにして、各種操作の時間計算量を \\(O(\\log n)\\) の水準に保ちます。言い換えると、追加・削除・探索・更新を頻繁に行う場面でも、AVL 木は常に高いデータ操作性能を維持でき、実用価値の高い構造です。</p>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL 木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#751-avl","level":2,"title":"7.5.1   AVL 木の基本用語","text":"<p>AVL 木は二分探索木であると同時に平衡二分木でもあり、これら 2 種類の二分木の性質をすべて満たします。したがって、平衡二分探索木（balanced binary search tree）の一種です。</p>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL 木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#1","level":3,"title":"1.   ノードの高さ","text":"<p>AVL 木の操作ではノードの高さを取得する必要があるため、ノードクラスに <code>height</code> 変数を追加します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>class TreeNode:\n    \"\"\"AVL 木ノードクラス\"\"\"\n    def __init__(self, val: int):\n        self.val: int = val                 # ノード値\n        self.height: int = 0                # ノードの高さ\n        self.left: TreeNode | None = None   # 左の子ノード参照\n        self.right: TreeNode | None = None  # 右の子ノード参照\n</code></pre> <pre><code>/* AVL 木ノードクラス */\nstruct TreeNode {\n    int val{};          // ノード値\n    int height = 0;     // ノードの高さ\n    TreeNode *left{};   // 左の子ノード\n    TreeNode *right{};  // 右の子ノード\n    TreeNode() = default;\n    explicit TreeNode(int x) : val(x){}\n};\n</code></pre> <pre><code>/* AVL 木ノードクラス */\nclass TreeNode {\n    public int val;        // ノード値\n    public int height;     // ノードの高さ\n    public TreeNode left;  // 左の子ノード\n    public TreeNode right; // 右の子ノード\n    public TreeNode(int x) { val = x; }\n}\n</code></pre> <pre><code>/* AVL 木ノードクラス */\nclass TreeNode(int? x) {\n    public int? val = x;    // ノード値\n    public int height;      // ノードの高さ\n    public TreeNode? left;  // 左の子ノード参照\n    public TreeNode? right; // 右の子ノード参照\n}\n</code></pre> <pre><code>/* AVL 木ノード構造体 */\ntype TreeNode struct {\n    Val    int       // ノード値\n    Height int       // ノードの高さ\n    Left   *TreeNode // 左の子ノード参照\n    Right  *TreeNode // 右の子ノード参照\n}\n</code></pre> <pre><code>/* AVL 木ノードクラス */\nclass TreeNode {\n    var val: Int // ノード値\n    var height: Int // ノードの高さ\n    var left: TreeNode? // 左の子ノード\n    var right: TreeNode? // 右の子ノード\n\n    init(x: Int) {\n        val = x\n        height = 0\n    }\n}\n</code></pre> <pre><code>/* AVL 木ノードクラス */\nclass TreeNode {\n    val; // ノード値\n    height; //ノードの高さ\n    left; // 左の子ノードポインタ\n    right; // 右の子ノードポインタ\n    constructor(val, left, right, height) {\n        this.val = val === undefined ? 0 : val;\n        this.height = height === undefined ? 0 : height;\n        this.left = left === undefined ? null : left;\n        this.right = right === undefined ? null : right;\n    }\n}\n</code></pre> <pre><code>/* AVL 木ノードクラス */\nclass TreeNode {\n    val: number;            // ノード値\n    height: number;         // ノードの高さ\n    left: TreeNode | null;  // 左の子ノードポインタ\n    right: TreeNode | null; // 右の子ノードポインタ\n    constructor(val?: number, height?: number, left?: TreeNode | null, right?: TreeNode | null) {\n        this.val = val === undefined ? 0 : val;\n        this.height = height === undefined ? 0 : height;\n        this.left = left === undefined ? null : left;\n        this.right = right === undefined ? null : right;\n    }\n}\n</code></pre> <pre><code>/* AVL 木ノードクラス */\nclass TreeNode {\n  int val;         // ノード値\n  int height;      // ノードの高さ\n  TreeNode? left;  // 左の子ノード\n  TreeNode? right; // 右の子ノード\n  TreeNode(this.val, [this.height = 0, this.left, this.right]);\n}\n</code></pre> <pre><code>use std::rc::Rc;\nuse std::cell::RefCell;\n\n/* AVL 木ノード構造体 */\nstruct TreeNode {\n    val: i32,                               // ノード値\n    height: i32,                            // ノードの高さ\n    left: Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,    // 左の子ノード\n    right: Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,   // 右の子ノード\n}\n\nimpl TreeNode {\n    /* コンストラクタ */\n    fn new(val: i32) -&gt; Rc&lt;RefCell&lt;Self&gt;&gt; {\n        Rc::new(RefCell::new(Self {\n            val,\n            height: 0,\n            left: None,\n            right: None\n        }))\n    }\n}\n</code></pre> <pre><code>/* AVL 木ノード構造体 */\ntypedef struct TreeNode {\n    int val;\n    int height;\n    struct TreeNode *left;\n    struct TreeNode *right;\n} TreeNode;\n\n/* コンストラクタ */\nTreeNode *newTreeNode(int val) {\n    TreeNode *node;\n\n    node = (TreeNode *)malloc(sizeof(TreeNode));\n    node-&gt;val = val;\n    node-&gt;height = 0;\n    node-&gt;left = NULL;\n    node-&gt;right = NULL;\n    return node;\n}\n</code></pre> <pre><code>/* AVL 木ノードクラス */\nclass TreeNode(val _val: Int) {  // ノード値\n    val height: Int = 0          // ノードの高さ\n    val left: TreeNode? = null   // 左の子ノード\n    val right: TreeNode? = null  // 右の子ノード\n}\n</code></pre> <pre><code>### AVL 木ノードクラス ###\nclass TreeNode\n  attr_accessor :val    # ノード値\n  attr_accessor :height # ノードの高さ\n  attr_accessor :left   # 左の子ノード参照\n  attr_accessor :right  # 右の子ノード参照\n\n  def initialize(val)\n    @val = val\n    @height = 0\n  end\nend\n</code></pre> <p>「ノードの高さ」とは、そのノードから最も遠い葉ノードまでの距離、すなわち通過する「辺」の本数を指します。特に、葉ノードの高さは \\(0\\)、空ノードの高さは \\(-1\\) です。ここでは、ノードの高さを取得・更新するための 2 つの補助関数を用意します：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def height(self, node: TreeNode | None) -&gt; int:\n    \"\"\"ノードの高さを取得\"\"\"\n    # 空ノードの高さは -1、葉ノードの高さは 0\n    if node is not None:\n        return node.height\n    return -1\n\ndef update_height(self, node: TreeNode | None):\n    \"\"\"ノードの高さを更新する\"\"\"\n    # ノードの高さは最も高い部分木の高さ + 1 に等しい\n    node.height = max([self.height(node.left), self.height(node.right)]) + 1\n</code></pre> avl_tree.cpp<pre><code>/* ノードの高さを取得 */\nint height(TreeNode *node) {\n    // 空ノードの高さは -1、葉ノードの高さは 0\n    return node == nullptr ? -1 : node-&gt;height;\n}\n\n/* ノードの高さを更新する */\nvoid updateHeight(TreeNode *node) {\n    // ノードの高さは最も高い部分木の高さ + 1 に等しい\n    node-&gt;height = max(height(node-&gt;left), height(node-&gt;right)) + 1;\n}\n</code></pre> avl_tree.java<pre><code>/* ノードの高さを取得 */\nint height(TreeNode node) {\n    // 空ノードの高さは -1、葉ノードの高さは 0\n    return node == null ? -1 : node.height;\n}\n\n/* ノードの高さを更新する */\nvoid updateHeight(TreeNode node) {\n    // ノードの高さは最も高い部分木の高さ + 1 に等しい\n    node.height = Math.max(height(node.left), height(node.right)) + 1;\n}\n</code></pre> avl_tree.cs<pre><code>/* ノードの高さを取得 */\nint Height(TreeNode? node) {\n    // 空ノードの高さは -1、葉ノードの高さは 0\n    return node == null ? -1 : node.height;\n}\n\n/* ノードの高さを更新する */\nvoid UpdateHeight(TreeNode node) {\n    // ノードの高さは最も高い部分木の高さ + 1 に等しい\n    node.height = Math.Max(Height(node.left), Height(node.right)) + 1;\n}\n</code></pre> avl_tree.go<pre><code>/* ノードの高さを取得 */\nfunc (t *aVLTree) height(node *TreeNode) int {\n    // 空ノードの高さは -1、葉ノードの高さは 0\n    if node != nil {\n        return node.Height\n    }\n    return -1\n}\n\n/* ノードの高さを更新する */\nfunc (t *aVLTree) updateHeight(node *TreeNode) {\n    lh := t.height(node.Left)\n    rh := t.height(node.Right)\n    // ノードの高さは最も高い部分木の高さ + 1 に等しい\n    if lh &gt; rh {\n        node.Height = lh + 1\n    } else {\n        node.Height = rh + 1\n    }\n}\n</code></pre> avl_tree.swift<pre><code>/* ノードの高さを取得 */\nfunc height(node: TreeNode?) -&gt; Int {\n    // 空ノードの高さは -1、葉ノードの高さは 0\n    node?.height ?? -1\n}\n\n/* ノードの高さを更新する */\nfunc updateHeight(node: TreeNode?) {\n    // ノードの高さは最も高い部分木の高さ + 1 に等しい\n    node?.height = max(height(node: node?.left), height(node: node?.right)) + 1\n}\n</code></pre> avl_tree.js<pre><code>/* ノードの高さを取得 */\nheight(node) {\n    // 空ノードの高さは -1、葉ノードの高さは 0\n    return node === null ? -1 : node.height;\n}\n\n/* ノードの高さを更新する */\n#updateHeight(node) {\n    // ノードの高さは最も高い部分木の高さ + 1 に等しい\n    node.height =\n        Math.max(this.height(node.left), this.height(node.right)) + 1;\n}\n</code></pre> avl_tree.ts<pre><code>/* ノードの高さを取得 */\nheight(node: TreeNode): number {\n    // 空ノードの高さは -1、葉ノードの高さは 0\n    return node === null ? -1 : node.height;\n}\n\n/* ノードの高さを更新する */\nupdateHeight(node: TreeNode): void {\n    // ノードの高さは最も高い部分木の高さ + 1 に等しい\n    node.height =\n        Math.max(this.height(node.left), this.height(node.right)) + 1;\n}\n</code></pre> avl_tree.dart<pre><code>/* ノードの高さを取得 */\nint height(TreeNode? node) {\n  // 空ノードの高さは -1、葉ノードの高さは 0\n  return node == null ? -1 : node.height;\n}\n\n/* ノードの高さを更新する */\nvoid updateHeight(TreeNode? node) {\n  // ノードの高さは最も高い部分木の高さ + 1 に等しい\n  node!.height = max(height(node.left), height(node.right)) + 1;\n}\n</code></pre> avl_tree.rs<pre><code>/* ノードの高さを取得 */\nfn height(node: OptionTreeNodeRc) -&gt; i32 {\n    // 空ノードの高さは -1、葉ノードの高さは 0\n    match node {\n        Some(node) =&gt; node.borrow().height,\n        None =&gt; -1,\n    }\n}\n\n/* ノードの高さを更新する */\nfn update_height(node: OptionTreeNodeRc) {\n    if let Some(node) = node {\n        let left = node.borrow().left.clone();\n        let right = node.borrow().right.clone();\n        // ノードの高さは最も高い部分木の高さ + 1 に等しい\n        node.borrow_mut().height = std::cmp::max(Self::height(left), Self::height(right)) + 1;\n    }\n}\n</code></pre> avl_tree.c<pre><code>/* ノードの高さを取得 */\nint height(TreeNode *node) {\n    // 空ノードの高さは -1、葉ノードの高さは 0\n    if (node != NULL) {\n        return node-&gt;height;\n    }\n    return -1;\n}\n\n/* ノードの高さを更新する */\nvoid updateHeight(TreeNode *node) {\n    int lh = height(node-&gt;left);\n    int rh = height(node-&gt;right);\n    // ノードの高さは最も高い部分木の高さ + 1 に等しい\n    if (lh &gt; rh) {\n        node-&gt;height = lh + 1;\n    } else {\n        node-&gt;height = rh + 1;\n    }\n}\n</code></pre> avl_tree.kt<pre><code>/* ノードの高さを取得 */\nfun height(node: TreeNode?): Int {\n    // 空ノードの高さは -1、葉ノードの高さは 0\n    return node?.height ?: -1\n}\n\n/* ノードの高さを更新する */\nfun updateHeight(node: TreeNode?) {\n    // ノードの高さは最も高い部分木の高さ + 1 に等しい\n    node?.height = max(height(node?.left), height(node?.right)) + 1\n}\n</code></pre> avl_tree.rb<pre><code>### ノードの高さを取得 ###\ndef height(node)\n  # 空ノードの高さは -1、葉ノードの高さは 0\n  return node.height unless node.nil?\n\n  -1\nend\n\n### ノードの高さを更新 ###\ndef update_height(node)\n  # ノードの高さは最も高い部分木の高さ + 1 に等しい\n  node.height = [height(node.left), height(node.right)].max + 1\nend\n</code></pre>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL 木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#2","level":3,"title":"2.   ノードの平衡係数","text":"<p>ノードの平衡係数（balance factor）は、左部分木の高さから右部分木の高さを引いた値と定義し、空ノードの平衡係数は \\(0\\) とします。同様に、ノードの平衡係数を取得する機能も関数にカプセル化して、後続で使いやすくします：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def balance_factor(self, node: TreeNode | None) -&gt; int:\n    \"\"\"平衡係数を取得\"\"\"\n    # 空ノードの平衡係数は 0\n    if node is None:\n        return 0\n    # ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ\n    return self.height(node.left) - self.height(node.right)\n</code></pre> avl_tree.cpp<pre><code>/* 平衡係数を取得 */\nint balanceFactor(TreeNode *node) {\n    // 空ノードの平衡係数は 0\n    if (node == nullptr)\n        return 0;\n    // ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ\n    return height(node-&gt;left) - height(node-&gt;right);\n}\n</code></pre> avl_tree.java<pre><code>/* 平衡係数を取得 */\nint balanceFactor(TreeNode node) {\n    // 空ノードの平衡係数は 0\n    if (node == null)\n        return 0;\n    // ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ\n    return height(node.left) - height(node.right);\n}\n</code></pre> avl_tree.cs<pre><code>/* 平衡係数を取得 */\nint BalanceFactor(TreeNode? node) {\n    // 空ノードの平衡係数は 0\n    if (node == null) return 0;\n    // ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ\n    return Height(node.left) - Height(node.right);\n}\n</code></pre> avl_tree.go<pre><code>/* 平衡係数を取得 */\nfunc (t *aVLTree) balanceFactor(node *TreeNode) int {\n    // 空ノードの平衡係数は 0\n    if node == nil {\n        return 0\n    }\n    // ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ\n    return t.height(node.Left) - t.height(node.Right)\n}\n</code></pre> avl_tree.swift<pre><code>/* 平衡係数を取得 */\nfunc balanceFactor(node: TreeNode?) -&gt; Int {\n    // 空ノードの平衡係数は 0\n    guard let node = node else { return 0 }\n    // ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ\n    return height(node: node.left) - height(node: node.right)\n}\n</code></pre> avl_tree.js<pre><code>/* 平衡係数を取得 */\nbalanceFactor(node) {\n    // 空ノードの平衡係数は 0\n    if (node === null) return 0;\n    // ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ\n    return this.height(node.left) - this.height(node.right);\n}\n</code></pre> avl_tree.ts<pre><code>/* 平衡係数を取得 */\nbalanceFactor(node: TreeNode): number {\n    // 空ノードの平衡係数は 0\n    if (node === null) return 0;\n    // ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ\n    return this.height(node.left) - this.height(node.right);\n}\n</code></pre> avl_tree.dart<pre><code>/* 平衡係数を取得 */\nint balanceFactor(TreeNode? node) {\n  // 空ノードの平衡係数は 0\n  if (node == null) return 0;\n  // ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ\n  return height(node.left) - height(node.right);\n}\n</code></pre> avl_tree.rs<pre><code>/* 平衡係数を取得 */\nfn balance_factor(node: OptionTreeNodeRc) -&gt; i32 {\n    match node {\n        // 空ノードの平衡係数は 0\n        None =&gt; 0,\n        // ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ\n        Some(node) =&gt; {\n            Self::height(node.borrow().left.clone()) - Self::height(node.borrow().right.clone())\n        }\n    }\n}\n</code></pre> avl_tree.c<pre><code>/* 平衡係数を取得 */\nint balanceFactor(TreeNode *node) {\n    // 空ノードの平衡係数は 0\n    if (node == NULL) {\n        return 0;\n    }\n    // ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ\n    return height(node-&gt;left) - height(node-&gt;right);\n}\n</code></pre> avl_tree.kt<pre><code>/* 平衡係数を取得 */\nfun balanceFactor(node: TreeNode?): Int {\n    // 空ノードの平衡係数は 0\n    if (node == null) return 0\n    // ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ\n    return height(node.left) - height(node.right)\n}\n</code></pre> avl_tree.rb<pre><code>### 平衡係数を取得 ###\ndef balance_factor(node)\n  # 空ノードの平衡係数は 0\n  return 0 if node.nil?\n\n  # ノードの平衡係数 = 左部分木の高さ - 右部分木の高さ\n  height(node.left) - height(node.right)\nend\n</code></pre> <p>Tip</p> <p>平衡係数を \\(f\\) とすると、AVL 木の任意のノードの平衡係数は常に \\(-1 \\le f \\le 1\\) を満たします。</p>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL 木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#752-avl","level":2,"title":"7.5.2   AVL 木の回転","text":"<p>AVL 木の特徴は「回転」操作にあり、二分木の中順走査列を変えずに、不平衡ノードを再び平衡に戻せます。言い換えると、回転操作は「二分探索木」の性質を保ちながら、木を再び「平衡二分木」に戻すことができます。</p> <p>平衡係数の絶対値が \\(&gt; 1\\) のノードを「不平衡ノード」と呼びます。ノードの不平衡の形に応じて、回転操作は 4 種類に分かれます。右回転、左回転、右回転してから左回転、左回転してから右回転です。以下でこれらを順に説明します。</p>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL 木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#1_1","level":3,"title":"1.   右回転","text":"<p>以下の図では、ノードの下に平衡係数を示しています。下から上へ見ると、二分木で最初に不平衡になるのは「ノード 3」です。この不平衡ノードを根とする部分木に注目し、そのノードを <code>node</code>、左の子ノードを <code>child</code> として、「右回転」を行います。右回転後、部分木は平衡を回復し、なおかつ二分探索木の性質も保たれます。</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p> 図 7-26   右回転の手順 </p> <p>以下の図に示すように、ノード <code>child</code> に右の子ノード（<code>grand_child</code> と記す）がある場合、右回転には 1 ステップ追加する必要があります。すなわち、<code>grand_child</code> を <code>node</code> の左の子ノードにします。</p> <p></p> <p> 図 7-27   grand_child を持つ右回転 </p> <p>「右に回転する」というのはあくまでイメージしやすい表現であり、実際にはノードポインタを変更して実現します。コードは次のとおりです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def right_rotate(self, node: TreeNode | None) -&gt; TreeNode | None:\n    \"\"\"右回転\"\"\"\n    child = node.left\n    grand_child = child.right\n    # child を支点として node を右回転させる\n    child.right = node\n    node.left = grand_child\n    # ノードの高さを更新する\n    self.update_height(node)\n    self.update_height(child)\n    # 回転後の部分木の根ノードを返す\n    return child\n</code></pre> avl_tree.cpp<pre><code>/* 右回転 */\nTreeNode *rightRotate(TreeNode *node) {\n    TreeNode *child = node-&gt;left;\n    TreeNode *grandChild = child-&gt;right;\n    // child を支点として node を右回転させる\n    child-&gt;right = node;\n    node-&gt;left = grandChild;\n    // ノードの高さを更新する\n    updateHeight(node);\n    updateHeight(child);\n    // 回転後の部分木の根ノードを返す\n    return child;\n}\n</code></pre> avl_tree.java<pre><code>/* 右回転 */\nTreeNode rightRotate(TreeNode node) {\n    TreeNode child = node.left;\n    TreeNode grandChild = child.right;\n    // child を支点として node を右回転させる\n    child.right = node;\n    node.left = grandChild;\n    // ノードの高さを更新する\n    updateHeight(node);\n    updateHeight(child);\n    // 回転後の部分木の根ノードを返す\n    return child;\n}\n</code></pre> avl_tree.cs<pre><code>/* 右回転 */\nTreeNode? RightRotate(TreeNode? node) {\n    TreeNode? child = node?.left;\n    TreeNode? grandChild = child?.right;\n    // child を支点として node を右回転させる\n    child.right = node;\n    node.left = grandChild;\n    // ノードの高さを更新する\n    UpdateHeight(node);\n    UpdateHeight(child);\n    // 回転後の部分木の根ノードを返す\n    return child;\n}\n</code></pre> avl_tree.go<pre><code>/* 右回転 */\nfunc (t *aVLTree) rightRotate(node *TreeNode) *TreeNode {\n    child := node.Left\n    grandChild := child.Right\n    // child を支点として node を右回転させる\n    child.Right = node\n    node.Left = grandChild\n    // ノードの高さを更新する\n    t.updateHeight(node)\n    t.updateHeight(child)\n    // 回転後の部分木の根ノードを返す\n    return child\n}\n</code></pre> avl_tree.swift<pre><code>/* 右回転 */\nfunc rightRotate(node: TreeNode?) -&gt; TreeNode? {\n    let child = node?.left\n    let grandChild = child?.right\n    // child を支点として node を右回転させる\n    child?.right = node\n    node?.left = grandChild\n    // ノードの高さを更新する\n    updateHeight(node: node)\n    updateHeight(node: child)\n    // 回転後の部分木の根ノードを返す\n    return child\n}\n</code></pre> avl_tree.js<pre><code>/* 右回転 */\n#rightRotate(node) {\n    const child = node.left;\n    const grandChild = child.right;\n    // child を支点として node を右回転させる\n    child.right = node;\n    node.left = grandChild;\n    // ノードの高さを更新する\n    this.#updateHeight(node);\n    this.#updateHeight(child);\n    // 回転後の部分木の根ノードを返す\n    return child;\n}\n</code></pre> avl_tree.ts<pre><code>/* 右回転 */\nrightRotate(node: TreeNode): TreeNode {\n    const child = node.left;\n    const grandChild = child.right;\n    // child を支点として node を右回転させる\n    child.right = node;\n    node.left = grandChild;\n    // ノードの高さを更新する\n    this.updateHeight(node);\n    this.updateHeight(child);\n    // 回転後の部分木の根ノードを返す\n    return child;\n}\n</code></pre> avl_tree.dart<pre><code>/* 右回転 */\nTreeNode? rightRotate(TreeNode? node) {\n  TreeNode? child = node!.left;\n  TreeNode? grandChild = child!.right;\n  // child を支点として node を右回転させる\n  child.right = node;\n  node.left = grandChild;\n  // ノードの高さを更新する\n  updateHeight(node);\n  updateHeight(child);\n  // 回転後の部分木の根ノードを返す\n  return child;\n}\n</code></pre> avl_tree.rs<pre><code>/* 右回転 */\nfn right_rotate(node: OptionTreeNodeRc) -&gt; OptionTreeNodeRc {\n    match node {\n        Some(node) =&gt; {\n            let child = node.borrow().left.clone().unwrap();\n            let grand_child = child.borrow().right.clone();\n            // child を支点として node を右回転させる\n            child.borrow_mut().right = Some(node.clone());\n            node.borrow_mut().left = grand_child;\n            // ノードの高さを更新する\n            Self::update_height(Some(node));\n            Self::update_height(Some(child.clone()));\n            // 回転後の部分木の根ノードを返す\n            Some(child)\n        }\n        None =&gt; None,\n    }\n}\n</code></pre> avl_tree.c<pre><code>/* 右回転 */\nTreeNode *rightRotate(TreeNode *node) {\n    TreeNode *child, *grandChild;\n    child = node-&gt;left;\n    grandChild = child-&gt;right;\n    // child を支点として node を右回転させる\n    child-&gt;right = node;\n    node-&gt;left = grandChild;\n    // ノードの高さを更新する\n    updateHeight(node);\n    updateHeight(child);\n    // 回転後の部分木の根ノードを返す\n    return child;\n}\n</code></pre> avl_tree.kt<pre><code>/* 右回転 */\nfun rightRotate(node: TreeNode?): TreeNode {\n    val child = node!!.left\n    val grandChild = child!!.right\n    // child を支点として node を右回転させる\n    child.right = node\n    node.left = grandChild\n    // ノードの高さを更新する\n    updateHeight(node)\n    updateHeight(child)\n    // 回転後の部分木の根ノードを返す\n    return child\n}\n</code></pre> avl_tree.rb<pre><code>### 右回転操作 ###\ndef right_rotate(node)\n  child = node.left\n  grand_child = child.right\n  # child を支点として node を右回転させる\n  child.right = node\n  node.left = grand_child\n  # ノードの高さを更新する\n  update_height(node)\n  update_height(child)\n  # 回転後の部分木の根ノードを返す\n  child\nend\n</code></pre>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL 木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#2_1","level":3,"title":"2.   左回転","text":"<p>対応する鏡像として、上記の不平衡二分木を左右反転して考えると、以下の図に示す「左回転」が必要になります。</p> <p></p> <p> 図 7-28   左回転 </p> <p>同様に、以下の図に示すように、ノード <code>child</code> に左の子ノード（<code>grand_child</code> と記す）がある場合、左回転にも 1 ステップ追加する必要があります。すなわち、<code>grand_child</code> を <code>node</code> の右の子ノードにします。</p> <p></p> <p> 図 7-29   grand_child を持つ左回転 </p> <p>分かるように、右回転と左回転は論理的に鏡像対称であり、それぞれが解決する 2 種類の不平衡も対称です。この対称性に基づけば、右回転の実装コードにあるすべての <code>left</code> を <code>right</code> に、すべての <code>right</code> を <code>left</code> に置き換えるだけで、左回転の実装コードが得られます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def left_rotate(self, node: TreeNode | None) -&gt; TreeNode | None:\n    \"\"\"左回転\"\"\"\n    child = node.right\n    grand_child = child.left\n    # child を支点として node を左回転させる\n    child.left = node\n    node.right = grand_child\n    # ノードの高さを更新する\n    self.update_height(node)\n    self.update_height(child)\n    # 回転後の部分木の根ノードを返す\n    return child\n</code></pre> avl_tree.cpp<pre><code>/* 左回転 */\nTreeNode *leftRotate(TreeNode *node) {\n    TreeNode *child = node-&gt;right;\n    TreeNode *grandChild = child-&gt;left;\n    // child を支点として node を左回転させる\n    child-&gt;left = node;\n    node-&gt;right = grandChild;\n    // ノードの高さを更新する\n    updateHeight(node);\n    updateHeight(child);\n    // 回転後の部分木の根ノードを返す\n    return child;\n}\n</code></pre> avl_tree.java<pre><code>/* 左回転 */\nTreeNode leftRotate(TreeNode node) {\n    TreeNode child = node.right;\n    TreeNode grandChild = child.left;\n    // child を支点として node を左回転させる\n    child.left = node;\n    node.right = grandChild;\n    // ノードの高さを更新する\n    updateHeight(node);\n    updateHeight(child);\n    // 回転後の部分木の根ノードを返す\n    return child;\n}\n</code></pre> avl_tree.cs<pre><code>/* 左回転 */\nTreeNode? LeftRotate(TreeNode? node) {\n    TreeNode? child = node?.right;\n    TreeNode? grandChild = child?.left;\n    // child を支点として node を左回転させる\n    child.left = node;\n    node.right = grandChild;\n    // ノードの高さを更新する\n    UpdateHeight(node);\n    UpdateHeight(child);\n    // 回転後の部分木の根ノードを返す\n    return child;\n}\n</code></pre> avl_tree.go<pre><code>/* 左回転 */\nfunc (t *aVLTree) leftRotate(node *TreeNode) *TreeNode {\n    child := node.Right\n    grandChild := child.Left\n    // child を支点として node を左回転させる\n    child.Left = node\n    node.Right = grandChild\n    // ノードの高さを更新する\n    t.updateHeight(node)\n    t.updateHeight(child)\n    // 回転後の部分木の根ノードを返す\n    return child\n}\n</code></pre> avl_tree.swift<pre><code>/* 左回転 */\nfunc leftRotate(node: TreeNode?) -&gt; TreeNode? {\n    let child = node?.right\n    let grandChild = child?.left\n    // child を支点として node を左回転させる\n    child?.left = node\n    node?.right = grandChild\n    // ノードの高さを更新する\n    updateHeight(node: node)\n    updateHeight(node: child)\n    // 回転後の部分木の根ノードを返す\n    return child\n}\n</code></pre> avl_tree.js<pre><code>/* 左回転 */\n#leftRotate(node) {\n    const child = node.right;\n    const grandChild = child.left;\n    // child を支点として node を左回転させる\n    child.left = node;\n    node.right = grandChild;\n    // ノードの高さを更新する\n    this.#updateHeight(node);\n    this.#updateHeight(child);\n    // 回転後の部分木の根ノードを返す\n    return child;\n}\n</code></pre> avl_tree.ts<pre><code>/* 左回転 */\nleftRotate(node: TreeNode): TreeNode {\n    const child = node.right;\n    const grandChild = child.left;\n    // child を支点として node を左回転させる\n    child.left = node;\n    node.right = grandChild;\n    // ノードの高さを更新する\n    this.updateHeight(node);\n    this.updateHeight(child);\n    // 回転後の部分木の根ノードを返す\n    return child;\n}\n</code></pre> avl_tree.dart<pre><code>/* 左回転 */\nTreeNode? leftRotate(TreeNode? node) {\n  TreeNode? child = node!.right;\n  TreeNode? grandChild = child!.left;\n  // child を支点として node を左回転させる\n  child.left = node;\n  node.right = grandChild;\n  // ノードの高さを更新する\n  updateHeight(node);\n  updateHeight(child);\n  // 回転後の部分木の根ノードを返す\n  return child;\n}\n</code></pre> avl_tree.rs<pre><code>/* 左回転 */\nfn left_rotate(node: OptionTreeNodeRc) -&gt; OptionTreeNodeRc {\n    match node {\n        Some(node) =&gt; {\n            let child = node.borrow().right.clone().unwrap();\n            let grand_child = child.borrow().left.clone();\n            // child を支点として node を左回転させる\n            child.borrow_mut().left = Some(node.clone());\n            node.borrow_mut().right = grand_child;\n            // ノードの高さを更新する\n            Self::update_height(Some(node));\n            Self::update_height(Some(child.clone()));\n            // 回転後の部分木の根ノードを返す\n            Some(child)\n        }\n        None =&gt; None,\n    }\n}\n</code></pre> avl_tree.c<pre><code>/* 左回転 */\nTreeNode *leftRotate(TreeNode *node) {\n    TreeNode *child, *grandChild;\n    child = node-&gt;right;\n    grandChild = child-&gt;left;\n    // child を支点として node を左回転させる\n    child-&gt;left = node;\n    node-&gt;right = grandChild;\n    // ノードの高さを更新する\n    updateHeight(node);\n    updateHeight(child);\n    // 回転後の部分木の根ノードを返す\n    return child;\n}\n</code></pre> avl_tree.kt<pre><code>/* 左回転 */\nfun leftRotate(node: TreeNode?): TreeNode {\n    val child = node!!.right\n    val grandChild = child!!.left\n    // child を支点として node を左回転させる\n    child.left = node\n    node.right = grandChild\n    // ノードの高さを更新する\n    updateHeight(node)\n    updateHeight(child)\n    // 回転後の部分木の根ノードを返す\n    return child\n}\n</code></pre> avl_tree.rb<pre><code>### 左回転操作 ###\ndef left_rotate(node)\n  child = node.right\n  grand_child = child.left\n  # child を支点として node を左回転させる\n  child.left = node\n  node.right = grand_child\n  # ノードの高さを更新する\n  update_height(node)\n  update_height(child)\n  # 回転後の部分木の根ノードを返す\n  child\nend\n</code></pre>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL 木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#3","level":3,"title":"3.   左回転してから右回転","text":"<p>以下の図の不平衡ノード 3 では、左回転だけでも右回転だけでも部分木を平衡に戻せません。この場合は、まず <code>child</code> に「左回転」を行い、次に <code>node</code> に「右回転」を行います。</p> <p></p> <p> 図 7-30   左回転してから右回転 </p>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL 木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#4","level":3,"title":"4.   右回転してから左回転","text":"<p>以下の図に示すように、上記の不平衡二分木の鏡像のケースでは、まず <code>child</code> に「右回転」を行い、次に <code>node</code> に「左回転」を行います。</p> <p></p> <p> 図 7-31   右回転してから左回転 </p>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL 木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#5","level":3,"title":"5.   回転の選択","text":"<p>以下の図に示す 4 種類の不平衡は、上の各ケースにそれぞれ対応しており、必要な操作は順に右回転、左回転してから右回転、右回転してから左回転、左回転です。</p> <p></p> <p> 図 7-32   AVL 木の 4 つの回転ケース </p> <p>以下の表に示すように、不平衡ノードの平衡係数と、高い側の子ノードの平衡係数の符号を判定することで、その不平衡ノードが上図のどのケースに属するかを判断できます。</p> <p> 表 7-3   4 種類の回転ケースの選択条件 </p> 不平衡ノードの平衡係数 子ノードの平衡係数 採用すべき回転方法 \\(&gt; 1\\) （左に偏った木） \\(\\geq 0\\) 右回転 \\(&gt; 1\\) （左に偏った木） \\(&lt;0\\) 左回転してから右回転 \\(&lt; -1\\) （右に偏った木） \\(\\leq 0\\) 左回転 \\(&lt; -1\\) （右に偏った木） \\(&gt;0\\) 右回転してから左回転 <p>使いやすくするために、回転操作を 1 つの関数にカプセル化します。この関数があれば、さまざまな不平衡ケースに対して回転を行い、不平衡ノードを再び平衡に戻せます。コードは次のとおりです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def rotate(self, node: TreeNode | None) -&gt; TreeNode | None:\n    \"\"\"回転操作を行い、この部分木の平衡を回復する\"\"\"\n    # ノード node の平衡係数を取得\n    balance_factor = self.balance_factor(node)\n    # 左に偏った木\n    if balance_factor &gt; 1:\n        if self.balance_factor(node.left) &gt;= 0:\n            # 右回転\n            return self.right_rotate(node)\n        else:\n            # 左回転してから右回転\n            node.left = self.left_rotate(node.left)\n            return self.right_rotate(node)\n    # 右に偏った木\n    elif balance_factor &lt; -1:\n        if self.balance_factor(node.right) &lt;= 0:\n            # 左回転\n            return self.left_rotate(node)\n        else:\n            # 右回転してから左回転\n            node.right = self.right_rotate(node.right)\n            return self.left_rotate(node)\n    # 平衡木なので回転不要、そのまま返す\n    return node\n</code></pre> avl_tree.cpp<pre><code>/* 回転操作を行い、この部分木の平衡を回復する */\nTreeNode *rotate(TreeNode *node) {\n    // ノード node の平衡係数を取得\n    int _balanceFactor = balanceFactor(node);\n    // 左に偏った木\n    if (_balanceFactor &gt; 1) {\n        if (balanceFactor(node-&gt;left) &gt;= 0) {\n            // 右回転\n            return rightRotate(node);\n        } else {\n            // 左回転してから右回転\n            node-&gt;left = leftRotate(node-&gt;left);\n            return rightRotate(node);\n        }\n    }\n    // 右に偏った木\n    if (_balanceFactor &lt; -1) {\n        if (balanceFactor(node-&gt;right) &lt;= 0) {\n            // 左回転\n            return leftRotate(node);\n        } else {\n            // 右回転してから左回転\n            node-&gt;right = rightRotate(node-&gt;right);\n            return leftRotate(node);\n        }\n    }\n    // 平衡木なので回転不要、そのまま返す\n    return node;\n}\n</code></pre> avl_tree.java<pre><code>/* 回転操作を行い、この部分木の平衡を回復する */\nTreeNode rotate(TreeNode node) {\n    // ノード node の平衡係数を取得\n    int balanceFactor = balanceFactor(node);\n    // 左に偏った木\n    if (balanceFactor &gt; 1) {\n        if (balanceFactor(node.left) &gt;= 0) {\n            // 右回転\n            return rightRotate(node);\n        } else {\n            // 左回転してから右回転\n            node.left = leftRotate(node.left);\n            return rightRotate(node);\n        }\n    }\n    // 右に偏った木\n    if (balanceFactor &lt; -1) {\n        if (balanceFactor(node.right) &lt;= 0) {\n            // 左回転\n            return leftRotate(node);\n        } else {\n            // 右回転してから左回転\n            node.right = rightRotate(node.right);\n            return leftRotate(node);\n        }\n    }\n    // 平衡木なので回転不要、そのまま返す\n    return node;\n}\n</code></pre> avl_tree.cs<pre><code>/* 回転操作を行い、この部分木の平衡を回復する */\nTreeNode? Rotate(TreeNode? node) {\n    // ノード node の平衡係数を取得\n    int balanceFactorInt = BalanceFactor(node);\n    // 左に偏った木\n    if (balanceFactorInt &gt; 1) {\n        if (BalanceFactor(node?.left) &gt;= 0) {\n            // 右回転\n            return RightRotate(node);\n        } else {\n            // 左回転してから右回転\n            node!.left = LeftRotate(node!.left);\n            return RightRotate(node);\n        }\n    }\n    // 右に偏った木\n    if (balanceFactorInt &lt; -1) {\n        if (BalanceFactor(node?.right) &lt;= 0) {\n            // 左回転\n            return LeftRotate(node);\n        } else {\n            // 右回転してから左回転\n            node!.right = RightRotate(node!.right);\n            return LeftRotate(node);\n        }\n    }\n    // 平衡木なので回転不要、そのまま返す\n    return node;\n}\n</code></pre> avl_tree.go<pre><code>/* 回転操作を行い、この部分木の平衡を回復する */\nfunc (t *aVLTree) rotate(node *TreeNode) *TreeNode {\n    // ノード `node` の平衡係数を取得する\n    // Go では短い変数名が推奨されるため、ここで `bf` は `t.balanceFactor` を表す\n    bf := t.balanceFactor(node)\n    // 左に偏った木\n    if bf &gt; 1 {\n        if t.balanceFactor(node.Left) &gt;= 0 {\n            // 右回転\n            return t.rightRotate(node)\n        } else {\n            // 左回転してから右回転\n            node.Left = t.leftRotate(node.Left)\n            return t.rightRotate(node)\n        }\n    }\n    // 右に偏った木\n    if bf &lt; -1 {\n        if t.balanceFactor(node.Right) &lt;= 0 {\n            // 左回転\n            return t.leftRotate(node)\n        } else {\n            // 右回転してから左回転\n            node.Right = t.rightRotate(node.Right)\n            return t.leftRotate(node)\n        }\n    }\n    // 平衡木なので回転不要、そのまま返す\n    return node\n}\n</code></pre> avl_tree.swift<pre><code>/* 回転操作を行い、この部分木の平衡を回復する */\nfunc rotate(node: TreeNode?) -&gt; TreeNode? {\n    // ノード node の平衡係数を取得\n    let balanceFactor = balanceFactor(node: node)\n    // 左に偏った木\n    if balanceFactor &gt; 1 {\n        if self.balanceFactor(node: node?.left) &gt;= 0 {\n            // 右回転\n            return rightRotate(node: node)\n        } else {\n            // 左回転してから右回転\n            node?.left = leftRotate(node: node?.left)\n            return rightRotate(node: node)\n        }\n    }\n    // 右に偏った木\n    if balanceFactor &lt; -1 {\n        if self.balanceFactor(node: node?.right) &lt;= 0 {\n            // 左回転\n            return leftRotate(node: node)\n        } else {\n            // 右回転してから左回転\n            node?.right = rightRotate(node: node?.right)\n            return leftRotate(node: node)\n        }\n    }\n    // 平衡木なので回転不要、そのまま返す\n    return node\n}\n</code></pre> avl_tree.js<pre><code>/* 回転操作を行い、この部分木の平衡を回復する */\n#rotate(node) {\n    // ノード node の平衡係数を取得\n    const balanceFactor = this.balanceFactor(node);\n    // 左に偏った木\n    if (balanceFactor &gt; 1) {\n        if (this.balanceFactor(node.left) &gt;= 0) {\n            // 右回転\n            return this.#rightRotate(node);\n        } else {\n            // 左回転してから右回転\n            node.left = this.#leftRotate(node.left);\n            return this.#rightRotate(node);\n        }\n    }\n    // 右に偏った木\n    if (balanceFactor &lt; -1) {\n        if (this.balanceFactor(node.right) &lt;= 0) {\n            // 左回転\n            return this.#leftRotate(node);\n        } else {\n            // 右回転してから左回転\n            node.right = this.#rightRotate(node.right);\n            return this.#leftRotate(node);\n        }\n    }\n    // 平衡木なので回転不要、そのまま返す\n    return node;\n}\n</code></pre> avl_tree.ts<pre><code>/* 回転操作を行い、この部分木の平衡を回復する */\nrotate(node: TreeNode): TreeNode {\n    // ノード node の平衡係数を取得\n    const balanceFactor = this.balanceFactor(node);\n    // 左に偏った木\n    if (balanceFactor &gt; 1) {\n        if (this.balanceFactor(node.left) &gt;= 0) {\n            // 右回転\n            return this.rightRotate(node);\n        } else {\n            // 左回転してから右回転\n            node.left = this.leftRotate(node.left);\n            return this.rightRotate(node);\n        }\n    }\n    // 右に偏った木\n    if (balanceFactor &lt; -1) {\n        if (this.balanceFactor(node.right) &lt;= 0) {\n            // 左回転\n            return this.leftRotate(node);\n        } else {\n            // 右回転してから左回転\n            node.right = this.rightRotate(node.right);\n            return this.leftRotate(node);\n        }\n    }\n    // 平衡木なので回転不要、そのまま返す\n    return node;\n}\n</code></pre> avl_tree.dart<pre><code>/* 回転操作を行い、この部分木の平衡を回復する */\nTreeNode? rotate(TreeNode? node) {\n  // ノード node の平衡係数を取得\n  int factor = balanceFactor(node);\n  // 左に偏った木\n  if (factor &gt; 1) {\n    if (balanceFactor(node!.left) &gt;= 0) {\n      // 右回転\n      return rightRotate(node);\n    } else {\n      // 左回転してから右回転\n      node.left = leftRotate(node.left);\n      return rightRotate(node);\n    }\n  }\n  // 右に偏った木\n  if (factor &lt; -1) {\n    if (balanceFactor(node!.right) &lt;= 0) {\n      // 左回転\n      return leftRotate(node);\n    } else {\n      // 右回転してから左回転\n      node.right = rightRotate(node.right);\n      return leftRotate(node);\n    }\n  }\n  // 平衡木なので回転不要、そのまま返す\n  return node;\n}\n</code></pre> avl_tree.rs<pre><code>/* 回転操作を行い、この部分木の平衡を回復する */\nfn rotate(node: OptionTreeNodeRc) -&gt; OptionTreeNodeRc {\n    // ノード node の平衡係数を取得\n    let balance_factor = Self::balance_factor(node.clone());\n    // 左に偏った木\n    if balance_factor &gt; 1 {\n        let node = node.unwrap();\n        if Self::balance_factor(node.borrow().left.clone()) &gt;= 0 {\n            // 右回転\n            Self::right_rotate(Some(node))\n        } else {\n            // 左回転してから右回転\n            let left = node.borrow().left.clone();\n            node.borrow_mut().left = Self::left_rotate(left);\n            Self::right_rotate(Some(node))\n        }\n    }\n    // 右に偏った木\n    else if balance_factor &lt; -1 {\n        let node = node.unwrap();\n        if Self::balance_factor(node.borrow().right.clone()) &lt;= 0 {\n            // 左回転\n            Self::left_rotate(Some(node))\n        } else {\n            // 右回転してから左回転\n            let right = node.borrow().right.clone();\n            node.borrow_mut().right = Self::right_rotate(right);\n            Self::left_rotate(Some(node))\n        }\n    } else {\n        // 平衡木なので回転不要、そのまま返す\n        node\n    }\n}\n</code></pre> avl_tree.c<pre><code>/* 回転操作を行い、この部分木の平衡を回復する */\nTreeNode *rotate(TreeNode *node) {\n    // ノード node の平衡係数を取得\n    int bf = balanceFactor(node);\n    // 左に偏った木\n    if (bf &gt; 1) {\n        if (balanceFactor(node-&gt;left) &gt;= 0) {\n            // 右回転\n            return rightRotate(node);\n        } else {\n            // 左回転してから右回転\n            node-&gt;left = leftRotate(node-&gt;left);\n            return rightRotate(node);\n        }\n    }\n    // 右に偏った木\n    if (bf &lt; -1) {\n        if (balanceFactor(node-&gt;right) &lt;= 0) {\n            // 左回転\n            return leftRotate(node);\n        } else {\n            // 右回転してから左回転\n            node-&gt;right = rightRotate(node-&gt;right);\n            return leftRotate(node);\n        }\n    }\n    // 平衡木なので回転不要、そのまま返す\n    return node;\n}\n</code></pre> avl_tree.kt<pre><code>/* 回転操作を行い、この部分木の平衡を回復する */\nfun rotate(node: TreeNode): TreeNode {\n    // ノード node の平衡係数を取得\n    val balanceFactor = balanceFactor(node)\n    // 左に偏った木\n    if (balanceFactor &gt; 1) {\n        if (balanceFactor(node.left) &gt;= 0) {\n            // 右回転\n            return rightRotate(node)\n        } else {\n            // 左回転してから右回転\n            node.left = leftRotate(node.left)\n            return rightRotate(node)\n        }\n    }\n    // 右に偏った木\n    if (balanceFactor &lt; -1) {\n        if (balanceFactor(node.right) &lt;= 0) {\n            // 左回転\n            return leftRotate(node)\n        } else {\n            // 右回転してから左回転\n            node.right = rightRotate(node.right)\n            return leftRotate(node)\n        }\n    }\n    // 平衡木なので回転不要、そのまま返す\n    return node\n}\n</code></pre> avl_tree.rb<pre><code>### 回転操作を行い、この部分木の平衡を回復する ###\ndef rotate(node)\n  # ノード node の平衡係数を取得\n  balance_factor = balance_factor(node)\n  # 左部分木をたどる\n  if balance_factor &gt; 1\n    if balance_factor(node.left) &gt;= 0\n      # 右回転\n      return right_rotate(node)\n    else\n      # 左回転してから右回転\n      node.left = left_rotate(node.left)\n      return right_rotate(node)\n    end\n  # 右に偏った木\n  elsif balance_factor &lt; -1\n    if balance_factor(node.right) &lt;= 0\n      # 左回転\n      return left_rotate(node)\n    else\n      # 右回転してから左回転\n      node.right = right_rotate(node.right)\n      return left_rotate(node)\n    end\n  end\n  # 平衡木なので回転不要、そのまま返す\n  node\nend\n</code></pre>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL 木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#753-avl","level":2,"title":"7.5.3   AVL 木の基本操作","text":"","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL 木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#1_2","level":3,"title":"1.   ノードの挿入","text":"<p>AVL 木のノード挿入は、基本的には二分探索木と同じです。唯一の違いは、AVL 木ではノード挿入後に、そのノードから根ノードまでの経路上に複数の不平衡ノードが現れる可能性があることです。したがって、このノードから開始して、下から上へ回転操作を行い、すべての不平衡ノードを平衡に戻す必要があります。コードは次のとおりです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def insert(self, val):\n    \"\"\"ノードを挿入\"\"\"\n    self._root = self.insert_helper(self._root, val)\n\ndef insert_helper(self, node: TreeNode | None, val: int) -&gt; TreeNode:\n    \"\"\"ノードを再帰的に挿入する（補助メソッド）\"\"\"\n    if node is None:\n        return TreeNode(val)\n    # 1. 挿入位置を探索してノードを挿入\n    if val &lt; node.val:\n        node.left = self.insert_helper(node.left, val)\n    elif val &gt; node.val:\n        node.right = self.insert_helper(node.right, val)\n    else:\n        # 重複ノードは挿入せず、そのまま返す\n        return node\n    # ノードの高さを更新する\n    self.update_height(node)\n    # 2. 回転操作を行い、部分木の平衡を回復する\n    return self.rotate(node)\n</code></pre> avl_tree.cpp<pre><code>/* ノードを挿入 */\nvoid insert(int val) {\n    root = insertHelper(root, val);\n}\n\n/* ノードを再帰的に挿入する（補助メソッド） */\nTreeNode *insertHelper(TreeNode *node, int val) {\n    if (node == nullptr)\n        return new TreeNode(val);\n    /* 1. 挿入位置を探索してノードを挿入 */\n    if (val &lt; node-&gt;val)\n        node-&gt;left = insertHelper(node-&gt;left, val);\n    else if (val &gt; node-&gt;val)\n        node-&gt;right = insertHelper(node-&gt;right, val);\n    else\n        return node;    // 重複ノードは挿入せず、そのまま返す\n    updateHeight(node); // ノードの高さを更新する\n    /* 2. 回転操作を行い、部分木の平衡を回復する */\n    node = rotate(node);\n    // 部分木の根ノードを返す\n    return node;\n}\n</code></pre> avl_tree.java<pre><code>/* ノードを挿入 */\nvoid insert(int val) {\n    root = insertHelper(root, val);\n}\n\n/* ノードを再帰的に挿入する（補助メソッド） */\nTreeNode insertHelper(TreeNode node, int val) {\n    if (node == null)\n        return new TreeNode(val);\n    /* 1. 挿入位置を探索してノードを挿入 */\n    if (val &lt; node.val)\n        node.left = insertHelper(node.left, val);\n    else if (val &gt; node.val)\n        node.right = insertHelper(node.right, val);\n    else\n        return node; // 重複ノードは挿入せず、そのまま返す\n    updateHeight(node); // ノードの高さを更新する\n    /* 2. 回転操作を行い、部分木の平衡を回復する */\n    node = rotate(node);\n    // 部分木の根ノードを返す\n    return node;\n}\n</code></pre> avl_tree.cs<pre><code>/* ノードを挿入 */\nvoid Insert(int val) {\n    root = InsertHelper(root, val);\n}\n\n/* ノードを再帰的に挿入する（補助メソッド） */\nTreeNode? InsertHelper(TreeNode? node, int val) {\n    if (node == null) return new TreeNode(val);\n    /* 1. 挿入位置を探索してノードを挿入 */\n    if (val &lt; node.val)\n        node.left = InsertHelper(node.left, val);\n    else if (val &gt; node.val)\n        node.right = InsertHelper(node.right, val);\n    else\n        return node;     // 重複ノードは挿入せず、そのまま返す\n    UpdateHeight(node);  // ノードの高さを更新する\n    /* 2. 回転操作を行い、部分木の平衡を回復する */\n    node = Rotate(node);\n    // 部分木の根ノードを返す\n    return node;\n}\n</code></pre> avl_tree.go<pre><code>/* ノードを挿入 */\nfunc (t *aVLTree) insert(val int) {\n    t.root = t.insertHelper(t.root, val)\n}\n\n/* ノードを再帰的に挿入する（補助関数） */\nfunc (t *aVLTree) insertHelper(node *TreeNode, val int) *TreeNode {\n    if node == nil {\n        return NewTreeNode(val)\n    }\n    /* 1. 挿入位置を探索してノードを挿入 */\n    if val &lt; node.Val.(int) {\n        node.Left = t.insertHelper(node.Left, val)\n    } else if val &gt; node.Val.(int) {\n        node.Right = t.insertHelper(node.Right, val)\n    } else {\n        // 重複ノードは挿入せず、そのまま返す\n        return node\n    }\n    // ノードの高さを更新する\n    t.updateHeight(node)\n    /* 2. 回転操作を行い、部分木の平衡を回復する */\n    node = t.rotate(node)\n    // 部分木の根ノードを返す\n    return node\n}\n</code></pre> avl_tree.swift<pre><code>/* ノードを挿入 */\nfunc insert(val: Int) {\n    root = insertHelper(node: root, val: val)\n}\n\n/* ノードを再帰的に挿入する（補助メソッド） */\nfunc insertHelper(node: TreeNode?, val: Int) -&gt; TreeNode? {\n    var node = node\n    if node == nil {\n        return TreeNode(x: val)\n    }\n    /* 1. 挿入位置を探索してノードを挿入 */\n    if val &lt; node!.val {\n        node?.left = insertHelper(node: node?.left, val: val)\n    } else if val &gt; node!.val {\n        node?.right = insertHelper(node: node?.right, val: val)\n    } else {\n        return node // 重複ノードは挿入せず、そのまま返す\n    }\n    updateHeight(node: node) // ノードの高さを更新する\n    /* 2. 回転操作を行い、部分木の平衡を回復する */\n    node = rotate(node: node)\n    // 部分木の根ノードを返す\n    return node\n}\n</code></pre> avl_tree.js<pre><code>/* ノードを挿入 */\ninsert(val) {\n    this.root = this.#insertHelper(this.root, val);\n}\n\n/* ノードを再帰的に挿入する（補助メソッド） */\n#insertHelper(node, val) {\n    if (node === null) return new TreeNode(val);\n    /* 1. 挿入位置を探索してノードを挿入 */\n    if (val &lt; node.val) node.left = this.#insertHelper(node.left, val);\n    else if (val &gt; node.val)\n        node.right = this.#insertHelper(node.right, val);\n    else return node; // 重複ノードは挿入せず、そのまま返す\n    this.#updateHeight(node); // ノードの高さを更新する\n    /* 2. 回転操作を行い、部分木の平衡を回復する */\n    node = this.#rotate(node);\n    // 部分木の根ノードを返す\n    return node;\n}\n</code></pre> avl_tree.ts<pre><code>/* ノードを挿入 */\ninsert(val: number): void {\n    this.root = this.insertHelper(this.root, val);\n}\n\n/* ノードを再帰的に挿入する（補助メソッド） */\ninsertHelper(node: TreeNode, val: number): TreeNode {\n    if (node === null) return new TreeNode(val);\n    /* 1. 挿入位置を探索してノードを挿入 */\n    if (val &lt; node.val) {\n        node.left = this.insertHelper(node.left, val);\n    } else if (val &gt; node.val) {\n        node.right = this.insertHelper(node.right, val);\n    } else {\n        return node; // 重複ノードは挿入せず、そのまま返す\n    }\n    this.updateHeight(node); // ノードの高さを更新する\n    /* 2. 回転操作を行い、部分木の平衡を回復する */\n    node = this.rotate(node);\n    // 部分木の根ノードを返す\n    return node;\n}\n</code></pre> avl_tree.dart<pre><code>/* ノードを挿入 */\nvoid insert(int val) {\n  root = insertHelper(root, val);\n}\n\n/* ノードを再帰的に挿入する（補助メソッド） */\nTreeNode? insertHelper(TreeNode? node, int val) {\n  if (node == null) return TreeNode(val);\n  /* 1. 挿入位置を探索してノードを挿入 */\n  if (val &lt; node.val)\n    node.left = insertHelper(node.left, val);\n  else if (val &gt; node.val)\n    node.right = insertHelper(node.right, val);\n  else\n    return node; // 重複ノードは挿入せず、そのまま返す\n  updateHeight(node); // ノードの高さを更新する\n  /* 2. 回転操作を行い、部分木の平衡を回復する */\n  node = rotate(node);\n  // 部分木の根ノードを返す\n  return node;\n}\n</code></pre> avl_tree.rs<pre><code>/* ノードを挿入 */\nfn insert(&amp;mut self, val: i32) {\n    self.root = Self::insert_helper(self.root.clone(), val);\n}\n\n/* ノードを再帰的に挿入する（補助メソッド） */\nfn insert_helper(node: OptionTreeNodeRc, val: i32) -&gt; OptionTreeNodeRc {\n    match node {\n        Some(mut node) =&gt; {\n            /* 1. 挿入位置を探索してノードを挿入 */\n            match {\n                let node_val = node.borrow().val;\n                node_val\n            }\n            .cmp(&amp;val)\n            {\n                Ordering::Greater =&gt; {\n                    let left = node.borrow().left.clone();\n                    node.borrow_mut().left = Self::insert_helper(left, val);\n                }\n                Ordering::Less =&gt; {\n                    let right = node.borrow().right.clone();\n                    node.borrow_mut().right = Self::insert_helper(right, val);\n                }\n                Ordering::Equal =&gt; {\n                    return Some(node); // 重複ノードは挿入せず、そのまま返す\n                }\n            }\n            Self::update_height(Some(node.clone())); // ノードの高さを更新する\n\n            /* 2. 回転操作を行い、部分木の平衡を回復する */\n            node = Self::rotate(Some(node)).unwrap();\n            // 部分木の根ノードを返す\n            Some(node)\n        }\n        None =&gt; Some(TreeNode::new(val)),\n    }\n}\n</code></pre> avl_tree.c<pre><code>/* ノードを挿入 */\nvoid insert(AVLTree *tree, int val) {\n    tree-&gt;root = insertHelper(tree-&gt;root, val);\n}\n\n/* ノードを再帰的に挿入する（補助関数） */\nTreeNode *insertHelper(TreeNode *node, int val) {\n    if (node == NULL) {\n        return newTreeNode(val);\n    }\n    /* 1. 挿入位置を探索してノードを挿入 */\n    if (val &lt; node-&gt;val) {\n        node-&gt;left = insertHelper(node-&gt;left, val);\n    } else if (val &gt; node-&gt;val) {\n        node-&gt;right = insertHelper(node-&gt;right, val);\n    } else {\n        // 重複ノードは挿入せず、そのまま返す\n        return node;\n    }\n    // ノードの高さを更新する\n    updateHeight(node);\n    /* 2. 回転操作を行い、部分木の平衡を回復する */\n    node = rotate(node);\n    // 部分木の根ノードを返す\n    return node;\n}\n</code></pre> avl_tree.kt<pre><code>/* ノードを挿入 */\nfun insert(_val: Int) {\n    root = insertHelper(root, _val)\n}\n\n/* ノードを再帰的に挿入する（補助メソッド） */\nfun insertHelper(n: TreeNode?, _val: Int): TreeNode {\n    if (n == null)\n        return TreeNode(_val)\n    var node = n\n    /* 1. 挿入位置を探索してノードを挿入 */\n    if (_val &lt; node._val)\n        node.left = insertHelper(node.left, _val)\n    else if (_val &gt; node._val)\n        node.right = insertHelper(node.right, _val)\n    else\n        return node // 重複ノードは挿入せず、そのまま返す\n    updateHeight(node) // ノードの高さを更新する\n    /* 2. 回転操作を行い、部分木の平衡を回復する */\n    node = rotate(node)\n    // 部分木の根ノードを返す\n    return node\n}\n</code></pre> avl_tree.rb<pre><code>### ノードを挿入 ###\ndef insert(val)\n  @root = insert_helper(@root, val)\nend\n\n### ノードを挿入 ###\ndef insert(val)\n  @root = insert_helper(@root, val)\nend\n\n# ## ノードを再帰的に挿入（補助メソッド）###\ndef insert_helper(node, val)\n  return TreeNode.new(val) if node.nil?\n  # 1. 挿入位置を探索してノードを挿入\n  if val &lt; node.val\n    node.left = insert_helper(node.left, val)\n  elsif val &gt; node.val\n    node.right = insert_helper(node.right, val)\n  else\n    # 重複ノードは挿入せず、そのまま返す\n    return node\n  end\n  # ノードの高さを更新する\n  update_height(node)\n  # 2. 回転操作を行い、部分木の平衡を回復する\n  rotate(node)\nend\n</code></pre>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL 木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#2_2","level":3,"title":"2.   ノードの削除","text":"<p>同様に、二分探索木のノード削除メソッドを土台として、下から上へ回転操作を行い、すべての不平衡ノードを平衡に戻す必要があります。コードは次のとおりです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def remove(self, val: int):\n    \"\"\"ノードを削除\"\"\"\n    self._root = self.remove_helper(self._root, val)\n\ndef remove_helper(self, node: TreeNode | None, val: int) -&gt; TreeNode | None:\n    \"\"\"ノードを再帰的に削除する（補助メソッド）\"\"\"\n    if node is None:\n        return None\n    # 1. ノードを探索して削除\n    if val &lt; node.val:\n        node.left = self.remove_helper(node.left, val)\n    elif val &gt; node.val:\n        node.right = self.remove_helper(node.right, val)\n    else:\n        if node.left is None or node.right is None:\n            child = node.left or node.right\n            # 子ノード数 = 0 の場合、node をそのまま削除して返す\n            if child is None:\n                return None\n            # 子ノード数 = 1 の場合、node をそのまま削除する\n            else:\n                node = child\n        else:\n            # 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える\n            temp = node.right\n            while temp.left is not None:\n                temp = temp.left\n            node.right = self.remove_helper(node.right, temp.val)\n            node.val = temp.val\n    # ノードの高さを更新する\n    self.update_height(node)\n    # 2. 回転操作を行い、部分木の平衡を回復する\n    return self.rotate(node)\n</code></pre> avl_tree.cpp<pre><code>/* ノードを削除 */\nvoid remove(int val) {\n    root = removeHelper(root, val);\n}\n\n/* ノードを再帰的に削除する（補助メソッド） */\nTreeNode *removeHelper(TreeNode *node, int val) {\n    if (node == nullptr)\n        return nullptr;\n    /* 1. ノードを探索して削除 */\n    if (val &lt; node-&gt;val)\n        node-&gt;left = removeHelper(node-&gt;left, val);\n    else if (val &gt; node-&gt;val)\n        node-&gt;right = removeHelper(node-&gt;right, val);\n    else {\n        if (node-&gt;left == nullptr || node-&gt;right == nullptr) {\n            TreeNode *child = node-&gt;left != nullptr ? node-&gt;left : node-&gt;right;\n            // 子ノード数 = 0 の場合、node をそのまま削除して返す\n            if (child == nullptr) {\n                delete node;\n                return nullptr;\n            }\n            // 子ノード数 = 1 の場合、node をそのまま削除する\n            else {\n                delete node;\n                node = child;\n            }\n        } else {\n            // 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える\n            TreeNode *temp = node-&gt;right;\n            while (temp-&gt;left != nullptr) {\n                temp = temp-&gt;left;\n            }\n            int tempVal = temp-&gt;val;\n            node-&gt;right = removeHelper(node-&gt;right, temp-&gt;val);\n            node-&gt;val = tempVal;\n        }\n    }\n    updateHeight(node); // ノードの高さを更新する\n    /* 2. 回転操作を行い、部分木の平衡を回復する */\n    node = rotate(node);\n    // 部分木の根ノードを返す\n    return node;\n}\n</code></pre> avl_tree.java<pre><code>/* ノードを削除 */\nvoid remove(int val) {\n    root = removeHelper(root, val);\n}\n\n/* ノードを再帰的に削除する（補助メソッド） */\nTreeNode removeHelper(TreeNode node, int val) {\n    if (node == null)\n        return null;\n    /* 1. ノードを探索して削除 */\n    if (val &lt; node.val)\n        node.left = removeHelper(node.left, val);\n    else if (val &gt; node.val)\n        node.right = removeHelper(node.right, val);\n    else {\n        if (node.left == null || node.right == null) {\n            TreeNode child = node.left != null ? node.left : node.right;\n            // 子ノード数 = 0 の場合、node をそのまま削除して返す\n            if (child == null)\n                return null;\n            // 子ノード数 = 1 の場合、node をそのまま削除する\n            else\n                node = child;\n        } else {\n            // 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える\n            TreeNode temp = node.right;\n            while (temp.left != null) {\n                temp = temp.left;\n            }\n            node.right = removeHelper(node.right, temp.val);\n            node.val = temp.val;\n        }\n    }\n    updateHeight(node); // ノードの高さを更新する\n    /* 2. 回転操作を行い、部分木の平衡を回復する */\n    node = rotate(node);\n    // 部分木の根ノードを返す\n    return node;\n}\n</code></pre> avl_tree.cs<pre><code>/* ノードを削除 */\nvoid Remove(int val) {\n    root = RemoveHelper(root, val);\n}\n\n/* ノードを再帰的に削除する（補助メソッド） */\nTreeNode? RemoveHelper(TreeNode? node, int val) {\n    if (node == null) return null;\n    /* 1. ノードを探索して削除 */\n    if (val &lt; node.val)\n        node.left = RemoveHelper(node.left, val);\n    else if (val &gt; node.val)\n        node.right = RemoveHelper(node.right, val);\n    else {\n        if (node.left == null || node.right == null) {\n            TreeNode? child = node.left ?? node.right;\n            // 子ノード数 = 0 の場合、node をそのまま削除して返す\n            if (child == null)\n                return null;\n            // 子ノード数 = 1 の場合、node をそのまま削除する\n            else\n                node = child;\n        } else {\n            // 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える\n            TreeNode? temp = node.right;\n            while (temp.left != null) {\n                temp = temp.left;\n            }\n            node.right = RemoveHelper(node.right, temp.val!.Value);\n            node.val = temp.val;\n        }\n    }\n    UpdateHeight(node);  // ノードの高さを更新する\n    /* 2. 回転操作を行い、部分木の平衡を回復する */\n    node = Rotate(node);\n    // 部分木の根ノードを返す\n    return node;\n}\n</code></pre> avl_tree.go<pre><code>/* ノードを削除 */\nfunc (t *aVLTree) remove(val int) {\n    t.root = t.removeHelper(t.root, val)\n}\n\n/* ノードを再帰的に削除する（補助関数） */\nfunc (t *aVLTree) removeHelper(node *TreeNode, val int) *TreeNode {\n    if node == nil {\n        return nil\n    }\n    /* 1. ノードを探索して削除 */\n    if val &lt; node.Val.(int) {\n        node.Left = t.removeHelper(node.Left, val)\n    } else if val &gt; node.Val.(int) {\n        node.Right = t.removeHelper(node.Right, val)\n    } else {\n        if node.Left == nil || node.Right == nil {\n            child := node.Left\n            if node.Right != nil {\n                child = node.Right\n            }\n            if child == nil {\n                // 子ノード数 = 0 の場合、node をそのまま削除して返す\n                return nil\n            } else {\n                // 子ノード数 = 1 の場合、node をそのまま削除する\n                node = child\n            }\n        } else {\n            // 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える\n            temp := node.Right\n            for temp.Left != nil {\n                temp = temp.Left\n            }\n            node.Right = t.removeHelper(node.Right, temp.Val.(int))\n            node.Val = temp.Val\n        }\n    }\n    // ノードの高さを更新する\n    t.updateHeight(node)\n    /* 2. 回転操作を行い、部分木の平衡を回復する */\n    node = t.rotate(node)\n    // 部分木の根ノードを返す\n    return node\n}\n</code></pre> avl_tree.swift<pre><code>/* ノードを削除 */\nfunc remove(val: Int) {\n    root = removeHelper(node: root, val: val)\n}\n\n/* ノードを再帰的に削除する（補助メソッド） */\nfunc removeHelper(node: TreeNode?, val: Int) -&gt; TreeNode? {\n    var node = node\n    if node == nil {\n        return nil\n    }\n    /* 1. ノードを探索して削除 */\n    if val &lt; node!.val {\n        node?.left = removeHelper(node: node?.left, val: val)\n    } else if val &gt; node!.val {\n        node?.right = removeHelper(node: node?.right, val: val)\n    } else {\n        if node?.left == nil || node?.right == nil {\n            let child = node?.left ?? node?.right\n            // 子ノード数 = 0 の場合、node をそのまま削除して返す\n            if child == nil {\n                return nil\n            }\n            // 子ノード数 = 1 の場合、node をそのまま削除する\n            else {\n                node = child\n            }\n        } else {\n            // 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える\n            var temp = node?.right\n            while temp?.left != nil {\n                temp = temp?.left\n            }\n            node?.right = removeHelper(node: node?.right, val: temp!.val)\n            node?.val = temp!.val\n        }\n    }\n    updateHeight(node: node) // ノードの高さを更新する\n    /* 2. 回転操作を行い、部分木の平衡を回復する */\n    node = rotate(node: node)\n    // 部分木の根ノードを返す\n    return node\n}\n</code></pre> avl_tree.js<pre><code>/* ノードを削除 */\nremove(val) {\n    this.root = this.#removeHelper(this.root, val);\n}\n\n/* ノードを再帰的に削除する（補助メソッド） */\n#removeHelper(node, val) {\n    if (node === null) return null;\n    /* 1. ノードを探索して削除 */\n    if (val &lt; node.val) node.left = this.#removeHelper(node.left, val);\n    else if (val &gt; node.val)\n        node.right = this.#removeHelper(node.right, val);\n    else {\n        if (node.left === null || node.right === null) {\n            const child = node.left !== null ? node.left : node.right;\n            // 子ノード数 = 0 の場合、node をそのまま削除して返す\n            if (child === null) return null;\n            // 子ノード数 = 1 の場合、node をそのまま削除する\n            else node = child;\n        } else {\n            // 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える\n            let temp = node.right;\n            while (temp.left !== null) {\n                temp = temp.left;\n            }\n            node.right = this.#removeHelper(node.right, temp.val);\n            node.val = temp.val;\n        }\n    }\n    this.#updateHeight(node); // ノードの高さを更新する\n    /* 2. 回転操作を行い、部分木の平衡を回復する */\n    node = this.#rotate(node);\n    // 部分木の根ノードを返す\n    return node;\n}\n</code></pre> avl_tree.ts<pre><code>/* ノードを削除 */\nremove(val: number): void {\n    this.root = this.removeHelper(this.root, val);\n}\n\n/* ノードを再帰的に削除する（補助メソッド） */\nremoveHelper(node: TreeNode, val: number): TreeNode {\n    if (node === null) return null;\n    /* 1. ノードを探索して削除 */\n    if (val &lt; node.val) {\n        node.left = this.removeHelper(node.left, val);\n    } else if (val &gt; node.val) {\n        node.right = this.removeHelper(node.right, val);\n    } else {\n        if (node.left === null || node.right === null) {\n            const child = node.left !== null ? node.left : node.right;\n            // 子ノード数 = 0 の場合、node をそのまま削除して返す\n            if (child === null) {\n                return null;\n            } else {\n                // 子ノード数 = 1 の場合、node をそのまま削除する\n                node = child;\n            }\n        } else {\n            // 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える\n            let temp = node.right;\n            while (temp.left !== null) {\n                temp = temp.left;\n            }\n            node.right = this.removeHelper(node.right, temp.val);\n            node.val = temp.val;\n        }\n    }\n    this.updateHeight(node); // ノードの高さを更新する\n    /* 2. 回転操作を行い、部分木の平衡を回復する */\n    node = this.rotate(node);\n    // 部分木の根ノードを返す\n    return node;\n}\n</code></pre> avl_tree.dart<pre><code>/* ノードを削除 */\nvoid remove(int val) {\n  root = removeHelper(root, val);\n}\n\n/* ノードを再帰的に削除する（補助メソッド） */\nTreeNode? removeHelper(TreeNode? node, int val) {\n  if (node == null) return null;\n  /* 1. ノードを探索して削除 */\n  if (val &lt; node.val)\n    node.left = removeHelper(node.left, val);\n  else if (val &gt; node.val)\n    node.right = removeHelper(node.right, val);\n  else {\n    if (node.left == null || node.right == null) {\n      TreeNode? child = node.left ?? node.right;\n      // 子ノード数 = 0 の場合、node をそのまま削除して返す\n      if (child == null)\n        return null;\n      // 子ノード数 = 1 の場合、node をそのまま削除する\n      else\n        node = child;\n    } else {\n      // 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える\n      TreeNode? temp = node.right;\n      while (temp!.left != null) {\n        temp = temp.left;\n      }\n      node.right = removeHelper(node.right, temp.val);\n      node.val = temp.val;\n    }\n  }\n  updateHeight(node); // ノードの高さを更新する\n  /* 2. 回転操作を行い、部分木の平衡を回復する */\n  node = rotate(node);\n  // 部分木の根ノードを返す\n  return node;\n}\n</code></pre> avl_tree.rs<pre><code>/* ノードを削除 */\nfn remove(&amp;self, val: i32) {\n    Self::remove_helper(self.root.clone(), val);\n}\n\n/* ノードを再帰的に削除する（補助メソッド） */\nfn remove_helper(node: OptionTreeNodeRc, val: i32) -&gt; OptionTreeNodeRc {\n    match node {\n        Some(mut node) =&gt; {\n            /* 1. ノードを探索して削除 */\n            if val &lt; node.borrow().val {\n                let left = node.borrow().left.clone();\n                node.borrow_mut().left = Self::remove_helper(left, val);\n            } else if val &gt; node.borrow().val {\n                let right = node.borrow().right.clone();\n                node.borrow_mut().right = Self::remove_helper(right, val);\n            } else if node.borrow().left.is_none() || node.borrow().right.is_none() {\n                let child = if node.borrow().left.is_some() {\n                    node.borrow().left.clone()\n                } else {\n                    node.borrow().right.clone()\n                };\n                match child {\n                    // 子ノード数 = 0 の場合、node をそのまま削除して返す\n                    None =&gt; {\n                        return None;\n                    }\n                    // 子ノード数 = 1 の場合、node をそのまま削除する\n                    Some(child) =&gt; node = child,\n                }\n            } else {\n                // 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える\n                let mut temp = node.borrow().right.clone().unwrap();\n                loop {\n                    let temp_left = temp.borrow().left.clone();\n                    if temp_left.is_none() {\n                        break;\n                    }\n                    temp = temp_left.unwrap();\n                }\n                let right = node.borrow().right.clone();\n                node.borrow_mut().right = Self::remove_helper(right, temp.borrow().val);\n                node.borrow_mut().val = temp.borrow().val;\n            }\n            Self::update_height(Some(node.clone())); // ノードの高さを更新する\n\n            /* 2. 回転操作を行い、部分木の平衡を回復する */\n            node = Self::rotate(Some(node)).unwrap();\n            // 部分木の根ノードを返す\n            Some(node)\n        }\n        None =&gt; None,\n    }\n}\n</code></pre> avl_tree.c<pre><code>/* ノードを削除 */\n// stdio.h を導入しているため、ここでは remove 識別子を使えない\nvoid removeItem(AVLTree *tree, int val) {\n    TreeNode *root = removeHelper(tree-&gt;root, val);\n}\n\n/* ノードを再帰的に削除する（補助関数） */\nTreeNode *removeHelper(TreeNode *node, int val) {\n    TreeNode *child, *grandChild;\n    if (node == NULL) {\n        return NULL;\n    }\n    /* 1. ノードを探索して削除 */\n    if (val &lt; node-&gt;val) {\n        node-&gt;left = removeHelper(node-&gt;left, val);\n    } else if (val &gt; node-&gt;val) {\n        node-&gt;right = removeHelper(node-&gt;right, val);\n    } else {\n        if (node-&gt;left == NULL || node-&gt;right == NULL) {\n            child = node-&gt;left;\n            if (node-&gt;right != NULL) {\n                child = node-&gt;right;\n            }\n            // 子ノード数 = 0 の場合、node をそのまま削除して返す\n            if (child == NULL) {\n                return NULL;\n            } else {\n                // 子ノード数 = 1 の場合、node をそのまま削除する\n                node = child;\n            }\n        } else {\n            // 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える\n            TreeNode *temp = node-&gt;right;\n            while (temp-&gt;left != NULL) {\n                temp = temp-&gt;left;\n            }\n            int tempVal = temp-&gt;val;\n            node-&gt;right = removeHelper(node-&gt;right, temp-&gt;val);\n            node-&gt;val = tempVal;\n        }\n    }\n    // ノードの高さを更新する\n    updateHeight(node);\n    /* 2. 回転操作を行い、部分木の平衡を回復する */\n    node = rotate(node);\n    // 部分木の根ノードを返す\n    return node;\n}\n</code></pre> avl_tree.kt<pre><code>/* ノードを削除 */\nfun remove(_val: Int) {\n    root = removeHelper(root, _val)\n}\n\n/* ノードを再帰的に削除する（補助メソッド） */\nfun removeHelper(n: TreeNode?, _val: Int): TreeNode? {\n    var node = n ?: return null\n    /* 1. ノードを探索して削除 */\n    if (_val &lt; node._val)\n        node.left = removeHelper(node.left, _val)\n    else if (_val &gt; node._val)\n        node.right = removeHelper(node.right, _val)\n    else {\n        if (node.left == null || node.right == null) {\n            val child = if (node.left != null)\n                node.left\n            else\n                node.right\n            // 子ノード数 = 0 の場合、node をそのまま削除して返す\n            if (child == null)\n                return null\n            // 子ノード数 = 1 の場合、node をそのまま削除する\n            else\n                node = child\n        } else {\n            // 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える\n            var temp = node.right\n            while (temp!!.left != null) {\n                temp = temp.left\n            }\n            node.right = removeHelper(node.right, temp._val)\n            node._val = temp._val\n        }\n    }\n    updateHeight(node) // ノードの高さを更新する\n    /* 2. 回転操作を行い、部分木の平衡を回復する */\n    node = rotate(node)\n    // 部分木の根ノードを返す\n    return node\n}\n</code></pre> avl_tree.rb<pre><code>### ノードを削除 ###\ndef remove(val)\n  @root = remove_helper(@root, val)\nend\n\n### ノードを削除 ###\ndef remove(val)\n  @root = remove_helper(@root, val)\nend\n\n# ## ノードを再帰的に削除（補助メソッド）###\ndef remove_helper(node, val)\n  return if node.nil?\n  # 1. ノードを探索して削除\n  if val &lt; node.val\n    node.left = remove_helper(node.left, val)\n  elsif val &gt; node.val\n    node.right = remove_helper(node.right, val)\n  else\n    if node.left.nil? || node.right.nil?\n      child = node.left || node.right\n      # 子ノード数 = 0 の場合、node をそのまま削除して返す\n      return if child.nil?\n      # 子ノード数 = 1 の場合、node をそのまま削除する\n      node = child\n    else\n      # 子ノード数 = 2 の場合、中順走査の次のノードを削除し、そのノードで現在のノードを置き換える\n      temp = node.right\n      while !temp.left.nil?\n        temp = temp.left\n      end\n      node.right = remove_helper(node.right, temp.val)\n      node.val = temp.val\n    end\n  end\n  # ノードの高さを更新する\n  update_height(node)\n  # 2. 回転操作を行い、部分木の平衡を回復する\n  rotate(node)\nend\n</code></pre>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL 木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#3_1","level":3,"title":"3.   ノードの探索","text":"<p>AVL 木のノード探索操作は二分探索木と同じなので、ここでは繰り返しません。</p>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL 木 *"],"tags":[]},{"location":"chapter_tree/avl_tree/#754-avl","level":2,"title":"7.5.4   AVL 木の代表的な応用","text":"<ul> <li>大規模データの整理・格納に用いられ、高頻度の探索と低頻度の追加・削除に適しています。</li> <li>データベースのインデックスシステムの構築に使われます。</li> <li>赤黒木も代表的な平衡二分探索木の一つです。AVL 木と比べると、赤黒木は平衡条件がより緩く、ノードの挿入・削除に必要な回転操作が少ないため、平均的な更新効率はより高くなります。</li> </ul>","path":["第 7 章 &nbsp; 木","7.5 &nbsp; AVL 木 *"],"tags":[]},{"location":"chapter_tree/binary_search_tree/","level":1,"title":"7.4   二分探索木","text":"<p>以下の図に示すように、二分探索木（binary search tree）は次の条件を満たします。</p> <ol> <li>根ノードについて、左部分木のすべてのノードの値 \\(&lt;\\) 根ノードの値 \\(&lt;\\) 右部分木のすべてのノードの値。</li> <li>任意のノードの左部分木と右部分木も二分探索木であり、すなわち条件 <code>1.</code> も満たします。</li> </ol> <p></p> <p> 図 7-16   二分探索木 </p>","path":["第 7 章 &nbsp; 木","7.4 &nbsp; 二分探索木"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#741","level":2,"title":"7.4.1   二分探索木の操作","text":"<p>二分探索木をクラス <code>BinarySearchTree</code> としてカプセル化し、木の根ノードを指すメンバ変数 <code>root</code> を宣言します。</p>","path":["第 7 章 &nbsp; 木","7.4 &nbsp; 二分探索木"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#1","level":3,"title":"1.   ノードの探索","text":"<p>目標ノードの値 <code>num</code> が与えられたら、二分探索木の性質に基づいて探索できます。以下の図に示すように、ノード <code>cur</code> を宣言し、二分木の根ノード <code>root</code> から出発して、ノード値 <code>cur.val</code> と <code>num</code> の大小関係を繰り返し比較します。</p> <ul> <li><code>cur.val &lt; num</code> の場合、目標ノードは <code>cur</code> の右部分木にあるため、<code>cur = cur.right</code> を実行します。</li> <li><code>cur.val &gt; num</code> の場合、目標ノードは <code>cur</code> の左部分木にあるため、<code>cur = cur.left</code> を実行します。</li> <li><code>cur.val = num</code> の場合、目標ノードが見つかったことを表し、ループを抜けてそのノードを返します。</li> </ul> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p> 図 7-17   二分探索木のノード探索例 </p> <p>二分探索木の探索操作は二分探索アルゴリズムと同じ原理で動作し、各ラウンドで半分の候補を除外します。ループ回数の上限は二分木の高さであり、二分木が平衡であれば \\(O(\\log n)\\) 時間です。コード例は次のとおりです。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_tree.py<pre><code>def search(self, num: int) -&gt; TreeNode | None:\n    \"\"\"ノードを探索\"\"\"\n    cur = self._root\n    # ループで探索し、葉ノードを越えたら抜ける\n    while cur is not None:\n        # 目標ノードは cur の右部分木にある\n        if cur.val &lt; num:\n            cur = cur.right\n        # 目標ノードは cur の左部分木にある\n        elif cur.val &gt; num:\n            cur = cur.left\n        # 目標ノードが見つかったらループを抜ける\n        else:\n            break\n    return cur\n</code></pre> binary_search_tree.cpp<pre><code>/* ノードを探索 */\nTreeNode *search(int num) {\n    TreeNode *cur = root;\n    // ループで探索し、葉ノードを越えたら抜ける\n    while (cur != nullptr) {\n        // 目標ノードは cur の右部分木にある\n        if (cur-&gt;val &lt; num)\n            cur = cur-&gt;right;\n        // 目標ノードは cur の左部分木にある\n        else if (cur-&gt;val &gt; num)\n            cur = cur-&gt;left;\n        // 目標ノードが見つかったらループを抜ける\n        else\n            break;\n    }\n    // 目標ノードを返す\n    return cur;\n}\n</code></pre> binary_search_tree.java<pre><code>/* ノードを探索 */\nTreeNode search(int num) {\n    TreeNode cur = root;\n    // ループで探索し、葉ノードを越えたら抜ける\n    while (cur != null) {\n        // 目標ノードは cur の右部分木にある\n        if (cur.val &lt; num)\n            cur = cur.right;\n        // 目標ノードは cur の左部分木にある\n        else if (cur.val &gt; num)\n            cur = cur.left;\n        // 目標ノードが見つかったらループを抜ける\n        else\n            break;\n    }\n    // 目標ノードを返す\n    return cur;\n}\n</code></pre> binary_search_tree.cs<pre><code>/* ノードを探索 */\nTreeNode? Search(int num) {\n    TreeNode? cur = root;\n    // ループで探索し、葉ノードを越えたら抜ける\n    while (cur != null) {\n        // 目標ノードは cur の右部分木にある\n        if (cur.val &lt; num) cur =\n            cur.right;\n        // 目標ノードは cur の左部分木にある\n        else if (cur.val &gt; num)\n            cur = cur.left;\n        // 目標ノードが見つかったらループを抜ける\n        else\n            break;\n    }\n    // 目標ノードを返す\n    return cur;\n}\n</code></pre> binary_search_tree.go<pre><code>/* ノードを探索 */\nfunc (bst *binarySearchTree) search(num int) *TreeNode {\n    node := bst.root\n    // ループで探索し、葉ノードを越えたら抜ける\n    for node != nil {\n        if node.Val.(int) &lt; num {\n            // 目標ノードは cur の右部分木にある\n            node = node.Right\n        } else if node.Val.(int) &gt; num {\n            // 目標ノードは cur の左部分木にある\n            node = node.Left\n        } else {\n            // 目標ノードが見つかったらループを抜ける\n            break\n        }\n    }\n    // 目標ノードを返す\n    return node\n}\n</code></pre> binary_search_tree.swift<pre><code>/* ノードを探索 */\nfunc search(num: Int) -&gt; TreeNode? {\n    var cur = root\n    // ループで探索し、葉ノードを越えたら抜ける\n    while cur != nil {\n        // 目標ノードは cur の右部分木にある\n        if cur!.val &lt; num {\n            cur = cur?.right\n        }\n        // 目標ノードは cur の左部分木にある\n        else if cur!.val &gt; num {\n            cur = cur?.left\n        }\n        // 目標ノードが見つかったらループを抜ける\n        else {\n            break\n        }\n    }\n    // 目標ノードを返す\n    return cur\n}\n</code></pre> binary_search_tree.js<pre><code>/* ノードを探索 */\nsearch(num) {\n    let cur = this.root;\n    // ループで探索し、葉ノードを越えたら抜ける\n    while (cur !== null) {\n        // 目標ノードは cur の右部分木にある\n        if (cur.val &lt; num) cur = cur.right;\n        // 目標ノードは cur の左部分木にある\n        else if (cur.val &gt; num) cur = cur.left;\n        // 目標ノードが見つかったらループを抜ける\n        else break;\n    }\n    // 目標ノードを返す\n    return cur;\n}\n</code></pre> binary_search_tree.ts<pre><code>/* ノードを探索 */\nsearch(num: number): TreeNode | null {\n    let cur = this.root;\n    // ループで探索し、葉ノードを越えたら抜ける\n    while (cur !== null) {\n        // 目標ノードは cur の右部分木にある\n        if (cur.val &lt; num) cur = cur.right;\n        // 目標ノードは cur の左部分木にある\n        else if (cur.val &gt; num) cur = cur.left;\n        // 目標ノードが見つかったらループを抜ける\n        else break;\n    }\n    // 目標ノードを返す\n    return cur;\n}\n</code></pre> binary_search_tree.dart<pre><code>/* ノードを探索 */\nTreeNode? search(int _num) {\n  TreeNode? cur = _root;\n  // ループで探索し、葉ノードを越えたら抜ける\n  while (cur != null) {\n    // 目標ノードは cur の右部分木にある\n    if (cur.val &lt; _num)\n      cur = cur.right;\n    // 目標ノードは cur の左部分木にある\n    else if (cur.val &gt; _num)\n      cur = cur.left;\n    // 目標ノードが見つかったらループを抜ける\n    else\n      break;\n  }\n  // 目標ノードを返す\n  return cur;\n}\n</code></pre> binary_search_tree.rs<pre><code>/* ノードを探索 */\npub fn search(&amp;self, num: i32) -&gt; OptionTreeNodeRc {\n    let mut cur = self.root.clone();\n    // ループで探索し、葉ノードを越えたら抜ける\n    while let Some(node) = cur.clone() {\n        match num.cmp(&amp;node.borrow().val) {\n            // 目標ノードは cur の右部分木にある\n            Ordering::Greater =&gt; cur = node.borrow().right.clone(),\n            // 目標ノードは cur の左部分木にある\n            Ordering::Less =&gt; cur = node.borrow().left.clone(),\n            // 目標ノードが見つかったらループを抜ける\n            Ordering::Equal =&gt; break,\n        }\n    }\n\n    // 目標ノードを返す\n    cur\n}\n</code></pre> binary_search_tree.c<pre><code>/* ノードを探索 */\nTreeNode *search(BinarySearchTree *bst, int num) {\n    TreeNode *cur = bst-&gt;root;\n    // ループで探索し、葉ノードを越えたら抜ける\n    while (cur != NULL) {\n        if (cur-&gt;val &lt; num) {\n            // 目標ノードは cur の右部分木にある\n            cur = cur-&gt;right;\n        } else if (cur-&gt;val &gt; num) {\n            // 目標ノードは cur の左部分木にある\n            cur = cur-&gt;left;\n        } else {\n            // 目標ノードが見つかったらループを抜ける\n            break;\n        }\n    }\n    // 目標ノードを返す\n    return cur;\n}\n</code></pre> binary_search_tree.kt<pre><code>/* ノードを探索 */\nfun search(num: Int): TreeNode? {\n    var cur = root\n    // ループで探索し、葉ノードを越えたら抜ける\n    while (cur != null) {\n        // 目標ノードは cur の右部分木にある\n        cur = if (cur._val &lt; num)\n            cur.right\n        // 目標ノードは cur の左部分木にある\n        else if (cur._val &gt; num)\n            cur.left\n        // 目標ノードが見つかったらループを抜ける\n        else\n            break\n    }\n    // 目標ノードを返す\n    return cur\n}\n</code></pre> binary_search_tree.rb<pre><code>### ノードを検索 ###\ndef search(num)\n  cur = @root\n\n  # ループで探索し、葉ノードを越えたら抜ける\n  while !cur.nil?\n    # 目標ノードは cur の右部分木にある\n    if cur.val &lt; num\n      cur = cur.right\n    # 目標ノードは cur の左部分木にある\n    elsif cur.val &gt; num\n      cur = cur.left\n    # 目標ノードが見つかったらループを抜ける\n    else\n      break\n    end\n  end\n\n  cur\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 7 章 &nbsp; 木","7.4 &nbsp; 二分探索木"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#2","level":3,"title":"2.   ノードの挿入","text":"<p>挿入する要素 <code>num</code> が与えられたとき、二分探索木の「左部分木 &lt; 根ノード &lt; 右部分木」という性質を保つため、挿入操作の流れは以下の図のようになります。</p> <ol> <li>挿入位置を探索する：探索操作と同様に、根ノードから出発し、現在のノード値と <code>num</code> の大小関係に基づいて下方向へ探索を繰り返し、葉ノードを越えて（<code>None</code> まで到達して）ループを抜けます。</li> <li>その位置にノードを挿入する：ノード <code>num</code> を初期化し、そのノードを <code>None</code> の位置に置きます。</li> </ol> <p></p> <p> 図 7-18   二分探索木にノードを挿入する </p> <p>コード実装では、次の 2 点に注意が必要です。</p> <ul> <li>二分探索木では重複ノードを許可しません。そうでないと定義に反するためです。したがって、挿入対象のノードが木内にすでに存在する場合は、挿入を行わずそのまま返します。</li> <li>ノード挿入を実現するために、ノード <code>pre</code> を用いて前回のループのノードを保持する必要があります。これにより、<code>None</code> までたどり着いたときにその親ノードを取得でき、ノード挿入を完了できます。</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_tree.py<pre><code>def insert(self, num: int):\n    \"\"\"ノードを挿入\"\"\"\n    # 木が空なら、根ノードを初期化する\n    if self._root is None:\n        self._root = TreeNode(num)\n        return\n    # ループで探索し、葉ノードを越えたら抜ける\n    cur, pre = self._root, None\n    while cur is not None:\n        # 重複ノードが見つかったら、直ちに返す\n        if cur.val == num:\n            return\n        pre = cur\n        # 挿入位置は cur の右部分木にある\n        if cur.val &lt; num:\n            cur = cur.right\n        # 挿入位置は cur の左部分木にある\n        else:\n            cur = cur.left\n    # ノードを挿入\n    node = TreeNode(num)\n    if pre.val &lt; num:\n        pre.right = node\n    else:\n        pre.left = node\n</code></pre> binary_search_tree.cpp<pre><code>/* ノードを挿入 */\nvoid insert(int num) {\n    // 木が空なら、根ノードを初期化する\n    if (root == nullptr) {\n        root = new TreeNode(num);\n        return;\n    }\n    TreeNode *cur = root, *pre = nullptr;\n    // ループで探索し、葉ノードを越えたら抜ける\n    while (cur != nullptr) {\n        // 重複ノードが見つかったら、直ちに返す\n        if (cur-&gt;val == num)\n            return;\n        pre = cur;\n        // 挿入位置は cur の右部分木にある\n        if (cur-&gt;val &lt; num)\n            cur = cur-&gt;right;\n        // 挿入位置は cur の左部分木にある\n        else\n            cur = cur-&gt;left;\n    }\n    // ノードを挿入\n    TreeNode *node = new TreeNode(num);\n    if (pre-&gt;val &lt; num)\n        pre-&gt;right = node;\n    else\n        pre-&gt;left = node;\n}\n</code></pre> binary_search_tree.java<pre><code>/* ノードを挿入 */\nvoid insert(int num) {\n    // 木が空なら、根ノードを初期化する\n    if (root == null) {\n        root = new TreeNode(num);\n        return;\n    }\n    TreeNode cur = root, pre = null;\n    // ループで探索し、葉ノードを越えたら抜ける\n    while (cur != null) {\n        // 重複ノードが見つかったら、直ちに返す\n        if (cur.val == num)\n            return;\n        pre = cur;\n        // 挿入位置は cur の右部分木にある\n        if (cur.val &lt; num)\n            cur = cur.right;\n        // 挿入位置は cur の左部分木にある\n        else\n            cur = cur.left;\n    }\n    // ノードを挿入\n    TreeNode node = new TreeNode(num);\n    if (pre.val &lt; num)\n        pre.right = node;\n    else\n        pre.left = node;\n}\n</code></pre> binary_search_tree.cs<pre><code>/* ノードを挿入 */\nvoid Insert(int num) {\n    // 木が空なら、根ノードを初期化する\n    if (root == null) {\n        root = new TreeNode(num);\n        return;\n    }\n    TreeNode? cur = root, pre = null;\n    // ループで探索し、葉ノードを越えたら抜ける\n    while (cur != null) {\n        // 重複ノードが見つかったら、直ちに返す\n        if (cur.val == num)\n            return;\n        pre = cur;\n        // 挿入位置は cur の右部分木にある\n        if (cur.val &lt; num)\n            cur = cur.right;\n        // 挿入位置は cur の左部分木にある\n        else\n            cur = cur.left;\n    }\n\n    // ノードを挿入\n    TreeNode node = new(num);\n    if (pre != null) {\n        if (pre.val &lt; num)\n            pre.right = node;\n        else\n            pre.left = node;\n    }\n}\n</code></pre> binary_search_tree.go<pre><code>/* ノードを挿入 */\nfunc (bst *binarySearchTree) insert(num int) {\n    cur := bst.root\n    // 木が空なら、根ノードを初期化する\n    if cur == nil {\n        bst.root = NewTreeNode(num)\n        return\n    }\n    // 挿入対象ノードの直前のノード位置\n    var pre *TreeNode = nil\n    // ループで探索し、葉ノードを越えたら抜ける\n    for cur != nil {\n        if cur.Val == num {\n            return\n        }\n        pre = cur\n        if cur.Val.(int) &lt; num {\n            cur = cur.Right\n        } else {\n            cur = cur.Left\n        }\n    }\n    // ノードを挿入\n    node := NewTreeNode(num)\n    if pre.Val.(int) &lt; num {\n        pre.Right = node\n    } else {\n        pre.Left = node\n    }\n}\n</code></pre> binary_search_tree.swift<pre><code>/* ノードを挿入 */\nfunc insert(num: Int) {\n    // 木が空なら、根ノードを初期化する\n    if root == nil {\n        root = TreeNode(x: num)\n        return\n    }\n    var cur = root\n    var pre: TreeNode?\n    // ループで探索し、葉ノードを越えたら抜ける\n    while cur != nil {\n        // 重複ノードが見つかったら、直ちに返す\n        if cur!.val == num {\n            return\n        }\n        pre = cur\n        // 挿入位置は cur の右部分木にある\n        if cur!.val &lt; num {\n            cur = cur?.right\n        }\n        // 挿入位置は cur の左部分木にある\n        else {\n            cur = cur?.left\n        }\n    }\n    // ノードを挿入\n    let node = TreeNode(x: num)\n    if pre!.val &lt; num {\n        pre?.right = node\n    } else {\n        pre?.left = node\n    }\n}\n</code></pre> binary_search_tree.js<pre><code>/* ノードを挿入 */\ninsert(num) {\n    // 木が空なら、根ノードを初期化する\n    if (this.root === null) {\n        this.root = new TreeNode(num);\n        return;\n    }\n    let cur = this.root,\n        pre = null;\n    // ループで探索し、葉ノードを越えたら抜ける\n    while (cur !== null) {\n        // 重複ノードが見つかったら、直ちに返す\n        if (cur.val === num) return;\n        pre = cur;\n        // 挿入位置は cur の右部分木にある\n        if (cur.val &lt; num) cur = cur.right;\n        // 挿入位置は cur の左部分木にある\n        else cur = cur.left;\n    }\n    // ノードを挿入\n    const node = new TreeNode(num);\n    if (pre.val &lt; num) pre.right = node;\n    else pre.left = node;\n}\n</code></pre> binary_search_tree.ts<pre><code>/* ノードを挿入 */\ninsert(num: number): void {\n    // 木が空なら、根ノードを初期化する\n    if (this.root === null) {\n        this.root = new TreeNode(num);\n        return;\n    }\n    let cur: TreeNode | null = this.root,\n        pre: TreeNode | null = null;\n    // ループで探索し、葉ノードを越えたら抜ける\n    while (cur !== null) {\n        // 重複ノードが見つかったら、直ちに返す\n        if (cur.val === num) return;\n        pre = cur;\n        // 挿入位置は cur の右部分木にある\n        if (cur.val &lt; num) cur = cur.right;\n        // 挿入位置は cur の左部分木にある\n        else cur = cur.left;\n    }\n    // ノードを挿入\n    const node = new TreeNode(num);\n    if (pre!.val &lt; num) pre!.right = node;\n    else pre!.left = node;\n}\n</code></pre> binary_search_tree.dart<pre><code>/* ノードを挿入 */\nvoid insert(int _num) {\n  // 木が空なら、根ノードを初期化する\n  if (_root == null) {\n    _root = TreeNode(_num);\n    return;\n  }\n  TreeNode? cur = _root;\n  TreeNode? pre = null;\n  // ループで探索し、葉ノードを越えたら抜ける\n  while (cur != null) {\n    // 重複ノードが見つかったら、直ちに返す\n    if (cur.val == _num) return;\n    pre = cur;\n    // 挿入位置は cur の右部分木にある\n    if (cur.val &lt; _num)\n      cur = cur.right;\n    // 挿入位置は cur の左部分木にある\n    else\n      cur = cur.left;\n  }\n  // ノードを挿入\n  TreeNode? node = TreeNode(_num);\n  if (pre!.val &lt; _num)\n    pre.right = node;\n  else\n    pre.left = node;\n}\n</code></pre> binary_search_tree.rs<pre><code>/* ノードを挿入 */\npub fn insert(&amp;mut self, num: i32) {\n    // 木が空なら、根ノードを初期化する\n    if self.root.is_none() {\n        self.root = Some(TreeNode::new(num));\n        return;\n    }\n    let mut cur = self.root.clone();\n    let mut pre = None;\n    // ループで探索し、葉ノードを越えたら抜ける\n    while let Some(node) = cur.clone() {\n        match num.cmp(&amp;node.borrow().val) {\n            // 重複ノードが見つかったら、直ちに返す\n            Ordering::Equal =&gt; return,\n            // 挿入位置は cur の右部分木にある\n            Ordering::Greater =&gt; {\n                pre = cur.clone();\n                cur = node.borrow().right.clone();\n            }\n            // 挿入位置は cur の左部分木にある\n            Ordering::Less =&gt; {\n                pre = cur.clone();\n                cur = node.borrow().left.clone();\n            }\n        }\n    }\n    // ノードを挿入\n    let pre = pre.unwrap();\n    let node = Some(TreeNode::new(num));\n    if num &gt; pre.borrow().val {\n        pre.borrow_mut().right = node;\n    } else {\n        pre.borrow_mut().left = node;\n    }\n}\n</code></pre> binary_search_tree.c<pre><code>/* ノードを挿入 */\nvoid insert(BinarySearchTree *bst, int num) {\n    // 木が空なら、根ノードを初期化する\n    if (bst-&gt;root == NULL) {\n        bst-&gt;root = newTreeNode(num);\n        return;\n    }\n    TreeNode *cur = bst-&gt;root, *pre = NULL;\n    // ループで探索し、葉ノードを越えたら抜ける\n    while (cur != NULL) {\n        // 重複ノードが見つかったら、直ちに返す\n        if (cur-&gt;val == num) {\n            return;\n        }\n        pre = cur;\n        if (cur-&gt;val &lt; num) {\n            // 挿入位置は cur の右部分木にある\n            cur = cur-&gt;right;\n        } else {\n            // 挿入位置は cur の左部分木にある\n            cur = cur-&gt;left;\n        }\n    }\n    // ノードを挿入\n    TreeNode *node = newTreeNode(num);\n    if (pre-&gt;val &lt; num) {\n        pre-&gt;right = node;\n    } else {\n        pre-&gt;left = node;\n    }\n}\n</code></pre> binary_search_tree.kt<pre><code>/* ノードを挿入 */\nfun insert(num: Int) {\n    // 木が空なら、根ノードを初期化する\n    if (root == null) {\n        root = TreeNode(num)\n        return\n    }\n    var cur = root\n    var pre: TreeNode? = null\n    // ループで探索し、葉ノードを越えたら抜ける\n    while (cur != null) {\n        // 重複ノードが見つかったら、直ちに返す\n        if (cur._val == num)\n            return\n        pre = cur\n        // 挿入位置は cur の右部分木にある\n        cur = if (cur._val &lt; num)\n            cur.right\n        // 挿入位置は cur の左部分木にある\n        else\n            cur.left\n    }\n    // ノードを挿入\n    val node = TreeNode(num)\n    if (pre?._val!! &lt; num)\n        pre.right = node\n    else\n        pre.left = node\n}\n</code></pre> binary_search_tree.rb<pre><code>### ノードを挿入 ###\ndef insert(num)\n  # 木が空なら、根ノードを初期化する\n  if @root.nil?\n    @root = TreeNode.new(num)\n    return\n  end\n\n  # ループで探索し、葉ノードを越えたら抜ける\n  cur, pre = @root, nil\n  while !cur.nil?\n    # 重複ノードが見つかったら、直ちに返す\n    return if cur.val == num\n\n    pre = cur\n    # 挿入位置は cur の右部分木にある\n    if cur.val &lt; num\n      cur = cur.right\n    # 挿入位置は cur の左部分木にある\n    else\n      cur = cur.left\n    end\n  end\n\n  # ノードを挿入\n  node = TreeNode.new(num)\n  if pre.val &lt; num\n    pre.right = node\n  else\n    pre.left = node\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>ノード探索と同様に、ノード挿入には \\(O(\\log n)\\) 時間を要します。</p>","path":["第 7 章 &nbsp; 木","7.4 &nbsp; 二分探索木"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#3","level":3,"title":"3.   ノードの削除","text":"<p>まず二分木内で目標ノードを見つけ、その後で削除します。ノード挿入と同様に、削除操作の完了後も二分探索木の「左部分木 &lt; 根ノード &lt; 右部分木」という性質が保たれる必要があります。そのため、目標ノードの子ノード数に応じて、0、1、2 の 3 つのケースに分けて対応する削除操作を行います。</p> <p>以下の図に示すように、削除対象ノードの次数が \\(0\\) のとき、そのノードは葉ノードであり、直接削除できます。</p> <p></p> <p> 図 7-19   二分探索木でノードを削除する（次数 0 ） </p> <p>以下の図に示すように、削除対象ノードの次数が \\(1\\) のとき、削除対象ノードをその子ノードで置き換えれば十分です。</p> <p></p> <p> 図 7-20   二分探索木でノードを削除する（次数 1 ） </p> <p>削除対象ノードの次数が \\(2\\) のときは、直接削除できず、別のノードでそのノードを置き換える必要があります。二分探索木の「左部分木 \\(&lt;\\) 根ノード \\(&lt;\\) 右部分木」という性質を保つ必要があるため、このノードには右部分木の最小ノードまたは左部分木の最大ノードを使えます。</p> <p>右部分木の最小ノード（中順走査で次のノード）を選ぶと仮定すると、削除操作の流れは以下の図のようになります。</p> <ol> <li>削除対象ノードの「中順走査列」における次のノードを見つけ、<code>tmp</code> と記します。</li> <li><code>tmp</code> の値で削除対象ノードの値を上書きし、木の中でノード <code>tmp</code> を再帰的に削除します。</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p> 図 7-21   二分探索木でノードを削除する（次数 2 ） </p> <p>ノード削除操作も同様に \\(O(\\log n)\\) 時間を要します。削除対象ノードの探索に \\(O(\\log n)\\) 時間、中順走査の後続ノードの取得に \\(O(\\log n)\\) 時間が必要です。コード例は次のとおりです。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_tree.py<pre><code>def remove(self, num: int):\n    \"\"\"ノードを削除\"\"\"\n    # 木が空なら、そのまま早期リターンする\n    if self._root is None:\n        return\n    # ループで探索し、葉ノードを越えたら抜ける\n    cur, pre = self._root, None\n    while cur is not None:\n        # 削除対象のノードが見つかったら、ループを抜ける\n        if cur.val == num:\n            break\n        pre = cur\n        # 削除対象ノードは cur の右部分木にある\n        if cur.val &lt; num:\n            cur = cur.right\n        # 削除対象ノードは cur の左部分木にある\n        else:\n            cur = cur.left\n    # 削除対象ノードがなければそのまま返す\n    if cur is None:\n        return\n\n    # 子ノード数 = 0 or 1\n    if cur.left is None or cur.right is None:\n        # 子ノード数が 0 / 1 のとき、child = null / その子ノード\n        child = cur.left or cur.right\n        # ノード cur を削除する\n        if cur != self._root:\n            if pre.left == cur:\n                pre.left = child\n            else:\n                pre.right = child\n        else:\n            # 削除ノードが根ノードなら、根ノードを再設定\n            self._root = child\n    # 子ノード数 = 2\n    else:\n        # 中順走査における cur の次ノードを取得\n        tmp: TreeNode = cur.right\n        while tmp.left is not None:\n            tmp = tmp.left\n        # ノード tmp を再帰的に削除\n        self.remove(tmp.val)\n        # tmp で cur を上書きする\n        cur.val = tmp.val\n</code></pre> binary_search_tree.cpp<pre><code>/* ノードを削除 */\nvoid remove(int num) {\n    // 木が空なら、そのまま早期リターンする\n    if (root == nullptr)\n        return;\n    TreeNode *cur = root, *pre = nullptr;\n    // ループで探索し、葉ノードを越えたら抜ける\n    while (cur != nullptr) {\n        // 削除対象のノードが見つかったら、ループを抜ける\n        if (cur-&gt;val == num)\n            break;\n        pre = cur;\n        // 削除対象ノードは cur の右部分木にある\n        if (cur-&gt;val &lt; num)\n            cur = cur-&gt;right;\n        // 削除対象ノードは cur の左部分木にある\n        else\n            cur = cur-&gt;left;\n    }\n    // 削除対象ノードがなければそのまま返す\n    if (cur == nullptr)\n        return;\n    // 子ノード数 = 0 or 1\n    if (cur-&gt;left == nullptr || cur-&gt;right == nullptr) {\n        // 子ノード数 = 0 / 1 のとき、child = nullptr / その子ノード\n        TreeNode *child = cur-&gt;left != nullptr ? cur-&gt;left : cur-&gt;right;\n        // ノード cur を削除する\n        if (cur != root) {\n            if (pre-&gt;left == cur)\n                pre-&gt;left = child;\n            else\n                pre-&gt;right = child;\n        } else {\n            // 削除ノードが根ノードなら、根ノードを再設定\n            root = child;\n        }\n        // メモリを解放する\n        delete cur;\n    }\n    // 子ノード数 = 2\n    else {\n        // 中順走査における cur の次ノードを取得\n        TreeNode *tmp = cur-&gt;right;\n        while (tmp-&gt;left != nullptr) {\n            tmp = tmp-&gt;left;\n        }\n        int tmpVal = tmp-&gt;val;\n        // ノード tmp を再帰的に削除\n        remove(tmp-&gt;val);\n        // tmp で cur を上書きする\n        cur-&gt;val = tmpVal;\n    }\n}\n</code></pre> binary_search_tree.java<pre><code>/* ノードを削除 */\nvoid remove(int num) {\n    // 木が空なら、そのまま早期リターンする\n    if (root == null)\n        return;\n    TreeNode cur = root, pre = null;\n    // ループで探索し、葉ノードを越えたら抜ける\n    while (cur != null) {\n        // 削除対象のノードが見つかったら、ループを抜ける\n        if (cur.val == num)\n            break;\n        pre = cur;\n        // 削除対象ノードは cur の右部分木にある\n        if (cur.val &lt; num)\n            cur = cur.right;\n        // 削除対象ノードは cur の左部分木にある\n        else\n            cur = cur.left;\n    }\n    // 削除対象ノードがなければそのまま返す\n    if (cur == null)\n        return;\n    // 子ノード数 = 0 or 1\n    if (cur.left == null || cur.right == null) {\n        // 子ノード数が 0 / 1 のとき、child = null / その子ノード\n        TreeNode child = cur.left != null ? cur.left : cur.right;\n        // ノード cur を削除する\n        if (cur != root) {\n            if (pre.left == cur)\n                pre.left = child;\n            else\n                pre.right = child;\n        } else {\n            // 削除ノードが根ノードなら、根ノードを再設定\n            root = child;\n        }\n    }\n    // 子ノード数 = 2\n    else {\n        // 中順走査における cur の次ノードを取得\n        TreeNode tmp = cur.right;\n        while (tmp.left != null) {\n            tmp = tmp.left;\n        }\n        // ノード tmp を再帰的に削除\n        remove(tmp.val);\n        // tmp で cur を上書きする\n        cur.val = tmp.val;\n    }\n}\n</code></pre> binary_search_tree.cs<pre><code>/* ノードを削除 */\nvoid Remove(int num) {\n    // 木が空なら、そのまま早期リターンする\n    if (root == null)\n        return;\n    TreeNode? cur = root, pre = null;\n    // ループで探索し、葉ノードを越えたら抜ける\n    while (cur != null) {\n        // 削除対象のノードが見つかったら、ループを抜ける\n        if (cur.val == num)\n            break;\n        pre = cur;\n        // 削除対象ノードは cur の右部分木にある\n        if (cur.val &lt; num)\n            cur = cur.right;\n        // 削除対象ノードは cur の左部分木にある\n        else\n            cur = cur.left;\n    }\n    // 削除対象ノードがなければそのまま返す\n    if (cur == null)\n        return;\n    // 子ノード数 = 0 or 1\n    if (cur.left == null || cur.right == null) {\n        // 子ノード数が 0 / 1 のとき、child = null / その子ノード\n        TreeNode? child = cur.left ?? cur.right;\n        // ノード cur を削除する\n        if (cur != root) {\n            if (pre!.left == cur)\n                pre.left = child;\n            else\n                pre.right = child;\n        } else {\n            // 削除ノードが根ノードなら、根ノードを再設定\n            root = child;\n        }\n    }\n    // 子ノード数 = 2\n    else {\n        // 中順走査における cur の次ノードを取得\n        TreeNode? tmp = cur.right;\n        while (tmp.left != null) {\n            tmp = tmp.left;\n        }\n        // ノード tmp を再帰的に削除\n        Remove(tmp.val!.Value);\n        // tmp で cur を上書きする\n        cur.val = tmp.val;\n    }\n}\n</code></pre> binary_search_tree.go<pre><code>/* ノードを削除 */\nfunc (bst *binarySearchTree) remove(num int) {\n    cur := bst.root\n    // 木が空なら、そのまま早期リターンする\n    if cur == nil {\n        return\n    }\n    // 削除対象ノードの直前のノード位置\n    var pre *TreeNode = nil\n    // ループで探索し、葉ノードを越えたら抜ける\n    for cur != nil {\n        if cur.Val == num {\n            break\n        }\n        pre = cur\n        if cur.Val.(int) &lt; num {\n            // 削除対象ノードは右部分木にある\n            cur = cur.Right\n        } else {\n            // 削除対象ノードは左部分木にある\n            cur = cur.Left\n        }\n    }\n    // 削除対象ノードがなければそのまま返す\n    if cur == nil {\n        return\n    }\n    // 子ノード数は 0 または 1\n    if cur.Left == nil || cur.Right == nil {\n        var child *TreeNode = nil\n        // 削除対象ノードの子ノードを取り出す\n        if cur.Left != nil {\n            child = cur.Left\n        } else {\n            child = cur.Right\n        }\n        // ノード cur を削除する\n        if cur != bst.root {\n            if pre.Left == cur {\n                pre.Left = child\n            } else {\n                pre.Right = child\n            }\n        } else {\n            // 削除ノードが根ノードなら、根ノードを再設定\n            bst.root = child\n        }\n        // 子ノード数は 2\n    } else {\n        // 中順走査で削除対象ノード `cur` の次のノードを取得する\n        tmp := cur.Right\n        for tmp.Left != nil {\n            tmp = tmp.Left\n        }\n        // ノード tmp を再帰的に削除\n        bst.remove(tmp.Val.(int))\n        // tmp で cur を上書きする\n        cur.Val = tmp.Val\n    }\n}\n</code></pre> binary_search_tree.swift<pre><code>/* ノードを削除 */\nfunc remove(num: Int) {\n    // 木が空なら、そのまま早期リターンする\n    if root == nil {\n        return\n    }\n    var cur = root\n    var pre: TreeNode?\n    // ループで探索し、葉ノードを越えたら抜ける\n    while cur != nil {\n        // 削除対象のノードが見つかったら、ループを抜ける\n        if cur!.val == num {\n            break\n        }\n        pre = cur\n        // 削除対象ノードは cur の右部分木にある\n        if cur!.val &lt; num {\n            cur = cur?.right\n        }\n        // 削除対象ノードは cur の左部分木にある\n        else {\n            cur = cur?.left\n        }\n    }\n    // 削除対象ノードがなければそのまま返す\n    if cur == nil {\n        return\n    }\n    // 子ノード数 = 0 or 1\n    if cur?.left == nil || cur?.right == nil {\n        // 子ノード数が 0 / 1 のとき、child = null / その子ノード\n        let child = cur?.left ?? cur?.right\n        // ノード cur を削除する\n        if cur !== root {\n            if pre?.left === cur {\n                pre?.left = child\n            } else {\n                pre?.right = child\n            }\n        } else {\n            // 削除ノードが根ノードなら、根ノードを再設定\n            root = child\n        }\n    }\n    // 子ノード数 = 2\n    else {\n        // 中順走査における cur の次ノードを取得\n        var tmp = cur?.right\n        while tmp?.left != nil {\n            tmp = tmp?.left\n        }\n        // ノード tmp を再帰的に削除\n        remove(num: tmp!.val)\n        // tmp で cur を上書きする\n        cur?.val = tmp!.val\n    }\n}\n</code></pre> binary_search_tree.js<pre><code>/* ノードを削除 */\nremove(num) {\n    // 木が空なら、そのまま早期リターンする\n    if (this.root === null) return;\n    let cur = this.root,\n        pre = null;\n    // ループで探索し、葉ノードを越えたら抜ける\n    while (cur !== null) {\n        // 削除対象のノードが見つかったら、ループを抜ける\n        if (cur.val === num) break;\n        pre = cur;\n        // 削除対象ノードは cur の右部分木にある\n        if (cur.val &lt; num) cur = cur.right;\n        // 削除対象ノードは cur の左部分木にある\n        else cur = cur.left;\n    }\n    // 削除対象ノードがなければそのまま返す\n    if (cur === null) return;\n    // 子ノード数 = 0 or 1\n    if (cur.left === null || cur.right === null) {\n        // 子ノード数が 0 / 1 のとき、child = null / その子ノード\n        const child = cur.left !== null ? cur.left : cur.right;\n        // ノード cur を削除する\n        if (cur !== this.root) {\n            if (pre.left === cur) pre.left = child;\n            else pre.right = child;\n        } else {\n            // 削除ノードが根ノードなら、根ノードを再設定\n            this.root = child;\n        }\n    }\n    // 子ノード数 = 2\n    else {\n        // 中順走査における cur の次ノードを取得\n        let tmp = cur.right;\n        while (tmp.left !== null) {\n            tmp = tmp.left;\n        }\n        // ノード tmp を再帰的に削除\n        this.remove(tmp.val);\n        // tmp で cur を上書きする\n        cur.val = tmp.val;\n    }\n}\n</code></pre> binary_search_tree.ts<pre><code>/* ノードを削除 */\nremove(num: number): void {\n    // 木が空なら、そのまま早期リターンする\n    if (this.root === null) return;\n    let cur: TreeNode | null = this.root,\n        pre: TreeNode | null = null;\n    // ループで探索し、葉ノードを越えたら抜ける\n    while (cur !== null) {\n        // 削除対象のノードが見つかったら、ループを抜ける\n        if (cur.val === num) break;\n        pre = cur;\n        // 削除対象ノードは cur の右部分木にある\n        if (cur.val &lt; num) cur = cur.right;\n        // 削除対象ノードは cur の左部分木にある\n        else cur = cur.left;\n    }\n    // 削除対象ノードがなければそのまま返す\n    if (cur === null) return;\n    // 子ノード数 = 0 or 1\n    if (cur.left === null || cur.right === null) {\n        // 子ノード数が 0 / 1 のとき、child = null / その子ノード\n        const child: TreeNode | null =\n            cur.left !== null ? cur.left : cur.right;\n        // ノード cur を削除する\n        if (cur !== this.root) {\n            if (pre!.left === cur) pre!.left = child;\n            else pre!.right = child;\n        } else {\n            // 削除ノードが根ノードなら、根ノードを再設定\n            this.root = child;\n        }\n    }\n    // 子ノード数 = 2\n    else {\n        // 中順走査における cur の次ノードを取得\n        let tmp: TreeNode | null = cur.right;\n        while (tmp!.left !== null) {\n            tmp = tmp!.left;\n        }\n        // ノード tmp を再帰的に削除\n        this.remove(tmp!.val);\n        // tmp で cur を上書きする\n        cur.val = tmp!.val;\n    }\n}\n</code></pre> binary_search_tree.dart<pre><code>/* ノードを削除 */\nvoid remove(int _num) {\n  // 木が空なら、そのまま早期リターンする\n  if (_root == null) return;\n  TreeNode? cur = _root;\n  TreeNode? pre = null;\n  // ループで探索し、葉ノードを越えたら抜ける\n  while (cur != null) {\n    // 削除対象のノードが見つかったら、ループを抜ける\n    if (cur.val == _num) break;\n    pre = cur;\n    // 削除対象ノードは cur の右部分木にある\n    if (cur.val &lt; _num)\n      cur = cur.right;\n    // 削除対象ノードは cur の左部分木にある\n    else\n      cur = cur.left;\n  }\n  // 削除対象ノードがない場合は、そのまま返す\n  if (cur == null) return;\n  // 子ノード数 = 0 or 1\n  if (cur.left == null || cur.right == null) {\n    // 子ノード数が 0 / 1 のとき、child = null / その子ノード\n    TreeNode? child = cur.left ?? cur.right;\n    // ノード cur を削除する\n    if (cur != _root) {\n      if (pre!.left == cur)\n        pre.left = child;\n      else\n        pre.right = child;\n    } else {\n      // 削除ノードが根ノードなら、根ノードを再設定\n      _root = child;\n    }\n  } else {\n    // 子ノード数 = 2\n    // 中順走査における cur の次のノードを取得\n    TreeNode? tmp = cur.right;\n    while (tmp!.left != null) {\n      tmp = tmp.left;\n    }\n    // ノード tmp を再帰的に削除\n    remove(tmp.val);\n    // tmp で cur を上書きする\n    cur.val = tmp.val;\n  }\n}\n</code></pre> binary_search_tree.rs<pre><code>/* ノードを削除 */\npub fn remove(&amp;mut self, num: i32) {\n    // 木が空なら、そのまま早期リターンする\n    if self.root.is_none() {\n        return;\n    }\n    let mut cur = self.root.clone();\n    let mut pre = None;\n    // ループで探索し、葉ノードを越えたら抜ける\n    while let Some(node) = cur.clone() {\n        match num.cmp(&amp;node.borrow().val) {\n            // 削除対象のノードが見つかったら、ループを抜ける\n            Ordering::Equal =&gt; break,\n            // 削除対象ノードは cur の右部分木にある\n            Ordering::Greater =&gt; {\n                pre = cur.clone();\n                cur = node.borrow().right.clone();\n            }\n            // 削除対象ノードは cur の左部分木にある\n            Ordering::Less =&gt; {\n                pre = cur.clone();\n                cur = node.borrow().left.clone();\n            }\n        }\n    }\n    // 削除対象ノードがなければそのまま返す\n    if cur.is_none() {\n        return;\n    }\n    let cur = cur.unwrap();\n    let (left_child, right_child) = (cur.borrow().left.clone(), cur.borrow().right.clone());\n    match (left_child.clone(), right_child.clone()) {\n        // 子ノード数 = 0 or 1\n        (None, None) | (Some(_), None) | (None, Some(_)) =&gt; {\n            // 子ノード数 = 0 / 1 のとき、child = nullptr / その子ノード\n            let child = left_child.or(right_child);\n            let pre = pre.unwrap();\n            // ノード cur を削除する\n            if !Rc::ptr_eq(&amp;cur, self.root.as_ref().unwrap()) {\n                let left = pre.borrow().left.clone();\n                if left.is_some() &amp;&amp; Rc::ptr_eq(left.as_ref().unwrap(), &amp;cur) {\n                    pre.borrow_mut().left = child;\n                } else {\n                    pre.borrow_mut().right = child;\n                }\n            } else {\n                // 削除ノードが根ノードなら、根ノードを再設定\n                self.root = child;\n            }\n        }\n        // 子ノード数 = 2\n        (Some(_), Some(_)) =&gt; {\n            // 中順走査における cur の次ノードを取得\n            let mut tmp = cur.borrow().right.clone();\n            while let Some(node) = tmp.clone() {\n                if node.borrow().left.is_some() {\n                    tmp = node.borrow().left.clone();\n                } else {\n                    break;\n                }\n            }\n            let tmp_val = tmp.unwrap().borrow().val;\n            // ノード tmp を再帰的に削除\n            self.remove(tmp_val);\n            // tmp で cur を上書きする\n            cur.borrow_mut().val = tmp_val;\n        }\n    }\n}\n</code></pre> binary_search_tree.c<pre><code>/* ノードを削除 */\n// stdio.h を導入しているため、ここでは remove 識別子を使えない\nvoid removeItem(BinarySearchTree *bst, int num) {\n    // 木が空なら、そのまま早期リターンする\n    if (bst-&gt;root == NULL)\n        return;\n    TreeNode *cur = bst-&gt;root, *pre = NULL;\n    // ループで探索し、葉ノードを越えたら抜ける\n    while (cur != NULL) {\n        // 削除対象のノードが見つかったら、ループを抜ける\n        if (cur-&gt;val == num)\n            break;\n        pre = cur;\n        if (cur-&gt;val &lt; num) {\n            // 削除対象ノードは root の右部分木にある\n            cur = cur-&gt;right;\n        } else {\n            // 削除対象ノードは root の左部分木にある\n            cur = cur-&gt;left;\n        }\n    }\n    // 削除対象ノードがなければそのまま返す\n    if (cur == NULL)\n        return;\n    // 削除対象ノードに子ノードがあるかを判定する\n    if (cur-&gt;left == NULL || cur-&gt;right == NULL) {\n        /* 子ノード数 = 0 or 1 */\n        // 子ノード数 = 0 / 1 のとき、child = nullptr / その子ノード\n        TreeNode *child = cur-&gt;left != NULL ? cur-&gt;left : cur-&gt;right;\n        // ノード cur を削除する\n        if (pre-&gt;left == cur) {\n            pre-&gt;left = child;\n        } else {\n            pre-&gt;right = child;\n        }\n        // メモリを解放する\n        free(cur);\n    } else {\n        /* 子ノード数 = 2 */\n        // 中順走査における cur の次ノードを取得\n        TreeNode *tmp = cur-&gt;right;\n        while (tmp-&gt;left != NULL) {\n            tmp = tmp-&gt;left;\n        }\n        int tmpVal = tmp-&gt;val;\n        // ノード tmp を再帰的に削除\n        removeItem(bst, tmp-&gt;val);\n        // tmp で cur を上書きする\n        cur-&gt;val = tmpVal;\n    }\n}\n</code></pre> binary_search_tree.kt<pre><code>/* ノードを削除 */\nfun remove(num: Int) {\n    // 木が空なら、そのまま早期リターンする\n    if (root == null)\n        return\n    var cur = root\n    var pre: TreeNode? = null\n    // ループで探索し、葉ノードを越えたら抜ける\n    while (cur != null) {\n        // 削除対象のノードが見つかったら、ループを抜ける\n        if (cur._val == num)\n            break\n        pre = cur\n        // 削除対象ノードは cur の右部分木にある\n        cur = if (cur._val &lt; num)\n            cur.right\n        // 削除対象ノードは cur の左部分木にある\n        else\n            cur.left\n    }\n    // 削除対象ノードがなければそのまま返す\n    if (cur == null)\n        return\n    // 子ノード数 = 0 or 1\n    if (cur.left == null || cur.right == null) {\n        // 子ノード数が 0 / 1 のとき、child = null / その子ノード\n        val child = if (cur.left != null)\n            cur.left\n        else\n            cur.right\n        // ノード cur を削除する\n        if (cur != root) {\n            if (pre!!.left == cur)\n                pre.left = child\n            else\n                pre.right = child\n        } else {\n            // 削除ノードが根ノードなら、根ノードを再設定\n            root = child\n        }\n        // 子ノード数 = 2\n    } else {\n        // 中順走査における cur の次ノードを取得\n        var tmp = cur.right\n        while (tmp!!.left != null) {\n            tmp = tmp.left\n        }\n        // ノード tmp を再帰的に削除\n        remove(tmp._val)\n        // tmp で cur を上書きする\n        cur._val = tmp._val\n    }\n}\n</code></pre> binary_search_tree.rb<pre><code>### ノードを削除 ###\ndef remove(num)\n  # 木が空なら、そのまま早期リターンする\n  return if @root.nil?\n\n  # ループで探索し、葉ノードを越えたら抜ける\n  cur, pre = @root, nil\n  while !cur.nil?\n    # 削除対象のノードが見つかったら、ループを抜ける\n    break if cur.val == num\n\n    pre = cur\n    # 削除対象ノードは cur の右部分木にある\n    if cur.val &lt; num\n      cur = cur.right\n    # 削除対象ノードは cur の左部分木にある\n    else\n      cur = cur.left\n    end\n  end\n  # 削除対象ノードがなければそのまま返す\n  return if cur.nil?\n\n  # 子ノード数 = 0 or 1\n  if cur.left.nil? || cur.right.nil?\n    # 子ノード数が 0 / 1 のとき、child = null / その子ノード\n    child = cur.left || cur.right\n    # ノード cur を削除する\n    if cur != @root\n      if pre.left == cur\n        pre.left = child\n      else\n        pre.right = child\n      end\n    else\n      # 削除ノードが根ノードなら、根ノードを再設定\n      @root = child\n    end\n  # 子ノード数 = 2\n  else\n    # 中順走査における cur の次ノードを取得\n    tmp = cur.right\n    while !tmp.left.nil?\n      tmp = tmp.left\n    end\n    # ノード tmp を再帰的に削除\n    remove(tmp.val)\n    # tmp で cur を上書きする\n    cur.val = tmp.val\n  end\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 7 章 &nbsp; 木","7.4 &nbsp; 二分探索木"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#4","level":3,"title":"4.   中順走査は昇順","text":"<p>以下の図に示すように、二分木の中順走査は「左 \\(\\rightarrow\\) 根 \\(\\rightarrow\\) 右」という順序に従い、二分探索木は「左子ノード \\(&lt;\\) 根ノード \\(&lt;\\) 右子ノード」という大小関係を満たします。</p> <p>これは、二分探索木で中順走査を行うと常に次の最小ノードが優先して走査されることを意味し、そこから重要な性質が導かれます。二分探索木の中順走査列は昇順です。</p> <p>中順走査が昇順になる性質を利用すれば、二分探索木から整列済みデータを取得するのに必要な時間は \\(O(n)\\) のみで、追加のソート操作は不要です。非常に効率的です。</p> <p></p> <p> 図 7-22   二分探索木の中順走査列 </p>","path":["第 7 章 &nbsp; 木","7.4 &nbsp; 二分探索木"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#742","level":2,"title":"7.4.2   二分探索木の効率","text":"<p>あるデータ集合が与えられたとき、配列または二分探索木で格納する場合を考えます。次の表を見ると、二分探索木の各操作の時間計算量はいずれも対数オーダーであり、安定して高効率です。高頻度の追加と低頻度の探索・削除という場面でのみ、配列のほうが二分探索木より効率的です。</p> <p> 表 7-2   配列と探索木の効率比較 </p> 無秩序配列 二分探索木 要素の探索 \\(O(n)\\) \\(O(\\log n)\\) 要素の挿入 \\(O(1)\\) \\(O(\\log n)\\) 要素の削除 \\(O(n)\\) \\(O(\\log n)\\) <p>理想的な状況では、二分探索木は「平衡」しており、その場合は \\(\\log n\\) 回のループ内で任意のノードを探索できます。</p> <p>しかし、二分探索木でノードの挿入と削除を繰り返すと、二分木が以下の図のような連結リストへ退化する可能性があり、このとき各操作の時間計算量も \\(O(n)\\) に退化します。</p> <p></p> <p> 図 7-23   二分探索木の退化 </p>","path":["第 7 章 &nbsp; 木","7.4 &nbsp; 二分探索木"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#743","level":2,"title":"7.4.3   二分探索木の代表的な応用","text":"<ul> <li>システム内の多段インデックスとして用いられ、効率的な探索、挿入、削除操作を実現します。</li> <li>一部の探索アルゴリズムの基盤データ構造として使われます。</li> <li>データストリームを格納し、その順序状態を保つために使われます。</li> </ul>","path":["第 7 章 &nbsp; 木","7.4 &nbsp; 二分探索木"],"tags":[]},{"location":"chapter_tree/binary_tree/","level":1,"title":"7.1   二分木","text":"<p>二分木（binary tree）は非線形データ構造の一種であり、「祖先」と「子孫」の派生関係を表し、「一つを二つに分ける」分割統治の考え方を体現しています。連結リストと同様に、二分木の基本単位はノードであり、各ノードは値、左子ノードへの参照、右子ノードへの参照を含みます。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>class TreeNode:\n    \"\"\"二分木ノードクラス\"\"\"\n    def __init__(self, val: int):\n        self.val: int = val                # ノード値\n        self.left: TreeNode | None = None  # 左子ノード参照\n        self.right: TreeNode | None = None # 右子ノード参照\n</code></pre> <pre><code>/* 二分木ノード構造体 */\nstruct TreeNode {\n    int val;          // ノード値\n    TreeNode *left;   // 左子ノードポインタ\n    TreeNode *right;  // 右子ノードポインタ\n    TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}\n};\n</code></pre> <pre><code>/* 二分木ノードクラス */\nclass TreeNode {\n    int val;         // ノード値\n    TreeNode left;   // 左子ノード参照\n    TreeNode right;  // 右子ノード参照\n    TreeNode(int x) { val = x; }\n}\n</code></pre> <pre><code>/* 二分木ノードクラス */\nclass TreeNode(int? x) {\n    public int? val = x;    // ノード値\n    public TreeNode? left;  // 左子ノード参照\n    public TreeNode? right; // 右子ノード参照\n}\n</code></pre> <pre><code>/* 二分木ノード構造体 */\ntype TreeNode struct {\n    Val   int\n    Left  *TreeNode\n    Right *TreeNode\n}\n/* コンストラクタ */\nfunc NewTreeNode(v int) *TreeNode {\n    return &amp;TreeNode{\n        Left:  nil, // 左子ノードポインタ\n        Right: nil, // 右子ノードポインタ\n        Val:   v,   // ノード値\n    }\n}\n</code></pre> <pre><code>/* 二分木ノードクラス */\nclass TreeNode {\n    var val: Int // ノード値\n    var left: TreeNode? // 左子ノード参照\n    var right: TreeNode? // 右子ノード参照\n\n    init(x: Int) {\n        val = x\n    }\n}\n</code></pre> <pre><code>/* 二分木ノードクラス */\nclass TreeNode {\n    val; // ノード値\n    left; // 左子ノードポインタ\n    right; // 右子ノードポインタ\n    constructor(val, left, right) {\n        this.val = val === undefined ? 0 : val;\n        this.left = left === undefined ? null : left;\n        this.right = right === undefined ? null : right;\n    }\n}\n</code></pre> <pre><code>/* 二分木ノードクラス */\nclass TreeNode {\n    val: number;\n    left: TreeNode | null;\n    right: TreeNode | null;\n\n    constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {\n        this.val = val === undefined ? 0 : val; // ノード値\n        this.left = left === undefined ? null : left; // 左子ノード参照\n        this.right = right === undefined ? null : right; // 右子ノード参照\n    }\n}\n</code></pre> <pre><code>/* 二分木ノードクラス */\nclass TreeNode {\n  int val;         // ノード値\n  TreeNode? left;  // 左子ノード参照\n  TreeNode? right; // 右子ノード参照\n  TreeNode(this.val, [this.left, this.right]);\n}\n</code></pre> <pre><code>use std::rc::Rc;\nuse std::cell::RefCell;\n\n/* 二分木ノード構造体 */\nstruct TreeNode {\n    val: i32,                               // ノード値\n    left: Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,    // 左子ノード参照\n    right: Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,   // 右子ノード参照\n}\n\nimpl TreeNode {\n    /* コンストラクタ */\n    fn new(val: i32) -&gt; Rc&lt;RefCell&lt;Self&gt;&gt; {\n        Rc::new(RefCell::new(Self {\n            val,\n            left: None,\n            right: None\n        }))\n    }\n}\n</code></pre> <pre><code>/* 二分木ノード構造体 */\ntypedef struct TreeNode {\n    int val;                // ノード値\n    int height;             // ノードの高さ\n    struct TreeNode *left;  // 左子ノードポインタ\n    struct TreeNode *right; // 右子ノードポインタ\n} TreeNode;\n\n/* コンストラクタ */\nTreeNode *newTreeNode(int val) {\n    TreeNode *node;\n\n    node = (TreeNode *)malloc(sizeof(TreeNode));\n    node-&gt;val = val;\n    node-&gt;height = 0;\n    node-&gt;left = NULL;\n    node-&gt;right = NULL;\n    return node;\n}\n</code></pre> <pre><code>/* 二分木ノードクラス */\nclass TreeNode(val _val: Int) {  // ノード値\n    val left: TreeNode? = null   // 左子ノード参照\n    val right: TreeNode? = null  // 右子ノード参照\n}\n</code></pre> <pre><code>### 二分木ノードクラス ###\nclass TreeNode\n  attr_accessor :val    # ノード値\n  attr_accessor :left   # 左子ノード参照\n  attr_accessor :right  # 右子ノード参照\n\n  def initialize(val)\n    @val = val\n  end\nend\n</code></pre> <p>各ノードは 2 つの参照（ポインタ）を持ち、それぞれ左子ノード（left-child node）と右子ノード（right-child node）を指します。このノードはこれら 2 つの子ノードの親ノード（parent node）と呼ばれます。二分木のあるノードが与えられたとき、そのノードの左子ノードとその配下のノードからなる木をそのノードの左部分木（left subtree）と呼び、同様に右部分木（right subtree）が定義されます。</p> <p>二分木では、葉ノードを除くすべてのノードが子ノードと空でない部分木を持ちます。以下の図に示すように、「ノード 2」を親ノードとみなすと、その左子ノードと右子ノードはそれぞれ「ノード 4」と「ノード 5」であり、左部分木は「ノード 4 とその配下のノードからなる木」、右部分木は「ノード 5 とその配下のノードからなる木」です。</p> <p></p> <p> 図 7-1   親ノード、子ノード、部分木 </p>","path":["第 7 章 &nbsp; 木","7.1 &nbsp; 二分木"],"tags":[]},{"location":"chapter_tree/binary_tree/#711","level":2,"title":"7.1.1   二分木のよく使われる用語","text":"<p>二分木でよく使われる用語を以下の図に示します。</p> <ul> <li>根ノード（root node）：二分木の最上位にあるノードで、親ノードを持ちません。</li> <li>葉ノード（leaf node）：子ノードを持たないノードで、2 本のポインタはいずれも <code>None</code> を指します。</li> <li>辺（edge）：2 つのノードを結ぶ線分、すなわちノード参照（ポインタ）です。</li> <li>ノードが属するレベル（level）：上から下へ向かって増加し、根ノードのレベルは 1 です。</li> <li>ノードの次数（degree）：ノードの子ノードの数。二分木では次数の取り得る値は 0、1、2 です。</li> <li>二分木の高さ（height）：根ノードから最も遠い葉ノードまでに通る辺の数。</li> <li>ノードの深さ（depth）：根ノードからそのノードまでに通る辺の数。</li> <li>ノードの高さ（height）：そのノードから最も遠い葉ノードまでに通る辺の数。</li> </ul> <p></p> <p> 図 7-2   二分木のよく使われる用語 </p> <p>Tip</p> <p>なお、通常「高さ」と「深さ」は「通過した辺の数」と定義しますが、問題や教材によっては「通過したノードの数」と定義する場合もあります。その場合、高さと深さはいずれも 1 を加える必要があります。</p>","path":["第 7 章 &nbsp; 木","7.1 &nbsp; 二分木"],"tags":[]},{"location":"chapter_tree/binary_tree/#712","level":2,"title":"7.1.2   二分木の基本操作","text":"","path":["第 7 章 &nbsp; 木","7.1 &nbsp; 二分木"],"tags":[]},{"location":"chapter_tree/binary_tree/#1","level":3,"title":"1.   二分木を初期化する","text":"<p>連結リストと同様に、まずノードを初期化し、その後で参照（ポインタ）を構築します。</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_tree.py<pre><code># 二分木を初期化する\n# ノードを初期化する\nn1 = TreeNode(val=1)\nn2 = TreeNode(val=2)\nn3 = TreeNode(val=3)\nn4 = TreeNode(val=4)\nn5 = TreeNode(val=5)\n# ノード間の参照（ポインタ）を構築する\nn1.left = n2\nn1.right = n3\nn2.left = n4\nn2.right = n5\n</code></pre> binary_tree.cpp<pre><code>/* 二分木を初期化する */\n// ノードを初期化する\nTreeNode* n1 = new TreeNode(1);\nTreeNode* n2 = new TreeNode(2);\nTreeNode* n3 = new TreeNode(3);\nTreeNode* n4 = new TreeNode(4);\nTreeNode* n5 = new TreeNode(5);\n// ノード間の参照（ポインタ）を構築する\nn1-&gt;left = n2;\nn1-&gt;right = n3;\nn2-&gt;left = n4;\nn2-&gt;right = n5;\n</code></pre> binary_tree.java<pre><code>// ノードを初期化する\nTreeNode n1 = new TreeNode(1);\nTreeNode n2 = new TreeNode(2);\nTreeNode n3 = new TreeNode(3);\nTreeNode n4 = new TreeNode(4);\nTreeNode n5 = new TreeNode(5);\n// ノード間の参照（ポインタ）を構築する\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.cs<pre><code>/* 二分木を初期化する */\n// ノードを初期化する\nTreeNode n1 = new(1);\nTreeNode n2 = new(2);\nTreeNode n3 = new(3);\nTreeNode n4 = new(4);\nTreeNode n5 = new(5);\n// ノード間の参照（ポインタ）を構築する\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.go<pre><code>/* 二分木を初期化する */\n// ノードを初期化する\nn1 := NewTreeNode(1)\nn2 := NewTreeNode(2)\nn3 := NewTreeNode(3)\nn4 := NewTreeNode(4)\nn5 := NewTreeNode(5)\n// ノード間の参照（ポインタ）を構築する\nn1.Left = n2\nn1.Right = n3\nn2.Left = n4\nn2.Right = n5\n</code></pre> binary_tree.swift<pre><code>// ノードを初期化する\nlet n1 = TreeNode(x: 1)\nlet n2 = TreeNode(x: 2)\nlet n3 = TreeNode(x: 3)\nlet n4 = TreeNode(x: 4)\nlet n5 = TreeNode(x: 5)\n// ノード間の参照（ポインタ）を構築する\nn1.left = n2\nn1.right = n3\nn2.left = n4\nn2.right = n5\n</code></pre> binary_tree.js<pre><code>/* 二分木を初期化する */\n// ノードを初期化する\nlet n1 = new TreeNode(1),\n    n2 = new TreeNode(2),\n    n3 = new TreeNode(3),\n    n4 = new TreeNode(4),\n    n5 = new TreeNode(5);\n// ノード間の参照（ポインタ）を構築する\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.ts<pre><code>/* 二分木を初期化する */\n// ノードを初期化する\nlet n1 = new TreeNode(1),\n    n2 = new TreeNode(2),\n    n3 = new TreeNode(3),\n    n4 = new TreeNode(4),\n    n5 = new TreeNode(5);\n// ノード間の参照（ポインタ）を構築する\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.dart<pre><code>/* 二分木を初期化する */\n// ノードを初期化する\nTreeNode n1 = new TreeNode(1);\nTreeNode n2 = new TreeNode(2);\nTreeNode n3 = new TreeNode(3);\nTreeNode n4 = new TreeNode(4);\nTreeNode n5 = new TreeNode(5);\n// ノード間の参照（ポインタ）を構築する\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.rs<pre><code>// ノードを初期化する\nlet n1 = TreeNode::new(1);\nlet n2 = TreeNode::new(2);\nlet n3 = TreeNode::new(3);\nlet n4 = TreeNode::new(4);\nlet n5 = TreeNode::new(5);\n// ノード間の参照（ポインタ）を構築する\nn1.borrow_mut().left = Some(n2.clone());\nn1.borrow_mut().right = Some(n3);\nn2.borrow_mut().left = Some(n4);\nn2.borrow_mut().right = Some(n5);\n</code></pre> binary_tree.c<pre><code>/* 二分木を初期化する */\n// ノードを初期化する\nTreeNode *n1 = newTreeNode(1);\nTreeNode *n2 = newTreeNode(2);\nTreeNode *n3 = newTreeNode(3);\nTreeNode *n4 = newTreeNode(4);\nTreeNode *n5 = newTreeNode(5);\n// ノード間の参照（ポインタ）を構築する\nn1-&gt;left = n2;\nn1-&gt;right = n3;\nn2-&gt;left = n4;\nn2-&gt;right = n5;\n</code></pre> binary_tree.kt<pre><code>// ノードを初期化する\nval n1 = TreeNode(1)\nval n2 = TreeNode(2)\nval n3 = TreeNode(3)\nval n4 = TreeNode(4)\nval n5 = TreeNode(5)\n// ノード間の参照（ポインタ）を構築する\nn1.left = n2\nn1.right = n3\nn2.left = n4\nn2.right = n5\n</code></pre> binary_tree.rb<pre><code># 二分木を初期化する\n# ノードを初期化する\nn1 = TreeNode.new(1)\nn2 = TreeNode.new(2)\nn3 = TreeNode.new(3)\nn4 = TreeNode.new(4)\nn5 = TreeNode.new(5)\n# ノード間の参照（ポインタ）を構築する\nn1.left = n2\nn1.right = n3\nn2.left = n4\nn2.right = n5\n</code></pre> 実行の可視化 <p>https://pythontutor.com/render.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%8F%89%E6%A0%91%E8%8A%82%E7%82%B9%E7%B1%BB%22%22%22%0A%20%20%20%20def%20__init__%28self,%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E8%8A%82%E7%82%B9%E5%80%BC%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%23%20%E5%8F%B3%E5%AD%90%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E4%BA%8C%E5%8F%89%E6%A0%91%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E8%8A%82%E7%82%B9%0A%20%20%20%20n1%20%3D%20TreeNode%28val%3D1%29%0A%20%20%20%20n2%20%3D%20TreeNode%28val%3D2%29%0A%20%20%20%20n3%20%3D%20TreeNode%28val%3D3%29%0A%20%20%20%20n4%20%3D%20TreeNode%28val%3D4%29%0A%20%20%20%20n5%20%3D%20TreeNode%28val%3D5%29%0A%20%20%20%20%23%20%E6%9E%84%E5%BB%BA%E8%8A%82%E7%82%B9%E4%B9%8B%E9%97%B4%E7%9A%84%E5%BC%95%E7%94%A8%EF%BC%88%E6%8C%87%E9%92%88%EF%BC%89%0A%20%20%20%20n1.left%20%3D%20n2%0A%20%20%20%20n1.right%20%3D%20n3%0A%20%20%20%20n2.left%20%3D%20n4%0A%20%20%20%20n2.right%20%3D%20n5&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["第 7 章 &nbsp; 木","7.1 &nbsp; 二分木"],"tags":[]},{"location":"chapter_tree/binary_tree/#2","level":3,"title":"2.   ノードの挿入と削除","text":"<p>連結リストと同様に、二分木でのノードの挿入と削除はポインタを変更することで実現できます。以下の図に 1 つの例を示します。</p> <p></p> <p> 図 7-3   二分木でノードを挿入・削除する </p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_tree.py<pre><code># ノードの挿入と削除\np = TreeNode(0)\n# n1 -&gt; n2 の間にノード P を挿入する\nn1.left = p\np.left = n2\n# ノード P を削除する\nn1.left = n2\n</code></pre> binary_tree.cpp<pre><code>/* ノードの挿入と削除 */\nTreeNode* P = new TreeNode(0);\n// n1 -&gt; n2 の間にノード P を挿入する\nn1-&gt;left = P;\nP-&gt;left = n2;\n// ノード P を削除する\nn1-&gt;left = n2;\n// メモリを解放する\ndelete P;\n</code></pre> binary_tree.java<pre><code>TreeNode P = new TreeNode(0);\n// n1 -&gt; n2 の間にノード P を挿入する\nn1.left = P;\nP.left = n2;\n// ノード P を削除する\nn1.left = n2;\n</code></pre> binary_tree.cs<pre><code>/* ノードの挿入と削除 */\nTreeNode P = new(0);\n// n1 -&gt; n2 の間にノード P を挿入する\nn1.left = P;\nP.left = n2;\n// ノード P を削除する\nn1.left = n2;\n</code></pre> binary_tree.go<pre><code>/* ノードの挿入と削除 */\n// n1 -&gt; n2 の間にノード P を挿入する\np := NewTreeNode(0)\nn1.Left = p\np.Left = n2\n// ノード P を削除する\nn1.Left = n2\n</code></pre> binary_tree.swift<pre><code>let P = TreeNode(x: 0)\n// n1 -&gt; n2 の間にノード P を挿入する\nn1.left = P\nP.left = n2\n// ノード P を削除する\nn1.left = n2\n</code></pre> binary_tree.js<pre><code>/* ノードの挿入と削除 */\nlet P = new TreeNode(0);\n// n1 -&gt; n2 の間にノード P を挿入する\nn1.left = P;\nP.left = n2;\n// ノード P を削除する\nn1.left = n2;\n</code></pre> binary_tree.ts<pre><code>/* ノードの挿入と削除 */\nconst P = new TreeNode(0);\n// n1 -&gt; n2 の間にノード P を挿入する\nn1.left = P;\nP.left = n2;\n// ノード P を削除する\nn1.left = n2;\n</code></pre> binary_tree.dart<pre><code>/* ノードの挿入と削除 */\nTreeNode P = new TreeNode(0);\n// n1 -&gt; n2 の間にノード P を挿入する\nn1.left = P;\nP.left = n2;\n// ノード P を削除する\nn1.left = n2;\n</code></pre> binary_tree.rs<pre><code>let p = TreeNode::new(0);\n// n1 -&gt; n2 の間にノード P を挿入する\nn1.borrow_mut().left = Some(p.clone());\np.borrow_mut().left = Some(n2.clone());\n// ノード p を削除する\nn1.borrow_mut().left = Some(n2);\n</code></pre> binary_tree.c<pre><code>/* ノードの挿入と削除 */\nTreeNode *P = newTreeNode(0);\n// n1 -&gt; n2 の間にノード P を挿入する\nn1-&gt;left = P;\nP-&gt;left = n2;\n// ノード P を削除する\nn1-&gt;left = n2;\n// メモリを解放する\nfree(P);\n</code></pre> binary_tree.kt<pre><code>val P = TreeNode(0)\n// n1 -&gt; n2 の間にノード P を挿入する\nn1.left = P\nP.left = n2\n// ノード P を削除する\nn1.left = n2\n</code></pre> binary_tree.rb<pre><code># ノードの挿入と削除\n_p = TreeNode.new(0)\n# n1 -&gt; n2 の間にノード _p を挿入する\nn1.left = _p\n_p.left = n2\n# ノードを削除する\nn1.left = n2\n</code></pre> 実行の可視化 <p>https://pythontutor.com/render.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%8F%89%E6%A0%91%E8%8A%82%E7%82%B9%E7%B1%BB%22%22%22%0A%20%20%20%20def%20__init__%28self,%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E8%8A%82%E7%82%B9%E5%80%BC%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%23%20%E5%8F%B3%E5%AD%90%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E4%BA%8C%E5%8F%89%E6%A0%91%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E8%8A%82%E7%82%B9%0A%20%20%20%20n1%20%3D%20TreeNode%28val%3D1%29%0A%20%20%20%20n2%20%3D%20TreeNode%28val%3D2%29%0A%20%20%20%20n3%20%3D%20TreeNode%28val%3D3%29%0A%20%20%20%20n4%20%3D%20TreeNode%28val%3D4%29%0A%20%20%20%20n5%20%3D%20TreeNode%28val%3D5%29%0A%20%20%20%20%23%20%E6%9E%84%E5%BB%BA%E8%8A%82%E7%82%B9%E4%B9%8B%E9%97%B4%E7%9A%84%E5%BC%95%E7%94%A8%EF%BC%88%E6%8C%87%E9%92%88%EF%BC%89%0A%20%20%20%20n1.left%20%3D%20n2%0A%20%20%20%20n1.right%20%3D%20n3%0A%20%20%20%20n2.left%20%3D%20n4%0A%20%20%20%20n2.right%20%3D%20n5%0A%0A%20%20%20%20%23%20%E6%8F%92%E5%85%A5%E4%B8%8E%E5%88%A0%E9%99%A4%E8%8A%82%E7%82%B9%0A%20%20%20%20p%20%3D%20TreeNode%280%29%0A%20%20%20%20%23%20%E5%9C%A8%20n1%20-%3E%20n2%20%E4%B8%AD%E9%97%B4%E6%8F%92%E5%85%A5%E8%8A%82%E7%82%B9%20P%0A%20%20%20%20n1.left%20%3D%20p%0A%20%20%20%20p.left%20%3D%20n2%0A%20%20%20%20%23%20%E5%88%A0%E9%99%A4%E8%8A%82%E7%82%B9%20P%0A%20%20%20%20n1.left%20%3D%20n2&amp;cumulative=false&amp;curInstr=37&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p> <p>Tip</p> <p>注意すべき点として、ノードの挿入は二分木の元の論理構造を変える可能性があり、ノードの削除は通常、そのノードと配下のすべての部分木の削除を意味します。そのため、二分木における挿入と削除は、実際に意味のある操作を実現するために、通常は一連の操作を組み合わせて行います。</p>","path":["第 7 章 &nbsp; 木","7.1 &nbsp; 二分木"],"tags":[]},{"location":"chapter_tree/binary_tree/#713","level":2,"title":"7.1.3   一般的な二分木の種類","text":"","path":["第 7 章 &nbsp; 木","7.1 &nbsp; 二分木"],"tags":[]},{"location":"chapter_tree/binary_tree/#1_1","level":3,"title":"1.   充足二分木","text":"<p>以下の図に示すように、充足二分木（perfect binary tree）ではすべてのレベルのノードが完全に埋まっています。充足二分木では、葉ノードの次数は \\(0\\) で、それ以外のすべてのノードの次数は \\(2\\) です。木の高さを \\(h\\) とすると、ノード総数は \\(2^{h+1} - 1\\) となり、標準的な指数関係を示して、自然界でよく見られる細胞分裂の現象を反映しています。</p> <p>Tip</p> <p>なお、中国語圏では充足二分木は満二分木と呼ばれることもあります。</p> <p></p> <p> 図 7-4   充足二分木 </p>","path":["第 7 章 &nbsp; 木","7.1 &nbsp; 二分木"],"tags":[]},{"location":"chapter_tree/binary_tree/#2_1","level":3,"title":"2.   完全二分木","text":"<p>以下の図に示すように、完全二分木（complete binary tree）では最下層のノードだけが完全に埋まっていなくてもよく、しかも最下層のノードは左から右へ連続して詰められていなければなりません。なお、充足二分木も完全二分木の一種です。</p> <p></p> <p> 図 7-5   完全二分木 </p>","path":["第 7 章 &nbsp; 木","7.1 &nbsp; 二分木"],"tags":[]},{"location":"chapter_tree/binary_tree/#3","level":3,"title":"3.   充満二分木","text":"<p>以下の図に示すように、充満二分木（full binary tree）では、葉ノードを除くすべてのノードが 2 つの子ノードを持ちます。</p> <p></p> <p> 図 7-6   充満二分木 </p>","path":["第 7 章 &nbsp; 木","7.1 &nbsp; 二分木"],"tags":[]},{"location":"chapter_tree/binary_tree/#4","level":3,"title":"4.   平衡二分木","text":"<p>以下の図に示すように、平衡二分木（balanced binary tree）では、任意のノードについて左部分木と右部分木の高さの差の絶対値が 1 を超えません。</p> <p></p> <p> 図 7-7   平衡二分木 </p>","path":["第 7 章 &nbsp; 木","7.1 &nbsp; 二分木"],"tags":[]},{"location":"chapter_tree/binary_tree/#714","level":2,"title":"7.1.4   二分木の退化","text":"<p>以下の図は、二分木の理想的な構造と退化した構造を示しています。二分木の各レベルのノードがすべて埋まっていると「充足二分木」となり、すべてのノードが片側に偏ると二分木は「連結リスト」へ退化します。</p> <ul> <li>充足二分木は理想的なケースであり、二分木の「分割統治」の利点を十分に発揮できます。</li> <li>連結リストはその対極にあり、各種操作はすべて線形操作となり、時間計算量は \\(O(n)\\) まで退化します。</li> </ul> <p></p> <p> 図 7-8   二分木の最良構造と最悪構造 </p> <p>以下の表に示すように、最良構造と最悪構造では、二分木の葉ノード数、ノード総数、高さなどが極大または極小になります。</p> <p> 表 7-1   二分木の最良構造と最悪構造 </p> 充足二分木 連結リスト 第 \\(i\\) レベルのノード数 \\(2^{i-1}\\) \\(1\\) 高さ \\(h\\) の木の葉ノード数 \\(2^h\\) \\(1\\) 高さ \\(h\\) の木のノード総数 \\(2^{h+1} - 1\\) \\(h + 1\\) ノード総数 \\(n\\) の木の高さ \\(\\log_2 (n+1) - 1\\) \\(n - 1\\)","path":["第 7 章 &nbsp; 木","7.1 &nbsp; 二分木"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/","level":1,"title":"7.2   二分木の走査","text":"<p>物理構造の観点から見ると、木は連結リストを基盤としたデータ構造であり、その走査はポインタを通じてノードへ順にアクセスすることで行われます。しかし、木は非線形データ構造であるため、木の走査は連結リストの走査よりも複雑であり、検索アルゴリズムを用いて実現する必要があります。</p> <p>二分木の一般的な走査方法には、レベル順走査、先行順走査、中間順走査、後行順走査などがあります。</p>","path":["第 7 章 &nbsp; 木","7.2 &nbsp; 二分木の走査"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/#721","level":2,"title":"7.2.1   レベル順走査","text":"<p>次の図に示すように、レベル順走査（level-order traversal）では、二分木を上から下へ層ごとに走査し、各層では左から右の順にノードへアクセスします。</p> <p>レベル順走査は本質的に幅優先走査（breadth-first traversal）に属し、幅優先探索（breadth-first search, BFS）とも呼ばれます。これは「同心円状に外側へ広がる」ような、層ごとの走査方法を表しています。</p> <p></p> <p> 図 7-9   二分木のレベル順走査 </p>","path":["第 7 章 &nbsp; 木","7.2 &nbsp; 二分木の走査"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/#1","level":3,"title":"1.   コードの実装","text":"<p>幅優先走査は通常「キュー」を用いて実装します。キューは「先入れ先出し」の規則に従い、幅優先走査は「層ごとに進む」という規則に従います。両者の背後にある考え方は一致しています。実装コードは次のとおりです：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_tree_bfs.py<pre><code>def level_order(root: TreeNode | None) -&gt; list[int]:\n    \"\"\"レベル順走査\"\"\"\n    # キューを初期化し、ルートノードを追加する\n    queue: deque[TreeNode] = deque()\n    queue.append(root)\n    # 走査順序を保存するためのリストを初期化する\n    res = []\n    while queue:\n        node: TreeNode = queue.popleft()  # デキュー\n        res.append(node.val)  # ノードの値を保存する\n        if node.left is not None:\n            queue.append(node.left)  # 左子ノードをキューに追加\n        if node.right is not None:\n            queue.append(node.right)  # 右子ノードをキューに追加\n    return res\n</code></pre> binary_tree_bfs.cpp<pre><code>/* レベル順走査 */\nvector&lt;int&gt; levelOrder(TreeNode *root) {\n    // キューを初期化し、ルートノードを追加する\n    queue&lt;TreeNode *&gt; queue;\n    queue.push(root);\n    // 走査順序を保存するためのリストを初期化する\n    vector&lt;int&gt; vec;\n    while (!queue.empty()) {\n        TreeNode *node = queue.front();\n        queue.pop();              // デキュー\n        vec.push_back(node-&gt;val); // ノードの値を保存する\n        if (node-&gt;left != nullptr)\n            queue.push(node-&gt;left); // 左子ノードをキューに追加\n        if (node-&gt;right != nullptr)\n            queue.push(node-&gt;right); // 右子ノードをキューに追加\n    }\n    return vec;\n}\n</code></pre> binary_tree_bfs.java<pre><code>/* レベル順走査 */\nList&lt;Integer&gt; levelOrder(TreeNode root) {\n    // キューを初期化し、ルートノードを追加する\n    Queue&lt;TreeNode&gt; queue = new LinkedList&lt;&gt;();\n    queue.add(root);\n    // 走査順序を保存するためのリストを初期化する\n    List&lt;Integer&gt; list = new ArrayList&lt;&gt;();\n    while (!queue.isEmpty()) {\n        TreeNode node = queue.poll(); // デキュー\n        list.add(node.val);           // ノードの値を保存する\n        if (node.left != null)\n            queue.offer(node.left);   // 左子ノードをキューに追加\n        if (node.right != null)\n            queue.offer(node.right);  // 右子ノードをキューに追加\n    }\n    return list;\n}\n</code></pre> binary_tree_bfs.cs<pre><code>/* レベル順走査 */\nList&lt;int&gt; LevelOrder(TreeNode root) {\n    // キューを初期化し、ルートノードを追加する\n    Queue&lt;TreeNode&gt; queue = new();\n    queue.Enqueue(root);\n    // 走査順序を保存するためのリストを初期化する\n    List&lt;int&gt; list = [];\n    while (queue.Count != 0) {\n        TreeNode node = queue.Dequeue(); // デキュー\n        list.Add(node.val!.Value);       // ノードの値を保存する\n        if (node.left != null)\n            queue.Enqueue(node.left);    // 左子ノードをキューに追加\n        if (node.right != null)\n            queue.Enqueue(node.right);   // 右子ノードをキューに追加\n    }\n    return list;\n}\n</code></pre> binary_tree_bfs.go<pre><code>/* レベル順走査 */\nfunc levelOrder(root *TreeNode) []any {\n    // キューを初期化し、ルートノードを追加する\n    queue := list.New()\n    queue.PushBack(root)\n    // 走査順を保存するためのスライスを初期化する\n    nums := make([]any, 0)\n    for queue.Len() &gt; 0 {\n        // デキュー\n        node := queue.Remove(queue.Front()).(*TreeNode)\n        // ノードの値を保存する\n        nums = append(nums, node.Val)\n        if node.Left != nil {\n            // 左子ノードをキューに追加\n            queue.PushBack(node.Left)\n        }\n        if node.Right != nil {\n            // 右子ノードをキューに追加\n            queue.PushBack(node.Right)\n        }\n    }\n    return nums\n}\n</code></pre> binary_tree_bfs.swift<pre><code>/* レベル順走査 */\nfunc levelOrder(root: TreeNode) -&gt; [Int] {\n    // キューを初期化し、ルートノードを追加する\n    var queue: [TreeNode] = [root]\n    // 走査順序を保存するためのリストを初期化する\n    var list: [Int] = []\n    while !queue.isEmpty {\n        let node = queue.removeFirst() // デキュー\n        list.append(node.val) // ノードの値を保存する\n        if let left = node.left {\n            queue.append(left) // 左子ノードをキューに追加\n        }\n        if let right = node.right {\n            queue.append(right) // 右子ノードをキューに追加\n        }\n    }\n    return list\n}\n</code></pre> binary_tree_bfs.js<pre><code>/* レベル順走査 */\nfunction levelOrder(root) {\n    // キューを初期化し、ルートノードを追加する\n    const queue = [root];\n    // 走査順序を保存するためのリストを初期化する\n    const list = [];\n    while (queue.length) {\n        let node = queue.shift(); // デキュー\n        list.push(node.val); // ノードの値を保存する\n        if (node.left) queue.push(node.left); // 左子ノードをキューに追加\n        if (node.right) queue.push(node.right); // 右子ノードをキューに追加\n    }\n    return list;\n}\n</code></pre> binary_tree_bfs.ts<pre><code>/* レベル順走査 */\nfunction levelOrder(root: TreeNode | null): number[] {\n    // キューを初期化し、ルートノードを追加する\n    const queue = [root];\n    // 走査順序を保存するためのリストを初期化する\n    const list: number[] = [];\n    while (queue.length) {\n        let node = queue.shift() as TreeNode; // デキュー\n        list.push(node.val); // ノードの値を保存する\n        if (node.left) {\n            queue.push(node.left); // 左子ノードをキューに追加\n        }\n        if (node.right) {\n            queue.push(node.right); // 右子ノードをキューに追加\n        }\n    }\n    return list;\n}\n</code></pre> binary_tree_bfs.dart<pre><code>/* レベル順走査 */\nList&lt;int&gt; levelOrder(TreeNode? root) {\n  // キューを初期化し、ルートノードを追加する\n  Queue&lt;TreeNode?&gt; queue = Queue();\n  queue.add(root);\n  // 走査順序を保存するためのリストを初期化する\n  List&lt;int&gt; res = [];\n  while (queue.isNotEmpty) {\n    TreeNode? node = queue.removeFirst(); // デキュー\n    res.add(node!.val); // ノードの値を保存する\n    if (node.left != null) queue.add(node.left); // 左子ノードをキューに追加\n    if (node.right != null) queue.add(node.right); // 右子ノードをキューに追加\n  }\n  return res;\n}\n</code></pre> binary_tree_bfs.rs<pre><code>/* レベル順走査 */\nfn level_order(root: &amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;) -&gt; Vec&lt;i32&gt; {\n    // キューを初期化し、ルートノードを追加する\n    let mut que = VecDeque::new();\n    que.push_back(root.clone());\n    // 走査順序を保存するためのリストを初期化する\n    let mut vec = Vec::new();\n\n    while let Some(node) = que.pop_front() {\n        // デキュー\n        vec.push(node.borrow().val); // ノードの値を保存する\n        if let Some(left) = node.borrow().left.as_ref() {\n            que.push_back(left.clone()); // 左子ノードをキューに追加\n        }\n        if let Some(right) = node.borrow().right.as_ref() {\n            que.push_back(right.clone()); // 右子ノードをキューに追加\n        };\n    }\n    vec\n}\n</code></pre> binary_tree_bfs.c<pre><code>/* レベル順走査 */\nint *levelOrder(TreeNode *root, int *size) {\n    /* 補助キュー */\n    int front, rear;\n    int index, *arr;\n    TreeNode *node;\n    TreeNode **queue;\n\n    /* 補助キュー */\n    queue = (TreeNode **)malloc(sizeof(TreeNode *) * MAX_SIZE);\n    // キューへのポインタ\n    front = 0, rear = 0;\n    // 根ノードを追加する\n    queue[rear++] = root;\n    // 走査順序を保存するためのリストを初期化する\n    /* 補助配列 */\n    arr = (int *)malloc(sizeof(int) * MAX_SIZE);\n    // 配列ポインタ\n    index = 0;\n    while (front &lt; rear) {\n        // デキュー\n        node = queue[front++];\n        // ノードの値を保存する\n        arr[index++] = node-&gt;val;\n        if (node-&gt;left != NULL) {\n            // 左子ノードをキューに追加\n            queue[rear++] = node-&gt;left;\n        }\n        if (node-&gt;right != NULL) {\n            // 右子ノードをキューに追加\n            queue[rear++] = node-&gt;right;\n        }\n    }\n    // 配列長の値を更新\n    *size = index;\n    arr = realloc(arr, sizeof(int) * (*size));\n\n    // 補助配列の領域を解放する\n    free(queue);\n    return arr;\n}\n</code></pre> binary_tree_bfs.kt<pre><code>/* レベル順走査 */\nfun levelOrder(root: TreeNode?): MutableList&lt;Int&gt; {\n    // キューを初期化し、ルートノードを追加する\n    val queue = LinkedList&lt;TreeNode?&gt;()\n    queue.add(root)\n    // 走査順序を保存するためのリストを初期化する\n    val list = mutableListOf&lt;Int&gt;()\n    while (queue.isNotEmpty()) {\n        val node = queue.poll()      // デキュー\n        list.add(node?._val!!)       // ノードの値を保存する\n        if (node.left != null)\n            queue.offer(node.left)   // 左子ノードをキューに追加\n        if (node.right != null)\n            queue.offer(node.right)  // 右子ノードをキューに追加\n    }\n    return list\n}\n</code></pre> binary_tree_bfs.rb<pre><code>### レベル順走査 ###\ndef level_order(root)\n  # キューを初期化し、ルートノードを追加する\n  queue = [root]\n  # 走査順序を保存するためのリストを初期化する\n  res = []\n  while !queue.empty?\n    node = queue.shift # デキュー\n    res &lt;&lt; node.val # ノードの値を保存する\n    queue &lt;&lt; node.left unless node.left.nil? # 左子ノードをキューに追加\n    queue &lt;&lt; node.right unless node.right.nil? # 右子ノードをキューに追加\n  end\n  res\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p>","path":["第 7 章 &nbsp; 木","7.2 &nbsp; 二分木の走査"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/#2","level":3,"title":"2.   計算量","text":"<ul> <li>時間計算量は \\(O(n)\\) ：すべてのノードを1回ずつ訪問するため、計算量は \\(O(n)\\) です。ここで、\\(n\\) はノード数です。</li> <li>空間計算量は \\(O(n)\\) ：最悪の場合、すなわち完全二分木では、最下層に到達する前に、キュー内には最大で同時に \\((n + 1) / 2\\) 個のノードが存在し、\\(O(n)\\) の空間を使用します。</li> </ul>","path":["第 7 章 &nbsp; 木","7.2 &nbsp; 二分木の走査"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/#722","level":2,"title":"7.2.2   先行順・中間順・後行順走査","text":"<p>同様に、先行順・中間順・後行順走査はいずれも深度優先走査（depth-first traversal）に属し、深度優先探索（depth-first search, DFS）とも呼ばれます。これは「まず行き止まりまで進み、その後で戻って続ける」という走査方法を表しています。</p> <p>次の図は、二分木に対して深度優先走査を行う仕組みを示しています。深度優先走査は、二分木全体の外周をぐるりと「一周する」ようなものです。各ノードでは3つの位置に出会い、それぞれが先行順走査・中間順走査・後行順走査に対応します。</p> <p></p> <p> 図 7-10   二分探索木の先行順・中間順・後行順走査 </p>","path":["第 7 章 &nbsp; 木","7.2 &nbsp; 二分木の走査"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/#1_1","level":3,"title":"1.   コードの実装","text":"<p>深度優先探索は通常、再帰に基づいて実装されます：</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_tree_dfs.py<pre><code>def pre_order(root: TreeNode | None):\n    \"\"\"先行順走査\"\"\"\n    if root is None:\n        return\n    # 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木\n    res.append(root.val)\n    pre_order(root=root.left)\n    pre_order(root=root.right)\n\ndef in_order(root: TreeNode | None):\n    \"\"\"中順走査\"\"\"\n    if root is None:\n        return\n    # 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木\n    in_order(root=root.left)\n    res.append(root.val)\n    in_order(root=root.right)\n\ndef post_order(root: TreeNode | None):\n    \"\"\"後順走査\"\"\"\n    if root is None:\n        return\n    # 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード\n    post_order(root=root.left)\n    post_order(root=root.right)\n    res.append(root.val)\n</code></pre> binary_tree_dfs.cpp<pre><code>/* 先行順走査 */\nvoid preOrder(TreeNode *root) {\n    if (root == nullptr)\n        return;\n    // 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木\n    vec.push_back(root-&gt;val);\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n}\n\n/* 中順走査 */\nvoid inOrder(TreeNode *root) {\n    if (root == nullptr)\n        return;\n    // 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木\n    inOrder(root-&gt;left);\n    vec.push_back(root-&gt;val);\n    inOrder(root-&gt;right);\n}\n\n/* 後順走査 */\nvoid postOrder(TreeNode *root) {\n    if (root == nullptr)\n        return;\n    // 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード\n    postOrder(root-&gt;left);\n    postOrder(root-&gt;right);\n    vec.push_back(root-&gt;val);\n}\n</code></pre> binary_tree_dfs.java<pre><code>/* 先行順走査 */\nvoid preOrder(TreeNode root) {\n    if (root == null)\n        return;\n    // 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木\n    list.add(root.val);\n    preOrder(root.left);\n    preOrder(root.right);\n}\n\n/* 中順走査 */\nvoid inOrder(TreeNode root) {\n    if (root == null)\n        return;\n    // 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木\n    inOrder(root.left);\n    list.add(root.val);\n    inOrder(root.right);\n}\n\n/* 後順走査 */\nvoid postOrder(TreeNode root) {\n    if (root == null)\n        return;\n    // 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード\n    postOrder(root.left);\n    postOrder(root.right);\n    list.add(root.val);\n}\n</code></pre> binary_tree_dfs.cs<pre><code>/* 先行順走査 */\nvoid PreOrder(TreeNode? root) {\n    if (root == null) return;\n    // 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木\n    list.Add(root.val!.Value);\n    PreOrder(root.left);\n    PreOrder(root.right);\n}\n\n/* 中順走査 */\nvoid InOrder(TreeNode? root) {\n    if (root == null) return;\n    // 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木\n    InOrder(root.left);\n    list.Add(root.val!.Value);\n    InOrder(root.right);\n}\n\n/* 後順走査 */\nvoid PostOrder(TreeNode? root) {\n    if (root == null) return;\n    // 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード\n    PostOrder(root.left);\n    PostOrder(root.right);\n    list.Add(root.val!.Value);\n}\n</code></pre> binary_tree_dfs.go<pre><code>/* 先行順走査 */\nfunc preOrder(node *TreeNode) {\n    if node == nil {\n        return\n    }\n    // 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木\n    nums = append(nums, node.Val)\n    preOrder(node.Left)\n    preOrder(node.Right)\n}\n\n/* 中順走査 */\nfunc inOrder(node *TreeNode) {\n    if node == nil {\n        return\n    }\n    // 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木\n    inOrder(node.Left)\n    nums = append(nums, node.Val)\n    inOrder(node.Right)\n}\n\n/* 後順走査 */\nfunc postOrder(node *TreeNode) {\n    if node == nil {\n        return\n    }\n    // 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード\n    postOrder(node.Left)\n    postOrder(node.Right)\n    nums = append(nums, node.Val)\n}\n</code></pre> binary_tree_dfs.swift<pre><code>/* 先行順走査 */\nfunc preOrder(root: TreeNode?) {\n    guard let root = root else {\n        return\n    }\n    // 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木\n    list.append(root.val)\n    preOrder(root: root.left)\n    preOrder(root: root.right)\n}\n\n/* 中順走査 */\nfunc inOrder(root: TreeNode?) {\n    guard let root = root else {\n        return\n    }\n    // 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木\n    inOrder(root: root.left)\n    list.append(root.val)\n    inOrder(root: root.right)\n}\n\n/* 後順走査 */\nfunc postOrder(root: TreeNode?) {\n    guard let root = root else {\n        return\n    }\n    // 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード\n    postOrder(root: root.left)\n    postOrder(root: root.right)\n    list.append(root.val)\n}\n</code></pre> binary_tree_dfs.js<pre><code>/* 先行順走査 */\nfunction preOrder(root) {\n    if (root === null) return;\n    // 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木\n    list.push(root.val);\n    preOrder(root.left);\n    preOrder(root.right);\n}\n\n/* 中順走査 */\nfunction inOrder(root) {\n    if (root === null) return;\n    // 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木\n    inOrder(root.left);\n    list.push(root.val);\n    inOrder(root.right);\n}\n\n/* 後順走査 */\nfunction postOrder(root) {\n    if (root === null) return;\n    // 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード\n    postOrder(root.left);\n    postOrder(root.right);\n    list.push(root.val);\n}\n</code></pre> binary_tree_dfs.ts<pre><code>/* 先行順走査 */\nfunction preOrder(root: TreeNode | null): void {\n    if (root === null) {\n        return;\n    }\n    // 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木\n    list.push(root.val);\n    preOrder(root.left);\n    preOrder(root.right);\n}\n\n/* 中順走査 */\nfunction inOrder(root: TreeNode | null): void {\n    if (root === null) {\n        return;\n    }\n    // 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木\n    inOrder(root.left);\n    list.push(root.val);\n    inOrder(root.right);\n}\n\n/* 後順走査 */\nfunction postOrder(root: TreeNode | null): void {\n    if (root === null) {\n        return;\n    }\n    // 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード\n    postOrder(root.left);\n    postOrder(root.right);\n    list.push(root.val);\n}\n</code></pre> binary_tree_dfs.dart<pre><code>/* 先行順走査 */\nvoid preOrder(TreeNode? node) {\n  if (node == null) return;\n  // 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木\n  list.add(node.val);\n  preOrder(node.left);\n  preOrder(node.right);\n}\n\n/* 中順走査 */\nvoid inOrder(TreeNode? node) {\n  if (node == null) return;\n  // 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木\n  inOrder(node.left);\n  list.add(node.val);\n  inOrder(node.right);\n}\n\n/* 後順走査 */\nvoid postOrder(TreeNode? node) {\n  if (node == null) return;\n  // 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード\n  postOrder(node.left);\n  postOrder(node.right);\n  list.add(node.val);\n}\n</code></pre> binary_tree_dfs.rs<pre><code>/* 先行順走査 */\nfn pre_order(root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;) -&gt; Vec&lt;i32&gt; {\n    let mut result = vec![];\n\n    fn dfs(root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;, res: &amp;mut Vec&lt;i32&gt;) {\n        if let Some(node) = root {\n            // 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木\n            let node = node.borrow();\n            res.push(node.val);\n            dfs(node.left.as_ref(), res);\n            dfs(node.right.as_ref(), res);\n        }\n    }\n    dfs(root, &amp;mut result);\n\n    result\n}\n\n/* 中順走査 */\nfn in_order(root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;) -&gt; Vec&lt;i32&gt; {\n    let mut result = vec![];\n\n    fn dfs(root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;, res: &amp;mut Vec&lt;i32&gt;) {\n        if let Some(node) = root {\n            // 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木\n            let node = node.borrow();\n            dfs(node.left.as_ref(), res);\n            res.push(node.val);\n            dfs(node.right.as_ref(), res);\n        }\n    }\n    dfs(root, &amp;mut result);\n\n    result\n}\n\n/* 後順走査 */\nfn post_order(root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;) -&gt; Vec&lt;i32&gt; {\n    let mut result = vec![];\n\n    fn dfs(root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;, res: &amp;mut Vec&lt;i32&gt;) {\n        if let Some(node) = root {\n            // 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード\n            let node = node.borrow();\n            dfs(node.left.as_ref(), res);\n            dfs(node.right.as_ref(), res);\n            res.push(node.val);\n        }\n    }\n\n    dfs(root, &amp;mut result);\n\n    result\n}\n</code></pre> binary_tree_dfs.c<pre><code>/* 先行順走査 */\nvoid preOrder(TreeNode *root, int *size) {\n    if (root == NULL)\n        return;\n    // 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木\n    arr[(*size)++] = root-&gt;val;\n    preOrder(root-&gt;left, size);\n    preOrder(root-&gt;right, size);\n}\n\n/* 中順走査 */\nvoid inOrder(TreeNode *root, int *size) {\n    if (root == NULL)\n        return;\n    // 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木\n    inOrder(root-&gt;left, size);\n    arr[(*size)++] = root-&gt;val;\n    inOrder(root-&gt;right, size);\n}\n\n/* 後順走査 */\nvoid postOrder(TreeNode *root, int *size) {\n    if (root == NULL)\n        return;\n    // 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード\n    postOrder(root-&gt;left, size);\n    postOrder(root-&gt;right, size);\n    arr[(*size)++] = root-&gt;val;\n}\n</code></pre> binary_tree_dfs.kt<pre><code>/* 先行順走査 */\nfun preOrder(root: TreeNode?) {\n    if (root == null) return\n    // 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木\n    list.add(root._val)\n    preOrder(root.left)\n    preOrder(root.right)\n}\n\n/* 中順走査 */\nfun inOrder(root: TreeNode?) {\n    if (root == null) return\n    // 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木\n    inOrder(root.left)\n    list.add(root._val)\n    inOrder(root.right)\n}\n\n/* 後順走査 */\nfun postOrder(root: TreeNode?) {\n    if (root == null) return\n    // 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード\n    postOrder(root.left)\n    postOrder(root.right)\n    list.add(root._val)\n}\n</code></pre> binary_tree_dfs.rb<pre><code>### 前順走査 ###\ndef pre_order(root)\n  return if root.nil?\n\n  # 訪問順序：根ノード -&gt; 左部分木 -&gt; 右部分木\n  $res &lt;&lt; root.val\n  pre_order(root.left)\n  pre_order(root.right)\nend\n\n### 中順走査 ###\ndef in_order(root)\n  return if root.nil?\n\n  # 訪問優先順: 左部分木 -&gt; 根ノード -&gt; 右部分木\n  in_order(root.left)\n  $res &lt;&lt; root.val\n  in_order(root.right)\nend\n\n### 後順走査 ###\ndef post_order(root)\n  return if root.nil?\n\n  # 訪問優先順: 左部分木 -&gt; 右部分木 -&gt; 根ノード\n  post_order(root.left)\n  post_order(root.right)\n  $res &lt;&lt; root.val\nend\n</code></pre> コードの可視化 <p> 全画面で見る &gt;</p> <p>Tip</p> <p>深度優先探索は反復によって実装することもできます。興味のある読者は自身で調べてみてください。</p> <p>次の図は、二分木の先行順走査における再帰の過程を示しており、「行き」と「帰り」という2つの逆向きの部分に分けられます。</p> <ol> <li>「行き」は新しいメソッドの開始を表し、この過程でプログラムは次のノードにアクセスします。</li> <li>「帰り」は関数の復帰を表し、現在のノードへのアクセスが完了したことを意味します。</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> 図 7-11   先行順走査の再帰過程 </p>","path":["第 7 章 &nbsp; 木","7.2 &nbsp; 二分木の走査"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/#2_1","level":3,"title":"2.   計算量","text":"<ul> <li>時間計算量は \\(O(n)\\) ：すべてのノードを1回ずつ訪問するため、計算量は \\(O(n)\\) です。</li> <li>空間計算量は \\(O(n)\\) ：最悪の場合、すなわち木が連結リストに退化したとき、再帰の深さは \\(n\\) に達し、システムは \\(O(n)\\) のスタックフレーム空間を使用します。</li> </ul>","path":["第 7 章 &nbsp; 木","7.2 &nbsp; 二分木の走査"],"tags":[]},{"location":"chapter_tree/summary/","level":1,"title":"7.6   まとめ","text":"","path":["第 7 章 &nbsp; 木","7.6 &nbsp; まとめ"],"tags":[]},{"location":"chapter_tree/summary/#1","level":3,"title":"1.   要点の振り返り","text":"<ul> <li>二分木は非線形データ構造の一種であり、「二分する」分割統治の考え方を体現している。各二分木ノードは 1 つの値と 2 本のポインタを持ち、それぞれ左子ノードと右子ノードを指す。</li> <li>二分木のあるノードについて、その左（右）子ノードおよびその配下から構成される木を、そのノードの左（右）部分木と呼ぶ。</li> <li>二分木に関する用語には、根ノード、葉ノード、レベル、次数、辺、高さ、深さなどがある。</li> <li>二分木の初期化、ノードの挿入、ノードの削除は、連結リストの操作方法と似ている。</li> <li>一般的な二分木の種類には、perfect 二分木、complete 二分木、full 二分木、平衡二分木がある。perfect 二分木が最も理想的な状態であり、連結リストは退化後の最悪の状態である。</li> <li>二分木は配列で表現できる。方法としては、ノード値と空き位置をレベル順走査の順に並べ、親ノードと子ノードのインデックス対応関係に基づいてポインタを実現する。</li> <li>二分木のレベル順走査は幅優先探索の一種であり、「同心円状に外へ広がる」ような逐次的な走査方式を表しており、通常はキューによって実装される。</li> <li>前順、中順、後順走査はいずれも深さ優先探索に属し、「まず末端まで進み、その後バックトラックして続ける」という走査方式を体現しており、通常は再帰で実装される。</li> <li>二分探索木は効率的な要素探索データ構造であり、探索、挿入、削除の時間計算量はいずれも \\(O(\\log n)\\) である。二分探索木が連結リストへ退化すると、各操作の時間計算量は \\(O(n)\\) まで悪化する。</li> <li>AVL 木は平衡二分探索木とも呼ばれ、回転操作によって、ノードの挿入と削除を繰り返した後も木が平衡を保つようにしている。</li> <li>AVL 木の回転操作には、右回転、左回転、右回転してから左回転、左回転してから右回転がある。ノードの挿入または削除の後、AVL 木は下から上へ回転操作を行い、木を再び平衡状態に戻す。</li> </ul>","path":["第 7 章 &nbsp; 木","7.6 &nbsp; まとめ"],"tags":[]},{"location":"chapter_tree/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q：ノードが 1 つしかない二分木では、木の高さと根ノードの深さはどちらも \\(0\\) ですか？</p> <p>はい。高さと深さは通常「通過した辺の本数」として定義されるからです。</p> <p>Q：二分木における挿入と削除は通常一連の操作を組み合わせて完了しますが、ここでいう「一連の操作」とは何を指すのでしょうか？リソースの子ノードに対するリソース解放と理解できますか？</p> <p>二分探索木を例にすると、ノード削除は 3 つのケースに分けて処理する必要があり、各ケースで複数段階のノード操作が必要になります。</p> <p>Q：なぜ DFS による二分木走査には前順・中順・後順の 3 種類があり、それぞれどのような用途があるのですか？</p> <p>配列の順方向走査と逆方向走査に似て、前順・中順・後順走査は二分木の 3 つの走査方法であり、特定の順序で走査結果を得るために使えます。たとえば二分探索木では、ノードの大小関係が <code>左子ノードの値 &lt; 根ノードの値 &lt; 右子ノードの値</code> を満たすため、「左 \\(\\rightarrow\\) 根 \\(\\rightarrow\\) 右」の優先順で木を走査すれば、整列済みのノード列を得られます。</p> <p>Q：右回転操作は不平衡ノード <code>node</code>、<code>child</code>、<code>grand_child</code> の関係を処理するものですが、<code>node</code> の親ノードと <code>node</code> の元の接続は維持しなくてよいのですか？右回転後に切れてしまいませんか？</p> <p>この問題は再帰の視点から考える必要があります。右回転操作 <code>right_rotate(root)</code> に渡されるのは部分木の根ノードであり、最終的に <code>return child</code> によって回転後の部分木の根ノードを返します。部分木の根ノードとその親ノードの接続は、この関数の返却後に行われるため、右回転操作自身が管理する範囲には含まれません。</p> <p>Q：C++ では関数を <code>private</code> と <code>public</code> に分けますが、この設計にはどのような考えがありますか？なぜ <code>height()</code> 関数と <code>updateHeight()</code> 関数をそれぞれ <code>public</code> と <code>private</code> に置くのですか？</p> <p>主に、そのメソッドの利用範囲を見て決めます。メソッドがクラス内部でしか使われないなら、<code>private</code> に設計します。たとえば、利用者が <code>updateHeight()</code> を単独で呼び出しても意味はなく、これは挿入や削除の途中の 1 ステップにすぎません。一方で <code>height()</code> はノードの高さにアクセスするためのもので、<code>vector.size()</code> に似た役割を持つため、使いやすいように <code>public</code> に設定します。</p> <p>Q：入力データの集合から二分探索木をどのように構築しますか？根ノードの選び方は重要ですか？</p> <p>はい。木の構築方法は、二分探索木のコード中の <code>build_tree()</code> メソッドですでに示されています。根ノードの選択については、通常は入力データをソートし、その中央の要素を根ノードにしてから、左右の部分木を再帰的に構築します。こうすることで、木の平衡性を最大限に保てます。</p> <p>Q：Java では、文字列比較には必ず <code>equals()</code> メソッドを使うべきですか？</p> <p>Java では、基本データ型については <code>==</code> を使って 2 つの変数の値が等しいかどうかを比較します。参照型については、この 2 つの記法の働き方は異なります。</p> <ul> <li><code>==</code> ：2 つの変数が同じオブジェクトを指しているか、つまりメモリ上の位置が同じかどうかを比較するために使います。</li> <li><code>equals()</code>：2 つのオブジェクトの値が等しいかどうかを比較するために使います。</li> </ul> <p>したがって、値を比較したい場合は <code>equals()</code> を使うべきです。ただし、<code>String a = \"hi\"; String b = \"hi\";</code> によって初期化された文字列は文字列定数プールに格納され、同じオブジェクトを指すため、<code>a == b</code> でも 2 つの文字列の内容を比較できます。</p> <p>Q：幅優先走査で最下層に到達する前、キュー内のノード数は \\(2^h\\) ですか？</p> <p>はい。たとえば高さ \\(h = 2\\) の充足二分木では、ノード総数は \\(n = 7\\) であり、最下層のノード数は \\(4 = 2^h = (n + 1) / 2\\) です。</p>","path":["第 7 章 &nbsp; 木","7.6 &nbsp; まとめ"],"tags":[]}]}
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diff --git a/ja/stylesheets/extra.css b/ja/stylesheets/extra.css
index f35b169d8..4bc4d3748 100644
--- a/ja/stylesheets/extra.css
+++ b/ja/stylesheets/extra.css
@@ -375,6 +375,14 @@ a:hover .text-button span {
   font-weight: normal;
 }
 
+.hero-div--en {
+  font-size: min(1.65vh, 2.3vw);
+}
+
+.hero-div--ru {
+  font-size: min(1.45vh, 2vw);
+}
+
 .hero-bg {
   height: 100%;
   width: 100%;
@@ -487,6 +495,11 @@ a:hover .text-button span {
   text-align: center;
 }
 
+.profile-cell a:hover b,
+.profile-cell a:focus-visible b {
+  text-decoration: underline;
+}
+
 .profile-img {
   width: 5em;
   border-radius: 50%;
@@ -768,4 +781,4 @@ html:has(body[data-md-color-scheme="default"]) {
 .md-typeset a:not(.md-button):focus-visible {
   text-decoration: underline;
 }
-/*! update cache: 20260329054750 */
+/*! update cache: 20260330081613 */
diff --git a/javascripts/katex.js b/javascripts/katex.js
index 615872276..6beb90293 100644
--- a/javascripts/katex.js
+++ b/javascripts/katex.js
@@ -8,4 +8,4 @@ document$.subscribe(({ body }) => {
     ],
   });
 });
-/*! update cache: 20260329054721 */
+/*! update cache: 20260330081538 */
diff --git a/javascripts/mathjax.js b/javascripts/mathjax.js
index 8add8c7bd..070f6c316 100644
--- a/javascripts/mathjax.js
+++ b/javascripts/mathjax.js
@@ -15,4 +15,4 @@ window.MathJax = {
 document$.subscribe(() => {
   MathJax.typesetPromise();
 });
-/*! update cache: 20260329054721 */
+/*! update cache: 20260330081538 */
diff --git a/javascripts/starfield.js b/javascripts/starfield.js
index b94ca8769..0fb623ac9 100644
--- a/javascripts/starfield.js
+++ b/javascripts/starfield.js
@@ -469,4 +469,4 @@
 
   return Starfield;
 });
-/*! update cache: 20260329054721 */
+/*! update cache: 20260330081538 */
diff --git a/ru/404.html b/ru/404.html
index d0739c001..39734f6fe 100644
--- a/ru/404.html
+++ b/ru/404.html
@@ -59,8 +59,8 @@
         
         
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-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
@@ -567,7 +567,7 @@
   <span class="md-ellipsis">
     
   
-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
     
@@ -589,7 +589,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
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-    1.2 Что такое структуры данных и алгоритмы
+    1.2 Что такое алгоритм
   
 
     
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+    Глава 4. Массивы и списки
   
 
     
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-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
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+    4.4 Оперативная память и кэш *
   
 
     
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   <span class="md-ellipsis">
     
   
-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
     
@@ -1606,7 +1606,7 @@
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-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
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+    Глава 7. Деревья
   
 
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-    7.6 Резюме
+    7.6 Краткие итоги
   
 
     
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-    8.3 Задача Top-K
+    8.3 Задача Top-k
   
 
     
@@ -2217,7 +2217,7 @@
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-    Глава 9. Граф
+    Глава 9. Графы
   
 
     
@@ -2239,7 +2239,7 @@
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+    Глава 9. Графы
   
 
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@@ -2289,7 +2289,7 @@
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@@ -3134,7 +3134,7 @@
   <span class="md-ellipsis">
     
   
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@@ -3664,7 +3664,7 @@
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rect{fill:var(--md-mermaid-edge-color)!important;stroke:none!important}.statediagram-cluster.statediagram-cluster .inner{fill:var(--md-default-bg-color)}.statediagram-cluster rect{fill:var(--md-mermaid-node-bg-color);stroke:var(--md-mermaid-node-fg-color)}.statediagram-state rect.divider{fill:var(--md-default-fg-color--lightest);stroke:var(--md-default-fg-color--lighter)}defs #statediagram-barbEnd{stroke:var(--md-mermaid-edge-color)}[id^=entity] path,[id^=entity] rect{fill:var(--md-default-bg-color)}.relationshipLine{stroke:var(--md-mermaid-edge-color)}defs .marker.oneOrMore.er *,defs .marker.onlyOne.er *,defs .marker.zeroOrMore.er *,defs .marker.zeroOrOne.er 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t.pipe(g(r=>R(Y(!0),Y(!1).pipe(It(2e3))).pipe(f(n=>({message:r,active:n})))))}function Fs(e,t){let r=G(".md-typeset",e);return j(()=>{let n=new I;return n.subscribe(({message:o,active:i})=>{e.classList.toggle("md-dialog--active",i),r.textContent=o}),dp(e,t).pipe($(o=>n.next(o)),V(()=>n.complete()),f(o=>H({ref:e},o)))})}function hp({viewport$:e}){if(!X("header.autohide"))return Y(!1);let t=e.pipe(f(({offset:{y:o}})=>o),Pt(2,1),f(([o,i])=>[o<i,i]),fe(0)),r=re([e,t]).pipe(L(([{offset:o},[,i]])=>Math.abs(i-o.y)>100),f(([,[o]])=>o),ie()),n=Tn("search");return re([e,n]).pipe(f(([{offset:o},i])=>o.y>400&&!i),ie(),g(o=>o?r:Y(!1)),J(!1))}function Us(e,t){return j(()=>re([Re(e),hp(t)])).pipe(f(([{height:r},n])=>({height:r,hidden:n})),ie((r,n)=>r.height===n.height&&r.hidden===n.hidden),se(1))}function Ns(e,{viewport$:t,header$:r,main$:n}){return j(()=>{let o=new 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Y(e)}function Mp(e){for(let n of["[data-md-component=announce]","[data-md-component=container]","[data-md-component=header-topic]","[data-md-component=outdated]","[data-md-component=logo]","[data-md-component=skip]",...X("navigation.tabs.sticky")?["[data-md-component=tabs]"]:[]]){let o=Le(n),i=Le(n,e);typeof o!="undefined"&&typeof i!="undefined"&&o.replaceWith(i)}let t=ac(document);for(let[n,o]of ac(e))t.has(n)?t.delete(n):document.head.appendChild(o);for(let n of t.values()){let o=n.getAttribute("name");o!=="theme-color"&&o!=="color-scheme"&&n.remove()}let r=ht("container");return nt(P("script",r)).pipe(g(n=>{let o=e.createElement("script");if(n.src){for(let i of n.getAttributeNames())o.setAttribute(i,n.getAttribute(i));return n.replaceWith(o),new U(i=>{o.onload=()=>i.complete()})}else return o.textContent=n.textContent,n.replaceWith(o),y}),he(),ye(document))}function cc({sitemap$:e,location$:t,viewport$:r,progress$:n}){if(location.protocol==="file:")return 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0:c.y)!=null?l:0):(history.scrollRestoration="auto",es(s.hash),history.scrollRestoration="manual")}),t.subscribe(()=>{history.scrollRestoration="manual"}),b(window,"beforeunload").subscribe(()=>{history.scrollRestoration="auto"}),r.pipe(fe("offset"),Be(100)).subscribe(({offset:s})=>{history.replaceState(s,"")}),X("navigation.instant.prefetch")&&R(b(document.body,"mousemove"),b(document.body,"focusin")).pipe(Ze(e),g(([s,c])=>ic(s,c)),Be(25),Yn(({href:s})=>s),cn(s=>{let c=document.createElement("link");return c.rel="prefetch",c.href=s.toString(),document.head.appendChild(c),b(c,"load").pipe(f(()=>c),Me(1))})).subscribe(s=>s.remove()),a}function lc(e){var u;let{selectedVersionSitemap:t,selectedVersionBaseURL:r,currentLocation:n,currentBaseURL:o}=e,i=(u=Ho(o))==null?void 0:u.pathname;if(i===void 0)return;let a=kp(n.pathname,i);if(a===void 0)return;let s=Cp(t.keys());if(!t.has(s))return;let c=Ho(a,s);if(!c||!t.has(c.href))return;let l=Ho(a,r);if(l)return l.hash=n.hash,l.search=n.search,l}function Ho(e,t){try{return new URL(e,t)}catch(r){return}}function kp(e,t){if(e.startsWith(t))return e.slice(t.length)}function Ap(e,t){let r=Math.min(e.length,t.length),n;for(n=0;n<r&&e[n]===t[n];++n);return n}function Cp(e){let t;for(let r of e)t===void 0?t=r:t=t.slice(0,Ap(t,r));return t!=null?t:""}function uc({document$:e}){let t=Ue(),r=et(new URL("../versions.json",t.base)).pipe(_e(()=>y)),n=r.pipe(f(o=>{let[,i]=t.base.match(/([^/]+)\/?$/);return o.find(({version:a,aliases:s})=>a===i||s.includes(i))||o[0]}));r.pipe(f(o=>new Map(o.map(i=>[`${new URL(`../${i.version}/`,t.base)}`,i]))),g(o=>b(document.body,"click").pipe(L(i=>!i.metaKey&&!i.ctrlKey),pe(n),g(([i,a])=>{if(i.target instanceof Element){let s=i.target.closest("a");if(s&&!s.target&&o.has(s.href)){let c=s.href;return!i.target.closest(".md-version")&&o.get(c)===a?y:(i.preventDefault(),Y(new URL(c)))}}return y}),g(i=>dr(i).pipe(f(a=>{var s;return(s=lc({selectedVersionSitemap:a,selectedVersionBaseURL:i,currentLocation:Ye(),currentBaseURL:t.base}))!=null?s:i})))))).subscribe(o=>dt(o,!0)),re([r,n]).subscribe(([o,i])=>{G(".md-header__topic").appendChild(_s(o,i))}),e.pipe(g(()=>n)).subscribe(o=>{var s;let i=new URL(t.base),a=__md_get("__outdated",sessionStorage,i);if(a===null){a=!0;let c=((s=t.version)==null?void 0:s.default)||"latest";Array.isArray(c)||(c=[c]);e:for(let l of c)for(let u of o.aliases.concat(o.version))if(new RegExp(l,"i").test(u)){a=!1;break e}__md_set("__outdated",a,sessionStorage,i)}if(a)for(let c of Ee("outdated"))c.hidden=!1})}function pc({document$:e,viewport$:t}){e.pipe(g(()=>P(".md-ellipsis")),oe(r=>Et(r).pipe(Q(e.pipe(ke(1))),L(n=>n),f(()=>r),Me(1))),L(r=>r.offsetWidth<r.scrollWidth),oe(r=>{let n=r.innerText,o=r.closest("a")||r;return o.title=n,X("content.tooltips")?Ge(o,{viewport$:t}).pipe(Q(e.pipe(ke(1))),V(()=>o.removeAttribute("title"))):y})).subscribe(),X("content.tooltips")&&e.pipe(g(()=>P(".md-status")),oe(r=>Ge(r,{viewport$:t}))).subscribe()}function fc({document$:e,tablet$:t}){e.pipe(g(()=>P(".md-toggle--indeterminate")),$(r=>{r.indeterminate=!0,r.checked=!1}),oe(r=>b(r,"change").pipe(Xn(()=>r.classList.contains("md-toggle--indeterminate")),f(()=>r))),pe(t)).subscribe(([r,n])=>{r.classList.remove("md-toggle--indeterminate"),n&&(r.checked=!1)})}function Hp(){return/(iPad|iPhone|iPod)/.test(navigator.userAgent)}function mc({document$:e}){e.pipe(g(()=>P("[data-md-scrollfix]")),$(t=>t.removeAttribute("data-md-scrollfix")),L(Hp),oe(t=>b(t,"touchstart").pipe(f(()=>t)))).subscribe(t=>{let r=t.scrollTop;r===0?t.scrollTop=1:r+t.offsetHeight===t.scrollHeight&&(t.scrollTop=r-1)})}Object.entries||(Object.entries=function(e){let t=[];for(let r of Object.keys(e))t.push([r,e[r]]);return t});Object.values||(Object.values=function(e){let t=[];for(let r of Object.keys(e))t.push(e[r]);return t});typeof Element!="undefined"&&(Element.prototype.scrollTo||(Element.prototype.scrollTo=function(e,t){typeof e=="object"?(this.scrollLeft=e.left,this.scrollTop=e.top):(this.scrollLeft=e,this.scrollTop=t)}),Element.prototype.replaceWith||(Element.prototype.replaceWith=function(...e){let t=this.parentNode;if(t){e.length===0&&t.removeChild(this);for(let r=e.length-1;r>=0;r--){let n=e[r];typeof n=="string"?n=document.createTextNode(n):n.parentNode&&n.parentNode.removeChild(n),r?t.insertBefore(this.previousSibling,n):t.replaceChild(n,this)}}}));function $p(){return location.protocol==="file:"?ar(`${new URL("search.js",Mn.base)}`).pipe(f(()=>__index),_e(()=>Ke),se(1)):et(new URL("search.json",Mn.base))}document.documentElement.classList.remove("no-js");document.documentElement.classList.add("js");var vt=Si(),Ur=Za(),hr=ts(Ur),hc=Xa(),ze=cs(),$o=Ir("(min-width: 60em)"),vc=Ir("(min-width: 76.25em)"),bc=rs(),Mn=Ue(),gc=Le(".md-search")?$p():Ke,Po=new I;oc({alert$:Po});nc({document$:vt});var Io=new I,_c=dr(Mn.base);X("navigation.instant")&&cc({sitemap$:_c,location$:Ur,viewport$:ze,progress$:Io}).subscribe(vt);var dc;((dc=Mn.version)==null?void 0:dc.provider)==="mike"&&uc({document$:vt});R(Ur,hr).pipe(It(125)).subscribe(()=>{Eo("drawer",!1),Eo("search",!1)});hc.pipe(L(({mode:e,meta:t})=>e==="global"&&!t)).subscribe(e=>{switch(e.type){case",":case"p":let t=document.querySelector("link[rel=prev]");t instanceof HTMLLinkElement&&dt(t);break;case".":case"n":let r=document.querySelector("link[rel=next]");r instanceof HTMLLinkElement&&dt(r);break;case"/":let n=document.querySelector("[data-md-component=search] button");n instanceof HTMLButtonElement&&n.click();break;case"Enter":let o=xt();o instanceof HTMLLabelElement&&o.click()}});pc({viewport$:ze,document$:vt});fc({document$:vt,tablet$:$o});mc({document$:vt});var Lt=Us(ht("header"),{viewport$:ze}),Fr=vt.pipe(f(()=>ht("main")),g(e=>Ws(e,{viewport$:ze,header$:Lt})),se(1)),Pp=R(...Ee("consent").map(e=>us(e,{target$:hr})),...Ee("dialog").map(e=>Fs(e,{alert$:Po})),...Ee("palette").map(e=>Vs(e)),...Ee("progress").map(e=>zs(e,{progress$:Io})),...Ee("search").map(e=>Ks(e,{index$:gc})),...Ee("source").map(e=>Zs(e))),Ip=j(()=>R(...Ee("announce").map(e=>ls(e)),...Ee("content").map(e=>js(e,{sitemap$:_c,viewport$:ze,target$:hr,print$:bc})),...Ee("content").map(e=>X("search.highlight")?Ys(e,{index$:gc,location$:Ur}):y),...Ee("header").map(e=>Ns(e,{viewport$:ze,header$:Lt,main$:Fr})),...Ee("header-title").map(e=>Ds(e,{viewport$:ze,header$:Lt})),...Ee("sidebar").map(e=>e.getAttribute("data-md-type")==="navigation"?yo(vc,()=>Ao(e,{viewport$:ze,header$:Lt,main$:Fr})):yo($o,()=>Ao(e,{viewport$:ze,header$:Lt,main$:Fr}))),...Ee("tabs").map(e=>Qs(e,{viewport$:ze,header$:Lt})),...Ee("toc").map(e=>ec(e,{viewport$:ze,header$:Lt,main$:Fr,target$:hr})),...Ee("top").map(e=>tc(e,{viewport$:ze,header$:Lt,main$:Fr,target$:hr})))),yc=vt.pipe(g(()=>Ip),Rt(Pp),se(1));yc.subscribe();window.document$=vt;window.location$=Ur;window.target$=hr;window.keyboard$=hc;window.viewport$=ze;window.tablet$=$o;window.screen$=vc;window.print$=bc;window.alert$=Po;window.progress$=Io;window.component$=yc;})();
-/*! update cache: 20260329054803 */
+/*! update cache: 20260330081625 */
diff --git a/ru/chapter_appendix/contribution/index.html b/ru/chapter_appendix/contribution/index.html
index 7022d46ac..99948bf17 100644
--- a/ru/chapter_appendix/contribution/index.html
+++ b/ru/chapter_appendix/contribution/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
@@ -574,7 +574,7 @@
   <span class="md-ellipsis">
     
   
-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
     
@@ -596,7 +596,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
           </label>
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 Что такое структуры данных и алгоритмы
+    1.2 Что такое алгоритм
   
 
     
@@ -1181,7 +1181,7 @@
   <span class="md-ellipsis">
     
   
-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
     
@@ -1203,7 +1203,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
           </label>
@@ -1309,7 +1309,7 @@
   <span class="md-ellipsis">
     
   
-    4.4 Память и кеш *
+    4.4 Оперативная память и кэш *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
           </label>
@@ -1691,7 +1691,7 @@
   <span class="md-ellipsis">
     
   
-    6.3 Хеш-алгоритмы
+    6.3 Алгоритмы хеширования
   
 
     
@@ -1786,7 +1786,7 @@
   <span class="md-ellipsis">
     
   
-    Глава 7. Дерево
+    Глава 7. Деревья
   
 
     
@@ -1808,7 +1808,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 7. Дерево
+    Глава 7. Деревья
   
 
           </label>
@@ -1886,7 +1886,7 @@
   <span class="md-ellipsis">
     
   
-    7.3 Представление дерева массивом
+    7.3 Представление двоичного дерева массивом
   
 
     
@@ -1970,7 +1970,7 @@
   <span class="md-ellipsis">
     
   
-    7.6 Резюме
+    7.6 Краткие итоги
   
 
     
@@ -2133,7 +2133,7 @@
   <span class="md-ellipsis">
     
   
-    8.3 Задача Top-K
+    8.3 Задача Top-k
   
 
     
@@ -2224,7 +2224,7 @@
   <span class="md-ellipsis">
     
   
-    Глава 9. Граф
+    Глава 9. Графы
   
 
     
@@ -2246,7 +2246,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 9. Граф
+    Глава 9. Графы
   
 
           </label>
@@ -2296,7 +2296,7 @@
   <span class="md-ellipsis">
     
   
-    9.2 Базовые операции над графами
+    9.2 Базовые операции графа
   
 
     
@@ -2352,7 +2352,7 @@
   <span class="md-ellipsis">
     
   
-    9.4 Резюме
+    9.4 Краткие итоги
   
 
     
@@ -2491,7 +2491,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 Точка вставки двоичного поиска
+    10.2 Двоичный поиск точки вставки
   
 
     
@@ -2519,7 +2519,7 @@
   <span class="md-ellipsis">
     
   
-    10.3 Граничные случаи двоичного поиска
+    10.3 Двоичный поиск границ
   
 
     
@@ -2547,7 +2547,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 Стратегия оптимизации через хеширование
+    10.4 Стратегии оптимизации хеширования
   
 
     
@@ -2575,7 +2575,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 Алгоритмы поиска: новый взгляд
+    10.5 Переосмысление алгоритмов поиска
   
 
     
@@ -2780,7 +2780,7 @@
   <span class="md-ellipsis">
     
   
-    11.3 Пузырьковая сортировка
+    11.3 Сортировка пузырьком
   
 
     
@@ -2808,7 +2808,7 @@
   <span class="md-ellipsis">
     
   
-    11.4 Сортировка вставкой
+    11.4 Сортировка вставками
   
 
     
@@ -3113,7 +3113,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 Алгоритмы разделяй и властвуй
+    12.1 Стратегия разделяй и властвуй
   
 
     
@@ -3141,7 +3141,7 @@
   <span class="md-ellipsis">
     
   
-    12.2 Стратегия поиска разделяй и властвуй
+    12.2 Поисковая стратегия разделяй и властвуй
   
 
     
@@ -3418,7 +3418,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 Задача о $n$ ферзях
+    13.4 Задача о n ферзях
   
 
     
@@ -3559,7 +3559,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 Введение в динамическое программирование
+    14.1 Первое знакомство с динамическим программированием
   
 
     
@@ -3671,7 +3671,7 @@
   <span class="md-ellipsis">
     
   
-    14.5 Задача о неограниченном рюкзаке
+    14.5 Задача о полном рюкзаке
   
 
     
@@ -4378,34 +4378,34 @@
 <!-- Page content -->
 <h1 id="162">16.2 &nbsp; Присоединяйтесь к созданию книги<a class="headerlink" href="#162" title="Permanent link">&para;</a></h1>
 <p>Возможности автора ограничены, поэтому в книге неизбежно могут встречаться упущения и ошибки. Просим отнестись к этому с пониманием. Если вы заметите опечатки, неработающие ссылки, пропуски в содержании, двусмысленные формулировки, неясные объяснения или неудачную структуру изложения, пожалуйста, помогите нам это исправить, чтобы читатели получили более качественный учебный ресурс.</p>
-<p>GitHub ID всех <a href="https://github.com/krahets/hello-algo/graphs/contributors">участников</a> будут указаны на главных страницах репозитория книги, веб-версии и PDF-версии в знак благодарности за их бескорыстный вклад в сообщество открытого исходного кода.</p>
+<p>Все GitHub ID <a href="https://github.com/krahets/hello-algo/graphs/contributors">авторов</a> будут указаны на главных страницах репозитория книги, веб-версии и PDF-версии в знак благодарности за их бескорыстный вклад в сообщество открытого исходного кода.</p>
 <div class="admonition success">
 <p class="admonition-title">Сила открытого исходного кода</p>
 <p>Интервал между двумя тиражами бумажной книги обычно довольно велик, поэтому обновлять содержание очень неудобно.</p>
 <p>В этой же открытой книге цикл обновления содержания сокращается до нескольких дней, а иногда даже до нескольких часов.</p>
 </div>
 <h3 id="1">1. &nbsp; Небольшие правки содержания<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>Как показано на рисунке 16-3, в правом верхнем углу каждой страницы есть "значок редактирования". Вы можете изменить текст или код следующим образом.</p>
+<p>Как показано на рисунке 16-3, в правом верхнем углу каждой страницы есть "значок редактирования". Текст или код можно изменить следующим образом.</p>
 <ol>
 <li>Нажмите на "значок редактирования". Если появится сообщение "You need to fork this repository", согласитесь с этим действием.</li>
 <li>Измените содержимое исходного Markdown-файла, проверьте корректность правок и постарайтесь сохранить единый стиль оформления.</li>
-<li>Внизу страницы заполните описание изменений, затем нажмите кнопку "Propose file change". После перехода на следующую страницу нажмите кнопку "Create pull request", чтобы создать pull request.</li>
+<li>Внизу страницы заполните описание изменений, затем нажмите кнопку "Propose file change". После перехода на следующую страницу нажмите кнопку "Create pull request", чтобы отправить pull request.</li>
 </ol>
 <p><img alt="Кнопка редактирования страницы" class="animation-figure" src="../contribution.assets/edit_markdown.png" /></p>
 <p align="center"> Рисунок 16-3 &nbsp; Кнопка редактирования страницы </p>
 
-<p>Изображения нельзя изменить напрямую, поэтому проблему с ними нужно описывать через новый <a href="https://github.com/krahets/hello-algo/issues">Issue</a> или комментарий. Мы постараемся как можно быстрее перерисовать и заменить изображение.</p>
+<p>Изображения нельзя изменить напрямую, поэтому проблему с ними нужно описывать через новый <a href="https://github.com/krahets/hello-algo/issues">Issue</a> или комментарий. Мы постараемся как можно быстрее исправить и обновить изображение.</p>
 <h3 id="2">2. &nbsp; Создание содержания<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>Если вам интересно участвовать в этом проекте с открытым исходным кодом, например переводить код на другие языки программирования или расширять содержание статей, то следует придерживаться следующего рабочего процесса Pull Request.</p>
+<p>Если вам интересно участвовать в этом проекте с открытым исходным кодом, например переводить код на другие языки программирования или расширять содержание статей, то следует придерживаться следующего процесса Pull Request.</p>
 <ol>
 <li>Войдите в GitHub и сделайте Fork <a href="https://github.com/krahets/hello-algo">репозитория книги</a> в свой личный аккаунт.</li>
 <li>Перейдите на страницу своего Fork-репозитория и с помощью команды <code>git clone</code> клонируйте репозиторий локально.</li>
 <li>Создавайте и редактируйте содержание локально, затем проведите полное тестирование и проверьте корректность кода.</li>
-<li>Сделайте Commit для локальных изменений, после чего выполните Push в удаленный репозиторий.</li>
-<li>Обновите страницу репозитория и нажмите кнопку "Create pull request", чтобы отправить pull request.</li>
+<li>Зафиксируйте локальные изменения, после чего выполните Push в удаленный репозиторий.</li>
+<li>Обновите страницу репозитория и нажмите кнопку "Create pull request", чтобы инициировать pull request.</li>
 </ol>
 <h3 id="3-docker">3. &nbsp; Развертывание Docker<a class="headerlink" href="#3-docker" title="Permanent link">&para;</a></h3>
-<p>В корневом каталоге <code>hello-algo</code> выполните следующий Docker-скрипт, после чего проект будет доступен по адресу <code>http://localhost:8000</code>:</p>
+<p>В корневом каталоге <code>hello-algo</code> выполните следующий Docker-скрипт, после чего проект станет доступен по адресу <code>http://localhost:8000</code>:</p>
 <div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a>docker-compose<span class="w"> </span>up<span class="w"> </span>-d
 </code></pre></div>
 <p>Удалить развертывание можно следующей командой:</p>
diff --git a/ru/chapter_appendix/index.html b/ru/chapter_appendix/index.html
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--- a/ru/chapter_appendix/index.html
+++ b/ru/chapter_appendix/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
@@ -574,7 +574,7 @@
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+    Глава 1. Введение в алгоритмы
   
 
     
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             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
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@@ -646,7 +646,7 @@
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-    1.2 Что такое структуры данных и алгоритмы
+    1.2 Что такое алгоритм
   
 
     
@@ -1181,7 +1181,7 @@
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-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
     
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             <span class="md-nav__icon md-icon"></span>
             
   
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+    Глава 4. Массивы и списки
   
 
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-    4.4 Память и кеш *
+    4.4 Оперативная память и кэш *
   
 
     
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   <span class="md-ellipsis">
     
   
-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
     
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             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
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@@ -1691,7 +1691,7 @@
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-    6.3 Хеш-алгоритмы
+    6.3 Алгоритмы хеширования
   
 
     
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+    Глава 7. Деревья
   
 
     
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-    Глава 7. Дерево
+    Глава 7. Деревья
   
 
           </label>
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-    7.3 Представление дерева массивом
+    7.3 Представление двоичного дерева массивом
   
 
     
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-    7.6 Резюме
+    7.6 Краткие итоги
   
 
     
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-    8.3 Задача Top-K
+    8.3 Задача Top-k
   
 
     
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-    Глава 9. Граф
+    Глава 9. Графы
   
 
     
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-    Глава 9. Граф
+    Глава 9. Графы
   
 
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+    9.2 Базовые операции графа
   
 
     
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-    9.4 Резюме
+    9.4 Краткие итоги
   
 
     
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+    10.2 Двоичный поиск точки вставки
   
 
     
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+    10.3 Двоичный поиск границ
   
 
     
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+    10.4 Стратегии оптимизации хеширования
   
 
     
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-    10.5 Алгоритмы поиска: новый взгляд
+    10.5 Переосмысление алгоритмов поиска
   
 
     
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+    12.1 Стратегия разделяй и властвуй
   
 
     
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         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
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 <!-- Page content -->
 <h1 id="161">16.1 &nbsp; Установка среды программирования<a class="headerlink" href="#161" title="Permanent link">&para;</a></h1>
 <h2 id="1611-ide">16.1.1 &nbsp; Установка IDE<a class="headerlink" href="#1611-ide" title="Permanent link">&para;</a></h2>
-<p>В качестве локальной интегрированной среды разработки (IDE) рекомендуется использовать открытую и легковесную VS Code. Перейдите на <a href="https://code.visualstudio.com/">официальный сайт VS Code</a>, выберите версию для своей операционной системы и установите ее.</p>
+<p>В качестве локальной интегрированной среды разработки (IDE) рекомендуется использовать открытую и быструю VS Code. Перейдите на <a href="https://code.visualstudio.com/">официальный сайт VS Code</a>, выберите версию для своей операционной системы и установите ее.</p>
 <p><img alt="Загрузка VS Code с официального сайта" class="animation-figure" src="../installation.assets/vscode_installation.png" /></p>
 <p align="center"> Рисунок 16-1 &nbsp; Загрузка VS Code с официального сайта </p>
 
-<p>VS Code обладает мощной экосистемой расширений и поддерживает запуск и отладку большинства языков программирования. Например, после установки расширения "Python Extension Pack" можно отлаживать код на Python. Процесс установки показан на рисунке 16-2.</p>
+<p>VS Code обладает мощной экосистемой расширений и поддерживает выполнение и отладку большинства языков программирования. Например, после установки расширения "Python Extension Pack" можно отлаживать код на Python. Процесс установки показан на рисунке 16-2.</p>
 <p><img alt="Установка расширений VS Code" class="animation-figure" src="../installation.assets/vscode_extension_installation.png" /></p>
 <p align="center"> Рисунок 16-2 &nbsp; Установка расширений VS Code </p>
 
 <h2 id="1612">16.1.2 &nbsp; Установка языковой среды<a class="headerlink" href="#1612" title="Permanent link">&para;</a></h2>
 <h3 id="1-python">1. &nbsp; Среда Python<a class="headerlink" href="#1-python" title="Permanent link">&para;</a></h3>
 <ol>
-<li>Загрузите и установите <a href="https://docs.conda.io/en/latest/miniconda.html">Miniconda3</a>, требуется Python 3.10 или более новая версия.</li>
+<li>Загрузите и установите <a href="https://docs.conda.io/en/latest/miniconda.html">Miniconda3</a>, требуется Python 3.10 или более поздняя версия.</li>
 <li>В магазине расширений VS Code найдите <code>python</code> и установите Python Extension Pack.</li>
 <li>(Необязательно) Введите в командной строке <code>pip install black</code>, чтобы установить инструмент форматирования кода.</li>
 </ol>
 <h3 id="2-cc">2. &nbsp; Среда C/C++<a class="headerlink" href="#2-cc" title="Permanent link">&para;</a></h3>
 <ol>
-<li>В Windows требуется установить <a href="https://sourceforge.net/projects/mingw-w64/files/">MinGW</a> (<a href="https://blog.csdn.net/qq_33698226/article/details/129031241">руководство по настройке</a>); в macOS Clang уже установлен по умолчанию.</li>
+<li>В Windows требуется установить <a href="https://sourceforge.net/projects/mingw-w64/files/">MinGW</a> (<a href="https://blog.csdn.net/qq_33698226/article/details/129031241">руководство по настройке</a>); в macOS компилятор Clang уже установлен по умолчанию.</li>
 <li>В магазине расширений VS Code найдите <code>c++</code> и установите C/C++ Extension Pack.</li>
 <li>(Необязательно) Откройте страницу Settings, найдите параметр форматирования <code>Clang_format_fallback Style</code> и задайте значение <code>{ BasedOnStyle: Microsoft, BreakBeforeBraces: Attach }</code>.</li>
 </ol>
diff --git a/ru/chapter_appendix/terminology/index.html b/ru/chapter_appendix/terminology/index.html
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+++ b/ru/chapter_appendix/terminology/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
@@ -574,7 +574,7 @@
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+    Глава 1. Введение в алгоритмы
   
 
     
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+    Глава 1. Введение в алгоритмы
   
 
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-    1.2 Что такое структуры данных и алгоритмы
+    1.2 Что такое алгоритм
   
 
     
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+    Глава 4. Массивы и списки
   
 
     
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-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
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+    4.4 Оперативная память и кэш *
   
 
     
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-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
     
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-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
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+    6.3 Алгоритмы хеширования
   
 
     
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+    7.3 Представление двоичного дерева массивом
   
 
     
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+    8.3 Задача Top-k
   
 
     
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+    Глава 9. Графы
   
 
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+    9.4 Краткие итоги
   
 
     
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+    10.2 Двоичный поиск точки вставки
   
 
     
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+    10.3 Двоичный поиск границ
   
 
     
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-    10.4 Стратегия оптимизации через хеширование
+    10.4 Стратегии оптимизации хеширования
   
 
     
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-    10.5 Алгоритмы поиска: новый взгляд
+    10.5 Переосмысление алгоритмов поиска
   
 
     
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+    11.3 Сортировка пузырьком
   
 
     
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+    12.1 Стратегия разделяй и властвуй
   
 
     
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+    13.4 Задача о n ферзях
   
 
     
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   <span class="md-ellipsis">
     
   
-    14.1 Введение в динамическое программирование
+    14.1 Первое знакомство с динамическим программированием
   
 
     
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   <span class="md-ellipsis">
     
   
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+    14.5 Задача о полном рюкзаке
   
 
     
@@ -4265,10 +4265,10 @@
 
 <!-- Page content -->
 <h1 id="163">16.3 &nbsp; Глоссарий<a class="headerlink" href="#163" title="Permanent link">&para;</a></h1>
-<p>В таблице 16-1 перечислены важные термины, встречающиеся в книге. Обратите внимание на следующие моменты.</p>
+<p>В таблице 16-1 приведены важные термины, встречающиеся в книге. Обратите внимание на следующие моменты.</p>
 <ul>
-<li>Рекомендуем запомнить английские названия терминов, чтобы легче читать англоязычную литературу.</li>
-<li>В русской версии приводится единый рекомендуемый перевод каждого термина.</li>
+<li>Рекомендуем запомнить английские названия терминов, чтобы легче читать англоязычные материалы.</li>
+<li>В русской версии для каждого термина приводится единый рекомендуемый перевод.</li>
 </ul>
 <p align="center"> Таблица 16-1 &nbsp; Важные термины по структурам данных и алгоритмам </p>
 
@@ -4451,7 +4451,7 @@
 </tr>
 <tr>
 <td>bucket</td>
-<td>корзина</td>
+<td>бакет</td>
 </tr>
 <tr>
 <td>hash function</td>
@@ -4543,11 +4543,11 @@
 </tr>
 <tr>
 <td>complete binary tree</td>
-<td>совершенное двоичное дерево</td>
+<td>полное двоичное дерево</td>
 </tr>
 <tr>
 <td>full binary tree</td>
-<td>полное двоичное дерево</td>
+<td>строгое двоичное дерево</td>
 </tr>
 <tr>
 <td>balanced binary tree</td>
@@ -4578,8 +4578,16 @@
 <td>обход в глубину</td>
 </tr>
 <tr>
-<td>binary search tree</td>
-<td>двоичное дерево поиска</td>
+<td>pre-order traversal</td>
+<td>прямой обход</td>
+</tr>
+<tr>
+<td>in-order traversal</td>
+<td>симметричный обход</td>
+</tr>
+<tr>
+<td>post-order traversal</td>
+<td>обратный обход</td>
 </tr>
 <tr>
 <td>balanced binary search tree</td>
diff --git a/ru/chapter_array_and_linkedlist/array/index.html b/ru/chapter_array_and_linkedlist/array/index.html
index 3821ab023..099232f8a 100644
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+++ b/ru/chapter_array_and_linkedlist/array/index.html
@@ -65,8 +65,8 @@
         
         
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-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
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   <span class="md-ellipsis">
     
   
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+    Глава 1. Введение в алгоритмы
   
 
     
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 <!-- Page content -->
 <h1 id="41">4.1 &nbsp; Массив<a class="headerlink" href="#41" title="Permanent link">&para;</a></h1>
-<p><u>Массив (array)</u> - это линейная структура данных, которая хранит элементы одного типа в непрерывной области памяти. Положение элемента в массиве называется его <u>индексом (index)</u>. На рисунке 4-1 показаны основные понятия, связанные с массивом, и способ его хранения.</p>
+<p><u>Массив (array)</u> - это линейная структура данных, в которой элементы одного типа хранятся в непрерывной области памяти. Положение элемента в массиве называется его <u>индексом (index)</u>. На рисунке 4-1 показаны основные понятия, связанные с массивом, и способ его хранения.</p>
 <p><img alt="Определение массива и способ хранения" class="animation-figure" src="../array.assets/array_definition.png" /></p>
 <p align="center"> Рисунок 4-1 &nbsp; Определение массива и способ хранения </p>
 
 <h2 id="411">4.1.1 &nbsp; Основные операции с массивом<a class="headerlink" href="#411" title="Permanent link">&para;</a></h2>
 <h3 id="1">1. &nbsp; Инициализация массива<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>В зависимости от задачи мы можем выбрать один из двух способов инициализации массива: без начальных значений или с заданными начальными значениями. Если начальные значения не указаны, большинство языков программирования инициализируют элементы массива значением <span class="arithmatex">\(0\)</span> :</p>
+<p>Существует два способа инициализации массива: без начальных значений и с заданными начальными значениями. Если начальные значения не указаны, большинство языков программирования инициализируют элементы массива нулями:</p>
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@@ -4649,11 +4649,11 @@
 <p>https://pythontutor.com/render.html#code=%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D0%BC%D0%B0%D1%81%D1%81%D0%B8%D0%B2%0Aarr%20%3D%20%5B0%5D%20%2A%205%20%20%23%20%5B%200%2C%200%2C%200%2C%200%2C%200%20%5D%0Anums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D&amp;cumulative=false&amp;curInstr=0&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>
 </details>
 <h3 id="2">2. &nbsp; Доступ к элементам<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>Элементы массива хранятся в непрерывной области памяти, а это означает, что вычислить адрес любого элемента очень просто. Зная адрес массива в памяти (то есть адрес первого элемента) и индекс некоторого элемента, мы можем по формуле с рисунка ниже вычислить адрес этого элемента и напрямую обратиться к нему.</p>
+<p>Элементы массива хранятся в непрерывной области памяти, что упрощает вычисление их адресов. Зная адрес массива в памяти (то есть адрес первого элемента) и индекс некоторого элемента, мы можем по формуле с рисунка ниже вычислить адрес этого элемента и напрямую обратиться к нему.</p>
 <p><img alt="Вычисление адреса элемента массива" class="animation-figure" src="../array.assets/array_memory_location_calculation.png" /></p>
 <p align="center"> Рисунок 4-2 &nbsp; Вычисление адреса элемента массива </p>
 
-<p>Если посмотреть на рисунок 4-2, можно заметить, что индекс первого элемента массива равен <span class="arithmatex">\(0\)</span> , и это кажется не слишком интуитивным, ведь естественнее было бы начинать счет с <span class="arithmatex">\(1\)</span> . Однако с точки зрения формулы адресации <strong>индекс по сути является смещением относительно адреса памяти</strong>. Смещение первого элемента равно <span class="arithmatex">\(0\)</span> , поэтому индекс <span class="arithmatex">\(0\)</span> вполне логичен.</p>
+<p>Если посмотреть на рисунок 4-2, можно заметить, что индекс первого элемента массива равен <span class="arithmatex">\(0\)</span> , и это кажется не слишком интуитивным, ведь естественнее было бы начинать счет с <span class="arithmatex">\(1\)</span> . Однако с точки зрения формулы адресации <strong>индекс по сути является смещением относительно адреса памяти</strong>. Смещение первого элемента равно <span class="arithmatex">\(0\)</span> , поэтому индекс <span class="arithmatex">\(0\)</span> полностью логичен.</p>
 <p>Доступ к элементам массива очень эффективен: любой элемент массива можно получить за <span class="arithmatex">\(O(1)\)</span> времени.</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
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@@ -4808,11 +4808,11 @@
 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=import%20random%0A%0Adef%20random_access%28nums%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%A1%D0%BB%D1%83%D1%87%D0%B0%D0%B9%D0%BD%D1%8B%D0%B9%20%D0%B4%D0%BE%D1%81%D1%82%D1%83%D0%BF%20%D0%BA%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D1%83%22%22%22%0A%20%20%20%20%23%20%D0%A1%D0%BB%D1%83%D1%87%D0%B0%D0%B9%D0%BD%D1%8B%D0%BC%20%D0%BE%D0%B1%D1%80%D0%B0%D0%B7%D0%BE%D0%BC%20%D0%B2%D1%8B%D0%B1%D1%80%D0%B0%D1%82%D1%8C%20%D1%87%D0%B8%D1%81%D0%BB%D0%BE%20%D0%B8%D0%B7%20%D0%B8%D0%BD%D1%82%D0%B5%D1%80%D0%B2%D0%B0%D0%BB%D0%B0%20%5B0%2C%20len%28nums%29-1%5D%0A%20%20%20%20random_index%20%3D%20random.randint%280%2C%20len%28nums%29%20-%201%29%0A%20%20%20%20%23%20%D0%9F%D0%BE%D0%BB%D1%83%D1%87%D0%B8%D1%82%D1%8C%20%D0%B8%20%D0%B2%D0%B5%D1%80%D0%BD%D1%83%D1%82%D1%8C%20%D1%81%D0%BB%D1%83%D1%87%D0%B0%D0%B9%D0%BD%D1%8B%D0%B9%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%0A%20%20%20%20random_num%20%3D%20nums%5Brandom_index%5D%0A%20%20%20%20return%20random_num%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%20%D0%BC%D0%B0%D1%81%D1%81%D0%B8%D0%B2%D0%B0%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20print%28%22%D0%9C%D0%B0%D1%81%D1%81%D0%B8%D0%B2%20nums%20%3D%22%2C%20nums%29%0A%0A%20%20%20%20%23%20%D0%A1%D0%BB%D1%83%D1%87%D0%B0%D0%B9%D0%BD%D1%8B%D0%B9%20%D0%B4%D0%BE%D1%81%D1%82%D1%83%D0%BF%0A%20%20%20%20random_num%3A%20int%20%3D%20random_access%28nums%29%0A%20%20%20%20print%28%22%D0%A1%D0%BB%D1%83%D1%87%D0%B0%D0%B9%D0%BD%D1%8B%D0%B9%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%B8%D0%B7%20nums%20%3D%22%2C%20random_num%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=7&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
 <h3 id="3">3. &nbsp; Вставка элемента<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
-<p>Элементы массива в памяти расположены "вплотную" друг к другу, и между ними нет места для размещения новых данных. Как показано на рисунке 4-3, если мы хотим вставить элемент в середину массива, то все элементы после этой позиции нужно сдвинуть на одну позицию вправо, а затем записать новое значение в освободившийся индекс.</p>
+<p>Элементы массива в памяти расположены вплотную друг к другу, и между ними нет места для размещения новых данных. Как показано на рисунке 4-3, если мы хотим вставить элемент в середину массива, то все элементы после этой позиции нужно сдвинуть на одну позицию вправо, а затем записать новое значение в освободившийся индекс.</p>
 <p><img alt="Пример вставки элемента в массив" class="animation-figure" src="../array.assets/array_insert_element.png" /></p>
 <p align="center"> Рисунок 4-3 &nbsp; Пример вставки элемента в массив </p>
 
-<p>Стоит отметить, что длина массива фиксирована, поэтому вставка нового элемента неизбежно приведет к "потере" элемента на конце массива. Решение этой проблемы мы оставим для обсуждения в разделе о "списках".</p>
+<p>Стоит отметить, что длина массива фиксирована, поэтому вставка нового элемента неизбежно приведет к потере элемента на конце массива. Решение этой проблемы мы оставим для обсуждения в разделе о "списках".</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label></div>
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 <p><img alt="Пример удаления элемента из массива" class="animation-figure" src="../array.assets/array_remove_element.png" /></p>
 <p align="center"> Рисунок 4-4 &nbsp; Пример удаления элемента из массива </p>
 
-<p>Обрати внимание: после удаления исходный последний элемент становится "бессмысленным", поэтому специально изменять его не требуется.</p>
+<p>Обрати внимание: после удаления исходный последний элемент становится бессмысленным, поэтому специально изменять его не требуется.</p>
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 <ul>
 <li><strong>Высокая временная сложность</strong>: средняя временная сложность и вставки, и удаления равна <span class="arithmatex">\(O(n)\)</span> , где <span class="arithmatex">\(n\)</span> - длина массива.</li>
 <li><strong>Потеря элементов</strong>: поскольку длина массива неизменяема, после вставки элементы, выходящие за пределы длины массива, будут потеряны.</li>
-<li><strong>Потери памяти</strong>: можно заранее инициализировать более длинный массив и использовать только его переднюю часть; тогда "теряемые" при вставке элементы на конце не будут нести смысла, но такой подход приводит к лишнему расходу памяти.</li>
+<li><strong>Потери памяти</strong>: можно заранее инициализировать более длинный массив и использовать только его переднюю часть; тогда теряемые при вставке элементы на конце не будут нести смысла, но такой подход приводит к лишнему расходу памяти.</li>
 </ul>
 <h3 id="5">5. &nbsp; Обход массива<a class="headerlink" href="#5" title="Permanent link">&para;</a></h3>
 <p>В большинстве языков программирования массив можно обходить как по индексу, так и напрямую перебирая каждый элемент:</p>
@@ -5346,7 +5346,7 @@
 </details>
 <h3 id="6">6. &nbsp; Поиск элемента<a class="headerlink" href="#6" title="Permanent link">&para;</a></h3>
 <p>Чтобы найти заданный элемент в массиве, нужно пройти по массиву и на каждой итерации проверять, совпадает ли значение; если совпадает, вернуть соответствующий индекс.</p>
-<p>Поскольку массив - это линейная структура данных, такая операция поиска называется "линейным поиском".</p>
+<p>Поскольку массив - это линейная структура данных, такая операция поиска называется линейным поиском.</p>
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@@ -5707,13 +5707,13 @@
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 </details>
 <h2 id="412">4.1.2 &nbsp; Преимущества и ограничения массива<a class="headerlink" href="#412" title="Permanent link">&para;</a></h2>
-<p>Массив хранится в непрерывной области памяти, и все его элементы имеют один и тот же тип. Такой подход содержит много априорной информации, которую система может использовать для оптимизации эффективности операций со структурой данных.</p>
+<p>Массив хранится в непрерывной области памяти, и все его элементы имеют один и тот же тип. Такой подход содержит богатую априорную информацию, которую система может использовать для оптимизации эффективности операций с этой структурой данных.</p>
 <ul>
 <li><strong>Высокая пространственная эффективность</strong>: массив выделяет для данных непрерывный блок памяти без дополнительного структурного накладного расхода.</li>
 <li><strong>Поддержка произвольного доступа</strong>: массив позволяет обращаться к любому элементу за <span class="arithmatex">\(O(1)\)</span> времени.</li>
 <li><strong>Локальность кэша</strong>: при обращении к элементу массива компьютер загружает не только сам элемент, но и соседние данные, что позволяет использовать кэш для ускорения последующих операций.</li>
 </ul>
-<p>Хранение в непрерывной области памяти - палка о двух концах, и у него есть следующие ограничения.</p>
+<p>Непрерывное хранение данных - это палка о двух концах, и у него есть следующие ограничения.</p>
 <ul>
 <li><strong>Низкая эффективность вставки и удаления</strong>: когда элементов в массиве много, вставка и удаление требуют сдвига большого количества элементов.</li>
 <li><strong>Неизменяемая длина</strong>: после инициализации длина массива фиксирована; расширение массива требует копирования всех данных в новый массив, что стоит дорого.</li>
@@ -5723,8 +5723,8 @@
 <p>Массив - это базовая и очень распространенная структура данных. Он часто используется как в различных алгоритмах, так и при реализации более сложных структур данных.</p>
 <ul>
 <li><strong>Произвольный доступ</strong>: если мы хотим случайным образом выбирать некоторые образцы, можно сохранить их в массиве и сгенерировать случайную последовательность индексов для выборки.</li>
-<li><strong>Сортировка и поиск</strong>: массив - самая распространенная структура данных для алгоритмов сортировки и поиска. Быстрая сортировка, сортировка слиянием, бинарный поиск и многие другие алгоритмы в основном работают именно с массивами.</li>
-<li><strong>Таблица поиска</strong>: когда нужно быстро находить элемент или его соответствие, массив можно использовать как lookup table. Например, если мы хотим реализовать отображение символов в коды ASCII, можно использовать значение ASCII как индекс, а соответствующий элемент хранить по этой позиции массива.</li>
+<li><strong>Сортировка и поиск</strong>: массив - самая распространенная структура данных для алгоритмов сортировки и поиска. Быстрая сортировка, сортировка слиянием, двоичный поиск и многие другие алгоритмы в основном работают именно с массивами.</li>
+<li><strong>Таблица поиска</strong>: когда нужно быстро находить элемент или его соответствие, массив можно использовать как таблицу поиска. Например, если мы хотим реализовать отображение символов в коды ASCII, можно использовать значение ASCII как индекс, а соответствующий элемент хранить по этой позиции массива.</li>
 <li><strong>Машинное обучение</strong>: в нейронных сетях широко используются операции линейной алгебры над векторами, матрицами и тензорами, и все эти данные строятся в форме массивов. Массив - самая часто используемая структура данных в программировании нейросетей.</li>
 <li><strong>Реализация структур данных</strong>: массивы можно использовать для реализации стеков, очередей, хеш-таблиц, куч, графов и других структур данных. Например, матрица смежности графа по сути является двумерным массивом.</li>
 </ul>
diff --git a/ru/chapter_array_and_linkedlist/index.html b/ru/chapter_array_and_linkedlist/index.html
index 137530cbd..e7a7141f8 100644
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+++ b/ru/chapter_array_and_linkedlist/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
@@ -574,7 +574,7 @@
   <span class="md-ellipsis">
     
   
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+    Глава 1. Введение в алгоритмы
   
 
     
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             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
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@@ -646,7 +646,7 @@
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-    1.2 Что такое структуры данных и алгоритмы
+    1.2 Что такое алгоритм
   
 
     
@@ -1183,7 +1183,7 @@
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-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
     
@@ -1205,7 +1205,7 @@
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-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
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@@ -1311,7 +1311,7 @@
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-    4.4 Память и кеш *
+    4.4 Оперативная память и кэш *
   
 
     
@@ -1593,7 +1593,7 @@
   <span class="md-ellipsis">
     
   
-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
     
@@ -1615,7 +1615,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
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@@ -1693,7 +1693,7 @@
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-    6.3 Хеш-алгоритмы
+    6.3 Алгоритмы хеширования
   
 
     
@@ -1788,7 +1788,7 @@
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-    Глава 7. Дерево
+    Глава 7. Деревья
   
 
     
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-    Глава 7. Дерево
+    Глава 7. Деревья
   
 
           </label>
@@ -1888,7 +1888,7 @@
   <span class="md-ellipsis">
     
   
-    7.3 Представление дерева массивом
+    7.3 Представление двоичного дерева массивом
   
 
     
@@ -1972,7 +1972,7 @@
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-    7.6 Резюме
+    7.6 Краткие итоги
   
 
     
@@ -2135,7 +2135,7 @@
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-    8.3 Задача Top-K
+    8.3 Задача Top-k
   
 
     
@@ -2226,7 +2226,7 @@
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-    Глава 9. Граф
+    Глава 9. Графы
   
 
     
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-    Глава 9. Граф
+    Глава 9. Графы
   
 
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@@ -2298,7 +2298,7 @@
   <span class="md-ellipsis">
     
   
-    9.2 Базовые операции над графами
+    9.2 Базовые операции графа
   
 
     
@@ -2354,7 +2354,7 @@
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-    9.4 Резюме
+    9.4 Краткие итоги
   
 
     
@@ -2493,7 +2493,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 Точка вставки двоичного поиска
+    10.2 Двоичный поиск точки вставки
   
 
     
@@ -2521,7 +2521,7 @@
   <span class="md-ellipsis">
     
   
-    10.3 Граничные случаи двоичного поиска
+    10.3 Двоичный поиск границ
   
 
     
@@ -2549,7 +2549,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 Стратегия оптимизации через хеширование
+    10.4 Стратегии оптимизации хеширования
   
 
     
@@ -2577,7 +2577,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 Алгоритмы поиска: новый взгляд
+    10.5 Переосмысление алгоритмов поиска
   
 
     
@@ -2782,7 +2782,7 @@
   <span class="md-ellipsis">
     
   
-    11.3 Пузырьковая сортировка
+    11.3 Сортировка пузырьком
   
 
     
@@ -2810,7 +2810,7 @@
   <span class="md-ellipsis">
     
   
-    11.4 Сортировка вставкой
+    11.4 Сортировка вставками
   
 
     
@@ -3115,7 +3115,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 Алгоритмы разделяй и властвуй
+    12.1 Стратегия разделяй и властвуй
   
 
     
@@ -3143,7 +3143,7 @@
   <span class="md-ellipsis">
     
   
-    12.2 Стратегия поиска разделяй и властвуй
+    12.2 Поисковая стратегия разделяй и властвуй
   
 
     
@@ -3420,7 +3420,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 Задача о $n$ ферзях
+    13.4 Задача о n ферзях
   
 
     
@@ -3561,7 +3561,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 Введение в динамическое программирование
+    14.1 Первое знакомство с динамическим программированием
   
 
     
@@ -3673,7 +3673,7 @@
   <span class="md-ellipsis">
     
   
-    14.5 Задача о неограниченном рюкзаке
+    14.5 Задача о полном рюкзаке
   
 
     
@@ -4278,14 +4278,14 @@
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
 <p>Мир структур данных напоминает прочную кирпичную стену.</p>
-<p>Кирпичи массива уложены ровно и плотно прилегают друг к другу. Кирпичи связного списка разбросаны в разных местах, а соединяющие их лозы свободно тянутся между щелями.</p>
+<p>Кирпичи массива уложены ровно и плотно прилегают друг к другу. Узлы связного списка, напротив, разбросаны в разных местах, а соединяющие их связи свободно тянутся между промежутками.</p>
 </div>
 <h2 id="_1">Содержание главы<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
 <li><a href="array/">4.1 &nbsp; Массив</a></li>
 <li><a href="linked_list/">4.2 &nbsp; Связный список</a></li>
 <li><a href="list/">4.3 &nbsp; Список</a></li>
-<li><a href="ram_and_cache/">4.4 &nbsp; Память и кеш *</a></li>
+<li><a href="ram_and_cache/">4.4 &nbsp; Оперативная память и кэш *</a></li>
 <li><a href="summary/">4.5 &nbsp; Резюме</a></li>
 </ul>
 
diff --git a/ru/chapter_array_and_linkedlist/linked_list/index.html b/ru/chapter_array_and_linkedlist/linked_list/index.html
index 49d98aacf..31104ec0a 100644
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@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
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+    Глава 1. Введение в алгоритмы
   
 
     
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+    Глава 1. Введение в алгоритмы
   
 
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-    1.2 Что такое структуры данных и алгоритмы
+    1.2 Что такое алгоритм
   
 
     
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-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
     
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-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
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+    4.4 Оперативная память и кэш *
   
 
     
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-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
     
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-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
           </label>
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-    6.3 Хеш-алгоритмы
+    6.3 Алгоритмы хеширования
   
 
     
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-    Глава 7. Дерево
+    Глава 7. Деревья
   
 
     
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-    Глава 7. Дерево
+    Глава 7. Деревья
   
 
           </label>
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-    7.3 Представление дерева массивом
+    7.3 Представление двоичного дерева массивом
   
 
     
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-    7.6 Резюме
+    7.6 Краткие итоги
   
 
     
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-    8.3 Задача Top-K
+    8.3 Задача Top-k
   
 
     
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-    Глава 9. Граф
+    Глава 9. Графы
   
 
     
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-    Глава 9. Граф
+    Глава 9. Графы
   
 
           </label>
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-    9.2 Базовые операции над графами
+    9.2 Базовые операции графа
   
 
     
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-    9.4 Резюме
+    9.4 Краткие итоги
   
 
     
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+    10.2 Двоичный поиск точки вставки
   
 
     
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+    10.3 Двоичный поиск границ
   
 
     
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-    10.5 Алгоритмы поиска: новый взгляд
+    10.5 Переосмысление алгоритмов поиска
   
 
     
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+    12.1 Стратегия разделяй и властвуй
   
 
     
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+    14.5 Задача о полном рюкзаке
   
 
     
@@ -4521,17 +4521,17 @@
 
 <!-- Page content -->
 <h1 id="42">4.2 &nbsp; Связный список<a class="headerlink" href="#42" title="Permanent link">&para;</a></h1>
-<p>Память является общим ресурсом для всех программ, и в сложной среде выполнения свободные участки памяти могут быть разбросаны по всему адресу памяти. Мы знаем, что память для хранения массива должна быть непрерывной, а если массив очень велик, память может не суметь предоставить столь большой непрерывный блок. Именно здесь проявляется преимущество гибкости связного списка.</p>
-<p><u>Связный список (linked list)</u> - это линейная структура данных, в которой каждый элемент представляет собой объект-узел, а сами узлы соединены между собой через "ссылки". Ссылка хранит адрес памяти следующего узла, благодаря чему из текущего узла можно получить доступ к следующему.</p>
-<p>Конструкция связного списка позволяет хранить отдельные узлы в разных местах памяти, и их адреса вовсе не обязаны быть непрерывными.</p>
+<p>Память - общий ресурс для всех программ, и в сложной среде выполнения свободные участки памяти могут быть разбросаны по всему адресному пространству. Мы знаем, что память для хранения массива должна быть непрерывной, а если массив очень велик, в памяти может не оказаться столь большого непрерывного блока. Именно здесь и проявляется преимущество гибкости связного списка.</p>
+<p><u>Связный список (linked list)</u> - это линейная структура данных, в которой каждый элемент представляет собой объект-узел, а сами узлы соединены между собой с помощью ссылок. Ссылка хранит адрес памяти следующего узла, благодаря чему из текущего узла можно перейти к следующему.</p>
+<p>Конструкция связного списка позволяет хранить отдельные узлы в разных местах памяти, и их адреса вовсе не обязаны быть последовательными.</p>
 <p><img alt="Определение связного списка и способ хранения" class="animation-figure" src="../linked_list.assets/linkedlist_definition.png" /></p>
 <p align="center"> Рисунок 4-5 &nbsp; Определение связного списка и способ хранения </p>
 
-<p>Если посмотреть на рисунок 4-5, можно заметить, что базовой единицей связного списка является объект <u>узел (node)</u>. Каждый узел содержит две части данных: "значение" узла и "ссылку" на следующий узел.</p>
+<p>Как видно на рисунке 4-5, базовой единицей связного списка является объект <u>узел (node)</u>. Каждый узел содержит две части данных: значение узла и ссылку на следующий узел.</p>
 <ul>
-<li>Первый узел связного списка называется "головным узлом", а последний - "хвостовым узлом".</li>
-<li>Хвостовой узел указывает на "пусто", что в Java, C++ и Python обозначается как <code>null</code> , <code>nullptr</code> и <code>None</code> соответственно.</li>
-<li>В языках, поддерживающих указатели, таких как C, C++, Go и Rust, упомянутую выше "ссылку" следует заменить на "указатель".</li>
+<li>Первый узел связного списка называется головным узлом, а последний - хвостовым узлом.</li>
+<li>Хвостовой узел указывает на пустое значение, что в Java, C++ и Python обозначается как <code>null</code> , <code>nullptr</code> и <code>None</code> соответственно.</li>
+<li>В языках, поддерживающих указатели, таких как C, C++, Go и Rust, упомянутую выше ссылку следует заменить на указатель.</li>
 </ul>
 <p>Как показано в коде ниже, узел связного списка <code>ListNode</code> хранит не только значение, но и дополнительную ссылку (указатель). Поэтому <strong>при одинаковом объеме данных связный список занимает больше памяти, чем массив</strong>.</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
@@ -4577,7 +4577,7 @@
 <a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">Next</span><span class="w"> </span><span class="o">*</span><span class="nx">ListNode</span><span class="w"> </span><span class="c1">// Указатель на следующий узел</span>
 <a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="p">}</span>
 <a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a>
-<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="c1">// NewListNode Конструктор, создает новый связный список</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="c1">// NewListNode Конструктор, создает новый узел</span>
 <a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="kd">func</span><span class="w"> </span><span class="nx">NewListNode</span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">ListNode</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">ListNode</span><span class="p">{</span>
 <a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">        </span><span class="nx">Val</span><span class="p">:</span><span class="w">  </span><span class="nx">val</span><span class="p">,</span>
@@ -4683,7 +4683,7 @@
 </div>
 <h2 id="421">4.2.1 &nbsp; Основные операции со связным списком<a class="headerlink" href="#421" title="Permanent link">&para;</a></h2>
 <h3 id="1">1. &nbsp; Инициализация связного списка<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>Построение связного списка состоит из двух шагов: сначала нужно инициализировать объекты всех узлов, затем установить связи-ссылки между ними. После завершения инициализации мы можем, начиная с головы списка, последовательно проходить все узлы по ссылке <code>next</code>.</p>
+<p>Построение связного списка состоит из двух шагов: сначала нужно инициализировать объекты всех узлов, затем установить ссылочные связи между ними. После завершения инициализации мы можем, начиная с головы списка, последовательно проходить все узлы по ссылке <code>next</code>.</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
@@ -4888,10 +4888,10 @@
 <summary>Визуализация выполнения</summary>
 <p>https://pythontutor.com/render.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%D1%81%D0%B2%D1%8F%D0%B7%D0%BD%D1%8B%D0%B9%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%D1%83%D0%B7%D0%B5%D0%BB%D0%BA%D0%BB%D0%B0%D1%81%D1%81%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%D0%97%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%83%D0%B7%D0%BB%D0%B0%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%D0%A1%D1%81%D1%8B%D0%BB%D0%BA%D0%B0%20%D0%BD%D0%B0%20%D1%81%D0%BB%D0%B5%D0%B4%D1%83%D1%8E%D1%89%D0%B8%D0%B9%20%D1%83%D0%B7%D0%B5%D0%BB%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%81%D0%B2%D1%8F%D0%B7%D0%BD%D1%8B%D0%B9%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%201%20-%3E%203%20-%3E%202%20-%3E%205%20-%3E%204%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D0%BA%D0%B0%D0%B6%D0%B4%D1%8B%D0%B9%20%D1%83%D0%B7%D0%B5%D0%BB%0A%20%20%20%20n0%20%3D%20ListNode%281%29%0A%20%20%20%20n1%20%3D%20ListNode%283%29%0A%20%20%20%20n2%20%3D%20ListNode%282%29%0A%20%20%20%20n3%20%3D%20ListNode%285%29%0A%20%20%20%20n4%20%3D%20ListNode%284%29%0A%20%20%20%20%23%20%D0%9F%D0%BE%D1%81%D1%82%D1%80%D0%BE%D0%B8%D1%82%D1%8C%20%D1%81%D1%81%D1%8B%D0%BB%D0%BA%D0%B8%20%D0%BC%D0%B5%D0%B6%D0%B4%D1%83%20%D1%83%D0%B7%D0%BB%D0%B0%D0%BC%D0%B8%0A%20%20%20%20n0.next%20%3D%20n1%0A%20%20%20%20n1.next%20%3D%20n2%0A%20%20%20%20n2.next%20%3D%20n3%0A%20%20%20%20n3.next%20%3D%20n4&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>
 </details>
-<p>Массив в целом - это одна переменная: например, массив <code>nums</code> содержит элементы <code>nums[0]</code> , <code>nums[1]</code> и т.д. Связный список же состоит из множества независимых объектов-узлов. <strong>Обычно в качестве обозначения всего связного списка используют головной узел</strong>; например, в приведенном выше коде связный список можно обозначить как список <code>n0</code> .</p>
+<p>Массив в целом - это одна переменная: например, массив <code>nums</code> содержит элементы <code>nums[0]</code> , <code>nums[1]</code> и т.д. Связный список же состоит из множества независимых объектов-узлов. <strong>Обычно в качестве обозначения всего связного списка используют головной узел</strong>; например, в приведенном выше коде связный список можно обозначить как <code>n0</code> .</p>
 <h3 id="2">2. &nbsp; Вставка узла<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
 <p>Вставить узел в связный список очень легко. Как показано на рисунке 4-6, предположим, что мы хотим вставить новый узел <code>P</code> между двумя соседними узлами <code>n0</code> и <code>n1</code> ; <strong>для этого нужно изменить всего две ссылки (указателя)</strong>, а временная сложность будет равна <span class="arithmatex">\(O(1)\)</span> .</p>
-<p>Для сравнения: временная сложность вставки элемента в массив составляет <span class="arithmatex">\(O(n)\)</span> , и при большом объеме данных это неэффективно.</p>
+<p>Для сравнения: временная сложность вставки элемента в массив составляет <span class="arithmatex">\(O(n)\)</span> , и при большом объеме данных это менее эффективно.</p>
 <p><img alt="Пример вставки узла в связный список" class="animation-figure" src="../linked_list.assets/linkedlist_insert_node.png" /></p>
 <p align="center"> Рисунок 4-6 &nbsp; Пример вставки узла в связный список </p>
 
@@ -5023,8 +5023,8 @@
 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%D0%9A%D0%BB%D0%B0%D1%81%D1%81%20%D1%83%D0%B7%D0%BB%D0%B0%20%D1%81%D0%B2%D1%8F%D0%B7%D0%BD%D0%BE%D0%B3%D0%BE%20%D1%81%D0%BF%D0%B8%D1%81%D0%BA%D0%B0%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%D0%97%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%83%D0%B7%D0%BB%D0%B0%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%D0%A1%D1%81%D1%8B%D0%BB%D0%BA%D0%B0%20%D0%BD%D0%B0%20%D1%83%D0%B7%D0%B5%D0%BB-%D0%BF%D1%80%D0%B5%D0%B5%D0%BC%D0%BD%D0%B8%D0%BA%0A%0Adef%20insert%28n0%3A%20ListNode%2C%20P%3A%20ListNode%29%3A%0A%20%20%20%20%22%22%22%D0%92%D1%81%D1%82%D0%B0%D0%B2%D0%B8%D1%82%D1%8C%20%D1%83%D0%B7%D0%B5%D0%BB%20P%20%D0%BF%D0%BE%D1%81%D0%BB%D0%B5%20%D1%83%D0%B7%D0%BB%D0%B0%20n0%20%D0%B2%20%D1%81%D0%B2%D1%8F%D0%B7%D0%BD%D0%BE%D0%BC%20%D1%81%D0%BF%D0%B8%D1%81%D0%BA%D0%B5%22%22%22%0A%20%20%20%20n1%20%3D%20n0.next%0A%20%20%20%20P.next%20%3D%20n1%0A%20%20%20%20n0.next%20%3D%20P%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%20%D1%81%D0%B2%D1%8F%D0%B7%D0%BD%D0%BE%D0%B3%D0%BE%20%D1%81%D0%BF%D0%B8%D1%81%D0%BA%D0%B0%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%20%D0%B2%D1%81%D0%B5%D1%85%20%D1%83%D0%B7%D0%BB%D0%BE%D0%B2%0A%20%20%20%20n0%20%3D%20ListNode%281%29%0A%20%20%20%20n1%20%3D%20ListNode%283%29%0A%20%20%20%20n2%20%3D%20ListNode%282%29%0A%20%20%20%20n3%20%3D%20ListNode%285%29%0A%20%20%20%20n4%20%3D%20ListNode%284%29%0A%20%20%20%20%23%20%D0%9F%D0%BE%D1%81%D1%82%D1%80%D0%BE%D0%B8%D1%82%D1%8C%20%D1%81%D1%81%D1%8B%D0%BB%D0%BA%D0%B8%20%D0%BC%D0%B5%D0%B6%D0%B4%D1%83%20%D1%83%D0%B7%D0%BB%D0%B0%D0%BC%D0%B8%0A%20%20%20%20n0.next%20%3D%20n1%0A%20%20%20%20n1.next%20%3D%20n2%0A%20%20%20%20n2.next%20%3D%20n3%0A%20%20%20%20n3.next%20%3D%20n4%0A%0A%20%20%20%20%23%20%D0%92%D1%81%D1%82%D0%B0%D0%B2%D0%BA%D0%B0%20%D1%83%D0%B7%D0%BB%D0%B0%0A%20%20%20%20p%20%3D%20ListNode%280%29%0A%20%20%20%20insert%28n0%2C%20p%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=39&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
 <h3 id="3">3. &nbsp; Удаление узла<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
-<p>Как показано на рисунке 4-7, удалить узел из связного списка тоже очень удобно: <strong>нужно изменить всего одну ссылку (указатель)</strong>.</p>
-<p>Обрати внимание: хотя после завершения операции удаления узел <code>P</code> все еще указывает на <code>n1</code> , при обходе связного списка до <code>P</code> уже нельзя добраться, а значит <code>P</code> больше не принадлежит данному списку.</p>
+<p>Как показано на рисунке 4-7, удалить узел из связного списка тоже очень просто: <strong>нужно изменить всего одну ссылку (указатель)</strong>.</p>
+<p>Стоит отметить, что хотя после завершения операции удаления узел <code>P</code> все еще указывает на <code>n1</code> , при обходе связного списка до <code>P</code> уже нельзя добраться. Это означает, что <code>P</code> фактически больше не принадлежит данному списку.</p>
 <p><img alt="Удаление узла из связного списка" class="animation-figure" src="../linked_list.assets/linkedlist_remove_node.png" /></p>
 <p align="center"> Рисунок 4-7 &nbsp; Удаление узла из связного списка </p>
 
@@ -5200,7 +5200,7 @@
 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%D0%9A%D0%BB%D0%B0%D1%81%D1%81%20%D1%83%D0%B7%D0%BB%D0%B0%20%D1%81%D0%B2%D1%8F%D0%B7%D0%BD%D0%BE%D0%B3%D0%BE%20%D1%81%D0%BF%D0%B8%D1%81%D0%BA%D0%B0%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%D0%97%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%83%D0%B7%D0%BB%D0%B0%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%D0%A1%D1%81%D1%8B%D0%BB%D0%BA%D0%B0%20%D0%BD%D0%B0%20%D1%83%D0%B7%D0%B5%D0%BB-%D0%BF%D1%80%D0%B5%D0%B5%D0%BC%D0%BD%D0%B8%D0%BA%0A%0Adef%20remove%28n0%3A%20ListNode%29%3A%0A%20%20%20%20%22%22%22%D0%A3%D0%B4%D0%B0%D0%BB%D0%B8%D1%82%D1%8C%20%D0%BF%D0%B5%D1%80%D0%B2%D1%8B%D0%B9%20%D1%83%D0%B7%D0%B5%D0%BB%20%D0%BF%D0%BE%D1%81%D0%BB%D0%B5%20%D1%83%D0%B7%D0%BB%D0%B0%20n0%20%D0%B2%20%D1%81%D0%B2%D1%8F%D0%B7%D0%BD%D0%BE%D0%BC%20%D1%81%D0%BF%D0%B8%D1%81%D0%BA%D0%B5%22%22%22%0A%20%20%20%20if%20not%20n0.next%3A%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20%23%20n0%20-%3E%20P%20-%3E%20n1%0A%20%20%20%20P%20%3D%20n0.next%0A%20%20%20%20n1%20%3D%20P.next%0A%20%20%20%20n0.next%20%3D%20n1%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%20%D1%81%D0%B2%D1%8F%D0%B7%D0%BD%D0%BE%D0%B3%D0%BE%20%D1%81%D0%BF%D0%B8%D1%81%D0%BA%D0%B0%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%20%D0%B2%D1%81%D0%B5%D1%85%20%D1%83%D0%B7%D0%BB%D0%BE%D0%B2%0A%20%20%20%20n0%20%3D%20ListNode%281%29%0A%20%20%20%20n1%20%3D%20ListNode%283%29%0A%20%20%20%20n2%20%3D%20ListNode%282%29%0A%20%20%20%20n3%20%3D%20ListNode%285%29%0A%20%20%20%20n4%20%3D%20ListNode%284%29%0A%20%20%20%20%23%20%D0%9F%D0%BE%D1%81%D1%82%D1%80%D0%BE%D0%B8%D1%82%D1%8C%20%D1%81%D1%81%D1%8B%D0%BB%D0%BA%D0%B8%20%D0%BC%D0%B5%D0%B6%D0%B4%D1%83%20%D1%83%D0%B7%D0%BB%D0%B0%D0%BC%D0%B8%0A%20%20%20%20n0.next%20%3D%20n1%0A%20%20%20%20n1.next%20%3D%20n2%0A%20%20%20%20n2.next%20%3D%20n3%0A%20%20%20%20n3.next%20%3D%20n4%0A%0A%20%20%20%20%23%20%D0%A3%D0%B4%D0%B0%D0%BB%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%83%D0%B7%D0%BB%D0%B0%0A%20%20%20%20remove%28n0%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=34&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
 <h3 id="4">4. &nbsp; Доступ к узлу<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
-<p><strong>Доступ к узлам в связном списке менее эффективен</strong>. Как уже обсуждалось в предыдущем разделе, к любому элементу массива можно обратиться за <span class="arithmatex">\(O(1)\)</span> времени. Со связным списком это не так: программе нужно стартовать от головного узла и последовательно двигаться дальше, пока не будет найден целевой узел. То есть для доступа к <span class="arithmatex">\(i\)</span> -му узлу списка нужно выполнить <span class="arithmatex">\(i - 1\)</span> итераций, а временная сложность составляет <span class="arithmatex">\(O(n)\)</span> .</p>
+<p><strong>Доступ к узлам в связном списке менее эффективен</strong>. Как уже обсуждалось в предыдущем разделе, к любому элементу массива можно обратиться за <span class="arithmatex">\(O(1)\)</span> времени. Со связным списком это не так: программе нужно начать с головного узла и последовательно двигаться дальше, пока не будет найден целевой узел. То есть для доступа к <span class="arithmatex">\(i\)</span> -му узлу списка нужно выполнить <span class="arithmatex">\(i - 1\)</span> итераций, а временная сложность составляет <span class="arithmatex">\(O(n)\)</span> .</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="5:13"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label></div>
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 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%D0%9A%D0%BB%D0%B0%D1%81%D1%81%20%D1%83%D0%B7%D0%BB%D0%B0%20%D1%81%D0%B2%D1%8F%D0%B7%D0%BD%D0%BE%D0%B3%D0%BE%20%D1%81%D0%BF%D0%B8%D1%81%D0%BA%D0%B0%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%D0%97%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%83%D0%B7%D0%BB%D0%B0%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%D0%A1%D1%81%D1%8B%D0%BB%D0%BA%D0%B0%20%D0%BD%D0%B0%20%D1%83%D0%B7%D0%B5%D0%BB-%D0%BF%D1%80%D0%B5%D0%B5%D0%BC%D0%BD%D0%B8%D0%BA%0A%0Adef%20access%28head%3A%20ListNode%2C%20index%3A%20int%29%20-%3E%20ListNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%D0%94%D0%BE%D1%81%D1%82%D1%83%D0%BF%20%D0%BA%20%D1%83%D0%B7%D0%BB%D1%83%20%D1%81%D0%B2%D1%8F%D0%B7%D0%BD%D0%BE%D0%B3%D0%BE%20%D1%81%D0%BF%D0%B8%D1%81%D0%BA%D0%B0%20%D0%BF%D0%BE%20%D0%B8%D0%BD%D0%B4%D0%B5%D0%BA%D1%81%D1%83%20index%22%22%22%0A%20%20%20%20for%20_%20in%20range%28index%29%3A%0A%20%20%20%20%20%20%20%20if%20not%20head%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%20%20%20%20head%20%3D%20head.next%0A%20%20%20%20return%20head%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%20%D1%81%D0%B2%D1%8F%D0%B7%D0%BD%D0%BE%D0%B3%D0%BE%20%D1%81%D0%BF%D0%B8%D1%81%D0%BA%D0%B0%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%20%D0%B2%D1%81%D0%B5%D1%85%20%D1%83%D0%B7%D0%BB%D0%BE%D0%B2%0A%20%20%20%20n0%20%3D%20ListNode%281%29%0A%20%20%20%20n1%20%3D%20ListNode%283%29%0A%20%20%20%20n2%20%3D%20ListNode%282%29%0A%20%20%20%20n3%20%3D%20ListNode%285%29%0A%20%20%20%20n4%20%3D%20ListNode%284%29%0A%20%20%20%20%23%20%D0%9F%D0%BE%D1%81%D1%82%D1%80%D0%BE%D0%B8%D1%82%D1%8C%20%D1%81%D1%81%D1%8B%D0%BB%D0%BA%D0%B8%20%D0%BC%D0%B5%D0%B6%D0%B4%D1%83%20%D1%83%D0%B7%D0%BB%D0%B0%D0%BC%D0%B8%0A%20%20%20%20n0.next%20%3D%20n1%0A%20%20%20%20n1.next%20%3D%20n2%0A%20%20%20%20n2.next%20%3D%20n3%0A%20%20%20%20n3.next%20%3D%20n4%0A%0A%20%20%20%20%23%20%D0%94%D0%BE%D1%81%D1%82%D1%83%D0%BF%20%D0%BA%20%D1%83%D0%B7%D0%BB%D1%83%0A%20%20%20%20node%20%3D%20access%28n0%2C%203%29%0A%20%20%20%20print%28%22%D0%97%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%83%D0%B7%D0%BB%D0%B0%20%D0%BF%D0%BE%20%D0%B8%D0%BD%D0%B4%D0%B5%D0%BA%D1%81%D1%83%203%20%D0%B2%20%D1%81%D0%B2%D1%8F%D0%B7%D0%BD%D0%BE%D0%BC%20%D1%81%D0%BF%D0%B8%D1%81%D0%BA%D0%B5%20%3D%20%7B%7D%22.format%28node.val%29%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=34&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
 <h3 id="5">5. &nbsp; Поиск узла<a class="headerlink" href="#5" title="Permanent link">&para;</a></h3>
-<p>Выполни обход связного списка, найди в нем узел со значением <code>target</code> и верни индекс этого узла в списке. Этот процесс тоже относится к линейному поиску. Код выглядит следующим образом:</p>
+<p>Поиск узла заключается в обходе связного списка, нахождении узла со значением <code>target</code> и возврате его индекса в списке. Этот процесс тоже относится к линейному поиску. Код выглядит следующим образом:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="6:13"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><input id="__tabbed_6_13" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Kotlin</label><label for="__tabbed_6_13">Ruby</label></div>
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@@ -5631,9 +5631,9 @@
 <h2 id="423">4.2.3 &nbsp; Основные типы связных списков<a class="headerlink" href="#423" title="Permanent link">&para;</a></h2>
 <p>Как показано на рисунке 4-8, существует три распространенных типа связных списков.</p>
 <ul>
-<li><strong>Односвязный список</strong>: это обычный связный список, рассмотренный выше. Узел односвязного списка содержит значение и ссылку на следующий узел. Первый узел называется головным, последний - хвостовым, и хвост указывает на пусто <code>None</code> .</li>
-<li><strong>Циклический список</strong>: если заставить хвостовой узел односвязного списка указывать на головной (то есть соединить хвост с головой), получится циклический список. В циклическом списке любой узел можно рассматривать как головной.</li>
-<li><strong>Двусвязный список</strong>: по сравнению с односвязным списком двусвязный хранит ссылки в двух направлениях. Определение узла двусвязного списка включает как ссылку на следующий узел, так и ссылку на предыдущий узел. По сравнению с односвязным списком двусвязный более гибок и позволяет проходить список в обе стороны, но за это приходится платить дополнительной памятью.</li>
+<li><strong>Односвязный список</strong>: это обычный связный список, рассмотренный выше. Узел односвязного списка содержит значение и ссылку на следующий узел. Первый узел называется головным, последний - хвостовым, и хвост указывает на <code>None</code> .</li>
+<li><strong>Циклический список</strong>: если заставить хвостовой узел односвязного списка указывать на головной, то есть соединить хвост с головой, получится циклический список. В циклическом списке любой узел можно рассматривать как головной.</li>
+<li><strong>Двусвязный список</strong>: по сравнению с односвязным списком двусвязный хранит ссылки в двух направлениях. Определение узла двусвязного списка включает как ссылку на следующий узел, так и ссылку на предыдущий узел. По сравнению с односвязным списком двусвязный более гибок и позволяет обходить список в обе стороны, но за это приходится платить дополнительной памятью.</li>
 </ul>
 <div class="tabbed-set tabbed-alternate" data-tabs="7:13"><input checked="checked" id="__tabbed_7_1" name="__tabbed_7" type="radio" /><input id="__tabbed_7_2" name="__tabbed_7" type="radio" /><input id="__tabbed_7_3" name="__tabbed_7" type="radio" /><input id="__tabbed_7_4" name="__tabbed_7" type="radio" /><input id="__tabbed_7_5" name="__tabbed_7" type="radio" /><input id="__tabbed_7_6" name="__tabbed_7" type="radio" /><input id="__tabbed_7_7" name="__tabbed_7" type="radio" /><input id="__tabbed_7_8" name="__tabbed_7" type="radio" /><input id="__tabbed_7_9" name="__tabbed_7" type="radio" /><input id="__tabbed_7_10" name="__tabbed_7" type="radio" /><input id="__tabbed_7_11" name="__tabbed_7" type="radio" /><input id="__tabbed_7_12" name="__tabbed_7" type="radio" /><input id="__tabbed_7_13" name="__tabbed_7" type="radio" /><div class="tabbed-labels"><label for="__tabbed_7_1">Python</label><label for="__tabbed_7_2">C++</label><label for="__tabbed_7_3">Java</label><label for="__tabbed_7_4">C#</label><label for="__tabbed_7_5">Go</label><label for="__tabbed_7_6">Swift</label><label for="__tabbed_7_7">JS</label><label for="__tabbed_7_8">TS</label><label for="__tabbed_7_9">Dart</label><label for="__tabbed_7_10">Rust</label><label for="__tabbed_7_11">C</label><label for="__tabbed_7_12">Kotlin</label><label for="__tabbed_7_13">Ruby</label></div>
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@@ -5824,10 +5824,10 @@
 <p>Двусвязные списки обычно используются там, где нужен быстрый доступ как к предыдущему, так и к следующему элементу.</p>
 <ul>
 <li><strong>Продвинутые структуры данных</strong>: например, в красно-черных деревьях и B-деревьях нам нужен доступ к родительскому узлу; этого можно добиться, сохранив в узле ссылку на родителя, по аналогии с двусвязным списком.</li>
-<li><strong>История браузера</strong>: когда пользователь в браузере нажимает кнопки "вперед" или "назад", браузеру нужно знать предыдущую и следующую веб-страницы, которые он посещал. Свойства двусвязного списка делают такую операцию простой.</li>
+<li><strong>История браузера</strong>: когда пользователь в браузере нажимает кнопки "вперед" или "назад", браузеру нужно знать предыдущую и следующую посещенные страницы. Свойства двусвязного списка делают такую операцию простой.</li>
 <li><strong>Алгоритм LRU</strong>: в алгоритмах вытеснения из кэша (LRU) нужно быстро находить наименее недавно использованные данные, а также быстро добавлять и удалять узлы. Для этого двусвязный список подходит очень хорошо.</li>
 </ul>
-<p>Циклические списки часто применяются в сценариях, требующих периодических операций, например при планировании ресурсов в операционной системе.</p>
+<p>Циклические списки часто применяются в сценариях, требующих циклических операций, например при планировании ресурсов в операционной системе.</p>
 <ul>
 <li><strong>Алгоритм циклического распределения кванта времени</strong>: в операционных системах round-robin scheduling - это распространенный алгоритм планирования CPU, который циклически обходит набор процессов. Каждому процессу выделяется квант времени, и когда он исчерпан, CPU переключается на следующий процесс. Такую циклическую операцию удобно реализовать с помощью кольцевого списка.</li>
 <li><strong>Буферы данных</strong>: в некоторых реализациях буферов данных также могут использоваться циклические списки. Например, в аудио- и видеоплеерах поток данных может делиться на несколько буферных блоков и помещаться в кольцевой список для обеспечения непрерывного воспроизведения.</li>
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+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
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 <p>На практике <strong>списки из стандартных библиотек многих языков программирования реализованы именно на основе динамических массивов</strong>, например <code>list</code> в Python, <code>ArrayList</code> в Java, <code>vector</code> в C++ и <code>List</code> в C#. В дальнейшем обсуждении мы будем считать понятия "список" и "динамический массив" эквивалентными.</p>
 <h2 id="431">4.3.1 &nbsp; Основные операции со списком<a class="headerlink" href="#431" title="Permanent link">&para;</a></h2>
 <h3 id="1">1. &nbsp; Инициализация списка<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>Обычно мы используем два способа инициализации: "без начальных значений" и "с начальными значениями":</p>
+<p>Обычно используются два способа инициализации: без начальных значений и с начальными значениями:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
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@@ -4623,7 +4623,7 @@
 <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%0A%20%20%20%20%23%20%D0%91%D0%B5%D0%B7%20%D0%BD%D0%B0%D1%87%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B%D1%85%20%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B9%0A%20%20%20%20nums1%20%3D%20%5B%5D%0A%20%20%20%20%23%20%D0%A1%20%D0%BD%D0%B0%D1%87%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B%D0%BC%D0%B8%20%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D1%8F%D0%BC%D0%B8%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D&amp;cumulative=false&amp;curInstr=4&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>
 </details>
 <h3 id="2">2. &nbsp; Доступ к элементам<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>Список по своей сути является массивом, поэтому доступ к элементам и их обновление можно выполнять за <span class="arithmatex">\(O(1)\)</span> времени, что очень эффективно.</p>
+<p>Поскольку в этом разделе список рассматривается как структура на основе динамического массива, доступ к элементам и их обновление можно выполнять за <span class="arithmatex">\(O(1)\)</span> времени, что очень эффективно.</p>
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 </details>
 <h3 id="3">3. &nbsp; Вставка и удаление элементов<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
-<p>По сравнению с массивами список позволяет свободно добавлять и удалять элементы. Добавление элемента в конец списка имеет временную сложность <span class="arithmatex">\(O(1)\)</span> , но операции вставки и удаления по-прежнему имеют ту же эффективность, что и у массива, то есть <span class="arithmatex">\(O(n)\)</span> .</p>
+<p>В отличие от массива список позволяет свободно добавлять и удалять элементы. Добавление элемента в конец списка имеет временную сложность <span class="arithmatex">\(O(1)\)</span> , но операции вставки и удаления по-прежнему имеют ту же эффективность, что и у массива, то есть <span class="arithmatex">\(O(n)\)</span> .</p>
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 </details>
 <h3 id="5">5. &nbsp; Конкатенация списков<a class="headerlink" href="#5" title="Permanent link">&para;</a></h3>
-<p>Если дан новый список <code>nums1</code> , мы можем присоединить его к хвосту исходного списка.</p>
+<p>Создав новый список <code>nums1</code> , мы можем присоединить его к хвосту исходного списка.</p>
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 </details>
 <h3 id="6">6. &nbsp; Сортировка списка<a class="headerlink" href="#6" title="Permanent link">&para;</a></h3>
-<p>После сортировки списка мы сможем применять алгоритмы "бинарный поиск" и "два указателя", которые очень часто встречаются в задачах по массивам.</p>
+<p>После сортировки списка мы сможем применять алгоритмы "двоичный поиск" и "два указателя", которые очень часто встречаются в задачах по массивам.</p>
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 </details>
 <h2 id="432">4.3.2 &nbsp; Реализация списка<a class="headerlink" href="#432" title="Permanent link">&para;</a></h2>
-<p>Во многих языках программирования списки встроены в стандартную библиотеку, например в Java, C++ и Python. Их реализация довольно сложна, а настройки параметров тщательно продуманы: начальная емкость, коэффициент расширения и так далее. Если тебе интересно, стоит заглянуть в исходный код.</p>
+<p>Во многих языках программирования списки встроены в стандартную библиотеку, например в Java, C++, Python и других языках. Их реализация довольно сложна, а настройки параметров тщательно продуманы: начальная емкость, коэффициент расширения и так далее. Если это интересно, стоит заглянуть в исходный код.</p>
 <p>Чтобы лучше понять принцип работы списка, попробуем реализовать его упрощенную версию, в которой есть три ключевых аспекта проектирования.</p>
 <ul>
 <li><strong>Начальная емкость</strong>: выбрать разумную начальную емкость внутреннего массива. В этом примере мы берем 10.</li>
-<li><strong>Учет количества элементов</strong>: объявить переменную <code>size</code> , которая будет хранить текущее число элементов в списке и обновляться в реальном времени при вставке и удалении элементов. С помощью этой переменной можно находить конец списка и понимать, требуется ли расширение.</li>
+<li><strong>Учет количества элементов</strong>: объявить переменную <code>size</code> , которая будет хранить текущее число элементов в списке и обновляться в реальном времени при вставке и удалении элементов. С помощью этой переменной можно определять конец списка и понимать, требуется ли расширение.</li>
 <li><strong>Механизм расширения</strong>: если при вставке элементов емкость списка исчерпана, нужно выполнить расширение. Для этого сначала создается больший массив с учетом коэффициента расширения, а затем все элементы текущего массива по порядку переносятся в новый. В этом примере мы считаем, что каждый раз массив расширяется в 2 раза.</li>
 </ul>
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@@ -6663,7 +6663,7 @@ aria-label="Нижний колонтитул"
   <a
     href="../ram_and_cache/"
     class="md-footer__link md-footer__link--next"
-    aria-label="Вперед: 4.4 Память и кеш *"
+    aria-label="Вперед: 4.4 Оперативная память и кэш *"
     rel="next"
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 <!-- Page content -->
 <h1 id="44">4.4 &nbsp; Оперативная память и кэш *<a class="headerlink" href="#44" title="Permanent link">&para;</a></h1>
-<p>В первых двух разделах этой главы мы разобрали массивы и связные списки - две фундаментальные и важные структуры данных, которые соответственно представляют две физические структуры хранения: "непрерывное хранение" и "разрозненное хранение".</p>
-<p>На практике <strong>физическая структура во многом определяет, насколько эффективно программа использует память и кэш</strong>, а это, в свою очередь, влияет на общую производительность алгоритмической программы.</p>
+<p>В первых двух разделах этой главы мы разобрали массивы и связные списки - две базовые и важные структуры данных, которые представляют соответственно непрерывное хранение и разрозненное хранение.</p>
+<p>На практике <strong>физическая структура во многом определяет, насколько эффективно программа использует память и кэш</strong>, а это, в свою очередь, влияет на общую производительность алгоритма.</p>
 <h2 id="441">4.4.1 &nbsp; Устройства хранения данных в компьютере<a class="headerlink" href="#441" title="Permanent link">&para;</a></h2>
-<p>В компьютере есть три типа устройств хранения данных: <u>жесткий диск (hard disk)</u> , <u>оперативная память (random-access memory, RAM)</u> и <u>кэш-память (cache memory)</u> . В таблице 4-2 показаны их различные роли и характеристики производительности в компьютерной системе.</p>
+<p>В компьютере есть три типа устройств хранения данных: <u>жесткий диск (hard disk)</u> , <u>оперативная память (random-access memory, RAM)</u> и <u>кэш-память (cache memory)</u> . В таблице 4-2 показаны их различные роли и характеристики в компьютерной системе.</p>
 <p align="center"> Таблица 4-2 &nbsp; Устройства хранения данных в компьютере </p>
 
 <div class="center-table">
@@ -4419,17 +4419,17 @@
 <td>Очень высокая, десятки и сотни GB/s</td>
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-<td>Цена (юани)</td>
-<td>Дешевый, от долей юаня до нескольких юаней за GB</td>
-<td>Дорогая, десятки и сотни юаней за GB</td>
-<td>Очень дорогой, входит в стоимость упаковки CPU</td>
+<td>Цена</td>
+<td>Низкая, единицы валюты за GB</td>
+<td>Высокая, десятки и сотни валютных единиц за GB</td>
+<td>Очень высокая, входит в стоимость CPU</td>
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 <p>Компьютерную систему хранения можно представить в виде пирамиды, показанной на рисунке 4-9. Чем ближе устройство хранения к вершине пирамиды, тем оно быстрее, тем меньше его емкость и тем выше его стоимость. Такая многоуровневая конструкция возникла не случайно, а стала результатом тщательных инженерных компромиссов.</p>
 <ul>
-<li><strong>Жесткий диск трудно заменить оперативной памятью</strong>. Во-первых, данные в оперативной памяти исчезают после отключения питания, поэтому она не подходит для долговременного хранения. Во-вторых, память стоит в десятки раз дороже жесткого диска, что мешает ее широкому применению в потребительском сегменте.</li>
+<li><strong>Жесткий диск трудно заменить оперативной памятью</strong>. Во-первых, данные в оперативной памяти исчезают после отключения питания, поэтому она не подходит для долговременного хранения. Во-вторых, память стоит в разы дороже жесткого диска, что мешает ее широкому применению.</li>
 <li><strong>Кэш не может одновременно быть и очень большим, и очень быстрым</strong>. По мере роста емкости кэшей L1, L2 и L3 их физический размер увеличивается, расстояние до ядра CPU становится больше, время передачи данных растет, а задержка доступа к элементам увеличивается. При текущем уровне технологий многоуровневая структура кэша является лучшим балансом между емкостью, скоростью и стоимостью.</li>
 </ul>
 <p><img alt="Система хранения данных компьютера" class="animation-figure" src="../ram_and_cache.assets/storage_pyramid.png" /></p>
@@ -4437,20 +4437,20 @@
 
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>Иерархия памяти компьютера отражает тонкий баланс между скоростью, емкостью и стоимостью. На самом деле подобные компромиссы встречаются почти во всех отраслях инженерии: приходится искать оптимальный баланс между преимуществами и ограничениями.</p>
+<p>Иерархия памяти компьютера отражает тонкий баланс между скоростью, емкостью и стоимостью. Подобные компромиссы встречаются почти во всех областях инженерии: приходится искать оптимальный баланс между преимуществами и ограничениями.</p>
 </div>
 <p>В итоге <strong>жесткий диск используется для долговременного хранения больших объемов данных, оперативная память - для временного хранения данных, с которыми программа работает прямо сейчас, а кэш - для хранения часто используемых данных и инструкций</strong>, чтобы ускорять выполнение программ. Все три уровня работают совместно и обеспечивают эффективную работу компьютерной системы.</p>
-<p>Как показано на рисунке 4-10, во время выполнения программы данные читаются с жесткого диска в оперативную память, а затем используются CPU в вычислениях. Кэш можно рассматривать как часть CPU: <strong>он интеллектуально подгружает данные из оперативной памяти</strong>, обеспечивая CPU высокоскоростной доступ и тем самым значительно ускоряя выполнение программы и уменьшая зависимость от более медленной RAM.</p>
+<p>Как показано на рисунке 4-10, во время выполнения программы данные читаются с жесткого диска в оперативную память, а затем используются CPU в вычислениях. Кэш можно рассматривать как часть CPU: <strong>он подгружает данные из оперативной памяти</strong>, обеспечивая CPU высокоскоростной доступ и тем самым значительно ускоряя выполнение программы и уменьшая зависимость от более медленной RAM.</p>
 <p><img alt="Поток данных между жестким диском, RAM и кэшем" class="animation-figure" src="../ram_and_cache.assets/computer_storage_devices.png" /></p>
 <p align="center"> Рисунок 4-10 &nbsp; Поток данных между жестким диском, RAM и кэшем </p>
 
 <h2 id="442">4.4.2 &nbsp; Эффективность использования памяти структурами данных<a class="headerlink" href="#442" title="Permanent link">&para;</a></h2>
 <p>С точки зрения использования пространства памяти массивы и связные списки имеют свои преимущества и ограничения.</p>
-<p>С одной стороны, <strong>память ограничена, и один и тот же участок памяти не может совместно использоваться несколькими программами</strong>, поэтому нам хочется, чтобы структуры данных использовали пространство как можно эффективнее. Элементы массива расположены плотно и не требуют дополнительного места для хранения ссылок (указателей) между узлами списка, поэтому массивы эффективнее по памяти. Однако массиву нужно сразу выделить достаточно большой непрерывный участок памяти, что может приводить к потерям пространства, а его расширение требует дополнительных затрат времени и памяти. Напротив, связные списки выполняют динамическое выделение и освобождение памяти "по узлам", что дает большую гибкость.</p>
+<p>С одной стороны, <strong>память ограничена, и один и тот же участок памяти не может совместно использоваться несколькими программами</strong>, поэтому нам хочется, чтобы структуры данных использовали пространство как можно эффективнее. Элементы массива расположены плотно и не требуют дополнительного места для хранения ссылок (указателей) между узлами списка, поэтому массивы эффективнее по памяти. Однако массиву нужно сразу выделить достаточно большой непрерывный участок памяти, что может приводить к потерям пространства, а его расширение требует дополнительных затрат времени и памяти. Напротив, связные списки выделяют и освобождают память на уровне узлов, что дает большую гибкость.</p>
 <p>С другой стороны, во время выполнения программы <strong>при многократном выделении и освобождении памяти фрагментация свободной памяти становится все более серьезной</strong>, что снижает эффективность ее использования. Массивы из-за непрерывного хранения относительно менее подвержены фрагментации. Напротив, элементы связного списка распределены по памяти, и частые операции вставки и удаления легче приводят к фрагментации.</p>
 <h2 id="443">4.4.3 &nbsp; Эффективность использования кэша структурами данных<a class="headerlink" href="#443" title="Permanent link">&para;</a></h2>
 <p>Хотя по объему кэш намного меньше оперативной памяти, он значительно быстрее и играет критически важную роль в скорости выполнения программ. Поскольку объем кэша ограничен и в нем можно хранить только небольшую долю часто используемых данных, когда CPU пытается обратиться к данным, которых в кэше нет, происходит <u>промах кэша (cache miss)</u> , и CPU вынужден загружать нужные данные из более медленной памяти.</p>
-<p>Очевидно, что <strong>чем меньше "промахов кэша", тем выше эффективность чтения и записи данных CPU</strong>, а значит, тем лучше производительность программы. Долю обращений, при которых CPU успешно получает данные из кэша, называют <u>коэффициентом попадания в кэш (cache hit rate)</u> ; этот показатель обычно используют для оценки эффективности кэша.</p>
+<p>Очевидно, что <strong>чем меньше промахов кэша, тем выше эффективность чтения и записи данных CPU</strong>, а значит, тем лучше производительность программы. Долю обращений, при которых CPU успешно получает данные из кэша, называют <u>коэффициентом попадания в кэш (cache hit rate)</u> ; этот показатель обычно используют для оценки эффективности кэша.</p>
 <p>Чтобы добиться как можно большей эффективности, кэш использует следующие механизмы загрузки данных.</p>
 <ul>
 <li><strong>Строки кэша</strong>: кэш хранит и загружает данные не по одному байту, а строками кэша. По сравнению с передачей по байтам это гораздо эффективнее.</li>
@@ -4461,8 +4461,8 @@
 <p>На практике <strong>массивы и связные списки по-разному используют кэш</strong>, и это проявляется в нескольких аспектах.</p>
 <ul>
 <li><strong>Занимаемое пространство</strong>: элементы связного списка занимают больше места, чем элементы массива, поэтому в кэше помещается меньше полезных данных.</li>
-<li><strong>Строки кэша</strong>: данные списка разбросаны по памяти, а кэш загружает данные "строками", поэтому доля бесполезно загружаемых данных оказывается выше.</li>
-<li><strong>Механизм предвыборки</strong>: шаблон доступа к данным у массивов более "предсказуем", чем у списков, то есть системе легче угадать, какие данные понадобятся следующими.</li>
+<li><strong>Строки кэша</strong>: данные списка разбросаны по памяти, а кэш загружает данные строками, поэтому доля бесполезно загружаемых данных оказывается выше.</li>
+<li><strong>Механизм предвыборки</strong>: шаблон доступа к данным у массивов более предсказуем, чем у списков, то есть системе легче угадать, какие данные понадобятся следующими.</li>
 <li><strong>Пространственная локальность</strong>: массив хранится в компактной области памяти, поэтому данные рядом с уже загруженными с большей вероятностью скоро будут использованы.</li>
 </ul>
 <p>В целом <strong>массивы имеют более высокий коэффициент попадания в кэш, поэтому по эффективности операций они обычно превосходят связные списки</strong>. Именно поэтому при решении алгоритмических задач структуры данных на основе массивов часто оказываются предпочтительнее.</p>
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 <h1 id="45">4.5 &nbsp; Резюме<a class="headerlink" href="#45" title="Permanent link">&para;</a></h1>
 <h3 id="1">1. &nbsp; Ключевые выводы<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
-<li>Массивы и связные списки - это две базовые структуры данных, представляющие два способа хранения данных в памяти компьютера: хранение в непрерывной области и хранение в разрозненных областях. Их свойства во многом взаимно дополняют друг друга.</li>
-<li>Массив поддерживает произвольный доступ и занимает меньше памяти; однако вставка и удаление элементов в нем неэффективны, а длина после инициализации неизменяема.</li>
-<li>Связный список позволяет эффективно вставлять и удалять узлы путем изменения ссылок (указателей), а также гибко менять длину; однако доступ к узлам неэффективен, а памяти он занимает больше. Распространенные типы списков включают односвязные, циклические и двусвязные списки.</li>
+<li>Массивы и связные списки - это две базовые структуры данных, представляющие два способа хранения данных в памяти компьютера: хранение в непрерывном пространстве и хранение в разрозненном пространстве. Их свойства во многом взаимно дополняют друг друга.</li>
+<li>Массив поддерживает произвольный доступ и занимает меньше памяти; однако вставка и удаление элементов в нем неэффективны, а длина после инициализации фиксирована.</li>
+<li>Связный список позволяет эффективно вставлять и удалять узлы путем изменения ссылок (указателей), а также гибко менять длину; однако доступ к узлам менее эффективен, а памяти он занимает больше. Распространенные типы списков включают односвязные, циклические и двусвязные списки.</li>
 <li>Список - это упорядоченная коллекция элементов, поддерживающая добавление, удаление, поиск и изменение, и обычно реализуемая на основе динамического массива. Он сохраняет преимущества массива и при этом может гибко менять длину.</li>
-<li>Появление списка значительно повысило практическую полезность массива, хотя это и может приводить к потерям части памяти.</li>
+<li>Появление списка значительно повысило практическую ценность массива, хотя это и может приводить к потере части памяти.</li>
 <li>Во время работы программы данные в основном хранятся в оперативной памяти. Массив обеспечивает более высокую эффективность использования пространства памяти, а связный список дает большую гибкость в использовании памяти.</li>
 <li>Кэш, используя строки кэша, механизм предвыборки, а также пространственную и временную локальность, предоставляет CPU быстрый доступ к данным и заметно повышает эффективность выполнения программ.</li>
 <li>Поскольку массивы обычно имеют более высокий коэффициент попадания в кэш, они в большинстве случаев работают эффективнее списков. При выборе структуры данных нужно исходить из конкретных требований и сценариев.</li>
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-    aria-label="Назад: 4.4 Память и кеш *"
+    aria-label="Назад: 4.4 Оперативная память и кэш *"
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-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
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+        13.1.6 &nbsp; Типичные задачи поиска с возвратом
       
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+        13.1.6 &nbsp; Типичные задачи поиска с возвратом
       
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 <!-- Page content -->
 <h1 id="131">13.1 &nbsp; Алгоритм поиска с возвратом<a class="headerlink" href="#131" title="Permanent link">&para;</a></h1>
 <p><u>Алгоритм поиска с возвратом (backtracking algorithm)</u> - это метод решения задач путем полного перебора. Его основная идея состоит в том, чтобы, начиная с некоторого исходного состояния, грубо перебрать все возможные решения, записывать корректные решения и продолжать поиск до тех пор, пока решение не будет найдено или пока не будут исчерпаны все возможные варианты.</p>
-<p>Обычно алгоритмы поиска с возвратом используют "поиск в глубину" для обхода пространства решений. В главе "Бинарные деревья" мы уже упоминали, что прямой, симметричный и обратный обходы относятся к поиску в глубину. Теперь мы на основе прямого обхода построим задачу backtracking и постепенно разберем принцип работы этого алгоритма.</p>
+<p>Обычно алгоритмы поиска с возвратом используют обход в глубину для обхода пространства решений. В главе "Бинарные деревья" мы уже упоминали, что прямой, симметричный и обратный обходы относятся к обходу в глубину. Теперь мы на основе прямого обхода построим задачу поиска с возвратом и постепенно разберем принцип работы этого алгоритма.</p>
 <div class="admonition question">
 <p class="admonition-title">Пример 1</p>
 <p>Дано двоичное дерево. Найдите и запишите все узлы со значением <span class="arithmatex">\(7\)</span> ; верните список этих узлов.</p>
@@ -4655,7 +4655,7 @@
 <p align="center"> Рисунок 13-1 &nbsp; Поиск узлов при прямом обходе </p>
 
 <h2 id="1311">13.1.1 &nbsp; Попытка и откат<a class="headerlink" href="#1311" title="Permanent link">&para;</a></h2>
-<p><strong>Алгоритм называется backtracking, потому что при поиске в пространстве решений он использует стратегию "попытка" и "откат"</strong>. Когда в процессе поиска алгоритм приходит в состояние, из которого нельзя двигаться дальше или нельзя получить удовлетворяющее условиям решение, он отменяет предыдущий выбор, возвращается к более раннему состоянию и пробует другие возможные варианты.</p>
+<p><strong>Алгоритм называется поиском с возвратом, потому что при поиске в пространстве решений он использует стратегию "попытка" и "откат"</strong>. Когда в процессе поиска алгоритм приходит в состояние, из которого нельзя двигаться дальше или нельзя получить удовлетворяющее условиям решение, он отменяет предыдущий выбор, возвращается к более раннему состоянию и пробует другие возможные варианты.</p>
 <p>Для примера 1 посещение каждого узла представляет собой "попытку", а прохождение листового узла или возврат к родителю через <code>return</code> означает "откат".</p>
 <p>Важно понимать, что <strong>откат не сводится только к возврату из функции</strong>. Чтобы показать это, слегка расширим пример 1.</p>
 <div class="admonition question">
@@ -4976,7 +4976,7 @@
 <p align="center"> Рисунок 13-2 &nbsp; Попытка и откат </p>
 
 <h2 id="1312">13.1.2 &nbsp; Обрезка<a class="headerlink" href="#1312" title="Permanent link">&para;</a></h2>
-<p>Сложные задачи backtracking обычно содержат одно или несколько ограничений, <strong>которые часто можно использовать для "обрезки"</strong>.</p>
+<p>Сложные задачи поиска с возвратом обычно содержат одно или несколько ограничений, <strong>которые часто можно использовать для "обрезки"</strong>.</p>
 <div class="admonition question">
 <p class="admonition-title">Пример 3</p>
 <p>Найдите в двоичном дереве все узлы со значением <span class="arithmatex">\(7\)</span> , верните пути от корня до этих узлов, <strong>причем путь не должен содержать узлы со значением <span class="arithmatex">\(3\)</span></strong>.</p>
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target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
-<p>Термин "обрезка" очень нагляден. Как показано на рисунке 13-3, во время поиска <strong>мы "срезаем" ветви поиска, не удовлетворяющие ограничениям</strong> , тем самым избегая множества бессмысленных попыток и повышая эффективность поиска.</p>
+<p>Термин "обрезка" очень нагляден. Как показано на рисунке 13-3, во время поиска <strong>мы отсекаем ветви, не удовлетворяющие ограничениям</strong> , тем самым избегая множества бессмысленных попыток и повышая эффективность поиска.</p>
 <p><img alt="Обрезка по условиям задачи" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_constrained_paths.png" /></p>
 <p align="center"> Рисунок 13-3 &nbsp; Обрезка по условиям задачи </p>
 
@@ -6246,10 +6246,10 @@
 <p><img alt="Сравнение поиска при сохранении и удалении return" class="animation-figure" src="../backtracking_algorithm.assets/backtrack_remove_return_or_not.png" /></p>
 <p align="center"> Рисунок 13-4 &nbsp; Сравнение поиска при сохранении и удалении return </p>
 
-<p>По сравнению с реализацией на основе прямого обхода, версия на основе общего каркаса backtracking выглядит более громоздкой, но при этом обладает лучшей универсальностью. На практике <strong>многие задачи backtracking можно решать в рамках этого каркаса</strong>. Для этого нужно лишь определить <code>state</code> и <code>choices</code> под конкретную задачу и реализовать соответствующие методы каркаса.</p>
+<p>По сравнению с реализацией на основе прямого обхода, версия на основе общего каркаса поиска с возвратом выглядит более громоздкой, но при этом обладает лучшей универсальностью. На практике <strong>многие задачи поиска с возвратом можно решать в рамках этого каркаса</strong>. Для этого нужно лишь определить <code>state</code> и <code>choices</code> под конкретную задачу и реализовать соответствующие методы каркаса.</p>
 <h2 id="1314">13.1.4 &nbsp; Часто используемые термины<a class="headerlink" href="#1314" title="Permanent link">&para;</a></h2>
-<p>Чтобы яснее анализировать алгоритмические задачи, подытожим значения часто используемых терминов backtracking и сопоставим их с примером 3, как показано в таблице 13-1.</p>
-<p align="center"> Таблица 13-1 &nbsp; Часто используемые термины алгоритма backtracking </p>
+<p>Чтобы яснее анализировать алгоритмические задачи, подытожим значения часто используемых терминов поиска с возвратом и сопоставим их с примером 3, как показано в таблице 13-1.</p>
+<p align="center"> Таблица 13-1 &nbsp; Часто используемые термины алгоритма поиска с возвратом </p>
 
 <div class="center-table">
 <table>
@@ -6296,21 +6296,21 @@
 </div>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>Такие понятия, как задача, решение и состояние, являются общими и встречаются не только в backtracking, но и в divide and conquer, динамическом программировании, жадных алгоритмах и других темах.</p>
+<p>Такие понятия, как задача, решение и состояние, являются общими и встречаются не только в поиске с возвратом, но и в "разделяй и властвуй", динамическом программировании, жадных алгоритмах и других темах.</p>
 </div>
 <h2 id="1315">13.1.5 &nbsp; Преимущества и ограничения<a class="headerlink" href="#1315" title="Permanent link">&para;</a></h2>
-<p>Алгоритм поиска с возвратом по своей сути является алгоритмом поиска в глубину, который перебирает все возможные решения, пока не найдет удовлетворяющее условиям. Преимущество этого подхода в том, что он позволяет находить все возможные решения и при разумной обрезке может работать весьма эффективно.</p>
-<p>Однако при работе с большими или сложными задачами <strong>эффективность backtracking может оказаться неприемлемой</strong>.</p>
+<p>Алгоритм поиска с возвратом по своей сути представляет собой алгоритм обхода в глубину, который перебирает все возможные решения, пока не найдет удовлетворяющее условиям. Преимущество этого подхода в том, что он позволяет находить все возможные решения и при разумной обрезке может работать весьма эффективно.</p>
+<p>Однако при работе с большими или сложными задачами <strong>эффективность поиска с возвратом может оказаться неприемлемой</strong>.</p>
 <ul>
-<li><strong>Время</strong>: backtracking обычно требует обхода всех возможных состояний пространства состояний, и его временная сложность может достигать экспоненциального или факториального порядка.</li>
+<li><strong>Время</strong>: поиск с возвратом обычно требует обхода всех возможных состояний пространства состояний, и его временная сложность может достигать экспоненциального или факториального порядка.</li>
 <li><strong>Память</strong>: при рекурсивных вызовах нужно хранить текущее состояние (например, путь, вспомогательные переменные для обрезки и т.д.), поэтому при большой глубине рекурсии потребность в памяти может стать значительной.</li>
 </ul>
-<p>Тем не менее <strong>backtracking по-прежнему остается лучшим решением для некоторых поисковых задач и задач удовлетворения ограничений</strong>. В таких задачах заранее невозможно предсказать, какие выборы приведут к эффективному решению, поэтому приходится перебирать все возможные варианты. В этой ситуации <strong>ключевым становится вопрос оптимизации эффективности</strong> , и для этого обычно используют две стратегии.</p>
+<p>Тем не менее <strong>поиск с возвратом по-прежнему остается лучшим решением для некоторых поисковых задач и задач удовлетворения ограничений</strong>. В таких задачах заранее невозможно предсказать, какие выборы приведут к эффективному решению, поэтому приходится перебирать все возможные варианты. В этой ситуации <strong>ключевым становится вопрос оптимизации эффективности</strong> , и для этого обычно используют две стратегии.</p>
 <ul>
 <li><strong>Обрезка</strong>: избегать поиска по тем путям, которые заведомо не приведут к решению, тем самым экономя время и память.</li>
 <li><strong>Эвристический поиск</strong>: вводить во время поиска дополнительные стратегии или оценки, чтобы в первую очередь исследовать пути, наиболее вероятно ведущие к эффективному решению.</li>
 </ul>
-<h2 id="1316-backtracking">13.1.6 &nbsp; Типичные задачи backtracking<a class="headerlink" href="#1316-backtracking" title="Permanent link">&para;</a></h2>
+<h2 id="1316">13.1.6 &nbsp; Типичные задачи поиска с возвратом<a class="headerlink" href="#1316" title="Permanent link">&para;</a></h2>
 <p>Алгоритм поиска с возвратом можно использовать для решения множества поисковых задач, задач удовлетворения ограничений и задач комбинаторной оптимизации.</p>
 <p><strong>Поисковые задачи</strong>: целью таких задач является поиск решений, удовлетворяющих определенным условиям.</p>
 <ul>
@@ -6330,7 +6330,7 @@
 <li>Задача коммивояжера: начиная из некоторой вершины графа, требуется посетить все остальные вершины ровно по одному разу и вернуться в исходную вершину, найдя при этом кратчайший путь.</li>
 <li>Задача о максимальной клике: дан неориентированный граф; требуется найти в нем максимальный полный подграф, то есть подграф, в котором любая пара вершин соединена ребром.</li>
 </ul>
-<p>Обратите внимание: для многих задач комбинаторной оптимизации backtracking не является оптимальным способом решения.</p>
+<p>Стоит отметить: для многих задач комбинаторной оптимизации поиск с возвратом не является оптимальным способом решения.</p>
 <ul>
 <li>Задача о рюкзаке 0-1 обычно решается с помощью динамического программирования, что дает более высокую временную эффективность.</li>
 <li>Задача коммивояжера является известной NP-Hard задачей; для ее решения часто используют генетические алгоритмы, муравьиные алгоритмы и другие методы.</li>
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-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
     
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-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
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 <li><a href="backtracking_algorithm/">13.1 &nbsp; Алгоритм поиска с возвратом</a></li>
 <li><a href="permutations_problem/">13.2 &nbsp; Задача о перестановках</a></li>
 <li><a href="subset_sum_problem/">13.3 &nbsp; Задача о сумме подмножеств</a></li>
-<li><a href="n_queens_problem/">13.4 &nbsp; Задача о <span class="arithmatex">\(n\)</span> ферзях</a></li>
+<li><a href="n_queens_problem/">13.4 &nbsp; Задача о n ферзях</a></li>
 <li><a href="summary/">13.5 &nbsp; Резюме</a></li>
 </ul>
 
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 <p class="admonition-title">Question</p>
 <p>Согласно правилам шахмат ферзь может атаковать фигуры, находящиеся с ним на одной строке, в одном столбце или на одной диагонали. Даны <span class="arithmatex">\(n\)</span> ферзей и шахматная доска размера <span class="arithmatex">\(n \times n\)</span> ; требуется найти такие расстановки, при которых ни одна пара ферзей не может атаковать друг друга.</p>
 </div>
-<p>Как показано на рисунке 13-15, при <span class="arithmatex">\(n = 4\)</span> существует два решения. С точки зрения backtracking доска размера <span class="arithmatex">\(n \times n\)</span> содержит <span class="arithmatex">\(n^2\)</span> клеток, которые образуют все возможные выборы <code>choices</code> . По мере поочередного размещения ферзей состояние доски непрерывно меняется, и текущее содержимое доски образует состояние <code>state</code> .</p>
+<p>Как показано на рисунке 13-15, при <span class="arithmatex">\(n = 4\)</span> существует два решения. С точки зрения поиска с возвратом доска размера <span class="arithmatex">\(n \times n\)</span> содержит <span class="arithmatex">\(n^2\)</span> клеток, которые образуют все возможные выборы <code>choices</code> . По мере поочередного размещения ферзей состояние доски непрерывно меняется, и текущее содержимое доски образует состояние <code>state</code> .</p>
 <p><img alt="Решения задачи о 4 ферзях" class="animation-figure" src="../n_queens_problem.assets/solution_4_queens.png" /></p>
 <p align="center"> Рисунок 13-15 &nbsp; Решения задачи о 4 ферзях </p>
 
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@@ -4522,8 +4522,8 @@
 <p class="admonition-title">Question</p>
 <p>Дан массив целых чисел, в котором нет повторяющихся элементов. Верните все возможные перестановки.</p>
 </div>
-<p>С точки зрения backtracking <strong>процесс построения перестановок можно представить как результат последовательности выборов</strong>. Пусть входной массив равен <span class="arithmatex">\([1, 2, 3]\)</span> ; если мы сначала выберем <span class="arithmatex">\(1\)</span> , затем <span class="arithmatex">\(3\)</span> , а потом <span class="arithmatex">\(2\)</span> , то получим перестановку <span class="arithmatex">\([1, 3, 2]\)</span> . Откат означает отмену одного из выборов с последующей попыткой других вариантов.</p>
-<p>С точки зрения кода backtracking множество кандидатов <code>choices</code> состоит из всех элементов входного массива, а состояние <code>state</code> - из элементов, уже выбранных к текущему моменту. Обратите внимание, что каждый элемент разрешено выбирать только один раз, <strong>поэтому все элементы в <code>state</code> должны быть уникальны</strong>.</p>
+<p>С точки зрения поиска с возвратом <strong>процесс построения перестановок можно представить как результат последовательности выборов</strong>. Пусть входной массив равен <span class="arithmatex">\([1, 2, 3]\)</span> ; если мы сначала выберем <span class="arithmatex">\(1\)</span> , затем <span class="arithmatex">\(3\)</span> , а потом <span class="arithmatex">\(2\)</span> , то получим перестановку <span class="arithmatex">\([1, 3, 2]\)</span> . Откат здесь означает отмену одного из выборов с последующей попыткой других вариантов.</p>
+<p>С точки зрения кода поиска с возвратом множество кандидатов <code>choices</code> состоит из всех элементов входного массива, а состояние <code>state</code> - из элементов, уже выбранных к текущему моменту. Поскольку каждый элемент разрешено выбирать только один раз, <strong>все элементы в <code>state</code> должны быть уникальны</strong>.</p>
 <p>Как показано на рисунке 13-5, процесс поиска можно развернуть в дерево рекурсии, где каждый узел представляет текущее состояние <code>state</code> . Начиная от корня, после трех раундов выбора мы попадаем в листья, и каждый лист соответствует одной перестановке.</p>
 <p><img alt="Дерево рекурсии для перестановок" class="animation-figure" src="../permutations_problem.assets/permutations_i.png" /></p>
 <p align="center"> Рисунок 13-5 &nbsp; Дерево рекурсии для перестановок </p>
@@ -4540,7 +4540,7 @@
 
 <p>Из рисунка видно, что такая обрезка уменьшает размер пространства поиска с <span class="arithmatex">\(O(n^n)\)</span> до <span class="arithmatex">\(O(n!)\)</span> .</p>
 <h3 id="2">2. &nbsp; Реализация кода<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>После прояснения всей логики можно просто "заполнить пропуски" в шаблоне backtracking. Чтобы сократить общий объем кода, мы не будем отдельно реализовывать каждую функцию из каркаса, а раскроем их прямо внутри <code>backtrack()</code> :</p>
+<p>После прояснения всей логики можно просто "заполнить пропуски" в шаблоне поиска с возвратом. Чтобы сократить общий объем кода, мы не будем отдельно реализовывать каждую функцию из каркаса, а раскроем их прямо внутри <code>backtrack()</code> :</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
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@@ -5021,7 +5021,7 @@
 <h3 id="1_1">1. &nbsp; Обрезка равных элементов<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
 <p>Посмотрите на рисунок 13-8: в первом раунде выбрать <span class="arithmatex">\(1\)</span> или выбрать <span class="arithmatex">\(\hat{1}\)</span> - это одно и то же, а значит, все перестановки, полученные из этих двух выборов, будут дублироваться. Поэтому ветвь <span class="arithmatex">\(\hat{1}\)</span> нужно отсечь.</p>
 <p>Точно так же, если в первом раунде выбрать <span class="arithmatex">\(2\)</span> , то во втором раунде выборы <span class="arithmatex">\(1\)</span> и <span class="arithmatex">\(\hat{1}\)</span> снова создадут дублирующиеся ветви, поэтому и в этом случае ветвь <span class="arithmatex">\(\hat{1}\)</span> нужно отсечь.</p>
-<p>По своей сути <strong>наша цель заключается в том, чтобы на каждом раунде выбора каждый из нескольких равных элементов выбирался только один раз</strong>.</p>
+<p>Иначе говоря, <strong>наша цель заключается в том, чтобы на каждом раунде выбора каждый из нескольких равных элементов выбирался только один раз</strong>.</p>
 <p><img alt="Обрезка повторяющихся перестановок" class="animation-figure" src="../permutations_problem.assets/permutations_ii_pruning.png" /></p>
 <p align="center"> Рисунок 13-8 &nbsp; Обрезка повторяющихся перестановок </p>
 
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+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
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 <p class="admonition-title">Question</p>
 <p>Дан массив положительных целых чисел <code>nums</code> и целое положительное значение <code>target</code> . Найдите все возможные комбинации, сумма элементов которых равна <code>target</code> . Во входном массиве нет повторяющихся элементов, и каждый элемент можно выбирать неограниченное число раз. Верните эти комбинации в виде списка; в результате не должно быть повторяющихся комбинаций.</p>
 </div>
-<p>Например, для входного множества <span class="arithmatex">\(\{3, 4, 5\}\)</span> и целевого значения <span class="arithmatex">\(9\)</span> решениями будут <span class="arithmatex">\(\{3, 3, 3\}\)</span> и <span class="arithmatex">\(\{4, 5\}\)</span> . При этом нужно обратить внимание на два обстоятельства.</p>
+<p>Например, для входного множества <span class="arithmatex">\(\{3, 4, 5\}\)</span> и целевого значения <span class="arithmatex">\(9\)</span> решениями будут <span class="arithmatex">\(\{3, 3, 3\}\)</span> и <span class="arithmatex">\(\{4, 5\}\)</span> . При этом важно учитывать два обстоятельства.</p>
 <ul>
 <li>Элементы входного множества можно выбирать повторно неограниченное число раз.</li>
 <li>Подмножество не различает порядок элементов, поэтому <span class="arithmatex">\(\{4, 5\}\)</span> и <span class="arithmatex">\(\{5, 4\}\)</span> считаются одним и тем же подмножеством.</li>
@@ -5002,7 +5002,7 @@
 <li>Если в первом и втором раундах выбрать соответственно <span class="arithmatex">\(3\)</span> и <span class="arithmatex">\(4\)</span> , то будут сгенерированы все подмножества, содержащие эти два элемента, и их можно обозначить как <span class="arithmatex">\([3, 4, \dots]\)</span> .</li>
 <li>После этого, если в первом раунде выбрать <span class="arithmatex">\(4\)</span> , <strong>то во втором раунде нужно пропустить <span class="arithmatex">\(3\)</span></strong> , потому что подмножества <span class="arithmatex">\([4, 3, \dots]\)</span> полностью дублируют подмножества, уже построенные на шаге <code>1.</code> .</li>
 </ol>
-<p>Во время поиска выборы на каждом уровне пробуются по одному слева направо, поэтому чем правее ветвь, тем больше ветвей оказывается отсечено.</p>
+<p>Во время поиска варианты на каждом уровне пробуются по одному слева направо, поэтому чем правее ветвь, тем больше ветвей оказывается отсечено.</p>
 <ol>
 <li>В первых двух раундах выбираются <span class="arithmatex">\(3\)</span> и <span class="arithmatex">\(5\)</span> , что дает подмножества <span class="arithmatex">\([3, 5, \dots]\)</span> .</li>
 <li>В первых двух раундах выбираются <span class="arithmatex">\(4\)</span> и <span class="arithmatex">\(5\)</span> , что дает подмножества <span class="arithmatex">\([4, 5, \dots]\)</span> .</li>
@@ -5517,9 +5517,9 @@
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target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
-<p>На рисунке 13-12 показан полный процесс backtracking для массива <span class="arithmatex">\([3, 4, 5]\)</span> и целевого значения <span class="arithmatex">\(9\)</span> .</p>
-<p><img alt="Процесс backtracking для задачи о сумме подмножеств I" class="animation-figure" src="../subset_sum_problem.assets/subset_sum_i.png" /></p>
-<p align="center"> Рисунок 13-12 &nbsp; Процесс backtracking для задачи о сумме подмножеств I </p>
+<p>На рисунке 13-12 показан полный процесс поиска с возвратом для массива <span class="arithmatex">\([3, 4, 5]\)</span> и целевого значения <span class="arithmatex">\(9\)</span> .</p>
+<p><img alt="Процесс поиска с возвратом для задачи о сумме подмножеств I" class="animation-figure" src="../subset_sum_problem.assets/subset_sum_i.png" /></p>
+<p align="center"> Рисунок 13-12 &nbsp; Процесс поиска с возвратом для задачи о сумме подмножеств I </p>
 
 <h2 id="1332">13.3.2 &nbsp; Учет повторяющихся элементов<a class="headerlink" href="#1332" title="Permanent link">&para;</a></h2>
 <div class="admonition question">
@@ -5532,7 +5532,7 @@
 <p align="center"> Рисунок 13-13 &nbsp; Повторяющиеся подмножества из-за равных элементов </p>
 
 <h3 id="1_1">1. &nbsp; Обрезка равных элементов<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
-<p>Чтобы решить эту проблему, <strong>нужно ограничить выбор равных элементов так, чтобы в каждом раунде каждый из них выбирался только один раз</strong>. Реализуется это довольно изящно: поскольку массив отсортирован, равные элементы стоят рядом. Значит, если в текущем раунде текущий элемент равен соседнему слева, то этот вариант уже был рассмотрен, и текущий элемент нужно пропустить.</p>
+<p>Чтобы решить эту проблему, <strong>нужно ограничить выбор равных элементов так, чтобы в каждом раунде каждый из них выбирался только один раз</strong>. Реализуется это довольно естественно: поскольку массив отсортирован, равные элементы стоят рядом. Значит, если в текущем раунде текущий элемент равен соседнему слева, то этот вариант уже был рассмотрен, и текущий элемент нужно пропустить.</p>
 <p>Одновременно <strong>по условию этой задачи каждый элемент массива можно выбрать только один раз</strong>. К счастью, это ограничение тоже можно реализовать через переменную <code>start</code> : после выбора элемента <span class="arithmatex">\(x_i\)</span> следующий раунд начинается с индекса <span class="arithmatex">\(i + 1\)</span> . Так мы одновременно убираем повторяющиеся подмножества и исключаем повторный выбор одного и того же элемента.</p>
 <h3 id="2_1">2. &nbsp; Реализация кода<a class="headerlink" href="#2_1" title="Permanent link">&para;</a></h3>
 <div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label></div>
@@ -6096,9 +6096,9 @@
 <p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20backtrack%28state%3A%20list%5Bint%5D%2C%20target%3A%20int%2C%20choices%3A%20list%5Bint%5D%2C%20start%3A%20int%2C%20res%3A%20list%5Blist%5Bint%5D%5D%29%3A%0A%20%20%20%20if%20target%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20res.append%28list%28state%29%29%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20for%20i%20in%20range%28start%2C%20len%28choices%29%29%3A%0A%20%20%20%20%20%20%20%20if%20target%20-%20choices%5Bi%5D%20%3C%200%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20if%20i%20%3E%20start%20and%20choices%5Bi%5D%20%3D%3D%20choices%5Bi%20-%201%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20continue%0A%20%20%20%20%20%20%20%20state.append%28choices%5Bi%5D%29%0A%20%20%20%20%20%20%20%20backtrack%28state%2C%20target%20-%20choices%5Bi%5D%2C%20choices%2C%20i%20%2B%201%2C%20res%29%0A%20%20%20%20%20%20%20%20state.pop%28%29%0A%0Adef%20subset_sum_ii%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20list%5Blist%5Bint%5D%5D%3A%0A%20%20%20%20state%20%3D%20%5B%5D%0A%20%20%20%20nums.sort%28%29%0A%20%20%20%20start%20%3D%200%0A%20%20%20%20res%20%3D%20%5B%5D%0A%20%20%20%20backtrack%28state%2C%20target%2C%20nums%2C%20start%2C%20res%29%0A%20%20%20%20return%20res%0A%27Driver%20Code%27%0Aif%20__name__%20%3D%3D%20%27__main__%27%3A%0A%20%20%20%20nums%20%3D%20%5B4%2C%204%2C%205%5D%0A%20%20%20%20target%20%3D%209%0A%20%20%20%20res%20%3D%20subset_sum_ii%28nums%2C%20target%29%0A%20%20%20%20print%28f%27%D0%92%D1%85%D0%BE%D0%B4%D0%BD%D0%BE%D0%B9%20%D0%BC%D0%B0%D1%81%D1%81%D0%B8%D0%B2%20nums%20%3D%20%7Bnums%7D%2C%20target%20%3D%20%7Btarget%7D%27%29%0A%20%20%20%20print%28f%27%D0%92%D1%81%D0%B5%20%D0%BF%D0%BE%D0%B4%D0%BC%D0%BD%D0%BE%D0%B6%D0%B5%D1%81%D1%82%D0%B2%D0%B0%20%D1%81%20%D1%81%D1%83%D0%BC%D0%BC%D0%BE%D0%B9%20%7Btarget%7D%3A%20res%20%3D%20%7Bres%7D%27%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=16&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20backtrack%28state%3A%20list%5Bint%5D%2C%20target%3A%20int%2C%20choices%3A%20list%5Bint%5D%2C%20start%3A%20int%2C%20res%3A%20list%5Blist%5Bint%5D%5D%29%3A%0A%20%20%20%20if%20target%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20res.append%28list%28state%29%29%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20for%20i%20in%20range%28start%2C%20len%28choices%29%29%3A%0A%20%20%20%20%20%20%20%20if%20target%20-%20choices%5Bi%5D%20%3C%200%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20if%20i%20%3E%20start%20and%20choices%5Bi%5D%20%3D%3D%20choices%5Bi%20-%201%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20continue%0A%20%20%20%20%20%20%20%20state.append%28choices%5Bi%5D%29%0A%20%20%20%20%20%20%20%20backtrack%28state%2C%20target%20-%20choices%5Bi%5D%2C%20choices%2C%20i%20%2B%201%2C%20res%29%0A%20%20%20%20%20%20%20%20state.pop%28%29%0A%0Adef%20subset_sum_ii%28nums%3A%20list%5Bint%5D%2C%20target%3A%20int%29%20-%3E%20list%5Blist%5Bint%5D%5D%3A%0A%20%20%20%20state%20%3D%20%5B%5D%0A%20%20%20%20nums.sort%28%29%0A%20%20%20%20start%20%3D%200%0A%20%20%20%20res%20%3D%20%5B%5D%0A%20%20%20%20backtrack%28state%2C%20target%2C%20nums%2C%20start%2C%20res%29%0A%20%20%20%20return%20res%0A%27Driver%20Code%27%0Aif%20__name__%20%3D%3D%20%27__main__%27%3A%0A%20%20%20%20nums%20%3D%20%5B4%2C%204%2C%205%5D%0A%20%20%20%20target%20%3D%209%0A%20%20%20%20res%20%3D%20subset_sum_ii%28nums%2C%20target%29%0A%20%20%20%20print%28f%27%D0%92%D1%85%D0%BE%D0%B4%D0%BD%D0%BE%D0%B9%20%D0%BC%D0%B0%D1%81%D1%81%D0%B8%D0%B2%20nums%20%3D%20%7Bnums%7D%2C%20target%20%3D%20%7Btarget%7D%27%29%0A%20%20%20%20print%28f%27%D0%92%D1%81%D0%B5%20%D0%BF%D0%BE%D0%B4%D0%BC%D0%BD%D0%BE%D0%B6%D0%B5%D1%81%D1%82%D0%B2%D0%B0%20%D1%81%20%D1%81%D1%83%D0%BC%D0%BC%D0%BE%D0%B9%20%7Btarget%7D%3A%20res%20%3D%20%7Bres%7D%27%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=16&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
-<p>На рисунке 13-14 показан процесс backtracking для массива <span class="arithmatex">\([4, 4, 5]\)</span> и целевого значения <span class="arithmatex">\(9\)</span> . В нем используются четыре вида обрезки. Попробуйте сопоставить рисунок с комментариями в коде, чтобы понять полный процесс поиска и то, как работает каждый тип обрезки.</p>
-<p><img alt="Процесс backtracking для задачи о сумме подмножеств II" class="animation-figure" src="../subset_sum_problem.assets/subset_sum_ii.png" /></p>
-<p align="center"> Рисунок 13-14 &nbsp; Процесс backtracking для задачи о сумме подмножеств II </p>
+<p>На рисунке 13-14 показан процесс поиска с возвратом для массива <span class="arithmatex">\([4, 4, 5]\)</span> и целевого значения <span class="arithmatex">\(9\)</span> . В нем используются четыре вида обрезки. Попробуйте сопоставить рисунок с комментариями в коде, чтобы понять полный процесс поиска и то, как работает каждый тип обрезки.</p>
+<p><img alt="Процесс поиска с возвратом для задачи о сумме подмножеств II" class="animation-figure" src="../subset_sum_problem.assets/subset_sum_ii.png" /></p>
+<p align="center"> Рисунок 13-14 &nbsp; Процесс поиска с возвратом для задачи о сумме подмножеств II </p>
 
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 <h3 id="1">1. &nbsp; Ключевые выводы<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
 <li>Алгоритм поиска с возвратом по своей сути является методом полного перебора: он ищет решения путем обхода пространства решений в глубину. Во время поиска он фиксирует решения, удовлетворяющие условиям, пока не найдет все такие решения или пока обход не завершится.</li>
-<li>Процесс backtracking состоит из двух частей: попытки и отката. Он с помощью поиска в глубину пробует разные варианты выбора; когда встречается состояние, не удовлетворяющее ограничениям, алгоритм отменяет предыдущий выбор, возвращается к прошлому состоянию и продолжает пробовать другие варианты. Попытка и откат являются двумя противоположными по направлению действиями.</li>
-<li>Задачи backtracking обычно содержат несколько ограничений, которые можно использовать для обрезки. Обрезка позволяет заранее завершать ненужные ветви поиска и тем самым значительно повышать эффективность.</li>
-<li>Алгоритм backtracking в первую очередь применяется для решения поисковых задач и задач с ограничениями. Задачи комбинаторной оптимизации тоже можно решать с его помощью, но для них часто существуют более эффективные или более подходящие методы.</li>
+<li>Процесс поиска с возвратом состоит из двух частей: попытки и отката. Он с помощью поиска в глубину пробует разные варианты выбора; когда встречается состояние, не удовлетворяющее ограничениям, алгоритм отменяет предыдущий выбор, возвращается к прошлому состоянию и продолжает пробовать другие варианты. Попытка и откат являются двумя противоположными по направлению действиями.</li>
+<li>Задачи поиска с возвратом обычно содержат несколько ограничений, которые можно использовать для обрезки. Обрезка позволяет заранее завершать ненужные ветви поиска и тем самым значительно повышать эффективность.</li>
+<li>Алгоритм поиска с возвратом в первую очередь применяется для решения поисковых задач и задач с ограничениями. Задачи комбинаторной оптимизации тоже можно решать с его помощью, но для них часто существуют более эффективные или более подходящие методы.</li>
 <li>Задача о перестановках нацелена на поиск всех возможных перестановок элементов данного множества. Мы используем массив для записи того, был ли выбран каждый элемент, и отсекаем ветви, где один и тот же элемент выбирается повторно, чтобы гарантировать однократный выбор каждого элемента.</li>
 <li>В задаче о перестановках, если во множестве присутствуют повторяющиеся элементы, в итоговом результате возникнут повторяющиеся перестановки. Поэтому нужно ограничить выбор равных элементов так, чтобы в каждом раунде каждый из них выбирался только один раз; обычно это реализуется с помощью хеш-множества.</li>
-<li>Цель задачи о сумме подмножеств - найти все подмножества данного множества, сумма которых равна целевому значению. В множестве порядок элементов не важен, однако процесс поиска порождает результаты во всех возможных порядках, из-за чего появляются повторяющиеся подмножества. Поэтому перед запуском backtracking мы сортируем данные и вводим переменную, указывающую начальную точку обхода в каждом раунде, чтобы отсечь ветви, создающие дубликаты.</li>
+<li>Цель задачи о сумме подмножеств - найти все подмножества данного множества, сумма которых равна целевому значению. В множестве порядок элементов не важен, однако процесс поиска порождает результаты во всех возможных порядках, из-за чего появляются повторяющиеся подмножества. Поэтому перед запуском поиска с возвратом мы сортируем данные и вводим переменную, указывающую начальную точку обхода в каждом раунде, чтобы отсечь ветви, создающие дубликаты.</li>
 <li>В задаче о сумме подмножеств равные элементы массива также порождают повторяющиеся множества. При наличии предварительной сортировки их можно отсекать, проверяя равенство соседних элементов, и тем самым гарантировать, что в каждом раунде равные элементы будут выбираться только один раз.</li>
 <li>Задача о <span class="arithmatex">\(n\)</span> ферзях состоит в поиске способов разместить <span class="arithmatex">\(n\)</span> ферзей на доске размера <span class="arithmatex">\(n \times n\)</span> так, чтобы никакие два ферзя не атаковали друг друга. Ограничения этой задачи включают строки, столбцы, главные диагонали и побочные диагонали. Чтобы выполнить ограничение по строкам, используется построчная стратегия размещения, гарантирующая по одному ферзю в каждой строке.</li>
 <li>Обработка ограничений по столбцам и диагоналям устроена похожим образом. Для ограничения по столбцам используется массив, фиксирующий наличие ферзя в каждом столбце. Для диагоналей используются два массива, записывающие наличие ферзей на главных и побочных диагоналях. Основная сложность здесь состоит в том, чтобы найти закономерность индексов строк и столбцов клеток, лежащих на одной и той же главной или побочной диагонали.</li>
 </ul>
-<h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
+<h3 id="2">2. &nbsp; Вопросы и ответы<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
 <p><strong>Q</strong>: Как понять связь между поиском с возвратом и рекурсией?</p>
-<p>В целом backtracking - это скорее "алгоритмическая стратегия", а рекурсия больше похожа на "инструмент".</p>
+<p>В целом поиск с возвратом - это скорее "алгоритмическая стратегия", а рекурсия больше похожа на "инструмент".</p>
 <ul>
-<li>Алгоритмы поиска с возвратом обычно реализуются на основе рекурсии. Однако backtracking - это лишь один из вариантов применения рекурсии, а именно ее использование в поисковых задачах.</li>
-<li>Структура рекурсии отражает парадигму разбиения на подзадачи и часто применяется для решения задач divide and conquer, backtracking, динамического программирования (мемоизированной рекурсии) и других подобных задач.</li>
+<li>Алгоритмы поиска с возвратом обычно реализуются на основе рекурсии. Однако поиск с возвратом - это лишь один из вариантов применения рекурсии, а именно ее использование в поисковых задачах.</li>
+<li>Структура рекурсии отражает парадигму разбиения на подзадачи и часто применяется для решения задач "разделяй и властвуй", поиска с возвратом, динамического программирования (мемоизированной рекурсии) и других подобных задач.</li>
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 <p><img alt="Анализ сложности" class="cover-image" src="../assets/covers/chapter_complexity_analysis.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>Анализ сложности подобен пространственно-временному проводнику в огромной вселенной алгоритмов.</p>
-<p>Он ведет нас вглубь двух измерений - времени и пространства, помогая искать более изящные решения.</p>
+<p>Анализ сложности подобен пространственно-временному проводнику в необъятной вселенной алгоритмов.</p>
+<p>Он ведет нас в глубину двух измерений - времени и пространства, помогая искать более изящные решения.</p>
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 <h2 id="_1">Содержание главы<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
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 <!-- Page content -->
 <h1 id="22">2.2 &nbsp; Итерация и рекурсия<a class="headerlink" href="#22" title="Permanent link">&para;</a></h1>
-<p>В алгоритмах очень часто приходится многократно выполнять одну и ту же задачу, и это тесно связано с анализом сложности. Поэтому, прежде чем переходить к временной и пространственной сложности, давай сначала разберемся, как в программах организуется повторяющееся выполнение задач, то есть с двумя базовыми управляющими структурами: итерацией и рекурсией.</p>
+<p>В алгоритмах часто требуется повторное выполнение определенной задачи, что тесно связано с анализом сложности. Поэтому, прежде чем перейти к обсуждению временной и пространственной сложности, рассмотрим, как реализовать повторное выполнение задач в программе, а именно две основные структуры управления программой: итерацию и рекурсию.</p>
 <h2 id="221">2.2.1 &nbsp; Итерация<a class="headerlink" href="#221" title="Permanent link">&para;</a></h2>
-<p><u>Итерация (iteration)</u> - это управляющая структура, предназначенная для многократного выполнения некоторой задачи. При итерации программа повторно выполняет определенный фрагмент кода при соблюдении некоторого условия, пока это условие не перестанет выполняться.</p>
+<p><u>Итерация (iteration)</u> - это структура управления, которая позволяет повторно выполнять определенную задачу. В итерации программа повторяет выполнение определенного участка кода, пока выполняется определенное условие.</p>
 <h3 id="1-for">1. &nbsp; Цикл for<a class="headerlink" href="#1-for" title="Permanent link">&para;</a></h3>
-<p>Цикл <code>for</code> - одна из самых распространенных форм итерации, <strong>она хорошо подходит в тех случаях, когда число повторений известно заранее</strong>.</p>
-<p>Следующая функция реализует вычисление суммы <span class="arithmatex">\(1 + 2 + \dots + n\)</span> на основе цикла <code>for</code> , а результат сохраняется в переменной <code>res</code> . Обрати внимание, что в Python <code>range(a, b)</code> соответствует "лево-замкнутому, право-открытому" интервалу, то есть перебираются значения <span class="arithmatex">\(a, a + 1, \dots, b-1\)</span> :</p>
+<p>Цикл <code>for</code> - одна из наиболее распространенных форм итерации, <strong>которая подходит для использования, когда количество итераций известно заранее</strong>.</p>
+<p>Следующая функция реализует суммирование <span class="arithmatex">\(1 + 2 + \dots + n\)</span> с использованием цикла <code>for</code> , а результат суммирования сохраняется в переменной <code>res</code> . Следует отметить, что в Python диапазон <code>range(a, b)</code> соответствует левому закрытому, правому открытому интервалу, то есть перебираются значения <span class="arithmatex">\(a, a + 1, \dots, b-1\)</span> :</p>
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 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20for_loop%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%A6%D0%B8%D0%BA%D0%BB%20for%22%22%22%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20%23%20%D0%A6%D0%B8%D0%BA%D0%BB%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B5%20%D1%81%D1%83%D0%BC%D0%BC%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5%201%2C%202%2C%20...%2C%20n-1%2C%20n%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20res%20%2B%3D%20i%0A%20%20%20%20return%20res%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20for_loop%28n%29%0A%20%20%20%20print%28f%22%5Cn%D0%A0%D0%B5%D0%B7%D1%83%D0%BB%D1%8C%D1%82%D0%B0%D1%82%20%D1%81%D1%83%D0%BC%D0%BC%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D1%8F%20%D0%B2%20%D1%86%D0%B8%D0%BA%D0%BB%D0%B5%20for%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
-<p>На рисунке 2-1 показана блок-схема этой функции суммирования.</p>
+<p>Ниже представлена блок-схема этой функции суммирования.</p>
 <p><img alt="Блок-схема функции суммирования" class="animation-figure" src="../iteration_and_recursion.assets/iteration.png" /></p>
 <p align="center"> Рисунок 2-1 &nbsp; Блок-схема функции суммирования </p>
 
-<p>Число операций в этой функции суммирования пропорционально размеру входных данных <span class="arithmatex">\(n\)</span> , то есть между ними существует "линейная зависимость". На самом деле <strong>временная сложность как раз и описывает такую "линейную зависимость"</strong>. Соответствующий материал будет подробно разобран в следующем разделе.</p>
+<p>Количество операций этой функции суммирования пропорционально размеру входных данных <span class="arithmatex">\(n\)</span> , или, другими словами, линейно зависит от него. <strong>На самом деле временная сложность описывает именно эту линейную зависимость</strong>. Соответствующий материал будет подробно рассмотрен в следующем разделе.</p>
 <h3 id="2-while">2. &nbsp; Цикл while<a class="headerlink" href="#2-while" title="Permanent link">&para;</a></h3>
-<p>Подобно циклу <code>for</code> , цикл <code>while</code> тоже является способом реализации итерации. В цикле <code>while</code> программа в каждом раунде сначала проверяет условие: если условие истинно, выполнение продолжается, иначе цикл завершается.</p>
-<p>Ниже мы используем цикл <code>while</code> для реализации суммы <span class="arithmatex">\(1 + 2 + \dots + n\)</span> :</p>
+<p>Подобно циклу <code>for</code> , цикл <code>while</code> также представляет собой метод реализации итерации. В цикле <code>while</code> программа перед каждой итерацией проверяет условие: если условие истинно, то выполнение продолжается, иначе цикл завершается.</p>
+<p>Ниже приведен пример реализации суммирования <span class="arithmatex">\(1 + 2 + \dots + n\)</span> с использованием цикла <code>while</code> :</p>
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 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20while_loop%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%A6%D0%B8%D0%BA%D0%BB%20while%22%22%22%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20i%20%3D%201%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%20%D1%83%D1%81%D0%BB%D0%BE%D0%B2%D0%BD%D0%BE%D0%B9%20%D0%BF%D0%B5%D1%80%D0%B5%D0%BC%D0%B5%D0%BD%D0%BD%D0%BE%D0%B9%0A%20%20%20%20%23%20%D0%A6%D0%B8%D0%BA%D0%BB%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B5%20%D1%81%D1%83%D0%BC%D0%BC%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5%201%2C%202%2C%20...%2C%20n-1%2C%20n%0A%20%20%20%20while%20i%20%3C%3D%20n%3A%0A%20%20%20%20%20%20%20%20res%20%2B%3D%20i%0A%20%20%20%20%20%20%20%20i%20%2B%3D%201%20%20%23%20%D0%9E%D0%B1%D0%BD%D0%BE%D0%B2%D0%B8%D1%82%D1%8C%20%D1%83%D1%81%D0%BB%D0%BE%D0%B2%D0%BD%D1%83%D1%8E%20%D0%BF%D0%B5%D1%80%D0%B5%D0%BC%D0%B5%D0%BD%D0%BD%D1%83%D1%8E%0A%20%20%20%20return%20res%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20while_loop%28n%29%0A%20%20%20%20print%28f%22%5Cn%D0%A0%D0%B5%D0%B7%D1%83%D0%BB%D1%8C%D1%82%D0%B0%D1%82%20%D1%81%D1%83%D0%BC%D0%BC%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D1%8F%20%D0%B2%20%D1%86%D0%B8%D0%BA%D0%BB%D0%B5%20while%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
-<p>**Цикл <code>while</code> обладает большей свободой, чем цикл <code>for</code> **. В цикле <code>while</code> мы можем свободно задавать шаги инициализации и обновления условной переменной.</p>
-<p>Например, в следующем коде условная переменная <span class="arithmatex">\(i\)</span> обновляется два раза за один проход, и такой случай уже не слишком удобно выражать через цикл <code>for</code> :</p>
+<p>**Цикл <code>while</code> обладает большей степенью свободы по сравнению с циклом <code>for</code> **. В цикле <code>while</code> можно свободно управлять инициализацией и обновлением условной переменной.</p>
+<p>Например, в следующем коде условная переменная <span class="arithmatex">\(i\)</span> обновляется дважды на каждой итерации, что затруднительно сделать с использованием цикла <code>for</code> :</p>
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 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20while_loop_ii%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%A6%D0%B8%D0%BA%D0%BB%20while%20%28%D0%B4%D0%B2%D0%BE%D0%B9%D0%BD%D0%BE%D0%B5%20%D0%BE%D0%B1%D0%BD%D0%BE%D0%B2%D0%BB%D0%B5%D0%BD%D0%B8%D0%B5%29%22%22%22%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20i%20%3D%201%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%20%D1%83%D1%81%D0%BB%D0%BE%D0%B2%D0%BD%D0%BE%D0%B9%20%D0%BF%D0%B5%D1%80%D0%B5%D0%BC%D0%B5%D0%BD%D0%BD%D0%BE%D0%B9%0A%20%20%20%20%23%20%D0%A6%D0%B8%D0%BA%D0%BB%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B5%20%D1%81%D1%83%D0%BC%D0%BC%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5%201%2C%204%2C%2010%2C%20...%0A%20%20%20%20while%20i%20%3C%3D%20n%3A%0A%20%20%20%20%20%20%20%20res%20%2B%3D%20i%0A%20%20%20%20%20%20%20%20%23%20%D0%9E%D0%B1%D0%BD%D0%BE%D0%B2%D0%B8%D1%82%D1%8C%20%D1%83%D1%81%D0%BB%D0%BE%D0%B2%D0%BD%D1%83%D1%8E%20%D0%BF%D0%B5%D1%80%D0%B5%D0%BC%D0%B5%D0%BD%D0%BD%D1%83%D1%8E%0A%20%20%20%20%20%20%20%20i%20%2B%3D%201%0A%20%20%20%20%20%20%20%20i%20%2A%3D%202%0A%20%20%20%20return%20res%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20while_loop_ii%28n%29%0A%20%20%20%20print%28f%22%5Cn%D0%A0%D0%B5%D0%B7%D1%83%D0%BB%D1%8C%D1%82%D0%B0%D1%82%20%D1%81%D1%83%D0%BC%D0%BC%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D1%8F%20%D0%B2%20%D1%86%D0%B8%D0%BA%D0%BB%D0%B5%20while%20%28%D0%B4%D0%B2%D0%BE%D0%B9%D0%BD%D0%BE%D0%B5%20%D0%BE%D0%B1%D0%BD%D0%BE%D0%B2%D0%BB%D0%B5%D0%BD%D0%B8%D0%B5%29%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
-<p>В целом <strong>код с <code>for</code> обычно компактнее, а <code>while</code> более гибок</strong>; обе конструкции позволяют реализовывать итерационные структуры. Выбор между ними должен определяться требованиями конкретной задачи.</p>
+<p>В целом <strong>код с использованием цикла <code>for</code> более компактный, а цикл <code>while</code> более гибкий</strong>. Но они оба могут реализовать итерационную структуру. Выбор между ними определяется требованиями конкретной задачи.</p>
 <h3 id="3">3. &nbsp; Вложенные циклы<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
-<p>Мы можем вкладывать одну циклическую структуру в другую; ниже показан пример на основе цикла <code>for</code> :</p>
+<p>Внутрь одной циклической структуры можно вложить другую, например используя два цикла <code>for</code> :</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="4:13"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label></div>
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 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20nested_for_loop%28n%3A%20int%29%20-%3E%20str%3A%0A%20%20%20%20%22%22%22%D0%94%D0%B2%D0%BE%D0%B9%D0%BD%D0%BE%D0%B9%20%D1%86%D0%B8%D0%BA%D0%BB%20for%22%22%22%0A%20%20%20%20res%20%3D%20%22%22%0A%20%20%20%20%23%20%D0%A6%D0%B8%D0%BA%D0%BB%20%D0%BF%D0%BE%20i%20%3D%201%2C%202%2C%20...%2C%20n-1%2C%20n%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%23%20%D0%A6%D0%B8%D0%BA%D0%BB%20%D0%BF%D0%BE%20j%20%3D%201%2C%202%2C%20...%2C%20n-1%2C%20n%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20res%20%2B%3D%20f%22%28%7Bi%7D%2C%20%7Bj%7D%29%2C%20%22%0A%20%20%20%20return%20res%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20nested_for_loop%28n%29%0A%20%20%20%20print%28f%22%5Cn%D0%A0%D0%B5%D0%B7%D1%83%D0%BB%D1%8C%D1%82%D0%B0%D1%82%20%D0%BE%D0%B1%D1%85%D0%BE%D0%B4%D0%B0%20%D0%B2%20%D0%B4%D0%B2%D0%BE%D0%B9%D0%BD%D0%BE%D0%BC%20%D1%86%D0%B8%D0%BA%D0%BB%D0%B5%20for%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
-<p>На рисунке 2-2 показана блок-схема такого вложенного цикла.</p>
+<p>Ниже приведена блок-схема такого вложенного цикла.</p>
 <p><img alt="Блок-схема вложенного цикла" class="animation-figure" src="../iteration_and_recursion.assets/nested_iteration.png" /></p>
 <p align="center"> Рисунок 2-2 &nbsp; Блок-схема вложенного цикла </p>
 
-<p>В этом случае число операций функции пропорционально <span class="arithmatex">\(n^2\)</span> , то есть время работы алгоритма и размер входных данных <span class="arithmatex">\(n\)</span> находятся в "квадратичной зависимости".</p>
-<p>Мы можем продолжать добавлять вложенные циклы, и каждое новое вложение будет означать очередное "повышение размерности", увеличивая временную сложность до "кубической зависимости", "зависимости четвертой степени" и так далее.</p>
+<p>В этом случае количество выполненных действий пропорционально <span class="arithmatex">\(n^2\)</span> , или, другими словами, время выполнения алгоритма и размер входных данных <span class="arithmatex">\(n\)</span> находятся в квадратичной зависимости.</p>
+<p>Можно и дальше добавлять вложенные циклы, тогда каждое вложение будет повышать размерность, увеличивая временную сложность до кубической зависимости, зависимости четвертой степени и так далее.</p>
 <h2 id="222">2.2.2 &nbsp; Рекурсия<a class="headerlink" href="#222" title="Permanent link">&para;</a></h2>
-<p><u>Рекурсия (recursion)</u> - это алгоритмическая стратегия, в которой функция решает задачу, вызывая саму себя. В основном она включает две фазы.</p>
+<p><u>Рекурсия (recursion)</u> - это стратегия алгоритма, при которой функция вызывает саму себя для решения задачи. Она включает два основных этапа.</p>
 <ol>
-<li><strong>Спуск</strong>: программа все глубже вызывает саму себя, обычно передавая меньшие или более упрощенные параметры, пока не достигнет "условия завершения".</li>
-<li><strong>Подъем</strong>: после срабатывания "условия завершения" программа начинает возвращаться от самой глубокой рекурсивной функции вверх, собирая результаты с каждого уровня.</li>
+<li><strong>Вызов</strong>: программа постоянно вызывает саму себя, обычно передавая меньшие или более упрощенные параметры, пока не будет достигнуто условие завершения.</li>
+<li><strong>Возврат</strong>: после срабатывания условия завершения программа начинает возвращаться из самой глубокой рекурсивной функции, объединяя результаты каждого уровня.</li>
 </ol>
-<p>С точки зрения реализации рекурсивный код в основном состоит из трех элементов.</p>
+<p>С точки зрения реализации рекурсивный код включает три основных элемента.</p>
 <ol>
-<li><strong>Условие завершения</strong>: определяет момент перехода от "спуска" к "подъему".</li>
-<li><strong>Рекурсивный вызов</strong>: соответствует "спуску", когда функция вызывает саму себя, обычно с меньшими или более упрощенными параметрами.</li>
-<li><strong>Возврат результата</strong>: соответствует "подъему", когда результат текущего уровня рекурсии передается предыдущему.</li>
+<li><strong>Условие завершения</strong>: используется для определения момента перехода от вызова к возврату.</li>
+<li><strong>Рекурсивный вызов</strong>: соответствует вызову, функция вызывает саму себя, обычно с меньшими или упрощенными параметрами.</li>
+<li><strong>Возврат результата</strong>: соответствует возврату, возвращает результат текущего уровня рекурсии на предыдущий уровень.</li>
 </ol>
-<p>Посмотри на следующий код: нам достаточно вызвать функцию <code>recur(n)</code>  , чтобы вычислить <span class="arithmatex">\(1 + 2 + \dots + n\)</span> :</p>
+<p>Рассмотрим следующий код: вызов функции <code>recur(n)</code> позволяет вычислить сумму <span class="arithmatex">\(1 + 2 + \dots + n\)</span> :</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="5:13"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label></div>
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 <p><div style="height: 459px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%A0%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D1%8F%22%22%22%0A%20%20%20%20%23%20%D0%A3%D1%81%D0%BB%D0%BE%D0%B2%D0%B8%D0%B5%20%D0%B7%D0%B0%D0%B2%D0%B5%D1%80%D1%88%D0%B5%D0%BD%D0%B8%D1%8F%0A%20%20%20%20if%20n%20%3D%3D%201%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20%23%20%D0%A0%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D1%8F%3A%20%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D1%8B%D0%B9%20%D0%B2%D1%8B%D0%B7%D0%BE%D0%B2%0A%20%20%20%20res%20%3D%20recur%28n%20-%201%29%0A%20%20%20%20%23%20%D0%92%D0%BE%D0%B7%D0%B2%D1%80%D0%B0%D1%82%3A%20%D0%B2%D0%B5%D1%80%D0%BD%D1%83%D1%82%D1%8C%20%D1%80%D0%B5%D0%B7%D1%83%D0%BB%D1%8C%D1%82%D0%B0%D1%82%0A%20%20%20%20return%20n%20%2B%20res%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20recur%28n%29%0A%20%20%20%20print%28f%22%5Cn%D0%A0%D0%B5%D0%B7%D1%83%D0%BB%D1%8C%D1%82%D0%B0%D1%82%20%D1%81%D1%83%D0%BC%D0%BC%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D1%8F%20%D0%B2%20%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D0%BE%D0%B9%20%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D0%B8%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%A0%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D1%8F%22%22%22%0A%20%20%20%20%23%20%D0%A3%D1%81%D0%BB%D0%BE%D0%B2%D0%B8%D0%B5%20%D0%B7%D0%B0%D0%B2%D0%B5%D1%80%D1%88%D0%B5%D0%BD%D0%B8%D1%8F%0A%20%20%20%20if%20n%20%3D%3D%201%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20%23%20%D0%A0%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D1%8F%3A%20%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D1%8B%D0%B9%20%D0%B2%D1%8B%D0%B7%D0%BE%D0%B2%0A%20%20%20%20res%20%3D%20recur%28n%20-%201%29%0A%20%20%20%20%23%20%D0%92%D0%BE%D0%B7%D0%B2%D1%80%D0%B0%D1%82%3A%20%D0%B2%D0%B5%D1%80%D0%BD%D1%83%D1%82%D1%8C%20%D1%80%D0%B5%D0%B7%D1%83%D0%BB%D1%8C%D1%82%D0%B0%D1%82%0A%20%20%20%20return%20n%20%2B%20res%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20recur%28n%29%0A%20%20%20%20print%28f%22%5Cn%D0%A0%D0%B5%D0%B7%D1%83%D0%BB%D1%8C%D1%82%D0%B0%D1%82%20%D1%81%D1%83%D0%BC%D0%BC%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D1%8F%20%D0%B2%20%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D0%BE%D0%B9%20%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D0%B8%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
-<p>На рисунке 2-3 показан рекурсивный процесс этой функции.</p>
+<p>Ниже представлен рекурсивный процесс этой функции.</p>
 <p><img alt="Рекурсивный процесс функции суммирования" class="animation-figure" src="../iteration_and_recursion.assets/recursion_sum.png" /></p>
 <p align="center"> Рисунок 2-3 &nbsp; Рекурсивный процесс функции суммирования </p>
 
-<p>Хотя с вычислительной точки зрения итерация и рекурсия могут давать один и тот же результат, <strong>они представляют собой две совершенно разные парадигмы мышления и решения задач</strong>.</p>
+<p>Хотя с точки зрения вычислений итерация и рекурсия могут давать одинаковый результат, <strong>они представляют собой совершенно разные парадигмы мышления и решения задач</strong>.</p>
 <ul>
-<li><strong>Итерация</strong>: решает задачу "снизу вверх". Мы начинаем с самых базовых шагов, а затем многократно повторяем или накапливаем их, пока задача не будет завершена.</li>
-<li><strong>Рекурсия</strong>: решает задачу "сверху вниз". Исходная задача разбивается на более мелкие подзадачи той же формы. Затем эти подзадачи продолжают разбиваться еще дальше, пока не будет достигнут базовый случай (для которого решение уже известно).</li>
+<li><strong>Итерация</strong>: решение задачи снизу вверх. Начинаем с самых базовых шагов, которые затем повторяются или накапливаются до завершения задачи.</li>
+<li><strong>Рекурсия</strong>: решение задачи сверху вниз. Исходная задача разбивается на более мелкие подзадачи, которые имеют ту же форму, что и исходная задача. Далее подзадачи продолжают делиться на еще более мелкие, пока не достигается базовый случай, решение которого известно.</li>
 </ul>
-<p>Возьмем в качестве примера указанную выше функцию суммирования и обозначим задачу как <span class="arithmatex">\(f(n) = 1 + 2 + \dots + n\)</span> .</p>
+<p>Рассмотрим в качестве примера вышеупомянутую функцию суммирования, где решается задача <span class="arithmatex">\(f(n) = 1 + 2 + \dots + n\)</span> .</p>
 <ul>
-<li><strong>Итерация</strong>: в цикле моделируется процесс суммирования от <span class="arithmatex">\(1\)</span> до <span class="arithmatex">\(n\)</span> , и на каждом шаге выполняется операция сложения, в результате чего получается <span class="arithmatex">\(f(n)\)</span> .</li>
-<li><strong>Рекурсия</strong>: задача раскладывается на подзадачу <span class="arithmatex">\(f(n) = n + f(n-1)\)</span> , а затем продолжает раскладываться (рекурсивно) до базового случая <span class="arithmatex">\(f(1) = 1\)</span> .</li>
+<li><strong>Итерация</strong>: моделирование процесса суммирования в цикле проходит от <span class="arithmatex">\(1\)</span> до <span class="arithmatex">\(n\)</span> , выполняя операцию суммирования на каждом шаге, чтобы получить итоговое значение <span class="arithmatex">\(f(n)\)</span> .</li>
+<li><strong>Рекурсия</strong>: последовательное разбиение задачи на подзадачи вида <span class="arithmatex">\(f(n) = n + f(n - 1)\)</span> до достижения базового случая <span class="arithmatex">\(f(1) = 1\)</span> .</li>
 </ul>
 <h3 id="1">1. &nbsp; Стек вызовов<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>Каждый раз, когда рекурсивная функция вызывает сама себя, система выделяет память для нового экземпляра функции, чтобы хранить локальные переменные, адрес возврата и другую информацию. Это приводит к двум последствиям.</p>
+<p>Каждый раз, когда рекурсивная функция вызывает саму себя, система выделяет память для нового вызова функции, чтобы хранить локальные переменные, адрес вызова и другую информацию. Это поведение имеет два последствия.</p>
 <ul>
-<li>Контекстные данные функции хранятся в области памяти, называемой "пространством кадра стека", и освобождаются только после возврата функции. Поэтому <strong>рекурсия обычно требует больше памяти, чем итерация</strong>.</li>
-<li>Вызов рекурсивной функции создает дополнительный накладной расход. <strong>Поэтому рекурсия обычно уступает циклам по временной эффективности</strong>.</li>
+<li>Контекстные данные функции хранятся в области памяти, называемой пространством стекового кадра, и освобождаются только после возврата функции. <strong>Поэтому рекурсия обычно требует больше памяти, чем итерация</strong>.</li>
+<li>Рекурсивный вызов функции создает дополнительные накладные расходы. <strong>Поэтому рекурсия обычно менее эффективна по времени, чем цикл</strong>.</li>
 </ul>
-<p>Как показано на рисунке 2-4, до срабатывания условия завершения одновременно существует <span class="arithmatex">\(n\)</span> еще не завершившихся рекурсивных вызовов, а <strong>глубина рекурсии равна <span class="arithmatex">\(n\)</span></strong> .</p>
+<p>Как показано на рисунке 2-4, до срабатывания условия завершения одновременно существует <span class="arithmatex">\(n\)</span> невозвращенных рекурсивных функций, а <strong>глубина рекурсии равна <span class="arithmatex">\(n\)</span></strong> .</p>
 <p><img alt="Глубина рекурсивного вызова" class="animation-figure" src="../iteration_and_recursion.assets/recursion_sum_depth.png" /></p>
 <p align="center"> Рисунок 2-4 &nbsp; Глубина рекурсивного вызова </p>
 
-<p>На практике разрешенная языком программирования глубина рекурсии обычно ограничена, и слишком глубокая рекурсия может привести к ошибке переполнения стека.</p>
+<p>На практике глубина рекурсии, разрешенная языком программирования, обычно ограничена, и слишком глубокая рекурсия может привести к ошибке переполнения стека.</p>
 <h3 id="2">2. &nbsp; Хвостовая рекурсия<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>Интересно, что <strong>если функция выполняет рекурсивный вызов в самом последнем действии перед возвратом</strong> , то компилятор или интерпретатор может оптимизировать такую функцию так, чтобы по использованию памяти она была сопоставима с итерацией. Такой случай называется <u>хвостовой рекурсией (tail recursion)</u>.</p>
+<p>Интересно, что <strong>если рекурсивный вызов происходит на последнем шаге перед возвратом функции</strong> , то компилятор или интерпретатор может оптимизировать этот вызов, сделав его по эффективности использования памяти сопоставимым с итерацией. Это называется <u>хвостовой рекурсией (tail recursion)</u>.</p>
 <ul>
-<li><strong>Обычная рекурсия</strong>: когда функция возвращается на предыдущий уровень, ей все еще нужно продолжать выполнять код, поэтому системе приходится сохранять контекст вызова предыдущего уровня.</li>
-<li><strong>Хвостовая рекурсия</strong>: рекурсивный вызов - это последняя операция перед возвратом, а значит, после возвращения на предыдущий уровень не требуется выполнять дополнительных действий, и системе не нужно сохранять контекст предыдущей функции.</li>
+<li><strong>Обычная рекурсия</strong>: когда функция возвращается на предыдущий уровень, необходимо продолжить выполнение кода, поэтому системе нужно сохранить контекст предыдущего вызова.</li>
+<li><strong>Хвостовая рекурсия</strong>: рекурсивный вызов является последней операцией перед возвратом функции, что означает, что после возврата на предыдущий уровень не требуется выполнять другие операции, поэтому системе не нужно сохранять контекст предыдущей функции.</li>
 </ul>
-<p>На примере вычисления <span class="arithmatex">\(1 + 2 + \dots + n\)</span> можно сделать переменную результата <code>res</code> параметром функции и тем самым реализовать хвостовую рекурсию:</p>
+<p>В качестве примера вычисления суммы <span class="arithmatex">\(1 + 2 + \dots + n\)</span> можно установить переменную результата <code>res</code> в качестве параметра функции, чтобы реализовать хвостовую рекурсию:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="6:13"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><input id="__tabbed_6_13" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Kotlin</label><label for="__tabbed_6_13">Ruby</label></div>
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@@ -5729,30 +5729,30 @@
 <p><div style="height: 423px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20tail_recur%28n%2C%20res%29%3A%0A%20%20%20%20%22%22%22%D0%A5%D0%B2%D0%BE%D1%81%D1%82%D0%BE%D0%B2%D0%B0%D1%8F%20%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D1%8F%22%22%22%0A%20%20%20%20%23%20%D0%A3%D1%81%D0%BB%D0%BE%D0%B2%D0%B8%D0%B5%20%D0%B7%D0%B0%D0%B2%D0%B5%D1%80%D1%88%D0%B5%D0%BD%D0%B8%D1%8F%0A%20%20%20%20if%20n%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20return%20res%0A%20%20%20%20%23%20%D0%A5%D0%B2%D0%BE%D1%81%D1%82%D0%BE%D0%B2%D0%BE%D0%B9%20%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D1%8B%D0%B9%20%D0%B2%D1%8B%D0%B7%D0%BE%D0%B2%0A%20%20%20%20return%20tail_recur%28n%20-%201%2C%20res%20%2B%20n%29%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20tail_recur%28n%2C%200%29%0A%20%20%20%20print%28f%22%5Cn%D0%A0%D0%B5%D0%B7%D1%83%D0%BB%D1%8C%D1%82%D0%B0%D1%82%20%D1%81%D1%83%D0%BC%D0%BC%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D1%8F%20%D0%B2%20%D1%85%D0%B2%D0%BE%D1%81%D1%82%D0%BE%D0%B2%D0%BE%D0%B9%20%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B8%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20tail_recur%28n%2C%20res%29%3A%0A%20%20%20%20%22%22%22%D0%A5%D0%B2%D0%BE%D1%81%D1%82%D0%BE%D0%B2%D0%B0%D1%8F%20%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D1%8F%22%22%22%0A%20%20%20%20%23%20%D0%A3%D1%81%D0%BB%D0%BE%D0%B2%D0%B8%D0%B5%20%D0%B7%D0%B0%D0%B2%D0%B5%D1%80%D1%88%D0%B5%D0%BD%D0%B8%D1%8F%0A%20%20%20%20if%20n%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20return%20res%0A%20%20%20%20%23%20%D0%A5%D0%B2%D0%BE%D1%81%D1%82%D0%BE%D0%B2%D0%BE%D0%B9%20%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D1%8B%D0%B9%20%D0%B2%D1%8B%D0%B7%D0%BE%D0%B2%0A%20%20%20%20return%20tail_recur%28n%20-%201%2C%20res%20%2B%20n%29%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20tail_recur%28n%2C%200%29%0A%20%20%20%20print%28f%22%5Cn%D0%A0%D0%B5%D0%B7%D1%83%D0%BB%D1%8C%D1%82%D0%B0%D1%82%20%D1%81%D1%83%D0%BC%D0%BC%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D1%8F%20%D0%B2%20%D1%85%D0%B2%D0%BE%D1%81%D1%82%D0%BE%D0%B2%D0%BE%D0%B9%20%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B8%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
-<p>Процесс выполнения хвостовой рекурсии показан на рисунке 2-5. Если сравнить обычную рекурсию и хвостовую рекурсию, то видно, что точка выполнения операции суммирования у них различается.</p>
+<p>Процесс выполнения хвостовой рекурсии показан на рисунке 2-5. Сравнивая обычную и хвостовую рекурсии, можно заметить, что точка выполнения операции суммирования у них различается.</p>
 <ul>
-<li><strong>Обычная рекурсия</strong>: операция суммирования выполняется в процессе "подъема", то есть после возврата с каждого уровня еще нужно выполнить очередное сложение.</li>
-<li><strong>Хвостовая рекурсия</strong>: операция суммирования выполняется в процессе "спуска", а сам "подъем" сводится лишь к последовательному возврату.</li>
+<li><strong>Обычная рекурсия</strong>: операция суммирования выполняется в процессе возврата, после каждого возврата необходимо снова выполнить операцию суммирования.</li>
+<li><strong>Хвостовая рекурсия</strong>: операция суммирования выполняется в процессе вызова, а процесс возврата требует только последовательного возврата.</li>
 </ul>
 <p><img alt="Процесс хвостовой рекурсии" class="animation-figure" src="../iteration_and_recursion.assets/tail_recursion_sum.png" /></p>
 <p align="center"> Рисунок 2-5 &nbsp; Процесс хвостовой рекурсии </p>
 
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>Обрати внимание: многие компиляторы и интерпретаторы не поддерживают оптимизацию хвостовой рекурсии. Например, Python по умолчанию такую оптимизацию не выполняет, поэтому даже функция в хвостово-рекурсивной форме все равно может привести к переполнению стека.</p>
+<p>Обратите внимание: многие компиляторы и интерпретаторы не поддерживают оптимизацию хвостовой рекурсии. Например, Python по умолчанию такую оптимизацию не выполняет, поэтому даже функция в хвостово-рекурсивной форме все равно может привести к переполнению стека.</p>
 </div>
 <h3 id="3_1">3. &nbsp; Дерево рекурсии<a class="headerlink" href="#3_1" title="Permanent link">&para;</a></h3>
-<p>При решении алгоритмических задач, связанных с "разделяй и властвуй", рекурсия часто дает более интуитивный способ рассуждения и более читаемый код, чем итерация. Возьмем в качестве примера "последовательность Фибоначчи".</p>
+<p>При решении задач, связанных с алгоритмами типа "разделяй и властвуй", рекурсия часто оказывается более интуитивной и читабельной, чем итерация. Рассмотрим в качестве примера последовательность Фибоначчи.</p>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
 <p>Дана последовательность Фибоначчи <span class="arithmatex">\(0, 1, 1, 2, 3, 5, 8, 13, \dots\)</span> ; найди <span class="arithmatex">\(n\)</span>-й элемент этой последовательности.</p>
 </div>
-<p>Обозначим <span class="arithmatex">\(n\)</span>-й элемент последовательности Фибоначчи как <span class="arithmatex">\(f(n)\)</span> . Тогда нетрудно получить два вывода.</p>
+<p>Обозначив <span class="arithmatex">\(n\)</span>-й член последовательности Фибоначчи как <span class="arithmatex">\(f(n)\)</span> , можно сформулировать два утверждения.</p>
 <ul>
-<li>Первые два числа последовательности равны <span class="arithmatex">\(f(1) = 0\)</span> и <span class="arithmatex">\(f(2) = 1\)</span> .</li>
-<li>Каждое последующее число равно сумме двух предыдущих, то есть <span class="arithmatex">\(f(n) = f(n - 1) + f(n - 2)\)</span> .</li>
+<li>Первые два числа последовательности: <span class="arithmatex">\(f(1) = 0\)</span> и <span class="arithmatex">\(f(2) = 1\)</span> .</li>
+<li>Каждое число последовательности является суммой двух предыдущих чисел, то есть <span class="arithmatex">\(f(n) = f(n - 1) + f(n - 2)\)</span> .</li>
 </ul>
-<p>Следуя рекуррентному соотношению и используя первые два числа как условия завершения, мы можем написать рекурсивный код. Вызов <code>fib(n)</code> даст нам <span class="arithmatex">\(n\)</span>-й элемент последовательности Фибоначчи:</p>
+<p>Используя рекурсивные вызовы в соответствии с рекуррентным соотношением и принимая первые два числа за условия остановки, можно написать рекурсивный код. Вызов <code>fib(n)</code> позволит получить <span class="arithmatex">\(n\)</span>-й член последовательности Фибоначчи:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="7:13"><input checked="checked" id="__tabbed_7_1" name="__tabbed_7" type="radio" /><input id="__tabbed_7_2" name="__tabbed_7" type="radio" /><input id="__tabbed_7_3" name="__tabbed_7" type="radio" /><input id="__tabbed_7_4" name="__tabbed_7" type="radio" /><input id="__tabbed_7_5" name="__tabbed_7" type="radio" /><input id="__tabbed_7_6" name="__tabbed_7" type="radio" /><input id="__tabbed_7_7" name="__tabbed_7" type="radio" /><input id="__tabbed_7_8" name="__tabbed_7" type="radio" /><input id="__tabbed_7_9" name="__tabbed_7" type="radio" /><input id="__tabbed_7_10" name="__tabbed_7" type="radio" /><input id="__tabbed_7_11" name="__tabbed_7" type="radio" /><input id="__tabbed_7_12" name="__tabbed_7" type="radio" /><input id="__tabbed_7_13" name="__tabbed_7" type="radio" /><div class="tabbed-labels"><label for="__tabbed_7_1">Python</label><label for="__tabbed_7_2">C++</label><label for="__tabbed_7_3">Java</label><label for="__tabbed_7_4">C#</label><label for="__tabbed_7_5">Go</label><label for="__tabbed_7_6">Swift</label><label for="__tabbed_7_7">JS</label><label for="__tabbed_7_8">TS</label><label for="__tabbed_7_9">Dart</label><label for="__tabbed_7_10">Rust</label><label for="__tabbed_7_11">C</label><label for="__tabbed_7_12">Kotlin</label><label for="__tabbed_7_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
@@ -5929,18 +5929,18 @@
 <p><div style="height: 459px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20fib%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%9F%D0%BE%D1%81%D0%BB%D0%B5%D0%B4%D0%BE%D0%B2%D0%B0%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D1%81%D1%82%D1%8C%20%D0%A4%D0%B8%D0%B1%D0%BE%D0%BD%D0%B0%D1%87%D1%87%D0%B8%3A%20%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D1%8F%22%22%22%0A%20%20%20%20%23%20%D0%A3%D1%81%D0%BB%D0%BE%D0%B2%D0%B8%D0%B5%20%D0%B7%D0%B0%D0%B2%D0%B5%D1%80%D1%88%D0%B5%D0%BD%D0%B8%D1%8F%3A%20f%281%29%20%3D%200%2C%20f%282%29%20%3D%201%0A%20%20%20%20if%20n%20%3D%3D%201%20or%20n%20%3D%3D%202%3A%0A%20%20%20%20%20%20%20%20return%20n%20-%201%0A%20%20%20%20%23%20%D0%A0%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D1%8B%D0%B9%20%D0%B2%D1%8B%D0%B7%D0%BE%D0%B2%20f%28n%29%20%3D%20f%28n-1%29%20%2B%20f%28n-2%29%0A%20%20%20%20res%20%3D%20fib%28n%20-%201%29%20%2B%20fib%28n%20-%202%29%0A%20%20%20%20%23%20%D0%92%D0%B5%D1%80%D0%BD%D1%83%D1%82%D1%8C%20%D1%80%D0%B5%D0%B7%D1%83%D0%BB%D1%8C%D1%82%D0%B0%D1%82%20f%28n%29%0A%20%20%20%20return%20res%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20fib%28n%29%0A%20%20%20%20print%28f%22%5Cn%D0%A7%D0%BB%D0%B5%D0%BD%20%D0%BF%D0%BE%D1%81%D0%BB%D0%B5%D0%B4%D0%BE%D0%B2%D0%B0%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%D0%A4%D0%B8%D0%B1%D0%BE%D0%BD%D0%B0%D1%87%D1%87%D0%B8%20%D1%81%20%D0%BD%D0%BE%D0%BC%D0%B5%D1%80%D0%BE%D0%BC%20%7Bn%7D%20%3D%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20fib%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%9F%D0%BE%D1%81%D0%BB%D0%B5%D0%B4%D0%BE%D0%B2%D0%B0%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D1%81%D1%82%D1%8C%20%D0%A4%D0%B8%D0%B1%D0%BE%D0%BD%D0%B0%D1%87%D1%87%D0%B8%3A%20%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D1%8F%22%22%22%0A%20%20%20%20%23%20%D0%A3%D1%81%D0%BB%D0%BE%D0%B2%D0%B8%D0%B5%20%D0%B7%D0%B0%D0%B2%D0%B5%D1%80%D1%88%D0%B5%D0%BD%D0%B8%D1%8F%3A%20f%281%29%20%3D%200%2C%20f%282%29%20%3D%201%0A%20%20%20%20if%20n%20%3D%3D%201%20or%20n%20%3D%3D%202%3A%0A%20%20%20%20%20%20%20%20return%20n%20-%201%0A%20%20%20%20%23%20%D0%A0%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D1%8B%D0%B9%20%D0%B2%D1%8B%D0%B7%D0%BE%D0%B2%20f%28n%29%20%3D%20f%28n-1%29%20%2B%20f%28n-2%29%0A%20%20%20%20res%20%3D%20fib%28n%20-%201%29%20%2B%20fib%28n%20-%202%29%0A%20%20%20%20%23%20%D0%92%D0%B5%D1%80%D0%BD%D1%83%D1%82%D1%8C%20%D1%80%D0%B5%D0%B7%D1%83%D0%BB%D1%8C%D1%82%D0%B0%D1%82%20f%28n%29%0A%20%20%20%20return%20res%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20fib%28n%29%0A%20%20%20%20print%28f%22%5Cn%D0%A7%D0%BB%D0%B5%D0%BD%20%D0%BF%D0%BE%D1%81%D0%BB%D0%B5%D0%B4%D0%BE%D0%B2%D0%B0%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%D0%A4%D0%B8%D0%B1%D0%BE%D0%BD%D0%B0%D1%87%D1%87%D0%B8%20%D1%81%20%D0%BD%D0%BE%D0%BC%D0%B5%D1%80%D0%BE%D0%BC%20%7Bn%7D%20%3D%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
-<p>Если посмотреть на приведенный код, внутри функции выполняются два рекурсивных вызова, <strong>а это означает, что один вызов рождает две ветви вызова</strong>. Как показано на рисунке 2-6, при таком продолжении рекурсивных вызовов в итоге получается <u>дерево рекурсии (recursion tree)</u> глубиной <span class="arithmatex">\(n\)</span> .</p>
+<p>Проанализировав приведенный код, можно заметить, что внутри функции осуществляется рекурсивный вызов двух функций, <strong>то есть из одного вызова образуются два ветвления</strong>. Как показано на рисунке 2-6, при последующем выполнении рекурсивных вызовов в итоге образуется <u>дерево рекурсии (recursion tree)</u> глубиной <span class="arithmatex">\(n\)</span> .</p>
 <p><img alt="Дерево рекурсии последовательности Фибоначчи" class="animation-figure" src="../iteration_and_recursion.assets/recursion_tree.png" /></p>
 <p align="center"> Рисунок 2-6 &nbsp; Дерево рекурсии последовательности Фибоначчи </p>
 
-<p>По своей сути рекурсия воплощает парадигму "разбиения задачи на более мелкие подзадачи", и именно поэтому стратегия разделяй-и-властвуй столь важна.</p>
+<p>По своей сути рекурсия отражает парадигму мышления "разбиение задачи на более мелкие подзадачи", что делает стратегию "разделяй и властвуй" крайне важной.</p>
 <ul>
-<li>С точки зрения алгоритмов многие важнейшие стратегии, такие как поиск, сортировка, бэктрекинг, разделяй-и-властвуй и динамическое программирование, прямо или косвенно используют такой образ мышления.</li>
-<li>С точки зрения структур данных рекурсия естественным образом подходит для решения задач, связанных со связными списками, деревьями и графами, потому что они хорошо поддаются анализу через идеи разделения задачи.</li>
+<li>С точки зрения <strong>алгоритмов</strong> многие важные алгоритмические стратегии, такие как поиск, сортировка, возврат, "разделяй и властвуй" и динамическое программирование, прямо или косвенно используют этот подход.</li>
+<li>С точки зрения <strong>структур данных</strong> рекурсия естественно подходит для решения задач, связанных со списками, деревьями и графами, поскольку они очень хорошо поддаются анализу с использованием идеи "разделяй и властвуй".</li>
 </ul>
-<h2 id="223">2.2.3 &nbsp; Сравнение двух подходов<a class="headerlink" href="#223" title="Permanent link">&para;</a></h2>
-<p>Обобщая все сказанное выше, можно представить различия между итерацией и рекурсией с точки зрения реализации, производительности и применимости в следующей таблице.</p>
-<p align="center"> Таблица 2-1 &nbsp; Сравнение характеристик итерации и рекурсии </p>
+<h2 id="223">2.2.3 &nbsp; Сравнение<a class="headerlink" href="#223" title="Permanent link">&para;</a></h2>
+<p>Подводя итог, можно сказать, что итерация и рекурсия различаются по реализации, производительности и применимости, как показано в таблице 2-1.</p>
+<p align="center"> Таблица 2-1 &nbsp; Сравнение итерации и рекурсии </p>
 
 <div class="center-table">
 <table>
@@ -5953,39 +5953,39 @@
 </thead>
 <tbody>
 <tr>
-<td>Реализация</td>
+<td>Способ реализации</td>
 <td>Циклическая структура</td>
-<td>Функция вызывает сама себя</td>
+<td>Функция вызывает саму себя</td>
 </tr>
 <tr>
 <td>Временная эффективность</td>
-<td>Обычно выше, так как нет накладных расходов на вызовы функций</td>
-<td>Каждый вызов функции создает накладные расходы</td>
+<td>Обычно высокая эффективность, нет затрат на вызов функции</td>
+<td>Каждый вызов функции создает затраты</td>
 </tr>
 <tr>
 <td>Использование памяти</td>
-<td>Обычно требуется фиксированный объем памяти</td>
-<td>Накопление вызовов функции может занимать много места в кадрах стека</td>
+<td>Обычно используется фиксированный объем памяти</td>
+<td>Накопление вызовов функции может использовать значительное количество пространства стека</td>
 </tr>
 <tr>
-<td>Подходящие задачи</td>
-<td>Хорошо подходит для простых циклических задач, код интуитивен и легко читается</td>
-<td>Хорошо подходит для разложения на подзадачи, например для деревьев, графов, разделяй-и-властвуй, бэктрекинга и т. д.; код при этом получается компактным и ясным</td>
+<td>Сфера использования</td>
+<td>Подходит для простых циклических задач, код интуитивно понятен и хорошо читаем</td>
+<td>Подходит для разбиения на подзадачи, для структур деревья и графы, алгоритмов "разделяй и властвуй", возврата и т. д.; структура кода проста и ясна</td>
 </tr>
 </tbody>
 </table>
 </div>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>Если тебе сложно понять дальнейшее содержание, можешь вернуться к нему после чтения главы о "стеке".</p>
+<p>Если дальнейшее содержание кажется сложным, можно вернуться к нему после чтения главы о "стеке".</p>
 </div>
-<p>Какова же внутренняя связь между итерацией и рекурсией? Если снова взять рекурсивную функцию выше, операция суммирования выполняется в фазе "подъема" рекурсии. Это означает, что функция, вызванная первой, на самом деле завершает сложение последней, <strong>и такой механизм очень похож на принцип стека "последним пришел - первым ушел"</strong>.</p>
-<p>На самом деле такие термины рекурсии, как "стек вызовов" и "пространство кадра стека", уже прямо намекают на тесную связь между рекурсией и стеком.</p>
+<p>Какова же внутренняя связь между итерацией и рекурсией? В рассмотренном примере рекурсивной функции операция сложения выполняется на этапе возврата рекурсии. Это означает, что функция, вызванная первой, фактически завершает операцию сложения последней, <strong>что соответствует принципу стека "первым пришел - последним вышел"</strong>.</p>
+<p>На самом деле такие термины рекурсии, как "стек вызовов" и "пространство стекового кадра", уже намекают на тесную связь между рекурсией и стеком.</p>
 <ol>
-<li><strong>Спуск</strong>: когда вызывается функция, система выделяет для нее новый кадр стека в "стеке вызовов", чтобы хранить локальные переменные, параметры, адрес возврата и другие данные.</li>
-<li><strong>Подъем</strong>: когда функция завершает выполнение и возвращается, соответствующий кадр стека удаляется из "стека вызовов", а среда выполнения предыдущей функции восстанавливается.</li>
+<li><strong>Вызов</strong>: когда вызывается функция, система выделяет для нее новый стековый кадр в "стеке вызовов" для хранения локальных переменных функции, параметров, адреса возврата и других данных.</li>
+<li><strong>Возврат</strong>: когда функция завершает выполнение и возвращает результат, соответствующий стековый кадр удаляется из "стека вызовов", восстанавливая среду выполнения предыдущей функции.</li>
 </ol>
-<p>Поэтому <strong>мы можем использовать явный стек для имитации поведения стека вызовов</strong> и тем самым преобразовать рекурсию в итеративную форму:</p>
+<p>Таким образом, <strong>можно использовать явный стек для моделирования поведения стека вызовов</strong>, чтобы преобразовать рекурсию в итеративную форму:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="8:13"><input checked="checked" id="__tabbed_8_1" name="__tabbed_8" type="radio" /><input id="__tabbed_8_2" name="__tabbed_8" type="radio" /><input id="__tabbed_8_3" name="__tabbed_8" type="radio" /><input id="__tabbed_8_4" name="__tabbed_8" type="radio" /><input id="__tabbed_8_5" name="__tabbed_8" type="radio" /><input id="__tabbed_8_6" name="__tabbed_8" type="radio" /><input id="__tabbed_8_7" name="__tabbed_8" type="radio" /><input id="__tabbed_8_8" name="__tabbed_8" type="radio" /><input id="__tabbed_8_9" name="__tabbed_8" type="radio" /><input id="__tabbed_8_10" name="__tabbed_8" type="radio" /><input id="__tabbed_8_11" name="__tabbed_8" type="radio" /><input id="__tabbed_8_12" name="__tabbed_8" type="radio" /><input id="__tabbed_8_13" name="__tabbed_8" type="radio" /><div class="tabbed-labels"><label for="__tabbed_8_1">Python</label><label for="__tabbed_8_2">C++</label><label for="__tabbed_8_3">Java</label><label for="__tabbed_8_4">C#</label><label for="__tabbed_8_5">Go</label><label for="__tabbed_8_6">Swift</label><label for="__tabbed_8_7">JS</label><label for="__tabbed_8_8">TS</label><label for="__tabbed_8_9">Dart</label><label for="__tabbed_8_10">Rust</label><label for="__tabbed_8_11">C</label><label for="__tabbed_8_12">Kotlin</label><label for="__tabbed_8_13">Ruby</label></div>
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 <div class="tabbed-block">
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 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20for_loop_recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%98%D0%BC%D0%B8%D1%82%D0%B0%D1%86%D0%B8%D1%8F%20%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B8%20%D0%B8%D1%82%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B5%D0%B9%22%22%22%0A%20%20%20%20%23%20%D0%98%D1%81%D0%BF%D0%BE%D0%BB%D1%8C%D0%B7%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%8F%D0%B2%D0%BD%D1%8B%D0%B9%20%D1%81%D1%82%D0%B5%D0%BA%20%D0%B4%D0%BB%D1%8F%20%D0%B8%D0%BC%D0%B8%D1%82%D0%B0%D1%86%D0%B8%D0%B8%20%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%BD%D0%BE%D0%B3%D0%BE%20%D1%81%D1%82%D0%B5%D0%BA%D0%B0%20%D0%B2%D1%8B%D0%B7%D0%BE%D0%B2%D0%BE%D0%B2%0A%20%20%20%20stack%20%3D%20%5B%5D%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20%23%20%D0%A0%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D1%8F%3A%20%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D1%8B%D0%B9%20%D0%B2%D1%8B%D0%B7%D0%BE%D0%B2%0A%20%20%20%20for%20i%20in%20range%28n%2C%200%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20%23%20%D0%98%D0%BC%D0%B8%D1%82%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%C2%AB%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D1%8E%C2%BB%20%D1%81%20%D0%BF%D0%BE%D0%BC%D0%BE%D1%89%D1%8C%D1%8E%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B8%20%D0%BF%D0%BE%D0%BC%D0%B5%D1%89%D0%B5%D0%BD%D0%B8%D1%8F%20%D0%B2%20%D1%81%D1%82%D0%B5%D0%BA%0A%20%20%20%20%20%20%20%20stack.append%28i%29%0A%20%20%20%20%23%20%D0%92%D0%BE%D0%B7%D0%B2%D1%80%D0%B0%D1%82%3A%20%D0%B2%D0%B5%D1%80%D0%BD%D1%83%D1%82%D1%8C%20%D1%80%D0%B5%D0%B7%D1%83%D0%BB%D1%8C%D1%82%D0%B0%D1%82%0A%20%20%20%20while%20stack%3A%0A%20%20%20%20%20%20%20%20%23%20%D0%98%D0%BC%D0%B8%D1%82%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%C2%AB%D0%B2%D0%BE%D0%B7%D0%B2%D1%80%D0%B0%D1%82%C2%BB%20%D1%81%20%D0%BF%D0%BE%D0%BC%D0%BE%D1%89%D1%8C%D1%8E%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B8%20%D0%B8%D0%B7%D0%B2%D0%BB%D0%B5%D1%87%D0%B5%D0%BD%D0%B8%D1%8F%20%D0%B8%D0%B7%20%D1%81%D1%82%D0%B5%D0%BA%D0%B0%0A%20%20%20%20%20%20%20%20res%20%2B%3D%20stack.pop%28%29%0A%20%20%20%20%23%20res%20%3D%201%2B2%2B3%2B...%2Bn%0A%20%20%20%20return%20res%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20res%20%3D%20for_loop_recur%28n%29%0A%20%20%20%20print%28f%22%5Cn%D0%A0%D0%B5%D0%B7%D1%83%D0%BB%D1%8C%D1%82%D0%B0%D1%82%20%D1%81%D1%83%D0%BC%D0%BC%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D1%8F%20%D0%BF%D1%80%D0%B8%20%D0%B8%D0%BC%D0%B8%D1%82%D0%B0%D1%86%D0%B8%D0%B8%20%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B8%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
-<p>Если посмотреть на приведенный выше код, видно, что после преобразования рекурсии в итерацию код становится сложнее. Хотя во многих случаях итерация и рекурсия действительно могут быть преобразованы друг в друга, это не всегда стоит делать по двум причинам.</p>
+<p>Наблюдая за приведенным выше кодом, можно заметить, что после преобразования рекурсии в итерацию код становится более сложным. Хотя во многих случаях итерация и рекурсия действительно могут быть преобразованы друг в друга, это не всегда стоит делать по двум причинам.</p>
 <ul>
 <li>Преобразованный код может стать труднее для понимания и менее читаемым.</li>
-<li>Для некоторых сложных задач имитация поведения системного стека вызовов может оказаться очень трудной.</li>
+<li>Для некоторых сложных задач моделирование поведения системного стека вызовов может оказаться очень трудным.</li>
 </ul>
-<p>Итак, <strong>выбор между итерацией и рекурсией зависит от природы конкретной задачи</strong>. В практическом программировании крайне важно взвешивать плюсы и минусы обоих подходов и выбирать подходящий метод с учетом контекста.</p>
+<p>Итак, <strong>выбор между итерацией и рекурсией зависит от природы конкретной задачи</strong>. В практическом программировании крайне важно взвешивать преимущества и недостатки обоих подходов и выбирать подходящий метод с учетом контекста.</p>
 
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 <!-- Page content -->
 <h1 id="21">2.1 &nbsp; Оценка эффективности алгоритмов<a class="headerlink" href="#21" title="Permanent link">&para;</a></h1>
-<p>При проектировании алгоритмов мы последовательно стремимся к двум уровням целей.</p>
+<p>В процессе разработки алгоритмов мы стремимся к достижению следующих целей.</p>
 <ol>
-<li><strong>Найти решение задачи</strong>: алгоритм должен надежно получать правильный ответ в заданном диапазоне входных данных.</li>
-<li><strong>Найти оптимальное решение</strong>: для одной и той же задачи может существовать несколько решений, и нам хочется выбрать максимально эффективный алгоритм.</li>
+<li><strong>Найти решение задачи</strong>: алгоритм должен надежно находить правильное решение задачи в заданных пределах входных данных.</li>
+<li><strong>Найти оптимальное решение</strong>: для одной и той же задачи может существовать несколько решений, и мы стремимся найти максимально эффективный алгоритм.</li>
 </ol>
-<p>Иными словами, если задача в принципе решается, эффективность алгоритма становится главным критерием оценки его качества. Она включает два следующих измерения.</p>
+<p>Таким образом, при условии возможности решения задачи эффективность алгоритма становится основным критерием его оценки, который включает два аспекта.</p>
 <ul>
-<li><strong>Временная эффективность</strong>: сколько времени работает алгоритм.</li>
-<li><strong>Пространственная эффективность</strong>: сколько памяти занимает алгоритм.</li>
+<li><strong>Временная эффективность</strong>: продолжительность выполнения алгоритма.</li>
+<li><strong>Пространственная эффективность</strong>: объем памяти, занимаемой алгоритмом.</li>
 </ul>
-<p>Короче говоря, <strong>наша цель - проектировать структуры данных и алгоритмы, которые "и быстры, и экономны по памяти"</strong>. Эффективная оценка алгоритмов крайне важна, потому что только так можно сравнивать разные алгоритмы и направлять процесс их проектирования и оптимизации.</p>
-<p>Методы оценки эффективности в основном делятся на два типа: практическое тестирование и теоретическая оценка.</p>
+<p>В двух словах, <strong>наша цель - разработка быстрых и экономных структур данных и алгоритмов</strong>. Эффективная оценка алгоритмов крайне важна, так как только так можно сравнивать различные алгоритмы и управлять процессом их разработки и оптимизации.</p>
+<p>Методы оценки эффективности делятся на два типа: практическое тестирование и теоретическую оценку.</p>
 <h2 id="211">2.1.1 &nbsp; Практическое тестирование<a class="headerlink" href="#211" title="Permanent link">&para;</a></h2>
-<p>Предположим, у нас есть алгоритм <code>A</code> и алгоритм <code>B</code>, оба решают одну и ту же задачу, и нам нужно сравнить их эффективность. Самый прямой способ - взять компьютер, запустить оба алгоритма и зафиксировать время работы и объем используемой памяти. Такой способ оценки отражает реальную ситуацию, но имеет и серьезные ограничения.</p>
-<p>С одной стороны, <strong>трудно исключить влияние факторов тестовой среды</strong>. Аппаратная конфигурация влияет на производительность алгоритма. Например, если алгоритм имеет высокий уровень параллелизма, он лучше подходит для многоядерных CPU; если алгоритм интенсивно работает с памятью, он покажет себя лучше на быстрой памяти. Иными словами, результаты тестирования одного и того же алгоритма на разных машинах могут различаться. Это означает, что пришлось бы тестировать на самых разных машинах и усреднять результаты, а на практике это нереалистично.</p>
-<p>С другой стороны, <strong>полное тестирование требует больших ресурсов</strong>. По мере изменения объема входных данных алгоритм может вести себя по-разному. Например, при небольшом объеме входных данных время работы алгоритма <code>A</code> может быть меньше, чем у алгоритма <code>B</code>; но при большом объеме результаты могут оказаться прямо противоположными. Поэтому для убедительных выводов пришлось бы тестировать входные данные множества разных масштабов, а это требует значительных вычислительных ресурсов.</p>
+<p>Предположим, у нас есть алгоритмы <code>A</code> и <code>B</code>, которые решают одну и ту же задачу, и необходимо сравнить их эффективность. Самый прямой метод - это запустить оба алгоритма на компьютере и зафиксировать время их выполнения и объем используемой памяти. Этот метод отражает реальную ситуацию, но имеет значительные ограничения.</p>
+<p>С одной стороны, <strong>сложно исключить влияние факторов тестовой среды</strong>. Аппаратная конфигурация влияет на производительность алгоритма. Например, если алгоритм обладает высокой степенью параллелизма, он будет лучше работать на многоядерных CPU; если алгоритм интенсивно использует память, его производительность будет выше на высокопроизводительной памяти. Это означает, что результаты тестирования на разных машинах могут значительно отличаться, а для получения средней эффективности пришлось бы тестировать на различных платформах, что крайне затруднительно.</p>
+<p>С другой стороны, <strong>проведение полного тестирования требует значительных ресурсов</strong>. С изменением объема входных данных алгоритмы демонстрируют разную эффективность. Например, при небольшом объеме данных алгоритм <code>A</code> может работать быстрее, чем алгоритм <code>B</code>, но при большом объеме данных результат может быть противоположным. Следовательно, для получения убедительных выводов необходимо тестировать различные масштабы входных данных, что требует значительных вычислительных ресурсов.</p>
 <h2 id="212">2.1.2 &nbsp; Теоретическая оценка<a class="headerlink" href="#212" title="Permanent link">&para;</a></h2>
-<p>Поскольку практическое тестирование имеет серьезные ограничения, можно попытаться оценить эффективность алгоритма только с помощью вычислений. Такой метод называется <u>асимптотическим анализом сложности (asymptotic complexity analysis)</u>, или сокращенно <u>анализом сложности</u>.</p>
-<p>Анализ сложности показывает зависимость между временем и пространственными ресурсами, требуемыми алгоритму, и масштабом входных данных. <strong>Он описывает тенденцию роста времени и памяти, необходимых алгоритму, по мере увеличения размера входных данных</strong>. Это определение звучит немного тяжеловесно, поэтому полезно разложить его на три ключевые идеи.</p>
+<p>Из-за значительных ограничений практического тестирования можно рассмотреть возможность оценки эффективности алгоритмов только с помощью вычислений. Такой метод называется <u>анализом асимптотической сложности (asymptotic complexity analysis)</u>, или сокращенно <u>анализом сложности</u>.</p>
+<p>Анализ сложности позволяет отразить зависимость между ресурсами времени и пространства, необходимыми для выполнения алгоритма, и размером входных данных. <strong>Он описывает тенденцию роста времени и пространства, необходимых для выполнения алгоритма, по мере увеличения размера входных данных</strong>. Это определение может показаться сложным, но его можно разбить на три ключевых момента.</p>
 <ul>
-<li>"Временные и пространственные ресурсы" соответствуют <u>временной сложности (time complexity)</u> и <u>пространственной сложности (space complexity)</u> соответственно.</li>
-<li>"По мере увеличения размера входных данных" означает, что сложность отражает связь между эффективностью алгоритма и масштабом входа.</li>
-<li>"Тенденция роста времени и пространства" означает, что анализ сложности интересуется не конкретными значениями времени или памяти, а тем, насколько быстро они растут.</li>
+<li>"Ресурсы времени и пространства" соответствуют <u>временной сложности (time complexity)</u> и <u>пространственной сложности (space complexity)</u>.</li>
+<li>"По мере увеличения размера входных данных" означает, что сложность отражает зависимость эффективности алгоритма от объема входных данных.</li>
+<li>"Тенденция роста времени и пространства" указывает, что анализ сложности фокусируется не на конкретных значениях времени выполнения или объема занимаемой памяти, а на скорости их роста.</li>
 </ul>
-<p><strong>Анализ сложности устраняет недостатки практического тестирования</strong>, что проявляется в следующих аспектах.</p>
+<p><strong>Анализ сложности преодолевает недостатки метода практического тестирования</strong>, что выражается в следующих аспектах.</p>
 <ul>
-<li>Для него не нужно реально запускать код, а значит, он экологичнее и экономит ресурсы.</li>
-<li>Он не зависит от тестовой среды, поэтому результаты анализа применимы ко всем платформам выполнения.</li>
-<li>Он позволяет увидеть эффективность алгоритма при разных объемах данных, особенно на больших данных.</li>
+<li>Он не требует фактического выполнения кода, что делает его более экологичным и энергосберегающим.</li>
+<li>Он независим от тестовой среды, а результаты анализа применимы ко всем платформам выполнения.</li>
+<li>Он может продемонстрировать эффективность алгоритма при различных объемах данных, особенно при больших объемах.</li>
 </ul>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>Если понятие сложности пока все еще кажется тебе запутанным, не переживай: мы подробно разберем его в следующих разделах.</p>
+<p>Если понятие сложности пока все еще кажется вам запутанным, не переживайте: мы подробно разберем его в следующих разделах.</p>
 </div>
-<p>Анализ сложности дает нам "линейку" для оценки эффективности алгоритмов, позволяя измерять, сколько времени и памяти требуется для выполнения конкретного алгоритма, и сравнивать эффективность разных алгоритмов между собой.</p>
-<p>Сложность - это математическое понятие, поэтому для начинающих оно может показаться довольно абстрактным и сравнительно трудным. С этой точки зрения анализ сложности, возможно, не лучший самый первый материал для знакомства. Однако, когда мы обсуждаем особенности конкретной структуры данных или алгоритма, почти невозможно не затронуть скорость его работы и использование памяти.</p>
-<p>В итоге рекомендуется еще до глубокого погружения в структуры данных и алгоритмы <strong>сформировать хотя бы первичное понимание анализа сложности, чтобы уметь выполнять анализ сложности простых алгоритмов</strong>.</p>
+<p>Анализ сложности предоставляет нам мерило оценки эффективности алгоритмов, позволяя измерять время и ресурсы, необходимые для выполнения конкретного алгоритма, а также сравнивать эффективность различных алгоритмов.</p>
+<p>Сложность - это математическое понятие, которое новичкам может показаться абстрактным и сложным для изучения. С этой точки зрения анализ сложности не то, с чего стоит начинать изучение алгоритмов. Однако, обсуждая особенности той или иной структуры данных или алгоритма, невозможно избежать анализа их скорости выполнения и использования памяти.</p>
+<p>Таким образом, перед погружением в изучение структур данных и алгоритмов рекомендуется получить базовое представление об анализе сложности, чтобы иметь возможность выполнять хотя бы базовую оценку их эффективности.</p>
 
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 <!-- Page content -->
 <h1 id="24">2.4 &nbsp; Пространственная сложность<a class="headerlink" href="#24" title="Permanent link">&para;</a></h1>
-<p><u>Пространственная сложность (space complexity)</u> используется для оценки того, как меняется объем памяти, занимаемой алгоритмом, по мере роста объема данных. Это понятие очень похоже на временную сложность, только вместо "времени выполнения" мы рассматриваем "объем используемой памяти".</p>
+<p><u>Пространственная сложность (space complexity)</u> служит для оценки того, как меняется объем памяти, требуемой алгоритму, по мере роста объема данных. Это понятие очень похоже на временную сложность, только вместо времени выполнения рассматривается объем используемой памяти.</p>
 <h2 id="241">2.4.1 &nbsp; Пространство, связанное с алгоритмом<a class="headerlink" href="#241" title="Permanent link">&para;</a></h2>
-<p>Память, которую использует алгоритм во время работы, в основном включает несколько следующих частей.</p>
+<p>Память, которую использует алгоритм во время работы, в основном делится на следующие части.</p>
 <ul>
 <li><strong>Входное пространство</strong>: используется для хранения входных данных алгоритма.</li>
 <li><strong>Временное пространство</strong>: используется для хранения переменных, объектов, контекста функций и других данных, возникающих во время выполнения алгоритма.</li>
 <li><strong>Выходное пространство</strong>: используется для хранения выходных данных алгоритма.</li>
 </ul>
-<p>В общем случае при анализе пространственной сложности в расчет включают "временное пространство" и "выходное пространство".</p>
+<p>Как правило, при анализе пространственной сложности в расчет включают временное пространство и выходное пространство.</p>
 <p>Временное пространство можно дополнительно разделить на три части.</p>
 <ul>
 <li><strong>Временные данные</strong>: используются для хранения различных констант, переменных, объектов и т.д., возникающих во время выполнения алгоритма.</li>
-<li><strong>Пространство кадров стека</strong>: используется для хранения контекстных данных вызываемых функций. Система при каждом вызове функции создает на вершине стека новый кадр; после возврата функции пространство этого кадра освобождается.</li>
+<li><strong>Пространство кадров стека</strong>: используется для хранения контекстных данных вызываемых функций. При каждом вызове функции система создает на вершине стека новый кадр; после возврата функции пространство этого кадра освобождается.</li>
 <li><strong>Пространство инструкций</strong>: используется для хранения скомпилированных инструкций программы и в реальном подсчете обычно не учитывается.</li>
 </ul>
-<p>При анализе пространственной сложности программы <strong>мы обычно учитываем три части: временные данные, пространство кадров стека и выходные данные</strong>, как показано на рисунке 2-15.</p>
+<p>При анализе пространственной сложности программы <strong>обычно учитываются временные данные, пространство стека и выходные данные</strong>, как показано на рисунке 2-15.</p>
 <p><img alt="Пространство, используемое алгоритмом" class="animation-figure" src="../space_complexity.assets/space_types.png" /></p>
 <p align="center"> Рисунок 2-15 &nbsp; Пространство, используемое алгоритмом </p>
 
-<p>Соответствующий код выглядит следующим образом:</p>
+<p>Ниже приведен соответствующий код:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
@@ -4857,12 +4857,12 @@
 </div>
 </div>
 <h2 id="242">2.4.2 &nbsp; Метод вывода<a class="headerlink" href="#242" title="Permanent link">&para;</a></h2>
-<p>Метод вывода пространственной сложности в целом аналогичен временному анализу: меняется только объект подсчета, с "количества операций" на "размер используемого пространства".</p>
-<p>В отличие от временной сложности, <strong>обычно мы рассматриваем только худшую пространственную сложность</strong>. Это связано с тем, что память является жестким ограничением: нам нужно гарантировать, что для любых входных данных у программы будет достаточно памяти.</p>
-<p>Рассмотрим следующий код. Слово "худшая" в "худшей пространственной сложности" имеет два значения.</p>
+<p>Метод вывода пространственной сложности в целом аналогичен выводу временной сложности: меняется только объект подсчета, с количества операций на размер используемого пространства.</p>
+<p>В отличие от временной сложности, <strong>обычно рассматривается только худшая пространственная сложность</strong>. Это связано с тем, что память является жестким ограничением: необходимо гарантировать, что для любых входных данных у программы будет достаточно памяти.</p>
+<p>Рассмотрим следующий код. Понятие худшей пространственной сложности здесь имеет два значения.</p>
 <ol>
 <li><strong>Ориентир на худшие входные данные</strong>: когда <span class="arithmatex">\(n &lt; 10\)</span> , пространственная сложность равна <span class="arithmatex">\(O(1)\)</span> ; но когда <span class="arithmatex">\(n &gt; 10\)</span> , инициализированный массив <code>nums</code> занимает <span class="arithmatex">\(O(n)\)</span> пространства, поэтому худшая пространственная сложность равна <span class="arithmatex">\(O(n)\)</span> .</li>
-<li><strong>Ориентир на пиковое потребление памяти во время выполнения алгоритма</strong>: например, до выполнения последней строки программа занимает <span class="arithmatex">\(O(1)\)</span> пространства; при инициализации массива <code>nums</code> она занимает <span class="arithmatex">\(O(n)\)</span> пространства, поэтому худшая пространственная сложность равна <span class="arithmatex">\(O(n)\)</span> .</li>
+<li><strong>Ориентир на пиковое использование памяти во время выполнения</strong>: например, до выполнения последней строки программа занимает <span class="arithmatex">\(O(1)\)</span> пространства; при инициализации массива <code>nums</code> она занимает <span class="arithmatex">\(O(n)\)</span> пространства, поэтому худшая пространственная сложность также равна <span class="arithmatex">\(O(n)\)</span> .</li>
 </ol>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
@@ -5248,7 +5248,7 @@
 <li>Рекурсивная функция <code>recur()</code> во время выполнения одновременно содержит <span class="arithmatex">\(n\)</span> еще не завершившихся экземпляров <code>recur()</code> , поэтому занимает <span class="arithmatex">\(O(n)\)</span> пространства кадров стека.</li>
 </ul>
 <h2 id="243">2.4.3 &nbsp; Распространенные типы<a class="headerlink" href="#243" title="Permanent link">&para;</a></h2>
-<p>Пусть размер входных данных равен <span class="arithmatex">\(n\)</span> . На рисунке 2-16 показаны распространенные типы пространственной сложности (в порядке от меньшей к большей).</p>
+<p>Пусть размер входных данных равен <span class="arithmatex">\(n\)</span> . На рисунке 2-16 показаны распространенные типы пространственной сложности в порядке от меньшей к большей.</p>
 <div class="arithmatex">\[
 \begin{aligned}
 O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
@@ -5259,7 +5259,7 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
 <p align="center"> Рисунок 2-16 &nbsp; Распространенные типы пространственной сложности </p>
 
 <h3 id="1-o1">1. &nbsp; Постоянная сложность <span class="arithmatex">\(O(1)\)</span><a class="headerlink" href="#1-o1" title="Permanent link">&para;</a></h3>
-<p>Постоянная сложность часто встречается у констант, переменных и объектов, количество которых не зависит от размера входных данных <span class="arithmatex">\(n\)</span> .</p>
+<p>Постоянная сложность обычно встречается у констант, переменных и объектов, количество которых не зависит от размера входных данных <span class="arithmatex">\(n\)</span> .</p>
 <p>Следует заметить, что память, занятая инициализацией переменных или вызовом функций внутри цикла, освобождается при переходе к следующей итерации, поэтому она не накапливается, и пространственная сложность по-прежнему остается <span class="arithmatex">\(O(1)\)</span> :</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="4:13"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label></div>
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@@ -5595,7 +5595,7 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%D0%9A%D0%BB%D0%B0%D1%81%D1%81%20%D1%83%D0%B7%D0%BB%D0%B0%20%D1%81%D0%B2%D1%8F%D0%B7%D0%BD%D0%BE%D0%B3%D0%BE%20%D1%81%D0%BF%D0%B8%D1%81%D0%BA%D0%B0%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%D0%97%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%83%D0%B7%D0%BB%D0%B0%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%D0%A1%D1%81%D1%8B%D0%BB%D0%BA%D0%B0%20%D0%BD%D0%B0%20%D1%83%D0%B7%D0%B5%D0%BB-%D0%BF%D1%80%D0%B5%D0%B5%D0%BC%D0%BD%D0%B8%D0%BA%0A%0Adef%20function%28%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F%22%22%22%0A%20%20%20%20%23%20%D0%92%D1%8B%D0%BF%D0%BE%D0%BB%D0%BD%D0%B8%D1%82%D1%8C%20%D0%BD%D0%B5%D0%BA%D0%BE%D1%82%D0%BE%D1%80%D1%8B%D0%B5%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B8%0A%20%20%20%20return%200%0A%0Adef%20constant%28n%3A%20int%29%3A%0A%20%20%20%20%22%22%22%D0%9F%D0%BE%D1%81%D1%82%D0%BE%D1%8F%D0%BD%D0%BD%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%22%22%22%0A%20%20%20%20%23%20%D0%9A%D0%BE%D0%BD%D1%81%D1%82%D0%B0%D0%BD%D1%82%D1%8B%2C%20%D0%BF%D0%B5%D1%80%D0%B5%D0%BC%D0%B5%D0%BD%D0%BD%D1%8B%D0%B5%20%D0%B8%20%D0%BE%D0%B1%D1%8A%D0%B5%D0%BA%D1%82%D1%8B%20%D0%B7%D0%B0%D0%BD%D0%B8%D0%BC%D0%B0%D1%8E%D1%82%20O%281%29%20%D0%BF%D0%B0%D0%BC%D1%8F%D1%82%D0%B8%0A%20%20%20%20a%20%3D%200%0A%20%20%20%20nums%20%3D%20%5B0%5D%20%2A%2010%0A%20%20%20%20node%20%3D%20ListNode%280%29%0A%20%20%20%20%23%20%D0%9F%D0%B5%D1%80%D0%B5%D0%BC%D0%B5%D0%BD%D0%BD%D1%8B%D0%B5%20%D0%B2%20%D1%86%D0%B8%D0%BA%D0%BB%D0%B5%20%D0%B7%D0%B0%D0%BD%D0%B8%D0%BC%D0%B0%D1%8E%D1%82%20O%281%29%20%D0%BF%D0%B0%D0%BC%D1%8F%D1%82%D0%B8%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20c%20%3D%200%0A%20%20%20%20%23%20%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D0%B8%20%D0%B2%20%D1%86%D0%B8%D0%BA%D0%BB%D0%B5%20%D0%B7%D0%B0%D0%BD%D0%B8%D0%BC%D0%B0%D1%8E%D1%82%20O%281%29%20%D0%BF%D0%B0%D0%BC%D1%8F%D1%82%D0%B8%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20function%28%29%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20%23%20%D0%9F%D0%BE%D1%81%D1%82%D0%BE%D1%8F%D0%BD%D0%BD%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%0A%20%20%20%20constant%28n%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
 <h3 id="2-on">2. &nbsp; Линейная сложность <span class="arithmatex">\(O(n)\)</span><a class="headerlink" href="#2-on" title="Permanent link">&para;</a></h3>
-<p>Линейная сложность часто встречается у массивов, связных списков, стеков, очередей и других структур, число элементов в которых пропорционально <span class="arithmatex">\(n\)</span> :</p>
+<p>Линейная сложность часто встречается у массивов, списков, стеков, очередей и других структур, число элементов в которых пропорционально <span class="arithmatex">\(n\)</span> :</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="5:13"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label></div>
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@@ -6373,7 +6373,7 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
 <p align="center"> Рисунок 2-18 &nbsp; Квадратичная пространственная сложность, порождаемая рекурсивной функцией </p>
 
 <h3 id="4-o2n">4. &nbsp; Экспоненциальная сложность <span class="arithmatex">\(O(2^n)\)</span><a class="headerlink" href="#4-o2n" title="Permanent link">&para;</a></h3>
-<p>Экспоненциальная сложность часто встречается у бинарных деревьев. Обрати внимание на рисунок 2-19: "полное бинарное дерево" с <span class="arithmatex">\(n\)</span> уровнями содержит <span class="arithmatex">\(2^n - 1\)</span> узлов и занимает <span class="arithmatex">\(O(2^n)\)</span> пространства:</p>
+<p>Экспоненциальная сложность часто встречается у бинарных деревьев. Полное бинарное дерево с <span class="arithmatex">\(n\)</span> уровнями содержит <span class="arithmatex">\(2^n - 1\)</span> узлов и занимает <span class="arithmatex">\(O(2^n)\)</span> пространства:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="9:13"><input checked="checked" id="__tabbed_9_1" name="__tabbed_9" type="radio" /><input id="__tabbed_9_2" name="__tabbed_9" type="radio" /><input id="__tabbed_9_3" name="__tabbed_9" type="radio" /><input id="__tabbed_9_4" name="__tabbed_9" type="radio" /><input id="__tabbed_9_5" name="__tabbed_9" type="radio" /><input id="__tabbed_9_6" name="__tabbed_9" type="radio" /><input id="__tabbed_9_7" name="__tabbed_9" type="radio" /><input id="__tabbed_9_8" name="__tabbed_9" type="radio" /><input id="__tabbed_9_9" name="__tabbed_9" type="radio" /><input id="__tabbed_9_10" name="__tabbed_9" type="radio" /><input id="__tabbed_9_11" name="__tabbed_9" type="radio" /><input id="__tabbed_9_12" name="__tabbed_9" type="radio" /><input id="__tabbed_9_13" name="__tabbed_9" type="radio" /><div class="tabbed-labels"><label for="__tabbed_9_1">Python</label><label for="__tabbed_9_2">C++</label><label for="__tabbed_9_3">Java</label><label for="__tabbed_9_4">C#</label><label for="__tabbed_9_5">Go</label><label for="__tabbed_9_6">Swift</label><label for="__tabbed_9_7">JS</label><label for="__tabbed_9_8">TS</label><label for="__tabbed_9_9">Dart</label><label for="__tabbed_9_10">Rust</label><label for="__tabbed_9_11">C</label><label for="__tabbed_9_12">Kotlin</label><label for="__tabbed_9_13">Ruby</label></div>
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@@ -6557,12 +6557,12 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
 <p align="center"> Рисунок 2-19 &nbsp; Экспоненциальная пространственная сложность, порождаемая полным бинарным деревом </p>
 
 <h3 id="5-olog-n">5. &nbsp; Логарифмическая сложность <span class="arithmatex">\(O(\log n)\)</span><a class="headerlink" href="#5-olog-n" title="Permanent link">&para;</a></h3>
-<p>Логарифмическая сложность часто встречается в алгоритмах "разделяй и властвуй". Например, при сортировке слиянием входной массив длины <span class="arithmatex">\(n\)</span> на каждом шаге рекурсии делится пополам по середине, образуя рекурсивное дерево высоты <span class="arithmatex">\(\log n\)</span> и используя <span class="arithmatex">\(O(\log n)\)</span> пространства кадров стека.</p>
+<p>Логарифмическая сложность часто встречается в алгоритмах "разделяй и властвуй". Например, при сортировке слиянием входной массив длины <span class="arithmatex">\(n\)</span> на каждом шаге рекурсии делится пополам, образуя рекурсивное дерево высоты <span class="arithmatex">\(\log n\)</span> и используя <span class="arithmatex">\(O(\log n)\)</span> пространства кадров стека.</p>
 <p>Еще один пример - преобразование числа в строку. Если задано положительное целое число <span class="arithmatex">\(n\)</span> , то количество его цифр равно <span class="arithmatex">\(\lfloor \log_{10} n \rfloor + 1\)</span> , то есть длина соответствующей строки тоже равна <span class="arithmatex">\(\lfloor \log_{10} n \rfloor + 1\)</span> , следовательно, пространственная сложность составляет <span class="arithmatex">\(O(\log_{10} n + 1) = O(\log n)\)</span> .</p>
 <h2 id="244">2.4.4 &nbsp; Компромисс между временем и пространством<a class="headerlink" href="#244" title="Permanent link">&para;</a></h2>
-<p>В идеале нам хотелось бы, чтобы и временная, и пространственная сложность алгоритма были оптимальными. Однако на практике одновременно оптимизировать и время, и память обычно очень трудно.</p>
-<p><strong>Снижение временной сложности обычно достигается ценой увеличения пространственной сложности, и наоборот</strong>. Подход, при котором мы жертвуем памятью ради ускорения работы алгоритма, называется "обмен пространства на время"; обратный подход называется "обмен времени на пространство".</p>
-<p>Выбор между этими двумя идеями зависит от того, что для нас важнее. В большинстве случаев время ценнее памяти, поэтому стратегия "обмена пространства на время" используется чаще. Но при очень больших объемах данных контроль пространственной сложности тоже становится крайне важным.</p>
+<p>В идеальных условиях хотелось бы, чтобы и временная, и пространственная сложность алгоритма были оптимальными. Однако на практике одновременно оптимизировать и время, и память обычно очень трудно.</p>
+<p><strong>Снижение временной сложности обычно достигается ценой увеличения пространственной сложности, и наоборот</strong>. Подход, при котором жертвуют памятью ради ускорения работы алгоритма, называется обменом пространства на время; обратный подход называется обменом времени на пространство.</p>
+<p>Выбор между этими двумя идеями зависит от того, что важнее в конкретной задаче. В большинстве случаев время ценнее памяти, поэтому стратегия обмена пространства на время используется чаще. Но при очень больших объемах данных контроль пространственной сложности тоже становится крайне важным.</p>
 
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 <h3 id="1">1. &nbsp; Ключевые выводы<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <p><strong>Оценка эффективности алгоритмов</strong></p>
 <ul>
-<li>Временная эффективность и пространственная эффективность - два главных показателя, по которым оценивают качество алгоритма.</li>
-<li>Мы можем оценивать эффективность алгоритма с помощью практического тестирования, но при этом трудно устранить влияние тестовой среды, а само тестирование потребляет много вычислительных ресурсов.</li>
-<li>Анализ сложности устраняет недостатки практического тестирования, дает результаты, применимые ко всем платформам выполнения, и позволяет увидеть эффективность алгоритма при разных масштабах данных.</li>
+<li>Временная и пространственная эффективность являются двумя основными критериями для оценки качества алгоритмов.</li>
+<li>Эффективность алгоритмов можно оценивать с помощью практических тестов, однако это сложно из-за влияния тестовой среды и значительных затрат вычислительных ресурсов.</li>
+<li>Анализ сложности позволяет устранить недостатки практических тестов, а результаты анализа применимы ко всем платформам и могут выявить эффективность алгоритма при различных объемах данных.</li>
 </ul>
 <p><strong>Временная сложность</strong></p>
 <ul>
-<li>Временная сложность используется для оценки того, как меняется время работы алгоритма с ростом объема данных. Она хорошо подходит для оценки эффективности, но в некоторых случаях может давать недостаточно точное сравнение, например когда входные данные малы или когда временные сложности совпадают.</li>
-<li>Худшая временная сложность обозначается с помощью нотации Big <span class="arithmatex">\(O\)</span> и соответствует асимптотической верхней границе функции, отражая уровень роста числа операций <span class="arithmatex">\(T(n)\)</span> при стремлении <span class="arithmatex">\(n\)</span> к положительной бесконечности.</li>
-<li>Вывод временной сложности включает два шага: сначала подсчитывается число операций, затем определяется асимптотическая верхняя граница.</li>
-<li>Распространенные временные сложности в порядке роста: <span class="arithmatex">\(O(1)\)</span>, <span class="arithmatex">\(O(\log n)\)</span>, <span class="arithmatex">\(O(n)\)</span>, <span class="arithmatex">\(O(n \log n)\)</span>, <span class="arithmatex">\(O(n^2)\)</span>, <span class="arithmatex">\(O(2^n)\)</span> и <span class="arithmatex">\(O(n!)\)</span>.</li>
-<li>Временная сложность некоторых алгоритмов не фиксирована, а зависит от распределения входных данных. Различают худшую, лучшую и среднюю временную сложность; лучшая временная сложность используется редко, потому что для ее достижения вход обычно должен удовлетворять строгим условиям.</li>
-<li>Средняя временная сложность отражает эффективность алгоритма на случайных входных данных и ближе всего к его поведению в практических сценариях. Для ее вычисления нужно знать распределение входных данных и рассчитать соответствующее математическое ожидание.</li>
+<li>Временная сложность используется для оценки тенденции изменения времени выполнения алгоритма с увеличением объема данных, что позволяет оценивать его эффективность. Однако в некоторых случаях она может работать не так хорошо, например когда объем входных данных мал или временная сложность одинакова, что не позволяет точно сравнить эффективность алгоритмов.</li>
+<li>Худшая временная сложность обозначается символом Big <span class="arithmatex">\(O\)</span> и соответствует асимптотической верхней границе, отражая уровень роста количества операций <span class="arithmatex">\(T(n)\)</span> при стремлении <span class="arithmatex">\(n\)</span> к бесконечности.</li>
+<li>Определение временной сложности включает два этапа: сначала подсчитывается количество операций, затем определяется асимптотическая верхняя граница.</li>
+<li>Наиболее распространенные временные сложности в порядке возрастания: <span class="arithmatex">\(O(1)\)</span>, <span class="arithmatex">\(O(\log n)\)</span>, <span class="arithmatex">\(O(n)\)</span>, <span class="arithmatex">\(O(n \log n)\)</span>, <span class="arithmatex">\(O(n^2)\)</span>, <span class="arithmatex">\(O(2^n)\)</span> и <span class="arithmatex">\(O(n!)\)</span>.</li>
+<li>Временная сложность некоторых алгоритмов не является фиксированной и зависит от распределения входных данных. Временная сложность делится на худшую, лучшую и среднюю. Лучшая временная сложность почти не используется, так как для достижения лучшего случая входные данные должны соответствовать строгим критериям.</li>
+<li>Средняя временная сложность отражает эффективность алгоритма при случайных входных данных и наиболее близка к реальной производительности алгоритма. Для расчета средней временной сложности необходимо учитывать распределение входных данных и математическое ожидание.</li>
 </ul>
 <p><strong>Пространственная сложность</strong></p>
 <ul>
-<li>Пространственная сложность играет роль, аналогичную временной: она показывает тенденцию роста потребления памяти по мере увеличения объема данных.</li>
-<li>Память, связанная с выполнением алгоритма, можно разделить на входное пространство, временное пространство и выходное пространство. Обычно входное пространство не включается в расчет пространственной сложности. Временное пространство можно разбить на временные данные, пространство кадров стека и пространство инструкций; при этом пространство кадров стека обычно влияет на сложность только в рекурсивных функциях.</li>
-<li>Обычно нас интересует только худшая пространственная сложность, то есть пространственная сложность алгоритма при худшем наборе входных данных и в худший момент времени выполнения.</li>
-<li>Распространенные пространственные сложности в порядке роста: <span class="arithmatex">\(O(1)\)</span>, <span class="arithmatex">\(O(\log n)\)</span>, <span class="arithmatex">\(O(n)\)</span>, <span class="arithmatex">\(O(n^2)\)</span> и <span class="arithmatex">\(O(2^n)\)</span>.</li>
+<li>Пространственная сложность аналогична временной сложности и используется для оценки тенденции изменения объема памяти, занимаемой алгоритмом, с увеличением объема данных.</li>
+<li>Память, используемую в процессе выполнения алгоритма, можно разделить на входное пространство, временное пространство и выходное пространство. Обычно при расчете пространственной сложности входное пространство не учитывается. Временное пространство делится на временные данные, пространство стека и пространство инструкций, причем пространство стека обычно влияет на сложность только в рекурсивных функциях.</li>
+<li>Обычно рассматривается только худшая пространственная сложность, то есть пространственная сложность алгоритма при худших входных данных и в худший момент выполнения.</li>
+<li>Наиболее распространенные пространственные сложности в порядке возрастания: <span class="arithmatex">\(O(1)\)</span>, <span class="arithmatex">\(O(\log n)\)</span>, <span class="arithmatex">\(O(n)\)</span>, <span class="arithmatex">\(O(n^2)\)</span> и <span class="arithmatex">\(O(2^n)\)</span>.</li>
 </ul>
 <h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
 <p><strong>Q</strong>: Является ли пространственная сложность хвостовой рекурсии равной <span class="arithmatex">\(O(1)\)</span>?</p>
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 <!-- Page content -->
 <h1 id="23">2.3 &nbsp; Временная сложность<a class="headerlink" href="#23" title="Permanent link">&para;</a></h1>
-<p>Время выполнения может наглядно и точно отражать эффективность алгоритма. Если мы хотим точно оценить время работы некоторого фрагмента кода, как это сделать?</p>
+<p>Время выполнения действительно может наглядно и точно отражать эффективность алгоритма. Но если мы захотим точно оценить время работы некоторого фрагмента кода, то столкнемся со следующими шагами.</p>
 <ol>
 <li><strong>Определить платформу выполнения</strong>, включая конфигурацию оборудования, язык программирования, системную среду и т.д., поскольку все эти факторы влияют на эффективность выполнения кода.</li>
 <li><strong>Оценить время выполнения различных вычислительных операций</strong>, например операция сложения <code>+</code> требует 1 нс , операция умножения <code>*</code> требует 10 нс , операция вывода <code>print()</code> требует 5 нс и т.д.</li>
@@ -4825,10 +4825,10 @@
 <div class="arithmatex">\[
 1 + 1 + 10 + (1 + 5) \times n = 6n + 12
 \]</div>
-<p>Но на практике <strong>подсчитывать реальное время выполнения алгоритма и неразумно, и нереалистично</strong>. Во-первых, мы не хотим привязывать оценку времени к конкретной платформе, потому что алгоритм должен запускаться на самых разных платформах. Во-вторых, нам трудно узнать время выполнения каждого типа операций, а это сильно усложняет оценку.</p>
+<p>Но на практике <strong>подсчитывать реальное время выполнения алгоритма и неразумно, и нереалистично</strong>. Во-первых, мы не хотим привязывать оценку времени к конкретной платформе, потому что алгоритм должен запускаться на самых разных платформах. Во-вторых, нам трудно определить время выполнения каждого типа операций, а это делает точную оценку крайне затруднительной.</p>
 <h2 id="231">2.3.1 &nbsp; Подсчет тенденции роста времени<a class="headerlink" href="#231" title="Permanent link">&para;</a></h2>
 <p>Анализ временной сложности оценивает не само время выполнения алгоритма, <strong>а тенденцию роста этого времени по мере увеличения объема данных</strong>.</p>
-<p>Понятие "тенденции роста времени" довольно абстрактно, поэтому разберем его на примере. Предположим, размер входных данных равен <span class="arithmatex">\(n\)</span> , и даны три алгоритма <code>A</code> , <code>B</code> и <code>C</code> :</p>
+<p>Понятие "тенденции роста времени" выглядит довольно абстрактным, поэтому разберем его на примере. Предположим, размер входных данных равен <span class="arithmatex">\(n\)</span> , и даны три алгоритма <code>A</code> , <code>B</code> и <code>C</code> :</p>
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 <div class="tabbed-content">
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@@ -5075,20 +5075,20 @@
 </div>
 </div>
 </div>
-<p>На рисунке 2-7 показана временная сложность трех функций алгоритмов выше.</p>
+<p>Ниже показаны временные сложности трех приведенных выше функций.</p>
 <ul>
-<li>У алгоритма <code>A</code> есть только 1 операция вывода, и время его работы не растет с увеличением <span class="arithmatex">\(n\)</span> . Мы называем такую временную сложность "постоянной".</li>
-<li>В алгоритме <code>B</code> операция вывода выполняется в цикле <span class="arithmatex">\(n\)</span> раз, поэтому время работы растет линейно по мере увеличения <span class="arithmatex">\(n\)</span> . Такая временная сложность называется "линейной".</li>
-<li>В алгоритме <code>C</code> операция вывода выполняется <span class="arithmatex">\(1000000\)</span> раз; хотя время работы велико, оно не зависит от размера входных данных <span class="arithmatex">\(n\)</span> . Поэтому временная сложность <code>C</code> такая же, как у <code>A</code> , и тоже является "постоянной".</li>
+<li>У алгоритма <code>A</code> есть только одна операция вывода, и время его работы не растет с увеличением <span class="arithmatex">\(n\)</span> . Такую временную сложность называют постоянной.</li>
+<li>В алгоритме <code>B</code> операция вывода выполняется в цикле <span class="arithmatex">\(n\)</span> раз, поэтому время работы растет линейно по мере увеличения <span class="arithmatex">\(n\)</span> . Такая временная сложность называется линейной.</li>
+<li>В алгоритме <code>C</code> операция вывода выполняется <span class="arithmatex">\(1000000\)</span> раз; хотя время работы велико, оно не зависит от размера входных данных <span class="arithmatex">\(n\)</span> . Поэтому временная сложность <code>C</code> такая же, как у <code>A</code> , и тоже является постоянной.</li>
 </ul>
 <p><img alt="Тенденции роста времени для алгоритмов A, B и C" class="animation-figure" src="../time_complexity.assets/time_complexity_simple_example.png" /></p>
 <p align="center"> Рисунок 2-7 &nbsp; Тенденции роста времени для алгоритмов A, B и C </p>
 
 <p>Какие особенности имеет анализ временной сложности по сравнению с непосредственным измерением времени работы алгоритма?</p>
 <ul>
-<li><strong>Временная сложность позволяет эффективно оценивать эффективность алгоритма</strong>. Например, время работы алгоритма <code>B</code> растет линейно: при <span class="arithmatex">\(n &gt; 1\)</span> он медленнее алгоритма <code>A</code> , а при <span class="arithmatex">\(n &gt; 1000000\)</span> медленнее алгоритма <code>C</code> . На самом деле, если размер входных данных <span class="arithmatex">\(n\)</span> достаточно велик, алгоритм с "постоянной" сложностью обязательно лучше алгоритма с "линейной" сложностью. В этом и состоит смысл тенденции роста времени.</li>
-<li><strong>Метод вывода временной сложности проще</strong>. Очевидно, что платформа выполнения и тип вычислительных операций не влияют на тенденцию роста времени работы алгоритма. Поэтому в анализе временной сложности мы можем считать время выполнения всех вычислительных операций одинаковым "единичным временем" и тем самым упростить "подсчет времени выполнения операций" до "подсчета количества операций", что существенно снижает сложность оценки.</li>
-<li><strong>У временной сложности есть и определенные ограничения</strong>. Например, хотя временная сложность алгоритмов <code>A</code> и <code>C</code> одинакова, их реальное время выполнения сильно различается. Точно так же, хотя временная сложность <code>B</code> выше, чем у <code>C</code> , при малых <span class="arithmatex">\(n\)</span> алгоритм <code>B</code> явно лучше <code>C</code> . В таких случаях нам часто трудно судить об эффективности алгоритма, опираясь только на временную сложность. Тем не менее, несмотря на эти ограничения, анализ сложности все равно остается самым эффективным и самым распространенным способом оценки алгоритмов.</li>
+<li><strong>Временная сложность позволяет эффективно оценивать эффективность алгоритма</strong>. Например, время работы алгоритма <code>B</code> растет линейно: при <span class="arithmatex">\(n &gt; 1\)</span> он медленнее алгоритма <code>A</code> , а при <span class="arithmatex">\(n &gt; 1000000\)</span> медленнее алгоритма <code>C</code> . Если размер входных данных достаточно велик, алгоритм с постоянной сложностью обязательно лучше алгоритма с линейной сложностью. В этом и состоит смысл тенденции роста времени.</li>
+<li><strong>Метод вывода временной сложности проще</strong>. Платформа выполнения и тип вычислительных операций не влияют на тенденцию роста времени работы алгоритма. Поэтому в анализе временной сложности можно считать время выполнения всех вычислительных операций одинаковым единичным временем и тем самым упростить подсчет времени выполнения до подсчета количества операций.</li>
+<li><strong>У временной сложности есть и определенные ограничения</strong>. Например, хотя временная сложность алгоритмов <code>A</code> и <code>C</code> одинакова, их реальное время выполнения сильно различается. Точно так же, хотя временная сложность <code>B</code> выше, чем у <code>C</code> , при малых <span class="arithmatex">\(n\)</span> алгоритм <code>B</code> очевидно лучше <code>C</code> . Несмотря на эти ограничения, анализ сложности все равно остается самым эффективным и самым распространенным способом оценки алгоритмов.</li>
 </ul>
 <h2 id="232">2.3.2 &nbsp; Асимптотическая верхняя граница функции<a class="headerlink" href="#232" title="Permanent link">&para;</a></h2>
 <p>Для функции с входным размером <span class="arithmatex">\(n\)</span> :</p>
@@ -5255,9 +5255,9 @@
 <div class="arithmatex">\[
 T(n) = 3 + 2n
 \]</div>
-<p><span class="arithmatex">\(T(n)\)</span> - линейная функция, а это означает, что тенденция роста времени работы линейна, следовательно, ее временная сложность является линейной.</p>
-<p>Линейную временную сложность мы записываем как <span class="arithmatex">\(O(n)\)</span> ; этот математический символ называется <u>нотацией Big <span class="arithmatex">\(O\)</span> (big-<span class="arithmatex">\(O\)</span> notation)</u> и обозначает <u>асимптотическую верхнюю границу (asymptotic upper bound)</u> функции <span class="arithmatex">\(T(n)\)</span> .</p>
-<p>По сути анализ временной сложности - это вычисление асимптотической верхней границы "количества операций <span class="arithmatex">\(T(n)\)</span>", и у него есть строгое математическое определение.</p>
+<p><span class="arithmatex">\(T(n)\)</span> - линейная функция, а это означает, что тенденция роста времени работы линейна, следовательно, временная сложность здесь тоже линейна.</p>
+<p>Линейную временную сложность записывают как <span class="arithmatex">\(O(n)\)</span> ; этот математический символ называется <u>нотацией Big <span class="arithmatex">\(O\)</span> (big-<span class="arithmatex">\(O\)</span> notation)</u> и обозначает <u>асимптотическую верхнюю границу (asymptotic upper bound)</u> функции <span class="arithmatex">\(T(n)\)</span> .</p>
+<p>Иными словами, анализ временной сложности сводится к определению асимптотической верхней границы числа операций <span class="arithmatex">\(T(n)\)</span>, и у этого понятия есть строгое математическое определение.</p>
 <div class="admonition note">
 <p class="admonition-title">Асимптотическая верхняя граница функции</p>
 <p>Если существуют положительное действительное число <span class="arithmatex">\(c\)</span> и действительное число <span class="arithmatex">\(n_0\)</span> , такие что для всех <span class="arithmatex">\(n &gt; n_0\)</span> выполняется <span class="arithmatex">\(T(n) \leq c \cdot f(n)\)</span> , то можно считать, что <span class="arithmatex">\(f(n)\)</span> задает асимптотическую верхнюю границу для <span class="arithmatex">\(T(n)\)</span> ; это записывается как <span class="arithmatex">\(T(n) = O(f(n))\)</span> .</p>
@@ -5267,10 +5267,10 @@ T(n) = 3 + 2n
 <p align="center"> Рисунок 2-8 &nbsp; Асимптотическая верхняя граница функции </p>
 
 <h2 id="233">2.3.3 &nbsp; Метод вывода<a class="headerlink" href="#233" title="Permanent link">&para;</a></h2>
-<p>Математическое определение асимптотической верхней границы выглядит довольно формально, и если ты понял его не до конца, переживать не стоит. Сначала можно освоить сам метод вывода, а в процессе дальнейшей практики постепенно почувствовать его математический смысл.</p>
-<p>Согласно определению, после того как мы определили <span class="arithmatex">\(f(n)\)</span> , мы можем получить временную сложность <span class="arithmatex">\(O(f(n))\)</span> . Но как определить саму асимптотическую верхнюю границу <span class="arithmatex">\(f(n)\)</span> ? В целом процесс состоит из двух шагов: сначала подсчитать количество операций, затем определить асимптотическую верхнюю границу.</p>
+<p>Математическое определение асимптотической верхней границы выглядит довольно формально, и если оно пока не до конца понятно, переживать не стоит. Сначала можно освоить сам метод вывода, а в процессе дальнейшей практики постепенно почувствовать его математический смысл.</p>
+<p>Согласно определению, после того как мы определили <span class="arithmatex">\(f(n)\)</span> , можно получить временную сложность <span class="arithmatex">\(O(f(n))\)</span> . Но как определить саму асимптотическую верхнюю границу <span class="arithmatex">\(f(n)\)</span> ? В целом процесс состоит из двух шагов: сначала подсчитать количество операций, затем определить асимптотическую верхнюю границу.</p>
 <h3 id="1-1">1. &nbsp; Шаг 1: подсчет количества операций<a class="headerlink" href="#1-1" title="Permanent link">&para;</a></h3>
-<p>Для кода это можно делать построчно сверху вниз. Однако, поскольку в выражении <span class="arithmatex">\(c \cdot f(n)\)</span> выше постоянный коэффициент <span class="arithmatex">\(c\)</span> может быть сколь угодно большим, <strong>различные коэффициенты и постоянные члены в числе операций <span class="arithmatex">\(T(n)\)</span> можно игнорировать</strong>. Исходя из этого принципа, можно сформулировать следующие упрощающие приемы подсчета.</p>
+<p>Для кода это можно делать построчно сверху вниз. Однако, поскольку в выражении <span class="arithmatex">\(c \cdot f(n)\)</span> постоянный коэффициент <span class="arithmatex">\(c\)</span> может быть сколь угодно большим, <strong>различные коэффициенты и постоянные члены в числе операций <span class="arithmatex">\(T(n)\)</span> можно игнорировать</strong>. Исходя из этого принципа, можно сформулировать следующие упрощающие приемы подсчета.</p>
 <ol>
 <li><strong>Игнорировать константы в <span class="arithmatex">\(T(n)\)</span></strong>. Они не зависят от <span class="arithmatex">\(n\)</span> , а значит не влияют на временную сложность.</li>
 <li><strong>Опускать все коэффициенты</strong>. Например, циклы на <span class="arithmatex">\(2n\)</span> раз или <span class="arithmatex">\(5n + 1\)</span> раз можно упростить до <span class="arithmatex">\(n\)</span> раз, потому что коэффициент перед <span class="arithmatex">\(n\)</span> не влияет на временную сложность.</li>
@@ -5506,7 +5506,7 @@ T(n) &amp; = n^2 + n &amp; \text{ленивый подсчет (o.O)}
 \]</div>
 <h3 id="2-2">2. &nbsp; Шаг 2: определение асимптотической верхней границы<a class="headerlink" href="#2-2" title="Permanent link">&para;</a></h3>
 <p>**Временная сложность определяется старшим по степени членом в <span class="arithmatex">\(T(n)\)</span> **. Это связано с тем, что при стремлении <span class="arithmatex">\(n\)</span> к бесконечности именно старший член начинает доминировать, а влиянием остальных членов можно пренебречь.</p>
-<p>В таблице 2-2 приведены несколько примеров. Некоторые значения специально сделаны преувеличенными, чтобы подчеркнуть вывод: "коэффициент не способен изменить порядок". Когда <span class="arithmatex">\(n\)</span> стремится к бесконечности, эти константы становятся несущественными.</p>
+<p>В таблице 2-2 приведены несколько примеров. Некоторые значения специально сделаны преувеличенными, чтобы подчеркнуть вывод: коэффициент не способен изменить порядок. Когда <span class="arithmatex">\(n\)</span> стремится к бесконечности, эти константы становятся несущественными.</p>
 <p align="center"> Таблица 2-2 &nbsp; Временная сложность, соответствующая разному количеству операций </p>
 
 <div class="center-table">
@@ -5542,7 +5542,7 @@ T(n) &amp; = n^2 + n &amp; \text{ленивый подсчет (o.O)}
 </table>
 </div>
 <h2 id="234">2.3.4 &nbsp; Распространенные типы<a class="headerlink" href="#234" title="Permanent link">&para;</a></h2>
-<p>Пусть размер входных данных равен <span class="arithmatex">\(n\)</span> ; распространенные типы временной сложности показаны на рисунке 2-9 (в порядке от меньшей к большей).</p>
+<p>Пусть размер входных данных равен <span class="arithmatex">\(n\)</span> ; распространенные типы временной сложности показаны на рисунке 2-9 в порядке от меньшей к большей.</p>
 <div class="arithmatex">\[
 \begin{aligned}
 O(1) &lt; O(\log n) &lt; O(n) &lt; O(n \log n) &lt; O(n^2) &lt; O(2^n) &lt; O(n!) \newline
@@ -5713,7 +5713,7 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n \log n) &lt; O(n^2) &lt; O(2^n) &lt; O(n!
 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20constant%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%9F%D0%BE%D1%81%D1%82%D0%BE%D1%8F%D0%BD%D0%BD%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20size%20%3D%2010%0A%20%20%20%20for%20_%20in%20range%28size%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20constant%28n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BA%D0%BE%D0%BD%D1%81%D1%82%D0%B0%D0%BD%D1%82%D0%BD%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
 <h3 id="2-on">2. &nbsp; Линейная сложность <span class="arithmatex">\(O(n)\)</span><a class="headerlink" href="#2-on" title="Permanent link">&para;</a></h3>
-<p>Число операций при линейной сложности растет линейно относительно размера входных данных <span class="arithmatex">\(n\)</span> . Линейная сложность обычно встречается в одноуровневых циклах:</p>
+<p>Линейная сложность характеризуется тем, что число операций растет линейно относительно размера входных данных <span class="arithmatex">\(n\)</span> . Линейная сложность обычно встречается в одноуровневых циклах:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="6:13"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><input id="__tabbed_6_13" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Kotlin</label><label for="__tabbed_6_13">Ruby</label></div>
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@@ -6027,9 +6027,9 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n \log n) &lt; O(n^2) &lt; O(2^n) &lt; O(n!
 <p><div style="height: 459px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20array_traversal%28nums%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%9B%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%20%28%D0%BE%D0%B1%D1%85%D0%BE%D0%B4%20%D0%BC%D0%B0%D1%81%D1%81%D0%B8%D0%B2%D0%B0%29%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%B8%D1%82%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BF%D1%80%D0%BE%D0%BF%D0%BE%D1%80%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%20%D0%B4%D0%BB%D0%B8%D0%BD%D0%B5%20%D0%BC%D0%B0%D1%81%D1%81%D0%B8%D0%B2%D0%B0%0A%20%20%20%20for%20num%20in%20nums%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20array_traversal%28%5B0%5D%20%2A%20n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%28%D0%BE%D0%B1%D1%85%D0%BE%D0%B4%20%D0%BC%D0%B0%D1%81%D1%81%D0%B8%D0%B2%D0%B0%29%20%3D%22%2C%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20array_traversal%28nums%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%9B%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%20%28%D0%BE%D0%B1%D1%85%D0%BE%D0%B4%20%D0%BC%D0%B0%D1%81%D1%81%D0%B8%D0%B2%D0%B0%29%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%B8%D1%82%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BF%D1%80%D0%BE%D0%BF%D0%BE%D1%80%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%20%D0%B4%D0%BB%D0%B8%D0%BD%D0%B5%20%D0%BC%D0%B0%D1%81%D1%81%D0%B8%D0%B2%D0%B0%0A%20%20%20%20for%20num%20in%20nums%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20array_traversal%28%5B0%5D%20%2A%20n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%28%D0%BE%D0%B1%D1%85%D0%BE%D0%B4%20%D0%BC%D0%B0%D1%81%D1%81%D0%B8%D0%B2%D0%B0%29%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
-<p>Стоит отметить, что <strong>размер входных данных <span class="arithmatex">\(n\)</span> нужно определять конкретно в зависимости от типа входа</strong>. Например, в первом примере переменная <span class="arithmatex">\(n\)</span> сама является размером входных данных; во втором примере размером данных служит длина массива <span class="arithmatex">\(n\)</span> .</p>
+<p>Стоит отметить, что <strong>размер входных данных <span class="arithmatex">\(n\)</span> нужно определять конкретно в зависимости от типа входа</strong>. Например, в первом примере переменная <span class="arithmatex">\(n\)</span> сама является размером входных данных; во втором примере размером данных служит длина массива.</p>
 <h3 id="3-on2">3. &nbsp; Квадратичная сложность <span class="arithmatex">\(O(n^2)\)</span><a class="headerlink" href="#3-on2" title="Permanent link">&para;</a></h3>
-<p>Число операций при квадратичной сложности растет квадратично относительно размера входных данных <span class="arithmatex">\(n\)</span> . Квадратичная сложность обычно встречается во вложенных циклах: временная сложность внешнего и внутреннего циклов равна <span class="arithmatex">\(O(n)\)</span> , поэтому общая временная сложность составляет <span class="arithmatex">\(O(n^2)\)</span> :</p>
+<p>Квадратичная сложность характеризуется тем, что число операций растет квадратично относительно размера входных данных <span class="arithmatex">\(n\)</span> . Квадратичная сложность обычно встречается во вложенных циклах: временная сложность внешнего и внутреннего циклов равна <span class="arithmatex">\(O(n)\)</span> , поэтому общая временная сложность составляет <span class="arithmatex">\(O(n^2)\)</span> :</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="8:13"><input checked="checked" id="__tabbed_8_1" name="__tabbed_8" type="radio" /><input id="__tabbed_8_2" name="__tabbed_8" type="radio" /><input id="__tabbed_8_3" name="__tabbed_8" type="radio" /><input id="__tabbed_8_4" name="__tabbed_8" type="radio" /><input id="__tabbed_8_5" name="__tabbed_8" type="radio" /><input id="__tabbed_8_6" name="__tabbed_8" type="radio" /><input id="__tabbed_8_7" name="__tabbed_8" type="radio" /><input id="__tabbed_8_8" name="__tabbed_8" type="radio" /><input id="__tabbed_8_9" name="__tabbed_8" type="radio" /><input id="__tabbed_8_10" name="__tabbed_8" type="radio" /><input id="__tabbed_8_11" name="__tabbed_8" type="radio" /><input id="__tabbed_8_12" name="__tabbed_8" type="radio" /><input id="__tabbed_8_13" name="__tabbed_8" type="radio" /><div class="tabbed-labels"><label for="__tabbed_8_1">Python</label><label for="__tabbed_8_2">C++</label><label for="__tabbed_8_3">Java</label><label for="__tabbed_8_4">C#</label><label for="__tabbed_8_5">Go</label><label for="__tabbed_8_6">Swift</label><label for="__tabbed_8_7">JS</label><label for="__tabbed_8_8">TS</label><label for="__tabbed_8_9">Dart</label><label for="__tabbed_8_10">Rust</label><label for="__tabbed_8_11">C</label><label for="__tabbed_8_12">Kotlin</label><label for="__tabbed_8_13">Ruby</label></div>
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@@ -6224,7 +6224,7 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n \log n) &lt; O(n^2) &lt; O(2^n) &lt; O(n!
 <p><img alt="Постоянная, линейная и квадратичная временная сложность" class="animation-figure" src="../time_complexity.assets/time_complexity_constant_linear_quadratic.png" /></p>
 <p align="center"> Рисунок 2-10 &nbsp; Постоянная, линейная и квадратичная временная сложность </p>
 
-<p>Возьмем в качестве примера пузырьковую сортировку: внешний цикл выполняется <span class="arithmatex">\(n - 1\)</span> раз, внутренний цикл выполняется <span class="arithmatex">\(n-1\)</span> , <span class="arithmatex">\(n-2\)</span> , <span class="arithmatex">\(\dots\)</span> , <span class="arithmatex">\(2\)</span> , <span class="arithmatex">\(1\)</span> раз, в среднем это <span class="arithmatex">\(n / 2\)</span> раз, поэтому временная сложность равна <span class="arithmatex">\(O((n - 1) n / 2) = O(n^2)\)</span> :</p>
+<p>Возьмем в качестве примера пузырьковую сортировку: внешний цикл выполняется <span class="arithmatex">\(n - 1\)</span> раз, внутренний цикл выполняется <span class="arithmatex">\(n-1\)</span> , <span class="arithmatex">\(n-2\)</span> , <span class="arithmatex">\(\dots\)</span> , <span class="arithmatex">\(2\)</span> , <span class="arithmatex">\(1\)</span> раз, в среднем это <span class="arithmatex">\(n / 2\)</span> раз, поэтому временная сложность равна <span class="arithmatex">\(O((n - 1)n / 2) = O(n^2)\)</span> :</p>
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@@ -6519,8 +6519,8 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n \log n) &lt; O(n^2) &lt; O(2^n) &lt; O(n!
 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20bubble_sort%28nums%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%9A%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%B8%D1%87%D0%BD%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%20%28%D0%BF%D1%83%D0%B7%D1%8B%D1%80%D1%8C%D0%BA%D0%BE%D0%B2%D0%B0%D1%8F%20%D1%81%D0%BE%D1%80%D1%82%D0%B8%D1%80%D0%BE%D0%B2%D0%BA%D0%B0%29%22%22%22%0A%20%20%20%20count%20%3D%200%20%20%23%20%D0%A1%D1%87%D0%B5%D1%82%D1%87%D0%B8%D0%BA%0A%20%20%20%20%23%20%D0%92%D0%BD%D0%B5%D1%88%D0%BD%D0%B8%D0%B9%20%D1%86%D0%B8%D0%BA%D0%BB%3A%20%D0%BD%D0%B5%D0%BE%D1%82%D1%81%D0%BE%D1%80%D1%82%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%BD%D1%8B%D0%B9%20%D0%B4%D0%B8%D0%B0%D0%BF%D0%B0%D0%B7%D0%BE%D0%BD%20%5B0%2C%20i%5D%0A%20%20%20%20for%20i%20in%20range%28len%28nums%29%20-%201%2C%200%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20%23%20%D0%92%D0%BD%D1%83%D1%82%D1%80%D0%B5%D0%BD%D0%BD%D0%B8%D0%B9%20%D1%86%D0%B8%D0%BA%D0%BB%3A%20%D0%BF%D0%B5%D1%80%D0%B5%D0%BC%D0%B5%D1%81%D1%82%D0%B8%D1%82%D1%8C%20%D0%BC%D0%B0%D0%BA%D1%81%D0%B8%D0%BC%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B%D0%B9%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%BD%D0%B5%D0%BE%D1%82%D1%81%D0%BE%D1%80%D1%82%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%BD%D0%BE%D0%B3%D0%BE%20%D0%B4%D0%B8%D0%B0%D0%BF%D0%B0%D0%B7%D0%BE%D0%BD%D0%B0%20%5B0%2C%20i%5D%20%D0%B2%20%D0%B5%D0%B3%D0%BE%20%D0%BF%D1%80%D0%B0%D0%B2%D1%8B%D0%B9%20%D0%BA%D0%BE%D0%BD%D0%B5%D1%86%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28i%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20nums%5Bj%5D%20%3E%20nums%5Bj%20%2B%201%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%D0%9F%D0%BE%D0%BC%D0%B5%D0%BD%D1%8F%D1%82%D1%8C%20%D0%BC%D0%B5%D1%81%D1%82%D0%B0%D0%BC%D0%B8%20nums%5Bj%5D%20%D0%B8%20nums%5Bj%20%2B%201%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20tmp%20%3D%20nums%5Bj%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20nums%5Bj%5D%20%3D%20nums%5Bj%20%2B%201%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20nums%5Bj%20%2B%201%5D%20%3D%20tmp%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20count%20%2B%3D%203%20%20%23%20%D0%9E%D0%B1%D0%BC%D0%B5%D0%BD%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D0%BE%D0%B2%20%D0%B2%D0%BA%D0%BB%D1%8E%D1%87%D0%B0%D0%B5%D1%82%203%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D0%B0%D1%80%D0%BD%D1%8B%D0%B5%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B8%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20nums%20%3D%20%5Bi%20for%20i%20in%20range%28n%2C%200%2C%20-1%29%5D%20%20%23%20%5Bn%2C%20n-1%2C%20...%2C%202%2C%201%5D%0A%20%20%20%20count%20%3D%20bubble_sort%28nums%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BA%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%B8%D1%87%D0%BD%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%28%D0%BF%D1%83%D0%B7%D1%8B%D1%80%D1%8C%D0%BA%D0%BE%D0%B2%D0%B0%D1%8F%20%D1%81%D0%BE%D1%80%D1%82%D0%B8%D1%80%D0%BE%D0%B2%D0%BA%D0%B0%29%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
 <h3 id="4-o2n">4. &nbsp; Экспоненциальная сложность <span class="arithmatex">\(O(2^n)\)</span><a class="headerlink" href="#4-o2n" title="Permanent link">&para;</a></h3>
-<p>Типичный пример экспоненциального роста в биологии - "деление клеток": в начальном состоянии есть 1 клетка, после одного деления их становится 2, после двух делений - 4 и так далее; после <span class="arithmatex">\(n\)</span> раундов деления клеток становится <span class="arithmatex">\(2^n\)</span> .</p>
-<p>На рисунке 2-11 и в следующем коде моделируется процесс деления клеток; временная сложность равна <span class="arithmatex">\(O(2^n)\)</span> . Обрати внимание, что входное значение <span class="arithmatex">\(n\)</span> обозначает число раундов деления, а возвращаемое значение <code>count</code> обозначает общее число делений.</p>
+<p>Типичный пример экспоненциального роста в биологии - деление клеток: в начальном состоянии есть одна клетка, после одного деления их становится 2, после двух делений - 4 и так далее; после <span class="arithmatex">\(n\)</span> раундов деления клеток становится <span class="arithmatex">\(2^n\)</span> .</p>
+<p>На рисунке 2-11 и в следующем коде моделируется процесс деления клеток; временная сложность равна <span class="arithmatex">\(O(2^n)\)</span> . Здесь входное значение <span class="arithmatex">\(n\)</span> обозначает число раундов деления, а возвращаемое значение <code>count</code> обозначает общее число делений.</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="10:13"><input checked="checked" id="__tabbed_10_1" name="__tabbed_10" type="radio" /><input id="__tabbed_10_2" name="__tabbed_10" type="radio" /><input id="__tabbed_10_3" name="__tabbed_10" type="radio" /><input id="__tabbed_10_4" name="__tabbed_10" type="radio" /><input id="__tabbed_10_5" name="__tabbed_10" type="radio" /><input id="__tabbed_10_6" name="__tabbed_10" type="radio" /><input id="__tabbed_10_7" name="__tabbed_10" type="radio" /><input id="__tabbed_10_8" name="__tabbed_10" type="radio" /><input id="__tabbed_10_9" name="__tabbed_10" type="radio" /><input id="__tabbed_10_10" name="__tabbed_10" type="radio" /><input id="__tabbed_10_11" name="__tabbed_10" type="radio" /><input id="__tabbed_10_12" name="__tabbed_10" type="radio" /><input id="__tabbed_10_13" name="__tabbed_10" type="radio" /><div class="tabbed-labels"><label for="__tabbed_10_1">Python</label><label for="__tabbed_10_2">C++</label><label for="__tabbed_10_3">Java</label><label for="__tabbed_10_4">C#</label><label for="__tabbed_10_5">Go</label><label for="__tabbed_10_6">Swift</label><label for="__tabbed_10_7">JS</label><label for="__tabbed_10_8">TS</label><label for="__tabbed_10_9">Dart</label><label for="__tabbed_10_10">Rust</label><label for="__tabbed_10_11">C</label><label for="__tabbed_10_12">Kotlin</label><label for="__tabbed_10_13">Ruby</label></div>
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@@ -6954,10 +6954,10 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n \log n) &lt; O(n^2) &lt; O(2^n) &lt; O(n!
 <p><div style="height: 423px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20exp_recur%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%AD%D0%BA%D1%81%D0%BF%D0%BE%D0%BD%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%20%28%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%22%22%22%0A%20%20%20%20if%20n%20%3D%3D%201%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20return%20exp_recur%28n%20-%201%29%20%2B%20exp_recur%28n%20-%201%29%20%2B%201%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%207%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20exp_recur%28n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D1%8D%D0%BA%D1%81%D0%BF%D0%BE%D0%BD%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%28%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%20%3D%22%2C%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20exp_recur%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%AD%D0%BA%D1%81%D0%BF%D0%BE%D0%BD%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%20%28%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%22%22%22%0A%20%20%20%20if%20n%20%3D%3D%201%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20return%20exp_recur%28n%20-%201%29%20%2B%20exp_recur%28n%20-%201%29%20%2B%201%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%207%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20exp_recur%28n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D1%8D%D0%BA%D1%81%D0%BF%D0%BE%D0%BD%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%28%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
-<p>Экспоненциальный рост происходит очень быстро и часто встречается в переборных методах (грубая сила, backtracking и т.д.). Для задач большого масштаба экспоненциальная сложность неприемлема, и обычно приходится применять динамическое программирование, жадные алгоритмы и другие подходы.</p>
+<p>Экспоненциальный рост происходит очень быстро и часто встречается в переборных методах, грубой силе, поиске с возвратом и тому подобных подходах. Для задач большого масштаба экспоненциальная сложность неприемлема, и обычно приходится применять динамическое программирование, жадные алгоритмы и другие стратегии.</p>
 <h3 id="5-olog-n">5. &nbsp; Логарифмическая сложность <span class="arithmatex">\(O(\log n)\)</span><a class="headerlink" href="#5-olog-n" title="Permanent link">&para;</a></h3>
-<p>В противоположность экспоненциальной, логарифмическая сложность описывает ситуацию "каждый раунд уменьшение вдвое". Пусть размер входных данных равен <span class="arithmatex">\(n\)</span> ; так как на каждом шаге размер уменьшается вдвое, число итераций равно <span class="arithmatex">\(\log_2 n\)</span> , то есть является обратной функцией к <span class="arithmatex">\(2^n\)</span> .</p>
-<p>На рисунке 2-12 и в следующем коде моделируется процесс "каждый раунд уменьшение вдвое"; временная сложность равна <span class="arithmatex">\(O(\log_2 n)\)</span> и кратко записывается как <span class="arithmatex">\(O(\log n)\)</span> :</p>
+<p>В противоположность экспоненциальной, логарифмическая сложность описывает ситуацию, когда <strong>в каждом раунде размер задачи уменьшается вдвое</strong>. Пусть размер входных данных равен <span class="arithmatex">\(n\)</span> ; так как на каждом шаге размер уменьшается вдвое, число итераций равно <span class="arithmatex">\(\log_2 n\)</span> , то есть является обратной функцией к <span class="arithmatex">\(2^n\)</span> .</p>
+<p>На рисунке 2-12 и в следующем коде моделируется процесс, в котором <strong>в каждом раунде размер задачи уменьшается вдвое</strong>; временная сложность равна <span class="arithmatex">\(O(\log_2 n)\)</span> и кратко записывается как <span class="arithmatex">\(O(\log n)\)</span> :</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="12:13"><input checked="checked" id="__tabbed_12_1" name="__tabbed_12" type="radio" /><input id="__tabbed_12_2" name="__tabbed_12" type="radio" /><input id="__tabbed_12_3" name="__tabbed_12" type="radio" /><input id="__tabbed_12_4" name="__tabbed_12" type="radio" /><input id="__tabbed_12_5" name="__tabbed_12" type="radio" /><input id="__tabbed_12_6" name="__tabbed_12" type="radio" /><input id="__tabbed_12_7" name="__tabbed_12" type="radio" /><input id="__tabbed_12_8" name="__tabbed_12" type="radio" /><input id="__tabbed_12_9" name="__tabbed_12" type="radio" /><input id="__tabbed_12_10" name="__tabbed_12" type="radio" /><input id="__tabbed_12_11" name="__tabbed_12" type="radio" /><input id="__tabbed_12_12" name="__tabbed_12" type="radio" /><input id="__tabbed_12_13" name="__tabbed_12" type="radio" /><div class="tabbed-labels"><label for="__tabbed_12_1">Python</label><label for="__tabbed_12_2">C++</label><label for="__tabbed_12_3">Java</label><label for="__tabbed_12_4">C#</label><label for="__tabbed_12_5">Go</label><label for="__tabbed_12_6">Swift</label><label for="__tabbed_12_7">JS</label><label for="__tabbed_12_8">TS</label><label for="__tabbed_12_9">Dart</label><label for="__tabbed_12_10">Rust</label><label for="__tabbed_12_11">C</label><label for="__tabbed_12_12">Kotlin</label><label for="__tabbed_12_13">Ruby</label></div>
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@@ -7374,7 +7374,7 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n \log n) &lt; O(n^2) &lt; O(2^n) &lt; O(n!
 <p><div style="height: 423px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20log_recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%9B%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%20%28%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%22%22%22%0A%20%20%20%20if%20n%20%3C%3D%201%3A%0A%20%20%20%20%20%20%20%20return%200%0A%20%20%20%20return%20log_recur%28n%20%2F%202%29%20%2B%201%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20log_recur%28n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%28%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%20%3D%22%2C%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20log_recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%9B%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C%20%28%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%22%22%22%0A%20%20%20%20if%20n%20%3C%3D%201%3A%0A%20%20%20%20%20%20%20%20return%200%0A%20%20%20%20return%20log_recur%28n%20%2F%202%29%20%2B%201%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D1%8B%D1%85%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20count%20%3D%20log_recur%28n%29%0A%20%20%20%20print%28%22%D0%A7%D0%B8%D1%81%D0%BB%D0%BE%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9%20%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%28%D1%80%D0%B5%D0%BA%D1%83%D1%80%D1%81%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%29%20%3D%22%2C%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
-<p>Логарифмическая сложность часто встречается в алгоритмах, основанных на стратегии "разделяй и властвуй", и отражает идеи "разделить одно на много" и "упростить сложное". Она растет медленно и является идеальной временной сложностью, уступающей только постоянной.</p>
+<p>Логарифмическая сложность часто встречается в алгоритмах, основанных на стратегии "разделяй и властвуй", и отражает идеи разбиения на части и упрощения сложной задачи. Она растет медленно и считается одной из самых желательных временных сложностей после константной.</p>
 <div class="admonition tip">
 <p class="admonition-title">Каково основание у <span class="arithmatex">\(O(\log n)\)</span> ?</p>
 <p>Точнее говоря, "разделение на <span class="arithmatex">\(m\)</span> частей" соответствует временной сложности <span class="arithmatex">\(O(\log_m n)\)</span> . А по формуле перехода к другому основанию логарифма мы получаем равные по сложности выражения с разными основаниями:</p>
@@ -7384,7 +7384,7 @@ O(\log_m n) = O(\log_k n / \log_k m) = O(\log_k n)
 <p>Иными словами, основание <span class="arithmatex">\(m\)</span> можно менять без влияния на сложность. Поэтому мы обычно опускаем основание <span class="arithmatex">\(m\)</span> и напрямую записываем логарифмическую сложность как <span class="arithmatex">\(O(\log n)\)</span> .</p>
 </div>
 <h3 id="6-on-log-n">6. &nbsp; Линейно-логарифмическая сложность <span class="arithmatex">\(O(n \log n)\)</span><a class="headerlink" href="#6-on-log-n" title="Permanent link">&para;</a></h3>
-<p>Линейно-логарифмическая сложность часто встречается во вложенных циклах, когда временная сложность двух уровней соответственно равна <span class="arithmatex">\(O(\log n)\)</span> и <span class="arithmatex">\(O(n)\)</span> . Соответствующий код выглядит следующим образом:</p>
+<p>Линейно-логарифмическая сложность часто встречается в рекурсивных разбиениях, где временная сложность одного измерения равна <span class="arithmatex">\(O(\log n)\)</span> , а другого - <span class="arithmatex">\(O(n)\)</span> . Соответствующий код выглядит следующим образом:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="14:13"><input checked="checked" id="__tabbed_14_1" name="__tabbed_14" type="radio" /><input id="__tabbed_14_2" name="__tabbed_14" type="radio" /><input id="__tabbed_14_3" name="__tabbed_14" type="radio" /><input id="__tabbed_14_4" name="__tabbed_14" type="radio" /><input id="__tabbed_14_5" name="__tabbed_14" type="radio" /><input id="__tabbed_14_6" name="__tabbed_14" type="radio" /><input id="__tabbed_14_7" name="__tabbed_14" type="radio" /><input id="__tabbed_14_8" name="__tabbed_14" type="radio" /><input id="__tabbed_14_9" name="__tabbed_14" type="radio" /><input id="__tabbed_14_10" name="__tabbed_14" type="radio" /><input id="__tabbed_14_11" name="__tabbed_14" type="radio" /><input id="__tabbed_14_12" name="__tabbed_14" type="radio" /><input id="__tabbed_14_13" name="__tabbed_14" type="radio" /><div class="tabbed-labels"><label for="__tabbed_14_1">Python</label><label for="__tabbed_14_2">C++</label><label for="__tabbed_14_3">Java</label><label for="__tabbed_14_4">C#</label><label for="__tabbed_14_5">Go</label><label for="__tabbed_14_6">Swift</label><label for="__tabbed_14_7">JS</label><label for="__tabbed_14_8">TS</label><label for="__tabbed_14_9">Dart</label><label for="__tabbed_14_10">Rust</label><label for="__tabbed_14_11">C</label><label for="__tabbed_14_12">Kotlin</label><label for="__tabbed_14_13">Ruby</label></div>
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@@ -7567,11 +7567,11 @@ O(\log_m n) = O(\log_k n / \log_k m) = O(\log_k n)
 
 <p>Временная сложность основных алгоритмов сортировки обычно равна <span class="arithmatex">\(O(n \log n)\)</span> , например у быстрой сортировки, сортировки слиянием, пирамидальной сортировки и т.д.</p>
 <h3 id="7-on">7. &nbsp; Факториальная сложность <span class="arithmatex">\(O(n!)\)</span><a class="headerlink" href="#7-on" title="Permanent link">&para;</a></h3>
-<p>Факториальная сложность соответствует математической задаче "все перестановки". Если даны <span class="arithmatex">\(n\)</span> попарно различных элементов, то число всех возможных перестановок равно:</p>
+<p>Факториальная сложность соответствует математической задаче полной перестановки. Если даны <span class="arithmatex">\(n\)</span> попарно различных элементов, то число всех возможных перестановок равно:</p>
 <div class="arithmatex">\[
 n! = n \times (n - 1) \times (n - 2) \times \dots \times 2 \times 1
 \]</div>
-<p>Факториал обычно реализуют через рекурсию. Как показано на рисунке 2-14 и в следующем коде, на первом уровне происходит ветвление на <span class="arithmatex">\(n\)</span> подзадач, на втором - на <span class="arithmatex">\(n - 1\)</span> и так далее, пока на <span class="arithmatex">\(n\)</span> -м уровне ветвление не прекращается:</p>
+<p>Факториал обычно реализуют через рекурсию. Как показано на рисунке 2-14 и в следующем коде, на первом уровне происходит ветвление на <span class="arithmatex">\(n\)</span> подзадач, на втором - на <span class="arithmatex">\(n - 1\)</span> и так далее, пока на <span class="arithmatex">\(n\)</span>-м уровне ветвление не прекращается:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="15:13"><input checked="checked" id="__tabbed_15_1" name="__tabbed_15" type="radio" /><input id="__tabbed_15_2" name="__tabbed_15" type="radio" /><input id="__tabbed_15_3" name="__tabbed_15" type="radio" /><input id="__tabbed_15_4" name="__tabbed_15" type="radio" /><input id="__tabbed_15_5" name="__tabbed_15" type="radio" /><input id="__tabbed_15_6" name="__tabbed_15" type="radio" /><input id="__tabbed_15_7" name="__tabbed_15" type="radio" /><input id="__tabbed_15_8" name="__tabbed_15" type="radio" /><input id="__tabbed_15_9" name="__tabbed_15" type="radio" /><input id="__tabbed_15_10" name="__tabbed_15" type="radio" /><input id="__tabbed_15_11" name="__tabbed_15" type="radio" /><input id="__tabbed_15_12" name="__tabbed_15" type="radio" /><input id="__tabbed_15_13" name="__tabbed_15" type="radio" /><div class="tabbed-labels"><label for="__tabbed_15_1">Python</label><label for="__tabbed_15_2">C++</label><label for="__tabbed_15_3">Java</label><label for="__tabbed_15_4">C#</label><label for="__tabbed_15_5">Go</label><label for="__tabbed_15_6">Swift</label><label for="__tabbed_15_7">JS</label><label for="__tabbed_15_8">TS</label><label for="__tabbed_15_9">Dart</label><label for="__tabbed_15_10">Rust</label><label for="__tabbed_15_11">C</label><label for="__tabbed_15_12">Kotlin</label><label for="__tabbed_15_13">Ruby</label></div>
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@@ -7771,14 +7771,14 @@ n! = n \times (n - 1) \times (n - 2) \times \dots \times 2 \times 1
 <p><img alt="Факториальная временная сложность" class="animation-figure" src="../time_complexity.assets/time_complexity_factorial.png" /></p>
 <p align="center"> Рисунок 2-14 &nbsp; Факториальная временная сложность </p>
 
-<p>Обрати внимание: поскольку при <span class="arithmatex">\(n \geq 4\)</span> всегда выполняется <span class="arithmatex">\(n! &gt; 2^n\)</span> , факториальная сложность растет еще быстрее, чем экспоненциальная, и при больших <span class="arithmatex">\(n\)</span> также неприемлема.</p>
+<p>Следует отметить, что поскольку при <span class="arithmatex">\(n \geq 4\)</span> всегда выполняется <span class="arithmatex">\(n! &gt; 2^n\)</span> , факториальная сложность растет еще быстрее, чем экспоненциальная, и при больших <span class="arithmatex">\(n\)</span> становится неприемлемой.</p>
 <h2 id="235">2.3.5 &nbsp; Худшая, лучшая и средняя временная сложность<a class="headerlink" href="#235" title="Permanent link">&para;</a></h2>
 <p><strong>Временная эффективность алгоритма часто не фиксирована, а зависит от распределения входных данных</strong>. Предположим, на вход подается массив <code>nums</code> длины <span class="arithmatex">\(n\)</span> , состоящий из чисел от <span class="arithmatex">\(1\)</span> до <span class="arithmatex">\(n\)</span> , каждое из которых встречается ровно один раз; при этом порядок элементов случайно перемешан. Задача состоит в том, чтобы вернуть индекс элемента <span class="arithmatex">\(1\)</span> . Тогда можно сделать следующие выводы.</p>
 <ul>
 <li>Когда <code>nums = [?, ?, ..., 1]</code> , то есть когда последний элемент равен <span class="arithmatex">\(1\)</span> , нужно полностью пройти по массиву, <strong>что дает худшую временную сложность <span class="arithmatex">\(O(n)\)</span></strong> .</li>
 <li>Когда <code>nums = [1, ?, ?, ...]</code> , то есть когда первый элемент равен <span class="arithmatex">\(1\)</span> , независимо от длины массива продолжать обход не нужно, <strong>что дает лучшую временную сложность <span class="arithmatex">\(\Omega(1)\)</span></strong> .</li>
 </ul>
-<p>"Худшая временная сложность" соответствует асимптотической верхней границе функции и обозначается нотацией Big <span class="arithmatex">\(O\)</span> . Соответственно, "лучшая временная сложность" соответствует асимптотической нижней границе функции и обозначается символом <span class="arithmatex">\(\Omega\)</span> :</p>
+<p>Худшая временная сложность соответствует асимптотической верхней границе функции и обозначается нотацией Big <span class="arithmatex">\(O\)</span> . Соответственно, лучшая временная сложность соответствует асимптотической нижней границе функции и обозначается символом <span class="arithmatex">\(\Omega\)</span> :</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="16:13"><input checked="checked" id="__tabbed_16_1" name="__tabbed_16" type="radio" /><input id="__tabbed_16_2" name="__tabbed_16" type="radio" /><input id="__tabbed_16_3" name="__tabbed_16" type="radio" /><input id="__tabbed_16_4" name="__tabbed_16" type="radio" /><input id="__tabbed_16_5" name="__tabbed_16" type="radio" /><input id="__tabbed_16_6" name="__tabbed_16" type="radio" /><input id="__tabbed_16_7" name="__tabbed_16" type="radio" /><input id="__tabbed_16_8" name="__tabbed_16" type="radio" /><input id="__tabbed_16_9" name="__tabbed_16" type="radio" /><input id="__tabbed_16_10" name="__tabbed_16" type="radio" /><input id="__tabbed_16_11" name="__tabbed_16" type="radio" /><input id="__tabbed_16_12" name="__tabbed_16" type="radio" /><input id="__tabbed_16_13" name="__tabbed_16" type="radio" /><div class="tabbed-labels"><label for="__tabbed_16_1">Python</label><label for="__tabbed_16_2">C++</label><label for="__tabbed_16_3">Java</label><label for="__tabbed_16_4">C#</label><label for="__tabbed_16_5">Go</label><label for="__tabbed_16_6">Swift</label><label for="__tabbed_16_7">JS</label><label for="__tabbed_16_8">TS</label><label for="__tabbed_16_9">Dart</label><label for="__tabbed_16_10">Rust</label><label for="__tabbed_16_11">C</label><label for="__tabbed_16_12">Kotlin</label><label for="__tabbed_16_13">Ruby</label></div>
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@@ -8136,10 +8136,10 @@ n! = n \times (n - 1) \times (n - 2) \times \dots \times 2 \times 1
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 </details>
-<p>Стоит отметить, что на практике мы редко используем лучшую временную сложность, поскольку обычно она достигается лишь с очень малой вероятностью и может вводить в заблуждение. <strong>Худшая временная сложность гораздо практичнее, потому что задает безопасную оценку эффективности</strong> и позволяет уверенно использовать алгоритм.</p>
-<p>Из приведенного выше примера видно, что худшая и лучшая временные сложности возникают только при "особых распределениях данных"; вероятность таких случаев может быть низкой, и они не всегда реально отражают эффективность алгоритма. Напротив, <strong>средняя временная сложность способна показать эффективность алгоритма на случайных входных данных</strong> и обозначается символом <span class="arithmatex">\(\Theta\)</span> .</p>
-<p>Для некоторых алгоритмов мы можем относительно просто вывести средний случай при случайном распределении данных. Например, в приведенном выше примере входной массив перемешан, а значит вероятность появления элемента <span class="arithmatex">\(1\)</span> на любом индексе одинакова; следовательно, среднее число итераций алгоритма равно половине длины массива, то есть <span class="arithmatex">\(n / 2\)</span> , а средняя временная сложность равна <span class="arithmatex">\(\Theta(n / 2) = \Theta(n)\)</span> .</p>
-<p>Но для более сложных алгоритмов вычислить среднюю временную сложность часто непросто, потому что трудно проанализировать полное математическое ожидание на заданном распределении данных. В таких случаях мы обычно используем худшую временную сложность как критерий оценки эффективности алгоритма.</p>
+<p>Стоит отметить, что на практике лучшая временная сложность используется редко, поскольку обычно она достигается лишь с очень малой вероятностью и может вводить в заблуждение. <strong>Худшая временная сложность гораздо практичнее, потому что задает безопасную оценку эффективности</strong> и позволяет уверенно использовать алгоритм.</p>
+<p>Из приведенного выше примера видно, что худшая и лучшая временные сложности возникают только при особых распределениях данных; вероятность таких случаев может быть низкой, и они не всегда реально отражают эффективность алгоритма. Напротив, <strong>средняя временная сложность способна показать эффективность алгоритма на случайных входных данных</strong> и обозначается символом <span class="arithmatex">\(\Theta\)</span> .</p>
+<p>Для некоторых алгоритмов можно относительно просто вывести средний случай при случайном распределении данных. Например, в приведенном выше примере входной массив перемешан, а вероятность появления элемента <span class="arithmatex">\(1\)</span> на любом индексе одинакова; следовательно, среднее число итераций алгоритма равно половине длины массива, то есть <span class="arithmatex">\(n / 2\)</span> , а средняя временная сложность равна <span class="arithmatex">\(\Theta(n / 2) = \Theta(n)\)</span> .</p>
+<p>Однако для более сложных алгоритмов вычислить среднюю временную сложность часто непросто, потому что трудно проанализировать полное математическое ожидание на заданном распределении данных. В таких случаях обычно используют худшую временную сложность как критерий оценки эффективности алгоритма.</p>
 <div class="admonition question">
 <p class="admonition-title">Почему символ <span class="arithmatex">\(\Theta\)</span> встречается так редко?</p>
 <p>Возможно, потому что символ <span class="arithmatex">\(O\)</span> звучит слишком привычно, и мы часто используем его для обозначения средней временной сложности. Но строго говоря, это некорректно. В этой книге и в других материалах, если встретится выражение вроде "средняя временная сложность <span class="arithmatex">\(O(n)\)</span>", просто понимай его как <span class="arithmatex">\(\Theta(n)\)</span> .</p>
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+    7.3 Представление двоичного дерева массивом
   
 
     
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-    7.6 Резюме
+    7.6 Краткие итоги
   
 
     
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-    8.3 Задача Top-K
+    8.3 Задача Top-k
   
 
     
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-    Глава 9. Граф
+    Глава 9. Графы
   
 
     
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-    Глава 9. Граф
+    Глава 9. Графы
   
 
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@@ -2308,7 +2308,7 @@
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-    9.2 Базовые операции над графами
+    9.2 Базовые операции графа
   
 
     
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-    9.4 Резюме
+    9.4 Краткие итоги
   
 
     
@@ -2503,7 +2503,7 @@
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-    10.2 Точка вставки двоичного поиска
+    10.2 Двоичный поиск точки вставки
   
 
     
@@ -2531,7 +2531,7 @@
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-    10.3 Граничные случаи двоичного поиска
+    10.3 Двоичный поиск границ
   
 
     
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-    10.4 Стратегия оптимизации через хеширование
+    10.4 Стратегии оптимизации хеширования
   
 
     
@@ -2587,7 +2587,7 @@
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-    10.5 Алгоритмы поиска: новый взгляд
+    10.5 Переосмысление алгоритмов поиска
   
 
     
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-    11.3 Пузырьковая сортировка
+    11.3 Сортировка пузырьком
   
 
     
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-    11.4 Сортировка вставкой
+    11.4 Сортировка вставками
   
 
     
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-    12.1 Алгоритмы разделяй и властвуй
+    12.1 Стратегия разделяй и властвуй
   
 
     
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-    12.2 Стратегия поиска разделяй и властвуй
+    12.2 Поисковая стратегия разделяй и властвуй
   
 
     
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-    13.4 Задача о $n$ ферзях
+    13.4 Задача о n ферзях
   
 
     
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-    14.1 Введение в динамическое программирование
+    14.1 Первое знакомство с динамическим программированием
   
 
     
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-    14.5 Задача о неограниченном рюкзаке
+    14.5 Задача о полном рюкзаке
   
 
     
@@ -4265,21 +4265,21 @@
 
 <!-- Page content -->
 <h1 id="32">3.2 &nbsp; Базовые типы данных<a class="headerlink" href="#32" title="Permanent link">&para;</a></h1>
-<p>Когда мы говорим о данных в компьютере, нам приходят на ум текст, изображения, видео, звук, 3D-модели и многие другие формы. Хотя эти данные организованы по-разному, все они состоят из различных базовых типов данных.</p>
-<p><strong>Базовые типы данных - это типы, с которыми CPU может работать напрямую</strong>; в алгоритмах они используются непосредственно и в основном включают следующее.</p>
+<p>Когда речь заходит о данных в компьютере, мы в первую очередь вспоминаем текст, изображения, видео, звук, 3D-модели и многие другие формы представления информации. Хотя способы организации этих данных различаются, все они строятся из базовых типов данных.</p>
+<p><strong>Базовые типы данных - это типы, которые процессор может обрабатывать непосредственно</strong>. В алгоритмах они используются напрямую и в основном включают следующее.</p>
 <ul>
 <li>Целочисленные типы <code>byte</code> , <code>short</code> , <code>int</code> , <code>long</code> .</li>
 <li>Типы с плавающей точкой <code>float</code> , <code>double</code> , используемые для представления дробных чисел.</li>
 <li>Символьный тип <code>char</code> , используемый для представления букв, знаков препинания и даже эмодзи в разных языках.</li>
 <li>Логический тип <code>bool</code> , используемый для представления суждений "да" и "нет".</li>
 </ul>
-<p><strong>Базовые типы данных хранятся в компьютере в двоичной форме</strong>. Один двоичный разряд равен <span class="arithmatex">\(1\)</span> биту. В подавляющем большинстве современных операционных систем <span class="arithmatex">\(1\)</span> байт (byte) состоит из <span class="arithmatex">\(8\)</span> битов (bit).</p>
+<p><strong>Базовые типы данных хранятся в компьютере в двоичной форме</strong>. Один двоичный разряд равен <span class="arithmatex">\(1\)</span> биту. В большинстве современных операционных систем <span class="arithmatex">\(1\)</span> байт (byte) состоит из <span class="arithmatex">\(8\)</span> битов (bit).</p>
 <p>Диапазон значений базовых типов данных зависит от объема занимаемого ими пространства. Ниже в качестве примера используется Java.</p>
 <ul>
 <li>Целочисленный тип <code>byte</code> занимает <span class="arithmatex">\(1\)</span> байт = <span class="arithmatex">\(8\)</span> бит и может представлять <span class="arithmatex">\(2^{8}\)</span> чисел.</li>
 <li>Целочисленный тип <code>int</code> занимает <span class="arithmatex">\(4\)</span> байта = <span class="arithmatex">\(32\)</span> бита и может представлять <span class="arithmatex">\(2^{32}\)</span> чисел.</li>
 </ul>
-<p>В таблице 3-1 перечислены объем памяти, диапазон значений и значения по умолчанию для различных базовых типов данных в Java. Заучивать эту таблицу наизусть не нужно; достаточно иметь общее представление и при необходимости обращаться к ней.</p>
+<p>В таблице 3-1 перечислены объем памяти, диапазон значений и значения по умолчанию для различных базовых типов данных в Java. Эту таблицу не нужно заучивать наизусть; достаточно иметь общее представление и при необходимости обращаться к ней.</p>
 <p align="center"> Таблица 3-1 &nbsp; Объем памяти и диапазоны значений базовых типов данных </p>
 
 <div class="center-table">
@@ -4362,31 +4362,31 @@
 </tbody>
 </table>
 </div>
-<p>Обрати внимание: приведенная выше таблица относится именно к базовым типам данных Java. В каждом языке программирования определения типов свои, поэтому объем памяти, диапазон значений и значения по умолчанию могут различаться.</p>
+<p>Обрати внимание: приведенная выше таблица относится именно к базовым типам данных Java. В каждом языке программирования свои определения типов, поэтому объем памяти, диапазон значений и значения по умолчанию могут различаться.</p>
 <ul>
-<li>В Python целочисленный тип <code>int</code> может иметь произвольный размер, ограниченный только доступной памятью; тип <code>float</code> использует двойную точность 64 бита; типа <code>char</code> нет, а одиночный символ на деле является строкой <code>str</code> длины 1.</li>
-<li>В C и C++ размер базовых типов данных явно не зафиксирован и зависит от реализации и платформы. таблица 3-1 соответствует модели данных LP64 <a href="https://en.cppreference.com/w/cpp/language/types#Properties">data model</a>, применяемой в 64-битных Unix-системах, включая Linux и macOS.</li>
+<li>В Python целочисленный тип <code>int</code> может иметь произвольный размер, ограниченный только доступной памятью; тип <code>float</code> является 64-битным числом двойной точности; типа <code>char</code> нет, а отдельный символ на деле является строкой <code>str</code> длины 1.</li>
+<li>В C и C++ размер базовых типов данных явно не зафиксирован и зависит от реализации и платформы. таблица 3-1 соответствует модели данных LP64 <a href="https://en.cppreference.com/w/cpp/language/types#Properties">data model</a>, используемой в 64-битных Unix-системах, включая Linux и macOS.</li>
 <li>Размер символа <code>char</code> в C и C++ составляет 1 байт, а в большинстве других языков программирования зависит от конкретного способа кодирования символов; подробнее это рассматривается в разделе "Кодирование символов".</li>
 <li>Хотя для представления логического значения достаточно 1 бита ( <span class="arithmatex">\(0\)</span> или <span class="arithmatex">\(1\)</span> ), в памяти оно обычно хранится как 1 байт. Это связано с тем, что современные CPU обычно используют 1 байт как минимальную адресуемую единицу памяти.</li>
 </ul>
-<p>Какова же связь между базовыми типами данных и структурами данных? Мы знаем, что структуры данных - это способы организации и хранения данных в компьютере. Подлежащее в этой фразе - "структура", а не "данные".</p>
-<p>Если мы хотим представить "ряд чисел", то естественно подумаем об использовании массива. Это связано с тем, что линейная структура массива может выразить отношения соседства и порядка между числами, а вот то, что именно хранится внутри - целые <code>int</code> , вещественные <code>float</code> или символы <code>char</code> , - к "структуре данных" отношения не имеет.</p>
+<p>Какова же связь между базовыми типами данных и структурами данных? Мы знаем, что структура данных - это способ организации и хранения данных в компьютере. Подлежащее в этой фразе - "структура", а не "данные".</p>
+<p>Если мы хотим представить "ряд чисел", то естественно подумаем об использовании массива. Это связано с тем, что линейная структура массива может выразить отношения соседства и порядка между числами, а то, что именно хранится внутри - целые <code>int</code> , вещественные <code>float</code> или символы <code>char</code> , - к "структуре данных" отношения не имеет.</p>
 <p>Иными словами, <strong>базовые типы данных задают "тип содержимого" данных, а структуры данных задают "способ организации" данных</strong>. Например, в следующем коде мы используем одну и ту же структуру данных (массив) для хранения и представления различных базовых типов данных, включая <code>int</code> , <code>float</code> , <code>char</code> , <code>bool</code> и т.д.</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># Инициализируем массивы с использованием разных базовых типов данных</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># Инициализируем массивы с использованием различных базовых типов данных</span>
 <a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="n">numbers</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">5</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="n">decimals</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">float</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">5</span>
-<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="c1"># В Python символы на деле являются строками длины 1</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="c1"># В Python символы фактически являются строками длины 1</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="n">characters</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">str</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;0&#39;</span><span class="p">]</span> <span class="o">*</span> <span class="mi">5</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="n">bools</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">bool</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="kc">False</span><span class="p">]</span> <span class="o">*</span> <span class="mi">5</span>
-<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="c1"># Списки Python могут свободно хранить разные базовые типы данных и ссылки на объекты</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="c1"># Списки Python могут свободно хранить различные базовые типы данных и ссылки на объекты</span>
 <a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="n">data</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="s1">&#39;a&#39;</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="n">ListNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)]</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="c1">// Инициализируем массивы с использованием разных базовых типов данных</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="c1">// Инициализируем массивы с использованием различных базовых типов данных</span>
 <a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">numbers</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="kt">float</span><span class="w"> </span><span class="n">decimals</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
 <a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="kt">char</span><span class="w"> </span><span class="n">characters</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
@@ -4394,7 +4394,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="c1">// Инициализируем массивы с использованием разных базовых типов данных</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="c1">// Инициализируем массивы с использованием различных базовых типов данных</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">numbers</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="mi">5</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="kt">float</span><span class="o">[]</span><span class="w"> </span><span class="n">decimals</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">float</span><span class="o">[</span><span class="mi">5</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="kt">char</span><span class="o">[]</span><span class="w"> </span><span class="n">characters</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">char</span><span class="o">[</span><span class="mi">5</span><span class="o">]</span><span class="p">;</span>
@@ -4402,7 +4402,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="c1">// Инициализируем массивы с использованием разных базовых типов данных</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="c1">// Инициализируем массивы с использованием различных базовых типов данных</span>
 <a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">numbers</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
 <a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="kt">float</span><span class="p">[]</span><span class="w"> </span><span class="n">decimals</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">float</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
 <a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="kt">char</span><span class="p">[]</span><span class="w"> </span><span class="n">characters</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">char</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
@@ -4410,7 +4410,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="c1">// Инициализируем массивы с использованием разных базовых типов данных</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="c1">// Инициализируем массивы с использованием различных базовых типов данных</span>
 <a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">var</span><span class="w"> </span><span class="nx">numbers</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="kt">int</span><span class="p">{}</span>
 <a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="kd">var</span><span class="w"> </span><span class="nx">decimals</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="kt">float64</span><span class="p">{}</span>
 <a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="kd">var</span><span class="w"> </span><span class="nx">characters</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="kt">byte</span><span class="p">{}</span>
@@ -4418,7 +4418,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="c1">// Инициализируем массивы с использованием разных базовых типов данных</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="c1">// Инициализируем массивы с использованием различных базовых типов данных</span>
 <a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">let</span><span class="w"> </span><span class="nv">numbers</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span>
 <a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">let</span><span class="w"> </span><span class="nv">decimals</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mf">0.0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span>
 <a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="kd">let</span><span class="w"> </span><span class="nv">characters</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Character</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="s">&quot;a&quot;</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span>
@@ -4426,19 +4426,19 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="c1">// Массивы JavaScript могут свободно хранить разные базовые типы данных и объекты</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="c1">// Массивы JavaScript могут свободно хранить различные базовые типы данных и объекты</span>
 <a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">array</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="mf">0.0</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;a&#39;</span><span class="p">,</span><span class="w"> </span><span class="kc">false</span><span class="p">];</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="c1">// Инициализируем массивы с использованием разных базовых типов данных</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="c1">// Инициализируем массивы с использованием различных базовых типов данных</span>
 <a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">numbers</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
 <a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="kd">const</span><span class="w"> </span><span class="nx">characters</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
 <a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="kd">const</span><span class="w"> </span><span class="nx">bools</span><span class="o">:</span><span class="w"> </span><span class="kt">boolean</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="c1">// Инициализируем массивы с использованием разных базовых типов данных</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="c1">// Инициализируем массивы с использованием различных базовых типов данных</span>
 <a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">numbers</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
 <a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">double</span><span class="o">&gt;</span><span class="w"> </span><span class="n">decimals</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="m">0.0</span><span class="p">);</span>
 <a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">characters</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;a&#39;</span><span class="p">);</span>
@@ -4446,7 +4446,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="c1">// Инициализируем массивы с использованием разных базовых типов данных</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="c1">// Инициализируем массивы с использованием различных базовых типов данных</span>
 <a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="kd">let</span><span class="w"> </span><span class="n">numbers</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="mi">5</span><span class="p">];</span>
 <a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="kd">let</span><span class="w"> </span><span class="n">decimals</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">f32</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mf">0.0</span><span class="p">;</span><span class="w"> </span><span class="mi">5</span><span class="p">];</span>
 <a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="kd">let</span><span class="w"> </span><span class="n">characters</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">char</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="sc">&#39;0&#39;</span><span class="p">;</span><span class="w"> </span><span class="mi">5</span><span class="p">];</span>
@@ -4454,7 +4454,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// Инициализируем массивы с использованием разных базовых типов данных</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// Инициализируем массивы с использованием различных базовых типов данных</span>
 <a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">numbers</span><span class="p">[</span><span class="mi">10</span><span class="p">];</span>
 <a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="kt">float</span><span class="w"> </span><span class="n">decimals</span><span class="p">[</span><span class="mi">10</span><span class="p">];</span>
 <a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="kt">char</span><span class="w"> </span><span class="n">characters</span><span class="p">[</span><span class="mi">10</span><span class="p">];</span>
@@ -4462,7 +4462,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="c1">// Инициализируем массивы с использованием разных базовых типов данных</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="c1">// Инициализируем массивы с использованием различных базовых типов данных</span>
 <a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">val</span><span class="w"> </span><span class="nv">numbers</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="m">5</span><span class="p">)</span>
 <a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="kd">val</span><span class="w"> </span><span class="nv">decinals</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">FloatArray</span><span class="p">(</span><span class="m">5</span><span class="p">)</span>
 <a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="kd">val</span><span class="w"> </span><span class="nv">characters</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">CharArray</span><span class="p">(</span><span class="m">5</span><span class="p">)</span>
@@ -4470,7 +4470,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1"># Списки Ruby могут свободно хранить разные базовые типы данных и ссылки на объекты</span>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1"># Списки Ruby могут свободно хранить различные базовые типы данных и ссылки на объекты</span>
 <a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="n">data</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="o">.</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;a&#39;</span><span class="p">,</span><span class="w"> </span><span class="kp">false</span><span class="p">,</span><span class="w"> </span><span class="no">ListNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="o">]</span>
 </code></pre></div>
 </div>
diff --git a/ru/chapter_data_structure/character_encoding/index.html b/ru/chapter_data_structure/character_encoding/index.html
index f01c5a15b..f88c39af1 100644
--- a/ru/chapter_data_structure/character_encoding/index.html
+++ b/ru/chapter_data_structure/character_encoding/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
@@ -574,7 +574,7 @@
   <span class="md-ellipsis">
     
   
-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
     
@@ -596,7 +596,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
           </label>
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 Что такое структуры данных и алгоритмы
+    1.2 Что такое алгоритм
   
 
     
@@ -1147,7 +1147,7 @@
   <a href="#341-ascii" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3.4.1 &nbsp; Набор символов ASCII
+        3.4.1 &nbsp; Таблица символов ASCII
       
     </span>
   </a>
@@ -1158,7 +1158,7 @@
   <a href="#342-gbk" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3.4.2 &nbsp; Набор символов GBK
+        3.4.2 &nbsp; Таблица символов GBK
       
     </span>
   </a>
@@ -1169,7 +1169,7 @@
   <a href="#343-unicode" class="md-nav__link">
     <span class="md-ellipsis">
       
-        3.4.3 &nbsp; Набор символов Unicode
+        3.4.3 &nbsp; Таблица символов Unicode
       
     </span>
   </a>
@@ -1286,7 +1286,7 @@
   <span class="md-ellipsis">
     
   
-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
     
@@ -1308,7 +1308,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
           </label>
@@ -1414,7 +1414,7 @@
   <span class="md-ellipsis">
     
   
-    4.4 Память и кеш *
+    4.4 Оперативная память и кэш *
   
 
     
@@ -1696,7 +1696,7 @@
   <span class="md-ellipsis">
     
   
-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
     
@@ -1718,7 +1718,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
           </label>
@@ -1796,7 +1796,7 @@
   <span class="md-ellipsis">
     
   
-    6.3 Хеш-алгоритмы
+    6.3 Алгоритмы хеширования
   
 
     
@@ -1891,7 +1891,7 @@
   <span class="md-ellipsis">
     
   
-    Глава 7. Дерево
+    Глава 7. Деревья
   
 
     
@@ -1913,7 +1913,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 7. Дерево
+    Глава 7. Деревья
   
 
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+    7.3 Представление двоичного дерева массивом
   
 
     
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-    7.6 Резюме
+    7.6 Краткие итоги
   
 
     
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+    8.3 Задача Top-k
   
 
     
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+    Глава 9. Графы
   
 
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+    9.4 Краткие итоги
   
 
     
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-    10.2 Точка вставки двоичного поиска
+    10.2 Двоичный поиск точки вставки
   
 
     
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+    10.3 Двоичный поиск границ
   
 
     
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-    10.4 Стратегия оптимизации через хеширование
+    10.4 Стратегии оптимизации хеширования
   
 
     
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-    10.5 Алгоритмы поиска: новый взгляд
+    10.5 Переосмысление алгоритмов поиска
   
 
     
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+    12.1 Стратегия разделяй и властвуй
   
 
     
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+    14.1 Первое знакомство с динамическим программированием
   
 
     
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-        3.4.1 &nbsp; Набор символов ASCII
+        3.4.1 &nbsp; Таблица символов ASCII
       
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-        3.4.3 &nbsp; Набор символов Unicode
+        3.4.3 &nbsp; Таблица символов Unicode
       
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 <!-- Page content -->
 <h1 id="34">3.4 &nbsp; Кодирование символов *<a class="headerlink" href="#34" title="Permanent link">&para;</a></h1>
-<p>В компьютере все данные хранятся в двоичной форме, и символ <code>char</code> не является исключением. Чтобы представлять символы, нам нужно определить "набор символов", задающий взаимно-однозначное соответствие между каждым символом и двоичным числом. Имея такой набор, компьютер может преобразовывать двоичные числа в символы простым поиском по таблице.</p>
-<h2 id="341-ascii">3.4.1 &nbsp; Набор символов ASCII<a class="headerlink" href="#341-ascii" title="Permanent link">&para;</a></h2>
-<p><u>Код ASCII</u> - это самый ранний набор символов; его полное название - American Standard Code for Information Interchange (американский стандартный код обмена информацией). Он использует 7 двоичных битов (нижние 7 битов одного байта) для представления одного символа и способен представлять не более 128 различных символов. Как показано на рисунке 3-6, ASCII включает заглавные и строчные английские буквы, цифры 0 ~ 9, некоторые знаки препинания и некоторые управляющие символы (например перевод строки и табуляцию).</p>
+<p>В компьютере все данные хранятся в виде двоичных чисел, и символьный тип данных <code>char</code> не является исключением. Для представления символов необходимо задать "таблицу символов", которая устанавливает взаимно-однозначное соответствие между каждым символом и двоичным числом. С помощью этой таблицы компьютер может преобразовывать двоичные числа в символы.</p>
+<h2 id="341-ascii">3.4.1 &nbsp; Таблица символов ASCII<a class="headerlink" href="#341-ascii" title="Permanent link">&para;</a></h2>
+<p><u>Код ASCII</u> - это самая ранняя таблица символов; ее полное название - American Standard Code for Information Interchange (американский стандартный код обмена информацией). Для представления символов в ней используются 7 двоичных битов (нижние 7 битов одного байта), что позволяет закодировать до 128 различных символов. Как показано на рисунке 3-6, ASCII включает заглавные и строчные буквы английского алфавита, цифры 0 ~ 9, некоторые знаки препинания, а также некоторые управляющие символы (например перевод строки и табуляцию).</p>
 <p><img alt="Таблица ASCII" class="animation-figure" src="../character_encoding.assets/ascii_table.png" /></p>
 <p align="center"> Рисунок 3-6 &nbsp; Таблица ASCII </p>
 
-<p>Однако <strong>код ASCII может представлять только английский язык</strong>. С глобализацией компьютерных технологий появился набор символов <u>EASCII</u>, способный покрывать больше языков. Он расширяет 7-битную основу ASCII до 8 битов и может представлять 256 различных символов.</p>
-<p>Во всем мире постепенно появились разные наборы EASCII, подходящие для разных регионов. Первые 128 символов в этих наборах одинаковы и соответствуют ASCII, а последние 128 символов определяются по-разному, чтобы удовлетворять потребностям разных языков.</p>
-<h2 id="342-gbk">3.4.2 &nbsp; Набор символов GBK<a class="headerlink" href="#342-gbk" title="Permanent link">&para;</a></h2>
-<p>Позже люди обнаружили, что <strong>кода EASCII все равно недостаточно для количества символов во многих языках</strong>. Например, китайских иероглифов существует почти сто тысяч, а в повседневном использовании нужны тысячи. В 1980 году Государственное управление стандартов Китая выпустило набор символов <u>GB2312</u>, включающий 6763 иероглифа, что в основном удовлетворило потребности компьютерной обработки китайского текста.</p>
-<p>Однако GB2312 не умеет работать с некоторыми редкими иероглифами и традиционными формами письма. Набор символов <u>GBK</u> - это расширение GB2312, содержащее в общей сложности 21886 иероглифов. В схеме кодирования GBK символы ASCII представляются одним байтом, а китайские иероглифы - двумя байтами.</p>
-<h2 id="343-unicode">3.4.3 &nbsp; Набор символов Unicode<a class="headerlink" href="#343-unicode" title="Permanent link">&para;</a></h2>
-<p>С бурным развитием компьютерной техники наборы символов и стандарты кодирования начали стремительно множиться, и это породило множество проблем. С одной стороны, такие наборы обычно определяли символы только для конкретных языков и не могли нормально работать в многоязычной среде. С другой стороны, для одного и того же языка существовало несколько стандартов кодирования; если две машины использовали разные стандарты, при обмене информацией возникали кракозябры.</p>
-<p>Исследователи той эпохи задумались: <strong>если создать достаточно полный набор символов, который включит все языки и знаки мира, разве это не решит проблемы межъязыковой среды и искаженного текста</strong>? Под влиянием этой идеи и появился большой и всеобъемлющий набор символов Unicode.</p>
-<p><u>Unicode</u> по-китайски называется "единый код" и теоретически способен вместить более миллиона символов. Его цель - собрать символы со всего мира в единый набор символов, предоставить универсальный стандарт для обработки и отображения текстов на разных языках и уменьшить количество проблем с искажением текста, вызванных различиями стандартов кодирования.</p>
-<p>С момента публикации в 1991 году Unicode непрерывно расширялся, добавляя новые языки и символы. По состоянию на сентябрь 2022 года Unicode уже включал 149186 символов, в том числе буквы разных языков, знаки, а также эмодзи. В огромном наборе символов Unicode часто используемые символы занимают 2 байта, а некоторые редкие символы - 3 байта и даже 4 байта.</p>
+<p>Однако <strong>код ASCII может представлять только английский язык</strong>. С развитием компьютерных технологий появилась таблица символов <u>EASCII</u>, способная охватывать больше языков. Она расширяет 7-битную основу ASCII до 8 битов и может представлять 256 различных символов.</p>
+<p>Во всем мире постепенно появились разные таблицы EASCII, подходящие для разных регионов. Первые 128 символов в этих таблицах одинаковы и соответствуют ASCII, а последние 128 символов определяются по-разному, чтобы удовлетворять потребностям разных языков.</p>
+<h2 id="342-gbk">3.4.2 &nbsp; Таблица символов GBK<a class="headerlink" href="#342-gbk" title="Permanent link">&para;</a></h2>
+<p>Позже люди обнаружили, что <strong>кодов EASCII все равно недостаточно для количества символов во многих языках</strong>. Например, китайских иероглифов существует почти сто тысяч, а в повседневном употреблении нужны тысячи. В 1980 году Государственное управление стандартов Китая выпустило таблицу символов <u>GB2312</u>, включающую 6763 иероглифа, что в основном удовлетворило потребности компьютерной обработки китайского текста.</p>
+<p>Однако GB2312 не умеет работать с некоторыми редкими иероглифами и традиционными формами письма. Таблица символов <u>GBK</u> представляет собой расширение GB2312 и в общей сложности содержит 21886 иероглифов. В схеме кодирования GBK символы ASCII представляются одним байтом, а китайские иероглифы - двумя байтами.</p>
+<h2 id="343-unicode">3.4.3 &nbsp; Таблица символов Unicode<a class="headerlink" href="#343-unicode" title="Permanent link">&para;</a></h2>
+<p>С бурным развитием компьютерной техники таблицы символов и стандарты кодирования начали стремительно множиться, и это породило множество проблем. С одной стороны, такие таблицы обычно определяли символы только для конкретных языков и не могли нормально работать в многоязычной среде. С другой стороны, для одного и того же языка существовало несколько стандартов кодирования; если две машины использовали разные стандарты, при обмене информацией возникали искажения текста.</p>
+<p>Исследователи той эпохи задумались: <strong>если создать достаточно полную таблицу символов, которая включит все языки и знаки мира, разве это не решит проблемы многоязычной среды и искаженного текста</strong>? Под влиянием этой идеи и появилась большая и всеобъемлющая таблица символов Unicode.</p>
+<p><u>Unicode</u> по-китайски называется "единый код" и теоретически способен вместить более миллиона символов. Его цель - собрать символы со всего мира в единую таблицу символов, предоставить универсальный стандарт для обработки и отображения текстов на разных языках и уменьшить количество проблем с искажением текста, вызванных различиями стандартов кодирования.</p>
+<p>С момента публикации в 1991 году Unicode непрерывно расширялся, добавляя новые языки и символы. По состоянию на сентябрь 2022 года Unicode уже включал 149186 символов, в том числе буквы разных языков, знаки, а также эмодзи. В огромной таблице символов Unicode часто используемые символы занимают 2 байта, а некоторые редкие символы - 3 байта и даже 4 байта.</p>
 <p>Unicode - это универсальный набор символов, который по сути просто присваивает каждому символу номер (так называемую "кодовую точку"), <strong>но не определяет, как именно хранить эти кодовые точки в компьютере</strong>. Тут неизбежно возникает вопрос: если в одном тексте одновременно встречаются кодовые точки Unicode разной длины, как система должна разбирать символы? Например, если дан код длиной 2 байта, как понять, является ли это одним 2-байтовым символом или двумя 1-байтовыми?</p>
 <p>Для этой проблемы <strong>прямолинейное решение состоит в том, чтобы хранить все символы в кодировке одинаковой длины</strong>. Как показано на рисунке 3-7, каждый символ в "Hello" занимает 1 байт, а каждый символ в "алгоритм" занимает 2 байта. Мы можем дополнить старшие биты нулями и закодировать все символы в "Hello алгоритм" в виде 2-байтовых единиц. Тогда система сможет считывать по одному символу каждые 2 байта и восстановить эту фразу.</p>
 <p><img alt="Пример кодирования Unicode" class="animation-figure" src="../character_encoding.assets/unicode_hello_algo.png" /></p>
diff --git a/ru/chapter_data_structure/classification_of_data_structure/index.html b/ru/chapter_data_structure/classification_of_data_structure/index.html
index f66a0fcd9..02a78a330 100644
--- a/ru/chapter_data_structure/classification_of_data_structure/index.html
+++ b/ru/chapter_data_structure/classification_of_data_structure/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
@@ -574,7 +574,7 @@
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-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
     
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+    Глава 1. Введение в алгоритмы
   
 
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@@ -646,7 +646,7 @@
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-    1.2 Что такое структуры данных и алгоритмы
+    1.2 Что такое алгоритм
   
 
     
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-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
     
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+    Глава 4. Массивы и списки
   
 
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+    4.4 Оперативная память и кэш *
   
 
     
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+    Глава 6. Хеш-таблицы
   
 
     
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+    Глава 6. Хеш-таблицы
   
 
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+    6.3 Алгоритмы хеширования
   
 
     
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+    Глава 9. Графы
   
 
     
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@@ -4355,25 +4355,25 @@
 
 <!-- Page content -->
 <h1 id="31">3.1 &nbsp; Классификация структур данных<a class="headerlink" href="#31" title="Permanent link">&para;</a></h1>
-<p>К распространенным структурам данных относятся массивы, связные списки, стеки, очереди, хеш-таблицы, деревья, кучи и графы; их можно классифицировать по двум измерениям: "логическая структура" и "физическая структура".</p>
+<p>К распространенным структурам данных относятся массивы, связные списки, стеки, очереди, хеш-таблицы, деревья, кучи и графы. Их можно классифицировать по двум измерениям: логической структуре и физической структуре.</p>
 <h2 id="311">3.1.1 &nbsp; Логическая структура: линейная и нелинейная<a class="headerlink" href="#311" title="Permanent link">&para;</a></h2>
-<p><strong>Логическая структура раскрывает логические связи между элементами данных</strong>. В массивах и связных списках данные располагаются в определенном порядке, отражая линейные отношения между элементами; в деревьях данные иерархически располагаются сверху вниз, проявляя производные отношения между "предками" и "потомками"; графы состоят из вершин и ребер и отражают сложные сетевые связи.</p>
-<p>Как показано на рисунке 3-1, логические структуры можно разделить на два больших класса: "линейные" и "нелинейные". Линейные структуры более интуитивны и означают, что данные логически выстроены в линию; нелинейные структуры, напротив, располагаются нелинейно.</p>
+<p><strong>Логическая структура раскрывает логические отношения между элементами данных</strong>. В массивах и связных списках данные расположены в определенном порядке, что отражает линейные отношения между элементами. В деревьях данные расположены по уровням сверху вниз, что демонстрирует отношения "предок" и "потомок". Графы состоят из вершин и ребер, отражая сложные сетевые отношения.</p>
+<p>Как показано на рисунке 3-1, логические структуры делятся на две большие категории: линейные и нелинейные. Линейные структуры более интуитивны, поскольку в них данные расположены линейно и логически связаны. Нелинейные структуры, напротив, представляют собой нелинейное расположение элементов данных.</p>
 <ul>
-<li><strong>Линейные структуры данных</strong>: массивы, связные списки, стеки, очереди, хеш-таблицы; между элементами существует отношение "один к одному".</li>
+<li><strong>Линейные структуры данных</strong>: массивы, связные списки, стеки, очереди, хеш-таблицы, в которых элементы связаны отношением "один к одному".</li>
 <li><strong>Нелинейные структуры данных</strong>: деревья, кучи, графы, хеш-таблицы.</li>
 </ul>
 <p>Нелинейные структуры данных можно дополнительно разделить на древовидные и сетевые.</p>
 <ul>
-<li><strong>Древовидные структуры</strong>: деревья, кучи, хеш-таблицы; между элементами существует отношение "один ко многим".</li>
-<li><strong>Сетевые структуры</strong>: графы; между элементами существует отношение "многие ко многим".</li>
+<li><strong>Древовидные структуры</strong>: деревья, кучи, хеш-таблицы, в которых элементы связаны отношением "один ко многим".</li>
+<li><strong>Сетевые структуры</strong>: графы, в которых элементы связаны отношением "многие ко многим".</li>
 </ul>
 <p><img alt="Линейные и нелинейные структуры данных" class="animation-figure" src="../classification_of_data_structure.assets/classification_logic_structure.png" /></p>
 <p align="center"> Рисунок 3-1 &nbsp; Линейные и нелинейные структуры данных </p>
 
 <h2 id="312">3.1.2 &nbsp; Физическая структура: непрерывная и разрозненная<a class="headerlink" href="#312" title="Permanent link">&para;</a></h2>
-<p><strong>Во время выполнения алгоритма обрабатываемые данные в основном хранятся в памяти</strong>. На рисунке 3-2 показана планка памяти компьютера, где каждый черный блок содержит некоторый участок памяти. Мы можем представить память как огромную таблицу Excel, в которой каждая ячейка способна хранить данные определенного размера.</p>
-<p><strong>Система обращается к данным по адресу памяти соответствующей позиции</strong>. Как показано на рисунке 3-2, компьютер по определенному правилу присваивает каждой ячейке в этой таблице номер, чтобы у каждого участка памяти был уникальный адрес. Имея эти адреса, программа может получать доступ к данным, находящимся в памяти.</p>
+<p><strong>Во время выполнения программы обрабатываемые данные в основном хранятся в памяти</strong>. На рисунке 3-2 показан модуль оперативной памяти компьютера, где каждый черный блок содержит определенный участок памяти. Память можно представить как огромную таблицу Excel, в которой каждая ячейка способна хранить данные определенного размера.</p>
+<p><strong>Система обращается к данным по адресам памяти соответствующих позиций</strong>. Как показано на рисунке 3-2, компьютер по определенным правилам присваивает каждой ячейке в этой таблице номер, чтобы каждый участок памяти имел уникальный адрес. Благодаря этим адресам программа получает доступ к данным, находящимся в памяти.</p>
 <p><img alt="Планка памяти, участок памяти и адрес памяти" class="animation-figure" src="../classification_of_data_structure.assets/computer_memory_location.png" /></p>
 <p align="center"> Рисунок 3-2 &nbsp; Планка памяти, участок памяти и адрес памяти </p>
 
@@ -4381,17 +4381,17 @@
 <p class="admonition-title">Tip</p>
 <p>Стоит отметить, что сравнение памяти с таблицей Excel - это упрощенная аналогия; реальный механизм работы памяти гораздо сложнее и включает такие понятия, как адресное пространство, управление памятью, кэш-механизмы, виртуальная и физическая память.</p>
 </div>
-<p>Память - общий ресурс для всех программ. Когда некоторый участок памяти занят одной программой, другие программы обычно не могут использовать его одновременно. <strong>Поэтому при проектировании структур данных и алгоритмов память является важным фактором</strong>. Например, пиковое потребление памяти алгоритмом не должно превышать доступную свободную память системы; если непрерывного крупного блока памяти недостаточно, выбранная структура данных должна уметь храниться в разрозненных областях памяти.</p>
-<p>Как показано на рисунке 3-3, <strong>физическая структура отражает способ хранения данных в памяти компьютера</strong>; ее можно разделить на хранение в непрерывном пространстве (массивы) и хранение в разрозненном пространстве (связные списки). Физическая структура на нижнем уровне определяет способы доступа к данным, их обновления, вставки и удаления; эти два типа физических структур взаимно дополняют друг друга по временной и пространственной эффективности.</p>
+<p>Память - общий ресурс для всех программ. Когда некоторый участок памяти занят одной программой, другие программы обычно не могут использовать его одновременно. <strong>Поэтому при проектировании структур данных и алгоритмов память занимает важное место</strong>. Например, пиковое потребление памяти алгоритмом не должно превышать объем доступной свободной памяти системы; если не хватает непрерывных крупных участков памяти, выбранная структура данных должна уметь размещаться в разрозненных областях памяти.</p>
+<p>Как показано на рисунке 3-3, <strong>физическая структура отражает способ хранения данных в памяти компьютера</strong>. Ее можно разделить на хранение в непрерывном пространстве (массивы) и хранение в разрозненном пространстве (связные списки). Физическая структура на низком уровне определяет способы доступа к данным, их обновления, вставки и удаления. Эти два типа физических структур взаимно дополняют друг друга по временной и пространственной эффективности.</p>
 <p><img alt="Хранение в непрерывном и разрозненном пространстве" class="animation-figure" src="../classification_of_data_structure.assets/classification_phisical_structure.png" /></p>
 <p align="center"> Рисунок 3-3 &nbsp; Хранение в непрерывном и разрозненном пространстве </p>
 
-<p>Стоит отметить, что <strong>все структуры данных реализуются на основе массивов, связных списков или их комбинации</strong>. Например, стеки и очереди можно реализовать как с помощью массивов, так и с помощью связных списков; а реализация хеш-таблицы может одновременно содержать массивы и связные списки.</p>
+<p>Стоит отметить, что <strong>все структуры данных реализуются на основе массивов, связных списков или их комбинации</strong>. Например, стек и очередь можно реализовать как с помощью массивов, так и с помощью связных списков; реализация хеш-таблицы также может одновременно включать массивы и связные списки.</p>
 <ul>
 <li><strong>Можно реализовать на основе массивов</strong>: стеки, очереди, хеш-таблицы, деревья, кучи, графы, матрицы, тензоры (массивы размерности <span class="arithmatex">\(\geq 3\)</span> ) и т.д.</li>
 <li><strong>Можно реализовать на основе связных списков</strong>: стеки, очереди, хеш-таблицы, деревья, кучи, графы и т.д.</li>
 </ul>
-<p>После инициализации длину связного списка все еще можно изменять во время выполнения программы, поэтому его также называют "динамической структурой данных". Длина массива после инициализации неизменна, поэтому его также называют "статической структурой данных". Стоит заметить, что массив может менять длину за счет повторного выделения памяти, тем самым приобретая определенную "динамичность".</p>
+<p>После инициализации длину связного списка все еще можно изменять во время выполнения программы, поэтому его также называют "динамической структурой данных". Длина массива после инициализации неизменна, поэтому его также называют "статической структурой данных". Стоит отметить, что массив может изменять длину за счет повторного выделения памяти, тем самым приобретая определенную "динамичность".</p>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
 <p>Если тебе пока трудно понять физическую структуру, рекомендуется сначала прочитать следующую главу, а затем вернуться к этому разделу.</p>
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-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
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+    Глава 1. Введение в алгоритмы
   
 
     
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+    Глава 1. Введение в алгоритмы
   
 
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-    1.2 Что такое структуры данных и алгоритмы
+    1.2 Что такое алгоритм
   
 
     
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-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
     
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+    4.4 Оперативная память и кэш *
   
 
     
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+    Глава 6. Хеш-таблицы
   
 
     
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+    7.3 Представление двоичного дерева массивом
   
 
     
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+    8.3 Задача Top-k
   
 
     
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+    Глава 9. Графы
   
 
     
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+    10.3 Двоичный поиск границ
   
 
     
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+    13.4 Задача о n ферзях
   
 
     
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-    14.1 Введение в динамическое программирование
+    14.1 Первое знакомство с динамическим программированием
   
 
     
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+    14.5 Задача о полном рюкзаке
   
 
     
@@ -4277,8 +4277,8 @@
 <p><img alt="Структуры данных" class="cover-image" src="../assets/covers/chapter_data_structure.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>Структуры данных подобны прочному и разнообразному каркасу.</p>
-<p>Они задают план упорядоченной организации данных, а алгоритмы на этой основе обретают жизнь.</p>
+<p>Структуры данных подобны прочному и многообразному каркасу.</p>
+<p>Они задают схему упорядоченной организации данных, на основе которой оживают алгоритмы.</p>
 </div>
 <h2 id="_1">Содержание главы<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
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+++ b/ru/chapter_data_structure/number_encoding/index.html
@@ -65,8 +65,8 @@
         
         
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-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
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+    Глава 1. Введение в алгоритмы
   
 
     
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+    1.2 Что такое алгоритм
   
 
     
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+    Глава 6. Хеш-таблицы
   
 
     
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-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
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+    6.3 Алгоритмы хеширования
   
 
     
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+    Глава 7. Деревья
   
 
     
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-    Глава 7. Дерево
+    Глава 7. Деревья
   
 
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+    7.3 Представление двоичного дерева массивом
   
 
     
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+    7.6 Краткие итоги
   
 
     
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+    9.4 Краткие итоги
   
 
     
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+    10.2 Двоичный поиск точки вставки
   
 
     
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+    10.3 Двоичный поиск границ
   
 
     
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-    10.4 Стратегия оптимизации через хеширование
+    10.4 Стратегии оптимизации хеширования
   
 
     
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-    10.5 Алгоритмы поиска: новый взгляд
+    10.5 Переосмысление алгоритмов поиска
   
 
     
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+    11.3 Сортировка пузырьком
   
 
     
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+    12.1 Стратегия разделяй и властвуй
   
 
     
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+    14.5 Задача о полном рюкзаке
   
 
     
@@ -4360,8 +4360,8 @@
 <p>В этой книге разделы, помеченные символом <code>*</code>, относятся к дополнительному чтению. Если у тебя мало времени или материал кажется трудным, можно сначала пропустить их и вернуться после изучения обязательных разделов.</p>
 </div>
 <h2 id="331">3.3.1 &nbsp; Прямой, обратный и дополнительный коды<a class="headerlink" href="#331" title="Permanent link">&para;</a></h2>
-<p>В таблице из предыдущего раздела мы заметили, что все целочисленные типы могут представлять на одно отрицательное число больше, чем положительных. Например, диапазон <code>byte</code> равен <span class="arithmatex">\([-128, 127]\)</span> . Это явление выглядит не слишком интуитивно, и его внутренняя причина связана с прямым, обратным и дополнительным кодами.</p>
-<p>Прежде всего нужно отметить, что <strong>числа хранятся в компьютере в форме "дополнительного кода"</strong>. Прежде чем разбирать причины такого решения, сначала дадим определения всем трем способам представления.</p>
+<p>В таблице из предыдущего раздела можно заметить, что все целочисленные типы могут представлять на одно отрицательное число больше, чем положительных. Например, диапазон <code>byte</code> равен <span class="arithmatex">\([-128, 127]\)</span> . Это выглядит не слишком интуитивно, и внутренняя причина связана с прямым, обратным и дополнительным кодами.</p>
+<p>Прежде всего нужно отметить, что <strong>числа хранятся в компьютере в виде "дополнительного кода"</strong>. Прежде чем разбирать причины такого решения, сначала дадим определения всем трем способам представления.</p>
 <ul>
 <li><strong>Прямой код</strong>: старший бит двоичного представления числа рассматривается как знаковый, где <span class="arithmatex">\(0\)</span> означает положительное число, а <span class="arithmatex">\(1\)</span> - отрицательное; остальные биты представляют значение числа.</li>
 <li><strong>Обратный код</strong>: для положительного числа обратный код совпадает с прямым; для отрицательного числа он получается инверсией всех битов прямого кода, кроме знакового бита.</li>
@@ -4408,7 +4408,7 @@
 \]</div>
 <p>При добавлении <span class="arithmatex">\(1\)</span> к обратному коду отрицательного нуля возникает перенос, но длина типа <code>byte</code> составляет всего 8 бит, поэтому переполнившаяся в 9-й бит единица отбрасывается. Иными словами, <strong>дополнительный код отрицательного нуля равен <span class="arithmatex">\(0000 \; 0000\)</span> и совпадает с дополнительным кодом положительного нуля</strong>. Значит, в представлении дополнительного кода существует только один ноль, и проблема неоднозначности положительного и отрицательного нуля тем самым устраняется.</p>
 <p>Остается последний вопрос: диапазон типа <code>byte</code> равен <span class="arithmatex">\([-128, 127]\)</span> , откуда берется лишнее отрицательное число <span class="arithmatex">\(-128\)</span> ? Мы замечаем, что у всех целых чисел из интервала <span class="arithmatex">\([-127, +127]\)</span> есть соответствующие прямой, обратный и дополнительный коды, а прямой и дополнительный коды можно преобразовывать друг в друга.</p>
-<p>Однако <strong>дополнительный код <span class="arithmatex">\(1000 \; 0000\)</span> является исключением: у него нет соответствующего прямого кода</strong>. Согласно правилу преобразования, прямой код для этого дополнительного кода должен быть равен <span class="arithmatex">\(0000 \; 0000\)</span> . Это, очевидно, противоречие, потому что такой прямой код обозначает число <span class="arithmatex">\(0\)</span> , а его дополнительный код должен совпадать с ним самим. Компьютер просто определяет, что этот особый дополнительный код <span class="arithmatex">\(1000 \; 0000\)</span> представляет число <span class="arithmatex">\(-128\)</span> . На самом деле результат вычисления <span class="arithmatex">\((-1) + (-127)\)</span> в дополнительном коде как раз и равен <span class="arithmatex">\(-128\)</span> .</p>
+<p>Однако <strong>дополнительный код <span class="arithmatex">\(1000 \; 0000\)</span> является исключением: у него нет соответствующего прямого кода</strong>. Согласно правилу преобразования, прямой код для этого дополнительного кода должен быть равен <span class="arithmatex">\(0000 \; 0000\)</span> . Это очевидное противоречие, потому что такой прямой код обозначает число <span class="arithmatex">\(0\)</span> , а его дополнительный код должен совпадать с ним самим. Компьютер просто определяет, что этот особый дополнительный код <span class="arithmatex">\(1000 \; 0000\)</span> представляет число <span class="arithmatex">\(-128\)</span> . На самом деле результат вычисления <span class="arithmatex">\((-1) + (-127)\)</span> в дополнительном коде как раз и равен <span class="arithmatex">\(-128\)</span> .</p>
 <div class="arithmatex">\[
 \begin{aligned}
 &amp; (-127) + (-1) \newline
@@ -4419,9 +4419,9 @@
 &amp; \rightarrow -128
 \end{aligned}
 \]</div>
-<p>Ты, вероятно, уже заметил, что все приведенные выше вычисления были операциями сложения. Это намекает на важный факт: <strong>аппаратные схемы внутри компьютера в основном проектируются на основе операций сложения</strong>. Причина в том, что сложение по сравнению с другими операциями (например умножением, делением и вычитанием) проще реализуется на аппаратном уровне, легче распараллеливается и выполняется быстрее.</p>
+<p>Ты, вероятно, уже заметил, что все приведенные выше вычисления были операциями сложения. Это указывает на важный факт: <strong>аппаратные схемы внутри компьютера в основном проектируются на основе операций сложения</strong>. Причина в том, что сложение по сравнению с другими операциями (например умножением, делением и вычитанием) проще реализуется на аппаратном уровне, легче распараллеливается и выполняется быстрее.</p>
 <p>Обрати внимание: это не означает, что компьютер умеет только складывать. <strong>Комбинируя сложение с некоторыми базовыми логическими операциями, компьютер может реализовать и другие математические операции</strong>. Например, вычитание <span class="arithmatex">\(a - b\)</span> можно преобразовать в сложение <span class="arithmatex">\(a + (-b)\)</span> ; умножение и деление можно свести к многократному сложению или вычитанию.</p>
-<p>Теперь можно подвести итог, почему компьютеры используют дополнительный код: с представлением в дополнительном коде компьютер может использовать одни и те же схемы и операции для сложения положительных и отрицательных чисел, без необходимости проектировать специальные аппаратные схемы для вычитания, и без особой обработки неоднозначности положительного и отрицательного нуля. Это значительно упрощает аппаратную архитектуру и повышает эффективность вычислений.</p>
+<p>Теперь можно подвести итог, почему компьютеры используют дополнительный код: с представлением в дополнительном коде компьютер может использовать одни и те же схемы и операции для сложения положительных и отрицательных чисел, без необходимости проектировать специальные аппаратные схемы для вычитания и без особой обработки неоднозначности положительного и отрицательного нуля. Это значительно упрощает аппаратную архитектуру и повышает эффективность вычислений.</p>
 <p>Идея дополнительного кода очень изящна; из-за ограничений по объему мы на этом остановимся. Если тебе интересно, стоит изучить эту тему глубже.</p>
 <h2 id="332">3.3.2 &nbsp; Кодирование чисел с плавающей точкой<a class="headerlink" href="#332" title="Permanent link">&para;</a></h2>
 <p>Внимательный читатель может заметить: <code>int</code> и <code>float</code> имеют одинаковую длину, по 4 байта , но почему диапазон значений у <code>float</code> намного больше, чем у <code>int</code> ? Это выглядит парадоксально, ведь <code>float</code> должен еще представлять дробные числа, а значит диапазон вроде бы должен быть меньше.</p>
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-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
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 <h1 id="35">3.5 &nbsp; Резюме<a class="headerlink" href="#35" title="Permanent link">&para;</a></h1>
 <h3 id="1">1. &nbsp; Ключевые выводы<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
-<li>Структуры данных можно классифицировать с двух точек зрения: логической структуры и физической структуры. Логическая структура описывает логические связи между элементами данных, а физическая структура описывает способ хранения данных в памяти компьютера.</li>
-<li>К распространенным логическим структурам относятся линейные, древовидные и сетевые. Обычно мы делим структуры данных по логической структуре на линейные (массивы, связные списки, стеки, очереди) и нелинейные (деревья, графы, кучи). Реализация хеш-таблицы может одновременно включать линейные и нелинейные структуры данных.</li>
-<li>Во время работы программы данные хранятся в памяти компьютера. У каждого участка памяти есть собственный адрес, и программа обращается к данным именно по этим адресам.</li>
-<li>Физическая структура в основном делится на хранение в непрерывном пространстве (массивы) и хранение в разрозненном пространстве (связные списки). Все структуры данных реализуются на основе массивов, связных списков или их комбинации.</li>
-<li>К базовым типам данных в компьютере относятся целые <code>byte</code> , <code>short</code> , <code>int</code> , <code>long</code> , числа с плавающей точкой <code>float</code> , <code>double</code> , символы <code>char</code> и логический тип <code>bool</code> . Их диапазон значений определяется объемом занимаемого пространства и способом представления.</li>
+<li>Структуры данных можно классифицировать с точки зрения логической и физической структуры. Логическая структура описывает логические отношения между элементами данных, а физическая структура описывает способ хранения данных в памяти компьютера.</li>
+<li>К распространенным логическим структурам относятся линейные, древовидные и сетевые. Обычно структуры данных делятся на линейные (массивы, связные списки, стеки, очереди) и нелинейные (деревья, графы, кучи). Реализация хеш-таблицы может включать как линейные, так и нелинейные структуры данных.</li>
+<li>При выполнении программы данные хранятся в памяти компьютера. Каждый участок памяти имеет соответствующий адрес, с помощью которого программа получает доступ к данным.</li>
+<li>Физическая структура делится на хранение в непрерывном пространстве (массивы) и хранение в разрозненном пространстве (связные списки). Все структуры данных реализуются на основе массивов, связных списков или их комбинации.</li>
+<li>Базовые типы данных в компьютере включают целые <code>byte</code> , <code>short</code> , <code>int</code> , <code>long</code> , числа с плавающей точкой <code>float</code> , <code>double</code> , символы <code>char</code> и логический тип <code>bool</code> . Их диапазон значений зависит от объема занимаемого пространства и способа представления.</li>
 <li>Прямой код, обратный код и дополнительный код - это три способа кодирования чисел в компьютере, между которыми можно выполнять взаимные преобразования. В прямом коде старший бит целого числа является знаковым, а остальные биты представляют значение числа.</li>
-<li>Целые числа в компьютере хранятся в виде дополнительного кода. В таком представлении компьютер может одинаково обрабатывать сложение положительных и отрицательных чисел, не проектируя специальную аппаратную схему отдельно для вычитания, и при этом не возникает неоднозначности положительного и отрицательного нуля.</li>
-<li>Кодирование числа с плавающей точкой состоит из 1 бита знака, 8 битов экспоненты и 23 битов мантиссы. Благодаря наличию экспоненты диапазон значений у чисел с плавающей точкой намного больше, чем у целых, но расплачиваться за это приходится точностью.</li>
+<li>Целые числа в компьютере хранятся в виде дополнительного кода. В таком представлении компьютер может одинаково обрабатывать сложение положительных и отрицательных чисел без специальной аппаратной схемы для вычитания, и при этом исчезает неоднозначность положительного и отрицательного нуля.</li>
+<li>Кодирование числа с плавающей точкой состоит из 1 бита знака, 8 битов экспоненты и 23 битов мантиссы. Благодаря наличию экспоненты диапазон значений у чисел с плавающей точкой намного больше, чем у целых, но это достигается ценой потери точности.</li>
 <li>ASCII - это самый ранний набор английских символов длиной 1 байт, включающий в общей сложности 127 символов. Набор GBK - распространенный китайский набор символов, включающий более двадцати тысяч иероглифов. Unicode стремится предоставить единый полный стандарт набора символов, включающий символы всех языков мира, чтобы решить проблемы искаженного текста, вызванные несовместимыми способами кодирования.</li>
 <li>UTF-8 - самый популярный способ кодирования Unicode, обладающий очень хорошей универсальностью. Это кодировка переменной длины, хорошо расширяемая и эффективно использующая память. UTF-16 и UTF-32 относятся к кодировкам фиксированной длины. При кодировании китайского текста UTF-16 занимает меньше места, чем UTF-8. Такие языки программирования, как Java и C#, по умолчанию используют UTF-16.</li>
 </ul>
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-        <title>12.2 Поисковая стратегия divide and conquer - Hello Algo</title>
+        <title>12.2 Поисковая стратегия разделяй и властвуй - Hello Algo</title>
       
     
     
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-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
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-        1. &nbsp; Реализация двоичного поиска на основе divide and conquer
+        1. &nbsp; Реализация двоичного поиска на основе "разделяй и властвуй"
       
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-        1. &nbsp; Реализация двоичного поиска на основе divide and conquer
+        1. &nbsp; Реализация двоичного поиска на основе "разделяй и властвуй"
       
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 <!-- Page content -->
-<h1 id="122-divide-and-conquer">12.2 &nbsp; Поисковая стратегия divide and conquer<a class="headerlink" href="#122-divide-and-conquer" title="Permanent link">&para;</a></h1>
+<h1 id="122">12.2 &nbsp; Поисковая стратегия разделяй и властвуй<a class="headerlink" href="#122" title="Permanent link">&para;</a></h1>
 <p>Мы уже знаем, что алгоритмы поиска делятся на две большие категории.</p>
 <ul>
 <li><strong>Полный перебор</strong>: реализуется через обход структуры данных, временная сложность равна <span class="arithmatex">\(O(n)\)</span> .</li>
 <li><strong>Адаптивный поиск</strong>: использует особую организацию данных или априорную информацию, временная сложность может достигать <span class="arithmatex">\(O(\log n)\)</span> и даже <span class="arithmatex">\(O(1)\)</span> .</li>
 </ul>
-<p>На практике <strong>алгоритмы поиска с временной сложностью <span class="arithmatex">\(O(\log n)\)</span> обычно реализуются на основе стратегии divide and conquer</strong>, например двоичный поиск и деревья.</p>
+<p>На практике <strong>алгоритмы поиска с временной сложностью <span class="arithmatex">\(O(\log n)\)</span> обычно реализуются на основе стратегии "разделяй и властвуй"</strong>, например двоичный поиск и деревья.</p>
 <ul>
 <li>На каждом шаге двоичный поиск раскладывает задачу (поиск целевого элемента в массиве) на более мелкую задачу (поиск целевого элемента в одной половине массива), и этот процесс продолжается, пока массив не станет пустым или пока не будет найден целевой элемент.</li>
-<li>Деревья являются типичными представителями идей divide and conquer; в таких структурах данных, как двоичное дерево поиска, AVL-дерево и куча, временная сложность различных операций равна <span class="arithmatex">\(O(\log n)\)</span> .</li>
+<li>Деревья являются типичными представителями идей "разделяй и властвуй"; в таких структурах данных, как двоичное дерево поиска, AVL-дерево и куча, временная сложность различных операций равна <span class="arithmatex">\(O(\log n)\)</span> .</li>
 </ul>
-<p>Стратегия divide and conquer для двоичного поиска выглядит следующим образом.</p>
+<p>Стратегия "разделяй и властвуй" для двоичного поиска выглядит следующим образом.</p>
 <ul>
 <li><strong>Задача раскладывается на части</strong>: двоичный поиск рекурсивно разбивает исходную задачу (поиск в массиве) на подзадачу (поиск в одной половине массива), и это достигается сравнением среднего элемента с целевым значением.</li>
 <li><strong>Подзадачи независимы</strong>: в двоичном поиске на каждом шаге обрабатывается только одна подзадача, и она не зависит от других подзадач.</li>
 <li><strong>Решения подзадач не нужно объединять</strong>: двоичный поиск нацелен на поиск конкретного элемента, поэтому объединять решения подзадач не требуется. Как только подзадача решена, одновременно считается решенной и исходная задача.</li>
 </ul>
-<p>По сути divide and conquer повышает эффективность поиска потому, что при полном переборе за один шаг удается исключить только один вариант, <strong>тогда как при поиске на основе divide and conquer за один шаг можно исключить половину вариантов</strong>.</p>
-<h3 id="1-divide-and-conquer">1. &nbsp; Реализация двоичного поиска на основе divide and conquer<a class="headerlink" href="#1-divide-and-conquer" title="Permanent link">&para;</a></h3>
-<p>В предыдущих главах двоичный поиск реализовывался через итерацию. Теперь реализуем его с помощью divide and conquer, то есть через рекурсию.</p>
+<p>Иными словами, стратегия "разделяй и властвуй" повышает эффективность поиска потому, что при полном переборе за один шаг удается исключить только один вариант, <strong>тогда как при поиске на основе "разделяй и властвуй" за один шаг можно исключить половину вариантов</strong>.</p>
+<h3 id="1">1. &nbsp; Реализация двоичного поиска на основе "разделяй и властвуй"<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>В предыдущих главах двоичный поиск реализовывался через итерацию. Теперь реализуем его с помощью стратегии "разделяй и властвуй", то есть через рекурсию.</p>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
 <p>Дан отсортированный массив <code>nums</code> длины <span class="arithmatex">\(n\)</span> , в котором все элементы уникальны. Найдите элемент <code>target</code> .</p>
 </div>
-<p>С точки зрения divide and conquer обозначим подзадачу, соответствующую интервалу поиска <span class="arithmatex">\([i, j]\)</span> , через <span class="arithmatex">\(f(i, j)\)</span> .</p>
+<p>С точки зрения стратегии "разделяй и властвуй" обозначим подзадачу, соответствующую интервалу поиска <span class="arithmatex">\([i, j]\)</span> , через <span class="arithmatex">\(f(i, j)\)</span> .</p>
 <p>Начиная с исходной задачи <span class="arithmatex">\(f(0, n-1)\)</span> , выполняем двоичный поиск по следующим шагам.</p>
 <ol>
 <li>Вычислить середину <span class="arithmatex">\(m\)</span> интервала поиска <span class="arithmatex">\([i, j]\)</span> и с ее помощью исключить половину интервала.</li>
 <li>Рекурсивно решить подзадачу вдвое меньшего размера; это может быть либо <span class="arithmatex">\(f(i, m-1)\)</span> , либо <span class="arithmatex">\(f(m+1, j)\)</span> .</li>
 <li>Повторять шаг <code>1.</code> и шаг <code>2.</code> , пока не будет найден <code>target</code> или пока интервал не станет пустым.</li>
 </ol>
-<p>На рисунке 12-4 показан процесс применения divide and conquer для поиска элемента <span class="arithmatex">\(6\)</span> в массиве.</p>
-<p><img alt="Процесс двоичного поиска в стиле divide and conquer" class="animation-figure" src="../binary_search_recur.assets/binary_search_recur.png" /></p>
-<p align="center"> Рисунок 12-4 &nbsp; Процесс двоичного поиска в стиле divide and conquer </p>
+<p>На рисунке 12-4 показан процесс применения стратегии "разделяй и властвуй" для поиска элемента <span class="arithmatex">\(6\)</span> в массиве.</p>
+<p><img alt="Процесс двоичного поиска в стиле разделяй и властвуй" class="animation-figure" src="../binary_search_recur.assets/binary_search_recur.png" /></p>
+<p align="center"> Рисунок 12-4 &nbsp; Процесс двоичного поиска в стиле разделяй и властвуй </p>
 
 <p>В реализации кода мы объявляем рекурсивную функцию <code>dfs()</code> для решения задачи <span class="arithmatex">\(f(i, j)\)</span> :</p>
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@@ -4406,15 +4406,15 @@
 <p><img alt="Пример данных для построения двоичного дерева" class="animation-figure" src="../build_binary_tree_problem.assets/build_tree_example.png" /></p>
 <p align="center"> Рисунок 12-5 &nbsp; Пример данных для построения двоичного дерева </p>
 
-<h3 id="1-divide-and-conquer">1. &nbsp; Проверка, является ли это задачей divide and conquer<a class="headerlink" href="#1-divide-and-conquer" title="Permanent link">&para;</a></h3>
-<p>Исходная задача - построить двоичное дерево по <code>preorder</code> и <code>inorder</code> - является типичной задачей divide and conquer.</p>
+<h3 id="1">1. &nbsp; Проверка, является ли это задачей "разделяй и властвуй"<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>Исходная задача - построить двоичное дерево по <code>preorder</code> и <code>inorder</code> - является типичной задачей для стратегии "разделяй и властвуй".</p>
 <ul>
-<li><strong>Задача раскладывается на части</strong>: если смотреть с точки зрения divide and conquer, исходную задачу можно разбить на две подзадачи: построение левого поддерева и построение правого поддерева, плюс одно действие: инициализация корневого узла. Для каждого поддерева (подзадачи) можно использовать тот же способ разбиения, пока не будет достигнута наименьшая подзадача (пустое поддерево).</li>
+<li><strong>Задача раскладывается на части</strong>: если смотреть с точки зрения стратегии "разделяй и властвуй", исходную задачу можно разбить на две подзадачи: построение левого поддерева и построение правого поддерева, плюс одно действие: инициализация корневого узла. Для каждого поддерева (подзадачи) можно использовать тот же способ разбиения, пока не будет достигнута наименьшая подзадача (пустое поддерево).</li>
 <li><strong>Подзадачи независимы</strong>: левое и правое поддеревья независимы друг от друга и не пересекаются. При построении левого поддерева нам нужно смотреть только на ту часть прямого и симметричного обходов, которая соответствует левому поддереву. Для правого поддерева рассуждение аналогично.</li>
 <li><strong>Решения подзадач можно объединить</strong>: когда левое и правое поддеревья (решения подзадач) уже построены, их можно присоединить к корневому узлу и тем самым получить решение исходной задачи.</li>
 </ul>
 <h3 id="2">2. &nbsp; Как разделить поддеревья<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>Из анализа выше видно, что эта задача действительно решается через divide and conquer, <strong>но как именно, имея прямой обход <code>preorder</code> и симметричный обход <code>inorder</code>, разделить левое и правое поддеревья</strong>?</p>
+<p>Из анализа выше видно, что эта задача действительно решается через "разделяй и властвуй", <strong>но как именно, имея прямой обход <code>preorder</code> и симметричный обход <code>inorder</code>, отделить левое и правое поддеревья</strong>?</p>
 <p>По определению и <code>preorder</code> , и <code>inorder</code> можно разбить на три части.</p>
 <ul>
 <li>Прямой обход: <code>[ корневой узел | левое поддерево | правое поддерево ]</code> , например для дерева на рисунке 12-5 это <code>[ 3 | 9 | 2 1 7 ]</code> .</li>
@@ -4467,7 +4467,7 @@
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 </table>
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-<p>Обратите внимание, что <span class="arithmatex">\((m-l)\)</span> в индексе корневого узла правого поддерева означает "число узлов в левом поддереве"; лучше всего понимать это выражение вместе с рисунком ниже.</p>
+<p>Стоит отметить, что <span class="arithmatex">\((m-l)\)</span> в индексе корневого узла правого поддерева означает число узлов в левом поддереве; лучше всего понимать это выражение вместе с рисунком ниже.</p>
 <p><img alt="Представление индексных интервалов корня и поддеревьев" class="animation-figure" src="../build_binary_tree_problem.assets/build_tree_division_pointers.png" /></p>
 <p align="center"> Рисунок 12-7 &nbsp; Представление индексных интервалов корня и поддеревьев </p>
 
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+        <title>12.1 Стратегия разделяй и властвуй - Hello Algo</title>
       
     
     
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-              12.1 &nbsp; Алгоритмы "разделяй и властвуй"
+              12.1 &nbsp; Стратегия разделяй и властвуй
             
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@@ -574,7 +574,7 @@
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-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
     
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-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
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-    1.2 Что такое структуры данных и алгоритмы
+    1.2 Что такое алгоритм
   
 
     
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-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
     
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-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
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-    4.4 Память и кеш *
+    4.4 Оперативная память и кэш *
   
 
     
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-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
     
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-    6.3 Хеш-алгоритмы
+    6.3 Алгоритмы хеширования
   
 
     
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-    7.3 Представление дерева массивом
+    7.3 Представление двоичного дерева массивом
   
 
     
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-    7.6 Резюме
+    7.6 Краткие итоги
   
 
     
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-    8.3 Задача Top-K
+    8.3 Задача Top-k
   
 
     
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+    Глава 9. Графы
   
 
     
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-    Глава 9. Граф
+    Глава 9. Графы
   
 
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-    9.2 Базовые операции над графами
+    9.2 Базовые операции графа
   
 
     
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+    9.4 Краткие итоги
   
 
     
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-    10.2 Точка вставки двоичного поиска
+    10.2 Двоичный поиск точки вставки
   
 
     
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-    10.3 Граничные случаи двоичного поиска
+    10.3 Двоичный поиск границ
   
 
     
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-    10.4 Стратегия оптимизации через хеширование
+    10.4 Стратегии оптимизации хеширования
   
 
     
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-    10.5 Алгоритмы поиска: новый взгляд
+    10.5 Переосмысление алгоритмов поиска
   
 
     
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-    11.3 Пузырьковая сортировка
+    11.3 Сортировка пузырьком
   
 
     
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-    11.4 Сортировка вставкой
+    11.4 Сортировка вставками
   
 
     
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-    12.1 Алгоритмы разделяй и властвуй
+    12.1 Стратегия разделяй и властвуй
   
 
     
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-    12.1 Алгоритмы разделяй и властвуй
+    12.1 Стратегия разделяй и властвуй
   
 
     
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-  <a href="#1211-divide-and-conquer" class="md-nav__link">
+  <a href="#1211" class="md-nav__link">
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-        12.1.1 &nbsp; Как определить задачу divide and conquer
+        12.1.1 &nbsp; Как определить задачу "разделяй и властвуй"
       
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+  <a href="#1212" class="md-nav__link">
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-        12.1.2 &nbsp; Повышение эффективности с помощью divide and conquer
+        12.1.2 &nbsp; Повышение эффективности с помощью "разделяй и властвуй"
       
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-    <nav class="md-nav" aria-label="12.1.2 Повышение эффективности с помощью divide and conquer">
+    <nav class="md-nav" aria-label="12.1.2 Повышение эффективности с помощью &quot;разделяй и властвуй&quot;">
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-        12.1.3 &nbsp; Типичные применения divide and conquer
+        12.1.3 &nbsp; Типичные применения стратегии "разделяй и властвуй"
       
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-    12.2 Стратегия поиска разделяй и властвуй
+    12.2 Поисковая стратегия разделяй и властвуй
   
 
     
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-    13.4 Задача о $n$ ферзях
+    13.4 Задача о n ферзях
   
 
     
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-    14.1 Введение в динамическое программирование
+    14.1 Первое знакомство с динамическим программированием
   
 
     
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-    14.5 Задача о неограниченном рюкзаке
+    14.5 Задача о полном рюкзаке
   
 
     
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-  <a href="#1211-divide-and-conquer" class="md-nav__link">
+  <a href="#1211" class="md-nav__link">
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-        12.1.1 &nbsp; Как определить задачу divide and conquer
+        12.1.1 &nbsp; Как определить задачу "разделяй и властвуй"
       
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-        12.1.2 &nbsp; Повышение эффективности с помощью divide and conquer
+        12.1.2 &nbsp; Повышение эффективности с помощью "разделяй и властвуй"
       
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-    <nav class="md-nav" aria-label="12.1.2 Повышение эффективности с помощью divide and conquer">
+    <nav class="md-nav" aria-label="12.1.2 Повышение эффективности с помощью &quot;разделяй и властвуй&quot;">
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-        12.1.3 &nbsp; Типичные применения divide and conquer
+        12.1.3 &nbsp; Типичные применения стратегии "разделяй и властвуй"
       
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@@ -4432,22 +4432,22 @@
 
 
 <!-- Page content -->
-<h1 id="121">12.1 &nbsp; Алгоритмы "разделяй и властвуй"<a class="headerlink" href="#121" title="Permanent link">&para;</a></h1>
-<p><u>Разделяй и властвуй (divide and conquer)</u> - это очень важная и широко используемая стратегия построения алгоритмов. Обычно она реализуется через рекурсию и включает два этапа: "разделение" и "решение".</p>
+<h1 id="121">12.1 &nbsp; Стратегия разделяй и властвуй<a class="headerlink" href="#121" title="Permanent link">&para;</a></h1>
+<p><u>Разделяй и властвуй (divide and conquer)</u> - это очень важная и широко используемая стратегия построения алгоритмов. Обычно она реализуется через рекурсию и включает два этапа: "разделение" и "объединение".</p>
 <ol>
 <li><strong>Разделение (этап декомпозиции)</strong>: рекурсивно разбить исходную задачу на две или более подзадачи, пока не будет достигнута наименьшая подзадача.</li>
-<li><strong>Решение (этап объединения)</strong>: начиная с уже известных решений наименьших подзадач, снизу вверх объединять решения подзадач и тем самым получать решение исходной задачи.</li>
+<li><strong>Объединение (этап синтеза)</strong>: начиная с уже известных решений наименьших подзадач, снизу вверх объединять решения подзадач и тем самым получать решение исходной задачи.</li>
 </ol>
 <p>Как показано на рисунке 12-1, "сортировка слиянием" является одним из типичных примеров применения стратегии "разделяй и властвуй".</p>
 <ol>
 <li><strong>Разделение</strong>: рекурсивно разделить исходный массив (исходную задачу) на два подмассива (подзадачи), пока в подмассиве не останется только один элемент (наименьшая подзадача).</li>
-<li><strong>Решение</strong>: снизу вверх объединять упорядоченные подмассивы (решения подзадач), чтобы получить упорядоченный исходный массив (решение исходной задачи).</li>
+<li><strong>Объединение</strong>: снизу вверх объединять упорядоченные подмассивы (решения подзадач), чтобы получить упорядоченный исходный массив (решение исходной задачи).</li>
 </ol>
-<p><img alt="Стратегия divide and conquer в сортировке слиянием" class="animation-figure" src="../divide_and_conquer.assets/divide_and_conquer_merge_sort.png" /></p>
-<p align="center"> Рисунок 12-1 &nbsp; Стратегия divide and conquer в сортировке слиянием </p>
+<p><img alt="Стратегия разделяй и властвуй в сортировке слиянием" class="animation-figure" src="../divide_and_conquer.assets/divide_and_conquer_merge_sort.png" /></p>
+<p align="center"> Рисунок 12-1 &nbsp; Стратегия разделяй и властвуй в сортировке слиянием </p>
 
-<h2 id="1211-divide-and-conquer">12.1.1 &nbsp; Как определить задачу divide and conquer<a class="headerlink" href="#1211-divide-and-conquer" title="Permanent link">&para;</a></h2>
-<p>Чтобы понять, подходит ли задача для решения методом divide and conquer, обычно можно ориентироваться на следующие критерии.</p>
+<h2 id="1211">12.1.1 &nbsp; Как определить задачу "разделяй и властвуй"<a class="headerlink" href="#1211" title="Permanent link">&para;</a></h2>
+<p>Чтобы понять, подходит ли задача для решения методом "разделяй и властвуй", обычно можно ориентироваться на следующие критерии.</p>
 <ol>
 <li><strong>Задача раскладывается на части</strong>: исходную задачу можно разбить на более мелкие и похожие подзадачи, причем такое разбиение можно применять рекурсивно.</li>
 <li><strong>Подзадачи независимы</strong>: подзадачи не пересекаются, не зависят друг от друга и могут решаться независимо.</li>
@@ -4459,9 +4459,9 @@
 <li><strong>Подзадачи независимы</strong>: каждый подмассив можно сортировать отдельно (то есть каждую подзадачу можно решать независимо).</li>
 <li><strong>Решения подзадач можно объединить</strong>: два упорядоченных подмассива (решения подзадач) можно объединить в один упорядоченный массив (решение исходной задачи).</li>
 </ol>
-<h2 id="1212-divide-and-conquer">12.1.2 &nbsp; Повышение эффективности с помощью divide and conquer<a class="headerlink" href="#1212-divide-and-conquer" title="Permanent link">&para;</a></h2>
-<p><strong>Стратегия divide and conquer не только позволяет эффективно решать алгоритмические задачи, но и часто повышает эффективность самих алгоритмов</strong>. Именно поэтому быстрая сортировка, сортировка слиянием и пирамидальная сортировка обычно работают быстрее, чем сортировка выбором, пузырьком и вставками.</p>
-<p>Тогда возникает естественный вопрос: <strong>почему divide and conquer повышает эффективность алгоритма и какова логика этого на более глубоком уровне</strong>? Иными словами, почему разбиение большой задачи на несколько подзадач, решение этих подзадач и последующее объединение их решений оказывается эффективнее, чем прямое решение исходной задачи? Этот вопрос можно рассмотреть с двух сторон: через число операций и через параллельные вычисления.</p>
+<h2 id="1212">12.1.2 &nbsp; Повышение эффективности с помощью "разделяй и властвуй"<a class="headerlink" href="#1212" title="Permanent link">&para;</a></h2>
+<p><strong>Стратегия "разделяй и властвуй" не только позволяет эффективно решать алгоритмические задачи, но и часто повышает эффективность самих алгоритмов</strong>. Именно поэтому быстрая сортировка, сортировка слиянием и пирамидальная сортировка обычно работают быстрее, чем сортировка выбором, пузырьком и вставками.</p>
+<p>Тогда возникает естественный вопрос: <strong>почему стратегия "разделяй и властвуй" повышает эффективность алгоритма и какова внутренняя логика этого подхода</strong>? Иными словами, почему разбиение большой задачи на несколько подзадач, решение этих подзадач и последующее объединение их решений оказывается эффективнее, чем прямое решение исходной задачи? Этот вопрос можно рассмотреть с двух сторон: через число операций и через параллельные вычисления.</p>
 <h3 id="1">1. &nbsp; Оптимизация числа операций<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <p>Рассмотрим "сортировку пузырьком": для массива длины <span class="arithmatex">\(n\)</span> ей требуется <span class="arithmatex">\(O(n^2)\)</span> времени. Предположим, что мы разделим массив на два подмассива в середине, как показано на рисунке 12-2. Тогда само разбиение потребует <span class="arithmatex">\(O(n)\)</span> времени, сортировка каждого подмассива займет <span class="arithmatex">\(O((n / 2)^2)\)</span> времени, а объединение двух подмассивов потребует еще <span class="arithmatex">\(O(n)\)</span> времени. Общая временная сложность будет равна:</p>
 <div class="arithmatex">\[
@@ -4480,34 +4480,34 @@ n(n - 4) &amp; &gt; 0
 \]</div>
 <p><strong>Это означает, что при <span class="arithmatex">\(n &gt; 4\)</span> число операций после разбиения становится меньше, а значит, сортировка должна работать быстрее</strong>. При этом важно заметить, что временная сложность после разбиения все еще остается квадратичной, то есть <span class="arithmatex">\(O(n^2)\)</span> ; уменьшается лишь константный множитель.</p>
 <p>Если пойти дальше и <strong>продолжать делить каждый подмассив пополам</strong>, пока в нем не останется только один элемент, то мы фактически получим "сортировку слиянием", чья временная сложность равна <span class="arithmatex">\(O(n \log n)\)</span> .</p>
-<p>Можно пойти еще дальше и спросить: <strong>что если задать несколько точек разделения</strong> и равномерно разбить исходный массив на <span class="arithmatex">\(k\)</span> подмассивов? Такая ситуация очень похожа на "блочную сортировку", которая особенно хорошо подходит для сортировки очень больших объемов данных и теоретически может достигать временной сложности <span class="arithmatex">\(O(n + k)\)</span> .</p>
+<p>Можно пойти еще дальше и спросить: <strong>что если задать несколько точек разделения</strong> и равномерно разбить исходный массив на <span class="arithmatex">\(k\)</span> подмассивов? Такая ситуация очень похожа на блочную сортировку, которая особенно хорошо подходит для сортировки очень больших объемов данных и теоретически может достигать временной сложности <span class="arithmatex">\(O(n + k)\)</span> .</p>
 <h3 id="2">2. &nbsp; Оптимизация параллельных вычислений<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>Мы знаем, что подзадачи, порождаемые divide and conquer, являются независимыми, <strong>а значит, их обычно можно решать параллельно</strong>. Иначе говоря, divide and conquer не только может уменьшить временную сложность алгоритма, <strong>но и хорошо сочетается с параллельной оптимизацией на уровне системы</strong>.</p>
+<p>Мы знаем, что подзадачи, порождаемые стратегией "разделяй и властвуй", являются независимыми, <strong>а значит, их обычно можно решать параллельно</strong>. Иначе говоря, "разделяй и властвуй" не только может уменьшить временную сложность алгоритма, <strong>но и хорошо сочетается с параллельной оптимизацией на уровне системы</strong>.</p>
 <p>Параллельная оптимизация особенно эффективна в среде с несколькими ядрами или несколькими процессорами, потому что система может одновременно обрабатывать разные подзадачи, лучше загружая вычислительные ресурсы и тем самым заметно сокращая общее время работы.</p>
 <p>Например, в показанной ниже "блочной сортировке" большой объем данных равномерно распределяется по блокам. Тогда сортировку каждого блока можно поручить отдельным вычислительным единицам, а после завершения просто объединить результаты.</p>
 <p><img alt="Параллельные вычисления в блочной сортировке" class="animation-figure" src="../divide_and_conquer.assets/divide_and_conquer_parallel_computing.png" /></p>
 <p align="center"> Рисунок 12-3 &nbsp; Параллельные вычисления в блочной сортировке </p>
 
-<h2 id="1213-divide-and-conquer">12.1.3 &nbsp; Типичные применения divide and conquer<a class="headerlink" href="#1213-divide-and-conquer" title="Permanent link">&para;</a></h2>
-<p>С одной стороны, divide and conquer можно использовать для решения многих классических алгоритмических задач.</p>
+<h2 id="1213">12.1.3 &nbsp; Типичные применения стратегии "разделяй и властвуй"<a class="headerlink" href="#1213" title="Permanent link">&para;</a></h2>
+<p>С одной стороны, стратегию "разделяй и властвуй" можно использовать для решения многих классических алгоритмических задач.</p>
 <ul>
 <li><strong>Поиск ближайшей пары точек</strong>: сначала множество точек делится на две части, затем ищется ближайшая пара в каждой части, а затем ближайшая пара, пересекающая границу между двумя частями.</li>
 <li><strong>Умножение больших чисел</strong>: например, алгоритм Карацубы, который раскладывает умножение больших чисел на несколько умножений и сложений меньших чисел.</li>
 <li><strong>Умножение матриц</strong>: например, алгоритм Штрассена, который раскладывает умножение больших матриц на несколько умножений и сложений матриц меньшего размера.</li>
-<li><strong>Задача о Ханойской башне</strong>: задача о Ханойской башне решается рекурсивно и является типичным примером применения divide and conquer.</li>
-<li><strong>Подсчет инверсий</strong>: если в последовательности предыдущее число больше следующего, то такая пара образует инверсию. Эту задачу можно решить с помощью идей divide and conquer, опираясь на сортировку слиянием.</li>
+<li><strong>Задача о Ханойской башне</strong>: задача о Ханойской башне решается рекурсивно и является типичным примером применения стратегии "разделяй и властвуй".</li>
+<li><strong>Подсчет инверсий</strong>: если в последовательности предыдущее число больше следующего, то такая пара образует инверсию. Эту задачу можно решить с помощью идей "разделяй и властвуй", опираясь на сортировку слиянием.</li>
 </ul>
-<p>С другой стороны, divide and conquer очень широко применяется при проектировании алгоритмов и структур данных.</p>
+<p>С другой стороны, стратегия "разделяй и властвуй" очень широко применяется при проектировании алгоритмов и структур данных.</p>
 <ul>
 <li><strong>Двоичный поиск</strong>: двоичный поиск делит отсортированный массив на две части по индексу середины, а затем, в зависимости от результата сравнения целевого значения со средним элементом, исключает одну из половин и повторяет ту же операцию на оставшемся интервале.</li>
 <li><strong>Сортировка слиянием</strong>: она уже была рассмотрена в начале этого раздела, поэтому не будем повторяться.</li>
 <li><strong>Быстрая сортировка</strong>: в ней выбирается опорное значение, после чего массив делится на два подмассива: один содержит элементы меньше опорного, а другой - больше. Затем такая же операция повторяется для обеих частей, пока в подмассиве не останется один элемент.</li>
 <li><strong>Блочная сортировка</strong>: ее основная идея заключается в распределении данных по нескольким блокам, сортировке элементов внутри каждого блока и последующем последовательном извлечении элементов из блоков для построения отсортированного массива.</li>
-<li><strong>Деревья</strong>: например, двоичные деревья поиска, AVL-деревья, красно-черные деревья, B-деревья, B+ деревья и т.д. Их операции поиска, вставки и удаления можно рассматривать как применение divide and conquer.</li>
-<li><strong>Кучи</strong>: куча является особым видом полного бинарного дерева, а такие операции, как вставка, удаление и упорядочивание, по сути содержат идеи divide and conquer.</li>
-<li><strong>Хеш-таблицы</strong>: хотя хеш-таблицы напрямую не используют divide and conquer, некоторые способы разрешения коллизий косвенно опираются на эту стратегию. Например, длинные цепочки в методе цепочек могут преобразовываться в красно-черные деревья для повышения эффективности поиска.</li>
+<li><strong>Деревья</strong>: например, двоичные деревья поиска, AVL-деревья, красно-черные деревья, B-деревья, B+ деревья и т.д. Их операции поиска, вставки и удаления можно рассматривать как применение стратегии "разделяй и властвуй".</li>
+<li><strong>Кучи</strong>: куча является особым видом полного двоичного дерева, а такие операции, как вставка, удаление и упорядочивание, по сути содержат идеи "разделяй и властвуй".</li>
+<li><strong>Хеш-таблицы</strong>: хотя хеш-таблицы напрямую не используют стратегию "разделяй и властвуй", некоторые способы разрешения коллизий косвенно опираются на эту идею. Например, длинные цепочки в методе цепочек могут преобразовываться в красно-черные деревья для повышения эффективности поиска.</li>
 </ul>
-<p>Нетрудно заметить, что <strong>divide and conquer - это "тихая" алгоритмическая идея</strong>, скрыто присутствующая внутри самых разных алгоритмов и структур данных.</p>
+<p>Нетрудно заметить, что <strong>"разделяй и властвуй" - это "тихая" алгоритмическая идея</strong>, скрыто присутствующая внутри самых разных алгоритмов и структур данных.</p>
 
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 <p>Процесс решения задачи <span class="arithmatex">\(f(2)\)</span> можно кратко описать так: <strong>переместить два диска с <code>A</code> на <code>C</code> с помощью <code>B</code></strong> . Здесь <code>C</code> называется целевым стержнем, а <code>B</code> - буферным стержнем.</p>
 <h3 id="2">2. &nbsp; Разбиение на подзадачи<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>Для задачи <span class="arithmatex">\(f(3)\)</span> , то есть когда имеется три диска, ситуация становится немного сложнее.</p>
-<p>Поскольку решения <span class="arithmatex">\(f(1)\)</span> и <span class="arithmatex">\(f(2)\)</span> уже известны, можно подойти к задаче с точки зрения divide and conquer и <strong>рассматривать два верхних диска на <code>A</code> как единое целое</strong>, выполняя шаги, показанные на рисунке 12-13. Так три диска успешно перемещаются с <code>A</code> на <code>C</code> .</p>
+<p>Для задачи <span class="arithmatex">\(f(3)\)</span> , то есть когда имеется три диска, ситуация становится сложнее.</p>
+<p>Поскольку решения <span class="arithmatex">\(f(1)\)</span> и <span class="arithmatex">\(f(2)\)</span> уже известны, можно подойти к задаче с точки зрения стратегии "разделяй и властвуй" и <strong>рассматривать два верхних диска на <code>A</code> как единое целое</strong>, выполняя шаги, показанные на рисунке 12-13. Так три диска успешно перемещаются с <code>A</code> на <code>C</code> .</p>
 <ol>
 <li>Сделать <code>B</code> целевым стержнем, а <code>C</code> буферным, и переместить два диска с <code>A</code> на <code>B</code> .</li>
 <li>Переместить оставшийся один диск с <code>A</code> напрямую на <code>C</code> .</li>
@@ -4456,16 +4456,16 @@
 </div>
 <p align="center"> Рисунок 12-13 &nbsp; Решение задачи размера 3 </p>
 
-<p>По своей сути <strong>мы разбиваем задачу <span class="arithmatex">\(f(3)\)</span> на две подзадачи <span class="arithmatex">\(f(2)\)</span> и одну подзадачу <span class="arithmatex">\(f(1)\)</span></strong> . Если последовательно решить эти три подзадачи, исходная задача тоже будет решена. Это показывает, что подзадачи независимы и что их решения можно объединить.</p>
-<p>Таким образом, можно сформулировать показанную на рисунке 12-14 стратегию divide and conquer для задачи о Ханойской башне: исходная задача <span class="arithmatex">\(f(n)\)</span> разбивается на две подзадачи <span class="arithmatex">\(f(n-1)\)</span> и одну подзадачу <span class="arithmatex">\(f(1)\)</span> , которые затем решаются в следующем порядке.</p>
+<p>Иначе говоря, <strong>мы разбиваем задачу <span class="arithmatex">\(f(3)\)</span> на две подзадачи <span class="arithmatex">\(f(2)\)</span> и одну подзадачу <span class="arithmatex">\(f(1)\)</span></strong> . Если последовательно решить эти три подзадачи, исходная задача тоже будет решена. Это показывает, что подзадачи независимы и что их решения можно объединить.</p>
+<p>Таким образом, можно сформулировать показанную на рисунке 12-14 стратегию "разделяй и властвуй" для задачи о Ханойской башне: исходная задача <span class="arithmatex">\(f(n)\)</span> разбивается на две подзадачи <span class="arithmatex">\(f(n-1)\)</span> и одну подзадачу <span class="arithmatex">\(f(1)\)</span> , которые затем решаются в следующем порядке.</p>
 <ol>
 <li>Переместить <span class="arithmatex">\(n-1\)</span> дисков с <code>A</code> на <code>B</code> с помощью <code>C</code> .</li>
 <li>Переместить оставшийся <span class="arithmatex">\(1\)</span> диск напрямую с <code>A</code> на <code>C</code> .</li>
 <li>Переместить <span class="arithmatex">\(n-1\)</span> дисков с <code>B</code> на <code>C</code> с помощью <code>A</code> .</li>
 </ol>
 <p>Для двух подзадач <span class="arithmatex">\(f(n-1)\)</span> <strong>можно применять тот же способ рекурсивного разбиения</strong>, пока не будет достигнута наименьшая подзадача <span class="arithmatex">\(f(1)\)</span> . А решение для <span class="arithmatex">\(f(1)\)</span> уже известно и требует всего одного перемещения.</p>
-<p><img alt="Стратегия divide and conquer для решения задачи о Ханойской башне" class="animation-figure" src="../hanota_problem.assets/hanota_divide_and_conquer.png" /></p>
-<p align="center"> Рисунок 12-14 &nbsp; Стратегия divide and conquer для решения задачи о Ханойской башне </p>
+<p><img alt="Стратегия разделяй и властвуй для решения задачи о Ханойской башне" class="animation-figure" src="../hanota_problem.assets/hanota_divide_and_conquer.png" /></p>
+<p align="center"> Рисунок 12-14 &nbsp; Стратегия разделяй и властвуй для решения задачи о Ханойской башне </p>
 
 <h3 id="3">3. &nbsp; Реализация кода<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
 <p>В коде мы объявляем рекурсивную функцию <code>dfs(i, src, buf, tar)</code> , которая перемещает <span class="arithmatex">\(i\)</span> верхних дисков со стержня <code>src</code> на целевой стержень <code>tar</code> с помощью буферного стержня <code>buf</code> :</p>
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+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
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+    10.3 Двоичный поиск границ
   
 
     
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+    10.4 Стратегии оптимизации хеширования
   
 
     
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+    10.5 Переосмысление алгоритмов поиска
   
 
     
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+    14.5 Задача о полном рюкзаке
   
 
     
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 </div>
 <h2 id="_1">Содержание главы<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
-<li><a href="divide_and_conquer/">12.1 &nbsp; Алгоритмы разделяй и властвуй</a></li>
-<li><a href="binary_search_recur/">12.2 &nbsp; Стратегия поиска разделяй и властвуй</a></li>
+<li><a href="divide_and_conquer/">12.1 &nbsp; Стратегия разделяй и властвуй</a></li>
+<li><a href="binary_search_recur/">12.2 &nbsp; Поисковая стратегия разделяй и властвуй</a></li>
 <li><a href="build_binary_tree_problem/">12.3 &nbsp; Задача построения двоичного дерева</a></li>
 <li><a href="hanota_problem/">12.4 &nbsp; Задача о Ханойской башне</a></li>
 <li><a href="summary/">12.5 &nbsp; Резюме</a></li>
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-    aria-label="Вперед: 12.1 Алгоритмы разделяй и властвуй"
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+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
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 <h1 id="125">12.5 &nbsp; Резюме<a class="headerlink" href="#125" title="Permanent link">&para;</a></h1>
 <h3 id="1">1. &nbsp; Ключевые выводы<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
-<li>Divide and conquer - это распространенная стратегия проектирования алгоритмов, которая включает два этапа: разделение (декомпозицию) и решение (объединение), и обычно реализуется с помощью рекурсии.</li>
+<li>"Разделяй и властвуй" - это распространенная стратегия проектирования алгоритмов, которая включает два этапа: разделение (декомпозицию) и объединение (синтез), и обычно реализуется с помощью рекурсии.</li>
 <li>Критерии применимости этой стратегии к задаче включают: возможность разложения задачи, независимость подзадач и возможность объединения их решений.</li>
-<li>Сортировка слиянием является типичным применением divide and conquer: она рекурсивно делит массив на два равных по длине подмассива, пока не останется массив из одного элемента, после чего начинает поэтапное объединение.</li>
-<li>Введение стратегии divide and conquer часто позволяет повысить эффективность алгоритма. С одной стороны, стратегия уменьшает число операций; с другой - после разбиения она способствует параллельной оптимизации на уровне системы.</li>
-<li>Divide and conquer не только помогает решать многие алгоритмические задачи, но и широко используется при проектировании структур данных и алгоритмов, поэтому его можно встретить буквально повсюду.</li>
-<li>По сравнению с полным перебором адаптивный поиск работает эффективнее. Алгоритмы поиска со сложностью <span class="arithmatex">\(O(\log n)\)</span> обычно реализуются на основе стратегии divide and conquer.</li>
-<li>Двоичный поиск - еще одно типичное применение divide and conquer, в котором отсутствует шаг объединения решений подзадач. Мы можем реализовать двоичный поиск рекурсивно, через divide and conquer.</li>
+<li>Сортировка слиянием является типичным применением стратегии "разделяй и властвуй": она рекурсивно делит массив на два равных по длине подмассива, пока не останется массив из одного элемента, после чего начинает поэтапное объединение.</li>
+<li>Использование стратегии "разделяй и властвуй" часто позволяет повысить эффективность алгоритма. С одной стороны, она уменьшает число операций; с другой - после разбиения способствует параллельной оптимизации на уровне системы.</li>
+<li>"Разделяй и властвуй" не только помогает решать многие алгоритмические задачи, но и широко используется при проектировании структур данных и алгоритмов, поэтому его можно встретить буквально повсюду.</li>
+<li>По сравнению с полным перебором адаптивный поиск работает эффективнее. Алгоритмы поиска со сложностью <span class="arithmatex">\(O(\log n)\)</span> обычно реализуются на основе стратегии "разделяй и властвуй".</li>
+<li>Двоичный поиск - еще одно типичное применение стратегии "разделяй и властвуй", в котором отсутствует шаг объединения решений подзадач. Его можно реализовать рекурсивно, опираясь на эту стратегию.</li>
 <li>В задаче построения двоичного дерева исходная задача построения дерева может быть разбита на две подзадачи: построение левого и правого поддеревьев, а реализуется это через разбиение индексных интервалов прямого и симметричного обходов.</li>
 <li>В задаче о Ханойской башне задача размера <span class="arithmatex">\(n\)</span> разбивается на две подзадачи размера <span class="arithmatex">\(n-1\)</span> и одну подзадачу размера <span class="arithmatex">\(1\)</span> . После последовательного решения этих трех подзадач исходная задача также оказывается решенной.</li>
 </ul>
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+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
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+    14.1 Первое знакомство с динамическим программированием
   
 
     
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 <!-- Page content -->
 <h1 id="142">14.2 &nbsp; Свойства задач динамического программирования<a class="headerlink" href="#142" title="Permanent link">&para;</a></h1>
-<p>В предыдущем разделе мы увидели, как динамическое программирование решает исходную задачу через разложение на подзадачи. На самом деле разложение на подзадачи - это общий алгоритмический подход, но в divide and conquer, динамическом программировании и backtracking акценты расставлены по-разному.</p>
+<p>В предыдущем разделе мы увидели, как динамическое программирование решает исходную задачу через разложение на подзадачи. На самом деле разложение на подзадачи - это общий алгоритмический подход, но в методе "разделяй и властвуй", динамическом программировании и поиске с возвратом акценты расставлены по-разному.</p>
 <ul>
-<li>Алгоритмы divide and conquer рекурсивно раскладывают исходную задачу на несколько независимых подзадач, пока не будет достигнута наименьшая подзадача, а затем в процессе возврата объединяют решения подзадач в решение исходной задачи.</li>
-<li>Динамическое программирование тоже раскладывает задачу рекурсивно, но его главное отличие от divide and conquer в том, что подзадачи здесь зависят друг от друга и в процессе разложения возникает много перекрывающихся подзадач.</li>
-<li>Алгоритм backtracking перебирает все возможные решения через попытки и откат и с помощью обрезки избегает ненужных ветвей поиска. Решение исходной задачи состоит из последовательности решений, и подзадачей можно считать префикс этой последовательности решений.</li>
+<li>Алгоритмы "разделяй и властвуй" рекурсивно раскладывают исходную задачу на несколько независимых подзадач, пока не будет достигнута наименьшая подзадача, а затем в процессе возврата объединяют решения подзадач в решение исходной задачи.</li>
+<li>Динамическое программирование тоже раскладывает задачу рекурсивно, но его главное отличие от метода "разделяй и властвуй" в том, что подзадачи здесь зависят друг от друга и в процессе разложения возникает много перекрывающихся подзадач.</li>
+<li>Алгоритм поиска с возвратом перебирает все возможные решения через попытки и откат и с помощью обрезки избегает ненужных ветвей поиска. Решение исходной задачи состоит из последовательности решений, и подзадачей можно считать префикс этой последовательности решений.</li>
 </ul>
 <p>На практике динамическое программирование часто применяется для задач оптимизации. Такие задачи не только содержат перекрывающиеся подзадачи, но и обладают еще двумя важными свойствами: оптимальной подструктурой и отсутствием последствий.</p>
 <h2 id="1421">14.2.1 &nbsp; Оптимальная подструктура<a class="headerlink" href="#1421" title="Permanent link">&para;</a></h2>
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     href="../intro_to_dynamic_programming/"
     class="md-footer__link md-footer__link--prev"
-    aria-label="Назад: 14.1 Введение в динамическое программирование"
+    aria-label="Назад: 14.1 Первое знакомство с динамическим программированием"
     rel="prev"
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+        14.1 Первое знакомство с динамическим программированием
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-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
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+    14.1 Первое знакомство с динамическим программированием
   
 
     
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+    14.5 Задача о полном рюкзаке
   
 
     
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 <li>С чего начинать решение такой задачи и как выглядит полный процесс решения?</li>
 </ol>
 <h2 id="1431">14.3.1 &nbsp; Определение задачи<a class="headerlink" href="#1431" title="Permanent link">&para;</a></h2>
-<p>В целом, если задача содержит перекрывающиеся подзадачи, оптимальную подструктуру и удовлетворяет свойству отсутствия последствий, то она обычно подходит для решения с помощью динамического программирования. Однако извлечь все эти свойства напрямую из формулировки задачи бывает трудно. Поэтому на практике мы обычно ослабляем требования и <strong>сначала смотрим, подходит ли задача для решения методом backtracking (полного перебора)</strong>.</p>
-<p><strong>Задачи, подходящие для backtracking, обычно удовлетворяют "модели дерева решений"</strong>. Такие задачи можно описать деревом, где каждый узел представляет одно решение, а каждый путь представляет последовательность решений.</p>
-<p>Иначе говоря, если в задаче есть четко выраженные решения и ответ порождается последовательностью таких решений, то она удовлетворяет модели дерева решений и обычно допускает решение через backtracking.</p>
+<p>В целом, если задача содержит перекрывающиеся подзадачи, оптимальную подструктуру и удовлетворяет свойству отсутствия последствий, то она обычно подходит для решения с помощью динамического программирования. Однако извлечь все эти свойства напрямую из формулировки задачи бывает трудно. Поэтому на практике мы обычно ослабляем требования и <strong>сначала смотрим, подходит ли задача для решения методом поиска с возвратом (полного перебора)</strong>.</p>
+<p><strong>Задачи, подходящие для поиска с возвратом, обычно удовлетворяют "модели дерева решений"</strong>. Такие задачи можно описать деревом, где каждый узел представляет одно решение, а каждый путь представляет последовательность решений.</p>
+<p>Иначе говоря, если в задаче есть четко выраженные решения и ответ порождается последовательностью таких решений, то она удовлетворяет модели дерева решений и обычно допускает решение через поиск с возвратом.</p>
 <p>Поверх этого у задач динамического программирования есть и некоторые дополнительные "плюсы".</p>
 <ul>
 <li>В условии задачи фигурируют слова "максимальный", "минимальный", "наибольший", "наименьший" и другие формулировки оптимизации.</li>
@@ -4495,7 +4495,7 @@
 
 <div class="admonition note">
 <p class="admonition-title">Note</p>
-<p>Как в динамическом программировании, так и в backtracking, решение задачи можно описать как последовательность решений, а состояние образуется всеми переменными решений. Оно должно содержать всю информацию, достаточную для вывода следующего состояния.</p>
+<p>Как в динамическом программировании, так и в поиске с возвратом, решение задачи можно описать как последовательность решений, а состояние образуется всеми переменными решений. Оно должно содержать всю информацию, достаточную для вывода следующего состояния.</p>
 <p>Каждому состоянию соответствует некоторая подзадача, и для хранения решений всех подзадач мы определяем таблицу <span class="arithmatex">\(dp\)</span> ; каждая независимая переменная состояния становится одним измерением таблицы <span class="arithmatex">\(dp\)</span> . По сути таблица <span class="arithmatex">\(dp\)</span> - это отображение от состояния к решению соответствующей подзадачи.</p>
 </div>
 <p><strong>Шаг 2: найти оптимальную подструктуру и на ее основе вывести уравнение перехода состояния</strong></p>
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 <!-- Page content -->
 <h1 id="146">14.6 &nbsp; Задача о расстоянии редактирования<a class="headerlink" href="#146" title="Permanent link">&para;</a></h1>
-<p>Расстояние редактирования, также называемое расстоянием Левенштейна, обозначает минимальное число правок, необходимых для взаимного преобразования двух строк. Обычно оно используется для измерения сходства двух последовательностей в информационном поиске и обработке естественного языка.</p>
+<p>Расстояние редактирования, также называемое расстоянием Левенштейна, - это минимальное количество изменений, необходимых для преобразования одной строки в другую. Обычно оно используется для измерения сходства двух последовательностей в информационном поиске и обработке естественного языка.</p>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
 <p>Даны две строки <span class="arithmatex">\(s\)</span> и <span class="arithmatex">\(t\)</span> . Верните минимальное число шагов редактирования, необходимое для преобразования <span class="arithmatex">\(s\)</span> в <span class="arithmatex">\(t\)</span> .</p>
@@ -4387,7 +4387,7 @@
 <p><img alt="Пример данных для задачи о расстоянии редактирования" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_example.png" /></p>
 <p align="center"> Рисунок 14-27 &nbsp; Пример данных для задачи о расстоянии редактирования </p>
 
-<p><strong>Задачу о расстоянии редактирования можно очень естественно описать через модель дерева решений</strong>. Строки соответствуют узлам дерева, а один раунд решения (одна операция редактирования) соответствует одному ребру дерева.</p>
+<p><strong>Задачу о расстоянии редактирования можно естественным образом объяснить с помощью модели дерева решений</strong>. Строки соответствуют узлам дерева, а один шаг решения, то есть одна операция редактирования, соответствует одному ребру дерева.</p>
 <p>Как показано на рисунке 14-28, если не ограничивать число операций, то каждый узел может порождать множество ребер, и каждое из них соответствует одному из вариантов преобразования. Это означает, что преобразовать <code>hello</code> в <code>algo</code> можно множеством разных путей.</p>
 <p>С точки зрения дерева решений цель этой задачи - найти кратчайший путь между узлом <code>hello</code> и узлом <code>algo</code> .</p>
 <p><img alt="Представление задачи о расстоянии редактирования через дерево решений" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_decision_tree.png" /></p>
@@ -4401,7 +4401,7 @@
 <li>Если <span class="arithmatex">\(s[n-1]\)</span> и <span class="arithmatex">\(t[m-1]\)</span> совпадают, их можно просто пропустить и сразу перейти к сравнению <span class="arithmatex">\(s[n-2]\)</span> и <span class="arithmatex">\(t[m-2]\)</span> .</li>
 <li>Если <span class="arithmatex">\(s[n-1]\)</span> и <span class="arithmatex">\(t[m-1]\)</span> различны, нужно выполнить над <span class="arithmatex">\(s\)</span> одну операцию редактирования (вставку, удаление или замену), чтобы последние символы стали одинаковыми, после чего можно перейти к задаче меньшего размера.</li>
 </ul>
-<p>Иначе говоря, каждое решение (операция редактирования), которое мы выполняем над строкой <span class="arithmatex">\(s\)</span> , меняет те символы, которые еще остаются несопоставленными в строках <span class="arithmatex">\(s\)</span> и <span class="arithmatex">\(t\)</span> . Поэтому состояние определяется текущими позициями рассматриваемых символов в <span class="arithmatex">\(s\)</span> и <span class="arithmatex">\(t\)</span> , то есть состоянием <span class="arithmatex">\([i, j]\)</span> .</p>
+<p>Иначе говоря, каждый шаг решения, то есть операция редактирования над строкой <span class="arithmatex">\(s\)</span> , меняет те символы, которые еще необходимо сопоставить в строках <span class="arithmatex">\(s\)</span> и <span class="arithmatex">\(t\)</span> . Поэтому состояние определяется текущими позициями рассматриваемых символов в <span class="arithmatex">\(s\)</span> и <span class="arithmatex">\(t\)</span> , то есть состоянием <span class="arithmatex">\([i, j]\)</span> .</p>
 <p>Подзадача, соответствующая состоянию <span class="arithmatex">\([i, j]\)</span> , такова: <strong>минимальное число операций редактирования, необходимое для преобразования первых <span class="arithmatex">\(i\)</span> символов строки <span class="arithmatex">\(s\)</span> в первые <span class="arithmatex">\(j\)</span> символов строки <span class="arithmatex">\(t\)</span></strong>.</p>
 <p>Отсюда получается двумерная таблица <span class="arithmatex">\(dp\)</span> размера <span class="arithmatex">\((i+1) \times (j+1)\)</span> .</p>
 <p><strong>Шаг 2: найти оптимальную подструктуру и на ее основе вывести уравнение перехода состояния</strong></p>
@@ -4414,7 +4414,7 @@
 <p><img alt="Переходы состояния в задаче о расстоянии редактирования" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_state_transfer.png" /></p>
 <p align="center"> Рисунок 14-29 &nbsp; Переходы состояния в задаче о расстоянии редактирования </p>
 
-<p>Согласно этому анализу оптимальная подструктура такова: минимальное число шагов редактирования для <span class="arithmatex">\(dp[i, j]\)</span> равно минимуму из трех значений - <span class="arithmatex">\(dp[i, j-1]\)</span> , <span class="arithmatex">\(dp[i-1, j]\)</span> и <span class="arithmatex">\(dp[i-1, j-1]\)</span> - плюс цена текущей операции редактирования <span class="arithmatex">\(1\)</span> . Значит, уравнение перехода состояния имеет вид:</p>
+<p>Согласно этому анализу оптимальная подструктура такова: минимальное число шагов редактирования для <span class="arithmatex">\(dp[i, j]\)</span> равно минимуму из трех значений - <span class="arithmatex">\(dp[i, j-1]\)</span> , <span class="arithmatex">\(dp[i-1, j]\)</span> и <span class="arithmatex">\(dp[i-1, j-1]\)</span> - плюс <span class="arithmatex">\(1\)</span> шаг за текущее редактирование. Значит, уравнение перехода состояния имеет вид:</p>
 <div class="arithmatex">\[
 dp[i, j] = \min(dp[i, j-1], dp[i-1, j], dp[i-1, j-1]) + 1
 \]</div>
@@ -4809,7 +4809,7 @@ dp[i, j] = dp[i-1, j-1]
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 </details>
-<p>Как показано на рисунке 14-30, процесс переходов состояния в задаче о расстоянии редактирования очень похож на процесс в задачах о рюкзаке: в обоих случаях это заполнение двумерной сетки.</p>
+<p>Как показано на рисунке 14-30, процесс переходов состояния в задаче о расстоянии редактирования очень похож на задачи о рюкзаке: и там и здесь его можно рассматривать как заполнение двумерной сетки.</p>
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@@ -4863,7 +4863,7 @@ dp[i, j] = dp[i-1, j-1]
 
 <h3 id="3">3. &nbsp; Оптимизация пространства<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
 <p>Поскольку <span class="arithmatex">\(dp[i,j]\)</span> зависит от значения сверху <span class="arithmatex">\(dp[i-1, j]\)</span> , слева <span class="arithmatex">\(dp[i, j-1]\)</span> и слева сверху <span class="arithmatex">\(dp[i-1, j-1]\)</span> , прямой обход после оптимизации памяти теряет значение слева сверху, а обратный обход не позволяет заранее построить значение слева <span class="arithmatex">\(dp[i, j-1]\)</span> . Значит, оба наивных варианта обхода здесь непригодны.</p>
-<p>Чтобы решить эту проблему, можно использовать переменную <code>leftup</code> для временного сохранения значения слева сверху <span class="arithmatex">\(dp[i-1, j-1]\)</span> ; после этого остается учитывать только верхнее и левое значения. Тогда ситуация становится эквивалентной задаче о полном рюкзаке, и можно выполнять прямой обход. Код приведен ниже:</p>
+<p>Чтобы решить эту проблему, можно использовать переменную <code>leftup</code> для временного сохранения значения слева сверху <span class="arithmatex">\(dp[i-1, j-1]\)</span> ; после этого остается учитывать только верхнее и левое значения. Тогда ситуация становится аналогичной задаче о полном рюкзаке, и можно выполнять прямой обход. Код приведен ниже:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label></div>
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     href="../unbounded_knapsack_problem/"
     class="md-footer__link md-footer__link--prev"
-    aria-label="Назад: 14.5 Задача о неограниченном рюкзаке"
+    aria-label="Назад: 14.5 Задача о полном рюкзаке"
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-        14.5 Задача о неограниченном рюкзаке
+        14.5 Задача о полном рюкзаке
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index 612b75d63..2fa43d0a2 100644
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+++ b/ru/chapter_dynamic_programming/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
@@ -574,7 +574,7 @@
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+    Глава 1. Введение в алгоритмы
   
 
     
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+    Глава 1. Введение в алгоритмы
   
 
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-    1.2 Что такое структуры данных и алгоритмы
+    1.2 Что такое алгоритм
   
 
     
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+    4.4 Оперативная память и кэш *
   
 
     
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+    Глава 6. Хеш-таблицы
   
 
     
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+    Глава 6. Хеш-таблицы
   
 
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+    Глава 9. Графы
   
 
     
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+    Глава 9. Графы
   
 
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+    9.2 Базовые операции графа
   
 
     
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+    9.4 Краткие итоги
   
 
     
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+    10.2 Двоичный поиск точки вставки
   
 
     
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+    10.3 Двоичный поиск границ
   
 
     
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+    10.4 Стратегии оптимизации хеширования
   
 
     
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-    10.5 Алгоритмы поиска: новый взгляд
+    10.5 Переосмысление алгоритмов поиска
   
 
     
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 </div>
 <h2 id="_1">Содержание главы<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
-<li><a href="intro_to_dynamic_programming/">14.1 &nbsp; Введение в динамическое программирование</a></li>
+<li><a href="intro_to_dynamic_programming/">14.1 &nbsp; Первое знакомство с динамическим программированием</a></li>
 <li><a href="dp_problem_features/">14.2 &nbsp; Свойства задач динамического программирования</a></li>
 <li><a href="dp_solution_pipeline/">14.3 &nbsp; Подход к решению задач динамического программирования</a></li>
 <li><a href="knapsack_problem/">14.4 &nbsp; Задача о рюкзаке 0-1</a></li>
-<li><a href="unbounded_knapsack_problem/">14.5 &nbsp; Задача о неограниченном рюкзаке</a></li>
+<li><a href="unbounded_knapsack_problem/">14.5 &nbsp; Задача о полном рюкзаке</a></li>
 <li><a href="edit_distance_problem/">14.6 &nbsp; Задача о расстоянии редактирования</a></li>
 <li><a href="summary/">14.7 &nbsp; Резюме</a></li>
 </ul>
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   <a
     href="./intro_to_dynamic_programming/"
     class="md-footer__link md-footer__link--next"
-    aria-label="Вперед: 14.1 Введение в динамическое программирование"
+    aria-label="Вперед: 14.1 Первое знакомство с динамическим программированием"
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+        14.1 Первое знакомство с динамическим программированием
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-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
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+    1.2 Что такое алгоритм
   
 
     
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+    4.4 Оперативная память и кэш *
   
 
     
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-    Глава 6. Хеширование
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 <!-- Page content -->
 <h1 id="141">14.1 &nbsp; Первое знакомство с динамическим программированием<a class="headerlink" href="#141" title="Permanent link">&para;</a></h1>
 <p><u>Динамическое программирование (dynamic programming)</u> - это важная алгоритмическая парадигма, которая разбивает задачу на последовательность более мелких подзадач и за счет хранения их решений избегает повторных вычислений, тем самым резко повышая эффективность по времени.</p>
-<p>В этом разделе мы начнем с классического примера: сначала запишем его грубое решение через backtracking, увидим в нем перекрывающиеся подзадачи, а затем постепенно выведем более эффективное решение на основе динамического программирования.</p>
+<p>В этом разделе мы начнем с классического примера: сначала представим его грубое решение методом поиска с возвратом, увидим в нем перекрывающиеся подзадачи, а затем постепенно выведем более эффективное решение на основе динамического программирования.</p>
 <div class="admonition question">
 <p class="admonition-title">Подъем по лестнице</p>
 <p>Дана лестница из <span class="arithmatex">\(n\)</span> ступеней. За один шаг можно подняться на <span class="arithmatex">\(1\)</span> или на <span class="arithmatex">\(2\)</span> ступени. Сколькими способами можно добраться до вершины?</p>
@@ -4409,7 +4409,7 @@
 <p><img alt="Число способов подняться на 3-ю ступень" class="animation-figure" src="../intro_to_dynamic_programming.assets/climbing_stairs_example.png" /></p>
 <p align="center"> Рисунок 14-1 &nbsp; Число способов подняться на 3-ю ступень </p>
 
-<p>Цель этой задачи - вычислить количество способов. <strong>Поэтому можно попробовать грубо перебрать все варианты с помощью backtracking</strong>. Если представить подъем по лестнице как последовательность решений, то мы начинаем от земли и на каждом раунде выбираем прыжок на <span class="arithmatex">\(1\)</span> или на <span class="arithmatex">\(2\)</span> ступени; всякий раз, когда достигаем вершины, увеличиваем число способов на <span class="arithmatex">\(1\)</span> , а если перескакиваем вершину, обрезаем эту ветвь. Код выглядит так:</p>
+<p>Цель этой задачи - вычислить количество способов. <strong>Поэтому можно попробовать использовать для ее решения метод поиска с возвратом</strong>. Если представить подъем по лестнице как последовательность решений, то мы начинаем от земли и на каждом раунде выбираем прыжок на <span class="arithmatex">\(1\)</span> или на <span class="arithmatex">\(2\)</span> ступени; всякий раз, когда достигаем вершины, увеличиваем число способов на <span class="arithmatex">\(1\)</span> , а если перескакиваем вершину, обрезаем эту ветвь. Код выглядит так:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
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@@ -4794,7 +4794,7 @@
 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20backtrack%28choices%3A%20list%5Bint%5D%2C%20state%3A%20int%2C%20n%3A%20int%2C%20res%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%91%D1%8D%D0%BA%D1%82%D1%80%D0%B5%D0%BA%D0%B8%D0%BD%D0%B3%22%22%22%0A%20%20%20%20%23%20%D0%9A%D0%BE%D0%B3%D0%B4%D0%B0%20%D0%BF%D0%BE%D0%B4%D1%8A%D0%B5%D0%BC%20%D0%B4%D0%BE%D1%81%D1%82%D0%B8%D0%B3%D0%B0%D0%B5%D1%82%20n-%D0%B9%20%D1%81%D1%82%D1%83%D0%BF%D0%B5%D0%BD%D0%B8%2C%20%D1%87%D0%B8%D1%81%D0%BB%D0%BE%20%D0%B2%D0%B0%D1%80%D0%B8%D0%B0%D0%BD%D1%82%D0%BE%D0%B2%20%D1%83%D0%B2%D0%B5%D0%BB%D0%B8%D1%87%D0%B8%D0%B2%D0%B0%D0%B5%D1%82%D1%81%D1%8F%20%D0%BD%D0%B0%201%0A%20%20%20%20if%20state%20%3D%3D%20n%3A%0A%20%20%20%20%20%20%20%20res%5B0%5D%20%2B%3D%201%0A%20%20%20%20%23%20%D0%9F%D0%B5%D1%80%D0%B5%D0%B1%D0%BE%D1%80%20%D0%B2%D1%81%D0%B5%D1%85%20%D0%B2%D0%B0%D1%80%D0%B8%D0%B0%D0%BD%D1%82%D0%BE%D0%B2%20%D0%B2%D1%8B%D0%B1%D0%BE%D1%80%D0%B0%0A%20%20%20%20for%20choice%20in%20choices%3A%0A%20%20%20%20%20%20%20%20%23%20%D0%9E%D1%82%D1%81%D0%B5%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%3A%20%D0%BD%D0%B5%D0%BB%D1%8C%D0%B7%D1%8F%20%D0%B2%D1%8B%D1%85%D0%BE%D0%B4%D0%B8%D1%82%D1%8C%20%D0%B7%D0%B0%20n-%D1%8E%20%D1%81%D1%82%D1%83%D0%BF%D0%B5%D0%BD%D1%8C%0A%20%20%20%20%20%20%20%20if%20state%20%2B%20choice%20%3E%20n%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20continue%0A%20%20%20%20%20%20%20%20%23%20%D0%9F%D0%BE%D0%BF%D1%8B%D1%82%D0%BA%D0%B0%3A%20%D1%81%D0%B4%D0%B5%D0%BB%D0%B0%D1%82%D1%8C%20%D0%B2%D1%8B%D0%B1%D0%BE%D1%80%20%D0%B8%20%D0%BE%D0%B1%D0%BD%D0%BE%D0%B2%D0%B8%D1%82%D1%8C%20%D1%81%D0%BE%D1%81%D1%82%D0%BE%D1%8F%D0%BD%D0%B8%D0%B5%0A%20%20%20%20%20%20%20%20backtrack%28choices%2C%20state%20%2B%20choice%2C%20n%2C%20res%29%0A%20%20%20%20%20%20%20%20%23%20%D0%9E%D1%82%D0%BA%D0%B0%D1%82%0A%0A%0Adef%20climbing_stairs_backtrack%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%D0%9F%D0%BE%D0%B4%D1%8A%D0%B5%D0%BC%20%D0%BF%D0%BE%20%D0%BB%D0%B5%D1%81%D1%82%D0%BD%D0%B8%D1%86%D0%B5%3A%20%D0%B1%D1%8D%D0%BA%D1%82%D1%80%D0%B5%D0%BA%D0%B8%D0%BD%D0%B3%22%22%22%0A%20%20%20%20choices%20%3D%20%5B1%2C%202%5D%20%20%23%20%D0%9C%D0%BE%D0%B6%D0%BD%D0%BE%20%D0%BF%D0%BE%D0%B4%D0%BD%D1%8F%D1%82%D1%8C%D1%81%D1%8F%20%D0%BD%D0%B0%201%20%D0%B8%D0%BB%D0%B8%202%20%D1%81%D1%82%D1%83%D0%BF%D0%B5%D0%BD%D0%B8%0A%20%20%20%20state%20%3D%200%20%20%23%20%D0%9D%D0%B0%D1%87%D0%B0%D1%82%D1%8C%20%D0%BF%D0%BE%D0%B4%D1%8A%D0%B5%D0%BC%20%D1%81%200-%D0%B9%20%D1%81%D1%82%D1%83%D0%BF%D0%B5%D0%BD%D0%B8%0A%20%20%20%20res%20%3D%20%5B0%5D%20%20%23%20%D0%98%D1%81%D0%BF%D0%BE%D0%BB%D1%8C%D0%B7%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20res%5B0%5D%20%D0%B4%D0%BB%D1%8F%20%D1%85%D1%80%D0%B0%D0%BD%D0%B5%D0%BD%D0%B8%D1%8F%20%D1%87%D0%B8%D1%81%D0%BB%D0%B0%20%D1%80%D0%B5%D1%88%D0%B5%D0%BD%D0%B8%D0%B9%0A%20%20%20%20backtrack%28choices%2C%20state%2C%20n%2C%20res%29%0A%20%20%20%20return%20res%5B0%5D%0A%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%204%0A%0A%20%20%20%20res%20%3D%20climbing_stairs_backtrack%28n%29%0A%20%20%20%20print%28f%22%D0%9A%D0%BE%D0%BB%D0%B8%D1%87%D0%B5%D1%81%D1%82%D0%B2%D0%BE%20%D1%81%D0%BF%D0%BE%D1%81%D0%BE%D0%B1%D0%BE%D0%B2%20%D0%BF%D0%BE%D0%B4%D0%BD%D1%8F%D1%82%D1%8C%D1%81%D1%8F%20%D0%BF%D0%BE%20%D0%BB%D0%B5%D1%81%D1%82%D0%BD%D0%B8%D1%86%D0%B5%20%D0%B8%D0%B7%20%7Bn%7D%20%D1%81%D1%82%D1%83%D0%BF%D0%B5%D0%BD%D0%B5%D0%B9%20%3D%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
 <h2 id="1411-1">14.1.1 &nbsp; Метод 1: полный перебор<a class="headerlink" href="#1411-1" title="Permanent link">&para;</a></h2>
-<p>Backtracking обычно не раскладывает задачу явно на подзадачи; вместо этого он рассматривает решение как последовательность решений, используя попытки и обрезку для поиска всех возможных ответов.</p>
+<p>Алгоритм поиска с возвратом обычно не раскладывает задачу явно на подзадачи; вместо этого он рассматривает решение как последовательность решений, используя попытки и обрезку для поиска всех возможных ответов.</p>
 <p>Попробуем посмотреть на задачу именно как на разложение подзадач. Пусть число способов добраться до ступени <span class="arithmatex">\(i\)</span> равно <span class="arithmatex">\(dp[i]\)</span> ; тогда <span class="arithmatex">\(dp[i]\)</span> - это исходная задача, а ее подзадачи включают:</p>
 <div class="arithmatex">\[
 dp[i-1], dp[i-2], \dots, dp[2], dp[1]
@@ -4809,7 +4809,7 @@ dp[i] = dp[i-1] + dp[i-2]
 <p align="center"> Рисунок 14-2 &nbsp; Рекуррентная связь числа способов </p>
 
 <p>По рекуррентной формуле можно получить решение полного перебора. Начиная с <span class="arithmatex">\(dp[n]\)</span> , <strong>мы рекурсивно разлагаем большую задачу в сумму двух меньших задач</strong> , пока не дойдем до наименьших подзадач <span class="arithmatex">\(dp[1]\)</span> и <span class="arithmatex">\(dp[2]\)</span> . Их решения уже известны: <span class="arithmatex">\(dp[1] = 1\)</span> и <span class="arithmatex">\(dp[2] = 2\)</span> , что означает <span class="arithmatex">\(1\)</span> и <span class="arithmatex">\(2\)</span> способа подняться соответственно на <span class="arithmatex">\(1\)</span>-ю и <span class="arithmatex">\(2\)</span>-ю ступени.</p>
-<p>Посмотрите на следующий код: как и стандартный backtracking, он относится к поиску в глубину, но выглядит более компактно:</p>
+<p>Посмотрите на следующий код: как и стандартный поиск с возвратом, он относится к поиску в глубину, но выглядит более компактно:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
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@@ -5626,7 +5626,7 @@ dp[i] = dp[i-1] + dp[i-2]
 <p><img alt="Процесс динамического программирования для подъема по лестнице" class="animation-figure" src="../intro_to_dynamic_programming.assets/climbing_stairs_dp.png" /></p>
 <p align="center"> Рисунок 14-5 &nbsp; Процесс динамического программирования для подъема по лестнице </p>
 
-<p>Как и в backtracking, в динамическом программировании используется понятие "состояние" для обозначения некоторого этапа решения задачи; каждое состояние соответствует одной подзадаче и ее локально оптимальному решению. Например, в задаче о лестнице состояние определяется текущим номером ступени <span class="arithmatex">\(i\)</span> .</p>
+<p>Как и в поиске с возвратом, в динамическом программировании используется понятие "состояние" для обозначения некоторого этапа решения задачи; каждое состояние соответствует одной подзадаче и ее локально оптимальному решению. Например, в задаче о лестнице состояние определяется текущим номером ступени <span class="arithmatex">\(i\)</span> .</p>
 <p>На основе сказанного можно подвести несколько часто используемых терминов динамического программирования.</p>
 <ul>
 <li>Массив <code>dp</code> называют <u>таблицей dp</u>, а <span class="arithmatex">\(dp[i]\)</span> обозначает решение подзадачи, соответствующей состоянию <span class="arithmatex">\(i\)</span> .</li>
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-    10.5 Алгоритмы поиска: новый взгляд
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-    12.1 Алгоритмы разделяй и властвуй
+    12.1 Стратегия разделяй и властвуй
   
 
     
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-    12.2 Стратегия поиска разделяй и властвуй
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+    13.4 Задача о n ферзях
   
 
     
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-    14.1 Введение в динамическое программирование
+    14.1 Первое знакомство с динамическим программированием
   
 
     
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   <a href="#2-2" class="md-nav__link">
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-        2. &nbsp; Метод 2: поиск с мемоизацией
+        2. &nbsp; Метод 2: мемоизация
       
     </span>
   </a>
@@ -3765,7 +3765,7 @@
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-    14.5 Задача о неограниченном рюкзаке
+    14.5 Задача о полном рюкзаке
   
 
     
@@ -4332,7 +4332,7 @@
   <a href="#2-2" class="md-nav__link">
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-        2. &nbsp; Метод 2: поиск с мемоизацией
+        2. &nbsp; Метод 2: мемоизация
       
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@@ -4399,7 +4399,7 @@
 
 <!-- Page content -->
 <h1 id="144-0-1">14.4 &nbsp; Задача о рюкзаке 0-1<a class="headerlink" href="#144-0-1" title="Permanent link">&para;</a></h1>
-<p>Задача о рюкзаке - это очень хороший вводный пример для динамического программирования и одна из самых типичных форм задач этого класса. У нее существует множество вариантов, например задача о рюкзаке 0-1, задача о полном рюкзаке, задача о многократном рюкзаке и т.д.</p>
+<p>Задача о рюкзаке является отличным примером для начала изучения динамического программирования и представляет собой одну из наиболее распространенных форм этой задачи. У нее существует множество вариантов, например задача о рюкзаке 0-1, задача о полном рюкзаке, задача о многократном рюкзаке и т.д.</p>
 <p>В этом разделе сначала разберем самый распространенный вариант - задачу о рюкзаке 0-1.</p>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
@@ -4409,8 +4409,8 @@
 <p><img alt="Пример данных для задачи о рюкзаке 0-1" class="animation-figure" src="../knapsack_problem.assets/knapsack_example.png" /></p>
 <p align="center"> Рисунок 14-17 &nbsp; Пример данных для задачи о рюкзаке 0-1 </p>
 
-<p>На задачу о рюкзаке 0-1 можно смотреть как на процесс из <span class="arithmatex">\(n\)</span> раундов решений: для каждого предмета есть два решения - не класть его в рюкзак или положить в рюкзак. Поэтому задача удовлетворяет модели дерева решений.</p>
-<p>Цель задачи - найти "максимальную суммарную стоимость при ограниченной вместимости рюкзака", значит, с большой вероятностью это задача динамического программирования.</p>
+<p>Задачу о рюкзаке 0-1 можно рассматривать как процесс из <span class="arithmatex">\(n\)</span> раундов принятия решений: для каждого предмета есть два решения - не класть его в рюкзак или положить в рюкзак. Поэтому задача удовлетворяет модели дерева решений.</p>
+<p>Цель задачи - найти "максимальную суммарную стоимость при ограниченной вместимости рюкзака", а это с большой вероятностью указывает на задачу динамического программирования.</p>
 <p><strong>Шаг 1: продумать решения на каждом раунде, определить состояние и тем самым получить таблицу <span class="arithmatex">\(dp\)</span></strong></p>
 <p>Для каждого предмета возможны два случая: не класть его в рюкзак, тогда вместимость не меняется; или положить его в рюкзак, тогда оставшаяся вместимость уменьшается. Отсюда получается определение состояния: текущий номер предмета <span class="arithmatex">\(i\)</span> и текущая вместимость рюкзака <span class="arithmatex">\(c\)</span> , то есть состояние обозначается как <span class="arithmatex">\([i, c]\)</span> .</p>
 <p>Подзадача, соответствующая состоянию <span class="arithmatex">\([i, c]\)</span> , такова: <strong>максимальная стоимость, которую можно получить, используя первые <span class="arithmatex">\(i\)</span> предметов и рюкзак вместимости <span class="arithmatex">\(c\)</span></strong>. Ее решение обозначается через <span class="arithmatex">\(dp[i, c]\)</span> .</p>
@@ -4702,7 +4702,7 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
 <p><img alt="Дерево полного перебора для задачи о рюкзаке 0-1" class="animation-figure" src="../knapsack_problem.assets/knapsack_dfs.png" /></p>
 <p align="center"> Рисунок 14-18 &nbsp; Дерево полного перебора для задачи о рюкзаке 0-1 </p>
 
-<h3 id="2-2">2. &nbsp; Метод 2: поиск с мемоизацией<a class="headerlink" href="#2-2" title="Permanent link">&para;</a></h3>
+<h3 id="2-2">2. &nbsp; Метод 2: мемоизация<a class="headerlink" href="#2-2" title="Permanent link">&para;</a></h3>
 <p>Чтобы каждая перекрывающаяся подзадача вычислялась только один раз, используем таблицу памяти <code>mem</code> для хранения решений подзадач, где <code>mem[i][c]</code> соответствует <span class="arithmatex">\(dp[i, c]\)</span> .</p>
 <p>После введения мемоизации <strong>временная сложность определяется числом подзадач</strong> , то есть равна <span class="arithmatex">\(O(n \times cap)\)</span> . Код выглядит так:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
@@ -5412,13 +5412,13 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
 <p align="center"> Рисунок 14-20 &nbsp; Процесс динамического программирования для задачи о рюкзаке 0-1 </p>
 
 <h3 id="4">4. &nbsp; Оптимизация пространства<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
-<p>Поскольку каждое состояние зависит только от состояния в предыдущей строке, можно использовать два массива, которые будут "перекатываться" вперед, и тем самым уменьшить пространственную сложность с <span class="arithmatex">\(O(n^2)\)</span> до <span class="arithmatex">\(O(n)\)</span> .</p>
+<p>Поскольку каждое состояние зависит только от состояния в предыдущей строке, можно использовать два массива, которые будут продвигаться вперед по очереди, и тем самым уменьшить пространственную сложность с <span class="arithmatex">\(O(n^2)\)</span> до <span class="arithmatex">\(O(n)\)</span> .</p>
 <p>Если пойти дальше, можно спросить: можно ли оптимизировать память так, чтобы использовать только один массив? Наблюдение показывает, что каждое состояние зависит от клетки прямо сверху и клетки слева сверху. Предположим, что у нас есть только один массив, и в момент начала обхода строки <span class="arithmatex">\(i\)</span> он еще хранит состояния строки <span class="arithmatex">\(i-1\)</span> .</p>
 <ul>
 <li>Если обходить массив слева направо, то к моменту вычисления <span class="arithmatex">\(dp[i, j]\)</span> значения слева сверху <span class="arithmatex">\(dp[i-1, 1]\)</span> ~ <span class="arithmatex">\(dp[i-1, j-1]\)</span> могут уже быть перезаписаны, и правильный результат перехода состояния получить не удастся.</li>
 <li>Если же обходить массив справа налево, проблема перезаписи не возникает, и переход состояния вычисляется корректно.</li>
 </ul>
-<p>На рисунке 14-21 показан процесс перехода от строки <span class="arithmatex">\(i = 1\)</span> к строке <span class="arithmatex">\(i = 2\)</span> при использовании одного массива. Попробуйте сопоставить его с разницей между прямым и обратным обходом.</p>
+<p>На рисунке 14-21 показан процесс перехода от строки <span class="arithmatex">\(i = 1\)</span> к строке <span class="arithmatex">\(i = 2\)</span> при использовании одного массива. С его помощью удобно понять различие между прямым и обратным обходом.</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="5:6"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">&lt;1&gt;</label><label for="__tabbed_5_2">&lt;2&gt;</label><label for="__tabbed_5_3">&lt;3&gt;</label><label for="__tabbed_5_4">&lt;4&gt;</label><label for="__tabbed_5_5">&lt;5&gt;</label><label for="__tabbed_5_6">&lt;6&gt;</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
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   <a
     href="../unbounded_knapsack_problem/"
     class="md-footer__link md-footer__link--next"
-    aria-label="Вперед: 14.5 Задача о неограниченном рюкзаке"
+    aria-label="Вперед: 14.5 Задача о полном рюкзаке"
     rel="next"
   >
     <div class="md-footer__title">
@@ -5779,7 +5779,7 @@ aria-label="Нижний колонтитул"
         Вперед
       </span>
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-        14.5 Задача о неограниченном рюкзаке
+        14.5 Задача о полном рюкзаке
       </div>
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+++ b/ru/chapter_dynamic_programming/summary/index.html
@@ -65,8 +65,8 @@
         
         
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-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
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-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
     
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-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
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-    1.2 Что такое структуры данных и алгоритмы
+    1.2 Что такое алгоритм
   
 
     
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-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
     
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+    Глава 4. Массивы и списки
   
 
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+    4.4 Оперативная память и кэш *
   
 
     
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+    7.3 Представление двоичного дерева массивом
   
 
     
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+    7.6 Краткие итоги
   
 
     
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+    8.3 Задача Top-k
   
 
     
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+    Глава 9. Графы
   
 
     
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+    10.2 Двоичный поиск точки вставки
   
 
     
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@@ -4336,9 +4336,9 @@
 <h3 id="1">1. &nbsp; Ключевые выводы<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
 <li>Динамическое программирование раскладывает задачу на подзадачи и повышает вычислительную эффективность за счет хранения решений этих подзадач и устранения повторных вычислений.</li>
-<li>Если не учитывать затраты времени, то любую задачу динамического программирования можно решить с помощью backtracking (полного перебора), однако в дереве рекурсии возникает множество перекрывающихся подзадач, из-за чего эффективность крайне низка. После введения таблицы памяти можно хранить решения всех уже вычисленных подзадач и гарантировать, что каждая перекрывающаяся подзадача будет вычисляться только один раз.</li>
+<li>Если не учитывать затраты времени, то любую задачу динамического программирования можно решить с помощью поиска с возвратом (полного перебора), однако в дереве рекурсии возникает множество перекрывающихся подзадач, из-за чего эффективность крайне низка. После введения таблицы памяти можно хранить решения всех уже вычисленных подзадач и гарантировать, что каждая перекрывающаяся подзадача будет вычисляться только один раз.</li>
 <li>Поиск с мемоизацией - это рекурсивный метод "сверху вниз", а соответствующее ему динамическое программирование - это итеративный метод "снизу вверх", похожий на заполнение таблицы. Поскольку текущее состояние обычно зависит только от части локальных состояний, можно убрать одно измерение таблицы <span class="arithmatex">\(dp\)</span> и тем самым снизить пространственную сложность.</li>
-<li>Разложение на подзадачи - это общий алгоритмический подход, но в divide and conquer, динамическом программировании и backtracking он имеет разные свойства.</li>
+<li>Разложение на подзадачи - это общий алгоритмический подход, но в методе "разделяй и властвуй", динамическом программировании и поиске с возвратом он имеет разные свойства.</li>
 <li>Для задач динамического программирования характерны три главных свойства: перекрывающиеся подзадачи, оптимальная подструктура и отсутствие последствий.</li>
 <li>Если оптимальное решение исходной задачи можно построить из оптимальных решений подзадач, то задача обладает оптимальной подструктурой.</li>
 <li>Отсутствие последствий означает, что для данного состояния его дальнейшее развитие определяется только этим состоянием и не зависит от всех прошлых состояний. Многие задачи комбинаторной оптимизации этим свойством не обладают и потому не могут эффективно решаться с помощью динамического программирования.</li>
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-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
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+    1.2 Что такое алгоритм
   
 
     
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+    4.4 Оперативная память и кэш *
   
 
     
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 <!-- Page content -->
 <h1 id="145">14.5 &nbsp; Задача о полном рюкзаке<a class="headerlink" href="#145" title="Permanent link">&para;</a></h1>
-<p>В этом разделе сначала решим еще один распространенный вариант задачи о рюкзаке - полный рюкзак, а затем рассмотрим одну из его типичных специальных форм: задачу о размене монет.</p>
+<p>В этом разделе сначала решим еще одну распространенную задачу о рюкзаке - задачу о полном рюкзаке, а затем рассмотрим один из ее типичных частных случаев: задачу о размене монет.</p>
 <h2 id="1451">14.5.1 &nbsp; Задача о полном рюкзаке<a class="headerlink" href="#1451" title="Permanent link">&para;</a></h2>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
@@ -4621,10 +4621,10 @@
 <p align="center"> Рисунок 14-22 &nbsp; Пример данных для задачи о полном рюкзаке </p>
 
 <h3 id="1">1. &nbsp; Идея динамического программирования<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>Задача о полном рюкзаке очень похожа на задачу о рюкзаке 0-1; <strong>разница состоит только в том, что число выборов каждого предмета не ограничено</strong>.</p>
+<p>Задача о полном рюкзаке очень похожа на задачу о рюкзаке 0-1; <strong>разница состоит только в том, что количество выборов каждого предмета не ограничено</strong>.</p>
 <ul>
 <li>В задаче о рюкзаке 0-1 каждого предмета существует только один экземпляр, поэтому после того как предмет <span class="arithmatex">\(i\)</span> помещен в рюкзак, выбирать можно только из первых <span class="arithmatex">\(i-1\)</span> предметов.</li>
-<li>В задаче о полном рюкзаке число экземпляров каждого предмета бесконечно, поэтому после того как предмет <span class="arithmatex">\(i\)</span> помещен в рюкзак, <strong>выбирать все еще можно из первых <span class="arithmatex">\(i\)</span> предметов</strong>.</li>
+<li>В задаче о полном рюкзаке количество предметов не ограничено, поэтому после того как предмет <span class="arithmatex">\(i\)</span> помещен в рюкзак, <strong>можно продолжать выбирать из первых <span class="arithmatex">\(i\)</span> предметов</strong>.</li>
 </ul>
 <p>При этом состояние <span class="arithmatex">\([i, c]\)</span> в задаче о полном рюкзаке может изменяться двумя способами.</p>
 <ul>
@@ -5315,9 +5315,9 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
 <p align="center"> Рисунок 14-24 &nbsp; Пример данных для задачи о размене монет </p>
 
 <h3 id="1_1">1. &nbsp; Идея динамического программирования<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
-<p><strong>Задачу о размене монет можно рассматривать как частный случай задачи о полном рюкзаке</strong> ; между ними существует следующая связь и следующие различия.</p>
+<p><strong>Задачу о размене монет можно рассматривать как частный случай задачи о полном рюкзаке</strong> ; между ними существуют следующие соответствия и различия.</p>
 <ul>
-<li>Эти две задачи можно взаимно переводить друг в друга: "предмет" соответствует "монете", "вес предмета" соответствует "номиналу монеты", а "вместимость рюкзака" соответствует "целевой сумме".</li>
+<li>Эти две задачи можно взаимно преобразовать: "предмет" соответствует "монете", "вес предмета" соответствует "номиналу монеты", а "вместимость рюкзака" соответствует "целевой сумме".</li>
 <li>Цель оптимизации противоположна: в задаче о полном рюкзаке нужно максимизировать стоимость предметов, а в задаче о размене монет - минимизировать число монет.</li>
 <li>В задаче о полном рюкзаке ищется решение, не превышающее вместимость, а в задаче о размене монет требуется <strong>ровно</strong> набрать целевую сумму.</li>
 </ul>
@@ -5337,7 +5337,7 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
 <p>Когда целевая сумма равна <span class="arithmatex">\(0\)</span> , минимальное число монет для ее набора равно <span class="arithmatex">\(0\)</span> , то есть весь первый столбец <span class="arithmatex">\(dp[i, 0]\)</span> заполняется нулями.</p>
 <p>Когда монет нет, <strong>невозможно набрать никакую целевую сумму <span class="arithmatex">\(&gt; 0\)</span></strong> ; это и есть недопустимое решение. Чтобы функция <span class="arithmatex">\(\min()\)</span> в уравнении перехода состояния могла распознавать и отбрасывать такие недопустимые решения, удобно использовать значение <span class="arithmatex">\(+ \infty\)</span> ; то есть всю первую строку <span class="arithmatex">\(dp[0, a]\)</span> нужно инициализировать значением <span class="arithmatex">\(+ \infty\)</span> .</p>
 <h3 id="2_1">2. &nbsp; Реализация кода<a class="headerlink" href="#2_1" title="Permanent link">&para;</a></h3>
-<p>Большинство языков программирования не предоставляет готовую переменную <span class="arithmatex">\(+ \infty\)</span> для целых чисел, поэтому обычно приходится заменять ее на максимальное значение типа <code>int</code> . Но тогда возникает риск переполнения: операция <span class="arithmatex">\(+ 1\)</span> в уравнении перехода может переполнить большое число.</p>
+<p>Большинство языков программирования не предоставляет представление для <span class="arithmatex">\(+ \infty\)</span> в целочисленном виде, поэтому обычно приходится заменять его на максимальное значение типа <code>int</code> . Но тогда возникает риск переполнения: операция <span class="arithmatex">\(+ 1\)</span> в уравнении перехода может переполнить большое число.</p>
 <p>Поэтому здесь мы используем число <span class="arithmatex">\(amt + 1\)</span> как обозначение недопустимого решения, потому что для набора суммы <span class="arithmatex">\(amt\)</span> максимум нужно не больше чем <span class="arithmatex">\(amt\)</span> монет. Перед возвратом результата проверяем, равно ли <span class="arithmatex">\(dp[n, amt]\)</span> значению <span class="arithmatex">\(amt + 1\)</span> ; если да, то возвращаем <span class="arithmatex">\(-1\)</span> , что означает невозможность набрать целевую сумму. Код приведен ниже:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="4:13"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label></div>
 <div class="tabbed-content">
@@ -6118,7 +6118,7 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
 <p align="center"> Рисунок 14-26 &nbsp; Пример данных для задачи о размене монет II </p>
 
 <h3 id="1_2">1. &nbsp; Идея динамического программирования<a class="headerlink" href="#1_2" title="Permanent link">&para;</a></h3>
-<p>По сравнению с предыдущей задачей теперь целью является число комбинаций. Поэтому подзадача меняется на следующую: <strong>число комбинаций из первых <span class="arithmatex">\(i\)</span> видов монет, которыми можно набрать сумму <span class="arithmatex">\(a\)</span></strong>. При этом таблица <span class="arithmatex">\(dp\)</span> по-прежнему остается двумерной матрицей размера <span class="arithmatex">\((n+1) \times (amt + 1)\)</span> .</p>
+<p>По сравнению с предыдущей задачей здесь целью является число комбинаций. Поэтому подзадача меняется на следующую: <strong>число комбинаций из первых <span class="arithmatex">\(i\)</span> видов монет, которыми можно набрать сумму <span class="arithmatex">\(a\)</span></strong>. При этом таблица <span class="arithmatex">\(dp\)</span> по-прежнему остается двумерной матрицей размера <span class="arithmatex">\((n+1) \times (amt + 1)\)</span> .</p>
 <p>Число комбинаций для текущего состояния равно сумме числа комбинаций для двух решений: не брать текущую монету и брать текущую монету. Поэтому уравнение перехода состояния принимает вид:</p>
 <div class="arithmatex">\[
 dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
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-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
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 <!-- Page content -->
 <h1 id="91">9.1 &nbsp; Граф<a class="headerlink" href="#91" title="Permanent link">&para;</a></h1>
-<p><u>Граф (graph)</u> - это нелинейная структура данных, состоящая из <u>вершин (vertex)</u> и <u>ребер (edge)</u>. Мы можем абстрактно представить граф <span class="arithmatex">\(G\)</span> как множество вершин <span class="arithmatex">\(V\)</span> и множество ребер <span class="arithmatex">\(E\)</span> . В примере ниже показан граф, содержащий 5 вершин и 7 ребер.</p>
+<p><u>Граф (graph)</u> - это нелинейная структура данных, состоящая из <u>вершин (vertex)</u> и <u>ребер (edge)</u>. Граф <span class="arithmatex">\(G\)</span> можно абстрактно представить как множество вершин <span class="arithmatex">\(V\)</span> и множество ребер <span class="arithmatex">\(E\)</span> . Ниже приведен пример графа, содержащего 5 вершин и 7 ребер.</p>
 <div class="arithmatex">\[
 \begin{aligned}
 V &amp; = \{ 1, 2, 3, 4, 5 \} \newline
@@ -4441,61 +4441,61 @@ E &amp; = \{ (1,2), (1,3), (1,5), (2,3), (2,4), (2,5), (4,5) \} \newline
 G &amp; = \{ V, E \} \newline
 \end{aligned}
 \]</div>
-<p>Если рассматривать вершины как узлы, а ребра как ссылки (указатели), соединяющие эти узлы, то граф можно считать структурой данных, выросшей из связного списка. Как показано на рисунке 9-1, <strong>по сравнению с линейными отношениями (связный список) и отношениями разделения (дерево), сетевые отношения (граф) обладают большей свободой</strong> , а потому и сложнее.</p>
+<p>Если рассматривать вершины как узлы, а ребра как ссылки, соединяющие узлы, граф можно считать структурой данных, расширяющей связный список. Как показано на рисунке 9-1, <strong>по сравнению с линейными отношениями (связный список) и отношениями разделения (дерево), сетевые отношения (граф) обладают большей свободой</strong> и потому являются более сложными.</p>
 <p><img alt="Связь между связным списком, деревом и графом" class="animation-figure" src="../graph.assets/linkedlist_tree_graph.png" /></p>
 <p align="center"> Рисунок 9-1 &nbsp; Связь между связным списком, деревом и графом </p>
 
 <h2 id="911">9.1.1 &nbsp; Распространенные типы и термины графов<a class="headerlink" href="#911" title="Permanent link">&para;</a></h2>
-<p>В зависимости от того, имеют ли ребра направление, графы делятся на <u>неориентированные графы (undirected graph)</u> и <u>ориентированные графы (directed graph)</u> , как показано на рисунке 9-2.</p>
+<p>В зависимости от наличия направления у ребер графы делятся на <u>неориентированные графы (undirected graph)</u> и <u>ориентированные графы (directed graph)</u> , как показано на рисунке 9-2.</p>
 <ul>
-<li>В неориентированном графе ребро означает "двустороннюю" связь между двумя вершинами, например отношение "друзья" в WeChat или QQ.</li>
-<li>В ориентированном графе ребро имеет направление, то есть ребра <span class="arithmatex">\(A \rightarrow B\)</span> и <span class="arithmatex">\(A \leftarrow B\)</span> независимы друг от друга, как, например, отношения "подписка" и "подписчик" в Weibo или Douyin.</li>
+<li>В неориентированном графе ребро представляет двустороннюю связь между двумя вершинами, например дружеские отношения в социальных сетях.</li>
+<li>В ориентированном графе ребро имеет направление, то есть ребра <span class="arithmatex">\(A \rightarrow B\)</span> и <span class="arithmatex">\(A \leftarrow B\)</span> независимы друг от друга, например отношения подписки и подписчиков.</li>
 </ul>
 <p><img alt="Ориентированный и неориентированный графы" class="animation-figure" src="../graph.assets/directed_graph.png" /></p>
 <p align="center"> Рисунок 9-2 &nbsp; Ориентированный и неориентированный графы </p>
 
-<p>В зависимости от того, достижимы ли все вершины друг из друга, граф делится на <u>связный граф (connected graph)</u> и <u>несвязный граф (disconnected graph)</u> , как показано на рисунке 9-3.</p>
+<p>В зависимости от того, связаны ли все вершины между собой, граф делится на <u>связный граф (connected graph)</u> и <u>несвязный граф (disconnected graph)</u> , как показано на рисунке 9-3.</p>
 <ul>
-<li>В связном графе, начиная из некоторой вершины, можно добраться до любой другой вершины.</li>
-<li>В несвязном графе, начиная из некоторой вершины, по крайней мере одна вершина оказывается недостижимой.</li>
+<li>В связном графе из любой вершины можно достичь любой другой вершины.</li>
+<li>В несвязном графе существует по крайней мере одна вершина, недостижимая из текущей.</li>
 </ul>
 <p><img alt="Связный и несвязный графы" class="animation-figure" src="../graph.assets/connected_graph.png" /></p>
 <p align="center"> Рисунок 9-3 &nbsp; Связный и несвязный графы </p>
 
-<p>Мы также можем добавить к ребрам переменную "вес" и тем самым получить <u>взвешенный граф (weighted graph)</u> , показанный на рисунке 9-4. Например, в мобильных играх вроде Honor of Kings система может вычислять "степень близости" между игроками по времени, проведенному в совместных играх; такую сеть близости можно описать взвешенным графом.</p>
+<p>Мы также можем добавить к ребрам переменную "вес" и получить показанный ниже <u>взвешенный граф (weighted graph)</u>. Например, в мобильных играх вроде Honor of Kings система рассчитывает "близость" между игроками по времени совместной игры, и такую сеть близости можно представить взвешенным графом.</p>
 <p><img alt="Взвешенный и невзвешенный графы" class="animation-figure" src="../graph.assets/weighted_graph.png" /></p>
 <p align="center"> Рисунок 9-4 &nbsp; Взвешенный и невзвешенный графы </p>
 
-<p>Для структуры данных "граф" используются следующие распространенные термины.</p>
+<p>Со структурой данных "граф" связаны следующие основные термины.</p>
 <ul>
-<li><u>Смежность (adjacency)</u>: если между двумя вершинами существует ребро, то эти вершины называются "смежными". На рисунке 9-4 вершинам 2, 3, 5 смежна вершина 1.</li>
-<li><u>Путь (path)</u>: последовательность ребер, ведущая из вершины A в вершину B, называется "путем" от A до B. На рисунке 9-4 последовательность ребер 1-5-2-4 представляет один из путей от вершины 1 к вершине 4.</li>
-<li><u>Степень (degree)</u>: число ребер, принадлежащих вершине. Для ориентированного графа <u>входящая степень (in-degree)</u> показывает число ребер, ведущих в вершину, а <u>исходящая степень (out-degree)</u> показывает число ребер, исходящих из вершины.</li>
+<li><u>Смежность (adjacency)</u>: если между двумя вершинами существует ребро, то такие вершины называются смежными. На рисунке 9-4 с вершиной 1 смежны вершины 2, 3 и 5.</li>
+<li><u>Путь (path)</u>: последовательность ребер от вершины A до вершины B называется путем из A в B. На рисунке 9-4 последовательность ребер 1-5-2-4 является одним из путей от вершины 1 к вершине 4.</li>
+<li><u>Степень (degree)</u>: количество ребер, принадлежащих вершине. Для ориентированного графа <u>входящая степень (in-degree)</u> показывает, сколько ребер входит в вершину, а <u>исходящая степень (out-degree)</u> показывает, сколько ребер из нее выходит.</li>
 </ul>
 <h2 id="912">9.1.2 &nbsp; Представление графа<a class="headerlink" href="#912" title="Permanent link">&para;</a></h2>
-<p>Распространенные способы представления графа включают "матрицу смежности" и "список смежности". Ниже в качестве примера используется неориентированный граф.</p>
+<p>Распространенные способы представления графа включают "матрицу смежности" и "список смежности". Ниже для примера рассматривается неориентированный граф.</p>
 <h3 id="1">1. &nbsp; Матрица смежности<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>Пусть число вершин графа равно <span class="arithmatex">\(n\)</span> ; тогда <u>матрица смежности (adjacency matrix)</u> использует матрицу размера <span class="arithmatex">\(n \times n\)</span> для представления графа: каждая строка и каждый столбец соответствуют вершине, а элементы матрицы отражают наличие ребра, то есть показывают, существует между двумя вершинами связь или нет.</p>
-<p>Как показано на рисунке 9-5, пусть матрица смежности обозначается как <span class="arithmatex">\(M\)</span> , а список вершин - как <span class="arithmatex">\(V\)</span> ; тогда элемент матрицы <span class="arithmatex">\(M[i, j] = 1\)</span> означает, что между вершинами <span class="arithmatex">\(V[i]\)</span> и <span class="arithmatex">\(V[j]\)</span> существует ребро, а элемент <span class="arithmatex">\(M[i, j] = 0\)</span> означает, что ребра между ними нет.</p>
+<p>Пусть число вершин графа равно <span class="arithmatex">\(n\)</span> ; тогда <u>матрица смежности (adjacency matrix)</u> использует матрицу размера <span class="arithmatex">\(n \times n\)</span> для представления графа, где каждая строка и каждый столбец соответствуют вершине, а элементы матрицы показывают наличие или отсутствие ребра.</p>
+<p>Как показано на рисунке 9-5, обозначим матрицу смежности через <span class="arithmatex">\(M\)</span> , а список вершин через <span class="arithmatex">\(V\)</span> ; тогда элемент матрицы <span class="arithmatex">\(M[i, j] = 1\)</span> означает наличие ребра между вершинами <span class="arithmatex">\(V[i]\)</span> и <span class="arithmatex">\(V[j]\)</span> , а элемент <span class="arithmatex">\(M[i, j] = 0\)</span> означает отсутствие ребра.</p>
 <p><img alt="Представление графа матрицей смежности" class="animation-figure" src="../graph.assets/adjacency_matrix.png" /></p>
 <p align="center"> Рисунок 9-5 &nbsp; Представление графа матрицей смежности </p>
 
 <p>Матрица смежности обладает следующими особенностями.</p>
 <ul>
-<li>В простом графе вершина не может соединяться сама с собой, поэтому элементы на главной диагонали матрицы смежности не имеют смысла.</li>
-<li>Для неориентированного графа ребра в двух направлениях эквивалентны, поэтому матрица смежности симметрична относительно главной диагонали.</li>
-<li>Если заменить в матрице смежности значения <span class="arithmatex">\(1\)</span> и <span class="arithmatex">\(0\)</span> на веса, то можно представить и взвешенный граф.</li>
+<li>В простом графе вершина не может соединяться сама с собой, поэтому элементы на главной диагонали матрицы смежности не имеют значения.</li>
+<li>Для неориентированного графа ребра в обоих направлениях эквивалентны, поэтому матрица смежности симметрична относительно главной диагонали.</li>
+<li>Если заменить в матрице смежности значения <span class="arithmatex">\(1\)</span> и <span class="arithmatex">\(0\)</span> на веса, то можно представить взвешенный граф.</li>
 </ul>
-<p>При представлении графа матрицей смежности мы можем напрямую обращаться к элементам матрицы, чтобы получить информацию о ребрах, поэтому операции добавления, удаления, поиска и изменения обладают высокой эффективностью, равной <span class="arithmatex">\(O(1)\)</span> . Однако пространственная сложность матрицы равна <span class="arithmatex">\(O(n^2)\)</span> , поэтому она занимает заметный объем памяти.</p>
+<p>При представлении графа матрицей смежности можно напрямую обращаться к элементам матрицы и получать сведения о ребрах, поэтому операции добавления, удаления, поиска и изменения обладают высокой эффективностью и выполняются за <span class="arithmatex">\(O(1)\)</span> . Однако пространственная сложность матрицы составляет <span class="arithmatex">\(O(n^2)\)</span> , поэтому она требует значительных затрат памяти.</p>
 <h3 id="2">2. &nbsp; Список смежности<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p><u>Список смежности (adjacency list)</u> использует <span class="arithmatex">\(n\)</span> связанных списков для представления графа, где узлы списка обозначают вершины. <span class="arithmatex">\(i\)</span>-й список соответствует вершине <span class="arithmatex">\(i\)</span> и хранит все вершины, смежные с ней, то есть все вершины, соединенные с этой вершиной. На рисунке 9-6 показан пример графа, представленного списком смежности.</p>
+<p><u>Список смежности (adjacency list)</u> использует <span class="arithmatex">\(n\)</span> списков для представления графа, где узлы списка обозначают вершины. <span class="arithmatex">\(i\)</span>-й список соответствует вершине <span class="arithmatex">\(i\)</span> и хранит все смежные с ней вершины, то есть все вершины, соединенные с данной вершиной. На рисунке 9-6 показан пример графа, представленного списком смежности.</p>
 <p><img alt="Представление графа списком смежности" class="animation-figure" src="../graph.assets/adjacency_list.png" /></p>
 <p align="center"> Рисунок 9-6 &nbsp; Представление графа списком смежности </p>
 
-<p>Список смежности хранит только реально существующие ребра, а общее число ребер обычно значительно меньше <span class="arithmatex">\(n^2\)</span> , поэтому этот способ существенно экономит пространство. Однако для поиска ребра в списке смежности нужно проходить по списку, поэтому по времени он уступает матрице смежности.</p>
-<p>Если посмотреть на рисунок 9-6, можно заметить, что <strong>структура списка смежности очень похожа на "метод цепочек" в хеш-таблице, поэтому для оптимизации эффективности здесь можно использовать сходные идеи</strong>. Например, когда список становится слишком длинным, его можно преобразовать в AVL-дерево или красно-черное дерево, чтобы улучшить временную сложность с <span class="arithmatex">\(O(n)\)</span> до <span class="arithmatex">\(O(\log n)\)</span> ; можно также превратить его в хеш-таблицу и снизить сложность до <span class="arithmatex">\(O(1)\)</span> .</p>
+<p>Список смежности хранит только реально существующие ребра, а общее число ребер обычно значительно меньше <span class="arithmatex">\(n^2\)</span> , поэтому он лучше экономит память. Однако для поиска ребра в списке смежности требуется обходить список, поэтому по времени он уступает матрице смежности.</p>
+<p>Если посмотреть на рисунок 9-6, можно заметить, что <strong>структура списка смежности очень похожа на цепную адресацию в хеш-таблицах, поэтому здесь можно использовать похожие методы оптимизации эффективности</strong>. Например, если список слишком длинный, его можно преобразовать в AVL-дерево или красно-черное дерево, чтобы снизить временную сложность с <span class="arithmatex">\(O(n)\)</span> до <span class="arithmatex">\(O(\log n)\)</span> ; также список можно преобразовать в хеш-таблицу, чтобы довести временную сложность до <span class="arithmatex">\(O(1)\)</span> .</p>
 <h2 id="913">9.1.3 &nbsp; Типичные применения графов<a class="headerlink" href="#913" title="Permanent link">&para;</a></h2>
-<p>Как показано в таблице 9-1, многие реальные системы можно моделировать графами, а соответствующие задачи затем сводить к задачам вычислений на графах.</p>
+<p>Как показано в таблице 9-1, многие реальные системы можно моделировать с помощью графов, а соответствующие задачи затем сводить к задачам вычислений на графах.</p>
 <p align="center"> Таблица 9-1 &nbsp; Распространенные графы в реальной жизни </p>
 
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 <!-- Page content -->
 <h1 id="92">9.2 &nbsp; Базовые операции графа<a class="headerlink" href="#92" title="Permanent link">&para;</a></h1>
-<p>Базовые операции графа можно разделить на операции над "ребрами" и операции над "вершинами". В двух способах представления - "матрица смежности" и "список смежности" - реализация будет различаться.</p>
+<p>Базовые операции графа можно разделить на операции над "ребрами" и операции над "вершинами". При двух способах представления, "матрице смежности" и "списке смежности", реализация этих операций различается.</p>
 <h2 id="921">9.2.1 &nbsp; Реализация на основе матрицы смежности<a class="headerlink" href="#921" title="Permanent link">&para;</a></h2>
 <p>Пусть дан неориентированный граф с числом вершин <span class="arithmatex">\(n\)</span> . Тогда способы реализации различных операций показаны на рисунках ниже.</p>
 <ul>
-<li><strong>Добавление или удаление ребра</strong>: достаточно изменить соответствующее ребро в матрице смежности, это требует <span class="arithmatex">\(O(1)\)</span> времени. Поскольку граф неориентированный, нужно одновременно обновлять ребра в обоих направлениях.</li>
-<li><strong>Добавление вершины</strong>: в конец матрицы смежности добавляется одна строка и один столбец, которые полностью заполняются нулями; это требует <span class="arithmatex">\(O(n)\)</span> времени.</li>
-<li><strong>Удаление вершины</strong>: из матрицы смежности удаляется одна строка и один столбец. В худшем случае, когда удаляются первая строка и первый столбец, приходится "сдвигать вверх-влево" <span class="arithmatex">\((n-1)^2\)</span> элементов, поэтому требуется <span class="arithmatex">\(O(n^2)\)</span> времени.</li>
+<li><strong>Добавление или удаление ребра</strong>: достаточно изменить соответствующее ребро в матрице смежности, что требует <span class="arithmatex">\(O(1)\)</span> времени. Поскольку граф неориентированный, необходимо одновременно обновить ребра в обоих направлениях.</li>
+<li><strong>Добавление вершины</strong>: в конец матрицы смежности добавляется строка и столбец, полностью заполненные нулями; это требует <span class="arithmatex">\(O(n)\)</span> времени.</li>
+<li><strong>Удаление вершины</strong>: из матрицы смежности удаляется строка и столбец. При удалении первой строки и первого столбца достигается худший случай, когда требуется "сдвинуть влево вверх" <span class="arithmatex">\((n-1)^2\)</span> элементов, поэтому используется <span class="arithmatex">\(O(n^2)\)</span> времени.</li>
 <li><strong>Инициализация</strong>: передаются <span class="arithmatex">\(n\)</span> вершин, затем инициализируется список вершин <code>vertices</code> длины <span class="arithmatex">\(n\)</span> , что требует <span class="arithmatex">\(O(n)\)</span> времени; после этого инициализируется матрица смежности <code>adjMat</code> размера <span class="arithmatex">\(n \times n\)</span> , что требует <span class="arithmatex">\(O(n^2)\)</span> времени.</li>
 </ul>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:5"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Инициализация матрицы смежности</label><label for="__tabbed_1_2">Добавление ребра</label><label for="__tabbed_1_3">Удаление ребра</label><label for="__tabbed_1_4">Добавление вершины</label><label for="__tabbed_1_5">Удаление вершины</label></div>
@@ -5566,8 +5566,8 @@
 <h2 id="922">9.2.2 &nbsp; Реализация на основе списка смежности<a class="headerlink" href="#922" title="Permanent link">&para;</a></h2>
 <p>Пусть неориентированный граф содержит в сумме <span class="arithmatex">\(n\)</span> вершин и <span class="arithmatex">\(m\)</span> ребер. Тогда различные операции можно реализовать способом, показанным на рисунках ниже.</p>
 <ul>
-<li><strong>Добавление ребра</strong>: достаточно добавить ребро в конец списка, соответствующего вершине; это требует <span class="arithmatex">\(O(1)\)</span> времени. Поскольку граф неориентированный, нужно одновременно добавлять ребра в обоих направлениях.</li>
-<li><strong>Удаление ребра</strong>: нужно найти и удалить указанное ребро в списке, соответствующем вершине; это требует <span class="arithmatex">\(O(m)\)</span> времени. В неориентированном графе нужно удалять ребра в обоих направлениях.</li>
+<li><strong>Добавление ребра</strong>: достаточно добавить ребро в конец списка, соответствующего вершине; это требует <span class="arithmatex">\(O(1)\)</span> времени. Поскольку граф неориентированный, необходимо одновременно добавить ребра в обоих направлениях.</li>
+<li><strong>Удаление ребра</strong>: нужно найти и удалить указанное ребро в списке, соответствующем вершине; это требует <span class="arithmatex">\(O(m)\)</span> времени. В неориентированном графе необходимо удалить ребра в обоих направлениях.</li>
 <li><strong>Добавление вершины</strong>: в список смежности добавляется еще один список, а новая вершина становится его головным узлом; это требует <span class="arithmatex">\(O(1)\)</span> времени.</li>
 <li><strong>Удаление вершины</strong>: требуется пройти по всему списку смежности и удалить все ребра, содержащие указанную вершину; это требует <span class="arithmatex">\(O(n + m)\)</span> времени.</li>
 <li><strong>Инициализация</strong>: в списке смежности создаются <span class="arithmatex">\(n\)</span> вершин и <span class="arithmatex">\(2m\)</span> ребер; это требует <span class="arithmatex">\(O(n + m)\)</span> времени.</li>
@@ -5595,10 +5595,10 @@
 
 <p>Ниже приведен код списка смежности. По сравнению с рисунками выше, реальная реализация имеет следующие отличия.</p>
 <ul>
-<li>Чтобы упростить добавление и удаление вершин, а также упростить код, мы используем список, то есть динамический массив, вместо связного списка.</li>
+<li>Чтобы упростить добавление и удаление вершин, а также сделать код проще, мы используем список, то есть динамический массив, вместо связного списка.</li>
 <li>Для хранения списка смежности используется хеш-таблица, где <code>key</code> - это экземпляр вершины, а <code>value</code> - список смежных вершин данной вершины.</li>
 </ul>
-<p>Кроме того, в списке смежности мы используем класс <code>Vertex</code> для представления вершины. Причина в следующем: если, как и в матрице смежности, различать вершины по индексам списка, то при удалении вершины с индексом <span class="arithmatex">\(i\)</span> пришлось бы обходить весь список смежности и уменьшать на <span class="arithmatex">\(1\)</span> все индексы, большие <span class="arithmatex">\(i\)</span> , что крайне неэффективно. Если же каждая вершина является уникальным экземпляром <code>Vertex</code> , то после удаления одной вершины остальные вершины менять уже не требуется.</p>
+<p>Кроме того, в списке смежности используется класс <code>Vertex</code> для представления вершины. Причина в том, что если, как и в матрице смежности, различать вершины по индексам списка, то при удалении вершины с индексом <span class="arithmatex">\(i\)</span> пришлось бы обходить весь список смежности и уменьшать на <span class="arithmatex">\(1\)</span> все индексы, большие <span class="arithmatex">\(i\)</span> , что крайне неэффективно. Если же каждая вершина является уникальным экземпляром <code>Vertex</code> , то после удаления одной вершины остальные вершины менять уже не требуется.</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="4:13"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label></div>
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 </details>
 <h2 id="923">9.2.3 &nbsp; Сравнение эффективности<a class="headerlink" href="#923" title="Permanent link">&para;</a></h2>
-<p>Пусть в графе имеется <span class="arithmatex">\(n\)</span> вершин и <span class="arithmatex">\(m\)</span> ребер. В таблице 9-2 сравниваются временная и пространственная эффективность матрицы смежности и списка смежности. Обрати внимание: список смежности (связный список) соответствует реализации из этой статьи, а список смежности (хеш-таблица) означает вариант, где все списки заменены хеш-таблицами.</p>
+<p>Пусть в графе имеется <span class="arithmatex">\(n\)</span> вершин и <span class="arithmatex">\(m\)</span> ребер. В таблице 9-2 сравниваются временная и пространственная эффективность матрицы смежности и списка смежности. Обратите внимание: список смежности (связный список) соответствует реализации из этой статьи, а список смежности (хеш-таблица) означает вариант, в котором все списки заменены хеш-таблицами.</p>
 <p align="center"> Таблица 9-2 &nbsp; Сравнение матрицы смежности и списка смежности </p>
 
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@@ -6755,7 +6755,7 @@
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 </div>
-<p>Если смотреть только на таблицу, может показаться, что список смежности на основе хеш-таблицы является лучшим и по времени, и по памяти. Но на практике операции над ребрами в матрице смежности часто выполняются быстрее, потому что там нужен лишь один доступ к массиву или одно присваивание. В целом матрица смежности воплощает принцип "обмен пространства на время", а список смежности - принцип "обмен времени на пространство".</p>
+<p>Если смотреть только на таблицу, может показаться, что список смежности на основе хеш-таблицы является лучшим и по времени, и по памяти. Но на практике операции над ребрами в матрице смежности обычно выполняются быстрее, потому что там нужен лишь один доступ к массиву или одно присваивание. В целом матрица смежности воплощает принцип "обмена пространства на время", а список смежности - принцип "обмена времени на пространство".</p>
 
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 <!-- Page content -->
 <h1 id="93">9.3 &nbsp; Обход графа<a class="headerlink" href="#93" title="Permanent link">&para;</a></h1>
-<p>Дерево представляет отношение "один ко многим", а граф имеет более высокую степень свободы и может выражать произвольные отношения "многие ко многим". Поэтому мы можем рассматривать дерево как частный случай графа. Очевидно, что <strong>операции обхода дерева также являются частным случаем операций обхода графа</strong>.</p>
-<p>И графы, и деревья требуют использования поисковых алгоритмов для реализации обхода. Способы обхода графа также делятся на два типа: <u>обход в ширину</u> и <u>обход в глубину</u>.</p>
+<p>Дерево представляет отношение "один ко многим", тогда как граф обладает большей свободой и может выражать произвольные отношения "многие ко многим". Поэтому дерево можно рассматривать как частный случай графа. Очевидно, что <strong>операции обхода дерева также являются частным случаем операций обхода графа</strong>.</p>
+<p>И графы, и деревья требуют применения алгоритмов обхода. Способы обхода графа также делятся на два типа: <u>обход в ширину</u> и <u>обход в глубину</u>.</p>
 <h2 id="931">9.3.1 &nbsp; Обход в ширину<a class="headerlink" href="#931" title="Permanent link">&para;</a></h2>
-<p><strong>Обход в ширину - это способ обхода "от близкого к далекому": начиная с некоторого узла, мы всегда в первую очередь посещаем ближайшие вершины и слой за слоем расширяемся наружу</strong>. Как показано на рисунке 9-9, начиная с вершины в левом верхнем углу, мы сначала обходим все смежные вершины этой вершины, затем все смежные вершины следующей вершины и так далее, пока не будут посещены все вершины.</p>
+<p><strong>Обход в ширину - это способ обхода от ближнего к дальнему, при котором начиная с некоторого узла сначала посещают ближайшие вершины, а затем слой за слоем расширяются наружу</strong>. Как показано на рисунке 9-9, начиная с вершины в левом верхнем углу, мы сначала обходим все смежные вершины этой вершины, затем все смежные вершины следующей вершины и так далее, пока не будут посещены все вершины.</p>
 <p><img alt="Обход графа в ширину" class="animation-figure" src="../graph_traversal.assets/graph_bfs.png" /></p>
 <p align="center"> Рисунок 9-9 &nbsp; Обход графа в ширину </p>
 
 <h3 id="1">1. &nbsp; Реализация алгоритма<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>BFS обычно реализуется с помощью очереди, код приведен ниже. Очередь обладает свойством "первым пришел - первым вышел", что хорошо соответствует идее BFS "от близкого к далекому".</p>
+<p>BFS обычно реализуется с помощью очереди, код приведен ниже. Очередь обладает свойством "первым пришел - первым вышел", что хорошо соответствует идее BFS "от ближнего к дальнему".</p>
 <ol>
 <li>Поместить стартовую вершину обхода <code>startVet</code> в очередь и запустить цикл.</li>
-<li>На каждой итерации цикла извлекать вершину из головы очереди и записывать факт ее посещения, после чего добавлять все смежные вершины этой вершины в хвост очереди.</li>
+<li>На каждой итерации цикла извлекать вершину из головы очереди и записывать ее посещение, после чего добавлять все смежные вершины этой вершины в хвост очереди.</li>
 <li>Повторять шаг <code>2.</code> до тех пор, пока не будут посещены все вершины.</li>
 </ol>
-<p>Чтобы предотвратить повторный обход вершин, нам нужен хеш-набор <code>visited</code> , в котором будет записываться, какие узлы уже посещены.</p>
+<p>Чтобы предотвратить повторный обход вершин, нам нужно хеш-множество <code>visited</code> , в котором записывается, какие вершины уже посещены.</p>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>Хеш-набор можно рассматривать как хеш-таблицу, которая хранит только <code>key</code> и не хранит <code>value</code> . Он позволяет выполнять добавление, удаление, поиск и изменение <code>key</code> за <span class="arithmatex">\(O(1)\)</span> времени. Благодаря уникальности <code>key</code> хеш-набор обычно используется, например, для устранения повторов.</p>
+<p>Хеш-множество можно рассматривать как хеш-таблицу, которая хранит только <code>key</code> и не хранит <code>value</code> . Оно позволяет выполнять добавление, удаление и проверку наличия <code>key</code> за <span class="arithmatex">\(O(1)\)</span> времени. Благодаря уникальности <code>key</code> хеш-множество обычно используется, например, для устранения повторов.</p>
 </div>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
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@@ -4956,18 +4956,18 @@
 
 <div class="admonition question">
 <p class="admonition-title">Является ли последовательность обхода в ширину единственной?</p>
-<p>Нет. Обход в ширину требует только соблюдения порядка "от близкого к далекому", <strong>а порядок обхода нескольких вершин на одинаковом расстоянии может произвольно меняться</strong>. Например, на рисунке 9-10 можно поменять местами порядок посещения вершин <span class="arithmatex">\(1\)</span> и <span class="arithmatex">\(3\)</span> , а также в произвольном порядке переставить вершины <span class="arithmatex">\(2\)</span>, <span class="arithmatex">\(4\)</span>, <span class="arithmatex">\(6\)</span> .</p>
+<p>Нет. Обход в ширину требует только соблюдения порядка "от ближнего к дальнему", <strong>а порядок обхода нескольких вершин на одинаковом расстоянии может произвольно меняться</strong>. Например, на рисунке 9-10 можно поменять местами порядок посещения вершин <span class="arithmatex">\(1\)</span> и <span class="arithmatex">\(3\)</span> , а вершины <span class="arithmatex">\(2\)</span>, <span class="arithmatex">\(4\)</span>, <span class="arithmatex">\(6\)</span> также можно переставлять произвольно.</p>
 </div>
 <h3 id="2">2. &nbsp; Анализ сложности<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
 <p><strong>Временная сложность</strong>: все вершины по одному разу помещаются в очередь и извлекаются из нее, что требует <span class="arithmatex">\(O(|V|)\)</span> времени; при обходе смежных вершин, поскольку граф неориентированный, все ребра будут посещены по <span class="arithmatex">\(2\)</span> раза, что требует <span class="arithmatex">\(O(2|E|)\)</span> времени; в сумме получается <span class="arithmatex">\(O(|V| + |E|)\)</span> .</p>
-<p><strong>Пространственная сложность</strong>: список <code>res</code> , хеш-набор <code>visited</code> и очередь <code>que</code> в худшем случае могут содержать до <span class="arithmatex">\(|V|\)</span> вершин, поэтому требуется <span class="arithmatex">\(O(|V|)\)</span> памяти.</p>
+<p><strong>Пространственная сложность</strong>: список <code>res</code> , хеш-множество <code>visited</code> и очередь <code>que</code> в худшем случае могут содержать до <span class="arithmatex">\(|V|\)</span> вершин, поэтому требуется <span class="arithmatex">\(O(|V|)\)</span> памяти.</p>
 <h2 id="932">9.3.2 &nbsp; Обход в глубину<a class="headerlink" href="#932" title="Permanent link">&para;</a></h2>
-<p><strong>Обход в глубину - это способ обхода, при котором сначала идут до самого конца, а когда дальше идти нельзя, откатываются назад</strong>. Как показано на рисунке 9-11, начиная с вершины в левом верхнем углу, мы выбираем некоторую смежную вершину текущей вершины, идем до упора, затем возвращаемся назад, снова идем до упора и так далее, пока не будут посещены все вершины.</p>
+<p><strong>Обход в глубину - это способ обхода, при котором сначала идут до самого конца, а когда дальше идти нельзя, возвращаются назад</strong>. Как показано на рисунке 9-11, начиная с вершины в левом верхнем углу, мы выбираем некоторую смежную вершину текущей вершины, идем до упора, затем возвращаемся назад, снова идем до упора и так далее, пока не будут посещены все вершины.</p>
 <p><img alt="Обход графа в глубину" class="animation-figure" src="../graph_traversal.assets/graph_dfs.png" /></p>
 <p align="center"> Рисунок 9-11 &nbsp; Обход графа в глубину </p>
 
 <h3 id="1_1">1. &nbsp; Реализация алгоритма<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
-<p>Такой алгоритмический шаблон "дойти до конца и вернуться" обычно реализуется через рекурсию. Подобно обходу в ширину, в обходе в глубину мы также используем хеш-набор <code>visited</code> для записи уже посещенных вершин и тем самым избегаем повторного посещения.</p>
+<p>Такой алгоритмический шаблон "дойти до конца и вернуться" обычно реализуется через рекурсию. Подобно обходу в ширину, в обходе в глубину мы также используем хеш-множество <code>visited</code> для записи уже посещенных вершин и тем самым избегаем повторного посещения.</p>
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@@ -5349,8 +5349,8 @@
 </details>
 <p>Алгоритмический процесс обхода в глубину показан на рисунках ниже.</p>
 <ul>
-<li><strong>Прямая пунктирная линия обозначает нисходящее рекурсивное развертывание</strong> , то есть запуск нового рекурсивного метода для посещения новой вершины.</li>
-<li><strong>Изогнутая пунктирная линия обозначает обратный возврат по рекурсии</strong> , то есть данный рекурсивный метод завершился и управление вернулось туда, откуда он был вызван.</li>
+<li><strong>Прямая пунктирная линия обозначает нисходящую рекурсию</strong> , то есть запуск нового рекурсивного метода для посещения новой вершины.</li>
+<li><strong>Изогнутая пунктирная линия обозначает восходящую рекурсию</strong> , то есть данный рекурсивный метод завершился и управление вернулось туда, откуда он был вызван.</li>
 </ul>
 <p>Чтобы лучше понять алгоритм, рекомендуется совместить рисунки ниже с кодом и мысленно проследить весь процесс DFS, включая моменты запуска и возврата каждого рекурсивного вызова.</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="4:11"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">&lt;1&gt;</label><label for="__tabbed_4_2">&lt;2&gt;</label><label for="__tabbed_4_3">&lt;3&gt;</label><label for="__tabbed_4_4">&lt;4&gt;</label><label for="__tabbed_4_5">&lt;5&gt;</label><label for="__tabbed_4_6">&lt;6&gt;</label><label for="__tabbed_4_7">&lt;7&gt;</label><label for="__tabbed_4_8">&lt;8&gt;</label><label for="__tabbed_4_9">&lt;9&gt;</label><label for="__tabbed_4_10">&lt;10&gt;</label><label for="__tabbed_4_11">&lt;11&gt;</label></div>
@@ -5399,7 +5399,7 @@
 </div>
 <h3 id="2_1">2. &nbsp; Анализ сложности<a class="headerlink" href="#2_1" title="Permanent link">&para;</a></h3>
 <p><strong>Временная сложность</strong>: все вершины будут посещены по <span class="arithmatex">\(1\)</span> разу, что требует <span class="arithmatex">\(O(|V|)\)</span> времени; все ребра будут посещены по <span class="arithmatex">\(2\)</span> раза, что требует <span class="arithmatex">\(O(2|E|)\)</span> времени; суммарно получается <span class="arithmatex">\(O(|V| + |E|)\)</span> .</p>
-<p><strong>Пространственная сложность</strong>: число вершин в списке <code>res</code> и хеш-наборе <code>visited</code> в худшем случае достигает <span class="arithmatex">\(|V|\)</span> , максимальная глубина рекурсии тоже равна <span class="arithmatex">\(|V|\)</span> , поэтому требуется <span class="arithmatex">\(O(|V|)\)</span> памяти.</p>
+<p><strong>Пространственная сложность</strong>: число вершин в списке <code>res</code> и хеш-множестве <code>visited</code> в худшем случае достигает <span class="arithmatex">\(|V|\)</span> , максимальная глубина рекурсии тоже равна <span class="arithmatex">\(|V|\)</span> , поэтому требуется <span class="arithmatex">\(O(|V|)\)</span> памяти.</p>
 
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@@ -4277,15 +4277,15 @@
 <p><img alt="Графы" class="cover-image" src="../assets/covers/chapter_graph.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>На жизненном пути мы подобны узлам, соединенным бесчисленными невидимыми ребрами.</p>
-<p>Каждая встреча и каждое расставание оставляют в этой огромной сети свой особый след.</p>
+<p>В жизни мы похожи на вершины, соединенные множеством невидимых ребер.</p>
+<p>Каждая встреча и каждое расставание оставляют в этой огромной сети свой след.</p>
 </div>
 <h2 id="_1">Содержание главы<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
 <li><a href="graph/">9.1 &nbsp; Граф</a></li>
-<li><a href="graph_operations/">9.2 &nbsp; Базовые операции над графами</a></li>
+<li><a href="graph_operations/">9.2 &nbsp; Базовые операции графа</a></li>
 <li><a href="graph_traversal/">9.3 &nbsp; Обход графа</a></li>
-<li><a href="summary/">9.4 &nbsp; Резюме</a></li>
+<li><a href="summary/">9.4 &nbsp; Краткие итоги</a></li>
 </ul>
 
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+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
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+    14.5 Задача о полном рюкзаке
   
 
     
@@ -4359,11 +4359,11 @@
 <ul>
 <li>Граф состоит из вершин и ребер и может быть задан как множество вершин и множество ребер.</li>
 <li>По сравнению с линейными отношениями (связный список) и отношениями разделения (дерево), сетевые отношения (граф) обладают большей свободой и потому более сложны.</li>
-<li>Ребра ориентированного графа имеют направление, в связном графе любые вершины достижимы друг из друга, а в взвешенном графе каждое ребро несет переменную веса.</li>
-<li>Матрица смежности использует матрицу для представления графа: каждая строка и каждый столбец соответствуют вершине, а элементы матрицы показывают, есть между двумя вершинами ребро или нет. Матрица смежности очень эффективна для операций добавления, удаления, поиска и изменения, но расходует больше памяти.</li>
+<li>Ребра ориентированного графа имеют направление, в связном графе любые вершины достижимы, а во взвешенном графе каждое ребро содержит переменную веса.</li>
+<li>Матрица смежности использует матрицу для представления графа: каждая строка и каждый столбец соответствуют вершине, а элементы матрицы показывают, есть между двумя вершинами ребро или нет. Матрица смежности эффективна в операциях добавления, удаления, поиска и изменения, но расходует больше памяти.</li>
 <li>Список смежности использует несколько списков для представления графа; <span class="arithmatex">\(i\)</span>-й список соответствует вершине <span class="arithmatex">\(i\)</span> и хранит все ее смежные вершины. По сравнению с матрицей смежности список смежности экономит пространство, но для поиска ребра в нем приходится обходить список, поэтому по времени он уступает.</li>
-<li>Когда списки в списке смежности становятся слишком длинными, их можно преобразовать в красно-черное дерево или хеш-таблицу, чтобы ускорить поиск.</li>
-<li>С точки зрения алгоритмической идеи матрица смежности отражает принцип "обмен пространства на время", а список смежности - принцип "обмена времени на пространство".</li>
+<li>Когда списки в списке смежности становятся слишком длинными, их можно преобразовать в красно-черное дерево или хеш-таблицу, чтобы повысить эффективность поиска.</li>
+<li>С точки зрения алгоритмической идеи матрица смежности отражает принцип "обмена пространства на время", а список смежности - принцип "обмена времени на пространство".</li>
 <li>Графы можно использовать для моделирования различных реальных систем, таких как социальные сети, линии метро и так далее.</li>
 <li>Дерево является частным случаем графа, а обход дерева - частным случаем обхода графа.</li>
 <li>Обход графа в ширину представляет собой способ поиска, который расширяется от ближнего к дальнему и обычно реализуется с помощью очереди.</li>
@@ -4371,7 +4371,7 @@
 </ul>
 <h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
 <p><strong>Q</strong>: Что считается путем: последовательность вершин или последовательность ребер?</p>
-<p>Определение в разных языковых версиях Википедии различается: в английской версии путь определяется как "последовательность ребер", а в китайской версии - как "последовательность вершин". В английской версии исходная формулировка выглядит так: In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices.</p>
+<p>Определение в разных языковых версиях Википедии различается: в английской версии путь определяется как "последовательность ребер", а в русской версии - как "последовательность вершин". В английской версии исходная формулировка выглядит так: In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices.</p>
 <p>В этой книге путь рассматривается как последовательность ребер, а не как последовательность вершин. Причина в том, что между двумя вершинами может существовать несколько ребер, и в таком случае каждому ребру соответствует свой путь.</p>
 <p><strong>Q</strong>: Есть ли в несвязном графе вершины, до которых нельзя дойти?</p>
 <p>В несвязном графе, начиная из некоторой вершины, по крайней мере одна вершина оказывается недостижимой. Чтобы обойти весь несвязный граф, нужно задать несколько стартовых точек и обойти все связные компоненты графа.</p>
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-    12.1 Алгоритмы разделяй и властвуй
+    12.1 Стратегия разделяй и властвуй
   
 
     
@@ -3141,7 +3141,7 @@
   <span class="md-ellipsis">
     
   
-    12.2 Стратегия поиска разделяй и властвуй
+    12.2 Поисковая стратегия разделяй и властвуй
   
 
     
@@ -3418,7 +3418,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 Задача о $n$ ферзях
+    13.4 Задача о n ферзях
   
 
     
@@ -3559,7 +3559,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 Введение в динамическое программирование
+    14.1 Первое знакомство с динамическим программированием
   
 
     
@@ -3671,7 +3671,7 @@
   <span class="md-ellipsis">
     
   
-    14.5 Задача о неограниченном рюкзаке
+    14.5 Задача о полном рюкзаке
   
 
     
@@ -4880,8 +4880,8 @@
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 </details>
-<p>Встроенный алгоритм сортировки обычно имеет временную сложность <span class="arithmatex">\(O(\log n)\)</span>, а пространственная сложность обычно равна <span class="arithmatex">\(O(\log n)\)</span> или <span class="arithmatex">\(O(n)\)</span>, в зависимости от конкретной реализации в языке программирования.</p>
-<p>Помимо сортировки, в худшем случае потребуется пройти весь список предметов, <strong>поэтому временная сложность равна <span class="arithmatex">\(O(n)\)</span></strong>, где <span class="arithmatex">\(n\)</span> - число предметов.</p>
+<p>Встроенный алгоритм сортировки обычно имеет временную сложность <span class="arithmatex">\(O(n \log n)\)</span>, а пространственная сложность обычно равна <span class="arithmatex">\(O(\log n)\)</span> или <span class="arithmatex">\(O(n)\)</span>, в зависимости от конкретной реализации в языке программирования.</p>
+<p>Помимо сортировки, в худшем случае потребуется пройти весь список предметов, но это не меняет асимптотику, <strong>поэтому итоговая временная сложность равна <span class="arithmatex">\(O(n \log n)\)</span></strong>, где <span class="arithmatex">\(n\)</span> - число предметов.</p>
 <p>Поскольку инициализируется список объектов <code>Item</code>, <strong>пространственная сложность равна <span class="arithmatex">\(O(n)\)</span></strong>.</p>
 <h3 id="3">3. &nbsp; Доказательство корректности<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
 <p>Используем доказательство от противного. Предположим, что предмет <span class="arithmatex">\(x\)</span> имеет наибольшую удельную ценность, некоторый алгоритм получил максимальную ценность <code>res</code>, но в найденном решении предмет <span class="arithmatex">\(x\)</span> отсутствует.</p>
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 <!-- Page content -->
 <h1 id="151">15.1 &nbsp; Жадный алгоритм<a class="headerlink" href="#151" title="Permanent link">&para;</a></h1>
-<p><u>Жадный алгоритм (greedy algorithm)</u> - это распространенный подход к решению задач оптимизации. Его основная идея состоит в том, чтобы на каждом этапе принятия решения выбирать вариант, который выглядит наилучшим прямо сейчас, то есть жадно принимать локально оптимальные решения в надежде получить глобально оптимальный результат. Жадные алгоритмы лаконичны и эффективны, поэтому широко применяются во многих практических задачах.</p>
-<p>Жадные алгоритмы и динамическое программирование часто используются для решения задач оптимизации. У них есть некоторое сходство, например оба опираются на свойство оптимальной подструктуры, но принципы работы различаются.</p>
+<p><u>Жадный алгоритм (greedy algorithm)</u> - это распространенный метод решения задач оптимизации. Его основная идея состоит в том, чтобы на каждом этапе принятия решения выбирать вариант, который выглядит наилучшим прямо сейчас, то есть жадно принимать локально оптимальные решения в надежде получить глобально оптимальный результат. Жадные алгоритмы просты и эффективны, поэтому широко применяются во многих практических задачах.</p>
+<p>Жадные алгоритмы и динамическое программирование часто используются для решения задач оптимизации. У них есть некоторое сходство, например оба метода опираются на свойство оптимальной подструктуры, но принципы работы различаются.</p>
 <ul>
-<li>Динамическое программирование учитывает все решения предыдущих этапов при выборе текущего решения и использует ответы для прошлых подзадач, чтобы построить ответ для текущей подзадачи.</li>
-<li>Жадный алгоритм не учитывает прошлые решения, а просто движется вперед, каждый раз делая жадный выбор, постепенно сужая область задачи, пока она не будет решена.</li>
+<li>Динамическое программирование при получении текущего решения учитывает все предыдущие решения и использует ответы для прошлых подзадач, чтобы построить ответ для текущей подзадачи.</li>
+<li>Жадный алгоритм не учитывает предыдущие решения, а просто движется вперед, каждый раз делая жадный выбор и постепенно сужая область задачи, пока она не будет решена.</li>
 </ul>
-<p>Сначала разберем принцип работы жадного алгоритма на примере задачи «размен монет». Эта задача уже встречалась в разделе «задача о полном рюкзаке», поэтому она наверняка вам знакома.</p>
+<p>Чтобы лучше понять принцип работы жадного алгоритма, разберем его на примере задачи «размен монет». Эта задача уже встречалась в разделе «задача о полном рюкзаке», поэтому она наверняка вам знакома.</p>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
 <p>Дано <span class="arithmatex">\(n\)</span> видов монет. Номинал монеты <span class="arithmatex">\(i\)</span> равен <span class="arithmatex">\(coins[i - 1]\)</span>, целевая сумма равна <span class="arithmatex">\(amt\)</span>, причем каждую монету можно брать неограниченное число раз. Требуется найти минимальное число монет, которыми можно набрать целевую сумму. Если набрать сумму невозможно, верните <span class="arithmatex">\(-1\)</span>.</p>
@@ -4414,7 +4414,7 @@
 <p><img alt="Жадная стратегия для задачи о размене монет" class="animation-figure" src="../greedy_algorithm.assets/coin_change_greedy_strategy.png" /></p>
 <p align="center"> Рисунок 15-1 &nbsp; Жадная стратегия для задачи о размене монет </p>
 
-<p>Код реализации выглядит следующим образом:</p>
+<p>Ниже приведен код реализации.</p>
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 </details>
-<p>У вас может невольно вырваться: So clean! Жадный алгоритм решает задачу размена монет всего примерно десятью строками кода.</p>
+<p>У вас может невольно вырваться: «Эврика!» Жадный алгоритм решает задачу размена монет всего примерно десятью строками кода.</p>
 <h2 id="1511">15.1.1 &nbsp; Преимущества и ограничения жадного алгоритма<a class="headerlink" href="#1511" title="Permanent link">&para;</a></h2>
-<p><strong>Жадный алгоритм не только прост в действиях и реализации, но и обычно очень эффективен</strong>. В приведенном выше коде обозначим минимальный номинал монеты через <span class="arithmatex">\(\min(coins)\)</span>, тогда жадный выбор выполняется не более чем <span class="arithmatex">\(amt / \min(coins)\)</span> раз, а временная сложность равна <span class="arithmatex">\(O(amt / \min(coins))\)</span>. Это на порядок меньше, чем временная сложность решения через динамическое программирование <span class="arithmatex">\(O(n \times amt)\)</span>.</p>
+<p><strong>Жадный алгоритм не только прост в реализации, но и обычно очень эффективен</strong>. В приведенном выше коде обозначим минимальный номинал монеты через <span class="arithmatex">\(\min(coins)\)</span>, тогда жадный выбор выполняется не более чем <span class="arithmatex">\(amt / \min(coins)\)</span> раз, а временная сложность равна <span class="arithmatex">\(O(amt / \min(coins))\)</span>. Это на порядок меньше, чем временная сложность решения через динамическое программирование <span class="arithmatex">\(O(n \times amt)\)</span>.</p>
 <p>Однако <strong>для некоторых наборов номиналов монет жадный алгоритм не может найти оптимальный ответ</strong>. Ниже показаны два примера.</p>
 <ul>
 <li><strong>Положительный пример <span class="arithmatex">\(coins = [1, 5, 10, 20, 50, 100]\)</span></strong>: для такого набора монет при любом <span class="arithmatex">\(amt\)</span> жадный алгоритм находит оптимальное решение.</li>
@@ -4723,7 +4723,7 @@
 </ol>
 <h2 id="1512">15.1.2 &nbsp; Свойства жадного алгоритма<a class="headerlink" href="#1512" title="Permanent link">&para;</a></h2>
 <p>Тогда возникает вопрос: какие задачи подходят для решения жадным алгоритмом? Или, другими словами, в каких случаях жадный алгоритм может гарантировать оптимальный ответ?</p>
-<p>По сравнению с динамическим программированием условия применения жадного алгоритма строже. В основном нас интересуют два свойства задачи.</p>
+<p>По сравнению с динамическим программированием условия применения жадного алгоритма более строгие. В основном нас интересуют два свойства задачи.</p>
 <ul>
 <li><strong>Свойство жадного выбора</strong>: только когда локально оптимальный выбор всегда может привести к глобально оптимальному решению, жадный алгоритм способен гарантировать оптимум.</li>
 <li><strong>Оптимальная подструктура</strong>: оптимальное решение исходной задачи содержит оптимальные решения подзадач.</li>
@@ -4737,7 +4737,7 @@
 <p>Pearson, D. A polynomial-time algorithm for the change-making problem[J]. Operations Research Letters, 2005, 33(3): 231-234.</p>
 </div>
 <h2 id="1513">15.1.3 &nbsp; Этапы решения задач жадным алгоритмом<a class="headerlink" href="#1513" title="Permanent link">&para;</a></h2>
-<p>В общем виде процесс решения жадной задачи можно разбить на три шага.</p>
+<p>Процесс решения жадной задачи в общем виде можно разбить на три шага.</p>
 <ol>
 <li><strong>Анализ задачи</strong>: разобраться в свойствах задачи, включая определение состояний, целевой функции и ограничений. Этот этап присутствует и в поиске с возвратом, и в динамическом программировании.</li>
 <li><strong>Определение жадной стратегии</strong>: определить, какой жадный выбор следует делать на каждом шаге. Эта стратегия должна уменьшать размер задачи на каждом этапе и в итоге привести к решению всей задачи.</li>
@@ -4751,7 +4751,7 @@
 <p>Чтобы гарантировать корректность, нужно дать строгое математическое доказательство жадной стратегии, <strong>обычно с использованием доказательства от противного или математической индукции</strong>.</p>
 <p>Однако и доказательство корректности может оказаться непростой задачей. Если идей нет, мы обычно начинаем отлаживать код на тестовых примерах, постепенно меняя и проверяя жадную стратегию.</p>
 <h2 id="1514">15.1.4 &nbsp; Типичные задачи для жадного алгоритма<a class="headerlink" href="#1514" title="Permanent link">&para;</a></h2>
-<p>Жадные алгоритмы часто применяются в задачах оптимизации, которые обладают свойством жадного выбора и оптимальной подструктурой. Ниже приведены некоторые типичные задачи, решаемые жадным подходом.</p>
+<p>Жадные алгоритмы часто применяются в задачах оптимизации, обладающих свойством жадного выбора и оптимальной подструктурой. Ниже приведены некоторые типичные задачи, решаемые жадным подходом.</p>
 <ul>
 <li><strong>Задача о размене монет</strong>: при некоторых системах монет жадный алгоритм всегда дает оптимальный ответ.</li>
 <li><strong>Задача о расписании интервалов</strong>: пусть есть несколько задач, каждая выполняется в некотором временном интервале, и требуется завершить как можно больше задач. Если каждый раз выбирать задачу с самым ранним временем окончания, то жадный алгоритм дает оптимальный ответ.</li>
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 <p align="center"> Рисунок 15-12 &nbsp; Состояния, пропущенные из-за смещения короткой перегородки </p>
 
 <p>Нетрудно заметить, что <strong>эти пропущенные состояния на самом деле и есть все состояния, в которых длинная перегородка <span class="arithmatex">\(j\)</span> сдвигается внутрь</strong>. Ранее мы уже доказали, что перемещение длинной перегородки внутрь обязательно уменьшает вместимость. Иными словами, пропущенные состояния не могут быть оптимальным решением, <strong>поэтому их пропуск не приводит к потере оптимума</strong>.</p>
-<p>Приведенный анализ показывает, что операция перемещения короткой перегородки является «безопасной», а жадная стратегия действительно эффективна.</p>
+<p>Приведенный анализ показывает, что операция перемещения короткой перегородки является «безопасной», а жадная стратегия действительно корректна.</p>
 
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 <li>Если остаток равен <span class="arithmatex">\(1\)</span>, то поскольку <span class="arithmatex">\(2 \times 2 &gt; 1 \times 3\)</span>, последний множитель <span class="arithmatex">\(3\)</span> следует заменить на <span class="arithmatex">\(2\)</span>.</li>
 </ol>
 <h3 id="2">2. &nbsp; Код реализации<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>Как показано на рисунке 15-16, нам не нужен цикл, чтобы выполнять разбиение числа. Можно использовать целочисленное деление вниз, чтобы получить число троек <span class="arithmatex">\(a\)</span>, и операцию взятия остатка, чтобы получить остаток <span class="arithmatex">\(b\)</span>. Тогда имеем:</p>
+<p>Как показано на рисунке 15-16, нам не нужен цикл, чтобы выполнять разбиение числа. Можно использовать целочисленное деление, чтобы получить число троек <span class="arithmatex">\(a\)</span>, и операцию взятия остатка, чтобы получить остаток <span class="arithmatex">\(b\)</span>. Тогда имеем:</p>
 <div class="arithmatex">\[
 n = 3 a + b
 \]</div>
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-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
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 <p>Из этой формулы видно: при фиксированной емкости хеш-таблицы <code>capacity</code> **выходное значение определяет именно хеш-алгоритм <code>hash()</code> **, а значит, именно он определяет распределение пар ключ-значение в хеш-таблице.</p>
 <p>Это означает, что для уменьшения вероятности хеш-коллизий нам следует сосредоточиться на проектировании хеш-алгоритма <code>hash()</code> .</p>
 <h2 id="631-">6.3.1 &nbsp; Цели хеш-алгоритма<a class="headerlink" href="#631-" title="Permanent link">&para;</a></h2>
-<p>Чтобы получить структуру данных хеш-таблицы, которая будет одновременно "быстрой и надежной", хеш-алгоритм должен обладать следующими свойствами.</p>
+<p>Чтобы получить структуру данных хеш-таблицы, которая будет одновременно быстрой и надежной, хеш-алгоритм должен обладать следующими свойствами.</p>
 <ul>
 <li><strong>Детерминированность</strong>: для одинакового входа хеш-алгоритм всегда должен выдавать одинаковый результат. Только так хеш-таблица остается надежной.</li>
 <li><strong>Высокая эффективность</strong>: вычисление хеш-значения должно быть достаточно быстрым. Чем меньше вычислительные затраты, тем выше практическая ценность хеш-таблицы.</li>
@@ -5030,7 +5030,7 @@
 <p>Следует отметить: если можно гарантировать, что <code>key</code> распределены случайно и равномерно, то выбор простого или составного числа в качестве модуля не так важен - оба варианта способны дать равномерное распределение хеш-значений. Но если в распределении <code>key</code> присутствует периодичность, то взятие по модулю составного числа гораздо легче приводит к кластеризации.</p>
 <p>Итак, на практике мы обычно выбираем простое число в качестве модуля, причем это простое число желательно брать достаточно большим, чтобы по возможности убрать периодические закономерности и повысить устойчивость хеш-алгоритма.</p>
 <h2 id="633-">6.3.3 &nbsp; Распространенные хеш-алгоритмы<a class="headerlink" href="#633-" title="Permanent link">&para;</a></h2>
-<p>Нетрудно заметить, что описанные выше простые хеш-алгоритмы довольно "хрупкие" и далеки от поставленных целей. Например, сложение и XOR подчиняются коммутативному закону, поэтому аддитивный хеш и XOR-хеш не различают строки, состоящие из одних и тех же символов, но в разном порядке. Это может усиливать хеш-коллизии и даже создавать некоторые проблемы безопасности.</p>
+<p>Нетрудно заметить, что описанные выше простые хеш-алгоритмы довольно хрупкие и далеки от поставленных целей. Например, сложение и XOR подчиняются коммутативному закону, поэтому аддитивный хеш и XOR-хеш не различают строки, состоящие из одних и тех же символов, но в разном порядке. Это может усиливать хеш-коллизии и даже создавать некоторые проблемы безопасности.</p>
 <p>На практике мы обычно используем стандартные хеш-алгоритмы, такие как MD5, SHA-1, SHA-2 и SHA-3. Они могут отображать входные данные произвольной длины в хеш-значения фиксированной длины.</p>
 <p>На протяжении почти ста лет хеш-алгоритмы непрерывно развивались и оптимизировались. Одни исследователи старались повысить их производительность, а другие исследователи и хакеры сосредоточивались на поиске уязвимостей в их безопасности. В таблице 6-2 приведены распространенные хеш-алгоритмы, которые часто встречаются в реальных приложениях.</p>
 <ul>
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 <!-- Page content -->
 <h1 id="62-">6.2 &nbsp; Хеш-коллизии<a class="headerlink" href="#62-" title="Permanent link">&para;</a></h1>
 <p>Как уже говорилось в предыдущем разделе, <strong>в обычных условиях входное пространство хеш-функции намного больше выходного пространства</strong> , поэтому теоретически хеш-коллизии неизбежны. Например, если входное пространство состоит из всех целых чисел, а выходное пространство ограничено размером массива, то неизбежно несколько целых чисел будут отображаться в один и тот же индекс бакета.</p>
-<p>Хеш-коллизии приводят к ошибочным результатам поиска и серьезно влияют на пригодность хеш-таблицы к использованию. Чтобы решить эту проблему, можно при каждом конфликте выполнять расширение хеш-таблицы, пока конфликт не исчезнет. Этот метод прост и груб, но слишком неэффективен, потому что расширение хеш-таблицы требует большого объема переноса данных и вычислений хеш-значений. Чтобы повысить эффективность, можно использовать следующие стратегии.</p>
+<p>Хеш-коллизии могут приводить к ошибочным результатам поиска и серьезно влиять на работоспособность хеш-таблицы. Чтобы решить эту проблему, можно при каждом конфликте выполнять расширение хеш-таблицы, пока конфликт не исчезнет. Этот метод понятен и прост, но слишком неэффективен, потому что расширение хеш-таблицы требует большого объема переноса данных и вычислений хеш-значений. Чтобы повысить эффективность, можно использовать следующие стратегии.</p>
 <ol>
 <li>Улучшить структуру данных хеш-таблицы, <strong>чтобы она могла корректно работать даже при возникновении хеш-коллизий</strong>.</li>
 <li>Выполнять расширение только тогда, когда это действительно необходимо, то есть когда хеш-коллизии становятся достаточно серьезными.</li>
 </ol>
-<p>Основные способы улучшения структуры хеш-таблицы включают "метод цепочек" и "открытую адресацию".</p>
+<p>Основные способы улучшения структуры хеш-таблицы включают метод цепочек и открытую адресацию.</p>
 <h2 id="621">6.2.1 &nbsp; Метод цепочек<a class="headerlink" href="#621" title="Permanent link">&para;</a></h2>
 <p>В исходной хеш-таблице каждый бакет может хранить только одну пару ключ-значение. <u>Метод цепочек (separate chaining)</u> превращает отдельный элемент в связный список: пары ключ-значение становятся узлами списка, и все конфликтующие пары ключ-значение хранятся в одном и том же списке. На рисунке 6-5 показан пример хеш-таблицы, реализованной методом цепочек.</p>
 <p><img alt="Хеш-таблица с методом цепочек" class="animation-figure" src="../hash_collision.assets/hash_table_chaining.png" /></p>
@@ -5946,9 +5946,9 @@
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 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20Pair%3A%0A%0A%20%20%20%20def%20__init__%28self%2C%20key%3A%20int%2C%20val%3A%20str%29%3A%0A%20%20%20%20%20%20%20%20self.key%20%3D%20key%0A%20%20%20%20%20%20%20%20self.val%20%3D%20val%0A%0Aclass%20HashMapChaining%3A%0A%0A%20%20%20%20def%20__init__%28self%29%3A%0A%20%20%20%20%20%20%20%20self.size%20%3D%200%0A%20%20%20%20%20%20%20%20self.capacity%20%3D%204%0A%20%20%20%20%20%20%20%20self.load_thres%20%3D%202.0%20%2F%203.0%0A%20%20%20%20%20%20%20%20self.extend_ratio%20%3D%202%0A%20%20%20%20%20%20%20%20self.buckets%20%3D%20%5B%5B%5D%20for%20_%20in%20range%28self.capacity%29%5D%0A%0A%20%20%20%20def%20hash_func%28self%2C%20key%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%20key%20%25%20self.capacity%0A%0A%20%20%20%20def%20load_factor%28self%29%20-%3E%20float%3A%0A%20%20%20%20%20%20%20%20return%20self.size%20%2F%20self.capacity%0A%0A%20%20%20%20def%20get%28self%2C%20key%3A%20int%29%20-%3E%20str%20%7C%20None%3A%0A%20%20%20%20%20%20%20%20index%20%3D%20self.hash_func%28key%29%0A%20%20%20%20%20%20%20%20bucket%20%3D%20self.buckets%5Bindex%5D%0A%20%20%20%20%20%20%20%20for%20pair%20in%20bucket%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20pair.key%20%3D%3D%20key%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20return%20pair.val%0A%20%20%20%20%20%20%20%20return%20None%0A%0A%20%20%20%20def%20put%28self%2C%20key%3A%20int%2C%20val%3A%20str%29%3A%0A%20%20%20%20%20%20%20%20if%20self.load_factor%28%29%20%3E%20self.load_thres%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.extend%28%29%0A%20%20%20%20%20%20%20%20index%20%3D%20self.hash_func%28key%29%0A%20%20%20%20%20%20%20%20bucket%20%3D%20self.buckets%5Bindex%5D%0A%20%20%20%20%20%20%20%20for%20pair%20in%20bucket%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20pair.key%20%3D%3D%20key%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20pair.val%20%3D%20val%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20return%0A%20%20%20%20%20%20%20%20pair%20%3D%20Pair%28key%2C%20val%29%0A%20%20%20%20%20%20%20%20bucket.append%28pair%29%0A%20%20%20%20%20%20%20%20self.size%20%2B%3D%201%0A%0A%20%20%20%20def%20remove%28self%2C%20key%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20index%20%3D%20self.hash_func%28key%29%0A%20%20%20%20%20%20%20%20bucket%20%3D%20self.buckets%5Bindex%5D%0A%20%20%20%20%20%20%20%20for%20pair%20in%20bucket%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20pair.key%20%3D%3D%20key%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20bucket.remove%28pair%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20self.size%20-%3D%201%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20break%0A%0A%20%20%20%20def%20extend%28self%29%3A%0A%20%20%20%20%20%20%20%20buckets%20%3D%20self.buckets%0A%20%20%20%20%20%20%20%20self.capacity%20%2A%3D%20self.extend_ratio%0A%20%20%20%20%20%20%20%20self.buckets%20%3D%20%5B%5B%5D%20for%20_%20in%20range%28self.capacity%29%5D%0A%20%20%20%20%20%20%20%20self.size%20%3D%200%0A%20%20%20%20%20%20%20%20for%20bucket%20in%20buckets%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20for%20pair%20in%20bucket%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20self.put%28pair.key%2C%20pair.val%29%0A%0A%20%20%20%20def%20print%28self%29%3A%0A%20%20%20%20%20%20%20%20for%20bucket%20in%20self.buckets%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20res%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20for%20pair%20in%20bucket%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20res.append%28str%28pair.key%29%20%2B%20%27%20-%3E%20%27%20%2B%20pair.val%29%0A%20%20%20%20%20%20%20%20%20%20%20%20print%28res%29%0A%27Driver%20Code%27%0Aif%20__name__%20%3D%3D%20%27__main__%27%3A%0A%20%20%20%20hashmap%20%3D%20HashMapChaining%28%29%0A%20%20%20%20hashmap.put%2812836%2C%20%27%D0%A1%D1%8F%D0%BE%20%D0%A5%D0%B0%27%29%0A%20%20%20%20hashmap.put%2815937%2C%20%27%D0%A1%D1%8F%D0%BE%20%D0%9B%D0%BE%27%29%0A%20%20%20%20hashmap.put%2816750%2C%20%27%D0%A1%D1%8F%D0%BE%20%D0%A1%D1%83%D0%B0%D0%BD%D1%8C%27%29%0A%20%20%20%20hashmap.put%2813276%2C%20%27%D0%A1%D1%8F%D0%BE%20%D0%A4%D0%B0%27%29%0A%20%20%20%20hashmap.put%2810583%2C%20%27%D0%A1%D1%8F%D0%BE%20%D0%AF%27%29%0A%20%20%20%20name%20%3D%20hashmap.get%2813276%29%0A%20%20%20%20hashmap.remove%2812836%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
-<p>Следует отметить, что когда связный список становится очень длинным, эффективность поиска <span class="arithmatex">\(O(n)\)</span> оказывается низкой. <strong>В этом случае список можно преобразовать в "AVL-дерево" или "красно-черное дерево"</strong> , чтобы оптимизировать временную сложность поиска до <span class="arithmatex">\(O(\log n)\)</span> .</p>
+<p>Следует отметить, что когда связный список становится очень длинным, эффективность поиска <span class="arithmatex">\(O(n)\)</span> оказывается низкой. <strong>В этом случае список можно преобразовать в AVL-дерево или красно-черное дерево</strong> , чтобы оптимизировать временную сложность поиска до <span class="arithmatex">\(O(\log n)\)</span> .</p>
 <h2 id="622">6.2.2 &nbsp; Открытая адресация<a class="headerlink" href="#622" title="Permanent link">&para;</a></h2>
-<p><u>Открытая адресация (open addressing)</u> не вводит дополнительных структур данных, а обрабатывает хеш-коллизии с помощью "многократного пробирования"; основные варианты пробирования включают линейное пробирование, квадратичное пробирование и повторное хеширование.</p>
+<p><u>Открытая адресация (open addressing)</u> не вводит дополнительных структур данных, а обрабатывает хеш-коллизии с помощью многократного пробирования; основные варианты пробирования включают линейное пробирование, квадратичное пробирование и повторное хеширование.</p>
 <p>Ниже на примере линейного пробирования рассмотрим механизм работы хеш-таблицы с открытой адресацией.</p>
 <h3 id="1">1. &nbsp; Линейное пробирование<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <p>Линейное пробирование использует линейный поиск с фиксированным шагом. Его методы работы отличаются от обычной хеш-таблицы.</p>
@@ -5960,7 +5960,7 @@
 <p><img alt="Распределение пар ключ-значение в хеш-таблице с открытой адресацией (линейное пробирование)" class="animation-figure" src="../hash_collision.assets/hash_table_linear_probing.png" /></p>
 <p align="center"> Рисунок 6-6 &nbsp; Распределение пар ключ-значение в хеш-таблице с открытой адресацией (линейное пробирование) </p>
 
-<p>Однако <strong>линейное пробирование легко приводит к "кластеризации"</strong>. Иначе говоря, чем длиннее непрерывная занятая область в массиве, тем выше вероятность новых коллизий в этой области, что еще сильнее способствует росту этой группы и в итоге ухудшает эффективность операций добавления, удаления, поиска и обновления.</p>
+<p>Однако <strong>линейное пробирование легко приводит к кластеризации</strong>. Иначе говоря, чем длиннее непрерывная занятая область в массиве, тем выше вероятность новых коллизий в этой области, что еще сильнее способствует росту этой группы и в итоге ухудшает эффективность операций добавления, удаления, поиска и обновления.</p>
 <p>Стоит заметить, что <strong>мы не можем напрямую удалять элементы из хеш-таблицы с открытой адресацией</strong>. Причина в том, что удаление создаст внутри массива пустой бакет <code>None</code> , а при поиске элемента линейное пробирование остановится на этом пустом бакете и вернет результат, из-за чего элементы ниже этого бакета уже не смогут быть найдены, и программа может ошибочно посчитать, что их не существует, как показано на рисунке 6-7.</p>
 <p><img alt="Проблема поиска после удаления элемента в открытой адресации" class="animation-figure" src="../hash_collision.assets/hash_table_open_addressing_deletion.png" /></p>
 <p align="center"> Рисунок 6-7 &nbsp; Проблема поиска после удаления элемента в открытой адресации </p>
@@ -5968,7 +5968,7 @@
 <p>Чтобы решить эту проблему, можно использовать механизм <u>ленивого удаления (lazy deletion)</u>: он не удаляет элемент из хеш-таблицы напрямую, **а помечает этот бакет специальной константой <code>TOMBSTONE</code> **. В этом механизме и <code>None</code> , и <code>TOMBSTONE</code> означают пустой бакет, и оба могут быть использованы для размещения пары ключ-значение. Но есть важное различие: при линейном пробировании, встретив <code>TOMBSTONE</code> , нужно продолжать обход, потому что ниже него все еще могут существовать пары ключ-значение.</p>
 <p>Однако <strong>ленивое удаление может ускорять деградацию производительности хеш-таблицы</strong>. Это связано с тем, что каждая операция удаления создает новую метку удаления; по мере роста числа <code>TOMBSTONE</code> время поиска тоже увеличивается, потому что линейное пробирование может быть вынуждено перескакивать через множество <code>TOMBSTONE</code> , прежде чем найдет целевой элемент.</p>
 <p>Поэтому имеет смысл при линейном пробировании запоминать индекс первого встреченного <code>TOMBSTONE</code> и затем менять найденный целевой элемент местами с этим <code>TOMBSTONE</code> . Преимущество такого подхода в том, что при каждом поиске или добавлении элемент будет перемещаться в бакет, расположенный ближе к его идеальной позиции (начальной точке пробирования), а значит, эффективность поиска улучшится.</p>
-<p>Ниже приведена реализация хеш-таблицы с открытой адресацией (линейное пробирование), включающая ленивое удаление. Чтобы пространство хеш-таблицы использовалось более полно, мы рассматриваем ее как "кольцевой массив": когда обход выходит за конец массива, он возвращается к началу и продолжается.</p>
+<p>Ниже приведена реализация хеш-таблицы с открытой адресацией, то есть с линейным пробированием, включающая ленивое удаление. Чтобы пространство хеш-таблицы использовалось более полно, мы рассматриваем ее как кольцевой массив: когда обход выходит за конец массива, он возвращается к началу и продолжается.</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
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@@ -7698,7 +7698,7 @@
 <ul>
 <li>Python использует открытую адресацию. В словаре <code>dict</code> для пробирования применяются псевдослучайные числа.</li>
 <li>Java использует метод цепочек. Начиная с JDK 1.8, когда длина массива внутри <code>HashMap</code> достигает 64, а длина списка достигает 8, этот список преобразуется в красно-черное дерево для повышения производительности поиска.</li>
-<li>Go использует метод цепочек. В Go установлено, что каждый бакет может хранить не более 8 пар ключ-значение; при переполнении подключается overflow-bucket, а когда таких bucket становится слишком много, выполняется специальное расширение того же масштаба, чтобы сохранить производительность.</li>
+<li>Go использует метод цепочек. В Go установлено, что каждый бакет может хранить не более 8 пар ключ-значение; при переполнении подключается overflow-бакет, а когда таких бакетов становится слишком много, выполняется специальное расширение того же масштаба, чтобы сохранить производительность.</li>
 </ul>
 
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-    aria-label="Вперед: 6.3 Хеш-алгоритмы"
+    aria-label="Вперед: 6.3 Алгоритмы хеширования"
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-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
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 <!-- Page content -->
 <h1 id="61-">6.1 &nbsp; Хеш-таблица<a class="headerlink" href="#61-" title="Permanent link">&para;</a></h1>
-<p><u>Хеш-таблица (hash table)</u>, также называемая <u>таблицей рассеяния</u>, обеспечивает эффективный поиск элементов за счет отображения между ключом <code>key</code> и значением <code>value</code> . Иначе говоря, если передать в хеш-таблицу ключ <code>key</code> , то можно за <span class="arithmatex">\(O(1)\)</span> времени получить соответствующее значение <code>value</code> .</p>
-<p>Как показано на рисунке 6-1, пусть есть <span class="arithmatex">\(n\)</span> студентов, и у каждого из них есть два поля данных: "имя" и "номер студенческого билета". Если мы хотим реализовать запрос вида "ввести номер студенческого билета и вернуть соответствующее имя", то для этого можно использовать показанную ниже хеш-таблицу.</p>
+<p><u>Хеш-таблица (hash table)</u>, также называемая <u>таблицей рассеяния</u>, реализует эффективный поиск элементов за счет установления соответствия между ключом <code>key</code> и значением <code>value</code> . Иначе говоря, если передать в хеш-таблицу ключ <code>key</code> , то можно за <span class="arithmatex">\(O(1)\)</span> времени получить соответствующее значение <code>value</code> .</p>
+<p>Как показано на рисунке 6-1, пусть есть <span class="arithmatex">\(n\)</span> студентов, и у каждого из них есть два поля данных: имя и номер студенческого билета. Если мы хотим реализовать запрос вида "ввести номер студенческого билета и вернуть соответствующее имя", то для этого можно использовать показанную ниже хеш-таблицу.</p>
 <p><img alt="Абстрактное представление хеш-таблицы" class="animation-figure" src="../hash_map.assets/hash_table_lookup.png" /></p>
 <p align="center"> Рисунок 6-1 &nbsp; Абстрактное представление хеш-таблицы </p>
 
-<p>Помимо хеш-таблицы, функции поиска можно реализовать и через массив, и через связный список. Сравнение их эффективности приведено в таблице 6-1.</p>
+<p>Помимо хеш-таблицы, функцией поиска также обладают массив и связный список. Сравнение их эффективности приведено в таблице 6-1.</p>
 <ul>
 <li><strong>Добавление элемента</strong>: нужно лишь добавить элемент в конец массива (или списка), что занимает <span class="arithmatex">\(O(1)\)</span> времени.</li>
 <li><strong>Поиск элемента</strong>: так как массив (или список) неупорядочен, приходится обходить все элементы, что занимает <span class="arithmatex">\(O(n)\)</span> времени.</li>
@@ -4422,7 +4422,7 @@
 </tbody>
 </table>
 </div>
-<p>Нетрудно заметить, что <strong>операции чтения, добавления, удаления и обновления в хеш-таблице имеют временную сложность <span class="arithmatex">\(O(1)\)</span></strong> , то есть выполняются очень эффективно.</p>
+<p>Нетрудно заметить, что <strong>операции поиска, добавления и удаления в хеш-таблице имеют временную сложность <span class="arithmatex">\(O(1)\)</span></strong> , то есть выполняются очень эффективно.</p>
 <h2 id="611-">6.1.1 &nbsp; Основные операции с хеш-таблицей<a class="headerlink" href="#611-" title="Permanent link">&para;</a></h2>
 <p>К базовым операциям хеш-таблицы относятся инициализация, поиск, добавление пар ключ-значение и удаление пар ключ-значение. Пример кода приведен ниже:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
@@ -4694,7 +4694,7 @@
 <summary>Визуализация выполнения</summary>
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 </details>
-<p>У хеш-таблицы есть три распространенных способа обхода: обход пар ключ-значение, обход ключей и обход значений. Примеры кода приведены ниже:</p>
+<p>Существует три распространенных способа обхода хеш-таблицы: обход пар ключ-значение, обход ключей и обход значений. Примеры кода приведены ниже:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
@@ -4894,7 +4894,7 @@
 </details>
 <h2 id="612-">6.1.2 &nbsp; Простая реализация хеш-таблицы<a class="headerlink" href="#612-" title="Permanent link">&para;</a></h2>
 <p>Сначала рассмотрим самый простой случай: <strong>реализуем хеш-таблицу только с помощью одного массива</strong>. В хеш-таблице каждую пустую ячейку массива мы называем <u>бакетом (bucket)</u>, и каждый бакет может хранить одну пару ключ-значение. Следовательно, операция поиска сводится к тому, чтобы найти бакет, соответствующий <code>key</code> , и получить из него <code>value</code> .</p>
-<p>Но как определить бакет, соответствующий заданному <code>key</code> ? Это делается с помощью <u>хеш-функции (hash function)</u>. Назначение хеш-функции - отображать большое входное пространство в меньшее выходное пространство. В хеш-таблице входным пространством являются все <code>key</code> , а выходным - все бакеты (индексы массива). Иначе говоря, передав <code>key</code> на вход, <strong>мы можем через хеш-функцию получить позицию хранения соответствующей пары ключ-значение в массиве</strong>.</p>
+<p>Но как определить бакет, соответствующий заданному <code>key</code> ? Это делается с помощью <u>хеш-функции (hash function)</u>. Назначение хеш-функции - отображать большое входное пространство в меньшее выходное пространство. В хеш-таблице входным пространством являются все <code>key</code> , а выходным - все бакеты, то есть индексы массива. Иначе говоря, передав <code>key</code> на вход, <strong>мы можем с помощью хеш-функции получить позицию хранения соответствующей пары ключ-значение в массиве</strong>.</p>
 <p>Процесс вычисления хеш-функции для одного <code>key</code> включает два шага.</p>
 <ol>
 <li>Сначала с помощью некоторого хеш-алгоритма <code>hash()</code> вычисляется хеш-значение.</li>
diff --git a/ru/chapter_hashing/index.html b/ru/chapter_hashing/index.html
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-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
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@@ -4277,14 +4277,14 @@
 <p><img alt="Хеш-таблицы" class="cover-image" src="../assets/covers/chapter_hashing.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>В мире компьютеров хеш-таблица похожа на сообразительного библиотекаря.</p>
-<p>Он умеет вычислять шифр хранения и потому быстро находит нужную книгу.</p>
+<p>Хеш-таблица устанавливает соответствие между ключом и значением.</p>
+<p>Благодаря этому она позволяет получать нужное значение по ключу за очень короткое время.</p>
 </div>
 <h2 id="_1">Содержание главы<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
 <li><a href="hash_map/">6.1 &nbsp; Хеш-таблица</a></li>
 <li><a href="hash_collision/">6.2 &nbsp; Хеш-коллизии</a></li>
-<li><a href="hash_algorithm/">6.3 &nbsp; Хеш-алгоритмы</a></li>
+<li><a href="hash_algorithm/">6.3 &nbsp; Алгоритмы хеширования</a></li>
 <li><a href="summary/">6.4 &nbsp; Резюме</a></li>
 </ul>
 
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-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
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+    Глава 9. Графы
   
 
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+        1. &nbsp; Ключевые выводы
       
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 <!-- Page content -->
-<h1 id="64">6.4 &nbsp; Краткие итоги<a class="headerlink" href="#64" title="Permanent link">&para;</a></h1>
-<h3 id="1">1. &nbsp; Основные моменты<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<h1 id="64">6.4 &nbsp; Резюме<a class="headerlink" href="#64" title="Permanent link">&para;</a></h1>
+<h3 id="1">1. &nbsp; Ключевые выводы<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
 <li>Передав <code>key</code> , мы можем получить <code>value</code> из хеш-таблицы за <span class="arithmatex">\(O(1)\)</span> времени, поэтому она очень эффективна.</li>
 <li>К типичным операциям хеш-таблицы относятся поиск, добавление пары ключ-значение, удаление пары ключ-значение и обход хеш-таблицы.</li>
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     href="../hash_algorithm/"
     class="md-footer__link md-footer__link--prev"
-    aria-label="Назад: 6.3 Хеш-алгоритмы"
+    aria-label="Назад: 6.3 Алгоритмы хеширования"
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-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
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 <!-- Page content -->
 <h1 id="82">8.2 &nbsp; Построение кучи<a class="headerlink" href="#82" title="Permanent link">&para;</a></h1>
-<p>В некоторых случаях мы хотим построить кучу, используя сразу все элементы списка. Этот процесс называется "построением кучи".</p>
+<p>В некоторых случаях требуется построить кучу, используя сразу все элементы списка. Этот процесс называется построением кучи.</p>
 <h2 id="821">8.2.1 &nbsp; Реализация через операцию добавления в кучу<a class="headerlink" href="#821" title="Permanent link">&para;</a></h2>
-<p>Сначала мы создаем пустую кучу, затем обходим список и для каждого элемента по очереди выполняем "операцию добавления в кучу": сначала помещаем элемент в хвост кучи, а затем выполняем для него упорядочивание "снизу вверх".</p>
-<p>Каждый раз, когда элемент добавляется в кучу, ее длина увеличивается на единицу. Поскольку узлы последовательно добавляются в двоичное дерево сверху вниз, куча строится "сверху вниз".</p>
+<p>Сначала мы создаем пустую кучу, затем обходим список и для каждого элемента по очереди выполняем операцию добавления в кучу: сначала помещаем элемент в хвост кучи, а затем выполняем для него упорядочивание снизу вверх.</p>
+<p>Каждый раз, когда элемент добавляется в кучу, ее длина увеличивается на единицу. Поскольку узлы последовательно добавляются в двоичное дерево сверху вниз, куча строится сверху вниз.</p>
 <p>Пусть число элементов равно <span class="arithmatex">\(n\)</span> ; так как каждая операция добавления требует <span class="arithmatex">\(O(\log{n})\)</span> времени, временная сложность такого построения кучи составляет <span class="arithmatex">\(O(n \log n)\)</span> .</p>
 <h2 id="822">8.2.2 &nbsp; Реализация через обход и упорядочивание<a class="headerlink" href="#822" title="Permanent link">&para;</a></h2>
 <p>На самом деле можно реализовать и более эффективный способ построения кучи, который состоит из двух шагов.</p>
 <ol>
 <li>Без изменений добавить все элементы списка в кучу; в этот момент свойства кучи еще не выполняются.</li>
-<li>Обойти кучу в обратном порядке, то есть в порядке, обратном обходу по уровням, и по очереди выполнить упорядочивание "сверху вниз" для каждого нелистового узла.</li>
+<li>Обойти кучу в обратном порядке, то есть в порядке, обратном обходу по уровням, и по очереди выполнить упорядочивание сверху вниз для каждого нелистового узла.</li>
 </ol>
-<p><strong>После того как некоторый узел был упорядочен, поддерево с этим узлом в качестве корня становится корректной подкучей</strong>. А поскольку обход выполняется в обратном порядке, куча строится "снизу вверх".</p>
+<p><strong>После того как некоторый узел был упорядочен, поддерево с этим узлом в качестве корня становится корректной подкучей</strong>. А поскольку обход выполняется в обратном порядке, куча строится снизу вверх.</p>
 <p>Причина выбора обратного обхода в том, что он гарантирует: поддеревья ниже текущего узла уже являются корректными подкучами, а значит, упорядочивание текущего узла действительно будет эффективным.</p>
 <p>Стоит отметить, что <strong>листовые узлы не имеют дочерних узлов, поэтому они естественным образом являются корректными подкучами и не требуют упорядочивания</strong>. Как показано в коде ниже, последний нелистовой узел является родителем последнего узла, и именно с него мы начинаем обратный обход и упорядочивание:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
@@ -4680,7 +4680,7 @@
 <p><img alt="Число узлов на каждом уровне идеального двоичного дерева" class="animation-figure" src="../build_heap.assets/heapify_operations_count.png" /></p>
 <p align="center"> Рисунок 8-5 &nbsp; Число узлов на каждом уровне идеального двоичного дерева </p>
 
-<p>Как показано на рисунке 8-5, максимальное число итераций упорядочивания "сверху вниз" для некоторого узла равно расстоянию от этого узла до листового узла, а это расстояние как раз и есть "высота узла". Поэтому мы можем просуммировать для каждого уровня выражение "число узлов <span class="arithmatex">\(\times\)</span> высота узла" и <strong>получить суммарное число итераций упорядочивания для всех узлов</strong>.</p>
+<p>Как показано на рисунке 8-5, максимальное число итераций упорядочивания сверху вниз для некоторого узла равно расстоянию от этого узла до листового узла, а это расстояние как раз и есть высота узла. Поэтому мы можем просуммировать для каждого уровня выражение "число узлов <span class="arithmatex">\(\times\)</span> высота узла" и <strong>получить суммарное число итераций упорядочивания для всех узлов</strong>.</p>
 <div class="arithmatex">\[
 T(h) = 2^0h + 2^1(h-1) + 2^2(h-2) + \dots + 2^{(h-1)}\times1
 \]</div>
@@ -4703,7 +4703,7 @@ T(h) &amp; = 2 \frac{1 - 2^h}{1 - 2} - h \newline
 &amp; = O(2^h)
 \end{aligned}
 \]</div>
-<p>Далее, число узлов идеального двоичного дерева высоты <span class="arithmatex">\(h\)</span> равно <span class="arithmatex">\(n = 2^{h+1} - 1\)</span> , поэтому несложно получить сложность <span class="arithmatex">\(O(2^h) = O(n)\)</span> . Из этого вывода следует, что <strong>построение кучи из входного списка имеет временную сложность <span class="arithmatex">\(O(n)\)</span> , что очень эффективно</strong>.</p>
+<p>Далее, число узлов идеального двоичного дерева высоты <span class="arithmatex">\(h\)</span> равно <span class="arithmatex">\(n = 2^{h+1} - 1\)</span> , поэтому несложно получить сложность <span class="arithmatex">\(O(2^h) = O(n)\)</span> . Из этого вывода следует, что <strong>построение кучи из входного списка имеет временную сложность <span class="arithmatex">\(O(n)\)</span> , то есть выполняется очень эффективно</strong>.</p>
 
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-    aria-label="Вперед: 8.3 Задача Top-K"
+    aria-label="Вперед: 8.3 Задача Top-k"
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-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
@@ -574,7 +574,7 @@
   <span class="md-ellipsis">
     
   
-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
     
@@ -596,7 +596,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
           </label>
@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 Что такое структуры данных и алгоритмы
+    1.2 Что такое алгоритм
   
 
     
@@ -1181,7 +1181,7 @@
   <span class="md-ellipsis">
     
   
-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
     
@@ -1203,7 +1203,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
           </label>
@@ -1309,7 +1309,7 @@
   <span class="md-ellipsis">
     
   
-    4.4 Память и кеш *
+    4.4 Оперативная память и кэш *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
           </label>
@@ -1691,7 +1691,7 @@
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-    6.3 Хеш-алгоритмы
+    6.3 Алгоритмы хеширования
   
 
     
@@ -1786,7 +1786,7 @@
   <span class="md-ellipsis">
     
   
-    Глава 7. Дерево
+    Глава 7. Деревья
   
 
     
@@ -1808,7 +1808,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 7. Дерево
+    Глава 7. Деревья
   
 
           </label>
@@ -1886,7 +1886,7 @@
   <span class="md-ellipsis">
     
   
-    7.3 Представление дерева массивом
+    7.3 Представление двоичного дерева массивом
   
 
     
@@ -1970,7 +1970,7 @@
   <span class="md-ellipsis">
     
   
-    7.6 Резюме
+    7.6 Краткие итоги
   
 
     
@@ -2266,7 +2266,7 @@
   <span class="md-ellipsis">
     
   
-    8.3 Задача Top-K
+    8.3 Задача Top-k
   
 
     
@@ -2357,7 +2357,7 @@
   <span class="md-ellipsis">
     
   
-    Глава 9. Граф
+    Глава 9. Графы
   
 
     
@@ -2379,7 +2379,7 @@
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-    Глава 9. Граф
+    Глава 9. Графы
   
 
           </label>
@@ -2429,7 +2429,7 @@
   <span class="md-ellipsis">
     
   
-    9.2 Базовые операции над графами
+    9.2 Базовые операции графа
   
 
     
@@ -2485,7 +2485,7 @@
   <span class="md-ellipsis">
     
   
-    9.4 Резюме
+    9.4 Краткие итоги
   
 
     
@@ -2624,7 +2624,7 @@
   <span class="md-ellipsis">
     
   
-    10.2 Точка вставки двоичного поиска
+    10.2 Двоичный поиск точки вставки
   
 
     
@@ -2652,7 +2652,7 @@
   <span class="md-ellipsis">
     
   
-    10.3 Граничные случаи двоичного поиска
+    10.3 Двоичный поиск границ
   
 
     
@@ -2680,7 +2680,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 Стратегия оптимизации через хеширование
+    10.4 Стратегии оптимизации хеширования
   
 
     
@@ -2708,7 +2708,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 Алгоритмы поиска: новый взгляд
+    10.5 Переосмысление алгоритмов поиска
   
 
     
@@ -2913,7 +2913,7 @@
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-    11.3 Пузырьковая сортировка
+    11.3 Сортировка пузырьком
   
 
     
@@ -2941,7 +2941,7 @@
   <span class="md-ellipsis">
     
   
-    11.4 Сортировка вставкой
+    11.4 Сортировка вставками
   
 
     
@@ -3246,7 +3246,7 @@
   <span class="md-ellipsis">
     
   
-    12.1 Алгоритмы разделяй и властвуй
+    12.1 Стратегия разделяй и властвуй
   
 
     
@@ -3274,7 +3274,7 @@
   <span class="md-ellipsis">
     
   
-    12.2 Стратегия поиска разделяй и властвуй
+    12.2 Поисковая стратегия разделяй и властвуй
   
 
     
@@ -3551,7 +3551,7 @@
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-    13.4 Задача о $n$ ферзях
+    13.4 Задача о n ферзях
   
 
     
@@ -3692,7 +3692,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 Введение в динамическое программирование
+    14.1 Первое знакомство с динамическим программированием
   
 
     
@@ -3804,7 +3804,7 @@
   <span class="md-ellipsis">
     
   
-    14.5 Задача о неограниченном рюкзаке
+    14.5 Задача о полном рюкзаке
   
 
     
@@ -4488,12 +4488,12 @@
 <p>Куча, являясь частным случаем полного двоичного дерева, обладает следующими свойствами.</p>
 <ul>
 <li>Узлы самого нижнего уровня заполняются слева, а все остальные уровни заполнены полностью.</li>
-<li>Корневой узел двоичного дерева мы называем "вершиной кучи", а самый правый узел нижнего уровня - "основанием кучи".</li>
+<li>Корневой узел двоичного дерева мы называем вершиной кучи, а самый правый узел нижнего уровня - основанием кучи.</li>
 <li>Для максимальной (минимальной) кучи значение элемента на вершине, то есть у корневого узла, является максимальным (минимальным).</li>
 </ul>
 <h2 id="811">8.1.1 &nbsp; Распространенные операции с кучей<a class="headerlink" href="#811" title="Permanent link">&para;</a></h2>
 <p>Нужно отметить, что многие языки программирования предоставляют не саму кучу, а <u>очередь с приоритетом (priority queue)</u> - абстрактную структуру данных, определяемую как очередь, в которой элементы извлекаются в соответствии с приоритетом.</p>
-<p>На практике <strong>куча обычно используется для реализации очереди с приоритетом, а максимальная куча эквивалентна очереди с приоритетом, в которой элементы извлекаются по убыванию</strong>. С точки зрения использования "очередь с приоритетом" и "куча" можно считать эквивалентными структурами данных. Поэтому в этой книге мы не будем специально различать их и в дальнейшем будем единообразно называть "кучей".</p>
+<p>На практике <strong>куча обычно используется для реализации очереди с приоритетом, а максимальная куча эквивалентна очереди с приоритетом, в которой элементы извлекаются по убыванию</strong>. С точки зрения использования очередь с приоритетом и куча могут считаться эквивалентными структурами данных. Поэтому в этой книге мы не будем специально различать их и в дальнейшем будем единообразно называть кучей.</p>
 <p>Распространенные операции с кучей приведены в таблице 8-1. Конкретные имена методов зависят от языка программирования.</p>
 <p align="center"> Таблица 8-1 &nbsp; Эффективность операций с кучей </p>
 
@@ -5227,7 +5227,7 @@
 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20MaxHeap%3A%0A%20%20%20%20%22%22%22%D0%9C%D0%B0%D0%BA%D1%81%D0%B8%D0%BC%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F%20%D0%BA%D1%83%D1%87%D0%B0%22%22%22%0A%0A%20%20%20%20def%20__init__%28self%2C%20nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%D0%9A%D0%BE%D0%BD%D1%81%D1%82%D1%80%D1%83%D0%BA%D1%82%D0%BE%D1%80%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%D0%94%D0%BE%D0%B1%D0%B0%D0%B2%D0%B8%D1%82%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D1%8B%20%D1%81%D0%BF%D0%B8%D1%81%D0%BA%D0%B0%20%D0%B2%20%D0%BA%D1%83%D1%87%D1%83%20%D0%B1%D0%B5%D0%B7%20%D0%B8%D0%B7%D0%BC%D0%B5%D0%BD%D0%B5%D0%BD%D0%B8%D0%B9%0A%20%20%20%20%20%20%20%20self.max_heap%20%3D%20nums%0A%0A%20%20%20%20def%20left%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%D0%9F%D0%BE%D0%BB%D1%83%D1%87%D0%B8%D1%82%D1%8C%20%D0%B8%D0%BD%D0%B4%D0%B5%D0%BA%D1%81%20%D0%BB%D0%B5%D0%B2%D0%BE%D0%B3%D0%BE%20%D0%B4%D0%BE%D1%87%D0%B5%D1%80%D0%BD%D0%B5%D0%B3%D0%BE%20%D1%83%D0%B7%D0%BB%D0%B0%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%D0%9F%D0%BE%D0%BB%D1%83%D1%87%D0%B8%D1%82%D1%8C%20%D0%B8%D0%BD%D0%B4%D0%B5%D0%BA%D1%81%20%D0%BF%D1%80%D0%B0%D0%B2%D0%BE%D0%B3%D0%BE%20%D0%B4%D0%BE%D1%87%D0%B5%D1%80%D0%BD%D0%B5%D0%B3%D0%BE%20%D1%83%D0%B7%D0%BB%D0%B0%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%D0%9F%D0%BE%D0%BB%D1%83%D1%87%D0%B8%D1%82%D1%8C%20%D0%B8%D0%BD%D0%B4%D0%B5%D0%BA%D1%81%20%D1%80%D0%BE%D0%B4%D0%B8%D1%82%D0%B5%D0%BB%D1%8C%D1%81%D0%BA%D0%BE%D0%B3%D0%BE%20%D1%83%D0%B7%D0%BB%D0%B0%22%22%22%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20%2F%2F%202%20%20%23%20%D0%9E%D0%BA%D1%80%D1%83%D0%B3%D0%BB%D0%B5%D0%BD%D0%B8%D0%B5%20%D0%B2%D0%BD%D0%B8%D0%B7%20%D0%BF%D1%80%D0%B8%20%D0%B4%D0%B5%D0%BB%D0%B5%D0%BD%D0%B8%D0%B8%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%D0%9F%D0%BE%D0%BB%D1%83%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%80%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%D0%B0%20%D0%BA%D1%83%D1%87%D0%B8%22%22%22%0A%20%20%20%20%20%20%20%20return%20len%28self.max_heap%29%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20%22%22%22%D0%9F%D1%80%D0%BE%D0%B2%D0%B5%D1%80%D0%BA%D0%B0%2C%20%D0%BF%D1%83%D1%81%D1%82%D0%B0%20%D0%BB%D0%B8%20%D0%BA%D1%83%D1%87%D0%B0%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.size%28%29%20%3D%3D%200%0A%0A%20%20%20%20def%20peek%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%D0%94%D0%BE%D1%81%D1%82%D1%83%D0%BF%20%D0%BA%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D1%83%20%D0%BD%D0%B0%20%D0%B2%D0%B5%D1%80%D1%88%D0%B8%D0%BD%D0%B5%20%D0%BA%D1%83%D1%87%D0%B8%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.max_heap%5B0%5D%0A%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F%20%D0%BC%D0%B0%D0%BA%D1%81%D0%B8%D0%BC%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%D0%B9%20%D0%BA%D1%83%D1%87%D0%B8%0A%20%20%20%20%23%20%D0%9E%D0%B1%D1%80%D0%B0%D1%82%D0%B8%D1%82%D0%B5%20%D0%B2%D0%BD%D0%B8%D0%BC%D0%B0%D0%BD%D0%B8%D0%B5%3A%20%D0%B2%D1%85%D0%BE%D0%B4%D0%BD%D0%BE%D0%B9%20%D0%BC%D0%B0%D1%81%D1%81%D0%B8%D0%B2%20%D1%83%D0%B6%D0%B5%20%D1%8F%D0%B2%D0%BB%D1%8F%D0%B5%D1%82%D1%81%D1%8F%20%D0%BA%D0%BE%D1%80%D1%80%D0%B5%D0%BA%D1%82%D0%BD%D0%BE%D0%B9%20%D0%BA%D1%83%D1%87%D0%B5%D0%B9%0A%20%20%20%20max_heap%20%3D%20MaxHeap%28%5B9%2C%208%2C%206%2C%206%2C%207%2C%205%2C%202%2C%201%2C%204%2C%203%2C%206%2C%202%5D%29%0A%0A%20%20%20%20%23%20%D0%9F%D0%BE%D0%BB%D1%83%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D0%B0%20%D1%81%20%D0%B2%D0%B5%D1%80%D1%88%D0%B8%D0%BD%D1%8B%20%D0%BA%D1%83%D1%87%D0%B8%0A%20%20%20%20peek%20%3D%20max_heap.peek%28%29%0A%20%20%20%20print%28f%22%5Cn%D0%AD%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%BD%D0%B0%20%D0%B2%D0%B5%D1%80%D1%88%D0%B8%D0%BD%D0%B5%20%D0%BA%D1%83%D1%87%D0%B8%20%3D%20%7Bpeek%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=7&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
 <h3 id="3">3. &nbsp; Добавление элемента в кучу<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
-<p>Пусть дан элемент <code>val</code> . Сначала мы помещаем его в основание кучи. После добавления свойства кучи могут нарушиться, потому что <code>val</code> может оказаться больше, чем другие элементы в куче. <strong>Поэтому необходимо восстановить порядок на пути от вставленного узла к корню</strong> ; эта операция называется <u>heapify</u>, то есть упорядочиванием кучи.</p>
+<p>Пусть дан элемент <code>val</code> . Сначала мы помещаем его в основание кучи. После добавления свойства кучи могут нарушиться, потому что <code>val</code> может оказаться больше, чем другие элементы в куче. <strong>Поэтому необходимо восстановить порядок на пути от вставленного узла к корню</strong> ; эта операция называется упорядочиванием кучи.</p>
 <p>Рассмотрим ситуацию, когда упорядочивание выполняется <strong>снизу вверх</strong>, начиная от только что вставленного узла. Как показано на рисунках ниже, мы сравниваем значение вставленного узла со значением его родителя; если вставленный узел больше, то меняем их местами. Затем продолжаем выполнять ту же операцию и последовательно восстанавливать корректность всех узлов по пути снизу вверх, пока не выйдем за корень или не встретим узел, для которого обмен не требуется.</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="4:9"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">&lt;1&gt;</label><label for="__tabbed_4_2">&lt;2&gt;</label><label for="__tabbed_4_3">&lt;3&gt;</label><label for="__tabbed_4_4">&lt;4&gt;</label><label for="__tabbed_4_5">&lt;5&gt;</label><label for="__tabbed_4_6">&lt;6&gt;</label><label for="__tabbed_4_7">&lt;7&gt;</label><label for="__tabbed_4_8">&lt;8&gt;</label><label for="__tabbed_4_9">&lt;9&gt;</label></div>
 <div class="tabbed-content">
@@ -5262,7 +5262,7 @@
 </div>
 <p align="center"> Рисунок 8-3 &nbsp; Шаги добавления элемента в кучу </p>
 
-<p>Пусть общее число узлов равно <span class="arithmatex">\(n\)</span> , тогда высота дерева равна <span class="arithmatex">\(O(\log n)\)</span> . Следовательно, максимальное число итераций операции heapify тоже не превышает <span class="arithmatex">\(O(\log n)\)</span> . Отсюда <strong>временная сложность добавления элемента в кучу равна <span class="arithmatex">\(O(\log n)\)</span></strong> . Код приведен ниже:</p>
+<p>Пусть общее число узлов равно <span class="arithmatex">\(n\)</span> , тогда высота дерева равна <span class="arithmatex">\(O(\log n)\)</span> . Следовательно, максимальное число итераций операции упорядочивания кучи тоже не превышает <span class="arithmatex">\(O(\log n)\)</span> . Отсюда <strong>временная сложность добавления элемента в кучу равна <span class="arithmatex">\(O(\log n)\)</span></strong> . Код приведен ниже:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="5:13"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label></div>
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@@ -5610,13 +5610,13 @@
 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20MaxHeap%3A%0A%0A%20%20%20%20def%20__init__%28self%2C%20nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%20%20%20%20self.max_heap%20%3D%20nums%0A%0A%20%20%20%20def%20left%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20%2F%2F%202%0A%0A%20%20%20%20def%20swap%28self%2C%20i%3A%20int%2C%20j%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%28self.max_heap%5Bi%5D%2C%20self.max_heap%5Bj%5D%29%20%3D%20%28self.max_heap%5Bj%5D%2C%20self.max_heap%5Bi%5D%29%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%20len%28self.max_heap%29%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20return%20self.size%28%29%20%3D%3D%200%0A%0A%20%20%20%20def%20push%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.max_heap.append%28val%29%0A%20%20%20%20%20%20%20%20self.sift_up%28self.size%28%29%20-%201%29%0A%0A%20%20%20%20def%20sift_up%28self%2C%20i%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20while%20True%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20p%20%3D%20self.parent%28i%29%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20p%20%3C%200%20or%20self.max_heap%5Bi%5D%20%3C%3D%20self.max_heap%5Bp%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20%20%20%20%20self.swap%28i%2C%20p%29%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%3D%20p%0A%27Driver%20Code%27%0Aif%20__name__%20%3D%3D%20%27__main__%27%3A%0A%20%20%20%20max_heap%20%3D%20MaxHeap%28%5B9%2C%208%2C%206%2C%206%2C%207%2C%205%2C%202%2C%201%2C%204%2C%203%2C%206%2C%202%5D%29%0A%20%20%20%20val%20%3D%207%0A%20%20%20%20max_heap.push%28val%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=8&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
 <h3 id="4">4. &nbsp; Извлечение элемента с вершины кучи<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
-<p>Элемент на вершине кучи - это корневой узел двоичного дерева, то есть первый элемент списка. Если просто удалить первый элемент списка, то индексы всех узлов двоичного дерева изменятся, и это сильно затруднит последующее восстановление структуры при помощи heapify. Чтобы по возможности минимизировать изменение индексов элементов, мы используем следующий порядок действий.</p>
+<p>Элемент на вершине кучи - это корневой узел двоичного дерева, то есть первый элемент списка. Если просто удалить первый элемент списка, то индексы всех узлов двоичного дерева изменятся, и это сильно затруднит последующее восстановление структуры при помощи упорядочивания кучи. Чтобы по возможности минимизировать изменение индексов элементов, мы используем следующий порядок действий.</p>
 <ol>
 <li>Поменять местами элемент на вершине кучи и элемент у основания кучи, то есть поменять корневой узел с самым правым листовым узлом.</li>
-<li>После обмена удалить основание кучи из списка. Обрати внимание: поскольку обмен уже выполнен, фактически удаляется исходный элемент вершины кучи.</li>
-<li>Начиная от корневого узла, <strong>выполнить heapify сверху вниз</strong>.</li>
+<li>После обмена удалить основание кучи из списка. Стоит отметить, что, поскольку обмен уже выполнен, фактически удаляется исходный элемент вершины кучи.</li>
+<li>Начиная от корневого узла, <strong>выполнить упорядочивание кучи сверху вниз</strong>.</li>
 </ol>
-<p>Как показано на рисунках ниже, <strong>направление операции "heapify сверху вниз" противоположно операции "heapify снизу вверх"</strong>. Мы сравниваем значение корневого узла со значениями двух дочерних узлов, выбираем больший дочерний узел и меняем его местами с корневым узлом. Затем циклически повторяем ту же операцию, пока не выйдем за листовой узел или не встретим узел, который уже не требует обмена.</p>
+<p>Как показано на рисунках ниже, <strong>направление операции упорядочивания кучи сверху вниз противоположно операции упорядочивания кучи снизу вверх</strong>. Мы сравниваем значение корневого узла со значениями двух дочерних узлов, выбираем больший дочерний узел и меняем его местами с корневым узлом. Затем циклически повторяем ту же операцию, пока не выйдем за листовой узел или не встретим узел, который уже не требует обмена.</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="6:10"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">&lt;1&gt;</label><label for="__tabbed_6_2">&lt;2&gt;</label><label for="__tabbed_6_3">&lt;3&gt;</label><label for="__tabbed_6_4">&lt;4&gt;</label><label for="__tabbed_6_5">&lt;5&gt;</label><label for="__tabbed_6_6">&lt;6&gt;</label><label for="__tabbed_6_7">&lt;7&gt;</label><label for="__tabbed_6_8">&lt;8&gt;</label><label for="__tabbed_6_9">&lt;9&gt;</label><label for="__tabbed_6_10">&lt;10&gt;</label></div>
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+++ b/ru/chapter_heap/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
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-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
     
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             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
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-    1.2 Что такое структуры данных и алгоритмы
+    1.2 Что такое алгоритм
   
 
     
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+    Глава 4. Массивы и списки
   
 
     
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+    Глава 4. Массивы и списки
   
 
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+    4.4 Оперативная память и кэш *
   
 
     
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+    7.3 Представление двоичного дерева массивом
   
 
     
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+    Глава 9. Графы
   
 
     
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+    9.2 Базовые операции графа
   
 
     
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+    9.4 Краткие итоги
   
 
     
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+    10.2 Двоичный поиск точки вставки
   
 
     
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+    10.3 Двоичный поиск границ
   
 
     
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+    10.4 Стратегии оптимизации хеширования
   
 
     
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+    10.5 Переосмысление алгоритмов поиска
   
 
     
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+    11.3 Сортировка пузырьком
   
 
     
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+    11.4 Сортировка вставками
   
 
     
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+    12.1 Стратегия разделяй и властвуй
   
 
     
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+    12.2 Поисковая стратегия разделяй и властвуй
   
 
     
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+    13.4 Задача о n ферзях
   
 
     
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+    14.1 Первое знакомство с динамическим программированием
   
 
     
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+    14.5 Задача о полном рюкзаке
   
 
     
@@ -4277,14 +4277,14 @@
 <p><img alt="Куча" class="cover-image" src="../assets/covers/chapter_heap.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>Куча похожа на горные вершины: ярусные, волнистые и самые разные по форме.</p>
-<p>Каждая вершина имеет свою высоту, но самая высокая всегда бросается в глаза первой.</p>
+<p>Куча - это полное двоичное дерево, удовлетворяющее определенным условиям.</p>
+<p>В максимальной и минимальной куче элемент на вершине всегда обладает самым выраженным приоритетом.</p>
 </div>
 <h2 id="_1">Содержание главы<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
 <li><a href="heap/">8.1 &nbsp; Куча</a></li>
 <li><a href="build_heap/">8.2 &nbsp; Построение кучи</a></li>
-<li><a href="top_k/">8.3 &nbsp; Задача Top-K</a></li>
+<li><a href="top_k/">8.3 &nbsp; Задача Top-k</a></li>
 <li><a href="summary/">8.4 &nbsp; Резюме</a></li>
 </ul>
 
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   <a
     href="../chapter_tree/summary/"
     class="md-footer__link md-footer__link--prev"
-    aria-label="Назад: 7.6 Резюме"
+    aria-label="Назад: 7.6 Краткие итоги"
     rel="prev"
   >
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+        7.6 Краткие итоги
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+        <title>8.4 Резюме - Hello Algo</title>
       
     
     
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-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
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+    1.2 Что такое алгоритм
   
 
     
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 <!-- Page content -->
-<h1 id="84">8.4 &nbsp; Краткие итоги<a class="headerlink" href="#84" title="Permanent link">&para;</a></h1>
-<h3 id="1">1. &nbsp; Основные моменты<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<h1 id="84">8.4 &nbsp; Резюме<a class="headerlink" href="#84" title="Permanent link">&para;</a></h1>
+<h3 id="1">1. &nbsp; Ключевые выводы<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
 <li>Куча представляет собой полное двоичное дерево и делится на максимальную кучу и минимальную кучу. Элемент на вершине максимальной (минимальной) кучи является наибольшим (наименьшим).</li>
 <li>Очередь с приоритетом определяется как очередь, элементы которой извлекаются в соответствии с приоритетом; обычно ее реализуют с помощью кучи.</li>
@@ -4367,7 +4367,7 @@
 </ul>
 <h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
 <p><strong>Q</strong>: Является ли "куча" как структура данных тем же самым понятием, что и "куча" в управлении памятью?</p>
-<p>Это не одно и то же, просто у них случайно совпало название. Куча в памяти компьютерной системы является частью динамического распределения памяти: во время выполнения программы она используется для хранения данных. Программа может запросить определенный объем памяти в куче для хранения сложных структур, таких как объекты и массивы. Когда эти данные больше не нужны, память нужно освободить, чтобы не допустить утечек. По сравнению со стековой памятью управление памятью в куче требует большей осторожности, а неправильное использование может привести к утечкам памяти, висячим указателям и другим проблемам.</p>
+<p>Это не одно и то же, просто у них случайно совпало название. Куча в памяти компьютерной системы является частью динамического распределения памяти: во время выполнения программы она используется для хранения данных. Программа может запросить определенный объем памяти в куче для хранения сложных структур, таких как объекты и массивы. Когда эти данные больше не нужны, память нужно освободить, чтобы не допустить утечек. По сравнению со стековой памятью управление памятью в куче требует большей осторожности, а неправильное использование может привести к утечкам памяти и проблемам с указателями.</p>
 
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+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
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 </div>
 <h2 id="832-2">8.3.2 &nbsp; Метод 2: сортировка<a class="headerlink" href="#832-2" title="Permanent link">&para;</a></h2>
 <p>Как показано на рисунке 8-7, можно сначала отсортировать массив <code>nums</code> , а затем вернуть его крайние правые <span class="arithmatex">\(k\)</span> элементов; временная сложность такого метода равна <span class="arithmatex">\(O(n \log n)\)</span> .</p>
-<p>Очевидно, что этот способ "делает слишком много", потому что нам нужно только найти наибольшие <span class="arithmatex">\(k\)</span> элементов, а сортировать остальные элементы совсем не обязательно.</p>
+<p>Очевидно, что этот способ делает слишком много, потому что нам нужно только найти наибольшие <span class="arithmatex">\(k\)</span> элементов, а сортировать остальные элементы совсем не обязательно.</p>
 <p><img alt="Поиск наибольших k элементов через сортировку" class="animation-figure" src="../top_k.assets/top_k_sorting.png" /></p>
 <p align="center"> Рисунок 8-7 &nbsp; Поиск наибольших k элементов через сортировку </p>
 
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 <!-- Page content -->
 <h1 id="_1">Перед началом<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h1>
-<p>Несколько лет назад я публиковал на LeetCode разборы серии задач "Sword for Offer" и получил поддержку и ободрение от многих читателей. Во время общения с ними чаще всего мне задавали один и тот же вопрос: "как начать изучать алгоритмы". Постепенно этот вопрос начал меня по-настоящему занимать.</p>
+<p>Несколько лет назад я публиковал на LeetCode разборы серии задач "Sword for Offer" и получил поддержку и ободрение от многих читателей. Во время общения с ними мне чаще всего задавали один и тот же вопрос: "как начать изучать алгоритмы?" Постепенно этот вопрос начал меня по-настоящему занимать.</p>
 <p>Слепо бросаться в решение задач кажется самым популярным способом: он прост, прямолинеен и действительно работает. Но решение задач похоже на игру в "Сапера": люди с сильными навыками самообучения способны обезвредить мины одну за другой, а тем, у кого не хватает базы, легко набить себе шишки и шаг за шагом отступить под давлением неудач. Полностью проходить учебники тоже принято часто, но для тех, кто готовится к поиску работы, диплом, резюме, письменные тесты и собеседования уже отнимают большую часть сил, и потому толстые книги нередко превращаются в тяжелое испытание.</p>
-<p>Если ты тоже сталкиваешься с такими трудностями, то можно сказать, что эта книга сама "нашла" тебя. Она стала моим ответом на этот вопрос: пусть не идеальным, но как минимум честной и активной попыткой. Эта книга сама по себе не гарантирует оффер, но поможет тебе увидеть "карту знаний" по структурам данных и алгоритмам, понять форму, размер и расположение разных "мин" и освоить разные "способы разминирования". Освоив это, ты сможешь увереннее решать задачи и читать технические материалы, шаг за шагом выстраивая целостную систему знаний.</p>
+<p>Если ты тоже сталкиваешься с такими трудностями, то можно сказать, что эта книга сама "нашла" тебя. Она стала моим ответом на этот вопрос: пусть и не идеальным, но как минимум честной и активной попыткой. Эта книга сама по себе не гарантирует предложения о работе, но поможет тебе увидеть "карту знаний" по структурам данных и алгоритмам, понять форму, размер и расположение разных "мин" и освоить разные "способы разминирования". Освоив это, ты сможешь увереннее решать задачи и читать технические материалы, шаг за шагом выстраивая целостную систему знаний.</p>
 <p>Я глубоко согласен со словами профессора Фейнмана: "Knowledge isn't free. You have to pay attention." В этом смысле книга не совсем "бесплатна". Чтобы не подвести то драгоценное "внимание", которое ты ей уделишь, я постараюсь вложить в ее создание максимум собственного "внимания".</p>
-<p>Я хорошо понимаю ограниченность собственных знаний. Хотя материал этой книги уже довольно долго шлифовался, в нем наверняка все еще осталось немало ошибок, поэтому я искренне прошу преподавателей и читателей указывать на неточности и недоработки.</p>
+<p>Я хорошо понимаю пределы собственных знаний. Хотя материал этой книги уже довольно долго шлифовался, в нем наверняка все еще осталось немало ошибок, поэтому я искренне прошу преподавателей и читателей указывать на неточности и недоработки.</p>
 <p><img alt="Hello Algo" class="cover-image" src="../assets/covers/chapter_hello_algo.jpg" /></p>
 <div style="text-align: center;">
-    <h2 style="margin-top: 0.8em; margin-bottom: 0.8em;">Hello, Алго!</h2>
+    <h2 style="margin-top: 0.8em; margin-bottom: 0.8em;">Hello, алгоритмы!</h2>
 </div>
 
-<p>Появление компьютеров радикально изменило мир. Благодаря высокой вычислительной скорости и отличной программируемости они стали идеальной средой для исполнения алгоритмов и обработки данных. Реалистичная графика в играх, интеллектуальные решения в автономном вождении, впечатляющие партии AlphaGo и естественное взаимодействие ChatGPT: все это изящные проявления алгоритмов на компьютере.</p>
+<p>Появление компьютеров радикально изменило мир. Благодаря высокой скорости вычислений и отличной программируемости они стали идеальной средой для исполнения алгоритмов и обработки данных. Реалистичная графика в играх, интеллектуальные решения в автономном вождении, впечатляющие партии AlphaGo и естественное взаимодействие ChatGPT: все это изящные проявления алгоритмов на компьютере.</p>
 <p>На самом деле еще до появления компьютеров алгоритмы и структуры данных уже существовали во всех уголках мира. Ранние алгоритмы были сравнительно простыми: например, древние способы счета или последовательности действий при изготовлении инструментов. По мере развития цивилизации алгоритмы становились тоньше и сложнее. За мастерством ремесленников, промышленными продуктами, освобождающими производительные силы, и даже за научными законами движения Вселенной почти всегда стоит изобретательная алгоритмическая мысль.</p>
 <p>Точно так же структуры данных встречаются повсюду: от социальных сетей до схем метро многие системы можно моделировать как "граф"; от государства до семьи основные формы общественной организации обладают свойствами "дерева"; зимняя одежда похожа на "стек", где то, что надевают первым, снимают последним; тубус для бадминтонных воланов похож на "очередь", где элементы добавляются с одного конца и извлекаются с другого; словарь похож на "хеш-таблицу", позволяющую быстро находить нужную статью.</p>
 <p>Эта книга стремится с помощью понятных анимированных иллюстраций и исполняемых примеров кода помочь читателю понять ключевые идеи алгоритмов и структур данных и научиться реализовывать их программно. На этой основе книга также пытается показать живые проявления алгоритмов в сложном мире и раскрыть их красоту. Надеюсь, она окажется для тебя полезной.</p>
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-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
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 <!-- Page content -->
 <h1 id="11">1.1 &nbsp; Алгоритмы повсюду<a class="headerlink" href="#11" title="Permanent link">&para;</a></h1>
-<p>Когда мы слышим слово "алгоритм", мы естественным образом думаем о математике. Однако на деле многие алгоритмы не связаны со сложной математикой, а в гораздо большей степени опираются на базовую логику, которую можно увидеть повсюду в повседневной жизни.</p>
-<p>Прежде чем официально перейти к разговору об алгоритмах, стоит поделиться одним любопытным фактом: <strong>ты уже незаметно для себя освоил множество алгоритмов и привык применять их в повседневной жизни</strong>. Ниже я приведу несколько конкретных примеров, чтобы это показать.</p>
-<p><strong>Пример 1: поиск в словаре</strong>. В английском словаре слова расположены в алфавитном порядке. Предположим, нам нужно найти слово, начинающееся на букву <span class="arithmatex">\(r\)</span>; обычно это делается так, как показано ниже.</p>
+<p>Говоря об алгоритмах, естественно вспомнить о математике. Однако на самом деле многие алгоритмы не связаны со сложной математикой, а больше полагаются на базовую логику, которая повсеместно встречается в нашей повседневной жизни.</p>
+<p>Прежде чем углубиться в обсуждение алгоритмов, стоит упомянуть интересный факт: <strong>вы уже точно освоили множество алгоритмов и привыкли применять их в повседневной жизни</strong>. Далее приведем несколько конкретных примеров, чтобы подтвердить этот факт.</p>
+<p><strong>Пример 1: поиск в словаре</strong>. В словаре все слова упорядочены по алфавиту. Предположим, нам нужно найти слово, начинающееся на букву <span class="arithmatex">\(r\)</span>; обычно для этого нужно выполнить следующие действия.</p>
 <ol>
-<li>Открой словарь примерно посередине и посмотри, с какой буквы начинается страница; предположим, это буква <span class="arithmatex">\(m\)</span>.</li>
-<li>Поскольку в алфавите <span class="arithmatex">\(r\)</span> идет после <span class="arithmatex">\(m\)</span>, первую половину словаря можно отбросить, и область поиска сузится до второй половины.</li>
-<li>Повторяй шаги <code>1.</code> и <code>2.</code> до тех пор, пока не найдешь страницу, на которой слово начинается с буквы <span class="arithmatex">\(r\)</span>.</li>
+<li>Откройте словарь примерно на половине страниц и посмотрите, какая буква является первой на этой странице; предположим, это буква <span class="arithmatex">\(m\)</span>.</li>
+<li>Поскольку в алфавите буква <span class="arithmatex">\(r\)</span> идет после <span class="arithmatex">\(m\)</span>, исключаем первую половину словаря, и область поиска сужается до второй половины.</li>
+<li>Продолжайте повторять шаги <code>1.</code> и <code>2.</code> , пока не найдете страницу, где первой буквой слов будет <span class="arithmatex">\(r\)</span>.</li>
 </ol>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:5"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label><label for="__tabbed_1_5">&lt;5&gt;</label></div>
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-<p><img alt="Процесс поиска в словаре" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step1.png" /></p>
+<p><img alt="Этапы поиска в словаре. Шаг 1" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step1.png" /></p>
 </div>
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-<p><img alt="Бинарный поиск в словаре, шаг 2" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step2.png" /></p>
+<p><img alt="Этапы поиска в словаре. Шаг 2" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step2.png" /></p>
 </div>
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-<p><img alt="Бинарный поиск в словаре, шаг 3" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step3.png" /></p>
+<p><img alt="Этапы поиска в словаре. Шаг 3" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step3.png" /></p>
 </div>
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-<p><img alt="Бинарный поиск в словаре, шаг 4" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step4.png" /></p>
+<p><img alt="Этапы поиска в словаре. Шаг 4" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step4.png" /></p>
 </div>
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-<p><img alt="Бинарный поиск в словаре, шаг 5" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step5.png" /></p>
+<p><img alt="Этапы поиска в словаре. Шаг 5" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step5.png" /></p>
 </div>
 </div>
 </div>
-<p align="center"> Рисунок 1-1 &nbsp; Процесс поиска в словаре </p>
+<p align="center"> Рисунок 1-1 &nbsp; Этапы поиска в словаре. Шаг 1 </p>
 
-<p>Поиск в словаре, обязательный навык для школьников, на самом деле и есть знаменитый алгоритм "двоичного поиска". С точки зрения структур данных словарь можно рассматривать как отсортированный "массив"; с точки зрения алгоритмов последовательность действий при поиске слова в словаре можно считать алгоритмом "двоичного поиска".</p>
-<p><strong>Пример 2: упорядочивание карт</strong>. Во время игры в карты нам нужно раскладывать карты в руке по возрастанию; процесс выглядит так, как показано ниже.</p>
+<p>Навык поиска в словаре, которым владеет каждый школьник, на самом деле является известным алгоритмом двоичного поиска. С точки зрения структуры данных словарь можно рассматривать как отсортированный массив; с точки зрения алгоритма последовательность операций по поиску в словаре можно считать двоичным поиском.</p>
+<p><strong>Пример 2: упорядочивание карт</strong>. Во время игры в карты необходимо каждый раз упорядочивать карты в руке от меньшего к большему. Для этого нужно выполнить следующие действия.</p>
 <ol>
-<li>Раздели карты на "упорядоченную" и "неупорядоченную" части и предположи, что в начальный момент самая левая карта уже стоит на правильном месте.</li>
-<li>Возьми одну карту из неупорядоченной части и вставь ее в правильную позицию внутри упорядоченной части; после этого две самые левые карты уже будут упорядочены.</li>
-<li>Повторяй шаг <code>2.</code> , каждый раз перенося одну карту из неупорядоченной части в упорядоченную, пока все карты не окажутся в порядке.</li>
+<li>Разделите карты на упорядоченную и неупорядоченную части, предполагая, что изначально самая левая карта уже упорядочена.</li>
+<li>Из неупорядоченной части извлеките одну карту и вставьте ее в правильное место в упорядоченной части; после этого две самые левые карты станут упорядоченными.</li>
+<li>Повторяйте шаг <code>2.</code> , каждый раз перемещая одну карту из неупорядоченной части в упорядоченную, пока все карты не станут упорядоченными.</li>
 </ol>
-<p><img alt="Процесс сортировки колоды карт" class="animation-figure" src="../algorithms_are_everywhere.assets/playing_cards_sorting.png" /></p>
-<p align="center"> Рисунок 1-2 &nbsp; Процесс сортировки колоды карт </p>
+<p><img alt="Этапы упорядочивания карт" class="animation-figure" src="../algorithms_are_everywhere.assets/playing_cards_sorting.png" /></p>
+<p align="center"> Рисунок 1-2 &nbsp; Этапы упорядочивания карт </p>
 
-<p>Описанный выше способ раскладывать карты по сути является алгоритмом "сортировки вставками", который очень эффективен на небольших наборах данных. Во многих языках программирования во встроенных функциях сортировки тоже можно увидеть этот алгоритм.</p>
-<p><strong>Пример 3: выдача сдачи</strong>. Предположим, в супермаркете мы купили товар на <span class="arithmatex">\(69\)</span> и дали кассиру <span class="arithmatex">\(100\)</span>, поэтому он должен вернуть нам <span class="arithmatex">\(31\)</span> сдачи. Этот процесс можно наглядно представить так, как показано на рисунке 1-3.</p>
+<p>Метод упорядочивания карт по своей сути является алгоритмом сортировки вставками, который весьма эффективен при обработке небольших наборов данных. Многие функции сортировки в библиотеках программирования используют именно этот алгоритм.</p>
+<p><strong>Пример 3: сдача</strong>. Предположим, что в супермаркете мы купили товар стоимостью <span class="arithmatex">\(69\)</span> руб. и дали кассиру купюру в <span class="arithmatex">\(100\)</span> руб. Кассир должен вернуть нам <span class="arithmatex">\(31\)</span> руб. Для этого ему нужно выполнить следующие действия.</p>
 <ol>
-<li>Доступные варианты - это купюры достоинством меньше <span class="arithmatex">\(31\)</span>, например <span class="arithmatex">\(1\)</span>, <span class="arithmatex">\(5\)</span>, <span class="arithmatex">\(10\)</span> и <span class="arithmatex">\(20\)</span>.</li>
-<li>Возьми самую большую купюру из доступных, то есть <span class="arithmatex">\(20\)</span>, тогда останется <span class="arithmatex">\(31 - 20 = 11\)</span>.</li>
-<li>Возьми самую большую купюру из оставшихся, то есть <span class="arithmatex">\(10\)</span>, тогда останется <span class="arithmatex">\(11 - 10 = 1\)</span>.</li>
-<li>Возьми самую большую купюру из оставшихся, то есть <span class="arithmatex">\(1\)</span>, тогда останется <span class="arithmatex">\(1 - 1 = 0\)</span>.</li>
-<li>Выдача сдачи завершена, итоговая комбинация: <span class="arithmatex">\(20 + 10 + 1 = 31\)</span>.</li>
+<li>Варианты выбора - это купюры номиналом меньше <span class="arithmatex">\(31\)</span> руб. Пусть у нас имеются номиналы <span class="arithmatex">\(1\)</span> , <span class="arithmatex">\(5\)</span> , <span class="arithmatex">\(10\)</span> и <span class="arithmatex">\(20\)</span> руб.</li>
+<li>Возьмем самую крупную доступную купюру в <span class="arithmatex">\(20\)</span> руб. Остаток сдачи составит <span class="arithmatex">\(31 - 20 = 11\)</span> руб.</li>
+<li>Возьмем самую крупную из оставшихся купюр в <span class="arithmatex">\(10\)</span> руб. Остаток составит <span class="arithmatex">\(11 - 10 = 1\)</span> руб.</li>
+<li>Возьмем самую крупную из оставшихся купюр в <span class="arithmatex">\(1\)</span> руб. Остаток составит <span class="arithmatex">\(1 - 1 = 0\)</span> руб.</li>
+<li>Завершим выдачу сдачи, схема: <span class="arithmatex">\(20 + 10 + 1 = 31\)</span> руб.</li>
 </ol>
-<p><img alt="Процесс выдачи сдачи" class="animation-figure" src="../algorithms_are_everywhere.assets/greedy_change.png" /></p>
-<p align="center"> Рисунок 1-3 &nbsp; Процесс выдачи сдачи </p>
+<p><img alt="Этапы выдачи сдачи" class="animation-figure" src="../algorithms_are_everywhere.assets/greedy_change.png" /></p>
+<p align="center"> Рисунок 1-3 &nbsp; Этапы выдачи сдачи </p>
 
-<p>В описанных шагах на каждом этапе выбирается наилучший вариант из доступных в текущий момент, то есть используется купюра наибольшего номинала; в результате получается рабочая схема выдачи сдачи. С точки зрения структур данных и алгоритмов такой подход называется "жадным" алгоритмом.</p>
-<p>От приготовления еды до межзвездных путешествий почти любое решение задачи связано с алгоритмами. Появление компьютеров позволило нам хранить структуры данных в памяти и писать код, который вызывает CPU и GPU для выполнения алгоритмов. Благодаря этому мы можем переносить реальные задачи в компьютер и решать самые разные сложные проблемы более эффективно.</p>
+<p>В этих шагах мы на каждом этапе выбираем наилучший вариант, используя купюры наибольшего номинала, и в итоге получаем рабочую схему сдачи. С точки зрения структуры данных и алгоритмов этот метод по своей сути является жадным алгоритмом.</p>
+<p>От приготовления блюда до межзвездных путешествий решение практически любой задачи неразрывно связано с алгоритмами. Появление компьютеров позволило нам с помощью программирования хранить структуры данных в памяти, а также писать код для вызовов к CPU и GPU для выполнения алгоритмов. Таким образом, мы можем переносить задачи из реальной жизни в компьютер и решать различные сложные проблемы более эффективно.</p>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>Если ты все еще смутно представляешь себе такие понятия, как структуры данных, алгоритмы, массивы и двоичный поиск, просто продолжай читать. Эта книга постепенно введет тебя в мир понимания структур данных и алгоритмов.</p>
+<p>Если представление о структурах данных, алгоритмах, массивах и двоичном поиске пока остается расплывчатым, просто продолжайте читать. Эта книга постепенно введет вас в мир структур данных и алгоритмов.</p>
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 <p><img alt="Введение в алгоритмы" class="cover-image" src="../assets/covers/chapter_introduction.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>Юная девушка легко кружится в танце среди данных, а подол ее платья струится мелодией алгоритмов.</p>
-<p>Она приглашает тебя присоединиться к танцу: следуй за ее шагами и войди в мир алгоритмов, полный логики и красоты.</p>
+<p>Юная девушка кружится в танце, переплетаясь с данными, а по подолу ее платья струится мелодия алгоритмов.</p>
+<p>Она приглашает вас присоединиться к танцу: следуйте за ее шагами и войдите в мир алгоритмов, полный логики и красоты.</p>
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 <h2 id="_1">Содержание главы<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
 <li><a href="algorithms_are_everywhere/">1.1 &nbsp; Алгоритмы повсюду</a></li>
-<li><a href="what_is_dsa/">1.2 &nbsp; Что такое структуры данных и алгоритмы</a></li>
+<li><a href="what_is_dsa/">1.2 &nbsp; Что такое алгоритм</a></li>
 <li><a href="summary/">1.3 &nbsp; Резюме</a></li>
 </ul>
 
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 <h1 id="13">1.3 &nbsp; Резюме<a class="headerlink" href="#13" title="Permanent link">&para;</a></h1>
 <h3 id="1">1. &nbsp; Ключевые выводы<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
-<li>Алгоритмы повсюду встречаются в повседневной жизни и вовсе не являются чем-то далеким и эзотерическим. На деле мы уже давно незаметно для себя освоили множество алгоритмов и используем их для решения самых разных жизненных задач.</li>
-<li>Принцип поиска в словаре соответствует алгоритму двоичного поиска. Двоичный поиск воплощает важную алгоритмическую идею "разделяй и властвуй".</li>
-<li>Процесс раскладывания карт очень похож на алгоритм сортировки вставками. Сортировка вставками подходит для упорядочивания небольших наборов данных.</li>
-<li>Выдача сдачи по шагам по своей сути является жадным алгоритмом, в котором на каждом этапе выбирается лучшее решение в текущей ситуации.</li>
-<li>Алгоритм - это набор инструкций или шагов, который решает конкретную задачу за конечное время, а структура данных - это способ, которым компьютер организует и хранит данные.</li>
-<li>Структуры данных и алгоритмы тесно связаны. Структуры данных являются основой алгоритмов, а алгоритмы оживляют структуры данных.</li>
-<li>Структуры данных и алгоритмы можно сравнить со сборкой конструктора: детали представляют данные, форма деталей и способ их соединения представляют структуру данных, а шаги сборки соответствуют алгоритму.</li>
+<li>Алгоритмы повсеместно присутствуют в нашей повседневной жизни и не являются недосягаемыми сложными знаниями. На самом деле мы уже освоили множество алгоритмов, которые помогают решать различные жизненные задачи.</li>
+<li>Принцип поиска в словаре соответствует алгоритму двоичного поиска. Двоичный поиск иллюстрирует важную идею алгоритмов "разделяй и властвуй".</li>
+<li>Процесс сортировки карт в колоде очень похож на алгоритм сортировки вставками, который хорошо подходит для сортировки небольших наборов данных.</li>
+<li>Процесс размена по своей сути является жадным алгоритмом, в котором на каждом этапе принимается наилучшее на данный момент решение.</li>
+<li>Алгоритм представляет собой набор инструкций или шагов, предназначенных для решения конкретной задачи в ограниченное время, а структура данных - это способ организации и хранения данных в компьютере.</li>
+<li>Структуры данных и алгоритмы тесно связаны. Структуры данных являются основой для алгоритмов, а алгоритмы оживляют структуры данных.</li>
+<li>Структуры данных и алгоритмы можно сравнить с конструктором: детали конструктора представляют данные, их форма и способы соединения - структуры данных, а этапы сборки конструктора соответствуют алгоритмам.</li>
 </ul>
 <h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
-<p><strong>Q</strong>: Я программист и в повседневной работе никогда не решал задачи "алгоритмами": распространенные алгоритмы уже инкапсулированы в языках программирования, и ими можно пользоваться напрямую. Значит ли это, что рабочие задачи еще не дошли до уровня, где действительно нужны алгоритмы?</p>
-<p>Если сравнить конкретные рабочие навыки с "приемами" в боевых искусствах, то фундаментальные дисциплины скорее напоминают "внутреннюю силу".</p>
-<p>Я считаю, что смысл изучения алгоритмов (и других фундаментальных дисциплин) не в том, чтобы каждый раз реализовывать их с нуля в работе, а в том, чтобы, опираясь на полученные знания, уметь профессионально реагировать и принимать решения при решении задач, тем самым повышая общее качество работы. Вот простой пример: в каждом языке программирования есть встроенная функция сортировки.</p>
+<p><strong>Q</strong>: Я программист и в повседневной работе никогда не использовал алгоритмы для решения задач, поскольку часто используемые алгоритмы уже встроены в языки программирования и ими можно пользоваться напрямую. Значит ли это, что рабочие задачи еще не требуют применения алгоритмов?</p>
+<p>Если сравнить конкретные профессиональные навыки с приемами в боевых искусствах, то базовые дисциплины скорее напоминают "внутреннюю силу".</p>
+<p>Я считаю, что изучение алгоритмов и других базовых дисциплин важно не для того, чтобы реализовывать их с нуля в работе, а для того, чтобы на основе полученных знаний принимать профессиональные решения и оценки при решении задач, тем самым повышая общее качество работы. Простой пример: каждый язык программирования имеет встроенные функции сортировки.</p>
 <ul>
-<li>Если мы не изучали структуры данных и алгоритмы, то для любых данных, скорее всего, просто отдали бы их этой функции сортировки. Все работает гладко, производительность хорошая, и на первый взгляд никаких проблем нет.</li>
-<li>Но если мы изучали алгоритмы, то знаем, что временная сложность встроенной сортировки равна <span class="arithmatex">\(O(n \log n)\)</span> ; однако если данные состоят из целых чисел фиксированной разрядности (например, номеров студентов), можно воспользоваться более эффективной "поразрядной сортировкой", снизив сложность до <span class="arithmatex">\(O(nk)\)</span> , где <span class="arithmatex">\(k\)</span> - число разрядов. Когда объем данных очень велик, сэкономленное время выполнения может принести заметную пользу, например снизить издержки и улучшить пользовательский опыт.</li>
+<li>Если бы мы не изучали структуры данных и алгоритмы, то, получив любые данные, возможно, просто передали бы их этой функции сортировки. Все работает гладко, производительность хорошая, и на первый взгляд проблем нет.</li>
+<li>Однако если мы изучили алгоритмы, то знаем, что временная сложность встроенной функции сортировки составляет <span class="arithmatex">\(O(n \log n)\)</span> ; если же данные представлены целыми числами фиксированной разрядности, например номерами студентов, то можно использовать более эффективный метод поразрядной сортировки, снизив временную сложность до <span class="arithmatex">\(O(nk)\)</span> , где <span class="arithmatex">\(k\)</span> - это количество разрядов, а при больших объемах данных выиграть во времени, затратах и пользовательском опыте.</li>
 </ul>
-<p>В инженерной практике огромное количество задач трудно довести до оптимального решения, и многие из них решаются лишь "примерно". Сложность задачи зависит, с одной стороны, от ее собственной природы, а с другой - от запаса знаний человека, который на нее смотрит. Чем полнее знания и чем больше опыт, тем глубже получается анализ задачи и тем изящнее ее можно решить.</p>
+<p>В инженерной практике множество задач трудно решить оптимальным образом, и многие из них решаются "как-то". Сложность задачи зависит как от ее природы, так и от уровня знаний и опыта человека, который ее анализирует. Чем более полными знаниями и большим опытом обладает человек, тем глубже он может проанализировать проблему и тем изящнее может быть ее решение.</p>
 
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+    9.2 Базовые операции графа
   
 
     
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+    12.1 Стратегия разделяй и властвуй
   
 
     
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+    14.1 Первое знакомство с динамическим программированием
   
 
     
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 <!-- Page content -->
 <h1 id="12">1.2 &nbsp; Что такое алгоритм<a class="headerlink" href="#12" title="Permanent link">&para;</a></h1>
 <h2 id="121">1.2.1 &nbsp; Определение алгоритма<a class="headerlink" href="#121" title="Permanent link">&para;</a></h2>
-<p><u>Алгоритм (algorithm)</u> - это набор инструкций или шагов, который решает конкретную задачу за конечное время. Он обладает следующими свойствами.</p>
+<p><u>Алгоритм (algorithm)</u> - это набор инструкций или шагов, предназначенных для решения конкретной задачи за ограниченное время. Он обладает следующими свойствами.</p>
 <ul>
-<li>Задача четко определена и имеет ясные определения входных и выходных данных.</li>
-<li>Алгоритм осуществим и может быть выполнен за конечное число шагов, времени и памяти.</li>
-<li>Каждый шаг имеет однозначный смысл, и при одинаковых входных данных и условиях выполнения результат всегда будет одинаковым.</li>
+<li>Задача четко определена и включает ясные определения входных и выходных данных.</li>
+<li>Обладает осуществимостью и может быть выполнен за ограниченное количество шагов, времени и памяти.</li>
+<li>Каждый шаг имеет определенное значение, и при одинаковых входных данных и условиях выполнения результат всегда будет одинаковым.</li>
 </ul>
 <h2 id="122">1.2.2 &nbsp; Определение структуры данных<a class="headerlink" href="#122" title="Permanent link">&para;</a></h2>
-<p><u>Структура данных (data structure)</u> - это способ организации и хранения данных, охватывающий само содержимое данных, связи между данными и методы работы с ними. У нее есть следующие цели проектирования.</p>
+<p><u>Структура данных (data structure)</u> - это способ организации и хранения данных, включающий содержимое данных, их взаимосвязи и методы операций с ними. Структура данных преследует следующие цели.</p>
 <ul>
-<li>Занимать как можно меньше места, чтобы экономить память компьютера.</li>
-<li>Выполнять операции над данными как можно быстрее, включая доступ, добавление, удаление, обновление и т. д.</li>
-<li>Предоставлять компактное представление данных и логическую информацию, чтобы алгоритмы могли работать эффективно.</li>
+<li>Минимизировать занимаемое пространство для экономии памяти компьютера.</li>
+<li>Обеспечивать максимально быструю обработку данных, включая доступ, добавление, удаление и обновление данных.</li>
+<li>Обеспечивать простое представление данных и логическую информацию для эффективного выполнения алгоритмов.</li>
 </ul>
-<p><strong>Проектирование структур данных - это процесс, полный компромиссов</strong>. Если мы хотим улучшить что-то одно, то часто вынуждены уступить в чем-то другом. Ниже приведены два примера.</p>
+<p><strong>Проектирование структуры данных - это процесс, полный компромиссов</strong>. Если вы хотите улучшить один аспект, часто приходится идти на уступки в другом. Приведем два примера.</p>
 <ul>
-<li>По сравнению с массивами связные списки удобнее для добавления и удаления данных, но жертвуют скоростью доступа к ним.</li>
-<li>По сравнению со связными списками графы предоставляют более богатую логическую информацию, но требуют большего объема памяти.</li>
+<li>Связный список, по сравнению с массивом, более удобен для добавления и удаления данных, но имеет проблемы со скоростью доступа к данным.</li>
+<li>Граф, по сравнению со связным списком, предоставляет более богатую логическую информацию, но требует большего объема памяти.</li>
 </ul>
 <h2 id="123">1.2.3 &nbsp; Связь между структурами данных и алгоритмами<a class="headerlink" href="#123" title="Permanent link">&para;</a></h2>
-<p>Как показано на рисунке 1-4, структуры данных и алгоритмы тесно связаны и сильно зависят друг от друга; это проявляется в следующих трех аспектах.</p>
+<p>Как показано на рисунке 1-4, структуры данных и алгоритмы тесно взаимосвязаны, что проявляется в следующих трех аспектах.</p>
 <ul>
-<li>Структуры данных служат фундаментом алгоритмов. Они дают алгоритмам структурированный способ хранения данных и методы работы с ними.</li>
-<li>Алгоритмы оживляют структуры данных. Сами по себе структуры данных лишь хранят информацию, а в сочетании с алгоритмами позволяют решать конкретные задачи.</li>
-<li>Алгоритмы обычно можно реализовать на основе разных структур данных, но эффективность выполнения может сильно различаться, поэтому выбор подходящей структуры данных является ключевым.</li>
+<li>Структуры данных являются основой алгоритмов. Они обеспечивают структурированное хранение данных и методы их обработки.</li>
+<li>Алгоритмы оживляют структуры данных. Сами по себе структуры данных лишь хранят информацию, но в сочетании с алгоритмами они позволяют решать конкретные задачи.</li>
+<li>Алгоритмы можно реализовать на основе различных структур данных, однако эффективность их выполнения может значительно различаться, поэтому выбор подходящей структуры данных является ключевым фактором.</li>
 </ul>
 <p><img alt="Связь между структурами данных и алгоритмами" class="animation-figure" src="../what_is_dsa.assets/relationship_between_data_structure_and_algorithm.png" /></p>
 <p align="center"> Рисунок 1-4 &nbsp; Связь между структурами данных и алгоритмами </p>
 
-<p>Структуры данных и алгоритмы похожи на сборку конструктора, показанную на рисунке 1-5. В набор конструктора, помимо множества деталей, входит и подробная инструкция по сборке. Если шаг за шагом следовать этой инструкции, можно собрать красивую модель.</p>
+<p>Структуры данных и алгоритмы подобны конструктору, как показано на рисунке 1-5. Комплект конструктора, помимо множества деталей, содержит также подробную инструкцию по сборке. Следуя этой инструкции шаг за шагом, можно собрать красивую модель.</p>
 <p><img alt="Сборка конструктора" class="animation-figure" src="../what_is_dsa.assets/assembling_blocks.png" /></p>
 <p align="center"> Рисунок 1-5 &nbsp; Сборка конструктора </p>
 
-<p>Подробное соответствие между ними показано в таблице 1-1.</p>
-<p align="center"> Таблица 1-1 &nbsp; Сравнение структур данных и алгоритмов со сборкой конструктора </p>
+<p>Подробное описание аналогии с конструктором представлено в таблице 1-1.</p>
+<p align="center"> Таблица 1-1 &nbsp; Сравнение структур данных и алгоритмов с конструктором </p>
 
 <div class="center-table">
 <table>
 <thead>
 <tr>
 <th>Структуры данных и алгоритмы</th>
-<th>Сборка конструктора</th>
+<th>Конструктор</th>
 </tr>
 </thead>
 <tbody>
@@ -4428,11 +4428,11 @@
 </tr>
 <tr>
 <td>Структура данных</td>
-<td>Организация деталей: форма, размер, способ соединения и т. д.</td>
+<td>Организация деталей конструктора, включая форму, размер, способы соединения и т. д.</td>
 </tr>
 <tr>
 <td>Алгоритм</td>
-<td>Последовательность шагов по сборке деталей в целевую форму</td>
+<td>Последовательность действий по сборке деталей в целевую модель</td>
 </tr>
 <tr>
 <td>Выходные данные</td>
@@ -4441,10 +4441,10 @@
 </tbody>
 </table>
 </div>
-<p>Стоит отметить, что структуры данных и алгоритмы не зависят от конкретного языка программирования. Именно поэтому эта книга может давать реализации на разных языках программирования.</p>
+<p>Стоит отметить, что структуры данных и алгоритмы не зависят от языка программирования. Именно поэтому данная книга предлагает их реализации на различных языках.</p>
 <div class="admonition tip">
 <p class="admonition-title">Принятое сокращение</p>
-<p>В реальных обсуждениях мы обычно сокращаем выражение "структуры данных и алгоритмы" до просто "алгоритмы". Например, хорошо известные алгоритмические задачи LeetCode на деле одновременно проверяют знания и по структурам данных, и по алгоритмам.</p>
+<p>В реальных обсуждениях выражение "структуры данных и алгоритмы" обычно сокращают до просто "алгоритмы". Например, хорошо известные задачи LeetCode на деле одновременно проверяют знания и по структурам данных, и по алгоритмам.</p>
 </div>
 
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+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
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 <!-- Page content -->
 <h1 id="01">0.1 &nbsp; Об этой книге<a class="headerlink" href="#01" title="Permanent link">&para;</a></h1>
-<p>Этот проект направлен на создание открытого, бесплатного и дружелюбного к новичкам вводного пособия по структурам данных и алгоритмам.</p>
+<p>Этот проект задуман как открытое, бесплатное и дружелюбное к новичкам введение в структуры данных и алгоритмы.</p>
 <ul>
-<li>Вся книга построена на анимированных иллюстрациях: материал изложен ясно и последовательно, а кривая обучения остается плавной, помогая начинающим постепенно увидеть карту знаний по структурам данных и алгоритмам.</li>
-<li>Исходный код можно запускать одним нажатием, что помогает читателю через практику развивать навыки программирования и понимать, как работают алгоритмы и как устроены структуры данных на базовом уровне.</li>
-<li>Мы призываем читателей учиться друг у друга: задавайте вопросы и делитесь своими наблюдениями в комментариях, чтобы вместе продвигаться вперед через обсуждение и обмен идеями.</li>
+<li>В книге используются анимированные иллюстрации: материал изложен ясно и последовательно, что облегчает освоение и помогает начинающим выстроить карту знаний по структурам данных и алгоритмам.</li>
+<li>Исходный код можно запустить одним нажатием, что позволяет тренироваться, развивать навыки программирования и понимать принципы работы алгоритмов и реализации структур данных на фундаментальном уровне.</li>
+<li>Мы призываем читателей к взаимопомощи: задавайте вопросы и делитесь идеями в комментариях. Обсуждения помогают двигаться вперед всем вместе.</li>
 </ul>
 <h2 id="011">0.1.1 &nbsp; Целевая аудитория<a class="headerlink" href="#011" title="Permanent link">&para;</a></h2>
-<p>Если ты только начинаешь изучать алгоритмы, никогда раньше с ними не сталкивался или уже решал некоторые задачи, но все еще смутно представляешь себе структуры данных и алгоритмы и постоянно колеблешься между "понимаю" и "не понимаю", то эта книга создана именно для тебя!</p>
-<p>Если у тебя уже накопился определенный опыт решения задач и ты знаком с большинством типовых вопросов, книга поможет тебе системно повторить и упорядочить знания об алгоритмах, а исходный код из репозитория можно использовать как "инструментарий для решения задач" или как "алгоритмический словарь".</p>
-<p>Если же ты уже настоящий "гуру" алгоритмов, мы будем рады получить твои ценные замечания или <a href="https://www.hello-algo.com/chapter_appendix/contribution/">создавать книгу вместе</a>.</p>
+<p>Если вы новичок в алгоритмах, никогда с ними не сталкивались или уже имеете некоторый опыт решения задач, но еще не обладаете четким пониманием структур данных и алгоритмов, эта книга создана специально для вас!</p>
+<p>Если у вас уже есть определенный опыт решения задач и вы знакомы с большинством типов задач, эта книга поможет вам освежить и систематизировать знания об алгоритмах, а исходный код может служить набором инструментов для решения задач или алгоритмическим словарем.</p>
+<p>Если вы владеете алгоритмами на экспертном уровне, мы будем рады вашим ценным советам или <a href="https://www.hello-algo.com/chapter_appendix/contribution/">совместному участию в создании книги</a>.</p>
 <div class="admonition success">
 <p class="admonition-title">Предварительные требования</p>
-<p>Тебе нужна хотя бы базовая подготовка в одном из языков программирования, чтобы читать и писать простой код.</p>
+<p>Необходимо иметь хотя бы базовую подготовку в одном из языков программирования, чтобы читать и писать простой код.</p>
 </div>
 <h2 id="012">0.1.2 &nbsp; Структура содержания<a class="headerlink" href="#012" title="Permanent link">&para;</a></h2>
-<p>Основное содержание книги показано на рисунке 0-1.</p>
+<p>Основное содержание книги представлено на рисунке 0-1.</p>
 <ul>
-<li><strong>Анализ сложности</strong>: измерения и методы оценки структур данных и алгоритмов. Способы вычисления временной и пространственной сложности, распространенные типы, примеры и т. д.</li>
-<li><strong>Структуры данных</strong>: способы классификации базовых типов данных и структур данных. Определения, достоинства и недостатки, основные операции, распространенные разновидности, типичные применения и методы реализации массивов, связных списков, стеков, очередей, хеш-таблиц, деревьев, куч, графов и других структур.</li>
-<li><strong>Алгоритмы</strong>: определения, достоинства и недостатки, эффективность, области применения, этапы решения и примеры задач для поиска, сортировки, разделяй-и-властвуй, поиска с возвратом, динамического программирования и жадных алгоритмов.</li>
+<li><strong>Анализ сложности</strong>: критерии и методы оценки структур данных и алгоритмов. Методы расчета временной и пространственной сложности, распространенные типы, примеры и т. д.</li>
+<li><strong>Структуры данных</strong>: классификация основных типов данных и структур данных. Определение, преимущества и недостатки, основные операции, распространенные типы, типичные приложения и методы реализации массивов, списков, стеков, очередей, хеш-таблиц, деревьев, куч и графов.</li>
+<li><strong>Алгоритмы</strong>: определение, преимущества и недостатки, эффективность, области применения, этапы решения и примеры задач для поиска, сортировки, алгоритма "разделяй и властвуй", поиска с возвратом, динамического программирования и жадных алгоритмов.</li>
 </ul>
 <p><img alt="Основное содержание книги" class="animation-figure" src="../about_the_book.assets/hello_algo_mindmap.png" /></p>
 <p align="center"> Рисунок 0-1 &nbsp; Основное содержание книги </p>
 
 <h2 id="013">0.1.3 &nbsp; Благодарности<a class="headerlink" href="#013" title="Permanent link">&para;</a></h2>
-<p>Эта книга непрерывно совершенствуется благодаря совместным усилиям множества участников сообщества open source. Спасибо каждому автору, который вложил свое время и силы; их имена перечислены в порядке, автоматически сгенерированном GitHub: krahets, coderonion, Gonglja, nuomi1, Reanon, justin-tse, hpstory, danielsss, curtishd, night-cruise, S-N-O-R-L-A-X, rongyi, msk397, gvenusleo, khoaxuantu, rivertwilight, K3v123, gyt95, zhuoqinyue, yuelinxin, Zuoxun, mingXta, Phoenix0415, FangYuan33, GN-Yu, longsizhuo, IsChristina, xBLACKICEx, guowei-gong, Cathay-Chen, pengchzn, QiLOL, magentaqin, hello-ikun, JoseHung, qualifier1024, thomasq0, sunshinesDL, L-Super, Guanngxu, Transmigration-zhou, WSL0809, Slone123c, lhxsm, yuan0221, what-is-me, Shyam-Chen, theNefelibatas, longranger2, codeberg-user, xiongsp, JeffersonHuang, prinpal, seven1240, Wonderdch, malone6, xiaomiusa87, gaofer, bluebean-cloud, a16su, SamJin98, hongyun-robot, nanlei, XiaChuerwu, yd-j, iron-irax, mgisr, steventimes, junminhong, heshuyue, danny900714, MolDuM, Nigh, Dr-XYZ, XC-Zero, reeswell, PXG-XPG, NI-SW, Horbin-Magician, Enlightenus, YangXuanyi, beatrix-chan, DullSword, xjr7670, jiaxianhua, qq909244296, iStig, boloboloda, hts0000, gledfish, wenjianmin, keshida, kilikilikid, lclc6, lwbaptx, linyejoe2, liuxjerry, llql1211, fbigm, echo1937, szu17dmy, dshlstarr, Yucao-cy, coderlef, czruby, bongbongbakudan, beintentional, ZongYangL, ZhongYuuu, ZhongGuanbin, hezhizhen, linzeyan, ZJKung, luluxia, xb534, ztkuaikuai, yw-1021, ElaBosak233, baagod, zhouLion, yishangzhang, yi427, yanedie, yabo083, weibk, wangwang105, th1nk3r-ing, tao363, 4yDX3906, syd168, sslmj2020, smilelsb, siqyka, selear, sdshaoda, Xi-Row, popozhu, nuquist19, noobcodemaker, XiaoK29, chadyi, lyl625760, lucaswangdev, 0130w, shanghai-Jerry, EJackYang, Javesun99, eltociear, lipusheng, KNChiu, BlindTerran, ShiMaRing, lovelock, FreddieLi, FloranceYeh, fanchenggang, gltianwen, goerll, nedchu, curly210102, CuB3y0nd, KraHsu, CarrotDLaw, youshaoXG, bubble9um, Asashishi, Asa0oo0o0o, fanenr, eagleanurag, akshiterate, 52coder, foursevenlove, KorsChen, GaochaoZhu, hopkings2008, yang-le, realwujing, Evilrabbit520, Umer-Jahangir, Turing-1024-Lee, Suremotoo, paoxiaomooo, Chieko-Seren, Allen-Scai, ymmmas, Risuntsy, Richard-Zhang1019, RafaelCaso, qingpeng9802, primexiao, Urbaner3, zhongfq, nidhoggfgg, MwumLi, CreatorMetaSky, martinx, ZnYang2018, hugtyftg, logan-qiu, psychelzh, Keynman, KeiichiKasai и KawaiiAsh.</p>
-<p>Рецензирование кода для этой книги выполнили coderonion, curtishd, Gonglja, gvenusleo, hpstory, justin-tse, khoaxuantu, krahets, night-cruise, nuomi1, Reanon и rongyi (в алфавитном порядке). Спасибо им за время и силы: именно они обеспечили единообразие и стандартизацию кода на разных языках.</p>
-<p>Традиционную китайскую версию книги вычитали Shyam-Chen и Dr-XYZ, английскую версию - yuelinxin, K3v123, QiLOL, Phoenix0415, SamJin98, yanedie, RafaelCaso, pengchzn, thomasq0 и magentaqin, а японскую версию - eltociear. Именно благодаря их постоянному вкладу эта книга может быть полезна более широкому кругу читателей, и мы искренне благодарим их.</p>
-<p>Инструмент генерации ePub-версии этой книги разработал zhongfq. Благодарим его за вклад, который дал читателям более гибкий способ чтения.</p>
-<p>Во время работы над этой книгой мне помогало очень много людей.</p>
+<p>Эта книга постоянно совершенствуется благодаря совместным усилиям множества участников открытого сообщества. Благодарим каждого автора, вложившего свое время и силы; их имена перечислены в порядке, автоматически сгенерированном GitHub: krahets, coderonion, Gonglja, nuomi1, Reanon, justin-tse, hpstory, danielsss, curtishd, night-cruise, S-N-O-R-L-A-X, rongyi, msk397, gvenusleo, khoaxuantu, rivertwilight, K3v123, gyt95, zhuoqinyue, yuelinxin, Zuoxun, mingXta, Phoenix0415, FangYuan33, GN-Yu, longsizhuo, IsChristina, xBLACKICEx, guowei-gong, Cathay-Chen, pengchzn, QiLOL, magentaqin, hello-ikun, JoseHung, qualifier1024, thomasq0, sunshinesDL, L-Super, Guanngxu, Transmigration-zhou, WSL0809, Slone123c, lhxsm, yuan0221, what-is-me, Shyam-Chen, theNefelibatas, longranger2, codeberg-user, xiongsp, JeffersonHuang, prinpal, seven1240, Wonderdch, malone6, xiaomiusa87, gaofer, bluebean-cloud, a16su, SamJin98, hongyun-robot, nanlei, XiaChuerwu, yd-j, iron-irax, mgisr, steventimes, junminhong, heshuyue, danny900714, MolDuM, Nigh, Dr-XYZ, XC-Zero, reeswell, PXG-XPG, NI-SW, Horbin-Magician, Enlightenus, YangXuanyi, beatrix-chan, DullSword, xjr7670, jiaxianhua, qq909244296, iStig, boloboloda, hts0000, gledfish, wenjianmin, keshida, kilikilikid, lclc6, lwbaptx, linyejoe2, liuxjerry, llql1211, fbigm, echo1937, szu17dmy, dshlstarr, Yucao-cy, coderlef, czruby, bongbongbakudan, beintentional, ZongYangL, ZhongYuuu, ZhongGuanbin, hezhizhen, linzeyan, ZJKung, luluxia, xb534, ztkuaikuai, yw-1021, ElaBosak233, baagod, zhouLion, yishangzhang, yi427, yanedie, yabo083, weibk, wangwang105, th1nk3r-ing, tao363, 4yDX3906, syd168, sslmj2020, smilelsb, siqyka, selear, sdshaoda, Xi-Row, popozhu, nuquist19, noobcodemaker, XiaoK29, chadyi, lyl625760, lucaswangdev, 0130w, shanghai-Jerry, EJackYang, Javesun99, eltociear, lipusheng, KNChiu, BlindTerran, ShiMaRing, lovelock, FreddieLi, FloranceYeh, fanchenggang, gltianwen, goerll, nedchu, curly210102, CuB3y0nd, KraHsu, CarrotDLaw, youshaoXG, bubble9um, Asashishi, Asa0oo0o0o, fanenr, eagleanurag, akshiterate, 52coder, foursevenlove, KorsChen, GaochaoZhu, hopkings2008, yang-le, realwujing, Evilrabbit520, Umer-Jahangir, Turing-1024-Lee, Suremotoo, paoxiaomooo, Chieko-Seren, Allen-Scai, ymmmas, Risuntsy, Richard-Zhang1019, RafaelCaso, qingpeng9802, primexiao, Urbaner3, zhongfq, nidhoggfgg, MwumLi, CreatorMetaSky, martinx, ZnYang2018, hugtyftg, logan-qiu, psychelzh, Keynman, KeiichiKasai и KawaiiAsh.</p>
+<p>Рецензирование кода книги выполнили coderonion, curtishd, Gonglja, gvenusleo, hpstory, justin-tse, khoaxuantu, krahets, night-cruise, nuomi1, Reanon и rongyi (в алфавитном порядке). Благодарим их за потраченное время и силы, которые обеспечили стандартизацию и единообразие кода на различных языках.</p>
+<p>Традиционную китайскую версию книги вычитали Shyam-Chen и Dr-XYZ, английскую версию - yuelinxin, K3v123, QiLOL, Phoenix0415, SamJin98, yanedie, RafaelCaso, pengchzn, thomasq0 и magentaqin, а японскую версию - eltociear. Именно благодаря их постоянному вкладу эта книга может служить более широкому кругу читателей, и мы искренне благодарим их.</p>
+<p>Инструмент генерации ePub-версии этой книги разработал zhongfq. Благодарим его за вклад, который дал читателям более свободный способ чтения.</p>
+<p>В процессе создания этой книги мне помогало много людей.</p>
 <ul>
-<li>Спасибо моему наставнику в компании, доктору Ли Си: в одной из бесед ты подтолкнул меня "быстрее начать", и это укрепило мою решимость написать эту книгу;</li>
-<li>Спасибо моей девушке Bubble, первому читателю этой книги: с позиции новичка в алгоритмах ты дала много ценных замечаний, благодаря которым книга стала понятнее для начинающих;</li>
-<li>Спасибо Tengbao, Qibao и Feibao за придуманное ими креативное название книги, которое возвращает нас к теплому воспоминанию о первой строке кода "Hello World!";</li>
-<li>Спасибо Xiaoquan за профессиональную помощь по вопросам интеллектуальной собственности: она сыграла важную роль в совершенствовании этой открытой книги;</li>
-<li>Спасибо Sutong за прекрасный дизайн обложки и логотипа, а также за терпеливые многочисленные правки, на которые тебя вдохновлял мой перфекционизм;</li>
-<li>Спасибо @squidfunk за советы по верстке и за созданную им открытую тему документации <a href="https://github.com/squidfunk/mkdocs-material/tree/master">Material-for-MkDocs</a>.</li>
+<li>Благодарю моего наставника в компании, доктора Ли Си: в одной из бесед вы вдохновили меня быстрее начать, что укрепило мою решимость написать эту книгу;</li>
+<li>Благодарю мою девушку Bubble, первого читателя этой книги: с позиции новичка в алгоритмах она дала много ценных советов, благодаря которым книга стала более понятной и доступной;</li>
+<li>Благодарю Tengbao, Qibao и Feibao за креативное название книги, которое навевает приятные воспоминания о первой строке кода "Hello World!";</li>
+<li>Благодарю Xiaoquan за профессиональную помощь в вопросах интеллектуальной собственности, что сыграло важную роль в совершенствовании этой открытой книги;</li>
+<li>Благодарю Sutong за дизайн обложки и логотипа книги, а также за терпение при многочисленных исправлениях по моим просьбам;</li>
+<li>Благодарю @squidfunk за советы по оформлению и за разработку открытой темы документации <a href="https://github.com/squidfunk/mkdocs-material/tree/master">Material-for-MkDocs</a>.</li>
 </ul>
-<p>Во время написания книги я прочитал множество учебников и статей по структурам данных и алгоритмам. Эти работы стали для книги прекрасными образцами и помогли обеспечить точность и качество материала. Я искренне благодарю всех преподавателей и предшественников за их выдающийся вклад!</p>
-<p>Эта книга пропагандирует способ обучения, в котором работают и руки, и голова; в этом отношении на меня сильно повлияла <a href="https://github.com/d2l-ai/d2l-zh">Dive into Deep Learning</a>. Я горячо рекомендую эту замечательную работу всем читателям.</p>
-<p><strong>От всего сердца благодарю моих родителей: именно ваша постоянная поддержка и ободрение дали мне возможность заниматься этим интересным делом</strong>.</p>
+<p>В процессе написания книги я ознакомился с множеством учебников и статей по структурам данных и алгоритмам. Эти работы послужили отличным образцом для этой книги, обеспечив ее точность и качество. Я искренне благодарю всех преподавателей и предшественников за их выдающийся вклад!</p>
+<p>Эта книга пропагандирует метод обучения, сочетающий умственную и практическую деятельность; в этом отношении на меня сильно повлияла <a href="https://github.com/d2l-ai/d2l-zh">Dive into Deep Learning</a>. Я настоятельно рекомендую эту замечательную работу всем читателям.</p>
+<p><strong>Сердечно благодарю моих родителей: именно ваша постоянная поддержка и ободрение дали мне возможность заняться этим увлекательным делом</strong>.</p>
 
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-    Глава 1. Знакомство с алгоритмами
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-    Глава 1. Знакомство с алгоритмами
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-    1.2 Что такое структуры данных и алгоритмы
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+    14.1 Первое знакомство с динамическим программированием
   
 
     
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+    14.5 Задача о полном рюкзаке
   
 
     
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 <p><img alt="Предисловие" class="cover-image" src="../assets/covers/chapter_preface.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>Алгоритмы подобны прекрасной симфонии, а каждая строка кода течет, как мелодия.</p>
-<p>Пусть эта книга мягко зазвучит в твоем сознании и оставит после себя особую и глубокую мелодию.</p>
+<p>Алгоритмы подобны прекрасной симфонии, а каждая строка кода льется подобно мелодии.</p>
+<p>Пусть эта книга тихо зазвучит в вашем сознании и оставит после себя особую и глубокую мелодию.</p>
 </div>
 <h2 id="_1">Содержание главы<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
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-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
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+    Глава 1. Введение в алгоритмы
   
 
     
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+    4.4 Оперативная память и кэш *
   
 
     
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-    Глава 6. Хеширование
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 <h1 id="02">0.2 &nbsp; Как пользоваться этой книгой<a class="headerlink" href="#02" title="Permanent link">&para;</a></h1>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>Чтобы получить наилучший опыт чтения, рекомендуется полностью прочитать этот раздел.</p>
+<p>Для получения наилучшего опыта чтения рекомендуется полностью прочитать этот раздел.</p>
 </div>
 <h2 id="021">0.2.1 &nbsp; Соглашения о стиле изложения<a class="headerlink" href="#021" title="Permanent link">&para;</a></h2>
 <ul>
-<li>Разделы, помеченные <code>*</code> в заголовке, являются дополнительными и сравнительно более сложными. Если времени мало, их можно пока пропустить.</li>
-<li>Технические термины будут выделяться полужирным шрифтом (в бумажной и PDF-версиях) или подчеркиванием (в веб-версии), например <u>массив (array)</u>. Рекомендуется запоминать их, чтобы легче читать техническую литературу.</li>
-<li>Ключевое содержание и итоговые формулировки будут <strong>выделяться полужирным</strong>, и на такие фрагменты стоит обращать особое внимание.</li>
+<li>Главы, помеченные <code>*</code> в заголовке, являются дополнительными и содержат более сложный материал. Если времени мало, их можно пропустить.</li>
+<li>Профессиональные термины выделяются полужирным шрифтом в печатной и PDF-версии или подчеркиванием в веб-версии, например <u>массив (array)</u>. Рекомендуется запоминать их для удобства чтения литературы.</li>
+<li>Важные моменты и обобщающие фразы будут <strong>выделяться полужирным шрифтом</strong>, и на такие тексты следует обращать особое внимание.</li>
 <li>Слова и выражения со специальным смыслом будут отмечаться "кавычками", чтобы избежать неоднозначности.</li>
-<li>Когда названия различаются между языками программирования, эта книга ориентируется на Python; например, для обозначения "пустого" значения используется <code>None</code>.</li>
-<li>В книге частично отказались от строгих правил оформления комментариев в языках программирования ради более компактной верстки. Комментарии в основном делятся на три типа: комментарии-заголовки, содержательные комментарии и многострочные комментарии.</li>
+<li>Когда термины различаются между языками программирования, в качестве стандарта используется Python; например, <code>None</code> применяется для обозначения "пустого" значения.</li>
+<li>В некоторых местах книга отходит от стандартов комментирования программного кода ради более компактного оформления. Комментарии в основном делятся на три типа: заголовочные, содержательные и многострочные.</li>
 </ul>
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 <div class="tabbed-content">
@@ -4580,49 +4580,49 @@
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 </div>
 <h2 id="022">0.2.2 &nbsp; Эффективное обучение с помощью анимированных иллюстраций<a class="headerlink" href="#022" title="Permanent link">&para;</a></h2>
-<p>По сравнению с текстом видео и изображения обладают большей информационной плотностью и более четкой структурой, поэтому их легче воспринимать. В этой книге <strong>ключевые и сложные идеи в основном будут показываться в виде анимированных иллюстраций</strong>, а текст будет играть роль пояснения и дополнения.</p>
-<p>Если во время чтения ты встречаешь фрагмент с анимированной иллюстрацией, как на рисунке 0-2, <strong>в первую очередь ориентируйся на изображение, а текст используй как дополнение</strong>, соединяя оба источника для понимания материала.</p>
+<p>По сравнению с текстом видео и изображения обладают более высокой плотностью информации и более четкой структурой, поэтому их легче воспринимать. В этой книге <strong>ключевые и сложные моменты в основном представлены в виде анимированных иллюстраций</strong>, а текст служит пояснением и дополнением.</p>
+<p>Если во время чтения вы встречаете фрагмент с анимированной иллюстрацией, как на рисунке 0-2, <strong>используйте иллюстрацию в качестве основного источника информации, а текст - в качестве вспомогательного</strong>, объединяя оба источника для понимания материала.</p>
 <p><img alt="Пример анимированной иллюстрации" class="animation-figure" src="../../index.assets/animation.gif" /></p>
 <p align="center"> Рисунок 0-2 &nbsp; Пример анимированной иллюстрации </p>
 
 <h2 id="023">0.2.3 &nbsp; Углубление понимания через практику кода<a class="headerlink" href="#023" title="Permanent link">&para;</a></h2>
-<p>Сопроводительный код этой книги размещен в <a href="https://github.com/krahets/hello-algo">репозитории GitHub</a>. Как показано ниже, <strong>исходный код снабжен тестовыми примерами и может запускаться одним нажатием</strong>.</p>
-<p>Если позволяет время, <strong>рекомендуется самостоятельно перепечатать код</strong>. Если времени на обучение мало, то хотя бы полностью прочитай и запусти весь код.</p>
-<p>По сравнению с простым чтением кода сам процесс его написания обычно дает больше пользы. <strong>Учиться на практике - значит учиться по-настоящему</strong>.</p>
+<p>Сопроводительный код этой книги размещен в <a href="https://github.com/krahets/hello-algo">репозитории GitHub</a>. Как показано ниже, <strong>исходный код содержит тестовые примеры и может быть запущен одним нажатием кнопки</strong>.</p>
+<p>Если позволяет время, <strong>рекомендуется самостоятельно набирать код</strong>. Если времени на обучение мало, по крайней мере <strong>просмотрите и выполните весь код</strong>.</p>
+<p>Процесс написания кода приносит больше пользы, чем его чтение. <strong>Настоящее обучение - это обучение на практике</strong>.</p>
 <p><img alt="Пример запуска кода" class="animation-figure" src="../../index.assets/running_code.gif" /></p>
 <p align="center"> Рисунок 0-3 &nbsp; Пример запуска кода </p>
 
-<p>Подготовка к запуску кода в основном состоит из трех шагов.</p>
-<p><strong>Шаг 1: установить локальную среду программирования</strong>. Воспользуйся <a href="https://www.hello-algo.com/chapter_appendix/installation/">руководством</a> из приложения. Если среда уже установлена, этот шаг можно пропустить.</p>
-<p><strong>Шаг 2: клонировать или скачать репозиторий с кодом</strong>. Перейди в <a href="https://github.com/krahets/hello-algo">репозиторий GitHub</a>. Если у тебя уже установлен <a href="https://git-scm.com/downloads">Git</a>, репозиторий можно клонировать следующей командой:</p>
+<p>Подготовка к запуску кода в основном состоит из трех этапов.</p>
+<p><strong>Шаг 1: установка локальной среды программирования</strong>. Воспользуйтесь <a href="https://www.hello-algo.com/chapter_appendix/installation/">руководством</a> из приложения. Если среда уже установлена, этот шаг можно пропустить.</p>
+<p><strong>Шаг 2: клонирование или загрузка репозитория кода</strong>. Перейдите в <a href="https://github.com/krahets/hello-algo">репозиторий GitHub</a>. Если у вас уже установлен <a href="https://git-scm.com/downloads">Git</a>, репозиторий можно клонировать следующей командой:</p>
 <div class="highlight"><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a>git<span class="w"> </span>clone<span class="w"> </span>https://github.com/krahets/hello-algo.git
 </code></pre></div>
-<p>Конечно, можно также нажать кнопку "Download ZIP" в месте, показанном на рисунке 0-4, напрямую скачать архив с кодом и затем распаковать его локально.</p>
+<p>Также можно нажать кнопку "Download ZIP" в месте, показанном на рисунке 0-4, напрямую скачать архив с кодом и затем распаковать его локально.</p>
 <p><img alt="Клонирование репозитория и загрузка кода" class="animation-figure" src="../suggestions.assets/download_code.png" /></p>
 <p align="center"> Рисунок 0-4 &nbsp; Клонирование репозитория и загрузка кода </p>
 
-<p><strong>Шаг 3: запустить исходный код</strong>. Как показано на рисунке 0-5, для блоков кода, у которых сверху указано имя файла, соответствующий исходный файл можно найти в папке <code>codes</code> репозитория. Эти файлы запускаются одним нажатием, что помогает не тратить лишнее время на отладку и сосредоточиться на изучении материала.</p>
+<p><strong>Шаг 3: запуск исходного кода</strong>. Как показано на рисунке 0-5, для блоков кода, у которых сверху указано имя файла, соответствующий исходный файл можно найти в папке <code>codes</code> репозитория. Исходные файлы запускаются одним нажатием, что помогает не тратить лишнее время на отладку и сосредоточиться на изучении материала.</p>
 <p><img alt="Блоки кода и соответствующие исходные файлы" class="animation-figure" src="../suggestions.assets/code_md_to_repo.png" /></p>
 <p align="center"> Рисунок 0-5 &nbsp; Блоки кода и соответствующие исходные файлы </p>
 
-<p>Помимо локального запуска, <strong>веб-версия также поддерживает визуальный запуск Python-кода</strong> (на базе <a href="https://pythontutor.com/">pythontutor</a>). Как показано ниже, можно нажать "Визуализировать выполнение" под блоком кода, чтобы раскрыть окно и наблюдать за выполнением алгоритма; также можно нажать "Полноэкранный режим", чтобы получить более удобный просмотр.</p>
+<p>Помимо локального запуска, <strong>веб-версия также поддерживает визуальное выполнение Python-кода</strong> (на базе <a href="https://pythontutor.com/">pythontutor</a>). Как показано ниже, можно нажать "Визуализировать выполнение" под блоком кода, чтобы раскрыть окно и наблюдать за выполнением алгоритма; также можно нажать "Полноэкранный режим" для более удобного просмотра.</p>
 <p><img alt="Визуальный запуск Python-кода" class="animation-figure" src="../suggestions.assets/pythontutor_example.png" /></p>
 <p align="center"> Рисунок 0-6 &nbsp; Визуальный запуск Python-кода </p>
 
 <h2 id="024">0.2.4 &nbsp; Совместный рост через вопросы и обсуждения<a class="headerlink" href="#024" title="Permanent link">&para;</a></h2>
-<p>Во время чтения книги не стоит легко пропускать те места, которые остались непонятными. <strong>Смело задавай свои вопросы в разделе комментариев</strong>: я и мои друзья постараемся ответить тебе как можно тщательнее, обычно в течение двух дней.</p>
-<p>Как показано на рисунке 0-7, в веб-версии у каждой главы внизу есть раздел комментариев. Надеюсь, ты будешь чаще обращать внимание на его содержание. С одной стороны, это поможет увидеть, с какими трудностями сталкиваются другие читатели, восполнить пробелы и подтолкнуть себя к более глубоким размышлениям. С другой стороны, буду рад, если ты щедро ответишь на вопросы других участников, поделишься своими наблюдениями и поможешь им продвинуться вперед.</p>
+<p>Во время чтения книги не стоит пропускать те места, которые остались непонятными. <strong>Мы призываем вас задавать вопросы в разделе комментариев</strong>: я и мои коллеги постараемся ответить вам как можно тщательнее, обычно в течение двух дней.</p>
+<p>Как показано на рисунке 0-7, в веб-версии у каждой главы внизу есть раздел комментариев. Рекомендуется уделять внимание его содержанию. С одной стороны, это поможет увидеть, с какими трудностями сталкиваются другие читатели, восполнить пробелы и подтолкнуть себя к более глубокому пониманию. С другой стороны, мы надеемся, что вы будете отвечать на вопросы других участников и делиться своими мнениями.</p>
 <p><img alt="Пример раздела комментариев" class="animation-figure" src="../../index.assets/comment.gif" /></p>
 <p align="center"> Рисунок 0-7 &nbsp; Пример раздела комментариев </p>
 
 <h2 id="025">0.2.5 &nbsp; Дорожная карта изучения алгоритмов<a class="headerlink" href="#025" title="Permanent link">&para;</a></h2>
 <p>В целом процесс изучения структур данных и алгоритмов можно разделить на три этапа.</p>
 <ol>
-<li><strong>Этап 1: введение в алгоритмы</strong>. Нужно познакомиться с особенностями и способами применения разных структур данных, а также изучить принципы, ход работы, назначение и эффективность различных алгоритмов.</li>
-<li><strong>Этап 2: решение алгоритмических задач</strong>. Рекомендуется начинать с популярных задач и сначала накопить не менее 100 решенных примеров, чтобы познакомиться с основными типами алгоритмических проблем. На первых порах "забывание знаний" может стать испытанием, но это нормально. Мы можем повторять задачи по "кривой забывания Эббингауза", и обычно после 3-5 циклов повторения материал прочно закрепляется. Рекомендуемые списки задач и планы практики см. в этом <a href="https://github.com/krahets/LeetCode-Book">репозитории GitHub</a>.</li>
-<li><strong>Этап 3: построение системы знаний</strong>. В учебной части можно читать статьи по алгоритмам, разбирать каркасы решений и учебники, чтобы постоянно обогащать свою систему знаний. В практической части можно пробовать более продвинутые стратегии, например классификацию по темам, несколько решений одной задачи или одно решение для нескольких задач; соответствующий опыт можно найти в разных сообществах.</li>
+<li><strong>Этап 1: введение в алгоритмы</strong>. Необходимо познакомиться с особенностями и применением различных структур данных, изучить принципы, процессы, назначение и эффективность различных алгоритмов.</li>
+<li><strong>Этап 2: решение алгоритмических задач</strong>. Рекомендуется начинать с популярных задач и решить не менее 100 из них, чтобы познакомиться с основными алгоритмическими проблемами. При первых попытках "забывание знаний" может стать испытанием, но это нормально. Следуйте при повторении задач "кривой забывания Эббингауза", и обычно после 3-5 циклов повторения материал хорошо запоминается. Рекомендуемые списки задач и планы практики см. в этом <a href="https://github.com/krahets/LeetCode-Book">репозитории GitHub</a>.</li>
+<li><strong>Этап 3: построение системы знаний</strong>. В процессе обучения можно читать статьи по алгоритмам, изучать каркасы решений и учебники, чтобы постоянно обогащать свою систему знаний. В решении задач можно применять продвинутые стратегии, например классификацию по темам, несколько решений одной задачи или одно решение для нескольких задач; соответствующий опыт можно найти в различных сообществах.</li>
 </ol>
-<p>Как показано на рисунке 0-8, содержание этой книги в основном покрывает "этап 1" и призвано помочь тебе более эффективно перейти к обучению на этапах 2 и 3.</p>
+<p>Как показано на рисунке 0-8, содержание этой книги в основном охватывает "этап 1" и призвано помочь вам более эффективно перейти к обучению на этапах 2 и 3.</p>
 <p><img alt="Дорожная карта изучения алгоритмов" class="animation-figure" src="../suggestions.assets/learning_route.png" /></p>
 <p align="center"> Рисунок 0-8 &nbsp; Дорожная карта изучения алгоритмов </p>
 
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+    Глава 1. Введение в алгоритмы
   
 
     
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+    Глава 1. Введение в алгоритмы
   
 
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+    Глава 4. Массивы и списки
   
 
     
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 <h1 id="03">0.3 &nbsp; Резюме<a class="headerlink" href="#03" title="Permanent link">&para;</a></h1>
 <h3 id="1">1. &nbsp; Ключевые выводы<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
-<li>Основная аудитория этой книги - новички в изучении алгоритмов. Если у тебя уже есть определенная база, книга поможет системно повторить знания, а исходный код можно использовать как "инструментарий для решения задач".</li>
-<li>Основное содержание книги состоит из трех частей: анализ сложности, структуры данных и алгоритмы; вместе они охватывают большую часть тем этой области.</li>
-<li>Для начинающих особенно важно на старте прочитать хорошее вводное пособие: это помогает избежать множества лишних обходных путей.</li>
-<li>Анимированные иллюстрации в книге обычно используются для объяснения ключевых и сложных идей. При чтении книги этим материалам стоит уделять больше внимания.</li>
-<li>Практика - лучший способ изучать программирование. Настоятельно рекомендуется запускать исходный код и набирать его самостоятельно.</li>
-<li>В веб-версии книги у каждой главы есть раздел комментариев, где можно в любой момент делиться вопросами и своими мыслями.</li>
+<li>Основная аудитория этой книги - новички в изучении алгоритмов. Если у вас уже есть определенная база, книга поможет систематизировать знания, а исходный код послужит инструментальной библиотекой для решения задач.</li>
+<li>Содержание книги включает три основные части - анализ сложности, структуры данных и алгоритмы - и охватывает большинство тем в этой области.</li>
+<li>Для новичков в алгоритмах крайне важно изучить начальные разделы книги, чтобы избежать множества ошибок в будущем.</li>
+<li>Анимированные иллюстрации в книге обычно используются для представления ключевых и сложных аспектов. При чтении книги следует уделять этим материалам больше внимания.</li>
+<li>Практика - лучший способ изучения программирования. Настоятельно рекомендуется запускать исходный код и самостоятельно писать программы.</li>
+<li>В веб-версии книги каждая глава имеет область комментариев, где можно задавать вопросы и делиться своими мыслями.</li>
 </ul>
 
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-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
@@ -572,7 +572,7 @@
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+    Глава 1. Введение в алгоритмы
   
 
     
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+    4.4 Оперативная память и кэш *
   
 
     
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+    13.4 Задача о n ферзях
   
 
     
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+    14.1 Первое знакомство с динамическим программированием
   
 
     
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+    14.5 Задача о полном рюкзаке
   
 
     
@@ -4253,16 +4253,16 @@
 
 <!-- Page content -->
 <h1 id="_1">Список литературы<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h1>
-<p>[1] Thomas H. Cormen, et al. Introduction to Algorithms (3<sup>rd</sup> Edition).</p>
+<p>[1] Thomas H. Cormen и др. Introduction to Algorithms (3<sup>rd</sup> Edition).</p>
 <p>[2] Aditya Bhargava. Grokking Algorithms: An Illustrated Guide for Programmers and Other Curious People (1<sup>st</sup> Edition).</p>
-<p>[3] Robert Sedgewick, et al. Algorithms (4<sup>th</sup> Edition).</p>
+<p>[3] Robert Sedgewick и др. Algorithms (4<sup>th</sup> Edition).</p>
 <p>[4] Yan Weimin. Data Structures (C Language Edition).</p>
 <p>[5] Deng Junhui. Data Structures (C++ Language Edition, 3<sup>rd</sup> Edition).</p>
-<p>[6] Mark Allen Weiss; translated by Chen Yue. Data Structures and Algorithm Analysis: Java Description (3<sup>rd</sup> Edition).</p>
+<p>[6] Mark Allen Weiss; пер. Chen Yue. Data Structures and Algorithm Analysis: Java Description (3<sup>rd</sup> Edition).</p>
 <p>[7] Cheng Jie. A Plainspoken Guide to Data Structures.</p>
 <p>[8] Wang Zheng. The Beauty of Data Structures and Algorithms.</p>
 <p>[9] Gayle Laakmann McDowell. Cracking the Coding Interview: 189 Programming Questions and Solutions (6<sup>th</sup> Edition).</p>
-<p>[10] Aston Zhang, et al. Dive into Deep Learning.</p>
+<p>[10] Aston Zhang и др. Dive into Deep Learning.</p>
 
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diff --git a/ru/chapter_searching/binary_search/index.html b/ru/chapter_searching/binary_search/index.html
index d8c091b0d..28ba00211 100644
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+++ b/ru/chapter_searching/binary_search/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
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+    Глава 1. Введение в алгоритмы
   
 
     
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             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
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-    1.2 Что такое структуры данных и алгоритмы
+    1.2 Что такое алгоритм
   
 
     
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+    Глава 4. Массивы и списки
   
 
     
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-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
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+    4.4 Оперативная память и кэш *
   
 
     
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+    Глава 6. Хеш-таблицы
   
 
     
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+    Глава 6. Хеш-таблицы
   
 
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+    7.3 Представление двоичного дерева массивом
   
 
     
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+    9.2 Базовые операции графа
   
 
     
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+    14.5 Задача о полном рюкзаке
   
 
     
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 <!-- Page content -->
 <h1 id="101">10.1 &nbsp; Двоичный поиск<a class="headerlink" href="#101" title="Permanent link">&para;</a></h1>
-<p><u>Двоичный поиск (binary search)</u> - это эффективный алгоритм поиска, основанный на стратегии "разделяй и властвуй". Он использует упорядоченность данных и на каждом шаге сокращает область поиска вдвое, пока не найдет целевой элемент или пока интервал поиска не опустеет.</p>
+<p><u>Двоичный поиск (binary search)</u> - это эффективный алгоритм поиска, основанный на стратегии "разделяй и властвуй". Он использует упорядоченность данных, сокращая на каждом шаге область поиска вдвое, пока не будет найден целевой элемент или пока интервал поиска не опустеет.</p>
 <div class="admonition question">
 <p class="admonition-title">Question</p>
 <p>Дан массив <code>nums</code> длины <span class="arithmatex">\(n\)</span>, элементы которого расположены в порядке возрастания и не повторяются. Найдите и верните индекс элемента <code>target</code> в этом массиве. Если массив не содержит этого элемента, верните <span class="arithmatex">\(-1\)</span> . Пример показан на рисунке 10-1.</p>
@@ -4699,7 +4699,7 @@
 <p><strong>Временная сложность равна <span class="arithmatex">\(O(\log n)\)</span></strong> : в цикле двоичного поиска интервал каждый раз сокращается вдвое, поэтому число итераций равно <span class="arithmatex">\(\log_2 n\)</span> .</p>
 <p><strong>Пространственная сложность равна <span class="arithmatex">\(O(1)\)</span></strong> : указатели <span class="arithmatex">\(i\)</span> и <span class="arithmatex">\(j\)</span> занимают константный объем памяти.</p>
 <h2 id="1011">10.1.1 &nbsp; Методы представления интервалов<a class="headerlink" href="#1011" title="Permanent link">&para;</a></h2>
-<p>Помимо описанного выше двойного замкнутого интервала, часто используется и интервал "слева закрыт, справа открыт", который задается как <span class="arithmatex">\([0, n)\)</span> , то есть левая граница включается, а правая - нет. В этом представлении интервал <span class="arithmatex">\([i, j)\)</span> пуст, когда <span class="arithmatex">\(i = j\)</span> .</p>
+<p>Помимо описанного выше двойного замкнутого интервала, часто используется и левозамкнутый правооткрытый интервал, который задается как <span class="arithmatex">\([0, n)\)</span> , то есть левая граница включается, а правая - нет. В этом представлении интервал <span class="arithmatex">\([i, j)\)</span> пуст, когда <span class="arithmatex">\(i = j\)</span> .</p>
 <p>На основе этого представления можно реализовать двоичный поиск с той же функциональностью:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label></div>
 <div class="tabbed-content">
@@ -5056,7 +5056,7 @@ aria-label="Нижний колонтитул"
   <a
     href="../binary_search_insertion/"
     class="md-footer__link md-footer__link--next"
-    aria-label="Вперед: 10.2 Точка вставки двоичного поиска"
+    aria-label="Вперед: 10.2 Двоичный поиск точки вставки"
     rel="next"
   >
     <div class="md-footer__title">
@@ -5064,7 +5064,7 @@ aria-label="Нижний колонтитул"
         Вперед
       </span>
       <div class="md-ellipsis">
-        10.2 Точка вставки двоичного поиска
+        10.2 Двоичный поиск точки вставки
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diff --git a/ru/chapter_searching/binary_search_edge/index.html b/ru/chapter_searching/binary_search_edge/index.html
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@@ -65,8 +65,8 @@
         
         
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-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
@@ -574,7 +574,7 @@
   <span class="md-ellipsis">
     
   
-    Глава 1. Знакомство с алгоритмами
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 <p class="admonition-title">Question</p>
 <p>Дан упорядоченный массив <code>nums</code> длины <span class="arithmatex">\(n\)</span>, который может содержать повторяющиеся элементы. Верните индекс самого левого элемента <code>target</code> в массиве. Если массив не содержит этот элемент, верните <span class="arithmatex">\(-1\)</span> .</p>
 </div>
-<p>Вспомним метод поиска точки вставки при двоичном поиске: после завершения поиска указатель <span class="arithmatex">\(i\)</span> указывает на самый левый <code>target</code> , <strong>поэтому поиск точки вставки по сути и есть поиск индекса самого левого <code>target</code></strong>.</p>
+<p>Вспомним метод поиска точки вставки при двоичном поиске: после завершения поиска указатель <span class="arithmatex">\(i\)</span> указывает на самый левый <code>target</code> , <strong>поэтому поиск точки вставки по сути является поиском индекса самого левого <code>target</code></strong>.</p>
 <p>Рассмотрим реализацию поиска левой границы через функцию поиска точки вставки. Обратите внимание: массив может не содержать <code>target</code> , и тогда возможны две ситуации.</p>
 <ul>
 <li>Индекс точки вставки <span class="arithmatex">\(i\)</span> выходит за границы массива.</li>
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 <!-- Page content -->
-<h1 id="102">10.2 &nbsp; Точка вставки при двоичном поиске<a class="headerlink" href="#102" title="Permanent link">&para;</a></h1>
+<h1 id="102">10.2 &nbsp; Двоичный поиск точки вставки<a class="headerlink" href="#102" title="Permanent link">&para;</a></h1>
 <p>Двоичный поиск можно использовать не только для поиска целевого элемента, но и для решения многих вариаций задачи, например для поиска позиции вставки целевого элемента.</p>
 <h2 id="1021">10.2.1 &nbsp; Случай без повторяющихся элементов<a class="headerlink" href="#1021" title="Permanent link">&para;</a></h2>
 <div class="admonition question">
@@ -4368,7 +4368,7 @@
 <p><strong>Вопрос 1</strong>: если массив содержит <code>target</code> , будет ли индекс вставки совпадать с индексом этого элемента?</p>
 <p>По условию <code>target</code> нужно вставить слева от равного элемента, а это означает, что новый <code>target</code> занимает место старого <code>target</code> . Иначе говоря, <strong>если массив содержит <code>target</code> , то индекс вставки совпадает с индексом этого <code>target</code></strong>.</p>
 <p><strong>Вопрос 2</strong>: если массив не содержит <code>target</code> , индекс какого элемента будет точкой вставки?</p>
-<p>Рассмотрим процесс двоичного поиска подробнее: когда <code>nums[m] &lt; target</code> , указатель <span class="arithmatex">\(i\)</span> сдвигается, а значит, приближается к элементу, который больше либо равен <code>target</code> . Аналогично указатель <span class="arithmatex">\(j\)</span> все время приближается к элементу, который меньше либо равен <code>target</code> .</p>
+<p>Рассмотрим процесс двоичного поиска подробнее: когда <code>nums[m] &lt; target</code> , указатель <span class="arithmatex">\(i\)</span> сдвигается вправо и тем самым приближается к элементу, который больше либо равен <code>target</code> . Аналогично указатель <span class="arithmatex">\(j\)</span> постепенно приближается к элементу, который меньше либо равен <code>target</code> .</p>
 <p>Следовательно, после завершения двоичного поиска обязательно выполняется следующее: указатель <span class="arithmatex">\(i\)</span> указывает на первый элемент, больший <code>target</code> , а указатель <span class="arithmatex">\(j\)</span> указывает на первый элемент, меньший <code>target</code> . <strong>Нетрудно сделать вывод, что если массив не содержит <code>target</code> , то индекс вставки равен <span class="arithmatex">\(i\)</span></strong> . Код приведен ниже:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
@@ -4691,7 +4691,7 @@
 </div>
 <p align="center"> Рисунок 10-6 &nbsp; Шаги поиска точки вставки для повторяющихся элементов </p>
 
-<p>Если посмотреть на следующий код, то видно, что операции в ветвях <code>nums[m] &gt; target</code> и <code>nums[m] == target</code> совпадают, поэтому эти две ветви можно объединить.</p>
+<p>Если посмотреть на следующий код, то видно, что действия в ветвях <code>nums[m] &gt; target</code> и <code>nums[m] == target</code> совпадают, поэтому эти две ветви можно объединить.</p>
 <p>Даже в этом случае можно оставить условия развернутыми, потому что так логика выглядит более ясной и код легче читать.</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label></div>
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@@ -4964,7 +4964,7 @@
 <p class="admonition-title">Tip</p>
 <p>Код в этом разделе записан в стиле "двойного замкнутого интервала". При желании можно самостоятельно реализовать вариант "слева закрыт, справа открыт".</p>
 </div>
-<p>Если смотреть в целом, суть двоичного поиска сводится к тому, что для указателей <span class="arithmatex">\(i\)</span> и <span class="arithmatex">\(j\)</span> заранее задаются цели поиска; целью может быть конкретный элемент (например, <code>target</code> ), а может быть и диапазон элементов (например, элементы, меньшие <code>target</code> ).</p>
+<p>Если смотреть в целом, суть двоичного поиска сводится к тому, что для указателей <span class="arithmatex">\(i\)</span> и <span class="arithmatex">\(j\)</span> заранее задаются ориентиры поиска; целью может быть конкретный элемент, например <code>target</code> , а может быть и диапазон элементов, например все элементы, меньшие <code>target</code> .</p>
 <p>В ходе непрерывного двоичного деления указатели <span class="arithmatex">\(i\)</span> и <span class="arithmatex">\(j\)</span> постепенно приближаются к заранее заданной цели. В конце они либо успешно находят ответ, либо останавливаются после выхода за границы.</p>
 
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 <p><img alt="Поиск" class="cover-image" src="../assets/covers/chapter_searching.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>Поиск - это приключение в неизвестность: иногда приходится пройти каждый уголок загадочного пространства, а иногда удается быстро зафиксировать цель.</p>
-<p>В этом путешествии каждый новый шаг может привести к ответу, которого мы не ожидали.</p>
+<p>Поиск - это движение в неизвестность: иногда приходится пройти каждый уголок пространства, а иногда удается быстро найти цель.</p>
+<p>В этом пути каждый новый шаг может привести к ответу, которого мы не ожидали.</p>
 </div>
 <h2 id="_1">Содержание главы<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
 <li><a href="binary_search/">10.1 &nbsp; Двоичный поиск</a></li>
-<li><a href="binary_search_insertion/">10.2 &nbsp; Точка вставки двоичного поиска</a></li>
-<li><a href="binary_search_edge/">10.3 &nbsp; Граничные случаи двоичного поиска</a></li>
-<li><a href="replace_linear_by_hashing/">10.4 &nbsp; Стратегия оптимизации через хеширование</a></li>
-<li><a href="searching_algorithm_revisited/">10.5 &nbsp; Алгоритмы поиска: новый взгляд</a></li>
+<li><a href="binary_search_insertion/">10.2 &nbsp; Двоичный поиск точки вставки</a></li>
+<li><a href="binary_search_edge/">10.3 &nbsp; Двоичный поиск границ</a></li>
+<li><a href="replace_linear_by_hashing/">10.4 &nbsp; Стратегии оптимизации хеширования</a></li>
+<li><a href="searching_algorithm_revisited/">10.5 &nbsp; Переосмысление алгоритмов поиска</a></li>
 <li><a href="summary/">10.6 &nbsp; Резюме</a></li>
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-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
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 <!-- Page content -->
-<h1 id="104-">10.4 &nbsp; Стратегии хеш-оптимизации<a class="headerlink" href="#104-" title="Permanent link">&para;</a></h1>
+<h1 id="104">10.4 &nbsp; Стратегии оптимизации хеширования<a class="headerlink" href="#104" title="Permanent link">&para;</a></h1>
 <p>В алгоритмических задачах <strong>мы часто заменяем линейный поиск на хеш-поиск, чтобы уменьшить временную сложность алгоритма</strong>. Разберем одну задачу, чтобы лучше понять этот прием.</p>
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-    aria-label="Назад: 10.3 Граничные случаи двоичного поиска"
+    aria-label="Назад: 10.3 Двоичный поиск границ"
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-    aria-label="Вперед: 10.5 Алгоритмы поиска: новый взгляд"
+    aria-label="Вперед: 10.5 Переосмысление алгоритмов поиска"
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+        10.5 Переосмысление алгоритмов поиска
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 <li><strong>Поиск целевого элемента путем обхода структуры данных</strong>, например обход массива, списка, дерева или графа.</li>
 <li><strong>Эффективный поиск элементов с использованием структуры организации данных или априорной информации</strong>, например двоичный поиск, хеш-поиск и поиск в двоичном дереве поиска.</li>
 </ul>
-<p>Нетрудно заметить, что эти темы уже рассматривались в предыдущих главах, поэтому алгоритмы поиска нам уже знакомы. В этом разделе мы еще раз посмотрим на них, но уже более системно.</p>
+<p>Нетрудно заметить, что эти темы уже рассматривались в предыдущих главах, поэтому алгоритмы поиска нам уже знакомы. В этом разделе мы систематизируем полученные ранее знания и еще раз посмотрим на них как на единую группу методов.</p>
 <h2 id="1051">10.5.1 &nbsp; Полный перебор<a class="headerlink" href="#1051" title="Permanent link">&para;</a></h2>
 <p>Полный перебор заключается в том, что мы обходим каждый элемент структуры данных, чтобы найти целевой элемент.</p>
 <ul>
 <li>"Линейный поиск" применяется к линейным структурам данных, таким как массивы и списки. Он начинается с одного конца структуры данных и последовательно проверяет элементы, пока не найдет целевой элемент или пока не достигнет другого конца структуры данных.</li>
-<li>"Поиск в ширину" и "поиск в глубину" - это две стратегии обхода графов и деревьев. Поиск в ширину стартует из начального узла и исследует все узлы текущего уровня, прежде чем переходить к следующему. Поиск в глубину стартует из начального узла, проходит один путь до конца, затем возвращается назад и пробует другие пути, пока не будет полностью пройдена вся структура данных.</li>
+<li>"Обход в ширину" и "обход в глубину" - это две стратегии обхода графов и деревьев. Обход в ширину стартует из начального узла и исследует все узлы текущего уровня, прежде чем переходить к следующему. Обход в глубину стартует из начального узла, проходит один путь до конца, затем возвращается назад и пробует другие пути, пока не будет полностью пройдена вся структура данных.</li>
 </ul>
 <p>Преимущество полного перебора состоит в его простоте и универсальности, <strong>поскольку он не требует предварительной обработки данных и использования дополнительных структур данных</strong>.</p>
 <p>Однако <strong>временная сложность таких алгоритмов равна <span class="arithmatex">\(O(n)\)</span></strong> , где <span class="arithmatex">\(n\)</span> - число элементов, поэтому при больших объемах данных их производительность невысока.</p>
@@ -4399,11 +4399,11 @@
 <li>"Хеш-поиск" использует хеш-таблицу для построения отображения между поисковыми данными и целевыми данными, благодаря чему запросы выполняются эффективно.</li>
 <li>"Поиск в дереве" ведется в конкретной древовидной структуре (например, в двоичном дереве поиска) и позволяет быстро отсекать узлы на основе сравнения значений, чтобы найти цель.</li>
 </ul>
-<p>Преимущество этих алгоритмов в высокой эффективности, <strong>их временная сложность может достигать <span class="arithmatex">\(O(\log n)\)</span> и даже <span class="arithmatex">\(O(1)\)</span></strong> .</p>
+<p>Преимущество этих алгоритмов заключается в высокой эффективности: <strong>их временная сложность может достигать <span class="arithmatex">\(O(\log n)\)</span> и даже <span class="arithmatex">\(O(1)\)</span></strong> .</p>
 <p>Однако <strong>для использования таких алгоритмов обычно требуется предварительная обработка данных</strong>. Например, для двоичного поиска нужно заранее отсортировать массив, а хеш-поиск и поиск в дереве требуют дополнительных структур данных, поддержание которых тоже отнимает время и память.</p>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
-<p>Адаптивные алгоритмы поиска часто называют алгоритмами поиска в узком смысле, <strong>поскольку они в основном предназначены для быстрого поиска целевого элемента в конкретной структуре данных</strong>.</p>
+<p>Адаптивные алгоритмы поиска часто называют алгоритмами поиска в узком смысле, <strong>поскольку они в основном предназначены для быстрого нахождения целевого элемента в конкретной структуре данных</strong>.</p>
 </div>
 <h2 id="1053">10.5.3 &nbsp; Выбор метода поиска<a class="headerlink" href="#1053" title="Permanent link">&para;</a></h2>
 <p>Для поиска целевого элемента в наборе данных размера <span class="arithmatex">\(n\)</span> можно использовать линейный поиск, двоичный поиск, поиск в дереве, хеш-поиск и другие методы. Принципы работы этих методов показаны на рисунке 10-11.</p>
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-    aria-label="Назад: 10.4 Стратегия оптимизации через хеширование"
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 <h3 id="1">1. &nbsp; Ключевые выводы<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
 <li>Двоичный поиск опирается на упорядоченность данных и выполняет поиск путем циклического сокращения интервала вдвое. Он требует упорядоченных входных данных и подходит только для массивов или структур данных, реализованных на их основе.</li>
-<li>Полный перебор находит данные путем обхода структуры данных. Линейный поиск подходит для массивов и списков, а поиск в ширину и поиск в глубину подходят для графов и деревьев. Эти алгоритмы универсальны и не требуют предварительной обработки данных, но их временная сложность <span class="arithmatex">\(O(n)\)</span> сравнительно велика.</li>
+<li>Полный перебор находит данные путем обхода структуры данных. Линейный поиск подходит для массивов и списков, а обход в ширину и обход в глубину подходят для графов и деревьев. Эти алгоритмы универсальны и не требуют предварительной обработки данных, но их временная сложность <span class="arithmatex">\(O(n)\)</span> сравнительно велика.</li>
 <li>Хеш-поиск, поиск в дереве и двоичный поиск относятся к эффективным методам поиска и позволяют быстро находить целевой элемент в конкретных структурах данных. Такие алгоритмы обладают высокой эффективностью, их временная сложность может достигать <span class="arithmatex">\(O(\log n)\)</span> и даже <span class="arithmatex">\(O(1)\)</span> , но обычно им нужны дополнительные структуры данных.</li>
 <li>На практике нужно анализировать размер данных, требования к производительности поиска, а также частоту запросов и обновлений данных, чтобы выбрать подходящий метод поиска.</li>
 <li>Линейный поиск подходит для небольших или часто обновляемых наборов данных; двоичный поиск - для больших отсортированных данных; хеш-поиск - для сценариев с высокими требованиями к скорости запросов и без необходимости поиска по диапазону; поиск в дереве - для больших динамических данных, где нужно поддерживать порядок и выполнять диапазонные запросы.</li>
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 <!-- Page content -->
 <h1 id="113">11.3 &nbsp; Сортировка пузырьком<a class="headerlink" href="#113" title="Permanent link">&para;</a></h1>
-<p><u>Сортировка пузырьком (bubble sort)</u> сортирует массив за счет непрерывного сравнения и обмена соседних элементов. Этот процесс напоминает всплытие пузырьков снизу вверх, откуда и произошло название алгоритма.</p>
+<p><u>Сортировка пузырьком (bubble sort)</u> реализует сортировку путем последовательного сравнения и обмена соседних элементов. Этот процесс напоминает всплытие пузырьков снизу вверх, откуда и произошло название алгоритма.</p>
 <p>Как показано на рисунке 11-4, процесс "всплытия" можно смоделировать через операцию обмена элементов: начиная от левого края массива и двигаясь вправо, мы последовательно сравниваем соседние элементы и, если "левый элемент &gt; правый элемент", меняем их местами. После завершения прохода максимальный элемент будет перемещен в самый правый конец массива.</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:7"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label><label for="__tabbed_1_5">&lt;5&gt;</label><label for="__tabbed_1_6">&lt;6&gt;</label><label for="__tabbed_1_7">&lt;7&gt;</label></div>
 <div class="tabbed-content">
@@ -4646,7 +4646,7 @@
 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20bubble_sort%28nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%22%22%22%D0%9F%D1%83%D0%B7%D1%8B%D1%80%D1%8C%D0%BA%D0%BE%D0%B2%D0%B0%D1%8F%20%D1%81%D0%BE%D1%80%D1%82%D0%B8%D1%80%D0%BE%D0%B2%D0%BA%D0%B0%22%22%22%0A%20%20%20%20n%20%3D%20len%28nums%29%0A%20%20%20%20%23%20%D0%92%D0%BD%D0%B5%D1%88%D0%BD%D0%B8%D0%B9%20%D1%86%D0%B8%D0%BA%D0%BB%3A%20%D0%BD%D0%B5%D0%BE%D1%82%D1%81%D0%BE%D1%80%D1%82%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%BD%D1%8B%D0%B9%20%D0%B4%D0%B8%D0%B0%D0%BF%D0%B0%D0%B7%D0%BE%D0%BD%20%5B0%2C%20i%5D%0A%20%20%20%20for%20i%20in%20range%28n%20-%201%2C%200%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20%23%20%D0%92%D0%BD%D1%83%D1%82%D1%80%D0%B5%D0%BD%D0%BD%D0%B8%D0%B9%20%D1%86%D0%B8%D0%BA%D0%BB%3A%20%D0%BF%D0%B5%D1%80%D0%B5%D0%BC%D0%B5%D1%81%D1%82%D0%B8%D1%82%D1%8C%20%D0%BC%D0%B0%D0%BA%D1%81%D0%B8%D0%BC%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B%D0%B9%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%BD%D0%B5%D0%BE%D1%82%D1%81%D0%BE%D1%80%D1%82%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%BD%D0%BE%D0%B3%D0%BE%20%D0%B4%D0%B8%D0%B0%D0%BF%D0%B0%D0%B7%D0%BE%D0%BD%D0%B0%20%5B0%2C%20i%5D%20%D0%B2%20%D0%B5%D0%B3%D0%BE%20%D0%BF%D1%80%D0%B0%D0%B2%D1%8B%D0%B9%20%D0%BA%D0%BE%D0%BD%D0%B5%D1%86%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28i%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20nums%5Bj%5D%20%3E%20nums%5Bj%20%2B%201%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%D0%9F%D0%BE%D0%BC%D0%B5%D0%BD%D1%8F%D1%82%D1%8C%20%D0%BC%D0%B5%D1%81%D1%82%D0%B0%D0%BC%D0%B8%20nums%5Bj%5D%20%D0%B8%20nums%5Bj%20%2B%201%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20nums%5Bj%5D%2C%20nums%5Bj%20%2B%201%5D%20%3D%20nums%5Bj%20%2B%201%5D%2C%20nums%5Bj%5D%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20nums%20%3D%20%5B4%2C%201%2C%203%2C%201%2C%205%2C%202%5D%0A%20%20%20%20bubble_sort%28nums%29%0A%20%20%20%20print%28%22%D0%9F%D0%BE%D1%81%D0%BB%D0%B5%20%D0%BF%D1%83%D0%B7%D1%8B%D1%80%D1%8C%D0%BA%D0%BE%D0%B2%D0%BE%D0%B9%20%D1%81%D0%BE%D1%80%D1%82%D0%B8%D1%80%D0%BE%D0%B2%D0%BA%D0%B8%20nums%20%3D%22%2C%20nums%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
 <h2 id="1132">11.3.2 &nbsp; Оптимизация эффективности<a class="headerlink" href="#1132" title="Permanent link">&para;</a></h2>
-<p>Мы замечаем, что если в каком-либо раунде "всплытия" не произошло ни одного обмена, значит, массив уже отсортирован и можно сразу вернуть результат. Поэтому можно добавить флаг <code>flag</code> для отслеживания этой ситуации и немедленного выхода.</p>
+<p>Если в каком-либо раунде "всплытия" не произошло ни одного обмена, значит, массив уже отсортирован и можно сразу вернуть результат. Поэтому можно добавить флаг <code>flag</code> для отслеживания этой ситуации и немедленного выхода.</p>
 <p>После такой оптимизации худшая и средняя временные сложности сортировки пузырьком по-прежнему равны <span class="arithmatex">\(O(n^2)\)</span> ; однако если входной массив уже полностью упорядочен, достигается лучшая временная сложность <span class="arithmatex">\(O(n)\)</span> .</p>
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 <!-- Page content -->
 <h1 id="118">11.8 &nbsp; Блочная сортировка<a class="headerlink" href="#118" title="Permanent link">&para;</a></h1>
 <p>Рассмотренные выше алгоритмы сортировки относятся к "сортировкам на основе сравнений": они упорядочивают данные, сравнивая элементы друг с другом. Временная сложность таких алгоритмов не может быть лучше <span class="arithmatex">\(O(n \log n)\)</span> . Далее мы рассмотрим несколько "сортировок без сравнений", чья временная сложность может достигать линейного порядка.</p>
-<p><u>Блочная сортировка (bucket sort)</u> является типичным применением стратегии "разделяй и властвуй". Она задает несколько упорядоченных по диапазонам блоков, каждый блок соответствует некоторому диапазону значений; затем данные равномерно распределяются по блокам, внутри каждого блока выполняется сортировка, а в конце результаты блоков объединяются по порядку.</p>
+<p><u>Блочная сортировка (bucket sort)</u> является типичным применением стратегии "разделяй и властвуй". Она создает набор упорядоченных по величине блоков, где каждый блок соответствует определенному диапазону данных; затем элементы равномерно распределяются по этим блокам, внутри каждого блока отдельно выполняется сортировка, а в конце результаты объединяются в порядке блоков.</p>
 <h2 id="1181">11.8.1 &nbsp; Алгоритм<a class="headerlink" href="#1181" title="Permanent link">&para;</a></h2>
 <p>Рассмотрим массив длины <span class="arithmatex">\(n\)</span>, элементы которого являются числами с плавающей запятой из диапазона <span class="arithmatex">\([0, 1)\)</span> . Процесс блочной сортировки показан на рисунке 11-13.</p>
 <ol>
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 <li>Является ли блочная сортировка стабильной, зависит от того, стабилен ли алгоритм сортировки внутри каждого блока.</li>
 </ul>
 <h2 id="1183">11.8.3 &nbsp; Как добиться равномерного распределения<a class="headerlink" href="#1183" title="Permanent link">&para;</a></h2>
-<p>Теоретически временная сложность блочной сортировки может достигать <span class="arithmatex">\(O(n)\)</span> ; <strong>ключ к этому - как можно более равномерно распределить элементы по блокам</strong>. На практике данные часто распределены неравномерно. Например, если нужно распределить все товары на Taobao по 10 блокам цен, количество товаров дешевле 100 юаней может быть очень большим, а товаров дороже 1000 юаней - очень маленьким. Если просто разбить диапазон цен на 10 равных частей, число товаров в каждом блоке будет сильно различаться.</p>
+<p>Теоретически временная сложность блочной сортировки может достигать <span class="arithmatex">\(O(n)\)</span> ; <strong>ключ к этому - как можно более равномерно распределить элементы по блокам</strong>. На практике данные часто распределены неравномерно. Например, если нужно распределить все товары на маркетплейсе по 10 ценовым блокам, количество товаров дешевле 100 рублей может быть очень большим, а товаров дороже 1000 рублей - очень маленьким. Если просто разбить диапазон цен на 10 равных частей, число товаров в каждом блоке будет сильно различаться.</p>
 <p>Чтобы добиться более равномерного распределения, можно сначала задать грубую линию раздела и приблизительно распределить данные по 3 блокам. <strong>После этого блоки с большим числом товаров можно снова делить на 3 блока и продолжать процесс до тех пор, пока число элементов в каждом блоке не станет примерно одинаковым</strong>.</p>
 <p>Как показано на рисунке 11-14, по сути этот метод строит рекурсивное дерево, цель которого - сделать значения в листьях как можно более равномерными. Конечно, совсем не обязательно каждый раз делить данные именно на 3 блока; конкретную схему разбиения можно выбирать в зависимости от свойств данных.</p>
 <p><img alt="Рекурсивное разбиение по блокам" class="animation-figure" src="../bucket_sort.assets/scatter_in_buckets_recursively.png" /></p>
 <p align="center"> Рисунок 11-14 &nbsp; Рекурсивное разбиение по блокам </p>
 
-<p>Если нам заранее известна вероятностная модель распределения цен товаров, <strong>то границы каждого блока можно задавать в соответствии с этим распределением</strong>. Важно отметить, что фактическое распределение данных не обязательно специально измерять - его можно приблизить некоторой вероятностной моделью исходя из свойств данных.</p>
+<p>Если нам заранее известна вероятностная модель распределения цен товаров, <strong>то границы цен для каждого блока можно задавать в соответствии с этим распределением</strong>. Важно отметить, что фактическое распределение данных не обязательно специально измерять - его можно приблизить некоторой вероятностной моделью исходя из свойств данных.</p>
 <p>Как показано на рисунке 11-15, если предположить, что цены товаров подчиняются нормальному распределению, то можно разумно задать интервалы цен и тем самым распределить товары по блокам достаточно равномерно.</p>
 <p><img alt="Разбиение блоков по вероятностному распределению" class="animation-figure" src="../bucket_sort.assets/scatter_in_buckets_distribution.png" /></p>
 <p align="center"> Рисунок 11-15 &nbsp; Разбиение блоков по вероятностному распределению </p>
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+    11.3 Сортировка пузырьком
   
 
     
@@ -2810,7 +2810,7 @@
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-    11.4 Сортировка вставкой
+    11.4 Сортировка вставками
   
 
     
@@ -3207,7 +3207,7 @@
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-    12.1 Алгоритмы разделяй и властвуй
+    12.1 Стратегия разделяй и властвуй
   
 
     
@@ -3235,7 +3235,7 @@
   <span class="md-ellipsis">
     
   
-    12.2 Стратегия поиска разделяй и властвуй
+    12.2 Поисковая стратегия разделяй и властвуй
   
 
     
@@ -3512,7 +3512,7 @@
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-    13.4 Задача о $n$ ферзях
+    13.4 Задача о n ферзях
   
 
     
@@ -3653,7 +3653,7 @@
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-    14.1 Введение в динамическое программирование
+    14.1 Первое знакомство с динамическим программированием
   
 
     
@@ -3765,7 +3765,7 @@
   <span class="md-ellipsis">
     
   
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+    14.5 Задача о полном рюкзаке
   
 
     
@@ -4399,7 +4399,7 @@
 
 <!-- Page content -->
 <h1 id="119">11.9 &nbsp; Сортировка подсчетом<a class="headerlink" href="#119" title="Permanent link">&para;</a></h1>
-<p><u>Сортировка подсчетом (counting sort)</u> реализует сортировку за счет подсчета количества элементов и обычно используется для массивов целых чисел.</p>
+<p><u>Сортировка подсчетом (counting sort)</u> реализует сортировку за счет подсчета количества вхождений элементов и обычно используется для массивов целых чисел.</p>
 <h2 id="1191">11.9.1 &nbsp; Простая реализация<a class="headerlink" href="#1191" title="Permanent link">&para;</a></h2>
 <p>Сначала рассмотрим простой пример. Дан массив <code>nums</code> длины <span class="arithmatex">\(n\)</span> , элементы которого являются "неотрицательными целыми числами". Общий процесс сортировки подсчетом показан на рисунке 11-16.</p>
 <ol>
@@ -4737,7 +4737,7 @@
 </details>
 <div class="admonition note">
 <p class="admonition-title">Связь между сортировкой подсчетом и блочной сортировкой</p>
-<p>Если посмотреть на сортировку подсчетом с точки зрения блочной сортировки, то каждый индекс массива <code>counter</code> можно рассматривать как отдельный блок, а процесс подсчета - как распределение элементов по соответствующим блокам. По сути, сортировка подсчетом является частным случаем блочной сортировки для целочисленных данных.</p>
+<p>Если посмотреть на сортировку подсчетом с точки зрения блочной сортировки, то каждый индекс массива <code>counter</code> можно рассматривать как отдельный блок, а процесс подсчета - как распределение элементов по соответствующим блокам. Иными словами, сортировка подсчетом является частным случаем блочной сортировки для целочисленных данных.</p>
 </div>
 <h2 id="1192">11.9.2 &nbsp; Полная реализация<a class="headerlink" href="#1192" title="Permanent link">&para;</a></h2>
 <p>Внимательный читатель мог заметить, что <strong>если входные данные представлены объектами, то описанный выше шаг <code>3.</code> перестает работать</strong>. Например, если входными данными являются объекты товаров и мы хотим отсортировать их по цене (полю класса), то описанный алгоритм сможет выдать только отсортированный ряд цен, но не исходные объекты в нужном порядке.</p>
diff --git a/ru/chapter_sorting/heap_sort/index.html b/ru/chapter_sorting/heap_sort/index.html
index fc684e4d1..97828285c 100644
--- a/ru/chapter_sorting/heap_sort/index.html
+++ b/ru/chapter_sorting/heap_sort/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
@@ -574,7 +574,7 @@
   <span class="md-ellipsis">
     
   
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+    Глава 1. Введение в алгоритмы
   
 
     
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             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
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-    1.2 Что такое структуры данных и алгоритмы
+    1.2 Что такое алгоритм
   
 
     
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-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
     
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             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
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-    4.4 Память и кеш *
+    4.4 Оперативная память и кэш *
   
 
     
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   <span class="md-ellipsis">
     
   
-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
     
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-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
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+    6.3 Алгоритмы хеширования
   
 
     
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+    7.3 Представление двоичного дерева массивом
   
 
     
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+    7.6 Краткие итоги
   
 
     
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+    8.3 Задача Top-k
   
 
     
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+    9.2 Базовые операции графа
   
 
     
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-    9.4 Резюме
+    9.4 Краткие итоги
   
 
     
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-    10.2 Точка вставки двоичного поиска
+    10.2 Двоичный поиск точки вставки
   
 
     
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+    10.3 Двоичный поиск границ
   
 
     
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-    10.4 Стратегия оптимизации через хеширование
+    10.4 Стратегии оптимизации хеширования
   
 
     
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-    10.5 Алгоритмы поиска: новый взгляд
+    10.5 Переосмысление алгоритмов поиска
   
 
     
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-    11.3 Пузырьковая сортировка
+    11.3 Сортировка пузырьком
   
 
     
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+    11.4 Сортировка вставками
   
 
     
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+    12.1 Стратегия разделяй и властвуй
   
 
     
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+    12.2 Поисковая стратегия разделяй и властвуй
   
 
     
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   <span class="md-ellipsis">
     
   
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+    13.4 Задача о n ферзях
   
 
     
@@ -3631,7 +3631,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 Введение в динамическое программирование
+    14.1 Первое знакомство с динамическим программированием
   
 
     
@@ -3743,7 +3743,7 @@
   <span class="md-ellipsis">
     
   
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+    14.5 Задача о полном рюкзаке
   
 
     
@@ -4364,13 +4364,13 @@
 <li>Подать на вход массив и построить из него мин-кучу; в этот момент минимальный элемент будет находиться в вершине кучи.</li>
 <li>Непрерывно выполнять извлечение из кучи и по порядку записывать извлеченные элементы - так получится последовательность, отсортированная по возрастанию.</li>
 </ol>
-<p>Хотя этот метод работоспособен, он требует дополнительного массива для хранения извлеченных элементов и потому расходует лишнюю память. На практике обычно используют более изящную реализацию.</p>
+<p>Хотя этот метод и работоспособен, он требует дополнительного массива для хранения извлеченных элементов и потому расходует лишнюю память. На практике обычно используют более изящную реализацию.</p>
 <h2 id="1171">11.7.1 &nbsp; Алгоритм<a class="headerlink" href="#1171" title="Permanent link">&para;</a></h2>
 <p>Пусть длина массива равна <span class="arithmatex">\(n\)</span> ; тогда процесс пирамидальной сортировки показан на рисунке 11-12.</p>
 <ol>
 <li>Подать на вход массив и построить из него макс-кучу. После этого максимальный элемент окажется в вершине кучи.</li>
 <li>Обменять элемент в вершине кучи (первый элемент) с элементом внизу кучи (последний элемент). После обмена длина кучи уменьшается на <span class="arithmatex">\(1\)</span> , а число уже отсортированных элементов увеличивается на <span class="arithmatex">\(1\)</span> .</li>
-<li>Начиная с вершины, выполнить просеивание вниз (sift down) сверху вниз. После этого свойство кучи будет восстановлено.</li>
+<li>Начиная с вершины, выполнить операцию просеивания сверху вниз. После этого свойство кучи будет восстановлено.</li>
 <li>Циклически повторять шаг <code>2.</code> и шаг <code>3.</code> . После <span class="arithmatex">\(n - 1\)</span> раундов массив будет полностью отсортирован.</li>
 </ol>
 <div class="admonition tip">
@@ -4419,7 +4419,7 @@
 </div>
 <p align="center"> Рисунок 11-12 &nbsp; Шаги пирамидальной сортировки </p>
 
-<p>В реализации кода используется та же функция просеивания сверху вниз <code>sift_down()</code>, что и в главе "Куча". Важно помнить, что длина кучи уменьшается по мере извлечения максимального элемента, поэтому функции <code>sift_down()</code> нужно передавать параметр длины <span class="arithmatex">\(n\)</span> , чтобы указать текущую эффективную длину кучи. Код приведен ниже:</p>
+<p>В коде используется та же функция просеивания сверху вниз <code>sift_down()</code>, что и в главе "Куча". Важно помнить, что длина кучи уменьшается по мере извлечения максимального элемента, поэтому функции <code>sift_down()</code> нужно передавать параметр длины <span class="arithmatex">\(n\)</span> , чтобы указать текущую действительную длину кучи. Код приведен ниже:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
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diff --git a/ru/chapter_sorting/index.html b/ru/chapter_sorting/index.html
index 191bb78f2..bd066a366 100644
--- a/ru/chapter_sorting/index.html
+++ b/ru/chapter_sorting/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
@@ -574,7 +574,7 @@
   <span class="md-ellipsis">
     
   
-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
     
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             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
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@@ -646,7 +646,7 @@
   <span class="md-ellipsis">
     
   
-    1.2 Что такое структуры данных и алгоритмы
+    1.2 Что такое алгоритм
   
 
     
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   <span class="md-ellipsis">
     
   
-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
     
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             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
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   <span class="md-ellipsis">
     
   
-    4.4 Память и кеш *
+    4.4 Оперативная память и кэш *
   
 
     
@@ -1591,7 +1591,7 @@
   <span class="md-ellipsis">
     
   
-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
     
@@ -1613,7 +1613,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
           </label>
@@ -1691,7 +1691,7 @@
   <span class="md-ellipsis">
     
   
-    6.3 Хеш-алгоритмы
+    6.3 Алгоритмы хеширования
   
 
     
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-    Глава 7. Дерево
+    Глава 7. Деревья
   
 
     
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-    Глава 7. Дерево
+    Глава 7. Деревья
   
 
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   <span class="md-ellipsis">
     
   
-    7.3 Представление дерева массивом
+    7.3 Представление двоичного дерева массивом
   
 
     
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   <span class="md-ellipsis">
     
   
-    7.6 Резюме
+    7.6 Краткие итоги
   
 
     
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-    8.3 Задача Top-K
+    8.3 Задача Top-k
   
 
     
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   <span class="md-ellipsis">
     
   
-    Глава 9. Граф
+    Глава 9. Графы
   
 
     
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+    Глава 9. Графы
   
 
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+    9.2 Базовые операции графа
   
 
     
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-    9.4 Резюме
+    9.4 Краткие итоги
   
 
     
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-    10.2 Точка вставки двоичного поиска
+    10.2 Двоичный поиск точки вставки
   
 
     
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+    10.3 Двоичный поиск границ
   
 
     
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+    10.4 Стратегии оптимизации хеширования
   
 
     
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-    10.5 Алгоритмы поиска: новый взгляд
+    10.5 Переосмысление алгоритмов поиска
   
 
     
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-    11.3 Пузырьковая сортировка
+    11.3 Сортировка пузырьком
   
 
     
@@ -2810,7 +2810,7 @@
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+    11.4 Сортировка вставками
   
 
     
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-    12.1 Алгоритмы разделяй и властвуй
+    12.1 Стратегия разделяй и властвуй
   
 
     
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   <span class="md-ellipsis">
     
   
-    12.2 Стратегия поиска разделяй и властвуй
+    12.2 Поисковая стратегия разделяй и властвуй
   
 
     
@@ -3420,7 +3420,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 Задача о $n$ ферзях
+    13.4 Задача о n ферзях
   
 
     
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   <span class="md-ellipsis">
     
   
-    14.1 Введение в динамическое программирование
+    14.1 Первое знакомство с динамическим программированием
   
 
     
@@ -3673,7 +3673,7 @@
   <span class="md-ellipsis">
     
   
-    14.5 Задача о неограниченном рюкзаке
+    14.5 Задача о полном рюкзаке
   
 
     
@@ -4284,8 +4284,8 @@
 <ul>
 <li><a href="sorting_algorithm/">11.1 &nbsp; Алгоритмы сортировки</a></li>
 <li><a href="selection_sort/">11.2 &nbsp; Сортировка выбором</a></li>
-<li><a href="bubble_sort/">11.3 &nbsp; Пузырьковая сортировка</a></li>
-<li><a href="insertion_sort/">11.4 &nbsp; Сортировка вставкой</a></li>
+<li><a href="bubble_sort/">11.3 &nbsp; Сортировка пузырьком</a></li>
+<li><a href="insertion_sort/">11.4 &nbsp; Сортировка вставками</a></li>
 <li><a href="quick_sort/">11.5 &nbsp; Быстрая сортировка</a></li>
 <li><a href="merge_sort/">11.6 &nbsp; Сортировка слиянием</a></li>
 <li><a href="heap_sort/">11.7 &nbsp; Пирамидальная сортировка</a></li>
diff --git a/ru/chapter_sorting/insertion_sort/index.html b/ru/chapter_sorting/insertion_sort/index.html
index b5df4a2e0..710aff9cf 100644
--- a/ru/chapter_sorting/insertion_sort/index.html
+++ b/ru/chapter_sorting/insertion_sort/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
@@ -574,7 +574,7 @@
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+    Глава 1. Введение в алгоритмы
   
 
     
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             <span class="md-nav__icon md-icon"></span>
             
   
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+    Глава 1. Введение в алгоритмы
   
 
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-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
     
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             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
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-    4.4 Память и кеш *
+    4.4 Оперативная память и кэш *
   
 
     
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-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
     
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+    Глава 6. Хеш-таблицы
   
 
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@@ -1691,7 +1691,7 @@
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+    6.3 Алгоритмы хеширования
   
 
     
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   <span class="md-ellipsis">
     
   
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+    7.3 Представление двоичного дерева массивом
   
 
     
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+    7.6 Краткие итоги
   
 
     
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-    8.3 Задача Top-K
+    8.3 Задача Top-k
   
 
     
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-    Глава 9. Граф
+    Глава 9. Графы
   
 
     
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-    Глава 9. Граф
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+    9.2 Базовые операции графа
   
 
     
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-    9.4 Резюме
+    9.4 Краткие итоги
   
 
     
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-    10.2 Точка вставки двоичного поиска
+    10.2 Двоичный поиск точки вставки
   
 
     
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-    10.3 Граничные случаи двоичного поиска
+    10.3 Двоичный поиск границ
   
 
     
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+    10.4 Стратегии оптимизации хеширования
   
 
     
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-    10.5 Алгоритмы поиска: новый взгляд
+    10.5 Переосмысление алгоритмов поиска
   
 
     
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+    12.1 Стратегия разделяй и властвуй
   
 
     
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-    12.2 Стратегия поиска разделяй и властвуй
+    12.2 Поисковая стратегия разделяй и властвуй
   
 
     
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+    13.4 Задача о n ферзях
   
 
     
@@ -3642,7 +3642,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 Введение в динамическое программирование
+    14.1 Первое знакомство с динамическим программированием
   
 
     
@@ -3754,7 +3754,7 @@
   <span class="md-ellipsis">
     
   
-    14.5 Задача о неограниченном рюкзаке
+    14.5 Задача о полном рюкзаке
   
 
     
@@ -4377,9 +4377,9 @@
 
 <!-- Page content -->
 <h1 id="114">11.4 &nbsp; Сортировка вставками<a class="headerlink" href="#114" title="Permanent link">&para;</a></h1>
-<p><u>Сортировка вставками (insertion sort)</u> - это простой алгоритм сортировки, принцип которого очень похож на ручное упорядочивание колоды карт.</p>
-<p>Точнее говоря, в неотсортированном диапазоне выбирается опорный элемент, после чего он поочередно сравнивается с элементами слева в уже отсортированном диапазоне и вставляется в правильную позицию.</p>
-<p>На рисунке 11-6 показан процесс вставки элемента в массив. Пусть опорный элемент обозначен как <code>base</code> ; нам нужно сдвинуть все элементы от целевого индекса до <code>base</code> на одну позицию вправо, а затем присвоить <code>base</code> значение в целевом индексе.</p>
+<p><u>Сортировка вставками (insertion sort)</u> - это простой алгоритм сортировки, принцип которого очень похож на ручную сортировку карт в колоде.</p>
+<p>Точнее говоря, в неотсортированном диапазоне выбирается опорный элемент, после чего он сравнивается с элементами слева в уже отсортированном диапазоне и вставляется в правильную позицию.</p>
+<p>На рисунке 11-6 показан процесс вставки элемента в массив. Пусть опорный элемент обозначен как <code>base</code> ; нам нужно сдвинуть все элементы от целевого индекса до <code>base</code> на одну позицию вправо, а затем записать <code>base</code> в целевой индекс.</p>
 <p><img alt="Одна операция вставки" class="animation-figure" src="../insertion_sort.assets/insertion_operation.png" /></p>
 <p align="center"> Рисунок 11-6 &nbsp; Одна операция вставки </p>
 
@@ -4387,8 +4387,8 @@
 <p>Общий процесс сортировки вставками показан на рисунке 11-7.</p>
 <ol>
 <li>В начальном состоянии отсортирован только первый элемент массива.</li>
-<li>Выбрать второй элемент массива как <code>base</code> ; после вставки в правильную позицию <strong>первые 2 элемента массива окажутся отсортированными</strong>.</li>
-<li>Выбрать третий элемент как <code>base</code> ; после вставки в правильную позицию <strong>первые 3 элемента массива окажутся отсортированными</strong>.</li>
+<li>Выбрать второй элемент массива как <code>base</code> ; после вставки в правильную позицию <strong>первые два элемента массива окажутся отсортированными</strong>.</li>
+<li>Выбрать третий элемент как <code>base</code> ; после вставки в правильную позицию <strong>первые три элемента массива окажутся отсортированными</strong>.</li>
 <li>Продолжать по аналогии; в последнем раунде в качестве <code>base</code> берется последний элемент, и после его вставки <strong>все элементы массива будут отсортированы</strong>.</li>
 </ol>
 <p><img alt="Процесс сортировки вставками" class="animation-figure" src="../insertion_sort.assets/insertion_sort_overview.png" /></p>
@@ -4657,7 +4657,7 @@ aria-label="Нижний колонтитул"
   <a
     href="../bubble_sort/"
     class="md-footer__link md-footer__link--prev"
-    aria-label="Назад: 11.3 Пузырьковая сортировка"
+    aria-label="Назад: 11.3 Сортировка пузырьком"
     rel="prev"
   >
     <div class="md-footer__button md-icon">
@@ -4669,7 +4669,7 @@ aria-label="Нижний колонтитул"
         Назад
       </span>
       <div class="md-ellipsis">
-        11.3 Пузырьковая сортировка
+        11.3 Сортировка пузырьком
       </div>
     </div>
   </a>
diff --git a/ru/chapter_sorting/merge_sort/index.html b/ru/chapter_sorting/merge_sort/index.html
index 5aa9f8b61..9c33a6ee1 100644
--- a/ru/chapter_sorting/merge_sort/index.html
+++ b/ru/chapter_sorting/merge_sort/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
@@ -574,7 +574,7 @@
   <span class="md-ellipsis">
     
   
-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
     
@@ -596,7 +596,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
           </label>
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+    1.2 Что такое алгоритм
   
 
     
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-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
     
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-    Глава 4. Массив и связный список
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-    4.4 Память и кеш *
+    4.4 Оперативная память и кэш *
   
 
     
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-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
     
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             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
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+    6.3 Алгоритмы хеширования
   
 
     
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+    7.3 Представление двоичного дерева массивом
   
 
     
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+    7.6 Краткие итоги
   
 
     
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-    8.3 Задача Top-K
+    8.3 Задача Top-k
   
 
     
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-    Глава 9. Граф
+    Глава 9. Графы
   
 
     
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           </label>
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+    9.2 Базовые операции графа
   
 
     
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-    9.4 Резюме
+    9.4 Краткие итоги
   
 
     
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-    10.2 Точка вставки двоичного поиска
+    10.2 Двоичный поиск точки вставки
   
 
     
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+    10.3 Двоичный поиск границ
   
 
     
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+    10.4 Стратегии оптимизации хеширования
   
 
     
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   <span class="md-ellipsis">
     
   
-    10.5 Алгоритмы поиска: новый взгляд
+    10.5 Переосмысление алгоритмов поиска
   
 
     
@@ -2782,7 +2782,7 @@
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+    11.3 Сортировка пузырьком
   
 
     
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+    11.4 Сортировка вставками
   
 
     
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+    12.1 Стратегия разделяй и властвуй
   
 
     
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+    12.2 Поисковая стратегия разделяй и властвуй
   
 
     
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+    14.1 Первое знакомство с динамическим программированием
   
 
     
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+    14.5 Задача о полном рюкзаке
   
 
     
@@ -4377,10 +4377,10 @@
 
 <!-- Page content -->
 <h1 id="116">11.6 &nbsp; Сортировка слиянием<a class="headerlink" href="#116" title="Permanent link">&para;</a></h1>
-<p><u>Сортировка слиянием (merge sort)</u> - это алгоритм сортировки на основе стратегии "разделяй и властвуй", который включает этапы "разделения" и "слияния", показанные на рисунке 11-10.</p>
+<p><u>Сортировка слиянием (merge sort)</u> - это алгоритм сортировки, основанный на стратегии "разделяй и властвуй", который включает этапы "разделения" и "слияния", показанные на рисунке 11-10.</p>
 <ol>
-<li><strong>Этап разделения</strong>: массив рекурсивно разбивается от середины, и задача сортировки длинного массива превращается в задачи сортировки более коротких массивов.</li>
-<li><strong>Этап слияния</strong>: когда длина подмассива становится равной 1, разделение завершается и начинается слияние; левые и правые короткие упорядоченные массивы непрерывно объединяются в более длинный упорядоченный массив, пока процесс не завершится.</li>
+<li><strong>Этап разделения</strong>: массив рекурсивно делится пополам, и задача сортировки длинного массива превращается в задачи сортировки более коротких массивов.</li>
+<li><strong>Этап слияния</strong>: когда длина подмассива становится равной 1, разделение завершается и начинается слияние; два коротких упорядоченных массива непрерывно объединяются в один более длинный упорядоченный массив, пока процесс не завершится.</li>
 </ol>
 <p><img alt="Этапы разделения и слияния в сортировке слиянием" class="animation-figure" src="../merge_sort.assets/merge_sort_overview.png" /></p>
 <p align="center"> Рисунок 11-10 &nbsp; Этапы разделения и слияния в сортировке слиянием </p>
@@ -4428,10 +4428,10 @@
 </div>
 <p align="center"> Рисунок 11-11 &nbsp; Шаги сортировки слиянием </p>
 
-<p>Нетрудно заметить, что порядок рекурсии в сортировке слиянием совпадает с порядком рекурсии при постфиксном обходе бинарного дерева.</p>
+<p>Нетрудно заметить, что порядок рекурсии в сортировке слиянием совпадает с порядком обхода в глубину двоичного дерева.</p>
 <ul>
-<li><strong>Постфиксный обход</strong>: сначала рекурсивно обходится левое поддерево, затем правое поддерево, а в конце обрабатывается корневой узел.</li>
-<li><strong>Сортировка слиянием</strong>: сначала рекурсивно обрабатывается левый подмассив, затем правый подмассив, а в конце выполняется слияние.</li>
+<li><strong>Обход в глубину</strong>: сначала рекурсивно обходится левое поддерево, затем правое поддерево, а в конце обрабатывается корневой узел.</li>
+<li><strong>Сортировка слиянием</strong>: сначала рекурсивно разделяется левый подмассив, затем правый подмассив, а в конце выполняется слияние.</li>
 </ul>
 <p>Реализация сортировки слиянием показана в коде ниже. Обратите внимание: в <code>nums</code> объединяемый интервал равен <code>[left, right]</code> , а соответствующий интервал в <code>tmp</code> равен <code>[0, right - left]</code> .</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
@@ -5047,7 +5047,7 @@
 <li><strong>Этап разделения</strong>: работу по разбиению списка можно реализовать с помощью "итерации" вместо "рекурсии", тем самым устранив расход памяти на стек вызовов.</li>
 <li><strong>Этап слияния</strong>: в связном списке добавление и удаление узлов требует только изменения ссылок (указателей), поэтому при слиянии двух коротких упорядоченных списков в один длинный упорядоченный список не нужно создавать дополнительный список.</li>
 </ul>
-<p>Детали реализации достаточно сложны; заинтересованные читатели могут изучить соответствующие материалы самостоятельно.</p>
+<p>Детали реализации достаточно сложны; заинтересованные читатели могут обратиться к соответствующим материалам самостоятельно.</p>
 
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diff --git a/ru/chapter_sorting/quick_sort/index.html b/ru/chapter_sorting/quick_sort/index.html
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@@ -65,8 +65,8 @@
         
         
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-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
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+    Глава 1. Введение в алгоритмы
   
 
     
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+    Глава 1. Введение в алгоритмы
   
 
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-    1.2 Что такое структуры данных и алгоритмы
+    1.2 Что такое алгоритм
   
 
     
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+    4.4 Оперативная память и кэш *
   
 
     
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+    Глава 6. Хеш-таблицы
   
 
     
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+    Глава 6. Хеш-таблицы
   
 
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+    6.3 Алгоритмы хеширования
   
 
     
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+    7.3 Представление двоичного дерева массивом
   
 
     
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-    7.6 Резюме
+    7.6 Краткие итоги
   
 
     
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-    8.3 Задача Top-K
+    8.3 Задача Top-k
   
 
     
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+    Глава 9. Графы
   
 
     
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+    Глава 9. Графы
   
 
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-    9.2 Базовые операции над графами
+    9.2 Базовые операции графа
   
 
     
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-    9.4 Резюме
+    9.4 Краткие итоги
   
 
     
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-    10.2 Точка вставки двоичного поиска
+    10.2 Двоичный поиск точки вставки
   
 
     
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+    10.3 Двоичный поиск границ
   
 
     
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+    10.4 Стратегии оптимизации хеширования
   
 
     
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-    10.5 Алгоритмы поиска: новый взгляд
+    10.5 Переосмысление алгоритмов поиска
   
 
     
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+    11.3 Сортировка пузырьком
   
 
     
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+    11.4 Сортировка вставками
   
 
     
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-    12.1 Алгоритмы разделяй и властвуй
+    12.1 Стратегия разделяй и властвуй
   
 
     
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-    12.2 Стратегия поиска разделяй и властвуй
+    12.2 Поисковая стратегия разделяй и властвуй
   
 
     
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-    13.4 Задача о $n$ ферзях
+    13.4 Задача о n ферзях
   
 
     
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-    14.1 Введение в динамическое программирование
+    14.1 Первое знакомство с динамическим программированием
   
 
     
@@ -3776,7 +3776,7 @@
   <span class="md-ellipsis">
     
   
-    14.5 Задача о неограниченном рюкзаке
+    14.5 Задача о полном рюкзаке
   
 
     
@@ -4463,8 +4463,8 @@
 
 <p>После завершения разделения исходный массив разбивается на три части: левый подмассив, опорный элемент и правый подмассив; при этом выполняется условие "любой элемент левого подмассива <span class="arithmatex">\(\leq\)</span> опорный элемент <span class="arithmatex">\(\leq\)</span> любой элемент правого подмассива". Следовательно, далее нам нужно лишь отсортировать эти два подмассива.</p>
 <div class="admonition note">
-<p class="admonition-title">Стратегия divide and conquer в быстрой сортировке</p>
-<p>По сути, разделение с опорным элементом сводит задачу сортировки длинного массива к двум задачам сортировки более коротких массивов.</p>
+<p class="admonition-title">Стратегия разделяй и властвуй в быстрой сортировке</p>
+<p>Иными словами, разделение с опорным элементом сводит задачу сортировки длинного массива к двум задачам сортировки более коротких массивов.</p>
 </div>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
 <div class="tabbed-content">
@@ -4985,9 +4985,9 @@
 <li><strong>Небольшой константный множитель в сложности</strong>: среди трех перечисленных алгоритмов у быстрой сортировки обычно меньше всего сравнений, присваиваний и обменов. Это похоже на причину, по которой "сортировка вставками" часто быстрее "сортировки пузырьком".</li>
 </ul>
 <h2 id="1154">11.5.4 &nbsp; Оптимизация выбора опорного элемента<a class="headerlink" href="#1154" title="Permanent link">&para;</a></h2>
-<p><strong>На некоторых входных данных временная эффективность быстрой сортировки может ухудшаться</strong>. Рассмотрим крайний случай: входной массив полностью отсортирован в обратном порядке. Поскольку в качестве опорного мы выбираем самый левый элемент, после разделения он будет обменян в самый правый конец массива, из-за чего длина левого подмассива станет <span class="arithmatex">\(n - 1\)</span> , а длина правого - <span class="arithmatex">\(0\)</span> . Если рекурсия будет продолжаться таким образом, то после каждого разделения один из подмассивов будет иметь длину <span class="arithmatex">\(0\)</span> , стратегия divide and conquer потеряет смысл, а быстрая сортировка выродится в нечто близкое к "сортировке пузырьком".</p>
-<p>Чтобы по возможности избежать такого сценария, <strong>мы можем улучшить стратегию выбора опорного элемента в процедуре разделения</strong>. Например, можно выбирать случайный элемент массива как опорный. Однако если не повезет и каждый раз будет выбираться неудачный опорный элемент, производительность все равно останется неудовлетворительной.</p>
-<p>Нужно учитывать, что языки программирования обычно генерируют "псевдослучайные числа". Если специально построить тестовый пример под такую последовательность, эффективность быстрой сортировки все равно может деградировать.</p>
+<p><strong>На некоторых входных данных временная эффективность быстрой сортировки может ухудшаться</strong>. Рассмотрим крайний случай: входной массив полностью отсортирован в обратном порядке. Поскольку в качестве опорного мы выбираем самый левый элемент, после разделения он будет обменян в самый правый конец массива, из-за чего длина левого подмассива станет <span class="arithmatex">\(n - 1\)</span> , а длина правого - <span class="arithmatex">\(0\)</span> . Если рекурсия будет продолжаться таким образом, то после каждого разделения один из подмассивов будет иметь длину <span class="arithmatex">\(0\)</span> , стратегия "разделяй и властвуй" потеряет смысл, а быстрая сортировка выродится в нечто близкое к "сортировке пузырьком".</p>
+<p>Чтобы по возможности избежать такого сценария, <strong>можно улучшить стратегию выбора опорного элемента в процедуре разделения</strong>. Например, можно выбирать случайный элемент массива как опорный. Однако если не повезет и каждый раз будет выбираться неудачный опорный элемент, производительность все равно останется неудовлетворительной.</p>
+<p>Стоит учитывать, что языки программирования обычно генерируют псевдослучайные числа. Если специально построить тестовый пример под такую последовательность, эффективность быстрой сортировки все равно может деградировать.</p>
 <p>Чтобы улучшить ситуацию, можно взять три кандидата (обычно первый, последний и средний элементы массива) и <strong>использовать медиану этих трех значений как опорный элемент</strong>. Благодаря этому вероятность того, что опорный элемент окажется "не слишком маленьким и не слишком большим", заметно возрастает. Конечно, можно брать и большее число кандидатов, чтобы еще сильнее повысить устойчивость алгоритма. После этого вероятность деградации временной сложности до <span class="arithmatex">\(O(n^2)\)</span> существенно уменьшается.</p>
 <p>Пример кода:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="4:13"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label></div>
@@ -5748,7 +5748,7 @@ aria-label="Нижний колонтитул"
   <a
     href="../insertion_sort/"
     class="md-footer__link md-footer__link--prev"
-    aria-label="Назад: 11.4 Сортировка вставкой"
+    aria-label="Назад: 11.4 Сортировка вставками"
     rel="prev"
   >
     <div class="md-footer__button md-icon">
@@ -5760,7 +5760,7 @@ aria-label="Нижний колонтитул"
         Назад
       </span>
       <div class="md-ellipsis">
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+        11.4 Сортировка вставками
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diff --git a/ru/chapter_sorting/radix_sort/index.html b/ru/chapter_sorting/radix_sort/index.html
index 8a394e54c..650efc3e2 100644
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+++ b/ru/chapter_sorting/radix_sort/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
@@ -574,7 +574,7 @@
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+    Глава 1. Введение в алгоритмы
   
 
     
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+    Глава 1. Введение в алгоритмы
   
 
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+    Глава 4. Массивы и списки
   
 
     
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-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
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+    4.4 Оперативная память и кэш *
   
 
     
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+    Глава 6. Хеш-таблицы
   
 
     
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-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
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+    6.3 Алгоритмы хеширования
   
 
     
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+    Глава 7. Деревья
   
 
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+    7.3 Представление двоичного дерева массивом
   
 
     
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+    7.6 Краткие итоги
   
 
     
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+    10.5 Переосмысление алгоритмов поиска
   
 
     
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+    11.3 Сортировка пузырьком
   
 
     
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+    12.1 Стратегия разделяй и властвуй
   
 
     
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+    12.2 Поисковая стратегия разделяй и властвуй
   
 
     
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+    13.4 Задача о n ферзях
   
 
     
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+    14.1 Первое знакомство с динамическим программированием
   
 
     
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+    14.5 Задача о полном рюкзаке
   
 
     
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 <!-- Page content -->
 <h1 id="1110">11.10 &nbsp; Поразрядная сортировка<a class="headerlink" href="#1110" title="Permanent link">&para;</a></h1>
-<p>В предыдущем разделе мы познакомились с сортировкой подсчетом: она подходит для случаев, когда объем данных <span class="arithmatex">\(n\)</span> велик, а диапазон значений <span class="arithmatex">\(m\)</span> сравнительно мал. Предположим теперь, что нужно отсортировать <span class="arithmatex">\(n = 10^6\)</span> студенческих идентификаторов, причем каждый идентификатор является <span class="arithmatex">\(8\)</span>-значным числом. Тогда диапазон данных <span class="arithmatex">\(m = 10^8\)</span> оказывается очень большим; сортировка подсчетом потребует огромного объема памяти, а поразрядная сортировка позволяет этого избежать.</p>
-<p><u>Поразрядная сортировка (radix sort)</u> по своей основной идее совпадает с сортировкой подсчетом и тоже реализует сортировку через подсчет количества. Поверх этого поразрядная сортировка использует иерархию разрядов числа и последовательно сортирует данные по каждому разряду, получая итоговый упорядоченный результат.</p>
+<p>В предыдущем разделе была рассмотрена сортировка подсчетом: она хорошо подходит для случаев, когда объем данных <span class="arithmatex">\(n\)</span> велик, а диапазон значений <span class="arithmatex">\(m\)</span> сравнительно мал. Предположим теперь, что нужно отсортировать <span class="arithmatex">\(n = 10^6\)</span> номеров студентов, причем каждый номер представляет собой <span class="arithmatex">\(8\)</span>-значное число. Тогда диапазон данных <span class="arithmatex">\(m = 10^8\)</span> оказывается очень большим; сортировка подсчетом потребует огромного объема памяти, а поразрядная сортировка позволяет этого избежать.</p>
+<p><u>Поразрядная сортировка (radix sort)</u> по своей основной идее совпадает с сортировкой подсчетом и тоже реализует сортировку через подсчет количества. При этом поразрядная сортировка использует соотношение между разрядами числа и последовательно сортирует данные по каждому разряду, получая итоговый упорядоченный результат.</p>
 <h2 id="11101">11.10.1 &nbsp; Алгоритм<a class="headerlink" href="#11101" title="Permanent link">&para;</a></h2>
 <p>Рассмотрим пример со студенческими номерами: будем считать, что младший разряд имеет номер <span class="arithmatex">\(1\)</span> , а старший - номер <span class="arithmatex">\(8\)</span> . Тогда процесс поразрядной сортировки показан на рисунке 11-18.</p>
 <ol>
@@ -4371,7 +4371,7 @@
 <div class="arithmatex">\[
 x_k = \lfloor\frac{x}{d^{k-1}}\rfloor \bmod d
 \]</div>
-<p>где <span class="arithmatex">\(\lfloor a \rfloor\)</span> обозначает округление числа <span class="arithmatex">\(a\)</span> вниз, а <span class="arithmatex">\(\bmod \: d\)</span> означает взятие остатка по модулю <span class="arithmatex">\(d\)</span> . Для студенческих идентификаторов выполняется <span class="arithmatex">\(d = 10\)</span> и <span class="arithmatex">\(k \in [1, 8]\)</span> .</p>
+<p>где <span class="arithmatex">\(\lfloor a \rfloor\)</span> обозначает округление числа <span class="arithmatex">\(a\)</span> вниз, а <span class="arithmatex">\(\bmod \: d\)</span> означает взятие остатка по модулю <span class="arithmatex">\(d\)</span> . Для студенческих номеров выполняется <span class="arithmatex">\(d = 10\)</span> и <span class="arithmatex">\(k \in [1, 8]\)</span> .</p>
 <p>Кроме того, нам нужно слегка изменить код сортировки подсчетом, чтобы он мог сортировать числа по их <span class="arithmatex">\(k\)</span>-му разряду:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
diff --git a/ru/chapter_sorting/selection_sort/index.html b/ru/chapter_sorting/selection_sort/index.html
index 40860c738..475e6266e 100644
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+++ b/ru/chapter_sorting/selection_sort/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
@@ -574,7 +574,7 @@
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-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
     
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             <span class="md-nav__icon md-icon"></span>
             
   
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+    Глава 1. Введение в алгоритмы
   
 
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+    1.2 Что такое алгоритм
   
 
     
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-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
     
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+    Глава 4. Массивы и списки
   
 
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+    4.4 Оперативная память и кэш *
   
 
     
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+    Глава 6. Хеш-таблицы
   
 
     
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+    Глава 6. Хеш-таблицы
   
 
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+    6.3 Алгоритмы хеширования
   
 
     
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+    7.3 Представление двоичного дерева массивом
   
 
     
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+    7.6 Краткие итоги
   
 
     
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+    8.3 Задача Top-k
   
 
     
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+    Глава 9. Графы
   
 
     
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+    10.3 Двоичный поиск границ
   
 
     
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+    10.4 Стратегии оптимизации хеширования
   
 
     
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+    14.5 Задача о полном рюкзаке
   
 
     
@@ -4337,8 +4337,8 @@
 <p>Пусть длина массива равна <span class="arithmatex">\(n\)</span> ; тогда процесс сортировки выбором выглядит так, как показано на рисунке 11-2.</p>
 <ol>
 <li>В начальном состоянии все элементы не отсортированы, то есть неотсортированный диапазон индексов равен <span class="arithmatex">\([0, n-1]\)</span> .</li>
-<li>Выбрать минимальный элемент из диапазона <span class="arithmatex">\([0, n-1]\)</span> и поменять его местами с элементом в позиции <span class="arithmatex">\(0\)</span> . После этого первые 1 элементов массива отсортированы.</li>
-<li>Выбрать минимальный элемент из диапазона <span class="arithmatex">\([1, n-1]\)</span> и поменять его местами с элементом в позиции <span class="arithmatex">\(1\)</span> . После этого первые 2 элементов массива отсортированы.</li>
+<li>Выбрать минимальный элемент из диапазона <span class="arithmatex">\([0, n-1]\)</span> и поменять его местами с элементом в позиции <span class="arithmatex">\(0\)</span> . После этого первый элемент массива отсортирован.</li>
+<li>Выбрать минимальный элемент из диапазона <span class="arithmatex">\([1, n-1]\)</span> и поменять его местами с элементом в позиции <span class="arithmatex">\(1\)</span> . После этого первые два элемента массива отсортированы.</li>
 <li>Продолжать по аналогии. После <span class="arithmatex">\(n - 1\)</span> раундов выбора и обмена первые <span class="arithmatex">\(n - 1\)</span> элементов массива будут отсортированы.</li>
 <li>Оставшийся элемент обязательно является максимальным, сортировать его не нужно, поэтому массив считается отсортированным.</li>
 </ol>
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 <!-- Page content -->
 <h1 id="111">11.1 &nbsp; Алгоритмы сортировки<a class="headerlink" href="#111" title="Permanent link">&para;</a></h1>
-<p><u>Алгоритмы сортировки (sorting algorithm)</u> используются для упорядочивания набора данных по определенному правилу. Они применяются очень широко, потому что упорядоченные данные обычно проще и быстрее искать, анализировать и обрабатывать.</p>
+<p><u>Алгоритмы сортировки (sorting algorithm)</u> используются для упорядочивания набора данных по определенному правилу. Они применяются очень широко, потому что упорядоченные данные обычно проще анализировать, обрабатывать и искать в них нужные элементы.</p>
 <p>Как показано на рисунке 11-1, данными в алгоритмах сортировки могут быть целые числа, числа с плавающей запятой, символы, строки и другие типы. Критерий сравнения тоже можно задать по-разному, например по величине чисел, по порядку ASCII-кодов символов или по пользовательскому правилу.</p>
 <p><img alt="Примеры типов данных и правил сравнения" class="animation-figure" src="../sorting_algorithm.assets/sorting_examples.png" /></p>
 <p align="center"> Рисунок 11-1 &nbsp; Примеры типов данных и правил сравнения </p>
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 <li>Блочная сортировка включает три этапа: распределение данных по блокам, сортировку внутри блоков и объединение результатов. Она тоже отражает стратегию "разделяй и властвуй" и подходит для очень больших объемов данных. Ключ к эффективности блочной сортировки - равномерное распределение данных.</li>
 <li>Сортировка подсчетом является частным случаем блочной сортировки; она реализует сортировку через подсчет числа вхождений данных. Сортировка подсчетом подходит для случаев, когда объем данных велик, но диапазон значений ограничен, и при этом данные можно преобразовать в положительные целые числа.</li>
 <li>Поразрядная сортировка выполняет сортировку данных путем последовательной сортировки по каждому разряду и требует, чтобы данные можно было представить в виде чисел фиксированной разрядности.</li>
-<li>В общем случае нам хотелось бы найти алгоритм сортировки, который одновременно обладал бы высокой эффективностью, стабильностью, свойством выполнения на месте и адаптивностью. Но, как и в других разделах алгоритмов и структур данных, не существует одного алгоритма сортировки, способного удовлетворить всем этим требованиям одновременно. На практике приходится выбирать подходящий алгоритм в зависимости от свойств данных.</li>
+<li>В общем случае нам хотелось бы найти алгоритм сортировки, который одновременно обладал бы высокой эффективностью, стабильностью, выполнением на месте и адаптивностью. Но, как и в других разделах алгоритмов и структур данных, не существует одного алгоритма сортировки, способного удовлетворить всем этим требованиям одновременно. На практике приходится выбирать подходящий алгоритм в зависимости от свойств данных.</li>
 <li>На рисунке 11-19 сравниваются эффективность, стабильность, выполнение на месте и адаптивность основных алгоритмов сортировки.</li>
 </ul>
 <p><img alt="Сравнение алгоритмов сортировки" class="animation-figure" src="../summary.assets/sorting_algorithms_comparison.png" /></p>
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 <!-- Page content -->
 <h1 id="53">5.3 &nbsp; Двусторонняя очередь<a class="headerlink" href="#53" title="Permanent link">&para;</a></h1>
-<p>В очереди мы можем удалять элементы только из головы или добавлять их только в хвост. Как показано на рисунке 5-7, <u>двусторонняя очередь (double-ended queue)</u> обеспечивает более высокую гибкость и позволяет выполнять добавление и удаление элементов как с головы, так и с хвоста.</p>
+<p>В обычной очереди мы можем удалять элементы только из головы и добавлять их только в хвост. Как показано на рисунке 5-7, <u>двусторонняя очередь (double-ended queue)</u> обеспечивает большую гибкость и позволяет выполнять добавление и удаление элементов как с головы, так и с хвоста.</p>
 <p><img alt="Операции двусторонней очереди" class="animation-figure" src="../deque.assets/deque_operations.png" /></p>
 <p align="center"> Рисунок 5-7 &nbsp; Операции двусторонней очереди </p>
 
@@ -4832,8 +4832,8 @@
 <h2 id="532">5.3.2 &nbsp; Реализация двусторонней очереди *<a class="headerlink" href="#532" title="Permanent link">&para;</a></h2>
 <p>Реализация двусторонней очереди похожа на реализацию обычной очереди: в качестве базовой структуры данных можно выбрать связный список или массив.</p>
 <h3 id="1">1. &nbsp; Реализация на основе двусвязного списка<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>Вспомним предыдущий раздел: там мы использовали обычный односвязный список для реализации очереди, потому что он позволяет удобно удалять головной узел (это соответствует операции dequeue) и добавлять новый узел после хвостового узла (это соответствует операции enqueue).</p>
-<p>Для двусторонней очереди и голова, и хвост допускают операции добавления и удаления элементов. Иначе говоря, двусторонняя очередь требует реализации еще одного симметричного направления операций. Поэтому в качестве базовой структуры данных двусторонней очереди мы используем "двусвязный список".</p>
+<p>Вспомним предыдущий раздел: там мы использовали обычный односвязный список для реализации очереди, потому что он позволяет удобно удалять головной узел, что соответствует операции <code>dequeue</code> , и добавлять новый узел после хвостового узла, что соответствует операции <code>enqueue</code> .</p>
+<p>Для двусторонней очереди и голова, и хвост допускают операции добавления и удаления элементов. Иначе говоря, двусторонняя очередь требует реализации еще одного симметричного направления операций. Поэтому в качестве базовой структуры данных двусторонней очереди удобно использовать двусвязный список.</p>
 <p>Как показано на рисунках ниже, мы рассматриваем головной и хвостовой узлы двусвязного списка как голову и хвост двусторонней очереди и одновременно реализуем функции добавления и удаления узлов с обеих сторон.</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:5"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">LinkedListDeque</label><label for="__tabbed_2_2">push_last()</label><label for="__tabbed_2_3">push_first()</label><label for="__tabbed_2_4">pop_last()</label><label for="__tabbed_2_5">pop_first()</label></div>
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 <h3 id="2">2. &nbsp; Реализация на основе массива<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>Как показано на рисунках ниже, аналогично реализации очереди на массиве мы также можем использовать кольцевой массив для реализации двусторонней очереди.</p>
+<p>Как показано на рисунках ниже, аналогично реализации обычной очереди на массиве мы также можем использовать кольцевой массив для реализации двусторонней очереди.</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="4:5"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">ArrayDeque</label><label for="__tabbed_4_2">push_last()</label><label for="__tabbed_4_3">push_first()</label><label for="__tabbed_4_4">pop_last()</label><label for="__tabbed_4_5">pop_first()</label></div>
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 </div>
 <p align="center"> Рисунок 5-9 &nbsp; Операции enqueue и dequeue для двусторонней очереди на массиве </p>
 
-<p>На основе реализации обычной очереди нужно лишь добавить методы "enqueue в голову" и "dequeue из хвоста":</p>
+<p>На основе реализации обычной очереди нужно лишь добавить методы добавления в голову очереди и удаления из хвоста:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="5:13"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label></div>
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 <h2 id="533">5.3.3 &nbsp; Применение двусторонней очереди<a class="headerlink" href="#533" title="Permanent link">&para;</a></h2>
 <p>Двусторонняя очередь сочетает в себе логику стека и очереди, <strong>поэтому она может покрыть все сценарии применения обеих структур и при этом предоставляет более высокую степень свободы</strong>.</p>
-<p>Мы знаем, что функция "undo" в программном обеспечении обычно реализуется с помощью стека: система <code>push</code>-ит каждое изменение в стек, а затем использует <code>pop</code> для отмены. Однако, учитывая ограниченность системных ресурсов, программы обычно ограничивают число шагов отмены (например, разрешают хранить только <span class="arithmatex">\(50\)</span> шагов). Когда длина стека превышает <span class="arithmatex">\(50\)</span>, программе нужно удалить элемент с дна стека (то есть с головы очереди). <strong>Но стек не может реализовать такую операцию, и в этом случае его приходится заменять двусторонней очередью</strong>. Обрати внимание: основная логика "undo" по-прежнему следует стековому правилу LIFO, просто двусторонняя очередь позволяет более гибко реализовать некоторые дополнительные механизмы.</p>
+<p>Мы знаем, что функция "undo" в программном обеспечении обычно реализуется с помощью стека: система помещает каждое изменение в стек с помощью <code>push</code> , а затем использует <code>pop</code> для отмены. Однако, учитывая ограниченность системных ресурсов, программы обычно ограничивают число шагов отмены, например разрешают хранить только <span class="arithmatex">\(50\)</span> шагов. Когда длина стека превышает этот предел, программе нужно удалить элемент с дна стека, то есть с головы очереди. <strong>Но стек не может реализовать такую операцию, и в этом случае его приходится заменять двусторонней очередью</strong>. Обрати внимание: основная логика "undo" по-прежнему следует стековому правилу LIFO, просто двусторонняя очередь позволяет более гибко реализовать некоторые дополнительные механизмы.</p>
 
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@@ -3561,7 +3561,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 Введение в динамическое программирование
+    14.1 Первое знакомство с динамическим программированием
   
 
     
@@ -3673,7 +3673,7 @@
   <span class="md-ellipsis">
     
   
-    14.5 Задача о неограниченном рюкзаке
+    14.5 Задача о полном рюкзаке
   
 
     
@@ -4277,8 +4277,8 @@
 <p><img alt="Стек и очередь" class="cover-image" src="../assets/covers/chapter_stack_and_queue.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>Стек похож на стопку кошек, а очередь - на очередь из кошек.</p>
-<p>Эти две структуры соответственно представляют отношения "последним пришел - первым вышел" и "первым пришел - первым вышел".</p>
+<p>Стек и очередь - две базовые линейные структуры данных.</p>
+<p>Они соответственно воплощают принципы "последним пришел - первым вышел" и "первым пришел - первым вышел".</p>
 </div>
 <h2 id="_1">Содержание главы<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
diff --git a/ru/chapter_stack_and_queue/queue/index.html b/ru/chapter_stack_and_queue/queue/index.html
index 816e8640a..aabbdf1e4 100644
--- a/ru/chapter_stack_and_queue/queue/index.html
+++ b/ru/chapter_stack_and_queue/queue/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}</style>
       
     
     
@@ -574,7 +574,7 @@
   <span class="md-ellipsis">
     
   
-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
     
@@ -596,7 +596,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 1. Знакомство с алгоритмами
+    Глава 1. Введение в алгоритмы
   
 
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@@ -646,7 +646,7 @@
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-    1.2 Что такое структуры данных и алгоритмы
+    1.2 Что такое алгоритм
   
 
     
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   <span class="md-ellipsis">
     
   
-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
     
@@ -1203,7 +1203,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 4. Массив и связный список
+    Глава 4. Массивы и списки
   
 
           </label>
@@ -1309,7 +1309,7 @@
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-    4.4 Память и кеш *
+    4.4 Оперативная память и кэш *
   
 
     
@@ -1702,7 +1702,7 @@
   <span class="md-ellipsis">
     
   
-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
     
@@ -1724,7 +1724,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 6. Хеширование
+    Глава 6. Хеш-таблицы
   
 
           </label>
@@ -1802,7 +1802,7 @@
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-    6.3 Хеш-алгоритмы
+    6.3 Алгоритмы хеширования
   
 
     
@@ -1897,7 +1897,7 @@
   <span class="md-ellipsis">
     
   
-    Глава 7. Дерево
+    Глава 7. Деревья
   
 
     
@@ -1919,7 +1919,7 @@
             <span class="md-nav__icon md-icon"></span>
             
   
-    Глава 7. Дерево
+    Глава 7. Деревья
   
 
           </label>
@@ -1997,7 +1997,7 @@
   <span class="md-ellipsis">
     
   
-    7.3 Представление дерева массивом
+    7.3 Представление двоичного дерева массивом
   
 
     
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-    7.6 Резюме
+    7.6 Краткие итоги
   
 
     
@@ -2244,7 +2244,7 @@
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-    8.3 Задача Top-K
+    8.3 Задача Top-k
   
 
     
@@ -2335,7 +2335,7 @@
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-    Глава 9. Граф
+    Глава 9. Графы
   
 
     
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-    Глава 9. Граф
+    Глава 9. Графы
   
 
           </label>
@@ -2407,7 +2407,7 @@
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-    9.2 Базовые операции над графами
+    9.2 Базовые операции графа
   
 
     
@@ -2463,7 +2463,7 @@
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-    9.4 Резюме
+    9.4 Краткие итоги
   
 
     
@@ -2602,7 +2602,7 @@
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-    10.2 Точка вставки двоичного поиска
+    10.2 Двоичный поиск точки вставки
   
 
     
@@ -2630,7 +2630,7 @@
   <span class="md-ellipsis">
     
   
-    10.3 Граничные случаи двоичного поиска
+    10.3 Двоичный поиск границ
   
 
     
@@ -2658,7 +2658,7 @@
   <span class="md-ellipsis">
     
   
-    10.4 Стратегия оптимизации через хеширование
+    10.4 Стратегии оптимизации хеширования
   
 
     
@@ -2686,7 +2686,7 @@
   <span class="md-ellipsis">
     
   
-    10.5 Алгоритмы поиска: новый взгляд
+    10.5 Переосмысление алгоритмов поиска
   
 
     
@@ -2891,7 +2891,7 @@
   <span class="md-ellipsis">
     
   
-    11.3 Пузырьковая сортировка
+    11.3 Сортировка пузырьком
   
 
     
@@ -2919,7 +2919,7 @@
   <span class="md-ellipsis">
     
   
-    11.4 Сортировка вставкой
+    11.4 Сортировка вставками
   
 
     
@@ -3224,7 +3224,7 @@
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-    12.1 Алгоритмы разделяй и властвуй
+    12.1 Стратегия разделяй и властвуй
   
 
     
@@ -3252,7 +3252,7 @@
   <span class="md-ellipsis">
     
   
-    12.2 Стратегия поиска разделяй и властвуй
+    12.2 Поисковая стратегия разделяй и властвуй
   
 
     
@@ -3529,7 +3529,7 @@
   <span class="md-ellipsis">
     
   
-    13.4 Задача о $n$ ферзях
+    13.4 Задача о n ферзях
   
 
     
@@ -3670,7 +3670,7 @@
   <span class="md-ellipsis">
     
   
-    14.1 Введение в динамическое программирование
+    14.1 Первое знакомство с динамическим программированием
   
 
     
@@ -3782,7 +3782,7 @@
   <span class="md-ellipsis">
     
   
-    14.5 Задача о неограниченном рюкзаке
+    14.5 Задача о полном рюкзаке
   
 
     
@@ -4434,7 +4434,7 @@
 <!-- Page content -->
 <h1 id="52">5.2 &nbsp; Очередь<a class="headerlink" href="#52" title="Permanent link">&para;</a></h1>
 <p><u>Очередь (queue)</u> - это линейная структура данных, подчиняющаяся правилу "первым пришел - первым вышел". Как видно из названия, очередь моделирует обычную ситуацию ожидания: новые люди непрерывно присоединяются к хвосту очереди, а стоящие в начале по одному уходят.</p>
-<p>Как показано на рисунке 5-4, начало очереди называется "головой очереди", а конец - "хвостом очереди"; операцию добавления элемента в хвост называют "enqueue", а операцию удаления элемента из головы - "dequeue".</p>
+<p>Как показано на рисунке 5-4, начало очереди называется головой очереди, а конец - хвостом очереди; операцию добавления элемента в хвост называют <code>enqueue</code>, а операцию удаления элемента из головы - <code>dequeue</code>.</p>
 <p><img alt="Правило FIFO для очереди" class="animation-figure" src="../queue.assets/queue_operations.png" /></p>
 <p align="center"> Рисунок 5-4 &nbsp; Правило FIFO для очереди </p>
 
@@ -4470,7 +4470,7 @@
 </tbody>
 </table>
 </div>
-<p>Мы можем напрямую использовать готовые классы очереди, предоставляемые языками программирования:</p>
+<p>Обычно достаточно использовать готовые классы очереди, предоставляемые языками программирования:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
@@ -4792,7 +4792,7 @@
 <h2 id="522">5.2.2 &nbsp; Реализация очереди<a class="headerlink" href="#522" title="Permanent link">&para;</a></h2>
 <p>Чтобы реализовать очередь, нам нужна такая структура данных, которая позволяет добавлять элементы с одного конца и удалять их с другого; и связный список, и массив этим требованиям удовлетворяют.</p>
 <h3 id="1">1. &nbsp; Реализация на основе связного списка<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-<p>Как показано на рисунке 5-5, мы можем рассматривать "головной узел" и "хвостовой узел" связного списка как "голову очереди" и "хвост очереди" соответственно, договорившись, что добавлять узлы можно только в хвост, а удалять - только из головы.</p>
+<p>Как показано на рисунке 5-5, мы можем рассматривать головной узел и хвостовой узел связного списка как голову очереди и хвост очереди соответственно, договорившись, что добавлять узлы можно только в хвост, а удалять - только из головы.</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:3"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">LinkedListQueue</label><label for="__tabbed_2_2">push()</label><label for="__tabbed_2_3">pop()</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
@@ -5712,14 +5712,14 @@
 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20ListNode%3A%0A%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%0A%0Aclass%20LinkedListQueue%3A%0A%0A%20%20%20%20def%20__init__%28self%29%3A%0A%20%20%20%20%20%20%20%20self._front%3A%20ListNode%20%7C%20None%20%3D%20None%0A%20%20%20%20%20%20%20%20self._rear%3A%20ListNode%20%7C%20None%20%3D%20None%0A%20%20%20%20%20%20%20%20self._size%3A%20int%20%3D%200%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%20self._size%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20return%20not%20self._front%0A%0A%20%20%20%20def%20push%28self%2C%20num%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20node%20%3D%20ListNode%28num%29%0A%20%20%20%20%20%20%20%20if%20self._front%20is%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self._front%20%3D%20node%0A%20%20%20%20%20%20%20%20%20%20%20%20self._rear%20%3D%20node%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self._rear.next%20%3D%20node%0A%20%20%20%20%20%20%20%20%20%20%20%20self._rear%20%3D%20node%0A%20%20%20%20%20%20%20%20self._size%20%2B%3D%201%0A%0A%20%20%20%20def%20pop%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20num%20%3D%20self.peek%28%29%0A%20%20%20%20%20%20%20%20self._front%20%3D%20self._front.next%0A%20%20%20%20%20%20%20%20self._size%20-%3D%201%0A%20%20%20%20%20%20%20%20return%20num%0A%0A%20%20%20%20def%20peek%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20if%20self.is_empty%28%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%27%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D1%8C%20%D0%BF%D1%83%D1%81%D1%82%D0%B0%27%29%0A%20%20%20%20%20%20%20%20return%20self._front.val%0A%0A%20%20%20%20def%20to_list%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20queue%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20temp%20%3D%20self._front%0A%20%20%20%20%20%20%20%20while%20temp%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20queue.append%28temp.val%29%0A%20%20%20%20%20%20%20%20%20%20%20%20temp%20%3D%20temp.next%0A%20%20%20%20%20%20%20%20return%20queue%0A%27Driver%20Code%27%0Aif%20__name__%20%3D%3D%20%27__main__%27%3A%0A%20%20%20%20queue%20%3D%20LinkedListQueue%28%29%0A%20%20%20%20queue.push%281%29%0A%20%20%20%20queue.push%283%29%0A%20%20%20%20queue.push%282%29%0A%20%20%20%20queue.push%285%29%0A%20%20%20%20queue.push%284%29%0A%20%20%20%20print%28%27%D0%9E%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D1%8C%20queue%20%3D%27%2C%20queue.to_list%28%29%29%0A%20%20%20%20peek%20%3D%20queue.peek%28%29%0A%20%20%20%20print%28%27%D0%9F%D0%B5%D1%80%D0%B2%D1%8B%D0%B9%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20front%20%3D%27%2C%20peek%29%0A%20%20%20%20pop_front%20%3D%20queue.pop%28%29%0A%20%20%20%20print%28%27%D0%98%D0%B7%D0%B2%D0%BB%D0%B5%D1%87%D0%B5%D0%BD%D0%BD%D1%8B%D0%B9%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20pop%20%3D%27%2C%20pop_front%29%0A%20%20%20%20print%28%27queue%20%D0%BF%D0%BE%D1%81%D0%BB%D0%B5%20%D0%B8%D0%B7%D0%B2%D0%BB%D0%B5%D1%87%D0%B5%D0%BD%D0%B8%D1%8F%20%3D%27%2C%20queue.to_list%28%29%29%0A%20%20%20%20size%20%3D%20queue.size%28%29%0A%20%20%20%20print%28%27%D0%94%D0%BB%D0%B8%D0%BD%D0%B0%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D0%B8%20size%20%3D%27%2C%20size%29%0A%20%20%20%20is_empty%20%3D%20queue.is_empty%28%29%0A%20%20%20%20print%28%27%D0%9F%D1%83%D1%81%D1%82%D0%B0%20%D0%BB%D0%B8%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D1%8C%20%3D%27%2C%20is_empty%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
 <h3 id="2">2. &nbsp; Реализация на основе массива<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>Удаление первого элемента из массива имеет временную сложность <span class="arithmatex">\(O(n)\)</span> , из-за чего операция dequeue оказывается неэффективной. Однако этого можно избежать с помощью следующего приема.</p>
+<p>Удаление первого элемента из массива имеет временную сложность <span class="arithmatex">\(O(n)\)</span> , из-за чего операция <code>dequeue</code> оказывается неэффективной. Однако этого можно избежать с помощью следующего приема.</p>
 <p>Мы можем использовать переменную <code>front</code> , указывающую на индекс элемента в голове очереди, и поддерживать переменную <code>size</code> , которая хранит длину очереди. Определим <code>rear = front + size</code> ; эта формула дает позицию <code>rear</code>, указывающую на ячейку сразу после хвоста очереди.</p>
 <p>Исходя из этого, <strong>эффективный диапазон элементов массива равен <code>[front, rear - 1]</code></strong>, а различные операции реализуются, как показано на рисунке 5-6.</p>
 <ul>
-<li>Операция enqueue: записать входной элемент по индексу <code>rear</code> и увеличить <code>size</code> на 1.</li>
-<li>Операция dequeue: просто увеличить <code>front</code> на 1 и уменьшить <code>size</code> на 1.</li>
+<li>Операция <code>enqueue</code>: записать входной элемент по индексу <code>rear</code> и увеличить <code>size</code> на 1.</li>
+<li>Операция <code>dequeue</code>: просто увеличить <code>front</code> на 1 и уменьшить <code>size</code> на 1.</li>
 </ul>
-<p>Можно увидеть, что и enqueue, и dequeue требуют всего одной операции, а значит обе имеют временную сложность <span class="arithmatex">\(O(1)\)</span> .</p>
+<p>Можно увидеть, что и <code>enqueue</code> , и <code>dequeue</code> требуют всего одной операции, а значит обе имеют временную сложность <span class="arithmatex">\(O(1)\)</span> .</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="4:3"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">ArrayQueue</label><label for="__tabbed_4_2">push()</label><label for="__tabbed_4_3">pop()</label></div>
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@@ -5735,7 +5735,7 @@
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 <p align="center"> Рисунок 5-6 &nbsp; Операции enqueue и dequeue в реализации очереди на массиве </p>
 
-<p>Ты можешь заметить еще одну проблему: при непрерывных операциях enqueue и dequeue значения <code>front</code> и <code>rear</code> оба движутся вправо, и <strong>когда они доходят до конца массива, дальше сдвигаться уже нельзя</strong>. Чтобы решить эту проблему, можно рассматривать массив как "кольцевой массив", у которого начало и конец соединены.</p>
+<p>Ты можешь заметить еще одну проблему: при непрерывных операциях <code>enqueue</code> и <code>dequeue</code> значения <code>front</code> и <code>rear</code> оба движутся вправо, и <strong>когда они доходят до конца массива, дальше сдвигаться уже нельзя</strong>. Чтобы решить эту проблему, можно рассматривать массив как кольцевой массив, у которого начало и конец соединены.</p>
 <p>Для кольцевого массива нужно сделать так, чтобы <code>front</code> или <code>rear</code>, перешагнув конец массива, сразу возвращались к его началу и продолжали движение. Такую периодичность удобно реализовать с помощью операции взятия остатка, как показано в коде ниже:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="5:13"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label></div>
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@@ -6666,7 +6666,7 @@
 <p>Выводы сравнения двух реализаций в целом такие же, как и для стека, поэтому здесь мы не будем повторяться.</p>
 <h2 id="523">5.2.3 &nbsp; Типичные применения очереди<a class="headerlink" href="#523" title="Permanent link">&para;</a></h2>
 <ul>
-<li><strong>Заказы на Taobao</strong>. После оформления заказа покупателем заказ попадает в очередь, а затем система обрабатывает заказы по порядку. Во время крупных распродаж, таких как Double 11, за короткое время возникает огромный поток заказов, и высокая конкурентная нагрузка становится ключевой инженерной проблемой.</li>
+<li><strong>Очереди заказов</strong>. После оформления заказа покупателем заказ попадает в очередь, а затем система обрабатывает заказы по порядку. Во время крупных распродаж за короткое время возникает огромный поток заказов, и высокая конкурентная нагрузка становится ключевой инженерной проблемой.</li>
 <li><strong>Различные отложенные задачи</strong>. Любой сценарий, где нужно реализовать принцип "кто раньше пришел, тот раньше обслуживается", например очередь заданий принтера или очередь блюд на кухне ресторана, хорошо моделируется очередью, которая эффективно поддерживает нужный порядок обработки.</li>
 </ul>
 
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 <!-- Page content -->
 <h1 id="51">5.1 &nbsp; Стек<a class="headerlink" href="#51" title="Permanent link">&para;</a></h1>
 <p><u>Стек (stack)</u> - это линейная структура данных, подчиняющаяся логике "последним пришел - первым вышел".</p>
-<p>Стек можно сравнить со стопкой тарелок на столе. Если разрешено перемещать только одну тарелку за раз, то, чтобы достать тарелку снизу, сначала придется по одной убрать все тарелки сверху. Если заменить тарелки различными элементами (например целыми числами, символами, объектами и т.д.), получится структура данных "стек".</p>
-<p>Как показано на рисунке 5-1, верхнюю часть стопки элементов мы называем "вершиной стека", а нижнюю - "основанием стека". Операция добавления элемента на вершину называется "push", а операция удаления верхнего элемента - "pop".</p>
+<p>Стек можно сравнить со стопкой тарелок на столе. Если разрешено перемещать только одну тарелку за раз, то, чтобы достать тарелку снизу, сначала придется по одной убрать все тарелки сверху. Если заменить тарелки различными элементами, например целыми числами, символами, объектами и т.д., получится структура данных "стек".</p>
+<p>Как показано на рисунке 5-1, верхнюю часть стопки элементов мы называем вершиной стека, а нижнюю - основанием стека. Операция добавления элемента на вершину называется <code>push</code>, а операция удаления верхнего элемента - <code>pop</code>.</p>
 <p><img alt="Правило LIFO для стека" class="animation-figure" src="../stack.assets/stack_operations.png" /></p>
 <p align="center"> Рисунок 5-1 &nbsp; Правило LIFO для стека </p>
 
@@ -4493,7 +4493,7 @@
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-<p>Обычно мы можем просто использовать встроенный стек, предоставляемый языком программирования. Однако в некоторых языках специальный класс стека может отсутствовать. В таком случае можно использовать "массив" или "связный список" этого языка как стек и в логике программы игнорировать операции, не относящиеся к стеку.</p>
+<p>Обычно достаточно использовать встроенный стек, предоставляемый языком программирования. Однако в некоторых языках специальный класс стека может отсутствовать. В таком случае можно использовать массив или связный список как стек и в логике программы игнорировать операции, не относящиеся к стеку.</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
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 <h2 id="512">5.1.2 &nbsp; Реализация стека<a class="headerlink" href="#512" title="Permanent link">&para;</a></h2>
 <p>Чтобы глубже понять механизм работы стека, попробуем самостоятельно реализовать класс стека.</p>
-<p>Стек подчиняется принципу LIFO, поэтому мы можем добавлять и удалять элементы только на вершине. Однако и массив, и связный список позволяют добавлять и удалять элементы в произвольном месте. <strong>Следовательно, стек можно рассматривать как ограниченный массив или связный список</strong>. Иными словами, мы можем "скрыть" часть нерелевантных операций массива или списка, так чтобы внешняя логика соответствовала свойствам стека.</p>
+<p>Стек подчиняется принципу LIFO, поэтому мы можем добавлять и удалять элементы только на вершине. Однако и массив, и связный список позволяют добавлять и удалять элементы в произвольном месте. <strong>Следовательно, стек можно рассматривать как ограниченный массив или связный список</strong>. Иными словами, мы можем скрыть часть нерелевантных операций массива или списка, так чтобы внешняя логика соответствовала свойствам стека.</p>
 <h3 id="1">1. &nbsp; Реализация на основе связного списка<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <p>Если реализовывать стек на основе связного списка, то головной узел списка можно рассматривать как вершину стека, а хвостовой - как основание.</p>
-<p>Как показано на рисунке 5-2, для операции push достаточно вставить элемент в голову связного списка. Такой способ вставки называется "вставкой в голову". Для операции pop достаточно удалить головной узел из списка.</p>
+<p>Как показано на рисунке 5-2, для операции <code>push</code> достаточно вставить элемент в голову связного списка. Такой способ вставки называется вставкой в голову. Для операции <code>pop</code> достаточно удалить головной узел из списка.</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:3"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">LinkedListStack</label><label for="__tabbed_2_2">push()</label><label for="__tabbed_2_3">pop()</label></div>
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 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20ListNode%3A%0A%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%0A%0Aclass%20LinkedListStack%3A%0A%0A%20%20%20%20def%20__init__%28self%29%3A%0A%20%20%20%20%20%20%20%20self._peek%3A%20ListNode%20%7C%20None%20%3D%20None%0A%20%20%20%20%20%20%20%20self._size%3A%20int%20%3D%200%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20return%20self._size%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20return%20not%20self._peek%0A%0A%20%20%20%20def%20push%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20node%20%3D%20ListNode%28val%29%0A%20%20%20%20%20%20%20%20node.next%20%3D%20self._peek%0A%20%20%20%20%20%20%20%20self._peek%20%3D%20node%0A%20%20%20%20%20%20%20%20self._size%20%2B%3D%201%0A%0A%20%20%20%20def%20pop%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20num%20%3D%20self.peek%28%29%0A%20%20%20%20%20%20%20%20self._peek%20%3D%20self._peek.next%0A%20%20%20%20%20%20%20%20self._size%20-%3D%201%0A%20%20%20%20%20%20%20%20return%20num%0A%0A%20%20%20%20def%20peek%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20if%20self.is_empty%28%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%27%D1%81%D1%82%D0%B5%D0%BA%20%D0%BF%D1%83%D1%81%D1%82%27%29%0A%20%20%20%20%20%20%20%20return%20self._peek.val%0A%0A%20%20%20%20def%20to_list%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20arr%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20node%20%3D%20self._peek%0A%20%20%20%20%20%20%20%20while%20node%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20arr.append%28node.val%29%0A%20%20%20%20%20%20%20%20%20%20%20%20node%20%3D%20node.next%0A%20%20%20%20%20%20%20%20arr.reverse%28%29%0A%20%20%20%20%20%20%20%20return%20arr%0A%27Driver%20Code%27%0Aif%20__name__%20%3D%3D%20%27__main__%27%3A%0A%20%20%20%20stack%20%3D%20LinkedListStack%28%29%0A%20%20%20%20stack.push%281%29%0A%20%20%20%20stack.push%283%29%0A%20%20%20%20stack.push%282%29%0A%20%20%20%20stack.push%285%29%0A%20%20%20%20stack.push%284%29%0A%20%20%20%20print%28%27%D0%A1%D1%82%D0%B5%D0%BA%20stack%20%3D%27%2C%20stack.to_list%28%29%29%0A%20%20%20%20peek%20%3D%20stack.peek%28%29%0A%20%20%20%20print%28%27%D0%92%D0%B5%D1%80%D1%85%D0%BD%D0%B8%D0%B9%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20peek%20%3D%27%2C%20peek%29%0A%20%20%20%20pop%20%3D%20stack.pop%28%29%0A%20%20%20%20print%28%27%D0%98%D0%B7%D0%B2%D0%BB%D0%B5%D1%87%D0%B5%D0%BD%D0%BD%D1%8B%D0%B9%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20pop%20%3D%27%2C%20pop%29%0A%20%20%20%20print%28%27stack%20%D0%BF%D0%BE%D1%81%D0%BB%D0%B5%20%D0%B8%D0%B7%D0%B2%D0%BB%D0%B5%D1%87%D0%B5%D0%BD%D0%B8%D1%8F%20%3D%27%2C%20stack.to_list%28%29%29%0A%20%20%20%20size%20%3D%20stack.size%28%29%0A%20%20%20%20print%28%27%D0%94%D0%BB%D0%B8%D0%BD%D0%B0%20%D1%81%D1%82%D0%B5%D0%BA%D0%B0%20size%20%3D%27%2C%20size%29%0A%20%20%20%20is_empty%20%3D%20stack.is_empty%28%29%0A%20%20%20%20print%28%27%D0%9F%D1%83%D1%81%D1%82%20%D0%BB%D0%B8%20%D1%81%D1%82%D0%B5%D0%BA%20%3D%27%2C%20is_empty%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Во весь экран &gt;</a></div></p>
 </details>
 <h3 id="2">2. &nbsp; Реализация на основе массива<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-<p>Если реализовывать стек на основе массива, то хвост массива можно рассматривать как вершину стека. Как показано на рисунке 5-3, операции push и pop соответствуют добавлению элемента в конец массива и удалению элемента из конца, обе имеют временную сложность <span class="arithmatex">\(O(1)\)</span> .</p>
+<p>Если реализовывать стек на основе массива, то хвост массива можно рассматривать как вершину стека. Как показано на рисунке 5-3, операции <code>push</code> и <code>pop</code> соответствуют добавлению элемента в конец массива и удалению элемента из конца, обе имеют временную сложность <span class="arithmatex">\(O(1)\)</span> .</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="4:3"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">ArrayStack</label><label for="__tabbed_4_2">push()</label><label for="__tabbed_4_3">pop()</label></div>
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@@ -6204,21 +6204,21 @@
 <p><strong>Поддерживаемые операции</strong></p>
 <p>Обе реализации поддерживают все операции, определенные для стека. Реализация на массиве дополнительно позволяет выполнять произвольный доступ, но это уже выходит за рамки определения стека и обычно не используется.</p>
 <p><strong>Временная эффективность</strong></p>
-<p>В реализации на массиве и push, и pop выполняются в заранее выделенной непрерывной памяти, которая хорошо использует локальность кэша, поэтому такие операции обычно эффективнее. Однако если при push емкость массива оказывается превышена, включается механизм расширения, и временная сложность конкретно этой операции push становится <span class="arithmatex">\(O(n)\)</span> .</p>
-<p>В реализации на связном списке расширение выполняется очень гибко, и проблемы падения эффективности из-за расширения массива здесь нет. Но сама операция push требует инициализации объекта-узла и изменения указателей, поэтому в среднем она немного менее эффективна. Впрочем, если помещаемые в стек элементы уже сами являются объектами-узлами, шаг инициализации можно пропустить и тем самым повысить эффективность.</p>
+<p>В реализации на массиве и <code>push</code> , и <code>pop</code> выполняются в заранее выделенной непрерывной памяти, которая хорошо использует локальность кэша, поэтому такие операции обычно эффективнее. Однако если при <code>push</code> емкость массива оказывается превышена, включается механизм расширения, и временная сложность именно этой операции становится <span class="arithmatex">\(O(n)\)</span> .</p>
+<p>В реализации на связном списке расширение выполняется очень гибко, и проблемы падения эффективности из-за расширения массива здесь нет. Но сама операция <code>push</code> требует инициализации объекта-узла и изменения указателей, поэтому в среднем она немного менее эффективна. Впрочем, если помещаемые в стек элементы уже сами являются объектами-узлами, шаг инициализации можно пропустить и тем самым повысить эффективность.</p>
 <p>Итак, когда элементами, помещаемыми и извлекаемыми из стека, являются базовые типы данных, например <code>int</code> или <code>double</code> , можно сделать следующие выводы.</p>
 <ul>
 <li>Стек на основе массива теряет в эффективности в моменты расширения, но поскольку расширение происходит редко, его средняя эффективность выше.</li>
 <li>Стек на основе связного списка может обеспечивать более стабильную производительность.</li>
 </ul>
 <p><strong>Пространственная эффективность</strong></p>
-<p>При инициализации списка система выделяет "начальную емкость", которая может превышать реальную потребность. Кроме того, механизм расширения обычно увеличивает емкость по некоторому коэффициенту (например в 2 раза), и расширенная емкость тоже может оказаться больше фактически необходимой. Поэтому <strong>реализация стека на основе массива может приводить к некоторым потерям памяти</strong>.</p>
+<p>При инициализации массива система выделяет начальную емкость, которая может превышать реальную потребность. Кроме того, механизм расширения обычно увеличивает емкость по некоторому коэффициенту, например в 2 раза, и расширенная емкость тоже может оказаться больше фактически необходимой. Поэтому <strong>реализация стека на основе массива может приводить к некоторым потерям памяти</strong>.</p>
 <p>Однако, поскольку узлы связного списка должны дополнительно хранить указатели, <strong>узлы списка сами по себе занимают больше пространства</strong>.</p>
 <p>В итоге нельзя просто сказать, какая из реализаций более экономна по памяти; это нужно анализировать в контексте конкретной задачи.</p>
 <h2 id="514">5.1.4 &nbsp; Типичные применения стека<a class="headerlink" href="#514" title="Permanent link">&para;</a></h2>
 <ul>
-<li><strong>Кнопки "назад" и "вперед" в браузере, undo и redo в программах</strong>. Каждый раз, когда мы открываем новую страницу, браузер помещает предыдущую страницу в стек, чтобы по операции "назад" можно было вернуться к ней. Операция "назад" по сути является pop. Если нужно одновременно поддерживать и "назад", и "вперед", то обычно используются два стека.</li>
-<li><strong>Управление памятью программы</strong>. Каждый раз при вызове функции система помещает на вершину стека стековый кадр, в котором хранится контекст функции. В рекурсивной функции на этапе углубления рекурсии непрерывно выполняются push-операции, а на этапе возврата - pop-операции.</li>
+<li><strong>Кнопки "назад" и "вперед" в браузере, undo и redo в программах</strong>. Каждый раз, когда мы открываем новую страницу, браузер помещает предыдущую страницу в стек, чтобы по операции "назад" можно было вернуться к ней. Операция "назад" по сути является <code>pop</code> . Если нужно одновременно поддерживать и "назад", и "вперед", то обычно используются два стека.</li>
+<li><strong>Управление памятью программы</strong>. Каждый раз при вызове функции система помещает на вершину стека стековый кадр, в котором хранится контекст функции. В рекурсивной функции на этапе углубления рекурсии непрерывно выполняются операции <code>push</code> , а на этапе возврата - операции <code>pop</code> .</li>
 </ul>
 
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-<h1 id="54">5.4 &nbsp; Краткие итоги<a class="headerlink" href="#54" title="Permanent link">&para;</a></h1>
-<h3 id="1">1. &nbsp; Основные моменты<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<h1 id="54">5.4 &nbsp; Резюме<a class="headerlink" href="#54" title="Permanent link">&para;</a></h1>
+<h3 id="1">1. &nbsp; Основные выводы<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
 <li>Стек - это структура данных, следующая правилу "последним пришел - первым вышел", и его можно реализовать с помощью массива или связного списка.</li>
-<li>С точки зрения временной эффективности реализация стека на массиве обычно работает быстрее в среднем, но во время расширения емкости временная сложность отдельной операции push может ухудшаться до <span class="arithmatex">\(O(n)\)</span> . Напротив, реализация стека на связном списке дает более стабильные характеристики.</li>
+<li>С точки зрения временной эффективности реализация стека на массиве обычно работает быстрее в среднем, но во время расширения емкости временная сложность отдельной операции <code>push</code> может ухудшаться до <span class="arithmatex">\(O(n)\)</span> . Напротив, реализация стека на связном списке дает более стабильные характеристики.</li>
 <li>С точки зрения использования памяти реализация стека на массиве может приводить к некоторой потере пространства. Однако следует учитывать, что узлы связного списка занимают больше памяти, чем элементы массива.</li>
 <li>Очередь - это структура данных, следующая правилу "первым пришел - первым вышел", и ее также можно реализовать с помощью массива или связного списка. Сравнение временной и пространственной эффективности для очереди в целом приводит к тем же выводам, что и для стека.</li>
-<li>Двусторонняя очередь - это очередь с более высокой степенью свободы, которая позволяет добавлять и удалять элементы с обеих сторон.</li>
+<li>Двусторонняя очередь - это очередь с более высокой степенью свободы, которая позволяет добавлять и удалять элементы с обоих концов.</li>
 </ul>
 <h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
 <p><strong>Q</strong>: Реализованы ли кнопки "вперед" и "назад" в браузере с помощью двусвязного списка?</p>
-<p>По сути, функция переходов "вперед/назад" в браузере отражает логику "стека". Когда пользователь открывает новую страницу, она помещается на вершину стека; когда пользователь нажимает кнопку "назад", эта страница снимается с вершины стека. Двусторонняя очередь позволяет удобно реализовать некоторые дополнительные операции, об этом уже упоминалось в разделе "Двусторонняя очередь".</p>
+<p>По сути, функция переходов "вперед/назад" в браузере отражает логику стека. Когда пользователь открывает новую страницу, она помещается на вершину стека; когда пользователь нажимает кнопку "назад", эта страница снимается с вершины стека. Двусторонняя очередь позволяет удобно реализовать некоторые дополнительные операции, об этом уже упоминалось в разделе "Двусторонняя очередь".</p>
 <p><strong>Q</strong>: Нужно ли освобождать память узла после извлечения его из стека?</p>
 <p>Если извлеченный узел еще понадобится, память освобождать не нужно. Если он больше не нужен, то в языках <code>Java</code> и <code>Python</code> есть автоматический сборщик мусора, поэтому ручное освобождение памяти не требуется; в <code>C</code> и <code>C++</code> память нужно освобождать вручную.</p>
 <p><strong>Q</strong>: Двусторонняя очередь выглядит как два соединенных стека. Для чего она нужна?</p>
-<p>Двусторонняя очередь похожа на комбинацию стека и очереди или на два соединенных стека. Она выражает логику "стек + очередь", поэтому может покрыть все применения стека и очереди и при этом остается более гибкой.</p>
+<p>Двусторонняя очередь похожа на комбинацию стека и очереди или на два соединенных стека. Она объединяет логику обеих структур, поэтому может покрыть все их применения и при этом остается более гибкой.</p>
 <p><strong>Q</strong>: Как именно реализуются отмена (undo) и повтор (redo)?</p>
 <p>Используются два стека: стек <code>A</code> для отмены и стек <code>B</code> для повтора.</p>
 <ol>
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 <p>Возникает вопрос: можно ли представить двоичное дерево с помощью массива? Ответ: да.</p>
 <h2 id="731">7.3.1 &nbsp; Представление идеального двоичного дерева<a class="headerlink" href="#731" title="Permanent link">&para;</a></h2>
 <p>Сначала разберем простой случай. Если дана идеальная двоичная структура и все ее узлы хранятся в массиве в порядке обхода по уровням, то каждому узлу будет соответствовать единственный индекс массива.</p>
-<p>Из свойств обхода по уровням можно вывести "формулу соответствия" между индексом родителя и индексами дочерних узлов: <strong>если индекс некоторого узла равен <span class="arithmatex">\(i\)</span> , то индекс его левого дочернего узла равен <span class="arithmatex">\(2i + 1\)</span> , а правого - <span class="arithmatex">\(2i + 2\)</span></strong> . На рисунке 7-12 показано соответствие между индексами разных узлов.</p>
+<p>Из свойств обхода по уровням можно вывести формулу соответствия между индексом родителя и индексами дочерних узлов: <strong>если индекс некоторого узла равен <span class="arithmatex">\(i\)</span> , то индекс его левого дочернего узла равен <span class="arithmatex">\(2i + 1\)</span> , а правого - <span class="arithmatex">\(2i + 2\)</span></strong> . На рисунке 7-12 показано соответствие между индексами разных узлов.</p>
 <p><img alt="Представление идеального двоичного дерева массивом" class="animation-figure" src="../array_representation_of_tree.assets/array_representation_binary_tree.png" /></p>
 <p align="center"> Рисунок 7-12 &nbsp; Представление идеального двоичного дерева массивом </p>
 
-<p><strong>Эта формула соответствия играет ту же роль, что и ссылки на узлы в связной структуре</strong> . Имея любой узел в массиве, мы можем по формуле получить доступ к его левому и правому дочерним узлам.</p>
+<p><strong>Эта формула соответствия играет ту же роль, что и ссылки на узлы в связной структуре</strong> . Имея любой узел в массиве, мы можем с ее помощью получить доступ к его левому и правому дочерним узлам.</p>
 <h2 id="732">7.3.2 &nbsp; Представление произвольного двоичного дерева<a class="headerlink" href="#732" title="Permanent link">&para;</a></h2>
 <p>Идеальное двоичное дерево - лишь частный случай; в обычной двоичной структуре на промежуточных уровнях часто существует множество <code>None</code> . Поскольку последовательность обхода по уровням не содержит этих <code>None</code> , мы не можем по одной лишь этой последовательности определить их количество и расположение. <strong>Это означает, что одному и тому же обходу по уровням может соответствовать сразу несколько различных структур двоичного дерева</strong>.</p>
 <p>Как показано на рисунке 7-13, для неполной двоичной структуры описанный выше способ представления массивом уже перестает работать.</p>
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-    aria-label="Вперед: 7.6 Резюме"
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 </div>
 <p align="center"> Рисунок 7-17 &nbsp; Пример поиска узла в двоичном дереве поиска </p>
 
-<p>Операция поиска в двоичном дереве поиска работает по тому же принципу, что и бинарный поиск: на каждом шаге она отбрасывает половину вариантов. Число итераций не превосходит высоты двоичного дерева, а когда дерево сбалансировано, требуется <span class="arithmatex">\(O(\log n)\)</span> времени. Пример кода приведен ниже:</p>
+<p>Операция поиска в двоичном дереве поиска работает по тому же принципу, что и двоичный поиск: на каждом шаге она отбрасывает половину вариантов. Число итераций не превосходит высоты двоичного дерева, а когда дерево сбалансировано, требуется <span class="arithmatex">\(O(\log n)\)</span> времени. Пример кода приведен ниже:</p>
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@@ -6000,7 +6000,7 @@
 <p align="center"> Рисунок 7-22 &nbsp; Последовательность симметричного обхода двоичного дерева поиска </p>
 
 <h2 id="742">7.4.2 &nbsp; Эффективность двоичного дерева поиска<a class="headerlink" href="#742" title="Permanent link">&para;</a></h2>
-<p>Для заданного набора данных можно рассмотреть хранение либо в массиве, либо в двоичном дереве поиска. Из таблицы ниже видно, что временная сложность операций двоичного дерева поиска имеет логарифмический порядок, поэтому его производительность стабильна и высока. Только в сценариях с очень частыми вставками и редкими поисками и удалениями массив может быть эффективнее, чем двоичное дерево поиска.</p>
+<p>Для заданного набора данных можно рассмотреть хранение либо в массиве, либо в двоичном дереве поиска. Из таблицы ниже видно, что временная сложность операций двоичного дерева поиска имеет логарифмический порядок и обеспечивает стабильную высокую производительность. Только в сценариях с очень частыми вставками и редкими поисками и удалениями массив может быть эффективнее, чем двоичное дерево поиска.</p>
 <p align="center"> Таблица 7-2 &nbsp; Сравнение эффективности массива и дерева поиска </p>
 
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-    aria-label="Назад: 7.3 Представление дерева массивом"
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-        <style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=PT+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
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 <!-- Page content -->
 <h1 id="71">7.1 &nbsp; Двоичное дерево<a class="headerlink" href="#71" title="Permanent link">&para;</a></h1>
-<p><u>Двоичное дерево (binary tree)</u> - это нелинейная структура данных, представляющая отношения порождения между "предками" и "потомками" и отражающая логику "разделения надвое". Подобно связному списку, базовой единицей двоичного дерева является узел; каждый узел содержит значение, ссылку на левого дочернего узла и ссылку на правого дочернего узла.</p>
+<p><u>Двоичное дерево (binary tree)</u> - это нелинейная структура данных, представляющая отношения между "предками" и "потомками" и отражающая логику "разделяй и властвуй". Подобно связному списку, базовой единицей двоичного дерева является узел; каждый узел содержит значение, ссылку на левого дочернего узла и ссылку на правого дочернего узла.</p>
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 <p>Каждый узел имеет две ссылки (указателя), которые соответственно указывают на <u>левого дочернего узла (left-child node)</u> и <u>правого дочернего узла (right-child node)</u>; данный узел называется <u>родительским узлом (parent node)</u> для этих двух дочерних узлов. Если задан некоторый узел двоичного дерева, то дерево, образованное его левым дочерним узлом и всеми узлами ниже него, называется <u>левым поддеревом (left subtree)</u> этого узла; аналогично определяется <u>правое поддерево (right subtree)</u>.</p>
-<p><strong>В двоичном дереве, кроме листовых узлов, все остальные узлы содержат дочерние узлы и непустые поддеревья</strong>. Как показано на рисунке 7-1, если рассматривать "узел 2" как родительский, то его левым и правым дочерними узлами будут "узел 4" и "узел 5"; левое поддерево - это "узел 4 и дерево ниже него", а правое поддерево - это "узел 5 и дерево ниже него".</p>
+<p><strong>Узлы, не имеющие дочерних узлов, называют листьями, а все остальные узлы содержат дочерние узлы и непустые поддеревья</strong>. Как показано на рисунке 7-1, если рассматривать "узел 2" как родительский, то его левым и правым дочерними узлами будут "узел 4" и "узел 5"; левое поддерево - это "узел 4 и дерево ниже него", а правое поддерево - это "узел 5 и дерево ниже него".</p>
 <p><img alt="Родительский узел, дочерние узлы и поддеревья" class="animation-figure" src="../binary_tree.assets/binary_tree_definition.png" /></p>
 <p align="center"> Рисунок 7-1 &nbsp; Родительский узел, дочерние узлы и поддеревья </p>
 
@@ -4755,7 +4755,7 @@
 
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-<p>Обрати внимание: обычно под "высотой" и "глубиной" понимают "число пройденных ребер", но в некоторых задачах или учебниках их могут определять как "число пройденных узлов". В таком случае и высоту, и глубину нужно увеличить на 1 .</p>
+<p>Обычно под "высотой" и "глубиной" понимают "число пройденных ребер", но в некоторых задачах или учебниках их могут определять как "число пройденных узлов". В таком случае и высоту, и глубину нужно увеличить на 1 .</p>
 </div>
 <h2 id="712">7.1.2 &nbsp; Базовые операции двоичного дерева<a class="headerlink" href="#712" title="Permanent link">&para;</a></h2>
 <h3 id="1">1. &nbsp; Инициализация двоичного дерева<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
@@ -5104,20 +5104,20 @@
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-<p>Обрати внимание: вставка узла может изменить исходную логическую структуру двоичного дерева, а удаление узла обычно означает удаление этого узла вместе со всеми его поддеревьями. Поэтому в двоичном дереве операции вставки и удаления обычно являются частью более крупного набора операций, который и реализует осмысленное действие.</p>
+<p>Стоит помнить, что вставка узла может изменить исходную логическую структуру двоичного дерева, а удаление узла обычно означает удаление этого узла вместе со всеми его поддеревьями. Поэтому в двоичном дереве операции вставки и удаления обычно являются частью более крупного набора операций, который и реализует осмысленное действие.</p>
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 <h2 id="713">7.1.3 &nbsp; Распространенные типы двоичных деревьев<a class="headerlink" href="#713" title="Permanent link">&para;</a></h2>
 <h3 id="1_1">1. &nbsp; Идеальное двоичное дерево<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
 <p>Как показано на рисунке 7-4, <u>идеальное двоичное дерево (perfect binary tree)</u> полностью заполнено на всех уровнях. В идеальном двоичном дереве степень листовых узлов равна <span class="arithmatex">\(0\)</span> , а у всех остальных узлов степень равна <span class="arithmatex">\(2\)</span> ; если высота дерева равна <span class="arithmatex">\(h\)</span> , то общее число узлов равно <span class="arithmatex">\(2^{h+1} - 1\)</span> , что образует стандартную экспоненциальную зависимость и отражает часто встречающееся в природе явление клеточного деления.</p>
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-<p>Обрати внимание: в китайскоязычном сообществе идеальное двоичное дерево часто называют <u>полностью заполненным двоичным деревом</u>.</p>
+<p>В китайскоязычном сообществе идеальное двоичное дерево часто называют <u>полностью заполненным двоичным деревом</u>.</p>
 </div>
 <p><img alt="Идеальное двоичное дерево" class="animation-figure" src="../binary_tree.assets/perfect_binary_tree.png" /></p>
 <p align="center"> Рисунок 7-4 &nbsp; Идеальное двоичное дерево </p>
 
 <h3 id="2_1">2. &nbsp; Полное двоичное дерево<a class="headerlink" href="#2_1" title="Permanent link">&para;</a></h3>
-<p>Как показано на рисунке 7-5, <u>полное двоичное дерево (complete binary tree)</u> допускает неполное заполнение только на самом нижнем уровне, причем узлы этого уровня должны непрерывно заполняться слева направо. Обрати внимание: идеальное двоичное дерево тоже является полным двоичным деревом.</p>
+<p>Как показано на рисунке 7-5, <u>полное двоичное дерево (complete binary tree)</u> допускает неполное заполнение только на самом нижнем уровне, причем узлы этого уровня должны непрерывно заполняться слева направо. Стоит отметить, что идеальное двоичное дерево тоже является полным двоичным деревом.</p>
 <p><img alt="Полное двоичное дерево" class="animation-figure" src="../binary_tree.assets/complete_binary_tree.png" /></p>
 <p align="center"> Рисунок 7-5 &nbsp; Полное двоичное дерево </p>
 
@@ -5134,7 +5134,7 @@
 <h2 id="714">7.1.4 &nbsp; Вырождение двоичного дерева<a class="headerlink" href="#714" title="Permanent link">&para;</a></h2>
 <p>На рисунке 7-8 показаны идеальная структура двоичного дерева и вырожденная структура. Когда каждый уровень двоичного дерева полностью заполнен узлами, мы получаем "идеальное двоичное дерево"; когда же все узлы смещаются к одной стороне, двоичное дерево вырождается в "связный список".</p>
 <ul>
-<li>Идеальное двоичное дерево соответствует лучшему случаю и позволяет полностью раскрыть преимущества двоичного дерева с точки зрения "разделяй и властвуй".</li>
+<li>Идеальное двоичное дерево соответствует лучшему случаю и позволяет в полной мере раскрыть преимущества подхода "разделяй и властвуй".</li>
 <li>Связный список представляет противоположную крайность: все операции становятся линейными, а временная сложность деградирует до <span class="arithmatex">\(O(n)\)</span> .</li>
 </ul>
 <p><img alt="Лучший и худший случаи структуры двоичного дерева" class="animation-figure" src="../binary_tree.assets/binary_tree_best_worst_cases.png" /></p>
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 <p>К распространенным способам обхода двоичного дерева относятся обход по уровням, прямой обход, симметричный обход и обратный обход.</p>
 <h2 id="721">7.2.1 &nbsp; Обход по уровням<a class="headerlink" href="#721" title="Permanent link">&para;</a></h2>
 <p>Как показано на рисунке 7-9, <u>обход по уровням (level-order traversal)</u> проходит двоичное дерево сверху вниз по уровням и на каждом уровне посещает узлы слева направо.</p>
-<p>По своей сути обход по уровням относится к <u>обходу в ширину (breadth-first traversal)</u>, также называемому <u>поиском в ширину (breadth-first search, BFS)</u>; он отражает идею "расширяться слой за слоем наружу".</p>
+<p>По своей сути обход по уровням относится к <u>обходу в ширину (breadth-first traversal)</u>, также называемому <u>поиском в ширину (breadth-first search, BFS)</u>; он отражает идею "расширяться от центра к периферии слой за слоем".</p>
 <p><img alt="Обход двоичного дерева по уровням" class="animation-figure" src="../binary_tree_traversal.assets/binary_tree_bfs.png" /></p>
 <p align="center"> Рисунок 7-9 &nbsp; Обход двоичного дерева по уровням </p>
 
@@ -4778,8 +4778,8 @@
 <li><strong>Пространственная сложность равна <span class="arithmatex">\(O(n)\)</span></strong> : в худшем случае, то есть для полной двоичной деревообразной структуры, до достижения самого нижнего уровня в очереди одновременно может находиться до <span class="arithmatex">\((n + 1) / 2\)</span> узлов, что требует <span class="arithmatex">\(O(n)\)</span> памяти.</li>
 </ul>
 <h2 id="722">7.2.2 &nbsp; Прямой, симметричный и обратный обходы<a class="headerlink" href="#722" title="Permanent link">&para;</a></h2>
-<p>Соответственно, прямой, симметричный и обратный обходы относятся к <u>обходу в глубину (depth-first traversal)</u>, также называемому <u>поиском в глубину (depth-first search, DFS)</u>; он отражает идею "сначала идти до конца, затем откатываться и продолжать".</p>
-<p>На рисунке 7-10 показан принцип работы обхода двоичного дерева в глубину. <strong>Обход в глубину похож на то, как будто мы обходим всю двоичную структуру по внешнему контуру</strong> , и у каждого узла встречаем три позиции, соответствующие прямому, симметричному и обратному обходам.</p>
+<p>Соответственно, прямой, симметричный и обратный обходы относятся к <u>обходу в глубину (depth-first traversal)</u>, также называемому <u>поиском в глубину (depth-first search, DFS)</u>; он отражает идею "сначала идти до конца, затем возвращаться и продолжать".</p>
+<p>На рисунке 7-10 показан принцип работы обхода двоичного дерева в глубину. <strong>Обход в глубину можно представить как обход всей двоичной структуры по внешнему контуру</strong> , и у каждого узла встречаются три позиции, соответствующие прямому, симметричному и обратному обходам.</p>
 <p><img alt="Прямой, симметричный и обратный обходы двоичного дерева поиска" class="animation-figure" src="../binary_tree_traversal.assets/binary_tree_dfs.png" /></p>
 <p align="center"> Рисунок 7-10 &nbsp; Прямой, симметричный и обратный обходы двоичного дерева поиска </p>
 
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 <p><img alt="Деревья" class="cover-image" src="../assets/covers/chapter_tree.jpg" /></p>
 <div class="admonition abstract">
 <p class="admonition-title">Abstract</p>
-<p>Высокое дерево полно жизни: мощные корни, густая крона и раскидистые ветви.</p>
-<p>Оно наглядно показывает нам форму данных, построенную на принципе "разделяй и властвуй".</p>
+<p>Высокое дерево полно жизни: мощные корни, густая листва и раскидистые ветви.</p>
+<p>Оно наглядно показывает нам живую форму данных, построенную на принципе "разделяй и властвуй".</p>
 </div>
 <h2 id="_1">Содержание главы<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
 <ul>
 <li><a href="binary_tree/">7.1 &nbsp; Двоичное дерево</a></li>
 <li><a href="binary_tree_traversal/">7.2 &nbsp; Обход двоичного дерева</a></li>
-<li><a href="array_representation_of_tree/">7.3 &nbsp; Представление дерева массивом</a></li>
+<li><a href="array_representation_of_tree/">7.3 &nbsp; Представление двоичного дерева массивом</a></li>
 <li><a href="binary_search_tree/">7.4 &nbsp; Двоичное дерево поиска</a></li>
 <li><a href="avl_tree/">7.5 &nbsp; AVL-дерево *</a></li>
-<li><a href="summary/">7.6 &nbsp; Резюме</a></li>
+<li><a href="summary/">7.6 &nbsp; Краткие итоги</a></li>
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 <h1 id="76">7.6 &nbsp; Краткие итоги<a class="headerlink" href="#76" title="Permanent link">&para;</a></h1>
 <h3 id="1">1. &nbsp; Основные моменты<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <ul>
-<li>Двоичное дерево - это нелинейная структура данных, отражающая логику "разделения надвое". Каждый узел двоичного дерева содержит значение и два указателя, которые соответственно ведут к левому и правому дочерним узлам.</li>
+<li>Двоичное дерево - это нелинейная структура данных, отражающая логику "разделяй и властвуй". Каждый узел двоичного дерева содержит значение и два указателя, которые соответственно ведут к левому и правому дочерним узлам.</li>
 <li>Для любого узла двоичного дерева дерево, образованное его левым (правым) дочерним узлом и всеми нижележащими узлами, называется левым (правым) поддеревом этого узла.</li>
 <li>К связанным с двоичным деревом терминам относятся корневой узел, листовой узел, уровень, степень, ребро, высота, глубина и так далее.</li>
-<li>Инициализация двоичного дерева, вставка узлов и удаление узлов похожи по способу реализации на операции со связным списком.</li>
+<li>Инициализация двоичного дерева, вставка узлов и удаление узлов аналогичны операциям со связным списком.</li>
 <li>К распространенным видам двоичного дерева относятся идеальное двоичное дерево, полное двоичное дерево, строгое двоичное дерево и сбалансированное двоичное дерево. Идеальное двоичное дерево - наиболее желательное состояние, а связный список - худший случай после вырождения.</li>
-<li>Двоичное дерево можно представить массивом: значения узлов и пустые позиции располагаются в порядке обхода по уровням, а связи между родителем и детьми реализуются через отображение индексов.</li>
-<li>Обход двоичного дерева по уровням является методом поиска в ширину; он отражает идею "расширяться слой за слоем наружу" и обычно реализуется через очередь.</li>
-<li>Прямой, симметричный и обратный обходы относятся к поиску в глубину; они отражают идею "сначала дойти до конца, затем откатиться и продолжить" и обычно реализуются рекурсивно.</li>
+<li>Двоичное дерево можно представить массивом: значения узлов и пустые позиции располагаются в порядке обхода по уровням, а связи между родителем и детьми реализуются через индексацию.</li>
+<li>Обход двоичного дерева по уровням является методом поиска в ширину; он отражает идею "расширяться от центра к периферии слой за слоем" и обычно реализуется через очередь.</li>
+<li>Прямой, симметричный и обратный обходы относятся к поиску в глубину; они отражают идею "сначала дойти до конца, затем вернуться и продолжить" и обычно реализуются рекурсивно.</li>
 <li>Двоичное дерево поиска - это эффективная структура данных для поиска элементов; его поиск, вставка и удаление имеют временную сложность <span class="arithmatex">\(O(\log n)\)</span> . Когда двоичное дерево поиска вырождается в связный список, все эти сложности деградируют до <span class="arithmatex">\(O(n)\)</span> .</li>
 <li>AVL-дерево, также называемое сбалансированным двоичным деревом поиска, с помощью вращений гарантирует, что после постоянных вставок и удалений узлов дерево остается сбалансированным.</li>
 <li>Вращения AVL-дерева включают правое вращение, левое вращение, сначала правое затем левое и сначала левое затем правое. После вставки или удаления узла AVL-дерево выполняет вращения снизу вверх, чтобы снова восстановить баланс.</li>
diff --git a/ru/index.html b/ru/index.html
index da4333653..7becd4d04 100644
--- a/ru/index.html
+++ b/ru/index.html
@@ -19,9 +19,9 @@
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-      :root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}
+      :root{--md-text-font:"PT Sans";--md-code-font:"JetBrains Mono"}
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     <script>
@@ -129,7 +129,7 @@
           <div class="starfield-origin">
           </div>
         </div>
-        <div class="hero-div">
+        <div class="hero-div hero-div--ru">
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           <a href="chapter_introduction/">
@@ -442,11 +442,13 @@
                 </b>
               </div>
               <div class="profile-cell translator-profile-cell">
-                <img alt="Translator: yuyanhuang" class="profile-img" src="../assets/avatar/avatar_xxx.jpg"/>
-                <br/>
-                <b>
-                  Yuyan Huang
-                </b>
+                <a href="https://github.com/veronicahuang2977">
+                  <img alt="Translator: yuyanhuang" class="profile-img" src="../assets/avatar/avatar_yuyanhuang.jpg"/>
+                  <br/>
+                  <b>
+                    Yuyan Huang
+                  </b>
+                </a>
               </div>
             </div>
           </div>
@@ -736,7 +738,7 @@
                             </path>
                           </svg>
                           <span class="md-ellipsis">
-                            Глава 1. Знакомство с алгоритмами
+                            Глава 1. Введение в алгоритмы
                           </span>
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                         <label class="md-nav__link" for="__nav_3" id="__nav_3_label" tabindex="0">
@@ -748,7 +750,7 @@
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                           <span class="md-nav__icon md-icon">
                           </span>
-                          Глава 1. Знакомство с алгоритмами
+                          Глава 1. Введение в алгоритмы
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@@ -761,7 +763,7 @@
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                               <span class="md-ellipsis">
-                                1.2 Что такое структуры данных и алгоритмы
+                                1.2 Что такое алгоритм
                               </span>
                             </a>
                           </li>
@@ -908,7 +910,7 @@
                             </path>
                           </svg>
                           <span class="md-ellipsis">
-                            Глава 4. Массив и связный список
+                            Глава 4. Массивы и списки
                           </span>
                         </a>
                         <label class="md-nav__link" for="__nav_6" id="__nav_6_label" tabindex="0">
@@ -920,7 +922,7 @@
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                           <span class="md-nav__icon md-icon">
                           </span>
-                          Глава 4. Массив и связный список
+                          Глава 4. Массивы и списки
                         </label>
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@@ -947,7 +949,7 @@
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_array_and_linkedlist/ram_and_cache/">
                               <span class="md-ellipsis">
-                                4.4 Память и кеш *
+                                4.4 Оперативная память и кэш *
                               </span>
                             </a>
                           </li>
@@ -1025,7 +1027,7 @@
                             </path>
                           </svg>
                           <span class="md-ellipsis">
-                            Глава 6. Хеширование
+                            Глава 6. Хеш-таблицы
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                         <label class="md-nav__link" for="__nav_8" id="__nav_8_label" tabindex="0">
@@ -1037,7 +1039,7 @@
                         <label class="md-nav__title" for="__nav_8">
                           <span class="md-nav__icon md-icon">
                           </span>
-                          Глава 6. Хеширование
+                          Глава 6. Хеш-таблицы
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                         <ul class="md-nav__list" data-md-scrollfix="">
                           <li class="md-nav__item">
@@ -1057,7 +1059,7 @@
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_hashing/hash_algorithm/">
                               <span class="md-ellipsis">
-                                6.3 Хеш-алгоритмы
+                                6.3 Алгоритмы хеширования
                               </span>
                             </a>
                           </li>
@@ -1080,7 +1082,7 @@
                             </path>
                           </svg>
                           <span class="md-ellipsis">
-                            Глава 7. Дерево
+                            Глава 7. Деревья
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@@ -1092,7 +1094,7 @@
                         <label class="md-nav__title" for="__nav_9">
                           <span class="md-nav__icon md-icon">
                           </span>
-                          Глава 7. Дерево
+                          Глава 7. Деревья
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@@ -1112,7 +1114,7 @@
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_tree/array_representation_of_tree/">
                               <span class="md-ellipsis">
-                                7.3 Представление дерева массивом
+                                7.3 Представление двоичного дерева массивом
                               </span>
                             </a>
                           </li>
@@ -1133,7 +1135,7 @@
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_tree/summary/">
                               <span class="md-ellipsis">
-                                7.6 Резюме
+                                7.6 Краткие итоги
                               </span>
                             </a>
                           </li>
@@ -1181,7 +1183,7 @@
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_heap/top_k/">
                               <span class="md-ellipsis">
-                                8.3 Задача Top-K
+                                8.3 Задача Top-k
                               </span>
                             </a>
                           </li>
@@ -1204,7 +1206,7 @@
                             </path>
                           </svg>
                           <span class="md-ellipsis">
-                            Глава 9. Граф
+                            Глава 9. Графы
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@@ -1216,7 +1218,7 @@
                         <label class="md-nav__title" for="__nav_11">
                           <span class="md-nav__icon md-icon">
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-                          Глава 9. Граф
+                          Глава 9. Графы
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@@ -1229,7 +1231,7 @@
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                             <a class="md-nav__link" href="./chapter_graph/graph_operations/">
                               <span class="md-ellipsis">
-                                9.2 Базовые операции над графами
+                                9.2 Базовые операции графа
                               </span>
                             </a>
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@@ -1243,7 +1245,7 @@
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_graph/summary/">
                               <span class="md-ellipsis">
-                                9.4 Резюме
+                                9.4 Краткие итоги
                               </span>
                             </a>
                           </li>
@@ -1284,28 +1286,28 @@
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_searching/binary_search_insertion/">
                               <span class="md-ellipsis">
-                                10.2 Точка вставки двоичного поиска
+                                10.2 Двоичный поиск точки вставки
                               </span>
                             </a>
                           </li>
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_searching/binary_search_edge/">
                               <span class="md-ellipsis">
-                                10.3 Граничные случаи двоичного поиска
+                                10.3 Двоичный поиск границ
                               </span>
                             </a>
                           </li>
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_searching/replace_linear_by_hashing/">
                               <span class="md-ellipsis">
-                                10.4 Стратегия оптимизации через хеширование
+                                10.4 Стратегии оптимизации хеширования
                               </span>
                             </a>
                           </li>
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_searching/searching_algorithm_revisited/">
                               <span class="md-ellipsis">
-                                10.5 Алгоритмы поиска: новый взгляд
+                                10.5 Переосмысление алгоритмов поиска
                               </span>
                             </a>
                           </li>
@@ -1360,14 +1362,14 @@
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_sorting/bubble_sort/">
                               <span class="md-ellipsis">
-                                11.3 Пузырьковая сортировка
+                                11.3 Сортировка пузырьком
                               </span>
                             </a>
                           </li>
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_sorting/insertion_sort/">
                               <span class="md-ellipsis">
-                                11.4 Сортировка вставкой
+                                11.4 Сортировка вставками
                               </span>
                             </a>
                           </li>
@@ -1450,14 +1452,14 @@
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_divide_and_conquer/divide_and_conquer/">
                               <span class="md-ellipsis">
-                                12.1 Алгоритмы разделяй и властвуй
+                                12.1 Стратегия разделяй и властвуй
                               </span>
                             </a>
                           </li>
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_divide_and_conquer/binary_search_recur/">
                               <span class="md-ellipsis">
-                                12.2 Стратегия поиска разделяй и властвуй
+                                12.2 Поисковая стратегия разделяй и властвуй
                               </span>
                             </a>
                           </li>
@@ -1533,7 +1535,7 @@
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_backtracking/n_queens_problem/">
                               <span class="md-ellipsis">
-                                13.4 Задача о $n$ ферзях
+                                13.4 Задача о n ферзях
                               </span>
                             </a>
                           </li>
@@ -1574,7 +1576,7 @@
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_dynamic_programming/intro_to_dynamic_programming/">
                               <span class="md-ellipsis">
-                                14.1 Введение в динамическое программирование
+                                14.1 Первое знакомство с динамическим программированием
                               </span>
                             </a>
                           </li>
@@ -1602,7 +1604,7 @@
                           <li class="md-nav__item">
                             <a class="md-nav__link" href="./chapter_dynamic_programming/unbounded_knapsack_problem/">
                               <span class="md-ellipsis">
-                                14.5 Задача о неограниченном рюкзаке
+                                14.5 Задача о полном рюкзаке
                               </span>
                             </a>
                           </li>
diff --git a/ru/javascripts/katex.js b/ru/javascripts/katex.js
index ae8ca26cc..e673fbeed 100644
--- a/ru/javascripts/katex.js
+++ b/ru/javascripts/katex.js
@@ -8,4 +8,4 @@ document$.subscribe(({ body }) => {
     ],
   });
 });
-/*! update cache: 20260329054803 */
+/*! update cache: 20260330081625 */
diff --git a/ru/javascripts/mathjax.js b/ru/javascripts/mathjax.js
index f41ea1ec5..af81815e2 100644
--- a/ru/javascripts/mathjax.js
+++ b/ru/javascripts/mathjax.js
@@ -15,4 +15,4 @@ window.MathJax = {
 document$.subscribe(() => {
   MathJax.typesetPromise();
 });
-/*! update cache: 20260329054803 */
+/*! update cache: 20260330081625 */
diff --git a/ru/javascripts/starfield.js b/ru/javascripts/starfield.js
index d8ebc0949..80c2d88c6 100644
--- a/ru/javascripts/starfield.js
+++ b/ru/javascripts/starfield.js
@@ -469,4 +469,4 @@
 
   return Starfield;
 });
-/*! update cache: 20260329054803 */
+/*! update cache: 20260330081625 */
diff --git a/ru/search.json b/ru/search.json
index abb4e2ce4..6059b2257 100644
--- a/ru/search.json
+++ b/ru/search.json
@@ -1 +1 @@
-{"config":{"separator":"[\\s\\-_,:!=\\[\\]()\\\\\"`/]+|\\.(?!\\d)"},"items":[{"location":"chapter_appendix/","level":1,"title":"Глава 16.   Приложение","text":"","path":["Глава 16. Приложение","Глава 16. &nbsp; Приложение"],"tags":[]},{"location":"chapter_appendix/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>16.1   Установка среды программирования</li> <li>16.2   Присоединяйтесь к созданию книги</li> <li>16.3   Глоссарий</li> </ul>","path":["Глава 16. Приложение","Глава 16. &nbsp; Приложение"],"tags":[]},{"location":"chapter_appendix/contribution/","level":1,"title":"16.2   Присоединяйтесь к созданию книги","text":"<p>Возможности автора ограничены, поэтому в книге неизбежно могут встречаться упущения и ошибки. Просим отнестись к этому с пониманием. Если вы заметите опечатки, неработающие ссылки, пропуски в содержании, двусмысленные формулировки, неясные объяснения или неудачную структуру изложения, пожалуйста, помогите нам это исправить, чтобы читатели получили более качественный учебный ресурс.</p> <p>GitHub ID всех участников будут указаны на главных страницах репозитория книги, веб-версии и PDF-версии в знак благодарности за их бескорыстный вклад в сообщество открытого исходного кода.</p> <p>Сила открытого исходного кода</p> <p>Интервал между двумя тиражами бумажной книги обычно довольно велик, поэтому обновлять содержание очень неудобно.</p> <p>В этой же открытой книге цикл обновления содержания сокращается до нескольких дней, а иногда даже до нескольких часов.</p>","path":["Глава 16. Приложение","16.2 &nbsp; Присоединяйтесь к созданию книги"],"tags":[]},{"location":"chapter_appendix/contribution/#1","level":3,"title":"1.   Небольшие правки содержания","text":"<p>Как показано на рисунке 16-3, в правом верхнем углу каждой страницы есть \"значок редактирования\". Вы можете изменить текст или код следующим образом.</p> <ol> <li>Нажмите на \"значок редактирования\". Если появится сообщение \"You need to fork this repository\", согласитесь с этим действием.</li> <li>Измените содержимое исходного Markdown-файла, проверьте корректность правок и постарайтесь сохранить единый стиль оформления.</li> <li>Внизу страницы заполните описание изменений, затем нажмите кнопку \"Propose file change\". После перехода на следующую страницу нажмите кнопку \"Create pull request\", чтобы создать pull request.</li> </ol> <p></p> <p> Рисунок 16-3   Кнопка редактирования страницы </p> <p>Изображения нельзя изменить напрямую, поэтому проблему с ними нужно описывать через новый Issue или комментарий. Мы постараемся как можно быстрее перерисовать и заменить изображение.</p>","path":["Глава 16. 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Приложение","16.2 &nbsp; Присоединяйтесь к созданию книги"],"tags":[]},{"location":"chapter_appendix/contribution/#3-docker","level":3,"title":"3.   Развертывание Docker","text":"<p>В корневом каталоге <code>hello-algo</code> выполните следующий Docker-скрипт, после чего проект будет доступен по адресу <code>http://localhost:8000</code>:</p> <pre><code>docker-compose up -d\n</code></pre> <p>Удалить развертывание можно следующей командой:</p> <pre><code>docker-compose down\n</code></pre>","path":["Глава 16. Приложение","16.2 &nbsp; Присоединяйтесь к созданию книги"],"tags":[]},{"location":"chapter_appendix/installation/","level":1,"title":"16.1   Установка среды программирования","text":"","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/installation/#1611-ide","level":2,"title":"16.1.1   Установка IDE","text":"<p>В качестве локальной интегрированной среды разработки (IDE) рекомендуется использовать открытую и легковесную VS Code. Перейдите на официальный сайт VS Code, выберите версию для своей операционной системы и установите ее.</p> <p></p> <p> Рисунок 16-1   Загрузка VS Code с официального сайта </p> <p>VS Code обладает мощной экосистемой расширений и поддерживает запуск и отладку большинства языков программирования. Например, после установки расширения \"Python Extension Pack\" можно отлаживать код на Python. Процесс установки показан на рисунке 16-2.</p> <p></p> <p> Рисунок 16-2   Установка расширений VS Code </p>","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/installation/#1612","level":2,"title":"16.1.2   Установка языковой среды","text":"","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/installation/#1-python","level":3,"title":"1.   Среда Python","text":"<ol> <li>Загрузите и установите Miniconda3, требуется Python 3.10 или более новая версия.</li> <li>В магазине расширений VS Code найдите <code>python</code> и установите Python Extension Pack.</li> <li>(Необязательно) Введите в командной строке <code>pip install black</code>, чтобы установить инструмент форматирования кода.</li> </ol>","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/installation/#2-cc","level":3,"title":"2.   Среда C/C++","text":"<ol> <li>В Windows требуется установить MinGW (руководство по настройке); в macOS Clang уже установлен по умолчанию.</li> <li>В магазине расширений VS Code найдите <code>c++</code> и установите C/C++ Extension Pack.</li> <li>(Необязательно) Откройте страницу Settings, найдите параметр форматирования <code>Clang_format_fallback Style</code> и задайте значение <code>{ BasedOnStyle: Microsoft, BreakBeforeBraces: Attach }</code>.</li> </ol>","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/installation/#3-java","level":3,"title":"3.   Среда Java","text":"<ol> <li>Загрузите и установите OpenJDK (требуемая версия: &gt; JDK 9).</li> <li>В магазине расширений VS Code найдите <code>java</code> и установите Extension Pack for Java.</li> </ol>","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/installation/#4-c","level":3,"title":"4.   Среда C","text":"<ol> <li>Загрузите и установите .Net 8.0.</li> <li>В магазине расширений VS Code найдите <code>C# Dev Kit</code> и установите C# Dev Kit (руководство по настройке).</li> <li>Также можно использовать Visual Studio (руководство по установке).</li> </ol>","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/installation/#5-go","level":3,"title":"5.   Среда Go","text":"<ol> <li>Загрузите и установите go.</li> <li>В магазине расширений VS Code найдите <code>go</code> и установите Go.</li> <li>Нажмите <code>Ctrl + Shift + P</code>, чтобы открыть командную палитру, введите <code>go</code>, выберите <code>Go: Install/Update Tools</code>, отметьте все инструменты и установите их.</li> </ol>","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/installation/#6-swift","level":3,"title":"6.   Среда Swift","text":"<ol> <li>Загрузите и установите Swift.</li> <li>В магазине расширений VS Code найдите <code>swift</code> и установите Swift for Visual Studio Code.</li> </ol>","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/installation/#7-javascript","level":3,"title":"7.   Среда JavaScript","text":"<ol> <li>Загрузите и установите Node.js.</li> <li>(Необязательно) В магазине расширений VS Code найдите <code>Prettier</code> и установите инструмент форматирования кода.</li> </ol>","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/installation/#8-typescript","level":3,"title":"8.   Среда TypeScript","text":"<ol> <li>Выполните те же шаги, что и для среды JavaScript.</li> <li>Установите TypeScript Execute (tsx).</li> <li>В магазине расширений VS Code найдите <code>typescript</code> и установите Pretty TypeScript Errors.</li> </ol>","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/installation/#9-dart","level":3,"title":"9.   Среда Dart","text":"<ol> <li>Загрузите и установите Dart.</li> <li>В магазине расширений VS Code найдите <code>dart</code> и установите Dart.</li> </ol>","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/installation/#10-rust","level":3,"title":"10.   Среда Rust","text":"<ol> <li>Загрузите и установите Rust.</li> <li>В магазине расширений VS Code найдите <code>rust</code> и установите rust-analyzer.</li> </ol>","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/terminology/","level":1,"title":"16.3   Глоссарий","text":"<p>В таблице 16-1 перечислены важные термины, встречающиеся в книге. Обратите внимание на следующие моменты.</p> <ul> <li>Рекомендуем запомнить английские названия терминов, чтобы легче читать англоязычную литературу.</li> <li>В русской версии приводится единый рекомендуемый перевод каждого термина.</li> </ul> <p> Таблица 16-1   Важные термины по структурам данных и алгоритмам </p> English Русский algorithm алгоритм data structure структура данных code код file файл function функция method метод variable переменная asymptotic complexity analysis асимптотический анализ сложности time complexity временная сложность space complexity пространственная сложность loop цикл iteration итерация recursion рекурсия tail recursion хвостовая рекурсия recursion tree дерево рекурсии big-\\(O\\) notation нотация big-\\(O\\) asymptotic upper bound асимптотическая верхняя граница sign-magnitude прямой код 1’s complement обратный код 2’s complement дополнительный код array массив index индекс linked list связный список linked list node, list node узел связного списка head node головной узел tail node хвостовой узел list список dynamic array динамический массив hard disk жесткий диск random-access memory (RAM) оперативная память cache memory кеш-память cache miss промах кеша cache hit rate коэффициент попадания в кеш stack стек top of the stack вершина стека bottom of the stack основание стека queue очередь double-ended queue двусторонняя очередь front of the queue голова очереди rear of the queue хвост очереди hash table хеш-таблица hash set хеш-набор bucket корзина hash function хеш-функция hash collision хеш-коллизия load factor коэффициент заполнения separate chaining цепная адресация open addressing открытая адресация linear probing линейное зондирование lazy deletion ленивое удаление binary tree двоичное дерево tree node узел дерева left-child node левый дочерний узел right-child node правый дочерний узел parent node родительский узел left subtree левое поддерево right subtree правое поддерево root node корневой узел leaf node листовой узел edge ребро level уровень degree степень height высота depth глубина perfect binary tree идеальное двоичное дерево complete binary tree совершенное двоичное дерево full binary tree полное двоичное дерево balanced binary tree сбалансированное двоичное дерево binary search tree двоичное дерево поиска AVL tree АВЛ-дерево red-black tree красно-черное дерево level-order traversal обход по уровням breadth-first traversal обход в ширину depth-first traversal обход в глубину binary search tree двоичное дерево поиска balanced binary search tree сбалансированное двоичное дерево поиска balance factor фактор баланса heap куча max heap максимальная куча min heap минимальная куча priority queue приоритетная очередь heapify упорядочивание кучи top-\\(k\\) problem поиск \\(k\\) наибольших элементов graph граф vertex вершина undirected graph неориентированный граф directed graph ориентированный граф connected graph связный граф disconnected graph несвязный граф weighted graph взвешенный граф adjacency смежность path путь in-degree входящая степень out-degree исходящая степень adjacency matrix матрица смежности adjacency list список смежности breadth-first search поиск в ширину depth-first search поиск в глубину binary search двоичный поиск searching algorithm алгоритм поиска sorting algorithm алгоритм сортировки selection sort сортировка выбором bubble sort сортировка пузырьком insertion sort сортировка вставкой quick sort быстрая сортировка merge sort сортировка слиянием heap sort пирамидальная сортировка bucket sort блочная сортировка counting sort сортировка подсчетом radix sort поразрядная сортировка divide and conquer разделяй и властвуй hanota problem задача о Ханойской башне backtracking algorithm алгоритм поиска с возвратом constraint ограничение solution решение state состояние pruning отсечение permutations problem задача о перестановках subset-sum problem задача о сумме подмножеств \\(n\\)-queens problem задача о \\(n\\) ферзях dynamic programming динамическое программирование initial state начальное состояние state-transition equation уравнение перехода состояния knapsack problem задача о рюкзаке edit distance problem задача о расстоянии редактирования greedy algorithm жадный алгоритм","path":["Глава 16. Приложение","16.3 &nbsp; Глоссарий"],"tags":[]},{"location":"chapter_array_and_linkedlist/","level":1,"title":"Глава 4.   Массивы и списки","text":"<p>Abstract</p> <p>Мир структур данных напоминает прочную кирпичную стену.</p> <p>Кирпичи массива уложены ровно и плотно прилегают друг к другу. Кирпичи связного списка разбросаны в разных местах, а соединяющие их лозы свободно тянутся между щелями.</p>","path":["Глава 4. Массив и связный список","Глава 4. &nbsp; Массивы и списки"],"tags":[]},{"location":"chapter_array_and_linkedlist/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>4.1   Массив</li> <li>4.2   Связный список</li> <li>4.3   Список</li> <li>4.4   Память и кеш *</li> <li>4.5   Резюме</li> </ul>","path":["Глава 4. Массив и связный список","Глава 4. &nbsp; Массивы и списки"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/","level":1,"title":"4.1   Массив","text":"<p>Массив (array) - это линейная структура данных, которая хранит элементы одного типа в непрерывной области памяти. Положение элемента в массиве называется его индексом (index). На рисунке 4-1 показаны основные понятия, связанные с массивом, и способ его хранения.</p> <p></p> <p> Рисунок 4-1   Определение массива и способ хранения </p>","path":["Глава 4. Массив и связный список","4.1 &nbsp; Массив"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#411","level":2,"title":"4.1.1   Основные операции с массивом","text":"","path":["Глава 4. Массив и связный список","4.1 &nbsp; Массив"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#1","level":3,"title":"1.   Инициализация массива","text":"<p>В зависимости от задачи мы можем выбрать один из двух способов инициализации массива: без начальных значений или с заданными начальными значениями. Если начальные значения не указаны, большинство языков программирования инициализируют элементы массива значением \\(0\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code># Инициализация массива\narr: list[int] = [0] * 5  # [ 0, 0, 0, 0, 0 ]\nnums: list[int] = [1, 3, 2, 5, 4]\n</code></pre> array.cpp<pre><code>/* Инициализация массива */\n// Хранится в стеке\nint arr[5];\nint nums[5] = { 1, 3, 2, 5, 4 };\n// Хранится в куче (требуется ручное освобождение памяти)\nint* arr1 = new int[5];\nint* nums1 = new int[5] { 1, 3, 2, 5, 4 };\n</code></pre> array.java<pre><code>/* Инициализация массива */\nint[] arr = new int[5]; // { 0, 0, 0, 0, 0 }\nint[] nums = { 1, 3, 2, 5, 4 };\n</code></pre> array.cs<pre><code>/* Инициализация массива */\nint[] arr = new int[5]; // [ 0, 0, 0, 0, 0 ]\nint[] nums = [1, 3, 2, 5, 4];\n</code></pre> array.go<pre><code>/* Инициализация массива */\nvar arr [5]int\n// В Go указание длины ([5]int) создает массив, а отсутствие длины ([]int) - срез\n// Поскольку длина массива в Go определяется на этапе компиляции, для задания длины можно использовать только константы\n// Чтобы упростить реализацию метода extend(), ниже будем рассматривать срезы (Slice) как массивы (Array)\nnums := []int{1, 3, 2, 5, 4}\n</code></pre> array.swift<pre><code>/* Инициализация массива */\nlet arr = Array(repeating: 0, count: 5) // [0, 0, 0, 0, 0]\nlet nums = [1, 3, 2, 5, 4]\n</code></pre> array.js<pre><code>/* Инициализация массива */\nvar arr = new Array(5).fill(0);\nvar nums = [1, 3, 2, 5, 4];\n</code></pre> array.ts<pre><code>/* Инициализация массива */\nlet arr: number[] = new Array(5).fill(0);\nlet nums: number[] = [1, 3, 2, 5, 4];\n</code></pre> array.dart<pre><code>/* Инициализация массива */\nList&lt;int&gt; arr = List.filled(5, 0); // [0, 0, 0, 0, 0]\nList&lt;int&gt; nums = [1, 3, 2, 5, 4];\n</code></pre> array.rs<pre><code>/* Инициализация массива */\nlet arr: [i32; 5] = [0; 5]; // [0, 0, 0, 0, 0]\nlet slice: &amp;[i32] = &amp;[0; 5];\n// В Rust указание длины ([i32; 5]) создает массив, а отсутствие длины (&amp;[i32]) - срез\n// Поскольку длина массива в Rust определяется на этапе компиляции, для задания длины можно использовать только константы\n// Vector в Rust обычно используется как динамический массив\n// Чтобы упростить реализацию метода extend(), ниже будем рассматривать vector как массив (array)\nlet nums: Vec&lt;i32&gt; = vec![1, 3, 2, 5, 4];\n</code></pre> array.c<pre><code>/* Инициализация массива */\nint arr[5] = { 0 }; // { 0, 0, 0, 0, 0 }\nint nums[5] = { 1, 3, 2, 5, 4 };\n</code></pre> array.kt<pre><code>/* Инициализация массива */\nvar arr = IntArray(5) // { 0, 0, 0, 0, 0 }\nvar nums = intArrayOf(1, 3, 2, 5, 4)\n</code></pre> array.rb<pre><code># Инициализация массива\narr = Array.new(5, 0)\nnums = [1, 3, 2, 5, 4]\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D0%BC%D0%B0%D1%81%D1%81%D0%B8%D0%B2%0Aarr%20%3D%20%5B0%5D%20%2A%205%20%20%23%20%5B%200%2C%200%2C%200%2C%200%2C%200%20%5D%0Anums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D&amp;cumulative=false&amp;curInstr=0&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 4. Массив и связный список","4.1 &nbsp; Массив"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#2","level":3,"title":"2.   Доступ к элементам","text":"<p>Элементы массива хранятся в непрерывной области памяти, а это означает, что вычислить адрес любого элемента очень просто. Зная адрес массива в памяти (то есть адрес первого элемента) и индекс некоторого элемента, мы можем по формуле с рисунка ниже вычислить адрес этого элемента и напрямую обратиться к нему.</p> <p></p> <p> Рисунок 4-2   Вычисление адреса элемента массива </p> <p>Если посмотреть на рисунок 4-2, можно заметить, что индекс первого элемента массива равен \\(0\\) , и это кажется не слишком интуитивным, ведь естественнее было бы начинать счет с \\(1\\) . Однако с точки зрения формулы адресации индекс по сути является смещением относительно адреса памяти. Смещение первого элемента равно \\(0\\) , поэтому индекс \\(0\\) вполне логичен.</p> <p>Доступ к элементам массива очень эффективен: любой элемент массива можно получить за \\(O(1)\\) времени.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code>def random_access(nums: list[int]) -&gt; int:\n    \"\"\"Случайный доступ к элементу\"\"\"\n    # Случайным образом выбрать число из интервала [0, len(nums)-1]\n    random_index = random.randint(0, len(nums) - 1)\n    # Получить и вернуть случайный элемент\n    random_num = nums[random_index]\n    return random_num\n</code></pre> array.cpp<pre><code>/* Случайный доступ к элементу */\nint randomAccess(int *nums, int size) {\n    // Случайным образом выбрать число из интервала [0, size)\n    int randomIndex = rand() % size;\n    // Получить и вернуть случайный элемент\n    int randomNum = nums[randomIndex];\n    return randomNum;\n}\n</code></pre> array.java<pre><code>/* Случайный доступ к элементу */\nint randomAccess(int[] nums) {\n    // Случайным образом выбрать число из интервала [0, nums.length)\n    int randomIndex = ThreadLocalRandom.current().nextInt(0, nums.length);\n    // Получить и вернуть случайный элемент\n    int randomNum = nums[randomIndex];\n    return randomNum;\n}\n</code></pre> array.cs<pre><code>/* Случайный доступ к элементу */\nint RandomAccess(int[] nums) {\n    Random random = new();\n    // Случайным образом выбрать число из интервала [0, nums.Length)\n    int randomIndex = random.Next(nums.Length);\n    // Получить и вернуть случайный элемент\n    int randomNum = nums[randomIndex];\n    return randomNum;\n}\n</code></pre> array.go<pre><code>/* Случайный доступ к элементу */\nfunc randomAccess(nums []int) (randomNum int) {\n    // Случайным образом выбрать число из интервала [0, nums.length)\n    randomIndex := rand.Intn(len(nums))\n    // Получить и вернуть случайный элемент\n    randomNum = nums[randomIndex]\n    return\n}\n</code></pre> array.swift<pre><code>/* Случайный доступ к элементу */\nfunc randomAccess(nums: [Int]) -&gt; Int {\n    // Случайным образом выбрать число из интервала [0, nums.count)\n    let randomIndex = nums.indices.randomElement()!\n    // Получить и вернуть случайный элемент\n    let randomNum = nums[randomIndex]\n    return randomNum\n}\n</code></pre> array.js<pre><code>/* Случайный доступ к элементу */\nfunction randomAccess(nums) {\n    // Случайным образом выбрать число из интервала [0, nums.length)\n    const random_index = Math.floor(Math.random() * nums.length);\n    // Получить и вернуть случайный элемент\n    const random_num = nums[random_index];\n    return random_num;\n}\n</code></pre> array.ts<pre><code>/* Случайный доступ к элементу */\nfunction randomAccess(nums: number[]): number {\n    // Случайным образом выбрать число из интервала [0, nums.length)\n    const random_index = Math.floor(Math.random() * nums.length);\n    // Получить и вернуть случайный элемент\n    const random_num = nums[random_index];\n    return random_num;\n}\n</code></pre> array.dart<pre><code>/* Случайный доступ к элементу */\nint randomAccess(List&lt;int&gt; nums) {\n  // Случайным образом выбрать число из интервала [0, nums.length)\n  int randomIndex = Random().nextInt(nums.length);\n  // Получить и вернуть случайный элемент\n  int randomNum = nums[randomIndex];\n  return randomNum;\n}\n</code></pre> array.rs<pre><code>/* Случайный доступ к элементу */\nfn random_access(nums: &amp;[i32]) -&gt; i32 {\n    // Случайным образом выбрать число из интервала [0, nums.len())\n    let random_index = rand::thread_rng().gen_range(0..nums.len());\n    // Получить и вернуть случайный элемент\n    let random_num = nums[random_index];\n    random_num\n}\n</code></pre> array.c<pre><code>/* Случайный доступ к элементу */\nint randomAccess(int *nums, int size) {\n    // Случайным образом выбрать число из интервала [0, size)\n    int randomIndex = rand() % size;\n    // Получить и вернуть случайный элемент\n    int randomNum = nums[randomIndex];\n    return randomNum;\n}\n</code></pre> array.kt<pre><code>/* Случайный доступ к элементу */\nfun randomAccess(nums: IntArray): Int {\n    // Случайным образом выбрать число из интервала [0, nums.size)\n    val randomIndex = ThreadLocalRandom.current().nextInt(0, nums.size)\n    // Получить и вернуть случайный элемент\n    val randomNum = nums[randomIndex]\n    return randomNum\n}\n</code></pre> array.rb<pre><code>### Случайный доступ к элементу ###\ndef random_access(nums)\n  # Случайным образом выбрать число из интервала [0, nums.length)\n  random_index = Random.rand(0...nums.length)\n\n  # Получить и вернуть случайный элемент\n  nums[random_index]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 4. Массив и связный список","4.1 &nbsp; Массив"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#3","level":3,"title":"3.   Вставка элемента","text":"<p>Элементы массива в памяти расположены \"вплотную\" друг к другу, и между ними нет места для размещения новых данных. Как показано на рисунке 4-3, если мы хотим вставить элемент в середину массива, то все элементы после этой позиции нужно сдвинуть на одну позицию вправо, а затем записать новое значение в освободившийся индекс.</p> <p></p> <p> Рисунок 4-3   Пример вставки элемента в массив </p> <p>Стоит отметить, что длина массива фиксирована, поэтому вставка нового элемента неизбежно приведет к \"потере\" элемента на конце массива. Решение этой проблемы мы оставим для обсуждения в разделе о \"списках\".</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code>def insert(nums: list[int], num: int, index: int):\n    \"\"\"Вставить элемент num по индексу index в массив\"\"\"\n    # Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n    for i in range(len(nums) - 1, index, -1):\n        nums[i] = nums[i - 1]\n    # Присвоить num элементу по индексу index\n    nums[index] = num\n</code></pre> array.cpp<pre><code>/* Вставить элемент num по индексу index в массив */\nvoid insert(int *nums, int size, int num, int index) {\n    // Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n    for (int i = size - 1; i &gt; index; i--) {\n        nums[i] = nums[i - 1];\n    }\n    // Присвоить num элементу по индексу index\n    nums[index] = num;\n}\n</code></pre> array.java<pre><code>/* Вставить элемент num по индексу index в массив */\nvoid insert(int[] nums, int num, int index) {\n    // Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n    for (int i = nums.length - 1; i &gt; index; i--) {\n        nums[i] = nums[i - 1];\n    }\n    // Присвоить num элементу по индексу index\n    nums[index] = num;\n}\n</code></pre> array.cs<pre><code>/* Вставить элемент num по индексу index в массив */\nvoid Insert(int[] nums, int num, int index) {\n    // Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n    for (int i = nums.Length - 1; i &gt; index; i--) {\n        nums[i] = nums[i - 1];\n    }\n    // Присвоить num элементу по индексу index\n    nums[index] = num;\n}\n</code></pre> array.go<pre><code>/* Вставить элемент num по индексу index в массив */\nfunc insert(nums []int, num int, index int) {\n    // Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n    for i := len(nums) - 1; i &gt; index; i-- {\n        nums[i] = nums[i-1]\n    }\n    // Присвоить num элементу по индексу index\n    nums[index] = num\n}\n</code></pre> array.swift<pre><code>/* Вставить элемент num по индексу index в массив */\nfunc insert(nums: inout [Int], num: Int, index: Int) {\n    // Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n    for i in nums.indices.dropFirst(index).reversed() {\n        nums[i] = nums[i - 1]\n    }\n    // Присвоить num элементу по индексу index\n    nums[index] = num\n}\n</code></pre> array.js<pre><code>/* Вставить элемент num по индексу index в массив */\nfunction insert(nums, num, index) {\n    // Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n    for (let i = nums.length - 1; i &gt; index; i--) {\n        nums[i] = nums[i - 1];\n    }\n    // Присвоить num элементу по индексу index\n    nums[index] = num;\n}\n</code></pre> array.ts<pre><code>/* Вставить элемент num по индексу index в массив */\nfunction insert(nums: number[], num: number, index: number): void {\n    // Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n    for (let i = nums.length - 1; i &gt; index; i--) {\n        nums[i] = nums[i - 1];\n    }\n    // Присвоить num элементу по индексу index\n    nums[index] = num;\n}\n</code></pre> array.dart<pre><code>/* Вставить элемент _num по индексу index в массив */\nvoid insert(List&lt;int&gt; nums, int _num, int index) {\n  // Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n  for (var i = nums.length - 1; i &gt; index; i--) {\n    nums[i] = nums[i - 1];\n  }\n  // Присвоить _num элементу по индексу index\n  nums[index] = _num;\n}\n</code></pre> array.rs<pre><code>/* Вставить элемент num по индексу index в массив */\nfn insert(nums: &amp;mut [i32], num: i32, index: usize) {\n    // Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n    for i in (index + 1..nums.len()).rev() {\n        nums[i] = nums[i - 1];\n    }\n    // Присвоить num элементу по индексу index\n    nums[index] = num;\n}\n</code></pre> array.c<pre><code>/* Вставить элемент num по индексу index в массив */\nvoid insert(int *nums, int size, int num, int index) {\n    // Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n    for (int i = size - 1; i &gt; index; i--) {\n        nums[i] = nums[i - 1];\n    }\n    // Присвоить num элементу по индексу index\n    nums[index] = num;\n}\n</code></pre> array.kt<pre><code>/* Вставить элемент num по индексу index в массив */\nfun insert(nums: IntArray, num: Int, index: Int) {\n    // Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n    for (i in nums.size - 1 downTo index + 1) {\n        nums[i] = nums[i - 1]\n    }\n    // Присвоить num элементу по индексу index\n    nums[index] = num\n}\n</code></pre> array.rb<pre><code>### Вставка элемента num по индексу index в массив ###\ndef insert(nums, num, index)\n  # Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n  for i in (nums.length - 1).downto(index + 1)\n    nums[i] = nums[i - 1]\n  end\n\n  # Присвоить num элементу по индексу index\n  nums[index] = num\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 4. Массив и связный список","4.1 &nbsp; Массив"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#4","level":3,"title":"4.   Удаление элемента","text":"<p>Аналогично, как показано на рисунке 4-4, если нужно удалить элемент по индексу \\(i\\) , то все элементы после индекса \\(i\\) необходимо сдвинуть на одну позицию влево.</p> <p></p> <p> Рисунок 4-4   Пример удаления элемента из массива </p> <p>Обрати внимание: после удаления исходный последний элемент становится \"бессмысленным\", поэтому специально изменять его не требуется.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code>def remove(nums: list[int], index: int):\n    \"\"\"Удалить элемент по индексу index\"\"\"\n    # Сдвинуть все элементы после индекса index на одну позицию вперед\n    for i in range(index, len(nums) - 1):\n        nums[i] = nums[i + 1]\n</code></pre> array.cpp<pre><code>/* Удалить элемент по индексу index */\nvoid remove(int *nums, int size, int index) {\n    // Сдвинуть все элементы после индекса index на одну позицию вперед\n    for (int i = index; i &lt; size - 1; i++) {\n        nums[i] = nums[i + 1];\n    }\n}\n</code></pre> array.java<pre><code>/* Удалить элемент по индексу index */\nvoid remove(int[] nums, int index) {\n    // Сдвинуть все элементы после индекса index на одну позицию вперед\n    for (int i = index; i &lt; nums.length - 1; i++) {\n        nums[i] = nums[i + 1];\n    }\n}\n</code></pre> array.cs<pre><code>/* Удалить элемент по индексу index */\nvoid Remove(int[] nums, int index) {\n    // Сдвинуть все элементы после индекса index на одну позицию вперед\n    for (int i = index; i &lt; nums.Length - 1; i++) {\n        nums[i] = nums[i + 1];\n    }\n}\n</code></pre> array.go<pre><code>/* Удалить элемент по индексу index */\nfunc remove(nums []int, index int) {\n    // Сдвинуть все элементы после индекса index на одну позицию вперед\n    for i := index; i &lt; len(nums)-1; i++ {\n        nums[i] = nums[i+1]\n    }\n}\n</code></pre> array.swift<pre><code>/* Удалить элемент по индексу index */\nfunc remove(nums: inout [Int], index: Int) {\n    // Сдвинуть все элементы после индекса index на одну позицию вперед\n    for i in nums.indices.dropFirst(index).dropLast() {\n        nums[i] = nums[i + 1]\n    }\n}\n</code></pre> array.js<pre><code>/* Удалить элемент по индексу index */\nfunction remove(nums, index) {\n    // Сдвинуть все элементы после индекса index на одну позицию вперед\n    for (let i = index; i &lt; nums.length - 1; i++) {\n        nums[i] = nums[i + 1];\n    }\n}\n</code></pre> array.ts<pre><code>/* Удалить элемент по индексу index */\nfunction remove(nums: number[], index: number): void {\n    // Сдвинуть все элементы после индекса index на одну позицию вперед\n    for (let i = index; i &lt; nums.length - 1; i++) {\n        nums[i] = nums[i + 1];\n    }\n}\n</code></pre> array.dart<pre><code>/* Удалить элемент по индексу index */\nvoid remove(List&lt;int&gt; nums, int index) {\n  // Сдвинуть все элементы после индекса index на одну позицию вперед\n  for (var i = index; i &lt; nums.length - 1; i++) {\n    nums[i] = nums[i + 1];\n  }\n}\n</code></pre> array.rs<pre><code>/* Удалить элемент по индексу index */\nfn remove(nums: &amp;mut [i32], index: usize) {\n    // Сдвинуть все элементы после индекса index на одну позицию вперед\n    for i in index..nums.len() - 1 {\n        nums[i] = nums[i + 1];\n    }\n}\n</code></pre> array.c<pre><code>/* Удалить элемент по индексу index */\n// Внимание: stdio.h уже использует ключевое слово remove\nvoid removeItem(int *nums, int size, int index) {\n    // Сдвинуть все элементы после индекса index на одну позицию вперед\n    for (int i = index; i &lt; size - 1; i++) {\n        nums[i] = nums[i + 1];\n    }\n}\n</code></pre> array.kt<pre><code>/* Удалить элемент по индексу index */\nfun remove(nums: IntArray, index: Int) {\n    // Сдвинуть все элементы после индекса index на одну позицию вперед\n    for (i in index..&lt;nums.size - 1) {\n        nums[i] = nums[i + 1]\n    }\n}\n</code></pre> array.rb<pre><code>### Удаление элемента по индексу index ###\ndef remove(nums, index)\n  # Сдвинуть все элементы после индекса index на одну позицию вперед\n  for i in index...(nums.length - 1)\n    nums[i] = nums[i + 1]\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>В целом операции вставки и удаления в массиве имеют следующие недостатки.</p> <ul> <li>Высокая временная сложность: средняя временная сложность и вставки, и удаления равна \\(O(n)\\) , где \\(n\\) - длина массива.</li> <li>Потеря элементов: поскольку длина массива неизменяема, после вставки элементы, выходящие за пределы длины массива, будут потеряны.</li> <li>Потери памяти: можно заранее инициализировать более длинный массив и использовать только его переднюю часть; тогда \"теряемые\" при вставке элементы на конце не будут нести смысла, но такой подход приводит к лишнему расходу памяти.</li> </ul>","path":["Глава 4. Массив и связный список","4.1 &nbsp; Массив"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#5","level":3,"title":"5.   Обход массива","text":"<p>В большинстве языков программирования массив можно обходить как по индексу, так и напрямую перебирая каждый элемент:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code>def traverse(nums: list[int]):\n    \"\"\"Обход массива\"\"\"\n    count = 0\n    # Обход массива по индексам\n    for i in range(len(nums)):\n        count += nums[i]\n    # Непосредственно обходить элементы массива\n    for num in nums:\n        count += num\n    # Одновременно обходить индексы и элементы данных\n    for i, num in enumerate(nums):\n        count += nums[i]\n        count += num\n</code></pre> array.cpp<pre><code>/* Обход массива */\nvoid traverse(int *nums, int size) {\n    int count = 0;\n    // Обход массива по индексам\n    for (int i = 0; i &lt; size; i++) {\n        count += nums[i];\n    }\n}\n</code></pre> array.java<pre><code>/* Обход массива */\nvoid traverse(int[] nums) {\n    int count = 0;\n    // Обход массива по индексам\n    for (int i = 0; i &lt; nums.length; i++) {\n        count += nums[i];\n    }\n    // Непосредственно обходить элементы массива\n    for (int num : nums) {\n        count += num;\n    }\n}\n</code></pre> array.cs<pre><code>/* Обход массива */\nvoid Traverse(int[] nums) {\n    int count = 0;\n    // Обход массива по индексам\n    for (int i = 0; i &lt; nums.Length; i++) {\n        count += nums[i];\n    }\n    // Непосредственно обходить элементы массива\n    foreach (int num in nums) {\n        count += num;\n    }\n}\n</code></pre> array.go<pre><code>/* Обход массива */\nfunc traverse(nums []int) {\n    count := 0\n    // Обход массива по индексам\n    for i := 0; i &lt; len(nums); i++ {\n        count += nums[i]\n    }\n    count = 0\n    // Непосредственно обходить элементы массива\n    for _, num := range nums {\n        count += num\n    }\n    // Одновременно обходить индексы и элементы данных\n    for i, num := range nums {\n        count += nums[i]\n        count += num\n    }\n}\n</code></pre> array.swift<pre><code>/* Обход массива */\nfunc traverse(nums: [Int]) {\n    var count = 0\n    // Обход массива по индексам\n    for i in nums.indices {\n        count += nums[i]\n    }\n    // Непосредственно обходить элементы массива\n    for num in nums {\n        count += num\n    }\n    // Одновременно обходить индексы и элементы данных\n    for (i, num) in nums.enumerated() {\n        count += nums[i]\n        count += num\n    }\n}\n</code></pre> array.js<pre><code>/* Обход массива */\nfunction traverse(nums) {\n    let count = 0;\n    // Обход массива по индексам\n    for (let i = 0; i &lt; nums.length; i++) {\n        count += nums[i];\n    }\n    // Непосредственно обходить элементы массива\n    for (const num of nums) {\n        count += num;\n    }\n}\n</code></pre> array.ts<pre><code>/* Обход массива */\nfunction traverse(nums: number[]): void {\n    let count = 0;\n    // Обход массива по индексам\n    for (let i = 0; i &lt; nums.length; i++) {\n        count += nums[i];\n    }\n    // Непосредственно обходить элементы массива\n    for (const num of nums) {\n        count += num;\n    }\n}\n</code></pre> array.dart<pre><code>/* Перебрать элементы массива */\nvoid traverse(List&lt;int&gt; nums) {\n  int count = 0;\n  // Обход массива по индексам\n  for (var i = 0; i &lt; nums.length; i++) {\n    count += nums[i];\n  }\n  // Непосредственно обходить элементы массива\n  for (int _num in nums) {\n    count += _num;\n  }\n  // Перебрать массив методом forEach\n  nums.forEach((_num) {\n    count += _num;\n  });\n}\n</code></pre> array.rs<pre><code>/* Обход массива */\nfn traverse(nums: &amp;[i32]) {\n    let mut _count = 0;\n    // Обход массива по индексам\n    for i in 0..nums.len() {\n        _count += nums[i];\n    }\n    // Непосредственно обходить элементы массива\n    _count = 0;\n    for &amp;num in nums {\n        _count += num;\n    }\n}\n</code></pre> array.c<pre><code>/* Обход массива */\nvoid traverse(int *nums, int size) {\n    int count = 0;\n    // Обход массива по индексам\n    for (int i = 0; i &lt; size; i++) {\n        count += nums[i];\n    }\n}\n</code></pre> array.kt<pre><code>/* Обход массива */\nfun traverse(nums: IntArray) {\n    var count = 0\n    // Обход массива по индексам\n    for (i in nums.indices) {\n        count += nums[i]\n    }\n    // Непосредственно обходить элементы массива\n    for (j in nums) {\n        count += j\n    }\n}\n</code></pre> array.rb<pre><code>### Обход массива ###\ndef traverse(nums)\n  count = 0\n\n  # Обход массива по индексам\n  for i in 0...nums.length\n    count += nums[i]\n  end\n\n  # Непосредственно обходить элементы массива\n  for num in nums\n    count += num\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 4. Массив и связный список","4.1 &nbsp; Массив"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#6","level":3,"title":"6.   Поиск элемента","text":"<p>Чтобы найти заданный элемент в массиве, нужно пройти по массиву и на каждой итерации проверять, совпадает ли значение; если совпадает, вернуть соответствующий индекс.</p> <p>Поскольку массив - это линейная структура данных, такая операция поиска называется \"линейным поиском\".</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code>def find(nums: list[int], target: int) -&gt; int:\n    \"\"\"Найти заданный элемент в массиве\"\"\"\n    for i in range(len(nums)):\n        if nums[i] == target:\n            return i\n    return -1\n</code></pre> array.cpp<pre><code>/* Найти заданный элемент в массиве */\nint find(int *nums, int size, int target) {\n    for (int i = 0; i &lt; size; i++) {\n        if (nums[i] == target)\n            return i;\n    }\n    return -1;\n}\n</code></pre> array.java<pre><code>/* Найти заданный элемент в массиве */\nint find(int[] nums, int target) {\n    for (int i = 0; i &lt; nums.length; i++) {\n        if (nums[i] == target)\n            return i;\n    }\n    return -1;\n}\n</code></pre> array.cs<pre><code>/* Найти заданный элемент в массиве */\nint Find(int[] nums, int target) {\n    for (int i = 0; i &lt; nums.Length; i++) {\n        if (nums[i] == target)\n            return i;\n    }\n    return -1;\n}\n</code></pre> array.go<pre><code>/* Найти заданный элемент в массиве */\nfunc find(nums []int, target int) (index int) {\n    index = -1\n    for i := 0; i &lt; len(nums); i++ {\n        if nums[i] == target {\n            index = i\n            break\n        }\n    }\n    return\n}\n</code></pre> array.swift<pre><code>/* Найти заданный элемент в массиве */\nfunc find(nums: [Int], target: Int) -&gt; Int {\n    for i in nums.indices {\n        if nums[i] == target {\n            return i\n        }\n    }\n    return -1\n}\n</code></pre> array.js<pre><code>/* Найти заданный элемент в массиве */\nfunction find(nums, target) {\n    for (let i = 0; i &lt; nums.length; i++) {\n        if (nums[i] === target) return i;\n    }\n    return -1;\n}\n</code></pre> array.ts<pre><code>/* Найти заданный элемент в массиве */\nfunction find(nums: number[], target: number): number {\n    for (let i = 0; i &lt; nums.length; i++) {\n        if (nums[i] === target) {\n            return i;\n        }\n    }\n    return -1;\n}\n</code></pre> array.dart<pre><code>/* Найти заданный элемент в массиве */\nint find(List&lt;int&gt; nums, int target) {\n  for (var i = 0; i &lt; nums.length; i++) {\n    if (nums[i] == target) return i;\n  }\n  return -1;\n}\n</code></pre> array.rs<pre><code>/* Найти заданный элемент в массиве */\nfn find(nums: &amp;[i32], target: i32) -&gt; Option&lt;usize&gt; {\n    for i in 0..nums.len() {\n        if nums[i] == target {\n            return Some(i);\n        }\n    }\n    None\n}\n</code></pre> array.c<pre><code>/* Найти заданный элемент в массиве */\nint find(int *nums, int size, int target) {\n    for (int i = 0; i &lt; size; i++) {\n        if (nums[i] == target)\n            return i;\n    }\n    return -1;\n}\n</code></pre> array.kt<pre><code>/* Найти заданный элемент в массиве */\nfun find(nums: IntArray, target: Int): Int {\n    for (i in nums.indices) {\n        if (nums[i] == target)\n            return i\n    }\n    return -1\n}\n</code></pre> array.rb<pre><code>### Поиск заданного элемента в массиве ###\ndef find(nums, target)\n  for i in 0...nums.length\n    return i if nums[i] == target\n  end\n\n  -1\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 4. Массив и связный список","4.1 &nbsp; Массив"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#7","level":3,"title":"7.   Расширение массива","text":"<p>В сложной системной среде программа не может гарантировать, что память сразу после массива доступна, поэтому безопасно расширить емкость массива невозможно. Поэтому в большинстве языков программирования длина массива неизменяема.</p> <p>Если мы хотим расширить массив, нужно заново создать больший массив и затем по одному скопировать в него элементы исходного массива. Это операция с временной сложностью \\(O(n)\\) , и при больших массивах она очень затратна. Соответствующий код показан ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code>def extend(nums: list[int], enlarge: int) -&gt; list[int]:\n    \"\"\"Увеличить длину массива\"\"\"\n    # Инициализировать массив увеличенной длины\n    res = [0] * (len(nums) + enlarge)\n    # Скопировать все элементы исходного массива в новый массив\n    for i in range(len(nums)):\n        res[i] = nums[i]\n    # Вернуть новый массив после расширения\n    return res\n</code></pre> array.cpp<pre><code>/* Увеличить длину массива */\nint *extend(int *nums, int size, int enlarge) {\n    // Инициализировать массив увеличенной длины\n    int *res = new int[size + enlarge];\n    // Скопировать все элементы исходного массива в новый массив\n    for (int i = 0; i &lt; size; i++) {\n        res[i] = nums[i];\n    }\n    // Освободить память\n    delete[] nums;\n    // Вернуть новый массив после расширения\n    return res;\n}\n</code></pre> array.java<pre><code>/* Увеличить длину массива */\nint[] extend(int[] nums, int enlarge) {\n    // Инициализировать массив увеличенной длины\n    int[] res = new int[nums.length + enlarge];\n    // Скопировать все элементы исходного массива в новый массив\n    for (int i = 0; i &lt; nums.length; i++) {\n        res[i] = nums[i];\n    }\n    // Вернуть новый массив после расширения\n    return res;\n}\n</code></pre> array.cs<pre><code>/* Увеличить длину массива */\nint[] Extend(int[] nums, int enlarge) {\n    // Инициализировать массив увеличенной длины\n    int[] res = new int[nums.Length + enlarge];\n    // Скопировать все элементы исходного массива в новый массив\n    for (int i = 0; i &lt; nums.Length; i++) {\n        res[i] = nums[i];\n    }\n    // Вернуть новый массив после расширения\n    return res;\n}\n</code></pre> array.go<pre><code>/* Увеличить длину массива */\nfunc extend(nums []int, enlarge int) []int {\n    // Инициализировать массив увеличенной длины\n    res := make([]int, len(nums)+enlarge)\n    // Скопировать все элементы исходного массива в новый массив\n    for i, num := range nums {\n        res[i] = num\n    }\n    // Вернуть новый массив после расширения\n    return res\n}\n</code></pre> array.swift<pre><code>/* Увеличить длину массива */\nfunc extend(nums: [Int], enlarge: Int) -&gt; [Int] {\n    // Инициализировать массив увеличенной длины\n    var res = Array(repeating: 0, count: nums.count + enlarge)\n    // Скопировать все элементы исходного массива в новый массив\n    for i in nums.indices {\n        res[i] = nums[i]\n    }\n    // Вернуть новый массив после расширения\n    return res\n}\n</code></pre> array.js<pre><code>/* Увеличить длину массива */\n// Обратите внимание: Array в JavaScript — это динамический массив, его можно расширять напрямую\n// Для удобства обучения в этой функции Array рассматривается как массив неизменяемой длины\nfunction extend(nums, enlarge) {\n    // Инициализировать массив увеличенной длины\n    const res = new Array(nums.length + enlarge).fill(0);\n    // Скопировать все элементы исходного массива в новый массив\n    for (let i = 0; i &lt; nums.length; i++) {\n        res[i] = nums[i];\n    }\n    // Вернуть новый массив после расширения\n    return res;\n}\n</code></pre> array.ts<pre><code>/* Увеличить длину массива */\n// Обратите внимание: Array в TypeScript — это динамический массив, его можно расширять напрямую\n// Для удобства обучения в этой функции Array рассматривается как массив неизменяемой длины\nfunction extend(nums: number[], enlarge: number): number[] {\n    // Инициализировать массив увеличенной длины\n    const res = new Array(nums.length + enlarge).fill(0);\n    // Скопировать все элементы исходного массива в новый массив\n    for (let i = 0; i &lt; nums.length; i++) {\n        res[i] = nums[i];\n    }\n    // Вернуть новый массив после расширения\n    return res;\n}\n</code></pre> array.dart<pre><code>/* Увеличить длину массива */\nList&lt;int&gt; extend(List&lt;int&gt; nums, int enlarge) {\n  // Инициализировать массив увеличенной длины\n  List&lt;int&gt; res = List.filled(nums.length + enlarge, 0);\n  // Скопировать все элементы исходного массива в новый массив\n  for (var i = 0; i &lt; nums.length; i++) {\n    res[i] = nums[i];\n  }\n  // Вернуть новый массив после расширения\n  return res;\n}\n</code></pre> array.rs<pre><code>/* Увеличить длину массива */\nfn extend(nums: &amp;[i32], enlarge: usize) -&gt; Vec&lt;i32&gt; {\n    // Инициализировать массив увеличенной длины\n    let mut res: Vec&lt;i32&gt; = vec![0; nums.len() + enlarge];\n    // Скопировать все элементы исходного массива в новый\n    res[0..nums.len()].copy_from_slice(nums);\n\n    // Вернуть новый массив после расширения\n    res\n}\n</code></pre> array.c<pre><code>/* Увеличить длину массива */\nint *extend(int *nums, int size, int enlarge) {\n    // Инициализировать массив увеличенной длины\n    int *res = (int *)malloc(sizeof(int) * (size + enlarge));\n    // Скопировать все элементы исходного массива в новый массив\n    for (int i = 0; i &lt; size; i++) {\n        res[i] = nums[i];\n    }\n    // Инициализировать расширенное пространство\n    for (int i = size; i &lt; size + enlarge; i++) {\n        res[i] = 0;\n    }\n    // Вернуть новый массив после расширения\n    return res;\n}\n</code></pre> array.kt<pre><code>/* Увеличить длину массива */\nfun extend(nums: IntArray, enlarge: Int): IntArray {\n    // Инициализировать массив увеличенной длины\n    val res = IntArray(nums.size + enlarge)\n    // Скопировать все элементы исходного массива в новый массив\n    for (i in nums.indices) {\n        res[i] = nums[i]\n    }\n    // Вернуть новый массив после расширения\n    return res\n}\n</code></pre> array.rb<pre><code>### Увеличить длину массива ###\n# Обратите внимание: Array в Ruby является динамическим массивом и может расширяться напрямую\n# Для удобства обучения в этой функции Array рассматривается как массив неизменяемой длины\ndef extend(nums, enlarge)\n  # Инициализировать массив увеличенной длины\n  res = Array.new(nums.length + enlarge, 0)\n\n  # Скопировать все элементы исходного массива в новый массив\n  for i in 0...nums.length\n    res[i] = nums[i]\n  end\n\n  # Вернуть новый массив после расширения\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 4. Массив и связный список","4.1 &nbsp; Массив"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#412","level":2,"title":"4.1.2   Преимущества и ограничения массива","text":"<p>Массив хранится в непрерывной области памяти, и все его элементы имеют один и тот же тип. Такой подход содержит много априорной информации, которую система может использовать для оптимизации эффективности операций со структурой данных.</p> <ul> <li>Высокая пространственная эффективность: массив выделяет для данных непрерывный блок памяти без дополнительного структурного накладного расхода.</li> <li>Поддержка произвольного доступа: массив позволяет обращаться к любому элементу за \\(O(1)\\) времени.</li> <li>Локальность кэша: при обращении к элементу массива компьютер загружает не только сам элемент, но и соседние данные, что позволяет использовать кэш для ускорения последующих операций.</li> </ul> <p>Хранение в непрерывной области памяти - палка о двух концах, и у него есть следующие ограничения.</p> <ul> <li>Низкая эффективность вставки и удаления: когда элементов в массиве много, вставка и удаление требуют сдвига большого количества элементов.</li> <li>Неизменяемая длина: после инициализации длина массива фиксирована; расширение массива требует копирования всех данных в новый массив, что стоит дорого.</li> <li>Потери памяти: если выделенный массив больше, чем реально необходимо, лишнее пространство пропадает впустую.</li> </ul>","path":["Глава 4. Массив и связный список","4.1 &nbsp; Массив"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#413","level":2,"title":"4.1.3   Типичные применения массива","text":"<p>Массив - это базовая и очень распространенная структура данных. Он часто используется как в различных алгоритмах, так и при реализации более сложных структур данных.</p> <ul> <li>Произвольный доступ: если мы хотим случайным образом выбирать некоторые образцы, можно сохранить их в массиве и сгенерировать случайную последовательность индексов для выборки.</li> <li>Сортировка и поиск: массив - самая распространенная структура данных для алгоритмов сортировки и поиска. Быстрая сортировка, сортировка слиянием, бинарный поиск и многие другие алгоритмы в основном работают именно с массивами.</li> <li>Таблица поиска: когда нужно быстро находить элемент или его соответствие, массив можно использовать как lookup table. Например, если мы хотим реализовать отображение символов в коды ASCII, можно использовать значение ASCII как индекс, а соответствующий элемент хранить по этой позиции массива.</li> <li>Машинное обучение: в нейронных сетях широко используются операции линейной алгебры над векторами, матрицами и тензорами, и все эти данные строятся в форме массивов. Массив - самая часто используемая структура данных в программировании нейросетей.</li> <li>Реализация структур данных: массивы можно использовать для реализации стеков, очередей, хеш-таблиц, куч, графов и других структур данных. Например, матрица смежности графа по сути является двумерным массивом.</li> </ul>","path":["Глава 4. Массив и связный список","4.1 &nbsp; Массив"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/","level":1,"title":"4.2   Связный список","text":"<p>Память является общим ресурсом для всех программ, и в сложной среде выполнения свободные участки памяти могут быть разбросаны по всему адресу памяти. Мы знаем, что память для хранения массива должна быть непрерывной, а если массив очень велик, память может не суметь предоставить столь большой непрерывный блок. Именно здесь проявляется преимущество гибкости связного списка.</p> <p>Связный список (linked list) - это линейная структура данных, в которой каждый элемент представляет собой объект-узел, а сами узлы соединены между собой через \"ссылки\". Ссылка хранит адрес памяти следующего узла, благодаря чему из текущего узла можно получить доступ к следующему.</p> <p>Конструкция связного списка позволяет хранить отдельные узлы в разных местах памяти, и их адреса вовсе не обязаны быть непрерывными.</p> <p></p> <p> Рисунок 4-5   Определение связного списка и способ хранения </p> <p>Если посмотреть на рисунок 4-5, можно заметить, что базовой единицей связного списка является объект узел (node). Каждый узел содержит две части данных: \"значение\" узла и \"ссылку\" на следующий узел.</p> <ul> <li>Первый узел связного списка называется \"головным узлом\", а последний - \"хвостовым узлом\".</li> <li>Хвостовой узел указывает на \"пусто\", что в Java, C++ и Python обозначается как <code>null</code> , <code>nullptr</code> и <code>None</code> соответственно.</li> <li>В языках, поддерживающих указатели, таких как C, C++, Go и Rust, упомянутую выше \"ссылку\" следует заменить на \"указатель\".</li> </ul> <p>Как показано в коде ниже, узел связного списка <code>ListNode</code> хранит не только значение, но и дополнительную ссылку (указатель). Поэтому при одинаковом объеме данных связный список занимает больше памяти, чем массив.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>class ListNode:\n    \"\"\"Класс узла связного списка\"\"\"\n    def __init__(self, val: int):\n        self.val: int = val               # Значение узла\n        self.next: ListNode | None = None # Ссылка на следующий узел\n</code></pre> <pre><code>/* Структура узла связного списка */\nstruct ListNode {\n    int val;         // Значение узла\n    ListNode *next;  // Указатель на следующий узел\n    ListNode(int x) : val(x), next(nullptr) {}  // Конструктор\n};\n</code></pre> <pre><code>/* Класс узла связного списка */\nclass ListNode {\n    int val;        // Значение узла\n    ListNode next;  // Ссылка на следующий узел\n    ListNode(int x) { val = x; }  // Конструктор\n}\n</code></pre> <pre><code>/* Класс узла связного списка */\nclass ListNode(int x) {  // Конструктор\n    int val = x;         // Значение узла\n    ListNode? next;      // Ссылка на следующий узел\n}\n</code></pre> <pre><code>/* Структура узла связного списка */\ntype ListNode struct {\n    Val  int       // Значение узла\n    Next *ListNode // Указатель на следующий узел\n}\n\n// NewListNode Конструктор, создает новый связный список\nfunc NewListNode(val int) *ListNode {\n    return &amp;ListNode{\n        Val:  val,\n        Next: nil,\n    }\n}\n</code></pre> <pre><code>/* Класс узла связного списка */\nclass ListNode {\n    var val: Int // Значение узла\n    var next: ListNode? // Ссылка на следующий узел\n\n    init(x: Int) { // Конструктор\n        val = x\n    }\n}\n</code></pre> <pre><code>/* Класс узла связного списка */\nclass ListNode {\n    constructor(val, next) {\n        this.val = (val === undefined ? 0 : val);       // Значение узла\n        this.next = (next === undefined ? null : next); // Ссылка на следующий узел\n    }\n}\n</code></pre> <pre><code>/* Класс узла связного списка */\nclass ListNode {\n    val: number;\n    next: ListNode | null;\n    constructor(val?: number, next?: ListNode | null) {\n        this.val = val === undefined ? 0 : val;        // Значение узла\n        this.next = next === undefined ? null : next;  // Ссылка на следующий узел\n    }\n}\n</code></pre> <pre><code>/* Класс узла связного списка */\nclass ListNode {\n  int val; // Значение узла\n  ListNode? next; // Ссылка на следующий узел\n  ListNode(this.val, [this.next]); // Конструктор\n}\n</code></pre> <pre><code>use std::rc::Rc;\nuse std::cell::RefCell;\n/* Класс узла связного списка */\n#[derive(Debug)]\nstruct ListNode {\n    val: i32, // Значение узла\n    next: Option&lt;Rc&lt;RefCell&lt;ListNode&gt;&gt;&gt;, // Указатель на следующий узел\n}\n</code></pre> <pre><code>/* Структура узла связного списка */\ntypedef struct ListNode {\n    int val;               // Значение узла\n    struct ListNode *next; // Указатель на следующий узел\n} ListNode;\n\n/* Конструктор */\nListNode *newListNode(int val) {\n    ListNode *node;\n    node = (ListNode *) malloc(sizeof(ListNode));\n    node-&gt;val = val;\n    node-&gt;next = NULL;\n    return node;\n}\n</code></pre> <pre><code>/* Класс узла связного списка */\n// Конструктор\nclass ListNode(x: Int) {\n    val _val: Int = x          // Значение узла\n    val next: ListNode? = null // Ссылка на следующий узел\n}\n</code></pre> <pre><code># Класс узла связного списка\nclass ListNode\n  attr_accessor :val  # Значение узла\n  attr_accessor :next # Ссылка на следующий узел\n\n  def initialize(val=0, next_node=nil)\n    @val = val\n    @next = next_node\n  end\nend\n</code></pre>","path":["Глава 4. Массив и связный список","4.2 &nbsp; Связный список"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#421","level":2,"title":"4.2.1   Основные операции со связным списком","text":"","path":["Глава 4. Массив и связный список","4.2 &nbsp; Связный список"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#1","level":3,"title":"1.   Инициализация связного списка","text":"<p>Построение связного списка состоит из двух шагов: сначала нужно инициализировать объекты всех узлов, затем установить связи-ссылки между ними. После завершения инициализации мы можем, начиная с головы списка, последовательно проходить все узлы по ссылке <code>next</code>.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linked_list.py<pre><code># Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4\n# Инициализация отдельных узлов\nn0 = ListNode(1)\nn1 = ListNode(3)\nn2 = ListNode(2)\nn3 = ListNode(5)\nn4 = ListNode(4)\n# Построение ссылок между узлами\nn0.next = n1\nn1.next = n2\nn2.next = n3\nn3.next = n4\n</code></pre> linked_list.cpp<pre><code>/* Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// Инициализация отдельных узлов\nListNode* n0 = new ListNode(1);\nListNode* n1 = new ListNode(3);\nListNode* n2 = new ListNode(2);\nListNode* n3 = new ListNode(5);\nListNode* n4 = new ListNode(4);\n// Построение ссылок между узлами\nn0-&gt;next = n1;\nn1-&gt;next = n2;\nn2-&gt;next = n3;\nn3-&gt;next = n4;\n</code></pre> linked_list.java<pre><code>/* Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// Инициализация отдельных узлов\nListNode n0 = new ListNode(1);\nListNode n1 = new ListNode(3);\nListNode n2 = new ListNode(2);\nListNode n3 = new ListNode(5);\nListNode n4 = new ListNode(4);\n// Построение ссылок между узлами\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.cs<pre><code>/* Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// Инициализация отдельных узлов\nListNode n0 = new(1);\nListNode n1 = new(3);\nListNode n2 = new(2);\nListNode n3 = new(5);\nListNode n4 = new(4);\n// Построение ссылок между узлами\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.go<pre><code>/* Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// Инициализация отдельных узлов\nn0 := NewListNode(1)\nn1 := NewListNode(3)\nn2 := NewListNode(2)\nn3 := NewListNode(5)\nn4 := NewListNode(4)\n// Построение ссылок между узлами\nn0.Next = n1\nn1.Next = n2\nn2.Next = n3\nn3.Next = n4\n</code></pre> linked_list.swift<pre><code>/* Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// Инициализация отдельных узлов\nlet n0 = ListNode(x: 1)\nlet n1 = ListNode(x: 3)\nlet n2 = ListNode(x: 2)\nlet n3 = ListNode(x: 5)\nlet n4 = ListNode(x: 4)\n// Построение ссылок между узлами\nn0.next = n1\nn1.next = n2\nn2.next = n3\nn3.next = n4\n</code></pre> linked_list.js<pre><code>/* Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// Инициализация отдельных узлов\nconst n0 = new ListNode(1);\nconst n1 = new ListNode(3);\nconst n2 = new ListNode(2);\nconst n3 = new ListNode(5);\nconst n4 = new ListNode(4);\n// Построение ссылок между узлами\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.ts<pre><code>/* Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// Инициализация отдельных узлов\nconst n0 = new ListNode(1);\nconst n1 = new ListNode(3);\nconst n2 = new ListNode(2);\nconst n3 = new ListNode(5);\nconst n4 = new ListNode(4);\n// Построение ссылок между узлами\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.dart<pre><code>/* Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\\\n// Инициализация отдельных узлов\nListNode n0 = ListNode(1);\nListNode n1 = ListNode(3);\nListNode n2 = ListNode(2);\nListNode n3 = ListNode(5);\nListNode n4 = ListNode(4);\n// Построение ссылок между узлами\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.rs<pre><code>/* Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// Инициализация отдельных узлов\nlet n0 = Rc::new(RefCell::new(ListNode { val: 1, next: None }));\nlet n1 = Rc::new(RefCell::new(ListNode { val: 3, next: None }));\nlet n2 = Rc::new(RefCell::new(ListNode { val: 2, next: None }));\nlet n3 = Rc::new(RefCell::new(ListNode { val: 5, next: None }));\nlet n4 = Rc::new(RefCell::new(ListNode { val: 4, next: None }));\n\n// Построение ссылок между узлами\nn0.borrow_mut().next = Some(n1.clone());\nn1.borrow_mut().next = Some(n2.clone());\nn2.borrow_mut().next = Some(n3.clone());\nn3.borrow_mut().next = Some(n4.clone());\n</code></pre> linked_list.c<pre><code>/* Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// Инициализация отдельных узлов\nListNode* n0 = newListNode(1);\nListNode* n1 = newListNode(3);\nListNode* n2 = newListNode(2);\nListNode* n3 = newListNode(5);\nListNode* n4 = newListNode(4);\n// Построение ссылок между узлами\nn0-&gt;next = n1;\nn1-&gt;next = n2;\nn2-&gt;next = n3;\nn3-&gt;next = n4;\n</code></pre> linked_list.kt<pre><code>/* Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// Инициализация отдельных узлов\nval n0 = ListNode(1)\nval n1 = ListNode(3)\nval n2 = ListNode(2)\nval n3 = ListNode(5)\nval n4 = ListNode(4)\n// Построение ссылок между узлами\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.rb<pre><code># Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4\n# Инициализация отдельных узлов\nn0 = ListNode.new(1)\nn1 = ListNode.new(3)\nn2 = ListNode.new(2)\nn3 = ListNode.new(5)\nn4 = ListNode.new(4)\n# Построение ссылок между узлами\nn0.next = n1\nn1.next = n2\nn2.next = n3\nn3.next = n4\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%D1%81%D0%B2%D1%8F%D0%B7%D0%BD%D1%8B%D0%B9%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%D1%83%D0%B7%D0%B5%D0%BB%D0%BA%D0%BB%D0%B0%D1%81%D1%81%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%D0%97%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%83%D0%B7%D0%BB%D0%B0%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%D0%A1%D1%81%D1%8B%D0%BB%D0%BA%D0%B0%20%D0%BD%D0%B0%20%D1%81%D0%BB%D0%B5%D0%B4%D1%83%D1%8E%D1%89%D0%B8%D0%B9%20%D1%83%D0%B7%D0%B5%D0%BB%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%81%D0%B2%D1%8F%D0%B7%D0%BD%D1%8B%D0%B9%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%201%20-%3E%203%20-%3E%202%20-%3E%205%20-%3E%204%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D0%BA%D0%B0%D0%B6%D0%B4%D1%8B%D0%B9%20%D1%83%D0%B7%D0%B5%D0%BB%0A%20%20%20%20n0%20%3D%20ListNode%281%29%0A%20%20%20%20n1%20%3D%20ListNode%283%29%0A%20%20%20%20n2%20%3D%20ListNode%282%29%0A%20%20%20%20n3%20%3D%20ListNode%285%29%0A%20%20%20%20n4%20%3D%20ListNode%284%29%0A%20%20%20%20%23%20%D0%9F%D0%BE%D1%81%D1%82%D1%80%D0%BE%D0%B8%D1%82%D1%8C%20%D1%81%D1%81%D1%8B%D0%BB%D0%BA%D0%B8%20%D0%BC%D0%B5%D0%B6%D0%B4%D1%83%20%D1%83%D0%B7%D0%BB%D0%B0%D0%BC%D0%B8%0A%20%20%20%20n0.next%20%3D%20n1%0A%20%20%20%20n1.next%20%3D%20n2%0A%20%20%20%20n2.next%20%3D%20n3%0A%20%20%20%20n3.next%20%3D%20n4&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p> <p>Массив в целом - это одна переменная: например, массив <code>nums</code> содержит элементы <code>nums[0]</code> , <code>nums[1]</code> и т.д. Связный список же состоит из множества независимых объектов-узлов. Обычно в качестве обозначения всего связного списка используют головной узел; например, в приведенном выше коде связный список можно обозначить как список <code>n0</code> .</p>","path":["Глава 4. Массив и связный список","4.2 &nbsp; Связный список"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#2","level":3,"title":"2.   Вставка узла","text":"<p>Вставить узел в связный список очень легко. Как показано на рисунке 4-6, предположим, что мы хотим вставить новый узел <code>P</code> между двумя соседними узлами <code>n0</code> и <code>n1</code> ; для этого нужно изменить всего две ссылки (указателя), а временная сложность будет равна \\(O(1)\\) .</p> <p>Для сравнения: временная сложность вставки элемента в массив составляет \\(O(n)\\) , и при большом объеме данных это неэффективно.</p> <p></p> <p> Рисунок 4-6   Пример вставки узла в связный список </p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linked_list.py<pre><code>def insert(n0: ListNode, P: ListNode):\n    \"\"\"Вставить узел P после узла n0 в связном списке\"\"\"\n    n1 = n0.next\n    P.next = n1\n    n0.next = P\n</code></pre> linked_list.cpp<pre><code>/* Вставить узел P после узла n0 в связном списке */\nvoid insert(ListNode *n0, ListNode *P) {\n    ListNode *n1 = n0-&gt;next;\n    P-&gt;next = n1;\n    n0-&gt;next = P;\n}\n</code></pre> linked_list.java<pre><code>/* Вставить узел P после узла n0 в связном списке */\nvoid insert(ListNode n0, ListNode P) {\n    ListNode n1 = n0.next;\n    P.next = n1;\n    n0.next = P;\n}\n</code></pre> linked_list.cs<pre><code>/* Вставить узел P после узла n0 в связном списке */\nvoid Insert(ListNode n0, ListNode P) {\n    ListNode? n1 = n0.next;\n    P.next = n1;\n    n0.next = P;\n}\n</code></pre> linked_list.go<pre><code>/* Вставить узел P после узла n0 в связном списке */\nfunc insertNode(n0 *ListNode, P *ListNode) {\n    n1 := n0.Next\n    P.Next = n1\n    n0.Next = P\n}\n</code></pre> linked_list.swift<pre><code>/* Вставить узел P после узла n0 в связном списке */\nfunc insert(n0: ListNode, P: ListNode) {\n    let n1 = n0.next\n    P.next = n1\n    n0.next = P\n}\n</code></pre> linked_list.js<pre><code>/* Вставить узел P после узла n0 в связном списке */\nfunction insert(n0, P) {\n    const n1 = n0.next;\n    P.next = n1;\n    n0.next = P;\n}\n</code></pre> linked_list.ts<pre><code>/* Вставить узел P после узла n0 в связном списке */\nfunction insert(n0: ListNode, P: ListNode): void {\n    const n1 = n0.next;\n    P.next = n1;\n    n0.next = P;\n}\n</code></pre> linked_list.dart<pre><code>/* Вставить узел P после узла n0 в связном списке */\nvoid insert(ListNode n0, ListNode P) {\n  ListNode? n1 = n0.next;\n  P.next = n1;\n  n0.next = P;\n}\n</code></pre> linked_list.rs<pre><code>/* Вставить узел P после узла n0 в связном списке */\n#[allow(non_snake_case)]\npub fn insert&lt;T&gt;(n0: &amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;, P: Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;) {\n    let n1 = n0.borrow_mut().next.take();\n    P.borrow_mut().next = n1;\n    n0.borrow_mut().next = Some(P);\n}\n</code></pre> linked_list.c<pre><code>/* Вставить узел P после узла n0 в связном списке */\nvoid insert(ListNode *n0, ListNode *P) {\n    ListNode *n1 = n0-&gt;next;\n    P-&gt;next = n1;\n    n0-&gt;next = P;\n}\n</code></pre> linked_list.kt<pre><code>/* Вставить узел P после узла n0 в связном списке */\nfun insert(n0: ListNode?, p: ListNode?) {\n    val n1 = n0?.next\n    p?.next = n1\n    n0?.next = p\n}\n</code></pre> linked_list.rb<pre><code>### Вставка узла _p после узла n0 в связном списке ###\n# В Ruby `p` является встроенной функцией, а `P` — константой, поэтому вместо них можно использовать `_p`\ndef insert(n0, _p)\n  n1 = n0.next\n  _p.next = n1\n  n0.next = _p\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 4. Массив и связный список","4.2 &nbsp; Связный список"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#3","level":3,"title":"3.   Удаление узла","text":"<p>Как показано на рисунке 4-7, удалить узел из связного списка тоже очень удобно: нужно изменить всего одну ссылку (указатель).</p> <p>Обрати внимание: хотя после завершения операции удаления узел <code>P</code> все еще указывает на <code>n1</code> , при обходе связного списка до <code>P</code> уже нельзя добраться, а значит <code>P</code> больше не принадлежит данному списку.</p> <p></p> <p> Рисунок 4-7   Удаление узла из связного списка </p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linked_list.py<pre><code>def remove(n0: ListNode):\n    \"\"\"Удалить первый узел после узла n0 в связном списке\"\"\"\n    if not n0.next:\n        return\n    # n0 -&gt; P -&gt; n1\n    P = n0.next\n    n1 = P.next\n    n0.next = n1\n</code></pre> linked_list.cpp<pre><code>/* Удалить первый узел после узла n0 в связном списке */\nvoid remove(ListNode *n0) {\n    if (n0-&gt;next == nullptr)\n        return;\n    // n0 -&gt; P -&gt; n1\n    ListNode *P = n0-&gt;next;\n    ListNode *n1 = P-&gt;next;\n    n0-&gt;next = n1;\n    // Освободить память\n    delete P;\n}\n</code></pre> linked_list.java<pre><code>/* Удалить первый узел после узла n0 в связном списке */\nvoid remove(ListNode n0) {\n    if (n0.next == null)\n        return;\n    // n0 -&gt; P -&gt; n1\n    ListNode P = n0.next;\n    ListNode n1 = P.next;\n    n0.next = n1;\n}\n</code></pre> linked_list.cs<pre><code>/* Удалить первый узел после узла n0 в связном списке */\nvoid Remove(ListNode n0) {\n    if (n0.next == null)\n        return;\n    // n0 -&gt; P -&gt; n1\n    ListNode P = n0.next;\n    ListNode? n1 = P.next;\n    n0.next = n1;\n}\n</code></pre> linked_list.go<pre><code>/* Удалить первый узел после узла n0 в связном списке */\nfunc removeItem(n0 *ListNode) {\n    if n0.Next == nil {\n        return\n    }\n    // n0 -&gt; P -&gt; n1\n    P := n0.Next\n    n1 := P.Next\n    n0.Next = n1\n}\n</code></pre> linked_list.swift<pre><code>/* Удалить первый узел после узла n0 в связном списке */\nfunc remove(n0: ListNode) {\n    if n0.next == nil {\n        return\n    }\n    // n0 -&gt; P -&gt; n1\n    let P = n0.next\n    let n1 = P?.next\n    n0.next = n1\n}\n</code></pre> linked_list.js<pre><code>/* Удалить первый узел после узла n0 в связном списке */\nfunction remove(n0) {\n    if (!n0.next) return;\n    // n0 -&gt; P -&gt; n1\n    const P = n0.next;\n    const n1 = P.next;\n    n0.next = n1;\n}\n</code></pre> linked_list.ts<pre><code>/* Удалить первый узел после узла n0 в связном списке */\nfunction remove(n0: ListNode): void {\n    if (!n0.next) {\n        return;\n    }\n    // n0 -&gt; P -&gt; n1\n    const P = n0.next;\n    const n1 = P.next;\n    n0.next = n1;\n}\n</code></pre> linked_list.dart<pre><code>/* Удалить первый узел после узла n0 в связном списке */\nvoid remove(ListNode n0) {\n  if (n0.next == null) return;\n  // n0 -&gt; P -&gt; n1\n  ListNode P = n0.next!;\n  ListNode? n1 = P.next;\n  n0.next = n1;\n}\n</code></pre> linked_list.rs<pre><code>/* Удалить первый узел после узла n0 в связном списке */\n#[allow(non_snake_case)]\npub fn remove&lt;T&gt;(n0: &amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;) {\n    // n0 -&gt; P -&gt; n1\n    let P = n0.borrow_mut().next.take();\n    if let Some(node) = P {\n        let n1 = node.borrow_mut().next.take();\n        n0.borrow_mut().next = n1;\n    }\n}\n</code></pre> linked_list.c<pre><code>/* Удалить первый узел после узла n0 в связном списке */\n// Внимание: stdio.h уже использует ключевое слово remove\nvoid removeItem(ListNode *n0) {\n    if (!n0-&gt;next)\n        return;\n    // n0 -&gt; P -&gt; n1\n    ListNode *P = n0-&gt;next;\n    ListNode *n1 = P-&gt;next;\n    n0-&gt;next = n1;\n    // Освободить память\n    free(P);\n}\n</code></pre> linked_list.kt<pre><code>/* Удалить первый узел после узла n0 в связном списке */\nfun remove(n0: ListNode?) {\n    if (n0?.next == null)\n        return\n    // n0 -&gt; P -&gt; n1\n    val p = n0.next\n    val n1 = p?.next\n    n0.next = n1\n}\n</code></pre> linked_list.rb<pre><code>### Удаление первого узла после узла n0 в связном списке ###\ndef remove(n0)\n  return if n0.next.nil?\n\n  # n0 -&gt; remove_node -&gt; n1\n  remove_node = n0.next\n  n1 = remove_node.next\n  n0.next = n1\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 4. Массив и связный список","4.2 &nbsp; Связный список"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#4","level":3,"title":"4.   Доступ к узлу","text":"<p>Доступ к узлам в связном списке менее эффективен. Как уже обсуждалось в предыдущем разделе, к любому элементу массива можно обратиться за \\(O(1)\\) времени. Со связным списком это не так: программе нужно стартовать от головного узла и последовательно двигаться дальше, пока не будет найден целевой узел. То есть для доступа к \\(i\\) -му узлу списка нужно выполнить \\(i - 1\\) итераций, а временная сложность составляет \\(O(n)\\) .</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linked_list.py<pre><code>def access(head: ListNode, index: int) -&gt; ListNode | None:\n    \"\"\"Доступ к узлу связного списка по индексу index\"\"\"\n    for _ in range(index):\n        if not head:\n            return None\n        head = head.next\n    return head\n</code></pre> linked_list.cpp<pre><code>/* Доступ к узлу связного списка по индексу index */\nListNode *access(ListNode *head, int index) {\n    for (int i = 0; i &lt; index; i++) {\n        if (head == nullptr)\n            return nullptr;\n        head = head-&gt;next;\n    }\n    return head;\n}\n</code></pre> linked_list.java<pre><code>/* Доступ к узлу связного списка по индексу index */\nListNode access(ListNode head, int index) {\n    for (int i = 0; i &lt; index; i++) {\n        if (head == null)\n            return null;\n        head = head.next;\n    }\n    return head;\n}\n</code></pre> linked_list.cs<pre><code>/* Доступ к узлу связного списка по индексу index */\nListNode? Access(ListNode? head, int index) {\n    for (int i = 0; i &lt; index; i++) {\n        if (head == null)\n            return null;\n        head = head.next;\n    }\n    return head;\n}\n</code></pre> linked_list.go<pre><code>/* Доступ к узлу связного списка по индексу index */\nfunc access(head *ListNode, index int) *ListNode {\n    for i := 0; i &lt; index; i++ {\n        if head == nil {\n            return nil\n        }\n        head = head.Next\n    }\n    return head\n}\n</code></pre> linked_list.swift<pre><code>/* Доступ к узлу связного списка по индексу index */\nfunc access(head: ListNode, index: Int) -&gt; ListNode? {\n    var head: ListNode? = head\n    for _ in 0 ..&lt; index {\n        if head == nil {\n            return nil\n        }\n        head = head?.next\n    }\n    return head\n}\n</code></pre> linked_list.js<pre><code>/* Доступ к узлу связного списка по индексу index */\nfunction access(head, index) {\n    for (let i = 0; i &lt; index; i++) {\n        if (!head) {\n            return null;\n        }\n        head = head.next;\n    }\n    return head;\n}\n</code></pre> linked_list.ts<pre><code>/* Доступ к узлу связного списка по индексу index */\nfunction access(head: ListNode | null, index: number): ListNode | null {\n    for (let i = 0; i &lt; index; i++) {\n        if (!head) {\n            return null;\n        }\n        head = head.next;\n    }\n    return head;\n}\n</code></pre> linked_list.dart<pre><code>/* Доступ к узлу связного списка по индексу index */\nListNode? access(ListNode? head, int index) {\n  for (var i = 0; i &lt; index; i++) {\n    if (head == null) return null;\n    head = head.next;\n  }\n  return head;\n}\n</code></pre> linked_list.rs<pre><code>/* Доступ к узлу связного списка по индексу index */\npub fn access&lt;T&gt;(head: Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;, index: i32) -&gt; Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt; {\n    fn dfs&lt;T&gt;(\n        head: Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;,\n        index: i32,\n    ) -&gt; Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt; {\n        if index &lt;= 0 {\n            return head.cloned();\n        }\n\n        if let Some(node) = head {\n            dfs(node.borrow().next.as_ref(), index - 1)\n        } else {\n            None\n        }\n    }\n\n    dfs(Some(head).as_ref(), index)\n}\n</code></pre> linked_list.c<pre><code>/* Доступ к узлу связного списка по индексу index */\nListNode *access(ListNode *head, int index) {\n    for (int i = 0; i &lt; index; i++) {\n        if (head == NULL)\n            return NULL;\n        head = head-&gt;next;\n    }\n    return head;\n}\n</code></pre> linked_list.kt<pre><code>/* Доступ к узлу связного списка по индексу index */\nfun access(head: ListNode?, index: Int): ListNode? {\n    var h = head\n    for (i in 0..&lt;index) {\n        if (h == null)\n            return null\n        h = h.next\n    }\n    return h\n}\n</code></pre> linked_list.rb<pre><code>### Доступ к узлу связного списка по индексу index ###\ndef access(head, index)\n  for i in 0...index\n    return nil if head.nil?\n    head = head.next\n  end\n\n  head\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 4. Массив и связный список","4.2 &nbsp; Связный список"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#5","level":3,"title":"5.   Поиск узла","text":"<p>Выполни обход связного списка, найди в нем узел со значением <code>target</code> и верни индекс этого узла в списке. Этот процесс тоже относится к линейному поиску. Код выглядит следующим образом:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linked_list.py<pre><code>def find(head: ListNode, target: int) -&gt; int:\n    \"\"\"Найти в связном списке первый узел со значением target\"\"\"\n    index = 0\n    while head:\n        if head.val == target:\n            return index\n        head = head.next\n        index += 1\n    return -1\n</code></pre> linked_list.cpp<pre><code>/* Найти в связном списке первый узел со значением target */\nint find(ListNode *head, int target) {\n    int index = 0;\n    while (head != nullptr) {\n        if (head-&gt;val == target)\n            return index;\n        head = head-&gt;next;\n        index++;\n    }\n    return -1;\n}\n</code></pre> linked_list.java<pre><code>/* Найти в связном списке первый узел со значением target */\nint find(ListNode head, int target) {\n    int index = 0;\n    while (head != null) {\n        if (head.val == target)\n            return index;\n        head = head.next;\n        index++;\n    }\n    return -1;\n}\n</code></pre> linked_list.cs<pre><code>/* Найти в связном списке первый узел со значением target */\nint Find(ListNode? head, int target) {\n    int index = 0;\n    while (head != null) {\n        if (head.val == target)\n            return index;\n        head = head.next;\n        index++;\n    }\n    return -1;\n}\n</code></pre> linked_list.go<pre><code>/* Найти в связном списке первый узел со значением target */\nfunc findNode(head *ListNode, target int) int {\n    index := 0\n    for head != nil {\n        if head.Val == target {\n            return index\n        }\n        head = head.Next\n        index++\n    }\n    return -1\n}\n</code></pre> linked_list.swift<pre><code>/* Найти в связном списке первый узел со значением target */\nfunc find(head: ListNode, target: Int) -&gt; Int {\n    var head: ListNode? = head\n    var index = 0\n    while head != nil {\n        if head?.val == target {\n            return index\n        }\n        head = head?.next\n        index += 1\n    }\n    return -1\n}\n</code></pre> linked_list.js<pre><code>/* Найти в связном списке первый узел со значением target */\nfunction find(head, target) {\n    let index = 0;\n    while (head !== null) {\n        if (head.val === target) {\n            return index;\n        }\n        head = head.next;\n        index += 1;\n    }\n    return -1;\n}\n</code></pre> linked_list.ts<pre><code>/* Найти в связном списке первый узел со значением target */\nfunction find(head: ListNode | null, target: number): number {\n    let index = 0;\n    while (head !== null) {\n        if (head.val === target) {\n            return index;\n        }\n        head = head.next;\n        index += 1;\n    }\n    return -1;\n}\n</code></pre> linked_list.dart<pre><code>/* Найти в связном списке первый узел со значением target */\nint find(ListNode? head, int target) {\n  int index = 0;\n  while (head != null) {\n    if (head.val == target) {\n      return index;\n    }\n    head = head.next;\n    index++;\n  }\n  return -1;\n}\n</code></pre> linked_list.rs<pre><code>/* Найти в связном списке первый узел со значением target */\npub fn find&lt;T: PartialEq&gt;(head: Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;, target: T) -&gt; i32 {\n    fn find&lt;T: PartialEq&gt;(head: Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;, target: T, idx: i32) -&gt; i32 {\n        if let Some(node) = head {\n            if node.borrow().val == target {\n                return idx;\n            }\n            return find(node.borrow().next.as_ref(), target, idx + 1);\n        } else {\n            -1\n        }\n    }\n\n    find(Some(head).as_ref(), target, 0)\n}\n</code></pre> linked_list.c<pre><code>/* Найти в связном списке первый узел со значением target */\nint find(ListNode *head, int target) {\n    int index = 0;\n    while (head) {\n        if (head-&gt;val == target)\n            return index;\n        head = head-&gt;next;\n        index++;\n    }\n    return -1;\n}\n</code></pre> linked_list.kt<pre><code>/* Найти в связном списке первый узел со значением target */\nfun find(head: ListNode?, target: Int): Int {\n    var index = 0\n    var h = head\n    while (h != null) {\n        if (h._val == target)\n            return index\n        h = h.next\n        index++\n    }\n    return -1\n}\n</code></pre> linked_list.rb<pre><code>### Поиск первого узла со значением target в связном списке ###\ndef find(head, target)\n  index = 0\n  while head\n    return index if head.val == target\n    head = head.next\n    index += 1\n  end\n\n  -1\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 4. Массив и связный список","4.2 &nbsp; Связный список"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#422","level":2,"title":"4.2.2   Сравнение массива и связного списка","text":"<p>В таблице 4-1 обобщаются свойства массива и связного списка, а также сравнивается эффективность соответствующих операций. Поскольку они используют противоположные стратегии хранения, их свойства и эффективность операций тоже во многом противоположны.</p> <p> Таблица 4-1   Сравнение эффективности массива и связного списка </p> Массив Связный список Способ хранения Непрерывная область памяти Разрозненная область памяти Расширение емкости Длина неизменяема Гибкое расширение Эффективность памяти Элементы занимают меньше памяти, но возможны потери пространства Элементы занимают больше памяти Доступ к элементу \\(O(1)\\) \\(O(n)\\) Добавление элемента \\(O(n)\\) \\(O(1)\\) Удаление элемента \\(O(n)\\) \\(O(1)\\)","path":["Глава 4. Массив и связный список","4.2 &nbsp; Связный список"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#423","level":2,"title":"4.2.3   Основные типы связных списков","text":"<p>Как показано на рисунке 4-8, существует три распространенных типа связных списков.</p> <ul> <li>Односвязный список: это обычный связный список, рассмотренный выше. Узел односвязного списка содержит значение и ссылку на следующий узел. Первый узел называется головным, последний - хвостовым, и хвост указывает на пусто <code>None</code> .</li> <li>Циклический список: если заставить хвостовой узел односвязного списка указывать на головной (то есть соединить хвост с головой), получится циклический список. В циклическом списке любой узел можно рассматривать как головной.</li> <li>Двусвязный список: по сравнению с односвязным списком двусвязный хранит ссылки в двух направлениях. Определение узла двусвязного списка включает как ссылку на следующий узел, так и ссылку на предыдущий узел. По сравнению с односвязным списком двусвязный более гибок и позволяет проходить список в обе стороны, но за это приходится платить дополнительной памятью.</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>class ListNode:\n    \"\"\"Класс узла двусвязного списка\"\"\"\n    def __init__(self, val: int):\n        self.val: int = val                # Значение узла\n        self.next: ListNode | None = None  # Ссылка на следующий узел\n        self.prev: ListNode | None = None  # Ссылка на предыдущий узел\n</code></pre> <pre><code>/* Структура узла двусвязного списка */\nstruct ListNode {\n    int val;         // Значение узла\n    ListNode *next;  // Указатель на следующий узел\n    ListNode *prev;  // Указатель на предыдущий узел\n    ListNode(int x) : val(x), next(nullptr), prev(nullptr) {}  // Конструктор\n};\n</code></pre> <pre><code>/* Класс узла двусвязного списка */\nclass ListNode {\n    int val;        // Значение узла\n    ListNode next;  // Ссылка на следующий узел\n    ListNode prev;  // Ссылка на предыдущий узел\n    ListNode(int x) { val = x; }  // Конструктор\n}\n</code></pre> <pre><code>/* Класс узла двусвязного списка */\nclass ListNode(int x) {  // Конструктор\n    int val = x;    // Значение узла\n    ListNode next;  // Ссылка на следующий узел\n    ListNode prev;  // Ссылка на предыдущий узел\n}\n</code></pre> <pre><code>/* Структура узла двусвязного списка */\ntype DoublyListNode struct {\n    Val  int             // Значение узла\n    Next *DoublyListNode // Указатель на следующий узел\n    Prev *DoublyListNode // Указатель на предыдущий узел\n}\n\n// NewDoublyListNode Инициализация\nfunc NewDoublyListNode(val int) *DoublyListNode {\n    return &amp;DoublyListNode{\n        Val:  val,\n        Next: nil,\n        Prev: nil,\n    }\n}\n</code></pre> <pre><code>/* Класс узла двусвязного списка */\nclass ListNode {\n    var val: Int // Значение узла\n    var next: ListNode? // Ссылка на следующий узел\n    var prev: ListNode? // Ссылка на предыдущий узел\n\n    init(x: Int) { // Конструктор\n        val = x\n    }\n}\n</code></pre> <pre><code>/* Класс узла двусвязного списка */\nclass ListNode {\n    constructor(val, next, prev) {\n        this.val = val  ===  undefined ? 0 : val;        // Значение узла\n        this.next = next  ===  undefined ? null : next;  // Ссылка на следующий узел\n        this.prev = prev  ===  undefined ? null : prev;  // Ссылка на предыдущий узел\n    }\n}\n</code></pre> <pre><code>/* Класс узла двусвязного списка */\nclass ListNode {\n    val: number;\n    next: ListNode | null;\n    prev: ListNode | null;\n    constructor(val?: number, next?: ListNode | null, prev?: ListNode | null) {\n        this.val = val  ===  undefined ? 0 : val;        // Значение узла\n        this.next = next  ===  undefined ? null : next;  // Ссылка на следующий узел\n        this.prev = prev  ===  undefined ? null : prev;  // Ссылка на предыдущий узел\n    }\n}\n</code></pre> <pre><code>/* Класс узла двусвязного списка */\nclass ListNode {\n    int val;        // Значение узла\n    ListNode? next;  // Ссылка на следующий узел\n    ListNode? prev;  // Ссылка на предыдущий узел\n    ListNode(this.val, [this.next, this.prev]);  // Конструктор\n}\n</code></pre> <pre><code>use std::rc::Rc;\nuse std::cell::RefCell;\n\n/* Тип узла двусвязного списка */\n#[derive(Debug)]\nstruct ListNode {\n    val: i32, // Значение узла\n    next: Option&lt;Rc&lt;RefCell&lt;ListNode&gt;&gt;&gt;, // Указатель на следующий узел\n    prev: Option&lt;Rc&lt;RefCell&lt;ListNode&gt;&gt;&gt;, // Указатель на предыдущий узел\n}\n\n/* Конструктор */\nimpl ListNode {\n    fn new(val: i32) -&gt; Self {\n        ListNode {\n            val,\n            next: None,\n            prev: None,\n        }\n    }\n}\n</code></pre> <pre><code>/* Структура узла двусвязного списка */\ntypedef struct ListNode {\n    int val;               // Значение узла\n    struct ListNode *next; // Указатель на следующий узел\n    struct ListNode *prev; // Указатель на предыдущий узел\n} ListNode;\n\n/* Конструктор */\nListNode *newListNode(int val) {\n    ListNode *node;\n    node = (ListNode *) malloc(sizeof(ListNode));\n    node-&gt;val = val;\n    node-&gt;next = NULL;\n    node-&gt;prev = NULL;\n    return node;\n}\n</code></pre> <pre><code>/* Класс узла двусвязного списка */\n// Конструктор\nclass ListNode(x: Int) {\n    val _val: Int = x           // Значение узла\n    val next: ListNode? = null  // Ссылка на следующий узел\n    val prev: ListNode? = null  // Ссылка на предыдущий узел\n}\n</code></pre> <pre><code># Класс узла двусвязного списка\nclass ListNode\n  attr_accessor :val    # Значение узла\n  attr_accessor :next   # Ссылка на следующий узел\n  attr_accessor :prev   # Ссылка на предыдущий узел\n\n  def initialize(val=0, next_node=nil, prev_node=nil)\n    @val = val\n    @next = next_node\n    @prev = prev_node\n  end\nend\n</code></pre> <p></p> <p> Рисунок 4-8   Распространенные типы связных списков </p>","path":["Глава 4. Массив и связный список","4.2 &nbsp; Связный список"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#424","level":2,"title":"4.2.4   Типичные применения связных списков","text":"<p>Односвязные списки обычно используются для реализации стеков, очередей, хеш-таблиц и графов.</p> <ul> <li>Стеки и очереди: если операции вставки и удаления выполняются на одном конце связного списка, он проявляет свойства LIFO, соответствующие стеку; если вставка происходит на одном конце, а удаление на другом, он проявляет свойства FIFO, соответствующие очереди.</li> <li>Хеш-таблицы: метод цепочек - один из основных способов разрешения коллизий в хеш-таблицах. В этом подходе все конфликтующие элементы помещаются в связный список.</li> <li>Графы: список смежности - это распространенный способ представления графа, при котором каждой вершине графа соответствует связный список, а каждый элемент этого списка представляет другую вершину, соединенную с данной.</li> </ul> <p>Двусвязные списки обычно используются там, где нужен быстрый доступ как к предыдущему, так и к следующему элементу.</p> <ul> <li>Продвинутые структуры данных: например, в красно-черных деревьях и B-деревьях нам нужен доступ к родительскому узлу; этого можно добиться, сохранив в узле ссылку на родителя, по аналогии с двусвязным списком.</li> <li>История браузера: когда пользователь в браузере нажимает кнопки \"вперед\" или \"назад\", браузеру нужно знать предыдущую и следующую веб-страницы, которые он посещал. Свойства двусвязного списка делают такую операцию простой.</li> <li>Алгоритм LRU: в алгоритмах вытеснения из кэша (LRU) нужно быстро находить наименее недавно использованные данные, а также быстро добавлять и удалять узлы. Для этого двусвязный список подходит очень хорошо.</li> </ul> <p>Циклические списки часто применяются в сценариях, требующих периодических операций, например при планировании ресурсов в операционной системе.</p> <ul> <li>Алгоритм циклического распределения кванта времени: в операционных системах round-robin scheduling - это распространенный алгоритм планирования CPU, который циклически обходит набор процессов. Каждому процессу выделяется квант времени, и когда он исчерпан, CPU переключается на следующий процесс. Такую циклическую операцию удобно реализовать с помощью кольцевого списка.</li> <li>Буферы данных: в некоторых реализациях буферов данных также могут использоваться циклические списки. Например, в аудио- и видеоплеерах поток данных может делиться на несколько буферных блоков и помещаться в кольцевой список для обеспечения непрерывного воспроизведения.</li> </ul>","path":["Глава 4. Массив и связный список","4.2 &nbsp; Связный список"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/","level":1,"title":"4.3   Список","text":"<p>Список (list) - это абстрактное понятие структуры данных, обозначающее упорядоченную коллекцию элементов, которая поддерживает доступ к элементам, их изменение, добавление, удаление и обход, не требуя от пользователя учитывать ограничения по емкости. Список может быть реализован как на основе связного списка, так и на основе массива.</p> <ul> <li>Связный список естественным образом можно рассматривать как список: он поддерживает операции добавления, удаления, поиска и изменения элементов и может гибко расширяться динамически.</li> <li>Массив тоже поддерживает операции добавления, удаления, поиска и изменения элементов, но из-за неизменяемости длины его можно считать лишь списком с ограниченной длиной.</li> </ul> <p>Когда список реализуется с помощью массива, неизменяемость длины снижает его практическую полезность. Причина в том, что мы обычно не можем заранее точно знать, сколько данных нужно хранить, а значит, трудно выбрать подходящую длину списка. Если длина слишком мала, она может не покрыть реальные потребности; если слишком велика, будет зря расходоваться память.</p> <p>Чтобы решить эту проблему, можно использовать динамический массив (dynamic array) для реализации списка. Он сохраняет все преимущества массива и при этом может динамически расширяться во время выполнения программы.</p> <p>На практике списки из стандартных библиотек многих языков программирования реализованы именно на основе динамических массивов, например <code>list</code> в Python, <code>ArrayList</code> в Java, <code>vector</code> в C++ и <code>List</code> в C#. В дальнейшем обсуждении мы будем считать понятия \"список\" и \"динамический массив\" эквивалентными.</p>","path":["Глава 4. Массив и связный список","4.3 &nbsp; Список"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#431","level":2,"title":"4.3.1   Основные операции со списком","text":"","path":["Глава 4. Массив и связный список","4.3 &nbsp; Список"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#1","level":3,"title":"1.   Инициализация списка","text":"<p>Обычно мы используем два способа инициализации: \"без начальных значений\" и \"с начальными значениями\":</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby list.py<pre><code># Инициализация списка\n# Без начальных значений\nnums1: list[int] = []\n# С начальными значениями\nnums: list[int] = [1, 3, 2, 5, 4]\n</code></pre> list.cpp<pre><code>/* Инициализация списка */\n// Обрати внимание: в C++ vector соответствует описываемому здесь nums\n// Без начальных значений\nvector&lt;int&gt; nums1;\n// С начальными значениями\nvector&lt;int&gt; nums = { 1, 3, 2, 5, 4 };\n</code></pre> list.java<pre><code>/* Инициализация списка */\n// Без начальных значений\nList&lt;Integer&gt; nums1 = new ArrayList&lt;&gt;();\n// С начальными значениями (обрати внимание: элементы массива должны использовать обертку Integer[] вместо int[])\nInteger[] numbers = new Integer[] { 1, 3, 2, 5, 4 };\nList&lt;Integer&gt; nums = new ArrayList&lt;&gt;(Arrays.asList(numbers));\n</code></pre> list.cs<pre><code>/* Инициализация списка */\n// Без начальных значений\nList&lt;int&gt; nums1 = [];\n// С начальными значениями\nint[] numbers = [1, 3, 2, 5, 4];\nList&lt;int&gt; nums = [.. numbers];\n</code></pre> list_test.go<pre><code>/* Инициализация списка */\n// Без начальных значений\nnums1 := []int{}\n// С начальными значениями\nnums := []int{1, 3, 2, 5, 4}\n</code></pre> list.swift<pre><code>/* Инициализация списка */\n// Без начальных значений\nlet nums1: [Int] = []\n// С начальными значениями\nvar nums = [1, 3, 2, 5, 4]\n</code></pre> list.js<pre><code>/* Инициализация списка */\n// Без начальных значений\nconst nums1 = [];\n// С начальными значениями\nconst nums = [1, 3, 2, 5, 4];\n</code></pre> list.ts<pre><code>/* Инициализация списка */\n// Без начальных значений\nconst nums1: number[] = [];\n// С начальными значениями\nconst nums: number[] = [1, 3, 2, 5, 4];\n</code></pre> list.dart<pre><code>/* Инициализация списка */\n// Без начальных значений\nList&lt;int&gt; nums1 = [];\n// С начальными значениями\nList&lt;int&gt; nums = [1, 3, 2, 5, 4];\n</code></pre> list.rs<pre><code>/* Инициализация списка */\n// Без начальных значений\nlet nums1: Vec&lt;i32&gt; = Vec::new();\n// С начальными значениями\nlet nums: Vec&lt;i32&gt; = vec![1, 3, 2, 5, 4];\n</code></pre> list.c<pre><code>// В C нет встроенного динамического массива\n</code></pre> list.kt<pre><code>/* Инициализация списка */\n// Без начальных значений\nvar nums1 = listOf&lt;Int&gt;()\n// С начальными значениями\nvar numbers = arrayOf(1, 3, 2, 5, 4)\nvar nums = numbers.toMutableList()\n</code></pre> list.rb<pre><code># Инициализация списка\n# Без начальных значений\nnums1 = []\n# С начальными значениями\nnums = [1, 3, 2, 5, 4]\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%0A%20%20%20%20%23%20%D0%91%D0%B5%D0%B7%20%D0%BD%D0%B0%D1%87%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B%D1%85%20%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B9%0A%20%20%20%20nums1%20%3D%20%5B%5D%0A%20%20%20%20%23%20%D0%A1%20%D0%BD%D0%B0%D1%87%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B%D0%BC%D0%B8%20%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D1%8F%D0%BC%D0%B8%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D&amp;cumulative=false&amp;curInstr=4&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 4. Массив и связный список","4.3 &nbsp; Список"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#2","level":3,"title":"2.   Доступ к элементам","text":"<p>Список по своей сути является массивом, поэтому доступ к элементам и их обновление можно выполнять за \\(O(1)\\) времени, что очень эффективно.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby list.py<pre><code># Доступ к элементу\nnum: int = nums[1]  # Доступ к элементу по индексу 1\n\n# Обновление элемента\nnums[1] = 0    # Обновить элемент по индексу 1 значением 0\n</code></pre> list.cpp<pre><code>/* Доступ к элементу */\nint num = nums[1];  // Доступ к элементу по индексу 1\n\n/* Обновление элемента */\nnums[1] = 0;  // Обновить элемент по индексу 1 значением 0\n</code></pre> list.java<pre><code>/* Доступ к элементу */\nint num = nums.get(1);  // Доступ к элементу по индексу 1\n\n/* Обновление элемента */\nnums.set(1, 0);  // Обновить элемент по индексу 1 значением 0\n</code></pre> list.cs<pre><code>/* Доступ к элементу */\nint num = nums[1];  // Доступ к элементу по индексу 1\n\n/* Обновление элемента */\nnums[1] = 0;  // Обновить элемент по индексу 1 значением 0\n</code></pre> list_test.go<pre><code>/* Доступ к элементу */\nnum := nums[1]  // Доступ к элементу по индексу 1\n\n/* Обновление элемента */\nnums[1] = 0     // Обновить элемент по индексу 1 значением 0\n</code></pre> list.swift<pre><code>/* Доступ к элементу */\nlet num = nums[1] // Доступ к элементу по индексу 1\n\n/* Обновление элемента */\nnums[1] = 0 // Обновить элемент по индексу 1 значением 0\n</code></pre> list.js<pre><code>/* Доступ к элементу */\nconst num = nums[1];  // Доступ к элементу по индексу 1\n\n/* Обновление элемента */\nnums[1] = 0;  // Обновить элемент по индексу 1 значением 0\n</code></pre> list.ts<pre><code>/* Доступ к элементу */\nconst num: number = nums[1];  // Доступ к элементу по индексу 1\n\n/* Обновление элемента */\nnums[1] = 0;  // Обновить элемент по индексу 1 значением 0\n</code></pre> list.dart<pre><code>/* Доступ к элементу */\nint num = nums[1];  // Доступ к элементу по индексу 1\n\n/* Обновление элемента */\nnums[1] = 0;  // Обновить элемент по индексу 1 значением 0\n</code></pre> list.rs<pre><code>/* Доступ к элементу */\nlet num: i32 = nums[1];  // Доступ к элементу по индексу 1\n/* Обновление элемента */\nnums[1] = 0;             // Обновить элемент по индексу 1 значением 0\n</code></pre> list.c<pre><code>// В C нет встроенного динамического массива\n</code></pre> list.kt<pre><code>/* Доступ к элементу */\nval num = nums[1]       // Доступ к элементу по индексу 1\n/* Обновление элемента */\nnums[1] = 0             // Обновить элемент по индексу 1 значением 0\n</code></pre> list.rb<pre><code># Доступ к элементу\nnum = nums[1] # Доступ к элементу по индексу 1\n# Обновление элемента\nnums[1] = 0 # Обновить элемент по индексу 1 значением 0\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%0A%20%20%20%20%23%20%D0%9F%D0%BE%D0%BB%D1%83%D1%87%D0%B8%D1%82%D1%8C%20%D0%B4%D0%BE%D1%81%D1%82%D1%83%D0%BF%20%D0%BA%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D1%83%0A%20%20%20%20num%20%3D%20nums%5B1%5D%20%20%23%20%D0%BE%D0%B1%D1%80%D0%B0%D1%82%D0%B8%D1%82%D1%8C%D1%81%D1%8F%20%D0%BA%D0%B8%D0%BD%D0%B4%D0%B5%D0%BA%D1%81%201%20%D0%BF%D0%BE%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%0A%0A%20%20%20%20%23%20%D0%9E%D0%B1%D0%BD%D0%BE%D0%B2%D0%B8%D1%82%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%0A%20%20%20%20nums%5B1%5D%20%3D%200%20%20%20%20%23%20%D0%9E%D0%B1%D0%BD%D0%BE%D0%B2%D0%B8%D1%82%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%BF%D0%BE%20%D0%B8%D0%BD%D0%B4%D0%B5%D0%BA%D1%81%D1%83%201%20%D0%B4%D0%BE%200&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 4. Массив и связный список","4.3 &nbsp; Список"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#3","level":3,"title":"3.   Вставка и удаление элементов","text":"<p>По сравнению с массивами список позволяет свободно добавлять и удалять элементы. Добавление элемента в конец списка имеет временную сложность \\(O(1)\\) , но операции вставки и удаления по-прежнему имеют ту же эффективность, что и у массива, то есть \\(O(n)\\) .</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby list.py<pre><code># Очистить список\nnums.clear()\n\n# Добавить элементы в конец\nnums.append(1)\nnums.append(3)\nnums.append(2)\nnums.append(5)\nnums.append(4)\n\n# Вставить элемент в середину\nnums.insert(3, 6)  # Вставить число 6 по индексу 3\n\n# Удалить элемент\nnums.pop(3)        # Удалить элемент по индексу 3\n</code></pre> list.cpp<pre><code>/* Очистить список */\nnums.clear();\n\n/* Добавить элементы в конец */\nnums.push_back(1);\nnums.push_back(3);\nnums.push_back(2);\nnums.push_back(5);\nnums.push_back(4);\n\n/* Вставить элемент в середину */\nnums.insert(nums.begin() + 3, 6);  // Вставить число 6 по индексу 3\n\n/* Удалить элемент */\nnums.erase(nums.begin() + 3);      // Удалить элемент по индексу 3\n</code></pre> list.java<pre><code>/* Очистить список */\nnums.clear();\n\n/* Добавить элементы в конец */\nnums.add(1);\nnums.add(3);\nnums.add(2);\nnums.add(5);\nnums.add(4);\n\n/* Вставить элемент в середину */\nnums.add(3, 6);  // Вставить число 6 по индексу 3\n\n/* Удалить элемент */\nnums.remove(3);  // Удалить элемент по индексу 3\n</code></pre> list.cs<pre><code>/* Очистить список */\nnums.Clear();\n\n/* Добавить элементы в конец */\nnums.Add(1);\nnums.Add(3);\nnums.Add(2);\nnums.Add(5);\nnums.Add(4);\n\n/* Вставить элемент в середину */\nnums.Insert(3, 6);  // Вставить число 6 по индексу 3\n\n/* Удалить элемент */\nnums.RemoveAt(3);  // Удалить элемент по индексу 3\n</code></pre> list_test.go<pre><code>/* Очистить список */\nnums = nil\n\n/* Добавить элементы в конец */\nnums = append(nums, 1)\nnums = append(nums, 3)\nnums = append(nums, 2)\nnums = append(nums, 5)\nnums = append(nums, 4)\n\n/* Вставить элемент в середину */\nnums = append(nums[:3], append([]int{6}, nums[3:]...)...) // Вставить число 6 по индексу 3\n\n/* Удалить элемент */\nnums = append(nums[:3], nums[4:]...) // Удалить элемент по индексу 3\n</code></pre> list.swift<pre><code>/* Очистить список */\nnums.removeAll()\n\n/* Добавить элементы в конец */\nnums.append(1)\nnums.append(3)\nnums.append(2)\nnums.append(5)\nnums.append(4)\n\n/* Вставить элемент в середину */\nnums.insert(6, at: 3) // Вставить число 6 по индексу 3\n\n/* Удалить элемент */\nnums.remove(at: 3) // Удалить элемент по индексу 3\n</code></pre> list.js<pre><code>/* Очистить список */\nnums.length = 0;\n\n/* Добавить элементы в конец */\nnums.push(1);\nnums.push(3);\nnums.push(2);\nnums.push(5);\nnums.push(4);\n\n/* Вставить элемент в середину */\nnums.splice(3, 0, 6); // Вставить число 6 по индексу 3\n\n/* Удалить элемент */\nnums.splice(3, 1);  // Удалить элемент по индексу 3\n</code></pre> list.ts<pre><code>/* Очистить список */\nnums.length = 0;\n\n/* Добавить элементы в конец */\nnums.push(1);\nnums.push(3);\nnums.push(2);\nnums.push(5);\nnums.push(4);\n\n/* Вставить элемент в середину */\nnums.splice(3, 0, 6); // Вставить число 6 по индексу 3\n\n/* Удалить элемент */\nnums.splice(3, 1);  // Удалить элемент по индексу 3\n</code></pre> list.dart<pre><code>/* Очистить список */\nnums.clear();\n\n/* Добавить элементы в конец */\nnums.add(1);\nnums.add(3);\nnums.add(2);\nnums.add(5);\nnums.add(4);\n\n/* Вставить элемент в середину */\nnums.insert(3, 6); // Вставить число 6 по индексу 3\n\n/* Удалить элемент */\nnums.removeAt(3); // Удалить элемент по индексу 3\n</code></pre> list.rs<pre><code>/* Очистить список */\nnums.clear();\n\n/* Добавить элементы в конец */\nnums.push(1);\nnums.push(3);\nnums.push(2);\nnums.push(5);\nnums.push(4);\n\n/* Вставить элемент в середину */\nnums.insert(3, 6);  // Вставить число 6 по индексу 3\n\n/* Удалить элемент */\nnums.remove(3);    // Удалить элемент по индексу 3\n</code></pre> list.c<pre><code>// В C нет встроенного динамического массива\n</code></pre> list.kt<pre><code>/* Очистить список */\nnums.clear();\n\n/* Добавить элементы в конец */\nnums.add(1);\nnums.add(3);\nnums.add(2);\nnums.add(5);\nnums.add(4);\n\n/* Вставить элемент в середину */\nnums.add(3, 6);  // Вставить число 6 по индексу 3\n\n/* Удалить элемент */\nnums.remove(3);  // Удалить элемент по индексу 3\n</code></pre> list.rb<pre><code># Очистить список\nnums.clear\n\n# Добавить элементы в конец\nnums &lt;&lt; 1\nnums &lt;&lt; 3\nnums &lt;&lt; 2\nnums &lt;&lt; 5\nnums &lt;&lt; 4\n\n# Вставить элемент в середину\nnums.insert(3, 6) # Вставить число 6 по индексу 3\n\n# Удалить элемент\nnums.delete_at(3) # Удалить элемент по индексу 3\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%A1%20%D0%BD%D0%B0%D1%87%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B%D0%BC%D0%B8%20%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D1%8F%D0%BC%D0%B8%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9E%D1%87%D0%B8%D1%81%D1%82%D0%B8%D1%82%D1%8C%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%0A%20%20%20%20nums.clear%28%29%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%94%D0%BE%D0%B1%D0%B0%D0%B2%D0%B8%D1%82%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%B2%20%D0%BA%D0%BE%D0%BD%D0%B5%D1%86%0A%20%20%20%20nums.append%281%29%0A%20%20%20%20nums.append%283%29%0A%20%20%20%20nums.append%282%29%0A%20%20%20%20nums.append%285%29%0A%20%20%20%20nums.append%284%29%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%92%D1%81%D1%82%D0%B0%D0%B2%D0%B8%D1%82%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%B2%20%D1%81%D0%B5%D1%80%D0%B5%D0%B4%D0%B8%D0%BD%D1%83%0A%20%20%20%20nums.insert%283%2C%206%29%20%20%23%20%D0%92%D1%81%D1%82%D0%B0%D0%B2%D0%B8%D1%82%D1%8C%20%D1%87%D0%B8%D1%81%D0%BB%D0%BE%206%20%D0%BF%D0%BE%20%D0%B8%D0%BD%D0%B4%D0%B5%D0%BA%D1%81%D1%83%203%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%A3%D0%B4%D0%B0%D0%BB%D0%B8%D1%82%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%0A%20%20%20%20nums.pop%283%29%20%20%20%20%20%20%20%20%23%20%D0%A3%D0%B4%D0%B0%D0%BB%D0%B8%D1%82%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%BF%D0%BE%20%D0%B8%D0%BD%D0%B4%D0%B5%D0%BA%D1%81%D1%83%203&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 4. Массив и связный список","4.3 &nbsp; Список"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#4","level":3,"title":"4.   Обход списка","text":"<p>Как и массив, список можно обходить как по индексам, так и напрямую по элементам.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby list.py<pre><code># Обход списка по индексам\ncount = 0\nfor i in range(len(nums)):\n    count += nums[i]\n\n# Прямой обход элементов списка\nfor num in nums:\n    count += num\n</code></pre> list.cpp<pre><code>/* Обход списка по индексам */\nint count = 0;\nfor (int i = 0; i &lt; nums.size(); i++) {\n    count += nums[i];\n}\n\n/* Прямой обход элементов списка */\ncount = 0;\nfor (int num : nums) {\n    count += num;\n}\n</code></pre> list.java<pre><code>/* Обход списка по индексам */\nint count = 0;\nfor (int i = 0; i &lt; nums.size(); i++) {\n    count += nums.get(i);\n}\n\n/* Прямой обход элементов списка */\nfor (int num : nums) {\n    count += num;\n}\n</code></pre> list.cs<pre><code>/* Обход списка по индексам */\nint count = 0;\nfor (int i = 0; i &lt; nums.Count; i++) {\n    count += nums[i];\n}\n\n/* Прямой обход элементов списка */\ncount = 0;\nforeach (int num in nums) {\n    count += num;\n}\n</code></pre> list_test.go<pre><code>/* Обход списка по индексам */\ncount := 0\nfor i := 0; i &lt; len(nums); i++ {\n    count += nums[i]\n}\n\n/* Прямой обход элементов списка */\ncount = 0\nfor _, num := range nums {\n    count += num\n}\n</code></pre> list.swift<pre><code>/* Обход списка по индексам */\nvar count = 0\nfor i in nums.indices {\n    count += nums[i]\n}\n\n/* Прямой обход элементов списка */\ncount = 0\nfor num in nums {\n    count += num\n}\n</code></pre> list.js<pre><code>/* Обход списка по индексам */\nlet count = 0;\nfor (let i = 0; i &lt; nums.length; i++) {\n    count += nums[i];\n}\n\n/* Прямой обход элементов списка */\ncount = 0;\nfor (const num of nums) {\n    count += num;\n}\n</code></pre> list.ts<pre><code>/* Обход списка по индексам */\nlet count = 0;\nfor (let i = 0; i &lt; nums.length; i++) {\n    count += nums[i];\n}\n\n/* Прямой обход элементов списка */\ncount = 0;\nfor (const num of nums) {\n    count += num;\n}\n</code></pre> list.dart<pre><code>/* Обход списка по индексам */\nint count = 0;\nfor (var i = 0; i &lt; nums.length; i++) {\n    count += nums[i];\n}\n\n/* Прямой обход элементов списка */\ncount = 0;\nfor (var num in nums) {\n    count += num;\n}\n</code></pre> list.rs<pre><code>// Обход списка по индексам\nlet mut _count = 0;\nfor i in 0..nums.len() {\n    _count += nums[i];\n}\n\n// Прямой обход элементов списка\n_count = 0;\nfor num in &amp;nums {\n    _count += num;\n}\n</code></pre> list.c<pre><code>// В C нет встроенного динамического массива\n</code></pre> list.kt<pre><code>/* Обход списка по индексам */\nvar count = 0\nfor (i in nums.indices) {\n    count += nums[i]\n}\n\n/* Прямой обход элементов списка */\nfor (num in nums) {\n    count += num\n}\n</code></pre> list.rb<pre><code># Обход списка по индексам\ncount = 0\nfor i in 0...nums.length\n    count += nums[i]\nend\n\n# Прямой обход элементов списка\ncount = 0\nfor num in nums\n    count += num\nend\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9E%D0%B1%D1%85%D0%BE%D0%B4%D0%B8%D1%82%D1%8C%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%20%D0%BF%D0%BE%20%D0%B8%D0%BD%D0%B4%D0%B5%D0%BA%D1%81%D0%B0%D0%BC%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20for%20i%20in%20range%28len%28nums%29%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%20nums%5Bi%5D%0A%0A%20%20%20%20%23%20%D0%9D%D0%B5%D0%BF%D0%BE%D1%81%D1%80%D0%B5%D0%B4%D1%81%D1%82%D0%B2%D0%B5%D0%BD%D0%BD%D0%BE%20%D0%BE%D0%B1%D1%85%D0%BE%D0%B4%D0%B8%D1%82%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D1%8B%20%D1%81%D0%BF%D0%B8%D1%81%D0%BA%D0%B0%0A%20%20%20%20for%20num%20in%20nums%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%20num&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 4. Массив и связный список","4.3 &nbsp; Список"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#5","level":3,"title":"5.   Конкатенация списков","text":"<p>Если дан новый список <code>nums1</code> , мы можем присоединить его к хвосту исходного списка.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby list.py<pre><code># Конкатенация двух списков\nnums1: list[int] = [6, 8, 7, 10, 9]\nnums += nums1  # Присоединить список nums1 к концу nums\n</code></pre> list.cpp<pre><code>/* Конкатенация двух списков */\nvector&lt;int&gt; nums1 = { 6, 8, 7, 10, 9 };\n// Присоединить список nums1 к концу nums\nnums.insert(nums.end(), nums1.begin(), nums1.end());\n</code></pre> list.java<pre><code>/* Конкатенация двух списков */\nList&lt;Integer&gt; nums1 = new ArrayList&lt;&gt;(Arrays.asList(new Integer[] { 6, 8, 7, 10, 9 }));\nnums.addAll(nums1);  // Присоединить список nums1 к концу nums\n</code></pre> list.cs<pre><code>/* Конкатенация двух списков */\nList&lt;int&gt; nums1 = [6, 8, 7, 10, 9];\nnums.AddRange(nums1);  // Присоединить список nums1 к концу nums\n</code></pre> list_test.go<pre><code>/* Конкатенация двух списков */\nnums1 := []int{6, 8, 7, 10, 9}\nnums = append(nums, nums1...)  // Присоединить список nums1 к концу nums\n</code></pre> list.swift<pre><code>/* Конкатенация двух списков */\nlet nums1 = [6, 8, 7, 10, 9]\nnums.append(contentsOf: nums1) // Присоединить список nums1 к концу nums\n</code></pre> list.js<pre><code>/* Конкатенация двух списков */\nconst nums1 = [6, 8, 7, 10, 9];\nnums.push(...nums1);  // Присоединить список nums1 к концу nums\n</code></pre> list.ts<pre><code>/* Конкатенация двух списков */\nconst nums1: number[] = [6, 8, 7, 10, 9];\nnums.push(...nums1);  // Присоединить список nums1 к концу nums\n</code></pre> list.dart<pre><code>/* Конкатенация двух списков */\nList&lt;int&gt; nums1 = [6, 8, 7, 10, 9];\nnums.addAll(nums1);  // Присоединить список nums1 к концу nums\n</code></pre> list.rs<pre><code>/* Конкатенация двух списков */\nlet nums1: Vec&lt;i32&gt; = vec![6, 8, 7, 10, 9];\nnums.extend(nums1);\n</code></pre> list.c<pre><code>// В C нет встроенного динамического массива\n</code></pre> list.kt<pre><code>/* Конкатенация двух списков */\nval nums1 = intArrayOf(6, 8, 7, 10, 9).toMutableList()\nnums.addAll(nums1)  // Присоединить список nums1 к концу nums\n</code></pre> list.rb<pre><code># Конкатенация двух списков\nnums1 = [6, 8, 7, 10, 9]\nnums += nums1\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9E%D0%B1%D1%8A%D0%B5%D0%B4%D0%B8%D0%BD%D0%B8%D1%82%D1%8C%20%D0%B4%D0%B2%D0%B0%20%D1%81%D0%BF%D0%B8%D1%81%D0%BA%D0%B0%0A%20%20%20%20nums1%20%3D%20%5B6%2C%208%2C%207%2C%2010%2C%209%5D%0A%20%20%20%20nums%20%2B%3D%20nums1%20%20%23%20%D0%9F%D1%80%D0%B8%D1%81%D0%BE%D0%B5%D0%B4%D0%B8%D0%BD%D0%B8%D1%82%D1%8C%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%20nums1%20%D0%BA%20nums&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 4. Массив и связный список","4.3 &nbsp; Список"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#6","level":3,"title":"6.   Сортировка списка","text":"<p>После сортировки списка мы сможем применять алгоритмы \"бинарный поиск\" и \"два указателя\", которые очень часто встречаются в задачах по массивам.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby list.py<pre><code># Отсортировать список\nnums.sort()  # После сортировки элементы списка идут по возрастанию\n</code></pre> list.cpp<pre><code>/* Отсортировать список */\nsort(nums.begin(), nums.end());  // После сортировки элементы списка идут по возрастанию\n</code></pre> list.java<pre><code>/* Отсортировать список */\nCollections.sort(nums);  // После сортировки элементы списка идут по возрастанию\n</code></pre> list.cs<pre><code>/* Отсортировать список */\nnums.Sort(); // После сортировки элементы списка идут по возрастанию\n</code></pre> list_test.go<pre><code>/* Отсортировать список */\nsort.Ints(nums)  // После сортировки элементы списка идут по возрастанию\n</code></pre> list.swift<pre><code>/* Отсортировать список */\nnums.sort() // После сортировки элементы списка идут по возрастанию\n</code></pre> list.js<pre><code>/* Отсортировать список */\nnums.sort((a, b) =&gt; a - b);  // После сортировки элементы списка идут по возрастанию\n</code></pre> list.ts<pre><code>/* Отсортировать список */\nnums.sort((a, b) =&gt; a - b);  // После сортировки элементы списка идут по возрастанию\n</code></pre> list.dart<pre><code>/* Отсортировать список */\nnums.sort(); // После сортировки элементы списка идут по возрастанию\n</code></pre> list.rs<pre><code>/* Отсортировать список */\nnums.sort(); // После сортировки элементы списка идут по возрастанию\n</code></pre> list.c<pre><code>// В C нет встроенного динамического массива\n</code></pre> list.kt<pre><code>/* Отсортировать список */\nnums.sort() // После сортировки элементы списка идут по возрастанию\n</code></pre> list.rb<pre><code># Отсортировать список\nnums = nums.sort { |a, b| a &lt;=&gt; b } # После сортировки элементы списка идут по возрастанию\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9E%D1%82%D1%81%D0%BE%D1%80%D1%82%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%0A%20%20%20%20nums.sort%28%29%20%20%23%20%D0%A1%D0%BE%D1%80%D1%82%D0%B8%D1%80%D0%BE%D0%B2%D0%BA%D0%B0%D0%BF%D0%BE%D1%81%D0%BB%D0%B5%2C%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D1%80%D0%B0%D1%81%D0%BF%D0%BE%D0%BB%D0%BE%D0%B6%D0%B5%D0%BD%D1%8B%20%D0%BF%D0%BE%20%D0%B2%D0%BE%D0%B7%D1%80%D0%B0%D1%81%D1%82%D0%B0%D0%BD%D0%B8%D1%8E&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 4. Массив и связный список","4.3 &nbsp; Список"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#432","level":2,"title":"4.3.2   Реализация списка","text":"<p>Во многих языках программирования списки встроены в стандартную библиотеку, например в Java, C++ и Python. Их реализация довольно сложна, а настройки параметров тщательно продуманы: начальная емкость, коэффициент расширения и так далее. Если тебе интересно, стоит заглянуть в исходный код.</p> <p>Чтобы лучше понять принцип работы списка, попробуем реализовать его упрощенную версию, в которой есть три ключевых аспекта проектирования.</p> <ul> <li>Начальная емкость: выбрать разумную начальную емкость внутреннего массива. В этом примере мы берем 10.</li> <li>Учет количества элементов: объявить переменную <code>size</code> , которая будет хранить текущее число элементов в списке и обновляться в реальном времени при вставке и удалении элементов. С помощью этой переменной можно находить конец списка и понимать, требуется ли расширение.</li> <li>Механизм расширения: если при вставке элементов емкость списка исчерпана, нужно выполнить расширение. Для этого сначала создается больший массив с учетом коэффициента расширения, а затем все элементы текущего массива по порядку переносятся в новый. В этом примере мы считаем, что каждый раз массив расширяется в 2 раза.</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby my_list.py<pre><code>class MyList:\n    \"\"\"Класс списка\"\"\"\n\n    def __init__(self):\n        \"\"\"Конструктор\"\"\"\n        self._capacity: int = 10  # Вместимость списка\n        self._arr: list[int] = [0] * self._capacity  # Массив (для хранения элементов списка)\n        self._size: int = 0  # Длина списка (текущее число элементов)\n        self._extend_ratio: int = 2  # Коэффициент увеличения списка при каждом расширении\n\n    def size(self) -&gt; int:\n        \"\"\"Получить длину списка (текущее число элементов)\"\"\"\n        return self._size\n\n    def capacity(self) -&gt; int:\n        \"\"\"Получить вместимость списка\"\"\"\n        return self._capacity\n\n    def get(self, index: int) -&gt; int:\n        \"\"\"Доступ к элементу\"\"\"\n        # Если индекс выходит за границы, выбрасывается исключение; далее аналогично\n        if index &lt; 0 or index &gt;= self._size:\n            raise IndexError(\"индекс выходит за границы\")\n        return self._arr[index]\n\n    def set(self, num: int, index: int):\n        \"\"\"Обновление элемента\"\"\"\n        if index &lt; 0 or index &gt;= self._size:\n            raise IndexError(\"индекс выходит за границы\")\n        self._arr[index] = num\n\n    def add(self, num: int):\n        \"\"\"Добавление элемента в конец\"\"\"\n        # При превышении вместимости по числу элементов запускается расширение\n        if self.size() == self.capacity():\n            self.extend_capacity()\n        self._arr[self._size] = num\n        self._size += 1\n\n    def insert(self, num: int, index: int):\n        \"\"\"Вставка элемента в середину\"\"\"\n        if index &lt; 0 or index &gt;= self._size:\n            raise IndexError(\"индекс выходит за границы\")\n        # При превышении вместимости по числу элементов запускается расширение\n        if self._size == self.capacity():\n            self.extend_capacity()\n        # Сдвинуть элемент с индексом index и все следующие элементы на одну позицию назад\n        for j in range(self._size - 1, index - 1, -1):\n            self._arr[j + 1] = self._arr[j]\n        self._arr[index] = num\n        # Обновить число элементов\n        self._size += 1\n\n    def remove(self, index: int) -&gt; int:\n        \"\"\"Удаление элемента\"\"\"\n        if index &lt; 0 or index &gt;= self._size:\n            raise IndexError(\"индекс выходит за границы\")\n        num = self._arr[index]\n        # Сдвинуть все элементы после индекса index на одну позицию вперед\n        for j in range(index, self._size - 1):\n            self._arr[j] = self._arr[j + 1]\n        # Обновить число элементов\n        self._size -= 1\n        # Вернуть удаленный элемент\n        return num\n\n    def extend_capacity(self):\n        \"\"\"Расширение списка\"\"\"\n        # Создать новый массив длиной в _extend_ratio раз больше исходного массива и скопировать в него исходный массив\n        self._arr = self._arr + [0] * self.capacity() * (self._extend_ratio - 1)\n        # Обновить вместимость списка\n        self._capacity = len(self._arr)\n\n    def to_array(self) -&gt; list[int]:\n        \"\"\"Вернуть список фактической длины\"\"\"\n        return self._arr[: self._size]\n</code></pre> my_list.cpp<pre><code>/* Класс списка */\nclass MyList {\n  private:\n    int *arr;             // Массив (для хранения элементов списка)\n    int arrCapacity = 10; // Вместимость списка\n    int arrSize = 0;      // Длина списка (текущее число элементов)\n    int extendRatio = 2;   // Коэффициент увеличения списка при каждом расширении\n\n  public:\n    /* Конструктор */\n    MyList() {\n        arr = new int[arrCapacity];\n    }\n\n    /* Метод-деструктор */\n    ~MyList() {\n        delete[] arr;\n    }\n\n    /* Получить длину списка (текущее число элементов) */\n    int size() {\n        return arrSize;\n    }\n\n    /* Получить вместимость списка */\n    int capacity() {\n        return arrCapacity;\n    }\n\n    /* Доступ к элементу */\n    int get(int index) {\n        // Если индекс выходит за границы, выбрасывается исключение; далее аналогично\n        if (index &lt; 0 || index &gt;= size())\n            throw out_of_range(\"индекс выходит за границы\");\n        return arr[index];\n    }\n\n    /* Обновление элемента */\n    void set(int index, int num) {\n        if (index &lt; 0 || index &gt;= size())\n            throw out_of_range(\"индекс выходит за границы\");\n        arr[index] = num;\n    }\n\n    /* Добавление элемента в конец */\n    void add(int num) {\n        // При превышении вместимости по числу элементов запускается расширение\n        if (size() == capacity())\n            extendCapacity();\n        arr[size()] = num;\n        // Обновить число элементов\n        arrSize++;\n    }\n\n    /* Вставка элемента в середину */\n    void insert(int index, int num) {\n        if (index &lt; 0 || index &gt;= size())\n            throw out_of_range(\"индекс выходит за границы\");\n        // При превышении вместимости по числу элементов запускается расширение\n        if (size() == capacity())\n            extendCapacity();\n        // Сдвинуть элемент с индексом index и все следующие элементы на одну позицию назад\n        for (int j = size() - 1; j &gt;= index; j--) {\n            arr[j + 1] = arr[j];\n        }\n        arr[index] = num;\n        // Обновить число элементов\n        arrSize++;\n    }\n\n    /* Удаление элемента */\n    int remove(int index) {\n        if (index &lt; 0 || index &gt;= size())\n            throw out_of_range(\"индекс выходит за границы\");\n        int num = arr[index];\n        // Сдвинуть все элементы после индекса index на одну позицию вперед\n        for (int j = index; j &lt; size() - 1; j++) {\n            arr[j] = arr[j + 1];\n        }\n        // Обновить число элементов\n        arrSize--;\n        // Вернуть удаленный элемент\n        return num;\n    }\n\n    /* Расширение списка */\n    void extendCapacity() {\n        // Создать новый массив длиной в extendRatio раз больше исходного массива\n        int newCapacity = capacity() * extendRatio;\n        int *tmp = arr;\n        arr = new int[newCapacity];\n        // Скопировать все элементы исходного массива в новый массив\n        for (int i = 0; i &lt; size(); i++) {\n            arr[i] = tmp[i];\n        }\n        // Освободить память\n        delete[] tmp;\n        arrCapacity = newCapacity;\n    }\n\n    /* Преобразовать список в Vector для вывода */\n    vector&lt;int&gt; toVector() {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        vector&lt;int&gt; vec(size());\n        for (int i = 0; i &lt; size(); i++) {\n            vec[i] = arr[i];\n        }\n        return vec;\n    }\n};\n</code></pre> my_list.java<pre><code>/* Класс списка */\nclass MyList {\n    private int[] arr; // Массив (для хранения элементов списка)\n    private int capacity = 10; // Вместимость списка\n    private int size = 0; // Длина списка (текущее число элементов)\n    private int extendRatio = 2; // Коэффициент увеличения списка при каждом расширении\n\n    /* Конструктор */\n    public MyList() {\n        arr = new int[capacity];\n    }\n\n    /* Получить длину списка (текущее число элементов) */\n    public int size() {\n        return size;\n    }\n\n    /* Получить вместимость списка */\n    public int capacity() {\n        return capacity;\n    }\n\n    /* Доступ к элементу */\n    public int get(int index) {\n        // Если индекс выходит за границы, выбрасывается исключение; далее аналогично\n        if (index &lt; 0 || index &gt;= size)\n            throw new IndexOutOfBoundsException(\"индекс выходит за границы\");\n        return arr[index];\n    }\n\n    /* Обновление элемента */\n    public void set(int index, int num) {\n        if (index &lt; 0 || index &gt;= size)\n            throw new IndexOutOfBoundsException(\"индекс выходит за границы\");\n        arr[index] = num;\n    }\n\n    /* Добавление элемента в конец */\n    public void add(int num) {\n        // При превышении вместимости по числу элементов запускается расширение\n        if (size == capacity())\n            extendCapacity();\n        arr[size] = num;\n        // Обновить число элементов\n        size++;\n    }\n\n    /* Вставка элемента в середину */\n    public void insert(int index, int num) {\n        if (index &lt; 0 || index &gt;= size)\n            throw new IndexOutOfBoundsException(\"индекс выходит за границы\");\n        // При превышении вместимости по числу элементов запускается расширение\n        if (size == capacity())\n            extendCapacity();\n        // Сдвинуть элемент с индексом index и все следующие элементы на одну позицию назад\n        for (int j = size - 1; j &gt;= index; j--) {\n            arr[j + 1] = arr[j];\n        }\n        arr[index] = num;\n        // Обновить число элементов\n        size++;\n    }\n\n    /* Удаление элемента */\n    public int remove(int index) {\n        if (index &lt; 0 || index &gt;= size)\n            throw new IndexOutOfBoundsException(\"индекс выходит за границы\");\n        int num = arr[index];\n        // Сдвинуть все элементы после индекса index на одну позицию вперед\n        for (int j = index; j &lt; size - 1; j++) {\n            arr[j] = arr[j + 1];\n        }\n        // Обновить число элементов\n        size--;\n        // Вернуть удаленный элемент\n        return num;\n    }\n\n    /* Расширение списка */\n    public void extendCapacity() {\n        // Создать новый массив длиной в extendRatio раз больше исходного и скопировать в него исходный массив\n        arr = Arrays.copyOf(arr, capacity() * extendRatio);\n        // Обновить вместимость списка\n        capacity = arr.length;\n    }\n\n    /* Преобразовать список в массив */\n    public int[] toArray() {\n        int size = size();\n        // Преобразовывать только элементы списка в пределах фактической длины\n        int[] arr = new int[size];\n        for (int i = 0; i &lt; size; i++) {\n            arr[i] = get(i);\n        }\n        return arr;\n    }\n}\n</code></pre> my_list.cs<pre><code>/* Класс списка */\nclass MyList {\n    private int[] arr;           // Массив (для хранения элементов списка)\n    private int arrCapacity = 10;    // Вместимость списка\n    private int arrSize = 0;         // Длина списка (текущее число элементов)\n    private readonly int extendRatio = 2;  // Коэффициент увеличения списка при каждом расширении\n\n    /* Конструктор */\n    public MyList() {\n        arr = new int[arrCapacity];\n    }\n\n    /* Получить длину списка (текущее число элементов) */\n    public int Size() {\n        return arrSize;\n    }\n\n    /* Получить вместимость списка */\n    public int Capacity() {\n        return arrCapacity;\n    }\n\n    /* Доступ к элементу */\n    public int Get(int index) {\n        // Если индекс выходит за границы, выбрасывается исключение; далее аналогично\n        if (index &lt; 0 || index &gt;= arrSize)\n            throw new IndexOutOfRangeException(\"индекс выходит за границы\");\n        return arr[index];\n    }\n\n    /* Обновление элемента */\n    public void Set(int index, int num) {\n        if (index &lt; 0 || index &gt;= arrSize)\n            throw new IndexOutOfRangeException(\"индекс выходит за границы\");\n        arr[index] = num;\n    }\n\n    /* Добавление элемента в конец */\n    public void Add(int num) {\n        // При превышении вместимости по числу элементов запускается расширение\n        if (arrSize == arrCapacity)\n            ExtendCapacity();\n        arr[arrSize] = num;\n        // Обновить число элементов\n        arrSize++;\n    }\n\n    /* Вставка элемента в середину */\n    public void Insert(int index, int num) {\n        if (index &lt; 0 || index &gt;= arrSize)\n            throw new IndexOutOfRangeException(\"индекс выходит за границы\");\n        // При превышении вместимости по числу элементов запускается расширение\n        if (arrSize == arrCapacity)\n            ExtendCapacity();\n        // Сдвинуть элемент с индексом index и все следующие элементы на одну позицию назад\n        for (int j = arrSize - 1; j &gt;= index; j--) {\n            arr[j + 1] = arr[j];\n        }\n        arr[index] = num;\n        // Обновить число элементов\n        arrSize++;\n    }\n\n    /* Удаление элемента */\n    public int Remove(int index) {\n        if (index &lt; 0 || index &gt;= arrSize)\n            throw new IndexOutOfRangeException(\"индекс выходит за границы\");\n        int num = arr[index];\n        // Сдвинуть все элементы после индекса index на одну позицию вперед\n        for (int j = index; j &lt; arrSize - 1; j++) {\n            arr[j] = arr[j + 1];\n        }\n        // Обновить число элементов\n        arrSize--;\n        // Вернуть удаленный элемент\n        return num;\n    }\n\n    /* Расширение списка */\n    public void ExtendCapacity() {\n        // Создать новый массив длиной arrCapacity * extendRatio и скопировать в него исходный массив\n        Array.Resize(ref arr, arrCapacity * extendRatio);\n        // Обновить вместимость списка\n        arrCapacity = arr.Length;\n    }\n\n    /* Преобразовать список в массив */\n    public int[] ToArray() {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        int[] arr = new int[arrSize];\n        for (int i = 0; i &lt; arrSize; i++) {\n            arr[i] = Get(i);\n        }\n        return arr;\n    }\n}\n</code></pre> my_list.go<pre><code>/* Класс списка */\ntype myList struct {\n    arrCapacity int\n    arr         []int\n    arrSize     int\n    extendRatio int\n}\n\n/* Конструктор */\nfunc newMyList() *myList {\n    return &amp;myList{\n        arrCapacity: 10,              // Вместимость списка\n        arr:         make([]int, 10), // Массив (для хранения элементов списка)\n        arrSize:     0,               // Длина списка (текущее число элементов)\n        extendRatio: 2,               // Коэффициент увеличения списка при каждом расширении\n    }\n}\n\n/* Получить длину списка (текущее число элементов) */\nfunc (l *myList) size() int {\n    return l.arrSize\n}\n\n/* Получить вместимость списка */\nfunc (l *myList) capacity() int {\n    return l.arrCapacity\n}\n\n/* Доступ к элементу */\nfunc (l *myList) get(index int) int {\n    // Если индекс выходит за границы, выбрасывается исключение; далее аналогично\n    if index &lt; 0 || index &gt;= l.arrSize {\n        panic(\"индекс выходит за границы\")\n    }\n    return l.arr[index]\n}\n\n/* Обновление элемента */\nfunc (l *myList) set(num, index int) {\n    if index &lt; 0 || index &gt;= l.arrSize {\n        panic(\"индекс выходит за границы\")\n    }\n    l.arr[index] = num\n}\n\n/* Добавление элемента в конец */\nfunc (l *myList) add(num int) {\n    // При превышении вместимости по числу элементов запускается расширение\n    if l.arrSize == l.arrCapacity {\n        l.extendCapacity()\n    }\n    l.arr[l.arrSize] = num\n    // Обновить число элементов\n    l.arrSize++\n}\n\n/* Вставка элемента в середину */\nfunc (l *myList) insert(num, index int) {\n    if index &lt; 0 || index &gt;= l.arrSize {\n        panic(\"индекс выходит за границы\")\n    }\n    // При превышении вместимости по числу элементов запускается расширение\n    if l.arrSize == l.arrCapacity {\n        l.extendCapacity()\n    }\n    // Сдвинуть элемент с индексом index и все следующие элементы на одну позицию назад\n    for j := l.arrSize - 1; j &gt;= index; j-- {\n        l.arr[j+1] = l.arr[j]\n    }\n    l.arr[index] = num\n    // Обновить число элементов\n    l.arrSize++\n}\n\n/* Удаление элемента */\nfunc (l *myList) remove(index int) int {\n    if index &lt; 0 || index &gt;= l.arrSize {\n        panic(\"индекс выходит за границы\")\n    }\n    num := l.arr[index]\n    // Сдвинуть все элементы после индекса index на одну позицию вперед\n    for j := index; j &lt; l.arrSize-1; j++ {\n        l.arr[j] = l.arr[j+1]\n    }\n    // Обновить число элементов\n    l.arrSize--\n    // Вернуть удаленный элемент\n    return num\n}\n\n/* Расширение списка */\nfunc (l *myList) extendCapacity() {\n    // Создать новый массив длиной в extendRatio раз больше исходного и скопировать в него исходный массив\n    l.arr = append(l.arr, make([]int, l.arrCapacity*(l.extendRatio-1))...)\n    // Обновить вместимость списка\n    l.arrCapacity = len(l.arr)\n}\n\n/* Вернуть список фактической длины */\nfunc (l *myList) toArray() []int {\n    // Преобразовывать только элементы списка в пределах фактической длины\n    return l.arr[:l.arrSize]\n}\n</code></pre> my_list.swift<pre><code>/* Класс списка */\nclass MyList {\n    private var arr: [Int] // Массив (для хранения элементов списка)\n    private var _capacity: Int // Вместимость списка\n    private var _size: Int // Длина списка (текущее число элементов)\n    private let extendRatio: Int // Коэффициент увеличения списка при каждом расширении\n\n    /* Конструктор */\n    init() {\n        _capacity = 10\n        _size = 0\n        extendRatio = 2\n        arr = Array(repeating: 0, count: _capacity)\n    }\n\n    /* Получить длину списка (текущее число элементов) */\n    func size() -&gt; Int {\n        _size\n    }\n\n    /* Получить вместимость списка */\n    func capacity() -&gt; Int {\n        _capacity\n    }\n\n    /* Доступ к элементу */\n    func get(index: Int) -&gt; Int {\n        // Если индекс выходит за границы, выбросить ошибку; далее аналогично\n        if index &lt; 0 || index &gt;= size() {\n            fatalError(\"индекс выходит за границы\")\n        }\n        return arr[index]\n    }\n\n    /* Обновление элемента */\n    func set(index: Int, num: Int) {\n        if index &lt; 0 || index &gt;= size() {\n            fatalError(\"индекс выходит за границы\")\n        }\n        arr[index] = num\n    }\n\n    /* Добавление элемента в конец */\n    func add(num: Int) {\n        // При превышении вместимости по числу элементов запускается расширение\n        if size() == capacity() {\n            extendCapacity()\n        }\n        arr[size()] = num\n        // Обновить число элементов\n        _size += 1\n    }\n\n    /* Вставка элемента в середину */\n    func insert(index: Int, num: Int) {\n        if index &lt; 0 || index &gt;= size() {\n            fatalError(\"индекс выходит за границы\")\n        }\n        // При превышении вместимости по числу элементов запускается расширение\n        if size() == capacity() {\n            extendCapacity()\n        }\n        // Сдвинуть элемент с индексом index и все следующие элементы на одну позицию назад\n        for j in (index ..&lt; size()).reversed() {\n            arr[j + 1] = arr[j]\n        }\n        arr[index] = num\n        // Обновить число элементов\n        _size += 1\n    }\n\n    /* Удаление элемента */\n    @discardableResult\n    func remove(index: Int) -&gt; Int {\n        if index &lt; 0 || index &gt;= size() {\n            fatalError(\"индекс выходит за границы\")\n        }\n        let num = arr[index]\n        // Сдвинуть все элементы после индекса index на одну позицию вперед\n        for j in index ..&lt; (size() - 1) {\n            arr[j] = arr[j + 1]\n        }\n        // Обновить число элементов\n        _size -= 1\n        // Вернуть удаленный элемент\n        return num\n    }\n\n    /* Расширение списка */\n    func extendCapacity() {\n        // Создать новый массив длиной в extendRatio раз больше исходного и скопировать в него исходный массив\n        arr = arr + Array(repeating: 0, count: capacity() * (extendRatio - 1))\n        // Обновить вместимость списка\n        _capacity = arr.count\n    }\n\n    /* Преобразовать список в массив */\n    func toArray() -&gt; [Int] {\n        Array(arr.prefix(size()))\n    }\n}\n</code></pre> my_list.js<pre><code>/* Класс списка */\nclass MyList {\n    #arr = new Array(); // Массив (для хранения элементов списка)\n    #capacity = 10; // Вместимость списка\n    #size = 0; // Длина списка (текущее число элементов)\n    #extendRatio = 2; // Коэффициент увеличения списка при каждом расширении\n\n    /* Конструктор */\n    constructor() {\n        this.#arr = new Array(this.#capacity);\n    }\n\n    /* Получить длину списка (текущее число элементов) */\n    size() {\n        return this.#size;\n    }\n\n    /* Получить вместимость списка */\n    capacity() {\n        return this.#capacity;\n    }\n\n    /* Доступ к элементу */\n    get(index) {\n        // Если индекс выходит за границы, выбрасывается исключение; далее аналогично\n        if (index &lt; 0 || index &gt;= this.#size) throw new Error('индекс выходит за границы');\n        return this.#arr[index];\n    }\n\n    /* Обновление элемента */\n    set(index, num) {\n        if (index &lt; 0 || index &gt;= this.#size) throw new Error('индекс выходит за границы');\n        this.#arr[index] = num;\n    }\n\n    /* Добавление элемента в конец */\n    add(num) {\n        // Если длина равна вместимости, требуется расширение\n        if (this.#size === this.#capacity) {\n            this.extendCapacity();\n        }\n        // Добавить новый элемент в конец списка\n        this.#arr[this.#size] = num;\n        this.#size++;\n    }\n\n    /* Вставка элемента в середину */\n    insert(index, num) {\n        if (index &lt; 0 || index &gt;= this.#size) throw new Error('индекс выходит за границы');\n        // При превышении вместимости по числу элементов запускается расширение\n        if (this.#size === this.#capacity) {\n            this.extendCapacity();\n        }\n        // Сдвинуть элемент с индексом index и все следующие элементы на одну позицию назад\n        for (let j = this.#size - 1; j &gt;= index; j--) {\n            this.#arr[j + 1] = this.#arr[j];\n        }\n        // Обновить число элементов\n        this.#arr[index] = num;\n        this.#size++;\n    }\n\n    /* Удаление элемента */\n    remove(index) {\n        if (index &lt; 0 || index &gt;= this.#size) throw new Error('индекс выходит за границы');\n        let num = this.#arr[index];\n        // Сдвинуть все элементы после индекса index на одну позицию вперед\n        for (let j = index; j &lt; this.#size - 1; j++) {\n            this.#arr[j] = this.#arr[j + 1];\n        }\n        // Обновить число элементов\n        this.#size--;\n        // Вернуть удаленный элемент\n        return num;\n    }\n\n    /* Расширение списка */\n    extendCapacity() {\n        // Создать новый массив длиной в extendRatio раз больше исходного и скопировать в него исходный массив\n        this.#arr = this.#arr.concat(\n            new Array(this.capacity() * (this.#extendRatio - 1))\n        );\n        // Обновить вместимость списка\n        this.#capacity = this.#arr.length;\n    }\n\n    /* Преобразовать список в массив */\n    toArray() {\n        let size = this.size();\n        // Преобразовывать только элементы списка в пределах фактической длины\n        const arr = new Array(size);\n        for (let i = 0; i &lt; size; i++) {\n            arr[i] = this.get(i);\n        }\n        return arr;\n    }\n}\n</code></pre> my_list.ts<pre><code>/* Класс списка */\nclass MyList {\n    private arr: Array&lt;number&gt;; // Массив (для хранения элементов списка)\n    private _capacity: number = 10; // Вместимость списка\n    private _size: number = 0; // Длина списка (текущее число элементов)\n    private extendRatio: number = 2; // Коэффициент увеличения списка при каждом расширении\n\n    /* Конструктор */\n    constructor() {\n        this.arr = new Array(this._capacity);\n    }\n\n    /* Получить длину списка (текущее число элементов) */\n    public size(): number {\n        return this._size;\n    }\n\n    /* Получить вместимость списка */\n    public capacity(): number {\n        return this._capacity;\n    }\n\n    /* Доступ к элементу */\n    public get(index: number): number {\n        // Если индекс выходит за границы, выбрасывается исключение; далее аналогично\n        if (index &lt; 0 || index &gt;= this._size) throw new Error('индекс выходит за границы');\n        return this.arr[index];\n    }\n\n    /* Обновление элемента */\n    public set(index: number, num: number): void {\n        if (index &lt; 0 || index &gt;= this._size) throw new Error('индекс выходит за границы');\n        this.arr[index] = num;\n    }\n\n    /* Добавление элемента в конец */\n    public add(num: number): void {\n        // Если длина равна вместимости, требуется расширение\n        if (this._size === this._capacity) this.extendCapacity();\n        // Добавить новый элемент в конец списка\n        this.arr[this._size] = num;\n        this._size++;\n    }\n\n    /* Вставка элемента в середину */\n    public insert(index: number, num: number): void {\n        if (index &lt; 0 || index &gt;= this._size) throw new Error('индекс выходит за границы');\n        // При превышении вместимости по числу элементов запускается расширение\n        if (this._size === this._capacity) {\n            this.extendCapacity();\n        }\n        // Сдвинуть элемент с индексом index и все следующие элементы на одну позицию назад\n        for (let j = this._size - 1; j &gt;= index; j--) {\n            this.arr[j + 1] = this.arr[j];\n        }\n        // Обновить число элементов\n        this.arr[index] = num;\n        this._size++;\n    }\n\n    /* Удаление элемента */\n    public remove(index: number): number {\n        if (index &lt; 0 || index &gt;= this._size) throw new Error('индекс выходит за границы');\n        let num = this.arr[index];\n        // Сдвинуть все элементы после индекса index на одну позицию вперед\n        for (let j = index; j &lt; this._size - 1; j++) {\n            this.arr[j] = this.arr[j + 1];\n        }\n        // Обновить число элементов\n        this._size--;\n        // Вернуть удаленный элемент\n        return num;\n    }\n\n    /* Расширение списка */\n    public extendCapacity(): void {\n        // Создать новый массив длиной size и скопировать в него исходный массив\n        this.arr = this.arr.concat(\n            new Array(this.capacity() * (this.extendRatio - 1))\n        );\n        // Обновить вместимость списка\n        this._capacity = this.arr.length;\n    }\n\n    /* Преобразовать список в массив */\n    public toArray(): number[] {\n        let size = this.size();\n        // Преобразовывать только элементы списка в пределах фактической длины\n        const arr = new Array(size);\n        for (let i = 0; i &lt; size; i++) {\n            arr[i] = this.get(i);\n        }\n        return arr;\n    }\n}\n</code></pre> my_list.dart<pre><code>/* Класс списка */\nclass MyList {\n  late List&lt;int&gt; _arr; // Массив (для хранения элементов списка)\n  int _capacity = 10; // Вместимость списка\n  int _size = 0; // Длина списка (текущее число элементов)\n  int _extendRatio = 2; // Коэффициент увеличения списка при каждом расширении\n\n  /* Конструктор */\n  MyList() {\n    _arr = List.filled(_capacity, 0);\n  }\n\n  /* Получить длину списка (текущее число элементов) */\n  int size() =&gt; _size;\n\n  /* Получить вместимость списка */\n  int capacity() =&gt; _capacity;\n\n  /* Доступ к элементу */\n  int get(int index) {\n    if (index &gt;= _size) throw RangeError('индекс выходит за границы');\n    return _arr[index];\n  }\n\n  /* Обновление элемента */\n  void set(int index, int _num) {\n    if (index &gt;= _size) throw RangeError('индекс выходит за границы');\n    _arr[index] = _num;\n  }\n\n  /* Добавление элемента в конец */\n  void add(int _num) {\n    // При превышении вместимости по числу элементов запускается расширение\n    if (_size == _capacity) extendCapacity();\n    _arr[_size] = _num;\n    // Обновить число элементов\n    _size++;\n  }\n\n  /* Вставка элемента в середину */\n  void insert(int index, int _num) {\n    if (index &gt;= _size) throw RangeError('индекс выходит за границы');\n    // При превышении вместимости по числу элементов запускается расширение\n    if (_size == _capacity) extendCapacity();\n    // Сдвинуть элемент с индексом index и все следующие элементы на одну позицию назад\n    for (var j = _size - 1; j &gt;= index; j--) {\n      _arr[j + 1] = _arr[j];\n    }\n    _arr[index] = _num;\n    // Обновить число элементов\n    _size++;\n  }\n\n  /* Удаление элемента */\n  int remove(int index) {\n    if (index &gt;= _size) throw RangeError('индекс выходит за границы');\n    int _num = _arr[index];\n    // Сдвинуть все элементы после индекса index на одну позицию вперед\n    for (var j = index; j &lt; _size - 1; j++) {\n      _arr[j] = _arr[j + 1];\n    }\n    // Обновить число элементов\n    _size--;\n    // Вернуть удаленный элемент\n    return _num;\n  }\n\n  /* Расширение списка */\n  void extendCapacity() {\n    // Создать новый массив длиной в _extendRatio раз больше исходного массива\n    final _newNums = List.filled(_capacity * _extendRatio, 0);\n    // Скопировать исходный массив в новый массив\n    List.copyRange(_newNums, 0, _arr);\n    // Обновить ссылку на _arr\n    _arr = _newNums;\n    // Обновить вместимость списка\n    _capacity = _arr.length;\n  }\n\n  /* Преобразовать список в массив */\n  List&lt;int&gt; toArray() {\n    List&lt;int&gt; arr = [];\n    for (var i = 0; i &lt; _size; i++) {\n      arr.add(get(i));\n    }\n    return arr;\n  }\n}\n</code></pre> my_list.rs<pre><code>/* Класс списка */\n#[allow(dead_code)]\nstruct MyList {\n    arr: Vec&lt;i32&gt;,       // Массив (для хранения элементов списка)\n    capacity: usize,     // Вместимость списка\n    size: usize,         // Длина списка (текущее число элементов)\n    extend_ratio: usize, // Коэффициент увеличения списка при каждом расширении\n}\n\n#[allow(unused, unused_comparisons)]\nimpl MyList {\n    /* Конструктор */\n    pub fn new(capacity: usize) -&gt; Self {\n        let mut vec = vec![0; capacity];\n        Self {\n            arr: vec,\n            capacity,\n            size: 0,\n            extend_ratio: 2,\n        }\n    }\n\n    /* Получить длину списка (текущее число элементов) */\n    pub fn size(&amp;self) -&gt; usize {\n        return self.size;\n    }\n\n    /* Получить вместимость списка */\n    pub fn capacity(&amp;self) -&gt; usize {\n        return self.capacity;\n    }\n\n    /* Доступ к элементу */\n    pub fn get(&amp;self, index: usize) -&gt; i32 {\n        // Если индекс выходит за границы, выбрасывается исключение; далее аналогично\n        if index &gt;= self.size {\n            panic!(\"индекс выходит за границы\")\n        };\n        return self.arr[index];\n    }\n\n    /* Обновление элемента */\n    pub fn set(&amp;mut self, index: usize, num: i32) {\n        if index &gt;= self.size {\n            panic!(\"индекс выходит за границы\")\n        };\n        self.arr[index] = num;\n    }\n\n    /* Добавление элемента в конец */\n    pub fn add(&amp;mut self, num: i32) {\n        // При превышении вместимости по числу элементов запускается расширение\n        if self.size == self.capacity() {\n            self.extend_capacity();\n        }\n        self.arr[self.size] = num;\n        // Обновить число элементов\n        self.size += 1;\n    }\n\n    /* Вставка элемента в середину */\n    pub fn insert(&amp;mut self, index: usize, num: i32) {\n        if index &gt;= self.size() {\n            panic!(\"индекс выходит за границы\")\n        };\n        // При превышении вместимости по числу элементов запускается расширение\n        if self.size == self.capacity() {\n            self.extend_capacity();\n        }\n        // Сдвинуть элемент с индексом index и все следующие элементы на одну позицию назад\n        for j in (index..self.size).rev() {\n            self.arr[j + 1] = self.arr[j];\n        }\n        self.arr[index] = num;\n        // Обновить число элементов\n        self.size += 1;\n    }\n\n    /* Удаление элемента */\n    pub fn remove(&amp;mut self, index: usize) -&gt; i32 {\n        if index &gt;= self.size() {\n            panic!(\"индекс выходит за границы\")\n        };\n        let num = self.arr[index];\n        // Сдвинуть все элементы после индекса index на одну позицию вперед\n        for j in index..self.size - 1 {\n            self.arr[j] = self.arr[j + 1];\n        }\n        // Обновить число элементов\n        self.size -= 1;\n        // Вернуть удаленный элемент\n        return num;\n    }\n\n    /* Расширение списка */\n    pub fn extend_capacity(&amp;mut self) {\n        // Создать новый массив длиной в extend_ratio раз больше исходного и скопировать в него исходный массив\n        let new_capacity = self.capacity * self.extend_ratio;\n        self.arr.resize(new_capacity, 0);\n        // Обновить вместимость списка\n        self.capacity = new_capacity;\n    }\n\n    /* Преобразовать список в массив */\n    pub fn to_array(&amp;self) -&gt; Vec&lt;i32&gt; {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        let mut arr = Vec::new();\n        for i in 0..self.size {\n            arr.push(self.get(i));\n        }\n        arr\n    }\n}\n</code></pre> my_list.c<pre><code>/* Класс списка */\ntypedef struct {\n    int *arr;        // Массив (для хранения элементов списка)\n    int capacity;    // Вместимость списка\n    int size;        // Размер списка\n    int extendRatio; // Коэффициент расширения списка при каждом увеличении\n} MyList;\n\n/* Конструктор */\nMyList *newMyList() {\n    MyList *nums = malloc(sizeof(MyList));\n    nums-&gt;capacity = 10;\n    nums-&gt;arr = malloc(sizeof(int) * nums-&gt;capacity);\n    nums-&gt;size = 0;\n    nums-&gt;extendRatio = 2;\n    return nums;\n}\n\n/* Деструктор */\nvoid delMyList(MyList *nums) {\n    free(nums-&gt;arr);\n    free(nums);\n}\n\n/* Получить длину списка */\nint size(MyList *nums) {\n    return nums-&gt;size;\n}\n\n/* Получить вместимость списка */\nint capacity(MyList *nums) {\n    return nums-&gt;capacity;\n}\n\n/* Доступ к элементу */\nint get(MyList *nums, int index) {\n    assert(index &gt;= 0 &amp;&amp; index &lt; nums-&gt;size);\n    return nums-&gt;arr[index];\n}\n\n/* Обновление элемента */\nvoid set(MyList *nums, int index, int num) {\n    assert(index &gt;= 0 &amp;&amp; index &lt; nums-&gt;size);\n    nums-&gt;arr[index] = num;\n}\n\n/* Добавление элемента в конец */\nvoid add(MyList *nums, int num) {\n    if (size(nums) == capacity(nums)) {\n        extendCapacity(nums); // Расширение емкости\n    }\n    nums-&gt;arr[size(nums)] = num;\n    nums-&gt;size++;\n}\n\n/* Вставка элемента в середину */\nvoid insert(MyList *nums, int index, int num) {\n    assert(index &gt;= 0 &amp;&amp; index &lt; size(nums));\n    // При превышении вместимости по числу элементов запускается расширение\n    if (size(nums) == capacity(nums)) {\n        extendCapacity(nums); // Расширение емкости\n    }\n    for (int i = size(nums); i &gt; index; --i) {\n        nums-&gt;arr[i] = nums-&gt;arr[i - 1];\n    }\n    nums-&gt;arr[index] = num;\n    nums-&gt;size++;\n}\n\n/* Удаление элемента */\n// Внимание: stdio.h уже использует ключевое слово remove\nint removeItem(MyList *nums, int index) {\n    assert(index &gt;= 0 &amp;&amp; index &lt; size(nums));\n    int num = nums-&gt;arr[index];\n    for (int i = index; i &lt; size(nums) - 1; i++) {\n        nums-&gt;arr[i] = nums-&gt;arr[i + 1];\n    }\n    nums-&gt;size--;\n    return num;\n}\n\n/* Расширение списка */\nvoid extendCapacity(MyList *nums) {\n    // Сначала выделить память\n    int newCapacity = capacity(nums) * nums-&gt;extendRatio;\n    int *extend = (int *)malloc(sizeof(int) * newCapacity);\n    int *temp = nums-&gt;arr;\n\n    // Скопировать старые данные в новые\n    for (int i = 0; i &lt; size(nums); i++)\n        extend[i] = nums-&gt;arr[i];\n\n    // Освободить старые данные\n    free(temp);\n\n    // Обновить новые данные\n    nums-&gt;arr = extend;\n    nums-&gt;capacity = newCapacity;\n}\n\n/* Преобразовать список в Array для вывода */\nint *toArray(MyList *nums) {\n    return nums-&gt;arr;\n}\n</code></pre> my_list.kt<pre><code>/* Класс списка */\nclass MyList {\n    private var arr: IntArray = intArrayOf() // Массив (для хранения элементов списка)\n    private var capacity: Int = 10 // Вместимость списка\n    private var size: Int = 0 // Длина списка (текущее число элементов)\n    private var extendRatio: Int = 2 // Коэффициент увеличения списка при каждом расширении\n\n    /* Конструктор */\n    init {\n        arr = IntArray(capacity)\n    }\n\n    /* Получить длину списка (текущее число элементов) */\n    fun size(): Int {\n        return size\n    }\n\n    /* Получить вместимость списка */\n    fun capacity(): Int {\n        return capacity\n    }\n\n    /* Доступ к элементу */\n    fun get(index: Int): Int {\n        // Если индекс выходит за границы, выбрасывается исключение; далее аналогично\n        if (index &lt; 0 || index &gt;= size)\n            throw IndexOutOfBoundsException(\"индекс выходит за границы\")\n        return arr[index]\n    }\n\n    /* Обновление элемента */\n    fun set(index: Int, num: Int) {\n        if (index &lt; 0 || index &gt;= size)\n            throw IndexOutOfBoundsException(\"индекс выходит за границы\")\n        arr[index] = num\n    }\n\n    /* Добавление элемента в конец */\n    fun add(num: Int) {\n        // При превышении вместимости по числу элементов запускается расширение\n        if (size == capacity())\n            extendCapacity()\n        arr[size] = num\n        // Обновить число элементов\n        size++\n    }\n\n    /* Вставка элемента в середину */\n    fun insert(index: Int, num: Int) {\n        if (index &lt; 0 || index &gt;= size)\n            throw IndexOutOfBoundsException(\"индекс выходит за границы\")\n        // При превышении вместимости по числу элементов запускается расширение\n        if (size == capacity())\n            extendCapacity()\n        // Сдвинуть элемент с индексом index и все следующие элементы на одну позицию назад\n        for (j in size - 1 downTo index)\n            arr[j + 1] = arr[j]\n        arr[index] = num\n        // Обновить число элементов\n        size++\n    }\n\n    /* Удаление элемента */\n    fun remove(index: Int): Int {\n        if (index &lt; 0 || index &gt;= size)\n            throw IndexOutOfBoundsException(\"индекс выходит за границы\")\n        val num = arr[index]\n        // Сдвинуть все элементы после индекса index на одну позицию вперед\n        for (j in index..&lt;size - 1)\n            arr[j] = arr[j + 1]\n        // Обновить число элементов\n        size--\n        // Вернуть удаленный элемент\n        return num\n    }\n\n    /* Расширение списка */\n    fun extendCapacity() {\n        // Создать новый массив длиной в extendRatio раз больше исходного и скопировать в него исходный массив\n        arr = arr.copyOf(capacity() * extendRatio)\n        // Обновить вместимость списка\n        capacity = arr.size\n    }\n\n    /* Преобразовать список в массив */\n    fun toArray(): IntArray {\n        val size = size()\n        // Преобразовывать только элементы списка в пределах фактической длины\n        val arr = IntArray(size)\n        for (i in 0..&lt;size) {\n            arr[i] = get(i)\n        }\n        return arr\n    }\n}\n</code></pre> my_list.rb<pre><code>### Класс списка ###\nclass MyList\n  attr_reader :size       # Получить длину списка (текущее число элементов)\n  attr_reader :capacity   # Получить вместимость списка\n\n  ### Конструктор ###\n  def initialize\n    @capacity = 10\n    @size = 0\n    @extend_ratio = 2\n    @arr = Array.new(capacity)\n  end\n\n  ### Доступ к элементу ###\n  def get(index)\n    # Если индекс выходит за границы, выбрасывается исключение; далее аналогично\n    raise IndexError, \"индекс выходит за границы\" if index &lt; 0 || index &gt;= size\n    @arr[index]\n  end\n\n  ### Доступ к элементу ###\n  def set(index, num)\n    raise IndexError, \"индекс выходит за границы\" if index &lt; 0 || index &gt;= size\n    @arr[index] = num\n  end\n\n  ### Добавление элемента в конец ###\n  def add(num)\n    # При превышении вместимости по числу элементов запускается расширение\n    extend_capacity if size == capacity\n    @arr[size] = num\n\n    # Обновить число элементов\n    @size += 1\n  end\n\n  ### Вставка элемента в середину ###\n  def insert(index, num)\n    raise IndexError, \"индекс выходит за границы\" if index &lt; 0 || index &gt;= size\n\n    # При превышении вместимости по числу элементов запускается расширение\n    extend_capacity if size == capacity\n\n    # Сдвинуть элемент с индексом index и все следующие элементы на одну позицию назад\n    for j in (size - 1).downto(index)\n      @arr[j + 1] = @arr[j]\n    end\n    @arr[index] = num\n\n    # Обновить число элементов\n    @size += 1\n  end\n\n  ### Удаление элемента ###\n  def remove(index)\n    raise IndexError, \"индекс выходит за границы\" if index &lt; 0 || index &gt;= size\n    num = @arr[index]\n\n    # Сдвинуть все элементы после индекса index на одну позицию вперед\n    for j in index...size\n      @arr[j] = @arr[j + 1]\n    end\n\n    # Обновить число элементов\n    @size -= 1\n\n    # Вернуть удаленный элемент\n    num\n  end\n\n  ### Расширение списка ###\n  def extend_capacity\n    # Создать новый массив длиной в extend_ratio раз больше исходного и скопировать в него исходный массив\n    arr = @arr.dup + Array.new(capacity * (@extend_ratio - 1))\n    # Обновить вместимость списка\n    @capacity = arr.length\n  end\n\n  ### Преобразование списка в массив ###\n  def to_array\n    sz = size\n    # Преобразовывать только элементы списка в пределах фактической длины\n    arr = Array.new(sz)\n    for i in 0...sz\n      arr[i] = get(i)\n    end\n    arr\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 4. Массив и связный список","4.3 &nbsp; Список"],"tags":[]},{"location":"chapter_array_and_linkedlist/ram_and_cache/","level":1,"title":"4.4   Оперативная память и кэш *","text":"<p>В первых двух разделах этой главы мы разобрали массивы и связные списки - две фундаментальные и важные структуры данных, которые соответственно представляют две физические структуры хранения: \"непрерывное хранение\" и \"разрозненное хранение\".</p> <p>На практике физическая структура во многом определяет, насколько эффективно программа использует память и кэш, а это, в свою очередь, влияет на общую производительность алгоритмической программы.</p>","path":["Глава 4. Массив и связный список","4.4 &nbsp; Оперативная память и кэш *"],"tags":[]},{"location":"chapter_array_and_linkedlist/ram_and_cache/#441","level":2,"title":"4.4.1   Устройства хранения данных в компьютере","text":"<p>В компьютере есть три типа устройств хранения данных: жесткий диск (hard disk) , оперативная память (random-access memory, RAM) и кэш-память (cache memory) . В таблице 4-2 показаны их различные роли и характеристики производительности в компьютерной системе.</p> <p> Таблица 4-2   Устройства хранения данных в компьютере </p> Жесткий диск Оперативная память Кэш Назначение Долговременное хранение данных, включая ОС, программы, файлы и т.д. Временное хранение выполняемых программ и обрабатываемых данных Хранение часто используемых данных и инструкций, уменьшающее число обращений CPU к памяти Энергозависимость Данные не теряются после отключения питания Данные теряются после отключения питания Данные теряются после отключения питания Емкость Большая, уровень TB Меньшая, уровень GB Очень малая, уровень MB Скорость Низкая, от сотен до тысяч MB/s Высокая, десятки GB/s Очень высокая, десятки и сотни GB/s Цена (юани) Дешевый, от долей юаня до нескольких юаней за GB Дорогая, десятки и сотни юаней за GB Очень дорогой, входит в стоимость упаковки CPU <p>Компьютерную систему хранения можно представить в виде пирамиды, показанной на рисунке 4-9. Чем ближе устройство хранения к вершине пирамиды, тем оно быстрее, тем меньше его емкость и тем выше его стоимость. Такая многоуровневая конструкция возникла не случайно, а стала результатом тщательных инженерных компромиссов.</p> <ul> <li>Жесткий диск трудно заменить оперативной памятью. Во-первых, данные в оперативной памяти исчезают после отключения питания, поэтому она не подходит для долговременного хранения. Во-вторых, память стоит в десятки раз дороже жесткого диска, что мешает ее широкому применению в потребительском сегменте.</li> <li>Кэш не может одновременно быть и очень большим, и очень быстрым. По мере роста емкости кэшей L1, L2 и L3 их физический размер увеличивается, расстояние до ядра CPU становится больше, время передачи данных растет, а задержка доступа к элементам увеличивается. При текущем уровне технологий многоуровневая структура кэша является лучшим балансом между емкостью, скоростью и стоимостью.</li> </ul> <p></p> <p> Рисунок 4-9   Система хранения данных компьютера </p> <p>Tip</p> <p>Иерархия памяти компьютера отражает тонкий баланс между скоростью, емкостью и стоимостью. На самом деле подобные компромиссы встречаются почти во всех отраслях инженерии: приходится искать оптимальный баланс между преимуществами и ограничениями.</p> <p>В итоге жесткий диск используется для долговременного хранения больших объемов данных, оперативная память - для временного хранения данных, с которыми программа работает прямо сейчас, а кэш - для хранения часто используемых данных и инструкций, чтобы ускорять выполнение программ. Все три уровня работают совместно и обеспечивают эффективную работу компьютерной системы.</p> <p>Как показано на рисунке 4-10, во время выполнения программы данные читаются с жесткого диска в оперативную память, а затем используются CPU в вычислениях. Кэш можно рассматривать как часть CPU: он интеллектуально подгружает данные из оперативной памяти, обеспечивая CPU высокоскоростной доступ и тем самым значительно ускоряя выполнение программы и уменьшая зависимость от более медленной RAM.</p> <p></p> <p> Рисунок 4-10   Поток данных между жестким диском, RAM и кэшем </p>","path":["Глава 4. Массив и связный список","4.4 &nbsp; Оперативная память и кэш *"],"tags":[]},{"location":"chapter_array_and_linkedlist/ram_and_cache/#442","level":2,"title":"4.4.2   Эффективность использования памяти структурами данных","text":"<p>С точки зрения использования пространства памяти массивы и связные списки имеют свои преимущества и ограничения.</p> <p>С одной стороны, память ограничена, и один и тот же участок памяти не может совместно использоваться несколькими программами, поэтому нам хочется, чтобы структуры данных использовали пространство как можно эффективнее. Элементы массива расположены плотно и не требуют дополнительного места для хранения ссылок (указателей) между узлами списка, поэтому массивы эффективнее по памяти. Однако массиву нужно сразу выделить достаточно большой непрерывный участок памяти, что может приводить к потерям пространства, а его расширение требует дополнительных затрат времени и памяти. Напротив, связные списки выполняют динамическое выделение и освобождение памяти \"по узлам\", что дает большую гибкость.</p> <p>С другой стороны, во время выполнения программы при многократном выделении и освобождении памяти фрагментация свободной памяти становится все более серьезной, что снижает эффективность ее использования. Массивы из-за непрерывного хранения относительно менее подвержены фрагментации. Напротив, элементы связного списка распределены по памяти, и частые операции вставки и удаления легче приводят к фрагментации.</p>","path":["Глава 4. Массив и связный список","4.4 &nbsp; Оперативная память и кэш *"],"tags":[]},{"location":"chapter_array_and_linkedlist/ram_and_cache/#443","level":2,"title":"4.4.3   Эффективность использования кэша структурами данных","text":"<p>Хотя по объему кэш намного меньше оперативной памяти, он значительно быстрее и играет критически важную роль в скорости выполнения программ. Поскольку объем кэша ограничен и в нем можно хранить только небольшую долю часто используемых данных, когда CPU пытается обратиться к данным, которых в кэше нет, происходит промах кэша (cache miss) , и CPU вынужден загружать нужные данные из более медленной памяти.</p> <p>Очевидно, что чем меньше \"промахов кэша\", тем выше эффективность чтения и записи данных CPU, а значит, тем лучше производительность программы. Долю обращений, при которых CPU успешно получает данные из кэша, называют коэффициентом попадания в кэш (cache hit rate) ; этот показатель обычно используют для оценки эффективности кэша.</p> <p>Чтобы добиться как можно большей эффективности, кэш использует следующие механизмы загрузки данных.</p> <ul> <li>Строки кэша: кэш хранит и загружает данные не по одному байту, а строками кэша. По сравнению с передачей по байтам это гораздо эффективнее.</li> <li>Механизм предвыборки: процессор старается предсказать шаблон доступа к данным (например последовательный доступ, доступ с фиксированным шагом и т.д.) и на основе этого шаблона заранее загружает данные в кэш, повышая вероятность попадания.</li> <li>Пространственная локальность: если к некоторым данным уже обратились, то велика вероятность, что в ближайшее время понадобятся и соседние данные. Поэтому, загружая некоторые данные, кэш часто подгружает и окружающие их данные.</li> <li>Временная локальность: если к данным уже обратились, то высока вероятность, что к ним снова обратятся в ближайшем будущем. Кэш использует это свойство, сохраняя недавно использованные данные.</li> </ul> <p>На практике массивы и связные списки по-разному используют кэш, и это проявляется в нескольких аспектах.</p> <ul> <li>Занимаемое пространство: элементы связного списка занимают больше места, чем элементы массива, поэтому в кэше помещается меньше полезных данных.</li> <li>Строки кэша: данные списка разбросаны по памяти, а кэш загружает данные \"строками\", поэтому доля бесполезно загружаемых данных оказывается выше.</li> <li>Механизм предвыборки: шаблон доступа к данным у массивов более \"предсказуем\", чем у списков, то есть системе легче угадать, какие данные понадобятся следующими.</li> <li>Пространственная локальность: массив хранится в компактной области памяти, поэтому данные рядом с уже загруженными с большей вероятностью скоро будут использованы.</li> </ul> <p>В целом массивы имеют более высокий коэффициент попадания в кэш, поэтому по эффективности операций они обычно превосходят связные списки. Именно поэтому при решении алгоритмических задач структуры данных на основе массивов часто оказываются предпочтительнее.</p> <p>Важно понимать, что высокая эффективность кэша не означает, что массивы во всех случаях лучше связных списков. В реальных приложениях выбор структуры данных должен определяться конкретными требованиями. Например, и массивы, и списки могут использоваться для реализации \"стека\" (подробнее об этом будет рассказано в следующей главе), но подходят они для разных сценариев.</p> <ul> <li>При решении алгоритмических задач мы обычно предпочитаем стек на основе массива, потому что он дает более высокую эффективность операций и поддерживает произвольный доступ, а цена за это - необходимость заранее выделить некоторый объем памяти под массив.</li> <li>Если объем данных очень велик, структура сильно динамична, а ожидаемый размер стека трудно оценить заранее, то более уместен стек на основе связного списка. Список позволяет распределить большой объем данных по разным участкам памяти и избегает накладных расходов, связанных с расширением массива.</li> </ul>","path":["Глава 4. Массив и связный список","4.4 &nbsp; Оперативная память и кэш *"],"tags":[]},{"location":"chapter_array_and_linkedlist/summary/","level":1,"title":"4.5   Резюме","text":"","path":["Глава 4. Массив и связный список","4.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_array_and_linkedlist/summary/#1","level":3,"title":"1.   Ключевые выводы","text":"<ul> <li>Массивы и связные списки - это две базовые структуры данных, представляющие два способа хранения данных в памяти компьютера: хранение в непрерывной области и хранение в разрозненных областях. Их свойства во многом взаимно дополняют друг друга.</li> <li>Массив поддерживает произвольный доступ и занимает меньше памяти; однако вставка и удаление элементов в нем неэффективны, а длина после инициализации неизменяема.</li> <li>Связный список позволяет эффективно вставлять и удалять узлы путем изменения ссылок (указателей), а также гибко менять длину; однако доступ к узлам неэффективен, а памяти он занимает больше. Распространенные типы списков включают односвязные, циклические и двусвязные списки.</li> <li>Список - это упорядоченная коллекция элементов, поддерживающая добавление, удаление, поиск и изменение, и обычно реализуемая на основе динамического массива. Он сохраняет преимущества массива и при этом может гибко менять длину.</li> <li>Появление списка значительно повысило практическую полезность массива, хотя это и может приводить к потерям части памяти.</li> <li>Во время работы программы данные в основном хранятся в оперативной памяти. Массив обеспечивает более высокую эффективность использования пространства памяти, а связный список дает большую гибкость в использовании памяти.</li> <li>Кэш, используя строки кэша, механизм предвыборки, а также пространственную и временную локальность, предоставляет CPU быстрый доступ к данным и заметно повышает эффективность выполнения программ.</li> <li>Поскольку массивы обычно имеют более высокий коэффициент попадания в кэш, они в большинстве случаев работают эффективнее списков. При выборе структуры данных нужно исходить из конкретных требований и сценариев.</li> </ul>","path":["Глава 4. Массив и связный список","4.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_array_and_linkedlist/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: Влияет ли хранение массива в стеке или в куче на временную и пространственную эффективность?</p> <p>Массивы, расположенные и в стеке, и в куче, все равно хранятся в непрерывной области памяти, поэтому эффективность операций с данными у них в целом одинакова. Однако у стека и кучи есть собственные особенности, из-за которых возникают следующие различия.</p> <ol> <li>Эффективность выделения и освобождения: стек представляет собой относительно небольшой участок памяти, а выделение в нем обычно выполняется автоматически компилятором; куча же обычно больше, может выделяться динамически из кода и легче фрагментируется. Поэтому выделение и освобождение памяти в куче обычно медленнее, чем в стеке.</li> <li>Ограничение размера: объем стека относительно невелик, а размер кучи обычно ограничивается доступной памятью. Поэтому куча лучше подходит для хранения больших массивов.</li> <li>Гибкость: размер массива в стеке должен быть известен во время компиляции, а размер массива в куче может определяться динамически во время выполнения.</li> </ol> <p>Q: Почему для массива требуется, чтобы все элементы были одного типа, а для связного списка это не подчеркивается?</p> <p>Связный список состоит из узлов, а узлы соединяются между собой через ссылки (указатели), поэтому каждый узел в принципе может хранить данные разного типа, например <code>int</code> , <code>double</code> , <code>string</code> , <code>object</code> и т.д.</p> <p>Напротив, элементы массива должны быть одного типа, иначе нельзя будет вычислять адрес элемента через смещение. Например, если массив одновременно содержит <code>int</code> и <code>long</code> , один элемент занимает 4 байта, а другой - 8 байт ; в этом случае формула ниже уже не позволит вычислить смещение, потому что в массиве будут присутствовать элементы разной длины.</p> <pre><code># Адрес элемента в памяти = адрес массива в памяти (адрес первого элемента) + длина элемента * индекс элемента\n</code></pre> <p>Q: После удаления узла <code>P</code> нужно ли присваивать <code>P.next = None</code> ?</p> <p>Можно и не изменять <code>P.next</code> . С точки зрения данного списка, при обходе от головы к хвосту узел <code>P</code> уже больше не встретится. Это означает, что узел <code>P</code> уже удален из списка, и то, куда он указывает после этого, на сам список больше не влияет.</p> <p>С точки зрения задач по структурам данных и алгоритмам, отсутствие такого разрыва обычно не критично, если логика программы остается корректной. Но с точки зрения стандартной библиотеки разорвать связь безопаснее и логичнее. Если этого не сделать и удаленный узел не будет нормально собран, он может мешать освобождению памяти последующих узлов.</p> <p>Q: Временная сложность вставки и удаления в связном списке равна \\(O(1)\\) . Но до вставки или удаления обычно еще нужно потратить \\(O(n)\\) на поиск элемента. Почему тогда общая сложность не \\(O(n)\\) ?</p> <p>Если сначала искать элемент, а потом удалять его, то временная сложность действительно будет \\(O(n)\\) . Однако преимущество связного списка с \\(O(1)\\) вставкой и удалением проявляется в других сценариях. Например, двустороннюю очередь удобно реализовывать именно на связном списке: мы поддерживаем указатели на голову и хвост, и тогда каждая операция вставки или удаления остается \\(O(1)\\) .</p> <p>Q: На рисунке \"Определение связного списка и способ хранения\" светло-голубой блок с указателем узла - это отдельный адрес памяти? Или он делит память пополам со значением узла?</p> <p>Этот рисунок дает только качественное представление; количественно все зависит от конкретных условий.</p> <ul> <li>Значения узлов разных типов занимают разный объем памяти, например <code>int</code> , <code>long</code> , <code>double</code> и объекты-экземпляры.</li> <li>Размер памяти, занимаемой переменной-указателем, зависит от операционной системы и среды компиляции и обычно составляет 8 байт или 4 байта.</li> </ul> <p>Q: Всегда ли добавление элемента в конец списка имеет сложность \\(O(1)\\) ?</p> <p>Если при добавлении элемента длина списка превышается, то сначала приходится расширять список, а уже затем добавлять новый элемент. Система выделяет новый участок памяти и переносит туда все элементы исходного списка, и в этот момент временная сложность становится \\(O(n)\\) .</p> <p>Q: В утверждении \"появление списка сильно повысило практическую полезность массива, но может приводить к потере части памяти\" под потерями памяти имеется в виду дополнительная память под такие переменные, как емкость, длина и коэффициент расширения?</p> <p>Потери памяти здесь в основном имеют два значения: во-первых, список обычно имеет некоторую начальную емкость, которая может быть нам не нужна целиком; во-вторых, чтобы избежать слишком частых расширений, емкость при расширении обычно умножается на некоторый коэффициент, например \\(\\times 1.5\\) . Из-за этого появляется много пустых слотов, которые обычно нельзя полностью заполнить.</p> <p>Q: В Python после инициализации <code>n = [1, 2, 3]</code> адреса этих трех элементов выглядят непрерывными, но после <code>m = [2, 1, 3]</code> можно заметить, что <code>id</code> элементов не идут подряд, а совпадают с одинаковыми числами из <code>n</code> . Если адреса элементов не непрерывны, остается ли <code>m</code> массивом?</p> <p>Предположим, что элементами списка являются узлы <code>n = [n1, n2, n3, n4, n5]</code> . Обычно эти 5 объектов-узлов тоже будут храниться в разных местах памяти. Однако, имея индекс списка, мы по-прежнему можем за \\(O(1)\\) получить адрес памяти соответствующего узла и обратиться к нему. Это связано с тем, что в массиве хранятся ссылки на узлы, а не сами узлы.</p> <p>В отличие от многих других языков, в Python даже числа обернуты в объекты, и в списке хранятся не сами числа, а ссылки на них. Поэтому мы и наблюдаем, что одинаковые числа в двух массивах имеют один и тот же <code>id</code> , а адреса этих чисел не обязаны быть непрерывными.</p> <p>Q: В C++ STL уже есть двусвязный список <code>std::list</code> , но в некоторых учебниках по алгоритмам им пользуются не так часто. Это связано с какими-то ограничениями?</p> <p>С одной стороны, при разработке алгоритмов мы обычно предпочитаем структуры на основе массива, а к связным спискам прибегаем только при необходимости, по двум главным причинам.</p> <ul> <li>Накладные расходы по памяти: поскольку каждому элементу нужны два дополнительных указателя (на предыдущий и следующий элементы), <code>std::list</code> обычно занимает больше памяти, чем <code>std::vector</code> .</li> <li>Низкая дружелюбность к кэшу: поскольку данные не лежат непрерывно, <code>std::list</code> хуже использует кэш. В большинстве случаев <code>std::vector</code> показывает лучшую производительность.</li> </ul> <p>С другой стороны, случаи, когда связный список действительно необходим, в основном возникают в деревьях и графах. Для стеков и очередей чаще используют предоставляемые языком <code>stack</code> и <code>queue</code> , а не связный список напрямую.</p> <p>Q: Операция <code>res = [[0]] * n</code> создает двумерный список. Каждый <code>[0]</code> в нем независим?</p> <p>Нет, они не независимы. В таком двумерном списке все <code>[0]</code> на самом деле являются ссылками на один и тот же объект. Если изменить один из них, окажется, что меняются и все остальные соответствующие элементы.</p> <p>Если нужно, чтобы каждый <code>[0]</code> был независимым, можно использовать <code>res = [[0] for _ in range(n)]</code> . В этом варианте создаются \\(n\\) независимых объектов-списков <code>[0]</code> .</p> <p>Q: Операция <code>res = [0] * n</code> создает список. Каждый целочисленный <code>0</code> в нем независим?</p> <p>В этом списке все целые числа <code>0</code> являются ссылками на один и тот же объект. Это связано с тем, что Python использует механизм кэш-пула для маленьких целых чисел (обычно от -5 до 256), чтобы максимально переиспользовать объекты и повысить производительность.</p> <p>Хотя все элементы указывают на один и тот же объект, мы все равно можем независимо изменять элементы списка, потому что целые числа в Python - это \"неизменяемые объекты\". Когда мы изменяем некоторый элемент, на самом деле происходит переключение ссылки на другой объект, а не изменение исходного объекта.</p> <p>Однако если элементами списка являются \"изменяемые объекты\" (например списки, словари или экземпляры классов), то изменение одного элемента прямо меняет сам объект, и все элементы, ссылающиеся на него, увидят одно и то же изменение.</p>","path":["Глава 4. Массив и связный список","4.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_backtracking/","level":1,"title":"Глава 13.   Поиск с возвратом","text":"<p>Abstract</p> <p>Мы словно исследователи в лабиринте: на пути вперед могут встречаться тупики и трудности.</p> <p>Сила возврата позволяет нам начать заново, пробовать снова и снова и в конце концов найти выход к свету.</p>","path":["Глава 13. Поиск с возвратом","Глава 13. &nbsp; Поиск с возвратом"],"tags":[]},{"location":"chapter_backtracking/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>13.1   Алгоритм поиска с возвратом</li> <li>13.2   Задача о перестановках</li> <li>13.3   Задача о сумме подмножеств</li> <li>13.4   Задача о \\(n\\) ферзях</li> <li>13.5   Резюме</li> </ul>","path":["Глава 13. Поиск с возвратом","Глава 13. &nbsp; Поиск с возвратом"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/","level":1,"title":"13.1   Алгоритм поиска с возвратом","text":"<p>Алгоритм поиска с возвратом (backtracking algorithm) - это метод решения задач путем полного перебора. Его основная идея состоит в том, чтобы, начиная с некоторого исходного состояния, грубо перебрать все возможные решения, записывать корректные решения и продолжать поиск до тех пор, пока решение не будет найдено или пока не будут исчерпаны все возможные варианты.</p> <p>Обычно алгоритмы поиска с возвратом используют \"поиск в глубину\" для обхода пространства решений. В главе \"Бинарные деревья\" мы уже упоминали, что прямой, симметричный и обратный обходы относятся к поиску в глубину. Теперь мы на основе прямого обхода построим задачу backtracking и постепенно разберем принцип работы этого алгоритма.</p> <p>Пример 1</p> <p>Дано двоичное дерево. Найдите и запишите все узлы со значением \\(7\\) ; верните список этих узлов.</p> <p>Для этой задачи мы выполняем прямой обход дерева и проверяем, равно ли значение текущего узла \\(7\\) ; если да, то добавляем значение этого узла в список результатов <code>res</code> . Соответствующий процесс показан на рисунке 13-1 и в коде:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby preorder_traversal_i_compact.py<pre><code>def pre_order(root: TreeNode):\n    \"\"\"Предварительный обход: пример 1\"\"\"\n    if root is None:\n        return\n    if root.val == 7:\n        # Записать решение\n        res.append(root)\n    pre_order(root.left)\n    pre_order(root.right)\n</code></pre> preorder_traversal_i_compact.cpp<pre><code>/* Предварительный обход: пример 1 */\nvoid preOrder(TreeNode *root) {\n    if (root == nullptr) {\n        return;\n    }\n    if (root-&gt;val == 7) {\n        // Записать решение\n        res.push_back(root);\n    }\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n}\n</code></pre> preorder_traversal_i_compact.java<pre><code>/* Предварительный обход: пример 1 */\nvoid preOrder(TreeNode root) {\n    if (root == null) {\n        return;\n    }\n    if (root.val == 7) {\n        // Записать решение\n        res.add(root);\n    }\n    preOrder(root.left);\n    preOrder(root.right);\n}\n</code></pre> preorder_traversal_i_compact.cs<pre><code>/* Предварительный обход: пример 1 */\nvoid PreOrder(TreeNode? root) {\n    if (root == null) {\n        return;\n    }\n    if (root.val == 7) {\n        // Записать решение\n        res.Add(root);\n    }\n    PreOrder(root.left);\n    PreOrder(root.right);\n}\n</code></pre> preorder_traversal_i_compact.go<pre><code>/* Предварительный обход: пример 1 */\nfunc preOrderI(root *TreeNode, res *[]*TreeNode) {\n    if root == nil {\n        return\n    }\n    if (root.Val).(int) == 7 {\n        // Записать решение\n        *res = append(*res, root)\n    }\n    preOrderI(root.Left, res)\n    preOrderI(root.Right, res)\n}\n</code></pre> preorder_traversal_i_compact.swift<pre><code>/* Предварительный обход: пример 1 */\nfunc preOrder(root: TreeNode?) {\n    guard let root = root else {\n        return\n    }\n    if root.val == 7 {\n        // Записать решение\n        res.append(root)\n    }\n    preOrder(root: root.left)\n    preOrder(root: root.right)\n}\n</code></pre> preorder_traversal_i_compact.js<pre><code>/* Предварительный обход: пример 1 */\nfunction preOrder(root, res) {\n    if (root === null) {\n        return;\n    }\n    if (root.val === 7) {\n        // Записать решение\n        res.push(root);\n    }\n    preOrder(root.left, res);\n    preOrder(root.right, res);\n}\n</code></pre> preorder_traversal_i_compact.ts<pre><code>/* Предварительный обход: пример 1 */\nfunction preOrder(root: TreeNode | null, res: TreeNode[]): void {\n    if (root === null) {\n        return;\n    }\n    if (root.val === 7) {\n        // Записать решение\n        res.push(root);\n    }\n    preOrder(root.left, res);\n    preOrder(root.right, res);\n}\n</code></pre> preorder_traversal_i_compact.dart<pre><code>/* Предварительный обход: пример 1 */\nvoid preOrder(TreeNode? root, List&lt;TreeNode&gt; res) {\n  if (root == null) {\n    return;\n  }\n  if (root.val == 7) {\n    // Записать решение\n    res.add(root);\n  }\n  preOrder(root.left, res);\n  preOrder(root.right, res);\n}\n</code></pre> preorder_traversal_i_compact.rs<pre><code>/* Предварительный обход: пример 1 */\nfn pre_order(res: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;, root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;) {\n    if root.is_none() {\n        return;\n    }\n    if let Some(node) = root {\n        if node.borrow().val == 7 {\n            // Записать решение\n            res.push(node.clone());\n        }\n        pre_order(res, node.borrow().left.as_ref());\n        pre_order(res, node.borrow().right.as_ref());\n    }\n}\n</code></pre> preorder_traversal_i_compact.c<pre><code>/* Предварительный обход: пример 1 */\nvoid preOrder(TreeNode *root) {\n    if (root == NULL) {\n        return;\n    }\n    if (root-&gt;val == 7) {\n        // Записать решение\n        res[resSize++] = root;\n    }\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n}\n</code></pre> preorder_traversal_i_compact.kt<pre><code>/* Предварительный обход: пример 1 */\nfun preOrder(root: TreeNode?) {\n    if (root == null) {\n        return\n    }\n    if (root._val == 7) {\n        // Записать решение\n        res!!.add(root)\n    }\n    preOrder(root.left)\n    preOrder(root.right)\n}\n</code></pre> preorder_traversal_i_compact.rb<pre><code>### Предварительный обход: пример 1 ###\ndef pre_order(root)\n  return unless root\n\n  # Записать решение\n  $res &lt;&lt; root if root.val == 7\n\n  pre_order(root.left)\n  pre_order(root.right)\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p></p> <p> Рисунок 13-1   Поиск узлов при прямом обходе </p>","path":["Глава 13. Поиск с возвратом","13.1 &nbsp; Алгоритм поиска с возвратом"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/#1311","level":2,"title":"13.1.1   Попытка и откат","text":"<p>Алгоритм называется backtracking, потому что при поиске в пространстве решений он использует стратегию \"попытка\" и \"откат\". Когда в процессе поиска алгоритм приходит в состояние, из которого нельзя двигаться дальше или нельзя получить удовлетворяющее условиям решение, он отменяет предыдущий выбор, возвращается к более раннему состоянию и пробует другие возможные варианты.</p> <p>Для примера 1 посещение каждого узла представляет собой \"попытку\", а прохождение листового узла или возврат к родителю через <code>return</code> означает \"откат\".</p> <p>Важно понимать, что откат не сводится только к возврату из функции. Чтобы показать это, слегка расширим пример 1.</p> <p>Пример 2</p> <p>Найдите в двоичном дереве все узлы со значением \\(7\\) и верните пути от корня до этих узлов.</p> <p>Взяв за основу код примера 1, добавим список <code>path</code> для записи пути посещенных узлов. Когда встречается узел со значением \\(7\\) , мы копируем <code>path</code> и добавляем его в список результатов <code>res</code> . После завершения обхода именно <code>res</code> будет содержать все решения. Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby preorder_traversal_ii_compact.py<pre><code>def pre_order(root: TreeNode):\n    \"\"\"Предварительный обход: пример 2\"\"\"\n    if root is None:\n        return\n    # Попытка\n    path.append(root)\n    if root.val == 7:\n        # Записать решение\n        res.append(list(path))\n    pre_order(root.left)\n    pre_order(root.right)\n    # Откат\n    path.pop()\n</code></pre> preorder_traversal_ii_compact.cpp<pre><code>/* Предварительный обход: пример 2 */\nvoid preOrder(TreeNode *root) {\n    if (root == nullptr) {\n        return;\n    }\n    // Попытка\n    path.push_back(root);\n    if (root-&gt;val == 7) {\n        // Записать решение\n        res.push_back(path);\n    }\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n    // Откат\n    path.pop_back();\n}\n</code></pre> preorder_traversal_ii_compact.java<pre><code>/* Предварительный обход: пример 2 */\nvoid preOrder(TreeNode root) {\n    if (root == null) {\n        return;\n    }\n    // Попытка\n    path.add(root);\n    if (root.val == 7) {\n        // Записать решение\n        res.add(new ArrayList&lt;&gt;(path));\n    }\n    preOrder(root.left);\n    preOrder(root.right);\n    // Откат\n    path.remove(path.size() - 1);\n}\n</code></pre> preorder_traversal_ii_compact.cs<pre><code>/* Предварительный обход: пример 2 */\nvoid PreOrder(TreeNode? root) {\n    if (root == null) {\n        return;\n    }\n    // Попытка\n    path.Add(root);\n    if (root.val == 7) {\n        // Записать решение\n        res.Add(new List&lt;TreeNode&gt;(path));\n    }\n    PreOrder(root.left);\n    PreOrder(root.right);\n    // Откат\n    path.RemoveAt(path.Count - 1);\n}\n</code></pre> preorder_traversal_ii_compact.go<pre><code>/* Предварительный обход: пример 2 */\nfunc preOrderII(root *TreeNode, res *[][]*TreeNode, path *[]*TreeNode) {\n    if root == nil {\n        return\n    }\n    // Попытка\n    *path = append(*path, root)\n    if root.Val.(int) == 7 {\n        // Записать решение\n        *res = append(*res, append([]*TreeNode{}, *path...))\n    }\n    preOrderII(root.Left, res, path)\n    preOrderII(root.Right, res, path)\n    // Откат\n    *path = (*path)[:len(*path)-1]\n}\n</code></pre> preorder_traversal_ii_compact.swift<pre><code>/* Предварительный обход: пример 2 */\nfunc preOrder(root: TreeNode?) {\n    guard let root = root else {\n        return\n    }\n    // Попытка\n    path.append(root)\n    if root.val == 7 {\n        // Записать решение\n        res.append(path)\n    }\n    preOrder(root: root.left)\n    preOrder(root: root.right)\n    // Откат\n    path.removeLast()\n}\n</code></pre> preorder_traversal_ii_compact.js<pre><code>/* Предварительный обход: пример 2 */\nfunction preOrder(root, path, res) {\n    if (root === null) {\n        return;\n    }\n    // Попытка\n    path.push(root);\n    if (root.val === 7) {\n        // Записать решение\n        res.push([...path]);\n    }\n    preOrder(root.left, path, res);\n    preOrder(root.right, path, res);\n    // Откат\n    path.pop();\n}\n</code></pre> preorder_traversal_ii_compact.ts<pre><code>/* Предварительный обход: пример 2 */\nfunction preOrder(\n    root: TreeNode | null,\n    path: TreeNode[],\n    res: TreeNode[][]\n): void {\n    if (root === null) {\n        return;\n    }\n    // Попытка\n    path.push(root);\n    if (root.val === 7) {\n        // Записать решение\n        res.push([...path]);\n    }\n    preOrder(root.left, path, res);\n    preOrder(root.right, path, res);\n    // Откат\n    path.pop();\n}\n</code></pre> preorder_traversal_ii_compact.dart<pre><code>/* Предварительный обход: пример 2 */\nvoid preOrder(\n  TreeNode? root,\n  List&lt;TreeNode&gt; path,\n  List&lt;List&lt;TreeNode&gt;&gt; res,\n) {\n  if (root == null) {\n    return;\n  }\n\n  // Попытка\n  path.add(root);\n  if (root.val == 7) {\n    // Записать решение\n    res.add(List.from(path));\n  }\n  preOrder(root.left, path, res);\n  preOrder(root.right, path, res);\n  // Откат\n  path.removeLast();\n}\n</code></pre> preorder_traversal_ii_compact.rs<pre><code>/* Предварительный обход: пример 2 */\nfn pre_order(\n    res: &amp;mut Vec&lt;Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;&gt;,\n    path: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,\n    root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,\n) {\n    if root.is_none() {\n        return;\n    }\n    if let Some(node) = root {\n        // Попытка\n        path.push(node.clone());\n        if node.borrow().val == 7 {\n            // Записать решение\n            res.push(path.clone());\n        }\n        pre_order(res, path, node.borrow().left.as_ref());\n        pre_order(res, path, node.borrow().right.as_ref());\n        // Откат\n        path.pop();\n    }\n}\n</code></pre> preorder_traversal_ii_compact.c<pre><code>/* Предварительный обход: пример 2 */\nvoid preOrder(TreeNode *root) {\n    if (root == NULL) {\n        return;\n    }\n    // Попытка\n    path[pathSize++] = root;\n    if (root-&gt;val == 7) {\n        // Записать решение\n        for (int i = 0; i &lt; pathSize; ++i) {\n            res[resSize][i] = path[i];\n        }\n        resSize++;\n    }\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n    // Откат\n    pathSize--;\n}\n</code></pre> preorder_traversal_ii_compact.kt<pre><code>/* Предварительный обход: пример 2 */\nfun preOrder(root: TreeNode?) {\n    if (root == null) {\n        return\n    }\n    // Попытка\n    path!!.add(root)\n    if (root._val == 7) {\n        // Записать решение\n        res!!.add(path!!.toMutableList())\n    }\n    preOrder(root.left)\n    preOrder(root.right)\n    // Откат\n    path!!.removeAt(path!!.size - 1)\n}\n</code></pre> preorder_traversal_ii_compact.rb<pre><code>### Предварительный обход: пример 2 ###\ndef pre_order(root)\n  return unless root\n\n  # Попытка\n  $path &lt;&lt; root\n\n  # Записать решение\n  $res &lt;&lt; $path.dup if root.val == 7\n\n  pre_order(root.left)\n  pre_order(root.right)\n\n  # Откат\n  $path.pop\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>В каждой \"попытке\" мы добавляем текущий узел в <code>path</code> , чтобы записать путь; а перед \"откатом\" нам нужно удалить этот узел из <code>path</code> , чтобы восстановить состояние, существовавшее до текущей попытки.</p> <p>Если посмотреть на процесс, изображенный на рисунке 13-2, то попытку и откат можно понимать как \"движение вперед\" и \"отмену\": это два взаимно противоположных действия.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 13-2   Попытка и откат </p>","path":["Глава 13. Поиск с возвратом","13.1 &nbsp; Алгоритм поиска с возвратом"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/#1312","level":2,"title":"13.1.2   Обрезка","text":"<p>Сложные задачи backtracking обычно содержат одно или несколько ограничений, которые часто можно использовать для \"обрезки\".</p> <p>Пример 3</p> <p>Найдите в двоичном дереве все узлы со значением \\(7\\) , верните пути от корня до этих узлов, причем путь не должен содержать узлы со значением \\(3\\).</p> <p>Чтобы выполнить это ограничение, нам нужно добавить операцию обрезки: во время поиска, если встречается узел со значением \\(3\\) , мы сразу возвращаемся и не продолжаем дальнейший поиск. Код выглядит так:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby preorder_traversal_iii_compact.py<pre><code>def pre_order(root: TreeNode):\n    \"\"\"Предварительный обход: пример 3\"\"\"\n    # Отсечение\n    if root is None or root.val == 3:\n        return\n    # Попытка\n    path.append(root)\n    if root.val == 7:\n        # Записать решение\n        res.append(list(path))\n    pre_order(root.left)\n    pre_order(root.right)\n    # Откат\n    path.pop()\n</code></pre> preorder_traversal_iii_compact.cpp<pre><code>/* Предварительный обход: пример 3 */\nvoid preOrder(TreeNode *root) {\n    // Отсечение\n    if (root == nullptr || root-&gt;val == 3) {\n        return;\n    }\n    // Попытка\n    path.push_back(root);\n    if (root-&gt;val == 7) {\n        // Записать решение\n        res.push_back(path);\n    }\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n    // Откат\n    path.pop_back();\n}\n</code></pre> preorder_traversal_iii_compact.java<pre><code>/* Предварительный обход: пример 3 */\nvoid preOrder(TreeNode root) {\n    // Отсечение\n    if (root == null || root.val == 3) {\n        return;\n    }\n    // Попытка\n    path.add(root);\n    if (root.val == 7) {\n        // Записать решение\n        res.add(new ArrayList&lt;&gt;(path));\n    }\n    preOrder(root.left);\n    preOrder(root.right);\n    // Откат\n    path.remove(path.size() - 1);\n}\n</code></pre> preorder_traversal_iii_compact.cs<pre><code>/* Предварительный обход: пример 3 */\nvoid PreOrder(TreeNode? root) {\n    // Отсечение\n    if (root == null || root.val == 3) {\n        return;\n    }\n    // Попытка\n    path.Add(root);\n    if (root.val == 7) {\n        // Записать решение\n        res.Add(new List&lt;TreeNode&gt;(path));\n    }\n    PreOrder(root.left);\n    PreOrder(root.right);\n    // Откат\n    path.RemoveAt(path.Count - 1);\n}\n</code></pre> preorder_traversal_iii_compact.go<pre><code>/* Предварительный обход: пример 3 */\nfunc preOrderIII(root *TreeNode, res *[][]*TreeNode, path *[]*TreeNode) {\n    // Отсечение\n    if root == nil || root.Val == 3 {\n        return\n    }\n    // Попытка\n    *path = append(*path, root)\n    if root.Val.(int) == 7 {\n        // Записать решение\n        *res = append(*res, append([]*TreeNode{}, *path...))\n    }\n    preOrderIII(root.Left, res, path)\n    preOrderIII(root.Right, res, path)\n    // Откат\n    *path = (*path)[:len(*path)-1]\n}\n</code></pre> preorder_traversal_iii_compact.swift<pre><code>/* Предварительный обход: пример 3 */\nfunc preOrder(root: TreeNode?) {\n    // Отсечение\n    guard let root = root, root.val != 3 else {\n        return\n    }\n    // Попытка\n    path.append(root)\n    if root.val == 7 {\n        // Записать решение\n        res.append(path)\n    }\n    preOrder(root: root.left)\n    preOrder(root: root.right)\n    // Откат\n    path.removeLast()\n}\n</code></pre> preorder_traversal_iii_compact.js<pre><code>/* Предварительный обход: пример 3 */\nfunction preOrder(root, path, res) {\n    // Отсечение\n    if (root === null || root.val === 3) {\n        return;\n    }\n    // Попытка\n    path.push(root);\n    if (root.val === 7) {\n        // Записать решение\n        res.push([...path]);\n    }\n    preOrder(root.left, path, res);\n    preOrder(root.right, path, res);\n    // Откат\n    path.pop();\n}\n</code></pre> preorder_traversal_iii_compact.ts<pre><code>/* Предварительный обход: пример 3 */\nfunction preOrder(\n    root: TreeNode | null,\n    path: TreeNode[],\n    res: TreeNode[][]\n): void {\n    // Отсечение\n    if (root === null || root.val === 3) {\n        return;\n    }\n    // Попытка\n    path.push(root);\n    if (root.val === 7) {\n        // Записать решение\n        res.push([...path]);\n    }\n    preOrder(root.left, path, res);\n    preOrder(root.right, path, res);\n    // Откат\n    path.pop();\n}\n</code></pre> preorder_traversal_iii_compact.dart<pre><code>/* Предварительный обход: пример 3 */\nvoid preOrder(\n  TreeNode? root,\n  List&lt;TreeNode&gt; path,\n  List&lt;List&lt;TreeNode&gt;&gt; res,\n) {\n  if (root == null || root.val == 3) {\n    return;\n  }\n\n  // Попытка\n  path.add(root);\n  if (root.val == 7) {\n    // Записать решение\n    res.add(List.from(path));\n  }\n  preOrder(root.left, path, res);\n  preOrder(root.right, path, res);\n  // Откат\n  path.removeLast();\n}\n</code></pre> preorder_traversal_iii_compact.rs<pre><code>/* Предварительный обход: пример 3 */\nfn pre_order(\n    res: &amp;mut Vec&lt;Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;&gt;,\n    path: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,\n    root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,\n) {\n    // Отсечение\n    if root.is_none() || root.as_ref().unwrap().borrow().val == 3 {\n        return;\n    }\n    if let Some(node) = root {\n        // Попытка\n        path.push(node.clone());\n        if node.borrow().val == 7 {\n            // Записать решение\n            res.push(path.clone());\n        }\n        pre_order(res, path, node.borrow().left.as_ref());\n        pre_order(res, path, node.borrow().right.as_ref());\n        // Откат\n        path.pop();\n    }\n}\n</code></pre> preorder_traversal_iii_compact.c<pre><code>/* Предварительный обход: пример 3 */\nvoid preOrder(TreeNode *root) {\n    // Отсечение\n    if (root == NULL || root-&gt;val == 3) {\n        return;\n    }\n    // Попытка\n    path[pathSize++] = root;\n    if (root-&gt;val == 7) {\n        // Записать решение\n        for (int i = 0; i &lt; pathSize; i++) {\n            res[resSize][i] = path[i];\n        }\n        resSize++;\n    }\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n    // Откат\n    pathSize--;\n}\n</code></pre> preorder_traversal_iii_compact.kt<pre><code>/* Предварительный обход: пример 3 */\nfun preOrder(root: TreeNode?) {\n    // Отсечение\n    if (root == null || root._val == 3) {\n        return\n    }\n    // Попытка\n    path!!.add(root)\n    if (root._val == 7) {\n        // Записать решение\n        res!!.add(path!!.toMutableList())\n    }\n    preOrder(root.left)\n    preOrder(root.right)\n    // Откат\n    path!!.removeAt(path!!.size - 1)\n}\n</code></pre> preorder_traversal_iii_compact.rb<pre><code>### Предварительный обход: пример 3 ###\ndef pre_order(root)\n  # Отсечение\n  return if !root || root.val == 3\n\n  # Попытка\n  $path.append(root)\n\n  # Записать решение\n  $res &lt;&lt; $path.dup if root.val == 7\n\n  pre_order(root.left)\n  pre_order(root.right)\n\n  # Откат\n  $path.pop\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Термин \"обрезка\" очень нагляден. Как показано на рисунке 13-3, во время поиска мы \"срезаем\" ветви поиска, не удовлетворяющие ограничениям , тем самым избегая множества бессмысленных попыток и повышая эффективность поиска.</p> <p></p> <p> Рисунок 13-3   Обрезка по условиям задачи </p>","path":["Глава 13. Поиск с возвратом","13.1 &nbsp; Алгоритм поиска с возвратом"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/#1313","level":2,"title":"13.1.3   Каркас кода","text":"<p>Теперь попробуем извлечь общий каркас из действий \"попытка\", \"откат\" и \"обрезка\", чтобы сделать код более универсальным.</p> <p>В следующем каркасе кода <code>state</code> обозначает текущее состояние задачи, а <code>choices</code> - список выборов, доступных в текущем состоянии:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>def backtrack(state: State, choices: list[choice], res: list[state]):\n    \"\"\"Каркас алгоритма поиска с возвратом\"\"\"\n    # Проверка, является ли текущее состояние решением\n    if is_solution(state):\n        # Запись решения\n        record_solution(state, res)\n        # Дальше не продолжаем поиск\n        return\n    # Перебор всех возможных выборов\n    for choice in choices:\n        # Обрезка: проверка допустимости выбора\n        if is_valid(state, choice):\n            # Попытка: сделать выбор и обновить состояние\n            make_choice(state, choice)\n            backtrack(state, choices, res)\n            # Откат: отменить выбор и восстановить предыдущее состояние\n            undo_choice(state, choice)\n</code></pre> <pre><code>/* Каркас алгоритма поиска с возвратом */\nvoid backtrack(State *state, vector&lt;Choice *&gt; &amp;choices, vector&lt;State *&gt; &amp;res) {\n    // Проверка, является ли текущее состояние решением\n    if (isSolution(state)) {\n        // Запись решения\n        recordSolution(state, res);\n        // Дальше не продолжаем поиск\n        return;\n    }\n    // Перебор всех возможных выборов\n    for (Choice choice : choices) {\n        // Обрезка: проверка допустимости выбора\n        if (isValid(state, choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, choice);\n            backtrack(state, choices, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* Каркас алгоритма поиска с возвратом */\nvoid backtrack(State state, List&lt;Choice&gt; choices, List&lt;State&gt; res) {\n    // Проверка, является ли текущее состояние решением\n    if (isSolution(state)) {\n        // Запись решения\n        recordSolution(state, res);\n        // Дальше не продолжаем поиск\n        return;\n    }\n    // Перебор всех возможных выборов\n    for (Choice choice : choices) {\n        // Обрезка: проверка допустимости выбора\n        if (isValid(state, choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, choice);\n            backtrack(state, choices, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* Каркас алгоритма поиска с возвратом */\nvoid Backtrack(State state, List&lt;Choice&gt; choices, List&lt;State&gt; res) {\n    // Проверка, является ли текущее состояние решением\n    if (IsSolution(state)) {\n        // Запись решения\n        RecordSolution(state, res);\n        // Дальше не продолжаем поиск\n        return;\n    }\n    // Перебор всех возможных выборов\n    foreach (Choice choice in choices) {\n        // Обрезка: проверка допустимости выбора\n        if (IsValid(state, choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            MakeChoice(state, choice);\n            Backtrack(state, choices, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            UndoChoice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* Каркас алгоритма поиска с возвратом */\nfunc backtrack(state *State, choices []Choice, res *[]State) {\n    // Проверка, является ли текущее состояние решением\n    if isSolution(state) {\n        // Запись решения\n        recordSolution(state, res)\n        // Дальше не продолжаем поиск\n        return\n    }\n    // Перебор всех возможных выборов\n    for _, choice := range choices {\n        // Обрезка: проверка допустимости выбора\n        if isValid(state, choice) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, choice)\n            backtrack(state, choices, res)\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state, choice)\n        }\n    }\n}\n</code></pre> <pre><code>/* Каркас алгоритма поиска с возвратом */\nfunc backtrack(state: inout State, choices: [Choice], res: inout [State]) {\n    // Проверка, является ли текущее состояние решением\n    if isSolution(state: state) {\n        // Запись решения\n        recordSolution(state: state, res: &amp;res)\n        // Дальше не продолжаем поиск\n        return\n    }\n    // Перебор всех возможных выборов\n    for choice in choices {\n        // Обрезка: проверка допустимости выбора\n        if isValid(state: state, choice: choice) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state: &amp;state, choice: choice)\n            backtrack(state: &amp;state, choices: choices, res: &amp;res)\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state: &amp;state, choice: choice)\n        }\n    }\n}\n</code></pre> <pre><code>/* Каркас алгоритма поиска с возвратом */\nfunction backtrack(state, choices, res) {\n    // Проверка, является ли текущее состояние решением\n    if (isSolution(state)) {\n        // Запись решения\n        recordSolution(state, res);\n        // Дальше не продолжаем поиск\n        return;\n    }\n    // Перебор всех возможных выборов\n    for (let choice of choices) {\n        // Обрезка: проверка допустимости выбора\n        if (isValid(state, choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, choice);\n            backtrack(state, choices, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* Каркас алгоритма поиска с возвратом */\nfunction backtrack(state: State, choices: Choice[], res: State[]): void {\n    // Проверка, является ли текущее состояние решением\n    if (isSolution(state)) {\n        // Запись решения\n        recordSolution(state, res);\n        // Дальше не продолжаем поиск\n        return;\n    }\n    // Перебор всех возможных выборов\n    for (let choice of choices) {\n        // Обрезка: проверка допустимости выбора\n        if (isValid(state, choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, choice);\n            backtrack(state, choices, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* Каркас алгоритма поиска с возвратом */\nvoid backtrack(State state, List&lt;Choice&gt;, List&lt;State&gt; res) {\n  // Проверка, является ли текущее состояние решением\n  if (isSolution(state)) {\n    // Запись решения\n    recordSolution(state, res);\n    // Дальше не продолжаем поиск\n    return;\n  }\n  // Перебор всех возможных выборов\n  for (Choice choice in choices) {\n    // Обрезка: проверка допустимости выбора\n    if (isValid(state, choice)) {\n      // Попытка: сделать выбор и обновить состояние\n      makeChoice(state, choice);\n      backtrack(state, choices, res);\n      // Откат: отменить выбор и восстановить предыдущее состояние\n      undoChoice(state, choice);\n    }\n  }\n}\n</code></pre> <pre><code>/* Каркас алгоритма поиска с возвратом */\nfn backtrack(state: &amp;mut State, choices: &amp;Vec&lt;Choice&gt;, res: &amp;mut Vec&lt;State&gt;) {\n    // Проверка, является ли текущее состояние решением\n    if is_solution(state) {\n        // Запись решения\n        record_solution(state, res);\n        // Дальше не продолжаем поиск\n        return;\n    }\n    // Перебор всех возможных выборов\n    for choice in choices {\n        // Обрезка: проверка допустимости выбора\n        if is_valid(state, choice) {\n            // Попытка: сделать выбор и обновить состояние\n            make_choice(state, choice);\n            backtrack(state, choices, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undo_choice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* Каркас алгоритма поиска с возвратом */\nvoid backtrack(State *state, Choice *choices, int numChoices, State *res, int numRes) {\n    // Проверка, является ли текущее состояние решением\n    if (isSolution(state)) {\n        // Запись решения\n        recordSolution(state, res, numRes);\n        // Дальше не продолжаем поиск\n        return;\n    }\n    // Перебор всех возможных выборов\n    for (int i = 0; i &lt; numChoices; i++) {\n        // Обрезка: проверка допустимости выбора\n        if (isValid(state, &amp;choices[i])) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, &amp;choices[i]);\n            backtrack(state, choices, numChoices, res, numRes);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state, &amp;choices[i]);\n        }\n    }\n}\n</code></pre> <pre><code>/* Каркас алгоритма поиска с возвратом */\nfun backtrack(state: State?, choices: List&lt;Choice?&gt;, res: List&lt;State?&gt;?) {\n    // Проверка, является ли текущее состояние решением\n    if (isSolution(state)) {\n        // Запись решения\n        recordSolution(state, res)\n        // Дальше не продолжаем поиск\n        return\n    }\n    // Перебор всех возможных выборов\n    for (choice in choices) {\n        // Обрезка: проверка допустимости выбора\n        if (isValid(state, choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, choice)\n            backtrack(state, choices, res)\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state, choice)\n        }\n    }\n}\n</code></pre> <pre><code>### Каркас алгоритма поиска с возвратом ###\ndef backtrack(state, choices, res)\n    # Проверка, является ли текущее состояние решением\n    if is_solution?(state)\n        # Запись решения\n        record_solution(state, res)\n        return\n    end\n\n    # Перебор всех возможных выборов\n    for choice in choices\n        # Обрезка: проверка допустимости выбора\n        if is_valid?(state, choice)\n            # Попытка: сделать выбор и обновить состояние\n            make_choice(state, choice)\n            backtrack(state, choices, res)\n            # Откат: отменить выбор и восстановить предыдущее состояние\n            undo_choice(state, choice)\n        end\n    end\nend\n</code></pre> <p>Теперь, опираясь на этот каркас, решим пример 3. Состояние <code>state</code> здесь - это путь обхода узлов, выбор <code>choices</code> - левый и правый потомки текущего узла, а результат <code>res</code> - список путей:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby preorder_traversal_iii_template.py<pre><code>def is_solution(state: list[TreeNode]) -&gt; bool:\n    \"\"\"Проверить, является ли текущее состояние решением\"\"\"\n    return state and state[-1].val == 7\n\ndef record_solution(state: list[TreeNode], res: list[list[TreeNode]]):\n    \"\"\"Записать решение\"\"\"\n    res.append(list(state))\n\ndef is_valid(state: list[TreeNode], choice: TreeNode) -&gt; bool:\n    \"\"\"Проверить, допустим ли этот выбор в текущем состоянии\"\"\"\n    return choice is not None and choice.val != 3\n\ndef make_choice(state: list[TreeNode], choice: TreeNode):\n    \"\"\"Обновить состояние\"\"\"\n    state.append(choice)\n\ndef undo_choice(state: list[TreeNode], choice: TreeNode):\n    \"\"\"Восстановить состояние\"\"\"\n    state.pop()\n\ndef backtrack(\n    state: list[TreeNode], choices: list[TreeNode], res: list[list[TreeNode]]\n):\n    \"\"\"Алгоритм бэктрекинга: пример 3\"\"\"\n    # Проверить, является ли текущее состояние решением\n    if is_solution(state):\n        # Записать решение\n        record_solution(state, res)\n    # Перебор всех вариантов выбора\n    for choice in choices:\n        # Отсечение: проверить допустимость выбора\n        if is_valid(state, choice):\n            # Попытка: сделать выбор и обновить состояние\n            make_choice(state, choice)\n            # Перейти к следующему выбору\n            backtrack(state, [choice.left, choice.right], res)\n            # Откат: отменить выбор и восстановить предыдущее состояние\n            undo_choice(state, choice)\n</code></pre> preorder_traversal_iii_template.cpp<pre><code>/* Проверить, является ли текущее состояние решением */\nbool isSolution(vector&lt;TreeNode *&gt; &amp;state) {\n    return !state.empty() &amp;&amp; state.back()-&gt;val == 7;\n}\n\n/* Записать решение */\nvoid recordSolution(vector&lt;TreeNode *&gt; &amp;state, vector&lt;vector&lt;TreeNode *&gt;&gt; &amp;res) {\n    res.push_back(state);\n}\n\n/* Проверить, допустим ли этот выбор в текущем состоянии */\nbool isValid(vector&lt;TreeNode *&gt; &amp;state, TreeNode *choice) {\n    return choice != nullptr &amp;&amp; choice-&gt;val != 3;\n}\n\n/* Обновить состояние */\nvoid makeChoice(vector&lt;TreeNode *&gt; &amp;state, TreeNode *choice) {\n    state.push_back(choice);\n}\n\n/* Восстановить состояние */\nvoid undoChoice(vector&lt;TreeNode *&gt; &amp;state, TreeNode *choice) {\n    state.pop_back();\n}\n\n/* Алгоритм бэктрекинга: пример 3 */\nvoid backtrack(vector&lt;TreeNode *&gt; &amp;state, vector&lt;TreeNode *&gt; &amp;choices, vector&lt;vector&lt;TreeNode *&gt;&gt; &amp;res) {\n    // Проверить, является ли текущее состояние решением\n    if (isSolution(state)) {\n        // Записать решение\n        recordSolution(state, res);\n    }\n    // Перебор всех вариантов выбора\n    for (TreeNode *choice : choices) {\n        // Отсечение: проверить допустимость выбора\n        if (isValid(state, choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, choice);\n            // Перейти к следующему выбору\n            vector&lt;TreeNode *&gt; nextChoices{choice-&gt;left, choice-&gt;right};\n            backtrack(state, nextChoices, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.java<pre><code>/* Проверить, является ли текущее состояние решением */\nboolean isSolution(List&lt;TreeNode&gt; state) {\n    return !state.isEmpty() &amp;&amp; state.get(state.size() - 1).val == 7;\n}\n\n/* Записать решение */\nvoid recordSolution(List&lt;TreeNode&gt; state, List&lt;List&lt;TreeNode&gt;&gt; res) {\n    res.add(new ArrayList&lt;&gt;(state));\n}\n\n/* Проверить, допустим ли этот выбор в текущем состоянии */\nboolean isValid(List&lt;TreeNode&gt; state, TreeNode choice) {\n    return choice != null &amp;&amp; choice.val != 3;\n}\n\n/* Обновить состояние */\nvoid makeChoice(List&lt;TreeNode&gt; state, TreeNode choice) {\n    state.add(choice);\n}\n\n/* Восстановить состояние */\nvoid undoChoice(List&lt;TreeNode&gt; state, TreeNode choice) {\n    state.remove(state.size() - 1);\n}\n\n/* Алгоритм бэктрекинга: пример 3 */\nvoid backtrack(List&lt;TreeNode&gt; state, List&lt;TreeNode&gt; choices, List&lt;List&lt;TreeNode&gt;&gt; res) {\n    // Проверить, является ли текущее состояние решением\n    if (isSolution(state)) {\n        // Записать решение\n        recordSolution(state, res);\n    }\n    // Перебор всех вариантов выбора\n    for (TreeNode choice : choices) {\n        // Отсечение: проверить допустимость выбора\n        if (isValid(state, choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, choice);\n            // Перейти к следующему выбору\n            backtrack(state, Arrays.asList(choice.left, choice.right), res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.cs<pre><code>/* Проверить, является ли текущее состояние решением */\nbool IsSolution(List&lt;TreeNode&gt; state) {\n    return state.Count != 0 &amp;&amp; state[^1].val == 7;\n}\n\n/* Записать решение */\nvoid RecordSolution(List&lt;TreeNode&gt; state, List&lt;List&lt;TreeNode&gt;&gt; res) {\n    res.Add(new List&lt;TreeNode&gt;(state));\n}\n\n/* Проверить, допустим ли этот выбор в текущем состоянии */\nbool IsValid(List&lt;TreeNode&gt; state, TreeNode choice) {\n    return choice != null &amp;&amp; choice.val != 3;\n}\n\n/* Обновить состояние */\nvoid MakeChoice(List&lt;TreeNode&gt; state, TreeNode choice) {\n    state.Add(choice);\n}\n\n/* Восстановить состояние */\nvoid UndoChoice(List&lt;TreeNode&gt; state, TreeNode choice) {\n    state.RemoveAt(state.Count - 1);\n}\n\n/* Алгоритм бэктрекинга: пример 3 */\nvoid Backtrack(List&lt;TreeNode&gt; state, List&lt;TreeNode&gt; choices, List&lt;List&lt;TreeNode&gt;&gt; res) {\n    // Проверить, является ли текущее состояние решением\n    if (IsSolution(state)) {\n        // Записать решение\n        RecordSolution(state, res);\n    }\n    // Перебор всех вариантов выбора\n    foreach (TreeNode choice in choices) {\n        // Отсечение: проверить допустимость выбора\n        if (IsValid(state, choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            MakeChoice(state, choice);\n            // Перейти к следующему выбору\n            Backtrack(state, [choice.left!, choice.right!], res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            UndoChoice(state, choice);\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.go<pre><code>/* Проверить, является ли текущее состояние решением */\nfunc isSolution(state *[]*TreeNode) bool {\n    return len(*state) != 0 &amp;&amp; (*state)[len(*state)-1].Val == 7\n}\n\n/* Записать решение */\nfunc recordSolution(state *[]*TreeNode, res *[][]*TreeNode) {\n    *res = append(*res, append([]*TreeNode{}, *state...))\n}\n\n/* Проверить, допустим ли этот выбор в текущем состоянии */\nfunc isValid(state *[]*TreeNode, choice *TreeNode) bool {\n    return choice != nil &amp;&amp; choice.Val != 3\n}\n\n/* Обновить состояние */\nfunc makeChoice(state *[]*TreeNode, choice *TreeNode) {\n    *state = append(*state, choice)\n}\n\n/* Восстановить состояние */\nfunc undoChoice(state *[]*TreeNode, choice *TreeNode) {\n    *state = (*state)[:len(*state)-1]\n}\n\n/* Алгоритм бэктрекинга: пример 3 */\nfunc backtrackIII(state *[]*TreeNode, choices *[]*TreeNode, res *[][]*TreeNode) {\n    // Проверить, является ли текущее состояние решением\n    if isSolution(state) {\n        // Записать решение\n        recordSolution(state, res)\n    }\n    // Перебор всех вариантов выбора\n    for _, choice := range *choices {\n        // Отсечение: проверить допустимость выбора\n        if isValid(state, choice) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, choice)\n            // Перейти к следующему выбору\n            temp := make([]*TreeNode, 0)\n            temp = append(temp, choice.Left, choice.Right)\n            backtrackIII(state, &amp;temp, res)\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state, choice)\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.swift<pre><code>/* Проверить, является ли текущее состояние решением */\nfunc isSolution(state: [TreeNode]) -&gt; Bool {\n    !state.isEmpty &amp;&amp; state.last!.val == 7\n}\n\n/* Записать решение */\nfunc recordSolution(state: [TreeNode], res: inout [[TreeNode]]) {\n    res.append(state)\n}\n\n/* Проверить, допустим ли этот выбор в текущем состоянии */\nfunc isValid(state: [TreeNode], choice: TreeNode?) -&gt; Bool {\n    choice != nil &amp;&amp; choice!.val != 3\n}\n\n/* Обновить состояние */\nfunc makeChoice(state: inout [TreeNode], choice: TreeNode) {\n    state.append(choice)\n}\n\n/* Восстановить состояние */\nfunc undoChoice(state: inout [TreeNode], choice: TreeNode) {\n    state.removeLast()\n}\n\n/* Алгоритм бэктрекинга: пример 3 */\nfunc backtrack(state: inout [TreeNode], choices: [TreeNode], res: inout [[TreeNode]]) {\n    // Проверить, является ли текущее состояние решением\n    if isSolution(state: state) {\n        recordSolution(state: state, res: &amp;res)\n    }\n    // Перебор всех вариантов выбора\n    for choice in choices {\n        // Отсечение: проверить допустимость выбора\n        if isValid(state: state, choice: choice) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state: &amp;state, choice: choice)\n            // Перейти к следующему выбору\n            backtrack(state: &amp;state, choices: [choice.left, choice.right].compactMap { $0 }, res: &amp;res)\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state: &amp;state, choice: choice)\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.js<pre><code>/* Проверить, является ли текущее состояние решением */\nfunction isSolution(state) {\n    return state &amp;&amp; state[state.length - 1]?.val === 7;\n}\n\n/* Записать решение */\nfunction recordSolution(state, res) {\n    res.push([...state]);\n}\n\n/* Проверить, допустим ли этот выбор в текущем состоянии */\nfunction isValid(state, choice) {\n    return choice !== null &amp;&amp; choice.val !== 3;\n}\n\n/* Обновить состояние */\nfunction makeChoice(state, choice) {\n    state.push(choice);\n}\n\n/* Восстановить состояние */\nfunction undoChoice(state) {\n    state.pop();\n}\n\n/* Алгоритм бэктрекинга: пример 3 */\nfunction backtrack(state, choices, res) {\n    // Проверить, является ли текущее состояние решением\n    if (isSolution(state)) {\n        // Записать решение\n        recordSolution(state, res);\n    }\n    // Перебор всех вариантов выбора\n    for (const choice of choices) {\n        // Отсечение: проверить допустимость выбора\n        if (isValid(state, choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, choice);\n            // Перейти к следующему выбору\n            backtrack(state, [choice.left, choice.right], res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state);\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.ts<pre><code>/* Проверить, является ли текущее состояние решением */\nfunction isSolution(state: TreeNode[]): boolean {\n    return state &amp;&amp; state[state.length - 1]?.val === 7;\n}\n\n/* Записать решение */\nfunction recordSolution(state: TreeNode[], res: TreeNode[][]): void {\n    res.push([...state]);\n}\n\n/* Проверить, допустим ли этот выбор в текущем состоянии */\nfunction isValid(state: TreeNode[], choice: TreeNode): boolean {\n    return choice !== null &amp;&amp; choice.val !== 3;\n}\n\n/* Обновить состояние */\nfunction makeChoice(state: TreeNode[], choice: TreeNode): void {\n    state.push(choice);\n}\n\n/* Восстановить состояние */\nfunction undoChoice(state: TreeNode[]): void {\n    state.pop();\n}\n\n/* Алгоритм бэктрекинга: пример 3 */\nfunction backtrack(\n    state: TreeNode[],\n    choices: TreeNode[],\n    res: TreeNode[][]\n): void {\n    // Проверить, является ли текущее состояние решением\n    if (isSolution(state)) {\n        // Записать решение\n        recordSolution(state, res);\n    }\n    // Перебор всех вариантов выбора\n    for (const choice of choices) {\n        // Отсечение: проверить допустимость выбора\n        if (isValid(state, choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, choice);\n            // Перейти к следующему выбору\n            backtrack(state, [choice.left, choice.right], res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state);\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.dart<pre><code>/* Проверить, является ли текущее состояние решением */\nbool isSolution(List&lt;TreeNode&gt; state) {\n  return state.isNotEmpty &amp;&amp; state.last.val == 7;\n}\n\n/* Записать решение */\nvoid recordSolution(List&lt;TreeNode&gt; state, List&lt;List&lt;TreeNode&gt;&gt; res) {\n  res.add(List.from(state));\n}\n\n/* Проверить, допустим ли этот выбор в текущем состоянии */\nbool isValid(List&lt;TreeNode&gt; state, TreeNode? choice) {\n  return choice != null &amp;&amp; choice.val != 3;\n}\n\n/* Обновить состояние */\nvoid makeChoice(List&lt;TreeNode&gt; state, TreeNode? choice) {\n  state.add(choice!);\n}\n\n/* Восстановить состояние */\nvoid undoChoice(List&lt;TreeNode&gt; state, TreeNode? choice) {\n  state.removeLast();\n}\n\n/* Алгоритм бэктрекинга: пример 3 */\nvoid backtrack(\n  List&lt;TreeNode&gt; state,\n  List&lt;TreeNode?&gt; choices,\n  List&lt;List&lt;TreeNode&gt;&gt; res,\n) {\n  // Проверить, является ли текущее состояние решением\n  if (isSolution(state)) {\n    // Записать решение\n    recordSolution(state, res);\n  }\n  // Перебор всех вариантов выбора\n  for (TreeNode? choice in choices) {\n    // Отсечение: проверить допустимость выбора\n    if (isValid(state, choice)) {\n      // Попытка: сделать выбор и обновить состояние\n      makeChoice(state, choice);\n      // Перейти к следующему выбору\n      backtrack(state, [choice!.left, choice.right], res);\n      // Откат: отменить выбор и восстановить предыдущее состояние\n      undoChoice(state, choice);\n    }\n  }\n}\n</code></pre> preorder_traversal_iii_template.rs<pre><code>/* Проверить, является ли текущее состояние решением */\nfn is_solution(state: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;) -&gt; bool {\n    return !state.is_empty() &amp;&amp; state.last().unwrap().borrow().val == 7;\n}\n\n/* Записать решение */\nfn record_solution(\n    state: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,\n    res: &amp;mut Vec&lt;Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;&gt;,\n) {\n    res.push(state.clone());\n}\n\n/* Проверить, допустим ли этот выбор в текущем состоянии */\nfn is_valid(_: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;, choice: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;) -&gt; bool {\n    return choice.is_some() &amp;&amp; choice.unwrap().borrow().val != 3;\n}\n\n/* Обновить состояние */\nfn make_choice(state: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;, choice: Rc&lt;RefCell&lt;TreeNode&gt;&gt;) {\n    state.push(choice);\n}\n\n/* Восстановить состояние */\nfn undo_choice(state: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;, _: Rc&lt;RefCell&lt;TreeNode&gt;&gt;) {\n    state.pop();\n}\n\n/* Алгоритм бэктрекинга: пример 3 */\nfn backtrack(\n    state: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,\n    choices: &amp;Vec&lt;Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;&gt;,\n    res: &amp;mut Vec&lt;Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;&gt;,\n) {\n    // Проверить, является ли текущее состояние решением\n    if is_solution(state) {\n        // Записать решение\n        record_solution(state, res);\n    }\n    // Перебор всех вариантов выбора\n    for &amp;choice in choices.iter() {\n        // Отсечение: проверить допустимость выбора\n        if is_valid(state, choice) {\n            // Попытка: сделать выбор и обновить состояние\n            make_choice(state, choice.unwrap().clone());\n            // Перейти к следующему выбору\n            backtrack(\n                state,\n                &amp;vec![\n                    choice.unwrap().borrow().left.as_ref(),\n                    choice.unwrap().borrow().right.as_ref(),\n                ],\n                res,\n            );\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undo_choice(state, choice.unwrap().clone());\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.c<pre><code>/* Проверить, является ли текущее состояние решением */\nbool isSolution(void) {\n    return pathSize &gt; 0 &amp;&amp; path[pathSize - 1]-&gt;val == 7;\n}\n\n/* Записать решение */\nvoid recordSolution(void) {\n    for (int i = 0; i &lt; pathSize; i++) {\n        res[resSize][i] = path[i];\n    }\n    resSize++;\n}\n\n/* Проверить, допустим ли этот выбор в текущем состоянии */\nbool isValid(TreeNode *choice) {\n    return choice != NULL &amp;&amp; choice-&gt;val != 3;\n}\n\n/* Обновить состояние */\nvoid makeChoice(TreeNode *choice) {\n    path[pathSize++] = choice;\n}\n\n/* Восстановить состояние */\nvoid undoChoice(void) {\n    pathSize--;\n}\n\n/* Алгоритм бэктрекинга: пример 3 */\nvoid backtrack(TreeNode *choices[2]) {\n    // Проверить, является ли текущее состояние решением\n    if (isSolution()) {\n        // Записать решение\n        recordSolution();\n    }\n    // Перебор всех вариантов выбора\n    for (int i = 0; i &lt; 2; i++) {\n        TreeNode *choice = choices[i];\n        // Отсечение: проверить допустимость выбора\n        if (isValid(choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(choice);\n            // Перейти к следующему выбору\n            TreeNode *nextChoices[2] = {choice-&gt;left, choice-&gt;right};\n            backtrack(nextChoices);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice();\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.kt<pre><code>/* Проверить, является ли текущее состояние решением */\nfun isSolution(state: MutableList&lt;TreeNode?&gt;): Boolean {\n    return state.isNotEmpty() &amp;&amp; state[state.size - 1]?._val == 7\n}\n\n/* Записать решение */\nfun recordSolution(state: MutableList&lt;TreeNode?&gt;?, res: MutableList&lt;MutableList&lt;TreeNode?&gt;?&gt;) {\n    res.add(state!!.toMutableList())\n}\n\n/* Проверить, допустим ли этот выбор в текущем состоянии */\nfun isValid(state: MutableList&lt;TreeNode?&gt;?, choice: TreeNode?): Boolean {\n    return choice != null &amp;&amp; choice._val != 3\n}\n\n/* Обновить состояние */\nfun makeChoice(state: MutableList&lt;TreeNode?&gt;, choice: TreeNode?) {\n    state.add(choice)\n}\n\n/* Восстановить состояние */\nfun undoChoice(state: MutableList&lt;TreeNode?&gt;, choice: TreeNode?) {\n    state.removeLast()\n}\n\n/* Алгоритм бэктрекинга: пример 3 */\nfun backtrack(\n    state: MutableList&lt;TreeNode?&gt;,\n    choices: MutableList&lt;TreeNode?&gt;,\n    res: MutableList&lt;MutableList&lt;TreeNode?&gt;?&gt;\n) {\n    // Проверить, является ли текущее состояние решением\n    if (isSolution(state)) {\n        // Записать решение\n        recordSolution(state, res)\n    }\n    // Перебор всех вариантов выбора\n    for (choice in choices) {\n        // Отсечение: проверить допустимость выбора\n        if (isValid(state, choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, choice)\n            // Перейти к следующему выбору\n            backtrack(state, mutableListOf(choice!!.left, choice.right), res)\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state, choice)\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.rb<pre><code>### Проверка, является ли текущее состояние решением ###\ndef is_solution?(state)\n  !state.empty? &amp;&amp; state.last.val == 7\nend\n\n### Записать решение ###\ndef record_solution(state, res)\n  res &lt;&lt; state.dup\nend\n\n### Проверка допустимости этого выбора в текущем состоянии ###\ndef is_valid?(state, choice)\n  choice &amp;&amp; choice.val != 3\nend\n\n### Обновить состояние ###\ndef make_choice(state, choice)\n  state &lt;&lt; choice\nend\n\n### Восстановить состояние ###\ndef undo_choice(state, choice)\n  state.pop\nend\n\n### Алгоритм бэктрекинга: пример 3 ###\ndef backtrack(state, choices, res)\n  # Проверить, является ли текущее состояние решением\n  record_solution(state, res) if is_solution?(state)\n\n  # Перебор всех вариантов выбора\n  for choice in choices\n    # Отсечение: проверить допустимость выбора\n    if is_valid?(state, choice)\n      # Попытка: сделать выбор и обновить состояние\n      make_choice(state, choice)\n      # Перейти к следующему выбору\n      backtrack(state, [choice.left, choice.right], res)\n      # Откат: отменить выбор и восстановить предыдущее состояние\n      undo_choice(state, choice)\n    end\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Согласно условию задачи, после нахождения узла со значением \\(7\\) мы должны продолжать поиск, поэтому оператор <code>return</code> после записи решения нужно удалить. На рисунке 13-4 сравниваются процессы поиска в случаях, когда <code>return</code> сохраняется и когда он удаляется.</p> <p></p> <p> Рисунок 13-4   Сравнение поиска при сохранении и удалении return </p> <p>По сравнению с реализацией на основе прямого обхода, версия на основе общего каркаса backtracking выглядит более громоздкой, но при этом обладает лучшей универсальностью. На практике многие задачи backtracking можно решать в рамках этого каркаса. Для этого нужно лишь определить <code>state</code> и <code>choices</code> под конкретную задачу и реализовать соответствующие методы каркаса.</p>","path":["Глава 13. Поиск с возвратом","13.1 &nbsp; Алгоритм поиска с возвратом"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/#1314","level":2,"title":"13.1.4   Часто используемые термины","text":"<p>Чтобы яснее анализировать алгоритмические задачи, подытожим значения часто используемых терминов backtracking и сопоставим их с примером 3, как показано в таблице 13-1.</p> <p> Таблица 13-1   Часто используемые термины алгоритма backtracking </p> Термин Определение Пример 3 Решение (solution) Решение - это ответ, удовлетворяющий условиям задачи; решений может быть одно или несколько Все пути от корня до узла \\(7\\) , удовлетворяющие ограничениям Ограничение (constraint) Ограничение определяет допустимость решения и обычно используется для обрезки Путь не содержит узлы со значением \\(3\\) Состояние (state) Состояние описывает ситуацию задачи в некоторый момент времени, включая уже сделанные выборы Текущий путь посещенных узлов, то есть список узлов <code>path</code> Попытка (attempt) Попытка - это исследование пространства решений на основе доступных выборов, включая выбор, обновление состояния и проверку, является ли состояние решением Рекурсивный переход к левому или правому потомку, добавление узла в <code>path</code> и проверка, равно ли значение узла \\(7\\) Откат (backtracking) Откат означает отмену предыдущих выборов и возврат к более раннему состоянию при встрече состояния, не удовлетворяющего ограничениям Завершение поиска при проходе через лист, окончании посещения узла или встрече узла со значением \\(3\\) , то есть возврат из функции Обрезка (pruning) Обрезка - это способ избегать бессмысленных путей поиска на основе свойств задачи и ее ограничений, повышающий эффективность При встрече узла со значением \\(3\\) поиск по этой ветви прекращается <p>Tip</p> <p>Такие понятия, как задача, решение и состояние, являются общими и встречаются не только в backtracking, но и в divide and conquer, динамическом программировании, жадных алгоритмах и других темах.</p>","path":["Глава 13. Поиск с возвратом","13.1 &nbsp; Алгоритм поиска с возвратом"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/#1315","level":2,"title":"13.1.5   Преимущества и ограничения","text":"<p>Алгоритм поиска с возвратом по своей сути является алгоритмом поиска в глубину, который перебирает все возможные решения, пока не найдет удовлетворяющее условиям. Преимущество этого подхода в том, что он позволяет находить все возможные решения и при разумной обрезке может работать весьма эффективно.</p> <p>Однако при работе с большими или сложными задачами эффективность backtracking может оказаться неприемлемой.</p> <ul> <li>Время: backtracking обычно требует обхода всех возможных состояний пространства состояний, и его временная сложность может достигать экспоненциального или факториального порядка.</li> <li>Память: при рекурсивных вызовах нужно хранить текущее состояние (например, путь, вспомогательные переменные для обрезки и т.д.), поэтому при большой глубине рекурсии потребность в памяти может стать значительной.</li> </ul> <p>Тем не менее backtracking по-прежнему остается лучшим решением для некоторых поисковых задач и задач удовлетворения ограничений. В таких задачах заранее невозможно предсказать, какие выборы приведут к эффективному решению, поэтому приходится перебирать все возможные варианты. В этой ситуации ключевым становится вопрос оптимизации эффективности , и для этого обычно используют две стратегии.</p> <ul> <li>Обрезка: избегать поиска по тем путям, которые заведомо не приведут к решению, тем самым экономя время и память.</li> <li>Эвристический поиск: вводить во время поиска дополнительные стратегии или оценки, чтобы в первую очередь исследовать пути, наиболее вероятно ведущие к эффективному решению.</li> </ul>","path":["Глава 13. Поиск с возвратом","13.1 &nbsp; Алгоритм поиска с возвратом"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/#1316-backtracking","level":2,"title":"13.1.6   Типичные задачи backtracking","text":"<p>Алгоритм поиска с возвратом можно использовать для решения множества поисковых задач, задач удовлетворения ограничений и задач комбинаторной оптимизации.</p> <p>Поисковые задачи: целью таких задач является поиск решений, удовлетворяющих определенным условиям.</p> <ul> <li>Задача о перестановках: дано множество, требуется найти все возможные перестановки его элементов.</li> <li>Задача о сумме подмножеств: даны множество и целевая сумма; нужно найти все подмножества, сумма элементов которых равна целевой.</li> <li>Задача о Ханойской башне: даны три стержня и набор дисков разного размера; требуется перенести все диски с одного стержня на другой, перемещая за раз только один диск и не помещая больший диск на меньший.</li> </ul> <p>Задачи удовлетворения ограничений: целью таких задач является поиск решений, удовлетворяющих всем ограничениям.</p> <ul> <li>Задача о \\(n\\) ферзях: разместить \\(n\\) ферзей на шахматной доске размера \\(n \\times n\\) так, чтобы они не атаковали друг друга.</li> <li>Судоку: заполнить сетку \\(9 \\times 9\\) числами от \\(1\\) до \\(9\\) так, чтобы в каждой строке, каждом столбце и каждом блоке \\(3 \\times 3\\) числа не повторялись.</li> <li>Задача раскраски графа: дан неориентированный граф; требуется раскрасить его вершины минимальным числом цветов так, чтобы соседние вершины имели разные цвета.</li> </ul> <p>Задачи комбинаторной оптимизации: целью таких задач является поиск оптимального решения в некотором комбинаторном пространстве при заданных ограничениях.</p> <ul> <li>Задача о рюкзаке 0-1: даны набор предметов и рюкзак; у каждого предмета есть ценность и вес, и нужно выбрать предметы так, чтобы при ограниченной вместимости рюкзака суммарная ценность была максимальной.</li> <li>Задача коммивояжера: начиная из некоторой вершины графа, требуется посетить все остальные вершины ровно по одному разу и вернуться в исходную вершину, найдя при этом кратчайший путь.</li> <li>Задача о максимальной клике: дан неориентированный граф; требуется найти в нем максимальный полный подграф, то есть подграф, в котором любая пара вершин соединена ребром.</li> </ul> <p>Обратите внимание: для многих задач комбинаторной оптимизации backtracking не является оптимальным способом решения.</p> <ul> <li>Задача о рюкзаке 0-1 обычно решается с помощью динамического программирования, что дает более высокую временную эффективность.</li> <li>Задача коммивояжера является известной NP-Hard задачей; для ее решения часто используют генетические алгоритмы, муравьиные алгоритмы и другие методы.</li> <li>Задача о максимальной клике является классической задачей теории графов и может решаться жадными и другими эвристическими алгоритмами.</li> </ul>","path":["Глава 13. Поиск с возвратом","13.1 &nbsp; Алгоритм поиска с возвратом"],"tags":[]},{"location":"chapter_backtracking/n_queens_problem/","level":1,"title":"13.4   Задача о n ферзях","text":"<p>Question</p> <p>Согласно правилам шахмат ферзь может атаковать фигуры, находящиеся с ним на одной строке, в одном столбце или на одной диагонали. Даны \\(n\\) ферзей и шахматная доска размера \\(n \\times n\\) ; требуется найти такие расстановки, при которых ни одна пара ферзей не может атаковать друг друга.</p> <p>Как показано на рисунке 13-15, при \\(n = 4\\) существует два решения. С точки зрения backtracking доска размера \\(n \\times n\\) содержит \\(n^2\\) клеток, которые образуют все возможные выборы <code>choices</code> . По мере поочередного размещения ферзей состояние доски непрерывно меняется, и текущее содержимое доски образует состояние <code>state</code> .</p> <p></p> <p> Рисунок 13-15   Решения задачи о 4 ферзях </p> <p>На рисунке 13-16 показаны три ограничения этой задачи: несколько ферзей не могут находиться на одной строке, в одном столбце или на одной диагонали. При этом нужно помнить, что диагонали бывают двух типов: главная <code>\\</code> и побочная <code>/</code> .</p> <p></p> <p> Рисунок 13-16   Ограничения задачи о n ферзях </p>","path":["Глава 13. Поиск с возвратом","13.4 &nbsp; Задача о n ферзях"],"tags":[]},{"location":"chapter_backtracking/n_queens_problem/#1","level":3,"title":"1.   Построчная стратегия размещения","text":"<p>Число ферзей и число строк доски одинаково и равно \\(n\\) , поэтому легко получить следующий вывод: в каждой строке доски разрешено и нужно разместить ровно одного ферзя.</p> <p>Иначе говоря, можно использовать построчную стратегию: начиная с первой строки, размещать по одному ферзю в каждой строке, пока не будет достигнута последняя.</p> <p>На рисунке 13-17 показан процесс построчного размещения для задачи о 4 ферзях. Из-за ограничений размера изображения на нем раскрыта только одна ветвь поиска для первой строки, а все варианты, не удовлетворяющие ограничениям по столбцам и диагоналям, были отсечены.</p> <p></p> <p> Рисунок 13-17   Построчная стратегия размещения </p> <p>По своей сути построчная стратегия сама по себе выполняет роль обрезки , потому что заранее исключает все ветви поиска, в которых в одной строке оказалось бы несколько ферзей.</p>","path":["Глава 13. Поиск с возвратом","13.4 &nbsp; Задача о n ферзях"],"tags":[]},{"location":"chapter_backtracking/n_queens_problem/#2","level":3,"title":"2.   Обрезка по столбцам и диагоналям","text":"<p>Чтобы удовлетворить ограничению по столбцам, можно использовать булев массив <code>cols</code> длины \\(n\\) , который записывает, есть ли ферзь в каждом столбце. Перед каждым размещением мы используем <code>cols</code> для отсечения столбцов, уже занятых ферзями, а затем динамически обновляем состояние <code>cols</code> во время отката.</p> <p>Tip</p> <p>Обратите внимание: начало координат матрицы находится в левом верхнем углу, при этом индексы строк растут сверху вниз, а индексы столбцов - слева направо.</p> <p>Как теперь обработать ограничения по диагоналям? Пусть клетка на доске имеет координаты \\((row, col)\\) . Выбрав некоторую главную диагональ в матрице, можно заметить, что разность индексов строки и столбца одинакова для всех клеток этой диагонали, то есть для всех клеток главной диагонали значение \\(row - col\\) постоянно.</p> <p>Это означает, что если для двух клеток выполняется равенство \\(row_1 - col_1 = row_2 - col_2\\) , то они обязательно лежат на одной и той же главной диагонали. Используя это правило, можно с помощью массива <code>diags1</code> , показанного на рисунке 13-18, отмечать наличие ферзя на каждой главной диагонали.</p> <p>Аналогично для всех клеток побочной диагонали значение \\(row + col\\) является постоянным. Поэтому для обработки ограничений по побочным диагоналям можно использовать еще один массив <code>diags2</code> .</p> <p></p> <p> Рисунок 13-18   Обработка ограничений по столбцам и диагоналям </p>","path":["Глава 13. Поиск с возвратом","13.4 &nbsp; Задача о n ферзях"],"tags":[]},{"location":"chapter_backtracking/n_queens_problem/#3","level":3,"title":"3.   Реализация кода","text":"<p>Заметим, что в квадратной матрице размера \\(n\\) диапазон значений \\(row - col\\) равен \\([-n + 1, n - 1]\\) , а диапазон значений \\(row + col\\) равен \\([0, 2n - 2]\\) . Следовательно, число главных и побочных диагоналей равно \\(2n - 1\\) , а значит, длины массивов <code>diags1</code> и <code>diags2</code> тоже равны \\(2n - 1\\) .</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby n_queens.py<pre><code>def backtrack(\n    row: int,\n    n: int,\n    state: list[list[str]],\n    res: list[list[list[str]]],\n    cols: list[bool],\n    diags1: list[bool],\n    diags2: list[bool],\n):\n    \"\"\"Алгоритм бэктрекинга: n ферзей\"\"\"\n    # Когда все строки уже обработаны, записать решение\n    if row == n:\n        res.append([list(row) for row in state])\n        return\n    # Обойти все столбцы\n    for col in range(n):\n        # Вычислить главную и побочную диагонали, соответствующие этой клетке\n        diag1 = row - col + n - 1\n        diag2 = row + col\n        # Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n        if not cols[col] and not diags1[diag1] and not diags2[diag2]:\n            # Попытка: поставить ферзя в эту клетку\n            state[row][col] = \"Q\"\n            cols[col] = diags1[diag1] = diags2[diag2] = True\n            # Перейти к размещению следующей строки\n            backtrack(row + 1, n, state, res, cols, diags1, diags2)\n            # Откат: восстановить эту клетку как пустую\n            state[row][col] = \"#\"\n            cols[col] = diags1[diag1] = diags2[diag2] = False\n\ndef n_queens(n: int) -&gt; list[list[list[str]]]:\n    \"\"\"Решить задачу о n ферзях\"\"\"\n    # Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n    state = [[\"#\" for _ in range(n)] for _ in range(n)]\n    cols = [False] * n  # Отмечать, есть ли ферзь в столбце\n    diags1 = [False] * (2 * n - 1)  # Отмечать наличие ферзя на главной диагонали\n    diags2 = [False] * (2 * n - 1)  # Отмечать наличие ферзя на побочной диагонали\n    res = []\n    backtrack(0, n, state, res, cols, diags1, diags2)\n\n    return res\n</code></pre> n_queens.cpp<pre><code>/* Алгоритм бэктрекинга: n ферзей */\nvoid backtrack(int row, int n, vector&lt;vector&lt;string&gt;&gt; &amp;state, vector&lt;vector&lt;vector&lt;string&gt;&gt;&gt; &amp;res, vector&lt;bool&gt; &amp;cols,\n               vector&lt;bool&gt; &amp;diags1, vector&lt;bool&gt; &amp;diags2) {\n    // Когда все строки уже обработаны, записать решение\n    if (row == n) {\n        res.push_back(state);\n        return;\n    }\n    // Обойти все столбцы\n    for (int col = 0; col &lt; n; col++) {\n        // Вычислить главную и побочную диагонали, соответствующие этой клетке\n        int diag1 = row - col + n - 1;\n        int diag2 = row + col;\n        // Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n        if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n            // Попытка: поставить ферзя в эту клетку\n            state[row][col] = \"Q\";\n            cols[col] = diags1[diag1] = diags2[diag2] = true;\n            // Перейти к размещению следующей строки\n            backtrack(row + 1, n, state, res, cols, diags1, diags2);\n            // Откат: восстановить эту клетку как пустую\n            state[row][col] = \"#\";\n            cols[col] = diags1[diag1] = diags2[diag2] = false;\n        }\n    }\n}\n\n/* Решить задачу о n ферзях */\nvector&lt;vector&lt;vector&lt;string&gt;&gt;&gt; nQueens(int n) {\n    // Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n    vector&lt;vector&lt;string&gt;&gt; state(n, vector&lt;string&gt;(n, \"#\"));\n    vector&lt;bool&gt; cols(n, false);           // Отмечать, есть ли ферзь в столбце\n    vector&lt;bool&gt; diags1(2 * n - 1, false); // Отмечать наличие ферзя на главной диагонали\n    vector&lt;bool&gt; diags2(2 * n - 1, false); // Отмечать наличие ферзя на побочной диагонали\n    vector&lt;vector&lt;vector&lt;string&gt;&gt;&gt; res;\n\n    backtrack(0, n, state, res, cols, diags1, diags2);\n\n    return res;\n}\n</code></pre> n_queens.java<pre><code>/* Алгоритм бэктрекинга: n ферзей */\nvoid backtrack(int row, int n, List&lt;List&lt;String&gt;&gt; state, List&lt;List&lt;List&lt;String&gt;&gt;&gt; res,\n        boolean[] cols, boolean[] diags1, boolean[] diags2) {\n    // Когда все строки уже обработаны, записать решение\n    if (row == n) {\n        List&lt;List&lt;String&gt;&gt; copyState = new ArrayList&lt;&gt;();\n        for (List&lt;String&gt; sRow : state) {\n            copyState.add(new ArrayList&lt;&gt;(sRow));\n        }\n        res.add(copyState);\n        return;\n    }\n    // Обойти все столбцы\n    for (int col = 0; col &lt; n; col++) {\n        // Вычислить главную и побочную диагонали, соответствующие этой клетке\n        int diag1 = row - col + n - 1;\n        int diag2 = row + col;\n        // Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n        if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n            // Попытка: поставить ферзя в эту клетку\n            state.get(row).set(col, \"Q\");\n            cols[col] = diags1[diag1] = diags2[diag2] = true;\n            // Перейти к размещению следующей строки\n            backtrack(row + 1, n, state, res, cols, diags1, diags2);\n            // Откат: восстановить эту клетку как пустую\n            state.get(row).set(col, \"#\");\n            cols[col] = diags1[diag1] = diags2[diag2] = false;\n        }\n    }\n}\n\n/* Решить задачу о n ферзях */\nList&lt;List&lt;List&lt;String&gt;&gt;&gt; nQueens(int n) {\n    // Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n    List&lt;List&lt;String&gt;&gt; state = new ArrayList&lt;&gt;();\n    for (int i = 0; i &lt; n; i++) {\n        List&lt;String&gt; row = new ArrayList&lt;&gt;();\n        for (int j = 0; j &lt; n; j++) {\n            row.add(\"#\");\n        }\n        state.add(row);\n    }\n    boolean[] cols = new boolean[n]; // Отмечать, есть ли ферзь в столбце\n    boolean[] diags1 = new boolean[2 * n - 1]; // Отмечать наличие ферзя на главной диагонали\n    boolean[] diags2 = new boolean[2 * n - 1]; // Отмечать наличие ферзя на побочной диагонали\n    List&lt;List&lt;List&lt;String&gt;&gt;&gt; res = new ArrayList&lt;&gt;();\n\n    backtrack(0, n, state, res, cols, diags1, diags2);\n\n    return res;\n}\n</code></pre> n_queens.cs<pre><code>/* Алгоритм бэктрекинга: n ферзей */\nvoid Backtrack(int row, int n, List&lt;List&lt;string&gt;&gt; state, List&lt;List&lt;List&lt;string&gt;&gt;&gt; res,\n        bool[] cols, bool[] diags1, bool[] diags2) {\n    // Когда все строки уже обработаны, записать решение\n    if (row == n) {\n        List&lt;List&lt;string&gt;&gt; copyState = [];\n        foreach (List&lt;string&gt; sRow in state) {\n            copyState.Add(new List&lt;string&gt;(sRow));\n        }\n        res.Add(copyState);\n        return;\n    }\n    // Обойти все столбцы\n    for (int col = 0; col &lt; n; col++) {\n        // Вычислить главную и побочную диагонали, соответствующие этой клетке\n        int diag1 = row - col + n - 1;\n        int diag2 = row + col;\n        // Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n        if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n            // Попытка: поставить ферзя в эту клетку\n            state[row][col] = \"Q\";\n            cols[col] = diags1[diag1] = diags2[diag2] = true;\n            // Перейти к размещению следующей строки\n            Backtrack(row + 1, n, state, res, cols, diags1, diags2);\n            // Откат: восстановить эту клетку как пустую\n            state[row][col] = \"#\";\n            cols[col] = diags1[diag1] = diags2[diag2] = false;\n        }\n    }\n}\n\n/* Решить задачу о n ферзях */\nList&lt;List&lt;List&lt;string&gt;&gt;&gt; NQueens(int n) {\n    // Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n    List&lt;List&lt;string&gt;&gt; state = [];\n    for (int i = 0; i &lt; n; i++) {\n        List&lt;string&gt; row = [];\n        for (int j = 0; j &lt; n; j++) {\n            row.Add(\"#\");\n        }\n        state.Add(row);\n    }\n    bool[] cols = new bool[n]; // Отмечать, есть ли ферзь в столбце\n    bool[] diags1 = new bool[2 * n - 1]; // Отмечать наличие ферзя на главной диагонали\n    bool[] diags2 = new bool[2 * n - 1]; // Отмечать наличие ферзя на побочной диагонали\n    List&lt;List&lt;List&lt;string&gt;&gt;&gt; res = [];\n\n    Backtrack(0, n, state, res, cols, diags1, diags2);\n\n    return res;\n}\n</code></pre> n_queens.go<pre><code>/* Алгоритм бэктрекинга: n ферзей */\nfunc backtrack(row, n int, state *[][]string, res *[][][]string, cols, diags1, diags2 *[]bool) {\n    // Когда все строки уже обработаны, записать решение\n    if row == n {\n        newState := make([][]string, len(*state))\n        for i, _ := range newState {\n            newState[i] = make([]string, len((*state)[0]))\n            copy(newState[i], (*state)[i])\n\n        }\n        *res = append(*res, newState)\n        return\n    }\n    // Обойти все столбцы\n    for col := 0; col &lt; n; col++ {\n        // Вычислить главную и побочную диагонали, соответствующие этой клетке\n        diag1 := row - col + n - 1\n        diag2 := row + col\n        // Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n        if !(*cols)[col] &amp;&amp; !(*diags1)[diag1] &amp;&amp; !(*diags2)[diag2] {\n            // Попытка: поставить ферзя в эту клетку\n            (*state)[row][col] = \"Q\"\n            (*cols)[col], (*diags1)[diag1], (*diags2)[diag2] = true, true, true\n            // Перейти к размещению следующей строки\n            backtrack(row+1, n, state, res, cols, diags1, diags2)\n            // Откат: восстановить эту клетку как пустую\n            (*state)[row][col] = \"#\"\n            (*cols)[col], (*diags1)[diag1], (*diags2)[diag2] = false, false, false\n        }\n    }\n}\n\n/* Решить задачу о n ферзях */\nfunc nQueens(n int) [][][]string {\n    // Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n    state := make([][]string, n)\n    for i := 0; i &lt; n; i++ {\n        row := make([]string, n)\n        for i := 0; i &lt; n; i++ {\n            row[i] = \"#\"\n        }\n        state[i] = row\n    }\n    // Отмечать, есть ли ферзь в столбце\n    cols := make([]bool, n)\n    diags1 := make([]bool, 2*n-1)\n    diags2 := make([]bool, 2*n-1)\n    res := make([][][]string, 0)\n    backtrack(0, n, &amp;state, &amp;res, &amp;cols, &amp;diags1, &amp;diags2)\n    return res\n}\n</code></pre> n_queens.swift<pre><code>/* Алгоритм бэктрекинга: n ферзей */\nfunc backtrack(row: Int, n: Int, state: inout [[String]], res: inout [[[String]]], cols: inout [Bool], diags1: inout [Bool], diags2: inout [Bool]) {\n    // Когда все строки уже обработаны, записать решение\n    if row == n {\n        res.append(state)\n        return\n    }\n    // Обойти все столбцы\n    for col in 0 ..&lt; n {\n        // Вычислить главную и побочную диагонали, соответствующие этой клетке\n        let diag1 = row - col + n - 1\n        let diag2 = row + col\n        // Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n        if !cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2] {\n            // Попытка: поставить ферзя в эту клетку\n            state[row][col] = \"Q\"\n            cols[col] = true\n            diags1[diag1] = true\n            diags2[diag2] = true\n            // Перейти к размещению следующей строки\n            backtrack(row: row + 1, n: n, state: &amp;state, res: &amp;res, cols: &amp;cols, diags1: &amp;diags1, diags2: &amp;diags2)\n            // Откат: восстановить эту клетку как пустую\n            state[row][col] = \"#\"\n            cols[col] = false\n            diags1[diag1] = false\n            diags2[diag2] = false\n        }\n    }\n}\n\n/* Решить задачу о n ферзях */\nfunc nQueens(n: Int) -&gt; [[[String]]] {\n    // Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n    var state = Array(repeating: Array(repeating: \"#\", count: n), count: n)\n    var cols = Array(repeating: false, count: n) // Отмечать, есть ли ферзь в столбце\n    var diags1 = Array(repeating: false, count: 2 * n - 1) // Отмечать наличие ферзя на главной диагонали\n    var diags2 = Array(repeating: false, count: 2 * n - 1) // Отмечать наличие ферзя на побочной диагонали\n    var res: [[[String]]] = []\n\n    backtrack(row: 0, n: n, state: &amp;state, res: &amp;res, cols: &amp;cols, diags1: &amp;diags1, diags2: &amp;diags2)\n\n    return res\n}\n</code></pre> n_queens.js<pre><code>/* Алгоритм бэктрекинга: n ферзей */\nfunction backtrack(row, n, state, res, cols, diags1, diags2) {\n    // Когда все строки уже обработаны, записать решение\n    if (row === n) {\n        res.push(state.map((row) =&gt; row.slice()));\n        return;\n    }\n    // Обойти все столбцы\n    for (let col = 0; col &lt; n; col++) {\n        // Вычислить главную и побочную диагонали, соответствующие этой клетке\n        const diag1 = row - col + n - 1;\n        const diag2 = row + col;\n        // Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n        if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n            // Попытка: поставить ферзя в эту клетку\n            state[row][col] = 'Q';\n            cols[col] = diags1[diag1] = diags2[diag2] = true;\n            // Перейти к размещению следующей строки\n            backtrack(row + 1, n, state, res, cols, diags1, diags2);\n            // Откат: восстановить эту клетку как пустую\n            state[row][col] = '#';\n            cols[col] = diags1[diag1] = diags2[diag2] = false;\n        }\n    }\n}\n\n/* Решить задачу о n ферзях */\nfunction nQueens(n) {\n    // Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n    const state = Array.from({ length: n }, () =&gt; Array(n).fill('#'));\n    const cols = Array(n).fill(false); // Отмечать, есть ли ферзь в столбце\n    const diags1 = Array(2 * n - 1).fill(false); // Отмечать наличие ферзя на главной диагонали\n    const diags2 = Array(2 * n - 1).fill(false); // Отмечать наличие ферзя на побочной диагонали\n    const res = [];\n\n    backtrack(0, n, state, res, cols, diags1, diags2);\n    return res;\n}\n</code></pre> n_queens.ts<pre><code>/* Алгоритм бэктрекинга: n ферзей */\nfunction backtrack(\n    row: number,\n    n: number,\n    state: string[][],\n    res: string[][][],\n    cols: boolean[],\n    diags1: boolean[],\n    diags2: boolean[]\n): void {\n    // Когда все строки уже обработаны, записать решение\n    if (row === n) {\n        res.push(state.map((row) =&gt; row.slice()));\n        return;\n    }\n    // Обойти все столбцы\n    for (let col = 0; col &lt; n; col++) {\n        // Вычислить главную и побочную диагонали, соответствующие этой клетке\n        const diag1 = row - col + n - 1;\n        const diag2 = row + col;\n        // Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n        if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n            // Попытка: поставить ферзя в эту клетку\n            state[row][col] = 'Q';\n            cols[col] = diags1[diag1] = diags2[diag2] = true;\n            // Перейти к размещению следующей строки\n            backtrack(row + 1, n, state, res, cols, diags1, diags2);\n            // Откат: восстановить эту клетку как пустую\n            state[row][col] = '#';\n            cols[col] = diags1[diag1] = diags2[diag2] = false;\n        }\n    }\n}\n\n/* Решить задачу о n ферзях */\nfunction nQueens(n: number): string[][][] {\n    // Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n    const state = Array.from({ length: n }, () =&gt; Array(n).fill('#'));\n    const cols = Array(n).fill(false); // Отмечать, есть ли ферзь в столбце\n    const diags1 = Array(2 * n - 1).fill(false); // Отмечать наличие ферзя на главной диагонали\n    const diags2 = Array(2 * n - 1).fill(false); // Отмечать наличие ферзя на побочной диагонали\n    const res: string[][][] = [];\n\n    backtrack(0, n, state, res, cols, diags1, diags2);\n    return res;\n}\n</code></pre> n_queens.dart<pre><code>/* Алгоритм бэктрекинга: n ферзей */\nvoid backtrack(\n  int row,\n  int n,\n  List&lt;List&lt;String&gt;&gt; state,\n  List&lt;List&lt;List&lt;String&gt;&gt;&gt; res,\n  List&lt;bool&gt; cols,\n  List&lt;bool&gt; diags1,\n  List&lt;bool&gt; diags2,\n) {\n  // Когда все строки уже обработаны, записать решение\n  if (row == n) {\n    List&lt;List&lt;String&gt;&gt; copyState = [];\n    for (List&lt;String&gt; sRow in state) {\n      copyState.add(List.from(sRow));\n    }\n    res.add(copyState);\n    return;\n  }\n  // Обойти все столбцы\n  for (int col = 0; col &lt; n; col++) {\n    // Вычислить главную и побочную диагонали, соответствующие этой клетке\n    int diag1 = row - col + n - 1;\n    int diag2 = row + col;\n    // Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n    if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n      // Попытка: поставить ферзя в эту клетку\n      state[row][col] = \"Q\";\n      cols[col] = true;\n      diags1[diag1] = true;\n      diags2[diag2] = true;\n      // Перейти к размещению следующей строки\n      backtrack(row + 1, n, state, res, cols, diags1, diags2);\n      // Откат: восстановить эту клетку как пустую\n      state[row][col] = \"#\";\n      cols[col] = false;\n      diags1[diag1] = false;\n      diags2[diag2] = false;\n    }\n  }\n}\n\n/* Решить задачу о n ферзях */\nList&lt;List&lt;List&lt;String&gt;&gt;&gt; nQueens(int n) {\n  // Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n  List&lt;List&lt;String&gt;&gt; state = List.generate(n, (index) =&gt; List.filled(n, \"#\"));\n  List&lt;bool&gt; cols = List.filled(n, false); // Отмечать, есть ли ферзь в столбце\n  List&lt;bool&gt; diags1 = List.filled(2 * n - 1, false); // Отмечать наличие ферзя на главной диагонали\n  List&lt;bool&gt; diags2 = List.filled(2 * n - 1, false); // Отмечать наличие ферзя на побочной диагонали\n  List&lt;List&lt;List&lt;String&gt;&gt;&gt; res = [];\n\n  backtrack(0, n, state, res, cols, diags1, diags2);\n\n  return res;\n}\n</code></pre> n_queens.rs<pre><code>/* Алгоритм бэктрекинга: n ферзей */\nfn backtrack(\n    row: usize,\n    n: usize,\n    state: &amp;mut Vec&lt;Vec&lt;String&gt;&gt;,\n    res: &amp;mut Vec&lt;Vec&lt;Vec&lt;String&gt;&gt;&gt;,\n    cols: &amp;mut [bool],\n    diags1: &amp;mut [bool],\n    diags2: &amp;mut [bool],\n) {\n    // Когда все строки уже обработаны, записать решение\n    if row == n {\n        res.push(state.clone());\n        return;\n    }\n    // Обойти все столбцы\n    for col in 0..n {\n        // Вычислить главную и побочную диагонали, соответствующие этой клетке\n        let diag1 = row + n - 1 - col;\n        let diag2 = row + col;\n        // Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n        if !cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2] {\n            // Попытка: поставить ферзя в эту клетку\n            state[row][col] = \"Q\".into();\n            (cols[col], diags1[diag1], diags2[diag2]) = (true, true, true);\n            // Перейти к размещению следующей строки\n            backtrack(row + 1, n, state, res, cols, diags1, diags2);\n            // Откат: восстановить эту клетку как пустую\n            state[row][col] = \"#\".into();\n            (cols[col], diags1[diag1], diags2[diag2]) = (false, false, false);\n        }\n    }\n}\n\n/* Решить задачу о n ферзях */\nfn n_queens(n: usize) -&gt; Vec&lt;Vec&lt;Vec&lt;String&gt;&gt;&gt; {\n    // Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n    let mut state: Vec&lt;Vec&lt;String&gt;&gt; = vec![vec![\"#\".to_string(); n]; n];\n    let mut cols = vec![false; n]; // Отмечать, есть ли ферзь в столбце\n    let mut diags1 = vec![false; 2 * n - 1]; // Отмечать наличие ферзя на главной диагонали\n    let mut diags2 = vec![false; 2 * n - 1]; // Отмечать наличие ферзя на побочной диагонали\n    let mut res: Vec&lt;Vec&lt;Vec&lt;String&gt;&gt;&gt; = Vec::new();\n\n    backtrack(\n        0,\n        n,\n        &amp;mut state,\n        &amp;mut res,\n        &amp;mut cols,\n        &amp;mut diags1,\n        &amp;mut diags2,\n    );\n\n    res\n}\n</code></pre> n_queens.c<pre><code>/* Алгоритм бэктрекинга: n ферзей */\nvoid backtrack(int row, int n, char state[MAX_SIZE][MAX_SIZE], char ***res, int *resSize, bool cols[MAX_SIZE],\n               bool diags1[2 * MAX_SIZE - 1], bool diags2[2 * MAX_SIZE - 1]) {\n    // Когда все строки уже обработаны, записать решение\n    if (row == n) {\n        res[*resSize] = (char **)malloc(sizeof(char *) * n);\n        for (int i = 0; i &lt; n; ++i) {\n            res[*resSize][i] = (char *)malloc(sizeof(char) * (n + 1));\n            strcpy(res[*resSize][i], state[i]);\n        }\n        (*resSize)++;\n        return;\n    }\n    // Обойти все столбцы\n    for (int col = 0; col &lt; n; col++) {\n        // Вычислить главную и побочную диагонали, соответствующие этой клетке\n        int diag1 = row - col + n - 1;\n        int diag2 = row + col;\n        // Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n        if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n            // Попытка: поставить ферзя в эту клетку\n            state[row][col] = 'Q';\n            cols[col] = diags1[diag1] = diags2[diag2] = true;\n            // Перейти к размещению следующей строки\n            backtrack(row + 1, n, state, res, resSize, cols, diags1, diags2);\n            // Откат: восстановить эту клетку как пустую\n            state[row][col] = '#';\n            cols[col] = diags1[diag1] = diags2[diag2] = false;\n        }\n    }\n}\n\n/* Решить задачу о n ферзях */\nchar ***nQueens(int n, int *returnSize) {\n    char state[MAX_SIZE][MAX_SIZE];\n    // Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n    for (int i = 0; i &lt; n; ++i) {\n        for (int j = 0; j &lt; n; ++j) {\n            state[i][j] = '#';\n        }\n        state[i][n] = '\\0';\n    }\n    bool cols[MAX_SIZE] = {false};           // Отмечать, есть ли ферзь в столбце\n    bool diags1[2 * MAX_SIZE - 1] = {false}; // Отмечать наличие ферзя на главной диагонали\n    bool diags2[2 * MAX_SIZE - 1] = {false}; // Отмечать наличие ферзя на побочной диагонали\n\n    char ***res = (char ***)malloc(sizeof(char **) * MAX_SIZE);\n    *returnSize = 0;\n    backtrack(0, n, state, res, returnSize, cols, diags1, diags2);\n    return res;\n}\n</code></pre> n_queens.kt<pre><code>/* Алгоритм бэктрекинга: n ферзей */\nfun backtrack(\n    row: Int,\n    n: Int,\n    state: MutableList&lt;MutableList&lt;String&gt;&gt;,\n    res: MutableList&lt;MutableList&lt;MutableList&lt;String&gt;&gt;?&gt;,\n    cols: BooleanArray,\n    diags1: BooleanArray,\n    diags2: BooleanArray\n) {\n    // Когда все строки уже обработаны, записать решение\n    if (row == n) {\n        val copyState = mutableListOf&lt;MutableList&lt;String&gt;&gt;()\n        for (sRow in state) {\n            copyState.add(sRow.toMutableList())\n        }\n        res.add(copyState)\n        return\n    }\n    // Обойти все столбцы\n    for (col in 0..&lt;n) {\n        // Вычислить главную и побочную диагонали, соответствующие этой клетке\n        val diag1 = row - col + n - 1\n        val diag2 = row + col\n        // Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n        if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n            // Попытка: поставить ферзя в эту клетку\n            state[row][col] = \"Q\"\n            diags2[diag2] = true\n            diags1[diag1] = diags2[diag2]\n            cols[col] = diags1[diag1]\n            // Перейти к размещению следующей строки\n            backtrack(row + 1, n, state, res, cols, diags1, diags2)\n            // Откат: восстановить эту клетку как пустую\n            state[row][col] = \"#\"\n            diags2[diag2] = false\n            diags1[diag1] = diags2[diag2]\n            cols[col] = diags1[diag1]\n        }\n    }\n}\n\n/* Решить задачу о n ферзях */\nfun nQueens(n: Int): MutableList&lt;MutableList&lt;MutableList&lt;String&gt;&gt;?&gt; {\n    // Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n    val state = mutableListOf&lt;MutableList&lt;String&gt;&gt;()\n    for (i in 0..&lt;n) {\n        val row = mutableListOf&lt;String&gt;()\n        for (j in 0..&lt;n) {\n            row.add(\"#\")\n        }\n        state.add(row)\n    }\n    val cols = BooleanArray(n) // Отмечать, есть ли ферзь в столбце\n    val diags1 = BooleanArray(2 * n - 1) // Отмечать наличие ферзя на главной диагонали\n    val diags2 = BooleanArray(2 * n - 1) // Отмечать наличие ферзя на побочной диагонали\n    val res = mutableListOf&lt;MutableList&lt;MutableList&lt;String&gt;&gt;?&gt;()\n\n    backtrack(0, n, state, res, cols, diags1, diags2)\n\n    return res\n}\n</code></pre> n_queens.rb<pre><code>### Алгоритм бэктрекинга: n ферзей ###\ndef backtrack(row, n, state, res, cols, diags1, diags2)\n  # Когда все строки уже обработаны, записать решение\n  if row == n\n    res &lt;&lt; state.map { |row| row.dup }\n    return\n  end\n\n  # Обойти все столбцы\n  for col in 0...n\n    # Вычислить главную и побочную диагонали, соответствующие этой клетке\n    diag1 = row - col + n - 1\n    diag2 = row + col\n    # Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n    if !cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]\n      # Попытка: поставить ферзя в эту клетку\n      state[row][col] = \"Q\"\n      cols[col] = diags1[diag1] = diags2[diag2] = true\n      # Перейти к размещению следующей строки\n      backtrack(row + 1, n, state, res, cols, diags1, diags2)\n      # Откат: восстановить эту клетку как пустую\n      state[row][col] = \"#\"\n      cols[col] = diags1[diag1] = diags2[diag2] = false\n    end\n  end\nend\n\n### Решить задачу о n ферзях ###\ndef n_queens(n)\n  # Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n  state = Array.new(n) { Array.new(n, \"#\") }\n  cols = Array.new(n, false) # Отмечать, есть ли ферзь в столбце\n  diags1 = Array.new(2 * n - 1, false) # Отмечать наличие ферзя на главной диагонали\n  diags2 = Array.new(2 * n - 1, false) # Отмечать наличие ферзя на побочной диагонали\n  res = []\n  backtrack(0, n, state, res, cols, diags1, diags2)\n\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Если размещать ферзей построчно \\(n\\) раз, учитывая ограничение по столбцам, то начиная с первой строки и заканчивая последней мы получаем соответственно \\(n\\), \\(n-1\\), \\(\\dots\\), \\(2\\), \\(1\\) вариантов выбора, что дает \\(O(n!)\\) времени. При записи решения нужно скопировать матрицу <code>state</code> и добавить ее в <code>res</code> , а копирование требует \\(O(n^2)\\) времени. Следовательно, общая временная сложность равна \\(O(n! \\cdot n^2)\\) . На практике обрезка по диагональным ограничениям дополнительно сильно уменьшает пространство поиска, поэтому фактическая эффективность часто лучше этой оценки.</p> <p>Массив <code>state</code> использует \\(O(n^2)\\) пространства, а массивы <code>cols</code> , <code>diags1</code> и <code>diags2</code> используют по \\(O(n)\\) пространства. Максимальная глубина рекурсии равна \\(n\\) , что требует \\(O(n)\\) памяти стека. Следовательно, пространственная сложность равна \\(O(n^2)\\) .</p>","path":["Глава 13. Поиск с возвратом","13.4 &nbsp; Задача о n ферзях"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/","level":1,"title":"13.2   Задача о перестановках","text":"<p>Задача о перестановках является типичным применением алгоритма поиска с возвратом. Ее определение состоит в том, чтобы для данного множества элементов (например, массива или строки) найти все возможные перестановки этих элементов.</p> <p>В таблице 13-2 приведено несколько примеров входных массивов и соответствующих им перестановок.</p> <p> Таблица 13-2   Примеры перестановок </p> Входной массив Все перестановки \\([1]\\) \\([1]\\) \\([1, 2]\\) \\([1, 2], [2, 1]\\) \\([1, 2, 3]\\) \\([1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]\\)","path":["Глава 13. Поиск с возвратом","13.2 &nbsp; Задача о перестановках"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#1321","level":2,"title":"13.2.1   Случай без равных элементов","text":"<p>Question</p> <p>Дан массив целых чисел, в котором нет повторяющихся элементов. Верните все возможные перестановки.</p> <p>С точки зрения backtracking процесс построения перестановок можно представить как результат последовательности выборов. Пусть входной массив равен \\([1, 2, 3]\\) ; если мы сначала выберем \\(1\\) , затем \\(3\\) , а потом \\(2\\) , то получим перестановку \\([1, 3, 2]\\) . Откат означает отмену одного из выборов с последующей попыткой других вариантов.</p> <p>С точки зрения кода backtracking множество кандидатов <code>choices</code> состоит из всех элементов входного массива, а состояние <code>state</code> - из элементов, уже выбранных к текущему моменту. Обратите внимание, что каждый элемент разрешено выбирать только один раз, поэтому все элементы в <code>state</code> должны быть уникальны.</p> <p>Как показано на рисунке 13-5, процесс поиска можно развернуть в дерево рекурсии, где каждый узел представляет текущее состояние <code>state</code> . Начиная от корня, после трех раундов выбора мы попадаем в листья, и каждый лист соответствует одной перестановке.</p> <p></p> <p> Рисунок 13-5   Дерево рекурсии для перестановок </p>","path":["Глава 13. Поиск с возвратом","13.2 &nbsp; Задача о перестановках"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#1","level":3,"title":"1.   Обрезка повторного выбора","text":"<p>Чтобы гарантировать, что каждый элемент выбирается только один раз, введем булев массив <code>selected</code> , где <code>selected[i]</code> обозначает, был ли уже выбран <code>choices[i]</code> , и на его основе выполним следующую обрезку.</p> <ul> <li>После того как сделан выбор <code>choice[i]</code> , мы присваиваем <code>selected[i]</code> значение \\(\\text{True}\\) , тем самым отмечая, что этот элемент уже выбран.</li> <li>При обходе списка вариантов <code>choices</code> пропускаем все уже выбранные элементы, то есть выполняем обрезку.</li> </ul> <p>Как показано на рисунке 13-6, если в первом раунде мы выберем 1 , во втором - 3 , а в третьем - 2 , то во втором раунде нужно отсечь ветвь элемента 1 , а в третьем - ветви элементов 1 и 3 .</p> <p></p> <p> Рисунок 13-6   Пример обрезки в задаче о перестановках </p> <p>Из рисунка видно, что такая обрезка уменьшает размер пространства поиска с \\(O(n^n)\\) до \\(O(n!)\\) .</p>","path":["Глава 13. Поиск с возвратом","13.2 &nbsp; Задача о перестановках"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#2","level":3,"title":"2.   Реализация кода","text":"<p>После прояснения всей логики можно просто \"заполнить пропуски\" в шаблоне backtracking. Чтобы сократить общий объем кода, мы не будем отдельно реализовывать каждую функцию из каркаса, а раскроем их прямо внутри <code>backtrack()</code> :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby permutations_i.py<pre><code>def backtrack(\n    state: list[int], choices: list[int], selected: list[bool], res: list[list[int]]\n):\n    \"\"\"Алгоритм бэктрекинга: все перестановки I\"\"\"\n    # Когда длина состояния равна числу элементов, записать решение\n    if len(state) == len(choices):\n        res.append(list(state))\n        return\n    # Перебор всех вариантов выбора\n    for i, choice in enumerate(choices):\n        # Отсечение: нельзя выбирать один и тот же элемент повторно\n        if not selected[i]:\n            # Попытка: сделать выбор и обновить состояние\n            selected[i] = True\n            state.append(choice)\n            # Перейти к следующему выбору\n            backtrack(state, choices, selected, res)\n            # Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = False\n            state.pop()\n\ndef permutations_i(nums: list[int]) -&gt; list[list[int]]:\n    \"\"\"Все перестановки I\"\"\"\n    res = []\n    backtrack(state=[], choices=nums, selected=[False] * len(nums), res=res)\n    return res\n</code></pre> permutations_i.cpp<pre><code>/* Алгоритм бэктрекинга: все перестановки I */\nvoid backtrack(vector&lt;int&gt; &amp;state, const vector&lt;int&gt; &amp;choices, vector&lt;bool&gt; &amp;selected, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (state.size() == choices.size()) {\n        res.push_back(state);\n        return;\n    }\n    // Перебор всех вариантов выбора\n    for (int i = 0; i &lt; choices.size(); i++) {\n        int choice = choices[i];\n        // Отсечение: нельзя выбирать один и тот же элемент повторно\n        if (!selected[i]) {\n            // Попытка: сделать выбор и обновить состояние\n            selected[i] = true;\n            state.push_back(choice);\n            // Перейти к следующему выбору\n            backtrack(state, choices, selected, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n            state.pop_back();\n        }\n    }\n}\n\n/* Все перестановки I */\nvector&lt;vector&lt;int&gt;&gt; permutationsI(vector&lt;int&gt; nums) {\n    vector&lt;int&gt; state;\n    vector&lt;bool&gt; selected(nums.size(), false);\n    vector&lt;vector&lt;int&gt;&gt; res;\n    backtrack(state, nums, selected, res);\n    return res;\n}\n</code></pre> permutations_i.java<pre><code>/* Алгоритм бэктрекинга: все перестановки I */\nvoid backtrack(List&lt;Integer&gt; state, int[] choices, boolean[] selected, List&lt;List&lt;Integer&gt;&gt; res) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (state.size() == choices.length) {\n        res.add(new ArrayList&lt;Integer&gt;(state));\n        return;\n    }\n    // Перебор всех вариантов выбора\n    for (int i = 0; i &lt; choices.length; i++) {\n        int choice = choices[i];\n        // Отсечение: нельзя выбирать один и тот же элемент повторно\n        if (!selected[i]) {\n            // Попытка: сделать выбор и обновить состояние\n            selected[i] = true;\n            state.add(choice);\n            // Перейти к следующему выбору\n            backtrack(state, choices, selected, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n            state.remove(state.size() - 1);\n        }\n    }\n}\n\n/* Все перестановки I */\nList&lt;List&lt;Integer&gt;&gt; permutationsI(int[] nums) {\n    List&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;List&lt;Integer&gt;&gt;();\n    backtrack(new ArrayList&lt;Integer&gt;(), nums, new boolean[nums.length], res);\n    return res;\n}\n</code></pre> permutations_i.cs<pre><code>/* Алгоритм бэктрекинга: все перестановки I */\nvoid Backtrack(List&lt;int&gt; state, int[] choices, bool[] selected, List&lt;List&lt;int&gt;&gt; res) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (state.Count == choices.Length) {\n        res.Add(new List&lt;int&gt;(state));\n        return;\n    }\n    // Перебор всех вариантов выбора\n    for (int i = 0; i &lt; choices.Length; i++) {\n        int choice = choices[i];\n        // Отсечение: нельзя выбирать один и тот же элемент повторно\n        if (!selected[i]) {\n            // Попытка: сделать выбор и обновить состояние\n            selected[i] = true;\n            state.Add(choice);\n            // Перейти к следующему выбору\n            Backtrack(state, choices, selected, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n            state.RemoveAt(state.Count - 1);\n        }\n    }\n}\n\n/* Все перестановки I */\nList&lt;List&lt;int&gt;&gt; PermutationsI(int[] nums) {\n    List&lt;List&lt;int&gt;&gt; res = [];\n    Backtrack([], nums, new bool[nums.Length], res);\n    return res;\n}\n</code></pre> permutations_i.go<pre><code>/* Алгоритм бэктрекинга: все перестановки I */\nfunc backtrackI(state *[]int, choices *[]int, selected *[]bool, res *[][]int) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if len(*state) == len(*choices) {\n        newState := append([]int{}, *state...)\n        *res = append(*res, newState)\n    }\n    // Перебор всех вариантов выбора\n    for i := 0; i &lt; len(*choices); i++ {\n        choice := (*choices)[i]\n        // Отсечение: нельзя выбирать один и тот же элемент повторно\n        if !(*selected)[i] {\n            // Попытка: сделать выбор и обновить состояние\n            (*selected)[i] = true\n            *state = append(*state, choice)\n            // Перейти к следующему выбору\n            backtrackI(state, choices, selected, res)\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            (*selected)[i] = false\n            *state = (*state)[:len(*state)-1]\n        }\n    }\n}\n\n/* Все перестановки I */\nfunc permutationsI(nums []int) [][]int {\n    res := make([][]int, 0)\n    state := make([]int, 0)\n    selected := make([]bool, len(nums))\n    backtrackI(&amp;state, &amp;nums, &amp;selected, &amp;res)\n    return res\n}\n</code></pre> permutations_i.swift<pre><code>/* Алгоритм бэктрекинга: все перестановки I */\nfunc backtrack(state: inout [Int], choices: [Int], selected: inout [Bool], res: inout [[Int]]) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if state.count == choices.count {\n        res.append(state)\n        return\n    }\n    // Перебор всех вариантов выбора\n    for (i, choice) in choices.enumerated() {\n        // Отсечение: нельзя выбирать один и тот же элемент повторно\n        if !selected[i] {\n            // Попытка: сделать выбор и обновить состояние\n            selected[i] = true\n            state.append(choice)\n            // Перейти к следующему выбору\n            backtrack(state: &amp;state, choices: choices, selected: &amp;selected, res: &amp;res)\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false\n            state.removeLast()\n        }\n    }\n}\n\n/* Все перестановки I */\nfunc permutationsI(nums: [Int]) -&gt; [[Int]] {\n    var state: [Int] = []\n    var selected = Array(repeating: false, count: nums.count)\n    var res: [[Int]] = []\n    backtrack(state: &amp;state, choices: nums, selected: &amp;selected, res: &amp;res)\n    return res\n}\n</code></pre> permutations_i.js<pre><code>/* Алгоритм бэктрекинга: все перестановки I */\nfunction backtrack(state, choices, selected, res) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (state.length === choices.length) {\n        res.push([...state]);\n        return;\n    }\n    // Перебор всех вариантов выбора\n    choices.forEach((choice, i) =&gt; {\n        // Отсечение: нельзя выбирать один и тот же элемент повторно\n        if (!selected[i]) {\n            // Попытка: сделать выбор и обновить состояние\n            selected[i] = true;\n            state.push(choice);\n            // Перейти к следующему выбору\n            backtrack(state, choices, selected, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n            state.pop();\n        }\n    });\n}\n\n/* Все перестановки I */\nfunction permutationsI(nums) {\n    const res = [];\n    backtrack([], nums, Array(nums.length).fill(false), res);\n    return res;\n}\n</code></pre> permutations_i.ts<pre><code>/* Алгоритм бэктрекинга: все перестановки I */\nfunction backtrack(\n    state: number[],\n    choices: number[],\n    selected: boolean[],\n    res: number[][]\n): void {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (state.length === choices.length) {\n        res.push([...state]);\n        return;\n    }\n    // Перебор всех вариантов выбора\n    choices.forEach((choice, i) =&gt; {\n        // Отсечение: нельзя выбирать один и тот же элемент повторно\n        if (!selected[i]) {\n            // Попытка: сделать выбор и обновить состояние\n            selected[i] = true;\n            state.push(choice);\n            // Перейти к следующему выбору\n            backtrack(state, choices, selected, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n            state.pop();\n        }\n    });\n}\n\n/* Все перестановки I */\nfunction permutationsI(nums: number[]): number[][] {\n    const res: number[][] = [];\n    backtrack([], nums, Array(nums.length).fill(false), res);\n    return res;\n}\n</code></pre> permutations_i.dart<pre><code>/* Алгоритм бэктрекинга: все перестановки I */\nvoid backtrack(\n  List&lt;int&gt; state,\n  List&lt;int&gt; choices,\n  List&lt;bool&gt; selected,\n  List&lt;List&lt;int&gt;&gt; res,\n) {\n  // Когда длина состояния равна числу элементов, записать решение\n  if (state.length == choices.length) {\n    res.add(List.from(state));\n    return;\n  }\n  // Перебор всех вариантов выбора\n  for (int i = 0; i &lt; choices.length; i++) {\n    int choice = choices[i];\n    // Отсечение: нельзя выбирать один и тот же элемент повторно\n    if (!selected[i]) {\n      // Попытка: сделать выбор и обновить состояние\n      selected[i] = true;\n      state.add(choice);\n      // Перейти к следующему выбору\n      backtrack(state, choices, selected, res);\n      // Откат: отменить выбор и восстановить предыдущее состояние\n      selected[i] = false;\n      state.removeLast();\n    }\n  }\n}\n\n/* Все перестановки I */\nList&lt;List&lt;int&gt;&gt; permutationsI(List&lt;int&gt; nums) {\n  List&lt;List&lt;int&gt;&gt; res = [];\n  backtrack([], nums, List.filled(nums.length, false), res);\n  return res;\n}\n</code></pre> permutations_i.rs<pre><code>/* Алгоритм бэктрекинга: все перестановки I */\nfn backtrack(mut state: Vec&lt;i32&gt;, choices: &amp;[i32], selected: &amp;mut [bool], res: &amp;mut Vec&lt;Vec&lt;i32&gt;&gt;) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if state.len() == choices.len() {\n        res.push(state);\n        return;\n    }\n    // Перебор всех вариантов выбора\n    for i in 0..choices.len() {\n        let choice = choices[i];\n        // Отсечение: нельзя выбирать один и тот же элемент повторно\n        if !selected[i] {\n            // Попытка: сделать выбор и обновить состояние\n            selected[i] = true;\n            state.push(choice);\n            // Перейти к следующему выбору\n            backtrack(state.clone(), choices, selected, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n            state.pop();\n        }\n    }\n}\n\n/* Все перестановки I */\nfn permutations_i(nums: &amp;mut [i32]) -&gt; Vec&lt;Vec&lt;i32&gt;&gt; {\n    let mut res = Vec::new(); // Состояние (подмножество)\n    backtrack(Vec::new(), nums, &amp;mut vec![false; nums.len()], &amp;mut res);\n    res\n}\n</code></pre> permutations_i.c<pre><code>/* Алгоритм бэктрекинга: все перестановки I */\nvoid backtrack(int *state, int stateSize, int *choices, int choicesSize, bool *selected, int **res, int *resSize) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (stateSize == choicesSize) {\n        res[*resSize] = (int *)malloc(choicesSize * sizeof(int));\n        for (int i = 0; i &lt; choicesSize; i++) {\n            res[*resSize][i] = state[i];\n        }\n        (*resSize)++;\n        return;\n    }\n    // Перебор всех вариантов выбора\n    for (int i = 0; i &lt; choicesSize; i++) {\n        int choice = choices[i];\n        // Отсечение: нельзя выбирать один и тот же элемент повторно\n        if (!selected[i]) {\n            // Попытка: сделать выбор и обновить состояние\n            selected[i] = true;\n            state[stateSize] = choice;\n            // Перейти к следующему выбору\n            backtrack(state, stateSize + 1, choices, choicesSize, selected, res, resSize);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n        }\n    }\n}\n\n/* Все перестановки I */\nint **permutationsI(int *nums, int numsSize, int *returnSize) {\n    int *state = (int *)malloc(numsSize * sizeof(int));\n    bool *selected = (bool *)malloc(numsSize * sizeof(bool));\n    for (int i = 0; i &lt; numsSize; i++) {\n        selected[i] = false;\n    }\n    int **res = (int **)malloc(MAX_SIZE * sizeof(int *));\n    *returnSize = 0;\n\n    backtrack(state, 0, nums, numsSize, selected, res, returnSize);\n\n    free(state);\n    free(selected);\n\n    return res;\n}\n</code></pre> permutations_i.kt<pre><code>/* Алгоритм бэктрекинга: все перестановки I */\nfun backtrack(\n    state: MutableList&lt;Int&gt;,\n    choices: IntArray,\n    selected: BooleanArray,\n    res: MutableList&lt;MutableList&lt;Int&gt;?&gt;\n) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (state.size == choices.size) {\n        res.add(state.toMutableList())\n        return\n    }\n    // Перебор всех вариантов выбора\n    for (i in choices.indices) {\n        val choice = choices[i]\n        // Отсечение: нельзя выбирать один и тот же элемент повторно\n        if (!selected[i]) {\n            // Попытка: сделать выбор и обновить состояние\n            selected[i] = true\n            state.add(choice)\n            // Перейти к следующему выбору\n            backtrack(state, choices, selected, res)\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false\n            state.removeAt(state.size - 1)\n        }\n    }\n}\n\n/* Все перестановки I */\nfun permutationsI(nums: IntArray): MutableList&lt;MutableList&lt;Int&gt;?&gt; {\n    val res = mutableListOf&lt;MutableList&lt;Int&gt;?&gt;()\n    backtrack(mutableListOf(), nums, BooleanArray(nums.size), res)\n    return res\n}\n</code></pre> permutations_i.rb<pre><code>### Алгоритм бэктрекинга: все перестановки I ###\ndef backtrack(state, choices, selected, res)\n  # Когда длина состояния равна числу элементов, записать решение\n  if state.length == choices.length\n    res &lt;&lt; state.dup\n    return\n  end\n\n  # Перебор всех вариантов выбора\n  choices.each_with_index do |choice, i|\n    # Отсечение: нельзя выбирать один и тот же элемент повторно\n    unless selected[i]\n      # Попытка: сделать выбор и обновить состояние\n      selected[i] = true\n      state &lt;&lt; choice\n      # Перейти к следующему выбору\n      backtrack(state, choices, selected, res)\n      # Откат: отменить выбор и восстановить предыдущее состояние\n      selected[i] = false\n      state.pop\n    end\n  end\nend\n\n### Все перестановки I ###\ndef permutations_i(nums)\n  res = []\n  backtrack([], nums, Array.new(nums.length, false), res)\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 13. Поиск с возвратом","13.2 &nbsp; Задача о перестановках"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#1322","level":2,"title":"13.2.2   Учет равных элементов","text":"<p>Question</p> <p>Дан массив целых чисел, который может содержать повторяющиеся элементы. Верните все неповторяющиеся перестановки.</p> <p>Пусть входной массив равен \\([1, 1, 2]\\) . Чтобы различать два одинаковых элемента \\(1\\) , будем обозначать второй из них как \\(\\hat{1}\\) .</p> <p>Как показано на рисунке 13-7, описанный выше метод создаст результат, половина которого окажется дублирующейся.</p> <p></p> <p> Рисунок 13-7   Повторяющиеся перестановки </p> <p>Как же убрать повторяющиеся перестановки? Самый прямолинейный способ - воспользоваться хеш-множеством и удалить дубликаты уже после генерации результата. Но это не слишком изящно, потому что ветви поиска, порождающие дубликаты, вообще не нужно посещать: их следует распознавать заранее и отсекать, что дополнительно повышает эффективность алгоритма.</p>","path":["Глава 13. Поиск с возвратом","13.2 &nbsp; Задача о перестановках"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#1_1","level":3,"title":"1.   Обрезка равных элементов","text":"<p>Посмотрите на рисунок 13-8: в первом раунде выбрать \\(1\\) или выбрать \\(\\hat{1}\\) - это одно и то же, а значит, все перестановки, полученные из этих двух выборов, будут дублироваться. Поэтому ветвь \\(\\hat{1}\\) нужно отсечь.</p> <p>Точно так же, если в первом раунде выбрать \\(2\\) , то во втором раунде выборы \\(1\\) и \\(\\hat{1}\\) снова создадут дублирующиеся ветви, поэтому и в этом случае ветвь \\(\\hat{1}\\) нужно отсечь.</p> <p>По своей сути наша цель заключается в том, чтобы на каждом раунде выбора каждый из нескольких равных элементов выбирался только один раз.</p> <p></p> <p> Рисунок 13-8   Обрезка повторяющихся перестановок </p>","path":["Глава 13. Поиск с возвратом","13.2 &nbsp; Задача о перестановках"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#2_1","level":3,"title":"2.   Реализация кода","text":"<p>На основе решения из предыдущей задачи можно на каждом раунде выбора заводить хеш-множество <code>duplicated</code> , которое будет записывать элементы, уже встречавшиеся в этом раунде, и отсекать повторы:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby permutations_ii.py<pre><code>def backtrack(\n    state: list[int], choices: list[int], selected: list[bool], res: list[list[int]]\n):\n    \"\"\"Алгоритм бэктрекинга: все перестановки II\"\"\"\n    # Когда длина состояния равна числу элементов, записать решение\n    if len(state) == len(choices):\n        res.append(list(state))\n        return\n    # Перебор всех вариантов выбора\n    duplicated = set[int]()\n    for i, choice in enumerate(choices):\n        # Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n        if not selected[i] and choice not in duplicated:\n            # Попытка: сделать выбор и обновить состояние\n            duplicated.add(choice)  # Записать значения уже выбранных элементов\n            selected[i] = True\n            state.append(choice)\n            # Перейти к следующему выбору\n            backtrack(state, choices, selected, res)\n            # Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = False\n            state.pop()\n\ndef permutations_ii(nums: list[int]) -&gt; list[list[int]]:\n    \"\"\"Все перестановки II\"\"\"\n    res = []\n    backtrack(state=[], choices=nums, selected=[False] * len(nums), res=res)\n    return res\n</code></pre> permutations_ii.cpp<pre><code>/* Алгоритм бэктрекинга: все перестановки II */\nvoid backtrack(vector&lt;int&gt; &amp;state, const vector&lt;int&gt; &amp;choices, vector&lt;bool&gt; &amp;selected, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (state.size() == choices.size()) {\n        res.push_back(state);\n        return;\n    }\n    // Перебор всех вариантов выбора\n    unordered_set&lt;int&gt; duplicated;\n    for (int i = 0; i &lt; choices.size(); i++) {\n        int choice = choices[i];\n        // Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n        if (!selected[i] &amp;&amp; duplicated.find(choice) == duplicated.end()) {\n            // Попытка: сделать выбор и обновить состояние\n            duplicated.emplace(choice); // Записать значения уже выбранных элементов\n            selected[i] = true;\n            state.push_back(choice);\n            // Перейти к следующему выбору\n            backtrack(state, choices, selected, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n            state.pop_back();\n        }\n    }\n}\n\n/* Все перестановки II */\nvector&lt;vector&lt;int&gt;&gt; permutationsII(vector&lt;int&gt; nums) {\n    vector&lt;int&gt; state;\n    vector&lt;bool&gt; selected(nums.size(), false);\n    vector&lt;vector&lt;int&gt;&gt; res;\n    backtrack(state, nums, selected, res);\n    return res;\n}\n</code></pre> permutations_ii.java<pre><code>/* Алгоритм бэктрекинга: все перестановки II */\nvoid backtrack(List&lt;Integer&gt; state, int[] choices, boolean[] selected, List&lt;List&lt;Integer&gt;&gt; res) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (state.size() == choices.length) {\n        res.add(new ArrayList&lt;Integer&gt;(state));\n        return;\n    }\n    // Перебор всех вариантов выбора\n    Set&lt;Integer&gt; duplicated = new HashSet&lt;Integer&gt;();\n    for (int i = 0; i &lt; choices.length; i++) {\n        int choice = choices[i];\n        // Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n        if (!selected[i] &amp;&amp; !duplicated.contains(choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            duplicated.add(choice); // Записать значения уже выбранных элементов\n            selected[i] = true;\n            state.add(choice);\n            // Перейти к следующему выбору\n            backtrack(state, choices, selected, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n            state.remove(state.size() - 1);\n        }\n    }\n}\n\n/* Все перестановки II */\nList&lt;List&lt;Integer&gt;&gt; permutationsII(int[] nums) {\n    List&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;List&lt;Integer&gt;&gt;();\n    backtrack(new ArrayList&lt;Integer&gt;(), nums, new boolean[nums.length], res);\n    return res;\n}\n</code></pre> permutations_ii.cs<pre><code>/* Алгоритм бэктрекинга: все перестановки II */\nvoid Backtrack(List&lt;int&gt; state, int[] choices, bool[] selected, List&lt;List&lt;int&gt;&gt; res) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (state.Count == choices.Length) {\n        res.Add(new List&lt;int&gt;(state));\n        return;\n    }\n    // Перебор всех вариантов выбора\n    HashSet&lt;int&gt; duplicated = [];\n    for (int i = 0; i &lt; choices.Length; i++) {\n        int choice = choices[i];\n        // Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n        if (!selected[i] &amp;&amp; !duplicated.Contains(choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            duplicated.Add(choice); // Записать значения уже выбранных элементов\n            selected[i] = true;\n            state.Add(choice);\n            // Перейти к следующему выбору\n            Backtrack(state, choices, selected, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n            state.RemoveAt(state.Count - 1);\n        }\n    }\n}\n\n/* Все перестановки II */\nList&lt;List&lt;int&gt;&gt; PermutationsII(int[] nums) {\n    List&lt;List&lt;int&gt;&gt; res = [];\n    Backtrack([], nums, new bool[nums.Length], res);\n    return res;\n}\n</code></pre> permutations_ii.go<pre><code>/* Алгоритм бэктрекинга: все перестановки II */\nfunc backtrackII(state *[]int, choices *[]int, selected *[]bool, res *[][]int) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if len(*state) == len(*choices) {\n        newState := append([]int{}, *state...)\n        *res = append(*res, newState)\n    }\n    // Перебор всех вариантов выбора\n    duplicated := make(map[int]struct{}, 0)\n    for i := 0; i &lt; len(*choices); i++ {\n        choice := (*choices)[i]\n        // Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n        if _, ok := duplicated[choice]; !ok &amp;&amp; !(*selected)[i] {\n            // Попробовать: сделать выбор, обновить состояние\n            // Записать значение уже выбранного элемента\n            duplicated[choice] = struct{}{}\n            (*selected)[i] = true\n            *state = append(*state, choice)\n            // Перейти к следующему выбору\n            backtrackII(state, choices, selected, res)\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            (*selected)[i] = false\n            *state = (*state)[:len(*state)-1]\n        }\n    }\n}\n\n/* Все перестановки II */\nfunc permutationsII(nums []int) [][]int {\n    res := make([][]int, 0)\n    state := make([]int, 0)\n    selected := make([]bool, len(nums))\n    backtrackII(&amp;state, &amp;nums, &amp;selected, &amp;res)\n    return res\n}\n</code></pre> permutations_ii.swift<pre><code>/* Алгоритм бэктрекинга: все перестановки II */\nfunc backtrack(state: inout [Int], choices: [Int], selected: inout [Bool], res: inout [[Int]]) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if state.count == choices.count {\n        res.append(state)\n        return\n    }\n    // Перебор всех вариантов выбора\n    var duplicated: Set&lt;Int&gt; = []\n    for (i, choice) in choices.enumerated() {\n        // Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n        if !selected[i], !duplicated.contains(choice) {\n            // Попытка: сделать выбор и обновить состояние\n            duplicated.insert(choice) // Записать значения уже выбранных элементов\n            selected[i] = true\n            state.append(choice)\n            // Перейти к следующему выбору\n            backtrack(state: &amp;state, choices: choices, selected: &amp;selected, res: &amp;res)\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false\n            state.removeLast()\n        }\n    }\n}\n\n/* Все перестановки II */\nfunc permutationsII(nums: [Int]) -&gt; [[Int]] {\n    var state: [Int] = []\n    var selected = Array(repeating: false, count: nums.count)\n    var res: [[Int]] = []\n    backtrack(state: &amp;state, choices: nums, selected: &amp;selected, res: &amp;res)\n    return res\n}\n</code></pre> permutations_ii.js<pre><code>/* Алгоритм бэктрекинга: все перестановки II */\nfunction backtrack(state, choices, selected, res) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (state.length === choices.length) {\n        res.push([...state]);\n        return;\n    }\n    // Перебор всех вариантов выбора\n    const duplicated = new Set();\n    choices.forEach((choice, i) =&gt; {\n        // Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n        if (!selected[i] &amp;&amp; !duplicated.has(choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            duplicated.add(choice); // Записать значения уже выбранных элементов\n            selected[i] = true;\n            state.push(choice);\n            // Перейти к следующему выбору\n            backtrack(state, choices, selected, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n            state.pop();\n        }\n    });\n}\n\n/* Все перестановки II */\nfunction permutationsII(nums) {\n    const res = [];\n    backtrack([], nums, Array(nums.length).fill(false), res);\n    return res;\n}\n</code></pre> permutations_ii.ts<pre><code>/* Алгоритм бэктрекинга: все перестановки II */\nfunction backtrack(\n    state: number[],\n    choices: number[],\n    selected: boolean[],\n    res: number[][]\n): void {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (state.length === choices.length) {\n        res.push([...state]);\n        return;\n    }\n    // Перебор всех вариантов выбора\n    const duplicated = new Set();\n    choices.forEach((choice, i) =&gt; {\n        // Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n        if (!selected[i] &amp;&amp; !duplicated.has(choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            duplicated.add(choice); // Записать значения уже выбранных элементов\n            selected[i] = true;\n            state.push(choice);\n            // Перейти к следующему выбору\n            backtrack(state, choices, selected, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n            state.pop();\n        }\n    });\n}\n\n/* Все перестановки II */\nfunction permutationsII(nums: number[]): number[][] {\n    const res: number[][] = [];\n    backtrack([], nums, Array(nums.length).fill(false), res);\n    return res;\n}\n</code></pre> permutations_ii.dart<pre><code>/* Алгоритм бэктрекинга: все перестановки II */\nvoid backtrack(\n  List&lt;int&gt; state,\n  List&lt;int&gt; choices,\n  List&lt;bool&gt; selected,\n  List&lt;List&lt;int&gt;&gt; res,\n) {\n  // Когда длина состояния равна числу элементов, записать решение\n  if (state.length == choices.length) {\n    res.add(List.from(state));\n    return;\n  }\n  // Перебор всех вариантов выбора\n  Set&lt;int&gt; duplicated = {};\n  for (int i = 0; i &lt; choices.length; i++) {\n    int choice = choices[i];\n    // Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n    if (!selected[i] &amp;&amp; !duplicated.contains(choice)) {\n      // Попытка: сделать выбор и обновить состояние\n      duplicated.add(choice); // Записать значения уже выбранных элементов\n      selected[i] = true;\n      state.add(choice);\n      // Перейти к следующему выбору\n      backtrack(state, choices, selected, res);\n      // Откат: отменить выбор и восстановить предыдущее состояние\n      selected[i] = false;\n      state.removeLast();\n    }\n  }\n}\n\n/* Все перестановки II */\nList&lt;List&lt;int&gt;&gt; permutationsII(List&lt;int&gt; nums) {\n  List&lt;List&lt;int&gt;&gt; res = [];\n  backtrack([], nums, List.filled(nums.length, false), res);\n  return res;\n}\n</code></pre> permutations_ii.rs<pre><code>/* Алгоритм бэктрекинга: все перестановки II */\nfn backtrack(mut state: Vec&lt;i32&gt;, choices: &amp;[i32], selected: &amp;mut [bool], res: &amp;mut Vec&lt;Vec&lt;i32&gt;&gt;) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if state.len() == choices.len() {\n        res.push(state);\n        return;\n    }\n    // Перебор всех вариантов выбора\n    let mut duplicated = HashSet::&lt;i32&gt;::new();\n    for i in 0..choices.len() {\n        let choice = choices[i];\n        // Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n        if !selected[i] &amp;&amp; !duplicated.contains(&amp;choice) {\n            // Попытка: сделать выбор и обновить состояние\n            duplicated.insert(choice); // Записать значения уже выбранных элементов\n            selected[i] = true;\n            state.push(choice);\n            // Перейти к следующему выбору\n            backtrack(state.clone(), choices, selected, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n            state.pop();\n        }\n    }\n}\n\n/* Все перестановки II */\nfn permutations_ii(nums: &amp;mut [i32]) -&gt; Vec&lt;Vec&lt;i32&gt;&gt; {\n    let mut res = Vec::new();\n    backtrack(Vec::new(), nums, &amp;mut vec![false; nums.len()], &amp;mut res);\n    res\n}\n</code></pre> permutations_ii.c<pre><code>/* Алгоритм бэктрекинга: все перестановки II */\nvoid backtrack(int *state, int stateSize, int *choices, int choicesSize, bool *selected, int **res, int *resSize) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (stateSize == choicesSize) {\n        res[*resSize] = (int *)malloc(choicesSize * sizeof(int));\n        for (int i = 0; i &lt; choicesSize; i++) {\n            res[*resSize][i] = state[i];\n        }\n        (*resSize)++;\n        return;\n    }\n    // Перебор всех вариантов выбора\n    bool duplicated[MAX_SIZE] = {false};\n    for (int i = 0; i &lt; choicesSize; i++) {\n        int choice = choices[i];\n        // Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n        if (!selected[i] &amp;&amp; !duplicated[choice]) {\n            // Попытка: сделать выбор и обновить состояние\n            duplicated[choice] = true; // Записать значения уже выбранных элементов\n            selected[i] = true;\n            state[stateSize] = choice;\n            // Перейти к следующему выбору\n            backtrack(state, stateSize + 1, choices, choicesSize, selected, res, resSize);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n        }\n    }\n}\n\n/* Все перестановки II */\nint **permutationsII(int *nums, int numsSize, int *returnSize) {\n    int *state = (int *)malloc(numsSize * sizeof(int));\n    bool *selected = (bool *)malloc(numsSize * sizeof(bool));\n    for (int i = 0; i &lt; numsSize; i++) {\n        selected[i] = false;\n    }\n    int **res = (int **)malloc(MAX_SIZE * sizeof(int *));\n    *returnSize = 0;\n\n    backtrack(state, 0, nums, numsSize, selected, res, returnSize);\n\n    free(state);\n    free(selected);\n\n    return res;\n}\n</code></pre> permutations_ii.kt<pre><code>/* Алгоритм бэктрекинга: все перестановки II */\nfun backtrack(\n    state: MutableList&lt;Int&gt;,\n    choices: IntArray,\n    selected: BooleanArray,\n    res: MutableList&lt;MutableList&lt;Int&gt;?&gt;\n) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (state.size == choices.size) {\n        res.add(state.toMutableList())\n        return\n    }\n    // Перебор всех вариантов выбора\n    val duplicated = HashSet&lt;Int&gt;()\n    for (i in choices.indices) {\n        val choice = choices[i]\n        // Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n        if (!selected[i] &amp;&amp; !duplicated.contains(choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            duplicated.add(choice) // Записать значения уже выбранных элементов\n            selected[i] = true\n            state.add(choice)\n            // Перейти к следующему выбору\n            backtrack(state, choices, selected, res)\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false\n            state.removeAt(state.size - 1)\n        }\n    }\n}\n\n/* Все перестановки II */\nfun permutationsII(nums: IntArray): MutableList&lt;MutableList&lt;Int&gt;?&gt; {\n    val res = mutableListOf&lt;MutableList&lt;Int&gt;?&gt;()\n    backtrack(mutableListOf(), nums, BooleanArray(nums.size), res)\n    return res\n}\n</code></pre> permutations_ii.rb<pre><code>### Алгоритм бэктрекинга: все перестановки II ###\ndef backtrack(state, choices, selected, res)\n  # Когда длина состояния равна числу элементов, записать решение\n  if state.length == choices.length\n    res &lt;&lt; state.dup\n    return\n  end\n\n  # Перебор всех вариантов выбора\n  duplicated = Set.new\n  choices.each_with_index do |choice, i|\n    # Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n    if !selected[i] &amp;&amp; !duplicated.include?(choice)\n      # Попытка: сделать выбор и обновить состояние\n      duplicated.add(choice)\n      selected[i] = true\n      state &lt;&lt; choice\n      # Перейти к следующему выбору\n      backtrack(state, choices, selected, res)\n      # Откат: отменить выбор и восстановить предыдущее состояние\n      selected[i] = false\n      state.pop\n    end\n  end\nend\n\n### Все перестановки II ###\ndef permutations_ii(nums)\n  res = []\n  backtrack([], nums, Array.new(nums.length, false), res)\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Если предположить, что все элементы попарно различны, то из \\(n\\) элементов можно получить \\(n!\\) перестановок; при записи результата требуется копировать список длины \\(n\\) , что занимает \\(O(n)\\) времени. Следовательно, временная сложность равна \\(O(n!n)\\) .</p> <p>Максимальная глубина рекурсии равна \\(n\\) , что требует \\(O(n)\\) стековой памяти. Массив <code>selected</code> занимает \\(O(n)\\) пространства. Одновременно может существовать до \\(n\\) хеш-множеств <code>duplicated</code> , что дает \\(O(n^2)\\) памяти. Следовательно, пространственная сложность равна \\(O(n^2)\\) .</p>","path":["Глава 13. Поиск с возвратом","13.2 &nbsp; Задача о перестановках"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#3","level":3,"title":"3.   Сравнение двух видов обрезки","text":"<p>Обратите внимание: хотя и <code>selected</code> , и <code>duplicated</code> используются для обрезки, их цели различаются.</p> <ul> <li>Обрезка повторного выбора: во всем процессе поиска существует только один <code>selected</code> . Он записывает, какие элементы уже входят в текущее состояние, и нужен для того, чтобы один и тот же элемент не появлялся в <code>state</code> дважды.</li> <li>Обрезка равных элементов: каждый раунд выбора (каждый вызов <code>backtrack</code>) содержит собственный <code>duplicated</code> . Он записывает, какие элементы уже выбирались в текущем раунде (<code>for</code> цикле), и нужен для того, чтобы равные элементы выбирались только один раз.</li> </ul> <p>На рисунке 13-9 показана область действия двух условий обрезки. Помните, что каждый узел дерева соответствует одному выбору, а путь от корня до листа образует одну перестановку.</p> <p></p> <p> Рисунок 13-9   Область действия двух условий обрезки </p>","path":["Глава 13. Поиск с возвратом","13.2 &nbsp; Задача о перестановках"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/","level":1,"title":"13.3   Задача о сумме подмножеств","text":"","path":["Глава 13. Поиск с возвратом","13.3 &nbsp; Задача о сумме подмножеств"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#1331","level":2,"title":"13.3.1   Случай без повторяющихся элементов","text":"<p>Question</p> <p>Дан массив положительных целых чисел <code>nums</code> и целое положительное значение <code>target</code> . Найдите все возможные комбинации, сумма элементов которых равна <code>target</code> . Во входном массиве нет повторяющихся элементов, и каждый элемент можно выбирать неограниченное число раз. Верните эти комбинации в виде списка; в результате не должно быть повторяющихся комбинаций.</p> <p>Например, для входного множества \\(\\{3, 4, 5\\}\\) и целевого значения \\(9\\) решениями будут \\(\\{3, 3, 3\\}\\) и \\(\\{4, 5\\}\\) . При этом нужно обратить внимание на два обстоятельства.</p> <ul> <li>Элементы входного множества можно выбирать повторно неограниченное число раз.</li> <li>Подмножество не различает порядок элементов, поэтому \\(\\{4, 5\\}\\) и \\(\\{5, 4\\}\\) считаются одним и тем же подмножеством.</li> </ul>","path":["Глава 13. Поиск с возвратом","13.3 &nbsp; Задача о сумме подмножеств"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#1","level":3,"title":"1.   Отталкиваемся от решения задачи о перестановках","text":"<p>Как и в задаче о перестановках, можно представлять построение подмножеств как результат последовательности выборов и во время выбора динамически обновлять \"сумму элементов\"; когда эта сумма становится равной <code>target</code> , соответствующее подмножество записывается в список результатов.</p> <p>Однако в отличие от задачи о перестановках в этой задаче элементы множества можно выбирать неограниченное число раз, поэтому нам не нужен булев список <code>selected</code> для записи того, был ли выбран элемент. Можно слегка изменить код для перестановок и получить первоначальную версию решения:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby subset_sum_i_naive.py<pre><code>def backtrack(\n    state: list[int],\n    target: int,\n    total: int,\n    choices: list[int],\n    res: list[list[int]],\n):\n    \"\"\"Алгоритм бэктрекинга: сумма подмножеств I\"\"\"\n    # Если сумма подмножества равна target, записать решение\n    if total == target:\n        res.append(list(state))\n        return\n    # Перебор всех вариантов выбора\n    for i in range(len(choices)):\n        # Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n        if total + choices[i] &gt; target:\n            continue\n        # Попытка: сделать выбор и обновить элемент и total\n        state.append(choices[i])\n        # Перейти к следующему выбору\n        backtrack(state, target, total + choices[i], choices, res)\n        # Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop()\n\ndef subset_sum_i_naive(nums: list[int], target: int) -&gt; list[list[int]]:\n    \"\"\"Решить задачу суммы подмножеств I (с повторяющимися подмножествами)\"\"\"\n    state = []  # Состояние (подмножество)\n    total = 0  # Сумма подмножеств\n    res = []  # Список результатов (список подмножеств)\n    backtrack(state, target, total, nums, res)\n    return res\n</code></pre> subset_sum_i_naive.cpp<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nvoid backtrack(vector&lt;int&gt; &amp;state, int target, int total, vector&lt;int&gt; &amp;choices, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n    // Если сумма подмножества равна target, записать решение\n    if (total == target) {\n        res.push_back(state);\n        return;\n    }\n    // Перебор всех вариантов выбора\n    for (size_t i = 0; i &lt; choices.size(); i++) {\n        // Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n        if (total + choices[i] &gt; target) {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить элемент и total\n        state.push_back(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target, total + choices[i], choices, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop_back();\n    }\n}\n\n/* Решить задачу суммы подмножеств I (с повторяющимися подмножествами) */\nvector&lt;vector&lt;int&gt;&gt; subsetSumINaive(vector&lt;int&gt; &amp;nums, int target) {\n    vector&lt;int&gt; state;       // Состояние (подмножество)\n    int total = 0;           // Сумма подмножеств\n    vector&lt;vector&lt;int&gt;&gt; res; // Список результатов (список подмножеств)\n    backtrack(state, target, total, nums, res);\n    return res;\n}\n</code></pre> subset_sum_i_naive.java<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nvoid backtrack(List&lt;Integer&gt; state, int target, int total, int[] choices, List&lt;List&lt;Integer&gt;&gt; res) {\n    // Если сумма подмножества равна target, записать решение\n    if (total == target) {\n        res.add(new ArrayList&lt;&gt;(state));\n        return;\n    }\n    // Перебор всех вариантов выбора\n    for (int i = 0; i &lt; choices.length; i++) {\n        // Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n        if (total + choices[i] &gt; target) {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить элемент и total\n        state.add(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target, total + choices[i], choices, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.remove(state.size() - 1);\n    }\n}\n\n/* Решить задачу суммы подмножеств I (с повторяющимися подмножествами) */\nList&lt;List&lt;Integer&gt;&gt; subsetSumINaive(int[] nums, int target) {\n    List&lt;Integer&gt; state = new ArrayList&lt;&gt;(); // Состояние (подмножество)\n    int total = 0; // Сумма подмножеств\n    List&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;&gt;(); // Список результатов (список подмножеств)\n    backtrack(state, target, total, nums, res);\n    return res;\n}\n</code></pre> subset_sum_i_naive.cs<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nvoid Backtrack(List&lt;int&gt; state, int target, int total, int[] choices, List&lt;List&lt;int&gt;&gt; res) {\n    // Если сумма подмножества равна target, записать решение\n    if (total == target) {\n        res.Add(new List&lt;int&gt;(state));\n        return;\n    }\n    // Перебор всех вариантов выбора\n    for (int i = 0; i &lt; choices.Length; i++) {\n        // Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n        if (total + choices[i] &gt; target) {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить элемент и total\n        state.Add(choices[i]);\n        // Перейти к следующему выбору\n        Backtrack(state, target, total + choices[i], choices, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.RemoveAt(state.Count - 1);\n    }\n}\n\n/* Решить задачу суммы подмножеств I (с повторяющимися подмножествами) */\nList&lt;List&lt;int&gt;&gt; SubsetSumINaive(int[] nums, int target) {\n    List&lt;int&gt; state = []; // Состояние (подмножество)\n    int total = 0; // Сумма подмножеств\n    List&lt;List&lt;int&gt;&gt; res = []; // Список результатов (список подмножеств)\n    Backtrack(state, target, total, nums, res);\n    return res;\n}\n</code></pre> subset_sum_i_naive.go<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nfunc backtrackSubsetSumINaive(total, target int, state, choices *[]int, res *[][]int) {\n    // Если сумма подмножества равна target, записать решение\n    if target == total {\n        newState := append([]int{}, *state...)\n        *res = append(*res, newState)\n        return\n    }\n    // Перебор всех вариантов выбора\n    for i := 0; i &lt; len(*choices); i++ {\n        // Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n        if total+(*choices)[i] &gt; target {\n            continue\n        }\n        // Попытка: сделать выбор и обновить элемент и total\n        *state = append(*state, (*choices)[i])\n        // Перейти к следующему выбору\n        backtrackSubsetSumINaive(total+(*choices)[i], target, state, choices, res)\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        *state = (*state)[:len(*state)-1]\n    }\n}\n\n/* Решить задачу суммы подмножеств I (с повторяющимися подмножествами) */\nfunc subsetSumINaive(nums []int, target int) [][]int {\n    state := make([]int, 0) // Состояние (подмножество)\n    total := 0              // Сумма подмножеств\n    res := make([][]int, 0) // Список результатов (список подмножеств)\n    backtrackSubsetSumINaive(total, target, &amp;state, &amp;nums, &amp;res)\n    return res\n}\n</code></pre> subset_sum_i_naive.swift<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nfunc backtrack(state: inout [Int], target: Int, total: Int, choices: [Int], res: inout [[Int]]) {\n    // Если сумма подмножества равна target, записать решение\n    if total == target {\n        res.append(state)\n        return\n    }\n    // Перебор всех вариантов выбора\n    for i in choices.indices {\n        // Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n        if total + choices[i] &gt; target {\n            continue\n        }\n        // Попытка: сделать выбор и обновить элемент и total\n        state.append(choices[i])\n        // Перейти к следующему выбору\n        backtrack(state: &amp;state, target: target, total: total + choices[i], choices: choices, res: &amp;res)\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.removeLast()\n    }\n}\n\n/* Решить задачу суммы подмножеств I (с повторяющимися подмножествами) */\nfunc subsetSumINaive(nums: [Int], target: Int) -&gt; [[Int]] {\n    var state: [Int] = [] // Состояние (подмножество)\n    let total = 0 // Сумма подмножеств\n    var res: [[Int]] = [] // Список результатов (список подмножеств)\n    backtrack(state: &amp;state, target: target, total: total, choices: nums, res: &amp;res)\n    return res\n}\n</code></pre> subset_sum_i_naive.js<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nfunction backtrack(state, target, total, choices, res) {\n    // Если сумма подмножества равна target, записать решение\n    if (total === target) {\n        res.push([...state]);\n        return;\n    }\n    // Перебор всех вариантов выбора\n    for (let i = 0; i &lt; choices.length; i++) {\n        // Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n        if (total + choices[i] &gt; target) {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить элемент и total\n        state.push(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target, total + choices[i], choices, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop();\n    }\n}\n\n/* Решить задачу суммы подмножеств I (с повторяющимися подмножествами) */\nfunction subsetSumINaive(nums, target) {\n    const state = []; // Состояние (подмножество)\n    const total = 0; // Сумма подмножеств\n    const res = []; // Список результатов (список подмножеств)\n    backtrack(state, target, total, nums, res);\n    return res;\n}\n</code></pre> subset_sum_i_naive.ts<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nfunction backtrack(\n    state: number[],\n    target: number,\n    total: number,\n    choices: number[],\n    res: number[][]\n): void {\n    // Если сумма подмножества равна target, записать решение\n    if (total === target) {\n        res.push([...state]);\n        return;\n    }\n    // Перебор всех вариантов выбора\n    for (let i = 0; i &lt; choices.length; i++) {\n        // Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n        if (total + choices[i] &gt; target) {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить элемент и total\n        state.push(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target, total + choices[i], choices, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop();\n    }\n}\n\n/* Решить задачу суммы подмножеств I (с повторяющимися подмножествами) */\nfunction subsetSumINaive(nums: number[], target: number): number[][] {\n    const state = []; // Состояние (подмножество)\n    const total = 0; // Сумма подмножеств\n    const res = []; // Список результатов (список подмножеств)\n    backtrack(state, target, total, nums, res);\n    return res;\n}\n</code></pre> subset_sum_i_naive.dart<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nvoid backtrack(\n  List&lt;int&gt; state,\n  int target,\n  int total,\n  List&lt;int&gt; choices,\n  List&lt;List&lt;int&gt;&gt; res,\n) {\n  // Если сумма подмножества равна target, записать решение\n  if (total == target) {\n    res.add(List.from(state));\n    return;\n  }\n  // Перебор всех вариантов выбора\n  for (int i = 0; i &lt; choices.length; i++) {\n    // Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n    if (total + choices[i] &gt; target) {\n      continue;\n    }\n    // Попытка: сделать выбор и обновить элемент и total\n    state.add(choices[i]);\n    // Перейти к следующему выбору\n    backtrack(state, target, total + choices[i], choices, res);\n    // Откат: отменить выбор и восстановить предыдущее состояние\n    state.removeLast();\n  }\n}\n\n/* Решить задачу суммы подмножеств I (с повторяющимися подмножествами) */\nList&lt;List&lt;int&gt;&gt; subsetSumINaive(List&lt;int&gt; nums, int target) {\n  List&lt;int&gt; state = []; // Состояние (подмножество)\n  int total = 0; // Сумма элементов\n  List&lt;List&lt;int&gt;&gt; res = []; // Список результатов (список подмножеств)\n  backtrack(state, target, total, nums, res);\n  return res;\n}\n</code></pre> subset_sum_i_naive.rs<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nfn backtrack(\n    state: &amp;mut Vec&lt;i32&gt;,\n    target: i32,\n    total: i32,\n    choices: &amp;[i32],\n    res: &amp;mut Vec&lt;Vec&lt;i32&gt;&gt;,\n) {\n    // Если сумма подмножества равна target, записать решение\n    if total == target {\n        res.push(state.clone());\n        return;\n    }\n    // Перебор всех вариантов выбора\n    for i in 0..choices.len() {\n        // Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n        if total + choices[i] &gt; target {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить элемент и total\n        state.push(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target, total + choices[i], choices, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop();\n    }\n}\n\n/* Решить задачу суммы подмножеств I (с повторяющимися подмножествами) */\nfn subset_sum_i_naive(nums: &amp;[i32], target: i32) -&gt; Vec&lt;Vec&lt;i32&gt;&gt; {\n    let mut state = Vec::new(); // Состояние (подмножество)\n    let total = 0; // Сумма подмножеств\n    let mut res = Vec::new(); // Список результатов (список подмножеств)\n    backtrack(&amp;mut state, target, total, nums, &amp;mut res);\n    res\n}\n</code></pre> subset_sum_i_naive.c<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nvoid backtrack(int target, int total, int *choices, int choicesSize) {\n    // Если сумма подмножества равна target, записать решение\n    if (total == target) {\n        for (int i = 0; i &lt; stateSize; i++) {\n            res[resSize][i] = state[i];\n        }\n        resColSizes[resSize++] = stateSize;\n        return;\n    }\n    // Перебор всех вариантов выбора\n    for (int i = 0; i &lt; choicesSize; i++) {\n        // Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n        if (total + choices[i] &gt; target) {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить элемент и total\n        state[stateSize++] = choices[i];\n        // Перейти к следующему выбору\n        backtrack(target, total + choices[i], choices, choicesSize);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        stateSize--;\n    }\n}\n\n/* Решить задачу суммы подмножеств I (с повторяющимися подмножествами) */\nvoid subsetSumINaive(int *nums, int numsSize, int target) {\n    resSize = 0; // Инициализировать число решений нулем\n    backtrack(target, 0, nums, numsSize);\n}\n</code></pre> subset_sum_i_naive.kt<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nfun backtrack(\n    state: MutableList&lt;Int&gt;,\n    target: Int,\n    total: Int,\n    choices: IntArray,\n    res: MutableList&lt;MutableList&lt;Int&gt;?&gt;\n) {\n    // Если сумма подмножества равна target, записать решение\n    if (total == target) {\n        res.add(state.toMutableList())\n        return\n    }\n    // Перебор всех вариантов выбора\n    for (i in choices.indices) {\n        // Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n        if (total + choices[i] &gt; target) {\n            continue\n        }\n        // Попытка: сделать выбор и обновить элемент и total\n        state.add(choices[i])\n        // Перейти к следующему выбору\n        backtrack(state, target, total + choices[i], choices, res)\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.removeAt(state.size - 1)\n    }\n}\n\n/* Решить задачу суммы подмножеств I (с повторяющимися подмножествами) */\nfun subsetSumINaive(nums: IntArray, target: Int): MutableList&lt;MutableList&lt;Int&gt;?&gt; {\n    val state = mutableListOf&lt;Int&gt;() // Состояние (подмножество)\n    val total = 0 // Сумма подмножеств\n    val res = mutableListOf&lt;MutableList&lt;Int&gt;?&gt;() // Список результатов (список подмножеств)\n    backtrack(state, target, total, nums, res)\n    return res\n}\n</code></pre> subset_sum_i_naive.rb<pre><code>### Алгоритм бэктрекинга: сумма подмножеств I ###\ndef backtrack(state, target, total, choices, res)\n  # Если сумма подмножества равна target, записать решение\n  if total == target\n    res &lt;&lt; state.dup\n    return\n  end\n\n  # Перебор всех вариантов выбора\n  for i in 0...choices.length\n    # Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n    next if total + choices[i] &gt; target\n    # Попытка: сделать выбор и обновить элемент и total\n    state &lt;&lt; choices[i]\n    # Перейти к следующему выбору\n    backtrack(state, target, total + choices[i], choices, res)\n    # Откат: отменить выбор и восстановить предыдущее состояние\n    state.pop\n  end\nend\n\n### Алгоритм бэктрекинга: сумма подмножеств I ###\ndef backtrack(state, target, total, choices, res)\n  # Если сумма подмножества равна target, записать решение\n  if total == target\n    res &lt;&lt; state.dup\n    return\n  end\n\n  # Перебор всех вариантов выбора\n  for i in 0...choices.length\n    # Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n    next if total + choices[i] &gt; target\n    # Попытка: сделать выбор и обновить элемент и total\n    state &lt;&lt; choices[i]\n    # Перейти к следующему выбору\n    backtrack(state, target, total + choices[i], choices, res)\n    # Откат: отменить выбор и восстановить предыдущее состояние\n    state.pop\n  end\nend\n\n# ## Решить задачу суммы подмножеств I (с повторяющимися подмножествами) ###\ndef subset_sum_i_naive(nums, target)\n  state = [] # Состояние (подмножество)\n  total = 0 # Сумма подмножеств\n  res = [] # Список результатов (список подмножеств)\n  backtrack(state, target, total, nums, res)\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Если подать на этот код массив \\([3, 4, 5]\\) и целевое значение \\(9\\) , то на выходе мы получим \\([3, 3, 3], [4, 5], [5, 4]\\) . Хотя все подмножества с суммой \\(9\\) успешно найдены, среди них все же присутствуют дубликаты: \\([4, 5]\\) и \\([5, 4]\\) .</p> <p>Причина в том, что процесс поиска различает порядок выбора, тогда как для подмножеств порядок не важен. Как показано на рисунке 13-10, сначала выбрать \\(4\\) , а затем \\(5\\) , и сначала выбрать \\(5\\) , а затем \\(4\\) - это разные ветви поиска, но им соответствует одно и то же подмножество.</p> <p></p> <p> Рисунок 13-10   Поиск подмножеств и обрезка по выходу за границу </p> <p>Чтобы убрать повторяющиеся подмножества, одна из прямых идей - удалить дубликаты уже из итогового списка результатов. Но это решение малоэффективно по двум причинам.</p> <ul> <li>Когда массив содержит много элементов, а особенно когда <code>target</code> велик, процесс поиска порождает огромное число повторяющихся подмножеств.</li> <li>Сравнение подмножеств (то есть массивов) само по себе довольно затратно: сначала приходится сортировать массивы, а затем поэлементно сравнивать их.</li> </ul>","path":["Глава 13. Поиск с возвратом","13.3 &nbsp; Задача о сумме подмножеств"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#2","level":3,"title":"2.   Обрезка повторяющихся подмножеств","text":"<p>Поэтому стоит выполнять устранение дубликатов прямо во время поиска, с помощью обрезки. Посмотрите на рисунок 13-11: повторяющиеся подмножества возникают тогда, когда элементы массива выбираются в разном порядке, например так.</p> <ol> <li>Если в первом и втором раундах выбрать соответственно \\(3\\) и \\(4\\) , то будут сгенерированы все подмножества, содержащие эти два элемента, и их можно обозначить как \\([3, 4, \\dots]\\) .</li> <li>После этого, если в первом раунде выбрать \\(4\\) , то во втором раунде нужно пропустить \\(3\\) , потому что подмножества \\([4, 3, \\dots]\\) полностью дублируют подмножества, уже построенные на шаге <code>1.</code> .</li> </ol> <p>Во время поиска выборы на каждом уровне пробуются по одному слева направо, поэтому чем правее ветвь, тем больше ветвей оказывается отсечено.</p> <ol> <li>В первых двух раундах выбираются \\(3\\) и \\(5\\) , что дает подмножества \\([3, 5, \\dots]\\) .</li> <li>В первых двух раундах выбираются \\(4\\) и \\(5\\) , что дает подмножества \\([4, 5, \\dots]\\) .</li> <li>Если же в первом раунде выбрать \\(5\\) , то во втором раунде нужно пропустить \\(3\\) и \\(4\\) , потому что подмножества \\([5, 3, \\dots]\\) и \\([5, 4, \\dots]\\) полностью дублируют случаи, описанные в шагах <code>1.</code> и <code>2.</code> .</li> </ol> <p></p> <p> Рисунок 13-11   Повторяющиеся подмножества из-за разного порядка выбора </p> <p>В общем виде, если входной массив имеет вид \\([x_1, x_2, \\dots, x_n]\\) , а последовательность выборов в ходе поиска равна \\([x_{i_1}, x_{i_2}, \\dots, x_{i_m}]\\) , то она должна удовлетворять условию \\(i_1 \\leq i_2 \\leq \\dots \\leq i_m\\) ; все последовательности выборов, не удовлетворяющие этому условию, приводят к дубликатам и должны отсекаться.</p>","path":["Глава 13. Поиск с возвратом","13.3 &nbsp; Задача о сумме подмножеств"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#3","level":3,"title":"3.   Реализация кода","text":"<p>Чтобы реализовать такую обрезку, инициализируем переменную <code>start</code> , которая будет указывать начальную точку обхода. После выбора элемента \\(x_i\\) следующий раунд начинается с индекса \\(i\\). Благодаря этому последовательность выборов всегда удовлетворяет условию \\(i_1 \\leq i_2 \\leq \\dots \\leq i_m\\) , а значит, каждое подмножество создается только один раз.</p> <p>Помимо этого, мы внесем в код еще два улучшения.</p> <ul> <li>Перед началом поиска отсортируем массив <code>nums</code> . Тогда при обходе всех вариантов можно сразу прервать цикл, как только сумма подмножества превысит <code>target</code> , потому что все последующие элементы будут еще больше и их сумма тоже превысит <code>target</code> .</li> <li>Откажемся от отдельной переменной суммы <code>total</code> и будем учитывать сумму через вычитание из <code>target</code> ; когда <code>target</code> станет равным \\(0\\) , решение фиксируется.</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby subset_sum_i.py<pre><code>def backtrack(\n    state: list[int], target: int, choices: list[int], start: int, res: list[list[int]]\n):\n    \"\"\"Алгоритм бэктрекинга: сумма подмножеств I\"\"\"\n    # Если сумма подмножества равна target, записать решение\n    if target == 0:\n        res.append(list(state))\n        return\n    # Обойти все варианты выбора\n    # Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    for i in range(start, len(choices)):\n        # Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        # Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if target - choices[i] &lt; 0:\n            break\n        # Попытка: сделать выбор и обновить target и start\n        state.append(choices[i])\n        # Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i, res)\n        # Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop()\n\ndef subset_sum_i(nums: list[int], target: int) -&gt; list[list[int]]:\n    \"\"\"Решить задачу суммы подмножеств I\"\"\"\n    state = []  # Состояние (подмножество)\n    nums.sort()  # Отсортировать nums\n    start = 0  # Стартовая вершина обхода\n    res = []  # Список результатов (список подмножеств)\n    backtrack(state, target, nums, start, res)\n    return res\n</code></pre> subset_sum_i.cpp<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nvoid backtrack(vector&lt;int&gt; &amp;state, int target, vector&lt;int&gt; &amp;choices, int start, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n    // Если сумма подмножества равна target, записать решение\n    if (target == 0) {\n        res.push_back(state);\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    for (int i = start; i &lt; choices.size(); i++) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.push_back(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop_back();\n    }\n}\n\n/* Решить задачу суммы подмножеств I */\nvector&lt;vector&lt;int&gt;&gt; subsetSumI(vector&lt;int&gt; &amp;nums, int target) {\n    vector&lt;int&gt; state;              // Состояние (подмножество)\n    sort(nums.begin(), nums.end()); // Отсортировать nums\n    int start = 0;                  // Стартовая вершина обхода\n    vector&lt;vector&lt;int&gt;&gt; res;        // Список результатов (список подмножеств)\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_i.java<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nvoid backtrack(List&lt;Integer&gt; state, int target, int[] choices, int start, List&lt;List&lt;Integer&gt;&gt; res) {\n    // Если сумма подмножества равна target, записать решение\n    if (target == 0) {\n        res.add(new ArrayList&lt;&gt;(state));\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    for (int i = start; i &lt; choices.length; i++) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.add(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.remove(state.size() - 1);\n    }\n}\n\n/* Решить задачу суммы подмножеств I */\nList&lt;List&lt;Integer&gt;&gt; subsetSumI(int[] nums, int target) {\n    List&lt;Integer&gt; state = new ArrayList&lt;&gt;(); // Состояние (подмножество)\n    Arrays.sort(nums); // Отсортировать nums\n    int start = 0; // Стартовая вершина обхода\n    List&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;&gt;(); // Список результатов (список подмножеств)\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_i.cs<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nvoid Backtrack(List&lt;int&gt; state, int target, int[] choices, int start, List&lt;List&lt;int&gt;&gt; res) {\n    // Если сумма подмножества равна target, записать решение\n    if (target == 0) {\n        res.Add(new List&lt;int&gt;(state));\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    for (int i = start; i &lt; choices.Length; i++) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.Add(choices[i]);\n        // Перейти к следующему выбору\n        Backtrack(state, target - choices[i], choices, i, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.RemoveAt(state.Count - 1);\n    }\n}\n\n/* Решить задачу суммы подмножеств I */\nList&lt;List&lt;int&gt;&gt; SubsetSumI(int[] nums, int target) {\n    List&lt;int&gt; state = []; // Состояние (подмножество)\n    Array.Sort(nums); // Отсортировать nums\n    int start = 0; // Стартовая вершина обхода\n    List&lt;List&lt;int&gt;&gt; res = []; // Список результатов (список подмножеств)\n    Backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_i.go<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nfunc backtrackSubsetSumI(start, target int, state, choices *[]int, res *[][]int) {\n    // Если сумма подмножества равна target, записать решение\n    if target == 0 {\n        newState := append([]int{}, *state...)\n        *res = append(*res, newState)\n        return\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    for i := start; i &lt; len(*choices); i++ {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if target-(*choices)[i] &lt; 0 {\n            break\n        }\n        // Попытка: сделать выбор и обновить target и start\n        *state = append(*state, (*choices)[i])\n        // Перейти к следующему выбору\n        backtrackSubsetSumI(i, target-(*choices)[i], state, choices, res)\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        *state = (*state)[:len(*state)-1]\n    }\n}\n\n/* Решить задачу суммы подмножеств I */\nfunc subsetSumI(nums []int, target int) [][]int {\n    state := make([]int, 0) // Состояние (подмножество)\n    sort.Ints(nums)         // Отсортировать nums\n    start := 0              // Стартовая вершина обхода\n    res := make([][]int, 0) // Список результатов (список подмножеств)\n    backtrackSubsetSumI(start, target, &amp;state, &amp;nums, &amp;res)\n    return res\n}\n</code></pre> subset_sum_i.swift<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nfunc backtrack(state: inout [Int], target: Int, choices: [Int], start: Int, res: inout [[Int]]) {\n    // Если сумма подмножества равна target, записать решение\n    if target == 0 {\n        res.append(state)\n        return\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    for i in choices.indices.dropFirst(start) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if target - choices[i] &lt; 0 {\n            break\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.append(choices[i])\n        // Перейти к следующему выбору\n        backtrack(state: &amp;state, target: target - choices[i], choices: choices, start: i, res: &amp;res)\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.removeLast()\n    }\n}\n\n/* Решить задачу суммы подмножеств I */\nfunc subsetSumI(nums: [Int], target: Int) -&gt; [[Int]] {\n    var state: [Int] = [] // Состояние (подмножество)\n    let nums = nums.sorted() // Отсортировать nums\n    let start = 0 // Стартовая вершина обхода\n    var res: [[Int]] = [] // Список результатов (список подмножеств)\n    backtrack(state: &amp;state, target: target, choices: nums, start: start, res: &amp;res)\n    return res\n}\n</code></pre> subset_sum_i.js<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nfunction backtrack(state, target, choices, start, res) {\n    // Если сумма подмножества равна target, записать решение\n    if (target === 0) {\n        res.push([...state]);\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    for (let i = start; i &lt; choices.length; i++) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.push(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop();\n    }\n}\n\n/* Решить задачу суммы подмножеств I */\nfunction subsetSumI(nums, target) {\n    const state = []; // Состояние (подмножество)\n    nums.sort((a, b) =&gt; a - b); // Отсортировать nums\n    const start = 0; // Стартовая вершина обхода\n    const res = []; // Список результатов (список подмножеств)\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_i.ts<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nfunction backtrack(\n    state: number[],\n    target: number,\n    choices: number[],\n    start: number,\n    res: number[][]\n): void {\n    // Если сумма подмножества равна target, записать решение\n    if (target === 0) {\n        res.push([...state]);\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    for (let i = start; i &lt; choices.length; i++) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.push(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop();\n    }\n}\n\n/* Решить задачу суммы подмножеств I */\nfunction subsetSumI(nums: number[], target: number): number[][] {\n    const state = []; // Состояние (подмножество)\n    nums.sort((a, b) =&gt; a - b); // Отсортировать nums\n    const start = 0; // Стартовая вершина обхода\n    const res = []; // Список результатов (список подмножеств)\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_i.dart<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nvoid backtrack(\n  List&lt;int&gt; state,\n  int target,\n  List&lt;int&gt; choices,\n  int start,\n  List&lt;List&lt;int&gt;&gt; res,\n) {\n  // Если сумма подмножества равна target, записать решение\n  if (target == 0) {\n    res.add(List.from(state));\n    return;\n  }\n  // Обойти все варианты выбора\n  // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n  for (int i = start; i &lt; choices.length; i++) {\n    // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n    // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n    if (target - choices[i] &lt; 0) {\n      break;\n    }\n    // Попытка: сделать выбор и обновить target и start\n    state.add(choices[i]);\n    // Перейти к следующему выбору\n    backtrack(state, target - choices[i], choices, i, res);\n    // Откат: отменить выбор и восстановить предыдущее состояние\n    state.removeLast();\n  }\n}\n\n/* Решить задачу суммы подмножеств I */\nList&lt;List&lt;int&gt;&gt; subsetSumI(List&lt;int&gt; nums, int target) {\n  List&lt;int&gt; state = []; // Состояние (подмножество)\n  nums.sort(); // Отсортировать nums\n  int start = 0; // Стартовая вершина обхода\n  List&lt;List&lt;int&gt;&gt; res = []; // Список результатов (список подмножеств)\n  backtrack(state, target, nums, start, res);\n  return res;\n}\n</code></pre> subset_sum_i.rs<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nfn backtrack(\n    state: &amp;mut Vec&lt;i32&gt;,\n    target: i32,\n    choices: &amp;[i32],\n    start: usize,\n    res: &amp;mut Vec&lt;Vec&lt;i32&gt;&gt;,\n) {\n    // Если сумма подмножества равна target, записать решение\n    if target == 0 {\n        res.push(state.clone());\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    for i in start..choices.len() {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if target - choices[i] &lt; 0 {\n            break;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.push(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop();\n    }\n}\n\n/* Решить задачу суммы подмножеств I */\nfn subset_sum_i(nums: &amp;mut [i32], target: i32) -&gt; Vec&lt;Vec&lt;i32&gt;&gt; {\n    let mut state = Vec::new(); // Состояние (подмножество)\n    nums.sort(); // Отсортировать nums\n    let start = 0; // Стартовая вершина обхода\n    let mut res = Vec::new(); // Список результатов (список подмножеств)\n    backtrack(&amp;mut state, target, nums, start, &amp;mut res);\n    res\n}\n</code></pre> subset_sum_i.c<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nvoid backtrack(int target, int *choices, int choicesSize, int start) {\n    // Если сумма подмножества равна target, записать решение\n    if (target == 0) {\n        for (int i = 0; i &lt; stateSize; ++i) {\n            res[resSize][i] = state[i];\n        }\n        resColSizes[resSize++] = stateSize;\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    for (int i = start; i &lt; choicesSize; i++) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state[stateSize] = choices[i];\n        stateSize++;\n        // Перейти к следующему выбору\n        backtrack(target - choices[i], choices, choicesSize, i);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        stateSize--;\n    }\n}\n\n/* Решить задачу суммы подмножеств I */\nvoid subsetSumI(int *nums, int numsSize, int target) {\n    qsort(nums, numsSize, sizeof(int), cmp); // Отсортировать nums\n    int start = 0;                           // Стартовая вершина обхода\n    backtrack(target, nums, numsSize, start);\n}\n</code></pre> subset_sum_i.kt<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nfun backtrack(\n    state: MutableList&lt;Int&gt;,\n    target: Int,\n    choices: IntArray,\n    start: Int,\n    res: MutableList&lt;MutableList&lt;Int&gt;?&gt;\n) {\n    // Если сумма подмножества равна target, записать решение\n    if (target == 0) {\n        res.add(state.toMutableList())\n        return\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    for (i in start..&lt;choices.size) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.add(choices[i])\n        // Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i, res)\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.removeAt(state.size - 1)\n    }\n}\n\n/* Решить задачу суммы подмножеств I */\nfun subsetSumI(nums: IntArray, target: Int): MutableList&lt;MutableList&lt;Int&gt;?&gt; {\n    val state = mutableListOf&lt;Int&gt;() // Состояние (подмножество)\n    nums.sort() // Отсортировать nums\n    val start = 0 // Стартовая вершина обхода\n    val res = mutableListOf&lt;MutableList&lt;Int&gt;?&gt;() // Список результатов (список подмножеств)\n    backtrack(state, target, nums, start, res)\n    return res\n}\n</code></pre> subset_sum_i.rb<pre><code>### Алгоритм бэктрекинга: сумма подмножеств I ###\ndef backtrack(state, target, choices, start, res)\n  # Если сумма подмножества равна target, записать решение\n  if target.zero?\n    res &lt;&lt; state.dup\n    return\n  end\n  # Обойти все варианты выбора\n  # Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n  for i in start...choices.length\n    # Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n    # Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n    break if target - choices[i] &lt; 0\n    # Попытка: сделать выбор и обновить target и start\n    state &lt;&lt; choices[i]\n    # Перейти к следующему выбору\n    backtrack(state, target - choices[i], choices, i, res)\n    # Откат: отменить выбор и восстановить предыдущее состояние\n    state.pop\n  end\nend\n\n### Решить задачу суммы подмножеств I ###\ndef subset_sum_i(nums, target)\n  state = [] # Состояние (подмножество)\n  nums.sort! # Отсортировать nums\n  start = 0 # Стартовая вершина обхода\n  res = [] # Список результатов (список подмножеств)\n  backtrack(state, target, nums, start, res)\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>На рисунке 13-12 показан полный процесс backtracking для массива \\([3, 4, 5]\\) и целевого значения \\(9\\) .</p> <p></p> <p> Рисунок 13-12   Процесс backtracking для задачи о сумме подмножеств I </p>","path":["Глава 13. Поиск с возвратом","13.3 &nbsp; Задача о сумме подмножеств"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#1332","level":2,"title":"13.3.2   Учет повторяющихся элементов","text":"<p>Question</p> <p>Дан массив положительных целых чисел <code>nums</code> и целое положительное значение <code>target</code> . Найдите все возможные комбинации, сумма элементов которых равна <code>target</code> . Во входном массиве могут присутствовать повторяющиеся элементы, и каждый элемент разрешено выбирать только один раз. Верните эти комбинации в виде списка; в результате не должно быть повторяющихся комбинаций.</p> <p>По сравнению с предыдущей задачей во входном массиве теперь могут присутствовать повторяющиеся элементы, и это создает новую проблему. Например, если дан массив \\([4, \\hat{4}, 5]\\) и целевое значение \\(9\\) , то существующий код вернет результат \\([4, 5], [\\hat{4}, 5]\\) , то есть с повторяющимся подмножеством.</p> <p>Причина появления дублей в том, что равные элементы выбираются несколько раз в одном и том же раунде. На рисунке 13-13 в первом раунде существует три варианта выбора, и два из них равны \\(4\\) ; из-за этого появляются две дублирующиеся ветви поиска и, соответственно, повторяющиеся подмножества. Точно так же два элемента \\(4\\) во втором раунде тоже порождают дубликаты.</p> <p></p> <p> Рисунок 13-13   Повторяющиеся подмножества из-за равных элементов </p>","path":["Глава 13. Поиск с возвратом","13.3 &nbsp; Задача о сумме подмножеств"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#1_1","level":3,"title":"1.   Обрезка равных элементов","text":"<p>Чтобы решить эту проблему, нужно ограничить выбор равных элементов так, чтобы в каждом раунде каждый из них выбирался только один раз. Реализуется это довольно изящно: поскольку массив отсортирован, равные элементы стоят рядом. Значит, если в текущем раунде текущий элемент равен соседнему слева, то этот вариант уже был рассмотрен, и текущий элемент нужно пропустить.</p> <p>Одновременно по условию этой задачи каждый элемент массива можно выбрать только один раз. К счастью, это ограничение тоже можно реализовать через переменную <code>start</code> : после выбора элемента \\(x_i\\) следующий раунд начинается с индекса \\(i + 1\\) . Так мы одновременно убираем повторяющиеся подмножества и исключаем повторный выбор одного и того же элемента.</p>","path":["Глава 13. Поиск с возвратом","13.3 &nbsp; Задача о сумме подмножеств"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#2_1","level":3,"title":"2.   Реализация кода","text":"PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby subset_sum_ii.py<pre><code>def backtrack(\n    state: list[int], target: int, choices: list[int], start: int, res: list[list[int]]\n):\n    \"\"\"Алгоритм бэктрекинга: сумма подмножеств II\"\"\"\n    # Если сумма подмножества равна target, записать решение\n    if target == 0:\n        res.append(list(state))\n        return\n    # Обойти все варианты выбора\n    # Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    # Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n    for i in range(start, len(choices)):\n        # Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        # Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if target - choices[i] &lt; 0:\n            break\n        # Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n        if i &gt; start and choices[i] == choices[i - 1]:\n            continue\n        # Попытка: сделать выбор и обновить target и start\n        state.append(choices[i])\n        # Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i + 1, res)\n        # Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop()\n\ndef subset_sum_ii(nums: list[int], target: int) -&gt; list[list[int]]:\n    \"\"\"Решить задачу суммы подмножеств II\"\"\"\n    state = []  # Состояние (подмножество)\n    nums.sort()  # Отсортировать nums\n    start = 0  # Стартовая вершина обхода\n    res = []  # Список результатов (список подмножеств)\n    backtrack(state, target, nums, start, res)\n    return res\n</code></pre> subset_sum_ii.cpp<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств II */\nvoid backtrack(vector&lt;int&gt; &amp;state, int target, vector&lt;int&gt; &amp;choices, int start, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n    // Если сумма подмножества равна target, записать решение\n    if (target == 0) {\n        res.push_back(state);\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    // Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n    for (int i = start; i &lt; choices.size(); i++) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n        if (i &gt; start &amp;&amp; choices[i] == choices[i - 1]) {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.push_back(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i + 1, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop_back();\n    }\n}\n\n/* Решить задачу суммы подмножеств II */\nvector&lt;vector&lt;int&gt;&gt; subsetSumII(vector&lt;int&gt; &amp;nums, int target) {\n    vector&lt;int&gt; state;              // Состояние (подмножество)\n    sort(nums.begin(), nums.end()); // Отсортировать nums\n    int start = 0;                  // Стартовая вершина обхода\n    vector&lt;vector&lt;int&gt;&gt; res;        // Список результатов (список подмножеств)\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_ii.java<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств II */\nvoid backtrack(List&lt;Integer&gt; state, int target, int[] choices, int start, List&lt;List&lt;Integer&gt;&gt; res) {\n    // Если сумма подмножества равна target, записать решение\n    if (target == 0) {\n        res.add(new ArrayList&lt;&gt;(state));\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    // Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n    for (int i = start; i &lt; choices.length; i++) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n        if (i &gt; start &amp;&amp; choices[i] == choices[i - 1]) {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.add(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i + 1, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.remove(state.size() - 1);\n    }\n}\n\n/* Решить задачу суммы подмножеств II */\nList&lt;List&lt;Integer&gt;&gt; subsetSumII(int[] nums, int target) {\n    List&lt;Integer&gt; state = new ArrayList&lt;&gt;(); // Состояние (подмножество)\n    Arrays.sort(nums); // Отсортировать nums\n    int start = 0; // Стартовая вершина обхода\n    List&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;&gt;(); // Список результатов (список подмножеств)\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_ii.cs<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств II */\nvoid Backtrack(List&lt;int&gt; state, int target, int[] choices, int start, List&lt;List&lt;int&gt;&gt; res) {\n    // Если сумма подмножества равна target, записать решение\n    if (target == 0) {\n        res.Add(new List&lt;int&gt;(state));\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    // Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n    for (int i = start; i &lt; choices.Length; i++) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n        if (i &gt; start &amp;&amp; choices[i] == choices[i - 1]) {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.Add(choices[i]);\n        // Перейти к следующему выбору\n        Backtrack(state, target - choices[i], choices, i + 1, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.RemoveAt(state.Count - 1);\n    }\n}\n\n/* Решить задачу суммы подмножеств II */\nList&lt;List&lt;int&gt;&gt; SubsetSumII(int[] nums, int target) {\n    List&lt;int&gt; state = []; // Состояние (подмножество)\n    Array.Sort(nums); // Отсортировать nums\n    int start = 0; // Стартовая вершина обхода\n    List&lt;List&lt;int&gt;&gt; res = []; // Список результатов (список подмножеств)\n    Backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_ii.go<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств II */\nfunc backtrackSubsetSumII(start, target int, state, choices *[]int, res *[][]int) {\n    // Если сумма подмножества равна target, записать решение\n    if target == 0 {\n        newState := append([]int{}, *state...)\n        *res = append(*res, newState)\n        return\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    // Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n    for i := start; i &lt; len(*choices); i++ {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if target-(*choices)[i] &lt; 0 {\n            break\n        }\n        // Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n        if i &gt; start &amp;&amp; (*choices)[i] == (*choices)[i-1] {\n            continue\n        }\n        // Попытка: сделать выбор и обновить target и start\n        *state = append(*state, (*choices)[i])\n        // Перейти к следующему выбору\n        backtrackSubsetSumII(i+1, target-(*choices)[i], state, choices, res)\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        *state = (*state)[:len(*state)-1]\n    }\n}\n\n/* Решить задачу суммы подмножеств II */\nfunc subsetSumII(nums []int, target int) [][]int {\n    state := make([]int, 0) // Состояние (подмножество)\n    sort.Ints(nums)         // Отсортировать nums\n    start := 0              // Стартовая вершина обхода\n    res := make([][]int, 0) // Список результатов (список подмножеств)\n    backtrackSubsetSumII(start, target, &amp;state, &amp;nums, &amp;res)\n    return res\n}\n</code></pre> subset_sum_ii.swift<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств II */\nfunc backtrack(state: inout [Int], target: Int, choices: [Int], start: Int, res: inout [[Int]]) {\n    // Если сумма подмножества равна target, записать решение\n    if target == 0 {\n        res.append(state)\n        return\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    // Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n    for i in choices.indices.dropFirst(start) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if target - choices[i] &lt; 0 {\n            break\n        }\n        // Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n        if i &gt; start, choices[i] == choices[i - 1] {\n            continue\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.append(choices[i])\n        // Перейти к следующему выбору\n        backtrack(state: &amp;state, target: target - choices[i], choices: choices, start: i + 1, res: &amp;res)\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.removeLast()\n    }\n}\n\n/* Решить задачу суммы подмножеств II */\nfunc subsetSumII(nums: [Int], target: Int) -&gt; [[Int]] {\n    var state: [Int] = [] // Состояние (подмножество)\n    let nums = nums.sorted() // Отсортировать nums\n    let start = 0 // Стартовая вершина обхода\n    var res: [[Int]] = [] // Список результатов (список подмножеств)\n    backtrack(state: &amp;state, target: target, choices: nums, start: start, res: &amp;res)\n    return res\n}\n</code></pre> subset_sum_ii.js<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств II */\nfunction backtrack(state, target, choices, start, res) {\n    // Если сумма подмножества равна target, записать решение\n    if (target === 0) {\n        res.push([...state]);\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    // Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n    for (let i = start; i &lt; choices.length; i++) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n        if (i &gt; start &amp;&amp; choices[i] === choices[i - 1]) {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.push(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i + 1, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop();\n    }\n}\n\n/* Решить задачу суммы подмножеств II */\nfunction subsetSumII(nums, target) {\n    const state = []; // Состояние (подмножество)\n    nums.sort((a, b) =&gt; a - b); // Отсортировать nums\n    const start = 0; // Стартовая вершина обхода\n    const res = []; // Список результатов (список подмножеств)\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_ii.ts<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств II */\nfunction backtrack(\n    state: number[],\n    target: number,\n    choices: number[],\n    start: number,\n    res: number[][]\n): void {\n    // Если сумма подмножества равна target, записать решение\n    if (target === 0) {\n        res.push([...state]);\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    // Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n    for (let i = start; i &lt; choices.length; i++) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n        if (i &gt; start &amp;&amp; choices[i] === choices[i - 1]) {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.push(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i + 1, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop();\n    }\n}\n\n/* Решить задачу суммы подмножеств II */\nfunction subsetSumII(nums: number[], target: number): number[][] {\n    const state = []; // Состояние (подмножество)\n    nums.sort((a, b) =&gt; a - b); // Отсортировать nums\n    const start = 0; // Стартовая вершина обхода\n    const res = []; // Список результатов (список подмножеств)\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_ii.dart<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств II */\nvoid backtrack(\n  List&lt;int&gt; state,\n  int target,\n  List&lt;int&gt; choices,\n  int start,\n  List&lt;List&lt;int&gt;&gt; res,\n) {\n  // Если сумма подмножества равна target, записать решение\n  if (target == 0) {\n    res.add(List.from(state));\n    return;\n  }\n  // Обойти все варианты выбора\n  // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n  // Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n  for (int i = start; i &lt; choices.length; i++) {\n    // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n    // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n    if (target - choices[i] &lt; 0) {\n      break;\n    }\n    // Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n    if (i &gt; start &amp;&amp; choices[i] == choices[i - 1]) {\n      continue;\n    }\n    // Попытка: сделать выбор и обновить target и start\n    state.add(choices[i]);\n    // Перейти к следующему выбору\n    backtrack(state, target - choices[i], choices, i + 1, res);\n    // Откат: отменить выбор и восстановить предыдущее состояние\n    state.removeLast();\n  }\n}\n\n/* Решить задачу суммы подмножеств II */\nList&lt;List&lt;int&gt;&gt; subsetSumII(List&lt;int&gt; nums, int target) {\n  List&lt;int&gt; state = []; // Состояние (подмножество)\n  nums.sort(); // Отсортировать nums\n  int start = 0; // Стартовая вершина обхода\n  List&lt;List&lt;int&gt;&gt; res = []; // Список результатов (список подмножеств)\n  backtrack(state, target, nums, start, res);\n  return res;\n}\n</code></pre> subset_sum_ii.rs<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств II */\nfn backtrack(\n    state: &amp;mut Vec&lt;i32&gt;,\n    target: i32,\n    choices: &amp;[i32],\n    start: usize,\n    res: &amp;mut Vec&lt;Vec&lt;i32&gt;&gt;,\n) {\n    // Если сумма подмножества равна target, записать решение\n    if target == 0 {\n        res.push(state.clone());\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    // Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n    for i in start..choices.len() {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if target - choices[i] &lt; 0 {\n            break;\n        }\n        // Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n        if i &gt; start &amp;&amp; choices[i] == choices[i - 1] {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.push(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i + 1, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop();\n    }\n}\n\n/* Решить задачу суммы подмножеств II */\nfn subset_sum_ii(nums: &amp;mut [i32], target: i32) -&gt; Vec&lt;Vec&lt;i32&gt;&gt; {\n    let mut state = Vec::new(); // Состояние (подмножество)\n    nums.sort(); // Отсортировать nums\n    let start = 0; // Стартовая вершина обхода\n    let mut res = Vec::new(); // Список результатов (список подмножеств)\n    backtrack(&amp;mut state, target, nums, start, &amp;mut res);\n    res\n}\n</code></pre> subset_sum_ii.c<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств II */\nvoid backtrack(int target, int *choices, int choicesSize, int start) {\n    // Если сумма подмножества равна target, записать решение\n    if (target == 0) {\n        for (int i = 0; i &lt; stateSize; i++) {\n            res[resSize][i] = state[i];\n        }\n        resColSizes[resSize++] = stateSize;\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    // Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n    for (int i = start; i &lt; choicesSize; i++) {\n        // Отсечение 1: если сумма подмножества превышает target, сразу пропустить\n        if (target - choices[i] &lt; 0) {\n            continue;\n        }\n        // Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n        if (i &gt; start &amp;&amp; choices[i] == choices[i - 1]) {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state[stateSize] = choices[i];\n        stateSize++;\n        // Перейти к следующему выбору\n        backtrack(target - choices[i], choices, choicesSize, i + 1);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        stateSize--;\n    }\n}\n\n/* Решить задачу суммы подмножеств II */\nvoid subsetSumII(int *nums, int numsSize, int target) {\n    // Отсортировать nums\n    qsort(nums, numsSize, sizeof(int), cmp);\n    // Начать бэктрекинг\n    backtrack(target, nums, numsSize, 0);\n}\n</code></pre> subset_sum_ii.kt<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств II */\nfun backtrack(\n    state: MutableList&lt;Int&gt;,\n    target: Int,\n    choices: IntArray,\n    start: Int,\n    res: MutableList&lt;MutableList&lt;Int&gt;?&gt;\n) {\n    // Если сумма подмножества равна target, записать решение\n    if (target == 0) {\n        res.add(state.toMutableList())\n        return\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    // Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n    for (i in start..&lt;choices.size) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break\n        }\n        // Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n        if (i &gt; start &amp;&amp; choices[i] == choices[i - 1]) {\n            continue\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.add(choices[i])\n        // Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i + 1, res)\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.removeAt(state.size - 1)\n    }\n}\n\n/* Решить задачу суммы подмножеств II */\nfun subsetSumII(nums: IntArray, target: Int): MutableList&lt;MutableList&lt;Int&gt;?&gt; {\n    val state = mutableListOf&lt;Int&gt;() // Состояние (подмножество)\n    nums.sort() // Отсортировать nums\n    val start = 0 // Стартовая вершина обхода\n    val res = mutableListOf&lt;MutableList&lt;Int&gt;?&gt;() // Список результатов (список подмножеств)\n    backtrack(state, target, nums, start, res)\n    return res\n}\n</code></pre> subset_sum_ii.rb<pre><code>### Алгоритм бэктрекинга: сумма подмножеств II ###\ndef backtrack(state, target, choices, start, res)\n  # Если сумма подмножества равна target, записать решение\n  if target.zero?\n    res &lt;&lt; state.dup\n    return\n  end\n\n  # Обойти все варианты выбора\n  # Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n  # Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n  for i in start...choices.length\n    # Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n    # Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n    break if target - choices[i] &lt; 0\n    # Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n    next if i &gt; start &amp;&amp; choices[i] == choices[i - 1]\n    # Попытка: сделать выбор и обновить target и start\n    state &lt;&lt; choices[i]\n    # Перейти к следующему выбору\n    backtrack(state, target - choices[i], choices, i + 1, res)\n    # Откат: отменить выбор и восстановить предыдущее состояние\n    state.pop\n  end\nend\n\n### Решить задачу суммы подмножеств II ###\ndef subset_sum_ii(nums, target)\n  state = [] # Состояние (подмножество)\n  nums.sort! # Отсортировать nums\n  start = 0 # Стартовая вершина обхода\n  res = [] # Список результатов (список подмножеств)\n  backtrack(state, target, nums, start, res)\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>На рисунке 13-14 показан процесс backtracking для массива \\([4, 4, 5]\\) и целевого значения \\(9\\) . В нем используются четыре вида обрезки. Попробуйте сопоставить рисунок с комментариями в коде, чтобы понять полный процесс поиска и то, как работает каждый тип обрезки.</p> <p></p> <p> Рисунок 13-14   Процесс backtracking для задачи о сумме подмножеств II </p>","path":["Глава 13. Поиск с возвратом","13.3 &nbsp; Задача о сумме подмножеств"],"tags":[]},{"location":"chapter_backtracking/summary/","level":1,"title":"13.5   Резюме","text":"","path":["Глава 13. Поиск с возвратом","13.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_backtracking/summary/#1","level":3,"title":"1.   Ключевые выводы","text":"<ul> <li>Алгоритм поиска с возвратом по своей сути является методом полного перебора: он ищет решения путем обхода пространства решений в глубину. Во время поиска он фиксирует решения, удовлетворяющие условиям, пока не найдет все такие решения или пока обход не завершится.</li> <li>Процесс backtracking состоит из двух частей: попытки и отката. Он с помощью поиска в глубину пробует разные варианты выбора; когда встречается состояние, не удовлетворяющее ограничениям, алгоритм отменяет предыдущий выбор, возвращается к прошлому состоянию и продолжает пробовать другие варианты. Попытка и откат являются двумя противоположными по направлению действиями.</li> <li>Задачи backtracking обычно содержат несколько ограничений, которые можно использовать для обрезки. Обрезка позволяет заранее завершать ненужные ветви поиска и тем самым значительно повышать эффективность.</li> <li>Алгоритм backtracking в первую очередь применяется для решения поисковых задач и задач с ограничениями. Задачи комбинаторной оптимизации тоже можно решать с его помощью, но для них часто существуют более эффективные или более подходящие методы.</li> <li>Задача о перестановках нацелена на поиск всех возможных перестановок элементов данного множества. Мы используем массив для записи того, был ли выбран каждый элемент, и отсекаем ветви, где один и тот же элемент выбирается повторно, чтобы гарантировать однократный выбор каждого элемента.</li> <li>В задаче о перестановках, если во множестве присутствуют повторяющиеся элементы, в итоговом результате возникнут повторяющиеся перестановки. Поэтому нужно ограничить выбор равных элементов так, чтобы в каждом раунде каждый из них выбирался только один раз; обычно это реализуется с помощью хеш-множества.</li> <li>Цель задачи о сумме подмножеств - найти все подмножества данного множества, сумма которых равна целевому значению. В множестве порядок элементов не важен, однако процесс поиска порождает результаты во всех возможных порядках, из-за чего появляются повторяющиеся подмножества. Поэтому перед запуском backtracking мы сортируем данные и вводим переменную, указывающую начальную точку обхода в каждом раунде, чтобы отсечь ветви, создающие дубликаты.</li> <li>В задаче о сумме подмножеств равные элементы массива также порождают повторяющиеся множества. При наличии предварительной сортировки их можно отсекать, проверяя равенство соседних элементов, и тем самым гарантировать, что в каждом раунде равные элементы будут выбираться только один раз.</li> <li>Задача о \\(n\\) ферзях состоит в поиске способов разместить \\(n\\) ферзей на доске размера \\(n \\times n\\) так, чтобы никакие два ферзя не атаковали друг друга. Ограничения этой задачи включают строки, столбцы, главные диагонали и побочные диагонали. Чтобы выполнить ограничение по строкам, используется построчная стратегия размещения, гарантирующая по одному ферзю в каждой строке.</li> <li>Обработка ограничений по столбцам и диагоналям устроена похожим образом. Для ограничения по столбцам используется массив, фиксирующий наличие ферзя в каждом столбце. Для диагоналей используются два массива, записывающие наличие ферзей на главных и побочных диагоналях. Основная сложность здесь состоит в том, чтобы найти закономерность индексов строк и столбцов клеток, лежащих на одной и той же главной или побочной диагонали.</li> </ul>","path":["Глава 13. Поиск с возвратом","13.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_backtracking/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: Как понять связь между поиском с возвратом и рекурсией?</p> <p>В целом backtracking - это скорее \"алгоритмическая стратегия\", а рекурсия больше похожа на \"инструмент\".</p> <ul> <li>Алгоритмы поиска с возвратом обычно реализуются на основе рекурсии. Однако backtracking - это лишь один из вариантов применения рекурсии, а именно ее использование в поисковых задачах.</li> <li>Структура рекурсии отражает парадигму разбиения на подзадачи и часто применяется для решения задач divide and conquer, backtracking, динамического программирования (мемоизированной рекурсии) и других подобных задач.</li> </ul>","path":["Глава 13. Поиск с возвратом","13.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_computational_complexity/","level":1,"title":"Глава 2.   Анализ сложности","text":"<p>Abstract</p> <p>Анализ сложности подобен пространственно-временному проводнику в огромной вселенной алгоритмов.</p> <p>Он ведет нас вглубь двух измерений - времени и пространства, помогая искать более изящные решения.</p>","path":["Глава 2. Анализ сложности","Глава 2. &nbsp; Анализ сложности"],"tags":[]},{"location":"chapter_computational_complexity/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>2.1   Оценка эффективности алгоритмов</li> <li>2.2   Итерация и рекурсия</li> <li>2.3   Временная сложность</li> <li>2.4   Пространственная сложность</li> <li>2.5   Резюме</li> </ul>","path":["Глава 2. Анализ сложности","Глава 2. &nbsp; Анализ сложности"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/","level":1,"title":"2.2   Итерация и рекурсия","text":"<p>В алгоритмах очень часто приходится многократно выполнять одну и ту же задачу, и это тесно связано с анализом сложности. Поэтому, прежде чем переходить к временной и пространственной сложности, давай сначала разберемся, как в программах организуется повторяющееся выполнение задач, то есть с двумя базовыми управляющими структурами: итерацией и рекурсией.</p>","path":["Глава 2. Анализ сложности","2.2 &nbsp; Итерация и рекурсия"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#221","level":2,"title":"2.2.1   Итерация","text":"<p>Итерация (iteration) - это управляющая структура, предназначенная для многократного выполнения некоторой задачи. При итерации программа повторно выполняет определенный фрагмент кода при соблюдении некоторого условия, пока это условие не перестанет выполняться.</p>","path":["Глава 2. Анализ сложности","2.2 &nbsp; Итерация и рекурсия"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#1-for","level":3,"title":"1.   Цикл for","text":"<p>Цикл <code>for</code> - одна из самых распространенных форм итерации, она хорошо подходит в тех случаях, когда число повторений известно заранее.</p> <p>Следующая функция реализует вычисление суммы \\(1 + 2 + \\dots + n\\) на основе цикла <code>for</code> , а результат сохраняется в переменной <code>res</code> . Обрати внимание, что в Python <code>range(a, b)</code> соответствует \"лево-замкнутому, право-открытому\" интервалу, то есть перебираются значения \\(a, a + 1, \\dots, b-1\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby iteration.py<pre><code>def for_loop(n: int) -&gt; int:\n    \"\"\"Цикл for\"\"\"\n    res = 0\n    # Циклическое суммирование 1, 2, ..., n-1, n\n    for i in range(1, n + 1):\n        res += i\n    return res\n</code></pre> iteration.cpp<pre><code>/* Цикл for */\nint forLoop(int n) {\n    int res = 0;\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    for (int i = 1; i &lt;= n; ++i) {\n        res += i;\n    }\n    return res;\n}\n</code></pre> iteration.java<pre><code>/* Цикл for */\nint forLoop(int n) {\n    int res = 0;\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    for (int i = 1; i &lt;= n; i++) {\n        res += i;\n    }\n    return res;\n}\n</code></pre> iteration.cs<pre><code>/* Цикл for */\nint ForLoop(int n) {\n    int res = 0;\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    for (int i = 1; i &lt;= n; i++) {\n        res += i;\n    }\n    return res;\n}\n</code></pre> iteration.go<pre><code>/* Цикл for */\nfunc forLoop(n int) int {\n    res := 0\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    for i := 1; i &lt;= n; i++ {\n        res += i\n    }\n    return res\n}\n</code></pre> iteration.swift<pre><code>/* Цикл for */\nfunc forLoop(n: Int) -&gt; Int {\n    var res = 0\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    for i in 1 ... n {\n        res += i\n    }\n    return res\n}\n</code></pre> iteration.js<pre><code>/* Цикл for */\nfunction forLoop(n) {\n    let res = 0;\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    for (let i = 1; i &lt;= n; i++) {\n        res += i;\n    }\n    return res;\n}\n</code></pre> iteration.ts<pre><code>/* Цикл for */\nfunction forLoop(n: number): number {\n    let res = 0;\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    for (let i = 1; i &lt;= n; i++) {\n        res += i;\n    }\n    return res;\n}\n</code></pre> iteration.dart<pre><code>/* Цикл for */\nint forLoop(int n) {\n  int res = 0;\n  // Циклическое суммирование 1, 2, ..., n-1, n\n  for (int i = 1; i &lt;= n; i++) {\n    res += i;\n  }\n  return res;\n}\n</code></pre> iteration.rs<pre><code>/* Цикл for */\nfn for_loop(n: i32) -&gt; i32 {\n    let mut res = 0;\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    for i in 1..=n {\n        res += i;\n    }\n    res\n}\n</code></pre> iteration.c<pre><code>/* Цикл for */\nint forLoop(int n) {\n    int res = 0;\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    for (int i = 1; i &lt;= n; i++) {\n        res += i;\n    }\n    return res;\n}\n</code></pre> iteration.kt<pre><code>/* Цикл for */\nfun forLoop(n: Int): Int {\n    var res = 0\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    for (i in 1..n) {\n        res += i\n    }\n    return res\n}\n</code></pre> iteration.rb<pre><code>### Цикл for ###\ndef for_loop(n)\n  res = 0\n\n  # Циклическое суммирование 1, 2, ..., n-1, n\n  for i in 1..n\n    res += i\n  end\n\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>На рисунке 2-1 показана блок-схема этой функции суммирования.</p> <p></p> <p> Рисунок 2-1   Блок-схема функции суммирования </p> <p>Число операций в этой функции суммирования пропорционально размеру входных данных \\(n\\) , то есть между ними существует \"линейная зависимость\". На самом деле временная сложность как раз и описывает такую \"линейную зависимость\". Соответствующий материал будет подробно разобран в следующем разделе.</p>","path":["Глава 2. Анализ сложности","2.2 &nbsp; Итерация и рекурсия"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#2-while","level":3,"title":"2.   Цикл while","text":"<p>Подобно циклу <code>for</code> , цикл <code>while</code> тоже является способом реализации итерации. В цикле <code>while</code> программа в каждом раунде сначала проверяет условие: если условие истинно, выполнение продолжается, иначе цикл завершается.</p> <p>Ниже мы используем цикл <code>while</code> для реализации суммы \\(1 + 2 + \\dots + n\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby iteration.py<pre><code>def while_loop(n: int) -&gt; int:\n    \"\"\"Цикл while\"\"\"\n    res = 0\n    i = 1  # Инициализация условной переменной\n    # Циклическое суммирование 1, 2, ..., n-1, n\n    while i &lt;= n:\n        res += i\n        i += 1  # Обновить условную переменную\n    return res\n</code></pre> iteration.cpp<pre><code>/* Цикл while */\nint whileLoop(int n) {\n    int res = 0;\n    int i = 1; // Инициализация условной переменной\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    while (i &lt;= n) {\n        res += i;\n        i++; // Обновить условную переменную\n    }\n    return res;\n}\n</code></pre> iteration.java<pre><code>/* Цикл while */\nint whileLoop(int n) {\n    int res = 0;\n    int i = 1; // Инициализация условной переменной\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    while (i &lt;= n) {\n        res += i;\n        i++; // Обновить условную переменную\n    }\n    return res;\n}\n</code></pre> iteration.cs<pre><code>/* Цикл while */\nint WhileLoop(int n) {\n    int res = 0;\n    int i = 1; // Инициализация условной переменной\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    while (i &lt;= n) {\n        res += i;\n        i += 1; // Обновить условную переменную\n    }\n    return res;\n}\n</code></pre> iteration.go<pre><code>/* Цикл while */\nfunc whileLoop(n int) int {\n    res := 0\n    // Инициализация условной переменной\n    i := 1\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    for i &lt;= n {\n        res += i\n        // Обновить условную переменную\n        i++\n    }\n    return res\n}\n</code></pre> iteration.swift<pre><code>/* Цикл while */\nfunc whileLoop(n: Int) -&gt; Int {\n    var res = 0\n    var i = 1 // Инициализация условной переменной\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    while i &lt;= n {\n        res += i\n        i += 1 // Обновить условную переменную\n    }\n    return res\n}\n</code></pre> iteration.js<pre><code>/* Цикл while */\nfunction whileLoop(n) {\n    let res = 0;\n    let i = 1; // Инициализация условной переменной\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    while (i &lt;= n) {\n        res += i;\n        i++; // Обновить условную переменную\n    }\n    return res;\n}\n</code></pre> iteration.ts<pre><code>/* Цикл while */\nfunction whileLoop(n: number): number {\n    let res = 0;\n    let i = 1; // Инициализация условной переменной\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    while (i &lt;= n) {\n        res += i;\n        i++; // Обновить условную переменную\n    }\n    return res;\n}\n</code></pre> iteration.dart<pre><code>/* Цикл while */\nint whileLoop(int n) {\n  int res = 0;\n  int i = 1; // Инициализация условной переменной\n  // Циклическое суммирование 1, 2, ..., n-1, n\n  while (i &lt;= n) {\n    res += i;\n    i++; // Обновить условную переменную\n  }\n  return res;\n}\n</code></pre> iteration.rs<pre><code>/* Цикл while */\nfn while_loop(n: i32) -&gt; i32 {\n    let mut res = 0;\n    let mut i = 1; // Инициализация условной переменной\n\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    while i &lt;= n {\n        res += i;\n        i += 1; // Обновить условную переменную\n    }\n    res\n}\n</code></pre> iteration.c<pre><code>/* Цикл while */\nint whileLoop(int n) {\n    int res = 0;\n    int i = 1; // Инициализация условной переменной\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    while (i &lt;= n) {\n        res += i;\n        i++; // Обновить условную переменную\n    }\n    return res;\n}\n</code></pre> iteration.kt<pre><code>/* Цикл while */\nfun whileLoop(n: Int): Int {\n    var res = 0\n    var i = 1 // Инициализация условной переменной\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    while (i &lt;= n) {\n        res += i\n        i++ // Обновить условную переменную\n    }\n    return res\n}\n</code></pre> iteration.rb<pre><code>### Цикл while ###\ndef while_loop(n)\n  res = 0\n  i = 1 # Инициализация условной переменной\n\n  # Циклическое суммирование 1, 2, ..., n-1, n\n  while i &lt;= n\n    res += i\n    i += 1 # Обновить условную переменную\n  end\n\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>**Цикл <code>while</code> обладает большей свободой, чем цикл <code>for</code> **. В цикле <code>while</code> мы можем свободно задавать шаги инициализации и обновления условной переменной.</p> <p>Например, в следующем коде условная переменная \\(i\\) обновляется два раза за один проход, и такой случай уже не слишком удобно выражать через цикл <code>for</code> :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby iteration.py<pre><code>def while_loop_ii(n: int) -&gt; int:\n    \"\"\"Цикл while (двойное обновление)\"\"\"\n    res = 0\n    i = 1  # Инициализация условной переменной\n    # Циклическое суммирование 1, 4, 10, ...\n    while i &lt;= n:\n        res += i\n        # Обновить условную переменную\n        i += 1\n        i *= 2\n    return res\n</code></pre> iteration.cpp<pre><code>/* Цикл while (двойное обновление) */\nint whileLoopII(int n) {\n    int res = 0;\n    int i = 1; // Инициализация условной переменной\n    // Циклическое суммирование 1, 4, 10, ...\n    while (i &lt;= n) {\n        res += i;\n        // Обновить условную переменную\n        i++;\n        i *= 2;\n    }\n    return res;\n}\n</code></pre> iteration.java<pre><code>/* Цикл while (двойное обновление) */\nint whileLoopII(int n) {\n    int res = 0;\n    int i = 1; // Инициализация условной переменной\n    // Циклическое суммирование 1, 4, 10, ...\n    while (i &lt;= n) {\n        res += i;\n        // Обновить условную переменную\n        i++;\n        i *= 2;\n    }\n    return res;\n}\n</code></pre> iteration.cs<pre><code>/* Цикл while (двойное обновление) */\nint WhileLoopII(int n) {\n    int res = 0;\n    int i = 1; // Инициализация условной переменной\n    // Циклическое суммирование 1, 4, 10, ...\n    while (i &lt;= n) {\n        res += i;\n        // Обновить условную переменную\n        i += 1; \n        i *= 2;\n    }\n    return res;\n}\n</code></pre> iteration.go<pre><code>/* Цикл while (двойное обновление) */\nfunc whileLoopII(n int) int {\n    res := 0\n    // Инициализация условной переменной\n    i := 1\n    // Циклическое суммирование 1, 4, 10, ...\n    for i &lt;= n {\n        res += i\n        // Обновить условную переменную\n        i++\n        i *= 2\n    }\n    return res\n}\n</code></pre> iteration.swift<pre><code>/* Цикл while (двойное обновление) */\nfunc whileLoopII(n: Int) -&gt; Int {\n    var res = 0\n    var i = 1 // Инициализация условной переменной\n    // Циклическое суммирование 1, 4, 10, ...\n    while i &lt;= n {\n        res += i\n        // Обновить условную переменную\n        i += 1\n        i *= 2\n    }\n    return res\n}\n</code></pre> iteration.js<pre><code>/* Цикл while (двойное обновление) */\nfunction whileLoopII(n) {\n    let res = 0;\n    let i = 1; // Инициализация условной переменной\n    // Циклическое суммирование 1, 4, 10, ...\n    while (i &lt;= n) {\n        res += i;\n        // Обновить условную переменную\n        i++;\n        i *= 2;\n    }\n    return res;\n}\n</code></pre> iteration.ts<pre><code>/* Цикл while (двойное обновление) */\nfunction whileLoopII(n: number): number {\n    let res = 0;\n    let i = 1; // Инициализация условной переменной\n    // Циклическое суммирование 1, 4, 10, ...\n    while (i &lt;= n) {\n        res += i;\n        // Обновить условную переменную\n        i++;\n        i *= 2;\n    }\n    return res;\n}\n</code></pre> iteration.dart<pre><code>/* Цикл while (двойное обновление) */\nint whileLoopII(int n) {\n  int res = 0;\n  int i = 1; // Инициализация условной переменной\n  // Циклическое суммирование 1, 4, 10, ...\n  while (i &lt;= n) {\n    res += i;\n    // Обновить условную переменную\n    i++;\n    i *= 2;\n  }\n  return res;\n}\n</code></pre> iteration.rs<pre><code>/* Цикл while (двойное обновление) */\nfn while_loop_ii(n: i32) -&gt; i32 {\n    let mut res = 0;\n    let mut i = 1; // Инициализация условной переменной\n\n    // Циклическое суммирование 1, 4, 10, ...\n    while i &lt;= n {\n        res += i;\n        // Обновить условную переменную\n        i += 1;\n        i *= 2;\n    }\n    res\n}\n</code></pre> iteration.c<pre><code>/* Цикл while (двойное обновление) */\nint whileLoopII(int n) {\n    int res = 0;\n    int i = 1; // Инициализация условной переменной\n    // Циклическое суммирование 1, 4, 10, ...\n    while (i &lt;= n) {\n        res += i;\n        // Обновить условную переменную\n        i++;\n        i *= 2;\n    }\n    return res;\n}\n</code></pre> iteration.kt<pre><code>/* Цикл while (двойное обновление) */\nfun whileLoopII(n: Int): Int {\n    var res = 0\n    var i = 1 // Инициализация условной переменной\n    // Циклическое суммирование 1, 4, 10, ...\n    while (i &lt;= n) {\n        res += i\n        // Обновить условную переменную\n        i++\n        i *= 2\n    }\n    return res\n}\n</code></pre> iteration.rb<pre><code>### Цикл while ###\ndef while_loop(n)\n  res = 0\n  i = 1 # Инициализация условной переменной\n\n  # Циклическое суммирование 1, 2, ..., n-1, n\n  while i &lt;= n\n    res += i\n    i += 1 # Обновить условную переменную\n  end\n\n  res\nend\n\n# ## Цикл while (двойное обновление) ###\ndef while_loop_ii(n)\n  res = 0\n  i = 1 # Инициализация условной переменной\n\n  # Циклическое суммирование 1, 4, 10, ...\n  while i &lt;= n\n    res += i\n    # Обновить условную переменную\n    i += 1\n    i *= 2\n  end\n\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>В целом код с <code>for</code> обычно компактнее, а <code>while</code> более гибок; обе конструкции позволяют реализовывать итерационные структуры. Выбор между ними должен определяться требованиями конкретной задачи.</p>","path":["Глава 2. Анализ сложности","2.2 &nbsp; Итерация и рекурсия"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#3","level":3,"title":"3.   Вложенные циклы","text":"<p>Мы можем вкладывать одну циклическую структуру в другую; ниже показан пример на основе цикла <code>for</code> :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby iteration.py<pre><code>def nested_for_loop(n: int) -&gt; str:\n    \"\"\"Двойной цикл for\"\"\"\n    res = \"\"\n    # Цикл по i = 1, 2, ..., n-1, n\n    for i in range(1, n + 1):\n        # Цикл по j = 1, 2, ..., n-1, n\n        for j in range(1, n + 1):\n            res += f\"({i}, {j}), \"\n    return res\n</code></pre> iteration.cpp<pre><code>/* Двойной цикл for */\nstring nestedForLoop(int n) {\n    ostringstream res;\n    // Цикл по i = 1, 2, ..., n-1, n\n    for (int i = 1; i &lt;= n; ++i) {\n        // Цикл по j = 1, 2, ..., n-1, n\n        for (int j = 1; j &lt;= n; ++j) {\n            res &lt;&lt; \"(\" &lt;&lt; i &lt;&lt; \", \" &lt;&lt; j &lt;&lt; \"), \";\n        }\n    }\n    return res.str();\n}\n</code></pre> iteration.java<pre><code>/* Двойной цикл for */\nString nestedForLoop(int n) {\n    StringBuilder res = new StringBuilder();\n    // Цикл по i = 1, 2, ..., n-1, n\n    for (int i = 1; i &lt;= n; i++) {\n        // Цикл по j = 1, 2, ..., n-1, n\n        for (int j = 1; j &lt;= n; j++) {\n            res.append(\"(\" + i + \", \" + j + \"), \");\n        }\n    }\n    return res.toString();\n}\n</code></pre> iteration.cs<pre><code>/* Двойной цикл for */\nstring NestedForLoop(int n) {\n    StringBuilder res = new();\n    // Цикл по i = 1, 2, ..., n-1, n\n    for (int i = 1; i &lt;= n; i++) {\n        // Цикл по j = 1, 2, ..., n-1, n\n        for (int j = 1; j &lt;= n; j++) {\n            res.Append($\"({i}, {j}), \");\n        }\n    }\n    return res.ToString();\n}\n</code></pre> iteration.go<pre><code>/* Двойной цикл for */\nfunc nestedForLoop(n int) string {\n    res := \"\"\n    // Цикл по i = 1, 2, ..., n-1, n\n    for i := 1; i &lt;= n; i++ {\n        for j := 1; j &lt;= n; j++ {\n            // Цикл по j = 1, 2, ..., n-1, n\n            res += fmt.Sprintf(\"(%d, %d), \", i, j)\n        }\n    }\n    return res\n}\n</code></pre> iteration.swift<pre><code>/* Двойной цикл for */\nfunc nestedForLoop(n: Int) -&gt; String {\n    var res = \"\"\n    // Цикл по i = 1, 2, ..., n-1, n\n    for i in 1 ... n {\n        // Цикл по j = 1, 2, ..., n-1, n\n        for j in 1 ... n {\n            res.append(\"(\\(i), \\(j)), \")\n        }\n    }\n    return res\n}\n</code></pre> iteration.js<pre><code>/* Двойной цикл for */\nfunction nestedForLoop(n) {\n    let res = '';\n    // Цикл по i = 1, 2, ..., n-1, n\n    for (let i = 1; i &lt;= n; i++) {\n        // Цикл по j = 1, 2, ..., n-1, n\n        for (let j = 1; j &lt;= n; j++) {\n            res += `(${i}, ${j}), `;\n        }\n    }\n    return res;\n}\n</code></pre> iteration.ts<pre><code>/* Двойной цикл for */\nfunction nestedForLoop(n: number): string {\n    let res = '';\n    // Цикл по i = 1, 2, ..., n-1, n\n    for (let i = 1; i &lt;= n; i++) {\n        // Цикл по j = 1, 2, ..., n-1, n\n        for (let j = 1; j &lt;= n; j++) {\n            res += `(${i}, ${j}), `;\n        }\n    }\n    return res;\n}\n</code></pre> iteration.dart<pre><code>/* Двойной цикл for */\nString nestedForLoop(int n) {\n  String res = \"\";\n  // Цикл по i = 1, 2, ..., n-1, n\n  for (int i = 1; i &lt;= n; i++) {\n    // Цикл по j = 1, 2, ..., n-1, n\n    for (int j = 1; j &lt;= n; j++) {\n      res += \"($i, $j), \";\n    }\n  }\n  return res;\n}\n</code></pre> iteration.rs<pre><code>/* Двойной цикл for */\nfn nested_for_loop(n: i32) -&gt; String {\n    let mut res = vec![];\n    // Цикл по i = 1, 2, ..., n-1, n\n    for i in 1..=n {\n        // Цикл по j = 1, 2, ..., n-1, n\n        for j in 1..=n {\n            res.push(format!(\"({}, {}), \", i, j));\n        }\n    }\n    res.join(\"\")\n}\n</code></pre> iteration.c<pre><code>/* Двойной цикл for */\nchar *nestedForLoop(int n) {\n    // n * n — это число соответствующих точек, а максимальная длина строки \"(i, j), \" равна 6+10*2, плюс дополнительное место для завершающего нулевого символа \\0\n    int size = n * n * 26 + 1;\n    char *res = malloc(size * sizeof(char));\n    // Цикл по i = 1, 2, ..., n-1, n\n    for (int i = 1; i &lt;= n; i++) {\n        // Цикл по j = 1, 2, ..., n-1, n\n        for (int j = 1; j &lt;= n; j++) {\n            char tmp[26];\n            snprintf(tmp, sizeof(tmp), \"(%d, %d), \", i, j);\n            strncat(res, tmp, size - strlen(res) - 1);\n        }\n    }\n    return res;\n}\n</code></pre> iteration.kt<pre><code>/* Двойной цикл for */\nfun nestedForLoop(n: Int): String {\n    val res = StringBuilder()\n    // Цикл по i = 1, 2, ..., n-1, n\n    for (i in 1..n) {\n        // Цикл по j = 1, 2, ..., n-1, n\n        for (j in 1..n) {\n            res.append(\" ($i, $j), \")\n        }\n    }\n    return res.toString()\n}\n</code></pre> iteration.rb<pre><code>### Двойной цикл for ###\ndef nested_for_loop(n)\n  res = \"\"\n\n  # Цикл по i = 1, 2, ..., n-1, n\n  for i in 1..n\n    # Цикл по j = 1, 2, ..., n-1, n\n    for j in 1..n\n      res += \"(#{i}, #{j}), \"\n    end\n  end\n\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>На рисунке 2-2 показана блок-схема такого вложенного цикла.</p> <p></p> <p> Рисунок 2-2   Блок-схема вложенного цикла </p> <p>В этом случае число операций функции пропорционально \\(n^2\\) , то есть время работы алгоритма и размер входных данных \\(n\\) находятся в \"квадратичной зависимости\".</p> <p>Мы можем продолжать добавлять вложенные циклы, и каждое новое вложение будет означать очередное \"повышение размерности\", увеличивая временную сложность до \"кубической зависимости\", \"зависимости четвертой степени\" и так далее.</p>","path":["Глава 2. Анализ сложности","2.2 &nbsp; Итерация и рекурсия"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#222","level":2,"title":"2.2.2   Рекурсия","text":"<p>Рекурсия (recursion) - это алгоритмическая стратегия, в которой функция решает задачу, вызывая саму себя. В основном она включает две фазы.</p> <ol> <li>Спуск: программа все глубже вызывает саму себя, обычно передавая меньшие или более упрощенные параметры, пока не достигнет \"условия завершения\".</li> <li>Подъем: после срабатывания \"условия завершения\" программа начинает возвращаться от самой глубокой рекурсивной функции вверх, собирая результаты с каждого уровня.</li> </ol> <p>С точки зрения реализации рекурсивный код в основном состоит из трех элементов.</p> <ol> <li>Условие завершения: определяет момент перехода от \"спуска\" к \"подъему\".</li> <li>Рекурсивный вызов: соответствует \"спуску\", когда функция вызывает саму себя, обычно с меньшими или более упрощенными параметрами.</li> <li>Возврат результата: соответствует \"подъему\", когда результат текущего уровня рекурсии передается предыдущему.</li> </ol> <p>Посмотри на следующий код: нам достаточно вызвать функцию <code>recur(n)</code>  , чтобы вычислить \\(1 + 2 + \\dots + n\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby recursion.py<pre><code>def recur(n: int) -&gt; int:\n    \"\"\"Рекурсия\"\"\"\n    # Условие завершения\n    if n == 1:\n        return 1\n    # Рекурсия: рекурсивный вызов\n    res = recur(n - 1)\n    # Возврат: вернуть результат\n    return n + res\n</code></pre> recursion.cpp<pre><code>/* Рекурсия */\nint recur(int n) {\n    // Условие завершения\n    if (n == 1)\n        return 1;\n    // Рекурсия: рекурсивный вызов\n    int res = recur(n - 1);\n    // Возврат: вернуть результат\n    return n + res;\n}\n</code></pre> recursion.java<pre><code>/* Рекурсия */\nint recur(int n) {\n    // Условие завершения\n    if (n == 1)\n        return 1;\n    // Рекурсия: рекурсивный вызов\n    int res = recur(n - 1);\n    // Возврат: вернуть результат\n    return n + res;\n}\n</code></pre> recursion.cs<pre><code>/* Рекурсия */\nint Recur(int n) {\n    // Условие завершения\n    if (n == 1)\n        return 1;\n    // Рекурсия: рекурсивный вызов\n    int res = Recur(n - 1);\n    // Возврат: вернуть результат\n    return n + res;\n}\n</code></pre> recursion.go<pre><code>/* Рекурсия */\nfunc recur(n int) int {\n    // Условие завершения\n    if n == 1 {\n        return 1\n    }\n    // Рекурсия: рекурсивный вызов\n    res := recur(n - 1)\n    // Возврат: вернуть результат\n    return n + res\n}\n</code></pre> recursion.swift<pre><code>/* Рекурсия */\nfunc recur(n: Int) -&gt; Int {\n    // Условие завершения\n    if n == 1 {\n        return 1\n    }\n    // Рекурсия: рекурсивный вызов\n    let res = recur(n: n - 1)\n    // Возврат: вернуть результат\n    return n + res\n}\n</code></pre> recursion.js<pre><code>/* Рекурсия */\nfunction recur(n) {\n    // Условие завершения\n    if (n === 1) return 1;\n    // Рекурсия: рекурсивный вызов\n    const res = recur(n - 1);\n    // Возврат: вернуть результат\n    return n + res;\n}\n</code></pre> recursion.ts<pre><code>/* Рекурсия */\nfunction recur(n: number): number {\n    // Условие завершения\n    if (n === 1) return 1;\n    // Рекурсия: рекурсивный вызов\n    const res = recur(n - 1);\n    // Возврат: вернуть результат\n    return n + res;\n}\n</code></pre> recursion.dart<pre><code>/* Рекурсия */\nint recur(int n) {\n  // Условие завершения\n  if (n == 1) return 1;\n  // Рекурсия: рекурсивный вызов\n  int res = recur(n - 1);\n  // Возврат: вернуть результат\n  return n + res;\n}\n</code></pre> recursion.rs<pre><code>/* Рекурсия */\nfn recur(n: i32) -&gt; i32 {\n    // Условие завершения\n    if n == 1 {\n        return 1;\n    }\n    // Рекурсия: рекурсивный вызов\n    let res = recur(n - 1);\n    // Возврат: вернуть результат\n    n + res\n}\n</code></pre> recursion.c<pre><code>/* Рекурсия */\nint recur(int n) {\n    // Условие завершения\n    if (n == 1)\n        return 1;\n    // Рекурсия: рекурсивный вызов\n    int res = recur(n - 1);\n    // Возврат: вернуть результат\n    return n + res;\n}\n</code></pre> recursion.kt<pre><code>/* Рекурсия */\nfun recur(n: Int): Int {\n    // Условие завершения\n    if (n == 1)\n        return 1\n    // Рекурсивный шаг: рекурсивный вызов\n    val res = recur(n - 1)\n    // Возврат: вернуть результат\n    return n + res\n}\n</code></pre> recursion.rb<pre><code>### Рекурсия ###\ndef recur(n)\n  # Условие завершения\n  return 1 if n == 1\n  # Рекурсия: рекурсивный вызов\n  res = recur(n - 1)\n  # Возврат: вернуть результат\n  n + res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>На рисунке 2-3 показан рекурсивный процесс этой функции.</p> <p></p> <p> Рисунок 2-3   Рекурсивный процесс функции суммирования </p> <p>Хотя с вычислительной точки зрения итерация и рекурсия могут давать один и тот же результат, они представляют собой две совершенно разные парадигмы мышления и решения задач.</p> <ul> <li>Итерация: решает задачу \"снизу вверх\". Мы начинаем с самых базовых шагов, а затем многократно повторяем или накапливаем их, пока задача не будет завершена.</li> <li>Рекурсия: решает задачу \"сверху вниз\". Исходная задача разбивается на более мелкие подзадачи той же формы. Затем эти подзадачи продолжают разбиваться еще дальше, пока не будет достигнут базовый случай (для которого решение уже известно).</li> </ul> <p>Возьмем в качестве примера указанную выше функцию суммирования и обозначим задачу как \\(f(n) = 1 + 2 + \\dots + n\\) .</p> <ul> <li>Итерация: в цикле моделируется процесс суммирования от \\(1\\) до \\(n\\) , и на каждом шаге выполняется операция сложения, в результате чего получается \\(f(n)\\) .</li> <li>Рекурсия: задача раскладывается на подзадачу \\(f(n) = n + f(n-1)\\) , а затем продолжает раскладываться (рекурсивно) до базового случая \\(f(1) = 1\\) .</li> </ul>","path":["Глава 2. Анализ сложности","2.2 &nbsp; Итерация и рекурсия"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#1","level":3,"title":"1.   Стек вызовов","text":"<p>Каждый раз, когда рекурсивная функция вызывает сама себя, система выделяет память для нового экземпляра функции, чтобы хранить локальные переменные, адрес возврата и другую информацию. Это приводит к двум последствиям.</p> <ul> <li>Контекстные данные функции хранятся в области памяти, называемой \"пространством кадра стека\", и освобождаются только после возврата функции. Поэтому рекурсия обычно требует больше памяти, чем итерация.</li> <li>Вызов рекурсивной функции создает дополнительный накладной расход. Поэтому рекурсия обычно уступает циклам по временной эффективности.</li> </ul> <p>Как показано на рисунке 2-4, до срабатывания условия завершения одновременно существует \\(n\\) еще не завершившихся рекурсивных вызовов, а глубина рекурсии равна \\(n\\) .</p> <p></p> <p> Рисунок 2-4   Глубина рекурсивного вызова </p> <p>На практике разрешенная языком программирования глубина рекурсии обычно ограничена, и слишком глубокая рекурсия может привести к ошибке переполнения стека.</p>","path":["Глава 2. Анализ сложности","2.2 &nbsp; Итерация и рекурсия"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#2","level":3,"title":"2.   Хвостовая рекурсия","text":"<p>Интересно, что если функция выполняет рекурсивный вызов в самом последнем действии перед возвратом , то компилятор или интерпретатор может оптимизировать такую функцию так, чтобы по использованию памяти она была сопоставима с итерацией. Такой случай называется хвостовой рекурсией (tail recursion).</p> <ul> <li>Обычная рекурсия: когда функция возвращается на предыдущий уровень, ей все еще нужно продолжать выполнять код, поэтому системе приходится сохранять контекст вызова предыдущего уровня.</li> <li>Хвостовая рекурсия: рекурсивный вызов - это последняя операция перед возвратом, а значит, после возвращения на предыдущий уровень не требуется выполнять дополнительных действий, и системе не нужно сохранять контекст предыдущей функции.</li> </ul> <p>На примере вычисления \\(1 + 2 + \\dots + n\\) можно сделать переменную результата <code>res</code> параметром функции и тем самым реализовать хвостовую рекурсию:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby recursion.py<pre><code>def tail_recur(n, res):\n    \"\"\"Хвостовая рекурсия\"\"\"\n    # Условие завершения\n    if n == 0:\n        return res\n    # Хвостовой рекурсивный вызов\n    return tail_recur(n - 1, res + n)\n</code></pre> recursion.cpp<pre><code>/* Хвостовая рекурсия */\nint tailRecur(int n, int res) {\n    // Условие завершения\n    if (n == 0)\n        return res;\n    // Хвостовой рекурсивный вызов\n    return tailRecur(n - 1, res + n);\n}\n</code></pre> recursion.java<pre><code>/* Хвостовая рекурсия */\nint tailRecur(int n, int res) {\n    // Условие завершения\n    if (n == 0)\n        return res;\n    // Хвостовой рекурсивный вызов\n    return tailRecur(n - 1, res + n);\n}\n</code></pre> recursion.cs<pre><code>/* Хвостовая рекурсия */\nint TailRecur(int n, int res) {\n    // Условие завершения\n    if (n == 0)\n        return res;\n    // Хвостовой рекурсивный вызов\n    return TailRecur(n - 1, res + n);\n}\n</code></pre> recursion.go<pre><code>/* Хвостовая рекурсия */\nfunc tailRecur(n int, res int) int {\n    // Условие завершения\n    if n == 0 {\n        return res\n    }\n    // Хвостовой рекурсивный вызов\n    return tailRecur(n-1, res+n)\n}\n</code></pre> recursion.swift<pre><code>/* Хвостовая рекурсия */\nfunc tailRecur(n: Int, res: Int) -&gt; Int {\n    // Условие завершения\n    if n == 0 {\n        return res\n    }\n    // Хвостовой рекурсивный вызов\n    return tailRecur(n: n - 1, res: res + n)\n}\n</code></pre> recursion.js<pre><code>/* Хвостовая рекурсия */\nfunction tailRecur(n, res) {\n    // Условие завершения\n    if (n === 0) return res;\n    // Хвостовой рекурсивный вызов\n    return tailRecur(n - 1, res + n);\n}\n</code></pre> recursion.ts<pre><code>/* Хвостовая рекурсия */\nfunction tailRecur(n: number, res: number): number {\n    // Условие завершения\n    if (n === 0) return res;\n    // Хвостовой рекурсивный вызов\n    return tailRecur(n - 1, res + n);\n}\n</code></pre> recursion.dart<pre><code>/* Хвостовая рекурсия */\nint tailRecur(int n, int res) {\n  // Условие завершения\n  if (n == 0) return res;\n  // Хвостовой рекурсивный вызов\n  return tailRecur(n - 1, res + n);\n}\n</code></pre> recursion.rs<pre><code>/* Хвостовая рекурсия */\nfn tail_recur(n: i32, res: i32) -&gt; i32 {\n    // Условие завершения\n    if n == 0 {\n        return res;\n    }\n    // Хвостовой рекурсивный вызов\n    tail_recur(n - 1, res + n)\n}\n</code></pre> recursion.c<pre><code>/* Хвостовая рекурсия */\nint tailRecur(int n, int res) {\n    // Условие завершения\n    if (n == 0)\n        return res;\n    // Хвостовой рекурсивный вызов\n    return tailRecur(n - 1, res + n);\n}\n</code></pre> recursion.kt<pre><code>/* Хвостовая рекурсия */\ntailrec fun tailRecur(n: Int, res: Int): Int {\n    // Добавить ключевое слово tailrec, чтобы включить оптимизацию хвостовой рекурсии\n    // Условие завершения\n    if (n == 0)\n        return res\n    // Хвостовой рекурсивный вызов\n    return tailRecur(n - 1, res + n)\n}\n</code></pre> recursion.rb<pre><code>### Хвостовая рекурсия ###\ndef tail_recur(n, res)\n  # Условие завершения\n  return res if n == 0\n  # Хвостовой рекурсивный вызов\n  tail_recur(n - 1, res + n)\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Процесс выполнения хвостовой рекурсии показан на рисунке 2-5. Если сравнить обычную рекурсию и хвостовую рекурсию, то видно, что точка выполнения операции суммирования у них различается.</p> <ul> <li>Обычная рекурсия: операция суммирования выполняется в процессе \"подъема\", то есть после возврата с каждого уровня еще нужно выполнить очередное сложение.</li> <li>Хвостовая рекурсия: операция суммирования выполняется в процессе \"спуска\", а сам \"подъем\" сводится лишь к последовательному возврату.</li> </ul> <p></p> <p> Рисунок 2-5   Процесс хвостовой рекурсии </p> <p>Tip</p> <p>Обрати внимание: многие компиляторы и интерпретаторы не поддерживают оптимизацию хвостовой рекурсии. Например, Python по умолчанию такую оптимизацию не выполняет, поэтому даже функция в хвостово-рекурсивной форме все равно может привести к переполнению стека.</p>","path":["Глава 2. Анализ сложности","2.2 &nbsp; Итерация и рекурсия"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#3_1","level":3,"title":"3.   Дерево рекурсии","text":"<p>При решении алгоритмических задач, связанных с \"разделяй и властвуй\", рекурсия часто дает более интуитивный способ рассуждения и более читаемый код, чем итерация. Возьмем в качестве примера \"последовательность Фибоначчи\".</p> <p>Question</p> <p>Дана последовательность Фибоначчи \\(0, 1, 1, 2, 3, 5, 8, 13, \\dots\\) ; найди \\(n\\)-й элемент этой последовательности.</p> <p>Обозначим \\(n\\)-й элемент последовательности Фибоначчи как \\(f(n)\\) . Тогда нетрудно получить два вывода.</p> <ul> <li>Первые два числа последовательности равны \\(f(1) = 0\\) и \\(f(2) = 1\\) .</li> <li>Каждое последующее число равно сумме двух предыдущих, то есть \\(f(n) = f(n - 1) + f(n - 2)\\) .</li> </ul> <p>Следуя рекуррентному соотношению и используя первые два числа как условия завершения, мы можем написать рекурсивный код. Вызов <code>fib(n)</code> даст нам \\(n\\)-й элемент последовательности Фибоначчи:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby recursion.py<pre><code>def fib(n: int) -&gt; int:\n    \"\"\"Последовательность Фибоначчи: рекурсия\"\"\"\n    # Условие завершения: f(1) = 0, f(2) = 1\n    if n == 1 or n == 2:\n        return n - 1\n    # Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n    res = fib(n - 1) + fib(n - 2)\n    # Вернуть результат f(n)\n    return res\n</code></pre> recursion.cpp<pre><code>/* Последовательность Фибоначчи: рекурсия */\nint fib(int n) {\n    // Условие завершения: f(1) = 0, f(2) = 1\n    if (n == 1 || n == 2)\n        return n - 1;\n    // Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n    int res = fib(n - 1) + fib(n - 2);\n    // Вернуть результат f(n)\n    return res;\n}\n</code></pre> recursion.java<pre><code>/* Последовательность Фибоначчи: рекурсия */\nint fib(int n) {\n    // Условие завершения: f(1) = 0, f(2) = 1\n    if (n == 1 || n == 2)\n        return n - 1;\n    // Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n    int res = fib(n - 1) + fib(n - 2);\n    // Вернуть результат f(n)\n    return res;\n}\n</code></pre> recursion.cs<pre><code>/* Последовательность Фибоначчи: рекурсия */\nint Fib(int n) {\n    // Условие завершения: f(1) = 0, f(2) = 1\n    if (n == 1 || n == 2)\n        return n - 1;\n    // Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n    int res = Fib(n - 1) + Fib(n - 2);\n    // Вернуть результат f(n)\n    return res;\n}\n</code></pre> recursion.go<pre><code>/* Последовательность Фибоначчи: рекурсия */\nfunc fib(n int) int {\n    // Условие завершения: f(1) = 0, f(2) = 1\n    if n == 1 || n == 2 {\n        return n - 1\n    }\n    // Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n    res := fib(n-1) + fib(n-2)\n    // Вернуть результат f(n)\n    return res\n}\n</code></pre> recursion.swift<pre><code>/* Последовательность Фибоначчи: рекурсия */\nfunc fib(n: Int) -&gt; Int {\n    // Условие завершения: f(1) = 0, f(2) = 1\n    if n == 1 || n == 2 {\n        return n - 1\n    }\n    // Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n    let res = fib(n: n - 1) + fib(n: n - 2)\n    // Вернуть результат f(n)\n    return res\n}\n</code></pre> recursion.js<pre><code>/* Последовательность Фибоначчи: рекурсия */\nfunction fib(n) {\n    // Условие завершения: f(1) = 0, f(2) = 1\n    if (n === 1 || n === 2) return n - 1;\n    // Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n    const res = fib(n - 1) + fib(n - 2);\n    // Вернуть результат f(n)\n    return res;\n}\n</code></pre> recursion.ts<pre><code>/* Последовательность Фибоначчи: рекурсия */\nfunction fib(n: number): number {\n    // Условие завершения: f(1) = 0, f(2) = 1\n    if (n === 1 || n === 2) return n - 1;\n    // Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n    const res = fib(n - 1) + fib(n - 2);\n    // Вернуть результат f(n)\n    return res;\n}\n</code></pre> recursion.dart<pre><code>/* Последовательность Фибоначчи: рекурсия */\nint fib(int n) {\n  // Условие завершения: f(1) = 0, f(2) = 1\n  if (n == 1 || n == 2) return n - 1;\n  // Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n  int res = fib(n - 1) + fib(n - 2);\n  // Вернуть результат f(n)\n  return res;\n}\n</code></pre> recursion.rs<pre><code>/* Последовательность Фибоначчи: рекурсия */\nfn fib(n: i32) -&gt; i32 {\n    // Условие завершения: f(1) = 0, f(2) = 1\n    if n == 1 || n == 2 {\n        return n - 1;\n    }\n    // Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n    let res = fib(n - 1) + fib(n - 2);\n    // Вернуть результат\n    res\n}\n</code></pre> recursion.c<pre><code>/* Последовательность Фибоначчи: рекурсия */\nint fib(int n) {\n    // Условие завершения: f(1) = 0, f(2) = 1\n    if (n == 1 || n == 2)\n        return n - 1;\n    // Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n    int res = fib(n - 1) + fib(n - 2);\n    // Вернуть результат f(n)\n    return res;\n}\n</code></pre> recursion.kt<pre><code>/* Последовательность Фибоначчи: рекурсия */\nfun fib(n: Int): Int {\n    // Условие завершения: f(1) = 0, f(2) = 1\n    if (n == 1 || n == 2)\n        return n - 1\n    // Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n    val res = fib(n - 1) + fib(n - 2)\n    // Вернуть результат f(n)\n    return res\n}\n</code></pre> recursion.rb<pre><code>### Последовательность Фибоначчи: рекурсия ###\ndef fib(n)\n  # Условие завершения: f(1) = 0, f(2) = 1\n  return n - 1 if n == 1 || n == 2\n  # Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n  res = fib(n - 1) + fib(n - 2)\n  # Вернуть результат f(n)\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Если посмотреть на приведенный код, внутри функции выполняются два рекурсивных вызова, а это означает, что один вызов рождает две ветви вызова. Как показано на рисунке 2-6, при таком продолжении рекурсивных вызовов в итоге получается дерево рекурсии (recursion tree) глубиной \\(n\\) .</p> <p></p> <p> Рисунок 2-6   Дерево рекурсии последовательности Фибоначчи </p> <p>По своей сути рекурсия воплощает парадигму \"разбиения задачи на более мелкие подзадачи\", и именно поэтому стратегия разделяй-и-властвуй столь важна.</p> <ul> <li>С точки зрения алгоритмов многие важнейшие стратегии, такие как поиск, сортировка, бэктрекинг, разделяй-и-властвуй и динамическое программирование, прямо или косвенно используют такой образ мышления.</li> <li>С точки зрения структур данных рекурсия естественным образом подходит для решения задач, связанных со связными списками, деревьями и графами, потому что они хорошо поддаются анализу через идеи разделения задачи.</li> </ul>","path":["Глава 2. Анализ сложности","2.2 &nbsp; Итерация и рекурсия"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#223","level":2,"title":"2.2.3   Сравнение двух подходов","text":"<p>Обобщая все сказанное выше, можно представить различия между итерацией и рекурсией с точки зрения реализации, производительности и применимости в следующей таблице.</p> <p> Таблица 2-1   Сравнение характеристик итерации и рекурсии </p> Итерация Рекурсия Реализация Циклическая структура Функция вызывает сама себя Временная эффективность Обычно выше, так как нет накладных расходов на вызовы функций Каждый вызов функции создает накладные расходы Использование памяти Обычно требуется фиксированный объем памяти Накопление вызовов функции может занимать много места в кадрах стека Подходящие задачи Хорошо подходит для простых циклических задач, код интуитивен и легко читается Хорошо подходит для разложения на подзадачи, например для деревьев, графов, разделяй-и-властвуй, бэктрекинга и т. д.; код при этом получается компактным и ясным <p>Tip</p> <p>Если тебе сложно понять дальнейшее содержание, можешь вернуться к нему после чтения главы о \"стеке\".</p> <p>Какова же внутренняя связь между итерацией и рекурсией? Если снова взять рекурсивную функцию выше, операция суммирования выполняется в фазе \"подъема\" рекурсии. Это означает, что функция, вызванная первой, на самом деле завершает сложение последней, и такой механизм очень похож на принцип стека \"последним пришел - первым ушел\".</p> <p>На самом деле такие термины рекурсии, как \"стек вызовов\" и \"пространство кадра стека\", уже прямо намекают на тесную связь между рекурсией и стеком.</p> <ol> <li>Спуск: когда вызывается функция, система выделяет для нее новый кадр стека в \"стеке вызовов\", чтобы хранить локальные переменные, параметры, адрес возврата и другие данные.</li> <li>Подъем: когда функция завершает выполнение и возвращается, соответствующий кадр стека удаляется из \"стека вызовов\", а среда выполнения предыдущей функции восстанавливается.</li> </ol> <p>Поэтому мы можем использовать явный стек для имитации поведения стека вызовов и тем самым преобразовать рекурсию в итеративную форму:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby recursion.py<pre><code>def for_loop_recur(n: int) -&gt; int:\n    \"\"\"Имитация рекурсии итерацией\"\"\"\n    # Использовать явный стек для имитации системного стека вызовов\n    stack = []\n    res = 0\n    # Рекурсия: рекурсивный вызов\n    for i in range(n, 0, -1):\n        # Имитировать «рекурсию» с помощью операции помещения в стек\n        stack.append(i)\n    # Возврат: вернуть результат\n    while stack:\n        # Имитировать «возврат» с помощью операции извлечения из стека\n        res += stack.pop()\n    # res = 1+2+3+...+n\n    return res\n</code></pre> recursion.cpp<pre><code>/* Имитация рекурсии итерацией */\nint forLoopRecur(int n) {\n    // Использовать явный стек для имитации системного стека вызовов\n    stack&lt;int&gt; stack;\n    int res = 0;\n    // Рекурсия: рекурсивный вызов\n    for (int i = n; i &gt; 0; i--) {\n        // Имитировать «рекурсию» с помощью операции помещения в стек\n        stack.push(i);\n    }\n    // Возврат: вернуть результат\n    while (!stack.empty()) {\n        // Имитировать «возврат» с помощью операции извлечения из стека\n        res += stack.top();\n        stack.pop();\n    }\n    // res = 1+2+3+...+n\n    return res;\n}\n</code></pre> recursion.java<pre><code>/* Имитация рекурсии итерацией */\nint forLoopRecur(int n) {\n    // Использовать явный стек для имитации системного стека вызовов\n    Stack&lt;Integer&gt; stack = new Stack&lt;&gt;();\n    int res = 0;\n    // Рекурсия: рекурсивный вызов\n    for (int i = n; i &gt; 0; i--) {\n        // Имитировать «рекурсию» с помощью операции помещения в стек\n        stack.push(i);\n    }\n    // Возврат: вернуть результат\n    while (!stack.isEmpty()) {\n        // Имитировать «возврат» с помощью операции извлечения из стека\n        res += stack.pop();\n    }\n    // res = 1+2+3+...+n\n    return res;\n}\n</code></pre> recursion.cs<pre><code>/* Имитация рекурсии итерацией */\nint ForLoopRecur(int n) {\n    // Использовать явный стек для имитации системного стека вызовов\n    Stack&lt;int&gt; stack = new();\n    int res = 0;\n    // Рекурсия: рекурсивный вызов\n    for (int i = n; i &gt; 0; i--) {\n        // Имитировать «рекурсию» с помощью операции помещения в стек\n        stack.Push(i);\n    }\n    // Возврат: вернуть результат\n    while (stack.Count &gt; 0) {\n        // Имитировать «возврат» с помощью операции извлечения из стека\n        res += stack.Pop();\n    }\n    // res = 1+2+3+...+n\n    return res;\n}\n</code></pre> recursion.go<pre><code>/* Имитация рекурсии итерацией */\nfunc forLoopRecur(n int) int {\n    // Использовать явный стек для имитации системного стека вызовов\n    stack := list.New()\n    res := 0\n    // Рекурсия: рекурсивный вызов\n    for i := n; i &gt; 0; i-- {\n        // Имитировать «рекурсию» с помощью операции помещения в стек\n        stack.PushBack(i)\n    }\n    // Возврат: вернуть результат\n    for stack.Len() != 0 {\n        // Имитировать «возврат» с помощью операции извлечения из стека\n        res += stack.Back().Value.(int)\n        stack.Remove(stack.Back())\n    }\n    // res = 1+2+3+...+n\n    return res\n}\n</code></pre> recursion.swift<pre><code>/* Имитация рекурсии итерацией */\nfunc forLoopRecur(n: Int) -&gt; Int {\n    // Использовать явный стек для имитации системного стека вызовов\n    var stack: [Int] = []\n    var res = 0\n    // Рекурсия: рекурсивный вызов\n    for i in (1 ... n).reversed() {\n        // Имитировать «рекурсию» с помощью операции помещения в стек\n        stack.append(i)\n    }\n    // Возврат: вернуть результат\n    while !stack.isEmpty {\n        // Имитировать «возврат» с помощью операции извлечения из стека\n        res += stack.removeLast()\n    }\n    // res = 1+2+3+...+n\n    return res\n}\n</code></pre> recursion.js<pre><code>/* Имитация рекурсии итерацией */\nfunction forLoopRecur(n) {\n    // Использовать явный стек для имитации системного стека вызовов\n    const stack = [];\n    let res = 0;\n    // Рекурсия: рекурсивный вызов\n    for (let i = n; i &gt; 0; i--) {\n        // Имитировать «рекурсию» с помощью операции помещения в стек\n        stack.push(i);\n    }\n    // Возврат: вернуть результат\n    while (stack.length) {\n        // Имитировать «возврат» с помощью операции извлечения из стека\n        res += stack.pop();\n    }\n    // res = 1+2+3+...+n\n    return res;\n}\n</code></pre> recursion.ts<pre><code>/* Имитация рекурсии итерацией */\nfunction forLoopRecur(n: number): number {\n    // Использовать явный стек для имитации системного стека вызовов\n    const stack: number[] = [];\n    let res: number = 0;\n    // Рекурсия: рекурсивный вызов\n    for (let i = n; i &gt; 0; i--) {\n        // Имитировать «рекурсию» с помощью операции помещения в стек\n        stack.push(i);\n    }\n    // Возврат: вернуть результат\n    while (stack.length) {\n        // Имитировать «возврат» с помощью операции извлечения из стека\n        res += stack.pop();\n    }\n    // res = 1+2+3+...+n\n    return res;\n}\n</code></pre> recursion.dart<pre><code>/* Имитация рекурсии итерацией */\nint forLoopRecur(int n) {\n  // Использовать явный стек для имитации системного стека вызовов\n  List&lt;int&gt; stack = [];\n  int res = 0;\n  // Рекурсия: рекурсивный вызов\n  for (int i = n; i &gt; 0; i--) {\n    // Имитировать «рекурсию» с помощью операции помещения в стек\n    stack.add(i);\n  }\n  // Возврат: вернуть результат\n  while (!stack.isEmpty) {\n    // Имитировать «возврат» с помощью операции извлечения из стека\n    res += stack.removeLast();\n  }\n  // res = 1+2+3+...+n\n  return res;\n}\n</code></pre> recursion.rs<pre><code>/* Имитация рекурсии итерацией */\nfn for_loop_recur(n: i32) -&gt; i32 {\n    // Использовать явный стек для имитации системного стека вызовов\n    let mut stack = Vec::new();\n    let mut res = 0;\n    // Рекурсия: рекурсивный вызов\n    for i in (1..=n).rev() {\n        // Имитировать «рекурсию» с помощью операции помещения в стек\n        stack.push(i);\n    }\n    // Возврат: вернуть результат\n    while !stack.is_empty() {\n        // Имитировать «возврат» с помощью операции извлечения из стека\n        res += stack.pop().unwrap();\n    }\n    // res = 1+2+3+...+n\n    res\n}\n</code></pre> recursion.c<pre><code>/* Имитация рекурсии итерацией */\nint forLoopRecur(int n) {\n    int stack[1000]; // Использовать большой массив для имитации стека\n    int top = -1;    // Индекс вершины стека\n    int res = 0;\n    // Рекурсия: рекурсивный вызов\n    for (int i = n; i &gt; 0; i--) {\n        // Имитировать «рекурсию» с помощью операции помещения в стек\n        stack[1 + top++] = i;\n    }\n    // Возврат: вернуть результат\n    while (top &gt;= 0) {\n        // Имитировать «возврат» с помощью операции извлечения из стека\n        res += stack[top--];\n    }\n    // res = 1+2+3+...+n\n    return res;\n}\n</code></pre> recursion.kt<pre><code>/* Имитация рекурсии итерацией */\nfun forLoopRecur(n: Int): Int {\n    // Использовать явный стек для имитации системного стека вызовов\n    val stack = Stack&lt;Int&gt;()\n    var res = 0\n    // Рекурсивный шаг: рекурсивный вызов\n    for (i in n downTo 0) {\n        // Имитировать «рекурсию» с помощью операции помещения в стек\n        stack.push(i)\n    }\n    // Возврат: вернуть результат\n    while (stack.isNotEmpty()) {\n        // Имитировать «возврат» с помощью операции извлечения из стека\n        res += stack.pop()\n    }\n    // res = 1+2+3+...+n\n    return res\n}\n</code></pre> recursion.rb<pre><code>### Имитация рекурсии итерацией ###\ndef for_loop_recur(n)\n  # Использовать явный стек для имитации системного стека вызовов\n  stack = []\n  res = 0\n\n  # Рекурсия: рекурсивный вызов\n  for i in n.downto(0)\n    # Имитировать «рекурсию» с помощью операции помещения в стек\n    stack &lt;&lt; i\n  end\n  # Возврат: вернуть результат\n  while !stack.empty?\n    res += stack.pop\n  end\n\n  # res = 1+2+3+...+n\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Если посмотреть на приведенный выше код, видно, что после преобразования рекурсии в итерацию код становится сложнее. Хотя во многих случаях итерация и рекурсия действительно могут быть преобразованы друг в друга, это не всегда стоит делать по двум причинам.</p> <ul> <li>Преобразованный код может стать труднее для понимания и менее читаемым.</li> <li>Для некоторых сложных задач имитация поведения системного стека вызовов может оказаться очень трудной.</li> </ul> <p>Итак, выбор между итерацией и рекурсией зависит от природы конкретной задачи. В практическом программировании крайне важно взвешивать плюсы и минусы обоих подходов и выбирать подходящий метод с учетом контекста.</p>","path":["Глава 2. Анализ сложности","2.2 &nbsp; Итерация и рекурсия"],"tags":[]},{"location":"chapter_computational_complexity/performance_evaluation/","level":1,"title":"2.1   Оценка эффективности алгоритмов","text":"<p>При проектировании алгоритмов мы последовательно стремимся к двум уровням целей.</p> <ol> <li>Найти решение задачи: алгоритм должен надежно получать правильный ответ в заданном диапазоне входных данных.</li> <li>Найти оптимальное решение: для одной и той же задачи может существовать несколько решений, и нам хочется выбрать максимально эффективный алгоритм.</li> </ol> <p>Иными словами, если задача в принципе решается, эффективность алгоритма становится главным критерием оценки его качества. Она включает два следующих измерения.</p> <ul> <li>Временная эффективность: сколько времени работает алгоритм.</li> <li>Пространственная эффективность: сколько памяти занимает алгоритм.</li> </ul> <p>Короче говоря, наша цель - проектировать структуры данных и алгоритмы, которые \"и быстры, и экономны по памяти\". Эффективная оценка алгоритмов крайне важна, потому что только так можно сравнивать разные алгоритмы и направлять процесс их проектирования и оптимизации.</p> <p>Методы оценки эффективности в основном делятся на два типа: практическое тестирование и теоретическая оценка.</p>","path":["Глава 2. Анализ сложности","2.1 &nbsp; Оценка эффективности алгоритмов"],"tags":[]},{"location":"chapter_computational_complexity/performance_evaluation/#211","level":2,"title":"2.1.1   Практическое тестирование","text":"<p>Предположим, у нас есть алгоритм <code>A</code> и алгоритм <code>B</code>, оба решают одну и ту же задачу, и нам нужно сравнить их эффективность. Самый прямой способ - взять компьютер, запустить оба алгоритма и зафиксировать время работы и объем используемой памяти. Такой способ оценки отражает реальную ситуацию, но имеет и серьезные ограничения.</p> <p>С одной стороны, трудно исключить влияние факторов тестовой среды. Аппаратная конфигурация влияет на производительность алгоритма. Например, если алгоритм имеет высокий уровень параллелизма, он лучше подходит для многоядерных CPU; если алгоритм интенсивно работает с памятью, он покажет себя лучше на быстрой памяти. Иными словами, результаты тестирования одного и того же алгоритма на разных машинах могут различаться. Это означает, что пришлось бы тестировать на самых разных машинах и усреднять результаты, а на практике это нереалистично.</p> <p>С другой стороны, полное тестирование требует больших ресурсов. По мере изменения объема входных данных алгоритм может вести себя по-разному. Например, при небольшом объеме входных данных время работы алгоритма <code>A</code> может быть меньше, чем у алгоритма <code>B</code>; но при большом объеме результаты могут оказаться прямо противоположными. Поэтому для убедительных выводов пришлось бы тестировать входные данные множества разных масштабов, а это требует значительных вычислительных ресурсов.</p>","path":["Глава 2. Анализ сложности","2.1 &nbsp; Оценка эффективности алгоритмов"],"tags":[]},{"location":"chapter_computational_complexity/performance_evaluation/#212","level":2,"title":"2.1.2   Теоретическая оценка","text":"<p>Поскольку практическое тестирование имеет серьезные ограничения, можно попытаться оценить эффективность алгоритма только с помощью вычислений. Такой метод называется асимптотическим анализом сложности (asymptotic complexity analysis), или сокращенно анализом сложности.</p> <p>Анализ сложности показывает зависимость между временем и пространственными ресурсами, требуемыми алгоритму, и масштабом входных данных. Он описывает тенденцию роста времени и памяти, необходимых алгоритму, по мере увеличения размера входных данных. Это определение звучит немного тяжеловесно, поэтому полезно разложить его на три ключевые идеи.</p> <ul> <li>\"Временные и пространственные ресурсы\" соответствуют временной сложности (time complexity) и пространственной сложности (space complexity) соответственно.</li> <li>\"По мере увеличения размера входных данных\" означает, что сложность отражает связь между эффективностью алгоритма и масштабом входа.</li> <li>\"Тенденция роста времени и пространства\" означает, что анализ сложности интересуется не конкретными значениями времени или памяти, а тем, насколько быстро они растут.</li> </ul> <p>Анализ сложности устраняет недостатки практического тестирования, что проявляется в следующих аспектах.</p> <ul> <li>Для него не нужно реально запускать код, а значит, он экологичнее и экономит ресурсы.</li> <li>Он не зависит от тестовой среды, поэтому результаты анализа применимы ко всем платформам выполнения.</li> <li>Он позволяет увидеть эффективность алгоритма при разных объемах данных, особенно на больших данных.</li> </ul> <p>Tip</p> <p>Если понятие сложности пока все еще кажется тебе запутанным, не переживай: мы подробно разберем его в следующих разделах.</p> <p>Анализ сложности дает нам \"линейку\" для оценки эффективности алгоритмов, позволяя измерять, сколько времени и памяти требуется для выполнения конкретного алгоритма, и сравнивать эффективность разных алгоритмов между собой.</p> <p>Сложность - это математическое понятие, поэтому для начинающих оно может показаться довольно абстрактным и сравнительно трудным. С этой точки зрения анализ сложности, возможно, не лучший самый первый материал для знакомства. Однако, когда мы обсуждаем особенности конкретной структуры данных или алгоритма, почти невозможно не затронуть скорость его работы и использование памяти.</p> <p>В итоге рекомендуется еще до глубокого погружения в структуры данных и алгоритмы сформировать хотя бы первичное понимание анализа сложности, чтобы уметь выполнять анализ сложности простых алгоритмов.</p>","path":["Глава 2. Анализ сложности","2.1 &nbsp; Оценка эффективности алгоритмов"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/","level":1,"title":"2.4   Пространственная сложность","text":"<p>Пространственная сложность (space complexity) используется для оценки того, как меняется объем памяти, занимаемой алгоритмом, по мере роста объема данных. Это понятие очень похоже на временную сложность, только вместо \"времени выполнения\" мы рассматриваем \"объем используемой памяти\".</p>","path":["Глава 2. Анализ сложности","2.4 &nbsp; Пространственная сложность"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#241","level":2,"title":"2.4.1   Пространство, связанное с алгоритмом","text":"<p>Память, которую использует алгоритм во время работы, в основном включает несколько следующих частей.</p> <ul> <li>Входное пространство: используется для хранения входных данных алгоритма.</li> <li>Временное пространство: используется для хранения переменных, объектов, контекста функций и других данных, возникающих во время выполнения алгоритма.</li> <li>Выходное пространство: используется для хранения выходных данных алгоритма.</li> </ul> <p>В общем случае при анализе пространственной сложности в расчет включают \"временное пространство\" и \"выходное пространство\".</p> <p>Временное пространство можно дополнительно разделить на три части.</p> <ul> <li>Временные данные: используются для хранения различных констант, переменных, объектов и т.д., возникающих во время выполнения алгоритма.</li> <li>Пространство кадров стека: используется для хранения контекстных данных вызываемых функций. Система при каждом вызове функции создает на вершине стека новый кадр; после возврата функции пространство этого кадра освобождается.</li> <li>Пространство инструкций: используется для хранения скомпилированных инструкций программы и в реальном подсчете обычно не учитывается.</li> </ul> <p>При анализе пространственной сложности программы мы обычно учитываем три части: временные данные, пространство кадров стека и выходные данные, как показано на рисунке 2-15.</p> <p></p> <p> Рисунок 2-15   Пространство, используемое алгоритмом </p> <p>Соответствующий код выглядит следующим образом:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>class Node:\n    \"\"\"Класс\"\"\"\n    def __init__(self, x: int):\n        self.val: int = x              # Значение узла\n        self.next: Node | None = None  # Ссылка на следующий узел\n\ndef function() -&gt; int:\n    \"\"\"Функция\"\"\"\n    # Выполнить некоторые операции...\n    return 0\n\ndef algorithm(n) -&gt; int:  # Входные данные\n    A = 0                 # Временные данные (константа, обычно обозначается заглавной буквой)\n    b = 0                 # Временные данные (переменная)\n    node = Node(0)        # Временные данные (объект)\n    c = function()        # Пространство кадра стека (вызов функции)\n    return A + b + c      # Выходные данные\n</code></pre> <pre><code>/* Структура */\nstruct Node {\n    int val;\n    Node *next;\n    Node(int x) : val(x), next(nullptr) {}\n};\n\n/* Функция */\nint func() {\n    // Выполнить некоторые операции...\n    return 0;\n}\n\nint algorithm(int n) {        // Входные данные\n    const int a = 0;          // Временные данные (константа)\n    int b = 0;                // Временные данные (переменная)\n    Node* node = new Node(0); // Временные данные (объект)\n    int c = func();           // Пространство кадра стека (вызов функции)\n    return a + b + c;         // Выходные данные\n}\n</code></pre> <pre><code>/* Класс */\nclass Node {\n    int val;\n    Node next;\n    Node(int x) { val = x; }\n}\n\n/* Функция */\nint function() {\n    // Выполнить некоторые операции...\n    return 0;\n}\n\nint algorithm(int n) {        // Входные данные\n    final int a = 0;          // Временные данные (константа)\n    int b = 0;                // Временные данные (переменная)\n    Node node = new Node(0);  // Временные данные (объект)\n    int c = function();       // Пространство кадра стека (вызов функции)\n    return a + b + c;         // Выходные данные\n}\n</code></pre> <pre><code>/* Класс */\nclass Node(int x) {\n    int val = x;\n    Node next;\n}\n\n/* Функция */\nint Function() {\n    // Выполнить некоторые операции...\n    return 0;\n}\n\nint Algorithm(int n) {        // Входные данные\n    const int a = 0;          // Временные данные (константа)\n    int b = 0;                // Временные данные (переменная)\n    Node node = new(0);       // Временные данные (объект)\n    int c = Function();       // Пространство кадра стека (вызов функции)\n    return a + b + c;         // Выходные данные\n}\n</code></pre> <pre><code>/* Структура */\ntype node struct {\n    val  int\n    next *node\n}\n\n/* Создать структуру node */\nfunc newNode(val int) *node {\n    return &amp;node{val: val}\n}\n\n/* Функция */\nfunc function() int {\n    // Выполнить некоторые операции...\n    return 0\n}\n\nfunc algorithm(n int) int { // Входные данные\n    const a = 0             // Временные данные (константа)\n    b := 0                  // Временные данные (переменная)\n    newNode(0)              // Временные данные (объект)\n    c := function()         // Пространство кадра стека (вызов функции)\n    return a + b + c        // Выходные данные\n}\n</code></pre> <pre><code>/* Класс */\nclass Node {\n    var val: Int\n    var next: Node?\n\n    init(x: Int) {\n        val = x\n    }\n}\n\n/* Функция */\nfunc function() -&gt; Int {\n    // Выполнить некоторые операции...\n    return 0\n}\n\nfunc algorithm(n: Int) -&gt; Int { // Входные данные\n    let a = 0             // Временные данные (константа)\n    var b = 0             // Временные данные (переменная)\n    let node = Node(x: 0) // Временные данные (объект)\n    let c = function()    // Пространство кадра стека (вызов функции)\n    return a + b + c      // Выходные данные\n}\n</code></pre> <pre><code>/* Класс */\nclass Node {\n    val;\n    next;\n    constructor(val) {\n        this.val = val === undefined ? 0 : val; // Значение узла\n        this.next = null;                       // Ссылка на следующий узел\n    }\n}\n\n/* Функция */\nfunction constFunc() {\n    // Выполнить некоторые операции\n    return 0;\n}\n\nfunction algorithm(n) {       // Входные данные\n    const a = 0;              // Временные данные (константа)\n    let b = 0;                // Временные данные (переменная)\n    const node = new Node(0); // Временные данные (объект)\n    const c = constFunc();    // Пространство кадра стека (вызов функции)\n    return a + b + c;         // Выходные данные\n}\n</code></pre> <pre><code>/* Класс */\nclass Node {\n    val: number;\n    next: Node | null;\n    constructor(val?: number) {\n        this.val = val === undefined ? 0 : val; // Значение узла\n        this.next = null;                       // Ссылка на следующий узел\n    }\n}\n\n/* Функция */\nfunction constFunc(): number {\n    // Выполнить некоторые операции\n    return 0;\n}\n\nfunction algorithm(n: number): number { // Входные данные\n    const a = 0;                        // Временные данные (константа)\n    let b = 0;                          // Временные данные (переменная)\n    const node = new Node(0);           // Временные данные (объект)\n    const c = constFunc();              // Пространство кадра стека (вызов функции)\n    return a + b + c;                   // Выходные данные\n}\n</code></pre> <pre><code>/* Класс */\nclass Node {\n  int val;\n  Node next;\n  Node(this.val, [this.next]);\n}\n\n/* Функция */\nint function() {\n  // Выполнить некоторые операции...\n  return 0;\n}\n\nint algorithm(int n) {  // Входные данные\n  const int a = 0;      // Временные данные (константа)\n  int b = 0;            // Временные данные (переменная)\n  Node node = Node(0);  // Временные данные (объект)\n  int c = function();   // Пространство кадра стека (вызов функции)\n  return a + b + c;     // Выходные данные\n}\n</code></pre> <pre><code>use std::rc::Rc;\nuse std::cell::RefCell;\n\n/* Структура */\nstruct Node {\n    val: i32,\n    next: Option&lt;Rc&lt;RefCell&lt;Node&gt;&gt;&gt;,\n}\n\n/* Создать структуру Node */\nimpl Node {\n    fn new(val: i32) -&gt; Self {\n        Self { val: val, next: None }\n    }\n}\n\n/* Функция */\nfn function() -&gt; i32 {      \n    // Выполнить некоторые операции...\n    return 0;\n}\n\nfn algorithm(n: i32) -&gt; i32 {       // Входные данные\n    const a: i32 = 0;               // Временные данные (константа)\n    let mut b = 0;                  // Временные данные (переменная)\n    let node = Node::new(0);        // Временные данные (объект)\n    let c = function();             // Пространство кадра стека (вызов функции)\n    return a + b + c;               // Выходные данные\n}\n</code></pre> <pre><code>/* Функция */\nint func() {\n    // Выполнить некоторые операции...\n    return 0;\n}\n\nint algorithm(int n) { // Входные данные\n    const int a = 0;   // Временные данные (константа)\n    int b = 0;         // Временные данные (переменная)\n    int c = func();    // Пространство кадра стека (вызов функции)\n    return a + b + c;  // Выходные данные\n}\n</code></pre> <pre><code>/* Класс */\nclass Node(var _val: Int) {\n    var next: Node? = null\n}\n\n/* Функция */\nfun function(): Int {\n    // Выполнить некоторые операции...\n    return 0\n}\n\nfun algorithm(n: Int): Int { // Входные данные\n    val a = 0                // Временные данные (константа)\n    var b = 0                // Временные данные (переменная)\n    val node = Node(0)       // Временные данные (объект)\n    val c = function()       // Пространство кадра стека (вызов функции)\n    return a + b + c         // Выходные данные\n}\n</code></pre> <pre><code>### Класс ###\nclass Node\n    attr_accessor :val      # Значение узла\n    attr_accessor :next     # Ссылка на следующий узел\n\n    def initialize(x)\n        @val = x\n    end\nend\n\n### Функция ###\ndef function\n    # Выполнить некоторые операции...\n    0\nend\n\n### Алгоритм ###\ndef algorithm(n)        # Входные данные\n    a = 0               # Временные данные (константа)\n    b = 0               # Временные данные (переменная)\n    node = Node.new(0)  # Временные данные (объект)\n    c = function        # Пространство кадра стека (вызов функции)\n    a + b + c           # Выходные данные\nend\n</code></pre>","path":["Глава 2. Анализ сложности","2.4 &nbsp; Пространственная сложность"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#242","level":2,"title":"2.4.2   Метод вывода","text":"<p>Метод вывода пространственной сложности в целом аналогичен временному анализу: меняется только объект подсчета, с \"количества операций\" на \"размер используемого пространства\".</p> <p>В отличие от временной сложности, обычно мы рассматриваем только худшую пространственную сложность. Это связано с тем, что память является жестким ограничением: нам нужно гарантировать, что для любых входных данных у программы будет достаточно памяти.</p> <p>Рассмотрим следующий код. Слово \"худшая\" в \"худшей пространственной сложности\" имеет два значения.</p> <ol> <li>Ориентир на худшие входные данные: когда \\(n &lt; 10\\) , пространственная сложность равна \\(O(1)\\) ; но когда \\(n &gt; 10\\) , инициализированный массив <code>nums</code> занимает \\(O(n)\\) пространства, поэтому худшая пространственная сложность равна \\(O(n)\\) .</li> <li>Ориентир на пиковое потребление памяти во время выполнения алгоритма: например, до выполнения последней строки программа занимает \\(O(1)\\) пространства; при инициализации массива <code>nums</code> она занимает \\(O(n)\\) пространства, поэтому худшая пространственная сложность равна \\(O(n)\\) .</li> </ol> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>def algorithm(n: int):\n    a = 0               # O(1)\n    b = [0] * 10000     # O(1)\n    if n &gt; 10:\n        nums = [0] * n  # O(n)\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 0;               // O(1)\n    vector&lt;int&gt; b(10000);    // O(1)\n    if (n &gt; 10)\n        vector&lt;int&gt; nums(n); // O(n)\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 0;                   // O(1)\n    int[] b = new int[10000];    // O(1)\n    if (n &gt; 10)\n        int[] nums = new int[n]; // O(n)\n}\n</code></pre> <pre><code>void Algorithm(int n) {\n    int a = 0;                   // O(1)\n    int[] b = new int[10000];    // O(1)\n    if (n &gt; 10) {\n        int[] nums = new int[n]; // O(n)\n    }\n}\n</code></pre> <pre><code>func algorithm(n int) {\n    a := 0                      // O(1)\n    b := make([]int, 10000)     // O(1)\n    var nums []int\n    if n &gt; 10 {\n        nums := make([]int, n)  // O(n)\n    }\n    fmt.Println(a, b, nums)\n}\n</code></pre> <pre><code>func algorithm(n: Int) {\n    let a = 0 // O(1)\n    let b = Array(repeating: 0, count: 10000) // O(1)\n    if n &gt; 10 {\n        let nums = Array(repeating: 0, count: n) // O(n)\n    }\n}\n</code></pre> <pre><code>function algorithm(n) {\n    const a = 0;                   // O(1)\n    const b = new Array(10000);    // O(1)\n    if (n &gt; 10) {\n        const nums = new Array(n); // O(n)\n    }\n}\n</code></pre> <pre><code>function algorithm(n: number): void {\n    const a = 0;                   // O(1)\n    const b = new Array(10000);    // O(1)\n    if (n &gt; 10) {\n        const nums = new Array(n); // O(n)\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n  int a = 0;                            // O(1)\n  List&lt;int&gt; b = List.filled(10000, 0);  // O(1)\n  if (n &gt; 10) {\n    List&lt;int&gt; nums = List.filled(n, 0); // O(n)\n  }\n}\n</code></pre> <pre><code>fn algorithm(n: i32) {\n    let a = 0;                              // O(1)\n    let b = [0; 10000];                     // O(1)\n    if n &gt; 10 {\n        let nums = vec![0; n as usize];     // O(n)\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 0;               // O(1)\n    int b[10000];            // O(1)\n    if (n &gt; 10)\n        int nums[n] = {0};   // O(n)\n}\n</code></pre> <pre><code>fun algorithm(n: Int) {\n    val a = 0                    // O(1)\n    val b = IntArray(10000)      // O(1)\n    if (n &gt; 10) {\n        val nums = IntArray(n)   // O(n)\n    }\n}\n</code></pre> <pre><code>def algorithm(n)\n    a = 0                           # O(1)\n    b = Array.new(10000)            # O(1)\n    nums = Array.new(n) if n &gt; 10   # O(n)\nend\n</code></pre> <p>В рекурсивных функциях необходимо учитывать пространство кадров стека. Рассмотрим следующий код:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>def function() -&gt; int:\n    # Выполнить некоторые операции\n    return 0\n\ndef loop(n: int):\n    \"\"\"Пространственная сложность цикла равна O(1)\"\"\"\n    for _ in range(n):\n        function()\n\ndef recur(n: int):\n    \"\"\"Пространственная сложность рекурсии равна O(n)\"\"\"\n    if n == 1:\n        return\n    return recur(n - 1)\n</code></pre> <pre><code>int func() {\n    // Выполнить некоторые операции\n    return 0;\n}\n/* Пространственная сложность цикла равна O(1) */\nvoid loop(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        func();\n    }\n}\n/* Пространственная сложность рекурсии равна O(n) */\nvoid recur(int n) {\n    if (n == 1) return;\n    recur(n - 1);\n}\n</code></pre> <pre><code>int function() {\n    // Выполнить некоторые операции\n    return 0;\n}\n/* Пространственная сложность цикла равна O(1) */\nvoid loop(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        function();\n    }\n}\n/* Пространственная сложность рекурсии равна O(n) */\nvoid recur(int n) {\n    if (n == 1) return;\n    recur(n - 1);\n}\n</code></pre> <pre><code>int Function() {\n    // Выполнить некоторые операции\n    return 0;\n}\n/* Пространственная сложность цикла равна O(1) */\nvoid Loop(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        Function();\n    }\n}\n/* Пространственная сложность рекурсии равна O(n) */\nint Recur(int n) {\n    if (n == 1) return 1;\n    return Recur(n - 1);\n}\n</code></pre> <pre><code>func function() int {\n    // Выполнить некоторые операции\n    return 0\n}\n\n/* Пространственная сложность цикла равна O(1) */\nfunc loop(n int) {\n    for i := 0; i &lt; n; i++ {\n        function()\n    }\n}\n\n/* Пространственная сложность рекурсии равна O(n) */\nfunc recur(n int) {\n    if n == 1 {\n        return\n    }\n    recur(n - 1)\n}\n</code></pre> <pre><code>@discardableResult\nfunc function() -&gt; Int {\n    // Выполнить некоторые операции\n    return 0\n}\n\n/* Пространственная сложность цикла равна O(1) */\nfunc loop(n: Int) {\n    for _ in 0 ..&lt; n {\n        function()\n    }\n}\n\n/* Пространственная сложность рекурсии равна O(n) */\nfunc recur(n: Int) {\n    if n == 1 {\n        return\n    }\n    recur(n: n - 1)\n}\n</code></pre> <pre><code>function constFunc() {\n    // Выполнить некоторые операции\n    return 0;\n}\n/* Пространственная сложность цикла равна O(1) */\nfunction loop(n) {\n    for (let i = 0; i &lt; n; i++) {\n        constFunc();\n    }\n}\n/* Пространственная сложность рекурсии равна O(n) */\nfunction recur(n) {\n    if (n === 1) return;\n    return recur(n - 1);\n}\n</code></pre> <pre><code>function constFunc(): number {\n    // Выполнить некоторые операции\n    return 0;\n}\n/* Пространственная сложность цикла равна O(1) */\nfunction loop(n: number): void {\n    for (let i = 0; i &lt; n; i++) {\n        constFunc();\n    }\n}\n/* Пространственная сложность рекурсии равна O(n) */\nfunction recur(n: number): void {\n    if (n === 1) return;\n    return recur(n - 1);\n}\n</code></pre> <pre><code>int function() {\n  // Выполнить некоторые операции\n  return 0;\n}\n/* Пространственная сложность цикла равна O(1) */\nvoid loop(int n) {\n  for (int i = 0; i &lt; n; i++) {\n    function();\n  }\n}\n/* Пространственная сложность рекурсии равна O(n) */\nvoid recur(int n) {\n  if (n == 1) return;\n  recur(n - 1);\n}\n</code></pre> <pre><code>fn function() -&gt; i32 {\n    // Выполнить некоторые операции\n    return 0;\n}\n/* Пространственная сложность цикла равна O(1) */\nfn loop(n: i32) {\n    for i in 0..n {\n        function();\n    }\n}\n/* Пространственная сложность рекурсии равна O(n) */\nfn recur(n: i32) {\n    if n == 1 {\n        return;\n    }\n    recur(n - 1);\n}\n</code></pre> <pre><code>int func() {\n    // Выполнить некоторые операции\n    return 0;\n}\n/* Пространственная сложность цикла равна O(1) */\nvoid loop(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        func();\n    }\n}\n/* Пространственная сложность рекурсии равна O(n) */\nvoid recur(int n) {\n    if (n == 1) return;\n    recur(n - 1);\n}\n</code></pre> <pre><code>fun function(): Int {\n    // Выполнить некоторые операции\n    return 0\n}\n/* Пространственная сложность цикла равна O(1) */\nfun loop(n: Int) {\n    for (i in 0..&lt;n) {\n        function()\n    }\n}\n/* Пространственная сложность рекурсии равна O(n) */\nfun recur(n: Int) {\n    if (n == 1) return\n    return recur(n - 1)\n}\n</code></pre> <pre><code>def function\n    # Выполнить некоторые операции\n    0\nend\n\n### Пространственная сложность цикла равна O(1) ###\ndef loop(n)\n    (0...n).each { function }\nend\n\n### Пространственная сложность рекурсии равна O(n) ###\ndef recur(n)\n    return if n == 1\n    recur(n - 1)\nend\n</code></pre> <p>Функции <code>loop()</code> и <code>recur()</code> имеют временную сложность \\(O(n)\\) , но их пространственная сложность различается.</p> <ul> <li>Функция <code>loop()</code> вызывает <code>function()</code> в цикле \\(n\\) раз; на каждой итерации <code>function()</code> возвращается и освобождает пространство своего кадра стека, поэтому пространственная сложность по-прежнему равна \\(O(1)\\) .</li> <li>Рекурсивная функция <code>recur()</code> во время выполнения одновременно содержит \\(n\\) еще не завершившихся экземпляров <code>recur()</code> , поэтому занимает \\(O(n)\\) пространства кадров стека.</li> </ul>","path":["Глава 2. Анализ сложности","2.4 &nbsp; Пространственная сложность"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#243","level":2,"title":"2.4.3   Распространенные типы","text":"<p>Пусть размер входных данных равен \\(n\\) . На рисунке 2-16 показаны распространенные типы пространственной сложности (в порядке от меньшей к большей).</p> \\[ \\begin{aligned} O(1) &lt; O(\\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \\newline \\text{Постоянная} &lt; \\text{Логарифмическая} &lt; \\text{Линейная} &lt; \\text{Квадратичная} &lt; \\text{Экспоненциальная} \\end{aligned} \\] <p></p> <p> Рисунок 2-16   Распространенные типы пространственной сложности </p>","path":["Глава 2. Анализ сложности","2.4 &nbsp; Пространственная сложность"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#1-o1","level":3,"title":"1.   Постоянная сложность \\(O(1)\\)","text":"<p>Постоянная сложность часто встречается у констант, переменных и объектов, количество которых не зависит от размера входных данных \\(n\\) .</p> <p>Следует заметить, что память, занятая инициализацией переменных или вызовом функций внутри цикла, освобождается при переходе к следующей итерации, поэтому она не накапливается, и пространственная сложность по-прежнему остается \\(O(1)\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby space_complexity.py<pre><code>def function() -&gt; int:\n    \"\"\"Функция\"\"\"\n    # Выполнить некоторые операции\n    return 0\n\ndef constant(n: int):\n    \"\"\"Постоянная сложность\"\"\"\n    # Константы, переменные и объекты занимают O(1) памяти\n    a = 0\n    nums = [0] * 10000\n    node = ListNode(0)\n    # Переменные в цикле занимают O(1) памяти\n    for _ in range(n):\n        c = 0\n    # Функции в цикле занимают O(1) памяти\n    for _ in range(n):\n        function()\n</code></pre> space_complexity.cpp<pre><code>/* Функция */\nint func() {\n    // Выполнить некоторые операции\n    return 0;\n}\n\n/* Постоянная сложность */\nvoid constant(int n) {\n    // Константы, переменные и объекты занимают O(1) памяти\n    const int a = 0;\n    int b = 0;\n    vector&lt;int&gt; nums(10000);\n    ListNode node(0);\n    // Переменные в цикле занимают O(1) памяти\n    for (int i = 0; i &lt; n; i++) {\n        int c = 0;\n    }\n    // Функции в цикле занимают O(1) памяти\n    for (int i = 0; i &lt; n; i++) {\n        func();\n    }\n}\n</code></pre> space_complexity.java<pre><code>/* Функция */\nint function() {\n    // Выполнить некоторые операции\n    return 0;\n}\n\n/* Постоянная сложность */\nvoid constant(int n) {\n    // Константы, переменные и объекты занимают O(1) памяти\n    final int a = 0;\n    int b = 0;\n    int[] nums = new int[10000];\n    ListNode node = new ListNode(0);\n    // Переменные в цикле занимают O(1) памяти\n    for (int i = 0; i &lt; n; i++) {\n        int c = 0;\n    }\n    // Функции в цикле занимают O(1) памяти\n    for (int i = 0; i &lt; n; i++) {\n        function();\n    }\n}\n</code></pre> space_complexity.cs<pre><code>/* Функция */\nint Function() {\n    // Выполнить некоторые операции\n    return 0;\n}\n\n/* Постоянная сложность */\nvoid Constant(int n) {\n    // Константы, переменные и объекты занимают O(1) памяти\n    int a = 0;\n    int b = 0;\n    int[] nums = new int[10000];\n    ListNode node = new(0);\n    // Переменные в цикле занимают O(1) памяти\n    for (int i = 0; i &lt; n; i++) {\n        int c = 0;\n    }\n    // Функции в цикле занимают O(1) памяти\n    for (int i = 0; i &lt; n; i++) {\n        Function();\n    }\n}\n</code></pre> space_complexity.go<pre><code>/* Функция */\nfunc function() int {\n    // Выполнить некоторые операции...\n    return 0\n}\n\n/* Постоянная сложность */\nfunc spaceConstant(n int) {\n    // Константы, переменные и объекты занимают O(1) памяти\n    const a = 0\n    b := 0\n    nums := make([]int, 10000)\n    node := newNode(0)\n    // Переменные в цикле занимают O(1) памяти\n    var c int\n    for i := 0; i &lt; n; i++ {\n        c = 0\n    }\n    // Функции в цикле занимают O(1) памяти\n    for i := 0; i &lt; n; i++ {\n        function()\n    }\n    b += 0\n    c += 0\n    nums[0] = 0\n    node.val = 0\n}\n</code></pre> space_complexity.swift<pre><code>/* Функция */\n@discardableResult\nfunc function() -&gt; Int {\n    // Выполнить некоторые операции\n    return 0\n}\n\n/* Постоянная сложность */\nfunc constant(n: Int) {\n    // Константы, переменные и объекты занимают O(1) памяти\n    let a = 0\n    var b = 0\n    let nums = Array(repeating: 0, count: 10000)\n    let node = ListNode(x: 0)\n    // Переменные в цикле занимают O(1) памяти\n    for _ in 0 ..&lt; n {\n        let c = 0\n    }\n    // Функции в цикле занимают O(1) памяти\n    for _ in 0 ..&lt; n {\n        function()\n    }\n}\n</code></pre> space_complexity.js<pre><code>/* Функция */\nfunction constFunc() {\n    // Выполнить некоторые операции\n    return 0;\n}\n\n/* Постоянная сложность */\nfunction constant(n) {\n    // Константы, переменные и объекты занимают O(1) памяти\n    const a = 0;\n    const b = 0;\n    const nums = new Array(10000);\n    const node = new ListNode(0);\n    // Переменные в цикле занимают O(1) памяти\n    for (let i = 0; i &lt; n; i++) {\n        const c = 0;\n    }\n    // Функции в цикле занимают O(1) памяти\n    for (let i = 0; i &lt; n; i++) {\n        constFunc();\n    }\n}\n</code></pre> space_complexity.ts<pre><code>/* Функция */\nfunction constFunc(): number {\n    // Выполнить некоторые операции\n    return 0;\n}\n\n/* Постоянная сложность */\nfunction constant(n: number): void {\n    // Константы, переменные и объекты занимают O(1) памяти\n    const a = 0;\n    const b = 0;\n    const nums = new Array(10000);\n    const node = new ListNode(0);\n    // Переменные в цикле занимают O(1) памяти\n    for (let i = 0; i &lt; n; i++) {\n        const c = 0;\n    }\n    // Функции в цикле занимают O(1) памяти\n    for (let i = 0; i &lt; n; i++) {\n        constFunc();\n    }\n}\n</code></pre> space_complexity.dart<pre><code>/* Функция */\nint function() {\n  // Выполнить некоторые операции\n  return 0;\n}\n\n/* Постоянная сложность */\nvoid constant(int n) {\n  // Константы, переменные и объекты занимают O(1) памяти\n  final int a = 0;\n  int b = 0;\n  List&lt;int&gt; nums = List.filled(10000, 0);\n  ListNode node = ListNode(0);\n  // Переменные в цикле занимают O(1) памяти\n  for (var i = 0; i &lt; n; i++) {\n    int c = 0;\n  }\n  // Функции в цикле занимают O(1) памяти\n  for (var i = 0; i &lt; n; i++) {\n    function();\n  }\n}\n</code></pre> space_complexity.rs<pre><code>/* Функция */\nfn function() -&gt; i32 {\n    // Выполнить некоторые операции\n    return 0;\n}\n\n/* Постоянная сложность */\n#[allow(unused)]\nfn constant(n: i32) {\n    // Константы, переменные и объекты занимают O(1) памяти\n    const A: i32 = 0;\n    let b = 0;\n    let nums = vec![0; 10000];\n    let node = ListNode::new(0);\n    // Переменные в цикле занимают O(1) памяти\n    for i in 0..n {\n        let c = 0;\n    }\n    // Функции в цикле занимают O(1) памяти\n    for i in 0..n {\n        function();\n    }\n}\n</code></pre> space_complexity.c<pre><code>/* Функция */\nint func() {\n    // Выполнить некоторые операции\n    return 0;\n}\n\n/* Постоянная сложность */\nvoid constant(int n) {\n    // Константы, переменные и объекты занимают O(1) памяти\n    const int a = 0;\n    int b = 0;\n    int nums[1000];\n    ListNode *node = newListNode(0);\n    free(node);\n    // Переменные в цикле занимают O(1) памяти\n    for (int i = 0; i &lt; n; i++) {\n        int c = 0;\n    }\n    // Функции в цикле занимают O(1) памяти\n    for (int i = 0; i &lt; n; i++) {\n        func();\n    }\n}\n</code></pre> space_complexity.kt<pre><code>/* Функция */\nfun function(): Int {\n    // Выполнить некоторые операции\n    return 0\n}\n\n/* Постоянная сложность */\nfun constant(n: Int) {\n    // Константы, переменные и объекты занимают O(1) памяти\n    val a = 0\n    var b = 0\n    val nums = Array(10000) { 0 }\n    val node = ListNode(0)\n    // Переменные в цикле занимают O(1) памяти\n    for (i in 0..&lt;n) {\n        val c = 0\n    }\n    // Функции в цикле занимают O(1) памяти\n    for (i in 0..&lt;n) {\n        function()\n    }\n}\n</code></pre> space_complexity.rb<pre><code>### Функция ###\ndef function\n  # Выполнить некоторые операции\n  0\nend\n\n### Постоянная сложность ###\ndef constant(n)\n  # Константы, переменные и объекты занимают O(1) памяти\n  a = 0\n  nums = [0] * 10000\n  node = ListNode.new\n\n  # Переменные в цикле занимают O(1) памяти\n  (0...n).each { c = 0 }\n  # Функции в цикле занимают O(1) памяти\n  (0...n).each { function }\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 2. Анализ сложности","2.4 &nbsp; Пространственная сложность"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#2-on","level":3,"title":"2.   Линейная сложность \\(O(n)\\)","text":"<p>Линейная сложность часто встречается у массивов, связных списков, стеков, очередей и других структур, число элементов в которых пропорционально \\(n\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby space_complexity.py<pre><code>def linear(n: int):\n    \"\"\"Линейная сложность\"\"\"\n    # Список длины n занимает O(n) памяти\n    nums = [0] * n\n    # Хеш-таблица длины n занимает O(n) памяти\n    hmap = dict[int, str]()\n    for i in range(n):\n        hmap[i] = str(i)\n</code></pre> space_complexity.cpp<pre><code>/* Линейная сложность */\nvoid linear(int n) {\n    // Массив длины n занимает O(n) памяти\n    vector&lt;int&gt; nums(n);\n    // Список длины n занимает O(n) памяти\n    vector&lt;ListNode&gt; nodes;\n    for (int i = 0; i &lt; n; i++) {\n        nodes.push_back(ListNode(i));\n    }\n    // Хеш-таблица длины n занимает O(n) памяти\n    unordered_map&lt;int, string&gt; map;\n    for (int i = 0; i &lt; n; i++) {\n        map[i] = to_string(i);\n    }\n}\n</code></pre> space_complexity.java<pre><code>/* Линейная сложность */\nvoid linear(int n) {\n    // Массив длины n занимает O(n) памяти\n    int[] nums = new int[n];\n    // Список длины n занимает O(n) памяти\n    List&lt;ListNode&gt; nodes = new ArrayList&lt;&gt;();\n    for (int i = 0; i &lt; n; i++) {\n        nodes.add(new ListNode(i));\n    }\n    // Хеш-таблица длины n занимает O(n) памяти\n    Map&lt;Integer, String&gt; map = new HashMap&lt;&gt;();\n    for (int i = 0; i &lt; n; i++) {\n        map.put(i, String.valueOf(i));\n    }\n}\n</code></pre> space_complexity.cs<pre><code>/* Линейная сложность */\nvoid Linear(int n) {\n    // Массив длины n занимает O(n) памяти\n    int[] nums = new int[n];\n    // Список длины n занимает O(n) памяти\n    List&lt;ListNode&gt; nodes = [];\n    for (int i = 0; i &lt; n; i++) {\n        nodes.Add(new ListNode(i));\n    }\n    // Хеш-таблица длины n занимает O(n) памяти\n    Dictionary&lt;int, string&gt; map = [];\n    for (int i = 0; i &lt; n; i++) {\n        map.Add(i, i.ToString());\n    }\n}\n</code></pre> space_complexity.go<pre><code>/* Линейная сложность */\nfunc spaceLinear(n int) {\n    // Массив длины n занимает O(n) памяти\n    _ = make([]int, n)\n    // Список длины n занимает O(n) памяти\n    var nodes []*node\n    for i := 0; i &lt; n; i++ {\n        nodes = append(nodes, newNode(i))\n    }\n    // Хеш-таблица длины n занимает O(n) памяти\n    m := make(map[int]string, n)\n    for i := 0; i &lt; n; i++ {\n        m[i] = strconv.Itoa(i)\n    }\n}\n</code></pre> space_complexity.swift<pre><code>/* Линейная сложность */\nfunc linear(n: Int) {\n    // Массив длины n занимает O(n) памяти\n    let nums = Array(repeating: 0, count: n)\n    // Список длины n занимает O(n) памяти\n    let nodes = (0 ..&lt; n).map { ListNode(x: $0) }\n    // Хеш-таблица длины n занимает O(n) памяти\n    let map = Dictionary(uniqueKeysWithValues: (0 ..&lt; n).map { ($0, \"\\($0)\") })\n}\n</code></pre> space_complexity.js<pre><code>/* Линейная сложность */\nfunction linear(n) {\n    // Массив длины n занимает O(n) памяти\n    const nums = new Array(n);\n    // Список длины n занимает O(n) памяти\n    const nodes = [];\n    for (let i = 0; i &lt; n; i++) {\n        nodes.push(new ListNode(i));\n    }\n    // Хеш-таблица длины n занимает O(n) памяти\n    const map = new Map();\n    for (let i = 0; i &lt; n; i++) {\n        map.set(i, i.toString());\n    }\n}\n</code></pre> space_complexity.ts<pre><code>/* Линейная сложность */\nfunction linear(n: number): void {\n    // Массив длины n занимает O(n) памяти\n    const nums = new Array(n);\n    // Список длины n занимает O(n) памяти\n    const nodes: ListNode[] = [];\n    for (let i = 0; i &lt; n; i++) {\n        nodes.push(new ListNode(i));\n    }\n    // Хеш-таблица длины n занимает O(n) памяти\n    const map = new Map();\n    for (let i = 0; i &lt; n; i++) {\n        map.set(i, i.toString());\n    }\n}\n</code></pre> space_complexity.dart<pre><code>/* Линейная сложность */\nvoid linear(int n) {\n  // Массив длины n занимает O(n) памяти\n  List&lt;int&gt; nums = List.filled(n, 0);\n  // Список длины n занимает O(n) памяти\n  List&lt;ListNode&gt; nodes = [];\n  for (var i = 0; i &lt; n; i++) {\n    nodes.add(ListNode(i));\n  }\n  // Хеш-таблица длины n занимает O(n) памяти\n  Map&lt;int, String&gt; map = HashMap();\n  for (var i = 0; i &lt; n; i++) {\n    map.putIfAbsent(i, () =&gt; i.toString());\n  }\n}\n</code></pre> space_complexity.rs<pre><code>/* Линейная сложность */\n#[allow(unused)]\nfn linear(n: i32) {\n    // Массив длины n занимает O(n) памяти\n    let mut nums = vec![0; n as usize];\n    // Список длины n занимает O(n) памяти\n    let mut nodes = Vec::new();\n    for i in 0..n {\n        nodes.push(ListNode::new(i))\n    }\n    // Хеш-таблица длины n занимает O(n) памяти\n    let mut map = HashMap::new();\n    for i in 0..n {\n        map.insert(i, i.to_string());\n    }\n}\n</code></pre> space_complexity.c<pre><code>/* Хеш-таблица */\ntypedef struct {\n    int key;\n    int val;\n    UT_hash_handle hh; // Реализовано на основе uthash.h\n} HashTable;\n\n/* Линейная сложность */\nvoid linear(int n) {\n    // Массив длины n занимает O(n) памяти\n    int *nums = malloc(sizeof(int) * n);\n    free(nums);\n\n    // Список длины n занимает O(n) памяти\n    ListNode **nodes = malloc(sizeof(ListNode *) * n);\n    for (int i = 0; i &lt; n; i++) {\n        nodes[i] = newListNode(i);\n    }\n    // Освобождение памяти\n    for (int i = 0; i &lt; n; i++) {\n        free(nodes[i]);\n    }\n    free(nodes);\n\n    // Хеш-таблица длины n занимает O(n) памяти\n    HashTable *h = NULL;\n    for (int i = 0; i &lt; n; i++) {\n        HashTable *tmp = malloc(sizeof(HashTable));\n        tmp-&gt;key = i;\n        tmp-&gt;val = i;\n        HASH_ADD_INT(h, key, tmp);\n    }\n\n    // Освобождение памяти\n    HashTable *curr, *tmp;\n    HASH_ITER(hh, h, curr, tmp) {\n        HASH_DEL(h, curr);\n        free(curr);\n    }\n}\n</code></pre> space_complexity.kt<pre><code>/* Линейная сложность */\nfun linear(n: Int) {\n    // Массив длины n занимает O(n) памяти\n    val nums = Array(n) { 0 }\n    // Список длины n занимает O(n) памяти\n    val nodes = mutableListOf&lt;ListNode&gt;()\n    for (i in 0..&lt;n) {\n        nodes.add(ListNode(i))\n    }\n    // Хеш-таблица длины n занимает O(n) памяти\n    val map = mutableMapOf&lt;Int, String&gt;()\n    for (i in 0..&lt;n) {\n        map[i] = i.toString()\n    }\n}\n</code></pre> space_complexity.rb<pre><code>### Линейная сложность ###\ndef linear(n)\n  # Список длины n занимает O(n) памяти\n  nums = Array.new(n, 0)\n\n  # Хеш-таблица длины n занимает O(n) памяти\n  hmap = {}\n  for i in 0...n\n    hmap[i] = i.to_s\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Как показано на рисунке 2-17, глубина рекурсии этой функции равна \\(n\\) , то есть одновременно существует \\(n\\) еще не завершившихся функций <code>linear_recur()</code> , которые используют \\(O(n)\\) пространства кадров стека:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby space_complexity.py<pre><code>def linear_recur(n: int):\n    \"\"\"Линейная сложность (рекурсивная реализация)\"\"\"\n    print(\"Рекурсия n =\", n)\n    if n == 1:\n        return\n    linear_recur(n - 1)\n</code></pre> space_complexity.cpp<pre><code>/* Линейная сложность (рекурсивная реализация) */\nvoid linearRecur(int n) {\n    cout &lt;&lt; \"Рекурсия n = \" &lt;&lt; n &lt;&lt; endl;\n    if (n == 1)\n        return;\n    linearRecur(n - 1);\n}\n</code></pre> space_complexity.java<pre><code>/* Линейная сложность (рекурсивная реализация) */\nvoid linearRecur(int n) {\n    System.out.println(\"Рекурсия n = \" + n);\n    if (n == 1)\n        return;\n    linearRecur(n - 1);\n}\n</code></pre> space_complexity.cs<pre><code>/* Линейная сложность (рекурсивная реализация) */\nvoid LinearRecur(int n) {\n    Console.WriteLine(\"Рекурсия n = \" + n);\n    if (n == 1) return;\n    LinearRecur(n - 1);\n}\n</code></pre> space_complexity.go<pre><code>/* Линейная сложность (рекурсивная реализация) */\nfunc spaceLinearRecur(n int) {\n    fmt.Println(\"Рекурсия n =\", n)\n    if n == 1 {\n        return\n    }\n    spaceLinearRecur(n - 1)\n}\n</code></pre> space_complexity.swift<pre><code>/* Линейная сложность (рекурсивная реализация) */\nfunc linearRecur(n: Int) {\n    print(\"Рекурсия n = \\(n)\")\n    if n == 1 {\n        return\n    }\n    linearRecur(n: n - 1)\n}\n</code></pre> space_complexity.js<pre><code>/* Линейная сложность (рекурсивная реализация) */\nfunction linearRecur(n) {\n    console.log(`Рекурсия n = ${n}`);\n    if (n === 1) return;\n    linearRecur(n - 1);\n}\n</code></pre> space_complexity.ts<pre><code>/* Линейная сложность (рекурсивная реализация) */\nfunction linearRecur(n: number): void {\n    console.log(`Рекурсия n = ${n}`);\n    if (n === 1) return;\n    linearRecur(n - 1);\n}\n</code></pre> space_complexity.dart<pre><code>/* Линейная сложность (рекурсивная реализация) */\nvoid linearRecur(int n) {\n  print('Рекурсия n = $n');\n  if (n == 1) return;\n  linearRecur(n - 1);\n}\n</code></pre> space_complexity.rs<pre><code>/* Линейная сложность (рекурсивная реализация) */\nfn linear_recur(n: i32) {\n    println!(\"Рекурсия n = {}\", n);\n    if n == 1 {\n        return;\n    };\n    linear_recur(n - 1);\n}\n</code></pre> space_complexity.c<pre><code>/* Линейная сложность (рекурсивная реализация) */\nvoid linearRecur(int n) {\n    printf(\"Рекурсия n = %d\\r\\n\", n);\n    if (n == 1)\n        return;\n    linearRecur(n - 1);\n}\n</code></pre> space_complexity.kt<pre><code>/* Линейная сложность (рекурсивная реализация) */\nfun linearRecur(n: Int) {\n    println(\"Рекурсия n = $n\")\n    if (n == 1)\n        return\n    linearRecur(n - 1)\n}\n</code></pre> space_complexity.rb<pre><code>### Линейная сложность ###\ndef linear(n)\n  # Список длины n занимает O(n) памяти\n  nums = Array.new(n, 0)\n\n  # Хеш-таблица длины n занимает O(n) памяти\n  hmap = {}\n  for i in 0...n\n    hmap[i] = i.to_s\n  end\nend\n\n# ## Линейная сложность (рекурсивная реализация) ###\ndef linear_recur(n)\n  puts \"Рекурсия n = #{n}\"\n  return if n == 1\n  linear_recur(n - 1)\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p></p> <p> Рисунок 2-17   Линейная пространственная сложность, порождаемая рекурсивной функцией </p>","path":["Глава 2. Анализ сложности","2.4 &nbsp; Пространственная сложность"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#3-on2","level":3,"title":"3.   Квадратичная сложность \\(O(n^2)\\)","text":"<p>Квадратичная сложность часто встречается у матриц и графов, где число элементов связано с \\(n\\) квадратичной зависимостью:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby space_complexity.py<pre><code>def quadratic(n: int):\n    \"\"\"Квадратичная сложность\"\"\"\n    # Двумерный список занимает O(n^2) памяти\n    num_matrix = [[0] * n for _ in range(n)]\n</code></pre> space_complexity.cpp<pre><code>/* Квадратичная сложность */\nvoid quadratic(int n) {\n    // Двумерный список занимает O(n^2) памяти\n    vector&lt;vector&lt;int&gt;&gt; numMatrix;\n    for (int i = 0; i &lt; n; i++) {\n        vector&lt;int&gt; tmp;\n        for (int j = 0; j &lt; n; j++) {\n            tmp.push_back(0);\n        }\n        numMatrix.push_back(tmp);\n    }\n}\n</code></pre> space_complexity.java<pre><code>/* Квадратичная сложность */\nvoid quadratic(int n) {\n    // Матрица занимает O(n^2) памяти\n    int[][] numMatrix = new int[n][n];\n    // Двумерный список занимает O(n^2) памяти\n    List&lt;List&lt;Integer&gt;&gt; numList = new ArrayList&lt;&gt;();\n    for (int i = 0; i &lt; n; i++) {\n        List&lt;Integer&gt; tmp = new ArrayList&lt;&gt;();\n        for (int j = 0; j &lt; n; j++) {\n            tmp.add(0);\n        }\n        numList.add(tmp);\n    }\n}\n</code></pre> space_complexity.cs<pre><code>/* Квадратичная сложность */\nvoid Quadratic(int n) {\n    // Матрица занимает O(n^2) памяти\n    int[,] numMatrix = new int[n, n];\n    // Двумерный список занимает O(n^2) памяти\n    List&lt;List&lt;int&gt;&gt; numList = [];\n    for (int i = 0; i &lt; n; i++) {\n        List&lt;int&gt; tmp = [];\n        for (int j = 0; j &lt; n; j++) {\n            tmp.Add(0);\n        }\n        numList.Add(tmp);\n    }\n}\n</code></pre> space_complexity.go<pre><code>/* Квадратичная сложность */\nfunc spaceQuadratic(n int) {\n    // Матрица занимает O(n^2) памяти\n    numMatrix := make([][]int, n)\n    for i := 0; i &lt; n; i++ {\n        numMatrix[i] = make([]int, n)\n    }\n}\n</code></pre> space_complexity.swift<pre><code>/* Квадратичная сложность */\nfunc quadratic(n: Int) {\n    // Двумерный список занимает O(n^2) памяти\n    let numList = Array(repeating: Array(repeating: 0, count: n), count: n)\n}\n</code></pre> space_complexity.js<pre><code>/* Квадратичная сложность */\nfunction quadratic(n) {\n    // Матрица занимает O(n^2) памяти\n    const numMatrix = Array(n)\n        .fill(null)\n        .map(() =&gt; Array(n).fill(null));\n    // Двумерный список занимает O(n^2) памяти\n    const numList = [];\n    for (let i = 0; i &lt; n; i++) {\n        const tmp = [];\n        for (let j = 0; j &lt; n; j++) {\n            tmp.push(0);\n        }\n        numList.push(tmp);\n    }\n}\n</code></pre> space_complexity.ts<pre><code>/* Квадратичная сложность */\nfunction quadratic(n: number): void {\n    // Матрица занимает O(n^2) памяти\n    const numMatrix = Array(n)\n        .fill(null)\n        .map(() =&gt; Array(n).fill(null));\n    // Двумерный список занимает O(n^2) памяти\n    const numList = [];\n    for (let i = 0; i &lt; n; i++) {\n        const tmp = [];\n        for (let j = 0; j &lt; n; j++) {\n            tmp.push(0);\n        }\n        numList.push(tmp);\n    }\n}\n</code></pre> space_complexity.dart<pre><code>/* Квадратичная сложность */\nvoid quadratic(int n) {\n  // Матрица занимает O(n^2) памяти\n  List&lt;List&lt;int&gt;&gt; numMatrix = List.generate(n, (_) =&gt; List.filled(n, 0));\n  // Двумерный список занимает O(n^2) памяти\n  List&lt;List&lt;int&gt;&gt; numList = [];\n  for (var i = 0; i &lt; n; i++) {\n    List&lt;int&gt; tmp = [];\n    for (int j = 0; j &lt; n; j++) {\n      tmp.add(0);\n    }\n    numList.add(tmp);\n  }\n}\n</code></pre> space_complexity.rs<pre><code>/* Квадратичная сложность */\n#[allow(unused)]\nfn quadratic(n: i32) {\n    // Матрица занимает O(n^2) памяти\n    let num_matrix = vec![vec![0; n as usize]; n as usize];\n    // Двумерный список занимает O(n^2) памяти\n    let mut num_list = Vec::new();\n    for i in 0..n {\n        let mut tmp = Vec::new();\n        for j in 0..n {\n            tmp.push(0);\n        }\n        num_list.push(tmp);\n    }\n}\n</code></pre> space_complexity.c<pre><code>/* Квадратичная сложность */\nvoid quadratic(int n) {\n    // Двумерный список занимает O(n^2) памяти\n    int **numMatrix = malloc(sizeof(int *) * n);\n    for (int i = 0; i &lt; n; i++) {\n        int *tmp = malloc(sizeof(int) * n);\n        for (int j = 0; j &lt; n; j++) {\n            tmp[j] = 0;\n        }\n        numMatrix[i] = tmp;\n    }\n\n    // Освобождение памяти\n    for (int i = 0; i &lt; n; i++) {\n        free(numMatrix[i]);\n    }\n    free(numMatrix);\n}\n</code></pre> space_complexity.kt<pre><code>/* Квадратичная сложность */\nfun quadratic(n: Int) {\n    // Матрица занимает O(n^2) памяти\n    val numMatrix = arrayOfNulls&lt;Array&lt;Int&gt;?&gt;(n)\n    // Двумерный список занимает O(n^2) памяти\n    val numList = mutableListOf&lt;MutableList&lt;Int&gt;&gt;()\n    for (i in 0..&lt;n) {\n        val tmp = mutableListOf&lt;Int&gt;()\n        for (j in 0..&lt;n) {\n            tmp.add(0)\n        }\n        numList.add(tmp)\n    }\n}\n</code></pre> space_complexity.rb<pre><code>### Квадратичная сложность ###\ndef quadratic(n)\n  # Двумерный список занимает O(n^2) памяти\n  Array.new(n) { Array.new(n, 0) }\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Как показано на рисунке 2-18, глубина рекурсии этой функции равна \\(n\\) , и в каждой рекурсивной функции инициализируется массив длины \\(n\\) , \\(n-1\\) , \\(\\dots\\) , \\(2\\) , \\(1\\) ; его средняя длина равна \\(n / 2\\) , поэтому в сумме используется \\(O(n^2)\\) пространства:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby space_complexity.py<pre><code>def quadratic_recur(n: int) -&gt; int:\n    \"\"\"Квадратичная сложность (рекурсивная реализация)\"\"\"\n    if n &lt;= 0:\n        return 0\n    # Длина массива nums равна n, n-1, ..., 2, 1\n    nums = [0] * n\n    return quadratic_recur(n - 1)\n</code></pre> space_complexity.cpp<pre><code>/* Квадратичная сложность (рекурсивная реализация) */\nint quadraticRecur(int n) {\n    if (n &lt;= 0)\n        return 0;\n    vector&lt;int&gt; nums(n);\n    cout &lt;&lt; \"Рекурсия n = \" &lt;&lt; n &lt;&lt; \" , длина nums = \" &lt;&lt; nums.size() &lt;&lt; endl;\n    return quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.java<pre><code>/* Квадратичная сложность (рекурсивная реализация) */\nint quadraticRecur(int n) {\n    if (n &lt;= 0)\n        return 0;\n    // Длина массива nums равна n, n-1, ..., 2, 1\n    int[] nums = new int[n];\n    System.out.println(\"В рекурсии n = \" + n + \", длина nums = \" + nums.length);\n    return quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.cs<pre><code>/* Квадратичная сложность (рекурсивная реализация) */\nint QuadraticRecur(int n) {\n    if (n &lt;= 0) return 0;\n    int[] nums = new int[n];\n    Console.WriteLine(\"В рекурсии n = \" + n + \", длина nums = \" + nums.Length);\n    return QuadraticRecur(n - 1);\n}\n</code></pre> space_complexity.go<pre><code>/* Квадратичная сложность (рекурсивная реализация) */\nfunc spaceQuadraticRecur(n int) int {\n    if n &lt;= 0 {\n        return 0\n    }\n    nums := make([]int, n)\n    fmt.Printf(\"В рекурсии n = %d, длина nums = %d\\n\", n, len(nums))\n    return spaceQuadraticRecur(n - 1)\n}\n</code></pre> space_complexity.swift<pre><code>/* Квадратичная сложность (рекурсивная реализация) */\n@discardableResult\nfunc quadraticRecur(n: Int) -&gt; Int {\n    if n &lt;= 0 {\n        return 0\n    }\n    // Длина массива nums равна n, n-1, ..., 2, 1\n    let nums = Array(repeating: 0, count: n)\n    print(\"В рекурсии n = \\(n), длина nums = \\(nums.count)\")\n    return quadraticRecur(n: n - 1)\n}\n</code></pre> space_complexity.js<pre><code>/* Квадратичная сложность (рекурсивная реализация) */\nfunction quadraticRecur(n) {\n    if (n &lt;= 0) return 0;\n    const nums = new Array(n);\n    console.log(`В рекурсии n = ${n} длина nums = ${nums.length}`);\n    return quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.ts<pre><code>/* Квадратичная сложность (рекурсивная реализация) */\nfunction quadraticRecur(n: number): number {\n    if (n &lt;= 0) return 0;\n    const nums = new Array(n);\n    console.log(`В рекурсии n = ${n} длина nums = ${nums.length}`);\n    return quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.dart<pre><code>/* Квадратичная сложность (рекурсивная реализация) */\nint quadraticRecur(int n) {\n  if (n &lt;= 0) return 0;\n  List&lt;int&gt; nums = List.filled(n, 0);\n  print('В рекурсии n = $n длина nums = ${nums.length}');\n  return quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.rs<pre><code>/* Квадратичная сложность (рекурсивная реализация) */\nfn quadratic_recur(n: i32) -&gt; i32 {\n    if n &lt;= 0 {\n        return 0;\n    };\n    // Длина массива nums равна n, n-1, ..., 2, 1\n    let nums = vec![0; n as usize];\n    println!(\"В рекурсии n = {} , длина nums = {}\", n, nums.len());\n    return quadratic_recur(n - 1);\n}\n</code></pre> space_complexity.c<pre><code>/* Квадратичная сложность (рекурсивная реализация) */\nint quadraticRecur(int n) {\n    if (n &lt;= 0)\n        return 0;\n    int *nums = malloc(sizeof(int) * n);\n    printf(\"Рекурсия n = %d, длина nums = %d\\r\\n\", n, n);\n    int res = quadraticRecur(n - 1);\n    free(nums);\n    return res;\n}\n</code></pre> space_complexity.kt<pre><code>/* Квадратичная сложность (рекурсивная реализация) */\ntailrec fun quadraticRecur(n: Int): Int {\n    if (n &lt;= 0)\n        return 0\n    // Длина массива nums равна n, n-1, ..., 2, 1\n    val nums = Array(n) { 0 }\n    println(\"В рекурсии n = $n длина nums = ${nums.size}\")\n    return quadraticRecur(n - 1)\n}\n</code></pre> space_complexity.rb<pre><code>### Квадратичная сложность ###\ndef quadratic(n)\n  # Двумерный список занимает O(n^2) памяти\n  Array.new(n) { Array.new(n, 0) }\nend\n\n# ## Квадратичная сложность (рекурсивная реализация) ###\ndef quadratic_recur(n)\n  return 0 unless n &gt; 0\n\n  # Длина массива nums равна n, n-1, ..., 2, 1\n  nums = Array.new(n, 0)\n  quadratic_recur(n - 1)\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p></p> <p> Рисунок 2-18   Квадратичная пространственная сложность, порождаемая рекурсивной функцией </p>","path":["Глава 2. Анализ сложности","2.4 &nbsp; Пространственная сложность"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#4-o2n","level":3,"title":"4.   Экспоненциальная сложность \\(O(2^n)\\)","text":"<p>Экспоненциальная сложность часто встречается у бинарных деревьев. Обрати внимание на рисунок 2-19: \"полное бинарное дерево\" с \\(n\\) уровнями содержит \\(2^n - 1\\) узлов и занимает \\(O(2^n)\\) пространства:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby space_complexity.py<pre><code>def build_tree(n: int) -&gt; TreeNode | None:\n    \"\"\"Экспоненциальная сложность (построение полного двоичного дерева)\"\"\"\n    if n == 0:\n        return None\n    root = TreeNode(0)\n    root.left = build_tree(n - 1)\n    root.right = build_tree(n - 1)\n    return root\n</code></pre> space_complexity.cpp<pre><code>/* Экспоненциальная сложность (построение полного двоичного дерева) */\nTreeNode *buildTree(int n) {\n    if (n == 0)\n        return nullptr;\n    TreeNode *root = new TreeNode(0);\n    root-&gt;left = buildTree(n - 1);\n    root-&gt;right = buildTree(n - 1);\n    return root;\n}\n</code></pre> space_complexity.java<pre><code>/* Экспоненциальная сложность (построение полного двоичного дерева) */\nTreeNode buildTree(int n) {\n    if (n == 0)\n        return null;\n    TreeNode root = new TreeNode(0);\n    root.left = buildTree(n - 1);\n    root.right = buildTree(n - 1);\n    return root;\n}\n</code></pre> space_complexity.cs<pre><code>/* Экспоненциальная сложность (построение полного двоичного дерева) */\nTreeNode? BuildTree(int n) {\n    if (n == 0) return null;\n    TreeNode root = new(0) {\n        left = BuildTree(n - 1),\n        right = BuildTree(n - 1)\n    };\n    return root;\n}\n</code></pre> space_complexity.go<pre><code>/* Экспоненциальная сложность (построение полного двоичного дерева) */\nfunc buildTree(n int) *TreeNode {\n    if n == 0 {\n        return nil\n    }\n    root := NewTreeNode(0)\n    root.Left = buildTree(n - 1)\n    root.Right = buildTree(n - 1)\n    return root\n}\n</code></pre> space_complexity.swift<pre><code>/* Экспоненциальная сложность (построение полного двоичного дерева) */\nfunc buildTree(n: Int) -&gt; TreeNode? {\n    if n == 0 {\n        return nil\n    }\n    let root = TreeNode(x: 0)\n    root.left = buildTree(n: n - 1)\n    root.right = buildTree(n: n - 1)\n    return root\n}\n</code></pre> space_complexity.js<pre><code>/* Экспоненциальная сложность (построение полного двоичного дерева) */\nfunction buildTree(n) {\n    if (n === 0) return null;\n    const root = new TreeNode(0);\n    root.left = buildTree(n - 1);\n    root.right = buildTree(n - 1);\n    return root;\n}\n</code></pre> space_complexity.ts<pre><code>/* Экспоненциальная сложность (построение полного двоичного дерева) */\nfunction buildTree(n: number): TreeNode | null {\n    if (n === 0) return null;\n    const root = new TreeNode(0);\n    root.left = buildTree(n - 1);\n    root.right = buildTree(n - 1);\n    return root;\n}\n</code></pre> space_complexity.dart<pre><code>/* Экспоненциальная сложность (построение полного двоичного дерева) */\nTreeNode? buildTree(int n) {\n  if (n == 0) return null;\n  TreeNode root = TreeNode(0);\n  root.left = buildTree(n - 1);\n  root.right = buildTree(n - 1);\n  return root;\n}\n</code></pre> space_complexity.rs<pre><code>/* Экспоненциальная сложность (построение полного двоичного дерева) */\nfn build_tree(n: i32) -&gt; Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt; {\n    if n == 0 {\n        return None;\n    };\n    let root = TreeNode::new(0);\n    root.borrow_mut().left = build_tree(n - 1);\n    root.borrow_mut().right = build_tree(n - 1);\n    return Some(root);\n}\n</code></pre> space_complexity.c<pre><code>/* Экспоненциальная сложность (построение полного двоичного дерева) */\nTreeNode *buildTree(int n) {\n    if (n == 0)\n        return NULL;\n    TreeNode *root = newTreeNode(0);\n    root-&gt;left = buildTree(n - 1);\n    root-&gt;right = buildTree(n - 1);\n    return root;\n}\n</code></pre> space_complexity.kt<pre><code>/* Экспоненциальная сложность (построение полного двоичного дерева) */\nfun buildTree(n: Int): TreeNode? {\n    if (n == 0)\n        return null\n    val root = TreeNode(0)\n    root.left = buildTree(n - 1)\n    root.right = buildTree(n - 1)\n    return root\n}\n</code></pre> space_complexity.rb<pre><code>### Квадратичная сложность ###\ndef quadratic(n)\n  # Двумерный список занимает O(n^2) памяти\n  Array.new(n) { Array.new(n, 0) }\nend\n\n# ## Квадратичная сложность (рекурсивная реализация) ###\ndef quadratic_recur(n)\n  return 0 unless n &gt; 0\n\n  # Длина массива nums равна n, n-1, ..., 2, 1\n  nums = Array.new(n, 0)\n  quadratic_recur(n - 1)\nend\n\n# ## Экспоненциальная сложность (построение полного двоичного дерева) ###\ndef build_tree(n)\n  return if n == 0\n\n  TreeNode.new.tap do |root|\n    root.left = build_tree(n - 1)\n    root.right = build_tree(n - 1)\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p></p> <p> Рисунок 2-19   Экспоненциальная пространственная сложность, порождаемая полным бинарным деревом </p>","path":["Глава 2. Анализ сложности","2.4 &nbsp; Пространственная сложность"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#5-olog-n","level":3,"title":"5.   Логарифмическая сложность \\(O(\\log n)\\)","text":"<p>Логарифмическая сложность часто встречается в алгоритмах \"разделяй и властвуй\". Например, при сортировке слиянием входной массив длины \\(n\\) на каждом шаге рекурсии делится пополам по середине, образуя рекурсивное дерево высоты \\(\\log n\\) и используя \\(O(\\log n)\\) пространства кадров стека.</p> <p>Еще один пример - преобразование числа в строку. Если задано положительное целое число \\(n\\) , то количество его цифр равно \\(\\lfloor \\log_{10} n \\rfloor + 1\\) , то есть длина соответствующей строки тоже равна \\(\\lfloor \\log_{10} n \\rfloor + 1\\) , следовательно, пространственная сложность составляет \\(O(\\log_{10} n + 1) = O(\\log n)\\) .</p>","path":["Глава 2. Анализ сложности","2.4 &nbsp; Пространственная сложность"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#244","level":2,"title":"2.4.4   Компромисс между временем и пространством","text":"<p>В идеале нам хотелось бы, чтобы и временная, и пространственная сложность алгоритма были оптимальными. Однако на практике одновременно оптимизировать и время, и память обычно очень трудно.</p> <p>Снижение временной сложности обычно достигается ценой увеличения пространственной сложности, и наоборот. Подход, при котором мы жертвуем памятью ради ускорения работы алгоритма, называется \"обмен пространства на время\"; обратный подход называется \"обмен времени на пространство\".</p> <p>Выбор между этими двумя идеями зависит от того, что для нас важнее. В большинстве случаев время ценнее памяти, поэтому стратегия \"обмена пространства на время\" используется чаще. Но при очень больших объемах данных контроль пространственной сложности тоже становится крайне важным.</p>","path":["Глава 2. Анализ сложности","2.4 &nbsp; Пространственная сложность"],"tags":[]},{"location":"chapter_computational_complexity/summary/","level":1,"title":"2.5   Резюме","text":"","path":["Глава 2. Анализ сложности","2.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_computational_complexity/summary/#1","level":3,"title":"1.   Ключевые выводы","text":"<p>Оценка эффективности алгоритмов</p> <ul> <li>Временная эффективность и пространственная эффективность - два главных показателя, по которым оценивают качество алгоритма.</li> <li>Мы можем оценивать эффективность алгоритма с помощью практического тестирования, но при этом трудно устранить влияние тестовой среды, а само тестирование потребляет много вычислительных ресурсов.</li> <li>Анализ сложности устраняет недостатки практического тестирования, дает результаты, применимые ко всем платформам выполнения, и позволяет увидеть эффективность алгоритма при разных масштабах данных.</li> </ul> <p>Временная сложность</p> <ul> <li>Временная сложность используется для оценки того, как меняется время работы алгоритма с ростом объема данных. Она хорошо подходит для оценки эффективности, но в некоторых случаях может давать недостаточно точное сравнение, например когда входные данные малы или когда временные сложности совпадают.</li> <li>Худшая временная сложность обозначается с помощью нотации Big \\(O\\) и соответствует асимптотической верхней границе функции, отражая уровень роста числа операций \\(T(n)\\) при стремлении \\(n\\) к положительной бесконечности.</li> <li>Вывод временной сложности включает два шага: сначала подсчитывается число операций, затем определяется асимптотическая верхняя граница.</li> <li>Распространенные временные сложности в порядке роста: \\(O(1)\\), \\(O(\\log n)\\), \\(O(n)\\), \\(O(n \\log n)\\), \\(O(n^2)\\), \\(O(2^n)\\) и \\(O(n!)\\).</li> <li>Временная сложность некоторых алгоритмов не фиксирована, а зависит от распределения входных данных. Различают худшую, лучшую и среднюю временную сложность; лучшая временная сложность используется редко, потому что для ее достижения вход обычно должен удовлетворять строгим условиям.</li> <li>Средняя временная сложность отражает эффективность алгоритма на случайных входных данных и ближе всего к его поведению в практических сценариях. Для ее вычисления нужно знать распределение входных данных и рассчитать соответствующее математическое ожидание.</li> </ul> <p>Пространственная сложность</p> <ul> <li>Пространственная сложность играет роль, аналогичную временной: она показывает тенденцию роста потребления памяти по мере увеличения объема данных.</li> <li>Память, связанная с выполнением алгоритма, можно разделить на входное пространство, временное пространство и выходное пространство. Обычно входное пространство не включается в расчет пространственной сложности. Временное пространство можно разбить на временные данные, пространство кадров стека и пространство инструкций; при этом пространство кадров стека обычно влияет на сложность только в рекурсивных функциях.</li> <li>Обычно нас интересует только худшая пространственная сложность, то есть пространственная сложность алгоритма при худшем наборе входных данных и в худший момент времени выполнения.</li> <li>Распространенные пространственные сложности в порядке роста: \\(O(1)\\), \\(O(\\log n)\\), \\(O(n)\\), \\(O(n^2)\\) и \\(O(2^n)\\).</li> </ul>","path":["Глава 2. Анализ сложности","2.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_computational_complexity/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: Является ли пространственная сложность хвостовой рекурсии равной \\(O(1)\\)?</p> <p>Теоретически пространственную сложность хвостово-рекурсивных функций можно оптимизировать до \\(O(1)\\) . Однако большинство языков программирования (например Java, Python, C++, Go, C# и другие) не поддерживают автоматическую оптимизацию хвостовой рекурсии, поэтому на практике пространственная сложность обычно считается равной \\(O(n)\\) .</p> <p>Q: В чем разница между терминами function и method?</p> <p>Функция (function) может выполняться независимо, и все ее параметры передаются явно. Метод (method) связан с объектом, неявно получает объект, который его вызывает, и может работать с данными, содержащимися в экземпляре класса.</p> <p>Ниже это проиллюстрировано на примере нескольких распространенных языков программирования.</p> <ul> <li>C - процедурный язык программирования без объектно-ориентированной модели, поэтому в нем есть только функции. Однако мы можем имитировать объектно-ориентированное программирование через структуры (<code>struct</code>), и функции, связанные со структурами, эквивалентны методам в других языках.</li> <li>Java и C# - объектно-ориентированные языки программирования, в которых блоки кода (методы) обычно являются частью класса. Статические методы по поведению похожи на функции, потому что они привязаны к классу и не могут обращаться к конкретным переменным экземпляра.</li> <li>C++ и Python поддерживают как процедурное программирование (функции), так и объектно-ориентированное программирование (методы).</li> </ul> <p>Q: Отражает ли диаграмма \"распространенных типов пространственной сложности\" абсолютный размер занятой памяти?</p> <p>Нет, эта диаграмма показывает пространственную сложность, а значит отражает именно тенденцию роста, а не абсолютный объем занятого пространства.</p> <p>Если взять \\(n = 8\\) , можно заметить, что значения на кривых не совпадают напрямую с соответствующими функциями. Это связано с тем, что каждая кривая содержит константный член, который сжимает диапазон значений до визуально удобного масштаба.</p> <p>На практике, поскольку мы обычно не знаем, какова \"константная\" сложность каждого метода, только по сложности мы, как правило, не можем выбрать оптимальное решение для случая \\(n = 8\\) . Но для \\(n = 8^5\\) выбор уже очевиден: в этой области доминирует именно тенденция роста.</p> <p>Q: Бывают ли случаи, когда в реальных сценариях алгоритм специально проектируют так, чтобы жертвовать временем ради пространства или пространством ради времени?</p> <p>На практике в большинстве случаев выбирают обмен пространства на время. Например, для индексов в базах данных обычно строят B+ деревья или хеш-индексы, расходуя значительный объем памяти ради эффективных запросов уровня \\(O(\\log n)\\) или даже \\(O(1)\\).</p> <p>В сценариях, где память особенно дорога, наоборот, могут жертвовать временем ради пространства. Например, в embedded-разработке память устройства очень ограничена, поэтому инженеры могут отказаться от хеш-таблиц и выбрать последовательный поиск по массиву, экономя память ценой более медленного поиска.</p>","path":["Глава 2. Анализ сложности","2.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/","level":1,"title":"2.3   Временная сложность","text":"<p>Время выполнения может наглядно и точно отражать эффективность алгоритма. Если мы хотим точно оценить время работы некоторого фрагмента кода, как это сделать?</p> <ol> <li>Определить платформу выполнения, включая конфигурацию оборудования, язык программирования, системную среду и т.д., поскольку все эти факторы влияют на эффективность выполнения кода.</li> <li>Оценить время выполнения различных вычислительных операций, например операция сложения <code>+</code> требует 1 нс , операция умножения <code>*</code> требует 10 нс , операция вывода <code>print()</code> требует 5 нс и т.д.</li> <li>Подсчитать все вычислительные операции в коде и суммировать время выполнения всех операций, чтобы получить общее время работы.</li> </ol> <p>Например, в следующем коде размер входных данных равен \\(n\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code># На некоторой платформе выполнения\ndef algorithm(n: int):\n    a = 2      # 1 нс\n    a = a + 1  # 1 нс\n    a = a * 2  # 10 нс\n    # Цикл выполняется n раз\n    for _ in range(n):  # 1 нс\n        print(0)        # 5 нс\n</code></pre> <pre><code>// На некоторой платформе выполнения\nvoid algorithm(int n) {\n    int a = 2;  // 1 нс\n    a = a + 1;  // 1 нс\n    a = a * 2;  // 10 нс\n    // Цикл выполняется n раз\n    for (int i = 0; i &lt; n; i++) {  // 1 нс\n        cout &lt;&lt; 0 &lt;&lt; endl;         // 5 нс\n    }\n}\n</code></pre> <pre><code>// На некоторой платформе выполнения\nvoid algorithm(int n) {\n    int a = 2;  // 1 нс\n    a = a + 1;  // 1 нс\n    a = a * 2;  // 10 нс\n    // Цикл выполняется n раз\n    for (int i = 0; i &lt; n; i++) {  // 1 нс\n        System.out.println(0);     // 5 нс\n    }\n}\n</code></pre> <pre><code>// На некоторой платформе выполнения\nvoid Algorithm(int n) {\n    int a = 2;  // 1 нс\n    a = a + 1;  // 1 нс\n    a = a * 2;  // 10 нс\n    // Цикл выполняется n раз\n    for (int i = 0; i &lt; n; i++) {  // 1 нс\n        Console.WriteLine(0);      // 5 нс\n    }\n}\n</code></pre> <pre><code>// На некоторой платформе выполнения\nfunc algorithm(n int) {\n    a := 2     // 1 нс\n    a = a + 1  // 1 нс\n    a = a * 2  // 10 нс\n    // Цикл выполняется n раз\n    for i := 0; i &lt; n; i++ {  // 1 нс\n        fmt.Println(a)        // 5 нс\n    }\n}\n</code></pre> <pre><code>// На некоторой платформе выполнения\nfunc algorithm(n: Int) {\n    var a = 2 // 1 нс\n    a = a + 1 // 1 нс\n    a = a * 2 // 10 нс\n    // Цикл выполняется n раз\n    for _ in 0 ..&lt; n { // 1 нс\n        print(0) // 5 нс\n    }\n}\n</code></pre> <pre><code>// На некоторой платформе выполнения\nfunction algorithm(n) {\n    var a = 2; // 1 нс\n    a = a + 1; // 1 нс\n    a = a * 2; // 10 нс\n    // Цикл выполняется n раз\n    for(let i = 0; i &lt; n; i++) { // 1 нс\n        console.log(0); // 5 нс\n    }\n}\n</code></pre> <pre><code>// На некоторой платформе выполнения\nfunction algorithm(n: number): void {\n    var a: number = 2; // 1 нс\n    a = a + 1; // 1 нс\n    a = a * 2; // 10 нс\n    // Цикл выполняется n раз\n    for(let i = 0; i &lt; n; i++) { // 1 нс\n        console.log(0); // 5 нс\n    }\n}\n</code></pre> <pre><code>// На некоторой платформе выполнения\nvoid algorithm(int n) {\n  int a = 2; // 1 нс\n  a = a + 1; // 1 нс\n  a = a * 2; // 10 нс\n  // Цикл выполняется n раз\n  for (int i = 0; i &lt; n; i++) { // 1 нс\n    print(0); // 5 нс\n  }\n}\n</code></pre> <pre><code>// На некоторой платформе выполнения\nfn algorithm(n: i32) {\n    let mut a = 2;      // 1 нс\n    a = a + 1;          // 1 нс\n    a = a * 2;          // 10 нс\n    // Цикл выполняется n раз\n    for _ in 0..n {     // 1 нс\n        println!(\"{}\", 0);  // 5 нс\n    }\n}\n</code></pre> <pre><code>// На некоторой платформе выполнения\nvoid algorithm(int n) {\n    int a = 2;  // 1 нс\n    a = a + 1;  // 1 нс\n    a = a * 2;  // 10 нс\n    // Цикл выполняется n раз\n    for (int i = 0; i &lt; n; i++) {   // 1 нс\n        printf(\"%d\", 0);            // 5 нс\n    }\n}\n</code></pre> <pre><code>// На некоторой платформе выполнения\nfun algorithm(n: Int) {\n    var a = 2 // 1 нс\n    a = a + 1 // 1 нс\n    a = a * 2 // 10 нс\n    // Цикл выполняется n раз\n    for (i in 0..&lt;n) {  // 1 нс\n        println(0)      // 5 нс\n    }\n}\n</code></pre> <pre><code># На некоторой платформе выполнения\ndef algorithm(n)\n    a = 2       # 1 нс\n    a = a + 1   # 1 нс\n    a = a * 2   # 10 нс\n    # Цикл выполняется n раз\n    (0...n).each do # 1 нс\n        puts 0      # 5 нс\n    end\nend\n</code></pre> <p>Согласно приведенному выше методу, время работы алгоритма равно \\((6n + 12)\\) нс :</p> \\[ 1 + 1 + 10 + (1 + 5) \\times n = 6n + 12 \\] <p>Но на практике подсчитывать реальное время выполнения алгоритма и неразумно, и нереалистично. Во-первых, мы не хотим привязывать оценку времени к конкретной платформе, потому что алгоритм должен запускаться на самых разных платформах. Во-вторых, нам трудно узнать время выполнения каждого типа операций, а это сильно усложняет оценку.</p>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#231","level":2,"title":"2.3.1   Подсчет тенденции роста времени","text":"<p>Анализ временной сложности оценивает не само время выполнения алгоритма, а тенденцию роста этого времени по мере увеличения объема данных.</p> <p>Понятие \"тенденции роста времени\" довольно абстрактно, поэтому разберем его на примере. Предположим, размер входных данных равен \\(n\\) , и даны три алгоритма <code>A</code> , <code>B</code> и <code>C</code> :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code># Временная сложность алгоритма A: постоянная\ndef algorithm_A(n: int):\n    print(0)\n# Временная сложность алгоритма B: линейная\ndef algorithm_B(n: int):\n    for _ in range(n):\n        print(0)\n# Временная сложность алгоритма C: постоянная\ndef algorithm_C(n: int):\n    for _ in range(1000000):\n        print(0)\n</code></pre> <pre><code>// Временная сложность алгоритма A: постоянная\nvoid algorithm_A(int n) {\n    cout &lt;&lt; 0 &lt;&lt; endl;\n}\n// Временная сложность алгоритма B: линейная\nvoid algorithm_B(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        cout &lt;&lt; 0 &lt;&lt; endl;\n    }\n}\n// Временная сложность алгоритма C: постоянная\nvoid algorithm_C(int n) {\n    for (int i = 0; i &lt; 1000000; i++) {\n        cout &lt;&lt; 0 &lt;&lt; endl;\n    }\n}\n</code></pre> <pre><code>// Временная сложность алгоритма A: постоянная\nvoid algorithm_A(int n) {\n    System.out.println(0);\n}\n// Временная сложность алгоритма B: линейная\nvoid algorithm_B(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        System.out.println(0);\n    }\n}\n// Временная сложность алгоритма C: постоянная\nvoid algorithm_C(int n) {\n    for (int i = 0; i &lt; 1000000; i++) {\n        System.out.println(0);\n    }\n}\n</code></pre> <pre><code>// Временная сложность алгоритма A: постоянная\nvoid AlgorithmA(int n) {\n    Console.WriteLine(0);\n}\n// Временная сложность алгоритма B: линейная\nvoid AlgorithmB(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        Console.WriteLine(0);\n    }\n}\n// Временная сложность алгоритма C: постоянная\nvoid AlgorithmC(int n) {\n    for (int i = 0; i &lt; 1000000; i++) {\n        Console.WriteLine(0);\n    }\n}\n</code></pre> <pre><code>// Временная сложность алгоритма A: постоянная\nfunc algorithm_A(n int) {\n    fmt.Println(0)\n}\n// Временная сложность алгоритма B: линейная\nfunc algorithm_B(n int) {\n    for i := 0; i &lt; n; i++ {\n        fmt.Println(0)\n    }\n}\n// Временная сложность алгоритма C: постоянная\nfunc algorithm_C(n int) {\n    for i := 0; i &lt; 1000000; i++ {\n        fmt.Println(0)\n    }\n}\n</code></pre> <pre><code>// Временная сложность алгоритма A: постоянная\nfunc algorithmA(n: Int) {\n    print(0)\n}\n\n// Временная сложность алгоритма B: линейная\nfunc algorithmB(n: Int) {\n    for _ in 0 ..&lt; n {\n        print(0)\n    }\n}\n\n// Временная сложность алгоритма C: постоянная\nfunc algorithmC(n: Int) {\n    for _ in 0 ..&lt; 1_000_000 {\n        print(0)\n    }\n}\n</code></pre> <pre><code>// Временная сложность алгоритма A: постоянная\nfunction algorithm_A(n) {\n    console.log(0);\n}\n// Временная сложность алгоритма B: линейная\nfunction algorithm_B(n) {\n    for (let i = 0; i &lt; n; i++) {\n        console.log(0);\n    }\n}\n// Временная сложность алгоритма C: постоянная\nfunction algorithm_C(n) {\n    for (let i = 0; i &lt; 1000000; i++) {\n        console.log(0);\n    }\n}\n</code></pre> <pre><code>// Временная сложность алгоритма A: постоянная\nfunction algorithm_A(n: number): void {\n    console.log(0);\n}\n// Временная сложность алгоритма B: линейная\nfunction algorithm_B(n: number): void {\n    for (let i = 0; i &lt; n; i++) {\n        console.log(0);\n    }\n}\n// Временная сложность алгоритма C: постоянная\nfunction algorithm_C(n: number): void {\n    for (let i = 0; i &lt; 1000000; i++) {\n        console.log(0);\n    }\n}\n</code></pre> <pre><code>// Временная сложность алгоритма A: постоянная\nvoid algorithmA(int n) {\n  print(0);\n}\n// Временная сложность алгоритма B: линейная\nvoid algorithmB(int n) {\n  for (int i = 0; i &lt; n; i++) {\n    print(0);\n  }\n}\n// Временная сложность алгоритма C: постоянная\nvoid algorithmC(int n) {\n  for (int i = 0; i &lt; 1000000; i++) {\n    print(0);\n  }\n}\n</code></pre> <pre><code>// Временная сложность алгоритма A: постоянная\nfn algorithm_A(n: i32) {\n    println!(\"{}\", 0);\n}\n// Временная сложность алгоритма B: линейная\nfn algorithm_B(n: i32) {\n    for _ in 0..n {\n        println!(\"{}\", 0);\n    }\n}\n// Временная сложность алгоритма C: постоянная\nfn algorithm_C(n: i32) {\n    for _ in 0..1000000 {\n        println!(\"{}\", 0);\n    }\n}\n</code></pre> <pre><code>// Временная сложность алгоритма A: постоянная\nvoid algorithm_A(int n) {\n    printf(\"%d\", 0);\n}\n// Временная сложность алгоритма B: линейная\nvoid algorithm_B(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        printf(\"%d\", 0);\n    }\n}\n// Временная сложность алгоритма C: постоянная\nvoid algorithm_C(int n) {\n    for (int i = 0; i &lt; 1000000; i++) {\n        printf(\"%d\", 0);\n    }\n}\n</code></pre> <pre><code>// Временная сложность алгоритма A: постоянная\nfun algoritm_A(n: Int) {\n    println(0)\n}\n// Временная сложность алгоритма B: линейная\nfun algorithm_B(n: Int) {\n    for (i in 0..&lt;n){\n        println(0)\n    }\n}\n// Временная сложность алгоритма C: постоянная\nfun algorithm_C(n: Int) {\n    for (i in 0..&lt;1000000) {\n        println(0)\n    }\n}\n</code></pre> <pre><code># Временная сложность алгоритма A: постоянная\ndef algorithm_A(n)\n    puts 0\nend\n\n# Временная сложность алгоритма B: линейная\ndef algorithm_B(n)\n    (0...n).each { puts 0 }\nend\n\n# Временная сложность алгоритма C: постоянная\ndef algorithm_C(n)\n    (0...1_000_000).each { puts 0 }\nend\n</code></pre> <p>На рисунке 2-7 показана временная сложность трех функций алгоритмов выше.</p> <ul> <li>У алгоритма <code>A</code> есть только 1 операция вывода, и время его работы не растет с увеличением \\(n\\) . Мы называем такую временную сложность \"постоянной\".</li> <li>В алгоритме <code>B</code> операция вывода выполняется в цикле \\(n\\) раз, поэтому время работы растет линейно по мере увеличения \\(n\\) . Такая временная сложность называется \"линейной\".</li> <li>В алгоритме <code>C</code> операция вывода выполняется \\(1000000\\) раз; хотя время работы велико, оно не зависит от размера входных данных \\(n\\) . Поэтому временная сложность <code>C</code> такая же, как у <code>A</code> , и тоже является \"постоянной\".</li> </ul> <p></p> <p> Рисунок 2-7   Тенденции роста времени для алгоритмов A, B и C </p> <p>Какие особенности имеет анализ временной сложности по сравнению с непосредственным измерением времени работы алгоритма?</p> <ul> <li>Временная сложность позволяет эффективно оценивать эффективность алгоритма. Например, время работы алгоритма <code>B</code> растет линейно: при \\(n &gt; 1\\) он медленнее алгоритма <code>A</code> , а при \\(n &gt; 1000000\\) медленнее алгоритма <code>C</code> . На самом деле, если размер входных данных \\(n\\) достаточно велик, алгоритм с \"постоянной\" сложностью обязательно лучше алгоритма с \"линейной\" сложностью. В этом и состоит смысл тенденции роста времени.</li> <li>Метод вывода временной сложности проще. Очевидно, что платформа выполнения и тип вычислительных операций не влияют на тенденцию роста времени работы алгоритма. Поэтому в анализе временной сложности мы можем считать время выполнения всех вычислительных операций одинаковым \"единичным временем\" и тем самым упростить \"подсчет времени выполнения операций\" до \"подсчета количества операций\", что существенно снижает сложность оценки.</li> <li>У временной сложности есть и определенные ограничения. Например, хотя временная сложность алгоритмов <code>A</code> и <code>C</code> одинакова, их реальное время выполнения сильно различается. Точно так же, хотя временная сложность <code>B</code> выше, чем у <code>C</code> , при малых \\(n\\) алгоритм <code>B</code> явно лучше <code>C</code> . В таких случаях нам часто трудно судить об эффективности алгоритма, опираясь только на временную сложность. Тем не менее, несмотря на эти ограничения, анализ сложности все равно остается самым эффективным и самым распространенным способом оценки алгоритмов.</li> </ul>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#232","level":2,"title":"2.3.2   Асимптотическая верхняя граница функции","text":"<p>Для функции с входным размером \\(n\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>def algorithm(n: int):\n    a = 1      # +1\n    a = a + 1  # +1\n    a = a * 2  # +1\n    # Цикл выполняется n раз\n    for i in range(n):  # +1\n        print(0)        # +1\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +1\n    a = a + 1;  // +1\n    a = a * 2;  // +1\n    // Цикл выполняется n раз\n    for (int i = 0; i &lt; n; i++) { // +1 (каждый раз выполняется i ++)\n        cout &lt;&lt; 0 &lt;&lt; endl;    // +1\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +1\n    a = a + 1;  // +1\n    a = a * 2;  // +1\n    // Цикл выполняется n раз\n    for (int i = 0; i &lt; n; i++) { // +1 (каждый раз выполняется i ++)\n        System.out.println(0);    // +1\n    }\n}\n</code></pre> <pre><code>void Algorithm(int n) {\n    int a = 1;  // +1\n    a = a + 1;  // +1\n    a = a * 2;  // +1\n    // Цикл выполняется n раз\n    for (int i = 0; i &lt; n; i++) {   // +1 (каждый раз выполняется i ++)\n        Console.WriteLine(0);   // +1\n    }\n}\n</code></pre> <pre><code>func algorithm(n int) {\n    a := 1      // +1\n    a = a + 1   // +1\n    a = a * 2   // +1\n    // Цикл выполняется n раз\n    for i := 0; i &lt; n; i++ {   // +1\n        fmt.Println(a)         // +1\n    }\n}\n</code></pre> <pre><code>func algorithm(n: Int) {\n    var a = 1 // +1\n    a = a + 1 // +1\n    a = a * 2 // +1\n    // Цикл выполняется n раз\n    for _ in 0 ..&lt; n { // +1\n        print(0) // +1\n    }\n}\n</code></pre> <pre><code>function algorithm(n) {\n    var a = 1; // +1\n    a += 1; // +1\n    a *= 2; // +1\n    // Цикл выполняется n раз\n    for(let i = 0; i &lt; n; i++){ // +1 (каждый раз выполняется i ++)\n        console.log(0); // +1\n    }\n}\n</code></pre> <pre><code>function algorithm(n: number): void{\n    var a: number = 1; // +1\n    a += 1; // +1\n    a *= 2; // +1\n    // Цикл выполняется n раз\n    for(let i = 0; i &lt; n; i++){ // +1 (каждый раз выполняется i ++)\n        console.log(0); // +1\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n  int a = 1; // +1\n  a = a + 1; // +1\n  a = a * 2; // +1\n  // Цикл выполняется n раз\n  for (int i = 0; i &lt; n; i++) { // +1 (каждый раз выполняется i ++)\n    print(0); // +1\n  }\n}\n</code></pre> <pre><code>fn algorithm(n: i32) {\n    let mut a = 1;   // +1\n    a = a + 1;      // +1\n    a = a * 2;      // +1\n\n    // Цикл выполняется n раз\n    for _ in 0..n { // +1 (каждый раз выполняется i ++)\n        println!(\"{}\", 0); // +1\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +1\n    a = a + 1;  // +1\n    a = a * 2;  // +1\n    // Цикл выполняется n раз\n    for (int i = 0; i &lt; n; i++) {   // +1 (каждый раз выполняется i ++)\n        printf(\"%d\", 0);            // +1\n    }\n}\n</code></pre> <pre><code>fun algorithm(n: Int) {\n    var a = 1 // +1\n    a = a + 1 // +1\n    a = a * 2 // +1\n    // Цикл выполняется n раз\n    for (i in 0..&lt;n) { // +1 (каждый раз выполняется i ++)\n        println(0) // +1\n    }\n}\n</code></pre> <pre><code>def algorithm(n)\n    a = 1       # +1\n    a = a + 1   # +1\n    a = a * 2   # +1\n    # Цикл выполняется n раз\n    (0...n).each do # +1\n        puts 0      # +1\n    end\nend\n</code></pre> <p>Пусть количество операций алгоритма является функцией от размера входных данных \\(n\\) и обозначается как \\(T(n)\\) ; тогда для приведенной выше функции число операций равно:</p> \\[ T(n) = 3 + 2n \\] <p>\\(T(n)\\) - линейная функция, а это означает, что тенденция роста времени работы линейна, следовательно, ее временная сложность является линейной.</p> <p>Линейную временную сложность мы записываем как \\(O(n)\\) ; этот математический символ называется нотацией Big \\(O\\) (big-\\(O\\) notation) и обозначает асимптотическую верхнюю границу (asymptotic upper bound) функции \\(T(n)\\) .</p> <p>По сути анализ временной сложности - это вычисление асимптотической верхней границы \"количества операций \\(T(n)\\)\", и у него есть строгое математическое определение.</p> <p>Асимптотическая верхняя граница функции</p> <p>Если существуют положительное действительное число \\(c\\) и действительное число \\(n_0\\) , такие что для всех \\(n &gt; n_0\\) выполняется \\(T(n) \\leq c \\cdot f(n)\\) , то можно считать, что \\(f(n)\\) задает асимптотическую верхнюю границу для \\(T(n)\\) ; это записывается как \\(T(n) = O(f(n))\\) .</p> <p>Как показано на рисунке 2-8, вычислить асимптотическую верхнюю границу - значит найти такую функцию \\(f(n)\\) , что при стремлении \\(n\\) к бесконечности функции \\(T(n)\\) и \\(f(n)\\) имеют один и тот же порядок роста и отличаются только постоянным коэффициентом \\(c\\).</p> <p></p> <p> Рисунок 2-8   Асимптотическая верхняя граница функции </p>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#233","level":2,"title":"2.3.3   Метод вывода","text":"<p>Математическое определение асимптотической верхней границы выглядит довольно формально, и если ты понял его не до конца, переживать не стоит. Сначала можно освоить сам метод вывода, а в процессе дальнейшей практики постепенно почувствовать его математический смысл.</p> <p>Согласно определению, после того как мы определили \\(f(n)\\) , мы можем получить временную сложность \\(O(f(n))\\) . Но как определить саму асимптотическую верхнюю границу \\(f(n)\\) ? В целом процесс состоит из двух шагов: сначала подсчитать количество операций, затем определить асимптотическую верхнюю границу.</p>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#1-1","level":3,"title":"1.   Шаг 1: подсчет количества операций","text":"<p>Для кода это можно делать построчно сверху вниз. Однако, поскольку в выражении \\(c \\cdot f(n)\\) выше постоянный коэффициент \\(c\\) может быть сколь угодно большим, различные коэффициенты и постоянные члены в числе операций \\(T(n)\\) можно игнорировать. Исходя из этого принципа, можно сформулировать следующие упрощающие приемы подсчета.</p> <ol> <li>Игнорировать константы в \\(T(n)\\). Они не зависят от \\(n\\) , а значит не влияют на временную сложность.</li> <li>Опускать все коэффициенты. Например, циклы на \\(2n\\) раз или \\(5n + 1\\) раз можно упростить до \\(n\\) раз, потому что коэффициент перед \\(n\\) не влияет на временную сложность.</li> <li>При вложенных циклах использовать умножение. Общее число операций равно произведению числа операций внешнего и внутреннего циклов; при этом для каждого уровня цикла по-прежнему можно применять приемы из пунктов <code>1.</code> и <code>2.</code> .</li> </ol> <p>Для заданной функции мы можем использовать перечисленные выше приемы и подсчитать число операций:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>def algorithm(n: int):\n    a = 1      # +0 (прием 1)\n    a = a + n  # +0 (прием 1)\n    # +n (прием 2)\n    for i in range(5 * n + 1):\n        print(0)\n    # +n*n (прием 3)\n    for i in range(2 * n):\n        for j in range(n + 1):\n            print(0)\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +0 (прием 1)\n    a = a + n;  // +0 (прием 1)\n    // +n (прием 2)\n    for (int i = 0; i &lt; 5 * n + 1; i++) {\n        cout &lt;&lt; 0 &lt;&lt; endl;\n    }\n    // +n*n (прием 3)\n    for (int i = 0; i &lt; 2 * n; i++) {\n        for (int j = 0; j &lt; n + 1; j++) {\n            cout &lt;&lt; 0 &lt;&lt; endl;\n        }\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +0 (прием 1)\n    a = a + n;  // +0 (прием 1)\n    // +n (прием 2)\n    for (int i = 0; i &lt; 5 * n + 1; i++) {\n        System.out.println(0);\n    }\n    // +n*n (прием 3)\n    for (int i = 0; i &lt; 2 * n; i++) {\n        for (int j = 0; j &lt; n + 1; j++) {\n            System.out.println(0);\n        }\n    }\n}\n</code></pre> <pre><code>void Algorithm(int n) {\n    int a = 1;  // +0 (прием 1)\n    a = a + n;  // +0 (прием 1)\n    // +n (прием 2)\n    for (int i = 0; i &lt; 5 * n + 1; i++) {\n        Console.WriteLine(0);\n    }\n    // +n*n (прием 3)\n    for (int i = 0; i &lt; 2 * n; i++) {\n        for (int j = 0; j &lt; n + 1; j++) {\n            Console.WriteLine(0);\n        }\n    }\n}\n</code></pre> <pre><code>func algorithm(n int) {\n    a := 1     // +0 (прием 1)\n    a = a + n  // +0 (прием 1)\n    // +n (прием 2)\n    for i := 0; i &lt; 5 * n + 1; i++ {\n        fmt.Println(0)\n    }\n    // +n*n (прием 3)\n    for i := 0; i &lt; 2 * n; i++ {\n        for j := 0; j &lt; n + 1; j++ {\n            fmt.Println(0)\n        }\n    }\n}\n</code></pre> <pre><code>func algorithm(n: Int) {\n    var a = 1 // +0 (прием 1)\n    a = a + n // +0 (прием 1)\n    // +n (прием 2)\n    for _ in 0 ..&lt; (5 * n + 1) {\n        print(0)\n    }\n    // +n*n (прием 3)\n    for _ in 0 ..&lt; (2 * n) {\n        for _ in 0 ..&lt; (n + 1) {\n            print(0)\n        }\n    }\n}\n</code></pre> <pre><code>function algorithm(n) {\n    let a = 1;  // +0 (прием 1)\n    a = a + n;  // +0 (прием 1)\n    // +n (прием 2)\n    for (let i = 0; i &lt; 5 * n + 1; i++) {\n        console.log(0);\n    }\n    // +n*n (прием 3)\n    for (let i = 0; i &lt; 2 * n; i++) {\n        for (let j = 0; j &lt; n + 1; j++) {\n            console.log(0);\n        }\n    }\n}\n</code></pre> <pre><code>function algorithm(n: number): void {\n    let a = 1;  // +0 (прием 1)\n    a = a + n;  // +0 (прием 1)\n    // +n (прием 2)\n    for (let i = 0; i &lt; 5 * n + 1; i++) {\n        console.log(0);\n    }\n    // +n*n (прием 3)\n    for (let i = 0; i &lt; 2 * n; i++) {\n        for (let j = 0; j &lt; n + 1; j++) {\n            console.log(0);\n        }\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n  int a = 1; // +0 (прием 1)\n  a = a + n; // +0 (прием 1)\n  // +n (прием 2)\n  for (int i = 0; i &lt; 5 * n + 1; i++) {\n    print(0);\n  }\n  // +n*n (прием 3)\n  for (int i = 0; i &lt; 2 * n; i++) {\n    for (int j = 0; j &lt; n + 1; j++) {\n      print(0);\n    }\n  }\n}\n</code></pre> <pre><code>fn algorithm(n: i32) {\n    let mut a = 1;     // +0 (прием 1)\n    a = a + n;        // +0 (прием 1)\n\n    // +n (прием 2)\n    for i in 0..(5 * n + 1) {\n        println!(\"{}\", 0);\n    }\n\n    // +n*n (прием 3)\n    for i in 0..(2 * n) {\n        for j in 0..(n + 1) {\n            println!(\"{}\", 0);\n        }\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +0 (прием 1)\n    a = a + n;  // +0 (прием 1)\n    // +n (прием 2)\n    for (int i = 0; i &lt; 5 * n + 1; i++) {\n        printf(\"%d\", 0);\n    }\n    // +n*n (прием 3)\n    for (int i = 0; i &lt; 2 * n; i++) {\n        for (int j = 0; j &lt; n + 1; j++) {\n            printf(\"%d\", 0);\n        }\n    }\n}\n</code></pre> <pre><code>fun algorithm(n: Int) {\n    var a = 1   // +0 (прием 1)\n    a = a + n   // +0 (прием 1)\n    // +n (прием 2)\n    for (i in 0..&lt;5 * n + 1) {\n        println(0)\n    }\n    // +n*n (прием 3)\n    for (i in 0..&lt;2 * n) {\n        for (j in 0..&lt;n + 1) {\n            println(0)\n        }\n    }\n}\n</code></pre> <pre><code>def algorithm(n)\n    a = 1       # +0 (прием 1)\n    a = a + n   # +0 (прием 1)\n    # +n (прием 2)\n    (0...(5 * n + 1)).each do { puts 0 }\n    # +n*n (прием 3)\n    (0...(2 * n)).each do\n        (0...(n + 1)).each do { puts 0 }\n    end\nend\n</code></pre> <p>Следующая формула показывает результаты подсчета до и после использования перечисленных выше приемов; в обоих случаях выводимая временная сложность равна \\(O(n^2)\\) .</p> \\[ \\begin{aligned} T(n) &amp; = 2n(n + 1) + (5n + 1) + 2 &amp; \\text{полный подсчет (-.-|||)} \\newline &amp; = 2n^2 + 7n + 3 \\newline T(n) &amp; = n^2 + n &amp; \\text{ленивый подсчет (o.O)} \\end{aligned} \\]","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#2-2","level":3,"title":"2.   Шаг 2: определение асимптотической верхней границы","text":"<p>**Временная сложность определяется старшим по степени членом в \\(T(n)\\) **. Это связано с тем, что при стремлении \\(n\\) к бесконечности именно старший член начинает доминировать, а влиянием остальных членов можно пренебречь.</p> <p>В таблице 2-2 приведены несколько примеров. Некоторые значения специально сделаны преувеличенными, чтобы подчеркнуть вывод: \"коэффициент не способен изменить порядок\". Когда \\(n\\) стремится к бесконечности, эти константы становятся несущественными.</p> <p> Таблица 2-2   Временная сложность, соответствующая разному количеству операций </p> Число операций \\(T(n)\\) Временная сложность \\(O(f(n))\\) \\(100000\\) \\(O(1)\\) \\(3n + 2\\) \\(O(n)\\) \\(2n^2 + 3n + 2\\) \\(O(n^2)\\) \\(n^3 + 10000n^2\\) \\(O(n^3)\\) \\(2^n + 10000n^{10000}\\) \\(O(2^n)\\)","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#234","level":2,"title":"2.3.4   Распространенные типы","text":"<p>Пусть размер входных данных равен \\(n\\) ; распространенные типы временной сложности показаны на рисунке 2-9 (в порядке от меньшей к большей).</p> \\[ \\begin{aligned} O(1) &lt; O(\\log n) &lt; O(n) &lt; O(n \\log n) &lt; O(n^2) &lt; O(2^n) &lt; O(n!) \\newline \\text{Постоянная} &lt; \\text{Логарифмическая} &lt; \\text{Линейная} &lt; \\text{Линейно-логарифмическая} &lt; \\text{Квадратичная} &lt; \\text{Экспоненциальная} &lt; \\text{Факториальная} \\end{aligned} \\] <p></p> <p> Рисунок 2-9   Распространенные типы временной сложности </p>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#1-o1","level":3,"title":"1.   Постоянная сложность \\(O(1)\\)","text":"<p>Число операций при постоянной сложности не зависит от размера входных данных \\(n\\) , то есть не изменяется вместе с изменением \\(n\\) .</p> <p>В следующей функции, хотя число операций <code>size</code> может быть большим, оно не зависит от размера входных данных \\(n\\) , поэтому временная сложность по-прежнему равна \\(O(1)\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def constant(n: int) -&gt; int:\n    \"\"\"Постоянная сложность\"\"\"\n    count = 0\n    size = 100000\n    for _ in range(size):\n        count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* Постоянная сложность */\nint constant(int n) {\n    int count = 0;\n    int size = 100000;\n    for (int i = 0; i &lt; size; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* Постоянная сложность */\nint constant(int n) {\n    int count = 0;\n    int size = 100000;\n    for (int i = 0; i &lt; size; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* Постоянная сложность */\nint Constant(int n) {\n    int count = 0;\n    int size = 100000;\n    for (int i = 0; i &lt; size; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* Постоянная сложность */\nfunc constant(n int) int {\n    count := 0\n    size := 100000\n    for i := 0; i &lt; size; i++ {\n        count++\n    }\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* Постоянная сложность */\nfunc constant(n: Int) -&gt; Int {\n    var count = 0\n    let size = 100_000\n    for _ in 0 ..&lt; size {\n        count += 1\n    }\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* Постоянная сложность */\nfunction constant(n) {\n    let count = 0;\n    const size = 100000;\n    for (let i = 0; i &lt; size; i++) count++;\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* Постоянная сложность */\nfunction constant(n: number): number {\n    let count = 0;\n    const size = 100000;\n    for (let i = 0; i &lt; size; i++) count++;\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* Постоянная сложность */\nint constant(int n) {\n  int count = 0;\n  int size = 100000;\n  for (var i = 0; i &lt; size; i++) {\n    count++;\n  }\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* Постоянная сложность */\nfn constant(n: i32) -&gt; i32 {\n    _ = n;\n    let mut count = 0;\n    let size = 100_000;\n    for _ in 0..size {\n        count += 1;\n    }\n    count\n}\n</code></pre> time_complexity.c<pre><code>/* Постоянная сложность */\nint constant(int n) {\n    int count = 0;\n    int size = 100000;\n    int i = 0;\n    for (int i = 0; i &lt; size; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* Постоянная сложность */\nfun constant(n: Int): Int {\n    var count = 0\n    val size = 100000\n    for (i in 0..&lt;size)\n        count++\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### Постоянная сложность ###\ndef constant(n)\n  count = 0\n  size = 100000\n\n  (0...size).each { count += 1 }\n\n  count\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#2-on","level":3,"title":"2.   Линейная сложность \\(O(n)\\)","text":"<p>Число операций при линейной сложности растет линейно относительно размера входных данных \\(n\\) . Линейная сложность обычно встречается в одноуровневых циклах:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def linear(n: int) -&gt; int:\n    \"\"\"Линейная сложность\"\"\"\n    count = 0\n    for _ in range(n):\n        count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* Линейная сложность */\nint linear(int n) {\n    int count = 0;\n    for (int i = 0; i &lt; n; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* Линейная сложность */\nint linear(int n) {\n    int count = 0;\n    for (int i = 0; i &lt; n; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* Линейная сложность */\nint Linear(int n) {\n    int count = 0;\n    for (int i = 0; i &lt; n; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* Линейная сложность */\nfunc linear(n int) int {\n    count := 0\n    for i := 0; i &lt; n; i++ {\n        count++\n    }\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* Линейная сложность */\nfunc linear(n: Int) -&gt; Int {\n    var count = 0\n    for _ in 0 ..&lt; n {\n        count += 1\n    }\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* Линейная сложность */\nfunction linear(n) {\n    let count = 0;\n    for (let i = 0; i &lt; n; i++) count++;\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* Линейная сложность */\nfunction linear(n: number): number {\n    let count = 0;\n    for (let i = 0; i &lt; n; i++) count++;\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* Линейная сложность */\nint linear(int n) {\n  int count = 0;\n  for (var i = 0; i &lt; n; i++) {\n    count++;\n  }\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* Линейная сложность */\nfn linear(n: i32) -&gt; i32 {\n    let mut count = 0;\n    for _ in 0..n {\n        count += 1;\n    }\n    count\n}\n</code></pre> time_complexity.c<pre><code>/* Линейная сложность */\nint linear(int n) {\n    int count = 0;\n    for (int i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* Линейная сложность */\nfun linear(n: Int): Int {\n    var count = 0\n    for (i in 0..&lt;n)\n        count++\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### Линейная сложность ###\ndef linear(n)\n  count = 0\n  (0...n).each { count += 1 }\n  count\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Операции обхода массива и обхода связного списка имеют временную сложность \\(O(n)\\) , где \\(n\\) - длина массива или списка:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def array_traversal(nums: list[int]) -&gt; int:\n    \"\"\"Линейная сложность (обход массива)\"\"\"\n    count = 0\n    # Число итераций пропорционально длине массива\n    for num in nums:\n        count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* Линейная сложность (обход массива) */\nint arrayTraversal(vector&lt;int&gt; &amp;nums) {\n    int count = 0;\n    // Число итераций пропорционально длине массива\n    for (int num : nums) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* Линейная сложность (обход массива) */\nint arrayTraversal(int[] nums) {\n    int count = 0;\n    // Число итераций пропорционально длине массива\n    for (int num : nums) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* Линейная сложность (обход массива) */\nint ArrayTraversal(int[] nums) {\n    int count = 0;\n    // Число итераций пропорционально длине массива\n    foreach (int num in nums) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* Линейная сложность (обход массива) */\nfunc arrayTraversal(nums []int) int {\n    count := 0\n    // Число итераций пропорционально длине массива\n    for range nums {\n        count++\n    }\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* Линейная сложность (обход массива) */\nfunc arrayTraversal(nums: [Int]) -&gt; Int {\n    var count = 0\n    // Число итераций пропорционально длине массива\n    for _ in nums {\n        count += 1\n    }\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* Линейная сложность (обход массива) */\nfunction arrayTraversal(nums) {\n    let count = 0;\n    // Число итераций пропорционально длине массива\n    for (let i = 0; i &lt; nums.length; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* Линейная сложность (обход массива) */\nfunction arrayTraversal(nums: number[]): number {\n    let count = 0;\n    // Число итераций пропорционально длине массива\n    for (let i = 0; i &lt; nums.length; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* Линейная сложность (обход массива) */\nint arrayTraversal(List&lt;int&gt; nums) {\n  int count = 0;\n  // Число итераций пропорционально длине массива\n  for (var _num in nums) {\n    count++;\n  }\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* Линейная сложность (обход массива) */\nfn array_traversal(nums: &amp;[i32]) -&gt; i32 {\n    let mut count = 0;\n    // Число итераций пропорционально длине массива\n    for _ in nums {\n        count += 1;\n    }\n    count\n}\n</code></pre> time_complexity.c<pre><code>/* Линейная сложность (обход массива) */\nint arrayTraversal(int *nums, int n) {\n    int count = 0;\n    // Число итераций пропорционально длине массива\n    for (int i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* Линейная сложность (обход массива) */\nfun arrayTraversal(nums: IntArray): Int {\n    var count = 0\n    // Число итераций пропорционально длине массива\n    for (num in nums) {\n        count++\n    }\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### Линейная сложность ###\ndef linear(n)\n  count = 0\n  (0...n).each { count += 1 }\n  count\nend\n\n# ## Линейная сложность (обход массива) ###\ndef array_traversal(nums)\n  count = 0\n\n  # Число итераций пропорционально длине массива\n  for num in nums\n    count += 1\n  end\n\n  count\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Стоит отметить, что размер входных данных \\(n\\) нужно определять конкретно в зависимости от типа входа. Например, в первом примере переменная \\(n\\) сама является размером входных данных; во втором примере размером данных служит длина массива \\(n\\) .</p>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#3-on2","level":3,"title":"3.   Квадратичная сложность \\(O(n^2)\\)","text":"<p>Число операций при квадратичной сложности растет квадратично относительно размера входных данных \\(n\\) . Квадратичная сложность обычно встречается во вложенных циклах: временная сложность внешнего и внутреннего циклов равна \\(O(n)\\) , поэтому общая временная сложность составляет \\(O(n^2)\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def quadratic(n: int) -&gt; int:\n    \"\"\"Квадратичная сложность\"\"\"\n    count = 0\n    # Число итераций квадратично зависит от размера данных n\n    for i in range(n):\n        for j in range(n):\n            count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* Квадратичная сложность */\nint quadratic(int n) {\n    int count = 0;\n    // Число итераций квадратично зависит от размера данных n\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; n; j++) {\n            count++;\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* Квадратичная сложность */\nint quadratic(int n) {\n    int count = 0;\n    // Число итераций квадратично зависит от размера данных n\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; n; j++) {\n            count++;\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* Квадратичная сложность */\nint Quadratic(int n) {\n    int count = 0;\n    // Число итераций квадратично зависит от размера данных n\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; n; j++) {\n            count++;\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* Квадратичная сложность */\nfunc quadratic(n int) int {\n    count := 0\n    // Число итераций квадратично зависит от размера данных n\n    for i := 0; i &lt; n; i++ {\n        for j := 0; j &lt; n; j++ {\n            count++\n        }\n    }\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* Квадратичная сложность */\nfunc quadratic(n: Int) -&gt; Int {\n    var count = 0\n    // Число итераций квадратично зависит от размера данных n\n    for _ in 0 ..&lt; n {\n        for _ in 0 ..&lt; n {\n            count += 1\n        }\n    }\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* Квадратичная сложность */\nfunction quadratic(n) {\n    let count = 0;\n    // Число итераций квадратично зависит от размера данных n\n    for (let i = 0; i &lt; n; i++) {\n        for (let j = 0; j &lt; n; j++) {\n            count++;\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* Квадратичная сложность */\nfunction quadratic(n: number): number {\n    let count = 0;\n    // Число итераций квадратично зависит от размера данных n\n    for (let i = 0; i &lt; n; i++) {\n        for (let j = 0; j &lt; n; j++) {\n            count++;\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* Квадратичная сложность */\nint quadratic(int n) {\n  int count = 0;\n  // Число итераций квадратично зависит от размера данных n\n  for (int i = 0; i &lt; n; i++) {\n    for (int j = 0; j &lt; n; j++) {\n      count++;\n    }\n  }\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* Квадратичная сложность */\nfn quadratic(n: i32) -&gt; i32 {\n    let mut count = 0;\n    // Число итераций квадратично зависит от размера данных n\n    for _ in 0..n {\n        for _ in 0..n {\n            count += 1;\n        }\n    }\n    count\n}\n</code></pre> time_complexity.c<pre><code>/* Квадратичная сложность */\nint quadratic(int n) {\n    int count = 0;\n    // Число итераций квадратично зависит от размера данных n\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; n; j++) {\n            count++;\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* Квадратичная сложность */\nfun quadratic(n: Int): Int {\n    var count = 0\n    // Число итераций квадратично зависит от размера данных n\n    for (i in 0..&lt;n) {\n        for (j in 0..&lt;n) {\n            count++\n        }\n    }\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### Квадратичная сложность ###\ndef quadratic(n)\n  count = 0\n\n  # Число итераций квадратично зависит от размера данных n\n  for i in 0...n\n    for j in 0...n\n      count += 1\n    end\n  end\n\n  count\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>На рисунке 2-10 сравниваются три временные сложности: постоянная, линейная и квадратичная.</p> <p></p> <p> Рисунок 2-10   Постоянная, линейная и квадратичная временная сложность </p> <p>Возьмем в качестве примера пузырьковую сортировку: внешний цикл выполняется \\(n - 1\\) раз, внутренний цикл выполняется \\(n-1\\) , \\(n-2\\) , \\(\\dots\\) , \\(2\\) , \\(1\\) раз, в среднем это \\(n / 2\\) раз, поэтому временная сложность равна \\(O((n - 1) n / 2) = O(n^2)\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def bubble_sort(nums: list[int]) -&gt; int:\n    \"\"\"Квадратичная сложность (пузырьковая сортировка)\"\"\"\n    count = 0  # Счетчик\n    # Внешний цикл: неотсортированный диапазон [0, i]\n    for i in range(len(nums) - 1, 0, -1):\n        # Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for j in range(i):\n            if nums[j] &gt; nums[j + 1]:\n                # Поменять местами nums[j] и nums[j + 1]\n                tmp: int = nums[j]\n                nums[j] = nums[j + 1]\n                nums[j + 1] = tmp\n                count += 3  # Обмен элементов включает 3 элементарные операции\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* Квадратичная сложность (пузырьковая сортировка) */\nint bubbleSort(vector&lt;int&gt; &amp;nums) {\n    int count = 0; // Счетчик\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (int i = nums.size() - 1; i &gt; 0; i--) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                int tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                count += 3; // Обмен элементов включает 3 элементарные операции\n            }\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* Квадратичная сложность (пузырьковая сортировка) */\nint bubbleSort(int[] nums) {\n    int count = 0; // Счетчик\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (int i = nums.length - 1; i &gt; 0; i--) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                int tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                count += 3; // Обмен элементов включает 3 элементарные операции\n            }\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* Квадратичная сложность (пузырьковая сортировка) */\nint BubbleSort(int[] nums) {\n    int count = 0;  // Счетчик\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (int i = nums.Length - 1; i &gt; 0; i--) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                (nums[j + 1], nums[j]) = (nums[j], nums[j + 1]);\n                count += 3;  // Обмен элементов включает 3 элементарные операции\n            }\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* Квадратичная сложность (пузырьковая сортировка) */\nfunc bubbleSort(nums []int) int {\n    count := 0 // Счетчик\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for i := len(nums) - 1; i &gt; 0; i-- {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for j := 0; j &lt; i; j++ {\n            if nums[j] &gt; nums[j+1] {\n                // Поменять местами nums[j] и nums[j + 1]\n                tmp := nums[j]\n                nums[j] = nums[j+1]\n                nums[j+1] = tmp\n                count += 3 // Обмен элементов включает 3 элементарные операции\n            }\n        }\n    }\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* Квадратичная сложность (пузырьковая сортировка) */\nfunc bubbleSort(nums: inout [Int]) -&gt; Int {\n    var count = 0 // Счетчик\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for i in nums.indices.dropFirst().reversed() {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for j in 0 ..&lt; i {\n            if nums[j] &gt; nums[j + 1] {\n                // Поменять местами nums[j] и nums[j + 1]\n                let tmp = nums[j]\n                nums[j] = nums[j + 1]\n                nums[j + 1] = tmp\n                count += 3 // Обмен элементов включает 3 элементарные операции\n            }\n        }\n    }\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* Квадратичная сложность (пузырьковая сортировка) */\nfunction bubbleSort(nums) {\n    let count = 0; // Счетчик\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (let i = nums.length - 1; i &gt; 0; i--) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (let j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                let tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                count += 3; // Обмен элементов включает 3 элементарные операции\n            }\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* Квадратичная сложность (пузырьковая сортировка) */\nfunction bubbleSort(nums: number[]): number {\n    let count = 0; // Счетчик\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (let i = nums.length - 1; i &gt; 0; i--) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (let j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                let tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                count += 3; // Обмен элементов включает 3 элементарные операции\n            }\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* Квадратичная сложность (пузырьковая сортировка) */\nint bubbleSort(List&lt;int&gt; nums) {\n  int count = 0; // Счетчик\n  // Внешний цикл: неотсортированный диапазон [0, i]\n  for (var i = nums.length - 1; i &gt; 0; i--) {\n    // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n    for (var j = 0; j &lt; i; j++) {\n      if (nums[j] &gt; nums[j + 1]) {\n        // Поменять местами nums[j] и nums[j + 1]\n        int tmp = nums[j];\n        nums[j] = nums[j + 1];\n        nums[j + 1] = tmp;\n        count += 3; // Обмен элементов включает 3 элементарные операции\n      }\n    }\n  }\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* Квадратичная сложность (пузырьковая сортировка) */\nfn bubble_sort(nums: &amp;mut [i32]) -&gt; i32 {\n    let mut count = 0; // Счетчик\n\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for i in (1..nums.len()).rev() {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for j in 0..i {\n            if nums[j] &gt; nums[j + 1] {\n                // Поменять местами nums[j] и nums[j + 1]\n                let tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                count += 3; // Обмен элементов включает 3 элементарные операции\n            }\n        }\n    }\n    count\n}\n</code></pre> time_complexity.c<pre><code>/* Квадратичная сложность (пузырьковая сортировка) */\nint bubbleSort(int *nums, int n) {\n    int count = 0; // Счетчик\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (int i = n - 1; i &gt; 0; i--) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                int tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                count += 3; // Обмен элементов включает 3 элементарные операции\n            }\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* Квадратичная сложность (пузырьковая сортировка) */\nfun bubbleSort(nums: IntArray): Int {\n    var count = 0 // Счетчик\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (i in nums.size - 1 downTo 1) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (j in 0..&lt;i) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                val temp = nums[j]\n                nums[j] = nums[j + 1]\n                nums[j + 1] = temp\n                count += 3 // Обмен элементов включает 3 элементарные операции\n            }\n        }\n    }\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### Квадратичная сложность ###\ndef quadratic(n)\n  count = 0\n\n  # Число итераций квадратично зависит от размера данных n\n  for i in 0...n\n    for j in 0...n\n      count += 1\n    end\n  end\n\n  count\nend\n\n# ## Квадратичная сложность (пузырьковая сортировка) ###\ndef bubble_sort(nums)\n  count = 0  # Счетчик\n\n  # Внешний цикл: неотсортированный диапазон [0, i]\n  for i in (nums.length - 1).downto(0)\n    # Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n    for j in 0...i\n      if nums[j] &gt; nums[j + 1]\n        # Поменять местами nums[j] и nums[j + 1]\n        tmp = nums[j]\n        nums[j] = nums[j + 1]\n        nums[j + 1] = tmp\n        count += 3 # Обмен элементов включает 3 элементарные операции\n      end\n    end\n  end\n\n  count\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#4-o2n","level":3,"title":"4.   Экспоненциальная сложность \\(O(2^n)\\)","text":"<p>Типичный пример экспоненциального роста в биологии - \"деление клеток\": в начальном состоянии есть 1 клетка, после одного деления их становится 2, после двух делений - 4 и так далее; после \\(n\\) раундов деления клеток становится \\(2^n\\) .</p> <p>На рисунке 2-11 и в следующем коде моделируется процесс деления клеток; временная сложность равна \\(O(2^n)\\) . Обрати внимание, что входное значение \\(n\\) обозначает число раундов деления, а возвращаемое значение <code>count</code> обозначает общее число делений.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def exponential(n: int) -&gt; int:\n    \"\"\"Экспоненциальная сложность (итеративная реализация)\"\"\"\n    count = 0\n    base = 1\n    # На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n    for _ in range(n):\n        for _ in range(base):\n            count += 1\n        base *= 2\n    # count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* Экспоненциальная сложность (итеративная реализация) */\nint exponential(int n) {\n    int count = 0, base = 1;\n    // На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; base; j++) {\n            count++;\n        }\n        base *= 2;\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* Экспоненциальная сложность (итеративная реализация) */\nint exponential(int n) {\n    int count = 0, base = 1;\n    // На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; base; j++) {\n            count++;\n        }\n        base *= 2;\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* Экспоненциальная сложность (итеративная реализация) */\nint Exponential(int n) {\n    int count = 0, bas = 1;\n    // На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; bas; j++) {\n            count++;\n        }\n        bas *= 2;\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* Экспоненциальная сложность (итеративная реализация) */\nfunc exponential(n int) int {\n    count, base := 0, 1\n    // На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n    for i := 0; i &lt; n; i++ {\n        for j := 0; j &lt; base; j++ {\n            count++\n        }\n        base *= 2\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* Экспоненциальная сложность (итеративная реализация) */\nfunc exponential(n: Int) -&gt; Int {\n    var count = 0\n    var base = 1\n    // На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n    for _ in 0 ..&lt; n {\n        for _ in 0 ..&lt; base {\n            count += 1\n        }\n        base *= 2\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* Экспоненциальная сложность (итеративная реализация) */\nfunction exponential(n) {\n    let count = 0,\n        base = 1;\n    // На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n    for (let i = 0; i &lt; n; i++) {\n        for (let j = 0; j &lt; base; j++) {\n            count++;\n        }\n        base *= 2;\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* Экспоненциальная сложность (итеративная реализация) */\nfunction exponential(n: number): number {\n    let count = 0,\n        base = 1;\n    // На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n    for (let i = 0; i &lt; n; i++) {\n        for (let j = 0; j &lt; base; j++) {\n            count++;\n        }\n        base *= 2;\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* Экспоненциальная сложность (итеративная реализация) */\nint exponential(int n) {\n  int count = 0, base = 1;\n  // На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n  for (var i = 0; i &lt; n; i++) {\n    for (var j = 0; j &lt; base; j++) {\n      count++;\n    }\n    base *= 2;\n  }\n  // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* Экспоненциальная сложность (итеративная реализация) */\nfn exponential(n: i32) -&gt; i32 {\n    let mut count = 0;\n    let mut base = 1;\n    // На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n    for _ in 0..n {\n        for _ in 0..base {\n            count += 1\n        }\n        base *= 2;\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    count\n}\n</code></pre> time_complexity.c<pre><code>/* Экспоненциальная сложность (итеративная реализация) */\nint exponential(int n) {\n    int count = 0;\n    int bas = 1;\n    // На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; bas; j++) {\n            count++;\n        }\n        bas *= 2;\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* Экспоненциальная сложность (итеративная реализация) */\nfun exponential(n: Int): Int {\n    var count = 0\n    var base = 1\n    // На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n    for (i in 0..&lt;n) {\n        for (j in 0..&lt;base) {\n            count++\n        }\n        base *= 2\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### Квадратичная сложность ###\ndef quadratic(n)\n  count = 0\n\n  # Число итераций квадратично зависит от размера данных n\n  for i in 0...n\n    for j in 0...n\n      count += 1\n    end\n  end\n\n  count\nend\n\n# ## Квадратичная сложность (пузырьковая сортировка) ###\ndef bubble_sort(nums)\n  count = 0  # Счетчик\n\n  # Внешний цикл: неотсортированный диапазон [0, i]\n  for i in (nums.length - 1).downto(0)\n    # Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n    for j in 0...i\n      if nums[j] &gt; nums[j + 1]\n        # Поменять местами nums[j] и nums[j + 1]\n        tmp = nums[j]\n        nums[j] = nums[j + 1]\n        nums[j + 1] = tmp\n        count += 3 # Обмен элементов включает 3 элементарные операции\n      end\n    end\n  end\n\n  count\nend\n\n# ## Экспоненциальная сложность (итеративная реализация) ###\ndef exponential(n)\n  count, base = 0, 1\n\n  # На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n  (0...n).each do\n    (0...base).each { count += 1 }\n    base *= 2\n  end\n\n  # count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n  count\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p></p> <p> Рисунок 2-11   Экспоненциальная временная сложность </p> <p>В реальных алгоритмах экспоненциальная сложность также часто встречается в рекурсивных функциях. Например, в следующем коде процесс рекурсивно делится надвое и останавливается после \\(n\\) разбиений:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def exp_recur(n: int) -&gt; int:\n    \"\"\"Экспоненциальная сложность (рекурсивная реализация)\"\"\"\n    if n == 1:\n        return 1\n    return exp_recur(n - 1) + exp_recur(n - 1) + 1\n</code></pre> time_complexity.cpp<pre><code>/* Экспоненциальная сложность (рекурсивная реализация) */\nint expRecur(int n) {\n    if (n == 1)\n        return 1;\n    return expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.java<pre><code>/* Экспоненциальная сложность (рекурсивная реализация) */\nint expRecur(int n) {\n    if (n == 1)\n        return 1;\n    return expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.cs<pre><code>/* Экспоненциальная сложность (рекурсивная реализация) */\nint ExpRecur(int n) {\n    if (n == 1) return 1;\n    return ExpRecur(n - 1) + ExpRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.go<pre><code>/* Экспоненциальная сложность (рекурсивная реализация) */\nfunc expRecur(n int) int {\n    if n == 1 {\n        return 1\n    }\n    return expRecur(n-1) + expRecur(n-1) + 1\n}\n</code></pre> time_complexity.swift<pre><code>/* Экспоненциальная сложность (рекурсивная реализация) */\nfunc expRecur(n: Int) -&gt; Int {\n    if n == 1 {\n        return 1\n    }\n    return expRecur(n: n - 1) + expRecur(n: n - 1) + 1\n}\n</code></pre> time_complexity.js<pre><code>/* Экспоненциальная сложность (рекурсивная реализация) */\nfunction expRecur(n) {\n    if (n === 1) return 1;\n    return expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.ts<pre><code>/* Экспоненциальная сложность (рекурсивная реализация) */\nfunction expRecur(n: number): number {\n    if (n === 1) return 1;\n    return expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.dart<pre><code>/* Экспоненциальная сложность (рекурсивная реализация) */\nint expRecur(int n) {\n  if (n == 1) return 1;\n  return expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.rs<pre><code>/* Экспоненциальная сложность (рекурсивная реализация) */\nfn exp_recur(n: i32) -&gt; i32 {\n    if n == 1 {\n        return 1;\n    }\n    exp_recur(n - 1) + exp_recur(n - 1) + 1\n}\n</code></pre> time_complexity.c<pre><code>/* Экспоненциальная сложность (рекурсивная реализация) */\nint expRecur(int n) {\n    if (n == 1)\n        return 1;\n    return expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.kt<pre><code>/* Экспоненциальная сложность (рекурсивная реализация) */\nfun expRecur(n: Int): Int {\n    if (n == 1) {\n        return 1\n    }\n    return expRecur(n - 1) + expRecur(n - 1) + 1\n}\n</code></pre> time_complexity.rb<pre><code>### Квадратичная сложность ###\ndef quadratic(n)\n  count = 0\n\n  # Число итераций квадратично зависит от размера данных n\n  for i in 0...n\n    for j in 0...n\n      count += 1\n    end\n  end\n\n  count\nend\n\n# ## Квадратичная сложность (пузырьковая сортировка) ###\ndef bubble_sort(nums)\n  count = 0  # Счетчик\n\n  # Внешний цикл: неотсортированный диапазон [0, i]\n  for i in (nums.length - 1).downto(0)\n    # Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n    for j in 0...i\n      if nums[j] &gt; nums[j + 1]\n        # Поменять местами nums[j] и nums[j + 1]\n        tmp = nums[j]\n        nums[j] = nums[j + 1]\n        nums[j + 1] = tmp\n        count += 3 # Обмен элементов включает 3 элементарные операции\n      end\n    end\n  end\n\n  count\nend\n\n# ## Экспоненциальная сложность (итеративная реализация) ###\ndef exponential(n)\n  count, base = 0, 1\n\n  # На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n  (0...n).each do\n    (0...base).each { count += 1 }\n    base *= 2\n  end\n\n  # count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n  count\nend\n\n# ## Экспоненциальная сложность (рекурсивная реализация) ###\ndef exp_recur(n)\n  return 1 if n == 1\n  exp_recur(n - 1) + exp_recur(n - 1) + 1\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Экспоненциальный рост происходит очень быстро и часто встречается в переборных методах (грубая сила, backtracking и т.д.). Для задач большого масштаба экспоненциальная сложность неприемлема, и обычно приходится применять динамическое программирование, жадные алгоритмы и другие подходы.</p>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#5-olog-n","level":3,"title":"5.   Логарифмическая сложность \\(O(\\log n)\\)","text":"<p>В противоположность экспоненциальной, логарифмическая сложность описывает ситуацию \"каждый раунд уменьшение вдвое\". Пусть размер входных данных равен \\(n\\) ; так как на каждом шаге размер уменьшается вдвое, число итераций равно \\(\\log_2 n\\) , то есть является обратной функцией к \\(2^n\\) .</p> <p>На рисунке 2-12 и в следующем коде моделируется процесс \"каждый раунд уменьшение вдвое\"; временная сложность равна \\(O(\\log_2 n)\\) и кратко записывается как \\(O(\\log n)\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def logarithmic(n: int) -&gt; int:\n    \"\"\"Логарифмическая сложность (итеративная реализация)\"\"\"\n    count = 0\n    while n &gt; 1:\n        n = n / 2\n        count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* Логарифмическая сложность (итеративная реализация) */\nint logarithmic(int n) {\n    int count = 0;\n    while (n &gt; 1) {\n        n = n / 2;\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* Логарифмическая сложность (итеративная реализация) */\nint logarithmic(int n) {\n    int count = 0;\n    while (n &gt; 1) {\n        n = n / 2;\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* Логарифмическая сложность (итеративная реализация) */\nint Logarithmic(int n) {\n    int count = 0;\n    while (n &gt; 1) {\n        n /= 2;\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* Логарифмическая сложность (итеративная реализация) */\nfunc logarithmic(n int) int {\n    count := 0\n    for n &gt; 1 {\n        n = n / 2\n        count++\n    }\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* Логарифмическая сложность (итеративная реализация) */\nfunc logarithmic(n: Int) -&gt; Int {\n    var count = 0\n    var n = n\n    while n &gt; 1 {\n        n = n / 2\n        count += 1\n    }\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* Логарифмическая сложность (итеративная реализация) */\nfunction logarithmic(n) {\n    let count = 0;\n    while (n &gt; 1) {\n        n = n / 2;\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* Логарифмическая сложность (итеративная реализация) */\nfunction logarithmic(n: number): number {\n    let count = 0;\n    while (n &gt; 1) {\n        n = n / 2;\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* Логарифмическая сложность (итеративная реализация) */\nint logarithmic(int n) {\n  int count = 0;\n  while (n &gt; 1) {\n    n = n ~/ 2;\n    count++;\n  }\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* Логарифмическая сложность (итеративная реализация) */\nfn logarithmic(mut n: i32) -&gt; i32 {\n    let mut count = 0;\n    while n &gt; 1 {\n        n = n / 2;\n        count += 1;\n    }\n    count\n}\n</code></pre> time_complexity.c<pre><code>/* Логарифмическая сложность (итеративная реализация) */\nint logarithmic(int n) {\n    int count = 0;\n    while (n &gt; 1) {\n        n = n / 2;\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* Логарифмическая сложность (итеративная реализация) */\nfun logarithmic(n: Int): Int {\n    var n1 = n\n    var count = 0\n    while (n1 &gt; 1) {\n        n1 /= 2\n        count++\n    }\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### Квадратичная сложность ###\ndef quadratic(n)\n  count = 0\n\n  # Число итераций квадратично зависит от размера данных n\n  for i in 0...n\n    for j in 0...n\n      count += 1\n    end\n  end\n\n  count\nend\n\n# ## Квадратичная сложность (пузырьковая сортировка) ###\ndef bubble_sort(nums)\n  count = 0  # Счетчик\n\n  # Внешний цикл: неотсортированный диапазон [0, i]\n  for i in (nums.length - 1).downto(0)\n    # Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n    for j in 0...i\n      if nums[j] &gt; nums[j + 1]\n        # Поменять местами nums[j] и nums[j + 1]\n        tmp = nums[j]\n        nums[j] = nums[j + 1]\n        nums[j + 1] = tmp\n        count += 3 # Обмен элементов включает 3 элементарные операции\n      end\n    end\n  end\n\n  count\nend\n\n# ## Экспоненциальная сложность (итеративная реализация) ###\ndef exponential(n)\n  count, base = 0, 1\n\n  # На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n  (0...n).each do\n    (0...base).each { count += 1 }\n    base *= 2\n  end\n\n  # count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n  count\nend\n\n# ## Экспоненциальная сложность (рекурсивная реализация) ###\ndef exp_recur(n)\n  return 1 if n == 1\n  exp_recur(n - 1) + exp_recur(n - 1) + 1\nend\n\n# ## Логарифмическая сложность (итеративная реализация) ###\ndef logarithmic(n)\n  count = 0\n\n  while n &gt; 1\n    n /= 2\n    count += 1\n  end\n\n  count\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p></p> <p> Рисунок 2-12   Логарифмическая временная сложность </p> <p>Подобно экспоненциальной сложности, логарифмическая также часто встречается в рекурсивных функциях. Следующий код формирует рекурсивное дерево высотой \\(\\log_2 n\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def log_recur(n: int) -&gt; int:\n    \"\"\"Логарифмическая сложность (рекурсивная реализация)\"\"\"\n    if n &lt;= 1:\n        return 0\n    return log_recur(n / 2) + 1\n</code></pre> time_complexity.cpp<pre><code>/* Логарифмическая сложность (рекурсивная реализация) */\nint logRecur(int n) {\n    if (n &lt;= 1)\n        return 0;\n    return logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.java<pre><code>/* Логарифмическая сложность (рекурсивная реализация) */\nint logRecur(int n) {\n    if (n &lt;= 1)\n        return 0;\n    return logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.cs<pre><code>/* Логарифмическая сложность (рекурсивная реализация) */\nint LogRecur(int n) {\n    if (n &lt;= 1) return 0;\n    return LogRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.go<pre><code>/* Логарифмическая сложность (рекурсивная реализация) */\nfunc logRecur(n int) int {\n    if n &lt;= 1 {\n        return 0\n    }\n    return logRecur(n/2) + 1\n}\n</code></pre> time_complexity.swift<pre><code>/* Логарифмическая сложность (рекурсивная реализация) */\nfunc logRecur(n: Int) -&gt; Int {\n    if n &lt;= 1 {\n        return 0\n    }\n    return logRecur(n: n / 2) + 1\n}\n</code></pre> time_complexity.js<pre><code>/* Логарифмическая сложность (рекурсивная реализация) */\nfunction logRecur(n) {\n    if (n &lt;= 1) return 0;\n    return logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.ts<pre><code>/* Логарифмическая сложность (рекурсивная реализация) */\nfunction logRecur(n: number): number {\n    if (n &lt;= 1) return 0;\n    return logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.dart<pre><code>/* Логарифмическая сложность (рекурсивная реализация) */\nint logRecur(int n) {\n  if (n &lt;= 1) return 0;\n  return logRecur(n ~/ 2) + 1;\n}\n</code></pre> time_complexity.rs<pre><code>/* Логарифмическая сложность (рекурсивная реализация) */\nfn log_recur(n: i32) -&gt; i32 {\n    if n &lt;= 1 {\n        return 0;\n    }\n    log_recur(n / 2) + 1\n}\n</code></pre> time_complexity.c<pre><code>/* Логарифмическая сложность (рекурсивная реализация) */\nint logRecur(int n) {\n    if (n &lt;= 1)\n        return 0;\n    return logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.kt<pre><code>/* Логарифмическая сложность (рекурсивная реализация) */\nfun logRecur(n: Int): Int {\n    if (n &lt;= 1)\n        return 0\n    return logRecur(n / 2) + 1\n}\n</code></pre> time_complexity.rb<pre><code>### Квадратичная сложность ###\ndef quadratic(n)\n  count = 0\n\n  # Число итераций квадратично зависит от размера данных n\n  for i in 0...n\n    for j in 0...n\n      count += 1\n    end\n  end\n\n  count\nend\n\n# ## Квадратичная сложность (пузырьковая сортировка) ###\ndef bubble_sort(nums)\n  count = 0  # Счетчик\n\n  # Внешний цикл: неотсортированный диапазон [0, i]\n  for i in (nums.length - 1).downto(0)\n    # Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n    for j in 0...i\n      if nums[j] &gt; nums[j + 1]\n        # Поменять местами nums[j] и nums[j + 1]\n        tmp = nums[j]\n        nums[j] = nums[j + 1]\n        nums[j + 1] = tmp\n        count += 3 # Обмен элементов включает 3 элементарные операции\n      end\n    end\n  end\n\n  count\nend\n\n# ## Экспоненциальная сложность (итеративная реализация) ###\ndef exponential(n)\n  count, base = 0, 1\n\n  # На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n  (0...n).each do\n    (0...base).each { count += 1 }\n    base *= 2\n  end\n\n  # count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n  count\nend\n\n# ## Экспоненциальная сложность (рекурсивная реализация) ###\ndef exp_recur(n)\n  return 1 if n == 1\n  exp_recur(n - 1) + exp_recur(n - 1) + 1\nend\n\n# ## Логарифмическая сложность (итеративная реализация) ###\ndef logarithmic(n)\n  count = 0\n\n  while n &gt; 1\n    n /= 2\n    count += 1\n  end\n\n  count\nend\n\n# ## Логарифмическая сложность (рекурсивная реализация) ###\ndef log_recur(n)\n  return 0 unless n &gt; 1\n  log_recur(n / 2) + 1\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Логарифмическая сложность часто встречается в алгоритмах, основанных на стратегии \"разделяй и властвуй\", и отражает идеи \"разделить одно на много\" и \"упростить сложное\". Она растет медленно и является идеальной временной сложностью, уступающей только постоянной.</p> <p>Каково основание у \\(O(\\log n)\\) ?</p> <p>Точнее говоря, \"разделение на \\(m\\) частей\" соответствует временной сложности \\(O(\\log_m n)\\) . А по формуле перехода к другому основанию логарифма мы получаем равные по сложности выражения с разными основаниями:</p> \\[ O(\\log_m n) = O(\\log_k n / \\log_k m) = O(\\log_k n) \\] <p>Иными словами, основание \\(m\\) можно менять без влияния на сложность. Поэтому мы обычно опускаем основание \\(m\\) и напрямую записываем логарифмическую сложность как \\(O(\\log n)\\) .</p>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#6-on-log-n","level":3,"title":"6.   Линейно-логарифмическая сложность \\(O(n \\log n)\\)","text":"<p>Линейно-логарифмическая сложность часто встречается во вложенных циклах, когда временная сложность двух уровней соответственно равна \\(O(\\log n)\\) и \\(O(n)\\) . Соответствующий код выглядит следующим образом:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def linear_log_recur(n: int) -&gt; int:\n    \"\"\"Линейно-логарифмическая сложность\"\"\"\n    if n &lt;= 1:\n        return 1\n    # Разделение надвое: размер подзадачи уменьшается вдвое\n    count = linear_log_recur(n // 2) + linear_log_recur(n // 2)\n    # Текущая подзадача содержит n операций\n    for _ in range(n):\n        count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* Линейно-логарифмическая сложность */\nint linearLogRecur(int n) {\n    if (n &lt;= 1)\n        return 1;\n    int count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\n    for (int i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* Линейно-логарифмическая сложность */\nint linearLogRecur(int n) {\n    if (n &lt;= 1)\n        return 1;\n    int count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\n    for (int i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* Линейно-логарифмическая сложность */\nint LinearLogRecur(int n) {\n    if (n &lt;= 1) return 1;\n    int count = LinearLogRecur(n / 2) + LinearLogRecur(n / 2);\n    for (int i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* Линейно-логарифмическая сложность */\nfunc linearLogRecur(n int) int {\n    if n &lt;= 1 {\n        return 1\n    }\n    count := linearLogRecur(n/2) + linearLogRecur(n/2)\n    for i := 0; i &lt; n; i++ {\n        count++\n    }\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* Линейно-логарифмическая сложность */\nfunc linearLogRecur(n: Int) -&gt; Int {\n    if n &lt;= 1 {\n        return 1\n    }\n    var count = linearLogRecur(n: n / 2) + linearLogRecur(n: n / 2)\n    for _ in stride(from: 0, to: n, by: 1) {\n        count += 1\n    }\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* Линейно-логарифмическая сложность */\nfunction linearLogRecur(n) {\n    if (n &lt;= 1) return 1;\n    let count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\n    for (let i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* Линейно-логарифмическая сложность */\nfunction linearLogRecur(n: number): number {\n    if (n &lt;= 1) return 1;\n    let count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\n    for (let i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* Линейно-логарифмическая сложность */\nint linearLogRecur(int n) {\n  if (n &lt;= 1) return 1;\n  int count = linearLogRecur(n ~/ 2) + linearLogRecur(n ~/ 2);\n  for (var i = 0; i &lt; n; i++) {\n    count++;\n  }\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* Линейно-логарифмическая сложность */\nfn linear_log_recur(n: i32) -&gt; i32 {\n    if n &lt;= 1 {\n        return 1;\n    }\n    let mut count = linear_log_recur(n / 2) + linear_log_recur(n / 2);\n    for _ in 0..n {\n        count += 1;\n    }\n    return count;\n}\n</code></pre> time_complexity.c<pre><code>/* Линейно-логарифмическая сложность */\nint linearLogRecur(int n) {\n    if (n &lt;= 1)\n        return 1;\n    int count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\n    for (int i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* Линейно-логарифмическая сложность */\nfun linearLogRecur(n: Int): Int {\n    if (n &lt;= 1)\n        return 1\n    var count = linearLogRecur(n / 2) + linearLogRecur(n / 2)\n    for (i in 0..&lt;n) {\n        count++\n    }\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### Линейно-логарифмическая сложность ###\ndef linear_log_recur(n)\n  return 1 unless n &gt; 1\n\n  count = linear_log_recur(n / 2) + linear_log_recur(n / 2)\n  (0...n).each { count += 1 }\n\n  count\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>На рисунке 2-13 показано, как возникает линейно-логарифмическая сложность. Общее число операций на каждом уровне бинарного дерева равно \\(n\\) , а дерево имеет \\(\\log_2 n + 1\\) уровней, поэтому временная сложность равна \\(O(n \\log n)\\) .</p> <p></p> <p> Рисунок 2-13   Линейно-логарифмическая временная сложность </p> <p>Временная сложность основных алгоритмов сортировки обычно равна \\(O(n \\log n)\\) , например у быстрой сортировки, сортировки слиянием, пирамидальной сортировки и т.д.</p>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#7-on","level":3,"title":"7.   Факториальная сложность \\(O(n!)\\)","text":"<p>Факториальная сложность соответствует математической задаче \"все перестановки\". Если даны \\(n\\) попарно различных элементов, то число всех возможных перестановок равно:</p> \\[ n! = n \\times (n - 1) \\times (n - 2) \\times \\dots \\times 2 \\times 1 \\] <p>Факториал обычно реализуют через рекурсию. Как показано на рисунке 2-14 и в следующем коде, на первом уровне происходит ветвление на \\(n\\) подзадач, на втором - на \\(n - 1\\) и так далее, пока на \\(n\\) -м уровне ветвление не прекращается:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def factorial_recur(n: int) -&gt; int:\n    \"\"\"Факториальная сложность (рекурсивная реализация)\"\"\"\n    if n == 0:\n        return 1\n    count = 0\n    # Из одного получается n\n    for _ in range(n):\n        count += factorial_recur(n - 1)\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* Факториальная сложность (рекурсивная реализация) */\nint factorialRecur(int n) {\n    if (n == 0)\n        return 1;\n    int count = 0;\n    // Из одного получается n\n    for (int i = 0; i &lt; n; i++) {\n        count += factorialRecur(n - 1);\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* Факториальная сложность (рекурсивная реализация) */\nint factorialRecur(int n) {\n    if (n == 0)\n        return 1;\n    int count = 0;\n    // Из одного получается n\n    for (int i = 0; i &lt; n; i++) {\n        count += factorialRecur(n - 1);\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* Факториальная сложность (рекурсивная реализация) */\nint FactorialRecur(int n) {\n    if (n == 0) return 1;\n    int count = 0;\n    // Из одного получается n\n    for (int i = 0; i &lt; n; i++) {\n        count += FactorialRecur(n - 1);\n    }\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* Факториальная сложность (рекурсивная реализация) */\nfunc factorialRecur(n int) int {\n    if n == 0 {\n        return 1\n    }\n    count := 0\n    // Из одного получается n\n    for i := 0; i &lt; n; i++ {\n        count += factorialRecur(n - 1)\n    }\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* Факториальная сложность (рекурсивная реализация) */\nfunc factorialRecur(n: Int) -&gt; Int {\n    if n == 0 {\n        return 1\n    }\n    var count = 0\n    // Из одного получается n\n    for _ in 0 ..&lt; n {\n        count += factorialRecur(n: n - 1)\n    }\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* Факториальная сложность (рекурсивная реализация) */\nfunction factorialRecur(n) {\n    if (n === 0) return 1;\n    let count = 0;\n    // Из одного получается n\n    for (let i = 0; i &lt; n; i++) {\n        count += factorialRecur(n - 1);\n    }\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* Факториальная сложность (рекурсивная реализация) */\nfunction factorialRecur(n: number): number {\n    if (n === 0) return 1;\n    let count = 0;\n    // Из одного получается n\n    for (let i = 0; i &lt; n; i++) {\n        count += factorialRecur(n - 1);\n    }\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* Факториальная сложность (рекурсивная реализация) */\nint factorialRecur(int n) {\n  if (n == 0) return 1;\n  int count = 0;\n  // Из одного получается n\n  for (var i = 0; i &lt; n; i++) {\n    count += factorialRecur(n - 1);\n  }\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* Факториальная сложность (рекурсивная реализация) */\nfn factorial_recur(n: i32) -&gt; i32 {\n    if n == 0 {\n        return 1;\n    }\n    let mut count = 0;\n    // Из одного получается n\n    for _ in 0..n {\n        count += factorial_recur(n - 1);\n    }\n    count\n}\n</code></pre> time_complexity.c<pre><code>/* Факториальная сложность (рекурсивная реализация) */\nint factorialRecur(int n) {\n    if (n == 0)\n        return 1;\n    int count = 0;\n    for (int i = 0; i &lt; n; i++) {\n        count += factorialRecur(n - 1);\n    }\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* Факториальная сложность (рекурсивная реализация) */\nfun factorialRecur(n: Int): Int {\n    if (n == 0)\n        return 1\n    var count = 0\n    // Из одного получается n\n    for (i in 0..&lt;n) {\n        count += factorialRecur(n - 1)\n    }\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### Линейно-логарифмическая сложность ###\ndef linear_log_recur(n)\n  return 1 unless n &gt; 1\n\n  count = linear_log_recur(n / 2) + linear_log_recur(n / 2)\n  (0...n).each { count += 1 }\n\n  count\nend\n\n# ## Факториальная сложность (рекурсивная реализация) ###\ndef factorial_recur(n)\n  return 1 if n == 0\n\n  count = 0\n  # Из одного получается n\n  (0...n).each { count += factorial_recur(n - 1) }\n\n  count\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p></p> <p> Рисунок 2-14   Факториальная временная сложность </p> <p>Обрати внимание: поскольку при \\(n \\geq 4\\) всегда выполняется \\(n! &gt; 2^n\\) , факториальная сложность растет еще быстрее, чем экспоненциальная, и при больших \\(n\\) также неприемлема.</p>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#235","level":2,"title":"2.3.5   Худшая, лучшая и средняя временная сложность","text":"<p>Временная эффективность алгоритма часто не фиксирована, а зависит от распределения входных данных. Предположим, на вход подается массив <code>nums</code> длины \\(n\\) , состоящий из чисел от \\(1\\) до \\(n\\) , каждое из которых встречается ровно один раз; при этом порядок элементов случайно перемешан. Задача состоит в том, чтобы вернуть индекс элемента \\(1\\) . Тогда можно сделать следующие выводы.</p> <ul> <li>Когда <code>nums = [?, ?, ..., 1]</code> , то есть когда последний элемент равен \\(1\\) , нужно полностью пройти по массиву, что дает худшую временную сложность \\(O(n)\\) .</li> <li>Когда <code>nums = [1, ?, ?, ...]</code> , то есть когда первый элемент равен \\(1\\) , независимо от длины массива продолжать обход не нужно, что дает лучшую временную сложность \\(\\Omega(1)\\) .</li> </ul> <p>\"Худшая временная сложность\" соответствует асимптотической верхней границе функции и обозначается нотацией Big \\(O\\) . Соответственно, \"лучшая временная сложность\" соответствует асимптотической нижней границе функции и обозначается символом \\(\\Omega\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby worst_best_time_complexity.py<pre><code>def random_numbers(n: int) -&gt; list[int]:\n    \"\"\"Сгенерировать массив с элементами 1, 2, ..., n в случайном порядке\"\"\"\n    # Создать массив nums =: 1, 2, 3, ..., n\n    nums = [i for i in range(1, n + 1)]\n    # Случайно перемешать элементы массива\n    random.shuffle(nums)\n    return nums\n\ndef find_one(nums: list[int]) -&gt; int:\n    \"\"\"Найти индекс числа 1 в массиве nums\"\"\"\n    for i in range(len(nums)):\n        # Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n        # Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n        if nums[i] == 1:\n            return i\n    return -1\n</code></pre> worst_best_time_complexity.cpp<pre><code>/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */\nvector&lt;int&gt; randomNumbers(int n) {\n    vector&lt;int&gt; nums(n);\n    // Создать массив nums = { 1, 2, 3, ..., n }\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = i + 1;\n    }\n    // Использовать системное время для генерации случайного seed\n    unsigned seed = chrono::system_clock::now().time_since_epoch().count();\n    // Случайно перемешать элементы массива\n    shuffle(nums.begin(), nums.end(), default_random_engine(seed));\n    return nums;\n}\n\n/* Найти индекс числа 1 в массиве nums */\nint findOne(vector&lt;int&gt; &amp;nums) {\n    for (int i = 0; i &lt; nums.size(); i++) {\n        // Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n        // Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n        if (nums[i] == 1)\n            return i;\n    }\n    return -1;\n}\n</code></pre> worst_best_time_complexity.java<pre><code>/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */\nint[] randomNumbers(int n) {\n    Integer[] nums = new Integer[n];\n    // Создать массив nums = { 1, 2, 3, ..., n }\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = i + 1;\n    }\n    // Случайно перемешать элементы массива\n    Collections.shuffle(Arrays.asList(nums));\n    // Integer[] -&gt; int[]\n    int[] res = new int[n];\n    for (int i = 0; i &lt; n; i++) {\n        res[i] = nums[i];\n    }\n    return res;\n}\n\n/* Найти индекс числа 1 в массиве nums */\nint findOne(int[] nums) {\n    for (int i = 0; i &lt; nums.length; i++) {\n        // Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n        // Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n        if (nums[i] == 1)\n            return i;\n    }\n    return -1;\n}\n</code></pre> worst_best_time_complexity.cs<pre><code>/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */\nint[] RandomNumbers(int n) {\n    int[] nums = new int[n];\n    // Создать массив nums = { 1, 2, 3, ..., n }\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = i + 1;\n    }\n\n    // Случайно перемешать элементы массива\n    for (int i = 0; i &lt; nums.Length; i++) {\n        int index = new Random().Next(i, nums.Length);\n        (nums[i], nums[index]) = (nums[index], nums[i]);\n    }\n    return nums;\n}\n\n/* Найти индекс числа 1 в массиве nums */\nint FindOne(int[] nums) {\n    for (int i = 0; i &lt; nums.Length; i++) {\n        // Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n        // Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n        if (nums[i] == 1)\n            return i;\n    }\n    return -1;\n}\n</code></pre> worst_best_time_complexity.go<pre><code>/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */\nfunc randomNumbers(n int) []int {\n    nums := make([]int, n)\n    // Создать массив nums = { 1, 2, 3, ..., n }\n    for i := 0; i &lt; n; i++ {\n        nums[i] = i + 1\n    }\n    // Случайно перемешать элементы массива\n    rand.Shuffle(len(nums), func(i, j int) {\n        nums[i], nums[j] = nums[j], nums[i]\n    })\n    return nums\n}\n\n/* Найти индекс числа 1 в массиве nums */\nfunc findOne(nums []int) int {\n    for i := 0; i &lt; len(nums); i++ {\n        // Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n        // Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n        if nums[i] == 1 {\n            return i\n        }\n    }\n    return -1\n}\n</code></pre> worst_best_time_complexity.swift<pre><code>/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */\nfunc randomNumbers(n: Int) -&gt; [Int] {\n    // Создать массив nums = { 1, 2, 3, ..., n }\n    var nums = Array(1 ... n)\n    // Случайно перемешать элементы массива\n    nums.shuffle()\n    return nums\n}\n\n/* Найти индекс числа 1 в массиве nums */\nfunc findOne(nums: [Int]) -&gt; Int {\n    for i in nums.indices {\n        // Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n        // Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n        if nums[i] == 1 {\n            return i\n        }\n    }\n    return -1\n}\n</code></pre> worst_best_time_complexity.js<pre><code>/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */\nfunction randomNumbers(n) {\n    const nums = Array(n);\n    // Создать массив nums = { 1, 2, 3, ..., n }\n    for (let i = 0; i &lt; n; i++) {\n        nums[i] = i + 1;\n    }\n    // Случайно перемешать элементы массива\n    for (let i = 0; i &lt; n; i++) {\n        const r = Math.floor(Math.random() * (i + 1));\n        const temp = nums[i];\n        nums[i] = nums[r];\n        nums[r] = temp;\n    }\n    return nums;\n}\n\n/* Найти индекс числа 1 в массиве nums */\nfunction findOne(nums) {\n    for (let i = 0; i &lt; nums.length; i++) {\n        // Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n        // Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n        if (nums[i] === 1) {\n            return i;\n        }\n    }\n    return -1;\n}\n</code></pre> worst_best_time_complexity.ts<pre><code>/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */\nfunction randomNumbers(n: number): number[] {\n    const nums = Array(n);\n    // Создать массив nums = { 1, 2, 3, ..., n }\n    for (let i = 0; i &lt; n; i++) {\n        nums[i] = i + 1;\n    }\n    // Случайно перемешать элементы массива\n    for (let i = 0; i &lt; n; i++) {\n        const r = Math.floor(Math.random() * (i + 1));\n        const temp = nums[i];\n        nums[i] = nums[r];\n        nums[r] = temp;\n    }\n    return nums;\n}\n\n/* Найти индекс числа 1 в массиве nums */\nfunction findOne(nums: number[]): number {\n    for (let i = 0; i &lt; nums.length; i++) {\n        // Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n        // Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n        if (nums[i] === 1) {\n            return i;\n        }\n    }\n    return -1;\n}\n</code></pre> worst_best_time_complexity.dart<pre><code>/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */\nList&lt;int&gt; randomNumbers(int n) {\n  final nums = List.filled(n, 0);\n  // Создать массив nums = { 1, 2, 3, ..., n }\n  for (var i = 0; i &lt; n; i++) {\n    nums[i] = i + 1;\n  }\n  // Случайно перемешать элементы массива\n  nums.shuffle();\n\n  return nums;\n}\n\n/* Найти индекс числа 1 в массиве nums */\nint findOne(List&lt;int&gt; nums) {\n  for (var i = 0; i &lt; nums.length; i++) {\n    // Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n    // Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n    if (nums[i] == 1) return i;\n  }\n\n  return -1;\n}\n</code></pre> worst_best_time_complexity.rs<pre><code>/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */\nfn random_numbers(n: i32) -&gt; Vec&lt;i32&gt; {\n    // Создать массив nums = { 1, 2, 3, ..., n }\n    let mut nums = (1..=n).collect::&lt;Vec&lt;i32&gt;&gt;();\n    // Случайно перемешать элементы массива\n    nums.shuffle(&amp;mut thread_rng());\n    nums\n}\n\n/* Найти индекс числа 1 в массиве nums */\nfn find_one(nums: &amp;[i32]) -&gt; Option&lt;usize&gt; {\n    for i in 0..nums.len() {\n        // Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n        // Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n        if nums[i] == 1 {\n            return Some(i);\n        }\n    }\n    None\n}\n</code></pre> worst_best_time_complexity.c<pre><code>/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */\nint *randomNumbers(int n) {\n    // Выделить память в куче (создать одномерный массив переменной длины: число элементов равно n, тип элементов — int)\n    int *nums = (int *)malloc(n * sizeof(int));\n    // Создать массив nums = { 1, 2, 3, ..., n }\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = i + 1;\n    }\n    // Случайно перемешать элементы массива\n    for (int i = n - 1; i &gt; 0; i--) {\n        int j = rand() % (i + 1);\n        int temp = nums[i];\n        nums[i] = nums[j];\n        nums[j] = temp;\n    }\n    return nums;\n}\n\n/* Найти индекс числа 1 в массиве nums */\nint findOne(int *nums, int n) {\n    for (int i = 0; i &lt; n; i++) {\n        // Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n        // Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n        if (nums[i] == 1)\n            return i;\n    }\n    return -1;\n}\n</code></pre> worst_best_time_complexity.kt<pre><code>/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */\nfun randomNumbers(n: Int): Array&lt;Int?&gt; {\n    val nums = IntArray(n)\n    // Создать массив nums = { 1, 2, 3, ..., n }\n    for (i in 0..&lt;n) {\n        nums[i] = i + 1\n    }\n    // Случайно перемешать элементы массива\n    nums.shuffle()\n    val res = arrayOfNulls&lt;Int&gt;(n)\n    for (i in 0..&lt;n) {\n        res[i] = nums[i]\n    }\n    return res\n}\n\n/* Найти индекс числа 1 в массиве nums */\nfun findOne(nums: Array&lt;Int?&gt;): Int {\n    for (i in nums.indices) {\n        // Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n        // Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n        if (nums[i] == 1)\n            return i\n    }\n    return -1\n}\n</code></pre> worst_best_time_complexity.rb<pre><code>### Создать массив с элементами: 1, 2, ..., n в случайном порядке ###\ndef random_numbers(n)\n  # Создать массив nums =: 1, 2, 3, ..., n\n  nums = Array.new(n) { |i| i + 1 }\n  # Случайно перемешать элементы массива\n  nums.shuffle!\nend\n\n### Найти индекс числа 1 в массиве nums ###\ndef find_one(nums)\n  for i in 0...nums.length\n    # Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n    # Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n    return i if nums[i] == 1\n  end\n\n  -1\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Стоит отметить, что на практике мы редко используем лучшую временную сложность, поскольку обычно она достигается лишь с очень малой вероятностью и может вводить в заблуждение. Худшая временная сложность гораздо практичнее, потому что задает безопасную оценку эффективности и позволяет уверенно использовать алгоритм.</p> <p>Из приведенного выше примера видно, что худшая и лучшая временные сложности возникают только при \"особых распределениях данных\"; вероятность таких случаев может быть низкой, и они не всегда реально отражают эффективность алгоритма. Напротив, средняя временная сложность способна показать эффективность алгоритма на случайных входных данных и обозначается символом \\(\\Theta\\) .</p> <p>Для некоторых алгоритмов мы можем относительно просто вывести средний случай при случайном распределении данных. Например, в приведенном выше примере входной массив перемешан, а значит вероятность появления элемента \\(1\\) на любом индексе одинакова; следовательно, среднее число итераций алгоритма равно половине длины массива, то есть \\(n / 2\\) , а средняя временная сложность равна \\(\\Theta(n / 2) = \\Theta(n)\\) .</p> <p>Но для более сложных алгоритмов вычислить среднюю временную сложность часто непросто, потому что трудно проанализировать полное математическое ожидание на заданном распределении данных. В таких случаях мы обычно используем худшую временную сложность как критерий оценки эффективности алгоритма.</p> <p>Почему символ \\(\\Theta\\) встречается так редко?</p> <p>Возможно, потому что символ \\(O\\) звучит слишком привычно, и мы часто используем его для обозначения средней временной сложности. Но строго говоря, это некорректно. В этой книге и в других материалах, если встретится выражение вроде \"средняя временная сложность \\(O(n)\\)\", просто понимай его как \\(\\Theta(n)\\) .</p>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_data_structure/","level":1,"title":"Глава 3.   Структуры данных","text":"<p>Abstract</p> <p>Структуры данных подобны прочному и разнообразному каркасу.</p> <p>Они задают план упорядоченной организации данных, а алгоритмы на этой основе обретают жизнь.</p>","path":["Глава 3. Структуры данных","Глава 3. &nbsp; Структуры данных"],"tags":[]},{"location":"chapter_data_structure/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>3.1   Классификация структур данных</li> <li>3.2   Базовые типы данных</li> <li>3.3   Кодирование чисел *</li> <li>3.4   Кодирование символов *</li> <li>3.5   Резюме</li> </ul>","path":["Глава 3. Структуры данных","Глава 3. &nbsp; Структуры данных"],"tags":[]},{"location":"chapter_data_structure/basic_data_types/","level":1,"title":"3.2   Базовые типы данных","text":"<p>Когда мы говорим о данных в компьютере, нам приходят на ум текст, изображения, видео, звук, 3D-модели и многие другие формы. Хотя эти данные организованы по-разному, все они состоят из различных базовых типов данных.</p> <p>Базовые типы данных - это типы, с которыми CPU может работать напрямую; в алгоритмах они используются непосредственно и в основном включают следующее.</p> <ul> <li>Целочисленные типы <code>byte</code> , <code>short</code> , <code>int</code> , <code>long</code> .</li> <li>Типы с плавающей точкой <code>float</code> , <code>double</code> , используемые для представления дробных чисел.</li> <li>Символьный тип <code>char</code> , используемый для представления букв, знаков препинания и даже эмодзи в разных языках.</li> <li>Логический тип <code>bool</code> , используемый для представления суждений \"да\" и \"нет\".</li> </ul> <p>Базовые типы данных хранятся в компьютере в двоичной форме. Один двоичный разряд равен \\(1\\) биту. В подавляющем большинстве современных операционных систем \\(1\\) байт (byte) состоит из \\(8\\) битов (bit).</p> <p>Диапазон значений базовых типов данных зависит от объема занимаемого ими пространства. Ниже в качестве примера используется Java.</p> <ul> <li>Целочисленный тип <code>byte</code> занимает \\(1\\) байт = \\(8\\) бит и может представлять \\(2^{8}\\) чисел.</li> <li>Целочисленный тип <code>int</code> занимает \\(4\\) байта = \\(32\\) бита и может представлять \\(2^{32}\\) чисел.</li> </ul> <p>В таблице 3-1 перечислены объем памяти, диапазон значений и значения по умолчанию для различных базовых типов данных в Java. Заучивать эту таблицу наизусть не нужно; достаточно иметь общее представление и при необходимости обращаться к ней.</p> <p> Таблица 3-1   Объем памяти и диапазоны значений базовых типов данных </p> Тип Обозначение Объем памяти Минимальное значение Максимальное значение Значение по умолчанию Целые <code>byte</code> 1 байт \\(-2^7\\) (\\(-128\\)) \\(2^7 - 1\\) (\\(127\\)) \\(0\\) <code>short</code> 2 байта \\(-2^{15}\\) \\(2^{15} - 1\\) \\(0\\) <code>int</code> 4 байта \\(-2^{31}\\) \\(2^{31} - 1\\) \\(0\\) <code>long</code> 8 байт \\(-2^{63}\\) \\(2^{63} - 1\\) \\(0\\) Вещественные <code>float</code> 4 байта \\(1.175 \\times 10^{-38}\\) \\(3.403 \\times 10^{38}\\) \\(0.0\\text{f}\\) <code>double</code> 8 байт \\(2.225 \\times 10^{-308}\\) \\(1.798 \\times 10^{308}\\) \\(0.0\\) Символы <code>char</code> 2 байта \\(0\\) \\(2^{16} - 1\\) \\(0\\) Логические <code>bool</code> 1 байт \\(\\text{false}\\) \\(\\text{true}\\) \\(\\text{false}\\) <p>Обрати внимание: приведенная выше таблица относится именно к базовым типам данных Java. В каждом языке программирования определения типов свои, поэтому объем памяти, диапазон значений и значения по умолчанию могут различаться.</p> <ul> <li>В Python целочисленный тип <code>int</code> может иметь произвольный размер, ограниченный только доступной памятью; тип <code>float</code> использует двойную точность 64 бита; типа <code>char</code> нет, а одиночный символ на деле является строкой <code>str</code> длины 1.</li> <li>В C и C++ размер базовых типов данных явно не зафиксирован и зависит от реализации и платформы. таблица 3-1 соответствует модели данных LP64 data model, применяемой в 64-битных Unix-системах, включая Linux и macOS.</li> <li>Размер символа <code>char</code> в C и C++ составляет 1 байт, а в большинстве других языков программирования зависит от конкретного способа кодирования символов; подробнее это рассматривается в разделе \"Кодирование символов\".</li> <li>Хотя для представления логического значения достаточно 1 бита ( \\(0\\) или \\(1\\) ), в памяти оно обычно хранится как 1 байт. Это связано с тем, что современные CPU обычно используют 1 байт как минимальную адресуемую единицу памяти.</li> </ul> <p>Какова же связь между базовыми типами данных и структурами данных? Мы знаем, что структуры данных - это способы организации и хранения данных в компьютере. Подлежащее в этой фразе - \"структура\", а не \"данные\".</p> <p>Если мы хотим представить \"ряд чисел\", то естественно подумаем об использовании массива. Это связано с тем, что линейная структура массива может выразить отношения соседства и порядка между числами, а вот то, что именно хранится внутри - целые <code>int</code> , вещественные <code>float</code> или символы <code>char</code> , - к \"структуре данных\" отношения не имеет.</p> <p>Иными словами, базовые типы данных задают \"тип содержимого\" данных, а структуры данных задают \"способ организации\" данных. Например, в следующем коде мы используем одну и ту же структуру данных (массив) для хранения и представления различных базовых типов данных, включая <code>int</code> , <code>float</code> , <code>char</code> , <code>bool</code> и т.д.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code># Инициализируем массивы с использованием разных базовых типов данных\nnumbers: list[int] = [0] * 5\ndecimals: list[float] = [0.0] * 5\n# В Python символы на деле являются строками длины 1\ncharacters: list[str] = ['0'] * 5\nbools: list[bool] = [False] * 5\n# Списки Python могут свободно хранить разные базовые типы данных и ссылки на объекты\ndata = [0, 0.0, 'a', False, ListNode(0)]\n</code></pre> <pre><code>// Инициализируем массивы с использованием разных базовых типов данных\nint numbers[5];\nfloat decimals[5];\nchar characters[5];\nbool bools[5];\n</code></pre> <pre><code>// Инициализируем массивы с использованием разных базовых типов данных\nint[] numbers = new int[5];\nfloat[] decimals = new float[5];\nchar[] characters = new char[5];\nboolean[] bools = new boolean[5];\n</code></pre> <pre><code>// Инициализируем массивы с использованием разных базовых типов данных\nint[] numbers = new int[5];\nfloat[] decimals = new float[5];\nchar[] characters = new char[5];\nbool[] bools = new bool[5];\n</code></pre> <pre><code>// Инициализируем массивы с использованием разных базовых типов данных\nvar numbers = [5]int{}\nvar decimals = [5]float64{}\nvar characters = [5]byte{}\nvar bools = [5]bool{}\n</code></pre> <pre><code>// Инициализируем массивы с использованием разных базовых типов данных\nlet numbers = Array(repeating: 0, count: 5)\nlet decimals = Array(repeating: 0.0, count: 5)\nlet characters: [Character] = Array(repeating: \"a\", count: 5)\nlet bools = Array(repeating: false, count: 5)\n</code></pre> <pre><code>// Массивы JavaScript могут свободно хранить разные базовые типы данных и объекты\nconst array = [0, 0.0, 'a', false];\n</code></pre> <pre><code>// Инициализируем массивы с использованием разных базовых типов данных\nconst numbers: number[] = [];\nconst characters: string[] = [];\nconst bools: boolean[] = [];\n</code></pre> <pre><code>// Инициализируем массивы с использованием разных базовых типов данных\nList&lt;int&gt; numbers = List.filled(5, 0);\nList&lt;double&gt; decimals = List.filled(5, 0.0);\nList&lt;String&gt; characters = List.filled(5, 'a');\nList&lt;bool&gt; bools = List.filled(5, false);\n</code></pre> <pre><code>// Инициализируем массивы с использованием разных базовых типов данных\nlet numbers: Vec&lt;i32&gt; = vec![0; 5];\nlet decimals: Vec&lt;f32&gt; = vec![0.0; 5];\nlet characters: Vec&lt;char&gt; = vec!['0'; 5];\nlet bools: Vec&lt;bool&gt; = vec![false; 5];\n</code></pre> <pre><code>// Инициализируем массивы с использованием разных базовых типов данных\nint numbers[10];\nfloat decimals[10];\nchar characters[10];\nbool bools[10];\n</code></pre> <pre><code>// Инициализируем массивы с использованием разных базовых типов данных\nval numbers = IntArray(5)\nval decinals = FloatArray(5)\nval characters = CharArray(5)\nval bools = BooleanArray(5)\n</code></pre> <pre><code># Списки Ruby могут свободно хранить разные базовые типы данных и ссылки на объекты\ndata = [0, 0.0, 'a', false, ListNode(0)]\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%D1%81%D0%B2%D1%8F%D0%B7%D0%BD%D1%8B%D0%B9%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%D1%83%D0%B7%D0%B5%D0%BB%D0%BA%D0%BB%D0%B0%D1%81%D1%81%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%D0%97%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%83%D0%B7%D0%BB%D0%B0%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%D0%A1%D1%81%D1%8B%D0%BB%D0%BA%D0%B0%20%D0%BD%D0%B0%20%D1%81%D0%BB%D0%B5%D0%B4%D1%83%D1%8E%D1%89%D0%B8%D0%B9%20%D1%83%D0%B7%D0%B5%D0%BB%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D0%BC%D0%B0%D1%81%D1%81%D0%B8%D0%B2%20%D1%81%20%D0%B8%D1%81%D0%BF%D0%BE%D0%BB%D1%8C%D0%B7%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5%D0%BC%20%D0%BD%D0%B5%D1%81%D0%BA%D0%BE%D0%BB%D1%8C%D0%BA%D0%B8%D1%85%20%D0%B1%D0%B0%D0%B7%D0%BE%D0%B2%D1%8B%D1%85%20%D1%82%D0%B8%D0%BF%D0%BE%D0%B2%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%0A%20%20%20%20numbers%20%3D%20%5B0%5D%20%2A%205%0A%20%20%20%20decimals%20%3D%20%5B0.0%5D%20%2A%205%0A%20%20%20%20%23%20%D0%92%20Python%20%D1%81%D0%B8%D0%BC%D0%B2%D0%BE%D0%BB%D1%8B%20%D0%BD%D0%B0%20%D1%81%D0%B0%D0%BC%D0%BE%D0%BC%20%D0%B4%D0%B5%D0%BB%D0%B5%20%D1%8F%D0%B2%D0%BB%D1%8F%D1%8E%D1%82%D1%81%D1%8F%20%D1%81%D1%82%D1%80%D0%BE%D0%BA%D0%B0%D0%BC%D0%B8%20%D0%B4%D0%BB%D0%B8%D0%BD%D1%8B%201%0A%20%20%20%20characters%20%3D%20%5B%270%27%5D%20%2A%205%0A%20%20%20%20bools%20%3D%20%5BFalse%5D%20%2A%205%0A%20%20%20%20%23%20%D0%A1%D0%BF%D0%B8%D1%81%D0%BA%D0%B8%20%D0%B2%20Python%20%D0%BC%D0%BE%D0%B3%D1%83%D1%82%20%D1%81%D0%B2%D0%BE%D0%B1%D0%BE%D0%B4%D0%BD%D0%BE%20%D1%85%D1%80%D0%B0%D0%BD%D0%B8%D1%82%D1%8C%20%D1%80%D0%B0%D0%B7%D0%BB%D0%B8%D1%87%D0%BD%D1%8B%D0%B5%20%D0%B1%D0%B0%D0%B7%D0%BE%D0%B2%D1%8B%D0%B5%20%D1%82%D0%B8%D0%BF%D1%8B%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20%D0%B8%20%D1%81%D1%81%D1%8B%D0%BB%D0%BA%D0%B8%20%D0%BD%D0%B0%20%D0%BE%D0%B1%D1%8A%D0%B5%D0%BA%D1%82%D1%8B%0A%20%20%20%20data%20%3D%20%5B0%2C%200.0%2C%20%27a%27%2C%20False%2C%20ListNode%280%29%5D&amp;cumulative=false&amp;curInstr=12&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 3. Структуры данных","3.2 &nbsp; Базовые типы данных"],"tags":[]},{"location":"chapter_data_structure/character_encoding/","level":1,"title":"3.4   Кодирование символов *","text":"<p>В компьютере все данные хранятся в двоичной форме, и символ <code>char</code> не является исключением. Чтобы представлять символы, нам нужно определить \"набор символов\", задающий взаимно-однозначное соответствие между каждым символом и двоичным числом. Имея такой набор, компьютер может преобразовывать двоичные числа в символы простым поиском по таблице.</p>","path":["Глава 3. Структуры данных","3.4 &nbsp; Кодирование символов *"],"tags":[]},{"location":"chapter_data_structure/character_encoding/#341-ascii","level":2,"title":"3.4.1   Набор символов ASCII","text":"<p>Код ASCII - это самый ранний набор символов; его полное название - American Standard Code for Information Interchange (американский стандартный код обмена информацией). Он использует 7 двоичных битов (нижние 7 битов одного байта) для представления одного символа и способен представлять не более 128 различных символов. Как показано на рисунке 3-6, ASCII включает заглавные и строчные английские буквы, цифры 0 ~ 9, некоторые знаки препинания и некоторые управляющие символы (например перевод строки и табуляцию).</p> <p></p> <p> Рисунок 3-6   Таблица ASCII </p> <p>Однако код ASCII может представлять только английский язык. С глобализацией компьютерных технологий появился набор символов EASCII, способный покрывать больше языков. Он расширяет 7-битную основу ASCII до 8 битов и может представлять 256 различных символов.</p> <p>Во всем мире постепенно появились разные наборы EASCII, подходящие для разных регионов. Первые 128 символов в этих наборах одинаковы и соответствуют ASCII, а последние 128 символов определяются по-разному, чтобы удовлетворять потребностям разных языков.</p>","path":["Глава 3. Структуры данных","3.4 &nbsp; Кодирование символов *"],"tags":[]},{"location":"chapter_data_structure/character_encoding/#342-gbk","level":2,"title":"3.4.2   Набор символов GBK","text":"<p>Позже люди обнаружили, что кода EASCII все равно недостаточно для количества символов во многих языках. Например, китайских иероглифов существует почти сто тысяч, а в повседневном использовании нужны тысячи. В 1980 году Государственное управление стандартов Китая выпустило набор символов GB2312, включающий 6763 иероглифа, что в основном удовлетворило потребности компьютерной обработки китайского текста.</p> <p>Однако GB2312 не умеет работать с некоторыми редкими иероглифами и традиционными формами письма. Набор символов GBK - это расширение GB2312, содержащее в общей сложности 21886 иероглифов. В схеме кодирования GBK символы ASCII представляются одним байтом, а китайские иероглифы - двумя байтами.</p>","path":["Глава 3. Структуры данных","3.4 &nbsp; Кодирование символов *"],"tags":[]},{"location":"chapter_data_structure/character_encoding/#343-unicode","level":2,"title":"3.4.3   Набор символов Unicode","text":"<p>С бурным развитием компьютерной техники наборы символов и стандарты кодирования начали стремительно множиться, и это породило множество проблем. С одной стороны, такие наборы обычно определяли символы только для конкретных языков и не могли нормально работать в многоязычной среде. С другой стороны, для одного и того же языка существовало несколько стандартов кодирования; если две машины использовали разные стандарты, при обмене информацией возникали кракозябры.</p> <p>Исследователи той эпохи задумались: если создать достаточно полный набор символов, который включит все языки и знаки мира, разве это не решит проблемы межъязыковой среды и искаженного текста? Под влиянием этой идеи и появился большой и всеобъемлющий набор символов Unicode.</p> <p>Unicode по-китайски называется \"единый код\" и теоретически способен вместить более миллиона символов. Его цель - собрать символы со всего мира в единый набор символов, предоставить универсальный стандарт для обработки и отображения текстов на разных языках и уменьшить количество проблем с искажением текста, вызванных различиями стандартов кодирования.</p> <p>С момента публикации в 1991 году Unicode непрерывно расширялся, добавляя новые языки и символы. По состоянию на сентябрь 2022 года Unicode уже включал 149186 символов, в том числе буквы разных языков, знаки, а также эмодзи. В огромном наборе символов Unicode часто используемые символы занимают 2 байта, а некоторые редкие символы - 3 байта и даже 4 байта.</p> <p>Unicode - это универсальный набор символов, который по сути просто присваивает каждому символу номер (так называемую \"кодовую точку\"), но не определяет, как именно хранить эти кодовые точки в компьютере. Тут неизбежно возникает вопрос: если в одном тексте одновременно встречаются кодовые точки Unicode разной длины, как система должна разбирать символы? Например, если дан код длиной 2 байта, как понять, является ли это одним 2-байтовым символом или двумя 1-байтовыми?</p> <p>Для этой проблемы прямолинейное решение состоит в том, чтобы хранить все символы в кодировке одинаковой длины. Как показано на рисунке 3-7, каждый символ в \"Hello\" занимает 1 байт, а каждый символ в \"алгоритм\" занимает 2 байта. Мы можем дополнить старшие биты нулями и закодировать все символы в \"Hello алгоритм\" в виде 2-байтовых единиц. Тогда система сможет считывать по одному символу каждые 2 байта и восстановить эту фразу.</p> <p></p> <p> Рисунок 3-7   Пример кодирования Unicode </p> <p>Однако ASCII уже показал нам, что для кодирования английского текста достаточно 1 байта. Если использовать описанную выше схему, английский текст будет занимать вдвое больше памяти, чем при ASCII, а это очень неэффективно. Поэтому нам нужен более эффективный способ кодирования Unicode.</p>","path":["Глава 3. Структуры данных","3.4 &nbsp; Кодирование символов *"],"tags":[]},{"location":"chapter_data_structure/character_encoding/#344-utf-8","level":2,"title":"3.4.4   Кодировка UTF-8","text":"<p>Сегодня UTF-8 стала самым широко используемым способом кодирования Unicode в мире. Это кодировка переменной длины, использующая от 1 до 4 байт на символ в зависимости от его сложности. Символам ASCII нужен только 1 байт, латинским и греческим буквам - 2 байта, часто используемым китайским символам - 3 байта, а некоторым редким символам - 4 байта.</p> <p>Правила кодирования UTF-8 не слишком сложны и делятся на два случая.</p> <ul> <li>Для символов длиной 1 байт старший бит устанавливается в \\(0\\) , а оставшиеся 7 битов содержат кодовую точку Unicode. Стоит отметить, что символы ASCII занимают первые 128 кодовых точек в наборе Unicode. Иными словами, кодировка UTF-8 обратно совместима с ASCII. Это означает, что мы можем использовать UTF-8 для разбора очень старых ASCII-текстов.</li> <li>Для символов длиной \\(n\\) байт (где \\(n &gt; 1\\)) старшие \\(n\\) битов первого байта устанавливаются в \\(1\\) , а \\((n + 1)\\)-й бит устанавливается в \\(0\\) ; начиная со второго байта, старшие 2 бита каждого байта устанавливаются в \\(10\\) ; все остальные биты используются для заполнения кодовой точки Unicode соответствующего символа.</li> </ul> <p>На рисунке 3-8 показана UTF-8-кодировка для строки \"Hello алгоритм\". Можно заметить, что поскольку старшие \\(n\\) битов установлены в \\(1\\) , система может определить длину символа как \\(n\\) , подсчитав число ведущих единиц.</p> <p>Но почему старшие 2 бита всех остальных байтов устанавливаются в \\(10\\) ? На самом деле это \\(10\\) играет роль контрольного маркера. Если система начнет разбирать текст с неверного байта, префикс \\(10\\) поможет быстро обнаружить аномалию.</p> <p>Причина выбора \\(10\\) в качестве контрольного маркера в том, что по правилам UTF-8 символ не может иметь старшие два бита, равные \\(10\\) . Это можно доказать от противного: если предположить, что у некоторого символа старшие два бита равны \\(10\\) , то длина такого символа должна быть 1 байт, то есть это ASCII. Но у ASCII старший бит обязан быть \\(0\\) , что противоречит предположению.</p> <p></p> <p> Рисунок 3-8   Пример кодировки UTF-8 </p> <p>Помимо UTF-8, распространены еще два следующих способа кодирования.</p> <ul> <li>Кодировка UTF-16: использует 2 или 4 байта для представления символа. Все символы ASCII и часто используемые неанглийские символы представляются 2 байтами; небольшая часть символов требует 4 байта. Для 2-байтовых символов кодировка UTF-16 совпадает с кодовой точкой Unicode.</li> <li>Кодировка UTF-32: каждый символ занимает 4 байта. Это означает, что UTF-32 требует больше места, чем UTF-8 и UTF-16, особенно в текстах с большой долей ASCII-символов.</li> </ul> <p>С точки зрения занимаемого места UTF-8 очень эффективна для английских символов, потому что им нужен всего 1 байт; а для некоторых неанглийских символов (например китайских) UTF-16 может быть эффективнее, потому что ей требуется только 2 байта, тогда как UTF-8 может потребовать 3 байта.</p> <p>С точки зрения совместимости у UTF-8 наилучшая универсальность, и многие инструменты и библиотеки в первую очередь поддерживают именно UTF-8.</p>","path":["Глава 3. Структуры данных","3.4 &nbsp; Кодирование символов *"],"tags":[]},{"location":"chapter_data_structure/character_encoding/#345","level":2,"title":"3.4.5   Кодирование символов в языках программирования","text":"<p>Для большинства языков программирования прошлого строки во время выполнения программы использовали фиксированные по длине кодировки, такие как UTF-16 или UTF-32. При кодировке фиксированной длины строку можно обрабатывать как массив, и такой подход дает следующие преимущества.</p> <ul> <li>Произвольный доступ: к строкам в UTF-16 легко осуществлять произвольный доступ. UTF-8 же является кодировкой переменной длины, поэтому, чтобы найти \\(i\\) -й символ, нужно пройти от начала строки до этого символа, а это требует \\(O(n)\\) времени.</li> <li>Подсчет длины строки: аналогично произвольному доступу, вычисление длины строки в UTF-16 - это операция \\(O(1)\\) . А вот вычисление длины строки в UTF-8 требует обхода всей строки.</li> <li>Строковые операции: многие операции со строками (разделение, конкатенация, вставка, удаление и т.д.) над строками в UTF-16 реализуются проще. При работе с UTF-8 обычно требуются дополнительные вычисления, чтобы не породить некорректную UTF-8-последовательность.</li> </ul> <p>Вообще говоря, проектирование схем кодирования символов в языках программирования - очень интересная тема, в которой учитывается множество факторов.</p> <ul> <li>Тип <code>String</code> в Java использует кодировку UTF-16, и каждый символ занимает 2 байта. Это связано с тем, что на раннем этапе проектирования Java считалось, что 16 битов достаточно для представления всех возможных символов. Но это оказалось неверным предположением. Позднее Unicode вышел за пределы 16 битов, поэтому символы в Java теперь могут представляться парой 16-битных значений (так называемой \"суррогатной парой\").</li> <li>Строки в JavaScript и TypeScript используют UTF-16 по причинам, похожим на Java. Когда Netscape впервые выпустила JavaScript в 1995 году, Unicode еще находился на ранней стадии развития, и 16-битного кодирования тогда было достаточно для представления всех символов Unicode.</li> <li>C# использует UTF-16 главным образом потому, что платформа .NET была разработана Microsoft, а многие технологии Microsoft (включая Windows) широко используют именно UTF-16.</li> </ul> <p>Из-за недооценки общего числа символов перечисленным выше языкам пришлось использовать \"суррогатные пары\" для представления Unicode-символов длиной больше 16 бит. Это вынужденный компромисс. С одной стороны, в строках с суррогатными парами один символ может занимать 2 байта или 4 байта, из-за чего теряется преимущество кодировки фиксированной длины. С другой стороны, обработка суррогатных пар требует дополнительного кода, что повышает сложность разработки и отладки.</p> <p>По этим причинам некоторые языки программирования предложили иные схемы кодирования.</p> <ul> <li><code>str</code> в Python использует Unicode и гибкое строковое представление, где длина хранимого символа зависит от наибольшей кодовой точки Unicode в строке. Если все символы строки принадлежат ASCII, каждый символ занимает 1 байт; если есть символы за пределами ASCII, но все они лежат в базовой многоязычной плоскости (BMP), каждый символ занимает 2 байта; если встречаются символы за пределами BMP, каждый символ занимает 4 байта.</li> <li>Тип <code>string</code> в Go внутри использует кодировку UTF-8. Язык Go также предоставляет тип <code>rune</code>, предназначенный для представления одной кодовой точки Unicode.</li> <li>Типы <code>str</code> и <code>String</code> в Rust внутри используют UTF-8. В Rust также есть тип <code>char</code>, представляющий одну кодовую точку Unicode.</li> </ul> <p>Следует помнить, что выше обсуждался способ хранения строк внутри языков программирования, а это не то же самое, что хранение строк в файлах или передача их по сети. При файловом хранении и сетевой передаче мы обычно кодируем строки в формате UTF-8, чтобы получить наилучшую совместимость и эффективность по занимаемому месту.</p>","path":["Глава 3. Структуры данных","3.4 &nbsp; Кодирование символов *"],"tags":[]},{"location":"chapter_data_structure/classification_of_data_structure/","level":1,"title":"3.1   Классификация структур данных","text":"<p>К распространенным структурам данных относятся массивы, связные списки, стеки, очереди, хеш-таблицы, деревья, кучи и графы; их можно классифицировать по двум измерениям: \"логическая структура\" и \"физическая структура\".</p>","path":["Глава 3. Структуры данных","3.1 &nbsp; Классификация структур данных"],"tags":[]},{"location":"chapter_data_structure/classification_of_data_structure/#311","level":2,"title":"3.1.1   Логическая структура: линейная и нелинейная","text":"<p>Логическая структура раскрывает логические связи между элементами данных. В массивах и связных списках данные располагаются в определенном порядке, отражая линейные отношения между элементами; в деревьях данные иерархически располагаются сверху вниз, проявляя производные отношения между \"предками\" и \"потомками\"; графы состоят из вершин и ребер и отражают сложные сетевые связи.</p> <p>Как показано на рисунке 3-1, логические структуры можно разделить на два больших класса: \"линейные\" и \"нелинейные\". Линейные структуры более интуитивны и означают, что данные логически выстроены в линию; нелинейные структуры, напротив, располагаются нелинейно.</p> <ul> <li>Линейные структуры данных: массивы, связные списки, стеки, очереди, хеш-таблицы; между элементами существует отношение \"один к одному\".</li> <li>Нелинейные структуры данных: деревья, кучи, графы, хеш-таблицы.</li> </ul> <p>Нелинейные структуры данных можно дополнительно разделить на древовидные и сетевые.</p> <ul> <li>Древовидные структуры: деревья, кучи, хеш-таблицы; между элементами существует отношение \"один ко многим\".</li> <li>Сетевые структуры: графы; между элементами существует отношение \"многие ко многим\".</li> </ul> <p></p> <p> Рисунок 3-1   Линейные и нелинейные структуры данных </p>","path":["Глава 3. Структуры данных","3.1 &nbsp; Классификация структур данных"],"tags":[]},{"location":"chapter_data_structure/classification_of_data_structure/#312","level":2,"title":"3.1.2   Физическая структура: непрерывная и разрозненная","text":"<p>Во время выполнения алгоритма обрабатываемые данные в основном хранятся в памяти. На рисунке 3-2 показана планка памяти компьютера, где каждый черный блок содержит некоторый участок памяти. Мы можем представить память как огромную таблицу Excel, в которой каждая ячейка способна хранить данные определенного размера.</p> <p>Система обращается к данным по адресу памяти соответствующей позиции. Как показано на рисунке 3-2, компьютер по определенному правилу присваивает каждой ячейке в этой таблице номер, чтобы у каждого участка памяти был уникальный адрес. Имея эти адреса, программа может получать доступ к данным, находящимся в памяти.</p> <p></p> <p> Рисунок 3-2   Планка памяти, участок памяти и адрес памяти </p> <p>Tip</p> <p>Стоит отметить, что сравнение памяти с таблицей Excel - это упрощенная аналогия; реальный механизм работы памяти гораздо сложнее и включает такие понятия, как адресное пространство, управление памятью, кэш-механизмы, виртуальная и физическая память.</p> <p>Память - общий ресурс для всех программ. Когда некоторый участок памяти занят одной программой, другие программы обычно не могут использовать его одновременно. Поэтому при проектировании структур данных и алгоритмов память является важным фактором. Например, пиковое потребление памяти алгоритмом не должно превышать доступную свободную память системы; если непрерывного крупного блока памяти недостаточно, выбранная структура данных должна уметь храниться в разрозненных областях памяти.</p> <p>Как показано на рисунке 3-3, физическая структура отражает способ хранения данных в памяти компьютера; ее можно разделить на хранение в непрерывном пространстве (массивы) и хранение в разрозненном пространстве (связные списки). Физическая структура на нижнем уровне определяет способы доступа к данным, их обновления, вставки и удаления; эти два типа физических структур взаимно дополняют друг друга по временной и пространственной эффективности.</p> <p></p> <p> Рисунок 3-3   Хранение в непрерывном и разрозненном пространстве </p> <p>Стоит отметить, что все структуры данных реализуются на основе массивов, связных списков или их комбинации. Например, стеки и очереди можно реализовать как с помощью массивов, так и с помощью связных списков; а реализация хеш-таблицы может одновременно содержать массивы и связные списки.</p> <ul> <li>Можно реализовать на основе массивов: стеки, очереди, хеш-таблицы, деревья, кучи, графы, матрицы, тензоры (массивы размерности \\(\\geq 3\\) ) и т.д.</li> <li>Можно реализовать на основе связных списков: стеки, очереди, хеш-таблицы, деревья, кучи, графы и т.д.</li> </ul> <p>После инициализации длину связного списка все еще можно изменять во время выполнения программы, поэтому его также называют \"динамической структурой данных\". Длина массива после инициализации неизменна, поэтому его также называют \"статической структурой данных\". Стоит заметить, что массив может менять длину за счет повторного выделения памяти, тем самым приобретая определенную \"динамичность\".</p> <p>Tip</p> <p>Если тебе пока трудно понять физическую структуру, рекомендуется сначала прочитать следующую главу, а затем вернуться к этому разделу.</p>","path":["Глава 3. Структуры данных","3.1 &nbsp; Классификация структур данных"],"tags":[]},{"location":"chapter_data_structure/number_encoding/","level":1,"title":"3.3   Кодирование чисел *","text":"<p>Tip</p> <p>В этой книге разделы, помеченные символом <code>*</code>, относятся к дополнительному чтению. Если у тебя мало времени или материал кажется трудным, можно сначала пропустить их и вернуться после изучения обязательных разделов.</p>","path":["Глава 3. Структуры данных","3.3 &nbsp; Кодирование чисел *"],"tags":[]},{"location":"chapter_data_structure/number_encoding/#331","level":2,"title":"3.3.1   Прямой, обратный и дополнительный коды","text":"<p>В таблице из предыдущего раздела мы заметили, что все целочисленные типы могут представлять на одно отрицательное число больше, чем положительных. Например, диапазон <code>byte</code> равен \\([-128, 127]\\) . Это явление выглядит не слишком интуитивно, и его внутренняя причина связана с прямым, обратным и дополнительным кодами.</p> <p>Прежде всего нужно отметить, что числа хранятся в компьютере в форме \"дополнительного кода\". Прежде чем разбирать причины такого решения, сначала дадим определения всем трем способам представления.</p> <ul> <li>Прямой код: старший бит двоичного представления числа рассматривается как знаковый, где \\(0\\) означает положительное число, а \\(1\\) - отрицательное; остальные биты представляют значение числа.</li> <li>Обратный код: для положительного числа обратный код совпадает с прямым; для отрицательного числа он получается инверсией всех битов прямого кода, кроме знакового бита.</li> <li>Дополнительный код: для положительного числа дополнительный код совпадает с прямым; для отрицательного числа он получается добавлением \\(1\\) к его обратному коду.</li> </ul> <p>На рисунке 3-4 показаны способы преобразования между прямым, обратным и дополнительным кодами.</p> <p></p> <p> Рисунок 3-4   Преобразования между прямым, обратным и дополнительным кодами </p> <p>Прямой код (sign-magnitude), хотя и является самым наглядным, имеет определенные ограничения. С одной стороны, прямой код отрицательных чисел нельзя напрямую использовать в вычислениях. Например, при вычислении \\(1 + (-2)\\) в прямом коде результатом будет \\(-3\\) , что, очевидно, неверно.</p> \\[ \\begin{aligned} &amp; 1 + (-2) \\newline &amp; \\rightarrow 0000 \\; 0001 + 1000 \\; 0010 \\newline &amp; = 1000 \\; 0011 \\newline &amp; \\rightarrow -3 \\end{aligned} \\] <p>Чтобы решить эту проблему, компьютеры ввели обратный код (1's complement). Если сначала преобразовать прямой код в обратный и выполнить вычисление \\(1 + (-2)\\) в обратном коде, а затем перевести результат обратно в прямой код, то получится правильный результат \\(-1\\) .</p> \\[ \\begin{aligned} &amp; 1 + (-2) \\newline &amp; \\rightarrow 0000 \\; 0001 \\; \\text{(прямой код)} + 1000 \\; 0010 \\; \\text{(прямой код)} \\newline &amp; = 0000 \\; 0001 \\; \\text{(обратный код)} + 1111  \\; 1101 \\; \\text{(обратный код)} \\newline &amp; = 1111 \\; 1110 \\; \\text{(обратный код)} \\newline &amp; = 1000 \\; 0001 \\; \\text{(прямой код)} \\newline &amp; \\rightarrow -1 \\end{aligned} \\] <p>С другой стороны, **в прямом коде у нуля есть два представления: \\(+0\\) и \\(-0\\) **. Это означает, что числу ноль соответствуют два разных двоичных кода, что может приводить к неоднозначности. Например, если в условном выражении не различать положительный и отрицательный ноль, можно получить ошибочный результат. А если специально обрабатывать такую неоднозначность, придется вводить дополнительные проверки, что может снизить вычислительную эффективность компьютера.</p> \\[ \\begin{aligned} +0 &amp; \\rightarrow 0000 \\; 0000 \\newline -0 &amp; \\rightarrow 1000 \\; 0000 \\end{aligned} \\] <p>Как и прямой код, обратный код тоже страдает от неоднозначности положительного и отрицательного нуля, поэтому компьютеры ввели дополнительный код (2's complement). Сначала посмотрим на процесс преобразования отрицательного нуля из прямого кода в обратный, а затем в дополнительный:</p> \\[ \\begin{aligned} -0 \\rightarrow \\; &amp; 1000 \\; 0000 \\; \\text{(прямой код)} \\newline = \\; &amp; 1111 \\; 1111 \\; \\text{(обратный код)} \\newline = 1 \\; &amp; 0000 \\; 0000 \\; \\text{(дополнительный код)} \\newline \\end{aligned} \\] <p>При добавлении \\(1\\) к обратному коду отрицательного нуля возникает перенос, но длина типа <code>byte</code> составляет всего 8 бит, поэтому переполнившаяся в 9-й бит единица отбрасывается. Иными словами, дополнительный код отрицательного нуля равен \\(0000 \\; 0000\\) и совпадает с дополнительным кодом положительного нуля. Значит, в представлении дополнительного кода существует только один ноль, и проблема неоднозначности положительного и отрицательного нуля тем самым устраняется.</p> <p>Остается последний вопрос: диапазон типа <code>byte</code> равен \\([-128, 127]\\) , откуда берется лишнее отрицательное число \\(-128\\) ? Мы замечаем, что у всех целых чисел из интервала \\([-127, +127]\\) есть соответствующие прямой, обратный и дополнительный коды, а прямой и дополнительный коды можно преобразовывать друг в друга.</p> <p>Однако дополнительный код \\(1000 \\; 0000\\) является исключением: у него нет соответствующего прямого кода. Согласно правилу преобразования, прямой код для этого дополнительного кода должен быть равен \\(0000 \\; 0000\\) . Это, очевидно, противоречие, потому что такой прямой код обозначает число \\(0\\) , а его дополнительный код должен совпадать с ним самим. Компьютер просто определяет, что этот особый дополнительный код \\(1000 \\; 0000\\) представляет число \\(-128\\) . На самом деле результат вычисления \\((-1) + (-127)\\) в дополнительном коде как раз и равен \\(-128\\) .</p> \\[ \\begin{aligned} &amp; (-127) + (-1) \\newline &amp; \\rightarrow 1111 \\; 1111 \\; \\text{(прямой код)} + 1000 \\; 0001 \\; \\text{(прямой код)} \\newline &amp; = 1000 \\; 0000 \\; \\text{(обратный код)} + 1111  \\; 1110 \\; \\text{(обратный код)} \\newline &amp; = 1000 \\; 0001 \\; \\text{(дополнительный код)} + 1111  \\; 1111 \\; \\text{(дополнительный код)} \\newline &amp; = 1000 \\; 0000 \\; \\text{(дополнительный код)} \\newline &amp; \\rightarrow -128 \\end{aligned} \\] <p>Ты, вероятно, уже заметил, что все приведенные выше вычисления были операциями сложения. Это намекает на важный факт: аппаратные схемы внутри компьютера в основном проектируются на основе операций сложения. Причина в том, что сложение по сравнению с другими операциями (например умножением, делением и вычитанием) проще реализуется на аппаратном уровне, легче распараллеливается и выполняется быстрее.</p> <p>Обрати внимание: это не означает, что компьютер умеет только складывать. Комбинируя сложение с некоторыми базовыми логическими операциями, компьютер может реализовать и другие математические операции. Например, вычитание \\(a - b\\) можно преобразовать в сложение \\(a + (-b)\\) ; умножение и деление можно свести к многократному сложению или вычитанию.</p> <p>Теперь можно подвести итог, почему компьютеры используют дополнительный код: с представлением в дополнительном коде компьютер может использовать одни и те же схемы и операции для сложения положительных и отрицательных чисел, без необходимости проектировать специальные аппаратные схемы для вычитания, и без особой обработки неоднозначности положительного и отрицательного нуля. Это значительно упрощает аппаратную архитектуру и повышает эффективность вычислений.</p> <p>Идея дополнительного кода очень изящна; из-за ограничений по объему мы на этом остановимся. Если тебе интересно, стоит изучить эту тему глубже.</p>","path":["Глава 3. Структуры данных","3.3 &nbsp; Кодирование чисел *"],"tags":[]},{"location":"chapter_data_structure/number_encoding/#332","level":2,"title":"3.3.2   Кодирование чисел с плавающей точкой","text":"<p>Внимательный читатель может заметить: <code>int</code> и <code>float</code> имеют одинаковую длину, по 4 байта , но почему диапазон значений у <code>float</code> намного больше, чем у <code>int</code> ? Это выглядит парадоксально, ведь <code>float</code> должен еще представлять дробные числа, а значит диапазон вроде бы должен быть меньше.</p> <p>На самом деле это связано с тем, что число с плавающей точкой <code>float</code> использует другой способ представления. Обозначим двоичное число длиной 32 бита как:</p> \\[ b_{31} b_{30} b_{29} \\ldots b_2 b_1 b_0 \\] <p>Согласно стандарту IEEE 754, 32-битный <code>float</code> состоит из следующих трех частей.</p> <ul> <li>Бит знака \\(\\mathrm{S}\\) : занимает 1 бит и соответствует \\(b_{31}\\) .</li> <li>Биты экспоненты \\(\\mathrm{E}\\) : занимают 8 бит и соответствуют \\(b_{30} b_{29} \\ldots b_{23}\\) .</li> <li>Биты мантиссы \\(\\mathrm{N}\\) : занимают 23 бита и соответствуют \\(b_{22} b_{21} \\ldots b_0\\) .</li> </ul> <p>Формула вычисления значения, соответствующего двоичному числу <code>float</code>, имеет вид:</p> \\[ \\text {val} = (-1)^{b_{31}} \\times 2^{\\left(b_{30} b_{29} \\ldots b_{23}\\right)_2-127} \\times\\left(1 . b_{22} b_{21} \\ldots b_0\\right)_2 \\] <p>Если перейти к десятичной записи, формула вычисления будет такой:</p> \\[ \\text {val}=(-1)^{\\mathrm{S}} \\times 2^{\\mathrm{E} -127} \\times (1 + \\mathrm{N}) \\] <p>Диапазоны значений соответствующих частей таковы:</p> \\[ \\begin{aligned} \\mathrm{S} \\in &amp; \\{ 0, 1\\}, \\quad \\mathrm{E} \\in \\{ 1, 2, \\dots, 254 \\} \\newline (1 + \\mathrm{N}) = &amp; (1 + \\sum_{i=1}^{23} b_{23-i} 2^{-i}) \\subset [1, 2 - 2^{-23}] \\end{aligned} \\] <p></p> <p> Рисунок 3-5   Пример вычисления float по стандарту IEEE 754 </p> <p>Посмотрим на рисунок 3-5: если взять пример \\(\\mathrm{S} = 0\\) , \\(\\mathrm{E} = 124\\) , \\(\\mathrm{N} = 2^{-2} + 2^{-3} = 0.375\\) , то получим:</p> \\[ \\text { val } = (-1)^0 \\times 2^{124 - 127} \\times (1 + 0.375) = 0.171875 \\] <p>Теперь мы можем ответить на исходный вопрос: в представлении <code>float</code> присутствуют биты экспоненты, поэтому его диапазон значений намного больше, чем у <code>int</code>. Согласно приведенным выше вычислениям, максимально возможное положительное число для <code>float</code> равно \\(2^{254 - 127} \\times (2 - 2^{-23}) \\approx 3.4 \\times 10^{38}\\) ; если изменить бит знака, получим минимальное отрицательное число.</p> <p>Хотя число с плавающей точкой <code>float</code> расширяет диапазон значений, побочным эффектом становится потеря точности. Целочисленный тип <code>int</code> использует все 32 бита для представления числа, и числа распределены равномерно; а из-за существования битов экспоненты у <code>float</code> чем больше число, тем больше обычно становится разница между двумя соседними представимыми значениями.</p> <p>Как показано в таблице 3-2, значения экспоненты \\(\\mathrm{E} = 0\\) и \\(\\mathrm{E} = 255\\) имеют специальный смысл и используются для представления нуля, бесконечности, \\(\\mathrm{NaN}\\) и т.д.</p> <p> Таблица 3-2   Значение поля экспоненты </p> Поле экспоненты E Поле мантиссы \\(\\mathrm{N} = 0\\) Поле мантиссы \\(\\mathrm{N} \\ne 0\\) Формула вычисления \\(0\\) \\(\\pm 0\\) Денормализованное число \\((-1)^{\\mathrm{S}} \\times 2^{-126} \\times (0.\\mathrm{N})\\) \\(1, 2, \\dots, 254\\) Нормализованное число Нормализованное число \\((-1)^{\\mathrm{S}} \\times 2^{(\\mathrm{E} -127)} \\times (1.\\mathrm{N})\\) \\(255\\) \\(\\pm \\infty\\) \\(\\mathrm{NaN}\\) <p>Стоит отметить, что денормализованные числа заметно повышают точность чисел с плавающей точкой. Наименьшее положительное нормализованное число равно \\(2^{-126}\\) , а наименьшее положительное денормализованное число равно \\(2^{-126} \\times 2^{-23}\\) .</p> <p>Двойная точность <code>double</code> использует способ представления, аналогичный <code>float</code> , поэтому здесь мы не будем подробно останавливаться на нем.</p>","path":["Глава 3. Структуры данных","3.3 &nbsp; Кодирование чисел *"],"tags":[]},{"location":"chapter_data_structure/summary/","level":1,"title":"3.5   Резюме","text":"","path":["Глава 3. Структуры данных","3.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_data_structure/summary/#1","level":3,"title":"1.   Ключевые выводы","text":"<ul> <li>Структуры данных можно классифицировать с двух точек зрения: логической структуры и физической структуры. Логическая структура описывает логические связи между элементами данных, а физическая структура описывает способ хранения данных в памяти компьютера.</li> <li>К распространенным логическим структурам относятся линейные, древовидные и сетевые. Обычно мы делим структуры данных по логической структуре на линейные (массивы, связные списки, стеки, очереди) и нелинейные (деревья, графы, кучи). Реализация хеш-таблицы может одновременно включать линейные и нелинейные структуры данных.</li> <li>Во время работы программы данные хранятся в памяти компьютера. У каждого участка памяти есть собственный адрес, и программа обращается к данным именно по этим адресам.</li> <li>Физическая структура в основном делится на хранение в непрерывном пространстве (массивы) и хранение в разрозненном пространстве (связные списки). Все структуры данных реализуются на основе массивов, связных списков или их комбинации.</li> <li>К базовым типам данных в компьютере относятся целые <code>byte</code> , <code>short</code> , <code>int</code> , <code>long</code> , числа с плавающей точкой <code>float</code> , <code>double</code> , символы <code>char</code> и логический тип <code>bool</code> . Их диапазон значений определяется объемом занимаемого пространства и способом представления.</li> <li>Прямой код, обратный код и дополнительный код - это три способа кодирования чисел в компьютере, между которыми можно выполнять взаимные преобразования. В прямом коде старший бит целого числа является знаковым, а остальные биты представляют значение числа.</li> <li>Целые числа в компьютере хранятся в виде дополнительного кода. В таком представлении компьютер может одинаково обрабатывать сложение положительных и отрицательных чисел, не проектируя специальную аппаратную схему отдельно для вычитания, и при этом не возникает неоднозначности положительного и отрицательного нуля.</li> <li>Кодирование числа с плавающей точкой состоит из 1 бита знака, 8 битов экспоненты и 23 битов мантиссы. Благодаря наличию экспоненты диапазон значений у чисел с плавающей точкой намного больше, чем у целых, но расплачиваться за это приходится точностью.</li> <li>ASCII - это самый ранний набор английских символов длиной 1 байт, включающий в общей сложности 127 символов. Набор GBK - распространенный китайский набор символов, включающий более двадцати тысяч иероглифов. Unicode стремится предоставить единый полный стандарт набора символов, включающий символы всех языков мира, чтобы решить проблемы искаженного текста, вызванные несовместимыми способами кодирования.</li> <li>UTF-8 - самый популярный способ кодирования Unicode, обладающий очень хорошей универсальностью. Это кодировка переменной длины, хорошо расширяемая и эффективно использующая память. UTF-16 и UTF-32 относятся к кодировкам фиксированной длины. При кодировании китайского текста UTF-16 занимает меньше места, чем UTF-8. Такие языки программирования, как Java и C#, по умолчанию используют UTF-16.</li> </ul>","path":["Глава 3. Структуры данных","3.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_data_structure/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: Почему хеш-таблица одновременно включает линейные и нелинейные структуры данных?</p> <p>В основе хеш-таблицы лежит массив, а для разрешения коллизий мы можем использовать \"цепочки адресации\" (об этом будет рассказано в последующем разделе \"Хеш-коллизии\"): каждый бакет массива указывает на связный список, а если длина списка превышает некоторый порог, он может быть преобразован в дерево (обычно в красно-черное дерево).</p> <p>С точки зрения хранения данных в основе хеш-таблицы находится массив, где каждый слот бакета может содержать либо отдельное значение, либо связный список, либо дерево. Поэтому хеш-таблица действительно может одновременно включать линейные структуры данных (массивы, списки) и нелинейные структуры данных (деревья).</p> <p>Q: Длина типа <code>char</code> равна 1 байту?</p> <p>Длина типа <code>char</code> определяется используемым в языке программирования способом кодирования. Например, Java, JavaScript, TypeScript и C# используют кодировку UTF-16 (для хранения кодовых точек Unicode), поэтому длина <code>char</code> у них равна 2 байтам.</p> <p>Q: Не является ли двусмысленным утверждение, что структуры данных, реализованные на основе массива, также называются \"статическими структурами данных\"? Ведь стек тоже поддерживает операции push и pop, а они явно \"динамические\".</p> <p>Стек действительно может поддерживать динамические операции над данными, но сама структура данных при этом остается \"статической\" (ее длина неизменна). Хотя структуры на основе массива могут динамически добавлять и удалять элементы, их емкость фиксирована. Если количество данных превышает заранее выделенный размер, приходится создавать новый, более крупный массив и копировать в него содержимое старого.</p> <p>Q: При построении стека (очереди) его размер не задается явно, почему же его относят к \"статическим структурам данных\"?</p> <p>В языках высокого уровня нам не нужно вручную задавать начальную емкость стека (очереди): это автоматически делает сама реализация класса. Например, начальная емкость <code>ArrayList</code> в Java обычно равна 10. Кроме того, автоматом реализуется и расширение емкости. Подробнее это рассматривается в последующем разделе о \"списках\".</p> <p>Q: Если метод преобразования из прямого кода в дополнительный - это \"сначала инвертировать, затем прибавить 1\", то обратное преобразование из дополнительного кода в прямой, по идее, должно быть обратной операцией \"сначала вычесть 1, затем инвертировать\". Почему же дополнительный код также можно перевести в прямой тем же способом \"сначала инвертировать, затем прибавить 1\"?</p> <p>Это связано с тем, что взаимное преобразование прямого и дополнительного кодов по сути является вычислением \"дополнения\". Сначала дадим определение дополнения: если \\(a + b = c\\) , то говорят, что \\(a\\) является дополнением числа \\(b\\) до \\(c\\) ; аналогично, \\(b\\) является дополнением числа \\(a\\) до \\(c\\) .</p> <p>Для двоичного числа длины \\(n = 4\\) со значением \\(0010\\) , если рассматривать его как прямой код (не учитывая знаковый бит), то его дополнительный код получается правилом \"сначала инвертировать, затем прибавить 1\":</p> \\[ 0010 \\rightarrow 1101 \\rightarrow 1110 \\] <p>Мы видим, что сумма прямого и дополнительного кодов равна \\(0010 + 1110 = 10000\\) , то есть дополнительный код \\(1110\\) является \"дополнением\" прямого кода \\(0010\\) до \\(10000\\) . **Это означает, что описанная выше операция \"сначала инвертировать, затем прибавить 1\" на самом деле вычисляет дополнение до \\(10000\\) **.</p> <p>Тогда чему равно \"дополнение\" дополнительного кода \\(1110\\) до \\(10000\\) ? Мы снова можем получить его правилом \"сначала инвертировать, затем прибавить 1\":</p> \\[ 1110 \\rightarrow 0001 \\rightarrow 0010 \\] <p>Иначе говоря, прямой и дополнительный коды являются взаимными \"дополнениями\" друг друга до \\(10000\\) , поэтому и \"прямой код -&gt; дополнительный код\", и \"дополнительный код -&gt; прямой код\" можно реализовать одной и той же операцией (сначала инвертировать, затем прибавить 1).</p> <p>Разумеется, можно получить прямой код из дополнительного кода \\(1110\\) и обратной операцией, то есть \"сначала вычесть 1, затем инвертировать\":</p> \\[ 1110 \\rightarrow 1101 \\rightarrow 0010 \\] <p>В итоге и \"сначала инвертировать, затем прибавить 1\", и \"сначала вычесть 1, затем инвертировать\" - это два эквивалентных способа вычисления дополнения до \\(10000\\) .</p> <p>По сути операция \"инвертировать\" сама по себе вычисляет дополнение до \\(1111\\) (потому что всегда выполняется <code>прямой код + обратный код = 1111</code> ); а дополнительный код, получающийся после добавления 1 к обратному коду, и есть дополнение до \\(10000\\) .</p> <p>Приведенный выше пример использовал \\(n = 4\\) , но его можно обобщить на двоичные числа любой длины.</p>","path":["Глава 3. Структуры данных","3.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_divide_and_conquer/","level":1,"title":"Глава 12.   Разделяй и властвуй","text":"<p>Abstract</p> <p>Сложная задача раскладывается слой за слоем, и каждое новое разбиение делает ее проще.</p> <p>Принцип \"разделяй и властвуй\" показывает важный факт: если начать с простого, многое перестает быть сложным.</p>","path":["Глава 12. Разделяй и властвуй","Глава 12. &nbsp; Разделяй и властвуй"],"tags":[]},{"location":"chapter_divide_and_conquer/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>12.1   Алгоритмы разделяй и властвуй</li> <li>12.2   Стратегия поиска разделяй и властвуй</li> <li>12.3   Задача построения двоичного дерева</li> <li>12.4   Задача о Ханойской башне</li> <li>12.5   Резюме</li> </ul>","path":["Глава 12. Разделяй и властвуй","Глава 12. &nbsp; Разделяй и властвуй"],"tags":[]},{"location":"chapter_divide_and_conquer/binary_search_recur/","level":1,"title":"12.2   Поисковая стратегия divide and conquer","text":"<p>Мы уже знаем, что алгоритмы поиска делятся на две большие категории.</p> <ul> <li>Полный перебор: реализуется через обход структуры данных, временная сложность равна \\(O(n)\\) .</li> <li>Адаптивный поиск: использует особую организацию данных или априорную информацию, временная сложность может достигать \\(O(\\log n)\\) и даже \\(O(1)\\) .</li> </ul> <p>На практике алгоритмы поиска с временной сложностью \\(O(\\log n)\\) обычно реализуются на основе стратегии divide and conquer, например двоичный поиск и деревья.</p> <ul> <li>На каждом шаге двоичный поиск раскладывает задачу (поиск целевого элемента в массиве) на более мелкую задачу (поиск целевого элемента в одной половине массива), и этот процесс продолжается, пока массив не станет пустым или пока не будет найден целевой элемент.</li> <li>Деревья являются типичными представителями идей divide and conquer; в таких структурах данных, как двоичное дерево поиска, AVL-дерево и куча, временная сложность различных операций равна \\(O(\\log n)\\) .</li> </ul> <p>Стратегия divide and conquer для двоичного поиска выглядит следующим образом.</p> <ul> <li>Задача раскладывается на части: двоичный поиск рекурсивно разбивает исходную задачу (поиск в массиве) на подзадачу (поиск в одной половине массива), и это достигается сравнением среднего элемента с целевым значением.</li> <li>Подзадачи независимы: в двоичном поиске на каждом шаге обрабатывается только одна подзадача, и она не зависит от других подзадач.</li> <li>Решения подзадач не нужно объединять: двоичный поиск нацелен на поиск конкретного элемента, поэтому объединять решения подзадач не требуется. Как только подзадача решена, одновременно считается решенной и исходная задача.</li> </ul> <p>По сути divide and conquer повышает эффективность поиска потому, что при полном переборе за один шаг удается исключить только один вариант, тогда как при поиске на основе divide and conquer за один шаг можно исключить половину вариантов.</p>","path":["Глава 12. Разделяй и властвуй","12.2 &nbsp; Поисковая стратегия divide and conquer"],"tags":[]},{"location":"chapter_divide_and_conquer/binary_search_recur/#1-divide-and-conquer","level":3,"title":"1.   Реализация двоичного поиска на основе divide and conquer","text":"<p>В предыдущих главах двоичный поиск реализовывался через итерацию. Теперь реализуем его с помощью divide and conquer, то есть через рекурсию.</p> <p>Question</p> <p>Дан отсортированный массив <code>nums</code> длины \\(n\\) , в котором все элементы уникальны. Найдите элемент <code>target</code> .</p> <p>С точки зрения divide and conquer обозначим подзадачу, соответствующую интервалу поиска \\([i, j]\\) , через \\(f(i, j)\\) .</p> <p>Начиная с исходной задачи \\(f(0, n-1)\\) , выполняем двоичный поиск по следующим шагам.</p> <ol> <li>Вычислить середину \\(m\\) интервала поиска \\([i, j]\\) и с ее помощью исключить половину интервала.</li> <li>Рекурсивно решить подзадачу вдвое меньшего размера; это может быть либо \\(f(i, m-1)\\) , либо \\(f(m+1, j)\\) .</li> <li>Повторять шаг <code>1.</code> и шаг <code>2.</code> , пока не будет найден <code>target</code> или пока интервал не станет пустым.</li> </ol> <p>На рисунке 12-4 показан процесс применения divide and conquer для поиска элемента \\(6\\) в массиве.</p> <p></p> <p> Рисунок 12-4   Процесс двоичного поиска в стиле divide and conquer </p> <p>В реализации кода мы объявляем рекурсивную функцию <code>dfs()</code> для решения задачи \\(f(i, j)\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_recur.py<pre><code>def dfs(nums: list[int], target: int, i: int, j: int) -&gt; int:\n    \"\"\"Бинарный поиск: задача f(i, j)\"\"\"\n    # Если интервал пуст, целевой элемент отсутствует, вернуть -1\n    if i &gt; j:\n        return -1\n    # Вычислить индекс середины m\n    m = (i + j) // 2\n    if nums[m] &lt; target:\n        # Рекурсивная подзадача f(m+1, j)\n        return dfs(nums, target, m + 1, j)\n    elif nums[m] &gt; target:\n        # Рекурсивная подзадача f(i, m-1)\n        return dfs(nums, target, i, m - 1)\n    else:\n        # Целевой элемент найден, вернуть его индекс\n        return m\n\ndef binary_search(nums: list[int], target: int) -&gt; int:\n    \"\"\"Бинарный поиск\"\"\"\n    n = len(nums)\n    # Решить задачу f(0, n-1)\n    return dfs(nums, target, 0, n - 1)\n</code></pre> binary_search_recur.cpp<pre><code>/* Бинарный поиск: задача f(i, j) */\nint dfs(vector&lt;int&gt; &amp;nums, int target, int i, int j) {\n    // Если интервал пуст, целевой элемент отсутствует, вернуть -1\n    if (i &gt; j) {\n        return -1;\n    }\n    // Вычислить индекс середины m\n    int m = (i + j) / 2;\n    if (nums[m] &lt; target) {\n        // Рекурсивная подзадача f(m+1, j)\n        return dfs(nums, target, m + 1, j);\n    } else if (nums[m] &gt; target) {\n        // Рекурсивная подзадача f(i, m-1)\n        return dfs(nums, target, i, m - 1);\n    } else {\n        // Целевой элемент найден, вернуть его индекс\n        return m;\n    }\n}\n\n/* Бинарный поиск */\nint binarySearch(vector&lt;int&gt; &amp;nums, int target) {\n    int n = nums.size();\n    // Решить задачу f(0, n-1)\n    return dfs(nums, target, 0, n - 1);\n}\n</code></pre> binary_search_recur.java<pre><code>/* Бинарный поиск: задача f(i, j) */\nint dfs(int[] nums, int target, int i, int j) {\n    // Если интервал пуст, целевой элемент отсутствует, вернуть -1\n    if (i &gt; j) {\n        return -1;\n    }\n    // Вычислить индекс середины m\n    int m = (i + j) / 2;\n    if (nums[m] &lt; target) {\n        // Рекурсивная подзадача f(m+1, j)\n        return dfs(nums, target, m + 1, j);\n    } else if (nums[m] &gt; target) {\n        // Рекурсивная подзадача f(i, m-1)\n        return dfs(nums, target, i, m - 1);\n    } else {\n        // Целевой элемент найден, вернуть его индекс\n        return m;\n    }\n}\n\n/* Бинарный поиск */\nint binarySearch(int[] nums, int target) {\n    int n = nums.length;\n    // Решить задачу f(0, n-1)\n    return dfs(nums, target, 0, n - 1);\n}\n</code></pre> binary_search_recur.cs<pre><code>/* Бинарный поиск: задача f(i, j) */\nint DFS(int[] nums, int target, int i, int j) {\n    // Если интервал пуст, целевой элемент отсутствует, вернуть -1\n    if (i &gt; j) {\n        return -1;\n    }\n    // Вычислить индекс середины m\n    int m = (i + j) / 2;\n    if (nums[m] &lt; target) {\n        // Рекурсивная подзадача f(m+1, j)\n        return DFS(nums, target, m + 1, j);\n    } else if (nums[m] &gt; target) {\n        // Рекурсивная подзадача f(i, m-1)\n        return DFS(nums, target, i, m - 1);\n    } else {\n        // Целевой элемент найден, вернуть его индекс\n        return m;\n    }\n}\n\n/* Бинарный поиск */\nint BinarySearch(int[] nums, int target) {\n    int n = nums.Length;\n    // Решить задачу f(0, n-1)\n    return DFS(nums, target, 0, n - 1);\n}\n</code></pre> binary_search_recur.go<pre><code>/* Бинарный поиск: задача f(i, j) */\nfunc dfs(nums []int, target, i, j int) int {\n    // Если интервал пуст, это означает отсутствие целевого элемента, вернуть -1\n    if i &gt; j {\n        return -1\n    }\n    // Вычислить средний индекс\n    m := i + ((j - i) &gt;&gt; 1)\n    // Сравнить середину и целевой элемент\n    if nums[m] &lt; target {\n        // Если меньше, рекурсивно обрабатывать правую половину массива\n        // Рекурсивная подзадача f(m+1, j)\n        return dfs(nums, target, m+1, j)\n    } else if nums[m] &gt; target {\n        // Если больше, рекурсивно обработать левую половину массива\n        // Рекурсивная подзадача f(i, m-1)\n        return dfs(nums, target, i, m-1)\n    } else {\n        // Целевой элемент найден, вернуть его индекс\n        return m\n    }\n}\n\n/* Бинарный поиск */\nfunc binarySearch(nums []int, target int) int {\n    n := len(nums)\n    return dfs(nums, target, 0, n-1)\n}\n</code></pre> binary_search_recur.swift<pre><code>/* Бинарный поиск: задача f(i, j) */\nfunc dfs(nums: [Int], target: Int, i: Int, j: Int) -&gt; Int {\n    // Если интервал пуст, целевой элемент отсутствует, вернуть -1\n    if i &gt; j {\n        return -1\n    }\n    // Вычислить индекс середины m\n    let m = (i + j) / 2\n    if nums[m] &lt; target {\n        // Рекурсивная подзадача f(m+1, j)\n        return dfs(nums: nums, target: target, i: m + 1, j: j)\n    } else if nums[m] &gt; target {\n        // Рекурсивная подзадача f(i, m-1)\n        return dfs(nums: nums, target: target, i: i, j: m - 1)\n    } else {\n        // Целевой элемент найден, вернуть его индекс\n        return m\n    }\n}\n\n/* Бинарный поиск */\nfunc binarySearch(nums: [Int], target: Int) -&gt; Int {\n    // Решить задачу f(0, n-1)\n    dfs(nums: nums, target: target, i: nums.startIndex, j: nums.endIndex - 1)\n}\n</code></pre> binary_search_recur.js<pre><code>/* Бинарный поиск: задача f(i, j) */\nfunction dfs(nums, target, i, j) {\n    // Если интервал пуст, целевой элемент отсутствует, вернуть -1\n    if (i &gt; j) {\n        return -1;\n    }\n    // Вычислить индекс середины m\n    const m = i + ((j - i) &gt;&gt; 1);\n    if (nums[m] &lt; target) {\n        // Рекурсивная подзадача f(m+1, j)\n        return dfs(nums, target, m + 1, j);\n    } else if (nums[m] &gt; target) {\n        // Рекурсивная подзадача f(i, m-1)\n        return dfs(nums, target, i, m - 1);\n    } else {\n        // Целевой элемент найден, вернуть его индекс\n        return m;\n    }\n}\n\n/* Бинарный поиск */\nfunction binarySearch(nums, target) {\n    const n = nums.length;\n    // Решить задачу f(0, n-1)\n    return dfs(nums, target, 0, n - 1);\n}\n</code></pre> binary_search_recur.ts<pre><code>/* Бинарный поиск: задача f(i, j) */\nfunction dfs(nums: number[], target: number, i: number, j: number): number {\n    // Если интервал пуст, целевой элемент отсутствует, вернуть -1\n    if (i &gt; j) {\n        return -1;\n    }\n    // Вычислить индекс середины m\n    const m = i + ((j - i) &gt;&gt; 1);\n    if (nums[m] &lt; target) {\n        // Рекурсивная подзадача f(m+1, j)\n        return dfs(nums, target, m + 1, j);\n    } else if (nums[m] &gt; target) {\n        // Рекурсивная подзадача f(i, m-1)\n        return dfs(nums, target, i, m - 1);\n    } else {\n        // Целевой элемент найден, вернуть его индекс\n        return m;\n    }\n}\n\n/* Бинарный поиск */\nfunction binarySearch(nums: number[], target: number): number {\n    const n = nums.length;\n    // Решить задачу f(0, n-1)\n    return dfs(nums, target, 0, n - 1);\n}\n</code></pre> binary_search_recur.dart<pre><code>/* Бинарный поиск: задача f(i, j) */\nint dfs(List&lt;int&gt; nums, int target, int i, int j) {\n  // Если интервал пуст, целевой элемент отсутствует, вернуть -1\n  if (i &gt; j) {\n    return -1;\n  }\n  // Вычислить индекс середины m\n  int m = (i + j) ~/ 2;\n  if (nums[m] &lt; target) {\n    // Рекурсивная подзадача f(m+1, j)\n    return dfs(nums, target, m + 1, j);\n  } else if (nums[m] &gt; target) {\n    // Рекурсивная подзадача f(i, m-1)\n    return dfs(nums, target, i, m - 1);\n  } else {\n    // Целевой элемент найден, вернуть его индекс\n    return m;\n  }\n}\n\n/* Бинарный поиск */\nint binarySearch(List&lt;int&gt; nums, int target) {\n  int n = nums.length;\n  // Решить задачу f(0, n-1)\n  return dfs(nums, target, 0, n - 1);\n}\n</code></pre> binary_search_recur.rs<pre><code>/* Бинарный поиск: задача f(i, j) */\nfn dfs(nums: &amp;[i32], target: i32, i: i32, j: i32) -&gt; i32 {\n    // Если интервал пуст, целевой элемент отсутствует, вернуть -1\n    if i &gt; j {\n        return -1;\n    }\n    let m: i32 = i + (j - i) / 2;\n    if nums[m as usize] &lt; target {\n        // Рекурсивная подзадача f(m+1, j)\n        return dfs(nums, target, m + 1, j);\n    } else if nums[m as usize] &gt; target {\n        // Рекурсивная подзадача f(i, m-1)\n        return dfs(nums, target, i, m - 1);\n    } else {\n        // Целевой элемент найден, вернуть его индекс\n        return m;\n    }\n}\n\n/* Бинарный поиск */\nfn binary_search(nums: &amp;[i32], target: i32) -&gt; i32 {\n    let n = nums.len() as i32;\n    // Решить задачу f(0, n-1)\n    dfs(nums, target, 0, n - 1)\n}\n</code></pre> binary_search_recur.c<pre><code>/* Бинарный поиск: задача f(i, j) */\nint dfs(int nums[], int target, int i, int j) {\n    // Если интервал пуст, целевой элемент отсутствует, вернуть -1\n    if (i &gt; j) {\n        return -1;\n    }\n    // Вычислить индекс середины m\n    int m = (i + j) / 2;\n    if (nums[m] &lt; target) {\n        // Рекурсивная подзадача f(m+1, j)\n        return dfs(nums, target, m + 1, j);\n    } else if (nums[m] &gt; target) {\n        // Рекурсивная подзадача f(i, m-1)\n        return dfs(nums, target, i, m - 1);\n    } else {\n        // Целевой элемент найден, вернуть его индекс\n        return m;\n    }\n}\n\n/* Бинарный поиск */\nint binarySearch(int nums[], int target, int numsSize) {\n    int n = numsSize;\n    // Решить задачу f(0, n-1)\n    return dfs(nums, target, 0, n - 1);\n}\n</code></pre> binary_search_recur.kt<pre><code>/* Бинарный поиск: задача f(i, j) */\nfun dfs(\n    nums: IntArray,\n    target: Int,\n    i: Int,\n    j: Int\n): Int {\n    // Если интервал пуст, целевой элемент отсутствует, вернуть -1\n    if (i &gt; j) {\n        return -1\n    }\n    // Вычислить индекс середины m\n    val m = (i + j) / 2\n    return if (nums[m] &lt; target) {\n        // Рекурсивная подзадача f(m+1, j)\n        dfs(nums, target, m + 1, j)\n    } else if (nums[m] &gt; target) {\n        // Рекурсивная подзадача f(i, m-1)\n        dfs(nums, target, i, m - 1)\n    } else {\n        // Целевой элемент найден, вернуть его индекс\n        m\n    }\n}\n\n/* Бинарный поиск */\nfun binarySearch(nums: IntArray, target: Int): Int {\n    val n = nums.size\n    // Решить задачу f(0, n-1)\n    return dfs(nums, target, 0, n - 1)\n}\n</code></pre> binary_search_recur.rb<pre><code>### Бинарный поиск: задача f(i, j) ###\ndef dfs(nums, target, i, j)\n  # Если интервал пуст, целевой элемент отсутствует, вернуть -1\n  return -1 if i &gt; j\n\n  # Вычислить индекс середины m\n  m = (i + j) / 2\n\n  if nums[m] &lt; target\n    # Рекурсивная подзадача f(m+1, j)\n    return dfs(nums, target, m + 1, j)\n  elsif nums[m] &gt; target\n    # Рекурсивная подзадача f(i, m-1)\n    return dfs(nums, target, i, m - 1)\n  else\n    # Целевой элемент найден, вернуть его индекс\n    return m\n  end\nend\n\n### Бинарный поиск ###\ndef binary_search(nums, target)\n  n = nums.length\n  # Решить задачу f(0, n-1)\n  dfs(nums, target, 0, n - 1)\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 12. Разделяй и властвуй","12.2 &nbsp; Поисковая стратегия divide and conquer"],"tags":[]},{"location":"chapter_divide_and_conquer/build_binary_tree_problem/","level":1,"title":"12.3   Задача построения двоичного дерева","text":"<p>Question</p> <p>Даны прямой обход <code>preorder</code> и симметричный обход <code>inorder</code> некоторого двоичного дерева. Постройте по ним двоичное дерево и верните его корневой узел. Предполагается, что в дереве нет узлов с одинаковыми значениями (как показано на рисунке 12-5).</p> <p></p> <p> Рисунок 12-5   Пример данных для построения двоичного дерева </p>","path":["Глава 12. Разделяй и властвуй","12.3 &nbsp; Задача построения двоичного дерева"],"tags":[]},{"location":"chapter_divide_and_conquer/build_binary_tree_problem/#1-divide-and-conquer","level":3,"title":"1.   Проверка, является ли это задачей divide and conquer","text":"<p>Исходная задача - построить двоичное дерево по <code>preorder</code> и <code>inorder</code> - является типичной задачей divide and conquer.</p> <ul> <li>Задача раскладывается на части: если смотреть с точки зрения divide and conquer, исходную задачу можно разбить на две подзадачи: построение левого поддерева и построение правого поддерева, плюс одно действие: инициализация корневого узла. Для каждого поддерева (подзадачи) можно использовать тот же способ разбиения, пока не будет достигнута наименьшая подзадача (пустое поддерево).</li> <li>Подзадачи независимы: левое и правое поддеревья независимы друг от друга и не пересекаются. При построении левого поддерева нам нужно смотреть только на ту часть прямого и симметричного обходов, которая соответствует левому поддереву. Для правого поддерева рассуждение аналогично.</li> <li>Решения подзадач можно объединить: когда левое и правое поддеревья (решения подзадач) уже построены, их можно присоединить к корневому узлу и тем самым получить решение исходной задачи.</li> </ul>","path":["Глава 12. Разделяй и властвуй","12.3 &nbsp; Задача построения двоичного дерева"],"tags":[]},{"location":"chapter_divide_and_conquer/build_binary_tree_problem/#2","level":3,"title":"2.   Как разделить поддеревья","text":"<p>Из анализа выше видно, что эта задача действительно решается через divide and conquer, но как именно, имея прямой обход <code>preorder</code> и симметричный обход <code>inorder</code>, разделить левое и правое поддеревья?</p> <p>По определению и <code>preorder</code> , и <code>inorder</code> можно разбить на три части.</p> <ul> <li>Прямой обход: <code>[ корневой узел | левое поддерево | правое поддерево ]</code> , например для дерева на рисунке 12-5 это <code>[ 3 | 9 | 2 1 7 ]</code> .</li> <li>Симметричный обход: <code>[ левое поддерево | корневой узел | правое поддерево ]</code> , например для дерева на рисунке 12-5 это <code>[ 9 | 3 | 1 2 7 ]</code> .</li> </ul> <p>На примере данных с рисунка можно получить результат разбиения по следующим шагам.</p> <ol> <li>Первый элемент прямого обхода, равный 3, является значением корневого узла.</li> <li>Найти индекс корневого узла 3 в <code>inorder</code> ; используя этот индекс, можно разбить <code>inorder</code> на <code>[ 9 | 3 | 1 2 7 ]</code> .</li> <li>По результату разбиения <code>inorder</code> нетрудно определить, что число узлов в левом и правом поддеревьях равно 1 и 3 соответственно, а значит, <code>preorder</code> можно разбить как <code>[ 3 | 9 | 2 1 7 ]</code> .</li> </ol> <p></p> <p> Рисунок 12-6   Разбиение поддеревьев в прямом и симметричном обходах </p>","path":["Глава 12. Разделяй и властвуй","12.3 &nbsp; Задача построения двоичного дерева"],"tags":[]},{"location":"chapter_divide_and_conquer/build_binary_tree_problem/#3","level":3,"title":"3.   Описание интервалов поддеревьев через переменные","text":"<p>Согласно описанному выше способу разбиения, мы уже получили интервалы индексов корневого узла, левого и правого поддеревьев в <code>preorder</code> и <code>inorder</code>. Чтобы описывать эти интервалы, нам понадобится несколько указателей-переменных.</p> <ul> <li>Обозначим индекс корневого узла текущего дерева в <code>preorder</code> через \\(i\\) .</li> <li>Обозначим индекс корневого узла текущего дерева в <code>inorder</code> через \\(m\\) .</li> <li>Обозначим интервал индексов текущего дерева в <code>inorder</code> через \\([l, r]\\) .</li> </ul> <p>Как показано в таблице 12-1, этих переменных достаточно для описания индекса корневого узла в <code>preorder</code> и интервалов поддеревьев в <code>inorder</code> .</p> <p> Таблица 12-1   Индексы корневого узла и поддеревьев в прямом и симметричном обходах </p> Индекс корневого узла в <code>preorder</code> Интервал индексов поддерева в <code>inorder</code> Текущее дерево \\(i\\) \\([l, r]\\) Левое поддерево \\(i + 1\\) \\([l, m-1]\\) Правое поддерево \\(i + 1 + (m - l)\\) \\([m+1, r]\\) <p>Обратите внимание, что \\((m-l)\\) в индексе корневого узла правого поддерева означает \"число узлов в левом поддереве\"; лучше всего понимать это выражение вместе с рисунком ниже.</p> <p></p> <p> Рисунок 12-7   Представление индексных интервалов корня и поддеревьев </p>","path":["Глава 12. Разделяй и властвуй","12.3 &nbsp; Задача построения двоичного дерева"],"tags":[]},{"location":"chapter_divide_and_conquer/build_binary_tree_problem/#4","level":3,"title":"4.   Реализация кода","text":"<p>Чтобы ускорить поиск \\(m\\) , мы используем хеш-таблицу <code>hmap</code> для хранения отображения значений массива <code>inorder</code> в индексы:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby build_tree.py<pre><code>def dfs(\n    preorder: list[int],\n    inorder_map: dict[int, int],\n    i: int,\n    l: int,\n    r: int,\n) -&gt; TreeNode | None:\n    \"\"\"Построить двоичное дерево: разделяй и властвуй\"\"\"\n    # Завершить при пустом диапазоне поддерева\n    if r - l &lt; 0:\n        return None\n    # Инициализировать корневой узел\n    root = TreeNode(preorder[i])\n    # Найти m, чтобы разделить левое и правое поддеревья\n    m = inorder_map[preorder[i]]\n    # Подзадача: построить левое поддерево\n    root.left = dfs(preorder, inorder_map, i + 1, l, m - 1)\n    # Подзадача: построить правое поддерево\n    root.right = dfs(preorder, inorder_map, i + 1 + m - l, m + 1, r)\n    # Вернуть корневой узел\n    return root\n\ndef build_tree(preorder: list[int], inorder: list[int]) -&gt; TreeNode | None:\n    \"\"\"Построить двоичное дерево\"\"\"\n    # Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n    inorder_map = {val: i for i, val in enumerate(inorder)}\n    root = dfs(preorder, inorder_map, 0, 0, len(inorder) - 1)\n    return root\n</code></pre> build_tree.cpp<pre><code>/* Построить двоичное дерево: разделяй и властвуй */\nTreeNode *dfs(vector&lt;int&gt; &amp;preorder, unordered_map&lt;int, int&gt; &amp;inorderMap, int i, int l, int r) {\n    // Завершить при пустом диапазоне поддерева\n    if (r - l &lt; 0)\n        return NULL;\n    // Инициализировать корневой узел\n    TreeNode *root = new TreeNode(preorder[i]);\n    // Найти m, чтобы разделить левое и правое поддеревья\n    int m = inorderMap[preorder[i]];\n    // Подзадача: построить левое поддерево\n    root-&gt;left = dfs(preorder, inorderMap, i + 1, l, m - 1);\n    // Подзадача: построить правое поддерево\n    root-&gt;right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r);\n    // Вернуть корневой узел\n    return root;\n}\n\n/* Построить двоичное дерево */\nTreeNode *buildTree(vector&lt;int&gt; &amp;preorder, vector&lt;int&gt; &amp;inorder) {\n    // Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n    unordered_map&lt;int, int&gt; inorderMap;\n    for (int i = 0; i &lt; inorder.size(); i++) {\n        inorderMap[inorder[i]] = i;\n    }\n    TreeNode *root = dfs(preorder, inorderMap, 0, 0, inorder.size() - 1);\n    return root;\n}\n</code></pre> build_tree.java<pre><code>/* Построить двоичное дерево: разделяй и властвуй */\nTreeNode dfs(int[] preorder, Map&lt;Integer, Integer&gt; inorderMap, int i, int l, int r) {\n    // Завершить при пустом диапазоне поддерева\n    if (r - l &lt; 0)\n        return null;\n    // Инициализировать корневой узел\n    TreeNode root = new TreeNode(preorder[i]);\n    // Найти m, чтобы разделить левое и правое поддеревья\n    int m = inorderMap.get(preorder[i]);\n    // Подзадача: построить левое поддерево\n    root.left = dfs(preorder, inorderMap, i + 1, l, m - 1);\n    // Подзадача: построить правое поддерево\n    root.right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r);\n    // Вернуть корневой узел\n    return root;\n}\n\n/* Построить двоичное дерево */\nTreeNode buildTree(int[] preorder, int[] inorder) {\n    // Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n    Map&lt;Integer, Integer&gt; inorderMap = new HashMap&lt;&gt;();\n    for (int i = 0; i &lt; inorder.length; i++) {\n        inorderMap.put(inorder[i], i);\n    }\n    TreeNode root = dfs(preorder, inorderMap, 0, 0, inorder.length - 1);\n    return root;\n}\n</code></pre> build_tree.cs<pre><code>/* Построить двоичное дерево: разделяй и властвуй */\nTreeNode? DFS(int[] preorder, Dictionary&lt;int, int&gt; inorderMap, int i, int l, int r) {\n    // Завершить при пустом диапазоне поддерева\n    if (r - l &lt; 0)\n        return null;\n    // Инициализировать корневой узел\n    TreeNode root = new(preorder[i]);\n    // Найти m, чтобы разделить левое и правое поддеревья\n    int m = inorderMap[preorder[i]];\n    // Подзадача: построить левое поддерево\n    root.left = DFS(preorder, inorderMap, i + 1, l, m - 1);\n    // Подзадача: построить правое поддерево\n    root.right = DFS(preorder, inorderMap, i + 1 + m - l, m + 1, r);\n    // Вернуть корневой узел\n    return root;\n}\n\n/* Построить двоичное дерево */\nTreeNode? BuildTree(int[] preorder, int[] inorder) {\n    // Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n    Dictionary&lt;int, int&gt; inorderMap = [];\n    for (int i = 0; i &lt; inorder.Length; i++) {\n        inorderMap.TryAdd(inorder[i], i);\n    }\n    TreeNode? root = DFS(preorder, inorderMap, 0, 0, inorder.Length - 1);\n    return root;\n}\n</code></pre> build_tree.go<pre><code>/* Построить двоичное дерево: разделяй и властвуй */\nfunc dfsBuildTree(preorder []int, inorderMap map[int]int, i, l, r int) *TreeNode {\n    // Завершить при пустом диапазоне поддерева\n    if r-l &lt; 0 {\n        return nil\n    }\n    // Инициализировать корневой узел\n    root := NewTreeNode(preorder[i])\n    // Найти m, чтобы разделить левое и правое поддеревья\n    m := inorderMap[preorder[i]]\n    // Подзадача: построить левое поддерево\n    root.Left = dfsBuildTree(preorder, inorderMap, i+1, l, m-1)\n    // Подзадача: построить правое поддерево\n    root.Right = dfsBuildTree(preorder, inorderMap, i+1+m-l, m+1, r)\n    // Вернуть корневой узел\n    return root\n}\n\n/* Построить двоичное дерево */\nfunc buildTree(preorder, inorder []int) *TreeNode {\n    // Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n    inorderMap := make(map[int]int, len(inorder))\n    for i := 0; i &lt; len(inorder); i++ {\n        inorderMap[inorder[i]] = i\n    }\n\n    root := dfsBuildTree(preorder, inorderMap, 0, 0, len(inorder)-1)\n    return root\n}\n</code></pre> build_tree.swift<pre><code>/* Построить двоичное дерево: разделяй и властвуй */\nfunc dfs(preorder: [Int], inorderMap: [Int: Int], i: Int, l: Int, r: Int) -&gt; TreeNode? {\n    // Завершить при пустом диапазоне поддерева\n    if r - l &lt; 0 {\n        return nil\n    }\n    // Инициализировать корневой узел\n    let root = TreeNode(x: preorder[i])\n    // Найти m, чтобы разделить левое и правое поддеревья\n    let m = inorderMap[preorder[i]]!\n    // Подзадача: построить левое поддерево\n    root.left = dfs(preorder: preorder, inorderMap: inorderMap, i: i + 1, l: l, r: m - 1)\n    // Подзадача: построить правое поддерево\n    root.right = dfs(preorder: preorder, inorderMap: inorderMap, i: i + 1 + m - l, l: m + 1, r: r)\n    // Вернуть корневой узел\n    return root\n}\n\n/* Построить двоичное дерево */\nfunc buildTree(preorder: [Int], inorder: [Int]) -&gt; TreeNode? {\n    // Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n    let inorderMap = inorder.enumerated().reduce(into: [:]) { $0[$1.element] = $1.offset }\n    return dfs(preorder: preorder, inorderMap: inorderMap, i: inorder.startIndex, l: inorder.startIndex, r: inorder.endIndex - 1)\n}\n</code></pre> build_tree.js<pre><code>/* Построить двоичное дерево: разделяй и властвуй */\nfunction dfs(preorder, inorderMap, i, l, r) {\n    // Завершить при пустом диапазоне поддерева\n    if (r - l &lt; 0) return null;\n    // Инициализировать корневой узел\n    const root = new TreeNode(preorder[i]);\n    // Найти m, чтобы разделить левое и правое поддеревья\n    const m = inorderMap.get(preorder[i]);\n    // Подзадача: построить левое поддерево\n    root.left = dfs(preorder, inorderMap, i + 1, l, m - 1);\n    // Подзадача: построить правое поддерево\n    root.right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r);\n    // Вернуть корневой узел\n    return root;\n}\n\n/* Построить двоичное дерево */\nfunction buildTree(preorder, inorder) {\n    // Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n    let inorderMap = new Map();\n    for (let i = 0; i &lt; inorder.length; i++) {\n        inorderMap.set(inorder[i], i);\n    }\n    const root = dfs(preorder, inorderMap, 0, 0, inorder.length - 1);\n    return root;\n}\n</code></pre> build_tree.ts<pre><code>/* Построить двоичное дерево: разделяй и властвуй */\nfunction dfs(\n    preorder: number[],\n    inorderMap: Map&lt;number, number&gt;,\n    i: number,\n    l: number,\n    r: number\n): TreeNode | null {\n    // Завершить при пустом диапазоне поддерева\n    if (r - l &lt; 0) return null;\n    // Инициализировать корневой узел\n    const root: TreeNode = new TreeNode(preorder[i]);\n    // Найти m, чтобы разделить левое и правое поддеревья\n    const m = inorderMap.get(preorder[i]);\n    // Подзадача: построить левое поддерево\n    root.left = dfs(preorder, inorderMap, i + 1, l, m - 1);\n    // Подзадача: построить правое поддерево\n    root.right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r);\n    // Вернуть корневой узел\n    return root;\n}\n\n/* Построить двоичное дерево */\nfunction buildTree(preorder: number[], inorder: number[]): TreeNode | null {\n    // Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n    let inorderMap = new Map&lt;number, number&gt;();\n    for (let i = 0; i &lt; inorder.length; i++) {\n        inorderMap.set(inorder[i], i);\n    }\n    const root = dfs(preorder, inorderMap, 0, 0, inorder.length - 1);\n    return root;\n}\n</code></pre> build_tree.dart<pre><code>/* Построить двоичное дерево: разделяй и властвуй */\nTreeNode? dfs(\n  List&lt;int&gt; preorder,\n  Map&lt;int, int&gt; inorderMap,\n  int i,\n  int l,\n  int r,\n) {\n  // Завершить при пустом диапазоне поддерева\n  if (r - l &lt; 0) {\n    return null;\n  }\n  // Инициализировать корневой узел\n  TreeNode? root = TreeNode(preorder[i]);\n  // Найти m, чтобы разделить левое и правое поддеревья\n  int m = inorderMap[preorder[i]]!;\n  // Подзадача: построить левое поддерево\n  root.left = dfs(preorder, inorderMap, i + 1, l, m - 1);\n  // Подзадача: построить правое поддерево\n  root.right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r);\n  // Вернуть корневой узел\n  return root;\n}\n\n/* Построить двоичное дерево */\nTreeNode? buildTree(List&lt;int&gt; preorder, List&lt;int&gt; inorder) {\n  // Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n  Map&lt;int, int&gt; inorderMap = {};\n  for (int i = 0; i &lt; inorder.length; i++) {\n    inorderMap[inorder[i]] = i;\n  }\n  TreeNode? root = dfs(preorder, inorderMap, 0, 0, inorder.length - 1);\n  return root;\n}\n</code></pre> build_tree.rs<pre><code>/* Построить двоичное дерево: разделяй и властвуй */\nfn dfs(\n    preorder: &amp;[i32],\n    inorder_map: &amp;HashMap&lt;i32, i32&gt;,\n    i: i32,\n    l: i32,\n    r: i32,\n) -&gt; Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt; {\n    // Завершить при пустом диапазоне поддерева\n    if r - l &lt; 0 {\n        return None;\n    }\n    // Инициализировать корневой узел\n    let root = TreeNode::new(preorder[i as usize]);\n    // Найти m, чтобы разделить левое и правое поддеревья\n    let m = inorder_map.get(&amp;preorder[i as usize]).unwrap();\n    // Подзадача: построить левое поддерево\n    root.borrow_mut().left = dfs(preorder, inorder_map, i + 1, l, m - 1);\n    // Подзадача: построить правое поддерево\n    root.borrow_mut().right = dfs(preorder, inorder_map, i + 1 + m - l, m + 1, r);\n    // Вернуть корневой узел\n    Some(root)\n}\n\n/* Построить двоичное дерево */\nfn build_tree(preorder: &amp;[i32], inorder: &amp;[i32]) -&gt; Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt; {\n    // Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n    let mut inorder_map: HashMap&lt;i32, i32&gt; = HashMap::new();\n    for i in 0..inorder.len() {\n        inorder_map.insert(inorder[i], i as i32);\n    }\n    let root = dfs(preorder, &amp;inorder_map, 0, 0, inorder.len() as i32 - 1);\n    root\n}\n</code></pre> build_tree.c<pre><code>/* Построить двоичное дерево: разделяй и властвуй */\nTreeNode *dfs(int *preorder, int *inorderMap, int i, int l, int r, int size) {\n    // Завершить при пустом диапазоне поддерева\n    if (r - l &lt; 0)\n        return NULL;\n    // Инициализировать корневой узел\n    TreeNode *root = (TreeNode *)malloc(sizeof(TreeNode));\n    root-&gt;val = preorder[i];\n    root-&gt;left = NULL;\n    root-&gt;right = NULL;\n    // Найти m, чтобы разделить левое и правое поддеревья\n    int m = inorderMap[preorder[i]];\n    // Подзадача: построить левое поддерево\n    root-&gt;left = dfs(preorder, inorderMap, i + 1, l, m - 1, size);\n    // Подзадача: построить правое поддерево\n    root-&gt;right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r, size);\n    // Вернуть корневой узел\n    return root;\n}\n\n/* Построить двоичное дерево */\nTreeNode *buildTree(int *preorder, int preorderSize, int *inorder, int inorderSize) {\n    // Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n    int *inorderMap = (int *)malloc(sizeof(int) * MAX_SIZE);\n    for (int i = 0; i &lt; inorderSize; i++) {\n        inorderMap[inorder[i]] = i;\n    }\n    TreeNode *root = dfs(preorder, inorderMap, 0, 0, inorderSize - 1, inorderSize);\n    free(inorderMap);\n    return root;\n}\n</code></pre> build_tree.kt<pre><code>/* Построить двоичное дерево: разделяй и властвуй */\nfun dfs(\n    preorder: IntArray,\n    inorderMap: Map&lt;Int?, Int?&gt;,\n    i: Int,\n    l: Int,\n    r: Int\n): TreeNode? {\n    // Завершить при пустом диапазоне поддерева\n    if (r - l &lt; 0) return null\n    // Инициализировать корневой узел\n    val root = TreeNode(preorder[i])\n    // Найти m, чтобы разделить левое и правое поддеревья\n    val m = inorderMap[preorder[i]]!!\n    // Подзадача: построить левое поддерево\n    root.left = dfs(preorder, inorderMap, i + 1, l, m - 1)\n    // Подзадача: построить правое поддерево\n    root.right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r)\n    // Вернуть корневой узел\n    return root\n}\n\n/* Построить двоичное дерево */\nfun buildTree(preorder: IntArray, inorder: IntArray): TreeNode? {\n    // Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n    val inorderMap = HashMap&lt;Int?, Int?&gt;()\n    for (i in inorder.indices) {\n        inorderMap[inorder[i]] = i\n    }\n    val root = dfs(preorder, inorderMap, 0, 0, inorder.size - 1)\n    return root\n}\n</code></pre> build_tree.rb<pre><code>### Построить двоичное дерево: разделяй и властвуй ###\ndef dfs(preorder, inorder_map, i, l, r)\n  # Завершить при пустом диапазоне поддерева\n  return if r - l &lt; 0\n\n  # Инициализировать корневой узел\n  root = TreeNode.new(preorder[i])\n  # Найти m, чтобы разделить левое и правое поддеревья\n  m = inorder_map[preorder[i]]\n  # Подзадача: построить левое поддерево\n  root.left = dfs(preorder, inorder_map, i + 1, l, m - 1)\n  # Подзадача: построить правое поддерево\n  root.right = dfs(preorder, inorder_map, i + 1 + m - l, m + 1, r)\n\n  # Вернуть корневой узел\n  root\nend\n\n### Построить двоичное дерево ###\ndef build_tree(preorder, inorder)\n  # Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n  inorder_map = {}\n  inorder.each_with_index { |val, i| inorder_map[val] = i }\n  dfs(preorder, inorder_map, 0, 0, inorder.length - 1)\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>На рисунке 12-8 показан рекурсивный процесс построения двоичного дерева: каждый узел создается в фазе \"спуска\", а каждое ребро (ссылка) формируется в фазе \"подъема\".</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 12-8   Рекурсивный процесс построения двоичного дерева </p> <p>Результаты разбиения <code>preorder</code> и <code>inorder</code> внутри каждого рекурсивного вызова показаны на рисунке 12-9.</p> <p></p> <p> Рисунок 12-9   Результаты разбиения в каждом рекурсивном вызове </p> <p>Пусть число узлов дерева равно \\(n\\) ; инициализация каждого узла (то есть выполнение одного рекурсивного вызова <code>dfs()</code> ) занимает \\(O(1)\\) времени. Следовательно, общая временная сложность равна \\(O(n)\\) .</p> <p>Хеш-таблица хранит отображение значений <code>inorder</code> в индексы, поэтому ее пространственная сложность равна \\(O(n)\\) . В худшем случае, когда двоичное дерево вырождается в связный список, глубина рекурсии достигает \\(n\\) и требует \\(O(n)\\) памяти стека. Следовательно, общая пространственная сложность также равна \\(O(n)\\) .</p>","path":["Глава 12. Разделяй и властвуй","12.3 &nbsp; Задача построения двоичного дерева"],"tags":[]},{"location":"chapter_divide_and_conquer/divide_and_conquer/","level":1,"title":"12.1   Алгоритмы \"разделяй и властвуй\"","text":"<p>Разделяй и властвуй (divide and conquer) - это очень важная и широко используемая стратегия построения алгоритмов. Обычно она реализуется через рекурсию и включает два этапа: \"разделение\" и \"решение\".</p> <ol> <li>Разделение (этап декомпозиции): рекурсивно разбить исходную задачу на две или более подзадачи, пока не будет достигнута наименьшая подзадача.</li> <li>Решение (этап объединения): начиная с уже известных решений наименьших подзадач, снизу вверх объединять решения подзадач и тем самым получать решение исходной задачи.</li> </ol> <p>Как показано на рисунке 12-1, \"сортировка слиянием\" является одним из типичных примеров применения стратегии \"разделяй и властвуй\".</p> <ol> <li>Разделение: рекурсивно разделить исходный массив (исходную задачу) на два подмассива (подзадачи), пока в подмассиве не останется только один элемент (наименьшая подзадача).</li> <li>Решение: снизу вверх объединять упорядоченные подмассивы (решения подзадач), чтобы получить упорядоченный исходный массив (решение исходной задачи).</li> </ol> <p></p> <p> Рисунок 12-1   Стратегия divide and conquer в сортировке слиянием </p>","path":["Глава 12. Разделяй и властвуй","12.1 &nbsp; Алгоритмы \"разделяй и властвуй\""],"tags":[]},{"location":"chapter_divide_and_conquer/divide_and_conquer/#1211-divide-and-conquer","level":2,"title":"12.1.1   Как определить задачу divide and conquer","text":"<p>Чтобы понять, подходит ли задача для решения методом divide and conquer, обычно можно ориентироваться на следующие критерии.</p> <ol> <li>Задача раскладывается на части: исходную задачу можно разбить на более мелкие и похожие подзадачи, причем такое разбиение можно применять рекурсивно.</li> <li>Подзадачи независимы: подзадачи не пересекаются, не зависят друг от друга и могут решаться независимо.</li> <li>Решения подзадач можно объединить: решение исходной задачи получается объединением решений подзадач.</li> </ol> <p>Очевидно, что сортировка слиянием удовлетворяет всем трем критериям.</p> <ol> <li>Задача раскладывается на части: массив (исходная задача) рекурсивно делится на два подмассива (подзадачи).</li> <li>Подзадачи независимы: каждый подмассив можно сортировать отдельно (то есть каждую подзадачу можно решать независимо).</li> <li>Решения подзадач можно объединить: два упорядоченных подмассива (решения подзадач) можно объединить в один упорядоченный массив (решение исходной задачи).</li> </ol>","path":["Глава 12. Разделяй и властвуй","12.1 &nbsp; Алгоритмы \"разделяй и властвуй\""],"tags":[]},{"location":"chapter_divide_and_conquer/divide_and_conquer/#1212-divide-and-conquer","level":2,"title":"12.1.2   Повышение эффективности с помощью divide and conquer","text":"<p>Стратегия divide and conquer не только позволяет эффективно решать алгоритмические задачи, но и часто повышает эффективность самих алгоритмов. Именно поэтому быстрая сортировка, сортировка слиянием и пирамидальная сортировка обычно работают быстрее, чем сортировка выбором, пузырьком и вставками.</p> <p>Тогда возникает естественный вопрос: почему divide and conquer повышает эффективность алгоритма и какова логика этого на более глубоком уровне? Иными словами, почему разбиение большой задачи на несколько подзадач, решение этих подзадач и последующее объединение их решений оказывается эффективнее, чем прямое решение исходной задачи? Этот вопрос можно рассмотреть с двух сторон: через число операций и через параллельные вычисления.</p>","path":["Глава 12. Разделяй и властвуй","12.1 &nbsp; Алгоритмы \"разделяй и властвуй\""],"tags":[]},{"location":"chapter_divide_and_conquer/divide_and_conquer/#1","level":3,"title":"1.   Оптимизация числа операций","text":"<p>Рассмотрим \"сортировку пузырьком\": для массива длины \\(n\\) ей требуется \\(O(n^2)\\) времени. Предположим, что мы разделим массив на два подмассива в середине, как показано на рисунке 12-2. Тогда само разбиение потребует \\(O(n)\\) времени, сортировка каждого подмассива займет \\(O((n / 2)^2)\\) времени, а объединение двух подмассивов потребует еще \\(O(n)\\) времени. Общая временная сложность будет равна:</p> \\[ O(n + (\\frac{n}{2})^2 \\times 2 + n) = O(\\frac{n^2}{2} + 2n) \\] <p></p> <p> Рисунок 12-2   Сортировка пузырьком до и после разбиения массива </p> <p>Теперь рассмотрим следующее неравенство, в котором левая и правая части обозначают общее число операций до разбиения и после него:</p> \\[ \\begin{aligned} n^2 &amp; &gt; \\frac{n^2}{2} + 2n \\newline n^2 - \\frac{n^2}{2} - 2n &amp; &gt; 0 \\newline n(n - 4) &amp; &gt; 0 \\end{aligned} \\] <p>Это означает, что при \\(n &gt; 4\\) число операций после разбиения становится меньше, а значит, сортировка должна работать быстрее. При этом важно заметить, что временная сложность после разбиения все еще остается квадратичной, то есть \\(O(n^2)\\) ; уменьшается лишь константный множитель.</p> <p>Если пойти дальше и продолжать делить каждый подмассив пополам, пока в нем не останется только один элемент, то мы фактически получим \"сортировку слиянием\", чья временная сложность равна \\(O(n \\log n)\\) .</p> <p>Можно пойти еще дальше и спросить: что если задать несколько точек разделения и равномерно разбить исходный массив на \\(k\\) подмассивов? Такая ситуация очень похожа на \"блочную сортировку\", которая особенно хорошо подходит для сортировки очень больших объемов данных и теоретически может достигать временной сложности \\(O(n + k)\\) .</p>","path":["Глава 12. Разделяй и властвуй","12.1 &nbsp; Алгоритмы \"разделяй и властвуй\""],"tags":[]},{"location":"chapter_divide_and_conquer/divide_and_conquer/#2","level":3,"title":"2.   Оптимизация параллельных вычислений","text":"<p>Мы знаем, что подзадачи, порождаемые divide and conquer, являются независимыми, а значит, их обычно можно решать параллельно. Иначе говоря, divide and conquer не только может уменьшить временную сложность алгоритма, но и хорошо сочетается с параллельной оптимизацией на уровне системы.</p> <p>Параллельная оптимизация особенно эффективна в среде с несколькими ядрами или несколькими процессорами, потому что система может одновременно обрабатывать разные подзадачи, лучше загружая вычислительные ресурсы и тем самым заметно сокращая общее время работы.</p> <p>Например, в показанной ниже \"блочной сортировке\" большой объем данных равномерно распределяется по блокам. Тогда сортировку каждого блока можно поручить отдельным вычислительным единицам, а после завершения просто объединить результаты.</p> <p></p> <p> Рисунок 12-3   Параллельные вычисления в блочной сортировке </p>","path":["Глава 12. Разделяй и властвуй","12.1 &nbsp; Алгоритмы \"разделяй и властвуй\""],"tags":[]},{"location":"chapter_divide_and_conquer/divide_and_conquer/#1213-divide-and-conquer","level":2,"title":"12.1.3   Типичные применения divide and conquer","text":"<p>С одной стороны, divide and conquer можно использовать для решения многих классических алгоритмических задач.</p> <ul> <li>Поиск ближайшей пары точек: сначала множество точек делится на две части, затем ищется ближайшая пара в каждой части, а затем ближайшая пара, пересекающая границу между двумя частями.</li> <li>Умножение больших чисел: например, алгоритм Карацубы, который раскладывает умножение больших чисел на несколько умножений и сложений меньших чисел.</li> <li>Умножение матриц: например, алгоритм Штрассена, который раскладывает умножение больших матриц на несколько умножений и сложений матриц меньшего размера.</li> <li>Задача о Ханойской башне: задача о Ханойской башне решается рекурсивно и является типичным примером применения divide and conquer.</li> <li>Подсчет инверсий: если в последовательности предыдущее число больше следующего, то такая пара образует инверсию. Эту задачу можно решить с помощью идей divide and conquer, опираясь на сортировку слиянием.</li> </ul> <p>С другой стороны, divide and conquer очень широко применяется при проектировании алгоритмов и структур данных.</p> <ul> <li>Двоичный поиск: двоичный поиск делит отсортированный массив на две части по индексу середины, а затем, в зависимости от результата сравнения целевого значения со средним элементом, исключает одну из половин и повторяет ту же операцию на оставшемся интервале.</li> <li>Сортировка слиянием: она уже была рассмотрена в начале этого раздела, поэтому не будем повторяться.</li> <li>Быстрая сортировка: в ней выбирается опорное значение, после чего массив делится на два подмассива: один содержит элементы меньше опорного, а другой - больше. Затем такая же операция повторяется для обеих частей, пока в подмассиве не останется один элемент.</li> <li>Блочная сортировка: ее основная идея заключается в распределении данных по нескольким блокам, сортировке элементов внутри каждого блока и последующем последовательном извлечении элементов из блоков для построения отсортированного массива.</li> <li>Деревья: например, двоичные деревья поиска, AVL-деревья, красно-черные деревья, B-деревья, B+ деревья и т.д. Их операции поиска, вставки и удаления можно рассматривать как применение divide and conquer.</li> <li>Кучи: куча является особым видом полного бинарного дерева, а такие операции, как вставка, удаление и упорядочивание, по сути содержат идеи divide and conquer.</li> <li>Хеш-таблицы: хотя хеш-таблицы напрямую не используют divide and conquer, некоторые способы разрешения коллизий косвенно опираются на эту стратегию. Например, длинные цепочки в методе цепочек могут преобразовываться в красно-черные деревья для повышения эффективности поиска.</li> </ul> <p>Нетрудно заметить, что divide and conquer - это \"тихая\" алгоритмическая идея, скрыто присутствующая внутри самых разных алгоритмов и структур данных.</p>","path":["Глава 12. Разделяй и властвуй","12.1 &nbsp; Алгоритмы \"разделяй и властвуй\""],"tags":[]},{"location":"chapter_divide_and_conquer/hanota_problem/","level":1,"title":"12.4   Задача о Ханойской башне","text":"<p>В задачах сортировки слиянием и построения двоичного дерева мы делили исходную задачу на две подзадачи, каждая из которых имела размер, равный примерно половине исходной задачи. Однако для задачи о Ханойской башне используется другая стратегия разбиения.</p> <p>Question</p> <p>Даны три стержня, обозначенные как <code>A</code> , <code>B</code> и <code>C</code> . В начальном состоянии на стержне <code>A</code> находятся \\(n\\) дисков, расположенных сверху вниз в порядке от меньшего к большему. Нужно переместить эти \\(n\\) дисков на стержень <code>C</code> , сохранив их исходный порядок (как показано на рисунке 12-10). Во время перемещения дисков необходимо соблюдать следующие правила.</p> <ol> <li>Диск можно снять только с вершины одного стержня и положить только на вершину другого стержня.</li> <li>За один раз можно перемещать только один диск.</li> <li>Меньший диск всегда должен лежать на большем.</li> </ol> <p></p> <p> Рисунок 12-10   Пример задачи о Ханойской башне </p> <p>Обозначим задачу о Ханойской башне размера \\(i\\) как \\(f(i)\\) . Например, \\(f(3)\\) означает задачу перемещения 3 дисков со стержня <code>A</code> на стержень <code>C</code> .</p>","path":["Глава 12. Разделяй и властвуй","12.4 &nbsp; Задача о Ханойской башне"],"tags":[]},{"location":"chapter_divide_and_conquer/hanota_problem/#1","level":3,"title":"1.   Рассмотрим базовые случаи","text":"<p>Как показано на рисунке 12-11, для задачи \\(f(1)\\) , то есть когда имеется только один диск, достаточно просто переместить его напрямую со стержня <code>A</code> на стержень <code>C</code> .</p> &lt;1&gt;&lt;2&gt; <p></p> <p></p> <p> Рисунок 12-11   Решение задачи размера 1 </p> <p>Как показано на рисунке 12-12, для задачи \\(f(2)\\) , то есть когда есть два диска, поскольку меньший диск все время должен лежать на большем, приходится использовать <code>B</code> как вспомогательный стержень.</p> <ol> <li>Сначала переместить верхний маленький диск с <code>A</code> на <code>B</code> .</li> <li>Затем переместить большой диск с <code>A</code> на <code>C</code> .</li> <li>Наконец, переместить маленький диск с <code>B</code> на <code>C</code> .</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p> Рисунок 12-12   Решение задачи размера 2 </p> <p>Процесс решения задачи \\(f(2)\\) можно кратко описать так: переместить два диска с <code>A</code> на <code>C</code> с помощью <code>B</code> . Здесь <code>C</code> называется целевым стержнем, а <code>B</code> - буферным стержнем.</p>","path":["Глава 12. Разделяй и властвуй","12.4 &nbsp; Задача о Ханойской башне"],"tags":[]},{"location":"chapter_divide_and_conquer/hanota_problem/#2","level":3,"title":"2.   Разбиение на подзадачи","text":"<p>Для задачи \\(f(3)\\) , то есть когда имеется три диска, ситуация становится немного сложнее.</p> <p>Поскольку решения \\(f(1)\\) и \\(f(2)\\) уже известны, можно подойти к задаче с точки зрения divide and conquer и рассматривать два верхних диска на <code>A</code> как единое целое, выполняя шаги, показанные на рисунке 12-13. Так три диска успешно перемещаются с <code>A</code> на <code>C</code> .</p> <ol> <li>Сделать <code>B</code> целевым стержнем, а <code>C</code> буферным, и переместить два диска с <code>A</code> на <code>B</code> .</li> <li>Переместить оставшийся один диск с <code>A</code> напрямую на <code>C</code> .</li> <li>Сделать <code>C</code> целевым стержнем, а <code>A</code> буферным, и переместить два диска с <code>B</code> на <code>C</code> .</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p> Рисунок 12-13   Решение задачи размера 3 </p> <p>По своей сути мы разбиваем задачу \\(f(3)\\) на две подзадачи \\(f(2)\\) и одну подзадачу \\(f(1)\\) . Если последовательно решить эти три подзадачи, исходная задача тоже будет решена. Это показывает, что подзадачи независимы и что их решения можно объединить.</p> <p>Таким образом, можно сформулировать показанную на рисунке 12-14 стратегию divide and conquer для задачи о Ханойской башне: исходная задача \\(f(n)\\) разбивается на две подзадачи \\(f(n-1)\\) и одну подзадачу \\(f(1)\\) , которые затем решаются в следующем порядке.</p> <ol> <li>Переместить \\(n-1\\) дисков с <code>A</code> на <code>B</code> с помощью <code>C</code> .</li> <li>Переместить оставшийся \\(1\\) диск напрямую с <code>A</code> на <code>C</code> .</li> <li>Переместить \\(n-1\\) дисков с <code>B</code> на <code>C</code> с помощью <code>A</code> .</li> </ol> <p>Для двух подзадач \\(f(n-1)\\) можно применять тот же способ рекурсивного разбиения, пока не будет достигнута наименьшая подзадача \\(f(1)\\) . А решение для \\(f(1)\\) уже известно и требует всего одного перемещения.</p> <p></p> <p> Рисунок 12-14   Стратегия divide and conquer для решения задачи о Ханойской башне </p>","path":["Глава 12. Разделяй и властвуй","12.4 &nbsp; Задача о Ханойской башне"],"tags":[]},{"location":"chapter_divide_and_conquer/hanota_problem/#3","level":3,"title":"3.   Реализация кода","text":"<p>В коде мы объявляем рекурсивную функцию <code>dfs(i, src, buf, tar)</code> , которая перемещает \\(i\\) верхних дисков со стержня <code>src</code> на целевой стержень <code>tar</code> с помощью буферного стержня <code>buf</code> :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby hanota.py<pre><code>def move(src: list[int], tar: list[int]):\n    \"\"\"Переместить один диск\"\"\"\n    # Снять диск с вершины src\n    pan = src.pop()\n    # Положить диск на вершину tar\n    tar.append(pan)\n\ndef dfs(i: int, src: list[int], buf: list[int], tar: list[int]):\n    \"\"\"Решить задачу Ханойской башни f(i)\"\"\"\n    # Если в src остался только один диск, сразу переместить его в tar\n    if i == 1:\n        move(src, tar)\n        return\n    # Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n    dfs(i - 1, src, tar, buf)\n    # Подзадача f(1): переместить оставшийся один диск из src в tar\n    move(src, tar)\n    # Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n    dfs(i - 1, buf, src, tar)\n\ndef solve_hanota(A: list[int], B: list[int], C: list[int]):\n    \"\"\"Решить задачу Ханойской башни\"\"\"\n    n = len(A)\n    # Переместить верхние n дисков из A в C с помощью B\n    dfs(n, A, B, C)\n</code></pre> hanota.cpp<pre><code>/* Переместить один диск */\nvoid move(vector&lt;int&gt; &amp;src, vector&lt;int&gt; &amp;tar) {\n    // Снять диск с вершины src\n    int pan = src.back();\n    src.pop_back();\n    // Положить диск на вершину tar\n    tar.push_back(pan);\n}\n\n/* Решить задачу Ханойской башни f(i) */\nvoid dfs(int i, vector&lt;int&gt; &amp;src, vector&lt;int&gt; &amp;buf, vector&lt;int&gt; &amp;tar) {\n    // Если в src остался только один диск, сразу переместить его в tar\n    if (i == 1) {\n        move(src, tar);\n        return;\n    }\n    // Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n    dfs(i - 1, src, tar, buf);\n    // Подзадача f(1): переместить оставшийся один диск из src в tar\n    move(src, tar);\n    // Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n    dfs(i - 1, buf, src, tar);\n}\n\n/* Решить задачу Ханойской башни */\nvoid solveHanota(vector&lt;int&gt; &amp;A, vector&lt;int&gt; &amp;B, vector&lt;int&gt; &amp;C) {\n    int n = A.size();\n    // Переместить верхние n дисков из A в C с помощью B\n    dfs(n, A, B, C);\n}\n</code></pre> hanota.java<pre><code>/* Переместить один диск */\nvoid move(List&lt;Integer&gt; src, List&lt;Integer&gt; tar) {\n    // Снять диск с вершины src\n    Integer pan = src.remove(src.size() - 1);\n    // Положить диск на вершину tar\n    tar.add(pan);\n}\n\n/* Решить задачу Ханойской башни f(i) */\nvoid dfs(int i, List&lt;Integer&gt; src, List&lt;Integer&gt; buf, List&lt;Integer&gt; tar) {\n    // Если в src остался только один диск, сразу переместить его в tar\n    if (i == 1) {\n        move(src, tar);\n        return;\n    }\n    // Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n    dfs(i - 1, src, tar, buf);\n    // Подзадача f(1): переместить оставшийся один диск из src в tar\n    move(src, tar);\n    // Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n    dfs(i - 1, buf, src, tar);\n}\n\n/* Решить задачу Ханойской башни */\nvoid solveHanota(List&lt;Integer&gt; A, List&lt;Integer&gt; B, List&lt;Integer&gt; C) {\n    int n = A.size();\n    // Переместить верхние n дисков из A в C с помощью B\n    dfs(n, A, B, C);\n}\n</code></pre> hanota.cs<pre><code>/* Переместить один диск */\nvoid Move(List&lt;int&gt; src, List&lt;int&gt; tar) {\n    // Снять диск с вершины src\n    int pan = src[^1];\n    src.RemoveAt(src.Count - 1);\n    // Положить диск на вершину tar\n    tar.Add(pan);\n}\n\n/* Решить задачу Ханойской башни f(i) */\nvoid DFS(int i, List&lt;int&gt; src, List&lt;int&gt; buf, List&lt;int&gt; tar) {\n    // Если в src остался только один диск, сразу переместить его в tar\n    if (i == 1) {\n        Move(src, tar);\n        return;\n    }\n    // Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n    DFS(i - 1, src, tar, buf);\n    // Подзадача f(1): переместить оставшийся один диск из src в tar\n    Move(src, tar);\n    // Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n    DFS(i - 1, buf, src, tar);\n}\n\n/* Решить задачу Ханойской башни */\nvoid SolveHanota(List&lt;int&gt; A, List&lt;int&gt; B, List&lt;int&gt; C) {\n    int n = A.Count;\n    // Переместить верхние n дисков из A в C с помощью B\n    DFS(n, A, B, C);\n}\n</code></pre> hanota.go<pre><code>/* Переместить один диск */\nfunc move(src, tar *list.List) {\n    // Снять диск с вершины src\n    pan := src.Back()\n    // Положить диск на вершину tar\n    tar.PushBack(pan.Value)\n    // Убрать верхний диск из src\n    src.Remove(pan)\n}\n\n/* Решить задачу Ханойской башни f(i) */\nfunc dfsHanota(i int, src, buf, tar *list.List) {\n    // Если в src остался только один диск, сразу переместить его в tar\n    if i == 1 {\n        move(src, tar)\n        return\n    }\n    // Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n    dfsHanota(i-1, src, tar, buf)\n    // Подзадача f(1): переместить оставшийся один диск из src в tar\n    move(src, tar)\n    // Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n    dfsHanota(i-1, buf, src, tar)\n}\n\n/* Решить задачу Ханойской башни */\nfunc solveHanota(A, B, C *list.List) {\n    n := A.Len()\n    // Переместить верхние n дисков из A в C с помощью B\n    dfsHanota(n, A, B, C)\n}\n</code></pre> hanota.swift<pre><code>/* Переместить один диск */\nfunc move(src: inout [Int], tar: inout [Int]) {\n    // Снять диск с вершины src\n    let pan = src.popLast()!\n    // Положить диск на вершину tar\n    tar.append(pan)\n}\n\n/* Решить задачу Ханойской башни f(i) */\nfunc dfs(i: Int, src: inout [Int], buf: inout [Int], tar: inout [Int]) {\n    // Если в src остался только один диск, сразу переместить его в tar\n    if i == 1 {\n        move(src: &amp;src, tar: &amp;tar)\n        return\n    }\n    // Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n    dfs(i: i - 1, src: &amp;src, buf: &amp;tar, tar: &amp;buf)\n    // Подзадача f(1): переместить оставшийся один диск из src в tar\n    move(src: &amp;src, tar: &amp;tar)\n    // Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n    dfs(i: i - 1, src: &amp;buf, buf: &amp;src, tar: &amp;tar)\n}\n\n/* Решить задачу Ханойской башни */\nfunc solveHanota(A: inout [Int], B: inout [Int], C: inout [Int]) {\n    let n = A.count\n    // Хвост списка соответствует вершине столбца\n    // Переместить верхние n дисков из src в C с помощью B\n    dfs(i: n, src: &amp;A, buf: &amp;B, tar: &amp;C)\n}\n</code></pre> hanota.js<pre><code>/* Переместить один диск */\nfunction move(src, tar) {\n    // Снять диск с вершины src\n    const pan = src.pop();\n    // Положить диск на вершину tar\n    tar.push(pan);\n}\n\n/* Решить задачу Ханойской башни f(i) */\nfunction dfs(i, src, buf, tar) {\n    // Если в src остался только один диск, сразу переместить его в tar\n    if (i === 1) {\n        move(src, tar);\n        return;\n    }\n    // Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n    dfs(i - 1, src, tar, buf);\n    // Подзадача f(1): переместить оставшийся один диск из src в tar\n    move(src, tar);\n    // Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n    dfs(i - 1, buf, src, tar);\n}\n\n/* Решить задачу Ханойской башни */\nfunction solveHanota(A, B, C) {\n    const n = A.length;\n    // Переместить верхние n дисков из A в C с помощью B\n    dfs(n, A, B, C);\n}\n</code></pre> hanota.ts<pre><code>/* Переместить один диск */\nfunction move(src: number[], tar: number[]): void {\n    // Снять диск с вершины src\n    const pan = src.pop();\n    // Положить диск на вершину tar\n    tar.push(pan);\n}\n\n/* Решить задачу Ханойской башни f(i) */\nfunction dfs(i: number, src: number[], buf: number[], tar: number[]): void {\n    // Если в src остался только один диск, сразу переместить его в tar\n    if (i === 1) {\n        move(src, tar);\n        return;\n    }\n    // Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n    dfs(i - 1, src, tar, buf);\n    // Подзадача f(1): переместить оставшийся один диск из src в tar\n    move(src, tar);\n    // Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n    dfs(i - 1, buf, src, tar);\n}\n\n/* Решить задачу Ханойской башни */\nfunction solveHanota(A: number[], B: number[], C: number[]): void {\n    const n = A.length;\n    // Переместить верхние n дисков из A в C с помощью B\n    dfs(n, A, B, C);\n}\n</code></pre> hanota.dart<pre><code>/* Переместить один диск */\nvoid move(List&lt;int&gt; src, List&lt;int&gt; tar) {\n  // Снять диск с вершины src\n  int pan = src.removeLast();\n  // Положить диск на вершину tar\n  tar.add(pan);\n}\n\n/* Решить задачу Ханойской башни f(i) */\nvoid dfs(int i, List&lt;int&gt; src, List&lt;int&gt; buf, List&lt;int&gt; tar) {\n  // Если в src остался только один диск, сразу переместить его в tar\n  if (i == 1) {\n    move(src, tar);\n    return;\n  }\n  // Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n  dfs(i - 1, src, tar, buf);\n  // Подзадача f(1): переместить оставшийся один диск из src в tar\n  move(src, tar);\n  // Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n  dfs(i - 1, buf, src, tar);\n}\n\n/* Решить задачу Ханойской башни */\nvoid solveHanota(List&lt;int&gt; A, List&lt;int&gt; B, List&lt;int&gt; C) {\n  int n = A.length;\n  // Переместить верхние n дисков из A в C с помощью B\n  dfs(n, A, B, C);\n}\n</code></pre> hanota.rs<pre><code>/* Переместить один диск */\nfn move_pan(src: &amp;mut Vec&lt;i32&gt;, tar: &amp;mut Vec&lt;i32&gt;) {\n    // Снять диск с вершины src\n    let pan = src.pop().unwrap();\n    // Положить диск на вершину tar\n    tar.push(pan);\n}\n\n/* Решить задачу Ханойской башни f(i) */\nfn dfs(i: i32, src: &amp;mut Vec&lt;i32&gt;, buf: &amp;mut Vec&lt;i32&gt;, tar: &amp;mut Vec&lt;i32&gt;) {\n    // Если в src остался только один диск, сразу переместить его в tar\n    if i == 1 {\n        move_pan(src, tar);\n        return;\n    }\n    // Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n    dfs(i - 1, src, tar, buf);\n    // Подзадача f(1): переместить оставшийся один диск из src в tar\n    move_pan(src, tar);\n    // Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n    dfs(i - 1, buf, src, tar);\n}\n\n/* Решить задачу Ханойской башни */\nfn solve_hanota(A: &amp;mut Vec&lt;i32&gt;, B: &amp;mut Vec&lt;i32&gt;, C: &amp;mut Vec&lt;i32&gt;) {\n    let n = A.len() as i32;\n    // Переместить верхние n дисков из A в C с помощью B\n    dfs(n, A, B, C);\n}\n</code></pre> hanota.c<pre><code>/* Переместить один диск */\nvoid move(int *src, int *srcSize, int *tar, int *tarSize) {\n    // Снять диск с вершины src\n    int pan = src[*srcSize - 1];\n    src[*srcSize - 1] = 0;\n    (*srcSize)--;\n    // Положить диск на вершину tar\n    tar[*tarSize] = pan;\n    (*tarSize)++;\n}\n\n/* Решить задачу Ханойской башни f(i) */\nvoid dfs(int i, int *src, int *srcSize, int *buf, int *bufSize, int *tar, int *tarSize) {\n    // Если в src остался только один диск, сразу переместить его в tar\n    if (i == 1) {\n        move(src, srcSize, tar, tarSize);\n        return;\n    }\n    // Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n    dfs(i - 1, src, srcSize, tar, tarSize, buf, bufSize);\n    // Подзадача f(1): переместить оставшийся один диск из src в tar\n    move(src, srcSize, tar, tarSize);\n    // Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n    dfs(i - 1, buf, bufSize, src, srcSize, tar, tarSize);\n}\n\n/* Решить задачу Ханойской башни */\nvoid solveHanota(int *A, int *ASize, int *B, int *BSize, int *C, int *CSize) {\n    // Переместить верхние n дисков из A в C с помощью B\n    dfs(*ASize, A, ASize, B, BSize, C, CSize);\n}\n</code></pre> hanota.kt<pre><code>/* Переместить один диск */\nfun move(src: MutableList&lt;Int&gt;, tar: MutableList&lt;Int&gt;) {\n    // Снять диск с вершины src\n    val pan = src.removeAt(src.size - 1)\n    // Положить диск на вершину tar\n    tar.add(pan)\n}\n\n/* Решить задачу Ханойской башни f(i) */\nfun dfs(i: Int, src: MutableList&lt;Int&gt;, buf: MutableList&lt;Int&gt;, tar: MutableList&lt;Int&gt;) {\n    // Если в src остался только один диск, сразу переместить его в tar\n    if (i == 1) {\n        move(src, tar)\n        return\n    }\n    // Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n    dfs(i - 1, src, tar, buf)\n    // Подзадача f(1): переместить оставшийся один диск из src в tar\n    move(src, tar)\n    // Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n    dfs(i - 1, buf, src, tar)\n}\n\n/* Решить задачу Ханойской башни */\nfun solveHanota(A: MutableList&lt;Int&gt;, B: MutableList&lt;Int&gt;, C: MutableList&lt;Int&gt;) {\n    val n = A.size\n    // Переместить верхние n дисков из A в C с помощью B\n    dfs(n, A, B, C)\n}\n</code></pre> hanota.rb<pre><code>### Переместить один диск ###\ndef move(src, tar)\n  # Снять диск с вершины src\n  pan = src.pop\n  # Положить диск на вершину tar\n  tar &lt;&lt; pan\nend\n\n### Решить задачу Ханойской башни f(i) ###\ndef dfs(i, src, buf, tar)\n  # Если в src остался только один диск, сразу переместить его в tar\n  if i == 1\n    move(src, tar)\n    return\n  end\n\n  # Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n  dfs(i - 1, src, tar, buf)\n  # Подзадача f(1): переместить оставшийся один диск из src в tar\n  move(src, tar)\n  # Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n  dfs(i - 1, buf, src, tar)\nend\n\n### Решить задачу Ханойской башни ###\ndef solve_hanota(_A, _B, _C)\n  n = _A.length\n  # Переместить верхние n дисков из A в C с помощью B\n  dfs(n, _A, _B, _C)\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Как показано на рисунке 12-15, задача о Ханойской башне формирует дерево рекурсии высоты \\(n\\) , в котором каждый узел представляет подзадачу и соответствует одному открытому вызову <code>dfs()</code> ; поэтому временная сложность равна \\(O(2^n)\\) , а пространственная сложность равна \\(O(n)\\) .</p> <p></p> <p> Рисунок 12-15   Дерево рекурсии задачи о Ханойской башне </p> <p>Quote</p> <p>Задача о Ханойской башне происходит из древней легенды. В одном из храмов древней Индии монахи имели три высоких алмазных стержня и \\(64\\) золотых диска разного размера. Монахи непрерывно перекладывали диски и верили, что в тот момент, когда последний диск будет правильно перенесен, мир подойдет к концу.</p> <p>Однако даже если бы монахи перемещали по одному диску в секунду, им понадобилось бы примерно \\(2^{64} \\approx 1.84×10^{19}\\) секунд, то есть около \\(585\\) миллиардов лет, что намного превышает текущую оценку возраста Вселенной. Поэтому, если легенда и верна, нам, вероятно, пока не о чем беспокоиться.</p>","path":["Глава 12. Разделяй и властвуй","12.4 &nbsp; Задача о Ханойской башне"],"tags":[]},{"location":"chapter_divide_and_conquer/summary/","level":1,"title":"12.5   Резюме","text":"","path":["Глава 12. Разделяй и властвуй","12.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_divide_and_conquer/summary/#1","level":3,"title":"1.   Ключевые выводы","text":"<ul> <li>Divide and conquer - это распространенная стратегия проектирования алгоритмов, которая включает два этапа: разделение (декомпозицию) и решение (объединение), и обычно реализуется с помощью рекурсии.</li> <li>Критерии применимости этой стратегии к задаче включают: возможность разложения задачи, независимость подзадач и возможность объединения их решений.</li> <li>Сортировка слиянием является типичным применением divide and conquer: она рекурсивно делит массив на два равных по длине подмассива, пока не останется массив из одного элемента, после чего начинает поэтапное объединение.</li> <li>Введение стратегии divide and conquer часто позволяет повысить эффективность алгоритма. С одной стороны, стратегия уменьшает число операций; с другой - после разбиения она способствует параллельной оптимизации на уровне системы.</li> <li>Divide and conquer не только помогает решать многие алгоритмические задачи, но и широко используется при проектировании структур данных и алгоритмов, поэтому его можно встретить буквально повсюду.</li> <li>По сравнению с полным перебором адаптивный поиск работает эффективнее. Алгоритмы поиска со сложностью \\(O(\\log n)\\) обычно реализуются на основе стратегии divide and conquer.</li> <li>Двоичный поиск - еще одно типичное применение divide and conquer, в котором отсутствует шаг объединения решений подзадач. Мы можем реализовать двоичный поиск рекурсивно, через divide and conquer.</li> <li>В задаче построения двоичного дерева исходная задача построения дерева может быть разбита на две подзадачи: построение левого и правого поддеревьев, а реализуется это через разбиение индексных интервалов прямого и симметричного обходов.</li> <li>В задаче о Ханойской башне задача размера \\(n\\) разбивается на две подзадачи размера \\(n-1\\) и одну подзадачу размера \\(1\\) . После последовательного решения этих трех подзадач исходная задача также оказывается решенной.</li> </ul>","path":["Глава 12. Разделяй и властвуй","12.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_dynamic_programming/","level":1,"title":"Глава 14.   Динамическое программирование","text":"<p>Abstract</p> <p>Ручьи впадают в реки, а реки вливаются в море.</p> <p>Динамическое программирование собирает решения малых задач в ответ на большую задачу и шаг за шагом ведет нас к ее решению.</p>","path":["Глава 14. Динамическое программирование","Глава 14. &nbsp; Динамическое программирование"],"tags":[]},{"location":"chapter_dynamic_programming/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>14.1   Введение в динамическое программирование</li> <li>14.2   Свойства задач динамического программирования</li> <li>14.3   Подход к решению задач динамического программирования</li> <li>14.4   Задача о рюкзаке 0-1</li> <li>14.5   Задача о неограниченном рюкзаке</li> <li>14.6   Задача о расстоянии редактирования</li> <li>14.7   Резюме</li> </ul>","path":["Глава 14. Динамическое программирование","Глава 14. &nbsp; Динамическое программирование"],"tags":[]},{"location":"chapter_dynamic_programming/dp_problem_features/","level":1,"title":"14.2   Свойства задач динамического программирования","text":"<p>В предыдущем разделе мы увидели, как динамическое программирование решает исходную задачу через разложение на подзадачи. На самом деле разложение на подзадачи - это общий алгоритмический подход, но в divide and conquer, динамическом программировании и backtracking акценты расставлены по-разному.</p> <ul> <li>Алгоритмы divide and conquer рекурсивно раскладывают исходную задачу на несколько независимых подзадач, пока не будет достигнута наименьшая подзадача, а затем в процессе возврата объединяют решения подзадач в решение исходной задачи.</li> <li>Динамическое программирование тоже раскладывает задачу рекурсивно, но его главное отличие от divide and conquer в том, что подзадачи здесь зависят друг от друга и в процессе разложения возникает много перекрывающихся подзадач.</li> <li>Алгоритм backtracking перебирает все возможные решения через попытки и откат и с помощью обрезки избегает ненужных ветвей поиска. Решение исходной задачи состоит из последовательности решений, и подзадачей можно считать префикс этой последовательности решений.</li> </ul> <p>На практике динамическое программирование часто применяется для задач оптимизации. Такие задачи не только содержат перекрывающиеся подзадачи, но и обладают еще двумя важными свойствами: оптимальной подструктурой и отсутствием последствий.</p>","path":["Глава 14. Динамическое программирование","14.2 &nbsp; Свойства задач динамического программирования"],"tags":[]},{"location":"chapter_dynamic_programming/dp_problem_features/#1421","level":2,"title":"14.2.1   Оптимальная подструктура","text":"<p>Немного изменим задачу о подъеме по лестнице, чтобы нагляднее показать понятие оптимальной подструктуры.</p> <p>Минимальная стоимость подъема по лестнице</p> <p>Дана лестница, по которой можно подниматься на \\(1\\) или на \\(2\\) ступени за раз. На каждой ступени указано неотрицательное целое число, обозначающее цену попадания на эту ступень. Дан массив неотрицательных целых чисел \\(cost\\) , где \\(cost[i]\\) - это цена для ступени \\(i\\) , а \\(cost[0]\\) соответствует земле (начальной позиции). Найдите минимальную суммарную стоимость, необходимую для достижения вершины.</p> <p>Как показано на рисунке 14-6, если цены для ступеней \\(1\\) , \\(2\\) и \\(3\\) равны соответственно \\(1\\) , \\(10\\) и \\(1\\) , то минимальная стоимость подъема с земли на третью ступень равна \\(2\\) .</p> <p></p> <p> Рисунок 14-6   Минимальная стоимость подъема на 3-ю ступень </p> <p>Пусть \\(dp[i]\\) обозначает накопленную стоимость подъема на ступень \\(i\\) . Поскольку на ступень \\(i\\) можно прийти только со ступени \\(i - 1\\) или со ступени \\(i - 2\\) , значение \\(dp[i]\\) может быть либо \\(dp[i - 1] + cost[i]\\) , либо \\(dp[i - 2] + cost[i]\\) . Чтобы минимизировать стоимость, нужно выбрать меньший из этих двух вариантов:</p> \\[ dp[i] = \\min(dp[i-1], dp[i-2]) + cost[i] \\] <p>Отсюда и возникает смысл оптимальной подструктуры: оптимальное решение исходной задачи строится из оптимальных решений подзадач.</p> <p>Очевидно, что эта задача обладает оптимальной подструктурой: мы берем лучшее из двух оптимальных решений подзадач \\(dp[i-1]\\) и \\(dp[i-2]\\) и на его основе строим оптимальное решение исходной задачи \\(dp[i]\\) .</p> <p>А обладает ли оптимальной подструктурой исходная задача о числе способов подъема по лестнице из прошлого раздела? Формально она не про оптимум, а про подсчет количества. Но если переформулировать ее как \"найдите максимальное количество способов\", мы неожиданно увидим, что хотя исходная задача осталась по сути той же, оптимальная подструктура стала явной: максимальное число способов добраться до ступени \\(n\\) равно сумме максимальных чисел способов добраться до ступеней \\(n-1\\) и \\(n-2\\) . То есть объяснение оптимальной подструктуры в разных задачах может быть довольно гибким.</p> <p>Зная уравнение перехода состояния, а также начальные состояния \\(dp[1] = cost[1]\\) и \\(dp[2] = cost[2]\\) , мы можем сразу написать код динамического программирования:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby min_cost_climbing_stairs_dp.py<pre><code>def min_cost_climbing_stairs_dp(cost: list[int]) -&gt; int:\n    \"\"\"Минимальная стоимость подъема по лестнице: динамическое программирование\"\"\"\n    n = len(cost) - 1\n    if n == 1 or n == 2:\n        return cost[n]\n    # Инициализация таблицы dp для хранения решений подзадач\n    dp = [0] * (n + 1)\n    # Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1], dp[2] = cost[1], cost[2]\n    # Переход состояний: постепенное решение больших подзадач через меньшие\n    for i in range(3, n + 1):\n        dp[i] = min(dp[i - 1], dp[i - 2]) + cost[i]\n    return dp[n]\n</code></pre> min_cost_climbing_stairs_dp.cpp<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование */\nint minCostClimbingStairsDP(vector&lt;int&gt; &amp;cost) {\n    int n = cost.size() - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    // Инициализация таблицы dp для хранения решений подзадач\n    vector&lt;int&gt; dp(n + 1);\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = cost[1];\n    dp[2] = cost[2];\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = min(dp[i - 1], dp[i - 2]) + cost[i];\n    }\n    return dp[n];\n}\n</code></pre> min_cost_climbing_stairs_dp.java<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование */\nint minCostClimbingStairsDP(int[] cost) {\n    int n = cost.length - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    // Инициализация таблицы dp для хранения решений подзадач\n    int[] dp = new int[n + 1];\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = cost[1];\n    dp[2] = cost[2];\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = Math.min(dp[i - 1], dp[i - 2]) + cost[i];\n    }\n    return dp[n];\n}\n</code></pre> min_cost_climbing_stairs_dp.cs<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование */\nint MinCostClimbingStairsDP(int[] cost) {\n    int n = cost.Length - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    // Инициализация таблицы dp для хранения решений подзадач\n    int[] dp = new int[n + 1];\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = cost[1];\n    dp[2] = cost[2];\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = Math.Min(dp[i - 1], dp[i - 2]) + cost[i];\n    }\n    return dp[n];\n}\n</code></pre> min_cost_climbing_stairs_dp.go<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование */\nfunc minCostClimbingStairsDP(cost []int) int {\n    n := len(cost) - 1\n    if n == 1 || n == 2 {\n        return cost[n]\n    }\n    min := func(a, b int) int {\n        if a &lt; b {\n            return a\n        }\n        return b\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    dp := make([]int, n+1)\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = cost[1]\n    dp[2] = cost[2]\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for i := 3; i &lt;= n; i++ {\n        dp[i] = min(dp[i-1], dp[i-2]) + cost[i]\n    }\n    return dp[n]\n}\n</code></pre> min_cost_climbing_stairs_dp.swift<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование */\nfunc minCostClimbingStairsDP(cost: [Int]) -&gt; Int {\n    let n = cost.count - 1\n    if n == 1 || n == 2 {\n        return cost[n]\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    var dp = Array(repeating: 0, count: n + 1)\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = cost[1]\n    dp[2] = cost[2]\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for i in 3 ... n {\n        dp[i] = min(dp[i - 1], dp[i - 2]) + cost[i]\n    }\n    return dp[n]\n}\n</code></pre> min_cost_climbing_stairs_dp.js<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование */\nfunction minCostClimbingStairsDP(cost) {\n    const n = cost.length - 1;\n    if (n === 1 || n === 2) {\n        return cost[n];\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    const dp = new Array(n + 1);\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = cost[1];\n    dp[2] = cost[2];\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (let i = 3; i &lt;= n; i++) {\n        dp[i] = Math.min(dp[i - 1], dp[i - 2]) + cost[i];\n    }\n    return dp[n];\n}\n</code></pre> min_cost_climbing_stairs_dp.ts<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование */\nfunction minCostClimbingStairsDP(cost: Array&lt;number&gt;): number {\n    const n = cost.length - 1;\n    if (n === 1 || n === 2) {\n        return cost[n];\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    const dp = new Array(n + 1);\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = cost[1];\n    dp[2] = cost[2];\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (let i = 3; i &lt;= n; i++) {\n        dp[i] = Math.min(dp[i - 1], dp[i - 2]) + cost[i];\n    }\n    return dp[n];\n}\n</code></pre> min_cost_climbing_stairs_dp.dart<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование */\nint minCostClimbingStairsDP(List&lt;int&gt; cost) {\n  int n = cost.length - 1;\n  if (n == 1 || n == 2) return cost[n];\n  // Инициализация таблицы dp для хранения решений подзадач\n  List&lt;int&gt; dp = List.filled(n + 1, 0);\n  // Начальное состояние: заранее задать решения наименьших подзадач\n  dp[1] = cost[1];\n  dp[2] = cost[2];\n  // Переход состояний: постепенное решение больших подзадач через меньшие\n  for (int i = 3; i &lt;= n; i++) {\n    dp[i] = min(dp[i - 1], dp[i - 2]) + cost[i];\n  }\n  return dp[n];\n}\n</code></pre> min_cost_climbing_stairs_dp.rs<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование */\nfn min_cost_climbing_stairs_dp(cost: &amp;[i32]) -&gt; i32 {\n    let n = cost.len() - 1;\n    if n == 1 || n == 2 {\n        return cost[n];\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    let mut dp = vec![-1; n + 1];\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = cost[1];\n    dp[2] = cost[2];\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for i in 3..=n {\n        dp[i] = cmp::min(dp[i - 1], dp[i - 2]) + cost[i];\n    }\n    dp[n]\n}\n</code></pre> min_cost_climbing_stairs_dp.c<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование */\nint minCostClimbingStairsDP(int cost[], int costSize) {\n    int n = costSize - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    // Инициализация таблицы dp для хранения решений подзадач\n    int *dp = calloc(n + 1, sizeof(int));\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = cost[1];\n    dp[2] = cost[2];\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = myMin(dp[i - 1], dp[i - 2]) + cost[i];\n    }\n    int res = dp[n];\n    // Освободить память\n    free(dp);\n    return res;\n}\n</code></pre> min_cost_climbing_stairs_dp.kt<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование */\nfun minCostClimbingStairsDP(cost: IntArray): Int {\n    val n = cost.size - 1\n    if (n == 1 || n == 2) return cost[n]\n    // Инициализация таблицы dp для хранения решений подзадач\n    val dp = IntArray(n + 1)\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = cost[1]\n    dp[2] = cost[2]\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (i in 3..n) {\n        dp[i] = min(dp[i - 1], dp[i - 2]) + cost[i]\n    }\n    return dp[n]\n}\n</code></pre> min_cost_climbing_stairs_dp.rb<pre><code>### Минимальная стоимость подъема по лестнице: динамическое программирование ###\ndef min_cost_climbing_stairs_dp(cost)\n  n = cost.length - 1\n  return cost[n] if n == 1 || n == 2\n  # Инициализация таблицы dp для хранения решений подзадач\n  dp = Array.new(n + 1, 0)\n  # Начальное состояние: заранее задать решения наименьших подзадач\n  dp[1], dp[2] = cost[1], cost[2]\n  # Переход состояний: постепенное решение больших подзадач через меньшие\n  (3...(n + 1)).each { |i| dp[i] = [dp[i - 1], dp[i - 2]].min + cost[i] }\n  dp[n]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>На рисунке 14-7 показан процесс динамического программирования для этой задачи.</p> <p></p> <p> Рисунок 14-7   Процесс динамического программирования для минимальной стоимости подъема </p> <p>В этой задаче тоже можно оптимизировать пространство, сжав одномерное состояние в нулевое измерение и тем самым уменьшив пространственную сложность с \\(O(n)\\) до \\(O(1)\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby min_cost_climbing_stairs_dp.py<pre><code>def min_cost_climbing_stairs_dp_comp(cost: list[int]) -&gt; int:\n    \"\"\"Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти\"\"\"\n    n = len(cost) - 1\n    if n == 1 or n == 2:\n        return cost[n]\n    a, b = cost[1], cost[2]\n    for i in range(3, n + 1):\n        a, b = b, min(a, b) + cost[i]\n    return b\n</code></pre> min_cost_climbing_stairs_dp.cpp<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти */\nint minCostClimbingStairsDPComp(vector&lt;int&gt; &amp;cost) {\n    int n = cost.size() - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    int a = cost[1], b = cost[2];\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = min(a, tmp) + cost[i];\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> min_cost_climbing_stairs_dp.java<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти */\nint minCostClimbingStairsDPComp(int[] cost) {\n    int n = cost.length - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    int a = cost[1], b = cost[2];\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = Math.min(a, tmp) + cost[i];\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> min_cost_climbing_stairs_dp.cs<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти */\nint MinCostClimbingStairsDPComp(int[] cost) {\n    int n = cost.Length - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    int a = cost[1], b = cost[2];\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = Math.Min(a, tmp) + cost[i];\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> min_cost_climbing_stairs_dp.go<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти */\nfunc minCostClimbingStairsDPComp(cost []int) int {\n    n := len(cost) - 1\n    if n == 1 || n == 2 {\n        return cost[n]\n    }\n    min := func(a, b int) int {\n        if a &lt; b {\n            return a\n        }\n        return b\n    }\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    a, b := cost[1], cost[2]\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for i := 3; i &lt;= n; i++ {\n        tmp := b\n        b = min(a, tmp) + cost[i]\n        a = tmp\n    }\n    return b\n}\n</code></pre> min_cost_climbing_stairs_dp.swift<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти */\nfunc minCostClimbingStairsDPComp(cost: [Int]) -&gt; Int {\n    let n = cost.count - 1\n    if n == 1 || n == 2 {\n        return cost[n]\n    }\n    var (a, b) = (cost[1], cost[2])\n    for i in 3 ... n {\n        (a, b) = (b, min(a, b) + cost[i])\n    }\n    return b\n}\n</code></pre> min_cost_climbing_stairs_dp.js<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти */\nfunction minCostClimbingStairsDPComp(cost) {\n    const n = cost.length - 1;\n    if (n === 1 || n === 2) {\n        return cost[n];\n    }\n    let a = cost[1],\n        b = cost[2];\n    for (let i = 3; i &lt;= n; i++) {\n        const tmp = b;\n        b = Math.min(a, tmp) + cost[i];\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> min_cost_climbing_stairs_dp.ts<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти */\nfunction minCostClimbingStairsDPComp(cost: Array&lt;number&gt;): number {\n    const n = cost.length - 1;\n    if (n === 1 || n === 2) {\n        return cost[n];\n    }\n    let a = cost[1],\n        b = cost[2];\n    for (let i = 3; i &lt;= n; i++) {\n        const tmp = b;\n        b = Math.min(a, tmp) + cost[i];\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> min_cost_climbing_stairs_dp.dart<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти */\nint minCostClimbingStairsDPComp(List&lt;int&gt; cost) {\n  int n = cost.length - 1;\n  if (n == 1 || n == 2) return cost[n];\n  int a = cost[1], b = cost[2];\n  for (int i = 3; i &lt;= n; i++) {\n    int tmp = b;\n    b = min(a, tmp) + cost[i];\n    a = tmp;\n  }\n  return b;\n}\n</code></pre> min_cost_climbing_stairs_dp.rs<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти */\nfn min_cost_climbing_stairs_dp_comp(cost: &amp;[i32]) -&gt; i32 {\n    let n = cost.len() - 1;\n    if n == 1 || n == 2 {\n        return cost[n];\n    };\n    let (mut a, mut b) = (cost[1], cost[2]);\n    for i in 3..=n {\n        let tmp = b;\n        b = cmp::min(a, tmp) + cost[i];\n        a = tmp;\n    }\n    b\n}\n</code></pre> min_cost_climbing_stairs_dp.c<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти */\nint minCostClimbingStairsDPComp(int cost[], int costSize) {\n    int n = costSize - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    int a = cost[1], b = cost[2];\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = myMin(a, tmp) + cost[i];\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> min_cost_climbing_stairs_dp.kt<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти */\nfun minCostClimbingStairsDPComp(cost: IntArray): Int {\n    val n = cost.size - 1\n    if (n == 1 || n == 2) return cost[n]\n    var a = cost[1]\n    var b = cost[2]\n    for (i in 3..n) {\n        val tmp = b\n        b = min(a, tmp) + cost[i]\n        a = tmp\n    }\n    return b\n}\n</code></pre> min_cost_climbing_stairs_dp.rb<pre><code>### Минимальная стоимость подъема по лестнице: динамическое программирование ###\ndef min_cost_climbing_stairs_dp(cost)\n  n = cost.length - 1\n  return cost[n] if n == 1 || n == 2\n  # Инициализация таблицы dp для хранения решений подзадач\n  dp = Array.new(n + 1, 0)\n  # Начальное состояние: заранее задать решения наименьших подзадач\n  dp[1], dp[2] = cost[1], cost[2]\n  # Переход состояний: постепенное решение больших подзадач через меньшие\n  (3...(n + 1)).each { |i| dp[i] = [dp[i - 1], dp[i - 2]].min + cost[i] }\n  dp[n]\nend\n\n# Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти\ndef min_cost_climbing_stairs_dp_comp(cost)\n  n = cost.length - 1\n  return cost[n] if n == 1 || n == 2\n  a, b = cost[1], cost[2]\n  (3...(n + 1)).each { |i| a, b = b, [a, b].min + cost[i] }\n  b\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 14. Динамическое программирование","14.2 &nbsp; Свойства задач динамического программирования"],"tags":[]},{"location":"chapter_dynamic_programming/dp_problem_features/#1422","level":2,"title":"14.2.2   Отсутствие последствий","text":"<p>Отсутствие последствий - одно из ключевых свойств, благодаря которому динамическое программирование вообще может эффективно работать. Его определение таково: если текущее состояние задано однозначно, то его дальнейшее развитие зависит только от него самого и не зависит от всей истории предыдущих состояний.</p> <p>Для примера снова рассмотрим задачу о лестнице. Если дано состояние \\(i\\) , то из него можно перейти в состояния \\(i+1\\) и \\(i+2\\) , соответствующие прыжкам на \\(1\\) и на \\(2\\) ступени. Чтобы сделать один из этих выборов, не нужно знать, какими были состояния до \\(i\\) ; на будущее влияет только текущее состояние \\(i\\) .</p> <p>Однако если добавить в задачу дополнительное ограничение, ситуация изменится.</p> <p>Подъем по лестнице с ограничением</p> <p>Дана лестница из \\(n\\) ступеней. За один шаг можно подняться на \\(1\\) или на \\(2\\) ступени, но нельзя два раунда подряд прыгать на \\(1\\) ступень. Сколькими способами можно добраться до вершины?</p> <p>Как показано на рисунке 14-8, на третью ступень теперь существует только \\(2\\) допустимых способа добраться: вариант с тремя последовательными прыжками на \\(1\\) не удовлетворяет ограничению и потому отбрасывается.</p> <p></p> <p> Рисунок 14-8   Число способов подняться на 3-ю ступень при наличии ограничения </p> <p>В этой задаче, если в предыдущем раунде был сделан прыжок на \\(1\\) ступень, то в следующем раунде уже обязательно нужно прыгнуть на \\(2\\) ступени. Иными словами, следующий выбор уже нельзя определить только по текущему состоянию (текущему номеру ступени) - он зависит еще и от предыдущего состояния (с какой ступени мы пришли в прошлый раз).</p> <p>Нетрудно заметить, что в таком виде задача больше не удовлетворяет свойству отсутствия последствий, а уравнение перехода состояния \\(dp[i] = dp[i-1] + dp[i-2]\\) перестает работать, потому что \\(dp[i-1]\\) соответствует прыжку на \\(1\\) ступень, но при этом включает множество вариантов, где предыдущий раунд тоже был прыжком на \\(1\\) ступень. Такие варианты уже нельзя напрямую учитывать в \\(dp[i]\\) , если мы хотим соблюдать ограничение.</p> <p>Поэтому нам нужно расширить определение состояния: состояние \\([i, j]\\) означает, что мы находимся на ступени \\(i\\) и в предыдущем раунде прыгнули на \\(j\\) ступеней, где \\(j \\in \\{1, 2\\}\\) . Такое определение состояния эффективно различает, был ли в прошлом раунде прыжок на \\(1\\) или на \\(2\\) ступени, и позволяет корректно определить, откуда произошло текущее состояние.</p> <ul> <li>Если в предыдущем раунде был прыжок на \\(1\\) ступень, то в раунде перед ним мог быть только прыжок на \\(2\\) ступени, то есть \\(dp[i, 1]\\) может перейти только из \\(dp[i-1, 2]\\) .</li> <li>Если в предыдущем раунде был прыжок на \\(2\\) ступени, то еще шагом раньше можно было прыгнуть либо на \\(1\\) , либо на \\(2\\) ступени, то есть \\(dp[i, 2]\\) может переходить из \\(dp[i-2, 1]\\) или из \\(dp[i-2, 2]\\) .</li> </ul> <p>Как показано на рисунке 14-9, при таком определении \\(dp[i, j]\\) обозначает число способов для состояния \\([i, j]\\) . Тогда уравнение перехода состояния имеет вид:</p> \\[ \\begin{cases} dp[i, 1] = dp[i-1, 2] \\\\ dp[i, 2] = dp[i-2, 1] + dp[i-2, 2] \\end{cases} \\] <p></p> <p> Рисунок 14-9   Рекуррентная связь с учетом ограничения </p> <p>В конце достаточно вернуть \\(dp[n, 1] + dp[n, 2]\\) ; эта сумма и представляет общее число способов добраться до ступени \\(n\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby climbing_stairs_constraint_dp.py<pre><code>def climbing_stairs_constraint_dp(n: int) -&gt; int:\n    \"\"\"Подъем по лестнице с ограничениями: динамическое программирование\"\"\"\n    if n == 1 or n == 2:\n        return 1\n    # Инициализация таблицы dp для хранения решений подзадач\n    dp = [[0] * 3 for _ in range(n + 1)]\n    # Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1][1], dp[1][2] = 1, 0\n    dp[2][1], dp[2][2] = 0, 1\n    # Переход состояний: постепенное решение больших подзадач через меньшие\n    for i in range(3, n + 1):\n        dp[i][1] = dp[i - 1][2]\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2]\n    return dp[n][1] + dp[n][2]\n</code></pre> climbing_stairs_constraint_dp.cpp<pre><code>/* Подъем по лестнице с ограничениями: динамическое программирование */\nint climbingStairsConstraintDP(int n) {\n    if (n == 1 || n == 2) {\n        return 1;\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(3, 0));\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1][1] = 1;\n    dp[1][2] = 0;\n    dp[2][1] = 0;\n    dp[2][2] = 1;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i][1] = dp[i - 1][2];\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2];\n    }\n    return dp[n][1] + dp[n][2];\n}\n</code></pre> climbing_stairs_constraint_dp.java<pre><code>/* Подъем по лестнице с ограничениями: динамическое программирование */\nint climbingStairsConstraintDP(int n) {\n    if (n == 1 || n == 2) {\n        return 1;\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    int[][] dp = new int[n + 1][3];\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1][1] = 1;\n    dp[1][2] = 0;\n    dp[2][1] = 0;\n    dp[2][2] = 1;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i][1] = dp[i - 1][2];\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2];\n    }\n    return dp[n][1] + dp[n][2];\n}\n</code></pre> climbing_stairs_constraint_dp.cs<pre><code>/* Подъем по лестнице с ограничениями: динамическое программирование */\nint ClimbingStairsConstraintDP(int n) {\n    if (n == 1 || n == 2) {\n        return 1;\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    int[,] dp = new int[n + 1, 3];\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1, 1] = 1;\n    dp[1, 2] = 0;\n    dp[2, 1] = 0;\n    dp[2, 2] = 1;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i, 1] = dp[i - 1, 2];\n        dp[i, 2] = dp[i - 2, 1] + dp[i - 2, 2];\n    }\n    return dp[n, 1] + dp[n, 2];\n}\n</code></pre> climbing_stairs_constraint_dp.go<pre><code>/* Подъем по лестнице с ограничениями: динамическое программирование */\nfunc climbingStairsConstraintDP(n int) int {\n    if n == 1 || n == 2 {\n        return 1\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    dp := make([][3]int, n+1)\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1][1] = 1\n    dp[1][2] = 0\n    dp[2][1] = 0\n    dp[2][2] = 1\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for i := 3; i &lt;= n; i++ {\n        dp[i][1] = dp[i-1][2]\n        dp[i][2] = dp[i-2][1] + dp[i-2][2]\n    }\n    return dp[n][1] + dp[n][2]\n}\n</code></pre> climbing_stairs_constraint_dp.swift<pre><code>/* Подъем по лестнице с ограничениями: динамическое программирование */\nfunc climbingStairsConstraintDP(n: Int) -&gt; Int {\n    if n == 1 || n == 2 {\n        return 1\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    var dp = Array(repeating: Array(repeating: 0, count: 3), count: n + 1)\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1][1] = 1\n    dp[1][2] = 0\n    dp[2][1] = 0\n    dp[2][2] = 1\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for i in 3 ... n {\n        dp[i][1] = dp[i - 1][2]\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2]\n    }\n    return dp[n][1] + dp[n][2]\n}\n</code></pre> climbing_stairs_constraint_dp.js<pre><code>/* Подъем по лестнице с ограничениями: динамическое программирование */\nfunction climbingStairsConstraintDP(n) {\n    if (n === 1 || n === 2) {\n        return 1;\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    const dp = Array.from(new Array(n + 1), () =&gt; new Array(3));\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1][1] = 1;\n    dp[1][2] = 0;\n    dp[2][1] = 0;\n    dp[2][2] = 1;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (let i = 3; i &lt;= n; i++) {\n        dp[i][1] = dp[i - 1][2];\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2];\n    }\n    return dp[n][1] + dp[n][2];\n}\n</code></pre> climbing_stairs_constraint_dp.ts<pre><code>/* Подъем по лестнице с ограничениями: динамическое программирование */\nfunction climbingStairsConstraintDP(n: number): number {\n    if (n === 1 || n === 2) {\n        return 1;\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    const dp = Array.from({ length: n + 1 }, () =&gt; new Array(3));\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1][1] = 1;\n    dp[1][2] = 0;\n    dp[2][1] = 0;\n    dp[2][2] = 1;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (let i = 3; i &lt;= n; i++) {\n        dp[i][1] = dp[i - 1][2];\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2];\n    }\n    return dp[n][1] + dp[n][2];\n}\n</code></pre> climbing_stairs_constraint_dp.dart<pre><code>/* Подъем по лестнице с ограничениями: динамическое программирование */\nint climbingStairsConstraintDP(int n) {\n  if (n == 1 || n == 2) {\n    return 1;\n  }\n  // Инициализация таблицы dp для хранения решений подзадач\n  List&lt;List&lt;int&gt;&gt; dp = List.generate(n + 1, (index) =&gt; List.filled(3, 0));\n  // Начальное состояние: заранее задать решения наименьших подзадач\n  dp[1][1] = 1;\n  dp[1][2] = 0;\n  dp[2][1] = 0;\n  dp[2][2] = 1;\n  // Переход состояний: постепенное решение больших подзадач через меньшие\n  for (int i = 3; i &lt;= n; i++) {\n    dp[i][1] = dp[i - 1][2];\n    dp[i][2] = dp[i - 2][1] + dp[i - 2][2];\n  }\n  return dp[n][1] + dp[n][2];\n}\n</code></pre> climbing_stairs_constraint_dp.rs<pre><code>/* Подъем по лестнице с ограничениями: динамическое программирование */\nfn climbing_stairs_constraint_dp(n: usize) -&gt; i32 {\n    if n == 1 || n == 2 {\n        return 1;\n    };\n    // Инициализация таблицы dp для хранения решений подзадач\n    let mut dp = vec![vec![-1; 3]; n + 1];\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1][1] = 1;\n    dp[1][2] = 0;\n    dp[2][1] = 0;\n    dp[2][2] = 1;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for i in 3..=n {\n        dp[i][1] = dp[i - 1][2];\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2];\n    }\n    dp[n][1] + dp[n][2]\n}\n</code></pre> climbing_stairs_constraint_dp.c<pre><code>/* Подъем по лестнице с ограничениями: динамическое программирование */\nint climbingStairsConstraintDP(int n) {\n    if (n == 1 || n == 2) {\n        return 1;\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    int **dp = malloc((n + 1) * sizeof(int *));\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i] = calloc(3, sizeof(int));\n    }\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1][1] = 1;\n    dp[1][2] = 0;\n    dp[2][1] = 0;\n    dp[2][2] = 1;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i][1] = dp[i - 1][2];\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2];\n    }\n    int res = dp[n][1] + dp[n][2];\n    // Освободить память\n    for (int i = 0; i &lt;= n; i++) {\n        free(dp[i]);\n    }\n    free(dp);\n    return res;\n}\n</code></pre> climbing_stairs_constraint_dp.kt<pre><code>/* Подъем по лестнице с ограничениями: динамическое программирование */\nfun climbingStairsConstraintDP(n: Int): Int {\n    if (n == 1 || n == 2) {\n        return 1\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    val dp = Array(n + 1) { IntArray(3) }\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1][1] = 1\n    dp[1][2] = 0\n    dp[2][1] = 0\n    dp[2][2] = 1\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (i in 3..n) {\n        dp[i][1] = dp[i - 1][2]\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2]\n    }\n    return dp[n][1] + dp[n][2]\n}\n</code></pre> climbing_stairs_constraint_dp.rb<pre><code>### Подъем по лестнице с ограничениями: динамическое программирование ###\ndef climbing_stairs_constraint_dp(n)\n  return 1 if n == 1 || n == 2\n\n  # Инициализация таблицы dp для хранения решений подзадач\n  dp = Array.new(n + 1) { Array.new(3, 0) }\n  # Начальное состояние: заранее задать решения наименьших подзадач\n  dp[1][1], dp[1][2] = 1, 0\n  dp[2][1], dp[2][2] = 0, 1\n  # Переход состояний: постепенное решение больших подзадач через меньшие\n  for i in 3...(n + 1)\n    dp[i][1] = dp[i - 1][2]\n    dp[i][2] = dp[i - 2][1] + dp[i - 2][2]\n  end\n\n  dp[n][1] + dp[n][2]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>В этом примере достаточно дополнительно учитывать только одно предыдущее состояние, поэтому после расширения определения состояния задача снова начинает удовлетворять свойству отсутствия последствий. Однако в некоторых задачах \"зависимость от прошлого\" бывает гораздо серьезнее.</p> <p>Подъем по лестнице с порождением препятствий</p> <p>Дана лестница из \\(n\\) ступеней. За один шаг можно подняться на \\(1\\) или на \\(2\\) ступени. При этом, если вы попали на ступень \\(i\\) , система автоматически создает препятствие на ступени \\(2i\\) , и на всех последующих шагах становиться на ступень \\(2i\\) уже нельзя. Например, если в первых двух раундах вы попали на ступени \\(2\\) и \\(3\\) , то после этого нельзя будет попадать на ступени \\(4\\) и \\(6\\) . Сколько существует способов добраться до вершины?</p> <p>В этой задаче следующий прыжок зависит от всех предыдущих состояний, потому что каждый прыжок порождает новое препятствие на более высокой ступени и тем самым влияет на все будущие прыжки. Для задач такого типа динамическое программирование обычно оказывается непригодным.</p> <p>Вообще, многие сложные задачи комбинаторной оптимизации (например, задача коммивояжера) не обладают свойством отсутствия последствий. Для таких задач обычно выбирают другие методы - например, эвристический поиск, генетические алгоритмы, обучение с подкреплением и т.д., - чтобы за ограниченное время получить пригодное локально оптимальное решение.</p>","path":["Глава 14. Динамическое программирование","14.2 &nbsp; Свойства задач динамического программирования"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/","level":1,"title":"14.3   Подход к решению задач динамического программирования","text":"<p>В двух предыдущих разделах были рассмотрены основные свойства задач динамического программирования. Теперь исследуем два более практических вопроса.</p> <ol> <li>Как определить, является ли некоторая задача задачей динамического программирования?</li> <li>С чего начинать решение такой задачи и как выглядит полный процесс решения?</li> </ol>","path":["Глава 14. Динамическое программирование","14.3 &nbsp; Подход к решению задач динамического программирования"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#1431","level":2,"title":"14.3.1   Определение задачи","text":"<p>В целом, если задача содержит перекрывающиеся подзадачи, оптимальную подструктуру и удовлетворяет свойству отсутствия последствий, то она обычно подходит для решения с помощью динамического программирования. Однако извлечь все эти свойства напрямую из формулировки задачи бывает трудно. Поэтому на практике мы обычно ослабляем требования и сначала смотрим, подходит ли задача для решения методом backtracking (полного перебора).</p> <p>Задачи, подходящие для backtracking, обычно удовлетворяют \"модели дерева решений\". Такие задачи можно описать деревом, где каждый узел представляет одно решение, а каждый путь представляет последовательность решений.</p> <p>Иначе говоря, если в задаче есть четко выраженные решения и ответ порождается последовательностью таких решений, то она удовлетворяет модели дерева решений и обычно допускает решение через backtracking.</p> <p>Поверх этого у задач динамического программирования есть и некоторые дополнительные \"плюсы\".</p> <ul> <li>В условии задачи фигурируют слова \"максимальный\", \"минимальный\", \"наибольший\", \"наименьший\" и другие формулировки оптимизации.</li> <li>Состояния задачи можно описать списком, многомерной матрицей или деревом, и между состоянием и соседними состояниями существует рекуррентная зависимость.</li> </ul> <p>Соответственно, существуют и некоторые \"минусы\".</p> <ul> <li>Цель задачи состоит в поиске всех возможных решений, а не одного оптимального решения.</li> <li>В формулировке явно присутствуют признаки комбинаторного перечисления, и требуется вернуть сразу много конкретных вариантов.</li> </ul> <p>Если задача удовлетворяет модели дерева решений и имеет достаточно явные \"плюсы\", мы можем предположить, что это задача динамического программирования, а затем проверить это предположение уже в процессе решения.</p>","path":["Глава 14. Динамическое программирование","14.3 &nbsp; Подход к решению задач динамического программирования"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#1432","level":2,"title":"14.3.2   Этапы решения задачи","text":"<p>Конкретный процесс решения задач динамического программирования зависит от природы и сложности задачи, но обычно включает следующие шаги: описание решений, определение состояний, построение таблицы \\(dp\\) , вывод уравнения перехода состояния, определение граничных условий и порядка переходов.</p> <p>Чтобы нагляднее показать этот процесс, рассмотрим классическую задачу \"минимальная сумма пути\".</p> <p>Question</p> <p>Дана двумерная сетка <code>grid</code> размера \\(n \\times m\\) , в каждой клетке которой записано неотрицательное целое число, означающее стоимость прохождения через эту клетку. Робот стартует из левой верхней клетки и за один шаг может двигаться только вправо или вниз, пока не достигнет правой нижней клетки. Верните минимальную сумму пути от левой верхней клетки до правой нижней.</p> <p>На рисунке 14-10 показан пример, в котором минимальная сумма пути равна \\(13\\) .</p> <p></p> <p> Рисунок 14-10   Пример данных для задачи о минимальной сумме пути </p> <p>Шаг 1: понять решения на каждом раунде, определить состояние и тем самым получить таблицу \\(dp\\)</p> <p>В этой задаче на каждом раунде решение состоит в том, чтобы из текущей клетки сделать один шаг вниз или вправо. Пусть индексы строки и столбца текущей клетки равны \\([i, j]\\) ; тогда после шага вниз или вправо индексы становятся равными \\([i+1, j]\\) или \\([i, j+1]\\) . Значит, состояние должно включать два переменных индекса: строки и столбца, то есть состояние обозначается как \\([i, j]\\) .</p> <p>Подзадача, соответствующая состоянию \\([i, j]\\) , такова: минимальная сумма пути от стартовой клетки \\([0, 0]\\) до клетки \\([i, j]\\) . Ее решение обозначается через \\(dp[i, j]\\) .</p> <p>На этом этапе мы получаем двумерную матрицу \\(dp\\) , показанную на рисунке 14-11, размер которой совпадает с размером входной сетки <code>grid</code> .</p> <p></p> <p> Рисунок 14-11   Определение состояния и таблицы dp </p> <p>Note</p> <p>Как в динамическом программировании, так и в backtracking, решение задачи можно описать как последовательность решений, а состояние образуется всеми переменными решений. Оно должно содержать всю информацию, достаточную для вывода следующего состояния.</p> <p>Каждому состоянию соответствует некоторая подзадача, и для хранения решений всех подзадач мы определяем таблицу \\(dp\\) ; каждая независимая переменная состояния становится одним измерением таблицы \\(dp\\) . По сути таблица \\(dp\\) - это отображение от состояния к решению соответствующей подзадачи.</p> <p>Шаг 2: найти оптимальную подструктуру и на ее основе вывести уравнение перехода состояния</p> <p>Для состояния \\([i, j]\\) возможны только два источника: клетка сверху \\([i-1, j]\\) и клетка слева \\([i, j-1]\\) . Следовательно, оптимальная подструктура выглядит так: минимальная сумма пути до \\([i, j]\\) определяется меньшим из двух значений - минимальной суммы пути до \\([i-1, j]\\) и минимальной суммы пути до \\([i, j-1]\\) .</p> <p>По этому рассуждению получается уравнение перехода состояния, показанное на рисунке 14-12:</p> \\[ dp[i, j] = \\min(dp[i-1, j], dp[i, j-1]) + grid[i, j] \\] <p></p> <p> Рисунок 14-12   Оптимальная подструктура и уравнение перехода состояния </p> <p>Note</p> <p>Опираясь на уже определенную таблицу \\(dp\\) , нужно продумать отношение между исходной задачей и подзадачами и найти способ построить оптимальное решение исходной задачи из оптимальных решений подзадач, то есть найти оптимальную подструктуру.</p> <p>Как только оптимальная подструктура найдена, на ее основе можно построить уравнение перехода состояния.</p> <p>Шаг 3: определить граничные условия и порядок переходов</p> <p>В этой задаче состояния в первой строке могут переходить только из клетки слева, а состояния в первом столбце - только из клетки сверху, поэтому первая строка \\(i = 0\\) и первый столбец \\(j = 0\\) образуют граничные условия.</p> <p>Как показано на рисунке 14-13, поскольку каждая клетка получается из клетки слева и клетки сверху, мы можем проходить матрицу циклами: внешний цикл по строкам, внутренний - по столбцам.</p> <p></p> <p> Рисунок 14-13   Граничные условия и порядок перехода состояний </p> <p>Note</p> <p>В динамическом программировании граничные условия используются для инициализации таблицы \\(dp\\) , а в поиске - для обрезки.</p> <p>Смысл порядка перехода состояния в том, чтобы к моменту вычисления текущей подзадачи все более мелкие подзадачи, от которых она зависит, уже были вычислены корректно.</p> <p>После этого анализа мы уже можем напрямую написать код динамического программирования. Однако разложение на подзадачи - это мышление \"сверху вниз\", поэтому с точки зрения мышления более естественно реализовывать задачу в порядке \"полный перебор \\(\\rightarrow\\) поиск с мемоизацией \\(\\rightarrow\\) динамическое программирование\".</p>","path":["Глава 14. Динамическое программирование","14.3 &nbsp; Подход к решению задач динамического программирования"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#1-1","level":3,"title":"1.   Метод 1: полный перебор","text":"<p>Начав со состояния \\([i, j]\\) , мы непрерывно раскладываем его на меньшие состояния \\([i-1, j]\\) и \\([i, j-1]\\) . Рекурсивная функция при этом имеет следующие элементы.</p> <ul> <li>Параметры рекурсии: состояние \\([i, j]\\) .</li> <li>Возвращаемое значение: минимальная сумма пути до \\([i, j]\\) , то есть \\(dp[i, j]\\) .</li> <li>Условие завершения: когда \\(i = 0\\) и \\(j = 0\\) , возвращается стоимость \\(grid[0, 0]\\) .</li> <li>Обрезка: если \\(i &lt; 0\\) или \\(j &lt; 0\\) , индекс выходит за границы, и в этом случае возвращается стоимость \\(+\\infty\\) , обозначающая невозможность.</li> </ul> <p>Код реализации:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby min_path_sum.py<pre><code>def min_path_sum_dfs(grid: list[list[int]], i: int, j: int) -&gt; int:\n    \"\"\"Минимальная сумма пути: полный перебор\"\"\"\n    # Если это верхняя левая ячейка, завершить поиск\n    if i == 0 and j == 0:\n        return grid[0][0]\n    # Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if i &lt; 0 or j &lt; 0:\n        return inf\n    # Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n    up = min_path_sum_dfs(grid, i - 1, j)\n    left = min_path_sum_dfs(grid, i, j - 1)\n    # Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    return min(left, up) + grid[i][j]\n</code></pre> min_path_sum.cpp<pre><code>/* Минимальная сумма пути: полный перебор */\nint minPathSumDFS(vector&lt;vector&lt;int&gt;&gt; &amp;grid, int i, int j) {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return INT_MAX;\n    }\n    // Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n    int up = minPathSumDFS(grid, i - 1, j);\n    int left = minPathSumDFS(grid, i, j - 1);\n    // Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    return min(left, up) != INT_MAX ? min(left, up) + grid[i][j] : INT_MAX;\n}\n</code></pre> min_path_sum.java<pre><code>/* Минимальная сумма пути: полный перебор */\nint minPathSumDFS(int[][] grid, int i, int j) {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return Integer.MAX_VALUE;\n    }\n    // Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n    int up = minPathSumDFS(grid, i - 1, j);\n    int left = minPathSumDFS(grid, i, j - 1);\n    // Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    return Math.min(left, up) + grid[i][j];\n}\n</code></pre> min_path_sum.cs<pre><code>/* Минимальная сумма пути: полный перебор */\nint MinPathSumDFS(int[][] grid, int i, int j) {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return int.MaxValue;\n    }\n    // Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n    int up = MinPathSumDFS(grid, i - 1, j);\n    int left = MinPathSumDFS(grid, i, j - 1);\n    // Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    return Math.Min(left, up) + grid[i][j];\n}\n</code></pre> min_path_sum.go<pre><code>/* Минимальная сумма пути: полный перебор */\nfunc minPathSumDFS(grid [][]int, i, j int) int {\n    // Если это верхняя левая ячейка, завершить поиск\n    if i == 0 &amp;&amp; j == 0 {\n        return grid[0][0]\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if i &lt; 0 || j &lt; 0 {\n        return math.MaxInt\n    }\n    // Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n    up := minPathSumDFS(grid, i-1, j)\n    left := minPathSumDFS(grid, i, j-1)\n    // Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    return int(math.Min(float64(left), float64(up))) + grid[i][j]\n}\n</code></pre> min_path_sum.swift<pre><code>/* Минимальная сумма пути: полный перебор */\nfunc minPathSumDFS(grid: [[Int]], i: Int, j: Int) -&gt; Int {\n    // Если это верхняя левая ячейка, завершить поиск\n    if i == 0, j == 0 {\n        return grid[0][0]\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if i &lt; 0 || j &lt; 0 {\n        return .max\n    }\n    // Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n    let up = minPathSumDFS(grid: grid, i: i - 1, j: j)\n    let left = minPathSumDFS(grid: grid, i: i, j: j - 1)\n    // Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    return min(left, up) + grid[i][j]\n}\n</code></pre> min_path_sum.js<pre><code>/* Минимальная сумма пути: полный перебор */\nfunction minPathSumDFS(grid, i, j) {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i === 0 &amp;&amp; j === 0) {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return Infinity;\n    }\n    // Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n    const up = minPathSumDFS(grid, i - 1, j);\n    const left = minPathSumDFS(grid, i, j - 1);\n    // Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    return Math.min(left, up) + grid[i][j];\n}\n</code></pre> min_path_sum.ts<pre><code>/* Минимальная сумма пути: полный перебор */\nfunction minPathSumDFS(\n    grid: Array&lt;Array&lt;number&gt;&gt;,\n    i: number,\n    j: number\n): number {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i === 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return Infinity;\n    }\n    // Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n    const up = minPathSumDFS(grid, i - 1, j);\n    const left = minPathSumDFS(grid, i, j - 1);\n    // Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    return Math.min(left, up) + grid[i][j];\n}\n</code></pre> min_path_sum.dart<pre><code>/* Минимальная сумма пути: полный перебор */\nint minPathSumDFS(List&lt;List&lt;int&gt;&gt; grid, int i, int j) {\n  // Если это верхняя левая ячейка, завершить поиск\n  if (i == 0 &amp;&amp; j == 0) {\n    return grid[0][0];\n  }\n  // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n  if (i &lt; 0 || j &lt; 0) {\n    // В Dart тип int — целое число фиксированного диапазона; значения, представляющего «бесконечность», не существует\n    return BigInt.from(2).pow(31).toInt();\n  }\n  // Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n  int up = minPathSumDFS(grid, i - 1, j);\n  int left = minPathSumDFS(grid, i, j - 1);\n  // Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n  return min(left, up) + grid[i][j];\n}\n</code></pre> min_path_sum.rs<pre><code>/* Минимальная сумма пути: полный перебор */\nfn min_path_sum_dfs(grid: &amp;Vec&lt;Vec&lt;i32&gt;&gt;, i: i32, j: i32) -&gt; i32 {\n    // Если это верхняя левая ячейка, завершить поиск\n    if i == 0 &amp;&amp; j == 0 {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if i &lt; 0 || j &lt; 0 {\n        return i32::MAX;\n    }\n    // Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n    let up = min_path_sum_dfs(grid, i - 1, j);\n    let left = min_path_sum_dfs(grid, i, j - 1);\n    // Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    std::cmp::min(left, up) + grid[i as usize][j as usize]\n}\n</code></pre> min_path_sum.c<pre><code>/* Минимальная сумма пути: полный перебор */\nint minPathSumDFS(int grid[MAX_SIZE][MAX_SIZE], int i, int j) {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return INT_MAX;\n    }\n    // Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n    int up = minPathSumDFS(grid, i - 1, j);\n    int left = minPathSumDFS(grid, i, j - 1);\n    // Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    return myMin(left, up) != INT_MAX ? myMin(left, up) + grid[i][j] : INT_MAX;\n}\n</code></pre> min_path_sum.kt<pre><code>/* Минимальная сумма пути: полный перебор */\nfun minPathSumDFS(grid: Array&lt;IntArray&gt;, i: Int, j: Int): Int {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0]\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return Int.MAX_VALUE\n    }\n    // Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n    val up = minPathSumDFS(grid, i - 1, j)\n    val left = minPathSumDFS(grid, i, j - 1)\n    // Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    return min(left, up) + grid[i][j]\n}\n</code></pre> min_path_sum.rb<pre><code>### Минимальная сумма пути: полный перебор ###\ndef min_path_sum_dfs(grid, i, j)\n  # Если это верхняя левая ячейка, завершить поиск\n  return grid[i][j] if i == 0 &amp;&amp; j == 0\n  # Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n  return Float::INFINITY if i &lt; 0 || j &lt; 0\n  # Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n  up = min_path_sum_dfs(grid, i - 1, j)\n  left = min_path_sum_dfs(grid, i, j - 1)\n  # Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n  [left, up].min + grid[i][j]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>На рисунке 14-14 показано дерево рекурсии с корнем в \\(dp[2, 1]\\) ; в нем содержатся перекрывающиеся подзадачи, и их число будет резко расти вместе с размером сетки <code>grid</code> .</p> <p>По своей сути причина появления перекрывающихся подзадач такова: существует много разных путей от левого верхнего угла до одной и той же клетки.</p> <p></p> <p> Рисунок 14-14   Дерево рекурсии полного перебора </p> <p>У каждого состояния есть два выбора - вниз и вправо, а от левого верхнего угла до правого нижнего нужно сделать всего \\(m + n - 2\\) шагов, поэтому худшая временная сложность равна \\(O(2^{m + n})\\) , где \\(n\\) и \\(m\\) - число строк и столбцов сетки соответственно. Заметим, что в этой оценке не учитывается близость к границам сетки: у граничных клеток остается только один выбор, так что фактическое число путей будет несколько меньше.</p>","path":["Глава 14. Динамическое программирование","14.3 &nbsp; Подход к решению задач динамического программирования"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#2-2","level":3,"title":"2.   Метод 2: поиск с мемоизацией","text":"<p>Введем список памяти <code>mem</code> того же размера, что и сетка <code>grid</code> , для хранения решений всех подзадач и отсечения перекрывающихся подзадач:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby min_path_sum.py<pre><code>def min_path_sum_dfs_mem(\n    grid: list[list[int]], mem: list[list[int]], i: int, j: int\n) -&gt; int:\n    \"\"\"Минимальная сумма пути: поиск с мемоизацией\"\"\"\n    # Если это верхняя левая ячейка, завершить поиск\n    if i == 0 and j == 0:\n        return grid[0][0]\n    # Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if i &lt; 0 or j &lt; 0:\n        return inf\n    # Если запись уже есть, вернуть сразу\n    if mem[i][j] != -1:\n        return mem[i][j]\n    # Минимальная стоимость пути для левой и верхней ячеек\n    up = min_path_sum_dfs_mem(grid, mem, i - 1, j)\n    left = min_path_sum_dfs_mem(grid, mem, i, j - 1)\n    # Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    mem[i][j] = min(left, up) + grid[i][j]\n    return mem[i][j]\n</code></pre> min_path_sum.cpp<pre><code>/* Минимальная сумма пути: поиск с мемоизацией */\nint minPathSumDFSMem(vector&lt;vector&lt;int&gt;&gt; &amp;grid, vector&lt;vector&lt;int&gt;&gt; &amp;mem, int i, int j) {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return INT_MAX;\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][j] != -1) {\n        return mem[i][j];\n    }\n    // Минимальная стоимость пути для левой и верхней ячеек\n    int up = minPathSumDFSMem(grid, mem, i - 1, j);\n    int left = minPathSumDFSMem(grid, mem, i, j - 1);\n    // Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    mem[i][j] = min(left, up) != INT_MAX ? min(left, up) + grid[i][j] : INT_MAX;\n    return mem[i][j];\n}\n</code></pre> min_path_sum.java<pre><code>/* Минимальная сумма пути: поиск с мемоизацией */\nint minPathSumDFSMem(int[][] grid, int[][] mem, int i, int j) {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return Integer.MAX_VALUE;\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][j] != -1) {\n        return mem[i][j];\n    }\n    // Минимальная стоимость пути для левой и верхней ячеек\n    int up = minPathSumDFSMem(grid, mem, i - 1, j);\n    int left = minPathSumDFSMem(grid, mem, i, j - 1);\n    // Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    mem[i][j] = Math.min(left, up) + grid[i][j];\n    return mem[i][j];\n}\n</code></pre> min_path_sum.cs<pre><code>/* Минимальная сумма пути: поиск с мемоизацией */\nint MinPathSumDFSMem(int[][] grid, int[][] mem, int i, int j) {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return int.MaxValue;\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][j] != -1) {\n        return mem[i][j];\n    }\n    // Минимальная стоимость пути для левой и верхней ячеек\n    int up = MinPathSumDFSMem(grid, mem, i - 1, j);\n    int left = MinPathSumDFSMem(grid, mem, i, j - 1);\n    // Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    mem[i][j] = Math.Min(left, up) + grid[i][j];\n    return mem[i][j];\n}\n</code></pre> min_path_sum.go<pre><code>/* Минимальная сумма пути: поиск с мемоизацией */\nfunc minPathSumDFSMem(grid, mem [][]int, i, j int) int {\n    // Если это верхняя левая ячейка, завершить поиск\n    if i == 0 &amp;&amp; j == 0 {\n        return grid[0][0]\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if i &lt; 0 || j &lt; 0 {\n        return math.MaxInt\n    }\n    // Если запись уже есть, вернуть сразу\n    if mem[i][j] != -1 {\n        return mem[i][j]\n    }\n    // Минимальная стоимость пути для левой и верхней ячеек\n    up := minPathSumDFSMem(grid, mem, i-1, j)\n    left := minPathSumDFSMem(grid, mem, i, j-1)\n    // Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    mem[i][j] = int(math.Min(float64(left), float64(up))) + grid[i][j]\n    return mem[i][j]\n}\n</code></pre> min_path_sum.swift<pre><code>/* Минимальная сумма пути: поиск с мемоизацией */\nfunc minPathSumDFSMem(grid: [[Int]], mem: inout [[Int]], i: Int, j: Int) -&gt; Int {\n    // Если это верхняя левая ячейка, завершить поиск\n    if i == 0, j == 0 {\n        return grid[0][0]\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if i &lt; 0 || j &lt; 0 {\n        return .max\n    }\n    // Если запись уже есть, вернуть сразу\n    if mem[i][j] != -1 {\n        return mem[i][j]\n    }\n    // Минимальная стоимость пути для левой и верхней ячеек\n    let up = minPathSumDFSMem(grid: grid, mem: &amp;mem, i: i - 1, j: j)\n    let left = minPathSumDFSMem(grid: grid, mem: &amp;mem, i: i, j: j - 1)\n    // Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    mem[i][j] = min(left, up) + grid[i][j]\n    return mem[i][j]\n}\n</code></pre> min_path_sum.js<pre><code>/* Минимальная сумма пути: поиск с мемоизацией */\nfunction minPathSumDFSMem(grid, mem, i, j) {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i === 0 &amp;&amp; j === 0) {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return Infinity;\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][j] !== -1) {\n        return mem[i][j];\n    }\n    // Минимальная стоимость пути для левой и верхней ячеек\n    const up = minPathSumDFSMem(grid, mem, i - 1, j);\n    const left = minPathSumDFSMem(grid, mem, i, j - 1);\n    // Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    mem[i][j] = Math.min(left, up) + grid[i][j];\n    return mem[i][j];\n}\n</code></pre> min_path_sum.ts<pre><code>/* Минимальная сумма пути: поиск с мемоизацией */\nfunction minPathSumDFSMem(\n    grid: Array&lt;Array&lt;number&gt;&gt;,\n    mem: Array&lt;Array&lt;number&gt;&gt;,\n    i: number,\n    j: number\n): number {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i === 0 &amp;&amp; j === 0) {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return Infinity;\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][j] != -1) {\n        return mem[i][j];\n    }\n    // Минимальная стоимость пути для левой и верхней ячеек\n    const up = minPathSumDFSMem(grid, mem, i - 1, j);\n    const left = minPathSumDFSMem(grid, mem, i, j - 1);\n    // Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    mem[i][j] = Math.min(left, up) + grid[i][j];\n    return mem[i][j];\n}\n</code></pre> min_path_sum.dart<pre><code>/* Минимальная сумма пути: поиск с мемоизацией */\nint minPathSumDFSMem(List&lt;List&lt;int&gt;&gt; grid, List&lt;List&lt;int&gt;&gt; mem, int i, int j) {\n  // Если это верхняя левая ячейка, завершить поиск\n  if (i == 0 &amp;&amp; j == 0) {\n    return grid[0][0];\n  }\n  // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n  if (i &lt; 0 || j &lt; 0) {\n    // В Dart тип int — целое число фиксированного диапазона; значения, представляющего «бесконечность», не существует\n    return BigInt.from(2).pow(31).toInt();\n  }\n  // Если запись уже есть, вернуть сразу\n  if (mem[i][j] != -1) {\n    return mem[i][j];\n  }\n  // Минимальная стоимость пути для левой и верхней ячеек\n  int up = minPathSumDFSMem(grid, mem, i - 1, j);\n  int left = minPathSumDFSMem(grid, mem, i, j - 1);\n  // Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n  mem[i][j] = min(left, up) + grid[i][j];\n  return mem[i][j];\n}\n</code></pre> min_path_sum.rs<pre><code>/* Минимальная сумма пути: поиск с мемоизацией */\nfn min_path_sum_dfs_mem(grid: &amp;Vec&lt;Vec&lt;i32&gt;&gt;, mem: &amp;mut Vec&lt;Vec&lt;i32&gt;&gt;, i: i32, j: i32) -&gt; i32 {\n    // Если это верхняя левая ячейка, завершить поиск\n    if i == 0 &amp;&amp; j == 0 {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if i &lt; 0 || j &lt; 0 {\n        return i32::MAX;\n    }\n    // Если запись уже есть, вернуть сразу\n    if mem[i as usize][j as usize] != -1 {\n        return mem[i as usize][j as usize];\n    }\n    // Минимальная стоимость пути для левой и верхней ячеек\n    let up = min_path_sum_dfs_mem(grid, mem, i - 1, j);\n    let left = min_path_sum_dfs_mem(grid, mem, i, j - 1);\n    // Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    mem[i as usize][j as usize] = std::cmp::min(left, up) + grid[i as usize][j as usize];\n    mem[i as usize][j as usize]\n}\n</code></pre> min_path_sum.c<pre><code>/* Минимальная сумма пути: поиск с мемоизацией */\nint minPathSumDFSMem(int grid[MAX_SIZE][MAX_SIZE], int mem[MAX_SIZE][MAX_SIZE], int i, int j) {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return INT_MAX;\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][j] != -1) {\n        return mem[i][j];\n    }\n    // Минимальная стоимость пути для левой и верхней ячеек\n    int up = minPathSumDFSMem(grid, mem, i - 1, j);\n    int left = minPathSumDFSMem(grid, mem, i, j - 1);\n    // Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    mem[i][j] = myMin(left, up) != INT_MAX ? myMin(left, up) + grid[i][j] : INT_MAX;\n    return mem[i][j];\n}\n</code></pre> min_path_sum.kt<pre><code>/* Минимальная сумма пути: поиск с мемоизацией */\nfun minPathSumDFSMem(\n    grid: Array&lt;IntArray&gt;,\n    mem: Array&lt;IntArray&gt;,\n    i: Int,\n    j: Int\n): Int {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0]\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return Int.MAX_VALUE\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][j] != -1) {\n        return mem[i][j]\n    }\n    // Минимальная стоимость пути для левой и верхней ячеек\n    val up = minPathSumDFSMem(grid, mem, i - 1, j)\n    val left = minPathSumDFSMem(grid, mem, i, j - 1)\n    // Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    mem[i][j] = min(left, up) + grid[i][j]\n    return mem[i][j]\n}\n</code></pre> min_path_sum.rb<pre><code>### Минимальная сумма пути: поиск с мемоизацией ###\ndef min_path_sum_dfs_mem(grid, mem, i, j)\n  # Если это верхняя левая ячейка, завершить поиск\n  return grid[0][0] if i == 0 &amp;&amp; j == 0\n  # Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n  return Float::INFINITY if i &lt; 0 || j &lt; 0\n  # Если запись уже есть, вернуть сразу\n  return mem[i][j] if mem[i][j] != -1\n  # Минимальная стоимость пути для левой и верхней ячеек\n  up = min_path_sum_dfs_mem(grid, mem, i - 1, j)\n  left = min_path_sum_dfs_mem(grid, mem, i, j - 1)\n  # Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n  mem[i][j] = [left, up].min + grid[i][j]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Как показано на рисунке 14-15, после добавления мемоизации решение каждой подзадачи вычисляется только один раз, поэтому временная сложность определяется общим числом состояний, то есть равна \\(O(nm)\\) .</p> <p></p> <p> Рисунок 14-15   Дерево рекурсии для поиска с мемоизацией </p>","path":["Глава 14. Динамическое программирование","14.3 &nbsp; Подход к решению задач динамического программирования"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#3-3","level":3,"title":"3.   Метод 3: динамическое программирование","text":"<p>Итеративная реализация динамического программирования выглядит так:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby min_path_sum.py<pre><code>def min_path_sum_dp(grid: list[list[int]]) -&gt; int:\n    \"\"\"Минимальная сумма пути: динамическое программирование\"\"\"\n    n, m = len(grid), len(grid[0])\n    # Инициализация таблицы dp\n    dp = [[0] * m for _ in range(n)]\n    dp[0][0] = grid[0][0]\n    # Переход состояний: первая строка\n    for j in range(1, m):\n        dp[0][j] = dp[0][j - 1] + grid[0][j]\n    # Переход состояний: первый столбец\n    for i in range(1, n):\n        dp[i][0] = dp[i - 1][0] + grid[i][0]\n    # Переход состояний: остальные строки и столбцы\n    for i in range(1, n):\n        for j in range(1, m):\n            dp[i][j] = min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j]\n    return dp[n - 1][m - 1]\n</code></pre> min_path_sum.cpp<pre><code>/* Минимальная сумма пути: динамическое программирование */\nint minPathSumDP(vector&lt;vector&lt;int&gt;&gt; &amp;grid) {\n    int n = grid.size(), m = grid[0].size();\n    // Инициализация таблицы dp\n    vector&lt;vector&lt;int&gt;&gt; dp(n, vector&lt;int&gt;(m));\n    dp[0][0] = grid[0][0];\n    // Переход состояний: первая строка\n    for (int j = 1; j &lt; m; j++) {\n        dp[0][j] = dp[0][j - 1] + grid[0][j];\n    }\n    // Переход состояний: первый столбец\n    for (int i = 1; i &lt; n; i++) {\n        dp[i][0] = dp[i - 1][0] + grid[i][0];\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (int i = 1; i &lt; n; i++) {\n        for (int j = 1; j &lt; m; j++) {\n            dp[i][j] = min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];\n        }\n    }\n    return dp[n - 1][m - 1];\n}\n</code></pre> min_path_sum.java<pre><code>/* Минимальная сумма пути: динамическое программирование */\nint minPathSumDP(int[][] grid) {\n    int n = grid.length, m = grid[0].length;\n    // Инициализация таблицы dp\n    int[][] dp = new int[n][m];\n    dp[0][0] = grid[0][0];\n    // Переход состояний: первая строка\n    for (int j = 1; j &lt; m; j++) {\n        dp[0][j] = dp[0][j - 1] + grid[0][j];\n    }\n    // Переход состояний: первый столбец\n    for (int i = 1; i &lt; n; i++) {\n        dp[i][0] = dp[i - 1][0] + grid[i][0];\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (int i = 1; i &lt; n; i++) {\n        for (int j = 1; j &lt; m; j++) {\n            dp[i][j] = Math.min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];\n        }\n    }\n    return dp[n - 1][m - 1];\n}\n</code></pre> min_path_sum.cs<pre><code>/* Минимальная сумма пути: динамическое программирование */\nint MinPathSumDP(int[][] grid) {\n    int n = grid.Length, m = grid[0].Length;\n    // Инициализация таблицы dp\n    int[,] dp = new int[n, m];\n    dp[0, 0] = grid[0][0];\n    // Переход состояний: первая строка\n    for (int j = 1; j &lt; m; j++) {\n        dp[0, j] = dp[0, j - 1] + grid[0][j];\n    }\n    // Переход состояний: первый столбец\n    for (int i = 1; i &lt; n; i++) {\n        dp[i, 0] = dp[i - 1, 0] + grid[i][0];\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (int i = 1; i &lt; n; i++) {\n        for (int j = 1; j &lt; m; j++) {\n            dp[i, j] = Math.Min(dp[i, j - 1], dp[i - 1, j]) + grid[i][j];\n        }\n    }\n    return dp[n - 1, m - 1];\n}\n</code></pre> min_path_sum.go<pre><code>/* Минимальная сумма пути: динамическое программирование */\nfunc minPathSumDP(grid [][]int) int {\n    n, m := len(grid), len(grid[0])\n    // Инициализация таблицы dp\n    dp := make([][]int, n)\n    for i := 0; i &lt; n; i++ {\n        dp[i] = make([]int, m)\n    }\n    dp[0][0] = grid[0][0]\n    // Переход состояний: первая строка\n    for j := 1; j &lt; m; j++ {\n        dp[0][j] = dp[0][j-1] + grid[0][j]\n    }\n    // Переход состояний: первый столбец\n    for i := 1; i &lt; n; i++ {\n        dp[i][0] = dp[i-1][0] + grid[i][0]\n    }\n    // Переход состояний: остальные строки и столбцы\n    for i := 1; i &lt; n; i++ {\n        for j := 1; j &lt; m; j++ {\n            dp[i][j] = int(math.Min(float64(dp[i][j-1]), float64(dp[i-1][j]))) + grid[i][j]\n        }\n    }\n    return dp[n-1][m-1]\n}\n</code></pre> min_path_sum.swift<pre><code>/* Минимальная сумма пути: динамическое программирование */\nfunc minPathSumDP(grid: [[Int]]) -&gt; Int {\n    let n = grid.count\n    let m = grid[0].count\n    // Инициализация таблицы dp\n    var dp = Array(repeating: Array(repeating: 0, count: m), count: n)\n    dp[0][0] = grid[0][0]\n    // Переход состояний: первая строка\n    for j in 1 ..&lt; m {\n        dp[0][j] = dp[0][j - 1] + grid[0][j]\n    }\n    // Переход состояний: первый столбец\n    for i in 1 ..&lt; n {\n        dp[i][0] = dp[i - 1][0] + grid[i][0]\n    }\n    // Переход состояний: остальные строки и столбцы\n    for i in 1 ..&lt; n {\n        for j in 1 ..&lt; m {\n            dp[i][j] = min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j]\n        }\n    }\n    return dp[n - 1][m - 1]\n}\n</code></pre> min_path_sum.js<pre><code>/* Минимальная сумма пути: динамическое программирование */\nfunction minPathSumDP(grid) {\n    const n = grid.length,\n        m = grid[0].length;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: n }, () =&gt;\n        Array.from({ length: m }, () =&gt; 0)\n    );\n    dp[0][0] = grid[0][0];\n    // Переход состояний: первая строка\n    for (let j = 1; j &lt; m; j++) {\n        dp[0][j] = dp[0][j - 1] + grid[0][j];\n    }\n    // Переход состояний: первый столбец\n    for (let i = 1; i &lt; n; i++) {\n        dp[i][0] = dp[i - 1][0] + grid[i][0];\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (let i = 1; i &lt; n; i++) {\n        for (let j = 1; j &lt; m; j++) {\n            dp[i][j] = Math.min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];\n        }\n    }\n    return dp[n - 1][m - 1];\n}\n</code></pre> min_path_sum.ts<pre><code>/* Минимальная сумма пути: динамическое программирование */\nfunction minPathSumDP(grid: Array&lt;Array&lt;number&gt;&gt;): number {\n    const n = grid.length,\n        m = grid[0].length;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: n }, () =&gt;\n        Array.from({ length: m }, () =&gt; 0)\n    );\n    dp[0][0] = grid[0][0];\n    // Переход состояний: первая строка\n    for (let j = 1; j &lt; m; j++) {\n        dp[0][j] = dp[0][j - 1] + grid[0][j];\n    }\n    // Переход состояний: первый столбец\n    for (let i = 1; i &lt; n; i++) {\n        dp[i][0] = dp[i - 1][0] + grid[i][0];\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (let i = 1; i &lt; n; i++) {\n        for (let j: number = 1; j &lt; m; j++) {\n            dp[i][j] = Math.min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];\n        }\n    }\n    return dp[n - 1][m - 1];\n}\n</code></pre> min_path_sum.dart<pre><code>/* Минимальная сумма пути: динамическое программирование */\nint minPathSumDP(List&lt;List&lt;int&gt;&gt; grid) {\n  int n = grid.length, m = grid[0].length;\n  // Инициализация таблицы dp\n  List&lt;List&lt;int&gt;&gt; dp = List.generate(n, (i) =&gt; List.filled(m, 0));\n  dp[0][0] = grid[0][0];\n  // Переход состояний: первая строка\n  for (int j = 1; j &lt; m; j++) {\n    dp[0][j] = dp[0][j - 1] + grid[0][j];\n  }\n  // Переход состояний: первый столбец\n  for (int i = 1; i &lt; n; i++) {\n    dp[i][0] = dp[i - 1][0] + grid[i][0];\n  }\n  // Переход состояний: остальные строки и столбцы\n  for (int i = 1; i &lt; n; i++) {\n    for (int j = 1; j &lt; m; j++) {\n      dp[i][j] = min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];\n    }\n  }\n  return dp[n - 1][m - 1];\n}\n</code></pre> min_path_sum.rs<pre><code>/* Минимальная сумма пути: динамическое программирование */\nfn min_path_sum_dp(grid: &amp;Vec&lt;Vec&lt;i32&gt;&gt;) -&gt; i32 {\n    let (n, m) = (grid.len(), grid[0].len());\n    // Инициализация таблицы dp\n    let mut dp = vec![vec![0; m]; n];\n    dp[0][0] = grid[0][0];\n    // Переход состояний: первая строка\n    for j in 1..m {\n        dp[0][j] = dp[0][j - 1] + grid[0][j];\n    }\n    // Переход состояний: первый столбец\n    for i in 1..n {\n        dp[i][0] = dp[i - 1][0] + grid[i][0];\n    }\n    // Переход состояний: остальные строки и столбцы\n    for i in 1..n {\n        for j in 1..m {\n            dp[i][j] = std::cmp::min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];\n        }\n    }\n    dp[n - 1][m - 1]\n}\n</code></pre> min_path_sum.c<pre><code>/* Минимальная сумма пути: динамическое программирование */\nint minPathSumDP(int grid[MAX_SIZE][MAX_SIZE], int n, int m) {\n    // Инициализация таблицы dp\n    int **dp = malloc(n * sizeof(int *));\n    for (int i = 0; i &lt; n; i++) {\n        dp[i] = calloc(m, sizeof(int));\n    }\n    dp[0][0] = grid[0][0];\n    // Переход состояний: первая строка\n    for (int j = 1; j &lt; m; j++) {\n        dp[0][j] = dp[0][j - 1] + grid[0][j];\n    }\n    // Переход состояний: первый столбец\n    for (int i = 1; i &lt; n; i++) {\n        dp[i][0] = dp[i - 1][0] + grid[i][0];\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (int i = 1; i &lt; n; i++) {\n        for (int j = 1; j &lt; m; j++) {\n            dp[i][j] = myMin(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];\n        }\n    }\n    int res = dp[n - 1][m - 1];\n    // Освободить память\n    for (int i = 0; i &lt; n; i++) {\n        free(dp[i]);\n    }\n    return res;\n}\n</code></pre> min_path_sum.kt<pre><code>/* Минимальная сумма пути: динамическое программирование */\nfun minPathSumDP(grid: Array&lt;IntArray&gt;): Int {\n    val n = grid.size\n    val m = grid[0].size\n    // Инициализация таблицы dp\n    val dp = Array(n) { IntArray(m) }\n    dp[0][0] = grid[0][0]\n    // Переход состояний: первая строка\n    for (j in 1..&lt;m) {\n        dp[0][j] = dp[0][j - 1] + grid[0][j]\n    }\n    // Переход состояний: первый столбец\n    for (i in 1..&lt;n) {\n        dp[i][0] = dp[i - 1][0] + grid[i][0]\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (i in 1..&lt;n) {\n        for (j in 1..&lt;m) {\n            dp[i][j] = min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j]\n        }\n    }\n    return dp[n - 1][m - 1]\n}\n</code></pre> min_path_sum.rb<pre><code>### Минимальная сумма пути: динамическое программирование ###\ndef min_path_sum_dp(grid)\n  n, m = grid.length, grid.first.length\n  # Инициализация таблицы dp\n  dp = Array.new(n) { Array.new(m, 0) }\n  dp[0][0] = grid[0][0]\n  # Переход состояний: первая строка\n  (1...m).each { |j| dp[0][j] = dp[0][j - 1] + grid[0][j] }\n  # Переход состояний: первый столбец\n  (1...n).each { |i| dp[i][0] = dp[i - 1][0] + grid[i][0] }\n  # Переход состояний: остальные строки и столбцы\n  for i in 1...n\n    for j in 1...m\n      dp[i][j] = [dp[i][j - 1], dp[i - 1][j]].min + grid[i][j]\n    end\n  end\n  dp[n -1][m -1]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>На рисунке 14-16 показан процесс переходов состояний в задаче о минимальной сумме пути. Он проходит по всей сетке, поэтому временная сложность равна \\(O(nm)\\) .</p> <p>Размер массива <code>dp</code> равен \\(n \\times m\\) , поэтому пространственная сложность равна \\(O(nm)\\) .</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 14-16   Процесс динамического программирования для минимальной суммы пути </p>","path":["Глава 14. Динамическое программирование","14.3 &nbsp; Подход к решению задач динамического программирования"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#4","level":3,"title":"4.   Оптимизация пространства","text":"<p>Поскольку каждая клетка зависит только от клетки слева и клетки сверху, таблицу \\(dp\\) можно реализовать с помощью одномерного массива, соответствующего одной строке.</p> <p>Обратите внимание: поскольку массив <code>dp</code> теперь может представлять только одну строку состояний, мы не можем заранее инициализировать состояния первого столбца, а должны обновлять их по мере обхода каждой строки:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby min_path_sum.py<pre><code>def min_path_sum_dp_comp(grid: list[list[int]]) -&gt; int:\n    \"\"\"Минимальная сумма пути: динамическое программирование с оптимизацией памяти\"\"\"\n    n, m = len(grid), len(grid[0])\n    # Инициализация таблицы dp\n    dp = [0] * m\n    # Переход состояний: первая строка\n    dp[0] = grid[0][0]\n    for j in range(1, m):\n        dp[j] = dp[j - 1] + grid[0][j]\n    # Переход состояний: остальные строки\n    for i in range(1, n):\n        # Переход состояний: первый столбец\n        dp[0] = dp[0] + grid[i][0]\n        # Переход состояний: остальные столбцы\n        for j in range(1, m):\n            dp[j] = min(dp[j - 1], dp[j]) + grid[i][j]\n    return dp[m - 1]\n</code></pre> min_path_sum.cpp<pre><code>/* Минимальная сумма пути: динамическое программирование с оптимизацией памяти */\nint minPathSumDPComp(vector&lt;vector&lt;int&gt;&gt; &amp;grid) {\n    int n = grid.size(), m = grid[0].size();\n    // Инициализация таблицы dp\n    vector&lt;int&gt; dp(m);\n    // Переход состояний: первая строка\n    dp[0] = grid[0][0];\n    for (int j = 1; j &lt; m; j++) {\n        dp[j] = dp[j - 1] + grid[0][j];\n    }\n    // Переход состояний: остальные строки\n    for (int i = 1; i &lt; n; i++) {\n        // Переход состояний: первый столбец\n        dp[0] = dp[0] + grid[i][0];\n        // Переход состояний: остальные столбцы\n        for (int j = 1; j &lt; m; j++) {\n            dp[j] = min(dp[j - 1], dp[j]) + grid[i][j];\n        }\n    }\n    return dp[m - 1];\n}\n</code></pre> min_path_sum.java<pre><code>/* Минимальная сумма пути: динамическое программирование с оптимизацией памяти */\nint minPathSumDPComp(int[][] grid) {\n    int n = grid.length, m = grid[0].length;\n    // Инициализация таблицы dp\n    int[] dp = new int[m];\n    // Переход состояний: первая строка\n    dp[0] = grid[0][0];\n    for (int j = 1; j &lt; m; j++) {\n        dp[j] = dp[j - 1] + grid[0][j];\n    }\n    // Переход состояний: остальные строки\n    for (int i = 1; i &lt; n; i++) {\n        // Переход состояний: первый столбец\n        dp[0] = dp[0] + grid[i][0];\n        // Переход состояний: остальные столбцы\n        for (int j = 1; j &lt; m; j++) {\n            dp[j] = Math.min(dp[j - 1], dp[j]) + grid[i][j];\n        }\n    }\n    return dp[m - 1];\n}\n</code></pre> min_path_sum.cs<pre><code>/* Минимальная сумма пути: динамическое программирование с оптимизацией памяти */\nint MinPathSumDPComp(int[][] grid) {\n    int n = grid.Length, m = grid[0].Length;\n    // Инициализация таблицы dp\n    int[] dp = new int[m];\n    dp[0] = grid[0][0];\n    // Переход состояний: первая строка\n    for (int j = 1; j &lt; m; j++) {\n        dp[j] = dp[j - 1] + grid[0][j];\n    }\n    // Переход состояний: остальные строки\n    for (int i = 1; i &lt; n; i++) {\n        // Переход состояний: первый столбец\n        dp[0] = dp[0] + grid[i][0];\n        // Переход состояний: остальные столбцы\n        for (int j = 1; j &lt; m; j++) {\n            dp[j] = Math.Min(dp[j - 1], dp[j]) + grid[i][j];\n        }\n    }\n    return dp[m - 1];\n}\n</code></pre> min_path_sum.go<pre><code>/* Минимальная сумма пути: динамическое программирование с оптимизацией памяти */\nfunc minPathSumDPComp(grid [][]int) int {\n    n, m := len(grid), len(grid[0])\n    // Инициализация таблицы dp\n    dp := make([]int, m)\n    // Переход состояний: первая строка\n    dp[0] = grid[0][0]\n    for j := 1; j &lt; m; j++ {\n        dp[j] = dp[j-1] + grid[0][j]\n    }\n    // Переход состояний: остальные строки и столбцы\n    for i := 1; i &lt; n; i++ {\n        // Переход состояний: первый столбец\n        dp[0] = dp[0] + grid[i][0]\n        // Переход состояний: остальные столбцы\n        for j := 1; j &lt; m; j++ {\n            dp[j] = int(math.Min(float64(dp[j-1]), float64(dp[j]))) + grid[i][j]\n        }\n    }\n    return dp[m-1]\n}\n</code></pre> min_path_sum.swift<pre><code>/* Минимальная сумма пути: динамическое программирование с оптимизацией памяти */\nfunc minPathSumDPComp(grid: [[Int]]) -&gt; Int {\n    let n = grid.count\n    let m = grid[0].count\n    // Инициализация таблицы dp\n    var dp = Array(repeating: 0, count: m)\n    // Переход состояний: первая строка\n    dp[0] = grid[0][0]\n    for j in 1 ..&lt; m {\n        dp[j] = dp[j - 1] + grid[0][j]\n    }\n    // Переход состояний: остальные строки\n    for i in 1 ..&lt; n {\n        // Переход состояний: первый столбец\n        dp[0] = dp[0] + grid[i][0]\n        // Переход состояний: остальные столбцы\n        for j in 1 ..&lt; m {\n            dp[j] = min(dp[j - 1], dp[j]) + grid[i][j]\n        }\n    }\n    return dp[m - 1]\n}\n</code></pre> min_path_sum.js<pre><code>/* Минимальная сумма пути: динамическое программирование с оптимизацией памяти */\nfunction minPathSumDPComp(grid) {\n    const n = grid.length,\n        m = grid[0].length;\n    // Инициализация таблицы dp\n    const dp = new Array(m);\n    // Переход состояний: первая строка\n    dp[0] = grid[0][0];\n    for (let j = 1; j &lt; m; j++) {\n        dp[j] = dp[j - 1] + grid[0][j];\n    }\n    // Переход состояний: остальные строки\n    for (let i = 1; i &lt; n; i++) {\n        // Переход состояний: первый столбец\n        dp[0] = dp[0] + grid[i][0];\n        // Переход состояний: остальные столбцы\n        for (let j = 1; j &lt; m; j++) {\n            dp[j] = Math.min(dp[j - 1], dp[j]) + grid[i][j];\n        }\n    }\n    return dp[m - 1];\n}\n</code></pre> min_path_sum.ts<pre><code>/* Минимальная сумма пути: динамическое программирование с оптимизацией памяти */\nfunction minPathSumDPComp(grid: Array&lt;Array&lt;number&gt;&gt;): number {\n    const n = grid.length,\n        m = grid[0].length;\n    // Инициализация таблицы dp\n    const dp = new Array(m);\n    // Переход состояний: первая строка\n    dp[0] = grid[0][0];\n    for (let j = 1; j &lt; m; j++) {\n        dp[j] = dp[j - 1] + grid[0][j];\n    }\n    // Переход состояний: остальные строки\n    for (let i = 1; i &lt; n; i++) {\n        // Переход состояний: первый столбец\n        dp[0] = dp[0] + grid[i][0];\n        // Переход состояний: остальные столбцы\n        for (let j = 1; j &lt; m; j++) {\n            dp[j] = Math.min(dp[j - 1], dp[j]) + grid[i][j];\n        }\n    }\n    return dp[m - 1];\n}\n</code></pre> min_path_sum.dart<pre><code>/* Минимальная сумма пути: динамическое программирование с оптимизацией памяти */\nint minPathSumDPComp(List&lt;List&lt;int&gt;&gt; grid) {\n  int n = grid.length, m = grid[0].length;\n  // Инициализация таблицы dp\n  List&lt;int&gt; dp = List.filled(m, 0);\n  dp[0] = grid[0][0];\n  for (int j = 1; j &lt; m; j++) {\n    dp[j] = dp[j - 1] + grid[0][j];\n  }\n  // Переход состояний: остальные строки\n  for (int i = 1; i &lt; n; i++) {\n    // Переход состояний: первый столбец\n    dp[0] = dp[0] + grid[i][0];\n    // Переход состояний: остальные столбцы\n    for (int j = 1; j &lt; m; j++) {\n      dp[j] = min(dp[j - 1], dp[j]) + grid[i][j];\n    }\n  }\n  return dp[m - 1];\n}\n</code></pre> min_path_sum.rs<pre><code>/* Минимальная сумма пути: динамическое программирование с оптимизацией памяти */\nfn min_path_sum_dp_comp(grid: &amp;Vec&lt;Vec&lt;i32&gt;&gt;) -&gt; i32 {\n    let (n, m) = (grid.len(), grid[0].len());\n    // Инициализация таблицы dp\n    let mut dp = vec![0; m];\n    // Переход состояний: первая строка\n    dp[0] = grid[0][0];\n    for j in 1..m {\n        dp[j] = dp[j - 1] + grid[0][j];\n    }\n    // Переход состояний: остальные строки\n    for i in 1..n {\n        // Переход состояний: первый столбец\n        dp[0] = dp[0] + grid[i][0];\n        // Переход состояний: остальные столбцы\n        for j in 1..m {\n            dp[j] = std::cmp::min(dp[j - 1], dp[j]) + grid[i][j];\n        }\n    }\n    dp[m - 1]\n}\n</code></pre> min_path_sum.c<pre><code>/* Минимальная сумма пути: динамическое программирование с оптимизацией памяти */\nint minPathSumDPComp(int grid[MAX_SIZE][MAX_SIZE], int n, int m) {\n    // Инициализация таблицы dp\n    int *dp = calloc(m, sizeof(int));\n    // Переход состояний: первая строка\n    dp[0] = grid[0][0];\n    for (int j = 1; j &lt; m; j++) {\n        dp[j] = dp[j - 1] + grid[0][j];\n    }\n    // Переход состояний: остальные строки\n    for (int i = 1; i &lt; n; i++) {\n        // Переход состояний: первый столбец\n        dp[0] = dp[0] + grid[i][0];\n        // Переход состояний: остальные столбцы\n        for (int j = 1; j &lt; m; j++) {\n            dp[j] = myMin(dp[j - 1], dp[j]) + grid[i][j];\n        }\n    }\n    int res = dp[m - 1];\n    // Освободить память\n    free(dp);\n    return res;\n}\n</code></pre> min_path_sum.kt<pre><code>/* Минимальная сумма пути: динамическое программирование с оптимизацией памяти */\nfun minPathSumDPComp(grid: Array&lt;IntArray&gt;): Int {\n    val n = grid.size\n    val m = grid[0].size\n    // Инициализация таблицы dp\n    val dp = IntArray(m)\n    // Переход состояний: первая строка\n    dp[0] = grid[0][0]\n    for (j in 1..&lt;m) {\n        dp[j] = dp[j - 1] + grid[0][j]\n    }\n    // Переход состояний: остальные строки\n    for (i in 1..&lt;n) {\n        // Переход состояний: первый столбец\n        dp[0] = dp[0] + grid[i][0]\n        // Переход состояний: остальные столбцы\n        for (j in 1..&lt;m) {\n            dp[j] = min(dp[j - 1], dp[j]) + grid[i][j]\n        }\n    }\n    return dp[m - 1]\n}\n</code></pre> min_path_sum.rb<pre><code>### Минимальная сумма пути: динамическое программирование с оптимизацией памяти ###\ndef min_path_sum_dp_comp(grid)\n  n, m = grid.length, grid.first.length\n  # Инициализация таблицы dp\n  dp = Array.new(m, 0)\n  # Переход состояний: первая строка\n  dp[0] = grid[0][0]\n  (1...m).each { |j| dp[j] = dp[j - 1] + grid[0][j] }\n  # Переход состояний: остальные строки\n  for i in 1...n\n    # Переход состояний: первый столбец\n    dp[0] = dp[0] + grid[i][0]\n    # Переход состояний: остальные столбцы\n    (1...m).each { |j| dp[j] = [dp[j - 1], dp[j]].min + grid[i][j] }\n  end\n  dp[m - 1]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 14. Динамическое программирование","14.3 &nbsp; Подход к решению задач динамического программирования"],"tags":[]},{"location":"chapter_dynamic_programming/edit_distance_problem/","level":1,"title":"14.6   Задача о расстоянии редактирования","text":"<p>Расстояние редактирования, также называемое расстоянием Левенштейна, обозначает минимальное число правок, необходимых для взаимного преобразования двух строк. Обычно оно используется для измерения сходства двух последовательностей в информационном поиске и обработке естественного языка.</p> <p>Question</p> <p>Даны две строки \\(s\\) и \\(t\\) . Верните минимальное число шагов редактирования, необходимое для преобразования \\(s\\) в \\(t\\) .</p> <p>Для строки допускаются три операции редактирования: вставка одного символа, удаление одного символа и замена одного символа на произвольный другой символ.</p> <p>Как показано на рисунке 14-27, для преобразования <code>kitten</code> в <code>sitting</code> требуется 3 шага редактирования: 2 операции замены и 1 операция вставки; для преобразования <code>hello</code> в <code>algo</code> также требуется 3 шага: 2 замены и 1 удаление.</p> <p></p> <p> Рисунок 14-27   Пример данных для задачи о расстоянии редактирования </p> <p>Задачу о расстоянии редактирования можно очень естественно описать через модель дерева решений. Строки соответствуют узлам дерева, а один раунд решения (одна операция редактирования) соответствует одному ребру дерева.</p> <p>Как показано на рисунке 14-28, если не ограничивать число операций, то каждый узел может порождать множество ребер, и каждое из них соответствует одному из вариантов преобразования. Это означает, что преобразовать <code>hello</code> в <code>algo</code> можно множеством разных путей.</p> <p>С точки зрения дерева решений цель этой задачи - найти кратчайший путь между узлом <code>hello</code> и узлом <code>algo</code> .</p> <p></p> <p> Рисунок 14-28   Представление задачи о расстоянии редактирования через дерево решений </p>","path":["Глава 14. Динамическое программирование","14.6 &nbsp; Задача о расстоянии редактирования"],"tags":[]},{"location":"chapter_dynamic_programming/edit_distance_problem/#1","level":3,"title":"1.   Идея динамического программирования","text":"<p>Шаг 1: продумать решения на каждом раунде, определить состояние и тем самым получить таблицу \\(dp\\)</p> <p>На каждом раунде решение состоит в выполнении одной операции редактирования над строкой \\(s\\) .</p> <p>Нам нужно, чтобы в ходе выполнения операций размер задачи постепенно уменьшался; только тогда можно строить подзадачи. Пусть длины строк \\(s\\) и \\(t\\) равны соответственно \\(n\\) и \\(m\\) ; сначала рассмотрим последние символы этих строк, то есть \\(s[n-1]\\) и \\(t[m-1]\\) .</p> <ul> <li>Если \\(s[n-1]\\) и \\(t[m-1]\\) совпадают, их можно просто пропустить и сразу перейти к сравнению \\(s[n-2]\\) и \\(t[m-2]\\) .</li> <li>Если \\(s[n-1]\\) и \\(t[m-1]\\) различны, нужно выполнить над \\(s\\) одну операцию редактирования (вставку, удаление или замену), чтобы последние символы стали одинаковыми, после чего можно перейти к задаче меньшего размера.</li> </ul> <p>Иначе говоря, каждое решение (операция редактирования), которое мы выполняем над строкой \\(s\\) , меняет те символы, которые еще остаются несопоставленными в строках \\(s\\) и \\(t\\) . Поэтому состояние определяется текущими позициями рассматриваемых символов в \\(s\\) и \\(t\\) , то есть состоянием \\([i, j]\\) .</p> <p>Подзадача, соответствующая состоянию \\([i, j]\\) , такова: минимальное число операций редактирования, необходимое для преобразования первых \\(i\\) символов строки \\(s\\) в первые \\(j\\) символов строки \\(t\\).</p> <p>Отсюда получается двумерная таблица \\(dp\\) размера \\((i+1) \\times (j+1)\\) .</p> <p>Шаг 2: найти оптимальную подструктуру и на ее основе вывести уравнение перехода состояния</p> <p>Рассмотрим подзадачу \\(dp[i, j]\\) . Ее последние символы - это \\(s[i-1]\\) и \\(t[j-1]\\) . В зависимости от операции редактирования возможны три случая, показанные на рисунке 14-29.</p> <ol> <li>Вставить после \\(s[i-1]\\) символ \\(t[j-1]\\) ; тогда остается подзадача \\(dp[i, j-1]\\) .</li> <li>Удалить \\(s[i-1]\\) ; тогда остается подзадача \\(dp[i-1, j]\\) .</li> <li>Заменить \\(s[i-1]\\) на \\(t[j-1]\\) ; тогда остается подзадача \\(dp[i-1, j-1]\\) .</li> </ol> <p></p> <p> Рисунок 14-29   Переходы состояния в задаче о расстоянии редактирования </p> <p>Согласно этому анализу оптимальная подструктура такова: минимальное число шагов редактирования для \\(dp[i, j]\\) равно минимуму из трех значений - \\(dp[i, j-1]\\) , \\(dp[i-1, j]\\) и \\(dp[i-1, j-1]\\) - плюс цена текущей операции редактирования \\(1\\) . Значит, уравнение перехода состояния имеет вид:</p> \\[ dp[i, j] = \\min(dp[i, j-1], dp[i-1, j], dp[i-1, j-1]) + 1 \\] <p>Заметим, что если символы \\(s[i-1]\\) и \\(t[j-1]\\) совпадают, то редактировать текущий символ не нужно. В этом случае уравнение перехода состояния имеет вид:</p> \\[ dp[i, j] = dp[i-1, j-1] \\] <p>Шаг 3: определить граничные условия и порядок переходов</p> <p>Когда обе строки пусты, число операций редактирования равно \\(0\\) , то есть \\(dp[0, 0] = 0\\) . Когда строка \\(s\\) пуста, а строка \\(t\\) непуста, минимальное число операций равно длине строки \\(t\\) , то есть вся первая строка инициализируется как \\(dp[0, j] = j\\) . Когда строка \\(s\\) непуста, а строка \\(t\\) пуста, минимальное число операций равно длине строки \\(s\\) , то есть весь первый столбец инициализируется как \\(dp[i, 0] = i\\) .</p> <p>Из уравнения перехода видно, что решение \\(dp[i, j]\\) зависит от значений слева, сверху и слева сверху, поэтому всю таблицу \\(dp\\) можно обходить двумя вложенными циклами в прямом порядке.</p>","path":["Глава 14. Динамическое программирование","14.6 &nbsp; Задача о расстоянии редактирования"],"tags":[]},{"location":"chapter_dynamic_programming/edit_distance_problem/#2","level":3,"title":"2.   Реализация кода","text":"PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby edit_distance.py<pre><code>def edit_distance_dp(s: str, t: str) -&gt; int:\n    \"\"\"Редакционное расстояние: динамическое программирование\"\"\"\n    n, m = len(s), len(t)\n    dp = [[0] * (m + 1) for _ in range(n + 1)]\n    # Переход состояний: первая строка и первый столбец\n    for i in range(1, n + 1):\n        dp[i][0] = i\n    for j in range(1, m + 1):\n        dp[0][j] = j\n    # Переход состояний: остальные строки и столбцы\n    for i in range(1, n + 1):\n        for j in range(1, m + 1):\n            if s[i - 1] == t[j - 1]:\n                # Если два символа равны, сразу пропустить их\n                dp[i][j] = dp[i - 1][j - 1]\n            else:\n                # Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[i][j] = min(dp[i][j - 1], dp[i - 1][j], dp[i - 1][j - 1]) + 1\n    return dp[n][m]\n</code></pre> edit_distance.cpp<pre><code>/* Редакционное расстояние: динамическое программирование */\nint editDistanceDP(string s, string t) {\n    int n = s.length(), m = t.length();\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(m + 1, 0));\n    // Переход состояний: первая строка и первый столбец\n    for (int i = 1; i &lt;= n; i++) {\n        dp[i][0] = i;\n    }\n    for (int j = 1; j &lt;= m; j++) {\n        dp[0][j] = j;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (int i = 1; i &lt;= n; i++) {\n        for (int j = 1; j &lt;= m; j++) {\n            if (s[i - 1] == t[j - 1]) {\n                // Если два символа равны, сразу пропустить их\n                dp[i][j] = dp[i - 1][j - 1];\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[i][j] = min(min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;\n            }\n        }\n    }\n    return dp[n][m];\n}\n</code></pre> edit_distance.java<pre><code>/* Редакционное расстояние: динамическое программирование */\nint editDistanceDP(String s, String t) {\n    int n = s.length(), m = t.length();\n    int[][] dp = new int[n + 1][m + 1];\n    // Переход состояний: первая строка и первый столбец\n    for (int i = 1; i &lt;= n; i++) {\n        dp[i][0] = i;\n    }\n    for (int j = 1; j &lt;= m; j++) {\n        dp[0][j] = j;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (int i = 1; i &lt;= n; i++) {\n        for (int j = 1; j &lt;= m; j++) {\n            if (s.charAt(i - 1) == t.charAt(j - 1)) {\n                // Если два символа равны, сразу пропустить их\n                dp[i][j] = dp[i - 1][j - 1];\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[i][j] = Math.min(Math.min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;\n            }\n        }\n    }\n    return dp[n][m];\n}\n</code></pre> edit_distance.cs<pre><code>/* Редакционное расстояние: динамическое программирование */\nint EditDistanceDP(string s, string t) {\n    int n = s.Length, m = t.Length;\n    int[,] dp = new int[n + 1, m + 1];\n    // Переход состояний: первая строка и первый столбец\n    for (int i = 1; i &lt;= n; i++) {\n        dp[i, 0] = i;\n    }\n    for (int j = 1; j &lt;= m; j++) {\n        dp[0, j] = j;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (int i = 1; i &lt;= n; i++) {\n        for (int j = 1; j &lt;= m; j++) {\n            if (s[i - 1] == t[j - 1]) {\n                // Если два символа равны, сразу пропустить их\n                dp[i, j] = dp[i - 1, j - 1];\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[i, j] = Math.Min(Math.Min(dp[i, j - 1], dp[i - 1, j]), dp[i - 1, j - 1]) + 1;\n            }\n        }\n    }\n    return dp[n, m];\n}\n</code></pre> edit_distance.go<pre><code>/* Редакционное расстояние: динамическое программирование */\nfunc editDistanceDP(s string, t string) int {\n    n := len(s)\n    m := len(t)\n    dp := make([][]int, n+1)\n    for i := 0; i &lt;= n; i++ {\n        dp[i] = make([]int, m+1)\n    }\n    // Переход состояний: первая строка и первый столбец\n    for i := 1; i &lt;= n; i++ {\n        dp[i][0] = i\n    }\n    for j := 1; j &lt;= m; j++ {\n        dp[0][j] = j\n    }\n    // Переход состояний: остальные строки и столбцы\n    for i := 1; i &lt;= n; i++ {\n        for j := 1; j &lt;= m; j++ {\n            if s[i-1] == t[j-1] {\n                // Если два символа равны, сразу пропустить их\n                dp[i][j] = dp[i-1][j-1]\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[i][j] = MinInt(MinInt(dp[i][j-1], dp[i-1][j]), dp[i-1][j-1]) + 1\n            }\n        }\n    }\n    return dp[n][m]\n}\n</code></pre> edit_distance.swift<pre><code>/* Редакционное расстояние: динамическое программирование */\nfunc editDistanceDP(s: String, t: String) -&gt; Int {\n    let n = s.utf8CString.count\n    let m = t.utf8CString.count\n    var dp = Array(repeating: Array(repeating: 0, count: m + 1), count: n + 1)\n    // Переход состояний: первая строка и первый столбец\n    for i in 1 ... n {\n        dp[i][0] = i\n    }\n    for j in 1 ... m {\n        dp[0][j] = j\n    }\n    // Переход состояний: остальные строки и столбцы\n    for i in 1 ... n {\n        for j in 1 ... m {\n            if s.utf8CString[i - 1] == t.utf8CString[j - 1] {\n                // Если два символа равны, сразу пропустить их\n                dp[i][j] = dp[i - 1][j - 1]\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[i][j] = min(min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1\n            }\n        }\n    }\n    return dp[n][m]\n}\n</code></pre> edit_distance.js<pre><code>/* Редакционное расстояние: динамическое программирование */\nfunction editDistanceDP(s, t) {\n    const n = s.length,\n        m = t.length;\n    const dp = Array.from({ length: n + 1 }, () =&gt; new Array(m + 1).fill(0));\n    // Переход состояний: первая строка и первый столбец\n    for (let i = 1; i &lt;= n; i++) {\n        dp[i][0] = i;\n    }\n    for (let j = 1; j &lt;= m; j++) {\n        dp[0][j] = j;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (let i = 1; i &lt;= n; i++) {\n        for (let j = 1; j &lt;= m; j++) {\n            if (s.charAt(i - 1) === t.charAt(j - 1)) {\n                // Если два символа равны, сразу пропустить их\n                dp[i][j] = dp[i - 1][j - 1];\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[i][j] =\n                    Math.min(dp[i][j - 1], dp[i - 1][j], dp[i - 1][j - 1]) + 1;\n            }\n        }\n    }\n    return dp[n][m];\n}\n</code></pre> edit_distance.ts<pre><code>/* Редакционное расстояние: динамическое программирование */\nfunction editDistanceDP(s: string, t: string): number {\n    const n = s.length,\n        m = t.length;\n    const dp = Array.from({ length: n + 1 }, () =&gt;\n        Array.from({ length: m + 1 }, () =&gt; 0)\n    );\n    // Переход состояний: первая строка и первый столбец\n    for (let i = 1; i &lt;= n; i++) {\n        dp[i][0] = i;\n    }\n    for (let j = 1; j &lt;= m; j++) {\n        dp[0][j] = j;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (let i = 1; i &lt;= n; i++) {\n        for (let j = 1; j &lt;= m; j++) {\n            if (s.charAt(i - 1) === t.charAt(j - 1)) {\n                // Если два символа равны, сразу пропустить их\n                dp[i][j] = dp[i - 1][j - 1];\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[i][j] =\n                    Math.min(dp[i][j - 1], dp[i - 1][j], dp[i - 1][j - 1]) + 1;\n            }\n        }\n    }\n    return dp[n][m];\n}\n</code></pre> edit_distance.dart<pre><code>/* Редакционное расстояние: динамическое программирование */\nint editDistanceDP(String s, String t) {\n  int n = s.length, m = t.length;\n  List&lt;List&lt;int&gt;&gt; dp = List.generate(n + 1, (_) =&gt; List.filled(m + 1, 0));\n  // Переход состояний: первая строка и первый столбец\n  for (int i = 1; i &lt;= n; i++) {\n    dp[i][0] = i;\n  }\n  for (int j = 1; j &lt;= m; j++) {\n    dp[0][j] = j;\n  }\n  // Переход состояний: остальные строки и столбцы\n  for (int i = 1; i &lt;= n; i++) {\n    for (int j = 1; j &lt;= m; j++) {\n      if (s[i - 1] == t[j - 1]) {\n        // Если два символа равны, сразу пропустить их\n        dp[i][j] = dp[i - 1][j - 1];\n      } else {\n        // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n        dp[i][j] = min(min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;\n      }\n    }\n  }\n  return dp[n][m];\n}\n</code></pre> edit_distance.rs<pre><code>/* Редакционное расстояние: динамическое программирование */\nfn edit_distance_dp(s: &amp;str, t: &amp;str) -&gt; i32 {\n    let (n, m) = (s.len(), t.len());\n    let mut dp = vec![vec![0; m + 1]; n + 1];\n    // Переход состояний: первая строка и первый столбец\n    for i in 1..=n {\n        dp[i][0] = i as i32;\n    }\n    for j in 1..m {\n        dp[0][j] = j as i32;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for i in 1..=n {\n        for j in 1..=m {\n            if s.chars().nth(i - 1) == t.chars().nth(j - 1) {\n                // Если два символа равны, сразу пропустить их\n                dp[i][j] = dp[i - 1][j - 1];\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[i][j] =\n                    std::cmp::min(std::cmp::min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;\n            }\n        }\n    }\n    dp[n][m]\n}\n</code></pre> edit_distance.c<pre><code>/* Редакционное расстояние: динамическое программирование */\nint editDistanceDP(char *s, char *t, int n, int m) {\n    int **dp = malloc((n + 1) * sizeof(int *));\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i] = calloc(m + 1, sizeof(int));\n    }\n    // Переход состояний: первая строка и первый столбец\n    for (int i = 1; i &lt;= n; i++) {\n        dp[i][0] = i;\n    }\n    for (int j = 1; j &lt;= m; j++) {\n        dp[0][j] = j;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (int i = 1; i &lt;= n; i++) {\n        for (int j = 1; j &lt;= m; j++) {\n            if (s[i - 1] == t[j - 1]) {\n                // Если два символа равны, сразу пропустить их\n                dp[i][j] = dp[i - 1][j - 1];\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[i][j] = myMin(myMin(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;\n            }\n        }\n    }\n    int res = dp[n][m];\n    // Освободить память\n    for (int i = 0; i &lt;= n; i++) {\n        free(dp[i]);\n    }\n    return res;\n}\n</code></pre> edit_distance.kt<pre><code>/* Редакционное расстояние: динамическое программирование */\nfun editDistanceDP(s: String, t: String): Int {\n    val n = s.length\n    val m = t.length\n    val dp = Array(n + 1) { IntArray(m + 1) }\n    // Переход состояний: первая строка и первый столбец\n    for (i in 1..n) {\n        dp[i][0] = i\n    }\n    for (j in 1..m) {\n        dp[0][j] = j\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (i in 1..n) {\n        for (j in 1..m) {\n            if (s[i - 1] == t[j - 1]) {\n                // Если два символа равны, сразу пропустить их\n                dp[i][j] = dp[i - 1][j - 1]\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[i][j] = min(min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1\n            }\n        }\n    }\n    return dp[n][m]\n}\n</code></pre> edit_distance.rb<pre><code>### Редакционное расстояние: динамическое программирование ###\ndef edit_distance_dp(s, t)\n  n, m = s.length, t.length\n  dp = Array.new(n + 1) { Array.new(m + 1, 0) }\n  # Переход состояний: первая строка и первый столбец\n  (1...(n + 1)).each { |i| dp[i][0] = i }\n  (1...(m + 1)).each { |j| dp[0][j] = j }\n  # Переход состояний: остальные строки и столбцы\n  for i in 1...(n + 1)\n    for j in 1...(m +1)\n      if s[i - 1] == t[j - 1]\n        # Если два символа равны, сразу пропустить их\n        dp[i][j] = dp[i - 1][j - 1]\n      else\n        # Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n        dp[i][j] = [dp[i][j - 1], dp[i - 1][j], dp[i - 1][j - 1]].min + 1\n      end\n    end\n  end\n  dp[n][m]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Как показано на рисунке 14-30, процесс переходов состояния в задаче о расстоянии редактирования очень похож на процесс в задачах о рюкзаке: в обоих случаях это заполнение двумерной сетки.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt;&lt;13&gt;&lt;14&gt;&lt;15&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 14-30   Процесс динамического программирования для расстояния редактирования </p>","path":["Глава 14. Динамическое программирование","14.6 &nbsp; Задача о расстоянии редактирования"],"tags":[]},{"location":"chapter_dynamic_programming/edit_distance_problem/#3","level":3,"title":"3.   Оптимизация пространства","text":"<p>Поскольку \\(dp[i,j]\\) зависит от значения сверху \\(dp[i-1, j]\\) , слева \\(dp[i, j-1]\\) и слева сверху \\(dp[i-1, j-1]\\) , прямой обход после оптимизации памяти теряет значение слева сверху, а обратный обход не позволяет заранее построить значение слева \\(dp[i, j-1]\\) . Значит, оба наивных варианта обхода здесь непригодны.</p> <p>Чтобы решить эту проблему, можно использовать переменную <code>leftup</code> для временного сохранения значения слева сверху \\(dp[i-1, j-1]\\) ; после этого остается учитывать только верхнее и левое значения. Тогда ситуация становится эквивалентной задаче о полном рюкзаке, и можно выполнять прямой обход. Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby edit_distance.py<pre><code>def edit_distance_dp_comp(s: str, t: str) -&gt; int:\n    \"\"\"Редакционное расстояние: динамическое программирование с оптимизацией памяти\"\"\"\n    n, m = len(s), len(t)\n    dp = [0] * (m + 1)\n    # Переход состояний: первая строка\n    for j in range(1, m + 1):\n        dp[j] = j\n    # Переход состояний: остальные строки\n    for i in range(1, n + 1):\n        # Переход состояний: первый столбец\n        leftup = dp[0]  # Временно сохранить dp[i-1, j-1]\n        dp[0] += 1\n        # Переход состояний: остальные столбцы\n        for j in range(1, m + 1):\n            temp = dp[j]\n            if s[i - 1] == t[j - 1]:\n                # Если два символа равны, сразу пропустить их\n                dp[j] = leftup\n            else:\n                # Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[j] = min(dp[j - 1], dp[j], leftup) + 1\n            leftup = temp  # Обновить до значения dp[i-1, j-1] для следующей итерации\n    return dp[m]\n</code></pre> edit_distance.cpp<pre><code>/* Редакционное расстояние: динамическое программирование с оптимизацией памяти */\nint editDistanceDPComp(string s, string t) {\n    int n = s.length(), m = t.length();\n    vector&lt;int&gt; dp(m + 1, 0);\n    // Переход состояний: первая строка\n    for (int j = 1; j &lt;= m; j++) {\n        dp[j] = j;\n    }\n    // Переход состояний: остальные строки\n    for (int i = 1; i &lt;= n; i++) {\n        // Переход состояний: первый столбец\n        int leftup = dp[0]; // Временно сохранить dp[i-1, j-1]\n        dp[0] = i;\n        // Переход состояний: остальные столбцы\n        for (int j = 1; j &lt;= m; j++) {\n            int temp = dp[j];\n            if (s[i - 1] == t[j - 1]) {\n                // Если два символа равны, сразу пропустить их\n                dp[j] = leftup;\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[j] = min(min(dp[j - 1], dp[j]), leftup) + 1;\n            }\n            leftup = temp; // Обновить до значения dp[i-1, j-1] для следующей итерации\n        }\n    }\n    return dp[m];\n}\n</code></pre> edit_distance.java<pre><code>/* Редакционное расстояние: динамическое программирование с оптимизацией памяти */\nint editDistanceDPComp(String s, String t) {\n    int n = s.length(), m = t.length();\n    int[] dp = new int[m + 1];\n    // Переход состояний: первая строка\n    for (int j = 1; j &lt;= m; j++) {\n        dp[j] = j;\n    }\n    // Переход состояний: остальные строки\n    for (int i = 1; i &lt;= n; i++) {\n        // Переход состояний: первый столбец\n        int leftup = dp[0]; // Временно сохранить dp[i-1, j-1]\n        dp[0] = i;\n        // Переход состояний: остальные столбцы\n        for (int j = 1; j &lt;= m; j++) {\n            int temp = dp[j];\n            if (s.charAt(i - 1) == t.charAt(j - 1)) {\n                // Если два символа равны, сразу пропустить их\n                dp[j] = leftup;\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[j] = Math.min(Math.min(dp[j - 1], dp[j]), leftup) + 1;\n            }\n            leftup = temp; // Обновить до значения dp[i-1, j-1] для следующей итерации\n        }\n    }\n    return dp[m];\n}\n</code></pre> edit_distance.cs<pre><code>/* Редакционное расстояние: динамическое программирование с оптимизацией памяти */\nint EditDistanceDPComp(string s, string t) {\n    int n = s.Length, m = t.Length;\n    int[] dp = new int[m + 1];\n    // Переход состояний: первая строка\n    for (int j = 1; j &lt;= m; j++) {\n        dp[j] = j;\n    }\n    // Переход состояний: остальные строки\n    for (int i = 1; i &lt;= n; i++) {\n        // Переход состояний: первый столбец\n        int leftup = dp[0]; // Временно сохранить dp[i-1, j-1]\n        dp[0] = i;\n        // Переход состояний: остальные столбцы\n        for (int j = 1; j &lt;= m; j++) {\n            int temp = dp[j];\n            if (s[i - 1] == t[j - 1]) {\n                // Если два символа равны, сразу пропустить их\n                dp[j] = leftup;\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[j] = Math.Min(Math.Min(dp[j - 1], dp[j]), leftup) + 1;\n            }\n            leftup = temp; // Обновить до значения dp[i-1, j-1] для следующей итерации\n        }\n    }\n    return dp[m];\n}\n</code></pre> edit_distance.go<pre><code>/* Редакционное расстояние: динамическое программирование с оптимизацией памяти */\nfunc editDistanceDPComp(s string, t string) int {\n    n := len(s)\n    m := len(t)\n    dp := make([]int, m+1)\n    // Переход состояний: первая строка\n    for j := 1; j &lt;= m; j++ {\n        dp[j] = j\n    }\n    // Переход состояний: остальные строки\n    for i := 1; i &lt;= n; i++ {\n        // Переход состояний: первый столбец\n        leftUp := dp[0] // Временно сохранить dp[i-1, j-1]\n        dp[0] = i\n        // Переход состояний: остальные столбцы\n        for j := 1; j &lt;= m; j++ {\n            temp := dp[j]\n            if s[i-1] == t[j-1] {\n                // Если два символа равны, сразу пропустить их\n                dp[j] = leftUp\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[j] = MinInt(MinInt(dp[j-1], dp[j]), leftUp) + 1\n            }\n            leftUp = temp // Обновить до значения dp[i-1, j-1] для следующей итерации\n        }\n    }\n    return dp[m]\n}\n</code></pre> edit_distance.swift<pre><code>/* Редакционное расстояние: динамическое программирование с оптимизацией памяти */\nfunc editDistanceDPComp(s: String, t: String) -&gt; Int {\n    let n = s.utf8CString.count\n    let m = t.utf8CString.count\n    var dp = Array(repeating: 0, count: m + 1)\n    // Переход состояний: первая строка\n    for j in 1 ... m {\n        dp[j] = j\n    }\n    // Переход состояний: остальные строки\n    for i in 1 ... n {\n        // Переход состояний: первый столбец\n        var leftup = dp[0] // Временно сохранить dp[i-1, j-1]\n        dp[0] = i\n        // Переход состояний: остальные столбцы\n        for j in 1 ... m {\n            let temp = dp[j]\n            if s.utf8CString[i - 1] == t.utf8CString[j - 1] {\n                // Если два символа равны, сразу пропустить их\n                dp[j] = leftup\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[j] = min(min(dp[j - 1], dp[j]), leftup) + 1\n            }\n            leftup = temp // Обновить до значения dp[i-1, j-1] для следующей итерации\n        }\n    }\n    return dp[m]\n}\n</code></pre> edit_distance.js<pre><code>/* Редакционное расстояние: динамическое программирование с оптимизацией памяти */\nfunction editDistanceDPComp(s, t) {\n    const n = s.length,\n        m = t.length;\n    const dp = new Array(m + 1).fill(0);\n    // Переход состояний: первая строка\n    for (let j = 1; j &lt;= m; j++) {\n        dp[j] = j;\n    }\n    // Переход состояний: остальные строки\n    for (let i = 1; i &lt;= n; i++) {\n        // Переход состояний: первый столбец\n        let leftup = dp[0]; // Временно сохранить dp[i-1, j-1]\n        dp[0] = i;\n        // Переход состояний: остальные столбцы\n        for (let j = 1; j &lt;= m; j++) {\n            const temp = dp[j];\n            if (s.charAt(i - 1) === t.charAt(j - 1)) {\n                // Если два символа равны, сразу пропустить их\n                dp[j] = leftup;\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[j] = Math.min(dp[j - 1], dp[j], leftup) + 1;\n            }\n            leftup = temp; // Обновить до значения dp[i-1, j-1] для следующей итерации\n        }\n    }\n    return dp[m];\n}\n</code></pre> edit_distance.ts<pre><code>/* Редакционное расстояние: динамическое программирование с оптимизацией памяти */\nfunction editDistanceDPComp(s: string, t: string): number {\n    const n = s.length,\n        m = t.length;\n    const dp = new Array(m + 1).fill(0);\n    // Переход состояний: первая строка\n    for (let j = 1; j &lt;= m; j++) {\n        dp[j] = j;\n    }\n    // Переход состояний: остальные строки\n    for (let i = 1; i &lt;= n; i++) {\n        // Переход состояний: первый столбец\n        let leftup = dp[0]; // Временно сохранить dp[i-1, j-1]\n        dp[0] = i;\n        // Переход состояний: остальные столбцы\n        for (let j = 1; j &lt;= m; j++) {\n            const temp = dp[j];\n            if (s.charAt(i - 1) === t.charAt(j - 1)) {\n                // Если два символа равны, сразу пропустить их\n                dp[j] = leftup;\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[j] = Math.min(dp[j - 1], dp[j], leftup) + 1;\n            }\n            leftup = temp; // Обновить до значения dp[i-1, j-1] для следующей итерации\n        }\n    }\n    return dp[m];\n}\n</code></pre> edit_distance.dart<pre><code>/* Редакционное расстояние: динамическое программирование с оптимизацией памяти */\nint editDistanceDPComp(String s, String t) {\n  int n = s.length, m = t.length;\n  List&lt;int&gt; dp = List.filled(m + 1, 0);\n  // Переход состояний: первая строка\n  for (int j = 1; j &lt;= m; j++) {\n    dp[j] = j;\n  }\n  // Переход состояний: остальные строки\n  for (int i = 1; i &lt;= n; i++) {\n    // Переход состояний: первый столбец\n    int leftup = dp[0]; // Временно сохранить dp[i-1, j-1]\n    dp[0] = i;\n    // Переход состояний: остальные столбцы\n    for (int j = 1; j &lt;= m; j++) {\n      int temp = dp[j];\n      if (s[i - 1] == t[j - 1]) {\n        // Если два символа равны, сразу пропустить их\n        dp[j] = leftup;\n      } else {\n        // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n        dp[j] = min(min(dp[j - 1], dp[j]), leftup) + 1;\n      }\n      leftup = temp; // Обновить до значения dp[i-1, j-1] для следующей итерации\n    }\n  }\n  return dp[m];\n}\n</code></pre> edit_distance.rs<pre><code>/* Редакционное расстояние: динамическое программирование с оптимизацией памяти */\nfn edit_distance_dp_comp(s: &amp;str, t: &amp;str) -&gt; i32 {\n    let (n, m) = (s.len(), t.len());\n    let mut dp = vec![0; m + 1];\n    // Переход состояний: первая строка\n    for j in 1..m {\n        dp[j] = j as i32;\n    }\n    // Переход состояний: остальные строки\n    for i in 1..=n {\n        // Переход состояний: первый столбец\n        let mut leftup = dp[0]; // Временно сохранить dp[i-1, j-1]\n        dp[0] = i as i32;\n        // Переход состояний: остальные столбцы\n        for j in 1..=m {\n            let temp = dp[j];\n            if s.chars().nth(i - 1) == t.chars().nth(j - 1) {\n                // Если два символа равны, сразу пропустить их\n                dp[j] = leftup;\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[j] = std::cmp::min(std::cmp::min(dp[j - 1], dp[j]), leftup) + 1;\n            }\n            leftup = temp; // Обновить до значения dp[i-1, j-1] для следующей итерации\n        }\n    }\n    dp[m]\n}\n</code></pre> edit_distance.c<pre><code>/* Редакционное расстояние: динамическое программирование с оптимизацией памяти */\nint editDistanceDPComp(char *s, char *t, int n, int m) {\n    int *dp = calloc(m + 1, sizeof(int));\n    // Переход состояний: первая строка\n    for (int j = 1; j &lt;= m; j++) {\n        dp[j] = j;\n    }\n    // Переход состояний: остальные строки\n    for (int i = 1; i &lt;= n; i++) {\n        // Переход состояний: первый столбец\n        int leftup = dp[0]; // Временно сохранить dp[i-1, j-1]\n        dp[0] = i;\n        // Переход состояний: остальные столбцы\n        for (int j = 1; j &lt;= m; j++) {\n            int temp = dp[j];\n            if (s[i - 1] == t[j - 1]) {\n                // Если два символа равны, сразу пропустить их\n                dp[j] = leftup;\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[j] = myMin(myMin(dp[j - 1], dp[j]), leftup) + 1;\n            }\n            leftup = temp; // Обновить до значения dp[i-1, j-1] для следующей итерации\n        }\n    }\n    int res = dp[m];\n    // Освободить память\n    free(dp);\n    return res;\n}\n</code></pre> edit_distance.kt<pre><code>/* Редакционное расстояние: динамическое программирование с оптимизацией памяти */\nfun editDistanceDPComp(s: String, t: String): Int {\n    val n = s.length\n    val m = t.length\n    val dp = IntArray(m + 1)\n    // Переход состояний: первая строка\n    for (j in 1..m) {\n        dp[j] = j\n    }\n    // Переход состояний: остальные строки\n    for (i in 1..n) {\n        // Переход состояний: первый столбец\n        var leftup = dp[0] // Временно сохранить dp[i-1, j-1]\n        dp[0] = i\n        // Переход состояний: остальные столбцы\n        for (j in 1..m) {\n            val temp = dp[j]\n            if (s[i - 1] == t[j - 1]) {\n                // Если два символа равны, сразу пропустить их\n                dp[j] = leftup\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[j] = min(min(dp[j - 1], dp[j]), leftup) + 1\n            }\n            leftup = temp // Обновить до значения dp[i-1, j-1] для следующей итерации\n        }\n    }\n    return dp[m]\n}\n</code></pre> edit_distance.rb<pre><code>### Редакционное расстояние: динамическое программирование с оптимизацией памяти ###\ndef edit_distance_dp_comp(s, t)\n  n, m = s.length, t.length\n  dp = Array.new(m + 1, 0)\n  # Переход состояний: первая строка\n  (1...(m + 1)).each { |j| dp[j] = j }\n  # Переход состояний: остальные строки\n  for i in 1...(n + 1)\n    # Переход состояний: первый столбец\n    leftup = dp.first # Временно сохранить dp[i-1, j-1]\n    dp[0] += 1\n    # Переход состояний: остальные столбцы\n    for j in 1...(m + 1)\n      temp = dp[j]\n      if s[i - 1] == t[j - 1]\n        # Если два символа равны, сразу пропустить их\n        dp[j] = leftup\n      else\n        # Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n        dp[j] = [dp[j - 1], dp[j], leftup].min + 1\n      end\n      leftup = temp # Обновить до значения dp[i-1, j-1] для следующей итерации\n    end\n  end\n  dp[m]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 14. Динамическое программирование","14.6 &nbsp; Задача о расстоянии редактирования"],"tags":[]},{"location":"chapter_dynamic_programming/intro_to_dynamic_programming/","level":1,"title":"14.1   Первое знакомство с динамическим программированием","text":"<p>Динамическое программирование (dynamic programming) - это важная алгоритмическая парадигма, которая разбивает задачу на последовательность более мелких подзадач и за счет хранения их решений избегает повторных вычислений, тем самым резко повышая эффективность по времени.</p> <p>В этом разделе мы начнем с классического примера: сначала запишем его грубое решение через backtracking, увидим в нем перекрывающиеся подзадачи, а затем постепенно выведем более эффективное решение на основе динамического программирования.</p> <p>Подъем по лестнице</p> <p>Дана лестница из \\(n\\) ступеней. За один шаг можно подняться на \\(1\\) или на \\(2\\) ступени. Сколькими способами можно добраться до вершины?</p> <p>Как показано на рисунке 14-1, для лестницы из \\(3\\) ступеней существует \\(3\\) способа добраться до вершины.</p> <p></p> <p> Рисунок 14-1   Число способов подняться на 3-ю ступень </p> <p>Цель этой задачи - вычислить количество способов. Поэтому можно попробовать грубо перебрать все варианты с помощью backtracking. Если представить подъем по лестнице как последовательность решений, то мы начинаем от земли и на каждом раунде выбираем прыжок на \\(1\\) или на \\(2\\) ступени; всякий раз, когда достигаем вершины, увеличиваем число способов на \\(1\\) , а если перескакиваем вершину, обрезаем эту ветвь. Код выглядит так:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby climbing_stairs_backtrack.py<pre><code>def backtrack(choices: list[int], state: int, n: int, res: list[int]) -&gt; int:\n    \"\"\"Бэктрекинг\"\"\"\n    # Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n    if state == n:\n        res[0] += 1\n    # Перебор всех вариантов выбора\n    for choice in choices:\n        # Отсечение: нельзя выходить за n-ю ступень\n        if state + choice &gt; n:\n            continue\n        # Попытка: сделать выбор и обновить состояние\n        backtrack(choices, state + choice, n, res)\n        # Откат\n\ndef climbing_stairs_backtrack(n: int) -&gt; int:\n    \"\"\"Подъем по лестнице: бэктрекинг\"\"\"\n    choices = [1, 2]  # Можно подняться на 1 или 2 ступени\n    state = 0  # Начать подъем с 0-й ступени\n    res = [0]  # Использовать res[0] для хранения числа решений\n    backtrack(choices, state, n, res)\n    return res[0]\n</code></pre> climbing_stairs_backtrack.cpp<pre><code>/* Бэктрекинг */\nvoid backtrack(vector&lt;int&gt; &amp;choices, int state, int n, vector&lt;int&gt; &amp;res) {\n    // Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n    if (state == n)\n        res[0]++;\n    // Перебор всех вариантов выбора\n    for (auto &amp;choice : choices) {\n        // Отсечение: нельзя выходить за n-ю ступень\n        if (state + choice &gt; n)\n            continue;\n        // Попытка: сделать выбор и обновить состояние\n        backtrack(choices, state + choice, n, res);\n        // Откат\n    }\n}\n\n/* Подъем по лестнице: бэктрекинг */\nint climbingStairsBacktrack(int n) {\n    vector&lt;int&gt; choices = {1, 2}; // Можно подняться на 1 или 2 ступени\n    int state = 0;                // Начать подъем с 0-й ступени\n    vector&lt;int&gt; res = {0};        // Использовать res[0] для хранения числа решений\n    backtrack(choices, state, n, res);\n    return res[0];\n}\n</code></pre> climbing_stairs_backtrack.java<pre><code>/* Бэктрекинг */\nvoid backtrack(List&lt;Integer&gt; choices, int state, int n, List&lt;Integer&gt; res) {\n    // Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n    if (state == n)\n        res.set(0, res.get(0) + 1);\n    // Перебор всех вариантов выбора\n    for (Integer choice : choices) {\n        // Отсечение: нельзя выходить за n-ю ступень\n        if (state + choice &gt; n)\n            continue;\n        // Попытка: сделать выбор и обновить состояние\n        backtrack(choices, state + choice, n, res);\n        // Откат\n    }\n}\n\n/* Подъем по лестнице: бэктрекинг */\nint climbingStairsBacktrack(int n) {\n    List&lt;Integer&gt; choices = Arrays.asList(1, 2); // Можно подняться на 1 или 2 ступени\n    int state = 0; // Начать подъем с 0-й ступени\n    List&lt;Integer&gt; res = new ArrayList&lt;&gt;();\n    res.add(0); // Использовать res[0] для хранения числа решений\n    backtrack(choices, state, n, res);\n    return res.get(0);\n}\n</code></pre> climbing_stairs_backtrack.cs<pre><code>/* Бэктрекинг */\nvoid Backtrack(List&lt;int&gt; choices, int state, int n, List&lt;int&gt; res) {\n    // Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n    if (state == n)\n        res[0]++;\n    // Перебор всех вариантов выбора\n    foreach (int choice in choices) {\n        // Отсечение: нельзя выходить за n-ю ступень\n        if (state + choice &gt; n)\n            continue;\n        // Попытка: сделать выбор и обновить состояние\n        Backtrack(choices, state + choice, n, res);\n        // Откат\n    }\n}\n\n/* Подъем по лестнице: бэктрекинг */\nint ClimbingStairsBacktrack(int n) {\n    List&lt;int&gt; choices = [1, 2]; // Можно подняться на 1 или 2 ступени\n    int state = 0; // Начать подъем с 0-й ступени\n    List&lt;int&gt; res = [0]; // Использовать res[0] для хранения числа решений\n    Backtrack(choices, state, n, res);\n    return res[0];\n}\n</code></pre> climbing_stairs_backtrack.go<pre><code>/* Бэктрекинг */\nfunc backtrack(choices []int, state, n int, res []int) {\n    // Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n    if state == n {\n        res[0] = res[0] + 1\n    }\n    // Перебор всех вариантов выбора\n    for _, choice := range choices {\n        // Отсечение: нельзя выходить за n-ю ступень\n        if state+choice &gt; n {\n            continue\n        }\n        // Попытка: сделать выбор и обновить состояние\n        backtrack(choices, state+choice, n, res)\n        // Откат\n    }\n}\n\n/* Подъем по лестнице: бэктрекинг */\nfunc climbingStairsBacktrack(n int) int {\n    // Можно подняться на 1 или 2 ступени\n    choices := []int{1, 2}\n    // Начать подъем с 0-й ступени\n    state := 0\n    res := make([]int, 1)\n    // Использовать res[0] для хранения числа решений\n    res[0] = 0\n    backtrack(choices, state, n, res)\n    return res[0]\n}\n</code></pre> climbing_stairs_backtrack.swift<pre><code>/* Бэктрекинг */\nfunc backtrack(choices: [Int], state: Int, n: Int, res: inout [Int]) {\n    // Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n    if state == n {\n        res[0] += 1\n    }\n    // Перебор всех вариантов выбора\n    for choice in choices {\n        // Отсечение: нельзя выходить за n-ю ступень\n        if state + choice &gt; n {\n            continue\n        }\n        // Попытка: сделать выбор и обновить состояние\n        backtrack(choices: choices, state: state + choice, n: n, res: &amp;res)\n        // Откат\n    }\n}\n\n/* Подъем по лестнице: бэктрекинг */\nfunc climbingStairsBacktrack(n: Int) -&gt; Int {\n    let choices = [1, 2] // Можно подняться на 1 или 2 ступени\n    let state = 0 // Начать подъем с 0-й ступени\n    var res: [Int] = []\n    res.append(0) // Использовать res[0] для хранения числа решений\n    backtrack(choices: choices, state: state, n: n, res: &amp;res)\n    return res[0]\n}\n</code></pre> climbing_stairs_backtrack.js<pre><code>/* Бэктрекинг */\nfunction backtrack(choices, state, n, res) {\n    // Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n    if (state === n) res.set(0, res.get(0) + 1);\n    // Перебор всех вариантов выбора\n    for (const choice of choices) {\n        // Отсечение: нельзя выходить за n-ю ступень\n        if (state + choice &gt; n) continue;\n        // Попытка: сделать выбор и обновить состояние\n        backtrack(choices, state + choice, n, res);\n        // Откат\n    }\n}\n\n/* Подъем по лестнице: бэктрекинг */\nfunction climbingStairsBacktrack(n) {\n    const choices = [1, 2]; // Можно подняться на 1 или 2 ступени\n    const state = 0; // Начать подъем с 0-й ступени\n    const res = new Map();\n    res.set(0, 0); // Использовать res[0] для хранения числа решений\n    backtrack(choices, state, n, res);\n    return res.get(0);\n}\n</code></pre> climbing_stairs_backtrack.ts<pre><code>/* Бэктрекинг */\nfunction backtrack(\n    choices: number[],\n    state: number,\n    n: number,\n    res: Map&lt;0, any&gt;\n): void {\n    // Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n    if (state === n) res.set(0, res.get(0) + 1);\n    // Перебор всех вариантов выбора\n    for (const choice of choices) {\n        // Отсечение: нельзя выходить за n-ю ступень\n        if (state + choice &gt; n) continue;\n        // Попытка: сделать выбор и обновить состояние\n        backtrack(choices, state + choice, n, res);\n        // Откат\n    }\n}\n\n/* Подъем по лестнице: бэктрекинг */\nfunction climbingStairsBacktrack(n: number): number {\n    const choices = [1, 2]; // Можно подняться на 1 или 2 ступени\n    const state = 0; // Начать подъем с 0-й ступени\n    const res = new Map();\n    res.set(0, 0); // Использовать res[0] для хранения числа решений\n    backtrack(choices, state, n, res);\n    return res.get(0);\n}\n</code></pre> climbing_stairs_backtrack.dart<pre><code>/* Бэктрекинг */\nvoid backtrack(List&lt;int&gt; choices, int state, int n, List&lt;int&gt; res) {\n  // Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n  if (state == n) {\n    res[0]++;\n  }\n  // Перебор всех вариантов выбора\n  for (int choice in choices) {\n    // Отсечение: нельзя выходить за n-ю ступень\n    if (state + choice &gt; n) continue;\n    // Попытка: сделать выбор и обновить состояние\n    backtrack(choices, state + choice, n, res);\n    // Откат\n  }\n}\n\n/* Подъем по лестнице: бэктрекинг */\nint climbingStairsBacktrack(int n) {\n  List&lt;int&gt; choices = [1, 2]; // Можно подняться на 1 или 2 ступени\n  int state = 0; // Начать подъем с 0-й ступени\n  List&lt;int&gt; res = [];\n  res.add(0); // Использовать res[0] для хранения числа решений\n  backtrack(choices, state, n, res);\n  return res[0];\n}\n</code></pre> climbing_stairs_backtrack.rs<pre><code>/* Бэктрекинг */\nfn backtrack(choices: &amp;[i32], state: i32, n: i32, res: &amp;mut [i32]) {\n    // Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n    if state == n {\n        res[0] = res[0] + 1;\n    }\n    // Перебор всех вариантов выбора\n    for &amp;choice in choices {\n        // Отсечение: нельзя выходить за n-ю ступень\n        if state + choice &gt; n {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить состояние\n        backtrack(choices, state + choice, n, res);\n        // Откат\n    }\n}\n\n/* Подъем по лестнице: бэктрекинг */\nfn climbing_stairs_backtrack(n: usize) -&gt; i32 {\n    let choices = vec![1, 2]; // Можно подняться на 1 или 2 ступени\n    let state = 0; // Начать подъем с 0-й ступени\n    let mut res = Vec::new();\n    res.push(0); // Использовать res[0] для хранения числа решений\n    backtrack(&amp;choices, state, n as i32, &amp;mut res);\n    res[0]\n}\n</code></pre> climbing_stairs_backtrack.c<pre><code>/* Бэктрекинг */\nvoid backtrack(int *choices, int state, int n, int *res, int len) {\n    // Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n    if (state == n)\n        res[0]++;\n    // Перебор всех вариантов выбора\n    for (int i = 0; i &lt; len; i++) {\n        int choice = choices[i];\n        // Отсечение: нельзя выходить за n-ю ступень\n        if (state + choice &gt; n)\n            continue;\n        // Попытка: сделать выбор и обновить состояние\n        backtrack(choices, state + choice, n, res, len);\n        // Откат\n    }\n}\n\n/* Подъем по лестнице: бэктрекинг */\nint climbingStairsBacktrack(int n) {\n    int choices[2] = {1, 2}; // Можно подняться на 1 или 2 ступени\n    int state = 0;           // Начать подъем с 0-й ступени\n    int *res = (int *)malloc(sizeof(int));\n    *res = 0; // Использовать res[0] для хранения числа решений\n    int len = sizeof(choices) / sizeof(int);\n    backtrack(choices, state, n, res, len);\n    int result = *res;\n    free(res);\n    return result;\n}\n</code></pre> climbing_stairs_backtrack.kt<pre><code>/* Бэктрекинг */\nfun backtrack(\n    choices: MutableList&lt;Int&gt;,\n    state: Int,\n    n: Int,\n    res: MutableList&lt;Int&gt;\n) {\n    // Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n    if (state == n)\n        res[0] = res[0] + 1\n    // Перебор всех вариантов выбора\n    for (choice in choices) {\n        // Отсечение: нельзя выходить за n-ю ступень\n        if (state + choice &gt; n) continue\n        // Попытка: сделать выбор и обновить состояние\n        backtrack(choices, state + choice, n, res)\n        // Откат\n    }\n}\n\n/* Подъем по лестнице: бэктрекинг */\nfun climbingStairsBacktrack(n: Int): Int {\n    val choices = mutableListOf(1, 2) // Можно подняться на 1 или 2 ступени\n    val state = 0 // Начать подъем с 0-й ступени\n    val res = mutableListOf&lt;Int&gt;()\n    res.add(0) // Использовать res[0] для хранения числа решений\n    backtrack(choices, state, n, res)\n    return res[0]\n}\n</code></pre> climbing_stairs_backtrack.rb<pre><code>### Бэктрекинг ###\ndef backtrack(choices, state, n, res)\n  # Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n  res[0] += 1 if state == n\n  # Перебор всех вариантов выбора\n  for choice in choices\n    # Отсечение: нельзя выходить за n-ю ступень\n    next if state + choice &gt; n\n\n    # Попытка: сделать выбор и обновить состояние\n    backtrack(choices, state + choice, n, res)\n  end\n  # Откат\nend\n\n### Подъем по лестнице: бэктрекинг ###\ndef climbing_stairs_backtrack(n)\n  choices = [1, 2] # Можно подняться на 1 или 2 ступени\n  state = 0 # Начать подъем с 0-й ступени\n  res = [0] # Использовать res[0] для хранения числа решений\n  backtrack(choices, state, n, res)\n  res.first\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 14. Динамическое программирование","14.1 &nbsp; Первое знакомство с динамическим программированием"],"tags":[]},{"location":"chapter_dynamic_programming/intro_to_dynamic_programming/#1411-1","level":2,"title":"14.1.1   Метод 1: полный перебор","text":"<p>Backtracking обычно не раскладывает задачу явно на подзадачи; вместо этого он рассматривает решение как последовательность решений, используя попытки и обрезку для поиска всех возможных ответов.</p> <p>Попробуем посмотреть на задачу именно как на разложение подзадач. Пусть число способов добраться до ступени \\(i\\) равно \\(dp[i]\\) ; тогда \\(dp[i]\\) - это исходная задача, а ее подзадачи включают:</p> \\[ dp[i-1], dp[i-2], \\dots, dp[2], dp[1] \\] <p>Поскольку за один раунд можно подняться только на \\(1\\) или на \\(2\\) ступени, стоя на ступени \\(i\\) , в предыдущий раунд мы могли находиться только на ступени \\(i - 1\\) или на ступени \\(i - 2\\) . Иначе говоря, на ступень \\(i\\) можно попасть только со ступени \\(i -1\\) или со ступени \\(i - 2\\) .</p> <p>Отсюда получается важный вывод: число способов добраться до ступени \\(i - 1\\) плюс число способов добраться до ступени \\(i - 2\\) равно числу способов добраться до ступени \\(i\\). Формула имеет вид:</p> \\[ dp[i] = dp[i-1] + dp[i-2] \\] <p>Это означает, что в задаче о подъеме по лестнице между подзадачами существует рекуррентная зависимость, и решение исходной задачи может быть построено на основе решений подзадач. Эта связь показана на рисунке 14-2.</p> <p></p> <p> Рисунок 14-2   Рекуррентная связь числа способов </p> <p>По рекуррентной формуле можно получить решение полного перебора. Начиная с \\(dp[n]\\) , мы рекурсивно разлагаем большую задачу в сумму двух меньших задач , пока не дойдем до наименьших подзадач \\(dp[1]\\) и \\(dp[2]\\) . Их решения уже известны: \\(dp[1] = 1\\) и \\(dp[2] = 2\\) , что означает \\(1\\) и \\(2\\) способа подняться соответственно на \\(1\\)-ю и \\(2\\)-ю ступени.</p> <p>Посмотрите на следующий код: как и стандартный backtracking, он относится к поиску в глубину, но выглядит более компактно:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby climbing_stairs_dfs.py<pre><code>def dfs(i: int) -&gt; int:\n    \"\"\"Поиск\"\"\"\n    # dp[1] и dp[2] уже известны, вернуть их\n    if i == 1 or i == 2:\n        return i\n    # dp[i] = dp[i-1] + dp[i-2]\n    count = dfs(i - 1) + dfs(i - 2)\n    return count\n\ndef climbing_stairs_dfs(n: int) -&gt; int:\n    \"\"\"Подъем по лестнице: поиск\"\"\"\n    return dfs(n)\n</code></pre> climbing_stairs_dfs.cpp<pre><code>/* Поиск */\nint dfs(int i) {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i == 1 || i == 2)\n        return i;\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1) + dfs(i - 2);\n    return count;\n}\n\n/* Подъем по лестнице: поиск */\nint climbingStairsDFS(int n) {\n    return dfs(n);\n}\n</code></pre> climbing_stairs_dfs.java<pre><code>/* Поиск */\nint dfs(int i) {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i == 1 || i == 2)\n        return i;\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1) + dfs(i - 2);\n    return count;\n}\n\n/* Подъем по лестнице: поиск */\nint climbingStairsDFS(int n) {\n    return dfs(n);\n}\n</code></pre> climbing_stairs_dfs.cs<pre><code>/* Поиск */\nint DFS(int i) {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i == 1 || i == 2)\n        return i;\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = DFS(i - 1) + DFS(i - 2);\n    return count;\n}\n\n/* Подъем по лестнице: поиск */\nint ClimbingStairsDFS(int n) {\n    return DFS(n);\n}\n</code></pre> climbing_stairs_dfs.go<pre><code>/* Поиск */\nfunc dfs(i int) int {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if i == 1 || i == 2 {\n        return i\n    }\n    // dp[i] = dp[i-1] + dp[i-2]\n    count := dfs(i-1) + dfs(i-2)\n    return count\n}\n\n/* Подъем по лестнице: поиск */\nfunc climbingStairsDFS(n int) int {\n    return dfs(n)\n}\n</code></pre> climbing_stairs_dfs.swift<pre><code>/* Поиск */\nfunc dfs(i: Int) -&gt; Int {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if i == 1 || i == 2 {\n        return i\n    }\n    // dp[i] = dp[i-1] + dp[i-2]\n    let count = dfs(i: i - 1) + dfs(i: i - 2)\n    return count\n}\n\n/* Подъем по лестнице: поиск */\nfunc climbingStairsDFS(n: Int) -&gt; Int {\n    dfs(i: n)\n}\n</code></pre> climbing_stairs_dfs.js<pre><code>/* Поиск */\nfunction dfs(i) {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i === 1 || i === 2) return i;\n    // dp[i] = dp[i-1] + dp[i-2]\n    const count = dfs(i - 1) + dfs(i - 2);\n    return count;\n}\n\n/* Подъем по лестнице: поиск */\nfunction climbingStairsDFS(n) {\n    return dfs(n);\n}\n</code></pre> climbing_stairs_dfs.ts<pre><code>/* Поиск */\nfunction dfs(i: number): number {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i === 1 || i === 2) return i;\n    // dp[i] = dp[i-1] + dp[i-2]\n    const count = dfs(i - 1) + dfs(i - 2);\n    return count;\n}\n\n/* Подъем по лестнице: поиск */\nfunction climbingStairsDFS(n: number): number {\n    return dfs(n);\n}\n</code></pre> climbing_stairs_dfs.dart<pre><code>/* Поиск */\nint dfs(int i) {\n  // dp[1] и dp[2] уже известны, вернуть их\n  if (i == 1 || i == 2) return i;\n  // dp[i] = dp[i-1] + dp[i-2]\n  int count = dfs(i - 1) + dfs(i - 2);\n  return count;\n}\n\n/* Подъем по лестнице: поиск */\nint climbingStairsDFS(int n) {\n  return dfs(n);\n}\n</code></pre> climbing_stairs_dfs.rs<pre><code>/* Поиск */\nfn dfs(i: usize) -&gt; i32 {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if i == 1 || i == 2 {\n        return i as i32;\n    }\n    // dp[i] = dp[i-1] + dp[i-2]\n    let count = dfs(i - 1) + dfs(i - 2);\n    count\n}\n\n/* Подъем по лестнице: поиск */\nfn climbing_stairs_dfs(n: usize) -&gt; i32 {\n    dfs(n)\n}\n</code></pre> climbing_stairs_dfs.c<pre><code>/* Поиск */\nint dfs(int i) {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i == 1 || i == 2)\n        return i;\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1) + dfs(i - 2);\n    return count;\n}\n\n/* Подъем по лестнице: поиск */\nint climbingStairsDFS(int n) {\n    return dfs(n);\n}\n</code></pre> climbing_stairs_dfs.kt<pre><code>/* Поиск */\nfun dfs(i: Int): Int {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i == 1 || i == 2) return i\n    // dp[i] = dp[i-1] + dp[i-2]\n    val count = dfs(i - 1) + dfs(i - 2)\n    return count\n}\n\n/* Подъем по лестнице: поиск */\nfun climbingStairsDFS(n: Int): Int {\n    return dfs(n)\n}\n</code></pre> climbing_stairs_dfs.rb<pre><code>### Поиск ###\ndef dfs(i)\n  # dp[1] и dp[2] уже известны, вернуть их\n  return i if i == 1 || i == 2\n  # dp[i] = dp[i-1] + dp[i-2]\n  dfs(i - 1) + dfs(i - 2)\nend\n\n### Подъем по лестнице: поиск ###\ndef climbing_stairs_dfs(n)\n  dfs(n)\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>На рисунке 14-3 показано дерево рекурсии, возникающее при полном переборе. Для задачи \\(dp[n]\\) глубина дерева рекурсии равна \\(n\\) , а временная сложность равна \\(O(2^n)\\) . Экспоненциальный рост взрывообразен: если подать на вход достаточно большое значение \\(n\\) , ожидание станет очень долгим.</p> <p></p> <p> Рисунок 14-3   Дерево рекурсии для подъема по лестнице </p> <p>Если посмотреть на рисунок 14-3, то видно, что экспоненциальная временная сложность порождается \"перекрывающимися подзадачами\". Например, \\(dp[9]\\) раскладывается в \\(dp[8]\\) и \\(dp[7]\\) , а \\(dp[8]\\) - в \\(dp[7]\\) и \\(dp[6]\\) ; обе ветви содержат подзадачу \\(dp[7]\\) .</p> <p>Продолжая это рассуждение, мы видим, что подзадачи порождают все более мелкие перекрывающиеся подзадачи без конца. Подавляющая часть вычислительных ресурсов уходит именно на них.</p>","path":["Глава 14. Динамическое программирование","14.1 &nbsp; Первое знакомство с динамическим программированием"],"tags":[]},{"location":"chapter_dynamic_programming/intro_to_dynamic_programming/#1412-2","level":2,"title":"14.1.2   Метод 2: поиск с мемоизацией","text":"<p>Чтобы ускорить алгоритм, мы хотим, чтобы каждая перекрывающаяся подзадача вычислялась только один раз. Для этого объявим массив <code>mem</code> для хранения решения каждой подзадачи и будем обрезать повторные вычисления в процессе поиска.</p> <ol> <li>Когда \\(dp[i]\\) вычисляется впервые, мы сохраняем его в <code>mem[i]</code> для последующего использования.</li> <li>Когда значение \\(dp[i]\\) требуется снова, мы просто берем его напрямую из <code>mem[i]</code> и тем самым избегаем повторного вычисления подзадачи.</li> </ol> <p>Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby climbing_stairs_dfs_mem.py<pre><code>def dfs(i: int, mem: list[int]) -&gt; int:\n    \"\"\"Поиск с мемоизацией\"\"\"\n    # dp[1] и dp[2] уже известны, вернуть их\n    if i == 1 or i == 2:\n        return i\n    # Если запись dp[i] существует, сразу вернуть ее\n    if mem[i] != -1:\n        return mem[i]\n    # dp[i] = dp[i-1] + dp[i-2]\n    count = dfs(i - 1, mem) + dfs(i - 2, mem)\n    # Сохранить dp[i]\n    mem[i] = count\n    return count\n\ndef climbing_stairs_dfs_mem(n: int) -&gt; int:\n    \"\"\"Подъем по лестнице: поиск с мемоизацией\"\"\"\n    # mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n    mem = [-1] * (n + 1)\n    return dfs(n, mem)\n</code></pre> climbing_stairs_dfs_mem.cpp<pre><code>/* Поиск с мемоизацией */\nint dfs(int i, vector&lt;int&gt; &amp;mem) {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i == 1 || i == 2)\n        return i;\n    // Если запись dp[i] существует, сразу вернуть ее\n    if (mem[i] != -1)\n        return mem[i];\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1, mem) + dfs(i - 2, mem);\n    // Сохранить dp[i]\n    mem[i] = count;\n    return count;\n}\n\n/* Подъем по лестнице: поиск с мемоизацией */\nint climbingStairsDFSMem(int n) {\n    // mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n    vector&lt;int&gt; mem(n + 1, -1);\n    return dfs(n, mem);\n}\n</code></pre> climbing_stairs_dfs_mem.java<pre><code>/* Поиск с мемоизацией */\nint dfs(int i, int[] mem) {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i == 1 || i == 2)\n        return i;\n    // Если запись dp[i] существует, сразу вернуть ее\n    if (mem[i] != -1)\n        return mem[i];\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1, mem) + dfs(i - 2, mem);\n    // Сохранить dp[i]\n    mem[i] = count;\n    return count;\n}\n\n/* Подъем по лестнице: поиск с мемоизацией */\nint climbingStairsDFSMem(int n) {\n    // mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n    int[] mem = new int[n + 1];\n    Arrays.fill(mem, -1);\n    return dfs(n, mem);\n}\n</code></pre> climbing_stairs_dfs_mem.cs<pre><code>/* Поиск с мемоизацией */\nint DFS(int i, int[] mem) {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i == 1 || i == 2)\n        return i;\n    // Если запись dp[i] существует, сразу вернуть ее\n    if (mem[i] != -1)\n        return mem[i];\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = DFS(i - 1, mem) + DFS(i - 2, mem);\n    // Сохранить dp[i]\n    mem[i] = count;\n    return count;\n}\n\n/* Подъем по лестнице: поиск с мемоизацией */\nint ClimbingStairsDFSMem(int n) {\n    // mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n    int[] mem = new int[n + 1];\n    Array.Fill(mem, -1);\n    return DFS(n, mem);\n}\n</code></pre> climbing_stairs_dfs_mem.go<pre><code>/* Поиск с мемоизацией */\nfunc dfsMem(i int, mem []int) int {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if i == 1 || i == 2 {\n        return i\n    }\n    // Если запись dp[i] существует, сразу вернуть ее\n    if mem[i] != -1 {\n        return mem[i]\n    }\n    // dp[i] = dp[i-1] + dp[i-2]\n    count := dfsMem(i-1, mem) + dfsMem(i-2, mem)\n    // Сохранить dp[i]\n    mem[i] = count\n    return count\n}\n\n/* Подъем по лестнице: поиск с мемоизацией */\nfunc climbingStairsDFSMem(n int) int {\n    // mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n    mem := make([]int, n+1)\n    for i := range mem {\n        mem[i] = -1\n    }\n    return dfsMem(n, mem)\n}\n</code></pre> climbing_stairs_dfs_mem.swift<pre><code>/* Поиск с мемоизацией */\nfunc dfs(i: Int, mem: inout [Int]) -&gt; Int {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if i == 1 || i == 2 {\n        return i\n    }\n    // Если запись dp[i] существует, сразу вернуть ее\n    if mem[i] != -1 {\n        return mem[i]\n    }\n    // dp[i] = dp[i-1] + dp[i-2]\n    let count = dfs(i: i - 1, mem: &amp;mem) + dfs(i: i - 2, mem: &amp;mem)\n    // Сохранить dp[i]\n    mem[i] = count\n    return count\n}\n\n/* Подъем по лестнице: поиск с мемоизацией */\nfunc climbingStairsDFSMem(n: Int) -&gt; Int {\n    // mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n    var mem = Array(repeating: -1, count: n + 1)\n    return dfs(i: n, mem: &amp;mem)\n}\n</code></pre> climbing_stairs_dfs_mem.js<pre><code>/* Поиск с мемоизацией */\nfunction dfs(i, mem) {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i === 1 || i === 2) return i;\n    // Если запись dp[i] существует, сразу вернуть ее\n    if (mem[i] != -1) return mem[i];\n    // dp[i] = dp[i-1] + dp[i-2]\n    const count = dfs(i - 1, mem) + dfs(i - 2, mem);\n    // Сохранить dp[i]\n    mem[i] = count;\n    return count;\n}\n\n/* Подъем по лестнице: поиск с мемоизацией */\nfunction climbingStairsDFSMem(n) {\n    // mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n    const mem = new Array(n + 1).fill(-1);\n    return dfs(n, mem);\n}\n</code></pre> climbing_stairs_dfs_mem.ts<pre><code>/* Поиск с мемоизацией */\nfunction dfs(i: number, mem: number[]): number {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i === 1 || i === 2) return i;\n    // Если запись dp[i] существует, сразу вернуть ее\n    if (mem[i] != -1) return mem[i];\n    // dp[i] = dp[i-1] + dp[i-2]\n    const count = dfs(i - 1, mem) + dfs(i - 2, mem);\n    // Сохранить dp[i]\n    mem[i] = count;\n    return count;\n}\n\n/* Подъем по лестнице: поиск с мемоизацией */\nfunction climbingStairsDFSMem(n: number): number {\n    // mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n    const mem = new Array(n + 1).fill(-1);\n    return dfs(n, mem);\n}\n</code></pre> climbing_stairs_dfs_mem.dart<pre><code>/* Поиск с мемоизацией */\nint dfs(int i, List&lt;int&gt; mem) {\n  // dp[1] и dp[2] уже известны, вернуть их\n  if (i == 1 || i == 2) return i;\n  // Если запись dp[i] существует, сразу вернуть ее\n  if (mem[i] != -1) return mem[i];\n  // dp[i] = dp[i-1] + dp[i-2]\n  int count = dfs(i - 1, mem) + dfs(i - 2, mem);\n  // Сохранить dp[i]\n  mem[i] = count;\n  return count;\n}\n\n/* Подъем по лестнице: поиск с мемоизацией */\nint climbingStairsDFSMem(int n) {\n  // mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n  List&lt;int&gt; mem = List.filled(n + 1, -1);\n  return dfs(n, mem);\n}\n</code></pre> climbing_stairs_dfs_mem.rs<pre><code>/* Поиск с мемоизацией */\nfn dfs(i: usize, mem: &amp;mut [i32]) -&gt; i32 {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if i == 1 || i == 2 {\n        return i as i32;\n    }\n    // Если запись dp[i] существует, сразу вернуть ее\n    if mem[i] != -1 {\n        return mem[i];\n    }\n    // dp[i] = dp[i-1] + dp[i-2]\n    let count = dfs(i - 1, mem) + dfs(i - 2, mem);\n    // Сохранить dp[i]\n    mem[i] = count;\n    count\n}\n\n/* Подъем по лестнице: поиск с мемоизацией */\nfn climbing_stairs_dfs_mem(n: usize) -&gt; i32 {\n    // mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n    let mut mem = vec![-1; n + 1];\n    dfs(n, &amp;mut mem)\n}\n</code></pre> climbing_stairs_dfs_mem.c<pre><code>/* Поиск с мемоизацией */\nint dfs(int i, int *mem) {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i == 1 || i == 2)\n        return i;\n    // Если запись dp[i] существует, сразу вернуть ее\n    if (mem[i] != -1)\n        return mem[i];\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1, mem) + dfs(i - 2, mem);\n    // Сохранить dp[i]\n    mem[i] = count;\n    return count;\n}\n\n/* Подъем по лестнице: поиск с мемоизацией */\nint climbingStairsDFSMem(int n) {\n    // mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n    int *mem = (int *)malloc((n + 1) * sizeof(int));\n    for (int i = 0; i &lt;= n; i++) {\n        mem[i] = -1;\n    }\n    int result = dfs(n, mem);\n    free(mem);\n    return result;\n}\n</code></pre> climbing_stairs_dfs_mem.kt<pre><code>/* Поиск с мемоизацией */\nfun dfs(i: Int, mem: IntArray): Int {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i == 1 || i == 2) return i\n    // Если запись dp[i] существует, сразу вернуть ее\n    if (mem[i] != -1) return mem[i]\n    // dp[i] = dp[i-1] + dp[i-2]\n    val count = dfs(i - 1, mem) + dfs(i - 2, mem)\n    // Сохранить dp[i]\n    mem[i] = count\n    return count\n}\n\n/* Подъем по лестнице: поиск с мемоизацией */\nfun climbingStairsDFSMem(n: Int): Int {\n    // mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n    val mem = IntArray(n + 1)\n    mem.fill(-1)\n    return dfs(n, mem)\n}\n</code></pre> climbing_stairs_dfs_mem.rb<pre><code>### Поиск с мемоизацией ###\ndef dfs(i, mem)\n  # dp[1] и dp[2] уже известны, вернуть их\n  return i if i == 1 || i == 2\n  # Если запись dp[i] существует, сразу вернуть ее\n  return mem[i] if mem[i] != -1\n\n  # dp[i] = dp[i-1] + dp[i-2]\n  count = dfs(i - 1, mem) + dfs(i - 2, mem)\n  # Сохранить dp[i]\n  mem[i] = count\nend\n\n### Подъем по лестнице: поиск с мемоизацией ###\ndef climbing_stairs_dfs_mem(n)\n  # mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n  mem = Array.new(n + 1, -1)\n  dfs(n, mem)\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Как показано на рисунке 14-4, после введения мемоизации каждая перекрывающаяся подзадача вычисляется только один раз, и временная сложность оптимизируется до \\(O(n)\\) . Это огромный скачок в эффективности.</p> <p></p> <p> Рисунок 14-4   Дерево рекурсии для поиска с мемоизацией </p>","path":["Глава 14. Динамическое программирование","14.1 &nbsp; Первое знакомство с динамическим программированием"],"tags":[]},{"location":"chapter_dynamic_programming/intro_to_dynamic_programming/#1413-3","level":2,"title":"14.1.3   Метод 3: динамическое программирование","text":"<p>Поиск с мемоизацией - это метод \"сверху вниз\" : мы начинаем с исходной задачи (корня), рекурсивно раскладываем более крупные подзадачи на меньшие, пока не достигнем наименьших подзадач с уже известным ответом (листьев). Затем в процессе возврата постепенно собираем решения подзадач и тем самым получаем решение исходной задачи.</p> <p>Напротив, динамическое программирование - это метод \"снизу вверх\" : начиная с решений наименьших подзадач, мы итеративно строим решения для более крупных подзадач, пока не получим ответ на исходную задачу.</p> <p>Поскольку в динамическом программировании нет этапа возврата, для его реализации достаточно обычных циклов, без рекурсии. В приведенном ниже коде мы инициализируем массив <code>dp</code> для хранения решений подзадач; он выполняет ту же роль, что и массив <code>mem</code> в мемоизированном поиске:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby climbing_stairs_dp.py<pre><code>def climbing_stairs_dp(n: int) -&gt; int:\n    \"\"\"Подъем по лестнице: динамическое программирование\"\"\"\n    if n == 1 or n == 2:\n        return n\n    # Инициализация таблицы dp для хранения решений подзадач\n    dp = [0] * (n + 1)\n    # Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1], dp[2] = 1, 2\n    # Переход состояний: постепенное решение больших подзадач через меньшие\n    for i in range(3, n + 1):\n        dp[i] = dp[i - 1] + dp[i - 2]\n    return dp[n]\n</code></pre> climbing_stairs_dp.cpp<pre><code>/* Подъем по лестнице: динамическое программирование */\nint climbingStairsDP(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    // Инициализация таблицы dp для хранения решений подзадач\n    vector&lt;int&gt; dp(n + 1);\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = 1;\n    dp[2] = 2;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    return dp[n];\n}\n</code></pre> climbing_stairs_dp.java<pre><code>/* Подъем по лестнице: динамическое программирование */\nint climbingStairsDP(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    // Инициализация таблицы dp для хранения решений подзадач\n    int[] dp = new int[n + 1];\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = 1;\n    dp[2] = 2;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    return dp[n];\n}\n</code></pre> climbing_stairs_dp.cs<pre><code>/* Подъем по лестнице: динамическое программирование */\nint ClimbingStairsDP(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    // Инициализация таблицы dp для хранения решений подзадач\n    int[] dp = new int[n + 1];\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = 1;\n    dp[2] = 2;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    return dp[n];\n}\n</code></pre> climbing_stairs_dp.go<pre><code>/* Подъем по лестнице: динамическое программирование */\nfunc climbingStairsDP(n int) int {\n    if n == 1 || n == 2 {\n        return n\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    dp := make([]int, n+1)\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = 1\n    dp[2] = 2\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for i := 3; i &lt;= n; i++ {\n        dp[i] = dp[i-1] + dp[i-2]\n    }\n    return dp[n]\n}\n</code></pre> climbing_stairs_dp.swift<pre><code>/* Подъем по лестнице: динамическое программирование */\nfunc climbingStairsDP(n: Int) -&gt; Int {\n    if n == 1 || n == 2 {\n        return n\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    var dp = Array(repeating: 0, count: n + 1)\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = 1\n    dp[2] = 2\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for i in 3 ... n {\n        dp[i] = dp[i - 1] + dp[i - 2]\n    }\n    return dp[n]\n}\n</code></pre> climbing_stairs_dp.js<pre><code>/* Подъем по лестнице: динамическое программирование */\nfunction climbingStairsDP(n) {\n    if (n === 1 || n === 2) return n;\n    // Инициализация таблицы dp для хранения решений подзадач\n    const dp = new Array(n + 1).fill(-1);\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = 1;\n    dp[2] = 2;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (let i = 3; i &lt;= n; i++) {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    return dp[n];\n}\n</code></pre> climbing_stairs_dp.ts<pre><code>/* Подъем по лестнице: динамическое программирование */\nfunction climbingStairsDP(n: number): number {\n    if (n === 1 || n === 2) return n;\n    // Инициализация таблицы dp для хранения решений подзадач\n    const dp = new Array(n + 1).fill(-1);\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = 1;\n    dp[2] = 2;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (let i = 3; i &lt;= n; i++) {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    return dp[n];\n}\n</code></pre> climbing_stairs_dp.dart<pre><code>/* Подъем по лестнице: динамическое программирование */\nint climbingStairsDP(int n) {\n  if (n == 1 || n == 2) return n;\n  // Инициализация таблицы dp для хранения решений подзадач\n  List&lt;int&gt; dp = List.filled(n + 1, 0);\n  // Начальное состояние: заранее задать решения наименьших подзадач\n  dp[1] = 1;\n  dp[2] = 2;\n  // Переход состояний: постепенное решение больших подзадач через меньшие\n  for (int i = 3; i &lt;= n; i++) {\n    dp[i] = dp[i - 1] + dp[i - 2];\n  }\n  return dp[n];\n}\n</code></pre> climbing_stairs_dp.rs<pre><code>/* Подъем по лестнице: динамическое программирование */\nfn climbing_stairs_dp(n: usize) -&gt; i32 {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if n == 1 || n == 2 {\n        return n as i32;\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    let mut dp = vec![-1; n + 1];\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = 1;\n    dp[2] = 2;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for i in 3..=n {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    dp[n]\n}\n</code></pre> climbing_stairs_dp.c<pre><code>/* Подъем по лестнице: динамическое программирование */\nint climbingStairsDP(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    // Инициализация таблицы dp для хранения решений подзадач\n    int *dp = (int *)malloc((n + 1) * sizeof(int));\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = 1;\n    dp[2] = 2;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    int result = dp[n];\n    free(dp);\n    return result;\n}\n</code></pre> climbing_stairs_dp.kt<pre><code>/* Подъем по лестнице: динамическое программирование */\nfun climbingStairsDP(n: Int): Int {\n    if (n == 1 || n == 2) return n\n    // Инициализация таблицы dp для хранения решений подзадач\n    val dp = IntArray(n + 1)\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = 1\n    dp[2] = 2\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (i in 3..n) {\n        dp[i] = dp[i - 1] + dp[i - 2]\n    }\n    return dp[n]\n}\n</code></pre> climbing_stairs_dp.rb<pre><code>### Подъем по лестнице: динамическое программирование ###\ndef climbing_stairs_dp(n)\n  return n  if n == 1 || n == 2\n\n  # Инициализация таблицы dp для хранения решений подзадач\n  dp = Array.new(n + 1, 0)\n  # Начальное состояние: заранее задать решения наименьших подзадач\n  dp[1], dp[2] = 1, 2\n  # Переход состояний: постепенное решение больших подзадач через меньшие\n  (3...(n + 1)).each { |i| dp[i] = dp[i - 1] + dp[i - 2] }\n\n  dp[n]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>На рисунке 14-5 смоделирован процесс выполнения этого кода.</p> <p></p> <p> Рисунок 14-5   Процесс динамического программирования для подъема по лестнице </p> <p>Как и в backtracking, в динамическом программировании используется понятие \"состояние\" для обозначения некоторого этапа решения задачи; каждое состояние соответствует одной подзадаче и ее локально оптимальному решению. Например, в задаче о лестнице состояние определяется текущим номером ступени \\(i\\) .</p> <p>На основе сказанного можно подвести несколько часто используемых терминов динамического программирования.</p> <ul> <li>Массив <code>dp</code> называют таблицей dp, а \\(dp[i]\\) обозначает решение подзадачи, соответствующей состоянию \\(i\\) .</li> <li>Состояния, соответствующие наименьшим подзадачам (первая и вторая ступени), называют начальными состояниями.</li> <li>Рекуррентную формулу \\(dp[i] = dp[i-1] + dp[i-2]\\) называют уравнением перехода состояния.</li> </ul>","path":["Глава 14. Динамическое программирование","14.1 &nbsp; Первое знакомство с динамическим программированием"],"tags":[]},{"location":"chapter_dynamic_programming/intro_to_dynamic_programming/#1414","level":2,"title":"14.1.4   Оптимизация пространства","text":"<p>Внимательный читатель мог заметить, что поскольку \\(dp[i]\\) зависит только от \\(dp[i-1]\\) и \\(dp[i-2]\\) , нам не нужен весь массив <code>dp</code> для хранения ответов всех подзадач ; достаточно двух переменных, которые будут \"перекатываться\" вперед. Код имеет вид:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby climbing_stairs_dp.py<pre><code>def climbing_stairs_dp_comp(n: int) -&gt; int:\n    \"\"\"Подъем по лестнице: динамическое программирование с оптимизацией памяти\"\"\"\n    if n == 1 or n == 2:\n        return n\n    a, b = 1, 2\n    for _ in range(3, n + 1):\n        a, b = b, a + b\n    return b\n</code></pre> climbing_stairs_dp.cpp<pre><code>/* Подъем по лестнице: динамическое программирование с оптимизацией памяти */\nint climbingStairsDPComp(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    int a = 1, b = 2;\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = a + b;\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> climbing_stairs_dp.java<pre><code>/* Подъем по лестнице: динамическое программирование с оптимизацией памяти */\nint climbingStairsDPComp(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    int a = 1, b = 2;\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = a + b;\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> climbing_stairs_dp.cs<pre><code>/* Подъем по лестнице: динамическое программирование с оптимизацией памяти */\nint ClimbingStairsDPComp(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    int a = 1, b = 2;\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = a + b;\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> climbing_stairs_dp.go<pre><code>/* Подъем по лестнице: динамическое программирование с оптимизацией памяти */\nfunc climbingStairsDPComp(n int) int {\n    if n == 1 || n == 2 {\n        return n\n    }\n    a, b := 1, 2\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for i := 3; i &lt;= n; i++ {\n        a, b = b, a+b\n    }\n    return b\n}\n</code></pre> climbing_stairs_dp.swift<pre><code>/* Подъем по лестнице: динамическое программирование с оптимизацией памяти */\nfunc climbingStairsDPComp(n: Int) -&gt; Int {\n    if n == 1 || n == 2 {\n        return n\n    }\n    var a = 1\n    var b = 2\n    for _ in 3 ... n {\n        (a, b) = (b, a + b)\n    }\n    return b\n}\n</code></pre> climbing_stairs_dp.js<pre><code>/* Подъем по лестнице: динамическое программирование с оптимизацией памяти */\nfunction climbingStairsDPComp(n) {\n    if (n === 1 || n === 2) return n;\n    let a = 1,\n        b = 2;\n    for (let i = 3; i &lt;= n; i++) {\n        const tmp = b;\n        b = a + b;\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> climbing_stairs_dp.ts<pre><code>/* Подъем по лестнице: динамическое программирование с оптимизацией памяти */\nfunction climbingStairsDPComp(n: number): number {\n    if (n === 1 || n === 2) return n;\n    let a = 1,\n        b = 2;\n    for (let i = 3; i &lt;= n; i++) {\n        const tmp = b;\n        b = a + b;\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> climbing_stairs_dp.dart<pre><code>/* Подъем по лестнице: динамическое программирование с оптимизацией памяти */\nint climbingStairsDPComp(int n) {\n  if (n == 1 || n == 2) return n;\n  int a = 1, b = 2;\n  for (int i = 3; i &lt;= n; i++) {\n    int tmp = b;\n    b = a + b;\n    a = tmp;\n  }\n  return b;\n}\n</code></pre> climbing_stairs_dp.rs<pre><code>/* Подъем по лестнице: динамическое программирование с оптимизацией памяти */\nfn climbing_stairs_dp_comp(n: usize) -&gt; i32 {\n    if n == 1 || n == 2 {\n        return n as i32;\n    }\n    let (mut a, mut b) = (1, 2);\n    for _ in 3..=n {\n        let tmp = b;\n        b = a + b;\n        a = tmp;\n    }\n    b\n}\n</code></pre> climbing_stairs_dp.c<pre><code>/* Подъем по лестнице: динамическое программирование с оптимизацией памяти */\nint climbingStairsDPComp(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    int a = 1, b = 2;\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = a + b;\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> climbing_stairs_dp.kt<pre><code>/* Подъем по лестнице: динамическое программирование с оптимизацией памяти */\nfun climbingStairsDPComp(n: Int): Int {\n    if (n == 1 || n == 2) return n\n    var a = 1\n    var b = 2\n    for (i in 3..n) {\n        val temp = b\n        b += a\n        a = temp\n    }\n    return b\n}\n</code></pre> climbing_stairs_dp.rb<pre><code>### Подъем по лестнице: динамическое программирование с оптимизацией памяти ###\ndef climbing_stairs_dp_comp(n)\n  return n if n == 1 || n == 2\n\n  a, b = 1, 2\n  (3...(n + 1)).each { a, b = b, a + b }\n\n  b\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Из кода видно, что после отказа от массива <code>dp</code> пространственная сложность уменьшается с \\(O(n)\\) до \\(O(1)\\) .</p> <p>Во многих задачах динамического программирования текущее состояние зависит лишь от ограниченного числа предыдущих состояний. Тогда можно сохранять только действительно нужные состояния и за счет \"уменьшения размерности\" экономить память. Этот прием оптимизации памяти называют \"скользящими переменными\" или \"скользящим массивом\".</p>","path":["Глава 14. Динамическое программирование","14.1 &nbsp; Первое знакомство с динамическим программированием"],"tags":[]},{"location":"chapter_dynamic_programming/knapsack_problem/","level":1,"title":"14.4   Задача о рюкзаке 0-1","text":"<p>Задача о рюкзаке - это очень хороший вводный пример для динамического программирования и одна из самых типичных форм задач этого класса. У нее существует множество вариантов, например задача о рюкзаке 0-1, задача о полном рюкзаке, задача о многократном рюкзаке и т.д.</p> <p>В этом разделе сначала разберем самый распространенный вариант - задачу о рюкзаке 0-1.</p> <p>Question</p> <p>Даны \\(n\\) предметов. Вес \\(i\\)-го предмета равен \\(wgt[i-1]\\) , стоимость равна \\(val[i-1]\\) . Также дан рюкзак вместимости \\(cap\\) . Каждый предмет можно выбрать только один раз. Найдите максимальную суммарную стоимость, которую можно поместить в рюкзак при заданной вместимости.</p> <p>Как видно на рисунке 14-17, поскольку номер предмета \\(i\\) начинается с \\(1\\) , а индексы массива начинаются с \\(0\\) , предмету \\(i\\) соответствуют вес \\(wgt[i-1]\\) и стоимость \\(val[i-1]\\) .</p> <p></p> <p> Рисунок 14-17   Пример данных для задачи о рюкзаке 0-1 </p> <p>На задачу о рюкзаке 0-1 можно смотреть как на процесс из \\(n\\) раундов решений: для каждого предмета есть два решения - не класть его в рюкзак или положить в рюкзак. Поэтому задача удовлетворяет модели дерева решений.</p> <p>Цель задачи - найти \"максимальную суммарную стоимость при ограниченной вместимости рюкзака\", значит, с большой вероятностью это задача динамического программирования.</p> <p>Шаг 1: продумать решения на каждом раунде, определить состояние и тем самым получить таблицу \\(dp\\)</p> <p>Для каждого предмета возможны два случая: не класть его в рюкзак, тогда вместимость не меняется; или положить его в рюкзак, тогда оставшаяся вместимость уменьшается. Отсюда получается определение состояния: текущий номер предмета \\(i\\) и текущая вместимость рюкзака \\(c\\) , то есть состояние обозначается как \\([i, c]\\) .</p> <p>Подзадача, соответствующая состоянию \\([i, c]\\) , такова: максимальная стоимость, которую можно получить, используя первые \\(i\\) предметов и рюкзак вместимости \\(c\\). Ее решение обозначается через \\(dp[i, c]\\) .</p> <p>Искомым значением является \\(dp[n, cap]\\) , значит, нам нужна двумерная таблица \\(dp\\) размера \\((n+1) \\times (cap+1)\\) .</p> <p>Шаг 2: найти оптимальную подструктуру и на ее основе вывести уравнение перехода состояния</p> <p>После того как мы принимаем решение по предмету \\(i\\) , остается подзадача, связанная с первыми \\(i-1\\) предметами. Здесь возможны два случая.</p> <ul> <li>Не класть предмет \\(i\\) : вместимость рюкзака не меняется, и состояние переходит в \\([i-1, c]\\) .</li> <li>Положить предмет \\(i\\) : вместимость рюкзака уменьшается на \\(wgt[i-1]\\) , а стоимость увеличивается на \\(val[i-1]\\) , и состояние переходит в \\([i-1, c-wgt[i-1]]\\) .</li> </ul> <p>Этот анализ и раскрывает оптимальную подструктуру задачи: максимальная стоимость \\(dp[i, c]\\) равна лучшему из двух вариантов - не брать предмет \\(i\\) или взять предмет \\(i\\). Отсюда получается уравнение перехода состояния:</p> \\[ dp[i, c] = \\max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1]) \\] <p>Нужно учитывать, что если вес текущего предмета \\(wgt[i - 1]\\) превышает оставшуюся вместимость \\(c\\) , то предмет можно только не брать.</p> <p>Шаг 3: определить граничные условия и порядок переходов</p> <p>Когда предметов нет или вместимость рюкзака равна \\(0\\) , максимальная стоимость равна \\(0\\) ; то есть весь первый столбец \\(dp[i, 0]\\) и вся первая строка \\(dp[0, c]\\) заполняются нулями.</p> <p>Текущее состояние \\([i, c]\\) зависит от состояния сверху \\([i-1, c]\\) и состояния слева сверху \\([i-1, c-wgt[i-1]]\\) , поэтому достаточно двумя вложенными циклами пройти по всей таблице \\(dp\\) в прямом порядке.</p> <p>После этого анализа реализуем по порядку: полный перебор, поиск с мемоизацией и динамическое программирование.</p>","path":["Глава 14. Динамическое программирование","14.4 &nbsp; Задача о рюкзаке 0-1"],"tags":[]},{"location":"chapter_dynamic_programming/knapsack_problem/#1-1","level":3,"title":"1.   Метод 1: полный перебор","text":"<p>Код поиска содержит следующие элементы.</p> <ul> <li>Параметры рекурсии: состояние \\([i, c]\\) .</li> <li>Возвращаемое значение: решение подзадачи \\(dp[i, c]\\) .</li> <li>Условие завершения: когда номер предмета выходит за границу, то есть \\(i = 0\\) , или оставшаяся вместимость равна \\(0\\) , рекурсия завершается и возвращается стоимость \\(0\\) .</li> <li>Обрезка: если вес текущего предмета превышает оставшуюся вместимость рюкзака, то можно только не класть этот предмет.</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby knapsack.py<pre><code>def knapsack_dfs(wgt: list[int], val: list[int], i: int, c: int) -&gt; int:\n    \"\"\"Рюкзак 0-1: полный перебор\"\"\"\n    # Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if i == 0 or c == 0:\n        return 0\n    # Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if wgt[i - 1] &gt; c:\n        return knapsack_dfs(wgt, val, i - 1, c)\n    # Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    no = knapsack_dfs(wgt, val, i - 1, c)\n    yes = knapsack_dfs(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1]\n    # Вернуть вариант с большей стоимостью из двух возможных\n    return max(no, yes)\n</code></pre> knapsack.cpp<pre><code>/* Рюкзак 0-1: полный перебор */\nint knapsackDFS(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int i, int c) {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFS(wgt, val, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    int no = knapsackDFS(wgt, val, i - 1, c);\n    int yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // Вернуть вариант с большей стоимостью из двух возможных\n    return max(no, yes);\n}\n</code></pre> knapsack.java<pre><code>/* Рюкзак 0-1: полный перебор */\nint knapsackDFS(int[] wgt, int[] val, int i, int c) {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFS(wgt, val, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    int no = knapsackDFS(wgt, val, i - 1, c);\n    int yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // Вернуть вариант с большей стоимостью из двух возможных\n    return Math.max(no, yes);\n}\n</code></pre> knapsack.cs<pre><code>/* Рюкзак 0-1: полный перебор */\nint KnapsackDFS(int[] weight, int[] val, int i, int c) {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (weight[i - 1] &gt; c) {\n        return KnapsackDFS(weight, val, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    int no = KnapsackDFS(weight, val, i - 1, c);\n    int yes = KnapsackDFS(weight, val, i - 1, c - weight[i - 1]) + val[i - 1];\n    // Вернуть вариант с большей стоимостью из двух возможных\n    return Math.Max(no, yes);\n}\n</code></pre> knapsack.go<pre><code>/* Рюкзак 0-1: полный перебор */\nfunc knapsackDFS(wgt, val []int, i, c int) int {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if i == 0 || c == 0 {\n        return 0\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if wgt[i-1] &gt; c {\n        return knapsackDFS(wgt, val, i-1, c)\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    no := knapsackDFS(wgt, val, i-1, c)\n    yes := knapsackDFS(wgt, val, i-1, c-wgt[i-1]) + val[i-1]\n    // Вернуть вариант с большей стоимостью из двух возможных\n    return int(math.Max(float64(no), float64(yes)))\n}\n</code></pre> knapsack.swift<pre><code>/* Рюкзак 0-1: полный перебор */\nfunc knapsackDFS(wgt: [Int], val: [Int], i: Int, c: Int) -&gt; Int {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if i == 0 || c == 0 {\n        return 0\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if wgt[i - 1] &gt; c {\n        return knapsackDFS(wgt: wgt, val: val, i: i - 1, c: c)\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    let no = knapsackDFS(wgt: wgt, val: val, i: i - 1, c: c)\n    let yes = knapsackDFS(wgt: wgt, val: val, i: i - 1, c: c - wgt[i - 1]) + val[i - 1]\n    // Вернуть вариант с большей стоимостью из двух возможных\n    return max(no, yes)\n}\n</code></pre> knapsack.js<pre><code>/* Рюкзак 0-1: полный перебор */\nfunction knapsackDFS(wgt, val, i, c) {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i === 0 || c === 0) {\n        return 0;\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFS(wgt, val, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    const no = knapsackDFS(wgt, val, i - 1, c);\n    const yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // Вернуть вариант с большей стоимостью из двух возможных\n    return Math.max(no, yes);\n}\n</code></pre> knapsack.ts<pre><code>/* Рюкзак 0-1: полный перебор */\nfunction knapsackDFS(\n    wgt: Array&lt;number&gt;,\n    val: Array&lt;number&gt;,\n    i: number,\n    c: number\n): number {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i === 0 || c === 0) {\n        return 0;\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFS(wgt, val, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    const no = knapsackDFS(wgt, val, i - 1, c);\n    const yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // Вернуть вариант с большей стоимостью из двух возможных\n    return Math.max(no, yes);\n}\n</code></pre> knapsack.dart<pre><code>/* Рюкзак 0-1: полный перебор */\nint knapsackDFS(List&lt;int&gt; wgt, List&lt;int&gt; val, int i, int c) {\n  // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n  if (i == 0 || c == 0) {\n    return 0;\n  }\n  // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n  if (wgt[i - 1] &gt; c) {\n    return knapsackDFS(wgt, val, i - 1, c);\n  }\n  // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n  int no = knapsackDFS(wgt, val, i - 1, c);\n  int yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];\n  // Вернуть вариант с большей стоимостью из двух возможных\n  return max(no, yes);\n}\n</code></pre> knapsack.rs<pre><code>/* Рюкзак 0-1: полный перебор */\nfn knapsack_dfs(wgt: &amp;[i32], val: &amp;[i32], i: usize, c: usize) -&gt; i32 {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if i == 0 || c == 0 {\n        return 0;\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if wgt[i - 1] &gt; c as i32 {\n        return knapsack_dfs(wgt, val, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    let no = knapsack_dfs(wgt, val, i - 1, c);\n    let yes = knapsack_dfs(wgt, val, i - 1, c - wgt[i - 1] as usize) + val[i - 1];\n    // Вернуть вариант с большей стоимостью из двух возможных\n    std::cmp::max(no, yes)\n}\n</code></pre> knapsack.c<pre><code>/* Рюкзак 0-1: полный перебор */\nint knapsackDFS(int wgt[], int val[], int i, int c) {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFS(wgt, val, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    int no = knapsackDFS(wgt, val, i - 1, c);\n    int yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // Вернуть вариант с большей стоимостью из двух возможных\n    return myMax(no, yes);\n}\n</code></pre> knapsack.kt<pre><code>/* Рюкзак 0-1: полный перебор */\nfun knapsackDFS(\n    wgt: IntArray,\n    _val: IntArray,\n    i: Int,\n    c: Int\n): Int {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i == 0 || c == 0) {\n        return 0\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFS(wgt, _val, i - 1, c)\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    val no = knapsackDFS(wgt, _val, i - 1, c)\n    val yes = knapsackDFS(wgt, _val, i - 1, c - wgt[i - 1]) + _val[i - 1]\n    // Вернуть вариант с большей стоимостью из двух возможных\n    return max(no, yes)\n}\n</code></pre> knapsack.rb<pre><code>### Рюкзак 0-1: полный перебор ###\ndef knapsack_dfs(wgt, val, i, c)\n  # Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n  return 0 if i == 0 || c == 0\n  # Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n  return knapsack_dfs(wgt, val, i - 1, c) if wgt[i - 1] &gt; c\n  # Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n  no = knapsack_dfs(wgt, val, i - 1, c)\n  yes = knapsack_dfs(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1]\n  # Вернуть вариант с большей стоимостью из двух возможных\n  [no, yes].max\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Как показано на рисунке 14-18, поскольку каждый предмет создает две ветви поиска - \"не брать\" и \"брать\", временная сложность равна \\(O(2^n)\\) .</p> <p>Посмотрев на дерево рекурсии, легко заметить наличие перекрывающихся подзадач, например \\(dp[1, 10]\\) и подобных. Когда число предметов растет, вместимость рюкзака велика, а особенно когда много предметов с одинаковым весом, количество перекрывающихся подзадач быстро увеличивается.</p> <p></p> <p> Рисунок 14-18   Дерево полного перебора для задачи о рюкзаке 0-1 </p>","path":["Глава 14. Динамическое программирование","14.4 &nbsp; Задача о рюкзаке 0-1"],"tags":[]},{"location":"chapter_dynamic_programming/knapsack_problem/#2-2","level":3,"title":"2.   Метод 2: поиск с мемоизацией","text":"<p>Чтобы каждая перекрывающаяся подзадача вычислялась только один раз, используем таблицу памяти <code>mem</code> для хранения решений подзадач, где <code>mem[i][c]</code> соответствует \\(dp[i, c]\\) .</p> <p>После введения мемоизации временная сложность определяется числом подзадач , то есть равна \\(O(n \\times cap)\\) . Код выглядит так:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby knapsack.py<pre><code>def knapsack_dfs_mem(\n    wgt: list[int], val: list[int], mem: list[list[int]], i: int, c: int\n) -&gt; int:\n    \"\"\"Рюкзак 0-1: поиск с мемоизацией\"\"\"\n    # Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if i == 0 or c == 0:\n        return 0\n    # Если запись уже есть, вернуть сразу\n    if mem[i][c] != -1:\n        return mem[i][c]\n    # Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if wgt[i - 1] &gt; c:\n        return knapsack_dfs_mem(wgt, val, mem, i - 1, c)\n    # Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    no = knapsack_dfs_mem(wgt, val, mem, i - 1, c)\n    yes = knapsack_dfs_mem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1]\n    # Сохранить и вернуть вариант с большей стоимостью из двух решений\n    mem[i][c] = max(no, yes)\n    return mem[i][c]\n</code></pre> knapsack.cpp<pre><code>/* Рюкзак 0-1: поиск с мемоизацией */\nint knapsackDFSMem(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, vector&lt;vector&lt;int&gt;&gt; &amp;mem, int i, int c) {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][c] != -1) {\n        return mem[i][c];\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFSMem(wgt, val, mem, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    int no = knapsackDFSMem(wgt, val, mem, i - 1, c);\n    int yes = knapsackDFSMem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // Сохранить и вернуть вариант с большей стоимостью из двух решений\n    mem[i][c] = max(no, yes);\n    return mem[i][c];\n}\n</code></pre> knapsack.java<pre><code>/* Рюкзак 0-1: поиск с мемоизацией */\nint knapsackDFSMem(int[] wgt, int[] val, int[][] mem, int i, int c) {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][c] != -1) {\n        return mem[i][c];\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFSMem(wgt, val, mem, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    int no = knapsackDFSMem(wgt, val, mem, i - 1, c);\n    int yes = knapsackDFSMem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // Сохранить и вернуть вариант с большей стоимостью из двух решений\n    mem[i][c] = Math.max(no, yes);\n    return mem[i][c];\n}\n</code></pre> knapsack.cs<pre><code>/* Рюкзак 0-1: поиск с мемоизацией */\nint KnapsackDFSMem(int[] weight, int[] val, int[][] mem, int i, int c) {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][c] != -1) {\n        return mem[i][c];\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (weight[i - 1] &gt; c) {\n        return KnapsackDFSMem(weight, val, mem, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    int no = KnapsackDFSMem(weight, val, mem, i - 1, c);\n    int yes = KnapsackDFSMem(weight, val, mem, i - 1, c - weight[i - 1]) + val[i - 1];\n    // Сохранить и вернуть вариант с большей стоимостью из двух решений\n    mem[i][c] = Math.Max(no, yes);\n    return mem[i][c];\n}\n</code></pre> knapsack.go<pre><code>/* Рюкзак 0-1: поиск с мемоизацией */\nfunc knapsackDFSMem(wgt, val []int, mem [][]int, i, c int) int {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if i == 0 || c == 0 {\n        return 0\n    }\n    // Если запись уже есть, вернуть сразу\n    if mem[i][c] != -1 {\n        return mem[i][c]\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if wgt[i-1] &gt; c {\n        return knapsackDFSMem(wgt, val, mem, i-1, c)\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    no := knapsackDFSMem(wgt, val, mem, i-1, c)\n    yes := knapsackDFSMem(wgt, val, mem, i-1, c-wgt[i-1]) + val[i-1]\n    // Вернуть вариант с большей стоимостью из двух возможных\n    mem[i][c] = int(math.Max(float64(no), float64(yes)))\n    return mem[i][c]\n}\n</code></pre> knapsack.swift<pre><code>/* Рюкзак 0-1: поиск с мемоизацией */\nfunc knapsackDFSMem(wgt: [Int], val: [Int], mem: inout [[Int]], i: Int, c: Int) -&gt; Int {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if i == 0 || c == 0 {\n        return 0\n    }\n    // Если запись уже есть, вернуть сразу\n    if mem[i][c] != -1 {\n        return mem[i][c]\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if wgt[i - 1] &gt; c {\n        return knapsackDFSMem(wgt: wgt, val: val, mem: &amp;mem, i: i - 1, c: c)\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    let no = knapsackDFSMem(wgt: wgt, val: val, mem: &amp;mem, i: i - 1, c: c)\n    let yes = knapsackDFSMem(wgt: wgt, val: val, mem: &amp;mem, i: i - 1, c: c - wgt[i - 1]) + val[i - 1]\n    // Сохранить и вернуть вариант с большей стоимостью из двух решений\n    mem[i][c] = max(no, yes)\n    return mem[i][c]\n}\n</code></pre> knapsack.js<pre><code>/* Рюкзак 0-1: поиск с мемоизацией */\nfunction knapsackDFSMem(wgt, val, mem, i, c) {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i === 0 || c === 0) {\n        return 0;\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][c] !== -1) {\n        return mem[i][c];\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFSMem(wgt, val, mem, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    const no = knapsackDFSMem(wgt, val, mem, i - 1, c);\n    const yes =\n        knapsackDFSMem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // Сохранить и вернуть вариант с большей стоимостью из двух решений\n    mem[i][c] = Math.max(no, yes);\n    return mem[i][c];\n}\n</code></pre> knapsack.ts<pre><code>/* Рюкзак 0-1: поиск с мемоизацией */\nfunction knapsackDFSMem(\n    wgt: Array&lt;number&gt;,\n    val: Array&lt;number&gt;,\n    mem: Array&lt;Array&lt;number&gt;&gt;,\n    i: number,\n    c: number\n): number {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i === 0 || c === 0) {\n        return 0;\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][c] !== -1) {\n        return mem[i][c];\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFSMem(wgt, val, mem, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    const no = knapsackDFSMem(wgt, val, mem, i - 1, c);\n    const yes =\n        knapsackDFSMem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // Сохранить и вернуть вариант с большей стоимостью из двух решений\n    mem[i][c] = Math.max(no, yes);\n    return mem[i][c];\n}\n</code></pre> knapsack.dart<pre><code>/* Рюкзак 0-1: поиск с мемоизацией */\nint knapsackDFSMem(\n  List&lt;int&gt; wgt,\n  List&lt;int&gt; val,\n  List&lt;List&lt;int&gt;&gt; mem,\n  int i,\n  int c,\n) {\n  // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n  if (i == 0 || c == 0) {\n    return 0;\n  }\n  // Если запись уже есть, вернуть сразу\n  if (mem[i][c] != -1) {\n    return mem[i][c];\n  }\n  // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n  if (wgt[i - 1] &gt; c) {\n    return knapsackDFSMem(wgt, val, mem, i - 1, c);\n  }\n  // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n  int no = knapsackDFSMem(wgt, val, mem, i - 1, c);\n  int yes = knapsackDFSMem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1];\n  // Сохранить и вернуть вариант с большей стоимостью из двух решений\n  mem[i][c] = max(no, yes);\n  return mem[i][c];\n}\n</code></pre> knapsack.rs<pre><code>/* Рюкзак 0-1: поиск с мемоизацией */\nfn knapsack_dfs_mem(wgt: &amp;[i32], val: &amp;[i32], mem: &amp;mut Vec&lt;Vec&lt;i32&gt;&gt;, i: usize, c: usize) -&gt; i32 {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if i == 0 || c == 0 {\n        return 0;\n    }\n    // Если запись уже есть, вернуть сразу\n    if mem[i][c] != -1 {\n        return mem[i][c];\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if wgt[i - 1] &gt; c as i32 {\n        return knapsack_dfs_mem(wgt, val, mem, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    let no = knapsack_dfs_mem(wgt, val, mem, i - 1, c);\n    let yes = knapsack_dfs_mem(wgt, val, mem, i - 1, c - wgt[i - 1] as usize) + val[i - 1];\n    // Сохранить и вернуть вариант с большей стоимостью из двух решений\n    mem[i][c] = std::cmp::max(no, yes);\n    mem[i][c]\n}\n</code></pre> knapsack.c<pre><code>/* Рюкзак 0-1: поиск с мемоизацией */\nint knapsackDFSMem(int wgt[], int val[], int memCols, int **mem, int i, int c) {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][c] != -1) {\n        return mem[i][c];\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFSMem(wgt, val, memCols, mem, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    int no = knapsackDFSMem(wgt, val, memCols, mem, i - 1, c);\n    int yes = knapsackDFSMem(wgt, val, memCols, mem, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // Сохранить и вернуть вариант с большей стоимостью из двух решений\n    mem[i][c] = myMax(no, yes);\n    return mem[i][c];\n}\n</code></pre> knapsack.kt<pre><code>/* Рюкзак 0-1: поиск с мемоизацией */\nfun knapsackDFSMem(\n    wgt: IntArray,\n    _val: IntArray,\n    mem: Array&lt;IntArray&gt;,\n    i: Int,\n    c: Int\n): Int {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i == 0 || c == 0) {\n        return 0\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][c] != -1) {\n        return mem[i][c]\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFSMem(wgt, _val, mem, i - 1, c)\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    val no = knapsackDFSMem(wgt, _val, mem, i - 1, c)\n    val yes = knapsackDFSMem(wgt, _val, mem, i - 1, c - wgt[i - 1]) + _val[i - 1]\n    // Сохранить и вернуть вариант с большей стоимостью из двух решений\n    mem[i][c] = max(no, yes)\n    return mem[i][c]\n}\n</code></pre> knapsack.rb<pre><code>### Рюкзак 0-1: поиск с мемоизацией ###\ndef knapsack_dfs_mem(wgt, val, mem, i, c)\n  # Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n  return 0 if i == 0 || c == 0\n  # Если запись уже есть, вернуть сразу\n  return mem[i][c] if mem[i][c] != -1\n  # Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n  return knapsack_dfs_mem(wgt, val, mem, i - 1, c) if wgt[i - 1] &gt; c\n  # Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n  no = knapsack_dfs_mem(wgt, val, mem, i - 1, c)\n  yes = knapsack_dfs_mem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1]\n  # Сохранить и вернуть вариант с большей стоимостью из двух решений\n  mem[i][c] = [no, yes].max\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>На рисунке 14-19 показаны ветви поиска, которые были отсечены благодаря мемоизации.</p> <p></p> <p> Рисунок 14-19   Дерево поиска с мемоизацией для задачи о рюкзаке 0-1 </p>","path":["Глава 14. Динамическое программирование","14.4 &nbsp; Задача о рюкзаке 0-1"],"tags":[]},{"location":"chapter_dynamic_programming/knapsack_problem/#3-3","level":3,"title":"3.   Метод 3: динамическое программирование","text":"<p>По своей сути динамическое программирование здесь - это процесс последовательного заполнения таблицы \\(dp\\) в соответствии с переходами состояний. Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby knapsack.py<pre><code>def knapsack_dp(wgt: list[int], val: list[int], cap: int) -&gt; int:\n    \"\"\"Рюкзак 0-1: динамическое программирование\"\"\"\n    n = len(wgt)\n    # Инициализация таблицы dp\n    dp = [[0] * (cap + 1) for _ in range(n + 1)]\n    # Переход состояний\n    for i in range(1, n + 1):\n        for c in range(1, cap + 1):\n            if wgt[i - 1] &gt; c:\n                # Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c]\n            else:\n                # Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1])\n    return dp[n][cap]\n</code></pre> knapsack.cpp<pre><code>/* Рюкзак 0-1: динамическое программирование */\nint knapsackDP(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int cap) {\n    int n = wgt.size();\n    // Инициализация таблицы dp\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(cap + 1, 0));\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> knapsack.java<pre><code>/* Рюкзак 0-1: динамическое программирование */\nint knapsackDP(int[] wgt, int[] val, int cap) {\n    int n = wgt.length;\n    // Инициализация таблицы dp\n    int[][] dp = new int[n + 1][cap + 1];\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = Math.max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> knapsack.cs<pre><code>/* Рюкзак 0-1: динамическое программирование */\nint KnapsackDP(int[] weight, int[] val, int cap) {\n    int n = weight.Length;\n    // Инициализация таблицы dp\n    int[,] dp = new int[n + 1, cap + 1];\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (weight[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i, c] = dp[i - 1, c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i, c] = Math.Max(dp[i - 1, c - weight[i - 1]] + val[i - 1], dp[i - 1, c]);\n            }\n        }\n    }\n    return dp[n, cap];\n}\n</code></pre> knapsack.go<pre><code>/* Рюкзак 0-1: динамическое программирование */\nfunc knapsackDP(wgt, val []int, cap int) int {\n    n := len(wgt)\n    // Инициализация таблицы dp\n    dp := make([][]int, n+1)\n    for i := 0; i &lt;= n; i++ {\n        dp[i] = make([]int, cap+1)\n    }\n    // Переход состояний\n    for i := 1; i &lt;= n; i++ {\n        for c := 1; c &lt;= cap; c++ {\n            if wgt[i-1] &gt; c {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i-1][c]\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = int(math.Max(float64(dp[i-1][c]), float64(dp[i-1][c-wgt[i-1]]+val[i-1])))\n            }\n        }\n    }\n    return dp[n][cap]\n}\n</code></pre> knapsack.swift<pre><code>/* Рюкзак 0-1: динамическое программирование */\nfunc knapsackDP(wgt: [Int], val: [Int], cap: Int) -&gt; Int {\n    let n = wgt.count\n    // Инициализация таблицы dp\n    var dp = Array(repeating: Array(repeating: 0, count: cap + 1), count: n + 1)\n    // Переход состояний\n    for i in 1 ... n {\n        for c in 1 ... cap {\n            if wgt[i - 1] &gt; c {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c]\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1])\n            }\n        }\n    }\n    return dp[n][cap]\n}\n</code></pre> knapsack.js<pre><code>/* Рюкзак 0-1: динамическое программирование */\nfunction knapsackDP(wgt, val, cap) {\n    const n = wgt.length;\n    // Инициализация таблицы dp\n    const dp = Array(n + 1)\n        .fill(0)\n        .map(() =&gt; Array(cap + 1).fill(0));\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        for (let c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = Math.max(\n                    dp[i - 1][c],\n                    dp[i - 1][c - wgt[i - 1]] + val[i - 1]\n                );\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> knapsack.ts<pre><code>/* Рюкзак 0-1: динамическое программирование */\nfunction knapsackDP(\n    wgt: Array&lt;number&gt;,\n    val: Array&lt;number&gt;,\n    cap: number\n): number {\n    const n = wgt.length;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: n + 1 }, () =&gt;\n        Array.from({ length: cap + 1 }, () =&gt; 0)\n    );\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        for (let c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = Math.max(\n                    dp[i - 1][c],\n                    dp[i - 1][c - wgt[i - 1]] + val[i - 1]\n                );\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> knapsack.dart<pre><code>/* Рюкзак 0-1: динамическое программирование */\nint knapsackDP(List&lt;int&gt; wgt, List&lt;int&gt; val, int cap) {\n  int n = wgt.length;\n  // Инициализация таблицы dp\n  List&lt;List&lt;int&gt;&gt; dp = List.generate(n + 1, (index) =&gt; List.filled(cap + 1, 0));\n  // Переход состояний\n  for (int i = 1; i &lt;= n; i++) {\n    for (int c = 1; c &lt;= cap; c++) {\n      if (wgt[i - 1] &gt; c) {\n        // Если вместимость рюкзака превышена, предмет i не выбирать\n        dp[i][c] = dp[i - 1][c];\n      } else {\n        // Большее из двух решений: не брать или взять предмет i\n        dp[i][c] = max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1]);\n      }\n    }\n  }\n  return dp[n][cap];\n}\n</code></pre> knapsack.rs<pre><code>/* Рюкзак 0-1: динамическое программирование */\nfn knapsack_dp(wgt: &amp;[i32], val: &amp;[i32], cap: usize) -&gt; i32 {\n    let n = wgt.len();\n    // Инициализация таблицы dp\n    let mut dp = vec![vec![0; cap + 1]; n + 1];\n    // Переход состояний\n    for i in 1..=n {\n        for c in 1..=cap {\n            if wgt[i - 1] &gt; c as i32 {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = std::cmp::max(\n                    dp[i - 1][c],\n                    dp[i - 1][c - wgt[i - 1] as usize] + val[i - 1],\n                );\n            }\n        }\n    }\n    dp[n][cap]\n}\n</code></pre> knapsack.c<pre><code>/* Рюкзак 0-1: динамическое программирование */\nint knapsackDP(int wgt[], int val[], int cap, int wgtSize) {\n    int n = wgtSize;\n    // Инициализация таблицы dp\n    int **dp = malloc((n + 1) * sizeof(int *));\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i] = calloc(cap + 1, sizeof(int));\n    }\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = myMax(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    int res = dp[n][cap];\n    // Освободить память\n    for (int i = 0; i &lt;= n; i++) {\n        free(dp[i]);\n    }\n    return res;\n}\n</code></pre> knapsack.kt<pre><code>/* Рюкзак 0-1: динамическое программирование */\nfun knapsackDP(wgt: IntArray, _val: IntArray, cap: Int): Int {\n    val n = wgt.size\n    // Инициализация таблицы dp\n    val dp = Array(n + 1) { IntArray(cap + 1) }\n    // Переход состояний\n    for (i in 1..n) {\n        for (c in 1..cap) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c]\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + _val[i - 1])\n            }\n        }\n    }\n    return dp[n][cap]\n}\n</code></pre> knapsack.rb<pre><code>### Рюкзак 0-1: динамическое программирование ###\ndef knapsack_dp(wgt, val, cap)\n  n = wgt.length\n  # Инициализация таблицы dp\n  dp = Array.new(n + 1) { Array.new(cap + 1, 0) }\n  # Переход состояний\n  for i in 1...(n + 1)\n    for c in 1...(cap + 1)\n      if wgt[i - 1] &gt; c\n        # Если вместимость рюкзака превышена, предмет i не выбирать\n        dp[i][c] = dp[i - 1][c]\n      else\n        # Большее из двух решений: не брать или взять предмет i\n        dp[i][c] = [dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1]].max\n      end\n    end\n  end\n  dp[n][cap]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Как показано на рисунке 14-20, и временная сложность, и пространственная сложность определяются размером массива <code>dp</code> , то есть равны \\(O(n \\times cap)\\) .</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt;&lt;13&gt;&lt;14&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 14-20   Процесс динамического программирования для задачи о рюкзаке 0-1 </p>","path":["Глава 14. Динамическое программирование","14.4 &nbsp; Задача о рюкзаке 0-1"],"tags":[]},{"location":"chapter_dynamic_programming/knapsack_problem/#4","level":3,"title":"4.   Оптимизация пространства","text":"<p>Поскольку каждое состояние зависит только от состояния в предыдущей строке, можно использовать два массива, которые будут \"перекатываться\" вперед, и тем самым уменьшить пространственную сложность с \\(O(n^2)\\) до \\(O(n)\\) .</p> <p>Если пойти дальше, можно спросить: можно ли оптимизировать память так, чтобы использовать только один массив? Наблюдение показывает, что каждое состояние зависит от клетки прямо сверху и клетки слева сверху. Предположим, что у нас есть только один массив, и в момент начала обхода строки \\(i\\) он еще хранит состояния строки \\(i-1\\) .</p> <ul> <li>Если обходить массив слева направо, то к моменту вычисления \\(dp[i, j]\\) значения слева сверху \\(dp[i-1, 1]\\) ~ \\(dp[i-1, j-1]\\) могут уже быть перезаписаны, и правильный результат перехода состояния получить не удастся.</li> <li>Если же обходить массив справа налево, проблема перезаписи не возникает, и переход состояния вычисляется корректно.</li> </ul> <p>На рисунке 14-21 показан процесс перехода от строки \\(i = 1\\) к строке \\(i = 2\\) при использовании одного массива. Попробуйте сопоставить его с разницей между прямым и обратным обходом.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 14-21   Процесс динамического программирования после оптимизации памяти для рюкзака 0-1 </p> <p>В коде для этого достаточно удалить первое измерение массива <code>dp</code> , а внутренний цикл заменить на обратный обход:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby knapsack.py<pre><code>def knapsack_dp_comp(wgt: list[int], val: list[int], cap: int) -&gt; int:\n    \"\"\"Рюкзак 0-1: динамическое программирование с оптимизацией памяти\"\"\"\n    n = len(wgt)\n    # Инициализация таблицы dp\n    dp = [0] * (cap + 1)\n    # Переход состояний\n    for i in range(1, n + 1):\n        # Обход в обратном порядке\n        for c in range(cap, 0, -1):\n            if wgt[i - 1] &gt; c:\n                # Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c]\n            else:\n                # Большее из двух решений: не брать или взять предмет i\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1])\n    return dp[cap]\n</code></pre> knapsack.cpp<pre><code>/* Рюкзак 0-1: динамическое программирование с оптимизацией памяти */\nint knapsackDPComp(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int cap) {\n    int n = wgt.size();\n    // Инициализация таблицы dp\n    vector&lt;int&gt; dp(cap + 1, 0);\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        // Обход в обратном порядке\n        for (int c = cap; c &gt;= 1; c--) {\n            if (wgt[i - 1] &lt;= c) {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> knapsack.java<pre><code>/* Рюкзак 0-1: динамическое программирование с оптимизацией памяти */\nint knapsackDPComp(int[] wgt, int[] val, int cap) {\n    int n = wgt.length;\n    // Инициализация таблицы dp\n    int[] dp = new int[cap + 1];\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        // Обход в обратном порядке\n        for (int c = cap; c &gt;= 1; c--) {\n            if (wgt[i - 1] &lt;= c) {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> knapsack.cs<pre><code>/* Рюкзак 0-1: динамическое программирование с оптимизацией памяти */\nint KnapsackDPComp(int[] weight, int[] val, int cap) {\n    int n = weight.Length;\n    // Инициализация таблицы dp\n    int[] dp = new int[cap + 1];\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        // Обход в обратном порядке\n        for (int c = cap; c &gt; 0; c--) {\n            if (weight[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = Math.Max(dp[c], dp[c - weight[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> knapsack.go<pre><code>/* Рюкзак 0-1: динамическое программирование с оптимизацией памяти */\nfunc knapsackDPComp(wgt, val []int, cap int) int {\n    n := len(wgt)\n    // Инициализация таблицы dp\n    dp := make([]int, cap+1)\n    // Переход состояний\n    for i := 1; i &lt;= n; i++ {\n        // Обход в обратном порядке\n        for c := cap; c &gt;= 1; c-- {\n            if wgt[i-1] &lt;= c {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = int(math.Max(float64(dp[c]), float64(dp[c-wgt[i-1]]+val[i-1])))\n            }\n        }\n    }\n    return dp[cap]\n}\n</code></pre> knapsack.swift<pre><code>/* Рюкзак 0-1: динамическое программирование с оптимизацией памяти */\nfunc knapsackDPComp(wgt: [Int], val: [Int], cap: Int) -&gt; Int {\n    let n = wgt.count\n    // Инициализация таблицы dp\n    var dp = Array(repeating: 0, count: cap + 1)\n    // Переход состояний\n    for i in 1 ... n {\n        // Обход в обратном порядке\n        for c in (1 ... cap).reversed() {\n            if wgt[i - 1] &lt;= c {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1])\n            }\n        }\n    }\n    return dp[cap]\n}\n</code></pre> knapsack.js<pre><code>/* Рюкзак 0-1: динамическое программирование с оптимизацией памяти */\nfunction knapsackDPComp(wgt, val, cap) {\n    const n = wgt.length;\n    // Инициализация таблицы dp\n    const dp = Array(cap + 1).fill(0);\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        // Обход в обратном порядке\n        for (let c = cap; c &gt;= 1; c--) {\n            if (wgt[i - 1] &lt;= c) {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> knapsack.ts<pre><code>/* Рюкзак 0-1: динамическое программирование с оптимизацией памяти */\nfunction knapsackDPComp(\n    wgt: Array&lt;number&gt;,\n    val: Array&lt;number&gt;,\n    cap: number\n): number {\n    const n = wgt.length;\n    // Инициализация таблицы dp\n    const dp = Array(cap + 1).fill(0);\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        // Обход в обратном порядке\n        for (let c = cap; c &gt;= 1; c--) {\n            if (wgt[i - 1] &lt;= c) {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> knapsack.dart<pre><code>/* Рюкзак 0-1: динамическое программирование с оптимизацией памяти */\nint knapsackDPComp(List&lt;int&gt; wgt, List&lt;int&gt; val, int cap) {\n  int n = wgt.length;\n  // Инициализация таблицы dp\n  List&lt;int&gt; dp = List.filled(cap + 1, 0);\n  // Переход состояний\n  for (int i = 1; i &lt;= n; i++) {\n    // Обход в обратном порядке\n    for (int c = cap; c &gt;= 1; c--) {\n      if (wgt[i - 1] &lt;= c) {\n        // Большее из двух решений: не брать или взять предмет i\n        dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n      }\n    }\n  }\n  return dp[cap];\n}\n</code></pre> knapsack.rs<pre><code>/* Рюкзак 0-1: динамическое программирование с оптимизацией памяти */\nfn knapsack_dp_comp(wgt: &amp;[i32], val: &amp;[i32], cap: usize) -&gt; i32 {\n    let n = wgt.len();\n    // Инициализация таблицы dp\n    let mut dp = vec![0; cap + 1];\n    // Переход состояний\n    for i in 1..=n {\n        // Обход в обратном порядке\n        for c in (1..=cap).rev() {\n            if wgt[i - 1] &lt;= c as i32 {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = std::cmp::max(dp[c], dp[c - wgt[i - 1] as usize] + val[i - 1]);\n            }\n        }\n    }\n    dp[cap]\n}\n</code></pre> knapsack.c<pre><code>/* Рюкзак 0-1: динамическое программирование с оптимизацией памяти */\nint knapsackDPComp(int wgt[], int val[], int cap, int wgtSize) {\n    int n = wgtSize;\n    // Инициализация таблицы dp\n    int *dp = calloc(cap + 1, sizeof(int));\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        // Обход в обратном порядке\n        for (int c = cap; c &gt;= 1; c--) {\n            if (wgt[i - 1] &lt;= c) {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = myMax(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    int res = dp[cap];\n    // Освободить память\n    free(dp);\n    return res;\n}\n</code></pre> knapsack.kt<pre><code>/* Рюкзак 0-1: динамическое программирование с оптимизацией памяти */\nfun knapsackDPComp(wgt: IntArray, _val: IntArray, cap: Int): Int {\n    val n = wgt.size\n    // Инициализация таблицы dp\n    val dp = IntArray(cap + 1)\n    // Переход состояний\n    for (i in 1..n) {\n        // Обход в обратном порядке\n        for (c in cap downTo 1) {\n            if (wgt[i - 1] &lt;= c) {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + _val[i - 1])\n            }\n        }\n    }\n    return dp[cap]\n}\n</code></pre> knapsack.rb<pre><code>### Рюкзак 0-1: динамическое программирование с оптимизацией памяти ###\ndef knapsack_dp_comp(wgt, val, cap)\n  n = wgt.length\n  # Инициализация таблицы dp\n  dp = Array.new(cap + 1, 0)\n  # Переход состояний\n  for i in 1...(n + 1)\n    # Обход в обратном порядке\n    for c in cap.downto(1)\n      if wgt[i - 1] &gt; c\n        # Если вместимость рюкзака превышена, предмет i не выбирать\n        dp[c] = dp[c]\n      else\n        # Большее из двух решений: не брать или взять предмет i\n        dp[c] = [dp[c], dp[c - wgt[i - 1]] + val[i - 1]].max\n      end\n    end\n  end\n  dp[cap]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 14. Динамическое программирование","14.4 &nbsp; Задача о рюкзаке 0-1"],"tags":[]},{"location":"chapter_dynamic_programming/summary/","level":1,"title":"14.7   Резюме","text":"","path":["Глава 14. Динамическое программирование","14.7 &nbsp; Резюме"],"tags":[]},{"location":"chapter_dynamic_programming/summary/#1","level":3,"title":"1.   Ключевые выводы","text":"<ul> <li>Динамическое программирование раскладывает задачу на подзадачи и повышает вычислительную эффективность за счет хранения решений этих подзадач и устранения повторных вычислений.</li> <li>Если не учитывать затраты времени, то любую задачу динамического программирования можно решить с помощью backtracking (полного перебора), однако в дереве рекурсии возникает множество перекрывающихся подзадач, из-за чего эффективность крайне низка. После введения таблицы памяти можно хранить решения всех уже вычисленных подзадач и гарантировать, что каждая перекрывающаяся подзадача будет вычисляться только один раз.</li> <li>Поиск с мемоизацией - это рекурсивный метод \"сверху вниз\", а соответствующее ему динамическое программирование - это итеративный метод \"снизу вверх\", похожий на заполнение таблицы. Поскольку текущее состояние обычно зависит только от части локальных состояний, можно убрать одно измерение таблицы \\(dp\\) и тем самым снизить пространственную сложность.</li> <li>Разложение на подзадачи - это общий алгоритмический подход, но в divide and conquer, динамическом программировании и backtracking он имеет разные свойства.</li> <li>Для задач динамического программирования характерны три главных свойства: перекрывающиеся подзадачи, оптимальная подструктура и отсутствие последствий.</li> <li>Если оптимальное решение исходной задачи можно построить из оптимальных решений подзадач, то задача обладает оптимальной подструктурой.</li> <li>Отсутствие последствий означает, что для данного состояния его дальнейшее развитие определяется только этим состоянием и не зависит от всех прошлых состояний. Многие задачи комбинаторной оптимизации этим свойством не обладают и потому не могут эффективно решаться с помощью динамического программирования.</li> </ul> <p>Задачи о рюкзаке</p> <ul> <li>Задача о рюкзаке - один из самых типичных классов задач динамического программирования; она включает варианты 0-1 рюкзака, полного рюкзака, многократного рюкзака и другие.</li> <li>В задаче о рюкзаке 0-1 состояние определяется как максимальная стоимость первых \\(i\\) предметов в рюкзаке вместимости \\(c\\) . Рассматривая два решения - не брать предмет и брать предмет, - можно получить оптимальную подструктуру и вывести уравнение перехода состояния. При оптимизации памяти, поскольку каждое состояние зависит от значения сверху и слева сверху, внутренний цикл нужно выполнять в обратном порядке, чтобы не перезаписать нужное значение.</li> <li>В задаче о полном рюкзаке число экземпляров каждого предмета не ограничено, поэтому при выборе предмета переход состояния отличается от варианта 0-1. Поскольку состояние зависит от значения сверху и слева, после оптимизации памяти внутренний цикл следует выполнять в прямом порядке.</li> <li>Задача о размене монет - это вариант задачи о полном рюкзаке. Здесь вместо \"максимальной стоимости\" ищется \"минимальное число монет\", поэтому в уравнении перехода \\(\\max()\\) заменяется на \\(\\min()\\) . Кроме того, вместо условия \"не превышать вместимость рюкзака\" нужно ровно набрать целевую сумму, поэтому значение \\(amt + 1\\) используется как обозначение недопустимого решения \"сумму набрать нельзя\".</li> <li>В задаче о размене монет II вместо \"минимального числа монет\" требуется найти \"число комбинаций монет\", поэтому в уравнении перехода оператор \\(\\min()\\) заменяется на суммирование.</li> </ul> <p>Задача о расстоянии редактирования</p> <ul> <li>Расстояние редактирования (расстояние Левенштейна) используется для измерения сходства двух строк и определяется как минимальное число операций редактирования, необходимых для преобразования одной строки в другую; допустимые операции - вставка, удаление и замена.</li> <li>В задаче о расстоянии редактирования состояние определяется как минимальное число шагов редактирования, необходимых для преобразования первых \\(i\\) символов строки \\(s\\) в первые \\(j\\) символов строки \\(t\\) . Если \\(s[i] \\ne t[j]\\) , то существуют три решения: вставка, удаление и замена, и каждому из них соответствует своя остаточная подзадача. На этой основе выводятся оптимальная подструктура и уравнение перехода состояния. Если же \\(s[i] = t[j]\\) , то редактировать текущий символ не нужно.</li> <li>В задаче о расстоянии редактирования состояние зависит от значений сверху, слева и слева сверху. Поэтому после оптимизации памяти ни прямой, ни обратный обход сам по себе не дает корректного перехода состояния. Для решения этой проблемы значение слева сверху временно сохраняется в отдельной переменной, что делает ситуацию эквивалентной задаче о полном рюкзаке и позволяет использовать прямой обход.</li> </ul>","path":["Глава 14. Динамическое программирование","14.7 &nbsp; Резюме"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/","level":1,"title":"14.5   Задача о полном рюкзаке","text":"<p>В этом разделе сначала решим еще один распространенный вариант задачи о рюкзаке - полный рюкзак, а затем рассмотрим одну из его типичных специальных форм: задачу о размене монет.</p>","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1451","level":2,"title":"14.5.1   Задача о полном рюкзаке","text":"<p>Question</p> <p>Даны \\(n\\) предметов. Вес \\(i\\)-го предмета равен \\(wgt[i-1]\\) , стоимость равна \\(val[i-1]\\) . Также дан рюкзак вместимости \\(cap\\) . Каждый предмет можно выбирать многократно. Найдите максимальную суммарную стоимость, которую можно поместить в рюкзак при заданной вместимости. Пример показан на рисунке 14-22.</p> <p></p> <p> Рисунок 14-22   Пример данных для задачи о полном рюкзаке </p>","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1","level":3,"title":"1.   Идея динамического программирования","text":"<p>Задача о полном рюкзаке очень похожа на задачу о рюкзаке 0-1; разница состоит только в том, что число выборов каждого предмета не ограничено.</p> <ul> <li>В задаче о рюкзаке 0-1 каждого предмета существует только один экземпляр, поэтому после того как предмет \\(i\\) помещен в рюкзак, выбирать можно только из первых \\(i-1\\) предметов.</li> <li>В задаче о полном рюкзаке число экземпляров каждого предмета бесконечно, поэтому после того как предмет \\(i\\) помещен в рюкзак, выбирать все еще можно из первых \\(i\\) предметов.</li> </ul> <p>При этом состояние \\([i, c]\\) в задаче о полном рюкзаке может изменяться двумя способами.</p> <ul> <li>Не брать предмет \\(i\\) : как и в задаче о рюкзаке 0-1, переход осуществляется в \\([i-1, c]\\) .</li> <li>Взять предмет \\(i\\) : в отличие от рюкзака 0-1 переход происходит в \\([i, c-wgt[i-1]]\\) .</li> </ul> <p>Следовательно, уравнение перехода состояния принимает вид:</p> \\[ dp[i, c] = \\max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1]) \\]","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#2","level":3,"title":"2.   Реализация кода","text":"<p>Если сравнить код этой задачи с кодом задачи о рюкзаке 0-1, то окажется, что в переходе состояний меняется только одна деталь: вместо \\(i-1\\) появляется \\(i\\) ; все остальное остается таким же:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby unbounded_knapsack.py<pre><code>def unbounded_knapsack_dp(wgt: list[int], val: list[int], cap: int) -&gt; int:\n    \"\"\"Полный рюкзак: динамическое программирование\"\"\"\n    n = len(wgt)\n    # Инициализация таблицы dp\n    dp = [[0] * (cap + 1) for _ in range(n + 1)]\n    # Переход состояний\n    for i in range(1, n + 1):\n        for c in range(1, cap + 1):\n            if wgt[i - 1] &gt; c:\n                # Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c]\n            else:\n                # Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1])\n    return dp[n][cap]\n</code></pre> unbounded_knapsack.cpp<pre><code>/* Полный рюкзак: динамическое программирование */\nint unboundedKnapsackDP(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int cap) {\n    int n = wgt.size();\n    // Инициализация таблицы dp\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(cap + 1, 0));\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> unbounded_knapsack.java<pre><code>/* Полный рюкзак: динамическое программирование */\nint unboundedKnapsackDP(int[] wgt, int[] val, int cap) {\n    int n = wgt.length;\n    // Инициализация таблицы dp\n    int[][] dp = new int[n + 1][cap + 1];\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = Math.max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> unbounded_knapsack.cs<pre><code>/* Полный рюкзак: динамическое программирование */\nint UnboundedKnapsackDP(int[] wgt, int[] val, int cap) {\n    int n = wgt.Length;\n    // Инициализация таблицы dp\n    int[,] dp = new int[n + 1, cap + 1];\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i, c] = dp[i - 1, c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i, c] = Math.Max(dp[i - 1, c], dp[i, c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n, cap];\n}\n</code></pre> unbounded_knapsack.go<pre><code>/* Полный рюкзак: динамическое программирование */\nfunc unboundedKnapsackDP(wgt, val []int, cap int) int {\n    n := len(wgt)\n    // Инициализация таблицы dp\n    dp := make([][]int, n+1)\n    for i := 0; i &lt;= n; i++ {\n        dp[i] = make([]int, cap+1)\n    }\n    // Переход состояний\n    for i := 1; i &lt;= n; i++ {\n        for c := 1; c &lt;= cap; c++ {\n            if wgt[i-1] &gt; c {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i-1][c]\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = int(math.Max(float64(dp[i-1][c]), float64(dp[i][c-wgt[i-1]]+val[i-1])))\n            }\n        }\n    }\n    return dp[n][cap]\n}\n</code></pre> unbounded_knapsack.swift<pre><code>/* Полный рюкзак: динамическое программирование */\nfunc unboundedKnapsackDP(wgt: [Int], val: [Int], cap: Int) -&gt; Int {\n    let n = wgt.count\n    // Инициализация таблицы dp\n    var dp = Array(repeating: Array(repeating: 0, count: cap + 1), count: n + 1)\n    // Переход состояний\n    for i in 1 ... n {\n        for c in 1 ... cap {\n            if wgt[i - 1] &gt; c {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c]\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1])\n            }\n        }\n    }\n    return dp[n][cap]\n}\n</code></pre> unbounded_knapsack.js<pre><code>/* Полный рюкзак: динамическое программирование */\nfunction unboundedKnapsackDP(wgt, val, cap) {\n    const n = wgt.length;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: n + 1 }, () =&gt;\n        Array.from({ length: cap + 1 }, () =&gt; 0)\n    );\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        for (let c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = Math.max(\n                    dp[i - 1][c],\n                    dp[i][c - wgt[i - 1]] + val[i - 1]\n                );\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> unbounded_knapsack.ts<pre><code>/* Полный рюкзак: динамическое программирование */\nfunction unboundedKnapsackDP(\n    wgt: Array&lt;number&gt;,\n    val: Array&lt;number&gt;,\n    cap: number\n): number {\n    const n = wgt.length;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: n + 1 }, () =&gt;\n        Array.from({ length: cap + 1 }, () =&gt; 0)\n    );\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        for (let c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = Math.max(\n                    dp[i - 1][c],\n                    dp[i][c - wgt[i - 1]] + val[i - 1]\n                );\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> unbounded_knapsack.dart<pre><code>/* Полный рюкзак: динамическое программирование */\nint unboundedKnapsackDP(List&lt;int&gt; wgt, List&lt;int&gt; val, int cap) {\n  int n = wgt.length;\n  // Инициализация таблицы dp\n  List&lt;List&lt;int&gt;&gt; dp = List.generate(n + 1, (index) =&gt; List.filled(cap + 1, 0));\n  // Переход состояний\n  for (int i = 1; i &lt;= n; i++) {\n    for (int c = 1; c &lt;= cap; c++) {\n      if (wgt[i - 1] &gt; c) {\n        // Если вместимость рюкзака превышена, предмет i не выбирать\n        dp[i][c] = dp[i - 1][c];\n      } else {\n        // Большее из двух решений: не брать или взять предмет i\n        dp[i][c] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]);\n      }\n    }\n  }\n  return dp[n][cap];\n}\n</code></pre> unbounded_knapsack.rs<pre><code>/* Полный рюкзак: динамическое программирование */\nfn unbounded_knapsack_dp(wgt: &amp;[i32], val: &amp;[i32], cap: usize) -&gt; i32 {\n    let n = wgt.len();\n    // Инициализация таблицы dp\n    let mut dp = vec![vec![0; cap + 1]; n + 1];\n    // Переход состояний\n    for i in 1..=n {\n        for c in 1..=cap {\n            if wgt[i - 1] &gt; c as i32 {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = std::cmp::max(dp[i - 1][c], dp[i][c - wgt[i - 1] as usize] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> unbounded_knapsack.c<pre><code>/* Полный рюкзак: динамическое программирование */\nint unboundedKnapsackDP(int wgt[], int val[], int cap, int wgtSize) {\n    int n = wgtSize;\n    // Инициализация таблицы dp\n    int **dp = malloc((n + 1) * sizeof(int *));\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i] = calloc(cap + 1, sizeof(int));\n    }\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = myMax(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    int res = dp[n][cap];\n    // Освободить память\n    for (int i = 0; i &lt;= n; i++) {\n        free(dp[i]);\n    }\n    return res;\n}\n</code></pre> unbounded_knapsack.kt<pre><code>/* Полный рюкзак: динамическое программирование */\nfun unboundedKnapsackDP(wgt: IntArray, _val: IntArray, cap: Int): Int {\n    val n = wgt.size\n    // Инициализация таблицы dp\n    val dp = Array(n + 1) { IntArray(cap + 1) }\n    // Переход состояний\n    for (i in 1..n) {\n        for (c in 1..cap) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c]\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + _val[i - 1])\n            }\n        }\n    }\n    return dp[n][cap]\n}\n</code></pre> unbounded_knapsack.rb<pre><code>### Полный рюкзак: динамическое программирование ###\ndef unbounded_knapsack_dp(wgt, val, cap)\n  n = wgt.length\n  # Инициализация таблицы dp\n  dp = Array.new(n + 1) { Array.new(cap + 1, 0) }\n  # Переход состояний\n  for i in 1...(n + 1)\n    for c in 1...(cap + 1)\n      if wgt[i - 1] &gt; c\n        # Если вместимость рюкзака превышена, предмет i не выбирать\n        dp[i][c] = dp[i - 1][c]\n      else\n        # Большее из двух решений: не брать или взять предмет i\n        dp[i][c] = [dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]].max\n      end\n    end\n  end\n  dp[n][cap]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#3","level":3,"title":"3.   Оптимизация пространства","text":"<p>Поскольку текущее состояние переходит из состояния слева и состояния сверху, после оптимизации памяти каждую строку таблицы \\(dp\\) нужно обходить слева направо.</p> <p>Этот порядок обхода как раз противоположен задаче о рюкзаке 0-1. Разницу удобно понять по рисунку ниже.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 14-23   Процесс динамического программирования после оптимизации памяти для полного рюкзака </p> <p>Код реализации здесь довольно прост: достаточно просто убрать первое измерение массива <code>dp</code> :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby unbounded_knapsack.py<pre><code>def unbounded_knapsack_dp_comp(wgt: list[int], val: list[int], cap: int) -&gt; int:\n    \"\"\"Полный рюкзак: динамическое программирование с оптимизацией памяти\"\"\"\n    n = len(wgt)\n    # Инициализация таблицы dp\n    dp = [0] * (cap + 1)\n    # Переход состояний\n    for i in range(1, n + 1):\n        # Прямой обход\n        for c in range(1, cap + 1):\n            if wgt[i - 1] &gt; c:\n                # Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c]\n            else:\n                # Большее из двух решений: не брать или взять предмет i\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1])\n    return dp[cap]\n</code></pre> unbounded_knapsack.cpp<pre><code>/* Полный рюкзак: динамическое программирование с оптимизацией памяти */\nint unboundedKnapsackDPComp(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int cap) {\n    int n = wgt.size();\n    // Инициализация таблицы dp\n    vector&lt;int&gt; dp(cap + 1, 0);\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> unbounded_knapsack.java<pre><code>/* Полный рюкзак: динамическое программирование с оптимизацией памяти */\nint unboundedKnapsackDPComp(int[] wgt, int[] val, int cap) {\n    int n = wgt.length;\n    // Инициализация таблицы dp\n    int[] dp = new int[cap + 1];\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> unbounded_knapsack.cs<pre><code>/* Полный рюкзак: динамическое программирование с оптимизацией памяти */\nint UnboundedKnapsackDPComp(int[] wgt, int[] val, int cap) {\n    int n = wgt.Length;\n    // Инициализация таблицы dp\n    int[] dp = new int[cap + 1];\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = Math.Max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> unbounded_knapsack.go<pre><code>/* Полный рюкзак: динамическое программирование с оптимизацией памяти */\nfunc unboundedKnapsackDPComp(wgt, val []int, cap int) int {\n    n := len(wgt)\n    // Инициализация таблицы dp\n    dp := make([]int, cap+1)\n    // Переход состояний\n    for i := 1; i &lt;= n; i++ {\n        for c := 1; c &lt;= cap; c++ {\n            if wgt[i-1] &gt; c {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c]\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = int(math.Max(float64(dp[c]), float64(dp[c-wgt[i-1]]+val[i-1])))\n            }\n        }\n    }\n    return dp[cap]\n}\n</code></pre> unbounded_knapsack.swift<pre><code>/* Полный рюкзак: динамическое программирование с оптимизацией памяти */\nfunc unboundedKnapsackDPComp(wgt: [Int], val: [Int], cap: Int) -&gt; Int {\n    let n = wgt.count\n    // Инициализация таблицы dp\n    var dp = Array(repeating: 0, count: cap + 1)\n    // Переход состояний\n    for i in 1 ... n {\n        for c in 1 ... cap {\n            if wgt[i - 1] &gt; c {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c]\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1])\n            }\n        }\n    }\n    return dp[cap]\n}\n</code></pre> unbounded_knapsack.js<pre><code>/* Полный рюкзак: динамическое программирование с оптимизацией памяти */\nfunction unboundedKnapsackDPComp(wgt, val, cap) {\n    const n = wgt.length;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: cap + 1 }, () =&gt; 0);\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        for (let c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> unbounded_knapsack.ts<pre><code>/* Полный рюкзак: динамическое программирование с оптимизацией памяти */\nfunction unboundedKnapsackDPComp(\n    wgt: Array&lt;number&gt;,\n    val: Array&lt;number&gt;,\n    cap: number\n): number {\n    const n = wgt.length;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: cap + 1 }, () =&gt; 0);\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        for (let c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> unbounded_knapsack.dart<pre><code>/* Полный рюкзак: динамическое программирование с оптимизацией памяти */\nint unboundedKnapsackDPComp(List&lt;int&gt; wgt, List&lt;int&gt; val, int cap) {\n  int n = wgt.length;\n  // Инициализация таблицы dp\n  List&lt;int&gt; dp = List.filled(cap + 1, 0);\n  // Переход состояний\n  for (int i = 1; i &lt;= n; i++) {\n    for (int c = 1; c &lt;= cap; c++) {\n      if (wgt[i - 1] &gt; c) {\n        // Если вместимость рюкзака превышена, предмет i не выбирать\n        dp[c] = dp[c];\n      } else {\n        // Большее из двух решений: не брать или взять предмет i\n        dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n      }\n    }\n  }\n  return dp[cap];\n}\n</code></pre> unbounded_knapsack.rs<pre><code>/* Полный рюкзак: динамическое программирование с оптимизацией памяти */\nfn unbounded_knapsack_dp_comp(wgt: &amp;[i32], val: &amp;[i32], cap: usize) -&gt; i32 {\n    let n = wgt.len();\n    // Инициализация таблицы dp\n    let mut dp = vec![0; cap + 1];\n    // Переход состояний\n    for i in 1..=n {\n        for c in 1..=cap {\n            if wgt[i - 1] &gt; c as i32 {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = std::cmp::max(dp[c], dp[c - wgt[i - 1] as usize] + val[i - 1]);\n            }\n        }\n    }\n    dp[cap]\n}\n</code></pre> unbounded_knapsack.c<pre><code>/* Полный рюкзак: динамическое программирование с оптимизацией памяти */\nint unboundedKnapsackDPComp(int wgt[], int val[], int cap, int wgtSize) {\n    int n = wgtSize;\n    // Инициализация таблицы dp\n    int *dp = calloc(cap + 1, sizeof(int));\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = myMax(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    int res = dp[cap];\n    // Освободить память\n    free(dp);\n    return res;\n}\n</code></pre> unbounded_knapsack.kt<pre><code>/* Полный рюкзак: динамическое программирование с оптимизацией памяти */\nfun unboundedKnapsackDPComp(\n    wgt: IntArray,\n    _val: IntArray,\n    cap: Int\n): Int {\n    val n = wgt.size\n    // Инициализация таблицы dp\n    val dp = IntArray(cap + 1)\n    // Переход состояний\n    for (i in 1..n) {\n        for (c in 1..cap) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c]\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + _val[i - 1])\n            }\n        }\n    }\n    return dp[cap]\n}\n</code></pre> unbounded_knapsack.rb<pre><code>### Полный рюкзак: динамическое программирование ###\ndef unbounded_knapsack_dp(wgt, val, cap)\n  n = wgt.length\n  # Инициализация таблицы dp\n  dp = Array.new(n + 1) { Array.new(cap + 1, 0) }\n  # Переход состояний\n  for i in 1...(n + 1)\n    for c in 1...(cap + 1)\n      if wgt[i - 1] &gt; c\n        # Если вместимость рюкзака превышена, предмет i не выбирать\n        dp[i][c] = dp[i - 1][c]\n      else\n        # Большее из двух решений: не брать или взять предмет i\n        dp[i][c] = [dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]].max\n      end\n    end\n  end\n  dp[n][cap]\nend\n\n# ## Полный рюкзак: динамическое программирование с оптимизацией памяти ##3\ndef unbounded_knapsack_dp_comp(wgt, val, cap)\n  n = wgt.length\n  # Инициализация таблицы dp\n  dp = Array.new(cap + 1, 0)\n  # Переход состояний\n  for i in 1...(n + 1)\n    # Прямой обход\n    for c in 1...(cap + 1)\n      if wgt[i -1] &gt; c\n        # Если вместимость рюкзака превышена, предмет i не выбирать\n        dp[c] = dp[c]\n      else\n        # Большее из двух решений: не брать или взять предмет i\n        dp[c] = [dp[c], dp[c - wgt[i - 1]] + val[i - 1]].max\n      end\n    end\n  end\n  dp[cap]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1452","level":2,"title":"14.5.2   Задача о размене монет","text":"<p>Задача о рюкзаке представляет собой целый класс задач динамического программирования, у которого есть множество вариантов, и одной из таких вариаций является задача о размене монет.</p> <p>Question</p> <p>Даны \\(n\\) видов монет, номинал монеты \\(i\\) равен \\(coins[i - 1]\\) , а целевая сумма равна \\(amt\\) . Монеты каждого вида можно брать многократно. Требуется найти минимальное число монет, которыми можно набрать целевую сумму. Если набрать сумму невозможно, верните \\(-1\\) . Пример показан на рисунке 14-24.</p> <p></p> <p> Рисунок 14-24   Пример данных для задачи о размене монет </p>","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1_1","level":3,"title":"1.   Идея динамического программирования","text":"<p>Задачу о размене монет можно рассматривать как частный случай задачи о полном рюкзаке ; между ними существует следующая связь и следующие различия.</p> <ul> <li>Эти две задачи можно взаимно переводить друг в друга: \"предмет\" соответствует \"монете\", \"вес предмета\" соответствует \"номиналу монеты\", а \"вместимость рюкзака\" соответствует \"целевой сумме\".</li> <li>Цель оптимизации противоположна: в задаче о полном рюкзаке нужно максимизировать стоимость предметов, а в задаче о размене монет - минимизировать число монет.</li> <li>В задаче о полном рюкзаке ищется решение, не превышающее вместимость, а в задаче о размене монет требуется ровно набрать целевую сумму.</li> </ul> <p>Шаг 1: продумать решения на каждом раунде, определить состояние и тем самым получить таблицу \\(dp\\)</p> <p>Подзадача, соответствующая состоянию \\([i, a]\\) , выглядит так: минимальное число монет из первых \\(i\\) видов, которыми можно набрать сумму \\(a\\). Решение этой подзадачи обозначается как \\(dp[i, a]\\) .</p> <p>Размер двумерной таблицы \\(dp\\) равен \\((n+1) \\times (amt+1)\\) .</p> <p>Шаг 2: найти оптимальную подструктуру и на ее основе вывести уравнение перехода состояния</p> <p>По сравнению с задачей о полном рюкзаке здесь есть два отличия в уравнении перехода состояния.</p> <ul> <li>Нужно искать минимум, а не максимум, поэтому оператор \\(\\max()\\) заменяется на \\(\\min()\\) .</li> <li>Оптимизируемое значение - это число монет, а не суммарная стоимость, поэтому при выборе монеты нужно просто прибавить \\(1\\) .</li> </ul> \\[ dp[i, a] = \\min(dp[i-1, a], dp[i, a - coins[i-1]] + 1) \\] <p>Шаг 3: определить граничные условия и порядок переходов</p> <p>Когда целевая сумма равна \\(0\\) , минимальное число монет для ее набора равно \\(0\\) , то есть весь первый столбец \\(dp[i, 0]\\) заполняется нулями.</p> <p>Когда монет нет, невозможно набрать никакую целевую сумму \\(&gt; 0\\) ; это и есть недопустимое решение. Чтобы функция \\(\\min()\\) в уравнении перехода состояния могла распознавать и отбрасывать такие недопустимые решения, удобно использовать значение \\(+ \\infty\\) ; то есть всю первую строку \\(dp[0, a]\\) нужно инициализировать значением \\(+ \\infty\\) .</p>","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#2_1","level":3,"title":"2.   Реализация кода","text":"<p>Большинство языков программирования не предоставляет готовую переменную \\(+ \\infty\\) для целых чисел, поэтому обычно приходится заменять ее на максимальное значение типа <code>int</code> . Но тогда возникает риск переполнения: операция \\(+ 1\\) в уравнении перехода может переполнить большое число.</p> <p>Поэтому здесь мы используем число \\(amt + 1\\) как обозначение недопустимого решения, потому что для набора суммы \\(amt\\) максимум нужно не больше чем \\(amt\\) монет. Перед возвратом результата проверяем, равно ли \\(dp[n, amt]\\) значению \\(amt + 1\\) ; если да, то возвращаем \\(-1\\) , что означает невозможность набрать целевую сумму. Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby coin_change.py<pre><code>def coin_change_dp(coins: list[int], amt: int) -&gt; int:\n    \"\"\"Размен монет: динамическое программирование\"\"\"\n    n = len(coins)\n    MAX = amt + 1\n    # Инициализация таблицы dp\n    dp = [[0] * (amt + 1) for _ in range(n + 1)]\n    # Переход состояний: первая строка и первый столбец\n    for a in range(1, amt + 1):\n        dp[0][a] = MAX\n    # Переход состояний: остальные строки и столбцы\n    for i in range(1, n + 1):\n        for a in range(1, amt + 1):\n            if coins[i - 1] &gt; a:\n                # Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a]\n            else:\n                # Меньшее из двух решений: не брать или взять монету i\n                dp[i][a] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1)\n    return dp[n][amt] if dp[n][amt] != MAX else -1\n</code></pre> coin_change.cpp<pre><code>/* Размен монет: динамическое программирование */\nint coinChangeDP(vector&lt;int&gt; &amp;coins, int amt) {\n    int n = coins.size();\n    int MAX = amt + 1;\n    // Инициализация таблицы dp\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(amt + 1, 0));\n    // Переход состояний: первая строка и первый столбец\n    for (int a = 1; a &lt;= amt; a++) {\n        dp[0][a] = MAX;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[i][a] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[n][amt] != MAX ? dp[n][amt] : -1;\n}\n</code></pre> coin_change.java<pre><code>/* Размен монет: динамическое программирование */\nint coinChangeDP(int[] coins, int amt) {\n    int n = coins.length;\n    int MAX = amt + 1;\n    // Инициализация таблицы dp\n    int[][] dp = new int[n + 1][amt + 1];\n    // Переход состояний: первая строка и первый столбец\n    for (int a = 1; a &lt;= amt; a++) {\n        dp[0][a] = MAX;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[i][a] = Math.min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[n][amt] != MAX ? dp[n][amt] : -1;\n}\n</code></pre> coin_change.cs<pre><code>/* Размен монет: динамическое программирование */\nint CoinChangeDP(int[] coins, int amt) {\n    int n = coins.Length;\n    int MAX = amt + 1;\n    // Инициализация таблицы dp\n    int[,] dp = new int[n + 1, amt + 1];\n    // Переход состояний: первая строка и первый столбец\n    for (int a = 1; a &lt;= amt; a++) {\n        dp[0, a] = MAX;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i, a] = dp[i - 1, a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[i, a] = Math.Min(dp[i - 1, a], dp[i, a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[n, amt] != MAX ? dp[n, amt] : -1;\n}\n</code></pre> coin_change.go<pre><code>/* Размен монет: динамическое программирование */\nfunc coinChangeDP(coins []int, amt int) int {\n    n := len(coins)\n    max := amt + 1\n    // Инициализация таблицы dp\n    dp := make([][]int, n+1)\n    for i := 0; i &lt;= n; i++ {\n        dp[i] = make([]int, amt+1)\n    }\n    // Переход состояний: первая строка и первый столбец\n    for a := 1; a &lt;= amt; a++ {\n        dp[0][a] = max\n    }\n    // Переход состояний: остальные строки и столбцы\n    for i := 1; i &lt;= n; i++ {\n        for a := 1; a &lt;= amt; a++ {\n            if coins[i-1] &gt; a {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i-1][a]\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[i][a] = int(math.Min(float64(dp[i-1][a]), float64(dp[i][a-coins[i-1]]+1)))\n            }\n        }\n    }\n    if dp[n][amt] != max {\n        return dp[n][amt]\n    }\n    return -1\n}\n</code></pre> coin_change.swift<pre><code>/* Размен монет: динамическое программирование */\nfunc coinChangeDP(coins: [Int], amt: Int) -&gt; Int {\n    let n = coins.count\n    let MAX = amt + 1\n    // Инициализация таблицы dp\n    var dp = Array(repeating: Array(repeating: 0, count: amt + 1), count: n + 1)\n    // Переход состояний: первая строка и первый столбец\n    for a in 1 ... amt {\n        dp[0][a] = MAX\n    }\n    // Переход состояний: остальные строки и столбцы\n    for i in 1 ... n {\n        for a in 1 ... amt {\n            if coins[i - 1] &gt; a {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a]\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[i][a] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1)\n            }\n        }\n    }\n    return dp[n][amt] != MAX ? dp[n][amt] : -1\n}\n</code></pre> coin_change.js<pre><code>/* Размен монет: динамическое программирование */\nfunction coinChangeDP(coins, amt) {\n    const n = coins.length;\n    const MAX = amt + 1;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: n + 1 }, () =&gt;\n        Array.from({ length: amt + 1 }, () =&gt; 0)\n    );\n    // Переход состояний: первая строка и первый столбец\n    for (let a = 1; a &lt;= amt; a++) {\n        dp[0][a] = MAX;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (let i = 1; i &lt;= n; i++) {\n        for (let a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[i][a] = Math.min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[n][amt] !== MAX ? dp[n][amt] : -1;\n}\n</code></pre> coin_change.ts<pre><code>/* Размен монет: динамическое программирование */\nfunction coinChangeDP(coins: Array&lt;number&gt;, amt: number): number {\n    const n = coins.length;\n    const MAX = amt + 1;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: n + 1 }, () =&gt;\n        Array.from({ length: amt + 1 }, () =&gt; 0)\n    );\n    // Переход состояний: первая строка и первый столбец\n    for (let a = 1; a &lt;= amt; a++) {\n        dp[0][a] = MAX;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (let i = 1; i &lt;= n; i++) {\n        for (let a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[i][a] = Math.min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[n][amt] !== MAX ? dp[n][amt] : -1;\n}\n</code></pre> coin_change.dart<pre><code>/* Размен монет: динамическое программирование */\nint coinChangeDP(List&lt;int&gt; coins, int amt) {\n  int n = coins.length;\n  int MAX = amt + 1;\n  // Инициализация таблицы dp\n  List&lt;List&lt;int&gt;&gt; dp = List.generate(n + 1, (index) =&gt; List.filled(amt + 1, 0));\n  // Переход состояний: первая строка и первый столбец\n  for (int a = 1; a &lt;= amt; a++) {\n    dp[0][a] = MAX;\n  }\n  // Переход состояний: остальные строки и столбцы\n  for (int i = 1; i &lt;= n; i++) {\n    for (int a = 1; a &lt;= amt; a++) {\n      if (coins[i - 1] &gt; a) {\n        // Если целевая сумма превышена, монету i не выбирать\n        dp[i][a] = dp[i - 1][a];\n      } else {\n        // Меньшее из двух решений: не брать или взять монету i\n        dp[i][a] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);\n      }\n    }\n  }\n  return dp[n][amt] != MAX ? dp[n][amt] : -1;\n}\n</code></pre> coin_change.rs<pre><code>/* Размен монет: динамическое программирование */\nfn coin_change_dp(coins: &amp;[i32], amt: usize) -&gt; i32 {\n    let n = coins.len();\n    let max = amt + 1;\n    // Инициализация таблицы dp\n    let mut dp = vec![vec![0; amt + 1]; n + 1];\n    // Переход состояний: первая строка и первый столбец\n    for a in 1..=amt {\n        dp[0][a] = max;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for i in 1..=n {\n        for a in 1..=amt {\n            if coins[i - 1] &gt; a as i32 {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[i][a] = std::cmp::min(dp[i - 1][a], dp[i][a - coins[i - 1] as usize] + 1);\n            }\n        }\n    }\n    if dp[n][amt] != max {\n        return dp[n][amt] as i32;\n    } else {\n        -1\n    }\n}\n</code></pre> coin_change.c<pre><code>/* Размен монет: динамическое программирование */\nint coinChangeDP(int coins[], int amt, int coinsSize) {\n    int n = coinsSize;\n    int MAX = amt + 1;\n    // Инициализация таблицы dp\n    int **dp = malloc((n + 1) * sizeof(int *));\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i] = calloc(amt + 1, sizeof(int));\n    }\n    // Переход состояний: первая строка и первый столбец\n    for (int a = 1; a &lt;= amt; a++) {\n        dp[0][a] = MAX;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[i][a] = myMin(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    int res = dp[n][amt] != MAX ? dp[n][amt] : -1;\n    // Освободить память\n    for (int i = 0; i &lt;= n; i++) {\n        free(dp[i]);\n    }\n    free(dp);\n    return res;\n}\n</code></pre> coin_change.kt<pre><code>/* Размен монет: динамическое программирование */\nfun coinChangeDP(coins: IntArray, amt: Int): Int {\n    val n = coins.size\n    val MAX = amt + 1\n    // Инициализация таблицы dp\n    val dp = Array(n + 1) { IntArray(amt + 1) }\n    // Переход состояний: первая строка и первый столбец\n    for (a in 1..amt) {\n        dp[0][a] = MAX\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (i in 1..n) {\n        for (a in 1..amt) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a]\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[i][a] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1)\n            }\n        }\n    }\n    return if (dp[n][amt] != MAX) dp[n][amt] else -1\n}\n</code></pre> coin_change.rb<pre><code>### Размен монет: динамическое программирование ###\ndef coin_change_dp(coins, amt)\n  n = coins.length\n  _MAX = amt + 1\n  # Инициализация таблицы dp\n  dp = Array.new(n + 1) { Array.new(amt + 1, 0) }\n  # Переход состояний: первая строка и первый столбец\n  (1...(amt + 1)).each { |a| dp[0][a] = _MAX }\n  # Переход состояний: остальные строки и столбцы\n  for i in 1...(n + 1)\n    for a in 1...(amt + 1)\n      if coins[i - 1] &gt; a\n        # Если целевая сумма превышена, монету i не выбирать\n        dp[i][a] = dp[i - 1][a]\n      else\n        # Меньшее из двух решений: не брать или взять монету i\n        dp[i][a] = [dp[i - 1][a], dp[i][a - coins[i - 1]] + 1].min\n      end\n    end\n  end\n  dp[n][amt] != _MAX ? dp[n][amt] : -1\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Как показано на рисунке 14-25, процесс динамического программирования для задачи о размене монет очень похож на задачу о полном рюкзаке.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt;&lt;13&gt;&lt;14&gt;&lt;15&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 14-25   Процесс динамического программирования для задачи о размене монет </p>","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#3_1","level":3,"title":"3.   Оптимизация пространства","text":"<p>Оптимизация пространства для задачи о размене монет выполняется так же, как и для полного рюкзака:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby coin_change.py<pre><code>def coin_change_dp_comp(coins: list[int], amt: int) -&gt; int:\n    \"\"\"Размен монет: динамическое программирование с оптимизацией памяти\"\"\"\n    n = len(coins)\n    MAX = amt + 1\n    # Инициализация таблицы dp\n    dp = [MAX] * (amt + 1)\n    dp[0] = 0\n    # Переход состояний\n    for i in range(1, n + 1):\n        # Прямой обход\n        for a in range(1, amt + 1):\n            if coins[i - 1] &gt; a:\n                # Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a]\n            else:\n                # Меньшее из двух решений: не брать или взять монету i\n                dp[a] = min(dp[a], dp[a - coins[i - 1]] + 1)\n    return dp[amt] if dp[amt] != MAX else -1\n</code></pre> coin_change.cpp<pre><code>/* Размен монет: динамическое программирование с оптимизацией памяти */\nint coinChangeDPComp(vector&lt;int&gt; &amp;coins, int amt) {\n    int n = coins.size();\n    int MAX = amt + 1;\n    // Инициализация таблицы dp\n    vector&lt;int&gt; dp(amt + 1, MAX);\n    dp[0] = 0;\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[a] = min(dp[a], dp[a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[amt] != MAX ? dp[amt] : -1;\n}\n</code></pre> coin_change.java<pre><code>/* Размен монет: динамическое программирование с оптимизацией памяти */\nint coinChangeDPComp(int[] coins, int amt) {\n    int n = coins.length;\n    int MAX = amt + 1;\n    // Инициализация таблицы dp\n    int[] dp = new int[amt + 1];\n    Arrays.fill(dp, MAX);\n    dp[0] = 0;\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[a] = Math.min(dp[a], dp[a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[amt] != MAX ? dp[amt] : -1;\n}\n</code></pre> coin_change.cs<pre><code>/* Размен монет: динамическое программирование с оптимизацией памяти */\nint CoinChangeDPComp(int[] coins, int amt) {\n    int n = coins.Length;\n    int MAX = amt + 1;\n    // Инициализация таблицы dp\n    int[] dp = new int[amt + 1];\n    Array.Fill(dp, MAX);\n    dp[0] = 0;\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[a] = Math.Min(dp[a], dp[a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[amt] != MAX ? dp[amt] : -1;\n}\n</code></pre> coin_change.go<pre><code>/* Размен монет: динамическое программирование */\nfunc coinChangeDPComp(coins []int, amt int) int {\n    n := len(coins)\n    max := amt + 1\n    // Инициализация таблицы dp\n    dp := make([]int, amt+1)\n    for i := 1; i &lt;= amt; i++ {\n        dp[i] = max\n    }\n    // Переход состояний\n    for i := 1; i &lt;= n; i++ {\n        // Прямой обход\n        for a := 1; a &lt;= amt; a++ {\n            if coins[i-1] &gt; a {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a]\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[a] = int(math.Min(float64(dp[a]), float64(dp[a-coins[i-1]]+1)))\n            }\n        }\n    }\n    if dp[amt] != max {\n        return dp[amt]\n    }\n    return -1\n}\n</code></pre> coin_change.swift<pre><code>/* Размен монет: динамическое программирование с оптимизацией памяти */\nfunc coinChangeDPComp(coins: [Int], amt: Int) -&gt; Int {\n    let n = coins.count\n    let MAX = amt + 1\n    // Инициализация таблицы dp\n    var dp = Array(repeating: MAX, count: amt + 1)\n    dp[0] = 0\n    // Переход состояний\n    for i in 1 ... n {\n        for a in 1 ... amt {\n            if coins[i - 1] &gt; a {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a]\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[a] = min(dp[a], dp[a - coins[i - 1]] + 1)\n            }\n        }\n    }\n    return dp[amt] != MAX ? dp[amt] : -1\n}\n</code></pre> coin_change.js<pre><code>/* Размен монет: динамическое программирование с оптимизацией памяти */\nfunction coinChangeDPComp(coins, amt) {\n    const n = coins.length;\n    const MAX = amt + 1;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: amt + 1 }, () =&gt; MAX);\n    dp[0] = 0;\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        for (let a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[a] = Math.min(dp[a], dp[a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[amt] !== MAX ? dp[amt] : -1;\n}\n</code></pre> coin_change.ts<pre><code>/* Размен монет: динамическое программирование с оптимизацией памяти */\nfunction coinChangeDPComp(coins: Array&lt;number&gt;, amt: number): number {\n    const n = coins.length;\n    const MAX = amt + 1;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: amt + 1 }, () =&gt; MAX);\n    dp[0] = 0;\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        for (let a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[a] = Math.min(dp[a], dp[a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[amt] !== MAX ? dp[amt] : -1;\n}\n</code></pre> coin_change.dart<pre><code>/* Размен монет: динамическое программирование с оптимизацией памяти */\nint coinChangeDPComp(List&lt;int&gt; coins, int amt) {\n  int n = coins.length;\n  int MAX = amt + 1;\n  // Инициализация таблицы dp\n  List&lt;int&gt; dp = List.filled(amt + 1, MAX);\n  dp[0] = 0;\n  // Переход состояний\n  for (int i = 1; i &lt;= n; i++) {\n    for (int a = 1; a &lt;= amt; a++) {\n      if (coins[i - 1] &gt; a) {\n        // Если целевая сумма превышена, монету i не выбирать\n        dp[a] = dp[a];\n      } else {\n        // Меньшее из двух решений: не брать или взять монету i\n        dp[a] = min(dp[a], dp[a - coins[i - 1]] + 1);\n      }\n    }\n  }\n  return dp[amt] != MAX ? dp[amt] : -1;\n}\n</code></pre> coin_change.rs<pre><code>/* Размен монет: динамическое программирование с оптимизацией памяти */\nfn coin_change_dp_comp(coins: &amp;[i32], amt: usize) -&gt; i32 {\n    let n = coins.len();\n    let max = amt + 1;\n    // Инициализация таблицы dp\n    let mut dp = vec![0; amt + 1];\n    dp.fill(max);\n    dp[0] = 0;\n    // Переход состояний\n    for i in 1..=n {\n        for a in 1..=amt {\n            if coins[i - 1] &gt; a as i32 {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[a] = std::cmp::min(dp[a], dp[a - coins[i - 1] as usize] + 1);\n            }\n        }\n    }\n    if dp[amt] != max {\n        return dp[amt] as i32;\n    } else {\n        -1\n    }\n}\n</code></pre> coin_change.c<pre><code>/* Размен монет: динамическое программирование с оптимизацией памяти */\nint coinChangeDPComp(int coins[], int amt, int coinsSize) {\n    int n = coinsSize;\n    int MAX = amt + 1;\n    // Инициализация таблицы dp\n    int *dp = malloc((amt + 1) * sizeof(int));\n    for (int j = 1; j &lt;= amt; j++) {\n        dp[j] = MAX;\n    } \n    dp[0] = 0;\n\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[a] = myMin(dp[a], dp[a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    int res = dp[amt] != MAX ? dp[amt] : -1;\n    // Освободить память\n    free(dp);\n    return res;\n}\n</code></pre> coin_change.kt<pre><code>/* Размен монет: динамическое программирование с оптимизацией памяти */\nfun coinChangeDPComp(coins: IntArray, amt: Int): Int {\n    val n = coins.size\n    val MAX = amt + 1\n    // Инициализация таблицы dp\n    val dp = IntArray(amt + 1)\n    dp.fill(MAX)\n    dp[0] = 0\n    // Переход состояний\n    for (i in 1..n) {\n        for (a in 1..amt) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a]\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[a] = min(dp[a], dp[a - coins[i - 1]] + 1)\n            }\n        }\n    }\n    return if (dp[amt] != MAX) dp[amt] else -1\n}\n</code></pre> coin_change.rb<pre><code>### Размен монет: динамическое программирование с оптимизацией памяти ###\ndef coin_change_dp_comp(coins, amt)\n  n = coins.length\n  _MAX = amt + 1\n  # Инициализация таблицы dp\n  dp = Array.new(amt + 1, _MAX)\n  dp[0] = 0\n  # Переход состояний\n  for i in 1...(n + 1)\n    # Прямой обход\n    for a in 1...(amt + 1)\n      if coins[i - 1] &gt; a\n        # Если целевая сумма превышена, монету i не выбирать\n        dp[a] = dp[a]\n      else\n        # Меньшее из двух решений: не брать или взять монету i\n        dp[a] = [dp[a], dp[a - coins[i - 1]] + 1].min\n      end\n    end\n  end\n  dp[amt] != _MAX ? dp[amt] : -1\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1453-ii","level":2,"title":"14.5.3   Задача о размене монет II","text":"<p>Question</p> <p>Даны \\(n\\) видов монет, номинал монеты \\(i\\) равен \\(coins[i - 1]\\) , а целевая сумма равна \\(amt\\) . Монеты каждого вида можно брать многократно. Найдите число различных комбинаций монет, которыми можно набрать целевую сумму. Пример показан на рисунке 14-26.</p> <p></p> <p> Рисунок 14-26   Пример данных для задачи о размене монет II </p>","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1_2","level":3,"title":"1.   Идея динамического программирования","text":"<p>По сравнению с предыдущей задачей теперь целью является число комбинаций. Поэтому подзадача меняется на следующую: число комбинаций из первых \\(i\\) видов монет, которыми можно набрать сумму \\(a\\). При этом таблица \\(dp\\) по-прежнему остается двумерной матрицей размера \\((n+1) \\times (amt + 1)\\) .</p> <p>Число комбинаций для текущего состояния равно сумме числа комбинаций для двух решений: не брать текущую монету и брать текущую монету. Поэтому уравнение перехода состояния принимает вид:</p> \\[ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]] \\] <p>Когда целевая сумма равна \\(0\\) , ее можно набрать, не выбирая ни одной монеты, поэтому весь первый столбец \\(dp[i, 0]\\) нужно инициализировать единицами. Когда монет нет, невозможно набрать никакую сумму \\(&gt;0\\) , поэтому вся первая строка \\(dp[0, a]\\) должна быть заполнена нулями.</p>","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#2_2","level":3,"title":"2.   Реализация кода","text":"PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby coin_change_ii.py<pre><code>def coin_change_ii_dp(coins: list[int], amt: int) -&gt; int:\n    \"\"\"Размен монет II: динамическое программирование\"\"\"\n    n = len(coins)\n    # Инициализация таблицы dp\n    dp = [[0] * (amt + 1) for _ in range(n + 1)]\n    # Инициализация первого столбца\n    for i in range(n + 1):\n        dp[i][0] = 1\n    # Переход состояний\n    for i in range(1, n + 1):\n        for a in range(1, amt + 1):\n            if coins[i - 1] &gt; a:\n                # Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a]\n            else:\n                # Сумма двух решений: не брать или взять монету i\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]]\n    return dp[n][amt]\n</code></pre> coin_change_ii.cpp<pre><code>/* Размен монет II: динамическое программирование */\nint coinChangeIIDP(vector&lt;int&gt; &amp;coins, int amt) {\n    int n = coins.size();\n    // Инициализация таблицы dp\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(amt + 1, 0));\n    // Инициализация первого столбца\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i][0] = 1;\n    }\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[n][amt];\n}\n</code></pre> coin_change_ii.java<pre><code>/* Размен монет II: динамическое программирование */\nint coinChangeIIDP(int[] coins, int amt) {\n    int n = coins.length;\n    // Инициализация таблицы dp\n    int[][] dp = new int[n + 1][amt + 1];\n    // Инициализация первого столбца\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i][0] = 1;\n    }\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[n][amt];\n}\n</code></pre> coin_change_ii.cs<pre><code>/* Размен монет II: динамическое программирование */\nint CoinChangeIIDP(int[] coins, int amt) {\n    int n = coins.Length;\n    // Инициализация таблицы dp\n    int[,] dp = new int[n + 1, amt + 1];\n    // Инициализация первого столбца\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i, 0] = 1;\n    }\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i, a] = dp[i - 1, a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[i, a] = dp[i - 1, a] + dp[i, a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[n, amt];\n}\n</code></pre> coin_change_ii.go<pre><code>/* Размен монет II: динамическое программирование */\nfunc coinChangeIIDP(coins []int, amt int) int {\n    n := len(coins)\n    // Инициализация таблицы dp\n    dp := make([][]int, n+1)\n    for i := 0; i &lt;= n; i++ {\n        dp[i] = make([]int, amt+1)\n    }\n    // Инициализация первого столбца\n    for i := 0; i &lt;= n; i++ {\n        dp[i][0] = 1\n    }\n    // Переход состояний: остальные строки и столбцы\n    for i := 1; i &lt;= n; i++ {\n        for a := 1; a &lt;= amt; a++ {\n            if coins[i-1] &gt; a {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i-1][a]\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[i][a] = dp[i-1][a] + dp[i][a-coins[i-1]]\n            }\n        }\n    }\n    return dp[n][amt]\n}\n</code></pre> coin_change_ii.swift<pre><code>/* Размен монет II: динамическое программирование */\nfunc coinChangeIIDP(coins: [Int], amt: Int) -&gt; Int {\n    let n = coins.count\n    // Инициализация таблицы dp\n    var dp = Array(repeating: Array(repeating: 0, count: amt + 1), count: n + 1)\n    // Инициализация первого столбца\n    for i in 0 ... n {\n        dp[i][0] = 1\n    }\n    // Переход состояний\n    for i in 1 ... n {\n        for a in 1 ... amt {\n            if coins[i - 1] &gt; a {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a]\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]]\n            }\n        }\n    }\n    return dp[n][amt]\n}\n</code></pre> coin_change_ii.js<pre><code>/* Размен монет II: динамическое программирование */\nfunction coinChangeIIDP(coins, amt) {\n    const n = coins.length;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: n + 1 }, () =&gt;\n        Array.from({ length: amt + 1 }, () =&gt; 0)\n    );\n    // Инициализация первого столбца\n    for (let i = 0; i &lt;= n; i++) {\n        dp[i][0] = 1;\n    }\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        for (let a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[n][amt];\n}\n</code></pre> coin_change_ii.ts<pre><code>/* Размен монет II: динамическое программирование */\nfunction coinChangeIIDP(coins: Array&lt;number&gt;, amt: number): number {\n    const n = coins.length;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: n + 1 }, () =&gt;\n        Array.from({ length: amt + 1 }, () =&gt; 0)\n    );\n    // Инициализация первого столбца\n    for (let i = 0; i &lt;= n; i++) {\n        dp[i][0] = 1;\n    }\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        for (let a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[n][amt];\n}\n</code></pre> coin_change_ii.dart<pre><code>/* Размен монет II: динамическое программирование */\nint coinChangeIIDP(List&lt;int&gt; coins, int amt) {\n  int n = coins.length;\n  // Инициализация таблицы dp\n  List&lt;List&lt;int&gt;&gt; dp = List.generate(n + 1, (index) =&gt; List.filled(amt + 1, 0));\n  // Инициализация первого столбца\n  for (int i = 0; i &lt;= n; i++) {\n    dp[i][0] = 1;\n  }\n  // Переход состояний\n  for (int i = 1; i &lt;= n; i++) {\n    for (int a = 1; a &lt;= amt; a++) {\n      if (coins[i - 1] &gt; a) {\n        // Если целевая сумма превышена, монету i не выбирать\n        dp[i][a] = dp[i - 1][a];\n      } else {\n        // Сумма двух решений: не брать или взять монету i\n        dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];\n      }\n    }\n  }\n  return dp[n][amt];\n}\n</code></pre> coin_change_ii.rs<pre><code>/* Размен монет II: динамическое программирование */\nfn coin_change_ii_dp(coins: &amp;[i32], amt: usize) -&gt; i32 {\n    let n = coins.len();\n    // Инициализация таблицы dp\n    let mut dp = vec![vec![0; amt + 1]; n + 1];\n    // Инициализация первого столбца\n    for i in 0..=n {\n        dp[i][0] = 1;\n    }\n    // Переход состояний\n    for i in 1..=n {\n        for a in 1..=amt {\n            if coins[i - 1] &gt; a as i32 {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1] as usize];\n            }\n        }\n    }\n    dp[n][amt]\n}\n</code></pre> coin_change_ii.c<pre><code>/* Размен монет II: динамическое программирование */\nint coinChangeIIDP(int coins[], int amt, int coinsSize) {\n    int n = coinsSize;\n    // Инициализация таблицы dp\n    int **dp = malloc((n + 1) * sizeof(int *));\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i] = calloc(amt + 1, sizeof(int));\n    }\n    // Инициализация первого столбца\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i][0] = 1;\n    }\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];\n            }\n        }\n    }\n    int res = dp[n][amt];\n    // Освободить память\n    for (int i = 0; i &lt;= n; i++) {\n        free(dp[i]);\n    }\n    free(dp);\n    return res;\n}\n</code></pre> coin_change_ii.kt<pre><code>/* Размен монет II: динамическое программирование */\nfun coinChangeIIDP(coins: IntArray, amt: Int): Int {\n    val n = coins.size\n    // Инициализация таблицы dp\n    val dp = Array(n + 1) { IntArray(amt + 1) }\n    // Инициализация первого столбца\n    for (i in 0..n) {\n        dp[i][0] = 1\n    }\n    // Переход состояний\n    for (i in 1..n) {\n        for (a in 1..amt) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a]\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]]\n            }\n        }\n    }\n    return dp[n][amt]\n}\n</code></pre> coin_change_ii.rb<pre><code>### Размен монет II: динамическое программирование ###\ndef coin_change_ii_dp(coins, amt)\n  n = coins.length\n  # Инициализация таблицы dp\n  dp = Array.new(n + 1) { Array.new(amt + 1, 0) }\n  # Инициализация первого столбца\n  (0...(n + 1)).each { |i| dp[i][0] = 1 }\n  # Переход состояний\n  for i in 1...(n + 1)\n    for a in 1...(amt + 1)\n      if coins[i - 1] &gt; a\n        # Если целевая сумма превышена, монету i не выбирать\n        dp[i][a] = dp[i - 1][a]\n      else\n        # Сумма двух решений: не брать или взять монету i\n        dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]]\n      end\n    end\n  end\n  dp[n][amt]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#3_2","level":3,"title":"3.   Оптимизация пространства","text":"<p>При оптимизации памяти способ остается тем же самым: достаточно убрать измерение, отвечающее за виды монет:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby coin_change_ii.py<pre><code>def coin_change_ii_dp_comp(coins: list[int], amt: int) -&gt; int:\n    \"\"\"Размен монет II: динамическое программирование с оптимизацией памяти\"\"\"\n    n = len(coins)\n    # Инициализация таблицы dp\n    dp = [0] * (amt + 1)\n    dp[0] = 1\n    # Переход состояний\n    for i in range(1, n + 1):\n        # Прямой обход\n        for a in range(1, amt + 1):\n            if coins[i - 1] &gt; a:\n                # Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a]\n            else:\n                # Сумма двух решений: не брать или взять монету i\n                dp[a] = dp[a] + dp[a - coins[i - 1]]\n    return dp[amt]\n</code></pre> coin_change_ii.cpp<pre><code>/* Размен монет II: динамическое программирование с оптимизацией памяти */\nint coinChangeIIDPComp(vector&lt;int&gt; &amp;coins, int amt) {\n    int n = coins.size();\n    // Инициализация таблицы dp\n    vector&lt;int&gt; dp(amt + 1, 0);\n    dp[0] = 1;\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[a] = dp[a] + dp[a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[amt];\n}\n</code></pre> coin_change_ii.java<pre><code>/* Размен монет II: динамическое программирование с оптимизацией памяти */\nint coinChangeIIDPComp(int[] coins, int amt) {\n    int n = coins.length;\n    // Инициализация таблицы dp\n    int[] dp = new int[amt + 1];\n    dp[0] = 1;\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[a] = dp[a] + dp[a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[amt];\n}\n</code></pre> coin_change_ii.cs<pre><code>/* Размен монет II: динамическое программирование с оптимизацией памяти */\nint CoinChangeIIDPComp(int[] coins, int amt) {\n    int n = coins.Length;\n    // Инициализация таблицы dp\n    int[] dp = new int[amt + 1];\n    dp[0] = 1;\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[a] = dp[a] + dp[a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[amt];\n}\n</code></pre> coin_change_ii.go<pre><code>/* Размен монет II: динамическое программирование с оптимизацией памяти */\nfunc coinChangeIIDPComp(coins []int, amt int) int {\n    n := len(coins)\n    // Инициализация таблицы dp\n    dp := make([]int, amt+1)\n    dp[0] = 1\n    // Переход состояний\n    for i := 1; i &lt;= n; i++ {\n        // Прямой обход\n        for a := 1; a &lt;= amt; a++ {\n            if coins[i-1] &gt; a {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a]\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[a] = dp[a] + dp[a-coins[i-1]]\n            }\n        }\n    }\n    return dp[amt]\n}\n</code></pre> coin_change_ii.swift<pre><code>/* Размен монет II: динамическое программирование с оптимизацией памяти */\nfunc coinChangeIIDPComp(coins: [Int], amt: Int) -&gt; Int {\n    let n = coins.count\n    // Инициализация таблицы dp\n    var dp = Array(repeating: 0, count: amt + 1)\n    dp[0] = 1\n    // Переход состояний\n    for i in 1 ... n {\n        for a in 1 ... amt {\n            if coins[i - 1] &gt; a {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a]\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[a] = dp[a] + dp[a - coins[i - 1]]\n            }\n        }\n    }\n    return dp[amt]\n}\n</code></pre> coin_change_ii.js<pre><code>/* Размен монет II: динамическое программирование с оптимизацией памяти */\nfunction coinChangeIIDPComp(coins, amt) {\n    const n = coins.length;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: amt + 1 }, () =&gt; 0);\n    dp[0] = 1;\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        for (let a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[a] = dp[a] + dp[a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[amt];\n}\n</code></pre> coin_change_ii.ts<pre><code>/* Размен монет II: динамическое программирование с оптимизацией памяти */\nfunction coinChangeIIDPComp(coins: Array&lt;number&gt;, amt: number): number {\n    const n = coins.length;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: amt + 1 }, () =&gt; 0);\n    dp[0] = 1;\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        for (let a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[a] = dp[a] + dp[a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[amt];\n}\n</code></pre> coin_change_ii.dart<pre><code>/* Размен монет II: динамическое программирование с оптимизацией памяти */\nint coinChangeIIDPComp(List&lt;int&gt; coins, int amt) {\n  int n = coins.length;\n  // Инициализация таблицы dp\n  List&lt;int&gt; dp = List.filled(amt + 1, 0);\n  dp[0] = 1;\n  // Переход состояний\n  for (int i = 1; i &lt;= n; i++) {\n    for (int a = 1; a &lt;= amt; a++) {\n      if (coins[i - 1] &gt; a) {\n        // Если целевая сумма превышена, монету i не выбирать\n        dp[a] = dp[a];\n      } else {\n        // Сумма двух решений: не брать или взять монету i\n        dp[a] = dp[a] + dp[a - coins[i - 1]];\n      }\n    }\n  }\n  return dp[amt];\n}\n</code></pre> coin_change_ii.rs<pre><code>/* Размен монет II: динамическое программирование с оптимизацией памяти */\nfn coin_change_ii_dp_comp(coins: &amp;[i32], amt: usize) -&gt; i32 {\n    let n = coins.len();\n    // Инициализация таблицы dp\n    let mut dp = vec![0; amt + 1];\n    dp[0] = 1;\n    // Переход состояний\n    for i in 1..=n {\n        for a in 1..=amt {\n            if coins[i - 1] &gt; a as i32 {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[a] = dp[a] + dp[a - coins[i - 1] as usize];\n            }\n        }\n    }\n    dp[amt]\n}\n</code></pre> coin_change_ii.c<pre><code>/* Размен монет II: динамическое программирование с оптимизацией памяти */\nint coinChangeIIDPComp(int coins[], int amt, int coinsSize) {\n    int n = coinsSize;\n    // Инициализация таблицы dp\n    int *dp = calloc(amt + 1, sizeof(int));\n    dp[0] = 1;\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[a] = dp[a] + dp[a - coins[i - 1]];\n            }\n        }\n    }\n    int res = dp[amt];\n    // Освободить память\n    free(dp);\n    return res;\n}\n</code></pre> coin_change_ii.kt<pre><code>/* Размен монет II: динамическое программирование с оптимизацией памяти */\nfun coinChangeIIDPComp(coins: IntArray, amt: Int): Int {\n    val n = coins.size\n    // Инициализация таблицы dp\n    val dp = IntArray(amt + 1)\n    dp[0] = 1\n    // Переход состояний\n    for (i in 1..n) {\n        for (a in 1..amt) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a]\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[a] = dp[a] + dp[a - coins[i - 1]]\n            }\n        }\n    }\n    return dp[amt]\n}\n</code></pre> coin_change_ii.rb<pre><code>### Размен монет II: динамическое программирование с оптимизацией памяти ###\ndef coin_change_ii_dp_comp(coins, amt)\n  n = coins.length\n  # Инициализация таблицы dp\n  dp = Array.new(amt + 1, 0)\n  dp[0] = 1\n  # Переход состояний\n  for i in 1...(n + 1)\n    # Прямой обход\n    for a in 1...(amt + 1)\n      if coins[i - 1] &gt; a\n        # Если целевая сумма превышена, монету i не выбирать\n        dp[a] = dp[a]\n      else\n        # Сумма двух решений: не брать или взять монету i\n        dp[a] = dp[a] + dp[a - coins[i - 1]]\n      end\n    end\n  end\n  dp[amt]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_graph/","level":1,"title":"Глава 9.   Графы","text":"<p>Abstract</p> <p>На жизненном пути мы подобны узлам, соединенным бесчисленными невидимыми ребрами.</p> <p>Каждая встреча и каждое расставание оставляют в этой огромной сети свой особый след.</p>","path":["Глава 9. Граф","Глава 9. &nbsp; Графы"],"tags":[]},{"location":"chapter_graph/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>9.1   Граф</li> <li>9.2   Базовые операции над графами</li> <li>9.3   Обход графа</li> <li>9.4   Резюме</li> </ul>","path":["Глава 9. Граф","Глава 9. &nbsp; Графы"],"tags":[]},{"location":"chapter_graph/graph/","level":1,"title":"9.1   Граф","text":"<p>Граф (graph) - это нелинейная структура данных, состоящая из вершин (vertex) и ребер (edge). Мы можем абстрактно представить граф \\(G\\) как множество вершин \\(V\\) и множество ребер \\(E\\) . В примере ниже показан граф, содержащий 5 вершин и 7 ребер.</p> \\[ \\begin{aligned} V &amp; = \\{ 1, 2, 3, 4, 5 \\} \\newline E &amp; = \\{ (1,2), (1,3), (1,5), (2,3), (2,4), (2,5), (4,5) \\} \\newline G &amp; = \\{ V, E \\} \\newline \\end{aligned} \\] <p>Если рассматривать вершины как узлы, а ребра как ссылки (указатели), соединяющие эти узлы, то граф можно считать структурой данных, выросшей из связного списка. Как показано на рисунке 9-1, по сравнению с линейными отношениями (связный список) и отношениями разделения (дерево), сетевые отношения (граф) обладают большей свободой , а потому и сложнее.</p> <p></p> <p> Рисунок 9-1   Связь между связным списком, деревом и графом </p>","path":["Глава 9. Граф","9.1 &nbsp; Граф"],"tags":[]},{"location":"chapter_graph/graph/#911","level":2,"title":"9.1.1   Распространенные типы и термины графов","text":"<p>В зависимости от того, имеют ли ребра направление, графы делятся на неориентированные графы (undirected graph) и ориентированные графы (directed graph) , как показано на рисунке 9-2.</p> <ul> <li>В неориентированном графе ребро означает \"двустороннюю\" связь между двумя вершинами, например отношение \"друзья\" в WeChat или QQ.</li> <li>В ориентированном графе ребро имеет направление, то есть ребра \\(A \\rightarrow B\\) и \\(A \\leftarrow B\\) независимы друг от друга, как, например, отношения \"подписка\" и \"подписчик\" в Weibo или Douyin.</li> </ul> <p></p> <p> Рисунок 9-2   Ориентированный и неориентированный графы </p> <p>В зависимости от того, достижимы ли все вершины друг из друга, граф делится на связный граф (connected graph) и несвязный граф (disconnected graph) , как показано на рисунке 9-3.</p> <ul> <li>В связном графе, начиная из некоторой вершины, можно добраться до любой другой вершины.</li> <li>В несвязном графе, начиная из некоторой вершины, по крайней мере одна вершина оказывается недостижимой.</li> </ul> <p></p> <p> Рисунок 9-3   Связный и несвязный графы </p> <p>Мы также можем добавить к ребрам переменную \"вес\" и тем самым получить взвешенный граф (weighted graph) , показанный на рисунке 9-4. Например, в мобильных играх вроде Honor of Kings система может вычислять \"степень близости\" между игроками по времени, проведенному в совместных играх; такую сеть близости можно описать взвешенным графом.</p> <p></p> <p> Рисунок 9-4   Взвешенный и невзвешенный графы </p> <p>Для структуры данных \"граф\" используются следующие распространенные термины.</p> <ul> <li>Смежность (adjacency): если между двумя вершинами существует ребро, то эти вершины называются \"смежными\". На рисунке 9-4 вершинам 2, 3, 5 смежна вершина 1.</li> <li>Путь (path): последовательность ребер, ведущая из вершины A в вершину B, называется \"путем\" от A до B. На рисунке 9-4 последовательность ребер 1-5-2-4 представляет один из путей от вершины 1 к вершине 4.</li> <li>Степень (degree): число ребер, принадлежащих вершине. Для ориентированного графа входящая степень (in-degree) показывает число ребер, ведущих в вершину, а исходящая степень (out-degree) показывает число ребер, исходящих из вершины.</li> </ul>","path":["Глава 9. Граф","9.1 &nbsp; Граф"],"tags":[]},{"location":"chapter_graph/graph/#912","level":2,"title":"9.1.2   Представление графа","text":"<p>Распространенные способы представления графа включают \"матрицу смежности\" и \"список смежности\". Ниже в качестве примера используется неориентированный граф.</p>","path":["Глава 9. Граф","9.1 &nbsp; Граф"],"tags":[]},{"location":"chapter_graph/graph/#1","level":3,"title":"1.   Матрица смежности","text":"<p>Пусть число вершин графа равно \\(n\\) ; тогда матрица смежности (adjacency matrix) использует матрицу размера \\(n \\times n\\) для представления графа: каждая строка и каждый столбец соответствуют вершине, а элементы матрицы отражают наличие ребра, то есть показывают, существует между двумя вершинами связь или нет.</p> <p>Как показано на рисунке 9-5, пусть матрица смежности обозначается как \\(M\\) , а список вершин - как \\(V\\) ; тогда элемент матрицы \\(M[i, j] = 1\\) означает, что между вершинами \\(V[i]\\) и \\(V[j]\\) существует ребро, а элемент \\(M[i, j] = 0\\) означает, что ребра между ними нет.</p> <p></p> <p> Рисунок 9-5   Представление графа матрицей смежности </p> <p>Матрица смежности обладает следующими особенностями.</p> <ul> <li>В простом графе вершина не может соединяться сама с собой, поэтому элементы на главной диагонали матрицы смежности не имеют смысла.</li> <li>Для неориентированного графа ребра в двух направлениях эквивалентны, поэтому матрица смежности симметрична относительно главной диагонали.</li> <li>Если заменить в матрице смежности значения \\(1\\) и \\(0\\) на веса, то можно представить и взвешенный граф.</li> </ul> <p>При представлении графа матрицей смежности мы можем напрямую обращаться к элементам матрицы, чтобы получить информацию о ребрах, поэтому операции добавления, удаления, поиска и изменения обладают высокой эффективностью, равной \\(O(1)\\) . Однако пространственная сложность матрицы равна \\(O(n^2)\\) , поэтому она занимает заметный объем памяти.</p>","path":["Глава 9. Граф","9.1 &nbsp; Граф"],"tags":[]},{"location":"chapter_graph/graph/#2","level":3,"title":"2.   Список смежности","text":"<p>Список смежности (adjacency list) использует \\(n\\) связанных списков для представления графа, где узлы списка обозначают вершины. \\(i\\)-й список соответствует вершине \\(i\\) и хранит все вершины, смежные с ней, то есть все вершины, соединенные с этой вершиной. На рисунке 9-6 показан пример графа, представленного списком смежности.</p> <p></p> <p> Рисунок 9-6   Представление графа списком смежности </p> <p>Список смежности хранит только реально существующие ребра, а общее число ребер обычно значительно меньше \\(n^2\\) , поэтому этот способ существенно экономит пространство. Однако для поиска ребра в списке смежности нужно проходить по списку, поэтому по времени он уступает матрице смежности.</p> <p>Если посмотреть на рисунок 9-6, можно заметить, что структура списка смежности очень похожа на \"метод цепочек\" в хеш-таблице, поэтому для оптимизации эффективности здесь можно использовать сходные идеи. Например, когда список становится слишком длинным, его можно преобразовать в AVL-дерево или красно-черное дерево, чтобы улучшить временную сложность с \\(O(n)\\) до \\(O(\\log n)\\) ; можно также превратить его в хеш-таблицу и снизить сложность до \\(O(1)\\) .</p>","path":["Глава 9. Граф","9.1 &nbsp; Граф"],"tags":[]},{"location":"chapter_graph/graph/#913","level":2,"title":"9.1.3   Типичные применения графов","text":"<p>Как показано в таблице 9-1, многие реальные системы можно моделировать графами, а соответствующие задачи затем сводить к задачам вычислений на графах.</p> <p> Таблица 9-1   Распространенные графы в реальной жизни </p> Вершина Ребро Задача вычислений на графе Социальные сети Пользователь Дружеская связь Рекомендация потенциальных друзей Линии метро Станция Связность между станциями Рекомендация кратчайшего маршрута Солнечная система Небесное тело Гравитационное взаимодействие между телами Вычисление орбит планет","path":["Глава 9. Граф","9.1 &nbsp; Граф"],"tags":[]},{"location":"chapter_graph/graph_operations/","level":1,"title":"9.2   Базовые операции графа","text":"<p>Базовые операции графа можно разделить на операции над \"ребрами\" и операции над \"вершинами\". В двух способах представления - \"матрица смежности\" и \"список смежности\" - реализация будет различаться.</p>","path":["Глава 9. Граф","9.2 &nbsp; Базовые операции графа"],"tags":[]},{"location":"chapter_graph/graph_operations/#921","level":2,"title":"9.2.1   Реализация на основе матрицы смежности","text":"<p>Пусть дан неориентированный граф с числом вершин \\(n\\) . Тогда способы реализации различных операций показаны на рисунках ниже.</p> <ul> <li>Добавление или удаление ребра: достаточно изменить соответствующее ребро в матрице смежности, это требует \\(O(1)\\) времени. Поскольку граф неориентированный, нужно одновременно обновлять ребра в обоих направлениях.</li> <li>Добавление вершины: в конец матрицы смежности добавляется одна строка и один столбец, которые полностью заполняются нулями; это требует \\(O(n)\\) времени.</li> <li>Удаление вершины: из матрицы смежности удаляется одна строка и один столбец. В худшем случае, когда удаляются первая строка и первый столбец, приходится \"сдвигать вверх-влево\" \\((n-1)^2\\) элементов, поэтому требуется \\(O(n^2)\\) времени.</li> <li>Инициализация: передаются \\(n\\) вершин, затем инициализируется список вершин <code>vertices</code> длины \\(n\\) , что требует \\(O(n)\\) времени; после этого инициализируется матрица смежности <code>adjMat</code> размера \\(n \\times n\\) , что требует \\(O(n^2)\\) времени.</li> </ul> Инициализация матрицы смежностиДобавление ребраУдаление ребраДобавление вершиныУдаление вершины <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 9-7   Инициализация матрицы смежности, добавление и удаление ребер и вершин </p> <p>Ниже приведен код реализации графа на основе матрицы смежности:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby graph_adjacency_matrix.py<pre><code>class GraphAdjMat:\n    \"\"\"Класс неориентированного графа на основе матрицы смежности\"\"\"\n\n    def __init__(self, vertices: list[int], edges: list[list[int]]):\n        \"\"\"Конструктор\"\"\"\n        # Список вершин: элементы представляют «значения вершин», а индексы — «индексы вершин»\n        self.vertices: list[int] = []\n        # Матрица смежности, где индексы строк и столбцов соответствуют «индексам вершин»\n        self.adj_mat: list[list[int]] = []\n        # Добавление вершины\n        for val in vertices:\n            self.add_vertex(val)\n        # Добавить ребра\n        # Обратите внимание: элементы edges представляют собой индексы вершин, то есть соответствуют индексам элементов vertices\n        for e in edges:\n            self.add_edge(e[0], e[1])\n\n    def size(self) -&gt; int:\n        \"\"\"Получить число вершин\"\"\"\n        return len(self.vertices)\n\n    def add_vertex(self, val: int):\n        \"\"\"Добавление вершины\"\"\"\n        n = self.size()\n        # Добавить значение новой вершины в список вершин\n        self.vertices.append(val)\n        # Добавить строку в матрицу смежности\n        new_row = [0] * n\n        self.adj_mat.append(new_row)\n        # Добавить столбец в матрицу смежности\n        for row in self.adj_mat:\n            row.append(0)\n\n    def remove_vertex(self, index: int):\n        \"\"\"Удаление вершины\"\"\"\n        if index &gt;= self.size():\n            raise IndexError()\n        # Удалить вершину с индексом index из списка вершин\n        self.vertices.pop(index)\n        # Удалить строку с индексом index из матрицы смежности\n        self.adj_mat.pop(index)\n        # Удалить столбец с индексом index из матрицы смежности\n        for row in self.adj_mat:\n            row.pop(index)\n\n    def add_edge(self, i: int, j: int):\n        \"\"\"Добавление ребра\"\"\"\n        # Параметры i и j соответствуют индексам элементов vertices\n        # Обработка выхода индекса за границы и случая равенства\n        if i &lt; 0 or j &lt; 0 or i &gt;= self.size() or j &gt;= self.size() or i == j:\n            raise IndexError()\n        # В неориентированном графе матрица смежности симметрична относительно главной диагонали, то есть выполняется (i, j) == (j, i)\n        self.adj_mat[i][j] = 1\n        self.adj_mat[j][i] = 1\n\n    def remove_edge(self, i: int, j: int):\n        \"\"\"Удаление ребра\"\"\"\n        # Параметры i и j соответствуют индексам элементов vertices\n        # Обработка выхода индекса за границы и случая равенства\n        if i &lt; 0 or j &lt; 0 or i &gt;= self.size() or j &gt;= self.size() or i == j:\n            raise IndexError()\n        self.adj_mat[i][j] = 0\n        self.adj_mat[j][i] = 0\n\n    def print(self):\n        \"\"\"Вывести матрицу смежности\"\"\"\n        print(\"Список вершин =\", self.vertices)\n        print(\"Матрица смежности =\")\n        print_matrix(self.adj_mat)\n</code></pre> graph_adjacency_matrix.cpp<pre><code>/* Класс неориентированного графа на основе матрицы смежности */\nclass GraphAdjMat {\n    vector&lt;int&gt; vertices;       // Список вершин: элементы представляют «значения вершин», а индексы — «индексы вершин»\n    vector&lt;vector&lt;int&gt;&gt; adjMat; // Матрица смежности, где индексы строк и столбцов соответствуют «индексам вершин»\n\n  public:\n    /* Конструктор */\n    GraphAdjMat(const vector&lt;int&gt; &amp;vertices, const vector&lt;vector&lt;int&gt;&gt; &amp;edges) {\n        // Добавление вершины\n        for (int val : vertices) {\n            addVertex(val);\n        }\n        // Добавить ребра\n        // Обратите внимание: элементы edges представляют собой индексы вершин, то есть соответствуют индексам элементов vertices\n        for (const vector&lt;int&gt; &amp;edge : edges) {\n            addEdge(edge[0], edge[1]);\n        }\n    }\n\n    /* Получить число вершин */\n    int size() const {\n        return vertices.size();\n    }\n\n    /* Добавление вершины */\n    void addVertex(int val) {\n        int n = size();\n        // Добавить значение новой вершины в список вершин\n        vertices.push_back(val);\n        // Добавить строку в матрицу смежности\n        adjMat.emplace_back(vector&lt;int&gt;(n, 0));\n        // Добавить столбец в матрицу смежности\n        for (vector&lt;int&gt; &amp;row : adjMat) {\n            row.push_back(0);\n        }\n    }\n\n    /* Удаление вершины */\n    void removeVertex(int index) {\n        if (index &gt;= size()) {\n            throw out_of_range(\"вершина не существует\");\n        }\n        // Удалить вершину с индексом index из списка вершин\n        vertices.erase(vertices.begin() + index);\n        // Удалить строку с индексом index из матрицы смежности\n        adjMat.erase(adjMat.begin() + index);\n        // Удалить столбец с индексом index из матрицы смежности\n        for (vector&lt;int&gt; &amp;row : adjMat) {\n            row.erase(row.begin() + index);\n        }\n    }\n\n    /* Добавление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    void addEdge(int i, int j) {\n        // Обработка выхода индекса за границы и случая равенства\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j) {\n            throw out_of_range(\"вершина не существует\");\n        }\n        // В неориентированном графе матрица смежности симметрична относительно главной диагонали, то есть выполняется (i, j) == (j, i)\n        adjMat[i][j] = 1;\n        adjMat[j][i] = 1;\n    }\n\n    /* Удаление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    void removeEdge(int i, int j) {\n        // Обработка выхода индекса за границы и случая равенства\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j) {\n            throw out_of_range(\"вершина не существует\");\n        }\n        adjMat[i][j] = 0;\n        adjMat[j][i] = 0;\n    }\n\n    /* Вывести матрицу смежности */\n    void print() {\n        cout &lt;&lt; \"Список вершин = \";\n        printVector(vertices);\n        cout &lt;&lt; \"Матрица смежности =\" &lt;&lt; endl;\n        printVectorMatrix(adjMat);\n    }\n};\n</code></pre> graph_adjacency_matrix.java<pre><code>/* Класс неориентированного графа на основе матрицы смежности */\nclass GraphAdjMat {\n    List&lt;Integer&gt; vertices; // Список вершин: элементы представляют «значения вершин», а индексы — «индексы вершин»\n    List&lt;List&lt;Integer&gt;&gt; adjMat; // Матрица смежности, где индексы строк и столбцов соответствуют «индексам вершин»\n\n    /* Конструктор */\n    public GraphAdjMat(int[] vertices, int[][] edges) {\n        this.vertices = new ArrayList&lt;&gt;();\n        this.adjMat = new ArrayList&lt;&gt;();\n        // Добавление вершины\n        for (int val : vertices) {\n            addVertex(val);\n        }\n        // Добавить ребра\n        // Обратите внимание: элементы edges представляют собой индексы вершин, то есть соответствуют индексам элементов vertices\n        for (int[] e : edges) {\n            addEdge(e[0], e[1]);\n        }\n    }\n\n    /* Получить число вершин */\n    public int size() {\n        return vertices.size();\n    }\n\n    /* Добавление вершины */\n    public void addVertex(int val) {\n        int n = size();\n        // Добавить значение новой вершины в список вершин\n        vertices.add(val);\n        // Добавить строку в матрицу смежности\n        List&lt;Integer&gt; newRow = new ArrayList&lt;&gt;(n);\n        for (int j = 0; j &lt; n; j++) {\n            newRow.add(0);\n        }\n        adjMat.add(newRow);\n        // Добавить столбец в матрицу смежности\n        for (List&lt;Integer&gt; row : adjMat) {\n            row.add(0);\n        }\n    }\n\n    /* Удаление вершины */\n    public void removeVertex(int index) {\n        if (index &gt;= size())\n            throw new IndexOutOfBoundsException();\n        // Удалить вершину с индексом index из списка вершин\n        vertices.remove(index);\n        // Удалить строку с индексом index из матрицы смежности\n        adjMat.remove(index);\n        // Удалить столбец с индексом index из матрицы смежности\n        for (List&lt;Integer&gt; row : adjMat) {\n            row.remove(index);\n        }\n    }\n\n    /* Добавление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    public void addEdge(int i, int j) {\n        // Обработка выхода индекса за границы и случая равенства\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j)\n            throw new IndexOutOfBoundsException();\n        // В неориентированном графе матрица смежности симметрична относительно главной диагонали, то есть выполняется (i, j) == (j, i)\n        adjMat.get(i).set(j, 1);\n        adjMat.get(j).set(i, 1);\n    }\n\n    /* Удаление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    public void removeEdge(int i, int j) {\n        // Обработка выхода индекса за границы и случая равенства\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j)\n            throw new IndexOutOfBoundsException();\n        adjMat.get(i).set(j, 0);\n        adjMat.get(j).set(i, 0);\n    }\n\n    /* Вывести матрицу смежности */\n    public void print() {\n        System.out.print(\"Список вершин = \");\n        System.out.println(vertices);\n        System.out.println(\"Матрица смежности =\");\n        PrintUtil.printMatrix(adjMat);\n    }\n}\n</code></pre> graph_adjacency_matrix.cs<pre><code>/* Класс неориентированного графа на основе матрицы смежности */\nclass GraphAdjMat {\n    List&lt;int&gt; vertices;     // Список вершин: элементы представляют «значения вершин», а индексы — «индексы вершин»\n    List&lt;List&lt;int&gt;&gt; adjMat; // Матрица смежности, где индексы строк и столбцов соответствуют «индексам вершин»\n\n    /* Конструктор */\n    public GraphAdjMat(int[] vertices, int[][] edges) {\n        this.vertices = [];\n        this.adjMat = [];\n        // Добавление вершины\n        foreach (int val in vertices) {\n            AddVertex(val);\n        }\n        // Добавить ребра\n        // Обратите внимание: элементы edges представляют собой индексы вершин, то есть соответствуют индексам элементов vertices\n        foreach (int[] e in edges) {\n            AddEdge(e[0], e[1]);\n        }\n    }\n\n    /* Получить число вершин */\n    int Size() {\n        return vertices.Count;\n    }\n\n    /* Добавление вершины */\n    public void AddVertex(int val) {\n        int n = Size();\n        // Добавить значение новой вершины в список вершин\n        vertices.Add(val);\n        // Добавить строку в матрицу смежности\n        List&lt;int&gt; newRow = new(n);\n        for (int j = 0; j &lt; n; j++) {\n            newRow.Add(0);\n        }\n        adjMat.Add(newRow);\n        // Добавить столбец в матрицу смежности\n        foreach (List&lt;int&gt; row in adjMat) {\n            row.Add(0);\n        }\n    }\n\n    /* Удаление вершины */\n    public void RemoveVertex(int index) {\n        if (index &gt;= Size())\n            throw new IndexOutOfRangeException();\n        // Удалить вершину с индексом index из списка вершин\n        vertices.RemoveAt(index);\n        // Удалить строку с индексом index из матрицы смежности\n        adjMat.RemoveAt(index);\n        // Удалить столбец с индексом index из матрицы смежности\n        foreach (List&lt;int&gt; row in adjMat) {\n            row.RemoveAt(index);\n        }\n    }\n\n    /* Добавление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    public void AddEdge(int i, int j) {\n        // Обработка выхода индекса за границы и случая равенства\n        if (i &lt; 0 || j &lt; 0 || i &gt;= Size() || j &gt;= Size() || i == j)\n            throw new IndexOutOfRangeException();\n        // В неориентированном графе матрица смежности симметрична относительно главной диагонали, то есть выполняется (i, j) == (j, i)\n        adjMat[i][j] = 1;\n        adjMat[j][i] = 1;\n    }\n\n    /* Удаление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    public void RemoveEdge(int i, int j) {\n        // Обработка выхода индекса за границы и случая равенства\n        if (i &lt; 0 || j &lt; 0 || i &gt;= Size() || j &gt;= Size() || i == j)\n            throw new IndexOutOfRangeException();\n        adjMat[i][j] = 0;\n        adjMat[j][i] = 0;\n    }\n\n    /* Вывести матрицу смежности */\n    public void Print() {\n        Console.Write(\"Список вершин = \");\n        PrintUtil.PrintList(vertices);\n        Console.WriteLine(\"Матрица смежности =\");\n        PrintUtil.PrintMatrix(adjMat);\n    }\n}\n</code></pre> graph_adjacency_matrix.go<pre><code>/* Класс неориентированного графа на основе матрицы смежности */\ntype graphAdjMat struct {\n    // Список вершин: элементы представляют «значения вершин», а индексы — «индексы вершин»\n    vertices []int\n    // Матрица смежности, где индексы строк и столбцов соответствуют «индексам вершин»\n    adjMat [][]int\n}\n\n/* Конструктор */\nfunc newGraphAdjMat(vertices []int, edges [][]int) *graphAdjMat {\n    // Добавление вершины\n    n := len(vertices)\n    adjMat := make([][]int, n)\n    for i := range adjMat {\n        adjMat[i] = make([]int, n)\n    }\n    // Инициализировать граф\n    g := &amp;graphAdjMat{\n        vertices: vertices,\n        adjMat:   adjMat,\n    }\n    // Добавить ребра\n    // Обратите внимание: элементы edges представляют собой индексы вершин, то есть соответствуют индексам элементов vertices\n    for i := range edges {\n        g.addEdge(edges[i][0], edges[i][1])\n    }\n    return g\n}\n\n/* Получить число вершин */\nfunc (g *graphAdjMat) size() int {\n    return len(g.vertices)\n}\n\n/* Добавление вершины */\nfunc (g *graphAdjMat) addVertex(val int) {\n    n := g.size()\n    // Добавить значение новой вершины в список вершин\n    g.vertices = append(g.vertices, val)\n    // Добавить строку в матрицу смежности\n    newRow := make([]int, n)\n    g.adjMat = append(g.adjMat, newRow)\n    // Добавить столбец в матрицу смежности\n    for i := range g.adjMat {\n        g.adjMat[i] = append(g.adjMat[i], 0)\n    }\n}\n\n/* Удаление вершины */\nfunc (g *graphAdjMat) removeVertex(index int) {\n    if index &gt;= g.size() {\n        return\n    }\n    // Удалить вершину с индексом index из списка вершин\n    g.vertices = append(g.vertices[:index], g.vertices[index+1:]...)\n    // Удалить строку с индексом index из матрицы смежности\n    g.adjMat = append(g.adjMat[:index], g.adjMat[index+1:]...)\n    // Удалить столбец с индексом index из матрицы смежности\n    for i := range g.adjMat {\n        g.adjMat[i] = append(g.adjMat[i][:index], g.adjMat[i][index+1:]...)\n    }\n}\n\n/* Добавление ребра */\n// Параметры i и j соответствуют индексам элементов vertices\nfunc (g *graphAdjMat) addEdge(i, j int) {\n    // Обработка выхода индекса за границы и случая равенства\n    if i &lt; 0 || j &lt; 0 || i &gt;= g.size() || j &gt;= g.size() || i == j {\n        fmt.Errorf(\"%s\", \"Index Out Of Bounds Exception\")\n    }\n    // В неориентированном графе матрица смежности симметрична относительно главной диагонали, то есть выполняется (i, j) == (j, i)\n    g.adjMat[i][j] = 1\n    g.adjMat[j][i] = 1\n}\n\n/* Удаление ребра */\n// Параметры i и j соответствуют индексам элементов vertices\nfunc (g *graphAdjMat) removeEdge(i, j int) {\n    // Обработка выхода индекса за границы и случая равенства\n    if i &lt; 0 || j &lt; 0 || i &gt;= g.size() || j &gt;= g.size() || i == j {\n        fmt.Errorf(\"%s\", \"Index Out Of Bounds Exception\")\n    }\n    g.adjMat[i][j] = 0\n    g.adjMat[j][i] = 0\n}\n\n/* Вывести матрицу смежности */\nfunc (g *graphAdjMat) print() {\n    fmt.Printf(\"\\tСписок вершин = %v\\n\", g.vertices)\n    fmt.Printf(\"\\tМатрица смежности = \\n\")\n    for i := range g.adjMat {\n        fmt.Printf(\"\\t\\t\\t%v\\n\", g.adjMat[i])\n    }\n}\n</code></pre> graph_adjacency_matrix.swift<pre><code>/* Класс неориентированного графа на основе матрицы смежности */\nclass GraphAdjMat {\n    private var vertices: [Int] // Список вершин: элементы представляют «значения вершин», а индексы — «индексы вершин»\n    private var adjMat: [[Int]] // Матрица смежности, где индексы строк и столбцов соответствуют «индексам вершин»\n\n    /* Конструктор */\n    init(vertices: [Int], edges: [[Int]]) {\n        self.vertices = []\n        adjMat = []\n        // Добавление вершины\n        for val in vertices {\n            addVertex(val: val)\n        }\n        // Добавить ребра\n        // Обратите внимание: элементы edges представляют собой индексы вершин, то есть соответствуют индексам элементов vertices\n        for e in edges {\n            addEdge(i: e[0], j: e[1])\n        }\n    }\n\n    /* Получить число вершин */\n    func size() -&gt; Int {\n        vertices.count\n    }\n\n    /* Добавление вершины */\n    func addVertex(val: Int) {\n        let n = size()\n        // Добавить значение новой вершины в список вершин\n        vertices.append(val)\n        // Добавить строку в матрицу смежности\n        let newRow = Array(repeating: 0, count: n)\n        adjMat.append(newRow)\n        // Добавить столбец в матрицу смежности\n        for i in adjMat.indices {\n            adjMat[i].append(0)\n        }\n    }\n\n    /* Удаление вершины */\n    func removeVertex(index: Int) {\n        if index &gt;= size() {\n            fatalError(\"Выход за границы диапазона\")\n        }\n        // Удалить вершину с индексом index из списка вершин\n        vertices.remove(at: index)\n        // Удалить строку с индексом index из матрицы смежности\n        adjMat.remove(at: index)\n        // Удалить столбец с индексом index из матрицы смежности\n        for i in adjMat.indices {\n            adjMat[i].remove(at: index)\n        }\n    }\n\n    /* Добавление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    func addEdge(i: Int, j: Int) {\n        // Обработка выхода индекса за границы и случая равенства\n        if i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j {\n            fatalError(\"Выход за границы диапазона\")\n        }\n        // В неориентированном графе матрица смежности симметрична относительно главной диагонали, то есть выполняется (i, j) == (j, i)\n        adjMat[i][j] = 1\n        adjMat[j][i] = 1\n    }\n\n    /* Удаление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    func removeEdge(i: Int, j: Int) {\n        // Обработка выхода индекса за границы и случая равенства\n        if i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j {\n            fatalError(\"Выход за границы диапазона\")\n        }\n        adjMat[i][j] = 0\n        adjMat[j][i] = 0\n    }\n\n    /* Вывести матрицу смежности */\n    func print() {\n        Swift.print(\"Список вершин = \", terminator: \"\")\n        Swift.print(vertices)\n        Swift.print(\"Матрица смежности =\")\n        PrintUtil.printMatrix(matrix: adjMat)\n    }\n}\n</code></pre> graph_adjacency_matrix.js<pre><code>/* Класс неориентированного графа на основе матрицы смежности */\nclass GraphAdjMat {\n    vertices; // Список вершин: элементы представляют «значения вершин», а индексы — «индексы вершин»\n    adjMat; // Матрица смежности, где индексы строк и столбцов соответствуют «индексам вершин»\n\n    /* Конструктор */\n    constructor(vertices, edges) {\n        this.vertices = [];\n        this.adjMat = [];\n        // Добавление вершины\n        for (const val of vertices) {\n            this.addVertex(val);\n        }\n        // Добавить ребра\n        // Обратите внимание: элементы edges представляют собой индексы вершин, то есть соответствуют индексам элементов vertices\n        for (const e of edges) {\n            this.addEdge(e[0], e[1]);\n        }\n    }\n\n    /* Получить число вершин */\n    size() {\n        return this.vertices.length;\n    }\n\n    /* Добавление вершины */\n    addVertex(val) {\n        const n = this.size();\n        // Добавить значение новой вершины в список вершин\n        this.vertices.push(val);\n        // Добавить строку в матрицу смежности\n        const newRow = [];\n        for (let j = 0; j &lt; n; j++) {\n            newRow.push(0);\n        }\n        this.adjMat.push(newRow);\n        // Добавить столбец в матрицу смежности\n        for (const row of this.adjMat) {\n            row.push(0);\n        }\n    }\n\n    /* Удаление вершины */\n    removeVertex(index) {\n        if (index &gt;= this.size()) {\n            throw new RangeError('Index Out Of Bounds Exception');\n        }\n        // Удалить вершину с индексом index из списка вершин\n        this.vertices.splice(index, 1);\n\n        // Удалить строку с индексом index из матрицы смежности\n        this.adjMat.splice(index, 1);\n        // Удалить столбец с индексом index из матрицы смежности\n        for (const row of this.adjMat) {\n            row.splice(index, 1);\n        }\n    }\n\n    /* Добавление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    addEdge(i, j) {\n        // Обработка выхода индекса за границы и случая равенства\n        if (i &lt; 0 || j &lt; 0 || i &gt;= this.size() || j &gt;= this.size() || i === j) {\n            throw new RangeError('Index Out Of Bounds Exception');\n        }\n        // В неориентированном графе матрица смежности симметрична относительно главной диагонали, то есть выполняется (i, j) === (j, i)\n        this.adjMat[i][j] = 1;\n        this.adjMat[j][i] = 1;\n    }\n\n    /* Удаление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    removeEdge(i, j) {\n        // Обработка выхода индекса за границы и случая равенства\n        if (i &lt; 0 || j &lt; 0 || i &gt;= this.size() || j &gt;= this.size() || i === j) {\n            throw new RangeError('Index Out Of Bounds Exception');\n        }\n        this.adjMat[i][j] = 0;\n        this.adjMat[j][i] = 0;\n    }\n\n    /* Вывести матрицу смежности */\n    print() {\n        console.log('Список вершин = ', this.vertices);\n        console.log('Матрица смежности =', this.adjMat);\n    }\n}\n</code></pre> graph_adjacency_matrix.ts<pre><code>/* Класс неориентированного графа на основе матрицы смежности */\nclass GraphAdjMat {\n    vertices: number[]; // Список вершин: элементы представляют «значения вершин», а индексы — «индексы вершин»\n    adjMat: number[][]; // Матрица смежности, где индексы строк и столбцов соответствуют «индексам вершин»\n\n    /* Конструктор */\n    constructor(vertices: number[], edges: number[][]) {\n        this.vertices = [];\n        this.adjMat = [];\n        // Добавление вершины\n        for (const val of vertices) {\n            this.addVertex(val);\n        }\n        // Добавить ребра\n        // Обратите внимание: элементы edges представляют собой индексы вершин, то есть соответствуют индексам элементов vertices\n        for (const e of edges) {\n            this.addEdge(e[0], e[1]);\n        }\n    }\n\n    /* Получить число вершин */\n    size(): number {\n        return this.vertices.length;\n    }\n\n    /* Добавление вершины */\n    addVertex(val: number): void {\n        const n: number = this.size();\n        // Добавить значение новой вершины в список вершин\n        this.vertices.push(val);\n        // Добавить строку в матрицу смежности\n        const newRow: number[] = [];\n        for (let j: number = 0; j &lt; n; j++) {\n            newRow.push(0);\n        }\n        this.adjMat.push(newRow);\n        // Добавить столбец в матрицу смежности\n        for (const row of this.adjMat) {\n            row.push(0);\n        }\n    }\n\n    /* Удаление вершины */\n    removeVertex(index: number): void {\n        if (index &gt;= this.size()) {\n            throw new RangeError('Index Out Of Bounds Exception');\n        }\n        // Удалить вершину с индексом index из списка вершин\n        this.vertices.splice(index, 1);\n\n        // Удалить строку с индексом index из матрицы смежности\n        this.adjMat.splice(index, 1);\n        // Удалить столбец с индексом index из матрицы смежности\n        for (const row of this.adjMat) {\n            row.splice(index, 1);\n        }\n    }\n\n    /* Добавление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    addEdge(i: number, j: number): void {\n        // Обработка выхода индекса за границы и случая равенства\n        if (i &lt; 0 || j &lt; 0 || i &gt;= this.size() || j &gt;= this.size() || i === j) {\n            throw new RangeError('Index Out Of Bounds Exception');\n        }\n        // В неориентированном графе матрица смежности симметрична относительно главной диагонали, то есть выполняется (i, j) === (j, i)\n        this.adjMat[i][j] = 1;\n        this.adjMat[j][i] = 1;\n    }\n\n    /* Удаление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    removeEdge(i: number, j: number): void {\n        // Обработка выхода индекса за границы и случая равенства\n        if (i &lt; 0 || j &lt; 0 || i &gt;= this.size() || j &gt;= this.size() || i === j) {\n            throw new RangeError('Index Out Of Bounds Exception');\n        }\n        this.adjMat[i][j] = 0;\n        this.adjMat[j][i] = 0;\n    }\n\n    /* Вывести матрицу смежности */\n    print(): void {\n        console.log('Список вершин = ', this.vertices);\n        console.log('Матрица смежности =', this.adjMat);\n    }\n}\n</code></pre> graph_adjacency_matrix.dart<pre><code>/* Класс неориентированного графа на основе матрицы смежности */\nclass GraphAdjMat {\n  List&lt;int&gt; vertices = []; // Элемент вершины: элемент представляет «значение вершины», индекс представляет «индекс вершины»\n  List&lt;List&lt;int&gt;&gt; adjMat = []; // Матрица смежности, где индексы строк и столбцов соответствуют «индексам вершин»\n\n  /* Конструктор */\n  GraphAdjMat(List&lt;int&gt; vertices, List&lt;List&lt;int&gt;&gt; edges) {\n    this.vertices = [];\n    this.adjMat = [];\n    // Добавление вершины\n    for (int val in vertices) {\n      addVertex(val);\n    }\n    // Добавить ребра\n    // Обратите внимание: элементы edges представляют собой индексы вершин, то есть соответствуют индексам элементов vertices\n    for (List&lt;int&gt; e in edges) {\n      addEdge(e[0], e[1]);\n    }\n  }\n\n  /* Получить число вершин */\n  int size() {\n    return vertices.length;\n  }\n\n  /* Добавление вершины */\n  void addVertex(int val) {\n    int n = size();\n    // Добавить значение новой вершины в список вершин\n    vertices.add(val);\n    // Добавить строку в матрицу смежности\n    List&lt;int&gt; newRow = List.filled(n, 0, growable: true);\n    adjMat.add(newRow);\n    // Добавить столбец в матрицу смежности\n    for (List&lt;int&gt; row in adjMat) {\n      row.add(0);\n    }\n  }\n\n  /* Удаление вершины */\n  void removeVertex(int index) {\n    if (index &gt;= size()) {\n      throw IndexError;\n    }\n    // Удалить вершину с индексом index из списка вершин\n    vertices.removeAt(index);\n    // Удалить строку с индексом index из матрицы смежности\n    adjMat.removeAt(index);\n    // Удалить столбец с индексом index из матрицы смежности\n    for (List&lt;int&gt; row in adjMat) {\n      row.removeAt(index);\n    }\n  }\n\n  /* Добавление ребра */\n  // Параметры i и j соответствуют индексам элементов vertices\n  void addEdge(int i, int j) {\n    // Обработка выхода индекса за границы и случая равенства\n    if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j) {\n      throw IndexError;\n    }\n    // В неориентированном графе матрица смежности симметрична относительно главной диагонали, то есть выполняется (i, j) == (j, i)\n    adjMat[i][j] = 1;\n    adjMat[j][i] = 1;\n  }\n\n  /* Удаление ребра */\n  // Параметры i и j соответствуют индексам элементов vertices\n  void removeEdge(int i, int j) {\n    // Обработка выхода индекса за границы и случая равенства\n    if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j) {\n      throw IndexError;\n    }\n    adjMat[i][j] = 0;\n    adjMat[j][i] = 0;\n  }\n\n  /* Вывести матрицу смежности */\n  void printAdjMat() {\n    print(\"Список вершин = $vertices\");\n    print(\"Матрица смежности = \");\n    printMatrix(adjMat);\n  }\n}\n</code></pre> graph_adjacency_matrix.rs<pre><code>/* Тип неориентированного графа на основе матрицы смежности */\npub struct GraphAdjMat {\n    // Список вершин: элементы представляют «значения вершин», а индексы — «индексы вершин»\n    pub vertices: Vec&lt;i32&gt;,\n    // Матрица смежности, где индексы строк и столбцов соответствуют «индексам вершин»\n    pub adj_mat: Vec&lt;Vec&lt;i32&gt;&gt;,\n}\n\nimpl GraphAdjMat {\n    /* Конструктор */\n    pub fn new(vertices: Vec&lt;i32&gt;, edges: Vec&lt;[usize; 2]&gt;) -&gt; Self {\n        let mut graph = GraphAdjMat {\n            vertices: vec![],\n            adj_mat: vec![],\n        };\n        // Добавление вершины\n        for val in vertices {\n            graph.add_vertex(val);\n        }\n        // Добавить ребра\n        // Обратите внимание: элементы edges представляют собой индексы вершин, то есть соответствуют индексам элементов vertices\n        for edge in edges {\n            graph.add_edge(edge[0], edge[1])\n        }\n\n        graph\n    }\n\n    /* Получить число вершин */\n    pub fn size(&amp;self) -&gt; usize {\n        self.vertices.len()\n    }\n\n    /* Добавление вершины */\n    pub fn add_vertex(&amp;mut self, val: i32) {\n        let n = self.size();\n        // Добавить значение новой вершины в список вершин\n        self.vertices.push(val);\n        // Добавить строку в матрицу смежности\n        self.adj_mat.push(vec![0; n]);\n        // Добавить столбец в матрицу смежности\n        for row in self.adj_mat.iter_mut() {\n            row.push(0);\n        }\n    }\n\n    /* Удаление вершины */\n    pub fn remove_vertex(&amp;mut self, index: usize) {\n        if index &gt;= self.size() {\n            panic!(\"index error\")\n        }\n        // Удалить вершину с индексом index из списка вершин\n        self.vertices.remove(index);\n        // Удалить строку с индексом index из матрицы смежности\n        self.adj_mat.remove(index);\n        // Удалить столбец с индексом index из матрицы смежности\n        for row in self.adj_mat.iter_mut() {\n            row.remove(index);\n        }\n    }\n\n    /* Добавление ребра */\n    pub fn add_edge(&amp;mut self, i: usize, j: usize) {\n        // Параметры i и j соответствуют индексам элементов vertices\n        // Обработка выхода индекса за границы и случая равенства\n        if i &gt;= self.size() || j &gt;= self.size() || i == j {\n            panic!(\"index error\")\n        }\n        // В неориентированном графе матрица смежности симметрична относительно главной диагонали, то есть выполняется (i, j) == (j, i)\n        self.adj_mat[i][j] = 1;\n        self.adj_mat[j][i] = 1;\n    }\n\n    /* Удаление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    pub fn remove_edge(&amp;mut self, i: usize, j: usize) {\n        // Параметры i и j соответствуют индексам элементов vertices\n        // Обработка выхода индекса за границы и случая равенства\n        if i &gt;= self.size() || j &gt;= self.size() || i == j {\n            panic!(\"index error\")\n        }\n        self.adj_mat[i][j] = 0;\n        self.adj_mat[j][i] = 0;\n    }\n\n    /* Вывести матрицу смежности */\n    pub fn print(&amp;self) {\n        println!(\"Список вершин = {:?}\", self.vertices);\n        println!(\"Матрица смежности =\");\n        println!(\"[\");\n        for row in &amp;self.adj_mat {\n            println!(\"  {:?},\", row);\n        }\n        println!(\"]\")\n    }\n}\n</code></pre> graph_adjacency_matrix.c<pre><code>/* Структура неориентированного графа на основе матрицы смежности */\ntypedef struct {\n    int vertices[MAX_SIZE];\n    int adjMat[MAX_SIZE][MAX_SIZE];\n    int size;\n} GraphAdjMat;\n\n/* Конструктор */\nGraphAdjMat *newGraphAdjMat() {\n    GraphAdjMat *graph = (GraphAdjMat *)malloc(sizeof(GraphAdjMat));\n    graph-&gt;size = 0;\n    for (int i = 0; i &lt; MAX_SIZE; i++) {\n        for (int j = 0; j &lt; MAX_SIZE; j++) {\n            graph-&gt;adjMat[i][j] = 0;\n        }\n    }\n    return graph;\n}\n\n/* Деструктор */\nvoid delGraphAdjMat(GraphAdjMat *graph) {\n    free(graph);\n}\n\n/* Добавление вершины */\nvoid addVertex(GraphAdjMat *graph, int val) {\n    if (graph-&gt;size == MAX_SIZE) {\n        fprintf(stderr, \"Количество вершин графа уже достигло максимума\\n\");\n        return;\n    }\n    // Добавить n-ю вершину и обнулить n-ю строку и столбец\n    int n = graph-&gt;size;\n    graph-&gt;vertices[n] = val;\n    for (int i = 0; i &lt;= n; i++) {\n        graph-&gt;adjMat[n][i] = graph-&gt;adjMat[i][n] = 0;\n    }\n    graph-&gt;size++;\n}\n\n/* Удаление вершины */\nvoid removeVertex(GraphAdjMat *graph, int index) {\n    if (index &lt; 0 || index &gt;= graph-&gt;size) {\n        fprintf(stderr, \"индекс вершины выходит за границы\\n\");\n        return;\n    }\n    // Удалить вершину с индексом index из списка вершин\n    for (int i = index; i &lt; graph-&gt;size - 1; i++) {\n        graph-&gt;vertices[i] = graph-&gt;vertices[i + 1];\n    }\n    // Удалить строку с индексом index из матрицы смежности\n    for (int i = index; i &lt; graph-&gt;size - 1; i++) {\n        for (int j = 0; j &lt; graph-&gt;size; j++) {\n            graph-&gt;adjMat[i][j] = graph-&gt;adjMat[i + 1][j];\n        }\n    }\n    // Удалить столбец с индексом index из матрицы смежности\n    for (int i = 0; i &lt; graph-&gt;size; i++) {\n        for (int j = index; j &lt; graph-&gt;size - 1; j++) {\n            graph-&gt;adjMat[i][j] = graph-&gt;adjMat[i][j + 1];\n        }\n    }\n    graph-&gt;size--;\n}\n\n/* Добавление ребра */\n// Параметры i и j соответствуют индексам элементов vertices\nvoid addEdge(GraphAdjMat *graph, int i, int j) {\n    if (i &lt; 0 || j &lt; 0 || i &gt;= graph-&gt;size || j &gt;= graph-&gt;size || i == j) {\n        fprintf(stderr, \"индексы ребра выходят за границы или совпадают\\n\");\n        return;\n    }\n    graph-&gt;adjMat[i][j] = 1;\n    graph-&gt;adjMat[j][i] = 1;\n}\n\n/* Удаление ребра */\n// Параметры i и j соответствуют индексам элементов vertices\nvoid removeEdge(GraphAdjMat *graph, int i, int j) {\n    if (i &lt; 0 || j &lt; 0 || i &gt;= graph-&gt;size || j &gt;= graph-&gt;size || i == j) {\n        fprintf(stderr, \"индексы ребра выходят за границы или совпадают\\n\");\n        return;\n    }\n    graph-&gt;adjMat[i][j] = 0;\n    graph-&gt;adjMat[j][i] = 0;\n}\n\n/* Вывести матрицу смежности */\nvoid printGraphAdjMat(GraphAdjMat *graph) {\n    printf(\"Список вершин = \");\n    printArray(graph-&gt;vertices, graph-&gt;size);\n    printf(\"Матрица смежности =\\n\");\n    for (int i = 0; i &lt; graph-&gt;size; i++) {\n        printArray(graph-&gt;adjMat[i], graph-&gt;size);\n    }\n}\n</code></pre> graph_adjacency_matrix.kt<pre><code>/* Класс неориентированного графа на основе матрицы смежности */\nclass GraphAdjMat(vertices: IntArray, edges: Array&lt;IntArray&gt;) {\n    val vertices = mutableListOf&lt;Int&gt;() // Список вершин: элементы представляют «значения вершин», а индексы — «индексы вершин»\n    val adjMat = mutableListOf&lt;MutableList&lt;Int&gt;&gt;() // Матрица смежности, где индексы строк и столбцов соответствуют «индексам вершин»\n\n    /* Конструктор */\n    init {\n        // Добавление вершины\n        for (vertex in vertices) {\n            addVertex(vertex)\n        }\n        // Добавить ребра\n        // Обратите внимание: элементы edges представляют собой индексы вершин, то есть соответствуют индексам элементов vertices\n        for (edge in edges) {\n            addEdge(edge[0], edge[1])\n        }\n    }\n\n    /* Получить число вершин */\n    fun size(): Int {\n        return vertices.size\n    }\n\n    /* Добавление вершины */\n    fun addVertex(_val: Int) {\n        val n = size()\n        // Добавить значение новой вершины в список вершин\n        vertices.add(_val)\n        // Добавить строку в матрицу смежности\n        val newRow = mutableListOf&lt;Int&gt;()\n        for (j in 0..&lt;n) {\n            newRow.add(0)\n        }\n        adjMat.add(newRow)\n        // Добавить столбец в матрицу смежности\n        for (row in adjMat) {\n            row.add(0)\n        }\n    }\n\n    /* Удаление вершины */\n    fun removeVertex(index: Int) {\n        if (index &gt;= size())\n            throw IndexOutOfBoundsException()\n        // Удалить вершину с индексом index из списка вершин\n        vertices.removeAt(index)\n        // Удалить строку с индексом index из матрицы смежности\n        adjMat.removeAt(index)\n        // Удалить столбец с индексом index из матрицы смежности\n        for (row in adjMat) {\n            row.removeAt(index)\n        }\n    }\n\n    /* Добавление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    fun addEdge(i: Int, j: Int) {\n        // Обработка выхода индекса за границы и случая равенства\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j)\n            throw IndexOutOfBoundsException()\n        // В неориентированном графе матрица смежности симметрична относительно главной диагонали, то есть выполняется (i, j) == (j, i)\n        adjMat[i][j] = 1\n        adjMat[j][i] = 1\n    }\n\n    /* Удаление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    fun removeEdge(i: Int, j: Int) {\n        // Обработка выхода индекса за границы и случая равенства\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j)\n            throw IndexOutOfBoundsException()\n        adjMat[i][j] = 0\n        adjMat[j][i] = 0\n    }\n\n    /* Вывести матрицу смежности */\n    fun print() {\n        print(\"Список вершин = \")\n        println(vertices)\n        println(\"Матрица смежности =\")\n        printMatrix(adjMat)\n    }\n}\n</code></pre> graph_adjacency_matrix.rb<pre><code>### Класс неориентированного графа на основе матрицы смежности ###\nclass GraphAdjMat\n  def initialize(vertices, edges)\n    ### Конструктор ###\n    # Список вершин: элементы представляют «значения вершин», а индексы — «индексы вершин»\n    @vertices = []\n    # Матрица смежности, где индексы строк и столбцов соответствуют «индексам вершин»\n    @adj_mat = []\n    # Добавление вершины\n    vertices.each { |val| add_vertex(val) }\n    # Добавить ребра\n    # Обратите внимание: элементы edges представляют собой индексы вершин, то есть соответствуют индексам элементов vertices\n    edges.each { |e| add_edge(e[0], e[1]) }\n  end\n\n  ### Получение числа вершин ###\n  def size\n    @vertices.length\n  end\n\n  ### Добавление вершины ###\n  def add_vertex(val)\n    n = size\n    # Добавить значение новой вершины в список вершин\n    @vertices &lt;&lt; val\n    # Добавить строку в матрицу смежности\n    new_row = Array.new(n, 0)\n    @adj_mat &lt;&lt; new_row\n    # Добавить столбец в матрицу смежности\n    @adj_mat.each { |row| row &lt;&lt; 0 }\n  end\n\n  ### Удаление вершины ###\n  def remove_vertex(index)\n    raise IndexError if index &gt;= size\n\n    # Удалить вершину с индексом index из списка вершин\n    @vertices.delete_at(index)\n    # Удалить строку с индексом index из матрицы смежности\n    @adj_mat.delete_at(index)\n    # Удалить столбец с индексом index из матрицы смежности\n    @adj_mat.each { |row| row.delete_at(index) }\n  end\n\n  ### Добавление ребра ###\n  def add_edge(i, j)\n    # Параметры i и j соответствуют индексам элементов vertices\n    # Обработка выхода индекса за границы и случая равенства\n    if i &lt; 0 || j &lt; 0 || i &gt;= size || j &gt;= size || i == j\n      raise IndexError\n    end\n    # В неориентированном графе матрица смежности симметрична относительно главной диагонали, то есть выполняется (i, j) == (j, i)\n    @adj_mat[i][j] = 1\n    @adj_mat[j][i] = 1\n  end\n\n  ### Удаление ребра ###\n  def remove_edge(i, j)\n    # Параметры i и j соответствуют индексам элементов vertices\n    # Обработка выхода индекса за границы и случая равенства\n    if i &lt; 0 || j &lt; 0 || i &gt;= size || j &gt;= size || i == j\n      raise IndexError\n    end\n    @adj_mat[i][j] = 0\n    @adj_mat[j][i] = 0\n  end\n\n  ### Вывести матрицу смежности ###\n  def __print__\n    puts \"Список вершин = #{@vertices}\"\n    puts 'Матрица смежности ='\n    print_matrix(@adj_mat)\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 9. Граф","9.2 &nbsp; Базовые операции графа"],"tags":[]},{"location":"chapter_graph/graph_operations/#922","level":2,"title":"9.2.2   Реализация на основе списка смежности","text":"<p>Пусть неориентированный граф содержит в сумме \\(n\\) вершин и \\(m\\) ребер. Тогда различные операции можно реализовать способом, показанным на рисунках ниже.</p> <ul> <li>Добавление ребра: достаточно добавить ребро в конец списка, соответствующего вершине; это требует \\(O(1)\\) времени. Поскольку граф неориентированный, нужно одновременно добавлять ребра в обоих направлениях.</li> <li>Удаление ребра: нужно найти и удалить указанное ребро в списке, соответствующем вершине; это требует \\(O(m)\\) времени. В неориентированном графе нужно удалять ребра в обоих направлениях.</li> <li>Добавление вершины: в список смежности добавляется еще один список, а новая вершина становится его головным узлом; это требует \\(O(1)\\) времени.</li> <li>Удаление вершины: требуется пройти по всему списку смежности и удалить все ребра, содержащие указанную вершину; это требует \\(O(n + m)\\) времени.</li> <li>Инициализация: в списке смежности создаются \\(n\\) вершин и \\(2m\\) ребер; это требует \\(O(n + m)\\) времени.</li> </ul> Инициализация списка смежностиДобавление ребраУдаление ребраДобавление вершиныУдаление вершины <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 9-8   Инициализация списка смежности, добавление и удаление ребер и вершин </p> <p>Ниже приведен код списка смежности. По сравнению с рисунками выше, реальная реализация имеет следующие отличия.</p> <ul> <li>Чтобы упростить добавление и удаление вершин, а также упростить код, мы используем список, то есть динамический массив, вместо связного списка.</li> <li>Для хранения списка смежности используется хеш-таблица, где <code>key</code> - это экземпляр вершины, а <code>value</code> - список смежных вершин данной вершины.</li> </ul> <p>Кроме того, в списке смежности мы используем класс <code>Vertex</code> для представления вершины. Причина в следующем: если, как и в матрице смежности, различать вершины по индексам списка, то при удалении вершины с индексом \\(i\\) пришлось бы обходить весь список смежности и уменьшать на \\(1\\) все индексы, большие \\(i\\) , что крайне неэффективно. Если же каждая вершина является уникальным экземпляром <code>Vertex</code> , то после удаления одной вершины остальные вершины менять уже не требуется.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby graph_adjacency_list.py<pre><code>class GraphAdjList:\n    \"\"\"Класс неориентированного графа на основе списка смежности\"\"\"\n\n    def __init__(self, edges: list[list[Vertex]]):\n        \"\"\"Конструктор\"\"\"\n        # Список смежности, где key — вершина, а value — все смежные ей вершины\n        self.adj_list = dict[Vertex, list[Vertex]]()\n        # Добавить все вершины и ребра\n        for edge in edges:\n            self.add_vertex(edge[0])\n            self.add_vertex(edge[1])\n            self.add_edge(edge[0], edge[1])\n\n    def size(self) -&gt; int:\n        \"\"\"Получить число вершин\"\"\"\n        return len(self.adj_list)\n\n    def add_edge(self, vet1: Vertex, vet2: Vertex):\n        \"\"\"Добавление ребра\"\"\"\n        if vet1 not in self.adj_list or vet2 not in self.adj_list or vet1 == vet2:\n            raise ValueError()\n        # Добавить ребро vet1 - vet2\n        self.adj_list[vet1].append(vet2)\n        self.adj_list[vet2].append(vet1)\n\n    def remove_edge(self, vet1: Vertex, vet2: Vertex):\n        \"\"\"Удаление ребра\"\"\"\n        if vet1 not in self.adj_list or vet2 not in self.adj_list or vet1 == vet2:\n            raise ValueError()\n        # Удалить ребро vet1 - vet2\n        self.adj_list[vet1].remove(vet2)\n        self.adj_list[vet2].remove(vet1)\n\n    def add_vertex(self, vet: Vertex):\n        \"\"\"Добавление вершины\"\"\"\n        if vet in self.adj_list:\n            return\n        # Добавить новый список в список смежности\n        self.adj_list[vet] = []\n\n    def remove_vertex(self, vet: Vertex):\n        \"\"\"Удаление вершины\"\"\"\n        if vet not in self.adj_list:\n            raise ValueError()\n        # Удалить из списка смежности список, соответствующий вершине vet\n        self.adj_list.pop(vet)\n        # Обойти списки других вершин и удалить все ребра, содержащие vet\n        for vertex in self.adj_list:\n            if vet in self.adj_list[vertex]:\n                self.adj_list[vertex].remove(vet)\n\n    def print(self):\n        \"\"\"Вывести список смежности\"\"\"\n        print(\"Список смежности =\")\n        for vertex in self.adj_list:\n            tmp = [v.val for v in self.adj_list[vertex]]\n            print(f\"{vertex.val}: {tmp},\")\n</code></pre> graph_adjacency_list.cpp<pre><code>/* Класс неориентированного графа на основе списка смежности */\nclass GraphAdjList {\n  public:\n    // Список смежности, где key — вершина, а value — все смежные ей вершины\n    unordered_map&lt;Vertex *, vector&lt;Vertex *&gt;&gt; adjList;\n\n    /* Удалить указанный узел из vector */\n    void remove(vector&lt;Vertex *&gt; &amp;vec, Vertex *vet) {\n        for (int i = 0; i &lt; vec.size(); i++) {\n            if (vec[i] == vet) {\n                vec.erase(vec.begin() + i);\n                break;\n            }\n        }\n    }\n\n    /* Конструктор */\n    GraphAdjList(const vector&lt;vector&lt;Vertex *&gt;&gt; &amp;edges) {\n        // Добавить все вершины и ребра\n        for (const vector&lt;Vertex *&gt; &amp;edge : edges) {\n            addVertex(edge[0]);\n            addVertex(edge[1]);\n            addEdge(edge[0], edge[1]);\n        }\n    }\n\n    /* Получить число вершин */\n    int size() {\n        return adjList.size();\n    }\n\n    /* Добавление ребра */\n    void addEdge(Vertex *vet1, Vertex *vet2) {\n        if (!adjList.count(vet1) || !adjList.count(vet2) || vet1 == vet2)\n            throw invalid_argument(\"вершина не существует\");\n        // Добавить ребро vet1 - vet2\n        adjList[vet1].push_back(vet2);\n        adjList[vet2].push_back(vet1);\n    }\n\n    /* Удаление ребра */\n    void removeEdge(Vertex *vet1, Vertex *vet2) {\n        if (!adjList.count(vet1) || !adjList.count(vet2) || vet1 == vet2)\n            throw invalid_argument(\"вершина не существует\");\n        // Удалить ребро vet1 - vet2\n        remove(adjList[vet1], vet2);\n        remove(adjList[vet2], vet1);\n    }\n\n    /* Добавление вершины */\n    void addVertex(Vertex *vet) {\n        if (adjList.count(vet))\n            return;\n        // Добавить новый список в список смежности\n        adjList[vet] = vector&lt;Vertex *&gt;();\n    }\n\n    /* Удаление вершины */\n    void removeVertex(Vertex *vet) {\n        if (!adjList.count(vet))\n            throw invalid_argument(\"вершина не существует\");\n        // Удалить из списка смежности список, соответствующий вершине vet\n        adjList.erase(vet);\n        // Обойти списки других вершин и удалить все ребра, содержащие vet\n        for (auto &amp;adj : adjList) {\n            remove(adj.second, vet);\n        }\n    }\n\n    /* Вывести список смежности */\n    void print() {\n        cout &lt;&lt; \"Список смежности =\" &lt;&lt; endl;\n        for (auto &amp;adj : adjList) {\n            const auto &amp;key = adj.first;\n            const auto &amp;vec = adj.second;\n            cout &lt;&lt; key-&gt;val &lt;&lt; \": \";\n            printVector(vetsToVals(vec));\n        }\n    }\n};\n</code></pre> graph_adjacency_list.java<pre><code>/* Класс неориентированного графа на основе списка смежности */\nclass GraphAdjList {\n    // Список смежности, где key — вершина, а value — все смежные ей вершины\n    Map&lt;Vertex, List&lt;Vertex&gt;&gt; adjList;\n\n    /* Конструктор */\n    public GraphAdjList(Vertex[][] edges) {\n        this.adjList = new HashMap&lt;&gt;();\n        // Добавить все вершины и ребра\n        for (Vertex[] edge : edges) {\n            addVertex(edge[0]);\n            addVertex(edge[1]);\n            addEdge(edge[0], edge[1]);\n        }\n    }\n\n    /* Получить число вершин */\n    public int size() {\n        return adjList.size();\n    }\n\n    /* Добавление ребра */\n    public void addEdge(Vertex vet1, Vertex vet2) {\n        if (!adjList.containsKey(vet1) || !adjList.containsKey(vet2) || vet1 == vet2)\n            throw new IllegalArgumentException();\n        // Добавить ребро vet1 - vet2\n        adjList.get(vet1).add(vet2);\n        adjList.get(vet2).add(vet1);\n    }\n\n    /* Удаление ребра */\n    public void removeEdge(Vertex vet1, Vertex vet2) {\n        if (!adjList.containsKey(vet1) || !adjList.containsKey(vet2) || vet1 == vet2)\n            throw new IllegalArgumentException();\n        // Удалить ребро vet1 - vet2\n        adjList.get(vet1).remove(vet2);\n        adjList.get(vet2).remove(vet1);\n    }\n\n    /* Добавление вершины */\n    public void addVertex(Vertex vet) {\n        if (adjList.containsKey(vet))\n            return;\n        // Добавить новый список в список смежности\n        adjList.put(vet, new ArrayList&lt;&gt;());\n    }\n\n    /* Удаление вершины */\n    public void removeVertex(Vertex vet) {\n        if (!adjList.containsKey(vet))\n            throw new IllegalArgumentException();\n        // Удалить из списка смежности список, соответствующий вершине vet\n        adjList.remove(vet);\n        // Обойти списки других вершин и удалить все ребра, содержащие vet\n        for (List&lt;Vertex&gt; list : adjList.values()) {\n            list.remove(vet);\n        }\n    }\n\n    /* Вывести список смежности */\n    public void print() {\n        System.out.println(\"Список смежности =\");\n        for (Map.Entry&lt;Vertex, List&lt;Vertex&gt;&gt; pair : adjList.entrySet()) {\n            List&lt;Integer&gt; tmp = new ArrayList&lt;&gt;();\n            for (Vertex vertex : pair.getValue())\n                tmp.add(vertex.val);\n            System.out.println(pair.getKey().val + \": \" + tmp + \",\");\n        }\n    }\n}\n</code></pre> graph_adjacency_list.cs<pre><code>/* Класс неориентированного графа на основе списка смежности */\nclass GraphAdjList {\n    // Список смежности, где key — вершина, а value — все смежные ей вершины\n    public Dictionary&lt;Vertex, List&lt;Vertex&gt;&gt; adjList;\n\n    /* Конструктор */\n    public GraphAdjList(Vertex[][] edges) {\n        adjList = [];\n        // Добавить все вершины и ребра\n        foreach (Vertex[] edge in edges) {\n            AddVertex(edge[0]);\n            AddVertex(edge[1]);\n            AddEdge(edge[0], edge[1]);\n        }\n    }\n\n    /* Получить число вершин */\n    int Size() {\n        return adjList.Count;\n    }\n\n    /* Добавление ребра */\n    public void AddEdge(Vertex vet1, Vertex vet2) {\n        if (!adjList.ContainsKey(vet1) || !adjList.ContainsKey(vet2) || vet1 == vet2)\n            throw new InvalidOperationException();\n        // Добавить ребро vet1 - vet2\n        adjList[vet1].Add(vet2);\n        adjList[vet2].Add(vet1);\n    }\n\n    /* Удаление ребра */\n    public void RemoveEdge(Vertex vet1, Vertex vet2) {\n        if (!adjList.ContainsKey(vet1) || !adjList.ContainsKey(vet2) || vet1 == vet2)\n            throw new InvalidOperationException();\n        // Удалить ребро vet1 - vet2\n        adjList[vet1].Remove(vet2);\n        adjList[vet2].Remove(vet1);\n    }\n\n    /* Добавление вершины */\n    public void AddVertex(Vertex vet) {\n        if (adjList.ContainsKey(vet))\n            return;\n        // Добавить новый список в список смежности\n        adjList.Add(vet, []);\n    }\n\n    /* Удаление вершины */\n    public void RemoveVertex(Vertex vet) {\n        if (!adjList.ContainsKey(vet))\n            throw new InvalidOperationException();\n        // Удалить из списка смежности список, соответствующий вершине vet\n        adjList.Remove(vet);\n        // Обойти списки других вершин и удалить все ребра, содержащие vet\n        foreach (List&lt;Vertex&gt; list in adjList.Values) {\n            list.Remove(vet);\n        }\n    }\n\n    /* Вывести список смежности */\n    public void Print() {\n        Console.WriteLine(\"Список смежности =\");\n        foreach (KeyValuePair&lt;Vertex, List&lt;Vertex&gt;&gt; pair in adjList) {\n            List&lt;int&gt; tmp = [];\n            foreach (Vertex vertex in pair.Value)\n                tmp.Add(vertex.val);\n            Console.WriteLine(pair.Key.val + \": [\" + string.Join(\", \", tmp) + \"],\");\n        }\n    }\n}\n</code></pre> graph_adjacency_list.go<pre><code>/* Класс неориентированного графа на основе списка смежности */\ntype graphAdjList struct {\n    // Список смежности, где key — вершина, а value — все смежные ей вершины\n    adjList map[Vertex][]Vertex\n}\n\n/* Конструктор */\nfunc newGraphAdjList(edges [][]Vertex) *graphAdjList {\n    g := &amp;graphAdjList{\n        adjList: make(map[Vertex][]Vertex),\n    }\n    // Добавить все вершины и ребра\n    for _, edge := range edges {\n        g.addVertex(edge[0])\n        g.addVertex(edge[1])\n        g.addEdge(edge[0], edge[1])\n    }\n    return g\n}\n\n/* Получить число вершин */\nfunc (g *graphAdjList) size() int {\n    return len(g.adjList)\n}\n\n/* Добавление ребра */\nfunc (g *graphAdjList) addEdge(vet1 Vertex, vet2 Vertex) {\n    _, ok1 := g.adjList[vet1]\n    _, ok2 := g.adjList[vet2]\n    if !ok1 || !ok2 || vet1 == vet2 {\n        panic(\"error\")\n    }\n    // Добавить ребро vet1 - vet2, добавив анонимную struct{}\n    g.adjList[vet1] = append(g.adjList[vet1], vet2)\n    g.adjList[vet2] = append(g.adjList[vet2], vet1)\n}\n\n/* Удаление ребра */\nfunc (g *graphAdjList) removeEdge(vet1 Vertex, vet2 Vertex) {\n    _, ok1 := g.adjList[vet1]\n    _, ok2 := g.adjList[vet2]\n    if !ok1 || !ok2 || vet1 == vet2 {\n        panic(\"error\")\n    }\n    // Удалить ребро vet1 - vet2\n    g.adjList[vet1] = DeleteSliceElms(g.adjList[vet1], vet2)\n    g.adjList[vet2] = DeleteSliceElms(g.adjList[vet2], vet1)\n}\n\n/* Добавление вершины */\nfunc (g *graphAdjList) addVertex(vet Vertex) {\n    _, ok := g.adjList[vet]\n    if ok {\n        return\n    }\n    // Добавить новый список в список смежности\n    g.adjList[vet] = make([]Vertex, 0)\n}\n\n/* Удаление вершины */\nfunc (g *graphAdjList) removeVertex(vet Vertex) {\n    _, ok := g.adjList[vet]\n    if !ok {\n        panic(\"error\")\n    }\n    // Удалить из списка смежности список, соответствующий вершине vet\n    delete(g.adjList, vet)\n    // Обойти списки других вершин и удалить все ребра, содержащие vet\n    for v, list := range g.adjList {\n        g.adjList[v] = DeleteSliceElms(list, vet)\n    }\n}\n\n/* Вывести список смежности */\nfunc (g *graphAdjList) print() {\n    var builder strings.Builder\n    fmt.Printf(\"Список смежности = \\n\")\n    for k, v := range g.adjList {\n        builder.WriteString(\"\\t\\t\" + strconv.Itoa(k.Val) + \": \")\n        for _, vet := range v {\n            builder.WriteString(strconv.Itoa(vet.Val) + \" \")\n        }\n        fmt.Println(builder.String())\n        builder.Reset()\n    }\n}\n</code></pre> graph_adjacency_list.swift<pre><code>/* Класс неориентированного графа на основе списка смежности */\nclass GraphAdjList {\n    // Список смежности, где key — вершина, а value — все смежные ей вершины\n    public private(set) var adjList: [Vertex: [Vertex]]\n\n    /* Конструктор */\n    public init(edges: [[Vertex]]) {\n        adjList = [:]\n        // Добавить все вершины и ребра\n        for edge in edges {\n            addVertex(vet: edge[0])\n            addVertex(vet: edge[1])\n            addEdge(vet1: edge[0], vet2: edge[1])\n        }\n    }\n\n    /* Получить число вершин */\n    public func size() -&gt; Int {\n        adjList.count\n    }\n\n    /* Добавление ребра */\n    public func addEdge(vet1: Vertex, vet2: Vertex) {\n        if adjList[vet1] == nil || adjList[vet2] == nil || vet1 == vet2 {\n            fatalError(\"Неверный аргумент\")\n        }\n        // Добавить ребро vet1 - vet2\n        adjList[vet1]?.append(vet2)\n        adjList[vet2]?.append(vet1)\n    }\n\n    /* Удаление ребра */\n    public func removeEdge(vet1: Vertex, vet2: Vertex) {\n        if adjList[vet1] == nil || adjList[vet2] == nil || vet1 == vet2 {\n            fatalError(\"Неверный аргумент\")\n        }\n        // Удалить ребро vet1 - vet2\n        adjList[vet1]?.removeAll { $0 == vet2 }\n        adjList[vet2]?.removeAll { $0 == vet1 }\n    }\n\n    /* Добавление вершины */\n    public func addVertex(vet: Vertex) {\n        if adjList[vet] != nil {\n            return\n        }\n        // Добавить новый список в список смежности\n        adjList[vet] = []\n    }\n\n    /* Удаление вершины */\n    public func removeVertex(vet: Vertex) {\n        if adjList[vet] == nil {\n            fatalError(\"Неверный аргумент\")\n        }\n        // Удалить из списка смежности список, соответствующий вершине vet\n        adjList.removeValue(forKey: vet)\n        // Обойти списки других вершин и удалить все ребра, содержащие vet\n        for key in adjList.keys {\n            adjList[key]?.removeAll { $0 == vet }\n        }\n    }\n\n    /* Вывести список смежности */\n    public func print() {\n        Swift.print(\"Список смежности =\")\n        for (vertex, list) in adjList {\n            let list = list.map { $0.val }\n            Swift.print(\"\\(vertex.val): \\(list),\")\n        }\n    }\n}\n</code></pre> graph_adjacency_list.js<pre><code>/* Класс неориентированного графа на основе списка смежности */\nclass GraphAdjList {\n    // Список смежности, где key — вершина, а value — все смежные ей вершины\n    adjList;\n\n    /* Конструктор */\n    constructor(edges) {\n        this.adjList = new Map();\n        // Добавить все вершины и ребра\n        for (const edge of edges) {\n            this.addVertex(edge[0]);\n            this.addVertex(edge[1]);\n            this.addEdge(edge[0], edge[1]);\n        }\n    }\n\n    /* Получить число вершин */\n    size() {\n        return this.adjList.size;\n    }\n\n    /* Добавление ребра */\n    addEdge(vet1, vet2) {\n        if (\n            !this.adjList.has(vet1) ||\n            !this.adjList.has(vet2) ||\n            vet1 === vet2\n        ) {\n            throw new Error('Illegal Argument Exception');\n        }\n        // Добавить ребро vet1 - vet2\n        this.adjList.get(vet1).push(vet2);\n        this.adjList.get(vet2).push(vet1);\n    }\n\n    /* Удаление ребра */\n    removeEdge(vet1, vet2) {\n        if (\n            !this.adjList.has(vet1) ||\n            !this.adjList.has(vet2) ||\n            vet1 === vet2 ||\n            this.adjList.get(vet1).indexOf(vet2) === -1\n        ) {\n            throw new Error('Illegal Argument Exception');\n        }\n        // Удалить ребро vet1 - vet2\n        this.adjList.get(vet1).splice(this.adjList.get(vet1).indexOf(vet2), 1);\n        this.adjList.get(vet2).splice(this.adjList.get(vet2).indexOf(vet1), 1);\n    }\n\n    /* Добавление вершины */\n    addVertex(vet) {\n        if (this.adjList.has(vet)) return;\n        // Добавить новый список в список смежности\n        this.adjList.set(vet, []);\n    }\n\n    /* Удаление вершины */\n    removeVertex(vet) {\n        if (!this.adjList.has(vet)) {\n            throw new Error('Illegal Argument Exception');\n        }\n        // Удалить из списка смежности список, соответствующий вершине vet\n        this.adjList.delete(vet);\n        // Обойти списки других вершин и удалить все ребра, содержащие vet\n        for (const set of this.adjList.values()) {\n            const index = set.indexOf(vet);\n            if (index &gt; -1) {\n                set.splice(index, 1);\n            }\n        }\n    }\n\n    /* Вывести список смежности */\n    print() {\n        console.log('Список смежности =');\n        for (const [key, value] of this.adjList) {\n            const tmp = [];\n            for (const vertex of value) {\n                tmp.push(vertex.val);\n            }\n            console.log(key.val + ': ' + tmp.join());\n        }\n    }\n}\n</code></pre> graph_adjacency_list.ts<pre><code>/* Класс неориентированного графа на основе списка смежности */\nclass GraphAdjList {\n    // Список смежности, где key — вершина, а value — все смежные ей вершины\n    adjList: Map&lt;Vertex, Vertex[]&gt;;\n\n    /* Конструктор */\n    constructor(edges: Vertex[][]) {\n        this.adjList = new Map();\n        // Добавить все вершины и ребра\n        for (const edge of edges) {\n            this.addVertex(edge[0]);\n            this.addVertex(edge[1]);\n            this.addEdge(edge[0], edge[1]);\n        }\n    }\n\n    /* Получить число вершин */\n    size(): number {\n        return this.adjList.size;\n    }\n\n    /* Добавление ребра */\n    addEdge(vet1: Vertex, vet2: Vertex): void {\n        if (\n            !this.adjList.has(vet1) ||\n            !this.adjList.has(vet2) ||\n            vet1 === vet2\n        ) {\n            throw new Error('Illegal Argument Exception');\n        }\n        // Добавить ребро vet1 - vet2\n        this.adjList.get(vet1).push(vet2);\n        this.adjList.get(vet2).push(vet1);\n    }\n\n    /* Удаление ребра */\n    removeEdge(vet1: Vertex, vet2: Vertex): void {\n        if (\n            !this.adjList.has(vet1) ||\n            !this.adjList.has(vet2) ||\n            vet1 === vet2 ||\n            this.adjList.get(vet1).indexOf(vet2) === -1\n        ) {\n            throw new Error('Illegal Argument Exception');\n        }\n        // Удалить ребро vet1 - vet2\n        this.adjList.get(vet1).splice(this.adjList.get(vet1).indexOf(vet2), 1);\n        this.adjList.get(vet2).splice(this.adjList.get(vet2).indexOf(vet1), 1);\n    }\n\n    /* Добавление вершины */\n    addVertex(vet: Vertex): void {\n        if (this.adjList.has(vet)) return;\n        // Добавить новый список в список смежности\n        this.adjList.set(vet, []);\n    }\n\n    /* Удаление вершины */\n    removeVertex(vet: Vertex): void {\n        if (!this.adjList.has(vet)) {\n            throw new Error('Illegal Argument Exception');\n        }\n        // Удалить из списка смежности список, соответствующий вершине vet\n        this.adjList.delete(vet);\n        // Обойти списки других вершин и удалить все ребра, содержащие vet\n        for (const set of this.adjList.values()) {\n            const index: number = set.indexOf(vet);\n            if (index &gt; -1) {\n                set.splice(index, 1);\n            }\n        }\n    }\n\n    /* Вывести список смежности */\n    print(): void {\n        console.log('Список смежности =');\n        for (const [key, value] of this.adjList.entries()) {\n            const tmp = [];\n            for (const vertex of value) {\n                tmp.push(vertex.val);\n            }\n            console.log(key.val + ': ' + tmp.join());\n        }\n    }\n}\n</code></pre> graph_adjacency_list.dart<pre><code>/* Класс неориентированного графа на основе списка смежности */\nclass GraphAdjList {\n  // Список смежности, где key — вершина, а value — все смежные ей вершины\n  Map&lt;Vertex, List&lt;Vertex&gt;&gt; adjList = {};\n\n  /* Конструктор */\n  GraphAdjList(List&lt;List&lt;Vertex&gt;&gt; edges) {\n    for (List&lt;Vertex&gt; edge in edges) {\n      addVertex(edge[0]);\n      addVertex(edge[1]);\n      addEdge(edge[0], edge[1]);\n    }\n  }\n\n  /* Получить число вершин */\n  int size() {\n    return adjList.length;\n  }\n\n  /* Добавление ребра */\n  void addEdge(Vertex vet1, Vertex vet2) {\n    if (!adjList.containsKey(vet1) ||\n        !adjList.containsKey(vet2) ||\n        vet1 == vet2) {\n      throw ArgumentError;\n    }\n    // Добавить ребро vet1 - vet2\n    adjList[vet1]!.add(vet2);\n    adjList[vet2]!.add(vet1);\n  }\n\n  /* Удаление ребра */\n  void removeEdge(Vertex vet1, Vertex vet2) {\n    if (!adjList.containsKey(vet1) ||\n        !adjList.containsKey(vet2) ||\n        vet1 == vet2) {\n      throw ArgumentError;\n    }\n    // Удалить ребро vet1 - vet2\n    adjList[vet1]!.remove(vet2);\n    adjList[vet2]!.remove(vet1);\n  }\n\n  /* Добавление вершины */\n  void addVertex(Vertex vet) {\n    if (adjList.containsKey(vet)) return;\n    // Добавить новый список в список смежности\n    adjList[vet] = [];\n  }\n\n  /* Удаление вершины */\n  void removeVertex(Vertex vet) {\n    if (!adjList.containsKey(vet)) {\n      throw ArgumentError;\n    }\n    // Удалить из списка смежности список, соответствующий вершине vet\n    adjList.remove(vet);\n    // Обойти списки других вершин и удалить все ребра, содержащие vet\n    adjList.forEach((key, value) {\n      value.remove(vet);\n    });\n  }\n\n  /* Вывести список смежности */\n  void printAdjList() {\n    print(\"Список смежности =\");\n    adjList.forEach((key, value) {\n      List&lt;int&gt; tmp = [];\n      for (Vertex vertex in value) {\n        tmp.add(vertex.val);\n      }\n      print(\"${key.val}: $tmp,\");\n    });\n  }\n}\n</code></pre> graph_adjacency_list.rs<pre><code>/* Тип неориентированного графа на основе списка смежности */\npub struct GraphAdjList {\n    // Список смежности, где key — вершина, а value — все смежные ей вершины\n    pub adj_list: HashMap&lt;Vertex, Vec&lt;Vertex&gt;&gt;, // maybe HashSet&lt;Vertex&gt; for value part is better?\n}\n\nimpl GraphAdjList {\n    /* Конструктор */\n    pub fn new(edges: Vec&lt;[Vertex; 2]&gt;) -&gt; Self {\n        let mut graph = GraphAdjList {\n            adj_list: HashMap::new(),\n        };\n        // Добавить все вершины и ребра\n        for edge in edges {\n            graph.add_vertex(edge[0]);\n            graph.add_vertex(edge[1]);\n            graph.add_edge(edge[0], edge[1]);\n        }\n\n        graph\n    }\n\n    /* Получить число вершин */\n    #[allow(unused)]\n    pub fn size(&amp;self) -&gt; usize {\n        self.adj_list.len()\n    }\n\n    /* Добавление ребра */\n    pub fn add_edge(&amp;mut self, vet1: Vertex, vet2: Vertex) {\n        if vet1 == vet2 {\n            panic!(\"value error\");\n        }\n        // Добавить ребро vet1 - vet2\n        self.adj_list.entry(vet1).or_default().push(vet2);\n        self.adj_list.entry(vet2).or_default().push(vet1);\n    }\n\n    /* Удаление ребра */\n    #[allow(unused)]\n    pub fn remove_edge(&amp;mut self, vet1: Vertex, vet2: Vertex) {\n        if vet1 == vet2 {\n            panic!(\"value error\");\n        }\n        // Удалить ребро vet1 - vet2\n        self.adj_list\n            .entry(vet1)\n            .and_modify(|v| v.retain(|&amp;e| e != vet2));\n        self.adj_list\n            .entry(vet2)\n            .and_modify(|v| v.retain(|&amp;e| e != vet1));\n    }\n\n    /* Добавление вершины */\n    pub fn add_vertex(&amp;mut self, vet: Vertex) {\n        if self.adj_list.contains_key(&amp;vet) {\n            return;\n        }\n        // Добавить новый список в список смежности\n        self.adj_list.insert(vet, vec![]);\n    }\n\n    /* Удаление вершины */\n    #[allow(unused)]\n    pub fn remove_vertex(&amp;mut self, vet: Vertex) {\n        // Удалить из списка смежности список, соответствующий вершине vet\n        self.adj_list.remove(&amp;vet);\n        // Обойти списки других вершин и удалить все ребра, содержащие vet\n        for list in self.adj_list.values_mut() {\n            list.retain(|&amp;v| v != vet);\n        }\n    }\n\n    /* Вывести список смежности */\n    pub fn print(&amp;self) {\n        println!(\"Список смежности =\");\n        for (vertex, list) in &amp;self.adj_list {\n            let list = list.iter().map(|vertex| vertex.val).collect::&lt;Vec&lt;i32&gt;&gt;();\n            println!(\"{}: {:?},\", vertex.val, list);\n        }\n    }\n}\n</code></pre> graph_adjacency_list.c<pre><code>/* Структура узла */\ntypedef struct AdjListNode {\n    Vertex *vertex;           // Вершина\n    struct AdjListNode *next; // Узел-преемник\n} AdjListNode;\n\n/* Найти узел, соответствующий вершине */\nAdjListNode *findNode(GraphAdjList *graph, Vertex *vet) {\n    for (int i = 0; i &lt; graph-&gt;size; i++) {\n        if (graph-&gt;heads[i]-&gt;vertex == vet) {\n            return graph-&gt;heads[i];\n        }\n    }\n    return NULL;\n}\n\n/* Вспомогательная функция добавления ребра */\nvoid addEdgeHelper(AdjListNode *head, Vertex *vet) {\n    AdjListNode *node = (AdjListNode *)malloc(sizeof(AdjListNode));\n    node-&gt;vertex = vet;\n    // Вставка в голову\n    node-&gt;next = head-&gt;next;\n    head-&gt;next = node;\n}\n\n/* Вспомогательная функция удаления ребра */\nvoid removeEdgeHelper(AdjListNode *head, Vertex *vet) {\n    AdjListNode *pre = head;\n    AdjListNode *cur = head-&gt;next;\n    // Искать в связном списке узел, соответствующий vet\n    while (cur != NULL &amp;&amp; cur-&gt;vertex != vet) {\n        pre = cur;\n        cur = cur-&gt;next;\n    }\n    if (cur == NULL)\n        return;\n    // Удалить из связного списка узел, соответствующий vet\n    pre-&gt;next = cur-&gt;next;\n    // Освободить память\n    free(cur);\n}\n\n/* Класс неориентированного графа на основе списка смежности */\ntypedef struct {\n    AdjListNode *heads[MAX_SIZE]; // Массив узлов\n    int size;                     // Количество узлов\n} GraphAdjList;\n\n/* Конструктор */\nGraphAdjList *newGraphAdjList() {\n    GraphAdjList *graph = (GraphAdjList *)malloc(sizeof(GraphAdjList));\n    if (!graph) {\n        return NULL;\n    }\n    graph-&gt;size = 0;\n    for (int i = 0; i &lt; MAX_SIZE; i++) {\n        graph-&gt;heads[i] = NULL;\n    }\n    return graph;\n}\n\n/* Деструктор */\nvoid delGraphAdjList(GraphAdjList *graph) {\n    for (int i = 0; i &lt; graph-&gt;size; i++) {\n        AdjListNode *cur = graph-&gt;heads[i];\n        while (cur != NULL) {\n            AdjListNode *next = cur-&gt;next;\n            if (cur != graph-&gt;heads[i]) {\n                free(cur);\n            }\n            cur = next;\n        }\n        free(graph-&gt;heads[i]-&gt;vertex);\n        free(graph-&gt;heads[i]);\n    }\n    free(graph);\n}\n\n/* Найти узел, соответствующий вершине */\nAdjListNode *findNode(GraphAdjList *graph, Vertex *vet) {\n    for (int i = 0; i &lt; graph-&gt;size; i++) {\n        if (graph-&gt;heads[i]-&gt;vertex == vet) {\n            return graph-&gt;heads[i];\n        }\n    }\n    return NULL;\n}\n\n/* Добавление ребра */\nvoid addEdge(GraphAdjList *graph, Vertex *vet1, Vertex *vet2) {\n    AdjListNode *head1 = findNode(graph, vet1);\n    AdjListNode *head2 = findNode(graph, vet2);\n    assert(head1 != NULL &amp;&amp; head2 != NULL &amp;&amp; head1 != head2);\n    // Добавить ребро vet1 - vet2\n    addEdgeHelper(head1, vet2);\n    addEdgeHelper(head2, vet1);\n}\n\n/* Удаление ребра */\nvoid removeEdge(GraphAdjList *graph, Vertex *vet1, Vertex *vet2) {\n    AdjListNode *head1 = findNode(graph, vet1);\n    AdjListNode *head2 = findNode(graph, vet2);\n    assert(head1 != NULL &amp;&amp; head2 != NULL);\n    // Удалить ребро vet1 - vet2\n    removeEdgeHelper(head1, head2-&gt;vertex);\n    removeEdgeHelper(head2, head1-&gt;vertex);\n}\n\n/* Добавление вершины */\nvoid addVertex(GraphAdjList *graph, Vertex *vet) {\n    assert(graph != NULL &amp;&amp; graph-&gt;size &lt; MAX_SIZE);\n    AdjListNode *head = (AdjListNode *)malloc(sizeof(AdjListNode));\n    head-&gt;vertex = vet;\n    head-&gt;next = NULL;\n    // Добавить новый список в список смежности\n    graph-&gt;heads[graph-&gt;size++] = head;\n}\n\n/* Удаление вершины */\nvoid removeVertex(GraphAdjList *graph, Vertex *vet) {\n    AdjListNode *node = findNode(graph, vet);\n    assert(node != NULL);\n    // Удалить из списка смежности список, соответствующий вершине vet\n    AdjListNode *cur = node, *pre = NULL;\n    while (cur) {\n        pre = cur;\n        cur = cur-&gt;next;\n        free(pre);\n    }\n    // Обойти списки других вершин и удалить все ребра, содержащие vet\n    for (int i = 0; i &lt; graph-&gt;size; i++) {\n        cur = graph-&gt;heads[i];\n        pre = NULL;\n        while (cur) {\n            pre = cur;\n            cur = cur-&gt;next;\n            if (cur &amp;&amp; cur-&gt;vertex == vet) {\n                pre-&gt;next = cur-&gt;next;\n                free(cur);\n                break;\n            }\n        }\n    }\n    // Сдвинуть вершины после данной вперед, чтобы заполнить образовавшийся пробел\n    int i;\n    for (i = 0; i &lt; graph-&gt;size; i++) {\n        if (graph-&gt;heads[i] == node)\n            break;\n    }\n    for (int j = i; j &lt; graph-&gt;size - 1; j++) {\n        graph-&gt;heads[j] = graph-&gt;heads[j + 1];\n    }\n    graph-&gt;size--;\n    free(vet);\n}\n</code></pre> graph_adjacency_list.kt<pre><code>/* Класс неориентированного графа на основе списка смежности */\nclass GraphAdjList(edges: Array&lt;Array&lt;Vertex?&gt;&gt;) {\n    // Список смежности, где key — вершина, а value — все смежные ей вершины\n    val adjList = HashMap&lt;Vertex, MutableList&lt;Vertex&gt;&gt;()\n\n    /* Конструктор */\n    init {\n        // Добавить все вершины и ребра\n        for (edge in edges) {\n            addVertex(edge[0]!!)\n            addVertex(edge[1]!!)\n            addEdge(edge[0]!!, edge[1]!!)\n        }\n    }\n\n    /* Получить число вершин */\n    fun size(): Int {\n        return adjList.size\n    }\n\n    /* Добавление ребра */\n    fun addEdge(vet1: Vertex, vet2: Vertex) {\n        if (!adjList.containsKey(vet1) || !adjList.containsKey(vet2) || vet1 == vet2)\n            throw IllegalArgumentException()\n        // Добавить ребро vet1 - vet2\n        adjList[vet1]?.add(vet2)\n        adjList[vet2]?.add(vet1)\n    }\n\n    /* Удаление ребра */\n    fun removeEdge(vet1: Vertex, vet2: Vertex) {\n        if (!adjList.containsKey(vet1) || !adjList.containsKey(vet2) || vet1 == vet2)\n            throw IllegalArgumentException()\n        // Удалить ребро vet1 - vet2\n        adjList[vet1]?.remove(vet2)\n        adjList[vet2]?.remove(vet1)\n    }\n\n    /* Добавление вершины */\n    fun addVertex(vet: Vertex) {\n        if (adjList.containsKey(vet))\n            return\n        // Добавить новый список в список смежности\n        adjList[vet] = mutableListOf()\n    }\n\n    /* Удаление вершины */\n    fun removeVertex(vet: Vertex) {\n        if (!adjList.containsKey(vet))\n            throw IllegalArgumentException()\n        // Удалить из списка смежности список, соответствующий вершине vet\n        adjList.remove(vet)\n        // Обойти списки других вершин и удалить все ребра, содержащие vet\n        for (list in adjList.values) {\n            list.remove(vet)\n        }\n    }\n\n    /* Вывести список смежности */\n    fun print() {\n        println(\"Список смежности =\")\n        for (pair in adjList.entries) {\n            val tmp = mutableListOf&lt;Int&gt;()\n            for (vertex in pair.value) {\n                tmp.add(vertex._val)\n            }\n            println(\"${pair.key._val}: $tmp,\")\n        }\n    }\n}\n</code></pre> graph_adjacency_list.rb<pre><code>### Класс неориентированного графа на основе списка смежности ###\nclass GraphAdjList\n  attr_reader :adj_list\n\n  ### Конструктор ###\n  def initialize(edges)\n    # Список смежности, где key — вершина, а value — все смежные ей вершины\n    @adj_list = {}\n    # Добавить все вершины и ребра\n    for edge in edges\n      add_vertex(edge[0])\n      add_vertex(edge[1])\n      add_edge(edge[0], edge[1])\n    end\n  end\n\n  ### Получение числа вершин ###\n  def size\n    @adj_list.length\n  end\n\n  ### Добавление ребра ###\n  def add_edge(vet1, vet2)\n    raise ArgumentError if !@adj_list.include?(vet1) || !@adj_list.include?(vet2)\n\n    @adj_list[vet1] &lt;&lt; vet2\n    @adj_list[vet2] &lt;&lt; vet1\n  end\n\n  ### Удаление ребра ###\n  def remove_edge(vet1, vet2)\n    raise ArgumentError if !@adj_list.include?(vet1) || !@adj_list.include?(vet2)\n\n    # Удалить ребро vet1 - vet2\n    @adj_list[vet1].delete(vet2)\n    @adj_list[vet2].delete(vet1)\n  end\n\n  ### Добавление вершины ###\n  def add_vertex(vet)\n    return if @adj_list.include?(vet)\n\n    # Добавить новый список в список смежности\n    @adj_list[vet] = []\n  end\n\n  ### Удаление вершины ###\n  def remove_vertex(vet)\n    raise ArgumentError unless @adj_list.include?(vet)\n\n    # Удалить из списка смежности список, соответствующий вершине vet\n    @adj_list.delete(vet)\n    # Обойти списки других вершин и удалить все ребра, содержащие vet\n    for vertex in @adj_list\n      @adj_list[vertex.first].delete(vet) if @adj_list[vertex.first].include?(vet)\n    end\n  end\n\n  ### Вывести список смежности ###\n  def __print__\n    puts 'Список смежности ='\n    for vertex in @adj_list\n      tmp = @adj_list[vertex.first].map { |v| v.val }\n      puts \"#{vertex.first.val}: #{tmp},\"\n    end\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 9. Граф","9.2 &nbsp; Базовые операции графа"],"tags":[]},{"location":"chapter_graph/graph_operations/#923","level":2,"title":"9.2.3   Сравнение эффективности","text":"<p>Пусть в графе имеется \\(n\\) вершин и \\(m\\) ребер. В таблице 9-2 сравниваются временная и пространственная эффективность матрицы смежности и списка смежности. Обрати внимание: список смежности (связный список) соответствует реализации из этой статьи, а список смежности (хеш-таблица) означает вариант, где все списки заменены хеш-таблицами.</p> <p> Таблица 9-2   Сравнение матрицы смежности и списка смежности </p> Матрица смежности Список смежности (связный список) Список смежности (хеш-таблица) Проверка смежности \\(O(1)\\) \\(O(n)\\) \\(O(1)\\) Добавление ребра \\(O(1)\\) \\(O(1)\\) \\(O(1)\\) Удаление ребра \\(O(1)\\) \\(O(n)\\) \\(O(1)\\) Добавление вершины \\(O(n)\\) \\(O(1)\\) \\(O(1)\\) Удаление вершины \\(O(n^2)\\) \\(O(n + m)\\) \\(O(n)\\) Занимаемая память \\(O(n^2)\\) \\(O(n + m)\\) \\(O(n + m)\\) <p>Если смотреть только на таблицу, может показаться, что список смежности на основе хеш-таблицы является лучшим и по времени, и по памяти. Но на практике операции над ребрами в матрице смежности часто выполняются быстрее, потому что там нужен лишь один доступ к массиву или одно присваивание. В целом матрица смежности воплощает принцип \"обмен пространства на время\", а список смежности - принцип \"обмен времени на пространство\".</p>","path":["Глава 9. Граф","9.2 &nbsp; Базовые операции графа"],"tags":[]},{"location":"chapter_graph/graph_traversal/","level":1,"title":"9.3   Обход графа","text":"<p>Дерево представляет отношение \"один ко многим\", а граф имеет более высокую степень свободы и может выражать произвольные отношения \"многие ко многим\". Поэтому мы можем рассматривать дерево как частный случай графа. Очевидно, что операции обхода дерева также являются частным случаем операций обхода графа.</p> <p>И графы, и деревья требуют использования поисковых алгоритмов для реализации обхода. Способы обхода графа также делятся на два типа: обход в ширину и обход в глубину.</p>","path":["Глава 9. Граф","9.3 &nbsp; Обход графа"],"tags":[]},{"location":"chapter_graph/graph_traversal/#931","level":2,"title":"9.3.1   Обход в ширину","text":"<p>Обход в ширину - это способ обхода \"от близкого к далекому\": начиная с некоторого узла, мы всегда в первую очередь посещаем ближайшие вершины и слой за слоем расширяемся наружу. Как показано на рисунке 9-9, начиная с вершины в левом верхнем углу, мы сначала обходим все смежные вершины этой вершины, затем все смежные вершины следующей вершины и так далее, пока не будут посещены все вершины.</p> <p></p> <p> Рисунок 9-9   Обход графа в ширину </p>","path":["Глава 9. Граф","9.3 &nbsp; Обход графа"],"tags":[]},{"location":"chapter_graph/graph_traversal/#1","level":3,"title":"1.   Реализация алгоритма","text":"<p>BFS обычно реализуется с помощью очереди, код приведен ниже. Очередь обладает свойством \"первым пришел - первым вышел\", что хорошо соответствует идее BFS \"от близкого к далекому\".</p> <ol> <li>Поместить стартовую вершину обхода <code>startVet</code> в очередь и запустить цикл.</li> <li>На каждой итерации цикла извлекать вершину из головы очереди и записывать факт ее посещения, после чего добавлять все смежные вершины этой вершины в хвост очереди.</li> <li>Повторять шаг <code>2.</code> до тех пор, пока не будут посещены все вершины.</li> </ol> <p>Чтобы предотвратить повторный обход вершин, нам нужен хеш-набор <code>visited</code> , в котором будет записываться, какие узлы уже посещены.</p> <p>Tip</p> <p>Хеш-набор можно рассматривать как хеш-таблицу, которая хранит только <code>key</code> и не хранит <code>value</code> . Он позволяет выполнять добавление, удаление, поиск и изменение <code>key</code> за \\(O(1)\\) времени. Благодаря уникальности <code>key</code> хеш-набор обычно используется, например, для устранения повторов.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby graph_bfs.py<pre><code>def graph_bfs(graph: GraphAdjList, start_vet: Vertex) -&gt; list[Vertex]:\n    \"\"\"Обход в ширину\"\"\"\n    # Использовать список смежности для представления графа, чтобы получать все смежные вершины заданной вершины\n    # Последовательность обхода вершин\n    res = []\n    # Хеш-множество для хранения уже посещенных вершин\n    visited = set[Vertex]([start_vet])\n    # Очередь используется для реализации BFS\n    que = deque[Vertex]([start_vet])\n    # Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n    while len(que) &gt; 0:\n        vet = que.popleft()  # Извлечь головную вершину из очереди\n        res.append(vet)  # Отметить посещенную вершину\n        # Обойти все смежные вершины данной вершины\n        for adj_vet in graph.adj_list[vet]:\n            if adj_vet in visited:\n                continue  # Пропустить уже посещенную вершину\n            que.append(adj_vet)  # Помещать в очередь только непосещенные вершины\n            visited.add(adj_vet)  # Отметить эту вершину как посещенную\n    # Вернуть последовательность обхода вершин\n    return res\n</code></pre> graph_bfs.cpp<pre><code>/* Обход в ширину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nvector&lt;Vertex *&gt; graphBFS(GraphAdjList &amp;graph, Vertex *startVet) {\n    // Последовательность обхода вершин\n    vector&lt;Vertex *&gt; res;\n    // Хеш-множество для хранения уже посещенных вершин\n    unordered_set&lt;Vertex *&gt; visited = {startVet};\n    // Очередь используется для реализации BFS\n    queue&lt;Vertex *&gt; que;\n    que.push(startVet);\n    // Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n    while (!que.empty()) {\n        Vertex *vet = que.front();\n        que.pop();          // Извлечь головную вершину из очереди\n        res.push_back(vet); // Отметить посещенную вершину\n        // Обойти все смежные вершины данной вершины\n        for (auto adjVet : graph.adjList[vet]) {\n            if (visited.count(adjVet))\n                continue;            // Пропустить уже посещенную вершину\n            que.push(adjVet);        // Помещать в очередь только непосещенные вершины\n            visited.emplace(adjVet); // Отметить эту вершину как посещенную\n        }\n    }\n    // Вернуть последовательность обхода вершин\n    return res;\n}\n</code></pre> graph_bfs.java<pre><code>/* Обход в ширину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nList&lt;Vertex&gt; graphBFS(GraphAdjList graph, Vertex startVet) {\n    // Последовательность обхода вершин\n    List&lt;Vertex&gt; res = new ArrayList&lt;&gt;();\n    // Хеш-множество для хранения уже посещенных вершин\n    Set&lt;Vertex&gt; visited = new HashSet&lt;&gt;();\n    visited.add(startVet);\n    // Очередь используется для реализации BFS\n    Queue&lt;Vertex&gt; que = new LinkedList&lt;&gt;();\n    que.offer(startVet);\n    // Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n    while (!que.isEmpty()) {\n        Vertex vet = que.poll(); // Извлечь головную вершину из очереди\n        res.add(vet);            // Отметить посещенную вершину\n        // Обойти все смежные вершины данной вершины\n        for (Vertex adjVet : graph.adjList.get(vet)) {\n            if (visited.contains(adjVet))\n                continue;        // Пропустить уже посещенную вершину\n            que.offer(adjVet);   // Помещать в очередь только непосещенные вершины\n            visited.add(adjVet); // Отметить эту вершину как посещенную\n        }\n    }\n    // Вернуть последовательность обхода вершин\n    return res;\n}\n</code></pre> graph_bfs.cs<pre><code>/* Обход в ширину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nList&lt;Vertex&gt; GraphBFS(GraphAdjList graph, Vertex startVet) {\n    // Последовательность обхода вершин\n    List&lt;Vertex&gt; res = [];\n    // Хеш-множество для хранения уже посещенных вершин\n    HashSet&lt;Vertex&gt; visited = [startVet];\n    // Очередь используется для реализации BFS\n    Queue&lt;Vertex&gt; que = new();\n    que.Enqueue(startVet);\n    // Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n    while (que.Count &gt; 0) {\n        Vertex vet = que.Dequeue(); // Извлечь головную вершину из очереди\n        res.Add(vet);               // Отметить посещенную вершину\n        foreach (Vertex adjVet in graph.adjList[vet]) {\n            if (visited.Contains(adjVet)) {\n                continue;          // Пропустить уже посещенную вершину\n            }\n            que.Enqueue(adjVet);   // Помещать в очередь только непосещенные вершины\n            visited.Add(adjVet);   // Отметить эту вершину как посещенную\n        }\n    }\n\n    // Вернуть последовательность обхода вершин\n    return res;\n}\n</code></pre> graph_bfs.go<pre><code>/* Обход в ширину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfunc graphBFS(g *graphAdjList, startVet Vertex) []Vertex {\n    // Последовательность обхода вершин\n    res := make([]Vertex, 0)\n    // Хеш-множество для хранения уже посещенных вершин\n    visited := make(map[Vertex]struct{})\n    visited[startVet] = struct{}{}\n    // Очередь используется для реализации BFS, срез используется для имитации очереди\n    queue := make([]Vertex, 0)\n    queue = append(queue, startVet)\n    // Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n    for len(queue) &gt; 0 {\n        // Извлечь головную вершину из очереди\n        vet := queue[0]\n        queue = queue[1:]\n        // Отметить посещенную вершину\n        res = append(res, vet)\n        // Обойти все смежные вершины данной вершины\n        for _, adjVet := range g.adjList[vet] {\n            _, isExist := visited[adjVet]\n            // Помещать в очередь только непосещенные вершины\n            if !isExist {\n                queue = append(queue, adjVet)\n                visited[adjVet] = struct{}{}\n            }\n        }\n    }\n    // Вернуть последовательность обхода вершин\n    return res\n}\n</code></pre> graph_bfs.swift<pre><code>/* Обход в ширину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfunc graphBFS(graph: GraphAdjList, startVet: Vertex) -&gt; [Vertex] {\n    // Последовательность обхода вершин\n    var res: [Vertex] = []\n    // Хеш-множество для хранения уже посещенных вершин\n    var visited: Set&lt;Vertex&gt; = [startVet]\n    // Очередь используется для реализации BFS\n    var que: [Vertex] = [startVet]\n    // Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n    while !que.isEmpty {\n        let vet = que.removeFirst() // Извлечь головную вершину из очереди\n        res.append(vet) // Отметить посещенную вершину\n        // Обойти все смежные вершины данной вершины\n        for adjVet in graph.adjList[vet] ?? [] {\n            if visited.contains(adjVet) {\n                continue // Пропустить уже посещенную вершину\n            }\n            que.append(adjVet) // Помещать в очередь только непосещенные вершины\n            visited.insert(adjVet) // Отметить эту вершину как посещенную\n        }\n    }\n    // Вернуть последовательность обхода вершин\n    return res\n}\n</code></pre> graph_bfs.js<pre><code>/* Обход в ширину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfunction graphBFS(graph, startVet) {\n    // Последовательность обхода вершин\n    const res = [];\n    // Хеш-множество для хранения уже посещенных вершин\n    const visited = new Set();\n    visited.add(startVet);\n    // Очередь используется для реализации BFS\n    const que = [startVet];\n    // Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n    while (que.length) {\n        const vet = que.shift(); // Извлечь головную вершину из очереди\n        res.push(vet); // Отметить посещенную вершину\n        // Обойти все смежные вершины данной вершины\n        for (const adjVet of graph.adjList.get(vet) ?? []) {\n            if (visited.has(adjVet)) {\n                continue; // Пропустить уже посещенную вершину\n            }\n            que.push(adjVet); // Помещать в очередь только непосещенные вершины\n            visited.add(adjVet); // Отметить эту вершину как посещенную\n        }\n    }\n    // Вернуть последовательность обхода вершин\n    return res;\n}\n</code></pre> graph_bfs.ts<pre><code>/* Обход в ширину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfunction graphBFS(graph: GraphAdjList, startVet: Vertex): Vertex[] {\n    // Последовательность обхода вершин\n    const res: Vertex[] = [];\n    // Хеш-множество для хранения уже посещенных вершин\n    const visited: Set&lt;Vertex&gt; = new Set();\n    visited.add(startVet);\n    // Очередь используется для реализации BFS\n    const que = [startVet];\n    // Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n    while (que.length) {\n        const vet = que.shift(); // Извлечь головную вершину из очереди\n        res.push(vet); // Отметить посещенную вершину\n        // Обойти все смежные вершины данной вершины\n        for (const adjVet of graph.adjList.get(vet) ?? []) {\n            if (visited.has(adjVet)) {\n                continue; // Пропустить уже посещенную вершину\n            }\n            que.push(adjVet); // Помещать в очередь только непосещенные вершины\n            visited.add(adjVet); // Отметить эту вершину как посещенную\n        }\n    }\n    // Вернуть последовательность обхода вершин\n    return res;\n}\n</code></pre> graph_bfs.dart<pre><code>/* Обход в ширину */\nList&lt;Vertex&gt; graphBFS(GraphAdjList graph, Vertex startVet) {\n  // Использовать список смежности для представления графа, чтобы получать все смежные вершины заданной вершины\n  // Последовательность обхода вершин\n  List&lt;Vertex&gt; res = [];\n  // Хеш-множество для хранения уже посещенных вершин\n  Set&lt;Vertex&gt; visited = {};\n  visited.add(startVet);\n  // Очередь используется для реализации BFS\n  Queue&lt;Vertex&gt; que = Queue();\n  que.add(startVet);\n  // Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n  while (que.isNotEmpty) {\n    Vertex vet = que.removeFirst(); // Извлечь головную вершину из очереди\n    res.add(vet); // Отметить посещенную вершину\n    // Обойти все смежные вершины данной вершины\n    for (Vertex adjVet in graph.adjList[vet]!) {\n      if (visited.contains(adjVet)) {\n        continue; // Пропустить уже посещенную вершину\n      }\n      que.add(adjVet); // Помещать в очередь только непосещенные вершины\n      visited.add(adjVet); // Отметить эту вершину как посещенную\n    }\n  }\n  // Вернуть последовательность обхода вершин\n  return res;\n}\n</code></pre> graph_bfs.rs<pre><code>/* Обход в ширину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfn graph_bfs(graph: GraphAdjList, start_vet: Vertex) -&gt; Vec&lt;Vertex&gt; {\n    // Последовательность обхода вершин\n    let mut res = vec![];\n    // Хеш-множество для хранения уже посещенных вершин\n    let mut visited = HashSet::new();\n    visited.insert(start_vet);\n    // Очередь используется для реализации BFS\n    let mut que = VecDeque::new();\n    que.push_back(start_vet);\n    // Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n    while let Some(vet) = que.pop_front() {\n        res.push(vet); // Отметить посещенную вершину\n\n        // Обойти все смежные вершины данной вершины\n        if let Some(adj_vets) = graph.adj_list.get(&amp;vet) {\n            for &amp;adj_vet in adj_vets {\n                if visited.contains(&amp;adj_vet) {\n                    continue; // Пропустить уже посещенную вершину\n                }\n                que.push_back(adj_vet); // Помещать в очередь только непосещенные вершины\n                visited.insert(adj_vet); // Отметить эту вершину как посещенную\n            }\n        }\n    }\n    // Вернуть последовательность обхода вершин\n    res\n}\n</code></pre> graph_bfs.c<pre><code>/* Структура очереди узлов */\ntypedef struct {\n    Vertex *vertices[MAX_SIZE];\n    int front, rear, size;\n} Queue;\n\n/* Конструктор */\nQueue *newQueue() {\n    Queue *q = (Queue *)malloc(sizeof(Queue));\n    q-&gt;front = q-&gt;rear = q-&gt;size = 0;\n    return q;\n}\n\n/* Проверка, пуста ли очередь */\nint isEmpty(Queue *q) {\n    return q-&gt;size == 0;\n}\n\n/* Операция добавления в очередь */\nvoid enqueue(Queue *q, Vertex *vet) {\n    q-&gt;vertices[q-&gt;rear] = vet;\n    q-&gt;rear = (q-&gt;rear + 1) % MAX_SIZE;\n    q-&gt;size++;\n}\n\n/* Операция извлечения из очереди */\nVertex *dequeue(Queue *q) {\n    Vertex *vet = q-&gt;vertices[q-&gt;front];\n    q-&gt;front = (q-&gt;front + 1) % MAX_SIZE;\n    q-&gt;size--;\n    return vet;\n}\n\n/* Проверить, была ли вершина уже посещена */\nint isVisited(Vertex **visited, int size, Vertex *vet) {\n    // Искать узел обходом за O(n) времени\n    for (int i = 0; i &lt; size; i++) {\n        if (visited[i] == vet)\n            return 1;\n    }\n    return 0;\n}\n\n/* Обход в ширину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nvoid graphBFS(GraphAdjList *graph, Vertex *startVet, Vertex **res, int *resSize, Vertex **visited, int *visitedSize) {\n    // Очередь используется для реализации BFS\n    Queue *queue = newQueue();\n    enqueue(queue, startVet);\n    visited[(*visitedSize)++] = startVet;\n    // Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n    while (!isEmpty(queue)) {\n        Vertex *vet = dequeue(queue); // Извлечь головную вершину из очереди\n        res[(*resSize)++] = vet;      // Отметить посещенную вершину\n        // Обойти все смежные вершины данной вершины\n        AdjListNode *node = findNode(graph, vet);\n        while (node != NULL) {\n            // Пропустить уже посещенную вершину\n            if (!isVisited(visited, *visitedSize, node-&gt;vertex)) {\n                enqueue(queue, node-&gt;vertex);             // Помещать в очередь только непосещенные вершины\n                visited[(*visitedSize)++] = node-&gt;vertex; // Отметить эту вершину как посещенную\n            }\n            node = node-&gt;next;\n        }\n    }\n    // Освободить память\n    free(queue);\n}\n</code></pre> graph_bfs.kt<pre><code>/* Обход в ширину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfun graphBFS(graph: GraphAdjList, startVet: Vertex): MutableList&lt;Vertex?&gt; {\n    // Последовательность обхода вершин\n    val res = mutableListOf&lt;Vertex?&gt;()\n    // Хеш-множество для хранения уже посещенных вершин\n    val visited = HashSet&lt;Vertex&gt;()\n    visited.add(startVet)\n    // Очередь используется для реализации BFS\n    val que = LinkedList&lt;Vertex&gt;()\n    que.offer(startVet)\n    // Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n    while (!que.isEmpty()) {\n        val vet = que.poll() // Извлечь головную вершину из очереди\n        res.add(vet)         // Отметить посещенную вершину\n        // Обойти все смежные вершины данной вершины\n        for (adjVet in graph.adjList[vet]!!) {\n            if (visited.contains(adjVet))\n                continue        // Пропустить уже посещенную вершину\n            que.offer(adjVet)   // Помещать в очередь только непосещенные вершины\n            visited.add(adjVet) // Отметить эту вершину как посещенную\n        }\n    }\n    // Вернуть последовательность обхода вершин\n    return res\n}\n</code></pre> graph_bfs.rb<pre><code>### Обход в ширину ###\ndef graph_bfs(graph, start_vet)\n  # Использовать список смежности для представления графа, чтобы получать все смежные вершины заданной вершины\n  # Последовательность обхода вершин\n  res = []\n  # Хеш-множество для хранения уже посещенных вершин\n  visited = Set.new([start_vet])\n  # Очередь используется для реализации BFS\n  que = [start_vet]\n  # Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n  while que.length &gt; 0\n    vet = que.shift # Извлечь головную вершину из очереди\n    res &lt;&lt; vet # Отметить посещенную вершину\n    # Обойти все смежные вершины данной вершины\n    for adj_vet in graph.adj_list[vet]\n      next if visited.include?(adj_vet) # Пропустить уже посещенную вершину\n      que &lt;&lt; adj_vet # Помещать в очередь только непосещенные вершины\n      visited.add(adj_vet) # Отметить эту вершину как посещенную\n    end\n  end\n  # Вернуть последовательность обхода вершин\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Код сравнительно абстрактен, поэтому рекомендуется сверяться с рисунками ниже для лучшего понимания.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 9-10   Шаги обхода графа в ширину </p> <p>Является ли последовательность обхода в ширину единственной?</p> <p>Нет. Обход в ширину требует только соблюдения порядка \"от близкого к далекому\", а порядок обхода нескольких вершин на одинаковом расстоянии может произвольно меняться. Например, на рисунке 9-10 можно поменять местами порядок посещения вершин \\(1\\) и \\(3\\) , а также в произвольном порядке переставить вершины \\(2\\), \\(4\\), \\(6\\) .</p>","path":["Глава 9. Граф","9.3 &nbsp; Обход графа"],"tags":[]},{"location":"chapter_graph/graph_traversal/#2","level":3,"title":"2.   Анализ сложности","text":"<p>Временная сложность: все вершины по одному разу помещаются в очередь и извлекаются из нее, что требует \\(O(|V|)\\) времени; при обходе смежных вершин, поскольку граф неориентированный, все ребра будут посещены по \\(2\\) раза, что требует \\(O(2|E|)\\) времени; в сумме получается \\(O(|V| + |E|)\\) .</p> <p>Пространственная сложность: список <code>res</code> , хеш-набор <code>visited</code> и очередь <code>que</code> в худшем случае могут содержать до \\(|V|\\) вершин, поэтому требуется \\(O(|V|)\\) памяти.</p>","path":["Глава 9. Граф","9.3 &nbsp; Обход графа"],"tags":[]},{"location":"chapter_graph/graph_traversal/#932","level":2,"title":"9.3.2   Обход в глубину","text":"<p>Обход в глубину - это способ обхода, при котором сначала идут до самого конца, а когда дальше идти нельзя, откатываются назад. Как показано на рисунке 9-11, начиная с вершины в левом верхнем углу, мы выбираем некоторую смежную вершину текущей вершины, идем до упора, затем возвращаемся назад, снова идем до упора и так далее, пока не будут посещены все вершины.</p> <p></p> <p> Рисунок 9-11   Обход графа в глубину </p>","path":["Глава 9. Граф","9.3 &nbsp; Обход графа"],"tags":[]},{"location":"chapter_graph/graph_traversal/#1_1","level":3,"title":"1.   Реализация алгоритма","text":"<p>Такой алгоритмический шаблон \"дойти до конца и вернуться\" обычно реализуется через рекурсию. Подобно обходу в ширину, в обходе в глубину мы также используем хеш-набор <code>visited</code> для записи уже посещенных вершин и тем самым избегаем повторного посещения.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby graph_dfs.py<pre><code>def dfs(graph: GraphAdjList, visited: set[Vertex], res: list[Vertex], vet: Vertex):\n    \"\"\"Вспомогательная функция обхода в глубину\"\"\"\n    res.append(vet)  # Отметить посещенную вершину\n    visited.add(vet)  # Отметить эту вершину как посещенную\n    # Обойти все смежные вершины данной вершины\n    for adjVet in graph.adj_list[vet]:\n        if adjVet in visited:\n            continue  # Пропустить уже посещенную вершину\n        # Рекурсивно обходить смежные вершины\n        dfs(graph, visited, res, adjVet)\n\ndef graph_dfs(graph: GraphAdjList, start_vet: Vertex) -&gt; list[Vertex]:\n    \"\"\"Обход в глубину\"\"\"\n    # Использовать список смежности для представления графа, чтобы получать все смежные вершины заданной вершины\n    # Последовательность обхода вершин\n    res = []\n    # Хеш-множество для хранения уже посещенных вершин\n    visited = set[Vertex]()\n    dfs(graph, visited, res, start_vet)\n    return res\n</code></pre> graph_dfs.cpp<pre><code>/* Вспомогательная функция обхода в глубину */\nvoid dfs(GraphAdjList &amp;graph, unordered_set&lt;Vertex *&gt; &amp;visited, vector&lt;Vertex *&gt; &amp;res, Vertex *vet) {\n    res.push_back(vet);   // Отметить посещенную вершину\n    visited.emplace(vet); // Отметить эту вершину как посещенную\n    // Обойти все смежные вершины данной вершины\n    for (Vertex *adjVet : graph.adjList[vet]) {\n        if (visited.count(adjVet))\n            continue; // Пропустить уже посещенную вершину\n        // Рекурсивно обходить смежные вершины\n        dfs(graph, visited, res, adjVet);\n    }\n}\n\n/* Обход в глубину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nvector&lt;Vertex *&gt; graphDFS(GraphAdjList &amp;graph, Vertex *startVet) {\n    // Последовательность обхода вершин\n    vector&lt;Vertex *&gt; res;\n    // Хеш-множество для хранения уже посещенных вершин\n    unordered_set&lt;Vertex *&gt; visited;\n    dfs(graph, visited, res, startVet);\n    return res;\n}\n</code></pre> graph_dfs.java<pre><code>/* Вспомогательная функция обхода в глубину */\nvoid dfs(GraphAdjList graph, Set&lt;Vertex&gt; visited, List&lt;Vertex&gt; res, Vertex vet) {\n    res.add(vet);     // Отметить посещенную вершину\n    visited.add(vet); // Отметить эту вершину как посещенную\n    // Обойти все смежные вершины данной вершины\n    for (Vertex adjVet : graph.adjList.get(vet)) {\n        if (visited.contains(adjVet))\n            continue; // Пропустить уже посещенную вершину\n        // Рекурсивно обходить смежные вершины\n        dfs(graph, visited, res, adjVet);\n    }\n}\n\n/* Обход в глубину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nList&lt;Vertex&gt; graphDFS(GraphAdjList graph, Vertex startVet) {\n    // Последовательность обхода вершин\n    List&lt;Vertex&gt; res = new ArrayList&lt;&gt;();\n    // Хеш-множество для хранения уже посещенных вершин\n    Set&lt;Vertex&gt; visited = new HashSet&lt;&gt;();\n    dfs(graph, visited, res, startVet);\n    return res;\n}\n</code></pre> graph_dfs.cs<pre><code>/* Вспомогательная функция обхода в глубину */\nvoid DFS(GraphAdjList graph, HashSet&lt;Vertex&gt; visited, List&lt;Vertex&gt; res, Vertex vet) {\n    res.Add(vet);     // Отметить посещенную вершину\n    visited.Add(vet); // Отметить эту вершину как посещенную\n    // Обойти все смежные вершины данной вершины\n    foreach (Vertex adjVet in graph.adjList[vet]) {\n        if (visited.Contains(adjVet)) {\n            continue; // Пропустить уже посещенную вершину\n        }\n        // Рекурсивно обходить смежные вершины\n        DFS(graph, visited, res, adjVet);\n    }\n}\n\n/* Обход в глубину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nList&lt;Vertex&gt; GraphDFS(GraphAdjList graph, Vertex startVet) {\n    // Последовательность обхода вершин\n    List&lt;Vertex&gt; res = [];\n    // Хеш-множество для хранения уже посещенных вершин\n    HashSet&lt;Vertex&gt; visited = [];\n    DFS(graph, visited, res, startVet);\n    return res;\n}\n</code></pre> graph_dfs.go<pre><code>/* Вспомогательная функция обхода в глубину */\nfunc dfs(g *graphAdjList, visited map[Vertex]struct{}, res *[]Vertex, vet Vertex) {\n    // Операция append возвращает новую ссылку, поэтому исходную ссылку нужно заново присвоить новому срезу\n    *res = append(*res, vet)\n    visited[vet] = struct{}{}\n    // Обойти все смежные вершины данной вершины\n    for _, adjVet := range g.adjList[vet] {\n        _, isExist := visited[adjVet]\n        // Рекурсивно обходить смежные вершины\n        if !isExist {\n            dfs(g, visited, res, adjVet)\n        }\n    }\n}\n\n/* Обход в глубину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfunc graphDFS(g *graphAdjList, startVet Vertex) []Vertex {\n    // Последовательность обхода вершин\n    res := make([]Vertex, 0)\n    // Хеш-множество для хранения уже посещенных вершин\n    visited := make(map[Vertex]struct{})\n    dfs(g, visited, &amp;res, startVet)\n    // Вернуть последовательность обхода вершин\n    return res\n}\n</code></pre> graph_dfs.swift<pre><code>/* Вспомогательная функция обхода в глубину */\nfunc dfs(graph: GraphAdjList, visited: inout Set&lt;Vertex&gt;, res: inout [Vertex], vet: Vertex) {\n    res.append(vet) // Отметить посещенную вершину\n    visited.insert(vet) // Отметить эту вершину как посещенную\n    // Обойти все смежные вершины данной вершины\n    for adjVet in graph.adjList[vet] ?? [] {\n        if visited.contains(adjVet) {\n            continue // Пропустить уже посещенную вершину\n        }\n        // Рекурсивно обходить смежные вершины\n        dfs(graph: graph, visited: &amp;visited, res: &amp;res, vet: adjVet)\n    }\n}\n\n/* Обход в глубину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfunc graphDFS(graph: GraphAdjList, startVet: Vertex) -&gt; [Vertex] {\n    // Последовательность обхода вершин\n    var res: [Vertex] = []\n    // Хеш-множество для хранения уже посещенных вершин\n    var visited: Set&lt;Vertex&gt; = []\n    dfs(graph: graph, visited: &amp;visited, res: &amp;res, vet: startVet)\n    return res\n}\n</code></pre> graph_dfs.js<pre><code>/* Обход в глубину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfunction dfs(graph, visited, res, vet) {\n    res.push(vet); // Отметить посещенную вершину\n    visited.add(vet); // Отметить эту вершину как посещенную\n    // Обойти все смежные вершины данной вершины\n    for (const adjVet of graph.adjList.get(vet)) {\n        if (visited.has(adjVet)) {\n            continue; // Пропустить уже посещенную вершину\n        }\n        // Рекурсивно обходить смежные вершины\n        dfs(graph, visited, res, adjVet);\n    }\n}\n\n/* Обход в глубину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfunction graphDFS(graph, startVet) {\n    // Последовательность обхода вершин\n    const res = [];\n    // Хеш-множество для хранения уже посещенных вершин\n    const visited = new Set();\n    dfs(graph, visited, res, startVet);\n    return res;\n}\n</code></pre> graph_dfs.ts<pre><code>/* Вспомогательная функция обхода в глубину */\nfunction dfs(\n    graph: GraphAdjList,\n    visited: Set&lt;Vertex&gt;,\n    res: Vertex[],\n    vet: Vertex\n): void {\n    res.push(vet); // Отметить посещенную вершину\n    visited.add(vet); // Отметить эту вершину как посещенную\n    // Обойти все смежные вершины данной вершины\n    for (const adjVet of graph.adjList.get(vet)) {\n        if (visited.has(adjVet)) {\n            continue; // Пропустить уже посещенную вершину\n        }\n        // Рекурсивно обходить смежные вершины\n        dfs(graph, visited, res, adjVet);\n    }\n}\n\n/* Обход в глубину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfunction graphDFS(graph: GraphAdjList, startVet: Vertex): Vertex[] {\n    // Последовательность обхода вершин\n    const res: Vertex[] = [];\n    // Хеш-множество для хранения уже посещенных вершин\n    const visited: Set&lt;Vertex&gt; = new Set();\n    dfs(graph, visited, res, startVet);\n    return res;\n}\n</code></pre> graph_dfs.dart<pre><code>/* Вспомогательная функция обхода в глубину */\nvoid dfs(\n  GraphAdjList graph,\n  Set&lt;Vertex&gt; visited,\n  List&lt;Vertex&gt; res,\n  Vertex vet,\n) {\n  res.add(vet); // Отметить посещенную вершину\n  visited.add(vet); // Отметить эту вершину как посещенную\n  // Обойти все смежные вершины данной вершины\n  for (Vertex adjVet in graph.adjList[vet]!) {\n    if (visited.contains(adjVet)) {\n      continue; // Пропустить уже посещенную вершину\n    }\n    // Рекурсивно обходить смежные вершины\n    dfs(graph, visited, res, adjVet);\n  }\n}\n\n/* Обход в глубину */\nList&lt;Vertex&gt; graphDFS(GraphAdjList graph, Vertex startVet) {\n  // Последовательность обхода вершин\n  List&lt;Vertex&gt; res = [];\n  // Хеш-множество для хранения уже посещенных вершин\n  Set&lt;Vertex&gt; visited = {};\n  dfs(graph, visited, res, startVet);\n  return res;\n}\n</code></pre> graph_dfs.rs<pre><code>/* Вспомогательная функция обхода в глубину */\nfn dfs(graph: &amp;GraphAdjList, visited: &amp;mut HashSet&lt;Vertex&gt;, res: &amp;mut Vec&lt;Vertex&gt;, vet: Vertex) {\n    res.push(vet); // Отметить посещенную вершину\n    visited.insert(vet); // Отметить эту вершину как посещенную\n                         // Обойти все смежные вершины данной вершины\n    if let Some(adj_vets) = graph.adj_list.get(&amp;vet) {\n        for &amp;adj_vet in adj_vets {\n            if visited.contains(&amp;adj_vet) {\n                continue; // Пропустить уже посещенную вершину\n            }\n            // Рекурсивно обходить смежные вершины\n            dfs(graph, visited, res, adj_vet);\n        }\n    }\n}\n\n/* Обход в глубину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfn graph_dfs(graph: GraphAdjList, start_vet: Vertex) -&gt; Vec&lt;Vertex&gt; {\n    // Последовательность обхода вершин\n    let mut res = vec![];\n    // Хеш-множество для хранения уже посещенных вершин\n    let mut visited = HashSet::new();\n    dfs(&amp;graph, &amp;mut visited, &amp;mut res, start_vet);\n\n    res\n}\n</code></pre> graph_dfs.c<pre><code>/* Проверить, была ли вершина уже посещена */\nint isVisited(Vertex **res, int size, Vertex *vet) {\n    // Искать узел обходом за O(n) времени\n    for (int i = 0; i &lt; size; i++) {\n        if (res[i] == vet) {\n            return 1;\n        }\n    }\n    return 0;\n}\n\n/* Вспомогательная функция обхода в глубину */\nvoid dfs(GraphAdjList *graph, Vertex **res, int *resSize, Vertex *vet) {\n    // Отметить посещенную вершину\n    res[(*resSize)++] = vet;\n    // Обойти все смежные вершины данной вершины\n    AdjListNode *node = findNode(graph, vet);\n    while (node != NULL) {\n        // Пропустить уже посещенную вершину\n        if (!isVisited(res, *resSize, node-&gt;vertex)) {\n            // Рекурсивно обходить смежные вершины\n            dfs(graph, res, resSize, node-&gt;vertex);\n        }\n        node = node-&gt;next;\n    }\n}\n\n/* Обход в глубину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nvoid graphDFS(GraphAdjList *graph, Vertex *startVet, Vertex **res, int *resSize) {\n    dfs(graph, res, resSize, startVet);\n}\n</code></pre> graph_dfs.kt<pre><code>/* Вспомогательная функция обхода в глубину */\nfun dfs(\n    graph: GraphAdjList,\n    visited: MutableSet&lt;Vertex?&gt;,\n    res: MutableList&lt;Vertex?&gt;,\n    vet: Vertex?\n) {\n    res.add(vet)     // Отметить посещенную вершину\n    visited.add(vet) // Отметить эту вершину как посещенную\n    // Обойти все смежные вершины данной вершины\n    for (adjVet in graph.adjList[vet]!!) {\n        if (visited.contains(adjVet))\n            continue  // Пропустить уже посещенную вершину\n        // Рекурсивно обходить смежные вершины\n        dfs(graph, visited, res, adjVet)\n    }\n}\n\n/* Обход в глубину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfun graphDFS(graph: GraphAdjList, startVet: Vertex?): MutableList&lt;Vertex?&gt; {\n    // Последовательность обхода вершин\n    val res = mutableListOf&lt;Vertex?&gt;()\n    // Хеш-множество для хранения уже посещенных вершин\n    val visited = HashSet&lt;Vertex?&gt;()\n    dfs(graph, visited, res, startVet)\n    return res\n}\n</code></pre> graph_dfs.rb<pre><code>### Вспомогательная функция обхода в глубину ###\ndef dfs(graph, visited, res, vet)\n  res &lt;&lt; vet # Отметить посещенную вершину\n  visited.add(vet) # Отметить эту вершину как посещенную\n  # Обойти все смежные вершины данной вершины\n  for adj_vet in graph.adj_list[vet]\n    next if visited.include?(adj_vet) # Пропустить уже посещенную вершину\n    # Рекурсивно обходить смежные вершины\n    dfs(graph, visited, res, adj_vet)\n  end\nend\n\n### Обход в глубину ###\ndef graph_dfs(graph, start_vet)\n  # Использовать список смежности для представления графа, чтобы получать все смежные вершины заданной вершины\n  # Последовательность обхода вершин\n  res = []\n  # Хеш-множество для хранения уже посещенных вершин\n  visited = Set.new\n  dfs(graph, visited, res, start_vet)\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Алгоритмический процесс обхода в глубину показан на рисунках ниже.</p> <ul> <li>Прямая пунктирная линия обозначает нисходящее рекурсивное развертывание , то есть запуск нового рекурсивного метода для посещения новой вершины.</li> <li>Изогнутая пунктирная линия обозначает обратный возврат по рекурсии , то есть данный рекурсивный метод завершился и управление вернулось туда, откуда он был вызван.</li> </ul> <p>Чтобы лучше понять алгоритм, рекомендуется совместить рисунки ниже с кодом и мысленно проследить весь процесс DFS, включая моменты запуска и возврата каждого рекурсивного вызова.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 9-12   Шаги обхода графа в глубину </p> <p>Является ли последовательность обхода в глубину единственной?</p> <p>Как и в случае обхода в ширину, последовательность DFS тоже не является единственной. Для заданной вершины допустимо сначала углубиться в любое направление, то есть порядок смежных вершин может быть произвольным, и все такие варианты будут корректными обходами в глубину.</p> <p>Если взять в качестве примера обход дерева, то варианты \"корень \\(\\rightarrow\\) лево \\(\\rightarrow\\) право\", \"лево \\(\\rightarrow\\) корень \\(\\rightarrow\\) право\" и \"лево \\(\\rightarrow\\) право \\(\\rightarrow\\) корень\" соответствуют прямому, симметричному и обратному обходам соответственно. Они показывают три разных приоритета обхода, но все они относятся к обходу в глубину.</p>","path":["Глава 9. Граф","9.3 &nbsp; Обход графа"],"tags":[]},{"location":"chapter_graph/graph_traversal/#2_1","level":3,"title":"2.   Анализ сложности","text":"<p>Временная сложность: все вершины будут посещены по \\(1\\) разу, что требует \\(O(|V|)\\) времени; все ребра будут посещены по \\(2\\) раза, что требует \\(O(2|E|)\\) времени; суммарно получается \\(O(|V| + |E|)\\) .</p> <p>Пространственная сложность: число вершин в списке <code>res</code> и хеш-наборе <code>visited</code> в худшем случае достигает \\(|V|\\) , максимальная глубина рекурсии тоже равна \\(|V|\\) , поэтому требуется \\(O(|V|)\\) памяти.</p>","path":["Глава 9. Граф","9.3 &nbsp; Обход графа"],"tags":[]},{"location":"chapter_graph/summary/","level":1,"title":"9.4   Краткие итоги","text":"","path":["Глава 9. Граф","9.4 &nbsp; Краткие итоги"],"tags":[]},{"location":"chapter_graph/summary/#1","level":3,"title":"1.   Основные моменты","text":"<ul> <li>Граф состоит из вершин и ребер и может быть задан как множество вершин и множество ребер.</li> <li>По сравнению с линейными отношениями (связный список) и отношениями разделения (дерево), сетевые отношения (граф) обладают большей свободой и потому более сложны.</li> <li>Ребра ориентированного графа имеют направление, в связном графе любые вершины достижимы друг из друга, а в взвешенном графе каждое ребро несет переменную веса.</li> <li>Матрица смежности использует матрицу для представления графа: каждая строка и каждый столбец соответствуют вершине, а элементы матрицы показывают, есть между двумя вершинами ребро или нет. Матрица смежности очень эффективна для операций добавления, удаления, поиска и изменения, но расходует больше памяти.</li> <li>Список смежности использует несколько списков для представления графа; \\(i\\)-й список соответствует вершине \\(i\\) и хранит все ее смежные вершины. По сравнению с матрицей смежности список смежности экономит пространство, но для поиска ребра в нем приходится обходить список, поэтому по времени он уступает.</li> <li>Когда списки в списке смежности становятся слишком длинными, их можно преобразовать в красно-черное дерево или хеш-таблицу, чтобы ускорить поиск.</li> <li>С точки зрения алгоритмической идеи матрица смежности отражает принцип \"обмен пространства на время\", а список смежности - принцип \"обмена времени на пространство\".</li> <li>Графы можно использовать для моделирования различных реальных систем, таких как социальные сети, линии метро и так далее.</li> <li>Дерево является частным случаем графа, а обход дерева - частным случаем обхода графа.</li> <li>Обход графа в ширину представляет собой способ поиска, который расширяется от ближнего к дальнему и обычно реализуется с помощью очереди.</li> <li>Обход графа в глубину представляет собой способ поиска, который сначала идет до самого конца, а затем возвращается назад, когда путь исчерпан; обычно он реализуется на основе рекурсии.</li> </ul>","path":["Глава 9. Граф","9.4 &nbsp; Краткие итоги"],"tags":[]},{"location":"chapter_graph/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: Что считается путем: последовательность вершин или последовательность ребер?</p> <p>Определение в разных языковых версиях Википедии различается: в английской версии путь определяется как \"последовательность ребер\", а в китайской версии - как \"последовательность вершин\". В английской версии исходная формулировка выглядит так: In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices.</p> <p>В этой книге путь рассматривается как последовательность ребер, а не как последовательность вершин. Причина в том, что между двумя вершинами может существовать несколько ребер, и в таком случае каждому ребру соответствует свой путь.</p> <p>Q: Есть ли в несвязном графе вершины, до которых нельзя дойти?</p> <p>В несвязном графе, начиная из некоторой вершины, по крайней мере одна вершина оказывается недостижимой. Чтобы обойти весь несвязный граф, нужно задать несколько стартовых точек и обойти все связные компоненты графа.</p> <p>Q: Есть ли требования к порядку вершин в списке \"всех вершин, соединенных с данной вершиной\" в списке смежности?</p> <p>Порядок может быть произвольным. Но на практике может понадобиться сортировка по определенному правилу, например по порядку добавления вершин или по возрастанию значений вершин; это помогает быстро находить вершины с некоторым экстремальным свойством.</p>","path":["Глава 9. Граф","9.4 &nbsp; Краткие итоги"],"tags":[]},{"location":"chapter_greedy/","level":1,"title":"Глава 15.   Жадность","text":"<p>Abstract</p> <p>Подсолнух поворачивается к солнцу, постоянно стремясь к наилучшим условиям для роста.</p> <p>Жадная стратегия через цепочку простых выборов постепенно приводит к наилучшему ответу.</p>","path":["Глава 15. Жадность","Глава 15. &nbsp; Жадность"],"tags":[]},{"location":"chapter_greedy/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>15.1   Жадный алгоритм</li> <li>15.2   Задача о дробном рюкзаке</li> <li>15.3   Задача о максимальной вместимости</li> <li>15.4   Задача о максимальном произведении разбиения</li> <li>15.5   Резюме</li> </ul>","path":["Глава 15. Жадность","Глава 15. &nbsp; Жадность"],"tags":[]},{"location":"chapter_greedy/fractional_knapsack_problem/","level":1,"title":"15.2   Задача о дробном рюкзаке","text":"<p>Question</p> <p>Дано \\(n\\) предметов. Вес предмета \\(i\\) равен \\(wgt[i-1]\\), ценность равна \\(val[i-1]\\), также дан рюкзак вместимостью \\(cap\\). Каждый предмет можно выбрать только один раз, но разрешается взять лишь часть предмета, а ценность вычисляется пропорционально взятому весу. Требуется найти максимальную ценность предметов в рюкзаке при ограниченной вместимости. Пример показан на рисунке 15-3.</p> <p></p> <p> Рисунок 15-3   Пример данных для задачи о дробном рюкзаке </p> <p>Задача о дробном рюкзаке в целом очень похожа на задачу о рюкзаке 0-1: состояние включает текущий предмет \\(i\\) и вместимость \\(c\\), а цель состоит в нахождении максимальной ценности при заданной вместимости рюкзака.</p> <p>Отличие в том, что здесь разрешено брать только часть предмета. Как показано на рисунке 15-4, мы можем произвольно делить предмет и вычислять соответствующую ценность пропорционально весу.</p> <ol> <li>Для предмета \\(i\\) его ценность на единицу веса равна \\(val[i-1] / wgt[i-1]\\), сокращенно - удельная ценность.</li> <li>Если взять часть предмета \\(i\\) весом \\(w\\), то ценность рюкзака увеличится на \\(w \\times val[i-1] / wgt[i-1]\\).</li> </ol> <p></p> <p> Рисунок 15-4   Ценность предмета на единицу веса </p>","path":["Глава 15. Жадность","15.2 &nbsp; Задача о дробном рюкзаке"],"tags":[]},{"location":"chapter_greedy/fractional_knapsack_problem/#1","level":3,"title":"1.   Определение жадной стратегии","text":"<p>Максимизация общей ценности предметов в рюкзаке по сути равносильна максимизации ценности на единицу веса. Отсюда естественно выводится следующая жадная стратегия.</p> <ol> <li>Отсортировать предметы по убыванию удельной ценности.</li> <li>Перебирать все предметы и на каждом шаге жадно выбирать предмет с наибольшей удельной ценностью.</li> <li>Если оставшейся вместимости рюкзака недостаточно, взять часть текущего предмета, чтобы заполнить рюкзак.</li> </ol> <p></p> <p> Рисунок 15-5   Жадная стратегия для задачи о дробном рюкзаке </p>","path":["Глава 15. Жадность","15.2 &nbsp; Задача о дробном рюкзаке"],"tags":[]},{"location":"chapter_greedy/fractional_knapsack_problem/#2","level":3,"title":"2.   Код реализации","text":"<p>Мы вводим класс <code>Item</code>, чтобы можно было сортировать предметы по удельной ценности. Далее циклически выполняем жадный выбор и, когда рюкзак заполнен, выходим и возвращаем ответ:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby fractional_knapsack.py<pre><code>class Item:\n    \"\"\"Предмет\"\"\"\n\n    def __init__(self, w: int, v: int):\n        self.w = w  # Вес предмета\n        self.v = v  # Стоимость предмета\n\ndef fractional_knapsack(wgt: list[int], val: list[int], cap: int) -&gt; int:\n    \"\"\"Дробный рюкзак: жадный алгоритм\"\"\"\n    # Создать список предметов с двумя свойствами: вес и стоимость\n    items = [Item(w, v) for w, v in zip(wgt, val)]\n    # Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n    items.sort(key=lambda item: item.v / item.w, reverse=True)\n    # Циклический жадный выбор\n    res = 0\n    for item in items:\n        if item.w &lt;= cap:\n            # Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n            res += item.v\n            cap -= item.w\n        else:\n            # Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n            res += (item.v / item.w) * cap\n            # Свободной вместимости больше не осталось, поэтому выйти из цикла\n            break\n    return res\n</code></pre> fractional_knapsack.cpp<pre><code>/* Предмет */\nclass Item {\n  public:\n    int w; // Вес предмета\n    int v; // Стоимость предмета\n\n    Item(int w, int v) : w(w), v(v) {\n    }\n};\n\n/* Дробный рюкзак: жадный алгоритм */\ndouble fractionalKnapsack(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int cap) {\n    // Создать список предметов с двумя свойствами: вес и стоимость\n    vector&lt;Item&gt; items;\n    for (int i = 0; i &lt; wgt.size(); i++) {\n        items.push_back(Item(wgt[i], val[i]));\n    }\n    // Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n    sort(items.begin(), items.end(), [](Item &amp;a, Item &amp;b) { return (double)a.v / a.w &gt; (double)b.v / b.w; });\n    // Циклический жадный выбор\n    double res = 0;\n    for (auto &amp;item : items) {\n        if (item.w &lt;= cap) {\n            // Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n            res += item.v;\n            cap -= item.w;\n        } else {\n            // Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n            res += (double)item.v / item.w * cap;\n            // Свободной вместимости больше не осталось, поэтому выйти из цикла\n            break;\n        }\n    }\n    return res;\n}\n</code></pre> fractional_knapsack.java<pre><code>/* Предмет */\nclass Item {\n    int w; // Вес предмета\n    int v; // Стоимость предмета\n\n    public Item(int w, int v) {\n        this.w = w;\n        this.v = v;\n    }\n}\n\n/* Дробный рюкзак: жадный алгоритм */\ndouble fractionalKnapsack(int[] wgt, int[] val, int cap) {\n    // Создать список предметов с двумя свойствами: вес и стоимость\n    Item[] items = new Item[wgt.length];\n    for (int i = 0; i &lt; wgt.length; i++) {\n        items[i] = new Item(wgt[i], val[i]);\n    }\n    // Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n    Arrays.sort(items, Comparator.comparingDouble(item -&gt; -((double) item.v / item.w)));\n    // Циклический жадный выбор\n    double res = 0;\n    for (Item item : items) {\n        if (item.w &lt;= cap) {\n            // Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n            res += item.v;\n            cap -= item.w;\n        } else {\n            // Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n            res += (double) item.v / item.w * cap;\n            // Свободной вместимости больше не осталось, поэтому выйти из цикла\n            break;\n        }\n    }\n    return res;\n}\n</code></pre> fractional_knapsack.cs<pre><code>/* Предмет */\nclass Item(int w, int v) {\n    public int w = w; // Вес предмета\n    public int v = v; // Стоимость предмета\n}\n\n/* Дробный рюкзак: жадный алгоритм */\ndouble FractionalKnapsack(int[] wgt, int[] val, int cap) {\n    // Создать список предметов с двумя свойствами: вес и стоимость\n    Item[] items = new Item[wgt.Length];\n    for (int i = 0; i &lt; wgt.Length; i++) {\n        items[i] = new Item(wgt[i], val[i]);\n    }\n    // Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n    Array.Sort(items, (x, y) =&gt; (y.v / y.w).CompareTo(x.v / x.w));\n    // Циклический жадный выбор\n    double res = 0;\n    foreach (Item item in items) {\n        if (item.w &lt;= cap) {\n            // Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n            res += item.v;\n            cap -= item.w;\n        } else {\n            // Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n            res += (double)item.v / item.w * cap;\n            // Свободной вместимости больше не осталось, поэтому выйти из цикла\n            break;\n        }\n    }\n    return res;\n}\n</code></pre> fractional_knapsack.go<pre><code>/* Предмет */\ntype Item struct {\n    w int // Вес предмета\n    v int // Стоимость предмета\n}\n\n/* Дробный рюкзак: жадный алгоритм */\nfunc fractionalKnapsack(wgt []int, val []int, cap int) float64 {\n    // Создать список предметов с двумя свойствами: вес и стоимость\n    items := make([]Item, len(wgt))\n    for i := 0; i &lt; len(wgt); i++ {\n        items[i] = Item{wgt[i], val[i]}\n    }\n    // Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n    sort.Slice(items, func(i, j int) bool {\n        return float64(items[i].v)/float64(items[i].w) &gt; float64(items[j].v)/float64(items[j].w)\n    })\n    // Циклический жадный выбор\n    res := 0.0\n    for _, item := range items {\n        if item.w &lt;= cap {\n            // Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n            res += float64(item.v)\n            cap -= item.w\n        } else {\n            // Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n            res += float64(item.v) / float64(item.w) * float64(cap)\n            // Свободной вместимости больше не осталось, поэтому выйти из цикла\n            break\n        }\n    }\n    return res\n}\n</code></pre> fractional_knapsack.swift<pre><code>/* Предмет */\nclass Item {\n    var w: Int // Вес предмета\n    var v: Int // Стоимость предмета\n\n    init(w: Int, v: Int) {\n        self.w = w\n        self.v = v\n    }\n}\n\n/* Дробный рюкзак: жадный алгоритм */\nfunc fractionalKnapsack(wgt: [Int], val: [Int], cap: Int) -&gt; Double {\n    // Создать список предметов с двумя свойствами: вес и стоимость\n    var items = zip(wgt, val).map { Item(w: $0, v: $1) }\n    // Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n    items.sort { -(Double($0.v) / Double($0.w)) &lt; -(Double($1.v) / Double($1.w)) }\n    // Циклический жадный выбор\n    var res = 0.0\n    var cap = cap\n    for item in items {\n        if item.w &lt;= cap {\n            // Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n            res += Double(item.v)\n            cap -= item.w\n        } else {\n            // Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n            res += Double(item.v) / Double(item.w) * Double(cap)\n            // Свободной вместимости больше не осталось, поэтому выйти из цикла\n            break\n        }\n    }\n    return res\n}\n</code></pre> fractional_knapsack.js<pre><code>/* Предмет */\nclass Item {\n    constructor(w, v) {\n        this.w = w; // Вес предмета\n        this.v = v; // Стоимость предмета\n    }\n}\n\n/* Дробный рюкзак: жадный алгоритм */\nfunction fractionalKnapsack(wgt, val, cap) {\n    // Создать список предметов с двумя свойствами: вес и стоимость\n    const items = wgt.map((w, i) =&gt; new Item(w, val[i]));\n    // Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n    items.sort((a, b) =&gt; b.v / b.w - a.v / a.w);\n    // Циклический жадный выбор\n    let res = 0;\n    for (const item of items) {\n        if (item.w &lt;= cap) {\n            // Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n            res += item.v;\n            cap -= item.w;\n        } else {\n            // Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n            res += (item.v / item.w) * cap;\n            // Свободной вместимости больше не осталось, поэтому выйти из цикла\n            break;\n        }\n    }\n    return res;\n}\n</code></pre> fractional_knapsack.ts<pre><code>/* Предмет */\nclass Item {\n    w: number; // Вес предмета\n    v: number; // Стоимость предмета\n\n    constructor(w: number, v: number) {\n        this.w = w;\n        this.v = v;\n    }\n}\n\n/* Дробный рюкзак: жадный алгоритм */\nfunction fractionalKnapsack(wgt: number[], val: number[], cap: number): number {\n    // Создать список предметов с двумя свойствами: вес и стоимость\n    const items: Item[] = wgt.map((w, i) =&gt; new Item(w, val[i]));\n    // Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n    items.sort((a, b) =&gt; b.v / b.w - a.v / a.w);\n    // Циклический жадный выбор\n    let res = 0;\n    for (const item of items) {\n        if (item.w &lt;= cap) {\n            // Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n            res += item.v;\n            cap -= item.w;\n        } else {\n            // Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n            res += (item.v / item.w) * cap;\n            // Свободной вместимости больше не осталось, поэтому выйти из цикла\n            break;\n        }\n    }\n    return res;\n}\n</code></pre> fractional_knapsack.dart<pre><code>/* Предмет */\nclass Item {\n  int w; // Вес предмета\n  int v; // Стоимость предмета\n\n  Item(this.w, this.v);\n}\n\n/* Дробный рюкзак: жадный алгоритм */\ndouble fractionalKnapsack(List&lt;int&gt; wgt, List&lt;int&gt; val, int cap) {\n  // Создать список предметов с двумя свойствами: вес и стоимость\n  List&lt;Item&gt; items = List.generate(wgt.length, (i) =&gt; Item(wgt[i], val[i]));\n  // Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n  items.sort((a, b) =&gt; (b.v / b.w).compareTo(a.v / a.w));\n  // Циклический жадный выбор\n  double res = 0;\n  for (Item item in items) {\n    if (item.w &lt;= cap) {\n      // Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n      res += item.v;\n      cap -= item.w;\n    } else {\n      // Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n      res += item.v / item.w * cap;\n      // Свободной вместимости больше не осталось, поэтому выйти из цикла\n      break;\n    }\n  }\n  return res;\n}\n</code></pre> fractional_knapsack.rs<pre><code>/* Предмет */\nstruct Item {\n    w: i32, // Вес предмета\n    v: i32, // Стоимость предмета\n}\n\nimpl Item {\n    fn new(w: i32, v: i32) -&gt; Self {\n        Self { w, v }\n    }\n}\n\n/* Дробный рюкзак: жадный алгоритм */\nfn fractional_knapsack(wgt: &amp;[i32], val: &amp;[i32], mut cap: i32) -&gt; f64 {\n    // Создать список предметов с двумя свойствами: вес и стоимость\n    let mut items = wgt\n        .iter()\n        .zip(val.iter())\n        .map(|(&amp;w, &amp;v)| Item::new(w, v))\n        .collect::&lt;Vec&lt;Item&gt;&gt;();\n    // Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n    items.sort_by(|a, b| {\n        (b.v as f64 / b.w as f64)\n            .partial_cmp(&amp;(a.v as f64 / a.w as f64))\n            .unwrap()\n    });\n    // Циклический жадный выбор\n    let mut res = 0.0;\n    for item in &amp;items {\n        if item.w &lt;= cap {\n            // Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n            res += item.v as f64;\n            cap -= item.w;\n        } else {\n            // Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n            res += item.v as f64 / item.w as f64 * cap as f64;\n            // Свободной вместимости больше не осталось, поэтому выйти из цикла\n            break;\n        }\n    }\n    res\n}\n</code></pre> fractional_knapsack.c<pre><code>/* Предмет */\ntypedef struct {\n    int w; // Вес предмета\n    int v; // Стоимость предмета\n} Item;\n\n/* Дробный рюкзак: жадный алгоритм */\nfloat fractionalKnapsack(int wgt[], int val[], int itemCount, int cap) {\n    // Создать список предметов с двумя свойствами: вес и стоимость\n    Item *items = malloc(sizeof(Item) * itemCount);\n    for (int i = 0; i &lt; itemCount; i++) {\n        items[i] = (Item){.w = wgt[i], .v = val[i]};\n    }\n    // Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n    qsort(items, (size_t)itemCount, sizeof(Item), sortByValueDensity);\n    // Циклический жадный выбор\n    float res = 0.0;\n    for (int i = 0; i &lt; itemCount; i++) {\n        if (items[i].w &lt;= cap) {\n            // Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n            res += items[i].v;\n            cap -= items[i].w;\n        } else {\n            // Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n            res += (float)cap / items[i].w * items[i].v;\n            cap = 0;\n            break;\n        }\n    }\n    free(items);\n    return res;\n}\n</code></pre> fractional_knapsack.kt<pre><code>/* Предмет */\nclass Item(\n    val w: Int, // Предмет\n    val v: Int  // Стоимость предмета\n)\n\n/* Дробный рюкзак: жадный алгоритм */\nfun fractionalKnapsack(wgt: IntArray, _val: IntArray, c: Int): Double {\n    // Создать список предметов с двумя свойствами: вес и стоимость\n    var cap = c\n    val items = arrayOfNulls&lt;Item&gt;(wgt.size)\n    for (i in wgt.indices) {\n        items[i] = Item(wgt[i], _val[i])\n    }\n    // Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n    items.sortBy { item: Item? -&gt; -(item!!.v.toDouble() / item.w) }\n    // Циклический жадный выбор\n    var res = 0.0\n    for (item in items) {\n        if (item!!.w &lt;= cap) {\n            // Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n            res += item.v\n            cap -= item.w\n        } else {\n            // Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n            res += item.v.toDouble() / item.w * cap\n            // Свободной вместимости больше не осталось, поэтому выйти из цикла\n            break\n        }\n    }\n    return res\n}\n</code></pre> fractional_knapsack.rb<pre><code>### Предмет ###\nclass Item\n  attr_accessor :w # Вес предмета\n  attr_accessor :v # Стоимость предмета\n\n  def initialize(w, v)\n    @w = w\n    @v = v\n  end\nend\n\n### Дробный рюкзак: жадный алгоритм ###\ndef fractional_knapsack(wgt, val, cap)\n  # Создать список предметов с двумя свойствами: вес и стоимость\n  items = wgt.each_with_index.map { |w, i| Item.new(w, val[i]) }\n  # Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n  items.sort! { |a, b| (b.v.to_f / b.w) &lt;=&gt; (a.v.to_f / a.w) }\n  # Циклический жадный выбор\n  res = 0\n  for item in items\n    if item.w &lt;= cap\n      # Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n      res += item.v\n      cap -= item.w\n    else\n      # Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n      res += (item.v.to_f / item.w) * cap\n      # Свободной вместимости больше не осталось, поэтому выйти из цикла\n      break\n    end\n  end\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Встроенный алгоритм сортировки обычно имеет временную сложность \\(O(\\log n)\\), а пространственная сложность обычно равна \\(O(\\log n)\\) или \\(O(n)\\), в зависимости от конкретной реализации в языке программирования.</p> <p>Помимо сортировки, в худшем случае потребуется пройти весь список предметов, поэтому временная сложность равна \\(O(n)\\), где \\(n\\) - число предметов.</p> <p>Поскольку инициализируется список объектов <code>Item</code>, пространственная сложность равна \\(O(n)\\).</p>","path":["Глава 15. Жадность","15.2 &nbsp; Задача о дробном рюкзаке"],"tags":[]},{"location":"chapter_greedy/fractional_knapsack_problem/#3","level":3,"title":"3.   Доказательство корректности","text":"<p>Используем доказательство от противного. Предположим, что предмет \\(x\\) имеет наибольшую удельную ценность, некоторый алгоритм получил максимальную ценность <code>res</code>, но в найденном решении предмет \\(x\\) отсутствует.</p> <p>Теперь вынем из рюкзака произвольный предмет единичного веса и заменим его на предмет \\(x\\) того же веса. Поскольку предмет \\(x\\) имеет наибольшую удельную ценность, общая ценность после замены обязательно станет больше <code>res</code>. Это противоречит тому, что <code>res</code> является оптимальным решением, а значит оптимальное решение обязательно содержит предмет \\(x\\).</p> <p>Для других предметов в этом решении можно построить аналогичное противоречие. Иными словами, предметы с большей удельной ценностью всегда являются более выгодным выбором, а значит жадная стратегия корректна.</p> <p>Как показано на рисунке 15-6, если рассматривать вес предметов и их удельную ценность как горизонтальную и вертикальную оси двумерной диаграммы, то задачу о дробном рюкзаке можно интерпретировать как «поиск максимальной площади, ограниченной конечным отрезком по горизонтали». Эта аналогия помогает понять корректность жадной стратегии с геометрической точки зрения.</p> <p></p> <p> Рисунок 15-6   Геометрическая интерпретация задачи о дробном рюкзаке </p>","path":["Глава 15. Жадность","15.2 &nbsp; Задача о дробном рюкзаке"],"tags":[]},{"location":"chapter_greedy/greedy_algorithm/","level":1,"title":"15.1   Жадный алгоритм","text":"<p>Жадный алгоритм (greedy algorithm) - это распространенный подход к решению задач оптимизации. Его основная идея состоит в том, чтобы на каждом этапе принятия решения выбирать вариант, который выглядит наилучшим прямо сейчас, то есть жадно принимать локально оптимальные решения в надежде получить глобально оптимальный результат. Жадные алгоритмы лаконичны и эффективны, поэтому широко применяются во многих практических задачах.</p> <p>Жадные алгоритмы и динамическое программирование часто используются для решения задач оптимизации. У них есть некоторое сходство, например оба опираются на свойство оптимальной подструктуры, но принципы работы различаются.</p> <ul> <li>Динамическое программирование учитывает все решения предыдущих этапов при выборе текущего решения и использует ответы для прошлых подзадач, чтобы построить ответ для текущей подзадачи.</li> <li>Жадный алгоритм не учитывает прошлые решения, а просто движется вперед, каждый раз делая жадный выбор, постепенно сужая область задачи, пока она не будет решена.</li> </ul> <p>Сначала разберем принцип работы жадного алгоритма на примере задачи «размен монет». Эта задача уже встречалась в разделе «задача о полном рюкзаке», поэтому она наверняка вам знакома.</p> <p>Question</p> <p>Дано \\(n\\) видов монет. Номинал монеты \\(i\\) равен \\(coins[i - 1]\\), целевая сумма равна \\(amt\\), причем каждую монету можно брать неограниченное число раз. Требуется найти минимальное число монет, которыми можно набрать целевую сумму. Если набрать сумму невозможно, верните \\(-1\\).</p> <p>Жадная стратегия для этой задачи показана на рисунке 15-1. Для заданной целевой суммы мы жадно выбираем монету, которая не превышает ее и находится к ней ближе всего, и повторяем этот шаг, пока не получим нужную сумму.</p> <p></p> <p> Рисунок 15-1   Жадная стратегия для задачи о размене монет </p> <p>Код реализации выглядит следующим образом:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby coin_change_greedy.py<pre><code>def coin_change_greedy(coins: list[int], amt: int) -&gt; int:\n    \"\"\"Размен монет: жадный алгоритм\"\"\"\n    # Предположить, что список coins упорядочен\n    i = len(coins) - 1\n    count = 0\n    # Циклически выполнять жадный выбор, пока не останется суммы\n    while amt &gt; 0:\n        # Найти монету, которая меньше остатка суммы и наиболее к нему близка\n        while i &gt; 0 and coins[i] &gt; amt:\n            i -= 1\n        # Выбрать coins[i]\n        amt -= coins[i]\n        count += 1\n    # Если допустимое решение не найдено, вернуть -1\n    return count if amt == 0 else -1\n</code></pre> coin_change_greedy.cpp<pre><code>/* Размен монет: жадный алгоритм */\nint coinChangeGreedy(vector&lt;int&gt; &amp;coins, int amt) {\n    // Предположить, что список coins упорядочен\n    int i = coins.size() - 1;\n    int count = 0;\n    // Циклически выполнять жадный выбор, пока не останется суммы\n    while (amt &gt; 0) {\n        // Найти монету, которая меньше остатка суммы и наиболее к нему близка\n        while (i &gt; 0 &amp;&amp; coins[i] &gt; amt) {\n            i--;\n        }\n        // Выбрать coins[i]\n        amt -= coins[i];\n        count++;\n    }\n    // Если допустимое решение не найдено, вернуть -1\n    return amt == 0 ? count : -1;\n}\n</code></pre> coin_change_greedy.java<pre><code>/* Размен монет: жадный алгоритм */\nint coinChangeGreedy(int[] coins, int amt) {\n    // Предположить, что список coins упорядочен\n    int i = coins.length - 1;\n    int count = 0;\n    // Циклически выполнять жадный выбор, пока не останется суммы\n    while (amt &gt; 0) {\n        // Найти монету, которая меньше остатка суммы и наиболее к нему близка\n        while (i &gt; 0 &amp;&amp; coins[i] &gt; amt) {\n            i--;\n        }\n        // Выбрать coins[i]\n        amt -= coins[i];\n        count++;\n    }\n    // Если допустимое решение не найдено, вернуть -1\n    return amt == 0 ? count : -1;\n}\n</code></pre> coin_change_greedy.cs<pre><code>/* Размен монет: жадный алгоритм */\nint CoinChangeGreedy(int[] coins, int amt) {\n    // Предположить, что список coins упорядочен\n    int i = coins.Length - 1;\n    int count = 0;\n    // Циклически выполнять жадный выбор, пока не останется суммы\n    while (amt &gt; 0) {\n        // Найти монету, которая меньше остатка суммы и наиболее к нему близка\n        while (i &gt; 0 &amp;&amp; coins[i] &gt; amt) {\n            i--;\n        }\n        // Выбрать coins[i]\n        amt -= coins[i];\n        count++;\n    }\n    // Если допустимое решение не найдено, вернуть -1\n    return amt == 0 ? count : -1;\n}\n</code></pre> coin_change_greedy.go<pre><code>/* Размен монет: жадный алгоритм */\nfunc coinChangeGreedy(coins []int, amt int) int {\n    // Предположить, что список coins упорядочен\n    i := len(coins) - 1\n    count := 0\n    // Циклически выполнять жадный выбор, пока не останется суммы\n    for amt &gt; 0 {\n        // Найти монету, которая меньше остатка суммы и наиболее к нему близка\n        for i &gt; 0 &amp;&amp; coins[i] &gt; amt {\n            i--\n        }\n        // Выбрать coins[i]\n        amt -= coins[i]\n        count++\n    }\n    // Если допустимое решение не найдено, вернуть -1\n    if amt != 0 {\n        return -1\n    }\n    return count\n}\n</code></pre> coin_change_greedy.swift<pre><code>/* Размен монет: жадный алгоритм */\nfunc coinChangeGreedy(coins: [Int], amt: Int) -&gt; Int {\n    // Предположить, что список coins упорядочен\n    var i = coins.count - 1\n    var count = 0\n    var amt = amt\n    // Циклически выполнять жадный выбор, пока не останется суммы\n    while amt &gt; 0 {\n        // Найти монету, которая меньше остатка суммы и наиболее к нему близка\n        while i &gt; 0 &amp;&amp; coins[i] &gt; amt {\n            i -= 1\n        }\n        // Выбрать coins[i]\n        amt -= coins[i]\n        count += 1\n    }\n    // Если допустимое решение не найдено, вернуть -1\n    return amt == 0 ? count : -1\n}\n</code></pre> coin_change_greedy.js<pre><code>/* Размен монет: жадный алгоритм */\nfunction coinChangeGreedy(coins, amt) {\n    // Предположить, что массив coins упорядочен\n    let i = coins.length - 1;\n    let count = 0;\n    // Циклически выполнять жадный выбор, пока не останется суммы\n    while (amt &gt; 0) {\n        // Найти монету, которая меньше остатка суммы и наиболее к нему близка\n        while (i &gt; 0 &amp;&amp; coins[i] &gt; amt) {\n            i--;\n        }\n        // Выбрать coins[i]\n        amt -= coins[i];\n        count++;\n    }\n    // Если допустимое решение не найдено, вернуть -1\n    return amt === 0 ? count : -1;\n}\n</code></pre> coin_change_greedy.ts<pre><code>/* Размен монет: жадный алгоритм */\nfunction coinChangeGreedy(coins: number[], amt: number): number {\n    // Предположить, что массив coins упорядочен\n    let i = coins.length - 1;\n    let count = 0;\n    // Циклически выполнять жадный выбор, пока не останется суммы\n    while (amt &gt; 0) {\n        // Найти монету, которая меньше остатка суммы и наиболее к нему близка\n        while (i &gt; 0 &amp;&amp; coins[i] &gt; amt) {\n            i--;\n        }\n        // Выбрать coins[i]\n        amt -= coins[i];\n        count++;\n    }\n    // Если допустимое решение не найдено, вернуть -1\n    return amt === 0 ? count : -1;\n}\n</code></pre> coin_change_greedy.dart<pre><code>/* Размен монет: жадный алгоритм */\nint coinChangeGreedy(List&lt;int&gt; coins, int amt) {\n  // Предположить, что список coins упорядочен\n  int i = coins.length - 1;\n  int count = 0;\n  // Циклически выполнять жадный выбор, пока не останется суммы\n  while (amt &gt; 0) {\n    // Найти монету, которая меньше остатка суммы и наиболее к нему близка\n    while (i &gt; 0 &amp;&amp; coins[i] &gt; amt) {\n      i--;\n    }\n    // Выбрать coins[i]\n    amt -= coins[i];\n    count++;\n  }\n  // Если допустимое решение не найдено, вернуть -1\n  return amt == 0 ? count : -1;\n}\n</code></pre> coin_change_greedy.rs<pre><code>/* Размен монет: жадный алгоритм */\nfn coin_change_greedy(coins: &amp;[i32], mut amt: i32) -&gt; i32 {\n    // Предположить, что список coins упорядочен\n    let mut i = coins.len() - 1;\n    let mut count = 0;\n    // Циклически выполнять жадный выбор, пока не останется суммы\n    while amt &gt; 0 {\n        // Найти монету, которая меньше остатка суммы и наиболее к нему близка\n        while i &gt; 0 &amp;&amp; coins[i] &gt; amt {\n            i -= 1;\n        }\n        // Выбрать coins[i]\n        amt -= coins[i];\n        count += 1;\n    }\n    // Если допустимое решение не найдено, вернуть -1\n    if amt == 0 {\n        count\n    } else {\n        -1\n    }\n}\n</code></pre> coin_change_greedy.c<pre><code>/* Размен монет: жадный алгоритм */\nint coinChangeGreedy(int *coins, int size, int amt) {\n    // Предположить, что список coins упорядочен\n    int i = size - 1;\n    int count = 0;\n    // Циклически выполнять жадный выбор, пока не останется суммы\n    while (amt &gt; 0) {\n        // Найти монету, которая меньше остатка суммы и наиболее к нему близка\n        while (i &gt; 0 &amp;&amp; coins[i] &gt; amt) {\n            i--;\n        }\n        // Выбрать coins[i]\n        amt -= coins[i];\n        count++;\n    }\n    // Если допустимое решение не найдено, вернуть -1\n    return amt == 0 ? count : -1;\n}\n</code></pre> coin_change_greedy.kt<pre><code>/* Размен монет: жадный алгоритм */\nfun coinChangeGreedy(coins: IntArray, amt: Int): Int {\n    // Предположить, что список coins упорядочен\n    var am = amt\n    var i = coins.size - 1\n    var count = 0\n    // Циклически выполнять жадный выбор, пока не останется суммы\n    while (am &gt; 0) {\n        // Найти монету, которая меньше остатка суммы и наиболее к нему близка\n        while (i &gt; 0 &amp;&amp; coins[i] &gt; am) {\n            i--\n        }\n        // Выбрать coins[i]\n        am -= coins[i]\n        count++\n    }\n    // Если допустимое решение не найдено, вернуть -1\n    return if (am == 0) count else -1\n}\n</code></pre> coin_change_greedy.rb<pre><code>### Размен монет: жадный алгоритм ###\ndef coin_change_greedy(coins, amt)\n  # Предположить, что список coins упорядочен\n  i = coins.length - 1\n  count = 0\n  # Циклически выполнять жадный выбор, пока не останется суммы\n  while amt &gt; 0\n    # Найти монету, которая меньше остатка суммы и наиболее к нему близка\n    while i &gt; 0 &amp;&amp; coins[i] &gt; amt\n      i -= 1\n    end\n    # Выбрать coins[i]\n    amt -= coins[i]\n    count += 1\n  end\n  # Если допустимое решение не найдено, вернуть -1\n  amt == 0 ? count : -1\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>У вас может невольно вырваться: So clean! Жадный алгоритм решает задачу размена монет всего примерно десятью строками кода.</p>","path":["Глава 15. Жадность","15.1 &nbsp; Жадный алгоритм"],"tags":[]},{"location":"chapter_greedy/greedy_algorithm/#1511","level":2,"title":"15.1.1   Преимущества и ограничения жадного алгоритма","text":"<p>Жадный алгоритм не только прост в действиях и реализации, но и обычно очень эффективен. В приведенном выше коде обозначим минимальный номинал монеты через \\(\\min(coins)\\), тогда жадный выбор выполняется не более чем \\(amt / \\min(coins)\\) раз, а временная сложность равна \\(O(amt / \\min(coins))\\). Это на порядок меньше, чем временная сложность решения через динамическое программирование \\(O(n \\times amt)\\).</p> <p>Однако для некоторых наборов номиналов монет жадный алгоритм не может найти оптимальный ответ. Ниже показаны два примера.</p> <ul> <li>Положительный пример \\(coins = [1, 5, 10, 20, 50, 100]\\): для такого набора монет при любом \\(amt\\) жадный алгоритм находит оптимальное решение.</li> <li>Отрицательный пример \\(coins = [1, 20, 50]\\): пусть \\(amt = 60\\). Жадный алгоритм найдет только комбинацию \\(50 + 1 \\times 10\\), то есть всего \\(11\\) монет, тогда как динамическое программирование находит оптимум \\(20 + 20 + 20\\), где требуется лишь \\(3\\) монеты.</li> <li>Отрицательный пример \\(coins = [1, 49, 50]\\): пусть \\(amt = 98\\). Жадный алгоритм найдет только комбинацию \\(50 + 1 \\times 48\\), то есть всего \\(49\\) монет, тогда как динамическое программирование находит оптимум \\(49 + 49\\), где требуется лишь \\(2\\) монеты.</li> </ul> <p></p> <p> Рисунок 15-2   Примеры, где жадный алгоритм не находит оптимального решения </p> <p>Иными словами, в задаче о размене монет жадный алгоритм не гарантирует нахождение глобально оптимального решения и иногда может приводить к очень плохому ответу. Для этой задачи больше подходит динамическое программирование.</p> <p>В общем случае жадный алгоритм применим в двух следующих ситуациях.</p> <ol> <li>Можно гарантировать нахождение оптимального решения: в таком случае жадный алгоритм часто является лучшим выбором, поскольку обычно он эффективнее, чем поиск с возвратом и динамическое программирование.</li> <li>Можно найти приближенно оптимальное решение: в таком случае жадный алгоритм тоже полезен. Для многих сложных задач поиск глобального оптимума очень труден, и возможность быстро найти субоптимальный ответ уже весьма ценна.</li> </ol>","path":["Глава 15. Жадность","15.1 &nbsp; Жадный алгоритм"],"tags":[]},{"location":"chapter_greedy/greedy_algorithm/#1512","level":2,"title":"15.1.2   Свойства жадного алгоритма","text":"<p>Тогда возникает вопрос: какие задачи подходят для решения жадным алгоритмом? Или, другими словами, в каких случаях жадный алгоритм может гарантировать оптимальный ответ?</p> <p>По сравнению с динамическим программированием условия применения жадного алгоритма строже. В основном нас интересуют два свойства задачи.</p> <ul> <li>Свойство жадного выбора: только когда локально оптимальный выбор всегда может привести к глобально оптимальному решению, жадный алгоритм способен гарантировать оптимум.</li> <li>Оптимальная подструктура: оптимальное решение исходной задачи содержит оптимальные решения подзадач.</li> </ul> <p>Оптимальная подструктура уже обсуждалась в главе «Динамическое программирование», поэтому здесь не будем повторяться. Стоит отметить, что у некоторых задач оптимальная подструктура не столь очевидна, но их все равно можно решать жадным алгоритмом.</p> <p>Основное внимание мы уделяем тому, как определить свойство жадного выбора. Хотя формулировка выглядит довольно простой, на практике для многих задач доказать свойство жадного выбора совсем не легко.</p> <p>Например, в задаче о размене монет легко привести контрпример и опровергнуть свойство жадного выбора, но вот доказать его истинность намного сложнее. Если спросить: для каких наборов монет можно использовать жадный алгоритм? - обычно удается дать лишь интуитивный или примерный ответ, а не строгое математическое доказательство.</p> <p>Quote</p> <p>Существует статья, в которой приводится алгоритм со временной сложностью \\(O(n^3)\\) для определения того, можно ли с помощью жадного алгоритма находить оптимальный размен для любой суммы в заданной системе монет.</p> <p>Pearson, D. A polynomial-time algorithm for the change-making problem[J]. Operations Research Letters, 2005, 33(3): 231-234.</p>","path":["Глава 15. Жадность","15.1 &nbsp; Жадный алгоритм"],"tags":[]},{"location":"chapter_greedy/greedy_algorithm/#1513","level":2,"title":"15.1.3   Этапы решения задач жадным алгоритмом","text":"<p>В общем виде процесс решения жадной задачи можно разбить на три шага.</p> <ol> <li>Анализ задачи: разобраться в свойствах задачи, включая определение состояний, целевой функции и ограничений. Этот этап присутствует и в поиске с возвратом, и в динамическом программировании.</li> <li>Определение жадной стратегии: определить, какой жадный выбор следует делать на каждом шаге. Эта стратегия должна уменьшать размер задачи на каждом этапе и в итоге привести к решению всей задачи.</li> <li>Доказательство корректности: обычно требуется доказать, что задача обладает свойством жадного выбора и оптимальной подструктурой. На этом этапе может понадобиться математическое доказательство, например индукция или доказательство от противного.</li> </ol> <p>Определение жадной стратегии - это ключевой этап решения, но на практике он часто оказывается непростым по следующим причинам.</p> <ul> <li>Жадные стратегии для разных задач сильно различаются. Для многих задач стратегия довольно очевидна, и до нее можно дойти за счет общих рассуждений и нескольких проб. Но в более сложных задачах жадная стратегия может быть очень скрытой, и тут уже многое зависит от опыта решения задач и алгоритмической подготовки.</li> <li>Некоторые жадные стратегии выглядят убедительно, но оказываются обманчивыми. Бывает, что мы с уверенностью придумали жадную стратегию, написали код и отправили его на проверку, а часть тестов не проходит. Причина в том, что спроектированная стратегия лишь «частично верна», и описанная выше задача о размене монет - типичный пример.</li> </ul> <p>Чтобы гарантировать корректность, нужно дать строгое математическое доказательство жадной стратегии, обычно с использованием доказательства от противного или математической индукции.</p> <p>Однако и доказательство корректности может оказаться непростой задачей. Если идей нет, мы обычно начинаем отлаживать код на тестовых примерах, постепенно меняя и проверяя жадную стратегию.</p>","path":["Глава 15. Жадность","15.1 &nbsp; Жадный алгоритм"],"tags":[]},{"location":"chapter_greedy/greedy_algorithm/#1514","level":2,"title":"15.1.4   Типичные задачи для жадного алгоритма","text":"<p>Жадные алгоритмы часто применяются в задачах оптимизации, которые обладают свойством жадного выбора и оптимальной подструктурой. Ниже приведены некоторые типичные задачи, решаемые жадным подходом.</p> <ul> <li>Задача о размене монет: при некоторых системах монет жадный алгоритм всегда дает оптимальный ответ.</li> <li>Задача о расписании интервалов: пусть есть несколько задач, каждая выполняется в некотором временном интервале, и требуется завершить как можно больше задач. Если каждый раз выбирать задачу с самым ранним временем окончания, то жадный алгоритм дает оптимальный ответ.</li> <li>Задача о дробном рюкзаке: дана группа предметов и грузоподъемность. Требуется выбрать предметы так, чтобы их общий вес не превышал ограничение, а общая ценность была максимальной. Если каждый раз выбирать предмет с наилучшим отношением стоимости к весу, то в некоторых случаях жадный алгоритм дает оптимальный ответ.</li> <li>Задача о покупке и продаже акций: дана история цен акции. Можно совершать несколько сделок, но если акция уже куплена, то до продажи покупать снова нельзя. Цель - получить максимальную прибыль.</li> <li>Код Хаффмана: это жадный алгоритм для сжатия данных без потерь. Построив дерево Хаффмана и каждый раз объединяя два узла с наименьшей частотой, мы получаем дерево с минимальной взвешенной длиной пути, то есть минимальной длиной кодирования.</li> <li>Алгоритм Дейкстры: это жадный алгоритм решения задачи о кратчайших путях от заданной исходной вершины до всех остальных вершин.</li> </ul>","path":["Глава 15. Жадность","15.1 &nbsp; Жадный алгоритм"],"tags":[]},{"location":"chapter_greedy/max_capacity_problem/","level":1,"title":"15.3   Задача о максимальной вместимости","text":"<p>Question</p> <p>Дан массив \\(ht\\), где каждый элемент обозначает высоту вертикальной перегородки. Любые две перегородки в массиве вместе с пространством между ними образуют контейнер.</p> <p>Вместимость контейнера равна произведению высоты и ширины (площади), где высота определяется более короткой перегородкой, а ширина - разностью индексов двух перегородок в массиве.</p> <p>Требуется выбрать две перегородки так, чтобы образованный ими контейнер имел максимальную вместимость. Пример показан на рисунке 15-7.</p> <p></p> <p> Рисунок 15-7   Пример данных для задачи о максимальной вместимости </p> <p>Контейнер образуется произвольными двумя перегородками, поэтому состоянием задачи служит пара индексов этих перегородок, обозначим ее как \\([i, j]\\).</p> <p>Согласно условию, вместимость равна произведению высоты на ширину, где высота определяется короткой перегородкой, а ширина - разностью индексов двух перегородок. Обозначим вместимость через \\(cap[i, j]\\), тогда формула принимает вид:</p> \\[ cap[i, j] = \\min(ht[i], ht[j]) \\times (j - i) \\] <p>Пусть длина массива равна \\(n\\). Тогда число пар перегородок, то есть общее число состояний, равно \\(C_n^2 = \\frac{n(n - 1)}{2}\\). Самый прямолинейный подход - перебрать все состояния, после чего найти максимальную вместимость. Его временная сложность равна \\(O(n^2)\\).</p>","path":["Глава 15. Жадность","15.3 &nbsp; Задача о максимальной вместимости"],"tags":[]},{"location":"chapter_greedy/max_capacity_problem/#1","level":3,"title":"1.   Определение жадной стратегии","text":"<p>У этой задачи есть и более эффективное решение. Как показано на рисунке 15-8, рассмотрим состояние \\([i, j]\\), где индексы удовлетворяют \\(i &lt; j\\), а высоты - условию \\(ht[i] &lt; ht[j]\\), то есть \\(i\\) - короткая перегородка, а \\(j\\) - длинная.</p> <p></p> <p> Рисунок 15-8   Начальное состояние </p> <p>Как показано на рисунке 15-9, если в этот момент сдвинуть длинную перегородку \\(j\\) ближе к короткой перегородке \\(i\\), то вместимость обязательно уменьшится.</p> <p>Причина в том, что после смещения длинной перегородки \\(j\\) ширина \\(j-i\\) обязательно станет меньше, а высота определяется короткой перегородкой, поэтому высота либо останется прежней (если \\(i\\) останется короткой перегородкой), либо уменьшится (если сдвинутая \\(j\\) станет короткой перегородкой).</p> <p></p> <p> Рисунок 15-9   Состояние после перемещения длинной перегородки внутрь </p> <p>Рассуждая в обратную сторону, только сдвигая короткую перегородку \\(i\\) внутрь, мы можем получить шанс увеличить вместимость. Хотя ширина при этом обязательно уменьшится, высота может возрасти (если после перемещения короткая перегородка \\(i\\) станет выше). Например, на рисунке 15-10 после перемещения короткой перегородки площадь увеличивается.</p> <p></p> <p> Рисунок 15-10   Состояние после перемещения короткой перегородки внутрь </p> <p>Отсюда и выводится жадная стратегия для этой задачи: инициализировать два указателя по краям контейнера и на каждом шаге сдвигать внутрь указатель, соответствующий короткой перегородке, пока указатели не встретятся.</p> <p>На рисунках ниже показан процесс выполнения этой жадной стратегии.</p> <ol> <li>В начальном состоянии указатели \\(i\\) и \\(j\\) стоят на двух концах массива.</li> <li>Вычислить вместимость текущего состояния \\(cap[i, j]\\) и обновить максимальную вместимость.</li> <li>Сравнить высоты перегородок \\(i\\) и \\(j\\), после чего сдвинуть короткую перегородку на одну позицию внутрь.</li> <li>Повторять шаги <code>2.</code> и <code>3.</code> до тех пор, пока \\(i\\) и \\(j\\) не встретятся.</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 15-11   Жадный процесс решения задачи о максимальной вместимости </p>","path":["Глава 15. Жадность","15.3 &nbsp; Задача о максимальной вместимости"],"tags":[]},{"location":"chapter_greedy/max_capacity_problem/#2","level":3,"title":"2.   Код реализации","text":"<p>Цикл в коде выполняется не более \\(n\\) раз, поэтому временная сложность равна \\(O(n)\\).</p> <p>Переменные \\(i\\), \\(j\\), \\(res\\) используют дополнительную память постоянного размера, поэтому пространственная сложность равна \\(O(1)\\).</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby max_capacity.py<pre><code>def max_capacity(ht: list[int]) -&gt; int:\n    \"\"\"Максимальная вместимость: жадный алгоритм\"\"\"\n    # Инициализировать i и j так, чтобы они располагались по двум концам массива\n    i, j = 0, len(ht) - 1\n    # Начальная максимальная вместимость равна 0\n    res = 0\n    # Выполнять жадный выбор в цикле, пока две доски не встретятся\n    while i &lt; j:\n        # Обновить максимальную вместимость\n        cap = min(ht[i], ht[j]) * (j - i)\n        res = max(res, cap)\n        # Сдвигать внутрь более короткую сторону\n        if ht[i] &lt; ht[j]:\n            i += 1\n        else:\n            j -= 1\n    return res\n</code></pre> max_capacity.cpp<pre><code>/* Максимальная вместимость: жадный алгоритм */\nint maxCapacity(vector&lt;int&gt; &amp;ht) {\n    // Инициализировать i и j так, чтобы они располагались по двум концам массива\n    int i = 0, j = ht.size() - 1;\n    // Начальная максимальная вместимость равна 0\n    int res = 0;\n    // Выполнять жадный выбор в цикле, пока две доски не встретятся\n    while (i &lt; j) {\n        // Обновить максимальную вместимость\n        int cap = min(ht[i], ht[j]) * (j - i);\n        res = max(res, cap);\n        // Сдвигать внутрь более короткую сторону\n        if (ht[i] &lt; ht[j]) {\n            i++;\n        } else {\n            j--;\n        }\n    }\n    return res;\n}\n</code></pre> max_capacity.java<pre><code>/* Максимальная вместимость: жадный алгоритм */\nint maxCapacity(int[] ht) {\n    // Инициализировать i и j так, чтобы они располагались по двум концам массива\n    int i = 0, j = ht.length - 1;\n    // Начальная максимальная вместимость равна 0\n    int res = 0;\n    // Выполнять жадный выбор в цикле, пока две доски не встретятся\n    while (i &lt; j) {\n        // Обновить максимальную вместимость\n        int cap = Math.min(ht[i], ht[j]) * (j - i);\n        res = Math.max(res, cap);\n        // Сдвигать внутрь более короткую сторону\n        if (ht[i] &lt; ht[j]) {\n            i++;\n        } else {\n            j--;\n        }\n    }\n    return res;\n}\n</code></pre> max_capacity.cs<pre><code>/* Максимальная вместимость: жадный алгоритм */\nint MaxCapacity(int[] ht) {\n    // Инициализировать i и j так, чтобы они располагались по двум концам массива\n    int i = 0, j = ht.Length - 1;\n    // Начальная максимальная вместимость равна 0\n    int res = 0;\n    // Выполнять жадный выбор в цикле, пока две доски не встретятся\n    while (i &lt; j) {\n        // Обновить максимальную вместимость\n        int cap = Math.Min(ht[i], ht[j]) * (j - i);\n        res = Math.Max(res, cap);\n        // Сдвигать внутрь более короткую сторону\n        if (ht[i] &lt; ht[j]) {\n            i++;\n        } else {\n            j--;\n        }\n    }\n    return res;\n}\n</code></pre> max_capacity.go<pre><code>/* Максимальная вместимость: жадный алгоритм */\nfunc maxCapacity(ht []int) int {\n    // Инициализировать i и j так, чтобы они располагались по двум концам массива\n    i, j := 0, len(ht)-1\n    // Начальная максимальная вместимость равна 0\n    res := 0\n    // Выполнять жадный выбор в цикле, пока две доски не встретятся\n    for i &lt; j {\n        // Обновить максимальную вместимость\n        capacity := int(math.Min(float64(ht[i]), float64(ht[j]))) * (j - i)\n        res = int(math.Max(float64(res), float64(capacity)))\n        // Сдвигать внутрь более короткую сторону\n        if ht[i] &lt; ht[j] {\n            i++\n        } else {\n            j--\n        }\n    }\n    return res\n}\n</code></pre> max_capacity.swift<pre><code>/* Максимальная вместимость: жадный алгоритм */\nfunc maxCapacity(ht: [Int]) -&gt; Int {\n    // Инициализировать i и j так, чтобы они располагались по двум концам массива\n    var i = ht.startIndex, j = ht.endIndex - 1\n    // Начальная максимальная вместимость равна 0\n    var res = 0\n    // Выполнять жадный выбор в цикле, пока две доски не встретятся\n    while i &lt; j {\n        // Обновить максимальную вместимость\n        let cap = min(ht[i], ht[j]) * (j - i)\n        res = max(res, cap)\n        // Сдвигать внутрь более короткую сторону\n        if ht[i] &lt; ht[j] {\n            i += 1\n        } else {\n            j -= 1\n        }\n    }\n    return res\n}\n</code></pre> max_capacity.js<pre><code>/* Максимальная вместимость: жадный алгоритм */\nfunction maxCapacity(ht) {\n    // Инициализировать i и j так, чтобы они располагались по двум концам массива\n    let i = 0,\n        j = ht.length - 1;\n    // Начальная максимальная вместимость равна 0\n    let res = 0;\n    // Выполнять жадный выбор в цикле, пока две доски не встретятся\n    while (i &lt; j) {\n        // Обновить максимальную вместимость\n        const cap = Math.min(ht[i], ht[j]) * (j - i);\n        res = Math.max(res, cap);\n        // Сдвигать внутрь более короткую сторону\n        if (ht[i] &lt; ht[j]) {\n            i += 1;\n        } else {\n            j -= 1;\n        }\n    }\n    return res;\n}\n</code></pre> max_capacity.ts<pre><code>/* Максимальная вместимость: жадный алгоритм */\nfunction maxCapacity(ht: number[]): number {\n    // Инициализировать i и j так, чтобы они располагались по двум концам массива\n    let i = 0,\n        j = ht.length - 1;\n    // Начальная максимальная вместимость равна 0\n    let res = 0;\n    // Выполнять жадный выбор в цикле, пока две доски не встретятся\n    while (i &lt; j) {\n        // Обновить максимальную вместимость\n        const cap: number = Math.min(ht[i], ht[j]) * (j - i);\n        res = Math.max(res, cap);\n        // Сдвигать внутрь более короткую сторону\n        if (ht[i] &lt; ht[j]) {\n            i += 1;\n        } else {\n            j -= 1;\n        }\n    }\n    return res;\n}\n</code></pre> max_capacity.dart<pre><code>/* Максимальная вместимость: жадный алгоритм */\nint maxCapacity(List&lt;int&gt; ht) {\n  // Инициализировать i и j так, чтобы они располагались по двум концам массива\n  int i = 0, j = ht.length - 1;\n  // Начальная максимальная вместимость равна 0\n  int res = 0;\n  // Выполнять жадный выбор в цикле, пока две доски не встретятся\n  while (i &lt; j) {\n    // Обновить максимальную вместимость\n    int cap = min(ht[i], ht[j]) * (j - i);\n    res = max(res, cap);\n    // Сдвигать внутрь более короткую сторону\n    if (ht[i] &lt; ht[j]) {\n      i++;\n    } else {\n      j--;\n    }\n  }\n  return res;\n}\n</code></pre> max_capacity.rs<pre><code>/* Максимальная вместимость: жадный алгоритм */\nfn max_capacity(ht: &amp;[i32]) -&gt; i32 {\n    // Инициализировать i и j так, чтобы они располагались по двум концам массива\n    let mut i = 0;\n    let mut j = ht.len() - 1;\n    // Начальная максимальная вместимость равна 0\n    let mut res = 0;\n    // Выполнять жадный выбор в цикле, пока две доски не встретятся\n    while i &lt; j {\n        // Обновить максимальную вместимость\n        let cap = std::cmp::min(ht[i], ht[j]) * (j - i) as i32;\n        res = std::cmp::max(res, cap);\n        // Сдвигать внутрь более короткую сторону\n        if ht[i] &lt; ht[j] {\n            i += 1;\n        } else {\n            j -= 1;\n        }\n    }\n    res\n}\n</code></pre> max_capacity.c<pre><code>/* Максимальная вместимость: жадный алгоритм */\nint maxCapacity(int ht[], int htLength) {\n    // Инициализировать i и j так, чтобы они располагались по двум концам массива\n    int i = 0;\n    int j = htLength - 1;\n    // Начальная максимальная вместимость равна 0\n    int res = 0;\n    // Выполнять жадный выбор в цикле, пока две доски не встретятся\n    while (i &lt; j) {\n        // Обновить максимальную вместимость\n        int capacity = myMin(ht[i], ht[j]) * (j - i);\n        res = myMax(res, capacity);\n        // Сдвигать внутрь более короткую сторону\n        if (ht[i] &lt; ht[j]) {\n            i++;\n        } else {\n            j--;\n        }\n    }\n    return res;\n}\n</code></pre> max_capacity.kt<pre><code>/* Максимальная вместимость: жадный алгоритм */\nfun maxCapacity(ht: IntArray): Int {\n    // Инициализировать i и j так, чтобы они располагались по двум концам массива\n    var i = 0\n    var j = ht.size - 1\n    // Начальная максимальная вместимость равна 0\n    var res = 0\n    // Выполнять жадный выбор в цикле, пока две доски не встретятся\n    while (i &lt; j) {\n        // Обновить максимальную вместимость\n        val cap = min(ht[i], ht[j]) * (j - i)\n        res = max(res, cap)\n        // Сдвигать внутрь более короткую сторону\n        if (ht[i] &lt; ht[j]) {\n            i++\n        } else {\n            j--\n        }\n    }\n    return res\n}\n</code></pre> max_capacity.rb<pre><code>### Максимальная вместимость: жадный алгоритм ###\ndef max_capacity(ht)\n  # Инициализировать i и j так, чтобы они располагались по двум концам массива\n  i, j = 0, ht.length - 1\n  # Начальная максимальная вместимость равна 0\n  res = 0\n\n  # Выполнять жадный выбор в цикле, пока две доски не встретятся\n  while i &lt; j\n    # Обновить максимальную вместимость\n    cap = [ht[i], ht[j]].min * (j - i)\n    res = [res, cap].max\n    # Сдвигать внутрь более короткую сторону\n    if ht[i] &lt; ht[j]\n      i += 1\n    else\n      j -= 1\n    end\n  end\n\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 15. Жадность","15.3 &nbsp; Задача о максимальной вместимости"],"tags":[]},{"location":"chapter_greedy/max_capacity_problem/#3","level":3,"title":"3.   Доказательство корректности","text":"<p>Жадный алгоритм быстрее полного перебора именно потому, что каждый жадный шаг «пропускает» часть состояний.</p> <p>Например, в состоянии \\(cap[i, j]\\) перегородка \\(i\\) является короткой, а \\(j\\) - длинной. Если жадно сдвинуть короткую перегородку \\(i\\) на одну позицию внутрь, то состояния, показанные на рисунке 15-12, будут «пропущены». Это означает, что позже мы уже не сможем проверить вместимость этих состояний.</p> \\[ cap[i, i+1], cap[i, i+2], \\dots, cap[i, j-2], cap[i, j-1] \\] <p></p> <p> Рисунок 15-12   Состояния, пропущенные из-за смещения короткой перегородки </p> <p>Нетрудно заметить, что эти пропущенные состояния на самом деле и есть все состояния, в которых длинная перегородка \\(j\\) сдвигается внутрь. Ранее мы уже доказали, что перемещение длинной перегородки внутрь обязательно уменьшает вместимость. Иными словами, пропущенные состояния не могут быть оптимальным решением, поэтому их пропуск не приводит к потере оптимума.</p> <p>Приведенный анализ показывает, что операция перемещения короткой перегородки является «безопасной», а жадная стратегия действительно эффективна.</p>","path":["Глава 15. Жадность","15.3 &nbsp; Задача о максимальной вместимости"],"tags":[]},{"location":"chapter_greedy/max_product_cutting_problem/","level":1,"title":"15.4   Задача о максимальном произведении разбиения","text":"<p>Question</p> <p>Дан положительный целый \\(n\\). Требуется разложить его в сумму как минимум двух положительных целых чисел и найти максимально возможное произведение всех полученных чисел, как показано на рисунке 15-13.</p> <p></p> <p> Рисунок 15-13   Определение задачи о максимальном произведении разбиения </p> <p>Предположим, что мы разбили \\(n\\) на \\(m\\) целочисленных множителей, где \\(i\\)-й множитель обозначим через \\(n_i\\), то есть</p> \\[ n = \\sum_{i=1}^{m}n_i \\] <p>Цель задачи - найти максимальное произведение всех целочисленных множителей, то есть</p> \\[ \\max(\\prod_{i=1}^{m}n_i) \\] <p>Нужно понять: каким должно быть число частей \\(m\\) и какими должны быть значения каждого \\(n_i\\)?</p>","path":["Глава 15. Жадность","15.4 &nbsp; Задача о максимальном произведении разбиения"],"tags":[]},{"location":"chapter_greedy/max_product_cutting_problem/#1","level":3,"title":"1.   Определение жадной стратегии","text":"<p>Из опыта известно, что произведение двух целых чисел часто больше их суммы. Предположим, что мы выделяем из \\(n\\) множитель \\(2\\), тогда произведение равно \\(2(n-2)\\). Сравним это выражение с \\(n\\):</p> \\[ \\begin{aligned} 2(n-2) &amp; \\geq n \\newline 2n - n - 4 &amp; \\geq 0 \\newline n &amp; \\geq 4 \\end{aligned} \\] <p>Как показано на рисунке 15-14, когда \\(n \\geq 4\\), выделение множителя \\(2\\) увеличивает произведение. Это означает, что все целые числа, большие либо равные \\(4\\), следует продолжать разбивать.</p> <p>Жадная стратегия 1: если в схеме разбиения присутствует множитель \\(\\geq 4\\), то его нужно дальше разбивать. В конечной схеме разбиения должны остаться только множители \\(1\\), \\(2\\), \\(3\\).</p> <p></p> <p> Рисунок 15-14   Разбиение увеличивает произведение </p> <p>Теперь подумаем, какой множитель является наилучшим. Среди \\(1\\), \\(2\\), \\(3\\) очевидно худшим является \\(1\\), потому что всегда выполняется \\(1 \\times (n-1) &lt; n\\), то есть выделение \\(1\\) уменьшает произведение.</p> <p>Как показано на рисунке 15-15, при \\(n = 6\\) имеем \\(3 \\times 3 &gt; 2 \\times 2 \\times 2\\). Это означает, что выделять \\(3\\) выгоднее, чем выделять \\(2\\).</p> <p>Жадная стратегия 2: в схеме разбиения должно быть не более двух множителей \\(2\\). Потому что три двойки всегда можно заменить двумя тройками и получить большее произведение.</p> <p></p> <p> Рисунок 15-15   Оптимальные множители разбиения </p> <p>Итак, получаем следующую жадную стратегию.</p> <ol> <li>Для заданного целого \\(n\\) непрерывно выделять из него множитель \\(3\\), пока остаток не станет равным \\(0\\), \\(1\\) или \\(2\\).</li> <li>Если остаток равен \\(0\\), это означает, что \\(n\\) кратно \\(3\\), и больше ничего делать не нужно.</li> <li>Если остаток равен \\(2\\), дальнейшее разбиение не требуется, его нужно сохранить.</li> <li>Если остаток равен \\(1\\), то поскольку \\(2 \\times 2 &gt; 1 \\times 3\\), последний множитель \\(3\\) следует заменить на \\(2\\).</li> </ol>","path":["Глава 15. Жадность","15.4 &nbsp; Задача о максимальном произведении разбиения"],"tags":[]},{"location":"chapter_greedy/max_product_cutting_problem/#2","level":3,"title":"2.   Код реализации","text":"<p>Как показано на рисунке 15-16, нам не нужен цикл, чтобы выполнять разбиение числа. Можно использовать целочисленное деление вниз, чтобы получить число троек \\(a\\), и операцию взятия остатка, чтобы получить остаток \\(b\\). Тогда имеем:</p> \\[ n = 3 a + b \\] <p>Обратите внимание, что для граничного случая \\(n \\leq 3\\) необходимо выделить множитель \\(1\\), и тогда произведение равно \\(1 \\times (n - 1)\\).</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby max_product_cutting.py<pre><code>def max_product_cutting(n: int) -&gt; int:\n    \"\"\"Максимальное произведение разрезания: жадный алгоритм\"\"\"\n    # Когда n &lt;= 3, обязательно нужно выделить одну 1\n    if n &lt;= 3:\n        return 1 * (n - 1)\n    # Жадно выделить множители 3, где a — число троек, а b — остаток\n    a, b = n // 3, n % 3\n    if b == 1:\n        # Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n        return int(math.pow(3, a - 1)) * 2 * 2\n    if b == 2:\n        # Если остаток равен 2, ничего не делать\n        return int(math.pow(3, a)) * 2\n    # Если остаток равен 0, ничего не делать\n    return int(math.pow(3, a))\n</code></pre> max_product_cutting.cpp<pre><code>/* Максимальное произведение разрезания: жадный алгоритм */\nint maxProductCutting(int n) {\n    // Когда n &lt;= 3, обязательно нужно выделить одну 1\n    if (n &lt;= 3) {\n        return 1 * (n - 1);\n    }\n    // Жадно выделить множители 3, где a — число троек, а b — остаток\n    int a = n / 3;\n    int b = n % 3;\n    if (b == 1) {\n        // Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n        return (int)pow(3, a - 1) * 2 * 2;\n    }\n    if (b == 2) {\n        // Если остаток равен 2, ничего не делать\n        return (int)pow(3, a) * 2;\n    }\n    // Если остаток равен 0, ничего не делать\n    return (int)pow(3, a);\n}\n</code></pre> max_product_cutting.java<pre><code>/* Максимальное произведение разрезания: жадный алгоритм */\nint maxProductCutting(int n) {\n    // Когда n &lt;= 3, обязательно нужно выделить одну 1\n    if (n &lt;= 3) {\n        return 1 * (n - 1);\n    }\n    // Жадно выделить множители 3, где a — число троек, а b — остаток\n    int a = n / 3;\n    int b = n % 3;\n    if (b == 1) {\n        // Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n        return (int) Math.pow(3, a - 1) * 2 * 2;\n    }\n    if (b == 2) {\n        // Если остаток равен 2, ничего не делать\n        return (int) Math.pow(3, a) * 2;\n    }\n    // Если остаток равен 0, ничего не делать\n    return (int) Math.pow(3, a);\n}\n</code></pre> max_product_cutting.cs<pre><code>/* Максимальное произведение разрезания: жадный алгоритм */\nint MaxProductCutting(int n) {\n    // Когда n &lt;= 3, обязательно нужно выделить одну 1\n    if (n &lt;= 3) {\n        return 1 * (n - 1);\n    }\n    // Жадно выделить множители 3, где a — число троек, а b — остаток\n    int a = n / 3;\n    int b = n % 3;\n    if (b == 1) {\n        // Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n        return (int)Math.Pow(3, a - 1) * 2 * 2;\n    }\n    if (b == 2) {\n        // Если остаток равен 2, ничего не делать\n        return (int)Math.Pow(3, a) * 2;\n    }\n    // Если остаток равен 0, ничего не делать\n    return (int)Math.Pow(3, a);\n}\n</code></pre> max_product_cutting.go<pre><code>/* Максимальное произведение разрезания: жадный алгоритм */\nfunc maxProductCutting(n int) int {\n    // Когда n &lt;= 3, обязательно нужно выделить одну 1\n    if n &lt;= 3 {\n        return 1 * (n - 1)\n    }\n    // Жадно выделить множители 3, где a — число троек, а b — остаток\n    a := n / 3\n    b := n % 3\n    if b == 1 {\n        // Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n        return int(math.Pow(3, float64(a-1))) * 2 * 2\n    }\n    if b == 2 {\n        // Если остаток равен 2, ничего не делать\n        return int(math.Pow(3, float64(a))) * 2\n    }\n    // Если остаток равен 0, ничего не делать\n    return int(math.Pow(3, float64(a)))\n}\n</code></pre> max_product_cutting.swift<pre><code>/* Максимальное произведение разрезания: жадный алгоритм */\nfunc maxProductCutting(n: Int) -&gt; Int {\n    // Когда n &lt;= 3, обязательно нужно выделить одну 1\n    if n &lt;= 3 {\n        return 1 * (n - 1)\n    }\n    // Жадно выделить множители 3, где a — число троек, а b — остаток\n    let a = n / 3\n    let b = n % 3\n    if b == 1 {\n        // Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n        return pow(3, a - 1) * 2 * 2\n    }\n    if b == 2 {\n        // Если остаток равен 2, ничего не делать\n        return pow(3, a) * 2\n    }\n    // Если остаток равен 0, ничего не делать\n    return pow(3, a)\n}\n</code></pre> max_product_cutting.js<pre><code>/* Максимальное произведение разрезания: жадный алгоритм */\nfunction maxProductCutting(n) {\n    // Когда n &lt;= 3, обязательно нужно выделить одну 1\n    if (n &lt;= 3) {\n        return 1 * (n - 1);\n    }\n    // Жадно выделить множители 3, где a — число троек, а b — остаток\n    let a = Math.floor(n / 3);\n    let b = n % 3;\n    if (b === 1) {\n        // Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n        return Math.pow(3, a - 1) * 2 * 2;\n    }\n    if (b === 2) {\n        // Если остаток равен 2, ничего не делать\n        return Math.pow(3, a) * 2;\n    }\n    // Если остаток равен 0, ничего не делать\n    return Math.pow(3, a);\n}\n</code></pre> max_product_cutting.ts<pre><code>/* Максимальное произведение разрезания: жадный алгоритм */\nfunction maxProductCutting(n: number): number {\n    // Когда n &lt;= 3, обязательно нужно выделить одну 1\n    if (n &lt;= 3) {\n        return 1 * (n - 1);\n    }\n    // Жадно выделить множители 3, где a — число троек, а b — остаток\n    let a: number = Math.floor(n / 3);\n    let b: number = n % 3;\n    if (b === 1) {\n        // Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n        return Math.pow(3, a - 1) * 2 * 2;\n    }\n    if (b === 2) {\n        // Если остаток равен 2, ничего не делать\n        return Math.pow(3, a) * 2;\n    }\n    // Если остаток равен 0, ничего не делать\n    return Math.pow(3, a);\n}\n</code></pre> max_product_cutting.dart<pre><code>/* Максимальное произведение разрезания: жадный алгоритм */\nint maxProductCutting(int n) {\n  // Когда n &lt;= 3, обязательно нужно выделить одну 1\n  if (n &lt;= 3) {\n    return 1 * (n - 1);\n  }\n  // Жадно выделить множители 3, где a — число троек, а b — остаток\n  int a = n ~/ 3;\n  int b = n % 3;\n  if (b == 1) {\n    // Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n    return (pow(3, a - 1) * 2 * 2).toInt();\n  }\n  if (b == 2) {\n    // Если остаток равен 2, ничего не делать\n    return (pow(3, a) * 2).toInt();\n  }\n  // Если остаток равен 0, ничего не делать\n  return pow(3, a).toInt();\n}\n</code></pre> max_product_cutting.rs<pre><code>/* Максимальное произведение разрезания: жадный алгоритм */\nfn max_product_cutting(n: i32) -&gt; i32 {\n    // Когда n &lt;= 3, обязательно нужно выделить одну 1\n    if n &lt;= 3 {\n        return 1 * (n - 1);\n    }\n    // Жадно выделить множители 3, где a — число троек, а b — остаток\n    let a = n / 3;\n    let b = n % 3;\n    if b == 1 {\n        // Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n        3_i32.pow(a as u32 - 1) * 2 * 2\n    } else if b == 2 {\n        // Если остаток равен 2, ничего не делать\n        3_i32.pow(a as u32) * 2\n    } else {\n        // Если остаток равен 0, ничего не делать\n        3_i32.pow(a as u32)\n    }\n}\n</code></pre> max_product_cutting.c<pre><code>/* Максимальное произведение разрезания: жадный алгоритм */\nint maxProductCutting(int n) {\n    // Когда n &lt;= 3, обязательно нужно выделить одну 1\n    if (n &lt;= 3) {\n        return 1 * (n - 1);\n    }\n    // Жадно выделить множители 3, где a — число троек, а b — остаток\n    int a = n / 3;\n    int b = n % 3;\n    if (b == 1) {\n        // Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n        return pow(3, a - 1) * 2 * 2;\n    }\n    if (b == 2) {\n        // Если остаток равен 2, ничего не делать\n        return pow(3, a) * 2;\n    }\n    // Если остаток равен 0, ничего не делать\n    return pow(3, a);\n}\n</code></pre> max_product_cutting.kt<pre><code>/* Максимальное произведение разрезания: жадный алгоритм */\nfun maxProductCutting(n: Int): Int {\n    // Когда n &lt;= 3, обязательно нужно выделить одну 1\n    if (n &lt;= 3) {\n        return 1 * (n - 1)\n    }\n    // Жадно выделить множители 3, где a — число троек, а b — остаток\n    val a = n / 3\n    val b = n % 3\n    if (b == 1) {\n        // Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n        return 3.0.pow((a - 1)).toInt() * 2 * 2\n    }\n    if (b == 2) {\n        // Если остаток равен 2, ничего не делать\n        return 3.0.pow(a).toInt() * 2 * 2\n    }\n    // Если остаток равен 0, ничего не делать\n    return 3.0.pow(a).toInt()\n}\n</code></pre> max_product_cutting.rb<pre><code>### Максимальное произведение разрезания: жадный алгоритм ###\ndef max_product_cutting(n)\n  # Когда n &lt;= 3, обязательно нужно выделить одну 1\n  return 1 * (n - 1) if n &lt;= 3\n  # Жадно выделить множители 3, где a — число троек, а b — остаток\n  a, b = n / 3, n % 3\n  # Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n  return (3.pow(a - 1) * 2 * 2).to_i if b == 1\n  # Если остаток равен 2, ничего не делать\n  return (3.pow(a) * 2).to_i if b == 2\n  # Если остаток равен 0, ничего не делать\n  3.pow(a).to_i\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p></p> <p> Рисунок 15-16   Метод вычисления максимального произведения разбиения </p> <p>Временная сложность зависит от того, как в языке программирования реализовано возведение в степень. Если взять Python, то обычно используются три распространенные функции для вычисления степени.</p> <ul> <li>Оператор <code>**</code> и функция <code>pow()</code> имеют временную сложность \\(O(\\log⁡ a)\\).</li> <li>Функция <code>math.pow()</code> внутри вызывает функцию <code>pow()</code> из библиотеки C, выполняющую возведение в степень с плавающей точкой, и ее временная сложность равна \\(O(1)\\).</li> </ul> <p>Переменные \\(a\\) и \\(b\\) занимают дополнительную память постоянного размера, поэтому пространственная сложность равна \\(O(1)\\).</p>","path":["Глава 15. Жадность","15.4 &nbsp; Задача о максимальном произведении разбиения"],"tags":[]},{"location":"chapter_greedy/max_product_cutting_problem/#3","level":3,"title":"3.   Доказательство корректности","text":"<p>Используем доказательство от противного и рассмотрим только случай \\(n \\geq 4\\).</p> <ol> <li>Все множители \\(\\leq 3\\): предположим, что в оптимальной схеме разбиения существует множитель \\(x \\geq 4\\). Тогда его можно дальше разложить в \\(2(x-2)\\) и получить большее или равное произведение. Это противоречит предположению.</li> <li>Схема разбиения не содержит \\(1\\): предположим, что в оптимальной схеме присутствует множитель \\(1\\). Тогда его можно объединить с другим множителем и получить большее произведение. Это противоречит предположению.</li> <li>Схема разбиения содержит не более двух \\(2\\): предположим, что в оптимальной схеме присутствуют три двойки. Тогда их можно заменить двумя тройками и получить большее произведение. Это противоречит предположению.</li> </ol>","path":["Глава 15. Жадность","15.4 &nbsp; Задача о максимальном произведении разбиения"],"tags":[]},{"location":"chapter_greedy/summary/","level":1,"title":"15.5   Резюме","text":"","path":["Глава 15. Жадность","15.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_greedy/summary/#1","level":3,"title":"1.   Ключевые моменты","text":"<ul> <li>Жадный алгоритм обычно используется для решения задач оптимизации. Его принцип состоит в том, чтобы на каждом этапе принятия решения делать локально оптимальный выбор в надежде получить глобально оптимальный ответ.</li> <li>Жадный алгоритм итеративно делает один жадный выбор за другим, на каждом шаге превращая задачу в подзадачу меньшего размера, пока задача не будет полностью решена.</li> <li>Жадный алгоритм не только прост в реализации, но и часто обладает высокой эффективностью. По сравнению с динамическим программированием его временная сложность обычно ниже.</li> <li>В задаче о размене монет для некоторых наборов монет жадный алгоритм способен гарантировать оптимальный ответ, а для других наборов - нет: он может дать очень плохое решение.</li> <li>Задачи, подходящие для жадного алгоритма, обладают двумя ключевыми свойствами: свойством жадного выбора и оптимальной подструктурой. Свойство жадного выбора отражает корректность жадной стратегии.</li> <li>Для некоторых сложных задач доказать свойство жадного выбора непросто. Относительно легче найти контрпример и опровергнуть его, как это видно на примере задачи о размене монет.</li> <li>Решение жадной задачи обычно состоит из трех шагов: анализ задачи, определение жадной стратегии и доказательство корректности. Из них ключевым является выбор жадной стратегии, а доказательство корректности часто оказывается самым трудным.</li> <li>В задаче о дробном рюкзаке, в отличие от задачи о рюкзаке 0-1, разрешено брать часть предмета, поэтому ее можно решать жадным алгоритмом. Корректность жадной стратегии доказывается методом от противного.</li> <li>Задачу о максимальной вместимости можно решать полным перебором со временной сложностью \\(O(n^2)\\). Разработав жадную стратегию со сдвигом короткой перегородки внутрь на каждом шаге, временную сложность можно оптимизировать до \\(O(n)\\).</li> <li>В задаче о максимальном произведении разбиения мы последовательно выводим две жадные стратегии: все целые числа \\(\\geq 4\\) следует дальше разбивать, а оптимальным множителем разбиения является \\(3\\). В коде присутствуют операции возведения в степень, поэтому временная сложность зависит от способа их реализации и обычно равна \\(O(1)\\) или \\(O(\\log n)\\).</li> </ul>","path":["Глава 15. Жадность","15.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_hashing/","level":1,"title":"Глава 6.   Хеш-таблицы","text":"<p>Abstract</p> <p>В мире компьютеров хеш-таблица похожа на сообразительного библиотекаря.</p> <p>Он умеет вычислять шифр хранения и потому быстро находит нужную книгу.</p>","path":["Глава 6. Хеширование","Глава 6. &nbsp; Хеш-таблицы"],"tags":[]},{"location":"chapter_hashing/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>6.1   Хеш-таблица</li> <li>6.2   Хеш-коллизии</li> <li>6.3   Хеш-алгоритмы</li> <li>6.4   Резюме</li> </ul>","path":["Глава 6. Хеширование","Глава 6. &nbsp; Хеш-таблицы"],"tags":[]},{"location":"chapter_hashing/hash_algorithm/","level":1,"title":"6.3   Алгоритмы хеширования","text":"<p>В двух предыдущих разделах мы рассмотрели принципы работы хеш-таблицы и способы обработки хеш-коллизий. Однако и открытая адресация, и метод цепочек лишь позволяют хеш-таблице корректно работать при возникновении коллизий, но не уменьшают вероятность появления самих коллизий.</p> <p>Если хеш-коллизии происходят слишком часто, производительность хеш-таблицы резко деградирует. Как показано на рисунке 6-8, для хеш-таблицы с методом цепочек в идеальном случае пары ключ-значение равномерно распределены по всем бакетам, и это дает наилучшую эффективность поиска; в худшем же случае все пары ключ-значение оказываются в одном бакете, и временная сложность вырождается до \\(O(n)\\) .</p> <p></p> <p> Рисунок 6-8   Лучший и худший случаи хеш-коллизий </p> <p>Распределение пар ключ-значение определяется хеш-функцией. Вспомним этапы вычисления хеш-функции: сначала вычисляется хеш-значение, затем оно берется по модулю длины массива:</p> <pre><code>index = hash(key) % capacity\n</code></pre> <p>Из этой формулы видно: при фиксированной емкости хеш-таблицы <code>capacity</code> **выходное значение определяет именно хеш-алгоритм <code>hash()</code> **, а значит, именно он определяет распределение пар ключ-значение в хеш-таблице.</p> <p>Это означает, что для уменьшения вероятности хеш-коллизий нам следует сосредоточиться на проектировании хеш-алгоритма <code>hash()</code> .</p>","path":["Глава 6. Хеширование","6.3 &nbsp; Алгоритмы хеширования"],"tags":[]},{"location":"chapter_hashing/hash_algorithm/#631-","level":2,"title":"6.3.1   Цели хеш-алгоритма","text":"<p>Чтобы получить структуру данных хеш-таблицы, которая будет одновременно \"быстрой и надежной\", хеш-алгоритм должен обладать следующими свойствами.</p> <ul> <li>Детерминированность: для одинакового входа хеш-алгоритм всегда должен выдавать одинаковый результат. Только так хеш-таблица остается надежной.</li> <li>Высокая эффективность: вычисление хеш-значения должно быть достаточно быстрым. Чем меньше вычислительные затраты, тем выше практическая ценность хеш-таблицы.</li> <li>Равномерное распределение: хеш-алгоритм должен стараться распределять пары ключ-значение в хеш-таблице равномерно. Чем равномернее распределение, тем ниже вероятность хеш-коллизий.</li> </ul> <p>На практике хеш-алгоритмы используются не только для реализации хеш-таблиц, но и во многих других областях.</p> <ul> <li>Хранение паролей: чтобы защищать пароли пользователей, система обычно хранит не сами пароли в открытом виде, а их хеш-значения. Когда пользователь вводит пароль, система вычисляет хеш-значение введенного пароля и сравнивает его с сохраненным значением. Если они совпадают, пароль считается правильным.</li> <li>Проверка целостности данных: отправитель может вычислить хеш-значение данных и отправить его вместе с самими данными; получатель затем вычисляет хеш-значение повторно и сравнивает его с полученным. Если они совпадают, данные считаются целостными.</li> </ul> <p>Для приложений, связанных с криптографией, чтобы не допустить восстановления исходного пароля по хеш-значению и иных форм обратного анализа, хеш-алгоритм должен обладать более строгими свойствами безопасности.</p> <ul> <li>Односторонность: по хеш-значению нельзя восстановить какую-либо информацию о входных данных.</li> <li>Устойчивость к коллизиям: должно быть крайне трудно найти два разных входа, имеющих одинаковое хеш-значение.</li> <li>Эффект лавины: даже небольшое изменение во входных данных должно приводить к заметному и непредсказуемому изменению результата.</li> </ul> <p>Обрати внимание: \"равномерное распределение\" и \"устойчивость к коллизиям\" - это два независимых понятия , и выполнение первого не означает автоматического выполнения второго. Например, при случайном распределении входных <code>key</code> хеш-функция <code>key % 100</code> может выдавать достаточно равномерное распределение. Однако этот хеш-алгоритм слишком прост: все <code>key</code> с одинаковыми двумя последними цифрами будут иметь одинаковый результат, а значит, по хеш-значению можно легко подобрать подходящие <code>key</code> и, например, взломать пароль.</p>","path":["Глава 6. Хеширование","6.3 &nbsp; Алгоритмы хеширования"],"tags":[]},{"location":"chapter_hashing/hash_algorithm/#632-","level":2,"title":"6.3.2   Проектирование хеш-алгоритма","text":"<p>Разработка хеш-алгоритма - это сложная задача, в которой нужно учитывать множество факторов. Однако для некоторых нетребовательных сценариев мы можем спроектировать и несколько простых хеш-алгоритмов.</p> <ul> <li>Аддитивный хеш: складываем ASCII-коды всех символов входной строки и используем полученную сумму как хеш-значение.</li> <li>Мультипликативный хеш: используем \"некоррелированность\" умножения; на каждом шаге умножаем текущее значение на константу и добавляем ASCII-код очередного символа.</li> <li>XOR-хеш: последовательно накапливаем элементы входных данных в одном хеш-значении через операцию XOR.</li> <li>Ротационный хеш: последовательно накапливаем ASCII-коды символов, причем перед каждым накоплением выполняем циклический сдвиг хеш-значения.</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby simple_hash.py<pre><code>def add_hash(key: str) -&gt; int:\n    \"\"\"Аддитивное хеширование\"\"\"\n    hash = 0\n    modulus = 1000000007\n    for c in key:\n        hash += ord(c)\n    return hash % modulus\n\ndef mul_hash(key: str) -&gt; int:\n    \"\"\"Мультипликативное хеширование\"\"\"\n    hash = 0\n    modulus = 1000000007\n    for c in key:\n        hash = 31 * hash + ord(c)\n    return hash % modulus\n\ndef xor_hash(key: str) -&gt; int:\n    \"\"\"XOR-хеширование\"\"\"\n    hash = 0\n    modulus = 1000000007\n    for c in key:\n        hash ^= ord(c)\n    return hash % modulus\n\ndef rot_hash(key: str) -&gt; int:\n    \"\"\"Хеширование с циклическим сдвигом\"\"\"\n    hash = 0\n    modulus = 1000000007\n    for c in key:\n        hash = (hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ ord(c)\n    return hash % modulus\n</code></pre> simple_hash.cpp<pre><code>/* Аддитивное хеширование */\nint addHash(string key) {\n    long long hash = 0;\n    const int MODULUS = 1000000007;\n    for (unsigned char c : key) {\n        hash = (hash + (int)c) % MODULUS;\n    }\n    return (int)hash;\n}\n\n/* Мультипликативное хеширование */\nint mulHash(string key) {\n    long long hash = 0;\n    const int MODULUS = 1000000007;\n    for (unsigned char c : key) {\n        hash = (31 * hash + (int)c) % MODULUS;\n    }\n    return (int)hash;\n}\n\n/* XOR-хеширование */\nint xorHash(string key) {\n    int hash = 0;\n    const int MODULUS = 1000000007;\n    for (unsigned char c : key) {\n        hash ^= (int)c;\n    }\n    return hash &amp; MODULUS;\n}\n\n/* Хеширование с циклическим сдвигом */\nint rotHash(string key) {\n    long long hash = 0;\n    const int MODULUS = 1000000007;\n    for (unsigned char c : key) {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ (int)c) % MODULUS;\n    }\n    return (int)hash;\n}\n</code></pre> simple_hash.java<pre><code>/* Аддитивное хеширование */\nint addHash(String key) {\n    long hash = 0;\n    final int MODULUS = 1000000007;\n    for (char c : key.toCharArray()) {\n        hash = (hash + (int) c) % MODULUS;\n    }\n    return (int) hash;\n}\n\n/* Мультипликативное хеширование */\nint mulHash(String key) {\n    long hash = 0;\n    final int MODULUS = 1000000007;\n    for (char c : key.toCharArray()) {\n        hash = (31 * hash + (int) c) % MODULUS;\n    }\n    return (int) hash;\n}\n\n/* XOR-хеширование */\nint xorHash(String key) {\n    int hash = 0;\n    final int MODULUS = 1000000007;\n    for (char c : key.toCharArray()) {\n        hash ^= (int) c;\n    }\n    return hash &amp; MODULUS;\n}\n\n/* Хеширование с циклическим сдвигом */\nint rotHash(String key) {\n    long hash = 0;\n    final int MODULUS = 1000000007;\n    for (char c : key.toCharArray()) {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ (int) c) % MODULUS;\n    }\n    return (int) hash;\n}\n</code></pre> simple_hash.cs<pre><code>/* Аддитивное хеширование */\nint AddHash(string key) {\n    long hash = 0;\n    const int MODULUS = 1000000007;\n    foreach (char c in key) {\n        hash = (hash + c) % MODULUS;\n    }\n    return (int)hash;\n}\n\n/* Мультипликативное хеширование */\nint MulHash(string key) {\n    long hash = 0;\n    const int MODULUS = 1000000007;\n    foreach (char c in key) {\n        hash = (31 * hash + c) % MODULUS;\n    }\n    return (int)hash;\n}\n\n/* XOR-хеширование */\nint XorHash(string key) {\n    int hash = 0;\n    const int MODULUS = 1000000007;\n    foreach (char c in key) {\n        hash ^= c;\n    }\n    return hash &amp; MODULUS;\n}\n\n/* Хеширование с циклическим сдвигом */\nint RotHash(string key) {\n    long hash = 0;\n    const int MODULUS = 1000000007;\n    foreach (char c in key) {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ c) % MODULUS;\n    }\n    return (int)hash;\n}\n</code></pre> simple_hash.go<pre><code>/* Аддитивное хеширование */\nfunc addHash(key string) int {\n    var hash int64\n    var modulus int64\n\n    modulus = 1000000007\n    for _, b := range []byte(key) {\n        hash = (hash + int64(b)) % modulus\n    }\n    return int(hash)\n}\n\n/* Мультипликативное хеширование */\nfunc mulHash(key string) int {\n    var hash int64\n    var modulus int64\n\n    modulus = 1000000007\n    for _, b := range []byte(key) {\n        hash = (31*hash + int64(b)) % modulus\n    }\n    return int(hash)\n}\n\n/* XOR-хеширование */\nfunc xorHash(key string) int {\n    hash := 0\n    modulus := 1000000007\n    for _, b := range []byte(key) {\n        fmt.Println(int(b))\n        hash ^= int(b)\n        hash = (31*hash + int(b)) % modulus\n    }\n    return hash &amp; modulus\n}\n\n/* Хеширование с циклическим сдвигом */\nfunc rotHash(key string) int {\n    var hash int64\n    var modulus int64\n\n    modulus = 1000000007\n    for _, b := range []byte(key) {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ int64(b)) % modulus\n    }\n    return int(hash)\n}\n</code></pre> simple_hash.swift<pre><code>/* Аддитивное хеширование */\nfunc addHash(key: String) -&gt; Int {\n    var hash = 0\n    let MODULUS = 1_000_000_007\n    for c in key {\n        for scalar in c.unicodeScalars {\n            hash = (hash + Int(scalar.value)) % MODULUS\n        }\n    }\n    return hash\n}\n\n/* Мультипликативное хеширование */\nfunc mulHash(key: String) -&gt; Int {\n    var hash = 0\n    let MODULUS = 1_000_000_007\n    for c in key {\n        for scalar in c.unicodeScalars {\n            hash = (31 * hash + Int(scalar.value)) % MODULUS\n        }\n    }\n    return hash\n}\n\n/* XOR-хеширование */\nfunc xorHash(key: String) -&gt; Int {\n    var hash = 0\n    let MODULUS = 1_000_000_007\n    for c in key {\n        for scalar in c.unicodeScalars {\n            hash ^= Int(scalar.value)\n        }\n    }\n    return hash &amp; MODULUS\n}\n\n/* Хеширование с циклическим сдвигом */\nfunc rotHash(key: String) -&gt; Int {\n    var hash = 0\n    let MODULUS = 1_000_000_007\n    for c in key {\n        for scalar in c.unicodeScalars {\n            hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ Int(scalar.value)) % MODULUS\n        }\n    }\n    return hash\n}\n</code></pre> simple_hash.js<pre><code>/* Аддитивное хеширование */\nfunction addHash(key) {\n    let hash = 0;\n    const MODULUS = 1000000007;\n    for (const c of key) {\n        hash = (hash + c.charCodeAt(0)) % MODULUS;\n    }\n    return hash;\n}\n\n/* Мультипликативное хеширование */\nfunction mulHash(key) {\n    let hash = 0;\n    const MODULUS = 1000000007;\n    for (const c of key) {\n        hash = (31 * hash + c.charCodeAt(0)) % MODULUS;\n    }\n    return hash;\n}\n\n/* XOR-хеширование */\nfunction xorHash(key) {\n    let hash = 0;\n    const MODULUS = 1000000007;\n    for (const c of key) {\n        hash ^= c.charCodeAt(0);\n    }\n    return hash % MODULUS;\n}\n\n/* Хеширование с циклическим сдвигом */\nfunction rotHash(key) {\n    let hash = 0;\n    const MODULUS = 1000000007;\n    for (const c of key) {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ c.charCodeAt(0)) % MODULUS;\n    }\n    return hash;\n}\n</code></pre> simple_hash.ts<pre><code>/* Аддитивное хеширование */\nfunction addHash(key: string): number {\n    let hash = 0;\n    const MODULUS = 1000000007;\n    for (const c of key) {\n        hash = (hash + c.charCodeAt(0)) % MODULUS;\n    }\n    return hash;\n}\n\n/* Мультипликативное хеширование */\nfunction mulHash(key: string): number {\n    let hash = 0;\n    const MODULUS = 1000000007;\n    for (const c of key) {\n        hash = (31 * hash + c.charCodeAt(0)) % MODULUS;\n    }\n    return hash;\n}\n\n/* XOR-хеширование */\nfunction xorHash(key: string): number {\n    let hash = 0;\n    const MODULUS = 1000000007;\n    for (const c of key) {\n        hash ^= c.charCodeAt(0);\n    }\n    return hash % MODULUS;\n}\n\n/* Хеширование с циклическим сдвигом */\nfunction rotHash(key: string): number {\n    let hash = 0;\n    const MODULUS = 1000000007;\n    for (const c of key) {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ c.charCodeAt(0)) % MODULUS;\n    }\n    return hash;\n}\n</code></pre> simple_hash.dart<pre><code>/* Аддитивное хеширование */\nint addHash(String key) {\n  int hash = 0;\n  final int MODULUS = 1000000007;\n  for (int i = 0; i &lt; key.length; i++) {\n    hash = (hash + key.codeUnitAt(i)) % MODULUS;\n  }\n  return hash;\n}\n\n/* Мультипликативное хеширование */\nint mulHash(String key) {\n  int hash = 0;\n  final int MODULUS = 1000000007;\n  for (int i = 0; i &lt; key.length; i++) {\n    hash = (31 * hash + key.codeUnitAt(i)) % MODULUS;\n  }\n  return hash;\n}\n\n/* XOR-хеширование */\nint xorHash(String key) {\n  int hash = 0;\n  final int MODULUS = 1000000007;\n  for (int i = 0; i &lt; key.length; i++) {\n    hash ^= key.codeUnitAt(i);\n  }\n  return hash &amp; MODULUS;\n}\n\n/* Хеширование с циклическим сдвигом */\nint rotHash(String key) {\n  int hash = 0;\n  final int MODULUS = 1000000007;\n  for (int i = 0; i &lt; key.length; i++) {\n    hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ key.codeUnitAt(i)) % MODULUS;\n  }\n  return hash;\n}\n</code></pre> simple_hash.rs<pre><code>/* Аддитивное хеширование */\nfn add_hash(key: &amp;str) -&gt; i32 {\n    let mut hash = 0_i64;\n    const MODULUS: i64 = 1000000007;\n\n    for c in key.chars() {\n        hash = (hash + c as i64) % MODULUS;\n    }\n\n    hash as i32\n}\n\n/* Мультипликативное хеширование */\nfn mul_hash(key: &amp;str) -&gt; i32 {\n    let mut hash = 0_i64;\n    const MODULUS: i64 = 1000000007;\n\n    for c in key.chars() {\n        hash = (31 * hash + c as i64) % MODULUS;\n    }\n\n    hash as i32\n}\n\n/* XOR-хеширование */\nfn xor_hash(key: &amp;str) -&gt; i32 {\n    let mut hash = 0_i64;\n    const MODULUS: i64 = 1000000007;\n\n    for c in key.chars() {\n        hash ^= c as i64;\n    }\n\n    (hash &amp; MODULUS) as i32\n}\n\n/* Хеширование с циклическим сдвигом */\nfn rot_hash(key: &amp;str) -&gt; i32 {\n    let mut hash = 0_i64;\n    const MODULUS: i64 = 1000000007;\n\n    for c in key.chars() {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ c as i64) % MODULUS;\n    }\n\n    hash as i32\n}\n</code></pre> simple_hash.c<pre><code>/* Аддитивное хеширование */\nint addHash(char *key) {\n    long long hash = 0;\n    const int MODULUS = 1000000007;\n    for (int i = 0; i &lt; strlen(key); i++) {\n        hash = (hash + (unsigned char)key[i]) % MODULUS;\n    }\n    return (int)hash;\n}\n\n/* Мультипликативное хеширование */\nint mulHash(char *key) {\n    long long hash = 0;\n    const int MODULUS = 1000000007;\n    for (int i = 0; i &lt; strlen(key); i++) {\n        hash = (31 * hash + (unsigned char)key[i]) % MODULUS;\n    }\n    return (int)hash;\n}\n\n/* XOR-хеширование */\nint xorHash(char *key) {\n    int hash = 0;\n    const int MODULUS = 1000000007;\n\n    for (int i = 0; i &lt; strlen(key); i++) {\n        hash ^= (unsigned char)key[i];\n    }\n    return hash &amp; MODULUS;\n}\n\n/* Хеширование с циклическим сдвигом */\nint rotHash(char *key) {\n    long long hash = 0;\n    const int MODULUS = 1000000007;\n    for (int i = 0; i &lt; strlen(key); i++) {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ (unsigned char)key[i]) % MODULUS;\n    }\n\n    return (int)hash;\n}\n</code></pre> simple_hash.kt<pre><code>/* Аддитивное хеширование */\nfun addHash(key: String): Int {\n    var hash = 0L\n    val MODULUS = 1000000007\n    for (c in key.toCharArray()) {\n        hash = (hash + c.code) % MODULUS\n    }\n    return hash.toInt()\n}\n\n/* Мультипликативное хеширование */\nfun mulHash(key: String): Int {\n    var hash = 0L\n    val MODULUS = 1000000007\n    for (c in key.toCharArray()) {\n        hash = (31 * hash + c.code) % MODULUS\n    }\n    return hash.toInt()\n}\n\n/* XOR-хеширование */\nfun xorHash(key: String): Int {\n    var hash = 0\n    val MODULUS = 1000000007\n    for (c in key.toCharArray()) {\n        hash = hash xor c.code\n    }\n    return hash and MODULUS\n}\n\n/* Хеширование с циклическим сдвигом */\nfun rotHash(key: String): Int {\n    var hash = 0L\n    val MODULUS = 1000000007\n    for (c in key.toCharArray()) {\n        hash = ((hash shl 4) xor (hash shr 28) xor c.code.toLong()) % MODULUS\n    }\n    return hash.toInt()\n}\n</code></pre> simple_hash.rb<pre><code>### Аддитивное хеширование ###\ndef add_hash(key)\n  hash = 0\n  modulus = 1_000_000_007\n\n  key.each_char { |c| hash += c.ord }\n\n  hash % modulus\nend\n\n### Мультипликативное хеширование ###\ndef mul_hash(key)\n  hash = 0\n  modulus = 1_000_000_007\n\n  key.each_char { |c| hash = 31 * hash + c.ord }\n\n  hash % modulus\nend\n\n### XOR-хеширование ###\ndef xor_hash(key)\n  hash = 0\n  modulus = 1_000_000_007\n\n  key.each_char { |c| hash ^= c.ord }\n\n  hash % modulus\nend\n\n### Хеширование с циклическим сдвигом ###\ndef rot_hash(key)\n  hash = 0\n  modulus = 1_000_000_007\n\n  key.each_char { |c| hash = (hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ c.ord }\n\n  hash % modulus\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Нетрудно заметить, что последний шаг каждого из этих хеш-алгоритмов - взятие по модулю большого простого числа \\(1000000007\\) , чтобы гарантировать, что хеш-значение остается в разумных границах. Стоит задуматься: почему подчеркивается именно взятие по модулю простого числа, и какие недостатки возникают при использовании составного модуля? Это интересный вопрос.</p> <p>Сначала дадим вывод: использование большого простого числа в качестве модуля позволяет в максимальной степени обеспечивать равномерное распределение хеш-значений. Поскольку простое число не имеет общих делителей с другими числами, это помогает уменьшить периодические закономерности, возникающие из-за операции взятия остатка, и тем самым снизить число хеш-коллизий.</p> <p>Рассмотрим пример. Предположим, мы выбрали составное число \\(9\\) в качестве модуля. Оно делится на \\(3\\) , поэтому все <code>key</code> , которые делятся на \\(3\\) , будут отображаться только в три хеш-значения: \\(0\\) , \\(3\\) , \\(6\\) .</p> \\[ \\begin{aligned} \\text{modulus} &amp; = 9 \\newline \\text{key} &amp; = \\{ 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, \\dots \\} \\newline \\text{hash} &amp; = \\{ 0, 3, 6, 0, 3, 6, 0, 3, 6, 0, 3, 6,\\dots \\} \\end{aligned} \\] <p>Если входные <code>key</code> как раз удовлетворяют такому распределению в виде арифметической прогрессии, то хеш-значения начнут скучиваться, а это усугубит хеш-коллизии. Теперь предположим, что мы заменили <code>modulus</code> на простое число \\(13\\) ; поскольку между <code>key</code> и <code>modulus</code> нет общих делителей, равномерность распределения хеш-значений заметно улучшится.</p> \\[ \\begin{aligned} \\text{modulus} &amp; = 13 \\newline \\text{key} &amp; = \\{ 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, \\dots \\} \\newline \\text{hash} &amp; = \\{ 0, 3, 6, 9, 12, 2, 5, 8, 11, 1, 4, 7, \\dots \\} \\end{aligned} \\] <p>Следует отметить: если можно гарантировать, что <code>key</code> распределены случайно и равномерно, то выбор простого или составного числа в качестве модуля не так важен - оба варианта способны дать равномерное распределение хеш-значений. Но если в распределении <code>key</code> присутствует периодичность, то взятие по модулю составного числа гораздо легче приводит к кластеризации.</p> <p>Итак, на практике мы обычно выбираем простое число в качестве модуля, причем это простое число желательно брать достаточно большим, чтобы по возможности убрать периодические закономерности и повысить устойчивость хеш-алгоритма.</p>","path":["Глава 6. Хеширование","6.3 &nbsp; Алгоритмы хеширования"],"tags":[]},{"location":"chapter_hashing/hash_algorithm/#633-","level":2,"title":"6.3.3   Распространенные хеш-алгоритмы","text":"<p>Нетрудно заметить, что описанные выше простые хеш-алгоритмы довольно \"хрупкие\" и далеки от поставленных целей. Например, сложение и XOR подчиняются коммутативному закону, поэтому аддитивный хеш и XOR-хеш не различают строки, состоящие из одних и тех же символов, но в разном порядке. Это может усиливать хеш-коллизии и даже создавать некоторые проблемы безопасности.</p> <p>На практике мы обычно используем стандартные хеш-алгоритмы, такие как MD5, SHA-1, SHA-2 и SHA-3. Они могут отображать входные данные произвольной длины в хеш-значения фиксированной длины.</p> <p>На протяжении почти ста лет хеш-алгоритмы непрерывно развивались и оптимизировались. Одни исследователи старались повысить их производительность, а другие исследователи и хакеры сосредоточивались на поиске уязвимостей в их безопасности. В таблице 6-2 приведены распространенные хеш-алгоритмы, которые часто встречаются в реальных приложениях.</p> <ul> <li>MD5 и SHA-1 уже многократно были успешно атакованы, поэтому они выведены из большинства сценариев, где требуется безопасность.</li> <li>SHA-256 из семейства SHA-2 является одним из самых надежных хеш-алгоритмов; на сегодняшний день не известно успешных практических атак, поэтому он широко используется в самых разных протоколах и системах безопасности.</li> <li>SHA-3 по сравнению с SHA-2 требует меньших затрат на реализацию и обеспечивает более высокую вычислительную эффективность, но на данный момент распространен слабее, чем семейство SHA-2.</li> </ul> <p> Таблица 6-2   Распространенные хеш-алгоритмы </p> MD5 SHA-1 SHA-2 SHA-3 Год появления 1992 1995 2002 2008 Длина вывода 128 bit 160 bit 256/512 bit 224/256/384/512 bit Хеш-коллизии Частые Частые Редкие Редкие Уровень безопасности Низкий, успешно атакован Низкий, успешно атакован Высокий Высокий Применение Устарел, но еще используется для проверки целостности данных Устарел Проверка криптовалютных транзакций, цифровые подписи и т. д. Может использоваться как замена SHA-2","path":["Глава 6. Хеширование","6.3 &nbsp; Алгоритмы хеширования"],"tags":[]},{"location":"chapter_hashing/hash_algorithm/#634-","level":2,"title":"6.3.4   Хеш-значения структур данных","text":"<p>Мы знаем, что <code>key</code> в хеш-таблице могут быть целыми числами, вещественными числами, строками и другими типами данных. Языки программирования обычно предоставляют встроенные хеш-алгоритмы для этих типов, чтобы вычислять индексы бакетов в хеш-таблице. Возьмем Python: в нем можно вызвать функцию <code>hash()</code> , чтобы вычислить хеш-значения для различных типов данных.</p> <ul> <li>Хеш-значение целого числа и булева значения совпадает с самим значением.</li> <li>Вычисление хеш-значений для вещественных чисел и строк устроено сложнее; интересующиеся читатели могут изучить это самостоятельно.</li> <li>Хеш-значение кортежа получается путем хеширования каждого элемента, а затем объединения этих хеш-значений в одно итоговое значение.</li> <li>Хеш-значение объекта обычно строится на основе его адреса в памяти. Если переопределить метод хеширования объекта, можно реализовать вычисление хеша по содержимому.</li> </ul> <p>Tip</p> <p>Обрати внимание: определения и способы вычисления встроенных хеш-значений в разных языках программирования отличаются.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby built_in_hash.py<pre><code>num = 3\nhash_num = hash(num)\n# Хеш-значение целого числа 3 равно 3\n\nbol = True\nhash_bol = hash(bol)\n# Хеш-значение булевого значения True равно 1\n\ndec = 3.14159\nhash_dec = hash(dec)\n# Хеш-значение числа 3.14159 равно 326484311674566659\n\nstr = \"Hello Algo\"\nhash_str = hash(str)\n# Хеш-значение строки \"Hello Algo\" равно 4617003410720528961\n\ntup = (12836, \"Сяо Ха\")\nhash_tup = hash(tup)\n# Хеш-значение кортежа (12836, \"Сяо Ха\") равно 1029005403108185979\n\nobj = ListNode(0)\nhash_obj = hash(obj)\n# Хеш-значение объекта узла &lt;ListNode object at 0x1058fd810&gt; равно 274267521\n</code></pre> built_in_hash.cpp<pre><code>int num = 3;\nsize_t hashNum = hash&lt;int&gt;()(num);\n// Хеш-значение целого числа 3 равно 3\n\nbool bol = true;\nsize_t hashBol = hash&lt;bool&gt;()(bol);\n// Хеш-значение булевого значения 1 равно 1\n\ndouble dec = 3.14159;\nsize_t hashDec = hash&lt;double&gt;()(dec);\n// Хеш-значение числа 3.14159 равно 4614256650576692846\n\nstring str = \"Hello Algo\";\nsize_t hashStr = hash&lt;string&gt;()(str);\n// Хеш-значение строки \"Hello Algo\" равно 15466937326284535026\n\n// В C++ встроенный std::hash() предоставляет вычисление хеша только для базовых типов данных\n// Для массивов и объектов хеш-значение обычно приходится реализовывать самостоятельно\n</code></pre> built_in_hash.java<pre><code>int num = 3;\nint hashNum = Integer.hashCode(num);\n// Хеш-значение целого числа 3 равно 3\n\nboolean bol = true;\nint hashBol = Boolean.hashCode(bol);\n// Хеш-значение булевого значения true равно 1231\n\ndouble dec = 3.14159;\nint hashDec = Double.hashCode(dec);\n// Хеш-значение числа 3.14159 равно -1340954729\n\nString str = \"Hello Algo\";\nint hashStr = str.hashCode();\n// Хеш-значение строки \"Hello Algo\" равно -727081396\n\nObject[] arr = { 12836, \"Сяо Ха\" };\nint hashTup = Arrays.hashCode(arr);\n// Хеш-значение массива [12836, Сяо Ха] равно 1151158\n\nListNode obj = new ListNode(0);\nint hashObj = obj.hashCode();\n// Хеш-значение объекта узла utils.ListNode@7dc5e7b4 равно 2110121908\n</code></pre> built_in_hash.cs<pre><code>int num = 3;\nint hashNum = num.GetHashCode();\n// Хеш-значение целого числа 3 равно 3;\n\nbool bol = true;\nint hashBol = bol.GetHashCode();\n// Хеш-значение булевого значения true равно 1;\n\ndouble dec = 3.14159;\nint hashDec = dec.GetHashCode();\n// Хеш-значение числа 3.14159 равно -1340954729;\n\nstring str = \"Hello Algo\";\nint hashStr = str.GetHashCode();\n// Хеш-значение строки \"Hello Algo\" равно -586107568;\n\nobject[] arr = [12836, \"Сяо Ха\"];\nint hashTup = arr.GetHashCode();\n// Хеш-значение массива [12836, Сяо Ха] равно 42931033;\n\nListNode obj = new(0);\nint hashObj = obj.GetHashCode();\n// Хеш-значение объекта узла 0 равно 39053774;\n</code></pre> built_in_hash.go<pre><code>// В Go нет встроенной функции hash code\n</code></pre> built_in_hash.swift<pre><code>let num = 3\nlet hashNum = num.hashValue\n// Хеш-значение целого числа 3 равно 9047044699613009734\n\nlet bol = true\nlet hashBol = bol.hashValue\n// Хеш-значение булевого значения true равно -4431640247352757451\n\nlet dec = 3.14159\nlet hashDec = dec.hashValue\n// Хеш-значение числа 3.14159 равно -2465384235396674631\n\nlet str = \"Hello Algo\"\nlet hashStr = str.hashValue\n// Хеш-значение строки \"Hello Algo\" равно -7850626797806988787\n\nlet arr = [AnyHashable(12836), AnyHashable(\"Сяо Ха\")]\nlet hashTup = arr.hashValue\n// Хеш-значение массива [AnyHashable(12836), AnyHashable(\"Сяо Ха\")] равно -2308633508154532996\n\nlet obj = ListNode(x: 0)\nlet hashObj = obj.hashValue\n// Хеш-значение объекта узла utils.ListNode равно -2434780518035996159\n</code></pre> built_in_hash.js<pre><code>// В JavaScript нет встроенной функции hash code\n</code></pre> built_in_hash.ts<pre><code>// В TypeScript нет встроенной функции hash code\n</code></pre> built_in_hash.dart<pre><code>int num = 3;\nint hashNum = num.hashCode;\n// Хеш-значение целого числа 3 равно 34803\n\nbool bol = true;\nint hashBol = bol.hashCode;\n// Хеш-значение булевого значения true равно 1231\n\ndouble dec = 3.14159;\nint hashDec = dec.hashCode;\n// Хеш-значение числа 3.14159 равно 2570631074981783\n\nString str = \"Hello Algo\";\nint hashStr = str.hashCode;\n// Хеш-значение строки \"Hello Algo\" равно 468167534\n\nList arr = [12836, \"Сяо Ха\"];\nint hashArr = arr.hashCode;\n// Хеш-значение массива [12836, Сяо Ха] равно 976512528\n\nListNode obj = new ListNode(0);\nint hashObj = obj.hashCode;\n// Хеш-значение объекта Instance of 'ListNode' равно 1033450432\n</code></pre> built_in_hash.rs<pre><code>use std::collections::hash_map::DefaultHasher;\nuse std::hash::{Hash, Hasher};\n\nlet num = 3;\nlet mut num_hasher = DefaultHasher::new();\nnum.hash(&amp;mut num_hasher);\nlet hash_num = num_hasher.finish();\n// Хеш-значение целого числа 3 равно 568126464209439262\n\nlet bol = true;\nlet mut bol_hasher = DefaultHasher::new();\nbol.hash(&amp;mut bol_hasher);\nlet hash_bol = bol_hasher.finish();\n// Хеш-значение булевого значения true равно 4952851536318644461\n\nlet dec: f32 = 3.14159;\nlet mut dec_hasher = DefaultHasher::new();\ndec.to_bits().hash(&amp;mut dec_hasher);\nlet hash_dec = dec_hasher.finish();\n// Хеш-значение числа 3.14159 равно 2566941990314602357\n\nlet str = \"Hello Algo\";\nlet mut str_hasher = DefaultHasher::new();\nstr.hash(&amp;mut str_hasher);\nlet hash_str = str_hasher.finish();\n// Хеш-значение строки \"Hello Algo\" равно 16092673739211250988\n\nlet arr = (&amp;12836, &amp;\"Сяо Ха\");\nlet mut tup_hasher = DefaultHasher::new();\narr.hash(&amp;mut tup_hasher);\nlet hash_tup = tup_hasher.finish();\n// Хеш-значение кортежа (12836, \"Сяо Ха\") равно 1885128010422702749\n\nlet node = ListNode::new(42);\nlet mut hasher = DefaultHasher::new();\nnode.borrow().val.hash(&amp;mut hasher);\nlet hash = hasher.finish();\n// Хеш-значение объекта RefCell { value: ListNode { val: 42, next: None } } равно 15387811073369036852\n</code></pre> built_in_hash.c<pre><code>// В C нет встроенной функции hash code\n</code></pre> built_in_hash.kt<pre><code>val num = 3\nval hashNum = num.hashCode()\n// Хеш-значение целого числа 3 равно 3\n\nval bol = true\nval hashBol = bol.hashCode()\n// Хеш-значение булевого значения true равно 1231\n\nval dec = 3.14159\nval hashDec = dec.hashCode()\n// Хеш-значение числа 3.14159 равно -1340954729\n\nval str = \"Hello Algo\"\nval hashStr = str.hashCode()\n// Хеш-значение строки \"Hello Algo\" равно -727081396\n\nval arr = arrayOf&lt;Any&gt;(12836, \"Сяо Ха\")\nval hashTup = arr.hashCode()\n// Хеш-значение массива [12836, Сяо Ха] равно 189568618\n\nval obj = ListNode(0)\nval hashObj = obj.hashCode()\n// Хеш-значение объекта узла utils.ListNode@1d81eb93 равно 495053715\n</code></pre> built_in_hash.rb<pre><code>num = 3\nhash_num = num.hash\n# Хеш-значение целого числа 3 равно -4385856518450339636\n\nbol = true\nhash_bol = bol.hash\n# Хеш-значение булевого значения true равно -1617938112149317027\n\ndec = 3.14159\nhash_dec = dec.hash\n# Хеш-значение числа 3.14159 равно -1479186995943067893\n\nstr = \"Hello Algo\"\nhash_str = str.hash\n# Хеш-значение строки \"Hello Algo\" равно -4075943250025831763\n\ntup = [12836, 'Сяо Ха']\nhash_tup = tup.hash\n# Хеш-значение кортежа (12836, 'Сяо Ха') равно 1999544809202288822\n\nobj = ListNode.new(0)\nhash_obj = obj.hash\n# Хеш-значение объекта #&lt;ListNode:0x000078133140ab70&gt; равно 4302940560806366381\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%D1%81%D0%B2%D1%8F%D0%B7%D0%BD%D1%8B%D0%B9%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%D1%83%D0%B7%D0%B5%D0%BB%D0%BA%D0%BB%D0%B0%D1%81%D1%81%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%D0%97%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%83%D0%B7%D0%BB%D0%B0%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%D0%A1%D1%81%D1%8B%D0%BB%D0%BA%D0%B0%20%D0%BD%D0%B0%20%D1%81%D0%BB%D0%B5%D0%B4%D1%83%D1%8E%D1%89%D0%B8%D0%B9%20%D1%83%D0%B7%D0%B5%D0%BB%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20num%20%3D%203%0A%20%20%20%20hash_num%20%3D%20hash%28num%29%0A%20%20%20%20%23%20%D0%A5%D0%B5%D1%88-%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%86%D0%B5%D0%BB%D0%BE%D0%B3%D0%BE%20%D1%87%D0%B8%D1%81%D0%BB%D0%B0%203%20%D1%80%D0%B0%D0%B2%D0%BD%D0%BE%203%0A%0A%20%20%20%20bol%20%3D%20True%0A%20%20%20%20hash_bol%20%3D%20hash%28bol%29%0A%20%20%20%20%23%20%D0%A5%D0%B5%D1%88-%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D0%B1%D1%83%D0%BB%D0%B5%D0%B2%D0%B0%20%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D1%8F%20True%20%D1%80%D0%B0%D0%B2%D0%BD%D0%BE%201%0A%0A%20%20%20%20dec%20%3D%203.14159%0A%20%20%20%20hash_dec%20%3D%20hash%28dec%29%0A%20%20%20%20%23%20%D0%A5%D0%B5%D1%88-%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%87%D0%B8%D1%81%D0%BB%D0%B0%203.14159%20%D1%80%D0%B0%D0%B2%D0%BD%D0%BE%20326484311674566659%0A%0A%20%20%20%20str%20%3D%20%22Hello%20Algo%22%0A%20%20%20%20hash_str%20%3D%20hash%28str%29%0A%20%20%20%20%23%20%D0%A5%D0%B5%D1%88-%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%81%D1%82%D1%80%D0%BE%D0%BA%D0%B8%20%22Hello%20Algo%22%20%D1%80%D0%B0%D0%B2%D0%BD%D0%BE%204617003410720528961%0A%0A%20%20%20%20tup%20%3D%20%2812836%2C%20%22%D0%A1%D1%8F%D0%BE%20%D0%A5%D0%B0%22%29%0A%20%20%20%20hash_tup%20%3D%20hash%28tup%29%0A%20%20%20%20%23%20%D0%A5%D0%B5%D1%88-%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D0%BA%D0%BE%D1%80%D1%82%D0%B5%D0%B6%D0%B0%20%2812836%2C%20%27%D0%A1%D1%8F%D0%BE%20%D0%A5%D0%B0%27%29%20%D1%80%D0%B0%D0%B2%D0%BD%D0%BE%201029005403108185979%0A%0A%20%20%20%20obj%20%3D%20ListNode%280%29%0A%20%20%20%20hash_obj%20%3D%20hash%28obj%29%0A%20%20%20%20%23%20%D0%A5%D0%B5%D1%88-%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D0%BE%D0%B1%D1%8A%D0%B5%D0%BA%D1%82%D0%B0%20%D1%83%D0%B7%D0%BB%D0%B0%20%3CListNode%20object%20at%200x1058fd810%3E%20%D1%80%D0%B0%D0%B2%D0%BD%D0%BE%20274267521&amp;cumulative=false&amp;curInstr=19&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p> <p>Во многих языках программирования в качестве <code>key</code> хеш-таблицы можно использовать только неизменяемые объекты . Если, например, использовать список (динамический массив) как <code>key</code> , то после изменения содержимого списка изменится и его хеш-значение, из-за чего мы уже не сможем найти прежнее <code>value</code> в хеш-таблице.</p> <p>Хотя у пользовательских объектов (например, у узла связного списка) поля являются изменяемыми, сам объект все же может быть хешируемым. Причина в том, что хеш-значение объекта обычно строится на основе адреса в памяти : даже если содержимое объекта меняется, его адрес памяти остается прежним, а значит, и хеш-значение не меняется.</p> <p>Внимательный читатель мог заметить, что при запуске программы в разных консолях выводимые хеш-значения отличаются. Это связано с тем, что интерпретатор Python при каждом запуске добавляет в хеш-функцию строк случайную соль (salt). Такой подход эффективно защищает от атак типа HashDoS и повышает безопасность хеш-алгоритма.</p>","path":["Глава 6. Хеширование","6.3 &nbsp; Алгоритмы хеширования"],"tags":[]},{"location":"chapter_hashing/hash_collision/","level":1,"title":"6.2   Хеш-коллизии","text":"<p>Как уже говорилось в предыдущем разделе, в обычных условиях входное пространство хеш-функции намного больше выходного пространства , поэтому теоретически хеш-коллизии неизбежны. Например, если входное пространство состоит из всех целых чисел, а выходное пространство ограничено размером массива, то неизбежно несколько целых чисел будут отображаться в один и тот же индекс бакета.</p> <p>Хеш-коллизии приводят к ошибочным результатам поиска и серьезно влияют на пригодность хеш-таблицы к использованию. Чтобы решить эту проблему, можно при каждом конфликте выполнять расширение хеш-таблицы, пока конфликт не исчезнет. Этот метод прост и груб, но слишком неэффективен, потому что расширение хеш-таблицы требует большого объема переноса данных и вычислений хеш-значений. Чтобы повысить эффективность, можно использовать следующие стратегии.</p> <ol> <li>Улучшить структуру данных хеш-таблицы, чтобы она могла корректно работать даже при возникновении хеш-коллизий.</li> <li>Выполнять расширение только тогда, когда это действительно необходимо, то есть когда хеш-коллизии становятся достаточно серьезными.</li> </ol> <p>Основные способы улучшения структуры хеш-таблицы включают \"метод цепочек\" и \"открытую адресацию\".</p>","path":["Глава 6. Хеширование","6.2 &nbsp; Хеш-коллизии"],"tags":[]},{"location":"chapter_hashing/hash_collision/#621","level":2,"title":"6.2.1   Метод цепочек","text":"<p>В исходной хеш-таблице каждый бакет может хранить только одну пару ключ-значение. Метод цепочек (separate chaining) превращает отдельный элемент в связный список: пары ключ-значение становятся узлами списка, и все конфликтующие пары ключ-значение хранятся в одном и том же списке. На рисунке 6-5 показан пример хеш-таблицы, реализованной методом цепочек.</p> <p></p> <p> Рисунок 6-5   Хеш-таблица с методом цепочек </p> <p>Методы работы с хеш-таблицей, построенной на основе метода цепочек, меняются следующим образом.</p> <ul> <li>Поиск элемента: передаем <code>key</code> , по хеш-функции получаем индекс бакета, после чего обращаемся к голове списка и обходим список, сравнивая <code>key</code> , пока не найдем целевую пару ключ-значение.</li> <li>Добавление элемента: сначала через хеш-функцию получаем голову списка, затем добавляем узел (пару ключ-значение) в этот список.</li> <li>Удаление элемента: по результату хеш-функции обращаемся к голове списка, затем обходим список, находим целевой узел и удаляем его.</li> </ul> <p>Метод цепочек имеет следующие ограничения.</p> <ul> <li>Рост потребления памяти: связный список содержит указатели на узлы, поэтому по сравнению с массивом он требует больше памяти.</li> <li>Снижение эффективности поиска: для нахождения нужного элемента нужно линейно обходить связный список.</li> </ul> <p>Ниже приведена простая реализация хеш-таблицы методом цепочек. Следует обратить внимание на два момента.</p> <ul> <li>Для упрощения кода вместо связного списка используется список (динамический массив). В этой реализации хеш-таблица (массив) содержит несколько бакетов, и каждый бакет представляет собой список.</li> <li>Ниже включен метод расширения хеш-таблицы. Когда коэффициент загрузки превышает \\(\\frac{2}{3}\\) , мы расширяем хеш-таблицу до \\(2\\) раз от прежней емкости.</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby hash_map_chaining.py<pre><code>class HashMapChaining:\n    \"\"\"Хеш-таблица с цепочками\"\"\"\n\n    def __init__(self):\n        \"\"\"Конструктор\"\"\"\n        self.size = 0  # Число пар ключ-значение\n        self.capacity = 4  # Вместимость хеш-таблицы\n        self.load_thres = 2.0 / 3.0  # Порог коэффициента загрузки для запуска расширения\n        self.extend_ratio = 2  # Коэффициент расширения\n        self.buckets = [[] for _ in range(self.capacity)]  # Массив корзин\n\n    def hash_func(self, key: int) -&gt; int:\n        \"\"\"Хеш-функция\"\"\"\n        return key % self.capacity\n\n    def load_factor(self) -&gt; float:\n        \"\"\"Коэффициент загрузки\"\"\"\n        return self.size / self.capacity\n\n    def get(self, key: int) -&gt; str | None:\n        \"\"\"Операция поиска\"\"\"\n        index = self.hash_func(key)\n        bucket = self.buckets[index]\n        # Обойти корзину; если найден key, вернуть соответствующее val\n        for pair in bucket:\n            if pair.key == key:\n                return pair.val\n        # Если key не найден, вернуть None\n        return None\n\n    def put(self, key: int, val: str):\n        \"\"\"Операция добавления\"\"\"\n        # Когда коэффициент загрузки превышает порог, выполнить расширение\n        if self.load_factor() &gt; self.load_thres:\n            self.extend()\n        index = self.hash_func(key)\n        bucket = self.buckets[index]\n        # Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n        for pair in bucket:\n            if pair.key == key:\n                pair.val = val\n                return\n        # Если такого key нет, добавить пару ключ-значение в конец\n        pair = Pair(key, val)\n        bucket.append(pair)\n        self.size += 1\n\n    def remove(self, key: int):\n        \"\"\"Операция удаления\"\"\"\n        index = self.hash_func(key)\n        bucket = self.buckets[index]\n        # Обойти корзину и удалить из нее пару ключ-значение\n        for pair in bucket:\n            if pair.key == key:\n                bucket.remove(pair)\n                self.size -= 1\n                break\n\n    def extend(self):\n        \"\"\"Расширить хеш-таблицу\"\"\"\n        # Временно сохранить исходную хеш-таблицу\n        buckets = self.buckets\n        # Инициализация новой хеш-таблицы после расширения\n        self.capacity *= self.extend_ratio\n        self.buckets = [[] for _ in range(self.capacity)]\n        self.size = 0\n        # Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for bucket in buckets:\n            for pair in bucket:\n                self.put(pair.key, pair.val)\n\n    def print(self):\n        \"\"\"Вывести хеш-таблицу\"\"\"\n        for bucket in self.buckets:\n            res = []\n            for pair in bucket:\n                res.append(str(pair.key) + \" -&gt; \" + pair.val)\n            print(res)\n</code></pre> hash_map_chaining.cpp<pre><code>/* Хеш-таблица с цепочками */\nclass HashMapChaining {\n  private:\n    int size;                       // Число пар ключ-значение\n    int capacity;                   // Вместимость хеш-таблицы\n    double loadThres;               // Порог коэффициента загрузки для запуска расширения\n    int extendRatio;                // Коэффициент расширения\n    vector&lt;vector&lt;Pair *&gt;&gt; buckets; // Массив корзин\n\n  public:\n    /* Конструктор */\n    HashMapChaining() : size(0), capacity(4), loadThres(2.0 / 3.0), extendRatio(2) {\n        buckets.resize(capacity);\n    }\n\n    /* Метод-деструктор */\n    ~HashMapChaining() {\n        for (auto &amp;bucket : buckets) {\n            for (Pair *pair : bucket) {\n                // Освободить память\n                delete pair;\n            }\n        }\n    }\n\n    /* Хеш-функция */\n    int hashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* Коэффициент загрузки */\n    double loadFactor() {\n        return (double)size / (double)capacity;\n    }\n\n    /* Операция поиска */\n    string get(int key) {\n        int index = hashFunc(key);\n        // Обойти корзину; если найден key, вернуть соответствующее val\n        for (Pair *pair : buckets[index]) {\n            if (pair-&gt;key == key) {\n                return pair-&gt;val;\n            }\n        }\n        // Если key не найден, вернуть пустую строку\n        return \"\";\n    }\n\n    /* Операция добавления */\n    void put(int key, string val) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if (loadFactor() &gt; loadThres) {\n            extend();\n        }\n        int index = hashFunc(key);\n        // Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n        for (Pair *pair : buckets[index]) {\n            if (pair-&gt;key == key) {\n                pair-&gt;val = val;\n                return;\n            }\n        }\n        // Если такого key нет, добавить пару ключ-значение в конец\n        buckets[index].push_back(new Pair(key, val));\n        size++;\n    }\n\n    /* Операция удаления */\n    void remove(int key) {\n        int index = hashFunc(key);\n        auto &amp;bucket = buckets[index];\n        // Обойти корзину и удалить из нее пару ключ-значение\n        for (int i = 0; i &lt; bucket.size(); i++) {\n            if (bucket[i]-&gt;key == key) {\n                Pair *tmp = bucket[i];\n                bucket.erase(bucket.begin() + i); // Удалить из него пару ключ-значение\n                delete tmp;                       // Освободить память\n                size--;\n                return;\n            }\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    void extend() {\n        // Временно сохранить исходную хеш-таблицу\n        vector&lt;vector&lt;Pair *&gt;&gt; bucketsTmp = buckets;\n        // Инициализация новой хеш-таблицы после расширения\n        capacity *= extendRatio;\n        buckets.clear();\n        buckets.resize(capacity);\n        size = 0;\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for (auto &amp;bucket : bucketsTmp) {\n            for (Pair *pair : bucket) {\n                put(pair-&gt;key, pair-&gt;val);\n                // Освободить память\n                delete pair;\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    void print() {\n        for (auto &amp;bucket : buckets) {\n            cout &lt;&lt; \"[\";\n            for (Pair *pair : bucket) {\n                cout &lt;&lt; pair-&gt;key &lt;&lt; \" -&gt; \" &lt;&lt; pair-&gt;val &lt;&lt; \", \";\n            }\n            cout &lt;&lt; \"]\\n\";\n        }\n    }\n};\n</code></pre> hash_map_chaining.java<pre><code>/* Хеш-таблица с цепочками */\nclass HashMapChaining {\n    int size; // Число пар ключ-значение\n    int capacity; // Вместимость хеш-таблицы\n    double loadThres; // Порог коэффициента загрузки для запуска расширения\n    int extendRatio; // Коэффициент расширения\n    List&lt;List&lt;Pair&gt;&gt; buckets; // Массив корзин\n\n    /* Конструктор */\n    public HashMapChaining() {\n        size = 0;\n        capacity = 4;\n        loadThres = 2.0 / 3.0;\n        extendRatio = 2;\n        buckets = new ArrayList&lt;&gt;(capacity);\n        for (int i = 0; i &lt; capacity; i++) {\n            buckets.add(new ArrayList&lt;&gt;());\n        }\n    }\n\n    /* Хеш-функция */\n    int hashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* Коэффициент загрузки */\n    double loadFactor() {\n        return (double) size / capacity;\n    }\n\n    /* Операция поиска */\n    String get(int key) {\n        int index = hashFunc(key);\n        List&lt;Pair&gt; bucket = buckets.get(index);\n        // Обойти корзину; если найден key, вернуть соответствующее val\n        for (Pair pair : bucket) {\n            if (pair.key == key) {\n                return pair.val;\n            }\n        }\n        // Если key не найден, вернуть null\n        return null;\n    }\n\n    /* Операция добавления */\n    void put(int key, String val) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if (loadFactor() &gt; loadThres) {\n            extend();\n        }\n        int index = hashFunc(key);\n        List&lt;Pair&gt; bucket = buckets.get(index);\n        // Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n        for (Pair pair : bucket) {\n            if (pair.key == key) {\n                pair.val = val;\n                return;\n            }\n        }\n        // Если такого key нет, добавить пару ключ-значение в конец\n        Pair pair = new Pair(key, val);\n        bucket.add(pair);\n        size++;\n    }\n\n    /* Операция удаления */\n    void remove(int key) {\n        int index = hashFunc(key);\n        List&lt;Pair&gt; bucket = buckets.get(index);\n        // Обойти корзину и удалить из нее пару ключ-значение\n        for (Pair pair : bucket) {\n            if (pair.key == key) {\n                bucket.remove(pair);\n                size--;\n                break;\n            }\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    void extend() {\n        // Временно сохранить исходную хеш-таблицу\n        List&lt;List&lt;Pair&gt;&gt; bucketsTmp = buckets;\n        // Инициализация новой хеш-таблицы после расширения\n        capacity *= extendRatio;\n        buckets = new ArrayList&lt;&gt;(capacity);\n        for (int i = 0; i &lt; capacity; i++) {\n            buckets.add(new ArrayList&lt;&gt;());\n        }\n        size = 0;\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for (List&lt;Pair&gt; bucket : bucketsTmp) {\n            for (Pair pair : bucket) {\n                put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    void print() {\n        for (List&lt;Pair&gt; bucket : buckets) {\n            List&lt;String&gt; res = new ArrayList&lt;&gt;();\n            for (Pair pair : bucket) {\n                res.add(pair.key + \" -&gt; \" + pair.val);\n            }\n            System.out.println(res);\n        }\n    }\n}\n</code></pre> hash_map_chaining.cs<pre><code>/* Хеш-таблица с цепочками */\nclass HashMapChaining {\n    int size; // Число пар ключ-значение\n    int capacity; // Вместимость хеш-таблицы\n    double loadThres; // Порог коэффициента загрузки для запуска расширения\n    int extendRatio; // Коэффициент расширения\n    List&lt;List&lt;Pair&gt;&gt; buckets; // Массив корзин\n\n    /* Конструктор */\n    public HashMapChaining() {\n        size = 0;\n        capacity = 4;\n        loadThres = 2.0 / 3.0;\n        extendRatio = 2;\n        buckets = new List&lt;List&lt;Pair&gt;&gt;(capacity);\n        for (int i = 0; i &lt; capacity; i++) {\n            buckets.Add([]);\n        }\n    }\n\n    /* Хеш-функция */\n    int HashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* Коэффициент загрузки */\n    double LoadFactor() {\n        return (double)size / capacity;\n    }\n\n    /* Операция поиска */\n    public string? Get(int key) {\n        int index = HashFunc(key);\n        // Обойти корзину; если найден key, вернуть соответствующее val\n        foreach (Pair pair in buckets[index]) {\n            if (pair.key == key) {\n                return pair.val;\n            }\n        }\n        // Если key не найден, вернуть null\n        return null;\n    }\n\n    /* Операция добавления */\n    public void Put(int key, string val) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if (LoadFactor() &gt; loadThres) {\n            Extend();\n        }\n        int index = HashFunc(key);\n        // Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n        foreach (Pair pair in buckets[index]) {\n            if (pair.key == key) {\n                pair.val = val;\n                return;\n            }\n        }\n        // Если такого key нет, добавить пару ключ-значение в конец\n        buckets[index].Add(new Pair(key, val));\n        size++;\n    }\n\n    /* Операция удаления */\n    public void Remove(int key) {\n        int index = HashFunc(key);\n        // Обойти корзину и удалить из нее пару ключ-значение\n        foreach (Pair pair in buckets[index].ToList()) {\n            if (pair.key == key) {\n                buckets[index].Remove(pair);\n                size--;\n                break;\n            }\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    void Extend() {\n        // Временно сохранить исходную хеш-таблицу\n        List&lt;List&lt;Pair&gt;&gt; bucketsTmp = buckets;\n        // Инициализация новой хеш-таблицы после расширения\n        capacity *= extendRatio;\n        buckets = new List&lt;List&lt;Pair&gt;&gt;(capacity);\n        for (int i = 0; i &lt; capacity; i++) {\n            buckets.Add([]);\n        }\n        size = 0;\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        foreach (List&lt;Pair&gt; bucket in bucketsTmp) {\n            foreach (Pair pair in bucket) {\n                Put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    public void Print() {\n        foreach (List&lt;Pair&gt; bucket in buckets) {\n            List&lt;string&gt; res = [];\n            foreach (Pair pair in bucket) {\n                res.Add(pair.key + \" -&gt; \" + pair.val);\n            }\n            foreach (string kv in res) {\n                Console.WriteLine(kv);\n            }\n        }\n    }\n}\n</code></pre> hash_map_chaining.go<pre><code>/* Хеш-таблица с цепочками */\ntype hashMapChaining struct {\n    size        int      // Число пар ключ-значение\n    capacity    int      // Вместимость хеш-таблицы\n    loadThres   float64  // Порог коэффициента загрузки для запуска расширения\n    extendRatio int      // Коэффициент расширения\n    buckets     [][]pair // Массив корзин\n}\n\n/* Конструктор */\nfunc newHashMapChaining() *hashMapChaining {\n    buckets := make([][]pair, 4)\n    for i := 0; i &lt; 4; i++ {\n        buckets[i] = make([]pair, 0)\n    }\n    return &amp;hashMapChaining{\n        size:        0,\n        capacity:    4,\n        loadThres:   2.0 / 3.0,\n        extendRatio: 2,\n        buckets:     buckets,\n    }\n}\n\n/* Хеш-функция */\nfunc (m *hashMapChaining) hashFunc(key int) int {\n    return key % m.capacity\n}\n\n/* Коэффициент загрузки */\nfunc (m *hashMapChaining) loadFactor() float64 {\n    return float64(m.size) / float64(m.capacity)\n}\n\n/* Операция поиска */\nfunc (m *hashMapChaining) get(key int) string {\n    idx := m.hashFunc(key)\n    bucket := m.buckets[idx]\n    // Обойти корзину; если найден key, вернуть соответствующее val\n    for _, p := range bucket {\n        if p.key == key {\n            return p.val\n        }\n    }\n    // Если key не найден, вернуть пустую строку\n    return \"\"\n}\n\n/* Операция добавления */\nfunc (m *hashMapChaining) put(key int, val string) {\n    // Когда коэффициент загрузки превышает порог, выполнить расширение\n    if m.loadFactor() &gt; m.loadThres {\n        m.extend()\n    }\n    idx := m.hashFunc(key)\n    // Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n    for i := range m.buckets[idx] {\n        if m.buckets[idx][i].key == key {\n            m.buckets[idx][i].val = val\n            return\n        }\n    }\n    // Если такого key нет, добавить пару ключ-значение в конец\n    p := pair{\n        key: key,\n        val: val,\n    }\n    m.buckets[idx] = append(m.buckets[idx], p)\n    m.size += 1\n}\n\n/* Операция удаления */\nfunc (m *hashMapChaining) remove(key int) {\n    idx := m.hashFunc(key)\n    // Обойти корзину и удалить из нее пару ключ-значение\n    for i, p := range m.buckets[idx] {\n        if p.key == key {\n            // Удаление из среза\n            m.buckets[idx] = append(m.buckets[idx][:i], m.buckets[idx][i+1:]...)\n            m.size -= 1\n            break\n        }\n    }\n}\n\n/* Расширить хеш-таблицу */\nfunc (m *hashMapChaining) extend() {\n    // Временно сохранить исходную хеш-таблицу\n    tmpBuckets := make([][]pair, len(m.buckets))\n    for i := 0; i &lt; len(m.buckets); i++ {\n        tmpBuckets[i] = make([]pair, len(m.buckets[i]))\n        copy(tmpBuckets[i], m.buckets[i])\n    }\n    // Инициализация новой хеш-таблицы после расширения\n    m.capacity *= m.extendRatio\n    m.buckets = make([][]pair, m.capacity)\n    for i := 0; i &lt; m.capacity; i++ {\n        m.buckets[i] = make([]pair, 0)\n    }\n    m.size = 0\n    // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n    for _, bucket := range tmpBuckets {\n        for _, p := range bucket {\n            m.put(p.key, p.val)\n        }\n    }\n}\n\n/* Вывести хеш-таблицу */\nfunc (m *hashMapChaining) print() {\n    var builder strings.Builder\n\n    for _, bucket := range m.buckets {\n        builder.WriteString(\"[\")\n        for _, p := range bucket {\n            builder.WriteString(strconv.Itoa(p.key) + \" -&gt; \" + p.val + \" \")\n        }\n        builder.WriteString(\"]\")\n        fmt.Println(builder.String())\n        builder.Reset()\n    }\n}\n</code></pre> hash_map_chaining.swift<pre><code>/* Хеш-таблица с цепочками */\nclass HashMapChaining {\n    var size: Int // Число пар ключ-значение\n    var capacity: Int // Вместимость хеш-таблицы\n    var loadThres: Double // Порог коэффициента загрузки для запуска расширения\n    var extendRatio: Int // Коэффициент расширения\n    var buckets: [[Pair]] // Массив корзин\n\n    /* Конструктор */\n    init() {\n        size = 0\n        capacity = 4\n        loadThres = 2.0 / 3.0\n        extendRatio = 2\n        buckets = Array(repeating: [], count: capacity)\n    }\n\n    /* Хеш-функция */\n    func hashFunc(key: Int) -&gt; Int {\n        key % capacity\n    }\n\n    /* Коэффициент загрузки */\n    func loadFactor() -&gt; Double {\n        Double(size) / Double(capacity)\n    }\n\n    /* Операция поиска */\n    func get(key: Int) -&gt; String? {\n        let index = hashFunc(key: key)\n        let bucket = buckets[index]\n        // Обойти корзину; если найден key, вернуть соответствующее val\n        for pair in bucket {\n            if pair.key == key {\n                return pair.val\n            }\n        }\n        // Если key не найден, вернуть nil\n        return nil\n    }\n\n    /* Операция добавления */\n    func put(key: Int, val: String) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if loadFactor() &gt; loadThres {\n            extend()\n        }\n        let index = hashFunc(key: key)\n        let bucket = buckets[index]\n        // Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n        for pair in bucket {\n            if pair.key == key {\n                pair.val = val\n                return\n            }\n        }\n        // Если такого key нет, добавить пару ключ-значение в конец\n        let pair = Pair(key: key, val: val)\n        buckets[index].append(pair)\n        size += 1\n    }\n\n    /* Операция удаления */\n    func remove(key: Int) {\n        let index = hashFunc(key: key)\n        let bucket = buckets[index]\n        // Обойти корзину и удалить из нее пару ключ-значение\n        for (pairIndex, pair) in bucket.enumerated() {\n            if pair.key == key {\n                buckets[index].remove(at: pairIndex)\n                size -= 1\n                break\n            }\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    func extend() {\n        // Временно сохранить исходную хеш-таблицу\n        let bucketsTmp = buckets\n        // Инициализация новой хеш-таблицы после расширения\n        capacity *= extendRatio\n        buckets = Array(repeating: [], count: capacity)\n        size = 0\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for bucket in bucketsTmp {\n            for pair in bucket {\n                put(key: pair.key, val: pair.val)\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    func print() {\n        for bucket in buckets {\n            let res = bucket.map { \"\\($0.key) -&gt; \\($0.val)\" }\n            Swift.print(res)\n        }\n    }\n}\n</code></pre> hash_map_chaining.js<pre><code>/* Хеш-таблица с цепочками */\nclass HashMapChaining {\n    #size; // Число пар ключ-значение\n    #capacity; // Вместимость хеш-таблицы\n    #loadThres; // Порог коэффициента загрузки для запуска расширения\n    #extendRatio; // Коэффициент расширения\n    #buckets; // Массив корзин\n\n    /* Конструктор */\n    constructor() {\n        this.#size = 0;\n        this.#capacity = 4;\n        this.#loadThres = 2.0 / 3.0;\n        this.#extendRatio = 2;\n        this.#buckets = new Array(this.#capacity).fill(null).map((x) =&gt; []);\n    }\n\n    /* Хеш-функция */\n    #hashFunc(key) {\n        return key % this.#capacity;\n    }\n\n    /* Коэффициент загрузки */\n    #loadFactor() {\n        return this.#size / this.#capacity;\n    }\n\n    /* Операция поиска */\n    get(key) {\n        const index = this.#hashFunc(key);\n        const bucket = this.#buckets[index];\n        // Обойти корзину; если найден key, вернуть соответствующее val\n        for (const pair of bucket) {\n            if (pair.key === key) {\n                return pair.val;\n            }\n        }\n        // Если key не найден, вернуть null\n        return null;\n    }\n\n    /* Операция добавления */\n    put(key, val) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if (this.#loadFactor() &gt; this.#loadThres) {\n            this.#extend();\n        }\n        const index = this.#hashFunc(key);\n        const bucket = this.#buckets[index];\n        // Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n        for (const pair of bucket) {\n            if (pair.key === key) {\n                pair.val = val;\n                return;\n            }\n        }\n        // Если такого key нет, добавить пару ключ-значение в конец\n        const pair = new Pair(key, val);\n        bucket.push(pair);\n        this.#size++;\n    }\n\n    /* Операция удаления */\n    remove(key) {\n        const index = this.#hashFunc(key);\n        let bucket = this.#buckets[index];\n        // Обойти корзину и удалить из нее пару ключ-значение\n        for (let i = 0; i &lt; bucket.length; i++) {\n            if (bucket[i].key === key) {\n                bucket.splice(i, 1);\n                this.#size--;\n                break;\n            }\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    #extend() {\n        // Временно сохранить исходную хеш-таблицу\n        const bucketsTmp = this.#buckets;\n        // Инициализация новой хеш-таблицы после расширения\n        this.#capacity *= this.#extendRatio;\n        this.#buckets = new Array(this.#capacity).fill(null).map((x) =&gt; []);\n        this.#size = 0;\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for (const bucket of bucketsTmp) {\n            for (const pair of bucket) {\n                this.put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    print() {\n        for (const bucket of this.#buckets) {\n            let res = [];\n            for (const pair of bucket) {\n                res.push(pair.key + ' -&gt; ' + pair.val);\n            }\n            console.log(res);\n        }\n    }\n}\n</code></pre> hash_map_chaining.ts<pre><code>/* Хеш-таблица с цепочками */\nclass HashMapChaining {\n    #size: number; // Число пар ключ-значение\n    #capacity: number; // Вместимость хеш-таблицы\n    #loadThres: number; // Порог коэффициента загрузки для запуска расширения\n    #extendRatio: number; // Коэффициент расширения\n    #buckets: Pair[][]; // Массив корзин\n\n    /* Конструктор */\n    constructor() {\n        this.#size = 0;\n        this.#capacity = 4;\n        this.#loadThres = 2.0 / 3.0;\n        this.#extendRatio = 2;\n        this.#buckets = new Array(this.#capacity).fill(null).map((x) =&gt; []);\n    }\n\n    /* Хеш-функция */\n    #hashFunc(key: number): number {\n        return key % this.#capacity;\n    }\n\n    /* Коэффициент загрузки */\n    #loadFactor(): number {\n        return this.#size / this.#capacity;\n    }\n\n    /* Операция поиска */\n    get(key: number): string | null {\n        const index = this.#hashFunc(key);\n        const bucket = this.#buckets[index];\n        // Обойти корзину; если найден key, вернуть соответствующее val\n        for (const pair of bucket) {\n            if (pair.key === key) {\n                return pair.val;\n            }\n        }\n        // Если key не найден, вернуть null\n        return null;\n    }\n\n    /* Операция добавления */\n    put(key: number, val: string): void {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if (this.#loadFactor() &gt; this.#loadThres) {\n            this.#extend();\n        }\n        const index = this.#hashFunc(key);\n        const bucket = this.#buckets[index];\n        // Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n        for (const pair of bucket) {\n            if (pair.key === key) {\n                pair.val = val;\n                return;\n            }\n        }\n        // Если такого key нет, добавить пару ключ-значение в конец\n        const pair = new Pair(key, val);\n        bucket.push(pair);\n        this.#size++;\n    }\n\n    /* Операция удаления */\n    remove(key: number): void {\n        const index = this.#hashFunc(key);\n        let bucket = this.#buckets[index];\n        // Обойти корзину и удалить из нее пару ключ-значение\n        for (let i = 0; i &lt; bucket.length; i++) {\n            if (bucket[i].key === key) {\n                bucket.splice(i, 1);\n                this.#size--;\n                break;\n            }\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    #extend(): void {\n        // Временно сохранить исходную хеш-таблицу\n        const bucketsTmp = this.#buckets;\n        // Инициализация новой хеш-таблицы после расширения\n        this.#capacity *= this.#extendRatio;\n        this.#buckets = new Array(this.#capacity).fill(null).map((x) =&gt; []);\n        this.#size = 0;\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for (const bucket of bucketsTmp) {\n            for (const pair of bucket) {\n                this.put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    print(): void {\n        for (const bucket of this.#buckets) {\n            let res = [];\n            for (const pair of bucket) {\n                res.push(pair.key + ' -&gt; ' + pair.val);\n            }\n            console.log(res);\n        }\n    }\n}\n</code></pre> hash_map_chaining.dart<pre><code>/* Хеш-таблица с цепочками */\nclass HashMapChaining {\n  late int size; // Число пар ключ-значение\n  late int capacity; // Вместимость хеш-таблицы\n  late double loadThres; // Порог коэффициента загрузки для запуска расширения\n  late int extendRatio; // Коэффициент расширения\n  late List&lt;List&lt;Pair&gt;&gt; buckets; // Массив корзин\n\n  /* Конструктор */\n  HashMapChaining() {\n    size = 0;\n    capacity = 4;\n    loadThres = 2.0 / 3.0;\n    extendRatio = 2;\n    buckets = List.generate(capacity, (_) =&gt; []);\n  }\n\n  /* Хеш-функция */\n  int hashFunc(int key) {\n    return key % capacity;\n  }\n\n  /* Коэффициент загрузки */\n  double loadFactor() {\n    return size / capacity;\n  }\n\n  /* Операция поиска */\n  String? get(int key) {\n    int index = hashFunc(key);\n    List&lt;Pair&gt; bucket = buckets[index];\n    // Обойти корзину; если найден key, вернуть соответствующее val\n    for (Pair pair in bucket) {\n      if (pair.key == key) {\n        return pair.val;\n      }\n    }\n    // Если key не найден, вернуть null\n    return null;\n  }\n\n  /* Операция добавления */\n  void put(int key, String val) {\n    // Когда коэффициент загрузки превышает порог, выполнить расширение\n    if (loadFactor() &gt; loadThres) {\n      extend();\n    }\n    int index = hashFunc(key);\n    List&lt;Pair&gt; bucket = buckets[index];\n    // Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n    for (Pair pair in bucket) {\n      if (pair.key == key) {\n        pair.val = val;\n        return;\n      }\n    }\n    // Если такого key нет, добавить пару ключ-значение в конец\n    Pair pair = Pair(key, val);\n    bucket.add(pair);\n    size++;\n  }\n\n  /* Операция удаления */\n  void remove(int key) {\n    int index = hashFunc(key);\n    List&lt;Pair&gt; bucket = buckets[index];\n    // Обойти корзину и удалить из нее пару ключ-значение\n    for (Pair pair in bucket) {\n      if (pair.key == key) {\n        bucket.remove(pair);\n        size--;\n        break;\n      }\n    }\n  }\n\n  /* Расширить хеш-таблицу */\n  void extend() {\n    // Временно сохранить исходную хеш-таблицу\n    List&lt;List&lt;Pair&gt;&gt; bucketsTmp = buckets;\n    // Инициализация новой хеш-таблицы после расширения\n    capacity *= extendRatio;\n    buckets = List.generate(capacity, (_) =&gt; []);\n    size = 0;\n    // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n    for (List&lt;Pair&gt; bucket in bucketsTmp) {\n      for (Pair pair in bucket) {\n        put(pair.key, pair.val);\n      }\n    }\n  }\n\n  /* Вывести хеш-таблицу */\n  void printHashMap() {\n    for (List&lt;Pair&gt; bucket in buckets) {\n      List&lt;String&gt; res = [];\n      for (Pair pair in bucket) {\n        res.add(\"${pair.key} -&gt; ${pair.val}\");\n      }\n      print(res);\n    }\n  }\n}\n</code></pre> hash_map_chaining.rs<pre><code>/* Хеш-таблица с цепочками */\nstruct HashMapChaining {\n    size: usize,\n    capacity: usize,\n    load_thres: f32,\n    extend_ratio: usize,\n    buckets: Vec&lt;Vec&lt;Pair&gt;&gt;,\n}\n\nimpl HashMapChaining {\n    /* Конструктор */\n    fn new() -&gt; Self {\n        Self {\n            size: 0,\n            capacity: 4,\n            load_thres: 2.0 / 3.0,\n            extend_ratio: 2,\n            buckets: vec![vec![]; 4],\n        }\n    }\n\n    /* Хеш-функция */\n    fn hash_func(&amp;self, key: i32) -&gt; usize {\n        key as usize % self.capacity\n    }\n\n    /* Коэффициент загрузки */\n    fn load_factor(&amp;self) -&gt; f32 {\n        self.size as f32 / self.capacity as f32\n    }\n\n    /* Операция удаления */\n    fn remove(&amp;mut self, key: i32) -&gt; Option&lt;String&gt; {\n        let index = self.hash_func(key);\n\n        // Обойти корзину и удалить из нее пару ключ-значение\n        for (i, p) in self.buckets[index].iter_mut().enumerate() {\n            if p.key == key {\n                let pair = self.buckets[index].remove(i);\n                self.size -= 1;\n                return Some(pair.val);\n            }\n        }\n\n        // Если key не найден, вернуть None\n        None\n    }\n\n    /* Расширить хеш-таблицу */\n    fn extend(&amp;mut self) {\n        // Временно сохранить исходную хеш-таблицу\n        let buckets_tmp = std::mem::take(&amp;mut self.buckets);\n\n        // Инициализация новой хеш-таблицы после расширения\n        self.capacity *= self.extend_ratio;\n        self.buckets = vec![Vec::new(); self.capacity as usize];\n        self.size = 0;\n\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for bucket in buckets_tmp {\n            for pair in bucket {\n                self.put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    fn print(&amp;self) {\n        for bucket in &amp;self.buckets {\n            let mut res = Vec::new();\n            for pair in bucket {\n                res.push(format!(\"{} -&gt; {}\", pair.key, pair.val));\n            }\n            println!(\"{:?}\", res);\n        }\n    }\n\n    /* Операция добавления */\n    fn put(&amp;mut self, key: i32, val: String) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if self.load_factor() &gt; self.load_thres {\n            self.extend();\n        }\n\n        let index = self.hash_func(key);\n\n        // Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n        for pair in self.buckets[index].iter_mut() {\n            if pair.key == key {\n                pair.val = val;\n                return;\n            }\n        }\n\n        // Если такого key нет, добавить пару ключ-значение в конец\n        let pair = Pair { key, val };\n        self.buckets[index].push(pair);\n        self.size += 1;\n    }\n\n    /* Операция поиска */\n    fn get(&amp;self, key: i32) -&gt; Option&lt;&amp;str&gt; {\n        let index = self.hash_func(key);\n\n        // Обойти корзину; если найден key, вернуть соответствующее val\n        for pair in self.buckets[index].iter() {\n            if pair.key == key {\n                return Some(&amp;pair.val);\n            }\n        }\n\n        // Если key не найден, вернуть None\n        None\n    }\n}\n</code></pre> hash_map_chaining.c<pre><code>/* Узел связного списка */\ntypedef struct Node {\n    Pair *pair;\n    struct Node *next;\n} Node;\n\n/* Хеш-таблица с цепочками */\ntypedef struct {\n    int size;         // Число пар ключ-значение\n    int capacity;     // Вместимость хеш-таблицы\n    double loadThres; // Порог коэффициента загрузки для запуска расширения\n    int extendRatio;  // Коэффициент расширения\n    Node **buckets;   // Массив корзин\n} HashMapChaining;\n\n/* Конструктор */\nHashMapChaining *newHashMapChaining() {\n    HashMapChaining *hashMap = (HashMapChaining *)malloc(sizeof(HashMapChaining));\n    hashMap-&gt;size = 0;\n    hashMap-&gt;capacity = 4;\n    hashMap-&gt;loadThres = 2.0 / 3.0;\n    hashMap-&gt;extendRatio = 2;\n    hashMap-&gt;buckets = (Node **)malloc(hashMap-&gt;capacity * sizeof(Node *));\n    for (int i = 0; i &lt; hashMap-&gt;capacity; i++) {\n        hashMap-&gt;buckets[i] = NULL;\n    }\n    return hashMap;\n}\n\n/* Деструктор */\nvoid delHashMapChaining(HashMapChaining *hashMap) {\n    for (int i = 0; i &lt; hashMap-&gt;capacity; i++) {\n        Node *cur = hashMap-&gt;buckets[i];\n        while (cur) {\n            Node *tmp = cur;\n            cur = cur-&gt;next;\n            free(tmp-&gt;pair);\n            free(tmp);\n        }\n    }\n    free(hashMap-&gt;buckets);\n    free(hashMap);\n}\n\n/* Хеш-функция */\nint hashFunc(HashMapChaining *hashMap, int key) {\n    return key % hashMap-&gt;capacity;\n}\n\n/* Коэффициент загрузки */\ndouble loadFactor(HashMapChaining *hashMap) {\n    return (double)hashMap-&gt;size / (double)hashMap-&gt;capacity;\n}\n\n/* Операция поиска */\nchar *get(HashMapChaining *hashMap, int key) {\n    int index = hashFunc(hashMap, key);\n    // Обойти корзину; если найден key, вернуть соответствующее val\n    Node *cur = hashMap-&gt;buckets[index];\n    while (cur) {\n        if (cur-&gt;pair-&gt;key == key) {\n            return cur-&gt;pair-&gt;val;\n        }\n        cur = cur-&gt;next;\n    }\n    return \"\"; // Если key не найден, вернуть пустую строку\n}\n\n/* Операция добавления */\nvoid put(HashMapChaining *hashMap, int key, const char *val) {\n    // Когда коэффициент загрузки превышает порог, выполнить расширение\n    if (loadFactor(hashMap) &gt; hashMap-&gt;loadThres) {\n        extend(hashMap);\n    }\n    int index = hashFunc(hashMap, key);\n    // Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n    Node *cur = hashMap-&gt;buckets[index];\n    while (cur) {\n        if (cur-&gt;pair-&gt;key == key) {\n            strcpy(cur-&gt;pair-&gt;val, val); // Если встретился указанный key, обновить соответствующий val и вернуть\n            return;\n        }\n        cur = cur-&gt;next;\n    }\n    // Если такого key нет, добавить пару ключ-значение в голову связного списка\n    Pair *newPair = (Pair *)malloc(sizeof(Pair));\n    newPair-&gt;key = key;\n    strcpy(newPair-&gt;val, val);\n    Node *newNode = (Node *)malloc(sizeof(Node));\n    newNode-&gt;pair = newPair;\n    newNode-&gt;next = hashMap-&gt;buckets[index];\n    hashMap-&gt;buckets[index] = newNode;\n    hashMap-&gt;size++;\n}\n\n/* Расширить хеш-таблицу */\nvoid extend(HashMapChaining *hashMap) {\n    // Временно сохранить исходную хеш-таблицу\n    int oldCapacity = hashMap-&gt;capacity;\n    Node **oldBuckets = hashMap-&gt;buckets;\n    // Инициализация новой хеш-таблицы после расширения\n    hashMap-&gt;capacity *= hashMap-&gt;extendRatio;\n    hashMap-&gt;buckets = (Node **)malloc(hashMap-&gt;capacity * sizeof(Node *));\n    for (int i = 0; i &lt; hashMap-&gt;capacity; i++) {\n        hashMap-&gt;buckets[i] = NULL;\n    }\n    hashMap-&gt;size = 0;\n    // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n    for (int i = 0; i &lt; oldCapacity; i++) {\n        Node *cur = oldBuckets[i];\n        while (cur) {\n            put(hashMap, cur-&gt;pair-&gt;key, cur-&gt;pair-&gt;val);\n            Node *temp = cur;\n            cur = cur-&gt;next;\n            // Освободить память\n            free(temp-&gt;pair);\n            free(temp);\n        }\n    }\n\n    free(oldBuckets);\n}\n\n/* Операция удаления */\nvoid removeItem(HashMapChaining *hashMap, int key) {\n    int index = hashFunc(hashMap, key);\n    Node *cur = hashMap-&gt;buckets[index];\n    Node *pre = NULL;\n    while (cur) {\n        if (cur-&gt;pair-&gt;key == key) {\n            // Удалить из него пару ключ-значение\n            if (pre) {\n                pre-&gt;next = cur-&gt;next;\n            } else {\n                hashMap-&gt;buckets[index] = cur-&gt;next;\n            }\n            // Освободить память\n            free(cur-&gt;pair);\n            free(cur);\n            hashMap-&gt;size--;\n            return;\n        }\n        pre = cur;\n        cur = cur-&gt;next;\n    }\n}\n\n/* Вывести хеш-таблицу */\nvoid print(HashMapChaining *hashMap) {\n    for (int i = 0; i &lt; hashMap-&gt;capacity; i++) {\n        Node *cur = hashMap-&gt;buckets[i];\n        printf(\"[\");\n        while (cur) {\n            printf(\"%d -&gt; %s, \", cur-&gt;pair-&gt;key, cur-&gt;pair-&gt;val);\n            cur = cur-&gt;next;\n        }\n        printf(\"]\\n\");\n    }\n}\n</code></pre> hash_map_chaining.kt<pre><code>/* Хеш-таблица с цепочками */\nclass HashMapChaining {\n    var size: Int // Число пар ключ-значение\n    var capacity: Int // Вместимость хеш-таблицы\n    val loadThres: Double // Порог коэффициента загрузки для запуска расширения\n    val extendRatio: Int // Коэффициент расширения\n    var buckets: MutableList&lt;MutableList&lt;Pair&gt;&gt; // Массив корзин\n\n    /* Конструктор */\n    init {\n        size = 0\n        capacity = 4\n        loadThres = 2.0 / 3.0\n        extendRatio = 2\n        buckets = mutableListOf()\n        for (i in 0..&lt;capacity) {\n            buckets.add(mutableListOf())\n        }\n    }\n\n    /* Хеш-функция */\n    fun hashFunc(key: Int): Int {\n        return key % capacity\n    }\n\n    /* Коэффициент загрузки */\n    fun loadFactor(): Double {\n        return (size / capacity).toDouble()\n    }\n\n    /* Операция поиска */\n    fun get(key: Int): String? {\n        val index = hashFunc(key)\n        val bucket = buckets[index]\n        // Обойти корзину; если найден key, вернуть соответствующее val\n        for (pair in bucket) {\n            if (pair.key == key) return pair._val\n        }\n        // Если key не найден, вернуть null\n        return null\n    }\n\n    /* Операция добавления */\n    fun put(key: Int, _val: String) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if (loadFactor() &gt; loadThres) {\n            extend()\n        }\n        val index = hashFunc(key)\n        val bucket = buckets[index]\n        // Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n        for (pair in bucket) {\n            if (pair.key == key) {\n                pair._val = _val\n                return\n            }\n        }\n        // Если такого key нет, добавить пару ключ-значение в конец\n        val pair = Pair(key, _val)\n        bucket.add(pair)\n        size++\n    }\n\n    /* Операция удаления */\n    fun remove(key: Int) {\n        val index = hashFunc(key)\n        val bucket = buckets[index]\n        // Обойти корзину и удалить из нее пару ключ-значение\n        for (pair in bucket) {\n            if (pair.key == key) {\n                bucket.remove(pair)\n                size--\n                break\n            }\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    fun extend() {\n        // Временно сохранить исходную хеш-таблицу\n        val bucketsTmp = buckets\n        // Инициализация новой хеш-таблицы после расширения\n        capacity *= extendRatio\n        // mutablelist не имеет фиксированного размера\n        buckets = mutableListOf()\n        for (i in 0..&lt;capacity) {\n            buckets.add(mutableListOf())\n        }\n        size = 0\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for (bucket in bucketsTmp) {\n            for (pair in bucket) {\n                put(pair.key, pair._val)\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    fun print() {\n        for (bucket in buckets) {\n            val res = mutableListOf&lt;String&gt;()\n            for (pair in bucket) {\n                val k = pair.key\n                val v = pair._val\n                res.add(\"$k -&gt; $v\")\n            }\n            println(res)\n        }\n    }\n}\n</code></pre> hash_map_chaining.rb<pre><code>### Хеш-таблица с цепочками ###\nclass HashMapChaining\n  ### Конструктор ###\n  def initialize\n    @size = 0 # Число пар ключ-значение\n    @capacity = 4 # Вместимость хеш-таблицы\n    @load_thres = 2.0 / 3.0 # Порог коэффициента загрузки для запуска расширения\n    @extend_ratio = 2 # Коэффициент расширения\n    @buckets = Array.new(@capacity) { [] } # Массив корзин\n  end\n\n  ### Хеш-функция ###\n  def hash_func(key)\n    key % @capacity\n  end\n\n  ### Коэффициент загрузки ###\n  def load_factor\n    @size / @capacity\n  end\n\n  ### Операция поиска ###\n  def get(key)\n    index = hash_func(key)\n    bucket = @buckets[index]\n    # Обойти корзину; если найден key, вернуть соответствующее val\n    for pair in bucket\n      return pair.val if pair.key == key\n    end\n    # Если key не найден, вернуть nil\n    nil\n  end\n\n  ### Операция добавления ###\n  def put(key, val)\n    # Когда коэффициент загрузки превышает порог, выполнить расширение\n    extend if load_factor &gt; @load_thres\n    index = hash_func(key)\n    bucket = @buckets[index]\n    # Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n    for pair in bucket\n      if pair.key == key\n        pair.val = val\n        return\n      end\n    end\n    # Если такого key нет, добавить пару ключ-значение в конец\n    pair = Pair.new(key, val)\n    bucket &lt;&lt; pair\n    @size += 1\n  end\n\n  ### Операция удаления ###\n  def remove(key)\n    index = hash_func(key)\n    bucket = @buckets[index]\n    # Обойти корзину и удалить из нее пару ключ-значение\n    for pair in bucket\n      if pair.key == key\n        bucket.delete(pair)\n        @size -= 1\n        break\n      end\n    end\n  end\n\n  ### Расширение хеш-таблицы ###\n  def extend\n    # Временно сохранить исходную хеш-таблицу\n    buckets = @buckets\n    # Инициализация новой хеш-таблицы после расширения\n    @capacity *= @extend_ratio\n    @buckets = Array.new(@capacity) { [] }\n    @size = 0\n    # Перенести пары ключ-значение из исходной хеш-таблицы в новую\n    for bucket in buckets\n      for pair in bucket\n        put(pair.key, pair.val)\n      end\n    end\n  end\n\n  ### Вывести хеш-таблицу ###\n  def print\n    for bucket in @buckets\n      res = []\n      for pair in bucket\n        res &lt;&lt; \"#{pair.key} -&gt; #{pair.val}\"\n      end\n      pp res\n    end\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Следует отметить, что когда связный список становится очень длинным, эффективность поиска \\(O(n)\\) оказывается низкой. В этом случае список можно преобразовать в \"AVL-дерево\" или \"красно-черное дерево\" , чтобы оптимизировать временную сложность поиска до \\(O(\\log n)\\) .</p>","path":["Глава 6. Хеширование","6.2 &nbsp; Хеш-коллизии"],"tags":[]},{"location":"chapter_hashing/hash_collision/#622","level":2,"title":"6.2.2   Открытая адресация","text":"<p>Открытая адресация (open addressing) не вводит дополнительных структур данных, а обрабатывает хеш-коллизии с помощью \"многократного пробирования\"; основные варианты пробирования включают линейное пробирование, квадратичное пробирование и повторное хеширование.</p> <p>Ниже на примере линейного пробирования рассмотрим механизм работы хеш-таблицы с открытой адресацией.</p>","path":["Глава 6. Хеширование","6.2 &nbsp; Хеш-коллизии"],"tags":[]},{"location":"chapter_hashing/hash_collision/#1","level":3,"title":"1.   Линейное пробирование","text":"<p>Линейное пробирование использует линейный поиск с фиксированным шагом. Его методы работы отличаются от обычной хеш-таблицы.</p> <ul> <li>Вставка элемента: по хеш-функции вычисляется индекс бакета; если бакет уже занят, то от места конфликта выполняется линейный обход вперед (шаг обычно равен \\(1\\) ), пока не будет найден пустой бакет, после чего элемент вставляется туда.</li> <li>Поиск элемента: если возник конфликт, то с тем же шагом продолжается линейный обход вперед, пока не будет найден целевой элемент и возвращено <code>value</code> ; если встречается пустой бакет, это означает, что искомого элемента в хеш-таблице нет, и возвращается <code>None</code> .</li> </ul> <p>На рисунке 6-6 показано распределение пар ключ-значение в хеш-таблице с открытой адресацией (линейное пробирование). Для этой хеш-функции все <code>key</code> с одинаковыми двумя последними цифрами отображаются в один и тот же бакет. Благодаря линейному пробированию они по очереди сохраняются в этом бакете и в следующих за ним бакетах.</p> <p></p> <p> Рисунок 6-6   Распределение пар ключ-значение в хеш-таблице с открытой адресацией (линейное пробирование) </p> <p>Однако линейное пробирование легко приводит к \"кластеризации\". Иначе говоря, чем длиннее непрерывная занятая область в массиве, тем выше вероятность новых коллизий в этой области, что еще сильнее способствует росту этой группы и в итоге ухудшает эффективность операций добавления, удаления, поиска и обновления.</p> <p>Стоит заметить, что мы не можем напрямую удалять элементы из хеш-таблицы с открытой адресацией. Причина в том, что удаление создаст внутри массива пустой бакет <code>None</code> , а при поиске элемента линейное пробирование остановится на этом пустом бакете и вернет результат, из-за чего элементы ниже этого бакета уже не смогут быть найдены, и программа может ошибочно посчитать, что их не существует, как показано на рисунке 6-7.</p> <p></p> <p> Рисунок 6-7   Проблема поиска после удаления элемента в открытой адресации </p> <p>Чтобы решить эту проблему, можно использовать механизм ленивого удаления (lazy deletion): он не удаляет элемент из хеш-таблицы напрямую, **а помечает этот бакет специальной константой <code>TOMBSTONE</code> **. В этом механизме и <code>None</code> , и <code>TOMBSTONE</code> означают пустой бакет, и оба могут быть использованы для размещения пары ключ-значение. Но есть важное различие: при линейном пробировании, встретив <code>TOMBSTONE</code> , нужно продолжать обход, потому что ниже него все еще могут существовать пары ключ-значение.</p> <p>Однако ленивое удаление может ускорять деградацию производительности хеш-таблицы. Это связано с тем, что каждая операция удаления создает новую метку удаления; по мере роста числа <code>TOMBSTONE</code> время поиска тоже увеличивается, потому что линейное пробирование может быть вынуждено перескакивать через множество <code>TOMBSTONE</code> , прежде чем найдет целевой элемент.</p> <p>Поэтому имеет смысл при линейном пробировании запоминать индекс первого встреченного <code>TOMBSTONE</code> и затем менять найденный целевой элемент местами с этим <code>TOMBSTONE</code> . Преимущество такого подхода в том, что при каждом поиске или добавлении элемент будет перемещаться в бакет, расположенный ближе к его идеальной позиции (начальной точке пробирования), а значит, эффективность поиска улучшится.</p> <p>Ниже приведена реализация хеш-таблицы с открытой адресацией (линейное пробирование), включающая ленивое удаление. Чтобы пространство хеш-таблицы использовалось более полно, мы рассматриваем ее как \"кольцевой массив\": когда обход выходит за конец массива, он возвращается к началу и продолжается.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby hash_map_open_addressing.py<pre><code>class HashMapOpenAddressing:\n    \"\"\"Хеш-таблица с открытой адресацией\"\"\"\n\n    def __init__(self):\n        \"\"\"Конструктор\"\"\"\n        self.size = 0  # Число пар ключ-значение\n        self.capacity = 4  # Вместимость хеш-таблицы\n        self.load_thres = 2.0 / 3.0  # Порог коэффициента загрузки для запуска расширения\n        self.extend_ratio = 2  # Коэффициент расширения\n        self.buckets: list[Pair | None] = [None] * self.capacity  # Массив корзин\n        self.TOMBSTONE = Pair(-1, \"-1\")  # Удалить метку\n\n    def hash_func(self, key: int) -&gt; int:\n        \"\"\"Хеш-функция\"\"\"\n        return key % self.capacity\n\n    def load_factor(self) -&gt; float:\n        \"\"\"Коэффициент загрузки\"\"\"\n        return self.size / self.capacity\n\n    def find_bucket(self, key: int) -&gt; int:\n        \"\"\"Найти индекс корзины, соответствующий key\"\"\"\n        index = self.hash_func(key)\n        first_tombstone = -1\n        # Выполнять линейное пробирование и завершить при встрече с пустой корзиной\n        while self.buckets[index] is not None:\n            # Если встретился key, вернуть соответствующий индекс корзины\n            if self.buckets[index].key == key:\n                # Если ранее встретилась метка удаления, переместить пару ключ-значение на этот индекс\n                if first_tombstone != -1:\n                    self.buckets[first_tombstone] = self.buckets[index]\n                    self.buckets[index] = self.TOMBSTONE\n                    return first_tombstone  # Вернуть индекс корзины после перемещения\n                return index  # Вернуть индекс корзины\n            # Записать первую встретившуюся метку удаления\n            if first_tombstone == -1 and self.buckets[index] is self.TOMBSTONE:\n                first_tombstone = index\n            # Вычислить индекс корзины; при выходе за конец вернуться к началу\n            index = (index + 1) % self.capacity\n        # Если key не существует, вернуть индекс точки добавления\n        return index if first_tombstone == -1 else first_tombstone\n\n    def get(self, key: int) -&gt; str:\n        \"\"\"Операция поиска\"\"\"\n        # Найти индекс корзины, соответствующий key\n        index = self.find_bucket(key)\n        # Если пара ключ-значение найдена, вернуть соответствующее val\n        if self.buckets[index] not in [None, self.TOMBSTONE]:\n            return self.buckets[index].val\n        # Если пара ключ-значение не существует, вернуть None\n        return None\n\n    def put(self, key: int, val: str):\n        \"\"\"Операция добавления\"\"\"\n        # Когда коэффициент загрузки превышает порог, выполнить расширение\n        if self.load_factor() &gt; self.load_thres:\n            self.extend()\n        # Найти индекс корзины, соответствующий key\n        index = self.find_bucket(key)\n        # Если пара ключ-значение найдена, перезаписать val и вернуть\n        if self.buckets[index] not in [None, self.TOMBSTONE]:\n            self.buckets[index].val = val\n            return\n        # Если пары ключ-значение нет, добавить ее\n        self.buckets[index] = Pair(key, val)\n        self.size += 1\n\n    def remove(self, key: int):\n        \"\"\"Операция удаления\"\"\"\n        # Найти индекс корзины, соответствующий key\n        index = self.find_bucket(key)\n        # Если пара ключ-значение найдена, заменить ее меткой удаления\n        if self.buckets[index] not in [None, self.TOMBSTONE]:\n            self.buckets[index] = self.TOMBSTONE\n            self.size -= 1\n\n    def extend(self):\n        \"\"\"Расширить хеш-таблицу\"\"\"\n        # Временно сохранить исходную хеш-таблицу\n        buckets_tmp = self.buckets\n        # Инициализация новой хеш-таблицы после расширения\n        self.capacity *= self.extend_ratio\n        self.buckets = [None] * self.capacity\n        self.size = 0\n        # Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for pair in buckets_tmp:\n            if pair not in [None, self.TOMBSTONE]:\n                self.put(pair.key, pair.val)\n\n    def print(self):\n        \"\"\"Вывести хеш-таблицу\"\"\"\n        for pair in self.buckets:\n            if pair is None:\n                print(\"None\")\n            elif pair is self.TOMBSTONE:\n                print(\"TOMBSTONE\")\n            else:\n                print(pair.key, \"-&gt;\", pair.val)\n</code></pre> hash_map_open_addressing.cpp<pre><code>/* Хеш-таблица с открытой адресацией */\nclass HashMapOpenAddressing {\n  private:\n    int size;                             // Число пар ключ-значение\n    int capacity = 4;                     // Вместимость хеш-таблицы\n    const double loadThres = 2.0 / 3.0;     // Порог коэффициента загрузки для запуска расширения\n    const int extendRatio = 2;            // Коэффициент расширения\n    vector&lt;Pair *&gt; buckets;               // Массив корзин\n    Pair *TOMBSTONE = new Pair(-1, \"-1\"); // Удалить метку\n\n  public:\n    /* Конструктор */\n    HashMapOpenAddressing() : size(0), buckets(capacity, nullptr) {\n    }\n\n    /* Метод-деструктор */\n    ~HashMapOpenAddressing() {\n        for (Pair *pair : buckets) {\n            if (pair != nullptr &amp;&amp; pair != TOMBSTONE) {\n                delete pair;\n            }\n        }\n        delete TOMBSTONE;\n    }\n\n    /* Хеш-функция */\n    int hashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* Коэффициент загрузки */\n    double loadFactor() {\n        return (double)size / capacity;\n    }\n\n    /* Найти индекс корзины, соответствующий key */\n    int findBucket(int key) {\n        int index = hashFunc(key);\n        int firstTombstone = -1;\n        // Выполнять линейное пробирование и завершить при встрече с пустой корзиной\n        while (buckets[index] != nullptr) {\n            // Если встретился key, вернуть соответствующий индекс корзины\n            if (buckets[index]-&gt;key == key) {\n                // Если ранее встретилась метка удаления, переместить пару ключ-значение на этот индекс\n                if (firstTombstone != -1) {\n                    buckets[firstTombstone] = buckets[index];\n                    buckets[index] = TOMBSTONE;\n                    return firstTombstone; // Вернуть индекс корзины после перемещения\n                }\n                return index; // Вернуть индекс корзины\n            }\n            // Записать первую встретившуюся метку удаления\n            if (firstTombstone == -1 &amp;&amp; buckets[index] == TOMBSTONE) {\n                firstTombstone = index;\n            }\n            // Вычислить индекс корзины; при выходе за конец вернуться к началу\n            index = (index + 1) % capacity;\n        }\n        // Если key не существует, вернуть индекс точки добавления\n        return firstTombstone == -1 ? index : firstTombstone;\n    }\n\n    /* Операция поиска */\n    string get(int key) {\n        // Найти индекс корзины, соответствующий key\n        int index = findBucket(key);\n        // Если пара ключ-значение найдена, вернуть соответствующее val\n        if (buckets[index] != nullptr &amp;&amp; buckets[index] != TOMBSTONE) {\n            return buckets[index]-&gt;val;\n        }\n        // Если пары ключ-значение не существует, вернуть пустую строку\n        return \"\";\n    }\n\n    /* Операция добавления */\n    void put(int key, string val) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if (loadFactor() &gt; loadThres) {\n            extend();\n        }\n        // Найти индекс корзины, соответствующий key\n        int index = findBucket(key);\n        // Если пара ключ-значение найдена, перезаписать val и вернуть\n        if (buckets[index] != nullptr &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index]-&gt;val = val;\n            return;\n        }\n        // Если пары ключ-значение нет, добавить ее\n        buckets[index] = new Pair(key, val);\n        size++;\n    }\n\n    /* Операция удаления */\n    void remove(int key) {\n        // Найти индекс корзины, соответствующий key\n        int index = findBucket(key);\n        // Если пара ключ-значение найдена, заменить ее меткой удаления\n        if (buckets[index] != nullptr &amp;&amp; buckets[index] != TOMBSTONE) {\n            delete buckets[index];\n            buckets[index] = TOMBSTONE;\n            size--;\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    void extend() {\n        // Временно сохранить исходную хеш-таблицу\n        vector&lt;Pair *&gt; bucketsTmp = buckets;\n        // Инициализация новой хеш-таблицы после расширения\n        capacity *= extendRatio;\n        buckets = vector&lt;Pair *&gt;(capacity, nullptr);\n        size = 0;\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for (Pair *pair : bucketsTmp) {\n            if (pair != nullptr &amp;&amp; pair != TOMBSTONE) {\n                put(pair-&gt;key, pair-&gt;val);\n                delete pair;\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    void print() {\n        for (Pair *pair : buckets) {\n            if (pair == nullptr) {\n                cout &lt;&lt; \"nullptr\" &lt;&lt; endl;\n            } else if (pair == TOMBSTONE) {\n                cout &lt;&lt; \"TOMBSTONE\" &lt;&lt; endl;\n            } else {\n                cout &lt;&lt; pair-&gt;key &lt;&lt; \" -&gt; \" &lt;&lt; pair-&gt;val &lt;&lt; endl;\n            }\n        }\n    }\n};\n</code></pre> hash_map_open_addressing.java<pre><code>/* Хеш-таблица с открытой адресацией */\nclass HashMapOpenAddressing {\n    private int size; // Число пар ключ-значение\n    private int capacity = 4; // Вместимость хеш-таблицы\n    private final double loadThres = 2.0 / 3.0; // Порог коэффициента загрузки для запуска расширения\n    private final int extendRatio = 2; // Коэффициент расширения\n    private Pair[] buckets; // Массив корзин\n    private final Pair TOMBSTONE = new Pair(-1, \"-1\"); // Удалить метку\n\n    /* Конструктор */\n    public HashMapOpenAddressing() {\n        size = 0;\n        buckets = new Pair[capacity];\n    }\n\n    /* Хеш-функция */\n    private int hashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* Коэффициент загрузки */\n    private double loadFactor() {\n        return (double) size / capacity;\n    }\n\n    /* Найти индекс корзины, соответствующий key */\n    private int findBucket(int key) {\n        int index = hashFunc(key);\n        int firstTombstone = -1;\n        // Выполнять линейное пробирование и завершить при встрече с пустой корзиной\n        while (buckets[index] != null) {\n            // Если встретился key, вернуть соответствующий индекс корзины\n            if (buckets[index].key == key) {\n                // Если ранее встретилась метка удаления, переместить пару ключ-значение на этот индекс\n                if (firstTombstone != -1) {\n                    buckets[firstTombstone] = buckets[index];\n                    buckets[index] = TOMBSTONE;\n                    return firstTombstone; // Вернуть индекс корзины после перемещения\n                }\n                return index; // Вернуть индекс корзины\n            }\n            // Записать первую встретившуюся метку удаления\n            if (firstTombstone == -1 &amp;&amp; buckets[index] == TOMBSTONE) {\n                firstTombstone = index;\n            }\n            // Вычислить индекс корзины; при выходе за конец вернуться к началу\n            index = (index + 1) % capacity;\n        }\n        // Если key не существует, вернуть индекс точки добавления\n        return firstTombstone == -1 ? index : firstTombstone;\n    }\n\n    /* Операция поиска */\n    public String get(int key) {\n        // Найти индекс корзины, соответствующий key\n        int index = findBucket(key);\n        // Если пара ключ-значение найдена, вернуть соответствующее val\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            return buckets[index].val;\n        }\n        // Если пары ключ-значение не существует, вернуть null\n        return null;\n    }\n\n    /* Операция добавления */\n    public void put(int key, String val) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if (loadFactor() &gt; loadThres) {\n            extend();\n        }\n        // Найти индекс корзины, соответствующий key\n        int index = findBucket(key);\n        // Если пара ключ-значение найдена, перезаписать val и вернуть\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index].val = val;\n            return;\n        }\n        // Если пары ключ-значение нет, добавить ее\n        buckets[index] = new Pair(key, val);\n        size++;\n    }\n\n    /* Операция удаления */\n    public void remove(int key) {\n        // Найти индекс корзины, соответствующий key\n        int index = findBucket(key);\n        // Если пара ключ-значение найдена, заменить ее меткой удаления\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index] = TOMBSTONE;\n            size--;\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    private void extend() {\n        // Временно сохранить исходную хеш-таблицу\n        Pair[] bucketsTmp = buckets;\n        // Инициализация новой хеш-таблицы после расширения\n        capacity *= extendRatio;\n        buckets = new Pair[capacity];\n        size = 0;\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for (Pair pair : bucketsTmp) {\n            if (pair != null &amp;&amp; pair != TOMBSTONE) {\n                put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    public void print() {\n        for (Pair pair : buckets) {\n            if (pair == null) {\n                System.out.println(\"null\");\n            } else if (pair == TOMBSTONE) {\n                System.out.println(\"TOMBSTONE\");\n            } else {\n                System.out.println(pair.key + \" -&gt; \" + pair.val);\n            }\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.cs<pre><code>/* Хеш-таблица с открытой адресацией */\nclass HashMapOpenAddressing {\n    int size; // Число пар ключ-значение\n    int capacity = 4; // Вместимость хеш-таблицы\n    double loadThres = 2.0 / 3.0; // Порог коэффициента загрузки для запуска расширения\n    int extendRatio = 2; // Коэффициент расширения\n    Pair[] buckets; // Массив корзин\n    Pair TOMBSTONE = new(-1, \"-1\"); // Удалить метку\n\n    /* Конструктор */\n    public HashMapOpenAddressing() {\n        size = 0;\n        buckets = new Pair[capacity];\n    }\n\n    /* Хеш-функция */\n    int HashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* Коэффициент загрузки */\n    double LoadFactor() {\n        return (double)size / capacity;\n    }\n\n    /* Найти индекс корзины, соответствующий key */\n    int FindBucket(int key) {\n        int index = HashFunc(key);\n        int firstTombstone = -1;\n        // Выполнять линейное пробирование и завершить при встрече с пустой корзиной\n        while (buckets[index] != null) {\n            // Если встретился key, вернуть соответствующий индекс корзины\n            if (buckets[index].key == key) {\n                // Если ранее встретилась метка удаления, переместить пару ключ-значение на этот индекс\n                if (firstTombstone != -1) {\n                    buckets[firstTombstone] = buckets[index];\n                    buckets[index] = TOMBSTONE;\n                    return firstTombstone; // Вернуть индекс корзины после перемещения\n                }\n                return index; // Вернуть индекс корзины\n            }\n            // Записать первую встретившуюся метку удаления\n            if (firstTombstone == -1 &amp;&amp; buckets[index] == TOMBSTONE) {\n                firstTombstone = index;\n            }\n            // Вычислить индекс корзины; при выходе за конец вернуться к началу\n            index = (index + 1) % capacity;\n        }\n        // Если key не существует, вернуть индекс точки добавления\n        return firstTombstone == -1 ? index : firstTombstone;\n    }\n\n    /* Операция поиска */\n    public string? Get(int key) {\n        // Найти индекс корзины, соответствующий key\n        int index = FindBucket(key);\n        // Если пара ключ-значение найдена, вернуть соответствующее val\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            return buckets[index].val;\n        }\n        // Если пары ключ-значение не существует, вернуть null\n        return null;\n    }\n\n    /* Операция добавления */\n    public void Put(int key, string val) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if (LoadFactor() &gt; loadThres) {\n            Extend();\n        }\n        // Найти индекс корзины, соответствующий key\n        int index = FindBucket(key);\n        // Если пара ключ-значение найдена, перезаписать val и вернуть\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index].val = val;\n            return;\n        }\n        // Если пары ключ-значение нет, добавить ее\n        buckets[index] = new Pair(key, val);\n        size++;\n    }\n\n    /* Операция удаления */\n    public void Remove(int key) {\n        // Найти индекс корзины, соответствующий key\n        int index = FindBucket(key);\n        // Если пара ключ-значение найдена, заменить ее меткой удаления\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index] = TOMBSTONE;\n            size--;\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    void Extend() {\n        // Временно сохранить исходную хеш-таблицу\n        Pair[] bucketsTmp = buckets;\n        // Инициализация новой хеш-таблицы после расширения\n        capacity *= extendRatio;\n        buckets = new Pair[capacity];\n        size = 0;\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        foreach (Pair pair in bucketsTmp) {\n            if (pair != null &amp;&amp; pair != TOMBSTONE) {\n                Put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    public void Print() {\n        foreach (Pair pair in buckets) {\n            if (pair == null) {\n                Console.WriteLine(\"null\");\n            } else if (pair == TOMBSTONE) {\n                Console.WriteLine(\"TOMBSTONE\");\n            } else {\n                Console.WriteLine(pair.key + \" -&gt; \" + pair.val);\n            }\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.go<pre><code>/* Хеш-таблица с открытой адресацией */\ntype hashMapOpenAddressing struct {\n    size        int     // Число пар ключ-значение\n    capacity    int     // Вместимость хеш-таблицы\n    loadThres   float64 // Порог коэффициента загрузки для запуска расширения\n    extendRatio int     // Коэффициент расширения\n    buckets     []*pair // Массив корзин\n    TOMBSTONE   *pair   // Удалить метку\n}\n\n/* Конструктор */\nfunc newHashMapOpenAddressing() *hashMapOpenAddressing {\n    return &amp;hashMapOpenAddressing{\n        size:        0,\n        capacity:    4,\n        loadThres:   2.0 / 3.0,\n        extendRatio: 2,\n        buckets:     make([]*pair, 4),\n        TOMBSTONE:   &amp;pair{-1, \"-1\"},\n    }\n}\n\n/* Хеш-функция */\nfunc (h *hashMapOpenAddressing) hashFunc(key int) int {\n    return key % h.capacity // Вычислить хеш-значение по ключу\n}\n\n/* Коэффициент загрузки */\nfunc (h *hashMapOpenAddressing) loadFactor() float64 {\n    return float64(h.size) / float64(h.capacity) // Вычислить текущий коэффициент загрузки\n}\n\n/* Найти индекс корзины, соответствующий key */\nfunc (h *hashMapOpenAddressing) findBucket(key int) int {\n    index := h.hashFunc(key) // Получить начальный индекс\n    firstTombstone := -1     // Запомнить положение первого TOMBSTONE\n    for h.buckets[index] != nil {\n        if h.buckets[index].key == key {\n            if firstTombstone != -1 {\n                // Если ранее встретилась метка удаления, переместить пару ключ-значение на этот индекс\n                h.buckets[firstTombstone] = h.buckets[index]\n                h.buckets[index] = h.TOMBSTONE\n                return firstTombstone // Вернуть индекс корзины после перемещения\n            }\n            return index // Вернуть найденный индекс\n        }\n        if firstTombstone == -1 &amp;&amp; h.buckets[index] == h.TOMBSTONE {\n            firstTombstone = index // Запомнить положение первой метки удаления\n        }\n        index = (index + 1) % h.capacity // Линейное пробирование: при выходе за хвост вернуться к началу\n    }\n    // Если key не существует, вернуть индекс точки добавления\n    if firstTombstone != -1 {\n        return firstTombstone\n    }\n    return index\n}\n\n/* Операция поиска */\nfunc (h *hashMapOpenAddressing) get(key int) string {\n    index := h.findBucket(key) // Найти индекс корзины, соответствующий key\n    if h.buckets[index] != nil &amp;&amp; h.buckets[index] != h.TOMBSTONE {\n        return h.buckets[index].val // Если пара ключ-значение найдена, вернуть соответствующее val\n    }\n    return \"\" // Если пара ключ-значение не существует, вернуть \"\"\n}\n\n/* Операция добавления */\nfunc (h *hashMapOpenAddressing) put(key int, val string) {\n    if h.loadFactor() &gt; h.loadThres {\n        h.extend() // Когда коэффициент загрузки превышает порог, выполнить расширение\n    }\n    index := h.findBucket(key) // Найти индекс корзины, соответствующий key\n    if h.buckets[index] == nil || h.buckets[index] == h.TOMBSTONE {\n        h.buckets[index] = &amp;pair{key, val} // Если пары ключ-значение нет, добавить ее\n        h.size++\n    } else {\n        h.buckets[index].val = val // Если пара ключ-значение найдена, перезаписать val\n    }\n}\n\n/* Операция удаления */\nfunc (h *hashMapOpenAddressing) remove(key int) {\n    index := h.findBucket(key) // Найти индекс корзины, соответствующий key\n    if h.buckets[index] != nil &amp;&amp; h.buckets[index] != h.TOMBSTONE {\n        h.buckets[index] = h.TOMBSTONE // Если пара ключ-значение найдена, заменить ее меткой удаления\n        h.size--\n    }\n}\n\n/* Расширить хеш-таблицу */\nfunc (h *hashMapOpenAddressing) extend() {\n    oldBuckets := h.buckets               // Временно сохранить исходную хеш-таблицу\n    h.capacity *= h.extendRatio           // Обновить емкость\n    h.buckets = make([]*pair, h.capacity) // Инициализация новой хеш-таблицы после расширения\n    h.size = 0                            // Сбросить размер\n    // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n    for _, pair := range oldBuckets {\n        if pair != nil &amp;&amp; pair != h.TOMBSTONE {\n            h.put(pair.key, pair.val)\n        }\n    }\n}\n\n/* Вывести хеш-таблицу */\nfunc (h *hashMapOpenAddressing) print() {\n    for _, pair := range h.buckets {\n        if pair == nil {\n            fmt.Println(\"nil\")\n        } else if pair == h.TOMBSTONE {\n            fmt.Println(\"TOMBSTONE\")\n        } else {\n            fmt.Printf(\"%d -&gt; %s\\n\", pair.key, pair.val)\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.swift<pre><code>/* Хеш-таблица с открытой адресацией */\nclass HashMapOpenAddressing {\n    var size: Int // Число пар ключ-значение\n    var capacity: Int // Вместимость хеш-таблицы\n    var loadThres: Double // Порог коэффициента загрузки для запуска расширения\n    var extendRatio: Int // Коэффициент расширения\n    var buckets: [Pair?] // Массив корзин\n    var TOMBSTONE: Pair // Удалить метку\n\n    /* Конструктор */\n    init() {\n        size = 0\n        capacity = 4\n        loadThres = 2.0 / 3.0\n        extendRatio = 2\n        buckets = Array(repeating: nil, count: capacity)\n        TOMBSTONE = Pair(key: -1, val: \"-1\")\n    }\n\n    /* Хеш-функция */\n    func hashFunc(key: Int) -&gt; Int {\n        key % capacity\n    }\n\n    /* Коэффициент загрузки */\n    func loadFactor() -&gt; Double {\n        Double(size) / Double(capacity)\n    }\n\n    /* Найти индекс корзины, соответствующий key */\n    func findBucket(key: Int) -&gt; Int {\n        var index = hashFunc(key: key)\n        var firstTombstone = -1\n        // Выполнять линейное пробирование и завершить при встрече с пустой корзиной\n        while buckets[index] != nil {\n            // Если встретился key, вернуть соответствующий индекс корзины\n            if buckets[index]!.key == key {\n                // Если ранее встретилась метка удаления, переместить пару ключ-значение на этот индекс\n                if firstTombstone != -1 {\n                    buckets[firstTombstone] = buckets[index]\n                    buckets[index] = TOMBSTONE\n                    return firstTombstone // Вернуть индекс корзины после перемещения\n                }\n                return index // Вернуть индекс корзины\n            }\n            // Записать первую встретившуюся метку удаления\n            if firstTombstone == -1 &amp;&amp; buckets[index] == TOMBSTONE {\n                firstTombstone = index\n            }\n            // Вычислить индекс корзины; при выходе за конец вернуться к началу\n            index = (index + 1) % capacity\n        }\n        // Если key не существует, вернуть индекс точки добавления\n        return firstTombstone == -1 ? index : firstTombstone\n    }\n\n    /* Операция поиска */\n    func get(key: Int) -&gt; String? {\n        // Найти индекс корзины, соответствующий key\n        let index = findBucket(key: key)\n        // Если пара ключ-значение найдена, вернуть соответствующее val\n        if buckets[index] != nil, buckets[index] != TOMBSTONE {\n            return buckets[index]!.val\n        }\n        // Если пары ключ-значение не существует, вернуть null\n        return nil\n    }\n\n    /* Операция добавления */\n    func put(key: Int, val: String) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if loadFactor() &gt; loadThres {\n            extend()\n        }\n        // Найти индекс корзины, соответствующий key\n        let index = findBucket(key: key)\n        // Если пара ключ-значение найдена, перезаписать val и вернуть\n        if buckets[index] != nil, buckets[index] != TOMBSTONE {\n            buckets[index]!.val = val\n            return\n        }\n        // Если пары ключ-значение нет, добавить ее\n        buckets[index] = Pair(key: key, val: val)\n        size += 1\n    }\n\n    /* Операция удаления */\n    func remove(key: Int) {\n        // Найти индекс корзины, соответствующий key\n        let index = findBucket(key: key)\n        // Если пара ключ-значение найдена, заменить ее меткой удаления\n        if buckets[index] != nil, buckets[index] != TOMBSTONE {\n            buckets[index] = TOMBSTONE\n            size -= 1\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    func extend() {\n        // Временно сохранить исходную хеш-таблицу\n        let bucketsTmp = buckets\n        // Инициализация новой хеш-таблицы после расширения\n        capacity *= extendRatio\n        buckets = Array(repeating: nil, count: capacity)\n        size = 0\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for pair in bucketsTmp {\n            if let pair, pair != TOMBSTONE {\n                put(key: pair.key, val: pair.val)\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    func print() {\n        for pair in buckets {\n            if pair == nil {\n                Swift.print(\"null\")\n            } else if pair == TOMBSTONE {\n                Swift.print(\"TOMBSTONE\")\n            } else {\n                Swift.print(\"\\(pair!.key) -&gt; \\(pair!.val)\")\n            }\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.js<pre><code>/* Хеш-таблица с открытой адресацией */\nclass HashMapOpenAddressing {\n    #size; // Число пар ключ-значение\n    #capacity; // Вместимость хеш-таблицы\n    #loadThres; // Порог коэффициента загрузки для запуска расширения\n    #extendRatio; // Коэффициент расширения\n    #buckets; // Массив корзин\n    #TOMBSTONE; // Удалить метку\n\n    /* Конструктор */\n    constructor() {\n        this.#size = 0; // Число пар ключ-значение\n        this.#capacity = 4; // Вместимость хеш-таблицы\n        this.#loadThres = 2.0 / 3.0; // Порог коэффициента загрузки для запуска расширения\n        this.#extendRatio = 2; // Коэффициент расширения\n        this.#buckets = Array(this.#capacity).fill(null); // Массив корзин\n        this.#TOMBSTONE = new Pair(-1, '-1'); // Удалить метку\n    }\n\n    /* Хеш-функция */\n    #hashFunc(key) {\n        return key % this.#capacity;\n    }\n\n    /* Коэффициент загрузки */\n    #loadFactor() {\n        return this.#size / this.#capacity;\n    }\n\n    /* Найти индекс корзины, соответствующий key */\n    #findBucket(key) {\n        let index = this.#hashFunc(key);\n        let firstTombstone = -1;\n        // Выполнять линейное пробирование и завершить при встрече с пустой корзиной\n        while (this.#buckets[index] !== null) {\n            // Если встретился key, вернуть соответствующий индекс корзины\n            if (this.#buckets[index].key === key) {\n                // Если ранее встретилась метка удаления, переместить пару ключ-значение на этот индекс\n                if (firstTombstone !== -1) {\n                    this.#buckets[firstTombstone] = this.#buckets[index];\n                    this.#buckets[index] = this.#TOMBSTONE;\n                    return firstTombstone; // Вернуть индекс корзины после перемещения\n                }\n                return index; // Вернуть индекс корзины\n            }\n            // Записать первую встретившуюся метку удаления\n            if (\n                firstTombstone === -1 &amp;&amp;\n                this.#buckets[index] === this.#TOMBSTONE\n            ) {\n                firstTombstone = index;\n            }\n            // Вычислить индекс корзины; при выходе за конец вернуться к началу\n            index = (index + 1) % this.#capacity;\n        }\n        // Если key не существует, вернуть индекс точки добавления\n        return firstTombstone === -1 ? index : firstTombstone;\n    }\n\n    /* Операция поиска */\n    get(key) {\n        // Найти индекс корзины, соответствующий key\n        const index = this.#findBucket(key);\n        // Если пара ключ-значение найдена, вернуть соответствующее val\n        if (\n            this.#buckets[index] !== null &amp;&amp;\n            this.#buckets[index] !== this.#TOMBSTONE\n        ) {\n            return this.#buckets[index].val;\n        }\n        // Если пары ключ-значение не существует, вернуть null\n        return null;\n    }\n\n    /* Операция добавления */\n    put(key, val) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if (this.#loadFactor() &gt; this.#loadThres) {\n            this.#extend();\n        }\n        // Найти индекс корзины, соответствующий key\n        const index = this.#findBucket(key);\n        // Если пара ключ-значение найдена, перезаписать val и вернуть\n        if (\n            this.#buckets[index] !== null &amp;&amp;\n            this.#buckets[index] !== this.#TOMBSTONE\n        ) {\n            this.#buckets[index].val = val;\n            return;\n        }\n        // Если пары ключ-значение нет, добавить ее\n        this.#buckets[index] = new Pair(key, val);\n        this.#size++;\n    }\n\n    /* Операция удаления */\n    remove(key) {\n        // Найти индекс корзины, соответствующий key\n        const index = this.#findBucket(key);\n        // Если пара ключ-значение найдена, заменить ее меткой удаления\n        if (\n            this.#buckets[index] !== null &amp;&amp;\n            this.#buckets[index] !== this.#TOMBSTONE\n        ) {\n            this.#buckets[index] = this.#TOMBSTONE;\n            this.#size--;\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    #extend() {\n        // Временно сохранить исходную хеш-таблицу\n        const bucketsTmp = this.#buckets;\n        // Инициализация новой хеш-таблицы после расширения\n        this.#capacity *= this.#extendRatio;\n        this.#buckets = Array(this.#capacity).fill(null);\n        this.#size = 0;\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for (const pair of bucketsTmp) {\n            if (pair !== null &amp;&amp; pair !== this.#TOMBSTONE) {\n                this.put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    print() {\n        for (const pair of this.#buckets) {\n            if (pair === null) {\n                console.log('null');\n            } else if (pair === this.#TOMBSTONE) {\n                console.log('TOMBSTONE');\n            } else {\n                console.log(pair.key + ' -&gt; ' + pair.val);\n            }\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.ts<pre><code>/* Хеш-таблица с открытой адресацией */\nclass HashMapOpenAddressing {\n    private size: number; // Число пар ключ-значение\n    private capacity: number; // Вместимость хеш-таблицы\n    private loadThres: number; // Порог коэффициента загрузки для запуска расширения\n    private extendRatio: number; // Коэффициент расширения\n    private buckets: Array&lt;Pair | null&gt;; // Массив корзин\n    private TOMBSTONE: Pair; // Удалить метку\n\n    /* Конструктор */\n    constructor() {\n        this.size = 0; // Число пар ключ-значение\n        this.capacity = 4; // Вместимость хеш-таблицы\n        this.loadThres = 2.0 / 3.0; // Порог коэффициента загрузки для запуска расширения\n        this.extendRatio = 2; // Коэффициент расширения\n        this.buckets = Array(this.capacity).fill(null); // Массив корзин\n        this.TOMBSTONE = new Pair(-1, '-1'); // Удалить метку\n    }\n\n    /* Хеш-функция */\n    private hashFunc(key: number): number {\n        return key % this.capacity;\n    }\n\n    /* Коэффициент загрузки */\n    private loadFactor(): number {\n        return this.size / this.capacity;\n    }\n\n    /* Найти индекс корзины, соответствующий key */\n    private findBucket(key: number): number {\n        let index = this.hashFunc(key);\n        let firstTombstone = -1;\n        // Выполнять линейное пробирование и завершить при встрече с пустой корзиной\n        while (this.buckets[index] !== null) {\n            // Если встретился key, вернуть соответствующий индекс корзины\n            if (this.buckets[index]!.key === key) {\n                // Если ранее встретилась метка удаления, переместить пару ключ-значение на этот индекс\n                if (firstTombstone !== -1) {\n                    this.buckets[firstTombstone] = this.buckets[index];\n                    this.buckets[index] = this.TOMBSTONE;\n                    return firstTombstone; // Вернуть индекс корзины после перемещения\n                }\n                return index; // Вернуть индекс корзины\n            }\n            // Записать первую встретившуюся метку удаления\n            if (\n                firstTombstone === -1 &amp;&amp;\n                this.buckets[index] === this.TOMBSTONE\n            ) {\n                firstTombstone = index;\n            }\n            // Вычислить индекс корзины; при выходе за конец вернуться к началу\n            index = (index + 1) % this.capacity;\n        }\n        // Если key не существует, вернуть индекс точки добавления\n        return firstTombstone === -1 ? index : firstTombstone;\n    }\n\n    /* Операция поиска */\n    get(key: number): string | null {\n        // Найти индекс корзины, соответствующий key\n        const index = this.findBucket(key);\n        // Если пара ключ-значение найдена, вернуть соответствующее val\n        if (\n            this.buckets[index] !== null &amp;&amp;\n            this.buckets[index] !== this.TOMBSTONE\n        ) {\n            return this.buckets[index]!.val;\n        }\n        // Если пары ключ-значение не существует, вернуть null\n        return null;\n    }\n\n    /* Операция добавления */\n    put(key: number, val: string): void {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if (this.loadFactor() &gt; this.loadThres) {\n            this.extend();\n        }\n        // Найти индекс корзины, соответствующий key\n        const index = this.findBucket(key);\n        // Если пара ключ-значение найдена, перезаписать val и вернуть\n        if (\n            this.buckets[index] !== null &amp;&amp;\n            this.buckets[index] !== this.TOMBSTONE\n        ) {\n            this.buckets[index]!.val = val;\n            return;\n        }\n        // Если пары ключ-значение нет, добавить ее\n        this.buckets[index] = new Pair(key, val);\n        this.size++;\n    }\n\n    /* Операция удаления */\n    remove(key: number): void {\n        // Найти индекс корзины, соответствующий key\n        const index = this.findBucket(key);\n        // Если пара ключ-значение найдена, заменить ее меткой удаления\n        if (\n            this.buckets[index] !== null &amp;&amp;\n            this.buckets[index] !== this.TOMBSTONE\n        ) {\n            this.buckets[index] = this.TOMBSTONE;\n            this.size--;\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    private extend(): void {\n        // Временно сохранить исходную хеш-таблицу\n        const bucketsTmp = this.buckets;\n        // Инициализация новой хеш-таблицы после расширения\n        this.capacity *= this.extendRatio;\n        this.buckets = Array(this.capacity).fill(null);\n        this.size = 0;\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for (const pair of bucketsTmp) {\n            if (pair !== null &amp;&amp; pair !== this.TOMBSTONE) {\n                this.put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    print(): void {\n        for (const pair of this.buckets) {\n            if (pair === null) {\n                console.log('null');\n            } else if (pair === this.TOMBSTONE) {\n                console.log('TOMBSTONE');\n            } else {\n                console.log(pair.key + ' -&gt; ' + pair.val);\n            }\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.dart<pre><code>/* Хеш-таблица с открытой адресацией */\nclass HashMapOpenAddressing {\n  late int _size; // Число пар ключ-значение\n  int _capacity = 4; // Вместимость хеш-таблицы\n  double _loadThres = 2.0 / 3.0; // Порог коэффициента загрузки для запуска расширения\n  int _extendRatio = 2; // Коэффициент расширения\n  late List&lt;Pair?&gt; _buckets; // Массив корзин\n  Pair _TOMBSTONE = Pair(-1, \"-1\"); // Удалить метку\n\n  /* Конструктор */\n  HashMapOpenAddressing() {\n    _size = 0;\n    _buckets = List.generate(_capacity, (index) =&gt; null);\n  }\n\n  /* Хеш-функция */\n  int hashFunc(int key) {\n    return key % _capacity;\n  }\n\n  /* Коэффициент загрузки */\n  double loadFactor() {\n    return _size / _capacity;\n  }\n\n  /* Найти индекс корзины, соответствующий key */\n  int findBucket(int key) {\n    int index = hashFunc(key);\n    int firstTombstone = -1;\n    // Выполнять линейное пробирование и завершить при встрече с пустой корзиной\n    while (_buckets[index] != null) {\n      // Если встретился key, вернуть соответствующий индекс корзины\n      if (_buckets[index]!.key == key) {\n        // Если ранее встретилась метка удаления, переместить пару ключ-значение на этот индекс\n        if (firstTombstone != -1) {\n          _buckets[firstTombstone] = _buckets[index];\n          _buckets[index] = _TOMBSTONE;\n          return firstTombstone; // Вернуть индекс корзины после перемещения\n        }\n        return index; // Вернуть индекс корзины\n      }\n      // Записать первую встретившуюся метку удаления\n      if (firstTombstone == -1 &amp;&amp; _buckets[index] == _TOMBSTONE) {\n        firstTombstone = index;\n      }\n      // Вычислить индекс корзины; при выходе за конец вернуться к началу\n      index = (index + 1) % _capacity;\n    }\n    // Если key не существует, вернуть индекс точки добавления\n    return firstTombstone == -1 ? index : firstTombstone;\n  }\n\n  /* Операция поиска */\n  String? get(int key) {\n    // Найти индекс корзины, соответствующий key\n    int index = findBucket(key);\n    // Если пара ключ-значение найдена, вернуть соответствующее val\n    if (_buckets[index] != null &amp;&amp; _buckets[index] != _TOMBSTONE) {\n      return _buckets[index]!.val;\n    }\n    // Если пары ключ-значение не существует, вернуть null\n    return null;\n  }\n\n  /* Операция добавления */\n  void put(int key, String val) {\n    // Когда коэффициент загрузки превышает порог, выполнить расширение\n    if (loadFactor() &gt; _loadThres) {\n      extend();\n    }\n    // Найти индекс корзины, соответствующий key\n    int index = findBucket(key);\n    // Если пара ключ-значение найдена, перезаписать val и вернуть\n    if (_buckets[index] != null &amp;&amp; _buckets[index] != _TOMBSTONE) {\n      _buckets[index]!.val = val;\n      return;\n    }\n    // Если пары ключ-значение нет, добавить ее\n    _buckets[index] = new Pair(key, val);\n    _size++;\n  }\n\n  /* Операция удаления */\n  void remove(int key) {\n    // Найти индекс корзины, соответствующий key\n    int index = findBucket(key);\n    // Если пара ключ-значение найдена, заменить ее меткой удаления\n    if (_buckets[index] != null &amp;&amp; _buckets[index] != _TOMBSTONE) {\n      _buckets[index] = _TOMBSTONE;\n      _size--;\n    }\n  }\n\n  /* Расширить хеш-таблицу */\n  void extend() {\n    // Временно сохранить исходную хеш-таблицу\n    List&lt;Pair?&gt; bucketsTmp = _buckets;\n    // Инициализация новой хеш-таблицы после расширения\n    _capacity *= _extendRatio;\n    _buckets = List.generate(_capacity, (index) =&gt; null);\n    _size = 0;\n    // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n    for (Pair? pair in bucketsTmp) {\n      if (pair != null &amp;&amp; pair != _TOMBSTONE) {\n        put(pair.key, pair.val);\n      }\n    }\n  }\n\n  /* Вывести хеш-таблицу */\n  void printHashMap() {\n    for (Pair? pair in _buckets) {\n      if (pair == null) {\n        print(\"null\");\n      } else if (pair == _TOMBSTONE) {\n        print(\"TOMBSTONE\");\n      } else {\n        print(\"${pair.key} -&gt; ${pair.val}\");\n      }\n    }\n  }\n}\n</code></pre> hash_map_open_addressing.rs<pre><code>/* Хеш-таблица с открытой адресацией */\nstruct HashMapOpenAddressing {\n    size: usize,                // Число пар ключ-значение\n    capacity: usize,            // Вместимость хеш-таблицы\n    load_thres: f64,            // Порог коэффициента загрузки для запуска расширения\n    extend_ratio: usize,        // Коэффициент расширения\n    buckets: Vec&lt;Option&lt;Pair&gt;&gt;, // Массив корзин\n    TOMBSTONE: Option&lt;Pair&gt;,    // Удалить метку\n}\n\nimpl HashMapOpenAddressing {\n    /* Конструктор */\n    fn new() -&gt; Self {\n        Self {\n            size: 0,\n            capacity: 4,\n            load_thres: 2.0 / 3.0,\n            extend_ratio: 2,\n            buckets: vec![None; 4],\n            TOMBSTONE: Some(Pair {\n                key: -1,\n                val: \"-1\".to_string(),\n            }),\n        }\n    }\n\n    /* Хеш-функция */\n    fn hash_func(&amp;self, key: i32) -&gt; usize {\n        (key % self.capacity as i32) as usize\n    }\n\n    /* Коэффициент загрузки */\n    fn load_factor(&amp;self) -&gt; f64 {\n        self.size as f64 / self.capacity as f64\n    }\n\n    /* Найти индекс корзины, соответствующий key */\n    fn find_bucket(&amp;mut self, key: i32) -&gt; usize {\n        let mut index = self.hash_func(key);\n        let mut first_tombstone = -1;\n        // Выполнять линейное пробирование и завершить при встрече с пустой корзиной\n        while self.buckets[index].is_some() {\n            // Если встретился key, вернуть соответствующий индекс корзины\n            if self.buckets[index].as_ref().unwrap().key == key {\n                // Если ранее встретилась метка удаления, переместить пару ключ-значение в этот индекс\n                if first_tombstone != -1 {\n                    self.buckets[first_tombstone as usize] = self.buckets[index].take();\n                    self.buckets[index] = self.TOMBSTONE.clone();\n                    return first_tombstone as usize; // Вернуть индекс корзины после перемещения\n                }\n                return index; // Вернуть индекс корзины\n            }\n            // Записать первую встретившуюся метку удаления\n            if first_tombstone == -1 &amp;&amp; self.buckets[index] == self.TOMBSTONE {\n                first_tombstone = index as i32;\n            }\n            // Вычислить индекс корзины; при выходе за конец вернуться к началу\n            index = (index + 1) % self.capacity;\n        }\n        // Если key не существует, вернуть индекс точки добавления\n        if first_tombstone == -1 {\n            index\n        } else {\n            first_tombstone as usize\n        }\n    }\n\n    /* Операция поиска */\n    fn get(&amp;mut self, key: i32) -&gt; Option&lt;&amp;str&gt; {\n        // Найти индекс корзины, соответствующий key\n        let index = self.find_bucket(key);\n        // Если пара ключ-значение найдена, вернуть соответствующее val\n        if self.buckets[index].is_some() &amp;&amp; self.buckets[index] != self.TOMBSTONE {\n            return self.buckets[index].as_ref().map(|pair| &amp;pair.val as &amp;str);\n        }\n        // Если пары ключ-значение не существует, вернуть null\n        None\n    }\n\n    /* Операция добавления */\n    fn put(&amp;mut self, key: i32, val: String) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if self.load_factor() &gt; self.load_thres {\n            self.extend();\n        }\n        // Найти индекс корзины, соответствующий key\n        let index = self.find_bucket(key);\n        // Если пара ключ-значение найдена, перезаписать val и вернуть\n        if self.buckets[index].is_some() &amp;&amp; self.buckets[index] != self.TOMBSTONE {\n            self.buckets[index].as_mut().unwrap().val = val;\n            return;\n        }\n        // Если пары ключ-значение нет, добавить ее\n        self.buckets[index] = Some(Pair { key, val });\n        self.size += 1;\n    }\n\n    /* Операция удаления */\n    fn remove(&amp;mut self, key: i32) {\n        // Найти индекс корзины, соответствующий key\n        let index = self.find_bucket(key);\n        // Если пара ключ-значение найдена, заменить ее меткой удаления\n        if self.buckets[index].is_some() &amp;&amp; self.buckets[index] != self.TOMBSTONE {\n            self.buckets[index] = self.TOMBSTONE.clone();\n            self.size -= 1;\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    fn extend(&amp;mut self) {\n        // Временно сохранить исходную хеш-таблицу\n        let buckets_tmp = self.buckets.clone();\n        // Инициализация новой хеш-таблицы после расширения\n        self.capacity *= self.extend_ratio;\n        self.buckets = vec![None; self.capacity];\n        self.size = 0;\n\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for pair in buckets_tmp {\n            if pair.is_none() || pair == self.TOMBSTONE {\n                continue;\n            }\n            let pair = pair.unwrap();\n\n            self.put(pair.key, pair.val);\n        }\n    }\n    /* Вывести хеш-таблицу */\n    fn print(&amp;self) {\n        for pair in &amp;self.buckets {\n            if pair.is_none() {\n                println!(\"null\");\n            } else if pair == &amp;self.TOMBSTONE {\n                println!(\"TOMBSTONE\");\n            } else {\n                let pair = pair.as_ref().unwrap();\n                println!(\"{} -&gt; {}\", pair.key, pair.val);\n            }\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.c<pre><code>/* Хеш-таблица с открытой адресацией */\ntypedef struct {\n    int size;         // Число пар ключ-значение\n    int capacity;     // Вместимость хеш-таблицы\n    double loadThres; // Порог коэффициента загрузки для запуска расширения\n    int extendRatio;  // Коэффициент расширения\n    Pair **buckets;   // Массив корзин\n    Pair *TOMBSTONE;  // Удалить метку\n} HashMapOpenAddressing;\n\n/* Конструктор */\nHashMapOpenAddressing *newHashMapOpenAddressing() {\n    HashMapOpenAddressing *hashMap = (HashMapOpenAddressing *)malloc(sizeof(HashMapOpenAddressing));\n    hashMap-&gt;size = 0;\n    hashMap-&gt;capacity = 4;\n    hashMap-&gt;loadThres = 2.0 / 3.0;\n    hashMap-&gt;extendRatio = 2;\n    hashMap-&gt;buckets = (Pair **)calloc(hashMap-&gt;capacity, sizeof(Pair *));\n    hashMap-&gt;TOMBSTONE = (Pair *)malloc(sizeof(Pair));\n    hashMap-&gt;TOMBSTONE-&gt;key = -1;\n    hashMap-&gt;TOMBSTONE-&gt;val = \"-1\";\n\n    return hashMap;\n}\n\n/* Деструктор */\nvoid delHashMapOpenAddressing(HashMapOpenAddressing *hashMap) {\n    for (int i = 0; i &lt; hashMap-&gt;capacity; i++) {\n        Pair *pair = hashMap-&gt;buckets[i];\n        if (pair != NULL &amp;&amp; pair != hashMap-&gt;TOMBSTONE) {\n            free(pair-&gt;val);\n            free(pair);\n        }\n    }\n    free(hashMap-&gt;buckets);\n    free(hashMap-&gt;TOMBSTONE);\n    free(hashMap);\n}\n\n/* Хеш-функция */\nint hashFunc(HashMapOpenAddressing *hashMap, int key) {\n    return key % hashMap-&gt;capacity;\n}\n\n/* Коэффициент загрузки */\ndouble loadFactor(HashMapOpenAddressing *hashMap) {\n    return (double)hashMap-&gt;size / (double)hashMap-&gt;capacity;\n}\n\n/* Найти индекс корзины, соответствующий key */\nint findBucket(HashMapOpenAddressing *hashMap, int key) {\n    int index = hashFunc(hashMap, key);\n    int firstTombstone = -1;\n    // Выполнять линейное пробирование и завершить при встрече с пустой корзиной\n    while (hashMap-&gt;buckets[index] != NULL) {\n        // Если встретился key, вернуть соответствующий индекс корзины\n        if (hashMap-&gt;buckets[index]-&gt;key == key) {\n            // Если ранее встретилась метка удаления, переместить пару ключ-значение на этот индекс\n            if (firstTombstone != -1) {\n                hashMap-&gt;buckets[firstTombstone] = hashMap-&gt;buckets[index];\n                hashMap-&gt;buckets[index] = hashMap-&gt;TOMBSTONE;\n                return firstTombstone; // Вернуть индекс корзины после перемещения\n            }\n            return index; // Вернуть индекс корзины\n        }\n        // Записать первую встретившуюся метку удаления\n        if (firstTombstone == -1 &amp;&amp; hashMap-&gt;buckets[index] == hashMap-&gt;TOMBSTONE) {\n            firstTombstone = index;\n        }\n        // Вычислить индекс корзины; при выходе за конец вернуться к началу\n        index = (index + 1) % hashMap-&gt;capacity;\n    }\n    // Если key не существует, вернуть индекс точки добавления\n    return firstTombstone == -1 ? index : firstTombstone;\n}\n\n/* Операция поиска */\nchar *get(HashMapOpenAddressing *hashMap, int key) {\n    // Найти индекс корзины, соответствующий key\n    int index = findBucket(hashMap, key);\n    // Если пара ключ-значение найдена, вернуть соответствующее val\n    if (hashMap-&gt;buckets[index] != NULL &amp;&amp; hashMap-&gt;buckets[index] != hashMap-&gt;TOMBSTONE) {\n        return hashMap-&gt;buckets[index]-&gt;val;\n    }\n    // Если пары ключ-значение не существует, вернуть пустую строку\n    return \"\";\n}\n\n/* Операция добавления */\nvoid put(HashMapOpenAddressing *hashMap, int key, char *val) {\n    // Когда коэффициент загрузки превышает порог, выполнить расширение\n    if (loadFactor(hashMap) &gt; hashMap-&gt;loadThres) {\n        extend(hashMap);\n    }\n    // Найти индекс корзины, соответствующий key\n    int index = findBucket(hashMap, key);\n    // Если пара ключ-значение найдена, перезаписать val и вернуть\n    if (hashMap-&gt;buckets[index] != NULL &amp;&amp; hashMap-&gt;buckets[index] != hashMap-&gt;TOMBSTONE) {\n        free(hashMap-&gt;buckets[index]-&gt;val);\n        hashMap-&gt;buckets[index]-&gt;val = (char *)malloc(sizeof(strlen(val) + 1));\n        strcpy(hashMap-&gt;buckets[index]-&gt;val, val);\n        hashMap-&gt;buckets[index]-&gt;val[strlen(val)] = '\\0';\n        return;\n    }\n    // Если пары ключ-значение нет, добавить ее\n    Pair *pair = (Pair *)malloc(sizeof(Pair));\n    pair-&gt;key = key;\n    pair-&gt;val = (char *)malloc(sizeof(strlen(val) + 1));\n    strcpy(pair-&gt;val, val);\n    pair-&gt;val[strlen(val)] = '\\0';\n\n    hashMap-&gt;buckets[index] = pair;\n    hashMap-&gt;size++;\n}\n\n/* Операция удаления */\nvoid removeItem(HashMapOpenAddressing *hashMap, int key) {\n    // Найти индекс корзины, соответствующий key\n    int index = findBucket(hashMap, key);\n    // Если пара ключ-значение найдена, заменить ее меткой удаления\n    if (hashMap-&gt;buckets[index] != NULL &amp;&amp; hashMap-&gt;buckets[index] != hashMap-&gt;TOMBSTONE) {\n        Pair *pair = hashMap-&gt;buckets[index];\n        free(pair-&gt;val);\n        free(pair);\n        hashMap-&gt;buckets[index] = hashMap-&gt;TOMBSTONE;\n        hashMap-&gt;size--;\n    }\n}\n\n/* Расширить хеш-таблицу */\nvoid extend(HashMapOpenAddressing *hashMap) {\n    // Временно сохранить исходную хеш-таблицу\n    Pair **bucketsTmp = hashMap-&gt;buckets;\n    int oldCapacity = hashMap-&gt;capacity;\n    // Инициализация новой хеш-таблицы после расширения\n    hashMap-&gt;capacity *= hashMap-&gt;extendRatio;\n    hashMap-&gt;buckets = (Pair **)calloc(hashMap-&gt;capacity, sizeof(Pair *));\n    hashMap-&gt;size = 0;\n    // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n    for (int i = 0; i &lt; oldCapacity; i++) {\n        Pair *pair = bucketsTmp[i];\n        if (pair != NULL &amp;&amp; pair != hashMap-&gt;TOMBSTONE) {\n            put(hashMap, pair-&gt;key, pair-&gt;val);\n            free(pair-&gt;val);\n            free(pair);\n        }\n    }\n    free(bucketsTmp);\n}\n\n/* Вывести хеш-таблицу */\nvoid print(HashMapOpenAddressing *hashMap) {\n    for (int i = 0; i &lt; hashMap-&gt;capacity; i++) {\n        Pair *pair = hashMap-&gt;buckets[i];\n        if (pair == NULL) {\n            printf(\"NULL\\n\");\n        } else if (pair == hashMap-&gt;TOMBSTONE) {\n            printf(\"TOMBSTONE\\n\");\n        } else {\n            printf(\"%d -&gt; %s\\n\", pair-&gt;key, pair-&gt;val);\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.kt<pre><code>/* Хеш-таблица с открытой адресацией */\nclass HashMapOpenAddressing {\n    private var size: Int               // Число пар ключ-значение\n    private var capacity: Int           // Вместимость хеш-таблицы\n    private val loadThres: Double       // Порог коэффициента загрузки для запуска расширения\n    private val extendRatio: Int        // Коэффициент расширения\n    private var buckets: Array&lt;Pair?&gt;   // Массив корзин\n    private val TOMBSTONE: Pair         // Удалить метку\n\n    /* Конструктор */\n    init {\n        size = 0\n        capacity = 4\n        loadThres = 2.0 / 3.0\n        extendRatio = 2\n        buckets = arrayOfNulls(capacity)\n        TOMBSTONE = Pair(-1, \"-1\")\n    }\n\n    /* Хеш-функция */\n    fun hashFunc(key: Int): Int {\n        return key % capacity\n    }\n\n    /* Коэффициент загрузки */\n    fun loadFactor(): Double {\n        return (size / capacity).toDouble()\n    }\n\n    /* Найти индекс корзины, соответствующий key */\n    fun findBucket(key: Int): Int {\n        var index = hashFunc(key)\n        var firstTombstone = -1\n        // Выполнять линейное пробирование и завершить при встрече с пустой корзиной\n        while (buckets[index] != null) {\n            // Если встретился key, вернуть соответствующий индекс корзины\n            if (buckets[index]?.key == key) {\n                // Если ранее встретилась метка удаления, переместить пару ключ-значение на этот индекс\n                if (firstTombstone != -1) {\n                    buckets[firstTombstone] = buckets[index]\n                    buckets[index] = TOMBSTONE\n                    return firstTombstone // Вернуть индекс корзины после перемещения\n                }\n                return index // Вернуть индекс корзины\n            }\n            // Записать первую встретившуюся метку удаления\n            if (firstTombstone == -1 &amp;&amp; buckets[index] == TOMBSTONE) {\n                firstTombstone = index\n            }\n            // Вычислить индекс корзины; при выходе за конец вернуться к началу\n            index = (index + 1) % capacity\n        }\n        // Если key не существует, вернуть индекс точки добавления\n        return if (firstTombstone == -1) index else firstTombstone\n    }\n\n    /* Операция поиска */\n    fun get(key: Int): String? {\n        // Найти индекс корзины, соответствующий key\n        val index = findBucket(key)\n        // Если пара ключ-значение найдена, вернуть соответствующее val\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            return buckets[index]?._val\n        }\n        // Если пары ключ-значение не существует, вернуть null\n        return null\n    }\n\n    /* Операция добавления */\n    fun put(key: Int, _val: String) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if (loadFactor() &gt; loadThres) {\n            extend()\n        }\n        // Найти индекс корзины, соответствующий key\n        val index = findBucket(key)\n        // Если пара ключ-значение найдена, перезаписать val и вернуть\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index]!!._val = _val\n            return\n        }\n        // Если пары ключ-значение нет, добавить ее\n        buckets[index] = Pair(key, _val)\n        size++\n    }\n\n    /* Операция удаления */\n    fun remove(key: Int) {\n        // Найти индекс корзины, соответствующий key\n        val index = findBucket(key)\n        // Если пара ключ-значение найдена, заменить ее меткой удаления\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index] = TOMBSTONE\n            size--\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    fun extend() {\n        // Временно сохранить исходную хеш-таблицу\n        val bucketsTmp = buckets\n        // Инициализация новой хеш-таблицы после расширения\n        capacity *= extendRatio\n        buckets = arrayOfNulls(capacity)\n        size = 0\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for (pair in bucketsTmp) {\n            if (pair != null &amp;&amp; pair != TOMBSTONE) {\n                put(pair.key, pair._val)\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    fun print() {\n        for (pair in buckets) {\n            if (pair == null) {\n                println(\"null\")\n            } else if (pair == TOMBSTONE) {\n                println(\"TOMESTOME\")\n            } else {\n                println(\"${pair.key} -&gt; ${pair._val}\")\n            }\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.rb<pre><code>### Хеш-таблица с открытой адресацией ###\nclass HashMapOpenAddressing\n  TOMBSTONE = Pair.new(-1, '-1') # Удалить метку\n\n  ### Конструктор ###\n  def initialize\n    @size = 0 # Число пар ключ-значение\n    @capacity = 4 # Вместимость хеш-таблицы\n    @load_thres = 2.0 / 3.0 # Порог коэффициента загрузки для запуска расширения\n    @extend_ratio = 2 # Коэффициент расширения\n    @buckets = Array.new(@capacity) # Массив корзин\n  end\n\n  ### Хеш-функция ###\n  def hash_func(key)\n    key % @capacity\n  end\n\n  ### Коэффициент загрузки ###\n  def load_factor\n    @size / @capacity\n  end\n\n  ### Найти индекс корзины, соответствующий key ###\n  def find_bucket(key)\n    index = hash_func(key)\n    first_tombstone = -1\n    # Выполнять линейное пробирование и завершить при встрече с пустой корзиной\n    while !@buckets[index].nil?\n      # Если встретился key, вернуть соответствующий индекс корзины\n      if @buckets[index].key == key\n        # Если ранее встретилась метка удаления, переместить пару ключ-значение на этот индекс\n        if first_tombstone != -1\n          @buckets[first_tombstone] = @buckets[index]\n          @buckets[index] = TOMBSTONE\n          return first_tombstone # Вернуть индекс корзины после перемещения\n        end\n        return index # Вернуть индекс корзины\n      end\n      # Записать первую встретившуюся метку удаления\n      first_tombstone = index if first_tombstone == -1 &amp;&amp; @buckets[index] == TOMBSTONE\n      # Вычислить индекс корзины; при выходе за конец вернуться к началу\n      index = (index + 1) % @capacity\n    end\n    # Если key не существует, вернуть индекс точки добавления\n    first_tombstone == -1 ? index : first_tombstone\n  end\n\n  ### Операция поиска ###\n  def get(key)\n    # Найти индекс корзины, соответствующий key\n    index = find_bucket(key)\n    # Если пара ключ-значение найдена, вернуть соответствующее val\n    return @buckets[index].val unless [nil, TOMBSTONE].include?(@buckets[index])\n    # Если пара ключ-значение не существует, вернуть nil\n    nil\n  end\n\n  ### Операция добавления ###\n  def put(key, val)\n    # Когда коэффициент загрузки превышает порог, выполнить расширение\n    extend if load_factor &gt; @load_thres\n    # Найти индекс корзины, соответствующий key\n    index = find_bucket(key)\n    # Если пара ключ-значение найдена, перезаписать val и вернуть\n    unless [nil, TOMBSTONE].include?(@buckets[index])\n      @buckets[index].val = val\n      return\n    end\n    # Если пары ключ-значение нет, добавить ее\n    @buckets[index] = Pair.new(key, val)\n    @size += 1\n  end\n\n  ### Операция удаления ###\n  def remove(key)\n    # Найти индекс корзины, соответствующий key\n    index = find_bucket(key)\n    # Если пара ключ-значение найдена, заменить ее меткой удаления\n    unless [nil, TOMBSTONE].include?(@buckets[index])\n      @buckets[index] = TOMBSTONE\n      @size -= 1\n    end\n  end\n\n  ### Расширение хеш-таблицы ###\n  def extend\n    # Временно сохранить исходную хеш-таблицу\n    buckets_tmp = @buckets\n    # Инициализация новой хеш-таблицы после расширения\n    @capacity *= @extend_ratio\n    @buckets = Array.new(@capacity)\n    @size = 0\n    # Перенести пары ключ-значение из исходной хеш-таблицы в новую\n    for pair in buckets_tmp\n      put(pair.key, pair.val) unless [nil, TOMBSTONE].include?(pair)\n    end\n  end\n\n  ### Вывести хеш-таблицу ###\n  def print\n    for pair in @buckets\n      if pair.nil?\n        puts \"Nil\"\n      elsif pair == TOMBSTONE\n        puts \"TOMBSTONE\"\n      else\n        puts \"#{pair.key} -&gt; #{pair.val}\"\n      end\n    end\n  end\nend\n</code></pre>","path":["Глава 6. Хеширование","6.2 &nbsp; Хеш-коллизии"],"tags":[]},{"location":"chapter_hashing/hash_collision/#2","level":3,"title":"2.   Квадратичное пробирование","text":"<p>Квадратичное пробирование похоже на линейное пробирование и тоже является одной из распространенных стратегий открытой адресации. При возникновении конфликта оно не пропускает фиксированное число шагов, а переходит на расстояние, равное \"квадрату числа попыток\", то есть на \\(1, 4, 9, \\dots\\) шагов.</p> <p>Квадратичное пробирование имеет следующие основные преимущества.</p> <ul> <li>Квадратичное пробирование пытается смягчить эффект кластеризации линейного пробирования, так как пропускает расстояния, равные квадрату номера попытки.</li> <li>Квадратичное пробирование перепрыгивает на более дальние позиции в поисках свободного места, что помогает распределять данные более равномерно.</li> </ul> <p>Однако квадратичное пробирование не является идеальным.</p> <ul> <li>Кластеризация все равно существует: некоторые позиции по-прежнему занимают чаще других.</li> <li>Из-за быстрого роста квадрата квадратичное пробирование может не охватить всю хеш-таблицу, а это означает, что даже при наличии пустых бакетов оно может так до них и не добраться.</li> </ul>","path":["Глава 6. Хеширование","6.2 &nbsp; Хеш-коллизии"],"tags":[]},{"location":"chapter_hashing/hash_collision/#3","level":3,"title":"3.   Повторное хеширование","text":"<p>Как видно из названия, метод повторного хеширования использует для пробирования несколько хеш-функций \\(f_1(x)\\), \\(f_2(x)\\), \\(f_3(x)\\), \\(\\dots\\) .</p> <ul> <li>Вставка элемента: если хеш-функция \\(f_1(x)\\) вызывает конфликт, то пробуем \\(f_2(x)\\) , и так далее, пока не будет найдено пустое место для вставки элемента.</li> <li>Поиск элемента: поиск идет в том же порядке хеш-функций, пока не будет найден целевой элемент; если встречается пустая позиция или уже были опробованы все хеш-функции, это означает, что элемента в хеш-таблице нет, и возвращается <code>None</code> .</li> </ul> <p>По сравнению с линейным пробированием метод повторного хеширования меньше подвержен кластеризации, но несколько хеш-функций приносят дополнительные вычислительные затраты.</p> <p>Tip</p> <p>Обрати внимание: у хеш-таблиц с открытой адресацией (линейное пробирование, квадратичное пробирование и повторное хеширование) есть общая проблема: в них нельзя напрямую удалять элементы.</p>","path":["Глава 6. Хеширование","6.2 &nbsp; Хеш-коллизии"],"tags":[]},{"location":"chapter_hashing/hash_collision/#623","level":2,"title":"6.2.3   Выбор в языках программирования","text":"<p>Разные языки программирования используют разные стратегии реализации хеш-таблиц. Ниже приведено несколько примеров.</p> <ul> <li>Python использует открытую адресацию. В словаре <code>dict</code> для пробирования применяются псевдослучайные числа.</li> <li>Java использует метод цепочек. Начиная с JDK 1.8, когда длина массива внутри <code>HashMap</code> достигает 64, а длина списка достигает 8, этот список преобразуется в красно-черное дерево для повышения производительности поиска.</li> <li>Go использует метод цепочек. В Go установлено, что каждый бакет может хранить не более 8 пар ключ-значение; при переполнении подключается overflow-bucket, а когда таких bucket становится слишком много, выполняется специальное расширение того же масштаба, чтобы сохранить производительность.</li> </ul>","path":["Глава 6. Хеширование","6.2 &nbsp; Хеш-коллизии"],"tags":[]},{"location":"chapter_hashing/hash_map/","level":1,"title":"6.1   Хеш-таблица","text":"<p>Хеш-таблица (hash table), также называемая таблицей рассеяния, обеспечивает эффективный поиск элементов за счет отображения между ключом <code>key</code> и значением <code>value</code> . Иначе говоря, если передать в хеш-таблицу ключ <code>key</code> , то можно за \\(O(1)\\) времени получить соответствующее значение <code>value</code> .</p> <p>Как показано на рисунке 6-1, пусть есть \\(n\\) студентов, и у каждого из них есть два поля данных: \"имя\" и \"номер студенческого билета\". Если мы хотим реализовать запрос вида \"ввести номер студенческого билета и вернуть соответствующее имя\", то для этого можно использовать показанную ниже хеш-таблицу.</p> <p></p> <p> Рисунок 6-1   Абстрактное представление хеш-таблицы </p> <p>Помимо хеш-таблицы, функции поиска можно реализовать и через массив, и через связный список. Сравнение их эффективности приведено в таблице 6-1.</p> <ul> <li>Добавление элемента: нужно лишь добавить элемент в конец массива (или списка), что занимает \\(O(1)\\) времени.</li> <li>Поиск элемента: так как массив (или список) неупорядочен, приходится обходить все элементы, что занимает \\(O(n)\\) времени.</li> <li>Удаление элемента: сначала нужно найти элемент, затем удалить его из массива (или списка), что занимает \\(O(n)\\) времени.</li> </ul> <p> Таблица 6-1   Сравнение эффективности поиска элементов </p> Массив Связный список Хеш-таблица Поиск элемента \\(O(n)\\) \\(O(n)\\) \\(O(1)\\) Добавление элемента \\(O(1)\\) \\(O(1)\\) \\(O(1)\\) Удаление элемента \\(O(n)\\) \\(O(n)\\) \\(O(1)\\) <p>Нетрудно заметить, что операции чтения, добавления, удаления и обновления в хеш-таблице имеют временную сложность \\(O(1)\\) , то есть выполняются очень эффективно.</p>","path":["Глава 6. Хеширование","6.1 &nbsp; Хеш-таблица"],"tags":[]},{"location":"chapter_hashing/hash_map/#611-","level":2,"title":"6.1.1   Основные операции с хеш-таблицей","text":"<p>К базовым операциям хеш-таблицы относятся инициализация, поиск, добавление пар ключ-значение и удаление пар ключ-значение. Пример кода приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby hash_map.py<pre><code># Инициализация хеш-таблицы\nhmap: dict = {}\n\n# Операция добавления\n# Добавить пару ключ-значение (key, value) в хеш-таблицу\nhmap[12836] = \"Сяо Ха\"\nhmap[15937] = \"Сяо Ло\"\nhmap[16750] = \"Сяо Суань\"\nhmap[13276] = \"Сяо Фа\"\nhmap[10583] = \"Сяо Я\"\n\n# Операция поиска\n# Передать в хеш-таблицу ключ key и получить значение value\nname: str = hmap[15937]\n\n# Операция удаления\n# Удалить пару ключ-значение (key, value) из хеш-таблицы\nhmap.pop(10583)\n</code></pre> hash_map.cpp<pre><code>/* Инициализация хеш-таблицы */\nunordered_map&lt;int, string&gt; map;\n\n/* Операция добавления */\n// Добавить пару ключ-значение (key, value) в хеш-таблицу\nmap[12836] = \"Сяо Ха\";\nmap[15937] = \"Сяо Ло\";\nmap[16750] = \"Сяо Суань\";\nmap[13276] = \"Сяо Фа\";\nmap[10583] = \"Сяо Я\";\n\n/* Операция поиска */\n// Передать в хеш-таблицу ключ key и получить значение value\nstring name = map[15937];\n\n/* Операция удаления */\n// Удалить пару ключ-значение (key, value) из хеш-таблицы\nmap.erase(10583);\n</code></pre> hash_map.java<pre><code>/* Инициализация хеш-таблицы */\nMap&lt;Integer, String&gt; map = new HashMap&lt;&gt;();\n\n/* Операция добавления */\n// Добавить пару ключ-значение (key, value) в хеш-таблицу\nmap.put(12836, \"Сяо Ха\");\nmap.put(15937, \"Сяо Ло\");\nmap.put(16750, \"Сяо Суань\");\nmap.put(13276, \"Сяо Фа\");\nmap.put(10583, \"Сяо Я\");\n\n/* Операция поиска */\n// Передать в хеш-таблицу ключ key и получить значение value\nString name = map.get(15937);\n\n/* Операция удаления */\n// Удалить пару ключ-значение (key, value) из хеш-таблицы\nmap.remove(10583);\n</code></pre> hash_map.cs<pre><code>/* Инициализация хеш-таблицы */\nDictionary&lt;int, string&gt; map = new() {\n    /* Операция добавления */\n    // Добавить пару ключ-значение (key, value) в хеш-таблицу\n    { 12836, \"Сяо Ха\" },\n    { 15937, \"Сяо Ло\" },\n    { 16750, \"Сяо Суань\" },\n    { 13276, \"Сяо Фа\" },\n    { 10583, \"Сяо Я\" }\n};\n\n/* Операция поиска */\n// Передать в хеш-таблицу ключ key и получить значение value\nstring name = map[15937];\n\n/* Операция удаления */\n// Удалить пару ключ-значение (key, value) из хеш-таблицы\nmap.Remove(10583);\n</code></pre> hash_map_test.go<pre><code>/* Инициализация хеш-таблицы */\nhmap := make(map[int]string)\n\n/* Операция добавления */\n// Добавить пару ключ-значение (key, value) в хеш-таблицу\nhmap[12836] = \"Сяо Ха\"\nhmap[15937] = \"Сяо Ло\"\nhmap[16750] = \"Сяо Суань\"\nhmap[13276] = \"Сяо Фа\"\nhmap[10583] = \"Сяо Я\"\n\n/* Операция поиска */\n// Передать в хеш-таблицу ключ key и получить значение value\nname := hmap[15937]\n\n/* Операция удаления */\n// Удалить пару ключ-значение (key, value) из хеш-таблицы\ndelete(hmap, 10583)\n</code></pre> hash_map.swift<pre><code>/* Инициализация хеш-таблицы */\nvar map: [Int: String] = [:]\n\n/* Операция добавления */\n// Добавить пару ключ-значение (key, value) в хеш-таблицу\nmap[12836] = \"Сяо Ха\"\nmap[15937] = \"Сяо Ло\"\nmap[16750] = \"Сяо Суань\"\nmap[13276] = \"Сяо Фа\"\nmap[10583] = \"Сяо Я\"\n\n/* Операция поиска */\n// Передать в хеш-таблицу ключ key и получить значение value\nlet name = map[15937]!\n\n/* Операция удаления */\n// Удалить пару ключ-значение (key, value) из хеш-таблицы\nmap.removeValue(forKey: 10583)\n</code></pre> hash_map.js<pre><code>/* Инициализация хеш-таблицы */\nconst map = new Map();\n/* Операция добавления */\n// Добавить пару ключ-значение (key, value) в хеш-таблицу\nmap.set(12836, 'Сяо Ха');\nmap.set(15937, 'Сяо Ло');\nmap.set(16750, 'Сяо Суань');\nmap.set(13276, 'Сяо Фа');\nmap.set(10583, 'Сяо Я');\n\n/* Операция поиска */\n// Передать в хеш-таблицу ключ key и получить значение value\nlet name = map.get(15937);\n\n/* Операция удаления */\n// Удалить пару ключ-значение (key, value) из хеш-таблицы\nmap.delete(10583);\n</code></pre> hash_map.ts<pre><code>/* Инициализация хеш-таблицы */\nconst map = new Map&lt;number, string&gt;();\n/* Операция добавления */\n// Добавить пару ключ-значение (key, value) в хеш-таблицу\nmap.set(12836, 'Сяо Ха');\nmap.set(15937, 'Сяо Ло');\nmap.set(16750, 'Сяо Суань');\nmap.set(13276, 'Сяо Фа');\nmap.set(10583, 'Сяо Я');\nconsole.info('\\nПосле добавления хеш-таблица имеет вид\\nKey -&gt; Value');\nconsole.info(map);\n\n/* Операция поиска */\n// Передать в хеш-таблицу ключ key и получить значение value\nlet name = map.get(15937);\nconsole.info('\\nПо номеру 15937 найдено имя ' + name);\n\n/* Операция удаления */\n// Удалить пару ключ-значение (key, value) из хеш-таблицы\nmap.delete(10583);\nconsole.info('\\nПосле удаления 10583 хеш-таблица имеет вид\\nKey -&gt; Value');\nconsole.info(map);\n</code></pre> hash_map.dart<pre><code>/* Инициализация хеш-таблицы */\nMap&lt;int, String&gt; map = {};\n\n/* Операция добавления */\n// Добавить пару ключ-значение (key, value) в хеш-таблицу\nmap[12836] = \"Сяо Ха\";\nmap[15937] = \"Сяо Ло\";\nmap[16750] = \"Сяо Суань\";\nmap[13276] = \"Сяо Фа\";\nmap[10583] = \"Сяо Я\";\n\n/* Операция поиска */\n// Передать в хеш-таблицу ключ key и получить значение value\nString name = map[15937];\n\n/* Операция удаления */\n// Удалить пару ключ-значение (key, value) из хеш-таблицы\nmap.remove(10583);\n</code></pre> hash_map.rs<pre><code>use std::collections::HashMap;\n\n/* Инициализация хеш-таблицы */\nlet mut map: HashMap&lt;i32, String&gt; = HashMap::new();\n\n/* Операция добавления */\n// Добавить пару ключ-значение (key, value) в хеш-таблицу\nmap.insert(12836, \"Сяо Ха\".to_string());\nmap.insert(15937, \"Сяо Ло\".to_string());\nmap.insert(16750, \"Сяо Суань\".to_string());\nmap.insert(13279, \"Сяо Фа\".to_string());\nmap.insert(10583, \"Сяо Я\".to_string());\n\n/* Операция поиска */\n// Передать в хеш-таблицу ключ key и получить значение value\nlet _name: Option&lt;&amp;String&gt; = map.get(&amp;15937);\n\n/* Операция удаления */\n// Удалить пару ключ-значение (key, value) из хеш-таблицы\nlet _removed_value: Option&lt;String&gt; = map.remove(&amp;10583);\n</code></pre> hash_map.c<pre><code>// В C нет встроенной хеш-таблицы\n</code></pre> hash_map.kt<pre><code>/* Инициализация хеш-таблицы */\nval map = HashMap&lt;Int,String&gt;()\n\n/* Операция добавления */\n// Добавить пару ключ-значение (key, value) в хеш-таблицу\nmap[12836] = \"Сяо Ха\"\nmap[15937] = \"Сяо Ло\"\nmap[16750] = \"Сяо Суань\"\nmap[13276] = \"Сяо Фа\"\nmap[10583] = \"Сяо Я\"\n\n/* Операция поиска */\n// Передать в хеш-таблицу ключ key и получить значение value\nval name = map[15937]\n\n/* Операция удаления */\n// Удалить пару ключ-значение (key, value) из хеш-таблицы\nmap.remove(10583)\n</code></pre> hash_map.rb<pre><code># Инициализация хеш-таблицы\nhmap = {}\n\n# Операция добавления\n# Добавить пару ключ-значение (key, value) в хеш-таблицу\nhmap[12836] = \"Сяо Ха\"\nhmap[15937] = \"Сяо Ло\"\nhmap[16750] = \"Сяо Суань\"\nhmap[13276] = \"Сяо Фа\"\nhmap[10583] = \"Сяо Я\"\n\n# Операция поиска\n# Передать в хеш-таблицу ключ key и получить значение value\nname = hmap[15937]\n\n# Операция удаления\n# Удалить пару ключ-значение (key, value) из хеш-таблицы\nhmap.delete(10583)\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%85%D0%B5%D1%88-%D1%82%D0%B0%D0%B1%D0%BB%D0%B8%D1%86%D1%83%0A%20%20%20%20hmap%20%3D%20%7B%7D%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9E%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%8F%20%D0%B4%D0%BE%D0%B1%D0%B0%D0%B2%D0%BB%D0%B5%D0%BD%D0%B8%D1%8F%0A%20%20%20%20%23%20%D0%94%D0%BE%D0%B1%D0%B0%D0%B2%D0%B8%D1%82%D1%8C%20%D0%B2%20%D1%85%D0%B5%D1%88-%D1%82%D0%B0%D0%B1%D0%BB%D0%B8%D1%86%D1%83%20%D0%BF%D0%B0%D1%80%D1%83%20%D0%BA%D0%BB%D1%8E%D1%87-%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%28key%2C%20value%29%0A%20%20%20%20hmap%5B12836%5D%20%3D%20%22%D0%A1%D1%8F%D0%BE%20%D0%A5%D0%B0%22%0A%20%20%20%20hmap%5B15937%5D%20%3D%20%22%D0%A1%D1%8F%D0%BE%20%D0%9B%D0%BE%22%0A%20%20%20%20hmap%5B16750%5D%20%3D%20%22%D0%A1%D1%8F%D0%BE%20%D0%A1%D1%83%D0%B0%D0%BD%D1%8C%22%0A%20%20%20%20hmap%5B13276%5D%20%3D%20%22%D0%A1%D1%8F%D0%BE%20%D0%A4%D0%B0%22%0A%20%20%20%20hmap%5B10583%5D%20%3D%20%22%D0%A3%D1%82%D0%B5%D0%BD%D0%BE%D0%BA%22%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9E%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%8F%20%D0%BF%D0%BE%D0%B8%D1%81%D0%BA%D0%B0%0A%20%20%20%20%23%20%D0%9F%D0%B5%D1%80%D0%B5%D0%B4%D0%B0%D1%82%D1%8C%20%D0%BA%D0%BB%D1%8E%D1%87%20key%20%D0%B2%20%D1%85%D0%B5%D1%88-%D1%82%D0%B0%D0%B1%D0%BB%D0%B8%D1%86%D1%83%20%D0%B8%20%D0%BF%D0%BE%D0%BB%D1%83%D1%87%D0%B8%D1%82%D1%8C%20%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20value%0A%20%20%20%20name%20%3D%20hmap%5B15937%5D%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9E%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%8F%20%D1%83%D0%B4%D0%B0%D0%BB%D0%B5%D0%BD%D0%B8%D1%8F%0A%20%20%20%20%23%20%D0%A3%D0%B4%D0%B0%D0%BB%D0%B8%D1%82%D1%8C%20%D0%B8%D0%B7%20%D1%85%D0%B5%D1%88-%D1%82%D0%B0%D0%B1%D0%BB%D0%B8%D1%86%D1%8B%20%D0%BF%D0%B0%D1%80%D1%83%20%D0%BA%D0%BB%D1%8E%D1%87-%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%28key%2C%20value%29%0A%20%20%20%20hmap.pop%2810583%29&amp;cumulative=false&amp;curInstr=2&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p> <p>У хеш-таблицы есть три распространенных способа обхода: обход пар ключ-значение, обход ключей и обход значений. Примеры кода приведены ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby hash_map.py<pre><code># Обход хеш-таблицы\n# Обход пар ключ-значение key-&gt;value\nfor key, value in hmap.items():\n    print(key, \"-&gt;\", value)\n# Обход только ключей key\nfor key in hmap.keys():\n    print(key)\n# Обход только значений value\nfor value in hmap.values():\n    print(value)\n</code></pre> hash_map.cpp<pre><code>/* Обход хеш-таблицы */\n// Обход пар ключ-значение key-&gt;value\nfor (auto kv: map) {\n    cout &lt;&lt; kv.first &lt;&lt; \" -&gt; \" &lt;&lt; kv.second &lt;&lt; endl;\n}\n// Обход key-&gt;value с помощью итератора\nfor (auto iter = map.begin(); iter != map.end(); iter++) {\n    cout &lt;&lt; iter-&gt;first &lt;&lt; \"-&gt;\" &lt;&lt; iter-&gt;second &lt;&lt; endl;\n}\n</code></pre> hash_map.java<pre><code>/* Обход хеш-таблицы */\n// Обход пар ключ-значение key-&gt;value\nfor (Map.Entry &lt;Integer, String&gt; kv: map.entrySet()) {\n    System.out.println(kv.getKey() + \" -&gt; \" + kv.getValue());\n}\n// Обход только ключей key\nfor (int key: map.keySet()) {\n    System.out.println(key);\n}\n// Обход только значений value\nfor (String val: map.values()) {\n    System.out.println(val);\n}\n</code></pre> hash_map.cs<pre><code>/* Обход хеш-таблицы */\n// Обход пар ключ-значение Key-&gt;Value\nforeach (var kv in map) {\n    Console.WriteLine(kv.Key + \" -&gt; \" + kv.Value);\n}\n// Обход только ключей key\nforeach (int key in map.Keys) {\n    Console.WriteLine(key);\n}\n// Обход только значений value\nforeach (string val in map.Values) {\n    Console.WriteLine(val);\n}\n</code></pre> hash_map_test.go<pre><code>/* Обход хеш-таблицы */\n// Обход пар ключ-значение key-&gt;value\nfor key, value := range hmap {\n    fmt.Println(key, \"-&gt;\", value)\n}\n// Обход только ключей key\nfor key := range hmap {\n    fmt.Println(key)\n}\n// Обход только значений value\nfor _, value := range hmap {\n    fmt.Println(value)\n}\n</code></pre> hash_map.swift<pre><code>/* Обход хеш-таблицы */\n// Обход пар ключ-значение Key-&gt;Value\nfor (key, value) in map {\n    print(\"\\(key) -&gt; \\(value)\")\n}\n// Обход только ключей Key\nfor key in map.keys {\n    print(key)\n}\n// Обход только значений Value\nfor value in map.values {\n    print(value)\n}\n</code></pre> hash_map.js<pre><code>/* Обход хеш-таблицы */\nconsole.info('\\nОбход пар ключ-значение Key-&gt;Value');\nfor (const [k, v] of map.entries()) {\n    console.info(k + ' -&gt; ' + v);\n}\nconsole.info('\\nОбход только ключей Key');\nfor (const k of map.keys()) {\n    console.info(k);\n}\nconsole.info('\\nОбход только значений Value');\nfor (const v of map.values()) {\n    console.info(v);\n}\n</code></pre> hash_map.ts<pre><code>/* Обход хеш-таблицы */\nconsole.info('\\nОбход пар ключ-значение Key-&gt;Value');\nfor (const [k, v] of map.entries()) {\n    console.info(k + ' -&gt; ' + v);\n}\nconsole.info('\\nОбход только ключей Key');\nfor (const k of map.keys()) {\n    console.info(k);\n}\nconsole.info('\\nОбход только значений Value');\nfor (const v of map.values()) {\n    console.info(v);\n}\n</code></pre> hash_map.dart<pre><code>/* Обход хеш-таблицы */\n// Обход пар ключ-значение Key-&gt;Value\nmap.forEach((key, value) {\n  print('$key -&gt; $value');\n});\n\n// Обход только ключей Key\nmap.keys.forEach((key) {\n  print(key);\n});\n\n// Обход только значений Value\nmap.values.forEach((value) {\n  print(value);\n});\n</code></pre> hash_map.rs<pre><code>/* Обход хеш-таблицы */\n// Обход пар ключ-значение Key-&gt;Value\nfor (key, value) in &amp;map {\n    println!(\"{key} -&gt; {value}\");\n}\n\n// Обход только ключей Key\nfor key in map.keys() {\n    println!(\"{key}\");\n}\n\n// Обход только значений Value\nfor value in map.values() {\n    println!(\"{value}\");\n}\n</code></pre> hash_map.c<pre><code>// В C нет встроенной хеш-таблицы\n</code></pre> hash_map.kt<pre><code>/* Обход хеш-таблицы */\n// Обход пар ключ-значение key-&gt;value\nfor ((key, value) in map) {\n    println(\"$key -&gt; $value\")\n}\n// Обход только ключей key\nfor (key in map.keys) {\n    println(key)\n}\n// Обход только значений value\nfor (_val in map.values) {\n    println(_val)\n}\n</code></pre> hash_map.rb<pre><code># Обход хеш-таблицы\n# Обход пар ключ-значение key-&gt;value\nhmap.entries.each { |key, value| puts \"#{key} -&gt; #{value}\" }\n\n# Обход только ключей key\nhmap.keys.each { |key| puts key }\n\n# Обход только значений value\nhmap.values.each { |val| puts val }\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%85%D0%B5%D1%88-%D1%82%D0%B0%D0%B1%D0%BB%D0%B8%D1%86%D1%83%0A%20%20%20%20hmap%20%3D%20%7B%7D%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9E%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%8F%20%D0%B4%D0%BE%D0%B1%D0%B0%D0%B2%D0%BB%D0%B5%D0%BD%D0%B8%D1%8F%0A%20%20%20%20%23%20%D0%94%D0%BE%D0%B1%D0%B0%D0%B2%D0%B8%D1%82%D1%8C%20%D0%B2%20%D1%85%D0%B5%D1%88-%D1%82%D0%B0%D0%B1%D0%BB%D0%B8%D1%86%D1%83%20%D0%BF%D0%B0%D1%80%D1%83%20%D0%BA%D0%BB%D1%8E%D1%87-%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%28key%2C%20value%29%0A%20%20%20%20hmap%5B12836%5D%20%3D%20%22%D0%A1%D1%8F%D0%BE%20%D0%A5%D0%B0%22%0A%20%20%20%20hmap%5B15937%5D%20%3D%20%22%D0%A1%D1%8F%D0%BE%20%D0%9B%D0%BE%22%0A%20%20%20%20hmap%5B16750%5D%20%3D%20%22%D0%A1%D1%8F%D0%BE%20%D0%A1%D1%83%D0%B0%D0%BD%D1%8C%22%0A%20%20%20%20hmap%5B13276%5D%20%3D%20%22%D0%A1%D1%8F%D0%BE%20%D0%A4%D0%B0%22%0A%20%20%20%20hmap%5B10583%5D%20%3D%20%22%D0%A3%D1%82%D0%B5%D0%BD%D0%BE%D0%BA%22%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9F%D0%B5%D1%80%D0%B5%D0%B1%D1%80%D0%B0%D1%82%D1%8C%20%D1%85%D0%B5%D1%88-%D1%82%D0%B0%D0%B1%D0%BB%D0%B8%D1%86%D1%83%0A%20%20%20%20%23%20%D0%9E%D0%B1%D0%BE%D0%B9%D1%82%D0%B8%D0%BF%D0%B0%D1%80%D0%B0%20%D0%BA%D0%BB%D1%8E%D1%87-%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20key-%3Evalue%0A%20%20%20%20for%20key%2C%20value%20in%20hmap.items%28%29%3A%0A%20%20%20%20%20%20%20%20print%28key%2C%20%22-%3E%22%2C%20value%29%0A%20%20%20%20%23%20%D0%BE%D1%82%D0%B4%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D0%9E%D0%B1%D0%BE%D0%B9%D1%82%D0%B8%D0%BA%D0%BB%D1%8E%D1%87%20key%0A%20%20%20%20for%20key%20in%20hmap.keys%28%29%3A%0A%20%20%20%20%20%20%20%20print%28key%29%0A%20%20%20%20%23%20%D0%BE%D1%82%D0%B4%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D0%9E%D0%B1%D0%BE%D0%B9%D1%82%D0%B8%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20value%0A%20%20%20%20for%20value%20in%20hmap.values%28%29%3A%0A%20%20%20%20%20%20%20%20print%28value%29&amp;cumulative=false&amp;curInstr=8&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 6. Хеширование","6.1 &nbsp; Хеш-таблица"],"tags":[]},{"location":"chapter_hashing/hash_map/#612-","level":2,"title":"6.1.2   Простая реализация хеш-таблицы","text":"<p>Сначала рассмотрим самый простой случай: реализуем хеш-таблицу только с помощью одного массива. В хеш-таблице каждую пустую ячейку массива мы называем бакетом (bucket), и каждый бакет может хранить одну пару ключ-значение. Следовательно, операция поиска сводится к тому, чтобы найти бакет, соответствующий <code>key</code> , и получить из него <code>value</code> .</p> <p>Но как определить бакет, соответствующий заданному <code>key</code> ? Это делается с помощью хеш-функции (hash function). Назначение хеш-функции - отображать большое входное пространство в меньшее выходное пространство. В хеш-таблице входным пространством являются все <code>key</code> , а выходным - все бакеты (индексы массива). Иначе говоря, передав <code>key</code> на вход, мы можем через хеш-функцию получить позицию хранения соответствующей пары ключ-значение в массиве.</p> <p>Процесс вычисления хеш-функции для одного <code>key</code> включает два шага.</p> <ol> <li>Сначала с помощью некоторого хеш-алгоритма <code>hash()</code> вычисляется хеш-значение.</li> <li>Затем хеш-значение берется по модулю числа бакетов (длины массива) <code>capacity</code> , чтобы получить бакет (индекс массива) <code>index</code> , соответствующий этому <code>key</code> .</li> </ol> <pre><code>index = hash(key) % capacity\n</code></pre> <p>После этого можно использовать <code>index</code> для доступа к соответствующему бакету в хеш-таблице и получения <code>value</code> .</p> <p>Пусть длина массива <code>capacity = 100</code> , а хеш-алгоритм <code>hash(key) = key</code> . Тогда легко получить хеш-функцию <code>key % 100</code> . На рисунке 6-2 на примере <code>key</code> \"номер студенческого билета\" и <code>value</code> \"имя\" показан принцип работы хеш-функции.</p> <p></p> <p> Рисунок 6-2   Принцип работы хеш-функции </p> <p>Ниже приведен код простой реализации хеш-таблицы. В нем мы инкапсулируем <code>key</code> и <code>value</code> в класс <code>Pair</code> , чтобы представить пару ключ-значение.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array_hash_map.py<pre><code>class Pair:\n    \"\"\"Пара ключ-значение\"\"\"\n\n    def __init__(self, key: int, val: str):\n        self.key = key\n        self.val = val\n\nclass ArrayHashMap:\n    \"\"\"Хеш-таблица на основе массива\"\"\"\n\n    def __init__(self):\n        \"\"\"Конструктор\"\"\"\n        # Инициализировать массив, содержащий 100 корзин\n        self.buckets: list[Pair | None] = [None] * 100\n\n    def hash_func(self, key: int) -&gt; int:\n        \"\"\"Хеш-функция\"\"\"\n        index = key % 100\n        return index\n\n    def get(self, key: int) -&gt; str | None:\n        \"\"\"Операция поиска\"\"\"\n        index: int = self.hash_func(key)\n        pair: Pair = self.buckets[index]\n        if pair is None:\n            return None\n        return pair.val\n\n    def put(self, key: int, val: str):\n        \"\"\"Операции добавления и обновления\"\"\"\n        pair = Pair(key, val)\n        index: int = self.hash_func(key)\n        self.buckets[index] = pair\n\n    def remove(self, key: int):\n        \"\"\"Операция удаления\"\"\"\n        index: int = self.hash_func(key)\n        # Присвоить None, что означает удаление\n        self.buckets[index] = None\n\n    def entry_set(self) -&gt; list[Pair]:\n        \"\"\"Получить все пары ключ-значение\"\"\"\n        result: list[Pair] = []\n        for pair in self.buckets:\n            if pair is not None:\n                result.append(pair)\n        return result\n\n    def key_set(self) -&gt; list[int]:\n        \"\"\"Получить все ключи\"\"\"\n        result = []\n        for pair in self.buckets:\n            if pair is not None:\n                result.append(pair.key)\n        return result\n\n    def value_set(self) -&gt; list[str]:\n        \"\"\"Получить все значения\"\"\"\n        result = []\n        for pair in self.buckets:\n            if pair is not None:\n                result.append(pair.val)\n        return result\n\n    def print(self):\n        \"\"\"Вывести хеш-таблицу\"\"\"\n        for pair in self.buckets:\n            if pair is not None:\n                print(pair.key, \"-&gt;\", pair.val)\n</code></pre> array_hash_map.cpp<pre><code>/* Пара ключ-значение */\nstruct Pair {\n  public:\n    int key;\n    string val;\n    Pair(int key, string val) {\n        this-&gt;key = key;\n        this-&gt;val = val;\n    }\n};\n\n/* Хеш-таблица на основе массива */\nclass ArrayHashMap {\n  private:\n    vector&lt;Pair *&gt; buckets;\n\n  public:\n    ArrayHashMap() {\n        // Инициализировать массив, содержащий 100 корзин\n        buckets = vector&lt;Pair *&gt;(100);\n    }\n\n    ~ArrayHashMap() {\n        // Освободить память\n        for (const auto &amp;bucket : buckets) {\n            delete bucket;\n        }\n        buckets.clear();\n    }\n\n    /* Хеш-функция */\n    int hashFunc(int key) {\n        int index = key % 100;\n        return index;\n    }\n\n    /* Операция поиска */\n    string get(int key) {\n        int index = hashFunc(key);\n        Pair *pair = buckets[index];\n        if (pair == nullptr)\n            return \"\";\n        return pair-&gt;val;\n    }\n\n    /* Операция добавления */\n    void put(int key, string val) {\n        Pair *pair = new Pair(key, val);\n        int index = hashFunc(key);\n        buckets[index] = pair;\n    }\n\n    /* Операция удаления */\n    void remove(int key) {\n        int index = hashFunc(key);\n        // Освободить память и присвоить nullptr\n        delete buckets[index];\n        buckets[index] = nullptr;\n    }\n\n    /* Получить все пары ключ-значение */\n    vector&lt;Pair *&gt; pairSet() {\n        vector&lt;Pair *&gt; pairSet;\n        for (Pair *pair : buckets) {\n            if (pair != nullptr) {\n                pairSet.push_back(pair);\n            }\n        }\n        return pairSet;\n    }\n\n    /* Получить все ключи */\n    vector&lt;int&gt; keySet() {\n        vector&lt;int&gt; keySet;\n        for (Pair *pair : buckets) {\n            if (pair != nullptr) {\n                keySet.push_back(pair-&gt;key);\n            }\n        }\n        return keySet;\n    }\n\n    /* Получить все значения */\n    vector&lt;string&gt; valueSet() {\n        vector&lt;string&gt; valueSet;\n        for (Pair *pair : buckets) {\n            if (pair != nullptr) {\n                valueSet.push_back(pair-&gt;val);\n            }\n        }\n        return valueSet;\n    }\n\n    /* Вывести хеш-таблицу */\n    void print() {\n        for (Pair *kv : pairSet()) {\n            cout &lt;&lt; kv-&gt;key &lt;&lt; \" -&gt; \" &lt;&lt; kv-&gt;val &lt;&lt; endl;\n        }\n    }\n};\n</code></pre> array_hash_map.java<pre><code>/* Пара ключ-значение */\nclass Pair {\n    public int key;\n    public String val;\n\n    public Pair(int key, String val) {\n        this.key = key;\n        this.val = val;\n    }\n}\n\n/* Хеш-таблица на основе массива */\nclass ArrayHashMap {\n    private List&lt;Pair&gt; buckets;\n\n    public ArrayHashMap() {\n        // Инициализировать массив, содержащий 100 корзин\n        buckets = new ArrayList&lt;&gt;();\n        for (int i = 0; i &lt; 100; i++) {\n            buckets.add(null);\n        }\n    }\n\n    /* Хеш-функция */\n    private int hashFunc(int key) {\n        int index = key % 100;\n        return index;\n    }\n\n    /* Операция поиска */\n    public String get(int key) {\n        int index = hashFunc(key);\n        Pair pair = buckets.get(index);\n        if (pair == null)\n            return null;\n        return pair.val;\n    }\n\n    /* Операция добавления */\n    public void put(int key, String val) {\n        Pair pair = new Pair(key, val);\n        int index = hashFunc(key);\n        buckets.set(index, pair);\n    }\n\n    /* Операция удаления */\n    public void remove(int key) {\n        int index = hashFunc(key);\n        // Присвоить null, что означает удаление\n        buckets.set(index, null);\n    }\n\n    /* Получить все пары ключ-значение */\n    public List&lt;Pair&gt; pairSet() {\n        List&lt;Pair&gt; pairSet = new ArrayList&lt;&gt;();\n        for (Pair pair : buckets) {\n            if (pair != null)\n                pairSet.add(pair);\n        }\n        return pairSet;\n    }\n\n    /* Получить все ключи */\n    public List&lt;Integer&gt; keySet() {\n        List&lt;Integer&gt; keySet = new ArrayList&lt;&gt;();\n        for (Pair pair : buckets) {\n            if (pair != null)\n                keySet.add(pair.key);\n        }\n        return keySet;\n    }\n\n    /* Получить все значения */\n    public List&lt;String&gt; valueSet() {\n        List&lt;String&gt; valueSet = new ArrayList&lt;&gt;();\n        for (Pair pair : buckets) {\n            if (pair != null)\n                valueSet.add(pair.val);\n        }\n        return valueSet;\n    }\n\n    /* Вывести хеш-таблицу */\n    public void print() {\n        for (Pair kv : pairSet()) {\n            System.out.println(kv.key + \" -&gt; \" + kv.val);\n        }\n    }\n}\n</code></pre> array_hash_map.cs<pre><code>/* Пара ключ-значение int-&gt;string */\nclass Pair(int key, string val) {\n    public int key = key;\n    public string val = val;\n}\n\n/* Хеш-таблица на основе массива */\nclass ArrayHashMap {\n    List&lt;Pair?&gt; buckets;\n    public ArrayHashMap() {\n        // Инициализировать массив, содержащий 100 корзин\n        buckets = [];\n        for (int i = 0; i &lt; 100; i++) {\n            buckets.Add(null);\n        }\n    }\n\n    /* Хеш-функция */\n    int HashFunc(int key) {\n        int index = key % 100;\n        return index;\n    }\n\n    /* Операция поиска */\n    public string? Get(int key) {\n        int index = HashFunc(key);\n        Pair? pair = buckets[index];\n        if (pair == null) return null;\n        return pair.val;\n    }\n\n    /* Операция добавления */\n    public void Put(int key, string val) {\n        Pair pair = new(key, val);\n        int index = HashFunc(key);\n        buckets[index] = pair;\n    }\n\n    /* Операция удаления */\n    public void Remove(int key) {\n        int index = HashFunc(key);\n        // Присвоить null, что означает удаление\n        buckets[index] = null;\n    }\n\n    /* Получить все пары ключ-значение */\n    public List&lt;Pair&gt; PairSet() {\n        List&lt;Pair&gt; pairSet = [];\n        foreach (Pair? pair in buckets) {\n            if (pair != null)\n                pairSet.Add(pair);\n        }\n        return pairSet;\n    }\n\n    /* Получить все ключи */\n    public List&lt;int&gt; KeySet() {\n        List&lt;int&gt; keySet = [];\n        foreach (Pair? pair in buckets) {\n            if (pair != null)\n                keySet.Add(pair.key);\n        }\n        return keySet;\n    }\n\n    /* Получить все значения */\n    public List&lt;string&gt; ValueSet() {\n        List&lt;string&gt; valueSet = [];\n        foreach (Pair? pair in buckets) {\n            if (pair != null)\n                valueSet.Add(pair.val);\n        }\n        return valueSet;\n    }\n\n    /* Вывести хеш-таблицу */\n    public void Print() {\n        foreach (Pair kv in PairSet()) {\n            Console.WriteLine(kv.key + \" -&gt; \" + kv.val);\n        }\n    }\n}\n</code></pre> array_hash_map.go<pre><code>/* Пара ключ-значение */\ntype pair struct {\n    key int\n    val string\n}\n\n/* Хеш-таблица на основе массива */\ntype arrayHashMap struct {\n    buckets []*pair\n}\n\n/* Инициализация хеш-таблицы */\nfunc newArrayHashMap() *arrayHashMap {\n    // Инициализировать массив, содержащий 100 корзин\n    buckets := make([]*pair, 100)\n    return &amp;arrayHashMap{buckets: buckets}\n}\n\n/* Хеш-функция */\nfunc (a *arrayHashMap) hashFunc(key int) int {\n    index := key % 100\n    return index\n}\n\n/* Операция поиска */\nfunc (a *arrayHashMap) get(key int) string {\n    index := a.hashFunc(key)\n    pair := a.buckets[index]\n    if pair == nil {\n        return \"Not Found\"\n    }\n    return pair.val\n}\n\n/* Операция добавления */\nfunc (a *arrayHashMap) put(key int, val string) {\n    pair := &amp;pair{key: key, val: val}\n    index := a.hashFunc(key)\n    a.buckets[index] = pair\n}\n\n/* Операция удаления */\nfunc (a *arrayHashMap) remove(key int) {\n    index := a.hashFunc(key)\n    // Присвоить nil, что означает удаление\n    a.buckets[index] = nil\n}\n\n/* Получить все ключи */\nfunc (a *arrayHashMap) pairSet() []*pair {\n    var pairs []*pair\n    for _, pair := range a.buckets {\n        if pair != nil {\n            pairs = append(pairs, pair)\n        }\n    }\n    return pairs\n}\n\n/* Получить все ключи */\nfunc (a *arrayHashMap) keySet() []int {\n    var keys []int\n    for _, pair := range a.buckets {\n        if pair != nil {\n            keys = append(keys, pair.key)\n        }\n    }\n    return keys\n}\n\n/* Получить все значения */\nfunc (a *arrayHashMap) valueSet() []string {\n    var values []string\n    for _, pair := range a.buckets {\n        if pair != nil {\n            values = append(values, pair.val)\n        }\n    }\n    return values\n}\n\n/* Вывести хеш-таблицу */\nfunc (a *arrayHashMap) print() {\n    for _, pair := range a.buckets {\n        if pair != nil {\n            fmt.Println(pair.key, \"-&gt;\", pair.val)\n        }\n    }\n}\n</code></pre> array_hash_map.swift<pre><code>/* Пара ключ-значение */\nclass Pair: Equatable {\n    public var key: Int\n    public var val: String\n\n    public init(key: Int, val: String) {\n        self.key = key\n        self.val = val\n    }\n\n    public static func == (lhs: Pair, rhs: Pair) -&gt; Bool {\n        lhs.key == rhs.key &amp;&amp; lhs.val == rhs.val\n    }\n}\n\n/* Хеш-таблица на основе массива */\nclass ArrayHashMap {\n    private var buckets: [Pair?]\n\n    init() {\n        // Инициализировать массив, содержащий 100 корзин\n        buckets = Array(repeating: nil, count: 100)\n    }\n\n    /* Хеш-функция */\n    private func hashFunc(key: Int) -&gt; Int {\n        let index = key % 100\n        return index\n    }\n\n    /* Операция поиска */\n    func get(key: Int) -&gt; String? {\n        let index = hashFunc(key: key)\n        let pair = buckets[index]\n        return pair?.val\n    }\n\n    /* Операция добавления */\n    func put(key: Int, val: String) {\n        let pair = Pair(key: key, val: val)\n        let index = hashFunc(key: key)\n        buckets[index] = pair\n    }\n\n    /* Операция удаления */\n    func remove(key: Int) {\n        let index = hashFunc(key: key)\n        // Присвоить nil, что означает удаление\n        buckets[index] = nil\n    }\n\n    /* Получить все пары ключ-значение */\n    func pairSet() -&gt; [Pair] {\n        buckets.compactMap { $0 }\n    }\n\n    /* Получить все ключи */\n    func keySet() -&gt; [Int] {\n        buckets.compactMap { $0?.key }\n    }\n\n    /* Получить все значения */\n    func valueSet() -&gt; [String] {\n        buckets.compactMap { $0?.val }\n    }\n\n    /* Вывести хеш-таблицу */\n    func print() {\n        for pair in pairSet() {\n            Swift.print(\"\\(pair.key) -&gt; \\(pair.val)\")\n        }\n    }\n}\n</code></pre> array_hash_map.js<pre><code>/* Пара ключ-значение Number -&gt; String */\nclass Pair {\n    constructor(key, val) {\n        this.key = key;\n        this.val = val;\n    }\n}\n\n/* Хеш-таблица на основе массива */\nclass ArrayHashMap {\n    #buckets;\n    constructor() {\n        // Инициализировать массив, содержащий 100 корзин\n        this.#buckets = new Array(100).fill(null);\n    }\n\n    /* Хеш-функция */\n    #hashFunc(key) {\n        return key % 100;\n    }\n\n    /* Операция поиска */\n    get(key) {\n        let index = this.#hashFunc(key);\n        let pair = this.#buckets[index];\n        if (pair === null) return null;\n        return pair.val;\n    }\n\n    /* Операция добавления */\n    set(key, val) {\n        let index = this.#hashFunc(key);\n        this.#buckets[index] = new Pair(key, val);\n    }\n\n    /* Операция удаления */\n    delete(key) {\n        let index = this.#hashFunc(key);\n        // Присвоить null, что означает удаление\n        this.#buckets[index] = null;\n    }\n\n    /* Получить все пары ключ-значение */\n    entries() {\n        let arr = [];\n        for (let i = 0; i &lt; this.#buckets.length; i++) {\n            if (this.#buckets[i]) {\n                arr.push(this.#buckets[i]);\n            }\n        }\n        return arr;\n    }\n\n    /* Получить все ключи */\n    keys() {\n        let arr = [];\n        for (let i = 0; i &lt; this.#buckets.length; i++) {\n            if (this.#buckets[i]) {\n                arr.push(this.#buckets[i].key);\n            }\n        }\n        return arr;\n    }\n\n    /* Получить все значения */\n    values() {\n        let arr = [];\n        for (let i = 0; i &lt; this.#buckets.length; i++) {\n            if (this.#buckets[i]) {\n                arr.push(this.#buckets[i].val);\n            }\n        }\n        return arr;\n    }\n\n    /* Вывести хеш-таблицу */\n    print() {\n        let pairSet = this.entries();\n        for (const pair of pairSet) {\n            console.info(`${pair.key} -&gt; ${pair.val}`);\n        }\n    }\n}\n</code></pre> array_hash_map.ts<pre><code>/* Пара ключ-значение Number -&gt; String */\nclass Pair {\n    public key: number;\n    public val: string;\n\n    constructor(key: number, val: string) {\n        this.key = key;\n        this.val = val;\n    }\n}\n\n/* Хеш-таблица на основе массива */\nclass ArrayHashMap {\n    private readonly buckets: (Pair | null)[];\n\n    constructor() {\n        // Инициализировать массив, содержащий 100 корзин\n        this.buckets = new Array(100).fill(null);\n    }\n\n    /* Хеш-функция */\n    private hashFunc(key: number): number {\n        return key % 100;\n    }\n\n    /* Операция поиска */\n    public get(key: number): string | null {\n        let index = this.hashFunc(key);\n        let pair = this.buckets[index];\n        if (pair === null) return null;\n        return pair.val;\n    }\n\n    /* Операция добавления */\n    public set(key: number, val: string) {\n        let index = this.hashFunc(key);\n        this.buckets[index] = new Pair(key, val);\n    }\n\n    /* Операция удаления */\n    public delete(key: number) {\n        let index = this.hashFunc(key);\n        // Присвоить null, что означает удаление\n        this.buckets[index] = null;\n    }\n\n    /* Получить все пары ключ-значение */\n    public entries(): (Pair | null)[] {\n        let arr: (Pair | null)[] = [];\n        for (let i = 0; i &lt; this.buckets.length; i++) {\n            if (this.buckets[i]) {\n                arr.push(this.buckets[i]);\n            }\n        }\n        return arr;\n    }\n\n    /* Получить все ключи */\n    public keys(): (number | undefined)[] {\n        let arr: (number | undefined)[] = [];\n        for (let i = 0; i &lt; this.buckets.length; i++) {\n            if (this.buckets[i]) {\n                arr.push(this.buckets[i].key);\n            }\n        }\n        return arr;\n    }\n\n    /* Получить все значения */\n    public values(): (string | undefined)[] {\n        let arr: (string | undefined)[] = [];\n        for (let i = 0; i &lt; this.buckets.length; i++) {\n            if (this.buckets[i]) {\n                arr.push(this.buckets[i].val);\n            }\n        }\n        return arr;\n    }\n\n    /* Вывести хеш-таблицу */\n    public print() {\n        let pairSet = this.entries();\n        for (const pair of pairSet) {\n            console.info(`${pair.key} -&gt; ${pair.val}`);\n        }\n    }\n}\n</code></pre> array_hash_map.dart<pre><code>/* Пара ключ-значение */\nclass Pair {\n  int key;\n  String val;\n  Pair(this.key, this.val);\n}\n\n/* Хеш-таблица на основе массива */\nclass ArrayHashMap {\n  late List&lt;Pair?&gt; _buckets;\n\n  ArrayHashMap() {\n    // Инициализировать массив, содержащий 100 корзин\n    _buckets = List.filled(100, null);\n  }\n\n  /* Хеш-функция */\n  int _hashFunc(int key) {\n    final int index = key % 100;\n    return index;\n  }\n\n  /* Операция поиска */\n  String? get(int key) {\n    final int index = _hashFunc(key);\n    final Pair? pair = _buckets[index];\n    if (pair == null) {\n      return null;\n    }\n    return pair.val;\n  }\n\n  /* Операция добавления */\n  void put(int key, String val) {\n    final Pair pair = Pair(key, val);\n    final int index = _hashFunc(key);\n    _buckets[index] = pair;\n  }\n\n  /* Операция удаления */\n  void remove(int key) {\n    final int index = _hashFunc(key);\n    _buckets[index] = null;\n  }\n\n  /* Получить все пары ключ-значение */\n  List&lt;Pair&gt; pairSet() {\n    List&lt;Pair&gt; pairSet = [];\n    for (final Pair? pair in _buckets) {\n      if (pair != null) {\n        pairSet.add(pair);\n      }\n    }\n    return pairSet;\n  }\n\n  /* Получить все ключи */\n  List&lt;int&gt; keySet() {\n    List&lt;int&gt; keySet = [];\n    for (final Pair? pair in _buckets) {\n      if (pair != null) {\n        keySet.add(pair.key);\n      }\n    }\n    return keySet;\n  }\n\n  /* Получить все значения */\n  List&lt;String&gt; values() {\n    List&lt;String&gt; valueSet = [];\n    for (final Pair? pair in _buckets) {\n      if (pair != null) {\n        valueSet.add(pair.val);\n      }\n    }\n    return valueSet;\n  }\n\n  /* Вывести хеш-таблицу */\n  void printHashMap() {\n    for (final Pair kv in pairSet()) {\n      print(\"${kv.key} -&gt; ${kv.val}\");\n    }\n  }\n}\n</code></pre> array_hash_map.rs<pre><code>/* Пара ключ-значение */\n#[derive(Debug, Clone, PartialEq)]\npub struct Pair {\n    pub key: i32,\n    pub val: String,\n}\n\n/* Хеш-таблица на основе массива */\npub struct ArrayHashMap {\n    buckets: Vec&lt;Option&lt;Pair&gt;&gt;,\n}\n\nimpl ArrayHashMap {\n    pub fn new() -&gt; ArrayHashMap {\n        // Инициализировать массив, содержащий 100 корзин\n        Self {\n            buckets: vec![None; 100],\n        }\n    }\n\n    /* Хеш-функция */\n    fn hash_func(&amp;self, key: i32) -&gt; usize {\n        key as usize % 100\n    }\n\n    /* Операция поиска */\n    pub fn get(&amp;self, key: i32) -&gt; Option&lt;&amp;String&gt; {\n        let index = self.hash_func(key);\n        self.buckets[index].as_ref().map(|pair| &amp;pair.val)\n    }\n\n    /* Операция добавления */\n    pub fn put(&amp;mut self, key: i32, val: &amp;str) {\n        let index = self.hash_func(key);\n        self.buckets[index] = Some(Pair {\n            key,\n            val: val.to_string(),\n        });\n    }\n\n    /* Операция удаления */\n    pub fn remove(&amp;mut self, key: i32) {\n        let index = self.hash_func(key);\n        // Присвоить None, что означает удаление\n        self.buckets[index] = None;\n    }\n\n    /* Получить все пары ключ-значение */\n    pub fn entry_set(&amp;self) -&gt; Vec&lt;&amp;Pair&gt; {\n        self.buckets\n            .iter()\n            .filter_map(|pair| pair.as_ref())\n            .collect()\n    }\n\n    /* Получить все ключи */\n    pub fn key_set(&amp;self) -&gt; Vec&lt;&amp;i32&gt; {\n        self.buckets\n            .iter()\n            .filter_map(|pair| pair.as_ref().map(|pair| &amp;pair.key))\n            .collect()\n    }\n\n    /* Получить все значения */\n    pub fn value_set(&amp;self) -&gt; Vec&lt;&amp;String&gt; {\n        self.buckets\n            .iter()\n            .filter_map(|pair| pair.as_ref().map(|pair| &amp;pair.val))\n            .collect()\n    }\n\n    /* Вывести хеш-таблицу */\n    pub fn print(&amp;self) {\n        for pair in self.entry_set() {\n            println!(\"{} -&gt; {}\", pair.key, pair.val);\n        }\n    }\n}\n</code></pre> array_hash_map.c<pre><code>/* Пара ключ-значение int-&gt;string */\ntypedef struct {\n    int key;\n    char *val;\n} Pair;\n\n/* Хеш-таблица на основе массива */\ntypedef struct {\n    Pair *buckets[MAX_SIZE];\n} ArrayHashMap;\n\n/* Конструктор */\nArrayHashMap *newArrayHashMap() {\n    ArrayHashMap *hmap = malloc(sizeof(ArrayHashMap));\n    for (int i=0; i &lt; MAX_SIZE; i++) {\n        hmap-&gt;buckets[i] = NULL;\n    }\n    return hmap;\n}\n\n/* Деструктор */\nvoid delArrayHashMap(ArrayHashMap *hmap) {\n    for (int i = 0; i &lt; MAX_SIZE; i++) {\n        if (hmap-&gt;buckets[i] != NULL) {\n            free(hmap-&gt;buckets[i]-&gt;val);\n            free(hmap-&gt;buckets[i]);\n        }\n    }\n    free(hmap);\n}\n\n/* Операция добавления */\nvoid put(ArrayHashMap *hmap, const int key, const char *val) {\n    Pair *Pair = malloc(sizeof(Pair));\n    Pair-&gt;key = key;\n    Pair-&gt;val = malloc(strlen(val) + 1);\n    strcpy(Pair-&gt;val, val);\n\n    int index = hashFunc(key);\n    hmap-&gt;buckets[index] = Pair;\n}\n\n/* Операция удаления */\nvoid removeItem(ArrayHashMap *hmap, const int key) {\n    int index = hashFunc(key);\n    free(hmap-&gt;buckets[index]-&gt;val);\n    free(hmap-&gt;buckets[index]);\n    hmap-&gt;buckets[index] = NULL;\n}\n\n/* Получить все пары ключ-значение */\nvoid pairSet(ArrayHashMap *hmap, MapSet *set) {\n    Pair *entries;\n    int i = 0, index = 0;\n    int total = 0;\n    /* Подсчитать число действительных пар ключ-значение */\n    for (i = 0; i &lt; MAX_SIZE; i++) {\n        if (hmap-&gt;buckets[i] != NULL) {\n            total++;\n        }\n    }\n    entries = malloc(sizeof(Pair) * total);\n    for (i = 0; i &lt; MAX_SIZE; i++) {\n        if (hmap-&gt;buckets[i] != NULL) {\n            entries[index].key = hmap-&gt;buckets[i]-&gt;key;\n            entries[index].val = malloc(strlen(hmap-&gt;buckets[i]-&gt;val) + 1);\n            strcpy(entries[index].val, hmap-&gt;buckets[i]-&gt;val);\n            index++;\n        }\n    }\n    set-&gt;set = entries;\n    set-&gt;len = total;\n}\n\n/* Получить все ключи */\nvoid keySet(ArrayHashMap *hmap, MapSet *set) {\n    int *keys;\n    int i = 0, index = 0;\n    int total = 0;\n    /* Подсчитать число действительных пар ключ-значение */\n    for (i = 0; i &lt; MAX_SIZE; i++) {\n        if (hmap-&gt;buckets[i] != NULL) {\n            total++;\n        }\n    }\n    keys = malloc(total * sizeof(int));\n    for (i = 0; i &lt; MAX_SIZE; i++) {\n        if (hmap-&gt;buckets[i] != NULL) {\n            keys[index] = hmap-&gt;buckets[i]-&gt;key;\n            index++;\n        }\n    }\n    set-&gt;set = keys;\n    set-&gt;len = total;\n}\n\n/* Получить все значения */\nvoid valueSet(ArrayHashMap *hmap, MapSet *set) {\n    char **vals;\n    int i = 0, index = 0;\n    int total = 0;\n    /* Подсчитать число действительных пар ключ-значение */\n    for (i = 0; i &lt; MAX_SIZE; i++) {\n        if (hmap-&gt;buckets[i] != NULL) {\n            total++;\n        }\n    }\n    vals = malloc(total * sizeof(char *));\n    for (i = 0; i &lt; MAX_SIZE; i++) {\n        if (hmap-&gt;buckets[i] != NULL) {\n            vals[index] = hmap-&gt;buckets[i]-&gt;val;\n            index++;\n        }\n    }\n    set-&gt;set = vals;\n    set-&gt;len = total;\n}\n\n/* Вывести хеш-таблицу */\nvoid print(ArrayHashMap *hmap) {\n    int i;\n    MapSet set;\n    pairSet(hmap, &amp;set);\n    Pair *entries = (Pair *)set.set;\n    for (i = 0; i &lt; set.len; i++) {\n        printf(\"%d -&gt; %s\\n\", entries[i].key, entries[i].val);\n    }\n    free(set.set);\n}\n</code></pre> array_hash_map.kt<pre><code>/* Пара ключ-значение */\nclass Pair(\n    var key: Int,\n    var _val: String\n)\n\n/* Хеш-таблица на основе массива */\nclass ArrayHashMap {\n    // Инициализировать массив, содержащий 100 корзин\n    private val buckets = arrayOfNulls&lt;Pair&gt;(100)\n\n    /* Хеш-функция */\n    fun hashFunc(key: Int): Int {\n        val index = key % 100\n        return index\n    }\n\n    /* Операция поиска */\n    fun get(key: Int): String? {\n        val index = hashFunc(key)\n        val pair = buckets[index] ?: return null\n        return pair._val\n    }\n\n    /* Операция добавления */\n    fun put(key: Int, _val: String) {\n        val pair = Pair(key, _val)\n        val index = hashFunc(key)\n        buckets[index] = pair\n    }\n\n    /* Операция удаления */\n    fun remove(key: Int) {\n        val index = hashFunc(key)\n        // Присвоить null, что означает удаление\n        buckets[index] = null\n    }\n\n    /* Получить все пары ключ-значение */\n    fun pairSet(): MutableList&lt;Pair&gt; {\n        val pairSet = mutableListOf&lt;Pair&gt;()\n        for (pair in buckets) {\n            if (pair != null)\n                pairSet.add(pair)\n        }\n        return pairSet\n    }\n\n    /* Получить все ключи */\n    fun keySet(): MutableList&lt;Int&gt; {\n        val keySet = mutableListOf&lt;Int&gt;()\n        for (pair in buckets) {\n            if (pair != null)\n                keySet.add(pair.key)\n        }\n        return keySet\n    }\n\n    /* Получить все значения */\n    fun valueSet(): MutableList&lt;String&gt; {\n        val valueSet = mutableListOf&lt;String&gt;()\n        for (pair in buckets) {\n            if (pair != null)\n                valueSet.add(pair._val)\n        }\n        return valueSet\n    }\n\n    /* Вывести хеш-таблицу */\n    fun print() {\n        for (kv in pairSet()) {\n            val key = kv.key\n            val _val = kv._val\n            println(\"$key -&gt; $_val\")\n        }\n    }\n}\n</code></pre> array_hash_map.rb<pre><code>### Пара ключ-значение ###\nclass Pair\n  attr_accessor :key, :val\n\n  def initialize(key, val)\n    @key = key\n    @val = val\n  end\nend\n\n### Хеш-таблица на основе массива ###\nclass ArrayHashMap\n  ### Конструктор ###\n  def initialize\n    # Инициализировать массив, содержащий 100 корзин\n    @buckets = Array.new(100)\n  end\n\n  ### Хеш-функция ###\n  def hash_func(key)\n    index = key % 100\n  end\n\n  ### Операция поиска ###\n  def get(key)\n    index = hash_func(key)\n    pair = @buckets[index]\n\n    return if pair.nil?\n    pair.val\n  end\n\n  ### Операция добавления ###\n  def put(key, val)\n    pair = Pair.new(key, val)\n    index = hash_func(key)\n    @buckets[index] = pair\n  end\n\n  ### Операция удаления ###\n  def remove(key)\n    index = hash_func(key)\n    # Присвоить nil, что означает удаление\n    @buckets[index] = nil\n  end\n\n  ### Получить все пары ключ-значение ###\n  def entry_set\n    result = []\n    @buckets.each { |pair| result &lt;&lt; pair unless pair.nil? }\n    result\n  end\n\n  ### Получить все ключи ###\n  def key_set\n    result = []\n    @buckets.each { |pair| result &lt;&lt; pair.key unless pair.nil? }\n    result\n  end\n\n  ### Получить все значения ###\n  def value_set\n    result = []\n    @buckets.each { |pair| result &lt;&lt; pair.val unless pair.nil? }\n    result\n  end\n\n  ### Вывести хеш-таблицу ###\n  def print\n    @buckets.each { |pair| puts \"#{pair.key} -&gt; #{pair.val}\" unless pair.nil? }\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 6. Хеширование","6.1 &nbsp; Хеш-таблица"],"tags":[]},{"location":"chapter_hashing/hash_map/#613-","level":2,"title":"6.1.3   Хеш-коллизии и расширение","text":"<p>По сути, хеш-функция отображает входное пространство, состоящее из всех <code>key</code> , в выходное пространство, состоящее из всех индексов массива, а входное пространство обычно значительно больше выходного. Поэтому теоретически неизбежно существование ситуации \"несколько входов соответствуют одному выходу\".</p> <p>Для хеш-функции из приведенного выше примера, если последние две цифры <code>key</code> совпадают, то совпадает и результат хеш-функции. Например, если искать студентов с номерами 12836 и 20336, то получим:</p> <pre><code>12836 % 100 = 36\n20336 % 100 = 36\n</code></pre> <p>Как показано на рисунке 6-3, два номера указывают на одно и то же имя, что, очевидно, неверно. Такую ситуацию, когда нескольким входам соответствует один и тот же выход, называют хеш-коллизией (hash collision).</p> <p></p> <p> Рисунок 6-3   Пример хеш-коллизии </p> <p>Легко понять, что чем больше емкость хеш-таблицы \\(n\\) , тем ниже вероятность того, что несколько <code>key</code> попадут в один и тот же бакет, а значит, тем меньше коллизий. Поэтому мы можем уменьшать число хеш-коллизий путем расширения хеш-таблицы.</p> <p>Как показано на рисунке 6-4, до расширения пары ключ-значение <code>(136, A)</code> и <code>(236, D)</code> конфликтовали, а после расширения коллизия исчезла.</p> <p></p> <p> Рисунок 6-4   Расширение хеш-таблицы </p> <p>Подобно расширению массива, расширение хеш-таблицы требует перенести все пары ключ-значение из старой таблицы в новую, а это очень затратно по времени; кроме того, поскольку емкость хеш-таблицы <code>capacity</code> изменилась, нам приходится с помощью хеш-функции заново вычислять позиции хранения всех пар ключ-значение, что дополнительно увеличивает вычислительные расходы процесса расширения. Поэтому языки программирования обычно заранее резервируют достаточно большую емкость хеш-таблицы, чтобы избежать частых расширений.</p> <p>Коэффициент загрузки (load factor) - важное понятие хеш-таблицы. Он определяется как отношение числа элементов в хеш-таблице к числу бакетов и используется для оценки степени серьезности хеш-коллизий, а также часто служит условием срабатывания расширения хеш-таблицы. Например, в Java, когда коэффициент загрузки превышает \\(0.75\\) , система расширяет хеш-таблицу до \\(2\\) раз от исходной емкости.</p>","path":["Глава 6. Хеширование","6.1 &nbsp; Хеш-таблица"],"tags":[]},{"location":"chapter_hashing/summary/","level":1,"title":"6.4   Краткие итоги","text":"","path":["Глава 6. Хеширование","6.4 &nbsp; Краткие итоги"],"tags":[]},{"location":"chapter_hashing/summary/#1","level":3,"title":"1.   Основные моменты","text":"<ul> <li>Передав <code>key</code> , мы можем получить <code>value</code> из хеш-таблицы за \\(O(1)\\) времени, поэтому она очень эффективна.</li> <li>К типичным операциям хеш-таблицы относятся поиск, добавление пары ключ-значение, удаление пары ключ-значение и обход хеш-таблицы.</li> <li>Хеш-функция отображает <code>key</code> в индекс массива, после чего можно обратиться к соответствующему бакету и получить <code>value</code> .</li> <li>Два разных <code>key</code> после хеш-функции могут дать один и тот же индекс массива, что приводит к ошибочному результату поиска; это явление называется хеш-коллизией.</li> <li>Чем больше емкость хеш-таблицы, тем ниже вероятность хеш-коллизий. Поэтому хеш-коллизии можно смягчать путем расширения хеш-таблицы. Как и у массива, операция расширения у хеш-таблицы очень затратна.</li> <li>Коэффициент загрузки определяется как отношение числа элементов в хеш-таблице к числу бакетов, отражает степень серьезности хеш-коллизий и часто используется как условие запуска расширения хеш-таблицы.</li> <li>Метод цепочек превращает одиночный элемент в связный список и хранит все конфликтующие элементы в одном списке. Однако слишком длинный список снижает эффективность поиска, поэтому его можно дополнительно преобразовать в красно-черное дерево.</li> <li>Открытая адресация обрабатывает хеш-коллизии за счет многократного пробирования. Линейное пробирование использует фиксированный шаг, его недостатки - невозможность прямого удаления элементов и склонность к кластеризации. Повторное хеширование использует несколько хеш-функций и по сравнению с линейным пробированием меньше подвержено кластеризации, но требует больше вычислений.</li> <li>Разные языки программирования выбирают разные стратегии реализации хеш-таблиц. Например, <code>HashMap</code> в Java использует метод цепочек, а <code>Dict</code> в Python - открытую адресацию.</li> <li>Для хеш-таблицы желательно, чтобы хеш-алгоритм был детерминированным, быстрым и обеспечивал равномерное распределение. В криптографии от него дополнительно требуют устойчивости к коллизиям и эффекта лавины.</li> <li>В качестве модуля хеш-алгоритмы обычно используют большое простое число, чтобы максимально обеспечить равномерность распределения хеш-значений и снизить число хеш-коллизий.</li> <li>К распространенным хеш-алгоритмам относятся MD5, SHA-1, SHA-2 и SHA-3. MD5 часто применяли для проверки целостности файлов, а SHA-2 широко используется в протоколах и приложениях, связанных с безопасностью.</li> <li>Языки программирования обычно предоставляют для типов данных встроенные хеш-алгоритмы, чтобы вычислять индексы бакетов в хеш-таблице. Как правило, хешируемыми могут быть только неизменяемые объекты.</li> </ul>","path":["Глава 6. Хеширование","6.4 &nbsp; Краткие итоги"],"tags":[]},{"location":"chapter_hashing/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: В каких случаях временная сложность хеш-таблицы становится \\(O(n)\\) ?</p> <p>Когда хеш-коллизии становятся достаточно серьезными, временная сложность хеш-таблицы деградирует до \\(O(n)\\) . Если хеш-функция спроектирована хорошо, емкость выбрана разумно, а конфликты распределены достаточно равномерно, то временная сложность обычно считается \\(O(1)\\) . При использовании встроенной хеш-таблицы языка программирования мы, как правило, и принимаем ее за \\(O(1)\\) .</p> <p>Q: Почему бы не использовать хеш-функцию \\(f(x) = x\\) ? Тогда ведь коллизий не будет.</p> <p>При хеш-функции \\(f(x) = x\\) каждому элементу соответствует уникальный индекс бакета, и такая структура становится эквивалентна массиву. Однако входное пространство обычно намного больше выходного пространства (длины массива), поэтому последним шагом хеш-функции обычно выступает взятие по модулю длины массива. Иначе говоря, цель хеш-таблицы состоит в том, чтобы отобразить большее пространство состояний в меньшее пространство и при этом обеспечить \\(O(1)\\) поиска.</p> <p>Q: В основе хеш-таблицы лежат массив, связный список и двоичное дерево. Почему же она может быть быстрее них?</p> <p>Во-первых, у хеш-таблицы повышается временная эффективность, но снижается пространственная эффективность. Значительная часть ее памяти остается неиспользованной.</p> <p>Во-вторых, она быстрее только в определенных сценариях. Если одну и ту же задачу можно реализовать на массиве или связном списке с той же асимптотикой, то часто такая реализация окажется быстрее, чем хеш-таблица. Причина в том, что вычисление хеш-функции само по себе стоит времени, то есть константа в сложности получается выше.</p> <p>Наконец, временная сложность хеш-таблицы тоже может деградировать. Например, при методе цепочек мы все равно выполняем поиск в связном списке или красно-черном дереве, поэтому риск деградации до \\(O(n)\\) сохраняется.</p> <p>Q: Есть ли у повторного хеширования недостаток \"нельзя напрямую удалять элементы\"? Можно ли повторно использовать место, помеченное как удаленное?</p> <p>Повторное хеширование - это разновидность открытой адресации, а у всех методов открытой адресации есть недостаток: элементы нельзя удалять напрямую, поэтому приходится использовать метку удаления. Пространство, помеченное как удаленное, можно использовать повторно. Когда новый элемент вставляется в хеш-таблицу и в процессе пробирования попадает на такую отмеченную позицию, эта позиция может быть занята новым элементом. Такой подход сохраняет последовательность пробирования и одновременно поддерживает приемлемую эффективность использования памяти.</p> <p>Q: Почему при линейном пробировании во время поиска элемента вообще возникает хеш-коллизия?</p> <p>Во время поиска мы через хеш-функцию находим соответствующий бакет и соответствующую пару ключ-значение, но видим, что <code>key</code> не совпадает, а это и означает наличие хеш-коллизии. Поэтому метод линейного пробирования в соответствии с заранее заданным шагом последовательно движется дальше, пока не найдет правильную пару ключ-значение или не убедится, что поиск завершился неудачей.</p> <p>Q: Почему расширение хеш-таблицы помогает смягчать хеш-коллизии?</p> <p>Последний шаг хеш-функции обычно состоит во взятии по модулю длины массива \\(n\\) , чтобы результат попадал в диапазон индексов массива; после расширения длина массива \\(n\\) меняется, а значит, может измениться и индекс, соответствующий данному <code>key</code> . Несколько <code>key</code> , которые раньше попадали в один бакет, после расширения могут распределиться по нескольким бакетам, и тем самым хеш-коллизии будут ослаблены.</p> <p>Q: Если нам нужен быстрый доступ, почему бы просто не использовать массив?</p> <p>Когда <code>key</code> данных - это непрерывные целые числа из маленького диапазона, действительно можно напрямую использовать массив: это просто и эффективно. Но если <code>key</code> имеют другой тип данных (например, строки), тогда нужен хеш-алгоритм, который отобразит <code>key</code> в индекс массива, а хранение элементов будет выполняться через массив бакетов. Такая структура и называется хеш-таблицей.</p>","path":["Глава 6. Хеширование","6.4 &nbsp; Краткие итоги"],"tags":[]},{"location":"chapter_heap/","level":1,"title":"Глава 8.   Куча","text":"<p>Abstract</p> <p>Куча похожа на горные вершины: ярусные, волнистые и самые разные по форме.</p> <p>Каждая вершина имеет свою высоту, но самая высокая всегда бросается в глаза первой.</p>","path":["Глава 8. Куча","Глава 8. &nbsp; Куча"],"tags":[]},{"location":"chapter_heap/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>8.1   Куча</li> <li>8.2   Построение кучи</li> <li>8.3   Задача Top-K</li> <li>8.4   Резюме</li> </ul>","path":["Глава 8. Куча","Глава 8. &nbsp; Куча"],"tags":[]},{"location":"chapter_heap/build_heap/","level":1,"title":"8.2   Построение кучи","text":"<p>В некоторых случаях мы хотим построить кучу, используя сразу все элементы списка. Этот процесс называется \"построением кучи\".</p>","path":["Глава 8. Куча","8.2 &nbsp; Построение кучи"],"tags":[]},{"location":"chapter_heap/build_heap/#821","level":2,"title":"8.2.1   Реализация через операцию добавления в кучу","text":"<p>Сначала мы создаем пустую кучу, затем обходим список и для каждого элемента по очереди выполняем \"операцию добавления в кучу\": сначала помещаем элемент в хвост кучи, а затем выполняем для него упорядочивание \"снизу вверх\".</p> <p>Каждый раз, когда элемент добавляется в кучу, ее длина увеличивается на единицу. Поскольку узлы последовательно добавляются в двоичное дерево сверху вниз, куча строится \"сверху вниз\".</p> <p>Пусть число элементов равно \\(n\\) ; так как каждая операция добавления требует \\(O(\\log{n})\\) времени, временная сложность такого построения кучи составляет \\(O(n \\log n)\\) .</p>","path":["Глава 8. Куча","8.2 &nbsp; Построение кучи"],"tags":[]},{"location":"chapter_heap/build_heap/#822","level":2,"title":"8.2.2   Реализация через обход и упорядочивание","text":"<p>На самом деле можно реализовать и более эффективный способ построения кучи, который состоит из двух шагов.</p> <ol> <li>Без изменений добавить все элементы списка в кучу; в этот момент свойства кучи еще не выполняются.</li> <li>Обойти кучу в обратном порядке, то есть в порядке, обратном обходу по уровням, и по очереди выполнить упорядочивание \"сверху вниз\" для каждого нелистового узла.</li> </ol> <p>После того как некоторый узел был упорядочен, поддерево с этим узлом в качестве корня становится корректной подкучей. А поскольку обход выполняется в обратном порядке, куча строится \"снизу вверх\".</p> <p>Причина выбора обратного обхода в том, что он гарантирует: поддеревья ниже текущего узла уже являются корректными подкучами, а значит, упорядочивание текущего узла действительно будет эффективным.</p> <p>Стоит отметить, что листовые узлы не имеют дочерних узлов, поэтому они естественным образом являются корректными подкучами и не требуют упорядочивания. Как показано в коде ниже, последний нелистовой узел является родителем последнего узла, и именно с него мы начинаем обратный обход и упорядочивание:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby my_heap.py<pre><code>def __init__(self, nums: list[int]):\n    \"\"\"Конструктор, строящий кучу по входному списку\"\"\"\n    # Добавить элементы списка в кучу без изменений\n    self.max_heap = nums\n    # Выполнить heapify для всех узлов, кроме листовых\n    for i in range(self.parent(self.size() - 1), -1, -1):\n        self.sift_down(i)\n</code></pre> my_heap.cpp<pre><code>/* Конструктор, строящий кучу по входному списку */\nMaxHeap(vector&lt;int&gt; nums) {\n    // Добавить элементы списка в кучу без изменений\n    maxHeap = nums;\n    // Выполнить heapify для всех узлов, кроме листовых\n    for (int i = parent(size() - 1); i &gt;= 0; i--) {\n        siftDown(i);\n    }\n}\n</code></pre> my_heap.java<pre><code>/* Конструктор, строящий кучу по входному списку */\nMaxHeap(List&lt;Integer&gt; nums) {\n    // Добавить элементы списка в кучу без изменений\n    maxHeap = new ArrayList&lt;&gt;(nums);\n    // Выполнить heapify для всех узлов, кроме листовых\n    for (int i = parent(size() - 1); i &gt;= 0; i--) {\n        siftDown(i);\n    }\n}\n</code></pre> my_heap.cs<pre><code>/* Конструктор: построить кучу по входному списку */\nMaxHeap(IEnumerable&lt;int&gt; nums) {\n    // Добавить элементы списка в кучу без изменений\n    maxHeap = new List&lt;int&gt;(nums);\n    // Выполнить heapify для всех узлов, кроме листовых\n    var size = Parent(this.Size() - 1);\n    for (int i = size; i &gt;= 0; i--) {\n        SiftDown(i);\n    }\n}\n</code></pre> my_heap.go<pre><code>/* Конструктор, строящий кучу по срезу */\nfunc newMaxHeap(nums []any) *maxHeap {\n    // Добавить элементы списка в кучу без изменений\n    h := &amp;maxHeap{data: nums}\n    for i := h.parent(len(h.data) - 1); i &gt;= 0; i-- {\n        // Выполнить heapify для всех узлов, кроме листовых\n        h.siftDown(i)\n    }\n    return h\n}\n</code></pre> my_heap.swift<pre><code>/* Конструктор, строящий кучу по входному списку */\ninit(nums: [Int]) {\n    // Добавить элементы списка в кучу без изменений\n    maxHeap = nums\n    // Выполнить heapify для всех узлов, кроме листовых\n    for i in (0 ... parent(i: size() - 1)).reversed() {\n        siftDown(i: i)\n    }\n}\n</code></pre> my_heap.js<pre><code>/* Конструктор, создающий пустую кучу или строящий кучу по входному списку */\nconstructor(nums) {\n    // Добавить элементы списка в кучу без изменений\n    this.#maxHeap = nums === undefined ? [] : [...nums];\n    // Выполнить heapify для всех узлов, кроме листовых\n    for (let i = this.#parent(this.size() - 1); i &gt;= 0; i--) {\n        this.#siftDown(i);\n    }\n}\n</code></pre> my_heap.ts<pre><code>/* Конструктор, создающий пустую кучу или строящий кучу по входному списку */\nconstructor(nums?: number[]) {\n    // Добавить элементы списка в кучу без изменений\n    this.maxHeap = nums === undefined ? [] : [...nums];\n    // Выполнить heapify для всех узлов, кроме листовых\n    for (let i = this.parent(this.size() - 1); i &gt;= 0; i--) {\n        this.siftDown(i);\n    }\n}\n</code></pre> my_heap.dart<pre><code>/* Конструктор, строящий кучу по входному списку */\nMaxHeap(List&lt;int&gt; nums) {\n  // Добавить элементы списка в кучу без изменений\n  _maxHeap = nums;\n  // Выполнить heapify для всех узлов, кроме листовых\n  for (int i = _parent(size() - 1); i &gt;= 0; i--) {\n    siftDown(i);\n  }\n}\n</code></pre> my_heap.rs<pre><code>/* Конструктор, строящий кучу по входному списку */\nfn new(nums: Vec&lt;i32&gt;) -&gt; Self {\n    // Добавить элементы списка в кучу без изменений\n    let mut heap = MaxHeap { max_heap: nums };\n    // Выполнить heapify для всех узлов, кроме листовых\n    for i in (0..=Self::parent(heap.size() - 1)).rev() {\n        heap.sift_down(i);\n    }\n    heap\n}\n</code></pre> my_heap.c<pre><code>/* Конструктор, строящий кучу по срезу */\nMaxHeap *newMaxHeap(int nums[], int size) {\n    // Поместить все элементы в кучу\n    MaxHeap *maxHeap = (MaxHeap *)malloc(sizeof(MaxHeap));\n    maxHeap-&gt;size = size;\n    memcpy(maxHeap-&gt;data, nums, size * sizeof(int));\n    for (int i = parent(maxHeap, size - 1); i &gt;= 0; i--) {\n        // Выполнить heapify для всех узлов, кроме листовых\n        siftDown(maxHeap, i);\n    }\n    return maxHeap;\n}\n</code></pre> my_heap.kt<pre><code>/* Максимальная куча */\nclass MaxHeap(nums: MutableList&lt;Int&gt;?) {\n    // Использовать список вместо массива, чтобы не учитывать проблему расширения\n    private val maxHeap = mutableListOf&lt;Int&gt;()\n\n    /* Конструктор, строящий кучу по входному списку */\n    init {\n        // Добавить элементы списка в кучу без изменений\n        maxHeap.addAll(nums!!)\n        // Выполнить heapify для всех узлов, кроме листовых\n        for (i in parent(size() - 1) downTo 0) {\n            siftDown(i)\n        }\n    }\n\n    /* Получить индекс левого дочернего узла */\n    private fun left(i: Int): Int {\n        return 2 * i + 1\n    }\n\n    /* Получить индекс правого дочернего узла */\n    private fun right(i: Int): Int {\n        return 2 * i + 2\n    }\n\n    /* Получить индекс родительского узла */\n    private fun parent(i: Int): Int {\n        return (i - 1) / 2 // Округление вниз при делении\n    }\n\n    /* Поменять элементы местами */\n    private fun swap(i: Int, j: Int) {\n        val temp = maxHeap[i]\n        maxHeap[i] = maxHeap[j]\n        maxHeap[j] = temp\n    }\n\n    /* Получение размера кучи */\n    fun size(): Int {\n        return maxHeap.size\n    }\n\n    /* Проверка, пуста ли куча */\n    fun isEmpty(): Boolean {\n        /* Проверка, пуста ли куча */\n        return size() == 0\n    }\n\n    /* Доступ к элементу на вершине кучи */\n    fun peek(): Int {\n        return maxHeap[0]\n    }\n\n    /* Добавление элемента в кучу */\n    fun push(_val: Int) {\n        // Добавление узла\n        maxHeap.add(_val)\n        // Просеивание снизу вверх\n        siftUp(size() - 1)\n    }\n\n    /* Начиная с узла i, выполнить просеивание снизу вверх */\n    private fun siftUp(it: Int) {\n        // Параметры функций в Kotlin неизменяемы, поэтому создается временная переменная\n        var i = it\n        while (true) {\n            // Получение родительского узла для узла i\n            val p = parent(i)\n            // Завершить heapify, когда «корневой узел уже пройден» или «узел не требует исправления»\n            if (p &lt; 0 || maxHeap[i] &lt;= maxHeap[p]) break\n            // Поменять два узла местами\n            swap(i, p)\n            // Циклическое просеивание вверх\n            i = p\n        }\n    }\n\n    /* Извлечение элемента из кучи */\n    fun pop(): Int {\n        // Обработка пустого случая\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n        swap(0, size() - 1)\n        // Удаление узла\n        val _val = maxHeap.removeAt(size() - 1)\n        // Просеивание сверху вниз\n        siftDown(0)\n        // Вернуть элемент с вершины кучи\n        return _val\n    }\n\n    /* Начиная с узла i, выполнить просеивание сверху вниз */\n    private fun siftDown(it: Int) {\n        // Параметры функций в Kotlin неизменяемы, поэтому создается временная переменная\n        var i = it\n        while (true) {\n            // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n            val l = left(i)\n            val r = right(i)\n            var ma = i\n            if (l &lt; size() &amp;&amp; maxHeap[l] &gt; maxHeap[ma]) ma = l\n            if (r &lt; size() &amp;&amp; maxHeap[r] &gt; maxHeap[ma]) ma = r\n            // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n            if (ma == i) break\n            // Поменять два узла местами\n            swap(i, ma)\n            // Циклическое просеивание вниз\n            i = ma\n        }\n    }\n\n    /* Вывести кучу (двоичное дерево) */\n    fun print() {\n        val queue = PriorityQueue { a: Int, b: Int -&gt; b - a }\n        queue.addAll(maxHeap)\n        printHeap(queue)\n    }\n}\n</code></pre> my_heap.rb<pre><code>### Конструктор, строящий кучу по входному списку ###\ndef initialize(nums)\n  # Добавить элементы списка в кучу без изменений\n  @max_heap = nums\n  # Выполнить heapify для всех узлов, кроме листовых\n  parent(size - 1).downto(0) do |i|\n    sift_down(i)\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 8. Куча","8.2 &nbsp; Построение кучи"],"tags":[]},{"location":"chapter_heap/build_heap/#823","level":2,"title":"8.2.3   Анализ сложности","text":"<p>Теперь попробуем оценить временную сложность второго способа построения кучи.</p> <ul> <li>Пусть число узлов полного двоичного дерева равно \\(n\\) , тогда число листовых узлов равно \\((n + 1) / 2\\) , где \\(/\\) означает целочисленное деление вниз. Следовательно, число узлов, которые нужно упорядочивать, равно \\((n - 1) / 2\\) .</li> <li>В процессе упорядочивания сверху вниз каждый узел в худшем случае может просеяться до листа, поэтому максимальное число итераций равно высоте двоичного дерева \\(\\log n\\) .</li> </ul> <p>Перемножив эти два значения, можно получить временную сложность построения кучи \\(O(n \\log n)\\) . Но эта оценка неточна, потому что мы не учли свойство двоичного дерева: на нижних уровнях узлов гораздо больше, чем на верхних.</p> <p>Далее выполним более точный расчет. Чтобы упростить вычисления, предположим, что дано \"идеальное двоичное дерево\" высоты \\(h\\) с числом узлов \\(n\\) ; это предположение не повлияет на корректность результата.</p> <p></p> <p> Рисунок 8-5   Число узлов на каждом уровне идеального двоичного дерева </p> <p>Как показано на рисунке 8-5, максимальное число итераций упорядочивания \"сверху вниз\" для некоторого узла равно расстоянию от этого узла до листового узла, а это расстояние как раз и есть \"высота узла\". Поэтому мы можем просуммировать для каждого уровня выражение \"число узлов \\(\\times\\) высота узла\" и получить суммарное число итераций упорядочивания для всех узлов.</p> \\[ T(h) = 2^0h + 2^1(h-1) + 2^2(h-2) + \\dots + 2^{(h-1)}\\times1 \\] <p>Чтобы упростить это выражение, воспользуемся школьными знаниями о последовательностях и сначала умножим \\(T(h)\\) на \\(2\\) :</p> \\[ \\begin{aligned} T(h) &amp; = 2^0h + 2^1(h-1) + 2^2(h-2) + \\dots + 2^{h-1}\\times1 \\newline 2 T(h) &amp; = 2^1h + 2^2(h-1) + 2^3(h-2) + \\dots + 2^{h}\\times1 \\newline \\end{aligned} \\] <p>Используя метод вычитания со сдвигом, вычтем из нижней строки \\(2 T(h)\\) верхнюю строку \\(T(h)\\) , тогда получим:</p> \\[ 2T(h) - T(h) = T(h) = -2^0h + 2^1 + 2^2 + \\dots + 2^{h-1} + 2^h \\] <p>Из этого выражения видно, что \\(T(h)\\) представляет собой геометрическую прогрессию, поэтому можно напрямую применить формулу суммы и получить временную сложность:</p> \\[ \\begin{aligned} T(h) &amp; = 2 \\frac{1 - 2^h}{1 - 2} - h \\newline &amp; = 2^{h+1} - h - 2 \\newline &amp; = O(2^h) \\end{aligned} \\] <p>Далее, число узлов идеального двоичного дерева высоты \\(h\\) равно \\(n = 2^{h+1} - 1\\) , поэтому несложно получить сложность \\(O(2^h) = O(n)\\) . Из этого вывода следует, что построение кучи из входного списка имеет временную сложность \\(O(n)\\) , что очень эффективно.</p>","path":["Глава 8. Куча","8.2 &nbsp; Построение кучи"],"tags":[]},{"location":"chapter_heap/heap/","level":1,"title":"8.1   Куча","text":"<p>Куча (heap) - это полное двоичное дерево, удовлетворяющее определенным условиям. Основных типов кучи два, как показано на рисунке 8-1.</p> <ul> <li>Минимальная куча (min heap): значение любого узла \\(\\leq\\) значения его дочерних узлов.</li> <li>Максимальная куча (max heap): значение любого узла \\(\\geq\\) значения его дочерних узлов.</li> </ul> <p></p> <p> Рисунок 8-1   Минимальная куча и максимальная куча </p> <p>Куча, являясь частным случаем полного двоичного дерева, обладает следующими свойствами.</p> <ul> <li>Узлы самого нижнего уровня заполняются слева, а все остальные уровни заполнены полностью.</li> <li>Корневой узел двоичного дерева мы называем \"вершиной кучи\", а самый правый узел нижнего уровня - \"основанием кучи\".</li> <li>Для максимальной (минимальной) кучи значение элемента на вершине, то есть у корневого узла, является максимальным (минимальным).</li> </ul>","path":["Глава 8. Куча","8.1 &nbsp; Куча"],"tags":[]},{"location":"chapter_heap/heap/#811","level":2,"title":"8.1.1   Распространенные операции с кучей","text":"<p>Нужно отметить, что многие языки программирования предоставляют не саму кучу, а очередь с приоритетом (priority queue) - абстрактную структуру данных, определяемую как очередь, в которой элементы извлекаются в соответствии с приоритетом.</p> <p>На практике куча обычно используется для реализации очереди с приоритетом, а максимальная куча эквивалентна очереди с приоритетом, в которой элементы извлекаются по убыванию. С точки зрения использования \"очередь с приоритетом\" и \"куча\" можно считать эквивалентными структурами данных. Поэтому в этой книге мы не будем специально различать их и в дальнейшем будем единообразно называть \"кучей\".</p> <p>Распространенные операции с кучей приведены в таблице 8-1. Конкретные имена методов зависят от языка программирования.</p> <p> Таблица 8-1   Эффективность операций с кучей </p> Имя метода Описание Временная сложность <code>push()</code> Поместить элемент в кучу \\(O(\\log n)\\) <code>pop()</code> Извлечь элемент с вершины кучи \\(O(\\log n)\\) <code>peek()</code> Получить доступ к вершине кучи (для max / min кучи это соответственно максимум / минимум) \\(O(1)\\) <code>size()</code> Получить число элементов в куче \\(O(1)\\) <code>isEmpty()</code> Проверить, пуста ли куча \\(O(1)\\) <p>В реальных приложениях мы можем напрямую использовать классы кучи, предоставляемые языком программирования, или классы очереди с приоритетом.</p> <p>Подобно сортировкам \"по возрастанию\" и \"по убыванию\", мы можем переключаться между \"минимальной кучей\" и \"максимальной кучей\", изменяя <code>flag</code> или модифицируя <code>Comparator</code> . Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby heap.py<pre><code># Инициализация минимальной кучи\nmin_heap, flag = [], 1\n# Инициализация максимальной кучи\nmax_heap, flag = [], -1\n\n# Модуль heapq в Python по умолчанию реализует минимальную кучу\n# Если инвертировать знак элемента перед добавлением, то отношение порядка перевернется и так реализуется максимальная куча\n# В этом примере flag = 1 соответствует минимальной куче, а flag = -1 - максимальной\n\n# Добавление элементов в кучу\nheapq.heappush(max_heap, flag * 1)\nheapq.heappush(max_heap, flag * 3)\nheapq.heappush(max_heap, flag * 2)\nheapq.heappush(max_heap, flag * 5)\nheapq.heappush(max_heap, flag * 4)\n\n# Получение элемента на вершине кучи\npeek: int = flag * max_heap[0] # 5\n\n# Извлечение элемента с вершины кучи\n# Извлеченные элементы образуют последовательность по убыванию\nval = flag * heapq.heappop(max_heap) # 5\nval = flag * heapq.heappop(max_heap) # 4\nval = flag * heapq.heappop(max_heap) # 3\nval = flag * heapq.heappop(max_heap) # 2\nval = flag * heapq.heappop(max_heap) # 1\n\n# Получение размера кучи\nsize: int = len(max_heap)\n\n# Проверка, пуста ли куча\nis_empty: bool = not max_heap\n\n# Построение кучи из входного списка\nmin_heap: list[int] = [1, 3, 2, 5, 4]\nheapq.heapify(min_heap)\n</code></pre> heap.cpp<pre><code>/* Инициализация кучи */\n// Инициализация минимальной кучи\npriority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; minHeap;\n// Инициализация максимальной кучи\npriority_queue&lt;int, vector&lt;int&gt;, less&lt;int&gt;&gt; maxHeap;\n\n/* Добавление элементов в кучу */\nmaxHeap.push(1);\nmaxHeap.push(3);\nmaxHeap.push(2);\nmaxHeap.push(5);\nmaxHeap.push(4);\n\n/* Получение элемента на вершине кучи */\nint peek = maxHeap.top(); // 5\n\n/* Извлечение элемента с вершины кучи */\n// Извлеченные элементы образуют последовательность по убыванию\nmaxHeap.pop(); // 5\nmaxHeap.pop(); // 4\nmaxHeap.pop(); // 3\nmaxHeap.pop(); // 2\nmaxHeap.pop(); // 1\n\n/* Получение размера кучи */\nint size = maxHeap.size();\n\n/* Проверка, пуста ли куча */\nbool isEmpty = maxHeap.empty();\n\n/* Построение кучи из входного списка */\nvector&lt;int&gt; input{1, 3, 2, 5, 4};\npriority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; minHeap(input.begin(), input.end());\n</code></pre> heap.java<pre><code>/* Инициализация кучи */\n// Инициализация минимальной кучи\nQueue&lt;Integer&gt; minHeap = new PriorityQueue&lt;&gt;();\n// Инициализация максимальной кучи (достаточно изменить Comparator через lambda)\nQueue&lt;Integer&gt; maxHeap = new PriorityQueue&lt;&gt;((a, b) -&gt; b - a);\n\n/* Добавление элементов в кучу */\nmaxHeap.offer(1);\nmaxHeap.offer(3);\nmaxHeap.offer(2);\nmaxHeap.offer(5);\nmaxHeap.offer(4);\n\n/* Получение элемента на вершине кучи */\nint peek = maxHeap.peek(); // 5\n\n/* Извлечение элемента с вершины кучи */\n// Извлеченные элементы образуют последовательность по убыванию\npeek = maxHeap.poll(); // 5\npeek = maxHeap.poll(); // 4\npeek = maxHeap.poll(); // 3\npeek = maxHeap.poll(); // 2\npeek = maxHeap.poll(); // 1\n\n/* Получение размера кучи */\nint size = maxHeap.size();\n\n/* Проверка, пуста ли куча */\nboolean isEmpty = maxHeap.isEmpty();\n\n/* Построение кучи из входного списка */\nminHeap = new PriorityQueue&lt;&gt;(Arrays.asList(1, 3, 2, 5, 4));\n</code></pre> heap.cs<pre><code>/* Инициализация кучи */\n// Инициализация минимальной кучи\nPriorityQueue&lt;int, int&gt; minHeap = new();\n// Инициализация максимальной кучи (достаточно изменить Comparer через lambda)\nPriorityQueue&lt;int, int&gt; maxHeap = new(Comparer&lt;int&gt;.Create((x, y) =&gt; y.CompareTo(x)));\n\n/* Добавление элементов в кучу */\nmaxHeap.Enqueue(1, 1);\nmaxHeap.Enqueue(3, 3);\nmaxHeap.Enqueue(2, 2);\nmaxHeap.Enqueue(5, 5);\nmaxHeap.Enqueue(4, 4);\n\n/* Получение элемента на вершине кучи */\nint peek = maxHeap.Peek();//5\n\n/* Извлечение элемента с вершины кучи */\n// Извлеченные элементы образуют последовательность по убыванию\npeek = maxHeap.Dequeue();  // 5\npeek = maxHeap.Dequeue();  // 4\npeek = maxHeap.Dequeue();  // 3\npeek = maxHeap.Dequeue();  // 2\npeek = maxHeap.Dequeue();  // 1\n\n/* Получение размера кучи */\nint size = maxHeap.Count;\n\n/* Проверка, пуста ли куча */\nbool isEmpty = maxHeap.Count == 0;\n\n/* Построение кучи из входного списка */\nminHeap = new PriorityQueue&lt;int, int&gt;([(1, 1), (3, 3), (2, 2), (5, 5), (4, 4)]);\n</code></pre> heap.go<pre><code>// В Go можно построить целочисленную максимальную кучу, реализовав heap.Interface\n// Для реализации heap.Interface также нужно реализовать sort.Interface\ntype intHeap []any\n\n// Метод Push из heap.Interface, реализует добавление элемента в кучу\nfunc (h *intHeap) Push(x any) {\n    // Push и Pop используют pointer receiver\n    // Потому что они не только изменяют содержимое среза, но и его длину\n    *h = append(*h, x.(int))\n}\n\n// Метод Pop из heap.Interface, реализует извлечение элемента с вершины кучи\nfunc (h *intHeap) Pop() any {\n    // Извлекаемый элемент хранится в конце\n    last := (*h)[len(*h)-1]\n    *h = (*h)[:len(*h)-1]\n    return last\n}\n\n// Метод Len из sort.Interface\nfunc (h *intHeap) Len() int {\n    return len(*h)\n}\n\n// Метод Less из sort.Interface\nfunc (h *intHeap) Less(i, j int) bool {\n    // Для минимальной кучи здесь нужно заменить сравнение на &lt;\n    return (*h)[i].(int) &gt; (*h)[j].(int)\n}\n\n// Метод Swap из sort.Interface\nfunc (h *intHeap) Swap(i, j int) {\n    (*h)[i], (*h)[j] = (*h)[j], (*h)[i]\n}\n\n// Top получает элемент на вершине кучи\nfunc (h *intHeap) Top() any {\n    return (*h)[0]\n}\n\n/* Driver Code */\nfunc TestHeap(t *testing.T) {\n    /* Инициализация кучи */\n    // Инициализация максимальной кучи\n    maxHeap := &amp;intHeap{}\n    heap.Init(maxHeap)\n    /* Добавление элементов в кучу */\n    // Вызываем методы heap.Interface для добавления элементов\n    heap.Push(maxHeap, 1)\n    heap.Push(maxHeap, 3)\n    heap.Push(maxHeap, 2)\n    heap.Push(maxHeap, 4)\n    heap.Push(maxHeap, 5)\n\n    /* Получение элемента на вершине кучи */\n    top := maxHeap.Top()\n    fmt.Printf(\"Элемент на вершине кучи: %d\\n\", top)\n\n    /* Извлечение элемента с вершины кучи */\n    // Вызываем методы heap.Interface для удаления элементов\n    heap.Pop(maxHeap) // 5\n    heap.Pop(maxHeap) // 4\n    heap.Pop(maxHeap) // 3\n    heap.Pop(maxHeap) // 2\n    heap.Pop(maxHeap) // 1\n\n    /* Получение размера кучи */\n    size := len(*maxHeap)\n    fmt.Printf(\"Число элементов в куче: %d\\n\", size)\n\n    /* Проверка, пуста ли куча */\n    isEmpty := len(*maxHeap) == 0\n    fmt.Printf(\"Пуста ли куча: %t\\n\", isEmpty)\n}\n</code></pre> heap.swift<pre><code>/* Инициализация кучи */\n// Тип Heap в Swift поддерживает и max-heap, и min-heap, но требует swift-collections\nvar heap = Heap&lt;Int&gt;()\n\n/* Добавление элементов в кучу */\nheap.insert(1)\nheap.insert(3)\nheap.insert(2)\nheap.insert(5)\nheap.insert(4)\n\n/* Получение элемента на вершине кучи */\nvar peek = heap.max()!\n\n/* Извлечение элемента с вершины кучи */\npeek = heap.removeMax() // 5\npeek = heap.removeMax() // 4\npeek = heap.removeMax() // 3\npeek = heap.removeMax() // 2\npeek = heap.removeMax() // 1\n\n/* Получение размера кучи */\nlet size = heap.count\n\n/* Проверка, пуста ли куча */\nlet isEmpty = heap.isEmpty\n\n/* Построение кучи из входного списка */\nlet heap2 = Heap([1, 3, 2, 5, 4])\n</code></pre> heap.js<pre><code>// В JavaScript нет встроенного класса Heap\n</code></pre> heap.ts<pre><code>// В TypeScript нет встроенного класса Heap\n</code></pre> heap.dart<pre><code>// В Dart нет встроенного класса Heap\n</code></pre> heap.rs<pre><code>use std::collections::BinaryHeap;\nuse std::cmp::Reverse;\n\n/* Инициализация кучи */\n// Инициализация минимальной кучи\nlet mut min_heap = BinaryHeap::&lt;Reverse&lt;i32&gt;&gt;::new();\n// Инициализация максимальной кучи\nlet mut max_heap = BinaryHeap::new();\n\n/* Добавление элементов в кучу */\nmax_heap.push(1);\nmax_heap.push(3);\nmax_heap.push(2);\nmax_heap.push(5);\nmax_heap.push(4);\n\n/* Получение элемента на вершине кучи */\nlet peek = max_heap.peek().unwrap();  // 5\n\n/* Извлечение элемента с вершины кучи */\n// Извлеченные элементы образуют последовательность по убыванию\nlet peek = max_heap.pop().unwrap();   // 5\nlet peek = max_heap.pop().unwrap();   // 4\nlet peek = max_heap.pop().unwrap();   // 3\nlet peek = max_heap.pop().unwrap();   // 2\nlet peek = max_heap.pop().unwrap();   // 1\n\n/* Получение размера кучи */\nlet size = max_heap.len();\n\n/* Проверка, пуста ли куча */\nlet is_empty = max_heap.is_empty();\n\n/* Построение кучи из входного списка */\nlet min_heap = BinaryHeap::from(vec![Reverse(1), Reverse(3), Reverse(2), Reverse(5), Reverse(4)]);\n</code></pre> heap.c<pre><code>// В C нет встроенного класса Heap\n</code></pre> heap.kt<pre><code>/* Инициализация кучи */\n// Инициализация минимальной кучи\nvar minHeap = PriorityQueue&lt;Int&gt;()\n// Инициализация максимальной кучи (достаточно изменить Comparator через lambda)\nval maxHeap = PriorityQueue { a: Int, b: Int -&gt; b - a }\n\n/* Добавление элементов в кучу */\nmaxHeap.offer(1)\nmaxHeap.offer(3)\nmaxHeap.offer(2)\nmaxHeap.offer(5)\nmaxHeap.offer(4)\n\n/* Получение элемента на вершине кучи */\nvar peek = maxHeap.peek() // 5\n\n/* Извлечение элемента с вершины кучи */\n// Извлеченные элементы образуют последовательность по убыванию\npeek = maxHeap.poll() // 5\npeek = maxHeap.poll() // 4\npeek = maxHeap.poll() // 3\npeek = maxHeap.poll() // 2\npeek = maxHeap.poll() // 1\n\n/* Получение размера кучи */\nval size = maxHeap.size\n\n/* Проверка, пуста ли куча */\nval isEmpty = maxHeap.isEmpty()\n\n/* Построение кучи из входного списка */\nminHeap = PriorityQueue(mutableListOf(1, 3, 2, 5, 4))\n</code></pre> heap.rb<pre><code># В Ruby нет встроенного класса Heap\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=import%20heapq%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20min-%D0%BA%D1%83%D1%87%D1%83%0A%20%20%20%20min_heap%2C%20flag%20%3D%20%5B%5D%2C%201%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20max-%D0%BA%D1%83%D1%87%D1%83%0A%20%20%20%20max_heap%2C%20flag%20%3D%20%5B%5D%2C%20-1%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8C%20heapq%20%D0%B2%20Python%20%D0%BF%D0%BE%20%D1%83%D0%BC%D0%BE%D0%BB%D1%87%D0%B0%D0%BD%D0%B8%D1%8E%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D1%83%D0%B5%D1%82%20min-%D0%BA%D1%83%D1%87%D1%83%0A%20%20%20%20%23%20%D0%95%D1%81%D0%BB%D0%B8%20%D0%BF%D0%B5%D1%80%D0%B5%D0%B4%20%D0%BF%D0%BE%D0%BC%D0%B5%D1%89%D0%B5%D0%BD%D0%B8%D0%B5%D0%BC%20%D0%B2%20%D0%BA%D1%83%D1%87%D1%83%20%D0%B1%D1%80%D0%B0%D1%82%D1%8C%20%D0%BE%D1%82%D1%80%D0%B8%D1%86%D0%B0%D0%BD%D0%B8%D0%B5%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D0%B0%2C%20%D0%BC%D0%BE%D0%B6%D0%BD%D0%BE%20%D0%BE%D0%B1%D1%80%D0%B0%D1%82%D0%B8%D1%82%D1%8C%20%D0%BE%D1%82%D0%BD%D0%BE%D1%88%D0%B5%D0%BD%D0%B8%D0%B5%20%D0%BF%D0%BE%D1%80%D1%8F%D0%B4%D0%BA%D0%B0%20%D0%B8%20%D1%82%D0%B5%D0%BC%20%D1%81%D0%B0%D0%BC%D1%8B%D0%BC%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20max-%D0%BA%D1%83%D1%87%D1%83%0A%20%20%20%20%23%20%D0%92%20%D1%8D%D1%82%D0%BE%D0%BC%20%D0%BF%D1%80%D0%B8%D0%BC%D0%B5%D1%80%D0%B5%20flag%20%3D%201%20%D1%81%D0%BE%D0%BE%D1%82%D0%B2%D0%B5%D1%82%D1%81%D1%82%D0%B2%D1%83%D0%B5%D1%82%20min-%D0%BA%D1%83%D1%87%D0%B5%2C%20%D0%B0%20flag%20%3D%20-1%20%D1%81%D0%BE%D0%BE%D1%82%D0%B2%D0%B5%D1%82%D1%81%D1%82%D0%B2%D1%83%D0%B5%D1%82%20max-%D0%BA%D1%83%D1%87%D0%B5%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%94%D0%BE%D0%B1%D0%B0%D0%B2%D0%B8%D1%82%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%B2%20%D0%BA%D1%83%D1%87%D1%83%0A%20%20%20%20heapq.heappush%28max_heap%2C%20flag%20%2A%201%29%0A%20%20%20%20heapq.heappush%28max_heap%2C%20flag%20%2A%203%29%0A%20%20%20%20heapq.heappush%28max_heap%2C%20flag%20%2A%202%29%0A%20%20%20%20heapq.heappush%28max_heap%2C%20flag%20%2A%205%29%0A%20%20%20%20heapq.heappush%28max_heap%2C%20flag%20%2A%204%29%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9F%D0%BE%D0%BB%D1%83%D1%87%D0%B8%D1%82%D1%8C%20%D0%B2%D0%B5%D1%80%D1%85%D0%BD%D0%B8%D0%B9%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%BA%D1%83%D1%87%D0%B8%0A%20%20%20%20peek%20%3D%20flag%20%2A%20max_heap%5B0%5D%20%23%205%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%98%D0%B7%D0%B2%D0%BB%D0%B5%D1%87%D1%8C%20%D0%B2%D0%B5%D1%80%D1%85%D0%BD%D0%B8%D0%B9%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%B8%D0%B7%20%D0%BA%D1%83%D1%87%D0%B8%0A%20%20%20%20%23%20%D0%98%D0%B7%D0%B2%D0%BB%D0%B5%D1%87%D0%B5%D0%BD%D0%BD%D1%8B%D0%B5%20%D0%B8%D0%B7%20%D0%BA%D1%83%D1%87%D0%B8%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D1%8B%20%D0%BE%D0%B1%D1%80%D0%B0%D0%B7%D1%83%D1%8E%D1%82%20%D0%BF%D0%BE%D1%81%D0%BB%D0%B5%D0%B4%D0%BE%D0%B2%D0%B0%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D1%81%D1%82%D1%8C%20%D0%BE%D1%82%20%D0%B1%D0%BE%D0%BB%D1%8C%D1%88%D0%B5%D0%B3%D0%BE%20%D0%BA%20%D0%BC%D0%B5%D0%BD%D1%8C%D1%88%D0%B5%D0%BC%D1%83%0A%20%20%20%20val%20%3D%20flag%20%2A%20heapq.heappop%28max_heap%29%20%23%205%0A%20%20%20%20val%20%3D%20flag%20%2A%20heapq.heappop%28max_heap%29%20%23%204%0A%20%20%20%20val%20%3D%20flag%20%2A%20heapq.heappop%28max_heap%29%20%23%203%0A%20%20%20%20val%20%3D%20flag%20%2A%20heapq.heappop%28max_heap%29%20%23%202%0A%20%20%20%20val%20%3D%20flag%20%2A%20heapq.heappop%28max_heap%29%20%23%201%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9F%D0%BE%D0%BB%D1%83%D1%87%D0%B8%D1%82%D1%8C%20%D1%80%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%BA%D1%83%D1%87%D0%B8%0A%20%20%20%20size%20%3D%20len%28max_heap%29%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9F%D1%80%D0%BE%D0%B2%D0%B5%D1%80%D0%B8%D1%82%D1%8C%2C%20%D0%BF%D1%83%D1%81%D1%82%D0%B0%20%D0%BB%D0%B8%20%D0%BA%D1%83%D1%87%D0%B0%0A%20%20%20%20is_empty%20%3D%20not%20max_heap%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%92%D1%85%D0%BE%D0%B4%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%D0%B8%D0%BF%D0%BE%D1%81%D1%82%D1%80%D0%BE%D0%B5%D0%BD%D0%B8%D0%B5%20%D0%BA%D1%83%D1%87%D0%B8%0A%20%20%20%20min_heap%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20heapq.heapify%28min_heap%29&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 8. Куча","8.1 &nbsp; Куча"],"tags":[]},{"location":"chapter_heap/heap/#812","level":2,"title":"8.1.2   Реализация кучи","text":"<p>Ниже реализуется максимальная куча. Чтобы преобразовать ее в минимальную кучу, достаточно инвертировать всю логику сравнений по величине, например заменить \\(\\geq\\) на \\(\\leq\\) . Заинтересованные читатели могут попробовать реализовать это самостоятельно.</p>","path":["Глава 8. Куча","8.1 &nbsp; Куча"],"tags":[]},{"location":"chapter_heap/heap/#1","level":3,"title":"1.   Хранение и представление кучи","text":"<p>В разделе \"Двоичные деревья\" мы уже говорили, что полное двоичное дерево очень удобно представлять массивом. Поскольку куча как раз и является полным двоичным деревом, для хранения кучи мы также будем использовать массив.</p> <p>Когда двоичное дерево представляется массивом, элементы массива соответствуют значениям узлов, а индексы - положениям этих узлов в двоичном дереве. Указатели на узлы реализуются через формулы отображения индексов.</p> <p>Как показано на рисунке 8-2, для заданного индекса \\(i\\) индекс левого дочернего узла равен \\(2i + 1\\) , правого дочернего узла - \\(2i + 2\\) , а родительского узла - \\((i - 1) / 2\\) с округлением вниз. Если индекс выходит за допустимые границы, это означает пустой узел или отсутствие узла.</p> <p></p> <p> Рисунок 8-2   Представление и хранение кучи </p> <p>Мы можем инкапсулировать формулы отображения индексов в функции, чтобы потом было удобнее ими пользоваться:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby my_heap.py<pre><code>def left(self, i: int) -&gt; int:\n    \"\"\"Получить индекс левого дочернего узла\"\"\"\n    return 2 * i + 1\n\ndef right(self, i: int) -&gt; int:\n    \"\"\"Получить индекс правого дочернего узла\"\"\"\n    return 2 * i + 2\n\ndef parent(self, i: int) -&gt; int:\n    \"\"\"Получить индекс родительского узла\"\"\"\n    return (i - 1) // 2  # Округление вниз при делении\n</code></pre> my_heap.cpp<pre><code>/* Получить индекс левого дочернего узла */\nint left(int i) {\n    return 2 * i + 1;\n}\n\n/* Получить индекс правого дочернего узла */\nint right(int i) {\n    return 2 * i + 2;\n}\n\n/* Получить индекс родительского узла */\nint parent(int i) {\n    return (i - 1) / 2; // Округление вниз при делении\n}\n</code></pre> my_heap.java<pre><code>/* Получить индекс левого дочернего узла */\nint left(int i) {\n    return 2 * i + 1;\n}\n\n/* Получить индекс правого дочернего узла */\nint right(int i) {\n    return 2 * i + 2;\n}\n\n/* Получить индекс родительского узла */\nint parent(int i) {\n    return (i - 1) / 2; // Округление вниз при делении\n}\n</code></pre> my_heap.cs<pre><code>/* Получить индекс левого дочернего узла */\nint Left(int i) {\n    return 2 * i + 1;\n}\n\n/* Получить индекс правого дочернего узла */\nint Right(int i) {\n    return 2 * i + 2;\n}\n\n/* Получить индекс родительского узла */\nint Parent(int i) {\n    return (i - 1) / 2; // Округление вниз при делении\n}\n</code></pre> my_heap.go<pre><code>/* Получить индекс левого дочернего узла */\nfunc (h *maxHeap) left(i int) int {\n    return 2*i + 1\n}\n\n/* Получить индекс правого дочернего узла */\nfunc (h *maxHeap) right(i int) int {\n    return 2*i + 2\n}\n\n/* Получить индекс родительского узла */\nfunc (h *maxHeap) parent(i int) int {\n    // Округление вниз при делении\n    return (i - 1) / 2\n}\n</code></pre> my_heap.swift<pre><code>/* Получить индекс левого дочернего узла */\nfunc left(i: Int) -&gt; Int {\n    2 * i + 1\n}\n\n/* Получить индекс правого дочернего узла */\nfunc right(i: Int) -&gt; Int {\n    2 * i + 2\n}\n\n/* Получить индекс родительского узла */\nfunc parent(i: Int) -&gt; Int {\n    (i - 1) / 2 // Округление вниз при делении\n}\n</code></pre> my_heap.js<pre><code>/* Получить индекс левого дочернего узла */\n#left(i) {\n    return 2 * i + 1;\n}\n\n/* Получить индекс правого дочернего узла */\n#right(i) {\n    return 2 * i + 2;\n}\n\n/* Получить индекс родительского узла */\n#parent(i) {\n    return Math.floor((i - 1) / 2); // Округление вниз при делении\n}\n</code></pre> my_heap.ts<pre><code>/* Получить индекс левого дочернего узла */\nleft(i: number): number {\n    return 2 * i + 1;\n}\n\n/* Получить индекс правого дочернего узла */\nright(i: number): number {\n    return 2 * i + 2;\n}\n\n/* Получить индекс родительского узла */\nparent(i: number): number {\n    return Math.floor((i - 1) / 2); // Округление вниз при делении\n}\n</code></pre> my_heap.dart<pre><code>/* Получить индекс левого дочернего узла */\nint _left(int i) {\n  return 2 * i + 1;\n}\n\n/* Получить индекс правого дочернего узла */\nint _right(int i) {\n  return 2 * i + 2;\n}\n\n/* Получить индекс родительского узла */\nint _parent(int i) {\n  return (i - 1) ~/ 2; // Округление вниз при делении\n}\n</code></pre> my_heap.rs<pre><code>/* Получить индекс левого дочернего узла */\nfn left(i: usize) -&gt; usize {\n    2 * i + 1\n}\n\n/* Получить индекс правого дочернего узла */\nfn right(i: usize) -&gt; usize {\n    2 * i + 2\n}\n\n/* Получить индекс родительского узла */\nfn parent(i: usize) -&gt; usize {\n    (i - 1) / 2 // Округление вниз при делении\n}\n</code></pre> my_heap.c<pre><code>/* Получить индекс левого дочернего узла */\nint left(MaxHeap *maxHeap, int i) {\n    return 2 * i + 1;\n}\n\n/* Получить индекс правого дочернего узла */\nint right(MaxHeap *maxHeap, int i) {\n    return 2 * i + 2;\n}\n\n/* Получить индекс родительского узла */\nint parent(MaxHeap *maxHeap, int i) {\n    return (i - 1) / 2; // Округление вниз\n}\n</code></pre> my_heap.kt<pre><code>/* Получить индекс левого дочернего узла */\nfun left(i: Int): Int {\n    return 2 * i + 1\n}\n\n/* Получить индекс правого дочернего узла */\nfun right(i: Int): Int {\n    return 2 * i + 2\n}\n\n/* Получить индекс родительского узла */\nfun parent(i: Int): Int {\n    return (i - 1) / 2 // Округление вниз при делении\n}\n</code></pre> my_heap.rb<pre><code>### Получить индекс левого дочернего узла ###\ndef left(i)\n  2 * i + 1\nend\n\n### Получить индекс правого дочернего узла ###\ndef right(i)\n  2 * i + 2\nend\n\n### Получить индекс родительского узла ###\ndef parent(i)\n  (i - 1) / 2     # Округление вниз при делении\nend\n</code></pre>","path":["Глава 8. Куча","8.1 &nbsp; Куча"],"tags":[]},{"location":"chapter_heap/heap/#2","level":3,"title":"2.   Доступ к элементу на вершине кучи","text":"<p>Элемент на вершине кучи - это корневой узел двоичного дерева, то есть первый элемент списка:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby my_heap.py<pre><code>def peek(self) -&gt; int:\n    \"\"\"Доступ к элементу на вершине кучи\"\"\"\n    return self.max_heap[0]\n</code></pre> my_heap.cpp<pre><code>/* Доступ к элементу на вершине кучи */\nint peek() {\n    return maxHeap[0];\n}\n</code></pre> my_heap.java<pre><code>/* Доступ к элементу на вершине кучи */\nint peek() {\n    return maxHeap.get(0);\n}\n</code></pre> my_heap.cs<pre><code>/* Доступ к элементу на вершине кучи */\nint Peek() {\n    return maxHeap[0];\n}\n</code></pre> my_heap.go<pre><code>/* Доступ к элементу на вершине кучи */\nfunc (h *maxHeap) peek() any {\n    return h.data[0]\n}\n</code></pre> my_heap.swift<pre><code>/* Доступ к элементу на вершине кучи */\nfunc peek() -&gt; Int {\n    maxHeap[0]\n}\n</code></pre> my_heap.js<pre><code>/* Доступ к элементу на вершине кучи */\npeek() {\n    return this.#maxHeap[0];\n}\n</code></pre> my_heap.ts<pre><code>/* Доступ к элементу на вершине кучи */\npeek(): number {\n    return this.maxHeap[0];\n}\n</code></pre> my_heap.dart<pre><code>/* Доступ к элементу на вершине кучи */\nint peek() {\n  return _maxHeap[0];\n}\n</code></pre> my_heap.rs<pre><code>/* Доступ к элементу на вершине кучи */\nfn peek(&amp;self) -&gt; Option&lt;i32&gt; {\n    self.max_heap.first().copied()\n}\n</code></pre> my_heap.c<pre><code>/* Доступ к элементу на вершине кучи */\nint peek(MaxHeap *maxHeap) {\n    return maxHeap-&gt;data[0];\n}\n</code></pre> my_heap.kt<pre><code>/* Доступ к элементу на вершине кучи */\nfun peek(): Int {\n    return maxHeap[0]\n}\n</code></pre> my_heap.rb<pre><code>### Доступ к элементу на вершине кучи ###\ndef peek\n  @max_heap[0]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 8. Куча","8.1 &nbsp; Куча"],"tags":[]},{"location":"chapter_heap/heap/#3","level":3,"title":"3.   Добавление элемента в кучу","text":"<p>Пусть дан элемент <code>val</code> . Сначала мы помещаем его в основание кучи. После добавления свойства кучи могут нарушиться, потому что <code>val</code> может оказаться больше, чем другие элементы в куче. Поэтому необходимо восстановить порядок на пути от вставленного узла к корню ; эта операция называется heapify, то есть упорядочиванием кучи.</p> <p>Рассмотрим ситуацию, когда упорядочивание выполняется снизу вверх, начиная от только что вставленного узла. Как показано на рисунках ниже, мы сравниваем значение вставленного узла со значением его родителя; если вставленный узел больше, то меняем их местами. Затем продолжаем выполнять ту же операцию и последовательно восстанавливать корректность всех узлов по пути снизу вверх, пока не выйдем за корень или не встретим узел, для которого обмен не требуется.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 8-3   Шаги добавления элемента в кучу </p> <p>Пусть общее число узлов равно \\(n\\) , тогда высота дерева равна \\(O(\\log n)\\) . Следовательно, максимальное число итераций операции heapify тоже не превышает \\(O(\\log n)\\) . Отсюда временная сложность добавления элемента в кучу равна \\(O(\\log n)\\) . Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby my_heap.py<pre><code>def push(self, val: int):\n    \"\"\"Добавление элемента в кучу\"\"\"\n    # Добавление узла\n    self.max_heap.append(val)\n    # Просеивание снизу вверх\n    self.sift_up(self.size() - 1)\n\ndef sift_up(self, i: int):\n    \"\"\"Начиная с узла i, выполнить просеивание снизу вверх\"\"\"\n    while True:\n        # Получение родительского узла для узла i\n        p = self.parent(i)\n        # Завершить heapify, когда «корневой узел уже пройден» или «узел не требует исправления»\n        if p &lt; 0 or self.max_heap[i] &lt;= self.max_heap[p]:\n            break\n        # Поменять два узла местами\n        self.swap(i, p)\n        # Циклическое просеивание вверх\n        i = p\n</code></pre> my_heap.cpp<pre><code>/* Добавление элемента в кучу */\nvoid push(int val) {\n    // Добавление узла\n    maxHeap.push_back(val);\n    // Просеивание снизу вверх\n    siftUp(size() - 1);\n}\n\n/* Начиная с узла i, выполнить просеивание снизу вверх */\nvoid siftUp(int i) {\n    while (true) {\n        // Получение родительского узла для узла i\n        int p = parent(i);\n        // Завершить heapify, когда «корневой узел уже пройден» или «узел не требует исправления»\n        if (p &lt; 0 || maxHeap[i] &lt;= maxHeap[p])\n            break;\n        // Поменять два узла местами\n        swap(maxHeap[i], maxHeap[p]);\n        // Циклическое просеивание вверх\n        i = p;\n    }\n}\n</code></pre> my_heap.java<pre><code>/* Добавление элемента в кучу */\nvoid push(int val) {\n    // Добавление узла\n    maxHeap.add(val);\n    // Просеивание снизу вверх\n    siftUp(size() - 1);\n}\n\n/* Начиная с узла i, выполнить просеивание снизу вверх */\nvoid siftUp(int i) {\n    while (true) {\n        // Получение родительского узла для узла i\n        int p = parent(i);\n        // Завершить heapify, когда «корневой узел уже пройден» или «узел не требует исправления»\n        if (p &lt; 0 || maxHeap.get(i) &lt;= maxHeap.get(p))\n            break;\n        // Поменять два узла местами\n        swap(i, p);\n        // Циклическое просеивание вверх\n        i = p;\n    }\n}\n</code></pre> my_heap.cs<pre><code>/* Добавление элемента в кучу */\nvoid Push(int val) {\n    // Добавление узла\n    maxHeap.Add(val);\n    // Просеивание снизу вверх\n    SiftUp(Size() - 1);\n}\n\n/* Начиная с узла i, выполнить просеивание снизу вверх */\nvoid SiftUp(int i) {\n    while (true) {\n        // Получение родительского узла для узла i\n        int p = Parent(i);\n        // Если «выход за пределы корневого узла» или «узел не требует исправления», завершить просеивание\n        if (p &lt; 0 || maxHeap[i] &lt;= maxHeap[p])\n            break;\n        // Поменять два узла местами\n        Swap(i, p);\n        // Циклическое просеивание вверх\n        i = p;\n    }\n}\n</code></pre> my_heap.go<pre><code>/* Добавление элемента в кучу */\nfunc (h *maxHeap) push(val any) {\n    // Добавление узла\n    h.data = append(h.data, val)\n    // Просеивание снизу вверх\n    h.siftUp(len(h.data) - 1)\n}\n\n/* Начиная с узла i, выполнить просеивание снизу вверх */\nfunc (h *maxHeap) siftUp(i int) {\n    for true {\n        // Получение родительского узла для узла i\n        p := h.parent(i)\n        // Завершить heapify, когда «корневой узел уже пройден» или «узел не требует исправления»\n        if p &lt; 0 || h.data[i].(int) &lt;= h.data[p].(int) {\n            break\n        }\n        // Поменять два узла местами\n        h.swap(i, p)\n        // Циклическое просеивание вверх\n        i = p\n    }\n}\n</code></pre> my_heap.swift<pre><code>/* Добавление элемента в кучу */\nfunc push(val: Int) {\n    // Добавление узла\n    maxHeap.append(val)\n    // Просеивание снизу вверх\n    siftUp(i: size() - 1)\n}\n\n/* Начиная с узла i, выполнить просеивание снизу вверх */\nfunc siftUp(i: Int) {\n    var i = i\n    while true {\n        // Получение родительского узла для узла i\n        let p = parent(i: i)\n        // Завершить heapify, когда «корневой узел уже пройден» или «узел не требует исправления»\n        if p &lt; 0 || maxHeap[i] &lt;= maxHeap[p] {\n            break\n        }\n        // Поменять два узла местами\n        swap(i: i, j: p)\n        // Циклическое просеивание вверх\n        i = p\n    }\n}\n</code></pre> my_heap.js<pre><code>/* Добавление элемента в кучу */\npush(val) {\n    // Добавление узла\n    this.#maxHeap.push(val);\n    // Просеивание снизу вверх\n    this.#siftUp(this.size() - 1);\n}\n\n/* Начиная с узла i, выполнить просеивание снизу вверх */\n#siftUp(i) {\n    while (true) {\n        // Получение родительского узла для узла i\n        const p = this.#parent(i);\n        // Завершить heapify, когда «корневой узел уже пройден» или «узел не требует исправления»\n        if (p &lt; 0 || this.#maxHeap[i] &lt;= this.#maxHeap[p]) break;\n        // Поменять два узла местами\n        this.#swap(i, p);\n        // Циклическое просеивание вверх\n        i = p;\n    }\n}\n</code></pre> my_heap.ts<pre><code>/* Добавление элемента в кучу */\npush(val: number): void {\n    // Добавление узла\n    this.maxHeap.push(val);\n    // Просеивание снизу вверх\n    this.siftUp(this.size() - 1);\n}\n\n/* Начиная с узла i, выполнить просеивание снизу вверх */\nsiftUp(i: number): void {\n    while (true) {\n        // Получение родительского узла для узла i\n        const p = this.parent(i);\n        // Завершить heapify, когда «корневой узел уже пройден» или «узел не требует исправления»\n        if (p &lt; 0 || this.maxHeap[i] &lt;= this.maxHeap[p]) break;\n        // Поменять два узла местами\n        this.swap(i, p);\n        // Циклическое просеивание вверх\n        i = p;\n    }\n}\n</code></pre> my_heap.dart<pre><code>/* Добавление элемента в кучу */\nvoid push(int val) {\n  // Добавление узла\n  _maxHeap.add(val);\n  // Просеивание снизу вверх\n  siftUp(size() - 1);\n}\n\n/* Начиная с узла i, выполнить просеивание снизу вверх */\nvoid siftUp(int i) {\n  while (true) {\n    // Получение родительского узла для узла i\n    int p = _parent(i);\n    // Завершить heapify, когда «корневой узел уже пройден» или «узел не требует исправления»\n    if (p &lt; 0 || _maxHeap[i] &lt;= _maxHeap[p]) {\n      break;\n    }\n    // Поменять два узла местами\n    _swap(i, p);\n    // Циклическое просеивание вверх\n    i = p;\n  }\n}\n</code></pre> my_heap.rs<pre><code>/* Добавление элемента в кучу */\nfn push(&amp;mut self, val: i32) {\n    // Добавление узла\n    self.max_heap.push(val);\n    // Просеивание снизу вверх\n    self.sift_up(self.size() - 1);\n}\n\n/* Начиная с узла i, выполнить просеивание снизу вверх */\nfn sift_up(&amp;mut self, mut i: usize) {\n    loop {\n        // Если узел i уже является вершиной кучи, завершить просеивание\n        if i == 0 {\n            break;\n        }\n        // Получение родительского узла для узла i\n        let p = Self::parent(i);\n        // Когда «узел не требует исправления», завершить просеивание\n        if self.max_heap[i] &lt;= self.max_heap[p] {\n            break;\n        }\n        // Поменять два узла местами\n        self.swap(i, p);\n        // Циклическое просеивание вверх\n        i = p;\n    }\n}\n</code></pre> my_heap.c<pre><code>/* Добавление элемента в кучу */\nvoid push(MaxHeap *maxHeap, int val) {\n    // По умолчанию не следует добавлять так много узлов\n    if (maxHeap-&gt;size == MAX_SIZE) {\n        printf(\"heap is full!\");\n        return;\n    }\n    // Добавление узла\n    maxHeap-&gt;data[maxHeap-&gt;size] = val;\n    maxHeap-&gt;size++;\n\n    // Просеивание снизу вверх\n    siftUp(maxHeap, maxHeap-&gt;size - 1);\n}\n\n/* Начиная с узла i, выполнить просеивание снизу вверх */\nvoid siftUp(MaxHeap *maxHeap, int i) {\n    while (true) {\n        // Получение родительского узла для узла i\n        int p = parent(maxHeap, i);\n        // Завершить heapify, когда «корневой узел уже пройден» или «узел не требует исправления»\n        if (p &lt; 0 || maxHeap-&gt;data[i] &lt;= maxHeap-&gt;data[p]) {\n            break;\n        }\n        // Поменять два узла местами\n        swap(maxHeap, i, p);\n        // Циклическое просеивание вверх\n        i = p;\n    }\n}\n</code></pre> my_heap.kt<pre><code>/* Добавление элемента в кучу */\nfun push(_val: Int) {\n    // Добавление узла\n    maxHeap.add(_val)\n    // Просеивание снизу вверх\n    siftUp(size() - 1)\n}\n\n/* Начиная с узла i, выполнить просеивание снизу вверх */\nfun siftUp(it: Int) {\n    // Параметры функций в Kotlin неизменяемы, поэтому создается временная переменная\n    var i = it\n    while (true) {\n        // Получение родительского узла для узла i\n        val p = parent(i)\n        // Завершить heapify, когда «корневой узел уже пройден» или «узел не требует исправления»\n        if (p &lt; 0 || maxHeap[i] &lt;= maxHeap[p]) break\n        // Поменять два узла местами\n        swap(i, p)\n        // Циклическое просеивание вверх\n        i = p\n    }\n}\n</code></pre> my_heap.rb<pre><code>### Добавление элемента в кучу ###\ndef push(val)\n  # Добавление узла\n  @max_heap &lt;&lt; val\n  # Просеивание снизу вверх\n  sift_up(size - 1)\nend\n\n### Начиная с узла i, выполнить просеивание снизу вверх ###\ndef sift_up(i)\n  loop do\n    # Получение родительского узла для узла i\n    p = parent(i)\n    # Завершить heapify, когда «корневой узел уже пройден» или «узел не требует исправления»\n    break if p &lt; 0 || @max_heap[i] &lt;= @max_heap[p]\n    # Поменять два узла местами\n    swap(i, p)\n    # Циклическое просеивание вверх\n    i = p\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 8. Куча","8.1 &nbsp; Куча"],"tags":[]},{"location":"chapter_heap/heap/#4","level":3,"title":"4.   Извлечение элемента с вершины кучи","text":"<p>Элемент на вершине кучи - это корневой узел двоичного дерева, то есть первый элемент списка. Если просто удалить первый элемент списка, то индексы всех узлов двоичного дерева изменятся, и это сильно затруднит последующее восстановление структуры при помощи heapify. Чтобы по возможности минимизировать изменение индексов элементов, мы используем следующий порядок действий.</p> <ol> <li>Поменять местами элемент на вершине кучи и элемент у основания кучи, то есть поменять корневой узел с самым правым листовым узлом.</li> <li>После обмена удалить основание кучи из списка. Обрати внимание: поскольку обмен уже выполнен, фактически удаляется исходный элемент вершины кучи.</li> <li>Начиная от корневого узла, выполнить heapify сверху вниз.</li> </ol> <p>Как показано на рисунках ниже, направление операции \"heapify сверху вниз\" противоположно операции \"heapify снизу вверх\". Мы сравниваем значение корневого узла со значениями двух дочерних узлов, выбираем больший дочерний узел и меняем его местами с корневым узлом. Затем циклически повторяем ту же операцию, пока не выйдем за листовой узел или не встретим узел, который уже не требует обмена.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 8-4   Шаги извлечения элемента с вершины кучи </p> <p>Как и операция добавления в кучу, операция извлечения элемента с вершины кучи также имеет временную сложность \\(O(\\log n)\\) . Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby my_heap.py<pre><code>def pop(self) -&gt; int:\n    \"\"\"Извлечение элемента из кучи\"\"\"\n    # Обработка пустого случая\n    if self.is_empty():\n        raise IndexError(\"куча пуста\")\n    # Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    self.swap(0, self.size() - 1)\n    # Удаление узла\n    val = self.max_heap.pop()\n    # Просеивание сверху вниз\n    self.sift_down(0)\n    # Вернуть элемент с вершины кучи\n    return val\n\ndef sift_down(self, i: int):\n    \"\"\"Начиная с узла i, выполнить просеивание сверху вниз\"\"\"\n    while True:\n        # Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        l, r, ma = self.left(i), self.right(i), i\n        if l &lt; self.size() and self.max_heap[l] &gt; self.max_heap[ma]:\n            ma = l\n        if r &lt; self.size() and self.max_heap[r] &gt; self.max_heap[ma]:\n            ma = r\n        # Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if ma == i:\n            break\n        # Поменять два узла местами\n        self.swap(i, ma)\n        # Циклическое просеивание вниз\n        i = ma\n</code></pre> my_heap.cpp<pre><code>/* Извлечение элемента из кучи */\nvoid pop() {\n    // Обработка пустого случая\n    if (isEmpty()) {\n        throw out_of_range(\"куча пуста\");\n    }\n    // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    swap(maxHeap[0], maxHeap[size() - 1]);\n    // Удаление узла\n    maxHeap.pop_back();\n    // Просеивание сверху вниз\n    siftDown(0);\n}\n\n/* Начиная с узла i, выполнить просеивание сверху вниз */\nvoid siftDown(int i) {\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        int l = left(i), r = right(i), ma = i;\n        if (l &lt; size() &amp;&amp; maxHeap[l] &gt; maxHeap[ma])\n            ma = l;\n        if (r &lt; size() &amp;&amp; maxHeap[r] &gt; maxHeap[ma])\n            ma = r;\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (ma == i)\n            break;\n        swap(maxHeap[i], maxHeap[ma]);\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n</code></pre> my_heap.java<pre><code>/* Извлечение элемента из кучи */\nint pop() {\n    // Обработка пустого случая\n    if (isEmpty())\n        throw new IndexOutOfBoundsException();\n    // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    swap(0, size() - 1);\n    // Удаление узла\n    int val = maxHeap.remove(size() - 1);\n    // Просеивание сверху вниз\n    siftDown(0);\n    // Вернуть элемент с вершины кучи\n    return val;\n}\n\n/* Начиная с узла i, выполнить просеивание сверху вниз */\nvoid siftDown(int i) {\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        int l = left(i), r = right(i), ma = i;\n        if (l &lt; size() &amp;&amp; maxHeap.get(l) &gt; maxHeap.get(ma))\n            ma = l;\n        if (r &lt; size() &amp;&amp; maxHeap.get(r) &gt; maxHeap.get(ma))\n            ma = r;\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (ma == i)\n            break;\n        // Поменять два узла местами\n        swap(i, ma);\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n</code></pre> my_heap.cs<pre><code>/* Извлечение элемента из кучи */\nint Pop() {\n    // Обработка пустого случая\n    if (IsEmpty())\n        throw new IndexOutOfRangeException();\n    // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    Swap(0, Size() - 1);\n    // Удаление узла\n    int val = maxHeap.Last();\n    maxHeap.RemoveAt(Size() - 1);\n    // Просеивание сверху вниз\n    SiftDown(0);\n    // Вернуть элемент с вершины кучи\n    return val;\n}\n\n/* Начиная с узла i, выполнить просеивание сверху вниз */\nvoid SiftDown(int i) {\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        int l = Left(i), r = Right(i), ma = i;\n        if (l &lt; Size() &amp;&amp; maxHeap[l] &gt; maxHeap[ma])\n            ma = l;\n        if (r &lt; Size() &amp;&amp; maxHeap[r] &gt; maxHeap[ma])\n            ma = r;\n        // Если «узел i максимален» или «выход за пределы листовых узлов», завершить просеивание\n        if (ma == i) break;\n        // Поменять два узла местами\n        Swap(i, ma);\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n</code></pre> my_heap.go<pre><code>/* Извлечение элемента из кучи */\nfunc (h *maxHeap) pop() any {\n    // Обработка пустого случая\n    if h.isEmpty() {\n        fmt.Println(\"error\")\n        return nil\n    }\n    // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    h.swap(0, h.size()-1)\n    // Удаление узла\n    val := h.data[len(h.data)-1]\n    h.data = h.data[:len(h.data)-1]\n    // Просеивание сверху вниз\n    h.siftDown(0)\n\n    // Вернуть элемент с вершины кучи\n    return val\n}\n\n/* Начиная с узла i, выполнить просеивание сверху вниз */\nfunc (h *maxHeap) siftDown(i int) {\n    for true {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как max\n        l, r, max := h.left(i), h.right(i), i\n        if l &lt; h.size() &amp;&amp; h.data[l].(int) &gt; h.data[max].(int) {\n            max = l\n        }\n        if r &lt; h.size() &amp;&amp; h.data[r].(int) &gt; h.data[max].(int) {\n            max = r\n        }\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if max == i {\n            break\n        }\n        // Поменять два узла местами\n        h.swap(i, max)\n        // Циклическое просеивание вниз\n        i = max\n    }\n}\n</code></pre> my_heap.swift<pre><code>/* Извлечение элемента из кучи */\nfunc pop() -&gt; Int {\n    // Обработка пустого случая\n    if isEmpty() {\n        fatalError(\"куча пуста\")\n    }\n    // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    swap(i: 0, j: size() - 1)\n    // Удаление узла\n    let val = maxHeap.remove(at: size() - 1)\n    // Просеивание сверху вниз\n    siftDown(i: 0)\n    // Вернуть элемент с вершины кучи\n    return val\n}\n\n/* Начиная с узла i, выполнить просеивание сверху вниз */\nfunc siftDown(i: Int) {\n    var i = i\n    while true {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        let l = left(i: i)\n        let r = right(i: i)\n        var ma = i\n        if l &lt; size(), maxHeap[l] &gt; maxHeap[ma] {\n            ma = l\n        }\n        if r &lt; size(), maxHeap[r] &gt; maxHeap[ma] {\n            ma = r\n        }\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if ma == i {\n            break\n        }\n        // Поменять два узла местами\n        swap(i: i, j: ma)\n        // Циклическое просеивание вниз\n        i = ma\n    }\n}\n</code></pre> my_heap.js<pre><code>/* Извлечение элемента из кучи */\npop() {\n    // Обработка пустого случая\n    if (this.isEmpty()) throw new Error('куча пуста');\n    // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    this.#swap(0, this.size() - 1);\n    // Удаление узла\n    const val = this.#maxHeap.pop();\n    // Просеивание сверху вниз\n    this.#siftDown(0);\n    // Вернуть элемент с вершины кучи\n    return val;\n}\n\n/* Начиная с узла i, выполнить просеивание сверху вниз */\n#siftDown(i) {\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        const l = this.#left(i),\n            r = this.#right(i);\n        let ma = i;\n        if (l &lt; this.size() &amp;&amp; this.#maxHeap[l] &gt; this.#maxHeap[ma]) ma = l;\n        if (r &lt; this.size() &amp;&amp; this.#maxHeap[r] &gt; this.#maxHeap[ma]) ma = r;\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (ma === i) break;\n        // Поменять два узла местами\n        this.#swap(i, ma);\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n</code></pre> my_heap.ts<pre><code>/* Извлечение элемента из кучи */\npop(): number {\n    // Обработка пустого случая\n    if (this.isEmpty()) throw new RangeError('Heap is empty.');\n    // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    this.swap(0, this.size() - 1);\n    // Удаление узла\n    const val = this.maxHeap.pop();\n    // Просеивание сверху вниз\n    this.siftDown(0);\n    // Вернуть элемент с вершины кучи\n    return val;\n}\n\n/* Начиная с узла i, выполнить просеивание сверху вниз */\nsiftDown(i: number): void {\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        const l = this.left(i),\n            r = this.right(i);\n        let ma = i;\n        if (l &lt; this.size() &amp;&amp; this.maxHeap[l] &gt; this.maxHeap[ma]) ma = l;\n        if (r &lt; this.size() &amp;&amp; this.maxHeap[r] &gt; this.maxHeap[ma]) ma = r;\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (ma === i) break;\n        // Поменять два узла местами\n        this.swap(i, ma);\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n</code></pre> my_heap.dart<pre><code>/* Извлечение элемента из кучи */\nint pop() {\n  // Обработка пустого случая\n  if (isEmpty()) throw Exception('куча пуста');\n  // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n  _swap(0, size() - 1);\n  // Удаление узла\n  int val = _maxHeap.removeLast();\n  // Просеивание сверху вниз\n  siftDown(0);\n  // Вернуть элемент с вершины кучи\n  return val;\n}\n\n/* Начиная с узла i, выполнить просеивание сверху вниз */\nvoid siftDown(int i) {\n  while (true) {\n    // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n    int l = _left(i);\n    int r = _right(i);\n    int ma = i;\n    if (l &lt; size() &amp;&amp; _maxHeap[l] &gt; _maxHeap[ma]) ma = l;\n    if (r &lt; size() &amp;&amp; _maxHeap[r] &gt; _maxHeap[ma]) ma = r;\n    // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n    if (ma == i) break;\n    // Поменять два узла местами\n    _swap(i, ma);\n    // Циклическое просеивание вниз\n    i = ma;\n  }\n}\n</code></pre> my_heap.rs<pre><code>/* Извлечение элемента из кучи */\nfn pop(&amp;mut self) -&gt; i32 {\n    // Обработка пустого случая\n    if self.is_empty() {\n        panic!(\"index out of bounds\");\n    }\n    // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    self.swap(0, self.size() - 1);\n    // Удаление узла\n    let val = self.max_heap.pop().unwrap();\n    // Просеивание сверху вниз\n    self.sift_down(0);\n    // Вернуть элемент с вершины кучи\n    val\n}\n\n/* Начиная с узла i, выполнить просеивание сверху вниз */\nfn sift_down(&amp;mut self, mut i: usize) {\n    loop {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        let (l, r, mut ma) = (Self::left(i), Self::right(i), i);\n        if l &lt; self.size() &amp;&amp; self.max_heap[l] &gt; self.max_heap[ma] {\n            ma = l;\n        }\n        if r &lt; self.size() &amp;&amp; self.max_heap[r] &gt; self.max_heap[ma] {\n            ma = r;\n        }\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if ma == i {\n            break;\n        }\n        // Поменять два узла местами\n        self.swap(i, ma);\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n</code></pre> my_heap.c<pre><code>/* Извлечение элемента из кучи */\nint pop(MaxHeap *maxHeap) {\n    // Обработка пустого случая\n    if (isEmpty(maxHeap)) {\n        printf(\"heap is empty!\");\n        return INT_MAX;\n    }\n    // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    swap(maxHeap, 0, size(maxHeap) - 1);\n    // Удаление узла\n    int val = maxHeap-&gt;data[maxHeap-&gt;size - 1];\n    maxHeap-&gt;size--;\n    // Просеивание сверху вниз\n    siftDown(maxHeap, 0);\n\n    // Вернуть элемент с вершины кучи\n    return val;\n}\n\n/* Начиная с узла i, выполнить просеивание сверху вниз */\nvoid siftDown(MaxHeap *maxHeap, int i) {\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как max\n        int l = left(maxHeap, i);\n        int r = right(maxHeap, i);\n        int max = i;\n        if (l &lt; size(maxHeap) &amp;&amp; maxHeap-&gt;data[l] &gt; maxHeap-&gt;data[max]) {\n            max = l;\n        }\n        if (r &lt; size(maxHeap) &amp;&amp; maxHeap-&gt;data[r] &gt; maxHeap-&gt;data[max]) {\n            max = r;\n        }\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (max == i) {\n            break;\n        }\n        // Поменять два узла местами\n        swap(maxHeap, i, max);\n        // Циклическое просеивание вниз\n        i = max;\n    }\n}\n</code></pre> my_heap.kt<pre><code>/* Извлечение элемента из кучи */\nfun pop(): Int {\n    // Обработка пустого случая\n    if (isEmpty()) throw IndexOutOfBoundsException()\n    // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    swap(0, size() - 1)\n    // Удаление узла\n    val _val = maxHeap.removeAt(size() - 1)\n    // Просеивание сверху вниз\n    siftDown(0)\n    // Вернуть элемент с вершины кучи\n    return _val\n}\n\n/* Начиная с узла i, выполнить просеивание сверху вниз */\nfun siftDown(it: Int) {\n    // Параметры функций в Kotlin неизменяемы, поэтому создается временная переменная\n    var i = it\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        val l = left(i)\n        val r = right(i)\n        var ma = i\n        if (l &lt; size() &amp;&amp; maxHeap[l] &gt; maxHeap[ma]) ma = l\n        if (r &lt; size() &amp;&amp; maxHeap[r] &gt; maxHeap[ma]) ma = r\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (ma == i) break\n        // Поменять два узла местами\n        swap(i, ma)\n        // Циклическое просеивание вниз\n        i = ma\n    }\n}\n</code></pre> my_heap.rb<pre><code>### Извлечение элемента из кучи ###\ndef pop\n  # Обработка пустого случая\n  raise IndexError, \"куча пуста\" if is_empty?\n  # Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n  swap(0, size - 1)\n  # Удаление узла\n  val = @max_heap.pop\n  # Просеивание сверху вниз\n  sift_down(0)\n  # Вернуть элемент с вершины кучи\n  val\nend\n\n### Начиная с узла i, выполнить просеивание сверху вниз ###\ndef sift_down(i)\n  loop do\n    # Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n    l, r, ma = left(i), right(i), i\n    ma = l if l &lt; size &amp;&amp; @max_heap[l] &gt; @max_heap[ma]\n    ma = r if r &lt; size &amp;&amp; @max_heap[r] &gt; @max_heap[ma]\n\n    # Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n    break if ma == i\n\n    # Поменять два узла местами\n    swap(i, ma)\n    # Циклическое просеивание вниз\n    i = ma\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 8. Куча","8.1 &nbsp; Куча"],"tags":[]},{"location":"chapter_heap/heap/#813","level":2,"title":"8.1.3   Типичные применения кучи","text":"<ul> <li>Очередь с приоритетом: куча обычно является предпочтительной структурой данных для реализации очереди с приоритетом; добавление и извлечение элементов имеют временную сложность \\(O(\\log n)\\) , а построение кучи - \\(O(n)\\) , и все эти операции выполняются очень эффективно.</li> <li>Пирамидальная сортировка: для заданного набора данных можно построить кучу, а затем непрерывно извлекать из нее элементы, получая отсортированные данные. Однако на практике мы обычно используем более изящную реализацию пирамидальной сортировки; подробности см. в разделе \"Пирамидальная сортировка\".</li> <li>Получение наибольших \\(k\\) элементов: это классическая алгоритмическая задача и одновременно типичное применение кучи. Например, выбор 10 самых горячих новостей для списка популярных тем или выбор 10 самых продаваемых товаров.</li> </ul>","path":["Глава 8. Куча","8.1 &nbsp; Куча"],"tags":[]},{"location":"chapter_heap/summary/","level":1,"title":"8.4   Краткие итоги","text":"","path":["Глава 8. Куча","8.4 &nbsp; Краткие итоги"],"tags":[]},{"location":"chapter_heap/summary/#1","level":3,"title":"1.   Основные моменты","text":"<ul> <li>Куча представляет собой полное двоичное дерево и делится на максимальную кучу и минимальную кучу. Элемент на вершине максимальной (минимальной) кучи является наибольшим (наименьшим).</li> <li>Очередь с приоритетом определяется как очередь, элементы которой извлекаются в соответствии с приоритетом; обычно ее реализуют с помощью кучи.</li> <li>К основным операциям кучи и их временным сложностям относятся: добавление элемента в кучу \\(O(\\log n)\\) , извлечение элемента с вершины кучи \\(O(\\log n)\\) и доступ к вершине кучи \\(O(1)\\) .</li> <li>Полное двоичное дерево очень удобно представлять массивом, поэтому кучу обычно тоже хранят в массиве.</li> <li>Операция упорядочивания кучи используется для поддержания свойств кучи и применяется как при добавлении элемента, так и при извлечении элемента.</li> <li>Временную сложность построения кучи из \\(n\\) элементов можно оптимизировать до \\(O(n)\\) , что очень эффективно.</li> <li>Top-k - это классическая алгоритмическая задача, которую можно эффективно решать с помощью кучи за \\(O(n \\log k)\\) .</li> </ul>","path":["Глава 8. Куча","8.4 &nbsp; Краткие итоги"],"tags":[]},{"location":"chapter_heap/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: Является ли \"куча\" как структура данных тем же самым понятием, что и \"куча\" в управлении памятью?</p> <p>Это не одно и то же, просто у них случайно совпало название. Куча в памяти компьютерной системы является частью динамического распределения памяти: во время выполнения программы она используется для хранения данных. Программа может запросить определенный объем памяти в куче для хранения сложных структур, таких как объекты и массивы. Когда эти данные больше не нужны, память нужно освободить, чтобы не допустить утечек. По сравнению со стековой памятью управление памятью в куче требует большей осторожности, а неправильное использование может привести к утечкам памяти, висячим указателям и другим проблемам.</p>","path":["Глава 8. Куча","8.4 &nbsp; Краткие итоги"],"tags":[]},{"location":"chapter_heap/top_k/","level":1,"title":"8.3   Задача Top-k","text":"<p>Question</p> <p>Дан неупорядоченный массив <code>nums</code> длины \\(n\\) . Требуется вернуть наибольшие \\(k\\) элементов массива.</p> <p>Для этой задачи мы сначала покажем два относительно прямолинейных способа решения, а затем более эффективный способ на основе кучи.</p>","path":["Глава 8. Куча","8.3 &nbsp; Задача Top-k"],"tags":[]},{"location":"chapter_heap/top_k/#831-1","level":2,"title":"8.3.1   Метод 1: выбор через обход","text":"<p>Как показано на рисунке 8-6, можно выполнить \\(k\\) проходов по массиву и на каждом проходе извлекать соответственно \\(1\\)-й, \\(2\\)-й, \\(\\dots\\) , \\(k\\)-й по величине элемент; временная сложность такого подхода равна \\(O(nk)\\) .</p> <p>Этот метод подходит только для случая \\(k \\ll n\\) , потому что когда \\(k\\) приближается к \\(n\\) , его временная сложность стремится к \\(O(n^2)\\) , а это уже очень затратно.</p> <p></p> <p> Рисунок 8-6   Поиск наибольших k элементов через обход </p> <p>Tip</p> <p>Когда \\(k = n\\) , мы получаем полную упорядоченную последовательность, и в этот момент задача становится эквивалентной алгоритму \"сортировка выбором\".</p>","path":["Глава 8. Куча","8.3 &nbsp; Задача Top-k"],"tags":[]},{"location":"chapter_heap/top_k/#832-2","level":2,"title":"8.3.2   Метод 2: сортировка","text":"<p>Как показано на рисунке 8-7, можно сначала отсортировать массив <code>nums</code> , а затем вернуть его крайние правые \\(k\\) элементов; временная сложность такого метода равна \\(O(n \\log n)\\) .</p> <p>Очевидно, что этот способ \"делает слишком много\", потому что нам нужно только найти наибольшие \\(k\\) элементов, а сортировать остальные элементы совсем не обязательно.</p> <p></p> <p> Рисунок 8-7   Поиск наибольших k элементов через сортировку </p>","path":["Глава 8. Куча","8.3 &nbsp; Задача Top-k"],"tags":[]},{"location":"chapter_heap/top_k/#833-3","level":2,"title":"8.3.3   Метод 3: куча","text":"<p>Задачу Top-k можно решить гораздо эффективнее с помощью кучи, как показано на рисунках ниже.</p> <ol> <li>Инициализировать минимальную кучу, у которой вершина содержит наименьший элемент.</li> <li>Сначала по очереди поместить в кучу первые \\(k\\) элементов массива.</li> <li>Начиная с элемента номер \\(k + 1\\) , если текущий элемент больше элемента на вершине кучи, то извлечь вершину кучи и поместить в кучу текущий элемент.</li> <li>После завершения обхода в куче будут храниться как раз наибольшие \\(k\\) элементов.</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 8-8   Поиск наибольших k элементов с помощью кучи </p> <p>Пример кода приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby top_k.py<pre><code>def top_k_heap(nums: list[int], k: int) -&gt; list[int]:\n    \"\"\"Найти k наибольших элементов массива с помощью кучи\"\"\"\n    # Инициализация минимальной кучи\n    heap = []\n    # Поместить первые k элементов массива в кучу\n    for i in range(k):\n        heapq.heappush(heap, nums[i])\n    # Начиная с элемента k+1, поддерживать длину кучи равной k\n    for i in range(k, len(nums)):\n        # Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n        if nums[i] &gt; heap[0]:\n            heapq.heappop(heap)\n            heapq.heappush(heap, nums[i])\n    return heap\n</code></pre> top_k.cpp<pre><code>/* Найти k наибольших элементов массива с помощью кучи */\npriority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; topKHeap(vector&lt;int&gt; &amp;nums, int k) {\n    // Инициализация минимальной кучи\n    priority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; heap;\n    // Поместить первые k элементов массива в кучу\n    for (int i = 0; i &lt; k; i++) {\n        heap.push(nums[i]);\n    }\n    // Начиная с элемента k+1, поддерживать длину кучи равной k\n    for (int i = k; i &lt; nums.size(); i++) {\n        // Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n        if (nums[i] &gt; heap.top()) {\n            heap.pop();\n            heap.push(nums[i]);\n        }\n    }\n    return heap;\n}\n</code></pre> top_k.java<pre><code>/* Найти k наибольших элементов массива с помощью кучи */\nQueue&lt;Integer&gt; topKHeap(int[] nums, int k) {\n    // Инициализация минимальной кучи\n    Queue&lt;Integer&gt; heap = new PriorityQueue&lt;Integer&gt;();\n    // Поместить первые k элементов массива в кучу\n    for (int i = 0; i &lt; k; i++) {\n        heap.offer(nums[i]);\n    }\n    // Начиная с элемента k+1, поддерживать длину кучи равной k\n    for (int i = k; i &lt; nums.length; i++) {\n        // Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n        if (nums[i] &gt; heap.peek()) {\n            heap.poll();\n            heap.offer(nums[i]);\n        }\n    }\n    return heap;\n}\n</code></pre> top_k.cs<pre><code>/* Найти k наибольших элементов массива с помощью кучи */\nPriorityQueue&lt;int, int&gt; TopKHeap(int[] nums, int k) {\n    // Инициализация минимальной кучи\n    PriorityQueue&lt;int, int&gt; heap = new();\n    // Поместить первые k элементов массива в кучу\n    for (int i = 0; i &lt; k; i++) {\n        heap.Enqueue(nums[i], nums[i]);\n    }\n    // Начиная с элемента k+1, поддерживать длину кучи равной k\n    for (int i = k; i &lt; nums.Length; i++) {\n        // Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n        if (nums[i] &gt; heap.Peek()) {\n            heap.Dequeue();\n            heap.Enqueue(nums[i], nums[i]);\n        }\n    }\n    return heap;\n}\n</code></pre> top_k.go<pre><code>/* Найти k наибольших элементов массива с помощью кучи */\nfunc topKHeap(nums []int, k int) *minHeap {\n    // Инициализация минимальной кучи\n    h := &amp;minHeap{}\n    heap.Init(h)\n    // Поместить первые k элементов массива в кучу\n    for i := 0; i &lt; k; i++ {\n        heap.Push(h, nums[i])\n    }\n    // Начиная с элемента k+1, поддерживать длину кучи равной k\n    for i := k; i &lt; len(nums); i++ {\n        // Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n        if nums[i] &gt; h.Top().(int) {\n            heap.Pop(h)\n            heap.Push(h, nums[i])\n        }\n    }\n    return h\n}\n</code></pre> top_k.swift<pre><code>/* Найти k наибольших элементов массива с помощью кучи */\nfunc topKHeap(nums: [Int], k: Int) -&gt; [Int] {\n    // Инициализировать минимальную кучу и построить ее по первым k элементам\n    var heap = Heap(nums.prefix(k))\n    // Начиная с элемента k+1, поддерживать длину кучи равной k\n    for i in nums.indices.dropFirst(k) {\n        // Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n        if nums[i] &gt; heap.min()! {\n            _ = heap.removeMin()\n            heap.insert(nums[i])\n        }\n    }\n    return heap.unordered\n}\n</code></pre> top_k.js<pre><code>/* Добавление элемента в кучу */\nfunction pushMinHeap(maxHeap, val) {\n    // Инвертировать знак элемента\n    maxHeap.push(-val);\n}\n\n/* Извлечение элемента из кучи */\nfunction popMinHeap(maxHeap) {\n    // Инвертировать знак элемента\n    return -maxHeap.pop();\n}\n\n/* Доступ к элементу на вершине кучи */\nfunction peekMinHeap(maxHeap) {\n    // Инвертировать знак элемента\n    return -maxHeap.peek();\n}\n\n/* Извлечь элементы из кучи */\nfunction getMinHeap(maxHeap) {\n    // Инвертировать знак элемента\n    return maxHeap.getMaxHeap().map((num) =&gt; -num);\n}\n\n/* Найти k наибольших элементов массива с помощью кучи */\nfunction topKHeap(nums, k) {\n    // Инициализация минимальной кучи\n    // Обратите внимание: мы инвертируем все элементы кучи, чтобы с помощью максимальной кучи имитировать минимальную\n    const maxHeap = new MaxHeap([]);\n    // Поместить первые k элементов массива в кучу\n    for (let i = 0; i &lt; k; i++) {\n        pushMinHeap(maxHeap, nums[i]);\n    }\n    // Начиная с элемента k+1, поддерживать длину кучи равной k\n    for (let i = k; i &lt; nums.length; i++) {\n        // Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n        if (nums[i] &gt; peekMinHeap(maxHeap)) {\n            popMinHeap(maxHeap);\n            pushMinHeap(maxHeap, nums[i]);\n        }\n    }\n    // Вернуть элементы кучи\n    return getMinHeap(maxHeap);\n}\n</code></pre> top_k.ts<pre><code>/* Добавление элемента в кучу */\nfunction pushMinHeap(maxHeap: MaxHeap, val: number): void {\n    // Инвертировать знак элемента\n    maxHeap.push(-val);\n}\n\n/* Извлечение элемента из кучи */\nfunction popMinHeap(maxHeap: MaxHeap): number {\n    // Инвертировать знак элемента\n    return -maxHeap.pop();\n}\n\n/* Доступ к элементу на вершине кучи */\nfunction peekMinHeap(maxHeap: MaxHeap): number {\n    // Инвертировать знак элемента\n    return -maxHeap.peek();\n}\n\n/* Извлечь элементы из кучи */\nfunction getMinHeap(maxHeap: MaxHeap): number[] {\n    // Инвертировать знак элемента\n    return maxHeap.getMaxHeap().map((num: number) =&gt; -num);\n}\n\n/* Найти k наибольших элементов массива с помощью кучи */\nfunction topKHeap(nums: number[], k: number): number[] {\n    // Инициализация минимальной кучи\n    // Обратите внимание: мы инвертируем все элементы кучи, чтобы с помощью максимальной кучи имитировать минимальную\n    const maxHeap = new MaxHeap([]);\n    // Поместить первые k элементов массива в кучу\n    for (let i = 0; i &lt; k; i++) {\n        pushMinHeap(maxHeap, nums[i]);\n    }\n    // Начиная с элемента k+1, поддерживать длину кучи равной k\n    for (let i = k; i &lt; nums.length; i++) {\n        // Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n        if (nums[i] &gt; peekMinHeap(maxHeap)) {\n            popMinHeap(maxHeap);\n            pushMinHeap(maxHeap, nums[i]);\n        }\n    }\n    // Вернуть элементы кучи\n    return getMinHeap(maxHeap);\n}\n</code></pre> top_k.dart<pre><code>/* Найти k наибольших элементов массива с помощью кучи */\nMinHeap topKHeap(List&lt;int&gt; nums, int k) {\n  // Инициализировать минимальную кучу, поместив в нее первые k элементов массива\n  MinHeap heap = MinHeap(nums.sublist(0, k));\n  // Начиная с элемента k+1, поддерживать длину кучи равной k\n  for (int i = k; i &lt; nums.length; i++) {\n    // Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n    if (nums[i] &gt; heap.peek()) {\n      heap.pop();\n      heap.push(nums[i]);\n    }\n  }\n  return heap;\n}\n</code></pre> top_k.rs<pre><code>/* Найти k наибольших элементов массива с помощью кучи */\nfn top_k_heap(nums: Vec&lt;i32&gt;, k: usize) -&gt; BinaryHeap&lt;Reverse&lt;i32&gt;&gt; {\n    // BinaryHeap — это максимальная куча; с помощью Reverse элементы инвертируются, чтобы реализовать минимальную кучу\n    let mut heap = BinaryHeap::&lt;Reverse&lt;i32&gt;&gt;::new();\n    // Поместить первые k элементов массива в кучу\n    for &amp;num in nums.iter().take(k) {\n        heap.push(Reverse(num));\n    }\n    // Начиная с элемента k+1, поддерживать длину кучи равной k\n    for &amp;num in nums.iter().skip(k) {\n        // Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n        if num &gt; heap.peek().unwrap().0 {\n            heap.pop();\n            heap.push(Reverse(num));\n        }\n    }\n    heap\n}\n</code></pre> top_k.c<pre><code>/* Добавление элемента в кучу */\nvoid pushMinHeap(MaxHeap *maxHeap, int val) {\n    // Инвертировать знак элемента\n    push(maxHeap, -val);\n}\n\n/* Извлечение элемента из кучи */\nint popMinHeap(MaxHeap *maxHeap) {\n    // Инвертировать знак элемента\n    return -pop(maxHeap);\n}\n\n/* Доступ к элементу на вершине кучи */\nint peekMinHeap(MaxHeap *maxHeap) {\n    // Инвертировать знак элемента\n    return -peek(maxHeap);\n}\n\n/* Извлечь элементы из кучи */\nint *getMinHeap(MaxHeap *maxHeap) {\n    // Инвертировать все элементы кучи и записать их в массив res\n    int *res = (int *)malloc(maxHeap-&gt;size * sizeof(int));\n    for (int i = 0; i &lt; maxHeap-&gt;size; i++) {\n        res[i] = -maxHeap-&gt;data[i];\n    }\n    return res;\n}\n\n/* Извлечь элементы из кучи */\nint *getMinHeap(MaxHeap *maxHeap) {\n    // Инвертировать все элементы кучи и записать их в массив res\n    int *res = (int *)malloc(maxHeap-&gt;size * sizeof(int));\n    for (int i = 0; i &lt; maxHeap-&gt;size; i++) {\n        res[i] = -maxHeap-&gt;data[i];\n    }\n    return res;\n}\n\n// Функция поиска k наибольших элементов массива на основе кучи\nint *topKHeap(int *nums, int sizeNums, int k) {\n    // Инициализация минимальной кучи\n    // Обратите внимание: мы инвертируем все элементы кучи, чтобы с помощью максимальной кучи имитировать минимальную\n    int *empty = (int *)malloc(0);\n    MaxHeap *maxHeap = newMaxHeap(empty, 0);\n    // Поместить первые k элементов массива в кучу\n    for (int i = 0; i &lt; k; i++) {\n        pushMinHeap(maxHeap, nums[i]);\n    }\n    // Начиная с элемента k+1, поддерживать длину кучи равной k\n    for (int i = k; i &lt; sizeNums; i++) {\n        // Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n        if (nums[i] &gt; peekMinHeap(maxHeap)) {\n            popMinHeap(maxHeap);\n            pushMinHeap(maxHeap, nums[i]);\n        }\n    }\n    int *res = getMinHeap(maxHeap);\n    // Освободить память\n    delMaxHeap(maxHeap);\n    return res;\n}\n</code></pre> top_k.kt<pre><code>/* Найти k наибольших элементов массива с помощью кучи */\nfun topKHeap(nums: IntArray, k: Int): Queue&lt;Int&gt; {\n    // Инициализация минимальной кучи\n    val heap = PriorityQueue&lt;Int&gt;()\n    // Поместить первые k элементов массива в кучу\n    for (i in 0..&lt;k) {\n        heap.offer(nums[i])\n    }\n    // Начиная с элемента k+1, поддерживать длину кучи равной k\n    for (i in k..&lt;nums.size) {\n        // Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n        if (nums[i] &gt; heap.peek()) {\n            heap.poll()\n            heap.offer(nums[i])\n        }\n    }\n    return heap\n}\n</code></pre> top_k.rb<pre><code>### Поиск k наибольших элементов массива с помощью кучи ###\ndef top_k_heap(nums, k)\n  # Инициализация минимальной кучи\n  # Обратите внимание: мы инвертируем все элементы кучи, чтобы с помощью максимальной кучи имитировать минимальную\n  max_heap = MaxHeap.new([])\n\n  # Поместить первые k элементов массива в кучу\n  for i in 0...k\n    push_min_heap(max_heap, nums[i])\n  end\n\n  # Начиная с элемента k+1, поддерживать длину кучи равной k\n  for i in k...nums.length\n    # Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n    if nums[i] &gt; peek_min_heap(max_heap)\n      pop_min_heap(max_heap)\n      push_min_heap(max_heap, nums[i])\n    end\n  end\n\n  get_min_heap(max_heap)\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Всего выполняется \\(n\\) операций добавления и извлечения из кучи, а максимальная длина кучи равна \\(k\\) , поэтому временная сложность равна \\(O(n \\log k)\\) . Этот метод очень эффективен: когда \\(k\\) мало, временная сложность стремится к \\(O(n)\\) ; когда \\(k\\) велико, она все равно не превышает \\(O(n \\log n)\\) .</p> <p>Кроме того, этот метод подходит и для сценариев с динамическим потоком данных. При непрерывном поступлении новых данных мы можем продолжать поддерживать содержимое кучи, тем самым динамически обновляя наибольшие \\(k\\) элементов.</p>","path":["Глава 8. Куча","8.3 &nbsp; Задача Top-k"],"tags":[]},{"location":"chapter_hello_algo/","level":1,"title":"Перед началом","text":"<p>Несколько лет назад я публиковал на LeetCode разборы серии задач \"Sword for Offer\" и получил поддержку и ободрение от многих читателей. Во время общения с ними чаще всего мне задавали один и тот же вопрос: \"как начать изучать алгоритмы\". Постепенно этот вопрос начал меня по-настоящему занимать.</p> <p>Слепо бросаться в решение задач кажется самым популярным способом: он прост, прямолинеен и действительно работает. Но решение задач похоже на игру в \"Сапера\": люди с сильными навыками самообучения способны обезвредить мины одну за другой, а тем, у кого не хватает базы, легко набить себе шишки и шаг за шагом отступить под давлением неудач. Полностью проходить учебники тоже принято часто, но для тех, кто готовится к поиску работы, диплом, резюме, письменные тесты и собеседования уже отнимают большую часть сил, и потому толстые книги нередко превращаются в тяжелое испытание.</p> <p>Если ты тоже сталкиваешься с такими трудностями, то можно сказать, что эта книга сама \"нашла\" тебя. Она стала моим ответом на этот вопрос: пусть не идеальным, но как минимум честной и активной попыткой. Эта книга сама по себе не гарантирует оффер, но поможет тебе увидеть \"карту знаний\" по структурам данных и алгоритмам, понять форму, размер и расположение разных \"мин\" и освоить разные \"способы разминирования\". Освоив это, ты сможешь увереннее решать задачи и читать технические материалы, шаг за шагом выстраивая целостную систему знаний.</p> <p>Я глубоко согласен со словами профессора Фейнмана: \"Knowledge isn't free. You have to pay attention.\" В этом смысле книга не совсем \"бесплатна\". Чтобы не подвести то драгоценное \"внимание\", которое ты ей уделишь, я постараюсь вложить в ее создание максимум собственного \"внимания\".</p> <p>Я хорошо понимаю ограниченность собственных знаний. Хотя материал этой книги уже довольно долго шлифовался, в нем наверняка все еще осталось немало ошибок, поэтому я искренне прошу преподавателей и читателей указывать на неточности и недоработки.</p> <p></p> Hello, Алго! <p>Появление компьютеров радикально изменило мир. Благодаря высокой вычислительной скорости и отличной программируемости они стали идеальной средой для исполнения алгоритмов и обработки данных. Реалистичная графика в играх, интеллектуальные решения в автономном вождении, впечатляющие партии AlphaGo и естественное взаимодействие ChatGPT: все это изящные проявления алгоритмов на компьютере.</p> <p>На самом деле еще до появления компьютеров алгоритмы и структуры данных уже существовали во всех уголках мира. Ранние алгоритмы были сравнительно простыми: например, древние способы счета или последовательности действий при изготовлении инструментов. По мере развития цивилизации алгоритмы становились тоньше и сложнее. За мастерством ремесленников, промышленными продуктами, освобождающими производительные силы, и даже за научными законами движения Вселенной почти всегда стоит изобретательная алгоритмическая мысль.</p> <p>Точно так же структуры данных встречаются повсюду: от социальных сетей до схем метро многие системы можно моделировать как \"граф\"; от государства до семьи основные формы общественной организации обладают свойствами \"дерева\"; зимняя одежда похожа на \"стек\", где то, что надевают первым, снимают последним; тубус для бадминтонных воланов похож на \"очередь\", где элементы добавляются с одного конца и извлекаются с другого; словарь похож на \"хеш-таблицу\", позволяющую быстро находить нужную статью.</p> <p>Эта книга стремится с помощью понятных анимированных иллюстраций и исполняемых примеров кода помочь читателю понять ключевые идеи алгоритмов и структур данных и научиться реализовывать их программно. На этой основе книга также пытается показать живые проявления алгоритмов в сложном мире и раскрыть их красоту. Надеюсь, она окажется для тебя полезной.</p>","path":["Перед началом"],"tags":[]},{"location":"chapter_introduction/","level":1,"title":"Глава 1.   Введение в алгоритмы","text":"<p>Abstract</p> <p>Юная девушка легко кружится в танце среди данных, а подол ее платья струится мелодией алгоритмов.</p> <p>Она приглашает тебя присоединиться к танцу: следуй за ее шагами и войди в мир алгоритмов, полный логики и красоты.</p>","path":["Глава 1. Знакомство с алгоритмами","Глава 1. &nbsp; Введение в алгоритмы"],"tags":[]},{"location":"chapter_introduction/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>1.1   Алгоритмы повсюду</li> <li>1.2   Что такое структуры данных и алгоритмы</li> <li>1.3   Резюме</li> </ul>","path":["Глава 1. Знакомство с алгоритмами","Глава 1. &nbsp; Введение в алгоритмы"],"tags":[]},{"location":"chapter_introduction/algorithms_are_everywhere/","level":1,"title":"1.1   Алгоритмы повсюду","text":"<p>Когда мы слышим слово \"алгоритм\", мы естественным образом думаем о математике. Однако на деле многие алгоритмы не связаны со сложной математикой, а в гораздо большей степени опираются на базовую логику, которую можно увидеть повсюду в повседневной жизни.</p> <p>Прежде чем официально перейти к разговору об алгоритмах, стоит поделиться одним любопытным фактом: ты уже незаметно для себя освоил множество алгоритмов и привык применять их в повседневной жизни. Ниже я приведу несколько конкретных примеров, чтобы это показать.</p> <p>Пример 1: поиск в словаре. В английском словаре слова расположены в алфавитном порядке. Предположим, нам нужно найти слово, начинающееся на букву \\(r\\); обычно это делается так, как показано ниже.</p> <ol> <li>Открой словарь примерно посередине и посмотри, с какой буквы начинается страница; предположим, это буква \\(m\\).</li> <li>Поскольку в алфавите \\(r\\) идет после \\(m\\), первую половину словаря можно отбросить, и область поиска сузится до второй половины.</li> <li>Повторяй шаги <code>1.</code> и <code>2.</code> до тех пор, пока не найдешь страницу, на которой слово начинается с буквы \\(r\\).</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 1-1   Процесс поиска в словаре </p> <p>Поиск в словаре, обязательный навык для школьников, на самом деле и есть знаменитый алгоритм \"двоичного поиска\". С точки зрения структур данных словарь можно рассматривать как отсортированный \"массив\"; с точки зрения алгоритмов последовательность действий при поиске слова в словаре можно считать алгоритмом \"двоичного поиска\".</p> <p>Пример 2: упорядочивание карт. Во время игры в карты нам нужно раскладывать карты в руке по возрастанию; процесс выглядит так, как показано ниже.</p> <ol> <li>Раздели карты на \"упорядоченную\" и \"неупорядоченную\" части и предположи, что в начальный момент самая левая карта уже стоит на правильном месте.</li> <li>Возьми одну карту из неупорядоченной части и вставь ее в правильную позицию внутри упорядоченной части; после этого две самые левые карты уже будут упорядочены.</li> <li>Повторяй шаг <code>2.</code> , каждый раз перенося одну карту из неупорядоченной части в упорядоченную, пока все карты не окажутся в порядке.</li> </ol> <p></p> <p> Рисунок 1-2   Процесс сортировки колоды карт </p> <p>Описанный выше способ раскладывать карты по сути является алгоритмом \"сортировки вставками\", который очень эффективен на небольших наборах данных. Во многих языках программирования во встроенных функциях сортировки тоже можно увидеть этот алгоритм.</p> <p>Пример 3: выдача сдачи. Предположим, в супермаркете мы купили товар на \\(69\\) и дали кассиру \\(100\\), поэтому он должен вернуть нам \\(31\\) сдачи. Этот процесс можно наглядно представить так, как показано на рисунке 1-3.</p> <ol> <li>Доступные варианты - это купюры достоинством меньше \\(31\\), например \\(1\\), \\(5\\), \\(10\\) и \\(20\\).</li> <li>Возьми самую большую купюру из доступных, то есть \\(20\\), тогда останется \\(31 - 20 = 11\\).</li> <li>Возьми самую большую купюру из оставшихся, то есть \\(10\\), тогда останется \\(11 - 10 = 1\\).</li> <li>Возьми самую большую купюру из оставшихся, то есть \\(1\\), тогда останется \\(1 - 1 = 0\\).</li> <li>Выдача сдачи завершена, итоговая комбинация: \\(20 + 10 + 1 = 31\\).</li> </ol> <p></p> <p> Рисунок 1-3   Процесс выдачи сдачи </p> <p>В описанных шагах на каждом этапе выбирается наилучший вариант из доступных в текущий момент, то есть используется купюра наибольшего номинала; в результате получается рабочая схема выдачи сдачи. С точки зрения структур данных и алгоритмов такой подход называется \"жадным\" алгоритмом.</p> <p>От приготовления еды до межзвездных путешествий почти любое решение задачи связано с алгоритмами. Появление компьютеров позволило нам хранить структуры данных в памяти и писать код, который вызывает CPU и GPU для выполнения алгоритмов. Благодаря этому мы можем переносить реальные задачи в компьютер и решать самые разные сложные проблемы более эффективно.</p> <p>Tip</p> <p>Если ты все еще смутно представляешь себе такие понятия, как структуры данных, алгоритмы, массивы и двоичный поиск, просто продолжай читать. Эта книга постепенно введет тебя в мир понимания структур данных и алгоритмов.</p>","path":["Глава 1. Знакомство с алгоритмами","1.1 &nbsp; Алгоритмы повсюду"],"tags":[]},{"location":"chapter_introduction/summary/","level":1,"title":"1.3   Резюме","text":"","path":["Глава 1. Знакомство с алгоритмами","1.3 &nbsp; Резюме"],"tags":[]},{"location":"chapter_introduction/summary/#1","level":3,"title":"1.   Ключевые выводы","text":"<ul> <li>Алгоритмы повсюду встречаются в повседневной жизни и вовсе не являются чем-то далеким и эзотерическим. На деле мы уже давно незаметно для себя освоили множество алгоритмов и используем их для решения самых разных жизненных задач.</li> <li>Принцип поиска в словаре соответствует алгоритму двоичного поиска. Двоичный поиск воплощает важную алгоритмическую идею \"разделяй и властвуй\".</li> <li>Процесс раскладывания карт очень похож на алгоритм сортировки вставками. Сортировка вставками подходит для упорядочивания небольших наборов данных.</li> <li>Выдача сдачи по шагам по своей сути является жадным алгоритмом, в котором на каждом этапе выбирается лучшее решение в текущей ситуации.</li> <li>Алгоритм - это набор инструкций или шагов, который решает конкретную задачу за конечное время, а структура данных - это способ, которым компьютер организует и хранит данные.</li> <li>Структуры данных и алгоритмы тесно связаны. Структуры данных являются основой алгоритмов, а алгоритмы оживляют структуры данных.</li> <li>Структуры данных и алгоритмы можно сравнить со сборкой конструктора: детали представляют данные, форма деталей и способ их соединения представляют структуру данных, а шаги сборки соответствуют алгоритму.</li> </ul>","path":["Глава 1. Знакомство с алгоритмами","1.3 &nbsp; Резюме"],"tags":[]},{"location":"chapter_introduction/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: Я программист и в повседневной работе никогда не решал задачи \"алгоритмами\": распространенные алгоритмы уже инкапсулированы в языках программирования, и ими можно пользоваться напрямую. Значит ли это, что рабочие задачи еще не дошли до уровня, где действительно нужны алгоритмы?</p> <p>Если сравнить конкретные рабочие навыки с \"приемами\" в боевых искусствах, то фундаментальные дисциплины скорее напоминают \"внутреннюю силу\".</p> <p>Я считаю, что смысл изучения алгоритмов (и других фундаментальных дисциплин) не в том, чтобы каждый раз реализовывать их с нуля в работе, а в том, чтобы, опираясь на полученные знания, уметь профессионально реагировать и принимать решения при решении задач, тем самым повышая общее качество работы. Вот простой пример: в каждом языке программирования есть встроенная функция сортировки.</p> <ul> <li>Если мы не изучали структуры данных и алгоритмы, то для любых данных, скорее всего, просто отдали бы их этой функции сортировки. Все работает гладко, производительность хорошая, и на первый взгляд никаких проблем нет.</li> <li>Но если мы изучали алгоритмы, то знаем, что временная сложность встроенной сортировки равна \\(O(n \\log n)\\) ; однако если данные состоят из целых чисел фиксированной разрядности (например, номеров студентов), можно воспользоваться более эффективной \"поразрядной сортировкой\", снизив сложность до \\(O(nk)\\) , где \\(k\\) - число разрядов. Когда объем данных очень велик, сэкономленное время выполнения может принести заметную пользу, например снизить издержки и улучшить пользовательский опыт.</li> </ul> <p>В инженерной практике огромное количество задач трудно довести до оптимального решения, и многие из них решаются лишь \"примерно\". Сложность задачи зависит, с одной стороны, от ее собственной природы, а с другой - от запаса знаний человека, который на нее смотрит. Чем полнее знания и чем больше опыт, тем глубже получается анализ задачи и тем изящнее ее можно решить.</p>","path":["Глава 1. Знакомство с алгоритмами","1.3 &nbsp; Резюме"],"tags":[]},{"location":"chapter_introduction/what_is_dsa/","level":1,"title":"1.2   Что такое алгоритм","text":"","path":["Глава 1. Знакомство с алгоритмами","1.2 &nbsp; Что такое алгоритм"],"tags":[]},{"location":"chapter_introduction/what_is_dsa/#121","level":2,"title":"1.2.1   Определение алгоритма","text":"<p>Алгоритм (algorithm) - это набор инструкций или шагов, который решает конкретную задачу за конечное время. Он обладает следующими свойствами.</p> <ul> <li>Задача четко определена и имеет ясные определения входных и выходных данных.</li> <li>Алгоритм осуществим и может быть выполнен за конечное число шагов, времени и памяти.</li> <li>Каждый шаг имеет однозначный смысл, и при одинаковых входных данных и условиях выполнения результат всегда будет одинаковым.</li> </ul>","path":["Глава 1. Знакомство с алгоритмами","1.2 &nbsp; Что такое алгоритм"],"tags":[]},{"location":"chapter_introduction/what_is_dsa/#122","level":2,"title":"1.2.2   Определение структуры данных","text":"<p>Структура данных (data structure) - это способ организации и хранения данных, охватывающий само содержимое данных, связи между данными и методы работы с ними. У нее есть следующие цели проектирования.</p> <ul> <li>Занимать как можно меньше места, чтобы экономить память компьютера.</li> <li>Выполнять операции над данными как можно быстрее, включая доступ, добавление, удаление, обновление и т. д.</li> <li>Предоставлять компактное представление данных и логическую информацию, чтобы алгоритмы могли работать эффективно.</li> </ul> <p>Проектирование структур данных - это процесс, полный компромиссов. Если мы хотим улучшить что-то одно, то часто вынуждены уступить в чем-то другом. Ниже приведены два примера.</p> <ul> <li>По сравнению с массивами связные списки удобнее для добавления и удаления данных, но жертвуют скоростью доступа к ним.</li> <li>По сравнению со связными списками графы предоставляют более богатую логическую информацию, но требуют большего объема памяти.</li> </ul>","path":["Глава 1. Знакомство с алгоритмами","1.2 &nbsp; Что такое алгоритм"],"tags":[]},{"location":"chapter_introduction/what_is_dsa/#123","level":2,"title":"1.2.3   Связь между структурами данных и алгоритмами","text":"<p>Как показано на рисунке 1-4, структуры данных и алгоритмы тесно связаны и сильно зависят друг от друга; это проявляется в следующих трех аспектах.</p> <ul> <li>Структуры данных служат фундаментом алгоритмов. Они дают алгоритмам структурированный способ хранения данных и методы работы с ними.</li> <li>Алгоритмы оживляют структуры данных. Сами по себе структуры данных лишь хранят информацию, а в сочетании с алгоритмами позволяют решать конкретные задачи.</li> <li>Алгоритмы обычно можно реализовать на основе разных структур данных, но эффективность выполнения может сильно различаться, поэтому выбор подходящей структуры данных является ключевым.</li> </ul> <p></p> <p> Рисунок 1-4   Связь между структурами данных и алгоритмами </p> <p>Структуры данных и алгоритмы похожи на сборку конструктора, показанную на рисунке 1-5. В набор конструктора, помимо множества деталей, входит и подробная инструкция по сборке. Если шаг за шагом следовать этой инструкции, можно собрать красивую модель.</p> <p></p> <p> Рисунок 1-5   Сборка конструктора </p> <p>Подробное соответствие между ними показано в таблице 1-1.</p> <p> Таблица 1-1   Сравнение структур данных и алгоритмов со сборкой конструктора </p> Структуры данных и алгоритмы Сборка конструктора Входные данные Несобранные детали конструктора Структура данных Организация деталей: форма, размер, способ соединения и т. д. Алгоритм Последовательность шагов по сборке деталей в целевую форму Выходные данные Собранная модель конструктора <p>Стоит отметить, что структуры данных и алгоритмы не зависят от конкретного языка программирования. Именно поэтому эта книга может давать реализации на разных языках программирования.</p> <p>Принятое сокращение</p> <p>В реальных обсуждениях мы обычно сокращаем выражение \"структуры данных и алгоритмы\" до просто \"алгоритмы\". Например, хорошо известные алгоритмические задачи LeetCode на деле одновременно проверяют знания и по структурам данных, и по алгоритмам.</p>","path":["Глава 1. Знакомство с алгоритмами","1.2 &nbsp; Что такое алгоритм"],"tags":[]},{"location":"chapter_preface/","level":1,"title":"Глава 0.   Предисловие","text":"<p>Abstract</p> <p>Алгоритмы подобны прекрасной симфонии, а каждая строка кода течет, как мелодия.</p> <p>Пусть эта книга мягко зазвучит в твоем сознании и оставит после себя особую и глубокую мелодию.</p>","path":["Глава 0. Предисловие","Глава 0. &nbsp; Предисловие"],"tags":[]},{"location":"chapter_preface/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>0.1   Об этой книге</li> <li>0.2   Как пользоваться этой книгой</li> <li>0.3   Резюме</li> </ul>","path":["Глава 0. Предисловие","Глава 0. &nbsp; Предисловие"],"tags":[]},{"location":"chapter_preface/about_the_book/","level":1,"title":"0.1   Об этой книге","text":"<p>Этот проект направлен на создание открытого, бесплатного и дружелюбного к новичкам вводного пособия по структурам данных и алгоритмам.</p> <ul> <li>Вся книга построена на анимированных иллюстрациях: материал изложен ясно и последовательно, а кривая обучения остается плавной, помогая начинающим постепенно увидеть карту знаний по структурам данных и алгоритмам.</li> <li>Исходный код можно запускать одним нажатием, что помогает читателю через практику развивать навыки программирования и понимать, как работают алгоритмы и как устроены структуры данных на базовом уровне.</li> <li>Мы призываем читателей учиться друг у друга: задавайте вопросы и делитесь своими наблюдениями в комментариях, чтобы вместе продвигаться вперед через обсуждение и обмен идеями.</li> </ul>","path":["Глава 0. Предисловие","0.1 &nbsp; Об этой книге"],"tags":[]},{"location":"chapter_preface/about_the_book/#011","level":2,"title":"0.1.1   Целевая аудитория","text":"<p>Если ты только начинаешь изучать алгоритмы, никогда раньше с ними не сталкивался или уже решал некоторые задачи, но все еще смутно представляешь себе структуры данных и алгоритмы и постоянно колеблешься между \"понимаю\" и \"не понимаю\", то эта книга создана именно для тебя!</p> <p>Если у тебя уже накопился определенный опыт решения задач и ты знаком с большинством типовых вопросов, книга поможет тебе системно повторить и упорядочить знания об алгоритмах, а исходный код из репозитория можно использовать как \"инструментарий для решения задач\" или как \"алгоритмический словарь\".</p> <p>Если же ты уже настоящий \"гуру\" алгоритмов, мы будем рады получить твои ценные замечания или создавать книгу вместе.</p> <p>Предварительные требования</p> <p>Тебе нужна хотя бы базовая подготовка в одном из языков программирования, чтобы читать и писать простой код.</p>","path":["Глава 0. Предисловие","0.1 &nbsp; Об этой книге"],"tags":[]},{"location":"chapter_preface/about_the_book/#012","level":2,"title":"0.1.2   Структура содержания","text":"<p>Основное содержание книги показано на рисунке 0-1.</p> <ul> <li>Анализ сложности: измерения и методы оценки структур данных и алгоритмов. Способы вычисления временной и пространственной сложности, распространенные типы, примеры и т. д.</li> <li>Структуры данных: способы классификации базовых типов данных и структур данных. Определения, достоинства и недостатки, основные операции, распространенные разновидности, типичные применения и методы реализации массивов, связных списков, стеков, очередей, хеш-таблиц, деревьев, куч, графов и других структур.</li> <li>Алгоритмы: определения, достоинства и недостатки, эффективность, области применения, этапы решения и примеры задач для поиска, сортировки, разделяй-и-властвуй, поиска с возвратом, динамического программирования и жадных алгоритмов.</li> </ul> <p></p> <p> Рисунок 0-1   Основное содержание книги </p>","path":["Глава 0. Предисловие","0.1 &nbsp; Об этой книге"],"tags":[]},{"location":"chapter_preface/about_the_book/#013","level":2,"title":"0.1.3   Благодарности","text":"<p>Эта книга непрерывно совершенствуется благодаря совместным усилиям множества участников сообщества open source. Спасибо каждому автору, который вложил свое время и силы; их имена перечислены в порядке, автоматически сгенерированном GitHub: krahets, coderonion, Gonglja, nuomi1, Reanon, justin-tse, hpstory, danielsss, curtishd, night-cruise, S-N-O-R-L-A-X, rongyi, msk397, gvenusleo, khoaxuantu, rivertwilight, K3v123, gyt95, zhuoqinyue, yuelinxin, Zuoxun, mingXta, Phoenix0415, FangYuan33, GN-Yu, longsizhuo, IsChristina, xBLACKICEx, guowei-gong, Cathay-Chen, pengchzn, QiLOL, magentaqin, hello-ikun, JoseHung, qualifier1024, thomasq0, sunshinesDL, L-Super, Guanngxu, Transmigration-zhou, WSL0809, Slone123c, lhxsm, yuan0221, what-is-me, Shyam-Chen, theNefelibatas, longranger2, codeberg-user, xiongsp, JeffersonHuang, prinpal, seven1240, Wonderdch, malone6, xiaomiusa87, gaofer, bluebean-cloud, a16su, SamJin98, hongyun-robot, nanlei, XiaChuerwu, yd-j, iron-irax, mgisr, steventimes, junminhong, heshuyue, danny900714, MolDuM, Nigh, Dr-XYZ, XC-Zero, reeswell, PXG-XPG, NI-SW, Horbin-Magician, Enlightenus, YangXuanyi, beatrix-chan, DullSword, xjr7670, jiaxianhua, qq909244296, iStig, boloboloda, hts0000, gledfish, wenjianmin, keshida, kilikilikid, lclc6, lwbaptx, linyejoe2, liuxjerry, llql1211, fbigm, echo1937, szu17dmy, dshlstarr, Yucao-cy, coderlef, czruby, bongbongbakudan, beintentional, ZongYangL, ZhongYuuu, ZhongGuanbin, hezhizhen, linzeyan, ZJKung, luluxia, xb534, ztkuaikuai, yw-1021, ElaBosak233, baagod, zhouLion, yishangzhang, yi427, yanedie, yabo083, weibk, wangwang105, th1nk3r-ing, tao363, 4yDX3906, syd168, sslmj2020, smilelsb, siqyka, selear, sdshaoda, Xi-Row, popozhu, nuquist19, noobcodemaker, XiaoK29, chadyi, lyl625760, lucaswangdev, 0130w, shanghai-Jerry, EJackYang, Javesun99, eltociear, lipusheng, KNChiu, BlindTerran, ShiMaRing, lovelock, FreddieLi, FloranceYeh, fanchenggang, gltianwen, goerll, nedchu, curly210102, CuB3y0nd, KraHsu, CarrotDLaw, youshaoXG, bubble9um, Asashishi, Asa0oo0o0o, fanenr, eagleanurag, akshiterate, 52coder, foursevenlove, KorsChen, GaochaoZhu, hopkings2008, yang-le, realwujing, Evilrabbit520, Umer-Jahangir, Turing-1024-Lee, Suremotoo, paoxiaomooo, Chieko-Seren, Allen-Scai, ymmmas, Risuntsy, Richard-Zhang1019, RafaelCaso, qingpeng9802, primexiao, Urbaner3, zhongfq, nidhoggfgg, MwumLi, CreatorMetaSky, martinx, ZnYang2018, hugtyftg, logan-qiu, psychelzh, Keynman, KeiichiKasai и KawaiiAsh.</p> <p>Рецензирование кода для этой книги выполнили coderonion, curtishd, Gonglja, gvenusleo, hpstory, justin-tse, khoaxuantu, krahets, night-cruise, nuomi1, Reanon и rongyi (в алфавитном порядке). Спасибо им за время и силы: именно они обеспечили единообразие и стандартизацию кода на разных языках.</p> <p>Традиционную китайскую версию книги вычитали Shyam-Chen и Dr-XYZ, английскую версию - yuelinxin, K3v123, QiLOL, Phoenix0415, SamJin98, yanedie, RafaelCaso, pengchzn, thomasq0 и magentaqin, а японскую версию - eltociear. Именно благодаря их постоянному вкладу эта книга может быть полезна более широкому кругу читателей, и мы искренне благодарим их.</p> <p>Инструмент генерации ePub-версии этой книги разработал zhongfq. Благодарим его за вклад, который дал читателям более гибкий способ чтения.</p> <p>Во время работы над этой книгой мне помогало очень много людей.</p> <ul> <li>Спасибо моему наставнику в компании, доктору Ли Си: в одной из бесед ты подтолкнул меня \"быстрее начать\", и это укрепило мою решимость написать эту книгу;</li> <li>Спасибо моей девушке Bubble, первому читателю этой книги: с позиции новичка в алгоритмах ты дала много ценных замечаний, благодаря которым книга стала понятнее для начинающих;</li> <li>Спасибо Tengbao, Qibao и Feibao за придуманное ими креативное название книги, которое возвращает нас к теплому воспоминанию о первой строке кода \"Hello World!\";</li> <li>Спасибо Xiaoquan за профессиональную помощь по вопросам интеллектуальной собственности: она сыграла важную роль в совершенствовании этой открытой книги;</li> <li>Спасибо Sutong за прекрасный дизайн обложки и логотипа, а также за терпеливые многочисленные правки, на которые тебя вдохновлял мой перфекционизм;</li> <li>Спасибо @squidfunk за советы по верстке и за созданную им открытую тему документации Material-for-MkDocs.</li> </ul> <p>Во время написания книги я прочитал множество учебников и статей по структурам данных и алгоритмам. Эти работы стали для книги прекрасными образцами и помогли обеспечить точность и качество материала. Я искренне благодарю всех преподавателей и предшественников за их выдающийся вклад!</p> <p>Эта книга пропагандирует способ обучения, в котором работают и руки, и голова; в этом отношении на меня сильно повлияла Dive into Deep Learning. Я горячо рекомендую эту замечательную работу всем читателям.</p> <p>От всего сердца благодарю моих родителей: именно ваша постоянная поддержка и ободрение дали мне возможность заниматься этим интересным делом.</p>","path":["Глава 0. Предисловие","0.1 &nbsp; Об этой книге"],"tags":[]},{"location":"chapter_preface/suggestions/","level":1,"title":"0.2   Как пользоваться этой книгой","text":"<p>Tip</p> <p>Чтобы получить наилучший опыт чтения, рекомендуется полностью прочитать этот раздел.</p>","path":["Глава 0. Предисловие","0.2 &nbsp; Как пользоваться этой книгой"],"tags":[]},{"location":"chapter_preface/suggestions/#021","level":2,"title":"0.2.1   Соглашения о стиле изложения","text":"<ul> <li>Разделы, помеченные <code>*</code> в заголовке, являются дополнительными и сравнительно более сложными. Если времени мало, их можно пока пропустить.</li> <li>Технические термины будут выделяться полужирным шрифтом (в бумажной и PDF-версиях) или подчеркиванием (в веб-версии), например массив (array). Рекомендуется запоминать их, чтобы легче читать техническую литературу.</li> <li>Ключевое содержание и итоговые формулировки будут выделяться полужирным, и на такие фрагменты стоит обращать особое внимание.</li> <li>Слова и выражения со специальным смыслом будут отмечаться \"кавычками\", чтобы избежать неоднозначности.</li> <li>Когда названия различаются между языками программирования, эта книга ориентируется на Python; например, для обозначения \"пустого\" значения используется <code>None</code>.</li> <li>В книге частично отказались от строгих правил оформления комментариев в языках программирования ради более компактной верстки. Комментарии в основном делятся на три типа: комментарии-заголовки, содержательные комментарии и многострочные комментарии.</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>\"\"\"Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п.\"\"\"\n\n# Содержательный комментарий: подробно поясняет код\n\n\"\"\"\nМногострочный\nкомментарий\n\"\"\"\n</code></pre> <pre><code>/* Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п. */\n\n// Содержательный комментарий: подробно поясняет код\n\n/**\n * Многострочный\n * комментарий\n */\n</code></pre> <pre><code>/* Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п. */\n\n// Содержательный комментарий: подробно поясняет код\n\n/**\n * Многострочный\n * комментарий\n */\n</code></pre> <pre><code>/* Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п. */\n\n// Содержательный комментарий: подробно поясняет код\n\n/**\n * Многострочный\n * комментарий\n */\n</code></pre> <pre><code>/* Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п. */\n\n// Содержательный комментарий: подробно поясняет код\n\n/**\n * Многострочный\n * комментарий\n */\n</code></pre> <pre><code>/* Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п. */\n\n// Содержательный комментарий: подробно поясняет код\n\n/**\n * Многострочный\n * комментарий\n */\n</code></pre> <pre><code>/* Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п. */\n\n// Содержательный комментарий: подробно поясняет код\n\n/**\n * Многострочный\n * комментарий\n */\n</code></pre> <pre><code>/* Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п. */\n\n// Содержательный комментарий: подробно поясняет код\n\n/**\n * Многострочный\n * комментарий\n */\n</code></pre> <pre><code>/* Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п. */\n\n// Содержательный комментарий: подробно поясняет код\n\n/**\n * Многострочный\n * комментарий\n */\n</code></pre> <pre><code>/* Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п. */\n\n// Содержательный комментарий: подробно поясняет код\n\n/**\n * Многострочный\n * комментарий\n */\n</code></pre> <pre><code>/* Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п. */\n\n// Содержательный комментарий: подробно поясняет код\n\n/**\n * Многострочный\n * комментарий\n */\n</code></pre> <pre><code>/* Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п. */\n\n// Содержательный комментарий: подробно поясняет код\n\n/**\n * Многострочный\n * комментарий\n */\n</code></pre> <pre><code>### Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п. ###\n\n# Содержательный комментарий: подробно поясняет код\n\n# Многострочный\n# комментарий\n</code></pre>","path":["Глава 0. Предисловие","0.2 &nbsp; Как пользоваться этой книгой"],"tags":[]},{"location":"chapter_preface/suggestions/#022","level":2,"title":"0.2.2   Эффективное обучение с помощью анимированных иллюстраций","text":"<p>По сравнению с текстом видео и изображения обладают большей информационной плотностью и более четкой структурой, поэтому их легче воспринимать. В этой книге ключевые и сложные идеи в основном будут показываться в виде анимированных иллюстраций, а текст будет играть роль пояснения и дополнения.</p> <p>Если во время чтения ты встречаешь фрагмент с анимированной иллюстрацией, как на рисунке 0-2, в первую очередь ориентируйся на изображение, а текст используй как дополнение, соединяя оба источника для понимания материала.</p> <p></p> <p> Рисунок 0-2   Пример анимированной иллюстрации </p>","path":["Глава 0. Предисловие","0.2 &nbsp; Как пользоваться этой книгой"],"tags":[]},{"location":"chapter_preface/suggestions/#023","level":2,"title":"0.2.3   Углубление понимания через практику кода","text":"<p>Сопроводительный код этой книги размещен в репозитории GitHub. Как показано ниже, исходный код снабжен тестовыми примерами и может запускаться одним нажатием.</p> <p>Если позволяет время, рекомендуется самостоятельно перепечатать код. Если времени на обучение мало, то хотя бы полностью прочитай и запусти весь код.</p> <p>По сравнению с простым чтением кода сам процесс его написания обычно дает больше пользы. Учиться на практике - значит учиться по-настоящему.</p> <p></p> <p> Рисунок 0-3   Пример запуска кода </p> <p>Подготовка к запуску кода в основном состоит из трех шагов.</p> <p>Шаг 1: установить локальную среду программирования. Воспользуйся руководством из приложения. Если среда уже установлена, этот шаг можно пропустить.</p> <p>Шаг 2: клонировать или скачать репозиторий с кодом. Перейди в репозиторий GitHub. Если у тебя уже установлен Git, репозиторий можно клонировать следующей командой:</p> <pre><code>git clone https://github.com/krahets/hello-algo.git\n</code></pre> <p>Конечно, можно также нажать кнопку \"Download ZIP\" в месте, показанном на рисунке 0-4, напрямую скачать архив с кодом и затем распаковать его локально.</p> <p></p> <p> Рисунок 0-4   Клонирование репозитория и загрузка кода </p> <p>Шаг 3: запустить исходный код. Как показано на рисунке 0-5, для блоков кода, у которых сверху указано имя файла, соответствующий исходный файл можно найти в папке <code>codes</code> репозитория. Эти файлы запускаются одним нажатием, что помогает не тратить лишнее время на отладку и сосредоточиться на изучении материала.</p> <p></p> <p> Рисунок 0-5   Блоки кода и соответствующие исходные файлы </p> <p>Помимо локального запуска, веб-версия также поддерживает визуальный запуск Python-кода (на базе pythontutor). Как показано ниже, можно нажать \"Визуализировать выполнение\" под блоком кода, чтобы раскрыть окно и наблюдать за выполнением алгоритма; также можно нажать \"Полноэкранный режим\", чтобы получить более удобный просмотр.</p> <p></p> <p> Рисунок 0-6   Визуальный запуск Python-кода </p>","path":["Глава 0. Предисловие","0.2 &nbsp; Как пользоваться этой книгой"],"tags":[]},{"location":"chapter_preface/suggestions/#024","level":2,"title":"0.2.4   Совместный рост через вопросы и обсуждения","text":"<p>Во время чтения книги не стоит легко пропускать те места, которые остались непонятными. Смело задавай свои вопросы в разделе комментариев: я и мои друзья постараемся ответить тебе как можно тщательнее, обычно в течение двух дней.</p> <p>Как показано на рисунке 0-7, в веб-версии у каждой главы внизу есть раздел комментариев. Надеюсь, ты будешь чаще обращать внимание на его содержание. С одной стороны, это поможет увидеть, с какими трудностями сталкиваются другие читатели, восполнить пробелы и подтолкнуть себя к более глубоким размышлениям. С другой стороны, буду рад, если ты щедро ответишь на вопросы других участников, поделишься своими наблюдениями и поможешь им продвинуться вперед.</p> <p></p> <p> Рисунок 0-7   Пример раздела комментариев </p>","path":["Глава 0. Предисловие","0.2 &nbsp; Как пользоваться этой книгой"],"tags":[]},{"location":"chapter_preface/suggestions/#025","level":2,"title":"0.2.5   Дорожная карта изучения алгоритмов","text":"<p>В целом процесс изучения структур данных и алгоритмов можно разделить на три этапа.</p> <ol> <li>Этап 1: введение в алгоритмы. Нужно познакомиться с особенностями и способами применения разных структур данных, а также изучить принципы, ход работы, назначение и эффективность различных алгоритмов.</li> <li>Этап 2: решение алгоритмических задач. Рекомендуется начинать с популярных задач и сначала накопить не менее 100 решенных примеров, чтобы познакомиться с основными типами алгоритмических проблем. На первых порах \"забывание знаний\" может стать испытанием, но это нормально. Мы можем повторять задачи по \"кривой забывания Эббингауза\", и обычно после 3-5 циклов повторения материал прочно закрепляется. Рекомендуемые списки задач и планы практики см. в этом репозитории GitHub.</li> <li>Этап 3: построение системы знаний. В учебной части можно читать статьи по алгоритмам, разбирать каркасы решений и учебники, чтобы постоянно обогащать свою систему знаний. В практической части можно пробовать более продвинутые стратегии, например классификацию по темам, несколько решений одной задачи или одно решение для нескольких задач; соответствующий опыт можно найти в разных сообществах.</li> </ol> <p>Как показано на рисунке 0-8, содержание этой книги в основном покрывает \"этап 1\" и призвано помочь тебе более эффективно перейти к обучению на этапах 2 и 3.</p> <p></p> <p> Рисунок 0-8   Дорожная карта изучения алгоритмов </p>","path":["Глава 0. Предисловие","0.2 &nbsp; Как пользоваться этой книгой"],"tags":[]},{"location":"chapter_preface/summary/","level":1,"title":"0.3   Резюме","text":"","path":["Глава 0. Предисловие","0.3 &nbsp; Резюме"],"tags":[]},{"location":"chapter_preface/summary/#1","level":3,"title":"1.   Ключевые выводы","text":"<ul> <li>Основная аудитория этой книги - новички в изучении алгоритмов. Если у тебя уже есть определенная база, книга поможет системно повторить знания, а исходный код можно использовать как \"инструментарий для решения задач\".</li> <li>Основное содержание книги состоит из трех частей: анализ сложности, структуры данных и алгоритмы; вместе они охватывают большую часть тем этой области.</li> <li>Для начинающих особенно важно на старте прочитать хорошее вводное пособие: это помогает избежать множества лишних обходных путей.</li> <li>Анимированные иллюстрации в книге обычно используются для объяснения ключевых и сложных идей. При чтении книги этим материалам стоит уделять больше внимания.</li> <li>Практика - лучший способ изучать программирование. Настоятельно рекомендуется запускать исходный код и набирать его самостоятельно.</li> <li>В веб-версии книги у каждой главы есть раздел комментариев, где можно в любой момент делиться вопросами и своими мыслями.</li> </ul>","path":["Глава 0. Предисловие","0.3 &nbsp; Резюме"],"tags":[]},{"location":"chapter_reference/","level":1,"title":"Список литературы","text":"<p>[1] Thomas H. Cormen, et al. Introduction to Algorithms (3<sup>rd</sup> Edition).</p> <p>[2] Aditya Bhargava. Grokking Algorithms: An Illustrated Guide for Programmers and Other Curious People (1<sup>st</sup> Edition).</p> <p>[3] Robert Sedgewick, et al. Algorithms (4<sup>th</sup> Edition).</p> <p>[4] Yan Weimin. Data Structures (C Language Edition).</p> <p>[5] Deng Junhui. Data Structures (C++ Language Edition, 3<sup>rd</sup> Edition).</p> <p>[6] Mark Allen Weiss; translated by Chen Yue. Data Structures and Algorithm Analysis: Java Description (3<sup>rd</sup> Edition).</p> <p>[7] Cheng Jie. A Plainspoken Guide to Data Structures.</p> <p>[8] Wang Zheng. The Beauty of Data Structures and Algorithms.</p> <p>[9] Gayle Laakmann McDowell. Cracking the Coding Interview: 189 Programming Questions and Solutions (6<sup>th</sup> Edition).</p> <p>[10] Aston Zhang, et al. Dive into Deep Learning.</p>","path":["Список литературы"],"tags":[]},{"location":"chapter_searching/","level":1,"title":"Глава 10.   Поиск","text":"<p>Abstract</p> <p>Поиск - это приключение в неизвестность: иногда приходится пройти каждый уголок загадочного пространства, а иногда удается быстро зафиксировать цель.</p> <p>В этом путешествии каждый новый шаг может привести к ответу, которого мы не ожидали.</p>","path":["Глава 10. Поиск","Глава 10. &nbsp; Поиск"],"tags":[]},{"location":"chapter_searching/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>10.1   Двоичный поиск</li> <li>10.2   Точка вставки двоичного поиска</li> <li>10.3   Граничные случаи двоичного поиска</li> <li>10.4   Стратегия оптимизации через хеширование</li> <li>10.5   Алгоритмы поиска: новый взгляд</li> <li>10.6   Резюме</li> </ul>","path":["Глава 10. Поиск","Глава 10. &nbsp; Поиск"],"tags":[]},{"location":"chapter_searching/binary_search/","level":1,"title":"10.1   Двоичный поиск","text":"<p>Двоичный поиск (binary search) - это эффективный алгоритм поиска, основанный на стратегии \"разделяй и властвуй\". Он использует упорядоченность данных и на каждом шаге сокращает область поиска вдвое, пока не найдет целевой элемент или пока интервал поиска не опустеет.</p> <p>Question</p> <p>Дан массив <code>nums</code> длины \\(n\\), элементы которого расположены в порядке возрастания и не повторяются. Найдите и верните индекс элемента <code>target</code> в этом массиве. Если массив не содержит этого элемента, верните \\(-1\\) . Пример показан на рисунке 10-1.</p> <p></p> <p> Рисунок 10-1   Пример данных для двоичного поиска </p> <p>Как показано на рисунке 10-2, сначала инициализируем указатели \\(i = 0\\) и \\(j = n - 1\\) , которые указывают на первый и последний элементы массива и задают интервал поиска \\([0, n - 1]\\) . Обратите внимание: квадратные скобки обозначают замкнутый интервал и включают граничные значения.</p> <p>Далее в цикле выполняются следующие два шага.</p> <ol> <li>Вычислить индекс середины \\(m = \\lfloor {(i + j) / 2} \\rfloor\\) , где \\(\\lfloor \\: \\rfloor\\) означает операцию округления вниз.</li> <li>Сравнить <code>nums[m]</code> и <code>target</code> , после чего возможны три случая.<ol> <li>Если <code>nums[m] &lt; target</code> , это означает, что <code>target</code> находится в интервале \\([m + 1, j]\\) , поэтому выполняется \\(i = m + 1\\) .</li> <li>Если <code>nums[m] &gt; target</code> , это означает, что <code>target</code> находится в интервале \\([i, m - 1]\\) , поэтому выполняется \\(j = m - 1\\) .</li> <li>Если <code>nums[m] = target</code> , значит, элемент <code>target</code> найден, поэтому возвращается индекс \\(m\\) .</li> </ol> </li> </ol> <p>Если массив не содержит целевой элемент, область поиска в итоге сузится до пустого интервала. В этом случае возвращается \\(-1\\) .</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 10-2   Процесс двоичного поиска </p> <p>Стоит отметить, что поскольку и \\(i\\) , и \\(j\\) имеют тип <code>int</code> , то сумма \\(i + j\\) может выйти за пределы диапазона типа <code>int</code>. Чтобы избежать переполнения, обычно используют формулу \\(m = \\lfloor {i + (j - i) / 2} \\rfloor\\) для вычисления середины.</p> <p>Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search.py<pre><code>def binary_search(nums: list[int], target: int) -&gt; int:\n    \"\"\"Бинарный поиск (двусторонне замкнутый интервал)\"\"\"\n    # Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n    i, j = 0, len(nums) - 1\n    # Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n    while i &lt;= j:\n        # Теоретически числа в Python могут быть сколь угодно большими (ограничены только объемом памяти), поэтому не нужно учитывать переполнение больших чисел\n        m = (i + j) // 2  # Вычислить индекс середины m\n        if nums[m] &lt; target:\n            i = m + 1  # Это означает, что target находится в интервале [m+1, j]\n        elif nums[m] &gt; target:\n            j = m - 1  # Это означает, что target находится в интервале [i, m-1]\n        else:\n            return m  # Целевой элемент найден, вернуть его индекс\n    return -1  # Целевой элемент не найден, вернуть -1\n</code></pre> binary_search.cpp<pre><code>/* Бинарный поиск (двусторонне замкнутый интервал) */\nint binarySearch(vector&lt;int&gt; &amp;nums, int target) {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n    int i = 0, j = nums.size() - 1;\n    // Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target)    // Это означает, что target находится в интервале [m+1, j]\n            i = m + 1;\n        else if (nums[m] &gt; target) // Это означает, что target находится в интервале [i, m-1]\n            j = m - 1;\n        else // Целевой элемент найден, вернуть его индекс\n            return m;\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1;\n}\n</code></pre> binary_search.java<pre><code>/* Бинарный поиск (двусторонне замкнутый интервал) */\nint binarySearch(int[] nums, int target) {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n    int i = 0, j = nums.length - 1;\n    // Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target) // Это означает, что target находится в интервале [m+1, j]\n            i = m + 1;\n        else if (nums[m] &gt; target) // Это означает, что target находится в интервале [i, m-1]\n            j = m - 1;\n        else // Целевой элемент найден, вернуть его индекс\n            return m;\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1;\n}\n</code></pre> binary_search.cs<pre><code>/* Бинарный поиск (двусторонне замкнутый интервал) */\nint BinarySearch(int[] nums, int target) {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n    int i = 0, j = nums.Length - 1;\n    // Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2;   // Вычислить индекс середины m\n        if (nums[m] &lt; target)      // Это означает, что target находится в интервале [m+1, j]\n            i = m + 1;\n        else if (nums[m] &gt; target) // Это означает, что target находится в интервале [i, m-1]\n            j = m - 1;\n        else                       // Целевой элемент найден, вернуть его индекс\n            return m;\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1;\n}\n</code></pre> binary_search.go<pre><code>/* Бинарный поиск (двусторонне замкнутый интервал) */\nfunc binarySearch(nums []int, target int) int {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n    i, j := 0, len(nums)-1\n    // Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n    for i &lt;= j {\n        m := i + (j-i)/2      // Вычислить индекс середины m\n        if nums[m] &lt; target { // Это означает, что target находится в интервале [m+1, j]\n            i = m + 1\n        } else if nums[m] &gt; target { // Это означает, что target находится в интервале [i, m-1]\n            j = m - 1\n        } else { // Целевой элемент найден, вернуть его индекс\n            return m\n        }\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1\n}\n</code></pre> binary_search.swift<pre><code>/* Бинарный поиск (двусторонне замкнутый интервал) */\nfunc binarySearch(nums: [Int], target: Int) -&gt; Int {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n    var i = nums.startIndex\n    var j = nums.endIndex - 1\n    // Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n    while i &lt;= j {\n        let m = i + (j - i) / 2 // Вычислить индекс середины m\n        if nums[m] &lt; target { // Это означает, что target находится в интервале [m+1, j]\n            i = m + 1\n        } else if nums[m] &gt; target { // Это означает, что target находится в интервале [i, m-1]\n            j = m - 1\n        } else { // Целевой элемент найден, вернуть его индекс\n            return m\n        }\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1\n}\n</code></pre> binary_search.js<pre><code>/* Бинарный поиск (двусторонне замкнутый интервал) */\nfunction binarySearch(nums, target) {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n    let i = 0,\n        j = nums.length - 1;\n    // Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n    while (i &lt;= j) {\n        // Вычислить индекс середины m, используя parseInt() для округления вниз\n        const m = parseInt(i + (j - i) / 2);\n        if (nums[m] &lt; target)\n            // Это означает, что target находится в интервале [m+1, j]\n            i = m + 1;\n        else if (nums[m] &gt; target)\n            // Это означает, что target находится в интервале [i, m-1]\n            j = m - 1;\n        else return m; // Целевой элемент найден, вернуть его индекс\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1;\n}\n</code></pre> binary_search.ts<pre><code>/* Бинарный поиск (двусторонне замкнутый интервал) */\nfunction binarySearch(nums: number[], target: number): number {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n    let i = 0,\n        j = nums.length - 1;\n    // Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n    while (i &lt;= j) {\n        // Вычислить индекс середины m\n        const m = Math.floor(i + (j - i) / 2);\n        if (nums[m] &lt; target) {\n            // Это означает, что target находится в интервале [m+1, j]\n            i = m + 1;\n        } else if (nums[m] &gt; target) {\n            // Это означает, что target находится в интервале [i, m-1]\n            j = m - 1;\n        } else {\n            // Целевой элемент найден, вернуть его индекс\n            return m;\n        }\n    }\n    return -1; // Целевой элемент не найден, вернуть -1\n}\n</code></pre> binary_search.dart<pre><code>/* Бинарный поиск (двусторонне замкнутый интервал) */\nint binarySearch(List&lt;int&gt; nums, int target) {\n  // Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n  int i = 0, j = nums.length - 1;\n  // Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n  while (i &lt;= j) {\n    int m = i + (j - i) ~/ 2; // Вычислить индекс середины m\n    if (nums[m] &lt; target) {\n      // Это означает, что target находится в интервале [m+1, j]\n      i = m + 1;\n    } else if (nums[m] &gt; target) {\n      // Это означает, что target находится в интервале [i, m-1]\n      j = m - 1;\n    } else {\n      // Целевой элемент найден, вернуть его индекс\n      return m;\n    }\n  }\n  // Целевой элемент не найден, вернуть -1\n  return -1;\n}\n</code></pre> binary_search.rs<pre><code>/* Бинарный поиск (двусторонне замкнутый интервал) */\nfn binary_search(nums: &amp;[i32], target: i32) -&gt; i32 {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n    let mut i = 0;\n    let mut j = nums.len() as i32 - 1;\n    // Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n    while i &lt;= j {\n        let m = i + (j - i) / 2; // Вычислить индекс середины m\n        if nums[m as usize] &lt; target {\n            // Это означает, что target находится в интервале [m+1, j]\n            i = m + 1;\n        } else if nums[m as usize] &gt; target {\n            // Это означает, что target находится в интервале [i, m-1]\n            j = m - 1;\n        } else {\n            // Целевой элемент найден, вернуть его индекс\n            return m;\n        }\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1;\n}\n</code></pre> binary_search.c<pre><code>/* Бинарный поиск (двусторонне замкнутый интервал) */\nint binarySearch(int *nums, int len, int target) {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n    int i = 0, j = len - 1;\n    // Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target)    // Это означает, что target находится в интервале [m+1, j]\n            i = m + 1;\n        else if (nums[m] &gt; target) // Это означает, что target находится в интервале [i, m-1]\n            j = m - 1;\n        else // Целевой элемент найден, вернуть его индекс\n            return m;\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1;\n}\n</code></pre> binary_search.kt<pre><code>/* Бинарный поиск (двусторонне замкнутый интервал) */\nfun binarySearch(nums: IntArray, target: Int): Int {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n    var i = 0\n    var j = nums.size - 1\n    // Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n    while (i &lt;= j) {\n        val m = i + (j - i) / 2 // Вычислить индекс середины m\n        if (nums[m] &lt; target) // Это означает, что target находится в интервале [m+1, j]\n            i = m + 1\n        else if (nums[m] &gt; target) // Это означает, что target находится в интервале [i, m-1]\n            j = m - 1\n        else  // Целевой элемент найден, вернуть его индекс\n            return m\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1\n}\n</code></pre> binary_search.rb<pre><code>### Бинарный поиск (двусторонне замкнутый интервал) ###\ndef binary_search(nums, target)\n  # Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n  i, j = 0, nums.length - 1\n\n  # Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n  while i &lt;= j\n    # Теоретически числа в Ruby могут быть сколь угодно большими (ограничены только объемом памяти), поэтому не нужно учитывать переполнение больших чисел\n    m = (i + j) / 2   # Вычислить индекс середины m\n\n    if nums[m] &lt; target\n      i = m + 1 # Это означает, что target находится в интервале [m+1, j]\n    elsif nums[m] &gt; target\n      j = m - 1 # Это означает, что target находится в интервале [i, m-1]\n    else\n      return m  # Целевой элемент найден, вернуть его индекс\n    end\n  end\n\n  -1  # Целевой элемент не найден, вернуть -1\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Временная сложность равна \\(O(\\log n)\\) : в цикле двоичного поиска интервал каждый раз сокращается вдвое, поэтому число итераций равно \\(\\log_2 n\\) .</p> <p>Пространственная сложность равна \\(O(1)\\) : указатели \\(i\\) и \\(j\\) занимают константный объем памяти.</p>","path":["Глава 10. Поиск","10.1 &nbsp; Двоичный поиск"],"tags":[]},{"location":"chapter_searching/binary_search/#1011","level":2,"title":"10.1.1   Методы представления интервалов","text":"<p>Помимо описанного выше двойного замкнутого интервала, часто используется и интервал \"слева закрыт, справа открыт\", который задается как \\([0, n)\\) , то есть левая граница включается, а правая - нет. В этом представлении интервал \\([i, j)\\) пуст, когда \\(i = j\\) .</p> <p>На основе этого представления можно реализовать двоичный поиск с той же функциональностью:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search.py<pre><code>def binary_search_lcro(nums: list[int], target: int) -&gt; int:\n    \"\"\"Бинарный поиск (лево замкнутый, право открытый интервал)\"\"\"\n    # Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n    i, j = 0, len(nums)\n    # Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n    while i &lt; j:\n        m = (i + j) // 2  # Вычислить индекс середины m\n        if nums[m] &lt; target:\n            i = m + 1  # Это означает, что target находится в интервале [m+1, j)\n        elif nums[m] &gt; target:\n            j = m  # Это означает, что target находится в интервале [i, m)\n        else:\n            return m  # Целевой элемент найден, вернуть его индекс\n    return -1  # Целевой элемент не найден, вернуть -1\n</code></pre> binary_search.cpp<pre><code>/* Бинарный поиск (лево замкнутый, право открытый интервал) */\nint binarySearchLCRO(vector&lt;int&gt; &amp;nums, int target) {\n    // Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n    int i = 0, j = nums.size();\n    // Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n    while (i &lt; j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target)    // Это означает, что target находится в интервале [m+1, j)\n            i = m + 1;\n        else if (nums[m] &gt; target) // Это означает, что target находится в интервале [i, m)\n            j = m;\n        else // Целевой элемент найден, вернуть его индекс\n            return m;\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1;\n}\n</code></pre> binary_search.java<pre><code>/* Бинарный поиск (лево замкнутый, право открытый интервал) */\nint binarySearchLCRO(int[] nums, int target) {\n    // Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n    int i = 0, j = nums.length;\n    // Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n    while (i &lt; j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target) // Это означает, что target находится в интервале [m+1, j)\n            i = m + 1;\n        else if (nums[m] &gt; target) // Это означает, что target находится в интервале [i, m)\n            j = m;\n        else // Целевой элемент найден, вернуть его индекс\n            return m;\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1;\n}\n</code></pre> binary_search.cs<pre><code>/* Бинарный поиск (лево замкнутый, право открытый интервал) */\nint BinarySearchLCRO(int[] nums, int target) {\n    // Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n    int i = 0, j = nums.Length;\n    // Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n    while (i &lt; j) {\n        int m = i + (j - i) / 2;   // Вычислить индекс середины m\n        if (nums[m] &lt; target)      // Это означает, что target находится в интервале [m+1, j)\n            i = m + 1;\n        else if (nums[m] &gt; target) // Это означает, что target находится в интервале [i, m)\n            j = m;\n        else                       // Целевой элемент найден, вернуть его индекс\n            return m;\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1;\n}\n</code></pre> binary_search.go<pre><code>/* Бинарный поиск (лево замкнутый, право открытый интервал) */\nfunc binarySearchLCRO(nums []int, target int) int {\n    // Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n    i, j := 0, len(nums)\n    // Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n    for i &lt; j {\n        m := i + (j-i)/2      // Вычислить индекс середины m\n        if nums[m] &lt; target { // Это означает, что target находится в интервале [m+1, j)\n            i = m + 1\n        } else if nums[m] &gt; target { // Это означает, что target находится в интервале [i, m)\n            j = m\n        } else { // Целевой элемент найден, вернуть его индекс\n            return m\n        }\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1\n}\n</code></pre> binary_search.swift<pre><code>/* Бинарный поиск (лево замкнутый, право открытый интервал) */\nfunc binarySearchLCRO(nums: [Int], target: Int) -&gt; Int {\n    // Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n    var i = nums.startIndex\n    var j = nums.endIndex\n    // Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n    while i &lt; j {\n        let m = i + (j - i) / 2 // Вычислить индекс середины m\n        if nums[m] &lt; target { // Это означает, что target находится в интервале [m+1, j)\n            i = m + 1\n        } else if nums[m] &gt; target { // Это означает, что target находится в интервале [i, m)\n            j = m\n        } else { // Целевой элемент найден, вернуть его индекс\n            return m\n        }\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1\n}\n</code></pre> binary_search.js<pre><code>/* Бинарный поиск (лево замкнутый, право открытый интервал) */\nfunction binarySearchLCRO(nums, target) {\n    // Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n    let i = 0,\n        j = nums.length;\n    // Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n    while (i &lt; j) {\n        // Вычислить индекс середины m, используя parseInt() для округления вниз\n        const m = parseInt(i + (j - i) / 2);\n        if (nums[m] &lt; target)\n            // Это означает, что target находится в интервале [m+1, j)\n            i = m + 1;\n        else if (nums[m] &gt; target)\n            // Это означает, что target находится в интервале [i, m)\n            j = m;\n        // Целевой элемент найден, вернуть его индекс\n        else return m;\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1;\n}\n</code></pre> binary_search.ts<pre><code>/* Бинарный поиск (лево замкнутый, право открытый интервал) */\nfunction binarySearchLCRO(nums: number[], target: number): number {\n    // Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n    let i = 0,\n        j = nums.length;\n    // Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n    while (i &lt; j) {\n        // Вычислить индекс середины m\n        const m = Math.floor(i + (j - i) / 2);\n        if (nums[m] &lt; target) {\n            // Это означает, что target находится в интервале [m+1, j)\n            i = m + 1;\n        } else if (nums[m] &gt; target) {\n            // Это означает, что target находится в интервале [i, m)\n            j = m;\n        } else {\n            // Целевой элемент найден, вернуть его индекс\n            return m;\n        }\n    }\n    return -1; // Целевой элемент не найден, вернуть -1\n}\n</code></pre> binary_search.dart<pre><code>/* Бинарный поиск (лево замкнутый, право открытый интервал) */\nint binarySearchLCRO(List&lt;int&gt; nums, int target) {\n  // Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n  int i = 0, j = nums.length;\n  // Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n  while (i &lt; j) {\n    int m = i + (j - i) ~/ 2; // Вычислить индекс середины m\n    if (nums[m] &lt; target) {\n      // Это означает, что target находится в интервале [m+1, j)\n      i = m + 1;\n    } else if (nums[m] &gt; target) {\n      // Это означает, что target находится в интервале [i, m)\n      j = m;\n    } else {\n      // Целевой элемент найден, вернуть его индекс\n      return m;\n    }\n  }\n  // Целевой элемент не найден, вернуть -1\n  return -1;\n}\n</code></pre> binary_search.rs<pre><code>/* Бинарный поиск (лево замкнутый, право открытый интервал) */\nfn binary_search_lcro(nums: &amp;[i32], target: i32) -&gt; i32 {\n    // Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n    let mut i = 0;\n    let mut j = nums.len() as i32;\n    // Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n    while i &lt; j {\n        let m = i + (j - i) / 2; // Вычислить индекс середины m\n        if nums[m as usize] &lt; target {\n            // Это означает, что target находится в интервале [m+1, j)\n            i = m + 1;\n        } else if nums[m as usize] &gt; target {\n            // Это означает, что target находится в интервале [i, m)\n            j = m;\n        } else {\n            // Целевой элемент найден, вернуть его индекс\n            return m;\n        }\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1;\n}\n</code></pre> binary_search.c<pre><code>/* Бинарный поиск (лево замкнутый, право открытый интервал) */\nint binarySearchLCRO(int *nums, int len, int target) {\n    // Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n    int i = 0, j = len;\n    // Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n    while (i &lt; j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target)    // Это означает, что target находится в интервале [m+1, j)\n            i = m + 1;\n        else if (nums[m] &gt; target) // Это означает, что target находится в интервале [i, m)\n            j = m;\n        else // Целевой элемент найден, вернуть его индекс\n            return m;\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1;\n}\n</code></pre> binary_search.kt<pre><code>/* Бинарный поиск (лево замкнутый, право открытый интервал) */\nfun binarySearchLCRO(nums: IntArray, target: Int): Int {\n    // Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n    var i = 0\n    var j = nums.size\n    // Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n    while (i &lt; j) {\n        val m = i + (j - i) / 2 // Вычислить индекс середины m\n        if (nums[m] &lt; target) // Это означает, что target находится в интервале [m+1, j)\n            i = m + 1\n        else if (nums[m] &gt; target) // Это означает, что target находится в интервале [i, m)\n            j = m\n        else  // Целевой элемент найден, вернуть его индекс\n            return m\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1\n}\n</code></pre> binary_search.rb<pre><code>### Бинарный поиск (лево замкнутый, право открытый интервал) ###\ndef binary_search_lcro(nums, target)\n  # Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n  i, j = 0, nums.length\n\n  # Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n  while i &lt; j\n    # Вычислить индекс середины m\n    m = (i + j) / 2\n\n    if nums[m] &lt; target\n      i = m + 1 # Это означает, что target находится в интервале [m+1, j)\n    elsif nums[m] &gt; target\n      j = m - 1 # Это означает, что target находится в интервале [i, m)\n    else\n      return m  # Целевой элемент найден, вернуть его индекс\n    end\n  end\n\n  -1  # Целевой элемент не найден, вернуть -1\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Как показано на рисунке 10-3, в этих двух вариантах представления интервала различаются инициализация, условие цикла и операция сужения интервала в алгоритме двоичного поиска.</p> <p>Поскольку в записи \"двойной замкнутый интервал\" обе границы являются закрытыми, операции сужения интервала при помощи указателей \\(i\\) и \\(j\\) тоже получаются симметричными. Из-за этого в таком варианте сложнее допустить ошибку, поэтому обычно рекомендуется использовать именно запись \"двойной замкнутый интервал\".</p> <p></p> <p> Рисунок 10-3   Два определения интервалов </p>","path":["Глава 10. Поиск","10.1 &nbsp; Двоичный поиск"],"tags":[]},{"location":"chapter_searching/binary_search/#1012","level":2,"title":"10.1.2   Преимущества и ограничения","text":"<p>Двоичный поиск показывает хорошие результаты и по времени, и по памяти.</p> <ul> <li>Двоичный поиск очень эффективен по времени. На больших объемах данных логарифмическая временная сложность дает заметное преимущество. Например, когда размер данных \\(n = 2^{20}\\) , линейный поиск потребует \\(2^{20} = 1048576\\) итераций, тогда как двоичный поиск выполнится всего за \\(\\log_2 2^{20} = 20\\) итераций.</li> <li>Двоичный поиск не требует дополнительной памяти. По сравнению с алгоритмами поиска, которым нужно внешнее пространство (например, с хеш-поиском), двоичный поиск заметно экономнее по памяти.</li> </ul> <p>Однако двоичный поиск подходит не для всех ситуаций, и основные причины таковы.</p> <ul> <li>Двоичный поиск применим только к упорядоченным данным. Если входные данные неупорядочены, специально сортировать их ради двоичного поиска невыгодно. Это связано с тем, что временная сложность алгоритмов сортировки обычно составляет \\(O(n \\log n)\\) , что выше, чем у линейного и двоичного поиска. Если элементы приходится часто вставлять, то для сохранения порядка в массиве их нужно помещать в конкретные позиции, а это требует \\(O(n)\\) времени и тоже обходится дорого.</li> <li>Двоичный поиск применим только к массивам. Для него нужен скачкообразный доступ к элементам, а в связном списке такой доступ малоэффективен, поэтому двоичный поиск не подходит для списков и структур данных, построенных на их основе.</li> <li>При малом объеме данных линейный поиск работает лучше. В линейном поиске на каждом шаге нужна всего одна операция сравнения; в двоичном поиске требуется 1 сложение, 1 деление, от 1 до 3 сравнений и еще 1 сложение или вычитание, то есть всего от 4 до 6 элементарных операций. Поэтому при небольшом \\(n\\) линейный поиск может оказаться быстрее двоичного.</li> </ul>","path":["Глава 10. Поиск","10.1 &nbsp; Двоичный поиск"],"tags":[]},{"location":"chapter_searching/binary_search_edge/","level":1,"title":"10.3   Двоичный поиск границ","text":"","path":["Глава 10. Поиск","10.3 &nbsp; Двоичный поиск границ"],"tags":[]},{"location":"chapter_searching/binary_search_edge/#1031","level":2,"title":"10.3.1   Поиск левой границы","text":"<p>Question</p> <p>Дан упорядоченный массив <code>nums</code> длины \\(n\\), который может содержать повторяющиеся элементы. Верните индекс самого левого элемента <code>target</code> в массиве. Если массив не содержит этот элемент, верните \\(-1\\) .</p> <p>Вспомним метод поиска точки вставки при двоичном поиске: после завершения поиска указатель \\(i\\) указывает на самый левый <code>target</code> , поэтому поиск точки вставки по сути и есть поиск индекса самого левого <code>target</code>.</p> <p>Рассмотрим реализацию поиска левой границы через функцию поиска точки вставки. Обратите внимание: массив может не содержать <code>target</code> , и тогда возможны две ситуации.</p> <ul> <li>Индекс точки вставки \\(i\\) выходит за границы массива.</li> <li>Элемент <code>nums[i]</code> не равен <code>target</code> .</li> </ul> <p>Если возникает любая из этих ситуаций, достаточно сразу вернуть \\(-1\\) . Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_edge.py<pre><code>def binary_search_left_edge(nums: list[int], target: int) -&gt; int:\n    \"\"\"Бинарный поиск самого левого target\"\"\"\n    # Эквивалентно поиску точки вставки target\n    i = binary_search_insertion(nums, target)\n    # target не найден, вернуть -1\n    if i == len(nums) or nums[i] != target:\n        return -1\n    # Найти target и вернуть индекс i\n    return i\n</code></pre> binary_search_edge.cpp<pre><code>/* Бинарный поиск самого левого target */\nint binarySearchLeftEdge(vector&lt;int&gt; &amp;nums, int target) {\n    // Эквивалентно поиску точки вставки target\n    int i = binarySearchInsertion(nums, target);\n    // target не найден, вернуть -1\n    if (i == nums.size() || nums[i] != target) {\n        return -1;\n    }\n    // Найти target и вернуть индекс i\n    return i;\n}\n</code></pre> binary_search_edge.java<pre><code>/* Бинарный поиск самого левого target */\nint binarySearchLeftEdge(int[] nums, int target) {\n    // Эквивалентно поиску точки вставки target\n    int i = binary_search_insertion.binarySearchInsertion(nums, target);\n    // target не найден, вернуть -1\n    if (i == nums.length || nums[i] != target) {\n        return -1;\n    }\n    // Найти target и вернуть индекс i\n    return i;\n}\n</code></pre> binary_search_edge.cs<pre><code>/* Бинарный поиск самого левого target */\nint BinarySearchLeftEdge(int[] nums, int target) {\n    // Эквивалентно поиску точки вставки target\n    int i = binary_search_insertion.BinarySearchInsertion(nums, target);\n    // target не найден, вернуть -1\n    if (i == nums.Length || nums[i] != target) {\n        return -1;\n    }\n    // Найти target и вернуть индекс i\n    return i;\n}\n</code></pre> binary_search_edge.go<pre><code>/* Бинарный поиск самого левого target */\nfunc binarySearchLeftEdge(nums []int, target int) int {\n    // Эквивалентно поиску точки вставки target\n    i := binarySearchInsertion(nums, target)\n    // target не найден, вернуть -1\n    if i == len(nums) || nums[i] != target {\n        return -1\n    }\n    // Найти target и вернуть индекс i\n    return i\n}\n</code></pre> binary_search_edge.swift<pre><code>/* Бинарный поиск самого левого target */\nfunc binarySearchLeftEdge(nums: [Int], target: Int) -&gt; Int {\n    // Эквивалентно поиску точки вставки target\n    let i = binarySearchInsertion(nums: nums, target: target)\n    // target не найден, вернуть -1\n    if i == nums.endIndex || nums[i] != target {\n        return -1\n    }\n    // Найти target и вернуть индекс i\n    return i\n}\n</code></pre> binary_search_edge.js<pre><code>/* Бинарный поиск самого левого target */\nfunction binarySearchLeftEdge(nums, target) {\n    // Эквивалентно поиску точки вставки target\n    const i = binarySearchInsertion(nums, target);\n    // target не найден, вернуть -1\n    if (i === nums.length || nums[i] !== target) {\n        return -1;\n    }\n    // Найти target и вернуть индекс i\n    return i;\n}\n</code></pre> binary_search_edge.ts<pre><code>/* Бинарный поиск самого левого target */\nfunction binarySearchLeftEdge(nums: Array&lt;number&gt;, target: number): number {\n    // Эквивалентно поиску точки вставки target\n    const i = binarySearchInsertion(nums, target);\n    // target не найден, вернуть -1\n    if (i === nums.length || nums[i] !== target) {\n        return -1;\n    }\n    // Найти target и вернуть индекс i\n    return i;\n}\n</code></pre> binary_search_edge.dart<pre><code>/* Бинарный поиск самого левого target */\nint binarySearchLeftEdge(List&lt;int&gt; nums, int target) {\n  // Эквивалентно поиску точки вставки target\n  int i = binarySearchInsertion(nums, target);\n  // target не найден, вернуть -1\n  if (i == nums.length || nums[i] != target) {\n    return -1;\n  }\n  // Найти target и вернуть индекс i\n  return i;\n}\n</code></pre> binary_search_edge.rs<pre><code>/* Бинарный поиск самого левого target */\nfn binary_search_left_edge(nums: &amp;[i32], target: i32) -&gt; i32 {\n    // Эквивалентно поиску точки вставки target\n    let i = binary_search_insertion(nums, target);\n    // target не найден, вернуть -1\n    if i == nums.len() as i32 || nums[i as usize] != target {\n        return -1;\n    }\n    // Найти target и вернуть индекс i\n    i\n}\n</code></pre> binary_search_edge.c<pre><code>/* Бинарный поиск самого левого target */\nint binarySearchLeftEdge(int *nums, int numSize, int target) {\n    // Эквивалентно поиску точки вставки target\n    int i = binarySearchInsertion(nums, numSize, target);\n    // target не найден, вернуть -1\n    if (i == numSize || nums[i] != target) {\n        return -1;\n    }\n    // Найти target и вернуть индекс i\n    return i;\n}\n</code></pre> binary_search_edge.kt<pre><code>/* Бинарный поиск самого левого target */\nfun binarySearchLeftEdge(nums: IntArray, target: Int): Int {\n    // Эквивалентно поиску точки вставки target\n    val i = binarySearchInsertion(nums, target)\n    // target не найден, вернуть -1\n    if (i == nums.size || nums[i] != target) {\n        return -1\n    }\n    // Найти target и вернуть индекс i\n    return i\n}\n</code></pre> binary_search_edge.rb<pre><code>### Бинарный поиск самого левого target ###\ndef binary_search_left_edge(nums, target)\n  # Эквивалентно поиску точки вставки target\n  i = binary_search_insertion(nums, target)\n\n  # target не найден, вернуть -1\n  return -1 if i == nums.length || nums[i] != target\n\n  i # Найти target и вернуть индекс i\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 10. Поиск","10.3 &nbsp; Двоичный поиск границ"],"tags":[]},{"location":"chapter_searching/binary_search_edge/#1032","level":2,"title":"10.3.2   Поиск правой границы","text":"<p>Как тогда найти самый правый <code>target</code> ? Самый прямой способ - изменить код, заменив операцию сужения указателя в случае <code>nums[m] == target</code> . Мы не будем приводить этот код, заинтересованные читатели могут реализовать его самостоятельно.</p> <p>Ниже представлены два более изящных способа.</p>","path":["Глава 10. Поиск","10.3 &nbsp; Двоичный поиск границ"],"tags":[]},{"location":"chapter_searching/binary_search_edge/#1","level":3,"title":"1.   Повторное использование поиска левой границы","text":"<p>На самом деле функцию поиска самого левого элемента можно использовать и для поиска самого правого элемента. Конкретная идея такова: преобразовать поиск самого правого <code>target</code> в поиск самого левого <code>target + 1</code>.</p> <p>Как показано на рисунке 10-7, после завершения поиска указатель \\(i\\) указывает на самый левый <code>target + 1</code> (если он существует), а указатель \\(j\\) указывает на самый правый <code>target</code> , поэтому достаточно вернуть \\(j\\).</p> <p></p> <p> Рисунок 10-7   Преобразование поиска правой границы в поиск левой </p> <p>Обратите внимание: функция возвращает точку вставки \\(i\\) , поэтому из нее нужно вычесть \\(1\\) , чтобы получить \\(j\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_edge.py<pre><code>def binary_search_right_edge(nums: list[int], target: int) -&gt; int:\n    \"\"\"Бинарный поиск самого правого target\"\"\"\n    # Преобразовать задачу в поиск самого левого target + 1\n    i = binary_search_insertion(nums, target + 1)\n    # j указывает на самый правый target, а i — на первый элемент больше target\n    j = i - 1\n    # target не найден, вернуть -1\n    if j == -1 or nums[j] != target:\n        return -1\n    # Найти target и вернуть индекс j\n    return j\n</code></pre> binary_search_edge.cpp<pre><code>/* Бинарный поиск самого правого target */\nint binarySearchRightEdge(vector&lt;int&gt; &amp;nums, int target) {\n    // Преобразовать задачу в поиск самого левого target + 1\n    int i = binarySearchInsertion(nums, target + 1);\n    // j указывает на самый правый target, а i — на первый элемент больше target\n    int j = i - 1;\n    // target не найден, вернуть -1\n    if (j == -1 || nums[j] != target) {\n        return -1;\n    }\n    // Найти target и вернуть индекс j\n    return j;\n}\n</code></pre> binary_search_edge.java<pre><code>/* Бинарный поиск самого правого target */\nint binarySearchRightEdge(int[] nums, int target) {\n    // Преобразовать задачу в поиск самого левого target + 1\n    int i = binary_search_insertion.binarySearchInsertion(nums, target + 1);\n    // j указывает на самый правый target, а i — на первый элемент больше target\n    int j = i - 1;\n    // target не найден, вернуть -1\n    if (j == -1 || nums[j] != target) {\n        return -1;\n    }\n    // Найти target и вернуть индекс j\n    return j;\n}\n</code></pre> binary_search_edge.cs<pre><code>/* Бинарный поиск самого правого target */\nint BinarySearchRightEdge(int[] nums, int target) {\n    // Преобразовать задачу в поиск самого левого target + 1\n    int i = binary_search_insertion.BinarySearchInsertion(nums, target + 1);\n    // j указывает на самый правый target, а i — на первый элемент больше target\n    int j = i - 1;\n    // target не найден, вернуть -1\n    if (j == -1 || nums[j] != target) {\n        return -1;\n    }\n    // Найти target и вернуть индекс j\n    return j;\n}\n</code></pre> binary_search_edge.go<pre><code>/* Бинарный поиск самого правого target */\nfunc binarySearchRightEdge(nums []int, target int) int {\n    // Преобразовать задачу в поиск самого левого target + 1\n    i := binarySearchInsertion(nums, target+1)\n    // j указывает на самый правый target, а i — на первый элемент больше target\n    j := i - 1\n    // target не найден, вернуть -1\n    if j == -1 || nums[j] != target {\n        return -1\n    }\n    // Найти target и вернуть индекс j\n    return j\n}\n</code></pre> binary_search_edge.swift<pre><code>/* Бинарный поиск самого правого target */\nfunc binarySearchRightEdge(nums: [Int], target: Int) -&gt; Int {\n    // Преобразовать задачу в поиск самого левого target + 1\n    let i = binarySearchInsertion(nums: nums, target: target + 1)\n    // j указывает на самый правый target, а i — на первый элемент больше target\n    let j = i - 1\n    // target не найден, вернуть -1\n    if j == -1 || nums[j] != target {\n        return -1\n    }\n    // Найти target и вернуть индекс j\n    return j\n}\n</code></pre> binary_search_edge.js<pre><code>/* Бинарный поиск самого правого target */\nfunction binarySearchRightEdge(nums, target) {\n    // Преобразовать задачу в поиск самого левого target + 1\n    const i = binarySearchInsertion(nums, target + 1);\n    // j указывает на самый правый target, а i — на первый элемент больше target\n    const j = i - 1;\n    // target не найден, вернуть -1\n    if (j === -1 || nums[j] !== target) {\n        return -1;\n    }\n    // Найти target и вернуть индекс j\n    return j;\n}\n</code></pre> binary_search_edge.ts<pre><code>/* Бинарный поиск самого правого target */\nfunction binarySearchRightEdge(nums: Array&lt;number&gt;, target: number): number {\n    // Преобразовать задачу в поиск самого левого target + 1\n    const i = binarySearchInsertion(nums, target + 1);\n    // j указывает на самый правый target, а i — на первый элемент больше target\n    const j = i - 1;\n    // target не найден, вернуть -1\n    if (j === -1 || nums[j] !== target) {\n        return -1;\n    }\n    // Найти target и вернуть индекс j\n    return j;\n}\n</code></pre> binary_search_edge.dart<pre><code>/* Бинарный поиск самого правого target */\nint binarySearchRightEdge(List&lt;int&gt; nums, int target) {\n  // Преобразовать задачу в поиск самого левого target + 1\n  int i = binarySearchInsertion(nums, target + 1);\n  // j указывает на самый правый target, а i — на первый элемент больше target\n  int j = i - 1;\n  // target не найден, вернуть -1\n  if (j == -1 || nums[j] != target) {\n    return -1;\n  }\n  // Найти target и вернуть индекс j\n  return j;\n}\n</code></pre> binary_search_edge.rs<pre><code>/* Бинарный поиск самого правого target */\nfn binary_search_right_edge(nums: &amp;[i32], target: i32) -&gt; i32 {\n    // Преобразовать задачу в поиск самого левого target + 1\n    let i = binary_search_insertion(nums, target + 1);\n    // j указывает на самый правый target, а i — на первый элемент больше target\n    let j = i - 1;\n    // target не найден, вернуть -1\n    if j == -1 || nums[j as usize] != target {\n        return -1;\n    }\n    // Найти target и вернуть индекс j\n    j\n}\n</code></pre> binary_search_edge.c<pre><code>/* Бинарный поиск самого правого target */\nint binarySearchRightEdge(int *nums, int numSize, int target) {\n    // Преобразовать задачу в поиск самого левого target + 1\n    int i = binarySearchInsertion(nums, numSize, target + 1);\n    // j указывает на самый правый target, а i — на первый элемент больше target\n    int j = i - 1;\n    // target не найден, вернуть -1\n    if (j == -1 || nums[j] != target) {\n        return -1;\n    }\n    // Найти target и вернуть индекс j\n    return j;\n}\n</code></pre> binary_search_edge.kt<pre><code>/* Бинарный поиск самого правого target */\nfun binarySearchRightEdge(nums: IntArray, target: Int): Int {\n    // Преобразовать задачу в поиск самого левого target + 1\n    val i = binarySearchInsertion(nums, target + 1)\n    // j указывает на самый правый target, а i — на первый элемент больше target\n    val j = i - 1\n    // target не найден, вернуть -1\n    if (j == -1 || nums[j] != target) {\n        return -1\n    }\n    // Найти target и вернуть индекс j\n    return j\n}\n</code></pre> binary_search_edge.rb<pre><code>### Бинарный поиск самого правого target ###\ndef binary_search_right_edge(nums, target)\n  # Преобразовать задачу в поиск самого левого target + 1\n  i = binary_search_insertion(nums, target + 1)\n\n  # j указывает на самый правый target, а i — на первый элемент больше target\n  j = i - 1\n\n  # target не найден, вернуть -1\n  return -1 if j == -1 || nums[j] != target\n\n  j # Найти target и вернуть индекс j\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 10. Поиск","10.3 &nbsp; Двоичный поиск границ"],"tags":[]},{"location":"chapter_searching/binary_search_edge/#2","level":3,"title":"2.   Преобразование в поиск элемента","text":"<p>Мы знаем, что если массив не содержит <code>target</code> , то в конце поиска указатели \\(i\\) и \\(j\\) будут указывать соответственно на первый элемент, больший <code>target</code> , и на первый элемент, меньший <code>target</code> .</p> <p>Следовательно, как показано на рисунке 10-8, для поиска левой и правой границы можно сконструировать элемент, которого нет в массиве.</p> <ul> <li>Поиск самого левого <code>target</code> : можно преобразовать в поиск <code>target - 0.5</code> и вернуть указатель \\(i\\) .</li> <li>Поиск самого правого <code>target</code> : можно преобразовать в поиск <code>target + 0.5</code> и вернуть указатель \\(j\\) .</li> </ul> <p></p> <p> Рисунок 10-8   Преобразование поиска границ в поиск элемента </p> <p>Код здесь опущен, но стоит обратить внимание на два момента.</p> <ul> <li>По условию массив не содержит дробных чисел, поэтому нам не нужно беспокоиться о том, как обрабатывать случай равенства другим элементам массива.</li> <li>Поскольку этот метод вводит дробные числа, переменную <code>target</code> в функции нужно изменить на тип с плавающей запятой (в Python менять ничего не требуется).</li> </ul>","path":["Глава 10. Поиск","10.3 &nbsp; Двоичный поиск границ"],"tags":[]},{"location":"chapter_searching/binary_search_insertion/","level":1,"title":"10.2   Точка вставки при двоичном поиске","text":"<p>Двоичный поиск можно использовать не только для поиска целевого элемента, но и для решения многих вариаций задачи, например для поиска позиции вставки целевого элемента.</p>","path":["Глава 10. Поиск","10.2 &nbsp; Точка вставки при двоичном поиске"],"tags":[]},{"location":"chapter_searching/binary_search_insertion/#1021","level":2,"title":"10.2.1   Случай без повторяющихся элементов","text":"<p>Question</p> <p>Дан упорядоченный массив <code>nums</code> длины \\(n\\) и элемент <code>target</code> , причем в массиве нет повторяющихся элементов. Нужно вставить <code>target</code> в массив <code>nums</code> , сохранив порядок. Если элемент <code>target</code> уже присутствует в массиве, вставьте его слева от него. Верните индекс, который будет иметь <code>target</code> после вставки. Пример показан на рисунке 10-4.</p> <p></p> <p> Рисунок 10-4   Пример данных для точки вставки </p> <p>Если мы хотим переиспользовать код двоичного поиска из предыдущего раздела, нужно ответить на два вопроса.</p> <p>Вопрос 1: если массив содержит <code>target</code> , будет ли индекс вставки совпадать с индексом этого элемента?</p> <p>По условию <code>target</code> нужно вставить слева от равного элемента, а это означает, что новый <code>target</code> занимает место старого <code>target</code> . Иначе говоря, если массив содержит <code>target</code> , то индекс вставки совпадает с индексом этого <code>target</code>.</p> <p>Вопрос 2: если массив не содержит <code>target</code> , индекс какого элемента будет точкой вставки?</p> <p>Рассмотрим процесс двоичного поиска подробнее: когда <code>nums[m] &lt; target</code> , указатель \\(i\\) сдвигается, а значит, приближается к элементу, который больше либо равен <code>target</code> . Аналогично указатель \\(j\\) все время приближается к элементу, который меньше либо равен <code>target</code> .</p> <p>Следовательно, после завершения двоичного поиска обязательно выполняется следующее: указатель \\(i\\) указывает на первый элемент, больший <code>target</code> , а указатель \\(j\\) указывает на первый элемент, меньший <code>target</code> . Нетрудно сделать вывод, что если массив не содержит <code>target</code> , то индекс вставки равен \\(i\\) . Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_insertion.py<pre><code>def binary_search_insertion_simple(nums: list[int], target: int) -&gt; int:\n    \"\"\"Бинарный поиск точки вставки (без повторяющихся элементов)\"\"\"\n    i, j = 0, len(nums) - 1  # Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while i &lt;= j:\n        m = (i + j) // 2  # Вычислить индекс середины m\n        if nums[m] &lt; target:\n            i = m + 1  # target находится в интервале [m+1, j]\n        elif nums[m] &gt; target:\n            j = m - 1  # target находится в интервале [i, m-1]\n        else:\n            return m  # Найти target и вернуть точку вставки m\n    # target не найден, вернуть точку вставки i\n    return i\n</code></pre> binary_search_insertion.cpp<pre><code>/* Бинарный поиск точки вставки (без повторяющихся элементов) */\nint binarySearchInsertionSimple(vector&lt;int&gt; &amp;nums, int target) {\n    int i = 0, j = nums.size() - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target) {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            return m; // Найти target и вернуть точку вставки m\n        }\n    }\n    // target не найден, вернуть точку вставки i\n    return i;\n}\n</code></pre> binary_search_insertion.java<pre><code>/* Бинарный поиск точки вставки (без повторяющихся элементов) */\nint binarySearchInsertionSimple(int[] nums, int target) {\n    int i = 0, j = nums.length - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target) {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            return m; // Найти target и вернуть точку вставки m\n        }\n    }\n    // target не найден, вернуть точку вставки i\n    return i;\n}\n</code></pre> binary_search_insertion.cs<pre><code>/* Бинарный поиск точки вставки (без повторяющихся элементов) */\nint BinarySearchInsertionSimple(int[] nums, int target) {\n    int i = 0, j = nums.Length - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target) {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            return m; // Найти target и вернуть точку вставки m\n        }\n    }\n    // target не найден, вернуть точку вставки i\n    return i;\n}\n</code></pre> binary_search_insertion.go<pre><code>/* Бинарный поиск точки вставки (без повторяющихся элементов) */\nfunc binarySearchInsertionSimple(nums []int, target int) int {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    i, j := 0, len(nums)-1\n    for i &lt;= j {\n        // Вычислить индекс середины m\n        m := i + (j-i)/2\n        if nums[m] &lt; target {\n            // target находится в интервале [m+1, j]\n            i = m + 1\n        } else if nums[m] &gt; target {\n            // target находится в интервале [i, m-1]\n            j = m - 1\n        } else {\n            // Найти target и вернуть точку вставки m\n            return m\n        }\n    }\n    // target не найден, вернуть точку вставки i\n    return i\n}\n</code></pre> binary_search_insertion.swift<pre><code>/* Бинарный поиск точки вставки (без повторяющихся элементов) */\nfunc binarySearchInsertionSimple(nums: [Int], target: Int) -&gt; Int {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    var i = nums.startIndex\n    var j = nums.endIndex - 1\n    while i &lt;= j {\n        let m = i + (j - i) / 2 // Вычислить индекс середины m\n        if nums[m] &lt; target {\n            i = m + 1 // target находится в интервале [m+1, j]\n        } else if nums[m] &gt; target {\n            j = m - 1 // target находится в интервале [i, m-1]\n        } else {\n            return m // Найти target и вернуть точку вставки m\n        }\n    }\n    // target не найден, вернуть точку вставки i\n    return i\n}\n</code></pre> binary_search_insertion.js<pre><code>/* Бинарный поиск точки вставки (без повторяющихся элементов) */\nfunction binarySearchInsertionSimple(nums, target) {\n    let i = 0,\n        j = nums.length - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        const m = Math.floor(i + (j - i) / 2); // Вычислить индекс середины m, используя Math.floor() для округления вниз\n        if (nums[m] &lt; target) {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            return m; // Найти target и вернуть точку вставки m\n        }\n    }\n    // target не найден, вернуть точку вставки i\n    return i;\n}\n</code></pre> binary_search_insertion.ts<pre><code>/* Бинарный поиск точки вставки (без повторяющихся элементов) */\nfunction binarySearchInsertionSimple(\n    nums: Array&lt;number&gt;,\n    target: number\n): number {\n    let i = 0,\n        j = nums.length - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        const m = Math.floor(i + (j - i) / 2); // Вычислить индекс середины m, используя Math.floor() для округления вниз\n        if (nums[m] &lt; target) {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            return m; // Найти target и вернуть точку вставки m\n        }\n    }\n    // target не найден, вернуть точку вставки i\n    return i;\n}\n</code></pre> binary_search_insertion.dart<pre><code>/* Бинарный поиск точки вставки (без повторяющихся элементов) */\nint binarySearchInsertionSimple(List&lt;int&gt; nums, int target) {\n  int i = 0, j = nums.length - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n  while (i &lt;= j) {\n    int m = i + (j - i) ~/ 2; // Вычислить индекс середины m\n    if (nums[m] &lt; target) {\n      i = m + 1; // target находится в интервале [m+1, j]\n    } else if (nums[m] &gt; target) {\n      j = m - 1; // target находится в интервале [i, m-1]\n    } else {\n      return m; // Найти target и вернуть точку вставки m\n    }\n  }\n  // target не найден, вернуть точку вставки i\n  return i;\n}\n</code></pre> binary_search_insertion.rs<pre><code>/* Бинарный поиск точки вставки (без повторяющихся элементов) */\nfn binary_search_insertion_simple(nums: &amp;[i32], target: i32) -&gt; i32 {\n    let (mut i, mut j) = (0, nums.len() as i32 - 1); // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while i &lt;= j {\n        let m = i + (j - i) / 2; // Вычислить индекс середины m\n        if nums[m as usize] &lt; target {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if nums[m as usize] &gt; target {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            return m;\n        }\n    }\n    // target не найден, вернуть точку вставки i\n    i\n}\n</code></pre> binary_search_insertion.c<pre><code>/* Бинарный поиск точки вставки (без повторяющихся элементов) */\nint binarySearchInsertionSimple(int *nums, int numSize, int target) {\n    int i = 0, j = numSize - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target) {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            return m; // Найти target и вернуть точку вставки m\n        }\n    }\n    // target не найден, вернуть точку вставки i\n    return i;\n}\n</code></pre> binary_search_insertion.kt<pre><code>/* Бинарный поиск точки вставки (без повторяющихся элементов) */\nfun binarySearchInsertionSimple(nums: IntArray, target: Int): Int {\n    var i = 0\n    var j = nums.size - 1 // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        val m = i + (j - i) / 2 // Вычислить индекс середины m\n        if (nums[m] &lt; target) {\n            i = m + 1 // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1 // target находится в интервале [i, m-1]\n        } else {\n            return m // Найти target и вернуть точку вставки m\n        }\n    }\n    // target не найден, вернуть точку вставки i\n    return i\n}\n</code></pre> binary_search_insertion.rb<pre><code>### Бинарный поиск точки вставки (без повторяющихся элементов) ###\ndef binary_search_insertion_simple(nums, target)\n  # Инициализировать двусторонне замкнутый интервал [0, n-1]\n  i, j = 0, nums.length - 1\n\n  while i &lt;= j\n    # Вычислить индекс середины m\n    m = (i + j) / 2\n\n    if nums[m] &lt; target\n      i = m + 1 # target находится в интервале [m+1, j]\n    elsif nums[m] &gt; target\n      j = m - 1 # target находится в интервале [i, m-1]\n    else\n      return m  # Найти target и вернуть точку вставки m\n    end\n  end\n\n  i # target не найден, вернуть точку вставки i\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 10. Поиск","10.2 &nbsp; Точка вставки при двоичном поиске"],"tags":[]},{"location":"chapter_searching/binary_search_insertion/#1022","level":2,"title":"10.2.2   Случай с повторяющимися элементами","text":"<p>Question</p> <p>В предыдущей задаче теперь допускается, что массив может содержать повторяющиеся элементы, а все остальные условия остаются без изменений.</p> <p>Если в массиве есть несколько элементов <code>target</code> , то обычный двоичный поиск сможет вернуть индекс только одного из них, но не позволит определить, сколько элементов <code>target</code> находится слева и справа от него.</p> <p>По условию целевой элемент нужно вставить в самую левую позицию, поэтому нам нужно найти индекс самого левого <code>target</code> в массиве. На первом этапе можно рассмотреть решение, показанное на рисунке 10-5.</p> <ol> <li>Выполнить двоичный поиск и получить индекс любого элемента <code>target</code> , обозначив его как \\(k\\) .</li> <li>Начиная с индекса \\(k\\) , линейно двигаться влево и вернуть результат, когда будет найден самый левый <code>target</code> .</li> </ol> <p></p> <p> Рисунок 10-5   Линейный поиск точки вставки среди повторяющихся элементов </p> <p>Этот метод применим на практике, однако в нем есть линейный поиск, поэтому его временная сложность равна \\(O(n)\\) . Когда в массиве имеется много повторяющихся <code>target</code> , такой подход работает неэффективно.</p> <p>Теперь рассмотрим расширение кода двоичного поиска. Как показано на рисунке 10-6, общий процесс остается прежним: на каждом шаге мы сначала вычисляем индекс середины \\(m\\) , а затем сравниваем <code>target</code> и <code>nums[m]</code> , после чего возможны следующие случаи.</p> <ul> <li>Когда <code>nums[m] &lt; target</code> или <code>nums[m] &gt; target</code> , это означает, что <code>target</code> еще не найден, поэтому используется стандартная операция сужения интервала в двоичном поиске, благодаря чему указатели \\(i\\) и \\(j\\) приближаются к <code>target</code>.</li> <li>Когда <code>nums[m] == target</code> , это означает, что элементы меньше <code>target</code> находятся в интервале \\([i, m - 1]\\) , поэтому мы используем \\(j = m - 1\\) для сужения интервала, тем самым приближая указатель \\(j\\) к элементам, меньшим <code>target</code>.</li> </ul> <p>После завершения цикла указатель \\(i\\) будет указывать на самый левый <code>target</code> , а указатель \\(j\\) - на первый элемент, меньший <code>target</code> , поэтому индекс \\(i\\) и является точкой вставки.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 10-6   Шаги поиска точки вставки для повторяющихся элементов </p> <p>Если посмотреть на следующий код, то видно, что операции в ветвях <code>nums[m] &gt; target</code> и <code>nums[m] == target</code> совпадают, поэтому эти две ветви можно объединить.</p> <p>Даже в этом случае можно оставить условия развернутыми, потому что так логика выглядит более ясной и код легче читать.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_insertion.py<pre><code>def binary_search_insertion(nums: list[int], target: int) -&gt; int:\n    \"\"\"Бинарный поиск точки вставки (с повторяющимися элементами)\"\"\"\n    i, j = 0, len(nums) - 1  # Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while i &lt;= j:\n        m = (i + j) // 2  # Вычислить индекс середины m\n        if nums[m] &lt; target:\n            i = m + 1  # target находится в интервале [m+1, j]\n        elif nums[m] &gt; target:\n            j = m - 1  # target находится в интервале [i, m-1]\n        else:\n            j = m - 1  # Первый элемент меньше target находится в интервале [i, m-1]\n    # Вернуть точку вставки i\n    return i\n</code></pre> binary_search_insertion.cpp<pre><code>/* Бинарный поиск точки вставки (с повторяющимися элементами) */\nint binarySearchInsertion(vector&lt;int&gt; &amp;nums, int target) {\n    int i = 0, j = nums.size() - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target) {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            j = m - 1; // Первый элемент меньше target находится в интервале [i, m-1]\n        }\n    }\n    // Вернуть точку вставки i\n    return i;\n}\n</code></pre> binary_search_insertion.java<pre><code>/* Бинарный поиск точки вставки (с повторяющимися элементами) */\nint binarySearchInsertion(int[] nums, int target) {\n    int i = 0, j = nums.length - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target) {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            j = m - 1; // Первый элемент меньше target находится в интервале [i, m-1]\n        }\n    }\n    // Вернуть точку вставки i\n    return i;\n}\n</code></pre> binary_search_insertion.cs<pre><code>/* Бинарный поиск точки вставки (с повторяющимися элементами) */\nint BinarySearchInsertion(int[] nums, int target) {\n    int i = 0, j = nums.Length - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target) {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            j = m - 1; // Первый элемент меньше target находится в интервале [i, m-1]\n        }\n    }\n    // Вернуть точку вставки i\n    return i;\n}\n</code></pre> binary_search_insertion.go<pre><code>/* Бинарный поиск точки вставки (с повторяющимися элементами) */\nfunc binarySearchInsertion(nums []int, target int) int {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    i, j := 0, len(nums)-1\n    for i &lt;= j {\n        // Вычислить индекс середины m\n        m := i + (j-i)/2\n        if nums[m] &lt; target {\n            // target находится в интервале [m+1, j]\n            i = m + 1\n        } else if nums[m] &gt; target {\n            // target находится в интервале [i, m-1]\n            j = m - 1\n        } else {\n            // Первый элемент меньше target находится в интервале [i, m-1]\n            j = m - 1\n        }\n    }\n    // Вернуть точку вставки i\n    return i\n}\n</code></pre> binary_search_insertion.swift<pre><code>/* Бинарный поиск точки вставки (с повторяющимися элементами) */\nfunc binarySearchInsertion(nums: [Int], target: Int) -&gt; Int {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    var i = nums.startIndex\n    var j = nums.endIndex - 1\n    while i &lt;= j {\n        let m = i + (j - i) / 2 // Вычислить индекс середины m\n        if nums[m] &lt; target {\n            i = m + 1 // target находится в интервале [m+1, j]\n        } else if nums[m] &gt; target {\n            j = m - 1 // target находится в интервале [i, m-1]\n        } else {\n            j = m - 1 // Первый элемент меньше target находится в интервале [i, m-1]\n        }\n    }\n    // Вернуть точку вставки i\n    return i\n}\n</code></pre> binary_search_insertion.js<pre><code>/* Бинарный поиск точки вставки (с повторяющимися элементами) */\nfunction binarySearchInsertion(nums, target) {\n    let i = 0,\n        j = nums.length - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        const m = Math.floor(i + (j - i) / 2); // Вычислить индекс середины m, используя Math.floor() для округления вниз\n        if (nums[m] &lt; target) {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            j = m - 1; // Первый элемент меньше target находится в интервале [i, m-1]\n        }\n    }\n    // Вернуть точку вставки i\n    return i;\n}\n</code></pre> binary_search_insertion.ts<pre><code>/* Бинарный поиск точки вставки (с повторяющимися элементами) */\nfunction binarySearchInsertion(nums: Array&lt;number&gt;, target: number): number {\n    let i = 0,\n        j = nums.length - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        const m = Math.floor(i + (j - i) / 2); // Вычислить индекс середины m, используя Math.floor() для округления вниз\n        if (nums[m] &lt; target) {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            j = m - 1; // Первый элемент меньше target находится в интервале [i, m-1]\n        }\n    }\n    // Вернуть точку вставки i\n    return i;\n}\n</code></pre> binary_search_insertion.dart<pre><code>/* Бинарный поиск точки вставки (с повторяющимися элементами) */\nint binarySearchInsertion(List&lt;int&gt; nums, int target) {\n  int i = 0, j = nums.length - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n  while (i &lt;= j) {\n    int m = i + (j - i) ~/ 2; // Вычислить индекс середины m\n    if (nums[m] &lt; target) {\n      i = m + 1; // target находится в интервале [m+1, j]\n    } else if (nums[m] &gt; target) {\n      j = m - 1; // target находится в интервале [i, m-1]\n    } else {\n      j = m - 1; // Первый элемент меньше target находится в интервале [i, m-1]\n    }\n  }\n  // Вернуть точку вставки i\n  return i;\n}\n</code></pre> binary_search_insertion.rs<pre><code>/* Бинарный поиск точки вставки (с повторяющимися элементами) */\npub fn binary_search_insertion(nums: &amp;[i32], target: i32) -&gt; i32 {\n    let (mut i, mut j) = (0, nums.len() as i32 - 1); // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while i &lt;= j {\n        let m = i + (j - i) / 2; // Вычислить индекс середины m\n        if nums[m as usize] &lt; target {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if nums[m as usize] &gt; target {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            j = m - 1; // Первый элемент меньше target находится в интервале [i, m-1]\n        }\n    }\n    // Вернуть точку вставки i\n    i\n}\n</code></pre> binary_search_insertion.c<pre><code>/* Бинарный поиск точки вставки (с повторяющимися элементами) */\nint binarySearchInsertion(int *nums, int numSize, int target) {\n    int i = 0, j = numSize - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target) {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            j = m - 1; // Первый элемент меньше target находится в интервале [i, m-1]\n        }\n    }\n    // Вернуть точку вставки i\n    return i;\n}\n</code></pre> binary_search_insertion.kt<pre><code>/* Бинарный поиск точки вставки (с повторяющимися элементами) */\nfun binarySearchInsertion(nums: IntArray, target: Int): Int {\n    var i = 0\n    var j = nums.size - 1 // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        val m = i + (j - i) / 2 // Вычислить индекс середины m\n        if (nums[m] &lt; target) {\n            i = m + 1 // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1 // target находится в интервале [i, m-1]\n        } else {\n            j = m - 1 // Первый элемент меньше target находится в интервале [i, m-1]\n        }\n    }\n    // Вернуть точку вставки i\n    return i\n}\n</code></pre> binary_search_insertion.rb<pre><code>### Бинарный поиск точки вставки (с повторяющимися элементами) ###\ndef binary_search_insertion(nums, target)\n  # Инициализировать двусторонне замкнутый интервал [0, n-1]\n  i, j = 0, nums.length - 1\n\n  while i &lt;= j\n    # Вычислить индекс середины m\n    m = (i + j) / 2\n\n    if nums[m] &lt; target\n      i = m + 1 # target находится в интервале [m+1, j]\n    elsif nums[m] &gt; target\n      j = m - 1 # target находится в интервале [i, m-1]\n    else\n      j = m - 1 # Первый элемент меньше target находится в интервале [i, m-1]\n    end\n  end\n\n  i # Вернуть точку вставки i\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Tip</p> <p>Код в этом разделе записан в стиле \"двойного замкнутого интервала\". При желании можно самостоятельно реализовать вариант \"слева закрыт, справа открыт\".</p> <p>Если смотреть в целом, суть двоичного поиска сводится к тому, что для указателей \\(i\\) и \\(j\\) заранее задаются цели поиска; целью может быть конкретный элемент (например, <code>target</code> ), а может быть и диапазон элементов (например, элементы, меньшие <code>target</code> ).</p> <p>В ходе непрерывного двоичного деления указатели \\(i\\) и \\(j\\) постепенно приближаются к заранее заданной цели. В конце они либо успешно находят ответ, либо останавливаются после выхода за границы.</p>","path":["Глава 10. Поиск","10.2 &nbsp; Точка вставки при двоичном поиске"],"tags":[]},{"location":"chapter_searching/replace_linear_by_hashing/","level":1,"title":"10.4   Стратегии хеш-оптимизации","text":"<p>В алгоритмических задачах мы часто заменяем линейный поиск на хеш-поиск, чтобы уменьшить временную сложность алгоритма. Разберем одну задачу, чтобы лучше понять этот прием.</p> <p>Question</p> <p>Дан массив целых чисел <code>nums</code> и целевой элемент <code>target</code> . Найдите в массиве два элемента, сумма которых равна <code>target</code> , и верните их индексы. Подойдет любой корректный ответ.</p>","path":["Глава 10. Поиск","10.4 &nbsp; Стратегии хеш-оптимизации"],"tags":[]},{"location":"chapter_searching/replace_linear_by_hashing/#1041","level":2,"title":"10.4.1   Линейный поиск: обмен времени на пространство","text":"<p>Рассмотрим прямой перебор всех возможных комбинаций. Как показано на рисунке 10-9, мы запускаем два вложенных цикла и на каждом шаге проверяем, равна ли сумма двух целых чисел <code>target</code> ; если да, то возвращаем их индексы.</p> <p></p> <p> Рисунок 10-9   Линейный поиск для задачи о двух суммах </p> <p>Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby two_sum.py<pre><code>def two_sum_brute_force(nums: list[int], target: int) -&gt; list[int]:\n    \"\"\"Метод 1: полный перебор\"\"\"\n    # Два вложенных цикла, временная сложность O(n^2)\n    for i in range(len(nums) - 1):\n        for j in range(i + 1, len(nums)):\n            if nums[i] + nums[j] == target:\n                return [i, j]\n    return []\n</code></pre> two_sum.cpp<pre><code>/* Метод 1: полный перебор */\nvector&lt;int&gt; twoSumBruteForce(vector&lt;int&gt; &amp;nums, int target) {\n    int size = nums.size();\n    // Два вложенных цикла, временная сложность O(n^2)\n    for (int i = 0; i &lt; size - 1; i++) {\n        for (int j = i + 1; j &lt; size; j++) {\n            if (nums[i] + nums[j] == target)\n                return {i, j};\n        }\n    }\n    return {};\n}\n</code></pre> two_sum.java<pre><code>/* Метод 1: полный перебор */\nint[] twoSumBruteForce(int[] nums, int target) {\n    int size = nums.length;\n    // Два вложенных цикла, временная сложность O(n^2)\n    for (int i = 0; i &lt; size - 1; i++) {\n        for (int j = i + 1; j &lt; size; j++) {\n            if (nums[i] + nums[j] == target)\n                return new int[] { i, j };\n        }\n    }\n    return new int[0];\n}\n</code></pre> two_sum.cs<pre><code>/* Метод 1: полный перебор */\nint[] TwoSumBruteForce(int[] nums, int target) {\n    int size = nums.Length;\n    // Два вложенных цикла, временная сложность O(n^2)\n    for (int i = 0; i &lt; size - 1; i++) {\n        for (int j = i + 1; j &lt; size; j++) {\n            if (nums[i] + nums[j] == target)\n                return [i, j];\n        }\n    }\n    return [];\n}\n</code></pre> two_sum.go<pre><code>/* Метод 1: полный перебор */\nfunc twoSumBruteForce(nums []int, target int) []int {\n    size := len(nums)\n    // Два вложенных цикла, временная сложность O(n^2)\n    for i := 0; i &lt; size-1; i++ {\n        for j := i + 1; j &lt; size; j++ {\n            if nums[i]+nums[j] == target {\n                return []int{i, j}\n            }\n        }\n    }\n    return nil\n}\n</code></pre> two_sum.swift<pre><code>/* Метод 1: полный перебор */\nfunc twoSumBruteForce(nums: [Int], target: Int) -&gt; [Int] {\n    // Два вложенных цикла, временная сложность O(n^2)\n    for i in nums.indices.dropLast() {\n        for j in nums.indices.dropFirst(i + 1) {\n            if nums[i] + nums[j] == target {\n                return [i, j]\n            }\n        }\n    }\n    return [0]\n}\n</code></pre> two_sum.js<pre><code>/* Метод 1: полный перебор */\nfunction twoSumBruteForce(nums, target) {\n    const n = nums.length;\n    // Два вложенных цикла, временная сложность O(n^2)\n    for (let i = 0; i &lt; n; i++) {\n        for (let j = i + 1; j &lt; n; j++) {\n            if (nums[i] + nums[j] === target) {\n                return [i, j];\n            }\n        }\n    }\n    return [];\n}\n</code></pre> two_sum.ts<pre><code>/* Метод 1: полный перебор */\nfunction twoSumBruteForce(nums: number[], target: number): number[] {\n    const n = nums.length;\n    // Два вложенных цикла, временная сложность O(n^2)\n    for (let i = 0; i &lt; n; i++) {\n        for (let j = i + 1; j &lt; n; j++) {\n            if (nums[i] + nums[j] === target) {\n                return [i, j];\n            }\n        }\n    }\n    return [];\n}\n</code></pre> two_sum.dart<pre><code>/* Способ 1: полный перебор */\nList&lt;int&gt; twoSumBruteForce(List&lt;int&gt; nums, int target) {\n  int size = nums.length;\n  // Два вложенных цикла, временная сложность O(n^2)\n  for (var i = 0; i &lt; size - 1; i++) {\n    for (var j = i + 1; j &lt; size; j++) {\n      if (nums[i] + nums[j] == target) return [i, j];\n    }\n  }\n  return [0];\n}\n</code></pre> two_sum.rs<pre><code>/* Метод 1: полный перебор */\npub fn two_sum_brute_force(nums: &amp;Vec&lt;i32&gt;, target: i32) -&gt; Option&lt;Vec&lt;i32&gt;&gt; {\n    let size = nums.len();\n    // Два вложенных цикла, временная сложность O(n^2)\n    for i in 0..size - 1 {\n        for j in i + 1..size {\n            if nums[i] + nums[j] == target {\n                return Some(vec![i as i32, j as i32]);\n            }\n        }\n    }\n    None\n}\n</code></pre> two_sum.c<pre><code>/* Метод 1: полный перебор */\nint *twoSumBruteForce(int *nums, int numsSize, int target, int *returnSize) {\n    for (int i = 0; i &lt; numsSize; ++i) {\n        for (int j = i + 1; j &lt; numsSize; ++j) {\n            if (nums[i] + nums[j] == target) {\n                int *res = malloc(sizeof(int) * 2);\n                res[0] = i, res[1] = j;\n                *returnSize = 2;\n                return res;\n            }\n        }\n    }\n    *returnSize = 0;\n    return NULL;\n}\n</code></pre> two_sum.kt<pre><code>/* Метод 1: полный перебор */\nfun twoSumBruteForce(nums: IntArray, target: Int): IntArray {\n    val size = nums.size\n    // Два вложенных цикла, временная сложность O(n^2)\n    for (i in 0..&lt;size - 1) {\n        for (j in i + 1..&lt;size) {\n            if (nums[i] + nums[j] == target) return intArrayOf(i, j)\n        }\n    }\n    return IntArray(0)\n}\n</code></pre> two_sum.rb<pre><code>### Метод 1: полный перебор ###\ndef two_sum_brute_force(nums, target)\n  # Два вложенных цикла, временная сложность O(n^2)\n  for i in 0...(nums.length - 1)\n    for j in (i + 1)...nums.length\n      return [i, j] if nums[i] + nums[j] == target\n    end\n  end\n\n  []\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Временная сложность этого метода равна \\(O(n^2)\\) , а пространственная сложность равна \\(O(1)\\) , поэтому на больших объемах данных он очень медленный.</p>","path":["Глава 10. Поиск","10.4 &nbsp; Стратегии хеш-оптимизации"],"tags":[]},{"location":"chapter_searching/replace_linear_by_hashing/#1042-","level":2,"title":"10.4.2   Хеш-поиск: обмен пространства на время","text":"<p>Рассмотрим вариант с использованием хеш-таблицы, где ключами и значениями будут элементы массива и их индексы. При циклическом обходе массива на каждом шаге выполняются действия, показанные на рисунке 10-10.</p> <ol> <li>Проверить, находится ли число <code>target - nums[i]</code> в хеш-таблице; если да, то сразу вернуть индексы этих двух элементов.</li> <li>Добавить в хеш-таблицу пару из ключа <code>nums[i]</code> и индекса <code>i</code> .</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt; <p></p> <p></p> <p></p> <p> Рисунок 10-10   Вспомогательная хеш-таблица для задачи о двух суммах </p> <p>Код реализации показан ниже, и для него достаточно одного цикла:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby two_sum.py<pre><code>def two_sum_hash_table(nums: list[int], target: int) -&gt; list[int]:\n    \"\"\"Метод 2: вспомогательная хеш-таблица\"\"\"\n    # Вспомогательная хеш-таблица, пространственная сложность O(n)\n    dic = {}\n    # Один цикл, временная сложность O(n)\n    for i in range(len(nums)):\n        if target - nums[i] in dic:\n            return [dic[target - nums[i]], i]\n        dic[nums[i]] = i\n    return []\n</code></pre> two_sum.cpp<pre><code>/* Метод 2: вспомогательная хеш-таблица */\nvector&lt;int&gt; twoSumHashTable(vector&lt;int&gt; &amp;nums, int target) {\n    int size = nums.size();\n    // Вспомогательная хеш-таблица, пространственная сложность O(n)\n    unordered_map&lt;int, int&gt; dic;\n    // Один цикл, временная сложность O(n)\n    for (int i = 0; i &lt; size; i++) {\n        if (dic.find(target - nums[i]) != dic.end()) {\n            return {dic[target - nums[i]], i};\n        }\n        dic.emplace(nums[i], i);\n    }\n    return {};\n}\n</code></pre> two_sum.java<pre><code>/* Метод 2: вспомогательная хеш-таблица */\nint[] twoSumHashTable(int[] nums, int target) {\n    int size = nums.length;\n    // Вспомогательная хеш-таблица, пространственная сложность O(n)\n    Map&lt;Integer, Integer&gt; dic = new HashMap&lt;&gt;();\n    // Один цикл, временная сложность O(n)\n    for (int i = 0; i &lt; size; i++) {\n        if (dic.containsKey(target - nums[i])) {\n            return new int[] { dic.get(target - nums[i]), i };\n        }\n        dic.put(nums[i], i);\n    }\n    return new int[0];\n}\n</code></pre> two_sum.cs<pre><code>/* Метод 2: вспомогательная хеш-таблица */\nint[] TwoSumHashTable(int[] nums, int target) {\n    int size = nums.Length;\n    // Вспомогательная хеш-таблица, пространственная сложность O(n)\n    Dictionary&lt;int, int&gt; dic = [];\n    // Один цикл, временная сложность O(n)\n    for (int i = 0; i &lt; size; i++) {\n        if (dic.ContainsKey(target - nums[i])) {\n            return [dic[target - nums[i]], i];\n        }\n        dic.Add(nums[i], i);\n    }\n    return [];\n}\n</code></pre> two_sum.go<pre><code>/* Метод 2: вспомогательная хеш-таблица */\nfunc twoSumHashTable(nums []int, target int) []int {\n    // Вспомогательная хеш-таблица, пространственная сложность O(n)\n    hashTable := map[int]int{}\n    // Один цикл, временная сложность O(n)\n    for idx, val := range nums {\n        if preIdx, ok := hashTable[target-val]; ok {\n            return []int{preIdx, idx}\n        }\n        hashTable[val] = idx\n    }\n    return nil\n}\n</code></pre> two_sum.swift<pre><code>/* Метод 2: вспомогательная хеш-таблица */\nfunc twoSumHashTable(nums: [Int], target: Int) -&gt; [Int] {\n    // Вспомогательная хеш-таблица, пространственная сложность O(n)\n    var dic: [Int: Int] = [:]\n    // Один цикл, временная сложность O(n)\n    for i in nums.indices {\n        if let j = dic[target - nums[i]] {\n            return [j, i]\n        }\n        dic[nums[i]] = i\n    }\n    return [0]\n}\n</code></pre> two_sum.js<pre><code>/* Метод 2: вспомогательная хеш-таблица */\nfunction twoSumHashTable(nums, target) {\n    // Вспомогательная хеш-таблица, пространственная сложность O(n)\n    let m = {};\n    // Один цикл, временная сложность O(n)\n    for (let i = 0; i &lt; nums.length; i++) {\n        if (m[target - nums[i]] !== undefined) {\n            return [m[target - nums[i]], i];\n        } else {\n            m[nums[i]] = i;\n        }\n    }\n    return [];\n}\n</code></pre> two_sum.ts<pre><code>/* Метод 2: вспомогательная хеш-таблица */\nfunction twoSumHashTable(nums: number[], target: number): number[] {\n    // Вспомогательная хеш-таблица, пространственная сложность O(n)\n    let m: Map&lt;number, number&gt; = new Map();\n    // Один цикл, временная сложность O(n)\n    for (let i = 0; i &lt; nums.length; i++) {\n        let index = m.get(target - nums[i]);\n        if (index !== undefined) {\n            return [index, i];\n        } else {\n            m.set(nums[i], i);\n        }\n    }\n    return [];\n}\n</code></pre> two_sum.dart<pre><code>/* Способ 2: вспомогательная хеш-таблица */\nList&lt;int&gt; twoSumHashTable(List&lt;int&gt; nums, int target) {\n  int size = nums.length;\n  // Вспомогательная хеш-таблица, пространственная сложность O(n)\n  Map&lt;int, int&gt; dic = HashMap();\n  // Один цикл, временная сложность O(n)\n  for (var i = 0; i &lt; size; i++) {\n    if (dic.containsKey(target - nums[i])) {\n      return [dic[target - nums[i]]!, i];\n    }\n    dic.putIfAbsent(nums[i], () =&gt; i);\n  }\n  return [0];\n}\n</code></pre> two_sum.rs<pre><code>/* Метод 2: вспомогательная хеш-таблица */\npub fn two_sum_hash_table(nums: &amp;Vec&lt;i32&gt;, target: i32) -&gt; Option&lt;Vec&lt;i32&gt;&gt; {\n    // Вспомогательная хеш-таблица, пространственная сложность O(n)\n    let mut dic = HashMap::new();\n    // Один цикл, временная сложность O(n)\n    for (i, num) in nums.iter().enumerate() {\n        match dic.get(&amp;(target - num)) {\n            Some(v) =&gt; return Some(vec![*v as i32, i as i32]),\n            None =&gt; dic.insert(num, i as i32),\n        };\n    }\n    None\n}\n</code></pre> two_sum.c<pre><code>/* Хеш-таблица */\ntypedef struct {\n    int key;\n    int val;\n    UT_hash_handle hh; // Реализовано на основе uthash.h\n} HashTable;\n\n/* Поиск в хеш-таблице */\nHashTable *find(HashTable *h, int key) {\n    HashTable *tmp;\n    HASH_FIND_INT(h, &amp;key, tmp);\n    return tmp;\n}\n\n/* Вставка элемента в хеш-таблицу */\nvoid insert(HashTable **h, int key, int val) {\n    HashTable *t = find(*h, key);\n    if (t == NULL) {\n        HashTable *tmp = malloc(sizeof(HashTable));\n        tmp-&gt;key = key, tmp-&gt;val = val;\n        HASH_ADD_INT(*h, key, tmp);\n    } else {\n        t-&gt;val = val;\n    }\n}\n\n/* Метод 2: вспомогательная хеш-таблица */\nint *twoSumHashTable(int *nums, int numsSize, int target, int *returnSize) {\n    HashTable *hashtable = NULL;\n    for (int i = 0; i &lt; numsSize; i++) {\n        HashTable *t = find(hashtable, target - nums[i]);\n        if (t != NULL) {\n            int *res = malloc(sizeof(int) * 2);\n            res[0] = t-&gt;val, res[1] = i;\n            *returnSize = 2;\n            return res;\n        }\n        insert(&amp;hashtable, nums[i], i);\n    }\n    *returnSize = 0;\n    return NULL;\n}\n</code></pre> two_sum.kt<pre><code>/* Метод 2: вспомогательная хеш-таблица */\nfun twoSumHashTable(nums: IntArray, target: Int): IntArray {\n    val size = nums.size\n    // Вспомогательная хеш-таблица, пространственная сложность O(n)\n    val dic = HashMap&lt;Int, Int&gt;()\n    // Один цикл, временная сложность O(n)\n    for (i in 0..&lt;size) {\n        if (dic.containsKey(target - nums[i])) {\n            return intArrayOf(dic[target - nums[i]]!!, i)\n        }\n        dic[nums[i]] = i\n    }\n    return IntArray(0)\n}\n</code></pre> two_sum.rb<pre><code>### Метод 2: вспомогательная хеш-таблица ###\ndef two_sum_hash_table(nums, target)\n  # Вспомогательная хеш-таблица, пространственная сложность O(n)\n  dic = {}\n  # Один цикл, временная сложность O(n)\n  for i in 0...nums.length\n    return [dic[target - nums[i]], i] if dic.has_key?(target - nums[i])\n\n    dic[nums[i]] = i\n  end\n\n  []\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Благодаря хеш-поиску этот метод снижает временную сложность с \\(O(n^2)\\) до \\(O(n)\\) , существенно повышая эффективность работы.</p> <p>Поскольку требуется поддерживать дополнительную хеш-таблицу, пространственная сложность составляет \\(O(n)\\) . Несмотря на это, в целом данный метод лучше сбалансирован по времени и памяти, поэтому именно он является оптимальным решением этой задачи.</p>","path":["Глава 10. Поиск","10.4 &nbsp; Стратегии хеш-оптимизации"],"tags":[]},{"location":"chapter_searching/searching_algorithm_revisited/","level":1,"title":"10.5   Переосмысление алгоритмов поиска","text":"<p>Алгоритмы поиска (searching algorithm) используются для того, чтобы находить один или несколько элементов, удовлетворяющих определенным условиям, в структурах данных, таких как массивы, списки, деревья или графы.</p> <p>Алгоритмы поиска можно разделить на две категории по способу реализации.</p> <ul> <li>Поиск целевого элемента путем обхода структуры данных, например обход массива, списка, дерева или графа.</li> <li>Эффективный поиск элементов с использованием структуры организации данных или априорной информации, например двоичный поиск, хеш-поиск и поиск в двоичном дереве поиска.</li> </ul> <p>Нетрудно заметить, что эти темы уже рассматривались в предыдущих главах, поэтому алгоритмы поиска нам уже знакомы. В этом разделе мы еще раз посмотрим на них, но уже более системно.</p>","path":["Глава 10. Поиск","10.5 &nbsp; Переосмысление алгоритмов поиска"],"tags":[]},{"location":"chapter_searching/searching_algorithm_revisited/#1051","level":2,"title":"10.5.1   Полный перебор","text":"<p>Полный перебор заключается в том, что мы обходим каждый элемент структуры данных, чтобы найти целевой элемент.</p> <ul> <li>\"Линейный поиск\" применяется к линейным структурам данных, таким как массивы и списки. Он начинается с одного конца структуры данных и последовательно проверяет элементы, пока не найдет целевой элемент или пока не достигнет другого конца структуры данных.</li> <li>\"Поиск в ширину\" и \"поиск в глубину\" - это две стратегии обхода графов и деревьев. Поиск в ширину стартует из начального узла и исследует все узлы текущего уровня, прежде чем переходить к следующему. Поиск в глубину стартует из начального узла, проходит один путь до конца, затем возвращается назад и пробует другие пути, пока не будет полностью пройдена вся структура данных.</li> </ul> <p>Преимущество полного перебора состоит в его простоте и универсальности, поскольку он не требует предварительной обработки данных и использования дополнительных структур данных.</p> <p>Однако временная сложность таких алгоритмов равна \\(O(n)\\) , где \\(n\\) - число элементов, поэтому при больших объемах данных их производительность невысока.</p>","path":["Глава 10. Поиск","10.5 &nbsp; Переосмысление алгоритмов поиска"],"tags":[]},{"location":"chapter_searching/searching_algorithm_revisited/#1052","level":2,"title":"10.5.2   Адаптивный поиск","text":"<p>Адаптивный поиск использует специфические свойства данных (например, упорядоченность), чтобы оптимизировать процесс поиска и тем самым эффективнее находить целевой элемент.</p> <ul> <li>\"Двоичный поиск\" использует упорядоченность данных для эффективного поиска и применим только к массивам.</li> <li>\"Хеш-поиск\" использует хеш-таблицу для построения отображения между поисковыми данными и целевыми данными, благодаря чему запросы выполняются эффективно.</li> <li>\"Поиск в дереве\" ведется в конкретной древовидной структуре (например, в двоичном дереве поиска) и позволяет быстро отсекать узлы на основе сравнения значений, чтобы найти цель.</li> </ul> <p>Преимущество этих алгоритмов в высокой эффективности, их временная сложность может достигать \\(O(\\log n)\\) и даже \\(O(1)\\) .</p> <p>Однако для использования таких алгоритмов обычно требуется предварительная обработка данных. Например, для двоичного поиска нужно заранее отсортировать массив, а хеш-поиск и поиск в дереве требуют дополнительных структур данных, поддержание которых тоже отнимает время и память.</p> <p>Tip</p> <p>Адаптивные алгоритмы поиска часто называют алгоритмами поиска в узком смысле, поскольку они в основном предназначены для быстрого поиска целевого элемента в конкретной структуре данных.</p>","path":["Глава 10. Поиск","10.5 &nbsp; Переосмысление алгоритмов поиска"],"tags":[]},{"location":"chapter_searching/searching_algorithm_revisited/#1053","level":2,"title":"10.5.3   Выбор метода поиска","text":"<p>Для поиска целевого элемента в наборе данных размера \\(n\\) можно использовать линейный поиск, двоичный поиск, поиск в дереве, хеш-поиск и другие методы. Принципы работы этих методов показаны на рисунке 10-11.</p> <p></p> <p> Рисунок 10-11   Различные стратегии поиска </p> <p>Эффективность и особенности перечисленных методов приведены в таблице 10-1.</p> <p> Таблица 10-1   Сравнение эффективности алгоритмов поиска </p> Линейный поиск Двоичный поиск Поиск в дереве Хеш-поиск Поиск элемента \\(O(n)\\) \\(O(\\log n)\\) \\(O(\\log n)\\) \\(O(1)\\) Вставка элемента \\(O(1)\\) \\(O(n)\\) \\(O(\\log n)\\) \\(O(1)\\) Удаление элемента \\(O(n)\\) \\(O(n)\\) \\(O(\\log n)\\) \\(O(1)\\) Дополнительное пространство \\(O(1)\\) \\(O(1)\\) \\(O(n)\\) \\(O(n)\\) Предварительная обработка / Сортировка \\(O(n \\log n)\\) Построение дерева \\(O(n \\log n)\\) Построение хеш-таблицы \\(O(n)\\) Упорядоченность данных Не требуется Требуется Требуется Не требуется <p>Выбор алгоритма поиска также зависит от масштаба данных, требований к производительности поиска, а также частоты запросов и обновлений данных.</p> <p>Линейный поиск</p> <ul> <li>Обладает хорошей универсальностью и не требует никакой предварительной обработки данных. Если нужно выполнить только один запрос, то время предварительной обработки для остальных трех методов окажется больше, чем время линейного поиска.</li> <li>Подходит для небольших объемов данных, потому что в этом случае влияние временной сложности на эффективность невелико.</li> <li>Подходит для сценариев с высокой частотой обновления данных, поскольку этот метод не требует никакого дополнительного обслуживания данных.</li> </ul> <p>Двоичный поиск</p> <ul> <li>Подходит для больших наборов данных и демонстрирует стабильную эффективность; его худшая временная сложность равна \\(O(\\log n)\\) .</li> <li>Объем данных не должен быть слишком большим, потому что массив требует непрерывного участка памяти.</li> <li>Не подходит для сценариев с частыми вставками и удалениями данных, так как поддержание массива в отсортированном виде требует больших затрат.</li> </ul> <p>Хеш-поиск</p> <ul> <li>Подходит для сценариев, в которых требования к скорости запросов очень высоки; средняя временная сложность равна \\(O(1)\\) .</li> <li>Не подходит для сценариев, где требуется упорядоченность данных или поиск по диапазону, потому что хеш-таблица не умеет поддерживать порядок данных.</li> <li>Сильно зависит от хеш-функции и стратегии обработки коллизий, поэтому риск деградации производительности сравнительно велик.</li> <li>Не подходит для слишком больших объемов данных, так как хеш-таблице требуется дополнительное пространство, чтобы максимально снизить число коллизий и обеспечить хорошую производительность поиска.</li> </ul> <p>Поиск в дереве</p> <ul> <li>Подходит для очень больших объемов данных, потому что узлы дерева распределены в памяти и не требуют непрерывного хранения.</li> <li>Подходит для сценариев, где нужно поддерживать упорядоченные данные или выполнять поиск по диапазону.</li> <li>В процессе постоянных вставок и удалений узлов двоичное дерево поиска может перекоситься, и тогда временная сложность деградирует до \\(O(n)\\) .</li> <li>Если использовать AVL-дерево или красно-черное дерево, то все операции могут стабильно выполняться за \\(O(\\log n)\\) , но поддержание баланса дерева увеличивает дополнительные накладные расходы.</li> </ul>","path":["Глава 10. Поиск","10.5 &nbsp; Переосмысление алгоритмов поиска"],"tags":[]},{"location":"chapter_searching/summary/","level":1,"title":"10.6   Резюме","text":"","path":["Глава 10. Поиск","10.6 &nbsp; Резюме"],"tags":[]},{"location":"chapter_searching/summary/#1","level":3,"title":"1.   Ключевые выводы","text":"<ul> <li>Двоичный поиск опирается на упорядоченность данных и выполняет поиск путем циклического сокращения интервала вдвое. Он требует упорядоченных входных данных и подходит только для массивов или структур данных, реализованных на их основе.</li> <li>Полный перебор находит данные путем обхода структуры данных. Линейный поиск подходит для массивов и списков, а поиск в ширину и поиск в глубину подходят для графов и деревьев. Эти алгоритмы универсальны и не требуют предварительной обработки данных, но их временная сложность \\(O(n)\\) сравнительно велика.</li> <li>Хеш-поиск, поиск в дереве и двоичный поиск относятся к эффективным методам поиска и позволяют быстро находить целевой элемент в конкретных структурах данных. Такие алгоритмы обладают высокой эффективностью, их временная сложность может достигать \\(O(\\log n)\\) и даже \\(O(1)\\) , но обычно им нужны дополнительные структуры данных.</li> <li>На практике нужно анализировать размер данных, требования к производительности поиска, а также частоту запросов и обновлений данных, чтобы выбрать подходящий метод поиска.</li> <li>Линейный поиск подходит для небольших или часто обновляемых наборов данных; двоичный поиск - для больших отсортированных данных; хеш-поиск - для сценариев с высокими требованиями к скорости запросов и без необходимости поиска по диапазону; поиск в дереве - для больших динамических данных, где нужно поддерживать порядок и выполнять диапазонные запросы.</li> <li>Замена линейного поиска на хеш-поиск - это распространенная стратегия ускорения, которая позволяет снизить временную сложность с \\(O(n)\\) до \\(O(1)\\) .</li> </ul>","path":["Глава 10. Поиск","10.6 &nbsp; Резюме"],"tags":[]},{"location":"chapter_sorting/","level":1,"title":"Глава 11.   Сортировка","text":"<p>Abstract</p> <p>Сортировка упорядочивает хаотичные данные и позволяет быстрее находить закономерности.</p> <p>За кажущейся простотой скрывается целая группа алгоритмов с разными достоинствами и ограничениями.</p>","path":["Глава 11. Сортировка","Глава 11. &nbsp; Сортировка"],"tags":[]},{"location":"chapter_sorting/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>11.1   Алгоритмы сортировки</li> <li>11.2   Сортировка выбором</li> <li>11.3   Пузырьковая сортировка</li> <li>11.4   Сортировка вставкой</li> <li>11.5   Быстрая сортировка</li> <li>11.6   Сортировка слиянием</li> <li>11.7   Пирамидальная сортировка</li> <li>11.8   Блочная сортировка</li> <li>11.9   Сортировка подсчетом</li> <li>11.10   Поразрядная сортировка</li> <li>11.11   Резюме</li> </ul>","path":["Глава 11. Сортировка","Глава 11. &nbsp; Сортировка"],"tags":[]},{"location":"chapter_sorting/bubble_sort/","level":1,"title":"11.3   Сортировка пузырьком","text":"<p>Сортировка пузырьком (bubble sort) сортирует массив за счет непрерывного сравнения и обмена соседних элементов. Этот процесс напоминает всплытие пузырьков снизу вверх, откуда и произошло название алгоритма.</p> <p>Как показано на рисунке 11-4, процесс \"всплытия\" можно смоделировать через операцию обмена элементов: начиная от левого края массива и двигаясь вправо, мы последовательно сравниваем соседние элементы и, если \"левый элемент &gt; правый элемент\", меняем их местами. После завершения прохода максимальный элемент будет перемещен в самый правый конец массива.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 11-4   Моделирование пузырька через обмен элементов </p>","path":["Глава 11. Сортировка","11.3 &nbsp; Сортировка пузырьком"],"tags":[]},{"location":"chapter_sorting/bubble_sort/#1131","level":2,"title":"11.3.1   Алгоритм","text":"<p>Пусть длина массива равна \\(n\\) ; тогда шаги сортировки пузырьком показаны на рисунке 11-5.</p> <ol> <li>Сначала выполнить один проход \"всплытия\" по \\(n\\) элементам, переместив максимальный элемент массива на правильную позицию.</li> <li>Затем выполнить \"всплытие\" по оставшимся \\(n - 1\\) элементам, переместив второй по величине элемент на правильную позицию.</li> <li>Продолжать по аналогии; после \\(n - 1\\) раундов \"всплытия\" первые \\(n - 1\\) по величине элементы окажутся на правильных позициях.</li> <li>Оставшийся единственный элемент обязательно является минимальным, сортировать его уже не нужно, поэтому сортировка завершена.</li> </ol> <p></p> <p> Рисунок 11-5   Процесс сортировки пузырьком </p> <p>Пример кода:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby bubble_sort.py<pre><code>def bubble_sort(nums: list[int]):\n    \"\"\"Пузырьковая сортировка\"\"\"\n    n = len(nums)\n    # Внешний цикл: неотсортированный диапазон [0, i]\n    for i in range(n - 1, 0, -1):\n        # Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for j in range(i):\n            if nums[j] &gt; nums[j + 1]:\n                # Поменять местами nums[j] и nums[j + 1]\n                nums[j], nums[j + 1] = nums[j + 1], nums[j]\n</code></pre> bubble_sort.cpp<pre><code>/* Пузырьковая сортировка */\nvoid bubbleSort(vector&lt;int&gt; &amp;nums) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (int i = nums.size() - 1; i &gt; 0; i--) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                // Здесь используется функция std::swap()\n                swap(nums[j], nums[j + 1]);\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.java<pre><code>/* Пузырьковая сортировка */\nvoid bubbleSort(int[] nums) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (int i = nums.length - 1; i &gt; 0; i--) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                int tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.cs<pre><code>/* Пузырьковая сортировка */\nvoid BubbleSort(int[] nums) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (int i = nums.Length - 1; i &gt; 0; i--) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                (nums[j + 1], nums[j]) = (nums[j], nums[j + 1]);\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.go<pre><code>/* Пузырьковая сортировка */\nfunc bubbleSort(nums []int) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for i := len(nums) - 1; i &gt; 0; i-- {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for j := 0; j &lt; i; j++ {\n            if nums[j] &gt; nums[j+1] {\n                // Поменять местами nums[j] и nums[j + 1]\n                nums[j], nums[j+1] = nums[j+1], nums[j]\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.swift<pre><code>/* Пузырьковая сортировка */\nfunc bubbleSort(nums: inout [Int]) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for i in nums.indices.dropFirst().reversed() {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for j in 0 ..&lt; i {\n            if nums[j] &gt; nums[j + 1] {\n                // Поменять местами nums[j] и nums[j + 1]\n                nums.swapAt(j, j + 1)\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.js<pre><code>/* Пузырьковая сортировка */\nfunction bubbleSort(nums) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (let i = nums.length - 1; i &gt; 0; i--) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (let j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                let tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.ts<pre><code>/* Пузырьковая сортировка */\nfunction bubbleSort(nums: number[]): void {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (let i = nums.length - 1; i &gt; 0; i--) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (let j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                let tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.dart<pre><code>/* Пузырьковая сортировка */\nvoid bubbleSort(List&lt;int&gt; nums) {\n  // Внешний цикл: неотсортированный диапазон [0, i]\n  for (int i = nums.length - 1; i &gt; 0; i--) {\n    // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n    for (int j = 0; j &lt; i; j++) {\n      if (nums[j] &gt; nums[j + 1]) {\n        // Поменять местами nums[j] и nums[j + 1]\n        int tmp = nums[j];\n        nums[j] = nums[j + 1];\n        nums[j + 1] = tmp;\n      }\n    }\n  }\n}\n</code></pre> bubble_sort.rs<pre><code>/* Пузырьковая сортировка */\nfn bubble_sort(nums: &amp;mut [i32]) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for i in (1..nums.len()).rev() {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for j in 0..i {\n            if nums[j] &gt; nums[j + 1] {\n                // Поменять местами nums[j] и nums[j + 1]\n                nums.swap(j, j + 1);\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.c<pre><code>/* Пузырьковая сортировка */\nvoid bubbleSort(int nums[], int size) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (int i = size - 1; i &gt; 0; i--) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                int temp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = temp;\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.kt<pre><code>/* Пузырьковая сортировка */\nfun bubbleSort(nums: IntArray) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (i in nums.size - 1 downTo 1) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (j in 0..&lt;i) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                val temp = nums[j]\n                nums[j] = nums[j + 1]\n                nums[j + 1] = temp\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.rb<pre><code>### Пузырьковая сортировка ###\ndef bubble_sort(nums)\n  n = nums.length\n  # Внешний цикл: неотсортированный диапазон [0, i]\n  for i in (n - 1).downto(1)\n    # Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n    for j in 0...i\n      if nums[j] &gt; nums[j + 1]\n        # Поменять местами nums[j] и nums[j + 1]\n        nums[j], nums[j + 1] = nums[j + 1], nums[j]\n      end\n    end\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 11. Сортировка","11.3 &nbsp; Сортировка пузырьком"],"tags":[]},{"location":"chapter_sorting/bubble_sort/#1132","level":2,"title":"11.3.2   Оптимизация эффективности","text":"<p>Мы замечаем, что если в каком-либо раунде \"всплытия\" не произошло ни одного обмена, значит, массив уже отсортирован и можно сразу вернуть результат. Поэтому можно добавить флаг <code>flag</code> для отслеживания этой ситуации и немедленного выхода.</p> <p>После такой оптимизации худшая и средняя временные сложности сортировки пузырьком по-прежнему равны \\(O(n^2)\\) ; однако если входной массив уже полностью упорядочен, достигается лучшая временная сложность \\(O(n)\\) .</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby bubble_sort.py<pre><code>def bubble_sort_with_flag(nums: list[int]):\n    \"\"\"Пузырьковая сортировка (оптимизация флагом)\"\"\"\n    n = len(nums)\n    # Внешний цикл: неотсортированный диапазон [0, i]\n    for i in range(n - 1, 0, -1):\n        flag = False  # Инициализировать флаг\n        # Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for j in range(i):\n            if nums[j] &gt; nums[j + 1]:\n                # Поменять местами nums[j] и nums[j + 1]\n                nums[j], nums[j + 1] = nums[j + 1], nums[j]\n                flag = True  # Записать обмен элементов\n        if not flag:\n            break  # На этой итерации «всплытия» не было ни одного обмена, сразу выйти\n</code></pre> bubble_sort.cpp<pre><code>/* Пузырьковая сортировка (оптимизация флагом) */\nvoid bubbleSortWithFlag(vector&lt;int&gt; &amp;nums) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (int i = nums.size() - 1; i &gt; 0; i--) {\n        bool flag = false; // Инициализировать флаг\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                // Здесь используется функция std::swap()\n                swap(nums[j], nums[j + 1]);\n                flag = true; // Записать обмен элементов\n            }\n        }\n        if (!flag)\n            break; // На этой итерации «всплытия» не было ни одного обмена, сразу выйти\n    }\n}\n</code></pre> bubble_sort.java<pre><code>/* Пузырьковая сортировка (оптимизация флагом) */\nvoid bubbleSortWithFlag(int[] nums) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (int i = nums.length - 1; i &gt; 0; i--) {\n        boolean flag = false; // Инициализировать флаг\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                int tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                flag = true; // Записать обмен элементов\n            }\n        }\n        if (!flag)\n            break; // На этой итерации «всплытия» не было ни одного обмена, сразу выйти\n    }\n}\n</code></pre> bubble_sort.cs<pre><code>/* Пузырьковая сортировка (оптимизация флагом) */\nvoid BubbleSortWithFlag(int[] nums) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (int i = nums.Length - 1; i &gt; 0; i--) {\n        bool flag = false; // Инициализировать флаг\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                (nums[j + 1], nums[j]) = (nums[j], nums[j + 1]);\n                flag = true;  // Записать обмен элементов\n            }\n        }\n        if (!flag) break;     // На этой итерации «всплытия» не было ни одного обмена, сразу выйти\n    }\n}\n</code></pre> bubble_sort.go<pre><code>/* Пузырьковая сортировка (оптимизация флагом) */\nfunc bubbleSortWithFlag(nums []int) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for i := len(nums) - 1; i &gt; 0; i-- {\n        flag := false // Инициализировать флаг\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for j := 0; j &lt; i; j++ {\n            if nums[j] &gt; nums[j+1] {\n                // Поменять местами nums[j] и nums[j + 1]\n                nums[j], nums[j+1] = nums[j+1], nums[j]\n                flag = true // Записать обмен элементов\n            }\n        }\n        if flag == false { // На этой итерации «всплытия» не было ни одного обмена, сразу выйти\n            break\n        }\n    }\n}\n</code></pre> bubble_sort.swift<pre><code>/* Пузырьковая сортировка (оптимизация флагом) */\nfunc bubbleSortWithFlag(nums: inout [Int]) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for i in nums.indices.dropFirst().reversed() {\n        var flag = false // Инициализировать флаг\n        for j in 0 ..&lt; i {\n            if nums[j] &gt; nums[j + 1] {\n                // Поменять местами nums[j] и nums[j + 1]\n                nums.swapAt(j, j + 1)\n                flag = true // Записать обмен элементов\n            }\n        }\n        if !flag { // На этой итерации «всплытия» не было ни одного обмена, сразу выйти\n            break\n        }\n    }\n}\n</code></pre> bubble_sort.js<pre><code>/* Пузырьковая сортировка (оптимизация флагом) */\nfunction bubbleSortWithFlag(nums) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (let i = nums.length - 1; i &gt; 0; i--) {\n        let flag = false; // Инициализировать флаг\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (let j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                let tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                flag = true; // Записать обмен элементов\n            }\n        }\n        if (!flag) break; // На этой итерации «всплытия» не было ни одного обмена, сразу выйти\n    }\n}\n</code></pre> bubble_sort.ts<pre><code>/* Пузырьковая сортировка (оптимизация флагом) */\nfunction bubbleSortWithFlag(nums: number[]): void {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (let i = nums.length - 1; i &gt; 0; i--) {\n        let flag = false; // Инициализировать флаг\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (let j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                let tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                flag = true; // Записать обмен элементов\n            }\n        }\n        if (!flag) break; // На этой итерации «всплытия» не было ни одного обмена, сразу выйти\n    }\n}\n</code></pre> bubble_sort.dart<pre><code>/* Пузырьковая сортировка (оптимизация флагом) */\nvoid bubbleSortWithFlag(List&lt;int&gt; nums) {\n  // Внешний цикл: неотсортированный диапазон [0, i]\n  for (int i = nums.length - 1; i &gt; 0; i--) {\n    bool flag = false; // Инициализировать флаг\n    // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n    for (int j = 0; j &lt; i; j++) {\n      if (nums[j] &gt; nums[j + 1]) {\n        // Поменять местами nums[j] и nums[j + 1]\n        int tmp = nums[j];\n        nums[j] = nums[j + 1];\n        nums[j + 1] = tmp;\n        flag = true; // Записать обмен элементов\n      }\n    }\n    if (!flag) break; // На этой итерации «всплытия» не было ни одного обмена, сразу выйти\n  }\n}\n</code></pre> bubble_sort.rs<pre><code>/* Пузырьковая сортировка (оптимизация флагом) */\nfn bubble_sort_with_flag(nums: &amp;mut [i32]) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for i in (1..nums.len()).rev() {\n        let mut flag = false; // Инициализировать флаг\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for j in 0..i {\n            if nums[j] &gt; nums[j + 1] {\n                // Поменять местами nums[j] и nums[j + 1]\n                nums.swap(j, j + 1);\n                flag = true; // Записать обмен элементов\n            }\n        }\n        if !flag {\n            break; // На этой итерации «всплытия» не было ни одного обмена, сразу выйти\n        };\n    }\n}\n</code></pre> bubble_sort.c<pre><code>/* Пузырьковая сортировка (оптимизация флагом) */\nvoid bubbleSortWithFlag(int nums[], int size) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (int i = size - 1; i &gt; 0; i--) {\n        bool flag = false;\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                int temp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = temp;\n                flag = true;\n            }\n        }\n        if (!flag)\n            break;\n    }\n}\n</code></pre> bubble_sort.kt<pre><code>/* Пузырьковая сортировка (оптимизация флагом) */\nfun bubbleSortWithFlag(nums: IntArray) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (i in nums.size - 1 downTo 1) {\n        var flag = false // Инициализировать флаг\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (j in 0..&lt;i) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                val temp = nums[j]\n                nums[j] = nums[j + 1]\n                nums[j + 1] = temp\n                flag = true // Записать обмен элементов\n            }\n        }\n        if (!flag) break // На этой итерации «всплытия» не было ни одного обмена, сразу выйти\n    }\n}\n</code></pre> bubble_sort.rb<pre><code>### Пузырьковая сортировка ###\ndef bubble_sort(nums)\n  n = nums.length\n  # Внешний цикл: неотсортированный диапазон [0, i]\n  for i in (n - 1).downto(1)\n    # Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n    for j in 0...i\n      if nums[j] &gt; nums[j + 1]\n        # Поменять местами nums[j] и nums[j + 1]\n        nums[j], nums[j + 1] = nums[j + 1], nums[j]\n      end\n    end\n  end\nend\n\n# ## Пузырьковая сортировка (оптимизация флагом) ###\ndef bubble_sort_with_flag(nums)\n  n = nums.length\n  # Внешний цикл: неотсортированный диапазон [0, i]\n  for i in (n - 1).downto(1)\n    flag = false # Инициализировать флаг\n\n    # Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n    for j in 0...i\n      if nums[j] &gt; nums[j + 1]\n        # Поменять местами nums[j] и nums[j + 1]\n        nums[j], nums[j + 1] = nums[j + 1], nums[j]\n        flag = true # Записать обмен элементов\n      end\n    end\n\n    break unless flag # На этой итерации «всплытия» не было ни одного обмена, сразу выйти\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 11. Сортировка","11.3 &nbsp; Сортировка пузырьком"],"tags":[]},{"location":"chapter_sorting/bubble_sort/#1133","level":2,"title":"11.3.3   Характеристики алгоритма","text":"<ul> <li>Временная сложность равна \\(O(n^2)\\), алгоритм адаптивен: длины диапазонов, проходящих \"всплытие\" в разных раундах, последовательно равны \\(n - 1\\), \\(n - 2\\), \\(\\dots\\), \\(2\\), \\(1\\) , а их сумма равна \\((n - 1) n / 2\\) . После добавления оптимизации с <code>flag</code> лучшая временная сложность может достигать \\(O(n)\\) .</li> <li>Пространственная сложность равна \\(O(1)\\), сортировка выполняется на месте: указатели \\(i\\) и \\(j\\) используют константный объем дополнительной памяти.</li> <li>Стабильная сортировка: поскольку при \"всплытии\" равные элементы не обмениваются местами.</li> </ul>","path":["Глава 11. Сортировка","11.3 &nbsp; Сортировка пузырьком"],"tags":[]},{"location":"chapter_sorting/bucket_sort/","level":1,"title":"11.8   Блочная сортировка","text":"<p>Рассмотренные выше алгоритмы сортировки относятся к \"сортировкам на основе сравнений\": они упорядочивают данные, сравнивая элементы друг с другом. Временная сложность таких алгоритмов не может быть лучше \\(O(n \\log n)\\) . Далее мы рассмотрим несколько \"сортировок без сравнений\", чья временная сложность может достигать линейного порядка.</p> <p>Блочная сортировка (bucket sort) является типичным применением стратегии \"разделяй и властвуй\". Она задает несколько упорядоченных по диапазонам блоков, каждый блок соответствует некоторому диапазону значений; затем данные равномерно распределяются по блокам, внутри каждого блока выполняется сортировка, а в конце результаты блоков объединяются по порядку.</p>","path":["Глава 11. Сортировка","11.8 &nbsp; Блочная сортировка"],"tags":[]},{"location":"chapter_sorting/bucket_sort/#1181","level":2,"title":"11.8.1   Алгоритм","text":"<p>Рассмотрим массив длины \\(n\\), элементы которого являются числами с плавающей запятой из диапазона \\([0, 1)\\) . Процесс блочной сортировки показан на рисунке 11-13.</p> <ol> <li>Инициализировать \\(k\\) блоков и распределить \\(n\\) элементов по этим \\(k\\) блокам.</li> <li>Отсортировать каждый блок по отдельности (здесь используется встроенная функция сортировки языка программирования).</li> <li>Объединить результаты в порядке следования блоков от меньшего к большему.</li> </ol> <p></p> <p> Рисунок 11-13   Процесс блочной сортировки </p> <p>Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby bucket_sort.py<pre><code>def bucket_sort(nums: list[float]):\n    \"\"\"Сортировка корзинами\"\"\"\n    # Инициализировать k = n/2 корзин, предполагая распределение 2 элементов в каждую корзину\n    k = len(nums) // 2\n    buckets = [[] for _ in range(k)]\n    # 1. Распределить элементы массива по корзинам\n    for num in nums:\n        # Входные данные лежат в диапазоне [0, 1); использовать num * k для отображения в диапазон индексов [0, k-1]\n        i = int(num * k)\n        # Добавить num в корзину i\n        buckets[i].append(num)\n    # 2. Выполнить сортировку внутри каждой корзины\n    for bucket in buckets:\n        # Использовать встроенную функцию сортировки; ее также можно заменить другим алгоритмом сортировки\n        bucket.sort()\n    # 3. Обойти корзины и объединить результаты\n    i = 0\n    for bucket in buckets:\n        for num in bucket:\n            nums[i] = num\n            i += 1\n</code></pre> bucket_sort.cpp<pre><code>/* Сортировка корзинами */\nvoid bucketSort(vector&lt;float&gt; &amp;nums) {\n    // Инициализировать k = n/2 корзин, предполагая распределение 2 элементов в каждую корзину\n    int k = nums.size() / 2;\n    vector&lt;vector&lt;float&gt;&gt; buckets(k);\n    // 1. Распределить элементы массива по корзинам\n    for (float num : nums) {\n        // Входные данные лежат в диапазоне [0, 1); использовать num * k для отображения в диапазон индексов [0, k-1]\n        int i = num * k;\n        // Добавить num в корзину bucket_idx\n        buckets[i].push_back(num);\n    }\n    // 2. Выполнить сортировку внутри каждой корзины\n    for (vector&lt;float&gt; &amp;bucket : buckets) {\n        // Использовать встроенную функцию сортировки; ее также можно заменить другим алгоритмом сортировки\n        sort(bucket.begin(), bucket.end());\n    }\n    // 3. Обойти корзины и объединить результаты\n    int i = 0;\n    for (vector&lt;float&gt; &amp;bucket : buckets) {\n        for (float num : bucket) {\n            nums[i++] = num;\n        }\n    }\n}\n</code></pre> bucket_sort.java<pre><code>/* Сортировка корзинами */\nvoid bucketSort(float[] nums) {\n    // Инициализировать k = n/2 корзин, предполагая распределение 2 элементов в каждую корзину\n    int k = nums.length / 2;\n    List&lt;List&lt;Float&gt;&gt; buckets = new ArrayList&lt;&gt;();\n    for (int i = 0; i &lt; k; i++) {\n        buckets.add(new ArrayList&lt;&gt;());\n    }\n    // 1. Распределить элементы массива по корзинам\n    for (float num : nums) {\n        // Входные данные лежат в диапазоне [0, 1); использовать num * k для отображения в диапазон индексов [0, k-1]\n        int i = (int) (num * k);\n        // Добавить num в корзину i\n        buckets.get(i).add(num);\n    }\n    // 2. Выполнить сортировку внутри каждой корзины\n    for (List&lt;Float&gt; bucket : buckets) {\n        // Использовать встроенную функцию сортировки; ее также можно заменить другим алгоритмом сортировки\n        Collections.sort(bucket);\n    }\n    // 3. Обойти корзины и объединить результаты\n    int i = 0;\n    for (List&lt;Float&gt; bucket : buckets) {\n        for (float num : bucket) {\n            nums[i++] = num;\n        }\n    }\n}\n</code></pre> bucket_sort.cs<pre><code>/* Сортировка корзинами */\nvoid BucketSort(float[] nums) {\n    // Инициализировать k = n/2 корзин, предполагая распределение 2 элементов в каждую корзину\n    int k = nums.Length / 2;\n    List&lt;List&lt;float&gt;&gt; buckets = [];\n    for (int i = 0; i &lt; k; i++) {\n        buckets.Add([]);\n    }\n    // 1. Распределить элементы массива по корзинам\n    foreach (float num in nums) {\n        // Входные данные лежат в диапазоне [0, 1); использовать num * k для отображения в диапазон индексов [0, k-1]\n        int i = (int)(num * k);\n        // Добавить num в корзину i\n        buckets[i].Add(num);\n    }\n    // 2. Выполнить сортировку внутри каждой корзины\n    foreach (List&lt;float&gt; bucket in buckets) {\n        // Использовать встроенную функцию сортировки; ее также можно заменить другим алгоритмом сортировки\n        bucket.Sort();\n    }\n    // 3. Обойти корзины и объединить результаты\n    int j = 0;\n    foreach (List&lt;float&gt; bucket in buckets) {\n        foreach (float num in bucket) {\n            nums[j++] = num;\n        }\n    }\n}\n</code></pre> bucket_sort.go<pre><code>/* Сортировка корзинами */\nfunc bucketSort(nums []float64) {\n    // Инициализировать k = n/2 корзин, предполагая распределение 2 элементов в каждую корзину\n    k := len(nums) / 2\n    buckets := make([][]float64, k)\n    for i := 0; i &lt; k; i++ {\n        buckets[i] = make([]float64, 0)\n    }\n    // 1. Распределить элементы массива по корзинам\n    for _, num := range nums {\n        // Входные данные лежат в диапазоне [0, 1); использовать num * k для отображения в диапазон индексов [0, k-1]\n        i := int(num * float64(k))\n        // Добавить num в корзину i\n        buckets[i] = append(buckets[i], num)\n    }\n    // 2. Выполнить сортировку внутри каждой корзины\n    for i := 0; i &lt; k; i++ {\n        // Использовать встроенную функцию сортировки среза; ее также можно заменить другим алгоритмом сортировки\n        sort.Float64s(buckets[i])\n    }\n    // 3. Обойти корзины и объединить результаты\n    i := 0\n    for _, bucket := range buckets {\n        for _, num := range bucket {\n            nums[i] = num\n            i++\n        }\n    }\n}\n</code></pre> bucket_sort.swift<pre><code>/* Сортировка корзинами */\nfunc bucketSort(nums: inout [Double]) {\n    // Инициализировать k = n/2 корзин, предполагая распределение 2 элементов в каждую корзину\n    let k = nums.count / 2\n    var buckets = (0 ..&lt; k).map { _ in [Double]() }\n    // 1. Распределить элементы массива по корзинам\n    for num in nums {\n        // Входные данные лежат в диапазоне [0, 1); использовать num * k для отображения в диапазон индексов [0, k-1]\n        let i = Int(num * Double(k))\n        // Добавить num в корзину i\n        buckets[i].append(num)\n    }\n    // 2. Выполнить сортировку внутри каждой корзины\n    for i in buckets.indices {\n        // Использовать встроенную функцию сортировки; ее также можно заменить другим алгоритмом сортировки\n        buckets[i].sort()\n    }\n    // 3. Обойти корзины и объединить результаты\n    var i = nums.startIndex\n    for bucket in buckets {\n        for num in bucket {\n            nums[i] = num\n            i += 1\n        }\n    }\n}\n</code></pre> bucket_sort.js<pre><code>/* Сортировка корзинами */\nfunction bucketSort(nums) {\n    // Инициализировать k = n/2 корзин, предполагая распределение 2 элементов в каждую корзину\n    const k = nums.length / 2;\n    const buckets = [];\n    for (let i = 0; i &lt; k; i++) {\n        buckets.push([]);\n    }\n    // 1. Распределить элементы массива по корзинам\n    for (const num of nums) {\n        // Входные данные лежат в диапазоне [0, 1); использовать num * k для отображения в диапазон индексов [0, k-1]\n        const i = Math.floor(num * k);\n        // Добавить num в корзину i\n        buckets[i].push(num);\n    }\n    // 2. Выполнить сортировку внутри каждой корзины\n    for (const bucket of buckets) {\n        // Использовать встроенную функцию сортировки; ее также можно заменить другим алгоритмом сортировки\n        bucket.sort((a, b) =&gt; a - b);\n    }\n    // 3. Обойти корзины и объединить результаты\n    let i = 0;\n    for (const bucket of buckets) {\n        for (const num of bucket) {\n            nums[i++] = num;\n        }\n    }\n}\n</code></pre> bucket_sort.ts<pre><code>/* Сортировка корзинами */\nfunction bucketSort(nums: number[]): void {\n    // Инициализировать k = n/2 корзин, предполагая распределение 2 элементов в каждую корзину\n    const k = nums.length / 2;\n    const buckets: number[][] = [];\n    for (let i = 0; i &lt; k; i++) {\n        buckets.push([]);\n    }\n    // 1. Распределить элементы массива по корзинам\n    for (const num of nums) {\n        // Входные данные лежат в диапазоне [0, 1); использовать num * k для отображения в диапазон индексов [0, k-1]\n        const i = Math.floor(num * k);\n        // Добавить num в корзину i\n        buckets[i].push(num);\n    }\n    // 2. Выполнить сортировку внутри каждой корзины\n    for (const bucket of buckets) {\n        // Использовать встроенную функцию сортировки; ее также можно заменить другим алгоритмом сортировки\n        bucket.sort((a, b) =&gt; a - b);\n    }\n    // 3. Обойти корзины и объединить результаты\n    let i = 0;\n    for (const bucket of buckets) {\n        for (const num of bucket) {\n            nums[i++] = num;\n        }\n    }\n}\n</code></pre> bucket_sort.dart<pre><code>/* Сортировка корзинами */\nvoid bucketSort(List&lt;double&gt; nums) {\n  // Инициализировать k = n/2 корзин, предполагая распределение 2 элементов в каждую корзину\n  int k = nums.length ~/ 2;\n  List&lt;List&lt;double&gt;&gt; buckets = List.generate(k, (index) =&gt; []);\n\n  // 1. Распределить элементы массива по корзинам\n  for (double _num in nums) {\n    // Входные данные находятся в диапазоне [0, 1), используем _num * k для отображения в диапазон индексов [0, k-1]\n    int i = (_num * k).toInt();\n    // Добавить _num в корзину bucket_idx\n    buckets[i].add(_num);\n  }\n  // 2. Выполнить сортировку внутри каждой корзины\n  for (List&lt;double&gt; bucket in buckets) {\n    bucket.sort();\n  }\n  // 3. Обойти корзины и объединить результаты\n  int i = 0;\n  for (List&lt;double&gt; bucket in buckets) {\n    for (double _num in bucket) {\n      nums[i++] = _num;\n    }\n  }\n}\n</code></pre> bucket_sort.rs<pre><code>/* Сортировка корзинами */\nfn bucket_sort(nums: &amp;mut [f64]) {\n    // Инициализировать k = n/2 корзин, предполагая распределение 2 элементов в каждую корзину\n    let k = nums.len() / 2;\n    let mut buckets = vec![vec![]; k];\n    // 1. Распределить элементы массива по корзинам\n    for &amp;num in nums.iter() {\n        // Входные данные лежат в диапазоне [0, 1); использовать num * k для отображения в диапазон индексов [0, k-1]\n        let i = (num * k as f64) as usize;\n        // Добавить num в корзину i\n        buckets[i].push(num);\n    }\n    // 2. Выполнить сортировку внутри каждой корзины\n    for bucket in &amp;mut buckets {\n        // Использовать встроенную функцию сортировки; ее также можно заменить другим алгоритмом сортировки\n        bucket.sort_by(|a, b| a.partial_cmp(b).unwrap());\n    }\n    // 3. Обойти корзины и объединить результаты\n    let mut i = 0;\n    for bucket in buckets.iter() {\n        for &amp;num in bucket.iter() {\n            nums[i] = num;\n            i += 1;\n        }\n    }\n}\n</code></pre> bucket_sort.c<pre><code>/* Сортировка корзинами */\nvoid bucketSort(float nums[], int n) {\n    int k = n / 2;                                 // Инициализировать k = n/2 корзин\n    int *sizes = malloc(k * sizeof(int));          // Записать размер каждой корзины\n    float **buckets = malloc(k * sizeof(float *)); // Массив динамических массивов (корзины)\n    // Предварительно выделить достаточно места для каждой корзины\n    for (int i = 0; i &lt; k; ++i) {\n        buckets[i] = (float *)malloc(n * sizeof(float));\n        sizes[i] = 0;\n    }\n    // 1. Распределить элементы массива по корзинам\n    for (int i = 0; i &lt; n; ++i) {\n        int idx = (int)(nums[i] * k);\n        buckets[idx][sizes[idx]++] = nums[i];\n    }\n    // 2. Выполнить сортировку внутри каждой корзины\n    for (int i = 0; i &lt; k; ++i) {\n        qsort(buckets[i], sizes[i], sizeof(float), compare);\n    }\n    // 3. Объединить отсортированные корзины\n    int idx = 0;\n    for (int i = 0; i &lt; k; ++i) {\n        for (int j = 0; j &lt; sizes[i]; ++j) {\n            nums[idx++] = buckets[i][j];\n        }\n        // Освободить память\n        free(buckets[i]);\n    }\n}\n</code></pre> bucket_sort.kt<pre><code>/* Сортировка корзинами */\nfun bucketSort(nums: FloatArray) {\n    // Инициализировать k = n/2 корзин, предполагая распределение 2 элементов в каждую корзину\n    val k = nums.size / 2\n    val buckets = mutableListOf&lt;MutableList&lt;Float&gt;&gt;()\n    for (i in 0..&lt;k) {\n        buckets.add(mutableListOf())\n    }\n    // 1. Распределить элементы массива по корзинам\n    for (num in nums) {\n        // Входные данные лежат в диапазоне [0, 1); использовать num * k для отображения в диапазон индексов [0, k-1]\n        val i = (num * k).toInt()\n        // Добавить num в корзину i\n        buckets[i].add(num)\n    }\n    // 2. Выполнить сортировку внутри каждой корзины\n    for (bucket in buckets) {\n        // Использовать встроенную функцию сортировки; ее также можно заменить другим алгоритмом сортировки\n        bucket.sort()\n    }\n    // 3. Обойти корзины и объединить результаты\n    var i = 0\n    for (bucket in buckets) {\n        for (num in bucket) {\n            nums[i++] = num\n        }\n    }\n}\n</code></pre> bucket_sort.rb<pre><code>### Сортировка корзинами ###\ndef bucket_sort(nums)\n  # Инициализировать k = n/2 корзин, предполагая распределение 2 элементов в каждую корзину\n  k = nums.length / 2\n  buckets = Array.new(k) { [] }\n\n  # 1. Распределить элементы массива по корзинам\n  nums.each do |num|\n    # Входные данные лежат в диапазоне [0, 1); использовать num * k для отображения в диапазон индексов [0, k-1]\n    i = (num * k).to_i\n    # Добавить num в корзину i\n    buckets[i] &lt;&lt; num\n  end\n\n  # 2. Выполнить сортировку внутри каждой корзины\n  buckets.each do |bucket|\n    # Использовать встроенную функцию сортировки; ее также можно заменить другим алгоритмом сортировки\n    bucket.sort!\n  end\n\n  # 3. Обойти корзины и объединить результаты\n  i = 0\n  buckets.each do |bucket|\n    bucket.each do |num|\n      nums[i] = num\n      i += 1\n    end\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 11. Сортировка","11.8 &nbsp; Блочная сортировка"],"tags":[]},{"location":"chapter_sorting/bucket_sort/#1182","level":2,"title":"11.8.2   Характеристики алгоритма","text":"<p>Блочная сортировка подходит для обработки очень больших объемов данных. Например, если вход содержит 1 миллион элементов и из-за ограничений памяти система не может загрузить их все сразу, можно разбить данные на 1000 блоков, отсортировать каждый блок отдельно, а затем объединить результаты.</p> <ul> <li>Временная сложность равна \\(O(n + k)\\) : если элементы распределены по блокам равномерно, то в каждом блоке будет \\(\\frac{n}{k}\\) элементов. Если сортировка одного блока требует \\(O(\\frac{n}{k} \\log\\frac{n}{k})\\) времени, то сортировка всех блоков потребует \\(O(n \\log\\frac{n}{k})\\) времени. Когда число блоков \\(k\\) достаточно велико, временная сложность приближается к \\(O(n)\\) . На объединение результатов требуется \\(O(n + k)\\) времени, потому что нужно пройти по всем блокам и элементам. В худшем случае все данные попадут в один блок, и если сортировка этого блока использует \\(O(n^2)\\) времени, общая сложность также станет \\(O(n^2)\\) .</li> <li>Пространственная сложность равна \\(O(n + k)\\), сортировка не выполняется на месте: требуются дополнительные блоки в количестве \\(k\\) и место для всех \\(n\\) элементов внутри них.</li> <li>Является ли блочная сортировка стабильной, зависит от того, стабилен ли алгоритм сортировки внутри каждого блока.</li> </ul>","path":["Глава 11. Сортировка","11.8 &nbsp; Блочная сортировка"],"tags":[]},{"location":"chapter_sorting/bucket_sort/#1183","level":2,"title":"11.8.3   Как добиться равномерного распределения","text":"<p>Теоретически временная сложность блочной сортировки может достигать \\(O(n)\\) ; ключ к этому - как можно более равномерно распределить элементы по блокам. На практике данные часто распределены неравномерно. Например, если нужно распределить все товары на Taobao по 10 блокам цен, количество товаров дешевле 100 юаней может быть очень большим, а товаров дороже 1000 юаней - очень маленьким. Если просто разбить диапазон цен на 10 равных частей, число товаров в каждом блоке будет сильно различаться.</p> <p>Чтобы добиться более равномерного распределения, можно сначала задать грубую линию раздела и приблизительно распределить данные по 3 блокам. После этого блоки с большим числом товаров можно снова делить на 3 блока и продолжать процесс до тех пор, пока число элементов в каждом блоке не станет примерно одинаковым.</p> <p>Как показано на рисунке 11-14, по сути этот метод строит рекурсивное дерево, цель которого - сделать значения в листьях как можно более равномерными. Конечно, совсем не обязательно каждый раз делить данные именно на 3 блока; конкретную схему разбиения можно выбирать в зависимости от свойств данных.</p> <p></p> <p> Рисунок 11-14   Рекурсивное разбиение по блокам </p> <p>Если нам заранее известна вероятностная модель распределения цен товаров, то границы каждого блока можно задавать в соответствии с этим распределением. Важно отметить, что фактическое распределение данных не обязательно специально измерять - его можно приблизить некоторой вероятностной моделью исходя из свойств данных.</p> <p>Как показано на рисунке 11-15, если предположить, что цены товаров подчиняются нормальному распределению, то можно разумно задать интервалы цен и тем самым распределить товары по блокам достаточно равномерно.</p> <p></p> <p> Рисунок 11-15   Разбиение блоков по вероятностному распределению </p>","path":["Глава 11. Сортировка","11.8 &nbsp; Блочная сортировка"],"tags":[]},{"location":"chapter_sorting/counting_sort/","level":1,"title":"11.9   Сортировка подсчетом","text":"<p>Сортировка подсчетом (counting sort) реализует сортировку за счет подсчета количества элементов и обычно используется для массивов целых чисел.</p>","path":["Глава 11. Сортировка","11.9 &nbsp; Сортировка подсчетом"],"tags":[]},{"location":"chapter_sorting/counting_sort/#1191","level":2,"title":"11.9.1   Простая реализация","text":"<p>Сначала рассмотрим простой пример. Дан массив <code>nums</code> длины \\(n\\) , элементы которого являются \"неотрицательными целыми числами\". Общий процесс сортировки подсчетом показан на рисунке 11-16.</p> <ol> <li>Пройти по массиву, найти в нем максимальное число, обозначить его как \\(m\\) , а затем создать вспомогательный массив <code>counter</code> длины \\(m + 1\\) .</li> <li>С помощью <code>counter</code> подсчитать, сколько раз каждое число встречается в <code>nums</code>; при этом <code>counter[num]</code> хранит число вхождений значения <code>num</code> . Делается это просто: достаточно пройти по <code>nums</code> (пусть текущее число равно <code>num</code> ) и на каждом шаге увеличить <code>counter[num]</code> на \\(1\\) .</li> <li>Поскольку индексы массива <code>counter</code> изначально упорядочены, можно считать, что все числа уже отсортированы. Далее остается пройти по <code>counter</code> и в соответствии с числом вхождений записать значения обратно в <code>nums</code> в порядке возрастания.</li> </ol> <p></p> <p> Рисунок 11-16   Процесс сортировки подсчетом </p> <p>Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby counting_sort.py<pre><code>def counting_sort_naive(nums: list[int]):\n    \"\"\"Сортировка подсчетом\"\"\"\n    # Простая реализация, не подходит для сортировки объектов\n    # 1. Найти максимальный элемент массива m\n    m = max(nums)\n    # 2. Подсчитать число появлений каждой цифры\n    # counter[num] обозначает число появлений num\n    counter = [0] * (m + 1)\n    for num in nums:\n        counter[num] += 1\n    # 3. Обойти counter и заполнить исходный массив nums элементами\n    i = 0\n    for num in range(m + 1):\n        for _ in range(counter[num]):\n            nums[i] = num\n            i += 1\n</code></pre> counting_sort.cpp<pre><code>/* Сортировка подсчетом */\n// Простая реализация, не подходит для сортировки объектов\nvoid countingSortNaive(vector&lt;int&gt; &amp;nums) {\n    // 1. Найти максимальный элемент массива m\n    int m = 0;\n    for (int num : nums) {\n        m = max(m, num);\n    }\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    vector&lt;int&gt; counter(m + 1, 0);\n    for (int num : nums) {\n        counter[num]++;\n    }\n    // 3. Обойти counter и заполнить исходный массив nums элементами\n    int i = 0;\n    for (int num = 0; num &lt; m + 1; num++) {\n        for (int j = 0; j &lt; counter[num]; j++, i++) {\n            nums[i] = num;\n        }\n    }\n}\n</code></pre> counting_sort.java<pre><code>/* Сортировка подсчетом */\n// Простая реализация, не подходит для сортировки объектов\nvoid countingSortNaive(int[] nums) {\n    // 1. Найти максимальный элемент массива m\n    int m = 0;\n    for (int num : nums) {\n        m = Math.max(m, num);\n    }\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    int[] counter = new int[m + 1];\n    for (int num : nums) {\n        counter[num]++;\n    }\n    // 3. Обойти counter и заполнить исходный массив nums элементами\n    int i = 0;\n    for (int num = 0; num &lt; m + 1; num++) {\n        for (int j = 0; j &lt; counter[num]; j++, i++) {\n            nums[i] = num;\n        }\n    }\n}\n</code></pre> counting_sort.cs<pre><code>/* Сортировка подсчетом */\n// Простая реализация, не подходит для сортировки объектов\nvoid CountingSortNaive(int[] nums) {\n    // 1. Найти максимальный элемент массива m\n    int m = 0;\n    foreach (int num in nums) {\n        m = Math.Max(m, num);\n    }\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    int[] counter = new int[m + 1];\n    foreach (int num in nums) {\n        counter[num]++;\n    }\n    // 3. Обойти counter и заполнить исходный массив nums элементами\n    int i = 0;\n    for (int num = 0; num &lt; m + 1; num++) {\n        for (int j = 0; j &lt; counter[num]; j++, i++) {\n            nums[i] = num;\n        }\n    }\n}\n</code></pre> counting_sort.go<pre><code>/* Сортировка подсчетом */\n// Простая реализация, не подходит для сортировки объектов\nfunc countingSortNaive(nums []int) {\n    // 1. Найти максимальный элемент массива m\n    m := 0\n    for _, num := range nums {\n        if num &gt; m {\n            m = num\n        }\n    }\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    counter := make([]int, m+1)\n    for _, num := range nums {\n        counter[num]++\n    }\n    // 3. Обойти counter и заполнить исходный массив nums элементами\n    for i, num := 0, 0; num &lt; m+1; num++ {\n        for j := 0; j &lt; counter[num]; j++ {\n            nums[i] = num\n            i++\n        }\n    }\n}\n</code></pre> counting_sort.swift<pre><code>/* Сортировка подсчетом */\n// Простая реализация, не подходит для сортировки объектов\nfunc countingSortNaive(nums: inout [Int]) {\n    // 1. Найти максимальный элемент массива m\n    let m = nums.max()!\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    var counter = Array(repeating: 0, count: m + 1)\n    for num in nums {\n        counter[num] += 1\n    }\n    // 3. Обойти counter и заполнить исходный массив nums элементами\n    var i = 0\n    for num in 0 ..&lt; m + 1 {\n        for _ in 0 ..&lt; counter[num] {\n            nums[i] = num\n            i += 1\n        }\n    }\n}\n</code></pre> counting_sort.js<pre><code>/* Сортировка подсчетом */\n// Простая реализация, не подходит для сортировки объектов\nfunction countingSortNaive(nums) {\n    // 1. Найти максимальный элемент массива m\n    let m = Math.max(...nums);\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    const counter = new Array(m + 1).fill(0);\n    for (const num of nums) {\n        counter[num]++;\n    }\n    // 3. Обойти counter и заполнить исходный массив nums элементами\n    let i = 0;\n    for (let num = 0; num &lt; m + 1; num++) {\n        for (let j = 0; j &lt; counter[num]; j++, i++) {\n            nums[i] = num;\n        }\n    }\n}\n</code></pre> counting_sort.ts<pre><code>/* Сортировка подсчетом */\n// Простая реализация, не подходит для сортировки объектов\nfunction countingSortNaive(nums: number[]): void {\n    // 1. Найти максимальный элемент массива m\n    let m: number = Math.max(...nums);\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    const counter: number[] = new Array&lt;number&gt;(m + 1).fill(0);\n    for (const num of nums) {\n        counter[num]++;\n    }\n    // 3. Обойти counter и заполнить исходный массив nums элементами\n    let i = 0;\n    for (let num = 0; num &lt; m + 1; num++) {\n        for (let j = 0; j &lt; counter[num]; j++, i++) {\n            nums[i] = num;\n        }\n    }\n}\n</code></pre> counting_sort.dart<pre><code>/* Сортировка подсчетом */\n// Простая реализация, не подходит для сортировки объектов\nvoid countingSortNaive(List&lt;int&gt; nums) {\n  // 1. Найти максимальный элемент массива m\n  int m = 0;\n  for (int _num in nums) {\n    m = max(m, _num);\n  }\n  // 2. Подсчитать число появлений каждой цифры\n  // counter[_num] обозначает число появлений _num\n  List&lt;int&gt; counter = List.filled(m + 1, 0);\n  for (int _num in nums) {\n    counter[_num]++;\n  }\n  // 3. Обойти counter и заполнить исходный массив nums элементами\n  int i = 0;\n  for (int _num = 0; _num &lt; m + 1; _num++) {\n    for (int j = 0; j &lt; counter[_num]; j++, i++) {\n      nums[i] = _num;\n    }\n  }\n}\n</code></pre> counting_sort.rs<pre><code>/* Сортировка подсчетом */\n// Простая реализация, не подходит для сортировки объектов\nfn counting_sort_naive(nums: &amp;mut [i32]) {\n    // 1. Найти максимальный элемент массива m\n    let m = *nums.iter().max().unwrap();\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    let mut counter = vec![0; m as usize + 1];\n    for &amp;num in nums.iter() {\n        counter[num as usize] += 1;\n    }\n    // 3. Обойти counter и заполнить исходный массив nums элементами\n    let mut i = 0;\n    for num in 0..m + 1 {\n        for _ in 0..counter[num as usize] {\n            nums[i] = num;\n            i += 1;\n        }\n    }\n}\n</code></pre> counting_sort.c<pre><code>/* Сортировка подсчетом */\n// Простая реализация, не подходит для сортировки объектов\nvoid countingSortNaive(int nums[], int size) {\n    // 1. Найти максимальный элемент массива m\n    int m = 0;\n    for (int i = 0; i &lt; size; i++) {\n        if (nums[i] &gt; m) {\n            m = nums[i];\n        }\n    }\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    int *counter = calloc(m + 1, sizeof(int));\n    for (int i = 0; i &lt; size; i++) {\n        counter[nums[i]]++;\n    }\n    // 3. Обойти counter и заполнить исходный массив nums элементами\n    int i = 0;\n    for (int num = 0; num &lt; m + 1; num++) {\n        for (int j = 0; j &lt; counter[num]; j++, i++) {\n            nums[i] = num;\n        }\n    }\n    // 4. Освободить память\n    free(counter);\n}\n</code></pre> counting_sort.kt<pre><code>/* Сортировка подсчетом */\n// Простая реализация, не подходит для сортировки объектов\nfun countingSortNaive(nums: IntArray) {\n    // 1. Найти максимальный элемент массива m\n    var m = 0\n    for (num in nums) {\n        m = max(m, num)\n    }\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    val counter = IntArray(m + 1)\n    for (num in nums) {\n        counter[num]++\n    }\n    // 3. Обойти counter и заполнить исходный массив nums элементами\n    var i = 0\n    for (num in 0..&lt;m + 1) {\n        var j = 0\n        while (j &lt; counter[num]) {\n            nums[i] = num\n            j++\n            i++\n        }\n    }\n}\n</code></pre> counting_sort.rb<pre><code>### Сортировка подсчетом ###\ndef counting_sort_naive(nums)\n  # Простая реализация, не подходит для сортировки объектов\n  # 1. Найти максимальный элемент массива m\n  m = 0\n  nums.each { |num| m = [m, num].max }\n  # 2. Подсчитать число появлений каждой цифры\n  # counter[num] обозначает число появлений num\n  counter = Array.new(m + 1, 0)\n  nums.each { |num| counter[num] += 1 }\n  # 3. Обойти counter и заполнить исходный массив nums элементами\n  i = 0\n  for num in 0...(m + 1)\n    (0...counter[num]).each do\n      nums[i] = num\n      i += 1\n    end\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Связь между сортировкой подсчетом и блочной сортировкой</p> <p>Если посмотреть на сортировку подсчетом с точки зрения блочной сортировки, то каждый индекс массива <code>counter</code> можно рассматривать как отдельный блок, а процесс подсчета - как распределение элементов по соответствующим блокам. По сути, сортировка подсчетом является частным случаем блочной сортировки для целочисленных данных.</p>","path":["Глава 11. Сортировка","11.9 &nbsp; Сортировка подсчетом"],"tags":[]},{"location":"chapter_sorting/counting_sort/#1192","level":2,"title":"11.9.2   Полная реализация","text":"<p>Внимательный читатель мог заметить, что если входные данные представлены объектами, то описанный выше шаг <code>3.</code> перестает работать. Например, если входными данными являются объекты товаров и мы хотим отсортировать их по цене (полю класса), то описанный алгоритм сможет выдать только отсортированный ряд цен, но не исходные объекты в нужном порядке.</p> <p>Как же получить корректный порядок исходных данных? Сначала вычислим \"префиксную сумму\" массива <code>counter</code> . Как следует из названия, префиксная сумма в индексе <code>i</code> , обозначаемая как <code>prefix[i]</code> , равна сумме первых <code>i</code> элементов массива:</p> \\[ \\text{prefix}[i] = \\sum_{j=0}^i \\text{counter[j]} \\] <p>Префиксная сумма имеет четкий смысл: <code>prefix[num] - 1</code> обозначает индекс последнего вхождения элемента <code>num</code> в результирующем массиве <code>res</code>. Это очень важная информация, потому что она указывает, в какую позицию результирующего массива должен попасть каждый элемент. Далее мы проходим исходный массив <code>nums</code> в обратном порядке и на каждой итерации для очередного элемента <code>num</code> выполняем два действия.</p> <ol> <li>Записать <code>num</code> в массив <code>res</code> по индексу <code>prefix[num] - 1</code> .</li> <li>Уменьшить префиксную сумму <code>prefix[num]</code> на \\(1\\) , чтобы получить индекс следующего размещения элемента <code>num</code> .</li> </ol> <p>После завершения прохода массив <code>res</code> будет содержать отсортированный результат; остается только переписать <code>res</code> обратно в <code>nums</code> . Полный процесс сортировки подсчетом показан на рисунке 11-17.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 11-17   Шаги сортировки подсчетом </p> <p>Код реализации сортировки подсчетом приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby counting_sort.py<pre><code>def counting_sort(nums: list[int]):\n    \"\"\"Сортировка подсчетом\"\"\"\n    # Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\n    # 1. Найти максимальный элемент массива m\n    m = max(nums)\n    # 2. Подсчитать число появлений каждой цифры\n    # counter[num] обозначает число появлений num\n    counter = [0] * (m + 1)\n    for num in nums:\n        counter[num] += 1\n    # 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n    # То есть counter[num]-1 — это индекс последнего появления num в res\n    for i in range(m):\n        counter[i + 1] += counter[i]\n    # 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n    # Инициализировать массив res для хранения результата\n    n = len(nums)\n    res = [0] * n\n    for i in range(n - 1, -1, -1):\n        num = nums[i]\n        res[counter[num] - 1] = num  # Поместить num по соответствующему индексу\n        counter[num] -= 1  # Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения num\n    # Перезаписать исходный массив nums массивом результата res\n    for i in range(n):\n        nums[i] = res[i]\n</code></pre> counting_sort.cpp<pre><code>/* Сортировка подсчетом */\n// Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\nvoid countingSort(vector&lt;int&gt; &amp;nums) {\n    // 1. Найти максимальный элемент массива m\n    int m = 0;\n    for (int num : nums) {\n        m = max(m, num);\n    }\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    vector&lt;int&gt; counter(m + 1, 0);\n    for (int num : nums) {\n        counter[num]++;\n    }\n    // 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n    // То есть counter[num]-1 — это индекс последнего появления num в res\n    for (int i = 0; i &lt; m; i++) {\n        counter[i + 1] += counter[i];\n    }\n    // 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n    // Инициализировать массив res для хранения результата\n    int n = nums.size();\n    vector&lt;int&gt; res(n);\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int num = nums[i];\n        res[counter[num] - 1] = num; // Поместить num по соответствующему индексу\n        counter[num]--;              // Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения num\n    }\n    // Перезаписать исходный массив nums массивом результата res\n    nums = res;\n}\n</code></pre> counting_sort.java<pre><code>/* Сортировка подсчетом */\n// Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\nvoid countingSort(int[] nums) {\n    // 1. Найти максимальный элемент массива m\n    int m = 0;\n    for (int num : nums) {\n        m = Math.max(m, num);\n    }\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    int[] counter = new int[m + 1];\n    for (int num : nums) {\n        counter[num]++;\n    }\n    // 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n    // То есть counter[num]-1 — это индекс последнего появления num в res\n    for (int i = 0; i &lt; m; i++) {\n        counter[i + 1] += counter[i];\n    }\n    // 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n    // Инициализировать массив res для хранения результата\n    int n = nums.length;\n    int[] res = new int[n];\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int num = nums[i];\n        res[counter[num] - 1] = num; // Поместить num по соответствующему индексу\n        counter[num]--; // Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения num\n    }\n    // Перезаписать исходный массив nums массивом результата res\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = res[i];\n    }\n}\n</code></pre> counting_sort.cs<pre><code>/* Сортировка подсчетом */\n// Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\nvoid CountingSort(int[] nums) {\n    // 1. Найти максимальный элемент массива m\n    int m = 0;\n    foreach (int num in nums) {\n        m = Math.Max(m, num);\n    }\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    int[] counter = new int[m + 1];\n    foreach (int num in nums) {\n        counter[num]++;\n    }\n    // 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n    // То есть counter[num]-1 — это индекс последнего появления num в res\n    for (int i = 0; i &lt; m; i++) {\n        counter[i + 1] += counter[i];\n    }\n    // 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n    // Инициализировать массив res для хранения результата\n    int n = nums.Length;\n    int[] res = new int[n];\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int num = nums[i];\n        res[counter[num] - 1] = num; // Поместить num по соответствующему индексу\n        counter[num]--; // Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения num\n    }\n    // Перезаписать исходный массив nums массивом результата res\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = res[i];\n    }\n}\n</code></pre> counting_sort.go<pre><code>/* Сортировка подсчетом */\n// Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\nfunc countingSort(nums []int) {\n    // 1. Найти максимальный элемент массива m\n    m := 0\n    for _, num := range nums {\n        if num &gt; m {\n            m = num\n        }\n    }\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    counter := make([]int, m+1)\n    for _, num := range nums {\n        counter[num]++\n    }\n    // 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n    // То есть counter[num]-1 — это индекс последнего появления num в res\n    for i := 0; i &lt; m; i++ {\n        counter[i+1] += counter[i]\n    }\n    // 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n    // Инициализировать массив res для хранения результата\n    n := len(nums)\n    res := make([]int, n)\n    for i := n - 1; i &gt;= 0; i-- {\n        num := nums[i]\n        // Поместить num по соответствующему индексу\n        res[counter[num]-1] = num\n        // Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения num\n        counter[num]--\n    }\n    // Перезаписать исходный массив nums массивом результата res\n    copy(nums, res)\n}\n</code></pre> counting_sort.swift<pre><code>/* Сортировка подсчетом */\n// Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\nfunc countingSort(nums: inout [Int]) {\n    // 1. Найти максимальный элемент массива m\n    let m = nums.max()!\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    var counter = Array(repeating: 0, count: m + 1)\n    for num in nums {\n        counter[num] += 1\n    }\n    // 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n    // То есть counter[num]-1 — это индекс последнего появления num в res\n    for i in 0 ..&lt; m {\n        counter[i + 1] += counter[i]\n    }\n    // 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n    // Инициализировать массив res для хранения результата\n    var res = Array(repeating: 0, count: nums.count)\n    for i in nums.indices.reversed() {\n        let num = nums[i]\n        res[counter[num] - 1] = num // Поместить num по соответствующему индексу\n        counter[num] -= 1 // Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения num\n    }\n    // Перезаписать исходный массив nums массивом результата res\n    for i in nums.indices {\n        nums[i] = res[i]\n    }\n}\n</code></pre> counting_sort.js<pre><code>/* Сортировка подсчетом */\n// Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\nfunction countingSort(nums) {\n    // 1. Найти максимальный элемент массива m\n    let m = Math.max(...nums);\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    const counter = new Array(m + 1).fill(0);\n    for (const num of nums) {\n        counter[num]++;\n    }\n    // 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n    // То есть counter[num]-1 — это индекс последнего появления num в res\n    for (let i = 0; i &lt; m; i++) {\n        counter[i + 1] += counter[i];\n    }\n    // 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n    // Инициализировать массив res для хранения результата\n    const n = nums.length;\n    const res = new Array(n);\n    for (let i = n - 1; i &gt;= 0; i--) {\n        const num = nums[i];\n        res[counter[num] - 1] = num; // Поместить num по соответствующему индексу\n        counter[num]--; // Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения num\n    }\n    // Перезаписать исходный массив nums массивом результата res\n    for (let i = 0; i &lt; n; i++) {\n        nums[i] = res[i];\n    }\n}\n</code></pre> counting_sort.ts<pre><code>/* Сортировка подсчетом */\n// Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\nfunction countingSort(nums: number[]): void {\n    // 1. Найти максимальный элемент массива m\n    let m: number = Math.max(...nums);\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    const counter: number[] = new Array&lt;number&gt;(m + 1).fill(0);\n    for (const num of nums) {\n        counter[num]++;\n    }\n    // 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n    // То есть counter[num]-1 — это индекс последнего появления num в res\n    for (let i = 0; i &lt; m; i++) {\n        counter[i + 1] += counter[i];\n    }\n    // 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n    // Инициализировать массив res для хранения результата\n    const n = nums.length;\n    const res: number[] = new Array&lt;number&gt;(n);\n    for (let i = n - 1; i &gt;= 0; i--) {\n        const num = nums[i];\n        res[counter[num] - 1] = num; // Поместить num по соответствующему индексу\n        counter[num]--; // Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения num\n    }\n    // Перезаписать исходный массив nums массивом результата res\n    for (let i = 0; i &lt; n; i++) {\n        nums[i] = res[i];\n    }\n}\n</code></pre> counting_sort.dart<pre><code>/* Сортировка подсчетом */\n// Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\nvoid countingSort(List&lt;int&gt; nums) {\n  // 1. Найти максимальный элемент массива m\n  int m = 0;\n  for (int _num in nums) {\n    m = max(m, _num);\n  }\n  // 2. Подсчитать число появлений каждой цифры\n  // counter[_num] обозначает число появлений _num\n  List&lt;int&gt; counter = List.filled(m + 1, 0);\n  for (int _num in nums) {\n    counter[_num]++;\n  }\n  // 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n  // То есть counter[_num]-1 — это индекс последнего появления _num в res\n  for (int i = 0; i &lt; m; i++) {\n    counter[i + 1] += counter[i];\n  }\n  // 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n  // Инициализировать массив res для хранения результата\n  int n = nums.length;\n  List&lt;int&gt; res = List.filled(n, 0);\n  for (int i = n - 1; i &gt;= 0; i--) {\n    int _num = nums[i];\n    res[counter[_num] - 1] = _num; // Поместить _num по соответствующему индексу\n    counter[_num]--; // Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения _num\n  }\n  // Перезаписать исходный массив nums массивом результата res\n  nums.setAll(0, res);\n}\n</code></pre> counting_sort.rs<pre><code>/* Сортировка подсчетом */\n// Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\nfn counting_sort(nums: &amp;mut [i32]) {\n    // 1. Найти максимальный элемент массива m\n    let m = *nums.iter().max().unwrap() as usize;\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    let mut counter = vec![0; m + 1];\n    for &amp;num in nums.iter() {\n        counter[num as usize] += 1;\n    }\n    // 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n    // То есть counter[num]-1 — это индекс последнего появления num в res\n    for i in 0..m {\n        counter[i + 1] += counter[i];\n    }\n    // 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n    // Инициализировать массив res для хранения результата\n    let n = nums.len();\n    let mut res = vec![0; n];\n    for i in (0..n).rev() {\n        let num = nums[i];\n        res[counter[num as usize] - 1] = num; // Поместить num по соответствующему индексу\n        counter[num as usize] -= 1; // Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения num\n    }\n    // Перезаписать исходный массив nums массивом результата res\n    nums.copy_from_slice(&amp;res)\n}\n</code></pre> counting_sort.c<pre><code>/* Сортировка подсчетом */\n// Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\nvoid countingSort(int nums[], int size) {\n    // 1. Найти максимальный элемент массива m\n    int m = 0;\n    for (int i = 0; i &lt; size; i++) {\n        if (nums[i] &gt; m) {\n            m = nums[i];\n        }\n    }\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    int *counter = calloc(m, sizeof(int));\n    for (int i = 0; i &lt; size; i++) {\n        counter[nums[i]]++;\n    }\n    // 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n    // То есть counter[num]-1 — это индекс последнего появления num в res\n    for (int i = 0; i &lt; m; i++) {\n        counter[i + 1] += counter[i];\n    }\n    // 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n    // Инициализировать массив res для хранения результата\n    int *res = malloc(sizeof(int) * size);\n    for (int i = size - 1; i &gt;= 0; i--) {\n        int num = nums[i];\n        res[counter[num] - 1] = num; // Поместить num по соответствующему индексу\n        counter[num]--;              // Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения num\n    }\n    // Перезаписать исходный массив nums массивом результата res\n    memcpy(nums, res, size * sizeof(int));\n    // 5. Освободить память\n    free(res);\n    free(counter);\n}\n</code></pre> counting_sort.kt<pre><code>/* Сортировка подсчетом */\n// Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\nfun countingSort(nums: IntArray) {\n    // 1. Найти максимальный элемент массива m\n    var m = 0\n    for (num in nums) {\n        m = max(m, num)\n    }\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    val counter = IntArray(m + 1)\n    for (num in nums) {\n        counter[num]++\n    }\n    // 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n    // То есть counter[num]-1 — это индекс последнего появления num в res\n    for (i in 0..&lt;m) {\n        counter[i + 1] += counter[i]\n    }\n    // 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n    // Инициализировать массив res для хранения результата\n    val n = nums.size\n    val res = IntArray(n)\n    for (i in n - 1 downTo 0) {\n        val num = nums[i]\n        res[counter[num] - 1] = num // Поместить num по соответствующему индексу\n        counter[num]-- // Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения num\n    }\n    // Перезаписать исходный массив nums массивом результата res\n    for (i in 0..&lt;n) {\n        nums[i] = res[i]\n    }\n}\n</code></pre> counting_sort.rb<pre><code>### Сортировка подсчетом ###\ndef counting_sort(nums)\n  # Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\n  # 1. Найти максимальный элемент массива m\n  m = nums.max\n  # 2. Подсчитать число появлений каждой цифры\n  # counter[num] обозначает число появлений num\n  counter = Array.new(m + 1, 0)\n  nums.each { |num| counter[num] += 1 }\n  # 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n  # То есть counter[num]-1 — это индекс последнего появления num в res\n  (0...m).each { |i| counter[i + 1] += counter[i] }\n  # 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n  # Инициализировать массив res для хранения результата\n  n = nums.length\n  res = Array.new(n, 0)\n  (n - 1).downto(0).each do |i|\n    num = nums[i]\n    res[counter[num] - 1] = num # Поместить num по соответствующему индексу\n    counter[num] -= 1 # Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения num\n  end\n  # Перезаписать исходный массив nums массивом результата res\n  (0...n).each { |i| nums[i] = res[i] }\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 11. Сортировка","11.9 &nbsp; Сортировка подсчетом"],"tags":[]},{"location":"chapter_sorting/counting_sort/#1193","level":2,"title":"11.9.3   Характеристики алгоритма","text":"<ul> <li>Временная сложность равна \\(O(n + m)\\), алгоритм не является адаптивным : необходимо пройти по <code>nums</code> и по <code>counter</code> , а оба этих прохода занимают линейное время. Обычно выполняется \\(n \\gg m\\) , поэтому временная сложность стремится к \\(O(n)\\) .</li> <li>Пространственная сложность равна \\(O(n + m)\\), сортировка не выполняется на месте: используются массивы <code>res</code> и <code>counter</code> длины \\(n\\) и \\(m\\) соответственно.</li> <li>Стабильная сортировка: порядок заполнения <code>res</code> идет \"справа налево\", поэтому обратный проход по <code>nums</code> позволяет сохранить относительный порядок равных элементов и тем самым реализовать стабильную сортировку. Вообще говоря, прямой проход по <code>nums</code> тоже даст правильный результат сортировки, но он будет нестабильным.</li> </ul>","path":["Глава 11. Сортировка","11.9 &nbsp; Сортировка подсчетом"],"tags":[]},{"location":"chapter_sorting/counting_sort/#1194","level":2,"title":"11.9.4   Ограничения","text":"<p>На этом этапе сортировка подсчетом может показаться очень изящной: она позволяет эффективно сортировать данные, опираясь только на подсчет числа вхождений. Однако условия ее применения довольно строгие.</p> <p>Сортировка подсчетом применима только к неотрицательным целым числам. Чтобы использовать ее для других типов данных, нужно убедиться, что эти данные можно преобразовать в неотрицательные целые числа и что при преобразовании относительный порядок элементов не изменится. Например, для массива целых чисел с отрицательными значениями можно сначала прибавить ко всем числам константу, превратив их в положительные, затем выполнить сортировку и после этого преобразовать значения обратно.</p> <p>Сортировка подсчетом подходит для случаев, когда объем данных велик, но диапазон значений невелик. Например, в приведенном выше примере \\(m\\) не должно быть слишком большим, иначе будет занято слишком много памяти. А когда \\(n \\ll m\\) , сортировка подсчетом использует \\(O(m)\\) времени и может оказаться медленнее, чем алгоритмы сортировки с \\(O(n \\log n)\\) .</p>","path":["Глава 11. Сортировка","11.9 &nbsp; Сортировка подсчетом"],"tags":[]},{"location":"chapter_sorting/heap_sort/","level":1,"title":"11.7   Пирамидальная сортировка","text":"<p>Tip</p> <p>Перед чтением этого раздела убедитесь, что вы уже изучили главу \"Куча\".</p> <p>Пирамидальная сортировка (heap sort) - это эффективный алгоритм сортировки, основанный на структуре данных \"куча\". Для его реализации можно использовать уже изученные нами \"построение кучи\" и \"извлечение элементов из кучи\".</p> <ol> <li>Подать на вход массив и построить из него мин-кучу; в этот момент минимальный элемент будет находиться в вершине кучи.</li> <li>Непрерывно выполнять извлечение из кучи и по порядку записывать извлеченные элементы - так получится последовательность, отсортированная по возрастанию.</li> </ol> <p>Хотя этот метод работоспособен, он требует дополнительного массива для хранения извлеченных элементов и потому расходует лишнюю память. На практике обычно используют более изящную реализацию.</p>","path":["Глава 11. Сортировка","11.7 &nbsp; Пирамидальная сортировка"],"tags":[]},{"location":"chapter_sorting/heap_sort/#1171","level":2,"title":"11.7.1   Алгоритм","text":"<p>Пусть длина массива равна \\(n\\) ; тогда процесс пирамидальной сортировки показан на рисунке 11-12.</p> <ol> <li>Подать на вход массив и построить из него макс-кучу. После этого максимальный элемент окажется в вершине кучи.</li> <li>Обменять элемент в вершине кучи (первый элемент) с элементом внизу кучи (последний элемент). После обмена длина кучи уменьшается на \\(1\\) , а число уже отсортированных элементов увеличивается на \\(1\\) .</li> <li>Начиная с вершины, выполнить просеивание вниз (sift down) сверху вниз. После этого свойство кучи будет восстановлено.</li> <li>Циклически повторять шаг <code>2.</code> и шаг <code>3.</code> . После \\(n - 1\\) раундов массив будет полностью отсортирован.</li> </ol> <p>Tip</p> <p>На самом деле операция извлечения из кучи тоже включает шаг <code>2.</code> и шаг <code>3.</code> , только дополнительно содержит действие по удалению элемента.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 11-12   Шаги пирамидальной сортировки </p> <p>В реализации кода используется та же функция просеивания сверху вниз <code>sift_down()</code>, что и в главе \"Куча\". Важно помнить, что длина кучи уменьшается по мере извлечения максимального элемента, поэтому функции <code>sift_down()</code> нужно передавать параметр длины \\(n\\) , чтобы указать текущую эффективную длину кучи. Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby heap_sort.py<pre><code>def sift_down(nums: list[int], n: int, i: int):\n    \"\"\"Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз\"\"\"\n    while True:\n        # Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        l = 2 * i + 1\n        r = 2 * i + 2\n        ma = i\n        if l &lt; n and nums[l] &gt; nums[ma]:\n            ma = l\n        if r &lt; n and nums[r] &gt; nums[ma]:\n            ma = r\n        # Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if ma == i:\n            break\n        # Поменять два узла местами\n        nums[i], nums[ma] = nums[ma], nums[i]\n        # Циклическое просеивание вниз\n        i = ma\n\ndef heap_sort(nums: list[int]):\n    \"\"\"Сортировка кучей\"\"\"\n    # Построение кучи: выполнить heapify для всех узлов, кроме листовых\n    for i in range(len(nums) // 2 - 1, -1, -1):\n        sift_down(nums, len(nums), i)\n    # Извлекать максимальный элемент из кучи в течение n-1 итераций\n    for i in range(len(nums) - 1, 0, -1):\n        # Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n        nums[0], nums[i] = nums[i], nums[0]\n        # Начиная с корневого узла, выполнить просеивание сверху вниз\n        sift_down(nums, i, 0)\n</code></pre> heap_sort.cpp<pre><code>/* Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз */\nvoid siftDown(vector&lt;int&gt; &amp;nums, int n, int i) {\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        int l = 2 * i + 1;\n        int r = 2 * i + 2;\n        int ma = i;\n        if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma])\n            ma = l;\n        if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma])\n            ma = r;\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (ma == i) {\n            break;\n        }\n        // Поменять два узла местами\n        swap(nums[i], nums[ma]);\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n\n/* Сортировка кучей */\nvoid heapSort(vector&lt;int&gt; &amp;nums) {\n    // Построение кучи: выполнить heapify для всех узлов, кроме листовых\n    for (int i = nums.size() / 2 - 1; i &gt;= 0; --i) {\n        siftDown(nums, nums.size(), i);\n    }\n    // Извлекать максимальный элемент из кучи в течение n-1 итераций\n    for (int i = nums.size() - 1; i &gt; 0; --i) {\n        // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n        swap(nums[0], nums[i]);\n        // Начиная с корневого узла, выполнить просеивание сверху вниз\n        siftDown(nums, i, 0);\n    }\n}\n</code></pre> heap_sort.java<pre><code>/* Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз */\nvoid siftDown(int[] nums, int n, int i) {\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        int l = 2 * i + 1;\n        int r = 2 * i + 2;\n        int ma = i;\n        if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma])\n            ma = l;\n        if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma])\n            ma = r;\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (ma == i)\n            break;\n        // Поменять два узла местами\n        int temp = nums[i];\n        nums[i] = nums[ma];\n        nums[ma] = temp;\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n\n/* Сортировка кучей */\nvoid heapSort(int[] nums) {\n    // Построение кучи: выполнить heapify для всех узлов, кроме листовых\n    for (int i = nums.length / 2 - 1; i &gt;= 0; i--) {\n        siftDown(nums, nums.length, i);\n    }\n    // Извлекать максимальный элемент из кучи в течение n-1 итераций\n    for (int i = nums.length - 1; i &gt; 0; i--) {\n        // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n        int tmp = nums[0];\n        nums[0] = nums[i];\n        nums[i] = tmp;\n        // Начиная с корневого узла, выполнить просеивание сверху вниз\n        siftDown(nums, i, 0);\n    }\n}\n</code></pre> heap_sort.cs<pre><code>/* Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз */\nvoid SiftDown(int[] nums, int n, int i) {\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        int l = 2 * i + 1;\n        int r = 2 * i + 2;\n        int ma = i;\n        if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma])\n            ma = l;\n        if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma])\n            ma = r;\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (ma == i)\n            break;\n        // Поменять два узла местами\n        (nums[ma], nums[i]) = (nums[i], nums[ma]);\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n\n/* Сортировка кучей */\nvoid HeapSort(int[] nums) {\n    // Построение кучи: выполнить heapify для всех узлов, кроме листовых\n    for (int i = nums.Length / 2 - 1; i &gt;= 0; i--) {\n        SiftDown(nums, nums.Length, i);\n    }\n    // Извлекать максимальный элемент из кучи в течение n-1 итераций\n    for (int i = nums.Length - 1; i &gt; 0; i--) {\n        // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n        (nums[i], nums[0]) = (nums[0], nums[i]);\n        // Начиная с корневого узла, выполнить просеивание сверху вниз\n        SiftDown(nums, i, 0);\n    }\n}\n</code></pre> heap_sort.go<pre><code>/* Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз */\nfunc siftDown(nums *[]int, n, i int) {\n    for true {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        l := 2*i + 1\n        r := 2*i + 2\n        ma := i\n        if l &lt; n &amp;&amp; (*nums)[l] &gt; (*nums)[ma] {\n            ma = l\n        }\n        if r &lt; n &amp;&amp; (*nums)[r] &gt; (*nums)[ma] {\n            ma = r\n        }\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if ma == i {\n            break\n        }\n        // Поменять два узла местами\n        (*nums)[i], (*nums)[ma] = (*nums)[ma], (*nums)[i]\n        // Циклическое просеивание вниз\n        i = ma\n    }\n}\n\n/* Сортировка кучей */\nfunc heapSort(nums *[]int) {\n    // Построение кучи: выполнить heapify для всех узлов, кроме листовых\n    for i := len(*nums)/2 - 1; i &gt;= 0; i-- {\n        siftDown(nums, len(*nums), i)\n    }\n    // Извлекать максимальный элемент из кучи в течение n-1 итераций\n    for i := len(*nums) - 1; i &gt; 0; i-- {\n        // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n        (*nums)[0], (*nums)[i] = (*nums)[i], (*nums)[0]\n        // Начиная с корневого узла, выполнить просеивание сверху вниз\n        siftDown(nums, i, 0)\n    }\n}\n</code></pre> heap_sort.swift<pre><code>/* Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз */\nfunc siftDown(nums: inout [Int], n: Int, i: Int) {\n    var i = i\n    while true {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        let l = 2 * i + 1\n        let r = 2 * i + 2\n        var ma = i\n        if l &lt; n, nums[l] &gt; nums[ma] {\n            ma = l\n        }\n        if r &lt; n, nums[r] &gt; nums[ma] {\n            ma = r\n        }\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if ma == i {\n            break\n        }\n        // Поменять два узла местами\n        nums.swapAt(i, ma)\n        // Циклическое просеивание вниз\n        i = ma\n    }\n}\n\n/* Сортировка кучей */\nfunc heapSort(nums: inout [Int]) {\n    // Построение кучи: выполнить heapify для всех узлов, кроме листовых\n    for i in stride(from: nums.count / 2 - 1, through: 0, by: -1) {\n        siftDown(nums: &amp;nums, n: nums.count, i: i)\n    }\n    // Извлекать максимальный элемент из кучи в течение n-1 итераций\n    for i in nums.indices.dropFirst().reversed() {\n        // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n        nums.swapAt(0, i)\n        // Начиная с корневого узла, выполнить просеивание сверху вниз\n        siftDown(nums: &amp;nums, n: i, i: 0)\n    }\n}\n</code></pre> heap_sort.js<pre><code>/* Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз */\nfunction siftDown(nums, n, i) {\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        let l = 2 * i + 1;\n        let r = 2 * i + 2;\n        let ma = i;\n        if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma]) {\n            ma = l;\n        }\n        if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma]) {\n            ma = r;\n        }\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (ma === i) {\n            break;\n        }\n        // Поменять два узла местами\n        [nums[i], nums[ma]] = [nums[ma], nums[i]];\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n\n/* Сортировка кучей */\nfunction heapSort(nums) {\n    // Построение кучи: выполнить heapify для всех узлов, кроме листовых\n    for (let i = Math.floor(nums.length / 2) - 1; i &gt;= 0; i--) {\n        siftDown(nums, nums.length, i);\n    }\n    // Извлекать максимальный элемент из кучи в течение n-1 итераций\n    for (let i = nums.length - 1; i &gt; 0; i--) {\n        // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n        [nums[0], nums[i]] = [nums[i], nums[0]];\n        // Начиная с корневого узла, выполнить просеивание сверху вниз\n        siftDown(nums, i, 0);\n    }\n}\n</code></pre> heap_sort.ts<pre><code>/* Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз */\nfunction siftDown(nums: number[], n: number, i: number): void {\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        let l = 2 * i + 1;\n        let r = 2 * i + 2;\n        let ma = i;\n        if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma]) {\n            ma = l;\n        }\n        if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma]) {\n            ma = r;\n        }\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (ma === i) {\n            break;\n        }\n        // Поменять два узла местами\n        [nums[i], nums[ma]] = [nums[ma], nums[i]];\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n\n/* Сортировка кучей */\nfunction heapSort(nums: number[]): void {\n    // Построение кучи: выполнить heapify для всех узлов, кроме листовых\n    for (let i = Math.floor(nums.length / 2) - 1; i &gt;= 0; i--) {\n        siftDown(nums, nums.length, i);\n    }\n    // Извлекать максимальный элемент из кучи в течение n-1 итераций\n    for (let i = nums.length - 1; i &gt; 0; i--) {\n        // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n        [nums[0], nums[i]] = [nums[i], nums[0]];\n        // Начиная с корневого узла, выполнить просеивание сверху вниз\n        siftDown(nums, i, 0);\n    }\n}\n</code></pre> heap_sort.dart<pre><code>/* Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз */\nvoid siftDown(List&lt;int&gt; nums, int n, int i) {\n  while (true) {\n    // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n    int l = 2 * i + 1;\n    int r = 2 * i + 2;\n    int ma = i;\n    if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma]) ma = l;\n    if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma]) ma = r;\n    // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n    if (ma == i) break;\n    // Поменять два узла местами\n    int temp = nums[i];\n    nums[i] = nums[ma];\n    nums[ma] = temp;\n    // Циклическое просеивание вниз\n    i = ma;\n  }\n}\n\n/* Сортировка кучей */\nvoid heapSort(List&lt;int&gt; nums) {\n  // Построение кучи: выполнить heapify для всех узлов, кроме листовых\n  for (int i = nums.length ~/ 2 - 1; i &gt;= 0; i--) {\n    siftDown(nums, nums.length, i);\n  }\n  // Извлекать максимальный элемент из кучи в течение n-1 итераций\n  for (int i = nums.length - 1; i &gt; 0; i--) {\n    // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    int tmp = nums[0];\n    nums[0] = nums[i];\n    nums[i] = tmp;\n    // Начиная с корневого узла, выполнить просеивание сверху вниз\n    siftDown(nums, i, 0);\n  }\n}\n</code></pre> heap_sort.rs<pre><code>/* Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз */\nfn sift_down(nums: &amp;mut [i32], n: usize, mut i: usize) {\n    loop {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        let l = 2 * i + 1;\n        let r = 2 * i + 2;\n        let mut ma = i;\n        if l &lt; n &amp;&amp; nums[l] &gt; nums[ma] {\n            ma = l;\n        }\n        if r &lt; n &amp;&amp; nums[r] &gt; nums[ma] {\n            ma = r;\n        }\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if ma == i {\n            break;\n        }\n        // Поменять два узла местами\n        nums.swap(i, ma);\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n\n/* Сортировка кучей */\nfn heap_sort(nums: &amp;mut [i32]) {\n    // Построение кучи: выполнить heapify для всех узлов, кроме листовых\n    for i in (0..nums.len() / 2).rev() {\n        sift_down(nums, nums.len(), i);\n    }\n    // Извлекать максимальный элемент из кучи в течение n-1 итераций\n    for i in (1..nums.len()).rev() {\n        // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n        nums.swap(0, i);\n        // Начиная с корневого узла, выполнить просеивание сверху вниз\n        sift_down(nums, i, 0);\n    }\n}\n</code></pre> heap_sort.c<pre><code>/* Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз */\nvoid siftDown(int nums[], int n, int i) {\n    while (1) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        int l = 2 * i + 1;\n        int r = 2 * i + 2;\n        int ma = i;\n        if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma])\n            ma = l;\n        if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma])\n            ma = r;\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (ma == i) {\n            break;\n        }\n        // Поменять два узла местами\n        int temp = nums[i];\n        nums[i] = nums[ma];\n        nums[ma] = temp;\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n\n/* Сортировка кучей */\nvoid heapSort(int nums[], int n) {\n    // Построение кучи: выполнить heapify для всех узлов, кроме листовых\n    for (int i = n / 2 - 1; i &gt;= 0; --i) {\n        siftDown(nums, n, i);\n    }\n    // Извлекать максимальный элемент из кучи в течение n-1 итераций\n    for (int i = n - 1; i &gt; 0; --i) {\n        // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n        int tmp = nums[0];\n        nums[0] = nums[i];\n        nums[i] = tmp;\n        // Начиная с корневого узла, выполнить просеивание сверху вниз\n        siftDown(nums, i, 0);\n    }\n}\n</code></pre> heap_sort.kt<pre><code>/* Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз */\nfun siftDown(nums: IntArray, n: Int, li: Int) {\n    var i = li\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        val l = 2 * i + 1\n        val r = 2 * i + 2\n        var ma = i\n        if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma]) \n            ma = l\n        if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma]) \n            ma = r\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (ma == i) \n            break\n        // Поменять два узла местами\n        val temp = nums[i]\n        nums[i] = nums[ma]\n        nums[ma] = temp\n        // Циклическое просеивание вниз\n        i = ma\n    }\n}\n\n/* Сортировка кучей */\nfun heapSort(nums: IntArray) {\n    // Построение кучи: выполнить heapify для всех узлов, кроме листовых\n    for (i in nums.size / 2 - 1 downTo 0) {\n        siftDown(nums, nums.size, i)\n    }\n    // Извлекать максимальный элемент из кучи в течение n-1 итераций\n    for (i in nums.size - 1 downTo 1) {\n        // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n        val temp = nums[0]\n        nums[0] = nums[i]\n        nums[i] = temp\n        // Начиная с корневого узла, выполнить просеивание сверху вниз\n        siftDown(nums, i, 0)\n    }\n}\n</code></pre> heap_sort.rb<pre><code>### Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз ###\ndef sift_down(nums, n, i)\n  while true\n    # Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n    l = 2 * i + 1\n    r = 2 * i + 2\n    ma = i\n    ma = l if l &lt; n &amp;&amp; nums[l] &gt; nums[ma]\n    ma = r if r &lt; n &amp;&amp; nums[r] &gt; nums[ma]\n    # Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n    break if ma == i\n    # Поменять два узла местами\n    nums[i], nums[ma] = nums[ma], nums[i]\n    # Циклическое просеивание вниз\n    i = ma\n  end\nend\n\n### Сортировка кучей ###\ndef heap_sort(nums)\n  # Построение кучи: выполнить heapify для всех узлов, кроме листовых\n  (nums.length / 2 - 1).downto(0) do |i|\n    sift_down(nums, nums.length, i)\n  end\n  # Извлекать максимальный элемент из кучи в течение n-1 итераций\n  (nums.length - 1).downto(1) do |i|\n    # Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    nums[0], nums[i] = nums[i], nums[0]\n    # Начиная с корневого узла, выполнить просеивание сверху вниз\n    sift_down(nums, i, 0)\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 11. Сортировка","11.7 &nbsp; Пирамидальная сортировка"],"tags":[]},{"location":"chapter_sorting/heap_sort/#1172","level":2,"title":"11.7.2   Характеристики алгоритма","text":"<ul> <li>Временная сложность равна \\(O(n \\log n)\\), алгоритм не является адаптивным: построение кучи занимает \\(O(n)\\) времени. Извлечение максимального элемента из кучи имеет временную сложность \\(O(\\log n)\\) и выполняется \\(n - 1\\) раз.</li> <li>Пространственная сложность равна \\(O(1)\\), сортировка выполняется на месте: несколько переменных-указателей используют \\(O(1)\\) памяти. Обмен элементов и операции просеивания выполняются прямо в исходном массиве.</li> <li>Нестабильная сортировка: при обмене вершины кучи и нижнего элемента относительный порядок равных элементов может измениться.</li> </ul>","path":["Глава 11. Сортировка","11.7 &nbsp; Пирамидальная сортировка"],"tags":[]},{"location":"chapter_sorting/insertion_sort/","level":1,"title":"11.4   Сортировка вставками","text":"<p>Сортировка вставками (insertion sort) - это простой алгоритм сортировки, принцип которого очень похож на ручное упорядочивание колоды карт.</p> <p>Точнее говоря, в неотсортированном диапазоне выбирается опорный элемент, после чего он поочередно сравнивается с элементами слева в уже отсортированном диапазоне и вставляется в правильную позицию.</p> <p>На рисунке 11-6 показан процесс вставки элемента в массив. Пусть опорный элемент обозначен как <code>base</code> ; нам нужно сдвинуть все элементы от целевого индекса до <code>base</code> на одну позицию вправо, а затем присвоить <code>base</code> значение в целевом индексе.</p> <p></p> <p> Рисунок 11-6   Одна операция вставки </p>","path":["Глава 11. Сортировка","11.4 &nbsp; Сортировка вставками"],"tags":[]},{"location":"chapter_sorting/insertion_sort/#1141","level":2,"title":"11.4.1   Алгоритм","text":"<p>Общий процесс сортировки вставками показан на рисунке 11-7.</p> <ol> <li>В начальном состоянии отсортирован только первый элемент массива.</li> <li>Выбрать второй элемент массива как <code>base</code> ; после вставки в правильную позицию первые 2 элемента массива окажутся отсортированными.</li> <li>Выбрать третий элемент как <code>base</code> ; после вставки в правильную позицию первые 3 элемента массива окажутся отсортированными.</li> <li>Продолжать по аналогии; в последнем раунде в качестве <code>base</code> берется последний элемент, и после его вставки все элементы массива будут отсортированы.</li> </ol> <p></p> <p> Рисунок 11-7   Процесс сортировки вставками </p> <p>Пример кода:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby insertion_sort.py<pre><code>def insertion_sort(nums: list[int]):\n    \"\"\"Сортировка вставками\"\"\"\n    # Внешний цикл: отсортированный диапазон [0, i-1]\n    for i in range(1, len(nums)):\n        base = nums[i]\n        j = i - 1\n        # Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n        while j &gt;= 0 and nums[j] &gt; base:\n            nums[j + 1] = nums[j]  # Сдвинуть nums[j] на одну позицию вправо\n            j -= 1\n        nums[j + 1] = base  # Поместить base в правильную позицию\n</code></pre> insertion_sort.cpp<pre><code>/* Сортировка вставками */\nvoid insertionSort(vector&lt;int&gt; &amp;nums) {\n    // Внешний цикл: отсортированный диапазон [0, i-1]\n    for (int i = 1; i &lt; nums.size(); i++) {\n        int base = nums[i], j = i - 1;\n        // Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n        while (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n            nums[j + 1] = nums[j]; // Сдвинуть nums[j] на одну позицию вправо\n            j--;\n        }\n        nums[j + 1] = base; // Поместить base в правильную позицию\n    }\n}\n</code></pre> insertion_sort.java<pre><code>/* Сортировка вставками */\nvoid insertionSort(int[] nums) {\n    // Внешний цикл: отсортированный диапазон [0, i-1]\n    for (int i = 1; i &lt; nums.length; i++) {\n        int base = nums[i], j = i - 1;\n        // Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n        while (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n            nums[j + 1] = nums[j]; // Сдвинуть nums[j] на одну позицию вправо\n            j--;\n        }\n        nums[j + 1] = base;        // Поместить base в правильную позицию\n    }\n}\n</code></pre> insertion_sort.cs<pre><code>/* Сортировка вставками */\nvoid InsertionSort(int[] nums) {\n    // Внешний цикл: отсортированный диапазон [0, i-1]\n    for (int i = 1; i &lt; nums.Length; i++) {\n        int bas = nums[i], j = i - 1;\n        // Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n        while (j &gt;= 0 &amp;&amp; nums[j] &gt; bas) {\n            nums[j + 1] = nums[j]; // Сдвинуть nums[j] на одну позицию вправо\n            j--;\n        }\n        nums[j + 1] = bas;         // Поместить base в правильную позицию\n    }\n}\n</code></pre> insertion_sort.go<pre><code>/* Сортировка вставками */\nfunc insertionSort(nums []int) {\n    // Внешний цикл: отсортированный диапазон [0, i-1]\n    for i := 1; i &lt; len(nums); i++ {\n        base := nums[i]\n        j := i - 1\n        // Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n        for j &gt;= 0 &amp;&amp; nums[j] &gt; base {\n            nums[j+1] = nums[j] // Сдвинуть nums[j] на одну позицию вправо\n            j--\n        }\n        nums[j+1] = base // Поместить base в правильную позицию\n    }\n}\n</code></pre> insertion_sort.swift<pre><code>/* Сортировка вставками */\nfunc insertionSort(nums: inout [Int]) {\n    // Внешний цикл: отсортированный диапазон [0, i-1]\n    for i in nums.indices.dropFirst() {\n        let base = nums[i]\n        var j = i - 1\n        // Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n        while j &gt;= 0, nums[j] &gt; base {\n            nums[j + 1] = nums[j] // Сдвинуть nums[j] на одну позицию вправо\n            j -= 1\n        }\n        nums[j + 1] = base // Поместить base в правильную позицию\n    }\n}\n</code></pre> insertion_sort.js<pre><code>/* Сортировка вставками */\nfunction insertionSort(nums) {\n    // Внешний цикл: отсортированный диапазон [0, i-1]\n    for (let i = 1; i &lt; nums.length; i++) {\n        let base = nums[i],\n            j = i - 1;\n        // Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n        while (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n            nums[j + 1] = nums[j]; // Сдвинуть nums[j] на одну позицию вправо\n            j--;\n        }\n        nums[j + 1] = base; // Поместить base в правильную позицию\n    }\n}\n</code></pre> insertion_sort.ts<pre><code>/* Сортировка вставками */\nfunction insertionSort(nums: number[]): void {\n    // Внешний цикл: отсортированный диапазон [0, i-1]\n    for (let i = 1; i &lt; nums.length; i++) {\n        const base = nums[i];\n        let j = i - 1;\n        // Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n        while (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n            nums[j + 1] = nums[j]; // Сдвинуть nums[j] на одну позицию вправо\n            j--;\n        }\n        nums[j + 1] = base; // Поместить base в правильную позицию\n    }\n}\n</code></pre> insertion_sort.dart<pre><code>/* Сортировка вставками */\nvoid insertionSort(List&lt;int&gt; nums) {\n  // Внешний цикл: отсортированный диапазон [0, i-1]\n  for (int i = 1; i &lt; nums.length; i++) {\n    int base = nums[i], j = i - 1;\n    // Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n    while (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n      nums[j + 1] = nums[j]; // Сдвинуть nums[j] на одну позицию вправо\n      j--;\n    }\n    nums[j + 1] = base; // Поместить base в правильную позицию\n  }\n}\n</code></pre> insertion_sort.rs<pre><code>/* Сортировка вставками */\nfn insertion_sort(nums: &amp;mut [i32]) {\n    // Внешний цикл: отсортированный диапазон [0, i-1]\n    for i in 1..nums.len() {\n        let (base, mut j) = (nums[i], (i - 1) as i32);\n        // Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n        while j &gt;= 0 &amp;&amp; nums[j as usize] &gt; base {\n            nums[(j + 1) as usize] = nums[j as usize]; // Сдвинуть nums[j] на одну позицию вправо\n            j -= 1;\n        }\n        nums[(j + 1) as usize] = base; // Поместить base в правильную позицию\n    }\n}\n</code></pre> insertion_sort.c<pre><code>/* Сортировка вставками */\nvoid insertionSort(int nums[], int size) {\n    // Внешний цикл: отсортированный диапазон [0, i-1]\n    for (int i = 1; i &lt; size; i++) {\n        int base = nums[i], j = i - 1;\n        // Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n        while (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n            // Сдвинуть nums[j] на одну позицию вправо\n            nums[j + 1] = nums[j];\n            j--;\n        }\n        // Поместить base в правильную позицию\n        nums[j + 1] = base;\n    }\n}\n</code></pre> insertion_sort.kt<pre><code>/* Сортировка вставками */\nfun insertionSort(nums: IntArray) {\n    // Внешний цикл: отсортированные элементы равны 1, 2, ..., n\n    for (i in nums.indices) {\n        val base = nums[i]\n        var j = i - 1\n        // Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n        while (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n            nums[j + 1] = nums[j] // Сдвинуть nums[j] на одну позицию вправо\n            j--\n        }\n        nums[j + 1] = base        // Поместить base в правильную позицию\n    }\n}\n</code></pre> insertion_sort.rb<pre><code>### Сортировка вставками ###\ndef insertion_sort(nums)\n  n = nums.length\n  # Внешний цикл: отсортированный диапазон [0, i-1]\n  for i in 1...n\n    base = nums[i]\n    j = i - 1\n    # Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n    while j &gt;= 0 &amp;&amp; nums[j] &gt; base\n      nums[j + 1] = nums[j] # Сдвинуть nums[j] на одну позицию вправо\n      j -= 1\n    end\n    nums[j + 1] = base # Поместить base в правильную позицию\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 11. Сортировка","11.4 &nbsp; Сортировка вставками"],"tags":[]},{"location":"chapter_sorting/insertion_sort/#1142","level":2,"title":"11.4.2   Характеристики алгоритма","text":"<ul> <li>Временная сложность равна \\(O(n^2)\\), алгоритм адаптивен: в худшем случае каждой операции вставки требуется соответственно \\(n - 1\\), \\(n-2\\), \\(\\dots\\), \\(2\\), \\(1\\) итераций, а их сумма равна \\((n - 1) n / 2\\) , поэтому временная сложность равна \\(O(n^2)\\) . Если входные данные уже упорядочены, операция вставки завершается раньше. Когда входной массив полностью отсортирован, сортировка вставками достигает лучшей временной сложности \\(O(n)\\) .</li> <li>Пространственная сложность равна \\(O(1)\\), сортировка выполняется на месте: указатели \\(i\\) и \\(j\\) используют константный объем дополнительной памяти.</li> <li>Стабильная сортировка: в процессе вставки элементы помещаются справа от равных им элементов, поэтому их относительный порядок не меняется.</li> </ul>","path":["Глава 11. Сортировка","11.4 &nbsp; Сортировка вставками"],"tags":[]},{"location":"chapter_sorting/insertion_sort/#1143","level":2,"title":"11.4.3   Преимущества сортировки вставками","text":"<p>Временная сложность сортировки вставками равна \\(O(n^2)\\) , а у быстрой сортировки, которую мы скоро изучим, временная сложность равна \\(O(n \\log n)\\) . Несмотря на более высокую асимптотическую сложность, на малых объемах данных сортировка вставками обычно работает быстрее.</p> <p>Этот вывод похож на сравнение линейного и двоичного поиска. Алгоритмы уровня \\(O(n \\log n)\\) , такие как быстрая сортировка, относятся к алгоритмам на основе стратегии \"разделяй и властвуй\" и обычно включают больше элементарных вычислений. Когда объем данных мал, значения \\(n^2\\) и \\(n \\log n\\) близки друг к другу, поэтому асимптотика не доминирует, а решающим становится число элементарных операций в каждом раунде.</p> <p>На практике встроенные функции сортировки во многих языках программирования (например, в Java) используют сортировку вставками. Общая идея такова: для длинных массивов применять алгоритмы сортировки на основе стратегии \"разделяй и властвуй\", например быструю сортировку; для коротких массивов сразу использовать сортировку вставками.</p> <p>Хотя сортировка пузырьком, выбором и вставками имеют одинаковую временную сложность \\(O(n^2)\\) , в реальных задачах сортировка вставками используется заметно чаще, чем сортировка пузырьком и сортировка выбором. Основные причины таковы.</p> <ul> <li>Сортировка пузырьком основана на обмене элементов, для чего нужна временная переменная и суммарно выполняются 3 элементарные операции; сортировка вставками основана на присваивании элементов и требует всего 1 элементарной операции. Поэтому вычислительные затраты сортировки пузырьком обычно выше, чем у сортировки вставками.</li> <li>Временная сложность сортировки выбором в любом случае равна \\(O(n^2)\\) . Если входные данные уже частично упорядочены, сортировка вставками обычно эффективнее сортировки выбором.</li> <li>Сортировка выбором нестабильна, поэтому ее нельзя использовать для многоуровневой сортировки.</li> </ul>","path":["Глава 11. Сортировка","11.4 &nbsp; Сортировка вставками"],"tags":[]},{"location":"chapter_sorting/merge_sort/","level":1,"title":"11.6   Сортировка слиянием","text":"<p>Сортировка слиянием (merge sort) - это алгоритм сортировки на основе стратегии \"разделяй и властвуй\", который включает этапы \"разделения\" и \"слияния\", показанные на рисунке 11-10.</p> <ol> <li>Этап разделения: массив рекурсивно разбивается от середины, и задача сортировки длинного массива превращается в задачи сортировки более коротких массивов.</li> <li>Этап слияния: когда длина подмассива становится равной 1, разделение завершается и начинается слияние; левые и правые короткие упорядоченные массивы непрерывно объединяются в более длинный упорядоченный массив, пока процесс не завершится.</li> </ol> <p></p> <p> Рисунок 11-10   Этапы разделения и слияния в сортировке слиянием </p>","path":["Глава 11. Сортировка","11.6 &nbsp; Сортировка слиянием"],"tags":[]},{"location":"chapter_sorting/merge_sort/#1161","level":2,"title":"11.6.1   Алгоритм","text":"<p>Как показано на рисунке 11-11, на этапе \"разделения\" массив рекурсивно разбивается сверху вниз по середине на два подмассива.</p> <ol> <li>Вычислить середину массива <code>mid</code> и рекурсивно разделить левый подмассив (интервал <code>[left, mid]</code> ) и правый подмассив (интервал <code>[mid + 1, right]</code> ).</li> <li>Рекурсивно повторять шаг <code>1.</code> , пока длина подмассива не станет равной 1.</li> </ol> <p>Этап \"слияния\" снизу вверх объединяет левый и правый подмассивы в один упорядоченный массив. Следует заметить, что начиная с подмассивов длины 1, каждый подмассив в фазе слияния уже является упорядоченным.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 11-11   Шаги сортировки слиянием </p> <p>Нетрудно заметить, что порядок рекурсии в сортировке слиянием совпадает с порядком рекурсии при постфиксном обходе бинарного дерева.</p> <ul> <li>Постфиксный обход: сначала рекурсивно обходится левое поддерево, затем правое поддерево, а в конце обрабатывается корневой узел.</li> <li>Сортировка слиянием: сначала рекурсивно обрабатывается левый подмассив, затем правый подмассив, а в конце выполняется слияние.</li> </ul> <p>Реализация сортировки слиянием показана в коде ниже. Обратите внимание: в <code>nums</code> объединяемый интервал равен <code>[left, right]</code> , а соответствующий интервал в <code>tmp</code> равен <code>[0, right - left]</code> .</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby merge_sort.py<pre><code>def merge(nums: list[int], left: int, mid: int, right: int):\n    \"\"\"Объединить левый и правый подмассивы\"\"\"\n    # Диапазон левого подмассива: [left, mid], диапазон правого подмассива: [mid+1, right]\n    # Создать временный массив tmp для хранения результата слияния\n    tmp = [0] * (right - left + 1)\n    # Инициализировать начальные индексы левого и правого подмассивов\n    i, j, k = left, mid + 1, 0\n    # Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n    while i &lt;= mid and j &lt;= right:\n        if nums[i] &lt;= nums[j]:\n            tmp[k] = nums[i]\n            i += 1\n        else:\n            tmp[k] = nums[j]\n            j += 1\n        k += 1\n    # Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n    while i &lt;= mid:\n        tmp[k] = nums[i]\n        i += 1\n        k += 1\n    while j &lt;= right:\n        tmp[k] = nums[j]\n        j += 1\n        k += 1\n    # Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n    for k in range(0, len(tmp)):\n        nums[left + k] = tmp[k]\n\ndef merge_sort(nums: list[int], left: int, right: int):\n    \"\"\"Сортировка слиянием\"\"\"\n    # Условие завершения\n    if left &gt;= right:\n        return  # Завершить рекурсию, когда длина подмассива равна 1\n    # Этап разбиения\n    mid = (left + right) // 2 # Вычислить середину\n    merge_sort(nums, left, mid)  # Рекурсивно обработать левый подмассив\n    merge_sort(nums, mid + 1, right)  # Рекурсивно обработать правый подмассив\n    # Этап слияния\n    merge(nums, left, mid, right)\n</code></pre> merge_sort.cpp<pre><code>/* Объединить левый и правый подмассивы */\nvoid merge(vector&lt;int&gt; &amp;nums, int left, int mid, int right) {\n    // Диапазон левого подмассива: [left, mid], диапазон правого подмассива: [mid+1, right]\n    // Создать временный массив tmp для хранения результата слияния\n    vector&lt;int&gt; tmp(right - left + 1);\n    // Инициализировать начальные индексы левого и правого подмассивов\n    int i = left, j = mid + 1, k = 0;\n    // Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n    while (i &lt;= mid &amp;&amp; j &lt;= right) {\n        if (nums[i] &lt;= nums[j])\n            tmp[k++] = nums[i++];\n        else\n            tmp[k++] = nums[j++];\n    }\n    // Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n    while (i &lt;= mid) {\n        tmp[k++] = nums[i++];\n    }\n    while (j &lt;= right) {\n        tmp[k++] = nums[j++];\n    }\n    // Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n    for (k = 0; k &lt; tmp.size(); k++) {\n        nums[left + k] = tmp[k];\n    }\n}\n\n/* Сортировка слиянием */\nvoid mergeSort(vector&lt;int&gt; &amp;nums, int left, int right) {\n    // Условие завершения\n    if (left &gt;= right)\n        return; // Завершить рекурсию, когда длина подмассива равна 1\n    // Этап разбиения\n    int mid = left + (right - left) / 2;    // Вычислить середину\n    mergeSort(nums, left, mid);      // Рекурсивно обработать левый подмассив\n    mergeSort(nums, mid + 1, right); // Рекурсивно обработать правый подмассив\n    // Этап слияния\n    merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.java<pre><code>/* Объединить левый и правый подмассивы */\nvoid merge(int[] nums, int left, int mid, int right) {\n    // Диапазон левого подмассива: [left, mid], диапазон правого подмассива: [mid+1, right]\n    // Создать временный массив tmp для хранения результата слияния\n    int[] tmp = new int[right - left + 1];\n    // Инициализировать начальные индексы левого и правого подмассивов\n    int i = left, j = mid + 1, k = 0;\n    // Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n    while (i &lt;= mid &amp;&amp; j &lt;= right) {\n        if (nums[i] &lt;= nums[j])\n            tmp[k++] = nums[i++];\n        else\n            tmp[k++] = nums[j++];\n    }\n    // Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n    while (i &lt;= mid) {\n        tmp[k++] = nums[i++];\n    }\n    while (j &lt;= right) {\n        tmp[k++] = nums[j++];\n    }\n    // Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n    for (k = 0; k &lt; tmp.length; k++) {\n        nums[left + k] = tmp[k];\n    }\n}\n\n/* Сортировка слиянием */\nvoid mergeSort(int[] nums, int left, int right) {\n    // Условие завершения\n    if (left &gt;= right)\n        return; // Завершить рекурсию, когда длина подмассива равна 1\n    // Этап разбиения\n    int mid = left + (right - left) / 2; // Вычислить середину\n    mergeSort(nums, left, mid); // Рекурсивно обработать левый подмассив\n    mergeSort(nums, mid + 1, right); // Рекурсивно обработать правый подмассив\n    // Этап слияния\n    merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.cs<pre><code>/* Объединить левый и правый подмассивы */\nvoid Merge(int[] nums, int left, int mid, int right) {\n    // Диапазон левого подмассива: [left, mid], диапазон правого подмассива: [mid+1, right]\n    // Создать временный массив tmp для хранения результата слияния\n    int[] tmp = new int[right - left + 1];\n    // Инициализировать начальные индексы левого и правого подмассивов\n    int i = left, j = mid + 1, k = 0;\n    // Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n    while (i &lt;= mid &amp;&amp; j &lt;= right) {\n        if (nums[i] &lt;= nums[j])\n            tmp[k++] = nums[i++];\n        else\n            tmp[k++] = nums[j++];\n    }\n    // Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n    while (i &lt;= mid) {\n        tmp[k++] = nums[i++];\n    }\n    while (j &lt;= right) {\n        tmp[k++] = nums[j++];\n    }\n    // Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n    for (k = 0; k &lt; tmp.Length; ++k) {\n        nums[left + k] = tmp[k];\n    }\n}\n\n/* Сортировка слиянием */\nvoid MergeSort(int[] nums, int left, int right) {\n    // Условие завершения\n    if (left &gt;= right) return;       // Завершить рекурсию, когда длина подмассива равна 1\n    // Этап разбиения\n    int mid = left + (right - left) / 2;    // Вычислить середину\n    MergeSort(nums, left, mid);      // Рекурсивно обработать левый подмассив\n    MergeSort(nums, mid + 1, right); // Рекурсивно обработать правый подмассив\n    // Этап слияния\n    Merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.go<pre><code>/* Объединить левый и правый подмассивы */\nfunc merge(nums []int, left, mid, right int) {\n    // Диапазон левого подмассива: [left, mid], диапазон правого подмассива: [mid+1, right]\n    // Создать временный массив tmp для хранения результата слияния\n    tmp := make([]int, right-left+1)\n    // Инициализировать начальные индексы левого и правого подмассивов\n    i, j, k := left, mid+1, 0\n    // Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n    for i &lt;= mid &amp;&amp; j &lt;= right {\n        if nums[i] &lt;= nums[j] {\n            tmp[k] = nums[i]\n            i++\n        } else {\n            tmp[k] = nums[j]\n            j++\n        }\n        k++\n    }\n    // Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n    for i &lt;= mid {\n        tmp[k] = nums[i]\n        i++\n        k++\n    }\n    for j &lt;= right {\n        tmp[k] = nums[j]\n        j++\n        k++\n    }\n    // Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n    for k := 0; k &lt; len(tmp); k++ {\n        nums[left+k] = tmp[k]\n    }\n}\n\n/* Сортировка слиянием */\nfunc mergeSort(nums []int, left, right int) {\n    // Условие завершения\n    if left &gt;= right {\n        return\n    }\n    // Этап разбиения\n    mid := left + (right - left) / 2\n    mergeSort(nums, left, mid)\n    mergeSort(nums, mid+1, right)\n    // Этап слияния\n    merge(nums, left, mid, right)\n}\n</code></pre> merge_sort.swift<pre><code>/* Объединить левый и правый подмассивы */\nfunc merge(nums: inout [Int], left: Int, mid: Int, right: Int) {\n    // Диапазон левого подмассива: [left, mid], диапазон правого подмассива: [mid+1, right]\n    // Создать временный массив tmp для хранения результата слияния\n    var tmp = Array(repeating: 0, count: right - left + 1)\n    // Инициализировать начальные индексы левого и правого подмассивов\n    var i = left, j = mid + 1, k = 0\n    // Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n    while i &lt;= mid, j &lt;= right {\n        if nums[i] &lt;= nums[j] {\n            tmp[k] = nums[i]\n            i += 1\n        } else {\n            tmp[k] = nums[j]\n            j += 1\n        }\n        k += 1\n    }\n    // Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n    while i &lt;= mid {\n        tmp[k] = nums[i]\n        i += 1\n        k += 1\n    }\n    while j &lt;= right {\n        tmp[k] = nums[j]\n        j += 1\n        k += 1\n    }\n    // Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n    for k in tmp.indices {\n        nums[left + k] = tmp[k]\n    }\n}\n\n/* Сортировка слиянием */\nfunc mergeSort(nums: inout [Int], left: Int, right: Int) {\n    // Условие завершения\n    if left &gt;= right { // Завершить рекурсию, когда длина подмассива равна 1\n        return\n    }\n    // Этап разбиения\n    let mid = left + (right - left) / 2 // Вычислить середину\n    mergeSort(nums: &amp;nums, left: left, right: mid) // Рекурсивно обработать левый подмассив\n    mergeSort(nums: &amp;nums, left: mid + 1, right: right) // Рекурсивно обработать правый подмассив\n    // Этап слияния\n    merge(nums: &amp;nums, left: left, mid: mid, right: right)\n}\n</code></pre> merge_sort.js<pre><code>/* Объединить левый и правый подмассивы */\nfunction merge(nums, left, mid, right) {\n    // Диапазон левого подмассива: [left, mid], диапазон правого подмассива: [mid+1, right]\n    // Создать временный массив tmp для хранения результата слияния\n    const tmp = new Array(right - left + 1);\n    // Инициализировать начальные индексы левого и правого подмассивов\n    let i = left,\n        j = mid + 1,\n        k = 0;\n    // Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n    while (i &lt;= mid &amp;&amp; j &lt;= right) {\n        if (nums[i] &lt;= nums[j]) {\n            tmp[k++] = nums[i++];\n        } else {\n            tmp[k++] = nums[j++];\n        }\n    }\n    // Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n    while (i &lt;= mid) {\n        tmp[k++] = nums[i++];\n    }\n    while (j &lt;= right) {\n        tmp[k++] = nums[j++];\n    }\n    // Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n    for (k = 0; k &lt; tmp.length; k++) {\n        nums[left + k] = tmp[k];\n    }\n}\n\n/* Сортировка слиянием */\nfunction mergeSort(nums, left, right) {\n    // Условие завершения\n    if (left &gt;= right) return; // Завершить рекурсию, когда длина подмассива равна 1\n    // Этап разбиения\n    let mid = Math.floor(left + (right - left) / 2); // Вычислить середину\n    mergeSort(nums, left, mid); // Рекурсивно обработать левый подмассив\n    mergeSort(nums, mid + 1, right); // Рекурсивно обработать правый подмассив\n    // Этап слияния\n    merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.ts<pre><code>/* Объединить левый и правый подмассивы */\nfunction merge(nums: number[], left: number, mid: number, right: number): void {\n    // Диапазон левого подмассива: [left, mid], диапазон правого подмассива: [mid+1, right]\n    // Создать временный массив tmp для хранения результата слияния\n    const tmp = new Array(right - left + 1);\n    // Инициализировать начальные индексы левого и правого подмассивов\n    let i = left,\n        j = mid + 1,\n        k = 0;\n    // Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n    while (i &lt;= mid &amp;&amp; j &lt;= right) {\n        if (nums[i] &lt;= nums[j]) {\n            tmp[k++] = nums[i++];\n        } else {\n            tmp[k++] = nums[j++];\n        }\n    }\n    // Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n    while (i &lt;= mid) {\n        tmp[k++] = nums[i++];\n    }\n    while (j &lt;= right) {\n        tmp[k++] = nums[j++];\n    }\n    // Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n    for (k = 0; k &lt; tmp.length; k++) {\n        nums[left + k] = tmp[k];\n    }\n}\n\n/* Сортировка слиянием */\nfunction mergeSort(nums: number[], left: number, right: number): void {\n    // Условие завершения\n    if (left &gt;= right) return; // Завершить рекурсию, когда длина подмассива равна 1\n    // Этап разбиения\n    let mid = Math.floor(left + (right - left) / 2); // Вычислить середину\n    mergeSort(nums, left, mid); // Рекурсивно обработать левый подмассив\n    mergeSort(nums, mid + 1, right); // Рекурсивно обработать правый подмассив\n    // Этап слияния\n    merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.dart<pre><code>/* Объединить левый и правый подмассивы */\nvoid merge(List&lt;int&gt; nums, int left, int mid, int right) {\n  // Диапазон левого подмассива: [left, mid], диапазон правого подмассива: [mid+1, right]\n  // Создать временный массив tmp для хранения результата слияния\n  List&lt;int&gt; tmp = List.filled(right - left + 1, 0);\n  // Инициализировать начальные индексы левого и правого подмассивов\n  int i = left, j = mid + 1, k = 0;\n  // Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n  while (i &lt;= mid &amp;&amp; j &lt;= right) {\n    if (nums[i] &lt;= nums[j])\n      tmp[k++] = nums[i++];\n    else\n      tmp[k++] = nums[j++];\n  }\n  // Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n  while (i &lt;= mid) {\n    tmp[k++] = nums[i++];\n  }\n  while (j &lt;= right) {\n    tmp[k++] = nums[j++];\n  }\n  // Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n  for (k = 0; k &lt; tmp.length; k++) {\n    nums[left + k] = tmp[k];\n  }\n}\n\n/* Сортировка слиянием */\nvoid mergeSort(List&lt;int&gt; nums, int left, int right) {\n  // Условие завершения\n  if (left &gt;= right) return; // Завершить рекурсию, когда длина подмассива равна 1\n  // Этап разбиения\n  int mid = left + (right - left) ~/ 2; // Вычислить середину\n  mergeSort(nums, left, mid); // Рекурсивно обработать левый подмассив\n  mergeSort(nums, mid + 1, right); // Рекурсивно обработать правый подмассив\n  // Этап слияния\n  merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.rs<pre><code>/* Объединить левый и правый подмассивы */\nfn merge(nums: &amp;mut [i32], left: usize, mid: usize, right: usize) {\n    // Диапазон левого подмассива: [left, mid], диапазон правого подмассива: [mid+1, right]\n    // Создать временный массив tmp для хранения результата слияния\n    let tmp_size = right - left + 1;\n    let mut tmp = vec![0; tmp_size];\n    // Инициализировать начальные индексы левого и правого подмассивов\n    let (mut i, mut j, mut k) = (left, mid + 1, 0);\n    // Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n    while i &lt;= mid &amp;&amp; j &lt;= right {\n        if nums[i] &lt;= nums[j] {\n            tmp[k] = nums[i];\n            i += 1;\n        } else {\n            tmp[k] = nums[j];\n            j += 1;\n        }\n        k += 1;\n    }\n    // Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n    while i &lt;= mid {\n        tmp[k] = nums[i];\n        k += 1;\n        i += 1;\n    }\n    while j &lt;= right {\n        tmp[k] = nums[j];\n        k += 1;\n        j += 1;\n    }\n    // Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n    for k in 0..tmp_size {\n        nums[left + k] = tmp[k];\n    }\n}\n\n/* Сортировка слиянием */\nfn merge_sort(nums: &amp;mut [i32], left: usize, right: usize) {\n    // Условие завершения\n    if left &gt;= right {\n        return; // Завершить рекурсию, когда длина подмассива равна 1\n    }\n\n    // Этап разбиения\n    let mid = left + (right - left) / 2; // Вычислить середину\n    merge_sort(nums, left, mid); // Рекурсивно обработать левый подмассив\n    merge_sort(nums, mid + 1, right); // Рекурсивно обработать правый подмассив\n\n    // Этап слияния\n    merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.c<pre><code>/* Объединить левый и правый подмассивы */\nvoid merge(int *nums, int left, int mid, int right) {\n    // Диапазон левого подмассива: [left, mid], диапазон правого подмассива: [mid+1, right]\n    // Создать временный массив tmp для хранения результата слияния\n    int tmpSize = right - left + 1;\n    int *tmp = (int *)malloc(tmpSize * sizeof(int));\n    // Инициализировать начальные индексы левого и правого подмассивов\n    int i = left, j = mid + 1, k = 0;\n    // Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n    while (i &lt;= mid &amp;&amp; j &lt;= right) {\n        if (nums[i] &lt;= nums[j]) {\n            tmp[k++] = nums[i++];\n        } else {\n            tmp[k++] = nums[j++];\n        }\n    }\n    // Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n    while (i &lt;= mid) {\n        tmp[k++] = nums[i++];\n    }\n    while (j &lt;= right) {\n        tmp[k++] = nums[j++];\n    }\n    // Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n    for (k = 0; k &lt; tmpSize; ++k) {\n        nums[left + k] = tmp[k];\n    }\n    // Освободить память\n    free(tmp);\n}\n\n/* Сортировка слиянием */\nvoid mergeSort(int *nums, int left, int right) {\n    // Условие завершения\n    if (left &gt;= right)\n        return; // Завершить рекурсию, когда длина подмассива равна 1\n    // Этап разбиения\n    int mid = left + (right - left) / 2;    // Вычислить середину\n    mergeSort(nums, left, mid);      // Рекурсивно обработать левый подмассив\n    mergeSort(nums, mid + 1, right); // Рекурсивно обработать правый подмассив\n    // Этап слияния\n    merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.kt<pre><code>/* Объединить левый и правый подмассивы */\nfun merge(nums: IntArray, left: Int, mid: Int, right: Int) {\n    // Диапазон левого подмассива: [left, mid], диапазон правого подмассива: [mid+1, right]\n    // Создать временный массив tmp для хранения результата слияния\n    val tmp = IntArray(right - left + 1)\n    // Инициализировать начальные индексы левого и правого подмассивов\n    var i = left\n    var j = mid + 1\n    var k = 0\n    // Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n    while (i &lt;= mid &amp;&amp; j &lt;= right) {\n        if (nums[i] &lt;= nums[j])\n            tmp[k++] = nums[i++]\n        else\n            tmp[k++] = nums[j++]\n    }\n    // Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n    while (i &lt;= mid) {\n        tmp[k++] = nums[i++]\n    }\n    while (j &lt;= right) {\n        tmp[k++] = nums[j++]\n    }\n    // Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n    for (l in tmp.indices) {\n        nums[left + l] = tmp[l]\n    }\n}\n\n/* Сортировка слиянием */\nfun mergeSort(nums: IntArray, left: Int, right: Int) {\n    // Условие завершения\n    if (left &gt;= right) return  // Завершить рекурсию, когда длина подмассива равна 1\n    // Этап разбиения\n    val mid = left + (right - left) / 2 // Вычислить середину\n    mergeSort(nums, left, mid) // Рекурсивно обработать левый подмассив\n    mergeSort(nums, mid + 1, right) // Рекурсивно обработать правый подмассив\n    // Этап слияния\n    merge(nums, left, mid, right)\n}\n</code></pre> merge_sort.rb<pre><code>### Слияние левого и правого подмассивов ###\ndef merge(nums, left, mid, right)\n  # Интервал левого подмассива: [left, mid], правого подмассива: [mid+1, right]\n  # Создать временный массив tmp для хранения результата слияния\n  tmp = Array.new(right - left + 1, 0)\n  # Инициализировать начальные индексы левого и правого подмассивов\n  i, j, k = left, mid + 1, 0\n  # Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n  while i &lt;= mid &amp;&amp; j &lt;= right\n    if nums[i] &lt;= nums[j]\n      tmp[k] = nums[i]\n      i += 1\n    else\n      tmp[k] = nums[j]\n      j += 1\n    end\n    k += 1\n  end\n  # Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n  while i &lt;= mid\n    tmp[k] = nums[i]\n    i += 1\n    k += 1\n  end\n  while j &lt;= right\n    tmp[k] = nums[j]\n    j += 1\n    k += 1\n  end\n  # Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n  (0...tmp.length).each do |k|\n    nums[left + k] = tmp[k]\n  end\nend\n\n### Сортировка слиянием ###\ndef merge_sort(nums, left, right)\n  # Условие завершения\n  # Когда длина подмассива равна 1, рекурсия завершается\n  return if left &gt;= right\n  # Этап разбиения\n  mid = left + (right - left) / 2 # Вычислить середину\n  merge_sort(nums, left, mid) # Рекурсивно обработать левый подмассив\n  merge_sort(nums, mid + 1, right) # Рекурсивно обработать правый подмассив\n  # Этап слияния\n  merge(nums, left, mid, right)\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 11. Сортировка","11.6 &nbsp; Сортировка слиянием"],"tags":[]},{"location":"chapter_sorting/merge_sort/#1162","level":2,"title":"11.6.2   Характеристики алгоритма","text":"<ul> <li>Временная сложность равна \\(O(n \\log n)\\), алгоритм не является адаптивным: этап разделения создает дерево рекурсии высоты \\(\\log n\\) , а суммарное число операций слияния на каждом уровне равно \\(n\\) , поэтому общая временная сложность составляет \\(O(n \\log n)\\) .</li> <li>Пространственная сложность равна \\(O(n)\\), сортировка не выполняется на месте: глубина рекурсии равна \\(\\log n\\) , из-за чего требуется \\(O(\\log n)\\) памяти под стек вызовов. Для этапа слияния нужен вспомогательный массив, поэтому дополнительно используется \\(O(n)\\) памяти.</li> <li>Стабильная сортировка: в процессе слияния относительный порядок равных элементов не меняется.</li> </ul>","path":["Глава 11. Сортировка","11.6 &nbsp; Сортировка слиянием"],"tags":[]},{"location":"chapter_sorting/merge_sort/#1163","level":2,"title":"11.6.3   Сортировка связного списка","text":"<p>Для связных списков сортировка слиянием имеет заметное преимущество перед другими алгоритмами сортировки: пространственную сложность задачи сортировки списка можно оптимизировать до \\(O(1)\\).</p> <ul> <li>Этап разделения: работу по разбиению списка можно реализовать с помощью \"итерации\" вместо \"рекурсии\", тем самым устранив расход памяти на стек вызовов.</li> <li>Этап слияния: в связном списке добавление и удаление узлов требует только изменения ссылок (указателей), поэтому при слиянии двух коротких упорядоченных списков в один длинный упорядоченный список не нужно создавать дополнительный список.</li> </ul> <p>Детали реализации достаточно сложны; заинтересованные читатели могут изучить соответствующие материалы самостоятельно.</p>","path":["Глава 11. Сортировка","11.6 &nbsp; Сортировка слиянием"],"tags":[]},{"location":"chapter_sorting/quick_sort/","level":1,"title":"11.5   Быстрая сортировка","text":"<p>Быстрая сортировка (quick sort) - это алгоритм сортировки, основанный на стратегии \"разделяй и властвуй\"; он работает эффективно и применяется очень широко.</p> <p>Ключевая операция быстрой сортировки - это \"разделение с опорным элементом\". Ее цель такова: выбрать некоторый элемент массива в качестве \"опорного\" и переместить все элементы меньше опорного влево от него, а все элементы больше опорного - вправо. Конкретный процесс показан на рисунке 11-8.</p> <ol> <li>Выбрать самый левый элемент массива как опорный и инициализировать два указателя <code>i</code> и <code>j</code> , направленные на левую и правую границы массива.</li> <li>Запустить цикл, в котором <code>i</code> и <code>j</code> ищут соответственно первый элемент, больший опорного, и первый элемент, меньший опорного, после чего эти два элемента меняются местами.</li> <li>Повторять шаг <code>2.</code> , пока указатели <code>i</code> и <code>j</code> не встретятся, а затем обменять опорный элемент с элементом на границе двух подмассивов.</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 11-8   Шаги разделения с опорным элементом </p> <p>После завершения разделения исходный массив разбивается на три части: левый подмассив, опорный элемент и правый подмассив; при этом выполняется условие \"любой элемент левого подмассива \\(\\leq\\) опорный элемент \\(\\leq\\) любой элемент правого подмассива\". Следовательно, далее нам нужно лишь отсортировать эти два подмассива.</p> <p>Стратегия divide and conquer в быстрой сортировке</p> <p>По сути, разделение с опорным элементом сводит задачу сортировки длинного массива к двум задачам сортировки более коротких массивов.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby quick_sort.py<pre><code>def partition(self, nums: list[int], left: int, right: int) -&gt; int:\n    \"\"\"Разбиение с опорными указателями\"\"\"\n    # Взять nums[left] в качестве опорного элемента\n    i, j = left, right\n    while i &lt; j:\n        while i &lt; j and nums[j] &gt;= nums[left]:\n            j -= 1  # Идти справа налево в поисках первого элемента меньше опорного\n        while i &lt; j and nums[i] &lt;= nums[left]:\n            i += 1  # Идти слева направо в поисках первого элемента больше опорного\n        # Обмен элементов\n        nums[i], nums[j] = nums[j], nums[i]\n    # Переместить опорный элемент на границу двух подмассивов\n    nums[i], nums[left] = nums[left], nums[i]\n    return i  # Вернуть индекс опорного элемента\n</code></pre> quick_sort.cpp<pre><code>/* Разбиение с опорными указателями */\nint partition(vector&lt;int&gt; &amp;nums, int left, int right) {\n    // Взять nums[left] в качестве опорного элемента\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--;                // Идти справа налево в поисках первого элемента меньше опорного\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;                // Идти слева направо в поисках первого элемента больше опорного\n        swap(nums[i], nums[j]); // Поменять эти два элемента местами\n    }\n    swap(nums[i], nums[left]);  // Переместить опорный элемент на границу двух подмассивов\n    return i;                   // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.java<pre><code>/* Обмен элементов */\nvoid swap(int[] nums, int i, int j) {\n    int tmp = nums[i];\n    nums[i] = nums[j];\n    nums[j] = tmp;\n}\n\n/* Разбиение с опорными указателями */\nint partition(int[] nums, int left, int right) {\n    // Взять nums[left] в качестве опорного элемента\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--;          // Идти справа налево в поисках первого элемента меньше опорного\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;          // Идти слева направо в поисках первого элемента больше опорного\n        swap(nums, i, j); // Поменять эти два элемента местами\n    }\n    swap(nums, i, left);  // Переместить опорный элемент на границу двух подмассивов\n    return i;             // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.cs<pre><code>/* Обмен элементов */\nvoid Swap(int[] nums, int i, int j) {\n    (nums[j], nums[i]) = (nums[i], nums[j]);\n}\n\n/* Разбиение с опорными указателями */\nint Partition(int[] nums, int left, int right) {\n    // Взять nums[left] в качестве опорного элемента\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--;          // Идти справа налево в поисках первого элемента меньше опорного\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;          // Идти слева направо в поисках первого элемента больше опорного\n        Swap(nums, i, j); // Поменять эти два элемента местами\n    }\n    Swap(nums, i, left);  // Переместить опорный элемент на границу двух подмассивов\n    return i;             // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.go<pre><code>/* Разбиение с опорными указателями */\nfunc (q *quickSort) partition(nums []int, left, right int) int {\n    // Взять nums[left] в качестве опорного элемента\n    i, j := left, right\n    for i &lt; j {\n        for i &lt; j &amp;&amp; nums[j] &gt;= nums[left] {\n            j-- // Идти справа налево в поисках первого элемента меньше опорного\n        }\n        for i &lt; j &amp;&amp; nums[i] &lt;= nums[left] {\n            i++ // Идти слева направо в поисках первого элемента больше опорного\n        }\n        // Обмен элементов\n        nums[i], nums[j] = nums[j], nums[i]\n    }\n    // Переместить опорный элемент на границу двух подмассивов\n    nums[i], nums[left] = nums[left], nums[i]\n    return i // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.swift<pre><code>/* Разбиение с опорными указателями */\nfunc partition(nums: inout [Int], left: Int, right: Int) -&gt; Int {\n    // Взять nums[left] в качестве опорного элемента\n    var i = left\n    var j = right\n    while i &lt; j {\n        while i &lt; j, nums[j] &gt;= nums[left] {\n            j -= 1 // Идти справа налево в поисках первого элемента меньше опорного\n        }\n        while i &lt; j, nums[i] &lt;= nums[left] {\n            i += 1 // Идти слева направо в поисках первого элемента больше опорного\n        }\n        nums.swapAt(i, j) // Поменять эти два элемента местами\n    }\n    nums.swapAt(i, left) // Переместить опорный элемент на границу двух подмассивов\n    return i // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.js<pre><code>/* Обмен элементов */\nswap(nums, i, j) {\n    let tmp = nums[i];\n    nums[i] = nums[j];\n    nums[j] = tmp;\n}\n\n/* Разбиение с опорными указателями */\npartition(nums, left, right) {\n    // Взять nums[left] в качестве опорного элемента\n    let i = left,\n        j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) {\n            j -= 1; // Идти справа налево в поисках первого элемента меньше опорного\n        }\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) {\n            i += 1; // Идти слева направо в поисках первого элемента больше опорного\n        }\n        // Обмен элементов\n        this.swap(nums, i, j); // Поменять эти два элемента местами\n    }\n    this.swap(nums, i, left); // Переместить опорный элемент на границу двух подмассивов\n    return i; // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.ts<pre><code>/* Обмен элементов */\nswap(nums: number[], i: number, j: number): void {\n    let tmp = nums[i];\n    nums[i] = nums[j];\n    nums[j] = tmp;\n}\n\n/* Разбиение с опорными указателями */\npartition(nums: number[], left: number, right: number): number {\n    // Взять nums[left] в качестве опорного элемента\n    let i = left,\n        j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) {\n            j -= 1; // Идти справа налево в поисках первого элемента меньше опорного\n        }\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) {\n            i += 1; // Идти слева направо в поисках первого элемента больше опорного\n        }\n        // Обмен элементов\n        this.swap(nums, i, j); // Поменять эти два элемента местами\n    }\n    this.swap(nums, i, left); // Переместить опорный элемент на границу двух подмассивов\n    return i; // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.dart<pre><code>/* Обмен элементов */\nvoid _swap(List&lt;int&gt; nums, int i, int j) {\n  int tmp = nums[i];\n  nums[i] = nums[j];\n  nums[j] = tmp;\n}\n\n/* Разбиение с опорными указателями */\nint _partition(List&lt;int&gt; nums, int left, int right) {\n  // Взять nums[left] в качестве опорного элемента\n  int i = left, j = right;\n  while (i &lt; j) {\n    while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) j--; // Идти справа налево в поисках первого элемента меньше опорного\n    while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) i++; // Идти слева направо в поисках первого элемента больше опорного\n    _swap(nums, i, j); // Поменять эти два элемента местами\n  }\n  _swap(nums, i, left); // Переместить опорный элемент на границу двух подмассивов\n  return i; // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.rs<pre><code>/* Разбиение с опорными указателями */\nfn partition(nums: &amp;mut [i32], left: usize, right: usize) -&gt; usize {\n    // Взять nums[left] в качестве опорного элемента\n    let (mut i, mut j) = (left, right);\n    while i &lt; j {\n        while i &lt; j &amp;&amp; nums[j] &gt;= nums[left] {\n            j -= 1; // Идти справа налево в поисках первого элемента меньше опорного\n        }\n        while i &lt; j &amp;&amp; nums[i] &lt;= nums[left] {\n            i += 1; // Идти слева направо в поисках первого элемента больше опорного\n        }\n        nums.swap(i, j); // Поменять эти два элемента местами\n    }\n    nums.swap(i, left); // Переместить опорный элемент на границу двух подмассивов\n    i // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.c<pre><code>/* Обмен элементов */\nvoid swap(int nums[], int i, int j) {\n    int tmp = nums[i];\n    nums[i] = nums[j];\n    nums[j] = tmp;\n}\n\n/* Разбиение с опорными указателями */\nint partition(int nums[], int left, int right) {\n    // Взять nums[left] в качестве опорного элемента\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) {\n            j--; // Идти справа налево в поисках первого элемента меньше опорного\n        }\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) {\n            i++; // Идти слева направо в поисках первого элемента больше опорного\n        }\n        // Поменять эти два элемента местами\n        swap(nums, i, j);\n    }\n    // Переместить опорный элемент на границу двух подмассивов\n    swap(nums, i, left);\n    // Вернуть индекс опорного элемента\n    return i;\n}\n</code></pre> quick_sort.kt<pre><code>/* Обмен элементов */\nfun swap(nums: IntArray, i: Int, j: Int) {\n    val temp = nums[i]\n    nums[i] = nums[j]\n    nums[j] = temp\n}\n\n/* Разбиение с опорными указателями */\nfun partition(nums: IntArray, left: Int, right: Int): Int {\n    // Взять nums[left] в качестве опорного элемента\n    var i = left\n    var j = right\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--           // Идти справа налево в поисках первого элемента меньше опорного\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++           // Идти слева направо в поисках первого элемента больше опорного\n        swap(nums, i, j)  // Поменять эти два элемента местами\n    }\n    swap(nums, i, left)   // Переместить опорный элемент на границу двух подмассивов\n    return i              // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.rb<pre><code>### Разбиение с опорными указателями ###\ndef partition(nums, left, right)\n  # Взять nums[left] в качестве опорного элемента\n  i, j = left, right\n  while i &lt; j\n    while i &lt; j &amp;&amp; nums[j] &gt;= nums[left]\n      j -= 1 # Идти справа налево в поисках первого элемента меньше опорного\n    end\n    while i &lt; j &amp;&amp; nums[i] &lt;= nums[left]\n      i += 1 # Идти слева направо в поисках первого элемента больше опорного\n    end\n    # Обмен элементов\n    nums[i], nums[j] = nums[j], nums[i]\n  end\n  # Переместить опорный элемент на границу двух подмассивов\n  nums[i], nums[left] = nums[left], nums[i]\n  i # Вернуть индекс опорного элемента\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 11. Сортировка","11.5 &nbsp; Быстрая сортировка"],"tags":[]},{"location":"chapter_sorting/quick_sort/#1151","level":2,"title":"11.5.1   Алгоритм","text":"<p>Общий процесс быстрой сортировки показан на рисунке 11-9.</p> <ol> <li>Сначала выполнить \"разделение с опорным элементом\" для исходного массива и получить неотсортированные левый и правый подмассивы.</li> <li>Затем рекурсивно выполнить \"разделение с опорным элементом\" для левого и правого подмассивов.</li> <li>Продолжать рекурсию до тех пор, пока длина подмассива не станет равной 1; после этого сортировка всего массива будет завершена.</li> </ol> <p></p> <p> Рисунок 11-9   Процесс быстрой сортировки </p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby quick_sort.py<pre><code>def quick_sort(self, nums: list[int], left: int, right: int):\n    \"\"\"Быстрая сортировка\"\"\"\n    # Завершить рекурсию, когда длина подмассива равна 1\n    if left &gt;= right:\n        return\n    # Разбиение с опорными указателями\n    pivot = self.partition(nums, left, right)\n    # Рекурсивно обработать левый и правый подмассивы\n    self.quick_sort(nums, left, pivot - 1)\n    self.quick_sort(nums, pivot + 1, right)\n</code></pre> quick_sort.cpp<pre><code>/* Быстрая сортировка */\nvoid quickSort(vector&lt;int&gt; &amp;nums, int left, int right) {\n    // Завершить рекурсию, когда длина подмассива равна 1\n    if (left &gt;= right)\n        return;\n    // Разбиение с опорными указателями\n    int pivot = partition(nums, left, right);\n    // Рекурсивно обработать левый и правый подмассивы\n    quickSort(nums, left, pivot - 1);\n    quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.java<pre><code>/* Быстрая сортировка */\nvoid quickSort(int[] nums, int left, int right) {\n    // Завершить рекурсию, когда длина подмассива равна 1\n    if (left &gt;= right)\n        return;\n    // Разбиение с опорными указателями\n    int pivot = partition(nums, left, right);\n    // Рекурсивно обработать левый и правый подмассивы\n    quickSort(nums, left, pivot - 1);\n    quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.cs<pre><code>/* Быстрая сортировка */\nvoid QuickSort(int[] nums, int left, int right) {\n    // Завершить рекурсию, когда длина подмассива равна 1\n    if (left &gt;= right)\n        return;\n    // Разбиение с опорными указателями\n    int pivot = Partition(nums, left, right);\n    // Рекурсивно обработать левый и правый подмассивы\n    QuickSort(nums, left, pivot - 1);\n    QuickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.go<pre><code>/* Быстрая сортировка */\nfunc (q *quickSort) quickSort(nums []int, left, right int) {\n    // Завершить рекурсию, когда длина подмассива равна 1\n    if left &gt;= right {\n        return\n    }\n    // Разбиение с опорными указателями\n    pivot := q.partition(nums, left, right)\n    // Рекурсивно обработать левый и правый подмассивы\n    q.quickSort(nums, left, pivot-1)\n    q.quickSort(nums, pivot+1, right)\n}\n</code></pre> quick_sort.swift<pre><code>/* Быстрая сортировка */\nfunc quickSort(nums: inout [Int], left: Int, right: Int) {\n    // Завершить рекурсию, когда длина подмассива равна 1\n    if left &gt;= right {\n        return\n    }\n    // Разбиение с опорными указателями\n    let pivot = partition(nums: &amp;nums, left: left, right: right)\n    // Рекурсивно обработать левый и правый подмассивы\n    quickSort(nums: &amp;nums, left: left, right: pivot - 1)\n    quickSort(nums: &amp;nums, left: pivot + 1, right: right)\n}\n</code></pre> quick_sort.js<pre><code>/* Быстрая сортировка */\nquickSort(nums, left, right) {\n    // Завершить рекурсию, когда длина подмассива равна 1\n    if (left &gt;= right) return;\n    // Разбиение с опорными указателями\n    const pivot = this.partition(nums, left, right);\n    // Рекурсивно обработать левый и правый подмассивы\n    this.quickSort(nums, left, pivot - 1);\n    this.quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.ts<pre><code>/* Быстрая сортировка */\nquickSort(nums: number[], left: number, right: number): void {\n    // Завершить рекурсию, когда длина подмассива равна 1\n    if (left &gt;= right) {\n        return;\n    }\n    // Разбиение с опорными указателями\n    const pivot = this.partition(nums, left, right);\n    // Рекурсивно обработать левый и правый подмассивы\n    this.quickSort(nums, left, pivot - 1);\n    this.quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.dart<pre><code>/* Быстрая сортировка */\nvoid quickSort(List&lt;int&gt; nums, int left, int right) {\n  // Завершить рекурсию, когда длина подмассива равна 1\n  if (left &gt;= right) return;\n  // Разбиение с опорными указателями\n  int pivot = _partition(nums, left, right);\n  // Рекурсивно обработать левый и правый подмассивы\n  quickSort(nums, left, pivot - 1);\n  quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.rs<pre><code>/* Быстрая сортировка */\npub fn quick_sort(left: i32, right: i32, nums: &amp;mut [i32]) {\n    // Завершить рекурсию, когда длина подмассива равна 1\n    if left &gt;= right {\n        return;\n    }\n    // Разбиение с опорными указателями\n    let pivot = Self::partition(nums, left as usize, right as usize) as i32;\n    // Рекурсивно обработать левый и правый подмассивы\n    Self::quick_sort(left, pivot - 1, nums);\n    Self::quick_sort(pivot + 1, right, nums);\n}\n</code></pre> quick_sort.c<pre><code>/* Быстрая сортировка */\nvoid quickSort(int nums[], int left, int right) {\n    // Завершить рекурсию, когда длина подмассива равна 1\n    if (left &gt;= right) {\n        return;\n    }\n    // Разбиение с опорными указателями\n    int pivot = partition(nums, left, right);\n    // Рекурсивно обработать левый и правый подмассивы\n    quickSort(nums, left, pivot - 1);\n    quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.kt<pre><code>/* Быстрая сортировка */\nfun quickSort(nums: IntArray, left: Int, right: Int) {\n    // Завершить рекурсию, когда длина подмассива равна 1\n    if (left &gt;= right) return\n    // Разбиение с опорными указателями\n    val pivot = partition(nums, left, right)\n    // Рекурсивно обработать левый и правый подмассивы\n    quickSort(nums, left, pivot - 1)\n    quickSort(nums, pivot + 1, right)\n}\n</code></pre> quick_sort.rb<pre><code>### Класс быстрой сортировки ###\ndef quick_sort(nums, left, right)\n  # Рекурсивно обрабатывать, пока длина подмассива не станет равной 1\n  if left &lt; right\n    # Разбиение с опорными указателями\n    pivot = partition(nums, left, right)\n    # Рекурсивно обработать левый и правый подмассивы\n    quick_sort(nums, left, pivot - 1)\n    quick_sort(nums, pivot + 1, right)\n  end\n  nums\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 11. Сортировка","11.5 &nbsp; Быстрая сортировка"],"tags":[]},{"location":"chapter_sorting/quick_sort/#1152","level":2,"title":"11.5.2   Характеристики алгоритма","text":"<ul> <li>Временная сложность равна \\(O(n \\log n)\\), алгоритм не является адаптивным: в среднем глубина рекурсии при разделении равна \\(\\log n\\) , а суммарное число циклов на каждом уровне равно \\(n\\) , поэтому общая сложность составляет \\(O(n \\log n)\\) . В худшем случае каждое разделение делит массив длины \\(n\\) на подмассивы длины \\(0\\) и \\(n - 1\\) ; тогда глубина рекурсии достигает \\(n\\) , на каждом уровне выполняется \\(n\\) операций, и общая временная сложность вырождается в \\(O(n^2)\\) .</li> <li>Пространственная сложность равна \\(O(n)\\), сортировка выполняется на месте: если входной массив полностью отсортирован в обратном порядке, глубина рекурсии достигает худшего случая \\(n\\) , что требует \\(O(n)\\) памяти под стек вызовов. При этом сама сортировка выполняется в исходном массиве без дополнительного массива.</li> <li>Нестабильная сортировка: на последнем шаге разделения опорный элемент может быть обменян вправо от равного ему элемента.</li> </ul>","path":["Глава 11. Сортировка","11.5 &nbsp; Быстрая сортировка"],"tags":[]},{"location":"chapter_sorting/quick_sort/#1153","level":2,"title":"11.5.3   Почему быстрая сортировка быстрая","text":"<p>Уже по названию понятно, что быстрая сортировка должна иметь преимущества по эффективности. Хотя ее средняя временная сложность совпадает со сложностью \"сортировки слиянием\" и \"пирамидальной сортировки\", на практике быстрая сортировка обычно работает быстрее. Основные причины таковы.</p> <ul> <li>Вероятность худшего случая очень мала: хотя худшая временная сложность быстрой сортировки равна \\(O(n^2)\\) и она не так стабильна, как сортировка слиянием, в подавляющем большинстве случаев она работает за \\(O(n \\log n)\\) .</li> <li>Высокая эффективность использования кэша: при выполнении разделения система может загрузить весь подмассив в кэш, поэтому доступ к элементам оказывается быстрым. Алгоритмы вроде \"пирамидальной сортировки\" требуют скачкообразного доступа к элементам и таким свойством не обладают.</li> <li>Небольшой константный множитель в сложности: среди трех перечисленных алгоритмов у быстрой сортировки обычно меньше всего сравнений, присваиваний и обменов. Это похоже на причину, по которой \"сортировка вставками\" часто быстрее \"сортировки пузырьком\".</li> </ul>","path":["Глава 11. Сортировка","11.5 &nbsp; Быстрая сортировка"],"tags":[]},{"location":"chapter_sorting/quick_sort/#1154","level":2,"title":"11.5.4   Оптимизация выбора опорного элемента","text":"<p>На некоторых входных данных временная эффективность быстрой сортировки может ухудшаться. Рассмотрим крайний случай: входной массив полностью отсортирован в обратном порядке. Поскольку в качестве опорного мы выбираем самый левый элемент, после разделения он будет обменян в самый правый конец массива, из-за чего длина левого подмассива станет \\(n - 1\\) , а длина правого - \\(0\\) . Если рекурсия будет продолжаться таким образом, то после каждого разделения один из подмассивов будет иметь длину \\(0\\) , стратегия divide and conquer потеряет смысл, а быстрая сортировка выродится в нечто близкое к \"сортировке пузырьком\".</p> <p>Чтобы по возможности избежать такого сценария, мы можем улучшить стратегию выбора опорного элемента в процедуре разделения. Например, можно выбирать случайный элемент массива как опорный. Однако если не повезет и каждый раз будет выбираться неудачный опорный элемент, производительность все равно останется неудовлетворительной.</p> <p>Нужно учитывать, что языки программирования обычно генерируют \"псевдослучайные числа\". Если специально построить тестовый пример под такую последовательность, эффективность быстрой сортировки все равно может деградировать.</p> <p>Чтобы улучшить ситуацию, можно взять три кандидата (обычно первый, последний и средний элементы массива) и использовать медиану этих трех значений как опорный элемент. Благодаря этому вероятность того, что опорный элемент окажется \"не слишком маленьким и не слишком большим\", заметно возрастает. Конечно, можно брать и большее число кандидатов, чтобы еще сильнее повысить устойчивость алгоритма. После этого вероятность деградации временной сложности до \\(O(n^2)\\) существенно уменьшается.</p> <p>Пример кода:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby quick_sort.py<pre><code>def median_three(self, nums: list[int], left: int, mid: int, right: int) -&gt; int:\n    \"\"\"Выбрать медиану из трех кандидатов\"\"\"\n    l, m, r = nums[left], nums[mid], nums[right]\n    if (l &lt;= m &lt;= r) or (r &lt;= m &lt;= l):\n        return mid  # m находится между l и r\n    if (m &lt;= l &lt;= r) or (r &lt;= l &lt;= m):\n        return left  # l находится между m и r\n    return right\n\ndef partition(self, nums: list[int], left: int, right: int) -&gt; int:\n    \"\"\"Разбиение с опорными указателями (медиана трех)\"\"\"\n    # Взять nums[left] в качестве опорного элемента\n    med = self.median_three(nums, left, (left + right) // 2, right)\n    # Переместить медиану в крайний левый элемент массива\n    nums[left], nums[med] = nums[med], nums[left]\n    # Взять nums[left] в качестве опорного элемента\n    i, j = left, right\n    while i &lt; j:\n        while i &lt; j and nums[j] &gt;= nums[left]:\n            j -= 1  # Идти справа налево в поисках первого элемента меньше опорного\n        while i &lt; j and nums[i] &lt;= nums[left]:\n            i += 1  # Идти слева направо в поисках первого элемента больше опорного\n        # Обмен элементов\n        nums[i], nums[j] = nums[j], nums[i]\n    # Переместить опорный элемент на границу двух подмассивов\n    nums[i], nums[left] = nums[left], nums[i]\n    return i  # Вернуть индекс опорного элемента\n</code></pre> quick_sort.cpp<pre><code>/* Выбрать медиану из трех кандидатов */\nint medianThree(vector&lt;int&gt; &amp;nums, int left, int mid, int right) {\n    int l = nums[left], m = nums[mid], r = nums[right];\n    if ((l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l))\n        return mid; // m находится между l и r\n    if ((m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m))\n        return left; // l находится между m и r\n    return right;\n}\n\n/* Разбиение с опорными указателями (медиана трех) */\nint partition(vector&lt;int&gt; &amp;nums, int left, int right) {\n    // Выбрать медиану из трех кандидатов\n    int med = medianThree(nums, left, (left + right) / 2, right);\n    // Переместить медиану в крайний левый элемент массива\n    swap(nums[left], nums[med]);\n    // Взять nums[left] в качестве опорного элемента\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--;                // Идти справа налево в поисках первого элемента меньше опорного\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;                // Идти слева направо в поисках первого элемента больше опорного\n        swap(nums[i], nums[j]); // Поменять эти два элемента местами\n    }\n    swap(nums[i], nums[left]);  // Переместить опорный элемент на границу двух подмассивов\n    return i;                   // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.java<pre><code>/* Выбрать медиану из трех кандидатов */\nint medianThree(int[] nums, int left, int mid, int right) {\n    int l = nums[left], m = nums[mid], r = nums[right];\n    if ((l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l))\n        return mid; // m находится между l и r\n    if ((m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m))\n        return left; // l находится между m и r\n    return right;\n}\n\n/* Разбиение с опорными указателями (медиана трех) */\nint partition(int[] nums, int left, int right) {\n    // Выбрать медиану из трех кандидатов\n    int med = medianThree(nums, left, (left + right) / 2, right);\n    // Переместить медиану в крайний левый элемент массива\n    swap(nums, left, med);\n    // Взять nums[left] в качестве опорного элемента\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--;          // Идти справа налево в поисках первого элемента меньше опорного\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;          // Идти слева направо в поисках первого элемента больше опорного\n        swap(nums, i, j); // Поменять эти два элемента местами\n    }\n    swap(nums, i, left);  // Переместить опорный элемент на границу двух подмассивов\n    return i;             // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.cs<pre><code>/* Выбрать медиану из трех кандидатов */\nint MedianThree(int[] nums, int left, int mid, int right) {\n    int l = nums[left], m = nums[mid], r = nums[right];\n    if ((l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l))\n        return mid; // m находится между l и r\n    if ((m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m))\n        return left; // l находится между m и r\n    return right;\n}\n\n/* Разбиение с опорными указателями (медиана трех) */\nint Partition(int[] nums, int left, int right) {\n    // Выбрать медиану из трех кандидатов\n    int med = MedianThree(nums, left, (left + right) / 2, right);\n    // Переместить медиану в крайний левый элемент массива\n    Swap(nums, left, med);\n    // Взять nums[left] в качестве опорного элемента\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--;          // Идти справа налево в поисках первого элемента меньше опорного\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;          // Идти слева направо в поисках первого элемента больше опорного\n        Swap(nums, i, j); // Поменять эти два элемента местами\n    }\n    Swap(nums, i, left);  // Переместить опорный элемент на границу двух подмассивов\n    return i;             // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.go<pre><code>/* Выбрать медиану из трех кандидатов */\nfunc (q *quickSortMedian) medianThree(nums []int, left, mid, right int) int {\n    l, m, r := nums[left], nums[mid], nums[right]\n    if (l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l) {\n        return mid // m находится между l и r\n    }\n    if (m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m) {\n        return left // l находится между m и r\n    }\n    return right\n}\n\n/* Разбиение с опорными указателями (медиана трех) */\nfunc (q *quickSortMedian) partition(nums []int, left, right int) int {\n    // Взять nums[left] в качестве опорного элемента\n    med := q.medianThree(nums, left, (left+right)/2, right)\n    // Переместить медиану в крайний левый элемент массива\n    nums[left], nums[med] = nums[med], nums[left]\n    // Взять nums[left] в качестве опорного элемента\n    i, j := left, right\n    for i &lt; j {\n        for i &lt; j &amp;&amp; nums[j] &gt;= nums[left] {\n            j-- // Идти справа налево в поисках первого элемента меньше опорного\n        }\n        for i &lt; j &amp;&amp; nums[i] &lt;= nums[left] {\n            i++ // Идти слева направо в поисках первого элемента больше опорного\n        }\n        // Обмен элементов\n        nums[i], nums[j] = nums[j], nums[i]\n    }\n    // Переместить опорный элемент на границу двух подмассивов\n    nums[i], nums[left] = nums[left], nums[i]\n    return i // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.swift<pre><code>/* Выбрать медиану из трех кандидатов */\nfunc medianThree(nums: [Int], left: Int, mid: Int, right: Int) -&gt; Int {\n    let l = nums[left]\n    let m = nums[mid]\n    let r = nums[right]\n    if (l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l) {\n        return mid // m находится между l и r\n    }\n    if (m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m) {\n        return left // l находится между m и r\n    }\n    return right\n}\n\n/* Разбиение с опорными указателями (медиана трех) */\nfunc partitionMedian(nums: inout [Int], left: Int, right: Int) -&gt; Int {\n    // Выбрать медиану из трех кандидатов\n    let med = medianThree(nums: nums, left: left, mid: left + (right - left) / 2, right: right)\n    // Переместить медиану в крайний левый элемент массива\n    nums.swapAt(left, med)\n    return partition(nums: &amp;nums, left: left, right: right)\n}\n</code></pre> quick_sort.js<pre><code>/* Выбрать медиану из трех кандидатов */\nmedianThree(nums, left, mid, right) {\n    let l = nums[left],\n        m = nums[mid],\n        r = nums[right];\n    // m находится между l и r\n    if ((l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l)) return mid;\n    // l находится между m и r\n    if ((m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m)) return left;\n    return right;\n}\n\n/* Разбиение с опорными указателями (медиана трех) */\npartition(nums, left, right) {\n    // Выбрать медиану из трех кандидатов\n    let med = this.medianThree(\n        nums,\n        left,\n        Math.floor((left + right) / 2),\n        right\n    );\n    // Переместить медиану в крайний левый элемент массива\n    this.swap(nums, left, med);\n    // Взять nums[left] в качестве опорного элемента\n    let i = left,\n        j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) j--; // Идти справа налево в поисках первого элемента меньше опорного\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) i++; // Идти слева направо в поисках первого элемента больше опорного\n        this.swap(nums, i, j); // Поменять эти два элемента местами\n    }\n    this.swap(nums, i, left); // Переместить опорный элемент на границу двух подмассивов\n    return i; // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.ts<pre><code>/* Выбрать медиану из трех кандидатов */\nmedianThree(\n    nums: number[],\n    left: number,\n    mid: number,\n    right: number\n): number {\n    let l = nums[left],\n        m = nums[mid],\n        r = nums[right];\n    // m находится между l и r\n    if ((l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l)) return mid;\n    // l находится между m и r\n    if ((m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m)) return left;\n    return right;\n}\n\n/* Разбиение с опорными указателями (медиана трех) */\npartition(nums: number[], left: number, right: number): number {\n    // Выбрать медиану из трех кандидатов\n    let med = this.medianThree(\n        nums,\n        left,\n        Math.floor((left + right) / 2),\n        right\n    );\n    // Переместить медиану в крайний левый элемент массива\n    this.swap(nums, left, med);\n    // Взять nums[left] в качестве опорного элемента\n    let i = left,\n        j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) {\n            j--; // Идти справа налево в поисках первого элемента меньше опорного\n        }\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) {\n            i++; // Идти слева направо в поисках первого элемента больше опорного\n        }\n        this.swap(nums, i, j); // Поменять эти два элемента местами\n    }\n    this.swap(nums, i, left); // Переместить опорный элемент на границу двух подмассивов\n    return i; // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.dart<pre><code>/* Выбрать медиану из трех кандидатов */\nint _medianThree(List&lt;int&gt; nums, int left, int mid, int right) {\n  int l = nums[left], m = nums[mid], r = nums[right];\n  if ((l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l))\n    return mid; // m находится между l и r\n  if ((m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m))\n    return left; // l находится между m и r\n  return right;\n}\n\n/* Разбиение с опорными указателями (медиана трех) */\nint _partition(List&lt;int&gt; nums, int left, int right) {\n  // Выбрать медиану из трех кандидатов\n  int med = _medianThree(nums, left, (left + right) ~/ 2, right);\n  // Переместить медиану в крайний левый элемент массива\n  _swap(nums, left, med);\n  // Взять nums[left] в качестве опорного элемента\n  int i = left, j = right;\n  while (i &lt; j) {\n    while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) j--; // Идти справа налево в поисках первого элемента меньше опорного\n    while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) i++; // Идти слева направо в поисках первого элемента больше опорного\n    _swap(nums, i, j); // Поменять эти два элемента местами\n  }\n  _swap(nums, i, left); // Переместить опорный элемент на границу двух подмассивов\n  return i; // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.rs<pre><code>/* Выбрать медиану из трех кандидатов */\nfn median_three(nums: &amp;mut [i32], left: usize, mid: usize, right: usize) -&gt; usize {\n    let (l, m, r) = (nums[left], nums[mid], nums[right]);\n    if (l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l) {\n        return mid; // m находится между l и r\n    }\n    if (m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m) {\n        return left; // l находится между m и r\n    }\n    right\n}\n\n/* Разбиение с опорными указателями (медиана трех) */\nfn partition(nums: &amp;mut [i32], left: usize, right: usize) -&gt; usize {\n    // Выбрать медиану из трех кандидатов\n    let med = Self::median_three(nums, left, (left + right) / 2, right);\n    // Переместить медиану в крайний левый элемент массива\n    nums.swap(left, med);\n    // Взять nums[left] в качестве опорного элемента\n    let (mut i, mut j) = (left, right);\n    while i &lt; j {\n        while i &lt; j &amp;&amp; nums[j] &gt;= nums[left] {\n            j -= 1; // Идти справа налево в поисках первого элемента меньше опорного\n        }\n        while i &lt; j &amp;&amp; nums[i] &lt;= nums[left] {\n            i += 1; // Идти слева направо в поисках первого элемента больше опорного\n        }\n        nums.swap(i, j); // Поменять эти два элемента местами\n    }\n    nums.swap(i, left); // Переместить опорный элемент на границу двух подмассивов\n    i // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.c<pre><code>/* Выбрать медиану из трех кандидатов */\nint medianThree(int nums[], int left, int mid, int right) {\n    int l = nums[left], m = nums[mid], r = nums[right];\n    if ((l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l))\n        return mid; // m находится между l и r\n    if ((m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m))\n        return left; // l находится между m и r\n    return right;\n}\n\n/* Разбиение с опорными указателями (медиана трех) */\nint partitionMedian(int nums[], int left, int right) {\n    // Выбрать медиану из трех кандидатов\n    int med = medianThree(nums, left, (left + right) / 2, right);\n    // Переместить медиану в крайний левый элемент массива\n    swap(nums, left, med);\n    // Взять nums[left] в качестве опорного элемента\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--; // Идти справа налево в поисках первого элемента меньше опорного\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;          // Идти слева направо в поисках первого элемента больше опорного\n        swap(nums, i, j); // Поменять эти два элемента местами\n    }\n    swap(nums, i, left); // Переместить опорный элемент на границу двух подмассивов\n    return i;            // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.kt<pre><code>/* Выбрать медиану из трех кандидатов */\nfun medianThree(nums: IntArray, left: Int, mid: Int, right: Int): Int {\n    val l = nums[left]\n    val m = nums[mid]\n    val r = nums[right]\n    if ((m in l..r) || (m in r..l))\n        return mid  // m находится между l и r\n    if ((l in m..r) || (l in r..m))\n        return left // l находится между m и r\n    return right\n}\n\n/* Разбиение с опорными указателями (медиана трех) */\nfun partitionMedian(nums: IntArray, left: Int, right: Int): Int {\n    // Выбрать медиану из трех кандидатов\n    val med = medianThree(nums, left, (left + right) / 2, right)\n    // Переместить медиану в крайний левый элемент массива\n    swap(nums, left, med)\n    // Взять nums[left] в качестве опорного элемента\n    var i = left\n    var j = right\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--                      // Идти справа налево в поисках первого элемента меньше опорного\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++                      // Идти слева направо в поисках первого элемента больше опорного\n        swap(nums, i, j)             // Поменять эти два элемента местами\n    }\n    swap(nums, i, left)              // Переместить опорный элемент на границу двух подмассивов\n    return i                         // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.rb<pre><code>### Выбрать медиану из трех кандидатов ###\ndef median_three(nums, left, mid, right)\n  # Выбрать медиану из трех кандидатов\n  _l, _m, _r = nums[left], nums[mid], nums[right]\n  # m находится между l и r\n  return mid if (_l &lt;= _m &amp;&amp; _m &lt;= _r) || (_r &lt;= _m &amp;&amp; _m &lt;= _l)\n  # l находится между m и r\n  return left if (_m &lt;= _l &amp;&amp; _l &lt;= _r) || (_r &lt;= _l &amp;&amp; _l &lt;= _m)\n  return right\nend\n\n### Выбрать медиану из трех кандидатов ###\ndef median_three(nums, left, mid, right)\n  # Выбрать медиану из трех кандидатов\n  _l, _m, _r = nums[left], nums[mid], nums[right]\n  # m находится между l и r\n  return mid if (_l &lt;= _m &amp;&amp; _m &lt;= _r) || (_r &lt;= _m &amp;&amp; _m &lt;= _l)\n  # l находится между m и r\n  return left if (_m &lt;= _l &amp;&amp; _l &lt;= _r) || (_r &lt;= _l &amp;&amp; _l &lt;= _m)\n  return right\nend\n\n# ## Разбиение с опорными указателями (медиана трех) ###\ndef partition(nums, left, right)\n  # ## Использовать nums[left] как опорный элемент\n  med = median_three(nums, left, (left + right) / 2, right)\n  # Переместить медиану в крайний левый элемент массива\n  nums[left], nums[med] = nums[med], nums[left]\n  i, j = left, right\n  while i &lt; j\n    while i &lt; j &amp;&amp; nums[j] &gt;= nums[left]\n      j -= 1 # Идти справа налево в поисках первого элемента меньше опорного\n    end\n    while i &lt; j &amp;&amp; nums[i] &lt;= nums[left]\n      i += 1 # Идти слева направо в поисках первого элемента больше опорного\n    end\n    # Обмен элементов\n    nums[i], nums[j] = nums[j], nums[i]\n  end\n  # Переместить опорный элемент на границу двух подмассивов\n  nums[i], nums[left] = nums[left], nums[i]\n  i # Вернуть индекс опорного элемента\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 11. Сортировка","11.5 &nbsp; Быстрая сортировка"],"tags":[]},{"location":"chapter_sorting/quick_sort/#1155","level":2,"title":"11.5.5   Оптимизация глубины рекурсии","text":"<p>На некоторых входных данных быстрая сортировка может занимать слишком много памяти. Рассмотрим полностью отсортированный входной массив. Пусть длина текущего подмассива в рекурсии равна \\(m\\) ; тогда после каждого разделения будут получаться левый подмассив длины \\(0\\) и правый подмассив длины \\(m - 1\\) . Это означает, что на каждом уровне размер задачи уменьшается совсем немного (лишь на один элемент), а высота дерева рекурсии достигает \\(n - 1\\) , поэтому требуется \\(O(n)\\) памяти под стек вызовов.</p> <p>Чтобы избежать накопления стековых кадров, после каждого разделения можно сравнивать длины двух подмассивов и рекурсивно обрабатывать только более короткий из них. Поскольку длина короткого подмассива не превысит \\(n / 2\\) , такой подход гарантирует, что глубина рекурсии не превысит \\(\\log n\\) , а худшая пространственная сложность будет оптимизирована до \\(O(\\log n)\\) . Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby quick_sort.py<pre><code>def quick_sort(self, nums: list[int], left: int, right: int):\n    \"\"\"Быстрая сортировка (оптимизация глубины рекурсии)\"\"\"\n    # Завершить, когда длина подмассива равна 1\n    while left &lt; right:\n        # Операция разбиения с опорными указателями\n        pivot = self.partition(nums, left, right)\n        # Выполнить быструю сортировку для более короткого из двух подмассивов\n        if pivot - left &lt; right - pivot:\n            self.quick_sort(nums, left, pivot - 1)  # Рекурсивно отсортировать левый подмассив\n            left = pivot + 1  # Оставшийся неотсортированный диапазон: [pivot + 1, right]\n        else:\n            self.quick_sort(nums, pivot + 1, right)  # Рекурсивно отсортировать правый подмассив\n            right = pivot - 1  # Оставшийся неотсортированный диапазон: [left, pivot - 1]\n</code></pre> quick_sort.cpp<pre><code>/* Быстрая сортировка (оптимизация глубины рекурсии) */\nvoid quickSort(vector&lt;int&gt; &amp;nums, int left, int right) {\n    // Завершить, когда длина подмассива равна 1\n    while (left &lt; right) {\n        // Операция разбиения с опорными указателями\n        int pivot = partition(nums, left, right);\n        // Выполнить быструю сортировку для более короткого из двух подмассивов\n        if (pivot - left &lt; right - pivot) {\n            quickSort(nums, left, pivot - 1); // Рекурсивно отсортировать левый подмассив\n            left = pivot + 1;                 // Оставшийся неотсортированный диапазон: [pivot + 1, right]\n        } else {\n            quickSort(nums, pivot + 1, right); // Рекурсивно отсортировать правый подмассив\n            right = pivot - 1;                 // Оставшийся неотсортированный диапазон: [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.java<pre><code>/* Быстрая сортировка (оптимизация глубины рекурсии) */\nvoid quickSort(int[] nums, int left, int right) {\n    // Завершить, когда длина подмассива равна 1\n    while (left &lt; right) {\n        // Операция разбиения с опорными указателями\n        int pivot = partition(nums, left, right);\n        // Выполнить быструю сортировку для более короткого из двух подмассивов\n        if (pivot - left &lt; right - pivot) {\n            quickSort(nums, left, pivot - 1); // Рекурсивно отсортировать левый подмассив\n            left = pivot + 1; // Оставшийся неотсортированный диапазон: [pivot + 1, right]\n        } else {\n            quickSort(nums, pivot + 1, right); // Рекурсивно отсортировать правый подмассив\n            right = pivot - 1; // Оставшийся неотсортированный диапазон: [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.cs<pre><code>/* Быстрая сортировка (оптимизация глубины рекурсии) */\nvoid QuickSort(int[] nums, int left, int right) {\n    // Завершить, когда длина подмассива равна 1\n    while (left &lt; right) {\n        // Операция разбиения с опорными указателями\n        int pivot = Partition(nums, left, right);\n        // Выполнить быструю сортировку для более короткого из двух подмассивов\n        if (pivot - left &lt; right - pivot) {\n            QuickSort(nums, left, pivot - 1);  // Рекурсивно отсортировать левый подмассив\n            left = pivot + 1;  // Оставшийся неотсортированный диапазон: [pivot + 1, right]\n        } else {\n            QuickSort(nums, pivot + 1, right); // Рекурсивно отсортировать правый подмассив\n            right = pivot - 1; // Оставшийся неотсортированный диапазон: [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.go<pre><code>/* Быстрая сортировка (оптимизация глубины рекурсии) */\nfunc (q *quickSortTailCall) quickSort(nums []int, left, right int) {\n    // Завершить, когда длина подмассива равна 1\n    for left &lt; right {\n        // Операция разбиения с опорными указателями\n        pivot := q.partition(nums, left, right)\n        // Выполнить быструю сортировку для более короткого из двух подмассивов\n        if pivot-left &lt; right-pivot {\n            q.quickSort(nums, left, pivot-1) // Рекурсивно отсортировать левый подмассив\n            left = pivot + 1                 // Оставшийся неотсортированный диапазон: [pivot + 1, right]\n        } else {\n            q.quickSort(nums, pivot+1, right) // Рекурсивно отсортировать правый подмассив\n            right = pivot - 1                 // Оставшийся неотсортированный диапазон: [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.swift<pre><code>/* Быстрая сортировка (оптимизация глубины рекурсии) */\nfunc quickSortTailCall(nums: inout [Int], left: Int, right: Int) {\n    var left = left\n    var right = right\n    // Завершить, когда длина подмассива равна 1\n    while left &lt; right {\n        // Операция разбиения с опорными указателями\n        let pivot = partition(nums: &amp;nums, left: left, right: right)\n        // Выполнить быструю сортировку для более короткого из двух подмассивов\n        if (pivot - left) &lt; (right - pivot) {\n            quickSortTailCall(nums: &amp;nums, left: left, right: pivot - 1) // Рекурсивно отсортировать левый подмассив\n            left = pivot + 1 // Оставшийся неотсортированный диапазон: [pivot + 1, right]\n        } else {\n            quickSortTailCall(nums: &amp;nums, left: pivot + 1, right: right) // Рекурсивно отсортировать правый подмассив\n            right = pivot - 1 // Оставшийся неотсортированный диапазон: [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.js<pre><code>/* Быстрая сортировка (оптимизация глубины рекурсии) */\nquickSort(nums, left, right) {\n    // Завершить, когда длина подмассива равна 1\n    while (left &lt; right) {\n        // Операция разбиения с опорными указателями\n        let pivot = this.partition(nums, left, right);\n        // Выполнить быструю сортировку для более короткого из двух подмассивов\n        if (pivot - left &lt; right - pivot) {\n            this.quickSort(nums, left, pivot - 1); // Рекурсивно отсортировать левый подмассив\n            left = pivot + 1; // Оставшийся неотсортированный диапазон: [pivot + 1, right]\n        } else {\n            this.quickSort(nums, pivot + 1, right); // Рекурсивно отсортировать правый подмассив\n            right = pivot - 1; // Оставшийся неотсортированный диапазон: [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.ts<pre><code>/* Быстрая сортировка (оптимизация глубины рекурсии) */\nquickSort(nums: number[], left: number, right: number): void {\n    // Завершить, когда длина подмассива равна 1\n    while (left &lt; right) {\n        // Операция разбиения с опорными указателями\n        let pivot = this.partition(nums, left, right);\n        // Выполнить быструю сортировку для более короткого из двух подмассивов\n        if (pivot - left &lt; right - pivot) {\n            this.quickSort(nums, left, pivot - 1); // Рекурсивно отсортировать левый подмассив\n            left = pivot + 1; // Оставшийся неотсортированный диапазон: [pivot + 1, right]\n        } else {\n            this.quickSort(nums, pivot + 1, right); // Рекурсивно отсортировать правый подмассив\n            right = pivot - 1; // Оставшийся неотсортированный диапазон: [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.dart<pre><code>/* Быстрая сортировка (оптимизация глубины рекурсии) */\nvoid quickSort(List&lt;int&gt; nums, int left, int right) {\n  // Завершить, когда длина подмассива равна 1\n  while (left &lt; right) {\n    // Операция разбиения с опорными указателями\n    int pivot = _partition(nums, left, right);\n    // Выполнить быструю сортировку для более короткого из двух подмассивов\n    if (pivot - left &lt; right - pivot) {\n      quickSort(nums, left, pivot - 1); // Рекурсивно отсортировать левый подмассив\n      left = pivot + 1; // Оставшийся неотсортированный диапазон: [pivot + 1, right]\n    } else {\n      quickSort(nums, pivot + 1, right); // Рекурсивно отсортировать правый подмассив\n      right = pivot - 1; // Оставшийся неотсортированный диапазон: [left, pivot - 1]\n    }\n  }\n}\n</code></pre> quick_sort.rs<pre><code>/* Быстрая сортировка (оптимизация глубины рекурсии) */\npub fn quick_sort(mut left: i32, mut right: i32, nums: &amp;mut [i32]) {\n    // Завершить, когда длина подмассива равна 1\n    while left &lt; right {\n        // Операция разбиения с опорными указателями\n        let pivot = Self::partition(nums, left as usize, right as usize) as i32;\n        // Выполнить быструю сортировку для более короткого из двух подмассивов\n        if pivot - left &lt; right - pivot {\n            Self::quick_sort(left, pivot - 1, nums); // Рекурсивно отсортировать левый подмассив\n            left = pivot + 1; // Оставшийся неотсортированный диапазон: [pivot + 1, right]\n        } else {\n            Self::quick_sort(pivot + 1, right, nums); // Рекурсивно отсортировать правый подмассив\n            right = pivot - 1; // Оставшийся неотсортированный диапазон: [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.c<pre><code>/* Быстрая сортировка (оптимизация глубины рекурсии) */\nvoid quickSortTailCall(int nums[], int left, int right) {\n    // Завершить, когда длина подмассива равна 1\n    while (left &lt; right) {\n        // Операция разбиения с опорными указателями\n        int pivot = partition(nums, left, right);\n        // Выполнить быструю сортировку для более короткого из двух подмассивов\n        if (pivot - left &lt; right - pivot) {\n            // Рекурсивно отсортировать левый подмассив\n            quickSortTailCall(nums, left, pivot - 1);\n            // Оставшийся неотсортированный диапазон: [pivot + 1, right]\n            left = pivot + 1;\n        } else {\n            // Рекурсивно отсортировать правый подмассив\n            quickSortTailCall(nums, pivot + 1, right);\n            // Оставшийся неотсортированный диапазон: [left, pivot - 1]\n            right = pivot - 1;\n        }\n    }\n}\n</code></pre> quick_sort.kt<pre><code>/* Быстрая сортировка (оптимизация глубины рекурсии) */\nfun quickSortTailCall(nums: IntArray, left: Int, right: Int) {\n    // Завершить, когда длина подмассива равна 1\n    var l = left\n    var r = right\n    while (l &lt; r) {\n        // Операция разбиения с опорными указателями\n        val pivot = partition(nums, l, r)\n        // Выполнить быструю сортировку для более короткого из двух подмассивов\n        if (pivot - l &lt; r - pivot) {\n            quickSort(nums, l, pivot - 1) // Рекурсивно отсортировать левый подмассив\n            l = pivot + 1 // Оставшийся неотсортированный диапазон: [pivot + 1, right]\n        } else {\n            quickSort(nums, pivot + 1, r) // Рекурсивно отсортировать правый подмассив\n            r = pivot - 1 // Оставшийся неотсортированный диапазон: [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.rb<pre><code>### Разбиение с опорными указателями ###\ndef partition(nums, left, right)\n  # Использовать nums[left] как опорный элемент\n  i = left\n  j = right\n  while i &lt; j\n    while i &lt; j &amp;&amp; nums[j] &gt;= nums[left]\n      j -= 1 # Идти справа налево в поисках первого элемента меньше опорного\n    end\n    while i &lt; j &amp;&amp; nums[i] &lt;= nums[left]\n      i += 1 # Идти слева направо в поисках первого элемента больше опорного\n    end\n    # Обмен элементов\n    nums[i], nums[j] = nums[j], nums[i]\n  end\n  # Переместить опорный элемент на границу двух подмассивов\n  nums[i], nums[left] = nums[left], nums[i]\n  i # Вернуть индекс опорного элемента\nend\n\n# ## Быстрая сортировка (оптимизация глубины рекурсии) ###\ndef quick_sort(nums, left, right)\n  # Рекурсивно обрабатывать, пока длина подмассива не станет равной 1\n  while left &lt; right\n    # Разбиение с опорными указателями\n    pivot = partition(nums, left, right)\n    # Выполнить быструю сортировку для более короткого из двух подмассивов\n    if pivot - left &lt; right - pivot\n      quick_sort(nums, left, pivot - 1)\n      left = pivot + 1 # Оставшийся неотсортированный диапазон: [pivot + 1, right]\n    else\n      quick_sort(nums, pivot + 1, right)\n      right = pivot - 1 # Оставшийся неотсортированный диапазон: [left, pivot - 1]\n    end\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 11. Сортировка","11.5 &nbsp; Быстрая сортировка"],"tags":[]},{"location":"chapter_sorting/radix_sort/","level":1,"title":"11.10   Поразрядная сортировка","text":"<p>В предыдущем разделе мы познакомились с сортировкой подсчетом: она подходит для случаев, когда объем данных \\(n\\) велик, а диапазон значений \\(m\\) сравнительно мал. Предположим теперь, что нужно отсортировать \\(n = 10^6\\) студенческих идентификаторов, причем каждый идентификатор является \\(8\\)-значным числом. Тогда диапазон данных \\(m = 10^8\\) оказывается очень большим; сортировка подсчетом потребует огромного объема памяти, а поразрядная сортировка позволяет этого избежать.</p> <p>Поразрядная сортировка (radix sort) по своей основной идее совпадает с сортировкой подсчетом и тоже реализует сортировку через подсчет количества. Поверх этого поразрядная сортировка использует иерархию разрядов числа и последовательно сортирует данные по каждому разряду, получая итоговый упорядоченный результат.</p>","path":["Глава 11. Сортировка","11.10 &nbsp; Поразрядная сортировка"],"tags":[]},{"location":"chapter_sorting/radix_sort/#11101","level":2,"title":"11.10.1   Алгоритм","text":"<p>Рассмотрим пример со студенческими номерами: будем считать, что младший разряд имеет номер \\(1\\) , а старший - номер \\(8\\) . Тогда процесс поразрядной сортировки показан на рисунке 11-18.</p> <ol> <li>Инициализировать номер разряда \\(k = 1\\) .</li> <li>Выполнить \"сортировку подсчетом\" по \\(k\\)-му разряду студенческого номера. После этого данные будут упорядочены по \\(k\\)-му разряду по возрастанию.</li> <li>Увеличить \\(k\\) на \\(1\\) и вернуться к шагу <code>2.</code> , продолжая процесс, пока сортировка не будет выполнена для всех разрядов.</li> </ol> <p></p> <p> Рисунок 11-18   Процесс поразрядной сортировки </p> <p>Ниже разберем реализацию кода. Для числа \\(x\\) в системе счисления с основанием \\(d\\) получить его \\(k\\)-й разряд \\(x_k\\) можно по формуле:</p> \\[ x_k = \\lfloor\\frac{x}{d^{k-1}}\\rfloor \\bmod d \\] <p>где \\(\\lfloor a \\rfloor\\) обозначает округление числа \\(a\\) вниз, а \\(\\bmod \\: d\\) означает взятие остатка по модулю \\(d\\) . Для студенческих идентификаторов выполняется \\(d = 10\\) и \\(k \\in [1, 8]\\) .</p> <p>Кроме того, нам нужно слегка изменить код сортировки подсчетом, чтобы он мог сортировать числа по их \\(k\\)-му разряду:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby radix_sort.py<pre><code>def digit(num: int, exp: int) -&gt; int:\n    \"\"\"Получить k-й разряд элемента num, где exp = 10^(k-1)\"\"\"\n    # Передача exp вместо k позволяет избежать повторного дорогостоящего вычисления степени\n    return (num // exp) % 10\n\ndef counting_sort_digit(nums: list[int], exp: int):\n    \"\"\"Сортировка подсчетом (сортировка по k-му разряду nums)\"\"\"\n    # Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n    counter = [0] * 10\n    n = len(nums)\n    # Подсчитать число появлений каждой цифры от 0 до 9\n    for i in range(n):\n        d = digit(nums[i], exp)  # Получить k-й разряд nums[i], обозначив его как d\n        counter[d] += 1  # Подсчитать число появлений цифры d\n    # Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n    for i in range(1, 10):\n        counter[i] += counter[i - 1]\n    # Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n    res = [0] * n\n    for i in range(n - 1, -1, -1):\n        d = digit(nums[i], exp)\n        j = counter[d] - 1  # Получить индекс j цифры d в массиве\n        res[j] = nums[i]  # Поместить текущий элемент по индексу j\n        counter[d] -= 1  # Уменьшить количество d на 1\n    # Перезаписать исходный массив nums результатом\n    for i in range(n):\n        nums[i] = res[i]\n\ndef radix_sort(nums: list[int]):\n    \"\"\"Поразрядная сортировка\"\"\"\n    # Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n    m = max(nums)\n    # Проходить разряды от младшего к старшему\n    exp = 1\n    while exp &lt;= m:\n        # Выполнить сортировку подсчетом по k-му разряду элементов массива\n        # k = 1 -&gt; exp = 1\n        # k = 2 -&gt; exp = 10\n        # то есть exp = 10^(k-1)\n        counting_sort_digit(nums, exp)\n        exp *= 10\n</code></pre> radix_sort.cpp<pre><code>/* Получить k-й разряд элемента num, где exp = 10^(k-1) */\nint digit(int num, int exp) {\n    // Передача exp вместо k позволяет избежать повторного дорогостоящего вычисления степени\n    return (num / exp) % 10;\n}\n\n/* Сортировка подсчетом (сортировка по k-му разряду nums) */\nvoid countingSortDigit(vector&lt;int&gt; &amp;nums, int exp) {\n    // Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n    vector&lt;int&gt; counter(10, 0);\n    int n = nums.size();\n    // Подсчитать число появлений каждой цифры от 0 до 9\n    for (int i = 0; i &lt; n; i++) {\n        int d = digit(nums[i], exp); // Получить k-й разряд nums[i], обозначив его как d\n        counter[d]++;                // Подсчитать число появлений цифры d\n    }\n    // Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n    for (int i = 1; i &lt; 10; i++) {\n        counter[i] += counter[i - 1];\n    }\n    // Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n    vector&lt;int&gt; res(n, 0);\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int d = digit(nums[i], exp);\n        int j = counter[d] - 1; // Получить индекс j цифры d в массиве\n        res[j] = nums[i];       // Поместить текущий элемент по индексу j\n        counter[d]--;           // Уменьшить количество d на 1\n    }\n    // Перезаписать исходный массив nums результатом\n    for (int i = 0; i &lt; n; i++)\n        nums[i] = res[i];\n}\n\n/* Поразрядная сортировка */\nvoid radixSort(vector&lt;int&gt; &amp;nums) {\n    // Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n    int m = *max_element(nums.begin(), nums.end());\n    // Проходить разряды от младшего к старшему\n    for (int exp = 1; exp &lt;= m; exp *= 10)\n        // Выполнить сортировку подсчетом по k-му разряду элементов массива\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // то есть exp = 10^(k-1)\n        countingSortDigit(nums, exp);\n}\n</code></pre> radix_sort.java<pre><code>/* Получить k-й разряд элемента num, где exp = 10^(k-1) */\nint digit(int num, int exp) {\n    // Передача exp вместо k позволяет избежать повторного дорогостоящего вычисления степени\n    return (num / exp) % 10;\n}\n\n/* Сортировка подсчетом (сортировка по k-му разряду nums) */\nvoid countingSortDigit(int[] nums, int exp) {\n    // Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n    int[] counter = new int[10];\n    int n = nums.length;\n    // Подсчитать число появлений каждой цифры от 0 до 9\n    for (int i = 0; i &lt; n; i++) {\n        int d = digit(nums[i], exp); // Получить k-й разряд nums[i], обозначив его как d\n        counter[d]++;                // Подсчитать число появлений цифры d\n    }\n    // Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n    for (int i = 1; i &lt; 10; i++) {\n        counter[i] += counter[i - 1];\n    }\n    // Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n    int[] res = new int[n];\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int d = digit(nums[i], exp);\n        int j = counter[d] - 1; // Получить индекс j цифры d в массиве\n        res[j] = nums[i];       // Поместить текущий элемент по индексу j\n        counter[d]--;           // Уменьшить количество d на 1\n    }\n    // Перезаписать исходный массив nums результатом\n    for (int i = 0; i &lt; n; i++)\n        nums[i] = res[i];\n}\n\n/* Поразрядная сортировка */\nvoid radixSort(int[] nums) {\n    // Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n    int m = Integer.MIN_VALUE;\n    for (int num : nums)\n        if (num &gt; m)\n            m = num;\n    // Проходить разряды от младшего к старшему\n    for (int exp = 1; exp &lt;= m; exp *= 10) {\n        // Выполнить сортировку подсчетом по k-му разряду элементов массива\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // то есть exp = 10^(k-1)\n        countingSortDigit(nums, exp);\n    }\n}\n</code></pre> radix_sort.cs<pre><code>/* Получить k-й разряд элемента num, где exp = 10^(k-1) */\nint Digit(int num, int exp) {\n    // Передача exp вместо k позволяет избежать повторного дорогостоящего вычисления степени\n    return (num / exp) % 10;\n}\n\n/* Сортировка подсчетом (сортировка по k-му разряду nums) */\nvoid CountingSortDigit(int[] nums, int exp) {\n    // Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n    int[] counter = new int[10];\n    int n = nums.Length;\n    // Подсчитать число появлений каждой цифры от 0 до 9\n    for (int i = 0; i &lt; n; i++) {\n        int d = Digit(nums[i], exp); // Получить k-й разряд nums[i], обозначив его как d\n        counter[d]++;                // Подсчитать число появлений цифры d\n    }\n    // Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n    for (int i = 1; i &lt; 10; i++) {\n        counter[i] += counter[i - 1];\n    }\n    // Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n    int[] res = new int[n];\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int d = Digit(nums[i], exp);\n        int j = counter[d] - 1; // Получить индекс j цифры d в массиве\n        res[j] = nums[i];       // Поместить текущий элемент по индексу j\n        counter[d]--;           // Уменьшить количество d на 1\n    }\n    // Перезаписать исходный массив nums результатом\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = res[i];\n    }\n}\n\n/* Поразрядная сортировка */\nvoid RadixSort(int[] nums) {\n    // Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n    int m = int.MinValue;\n    foreach (int num in nums) {\n        if (num &gt; m) m = num;\n    }\n    // Проходить разряды от младшего к старшему\n    for (int exp = 1; exp &lt;= m; exp *= 10) {\n        // Выполнить сортировку подсчетом по k-му разряду элементов массива\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // то есть exp = 10^(k-1)\n        CountingSortDigit(nums, exp);\n    }\n}\n</code></pre> radix_sort.go<pre><code>/* Получить k-й разряд элемента num, где exp = 10^(k-1) */\nfunc digit(num, exp int) int {\n    // Передача exp вместо k позволяет избежать повторного дорогостоящего вычисления степени\n    return (num / exp) % 10\n}\n\n/* Сортировка подсчетом (сортировка по k-му разряду nums) */\nfunc countingSortDigit(nums []int, exp int) {\n    // Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n    counter := make([]int, 10)\n    n := len(nums)\n    // Подсчитать число появлений каждой цифры от 0 до 9\n    for i := 0; i &lt; n; i++ {\n        d := digit(nums[i], exp) // Получить k-й разряд nums[i], обозначив его как d\n        counter[d]++             // Подсчитать число появлений цифры d\n    }\n    // Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n    for i := 1; i &lt; 10; i++ {\n        counter[i] += counter[i-1]\n    }\n    // Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n    res := make([]int, n)\n    for i := n - 1; i &gt;= 0; i-- {\n        d := digit(nums[i], exp)\n        j := counter[d] - 1 // Получить индекс j цифры d в массиве\n        res[j] = nums[i]    // Поместить текущий элемент по индексу j\n        counter[d]--        // Уменьшить количество d на 1\n    }\n    // Перезаписать исходный массив nums результатом\n    for i := 0; i &lt; n; i++ {\n        nums[i] = res[i]\n    }\n}\n\n/* Поразрядная сортировка */\nfunc radixSort(nums []int) {\n    // Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n    max := math.MinInt\n    for _, num := range nums {\n        if num &gt; max {\n            max = num\n        }\n    }\n    // Проходить разряды от младшего к старшему\n    for exp := 1; max &gt;= exp; exp *= 10 {\n        // Выполнить сортировку подсчетом по k-му разряду элементов массива\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // то есть exp = 10^(k-1)\n        countingSortDigit(nums, exp)\n    }\n}\n</code></pre> radix_sort.swift<pre><code>/* Получить k-й разряд элемента num, где exp = 10^(k-1) */\nfunc digit(num: Int, exp: Int) -&gt; Int {\n    // Передача exp вместо k позволяет избежать повторного дорогостоящего вычисления степени\n    (num / exp) % 10\n}\n\n/* Сортировка подсчетом (сортировка по k-му разряду nums) */\nfunc countingSortDigit(nums: inout [Int], exp: Int) {\n    // Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n    var counter = Array(repeating: 0, count: 10)\n    // Подсчитать число появлений каждой цифры от 0 до 9\n    for i in nums.indices {\n        let d = digit(num: nums[i], exp: exp) // Получить k-й разряд nums[i], обозначив его как d\n        counter[d] += 1 // Подсчитать число появлений цифры d\n    }\n    // Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n    for i in 1 ..&lt; 10 {\n        counter[i] += counter[i - 1]\n    }\n    // Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n    var res = Array(repeating: 0, count: nums.count)\n    for i in nums.indices.reversed() {\n        let d = digit(num: nums[i], exp: exp)\n        let j = counter[d] - 1 // Получить индекс j цифры d в массиве\n        res[j] = nums[i] // Поместить текущий элемент по индексу j\n        counter[d] -= 1 // Уменьшить количество d на 1\n    }\n    // Перезаписать исходный массив nums результатом\n    for i in nums.indices {\n        nums[i] = res[i]\n    }\n}\n\n/* Поразрядная сортировка */\nfunc radixSort(nums: inout [Int]) {\n    // Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n    var m = Int.min\n    for num in nums {\n        if num &gt; m {\n            m = num\n        }\n    }\n    // Проходить разряды от младшего к старшему\n    for exp in sequence(first: 1, next: { m &gt;= ($0 * 10) ? $0 * 10 : nil }) {\n        // Выполнить сортировку подсчетом по k-му разряду элементов массива\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // то есть exp = 10^(k-1)\n        countingSortDigit(nums: &amp;nums, exp: exp)\n    }\n}\n</code></pre> radix_sort.js<pre><code>/* Получить k-й разряд элемента num, где exp = 10^(k-1) */\nfunction digit(num, exp) {\n    // Передача exp вместо k позволяет избежать повторного дорогостоящего вычисления степени\n    return Math.floor(num / exp) % 10;\n}\n\n/* Сортировка подсчетом (сортировка по k-му разряду nums) */\nfunction countingSortDigit(nums, exp) {\n    // Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n    const counter = new Array(10).fill(0);\n    const n = nums.length;\n    // Подсчитать число появлений каждой цифры от 0 до 9\n    for (let i = 0; i &lt; n; i++) {\n        const d = digit(nums[i], exp); // Получить k-й разряд nums[i], обозначив его как d\n        counter[d]++; // Подсчитать число появлений цифры d\n    }\n    // Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n    for (let i = 1; i &lt; 10; i++) {\n        counter[i] += counter[i - 1];\n    }\n    // Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n    const res = new Array(n).fill(0);\n    for (let i = n - 1; i &gt;= 0; i--) {\n        const d = digit(nums[i], exp);\n        const j = counter[d] - 1; // Получить индекс j цифры d в массиве\n        res[j] = nums[i]; // Поместить текущий элемент по индексу j\n        counter[d]--; // Уменьшить количество d на 1\n    }\n    // Перезаписать исходный массив nums результатом\n    for (let i = 0; i &lt; n; i++) {\n        nums[i] = res[i];\n    }\n}\n\n/* Поразрядная сортировка */\nfunction radixSort(nums) {\n    // Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n    let m = Math.max(... nums);\n    // Проходить разряды от младшего к старшему\n    for (let exp = 1; exp &lt;= m; exp *= 10) {\n        // Выполнить сортировку подсчетом по k-му разряду элементов массива\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // то есть exp = 10^(k-1)\n        countingSortDigit(nums, exp);\n    }\n}\n</code></pre> radix_sort.ts<pre><code>/* Получить k-й разряд элемента num, где exp = 10^(k-1) */\nfunction digit(num: number, exp: number): number {\n    // Передача exp вместо k позволяет избежать повторного дорогостоящего вычисления степени\n    return Math.floor(num / exp) % 10;\n}\n\n/* Сортировка подсчетом (сортировка по k-му разряду nums) */\nfunction countingSortDigit(nums: number[], exp: number): void {\n    // Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n    const counter = new Array(10).fill(0);\n    const n = nums.length;\n    // Подсчитать число появлений каждой цифры от 0 до 9\n    for (let i = 0; i &lt; n; i++) {\n        const d = digit(nums[i], exp); // Получить k-й разряд nums[i], обозначив его как d\n        counter[d]++; // Подсчитать число появлений цифры d\n    }\n    // Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n    for (let i = 1; i &lt; 10; i++) {\n        counter[i] += counter[i - 1];\n    }\n    // Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n    const res = new Array(n).fill(0);\n    for (let i = n - 1; i &gt;= 0; i--) {\n        const d = digit(nums[i], exp);\n        const j = counter[d] - 1; // Получить индекс j цифры d в массиве\n        res[j] = nums[i]; // Поместить текущий элемент по индексу j\n        counter[d]--; // Уменьшить количество d на 1\n    }\n    // Перезаписать исходный массив nums результатом\n    for (let i = 0; i &lt; n; i++) {\n        nums[i] = res[i];\n    }\n}\n\n/* Поразрядная сортировка */\nfunction radixSort(nums: number[]): void {\n    // Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n    let m: number = Math.max(... nums);\n    // Проходить разряды от младшего к старшему\n    for (let exp = 1; exp &lt;= m; exp *= 10) {\n        // Выполнить сортировку подсчетом по k-му разряду элементов массива\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // то есть exp = 10^(k-1)\n        countingSortDigit(nums, exp);\n    }\n}\n</code></pre> radix_sort.dart<pre><code>/* Получить k-й разряд элемента _num, где exp = 10^(k-1) */\nint digit(int _num, int exp) {\n  // Передача exp вместо k позволяет избежать повторного дорогостоящего вычисления степени\n  return (_num ~/ exp) % 10;\n}\n\n/* Сортировка подсчетом (сортировка по k-му разряду nums) */\nvoid countingSortDigit(List&lt;int&gt; nums, int exp) {\n  // Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n  List&lt;int&gt; counter = List&lt;int&gt;.filled(10, 0);\n  int n = nums.length;\n  // Подсчитать число появлений каждой цифры от 0 до 9\n  for (int i = 0; i &lt; n; i++) {\n    int d = digit(nums[i], exp); // Получить k-й разряд nums[i], обозначив его как d\n    counter[d]++; // Подсчитать число появлений цифры d\n  }\n  // Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n  for (int i = 1; i &lt; 10; i++) {\n    counter[i] += counter[i - 1];\n  }\n  // Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n  List&lt;int&gt; res = List&lt;int&gt;.filled(n, 0);\n  for (int i = n - 1; i &gt;= 0; i--) {\n    int d = digit(nums[i], exp);\n    int j = counter[d] - 1; // Получить индекс j цифры d в массиве\n    res[j] = nums[i]; // Поместить текущий элемент по индексу j\n    counter[d]--; // Уменьшить количество d на 1\n  }\n  // Перезаписать исходный массив nums результатом\n  for (int i = 0; i &lt; n; i++) nums[i] = res[i];\n}\n\n/* Поразрядная сортировка */\nvoid radixSort(List&lt;int&gt; nums) {\n  // Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n  // В dart длина int составляет 64 бита\n  int m = -1 &lt;&lt; 63;\n  for (int _num in nums) if (_num &gt; m) m = _num;\n  // Проходить разряды от младшего к старшему\n  for (int exp = 1; exp &lt;= m; exp *= 10)\n    // Выполнить сортировку подсчетом по k-му разряду элементов массива\n    // k = 1 -&gt; exp = 1\n    // k = 2 -&gt; exp = 10\n    // то есть exp = 10^(k-1)\n    countingSortDigit(nums, exp);\n}\n</code></pre> radix_sort.rs<pre><code>/* Получить k-й разряд элемента num, где exp = 10^(k-1) */\nfn digit(num: i32, exp: i32) -&gt; usize {\n    // Передача exp вместо k позволяет избежать повторного дорогостоящего вычисления степени\n    return ((num / exp) % 10) as usize;\n}\n\n/* Сортировка подсчетом (сортировка по k-му разряду nums) */\nfn counting_sort_digit(nums: &amp;mut [i32], exp: i32) {\n    // Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n    let mut counter = [0; 10];\n    let n = nums.len();\n    // Подсчитать число появлений каждой цифры от 0 до 9\n    for i in 0..n {\n        let d = digit(nums[i], exp); // Получить k-й разряд nums[i], обозначив его как d\n        counter[d] += 1; // Подсчитать число появлений цифры d\n    }\n    // Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n    for i in 1..10 {\n        counter[i] += counter[i - 1];\n    }\n    // Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n    let mut res = vec![0; n];\n    for i in (0..n).rev() {\n        let d = digit(nums[i], exp);\n        let j = counter[d] - 1; // Получить индекс j цифры d в массиве\n        res[j] = nums[i]; // Поместить текущий элемент по индексу j\n        counter[d] -= 1; // Уменьшить количество d на 1\n    }\n    // Перезаписать исходный массив nums результатом\n    nums.copy_from_slice(&amp;res);\n}\n\n/* Поразрядная сортировка */\nfn radix_sort(nums: &amp;mut [i32]) {\n    // Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n    let m = *nums.into_iter().max().unwrap();\n    // Проходить разряды от младшего к старшему\n    let mut exp = 1;\n    while exp &lt;= m {\n        counting_sort_digit(nums, exp);\n        exp *= 10;\n    }\n}\n</code></pre> radix_sort.c<pre><code>/* Получить k-й разряд элемента num, где exp = 10^(k-1) */\nint digit(int num, int exp) {\n    // Передача exp вместо k позволяет избежать повторного дорогостоящего вычисления степени\n    return (num / exp) % 10;\n}\n\n/* Сортировка подсчетом (сортировка по k-му разряду nums) */\nvoid countingSortDigit(int nums[], int size, int exp) {\n    // Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n    int *counter = (int *)malloc((sizeof(int) * 10));\n    memset(counter, 0, sizeof(int) * 10); // Инициализировать нулем для последующего освобождения памяти\n    // Подсчитать число появлений каждой цифры от 0 до 9\n    for (int i = 0; i &lt; size; i++) {\n        // Получить k-й разряд nums[i], обозначив его как d\n        int d = digit(nums[i], exp);\n        // Подсчитать число появлений цифры d\n        counter[d]++;\n    }\n    // Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n    for (int i = 1; i &lt; 10; i++) {\n        counter[i] += counter[i - 1];\n    }\n    // Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n    int *res = (int *)malloc(sizeof(int) * size);\n    for (int i = size - 1; i &gt;= 0; i--) {\n        int d = digit(nums[i], exp);\n        int j = counter[d] - 1; // Получить индекс j цифры d в массиве\n        res[j] = nums[i];       // Поместить текущий элемент по индексу j\n        counter[d]--;           // Уменьшить количество d на 1\n    }\n    // Перезаписать исходный массив nums результатом\n    for (int i = 0; i &lt; size; i++) {\n        nums[i] = res[i];\n    }\n    // Освободить память\n    free(res);\n    free(counter);\n}\n\n/* Поразрядная сортировка */\nvoid radixSort(int nums[], int size) {\n    // Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n    int max = INT32_MIN;\n    for (int i = 0; i &lt; size; i++) {\n        if (nums[i] &gt; max) {\n            max = nums[i];\n        }\n    }\n    // Проходить разряды от младшего к старшему\n    for (int exp = 1; max &gt;= exp; exp *= 10)\n        // Выполнить сортировку подсчетом по k-му разряду элементов массива\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // то есть exp = 10^(k-1)\n        countingSortDigit(nums, size, exp);\n}\n</code></pre> radix_sort.kt<pre><code>/* Получить k-й разряд элемента num, где exp = 10^(k-1) */\nfun digit(num: Int, exp: Int): Int {\n    // Передача exp вместо k позволяет избежать повторного дорогостоящего вычисления степени\n    return (num / exp) % 10\n}\n\n/* Сортировка подсчетом (сортировка по k-му разряду nums) */\nfun countingSortDigit(nums: IntArray, exp: Int) {\n    // Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n    val counter = IntArray(10)\n    val n = nums.size\n    // Подсчитать число появлений каждой цифры от 0 до 9\n    for (i in 0..&lt;n) {\n        val d = digit(nums[i], exp) // Получить k-й разряд nums[i], обозначив его как d\n        counter[d]++                // Подсчитать число появлений цифры d\n    }\n    // Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n    for (i in 1..9) {\n        counter[i] += counter[i - 1]\n    }\n    // Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n    val res = IntArray(n)\n    for (i in n - 1 downTo 0) {\n        val d = digit(nums[i], exp)\n        val j = counter[d] - 1 // Получить индекс j цифры d в массиве\n        res[j] = nums[i]       // Поместить текущий элемент по индексу j\n        counter[d]--           // Уменьшить количество d на 1\n    }\n    // Перезаписать исходный массив nums результатом\n    for (i in 0..&lt;n)\n        nums[i] = res[i]\n}\n\n/* Поразрядная сортировка */\nfun radixSort(nums: IntArray) {\n    // Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n    var m = Int.MIN_VALUE\n    for (num in nums) if (num &gt; m) m = num\n    var exp = 1\n    // Проходить разряды от младшего к старшему\n    while (exp &lt;= m) {\n        // Выполнить сортировку подсчетом по k-му разряду элементов массива\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // то есть exp = 10^(k-1)\n        countingSortDigit(nums, exp)\n        exp *= 10\n    }\n}\n</code></pre> radix_sort.rb<pre><code>### Получить k-й разряд элемента num, где exp = 10^(k-1) ###\ndef digit(num, exp)\n  # Передача exp вместо k позволяет избежать повторного выполнения дорогостоящих вычислений степени\n  (num / exp) % 10\nend\n\n### Получить k-й разряд элемента num, где exp = 10^(k-1) ###\ndef digit(num, exp)\n  # Передача exp вместо k позволяет избежать повторного выполнения дорогостоящих вычислений степени\n  (num / exp) % 10\nend\n\n# ## Сортировка подсчетом (сортировка по k-му разряду nums) ###\ndef counting_sort_digit(nums, exp)\n  # Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n  counter = Array.new(10, 0)\n  n = nums.length\n  # Подсчитать число появлений каждой цифры от 0 до 9\n  for i in 0...n\n    d = digit(nums[i], exp) # Получить k-й разряд nums[i], обозначив его как d\n    counter[d] += 1 # Подсчитать число появлений цифры d\n  end\n  # Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n  (1...10).each { |i| counter[i] += counter[i - 1] }\n  # Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n  res = Array.new(n, 0)\n  for i in (n - 1).downto(0)\n    d = digit(nums[i], exp)\n    j = counter[d] - 1 # Получить индекс j цифры d в массиве\n    res[j] = nums[i] # Поместить текущий элемент по индексу j\n    counter[d] -= 1 # Уменьшить количество d на 1\n  end\n  # Перезаписать исходный массив nums результатом\n  (0...n).each { |i| nums[i] = res[i] }\nend\n\n### Поразрядная сортировка ###\ndef radix_sort(nums)\n  # Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n  m = nums.max\n  # Проходить разряды от младшего к старшему\n  exp = 1\n  while exp &lt;= m\n    # Выполнить сортировку подсчетом по k-му разряду элементов массива\n    # k = 1 -&gt; exp = 1\n    # k = 2 -&gt; exp = 10\n    # то есть exp = 10^(k-1)\n    counting_sort_digit(nums, exp)\n    exp *= 10\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Почему сортировка выполняется от младшего разряда к старшему?</p> <p>В последовательных раундах сортировки результаты более позднего раунда перекрывают результаты предыдущего. Например, если после первого раунда получилось \\(a &lt; b\\) , а после второго - \\(a &gt; b\\) , то именно результат второго раунда станет окончательным. Поскольку старшие разряды имеют более высокий приоритет, сначала нужно сортировать по младшим разрядам, а затем по старшим.</p>","path":["Глава 11. Сортировка","11.10 &nbsp; Поразрядная сортировка"],"tags":[]},{"location":"chapter_sorting/radix_sort/#11102","level":2,"title":"11.10.2   Характеристики алгоритма","text":"<p>По сравнению с сортировкой подсчетом поразрядная сортировка подходит для случаев с большим диапазоном чисел, но только при условии, что данные можно представить в виде чисел фиксированной длины и число разрядов не слишком велико. Например, числа с плавающей запятой плохо подходят для поразрядной сортировки, потому что число разрядов \\(k\\) слишком велико и может привести к ситуации \\(O(nk) \\gg O(n^2)\\) .</p> <ul> <li>Временная сложность равна \\(O(nk)\\), алгоритм не является адаптивным: пусть объем данных равен \\(n\\) , числа записаны в системе счисления с основанием \\(d\\) , а максимальное число разрядов равно \\(k\\) . Тогда выполнение сортировки подсчетом для одного разряда требует \\(O(n + d)\\) времени, а сортировка по всем \\(k\\) разрядам требует \\(O((n + d)k)\\) времени. Обычно \\(d\\) и \\(k\\) сравнительно малы, поэтому временная сложность стремится к \\(O(n)\\) .</li> <li>Пространственная сложность равна \\(O(n + d)\\), сортировка не выполняется на месте: как и в сортировке подсчетом, здесь требуются массивы <code>res</code> и <code>counter</code> длины \\(n\\) и \\(d\\) .</li> <li>Стабильная сортировка: если сортировка подсчетом стабильна, то и поразрядная сортировка стабильна; если же сортировка подсчетом нестабильна, поразрядная сортировка не может гарантировать корректный результат.</li> </ul>","path":["Глава 11. Сортировка","11.10 &nbsp; Поразрядная сортировка"],"tags":[]},{"location":"chapter_sorting/selection_sort/","level":1,"title":"11.2   Сортировка выбором","text":"<p>Сортировка выбором (selection sort) работает очень просто: запускается цикл, и на каждом шаге из неотсортированного диапазона выбирается минимальный элемент, после чего он переносится в конец уже отсортированного диапазона.</p> <p>Пусть длина массива равна \\(n\\) ; тогда процесс сортировки выбором выглядит так, как показано на рисунке 11-2.</p> <ol> <li>В начальном состоянии все элементы не отсортированы, то есть неотсортированный диапазон индексов равен \\([0, n-1]\\) .</li> <li>Выбрать минимальный элемент из диапазона \\([0, n-1]\\) и поменять его местами с элементом в позиции \\(0\\) . После этого первые 1 элементов массива отсортированы.</li> <li>Выбрать минимальный элемент из диапазона \\([1, n-1]\\) и поменять его местами с элементом в позиции \\(1\\) . После этого первые 2 элементов массива отсортированы.</li> <li>Продолжать по аналогии. После \\(n - 1\\) раундов выбора и обмена первые \\(n - 1\\) элементов массива будут отсортированы.</li> <li>Оставшийся элемент обязательно является максимальным, сортировать его не нужно, поэтому массив считается отсортированным.</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 11-2   Шаги сортировки выбором </p> <p>В коде мы используем \\(k\\) для записи минимального элемента в пределах неотсортированного диапазона:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby selection_sort.py<pre><code>def selection_sort(nums: list[int]):\n    \"\"\"Сортировка выбором\"\"\"\n    n = len(nums)\n    # Внешний цикл: неотсортированный диапазон [i, n-1]\n    for i in range(n - 1):\n        # Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n        k = i\n        for j in range(i + 1, n):\n            if nums[j] &lt; nums[k]:\n                k = j  # Записать индекс минимального элемента\n        # Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n        nums[i], nums[k] = nums[k], nums[i]\n</code></pre> selection_sort.cpp<pre><code>/* Сортировка выбором */\nvoid selectionSort(vector&lt;int&gt; &amp;nums) {\n    int n = nums.size();\n    // Внешний цикл: неотсортированный диапазон [i, n-1]\n    for (int i = 0; i &lt; n - 1; i++) {\n        // Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n        int k = i;\n        for (int j = i + 1; j &lt; n; j++) {\n            if (nums[j] &lt; nums[k])\n                k = j; // Записать индекс минимального элемента\n        }\n        // Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n        swap(nums[i], nums[k]);\n    }\n}\n</code></pre> selection_sort.java<pre><code>/* Сортировка выбором */\nvoid selectionSort(int[] nums) {\n    int n = nums.length;\n    // Внешний цикл: неотсортированный диапазон [i, n-1]\n    for (int i = 0; i &lt; n - 1; i++) {\n        // Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n        int k = i;\n        for (int j = i + 1; j &lt; n; j++) {\n            if (nums[j] &lt; nums[k])\n                k = j; // Записать индекс минимального элемента\n        }\n        // Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n        int temp = nums[i];\n        nums[i] = nums[k];\n        nums[k] = temp;\n    }\n}\n</code></pre> selection_sort.cs<pre><code>/* Сортировка выбором */\nvoid SelectionSort(int[] nums) {\n    int n = nums.Length;\n    // Внешний цикл: неотсортированный диапазон [i, n-1]\n    for (int i = 0; i &lt; n - 1; i++) {\n        // Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n        int k = i;\n        for (int j = i + 1; j &lt; n; j++) {\n            if (nums[j] &lt; nums[k])\n                k = j; // Записать индекс минимального элемента\n        }\n        // Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n        (nums[k], nums[i]) = (nums[i], nums[k]);\n    }\n}\n</code></pre> selection_sort.go<pre><code>/* Сортировка выбором */\nfunc selectionSort(nums []int) {\n    n := len(nums)\n    // Внешний цикл: неотсортированный диапазон [i, n-1]\n    for i := 0; i &lt; n-1; i++ {\n        // Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n        k := i\n        for j := i + 1; j &lt; n; j++ {\n            if nums[j] &lt; nums[k] {\n                // Записать индекс минимального элемента\n                k = j\n            }\n        }\n        // Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n        nums[i], nums[k] = nums[k], nums[i]\n\n    }\n}\n</code></pre> selection_sort.swift<pre><code>/* Сортировка выбором */\nfunc selectionSort(nums: inout [Int]) {\n    // Внешний цикл: неотсортированный диапазон [i, n-1]\n    for i in nums.indices.dropLast() {\n        // Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n        var k = i\n        for j in nums.indices.dropFirst(i + 1) {\n            if nums[j] &lt; nums[k] {\n                k = j // Записать индекс минимального элемента\n            }\n        }\n        // Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n        nums.swapAt(i, k)\n    }\n}\n</code></pre> selection_sort.js<pre><code>/* Сортировка выбором */\nfunction selectionSort(nums) {\n    let n = nums.length;\n    // Внешний цикл: неотсортированный диапазон [i, n-1]\n    for (let i = 0; i &lt; n - 1; i++) {\n        // Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n        let k = i;\n        for (let j = i + 1; j &lt; n; j++) {\n            if (nums[j] &lt; nums[k]) {\n                k = j; // Записать индекс минимального элемента\n            }\n        }\n        // Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n        [nums[i], nums[k]] = [nums[k], nums[i]];\n    }\n}\n</code></pre> selection_sort.ts<pre><code>/* Сортировка выбором */\nfunction selectionSort(nums: number[]): void {\n    let n = nums.length;\n    // Внешний цикл: неотсортированный диапазон [i, n-1]\n    for (let i = 0; i &lt; n - 1; i++) {\n        // Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n        let k = i;\n        for (let j = i + 1; j &lt; n; j++) {\n            if (nums[j] &lt; nums[k]) {\n                k = j; // Записать индекс минимального элемента\n            }\n        }\n        // Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n        [nums[i], nums[k]] = [nums[k], nums[i]];\n    }\n}\n</code></pre> selection_sort.dart<pre><code>/* Сортировка выбором */\nvoid selectionSort(List&lt;int&gt; nums) {\n  int n = nums.length;\n  // Внешний цикл: неотсортированный диапазон [i, n-1]\n  for (int i = 0; i &lt; n - 1; i++) {\n    // Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n    int k = i;\n    for (int j = i + 1; j &lt; n; j++) {\n      if (nums[j] &lt; nums[k]) k = j; // Записать индекс минимального элемента\n    }\n    // Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n    int temp = nums[i];\n    nums[i] = nums[k];\n    nums[k] = temp;\n  }\n}\n</code></pre> selection_sort.rs<pre><code>/* Сортировка выбором */\nfn selection_sort(nums: &amp;mut [i32]) {\n    if nums.is_empty() {\n        return;\n    }\n    let n = nums.len();\n    // Внешний цикл: неотсортированный диапазон [i, n-1]\n    for i in 0..n - 1 {\n        // Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n        let mut k = i;\n        for j in i + 1..n {\n            if nums[j] &lt; nums[k] {\n                k = j; // Записать индекс минимального элемента\n            }\n        }\n        // Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n        nums.swap(i, k);\n    }\n}\n</code></pre> selection_sort.c<pre><code>/* Сортировка выбором */\nvoid selectionSort(int nums[], int n) {\n    // Внешний цикл: неотсортированный диапазон [i, n-1]\n    for (int i = 0; i &lt; n - 1; i++) {\n        // Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n        int k = i;\n        for (int j = i + 1; j &lt; n; j++) {\n            if (nums[j] &lt; nums[k])\n                k = j; // Записать индекс минимального элемента\n        }\n        // Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n        int temp = nums[i];\n        nums[i] = nums[k];\n        nums[k] = temp;\n    }\n}\n</code></pre> selection_sort.kt<pre><code>/* Сортировка выбором */\nfun selectionSort(nums: IntArray) {\n    val n = nums.size\n    // Внешний цикл: неотсортированный диапазон [i, n-1]\n    for (i in 0..&lt;n - 1) {\n        var k = i\n        // Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n        for (j in i + 1..&lt;n) {\n            if (nums[j] &lt; nums[k])\n                k = j // Записать индекс минимального элемента\n        }\n        // Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n        val temp = nums[i]\n        nums[i] = nums[k]\n        nums[k] = temp\n    }\n}\n</code></pre> selection_sort.rb<pre><code>### Сортировка выбором ###\ndef selection_sort(nums)\n  n = nums.length\n  # Внешний цикл: неотсортированный диапазон [i, n-1]\n  for i in 0...(n - 1)\n    # Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n    k = i\n    for j in (i + 1)...n\n      if nums[j] &lt; nums[k]\n        k = j # Записать индекс минимального элемента\n      end\n    end\n    # Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n    nums[i], nums[k] = nums[k], nums[i]\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 11. Сортировка","11.2 &nbsp; Сортировка выбором"],"tags":[]},{"location":"chapter_sorting/selection_sort/#1121","level":2,"title":"11.2.1   Характеристики алгоритма","text":"<ul> <li>Временная сложность равна \\(O(n^2)\\), сортировка не является адаптивной: внешний цикл выполняется \\(n - 1\\) раз; в первом раунде длина неотсортированного диапазона равна \\(n\\) , а в последнем - \\(2\\) , то есть отдельные раунды содержат \\(n\\), \\(n - 1\\), \\(\\dots\\), \\(3\\), \\(2\\) проходов внутреннего цикла, их сумма равна \\(\\frac{(n - 1)(n + 2)}{2}\\) .</li> <li>Пространственная сложность равна \\(O(1)\\), сортировка выполняется на месте: указатели \\(i\\) и \\(j\\) используют константный объем дополнительной памяти.</li> <li>Нестабильная сортировка: как показано на рисунке 11-3, элемент <code>nums[i]</code> может быть переставлен вправо от другого равного ему элемента, из-за чего их относительный порядок изменится.</li> </ul> <p> Рисунок 11-3   Пример нестабильности сортировки выбором </p>","path":["Глава 11. Сортировка","11.2 &nbsp; Сортировка выбором"],"tags":[]},{"location":"chapter_sorting/sorting_algorithm/","level":1,"title":"11.1   Алгоритмы сортировки","text":"<p>Алгоритмы сортировки (sorting algorithm) используются для упорядочивания набора данных по определенному правилу. Они применяются очень широко, потому что упорядоченные данные обычно проще и быстрее искать, анализировать и обрабатывать.</p> <p>Как показано на рисунке 11-1, данными в алгоритмах сортировки могут быть целые числа, числа с плавающей запятой, символы, строки и другие типы. Критерий сравнения тоже можно задать по-разному, например по величине чисел, по порядку ASCII-кодов символов или по пользовательскому правилу.</p> <p></p> <p> Рисунок 11-1   Примеры типов данных и правил сравнения </p>","path":["Глава 11. Сортировка","11.1 &nbsp; Алгоритмы сортировки"],"tags":[]},{"location":"chapter_sorting/sorting_algorithm/#1111","level":2,"title":"11.1.1   Критерии оценки","text":"<p>Скорость выполнения: мы ожидаем, что временная сложность алгоритма сортировки будет как можно ниже, а общее число операций будет как можно меньше (то есть константа во временной сложности будет небольшой). Для больших объемов данных этот критерий особенно важен.</p> <p>Сортировка на месте: как следует из названия, сортировка на месте выполняется прямо в исходном массиве и не требует дополнительного вспомогательного массива, что позволяет экономить память. Обычно при сортировке на месте переносов данных меньше, а скорость работы выше.</p> <p>Стабильность: стабильная сортировка после завершения не меняет относительный порядок одинаковых элементов в массиве.</p> <p>Стабильность является необходимым условием для многоуровневой сортировки. Предположим, у нас есть таблица со сведениями о студентах, где в первом и втором столбцах записаны имя и возраст. В этом случае нестабильная сортировка может разрушить уже существующий порядок входных данных:</p> <pre><code># Входные данные уже отсортированы по имени\n# (name, age)\n  ('A', 19)\n  ('B', 18)\n  ('C', 21)\n  ('D', 19)\n  ('E', 23)\n\n# Если затем нестабильным алгоритмом отсортировать список по возрасту,\n# относительный порядок ('D', 19) и ('A', 19) изменится,\n# и свойство упорядоченности по имени будет потеряно\n  ('B', 18)\n  ('D', 19)\n  ('A', 19)\n  ('C', 21)\n  ('E', 23)\n</code></pre> <p>Адаптивность: адаптивная сортировка умеет использовать уже существующий порядок входных данных, чтобы сократить вычисления и добиться лучшей эффективности. Лучшая временная сложность адаптивных алгоритмов обычно лучше их средней временной сложности.</p> <p>Основанность на сравнении: сортировка на основе сравнений использует операторы сравнения (\\(&lt;\\), \\(=\\), \\(&gt;\\)), чтобы определить относительный порядок элементов и отсортировать массив; ее теоретически лучшая временная сложность равна \\(O(n \\log n)\\) . А вот сортировка без сравнений не опирается на операторы сравнения, поэтому может достигать \\(O(n)\\) , но универсальность у нее ниже.</p>","path":["Глава 11. Сортировка","11.1 &nbsp; Алгоритмы сортировки"],"tags":[]},{"location":"chapter_sorting/sorting_algorithm/#1112","level":2,"title":"11.1.2   Идеальный алгоритм сортировки","text":"<p>Быстрый, выполняющийся на месте, стабильный, адаптивный и универсальный. Очевидно, что на сегодняшний день не существует алгоритма сортировки, который одновременно обладал бы всеми этими свойствами. Поэтому при выборе алгоритма сортировки нужно исходить из конкретных особенностей данных и требований задачи.</p> <p>Далее мы последовательно изучим разные алгоритмы сортировки и на основании приведенных выше критериев разберем их преимущества и недостатки.</p>","path":["Глава 11. Сортировка","11.1 &nbsp; Алгоритмы сортировки"],"tags":[]},{"location":"chapter_sorting/summary/","level":1,"title":"11.11   Резюме","text":"","path":["Глава 11. Сортировка","11.11 &nbsp; Резюме"],"tags":[]},{"location":"chapter_sorting/summary/#1","level":3,"title":"1.   Ключевые выводы","text":"<ul> <li>Сортировка пузырьком выполняет сортировку за счет обмена соседних элементов. Если добавить флаг для досрочного выхода, лучшую временную сложность пузырьковой сортировки можно оптимизировать до \\(O(n)\\) .</li> <li>Сортировка вставками на каждом раунде вставляет элемент из неотсортированного диапазона в правильную позицию внутри отсортированного диапазона. Хотя ее временная сложность равна \\(O(n^2)\\) , она очень популярна для задач сортировки небольших массивов, поскольку число элементарных операций у нее сравнительно невелико.</li> <li>Быстрая сортировка основана на операции разделения с опорным элементом. При неудачном выборе опорного элемента на каждом раунде ее временная сложность может деградировать до \\(O(n^2)\\) . Использование медианы трех элементов или случайного опорного элемента уменьшает вероятность этой деградации. Если всегда рекурсивно обрабатывать более короткий поддиапазон первым, можно эффективно уменьшить глубину рекурсии и оптимизировать пространственную сложность до \\(O(\\log n)\\) .</li> <li>Сортировка слиянием включает этапы разделения и слияния и служит типичным проявлением стратегии \"разделяй и властвуй\". Для сортировки массива ей требуется вспомогательный массив, поэтому пространственная сложность равна \\(O(n)\\) ; однако при сортировке связного списка пространственную сложность можно оптимизировать до \\(O(1)\\) .</li> <li>Блочная сортировка включает три этапа: распределение данных по блокам, сортировку внутри блоков и объединение результатов. Она тоже отражает стратегию \"разделяй и властвуй\" и подходит для очень больших объемов данных. Ключ к эффективности блочной сортировки - равномерное распределение данных.</li> <li>Сортировка подсчетом является частным случаем блочной сортировки; она реализует сортировку через подсчет числа вхождений данных. Сортировка подсчетом подходит для случаев, когда объем данных велик, но диапазон значений ограничен, и при этом данные можно преобразовать в положительные целые числа.</li> <li>Поразрядная сортировка выполняет сортировку данных путем последовательной сортировки по каждому разряду и требует, чтобы данные можно было представить в виде чисел фиксированной разрядности.</li> <li>В общем случае нам хотелось бы найти алгоритм сортировки, который одновременно обладал бы высокой эффективностью, стабильностью, свойством выполнения на месте и адаптивностью. Но, как и в других разделах алгоритмов и структур данных, не существует одного алгоритма сортировки, способного удовлетворить всем этим требованиям одновременно. На практике приходится выбирать подходящий алгоритм в зависимости от свойств данных.</li> <li>На рисунке 11-19 сравниваются эффективность, стабильность, выполнение на месте и адаптивность основных алгоритмов сортировки.</li> </ul> <p> Рисунок 11-19   Сравнение алгоритмов сортировки </p>","path":["Глава 11. Сортировка","11.11 &nbsp; Резюме"],"tags":[]},{"location":"chapter_sorting/summary/#2","level":3,"title":"2.   Вопросы и ответы","text":"<p>В: В каких случаях стабильность алгоритма сортировки является обязательной?</p> <p>В реальных задачах нам может понадобиться сортировать объекты по некоторому атрибуту. Например, у студентов есть два атрибута: имя и рост. Мы хотим выполнить многоуровневую сортировку: сначала отсортировать по имени и получить <code>(A, 180) (B, 185) (C, 170) (D, 170)</code> , а затем отсортировать по росту. Если используемый алгоритм сортировки нестабилен, то мы можем получить <code>(D, 170) (C, 170) (A, 180) (B, 185)</code> .</p> <p>Нетрудно увидеть, что в этом случае студенты D и C поменялись местами, порядок по имени разрушился, а именно этого мы и не хотим.</p> <p>В: Можно ли поменять местами порядок \"поиска справа налево\" и \"поиска слева направо\" в разделении с опорным элементом?</p> <p>Нет. Если в качестве опорного элемента выбирается самый левый элемент, необходимо сначала выполнять \"поиск справа налево\", а уже затем - \"поиск слева направо\". Этот вывод кажется немного неочевидным, поэтому разберем его подробнее.</p> <p>Последний шаг <code>partition()</code> - это обмен <code>nums[left]</code> и <code>nums[i]</code> . После обмена все элементы слева от опорного должны быть <code>&lt;=</code> опорного, а значит, перед этим обменом должно выполняться условие <code>nums[left] &gt;= nums[i]</code>. Если сначала выполнять \"поиск слева направо\", то в случае, когда не удается найти элемент больше опорного, цикл завершится в состоянии <code>i == j</code> , и при этом может оказаться, что <code>nums[j] == nums[i] &gt; nums[left]</code>. Иными словами, на последнем шаге обмена элемент, больший опорного, будет помещен в начало массива, из-за чего разделение завершится неверно.</p> <p>Например, для массива <code>[0, 0, 0, 0, 1]</code> , если сначала выполнять \"поиск слева направо\", после разделения получится <code>[1, 0, 0, 0, 0]</code> , а это неправильный результат.</p> <p>Если же выбрать <code>nums[right]</code> в качестве опорного элемента, то ситуация станет противоположной, и тогда сначала нужно выполнять \"поиск слева направо\".</p> <p>В: Почему при оптимизации глубины рекурсии в быстрой сортировке выбор короткого массива гарантирует, что глубина рекурсии не превысит \\(\\log n\\) ?</p> <p>Глубина рекурсии - это число текущих рекурсивных вызовов, которые еще не завершились. На каждом раунде разделения исходный массив разбивается на два подмассива. После оптимизации глубины рекурсии длина подмассива, в который мы продолжаем рекурсивный спуск, не превышает половины длины исходного массива. Если рассматривать худший случай, когда длина каждый раз становится ровно вдвое меньше, итоговая глубина рекурсии и будет равна \\(\\log n\\) .</p> <p>В исходной версии быстрой сортировки может происходить последовательный рекурсивный вызов для более длинных массивов; в худшем случае это будут длины \\(n\\) , \\(n - 1\\) , \\(\\dots\\) , \\(2\\) , \\(1\\) , а глубина рекурсии окажется равной \\(n\\) . Оптимизация глубины рекурсии как раз и позволяет избежать такого сценария.</p> <p>В: Если все элементы массива равны, будет ли временная сложность быстрой сортировки равна \\(O(n^2)\\) ? Как справиться с таким вырождением?</p> <p>Да. Для этого случая можно рассмотреть разделение массива на три части: элементы меньше опорного, равные опорному и большие опорного. Рекурсию нужно продолжать только для частей меньше и больше опорного. При таком подходе массив, целиком состоящий из одинаковых элементов, будет отсортирован всего за один раунд разделения.</p> <p>В: Почему худшая временная сложность блочной сортировки равна \\(O(n^2)\\) ?</p> <p>В худшем случае все элементы попадут в один и тот же блок. Если затем сортировать этот блок алгоритмом со сложностью \\(O(n^2)\\) , то общая временная сложность тоже станет \\(O(n^2)\\) .</p>","path":["Глава 11. Сортировка","11.11 &nbsp; Резюме"],"tags":[]},{"location":"chapter_stack_and_queue/","level":1,"title":"Глава 5.   Стек и очередь","text":"<p>Abstract</p> <p>Стек похож на стопку кошек, а очередь - на очередь из кошек.</p> <p>Эти две структуры соответственно представляют отношения \"последним пришел - первым вышел\" и \"первым пришел - первым вышел\".</p>","path":["Глава 5. Стек и очередь","Глава 5. &nbsp; Стек и очередь"],"tags":[]},{"location":"chapter_stack_and_queue/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>5.1   Стек</li> <li>5.2   Очередь</li> <li>5.3   Двусторонняя очередь</li> <li>5.4   Резюме</li> </ul>","path":["Глава 5. Стек и очередь","Глава 5. &nbsp; Стек и очередь"],"tags":[]},{"location":"chapter_stack_and_queue/deque/","level":1,"title":"5.3   Двусторонняя очередь","text":"<p>В очереди мы можем удалять элементы только из головы или добавлять их только в хвост. Как показано на рисунке 5-7, двусторонняя очередь (double-ended queue) обеспечивает более высокую гибкость и позволяет выполнять добавление и удаление элементов как с головы, так и с хвоста.</p> <p></p> <p> Рисунок 5-7   Операции двусторонней очереди </p>","path":["Глава 5. Стек и очередь","5.3 &nbsp; Двусторонняя очередь"],"tags":[]},{"location":"chapter_stack_and_queue/deque/#531","level":2,"title":"5.3.1   Основные операции с двусторонней очередью","text":"<p>Распространенные операции двусторонней очереди приведены в таблице 5-3. Конкретные названия методов зависят от используемого языка программирования.</p> <p> Таблица 5-3   Эффективность операций двусторонней очереди </p> Имя метода Описание Временная сложность <code>push_first()</code> Добавить элемент в голову очереди \\(O(1)\\) <code>push_last()</code> Добавить элемент в хвост очереди \\(O(1)\\) <code>pop_first()</code> Удалить элемент из головы очереди \\(O(1)\\) <code>pop_last()</code> Удалить элемент из хвоста очереди \\(O(1)\\) <code>peek_first()</code> Просмотреть элемент в голове очереди \\(O(1)\\) <code>peek_last()</code> Просмотреть элемент в хвосте очереди \\(O(1)\\) <p>Точно так же мы можем напрямую использовать уже реализованные в языках программирования классы двусторонней очереди:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby deque.py<pre><code>from collections import deque\n\n# Инициализация двусторонней очереди\ndeq: deque[int] = deque()\n\n# Поместить элементы в очередь\ndeq.append(2)      # Добавить в хвост\ndeq.append(5)\ndeq.append(4)\ndeq.appendleft(3)  # Добавить в голову\ndeq.appendleft(1)\n\n# Просмотреть элементы\nfront: int = deq[0]  # Элемент в голове\nrear: int = deq[-1]  # Элемент в хвосте\n\n# Извлечь элементы из очереди\npop_front: int = deq.popleft()  # Извлечь элемент из головы\npop_rear: int = deq.pop()       # Извлечь элемент из хвоста\n\n# Получить длину двусторонней очереди\nsize: int = len(deq)\n\n# Проверить, пуста ли двусторонняя очередь\nis_empty: bool = len(deq) == 0\n</code></pre> deque.cpp<pre><code>/* Инициализация двусторонней очереди */\ndeque&lt;int&gt; deque;\n\n/* Поместить элементы в очередь */\ndeque.push_back(2);   // Добавить в хвост\ndeque.push_back(5);\ndeque.push_back(4);\ndeque.push_front(3);  // Добавить в голову\ndeque.push_front(1);\n\n/* Просмотреть элементы */\nint front = deque.front(); // Элемент в голове\nint back = deque.back();   // Элемент в хвосте\n\n/* Извлечь элементы из очереди */\ndeque.pop_front();  // Извлечь элемент из головы\ndeque.pop_back();   // Извлечь элемент из хвоста\n\n/* Получить длину двусторонней очереди */\nint size = deque.size();\n\n/* Проверить, пуста ли двусторонняя очередь */\nbool empty = deque.empty();\n</code></pre> deque.java<pre><code>/* Инициализация двусторонней очереди */\nDeque&lt;Integer&gt; deque = new LinkedList&lt;&gt;();\n\n/* Поместить элементы в очередь */\ndeque.offerLast(2);   // Добавить в хвост\ndeque.offerLast(5);\ndeque.offerLast(4);\ndeque.offerFirst(3);  // Добавить в голову\ndeque.offerFirst(1);\n\n/* Просмотреть элементы */\nint peekFirst = deque.peekFirst();  // Элемент в голове\nint peekLast = deque.peekLast();    // Элемент в хвосте\n\n/* Извлечь элементы из очереди */\nint popFirst = deque.pollFirst();  // Извлечь элемент из головы\nint popLast = deque.pollLast();    // Извлечь элемент из хвоста\n\n/* Получить длину двусторонней очереди */\nint size = deque.size();\n\n/* Проверить, пуста ли двусторонняя очередь */\nboolean isEmpty = deque.isEmpty();\n</code></pre> deque.cs<pre><code>/* Инициализация двусторонней очереди */\n// В C# двустороннюю очередь обычно моделируют через связный список LinkedList\nLinkedList&lt;int&gt; deque = new();\n\n/* Поместить элементы в очередь */\ndeque.AddLast(2);   // Добавить в хвост\ndeque.AddLast(5);\ndeque.AddLast(4);\ndeque.AddFirst(3);  // Добавить в голову\ndeque.AddFirst(1);\n\n/* Просмотреть элементы */\nint peekFirst = deque.First.Value;  // Элемент в голове\nint peekLast = deque.Last.Value;    // Элемент в хвосте\n\n/* Извлечь элементы из очереди */\ndeque.RemoveFirst();  // Извлечь элемент из головы\ndeque.RemoveLast();   // Извлечь элемент из хвоста\n\n/* Получить длину двусторонней очереди */\nint size = deque.Count;\n\n/* Проверить, пуста ли двусторонняя очередь */\nbool isEmpty = deque.Count == 0;\n</code></pre> deque_test.go<pre><code>/* Инициализация двусторонней очереди */\n// В Go list обычно используется как двусторонняя очередь\ndeque := list.New()\n\n/* Поместить элементы в очередь */\ndeque.PushBack(2)      // Добавить в хвост\ndeque.PushBack(5)\ndeque.PushBack(4)\ndeque.PushFront(3)     // Добавить в голову\ndeque.PushFront(1)\n\n/* Просмотреть элементы */\nfront := deque.Front() // Элемент в голове\nrear := deque.Back()   // Элемент в хвосте\n\n/* Извлечь элементы из очереди */\ndeque.Remove(front)    // Извлечь элемент из головы\ndeque.Remove(rear)     // Извлечь элемент из хвоста\n\n/* Получить длину двусторонней очереди */\nsize := deque.Len()\n\n/* Проверить, пуста ли двусторонняя очередь */\nisEmpty := deque.Len() == 0\n</code></pre> deque.swift<pre><code>/* Инициализация двусторонней очереди */\n// В Swift нет встроенного класса двусторонней очереди, поэтому можно использовать Array как двустороннюю очередь\nvar deque: [Int] = []\n\n/* Поместить элементы в очередь */\ndeque.append(2) // Добавить в хвост\ndeque.append(5)\ndeque.append(4)\ndeque.insert(3, at: 0) // Добавить в голову\ndeque.insert(1, at: 0)\n\n/* Просмотреть элементы */\nlet peekFirst = deque.first! // Элемент в голове\nlet peekLast = deque.last! // Элемент в хвосте\n\n/* Извлечь элементы из очереди */\n// При моделировании через Array сложность popFirst равна O(n)\nlet popFirst = deque.removeFirst() // Извлечь элемент из головы\nlet popLast = deque.removeLast() // Извлечь элемент из хвоста\n\n/* Получить длину двусторонней очереди */\nlet size = deque.count\n\n/* Проверить, пуста ли двусторонняя очередь */\nlet isEmpty = deque.isEmpty\n</code></pre> deque.js<pre><code>/* Инициализация двусторонней очереди */\n// В JavaScript нет встроенной двусторонней очереди, поэтому можно использовать Array как двустороннюю очередь\nconst deque = [];\n\n/* Поместить элементы в очередь */\ndeque.push(2);\ndeque.push(5);\ndeque.push(4);\n// Обрати внимание: поскольку это массив, метод unshift() имеет сложность O(n)\ndeque.unshift(3);\ndeque.unshift(1);\n\n/* Просмотреть элементы */\nconst peekFirst = deque[0];\nconst peekLast = deque[deque.length - 1];\n\n/* Извлечь элементы из очереди */\n// Обрати внимание: поскольку это массив, метод shift() имеет сложность O(n)\nconst popFront = deque.shift();\nconst popBack = deque.pop();\n\n/* Получить длину двусторонней очереди */\nconst size = deque.length;\n\n/* Проверить, пуста ли двусторонняя очередь */\nconst isEmpty = size === 0;\n</code></pre> deque.ts<pre><code>/* Инициализация двусторонней очереди */\n// В TypeScript нет встроенной двусторонней очереди, поэтому можно использовать Array как двустороннюю очередь\nconst deque: number[] = [];\n\n/* Поместить элементы в очередь */\ndeque.push(2);\ndeque.push(5);\ndeque.push(4);\n// Обрати внимание: поскольку это массив, метод unshift() имеет сложность O(n)\ndeque.unshift(3);\ndeque.unshift(1);\n\n/* Просмотреть элементы */\nconst peekFirst: number = deque[0];\nconst peekLast: number = deque[deque.length - 1];\n\n/* Извлечь элементы из очереди */\n// Обрати внимание: поскольку это массив, метод shift() имеет сложность O(n)\nconst popFront: number = deque.shift() as number;\nconst popBack: number = deque.pop() as number;\n\n/* Получить длину двусторонней очереди */\nconst size: number = deque.length;\n\n/* Проверить, пуста ли двусторонняя очередь */\nconst isEmpty: boolean = size === 0;\n</code></pre> deque.dart<pre><code>/* Инициализация двусторонней очереди */\n// В Dart Queue определена как двусторонняя очередь\nQueue&lt;int&gt; deque = Queue&lt;int&gt;();\n\n/* Поместить элементы в очередь */\ndeque.addLast(2);  // Добавить в хвост\ndeque.addLast(5);\ndeque.addLast(4);\ndeque.addFirst(3); // Добавить в голову\ndeque.addFirst(1);\n\n/* Просмотреть элементы */\nint peekFirst = deque.first; // Элемент в голове\nint peekLast = deque.last;   // Элемент в хвосте\n\n/* Извлечь элементы из очереди */\nint popFirst = deque.removeFirst(); // Извлечь элемент из головы\nint popLast = deque.removeLast();   // Извлечь элемент из хвоста\n\n/* Получить длину двусторонней очереди */\nint size = deque.length;\n\n/* Проверить, пуста ли двусторонняя очередь */\nbool isEmpty = deque.isEmpty;\n</code></pre> deque.rs<pre><code>/* Инициализация двусторонней очереди */\nlet mut deque: VecDeque&lt;u32&gt; = VecDeque::new();\n\n/* Поместить элементы в очередь */\ndeque.push_back(2);  // Добавить в хвост\ndeque.push_back(5);\ndeque.push_back(4);\ndeque.push_front(3); // Добавить в голову\ndeque.push_front(1);\n\n/* Просмотреть элементы */\nif let Some(front) = deque.front() { // Элемент в голове\n}\nif let Some(rear) = deque.back() {   // Элемент в хвосте\n}\n\n/* Извлечь элементы из очереди */\nif let Some(pop_front) = deque.pop_front() { // Извлечь элемент из головы\n}\nif let Some(pop_rear) = deque.pop_back() {   // Извлечь элемент из хвоста\n}\n\n/* Получить длину двусторонней очереди */\nlet size = deque.len();\n\n/* Проверить, пуста ли двусторонняя очередь */\nlet is_empty = deque.is_empty();\n</code></pre> deque.c<pre><code>// В C нет встроенной двусторонней очереди\n</code></pre> deque.kt<pre><code>/* Инициализация двусторонней очереди */\nval deque = LinkedList&lt;Int&gt;()\n\n/* Поместить элементы в очередь */\ndeque.offerLast(2)  // Добавить в хвост\ndeque.offerLast(5)\ndeque.offerLast(4)\ndeque.offerFirst(3) // Добавить в голову\ndeque.offerFirst(1)\n\n/* Просмотреть элементы */\nval peekFirst = deque.peekFirst() // Элемент в голове\nval peekLast = deque.peekLast()   // Элемент в хвосте\n\n/* Извлечь элементы из очереди */\nval popFirst = deque.pollFirst() // Извлечь элемент из головы\nval popLast = deque.pollLast()   // Извлечь элемент из хвоста\n\n/* Получить длину двусторонней очереди */\nval size = deque.size\n\n/* Проверить, пуста ли двусторонняя очередь */\nval isEmpty = deque.isEmpty()\n</code></pre> deque.rb<pre><code># Инициализация двусторонней очереди\n# В Ruby нет встроенной двусторонней очереди, поэтому можно использовать Array как двустороннюю очередь\ndeque = []\n\n# Поместить элементы в очередь\ndeque &lt;&lt; 2\ndeque &lt;&lt; 5\ndeque &lt;&lt; 4\n# Обрати внимание: поскольку это массив, метод Array#unshift имеет сложность O(n)\ndeque.unshift(3)\ndeque.unshift(1)\n\n# Просмотреть элементы\npeek_first = deque.first\npeek_last = deque.last\n\n# Извлечь элементы из очереди\n# Обрати внимание: поскольку это массив, метод Array#shift имеет сложность O(n)\npop_front = deque.shift\npop_back = deque.pop\n\n# Получить длину двусторонней очереди\nsize = deque.length\n\n# Проверить, пуста ли двусторонняя очередь\nis_empty = size.zero?\n</code></pre> Визуализация выполнения 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rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 5. Стек и очередь","5.3 &nbsp; Двусторонняя очередь"],"tags":[]},{"location":"chapter_stack_and_queue/deque/#532","level":2,"title":"5.3.2   Реализация двусторонней очереди *","text":"<p>Реализация двусторонней очереди похожа на реализацию обычной очереди: в качестве базовой структуры данных можно выбрать связный список или массив.</p>","path":["Глава 5. Стек и очередь","5.3 &nbsp; Двусторонняя очередь"],"tags":[]},{"location":"chapter_stack_and_queue/deque/#1","level":3,"title":"1.   Реализация на основе двусвязного списка","text":"<p>Вспомним предыдущий раздел: там мы использовали обычный односвязный список для реализации очереди, потому что он позволяет удобно удалять головной узел (это соответствует операции dequeue) и добавлять новый узел после хвостового узла (это соответствует операции enqueue).</p> <p>Для двусторонней очереди и голова, и хвост допускают операции добавления и удаления элементов. Иначе говоря, двусторонняя очередь требует реализации еще одного симметричного направления операций. Поэтому в качестве базовой структуры данных двусторонней очереди мы используем \"двусвязный список\".</p> <p>Как показано на рисунках ниже, мы рассматриваем головной и хвостовой узлы двусвязного списка как голову и хвост двусторонней очереди и одновременно реализуем функции добавления и удаления узлов с обеих сторон.</p> LinkedListDequepush_last()push_first()pop_last()pop_first() <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 5-8   Операции enqueue и dequeue для двусторонней очереди на связном списке </p> <p>Код реализации приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linkedlist_deque.py<pre><code>class ListNode:\n    \"\"\"Узел двусвязного списка\"\"\"\n\n    def __init__(self, val: int):\n        \"\"\"Конструктор\"\"\"\n        self.val: int = val\n        self.next: ListNode | None = None  # Ссылка на узел-преемник\n        self.prev: ListNode | None = None  # Ссылка на узел-предшественник\n\nclass LinkedListDeque:\n    \"\"\"Двусторонняя очередь на основе двусвязного списка\"\"\"\n\n    def __init__(self):\n        \"\"\"Конструктор\"\"\"\n        self._front: ListNode | None = None  # Головной узел front\n        self._rear: ListNode | None = None  # Хвостовой узел rear\n        self._size: int = 0  # Длина двусторонней очереди\n\n    def size(self) -&gt; int:\n        \"\"\"Получение длины двусторонней очереди\"\"\"\n        return self._size\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"Проверка, пуста ли двусторонняя очередь\"\"\"\n        return self._size == 0\n\n    def push(self, num: int, is_front: bool):\n        \"\"\"Операция добавления в очередь\"\"\"\n        node = ListNode(num)\n        # Если связный список пуст, сделать так, чтобы и front, и rear указывали на node\n        if self.is_empty():\n            self._front = self._rear = node\n        # Операция добавления в голову очереди\n        elif is_front:\n            # Добавить node в голову списка\n            self._front.prev = node\n            node.next = self._front\n            self._front = node  # Обновить головной узел\n        # Операция добавления в хвост очереди\n        else:\n            # Добавить node в хвост списка\n            self._rear.next = node\n            node.prev = self._rear\n            self._rear = node  # Обновить хвостовой узел\n        self._size += 1  # Обновить длину очереди\n\n    def push_first(self, num: int):\n        \"\"\"Добавление в голову очереди\"\"\"\n        self.push(num, True)\n\n    def push_last(self, num: int):\n        \"\"\"Добавление в хвост очереди\"\"\"\n        self.push(num, False)\n\n    def pop(self, is_front: bool) -&gt; int:\n        \"\"\"Операция извлечения из очереди\"\"\"\n        if self.is_empty():\n            raise IndexError(\"двусторонняя очередь пуста\")\n        # Операция извлечения из головы очереди\n        if is_front:\n            val: int = self._front.val  # Временно сохранить значение головного узла\n            # Удалить головной узел\n            fnext: ListNode | None = self._front.next\n            if fnext is not None:\n                fnext.prev = None\n                self._front.next = None\n            self._front = fnext  # Обновить головной узел\n        # Операция извлечения из хвоста очереди\n        else:\n            val: int = self._rear.val  # Временно сохранить значение хвостового узла\n            # Удалить хвостовой узел\n            rprev: ListNode | None = self._rear.prev\n            if rprev is not None:\n                rprev.next = None\n                self._rear.prev = None\n            self._rear = rprev  # Обновить хвостовой узел\n        self._size -= 1  # Обновить длину очереди\n        return val\n\n    def pop_first(self) -&gt; int:\n        \"\"\"Извлечение из головы очереди\"\"\"\n        return self.pop(True)\n\n    def pop_last(self) -&gt; int:\n        \"\"\"Извлечение из хвоста очереди\"\"\"\n        return self.pop(False)\n\n    def peek_first(self) -&gt; int:\n        \"\"\"Доступ к элементу в начале очереди\"\"\"\n        if self.is_empty():\n            raise IndexError(\"двусторонняя очередь пуста\")\n        return self._front.val\n\n    def peek_last(self) -&gt; int:\n        \"\"\"Доступ к элементу в конце очереди\"\"\"\n        if self.is_empty():\n            raise IndexError(\"двусторонняя очередь пуста\")\n        return self._rear.val\n\n    def to_array(self) -&gt; list[int]:\n        \"\"\"Вернуть массив для вывода\"\"\"\n        node = self._front\n        res = [0] * self.size()\n        for i in range(self.size()):\n            res[i] = node.val\n            node = node.next\n        return res\n</code></pre> linkedlist_deque.cpp<pre><code>/* Узел двусвязного списка */\nstruct DoublyListNode {\n    int val;              // Значение узла\n    DoublyListNode *next; // Указатель на узел-преемник\n    DoublyListNode *prev; // Указатель на узел-предшественник\n    DoublyListNode(int val) : val(val), prev(nullptr), next(nullptr) {\n    }\n};\n\n/* Двусторонняя очередь на основе двусвязного списка */\nclass LinkedListDeque {\n  private:\n    DoublyListNode *front, *rear; // Головной узел front, хвостовой узел rear\n    int queSize = 0;              // Длина двусторонней очереди\n\n  public:\n    /* Конструктор */\n    LinkedListDeque() : front(nullptr), rear(nullptr) {\n    }\n\n    /* Метод-деструктор */\n    ~LinkedListDeque() {\n        // Обходить связный список, удалять узлы и освобождать память\n        DoublyListNode *pre, *cur = front;\n        while (cur != nullptr) {\n            pre = cur;\n            cur = cur-&gt;next;\n            delete pre;\n        }\n    }\n\n    /* Получение длины двусторонней очереди */\n    int size() {\n        return queSize;\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    bool isEmpty() {\n        return size() == 0;\n    }\n\n    /* Операция добавления в очередь */\n    void push(int num, bool isFront) {\n        DoublyListNode *node = new DoublyListNode(num);\n        // Если связный список пуст, сделать так, чтобы и front, и rear указывали на node\n        if (isEmpty())\n            front = rear = node;\n        // Операция добавления в голову очереди\n        else if (isFront) {\n            // Добавить node в голову списка\n            front-&gt;prev = node;\n            node-&gt;next = front;\n            front = node; // Обновить головной узел\n        // Операция добавления в хвост очереди\n        } else {\n            // Добавить node в хвост списка\n            rear-&gt;next = node;\n            node-&gt;prev = rear;\n            rear = node; // Обновить хвостовой узел\n        }\n        queSize++; // Обновить длину очереди\n    }\n\n    /* Добавление в голову очереди */\n    void pushFirst(int num) {\n        push(num, true);\n    }\n\n    /* Добавление в хвост очереди */\n    void pushLast(int num) {\n        push(num, false);\n    }\n\n    /* Операция извлечения из очереди */\n    int pop(bool isFront) {\n        if (isEmpty())\n            throw out_of_range(\"очередь пуста\");\n        int val;\n        // Операция извлечения из головы очереди\n        if (isFront) {\n            val = front-&gt;val; // Временно сохранить значение головного узла\n            // Удалить головной узел\n            DoublyListNode *fNext = front-&gt;next;\n            if (fNext != nullptr) {\n                fNext-&gt;prev = nullptr;\n                front-&gt;next = nullptr;\n            }\n            delete front;\n            front = fNext; // Обновить головной узел\n        // Операция извлечения из хвоста очереди\n        } else {\n            val = rear-&gt;val; // Временно сохранить значение хвостового узла\n            // Удалить хвостовой узел\n            DoublyListNode *rPrev = rear-&gt;prev;\n            if (rPrev != nullptr) {\n                rPrev-&gt;next = nullptr;\n                rear-&gt;prev = nullptr;\n            }\n            delete rear;\n            rear = rPrev; // Обновить хвостовой узел\n        }\n        queSize--; // Обновить длину очереди\n        return val;\n    }\n\n    /* Извлечение из головы очереди */\n    int popFirst() {\n        return pop(true);\n    }\n\n    /* Извлечение из хвоста очереди */\n    int popLast() {\n        return pop(false);\n    }\n\n    /* Доступ к элементу в начале очереди */\n    int peekFirst() {\n        if (isEmpty())\n            throw out_of_range(\"двусторонняя очередь пуста\");\n        return front-&gt;val;\n    }\n\n    /* Доступ к элементу в конце очереди */\n    int peekLast() {\n        if (isEmpty())\n            throw out_of_range(\"двусторонняя очередь пуста\");\n        return rear-&gt;val;\n    }\n\n    /* Вернуть массив для вывода */\n    vector&lt;int&gt; toVector() {\n        DoublyListNode *node = front;\n        vector&lt;int&gt; res(size());\n        for (int i = 0; i &lt; res.size(); i++) {\n            res[i] = node-&gt;val;\n            node = node-&gt;next;\n        }\n        return res;\n    }\n};\n</code></pre> linkedlist_deque.java<pre><code>/* Узел двусвязного списка */\nclass ListNode {\n    int val; // Значение узла\n    ListNode next; // Ссылка на узел-преемник\n    ListNode prev; // Ссылка на узел-предшественник\n\n    ListNode(int val) {\n        this.val = val;\n        prev = next = null;\n    }\n}\n\n/* Двусторонняя очередь на основе двусвязного списка */\nclass LinkedListDeque {\n    private ListNode front, rear; // Головной узел front, хвостовой узел rear\n    private int queSize = 0; // Длина двусторонней очереди\n\n    public LinkedListDeque() {\n        front = rear = null;\n    }\n\n    /* Получение длины двусторонней очереди */\n    public int size() {\n        return queSize;\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    public boolean isEmpty() {\n        return size() == 0;\n    }\n\n    /* Операция добавления в очередь */\n    private void push(int num, boolean isFront) {\n        ListNode node = new ListNode(num);\n        // Если связный список пуст, сделать так, чтобы и front, и rear указывали на node\n        if (isEmpty())\n            front = rear = node;\n        // Операция добавления в голову очереди\n        else if (isFront) {\n            // Добавить node в голову списка\n            front.prev = node;\n            node.next = front;\n            front = node; // Обновить головной узел\n        // Операция добавления в хвост очереди\n        } else {\n            // Добавить node в хвост списка\n            rear.next = node;\n            node.prev = rear;\n            rear = node; // Обновить хвостовой узел\n        }\n        queSize++; // Обновить длину очереди\n    }\n\n    /* Добавление в голову очереди */\n    public void pushFirst(int num) {\n        push(num, true);\n    }\n\n    /* Добавление в хвост очереди */\n    public void pushLast(int num) {\n        push(num, false);\n    }\n\n    /* Операция извлечения из очереди */\n    private int pop(boolean isFront) {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        int val;\n        // Операция извлечения из головы очереди\n        if (isFront) {\n            val = front.val; // Временно сохранить значение головного узла\n            // Удалить головной узел\n            ListNode fNext = front.next;\n            if (fNext != null) {\n                fNext.prev = null;\n                front.next = null;\n            }\n            front = fNext; // Обновить головной узел\n        // Операция извлечения из хвоста очереди\n        } else {\n            val = rear.val; // Временно сохранить значение хвостового узла\n            // Удалить хвостовой узел\n            ListNode rPrev = rear.prev;\n            if (rPrev != null) {\n                rPrev.next = null;\n                rear.prev = null;\n            }\n            rear = rPrev; // Обновить хвостовой узел\n        }\n        queSize--; // Обновить длину очереди\n        return val;\n    }\n\n    /* Извлечение из головы очереди */\n    public int popFirst() {\n        return pop(true);\n    }\n\n    /* Извлечение из хвоста очереди */\n    public int popLast() {\n        return pop(false);\n    }\n\n    /* Доступ к элементу в начале очереди */\n    public int peekFirst() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return front.val;\n    }\n\n    /* Доступ к элементу в конце очереди */\n    public int peekLast() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return rear.val;\n    }\n\n    /* Вернуть массив для вывода */\n    public int[] toArray() {\n        ListNode node = front;\n        int[] res = new int[size()];\n        for (int i = 0; i &lt; res.length; i++) {\n            res[i] = node.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_deque.cs<pre><code>/* Узел двусвязного списка */\nclass ListNode(int val) {\n    public int val = val;       // Значение узла\n    public ListNode? next = null; // Ссылка на узел-преемник\n    public ListNode? prev = null; // Ссылка на узел-предшественник\n}\n\n/* Двусторонняя очередь на основе двусвязного списка */\nclass LinkedListDeque {\n    ListNode? front, rear; // Головной узел front, хвостовой узел rear\n    int queSize = 0;      // Длина двусторонней очереди\n\n    public LinkedListDeque() {\n        front = null;\n        rear = null;\n    }\n\n    /* Получение длины двусторонней очереди */\n    public int Size() {\n        return queSize;\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    public bool IsEmpty() {\n        return Size() == 0;\n    }\n\n    /* Операция добавления в очередь */\n    void Push(int num, bool isFront) {\n        ListNode node = new(num);\n        // Если связный список пуст, сделать так, чтобы и front, и rear указывали на node\n        if (IsEmpty()) {\n            front = node;\n            rear = node;\n        }\n        // Операция добавления в голову очереди\n        else if (isFront) {\n            // Добавить node в голову списка\n            front!.prev = node;\n            node.next = front;\n            front = node; // Обновить головной узел\n        }\n        // Операция добавления в хвост очереди\n        else {\n            // Добавить node в хвост списка\n            rear!.next = node;\n            node.prev = rear;\n            rear = node;  // Обновить хвостовой узел\n        }\n\n        queSize++; // Обновить длину очереди\n    }\n\n    /* Добавление в голову очереди */\n    public void PushFirst(int num) {\n        Push(num, true);\n    }\n\n    /* Добавление в хвост очереди */\n    public void PushLast(int num) {\n        Push(num, false);\n    }\n\n    /* Операция извлечения из очереди */\n    int? Pop(bool isFront) {\n        if (IsEmpty())\n            throw new Exception();\n        int? val;\n        // Операция извлечения из головы очереди\n        if (isFront) {\n            val = front?.val; // Временно сохранить значение головного узла\n            // Удалить головной узел\n            ListNode? fNext = front?.next;\n            if (fNext != null) {\n                fNext.prev = null;\n                front!.next = null;\n            }\n            front = fNext;   // Обновить головной узел\n        }\n        // Операция извлечения из хвоста очереди\n        else {\n            val = rear?.val;  // Временно сохранить значение хвостового узла\n            // Удалить хвостовой узел\n            ListNode? rPrev = rear?.prev;\n            if (rPrev != null) {\n                rPrev.next = null;\n                rear!.prev = null;\n            }\n            rear = rPrev;    // Обновить хвостовой узел\n        }\n\n        queSize--; // Обновить длину очереди\n        return val;\n    }\n\n    /* Извлечение из головы очереди */\n    public int? PopFirst() {\n        return Pop(true);\n    }\n\n    /* Извлечение из хвоста очереди */\n    public int? PopLast() {\n        return Pop(false);\n    }\n\n    /* Доступ к элементу в начале очереди */\n    public int? PeekFirst() {\n        if (IsEmpty())\n            throw new Exception();\n        return front?.val;\n    }\n\n    /* Доступ к элементу в конце очереди */\n    public int? PeekLast() {\n        if (IsEmpty())\n            throw new Exception();\n        return rear?.val;\n    }\n\n    /* Вернуть массив для вывода */\n    public int?[] ToArray() {\n        ListNode? node = front;\n        int?[] res = new int?[Size()];\n        for (int i = 0; i &lt; res.Length; i++) {\n            res[i] = node?.val;\n            node = node?.next;\n        }\n\n        return res;\n    }\n}\n</code></pre> linkedlist_deque.go<pre><code>/* Двусторонняя очередь на основе двусвязного списка */\ntype linkedListDeque struct {\n    // Использовать встроенный пакет list\n    data *list.List\n}\n\n/* Инициализировать двустороннюю очередь */\nfunc newLinkedListDeque() *linkedListDeque {\n    return &amp;linkedListDeque{\n        data: list.New(),\n    }\n}\n\n/* Поместить элемент в голову очереди */\nfunc (s *linkedListDeque) pushFirst(value any) {\n    s.data.PushFront(value)\n}\n\n/* Поместить элемент в хвост очереди */\nfunc (s *linkedListDeque) pushLast(value any) {\n    s.data.PushBack(value)\n}\n\n/* Извлечь элемент из головы очереди */\nfunc (s *linkedListDeque) popFirst() any {\n    if s.isEmpty() {\n        return nil\n    }\n    e := s.data.Front()\n    s.data.Remove(e)\n    return e.Value\n}\n\n/* Извлечь элемент из хвоста очереди */\nfunc (s *linkedListDeque) popLast() any {\n    if s.isEmpty() {\n        return nil\n    }\n    e := s.data.Back()\n    s.data.Remove(e)\n    return e.Value\n}\n\n/* Доступ к элементу в начале очереди */\nfunc (s *linkedListDeque) peekFirst() any {\n    if s.isEmpty() {\n        return nil\n    }\n    e := s.data.Front()\n    return e.Value\n}\n\n/* Доступ к элементу в конце очереди */\nfunc (s *linkedListDeque) peekLast() any {\n    if s.isEmpty() {\n        return nil\n    }\n    e := s.data.Back()\n    return e.Value\n}\n\n/* Получение длины очереди */\nfunc (s *linkedListDeque) size() int {\n    return s.data.Len()\n}\n\n/* Проверка, пуста ли очередь */\nfunc (s *linkedListDeque) isEmpty() bool {\n    return s.data.Len() == 0\n}\n\n/* Получить List для вывода */\nfunc (s *linkedListDeque) toList() *list.List {\n    return s.data\n}\n</code></pre> linkedlist_deque.swift<pre><code>/* Узел двусвязного списка */\nclass ListNode {\n    var val: Int // Значение узла\n    var next: ListNode? // Ссылка на узел-преемник\n    weak var prev: ListNode? // Ссылка на узел-предшественник\n\n    init(val: Int) {\n        self.val = val\n    }\n}\n\n/* Двусторонняя очередь на основе двусвязного списка */\nclass LinkedListDeque {\n    private var front: ListNode? // Головной узел front\n    private var rear: ListNode? // Хвостовой узел rear\n    private var _size: Int // Длина двусторонней очереди\n\n    init() {\n        _size = 0\n    }\n\n    /* Получение длины двусторонней очереди */\n    func size() -&gt; Int {\n        _size\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    func isEmpty() -&gt; Bool {\n        size() == 0\n    }\n\n    /* Операция добавления в очередь */\n    private func push(num: Int, isFront: Bool) {\n        let node = ListNode(val: num)\n        // Если связный список пуст, сделать так, чтобы и front, и rear указывали на node\n        if isEmpty() {\n            front = node\n            rear = node\n        }\n        // Операция добавления в голову очереди\n        else if isFront {\n            // Добавить node в голову списка\n            front?.prev = node\n            node.next = front\n            front = node // Обновить головной узел\n        }\n        // Операция добавления в хвост очереди\n        else {\n            // Добавить node в хвост списка\n            rear?.next = node\n            node.prev = rear\n            rear = node // Обновить хвостовой узел\n        }\n        _size += 1 // Обновить длину очереди\n    }\n\n    /* Добавление в голову очереди */\n    func pushFirst(num: Int) {\n        push(num: num, isFront: true)\n    }\n\n    /* Добавление в хвост очереди */\n    func pushLast(num: Int) {\n        push(num: num, isFront: false)\n    }\n\n    /* Операция извлечения из очереди */\n    private func pop(isFront: Bool) -&gt; Int {\n        if isEmpty() {\n            fatalError(\"двусторонняя очередь пуста\")\n        }\n        let val: Int\n        // Операция извлечения из головы очереди\n        if isFront {\n            val = front!.val // Временно сохранить значение головного узла\n            // Удалить головной узел\n            let fNext = front?.next\n            if fNext != nil {\n                fNext?.prev = nil\n                front?.next = nil\n            }\n            front = fNext // Обновить головной узел\n        }\n        // Операция извлечения из хвоста очереди\n        else {\n            val = rear!.val // Временно сохранить значение хвостового узла\n            // Удалить хвостовой узел\n            let rPrev = rear?.prev\n            if rPrev != nil {\n                rPrev?.next = nil\n                rear?.prev = nil\n            }\n            rear = rPrev // Обновить хвостовой узел\n        }\n        _size -= 1 // Обновить длину очереди\n        return val\n    }\n\n    /* Извлечение из головы очереди */\n    func popFirst() -&gt; Int {\n        pop(isFront: true)\n    }\n\n    /* Извлечение из хвоста очереди */\n    func popLast() -&gt; Int {\n        pop(isFront: false)\n    }\n\n    /* Доступ к элементу в начале очереди */\n    func peekFirst() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"двусторонняя очередь пуста\")\n        }\n        return front!.val\n    }\n\n    /* Доступ к элементу в конце очереди */\n    func peekLast() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"двусторонняя очередь пуста\")\n        }\n        return rear!.val\n    }\n\n    /* Вернуть массив для вывода */\n    func toArray() -&gt; [Int] {\n        var node = front\n        var res = Array(repeating: 0, count: size())\n        for i in res.indices {\n            res[i] = node!.val\n            node = node?.next\n        }\n        return res\n    }\n}\n</code></pre> linkedlist_deque.js<pre><code>/* Узел двусвязного списка */\nclass ListNode {\n    prev; // Ссылка на узел-предшественник (указатель)\n    next; // Ссылка на узел-преемник (указатель)\n    val; // Значение узла\n\n    constructor(val) {\n        this.val = val;\n        this.next = null;\n        this.prev = null;\n    }\n}\n\n/* Двусторонняя очередь на основе двусвязного списка */\nclass LinkedListDeque {\n    #front; // Головной узел front\n    #rear; // Хвостовой узел rear\n    #queSize; // Длина двусторонней очереди\n\n    constructor() {\n        this.#front = null;\n        this.#rear = null;\n        this.#queSize = 0;\n    }\n\n    /* Операция добавления в хвост очереди */\n    pushLast(val) {\n        const node = new ListNode(val);\n        // Если связный список пуст, сделать так, чтобы и front, и rear указывали на node\n        if (this.#queSize === 0) {\n            this.#front = node;\n            this.#rear = node;\n        } else {\n            // Добавить node в хвост списка\n            this.#rear.next = node;\n            node.prev = this.#rear;\n            this.#rear = node; // Обновить хвостовой узел\n        }\n        this.#queSize++;\n    }\n\n    /* Операция добавления в голову очереди */\n    pushFirst(val) {\n        const node = new ListNode(val);\n        // Если связный список пуст, сделать так, чтобы и front, и rear указывали на node\n        if (this.#queSize === 0) {\n            this.#front = node;\n            this.#rear = node;\n        } else {\n            // Добавить node в голову списка\n            this.#front.prev = node;\n            node.next = this.#front;\n            this.#front = node; // Обновить головной узел\n        }\n        this.#queSize++;\n    }\n\n    /* Операция извлечения из хвоста очереди */\n    popLast() {\n        if (this.#queSize === 0) {\n            return null;\n        }\n        const value = this.#rear.val; // Сохранить значение хвостового узла\n        // Удалить хвостовой узел\n        let temp = this.#rear.prev;\n        if (temp !== null) {\n            temp.next = null;\n            this.#rear.prev = null;\n        }\n        this.#rear = temp; // Обновить хвостовой узел\n        this.#queSize--;\n        return value;\n    }\n\n    /* Операция извлечения из головы очереди */\n    popFirst() {\n        if (this.#queSize === 0) {\n            return null;\n        }\n        const value = this.#front.val; // Сохранить значение хвостового узла\n        // Удалить головной узел\n        let temp = this.#front.next;\n        if (temp !== null) {\n            temp.prev = null;\n            this.#front.next = null;\n        }\n        this.#front = temp; // Обновить головной узел\n        this.#queSize--;\n        return value;\n    }\n\n    /* Доступ к элементу в конце очереди */\n    peekLast() {\n        return this.#queSize === 0 ? null : this.#rear.val;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    peekFirst() {\n        return this.#queSize === 0 ? null : this.#front.val;\n    }\n\n    /* Получение длины двусторонней очереди */\n    size() {\n        return this.#queSize;\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    isEmpty() {\n        return this.#queSize === 0;\n    }\n\n    /* Вывести двустороннюю очередь */\n    print() {\n        const arr = [];\n        let temp = this.#front;\n        while (temp !== null) {\n            arr.push(temp.val);\n            temp = temp.next;\n        }\n        console.log('[' + arr.join(', ') + ']');\n    }\n}\n</code></pre> linkedlist_deque.ts<pre><code>/* Узел двусвязного списка */\nclass ListNode {\n    prev: ListNode; // Ссылка на узел-предшественник (указатель)\n    next: ListNode; // Ссылка на узел-преемник (указатель)\n    val: number; // Значение узла\n\n    constructor(val: number) {\n        this.val = val;\n        this.next = null;\n        this.prev = null;\n    }\n}\n\n/* Двусторонняя очередь на основе двусвязного списка */\nclass LinkedListDeque {\n    private front: ListNode; // Головной узел front\n    private rear: ListNode; // Хвостовой узел rear\n    private queSize: number; // Длина двусторонней очереди\n\n    constructor() {\n        this.front = null;\n        this.rear = null;\n        this.queSize = 0;\n    }\n\n    /* Операция добавления в хвост очереди */\n    pushLast(val: number): void {\n        const node: ListNode = new ListNode(val);\n        // Если связный список пуст, сделать так, чтобы и front, и rear указывали на node\n        if (this.queSize === 0) {\n            this.front = node;\n            this.rear = node;\n        } else {\n            // Добавить node в хвост списка\n            this.rear.next = node;\n            node.prev = this.rear;\n            this.rear = node; // Обновить хвостовой узел\n        }\n        this.queSize++;\n    }\n\n    /* Операция добавления в голову очереди */\n    pushFirst(val: number): void {\n        const node: ListNode = new ListNode(val);\n        // Если связный список пуст, сделать так, чтобы и front, и rear указывали на node\n        if (this.queSize === 0) {\n            this.front = node;\n            this.rear = node;\n        } else {\n            // Добавить node в голову списка\n            this.front.prev = node;\n            node.next = this.front;\n            this.front = node; // Обновить головной узел\n        }\n        this.queSize++;\n    }\n\n    /* Операция извлечения из хвоста очереди */\n    popLast(): number {\n        if (this.queSize === 0) {\n            return null;\n        }\n        const value: number = this.rear.val; // Сохранить значение хвостового узла\n        // Удалить хвостовой узел\n        let temp: ListNode = this.rear.prev;\n        if (temp !== null) {\n            temp.next = null;\n            this.rear.prev = null;\n        }\n        this.rear = temp; // Обновить хвостовой узел\n        this.queSize--;\n        return value;\n    }\n\n    /* Операция извлечения из головы очереди */\n    popFirst(): number {\n        if (this.queSize === 0) {\n            return null;\n        }\n        const value: number = this.front.val; // Сохранить значение хвостового узла\n        // Удалить головной узел\n        let temp: ListNode = this.front.next;\n        if (temp !== null) {\n            temp.prev = null;\n            this.front.next = null;\n        }\n        this.front = temp; // Обновить головной узел\n        this.queSize--;\n        return value;\n    }\n\n    /* Доступ к элементу в конце очереди */\n    peekLast(): number {\n        return this.queSize === 0 ? null : this.rear.val;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    peekFirst(): number {\n        return this.queSize === 0 ? null : this.front.val;\n    }\n\n    /* Получение длины двусторонней очереди */\n    size(): number {\n        return this.queSize;\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    isEmpty(): boolean {\n        return this.queSize === 0;\n    }\n\n    /* Вывести двустороннюю очередь */\n    print(): void {\n        const arr: number[] = [];\n        let temp: ListNode = this.front;\n        while (temp !== null) {\n            arr.push(temp.val);\n            temp = temp.next;\n        }\n        console.log('[' + arr.join(', ') + ']');\n    }\n}\n</code></pre> linkedlist_deque.dart<pre><code>/* Узел двусвязного списка */\nclass ListNode {\n  int val; // Значение узла\n  ListNode? next; // Ссылка на узел-преемник\n  ListNode? prev; // Ссылка на узел-предшественник\n\n  ListNode(this.val, {this.next, this.prev});\n}\n\n/* Двусторонняя очередь на основе двусвязного списка */\nclass LinkedListDeque {\n  late ListNode? _front; // Головной узел _front\n  late ListNode? _rear; // Хвостовой узел _rear\n  int _queSize = 0; // Длина двусторонней очереди\n\n  LinkedListDeque() {\n    this._front = null;\n    this._rear = null;\n  }\n\n  /* Получить длину двусторонней очереди */\n  int size() {\n    return this._queSize;\n  }\n\n  /* Проверка, пуста ли двусторонняя очередь */\n  bool isEmpty() {\n    return size() == 0;\n  }\n\n  /* Операция добавления в очередь */\n  void push(int _num, bool isFront) {\n    final ListNode node = ListNode(_num);\n    if (isEmpty()) {\n      // Если связный список пуст, пусть _front и _rear оба указывают на node\n      _front = _rear = node;\n    } else if (isFront) {\n      // Операция добавления в голову очереди\n      // Добавить node в начало связного списка\n      _front!.prev = node;\n      node.next = _front;\n      _front = node; // Обновить головной узел\n    } else {\n      // Операция добавления в хвост очереди\n      // Добавить node в конец связного списка\n      _rear!.next = node;\n      node.prev = _rear;\n      _rear = node; // Обновить хвостовой узел\n    }\n    _queSize++; // Обновить длину очереди\n  }\n\n  /* Добавление в голову очереди */\n  void pushFirst(int _num) {\n    push(_num, true);\n  }\n\n  /* Добавление в хвост очереди */\n  void pushLast(int _num) {\n    push(_num, false);\n  }\n\n  /* Операция извлечения из очереди */\n  int? pop(bool isFront) {\n    // Если очередь пуста, сразу вернуть null\n    if (isEmpty()) {\n      return null;\n    }\n    final int val;\n    if (isFront) {\n      // Операция извлечения из головы очереди\n      val = _front!.val; // Временно сохранить значение головного узла\n      // Удалить головной узел\n      ListNode? fNext = _front!.next;\n      if (fNext != null) {\n        fNext.prev = null;\n        _front!.next = null;\n      }\n      _front = fNext; // Обновить головной узел\n    } else {\n      // Операция извлечения из хвоста очереди\n      val = _rear!.val; // Временно сохранить значение хвостового узла\n      // Удалить хвостовой узел\n      ListNode? rPrev = _rear!.prev;\n      if (rPrev != null) {\n        rPrev.next = null;\n        _rear!.prev = null;\n      }\n      _rear = rPrev; // Обновить хвостовой узел\n    }\n    _queSize--; // Обновить длину очереди\n    return val;\n  }\n\n  /* Извлечение из головы очереди */\n  int? popFirst() {\n    return pop(true);\n  }\n\n  /* Извлечение из хвоста очереди */\n  int? popLast() {\n    return pop(false);\n  }\n\n  /* Доступ к элементу в начале очереди */\n  int? peekFirst() {\n    return _front?.val;\n  }\n\n  /* Доступ к элементу в конце очереди */\n  int? peekLast() {\n    return _rear?.val;\n  }\n\n  /* Вернуть массив для вывода */\n  List&lt;int&gt; toArray() {\n    ListNode? node = _front;\n    final List&lt;int&gt; res = [];\n    for (int i = 0; i &lt; _queSize; i++) {\n      res.add(node!.val);\n      node = node.next;\n    }\n    return res;\n  }\n}\n</code></pre> linkedlist_deque.rs<pre><code>/* Узел двусвязного списка */\npub struct ListNode&lt;T&gt; {\n    pub val: T,                                 // Значение узла\n    pub next: Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;, // Указатель на узел-преемник\n    pub prev: Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;, // Указатель на узел-предшественник\n}\n\nimpl&lt;T&gt; ListNode&lt;T&gt; {\n    pub fn new(val: T) -&gt; Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt; {\n        Rc::new(RefCell::new(ListNode {\n            val,\n            next: None,\n            prev: None,\n        }))\n    }\n}\n\n/* Двусторонняя очередь на основе двусвязного списка */\n#[allow(dead_code)]\npub struct LinkedListDeque&lt;T&gt; {\n    front: Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;, // Головной узел front\n    rear: Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;,  // Хвостовой узел rear\n    que_size: usize,                         // Длина двусторонней очереди\n}\n\nimpl&lt;T: Copy&gt; LinkedListDeque&lt;T&gt; {\n    pub fn new() -&gt; Self {\n        Self {\n            front: None,\n            rear: None,\n            que_size: 0,\n        }\n    }\n\n    /* Получение длины двусторонней очереди */\n    pub fn size(&amp;self) -&gt; usize {\n        return self.que_size;\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    pub fn is_empty(&amp;self) -&gt; bool {\n        return self.que_size == 0;\n    }\n\n    /* Операция добавления в очередь */\n    fn push(&amp;mut self, num: T, is_front: bool) {\n        let node = ListNode::new(num);\n        // Операция добавления в голову очереди\n        if is_front {\n            match self.front.take() {\n                // Если связный список пуст, сделать так, чтобы и front, и rear указывали на node\n                None =&gt; {\n                    self.rear = Some(node.clone());\n                    self.front = Some(node);\n                }\n                // Добавить node в голову списка\n                Some(old_front) =&gt; {\n                    old_front.borrow_mut().prev = Some(node.clone());\n                    node.borrow_mut().next = Some(old_front);\n                    self.front = Some(node); // Обновить головной узел\n                }\n            }\n        }\n        // Операция добавления в хвост очереди\n        else {\n            match self.rear.take() {\n                // Если связный список пуст, сделать так, чтобы и front, и rear указывали на node\n                None =&gt; {\n                    self.front = Some(node.clone());\n                    self.rear = Some(node);\n                }\n                // Добавить node в хвост списка\n                Some(old_rear) =&gt; {\n                    old_rear.borrow_mut().next = Some(node.clone());\n                    node.borrow_mut().prev = Some(old_rear);\n                    self.rear = Some(node); // Обновить хвостовой узел\n                }\n            }\n        }\n        self.que_size += 1; // Обновить длину очереди\n    }\n\n    /* Добавление в голову очереди */\n    pub fn push_first(&amp;mut self, num: T) {\n        self.push(num, true);\n    }\n\n    /* Добавление в хвост очереди */\n    pub fn push_last(&amp;mut self, num: T) {\n        self.push(num, false);\n    }\n\n    /* Операция извлечения из очереди */\n    fn pop(&amp;mut self, is_front: bool) -&gt; Option&lt;T&gt; {\n        // Если очередь пуста, сразу вернуть None\n        if self.is_empty() {\n            return None;\n        };\n        // Операция извлечения из головы очереди\n        if is_front {\n            self.front.take().map(|old_front| {\n                match old_front.borrow_mut().next.take() {\n                    Some(new_front) =&gt; {\n                        new_front.borrow_mut().prev.take();\n                        self.front = Some(new_front); // Обновить головной узел\n                    }\n                    None =&gt; {\n                        self.rear.take();\n                    }\n                }\n                self.que_size -= 1; // Обновить длину очереди\n                old_front.borrow().val\n            })\n        }\n        // Операция извлечения из хвоста очереди\n        else {\n            self.rear.take().map(|old_rear| {\n                match old_rear.borrow_mut().prev.take() {\n                    Some(new_rear) =&gt; {\n                        new_rear.borrow_mut().next.take();\n                        self.rear = Some(new_rear); // Обновить хвостовой узел\n                    }\n                    None =&gt; {\n                        self.front.take();\n                    }\n                }\n                self.que_size -= 1; // Обновить длину очереди\n                old_rear.borrow().val\n            })\n        }\n    }\n\n    /* Извлечение из головы очереди */\n    pub fn pop_first(&amp;mut self) -&gt; Option&lt;T&gt; {\n        return self.pop(true);\n    }\n\n    /* Извлечение из хвоста очереди */\n    pub fn pop_last(&amp;mut self) -&gt; Option&lt;T&gt; {\n        return self.pop(false);\n    }\n\n    /* Доступ к элементу в начале очереди */\n    pub fn peek_first(&amp;self) -&gt; Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt; {\n        self.front.as_ref()\n    }\n\n    /* Доступ к элементу в конце очереди */\n    pub fn peek_last(&amp;self) -&gt; Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt; {\n        self.rear.as_ref()\n    }\n\n    /* Вернуть массив для вывода */\n    pub fn to_array(&amp;self, head: Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;) -&gt; Vec&lt;T&gt; {\n        let mut res: Vec&lt;T&gt; = Vec::new();\n        fn recur&lt;T: Copy&gt;(cur: Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;, res: &amp;mut Vec&lt;T&gt;) {\n            if let Some(cur) = cur {\n                res.push(cur.borrow().val);\n                recur(cur.borrow().next.as_ref(), res);\n            }\n        }\n\n        recur(head, &amp;mut res);\n        res\n    }\n}\n</code></pre> linkedlist_deque.c<pre><code>/* Узел двусвязного списка */\ntypedef struct DoublyListNode {\n    int val;                     // Значение узла\n    struct DoublyListNode *next; // Узел-преемник\n    struct DoublyListNode *prev; // Узел-предшественник\n} DoublyListNode;\n\n/* Конструктор */\nDoublyListNode *newDoublyListNode(int num) {\n    DoublyListNode *new = (DoublyListNode *)malloc(sizeof(DoublyListNode));\n    new-&gt;val = num;\n    new-&gt;next = NULL;\n    new-&gt;prev = NULL;\n    return new;\n}\n\n/* Деструктор */\nvoid delDoublyListNode(DoublyListNode *node) {\n    free(node);\n}\n\n/* Двусторонняя очередь на основе двусвязного списка */\ntypedef struct {\n    DoublyListNode *front, *rear; // Головной узел front, хвостовой узел rear\n    int queSize;                  // Длина двусторонней очереди\n} LinkedListDeque;\n\n/* Конструктор */\nLinkedListDeque *newLinkedListDeque() {\n    LinkedListDeque *deque = (LinkedListDeque *)malloc(sizeof(LinkedListDeque));\n    deque-&gt;front = NULL;\n    deque-&gt;rear = NULL;\n    deque-&gt;queSize = 0;\n    return deque;\n}\n\n/* Деструктор */\nvoid delLinkedListdeque(LinkedListDeque *deque) {\n    // Освободить все узлы\n    for (int i = 0; i &lt; deque-&gt;queSize &amp;&amp; deque-&gt;front != NULL; i++) {\n        DoublyListNode *tmp = deque-&gt;front;\n        deque-&gt;front = deque-&gt;front-&gt;next;\n        free(tmp);\n    }\n    // Освободить структуру deque\n    free(deque);\n}\n\n/* Получение длины очереди */\nint size(LinkedListDeque *deque) {\n    return deque-&gt;queSize;\n}\n\n/* Проверка, пуста ли очередь */\nbool empty(LinkedListDeque *deque) {\n    return (size(deque) == 0);\n}\n\n/* Поместить в очередь */\nvoid push(LinkedListDeque *deque, int num, bool isFront) {\n    DoublyListNode *node = newDoublyListNode(num);\n    // Если связный список пуст, пусть front и rear оба указывают на node\n    if (empty(deque)) {\n        deque-&gt;front = deque-&gt;rear = node;\n    }\n    // Операция добавления в голову очереди\n    else if (isFront) {\n        // Добавить node в голову списка\n        deque-&gt;front-&gt;prev = node;\n        node-&gt;next = deque-&gt;front;\n        deque-&gt;front = node; // Обновить головной узел\n    }\n    // Операция добавления в хвост очереди\n    else {\n        // Добавить node в хвост списка\n        deque-&gt;rear-&gt;next = node;\n        node-&gt;prev = deque-&gt;rear;\n        deque-&gt;rear = node;\n    }\n    deque-&gt;queSize++; // Обновить длину очереди\n}\n\n/* Добавление в голову очереди */\nvoid pushFirst(LinkedListDeque *deque, int num) {\n    push(deque, num, true);\n}\n\n/* Добавление в хвост очереди */\nvoid pushLast(LinkedListDeque *deque, int num) {\n    push(deque, num, false);\n}\n\n/* Доступ к элементу в начале очереди */\nint peekFirst(LinkedListDeque *deque) {\n    assert(size(deque) &amp;&amp; deque-&gt;front);\n    return deque-&gt;front-&gt;val;\n}\n\n/* Доступ к элементу в конце очереди */\nint peekLast(LinkedListDeque *deque) {\n    assert(size(deque) &amp;&amp; deque-&gt;rear);\n    return deque-&gt;rear-&gt;val;\n}\n\n/* Извлечь из очереди */\nint pop(LinkedListDeque *deque, bool isFront) {\n    if (empty(deque))\n        return -1;\n    int val;\n    // Операция извлечения из головы очереди\n    if (isFront) {\n        val = peekFirst(deque); // Временно сохранить значение головного узла\n        DoublyListNode *fNext = deque-&gt;front-&gt;next;\n        if (fNext) {\n            fNext-&gt;prev = NULL;\n            deque-&gt;front-&gt;next = NULL;\n        }\n        delDoublyListNode(deque-&gt;front);\n        deque-&gt;front = fNext; // Обновить головной узел\n    }\n    // Операция извлечения из хвоста очереди\n    else {\n        val = peekLast(deque); // Временно сохранить значение хвостового узла\n        DoublyListNode *rPrev = deque-&gt;rear-&gt;prev;\n        if (rPrev) {\n            rPrev-&gt;next = NULL;\n            deque-&gt;rear-&gt;prev = NULL;\n        }\n        delDoublyListNode(deque-&gt;rear);\n        deque-&gt;rear = rPrev; // Обновить хвостовой узел\n    }\n    deque-&gt;queSize--; // Обновить длину очереди\n    return val;\n}\n\n/* Извлечение из головы очереди */\nint popFirst(LinkedListDeque *deque) {\n    return pop(deque, true);\n}\n\n/* Извлечение из хвоста очереди */\nint popLast(LinkedListDeque *deque) {\n    return pop(deque, false);\n}\n\n/* Вывести очередь */\nvoid printLinkedListDeque(LinkedListDeque *deque) {\n    int *arr = malloc(sizeof(int) * deque-&gt;queSize);\n    // Скопировать данные связного списка в массив\n    int i;\n    DoublyListNode *node;\n    for (i = 0, node = deque-&gt;front; i &lt; deque-&gt;queSize; i++) {\n        arr[i] = node-&gt;val;\n        node = node-&gt;next;\n    }\n    printArray(arr, deque-&gt;queSize);\n    free(arr);\n}\n</code></pre> linkedlist_deque.kt<pre><code>/* Узел двусвязного списка */\nclass ListNode(var _val: Int) {\n    // Значение узла\n    var next: ListNode? = null // Ссылка на узел-преемник\n    var prev: ListNode? = null // Ссылка на узел-предшественник\n}\n\n/* Двусторонняя очередь на основе двусвязного списка */\nclass LinkedListDeque {\n    private var front: ListNode? = null // Головной узел front\n    private var rear: ListNode? = null // Хвостовой узел rear\n    private var queSize: Int = 0 // Длина двусторонней очереди\n\n    /* Получение длины двусторонней очереди */\n    fun size(): Int {\n        return queSize\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    fun isEmpty(): Boolean {\n        return size() == 0\n    }\n\n    /* Операция добавления в очередь */\n    fun push(num: Int, isFront: Boolean) {\n        val node = ListNode(num)\n        // Если связный список пуст, сделать так, чтобы и front, и rear указывали на node\n        if (isEmpty()) {\n            rear = node\n            front = rear\n            // Операция добавления в голову очереди\n        } else if (isFront) {\n            // Добавить node в голову списка\n            front?.prev = node\n            node.next = front\n            front = node // Обновить головной узел\n            // Операция добавления в хвост очереди\n        } else {\n            // Добавить node в хвост списка\n            rear?.next = node\n            node.prev = rear\n            rear = node // Обновить хвостовой узел\n        }\n        queSize++ // Обновить длину очереди\n    }\n\n    /* Добавление в голову очереди */\n    fun pushFirst(num: Int) {\n        push(num, true)\n    }\n\n    /* Добавление в хвост очереди */\n    fun pushLast(num: Int) {\n        push(num, false)\n    }\n\n    /* Операция извлечения из очереди */\n    fun pop(isFront: Boolean): Int {\n        if (isEmpty()) \n            throw IndexOutOfBoundsException()\n        val _val: Int\n        // Операция извлечения из головы очереди\n        if (isFront) {\n            _val = front!!._val // Временно сохранить значение головного узла\n            // Удалить головной узел\n            val fNext = front!!.next\n            if (fNext != null) {\n                fNext.prev = null\n                front!!.next = null\n            }\n            front = fNext // Обновить головной узел\n            // Операция извлечения из хвоста очереди\n        } else {\n            _val = rear!!._val // Временно сохранить значение хвостового узла\n            // Удалить хвостовой узел\n            val rPrev = rear!!.prev\n            if (rPrev != null) {\n                rPrev.next = null\n                rear!!.prev = null\n            }\n            rear = rPrev // Обновить хвостовой узел\n        }\n        queSize-- // Обновить длину очереди\n        return _val\n    }\n\n    /* Извлечение из головы очереди */\n    fun popFirst(): Int {\n        return pop(true)\n    }\n\n    /* Извлечение из хвоста очереди */\n    fun popLast(): Int {\n        return pop(false)\n    }\n\n    /* Доступ к элементу в начале очереди */\n    fun peekFirst(): Int {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        return front!!._val\n    }\n\n    /* Доступ к элементу в конце очереди */\n    fun peekLast(): Int {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        return rear!!._val\n    }\n\n    /* Вернуть массив для вывода */\n    fun toArray(): IntArray {\n        var node = front\n        val res = IntArray(size())\n        for (i in res.indices) {\n            res[i] = node!!._val\n            node = node.next\n        }\n        return res\n    }\n}\n</code></pre> linkedlist_deque.rb<pre><code>=begin\nFile: linkedlist_deque.rb\nCreated Time: 2024-04-06\nAuthor: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)\n=end\n\n# ## Узел двусвязного списка\nclass ListNode\n  attr_accessor :val\n  attr_accessor :next # Ссылка на узел-преемник\n  attr_accessor :prev # Ссылка на узел-предшественник\n\n  ### Конструктор ###\n  def initialize(val)\n    @val = val\n  end\nend\n\n### Двусторонняя очередь на основе двусвязного списка ###\nclass LinkedListDeque\n  ### Получение длины двусторонней очереди ###\n  attr_reader :size\n\n  ### Конструктор ###\n  def initialize\n    @front = nil  # Головной узел front\n    @rear = nil   # Хвостовой узел rear\n    @size = 0     # Длина двусторонней очереди\n  end\n\n  ### Проверка, пуста ли двусторонняя очередь ###\n  def is_empty?\n    size.zero?\n  end\n\n  ### Операция добавления в очередь ###\n  def push(num, is_front)\n    node = ListNode.new(num)\n    # Если связный список пуст, пусть front и rear оба указывают на node\n    if is_empty?\n      @front = @rear = node\n    # Операция добавления в голову очереди\n    elsif is_front\n      # Добавить node в голову списка\n      @front.prev = node\n      node.next = @front\n      @front = node # Обновить головной узел\n    # Операция добавления в хвост очереди\n    else\n      # Добавить node в хвост списка\n      @rear.next = node\n      node.prev = @rear\n      @rear = node # Обновить хвостовой узел\n    end\n    @size += 1 # Обновить длину очереди\n  end\n\n  ### Добавление в голову очереди ###\n  def push_first(num)\n    push(num, true)\n  end\n\n  ### Добавление в хвост очереди ###\n  def push_last(num)\n    push(num, false)\n  end\n\n  ### Операция извлечения из очереди ###\n  def pop(is_front)\n    raise IndexError, 'двусторонняя очередь пуста' if is_empty?\n\n    # Операция извлечения из головы очереди\n    if is_front\n      val = @front.val # Временно сохранить значение головного узла\n      # Удалить головной узел\n      fnext = @front.next\n      unless fnext.nil?\n        fnext.prev = nil\n        @front.next = nil\n      end\n      @front = fnext # Обновить головной узел\n    # Операция извлечения из хвоста очереди\n    else\n      val = @rear.val # Временно сохранить значение хвостового узла\n      # Удалить хвостовой узел\n      rprev = @rear.prev\n      unless rprev.nil?\n        rprev.next = nil\n        @rear.prev = nil\n      end\n      @rear = rprev # Обновить хвостовой узел\n    end\n    @size -= 1 # Обновить длину очереди\n\n    val\n  end\n\n  ### Извлечение из головы очереди ###\n  def pop_first\n    pop(true)\n  end\n\n  ### Извлечение из головы очереди ###\n  def pop_last\n    pop(false)\n  end\n\n  ### Доступ к элементу в начале очереди ###\n  def peek_first\n    raise IndexError, 'двусторонняя очередь пуста' if is_empty?\n\n    @front.val\n  end\n\n  ### Доступ к элементу в хвосте очереди ###\n  def peek_last\n    raise IndexError, 'двусторонняя очередь пуста' if is_empty?\n\n    @rear.val\n  end\n\n  ### Вернуть массив для вывода ###\n  def to_array\n    node = @front\n    res = Array.new(size, 0)\n    for i in 0...size\n      res[i] = node.val\n      node = node.next\n    end\n    res\n  end\nend\n</code></pre>","path":["Глава 5. Стек и очередь","5.3 &nbsp; Двусторонняя очередь"],"tags":[]},{"location":"chapter_stack_and_queue/deque/#2","level":3,"title":"2.   Реализация на основе массива","text":"<p>Как показано на рисунках ниже, аналогично реализации очереди на массиве мы также можем использовать кольцевой массив для реализации двусторонней очереди.</p> ArrayDequepush_last()push_first()pop_last()pop_first() <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 5-9   Операции enqueue и dequeue для двусторонней очереди на массиве </p> <p>На основе реализации обычной очереди нужно лишь добавить методы \"enqueue в голову\" и \"dequeue из хвоста\":</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array_deque.py<pre><code>class ArrayDeque:\n    \"\"\"Двусторонняя очередь на основе кольцевого массива\"\"\"\n\n    def __init__(self, capacity: int):\n        \"\"\"Конструктор\"\"\"\n        self._nums: list[int] = [0] * capacity\n        self._front: int = 0\n        self._size: int = 0\n\n    def capacity(self) -&gt; int:\n        \"\"\"Получить вместимость двусторонней очереди\"\"\"\n        return len(self._nums)\n\n    def size(self) -&gt; int:\n        \"\"\"Получение длины двусторонней очереди\"\"\"\n        return self._size\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"Проверка, пуста ли двусторонняя очередь\"\"\"\n        return self._size == 0\n\n    def index(self, i: int) -&gt; int:\n        \"\"\"Вычислить индекс в кольцевом массиве\"\"\"\n        # С помощью операции взятия по модулю соединить начало и конец массива\n        # Когда i выходит за конец массива, он возвращается в начало\n        # Когда i выходит за начало массива, он возвращается в конец\n        return (i + self.capacity()) % self.capacity()\n\n    def push_first(self, num: int):\n        \"\"\"Добавление в голову очереди\"\"\"\n        if self._size == self.capacity():\n            print(\"Двусторонняя очередь заполнена\")\n            return\n        # Указатель головы сдвигается на одну позицию влево\n        # С помощью операции взятия по модулю front после выхода за начало массива возвращается в хвост\n        self._front = self.index(self._front - 1)\n        # Добавить num в голову очереди\n        self._nums[self._front] = num\n        self._size += 1\n\n    def push_last(self, num: int):\n        \"\"\"Добавление в хвост очереди\"\"\"\n        if self._size == self.capacity():\n            print(\"Двусторонняя очередь заполнена\")\n            return\n        # Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        rear = self.index(self._front + self._size)\n        # Добавить num в хвост очереди\n        self._nums[rear] = num\n        self._size += 1\n\n    def pop_first(self) -&gt; int:\n        \"\"\"Извлечение из головы очереди\"\"\"\n        num = self.peek_first()\n        # Указатель головы сдвигается на одну позицию назад\n        self._front = self.index(self._front + 1)\n        self._size -= 1\n        return num\n\n    def pop_last(self) -&gt; int:\n        \"\"\"Извлечение из хвоста очереди\"\"\"\n        num = self.peek_last()\n        self._size -= 1\n        return num\n\n    def peek_first(self) -&gt; int:\n        \"\"\"Доступ к элементу в начале очереди\"\"\"\n        if self.is_empty():\n            raise IndexError(\"двусторонняя очередь пуста\")\n        return self._nums[self._front]\n\n    def peek_last(self) -&gt; int:\n        \"\"\"Доступ к элементу в конце очереди\"\"\"\n        if self.is_empty():\n            raise IndexError(\"двусторонняя очередь пуста\")\n        # Вычислить индекс хвостового элемента\n        last = self.index(self._front + self._size - 1)\n        return self._nums[last]\n\n    def to_array(self) -&gt; list[int]:\n        \"\"\"Вернуть массив для вывода\"\"\"\n        # Преобразовывать только элементы списка в пределах фактической длины\n        res = []\n        for i in range(self._size):\n            res.append(self._nums[self.index(self._front + i)])\n        return res\n</code></pre> array_deque.cpp<pre><code>/* Двусторонняя очередь на основе кольцевого массива */\nclass ArrayDeque {\n  private:\n    vector&lt;int&gt; nums; // Массив для хранения элементов двусторонней очереди\n    int front;        // Указатель head, указывающий на первый элемент очереди\n    int queSize;      // Длина двусторонней очереди\n\n  public:\n    /* Конструктор */\n    ArrayDeque(int capacity) {\n        nums.resize(capacity);\n        front = queSize = 0;\n    }\n\n    /* Получить вместимость двусторонней очереди */\n    int capacity() {\n        return nums.size();\n    }\n\n    /* Получение длины двусторонней очереди */\n    int size() {\n        return queSize;\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    bool isEmpty() {\n        return queSize == 0;\n    }\n\n    /* Вычислить индекс в кольцевом массиве */\n    int index(int i) {\n        // С помощью операции взятия по модулю соединить начало и конец массива\n        // Когда i выходит за конец массива, он возвращается в начало\n        // Когда i выходит за начало массива, он возвращается в конец\n        return (i + capacity()) % capacity();\n    }\n\n    /* Добавление в голову очереди */\n    void pushFirst(int num) {\n        if (queSize == capacity()) {\n            cout &lt;&lt; \"Двусторонняя очередь заполнена\" &lt;&lt; endl;\n            return;\n        }\n        // Указатель головы сдвигается на одну позицию влево\n        // С помощью операции взятия по модулю front после выхода за начало массива возвращается в хвост\n        front = index(front - 1);\n        // Добавить num в голову очереди\n        nums[front] = num;\n        queSize++;\n    }\n\n    /* Добавление в хвост очереди */\n    void pushLast(int num) {\n        if (queSize == capacity()) {\n            cout &lt;&lt; \"Двусторонняя очередь заполнена\" &lt;&lt; endl;\n            return;\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        int rear = index(front + queSize);\n        // Добавить num в хвост очереди\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* Извлечение из головы очереди */\n    int popFirst() {\n        int num = peekFirst();\n        // Указатель головы сдвигается на одну позицию назад\n        front = index(front + 1);\n        queSize--;\n        return num;\n    }\n\n    /* Извлечение из хвоста очереди */\n    int popLast() {\n        int num = peekLast();\n        queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    int peekFirst() {\n        if (isEmpty())\n            throw out_of_range(\"двусторонняя очередь пуста\");\n        return nums[front];\n    }\n\n    /* Доступ к элементу в конце очереди */\n    int peekLast() {\n        if (isEmpty())\n            throw out_of_range(\"двусторонняя очередь пуста\");\n        // Вычислить индекс хвостового элемента\n        int last = index(front + queSize - 1);\n        return nums[last];\n    }\n\n    /* Вернуть массив для вывода */\n    vector&lt;int&gt; toVector() {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        vector&lt;int&gt; res(queSize);\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            res[i] = nums[index(j)];\n        }\n        return res;\n    }\n};\n</code></pre> array_deque.java<pre><code>/* Двусторонняя очередь на основе кольцевого массива */\nclass ArrayDeque {\n    private int[] nums; // Массив для хранения элементов двусторонней очереди\n    private int front; // Указатель head, указывающий на первый элемент очереди\n    private int queSize; // Длина двусторонней очереди\n\n    /* Конструктор */\n    public ArrayDeque(int capacity) {\n        this.nums = new int[capacity];\n        front = queSize = 0;\n    }\n\n    /* Получить вместимость двусторонней очереди */\n    public int capacity() {\n        return nums.length;\n    }\n\n    /* Получение длины двусторонней очереди */\n    public int size() {\n        return queSize;\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    public boolean isEmpty() {\n        return queSize == 0;\n    }\n\n    /* Вычислить индекс в кольцевом массиве */\n    private int index(int i) {\n        // С помощью операции взятия по модулю соединить начало и конец массива\n        // Когда i выходит за конец массива, он возвращается в начало\n        // Когда i выходит за начало массива, он возвращается в конец\n        return (i + capacity()) % capacity();\n    }\n\n    /* Добавление в голову очереди */\n    public void pushFirst(int num) {\n        if (queSize == capacity()) {\n            System.out.println(\"Двусторонняя очередь заполнена\");\n            return;\n        }\n        // Указатель головы сдвигается на одну позицию влево\n        // С помощью операции взятия по модулю front после выхода за начало массива возвращается в хвост\n        front = index(front - 1);\n        // Добавить num в голову очереди\n        nums[front] = num;\n        queSize++;\n    }\n\n    /* Добавление в хвост очереди */\n    public void pushLast(int num) {\n        if (queSize == capacity()) {\n            System.out.println(\"Двусторонняя очередь заполнена\");\n            return;\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        int rear = index(front + queSize);\n        // Добавить num в хвост очереди\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* Извлечение из головы очереди */\n    public int popFirst() {\n        int num = peekFirst();\n        // Указатель головы сдвигается на одну позицию назад\n        front = index(front + 1);\n        queSize--;\n        return num;\n    }\n\n    /* Извлечение из хвоста очереди */\n    public int popLast() {\n        int num = peekLast();\n        queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    public int peekFirst() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return nums[front];\n    }\n\n    /* Доступ к элементу в конце очереди */\n    public int peekLast() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        // Вычислить индекс хвостового элемента\n        int last = index(front + queSize - 1);\n        return nums[last];\n    }\n\n    /* Вернуть массив для вывода */\n    public int[] toArray() {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        int[] res = new int[queSize];\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            res[i] = nums[index(j)];\n        }\n        return res;\n    }\n}\n</code></pre> array_deque.cs<pre><code>/* Двусторонняя очередь на основе кольцевого массива */\nclass ArrayDeque {\n    int[] nums;  // Массив для хранения элементов двусторонней очереди\n    int front;   // Указатель head, указывающий на первый элемент очереди\n    int queSize; // Длина двусторонней очереди\n\n    /* Конструктор */\n    public ArrayDeque(int capacity) {\n        nums = new int[capacity];\n        front = queSize = 0;\n    }\n\n    /* Получить вместимость двусторонней очереди */\n    int Capacity() {\n        return nums.Length;\n    }\n\n    /* Получение длины двусторонней очереди */\n    public int Size() {\n        return queSize;\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    public bool IsEmpty() {\n        return queSize == 0;\n    }\n\n    /* Вычислить индекс в кольцевом массиве */\n    int Index(int i) {\n        // С помощью операции взятия по модулю соединить начало и конец массива\n        // Когда i выходит за конец массива, он возвращается в начало\n        // Когда i выходит за начало массива, он возвращается в конец\n        return (i + Capacity()) % Capacity();\n    }\n\n    /* Добавление в голову очереди */\n    public void PushFirst(int num) {\n        if (queSize == Capacity()) {\n            Console.WriteLine(\"Двусторонняя очередь заполнена\");\n            return;\n        }\n        // Указатель головы сдвигается на одну позицию влево\n        // С помощью операции взятия по модулю front после выхода за начало массива возвращается в хвост\n        front = Index(front - 1);\n        // Добавить num в голову очереди\n        nums[front] = num;\n        queSize++;\n    }\n\n    /* Добавление в хвост очереди */\n    public void PushLast(int num) {\n        if (queSize == Capacity()) {\n            Console.WriteLine(\"Двусторонняя очередь заполнена\");\n            return;\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        int rear = Index(front + queSize);\n        // Добавить num в хвост очереди\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* Извлечение из головы очереди */\n    public int PopFirst() {\n        int num = PeekFirst();\n        // Указатель головы сдвигается на одну позицию назад\n        front = Index(front + 1);\n        queSize--;\n        return num;\n    }\n\n    /* Извлечение из хвоста очереди */\n    public int PopLast() {\n        int num = PeekLast();\n        queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    public int PeekFirst() {\n        if (IsEmpty()) {\n            throw new InvalidOperationException();\n        }\n        return nums[front];\n    }\n\n    /* Доступ к элементу в конце очереди */\n    public int PeekLast() {\n        if (IsEmpty()) {\n            throw new InvalidOperationException();\n        }\n        // Вычислить индекс хвостового элемента\n        int last = Index(front + queSize - 1);\n        return nums[last];\n    }\n\n    /* Вернуть массив для вывода */\n    public int[] ToArray() {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        int[] res = new int[queSize];\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            res[i] = nums[Index(j)];\n        }\n        return res;\n    }\n}\n</code></pre> array_deque.go<pre><code>/* Двусторонняя очередь на основе кольцевого массива */\ntype arrayDeque struct {\n    nums        []int // Массив для хранения элементов двусторонней очереди\n    front       int   // Указатель head, указывающий на первый элемент очереди\n    queSize     int   // Длина двусторонней очереди\n    queCapacity int   // Вместимость очереди (то есть максимальное число элементов)\n}\n\n/* Инициализация очереди */\nfunc newArrayDeque(queCapacity int) *arrayDeque {\n    return &amp;arrayDeque{\n        nums:        make([]int, queCapacity),\n        queCapacity: queCapacity,\n        front:       0,\n        queSize:     0,\n    }\n}\n\n/* Получение длины двусторонней очереди */\nfunc (q *arrayDeque) size() int {\n    return q.queSize\n}\n\n/* Проверка, пуста ли двусторонняя очередь */\nfunc (q *arrayDeque) isEmpty() bool {\n    return q.queSize == 0\n}\n\n/* Вычислить индекс в кольцевом массиве */\nfunc (q *arrayDeque) index(i int) int {\n    // С помощью операции взятия по модулю соединить начало и конец массива\n    // Когда i выходит за конец массива, он возвращается в начало\n    // Когда i выходит за начало массива, он возвращается в конец\n    return (i + q.queCapacity) % q.queCapacity\n}\n\n/* Добавление в голову очереди */\nfunc (q *arrayDeque) pushFirst(num int) {\n    if q.queSize == q.queCapacity {\n        fmt.Println(\"Двусторонняя очередь заполнена\")\n        return\n    }\n    // Указатель головы сдвигается на одну позицию влево\n    // С помощью операции взятия по модулю front после выхода за начало массива возвращается в хвост\n    q.front = q.index(q.front - 1)\n    // Добавить num в голову очереди\n    q.nums[q.front] = num\n    q.queSize++\n}\n\n/* Добавление в хвост очереди */\nfunc (q *arrayDeque) pushLast(num int) {\n    if q.queSize == q.queCapacity {\n        fmt.Println(\"Двусторонняя очередь заполнена\")\n        return\n    }\n    // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n    rear := q.index(q.front + q.queSize)\n    // Добавить num в хвост очереди\n    q.nums[rear] = num\n    q.queSize++\n}\n\n/* Извлечение из головы очереди */\nfunc (q *arrayDeque) popFirst() any {\n    num := q.peekFirst()\n    if num == nil {\n        return nil\n    }\n    // Указатель головы сдвигается на одну позицию назад\n    q.front = q.index(q.front + 1)\n    q.queSize--\n    return num\n}\n\n/* Извлечение из хвоста очереди */\nfunc (q *arrayDeque) popLast() any {\n    num := q.peekLast()\n    if num == nil {\n        return nil\n    }\n    q.queSize--\n    return num\n}\n\n/* Доступ к элементу в начале очереди */\nfunc (q *arrayDeque) peekFirst() any {\n    if q.isEmpty() {\n        return nil\n    }\n    return q.nums[q.front]\n}\n\n/* Доступ к элементу в конце очереди */\nfunc (q *arrayDeque) peekLast() any {\n    if q.isEmpty() {\n        return nil\n    }\n    // Вычислить индекс хвостового элемента\n    last := q.index(q.front + q.queSize - 1)\n    return q.nums[last]\n}\n\n/* Получить Slice для вывода */\nfunc (q *arrayDeque) toSlice() []int {\n    // Преобразовывать только элементы списка в пределах фактической длины\n    res := make([]int, q.queSize)\n    for i, j := 0, q.front; i &lt; q.queSize; i++ {\n        res[i] = q.nums[q.index(j)]\n        j++\n    }\n    return res\n}\n</code></pre> array_deque.swift<pre><code>/* Двусторонняя очередь на основе кольцевого массива */\nclass ArrayDeque {\n    private var nums: [Int] // Массив для хранения элементов двусторонней очереди\n    private var front: Int // Указатель head, указывающий на первый элемент очереди\n    private var _size: Int // Длина двусторонней очереди\n\n    /* Конструктор */\n    init(capacity: Int) {\n        nums = Array(repeating: 0, count: capacity)\n        front = 0\n        _size = 0\n    }\n\n    /* Получить вместимость двусторонней очереди */\n    func capacity() -&gt; Int {\n        nums.count\n    }\n\n    /* Получение длины двусторонней очереди */\n    func size() -&gt; Int {\n        _size\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    func isEmpty() -&gt; Bool {\n        size() == 0\n    }\n\n    /* Вычислить индекс в кольцевом массиве */\n    private func index(i: Int) -&gt; Int {\n        // С помощью операции взятия по модулю соединить начало и конец массива\n        // Когда i выходит за конец массива, он возвращается в начало\n        // Когда i выходит за начало массива, он возвращается в конец\n        (i + capacity()) % capacity()\n    }\n\n    /* Добавление в голову очереди */\n    func pushFirst(num: Int) {\n        if size() == capacity() {\n            print(\"Двусторонняя очередь заполнена\")\n            return\n        }\n        // Указатель головы сдвигается на одну позицию влево\n        // С помощью операции взятия по модулю front после выхода за начало массива возвращается в хвост\n        front = index(i: front - 1)\n        // Добавить num в голову очереди\n        nums[front] = num\n        _size += 1\n    }\n\n    /* Добавление в хвост очереди */\n    func pushLast(num: Int) {\n        if size() == capacity() {\n            print(\"Двусторонняя очередь заполнена\")\n            return\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        let rear = index(i: front + size())\n        // Добавить num в хвост очереди\n        nums[rear] = num\n        _size += 1\n    }\n\n    /* Извлечение из головы очереди */\n    func popFirst() -&gt; Int {\n        let num = peekFirst()\n        // Указатель головы сдвигается на одну позицию назад\n        front = index(i: front + 1)\n        _size -= 1\n        return num\n    }\n\n    /* Извлечение из хвоста очереди */\n    func popLast() -&gt; Int {\n        let num = peekLast()\n        _size -= 1\n        return num\n    }\n\n    /* Доступ к элементу в начале очереди */\n    func peekFirst() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"двусторонняя очередь пуста\")\n        }\n        return nums[front]\n    }\n\n    /* Доступ к элементу в конце очереди */\n    func peekLast() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"двусторонняя очередь пуста\")\n        }\n        // Вычислить индекс хвостового элемента\n        let last = index(i: front + size() - 1)\n        return nums[last]\n    }\n\n    /* Вернуть массив для вывода */\n    func toArray() -&gt; [Int] {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        (front ..&lt; front + size()).map { nums[index(i: $0)] }\n    }\n}\n</code></pre> array_deque.js<pre><code>/* Двусторонняя очередь на основе кольцевого массива */\nclass ArrayDeque {\n    #nums; // Массив для хранения элементов двусторонней очереди\n    #front; // Указатель head, указывающий на первый элемент очереди\n    #queSize; // Длина двусторонней очереди\n\n    /* Конструктор */\n    constructor(capacity) {\n        this.#nums = new Array(capacity);\n        this.#front = 0;\n        this.#queSize = 0;\n    }\n\n    /* Получить вместимость двусторонней очереди */\n    capacity() {\n        return this.#nums.length;\n    }\n\n    /* Получение длины двусторонней очереди */\n    size() {\n        return this.#queSize;\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    isEmpty() {\n        return this.#queSize === 0;\n    }\n\n    /* Вычислить индекс в кольцевом массиве */\n    index(i) {\n        // С помощью операции взятия по модулю соединить начало и конец массива\n        // Когда i выходит за конец массива, он возвращается в начало\n        // Когда i выходит за начало массива, он возвращается в конец\n        return (i + this.capacity()) % this.capacity();\n    }\n\n    /* Добавление в голову очереди */\n    pushFirst(num) {\n        if (this.#queSize === this.capacity()) {\n            console.log('Двусторонняя очередь заполнена');\n            return;\n        }\n        // Указатель головы сдвигается на одну позицию влево\n        // С помощью операции взятия по модулю front после выхода за начало массива возвращается в хвост\n        this.#front = this.index(this.#front - 1);\n        // Добавить num в голову очереди\n        this.#nums[this.#front] = num;\n        this.#queSize++;\n    }\n\n    /* Добавление в хвост очереди */\n    pushLast(num) {\n        if (this.#queSize === this.capacity()) {\n            console.log('Двусторонняя очередь заполнена');\n            return;\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        const rear = this.index(this.#front + this.#queSize);\n        // Добавить num в хвост очереди\n        this.#nums[rear] = num;\n        this.#queSize++;\n    }\n\n    /* Извлечение из головы очереди */\n    popFirst() {\n        const num = this.peekFirst();\n        // Указатель головы сдвигается на одну позицию назад\n        this.#front = this.index(this.#front + 1);\n        this.#queSize--;\n        return num;\n    }\n\n    /* Извлечение из хвоста очереди */\n    popLast() {\n        const num = this.peekLast();\n        this.#queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    peekFirst() {\n        if (this.isEmpty()) throw new Error('The Deque Is Empty.');\n        return this.#nums[this.#front];\n    }\n\n    /* Доступ к элементу в конце очереди */\n    peekLast() {\n        if (this.isEmpty()) throw new Error('The Deque Is Empty.');\n        // Вычислить индекс хвостового элемента\n        const last = this.index(this.#front + this.#queSize - 1);\n        return this.#nums[last];\n    }\n\n    /* Вернуть массив для вывода */\n    toArray() {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        const res = [];\n        for (let i = 0, j = this.#front; i &lt; this.#queSize; i++, j++) {\n            res[i] = this.#nums[this.index(j)];\n        }\n        return res;\n    }\n}\n</code></pre> array_deque.ts<pre><code>/* Двусторонняя очередь на основе кольцевого массива */\nclass ArrayDeque {\n    private nums: number[]; // Массив для хранения элементов двусторонней очереди\n    private front: number; // Указатель head, указывающий на первый элемент очереди\n    private queSize: number; // Длина двусторонней очереди\n\n    /* Конструктор */\n    constructor(capacity: number) {\n        this.nums = new Array(capacity);\n        this.front = 0;\n        this.queSize = 0;\n    }\n\n    /* Получить вместимость двусторонней очереди */\n    capacity(): number {\n        return this.nums.length;\n    }\n\n    /* Получение длины двусторонней очереди */\n    size(): number {\n        return this.queSize;\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    isEmpty(): boolean {\n        return this.queSize === 0;\n    }\n\n    /* Вычислить индекс в кольцевом массиве */\n    index(i: number): number {\n        // С помощью операции взятия по модулю соединить начало и конец массива\n        // Когда i выходит за конец массива, он возвращается в начало\n        // Когда i выходит за начало массива, он возвращается в конец\n        return (i + this.capacity()) % this.capacity();\n    }\n\n    /* Добавление в голову очереди */\n    pushFirst(num: number): void {\n        if (this.queSize === this.capacity()) {\n            console.log('Двусторонняя очередь заполнена');\n            return;\n        }\n        // Указатель головы сдвигается на одну позицию влево\n        // С помощью операции взятия по модулю front после выхода за начало массива возвращается в хвост\n        this.front = this.index(this.front - 1);\n        // Добавить num в голову очереди\n        this.nums[this.front] = num;\n        this.queSize++;\n    }\n\n    /* Добавление в хвост очереди */\n    pushLast(num: number): void {\n        if (this.queSize === this.capacity()) {\n            console.log('Двусторонняя очередь заполнена');\n            return;\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        const rear: number = this.index(this.front + this.queSize);\n        // Добавить num в хвост очереди\n        this.nums[rear] = num;\n        this.queSize++;\n    }\n\n    /* Извлечение из головы очереди */\n    popFirst(): number {\n        const num: number = this.peekFirst();\n        // Указатель головы сдвигается на одну позицию назад\n        this.front = this.index(this.front + 1);\n        this.queSize--;\n        return num;\n    }\n\n    /* Извлечение из хвоста очереди */\n    popLast(): number {\n        const num: number = this.peekLast();\n        this.queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    peekFirst(): number {\n        if (this.isEmpty()) throw new Error('The Deque Is Empty.');\n        return this.nums[this.front];\n    }\n\n    /* Доступ к элементу в конце очереди */\n    peekLast(): number {\n        if (this.isEmpty()) throw new Error('The Deque Is Empty.');\n        // Вычислить индекс хвостового элемента\n        const last = this.index(this.front + this.queSize - 1);\n        return this.nums[last];\n    }\n\n    /* Вернуть массив для вывода */\n    toArray(): number[] {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        const res: number[] = [];\n        for (let i = 0, j = this.front; i &lt; this.queSize; i++, j++) {\n            res[i] = this.nums[this.index(j)];\n        }\n        return res;\n    }\n}\n</code></pre> array_deque.dart<pre><code>/* Двусторонняя очередь на основе кольцевого массива */\nclass ArrayDeque {\n  late List&lt;int&gt; _nums; // Массив для хранения элементов двусторонней очереди\n  late int _front; // Указатель head, указывающий на первый элемент очереди\n  late int _queSize; // Длина двусторонней очереди\n\n  /* Конструктор */\n  ArrayDeque(int capacity) {\n    this._nums = List.filled(capacity, 0);\n    this._front = this._queSize = 0;\n  }\n\n  /* Получить вместимость двусторонней очереди */\n  int capacity() {\n    return _nums.length;\n  }\n\n  /* Получение длины двусторонней очереди */\n  int size() {\n    return _queSize;\n  }\n\n  /* Проверка, пуста ли двусторонняя очередь */\n  bool isEmpty() {\n    return _queSize == 0;\n  }\n\n  /* Вычислить индекс в кольцевом массиве */\n  int index(int i) {\n    // С помощью операции взятия по модулю соединить начало и конец массива\n    // Когда i выходит за конец массива, он возвращается в начало\n    // Когда i выходит за начало массива, он возвращается в конец\n    return (i + capacity()) % capacity();\n  }\n\n  /* Добавление в голову очереди */\n  void pushFirst(int _num) {\n    if (_queSize == capacity()) {\n      throw Exception(\"Двусторонняя очередь заполнена\");\n    }\n    // Указатель головы сместить влево на одну позицию\n    // С помощью операции взятия остатка реализовать возврат _front к хвосту после выхода за начало массива\n    _front = index(_front - 1);\n    // Добавить _num в голову очереди\n    _nums[_front] = _num;\n    _queSize++;\n  }\n\n  /* Добавление в хвост очереди */\n  void pushLast(int _num) {\n    if (_queSize == capacity()) {\n      throw Exception(\"Двусторонняя очередь заполнена\");\n    }\n    // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n    int rear = index(_front + _queSize);\n    // Добавить _num в хвост очереди\n    _nums[rear] = _num;\n    _queSize++;\n  }\n\n  /* Извлечение из головы очереди */\n  int popFirst() {\n    int _num = peekFirst();\n    // Указатель головы сместить вправо на одну позицию\n    _front = index(_front + 1);\n    _queSize--;\n    return _num;\n  }\n\n  /* Извлечение из хвоста очереди */\n  int popLast() {\n    int _num = peekLast();\n    _queSize--;\n    return _num;\n  }\n\n  /* Доступ к элементу в начале очереди */\n  int peekFirst() {\n    if (isEmpty()) {\n      throw Exception(\"двусторонняя очередь пуста\");\n    }\n    return _nums[_front];\n  }\n\n  /* Доступ к элементу в конце очереди */\n  int peekLast() {\n    if (isEmpty()) {\n      throw Exception(\"двусторонняя очередь пуста\");\n    }\n    // Вычислить индекс хвостового элемента\n    int last = index(_front + _queSize - 1);\n    return _nums[last];\n  }\n\n  /* Вернуть массив для вывода */\n  List&lt;int&gt; toArray() {\n    // Преобразовывать только элементы списка в пределах фактической длины\n    List&lt;int&gt; res = List.filled(_queSize, 0);\n    for (int i = 0, j = _front; i &lt; _queSize; i++, j++) {\n      res[i] = _nums[index(j)];\n    }\n    return res;\n  }\n}\n</code></pre> array_deque.rs<pre><code>/* Двусторонняя очередь на основе кольцевого массива */\nstruct ArrayDeque&lt;T&gt; {\n    nums: Vec&lt;T&gt;,    // Массив для хранения элементов двусторонней очереди\n    front: usize,    // Указатель head, указывающий на первый элемент очереди\n    que_size: usize, // Длина двусторонней очереди\n}\n\nimpl&lt;T: Copy + Default&gt; ArrayDeque&lt;T&gt; {\n    /* Конструктор */\n    pub fn new(capacity: usize) -&gt; Self {\n        Self {\n            nums: vec![T::default(); capacity],\n            front: 0,\n            que_size: 0,\n        }\n    }\n\n    /* Получить вместимость двусторонней очереди */\n    pub fn capacity(&amp;self) -&gt; usize {\n        self.nums.len()\n    }\n\n    /* Получение длины двусторонней очереди */\n    pub fn size(&amp;self) -&gt; usize {\n        self.que_size\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    pub fn is_empty(&amp;self) -&gt; bool {\n        self.que_size == 0\n    }\n\n    /* Вычислить индекс в кольцевом массиве */\n    fn index(&amp;self, i: i32) -&gt; usize {\n        // С помощью операции взятия по модулю соединить начало и конец массива\n        // Когда i выходит за конец массива, он возвращается в начало\n        // Когда i выходит за начало массива, он возвращается в конец\n        ((i + self.capacity() as i32) % self.capacity() as i32) as usize\n    }\n\n    /* Добавление в голову очереди */\n    pub fn push_first(&amp;mut self, num: T) {\n        if self.que_size == self.capacity() {\n            println!(\"Двусторонняя очередь заполнена\");\n            return;\n        }\n        // Указатель головы сдвигается на одну позицию влево\n        // С помощью операции взятия по модулю front после выхода за начало массива возвращается в хвост\n        self.front = self.index(self.front as i32 - 1);\n        // Добавить num в голову очереди\n        self.nums[self.front] = num;\n        self.que_size += 1;\n    }\n\n    /* Добавление в хвост очереди */\n    pub fn push_last(&amp;mut self, num: T) {\n        if self.que_size == self.capacity() {\n            println!(\"Двусторонняя очередь заполнена\");\n            return;\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        let rear = self.index(self.front as i32 + self.que_size as i32);\n        // Добавить num в хвост очереди\n        self.nums[rear] = num;\n        self.que_size += 1;\n    }\n\n    /* Извлечение из головы очереди */\n    fn pop_first(&amp;mut self) -&gt; T {\n        let num = self.peek_first();\n        // Указатель головы сдвигается на одну позицию назад\n        self.front = self.index(self.front as i32 + 1);\n        self.que_size -= 1;\n        num\n    }\n\n    /* Извлечение из хвоста очереди */\n    fn pop_last(&amp;mut self) -&gt; T {\n        let num = self.peek_last();\n        self.que_size -= 1;\n        num\n    }\n\n    /* Доступ к элементу в начале очереди */\n    fn peek_first(&amp;self) -&gt; T {\n        if self.is_empty() {\n            panic!(\"двусторонняя очередь пуста\")\n        };\n        self.nums[self.front]\n    }\n\n    /* Доступ к элементу в конце очереди */\n    fn peek_last(&amp;self) -&gt; T {\n        if self.is_empty() {\n            panic!(\"двусторонняя очередь пуста\")\n        };\n        // Вычислить индекс хвостового элемента\n        let last = self.index(self.front as i32 + self.que_size as i32 - 1);\n        self.nums[last]\n    }\n\n    /* Вернуть массив для вывода */\n    fn to_array(&amp;self) -&gt; Vec&lt;T&gt; {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        let mut res = vec![T::default(); self.que_size];\n        let mut j = self.front;\n        for i in 0..self.que_size {\n            res[i] = self.nums[self.index(j as i32)];\n            j += 1;\n        }\n        res\n    }\n}\n</code></pre> array_deque.c<pre><code>/* Двусторонняя очередь на основе кольцевого массива */\ntypedef struct {\n    int *nums;       // Массив для хранения элементов очереди\n    int front;       // Указатель head, указывающий на первый элемент очереди\n    int queSize;     // Указатель хвоста, указывающий на позицию после хвоста\n    int queCapacity; // Вместимость очереди\n} ArrayDeque;\n\n/* Конструктор */\nArrayDeque *newArrayDeque(int capacity) {\n    ArrayDeque *deque = (ArrayDeque *)malloc(sizeof(ArrayDeque));\n    // Инициализация массива\n    deque-&gt;queCapacity = capacity;\n    deque-&gt;nums = (int *)malloc(sizeof(int) * deque-&gt;queCapacity);\n    deque-&gt;front = deque-&gt;queSize = 0;\n    return deque;\n}\n\n/* Деструктор */\nvoid delArrayDeque(ArrayDeque *deque) {\n    free(deque-&gt;nums);\n    free(deque);\n}\n\n/* Получить вместимость двусторонней очереди */\nint capacity(ArrayDeque *deque) {\n    return deque-&gt;queCapacity;\n}\n\n/* Получение длины двусторонней очереди */\nint size(ArrayDeque *deque) {\n    return deque-&gt;queSize;\n}\n\n/* Проверка, пуста ли двусторонняя очередь */\nbool empty(ArrayDeque *deque) {\n    return deque-&gt;queSize == 0;\n}\n\n/* Вычислить индекс в кольцевом массиве */\nint dequeIndex(ArrayDeque *deque, int i) {\n    // С помощью операции взятия остатка соединить начало и конец массива\n    // Когда i выходит за хвост массива, вернуться к началу\n    // Когда i выходит за голову массива, вернуться к концу\n    return ((i + capacity(deque)) % capacity(deque));\n}\n\n/* Добавление в голову очереди */\nvoid pushFirst(ArrayDeque *deque, int num) {\n    if (deque-&gt;queSize == capacity(deque)) {\n        printf(\"Дек заполнен\\r\\n\");\n        return;\n    }\n    // Указатель головы сместить влево на одну позицию\n    // С помощью операции взятия остатка реализовать возврат front к хвосту после выхода за начало массива\n    deque-&gt;front = dequeIndex(deque, deque-&gt;front - 1);\n    // Добавить num в голову очереди\n    deque-&gt;nums[deque-&gt;front] = num;\n    deque-&gt;queSize++;\n}\n\n/* Добавление в хвост очереди */\nvoid pushLast(ArrayDeque *deque, int num) {\n    if (deque-&gt;queSize == capacity(deque)) {\n        printf(\"Дек заполнен\\r\\n\");\n        return;\n    }\n    // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n    int rear = dequeIndex(deque, deque-&gt;front + deque-&gt;queSize);\n    // Добавить num в хвост очереди\n    deque-&gt;nums[rear] = num;\n    deque-&gt;queSize++;\n}\n\n/* Доступ к элементу в начале очереди */\nint peekFirst(ArrayDeque *deque) {\n    // Ошибка доступа: двусторонняя очередь пуста\n    assert(empty(deque) == 0);\n    return deque-&gt;nums[deque-&gt;front];\n}\n\n/* Доступ к элементу в конце очереди */\nint peekLast(ArrayDeque *deque) {\n    // Ошибка доступа: двусторонняя очередь пуста\n    assert(empty(deque) == 0);\n    int last = dequeIndex(deque, deque-&gt;front + deque-&gt;queSize - 1);\n    return deque-&gt;nums[last];\n}\n\n/* Извлечение из головы очереди */\nint popFirst(ArrayDeque *deque) {\n    int num = peekFirst(deque);\n    // Указатель головы сдвигается на одну позицию назад\n    deque-&gt;front = dequeIndex(deque, deque-&gt;front + 1);\n    deque-&gt;queSize--;\n    return num;\n}\n\n/* Извлечение из хвоста очереди */\nint popLast(ArrayDeque *deque) {\n    int num = peekLast(deque);\n    deque-&gt;queSize--;\n    return num;\n}\n\n/* Вернуть массив для вывода */\nint *toArray(ArrayDeque *deque, int *queSize) {\n    *queSize = deque-&gt;queSize;\n    int *res = (int *)calloc(deque-&gt;queSize, sizeof(int));\n    int j = deque-&gt;front;\n    for (int i = 0; i &lt; deque-&gt;queSize; i++) {\n        res[i] = deque-&gt;nums[j % deque-&gt;queCapacity];\n        j++;\n    }\n    return res;\n}\n</code></pre> array_deque.kt<pre><code>/* Конструктор */\nclass ArrayDeque(capacity: Int) {\n    private var nums: IntArray = IntArray(capacity) // Массив для хранения элементов двусторонней очереди\n    private var front: Int = 0 // Указатель head, указывающий на первый элемент очереди\n    private var queSize: Int = 0 // Длина двусторонней очереди\n\n    /* Получить вместимость двусторонней очереди */\n    fun capacity(): Int {\n        return nums.size\n    }\n\n    /* Получение длины двусторонней очереди */\n    fun size(): Int {\n        return queSize\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    fun isEmpty(): Boolean {\n        return queSize == 0\n    }\n\n    /* Вычислить индекс в кольцевом массиве */\n    private fun index(i: Int): Int {\n        // С помощью операции взятия по модулю соединить начало и конец массива\n        // Когда i выходит за конец массива, он возвращается в начало\n        // Когда i выходит за начало массива, он возвращается в конец\n        return (i + capacity()) % capacity()\n    }\n\n    /* Добавление в голову очереди */\n    fun pushFirst(num: Int) {\n        if (queSize == capacity()) {\n            println(\"Двусторонняя очередь заполнена\")\n            return\n        }\n        // Указатель головы сдвигается на одну позицию влево\n        // С помощью операции взятия по модулю front после выхода за начало массива возвращается в хвост\n        front = index(front - 1)\n        // Добавить num в голову очереди\n        nums[front] = num\n        queSize++\n    }\n\n    /* Добавление в хвост очереди */\n    fun pushLast(num: Int) {\n        if (queSize == capacity()) {\n            println(\"Двусторонняя очередь заполнена\")\n            return\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        val rear = index(front + queSize)\n        // Добавить num в хвост очереди\n        nums[rear] = num\n        queSize++\n    }\n\n    /* Извлечение из головы очереди */\n    fun popFirst(): Int {\n        val num = peekFirst()\n        // Указатель головы сдвигается на одну позицию назад\n        front = index(front + 1)\n        queSize--\n        return num\n    }\n\n    /* Извлечение из хвоста очереди */\n    fun popLast(): Int {\n        val num = peekLast()\n        queSize--\n        return num\n    }\n\n    /* Доступ к элементу в начале очереди */\n    fun peekFirst(): Int {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        return nums[front]\n    }\n\n    /* Доступ к элементу в конце очереди */\n    fun peekLast(): Int {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        // Вычислить индекс хвостового элемента\n        val last = index(front + queSize - 1)\n        return nums[last]\n    }\n\n    /* Вернуть массив для вывода */\n    fun toArray(): IntArray {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        val res = IntArray(queSize)\n        var i = 0\n        var j = front\n        while (i &lt; queSize) {\n            res[i] = nums[index(j)]\n            i++\n            j++\n        }\n        return res\n    }\n}\n</code></pre> array_deque.rb<pre><code>### Двусторонняя очередь на основе кольцевого массива ###\nclass ArrayDeque\n  ### Получение длины двусторонней очереди ###\n  attr_reader :size\n\n  ### Конструктор ###\n  def initialize(capacity)\n    @nums = Array.new(capacity, 0)\n    @front = 0\n    @size = 0\n  end\n\n  ### Получить вместимость двусторонней очереди ###\n  def capacity\n    @nums.length\n  end\n\n  ### Проверка, пуста ли двусторонняя очередь ###\n  def is_empty?\n    size.zero?\n  end\n\n  ### Добавление в голову очереди ###\n  def push_first(num)\n    if size == capacity\n      puts 'Двусторонняя очередь заполнена'\n      return\n    end\n\n    # Указатель головы сдвигается на одну позицию влево\n    # С помощью операции взятия по модулю front после выхода за начало массива возвращается в хвост\n    @front = index(@front - 1)\n    # Добавить num в голову очереди\n    @nums[@front] = num\n    @size += 1\n  end\n\n  ### Добавление в хвост очереди ###\n  def push_last(num)\n    if size == capacity\n      puts 'Двусторонняя очередь заполнена'\n      return\n    end\n\n    # Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n    rear = index(@front + size)\n    # Добавить num в хвост очереди\n    @nums[rear] = num\n    @size += 1\n  end\n\n  ### Извлечение из головы очереди ###\n  def pop_first\n    num = peek_first\n    # Указатель головы сдвигается на одну позицию назад\n    @front = index(@front + 1)\n    @size -= 1\n    num\n  end\n\n  ### Извлечение из хвоста очереди ###\n  def pop_last\n    num = peek_last\n    @size -= 1\n    num\n  end\n\n  ### Доступ к элементу в начале очереди ###\n  def peek_first\n    raise IndexError, 'двусторонняя очередь пуста' if is_empty?\n\n    @nums[@front]\n  end\n\n  ### Доступ к элементу в хвосте очереди ###\n  def peek_last\n    raise IndexError, 'двусторонняя очередь пуста' if is_empty?\n\n    # Вычислить индекс хвостового элемента\n    last = index(@front + size - 1)\n    @nums[last]\n  end\n\n  ### Вернуть массив для вывода ###\n  def to_array\n    # Преобразовывать только элементы списка в пределах фактической длины\n    res = []\n    for i in 0...size\n      res &lt;&lt; @nums[index(@front + i)]\n    end\n    res\n  end\n\n  private\n\n  ### Вычислить индекс в кольцевом массиве ###\n  def index(i)\n    # С помощью операции взятия по модулю соединить начало и конец массива\n    # Когда i выходит за конец массива, он возвращается в начало\n    # Когда i выходит за начало массива, он возвращается в конец\n    (i + capacity) % capacity\n  end\nend\n</code></pre>","path":["Глава 5. Стек и очередь","5.3 &nbsp; Двусторонняя очередь"],"tags":[]},{"location":"chapter_stack_and_queue/deque/#533","level":2,"title":"5.3.3   Применение двусторонней очереди","text":"<p>Двусторонняя очередь сочетает в себе логику стека и очереди, поэтому она может покрыть все сценарии применения обеих структур и при этом предоставляет более высокую степень свободы.</p> <p>Мы знаем, что функция \"undo\" в программном обеспечении обычно реализуется с помощью стека: система <code>push</code>-ит каждое изменение в стек, а затем использует <code>pop</code> для отмены. Однако, учитывая ограниченность системных ресурсов, программы обычно ограничивают число шагов отмены (например, разрешают хранить только \\(50\\) шагов). Когда длина стека превышает \\(50\\), программе нужно удалить элемент с дна стека (то есть с головы очереди). Но стек не может реализовать такую операцию, и в этом случае его приходится заменять двусторонней очередью. Обрати внимание: основная логика \"undo\" по-прежнему следует стековому правилу LIFO, просто двусторонняя очередь позволяет более гибко реализовать некоторые дополнительные механизмы.</p>","path":["Глава 5. Стек и очередь","5.3 &nbsp; Двусторонняя очередь"],"tags":[]},{"location":"chapter_stack_and_queue/queue/","level":1,"title":"5.2   Очередь","text":"<p>Очередь (queue) - это линейная структура данных, подчиняющаяся правилу \"первым пришел - первым вышел\". Как видно из названия, очередь моделирует обычную ситуацию ожидания: новые люди непрерывно присоединяются к хвосту очереди, а стоящие в начале по одному уходят.</p> <p>Как показано на рисунке 5-4, начало очереди называется \"головой очереди\", а конец - \"хвостом очереди\"; операцию добавления элемента в хвост называют \"enqueue\", а операцию удаления элемента из головы - \"dequeue\".</p> <p></p> <p> Рисунок 5-4   Правило FIFO для очереди </p>","path":["Глава 5. Стек и очередь","5.2 &nbsp; Очередь"],"tags":[]},{"location":"chapter_stack_and_queue/queue/#521","level":2,"title":"5.2.1   Основные операции с очередью","text":"<p>Распространенные операции с очередью показаны в таблице 5-2. Следует учитывать, что названия методов в разных языках могут различаться. Здесь мы используем те же названия, что и для стека.</p> <p> Таблица 5-2   Эффективность операций с очередью </p> Имя метода Описание Временная сложность <code>push()</code> Поместить элемент в очередь, то есть добавить его в хвост \\(O(1)\\) <code>pop()</code> Извлечь элемент из головы очереди \\(O(1)\\) <code>peek()</code> Просмотреть элемент в голове очереди \\(O(1)\\) <p>Мы можем напрямую использовать готовые классы очереди, предоставляемые языками программирования:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby queue.py<pre><code>from collections import deque\n\n# Инициализация очереди\n# В Python обычно используют двустороннюю очередь deque как обычную очередь\n# Хотя queue.Queue() является \"чистой\" очередью, она не слишком удобна, поэтому ее не рекомендуют\nque: deque[int] = deque()\n\n# Поместить элементы в очередь\nque.append(1)\nque.append(3)\nque.append(2)\nque.append(5)\nque.append(4)\n\n# Просмотреть элемент в голове очереди\nfront: int = que[0]\n\n# Извлечь элемент из очереди\npop: int = que.popleft()\n\n# Получить длину очереди\nsize: int = len(que)\n\n# Проверить, пуста ли очередь\nis_empty: bool = len(que) == 0\n</code></pre> queue.cpp<pre><code>/* Инициализация очереди */\nqueue&lt;int&gt; queue;\n\n/* Поместить элементы в очередь */\nqueue.push(1);\nqueue.push(3);\nqueue.push(2);\nqueue.push(5);\nqueue.push(4);\n\n/* Просмотреть элемент в голове очереди */\nint front = queue.front();\n\n/* Извлечь элемент из очереди */\nqueue.pop();\n\n/* Получить длину очереди */\nint size = queue.size();\n\n/* Проверить, пуста ли очередь */\nbool empty = queue.empty();\n</code></pre> queue.java<pre><code>/* Инициализация очереди */\nQueue&lt;Integer&gt; queue = new LinkedList&lt;&gt;();\n\n/* Поместить элементы в очередь */\nqueue.offer(1);\nqueue.offer(3);\nqueue.offer(2);\nqueue.offer(5);\nqueue.offer(4);\n\n/* Просмотреть элемент в голове очереди */\nint peek = queue.peek();\n\n/* Извлечь элемент из очереди */\nint pop = queue.poll();\n\n/* Получить длину очереди */\nint size = queue.size();\n\n/* Проверить, пуста ли очередь */\nboolean isEmpty = queue.isEmpty();\n</code></pre> queue.cs<pre><code>/* Инициализация очереди */\nQueue&lt;int&gt; queue = new();\n\n/* Поместить элементы в очередь */\nqueue.Enqueue(1);\nqueue.Enqueue(3);\nqueue.Enqueue(2);\nqueue.Enqueue(5);\nqueue.Enqueue(4);\n\n/* Просмотреть элемент в голове очереди */\nint peek = queue.Peek();\n\n/* Извлечь элемент из очереди */\nint pop = queue.Dequeue();\n\n/* Получить длину очереди */\nint size = queue.Count;\n\n/* Проверить, пуста ли очередь */\nbool isEmpty = queue.Count == 0;\n</code></pre> queue_test.go<pre><code>/* Инициализация очереди */\n// В Go очередь обычно реализуют через list\nqueue := list.New()\n\n/* Поместить элементы в очередь */\nqueue.PushBack(1)\nqueue.PushBack(3)\nqueue.PushBack(2)\nqueue.PushBack(5)\nqueue.PushBack(4)\n\n/* Просмотреть элемент в голове очереди */\npeek := queue.Front()\n\n/* Извлечь элемент из очереди */\npop := queue.Front()\nqueue.Remove(pop)\n\n/* Получить длину очереди */\nsize := queue.Len()\n\n/* Проверить, пуста ли очередь */\nisEmpty := queue.Len() == 0\n</code></pre> queue.swift<pre><code>/* Инициализация очереди */\n// В Swift нет встроенного класса очереди, поэтому можно использовать Array как очередь\nvar queue: [Int] = []\n\n/* Поместить элементы в очередь */\nqueue.append(1)\nqueue.append(3)\nqueue.append(2)\nqueue.append(5)\nqueue.append(4)\n\n/* Просмотреть элемент в голове очереди */\nlet peek = queue.first!\n\n/* Извлечь элемент из очереди */\n// Поскольку в основе лежит массив, removeFirst имеет сложность O(n)\nlet pool = queue.removeFirst()\n\n/* Получить длину очереди */\nlet size = queue.count\n\n/* Проверить, пуста ли очередь */\nlet isEmpty = queue.isEmpty\n</code></pre> queue.js<pre><code>/* Инициализация очереди */\n// В JavaScript нет встроенной очереди, поэтому можно использовать Array как очередь\nconst queue = [];\n\n/* Поместить элементы в очередь */\nqueue.push(1);\nqueue.push(3);\nqueue.push(2);\nqueue.push(5);\nqueue.push(4);\n\n/* Просмотреть элемент в голове очереди */\nconst peek = queue[0];\n\n/* Извлечь элемент из очереди */\n// В основе лежит массив, поэтому shift() имеет сложность O(n)\nconst pop = queue.shift();\n\n/* Получить длину очереди */\nconst size = queue.length;\n\n/* Проверить, пуста ли очередь */\nconst empty = queue.length === 0;\n</code></pre> queue.ts<pre><code>/* Инициализация очереди */\n// В TypeScript нет встроенной очереди, поэтому можно использовать Array как очередь\nconst queue: number[] = [];\n\n/* Поместить элементы в очередь */\nqueue.push(1);\nqueue.push(3);\nqueue.push(2);\nqueue.push(5);\nqueue.push(4);\n\n/* Просмотреть элемент в голове очереди */\nconst peek = queue[0];\n\n/* Извлечь элемент из очереди */\n// В основе лежит массив, поэтому shift() имеет сложность O(n)\nconst pop = queue.shift();\n\n/* Получить длину очереди */\nconst size = queue.length;\n\n/* Проверить, пуста ли очередь */\nconst empty = queue.length === 0;\n</code></pre> queue.dart<pre><code>/* Инициализация очереди */\n// В Dart класс Queue является двусторонней очередью и может использоваться как обычная очередь\nQueue&lt;int&gt; queue = Queue();\n\n/* Поместить элементы в очередь */\nqueue.add(1);\nqueue.add(3);\nqueue.add(2);\nqueue.add(5);\nqueue.add(4);\n\n/* Просмотреть элемент в голове очереди */\nint peek = queue.first;\n\n/* Извлечь элемент из очереди */\nint pop = queue.removeFirst();\n\n/* Получить длину очереди */\nint size = queue.length;\n\n/* Проверить, пуста ли очередь */\nbool isEmpty = queue.isEmpty;\n</code></pre> queue.rs<pre><code>/* Инициализация двусторонней очереди */\n// В Rust двусторонняя очередь может использоваться как обычная очередь\nlet mut deque: VecDeque&lt;u32&gt; = VecDeque::new();\n\n/* Поместить элементы в очередь */\ndeque.push_back(1);\ndeque.push_back(3);\ndeque.push_back(2);\ndeque.push_back(5);\ndeque.push_back(4);\n\n/* Просмотреть элемент в голове очереди */\nif let Some(front) = deque.front() {\n}\n\n/* Извлечь элемент из очереди */\nif let Some(pop) = deque.pop_front() {\n}\n\n/* Получить длину очереди */\nlet size = deque.len();\n\n/* Проверить, пуста ли очередь */\nlet is_empty = deque.is_empty();\n</code></pre> queue.c<pre><code>// В C нет встроенной очереди\n</code></pre> queue.kt<pre><code>/* Инициализация очереди */\nval queue = LinkedList&lt;Int&gt;()\n\n/* Поместить элементы в очередь */\nqueue.offer(1)\nqueue.offer(3)\nqueue.offer(2)\nqueue.offer(5)\nqueue.offer(4)\n\n/* Просмотреть элемент в голове очереди */\nval peek = queue.peek()\n\n/* Извлечь элемент из очереди */\nval pop = queue.poll()\n\n/* Получить длину очереди */\nval size = queue.size\n\n/* Проверить, пуста ли очередь */\nval isEmpty = queue.isEmpty()\n</code></pre> queue.rb<pre><code># Инициализация очереди\n# Встроенная очередь в Ruby (Thread::Queue) не имеет методов peek и traverse, поэтому можно использовать Array как очередь\nqueue = []\n\n# Поместить элементы в очередь\nqueue.push(1)\nqueue.push(3)\nqueue.push(2)\nqueue.push(5)\nqueue.push(4)\n\n# Просмотреть элемент очереди\npeek = queue.first\n\n# Извлечь элемент из очереди\n# Обрати внимание: поскольку это массив, метод Array#shift имеет сложность O(n)\npop = queue.shift\n\n# Получить длину очереди\nsize = queue.length\n\n# Проверить, пуста ли очередь\nis_empty = queue.empty?\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=from%20collections%20import%20deque%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D1%8C%0A%20%20%20%20%23%20%D0%92%20Python%20%D0%B4%D0%B2%D1%83%D1%81%D1%82%D0%BE%D1%80%D0%BE%D0%BD%D0%BD%D1%8E%D1%8E%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D1%8C%20deque%20%D0%BE%D0%B1%D1%8B%D1%87%D0%BD%D0%BE%20%D0%B8%D1%81%D0%BF%D0%BE%D0%BB%D1%8C%D0%B7%D1%83%D1%8E%D1%82%20%D0%BA%D0%B0%D0%BA%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D1%8C%0A%20%20%20%20%23%20%D0%A5%D0%BE%D1%82%D1%8F%20queue.Queue%28%29%20%D1%8F%D0%B2%D0%BB%D1%8F%D0%B5%D1%82%D1%81%D1%8F%20%D0%BD%D0%B0%D1%81%D1%82%D0%BE%D1%8F%D1%89%D0%B8%D0%BC%20%D0%BA%D0%BB%D0%B0%D1%81%D1%81%D0%BE%D0%BC%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D0%B8%2C%20%D0%BF%D0%BE%D0%BB%D1%8C%D0%B7%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%D1%81%D1%8F%20%D0%B8%D0%BC%20%D0%BD%D0%B5%20%D1%81%D0%BB%D0%B8%D1%88%D0%BA%D0%BE%D0%BC%20%D1%83%D0%B4%D0%BE%D0%B1%D0%BD%D0%BE%0A%20%20%20%20que%20%3D%20deque%28%29%0A%0A%20%20%20%20%23%20%D0%9F%D0%BE%D0%BC%D0%B5%D1%81%D1%82%D0%B8%D1%82%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%B2%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D1%8C%0A%20%20%20%20que.append%281%29%0A%20%20%20%20que.append%283%29%0A%20%20%20%20que.append%282%29%0A%20%20%20%20que.append%285%29%0A%20%20%20%20que.append%284%29%0A%20%20%20%20print%28%22%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D1%8C%20que%20%3D%22%2C%20que%29%0A%0A%20%20%20%20%23%20%D0%9F%D0%BE%D0%BB%D1%83%D1%87%D0%B8%D1%82%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%B2%20%D0%BD%D0%B0%D1%87%D0%B0%D0%BB%D0%B5%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D0%B8%0A%20%20%20%20front%20%3D%20que%5B0%5D%0A%20%20%20%20print%28%22%D0%AD%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%B2%20%D0%BD%D0%B0%D1%87%D0%B0%D0%BB%D0%B5%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D0%B8%20front%20%3D%22%2C%20front%29%0A%0A%20%20%20%20%23%20%D0%98%D0%B7%D0%B2%D0%BB%D0%B5%D1%87%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%B8%D0%B7%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D0%B8%0A%20%20%20%20pop%20%3D%20que.popleft%28%29%0A%20%20%20%20print%28%22%D0%98%D0%B7%D0%B2%D0%BB%D0%B5%D1%87%D0%B5%D0%BD%D0%BD%D1%8B%D0%B9%20%D0%B8%D0%B7%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D0%B8%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20pop%20%3D%22%2C%20pop%29%0A%20%20%20%20print%28%22que%20%D0%BF%D0%BE%D1%81%D0%BB%D0%B5%20%D0%B8%D0%B7%D0%B2%D0%BB%D0%B5%D1%87%D0%B5%D0%BD%D0%B8%D1%8F%20%3D%22%2C%20que%29%0A%0A%20%20%20%20%23%20%D0%9F%D0%BE%D0%BB%D1%83%D1%87%D0%B8%D1%82%D1%8C%20%D0%B4%D0%BB%D0%B8%D0%BD%D1%83%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D0%B8%0A%20%20%20%20size%20%3D%20len%28que%29%0A%20%20%20%20print%28%22%D0%94%D0%BB%D0%B8%D0%BD%D0%B0%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D0%B8%20size%20%3D%22%2C%20size%29%0A%0A%20%20%20%20%23%20%D0%9F%D1%80%D0%BE%D0%B2%D0%B5%D1%80%D0%B8%D1%82%D1%8C%2C%20%D0%BF%D1%83%D1%81%D1%82%D0%B0%20%D0%BB%D0%B8%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D1%8C%0A%20%20%20%20is_empty%20%3D%20len%28que%29%20%3D%3D%200%0A%20%20%20%20print%28%22%D0%9F%D1%83%D1%81%D1%82%D0%B0%20%D0%BB%D0%B8%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D1%8C%20%3D%22%2C%20is_empty%29&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 5. Стек и очередь","5.2 &nbsp; Очередь"],"tags":[]},{"location":"chapter_stack_and_queue/queue/#522","level":2,"title":"5.2.2   Реализация очереди","text":"<p>Чтобы реализовать очередь, нам нужна такая структура данных, которая позволяет добавлять элементы с одного конца и удалять их с другого; и связный список, и массив этим требованиям удовлетворяют.</p>","path":["Глава 5. Стек и очередь","5.2 &nbsp; Очередь"],"tags":[]},{"location":"chapter_stack_and_queue/queue/#1","level":3,"title":"1.   Реализация на основе связного списка","text":"<p>Как показано на рисунке 5-5, мы можем рассматривать \"головной узел\" и \"хвостовой узел\" связного списка как \"голову очереди\" и \"хвост очереди\" соответственно, договорившись, что добавлять узлы можно только в хвост, а удалять - только из головы.</p> LinkedListQueuepush()pop() <p></p> <p></p> <p></p> <p> Рисунок 5-5   Операции enqueue и dequeue в реализации очереди на связном списке </p> <p>Ниже приведен код реализации очереди на связном списке:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linkedlist_queue.py<pre><code>class LinkedListQueue:\n    \"\"\"Очередь на основе связного списка\"\"\"\n\n    def __init__(self):\n        \"\"\"Конструктор\"\"\"\n        self._front: ListNode | None = None  # Головной узел front\n        self._rear: ListNode | None = None  # Хвостовой узел rear\n        self._size: int = 0\n\n    def size(self) -&gt; int:\n        \"\"\"Получение длины очереди\"\"\"\n        return self._size\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"Проверка, пуста ли очередь\"\"\"\n        return self._size == 0\n\n    def push(self, num: int):\n        \"\"\"Поместить в очередь\"\"\"\n        # Добавить num после хвостового узла\n        node = ListNode(num)\n        # Если очередь пуста, сделать так, чтобы и head, и tail указывали на этот узел\n        if self._front is None:\n            self._front = node\n            self._rear = node\n        # Если очередь не пуста, добавить этот узел после хвостового узла\n        else:\n            self._rear.next = node\n            self._rear = node\n        self._size += 1\n\n    def pop(self) -&gt; int:\n        \"\"\"Извлечь из очереди\"\"\"\n        num = self.peek()\n        # Удалить головной узел\n        self._front = self._front.next\n        self._size -= 1\n        return num\n\n    def peek(self) -&gt; int:\n        \"\"\"Доступ к элементу в начале очереди\"\"\"\n        if self.is_empty():\n            raise IndexError(\"очередь пуста\")\n        return self._front.val\n\n    def to_list(self) -&gt; list[int]:\n        \"\"\"Преобразовать в список для вывода\"\"\"\n        queue = []\n        temp = self._front\n        while temp:\n            queue.append(temp.val)\n            temp = temp.next\n        return queue\n</code></pre> linkedlist_queue.cpp<pre><code>/* Очередь на основе связного списка */\nclass LinkedListQueue {\n  private:\n    ListNode *front, *rear; // Головной узел front, хвостовой узел rear\n    int queSize;\n\n  public:\n    LinkedListQueue() {\n        front = nullptr;\n        rear = nullptr;\n        queSize = 0;\n    }\n\n    ~LinkedListQueue() {\n        // Обходить связный список, удалять узлы и освобождать память\n        freeMemoryLinkedList(front);\n    }\n\n    /* Получение длины очереди */\n    int size() {\n        return queSize;\n    }\n\n    /* Проверка, пуста ли очередь */\n    bool isEmpty() {\n        return queSize == 0;\n    }\n\n    /* Поместить в очередь */\n    void push(int num) {\n        // Добавить num после хвостового узла\n        ListNode *node = new ListNode(num);\n        // Если очередь пуста, сделать так, чтобы и head, и tail указывали на этот узел\n        if (front == nullptr) {\n            front = node;\n            rear = node;\n        }\n        // Если очередь не пуста, добавить этот узел после хвостового узла\n        else {\n            rear-&gt;next = node;\n            rear = node;\n        }\n        queSize++;\n    }\n\n    /* Извлечь из очереди */\n    int pop() {\n        int num = peek();\n        // Удалить головной узел\n        ListNode *tmp = front;\n        front = front-&gt;next;\n        // Освободить память\n        delete tmp;\n        queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    int peek() {\n        if (size() == 0)\n            throw out_of_range(\"очередь пуста\");\n        return front-&gt;val;\n    }\n\n    /* Преобразовать связный список в Vector и вернуть */\n    vector&lt;int&gt; toVector() {\n        ListNode *node = front;\n        vector&lt;int&gt; res(size());\n        for (int i = 0; i &lt; res.size(); i++) {\n            res[i] = node-&gt;val;\n            node = node-&gt;next;\n        }\n        return res;\n    }\n};\n</code></pre> linkedlist_queue.java<pre><code>/* Очередь на основе связного списка */\nclass LinkedListQueue {\n    private ListNode front, rear; // Головной узел front, хвостовой узел rear\n    private int queSize = 0;\n\n    public LinkedListQueue() {\n        front = null;\n        rear = null;\n    }\n\n    /* Получение длины очереди */\n    public int size() {\n        return queSize;\n    }\n\n    /* Проверка, пуста ли очередь */\n    public boolean isEmpty() {\n        return size() == 0;\n    }\n\n    /* Поместить в очередь */\n    public void push(int num) {\n        // Добавить num после хвостового узла\n        ListNode node = new ListNode(num);\n        // Если очередь пуста, сделать так, чтобы и head, и tail указывали на этот узел\n        if (front == null) {\n            front = node;\n            rear = node;\n        // Если очередь не пуста, добавить этот узел после хвостового узла\n        } else {\n            rear.next = node;\n            rear = node;\n        }\n        queSize++;\n    }\n\n    /* Извлечь из очереди */\n    public int pop() {\n        int num = peek();\n        // Удалить головной узел\n        front = front.next;\n        queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    public int peek() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return front.val;\n    }\n\n    /* Преобразовать связный список в Array и вернуть */\n    public int[] toArray() {\n        ListNode node = front;\n        int[] res = new int[size()];\n        for (int i = 0; i &lt; res.length; i++) {\n            res[i] = node.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_queue.cs<pre><code>/* Очередь на основе связного списка */\nclass LinkedListQueue {\n    ListNode? front, rear;  // Головной узел front, хвостовой узел rear\n    int queSize = 0;\n\n    public LinkedListQueue() {\n        front = null;\n        rear = null;\n    }\n\n    /* Получение длины очереди */\n    public int Size() {\n        return queSize;\n    }\n\n    /* Проверка, пуста ли очередь */\n    public bool IsEmpty() {\n        return Size() == 0;\n    }\n\n    /* Поместить в очередь */\n    public void Push(int num) {\n        // Добавить num после хвостового узла\n        ListNode node = new(num);\n        // Если очередь пуста, сделать так, чтобы и head, и tail указывали на этот узел\n        if (front == null) {\n            front = node;\n            rear = node;\n            // Если очередь не пуста, добавить этот узел после хвостового узла\n        } else if (rear != null) {\n            rear.next = node;\n            rear = node;\n        }\n        queSize++;\n    }\n\n    /* Извлечь из очереди */\n    public int Pop() {\n        int num = Peek();\n        // Удалить головной узел\n        front = front?.next;\n        queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    public int Peek() {\n        if (IsEmpty())\n            throw new Exception();\n        return front!.val;\n    }\n\n    /* Преобразовать связный список в Array и вернуть */\n    public int[] ToArray() {\n        if (front == null)\n            return [];\n\n        ListNode? node = front;\n        int[] res = new int[Size()];\n        for (int i = 0; i &lt; res.Length; i++) {\n            res[i] = node!.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_queue.go<pre><code>/* Очередь на основе связного списка */\ntype linkedListQueue struct {\n    // Использовать встроенный пакет list для реализации очереди\n    data *list.List\n}\n\n/* Инициализация очереди */\nfunc newLinkedListQueue() *linkedListQueue {\n    return &amp;linkedListQueue{\n        data: list.New(),\n    }\n}\n\n/* Поместить в очередь */\nfunc (s *linkedListQueue) push(value any) {\n    s.data.PushBack(value)\n}\n\n/* Извлечь из очереди */\nfunc (s *linkedListQueue) pop() any {\n    if s.isEmpty() {\n        return nil\n    }\n    e := s.data.Front()\n    s.data.Remove(e)\n    return e.Value\n}\n\n/* Доступ к элементу в начале очереди */\nfunc (s *linkedListQueue) peek() any {\n    if s.isEmpty() {\n        return nil\n    }\n    e := s.data.Front()\n    return e.Value\n}\n\n/* Получение длины очереди */\nfunc (s *linkedListQueue) size() int {\n    return s.data.Len()\n}\n\n/* Проверка, пуста ли очередь */\nfunc (s *linkedListQueue) isEmpty() bool {\n    return s.data.Len() == 0\n}\n\n/* Получить List для вывода */\nfunc (s *linkedListQueue) toList() *list.List {\n    return s.data\n}\n</code></pre> linkedlist_queue.swift<pre><code>/* Очередь на основе связного списка */\nclass LinkedListQueue {\n    private var front: ListNode? // Головной узел\n    private var rear: ListNode? // Хвостовой узел\n    private var _size: Int\n\n    init() {\n        _size = 0\n    }\n\n    /* Получение длины очереди */\n    func size() -&gt; Int {\n        _size\n    }\n\n    /* Проверка, пуста ли очередь */\n    func isEmpty() -&gt; Bool {\n        size() == 0\n    }\n\n    /* Поместить в очередь */\n    func push(num: Int) {\n        // Добавить num после хвостового узла\n        let node = ListNode(x: num)\n        // Если очередь пуста, сделать так, чтобы и head, и tail указывали на этот узел\n        if front == nil {\n            front = node\n            rear = node\n        }\n        // Если очередь не пуста, добавить этот узел после хвостового узла\n        else {\n            rear?.next = node\n            rear = node\n        }\n        _size += 1\n    }\n\n    /* Извлечь из очереди */\n    @discardableResult\n    func pop() -&gt; Int {\n        let num = peek()\n        // Удалить головной узел\n        front = front?.next\n        _size -= 1\n        return num\n    }\n\n    /* Доступ к элементу в начале очереди */\n    func peek() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"очередь пуста\")\n        }\n        return front!.val\n    }\n\n    /* Преобразовать связный список в Array и вернуть */\n    func toArray() -&gt; [Int] {\n        var node = front\n        var res = Array(repeating: 0, count: size())\n        for i in res.indices {\n            res[i] = node!.val\n            node = node?.next\n        }\n        return res\n    }\n}\n</code></pre> linkedlist_queue.js<pre><code>/* Очередь на основе связного списка */\nclass LinkedListQueue {\n    #front; // Головной узел #front\n    #rear; // Хвостовой узел #rear\n    #queSize = 0;\n\n    constructor() {\n        this.#front = null;\n        this.#rear = null;\n    }\n\n    /* Получение длины очереди */\n    get size() {\n        return this.#queSize;\n    }\n\n    /* Проверка, пуста ли очередь */\n    isEmpty() {\n        return this.size === 0;\n    }\n\n    /* Поместить в очередь */\n    push(num) {\n        // Добавить num после хвостового узла\n        const node = new ListNode(num);\n        // Если очередь пуста, сделать так, чтобы и head, и tail указывали на этот узел\n        if (!this.#front) {\n            this.#front = node;\n            this.#rear = node;\n            // Если очередь не пуста, добавить этот узел после хвостового узла\n        } else {\n            this.#rear.next = node;\n            this.#rear = node;\n        }\n        this.#queSize++;\n    }\n\n    /* Извлечь из очереди */\n    pop() {\n        const num = this.peek();\n        // Удалить головной узел\n        this.#front = this.#front.next;\n        this.#queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    peek() {\n        if (this.size === 0) throw new Error('очередь пуста');\n        return this.#front.val;\n    }\n\n    /* Преобразовать связный список в Array и вернуть */\n    toArray() {\n        let node = this.#front;\n        const res = new Array(this.size);\n        for (let i = 0; i &lt; res.length; i++) {\n            res[i] = node.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_queue.ts<pre><code>/* Очередь на основе связного списка */\nclass LinkedListQueue {\n    private front: ListNode | null; // Головной узел front\n    private rear: ListNode | null; // Хвостовой узел rear\n    private queSize: number = 0;\n\n    constructor() {\n        this.front = null;\n        this.rear = null;\n    }\n\n    /* Получение длины очереди */\n    get size(): number {\n        return this.queSize;\n    }\n\n    /* Проверка, пуста ли очередь */\n    isEmpty(): boolean {\n        return this.size === 0;\n    }\n\n    /* Поместить в очередь */\n    push(num: number): void {\n        // Добавить num после хвостового узла\n        const node = new ListNode(num);\n        // Если очередь пуста, сделать так, чтобы и head, и tail указывали на этот узел\n        if (!this.front) {\n            this.front = node;\n            this.rear = node;\n            // Если очередь не пуста, добавить этот узел после хвостового узла\n        } else {\n            this.rear!.next = node;\n            this.rear = node;\n        }\n        this.queSize++;\n    }\n\n    /* Извлечь из очереди */\n    pop(): number {\n        const num = this.peek();\n        if (!this.front) throw new Error('очередь пуста');\n        // Удалить головной узел\n        this.front = this.front.next;\n        this.queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    peek(): number {\n        if (this.size === 0) throw new Error('очередь пуста');\n        return this.front!.val;\n    }\n\n    /* Преобразовать связный список в Array и вернуть */\n    toArray(): number[] {\n        let node = this.front;\n        const res = new Array&lt;number&gt;(this.size);\n        for (let i = 0; i &lt; res.length; i++) {\n            res[i] = node!.val;\n            node = node!.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_queue.dart<pre><code>/* Очередь на основе связного списка */\nclass LinkedListQueue {\n  ListNode? _front; // Головной узел _front\n  ListNode? _rear; // Хвостовой узел _rear\n  int _queSize = 0; // Длина очереди\n\n  LinkedListQueue() {\n    _front = null;\n    _rear = null;\n  }\n\n  /* Получение длины очереди */\n  int size() {\n    return _queSize;\n  }\n\n  /* Проверка, пуста ли очередь */\n  bool isEmpty() {\n    return _queSize == 0;\n  }\n\n  /* Поместить в очередь */\n  void push(int _num) {\n    // Добавить _num после хвостового узла\n    final node = ListNode(_num);\n    // Если очередь пуста, сделать так, чтобы и head, и tail указывали на этот узел\n    if (_front == null) {\n      _front = node;\n      _rear = node;\n    } else {\n      // Если очередь не пуста, добавить этот узел после хвостового узла\n      _rear!.next = node;\n      _rear = node;\n    }\n    _queSize++;\n  }\n\n  /* Извлечь из очереди */\n  int pop() {\n    final int _num = peek();\n    // Удалить головной узел\n    _front = _front!.next;\n    _queSize--;\n    return _num;\n  }\n\n  /* Доступ к элементу в начале очереди */\n  int peek() {\n    if (_queSize == 0) {\n      throw Exception('очередь пуста');\n    }\n    return _front!.val;\n  }\n\n  /* Преобразовать связный список в Array и вернуть */\n  List&lt;int&gt; toArray() {\n    ListNode? node = _front;\n    final List&lt;int&gt; queue = [];\n    while (node != null) {\n      queue.add(node.val);\n      node = node.next;\n    }\n    return queue;\n  }\n}\n</code></pre> linkedlist_queue.rs<pre><code>/* Очередь на основе связного списка */\n#[allow(dead_code)]\npub struct LinkedListQueue&lt;T&gt; {\n    front: Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;, // Головной узел front\n    rear: Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;,  // Хвостовой узел rear\n    que_size: usize,                         // Длина очереди\n}\n\nimpl&lt;T: Copy&gt; LinkedListQueue&lt;T&gt; {\n    pub fn new() -&gt; Self {\n        Self {\n            front: None,\n            rear: None,\n            que_size: 0,\n        }\n    }\n\n    /* Получение длины очереди */\n    pub fn size(&amp;self) -&gt; usize {\n        return self.que_size;\n    }\n\n    /* Проверка, пуста ли очередь */\n    pub fn is_empty(&amp;self) -&gt; bool {\n        return self.que_size == 0;\n    }\n\n    /* Поместить в очередь */\n    pub fn push(&amp;mut self, num: T) {\n        // Добавить num после хвостового узла\n        let new_rear = ListNode::new(num);\n        match self.rear.take() {\n            // Если очередь не пуста, добавить этот узел после хвостового узла\n            Some(old_rear) =&gt; {\n                old_rear.borrow_mut().next = Some(new_rear.clone());\n                self.rear = Some(new_rear);\n            }\n            // Если очередь пуста, сделать так, чтобы и head, и tail указывали на этот узел\n            None =&gt; {\n                self.front = Some(new_rear.clone());\n                self.rear = Some(new_rear);\n            }\n        }\n        self.que_size += 1;\n    }\n\n    /* Извлечь из очереди */\n    pub fn pop(&amp;mut self) -&gt; Option&lt;T&gt; {\n        self.front.take().map(|old_front| {\n            match old_front.borrow_mut().next.take() {\n                Some(new_front) =&gt; {\n                    self.front = Some(new_front);\n                }\n                None =&gt; {\n                    self.rear.take();\n                }\n            }\n            self.que_size -= 1;\n            old_front.borrow().val\n        })\n    }\n\n    /* Доступ к элементу в начале очереди */\n    pub fn peek(&amp;self) -&gt; Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt; {\n        self.front.as_ref()\n    }\n\n    /* Преобразовать связный список в Array и вернуть */\n    pub fn to_array(&amp;self, head: Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;) -&gt; Vec&lt;T&gt; {\n        let mut res: Vec&lt;T&gt; = Vec::new();\n\n        fn recur&lt;T: Copy&gt;(cur: Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;, res: &amp;mut Vec&lt;T&gt;) {\n            if let Some(cur) = cur {\n                res.push(cur.borrow().val);\n                recur(cur.borrow().next.as_ref(), res);\n            }\n        }\n\n        recur(head, &amp;mut res);\n\n        res\n    }\n}\n</code></pre> linkedlist_queue.c<pre><code>/* Очередь на основе связного списка */\ntypedef struct {\n    ListNode *front, *rear;\n    int queSize;\n} LinkedListQueue;\n\n/* Конструктор */\nLinkedListQueue *newLinkedListQueue() {\n    LinkedListQueue *queue = (LinkedListQueue *)malloc(sizeof(LinkedListQueue));\n    queue-&gt;front = NULL;\n    queue-&gt;rear = NULL;\n    queue-&gt;queSize = 0;\n    return queue;\n}\n\n/* Деструктор */\nvoid delLinkedListQueue(LinkedListQueue *queue) {\n    // Освободить все узлы\n    while (queue-&gt;front != NULL) {\n        ListNode *tmp = queue-&gt;front;\n        queue-&gt;front = queue-&gt;front-&gt;next;\n        free(tmp);\n    }\n    // Освободить структуру queue\n    free(queue);\n}\n\n/* Получение длины очереди */\nint size(LinkedListQueue *queue) {\n    return queue-&gt;queSize;\n}\n\n/* Проверка, пуста ли очередь */\nbool empty(LinkedListQueue *queue) {\n    return (size(queue) == 0);\n}\n\n/* Поместить в очередь */\nvoid push(LinkedListQueue *queue, int num) {\n    // Добавить node в хвост\n    ListNode *node = newListNode(num);\n    // Если очередь пуста, сделать так, чтобы и head, и tail указывали на этот узел\n    if (queue-&gt;front == NULL) {\n        queue-&gt;front = node;\n        queue-&gt;rear = node;\n    }\n    // Если очередь не пуста, добавить этот узел после хвостового узла\n    else {\n        queue-&gt;rear-&gt;next = node;\n        queue-&gt;rear = node;\n    }\n    queue-&gt;queSize++;\n}\n\n/* Доступ к элементу в начале очереди */\nint peek(LinkedListQueue *queue) {\n    assert(size(queue) &amp;&amp; queue-&gt;front);\n    return queue-&gt;front-&gt;val;\n}\n\n/* Извлечь из очереди */\nint pop(LinkedListQueue *queue) {\n    int num = peek(queue);\n    ListNode *tmp = queue-&gt;front;\n    queue-&gt;front = queue-&gt;front-&gt;next;\n    free(tmp);\n    queue-&gt;queSize--;\n    return num;\n}\n\n/* Вывести очередь */\nvoid printLinkedListQueue(LinkedListQueue *queue) {\n    int *arr = malloc(sizeof(int) * queue-&gt;queSize);\n    // Скопировать данные связного списка в массив\n    int i;\n    ListNode *node;\n    for (i = 0, node = queue-&gt;front; i &lt; queue-&gt;queSize; i++) {\n        arr[i] = node-&gt;val;\n        node = node-&gt;next;\n    }\n    printArray(arr, queue-&gt;queSize);\n    free(arr);\n}\n</code></pre> linkedlist_queue.kt<pre><code>/* Очередь на основе связного списка */\nclass LinkedListQueue(\n    // Головной узел front, хвостовой узел rear\n    private var front: ListNode? = null,\n    private var rear: ListNode? = null,\n    private var queSize: Int = 0\n) {\n\n    /* Получение длины очереди */\n    fun size(): Int {\n        return queSize\n    }\n\n    /* Проверка, пуста ли очередь */\n    fun isEmpty(): Boolean {\n        return size() == 0\n    }\n\n    /* Поместить в очередь */\n    fun push(num: Int) {\n        // Добавить num после хвостового узла\n        val node = ListNode(num)\n        // Если очередь пуста, сделать так, чтобы и head, и tail указывали на этот узел\n        if (front == null) {\n            front = node\n            rear = node\n            // Если очередь не пуста, добавить этот узел после хвостового узла\n        } else {\n            rear?.next = node\n            rear = node\n        }\n        queSize++\n    }\n\n    /* Извлечь из очереди */\n    fun pop(): Int {\n        val num = peek()\n        // Удалить головной узел\n        front = front?.next\n        queSize--\n        return num\n    }\n\n    /* Доступ к элементу в начале очереди */\n    fun peek(): Int {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        return front!!._val\n    }\n\n    /* Преобразовать связный список в Array и вернуть */\n    fun toArray(): IntArray {\n        var node = front\n        val res = IntArray(size())\n        for (i in res.indices) {\n            res[i] = node!!._val\n            node = node.next\n        }\n        return res\n    }\n}\n</code></pre> linkedlist_queue.rb<pre><code>### Очередь на основе связного списка ###\nclass LinkedListQueue\n  ### Получение длины очереди ###\n  attr_reader :size\n\n  ### Конструктор ###\n  def initialize\n    @front = nil  # Головной узел front\n    @rear = nil   # Хвостовой узел rear\n    @size = 0\n  end\n\n  ### Проверка, пуста ли очередь ###\n  def is_empty?\n    @front.nil?\n  end\n\n  ### Добавление в очередь ###\n  def push(num)\n    # Добавить num после хвостового узла\n    node = ListNode.new(num)\n\n    # Если очередь пуста, сделать так, чтобы и head, и tail указывали на этот узел\n    if @front.nil?\n      @front = node\n      @rear = node\n    # Если очередь не пуста, добавить этот узел после хвостового узла\n    else\n      @rear.next = node\n      @rear = node\n    end\n\n    @size += 1\n  end\n\n  ### Извлечение из очереди ###\n  def pop\n    num = peek\n    # Удалить головной узел\n    @front = @front.next\n    @size -= 1\n    num\n  end\n\n  ### Доступ к элементу в начале очереди ###\n  def peek\n    raise IndexError, 'очередь пуста' if is_empty?\n\n    @front.val\n  end\n\n  ### Преобразовать связный список в Array и вернуть ###\n  def to_array\n    queue = []\n    temp = @front\n    while temp\n      queue &lt;&lt; temp.val\n      temp = temp.next\n    end\n    queue\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 5. Стек и очередь","5.2 &nbsp; Очередь"],"tags":[]},{"location":"chapter_stack_and_queue/queue/#2","level":3,"title":"2.   Реализация на основе массива","text":"<p>Удаление первого элемента из массива имеет временную сложность \\(O(n)\\) , из-за чего операция dequeue оказывается неэффективной. Однако этого можно избежать с помощью следующего приема.</p> <p>Мы можем использовать переменную <code>front</code> , указывающую на индекс элемента в голове очереди, и поддерживать переменную <code>size</code> , которая хранит длину очереди. Определим <code>rear = front + size</code> ; эта формула дает позицию <code>rear</code>, указывающую на ячейку сразу после хвоста очереди.</p> <p>Исходя из этого, эффективный диапазон элементов массива равен <code>[front, rear - 1]</code>, а различные операции реализуются, как показано на рисунке 5-6.</p> <ul> <li>Операция enqueue: записать входной элемент по индексу <code>rear</code> и увеличить <code>size</code> на 1.</li> <li>Операция dequeue: просто увеличить <code>front</code> на 1 и уменьшить <code>size</code> на 1.</li> </ul> <p>Можно увидеть, что и enqueue, и dequeue требуют всего одной операции, а значит обе имеют временную сложность \\(O(1)\\) .</p> ArrayQueuepush()pop() <p></p> <p></p> <p></p> <p> Рисунок 5-6   Операции enqueue и dequeue в реализации очереди на массиве </p> <p>Ты можешь заметить еще одну проблему: при непрерывных операциях enqueue и dequeue значения <code>front</code> и <code>rear</code> оба движутся вправо, и когда они доходят до конца массива, дальше сдвигаться уже нельзя. Чтобы решить эту проблему, можно рассматривать массив как \"кольцевой массив\", у которого начало и конец соединены.</p> <p>Для кольцевого массива нужно сделать так, чтобы <code>front</code> или <code>rear</code>, перешагнув конец массива, сразу возвращались к его началу и продолжали движение. Такую периодичность удобно реализовать с помощью операции взятия остатка, как показано в коде ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array_queue.py<pre><code>class ArrayQueue:\n    \"\"\"Очередь на основе кольцевого массива\"\"\"\n\n    def __init__(self, size: int):\n        \"\"\"Конструктор\"\"\"\n        self._nums: list[int] = [0] * size  # Массив для хранения элементов очереди\n        self._front: int = 0  # Указатель head, указывающий на первый элемент очереди\n        self._size: int = 0  # Длина очереди\n\n    def capacity(self) -&gt; int:\n        \"\"\"Получить вместимость очереди\"\"\"\n        return len(self._nums)\n\n    def size(self) -&gt; int:\n        \"\"\"Получение длины очереди\"\"\"\n        return self._size\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"Проверка, пуста ли очередь\"\"\"\n        return self._size == 0\n\n    def push(self, num: int):\n        \"\"\"Поместить в очередь\"\"\"\n        if self._size == self.capacity():\n            raise IndexError(\"очередь заполнена\")\n        # Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        # С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n        rear: int = (self._front + self._size) % self.capacity()\n        # Добавить num в хвост очереди\n        self._nums[rear] = num\n        self._size += 1\n\n    def pop(self) -&gt; int:\n        \"\"\"Извлечь из очереди\"\"\"\n        num: int = self.peek()\n        # Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n        self._front = (self._front + 1) % self.capacity()\n        self._size -= 1\n        return num\n\n    def peek(self) -&gt; int:\n        \"\"\"Доступ к элементу в начале очереди\"\"\"\n        if self.is_empty():\n            raise IndexError(\"очередь пуста\")\n        return self._nums[self._front]\n\n    def to_list(self) -&gt; list[int]:\n        \"\"\"Вернуть список для вывода\"\"\"\n        res = [0] * self.size()\n        j: int = self._front\n        for i in range(self.size()):\n            res[i] = self._nums[(j % self.capacity())]\n            j += 1\n        return res\n</code></pre> array_queue.cpp<pre><code>/* Очередь на основе кольцевого массива */\nclass ArrayQueue {\n  private:\n    int *nums;       // Массив для хранения элементов очереди\n    int front;       // Указатель head, указывающий на первый элемент очереди\n    int queSize;     // Длина очереди\n    int queCapacity; // Вместимость очереди\n\n  public:\n    ArrayQueue(int capacity) {\n        // Инициализация массива\n        nums = new int[capacity];\n        queCapacity = capacity;\n        front = queSize = 0;\n    }\n\n    ~ArrayQueue() {\n        delete[] nums;\n    }\n\n    /* Получить вместимость очереди */\n    int capacity() {\n        return queCapacity;\n    }\n\n    /* Получение длины очереди */\n    int size() {\n        return queSize;\n    }\n\n    /* Проверка, пуста ли очередь */\n    bool isEmpty() {\n        return size() == 0;\n    }\n\n    /* Поместить в очередь */\n    void push(int num) {\n        if (queSize == queCapacity) {\n            cout &lt;&lt; \"Очередь заполнена\" &lt;&lt; endl;\n            return;\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        // С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n        int rear = (front + queSize) % queCapacity;\n        // Добавить num в хвост очереди\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* Извлечь из очереди */\n    int pop() {\n        int num = peek();\n        // Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n        front = (front + 1) % queCapacity;\n        queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    int peek() {\n        if (isEmpty())\n            throw out_of_range(\"очередь пуста\");\n        return nums[front];\n    }\n\n    /* Преобразовать массив в Vector и вернуть */\n    vector&lt;int&gt; toVector() {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        vector&lt;int&gt; arr(queSize);\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            arr[i] = nums[j % queCapacity];\n        }\n        return arr;\n    }\n};\n</code></pre> array_queue.java<pre><code>/* Очередь на основе кольцевого массива */\nclass ArrayQueue {\n    private int[] nums; // Массив для хранения элементов очереди\n    private int front; // Указатель head, указывающий на первый элемент очереди\n    private int queSize; // Длина очереди\n\n    public ArrayQueue(int capacity) {\n        nums = new int[capacity];\n        front = queSize = 0;\n    }\n\n    /* Получить вместимость очереди */\n    public int capacity() {\n        return nums.length;\n    }\n\n    /* Получение длины очереди */\n    public int size() {\n        return queSize;\n    }\n\n    /* Проверка, пуста ли очередь */\n    public boolean isEmpty() {\n        return queSize == 0;\n    }\n\n    /* Поместить в очередь */\n    public void push(int num) {\n        if (queSize == capacity()) {\n            System.out.println(\"Очередь заполнена\");\n            return;\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        // С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n        int rear = (front + queSize) % capacity();\n        // Добавить num в хвост очереди\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* Извлечь из очереди */\n    public int pop() {\n        int num = peek();\n        // Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n        front = (front + 1) % capacity();\n        queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    public int peek() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return nums[front];\n    }\n\n    /* Вернуть массив */\n    public int[] toArray() {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        int[] res = new int[queSize];\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            res[i] = nums[j % capacity()];\n        }\n        return res;\n    }\n}\n</code></pre> array_queue.cs<pre><code>/* Очередь на основе кольцевого массива */\nclass ArrayQueue {\n    int[] nums;  // Массив для хранения элементов очереди\n    int front;   // Указатель head, указывающий на первый элемент очереди\n    int queSize; // Длина очереди\n\n    public ArrayQueue(int capacity) {\n        nums = new int[capacity];\n        front = queSize = 0;\n    }\n\n    /* Получить вместимость очереди */\n    int Capacity() {\n        return nums.Length;\n    }\n\n    /* Получение длины очереди */\n    public int Size() {\n        return queSize;\n    }\n\n    /* Проверка, пуста ли очередь */\n    public bool IsEmpty() {\n        return queSize == 0;\n    }\n\n    /* Поместить в очередь */\n    public void Push(int num) {\n        if (queSize == Capacity()) {\n            Console.WriteLine(\"Очередь заполнена\");\n            return;\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        // С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n        int rear = (front + queSize) % Capacity();\n        // Добавить num в хвост очереди\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* Извлечь из очереди */\n    public int Pop() {\n        int num = Peek();\n        // Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n        front = (front + 1) % Capacity();\n        queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    public int Peek() {\n        if (IsEmpty())\n            throw new Exception();\n        return nums[front];\n    }\n\n    /* Вернуть массив */\n    public int[] ToArray() {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        int[] res = new int[queSize];\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            res[i] = nums[j % this.Capacity()];\n        }\n        return res;\n    }\n}\n</code></pre> array_queue.go<pre><code>/* Очередь на основе кольцевого массива */\ntype arrayQueue struct {\n    nums        []int // Массив для хранения элементов очереди\n    front       int   // Указатель head, указывающий на первый элемент очереди\n    queSize     int   // Длина очереди\n    queCapacity int   // Вместимость очереди (то есть максимальное число элементов)\n}\n\n/* Инициализация очереди */\nfunc newArrayQueue(queCapacity int) *arrayQueue {\n    return &amp;arrayQueue{\n        nums:        make([]int, queCapacity),\n        queCapacity: queCapacity,\n        front:       0,\n        queSize:     0,\n    }\n}\n\n/* Получение длины очереди */\nfunc (q *arrayQueue) size() int {\n    return q.queSize\n}\n\n/* Проверка, пуста ли очередь */\nfunc (q *arrayQueue) isEmpty() bool {\n    return q.queSize == 0\n}\n\n/* Поместить в очередь */\nfunc (q *arrayQueue) push(num int) {\n    // Когда rear == queCapacity, очередь заполнена\n    if q.queSize == q.queCapacity {\n        return\n    }\n    // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n    // С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n    rear := (q.front + q.queSize) % q.queCapacity\n    // Добавить num в хвост очереди\n    q.nums[rear] = num\n    q.queSize++\n}\n\n/* Извлечь из очереди */\nfunc (q *arrayQueue) pop() any {\n    num := q.peek()\n    if num == nil {\n        return nil\n    }\n\n    // Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n    q.front = (q.front + 1) % q.queCapacity\n    q.queSize--\n    return num\n}\n\n/* Доступ к элементу в начале очереди */\nfunc (q *arrayQueue) peek() any {\n    if q.isEmpty() {\n        return nil\n    }\n    return q.nums[q.front]\n}\n\n/* Получить Slice для вывода */\nfunc (q *arrayQueue) toSlice() []int {\n    rear := (q.front + q.queSize)\n    if rear &gt;= q.queCapacity {\n        rear %= q.queCapacity\n        return append(q.nums[q.front:], q.nums[:rear]...)\n    }\n    return q.nums[q.front:rear]\n}\n</code></pre> array_queue.swift<pre><code>/* Очередь на основе кольцевого массива */\nclass ArrayQueue {\n    private var nums: [Int] // Массив для хранения элементов очереди\n    private var front: Int // Указатель head, указывающий на первый элемент очереди\n    private var _size: Int // Длина очереди\n\n    init(capacity: Int) {\n        // Инициализация массива\n        nums = Array(repeating: 0, count: capacity)\n        front = 0\n        _size = 0\n    }\n\n    /* Получить вместимость очереди */\n    func capacity() -&gt; Int {\n        nums.count\n    }\n\n    /* Получение длины очереди */\n    func size() -&gt; Int {\n        _size\n    }\n\n    /* Проверка, пуста ли очередь */\n    func isEmpty() -&gt; Bool {\n        size() == 0\n    }\n\n    /* Поместить в очередь */\n    func push(num: Int) {\n        if size() == capacity() {\n            print(\"Очередь заполнена\")\n            return\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        // С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n        let rear = (front + size()) % capacity()\n        // Добавить num в хвост очереди\n        nums[rear] = num\n        _size += 1\n    }\n\n    /* Извлечь из очереди */\n    @discardableResult\n    func pop() -&gt; Int {\n        let num = peek()\n        // Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n        front = (front + 1) % capacity()\n        _size -= 1\n        return num\n    }\n\n    /* Доступ к элементу в начале очереди */\n    func peek() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"очередь пуста\")\n        }\n        return nums[front]\n    }\n\n    /* Вернуть массив */\n    func toArray() -&gt; [Int] {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        (front ..&lt; front + size()).map { nums[$0 % capacity()] }\n    }\n}\n</code></pre> array_queue.js<pre><code>/* Очередь на основе кольцевого массива */\nclass ArrayQueue {\n    #nums; // Массив для хранения элементов очереди\n    #front = 0; // Указатель head, указывающий на первый элемент очереди\n    #queSize = 0; // Длина очереди\n\n    constructor(capacity) {\n        this.#nums = new Array(capacity);\n    }\n\n    /* Получить вместимость очереди */\n    get capacity() {\n        return this.#nums.length;\n    }\n\n    /* Получение длины очереди */\n    get size() {\n        return this.#queSize;\n    }\n\n    /* Проверка, пуста ли очередь */\n    isEmpty() {\n        return this.#queSize === 0;\n    }\n\n    /* Поместить в очередь */\n    push(num) {\n        if (this.size === this.capacity) {\n            console.log('Очередь заполнена');\n            return;\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        // С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n        const rear = (this.#front + this.size) % this.capacity;\n        // Добавить num в хвост очереди\n        this.#nums[rear] = num;\n        this.#queSize++;\n    }\n\n    /* Извлечь из очереди */\n    pop() {\n        const num = this.peek();\n        // Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n        this.#front = (this.#front + 1) % this.capacity;\n        this.#queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    peek() {\n        if (this.isEmpty()) throw new Error('очередь пуста');\n        return this.#nums[this.#front];\n    }\n\n    /* Вернуть Array */\n    toArray() {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        const arr = new Array(this.size);\n        for (let i = 0, j = this.#front; i &lt; this.size; i++, j++) {\n            arr[i] = this.#nums[j % this.capacity];\n        }\n        return arr;\n    }\n}\n</code></pre> array_queue.ts<pre><code>/* Очередь на основе кольцевого массива */\nclass ArrayQueue {\n    private nums: number[]; // Массив для хранения элементов очереди\n    private front: number; // Указатель head, указывающий на первый элемент очереди\n    private queSize: number; // Длина очереди\n\n    constructor(capacity: number) {\n        this.nums = new Array(capacity);\n        this.front = this.queSize = 0;\n    }\n\n    /* Получить вместимость очереди */\n    get capacity(): number {\n        return this.nums.length;\n    }\n\n    /* Получение длины очереди */\n    get size(): number {\n        return this.queSize;\n    }\n\n    /* Проверка, пуста ли очередь */\n    isEmpty(): boolean {\n        return this.queSize === 0;\n    }\n\n    /* Поместить в очередь */\n    push(num: number): void {\n        if (this.size === this.capacity) {\n            console.log('Очередь заполнена');\n            return;\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        // С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n        const rear = (this.front + this.queSize) % this.capacity;\n        // Добавить num в хвост очереди\n        this.nums[rear] = num;\n        this.queSize++;\n    }\n\n    /* Извлечь из очереди */\n    pop(): number {\n        const num = this.peek();\n        // Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n        this.front = (this.front + 1) % this.capacity;\n        this.queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    peek(): number {\n        if (this.isEmpty()) throw new Error('очередь пуста');\n        return this.nums[this.front];\n    }\n\n    /* Вернуть Array */\n    toArray(): number[] {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        const arr = new Array(this.size);\n        for (let i = 0, j = this.front; i &lt; this.size; i++, j++) {\n            arr[i] = this.nums[j % this.capacity];\n        }\n        return arr;\n    }\n}\n</code></pre> array_queue.dart<pre><code>/* Очередь на основе кольцевого массива */\nclass ArrayQueue {\n  late List&lt;int&gt; _nums; // Массив для хранения элементов очереди\n  late int _front; // Указатель head, указывающий на первый элемент очереди\n  late int _queSize; // Длина очереди\n\n  ArrayQueue(int capacity) {\n    _nums = List.filled(capacity, 0);\n    _front = _queSize = 0;\n  }\n\n  /* Получить вместимость очереди */\n  int capaCity() {\n    return _nums.length;\n  }\n\n  /* Получение длины очереди */\n  int size() {\n    return _queSize;\n  }\n\n  /* Проверка, пуста ли очередь */\n  bool isEmpty() {\n    return _queSize == 0;\n  }\n\n  /* Поместить в очередь */\n  void push(int _num) {\n    if (_queSize == capaCity()) {\n      throw Exception(\"Очередь заполнена\");\n    }\n    // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n    // С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n    int rear = (_front + _queSize) % capaCity();\n    // Добавить _num в хвост очереди\n    _nums[rear] = _num;\n    _queSize++;\n  }\n\n  /* Извлечь из очереди */\n  int pop() {\n    int _num = peek();\n    // Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n    _front = (_front + 1) % capaCity();\n    _queSize--;\n    return _num;\n  }\n\n  /* Доступ к элементу в начале очереди */\n  int peek() {\n    if (isEmpty()) {\n      throw Exception(\"очередь пуста\");\n    }\n    return _nums[_front];\n  }\n\n  /* Вернуть Array */\n  List&lt;int&gt; toArray() {\n    // Преобразовывать только элементы списка в пределах фактической длины\n    final List&lt;int&gt; res = List.filled(_queSize, 0);\n    for (int i = 0, j = _front; i &lt; _queSize; i++, j++) {\n      res[i] = _nums[j % capaCity()];\n    }\n    return res;\n  }\n}\n</code></pre> array_queue.rs<pre><code>/* Очередь на основе кольцевого массива */\nstruct ArrayQueue&lt;T&gt; {\n    nums: Vec&lt;T&gt;,      // Массив для хранения элементов очереди\n    front: i32,        // Указатель head, указывающий на первый элемент очереди\n    que_size: i32,     // Длина очереди\n    que_capacity: i32, // Вместимость очереди\n}\n\nimpl&lt;T: Copy + Default&gt; ArrayQueue&lt;T&gt; {\n    /* Конструктор */\n    fn new(capacity: i32) -&gt; ArrayQueue&lt;T&gt; {\n        ArrayQueue {\n            nums: vec![T::default(); capacity as usize],\n            front: 0,\n            que_size: 0,\n            que_capacity: capacity,\n        }\n    }\n\n    /* Получить вместимость очереди */\n    fn capacity(&amp;self) -&gt; i32 {\n        self.que_capacity\n    }\n\n    /* Получение длины очереди */\n    fn size(&amp;self) -&gt; i32 {\n        self.que_size\n    }\n\n    /* Проверка, пуста ли очередь */\n    fn is_empty(&amp;self) -&gt; bool {\n        self.que_size == 0\n    }\n\n    /* Поместить в очередь */\n    fn push(&amp;mut self, num: T) {\n        if self.que_size == self.capacity() {\n            println!(\"Очередь заполнена\");\n            return;\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        // С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n        let rear = (self.front + self.que_size) % self.que_capacity;\n        // Добавить num в хвост очереди\n        self.nums[rear as usize] = num;\n        self.que_size += 1;\n    }\n\n    /* Извлечь из очереди */\n    fn pop(&amp;mut self) -&gt; T {\n        let num = self.peek();\n        // Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n        self.front = (self.front + 1) % self.que_capacity;\n        self.que_size -= 1;\n        num\n    }\n\n    /* Доступ к элементу в начале очереди */\n    fn peek(&amp;self) -&gt; T {\n        if self.is_empty() {\n            panic!(\"index out of bounds\");\n        }\n        self.nums[self.front as usize]\n    }\n\n    /* Вернуть массив */\n    fn to_vector(&amp;self) -&gt; Vec&lt;T&gt; {\n        let cap = self.que_capacity;\n        let mut j = self.front;\n        let mut arr = vec![T::default(); cap as usize];\n        for i in 0..self.que_size {\n            arr[i as usize] = self.nums[(j % cap) as usize];\n            j += 1;\n        }\n        arr\n    }\n}\n</code></pre> array_queue.c<pre><code>/* Очередь на основе кольцевого массива */\ntypedef struct {\n    int *nums;       // Массив для хранения элементов очереди\n    int front;       // Указатель head, указывающий на первый элемент очереди\n    int queSize;     // Указатель хвоста, указывающий на позицию после хвоста\n    int queCapacity; // Вместимость очереди\n} ArrayQueue;\n\n/* Конструктор */\nArrayQueue *newArrayQueue(int capacity) {\n    ArrayQueue *queue = (ArrayQueue *)malloc(sizeof(ArrayQueue));\n    // Инициализация массива\n    queue-&gt;queCapacity = capacity;\n    queue-&gt;nums = (int *)malloc(sizeof(int) * queue-&gt;queCapacity);\n    queue-&gt;front = queue-&gt;queSize = 0;\n    return queue;\n}\n\n/* Деструктор */\nvoid delArrayQueue(ArrayQueue *queue) {\n    free(queue-&gt;nums);\n    free(queue);\n}\n\n/* Получить вместимость очереди */\nint capacity(ArrayQueue *queue) {\n    return queue-&gt;queCapacity;\n}\n\n/* Получение длины очереди */\nint size(ArrayQueue *queue) {\n    return queue-&gt;queSize;\n}\n\n/* Проверка, пуста ли очередь */\nbool empty(ArrayQueue *queue) {\n    return queue-&gt;queSize == 0;\n}\n\n/* Доступ к элементу в начале очереди */\nint peek(ArrayQueue *queue) {\n    assert(size(queue) != 0);\n    return queue-&gt;nums[queue-&gt;front];\n}\n\n/* Поместить в очередь */\nvoid push(ArrayQueue *queue, int num) {\n    if (size(queue) == capacity(queue)) {\n        printf(\"Очередь заполнена\\r\\n\");\n        return;\n    }\n    // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n    // С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n    int rear = (queue-&gt;front + queue-&gt;queSize) % queue-&gt;queCapacity;\n    // Добавить num в хвост очереди\n    queue-&gt;nums[rear] = num;\n    queue-&gt;queSize++;\n}\n\n/* Извлечь из очереди */\nint pop(ArrayQueue *queue) {\n    int num = peek(queue);\n    // Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n    queue-&gt;front = (queue-&gt;front + 1) % queue-&gt;queCapacity;\n    queue-&gt;queSize--;\n    return num;\n}\n\n/* Вернуть массив для вывода */\nint *toArray(ArrayQueue *queue, int *queSize) {\n    *queSize = queue-&gt;queSize;\n    int *res = (int *)calloc(queue-&gt;queSize, sizeof(int));\n    int j = queue-&gt;front;\n    for (int i = 0; i &lt; queue-&gt;queSize; i++) {\n        res[i] = queue-&gt;nums[j % queue-&gt;queCapacity];\n        j++;\n    }\n    return res;\n}\n</code></pre> array_queue.kt<pre><code>/* Очередь на основе кольцевого массива */\nclass ArrayQueue(capacity: Int) {\n    private val nums: IntArray = IntArray(capacity) // Массив для хранения элементов очереди\n    private var front: Int = 0 // Указатель head, указывающий на первый элемент очереди\n    private var queSize: Int = 0 // Длина очереди\n\n    /* Получить вместимость очереди */\n    fun capacity(): Int {\n        return nums.size\n    }\n\n    /* Получение длины очереди */\n    fun size(): Int {\n        return queSize\n    }\n\n    /* Проверка, пуста ли очередь */\n    fun isEmpty(): Boolean {\n        return queSize == 0\n    }\n\n    /* Поместить в очередь */\n    fun push(num: Int) {\n        if (queSize == capacity()) {\n            println(\"Очередь заполнена\")\n            return\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        // С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n        val rear = (front + queSize) % capacity()\n        // Добавить num в хвост очереди\n        nums[rear] = num\n        queSize++\n    }\n\n    /* Извлечь из очереди */\n    fun pop(): Int {\n        val num = peek()\n        // Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n        front = (front + 1) % capacity()\n        queSize--\n        return num\n    }\n\n    /* Доступ к элементу в начале очереди */\n    fun peek(): Int {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        return nums[front]\n    }\n\n    /* Вернуть массив */\n    fun toArray(): IntArray {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        val res = IntArray(queSize)\n        var i = 0\n        var j = front\n        while (i &lt; queSize) {\n            res[i] = nums[j % capacity()]\n            i++\n            j++\n        }\n        return res\n    }\n}\n</code></pre> array_queue.rb<pre><code>### Очередь на основе кольцевого массива ###\nclass ArrayQueue\n  ### Получение длины очереди ###\n  attr_reader :size\n\n  ### Конструктор ###\n  def initialize(size)\n    @nums = Array.new(size, 0) # Массив для хранения элементов очереди\n    @front = 0 # Указатель head, указывающий на первый элемент очереди\n    @size = 0 # Длина очереди\n  end\n\n  ### Получить вместимость очереди ###\n  def capacity\n    @nums.length\n  end\n\n  ### Проверка, пуста ли очередь ###\n  def is_empty?\n    size.zero?\n  end\n\n  ### Добавление в очередь ###\n  def push(num)\n    raise IndexError, 'очередь заполнена' if size == capacity\n\n    # Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n    # С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n    rear = (@front + size) % capacity\n    # Добавить num в хвост очереди\n    @nums[rear] = num\n    @size += 1\n  end\n\n  ### Извлечение из очереди ###\n  def pop\n    num = peek\n    # Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n    @front = (@front + 1) % capacity\n    @size -= 1\n    num\n  end\n\n  ### Доступ к элементу в начале очереди ###\n  def peek\n    raise IndexError, 'очередь пуста' if is_empty?\n\n    @nums[@front]\n  end\n\n  ### Вернуть список для вывода ###\n  def to_array\n    res = Array.new(size, 0)\n    j = @front\n\n    for i in 0...size\n      res[i] = @nums[j % capacity]\n      j += 1\n    end\n\n    res\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Даже такая реализация очереди остается ограниченной: ее длина неизменяема. Однако это несложно исправить, заменив массив на динамический массив и тем самым введя механизм расширения. Заинтересованные читатели могут попробовать реализовать это самостоятельно.</p> <p>Выводы сравнения двух реализаций в целом такие же, как и для стека, поэтому здесь мы не будем повторяться.</p>","path":["Глава 5. Стек и очередь","5.2 &nbsp; Очередь"],"tags":[]},{"location":"chapter_stack_and_queue/queue/#523","level":2,"title":"5.2.3   Типичные применения очереди","text":"<ul> <li>Заказы на Taobao. После оформления заказа покупателем заказ попадает в очередь, а затем система обрабатывает заказы по порядку. Во время крупных распродаж, таких как Double 11, за короткое время возникает огромный поток заказов, и высокая конкурентная нагрузка становится ключевой инженерной проблемой.</li> <li>Различные отложенные задачи. Любой сценарий, где нужно реализовать принцип \"кто раньше пришел, тот раньше обслуживается\", например очередь заданий принтера или очередь блюд на кухне ресторана, хорошо моделируется очередью, которая эффективно поддерживает нужный порядок обработки.</li> </ul>","path":["Глава 5. Стек и очередь","5.2 &nbsp; Очередь"],"tags":[]},{"location":"chapter_stack_and_queue/stack/","level":1,"title":"5.1   Стек","text":"<p>Стек (stack) - это линейная структура данных, подчиняющаяся логике \"последним пришел - первым вышел\".</p> <p>Стек можно сравнить со стопкой тарелок на столе. Если разрешено перемещать только одну тарелку за раз, то, чтобы достать тарелку снизу, сначала придется по одной убрать все тарелки сверху. Если заменить тарелки различными элементами (например целыми числами, символами, объектами и т.д.), получится структура данных \"стек\".</p> <p>Как показано на рисунке 5-1, верхнюю часть стопки элементов мы называем \"вершиной стека\", а нижнюю - \"основанием стека\". Операция добавления элемента на вершину называется \"push\", а операция удаления верхнего элемента - \"pop\".</p> <p></p> <p> Рисунок 5-1   Правило LIFO для стека </p>","path":["Глава 5. Стек и очередь","5.1 &nbsp; Стек"],"tags":[]},{"location":"chapter_stack_and_queue/stack/#511","level":2,"title":"5.1.1   Основные операции со стеком","text":"<p>Основные операции со стеком показаны в таблице 5-1. Конкретные имена методов зависят от используемого языка программирования. Здесь в качестве примера используются распространенные названия <code>push()</code> , <code>pop()</code> и <code>peek()</code> .</p> <p> Таблица 5-1   Эффективность операций со стеком </p> Метод Описание Временная сложность <code>push()</code> Поместить элемент в стек (на вершину) \\(O(1)\\) <code>pop()</code> Извлечь верхний элемент стека \\(O(1)\\) <code>peek()</code> Просмотреть верхний элемент \\(O(1)\\) <p>Обычно мы можем просто использовать встроенный стек, предоставляемый языком программирования. Однако в некоторых языках специальный класс стека может отсутствовать. В таком случае можно использовать \"массив\" или \"связный список\" этого языка как стек и в логике программы игнорировать операции, не относящиеся к стеку.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby stack.py<pre><code># Инициализация стека\n# В Python нет встроенного класса стека, поэтому можно использовать list как стек\nstack: list[int] = []\n\n# Поместить элементы в стек\nstack.append(1)\nstack.append(3)\nstack.append(2)\nstack.append(5)\nstack.append(4)\n\n# Просмотреть верхний элемент\npeek: int = stack[-1]\n\n# Извлечь элемент\npop: int = stack.pop()\n\n# Получить длину стека\nsize: int = len(stack)\n\n# Проверить, пуст ли стек\nis_empty: bool = len(stack) == 0\n</code></pre> stack.cpp<pre><code>/* Инициализация стека */\nstack&lt;int&gt; stack;\n\n/* Поместить элементы в стек */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n\n/* Просмотреть верхний элемент */\nint top = stack.top();\n\n/* Извлечь элемент */\nstack.pop(); // Без возвращаемого значения\n\n/* Получить длину стека */\nint size = stack.size();\n\n/* Проверить, пуст ли стек */\nbool empty = stack.empty();\n</code></pre> stack.java<pre><code>/* Инициализация стека */\nStack&lt;Integer&gt; stack = new Stack&lt;&gt;();\n\n/* Поместить элементы в стек */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n\n/* Просмотреть верхний элемент */\nint peek = stack.peek();\n\n/* Извлечь элемент */\nint pop = stack.pop();\n\n/* Получить длину стека */\nint size = stack.size();\n\n/* Проверить, пуст ли стек */\nboolean isEmpty = stack.isEmpty();\n</code></pre> stack.cs<pre><code>/* Инициализация стека */\nStack&lt;int&gt; stack = new();\n\n/* Поместить элементы в стек */\nstack.Push(1);\nstack.Push(3);\nstack.Push(2);\nstack.Push(5);\nstack.Push(4);\n\n/* Просмотреть верхний элемент */\nint peek = stack.Peek();\n\n/* Извлечь элемент */\nint pop = stack.Pop();\n\n/* Получить длину стека */\nint size = stack.Count;\n\n/* Проверить, пуст ли стек */\nbool isEmpty = stack.Count == 0;\n</code></pre> stack_test.go<pre><code>/* Инициализация стека */\n// В Go рекомендуется использовать Slice как стек\nvar stack []int\n\n/* Поместить элементы в стек */\nstack = append(stack, 1)\nstack = append(stack, 3)\nstack = append(stack, 2)\nstack = append(stack, 5)\nstack = append(stack, 4)\n\n/* Просмотреть верхний элемент */\npeek := stack[len(stack)-1]\n\n/* Извлечь элемент */\npop := stack[len(stack)-1]\nstack = stack[:len(stack)-1]\n\n/* Получить длину стека */\nsize := len(stack)\n\n/* Проверить, пуст ли стек */\nisEmpty := len(stack) == 0\n</code></pre> stack.swift<pre><code>/* Инициализация стека */\n// В Swift нет встроенного класса стека, поэтому можно использовать Array как стек\nvar stack: [Int] = []\n\n/* Поместить элементы в стек */\nstack.append(1)\nstack.append(3)\nstack.append(2)\nstack.append(5)\nstack.append(4)\n\n/* Просмотреть верхний элемент */\nlet peek = stack.last!\n\n/* Извлечь элемент */\nlet pop = stack.removeLast()\n\n/* Получить длину стека */\nlet size = stack.count\n\n/* Проверить, пуст ли стек */\nlet isEmpty = stack.isEmpty\n</code></pre> stack.js<pre><code>/* Инициализация стека */\n// В JavaScript нет встроенного класса стека, поэтому можно использовать Array как стек\nconst stack = [];\n\n/* Поместить элементы в стек */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n\n/* Просмотреть верхний элемент */\nconst peek = stack[stack.length-1];\n\n/* Извлечь элемент */\nconst pop = stack.pop();\n\n/* Получить длину стека */\nconst size = stack.length;\n\n/* Проверить, пуст ли стек */\nconst is_empty = stack.length === 0;\n</code></pre> stack.ts<pre><code>/* Инициализация стека */\n// В TypeScript нет встроенного класса стека, поэтому можно использовать Array как стек\nconst stack: number[] = [];\n\n/* Поместить элементы в стек */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n\n/* Просмотреть верхний элемент */\nconst peek = stack[stack.length - 1];\n\n/* Извлечь элемент */\nconst pop = stack.pop();\n\n/* Получить длину стека */\nconst size = stack.length;\n\n/* Проверить, пуст ли стек */\nconst is_empty = stack.length === 0;\n</code></pre> stack.dart<pre><code>/* Инициализация стека */\n// В Dart нет встроенного класса стека, поэтому можно использовать List как стек\nList&lt;int&gt; stack = [];\n\n/* Поместить элементы в стек */\nstack.add(1);\nstack.add(3);\nstack.add(2);\nstack.add(5);\nstack.add(4);\n\n/* Просмотреть верхний элемент */\nint peek = stack.last;\n\n/* Извлечь элемент */\nint pop = stack.removeLast();\n\n/* Получить длину стека */\nint size = stack.length;\n\n/* Проверить, пуст ли стек */\nbool isEmpty = stack.isEmpty;\n</code></pre> stack.rs<pre><code>/* Инициализация стека */\n// Используем Vec как стек\nlet mut stack: Vec&lt;i32&gt; = Vec::new();\n\n/* Поместить элементы в стек */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n\n/* Просмотреть верхний элемент */\nlet top = stack.last().unwrap();\n\n/* Извлечь элемент */\nlet pop = stack.pop().unwrap();\n\n/* Получить длину стека */\nlet size = stack.len();\n\n/* Проверить, пуст ли стек */\nlet is_empty = stack.is_empty();\n</code></pre> stack.c<pre><code>// В C нет встроенного стека\n</code></pre> stack.kt<pre><code>/* Инициализация стека */\nval stack = Stack&lt;Int&gt;()\n\n/* Поместить элементы в стек */\nstack.push(1)\nstack.push(3)\nstack.push(2)\nstack.push(5)\nstack.push(4)\n\n/* Просмотреть верхний элемент */\nval peek = stack.peek()\n\n/* Извлечь элемент */\nval pop = stack.pop()\n\n/* Получить длину стека */\nval size = stack.size\n\n/* Проверить, пуст ли стек */\nval isEmpty = stack.isEmpty()\n</code></pre> stack.rb<pre><code># Инициализация стека\n# В Ruby нет встроенного класса стека, поэтому можно использовать Array как стек\nstack = []\n\n# Поместить элементы в стек\nstack &lt;&lt; 1\nstack &lt;&lt; 3\nstack &lt;&lt; 2\nstack &lt;&lt; 5\nstack &lt;&lt; 4\n\n# Просмотреть верхний элемент\npeek = stack.last\n\n# Извлечь элемент\npop = stack.pop\n\n# Получить длину стека\nsize = stack.length\n\n# Проверить, пуст ли стек\nis_empty = stack.empty?\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%81%D1%82%D0%B5%D0%BA%0A%20%20%20%20%23%20%D0%92%20Python%20%D0%BD%D0%B5%D1%82%20%D0%B2%D1%81%D1%82%D1%80%D0%BE%D0%B5%D0%BD%D0%BD%D0%BE%D0%B3%D0%BE%20%D0%BA%D0%BB%D0%B0%D1%81%D1%81%D0%B0%20%D1%81%D1%82%D0%B5%D0%BA%D0%B0%2C%20%D0%BF%D0%BE%D1%8D%D1%82%D0%BE%D0%BC%D1%83%20list%20%D0%BC%D0%BE%D0%B6%D0%BD%D0%BE%20%D0%B8%D1%81%D0%BF%D0%BE%D0%BB%D1%8C%D0%B7%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D0%BA%D0%B0%D0%BA%20%D1%81%D1%82%D0%B5%D0%BA%0A%20%20%20%20stack%20%3D%20%5B%5D%0A%0A%20%20%20%20%23%20%D0%9F%D0%BE%D0%BC%D0%B5%D1%81%D1%82%D0%B8%D1%82%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%B2%20%D1%81%D1%82%D0%B5%D0%BA%0A%20%20%20%20stack.append%281%29%0A%20%20%20%20stack.append%283%29%0A%20%20%20%20stack.append%282%29%0A%20%20%20%20stack.append%285%29%0A%20%20%20%20stack.append%284%29%0A%20%20%20%20print%28%22%D1%81%D1%82%D0%B5%D0%BA%20stack%20%3D%22%2C%20stack%29%0A%0A%20%20%20%20%23%20%D0%9F%D0%BE%D0%BB%D1%83%D1%87%D0%B8%D1%82%D1%8C%20%D0%B2%D0%B5%D1%80%D1%85%D0%BD%D0%B8%D0%B9%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D1%81%D1%82%D0%B5%D0%BA%D0%B0%0A%20%20%20%20peek%20%3D%20stack%5B-1%5D%0A%20%20%20%20print%28%22%D0%92%D0%B5%D1%80%D1%85%D0%BD%D0%B8%D0%B9%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D1%81%D1%82%D0%B5%D0%BA%D0%B0%20peek%20%3D%22%2C%20peek%29%0A%0A%20%20%20%20%23%20%D0%98%D0%B7%D0%B2%D0%BB%D0%B5%D1%87%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%B8%D0%B7%20%D1%81%D1%82%D0%B5%D0%BA%D0%B0%0A%20%20%20%20pop%20%3D%20stack.pop%28%29%0A%20%20%20%20print%28%22%D0%98%D0%B7%D0%B2%D0%BB%D0%B5%D1%87%D0%B5%D0%BD%D0%BD%D1%8B%D0%B9%20%D0%B8%D0%B7%20%D1%81%D1%82%D0%B5%D0%BA%D0%B0%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20pop%20%3D%22%2C%20pop%29%0A%20%20%20%20print%28%22%D0%9F%D0%BE%D1%81%D0%BB%D0%B5%20%D0%B8%D0%B7%D0%B2%D0%BB%D0%B5%D1%87%D0%B5%D0%BD%D0%B8%D1%8F%20stack%20%3D%22%2C%20stack%29%0A%0A%20%20%20%20%23%20%D0%9F%D0%BE%D0%BB%D1%83%D1%87%D0%B8%D1%82%D1%8C%20%D0%B4%D0%BB%D0%B8%D0%BD%D1%83%20%D1%81%D1%82%D0%B5%D0%BA%D0%B0%0A%20%20%20%20size%20%3D%20len%28stack%29%0A%20%20%20%20print%28%22%D0%94%D0%BB%D0%B8%D0%BD%D0%B0%20%D1%81%D1%82%D0%B5%D0%BA%D0%B0%20size%20%3D%22%2C%20size%29%0A%0A%20%20%20%20%23%20%D0%9F%D1%80%D0%BE%D0%B2%D0%B5%D1%80%D0%B8%D1%82%D1%8C%2C%20%D0%BF%D1%83%D1%81%D1%82%D0%B0%20%D0%BB%D0%B8%20%D1%81%D1%82%D1%80%D1%83%D0%BA%D1%82%D1%83%D1%80%D0%B0%0A%20%20%20%20is_empty%20%3D%20len%28stack%29%20%3D%3D%200%0A%20%20%20%20print%28%22%D0%9F%D1%83%D1%81%D1%82%20%D0%BB%D0%B8%20%D1%81%D1%82%D0%B5%D0%BA%20%3D%22%2C%20is_empty%29&amp;cumulative=false&amp;curInstr=2&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 5. Стек и очередь","5.1 &nbsp; Стек"],"tags":[]},{"location":"chapter_stack_and_queue/stack/#512","level":2,"title":"5.1.2   Реализация стека","text":"<p>Чтобы глубже понять механизм работы стека, попробуем самостоятельно реализовать класс стека.</p> <p>Стек подчиняется принципу LIFO, поэтому мы можем добавлять и удалять элементы только на вершине. Однако и массив, и связный список позволяют добавлять и удалять элементы в произвольном месте. Следовательно, стек можно рассматривать как ограниченный массив или связный список. Иными словами, мы можем \"скрыть\" часть нерелевантных операций массива или списка, так чтобы внешняя логика соответствовала свойствам стека.</p>","path":["Глава 5. Стек и очередь","5.1 &nbsp; Стек"],"tags":[]},{"location":"chapter_stack_and_queue/stack/#1","level":3,"title":"1.   Реализация на основе связного списка","text":"<p>Если реализовывать стек на основе связного списка, то головной узел списка можно рассматривать как вершину стека, а хвостовой - как основание.</p> <p>Как показано на рисунке 5-2, для операции push достаточно вставить элемент в голову связного списка. Такой способ вставки называется \"вставкой в голову\". Для операции pop достаточно удалить головной узел из списка.</p> LinkedListStackpush()pop() <p></p> <p></p> <p></p> <p> Рисунок 5-2   Операции push и pop в реализации стека на связном списке </p> <p>Ниже приведен пример кода реализации стека на основе связного списка:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linkedlist_stack.py<pre><code>class LinkedListStack:\n    \"\"\"Стек на основе связного списка\"\"\"\n\n    def __init__(self):\n        \"\"\"Конструктор\"\"\"\n        self._peek: ListNode | None = None\n        self._size: int = 0\n\n    def size(self) -&gt; int:\n        \"\"\"Получение длины стека\"\"\"\n        return self._size\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"Проверка, пуст ли стек\"\"\"\n        return self._size == 0\n\n    def push(self, val: int):\n        \"\"\"Поместить в стек\"\"\"\n        node = ListNode(val)\n        node.next = self._peek\n        self._peek = node\n        self._size += 1\n\n    def pop(self) -&gt; int:\n        \"\"\"Извлечь из стека\"\"\"\n        num = self.peek()\n        self._peek = self._peek.next\n        self._size -= 1\n        return num\n\n    def peek(self) -&gt; int:\n        \"\"\"Доступ к верхнему элементу стека\"\"\"\n        if self.is_empty():\n            raise IndexError(\"стек пуст\")\n        return self._peek.val\n\n    def to_list(self) -&gt; list[int]:\n        \"\"\"Преобразовать в список для вывода\"\"\"\n        arr = []\n        node = self._peek\n        while node:\n            arr.append(node.val)\n            node = node.next\n        arr.reverse()\n        return arr\n</code></pre> linkedlist_stack.cpp<pre><code>/* Стек на основе связного списка */\nclass LinkedListStack {\n  private:\n    ListNode *stackTop; // Использовать головной узел как вершину стека\n    int stkSize;        // Длина стека\n\n  public:\n    LinkedListStack() {\n        stackTop = nullptr;\n        stkSize = 0;\n    }\n\n    ~LinkedListStack() {\n        // Обходить связный список, удалять узлы и освобождать память\n        freeMemoryLinkedList(stackTop);\n    }\n\n    /* Получение длины стека */\n    int size() {\n        return stkSize;\n    }\n\n    /* Проверка, пуст ли стек */\n    bool isEmpty() {\n        return size() == 0;\n    }\n\n    /* Поместить в стек */\n    void push(int num) {\n        ListNode *node = new ListNode(num);\n        node-&gt;next = stackTop;\n        stackTop = node;\n        stkSize++;\n    }\n\n    /* Извлечь из стека */\n    int pop() {\n        int num = top();\n        ListNode *tmp = stackTop;\n        stackTop = stackTop-&gt;next;\n        // Освободить память\n        delete tmp;\n        stkSize--;\n        return num;\n    }\n\n    /* Доступ к верхнему элементу стека */\n    int top() {\n        if (isEmpty())\n            throw out_of_range(\"стек пуст\");\n        return stackTop-&gt;val;\n    }\n\n    /* Преобразовать List в Array и вернуть */\n    vector&lt;int&gt; toVector() {\n        ListNode *node = stackTop;\n        vector&lt;int&gt; res(size());\n        for (int i = res.size() - 1; i &gt;= 0; i--) {\n            res[i] = node-&gt;val;\n            node = node-&gt;next;\n        }\n        return res;\n    }\n};\n</code></pre> linkedlist_stack.java<pre><code>/* Стек на основе связного списка */\nclass LinkedListStack {\n    private ListNode stackPeek; // Использовать головной узел как вершину стека\n    private int stkSize = 0; // Длина стека\n\n    public LinkedListStack() {\n        stackPeek = null;\n    }\n\n    /* Получение длины стека */\n    public int size() {\n        return stkSize;\n    }\n\n    /* Проверка, пуст ли стек */\n    public boolean isEmpty() {\n        return size() == 0;\n    }\n\n    /* Поместить в стек */\n    public void push(int num) {\n        ListNode node = new ListNode(num);\n        node.next = stackPeek;\n        stackPeek = node;\n        stkSize++;\n    }\n\n    /* Извлечь из стека */\n    public int pop() {\n        int num = peek();\n        stackPeek = stackPeek.next;\n        stkSize--;\n        return num;\n    }\n\n    /* Доступ к верхнему элементу стека */\n    public int peek() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return stackPeek.val;\n    }\n\n    /* Преобразовать List в Array и вернуть */\n    public int[] toArray() {\n        ListNode node = stackPeek;\n        int[] res = new int[size()];\n        for (int i = res.length - 1; i &gt;= 0; i--) {\n            res[i] = node.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_stack.cs<pre><code>/* Стек на основе связного списка */\nclass LinkedListStack {\n    ListNode? stackPeek;  // Использовать головной узел как вершину стека\n    int stkSize = 0;   // Длина стека\n\n    public LinkedListStack() {\n        stackPeek = null;\n    }\n\n    /* Получение длины стека */\n    public int Size() {\n        return stkSize;\n    }\n\n    /* Проверка, пуст ли стек */\n    public bool IsEmpty() {\n        return Size() == 0;\n    }\n\n    /* Поместить в стек */\n    public void Push(int num) {\n        ListNode node = new(num) {\n            next = stackPeek\n        };\n        stackPeek = node;\n        stkSize++;\n    }\n\n    /* Извлечь из стека */\n    public int Pop() {\n        int num = Peek();\n        stackPeek = stackPeek!.next;\n        stkSize--;\n        return num;\n    }\n\n    /* Доступ к верхнему элементу стека */\n    public int Peek() {\n        if (IsEmpty())\n            throw new Exception();\n        return stackPeek!.val;\n    }\n\n    /* Преобразовать List в Array и вернуть */\n    public int[] ToArray() {\n        if (stackPeek == null)\n            return [];\n\n        ListNode? node = stackPeek;\n        int[] res = new int[Size()];\n        for (int i = res.Length - 1; i &gt;= 0; i--) {\n            res[i] = node!.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_stack.go<pre><code>/* Стек на основе связного списка */\ntype linkedListStack struct {\n    // Использовать встроенный пакет list для реализации стека\n    data *list.List\n}\n\n/* Инициализация стека */\nfunc newLinkedListStack() *linkedListStack {\n    return &amp;linkedListStack{\n        data: list.New(),\n    }\n}\n\n/* Поместить в стек */\nfunc (s *linkedListStack) push(value int) {\n    s.data.PushBack(value)\n}\n\n/* Извлечь из стека */\nfunc (s *linkedListStack) pop() any {\n    if s.isEmpty() {\n        return nil\n    }\n    e := s.data.Back()\n    s.data.Remove(e)\n    return e.Value\n}\n\n/* Доступ к верхнему элементу стека */\nfunc (s *linkedListStack) peek() any {\n    if s.isEmpty() {\n        return nil\n    }\n    e := s.data.Back()\n    return e.Value\n}\n\n/* Получение длины стека */\nfunc (s *linkedListStack) size() int {\n    return s.data.Len()\n}\n\n/* Проверка, пуст ли стек */\nfunc (s *linkedListStack) isEmpty() bool {\n    return s.data.Len() == 0\n}\n\n/* Получить List для вывода */\nfunc (s *linkedListStack) toList() *list.List {\n    return s.data\n}\n</code></pre> linkedlist_stack.swift<pre><code>/* Стек на основе связного списка */\nclass LinkedListStack {\n    private var _peek: ListNode? // Использовать головной узел как вершину стека\n    private var _size: Int // Длина стека\n\n    init() {\n        _size = 0\n    }\n\n    /* Получение длины стека */\n    func size() -&gt; Int {\n        _size\n    }\n\n    /* Проверка, пуст ли стек */\n    func isEmpty() -&gt; Bool {\n        size() == 0\n    }\n\n    /* Поместить в стек */\n    func push(num: Int) {\n        let node = ListNode(x: num)\n        node.next = _peek\n        _peek = node\n        _size += 1\n    }\n\n    /* Извлечь из стека */\n    @discardableResult\n    func pop() -&gt; Int {\n        let num = peek()\n        _peek = _peek?.next\n        _size -= 1\n        return num\n    }\n\n    /* Доступ к верхнему элементу стека */\n    func peek() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"стек пуст\")\n        }\n        return _peek!.val\n    }\n\n    /* Преобразовать List в Array и вернуть */\n    func toArray() -&gt; [Int] {\n        var node = _peek\n        var res = Array(repeating: 0, count: size())\n        for i in res.indices.reversed() {\n            res[i] = node!.val\n            node = node?.next\n        }\n        return res\n    }\n}\n</code></pre> linkedlist_stack.js<pre><code>/* Стек на основе связного списка */\nclass LinkedListStack {\n    #stackPeek; // Использовать головной узел как вершину стека\n    #stkSize = 0; // Длина стека\n\n    constructor() {\n        this.#stackPeek = null;\n    }\n\n    /* Получение длины стека */\n    get size() {\n        return this.#stkSize;\n    }\n\n    /* Проверка, пуст ли стек */\n    isEmpty() {\n        return this.size === 0;\n    }\n\n    /* Поместить в стек */\n    push(num) {\n        const node = new ListNode(num);\n        node.next = this.#stackPeek;\n        this.#stackPeek = node;\n        this.#stkSize++;\n    }\n\n    /* Извлечь из стека */\n    pop() {\n        const num = this.peek();\n        this.#stackPeek = this.#stackPeek.next;\n        this.#stkSize--;\n        return num;\n    }\n\n    /* Доступ к верхнему элементу стека */\n    peek() {\n        if (!this.#stackPeek) throw new Error('стек пуст');\n        return this.#stackPeek.val;\n    }\n\n    /* Преобразовать связный список в Array и вернуть */\n    toArray() {\n        let node = this.#stackPeek;\n        const res = new Array(this.size);\n        for (let i = res.length - 1; i &gt;= 0; i--) {\n            res[i] = node.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_stack.ts<pre><code>/* Стек на основе связного списка */\nclass LinkedListStack {\n    private stackPeek: ListNode | null; // Использовать головной узел как вершину стека\n    private stkSize: number = 0; // Длина стека\n\n    constructor() {\n        this.stackPeek = null;\n    }\n\n    /* Получение длины стека */\n    get size(): number {\n        return this.stkSize;\n    }\n\n    /* Проверка, пуст ли стек */\n    isEmpty(): boolean {\n        return this.size === 0;\n    }\n\n    /* Поместить в стек */\n    push(num: number): void {\n        const node = new ListNode(num);\n        node.next = this.stackPeek;\n        this.stackPeek = node;\n        this.stkSize++;\n    }\n\n    /* Извлечь из стека */\n    pop(): number {\n        const num = this.peek();\n        if (!this.stackPeek) throw new Error('стек пуст');\n        this.stackPeek = this.stackPeek.next;\n        this.stkSize--;\n        return num;\n    }\n\n    /* Доступ к верхнему элементу стека */\n    peek(): number {\n        if (!this.stackPeek) throw new Error('стек пуст');\n        return this.stackPeek.val;\n    }\n\n    /* Преобразовать связный список в Array и вернуть */\n    toArray(): number[] {\n        let node = this.stackPeek;\n        const res = new Array&lt;number&gt;(this.size);\n        for (let i = res.length - 1; i &gt;= 0; i--) {\n            res[i] = node!.val;\n            node = node!.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_stack.dart<pre><code>/* Стек на основе класса связного списка */\nclass LinkedListStack {\n  ListNode? _stackPeek; // Использовать головной узел как вершину стека\n  int _stkSize = 0; // Длина стека\n\n  LinkedListStack() {\n    _stackPeek = null;\n  }\n\n  /* Получение длины стека */\n  int size() {\n    return _stkSize;\n  }\n\n  /* Проверка, пуст ли стек */\n  bool isEmpty() {\n    return _stkSize == 0;\n  }\n\n  /* Поместить в стек */\n  void push(int _num) {\n    final ListNode node = ListNode(_num);\n    node.next = _stackPeek;\n    _stackPeek = node;\n    _stkSize++;\n  }\n\n  /* Извлечь из стека */\n  int pop() {\n    final int _num = peek();\n    _stackPeek = _stackPeek!.next;\n    _stkSize--;\n    return _num;\n  }\n\n  /* Доступ к верхнему элементу стека */\n  int peek() {\n    if (_stackPeek == null) {\n      throw Exception(\"стек пуст\");\n    }\n    return _stackPeek!.val;\n  }\n\n  /* Преобразовать связный список в List и вернуть */\n  List&lt;int&gt; toList() {\n    ListNode? node = _stackPeek;\n    List&lt;int&gt; list = [];\n    while (node != null) {\n      list.add(node.val);\n      node = node.next;\n    }\n    list = list.reversed.toList();\n    return list;\n  }\n}\n</code></pre> linkedlist_stack.rs<pre><code>/* Стек на основе связного списка */\n#[allow(dead_code)]\npub struct LinkedListStack&lt;T&gt; {\n    stack_peek: Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;, // Использовать головной узел как вершину стека\n    stk_size: usize,                              // Длина стека\n}\n\nimpl&lt;T: Copy&gt; LinkedListStack&lt;T&gt; {\n    pub fn new() -&gt; Self {\n        Self {\n            stack_peek: None,\n            stk_size: 0,\n        }\n    }\n\n    /* Получение длины стека */\n    pub fn size(&amp;self) -&gt; usize {\n        return self.stk_size;\n    }\n\n    /* Проверка, пуст ли стек */\n    pub fn is_empty(&amp;self) -&gt; bool {\n        return self.size() == 0;\n    }\n\n    /* Поместить в стек */\n    pub fn push(&amp;mut self, num: T) {\n        let node = ListNode::new(num);\n        node.borrow_mut().next = self.stack_peek.take();\n        self.stack_peek = Some(node);\n        self.stk_size += 1;\n    }\n\n    /* Извлечь из стека */\n    pub fn pop(&amp;mut self) -&gt; Option&lt;T&gt; {\n        self.stack_peek.take().map(|old_head| {\n            self.stack_peek = old_head.borrow_mut().next.take();\n            self.stk_size -= 1;\n\n            old_head.borrow().val\n        })\n    }\n\n    /* Доступ к верхнему элементу стека */\n    pub fn peek(&amp;self) -&gt; Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt; {\n        self.stack_peek.as_ref()\n    }\n\n    /* Преобразовать List в Array и вернуть */\n    pub fn to_array(&amp;self) -&gt; Vec&lt;T&gt; {\n        fn _to_array&lt;T: Sized + Copy&gt;(head: Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;) -&gt; Vec&lt;T&gt; {\n            if let Some(node) = head {\n                let mut nums = _to_array(node.borrow().next.as_ref());\n                nums.push(node.borrow().val);\n                return nums;\n            }\n            return Vec::new();\n        }\n\n        _to_array(self.peek())\n    }\n}\n</code></pre> linkedlist_stack.c<pre><code>/* Стек на основе связного списка */\ntypedef struct {\n    ListNode *top; // Использовать головной узел как вершину стека\n    int size;      // Длина стека\n} LinkedListStack;\n\n/* Конструктор */\nLinkedListStack *newLinkedListStack() {\n    LinkedListStack *s = malloc(sizeof(LinkedListStack));\n    s-&gt;top = NULL;\n    s-&gt;size = 0;\n    return s;\n}\n\n/* Деструктор */\nvoid delLinkedListStack(LinkedListStack *s) {\n    while (s-&gt;top) {\n        ListNode *n = s-&gt;top-&gt;next;\n        free(s-&gt;top);\n        s-&gt;top = n;\n    }\n    free(s);\n}\n\n/* Получение длины стека */\nint size(LinkedListStack *s) {\n    return s-&gt;size;\n}\n\n/* Проверка, пуст ли стек */\nbool isEmpty(LinkedListStack *s) {\n    return size(s) == 0;\n}\n\n/* Поместить в стек */\nvoid push(LinkedListStack *s, int num) {\n    ListNode *node = (ListNode *)malloc(sizeof(ListNode));\n    node-&gt;next = s-&gt;top; // Обновить поле указателя нового узла\n    node-&gt;val = num;     // Обновить поле данных нового узла\n    s-&gt;top = node;       // Обновить вершину стека\n    s-&gt;size++;           // Обновить размер стека\n}\n\n/* Доступ к верхнему элементу стека */\nint peek(LinkedListStack *s) {\n    if (s-&gt;size == 0) {\n        printf(\"стек пуст\\n\");\n        return INT_MAX;\n    }\n    return s-&gt;top-&gt;val;\n}\n\n/* Извлечь из стека */\nint pop(LinkedListStack *s) {\n    int val = peek(s);\n    ListNode *tmp = s-&gt;top;\n    s-&gt;top = s-&gt;top-&gt;next;\n    // Освободить память\n    free(tmp);\n    s-&gt;size--;\n    return val;\n}\n</code></pre> linkedlist_stack.kt<pre><code>/* Стек на основе связного списка */\nclass LinkedListStack(\n    private var stackPeek: ListNode? = null, // Использовать головной узел как вершину стека\n    private var stkSize: Int = 0 // Длина стека\n) {\n\n    /* Получение длины стека */\n    fun size(): Int {\n        return stkSize\n    }\n\n    /* Проверка, пуст ли стек */\n    fun isEmpty(): Boolean {\n        return size() == 0\n    }\n\n    /* Поместить в стек */\n    fun push(num: Int) {\n        val node = ListNode(num)\n        node.next = stackPeek\n        stackPeek = node\n        stkSize++\n    }\n\n    /* Извлечь из стека */\n    fun pop(): Int? {\n        val num = peek()\n        stackPeek = stackPeek?.next\n        stkSize--\n        return num\n    }\n\n    /* Доступ к верхнему элементу стека */\n    fun peek(): Int? {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        return stackPeek?._val\n    }\n\n    /* Преобразовать List в Array и вернуть */\n    fun toArray(): IntArray {\n        var node = stackPeek\n        val res = IntArray(size())\n        for (i in res.size - 1 downTo 0) {\n            res[i] = node?._val!!\n            node = node.next\n        }\n        return res\n    }\n}\n</code></pre> linkedlist_stack.rb<pre><code>### Стек на основе связного списка ###\nclass LinkedListStack\n  attr_reader :size\n\n  ### Конструктор ###\n  def initialize\n    @size = 0\n  end\n\n  ### Проверка, пуст ли стек ###\n  def is_empty?\n    @peek.nil?\n  end\n\n  ### Помещение в стек ###\n  def push(val)\n    node = ListNode.new(val)\n    node.next = @peek\n    @peek = node\n    @size += 1\n  end\n\n  ### Извлечение из стека ###\n  def pop\n    num = peek\n    @peek = @peek.next\n    @size -= 1\n    num\n  end\n\n  ### Доступ к верхнему элементу стека ###\n  def peek\n    raise IndexError, 'стек пуст' if is_empty?\n\n    @peek.val\n  end\n\n  ### Преобразовать связный список в Array и вернуть ###\n  def to_array\n    arr = []\n    node = @peek\n    while node\n      arr &lt;&lt; node.val\n      node = node.next\n    end\n    arr.reverse\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 5. Стек и очередь","5.1 &nbsp; Стек"],"tags":[]},{"location":"chapter_stack_and_queue/stack/#2","level":3,"title":"2.   Реализация на основе массива","text":"<p>Если реализовывать стек на основе массива, то хвост массива можно рассматривать как вершину стека. Как показано на рисунке 5-3, операции push и pop соответствуют добавлению элемента в конец массива и удалению элемента из конца, обе имеют временную сложность \\(O(1)\\) .</p> ArrayStackpush()pop() <p></p> <p></p> <p></p> <p> Рисунок 5-3   Операции push и pop в реализации стека на массиве </p> <p>Поскольку количество элементов, помещаемых в стек, может непрерывно расти, мы можем использовать динамический массив и тем самым не заниматься расширением массива вручную. Ниже приведен пример кода:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array_stack.py<pre><code>class ArrayStack:\n    \"\"\"Стек на основе массива\"\"\"\n\n    def __init__(self):\n        \"\"\"Конструктор\"\"\"\n        self._stack: list[int] = []\n\n    def size(self) -&gt; int:\n        \"\"\"Получение длины стека\"\"\"\n        return len(self._stack)\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"Проверка, пуст ли стек\"\"\"\n        return self.size() == 0\n\n    def push(self, item: int):\n        \"\"\"Поместить в стек\"\"\"\n        self._stack.append(item)\n\n    def pop(self) -&gt; int:\n        \"\"\"Извлечь из стека\"\"\"\n        if self.is_empty():\n            raise IndexError(\"стек пуст\")\n        return self._stack.pop()\n\n    def peek(self) -&gt; int:\n        \"\"\"Доступ к верхнему элементу стека\"\"\"\n        if self.is_empty():\n            raise IndexError(\"стек пуст\")\n        return self._stack[-1]\n\n    def to_list(self) -&gt; list[int]:\n        \"\"\"Вернуть список для вывода\"\"\"\n        return self._stack\n</code></pre> array_stack.cpp<pre><code>/* Стек на основе массива */\nclass ArrayStack {\n  private:\n    vector&lt;int&gt; stack;\n\n  public:\n    /* Получение длины стека */\n    int size() {\n        return stack.size();\n    }\n\n    /* Проверка, пуст ли стек */\n    bool isEmpty() {\n        return stack.size() == 0;\n    }\n\n    /* Поместить в стек */\n    void push(int num) {\n        stack.push_back(num);\n    }\n\n    /* Извлечь из стека */\n    int pop() {\n        int num = top();\n        stack.pop_back();\n        return num;\n    }\n\n    /* Доступ к верхнему элементу стека */\n    int top() {\n        if (isEmpty())\n            throw out_of_range(\"стек пуст\");\n        return stack.back();\n    }\n\n    /* Вернуть Vector */\n    vector&lt;int&gt; toVector() {\n        return stack;\n    }\n};\n</code></pre> array_stack.java<pre><code>/* Стек на основе массива */\nclass ArrayStack {\n    private ArrayList&lt;Integer&gt; stack;\n\n    public ArrayStack() {\n        // Инициализация списка (динамического массива)\n        stack = new ArrayList&lt;&gt;();\n    }\n\n    /* Получение длины стека */\n    public int size() {\n        return stack.size();\n    }\n\n    /* Проверка, пуст ли стек */\n    public boolean isEmpty() {\n        return size() == 0;\n    }\n\n    /* Поместить в стек */\n    public void push(int num) {\n        stack.add(num);\n    }\n\n    /* Извлечь из стека */\n    public int pop() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return stack.remove(size() - 1);\n    }\n\n    /* Доступ к верхнему элементу стека */\n    public int peek() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return stack.get(size() - 1);\n    }\n\n    /* Преобразовать List в Array и вернуть */\n    public Object[] toArray() {\n        return stack.toArray();\n    }\n}\n</code></pre> array_stack.cs<pre><code>/* Стек на основе массива */\nclass ArrayStack {\n    List&lt;int&gt; stack;\n    public ArrayStack() {\n        // Инициализация списка (динамического массива)\n        stack = [];\n    }\n\n    /* Получение длины стека */\n    public int Size() {\n        return stack.Count;\n    }\n\n    /* Проверка, пуст ли стек */\n    public bool IsEmpty() {\n        return Size() == 0;\n    }\n\n    /* Поместить в стек */\n    public void Push(int num) {\n        stack.Add(num);\n    }\n\n    /* Извлечь из стека */\n    public int Pop() {\n        if (IsEmpty())\n            throw new Exception();\n        var val = Peek();\n        stack.RemoveAt(Size() - 1);\n        return val;\n    }\n\n    /* Доступ к верхнему элементу стека */\n    public int Peek() {\n        if (IsEmpty())\n            throw new Exception();\n        return stack[Size() - 1];\n    }\n\n    /* Преобразовать List в Array и вернуть */\n    public int[] ToArray() {\n        return [.. stack];\n    }\n}\n</code></pre> array_stack.go<pre><code>/* Стек на основе массива */\ntype arrayStack struct {\n    data []int // Данные\n}\n\n/* Инициализация стека */\nfunc newArrayStack() *arrayStack {\n    return &amp;arrayStack{\n        // Установить длину стека равной 0, а емкость равной 16\n        data: make([]int, 0, 16),\n    }\n}\n\n/* Длина стека */\nfunc (s *arrayStack) size() int {\n    return len(s.data)\n}\n\n/* Пуст ли стек */\nfunc (s *arrayStack) isEmpty() bool {\n    return s.size() == 0\n}\n\n/* Поместить в стек */\nfunc (s *arrayStack) push(v int) {\n    // Срез автоматически расширяется\n    s.data = append(s.data, v)\n}\n\n/* Извлечь из стека */\nfunc (s *arrayStack) pop() any {\n    val := s.peek()\n    s.data = s.data[:len(s.data)-1]\n    return val\n}\n\n/* Получить элемент на вершине стека */\nfunc (s *arrayStack) peek() any {\n    if s.isEmpty() {\n        return nil\n    }\n    val := s.data[len(s.data)-1]\n    return val\n}\n\n/* Получить Slice для вывода */\nfunc (s *arrayStack) toSlice() []int {\n    return s.data\n}\n</code></pre> array_stack.swift<pre><code>/* Стек на основе массива */\nclass ArrayStack {\n    private var stack: [Int]\n\n    init() {\n        // Инициализация списка (динамического массива)\n        stack = []\n    }\n\n    /* Получение длины стека */\n    func size() -&gt; Int {\n        stack.count\n    }\n\n    /* Проверка, пуст ли стек */\n    func isEmpty() -&gt; Bool {\n        stack.isEmpty\n    }\n\n    /* Поместить в стек */\n    func push(num: Int) {\n        stack.append(num)\n    }\n\n    /* Извлечь из стека */\n    @discardableResult\n    func pop() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"стек пуст\")\n        }\n        return stack.removeLast()\n    }\n\n    /* Доступ к верхнему элементу стека */\n    func peek() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"стек пуст\")\n        }\n        return stack.last!\n    }\n\n    /* Преобразовать List в Array и вернуть */\n    func toArray() -&gt; [Int] {\n        stack\n    }\n}\n</code></pre> array_stack.js<pre><code>/* Стек на основе массива */\nclass ArrayStack {\n    #stack;\n    constructor() {\n        this.#stack = [];\n    }\n\n    /* Получение длины стека */\n    get size() {\n        return this.#stack.length;\n    }\n\n    /* Проверка, пуст ли стек */\n    isEmpty() {\n        return this.#stack.length === 0;\n    }\n\n    /* Поместить в стек */\n    push(num) {\n        this.#stack.push(num);\n    }\n\n    /* Извлечь из стека */\n    pop() {\n        if (this.isEmpty()) throw new Error('стек пуст');\n        return this.#stack.pop();\n    }\n\n    /* Доступ к верхнему элементу стека */\n    top() {\n        if (this.isEmpty()) throw new Error('стек пуст');\n        return this.#stack[this.#stack.length - 1];\n    }\n\n    /* Вернуть Array */\n    toArray() {\n        return this.#stack;\n    }\n}\n</code></pre> array_stack.ts<pre><code>/* Стек на основе массива */\nclass ArrayStack {\n    private stack: number[];\n    constructor() {\n        this.stack = [];\n    }\n\n    /* Получение длины стека */\n    get size(): number {\n        return this.stack.length;\n    }\n\n    /* Проверка, пуст ли стек */\n    isEmpty(): boolean {\n        return this.stack.length === 0;\n    }\n\n    /* Поместить в стек */\n    push(num: number): void {\n        this.stack.push(num);\n    }\n\n    /* Извлечь из стека */\n    pop(): number | undefined {\n        if (this.isEmpty()) throw new Error('стек пуст');\n        return this.stack.pop();\n    }\n\n    /* Доступ к верхнему элементу стека */\n    top(): number | undefined {\n        if (this.isEmpty()) throw new Error('стек пуст');\n        return this.stack[this.stack.length - 1];\n    }\n\n    /* Вернуть Array */\n    toArray() {\n        return this.stack;\n    }\n}\n</code></pre> array_stack.dart<pre><code>/* Стек на основе массива */\nclass ArrayStack {\n  late List&lt;int&gt; _stack;\n  ArrayStack() {\n    _stack = [];\n  }\n\n  /* Получение длины стека */\n  int size() {\n    return _stack.length;\n  }\n\n  /* Проверка, пуст ли стек */\n  bool isEmpty() {\n    return _stack.isEmpty;\n  }\n\n  /* Поместить в стек */\n  void push(int _num) {\n    _stack.add(_num);\n  }\n\n  /* Извлечь из стека */\n  int pop() {\n    if (isEmpty()) {\n      throw Exception(\"стек пуст\");\n    }\n    return _stack.removeLast();\n  }\n\n  /* Доступ к верхнему элементу стека */\n  int peek() {\n    if (isEmpty()) {\n      throw Exception(\"стек пуст\");\n    }\n    return _stack.last;\n  }\n\n  /* Преобразовать стек в Array и вернуть */\n  List&lt;int&gt; toArray() =&gt; _stack;\n}\n</code></pre> array_stack.rs<pre><code>/* Стек на основе массива */\nstruct ArrayStack&lt;T&gt; {\n    stack: Vec&lt;T&gt;,\n}\n\nimpl&lt;T&gt; ArrayStack&lt;T&gt; {\n    /* Инициализация стека */\n    fn new() -&gt; ArrayStack&lt;T&gt; {\n        ArrayStack::&lt;T&gt; {\n            stack: Vec::&lt;T&gt;::new(),\n        }\n    }\n\n    /* Получение длины стека */\n    fn size(&amp;self) -&gt; usize {\n        self.stack.len()\n    }\n\n    /* Проверка, пуст ли стек */\n    fn is_empty(&amp;self) -&gt; bool {\n        self.size() == 0\n    }\n\n    /* Поместить в стек */\n    fn push(&amp;mut self, num: T) {\n        self.stack.push(num);\n    }\n\n    /* Извлечь из стека */\n    fn pop(&amp;mut self) -&gt; Option&lt;T&gt; {\n        self.stack.pop()\n    }\n\n    /* Доступ к верхнему элементу стека */\n    fn peek(&amp;self) -&gt; Option&lt;&amp;T&gt; {\n        if self.is_empty() {\n            panic!(\"стек пуст\")\n        };\n        self.stack.last()\n    }\n\n    /* Вернуть &amp;Vec */\n    fn to_array(&amp;self) -&gt; &amp;Vec&lt;T&gt; {\n        &amp;self.stack\n    }\n}\n</code></pre> array_stack.c<pre><code>/* Стек на основе массива */\ntypedef struct {\n    int *data;\n    int size;\n} ArrayStack;\n\n/* Конструктор */\nArrayStack *newArrayStack() {\n    ArrayStack *stack = malloc(sizeof(ArrayStack));\n    // Инициализировать большую вместимость, чтобы избежать расширения\n    stack-&gt;data = malloc(sizeof(int) * MAX_SIZE);\n    stack-&gt;size = 0;\n    return stack;\n}\n\n/* Деструктор */\nvoid delArrayStack(ArrayStack *stack) {\n    free(stack-&gt;data);\n    free(stack);\n}\n\n/* Получение длины стека */\nint size(ArrayStack *stack) {\n    return stack-&gt;size;\n}\n\n/* Проверка, пуст ли стек */\nbool isEmpty(ArrayStack *stack) {\n    return stack-&gt;size == 0;\n}\n\n/* Поместить в стек */\nvoid push(ArrayStack *stack, int num) {\n    if (stack-&gt;size == MAX_SIZE) {\n        printf(\"Стек заполнен\\n\");\n        return;\n    }\n    stack-&gt;data[stack-&gt;size] = num;\n    stack-&gt;size++;\n}\n\n/* Доступ к верхнему элементу стека */\nint peek(ArrayStack *stack) {\n    if (stack-&gt;size == 0) {\n        printf(\"стек пуст\\n\");\n        return INT_MAX;\n    }\n    return stack-&gt;data[stack-&gt;size - 1];\n}\n\n/* Извлечь из стека */\nint pop(ArrayStack *stack) {\n    int val = peek(stack);\n    stack-&gt;size--;\n    return val;\n}\n</code></pre> array_stack.kt<pre><code>/* Стек на основе массива */\nclass ArrayStack {\n    // Инициализация списка (динамического массива)\n    private val stack = mutableListOf&lt;Int&gt;()\n\n    /* Получение длины стека */\n    fun size(): Int {\n        return stack.size\n    }\n\n    /* Проверка, пуст ли стек */\n    fun isEmpty(): Boolean {\n        return size() == 0\n    }\n\n    /* Поместить в стек */\n    fun push(num: Int) {\n        stack.add(num)\n    }\n\n    /* Извлечь из стека */\n    fun pop(): Int {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        return stack.removeAt(size() - 1)\n    }\n\n    /* Доступ к верхнему элементу стека */\n    fun peek(): Int {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        return stack[size() - 1]\n    }\n\n    /* Преобразовать List в Array и вернуть */\n    fun toArray(): Array&lt;Any&gt; {\n        return stack.toTypedArray()\n    }\n}\n</code></pre> array_stack.rb<pre><code>### Стек на основе массива ###\nclass ArrayStack\n  ### Конструктор ###\n  def initialize\n    @stack = []\n  end\n\n  ### Получить длину стека ###\n  def size\n    @stack.length\n  end\n\n  ### Проверка, пуст ли стек ###\n  def is_empty?\n    @stack.empty?\n  end\n\n  ### Помещение в стек ###\n  def push(item)\n    @stack &lt;&lt; item\n  end\n\n  ### Извлечение из стека ###\n  def pop\n    raise IndexError, 'стек пуст' if is_empty?\n\n    @stack.pop\n  end\n\n  ### Доступ к верхнему элементу стека ###\n  def peek\n    raise IndexError, 'стек пуст' if is_empty?\n\n    @stack.last\n  end\n\n  ### Вернуть список для вывода ###\n  def to_array\n    @stack\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 5. Стек и очередь","5.1 &nbsp; Стек"],"tags":[]},{"location":"chapter_stack_and_queue/stack/#513","level":2,"title":"5.1.3   Сравнение двух реализаций","text":"<p>Поддерживаемые операции</p> <p>Обе реализации поддерживают все операции, определенные для стека. Реализация на массиве дополнительно позволяет выполнять произвольный доступ, но это уже выходит за рамки определения стека и обычно не используется.</p> <p>Временная эффективность</p> <p>В реализации на массиве и push, и pop выполняются в заранее выделенной непрерывной памяти, которая хорошо использует локальность кэша, поэтому такие операции обычно эффективнее. Однако если при push емкость массива оказывается превышена, включается механизм расширения, и временная сложность конкретно этой операции push становится \\(O(n)\\) .</p> <p>В реализации на связном списке расширение выполняется очень гибко, и проблемы падения эффективности из-за расширения массива здесь нет. Но сама операция push требует инициализации объекта-узла и изменения указателей, поэтому в среднем она немного менее эффективна. Впрочем, если помещаемые в стек элементы уже сами являются объектами-узлами, шаг инициализации можно пропустить и тем самым повысить эффективность.</p> <p>Итак, когда элементами, помещаемыми и извлекаемыми из стека, являются базовые типы данных, например <code>int</code> или <code>double</code> , можно сделать следующие выводы.</p> <ul> <li>Стек на основе массива теряет в эффективности в моменты расширения, но поскольку расширение происходит редко, его средняя эффективность выше.</li> <li>Стек на основе связного списка может обеспечивать более стабильную производительность.</li> </ul> <p>Пространственная эффективность</p> <p>При инициализации списка система выделяет \"начальную емкость\", которая может превышать реальную потребность. Кроме того, механизм расширения обычно увеличивает емкость по некоторому коэффициенту (например в 2 раза), и расширенная емкость тоже может оказаться больше фактически необходимой. Поэтому реализация стека на основе массива может приводить к некоторым потерям памяти.</p> <p>Однако, поскольку узлы связного списка должны дополнительно хранить указатели, узлы списка сами по себе занимают больше пространства.</p> <p>В итоге нельзя просто сказать, какая из реализаций более экономна по памяти; это нужно анализировать в контексте конкретной задачи.</p>","path":["Глава 5. Стек и очередь","5.1 &nbsp; Стек"],"tags":[]},{"location":"chapter_stack_and_queue/stack/#514","level":2,"title":"5.1.4   Типичные применения стека","text":"<ul> <li>Кнопки \"назад\" и \"вперед\" в браузере, undo и redo в программах. Каждый раз, когда мы открываем новую страницу, браузер помещает предыдущую страницу в стек, чтобы по операции \"назад\" можно было вернуться к ней. Операция \"назад\" по сути является pop. Если нужно одновременно поддерживать и \"назад\", и \"вперед\", то обычно используются два стека.</li> <li>Управление памятью программы. Каждый раз при вызове функции система помещает на вершину стека стековый кадр, в котором хранится контекст функции. В рекурсивной функции на этапе углубления рекурсии непрерывно выполняются push-операции, а на этапе возврата - pop-операции.</li> </ul>","path":["Глава 5. Стек и очередь","5.1 &nbsp; Стек"],"tags":[]},{"location":"chapter_stack_and_queue/summary/","level":1,"title":"5.4   Краткие итоги","text":"","path":["Глава 5. Стек и очередь","5.4 &nbsp; Краткие итоги"],"tags":[]},{"location":"chapter_stack_and_queue/summary/#1","level":3,"title":"1.   Основные моменты","text":"<ul> <li>Стек - это структура данных, следующая правилу \"последним пришел - первым вышел\", и его можно реализовать с помощью массива или связного списка.</li> <li>С точки зрения временной эффективности реализация стека на массиве обычно работает быстрее в среднем, но во время расширения емкости временная сложность отдельной операции push может ухудшаться до \\(O(n)\\) . Напротив, реализация стека на связном списке дает более стабильные характеристики.</li> <li>С точки зрения использования памяти реализация стека на массиве может приводить к некоторой потере пространства. Однако следует учитывать, что узлы связного списка занимают больше памяти, чем элементы массива.</li> <li>Очередь - это структура данных, следующая правилу \"первым пришел - первым вышел\", и ее также можно реализовать с помощью массива или связного списка. Сравнение временной и пространственной эффективности для очереди в целом приводит к тем же выводам, что и для стека.</li> <li>Двусторонняя очередь - это очередь с более высокой степенью свободы, которая позволяет добавлять и удалять элементы с обеих сторон.</li> </ul>","path":["Глава 5. Стек и очередь","5.4 &nbsp; Краткие итоги"],"tags":[]},{"location":"chapter_stack_and_queue/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: Реализованы ли кнопки \"вперед\" и \"назад\" в браузере с помощью двусвязного списка?</p> <p>По сути, функция переходов \"вперед/назад\" в браузере отражает логику \"стека\". Когда пользователь открывает новую страницу, она помещается на вершину стека; когда пользователь нажимает кнопку \"назад\", эта страница снимается с вершины стека. Двусторонняя очередь позволяет удобно реализовать некоторые дополнительные операции, об этом уже упоминалось в разделе \"Двусторонняя очередь\".</p> <p>Q: Нужно ли освобождать память узла после извлечения его из стека?</p> <p>Если извлеченный узел еще понадобится, память освобождать не нужно. Если он больше не нужен, то в языках <code>Java</code> и <code>Python</code> есть автоматический сборщик мусора, поэтому ручное освобождение памяти не требуется; в <code>C</code> и <code>C++</code> память нужно освобождать вручную.</p> <p>Q: Двусторонняя очередь выглядит как два соединенных стека. Для чего она нужна?</p> <p>Двусторонняя очередь похожа на комбинацию стека и очереди или на два соединенных стека. Она выражает логику \"стек + очередь\", поэтому может покрыть все применения стека и очереди и при этом остается более гибкой.</p> <p>Q: Как именно реализуются отмена (undo) и повтор (redo)?</p> <p>Используются два стека: стек <code>A</code> для отмены и стек <code>B</code> для повтора.</p> <ol> <li>Каждый раз, когда пользователь выполняет действие, это действие помещается в стек <code>A</code> , а стек <code>B</code> очищается.</li> <li>Когда пользователь выполняет \"undo\", последнее действие извлекается из стека <code>A</code> и помещается в стек <code>B</code> .</li> <li>Когда пользователь выполняет \"redo\", последнее действие извлекается из стека <code>B</code> и помещается обратно в стек <code>A</code> .</li> </ol>","path":["Глава 5. Стек и очередь","5.4 &nbsp; Краткие итоги"],"tags":[]},{"location":"chapter_tree/","level":1,"title":"Глава 7.   Деревья","text":"<p>Abstract</p> <p>Высокое дерево полно жизни: мощные корни, густая крона и раскидистые ветви.</p> <p>Оно наглядно показывает нам форму данных, построенную на принципе \"разделяй и властвуй\".</p>","path":["Глава 7. Дерево","Глава 7. &nbsp; Деревья"],"tags":[]},{"location":"chapter_tree/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>7.1   Двоичное дерево</li> <li>7.2   Обход двоичного дерева</li> <li>7.3   Представление дерева массивом</li> <li>7.4   Двоичное дерево поиска</li> <li>7.5   AVL-дерево *</li> <li>7.6   Резюме</li> </ul>","path":["Глава 7. Дерево","Глава 7. &nbsp; Деревья"],"tags":[]},{"location":"chapter_tree/array_representation_of_tree/","level":1,"title":"7.3   Представление двоичного дерева массивом","text":"<p>В представлении через связную структуру единицей хранения двоичного дерева является узел <code>TreeNode</code> , а между узлами существуют связи через указатели. В предыдущем разделе были рассмотрены основные операции двоичного дерева в таком представлении.</p> <p>Возникает вопрос: можно ли представить двоичное дерево с помощью массива? Ответ: да.</p>","path":["Глава 7. Дерево","7.3 &nbsp; Представление двоичного дерева массивом"],"tags":[]},{"location":"chapter_tree/array_representation_of_tree/#731","level":2,"title":"7.3.1   Представление идеального двоичного дерева","text":"<p>Сначала разберем простой случай. Если дана идеальная двоичная структура и все ее узлы хранятся в массиве в порядке обхода по уровням, то каждому узлу будет соответствовать единственный индекс массива.</p> <p>Из свойств обхода по уровням можно вывести \"формулу соответствия\" между индексом родителя и индексами дочерних узлов: если индекс некоторого узла равен \\(i\\) , то индекс его левого дочернего узла равен \\(2i + 1\\) , а правого - \\(2i + 2\\) . На рисунке 7-12 показано соответствие между индексами разных узлов.</p> <p></p> <p> Рисунок 7-12   Представление идеального двоичного дерева массивом </p> <p>Эта формула соответствия играет ту же роль, что и ссылки на узлы в связной структуре . Имея любой узел в массиве, мы можем по формуле получить доступ к его левому и правому дочерним узлам.</p>","path":["Глава 7. Дерево","7.3 &nbsp; Представление двоичного дерева массивом"],"tags":[]},{"location":"chapter_tree/array_representation_of_tree/#732","level":2,"title":"7.3.2   Представление произвольного двоичного дерева","text":"<p>Идеальное двоичное дерево - лишь частный случай; в обычной двоичной структуре на промежуточных уровнях часто существует множество <code>None</code> . Поскольку последовательность обхода по уровням не содержит этих <code>None</code> , мы не можем по одной лишь этой последовательности определить их количество и расположение. Это означает, что одному и тому же обходу по уровням может соответствовать сразу несколько различных структур двоичного дерева.</p> <p>Как показано на рисунке 7-13, для неполной двоичной структуры описанный выше способ представления массивом уже перестает работать.</p> <p></p> <p> Рисунок 7-13   Одной последовательности обхода по уровням соответствуют разные двоичные структуры </p> <p>Чтобы решить эту проблему, мы можем явно записывать все <code>None</code> в последовательности обхода по уровням . Как показано на рисунке 7-14, после такой обработки последовательность обхода по уровням уже сможет однозначно задавать двоичное дерево. Пример кода приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code># Представление двоичного дерева массивом\n# Используем None для обозначения пустых позиций\ntree = [1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, None, None, 15]\n</code></pre> <pre><code>/* Представление двоичного дерева массивом */\n// Используем максимальное значение int, INT_MAX, для обозначения пустых позиций\nvector&lt;int&gt; tree = {1, 2, 3, 4, INT_MAX, 6, 7, 8, 9, INT_MAX, INT_MAX, 12, INT_MAX, INT_MAX, 15};\n</code></pre> <pre><code>/* Представление двоичного дерева массивом */\n// Используя обертку Integer для int, можно применять null для обозначения пустых позиций\nInteger[] tree = { 1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15 };\n</code></pre> <pre><code>/* Представление двоичного дерева массивом */\n// Используя nullable-тип int? , можно применять null для обозначения пустых позиций\nint?[] tree = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <pre><code>/* Представление двоичного дерева массивом */\n// Используем срез типа any, чтобы можно было применять nil для обозначения пустых позиций\ntree := []any{1, 2, 3, 4, nil, 6, 7, 8, 9, nil, nil, 12, nil, nil, 15}\n</code></pre> <pre><code>/* Представление двоичного дерева массивом */\n// Используя nullable-тип Int? , можно применять nil для обозначения пустых позиций\nlet tree: [Int?] = [1, 2, 3, 4, nil, 6, 7, 8, 9, nil, nil, 12, nil, nil, 15]\n</code></pre> <pre><code>/* Представление двоичного дерева массивом */\n// Используем null для обозначения пустых позиций\nlet tree = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <pre><code>/* Представление двоичного дерева массивом */\n// Используем null для обозначения пустых позиций\nlet tree: (number | null)[] = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <pre><code>/* Представление двоичного дерева массивом */\n// Используя nullable-тип int? , можно применять null для обозначения пустых позиций\nList&lt;int?&gt; tree = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <pre><code>/* Представление двоичного дерева массивом */\n// Используем None для обозначения пустых позиций\nlet tree = [Some(1), Some(2), Some(3), Some(4), None, Some(6), Some(7), Some(8), Some(9), None, None, Some(12), None, None, Some(15)];\n</code></pre> <pre><code>/* Представление двоичного дерева массивом */\n// Используем максимальное значение int для обозначения пустых позиций, поэтому узлы не должны принимать значение INT_MAX\nint tree[] = {1, 2, 3, 4, INT_MAX, 6, 7, 8, 9, INT_MAX, INT_MAX, 12, INT_MAX, INT_MAX, 15};\n</code></pre> <pre><code>/* Представление двоичного дерева массивом */\n// Используем null для обозначения пустых позиций\nval tree = arrayOf( 1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15 )\n</code></pre> <pre><code>### Представление двоичного дерева массивом ###\n# Используем nil для обозначения пустых позиций\ntree = [1, 2, 3, 4, nil, 6, 7, 8, 9, nil, nil, 12, nil, nil, 15]\n</code></pre> <p></p> <p> Рисунок 7-14   Представление произвольного двоичного дерева массивом </p> <p>Стоит отметить, что полное двоичное дерево очень удобно представлять массивом . Если вспомнить определение полного двоичного дерева, то <code>None</code> появляются только на самом нижнем уровне и справа, а значит, все <code>None</code> обязательно находятся в конце последовательности обхода по уровням.</p> <p>Это означает, что при представлении полного двоичного дерева массивом можно не хранить все <code>None</code> , что очень удобно. На рисунке 7-15 приведен пример.</p> <p></p> <p> Рисунок 7-15   Представление полного двоичного дерева массивом </p> <p>Ниже приведен код реализации двоичного дерева, представленного массивом. Он включает следующие операции.</p> <ul> <li>Для заданного узла получить его значение, левого дочернего узла, правого дочернего узла и родительский узел.</li> <li>Получить последовательности прямого, симметричного, обратного обходов и обхода по уровням.</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array_binary_tree.py<pre><code>class ArrayBinaryTree:\n    \"\"\"Класс двоичного дерева в массивном представлении\"\"\"\n\n    def __init__(self, arr: list[int | None]):\n        \"\"\"Конструктор\"\"\"\n        self._tree = list(arr)\n\n    def size(self):\n        \"\"\"Вместимость списка\"\"\"\n        return len(self._tree)\n\n    def val(self, i: int) -&gt; int | None:\n        \"\"\"Получить значение узла с индексом i\"\"\"\n        # Если индекс выходит за границы, вернуть None, обозначающий пустую позицию\n        if i &lt; 0 or i &gt;= self.size():\n            return None\n        return self._tree[i]\n\n    def left(self, i: int) -&gt; int | None:\n        \"\"\"Получить индекс левого дочернего узла узла с индексом i\"\"\"\n        return 2 * i + 1\n\n    def right(self, i: int) -&gt; int | None:\n        \"\"\"Получить индекс правого дочернего узла узла с индексом i\"\"\"\n        return 2 * i + 2\n\n    def parent(self, i: int) -&gt; int | None:\n        \"\"\"Получить индекс родительского узла узла с индексом i\"\"\"\n        return (i - 1) // 2\n\n    def level_order(self) -&gt; list[int]:\n        \"\"\"Обход в ширину\"\"\"\n        self.res = []\n        # Непосредственно обходить массив\n        for i in range(self.size()):\n            if self.val(i) is not None:\n                self.res.append(self.val(i))\n        return self.res\n\n    def dfs(self, i: int, order: str):\n        \"\"\"Обход в глубину\"\"\"\n        if self.val(i) is None:\n            return\n        # Предварительный обход\n        if order == \"pre\":\n            self.res.append(self.val(i))\n        self.dfs(self.left(i), order)\n        # Симметричный обход\n        if order == \"in\":\n            self.res.append(self.val(i))\n        self.dfs(self.right(i), order)\n        # Обратный обход\n        if order == \"post\":\n            self.res.append(self.val(i))\n\n    def pre_order(self) -&gt; list[int]:\n        \"\"\"Предварительный обход\"\"\"\n        self.res = []\n        self.dfs(0, order=\"pre\")\n        return self.res\n\n    def in_order(self) -&gt; list[int]:\n        \"\"\"Симметричный обход\"\"\"\n        self.res = []\n        self.dfs(0, order=\"in\")\n        return self.res\n\n    def post_order(self) -&gt; list[int]:\n        \"\"\"Обратный обход\"\"\"\n        self.res = []\n        self.dfs(0, order=\"post\")\n        return self.res\n</code></pre> array_binary_tree.cpp<pre><code>/* Класс двоичного дерева в массивном представлении */\nclass ArrayBinaryTree {\n  public:\n    /* Конструктор */\n    ArrayBinaryTree(vector&lt;int&gt; arr) {\n        tree = arr;\n    }\n\n    /* Вместимость списка */\n    int size() {\n        return tree.size();\n    }\n\n    /* Получить значение узла с индексом i */\n    int val(int i) {\n        // Если индекс выходит за границы, вернуть INT_MAX, обозначающий пустую позицию\n        if (i &lt; 0 || i &gt;= size())\n            return INT_MAX;\n        return tree[i];\n    }\n\n    /* Получить индекс левого дочернего узла узла с индексом i */\n    int left(int i) {\n        return 2 * i + 1;\n    }\n\n    /* Получить индекс правого дочернего узла узла с индексом i */\n    int right(int i) {\n        return 2 * i + 2;\n    }\n\n    /* Получить индекс родительского узла узла с индексом i */\n    int parent(int i) {\n        return (i - 1) / 2;\n    }\n\n    /* Обход в ширину */\n    vector&lt;int&gt; levelOrder() {\n        vector&lt;int&gt; res;\n        // Непосредственно обходить массив\n        for (int i = 0; i &lt; size(); i++) {\n            if (val(i) != INT_MAX)\n                res.push_back(val(i));\n        }\n        return res;\n    }\n\n    /* Предварительный обход */\n    vector&lt;int&gt; preOrder() {\n        vector&lt;int&gt; res;\n        dfs(0, \"pre\", res);\n        return res;\n    }\n\n    /* Симметричный обход */\n    vector&lt;int&gt; inOrder() {\n        vector&lt;int&gt; res;\n        dfs(0, \"in\", res);\n        return res;\n    }\n\n    /* Обратный обход */\n    vector&lt;int&gt; postOrder() {\n        vector&lt;int&gt; res;\n        dfs(0, \"post\", res);\n        return res;\n    }\n\n  private:\n    vector&lt;int&gt; tree;\n\n    /* Обход в глубину */\n    void dfs(int i, string order, vector&lt;int&gt; &amp;res) {\n        // Если это пустая позиция, вернуть\n        if (val(i) == INT_MAX)\n            return;\n        // Предварительный обход\n        if (order == \"pre\")\n            res.push_back(val(i));\n        dfs(left(i), order, res);\n        // Симметричный обход\n        if (order == \"in\")\n            res.push_back(val(i));\n        dfs(right(i), order, res);\n        // Обратный обход\n        if (order == \"post\")\n            res.push_back(val(i));\n    }\n};\n</code></pre> array_binary_tree.java<pre><code>/* Класс двоичного дерева в массивном представлении */\nclass ArrayBinaryTree {\n    private List&lt;Integer&gt; tree;\n\n    /* Конструктор */\n    public ArrayBinaryTree(List&lt;Integer&gt; arr) {\n        tree = new ArrayList&lt;&gt;(arr);\n    }\n\n    /* Вместимость списка */\n    public int size() {\n        return tree.size();\n    }\n\n    /* Получить значение узла с индексом i */\n    public Integer val(int i) {\n        // Если индекс выходит за границы, вернуть null, обозначающий пустую позицию\n        if (i &lt; 0 || i &gt;= size())\n            return null;\n        return tree.get(i);\n    }\n\n    /* Получить индекс левого дочернего узла узла с индексом i */\n    public Integer left(int i) {\n        return 2 * i + 1;\n    }\n\n    /* Получить индекс правого дочернего узла узла с индексом i */\n    public Integer right(int i) {\n        return 2 * i + 2;\n    }\n\n    /* Получить индекс родительского узла узла с индексом i */\n    public Integer parent(int i) {\n        return (i - 1) / 2;\n    }\n\n    /* Обход в ширину */\n    public List&lt;Integer&gt; levelOrder() {\n        List&lt;Integer&gt; res = new ArrayList&lt;&gt;();\n        // Непосредственно обходить массив\n        for (int i = 0; i &lt; size(); i++) {\n            if (val(i) != null)\n                res.add(val(i));\n        }\n        return res;\n    }\n\n    /* Обход в глубину */\n    private void dfs(Integer i, String order, List&lt;Integer&gt; res) {\n        // Если это пустая позиция, вернуть\n        if (val(i) == null)\n            return;\n        // Предварительный обход\n        if (\"pre\".equals(order))\n            res.add(val(i));\n        dfs(left(i), order, res);\n        // Симметричный обход\n        if (\"in\".equals(order))\n            res.add(val(i));\n        dfs(right(i), order, res);\n        // Обратный обход\n        if (\"post\".equals(order))\n            res.add(val(i));\n    }\n\n    /* Предварительный обход */\n    public List&lt;Integer&gt; preOrder() {\n        List&lt;Integer&gt; res = new ArrayList&lt;&gt;();\n        dfs(0, \"pre\", res);\n        return res;\n    }\n\n    /* Симметричный обход */\n    public List&lt;Integer&gt; inOrder() {\n        List&lt;Integer&gt; res = new ArrayList&lt;&gt;();\n        dfs(0, \"in\", res);\n        return res;\n    }\n\n    /* Обратный обход */\n    public List&lt;Integer&gt; postOrder() {\n        List&lt;Integer&gt; res = new ArrayList&lt;&gt;();\n        dfs(0, \"post\", res);\n        return res;\n    }\n}\n</code></pre> array_binary_tree.cs<pre><code>/* Класс двоичного дерева в массивном представлении */\nclass ArrayBinaryTree(List&lt;int?&gt; arr) {\n    List&lt;int?&gt; tree = new(arr);\n\n    /* Вместимость списка */\n    public int Size() {\n        return tree.Count;\n    }\n\n    /* Получить значение узла с индексом i */\n    public int? Val(int i) {\n        // Если индекс выходит за границы, вернуть null, обозначающий пустую позицию\n        if (i &lt; 0 || i &gt;= Size())\n            return null;\n        return tree[i];\n    }\n\n    /* Получить индекс левого дочернего узла узла с индексом i */\n    public int Left(int i) {\n        return 2 * i + 1;\n    }\n\n    /* Получить индекс правого дочернего узла узла с индексом i */\n    public int Right(int i) {\n        return 2 * i + 2;\n    }\n\n    /* Получить индекс родительского узла узла с индексом i */\n    public int Parent(int i) {\n        return (i - 1) / 2;\n    }\n\n    /* Обход в ширину */\n    public List&lt;int&gt; LevelOrder() {\n        List&lt;int&gt; res = [];\n        // Непосредственно обходить массив\n        for (int i = 0; i &lt; Size(); i++) {\n            if (Val(i).HasValue)\n                res.Add(Val(i)!.Value);\n        }\n        return res;\n    }\n\n    /* Обход в глубину */\n    void DFS(int i, string order, List&lt;int&gt; res) {\n        // Если это пустая позиция, вернуть\n        if (!Val(i).HasValue)\n            return;\n        // Предварительный обход\n        if (order == \"pre\")\n            res.Add(Val(i)!.Value);\n        DFS(Left(i), order, res);\n        // Симметричный обход\n        if (order == \"in\")\n            res.Add(Val(i)!.Value);\n        DFS(Right(i), order, res);\n        // Обратный обход\n        if (order == \"post\")\n            res.Add(Val(i)!.Value);\n    }\n\n    /* Предварительный обход */\n    public List&lt;int&gt; PreOrder() {\n        List&lt;int&gt; res = [];\n        DFS(0, \"pre\", res);\n        return res;\n    }\n\n    /* Симметричный обход */\n    public List&lt;int&gt; InOrder() {\n        List&lt;int&gt; res = [];\n        DFS(0, \"in\", res);\n        return res;\n    }\n\n    /* Обратный обход */\n    public List&lt;int&gt; PostOrder() {\n        List&lt;int&gt; res = [];\n        DFS(0, \"post\", res);\n        return res;\n    }\n}\n</code></pre> array_binary_tree.go<pre><code>/* Класс двоичного дерева в массивном представлении */\ntype arrayBinaryTree struct {\n    tree []any\n}\n\n/* Конструктор */\nfunc newArrayBinaryTree(arr []any) *arrayBinaryTree {\n    return &amp;arrayBinaryTree{\n        tree: arr,\n    }\n}\n\n/* Вместимость списка */\nfunc (abt *arrayBinaryTree) size() int {\n    return len(abt.tree)\n}\n\n/* Получить значение узла с индексом i */\nfunc (abt *arrayBinaryTree) val(i int) any {\n    // Если индекс выходит за границы, вернуть null, обозначающий пустую позицию\n    if i &lt; 0 || i &gt;= abt.size() {\n        return nil\n    }\n    return abt.tree[i]\n}\n\n/* Получить индекс левого дочернего узла узла с индексом i */\nfunc (abt *arrayBinaryTree) left(i int) int {\n    return 2*i + 1\n}\n\n/* Получить индекс правого дочернего узла узла с индексом i */\nfunc (abt *arrayBinaryTree) right(i int) int {\n    return 2*i + 2\n}\n\n/* Получить индекс родительского узла узла с индексом i */\nfunc (abt *arrayBinaryTree) parent(i int) int {\n    return (i - 1) / 2\n}\n\n/* Обход в ширину */\nfunc (abt *arrayBinaryTree) levelOrder() []any {\n    var res []any\n    // Непосредственно обходить массив\n    for i := 0; i &lt; abt.size(); i++ {\n        if abt.val(i) != nil {\n            res = append(res, abt.val(i))\n        }\n    }\n    return res\n}\n\n/* Обход в глубину */\nfunc (abt *arrayBinaryTree) dfs(i int, order string, res *[]any) {\n    // Если это пустая позиция, вернуть\n    if abt.val(i) == nil {\n        return\n    }\n    // Предварительный обход\n    if order == \"pre\" {\n        *res = append(*res, abt.val(i))\n    }\n    abt.dfs(abt.left(i), order, res)\n    // Симметричный обход\n    if order == \"in\" {\n        *res = append(*res, abt.val(i))\n    }\n    abt.dfs(abt.right(i), order, res)\n    // Обратный обход\n    if order == \"post\" {\n        *res = append(*res, abt.val(i))\n    }\n}\n\n/* Предварительный обход */\nfunc (abt *arrayBinaryTree) preOrder() []any {\n    var res []any\n    abt.dfs(0, \"pre\", &amp;res)\n    return res\n}\n\n/* Симметричный обход */\nfunc (abt *arrayBinaryTree) inOrder() []any {\n    var res []any\n    abt.dfs(0, \"in\", &amp;res)\n    return res\n}\n\n/* Обратный обход */\nfunc (abt *arrayBinaryTree) postOrder() []any {\n    var res []any\n    abt.dfs(0, \"post\", &amp;res)\n    return res\n}\n</code></pre> array_binary_tree.swift<pre><code>/* Класс двоичного дерева в массивном представлении */\nclass ArrayBinaryTree {\n    private var tree: [Int?]\n\n    /* Конструктор */\n    init(arr: [Int?]) {\n        tree = arr\n    }\n\n    /* Вместимость списка */\n    func size() -&gt; Int {\n        tree.count\n    }\n\n    /* Получить значение узла с индексом i */\n    func val(i: Int) -&gt; Int? {\n        // Если индекс выходит за границы, вернуть null, обозначающий пустую позицию\n        if i &lt; 0 || i &gt;= size() {\n            return nil\n        }\n        return tree[i]\n    }\n\n    /* Получить индекс левого дочернего узла узла с индексом i */\n    func left(i: Int) -&gt; Int {\n        2 * i + 1\n    }\n\n    /* Получить индекс правого дочернего узла узла с индексом i */\n    func right(i: Int) -&gt; Int {\n        2 * i + 2\n    }\n\n    /* Получить индекс родительского узла узла с индексом i */\n    func parent(i: Int) -&gt; Int {\n        (i - 1) / 2\n    }\n\n    /* Обход в ширину */\n    func levelOrder() -&gt; [Int] {\n        var res: [Int] = []\n        // Непосредственно обходить массив\n        for i in 0 ..&lt; size() {\n            if let val = val(i: i) {\n                res.append(val)\n            }\n        }\n        return res\n    }\n\n    /* Обход в глубину */\n    private func dfs(i: Int, order: String, res: inout [Int]) {\n        // Если это пустая позиция, вернуть\n        guard let val = val(i: i) else {\n            return\n        }\n        // Предварительный обход\n        if order == \"pre\" {\n            res.append(val)\n        }\n        dfs(i: left(i: i), order: order, res: &amp;res)\n        // Симметричный обход\n        if order == \"in\" {\n            res.append(val)\n        }\n        dfs(i: right(i: i), order: order, res: &amp;res)\n        // Обратный обход\n        if order == \"post\" {\n            res.append(val)\n        }\n    }\n\n    /* Предварительный обход */\n    func preOrder() -&gt; [Int] {\n        var res: [Int] = []\n        dfs(i: 0, order: \"pre\", res: &amp;res)\n        return res\n    }\n\n    /* Симметричный обход */\n    func inOrder() -&gt; [Int] {\n        var res: [Int] = []\n        dfs(i: 0, order: \"in\", res: &amp;res)\n        return res\n    }\n\n    /* Обратный обход */\n    func postOrder() -&gt; [Int] {\n        var res: [Int] = []\n        dfs(i: 0, order: \"post\", res: &amp;res)\n        return res\n    }\n}\n</code></pre> array_binary_tree.js<pre><code>/* Класс двоичного дерева в массивном представлении */\nclass ArrayBinaryTree {\n    #tree;\n\n    /* Конструктор */\n    constructor(arr) {\n        this.#tree = arr;\n    }\n\n    /* Вместимость списка */\n    size() {\n        return this.#tree.length;\n    }\n\n    /* Получить значение узла с индексом i */\n    val(i) {\n        // Если индекс выходит за границы, вернуть null, обозначающий пустую позицию\n        if (i &lt; 0 || i &gt;= this.size()) return null;\n        return this.#tree[i];\n    }\n\n    /* Получить индекс левого дочернего узла узла с индексом i */\n    left(i) {\n        return 2 * i + 1;\n    }\n\n    /* Получить индекс правого дочернего узла узла с индексом i */\n    right(i) {\n        return 2 * i + 2;\n    }\n\n    /* Получить индекс родительского узла узла с индексом i */\n    parent(i) {\n        return Math.floor((i - 1) / 2); // Округление вниз при делении\n    }\n\n    /* Обход в ширину */\n    levelOrder() {\n        let res = [];\n        // Непосредственно обходить массив\n        for (let i = 0; i &lt; this.size(); i++) {\n            if (this.val(i) !== null) res.push(this.val(i));\n        }\n        return res;\n    }\n\n    /* Обход в глубину */\n    #dfs(i, order, res) {\n        // Если это пустая позиция, вернуть\n        if (this.val(i) === null) return;\n        // Предварительный обход\n        if (order === 'pre') res.push(this.val(i));\n        this.#dfs(this.left(i), order, res);\n        // Симметричный обход\n        if (order === 'in') res.push(this.val(i));\n        this.#dfs(this.right(i), order, res);\n        // Обратный обход\n        if (order === 'post') res.push(this.val(i));\n    }\n\n    /* Предварительный обход */\n    preOrder() {\n        const res = [];\n        this.#dfs(0, 'pre', res);\n        return res;\n    }\n\n    /* Симметричный обход */\n    inOrder() {\n        const res = [];\n        this.#dfs(0, 'in', res);\n        return res;\n    }\n\n    /* Обратный обход */\n    postOrder() {\n        const res = [];\n        this.#dfs(0, 'post', res);\n        return res;\n    }\n}\n</code></pre> array_binary_tree.ts<pre><code>/* Класс двоичного дерева в массивном представлении */\nclass ArrayBinaryTree {\n    #tree: (number | null)[];\n\n    /* Конструктор */\n    constructor(arr: (number | null)[]) {\n        this.#tree = arr;\n    }\n\n    /* Вместимость списка */\n    size(): number {\n        return this.#tree.length;\n    }\n\n    /* Получить значение узла с индексом i */\n    val(i: number): number | null {\n        // Если индекс выходит за границы, вернуть null, обозначающий пустую позицию\n        if (i &lt; 0 || i &gt;= this.size()) return null;\n        return this.#tree[i];\n    }\n\n    /* Получить индекс левого дочернего узла узла с индексом i */\n    left(i: number): number {\n        return 2 * i + 1;\n    }\n\n    /* Получить индекс правого дочернего узла узла с индексом i */\n    right(i: number): number {\n        return 2 * i + 2;\n    }\n\n    /* Получить индекс родительского узла узла с индексом i */\n    parent(i: number): number {\n        return Math.floor((i - 1) / 2); // Округление вниз при делении\n    }\n\n    /* Обход в ширину */\n    levelOrder(): number[] {\n        let res = [];\n        // Непосредственно обходить массив\n        for (let i = 0; i &lt; this.size(); i++) {\n            if (this.val(i) !== null) res.push(this.val(i));\n        }\n        return res;\n    }\n\n    /* Обход в глубину */\n    #dfs(i: number, order: Order, res: (number | null)[]): void {\n        // Если это пустая позиция, вернуть\n        if (this.val(i) === null) return;\n        // Предварительный обход\n        if (order === 'pre') res.push(this.val(i));\n        this.#dfs(this.left(i), order, res);\n        // Симметричный обход\n        if (order === 'in') res.push(this.val(i));\n        this.#dfs(this.right(i), order, res);\n        // Обратный обход\n        if (order === 'post') res.push(this.val(i));\n    }\n\n    /* Предварительный обход */\n    preOrder(): (number | null)[] {\n        const res = [];\n        this.#dfs(0, 'pre', res);\n        return res;\n    }\n\n    /* Симметричный обход */\n    inOrder(): (number | null)[] {\n        const res = [];\n        this.#dfs(0, 'in', res);\n        return res;\n    }\n\n    /* Обратный обход */\n    postOrder(): (number | null)[] {\n        const res = [];\n        this.#dfs(0, 'post', res);\n        return res;\n    }\n}\n</code></pre> array_binary_tree.dart<pre><code>/* Класс двоичного дерева в массивном представлении */\nclass ArrayBinaryTree {\n  late List&lt;int?&gt; _tree;\n\n  /* Конструктор */\n  ArrayBinaryTree(this._tree);\n\n  /* Вместимость списка */\n  int size() {\n    return _tree.length;\n  }\n\n  /* Получить значение узла с индексом i */\n  int? val(int i) {\n    // Если индекс выходит за границы, вернуть null, обозначающий пустую позицию\n    if (i &lt; 0 || i &gt;= size()) {\n      return null;\n    }\n    return _tree[i];\n  }\n\n  /* Получить индекс левого дочернего узла узла с индексом i */\n  int? left(int i) {\n    return 2 * i + 1;\n  }\n\n  /* Получить индекс правого дочернего узла узла с индексом i */\n  int? right(int i) {\n    return 2 * i + 2;\n  }\n\n  /* Получить индекс родительского узла узла с индексом i */\n  int? parent(int i) {\n    return (i - 1) ~/ 2;\n  }\n\n  /* Обход в ширину */\n  List&lt;int&gt; levelOrder() {\n    List&lt;int&gt; res = [];\n    for (int i = 0; i &lt; size(); i++) {\n      if (val(i) != null) {\n        res.add(val(i)!);\n      }\n    }\n    return res;\n  }\n\n  /* Обход в глубину */\n  void dfs(int i, String order, List&lt;int?&gt; res) {\n    // Если это пустая позиция, вернуть\n    if (val(i) == null) {\n      return;\n    }\n    // Предварительный обход\n    if (order == 'pre') {\n      res.add(val(i));\n    }\n    dfs(left(i)!, order, res);\n    // Симметричный обход\n    if (order == 'in') {\n      res.add(val(i));\n    }\n    dfs(right(i)!, order, res);\n    // Обратный обход\n    if (order == 'post') {\n      res.add(val(i));\n    }\n  }\n\n  /* Предварительный обход */\n  List&lt;int?&gt; preOrder() {\n    List&lt;int?&gt; res = [];\n    dfs(0, 'pre', res);\n    return res;\n  }\n\n  /* Симметричный обход */\n  List&lt;int?&gt; inOrder() {\n    List&lt;int?&gt; res = [];\n    dfs(0, 'in', res);\n    return res;\n  }\n\n  /* Обратный обход */\n  List&lt;int?&gt; postOrder() {\n    List&lt;int?&gt; res = [];\n    dfs(0, 'post', res);\n    return res;\n  }\n}\n</code></pre> array_binary_tree.rs<pre><code>/* Класс двоичного дерева в массивном представлении */\nstruct ArrayBinaryTree {\n    tree: Vec&lt;Option&lt;i32&gt;&gt;,\n}\n\nimpl ArrayBinaryTree {\n    /* Конструктор */\n    fn new(arr: Vec&lt;Option&lt;i32&gt;&gt;) -&gt; Self {\n        Self { tree: arr }\n    }\n\n    /* Вместимость списка */\n    fn size(&amp;self) -&gt; i32 {\n        self.tree.len() as i32\n    }\n\n    /* Получить значение узла с индексом i */\n    fn val(&amp;self, i: i32) -&gt; Option&lt;i32&gt; {\n        // Если индекс выходит за границы, вернуть None, обозначающий пустую позицию\n        if i &lt; 0 || i &gt;= self.size() {\n            None\n        } else {\n            self.tree[i as usize]\n        }\n    }\n\n    /* Получить индекс левого дочернего узла узла с индексом i */\n    fn left(&amp;self, i: i32) -&gt; i32 {\n        2 * i + 1\n    }\n\n    /* Получить индекс правого дочернего узла узла с индексом i */\n    fn right(&amp;self, i: i32) -&gt; i32 {\n        2 * i + 2\n    }\n\n    /* Получить индекс родительского узла узла с индексом i */\n    fn parent(&amp;self, i: i32) -&gt; i32 {\n        (i - 1) / 2\n    }\n\n    /* Обход в ширину */\n    fn level_order(&amp;self) -&gt; Vec&lt;i32&gt; {\n        self.tree.iter().filter_map(|&amp;x| x).collect()\n    }\n\n    /* Обход в глубину */\n    fn dfs(&amp;self, i: i32, order: &amp;'static str, res: &amp;mut Vec&lt;i32&gt;) {\n        if self.val(i).is_none() {\n            return;\n        }\n        let val = self.val(i).unwrap();\n        // Предварительный обход\n        if order == \"pre\" {\n            res.push(val);\n        }\n        self.dfs(self.left(i), order, res);\n        // Симметричный обход\n        if order == \"in\" {\n            res.push(val);\n        }\n        self.dfs(self.right(i), order, res);\n        // Обратный обход\n        if order == \"post\" {\n            res.push(val);\n        }\n    }\n\n    /* Предварительный обход */\n    fn pre_order(&amp;self) -&gt; Vec&lt;i32&gt; {\n        let mut res = vec![];\n        self.dfs(0, \"pre\", &amp;mut res);\n        res\n    }\n\n    /* Симметричный обход */\n    fn in_order(&amp;self) -&gt; Vec&lt;i32&gt; {\n        let mut res = vec![];\n        self.dfs(0, \"in\", &amp;mut res);\n        res\n    }\n\n    /* Обратный обход */\n    fn post_order(&amp;self) -&gt; Vec&lt;i32&gt; {\n        let mut res = vec![];\n        self.dfs(0, \"post\", &amp;mut res);\n        res\n    }\n}\n</code></pre> array_binary_tree.c<pre><code>/* Структура двоичного дерева в представлении массивом */\ntypedef struct {\n    int *tree;\n    int size;\n} ArrayBinaryTree;\n\n/* Конструктор */\nArrayBinaryTree *newArrayBinaryTree(int *arr, int arrSize) {\n    ArrayBinaryTree *abt = (ArrayBinaryTree *)malloc(sizeof(ArrayBinaryTree));\n    abt-&gt;tree = malloc(sizeof(int) * arrSize);\n    memcpy(abt-&gt;tree, arr, sizeof(int) * arrSize);\n    abt-&gt;size = arrSize;\n    return abt;\n}\n\n/* Деструктор */\nvoid delArrayBinaryTree(ArrayBinaryTree *abt) {\n    free(abt-&gt;tree);\n    free(abt);\n}\n\n/* Вместимость списка */\nint size(ArrayBinaryTree *abt) {\n    return abt-&gt;size;\n}\n\n/* Получить значение узла с индексом i */\nint val(ArrayBinaryTree *abt, int i) {\n    // Если индекс выходит за границы, вернуть INT_MAX, обозначающий пустую позицию\n    if (i &lt; 0 || i &gt;= size(abt))\n        return INT_MAX;\n    return abt-&gt;tree[i];\n}\n\n/* Обход в ширину */\nint *levelOrder(ArrayBinaryTree *abt, int *returnSize) {\n    int *res = (int *)malloc(sizeof(int) * size(abt));\n    int index = 0;\n    // Непосредственно обходить массив\n    for (int i = 0; i &lt; size(abt); i++) {\n        if (val(abt, i) != INT_MAX)\n            res[index++] = val(abt, i);\n    }\n    *returnSize = index;\n    return res;\n}\n\n/* Обход в глубину */\nvoid dfs(ArrayBinaryTree *abt, int i, char *order, int *res, int *index) {\n    // Если это пустая позиция, вернуть\n    if (val(abt, i) == INT_MAX)\n        return;\n    // Предварительный обход\n    if (strcmp(order, \"pre\") == 0)\n        res[(*index)++] = val(abt, i);\n    dfs(abt, left(i), order, res, index);\n    // Симметричный обход\n    if (strcmp(order, \"in\") == 0)\n        res[(*index)++] = val(abt, i);\n    dfs(abt, right(i), order, res, index);\n    // Обратный обход\n    if (strcmp(order, \"post\") == 0)\n        res[(*index)++] = val(abt, i);\n}\n\n/* Предварительный обход */\nint *preOrder(ArrayBinaryTree *abt, int *returnSize) {\n    int *res = (int *)malloc(sizeof(int) * size(abt));\n    int index = 0;\n    dfs(abt, 0, \"pre\", res, &amp;index);\n    *returnSize = index;\n    return res;\n}\n\n/* Симметричный обход */\nint *inOrder(ArrayBinaryTree *abt, int *returnSize) {\n    int *res = (int *)malloc(sizeof(int) * size(abt));\n    int index = 0;\n    dfs(abt, 0, \"in\", res, &amp;index);\n    *returnSize = index;\n    return res;\n}\n\n/* Обратный обход */\nint *postOrder(ArrayBinaryTree *abt, int *returnSize) {\n    int *res = (int *)malloc(sizeof(int) * size(abt));\n    int index = 0;\n    dfs(abt, 0, \"post\", res, &amp;index);\n    *returnSize = index;\n    return res;\n}\n</code></pre> array_binary_tree.kt<pre><code>/* Класс двоичного дерева в массивном представлении */\nclass ArrayBinaryTree(val tree: MutableList&lt;Int?&gt;) {\n    /* Вместимость списка */\n    fun size(): Int {\n        return tree.size\n    }\n\n    /* Получить значение узла с индексом i */\n    fun _val(i: Int): Int? {\n        // Если индекс выходит за границы, вернуть null, обозначающий пустую позицию\n        if (i &lt; 0 || i &gt;= size()) return null\n        return tree[i]\n    }\n\n    /* Получить индекс левого дочернего узла узла с индексом i */\n    fun left(i: Int): Int {\n        return 2 * i + 1\n    }\n\n    /* Получить индекс правого дочернего узла узла с индексом i */\n    fun right(i: Int): Int {\n        return 2 * i + 2\n    }\n\n    /* Получить индекс родительского узла узла с индексом i */\n    fun parent(i: Int): Int {\n        return (i - 1) / 2\n    }\n\n    /* Обход в ширину */\n    fun levelOrder(): MutableList&lt;Int?&gt; {\n        val res = mutableListOf&lt;Int?&gt;()\n        // Непосредственно обходить массив\n        for (i in 0..&lt;size()) {\n            if (_val(i) != null)\n                res.add(_val(i))\n        }\n        return res\n    }\n\n    /* Обход в глубину */\n    fun dfs(i: Int, order: String, res: MutableList&lt;Int?&gt;) {\n        // Если это пустая позиция, вернуть\n        if (_val(i) == null)\n            return\n        // Предварительный обход\n        if (\"pre\" == order)\n            res.add(_val(i))\n        dfs(left(i), order, res)\n        // Симметричный обход\n        if (\"in\" == order)\n            res.add(_val(i))\n        dfs(right(i), order, res)\n        // Обратный обход\n        if (\"post\" == order)\n            res.add(_val(i))\n    }\n\n    /* Предварительный обход */\n    fun preOrder(): MutableList&lt;Int?&gt; {\n        val res = mutableListOf&lt;Int?&gt;()\n        dfs(0, \"pre\", res)\n        return res\n    }\n\n    /* Симметричный обход */\n    fun inOrder(): MutableList&lt;Int?&gt; {\n        val res = mutableListOf&lt;Int?&gt;()\n        dfs(0, \"in\", res)\n        return res\n    }\n\n    /* Обратный обход */\n    fun postOrder(): MutableList&lt;Int?&gt; {\n        val res = mutableListOf&lt;Int?&gt;()\n        dfs(0, \"post\", res)\n        return res\n    }\n}\n</code></pre> array_binary_tree.rb<pre><code>### Класс двоичного дерева в массивном представлении ###\nclass ArrayBinaryTree\n  ### Конструктор ###\n  def initialize(arr)\n    @tree = arr.to_a\n  end\n\n  ### Вместимость списка ###\n  def size\n    @tree.length\n  end\n\n  ### Получить значение узла с индексом i ###\n  def val(i)\n    # Если индекс выходит за границы, вернуть nil, обозначающий пустую ячейку\n    return if i &lt; 0 || i &gt;= size\n\n    @tree[i]\n  end\n\n  ### Получить индекс левого дочернего узла узла с индексом i ###\n  def left(i)\n    2 * i + 1\n  end\n\n  ### Получить индекс правого дочернего узла узла с индексом i ###\n  def right(i)\n    2 * i + 2\n  end\n\n  ### Получить индекс родительского узла узла с индексом i ###\n  def parent(i)\n    (i - 1) / 2\n  end\n\n  ### Обход в ширину ###\n  def level_order\n    @res = []\n\n    # Непосредственно обходить массив\n    for i in 0...size\n      @res &lt;&lt; val(i) unless val(i).nil?\n    end\n\n    @res\n  end\n\n  ### Обход в глубину ###\n  def dfs(i, order)\n    return if val(i).nil?\n    # Предварительный обход\n    @res &lt;&lt; val(i) if order == :pre\n    dfs(left(i), order)\n    # Симметричный обход\n    @res &lt;&lt; val(i) if order == :in\n    dfs(right(i), order)\n    # Обратный обход\n    @res &lt;&lt; val(i) if order == :post\n  end\n\n  ### Предварительный обход ###\n  def pre_order\n    @res = []\n    dfs(0, :pre)\n    @res\n  end\n\n  ### Симметричный обход ###\n  def in_order\n    @res = []\n    dfs(0, :in)\n    @res\n  end\n\n  ### Обратный обход ###\n  def post_order\n    @res = []\n    dfs(0, :post)\n    @res\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 7. Дерево","7.3 &nbsp; Представление двоичного дерева массивом"],"tags":[]},{"location":"chapter_tree/array_representation_of_tree/#733","level":2,"title":"7.3.3   Преимущества и ограничения","text":"<p>Представление двоичного дерева массивом имеет в основном следующие преимущества.</p> <ul> <li>Массив хранится в непрерывной области памяти, хорошо работает с кешем и обеспечивает высокую скорость доступа и обхода.</li> <li>Не нужно хранить указатели, поэтому память расходуется экономнее.</li> <li>Разрешается произвольный доступ к узлам.</li> </ul> <p>Однако у представления массивом есть и некоторые ограничения.</p> <ul> <li>Для хранения массива требуется непрерывная область памяти, поэтому такой способ не подходит для деревьев с очень большим объемом данных.</li> <li>Добавление и удаление узлов приходится реализовывать через вставку и удаление элементов массива, а это не слишком эффективно.</li> <li>Когда в двоичном дереве имеется большое число <code>None</code> , доля действительно полезных данных в массиве оказывается низкой, и эффективность использования пространства падает.</li> </ul>","path":["Глава 7. Дерево","7.3 &nbsp; Представление двоичного дерева массивом"],"tags":[]},{"location":"chapter_tree/avl_tree/","level":1,"title":"7.5   AVL-дерево *","text":"<p>В разделе \"Двоичное дерево поиска\" мы упоминали, что после многократных операций вставки и удаления узлов двоичное дерево поиска может выродиться в связный список. В таком случае временная сложность всех операций ухудшается с \\(O(\\log n)\\) до \\(O(n)\\) .</p> <p>Как показано на рисунке 7-24, после двух операций удаления узлов это двоичное дерево поиска вырождается в связный список.</p> <p></p> <p> Рисунок 7-24   Деградация AVL-дерева после удаления узлов </p> <p>Другой пример: если в идеальное двоичное дерево, показанное на рисунке 7-25, вставить два узла, то дерево сильно наклонится влево, а временная сложность поиска тоже ухудшится.</p> <p></p> <p> Рисунок 7-25   Деградация AVL-дерева после вставки узлов </p> <p>В 1962 году Г. М. Adelson-Velsky и Е. М. Landis в статье \"An algorithm for the organization of information\" предложили AVL-дерево. В статье подробно описан набор операций, гарантирующий, что при непрерывном добавлении и удалении узлов AVL-дерево не вырождается, благодаря чему временная сложность различных операций сохраняется на уровне \\(O(\\log n)\\) . Иначе говоря, в сценариях, где часто выполняются вставка, удаление, поиск и изменение, AVL-дерево всегда поддерживает эффективную работу с данными и потому имеет высокую практическую ценность.</p>","path":["Глава 7. Дерево","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#751-avl-","level":2,"title":"7.5.1   Распространенные термины AVL-дерева","text":"<p>AVL-дерево одновременно является и двоичным деревом поиска, и сбалансированным двоичным деревом, то есть одновременно удовлетворяет всем свойствам обеих этих структур. Поэтому AVL-дерево является разновидностью сбалансированного двоичного дерева поиска (balanced binary search tree).</p>","path":["Глава 7. Дерево","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#1","level":3,"title":"1.   Высота узла","text":"<p>Поскольку операции AVL-дерева требуют получать высоту узла, нам нужно добавить в класс узла переменную <code>height</code> :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>class TreeNode:\n    \"\"\"Класс узла AVL-дерева\"\"\"\n    def __init__(self, val: int):\n        self.val: int = val                 # Значение узла\n        self.height: int = 0                # Высота узла\n        self.left: TreeNode | None = None   # Ссылка на левого дочернего узла\n        self.right: TreeNode | None = None  # Ссылка на правого дочернего узла\n</code></pre> <pre><code>/* Класс узла AVL-дерева */\nstruct TreeNode {\n    int val{};          // Значение узла\n    int height = 0;     // Высота узла\n    TreeNode *left{};   // Левый дочерний узел\n    TreeNode *right{};  // Правый дочерний узел\n    TreeNode() = default;\n    explicit TreeNode(int x) : val(x){}\n};\n</code></pre> <pre><code>/* Класс узла AVL-дерева */\nclass TreeNode {\n    public int val;        // Значение узла\n    public int height;     // Высота узла\n    public TreeNode left;  // Левый дочерний узел\n    public TreeNode right; // Правый дочерний узел\n    public TreeNode(int x) { val = x; }\n}\n</code></pre> <pre><code>/* Класс узла AVL-дерева */\nclass TreeNode(int? x) {\n    public int? val = x;    // Значение узла\n    public int height;      // Высота узла\n    public TreeNode? left;  // Ссылка на левого дочернего узла\n    public TreeNode? right; // Ссылка на правого дочернего узла\n}\n</code></pre> <pre><code>/* Структура узла AVL-дерева */\ntype TreeNode struct {\n    Val    int       // Значение узла\n    Height int       // Высота узла\n    Left   *TreeNode // Ссылка на левого дочернего узла\n    Right  *TreeNode // Ссылка на правого дочернего узла\n}\n</code></pre> <pre><code>/* Класс узла AVL-дерева */\nclass TreeNode {\n    var val: Int // Значение узла\n    var height: Int // Высота узла\n    var left: TreeNode? // Левый дочерний узел\n    var right: TreeNode? // Правый дочерний узел\n\n    init(x: Int) {\n        val = x\n        height = 0\n    }\n}\n</code></pre> <pre><code>/* Класс узла AVL-дерева */\nclass TreeNode {\n    val; // Значение узла\n    height; // Высота узла\n    left; // Указатель на левого дочернего узла\n    right; // Указатель на правого дочернего узла\n    constructor(val, left, right, height) {\n        this.val = val === undefined ? 0 : val;\n        this.height = height === undefined ? 0 : height;\n        this.left = left === undefined ? null : left;\n        this.right = right === undefined ? null : right;\n    }\n}\n</code></pre> <pre><code>/* Класс узла AVL-дерева */\nclass TreeNode {\n    val: number;            // Значение узла\n    height: number;         // Высота узла\n    left: TreeNode | null;  // Указатель на левого дочернего узла\n    right: TreeNode | null; // Указатель на правого дочернего узла\n    constructor(val?: number, height?: number, left?: TreeNode | null, right?: TreeNode | null) {\n        this.val = val === undefined ? 0 : val;\n        this.height = height === undefined ? 0 : height;\n        this.left = left === undefined ? null : left;\n        this.right = right === undefined ? null : right;\n    }\n}\n</code></pre> <pre><code>/* Класс узла AVL-дерева */\nclass TreeNode {\n  int val;         // Значение узла\n  int height;      // Высота узла\n  TreeNode? left;  // Левый дочерний узел\n  TreeNode? right; // Правый дочерний узел\n  TreeNode(this.val, [this.height = 0, this.left, this.right]);\n}\n</code></pre> <pre><code>use std::rc::Rc;\nuse std::cell::RefCell;\n\n/* Структура узла AVL-дерева */\nstruct TreeNode {\n    val: i32,                               // Значение узла\n    height: i32,                            // Высота узла\n    left: Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,    // Левый дочерний узел\n    right: Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,   // Правый дочерний узел\n}\n\nimpl TreeNode {\n    /* Конструктор */\n    fn new(val: i32) -&gt; Rc&lt;RefCell&lt;Self&gt;&gt; {\n        Rc::new(RefCell::new(Self {\n            val,\n            height: 0,\n            left: None,\n            right: None\n        }))\n    }\n}\n</code></pre> <pre><code>/* Структура узла AVL-дерева */\ntypedef struct TreeNode {\n    int val;\n    int height;\n    struct TreeNode *left;\n    struct TreeNode *right;\n} TreeNode;\n\n/* Конструктор */\nTreeNode *newTreeNode(int val) {\n    TreeNode *node;\n\n    node = (TreeNode *)malloc(sizeof(TreeNode));\n    node-&gt;val = val;\n    node-&gt;height = 0;\n    node-&gt;left = NULL;\n    node-&gt;right = NULL;\n    return node;\n}\n</code></pre> <pre><code>/* Класс узла AVL-дерева */\nclass TreeNode(val _val: Int) {  // Значение узла\n    val height: Int = 0          // Высота узла\n    val left: TreeNode? = null   // Левый дочерний узел\n    val right: TreeNode? = null  // Правый дочерний узел\n}\n</code></pre> <pre><code>### Класс узла AVL-дерева ###\nclass TreeNode\n  attr_accessor :val    # Значение узла\n  attr_accessor :height # Высота узла\n  attr_accessor :left   # Ссылка на левого дочернего узла\n  attr_accessor :right  # Ссылка на правого дочернего узла\n\n  def initialize(val)\n    @val = val\n    @height = 0\n  end\nend\n</code></pre> <p>\"Высота узла\" означает расстояние от этого узла до самого удаленного листового узла, то есть число пройденных \"ребер\". Особенно важно помнить, что высота листового узла равна \\(0\\) , а высота пустого узла равна \\(-1\\) . Мы создадим две вспомогательные функции: одну для получения высоты узла, другую для ее обновления:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def height(self, node: TreeNode | None) -&gt; int:\n    \"\"\"Получить высоту узла\"\"\"\n    # Высота пустого узла равна -1, высота листового узла равна 0\n    if node is not None:\n        return node.height\n    return -1\n\ndef update_height(self, node: TreeNode | None):\n    \"\"\"Обновить высоту узла\"\"\"\n    # Высота узла равна высоте более высокого поддерева + 1\n    node.height = max([self.height(node.left), self.height(node.right)]) + 1\n</code></pre> avl_tree.cpp<pre><code>/* Получить высоту узла */\nint height(TreeNode *node) {\n    // Высота пустого узла равна -1, высота листового узла равна 0\n    return node == nullptr ? -1 : node-&gt;height;\n}\n\n/* Обновить высоту узла */\nvoid updateHeight(TreeNode *node) {\n    // Высота узла равна высоте более высокого поддерева + 1\n    node-&gt;height = max(height(node-&gt;left), height(node-&gt;right)) + 1;\n}\n</code></pre> avl_tree.java<pre><code>/* Получить высоту узла */\nint height(TreeNode node) {\n    // Высота пустого узла равна -1, высота листового узла равна 0\n    return node == null ? -1 : node.height;\n}\n\n/* Обновить высоту узла */\nvoid updateHeight(TreeNode node) {\n    // Высота узла равна высоте более высокого поддерева + 1\n    node.height = Math.max(height(node.left), height(node.right)) + 1;\n}\n</code></pre> avl_tree.cs<pre><code>/* Получить высоту узла */\nint Height(TreeNode? node) {\n    // Высота пустого узла равна -1, высота листового узла равна 0\n    return node == null ? -1 : node.height;\n}\n\n/* Обновить высоту узла */\nvoid UpdateHeight(TreeNode node) {\n    // Высота узла равна высоте более высокого поддерева + 1\n    node.height = Math.Max(Height(node.left), Height(node.right)) + 1;\n}\n</code></pre> avl_tree.go<pre><code>/* Получить высоту узла */\nfunc (t *aVLTree) height(node *TreeNode) int {\n    // Высота пустого узла равна -1, высота листового узла равна 0\n    if node != nil {\n        return node.Height\n    }\n    return -1\n}\n\n/* Обновить высоту узла */\nfunc (t *aVLTree) updateHeight(node *TreeNode) {\n    lh := t.height(node.Left)\n    rh := t.height(node.Right)\n    // Высота узла равна высоте более высокого поддерева + 1\n    if lh &gt; rh {\n        node.Height = lh + 1\n    } else {\n        node.Height = rh + 1\n    }\n}\n</code></pre> avl_tree.swift<pre><code>/* Получить высоту узла */\nfunc height(node: TreeNode?) -&gt; Int {\n    // Высота пустого узла равна -1, высота листового узла равна 0\n    node?.height ?? -1\n}\n\n/* Обновить высоту узла */\nfunc updateHeight(node: TreeNode?) {\n    // Высота узла равна высоте более высокого поддерева + 1\n    node?.height = max(height(node: node?.left), height(node: node?.right)) + 1\n}\n</code></pre> avl_tree.js<pre><code>/* Получить высоту узла */\nheight(node) {\n    // Высота пустого узла равна -1, высота листового узла равна 0\n    return node === null ? -1 : node.height;\n}\n\n/* Обновить высоту узла */\n#updateHeight(node) {\n    // Высота узла равна высоте более высокого поддерева + 1\n    node.height =\n        Math.max(this.height(node.left), this.height(node.right)) + 1;\n}\n</code></pre> avl_tree.ts<pre><code>/* Получить высоту узла */\nheight(node: TreeNode): number {\n    // Высота пустого узла равна -1, высота листового узла равна 0\n    return node === null ? -1 : node.height;\n}\n\n/* Обновить высоту узла */\nupdateHeight(node: TreeNode): void {\n    // Высота узла равна высоте более высокого поддерева + 1\n    node.height =\n        Math.max(this.height(node.left), this.height(node.right)) + 1;\n}\n</code></pre> avl_tree.dart<pre><code>/* Получить высоту узла */\nint height(TreeNode? node) {\n  // Высота пустого узла равна -1, высота листового узла равна 0\n  return node == null ? -1 : node.height;\n}\n\n/* Обновить высоту узла */\nvoid updateHeight(TreeNode? node) {\n  // Высота узла равна высоте более высокого поддерева + 1\n  node!.height = max(height(node.left), height(node.right)) + 1;\n}\n</code></pre> avl_tree.rs<pre><code>/* Получить высоту узла */\nfn height(node: OptionTreeNodeRc) -&gt; i32 {\n    // Высота пустого узла равна -1, высота листового узла равна 0\n    match node {\n        Some(node) =&gt; node.borrow().height,\n        None =&gt; -1,\n    }\n}\n\n/* Обновить высоту узла */\nfn update_height(node: OptionTreeNodeRc) {\n    if let Some(node) = node {\n        let left = node.borrow().left.clone();\n        let right = node.borrow().right.clone();\n        // Высота узла равна высоте более высокого поддерева + 1\n        node.borrow_mut().height = std::cmp::max(Self::height(left), Self::height(right)) + 1;\n    }\n}\n</code></pre> avl_tree.c<pre><code>/* Получить высоту узла */\nint height(TreeNode *node) {\n    // Высота пустого узла равна -1, высота листового узла равна 0\n    if (node != NULL) {\n        return node-&gt;height;\n    }\n    return -1;\n}\n\n/* Обновить высоту узла */\nvoid updateHeight(TreeNode *node) {\n    int lh = height(node-&gt;left);\n    int rh = height(node-&gt;right);\n    // Высота узла равна высоте более высокого поддерева + 1\n    if (lh &gt; rh) {\n        node-&gt;height = lh + 1;\n    } else {\n        node-&gt;height = rh + 1;\n    }\n}\n</code></pre> avl_tree.kt<pre><code>/* Получить высоту узла */\nfun height(node: TreeNode?): Int {\n    // Высота пустого узла равна -1, высота листового узла равна 0\n    return node?.height ?: -1\n}\n\n/* Обновить высоту узла */\nfun updateHeight(node: TreeNode?) {\n    // Высота узла равна высоте более высокого поддерева + 1\n    node?.height = max(height(node?.left), height(node?.right)) + 1\n}\n</code></pre> avl_tree.rb<pre><code>### Получить высоту узла ###\ndef height(node)\n  # Высота пустого узла равна -1, высота листового узла равна 0\n  return node.height unless node.nil?\n\n  -1\nend\n\n### Обновить высоту узла ###\ndef update_height(node)\n  # Высота узла равна высоте более высокого поддерева + 1\n  node.height = [height(node.left), height(node.right)].max + 1\nend\n</code></pre>","path":["Глава 7. Дерево","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#2-","level":3,"title":"2.   Баланс-фактор узла","text":"<p>Баланс-фактор (balance factor) узла определяется как высота левого поддерева минус высота правого поддерева; при этом баланс-фактор пустого узла считается равным \\(0\\) . Мы также инкапсулируем получение баланс-фактора в отдельную функцию, чтобы потом было удобнее ее использовать:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def balance_factor(self, node: TreeNode | None) -&gt; int:\n    \"\"\"Получить коэффициент баланса\"\"\"\n    # Коэффициент баланса пустого узла равен 0\n    if node is None:\n        return 0\n    # Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n    return self.height(node.left) - self.height(node.right)\n</code></pre> avl_tree.cpp<pre><code>/* Получить коэффициент баланса */\nint balanceFactor(TreeNode *node) {\n    // Коэффициент баланса пустого узла равен 0\n    if (node == nullptr)\n        return 0;\n    // Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n    return height(node-&gt;left) - height(node-&gt;right);\n}\n</code></pre> avl_tree.java<pre><code>/* Получить коэффициент баланса */\nint balanceFactor(TreeNode node) {\n    // Коэффициент баланса пустого узла равен 0\n    if (node == null)\n        return 0;\n    // Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n    return height(node.left) - height(node.right);\n}\n</code></pre> avl_tree.cs<pre><code>/* Получить коэффициент баланса */\nint BalanceFactor(TreeNode? node) {\n    // Коэффициент баланса пустого узла равен 0\n    if (node == null) return 0;\n    // Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n    return Height(node.left) - Height(node.right);\n}\n</code></pre> avl_tree.go<pre><code>/* Получить коэффициент баланса */\nfunc (t *aVLTree) balanceFactor(node *TreeNode) int {\n    // Коэффициент баланса пустого узла равен 0\n    if node == nil {\n        return 0\n    }\n    // Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n    return t.height(node.Left) - t.height(node.Right)\n}\n</code></pre> avl_tree.swift<pre><code>/* Получить коэффициент баланса */\nfunc balanceFactor(node: TreeNode?) -&gt; Int {\n    // Коэффициент баланса пустого узла равен 0\n    guard let node = node else { return 0 }\n    // Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n    return height(node: node.left) - height(node: node.right)\n}\n</code></pre> avl_tree.js<pre><code>/* Получить коэффициент баланса */\nbalanceFactor(node) {\n    // Коэффициент баланса пустого узла равен 0\n    if (node === null) return 0;\n    // Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n    return this.height(node.left) - this.height(node.right);\n}\n</code></pre> avl_tree.ts<pre><code>/* Получить коэффициент баланса */\nbalanceFactor(node: TreeNode): number {\n    // Коэффициент баланса пустого узла равен 0\n    if (node === null) return 0;\n    // Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n    return this.height(node.left) - this.height(node.right);\n}\n</code></pre> avl_tree.dart<pre><code>/* Получить коэффициент баланса */\nint balanceFactor(TreeNode? node) {\n  // Коэффициент баланса пустого узла равен 0\n  if (node == null) return 0;\n  // Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n  return height(node.left) - height(node.right);\n}\n</code></pre> avl_tree.rs<pre><code>/* Получить коэффициент баланса */\nfn balance_factor(node: OptionTreeNodeRc) -&gt; i32 {\n    match node {\n        // Коэффициент баланса пустого узла равен 0\n        None =&gt; 0,\n        // Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n        Some(node) =&gt; {\n            Self::height(node.borrow().left.clone()) - Self::height(node.borrow().right.clone())\n        }\n    }\n}\n</code></pre> avl_tree.c<pre><code>/* Получить коэффициент баланса */\nint balanceFactor(TreeNode *node) {\n    // Коэффициент баланса пустого узла равен 0\n    if (node == NULL) {\n        return 0;\n    }\n    // Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n    return height(node-&gt;left) - height(node-&gt;right);\n}\n</code></pre> avl_tree.kt<pre><code>/* Получить коэффициент баланса */\nfun balanceFactor(node: TreeNode?): Int {\n    // Коэффициент баланса пустого узла равен 0\n    if (node == null) return 0\n    // Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n    return height(node.left) - height(node.right)\n}\n</code></pre> avl_tree.rb<pre><code>### Получить коэффициент баланса ###\ndef balance_factor(node)\n  # Коэффициент баланса пустого узла равен 0\n  return 0 if node.nil?\n\n  # Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n  height(node.left) - height(node.right)\nend\n</code></pre> <p>Tip</p> <p>Пусть баланс-фактор равен \\(f\\) ; тогда для любого узла AVL-дерева выполняется \\(-1 \\le f \\le 1\\) .</p>","path":["Глава 7. Дерево","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#752-avl-","level":2,"title":"7.5.2   Вращения AVL-дерева","text":"<p>Особенность AVL-дерева заключается в операции \"вращения\", которая позволяет заново сбалансировать разбалансированный узел, не нарушая последовательность симметричного обхода двоичного дерева. Иначе говоря, операция вращения одновременно сохраняет свойство \"двоичного дерева поиска\" и возвращает дерево в состояние \"сбалансированного двоичного дерева\".</p> <p>Узлы, для которых абсолютное значение баланс-фактора больше \\(1\\) , мы называем \"разбалансированными узлами\". В зависимости от вида разбаланса вращения делятся на четыре типа: правое вращение, левое вращение, сначала левое затем правое, и сначала правое затем левое. Ниже разберем их подробно.</p>","path":["Глава 7. Дерево","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#1_1","level":3,"title":"1.   Правое вращение","text":"<p>Как показано на рисунках ниже, под узлом указан его баланс-фактор. Если двигаться снизу вверх, то первым разбалансированным узлом в двоичном дереве будет \"узел 3\". Рассмотрим поддерево с этим узлом в качестве корня, обозначим данный узел как <code>node</code> , его левого дочернего узла как <code>child</code> и выполним \"правое вращение\". После завершения правого вращения поддерево снова станет сбалансированным и при этом сохранит свойство двоичного дерева поиска.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p> Рисунок 7-26   Шаги правого вращения </p> <p>Как показано на рисунке 7-27, когда у узла <code>child</code> есть правый дочерний узел, который мы обозначим как <code>grand_child</code> , в правое вращение нужно добавить еще один шаг: сделать <code>grand_child</code> левым дочерним узлом <code>node</code> .</p> <p></p> <p> Рисунок 7-27   Правое вращение при наличии grand_child </p> <p>\"Поворот вправо\" - это лишь образное описание; в реальности он реализуется через изменение указателей узлов. Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def right_rotate(self, node: TreeNode | None) -&gt; TreeNode | None:\n    \"\"\"Операция правого вращения\"\"\"\n    child = node.left\n    grand_child = child.right\n    # Выполнить правое вращение узла node вокруг child\n    child.right = node\n    node.left = grand_child\n    # Обновить высоту узла\n    self.update_height(node)\n    self.update_height(child)\n    # Вернуть корневой узел поддерева после вращения\n    return child\n</code></pre> avl_tree.cpp<pre><code>/* Операция правого вращения */\nTreeNode *rightRotate(TreeNode *node) {\n    TreeNode *child = node-&gt;left;\n    TreeNode *grandChild = child-&gt;right;\n    // Выполнить правое вращение узла node вокруг child\n    child-&gt;right = node;\n    node-&gt;left = grandChild;\n    // Обновить высоту узла\n    updateHeight(node);\n    updateHeight(child);\n    // Вернуть корневой узел поддерева после вращения\n    return child;\n}\n</code></pre> avl_tree.java<pre><code>/* Операция правого вращения */\nTreeNode rightRotate(TreeNode node) {\n    TreeNode child = node.left;\n    TreeNode grandChild = child.right;\n    // Выполнить правое вращение узла node вокруг child\n    child.right = node;\n    node.left = grandChild;\n    // Обновить высоту узла\n    updateHeight(node);\n    updateHeight(child);\n    // Вернуть корневой узел поддерева после вращения\n    return child;\n}\n</code></pre> avl_tree.cs<pre><code>/* Операция правого вращения */\nTreeNode? RightRotate(TreeNode? node) {\n    TreeNode? child = node?.left;\n    TreeNode? grandChild = child?.right;\n    // Выполнить правое вращение узла node вокруг child\n    child.right = node;\n    node.left = grandChild;\n    // Обновить высоту узла\n    UpdateHeight(node);\n    UpdateHeight(child);\n    // Вернуть корневой узел поддерева после вращения\n    return child;\n}\n</code></pre> avl_tree.go<pre><code>/* Операция правого вращения */\nfunc (t *aVLTree) rightRotate(node *TreeNode) *TreeNode {\n    child := node.Left\n    grandChild := child.Right\n    // Выполнить правое вращение узла node вокруг child\n    child.Right = node\n    node.Left = grandChild\n    // Обновить высоту узла\n    t.updateHeight(node)\n    t.updateHeight(child)\n    // Вернуть корневой узел поддерева после вращения\n    return child\n}\n</code></pre> avl_tree.swift<pre><code>/* Операция правого вращения */\nfunc rightRotate(node: TreeNode?) -&gt; TreeNode? {\n    let child = node?.left\n    let grandChild = child?.right\n    // Выполнить правое вращение узла node вокруг child\n    child?.right = node\n    node?.left = grandChild\n    // Обновить высоту узла\n    updateHeight(node: node)\n    updateHeight(node: child)\n    // Вернуть корневой узел поддерева после вращения\n    return child\n}\n</code></pre> avl_tree.js<pre><code>/* Операция правого вращения */\n#rightRotate(node) {\n    const child = node.left;\n    const grandChild = child.right;\n    // Выполнить правое вращение узла node вокруг child\n    child.right = node;\n    node.left = grandChild;\n    // Обновить высоту узла\n    this.#updateHeight(node);\n    this.#updateHeight(child);\n    // Вернуть корневой узел поддерева после вращения\n    return child;\n}\n</code></pre> avl_tree.ts<pre><code>/* Операция правого вращения */\nrightRotate(node: TreeNode): TreeNode {\n    const child = node.left;\n    const grandChild = child.right;\n    // Выполнить правое вращение узла node вокруг child\n    child.right = node;\n    node.left = grandChild;\n    // Обновить высоту узла\n    this.updateHeight(node);\n    this.updateHeight(child);\n    // Вернуть корневой узел поддерева после вращения\n    return child;\n}\n</code></pre> avl_tree.dart<pre><code>/* Операция правого вращения */\nTreeNode? rightRotate(TreeNode? node) {\n  TreeNode? child = node!.left;\n  TreeNode? grandChild = child!.right;\n  // Выполнить правое вращение узла node вокруг child\n  child.right = node;\n  node.left = grandChild;\n  // Обновить высоту узла\n  updateHeight(node);\n  updateHeight(child);\n  // Вернуть корневой узел поддерева после вращения\n  return child;\n}\n</code></pre> avl_tree.rs<pre><code>/* Операция правого вращения */\nfn right_rotate(node: OptionTreeNodeRc) -&gt; OptionTreeNodeRc {\n    match node {\n        Some(node) =&gt; {\n            let child = node.borrow().left.clone().unwrap();\n            let grand_child = child.borrow().right.clone();\n            // Выполнить правое вращение узла node вокруг child\n            child.borrow_mut().right = Some(node.clone());\n            node.borrow_mut().left = grand_child;\n            // Обновить высоту узла\n            Self::update_height(Some(node));\n            Self::update_height(Some(child.clone()));\n            // Вернуть корневой узел поддерева после вращения\n            Some(child)\n        }\n        None =&gt; None,\n    }\n}\n</code></pre> avl_tree.c<pre><code>/* Операция правого вращения */\nTreeNode *rightRotate(TreeNode *node) {\n    TreeNode *child, *grandChild;\n    child = node-&gt;left;\n    grandChild = child-&gt;right;\n    // Выполнить правое вращение узла node вокруг child\n    child-&gt;right = node;\n    node-&gt;left = grandChild;\n    // Обновить высоту узла\n    updateHeight(node);\n    updateHeight(child);\n    // Вернуть корневой узел поддерева после вращения\n    return child;\n}\n</code></pre> avl_tree.kt<pre><code>/* Операция правого вращения */\nfun rightRotate(node: TreeNode?): TreeNode {\n    val child = node!!.left\n    val grandChild = child!!.right\n    // Выполнить правое вращение узла node вокруг child\n    child.right = node\n    node.left = grandChild\n    // Обновить высоту узла\n    updateHeight(node)\n    updateHeight(child)\n    // Вернуть корневой узел поддерева после вращения\n    return child\n}\n</code></pre> avl_tree.rb<pre><code>### Операция правого вращения ###\ndef right_rotate(node)\n  child = node.left\n  grand_child = child.right\n  # Выполнить правое вращение узла node вокруг child\n  child.right = node\n  node.left = grand_child\n  # Обновить высоту узла\n  update_height(node)\n  update_height(child)\n  # Вернуть корневой узел поддерева после вращения\n  child\nend\n</code></pre>","path":["Глава 7. Дерево","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#2","level":3,"title":"2.   Левое вращение","text":"<p>Соответственно, если рассмотреть \"зеркальную\" версию приведенного выше разбалансированного двоичного дерева, то понадобится выполнить \"левое вращение\", показанное на рисунке 7-28.</p> <p></p> <p> Рисунок 7-28   Левое вращение </p> <p>По той же причине, когда у узла <code>child</code> есть левый дочерний узел, который обозначим как <code>grand_child</code> , в левое вращение также требуется добавить шаг: сделать <code>grand_child</code> правым дочерним узлом <code>node</code> .</p> <p></p> <p> Рисунок 7-29   Левое вращение при наличии grand_child </p> <p>Можно заметить, что операции правого и левого вращения логически зеркально симметричны, и два вида разбаланса, которые они исправляют, тоже симметричны. Поэтому, опираясь на эту симметрию, достаточно заменить в коде правого вращения все <code>left</code> на <code>right</code> , а все <code>right</code> на <code>left</code> , чтобы получить реализацию левого вращения:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def left_rotate(self, node: TreeNode | None) -&gt; TreeNode | None:\n    \"\"\"Операция левого вращения\"\"\"\n    child = node.right\n    grand_child = child.left\n    # Выполнить левое вращение узла node вокруг child\n    child.left = node\n    node.right = grand_child\n    # Обновить высоту узла\n    self.update_height(node)\n    self.update_height(child)\n    # Вернуть корневой узел поддерева после вращения\n    return child\n</code></pre> avl_tree.cpp<pre><code>/* Операция левого вращения */\nTreeNode *leftRotate(TreeNode *node) {\n    TreeNode *child = node-&gt;right;\n    TreeNode *grandChild = child-&gt;left;\n    // Выполнить левое вращение узла node вокруг child\n    child-&gt;left = node;\n    node-&gt;right = grandChild;\n    // Обновить высоту узла\n    updateHeight(node);\n    updateHeight(child);\n    // Вернуть корневой узел поддерева после вращения\n    return child;\n}\n</code></pre> avl_tree.java<pre><code>/* Операция левого вращения */\nTreeNode leftRotate(TreeNode node) {\n    TreeNode child = node.right;\n    TreeNode grandChild = child.left;\n    // Выполнить левое вращение узла node вокруг child\n    child.left = node;\n    node.right = grandChild;\n    // Обновить высоту узла\n    updateHeight(node);\n    updateHeight(child);\n    // Вернуть корневой узел поддерева после вращения\n    return child;\n}\n</code></pre> avl_tree.cs<pre><code>/* Операция левого вращения */\nTreeNode? LeftRotate(TreeNode? node) {\n    TreeNode? child = node?.right;\n    TreeNode? grandChild = child?.left;\n    // Выполнить левое вращение узла node вокруг child\n    child.left = node;\n    node.right = grandChild;\n    // Обновить высоту узла\n    UpdateHeight(node);\n    UpdateHeight(child);\n    // Вернуть корневой узел поддерева после вращения\n    return child;\n}\n</code></pre> avl_tree.go<pre><code>/* Операция левого вращения */\nfunc (t *aVLTree) leftRotate(node *TreeNode) *TreeNode {\n    child := node.Right\n    grandChild := child.Left\n    // Выполнить левое вращение узла node вокруг child\n    child.Left = node\n    node.Right = grandChild\n    // Обновить высоту узла\n    t.updateHeight(node)\n    t.updateHeight(child)\n    // Вернуть корневой узел поддерева после вращения\n    return child\n}\n</code></pre> avl_tree.swift<pre><code>/* Операция левого вращения */\nfunc leftRotate(node: TreeNode?) -&gt; TreeNode? {\n    let child = node?.right\n    let grandChild = child?.left\n    // Выполнить левое вращение узла node вокруг child\n    child?.left = node\n    node?.right = grandChild\n    // Обновить высоту узла\n    updateHeight(node: node)\n    updateHeight(node: child)\n    // Вернуть корневой узел поддерева после вращения\n    return child\n}\n</code></pre> avl_tree.js<pre><code>/* Операция левого вращения */\n#leftRotate(node) {\n    const child = node.right;\n    const grandChild = child.left;\n    // Выполнить левое вращение узла node вокруг child\n    child.left = node;\n    node.right = grandChild;\n    // Обновить высоту узла\n    this.#updateHeight(node);\n    this.#updateHeight(child);\n    // Вернуть корневой узел поддерева после вращения\n    return child;\n}\n</code></pre> avl_tree.ts<pre><code>/* Операция левого вращения */\nleftRotate(node: TreeNode): TreeNode {\n    const child = node.right;\n    const grandChild = child.left;\n    // Выполнить левое вращение узла node вокруг child\n    child.left = node;\n    node.right = grandChild;\n    // Обновить высоту узла\n    this.updateHeight(node);\n    this.updateHeight(child);\n    // Вернуть корневой узел поддерева после вращения\n    return child;\n}\n</code></pre> avl_tree.dart<pre><code>/* Операция левого вращения */\nTreeNode? leftRotate(TreeNode? node) {\n  TreeNode? child = node!.right;\n  TreeNode? grandChild = child!.left;\n  // Выполнить левое вращение узла node вокруг child\n  child.left = node;\n  node.right = grandChild;\n  // Обновить высоту узла\n  updateHeight(node);\n  updateHeight(child);\n  // Вернуть корневой узел поддерева после вращения\n  return child;\n}\n</code></pre> avl_tree.rs<pre><code>/* Операция левого вращения */\nfn left_rotate(node: OptionTreeNodeRc) -&gt; OptionTreeNodeRc {\n    match node {\n        Some(node) =&gt; {\n            let child = node.borrow().right.clone().unwrap();\n            let grand_child = child.borrow().left.clone();\n            // Выполнить левое вращение узла node вокруг child\n            child.borrow_mut().left = Some(node.clone());\n            node.borrow_mut().right = grand_child;\n            // Обновить высоту узла\n            Self::update_height(Some(node));\n            Self::update_height(Some(child.clone()));\n            // Вернуть корневой узел поддерева после вращения\n            Some(child)\n        }\n        None =&gt; None,\n    }\n}\n</code></pre> avl_tree.c<pre><code>/* Операция левого вращения */\nTreeNode *leftRotate(TreeNode *node) {\n    TreeNode *child, *grandChild;\n    child = node-&gt;right;\n    grandChild = child-&gt;left;\n    // Выполнить левое вращение узла node вокруг child\n    child-&gt;left = node;\n    node-&gt;right = grandChild;\n    // Обновить высоту узла\n    updateHeight(node);\n    updateHeight(child);\n    // Вернуть корневой узел поддерева после вращения\n    return child;\n}\n</code></pre> avl_tree.kt<pre><code>/* Операция левого вращения */\nfun leftRotate(node: TreeNode?): TreeNode {\n    val child = node!!.right\n    val grandChild = child!!.left\n    // Выполнить левое вращение узла node вокруг child\n    child.left = node\n    node.right = grandChild\n    // Обновить высоту узла\n    updateHeight(node)\n    updateHeight(child)\n    // Вернуть корневой узел поддерева после вращения\n    return child\n}\n</code></pre> avl_tree.rb<pre><code>### Операция левого вращения ###\ndef left_rotate(node)\n  child = node.right\n  grand_child = child.left\n  # Выполнить левое вращение узла node вокруг child\n  child.left = node\n  node.right = grand_child\n  # Обновить высоту узла\n  update_height(node)\n  update_height(child)\n  # Вернуть корневой узел поддерева после вращения\n  child\nend\n</code></pre>","path":["Глава 7. Дерево","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#3","level":3,"title":"3.   Сначала левое, затем правое вращение","text":"<p>Для разбалансированного узла 3 на рисунке 7-30 ни одно лишь левое вращение, ни одно лишь правое вращение не способны вернуть поддерево в баланс. В этом случае нужно сначала выполнить \"левое вращение\" для <code>child</code> , а затем выполнить \"правое вращение\" для <code>node</code> .</p> <p></p> <p> Рисунок 7-30   Сначала левое, затем правое вращение </p>","path":["Глава 7. Дерево","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#4","level":3,"title":"4.   Сначала правое, затем левое вращение","text":"<p>Как показано на рисунке 7-31, для зеркальной ситуации предыдущего разбалансированного двоичного дерева нужно сначала выполнить \"правое вращение\" для <code>child</code> , а затем \"левое вращение\" для <code>node</code> .</p> <p></p> <p> Рисунок 7-31   Сначала правое, затем левое вращение </p>","path":["Глава 7. Дерево","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#5","level":3,"title":"5.   Выбор вращения","text":"<p>Четыре вида разбаланса, показанные на рисунке 7-32, по одному соответствуют рассмотренным выше случаям; для них соответственно требуются правое вращение, сначала левое затем правое, сначала правое затем левое и левое вращение.</p> <p></p> <p> Рисунок 7-32   Четыре случая вращений AVL-дерева </p> <p>Как показано в таблице 7-3, мы определяем, какому из этих четырех случаев соответствует разбалансированный узел, по знаку баланс-фактора самого разбалансированного узла и по знаку баланс-фактора дочернего узла на более высокой стороне.</p> <p> Таблица 7-3   Условия выбора для четырех случаев вращений </p> Баланс-фактор разбалансированного узла Баланс-фактор дочернего узла Какое вращение использовать \\(&gt; 1\\) (левостороннее дерево) \\(\\geq 0\\) Правое вращение \\(&gt; 1\\) (левостороннее дерево) \\(&lt;0\\) Сначала левое, затем правое \\(&lt; -1\\) (правостороннее дерево) \\(\\leq 0\\) Левое вращение \\(&lt; -1\\) (правостороннее дерево) \\(&gt;0\\) Сначала правое, затем левое <p>Для удобства мы инкапсулируем операцию вращения в отдельную функцию. С помощью этой функции можно выполнить корректное вращение для любой ситуации разбаланса и снова привести узел в сбалансированное состояние. Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def rotate(self, node: TreeNode | None) -&gt; TreeNode | None:\n    \"\"\"Выполнить вращение, чтобы снова сбалансировать поддерево\"\"\"\n    # Получить коэффициент баланса узла node\n    balance_factor = self.balance_factor(node)\n    # Левосторонне перекошенное дерево\n    if balance_factor &gt; 1:\n        if self.balance_factor(node.left) &gt;= 0:\n            # Правое вращение\n            return self.right_rotate(node)\n        else:\n            # Сначала левое вращение, затем правое\n            node.left = self.left_rotate(node.left)\n            return self.right_rotate(node)\n    # Правосторонне перекошенное дерево\n    elif balance_factor &lt; -1:\n        if self.balance_factor(node.right) &lt;= 0:\n            # Левое вращение\n            return self.left_rotate(node)\n        else:\n            # Сначала правое вращение, затем левое\n            node.right = self.right_rotate(node.right)\n            return self.left_rotate(node)\n    # Дерево сбалансировано, вращение не требуется, вернуть сразу\n    return node\n</code></pre> avl_tree.cpp<pre><code>/* Выполнить вращение, чтобы снова сбалансировать поддерево */\nTreeNode *rotate(TreeNode *node) {\n    // Получить коэффициент баланса узла node\n    int _balanceFactor = balanceFactor(node);\n    // Левосторонне перекошенное дерево\n    if (_balanceFactor &gt; 1) {\n        if (balanceFactor(node-&gt;left) &gt;= 0) {\n            // Правое вращение\n            return rightRotate(node);\n        } else {\n            // Сначала левое вращение, затем правое\n            node-&gt;left = leftRotate(node-&gt;left);\n            return rightRotate(node);\n        }\n    }\n    // Правосторонне перекошенное дерево\n    if (_balanceFactor &lt; -1) {\n        if (balanceFactor(node-&gt;right) &lt;= 0) {\n            // Левое вращение\n            return leftRotate(node);\n        } else {\n            // Сначала правое вращение, затем левое\n            node-&gt;right = rightRotate(node-&gt;right);\n            return leftRotate(node);\n        }\n    }\n    // Дерево сбалансировано, вращение не требуется, вернуть сразу\n    return node;\n}\n</code></pre> avl_tree.java<pre><code>/* Выполнить вращение, чтобы снова сбалансировать поддерево */\nTreeNode rotate(TreeNode node) {\n    // Получить коэффициент баланса узла node\n    int balanceFactor = balanceFactor(node);\n    // Левосторонне перекошенное дерево\n    if (balanceFactor &gt; 1) {\n        if (balanceFactor(node.left) &gt;= 0) {\n            // Правое вращение\n            return rightRotate(node);\n        } else {\n            // Сначала левое вращение, затем правое\n            node.left = leftRotate(node.left);\n            return rightRotate(node);\n        }\n    }\n    // Правосторонне перекошенное дерево\n    if (balanceFactor &lt; -1) {\n        if (balanceFactor(node.right) &lt;= 0) {\n            // Левое вращение\n            return leftRotate(node);\n        } else {\n            // Сначала правое вращение, затем левое\n            node.right = rightRotate(node.right);\n            return leftRotate(node);\n        }\n    }\n    // Дерево сбалансировано, вращение не требуется, вернуть сразу\n    return node;\n}\n</code></pre> avl_tree.cs<pre><code>/* Выполнить вращение, чтобы снова сбалансировать поддерево */\nTreeNode? Rotate(TreeNode? node) {\n    // Получить коэффициент баланса узла node\n    int balanceFactorInt = BalanceFactor(node);\n    // Левосторонне перекошенное дерево\n    if (balanceFactorInt &gt; 1) {\n        if (BalanceFactor(node?.left) &gt;= 0) {\n            // Правое вращение\n            return RightRotate(node);\n        } else {\n            // Сначала левое вращение, затем правое\n            node!.left = LeftRotate(node!.left);\n            return RightRotate(node);\n        }\n    }\n    // Правосторонне перекошенное дерево\n    if (balanceFactorInt &lt; -1) {\n        if (BalanceFactor(node?.right) &lt;= 0) {\n            // Левое вращение\n            return LeftRotate(node);\n        } else {\n            // Сначала правое вращение, затем левое\n            node!.right = RightRotate(node!.right);\n            return LeftRotate(node);\n        }\n    }\n    // Дерево сбалансировано, вращение не требуется, вернуть сразу\n    return node;\n}\n</code></pre> avl_tree.go<pre><code>/* Выполнить вращение, чтобы снова сбалансировать поддерево */\nfunc (t *aVLTree) rotate(node *TreeNode) *TreeNode {\n    // Получить коэффициент баланса узла node\n    // В Go рекомендуется использовать короткие имена переменных, здесь bf обозначает t.balanceFactor\n    bf := t.balanceFactor(node)\n    // Левосторонне перекошенное дерево\n    if bf &gt; 1 {\n        if t.balanceFactor(node.Left) &gt;= 0 {\n            // Правое вращение\n            return t.rightRotate(node)\n        } else {\n            // Сначала левое вращение, затем правое\n            node.Left = t.leftRotate(node.Left)\n            return t.rightRotate(node)\n        }\n    }\n    // Правосторонне перекошенное дерево\n    if bf &lt; -1 {\n        if t.balanceFactor(node.Right) &lt;= 0 {\n            // Левое вращение\n            return t.leftRotate(node)\n        } else {\n            // Сначала правое вращение, затем левое\n            node.Right = t.rightRotate(node.Right)\n            return t.leftRotate(node)\n        }\n    }\n    // Дерево сбалансировано, вращение не требуется, вернуть сразу\n    return node\n}\n</code></pre> avl_tree.swift<pre><code>/* Выполнить вращение, чтобы снова сбалансировать поддерево */\nfunc rotate(node: TreeNode?) -&gt; TreeNode? {\n    // Получить коэффициент баланса узла node\n    let balanceFactor = balanceFactor(node: node)\n    // Левосторонне перекошенное дерево\n    if balanceFactor &gt; 1 {\n        if self.balanceFactor(node: node?.left) &gt;= 0 {\n            // Правое вращение\n            return rightRotate(node: node)\n        } else {\n            // Сначала левое вращение, затем правое\n            node?.left = leftRotate(node: node?.left)\n            return rightRotate(node: node)\n        }\n    }\n    // Правосторонне перекошенное дерево\n    if balanceFactor &lt; -1 {\n        if self.balanceFactor(node: node?.right) &lt;= 0 {\n            // Левое вращение\n            return leftRotate(node: node)\n        } else {\n            // Сначала правое вращение, затем левое\n            node?.right = rightRotate(node: node?.right)\n            return leftRotate(node: node)\n        }\n    }\n    // Дерево сбалансировано, вращение не требуется, вернуть сразу\n    return node\n}\n</code></pre> avl_tree.js<pre><code>/* Выполнить вращение, чтобы снова сбалансировать поддерево */\n#rotate(node) {\n    // Получить коэффициент баланса узла node\n    const balanceFactor = this.balanceFactor(node);\n    // Левосторонне перекошенное дерево\n    if (balanceFactor &gt; 1) {\n        if (this.balanceFactor(node.left) &gt;= 0) {\n            // Правое вращение\n            return this.#rightRotate(node);\n        } else {\n            // Сначала левое вращение, затем правое\n            node.left = this.#leftRotate(node.left);\n            return this.#rightRotate(node);\n        }\n    }\n    // Правосторонне перекошенное дерево\n    if (balanceFactor &lt; -1) {\n        if (this.balanceFactor(node.right) &lt;= 0) {\n            // Левое вращение\n            return this.#leftRotate(node);\n        } else {\n            // Сначала правое вращение, затем левое\n            node.right = this.#rightRotate(node.right);\n            return this.#leftRotate(node);\n        }\n    }\n    // Дерево сбалансировано, вращение не требуется, вернуть сразу\n    return node;\n}\n</code></pre> avl_tree.ts<pre><code>/* Выполнить вращение, чтобы снова сбалансировать поддерево */\nrotate(node: TreeNode): TreeNode {\n    // Получить коэффициент баланса узла node\n    const balanceFactor = this.balanceFactor(node);\n    // Левосторонне перекошенное дерево\n    if (balanceFactor &gt; 1) {\n        if (this.balanceFactor(node.left) &gt;= 0) {\n            // Правое вращение\n            return this.rightRotate(node);\n        } else {\n            // Сначала левое вращение, затем правое\n            node.left = this.leftRotate(node.left);\n            return this.rightRotate(node);\n        }\n    }\n    // Правосторонне перекошенное дерево\n    if (balanceFactor &lt; -1) {\n        if (this.balanceFactor(node.right) &lt;= 0) {\n            // Левое вращение\n            return this.leftRotate(node);\n        } else {\n            // Сначала правое вращение, затем левое\n            node.right = this.rightRotate(node.right);\n            return this.leftRotate(node);\n        }\n    }\n    // Дерево сбалансировано, вращение не требуется, вернуть сразу\n    return node;\n}\n</code></pre> avl_tree.dart<pre><code>/* Выполнить вращение, чтобы снова сбалансировать поддерево */\nTreeNode? rotate(TreeNode? node) {\n  // Получить коэффициент баланса узла node\n  int factor = balanceFactor(node);\n  // Левосторонне перекошенное дерево\n  if (factor &gt; 1) {\n    if (balanceFactor(node!.left) &gt;= 0) {\n      // Правое вращение\n      return rightRotate(node);\n    } else {\n      // Сначала левое вращение, затем правое\n      node.left = leftRotate(node.left);\n      return rightRotate(node);\n    }\n  }\n  // Правосторонне перекошенное дерево\n  if (factor &lt; -1) {\n    if (balanceFactor(node!.right) &lt;= 0) {\n      // Левое вращение\n      return leftRotate(node);\n    } else {\n      // Сначала правое вращение, затем левое\n      node.right = rightRotate(node.right);\n      return leftRotate(node);\n    }\n  }\n  // Дерево сбалансировано, вращение не требуется, вернуть сразу\n  return node;\n}\n</code></pre> avl_tree.rs<pre><code>/* Выполнить вращение, чтобы снова сбалансировать поддерево */\nfn rotate(node: OptionTreeNodeRc) -&gt; OptionTreeNodeRc {\n    // Получить коэффициент баланса узла node\n    let balance_factor = Self::balance_factor(node.clone());\n    // Левосторонне перекошенное дерево\n    if balance_factor &gt; 1 {\n        let node = node.unwrap();\n        if Self::balance_factor(node.borrow().left.clone()) &gt;= 0 {\n            // Правое вращение\n            Self::right_rotate(Some(node))\n        } else {\n            // Сначала левое вращение, затем правое\n            let left = node.borrow().left.clone();\n            node.borrow_mut().left = Self::left_rotate(left);\n            Self::right_rotate(Some(node))\n        }\n    }\n    // Правосторонне перекошенное дерево\n    else if balance_factor &lt; -1 {\n        let node = node.unwrap();\n        if Self::balance_factor(node.borrow().right.clone()) &lt;= 0 {\n            // Левое вращение\n            Self::left_rotate(Some(node))\n        } else {\n            // Сначала правое вращение, затем левое\n            let right = node.borrow().right.clone();\n            node.borrow_mut().right = Self::right_rotate(right);\n            Self::left_rotate(Some(node))\n        }\n    } else {\n        // Дерево сбалансировано, вращение не требуется, вернуть сразу\n        node\n    }\n}\n</code></pre> avl_tree.c<pre><code>/* Выполнить вращение, чтобы снова сбалансировать поддерево */\nTreeNode *rotate(TreeNode *node) {\n    // Получить коэффициент баланса узла node\n    int bf = balanceFactor(node);\n    // Левосторонне перекошенное дерево\n    if (bf &gt; 1) {\n        if (balanceFactor(node-&gt;left) &gt;= 0) {\n            // Правое вращение\n            return rightRotate(node);\n        } else {\n            // Сначала левое вращение, затем правое\n            node-&gt;left = leftRotate(node-&gt;left);\n            return rightRotate(node);\n        }\n    }\n    // Правосторонне перекошенное дерево\n    if (bf &lt; -1) {\n        if (balanceFactor(node-&gt;right) &lt;= 0) {\n            // Левое вращение\n            return leftRotate(node);\n        } else {\n            // Сначала правое вращение, затем левое\n            node-&gt;right = rightRotate(node-&gt;right);\n            return leftRotate(node);\n        }\n    }\n    // Дерево сбалансировано, вращение не требуется, вернуть сразу\n    return node;\n}\n</code></pre> avl_tree.kt<pre><code>/* Выполнить вращение, чтобы снова сбалансировать поддерево */\nfun rotate(node: TreeNode): TreeNode {\n    // Получить коэффициент баланса узла node\n    val balanceFactor = balanceFactor(node)\n    // Левосторонне перекошенное дерево\n    if (balanceFactor &gt; 1) {\n        if (balanceFactor(node.left) &gt;= 0) {\n            // Правое вращение\n            return rightRotate(node)\n        } else {\n            // Сначала левое вращение, затем правое\n            node.left = leftRotate(node.left)\n            return rightRotate(node)\n        }\n    }\n    // Правосторонне перекошенное дерево\n    if (balanceFactor &lt; -1) {\n        if (balanceFactor(node.right) &lt;= 0) {\n            // Левое вращение\n            return leftRotate(node)\n        } else {\n            // Сначала правое вращение, затем левое\n            node.right = rightRotate(node.right)\n            return leftRotate(node)\n        }\n    }\n    // Дерево сбалансировано, вращение не требуется, вернуть сразу\n    return node\n}\n</code></pre> avl_tree.rb<pre><code>### Выполнить вращение, чтобы снова сбалансировать поддерево ###\ndef rotate(node)\n  # Получить коэффициент баланса узла node\n  balance_factor = balance_factor(node)\n  # Обойти левое поддерево\n  if balance_factor &gt; 1\n    if balance_factor(node.left) &gt;= 0\n      # Правое вращение\n      return right_rotate(node)\n    else\n      # Сначала левое вращение, затем правое\n      node.left = left_rotate(node.left)\n      return right_rotate(node)\n    end\n  # Правостороннее дерево обхода\n  elsif balance_factor &lt; -1\n    if balance_factor(node.right) &lt;= 0\n      # Левое вращение\n      return left_rotate(node)\n    else\n      # Сначала правое вращение, затем левое\n      node.right = right_rotate(node.right)\n      return left_rotate(node)\n    end\n  end\n  # Дерево сбалансировано, вращение не требуется, вернуть сразу\n  node\nend\n</code></pre>","path":["Глава 7. Дерево","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#753-avl-","level":2,"title":"7.5.3   Распространенные операции AVL-дерева","text":"","path":["Глава 7. Дерево","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#1_2","level":3,"title":"1.   Вставка узла","text":"<p>Операция вставки узла в AVL-дерево по основному процессу похожа на вставку в двоичное дерево поиска. Единственная разница состоит в том, что после вставки в AVL-дерево на пути от вставленного узла к корню может появиться цепочка разбалансированных узлов. Поэтому начиная от этого узла, мы должны выполнять вращения снизу вверх, чтобы вернуть в баланс все разбалансированные узлы. Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def insert(self, val):\n    \"\"\"Вставка узла\"\"\"\n    self._root = self.insert_helper(self._root, val)\n\ndef insert_helper(self, node: TreeNode | None, val: int) -&gt; TreeNode:\n    \"\"\"Рекурсивная вставка узла (вспомогательный метод)\"\"\"\n    if node is None:\n        return TreeNode(val)\n    # 1. Найти позицию вставки и вставить узел\n    if val &lt; node.val:\n        node.left = self.insert_helper(node.left, val)\n    elif val &gt; node.val:\n        node.right = self.insert_helper(node.right, val)\n    else:\n        # Повторяющийся узел не вставлять, сразу вернуть\n        return node\n    # Обновить высоту узла\n    self.update_height(node)\n    # 2. Выполнить вращение, чтобы снова сбалансировать поддерево\n    return self.rotate(node)\n</code></pre> avl_tree.cpp<pre><code>/* Вставка узла */\nvoid insert(int val) {\n    root = insertHelper(root, val);\n}\n\n/* Рекурсивная вставка узла (вспомогательный метод) */\nTreeNode *insertHelper(TreeNode *node, int val) {\n    if (node == nullptr)\n        return new TreeNode(val);\n    /* 1. Найти позицию вставки и вставить узел */\n    if (val &lt; node-&gt;val)\n        node-&gt;left = insertHelper(node-&gt;left, val);\n    else if (val &gt; node-&gt;val)\n        node-&gt;right = insertHelper(node-&gt;right, val);\n    else\n        return node;    // Повторяющийся узел не вставлять, сразу вернуть\n    updateHeight(node); // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = rotate(node);\n    // Вернуть корневой узел поддерева\n    return node;\n}\n</code></pre> avl_tree.java<pre><code>/* Вставка узла */\nvoid insert(int val) {\n    root = insertHelper(root, val);\n}\n\n/* Рекурсивная вставка узла (вспомогательный метод) */\nTreeNode insertHelper(TreeNode node, int val) {\n    if (node == null)\n        return new TreeNode(val);\n    /* 1. Найти позицию вставки и вставить узел */\n    if (val &lt; node.val)\n        node.left = insertHelper(node.left, val);\n    else if (val &gt; node.val)\n        node.right = insertHelper(node.right, val);\n    else\n        return node; // Повторяющийся узел не вставлять, сразу вернуть\n    updateHeight(node); // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = rotate(node);\n    // Вернуть корневой узел поддерева\n    return node;\n}\n</code></pre> avl_tree.cs<pre><code>/* Вставка узла */\nvoid Insert(int val) {\n    root = InsertHelper(root, val);\n}\n\n/* Рекурсивная вставка узла (вспомогательный метод) */\nTreeNode? InsertHelper(TreeNode? node, int val) {\n    if (node == null) return new TreeNode(val);\n    /* 1. Найти позицию вставки и вставить узел */\n    if (val &lt; node.val)\n        node.left = InsertHelper(node.left, val);\n    else if (val &gt; node.val)\n        node.right = InsertHelper(node.right, val);\n    else\n        return node;     // Повторяющийся узел не вставлять, сразу вернуть\n    UpdateHeight(node);  // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = Rotate(node);\n    // Вернуть корневой узел поддерева\n    return node;\n}\n</code></pre> avl_tree.go<pre><code>/* Вставка узла */\nfunc (t *aVLTree) insert(val int) {\n    t.root = t.insertHelper(t.root, val)\n}\n\n/* Рекурсивная вставка узла (вспомогательная функция) */\nfunc (t *aVLTree) insertHelper(node *TreeNode, val int) *TreeNode {\n    if node == nil {\n        return NewTreeNode(val)\n    }\n    /* 1. Найти позицию вставки и вставить узел */\n    if val &lt; node.Val.(int) {\n        node.Left = t.insertHelper(node.Left, val)\n    } else if val &gt; node.Val.(int) {\n        node.Right = t.insertHelper(node.Right, val)\n    } else {\n        // Повторяющийся узел не вставлять, сразу вернуть\n        return node\n    }\n    // Обновить высоту узла\n    t.updateHeight(node)\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = t.rotate(node)\n    // Вернуть корневой узел поддерева\n    return node\n}\n</code></pre> avl_tree.swift<pre><code>/* Вставка узла */\nfunc insert(val: Int) {\n    root = insertHelper(node: root, val: val)\n}\n\n/* Рекурсивная вставка узла (вспомогательный метод) */\nfunc insertHelper(node: TreeNode?, val: Int) -&gt; TreeNode? {\n    var node = node\n    if node == nil {\n        return TreeNode(x: val)\n    }\n    /* 1. Найти позицию вставки и вставить узел */\n    if val &lt; node!.val {\n        node?.left = insertHelper(node: node?.left, val: val)\n    } else if val &gt; node!.val {\n        node?.right = insertHelper(node: node?.right, val: val)\n    } else {\n        return node // Повторяющийся узел не вставлять, сразу вернуть\n    }\n    updateHeight(node: node) // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = rotate(node: node)\n    // Вернуть корневой узел поддерева\n    return node\n}\n</code></pre> avl_tree.js<pre><code>/* Вставка узла */\ninsert(val) {\n    this.root = this.#insertHelper(this.root, val);\n}\n\n/* Рекурсивная вставка узла (вспомогательный метод) */\n#insertHelper(node, val) {\n    if (node === null) return new TreeNode(val);\n    /* 1. Найти позицию вставки и вставить узел */\n    if (val &lt; node.val) node.left = this.#insertHelper(node.left, val);\n    else if (val &gt; node.val)\n        node.right = this.#insertHelper(node.right, val);\n    else return node; // Повторяющийся узел не вставлять, сразу вернуть\n    this.#updateHeight(node); // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = this.#rotate(node);\n    // Вернуть корневой узел поддерева\n    return node;\n}\n</code></pre> avl_tree.ts<pre><code>/* Вставка узла */\ninsert(val: number): void {\n    this.root = this.insertHelper(this.root, val);\n}\n\n/* Рекурсивная вставка узла (вспомогательный метод) */\ninsertHelper(node: TreeNode, val: number): TreeNode {\n    if (node === null) return new TreeNode(val);\n    /* 1. Найти позицию вставки и вставить узел */\n    if (val &lt; node.val) {\n        node.left = this.insertHelper(node.left, val);\n    } else if (val &gt; node.val) {\n        node.right = this.insertHelper(node.right, val);\n    } else {\n        return node; // Повторяющийся узел не вставлять, сразу вернуть\n    }\n    this.updateHeight(node); // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = this.rotate(node);\n    // Вернуть корневой узел поддерева\n    return node;\n}\n</code></pre> avl_tree.dart<pre><code>/* Вставка узла */\nvoid insert(int val) {\n  root = insertHelper(root, val);\n}\n\n/* Рекурсивная вставка узла (вспомогательный метод) */\nTreeNode? insertHelper(TreeNode? node, int val) {\n  if (node == null) return TreeNode(val);\n  /* 1. Найти позицию вставки и вставить узел */\n  if (val &lt; node.val)\n    node.left = insertHelper(node.left, val);\n  else if (val &gt; node.val)\n    node.right = insertHelper(node.right, val);\n  else\n    return node; // Повторяющийся узел не вставлять, сразу вернуть\n  updateHeight(node); // Обновить высоту узла\n  /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n  node = rotate(node);\n  // Вернуть корневой узел поддерева\n  return node;\n}\n</code></pre> avl_tree.rs<pre><code>/* Вставка узла */\nfn insert(&amp;mut self, val: i32) {\n    self.root = Self::insert_helper(self.root.clone(), val);\n}\n\n/* Рекурсивная вставка узла (вспомогательный метод) */\nfn insert_helper(node: OptionTreeNodeRc, val: i32) -&gt; OptionTreeNodeRc {\n    match node {\n        Some(mut node) =&gt; {\n            /* 1. Найти позицию вставки и вставить узел */\n            match {\n                let node_val = node.borrow().val;\n                node_val\n            }\n            .cmp(&amp;val)\n            {\n                Ordering::Greater =&gt; {\n                    let left = node.borrow().left.clone();\n                    node.borrow_mut().left = Self::insert_helper(left, val);\n                }\n                Ordering::Less =&gt; {\n                    let right = node.borrow().right.clone();\n                    node.borrow_mut().right = Self::insert_helper(right, val);\n                }\n                Ordering::Equal =&gt; {\n                    return Some(node); // Повторяющийся узел не вставлять, сразу вернуть\n                }\n            }\n            Self::update_height(Some(node.clone())); // Обновить высоту узла\n\n            /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n            node = Self::rotate(Some(node)).unwrap();\n            // Вернуть корневой узел поддерева\n            Some(node)\n        }\n        None =&gt; Some(TreeNode::new(val)),\n    }\n}\n</code></pre> avl_tree.c<pre><code>/* Вставка узла */\nvoid insert(AVLTree *tree, int val) {\n    tree-&gt;root = insertHelper(tree-&gt;root, val);\n}\n\n/* Рекурсивная вставка узла (вспомогательная функция) */\nTreeNode *insertHelper(TreeNode *node, int val) {\n    if (node == NULL) {\n        return newTreeNode(val);\n    }\n    /* 1. Найти позицию вставки и вставить узел */\n    if (val &lt; node-&gt;val) {\n        node-&gt;left = insertHelper(node-&gt;left, val);\n    } else if (val &gt; node-&gt;val) {\n        node-&gt;right = insertHelper(node-&gt;right, val);\n    } else {\n        // Повторяющийся узел не вставлять, сразу вернуть\n        return node;\n    }\n    // Обновить высоту узла\n    updateHeight(node);\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = rotate(node);\n    // Вернуть корневой узел поддерева\n    return node;\n}\n</code></pre> avl_tree.kt<pre><code>/* Вставка узла */\nfun insert(_val: Int) {\n    root = insertHelper(root, _val)\n}\n\n/* Рекурсивная вставка узла (вспомогательный метод) */\nfun insertHelper(n: TreeNode?, _val: Int): TreeNode {\n    if (n == null)\n        return TreeNode(_val)\n    var node = n\n    /* 1. Найти позицию вставки и вставить узел */\n    if (_val &lt; node._val)\n        node.left = insertHelper(node.left, _val)\n    else if (_val &gt; node._val)\n        node.right = insertHelper(node.right, _val)\n    else\n        return node // Повторяющийся узел не вставлять, сразу вернуть\n    updateHeight(node) // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = rotate(node)\n    // Вернуть корневой узел поддерева\n    return node\n}\n</code></pre> avl_tree.rb<pre><code>### Вставка узла ###\ndef insert(val)\n  @root = insert_helper(@root, val)\nend\n\n### Вставка узла ###\ndef insert(val)\n  @root = insert_helper(@root, val)\nend\n\n# ## Рекурсивная вставка узла (вспомогательный метод) ###\ndef insert_helper(node, val)\n  return TreeNode.new(val) if node.nil?\n  # 1. Найти позицию вставки и вставить узел\n  if val &lt; node.val\n    node.left = insert_helper(node.left, val)\n  elsif val &gt; node.val\n    node.right = insert_helper(node.right, val)\n  else\n    # Повторяющийся узел не вставлять, сразу вернуть\n    return node\n  end\n  # Обновить высоту узла\n  update_height(node)\n  # 2. Выполнить вращение, чтобы снова сбалансировать поддерево\n  rotate(node)\nend\n</code></pre>","path":["Глава 7. Дерево","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#2_1","level":3,"title":"2.   Удаление узла","text":"<p>Аналогично, на основе метода удаления узла из двоичного дерева поиска нужно добавить вращения снизу вверх, чтобы восстановить баланс всех разбалансированных узлов. Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def remove(self, val: int):\n    \"\"\"Удаление узла\"\"\"\n    self._root = self.remove_helper(self._root, val)\n\ndef remove_helper(self, node: TreeNode | None, val: int) -&gt; TreeNode | None:\n    \"\"\"Рекурсивное удаление узла (вспомогательный метод)\"\"\"\n    if node is None:\n        return None\n    # 1. Найти узел и удалить его\n    if val &lt; node.val:\n        node.left = self.remove_helper(node.left, val)\n    elif val &gt; node.val:\n        node.right = self.remove_helper(node.right, val)\n    else:\n        if node.left is None or node.right is None:\n            child = node.left or node.right\n            # Число дочерних узлов = 0, удалить node и сразу вернуть\n            if child is None:\n                return None\n            # Число дочерних узлов = 1, удалить node напрямую\n            else:\n                node = child\n        else:\n            # Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n            temp = node.right\n            while temp.left is not None:\n                temp = temp.left\n            node.right = self.remove_helper(node.right, temp.val)\n            node.val = temp.val\n    # Обновить высоту узла\n    self.update_height(node)\n    # 2. Выполнить вращение, чтобы снова сбалансировать поддерево\n    return self.rotate(node)\n</code></pre> avl_tree.cpp<pre><code>/* Удаление узла */\nvoid remove(int val) {\n    root = removeHelper(root, val);\n}\n\n/* Рекурсивное удаление узла (вспомогательный метод) */\nTreeNode *removeHelper(TreeNode *node, int val) {\n    if (node == nullptr)\n        return nullptr;\n    /* 1. Найти узел и удалить его */\n    if (val &lt; node-&gt;val)\n        node-&gt;left = removeHelper(node-&gt;left, val);\n    else if (val &gt; node-&gt;val)\n        node-&gt;right = removeHelper(node-&gt;right, val);\n    else {\n        if (node-&gt;left == nullptr || node-&gt;right == nullptr) {\n            TreeNode *child = node-&gt;left != nullptr ? node-&gt;left : node-&gt;right;\n            // Число дочерних узлов = 0, удалить node и сразу вернуть\n            if (child == nullptr) {\n                delete node;\n                return nullptr;\n            }\n            // Число дочерних узлов = 1, удалить node напрямую\n            else {\n                delete node;\n                node = child;\n            }\n        } else {\n            // Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n            TreeNode *temp = node-&gt;right;\n            while (temp-&gt;left != nullptr) {\n                temp = temp-&gt;left;\n            }\n            int tempVal = temp-&gt;val;\n            node-&gt;right = removeHelper(node-&gt;right, temp-&gt;val);\n            node-&gt;val = tempVal;\n        }\n    }\n    updateHeight(node); // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = rotate(node);\n    // Вернуть корневой узел поддерева\n    return node;\n}\n</code></pre> avl_tree.java<pre><code>/* Удаление узла */\nvoid remove(int val) {\n    root = removeHelper(root, val);\n}\n\n/* Рекурсивное удаление узла (вспомогательный метод) */\nTreeNode removeHelper(TreeNode node, int val) {\n    if (node == null)\n        return null;\n    /* 1. Найти узел и удалить его */\n    if (val &lt; node.val)\n        node.left = removeHelper(node.left, val);\n    else if (val &gt; node.val)\n        node.right = removeHelper(node.right, val);\n    else {\n        if (node.left == null || node.right == null) {\n            TreeNode child = node.left != null ? node.left : node.right;\n            // Число дочерних узлов = 0, удалить node и сразу вернуть\n            if (child == null)\n                return null;\n            // Число дочерних узлов = 1, удалить node напрямую\n            else\n                node = child;\n        } else {\n            // Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n            TreeNode temp = node.right;\n            while (temp.left != null) {\n                temp = temp.left;\n            }\n            node.right = removeHelper(node.right, temp.val);\n            node.val = temp.val;\n        }\n    }\n    updateHeight(node); // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = rotate(node);\n    // Вернуть корневой узел поддерева\n    return node;\n}\n</code></pre> avl_tree.cs<pre><code>/* Удаление узла */\nvoid Remove(int val) {\n    root = RemoveHelper(root, val);\n}\n\n/* Рекурсивное удаление узла (вспомогательный метод) */\nTreeNode? RemoveHelper(TreeNode? node, int val) {\n    if (node == null) return null;\n    /* 1. Найти узел и удалить его */\n    if (val &lt; node.val)\n        node.left = RemoveHelper(node.left, val);\n    else if (val &gt; node.val)\n        node.right = RemoveHelper(node.right, val);\n    else {\n        if (node.left == null || node.right == null) {\n            TreeNode? child = node.left ?? node.right;\n            // Число дочерних узлов = 0, удалить node и сразу вернуть\n            if (child == null)\n                return null;\n            // Число дочерних узлов = 1, удалить node напрямую\n            else\n                node = child;\n        } else {\n            // Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n            TreeNode? temp = node.right;\n            while (temp.left != null) {\n                temp = temp.left;\n            }\n            node.right = RemoveHelper(node.right, temp.val!.Value);\n            node.val = temp.val;\n        }\n    }\n    UpdateHeight(node);  // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = Rotate(node);\n    // Вернуть корневой узел поддерева\n    return node;\n}\n</code></pre> avl_tree.go<pre><code>/* Удаление узла */\nfunc (t *aVLTree) remove(val int) {\n    t.root = t.removeHelper(t.root, val)\n}\n\n/* Рекурсивное удаление узла (вспомогательная функция) */\nfunc (t *aVLTree) removeHelper(node *TreeNode, val int) *TreeNode {\n    if node == nil {\n        return nil\n    }\n    /* 1. Найти узел и удалить его */\n    if val &lt; node.Val.(int) {\n        node.Left = t.removeHelper(node.Left, val)\n    } else if val &gt; node.Val.(int) {\n        node.Right = t.removeHelper(node.Right, val)\n    } else {\n        if node.Left == nil || node.Right == nil {\n            child := node.Left\n            if node.Right != nil {\n                child = node.Right\n            }\n            if child == nil {\n                // Число дочерних узлов = 0, удалить node и сразу вернуть\n                return nil\n            } else {\n                // Число дочерних узлов = 1, удалить node напрямую\n                node = child\n            }\n        } else {\n            // Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n            temp := node.Right\n            for temp.Left != nil {\n                temp = temp.Left\n            }\n            node.Right = t.removeHelper(node.Right, temp.Val.(int))\n            node.Val = temp.Val\n        }\n    }\n    // Обновить высоту узла\n    t.updateHeight(node)\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = t.rotate(node)\n    // Вернуть корневой узел поддерева\n    return node\n}\n</code></pre> avl_tree.swift<pre><code>/* Удаление узла */\nfunc remove(val: Int) {\n    root = removeHelper(node: root, val: val)\n}\n\n/* Рекурсивное удаление узла (вспомогательный метод) */\nfunc removeHelper(node: TreeNode?, val: Int) -&gt; TreeNode? {\n    var node = node\n    if node == nil {\n        return nil\n    }\n    /* 1. Найти узел и удалить его */\n    if val &lt; node!.val {\n        node?.left = removeHelper(node: node?.left, val: val)\n    } else if val &gt; node!.val {\n        node?.right = removeHelper(node: node?.right, val: val)\n    } else {\n        if node?.left == nil || node?.right == nil {\n            let child = node?.left ?? node?.right\n            // Число дочерних узлов = 0, удалить node и сразу вернуть\n            if child == nil {\n                return nil\n            }\n            // Число дочерних узлов = 1, удалить node напрямую\n            else {\n                node = child\n            }\n        } else {\n            // Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n            var temp = node?.right\n            while temp?.left != nil {\n                temp = temp?.left\n            }\n            node?.right = removeHelper(node: node?.right, val: temp!.val)\n            node?.val = temp!.val\n        }\n    }\n    updateHeight(node: node) // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = rotate(node: node)\n    // Вернуть корневой узел поддерева\n    return node\n}\n</code></pre> avl_tree.js<pre><code>/* Удаление узла */\nremove(val) {\n    this.root = this.#removeHelper(this.root, val);\n}\n\n/* Рекурсивное удаление узла (вспомогательный метод) */\n#removeHelper(node, val) {\n    if (node === null) return null;\n    /* 1. Найти узел и удалить его */\n    if (val &lt; node.val) node.left = this.#removeHelper(node.left, val);\n    else if (val &gt; node.val)\n        node.right = this.#removeHelper(node.right, val);\n    else {\n        if (node.left === null || node.right === null) {\n            const child = node.left !== null ? node.left : node.right;\n            // Число дочерних узлов = 0, удалить node и сразу вернуть\n            if (child === null) return null;\n            // Число дочерних узлов = 1, удалить node напрямую\n            else node = child;\n        } else {\n            // Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n            let temp = node.right;\n            while (temp.left !== null) {\n                temp = temp.left;\n            }\n            node.right = this.#removeHelper(node.right, temp.val);\n            node.val = temp.val;\n        }\n    }\n    this.#updateHeight(node); // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = this.#rotate(node);\n    // Вернуть корневой узел поддерева\n    return node;\n}\n</code></pre> avl_tree.ts<pre><code>/* Удаление узла */\nremove(val: number): void {\n    this.root = this.removeHelper(this.root, val);\n}\n\n/* Рекурсивное удаление узла (вспомогательный метод) */\nremoveHelper(node: TreeNode, val: number): TreeNode {\n    if (node === null) return null;\n    /* 1. Найти узел и удалить его */\n    if (val &lt; node.val) {\n        node.left = this.removeHelper(node.left, val);\n    } else if (val &gt; node.val) {\n        node.right = this.removeHelper(node.right, val);\n    } else {\n        if (node.left === null || node.right === null) {\n            const child = node.left !== null ? node.left : node.right;\n            // Число дочерних узлов = 0, удалить node и сразу вернуть\n            if (child === null) {\n                return null;\n            } else {\n                // Число дочерних узлов = 1, удалить node напрямую\n                node = child;\n            }\n        } else {\n            // Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n            let temp = node.right;\n            while (temp.left !== null) {\n                temp = temp.left;\n            }\n            node.right = this.removeHelper(node.right, temp.val);\n            node.val = temp.val;\n        }\n    }\n    this.updateHeight(node); // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = this.rotate(node);\n    // Вернуть корневой узел поддерева\n    return node;\n}\n</code></pre> avl_tree.dart<pre><code>/* Удаление узла */\nvoid remove(int val) {\n  root = removeHelper(root, val);\n}\n\n/* Рекурсивное удаление узла (вспомогательный метод) */\nTreeNode? removeHelper(TreeNode? node, int val) {\n  if (node == null) return null;\n  /* 1. Найти узел и удалить его */\n  if (val &lt; node.val)\n    node.left = removeHelper(node.left, val);\n  else if (val &gt; node.val)\n    node.right = removeHelper(node.right, val);\n  else {\n    if (node.left == null || node.right == null) {\n      TreeNode? child = node.left ?? node.right;\n      // Число дочерних узлов = 0, удалить node и сразу вернуть\n      if (child == null)\n        return null;\n      // Число дочерних узлов = 1, удалить node напрямую\n      else\n        node = child;\n    } else {\n      // Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n      TreeNode? temp = node.right;\n      while (temp!.left != null) {\n        temp = temp.left;\n      }\n      node.right = removeHelper(node.right, temp.val);\n      node.val = temp.val;\n    }\n  }\n  updateHeight(node); // Обновить высоту узла\n  /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n  node = rotate(node);\n  // Вернуть корневой узел поддерева\n  return node;\n}\n</code></pre> avl_tree.rs<pre><code>/* Удаление узла */\nfn remove(&amp;self, val: i32) {\n    Self::remove_helper(self.root.clone(), val);\n}\n\n/* Рекурсивное удаление узла (вспомогательный метод) */\nfn remove_helper(node: OptionTreeNodeRc, val: i32) -&gt; OptionTreeNodeRc {\n    match node {\n        Some(mut node) =&gt; {\n            /* 1. Найти узел и удалить его */\n            if val &lt; node.borrow().val {\n                let left = node.borrow().left.clone();\n                node.borrow_mut().left = Self::remove_helper(left, val);\n            } else if val &gt; node.borrow().val {\n                let right = node.borrow().right.clone();\n                node.borrow_mut().right = Self::remove_helper(right, val);\n            } else if node.borrow().left.is_none() || node.borrow().right.is_none() {\n                let child = if node.borrow().left.is_some() {\n                    node.borrow().left.clone()\n                } else {\n                    node.borrow().right.clone()\n                };\n                match child {\n                    // Число дочерних узлов = 0, удалить node и сразу вернуть\n                    None =&gt; {\n                        return None;\n                    }\n                    // Число дочерних узлов = 1, удалить node напрямую\n                    Some(child) =&gt; node = child,\n                }\n            } else {\n                // Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n                let mut temp = node.borrow().right.clone().unwrap();\n                loop {\n                    let temp_left = temp.borrow().left.clone();\n                    if temp_left.is_none() {\n                        break;\n                    }\n                    temp = temp_left.unwrap();\n                }\n                let right = node.borrow().right.clone();\n                node.borrow_mut().right = Self::remove_helper(right, temp.borrow().val);\n                node.borrow_mut().val = temp.borrow().val;\n            }\n            Self::update_height(Some(node.clone())); // Обновить высоту узла\n\n            /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n            node = Self::rotate(Some(node)).unwrap();\n            // Вернуть корневой узел поддерева\n            Some(node)\n        }\n        None =&gt; None,\n    }\n}\n</code></pre> avl_tree.c<pre><code>/* Удаление узла */\n// Из-за подключения stdio.h здесь нельзя использовать ключевое слово remove\nvoid removeItem(AVLTree *tree, int val) {\n    TreeNode *root = removeHelper(tree-&gt;root, val);\n}\n\n/* Рекурсивное удаление узла (вспомогательная функция) */\nTreeNode *removeHelper(TreeNode *node, int val) {\n    TreeNode *child, *grandChild;\n    if (node == NULL) {\n        return NULL;\n    }\n    /* 1. Найти узел и удалить его */\n    if (val &lt; node-&gt;val) {\n        node-&gt;left = removeHelper(node-&gt;left, val);\n    } else if (val &gt; node-&gt;val) {\n        node-&gt;right = removeHelper(node-&gt;right, val);\n    } else {\n        if (node-&gt;left == NULL || node-&gt;right == NULL) {\n            child = node-&gt;left;\n            if (node-&gt;right != NULL) {\n                child = node-&gt;right;\n            }\n            // Число дочерних узлов = 0, удалить node и сразу вернуть\n            if (child == NULL) {\n                return NULL;\n            } else {\n                // Число дочерних узлов = 1, удалить node напрямую\n                node = child;\n            }\n        } else {\n            // Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n            TreeNode *temp = node-&gt;right;\n            while (temp-&gt;left != NULL) {\n                temp = temp-&gt;left;\n            }\n            int tempVal = temp-&gt;val;\n            node-&gt;right = removeHelper(node-&gt;right, temp-&gt;val);\n            node-&gt;val = tempVal;\n        }\n    }\n    // Обновить высоту узла\n    updateHeight(node);\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = rotate(node);\n    // Вернуть корневой узел поддерева\n    return node;\n}\n</code></pre> avl_tree.kt<pre><code>/* Удаление узла */\nfun remove(_val: Int) {\n    root = removeHelper(root, _val)\n}\n\n/* Рекурсивное удаление узла (вспомогательный метод) */\nfun removeHelper(n: TreeNode?, _val: Int): TreeNode? {\n    var node = n ?: return null\n    /* 1. Найти узел и удалить его */\n    if (_val &lt; node._val)\n        node.left = removeHelper(node.left, _val)\n    else if (_val &gt; node._val)\n        node.right = removeHelper(node.right, _val)\n    else {\n        if (node.left == null || node.right == null) {\n            val child = if (node.left != null)\n                node.left\n            else\n                node.right\n            // Число дочерних узлов = 0, удалить node и сразу вернуть\n            if (child == null)\n                return null\n            // Число дочерних узлов = 1, удалить node напрямую\n            else\n                node = child\n        } else {\n            // Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n            var temp = node.right\n            while (temp!!.left != null) {\n                temp = temp.left\n            }\n            node.right = removeHelper(node.right, temp._val)\n            node._val = temp._val\n        }\n    }\n    updateHeight(node) // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = rotate(node)\n    // Вернуть корневой узел поддерева\n    return node\n}\n</code></pre> avl_tree.rb<pre><code>### Удаление узла ###\ndef remove(val)\n  @root = remove_helper(@root, val)\nend\n\n### Удаление узла ###\ndef remove(val)\n  @root = remove_helper(@root, val)\nend\n\n# ## Рекурсивное удаление узла (вспомогательный метод) ###\ndef remove_helper(node, val)\n  return if node.nil?\n  # 1. Найти узел и удалить его\n  if val &lt; node.val\n    node.left = remove_helper(node.left, val)\n  elsif val &gt; node.val\n    node.right = remove_helper(node.right, val)\n  else\n    if node.left.nil? || node.right.nil?\n      child = node.left || node.right\n      # Число дочерних узлов = 0, удалить node и сразу вернуть\n      return if child.nil?\n      # Число дочерних узлов = 1, удалить node напрямую\n      node = child\n    else\n      # Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n      temp = node.right\n      while !temp.left.nil?\n        temp = temp.left\n      end\n      node.right = remove_helper(node.right, temp.val)\n      node.val = temp.val\n    end\n  end\n  # Обновить высоту узла\n  update_height(node)\n  # 2. Выполнить вращение, чтобы снова сбалансировать поддерево\n  rotate(node)\nend\n</code></pre>","path":["Глава 7. Дерево","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#3_1","level":3,"title":"3.   Поиск узла","text":"<p>Операция поиска узла в AVL-дереве совпадает с поиском в двоичном дереве поиска, поэтому здесь она повторно не рассматривается.</p>","path":["Глава 7. Дерево","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#754-avl-","level":2,"title":"7.5.4   Типичные применения AVL-дерева","text":"<ul> <li>Организация и хранение больших массивов данных, особенно в сценариях с частым поиском и относительно редкими вставками и удалениями.</li> <li>Использование при построении индексных систем в базах данных.</li> <li>Красно-черное дерево тоже является распространенным видом сбалансированного двоичного дерева поиска. По сравнению с AVL-деревом условия баланса у красно-черного дерева мягче, поэтому при вставке и удалении требуется меньше вращений, а средняя эффективность операций добавления и удаления выше.</li> </ul>","path":["Глава 7. Дерево","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/binary_search_tree/","level":1,"title":"7.4   Двоичное дерево поиска","text":"<p>Как показано на рисунке 7-16, двоичное дерево поиска (binary search tree) удовлетворяет следующим условиям.</p> <ol> <li>Для корневого узла все значения в левом поддереве меньше значения корневого узла, а все значения в правом поддереве больше значения корневого узла.</li> <li>Левое и правое поддеревья любого узла также являются двоичными деревьями поиска, то есть тоже удовлетворяют условию <code>1.</code> .</li> </ol> <p></p> <p> Рисунок 7-16   Двоичное дерево поиска </p>","path":["Глава 7. Дерево","7.4 &nbsp; Двоичное дерево поиска"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#741","level":2,"title":"7.4.1   Операции с двоичным деревом поиска","text":"<p>Мы инкапсулируем двоичное дерево поиска в класс <code>BinarySearchTree</code> и объявляем переменную-член <code>root</code> , которая указывает на корневой узел дерева.</p>","path":["Глава 7. Дерево","7.4 &nbsp; Двоичное дерево поиска"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#1","level":3,"title":"1.   Поиск узла","text":"<p>Для заданного целевого значения узла <code>num</code> можно выполнить поиск, опираясь на свойства двоичного дерева поиска. Как показано на рисунках ниже, мы объявляем узел <code>cur</code> , стартуем от корня дерева <code>root</code> и циклически сравниваем значения <code>cur.val</code> и <code>num</code> .</p> <ul> <li>Если <code>cur.val &lt; num</code> , это означает, что целевой узел находится в правом поддереве <code>cur</code> , поэтому выполняем <code>cur = cur.right</code> .</li> <li>Если <code>cur.val &gt; num</code> , это означает, что целевой узел находится в левом поддереве <code>cur</code> , поэтому выполняем <code>cur = cur.left</code> .</li> <li>Если <code>cur.val = num</code> , это означает, что целевой узел найден, и мы выходим из цикла, возвращая этот узел.</li> </ul> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p> Рисунок 7-17   Пример поиска узла в двоичном дереве поиска </p> <p>Операция поиска в двоичном дереве поиска работает по тому же принципу, что и бинарный поиск: на каждом шаге она отбрасывает половину вариантов. Число итераций не превосходит высоты двоичного дерева, а когда дерево сбалансировано, требуется \\(O(\\log n)\\) времени. Пример кода приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_tree.py<pre><code>def search(self, num: int) -&gt; TreeNode | None:\n    \"\"\"Поиск узла\"\"\"\n    cur = self._root\n    # Искать в цикле и выйти после прохода за листовой узел\n    while cur is not None:\n        # Целевой узел находится в правом поддереве cur\n        if cur.val &lt; num:\n            cur = cur.right\n        # Целевой узел находится в левом поддереве cur\n        elif cur.val &gt; num:\n            cur = cur.left\n        # Найти целевой узел и выйти из цикла\n        else:\n            break\n    return cur\n</code></pre> binary_search_tree.cpp<pre><code>/* Поиск узла */\nTreeNode *search(int num) {\n    TreeNode *cur = root;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != nullptr) {\n        // Целевой узел находится в правом поддереве cur\n        if (cur-&gt;val &lt; num)\n            cur = cur-&gt;right;\n        // Целевой узел находится в левом поддереве cur\n        else if (cur-&gt;val &gt; num)\n            cur = cur-&gt;left;\n        // Найти целевой узел и выйти из цикла\n        else\n            break;\n    }\n    // Вернуть целевой узел\n    return cur;\n}\n</code></pre> binary_search_tree.java<pre><code>/* Поиск узла */\nTreeNode search(int num) {\n    TreeNode cur = root;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != null) {\n        // Целевой узел находится в правом поддереве cur\n        if (cur.val &lt; num)\n            cur = cur.right;\n        // Целевой узел находится в левом поддереве cur\n        else if (cur.val &gt; num)\n            cur = cur.left;\n        // Найти целевой узел и выйти из цикла\n        else\n            break;\n    }\n    // Вернуть целевой узел\n    return cur;\n}\n</code></pre> binary_search_tree.cs<pre><code>/* Поиск узла */\nTreeNode? Search(int num) {\n    TreeNode? cur = root;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != null) {\n        // Целевой узел находится в правом поддереве cur\n        if (cur.val &lt; num) cur =\n            cur.right;\n        // Целевой узел находится в левом поддереве cur\n        else if (cur.val &gt; num)\n            cur = cur.left;\n        // Найти целевой узел и выйти из цикла\n        else\n            break;\n    }\n    // Вернуть целевой узел\n    return cur;\n}\n</code></pre> binary_search_tree.go<pre><code>/* Поиск узла */\nfunc (bst *binarySearchTree) search(num int) *TreeNode {\n    node := bst.root\n    // Искать в цикле и выйти после прохода за листовой узел\n    for node != nil {\n        if node.Val.(int) &lt; num {\n            // Целевой узел находится в правом поддереве cur\n            node = node.Right\n        } else if node.Val.(int) &gt; num {\n            // Целевой узел находится в левом поддереве cur\n            node = node.Left\n        } else {\n            // Найти целевой узел и выйти из цикла\n            break\n        }\n    }\n    // Вернуть целевой узел\n    return node\n}\n</code></pre> binary_search_tree.swift<pre><code>/* Поиск узла */\nfunc search(num: Int) -&gt; TreeNode? {\n    var cur = root\n    // Искать в цикле и выйти после прохода за листовой узел\n    while cur != nil {\n        // Целевой узел находится в правом поддереве cur\n        if cur!.val &lt; num {\n            cur = cur?.right\n        }\n        // Целевой узел находится в левом поддереве cur\n        else if cur!.val &gt; num {\n            cur = cur?.left\n        }\n        // Найти целевой узел и выйти из цикла\n        else {\n            break\n        }\n    }\n    // Вернуть целевой узел\n    return cur\n}\n</code></pre> binary_search_tree.js<pre><code>/* Поиск узла */\nsearch(num) {\n    let cur = this.root;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur !== null) {\n        // Целевой узел находится в правом поддереве cur\n        if (cur.val &lt; num) cur = cur.right;\n        // Целевой узел находится в левом поддереве cur\n        else if (cur.val &gt; num) cur = cur.left;\n        // Найти целевой узел и выйти из цикла\n        else break;\n    }\n    // Вернуть целевой узел\n    return cur;\n}\n</code></pre> binary_search_tree.ts<pre><code>/* Поиск узла */\nsearch(num: number): TreeNode | null {\n    let cur = this.root;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur !== null) {\n        // Целевой узел находится в правом поддереве cur\n        if (cur.val &lt; num) cur = cur.right;\n        // Целевой узел находится в левом поддереве cur\n        else if (cur.val &gt; num) cur = cur.left;\n        // Найти целевой узел и выйти из цикла\n        else break;\n    }\n    // Вернуть целевой узел\n    return cur;\n}\n</code></pre> binary_search_tree.dart<pre><code>/* Поиск узла */\nTreeNode? search(int _num) {\n  TreeNode? cur = _root;\n  // Искать в цикле и выйти после прохода за листовой узел\n  while (cur != null) {\n    // Целевой узел находится в правом поддереве cur\n    if (cur.val &lt; _num)\n      cur = cur.right;\n    // Целевой узел находится в левом поддереве cur\n    else if (cur.val &gt; _num)\n      cur = cur.left;\n    // Найти целевой узел и выйти из цикла\n    else\n      break;\n  }\n  // Вернуть целевой узел\n  return cur;\n}\n</code></pre> binary_search_tree.rs<pre><code>/* Поиск узла */\npub fn search(&amp;self, num: i32) -&gt; OptionTreeNodeRc {\n    let mut cur = self.root.clone();\n    // Искать в цикле и выйти после прохода за листовой узел\n    while let Some(node) = cur.clone() {\n        match num.cmp(&amp;node.borrow().val) {\n            // Целевой узел находится в правом поддереве cur\n            Ordering::Greater =&gt; cur = node.borrow().right.clone(),\n            // Целевой узел находится в левом поддереве cur\n            Ordering::Less =&gt; cur = node.borrow().left.clone(),\n            // Найти целевой узел и выйти из цикла\n            Ordering::Equal =&gt; break,\n        }\n    }\n\n    // Вернуть целевой узел\n    cur\n}\n</code></pre> binary_search_tree.c<pre><code>/* Поиск узла */\nTreeNode *search(BinarySearchTree *bst, int num) {\n    TreeNode *cur = bst-&gt;root;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != NULL) {\n        if (cur-&gt;val &lt; num) {\n            // Целевой узел находится в правом поддереве cur\n            cur = cur-&gt;right;\n        } else if (cur-&gt;val &gt; num) {\n            // Целевой узел находится в левом поддереве cur\n            cur = cur-&gt;left;\n        } else {\n            // Найти целевой узел и выйти из цикла\n            break;\n        }\n    }\n    // Вернуть целевой узел\n    return cur;\n}\n</code></pre> binary_search_tree.kt<pre><code>/* Поиск узла */\nfun search(num: Int): TreeNode? {\n    var cur = root\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != null) {\n        // Целевой узел находится в правом поддереве cur\n        cur = if (cur._val &lt; num)\n            cur.right\n        // Целевой узел находится в левом поддереве cur\n        else if (cur._val &gt; num)\n            cur.left\n        // Найти целевой узел и выйти из цикла\n        else\n            break\n    }\n    // Вернуть целевой узел\n    return cur\n}\n</code></pre> binary_search_tree.rb<pre><code>### Поиск узла ###\ndef search(num)\n  cur = @root\n\n  # Искать в цикле и выйти после прохода за листовой узел\n  while !cur.nil?\n    # Целевой узел находится в правом поддереве cur\n    if cur.val &lt; num\n      cur = cur.right\n    # Целевой узел находится в левом поддереве cur\n    elsif cur.val &gt; num\n      cur = cur.left\n    # Найти целевой узел и выйти из цикла\n    else\n      break\n    end\n  end\n\n  cur\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 7. Дерево","7.4 &nbsp; Двоичное дерево поиска"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#2","level":3,"title":"2.   Вставка узла","text":"<p>Пусть дан элемент <code>num</code> , который нужно вставить. Чтобы сохранить свойство двоичного дерева поиска \"левое поддерево &lt; корень &lt; правое поддерево\", процесс вставки выглядит следующим образом.</p> <ol> <li>Найти позицию для вставки: как и в операции поиска, начиная от корня, мы циклически спускаемся вниз в зависимости от соотношения между текущим значением узла и <code>num</code> , пока не выйдем за листовой узел (то есть не дойдем до <code>None</code> ).</li> <li>Вставить узел в найденную позицию: инициализировать узел <code>num</code> и поставить его на место этого <code>None</code> .</li> </ol> <p></p> <p> Рисунок 7-18   Вставка узла в двоичное дерево поиска </p> <p>В реализации кода нужно обратить внимание на следующие два момента.</p> <ul> <li>Двоичное дерево поиска не допускает дублирующихся узлов, иначе его определение будет нарушено. Поэтому если вставляемый узел уже существует в дереве, вставка не выполняется и функция сразу возвращается.</li> <li>Чтобы реализовать вставку, нам нужно использовать узел <code>pre</code> для сохранения узла предыдущей итерации цикла. Тогда, когда обход дойдет до <code>None</code> , мы сможем получить его родителя и завершить вставку.</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_tree.py<pre><code>def insert(self, num: int):\n    \"\"\"Вставка узла\"\"\"\n    # Если дерево пусто, инициализировать корневой узел\n    if self._root is None:\n        self._root = TreeNode(num)\n        return\n    # Искать в цикле и выйти после прохода за листовой узел\n    cur, pre = self._root, None\n    while cur is not None:\n        # Найти повторяющийся узел и сразу вернуть\n        if cur.val == num:\n            return\n        pre = cur\n        # Позиция вставки находится в правом поддереве cur\n        if cur.val &lt; num:\n            cur = cur.right\n        # Позиция вставки находится в левом поддереве cur\n        else:\n            cur = cur.left\n    # Вставка узла\n    node = TreeNode(num)\n    if pre.val &lt; num:\n        pre.right = node\n    else:\n        pre.left = node\n</code></pre> binary_search_tree.cpp<pre><code>/* Вставка узла */\nvoid insert(int num) {\n    // Если дерево пусто, инициализировать корневой узел\n    if (root == nullptr) {\n        root = new TreeNode(num);\n        return;\n    }\n    TreeNode *cur = root, *pre = nullptr;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != nullptr) {\n        // Найти повторяющийся узел и сразу вернуть\n        if (cur-&gt;val == num)\n            return;\n        pre = cur;\n        // Позиция вставки находится в правом поддереве cur\n        if (cur-&gt;val &lt; num)\n            cur = cur-&gt;right;\n        // Позиция вставки находится в левом поддереве cur\n        else\n            cur = cur-&gt;left;\n    }\n    // Вставка узла\n    TreeNode *node = new TreeNode(num);\n    if (pre-&gt;val &lt; num)\n        pre-&gt;right = node;\n    else\n        pre-&gt;left = node;\n}\n</code></pre> binary_search_tree.java<pre><code>/* Вставка узла */\nvoid insert(int num) {\n    // Если дерево пусто, инициализировать корневой узел\n    if (root == null) {\n        root = new TreeNode(num);\n        return;\n    }\n    TreeNode cur = root, pre = null;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != null) {\n        // Найти повторяющийся узел и сразу вернуть\n        if (cur.val == num)\n            return;\n        pre = cur;\n        // Позиция вставки находится в правом поддереве cur\n        if (cur.val &lt; num)\n            cur = cur.right;\n        // Позиция вставки находится в левом поддереве cur\n        else\n            cur = cur.left;\n    }\n    // Вставка узла\n    TreeNode node = new TreeNode(num);\n    if (pre.val &lt; num)\n        pre.right = node;\n    else\n        pre.left = node;\n}\n</code></pre> binary_search_tree.cs<pre><code>/* Вставка узла */\nvoid Insert(int num) {\n    // Если дерево пусто, инициализировать корневой узел\n    if (root == null) {\n        root = new TreeNode(num);\n        return;\n    }\n    TreeNode? cur = root, pre = null;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != null) {\n        // Найти повторяющийся узел и сразу вернуть\n        if (cur.val == num)\n            return;\n        pre = cur;\n        // Позиция вставки находится в правом поддереве cur\n        if (cur.val &lt; num)\n            cur = cur.right;\n        // Позиция вставки находится в левом поддереве cur\n        else\n            cur = cur.left;\n    }\n\n    // Вставка узла\n    TreeNode node = new(num);\n    if (pre != null) {\n        if (pre.val &lt; num)\n            pre.right = node;\n        else\n            pre.left = node;\n    }\n}\n</code></pre> binary_search_tree.go<pre><code>/* Вставка узла */\nfunc (bst *binarySearchTree) insert(num int) {\n    cur := bst.root\n    // Если дерево пусто, инициализировать корневой узел\n    if cur == nil {\n        bst.root = NewTreeNode(num)\n        return\n    }\n    // Позиция узла, предшествующего вставляемому\n    var pre *TreeNode = nil\n    // Искать в цикле и выйти после прохода за листовой узел\n    for cur != nil {\n        if cur.Val == num {\n            return\n        }\n        pre = cur\n        if cur.Val.(int) &lt; num {\n            cur = cur.Right\n        } else {\n            cur = cur.Left\n        }\n    }\n    // Вставка узла\n    node := NewTreeNode(num)\n    if pre.Val.(int) &lt; num {\n        pre.Right = node\n    } else {\n        pre.Left = node\n    }\n}\n</code></pre> binary_search_tree.swift<pre><code>/* Вставка узла */\nfunc insert(num: Int) {\n    // Если дерево пусто, инициализировать корневой узел\n    if root == nil {\n        root = TreeNode(x: num)\n        return\n    }\n    var cur = root\n    var pre: TreeNode?\n    // Искать в цикле и выйти после прохода за листовой узел\n    while cur != nil {\n        // Найти повторяющийся узел и сразу вернуть\n        if cur!.val == num {\n            return\n        }\n        pre = cur\n        // Позиция вставки находится в правом поддереве cur\n        if cur!.val &lt; num {\n            cur = cur?.right\n        }\n        // Позиция вставки находится в левом поддереве cur\n        else {\n            cur = cur?.left\n        }\n    }\n    // Вставка узла\n    let node = TreeNode(x: num)\n    if pre!.val &lt; num {\n        pre?.right = node\n    } else {\n        pre?.left = node\n    }\n}\n</code></pre> binary_search_tree.js<pre><code>/* Вставка узла */\ninsert(num) {\n    // Если дерево пусто, инициализировать корневой узел\n    if (this.root === null) {\n        this.root = new TreeNode(num);\n        return;\n    }\n    let cur = this.root,\n        pre = null;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur !== null) {\n        // Найти повторяющийся узел и сразу вернуть\n        if (cur.val === num) return;\n        pre = cur;\n        // Позиция вставки находится в правом поддереве cur\n        if (cur.val &lt; num) cur = cur.right;\n        // Позиция вставки находится в левом поддереве cur\n        else cur = cur.left;\n    }\n    // Вставка узла\n    const node = new TreeNode(num);\n    if (pre.val &lt; num) pre.right = node;\n    else pre.left = node;\n}\n</code></pre> binary_search_tree.ts<pre><code>/* Вставка узла */\ninsert(num: number): void {\n    // Если дерево пусто, инициализировать корневой узел\n    if (this.root === null) {\n        this.root = new TreeNode(num);\n        return;\n    }\n    let cur: TreeNode | null = this.root,\n        pre: TreeNode | null = null;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur !== null) {\n        // Найти повторяющийся узел и сразу вернуть\n        if (cur.val === num) return;\n        pre = cur;\n        // Позиция вставки находится в правом поддереве cur\n        if (cur.val &lt; num) cur = cur.right;\n        // Позиция вставки находится в левом поддереве cur\n        else cur = cur.left;\n    }\n    // Вставка узла\n    const node = new TreeNode(num);\n    if (pre!.val &lt; num) pre!.right = node;\n    else pre!.left = node;\n}\n</code></pre> binary_search_tree.dart<pre><code>/* Вставка узла */\nvoid insert(int _num) {\n  // Если дерево пусто, инициализировать корневой узел\n  if (_root == null) {\n    _root = TreeNode(_num);\n    return;\n  }\n  TreeNode? cur = _root;\n  TreeNode? pre = null;\n  // Искать в цикле и выйти после прохода за листовой узел\n  while (cur != null) {\n    // Найти повторяющийся узел и сразу вернуть\n    if (cur.val == _num) return;\n    pre = cur;\n    // Позиция вставки находится в правом поддереве cur\n    if (cur.val &lt; _num)\n      cur = cur.right;\n    // Позиция вставки находится в левом поддереве cur\n    else\n      cur = cur.left;\n  }\n  // Вставка узла\n  TreeNode? node = TreeNode(_num);\n  if (pre!.val &lt; _num)\n    pre.right = node;\n  else\n    pre.left = node;\n}\n</code></pre> binary_search_tree.rs<pre><code>/* Вставка узла */\npub fn insert(&amp;mut self, num: i32) {\n    // Если дерево пусто, инициализировать корневой узел\n    if self.root.is_none() {\n        self.root = Some(TreeNode::new(num));\n        return;\n    }\n    let mut cur = self.root.clone();\n    let mut pre = None;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while let Some(node) = cur.clone() {\n        match num.cmp(&amp;node.borrow().val) {\n            // Найти повторяющийся узел и сразу вернуть\n            Ordering::Equal =&gt; return,\n            // Позиция вставки находится в правом поддереве cur\n            Ordering::Greater =&gt; {\n                pre = cur.clone();\n                cur = node.borrow().right.clone();\n            }\n            // Позиция вставки находится в левом поддереве cur\n            Ordering::Less =&gt; {\n                pre = cur.clone();\n                cur = node.borrow().left.clone();\n            }\n        }\n    }\n    // Вставка узла\n    let pre = pre.unwrap();\n    let node = Some(TreeNode::new(num));\n    if num &gt; pre.borrow().val {\n        pre.borrow_mut().right = node;\n    } else {\n        pre.borrow_mut().left = node;\n    }\n}\n</code></pre> binary_search_tree.c<pre><code>/* Вставка узла */\nvoid insert(BinarySearchTree *bst, int num) {\n    // Если дерево пусто, инициализировать корневой узел\n    if (bst-&gt;root == NULL) {\n        bst-&gt;root = newTreeNode(num);\n        return;\n    }\n    TreeNode *cur = bst-&gt;root, *pre = NULL;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != NULL) {\n        // Найти повторяющийся узел и сразу вернуть\n        if (cur-&gt;val == num) {\n            return;\n        }\n        pre = cur;\n        if (cur-&gt;val &lt; num) {\n            // Позиция вставки находится в правом поддереве cur\n            cur = cur-&gt;right;\n        } else {\n            // Позиция вставки находится в левом поддереве cur\n            cur = cur-&gt;left;\n        }\n    }\n    // Вставка узла\n    TreeNode *node = newTreeNode(num);\n    if (pre-&gt;val &lt; num) {\n        pre-&gt;right = node;\n    } else {\n        pre-&gt;left = node;\n    }\n}\n</code></pre> binary_search_tree.kt<pre><code>/* Вставка узла */\nfun insert(num: Int) {\n    // Если дерево пусто, инициализировать корневой узел\n    if (root == null) {\n        root = TreeNode(num)\n        return\n    }\n    var cur = root\n    var pre: TreeNode? = null\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != null) {\n        // Найти повторяющийся узел и сразу вернуть\n        if (cur._val == num)\n            return\n        pre = cur\n        // Позиция вставки находится в правом поддереве cur\n        cur = if (cur._val &lt; num)\n            cur.right\n        // Позиция вставки находится в левом поддереве cur\n        else\n            cur.left\n    }\n    // Вставка узла\n    val node = TreeNode(num)\n    if (pre?._val!! &lt; num)\n        pre.right = node\n    else\n        pre.left = node\n}\n</code></pre> binary_search_tree.rb<pre><code>### Вставка узла ###\ndef insert(num)\n  # Если дерево пусто, инициализировать корневой узел\n  if @root.nil?\n    @root = TreeNode.new(num)\n    return\n  end\n\n  # Искать в цикле и выйти после прохода за листовой узел\n  cur, pre = @root, nil\n  while !cur.nil?\n    # Найти повторяющийся узел и сразу вернуть\n    return if cur.val == num\n\n    pre = cur\n    # Позиция вставки находится в правом поддереве cur\n    if cur.val &lt; num\n      cur = cur.right\n    # Позиция вставки находится в левом поддереве cur\n    else\n      cur = cur.left\n    end\n  end\n\n  # Вставка узла\n  node = TreeNode.new(num)\n  if pre.val &lt; num\n    pre.right = node\n  else\n    pre.left = node\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Как и поиск узла, вставка узла требует \\(O(\\log n)\\) времени.</p>","path":["Глава 7. Дерево","7.4 &nbsp; Двоичное дерево поиска"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#3","level":3,"title":"3.   Удаление узла","text":"<p>Сначала нужно найти в двоичном дереве целевой узел, а затем удалить его. Как и при вставке, после удаления необходимо сохранить свойство двоичного дерева поиска: \"левое поддерево &lt; корень &lt; правое поддерево\". Поэтому в зависимости от числа дочерних узлов у удаляемого узла, то есть для случаев со степенью 0, 1 и 2, выполняются разные операции удаления.</p> <p>Как показано на рисунке 7-19, когда степень удаляемого узла равна \\(0\\) , это значит, что узел является листом и может быть удален напрямую.</p> <p></p> <p> Рисунок 7-19   Удаление узла в двоичном дереве поиска (степень 0) </p> <p>Как показано на рисунке 7-20, когда степень удаляемого узла равна \\(1\\) , достаточно заменить удаляемый узел его дочерним узлом.</p> <p></p> <p> Рисунок 7-20   Удаление узла в двоичном дереве поиска (степень 1) </p> <p>Когда степень удаляемого узла равна \\(2\\) , мы уже не можем удалить его напрямую и должны использовать для замены другой узел. Чтобы сохранить свойство двоичного дерева поиска \"левое поддерево \\(&lt;\\) корень \\(&lt;\\) правое поддерево\", этим узлом может быть минимальный узел правого поддерева или максимальный узел левого поддерева.</p> <p>Предположим, мы выбираем минимальный узел правого поддерева, то есть следующий узел в симметричном обходе. Тогда процесс удаления выглядит так.</p> <ol> <li>Найти следующий узел в \"последовательности симметричного обхода\" для удаляемого узла и обозначить его как <code>tmp</code> .</li> <li>Значением <code>tmp</code> перезаписать значение удаляемого узла, а затем рекурсивно удалить узел <code>tmp</code> из дерева.</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p> Рисунок 7-21   Удаление узла в двоичном дереве поиска (степень 2) </p> <p>Операция удаления узла также требует \\(O(\\log n)\\) времени, где поиск удаляемого узла стоит \\(O(\\log n)\\) , а получение следующего узла симметричного обхода также требует \\(O(\\log n)\\) . Пример кода приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_tree.py<pre><code>def remove(self, num: int):\n    \"\"\"Удаление узла\"\"\"\n    # Если дерево пусто, сразу вернуть\n    if self._root is None:\n        return\n    # Искать в цикле и выйти после прохода за листовой узел\n    cur, pre = self._root, None\n    while cur is not None:\n        # Найти узел для удаления и выйти из цикла\n        if cur.val == num:\n            break\n        pre = cur\n        # Узел для удаления находится в правом поддереве cur\n        if cur.val &lt; num:\n            cur = cur.right\n        # Узел для удаления находится в левом поддереве cur\n        else:\n            cur = cur.left\n    # Если узел для удаления отсутствует, сразу вернуть\n    if cur is None:\n        return\n\n    # Число дочерних узлов = 0 или 1\n    if cur.left is None or cur.right is None:\n        # Когда число дочерних узлов = 0 / 1, child = null / этот дочерний узел\n        child = cur.left or cur.right\n        # Удалить узел cur\n        if cur != self._root:\n            if pre.left == cur:\n                pre.left = child\n            else:\n                pre.right = child\n        else:\n            # Если удаляемый узел является корнем, заново назначить корневой узел\n            self._root = child\n    # Число дочерних узлов = 2\n    else:\n        # Получить следующий узел после cur в симметричном обходе\n        tmp: TreeNode = cur.right\n        while tmp.left is not None:\n            tmp = tmp.left\n        # Рекурсивно удалить узел tmp\n        self.remove(tmp.val)\n        # Перезаписать cur значением tmp\n        cur.val = tmp.val\n</code></pre> binary_search_tree.cpp<pre><code>/* Удаление узла */\nvoid remove(int num) {\n    // Если дерево пусто, сразу вернуть\n    if (root == nullptr)\n        return;\n    TreeNode *cur = root, *pre = nullptr;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != nullptr) {\n        // Найти узел для удаления и выйти из цикла\n        if (cur-&gt;val == num)\n            break;\n        pre = cur;\n        // Узел для удаления находится в правом поддереве cur\n        if (cur-&gt;val &lt; num)\n            cur = cur-&gt;right;\n        // Узел для удаления находится в левом поддереве cur\n        else\n            cur = cur-&gt;left;\n    }\n    // Если узел для удаления отсутствует, сразу вернуть\n    if (cur == nullptr)\n        return;\n    // Число дочерних узлов = 0 или 1\n    if (cur-&gt;left == nullptr || cur-&gt;right == nullptr) {\n        // Когда число дочерних узлов = 0 / 1, child = nullptr / этот дочерний узел\n        TreeNode *child = cur-&gt;left != nullptr ? cur-&gt;left : cur-&gt;right;\n        // Удалить узел cur\n        if (cur != root) {\n            if (pre-&gt;left == cur)\n                pre-&gt;left = child;\n            else\n                pre-&gt;right = child;\n        } else {\n            // Если удаляемый узел является корнем, заново назначить корневой узел\n            root = child;\n        }\n        // Освободить память\n        delete cur;\n    }\n    // Число дочерних узлов = 2\n    else {\n        // Получить следующий узел после cur в симметричном обходе\n        TreeNode *tmp = cur-&gt;right;\n        while (tmp-&gt;left != nullptr) {\n            tmp = tmp-&gt;left;\n        }\n        int tmpVal = tmp-&gt;val;\n        // Рекурсивно удалить узел tmp\n        remove(tmp-&gt;val);\n        // Перезаписать cur значением tmp\n        cur-&gt;val = tmpVal;\n    }\n}\n</code></pre> binary_search_tree.java<pre><code>/* Удаление узла */\nvoid remove(int num) {\n    // Если дерево пусто, сразу вернуть\n    if (root == null)\n        return;\n    TreeNode cur = root, pre = null;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != null) {\n        // Найти узел для удаления и выйти из цикла\n        if (cur.val == num)\n            break;\n        pre = cur;\n        // Узел для удаления находится в правом поддереве cur\n        if (cur.val &lt; num)\n            cur = cur.right;\n        // Узел для удаления находится в левом поддереве cur\n        else\n            cur = cur.left;\n    }\n    // Если узел для удаления отсутствует, сразу вернуть\n    if (cur == null)\n        return;\n    // Число дочерних узлов = 0 или 1\n    if (cur.left == null || cur.right == null) {\n        // Когда число дочерних узлов = 0 / 1, child = null / этот дочерний узел\n        TreeNode child = cur.left != null ? cur.left : cur.right;\n        // Удалить узел cur\n        if (cur != root) {\n            if (pre.left == cur)\n                pre.left = child;\n            else\n                pre.right = child;\n        } else {\n            // Если удаляемый узел является корнем, заново назначить корневой узел\n            root = child;\n        }\n    }\n    // Число дочерних узлов = 2\n    else {\n        // Получить следующий узел после cur в симметричном обходе\n        TreeNode tmp = cur.right;\n        while (tmp.left != null) {\n            tmp = tmp.left;\n        }\n        // Рекурсивно удалить узел tmp\n        remove(tmp.val);\n        // Перезаписать cur значением tmp\n        cur.val = tmp.val;\n    }\n}\n</code></pre> binary_search_tree.cs<pre><code>/* Удаление узла */\nvoid Remove(int num) {\n    // Если дерево пусто, сразу вернуть\n    if (root == null)\n        return;\n    TreeNode? cur = root, pre = null;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != null) {\n        // Найти узел для удаления и выйти из цикла\n        if (cur.val == num)\n            break;\n        pre = cur;\n        // Узел для удаления находится в правом поддереве cur\n        if (cur.val &lt; num)\n            cur = cur.right;\n        // Узел для удаления находится в левом поддереве cur\n        else\n            cur = cur.left;\n    }\n    // Если узел для удаления отсутствует, сразу вернуть\n    if (cur == null)\n        return;\n    // Число дочерних узлов = 0 или 1\n    if (cur.left == null || cur.right == null) {\n        // Когда число дочерних узлов = 0 / 1, child = null / этот дочерний узел\n        TreeNode? child = cur.left ?? cur.right;\n        // Удалить узел cur\n        if (cur != root) {\n            if (pre!.left == cur)\n                pre.left = child;\n            else\n                pre.right = child;\n        } else {\n            // Если удаляемый узел является корнем, заново назначить корневой узел\n            root = child;\n        }\n    }\n    // Число дочерних узлов = 2\n    else {\n        // Получить следующий узел после cur в симметричном обходе\n        TreeNode? tmp = cur.right;\n        while (tmp.left != null) {\n            tmp = tmp.left;\n        }\n        // Рекурсивно удалить узел tmp\n        Remove(tmp.val!.Value);\n        // Перезаписать cur значением tmp\n        cur.val = tmp.val;\n    }\n}\n</code></pre> binary_search_tree.go<pre><code>/* Удаление узла */\nfunc (bst *binarySearchTree) remove(num int) {\n    cur := bst.root\n    // Если дерево пусто, сразу вернуть\n    if cur == nil {\n        return\n    }\n    // Позиция узла, предшествующего удаляемому\n    var pre *TreeNode = nil\n    // Искать в цикле и выйти после прохода за листовой узел\n    for cur != nil {\n        if cur.Val == num {\n            break\n        }\n        pre = cur\n        if cur.Val.(int) &lt; num {\n            // Удаляемый узел находится в правом поддереве\n            cur = cur.Right\n        } else {\n            // Удаляемый узел находится в левом поддереве\n            cur = cur.Left\n        }\n    }\n    // Если узел для удаления отсутствует, сразу вернуть\n    if cur == nil {\n        return\n    }\n    // Число дочерних узлов равно 0 или 1\n    if cur.Left == nil || cur.Right == nil {\n        var child *TreeNode = nil\n        // Извлечь дочерний узел удаляемого узла\n        if cur.Left != nil {\n            child = cur.Left\n        } else {\n            child = cur.Right\n        }\n        // Удалить узел cur\n        if cur != bst.root {\n            if pre.Left == cur {\n                pre.Left = child\n            } else {\n                pre.Right = child\n            }\n        } else {\n            // Если удаляемый узел является корнем, заново назначить корневой узел\n            bst.root = child\n        }\n        // Число дочерних узлов равно 2\n    } else {\n        // Получить следующий после cur узел в симметричном обходе для удаляемого узла\n        tmp := cur.Right\n        for tmp.Left != nil {\n            tmp = tmp.Left\n        }\n        // Рекурсивно удалить узел tmp\n        bst.remove(tmp.Val.(int))\n        // Перезаписать cur значением tmp\n        cur.Val = tmp.Val\n    }\n}\n</code></pre> binary_search_tree.swift<pre><code>/* Удаление узла */\nfunc remove(num: Int) {\n    // Если дерево пусто, сразу вернуть\n    if root == nil {\n        return\n    }\n    var cur = root\n    var pre: TreeNode?\n    // Искать в цикле и выйти после прохода за листовой узел\n    while cur != nil {\n        // Найти узел для удаления и выйти из цикла\n        if cur!.val == num {\n            break\n        }\n        pre = cur\n        // Узел для удаления находится в правом поддереве cur\n        if cur!.val &lt; num {\n            cur = cur?.right\n        }\n        // Узел для удаления находится в левом поддереве cur\n        else {\n            cur = cur?.left\n        }\n    }\n    // Если узел для удаления отсутствует, сразу вернуть\n    if cur == nil {\n        return\n    }\n    // Число дочерних узлов = 0 или 1\n    if cur?.left == nil || cur?.right == nil {\n        // Когда число дочерних узлов = 0 / 1, child = null / этот дочерний узел\n        let child = cur?.left ?? cur?.right\n        // Удалить узел cur\n        if cur !== root {\n            if pre?.left === cur {\n                pre?.left = child\n            } else {\n                pre?.right = child\n            }\n        } else {\n            // Если удаляемый узел является корнем, заново назначить корневой узел\n            root = child\n        }\n    }\n    // Число дочерних узлов = 2\n    else {\n        // Получить следующий узел после cur в симметричном обходе\n        var tmp = cur?.right\n        while tmp?.left != nil {\n            tmp = tmp?.left\n        }\n        // Рекурсивно удалить узел tmp\n        remove(num: tmp!.val)\n        // Перезаписать cur значением tmp\n        cur?.val = tmp!.val\n    }\n}\n</code></pre> binary_search_tree.js<pre><code>/* Удаление узла */\nremove(num) {\n    // Если дерево пусто, сразу вернуть\n    if (this.root === null) return;\n    let cur = this.root,\n        pre = null;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur !== null) {\n        // Найти узел для удаления и выйти из цикла\n        if (cur.val === num) break;\n        pre = cur;\n        // Узел для удаления находится в правом поддереве cur\n        if (cur.val &lt; num) cur = cur.right;\n        // Узел для удаления находится в левом поддереве cur\n        else cur = cur.left;\n    }\n    // Если узел для удаления отсутствует, сразу вернуть\n    if (cur === null) return;\n    // Число дочерних узлов = 0 или 1\n    if (cur.left === null || cur.right === null) {\n        // Когда число дочерних узлов = 0 / 1, child = null / этот дочерний узел\n        const child = cur.left !== null ? cur.left : cur.right;\n        // Удалить узел cur\n        if (cur !== this.root) {\n            if (pre.left === cur) pre.left = child;\n            else pre.right = child;\n        } else {\n            // Если удаляемый узел является корнем, заново назначить корневой узел\n            this.root = child;\n        }\n    }\n    // Число дочерних узлов = 2\n    else {\n        // Получить следующий узел после cur в симметричном обходе\n        let tmp = cur.right;\n        while (tmp.left !== null) {\n            tmp = tmp.left;\n        }\n        // Рекурсивно удалить узел tmp\n        this.remove(tmp.val);\n        // Перезаписать cur значением tmp\n        cur.val = tmp.val;\n    }\n}\n</code></pre> binary_search_tree.ts<pre><code>/* Удаление узла */\nremove(num: number): void {\n    // Если дерево пусто, сразу вернуть\n    if (this.root === null) return;\n    let cur: TreeNode | null = this.root,\n        pre: TreeNode | null = null;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur !== null) {\n        // Найти узел для удаления и выйти из цикла\n        if (cur.val === num) break;\n        pre = cur;\n        // Узел для удаления находится в правом поддереве cur\n        if (cur.val &lt; num) cur = cur.right;\n        // Узел для удаления находится в левом поддереве cur\n        else cur = cur.left;\n    }\n    // Если узел для удаления отсутствует, сразу вернуть\n    if (cur === null) return;\n    // Число дочерних узлов = 0 или 1\n    if (cur.left === null || cur.right === null) {\n        // Когда число дочерних узлов = 0 / 1, child = null / этот дочерний узел\n        const child: TreeNode | null =\n            cur.left !== null ? cur.left : cur.right;\n        // Удалить узел cur\n        if (cur !== this.root) {\n            if (pre!.left === cur) pre!.left = child;\n            else pre!.right = child;\n        } else {\n            // Если удаляемый узел является корнем, заново назначить корневой узел\n            this.root = child;\n        }\n    }\n    // Число дочерних узлов = 2\n    else {\n        // Получить следующий узел после cur в симметричном обходе\n        let tmp: TreeNode | null = cur.right;\n        while (tmp!.left !== null) {\n            tmp = tmp!.left;\n        }\n        // Рекурсивно удалить узел tmp\n        this.remove(tmp!.val);\n        // Перезаписать cur значением tmp\n        cur.val = tmp!.val;\n    }\n}\n</code></pre> binary_search_tree.dart<pre><code>/* Удаление узла */\nvoid remove(int _num) {\n  // Если дерево пусто, сразу вернуть\n  if (_root == null) return;\n  TreeNode? cur = _root;\n  TreeNode? pre = null;\n  // Искать в цикле и выйти после прохода за листовой узел\n  while (cur != null) {\n    // Найти узел для удаления и выйти из цикла\n    if (cur.val == _num) break;\n    pre = cur;\n    // Узел для удаления находится в правом поддереве cur\n    if (cur.val &lt; _num)\n      cur = cur.right;\n    // Узел для удаления находится в левом поддереве cur\n    else\n      cur = cur.left;\n  }\n  // Если удаляемого узла нет, сразу вернуть\n  if (cur == null) return;\n  // Число дочерних узлов = 0 или 1\n  if (cur.left == null || cur.right == null) {\n    // Когда число дочерних узлов = 0 / 1, child = null / этот дочерний узел\n    TreeNode? child = cur.left ?? cur.right;\n    // Удалить узел cur\n    if (cur != _root) {\n      if (pre!.left == cur)\n        pre.left = child;\n      else\n        pre.right = child;\n    } else {\n      // Если удаляемый узел является корнем, заново назначить корневой узел\n      _root = child;\n    }\n  } else {\n    // Число дочерних узлов = 2\n    // Получить следующий узел после cur в симметричном обходе\n    TreeNode? tmp = cur.right;\n    while (tmp!.left != null) {\n      tmp = tmp.left;\n    }\n    // Рекурсивно удалить узел tmp\n    remove(tmp.val);\n    // Перезаписать cur значением tmp\n    cur.val = tmp.val;\n  }\n}\n</code></pre> binary_search_tree.rs<pre><code>/* Удаление узла */\npub fn remove(&amp;mut self, num: i32) {\n    // Если дерево пусто, сразу вернуть\n    if self.root.is_none() {\n        return;\n    }\n    let mut cur = self.root.clone();\n    let mut pre = None;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while let Some(node) = cur.clone() {\n        match num.cmp(&amp;node.borrow().val) {\n            // Найти узел для удаления и выйти из цикла\n            Ordering::Equal =&gt; break,\n            // Узел для удаления находится в правом поддереве cur\n            Ordering::Greater =&gt; {\n                pre = cur.clone();\n                cur = node.borrow().right.clone();\n            }\n            // Узел для удаления находится в левом поддереве cur\n            Ordering::Less =&gt; {\n                pre = cur.clone();\n                cur = node.borrow().left.clone();\n            }\n        }\n    }\n    // Если узел для удаления отсутствует, сразу вернуть\n    if cur.is_none() {\n        return;\n    }\n    let cur = cur.unwrap();\n    let (left_child, right_child) = (cur.borrow().left.clone(), cur.borrow().right.clone());\n    match (left_child.clone(), right_child.clone()) {\n        // Число дочерних узлов = 0 или 1\n        (None, None) | (Some(_), None) | (None, Some(_)) =&gt; {\n            // Когда число дочерних узлов = 0 / 1, child = nullptr / этот дочерний узел\n            let child = left_child.or(right_child);\n            let pre = pre.unwrap();\n            // Удалить узел cur\n            if !Rc::ptr_eq(&amp;cur, self.root.as_ref().unwrap()) {\n                let left = pre.borrow().left.clone();\n                if left.is_some() &amp;&amp; Rc::ptr_eq(left.as_ref().unwrap(), &amp;cur) {\n                    pre.borrow_mut().left = child;\n                } else {\n                    pre.borrow_mut().right = child;\n                }\n            } else {\n                // Если удаляемый узел является корнем, заново назначить корневой узел\n                self.root = child;\n            }\n        }\n        // Число дочерних узлов = 2\n        (Some(_), Some(_)) =&gt; {\n            // Получить следующий узел после cur в симметричном обходе\n            let mut tmp = cur.borrow().right.clone();\n            while let Some(node) = tmp.clone() {\n                if node.borrow().left.is_some() {\n                    tmp = node.borrow().left.clone();\n                } else {\n                    break;\n                }\n            }\n            let tmp_val = tmp.unwrap().borrow().val;\n            // Рекурсивно удалить узел tmp\n            self.remove(tmp_val);\n            // Перезаписать cur значением tmp\n            cur.borrow_mut().val = tmp_val;\n        }\n    }\n}\n</code></pre> binary_search_tree.c<pre><code>/* Удаление узла */\n// Из-за подключения stdio.h здесь нельзя использовать ключевое слово remove\nvoid removeItem(BinarySearchTree *bst, int num) {\n    // Если дерево пусто, сразу вернуть\n    if (bst-&gt;root == NULL)\n        return;\n    TreeNode *cur = bst-&gt;root, *pre = NULL;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != NULL) {\n        // Найти узел для удаления и выйти из цикла\n        if (cur-&gt;val == num)\n            break;\n        pre = cur;\n        if (cur-&gt;val &lt; num) {\n            // Удаляемый узел находится в правом поддереве root\n            cur = cur-&gt;right;\n        } else {\n            // Удаляемый узел находится в левом поддереве root\n            cur = cur-&gt;left;\n        }\n    }\n    // Если узел для удаления отсутствует, сразу вернуть\n    if (cur == NULL)\n        return;\n    // Проверить, есть ли дочерние узлы у удаляемого узла\n    if (cur-&gt;left == NULL || cur-&gt;right == NULL) {\n        /* Число дочерних узлов = 0 или 1 */\n        // Когда число дочерних узлов = 0 / 1, child = nullptr / этот дочерний узел\n        TreeNode *child = cur-&gt;left != NULL ? cur-&gt;left : cur-&gt;right;\n        // Удалить узел cur\n        if (pre-&gt;left == cur) {\n            pre-&gt;left = child;\n        } else {\n            pre-&gt;right = child;\n        }\n        // Освободить память\n        free(cur);\n    } else {\n        /* Число дочерних узлов = 2 */\n        // Получить следующий узел после cur в симметричном обходе\n        TreeNode *tmp = cur-&gt;right;\n        while (tmp-&gt;left != NULL) {\n            tmp = tmp-&gt;left;\n        }\n        int tmpVal = tmp-&gt;val;\n        // Рекурсивно удалить узел tmp\n        removeItem(bst, tmp-&gt;val);\n        // Перезаписать cur значением tmp\n        cur-&gt;val = tmpVal;\n    }\n}\n</code></pre> binary_search_tree.kt<pre><code>/* Удаление узла */\nfun remove(num: Int) {\n    // Если дерево пусто, сразу вернуть\n    if (root == null)\n        return\n    var cur = root\n    var pre: TreeNode? = null\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != null) {\n        // Найти узел для удаления и выйти из цикла\n        if (cur._val == num)\n            break\n        pre = cur\n        // Узел для удаления находится в правом поддереве cur\n        cur = if (cur._val &lt; num)\n            cur.right\n        // Узел для удаления находится в левом поддереве cur\n        else\n            cur.left\n    }\n    // Если узел для удаления отсутствует, сразу вернуть\n    if (cur == null)\n        return\n    // Число дочерних узлов = 0 или 1\n    if (cur.left == null || cur.right == null) {\n        // Когда число дочерних узлов = 0 / 1, child = null / этот дочерний узел\n        val child = if (cur.left != null)\n            cur.left\n        else\n            cur.right\n        // Удалить узел cur\n        if (cur != root) {\n            if (pre!!.left == cur)\n                pre.left = child\n            else\n                pre.right = child\n        } else {\n            // Если удаляемый узел является корнем, заново назначить корневой узел\n            root = child\n        }\n        // Число дочерних узлов = 2\n    } else {\n        // Получить следующий узел после cur в симметричном обходе\n        var tmp = cur.right\n        while (tmp!!.left != null) {\n            tmp = tmp.left\n        }\n        // Рекурсивно удалить узел tmp\n        remove(tmp._val)\n        // Перезаписать cur значением tmp\n        cur._val = tmp._val\n    }\n}\n</code></pre> binary_search_tree.rb<pre><code>### Удаление узла ###\ndef remove(num)\n  # Если дерево пусто, сразу вернуть\n  return if @root.nil?\n\n  # Искать в цикле и выйти после прохода за листовой узел\n  cur, pre = @root, nil\n  while !cur.nil?\n    # Найти узел для удаления и выйти из цикла\n    break if cur.val == num\n\n    pre = cur\n    # Узел для удаления находится в правом поддереве cur\n    if cur.val &lt; num\n      cur = cur.right\n    # Узел для удаления находится в левом поддереве cur\n    else\n      cur = cur.left\n    end\n  end\n  # Если узел для удаления отсутствует, сразу вернуть\n  return if cur.nil?\n\n  # Число дочерних узлов = 0 или 1\n  if cur.left.nil? || cur.right.nil?\n    # Когда число дочерних узлов = 0 / 1, child = null / этот дочерний узел\n    child = cur.left || cur.right\n    # Удалить узел cur\n    if cur != @root\n      if pre.left == cur\n        pre.left = child\n      else\n        pre.right = child\n      end\n    else\n      # Если удаляемый узел является корнем, заново назначить корневой узел\n      @root = child\n    end\n  # Число дочерних узлов = 2\n  else\n    # Получить следующий узел после cur в симметричном обходе\n    tmp = cur.right\n    while !tmp.left.nil?\n      tmp = tmp.left\n    end\n    # Рекурсивно удалить узел tmp\n    remove(tmp.val)\n    # Перезаписать cur значением tmp\n    cur.val = tmp.val\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 7. Дерево","7.4 &nbsp; Двоичное дерево поиска"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#4","level":3,"title":"4.   Упорядоченность симметричного обхода","text":"<p>Как показано на рисунке 7-22, симметричный обход двоичного дерева следует порядку \"лево \\(\\rightarrow\\) корень \\(\\rightarrow\\) право\", а двоичное дерево поиска удовлетворяет соотношению \"левый дочерний узел \\(&lt;\\) корень \\(&lt;\\) правый дочерний узел\".</p> <p>Это означает, что при симметричном обходе двоичного дерева поиска мы всегда сначала будем посещать следующий минимальный узел, и отсюда получается важное свойство: последовательность симметричного обхода двоичного дерева поиска является возрастающей.</p> <p>Используя это свойство возрастающей последовательности симметричного обхода, мы можем получить отсортированные данные из двоичного дерева поиска всего за \\(O(n)\\) времени, без дополнительной сортировки, что очень эффективно.</p> <p></p> <p> Рисунок 7-22   Последовательность симметричного обхода двоичного дерева поиска </p>","path":["Глава 7. Дерево","7.4 &nbsp; Двоичное дерево поиска"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#742","level":2,"title":"7.4.2   Эффективность двоичного дерева поиска","text":"<p>Для заданного набора данных можно рассмотреть хранение либо в массиве, либо в двоичном дереве поиска. Из таблицы ниже видно, что временная сложность операций двоичного дерева поиска имеет логарифмический порядок, поэтому его производительность стабильна и высока. Только в сценариях с очень частыми вставками и редкими поисками и удалениями массив может быть эффективнее, чем двоичное дерево поиска.</p> <p> Таблица 7-2   Сравнение эффективности массива и дерева поиска </p> Неупорядоченный массив Двоичное дерево поиска Поиск элемента \\(O(n)\\) \\(O(\\log n)\\) Вставка элемента \\(O(1)\\) \\(O(\\log n)\\) Удаление элемента \\(O(n)\\) \\(O(\\log n)\\) <p>В идеальном случае двоичное дерево поиска является \"сбалансированным\", и тогда любой узел можно найти за \\(\\log n\\) итераций.</p> <p>Однако если в двоичное дерево поиска непрерывно вставлять и удалять узлы, оно может выродиться в связный список, как показано на рисунке 7-23. Тогда временная сложность различных операций тоже вырождается до \\(O(n)\\) .</p> <p></p> <p> Рисунок 7-23   Деградация двоичного дерева поиска </p>","path":["Глава 7. Дерево","7.4 &nbsp; Двоичное дерево поиска"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#743","level":2,"title":"7.4.3   Типичные применения двоичного дерева поиска","text":"<ul> <li>Используется как многоуровневый индекс в системах, обеспечивая эффективный поиск, вставку и удаление.</li> <li>Служит базовой структурой данных для некоторых поисковых алгоритмов.</li> <li>Применяется для хранения потока данных в отсортированном состоянии.</li> </ul>","path":["Глава 7. Дерево","7.4 &nbsp; Двоичное дерево поиска"],"tags":[]},{"location":"chapter_tree/binary_tree/","level":1,"title":"7.1   Двоичное дерево","text":"<p>Двоичное дерево (binary tree) - это нелинейная структура данных, представляющая отношения порождения между \"предками\" и \"потомками\" и отражающая логику \"разделения надвое\". Подобно связному списку, базовой единицей двоичного дерева является узел; каждый узел содержит значение, ссылку на левого дочернего узла и ссылку на правого дочернего узла.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>class TreeNode:\n    \"\"\"Класс узла двоичного дерева\"\"\"\n    def __init__(self, val: int):\n        self.val: int = val                # Значение узла\n        self.left: TreeNode | None = None  # Ссылка на левого дочернего узла\n        self.right: TreeNode | None = None # Ссылка на правого дочернего узла\n</code></pre> <pre><code>/* Структура узла двоичного дерева */\nstruct TreeNode {\n    int val;          // Значение узла\n    TreeNode *left;   // Указатель на левого дочернего узла\n    TreeNode *right;  // Указатель на правого дочернего узла\n    TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}\n};\n</code></pre> <pre><code>/* Класс узла двоичного дерева */\nclass TreeNode {\n    int val;         // Значение узла\n    TreeNode left;   // Ссылка на левого дочернего узла\n    TreeNode right;  // Ссылка на правого дочернего узла\n    TreeNode(int x) { val = x; }\n}\n</code></pre> <pre><code>/* Класс узла двоичного дерева */\nclass TreeNode(int? x) {\n    public int? val = x;    // Значение узла\n    public TreeNode? left;  // Ссылка на левого дочернего узла\n    public TreeNode? right; // Ссылка на правого дочернего узла\n}\n</code></pre> <pre><code>/* Структура узла двоичного дерева */\ntype TreeNode struct {\n    Val   int\n    Left  *TreeNode\n    Right *TreeNode\n}\n/* Конструктор */\nfunc NewTreeNode(v int) *TreeNode {\n    return &amp;TreeNode{\n        Left:  nil, // Указатель на левого дочернего узла\n        Right: nil, // Указатель на правого дочернего узла\n        Val:   v,   // Значение узла\n    }\n}\n</code></pre> <pre><code>/* Класс узла двоичного дерева */\nclass TreeNode {\n    var val: Int // Значение узла\n    var left: TreeNode? // Ссылка на левого дочернего узла\n    var right: TreeNode? // Ссылка на правого дочернего узла\n\n    init(x: Int) {\n        val = x\n    }\n}\n</code></pre> <pre><code>/* Класс узла двоичного дерева */\nclass TreeNode {\n    val; // Значение узла\n    left; // Указатель на левого дочернего узла\n    right; // Указатель на правого дочернего узла\n    constructor(val, left, right) {\n        this.val = val === undefined ? 0 : val;\n        this.left = left === undefined ? null : left;\n        this.right = right === undefined ? null : right;\n    }\n}\n</code></pre> <pre><code>/* Класс узла двоичного дерева */\nclass TreeNode {\n    val: number;\n    left: TreeNode | null;\n    right: TreeNode | null;\n\n    constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {\n        this.val = val === undefined ? 0 : val; // Значение узла\n        this.left = left === undefined ? null : left; // Ссылка на левого дочернего узла\n        this.right = right === undefined ? null : right; // Ссылка на правого дочернего узла\n    }\n}\n</code></pre> <pre><code>/* Класс узла двоичного дерева */\nclass TreeNode {\n  int val;         // Значение узла\n  TreeNode? left;  // Ссылка на левого дочернего узла\n  TreeNode? right; // Ссылка на правого дочернего узла\n  TreeNode(this.val, [this.left, this.right]);\n}\n</code></pre> <pre><code>use std::rc::Rc;\nuse std::cell::RefCell;\n\n/* Структура узла двоичного дерева */\nstruct TreeNode {\n    val: i32,                               // Значение узла\n    left: Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,    // Ссылка на левого дочернего узла\n    right: Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,   // Ссылка на правого дочернего узла\n}\n\nimpl TreeNode {\n    /* Конструктор */\n    fn new(val: i32) -&gt; Rc&lt;RefCell&lt;Self&gt;&gt; {\n        Rc::new(RefCell::new(Self {\n            val,\n            left: None,\n            right: None\n        }))\n    }\n}\n</code></pre> <pre><code>/* Структура узла двоичного дерева */\ntypedef struct TreeNode {\n    int val;                // Значение узла\n    int height;             // Высота узла\n    struct TreeNode *left;  // Указатель на левого дочернего узла\n    struct TreeNode *right; // Указатель на правого дочернего узла\n} TreeNode;\n\n/* Конструктор */\nTreeNode *newTreeNode(int val) {\n    TreeNode *node;\n\n    node = (TreeNode *)malloc(sizeof(TreeNode));\n    node-&gt;val = val;\n    node-&gt;height = 0;\n    node-&gt;left = NULL;\n    node-&gt;right = NULL;\n    return node;\n}\n</code></pre> <pre><code>/* Класс узла двоичного дерева */\nclass TreeNode(val _val: Int) {  // Значение узла\n    val left: TreeNode? = null   // Ссылка на левого дочернего узла\n    val right: TreeNode? = null  // Ссылка на правого дочернего узла\n}\n</code></pre> <pre><code>### Класс узла двоичного дерева ###\nclass TreeNode\n  attr_accessor :val    # Значение узла\n  attr_accessor :left   # Ссылка на левого дочернего узла\n  attr_accessor :right  # Ссылка на правого дочернего узла\n\n  def initialize(val)\n    @val = val\n  end\nend\n</code></pre> <p>Каждый узел имеет две ссылки (указателя), которые соответственно указывают на левого дочернего узла (left-child node) и правого дочернего узла (right-child node); данный узел называется родительским узлом (parent node) для этих двух дочерних узлов. Если задан некоторый узел двоичного дерева, то дерево, образованное его левым дочерним узлом и всеми узлами ниже него, называется левым поддеревом (left subtree) этого узла; аналогично определяется правое поддерево (right subtree).</p> <p>В двоичном дереве, кроме листовых узлов, все остальные узлы содержат дочерние узлы и непустые поддеревья. Как показано на рисунке 7-1, если рассматривать \"узел 2\" как родительский, то его левым и правым дочерними узлами будут \"узел 4\" и \"узел 5\"; левое поддерево - это \"узел 4 и дерево ниже него\", а правое поддерево - это \"узел 5 и дерево ниже него\".</p> <p></p> <p> Рисунок 7-1   Родительский узел, дочерние узлы и поддеревья </p>","path":["Глава 7. Дерево","7.1 &nbsp; Двоичное дерево"],"tags":[]},{"location":"chapter_tree/binary_tree/#711","level":2,"title":"7.1.1   Распространенные термины двоичного дерева","text":"<p>Распространенные термины двоичного дерева показаны на рисунке 7-2.</p> <ul> <li>Корневой узел (root node): узел, расположенный на верхнем уровне двоичного дерева и не имеющий родительского узла.</li> <li>Листовой узел (leaf node): узел без дочерних узлов; оба его указателя направлены на <code>None</code> .</li> <li>Ребро (edge): отрезок, соединяющий два узла, то есть ссылка (указатель) между узлами.</li> <li>Уровень (level) узла: увеличивается сверху вниз; уровень корневого узла равен 1 .</li> <li>Степень (degree) узла: число дочерних узлов данного узла. В двоичном дереве возможны степени 0, 1, 2 .</li> <li>Высота (height) двоичного дерева: число ребер от корневого узла до самого удаленного листового узла.</li> <li>Глубина (depth) узла: число ребер от корневого узла до данного узла.</li> <li>Высота (height) узла: число ребер от самого удаленного листового узла до данного узла.</li> </ul> <p></p> <p> Рисунок 7-2   Распространенные термины двоичного дерева </p> <p>Tip</p> <p>Обрати внимание: обычно под \"высотой\" и \"глубиной\" понимают \"число пройденных ребер\", но в некоторых задачах или учебниках их могут определять как \"число пройденных узлов\". В таком случае и высоту, и глубину нужно увеличить на 1 .</p>","path":["Глава 7. Дерево","7.1 &nbsp; Двоичное дерево"],"tags":[]},{"location":"chapter_tree/binary_tree/#712","level":2,"title":"7.1.2   Базовые операции двоичного дерева","text":"","path":["Глава 7. Дерево","7.1 &nbsp; Двоичное дерево"],"tags":[]},{"location":"chapter_tree/binary_tree/#1","level":3,"title":"1.   Инициализация двоичного дерева","text":"<p>Как и в связном списке, сначала инициализируются узлы, а затем между ними строятся ссылки (указатели).</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_tree.py<pre><code># Инициализация двоичного дерева\n# Инициализация узлов\nn1 = TreeNode(val=1)\nn2 = TreeNode(val=2)\nn3 = TreeNode(val=3)\nn4 = TreeNode(val=4)\nn5 = TreeNode(val=5)\n# Построение ссылок (указателей) между узлами\nn1.left = n2\nn1.right = n3\nn2.left = n4\nn2.right = n5\n</code></pre> binary_tree.cpp<pre><code>/* Инициализация двоичного дерева */\n// Инициализация узлов\nTreeNode* n1 = new TreeNode(1);\nTreeNode* n2 = new TreeNode(2);\nTreeNode* n3 = new TreeNode(3);\nTreeNode* n4 = new TreeNode(4);\nTreeNode* n5 = new TreeNode(5);\n// Построение ссылок (указателей) между узлами\nn1-&gt;left = n2;\nn1-&gt;right = n3;\nn2-&gt;left = n4;\nn2-&gt;right = n5;\n</code></pre> binary_tree.java<pre><code>// Инициализация узлов\nTreeNode n1 = new TreeNode(1);\nTreeNode n2 = new TreeNode(2);\nTreeNode n3 = new TreeNode(3);\nTreeNode n4 = new TreeNode(4);\nTreeNode n5 = new TreeNode(5);\n// Построение ссылок (указателей) между узлами\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.cs<pre><code>/* Инициализация двоичного дерева */\n// Инициализация узлов\nTreeNode n1 = new(1);\nTreeNode n2 = new(2);\nTreeNode n3 = new(3);\nTreeNode n4 = new(4);\nTreeNode n5 = new(5);\n// Построение ссылок (указателей) между узлами\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.go<pre><code>/* Инициализация двоичного дерева */\n// Инициализация узлов\nn1 := NewTreeNode(1)\nn2 := NewTreeNode(2)\nn3 := NewTreeNode(3)\nn4 := NewTreeNode(4)\nn5 := NewTreeNode(5)\n// Построение ссылок (указателей) между узлами\nn1.Left = n2\nn1.Right = n3\nn2.Left = n4\nn2.Right = n5\n</code></pre> binary_tree.swift<pre><code>// Инициализация узлов\nlet n1 = TreeNode(x: 1)\nlet n2 = TreeNode(x: 2)\nlet n3 = TreeNode(x: 3)\nlet n4 = TreeNode(x: 4)\nlet n5 = TreeNode(x: 5)\n// Построение ссылок (указателей) между узлами\nn1.left = n2\nn1.right = n3\nn2.left = n4\nn2.right = n5\n</code></pre> binary_tree.js<pre><code>/* Инициализация двоичного дерева */\n// Инициализация узлов\nlet n1 = new TreeNode(1),\n    n2 = new TreeNode(2),\n    n3 = new TreeNode(3),\n    n4 = new TreeNode(4),\n    n5 = new TreeNode(5);\n// Построение ссылок (указателей) между узлами\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.ts<pre><code>/* Инициализация двоичного дерева */\n// Инициализация узлов\nlet n1 = new TreeNode(1),\n    n2 = new TreeNode(2),\n    n3 = new TreeNode(3),\n    n4 = new TreeNode(4),\n    n5 = new TreeNode(5);\n// Построение ссылок (указателей) между узлами\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.dart<pre><code>/* Инициализация двоичного дерева */\n// Инициализация узлов\nTreeNode n1 = new TreeNode(1);\nTreeNode n2 = new TreeNode(2);\nTreeNode n3 = new TreeNode(3);\nTreeNode n4 = new TreeNode(4);\nTreeNode n5 = new TreeNode(5);\n// Построение ссылок (указателей) между узлами\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.rs<pre><code>// Инициализация узлов\nlet n1 = TreeNode::new(1);\nlet n2 = TreeNode::new(2);\nlet n3 = TreeNode::new(3);\nlet n4 = TreeNode::new(4);\nlet n5 = TreeNode::new(5);\n// Построение ссылок (указателей) между узлами\nn1.borrow_mut().left = Some(n2.clone());\nn1.borrow_mut().right = Some(n3);\nn2.borrow_mut().left = Some(n4);\nn2.borrow_mut().right = Some(n5);\n</code></pre> binary_tree.c<pre><code>/* Инициализация двоичного дерева */\n// Инициализация узлов\nTreeNode *n1 = newTreeNode(1);\nTreeNode *n2 = newTreeNode(2);\nTreeNode *n3 = newTreeNode(3);\nTreeNode *n4 = newTreeNode(4);\nTreeNode *n5 = newTreeNode(5);\n// Построение ссылок (указателей) между узлами\nn1-&gt;left = n2;\nn1-&gt;right = n3;\nn2-&gt;left = n4;\nn2-&gt;right = n5;\n</code></pre> binary_tree.kt<pre><code>// Инициализация узлов\nval n1 = TreeNode(1)\nval n2 = TreeNode(2)\nval n3 = TreeNode(3)\nval n4 = TreeNode(4)\nval n5 = TreeNode(5)\n// Построение ссылок (указателей) между узлами\nn1.left = n2\nn1.right = n3\nn2.left = n4\nn2.right = n5\n</code></pre> binary_tree.rb<pre><code># Инициализация двоичного дерева\n# Инициализация узлов\nn1 = TreeNode.new(1)\nn2 = TreeNode.new(2)\nn3 = TreeNode.new(3)\nn4 = TreeNode.new(4)\nn5 = TreeNode.new(5)\n# Построение ссылок (указателей) между узлами\nn1.left = n2\nn1.right = n3\nn2.left = n4\nn2.right = n5\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%D0%9A%D0%BB%D0%B0%D1%81%D1%81%20%D1%83%D0%B7%D0%BB%D0%B0%20%D0%B4%D0%B2%D0%BE%D0%B8%D1%87%D0%BD%D0%BE%D0%B3%D0%BE%20%D0%B4%D0%B5%D1%80%D0%B5%D0%B2%D0%B0%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%D0%97%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%83%D0%B7%D0%BB%D0%B0%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%D0%A1%D1%81%D1%8B%D0%BB%D0%BA%D0%B0%20%D0%BD%D0%B0%20%D0%BB%D0%B5%D0%B2%D1%8B%D0%B9%20%D0%B4%D0%BE%D1%87%D0%B5%D1%80%D0%BD%D0%B8%D0%B9%20%D1%83%D0%B7%D0%B5%D0%BB%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%23%20%D0%A1%D1%81%D1%8B%D0%BB%D0%BA%D0%B0%20%D0%BD%D0%B0%20%D0%BF%D1%80%D0%B0%D0%B2%D1%8B%D0%B9%20%D0%B4%D0%BE%D1%87%D0%B5%D1%80%D0%BD%D0%B8%D0%B9%20%D1%83%D0%B7%D0%B5%D0%BB%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D0%B4%D0%B2%D0%BE%D0%B8%D1%87%D0%BD%D0%BE%D0%B5%20%D0%B4%D0%B5%D1%80%D0%B5%D0%B2%D0%BE%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%83%D0%B7%D0%B5%D0%BB%0A%20%20%20%20n1%20%3D%20TreeNode%28val%3D1%29%0A%20%20%20%20n2%20%3D%20TreeNode%28val%3D2%29%0A%20%20%20%20n3%20%3D%20TreeNode%28val%3D3%29%0A%20%20%20%20n4%20%3D%20TreeNode%28val%3D4%29%0A%20%20%20%20n5%20%3D%20TreeNode%28val%3D5%29%0A%20%20%20%20%23%20%D0%9F%D0%BE%D1%81%D1%82%D1%80%D0%BE%D0%B8%D1%82%D1%8C%20%D1%81%D1%81%D1%8B%D0%BB%D0%BA%D0%B8%20%D0%BC%D0%B5%D0%B6%D0%B4%D1%83%20%D1%83%D0%B7%D0%BB%D0%B0%D0%BC%D0%B8%20%28%D1%83%D0%BA%D0%B0%D0%B7%D0%B0%D1%82%D0%B5%D0%BB%D0%B8%29%0A%20%20%20%20n1.left%20%3D%20n2%0A%20%20%20%20n1.right%20%3D%20n3%0A%20%20%20%20n2.left%20%3D%20n4%0A%20%20%20%20n2.right%20%3D%20n5&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 7. Дерево","7.1 &nbsp; Двоичное дерево"],"tags":[]},{"location":"chapter_tree/binary_tree/#2","level":3,"title":"2.   Вставка и удаление узлов","text":"<p>Как и в связном списке, вставка и удаление узлов в двоичном дереве могут выполняться через изменение указателей. На рисунке 7-3 приведен пример.</p> <p></p> <p> Рисунок 7-3   Вставка и удаление узлов в двоичном дереве </p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_tree.py<pre><code># Вставка и удаление узлов\np = TreeNode(0)\n# Вставить узел P между n1 -&gt; n2\nn1.left = p\np.left = n2\n# Удалить узел P\nn1.left = n2\n</code></pre> binary_tree.cpp<pre><code>/* Вставка и удаление узлов */\nTreeNode* P = new TreeNode(0);\n// Вставить узел P между n1 -&gt; n2\nn1-&gt;left = P;\nP-&gt;left = n2;\n// Удалить узел P\nn1-&gt;left = n2;\n// Освободить память\ndelete P;\n</code></pre> binary_tree.java<pre><code>TreeNode P = new TreeNode(0);\n// Вставить узел P между n1 -&gt; n2\nn1.left = P;\nP.left = n2;\n// Удалить узел P\nn1.left = n2;\n</code></pre> binary_tree.cs<pre><code>/* Вставка и удаление узлов */\nTreeNode P = new(0);\n// Вставить узел P между n1 -&gt; n2\nn1.left = P;\nP.left = n2;\n// Удалить узел P\nn1.left = n2;\n</code></pre> binary_tree.go<pre><code>/* Вставка и удаление узлов */\n// Вставить узел P между n1 -&gt; n2\np := NewTreeNode(0)\nn1.Left = p\np.Left = n2\n// Удалить узел P\nn1.Left = n2\n</code></pre> binary_tree.swift<pre><code>let P = TreeNode(x: 0)\n// Вставить узел P между n1 -&gt; n2\nn1.left = P\nP.left = n2\n// Удалить узел P\nn1.left = n2\n</code></pre> binary_tree.js<pre><code>/* Вставка и удаление узлов */\nlet P = new TreeNode(0);\n// Вставить узел P между n1 -&gt; n2\nn1.left = P;\nP.left = n2;\n// Удалить узел P\nn1.left = n2;\n</code></pre> binary_tree.ts<pre><code>/* Вставка и удаление узлов */\nconst P = new TreeNode(0);\n// Вставить узел P между n1 -&gt; n2\nn1.left = P;\nP.left = n2;\n// Удалить узел P\nn1.left = n2;\n</code></pre> binary_tree.dart<pre><code>/* Вставка и удаление узлов */\nTreeNode P = new TreeNode(0);\n// Вставить узел P между n1 -&gt; n2\nn1.left = P;\nP.left = n2;\n// Удалить узел P\nn1.left = n2;\n</code></pre> binary_tree.rs<pre><code>let p = TreeNode::new(0);\n// Вставить узел P между n1 -&gt; n2\nn1.borrow_mut().left = Some(p.clone());\np.borrow_mut().left = Some(n2.clone());\n// Удалить узел p\nn1.borrow_mut().left = Some(n2);\n</code></pre> binary_tree.c<pre><code>/* Вставка и удаление узлов */\nTreeNode *P = newTreeNode(0);\n// Вставить узел P между n1 -&gt; n2\nn1-&gt;left = P;\nP-&gt;left = n2;\n// Удалить узел P\nn1-&gt;left = n2;\n// Освободить память\nfree(P);\n</code></pre> binary_tree.kt<pre><code>val P = TreeNode(0)\n// Вставить узел P между n1 -&gt; n2\nn1.left = P\nP.left = n2\n// Удалить узел P\nn1.left = n2\n</code></pre> binary_tree.rb<pre><code># Вставка и удаление узлов\n_p = TreeNode.new(0)\n# Вставить узел _p между n1 -&gt; n2\nn1.left = _p\n_p.left = n2\n# Удалить узел\nn1.left = n2\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%D0%9A%D0%BB%D0%B0%D1%81%D1%81%20%D1%83%D0%B7%D0%BB%D0%B0%20%D0%B4%D0%B2%D0%BE%D0%B8%D1%87%D0%BD%D0%BE%D0%B3%D0%BE%20%D0%B4%D0%B5%D1%80%D0%B5%D0%B2%D0%B0%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%D0%97%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%83%D0%B7%D0%BB%D0%B0%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%D0%A1%D1%81%D1%8B%D0%BB%D0%BA%D0%B0%20%D0%BD%D0%B0%20%D0%BB%D0%B5%D0%B2%D1%8B%D0%B9%20%D0%B4%D0%BE%D1%87%D0%B5%D1%80%D0%BD%D0%B8%D0%B9%20%D1%83%D0%B7%D0%B5%D0%BB%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%23%20%D0%A1%D1%81%D1%8B%D0%BB%D0%BA%D0%B0%20%D0%BD%D0%B0%20%D0%BF%D1%80%D0%B0%D0%B2%D1%8B%D0%B9%20%D0%B4%D0%BE%D1%87%D0%B5%D1%80%D0%BD%D0%B8%D0%B9%20%D1%83%D0%B7%D0%B5%D0%BB%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D0%B4%D0%B2%D0%BE%D0%B8%D1%87%D0%BD%D0%BE%D0%B5%20%D0%B4%D0%B5%D1%80%D0%B5%D0%B2%D0%BE%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%83%D0%B7%D0%B5%D0%BB%0A%20%20%20%20n1%20%3D%20TreeNode%28val%3D1%29%0A%20%20%20%20n2%20%3D%20TreeNode%28val%3D2%29%0A%20%20%20%20n3%20%3D%20TreeNode%28val%3D3%29%0A%20%20%20%20n4%20%3D%20TreeNode%28val%3D4%29%0A%20%20%20%20n5%20%3D%20TreeNode%28val%3D5%29%0A%20%20%20%20%23%20%D0%9F%D0%BE%D1%81%D1%82%D1%80%D0%BE%D0%B8%D1%82%D1%8C%20%D1%81%D1%81%D1%8B%D0%BB%D0%BA%D0%B8%20%D0%BC%D0%B5%D0%B6%D0%B4%D1%83%20%D1%83%D0%B7%D0%BB%D0%B0%D0%BC%D0%B8%20%28%D1%83%D0%BA%D0%B0%D0%B7%D0%B0%D1%82%D0%B5%D0%BB%D0%B8%29%0A%20%20%20%20n1.left%20%3D%20n2%0A%20%20%20%20n1.right%20%3D%20n3%0A%20%20%20%20n2.left%20%3D%20n4%0A%20%20%20%20n2.right%20%3D%20n5%0A%0A%20%20%20%20%23%20%D0%92%D1%81%D1%82%D0%B0%D0%B2%D0%BA%D0%B0%20%D0%B8%20%D1%83%D0%B4%D0%B0%D0%BB%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%83%D0%B7%D0%BB%D0%BE%D0%B2%0A%20%20%20%20p%20%3D%20TreeNode%280%29%0A%20%20%20%20%23%20%D0%92%D1%81%D1%82%D0%B0%D0%B2%D0%B8%D1%82%D1%8C%20%D1%83%D0%B7%D0%B5%D0%BB%20P%20%D0%BC%D0%B5%D0%B6%D0%B4%D1%83%20n1%20-%3E%20n2%0A%20%20%20%20n1.left%20%3D%20p%0A%20%20%20%20p.left%20%3D%20n2%0A%20%20%20%20%23%20%D0%A3%D0%B4%D0%B0%D0%BB%D0%B8%D1%82%D1%8C%20%D1%83%D0%B7%D0%B5%D0%BB%20P%0A%20%20%20%20n1.left%20%3D%20n2&amp;cumulative=false&amp;curInstr=37&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p> <p>Tip</p> <p>Обрати внимание: вставка узла может изменить исходную логическую структуру двоичного дерева, а удаление узла обычно означает удаление этого узла вместе со всеми его поддеревьями. Поэтому в двоичном дереве операции вставки и удаления обычно являются частью более крупного набора операций, который и реализует осмысленное действие.</p>","path":["Глава 7. Дерево","7.1 &nbsp; Двоичное дерево"],"tags":[]},{"location":"chapter_tree/binary_tree/#713","level":2,"title":"7.1.3   Распространенные типы двоичных деревьев","text":"","path":["Глава 7. Дерево","7.1 &nbsp; Двоичное дерево"],"tags":[]},{"location":"chapter_tree/binary_tree/#1_1","level":3,"title":"1.   Идеальное двоичное дерево","text":"<p>Как показано на рисунке 7-4, идеальное двоичное дерево (perfect binary tree) полностью заполнено на всех уровнях. В идеальном двоичном дереве степень листовых узлов равна \\(0\\) , а у всех остальных узлов степень равна \\(2\\) ; если высота дерева равна \\(h\\) , то общее число узлов равно \\(2^{h+1} - 1\\) , что образует стандартную экспоненциальную зависимость и отражает часто встречающееся в природе явление клеточного деления.</p> <p>Tip</p> <p>Обрати внимание: в китайскоязычном сообществе идеальное двоичное дерево часто называют полностью заполненным двоичным деревом.</p> <p></p> <p> Рисунок 7-4   Идеальное двоичное дерево </p>","path":["Глава 7. Дерево","7.1 &nbsp; Двоичное дерево"],"tags":[]},{"location":"chapter_tree/binary_tree/#2_1","level":3,"title":"2.   Полное двоичное дерево","text":"<p>Как показано на рисунке 7-5, полное двоичное дерево (complete binary tree) допускает неполное заполнение только на самом нижнем уровне, причем узлы этого уровня должны непрерывно заполняться слева направо. Обрати внимание: идеальное двоичное дерево тоже является полным двоичным деревом.</p> <p></p> <p> Рисунок 7-5   Полное двоичное дерево </p>","path":["Глава 7. Дерево","7.1 &nbsp; Двоичное дерево"],"tags":[]},{"location":"chapter_tree/binary_tree/#3","level":3,"title":"3.   Строгое двоичное дерево","text":"<p>Как показано на рисунке 7-6, строгое двоичное дерево (full binary tree) имеет у всех нелистовых узлов ровно двух дочерних узлов.</p> <p></p> <p> Рисунок 7-6   Строгое двоичное дерево </p>","path":["Глава 7. Дерево","7.1 &nbsp; Двоичное дерево"],"tags":[]},{"location":"chapter_tree/binary_tree/#4","level":3,"title":"4.   Сбалансированное двоичное дерево","text":"<p>Как показано на рисунке 7-7, в сбалансированном двоичном дереве (balanced binary tree) для любого узла абсолютное значение разности высот левого и правого поддеревьев не превышает 1 .</p> <p></p> <p> Рисунок 7-7   Сбалансированное двоичное дерево </p>","path":["Глава 7. Дерево","7.1 &nbsp; Двоичное дерево"],"tags":[]},{"location":"chapter_tree/binary_tree/#714","level":2,"title":"7.1.4   Вырождение двоичного дерева","text":"<p>На рисунке 7-8 показаны идеальная структура двоичного дерева и вырожденная структура. Когда каждый уровень двоичного дерева полностью заполнен узлами, мы получаем \"идеальное двоичное дерево\"; когда же все узлы смещаются к одной стороне, двоичное дерево вырождается в \"связный список\".</p> <ul> <li>Идеальное двоичное дерево соответствует лучшему случаю и позволяет полностью раскрыть преимущества двоичного дерева с точки зрения \"разделяй и властвуй\".</li> <li>Связный список представляет противоположную крайность: все операции становятся линейными, а временная сложность деградирует до \\(O(n)\\) .</li> </ul> <p></p> <p> Рисунок 7-8   Лучший и худший случаи структуры двоичного дерева </p> <p>Как показано в таблице 7-1, в лучшем и худшем случаях число листовых узлов, общее число узлов, высота и другие характеристики двоичного дерева достигают максимума или минимума.</p> <p> Таблица 7-1   Лучший и худший случаи структуры двоичного дерева </p> Идеальное двоичное дерево Связный список Число узлов на уровне \\(i\\) \\(2^{i-1}\\) \\(1\\) Число листьев у дерева высоты \\(h\\) \\(2^h\\) \\(1\\) Общее число узлов у дерева высоты \\(h\\) \\(2^{h+1} - 1\\) \\(h + 1\\) Высота дерева с \\(n\\) узлами \\(\\log_2 (n+1) - 1\\) \\(n - 1\\)","path":["Глава 7. Дерево","7.1 &nbsp; Двоичное дерево"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/","level":1,"title":"7.2   Обход двоичного дерева","text":"<p>С точки зрения физической структуры дерево представляет собой разновидность структуры данных на основе связей, поэтому его обход выполняется через последовательный доступ к узлам по указателям. Однако дерево является нелинейной структурой данных, а значит, его обход сложнее, чем обход связного списка, и для него требуется использовать поисковые алгоритмы.</p> <p>К распространенным способам обхода двоичного дерева относятся обход по уровням, прямой обход, симметричный обход и обратный обход.</p>","path":["Глава 7. Дерево","7.2 &nbsp; Обход двоичного дерева"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/#721","level":2,"title":"7.2.1   Обход по уровням","text":"<p>Как показано на рисунке 7-9, обход по уровням (level-order traversal) проходит двоичное дерево сверху вниз по уровням и на каждом уровне посещает узлы слева направо.</p> <p>По своей сути обход по уровням относится к обходу в ширину (breadth-first traversal), также называемому поиском в ширину (breadth-first search, BFS); он отражает идею \"расширяться слой за слоем наружу\".</p> <p></p> <p> Рисунок 7-9   Обход двоичного дерева по уровням </p>","path":["Глава 7. Дерево","7.2 &nbsp; Обход двоичного дерева"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/#1","level":3,"title":"1.   Код реализации","text":"<p>Обход в ширину обычно реализуется с помощью \"очереди\". Очередь подчиняется правилу \"первым пришел - первым вышел\", а обход в ширину подчиняется правилу \"продвигаться по уровням\", поэтому стоящая за ними идея согласована. Код реализации приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_tree_bfs.py<pre><code>def level_order(root: TreeNode | None) -&gt; list[int]:\n    \"\"\"Обход в ширину\"\"\"\n    # Инициализировать очередь и добавить корневой узел\n    queue: deque[TreeNode] = deque()\n    queue.append(root)\n    # Инициализировать список для хранения последовательности обхода\n    res = []\n    while queue:\n        node: TreeNode = queue.popleft()  # Извлечение из очереди\n        res.append(node.val)  # Сохранить значение узла\n        if node.left is not None:\n            queue.append(node.left)  # Поместить левый дочерний узел в очередь\n        if node.right is not None:\n            queue.append(node.right)  # Поместить правый дочерний узел в очередь\n    return res\n</code></pre> binary_tree_bfs.cpp<pre><code>/* Обход в ширину */\nvector&lt;int&gt; levelOrder(TreeNode *root) {\n    // Инициализировать очередь и добавить корневой узел\n    queue&lt;TreeNode *&gt; queue;\n    queue.push(root);\n    // Инициализировать список для хранения последовательности обхода\n    vector&lt;int&gt; vec;\n    while (!queue.empty()) {\n        TreeNode *node = queue.front();\n        queue.pop();              // Извлечение из очереди\n        vec.push_back(node-&gt;val); // Сохранить значение узла\n        if (node-&gt;left != nullptr)\n            queue.push(node-&gt;left); // Поместить левый дочерний узел в очередь\n        if (node-&gt;right != nullptr)\n            queue.push(node-&gt;right); // Поместить правый дочерний узел в очередь\n    }\n    return vec;\n}\n</code></pre> binary_tree_bfs.java<pre><code>/* Обход в ширину */\nList&lt;Integer&gt; levelOrder(TreeNode root) {\n    // Инициализировать очередь и добавить корневой узел\n    Queue&lt;TreeNode&gt; queue = new LinkedList&lt;&gt;();\n    queue.add(root);\n    // Инициализировать список для хранения последовательности обхода\n    List&lt;Integer&gt; list = new ArrayList&lt;&gt;();\n    while (!queue.isEmpty()) {\n        TreeNode node = queue.poll(); // Извлечение из очереди\n        list.add(node.val);           // Сохранить значение узла\n        if (node.left != null)\n            queue.offer(node.left);   // Поместить левый дочерний узел в очередь\n        if (node.right != null)\n            queue.offer(node.right);  // Поместить правый дочерний узел в очередь\n    }\n    return list;\n}\n</code></pre> binary_tree_bfs.cs<pre><code>/* Обход в ширину */\nList&lt;int&gt; LevelOrder(TreeNode root) {\n    // Инициализировать очередь и добавить корневой узел\n    Queue&lt;TreeNode&gt; queue = new();\n    queue.Enqueue(root);\n    // Инициализировать список для хранения последовательности обхода\n    List&lt;int&gt; list = [];\n    while (queue.Count != 0) {\n        TreeNode node = queue.Dequeue(); // Извлечение из очереди\n        list.Add(node.val!.Value);       // Сохранить значение узла\n        if (node.left != null)\n            queue.Enqueue(node.left);    // Поместить левый дочерний узел в очередь\n        if (node.right != null)\n            queue.Enqueue(node.right);   // Поместить правый дочерний узел в очередь\n    }\n    return list;\n}\n</code></pre> binary_tree_bfs.go<pre><code>/* Обход в ширину */\nfunc levelOrder(root *TreeNode) []any {\n    // Инициализировать очередь и добавить корневой узел\n    queue := list.New()\n    queue.PushBack(root)\n    // Инициализировать срез для хранения последовательности обхода\n    nums := make([]any, 0)\n    for queue.Len() &gt; 0 {\n        // Извлечение из очереди\n        node := queue.Remove(queue.Front()).(*TreeNode)\n        // Сохранить значение узла\n        nums = append(nums, node.Val)\n        if node.Left != nil {\n            // Поместить левый дочерний узел в очередь\n            queue.PushBack(node.Left)\n        }\n        if node.Right != nil {\n            // Поместить правый дочерний узел в очередь\n            queue.PushBack(node.Right)\n        }\n    }\n    return nums\n}\n</code></pre> binary_tree_bfs.swift<pre><code>/* Обход в ширину */\nfunc levelOrder(root: TreeNode) -&gt; [Int] {\n    // Инициализировать очередь и добавить корневой узел\n    var queue: [TreeNode] = [root]\n    // Инициализировать список для хранения последовательности обхода\n    var list: [Int] = []\n    while !queue.isEmpty {\n        let node = queue.removeFirst() // Извлечение из очереди\n        list.append(node.val) // Сохранить значение узла\n        if let left = node.left {\n            queue.append(left) // Поместить левый дочерний узел в очередь\n        }\n        if let right = node.right {\n            queue.append(right) // Поместить правый дочерний узел в очередь\n        }\n    }\n    return list\n}\n</code></pre> binary_tree_bfs.js<pre><code>/* Обход в ширину */\nfunction levelOrder(root) {\n    // Инициализировать очередь и добавить корневой узел\n    const queue = [root];\n    // Инициализировать список для хранения последовательности обхода\n    const list = [];\n    while (queue.length) {\n        let node = queue.shift(); // Извлечение из очереди\n        list.push(node.val); // Сохранить значение узла\n        if (node.left) queue.push(node.left); // Поместить левый дочерний узел в очередь\n        if (node.right) queue.push(node.right); // Поместить правый дочерний узел в очередь\n    }\n    return list;\n}\n</code></pre> binary_tree_bfs.ts<pre><code>/* Обход в ширину */\nfunction levelOrder(root: TreeNode | null): number[] {\n    // Инициализировать очередь и добавить корневой узел\n    const queue = [root];\n    // Инициализировать список для хранения последовательности обхода\n    const list: number[] = [];\n    while (queue.length) {\n        let node = queue.shift() as TreeNode; // Извлечение из очереди\n        list.push(node.val); // Сохранить значение узла\n        if (node.left) {\n            queue.push(node.left); // Поместить левый дочерний узел в очередь\n        }\n        if (node.right) {\n            queue.push(node.right); // Поместить правый дочерний узел в очередь\n        }\n    }\n    return list;\n}\n</code></pre> binary_tree_bfs.dart<pre><code>/* Обход в ширину */\nList&lt;int&gt; levelOrder(TreeNode? root) {\n  // Инициализировать очередь и добавить корневой узел\n  Queue&lt;TreeNode?&gt; queue = Queue();\n  queue.add(root);\n  // Инициализировать список для хранения последовательности обхода\n  List&lt;int&gt; res = [];\n  while (queue.isNotEmpty) {\n    TreeNode? node = queue.removeFirst(); // Извлечение из очереди\n    res.add(node!.val); // Сохранить значение узла\n    if (node.left != null) queue.add(node.left); // Поместить левый дочерний узел в очередь\n    if (node.right != null) queue.add(node.right); // Поместить правый дочерний узел в очередь\n  }\n  return res;\n}\n</code></pre> binary_tree_bfs.rs<pre><code>/* Обход в ширину */\nfn level_order(root: &amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;) -&gt; Vec&lt;i32&gt; {\n    // Инициализировать очередь и добавить корневой узел\n    let mut que = VecDeque::new();\n    que.push_back(root.clone());\n    // Инициализировать список для хранения последовательности обхода\n    let mut vec = Vec::new();\n\n    while let Some(node) = que.pop_front() {\n        // Извлечение из очереди\n        vec.push(node.borrow().val); // Сохранить значение узла\n        if let Some(left) = node.borrow().left.as_ref() {\n            que.push_back(left.clone()); // Поместить левый дочерний узел в очередь\n        }\n        if let Some(right) = node.borrow().right.as_ref() {\n            que.push_back(right.clone()); // Поместить правый дочерний узел в очередь\n        };\n    }\n    vec\n}\n</code></pre> binary_tree_bfs.c<pre><code>/* Обход в ширину */\nint *levelOrder(TreeNode *root, int *size) {\n    /* Вспомогательная очередь */\n    int front, rear;\n    int index, *arr;\n    TreeNode *node;\n    TreeNode **queue;\n\n    /* Вспомогательная очередь */\n    queue = (TreeNode **)malloc(sizeof(TreeNode *) * MAX_SIZE);\n    // Указатель очереди\n    front = 0, rear = 0;\n    // Добавить корневой узел\n    queue[rear++] = root;\n    // Инициализировать список для хранения последовательности обхода\n    /* Вспомогательный массив */\n    arr = (int *)malloc(sizeof(int) * MAX_SIZE);\n    // Указатель на массив\n    index = 0;\n    while (front &lt; rear) {\n        // Извлечение из очереди\n        node = queue[front++];\n        // Сохранить значение узла\n        arr[index++] = node-&gt;val;\n        if (node-&gt;left != NULL) {\n            // Поместить левый дочерний узел в очередь\n            queue[rear++] = node-&gt;left;\n        }\n        if (node-&gt;right != NULL) {\n            // Поместить правый дочерний узел в очередь\n            queue[rear++] = node-&gt;right;\n        }\n    }\n    // Обновить значение длины массива\n    *size = index;\n    arr = realloc(arr, sizeof(int) * (*size));\n\n    // Освободить память вспомогательного массива\n    free(queue);\n    return arr;\n}\n</code></pre> binary_tree_bfs.kt<pre><code>/* Обход в ширину */\nfun levelOrder(root: TreeNode?): MutableList&lt;Int&gt; {\n    // Инициализировать очередь и добавить корневой узел\n    val queue = LinkedList&lt;TreeNode?&gt;()\n    queue.add(root)\n    // Инициализировать список для хранения последовательности обхода\n    val list = mutableListOf&lt;Int&gt;()\n    while (queue.isNotEmpty()) {\n        val node = queue.poll()      // Извлечение из очереди\n        list.add(node?._val!!)       // Сохранить значение узла\n        if (node.left != null)\n            queue.offer(node.left)   // Поместить левый дочерний узел в очередь\n        if (node.right != null)\n            queue.offer(node.right)  // Поместить правый дочерний узел в очередь\n    }\n    return list\n}\n</code></pre> binary_tree_bfs.rb<pre><code>### Обход в ширину ###\ndef level_order(root)\n  # Инициализировать очередь и добавить корневой узел\n  queue = [root]\n  # Инициализировать список для хранения последовательности обхода\n  res = []\n  while !queue.empty?\n    node = queue.shift # Извлечение из очереди\n    res &lt;&lt; node.val # Сохранить значение узла\n    queue &lt;&lt; node.left unless node.left.nil? # Поместить левый дочерний узел в очередь\n    queue &lt;&lt; node.right unless node.right.nil? # Поместить правый дочерний узел в очередь\n  end\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 7. Дерево","7.2 &nbsp; Обход двоичного дерева"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/#2","level":3,"title":"2.   Анализ сложности","text":"<ul> <li>Временная сложность равна \\(O(n)\\) : все узлы посещаются по одному разу, поэтому требуется \\(O(n)\\) времени, где \\(n\\) - число узлов.</li> <li>Пространственная сложность равна \\(O(n)\\) : в худшем случае, то есть для полной двоичной деревообразной структуры, до достижения самого нижнего уровня в очереди одновременно может находиться до \\((n + 1) / 2\\) узлов, что требует \\(O(n)\\) памяти.</li> </ul>","path":["Глава 7. Дерево","7.2 &nbsp; Обход двоичного дерева"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/#722","level":2,"title":"7.2.2   Прямой, симметричный и обратный обходы","text":"<p>Соответственно, прямой, симметричный и обратный обходы относятся к обходу в глубину (depth-first traversal), также называемому поиском в глубину (depth-first search, DFS); он отражает идею \"сначала идти до конца, затем откатываться и продолжать\".</p> <p>На рисунке 7-10 показан принцип работы обхода двоичного дерева в глубину. Обход в глубину похож на то, как будто мы обходим всю двоичную структуру по внешнему контуру , и у каждого узла встречаем три позиции, соответствующие прямому, симметричному и обратному обходам.</p> <p></p> <p> Рисунок 7-10   Прямой, симметричный и обратный обходы двоичного дерева поиска </p>","path":["Глава 7. Дерево","7.2 &nbsp; Обход двоичного дерева"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/#1_1","level":3,"title":"1.   Код реализации","text":"<p>Поиск в глубину обычно реализуется через рекурсию:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_tree_dfs.py<pre><code>def pre_order(root: TreeNode | None):\n    \"\"\"Предварительный обход\"\"\"\n    if root is None:\n        return\n    # Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n    res.append(root.val)\n    pre_order(root=root.left)\n    pre_order(root=root.right)\n\ndef in_order(root: TreeNode | None):\n    \"\"\"Симметричный обход\"\"\"\n    if root is None:\n        return\n    # Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n    in_order(root=root.left)\n    res.append(root.val)\n    in_order(root=root.right)\n\ndef post_order(root: TreeNode | None):\n    \"\"\"Обратный обход\"\"\"\n    if root is None:\n        return\n    # Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n    post_order(root=root.left)\n    post_order(root=root.right)\n    res.append(root.val)\n</code></pre> binary_tree_dfs.cpp<pre><code>/* Предварительный обход */\nvoid preOrder(TreeNode *root) {\n    if (root == nullptr)\n        return;\n    // Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n    vec.push_back(root-&gt;val);\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n}\n\n/* Симметричный обход */\nvoid inOrder(TreeNode *root) {\n    if (root == nullptr)\n        return;\n    // Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n    inOrder(root-&gt;left);\n    vec.push_back(root-&gt;val);\n    inOrder(root-&gt;right);\n}\n\n/* Обратный обход */\nvoid postOrder(TreeNode *root) {\n    if (root == nullptr)\n        return;\n    // Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n    postOrder(root-&gt;left);\n    postOrder(root-&gt;right);\n    vec.push_back(root-&gt;val);\n}\n</code></pre> binary_tree_dfs.java<pre><code>/* Предварительный обход */\nvoid preOrder(TreeNode root) {\n    if (root == null)\n        return;\n    // Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n    list.add(root.val);\n    preOrder(root.left);\n    preOrder(root.right);\n}\n\n/* Симметричный обход */\nvoid inOrder(TreeNode root) {\n    if (root == null)\n        return;\n    // Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n    inOrder(root.left);\n    list.add(root.val);\n    inOrder(root.right);\n}\n\n/* Обратный обход */\nvoid postOrder(TreeNode root) {\n    if (root == null)\n        return;\n    // Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n    postOrder(root.left);\n    postOrder(root.right);\n    list.add(root.val);\n}\n</code></pre> binary_tree_dfs.cs<pre><code>/* Предварительный обход */\nvoid PreOrder(TreeNode? root) {\n    if (root == null) return;\n    // Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n    list.Add(root.val!.Value);\n    PreOrder(root.left);\n    PreOrder(root.right);\n}\n\n/* Симметричный обход */\nvoid InOrder(TreeNode? root) {\n    if (root == null) return;\n    // Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n    InOrder(root.left);\n    list.Add(root.val!.Value);\n    InOrder(root.right);\n}\n\n/* Обратный обход */\nvoid PostOrder(TreeNode? root) {\n    if (root == null) return;\n    // Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n    PostOrder(root.left);\n    PostOrder(root.right);\n    list.Add(root.val!.Value);\n}\n</code></pre> binary_tree_dfs.go<pre><code>/* Предварительный обход */\nfunc preOrder(node *TreeNode) {\n    if node == nil {\n        return\n    }\n    // Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n    nums = append(nums, node.Val)\n    preOrder(node.Left)\n    preOrder(node.Right)\n}\n\n/* Симметричный обход */\nfunc inOrder(node *TreeNode) {\n    if node == nil {\n        return\n    }\n    // Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n    inOrder(node.Left)\n    nums = append(nums, node.Val)\n    inOrder(node.Right)\n}\n\n/* Обратный обход */\nfunc postOrder(node *TreeNode) {\n    if node == nil {\n        return\n    }\n    // Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n    postOrder(node.Left)\n    postOrder(node.Right)\n    nums = append(nums, node.Val)\n}\n</code></pre> binary_tree_dfs.swift<pre><code>/* Предварительный обход */\nfunc preOrder(root: TreeNode?) {\n    guard let root = root else {\n        return\n    }\n    // Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n    list.append(root.val)\n    preOrder(root: root.left)\n    preOrder(root: root.right)\n}\n\n/* Симметричный обход */\nfunc inOrder(root: TreeNode?) {\n    guard let root = root else {\n        return\n    }\n    // Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n    inOrder(root: root.left)\n    list.append(root.val)\n    inOrder(root: root.right)\n}\n\n/* Обратный обход */\nfunc postOrder(root: TreeNode?) {\n    guard let root = root else {\n        return\n    }\n    // Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n    postOrder(root: root.left)\n    postOrder(root: root.right)\n    list.append(root.val)\n}\n</code></pre> binary_tree_dfs.js<pre><code>/* Предварительный обход */\nfunction preOrder(root) {\n    if (root === null) return;\n    // Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n    list.push(root.val);\n    preOrder(root.left);\n    preOrder(root.right);\n}\n\n/* Симметричный обход */\nfunction inOrder(root) {\n    if (root === null) return;\n    // Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n    inOrder(root.left);\n    list.push(root.val);\n    inOrder(root.right);\n}\n\n/* Обратный обход */\nfunction postOrder(root) {\n    if (root === null) return;\n    // Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n    postOrder(root.left);\n    postOrder(root.right);\n    list.push(root.val);\n}\n</code></pre> binary_tree_dfs.ts<pre><code>/* Предварительный обход */\nfunction preOrder(root: TreeNode | null): void {\n    if (root === null) {\n        return;\n    }\n    // Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n    list.push(root.val);\n    preOrder(root.left);\n    preOrder(root.right);\n}\n\n/* Симметричный обход */\nfunction inOrder(root: TreeNode | null): void {\n    if (root === null) {\n        return;\n    }\n    // Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n    inOrder(root.left);\n    list.push(root.val);\n    inOrder(root.right);\n}\n\n/* Обратный обход */\nfunction postOrder(root: TreeNode | null): void {\n    if (root === null) {\n        return;\n    }\n    // Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n    postOrder(root.left);\n    postOrder(root.right);\n    list.push(root.val);\n}\n</code></pre> binary_tree_dfs.dart<pre><code>/* Предварительный обход */\nvoid preOrder(TreeNode? node) {\n  if (node == null) return;\n  // Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n  list.add(node.val);\n  preOrder(node.left);\n  preOrder(node.right);\n}\n\n/* Симметричный обход */\nvoid inOrder(TreeNode? node) {\n  if (node == null) return;\n  // Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n  inOrder(node.left);\n  list.add(node.val);\n  inOrder(node.right);\n}\n\n/* Обратный обход */\nvoid postOrder(TreeNode? node) {\n  if (node == null) return;\n  // Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n  postOrder(node.left);\n  postOrder(node.right);\n  list.add(node.val);\n}\n</code></pre> binary_tree_dfs.rs<pre><code>/* Предварительный обход */\nfn pre_order(root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;) -&gt; Vec&lt;i32&gt; {\n    let mut result = vec![];\n\n    fn dfs(root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;, res: &amp;mut Vec&lt;i32&gt;) {\n        if let Some(node) = root {\n            // Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n            let node = node.borrow();\n            res.push(node.val);\n            dfs(node.left.as_ref(), res);\n            dfs(node.right.as_ref(), res);\n        }\n    }\n    dfs(root, &amp;mut result);\n\n    result\n}\n\n/* Симметричный обход */\nfn in_order(root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;) -&gt; Vec&lt;i32&gt; {\n    let mut result = vec![];\n\n    fn dfs(root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;, res: &amp;mut Vec&lt;i32&gt;) {\n        if let Some(node) = root {\n            // Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n            let node = node.borrow();\n            dfs(node.left.as_ref(), res);\n            res.push(node.val);\n            dfs(node.right.as_ref(), res);\n        }\n    }\n    dfs(root, &amp;mut result);\n\n    result\n}\n\n/* Обратный обход */\nfn post_order(root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;) -&gt; Vec&lt;i32&gt; {\n    let mut result = vec![];\n\n    fn dfs(root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;, res: &amp;mut Vec&lt;i32&gt;) {\n        if let Some(node) = root {\n            // Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n            let node = node.borrow();\n            dfs(node.left.as_ref(), res);\n            dfs(node.right.as_ref(), res);\n            res.push(node.val);\n        }\n    }\n\n    dfs(root, &amp;mut result);\n\n    result\n}\n</code></pre> binary_tree_dfs.c<pre><code>/* Предварительный обход */\nvoid preOrder(TreeNode *root, int *size) {\n    if (root == NULL)\n        return;\n    // Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n    arr[(*size)++] = root-&gt;val;\n    preOrder(root-&gt;left, size);\n    preOrder(root-&gt;right, size);\n}\n\n/* Симметричный обход */\nvoid inOrder(TreeNode *root, int *size) {\n    if (root == NULL)\n        return;\n    // Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n    inOrder(root-&gt;left, size);\n    arr[(*size)++] = root-&gt;val;\n    inOrder(root-&gt;right, size);\n}\n\n/* Обратный обход */\nvoid postOrder(TreeNode *root, int *size) {\n    if (root == NULL)\n        return;\n    // Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n    postOrder(root-&gt;left, size);\n    postOrder(root-&gt;right, size);\n    arr[(*size)++] = root-&gt;val;\n}\n</code></pre> binary_tree_dfs.kt<pre><code>/* Предварительный обход */\nfun preOrder(root: TreeNode?) {\n    if (root == null) return\n    // Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n    list.add(root._val)\n    preOrder(root.left)\n    preOrder(root.right)\n}\n\n/* Симметричный обход */\nfun inOrder(root: TreeNode?) {\n    if (root == null) return\n    // Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n    inOrder(root.left)\n    list.add(root._val)\n    inOrder(root.right)\n}\n\n/* Обратный обход */\nfun postOrder(root: TreeNode?) {\n    if (root == null) return\n    // Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n    postOrder(root.left)\n    postOrder(root.right)\n    list.add(root._val)\n}\n</code></pre> binary_tree_dfs.rb<pre><code>### Предварительный обход ###\ndef pre_order(root)\n  return if root.nil?\n\n  # Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n  $res &lt;&lt; root.val\n  pre_order(root.left)\n  pre_order(root.right)\nend\n\n### Симметричный обход ###\ndef in_order(root)\n  return if root.nil?\n\n  # Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n  in_order(root.left)\n  $res &lt;&lt; root.val\n  in_order(root.right)\nend\n\n### Обратный обход ###\ndef post_order(root)\n  return if root.nil?\n\n  # Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n  post_order(root.left)\n  post_order(root.right)\n  $res &lt;&lt; root.val\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Tip</p> <p>Поиск в глубину можно реализовать и итеративно; заинтересованные читатели могут изучить это самостоятельно.</p> <p>На рисунках ниже показан рекурсивный процесс прямого обхода двоичного дерева. Его можно разделить на две противоположные части: \"вход в рекурсию\" и \"возврат\".</p> <ol> <li>\"Вход в рекурсию\" означает запуск нового вызова функции; в этом процессе программа переходит к следующему узлу.</li> <li>\"Возврат\" означает завершение вызова функции и возврат назад, то есть текущий узел уже полностью обработан.</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 7-11   Рекурсивный процесс прямого обхода </p>","path":["Глава 7. Дерево","7.2 &nbsp; Обход двоичного дерева"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/#2_1","level":3,"title":"2.   Анализ сложности","text":"<ul> <li>Временная сложность равна \\(O(n)\\) : все узлы посещаются по одному разу, поэтому требуется \\(O(n)\\) времени.</li> <li>Пространственная сложность равна \\(O(n)\\) : в худшем случае, когда дерево вырождается в связный список, глубина рекурсии достигает \\(n\\) , и система тратит \\(O(n)\\) памяти на стек вызовов.</li> </ul>","path":["Глава 7. Дерево","7.2 &nbsp; Обход двоичного дерева"],"tags":[]},{"location":"chapter_tree/summary/","level":1,"title":"7.6   Краткие итоги","text":"","path":["Глава 7. Дерево","7.6 &nbsp; Краткие итоги"],"tags":[]},{"location":"chapter_tree/summary/#1","level":3,"title":"1.   Основные моменты","text":"<ul> <li>Двоичное дерево - это нелинейная структура данных, отражающая логику \"разделения надвое\". Каждый узел двоичного дерева содержит значение и два указателя, которые соответственно ведут к левому и правому дочерним узлам.</li> <li>Для любого узла двоичного дерева дерево, образованное его левым (правым) дочерним узлом и всеми нижележащими узлами, называется левым (правым) поддеревом этого узла.</li> <li>К связанным с двоичным деревом терминам относятся корневой узел, листовой узел, уровень, степень, ребро, высота, глубина и так далее.</li> <li>Инициализация двоичного дерева, вставка узлов и удаление узлов похожи по способу реализации на операции со связным списком.</li> <li>К распространенным видам двоичного дерева относятся идеальное двоичное дерево, полное двоичное дерево, строгое двоичное дерево и сбалансированное двоичное дерево. Идеальное двоичное дерево - наиболее желательное состояние, а связный список - худший случай после вырождения.</li> <li>Двоичное дерево можно представить массивом: значения узлов и пустые позиции располагаются в порядке обхода по уровням, а связи между родителем и детьми реализуются через отображение индексов.</li> <li>Обход двоичного дерева по уровням является методом поиска в ширину; он отражает идею \"расширяться слой за слоем наружу\" и обычно реализуется через очередь.</li> <li>Прямой, симметричный и обратный обходы относятся к поиску в глубину; они отражают идею \"сначала дойти до конца, затем откатиться и продолжить\" и обычно реализуются рекурсивно.</li> <li>Двоичное дерево поиска - это эффективная структура данных для поиска элементов; его поиск, вставка и удаление имеют временную сложность \\(O(\\log n)\\) . Когда двоичное дерево поиска вырождается в связный список, все эти сложности деградируют до \\(O(n)\\) .</li> <li>AVL-дерево, также называемое сбалансированным двоичным деревом поиска, с помощью вращений гарантирует, что после постоянных вставок и удалений узлов дерево остается сбалансированным.</li> <li>Вращения AVL-дерева включают правое вращение, левое вращение, сначала правое затем левое и сначала левое затем правое. После вставки или удаления узла AVL-дерево выполняет вращения снизу вверх, чтобы снова восстановить баланс.</li> </ul>","path":["Глава 7. Дерево","7.6 &nbsp; Краткие итоги"],"tags":[]},{"location":"chapter_tree/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: Для двоичного дерева, состоящего из одного узла, высота дерева и глубина корня обе равны \\(0\\) ?</p> <p>Да, потому что высота и глубина обычно определяются как \"число пройденных ребер\".</p> <p>Q: Вставка и удаление в двоичном дереве обычно выполняются в составе набора операций. Что именно означает этот \"набор операций\"? Можно ли понимать это как освобождение ресурсов у дочерних узлов ресурса?</p> <p>Возьмем в качестве примера двоичное дерево поиска: операция удаления узла делится на три случая, и каждый из этих случаев требует нескольких последовательных шагов работы с узлами.</p> <p>Q: Почему у DFS для двоичного дерева есть три порядка: прямой, симметричный и обратный? Для чего они нужны?</p> <p>Подобно прямому и обратному обходу массива, прямой, симметричный и обратный обходы - это три способа обхода двоичного дерева, с помощью которых можно получить результаты в определенном порядке. Например, в двоичном дереве поиска, где соблюдается отношение <code>значение левого дочернего узла &lt; значение корня &lt; значение правого дочернего узла</code> , если обходить дерево с приоритетом \"лево \\(\\rightarrow\\) корень \\(\\rightarrow\\) право\", то получится упорядоченная последовательность узлов.</p> <p>Q: Правое вращение работает с отношениями между <code>node</code> , <code>child</code> и <code>grand_child</code> . А связь между <code>node</code> и его исходным родителем разве не нужно поддерживать? После правого вращения она ведь не оборвется?</p> <p>На это нужно смотреть с точки зрения рекурсии. В правое вращение <code>right_rotate(root)</code> передается корень поддерева, а затем через <code>return child</code> возвращается корень этого поддерева уже после вращения. Соединение между новым корнем поддерева и его родителем восстанавливается после возврата функции и не входит в обязанности самой операции правого вращения.</p> <p>Q: В C++ функции делятся на <code>private</code> и <code>public</code> . Какая логика стоит за этим? Почему <code>height()</code> и <code>updateHeight()</code> помещают в разные области видимости?</p> <p>Главный критерий - область использования метода. Если метод нужен только внутри класса, его следует проектировать как <code>private</code> . Например, самостоятельный вызов <code>updateHeight()</code> пользователем не имеет смысла: это лишь один из шагов внутри вставки или удаления. А <code>height()</code> используется для чтения высоты узла, подобно <code>vector.size()</code> , поэтому его разумно делать <code>public</code> .</p> <p>Q: Как построить двоичное дерево поиска из набора входных данных? Важен ли выбор корневого узла?</p> <p>Да, важен. Способ построения дерева уже показан в методе <code>build_tree()</code> в коде двоичного дерева поиска. Что касается выбора корня, обычно входные данные сортируют, берут средний элемент как корень, а затем рекурсивно строят левое и правое поддеревья. Это позволяет в наибольшей степени сохранить баланс дерева.</p> <p>Q: Нужно ли в Java всегда использовать <code>equals()</code> для сравнения строк?</p> <p>В Java для базовых типов <code>==</code> используется, чтобы сравнивать, равны ли значения двух переменных. Для ссылочных типов логика у этих двух способов уже разная.</p> <ul> <li><code>==</code> : сравнивает, ссылаются ли две переменные на один и тот же объект, то есть совпадает ли их адрес в памяти.</li> <li><code>equals()</code>: сравнивает, равны ли значения двух объектов.</li> </ul> <p>Поэтому если нужно сравнить значения, то следует использовать <code>equals()</code> . Но строки, инициализированные как <code>String a = \"hi\"; String b = \"hi\";</code> , хранятся в строковом пуле констант и указывают на один и тот же объект, поэтому в таком случае <code>a == b</code> тоже может дать истинный результат при сравнении содержимого.</p> <p>Q: До достижения самого нижнего уровня при обходе в ширину число узлов в очереди равно \\(2^h\\) ?</p> <p>Да. Например, для полного двоичного дерева высоты \\(h = 2\\) общее число узлов равно \\(n = 7\\) , а число узлов на нижнем уровне равно \\(4 = 2^h = (n + 1) / 2\\) .</p>","path":["Глава 7. Дерево","7.6 &nbsp; Краткие итоги"],"tags":[]}]}
\ No newline at end of file
+{"config":{"separator":"[\\s\\-_,:!=\\[\\]()\\\\\"`/]+|\\.(?!\\d)"},"items":[{"location":"chapter_appendix/","level":1,"title":"Глава 16.   Приложение","text":"","path":["Глава 16. Приложение","Глава 16. &nbsp; Приложение"],"tags":[]},{"location":"chapter_appendix/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>16.1   Установка среды программирования</li> <li>16.2   Присоединяйтесь к созданию книги</li> <li>16.3   Глоссарий</li> </ul>","path":["Глава 16. Приложение","Глава 16. &nbsp; Приложение"],"tags":[]},{"location":"chapter_appendix/contribution/","level":1,"title":"16.2   Присоединяйтесь к созданию книги","text":"<p>Возможности автора ограничены, поэтому в книге неизбежно могут встречаться упущения и ошибки. Просим отнестись к этому с пониманием. Если вы заметите опечатки, неработающие ссылки, пропуски в содержании, двусмысленные формулировки, неясные объяснения или неудачную структуру изложения, пожалуйста, помогите нам это исправить, чтобы читатели получили более качественный учебный ресурс.</p> <p>Все GitHub ID авторов будут указаны на главных страницах репозитория книги, веб-версии и PDF-версии в знак благодарности за их бескорыстный вклад в сообщество открытого исходного кода.</p> <p>Сила открытого исходного кода</p> <p>Интервал между двумя тиражами бумажной книги обычно довольно велик, поэтому обновлять содержание очень неудобно.</p> <p>В этой же открытой книге цикл обновления содержания сокращается до нескольких дней, а иногда даже до нескольких часов.</p>","path":["Глава 16. Приложение","16.2 &nbsp; Присоединяйтесь к созданию книги"],"tags":[]},{"location":"chapter_appendix/contribution/#1","level":3,"title":"1.   Небольшие правки содержания","text":"<p>Как показано на рисунке 16-3, в правом верхнем углу каждой страницы есть \"значок редактирования\". Текст или код можно изменить следующим образом.</p> <ol> <li>Нажмите на \"значок редактирования\". Если появится сообщение \"You need to fork this repository\", согласитесь с этим действием.</li> <li>Измените содержимое исходного Markdown-файла, проверьте корректность правок и постарайтесь сохранить единый стиль оформления.</li> <li>Внизу страницы заполните описание изменений, затем нажмите кнопку \"Propose file change\". После перехода на следующую страницу нажмите кнопку \"Create pull request\", чтобы отправить pull request.</li> </ol> <p></p> <p> Рисунок 16-3   Кнопка редактирования страницы </p> <p>Изображения нельзя изменить напрямую, поэтому проблему с ними нужно описывать через новый Issue или комментарий. Мы постараемся как можно быстрее исправить и обновить изображение.</p>","path":["Глава 16. Приложение","16.2 &nbsp; Присоединяйтесь к созданию книги"],"tags":[]},{"location":"chapter_appendix/contribution/#2","level":3,"title":"2.   Создание содержания","text":"<p>Если вам интересно участвовать в этом проекте с открытым исходным кодом, например переводить код на другие языки программирования или расширять содержание статей, то следует придерживаться следующего процесса Pull Request.</p> <ol> <li>Войдите в GitHub и сделайте Fork репозитория книги в свой личный аккаунт.</li> <li>Перейдите на страницу своего Fork-репозитория и с помощью команды <code>git clone</code> клонируйте репозиторий локально.</li> <li>Создавайте и редактируйте содержание локально, затем проведите полное тестирование и проверьте корректность кода.</li> <li>Зафиксируйте локальные изменения, после чего выполните Push в удаленный репозиторий.</li> <li>Обновите страницу репозитория и нажмите кнопку \"Create pull request\", чтобы инициировать pull request.</li> </ol>","path":["Глава 16. Приложение","16.2 &nbsp; Присоединяйтесь к созданию книги"],"tags":[]},{"location":"chapter_appendix/contribution/#3-docker","level":3,"title":"3.   Развертывание Docker","text":"<p>В корневом каталоге <code>hello-algo</code> выполните следующий Docker-скрипт, после чего проект станет доступен по адресу <code>http://localhost:8000</code>:</p> <pre><code>docker-compose up -d\n</code></pre> <p>Удалить развертывание можно следующей командой:</p> <pre><code>docker-compose down\n</code></pre>","path":["Глава 16. Приложение","16.2 &nbsp; Присоединяйтесь к созданию книги"],"tags":[]},{"location":"chapter_appendix/installation/","level":1,"title":"16.1   Установка среды программирования","text":"","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/installation/#1611-ide","level":2,"title":"16.1.1   Установка IDE","text":"<p>В качестве локальной интегрированной среды разработки (IDE) рекомендуется использовать открытую и быструю VS Code. Перейдите на официальный сайт VS Code, выберите версию для своей операционной системы и установите ее.</p> <p></p> <p> Рисунок 16-1   Загрузка VS Code с официального сайта </p> <p>VS Code обладает мощной экосистемой расширений и поддерживает выполнение и отладку большинства языков программирования. Например, после установки расширения \"Python Extension Pack\" можно отлаживать код на Python. Процесс установки показан на рисунке 16-2.</p> <p></p> <p> Рисунок 16-2   Установка расширений VS Code </p>","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/installation/#1612","level":2,"title":"16.1.2   Установка языковой среды","text":"","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/installation/#1-python","level":3,"title":"1.   Среда Python","text":"<ol> <li>Загрузите и установите Miniconda3, требуется Python 3.10 или более поздняя версия.</li> <li>В магазине расширений VS Code найдите <code>python</code> и установите Python Extension Pack.</li> <li>(Необязательно) Введите в командной строке <code>pip install black</code>, чтобы установить инструмент форматирования кода.</li> </ol>","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/installation/#2-cc","level":3,"title":"2.   Среда C/C++","text":"<ol> <li>В Windows требуется установить MinGW (руководство по настройке); в macOS компилятор Clang уже установлен по умолчанию.</li> <li>В магазине расширений VS Code найдите <code>c++</code> и установите C/C++ Extension Pack.</li> <li>(Необязательно) Откройте страницу Settings, найдите параметр форматирования <code>Clang_format_fallback Style</code> и задайте значение <code>{ BasedOnStyle: Microsoft, BreakBeforeBraces: Attach }</code>.</li> </ol>","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/installation/#3-java","level":3,"title":"3.   Среда Java","text":"<ol> <li>Загрузите и установите OpenJDK (требуемая версия: &gt; JDK 9).</li> <li>В магазине расширений VS Code найдите <code>java</code> и установите Extension Pack for Java.</li> </ol>","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/installation/#4-c","level":3,"title":"4.   Среда C","text":"<ol> <li>Загрузите и установите .Net 8.0.</li> <li>В магазине расширений VS Code найдите <code>C# Dev Kit</code> и установите C# Dev Kit (руководство по настройке).</li> <li>Также можно использовать Visual Studio (руководство по установке).</li> </ol>","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/installation/#5-go","level":3,"title":"5.   Среда Go","text":"<ol> <li>Загрузите и установите go.</li> <li>В магазине расширений VS Code найдите <code>go</code> и установите Go.</li> <li>Нажмите <code>Ctrl + Shift + P</code>, чтобы открыть командную палитру, введите <code>go</code>, выберите <code>Go: Install/Update Tools</code>, отметьте все инструменты и установите их.</li> </ol>","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/installation/#6-swift","level":3,"title":"6.   Среда Swift","text":"<ol> <li>Загрузите и установите Swift.</li> <li>В магазине расширений VS Code найдите <code>swift</code> и установите Swift for Visual Studio Code.</li> </ol>","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/installation/#7-javascript","level":3,"title":"7.   Среда JavaScript","text":"<ol> <li>Загрузите и установите Node.js.</li> <li>(Необязательно) В магазине расширений VS Code найдите <code>Prettier</code> и установите инструмент форматирования кода.</li> </ol>","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/installation/#8-typescript","level":3,"title":"8.   Среда TypeScript","text":"<ol> <li>Выполните те же шаги, что и для среды JavaScript.</li> <li>Установите TypeScript Execute (tsx).</li> <li>В магазине расширений VS Code найдите <code>typescript</code> и установите Pretty TypeScript Errors.</li> </ol>","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/installation/#9-dart","level":3,"title":"9.   Среда Dart","text":"<ol> <li>Загрузите и установите Dart.</li> <li>В магазине расширений VS Code найдите <code>dart</code> и установите Dart.</li> </ol>","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/installation/#10-rust","level":3,"title":"10.   Среда Rust","text":"<ol> <li>Загрузите и установите Rust.</li> <li>В магазине расширений VS Code найдите <code>rust</code> и установите rust-analyzer.</li> </ol>","path":["Глава 16. Приложение","16.1 &nbsp; Установка среды программирования"],"tags":[]},{"location":"chapter_appendix/terminology/","level":1,"title":"16.3   Глоссарий","text":"<p>В таблице 16-1 приведены важные термины, встречающиеся в книге. Обратите внимание на следующие моменты.</p> <ul> <li>Рекомендуем запомнить английские названия терминов, чтобы легче читать англоязычные материалы.</li> <li>В русской версии для каждого термина приводится единый рекомендуемый перевод.</li> </ul> <p> Таблица 16-1   Важные термины по структурам данных и алгоритмам </p> English Русский algorithm алгоритм data structure структура данных code код file файл function функция method метод variable переменная asymptotic complexity analysis асимптотический анализ сложности time complexity временная сложность space complexity пространственная сложность loop цикл iteration итерация recursion рекурсия tail recursion хвостовая рекурсия recursion tree дерево рекурсии big-\\(O\\) notation нотация big-\\(O\\) asymptotic upper bound асимптотическая верхняя граница sign-magnitude прямой код 1’s complement обратный код 2’s complement дополнительный код array массив index индекс linked list связный список linked list node, list node узел связного списка head node головной узел tail node хвостовой узел list список dynamic array динамический массив hard disk жесткий диск random-access memory (RAM) оперативная память cache memory кеш-память cache miss промах кеша cache hit rate коэффициент попадания в кеш stack стек top of the stack вершина стека bottom of the stack основание стека queue очередь double-ended queue двусторонняя очередь front of the queue голова очереди rear of the queue хвост очереди hash table хеш-таблица hash set хеш-набор bucket бакет hash function хеш-функция hash collision хеш-коллизия load factor коэффициент заполнения separate chaining цепная адресация open addressing открытая адресация linear probing линейное зондирование lazy deletion ленивое удаление binary tree двоичное дерево tree node узел дерева left-child node левый дочерний узел right-child node правый дочерний узел parent node родительский узел left subtree левое поддерево right subtree правое поддерево root node корневой узел leaf node листовой узел edge ребро level уровень degree степень height высота depth глубина perfect binary tree идеальное двоичное дерево complete binary tree полное двоичное дерево full binary tree строгое двоичное дерево balanced binary tree сбалансированное двоичное дерево binary search tree двоичное дерево поиска AVL tree АВЛ-дерево red-black tree красно-черное дерево level-order traversal обход по уровням breadth-first traversal обход в ширину depth-first traversal обход в глубину pre-order traversal прямой обход in-order traversal симметричный обход post-order traversal обратный обход balanced binary search tree сбалансированное двоичное дерево поиска balance factor фактор баланса heap куча max heap максимальная куча min heap минимальная куча priority queue приоритетная очередь heapify упорядочивание кучи top-\\(k\\) problem поиск \\(k\\) наибольших элементов graph граф vertex вершина undirected graph неориентированный граф directed graph ориентированный граф connected graph связный граф disconnected graph несвязный граф weighted graph взвешенный граф adjacency смежность path путь in-degree входящая степень out-degree исходящая степень adjacency matrix матрица смежности adjacency list список смежности breadth-first search поиск в ширину depth-first search поиск в глубину binary search двоичный поиск searching algorithm алгоритм поиска sorting algorithm алгоритм сортировки selection sort сортировка выбором bubble sort сортировка пузырьком insertion sort сортировка вставкой quick sort быстрая сортировка merge sort сортировка слиянием heap sort пирамидальная сортировка bucket sort блочная сортировка counting sort сортировка подсчетом radix sort поразрядная сортировка divide and conquer разделяй и властвуй hanota problem задача о Ханойской башне backtracking algorithm алгоритм поиска с возвратом constraint ограничение solution решение state состояние pruning отсечение permutations problem задача о перестановках subset-sum problem задача о сумме подмножеств \\(n\\)-queens problem задача о \\(n\\) ферзях dynamic programming динамическое программирование initial state начальное состояние state-transition equation уравнение перехода состояния knapsack problem задача о рюкзаке edit distance problem задача о расстоянии редактирования greedy algorithm жадный алгоритм","path":["Глава 16. Приложение","16.3 &nbsp; Глоссарий"],"tags":[]},{"location":"chapter_array_and_linkedlist/","level":1,"title":"Глава 4.   Массивы и списки","text":"<p>Abstract</p> <p>Мир структур данных напоминает прочную кирпичную стену.</p> <p>Кирпичи массива уложены ровно и плотно прилегают друг к другу. Узлы связного списка, напротив, разбросаны в разных местах, а соединяющие их связи свободно тянутся между промежутками.</p>","path":["Глава 4. Массивы и списки","Глава 4. &nbsp; Массивы и списки"],"tags":[]},{"location":"chapter_array_and_linkedlist/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>4.1   Массив</li> <li>4.2   Связный список</li> <li>4.3   Список</li> <li>4.4   Оперативная память и кэш *</li> <li>4.5   Резюме</li> </ul>","path":["Глава 4. Массивы и списки","Глава 4. &nbsp; Массивы и списки"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/","level":1,"title":"4.1   Массив","text":"<p>Массив (array) - это линейная структура данных, в которой элементы одного типа хранятся в непрерывной области памяти. Положение элемента в массиве называется его индексом (index). На рисунке 4-1 показаны основные понятия, связанные с массивом, и способ его хранения.</p> <p></p> <p> Рисунок 4-1   Определение массива и способ хранения </p>","path":["Глава 4. Массивы и списки","4.1 &nbsp; Массив"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#411","level":2,"title":"4.1.1   Основные операции с массивом","text":"","path":["Глава 4. Массивы и списки","4.1 &nbsp; Массив"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#1","level":3,"title":"1.   Инициализация массива","text":"<p>Существует два способа инициализации массива: без начальных значений и с заданными начальными значениями. Если начальные значения не указаны, большинство языков программирования инициализируют элементы массива нулями:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code># Инициализация массива\narr: list[int] = [0] * 5  # [ 0, 0, 0, 0, 0 ]\nnums: list[int] = [1, 3, 2, 5, 4]\n</code></pre> array.cpp<pre><code>/* Инициализация массива */\n// Хранится в стеке\nint arr[5];\nint nums[5] = { 1, 3, 2, 5, 4 };\n// Хранится в куче (требуется ручное освобождение памяти)\nint* arr1 = new int[5];\nint* nums1 = new int[5] { 1, 3, 2, 5, 4 };\n</code></pre> array.java<pre><code>/* Инициализация массива */\nint[] arr = new int[5]; // { 0, 0, 0, 0, 0 }\nint[] nums = { 1, 3, 2, 5, 4 };\n</code></pre> array.cs<pre><code>/* Инициализация массива */\nint[] arr = new int[5]; // [ 0, 0, 0, 0, 0 ]\nint[] nums = [1, 3, 2, 5, 4];\n</code></pre> array.go<pre><code>/* Инициализация массива */\nvar arr [5]int\n// В Go указание длины ([5]int) создает массив, а отсутствие длины ([]int) - срез\n// Поскольку длина массива в Go определяется на этапе компиляции, для задания длины можно использовать только константы\n// Чтобы упростить реализацию метода extend(), ниже будем рассматривать срезы (Slice) как массивы (Array)\nnums := []int{1, 3, 2, 5, 4}\n</code></pre> array.swift<pre><code>/* Инициализация массива */\nlet arr = Array(repeating: 0, count: 5) // [0, 0, 0, 0, 0]\nlet nums = [1, 3, 2, 5, 4]\n</code></pre> array.js<pre><code>/* Инициализация массива */\nvar arr = new Array(5).fill(0);\nvar nums = [1, 3, 2, 5, 4];\n</code></pre> array.ts<pre><code>/* Инициализация массива */\nlet arr: number[] = new Array(5).fill(0);\nlet nums: number[] = [1, 3, 2, 5, 4];\n</code></pre> array.dart<pre><code>/* Инициализация массива */\nList&lt;int&gt; arr = List.filled(5, 0); // [0, 0, 0, 0, 0]\nList&lt;int&gt; nums = [1, 3, 2, 5, 4];\n</code></pre> array.rs<pre><code>/* Инициализация массива */\nlet arr: [i32; 5] = [0; 5]; // [0, 0, 0, 0, 0]\nlet slice: &amp;[i32] = &amp;[0; 5];\n// В Rust указание длины ([i32; 5]) создает массив, а отсутствие длины (&amp;[i32]) - срез\n// Поскольку длина массива в Rust определяется на этапе компиляции, для задания длины можно использовать только константы\n// Vector в Rust обычно используется как динамический массив\n// Чтобы упростить реализацию метода extend(), ниже будем рассматривать vector как массив (array)\nlet nums: Vec&lt;i32&gt; = vec![1, 3, 2, 5, 4];\n</code></pre> array.c<pre><code>/* Инициализация массива */\nint arr[5] = { 0 }; // { 0, 0, 0, 0, 0 }\nint nums[5] = { 1, 3, 2, 5, 4 };\n</code></pre> array.kt<pre><code>/* Инициализация массива */\nvar arr = IntArray(5) // { 0, 0, 0, 0, 0 }\nvar nums = intArrayOf(1, 3, 2, 5, 4)\n</code></pre> array.rb<pre><code># Инициализация массива\narr = Array.new(5, 0)\nnums = [1, 3, 2, 5, 4]\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D0%BC%D0%B0%D1%81%D1%81%D0%B8%D0%B2%0Aarr%20%3D%20%5B0%5D%20%2A%205%20%20%23%20%5B%200%2C%200%2C%200%2C%200%2C%200%20%5D%0Anums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D&amp;cumulative=false&amp;curInstr=0&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 4. Массивы и списки","4.1 &nbsp; Массив"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#2","level":3,"title":"2.   Доступ к элементам","text":"<p>Элементы массива хранятся в непрерывной области памяти, что упрощает вычисление их адресов. Зная адрес массива в памяти (то есть адрес первого элемента) и индекс некоторого элемента, мы можем по формуле с рисунка ниже вычислить адрес этого элемента и напрямую обратиться к нему.</p> <p></p> <p> Рисунок 4-2   Вычисление адреса элемента массива </p> <p>Если посмотреть на рисунок 4-2, можно заметить, что индекс первого элемента массива равен \\(0\\) , и это кажется не слишком интуитивным, ведь естественнее было бы начинать счет с \\(1\\) . Однако с точки зрения формулы адресации индекс по сути является смещением относительно адреса памяти. Смещение первого элемента равно \\(0\\) , поэтому индекс \\(0\\) полностью логичен.</p> <p>Доступ к элементам массива очень эффективен: любой элемент массива можно получить за \\(O(1)\\) времени.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code>def random_access(nums: list[int]) -&gt; int:\n    \"\"\"Случайный доступ к элементу\"\"\"\n    # Случайным образом выбрать число из интервала [0, len(nums)-1]\n    random_index = random.randint(0, len(nums) - 1)\n    # Получить и вернуть случайный элемент\n    random_num = nums[random_index]\n    return random_num\n</code></pre> array.cpp<pre><code>/* Случайный доступ к элементу */\nint randomAccess(int *nums, int size) {\n    // Случайным образом выбрать число из интервала [0, size)\n    int randomIndex = rand() % size;\n    // Получить и вернуть случайный элемент\n    int randomNum = nums[randomIndex];\n    return randomNum;\n}\n</code></pre> array.java<pre><code>/* Случайный доступ к элементу */\nint randomAccess(int[] nums) {\n    // Случайным образом выбрать число из интервала [0, nums.length)\n    int randomIndex = ThreadLocalRandom.current().nextInt(0, nums.length);\n    // Получить и вернуть случайный элемент\n    int randomNum = nums[randomIndex];\n    return randomNum;\n}\n</code></pre> array.cs<pre><code>/* Случайный доступ к элементу */\nint RandomAccess(int[] nums) {\n    Random random = new();\n    // Случайным образом выбрать число из интервала [0, nums.Length)\n    int randomIndex = random.Next(nums.Length);\n    // Получить и вернуть случайный элемент\n    int randomNum = nums[randomIndex];\n    return randomNum;\n}\n</code></pre> array.go<pre><code>/* Случайный доступ к элементу */\nfunc randomAccess(nums []int) (randomNum int) {\n    // Случайным образом выбрать число из интервала [0, nums.length)\n    randomIndex := rand.Intn(len(nums))\n    // Получить и вернуть случайный элемент\n    randomNum = nums[randomIndex]\n    return\n}\n</code></pre> array.swift<pre><code>/* Случайный доступ к элементу */\nfunc randomAccess(nums: [Int]) -&gt; Int {\n    // Случайным образом выбрать число из интервала [0, nums.count)\n    let randomIndex = nums.indices.randomElement()!\n    // Получить и вернуть случайный элемент\n    let randomNum = nums[randomIndex]\n    return randomNum\n}\n</code></pre> array.js<pre><code>/* Случайный доступ к элементу */\nfunction randomAccess(nums) {\n    // Случайным образом выбрать число из интервала [0, nums.length)\n    const random_index = Math.floor(Math.random() * nums.length);\n    // Получить и вернуть случайный элемент\n    const random_num = nums[random_index];\n    return random_num;\n}\n</code></pre> array.ts<pre><code>/* Случайный доступ к элементу */\nfunction randomAccess(nums: number[]): number {\n    // Случайным образом выбрать число из интервала [0, nums.length)\n    const random_index = Math.floor(Math.random() * nums.length);\n    // Получить и вернуть случайный элемент\n    const random_num = nums[random_index];\n    return random_num;\n}\n</code></pre> array.dart<pre><code>/* Случайный доступ к элементу */\nint randomAccess(List&lt;int&gt; nums) {\n  // Случайным образом выбрать число из интервала [0, nums.length)\n  int randomIndex = Random().nextInt(nums.length);\n  // Получить и вернуть случайный элемент\n  int randomNum = nums[randomIndex];\n  return randomNum;\n}\n</code></pre> array.rs<pre><code>/* Случайный доступ к элементу */\nfn random_access(nums: &amp;[i32]) -&gt; i32 {\n    // Случайным образом выбрать число из интервала [0, nums.len())\n    let random_index = rand::thread_rng().gen_range(0..nums.len());\n    // Получить и вернуть случайный элемент\n    let random_num = nums[random_index];\n    random_num\n}\n</code></pre> array.c<pre><code>/* Случайный доступ к элементу */\nint randomAccess(int *nums, int size) {\n    // Случайным образом выбрать число из интервала [0, size)\n    int randomIndex = rand() % size;\n    // Получить и вернуть случайный элемент\n    int randomNum = nums[randomIndex];\n    return randomNum;\n}\n</code></pre> array.kt<pre><code>/* Случайный доступ к элементу */\nfun randomAccess(nums: IntArray): Int {\n    // Случайным образом выбрать число из интервала [0, nums.size)\n    val randomIndex = ThreadLocalRandom.current().nextInt(0, nums.size)\n    // Получить и вернуть случайный элемент\n    val randomNum = nums[randomIndex]\n    return randomNum\n}\n</code></pre> array.rb<pre><code>### Случайный доступ к элементу ###\ndef random_access(nums)\n  # Случайным образом выбрать число из интервала [0, nums.length)\n  random_index = Random.rand(0...nums.length)\n\n  # Получить и вернуть случайный элемент\n  nums[random_index]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 4. Массивы и списки","4.1 &nbsp; Массив"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#3","level":3,"title":"3.   Вставка элемента","text":"<p>Элементы массива в памяти расположены вплотную друг к другу, и между ними нет места для размещения новых данных. Как показано на рисунке 4-3, если мы хотим вставить элемент в середину массива, то все элементы после этой позиции нужно сдвинуть на одну позицию вправо, а затем записать новое значение в освободившийся индекс.</p> <p></p> <p> Рисунок 4-3   Пример вставки элемента в массив </p> <p>Стоит отметить, что длина массива фиксирована, поэтому вставка нового элемента неизбежно приведет к потере элемента на конце массива. Решение этой проблемы мы оставим для обсуждения в разделе о \"списках\".</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code>def insert(nums: list[int], num: int, index: int):\n    \"\"\"Вставить элемент num по индексу index в массив\"\"\"\n    # Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n    for i in range(len(nums) - 1, index, -1):\n        nums[i] = nums[i - 1]\n    # Присвоить num элементу по индексу index\n    nums[index] = num\n</code></pre> array.cpp<pre><code>/* Вставить элемент num по индексу index в массив */\nvoid insert(int *nums, int size, int num, int index) {\n    // Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n    for (int i = size - 1; i &gt; index; i--) {\n        nums[i] = nums[i - 1];\n    }\n    // Присвоить num элементу по индексу index\n    nums[index] = num;\n}\n</code></pre> array.java<pre><code>/* Вставить элемент num по индексу index в массив */\nvoid insert(int[] nums, int num, int index) {\n    // Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n    for (int i = nums.length - 1; i &gt; index; i--) {\n        nums[i] = nums[i - 1];\n    }\n    // Присвоить num элементу по индексу index\n    nums[index] = num;\n}\n</code></pre> array.cs<pre><code>/* Вставить элемент num по индексу index в массив */\nvoid Insert(int[] nums, int num, int index) {\n    // Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n    for (int i = nums.Length - 1; i &gt; index; i--) {\n        nums[i] = nums[i - 1];\n    }\n    // Присвоить num элементу по индексу index\n    nums[index] = num;\n}\n</code></pre> array.go<pre><code>/* Вставить элемент num по индексу index в массив */\nfunc insert(nums []int, num int, index int) {\n    // Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n    for i := len(nums) - 1; i &gt; index; i-- {\n        nums[i] = nums[i-1]\n    }\n    // Присвоить num элементу по индексу index\n    nums[index] = num\n}\n</code></pre> array.swift<pre><code>/* Вставить элемент num по индексу index в массив */\nfunc insert(nums: inout [Int], num: Int, index: Int) {\n    // Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n    for i in nums.indices.dropFirst(index).reversed() {\n        nums[i] = nums[i - 1]\n    }\n    // Присвоить num элементу по индексу index\n    nums[index] = num\n}\n</code></pre> array.js<pre><code>/* Вставить элемент num по индексу index в массив */\nfunction insert(nums, num, index) {\n    // Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n    for (let i = nums.length - 1; i &gt; index; i--) {\n        nums[i] = nums[i - 1];\n    }\n    // Присвоить num элементу по индексу index\n    nums[index] = num;\n}\n</code></pre> array.ts<pre><code>/* Вставить элемент num по индексу index в массив */\nfunction insert(nums: number[], num: number, index: number): void {\n    // Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n    for (let i = nums.length - 1; i &gt; index; i--) {\n        nums[i] = nums[i - 1];\n    }\n    // Присвоить num элементу по индексу index\n    nums[index] = num;\n}\n</code></pre> array.dart<pre><code>/* Вставить элемент _num по индексу index в массив */\nvoid insert(List&lt;int&gt; nums, int _num, int index) {\n  // Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n  for (var i = nums.length - 1; i &gt; index; i--) {\n    nums[i] = nums[i - 1];\n  }\n  // Присвоить _num элементу по индексу index\n  nums[index] = _num;\n}\n</code></pre> array.rs<pre><code>/* Вставить элемент num по индексу index в массив */\nfn insert(nums: &amp;mut [i32], num: i32, index: usize) {\n    // Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n    for i in (index + 1..nums.len()).rev() {\n        nums[i] = nums[i - 1];\n    }\n    // Присвоить num элементу по индексу index\n    nums[index] = num;\n}\n</code></pre> array.c<pre><code>/* Вставить элемент num по индексу index в массив */\nvoid insert(int *nums, int size, int num, int index) {\n    // Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n    for (int i = size - 1; i &gt; index; i--) {\n        nums[i] = nums[i - 1];\n    }\n    // Присвоить num элементу по индексу index\n    nums[index] = num;\n}\n</code></pre> array.kt<pre><code>/* Вставить элемент num по индексу index в массив */\nfun insert(nums: IntArray, num: Int, index: Int) {\n    // Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n    for (i in nums.size - 1 downTo index + 1) {\n        nums[i] = nums[i - 1]\n    }\n    // Присвоить num элементу по индексу index\n    nums[index] = num\n}\n</code></pre> array.rb<pre><code>### Вставка элемента num по индексу index в массив ###\ndef insert(nums, num, index)\n  # Сдвинуть элемент с индексом index и все последующие элементы на одну позицию назад\n  for i in (nums.length - 1).downto(index + 1)\n    nums[i] = nums[i - 1]\n  end\n\n  # Присвоить num элементу по индексу index\n  nums[index] = num\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 4. Массивы и списки","4.1 &nbsp; Массив"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#4","level":3,"title":"4.   Удаление элемента","text":"<p>Аналогично, как показано на рисунке 4-4, если нужно удалить элемент по индексу \\(i\\) , то все элементы после индекса \\(i\\) необходимо сдвинуть на одну позицию влево.</p> <p></p> <p> Рисунок 4-4   Пример удаления элемента из массива </p> <p>Обрати внимание: после удаления исходный последний элемент становится бессмысленным, поэтому специально изменять его не требуется.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code>def remove(nums: list[int], index: int):\n    \"\"\"Удалить элемент по индексу index\"\"\"\n    # Сдвинуть все элементы после индекса index на одну позицию вперед\n    for i in range(index, len(nums) - 1):\n        nums[i] = nums[i + 1]\n</code></pre> array.cpp<pre><code>/* Удалить элемент по индексу index */\nvoid remove(int *nums, int size, int index) {\n    // Сдвинуть все элементы после индекса index на одну позицию вперед\n    for (int i = index; i &lt; size - 1; i++) {\n        nums[i] = nums[i + 1];\n    }\n}\n</code></pre> array.java<pre><code>/* Удалить элемент по индексу index */\nvoid remove(int[] nums, int index) {\n    // Сдвинуть все элементы после индекса index на одну позицию вперед\n    for (int i = index; i &lt; nums.length - 1; i++) {\n        nums[i] = nums[i + 1];\n    }\n}\n</code></pre> array.cs<pre><code>/* Удалить элемент по индексу index */\nvoid Remove(int[] nums, int index) {\n    // Сдвинуть все элементы после индекса index на одну позицию вперед\n    for (int i = index; i &lt; nums.Length - 1; i++) {\n        nums[i] = nums[i + 1];\n    }\n}\n</code></pre> array.go<pre><code>/* Удалить элемент по индексу index */\nfunc remove(nums []int, index int) {\n    // Сдвинуть все элементы после индекса index на одну позицию вперед\n    for i := index; i &lt; len(nums)-1; i++ {\n        nums[i] = nums[i+1]\n    }\n}\n</code></pre> array.swift<pre><code>/* Удалить элемент по индексу index */\nfunc remove(nums: inout [Int], index: Int) {\n    // Сдвинуть все элементы после индекса index на одну позицию вперед\n    for i in nums.indices.dropFirst(index).dropLast() {\n        nums[i] = nums[i + 1]\n    }\n}\n</code></pre> array.js<pre><code>/* Удалить элемент по индексу index */\nfunction remove(nums, index) {\n    // Сдвинуть все элементы после индекса index на одну позицию вперед\n    for (let i = index; i &lt; nums.length - 1; i++) {\n        nums[i] = nums[i + 1];\n    }\n}\n</code></pre> array.ts<pre><code>/* Удалить элемент по индексу index */\nfunction remove(nums: number[], index: number): void {\n    // Сдвинуть все элементы после индекса index на одну позицию вперед\n    for (let i = index; i &lt; nums.length - 1; i++) {\n        nums[i] = nums[i + 1];\n    }\n}\n</code></pre> array.dart<pre><code>/* Удалить элемент по индексу index */\nvoid remove(List&lt;int&gt; nums, int index) {\n  // Сдвинуть все элементы после индекса index на одну позицию вперед\n  for (var i = index; i &lt; nums.length - 1; i++) {\n    nums[i] = nums[i + 1];\n  }\n}\n</code></pre> array.rs<pre><code>/* Удалить элемент по индексу index */\nfn remove(nums: &amp;mut [i32], index: usize) {\n    // Сдвинуть все элементы после индекса index на одну позицию вперед\n    for i in index..nums.len() - 1 {\n        nums[i] = nums[i + 1];\n    }\n}\n</code></pre> array.c<pre><code>/* Удалить элемент по индексу index */\n// Внимание: stdio.h уже использует ключевое слово remove\nvoid removeItem(int *nums, int size, int index) {\n    // Сдвинуть все элементы после индекса index на одну позицию вперед\n    for (int i = index; i &lt; size - 1; i++) {\n        nums[i] = nums[i + 1];\n    }\n}\n</code></pre> array.kt<pre><code>/* Удалить элемент по индексу index */\nfun remove(nums: IntArray, index: Int) {\n    // Сдвинуть все элементы после индекса index на одну позицию вперед\n    for (i in index..&lt;nums.size - 1) {\n        nums[i] = nums[i + 1]\n    }\n}\n</code></pre> array.rb<pre><code>### Удаление элемента по индексу index ###\ndef remove(nums, index)\n  # Сдвинуть все элементы после индекса index на одну позицию вперед\n  for i in index...(nums.length - 1)\n    nums[i] = nums[i + 1]\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>В целом операции вставки и удаления в массиве имеют следующие недостатки.</p> <ul> <li>Высокая временная сложность: средняя временная сложность и вставки, и удаления равна \\(O(n)\\) , где \\(n\\) - длина массива.</li> <li>Потеря элементов: поскольку длина массива неизменяема, после вставки элементы, выходящие за пределы длины массива, будут потеряны.</li> <li>Потери памяти: можно заранее инициализировать более длинный массив и использовать только его переднюю часть; тогда теряемые при вставке элементы на конце не будут нести смысла, но такой подход приводит к лишнему расходу памяти.</li> </ul>","path":["Глава 4. Массивы и списки","4.1 &nbsp; Массив"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#5","level":3,"title":"5.   Обход массива","text":"<p>В большинстве языков программирования массив можно обходить как по индексу, так и напрямую перебирая каждый элемент:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code>def traverse(nums: list[int]):\n    \"\"\"Обход массива\"\"\"\n    count = 0\n    # Обход массива по индексам\n    for i in range(len(nums)):\n        count += nums[i]\n    # Непосредственно обходить элементы массива\n    for num in nums:\n        count += num\n    # Одновременно обходить индексы и элементы данных\n    for i, num in enumerate(nums):\n        count += nums[i]\n        count += num\n</code></pre> array.cpp<pre><code>/* Обход массива */\nvoid traverse(int *nums, int size) {\n    int count = 0;\n    // Обход массива по индексам\n    for (int i = 0; i &lt; size; i++) {\n        count += nums[i];\n    }\n}\n</code></pre> array.java<pre><code>/* Обход массива */\nvoid traverse(int[] nums) {\n    int count = 0;\n    // Обход массива по индексам\n    for (int i = 0; i &lt; nums.length; i++) {\n        count += nums[i];\n    }\n    // Непосредственно обходить элементы массива\n    for (int num : nums) {\n        count += num;\n    }\n}\n</code></pre> array.cs<pre><code>/* Обход массива */\nvoid Traverse(int[] nums) {\n    int count = 0;\n    // Обход массива по индексам\n    for (int i = 0; i &lt; nums.Length; i++) {\n        count += nums[i];\n    }\n    // Непосредственно обходить элементы массива\n    foreach (int num in nums) {\n        count += num;\n    }\n}\n</code></pre> array.go<pre><code>/* Обход массива */\nfunc traverse(nums []int) {\n    count := 0\n    // Обход массива по индексам\n    for i := 0; i &lt; len(nums); i++ {\n        count += nums[i]\n    }\n    count = 0\n    // Непосредственно обходить элементы массива\n    for _, num := range nums {\n        count += num\n    }\n    // Одновременно обходить индексы и элементы данных\n    for i, num := range nums {\n        count += nums[i]\n        count += num\n    }\n}\n</code></pre> array.swift<pre><code>/* Обход массива */\nfunc traverse(nums: [Int]) {\n    var count = 0\n    // Обход массива по индексам\n    for i in nums.indices {\n        count += nums[i]\n    }\n    // Непосредственно обходить элементы массива\n    for num in nums {\n        count += num\n    }\n    // Одновременно обходить индексы и элементы данных\n    for (i, num) in nums.enumerated() {\n        count += nums[i]\n        count += num\n    }\n}\n</code></pre> array.js<pre><code>/* Обход массива */\nfunction traverse(nums) {\n    let count = 0;\n    // Обход массива по индексам\n    for (let i = 0; i &lt; nums.length; i++) {\n        count += nums[i];\n    }\n    // Непосредственно обходить элементы массива\n    for (const num of nums) {\n        count += num;\n    }\n}\n</code></pre> array.ts<pre><code>/* Обход массива */\nfunction traverse(nums: number[]): void {\n    let count = 0;\n    // Обход массива по индексам\n    for (let i = 0; i &lt; nums.length; i++) {\n        count += nums[i];\n    }\n    // Непосредственно обходить элементы массива\n    for (const num of nums) {\n        count += num;\n    }\n}\n</code></pre> array.dart<pre><code>/* Перебрать элементы массива */\nvoid traverse(List&lt;int&gt; nums) {\n  int count = 0;\n  // Обход массива по индексам\n  for (var i = 0; i &lt; nums.length; i++) {\n    count += nums[i];\n  }\n  // Непосредственно обходить элементы массива\n  for (int _num in nums) {\n    count += _num;\n  }\n  // Перебрать массив методом forEach\n  nums.forEach((_num) {\n    count += _num;\n  });\n}\n</code></pre> array.rs<pre><code>/* Обход массива */\nfn traverse(nums: &amp;[i32]) {\n    let mut _count = 0;\n    // Обход массива по индексам\n    for i in 0..nums.len() {\n        _count += nums[i];\n    }\n    // Непосредственно обходить элементы массива\n    _count = 0;\n    for &amp;num in nums {\n        _count += num;\n    }\n}\n</code></pre> array.c<pre><code>/* Обход массива */\nvoid traverse(int *nums, int size) {\n    int count = 0;\n    // Обход массива по индексам\n    for (int i = 0; i &lt; size; i++) {\n        count += nums[i];\n    }\n}\n</code></pre> array.kt<pre><code>/* Обход массива */\nfun traverse(nums: IntArray) {\n    var count = 0\n    // Обход массива по индексам\n    for (i in nums.indices) {\n        count += nums[i]\n    }\n    // Непосредственно обходить элементы массива\n    for (j in nums) {\n        count += j\n    }\n}\n</code></pre> array.rb<pre><code>### Обход массива ###\ndef traverse(nums)\n  count = 0\n\n  # Обход массива по индексам\n  for i in 0...nums.length\n    count += nums[i]\n  end\n\n  # Непосредственно обходить элементы массива\n  for num in nums\n    count += num\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 4. Массивы и списки","4.1 &nbsp; Массив"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#6","level":3,"title":"6.   Поиск элемента","text":"<p>Чтобы найти заданный элемент в массиве, нужно пройти по массиву и на каждой итерации проверять, совпадает ли значение; если совпадает, вернуть соответствующий индекс.</p> <p>Поскольку массив - это линейная структура данных, такая операция поиска называется линейным поиском.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code>def find(nums: list[int], target: int) -&gt; int:\n    \"\"\"Найти заданный элемент в массиве\"\"\"\n    for i in range(len(nums)):\n        if nums[i] == target:\n            return i\n    return -1\n</code></pre> array.cpp<pre><code>/* Найти заданный элемент в массиве */\nint find(int *nums, int size, int target) {\n    for (int i = 0; i &lt; size; i++) {\n        if (nums[i] == target)\n            return i;\n    }\n    return -1;\n}\n</code></pre> array.java<pre><code>/* Найти заданный элемент в массиве */\nint find(int[] nums, int target) {\n    for (int i = 0; i &lt; nums.length; i++) {\n        if (nums[i] == target)\n            return i;\n    }\n    return -1;\n}\n</code></pre> array.cs<pre><code>/* Найти заданный элемент в массиве */\nint Find(int[] nums, int target) {\n    for (int i = 0; i &lt; nums.Length; i++) {\n        if (nums[i] == target)\n            return i;\n    }\n    return -1;\n}\n</code></pre> array.go<pre><code>/* Найти заданный элемент в массиве */\nfunc find(nums []int, target int) (index int) {\n    index = -1\n    for i := 0; i &lt; len(nums); i++ {\n        if nums[i] == target {\n            index = i\n            break\n        }\n    }\n    return\n}\n</code></pre> array.swift<pre><code>/* Найти заданный элемент в массиве */\nfunc find(nums: [Int], target: Int) -&gt; Int {\n    for i in nums.indices {\n        if nums[i] == target {\n            return i\n        }\n    }\n    return -1\n}\n</code></pre> array.js<pre><code>/* Найти заданный элемент в массиве */\nfunction find(nums, target) {\n    for (let i = 0; i &lt; nums.length; i++) {\n        if (nums[i] === target) return i;\n    }\n    return -1;\n}\n</code></pre> array.ts<pre><code>/* Найти заданный элемент в массиве */\nfunction find(nums: number[], target: number): number {\n    for (let i = 0; i &lt; nums.length; i++) {\n        if (nums[i] === target) {\n            return i;\n        }\n    }\n    return -1;\n}\n</code></pre> array.dart<pre><code>/* Найти заданный элемент в массиве */\nint find(List&lt;int&gt; nums, int target) {\n  for (var i = 0; i &lt; nums.length; i++) {\n    if (nums[i] == target) return i;\n  }\n  return -1;\n}\n</code></pre> array.rs<pre><code>/* Найти заданный элемент в массиве */\nfn find(nums: &amp;[i32], target: i32) -&gt; Option&lt;usize&gt; {\n    for i in 0..nums.len() {\n        if nums[i] == target {\n            return Some(i);\n        }\n    }\n    None\n}\n</code></pre> array.c<pre><code>/* Найти заданный элемент в массиве */\nint find(int *nums, int size, int target) {\n    for (int i = 0; i &lt; size; i++) {\n        if (nums[i] == target)\n            return i;\n    }\n    return -1;\n}\n</code></pre> array.kt<pre><code>/* Найти заданный элемент в массиве */\nfun find(nums: IntArray, target: Int): Int {\n    for (i in nums.indices) {\n        if (nums[i] == target)\n            return i\n    }\n    return -1\n}\n</code></pre> array.rb<pre><code>### Поиск заданного элемента в массиве ###\ndef find(nums, target)\n  for i in 0...nums.length\n    return i if nums[i] == target\n  end\n\n  -1\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 4. Массивы и списки","4.1 &nbsp; Массив"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#7","level":3,"title":"7.   Расширение массива","text":"<p>В сложной системной среде программа не может гарантировать, что память сразу после массива доступна, поэтому безопасно расширить емкость массива невозможно. Поэтому в большинстве языков программирования длина массива неизменяема.</p> <p>Если мы хотим расширить массив, нужно заново создать больший массив и затем по одному скопировать в него элементы исходного массива. Это операция с временной сложностью \\(O(n)\\) , и при больших массивах она очень затратна. Соответствующий код показан ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array.py<pre><code>def extend(nums: list[int], enlarge: int) -&gt; list[int]:\n    \"\"\"Увеличить длину массива\"\"\"\n    # Инициализировать массив увеличенной длины\n    res = [0] * (len(nums) + enlarge)\n    # Скопировать все элементы исходного массива в новый массив\n    for i in range(len(nums)):\n        res[i] = nums[i]\n    # Вернуть новый массив после расширения\n    return res\n</code></pre> array.cpp<pre><code>/* Увеличить длину массива */\nint *extend(int *nums, int size, int enlarge) {\n    // Инициализировать массив увеличенной длины\n    int *res = new int[size + enlarge];\n    // Скопировать все элементы исходного массива в новый массив\n    for (int i = 0; i &lt; size; i++) {\n        res[i] = nums[i];\n    }\n    // Освободить память\n    delete[] nums;\n    // Вернуть новый массив после расширения\n    return res;\n}\n</code></pre> array.java<pre><code>/* Увеличить длину массива */\nint[] extend(int[] nums, int enlarge) {\n    // Инициализировать массив увеличенной длины\n    int[] res = new int[nums.length + enlarge];\n    // Скопировать все элементы исходного массива в новый массив\n    for (int i = 0; i &lt; nums.length; i++) {\n        res[i] = nums[i];\n    }\n    // Вернуть новый массив после расширения\n    return res;\n}\n</code></pre> array.cs<pre><code>/* Увеличить длину массива */\nint[] Extend(int[] nums, int enlarge) {\n    // Инициализировать массив увеличенной длины\n    int[] res = new int[nums.Length + enlarge];\n    // Скопировать все элементы исходного массива в новый массив\n    for (int i = 0; i &lt; nums.Length; i++) {\n        res[i] = nums[i];\n    }\n    // Вернуть новый массив после расширения\n    return res;\n}\n</code></pre> array.go<pre><code>/* Увеличить длину массива */\nfunc extend(nums []int, enlarge int) []int {\n    // Инициализировать массив увеличенной длины\n    res := make([]int, len(nums)+enlarge)\n    // Скопировать все элементы исходного массива в новый массив\n    for i, num := range nums {\n        res[i] = num\n    }\n    // Вернуть новый массив после расширения\n    return res\n}\n</code></pre> array.swift<pre><code>/* Увеличить длину массива */\nfunc extend(nums: [Int], enlarge: Int) -&gt; [Int] {\n    // Инициализировать массив увеличенной длины\n    var res = Array(repeating: 0, count: nums.count + enlarge)\n    // Скопировать все элементы исходного массива в новый массив\n    for i in nums.indices {\n        res[i] = nums[i]\n    }\n    // Вернуть новый массив после расширения\n    return res\n}\n</code></pre> array.js<pre><code>/* Увеличить длину массива */\n// Обратите внимание: Array в JavaScript — это динамический массив, его можно расширять напрямую\n// Для удобства обучения в этой функции Array рассматривается как массив неизменяемой длины\nfunction extend(nums, enlarge) {\n    // Инициализировать массив увеличенной длины\n    const res = new Array(nums.length + enlarge).fill(0);\n    // Скопировать все элементы исходного массива в новый массив\n    for (let i = 0; i &lt; nums.length; i++) {\n        res[i] = nums[i];\n    }\n    // Вернуть новый массив после расширения\n    return res;\n}\n</code></pre> array.ts<pre><code>/* Увеличить длину массива */\n// Обратите внимание: Array в TypeScript — это динамический массив, его можно расширять напрямую\n// Для удобства обучения в этой функции Array рассматривается как массив неизменяемой длины\nfunction extend(nums: number[], enlarge: number): number[] {\n    // Инициализировать массив увеличенной длины\n    const res = new Array(nums.length + enlarge).fill(0);\n    // Скопировать все элементы исходного массива в новый массив\n    for (let i = 0; i &lt; nums.length; i++) {\n        res[i] = nums[i];\n    }\n    // Вернуть новый массив после расширения\n    return res;\n}\n</code></pre> array.dart<pre><code>/* Увеличить длину массива */\nList&lt;int&gt; extend(List&lt;int&gt; nums, int enlarge) {\n  // Инициализировать массив увеличенной длины\n  List&lt;int&gt; res = List.filled(nums.length + enlarge, 0);\n  // Скопировать все элементы исходного массива в новый массив\n  for (var i = 0; i &lt; nums.length; i++) {\n    res[i] = nums[i];\n  }\n  // Вернуть новый массив после расширения\n  return res;\n}\n</code></pre> array.rs<pre><code>/* Увеличить длину массива */\nfn extend(nums: &amp;[i32], enlarge: usize) -&gt; Vec&lt;i32&gt; {\n    // Инициализировать массив увеличенной длины\n    let mut res: Vec&lt;i32&gt; = vec![0; nums.len() + enlarge];\n    // Скопировать все элементы исходного массива в новый\n    res[0..nums.len()].copy_from_slice(nums);\n\n    // Вернуть новый массив после расширения\n    res\n}\n</code></pre> array.c<pre><code>/* Увеличить длину массива */\nint *extend(int *nums, int size, int enlarge) {\n    // Инициализировать массив увеличенной длины\n    int *res = (int *)malloc(sizeof(int) * (size + enlarge));\n    // Скопировать все элементы исходного массива в новый массив\n    for (int i = 0; i &lt; size; i++) {\n        res[i] = nums[i];\n    }\n    // Инициализировать расширенное пространство\n    for (int i = size; i &lt; size + enlarge; i++) {\n        res[i] = 0;\n    }\n    // Вернуть новый массив после расширения\n    return res;\n}\n</code></pre> array.kt<pre><code>/* Увеличить длину массива */\nfun extend(nums: IntArray, enlarge: Int): IntArray {\n    // Инициализировать массив увеличенной длины\n    val res = IntArray(nums.size + enlarge)\n    // Скопировать все элементы исходного массива в новый массив\n    for (i in nums.indices) {\n        res[i] = nums[i]\n    }\n    // Вернуть новый массив после расширения\n    return res\n}\n</code></pre> array.rb<pre><code>### Увеличить длину массива ###\n# Обратите внимание: Array в Ruby является динамическим массивом и может расширяться напрямую\n# Для удобства обучения в этой функции Array рассматривается как массив неизменяемой длины\ndef extend(nums, enlarge)\n  # Инициализировать массив увеличенной длины\n  res = Array.new(nums.length + enlarge, 0)\n\n  # Скопировать все элементы исходного массива в новый массив\n  for i in 0...nums.length\n    res[i] = nums[i]\n  end\n\n  # Вернуть новый массив после расширения\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 4. Массивы и списки","4.1 &nbsp; Массив"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#412","level":2,"title":"4.1.2   Преимущества и ограничения массива","text":"<p>Массив хранится в непрерывной области памяти, и все его элементы имеют один и тот же тип. Такой подход содержит богатую априорную информацию, которую система может использовать для оптимизации эффективности операций с этой структурой данных.</p> <ul> <li>Высокая пространственная эффективность: массив выделяет для данных непрерывный блок памяти без дополнительного структурного накладного расхода.</li> <li>Поддержка произвольного доступа: массив позволяет обращаться к любому элементу за \\(O(1)\\) времени.</li> <li>Локальность кэша: при обращении к элементу массива компьютер загружает не только сам элемент, но и соседние данные, что позволяет использовать кэш для ускорения последующих операций.</li> </ul> <p>Непрерывное хранение данных - это палка о двух концах, и у него есть следующие ограничения.</p> <ul> <li>Низкая эффективность вставки и удаления: когда элементов в массиве много, вставка и удаление требуют сдвига большого количества элементов.</li> <li>Неизменяемая длина: после инициализации длина массива фиксирована; расширение массива требует копирования всех данных в новый массив, что стоит дорого.</li> <li>Потери памяти: если выделенный массив больше, чем реально необходимо, лишнее пространство пропадает впустую.</li> </ul>","path":["Глава 4. Массивы и списки","4.1 &nbsp; Массив"],"tags":[]},{"location":"chapter_array_and_linkedlist/array/#413","level":2,"title":"4.1.3   Типичные применения массива","text":"<p>Массив - это базовая и очень распространенная структура данных. Он часто используется как в различных алгоритмах, так и при реализации более сложных структур данных.</p> <ul> <li>Произвольный доступ: если мы хотим случайным образом выбирать некоторые образцы, можно сохранить их в массиве и сгенерировать случайную последовательность индексов для выборки.</li> <li>Сортировка и поиск: массив - самая распространенная структура данных для алгоритмов сортировки и поиска. Быстрая сортировка, сортировка слиянием, двоичный поиск и многие другие алгоритмы в основном работают именно с массивами.</li> <li>Таблица поиска: когда нужно быстро находить элемент или его соответствие, массив можно использовать как таблицу поиска. Например, если мы хотим реализовать отображение символов в коды ASCII, можно использовать значение ASCII как индекс, а соответствующий элемент хранить по этой позиции массива.</li> <li>Машинное обучение: в нейронных сетях широко используются операции линейной алгебры над векторами, матрицами и тензорами, и все эти данные строятся в форме массивов. Массив - самая часто используемая структура данных в программировании нейросетей.</li> <li>Реализация структур данных: массивы можно использовать для реализации стеков, очередей, хеш-таблиц, куч, графов и других структур данных. Например, матрица смежности графа по сути является двумерным массивом.</li> </ul>","path":["Глава 4. Массивы и списки","4.1 &nbsp; Массив"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/","level":1,"title":"4.2   Связный список","text":"<p>Память - общий ресурс для всех программ, и в сложной среде выполнения свободные участки памяти могут быть разбросаны по всему адресному пространству. Мы знаем, что память для хранения массива должна быть непрерывной, а если массив очень велик, в памяти может не оказаться столь большого непрерывного блока. Именно здесь и проявляется преимущество гибкости связного списка.</p> <p>Связный список (linked list) - это линейная структура данных, в которой каждый элемент представляет собой объект-узел, а сами узлы соединены между собой с помощью ссылок. Ссылка хранит адрес памяти следующего узла, благодаря чему из текущего узла можно перейти к следующему.</p> <p>Конструкция связного списка позволяет хранить отдельные узлы в разных местах памяти, и их адреса вовсе не обязаны быть последовательными.</p> <p></p> <p> Рисунок 4-5   Определение связного списка и способ хранения </p> <p>Как видно на рисунке 4-5, базовой единицей связного списка является объект узел (node). Каждый узел содержит две части данных: значение узла и ссылку на следующий узел.</p> <ul> <li>Первый узел связного списка называется головным узлом, а последний - хвостовым узлом.</li> <li>Хвостовой узел указывает на пустое значение, что в Java, C++ и Python обозначается как <code>null</code> , <code>nullptr</code> и <code>None</code> соответственно.</li> <li>В языках, поддерживающих указатели, таких как C, C++, Go и Rust, упомянутую выше ссылку следует заменить на указатель.</li> </ul> <p>Как показано в коде ниже, узел связного списка <code>ListNode</code> хранит не только значение, но и дополнительную ссылку (указатель). Поэтому при одинаковом объеме данных связный список занимает больше памяти, чем массив.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>class ListNode:\n    \"\"\"Класс узла связного списка\"\"\"\n    def __init__(self, val: int):\n        self.val: int = val               # Значение узла\n        self.next: ListNode | None = None # Ссылка на следующий узел\n</code></pre> <pre><code>/* Структура узла связного списка */\nstruct ListNode {\n    int val;         // Значение узла\n    ListNode *next;  // Указатель на следующий узел\n    ListNode(int x) : val(x), next(nullptr) {}  // Конструктор\n};\n</code></pre> <pre><code>/* Класс узла связного списка */\nclass ListNode {\n    int val;        // Значение узла\n    ListNode next;  // Ссылка на следующий узел\n    ListNode(int x) { val = x; }  // Конструктор\n}\n</code></pre> <pre><code>/* Класс узла связного списка */\nclass ListNode(int x) {  // Конструктор\n    int val = x;         // Значение узла\n    ListNode? next;      // Ссылка на следующий узел\n}\n</code></pre> <pre><code>/* Структура узла связного списка */\ntype ListNode struct {\n    Val  int       // Значение узла\n    Next *ListNode // Указатель на следующий узел\n}\n\n// NewListNode Конструктор, создает новый узел\nfunc NewListNode(val int) *ListNode {\n    return &amp;ListNode{\n        Val:  val,\n        Next: nil,\n    }\n}\n</code></pre> <pre><code>/* Класс узла связного списка */\nclass ListNode {\n    var val: Int // Значение узла\n    var next: ListNode? // Ссылка на следующий узел\n\n    init(x: Int) { // Конструктор\n        val = x\n    }\n}\n</code></pre> <pre><code>/* Класс узла связного списка */\nclass ListNode {\n    constructor(val, next) {\n        this.val = (val === undefined ? 0 : val);       // Значение узла\n        this.next = (next === undefined ? null : next); // Ссылка на следующий узел\n    }\n}\n</code></pre> <pre><code>/* Класс узла связного списка */\nclass ListNode {\n    val: number;\n    next: ListNode | null;\n    constructor(val?: number, next?: ListNode | null) {\n        this.val = val === undefined ? 0 : val;        // Значение узла\n        this.next = next === undefined ? null : next;  // Ссылка на следующий узел\n    }\n}\n</code></pre> <pre><code>/* Класс узла связного списка */\nclass ListNode {\n  int val; // Значение узла\n  ListNode? next; // Ссылка на следующий узел\n  ListNode(this.val, [this.next]); // Конструктор\n}\n</code></pre> <pre><code>use std::rc::Rc;\nuse std::cell::RefCell;\n/* Класс узла связного списка */\n#[derive(Debug)]\nstruct ListNode {\n    val: i32, // Значение узла\n    next: Option&lt;Rc&lt;RefCell&lt;ListNode&gt;&gt;&gt;, // Указатель на следующий узел\n}\n</code></pre> <pre><code>/* Структура узла связного списка */\ntypedef struct ListNode {\n    int val;               // Значение узла\n    struct ListNode *next; // Указатель на следующий узел\n} ListNode;\n\n/* Конструктор */\nListNode *newListNode(int val) {\n    ListNode *node;\n    node = (ListNode *) malloc(sizeof(ListNode));\n    node-&gt;val = val;\n    node-&gt;next = NULL;\n    return node;\n}\n</code></pre> <pre><code>/* Класс узла связного списка */\n// Конструктор\nclass ListNode(x: Int) {\n    val _val: Int = x          // Значение узла\n    val next: ListNode? = null // Ссылка на следующий узел\n}\n</code></pre> <pre><code># Класс узла связного списка\nclass ListNode\n  attr_accessor :val  # Значение узла\n  attr_accessor :next # Ссылка на следующий узел\n\n  def initialize(val=0, next_node=nil)\n    @val = val\n    @next = next_node\n  end\nend\n</code></pre>","path":["Глава 4. Массивы и списки","4.2 &nbsp; Связный список"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#421","level":2,"title":"4.2.1   Основные операции со связным списком","text":"","path":["Глава 4. Массивы и списки","4.2 &nbsp; Связный список"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#1","level":3,"title":"1.   Инициализация связного списка","text":"<p>Построение связного списка состоит из двух шагов: сначала нужно инициализировать объекты всех узлов, затем установить ссылочные связи между ними. После завершения инициализации мы можем, начиная с головы списка, последовательно проходить все узлы по ссылке <code>next</code>.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linked_list.py<pre><code># Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4\n# Инициализация отдельных узлов\nn0 = ListNode(1)\nn1 = ListNode(3)\nn2 = ListNode(2)\nn3 = ListNode(5)\nn4 = ListNode(4)\n# Построение ссылок между узлами\nn0.next = n1\nn1.next = n2\nn2.next = n3\nn3.next = n4\n</code></pre> linked_list.cpp<pre><code>/* Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// Инициализация отдельных узлов\nListNode* n0 = new ListNode(1);\nListNode* n1 = new ListNode(3);\nListNode* n2 = new ListNode(2);\nListNode* n3 = new ListNode(5);\nListNode* n4 = new ListNode(4);\n// Построение ссылок между узлами\nn0-&gt;next = n1;\nn1-&gt;next = n2;\nn2-&gt;next = n3;\nn3-&gt;next = n4;\n</code></pre> linked_list.java<pre><code>/* Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// Инициализация отдельных узлов\nListNode n0 = new ListNode(1);\nListNode n1 = new ListNode(3);\nListNode n2 = new ListNode(2);\nListNode n3 = new ListNode(5);\nListNode n4 = new ListNode(4);\n// Построение ссылок между узлами\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.cs<pre><code>/* Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// Инициализация отдельных узлов\nListNode n0 = new(1);\nListNode n1 = new(3);\nListNode n2 = new(2);\nListNode n3 = new(5);\nListNode n4 = new(4);\n// Построение ссылок между узлами\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.go<pre><code>/* Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// Инициализация отдельных узлов\nn0 := NewListNode(1)\nn1 := NewListNode(3)\nn2 := NewListNode(2)\nn3 := NewListNode(5)\nn4 := NewListNode(4)\n// Построение ссылок между узлами\nn0.Next = n1\nn1.Next = n2\nn2.Next = n3\nn3.Next = n4\n</code></pre> linked_list.swift<pre><code>/* Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// Инициализация отдельных узлов\nlet n0 = ListNode(x: 1)\nlet n1 = ListNode(x: 3)\nlet n2 = ListNode(x: 2)\nlet n3 = ListNode(x: 5)\nlet n4 = ListNode(x: 4)\n// Построение ссылок между узлами\nn0.next = n1\nn1.next = n2\nn2.next = n3\nn3.next = n4\n</code></pre> linked_list.js<pre><code>/* Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// Инициализация отдельных узлов\nconst n0 = new ListNode(1);\nconst n1 = new ListNode(3);\nconst n2 = new ListNode(2);\nconst n3 = new ListNode(5);\nconst n4 = new ListNode(4);\n// Построение ссылок между узлами\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.ts<pre><code>/* Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// Инициализация отдельных узлов\nconst n0 = new ListNode(1);\nconst n1 = new ListNode(3);\nconst n2 = new ListNode(2);\nconst n3 = new ListNode(5);\nconst n4 = new ListNode(4);\n// Построение ссылок между узлами\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.dart<pre><code>/* Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\\\n// Инициализация отдельных узлов\nListNode n0 = ListNode(1);\nListNode n1 = ListNode(3);\nListNode n2 = ListNode(2);\nListNode n3 = ListNode(5);\nListNode n4 = ListNode(4);\n// Построение ссылок между узлами\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.rs<pre><code>/* Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// Инициализация отдельных узлов\nlet n0 = Rc::new(RefCell::new(ListNode { val: 1, next: None }));\nlet n1 = Rc::new(RefCell::new(ListNode { val: 3, next: None }));\nlet n2 = Rc::new(RefCell::new(ListNode { val: 2, next: None }));\nlet n3 = Rc::new(RefCell::new(ListNode { val: 5, next: None }));\nlet n4 = Rc::new(RefCell::new(ListNode { val: 4, next: None }));\n\n// Построение ссылок между узлами\nn0.borrow_mut().next = Some(n1.clone());\nn1.borrow_mut().next = Some(n2.clone());\nn2.borrow_mut().next = Some(n3.clone());\nn3.borrow_mut().next = Some(n4.clone());\n</code></pre> linked_list.c<pre><code>/* Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// Инициализация отдельных узлов\nListNode* n0 = newListNode(1);\nListNode* n1 = newListNode(3);\nListNode* n2 = newListNode(2);\nListNode* n3 = newListNode(5);\nListNode* n4 = newListNode(4);\n// Построение ссылок между узлами\nn0-&gt;next = n1;\nn1-&gt;next = n2;\nn2-&gt;next = n3;\nn3-&gt;next = n4;\n</code></pre> linked_list.kt<pre><code>/* Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// Инициализация отдельных узлов\nval n0 = ListNode(1)\nval n1 = ListNode(3)\nval n2 = ListNode(2)\nval n3 = ListNode(5)\nval n4 = ListNode(4)\n// Построение ссылок между узлами\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.rb<pre><code># Инициализация связного списка 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4\n# Инициализация отдельных узлов\nn0 = ListNode.new(1)\nn1 = ListNode.new(3)\nn2 = ListNode.new(2)\nn3 = ListNode.new(5)\nn4 = ListNode.new(4)\n# Построение ссылок между узлами\nn0.next = n1\nn1.next = n2\nn2.next = n3\nn3.next = n4\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%D1%81%D0%B2%D1%8F%D0%B7%D0%BD%D1%8B%D0%B9%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%D1%83%D0%B7%D0%B5%D0%BB%D0%BA%D0%BB%D0%B0%D1%81%D1%81%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%D0%97%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%83%D0%B7%D0%BB%D0%B0%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%D0%A1%D1%81%D1%8B%D0%BB%D0%BA%D0%B0%20%D0%BD%D0%B0%20%D1%81%D0%BB%D0%B5%D0%B4%D1%83%D1%8E%D1%89%D0%B8%D0%B9%20%D1%83%D0%B7%D0%B5%D0%BB%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%81%D0%B2%D1%8F%D0%B7%D0%BD%D1%8B%D0%B9%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%201%20-%3E%203%20-%3E%202%20-%3E%205%20-%3E%204%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D0%BA%D0%B0%D0%B6%D0%B4%D1%8B%D0%B9%20%D1%83%D0%B7%D0%B5%D0%BB%0A%20%20%20%20n0%20%3D%20ListNode%281%29%0A%20%20%20%20n1%20%3D%20ListNode%283%29%0A%20%20%20%20n2%20%3D%20ListNode%282%29%0A%20%20%20%20n3%20%3D%20ListNode%285%29%0A%20%20%20%20n4%20%3D%20ListNode%284%29%0A%20%20%20%20%23%20%D0%9F%D0%BE%D1%81%D1%82%D1%80%D0%BE%D0%B8%D1%82%D1%8C%20%D1%81%D1%81%D1%8B%D0%BB%D0%BA%D0%B8%20%D0%BC%D0%B5%D0%B6%D0%B4%D1%83%20%D1%83%D0%B7%D0%BB%D0%B0%D0%BC%D0%B8%0A%20%20%20%20n0.next%20%3D%20n1%0A%20%20%20%20n1.next%20%3D%20n2%0A%20%20%20%20n2.next%20%3D%20n3%0A%20%20%20%20n3.next%20%3D%20n4&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p> <p>Массив в целом - это одна переменная: например, массив <code>nums</code> содержит элементы <code>nums[0]</code> , <code>nums[1]</code> и т.д. Связный список же состоит из множества независимых объектов-узлов. Обычно в качестве обозначения всего связного списка используют головной узел; например, в приведенном выше коде связный список можно обозначить как <code>n0</code> .</p>","path":["Глава 4. Массивы и списки","4.2 &nbsp; Связный список"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#2","level":3,"title":"2.   Вставка узла","text":"<p>Вставить узел в связный список очень легко. Как показано на рисунке 4-6, предположим, что мы хотим вставить новый узел <code>P</code> между двумя соседними узлами <code>n0</code> и <code>n1</code> ; для этого нужно изменить всего две ссылки (указателя), а временная сложность будет равна \\(O(1)\\) .</p> <p>Для сравнения: временная сложность вставки элемента в массив составляет \\(O(n)\\) , и при большом объеме данных это менее эффективно.</p> <p></p> <p> Рисунок 4-6   Пример вставки узла в связный список </p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linked_list.py<pre><code>def insert(n0: ListNode, P: ListNode):\n    \"\"\"Вставить узел P после узла n0 в связном списке\"\"\"\n    n1 = n0.next\n    P.next = n1\n    n0.next = P\n</code></pre> linked_list.cpp<pre><code>/* Вставить узел P после узла n0 в связном списке */\nvoid insert(ListNode *n0, ListNode *P) {\n    ListNode *n1 = n0-&gt;next;\n    P-&gt;next = n1;\n    n0-&gt;next = P;\n}\n</code></pre> linked_list.java<pre><code>/* Вставить узел P после узла n0 в связном списке */\nvoid insert(ListNode n0, ListNode P) {\n    ListNode n1 = n0.next;\n    P.next = n1;\n    n0.next = P;\n}\n</code></pre> linked_list.cs<pre><code>/* Вставить узел P после узла n0 в связном списке */\nvoid Insert(ListNode n0, ListNode P) {\n    ListNode? n1 = n0.next;\n    P.next = n1;\n    n0.next = P;\n}\n</code></pre> linked_list.go<pre><code>/* Вставить узел P после узла n0 в связном списке */\nfunc insertNode(n0 *ListNode, P *ListNode) {\n    n1 := n0.Next\n    P.Next = n1\n    n0.Next = P\n}\n</code></pre> linked_list.swift<pre><code>/* Вставить узел P после узла n0 в связном списке */\nfunc insert(n0: ListNode, P: ListNode) {\n    let n1 = n0.next\n    P.next = n1\n    n0.next = P\n}\n</code></pre> linked_list.js<pre><code>/* Вставить узел P после узла n0 в связном списке */\nfunction insert(n0, P) {\n    const n1 = n0.next;\n    P.next = n1;\n    n0.next = P;\n}\n</code></pre> linked_list.ts<pre><code>/* Вставить узел P после узла n0 в связном списке */\nfunction insert(n0: ListNode, P: ListNode): void {\n    const n1 = n0.next;\n    P.next = n1;\n    n0.next = P;\n}\n</code></pre> linked_list.dart<pre><code>/* Вставить узел P после узла n0 в связном списке */\nvoid insert(ListNode n0, ListNode P) {\n  ListNode? n1 = n0.next;\n  P.next = n1;\n  n0.next = P;\n}\n</code></pre> linked_list.rs<pre><code>/* Вставить узел P после узла n0 в связном списке */\n#[allow(non_snake_case)]\npub fn insert&lt;T&gt;(n0: &amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;, P: Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;) {\n    let n1 = n0.borrow_mut().next.take();\n    P.borrow_mut().next = n1;\n    n0.borrow_mut().next = Some(P);\n}\n</code></pre> linked_list.c<pre><code>/* Вставить узел P после узла n0 в связном списке */\nvoid insert(ListNode *n0, ListNode *P) {\n    ListNode *n1 = n0-&gt;next;\n    P-&gt;next = n1;\n    n0-&gt;next = P;\n}\n</code></pre> linked_list.kt<pre><code>/* Вставить узел P после узла n0 в связном списке */\nfun insert(n0: ListNode?, p: ListNode?) {\n    val n1 = n0?.next\n    p?.next = n1\n    n0?.next = p\n}\n</code></pre> linked_list.rb<pre><code>### Вставка узла _p после узла n0 в связном списке ###\n# В Ruby `p` является встроенной функцией, а `P` — константой, поэтому вместо них можно использовать `_p`\ndef insert(n0, _p)\n  n1 = n0.next\n  _p.next = n1\n  n0.next = _p\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 4. Массивы и списки","4.2 &nbsp; Связный список"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#3","level":3,"title":"3.   Удаление узла","text":"<p>Как показано на рисунке 4-7, удалить узел из связного списка тоже очень просто: нужно изменить всего одну ссылку (указатель).</p> <p>Стоит отметить, что хотя после завершения операции удаления узел <code>P</code> все еще указывает на <code>n1</code> , при обходе связного списка до <code>P</code> уже нельзя добраться. Это означает, что <code>P</code> фактически больше не принадлежит данному списку.</p> <p></p> <p> Рисунок 4-7   Удаление узла из связного списка </p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linked_list.py<pre><code>def remove(n0: ListNode):\n    \"\"\"Удалить первый узел после узла n0 в связном списке\"\"\"\n    if not n0.next:\n        return\n    # n0 -&gt; P -&gt; n1\n    P = n0.next\n    n1 = P.next\n    n0.next = n1\n</code></pre> linked_list.cpp<pre><code>/* Удалить первый узел после узла n0 в связном списке */\nvoid remove(ListNode *n0) {\n    if (n0-&gt;next == nullptr)\n        return;\n    // n0 -&gt; P -&gt; n1\n    ListNode *P = n0-&gt;next;\n    ListNode *n1 = P-&gt;next;\n    n0-&gt;next = n1;\n    // Освободить память\n    delete P;\n}\n</code></pre> linked_list.java<pre><code>/* Удалить первый узел после узла n0 в связном списке */\nvoid remove(ListNode n0) {\n    if (n0.next == null)\n        return;\n    // n0 -&gt; P -&gt; n1\n    ListNode P = n0.next;\n    ListNode n1 = P.next;\n    n0.next = n1;\n}\n</code></pre> linked_list.cs<pre><code>/* Удалить первый узел после узла n0 в связном списке */\nvoid Remove(ListNode n0) {\n    if (n0.next == null)\n        return;\n    // n0 -&gt; P -&gt; n1\n    ListNode P = n0.next;\n    ListNode? n1 = P.next;\n    n0.next = n1;\n}\n</code></pre> linked_list.go<pre><code>/* Удалить первый узел после узла n0 в связном списке */\nfunc removeItem(n0 *ListNode) {\n    if n0.Next == nil {\n        return\n    }\n    // n0 -&gt; P -&gt; n1\n    P := n0.Next\n    n1 := P.Next\n    n0.Next = n1\n}\n</code></pre> linked_list.swift<pre><code>/* Удалить первый узел после узла n0 в связном списке */\nfunc remove(n0: ListNode) {\n    if n0.next == nil {\n        return\n    }\n    // n0 -&gt; P -&gt; n1\n    let P = n0.next\n    let n1 = P?.next\n    n0.next = n1\n}\n</code></pre> linked_list.js<pre><code>/* Удалить первый узел после узла n0 в связном списке */\nfunction remove(n0) {\n    if (!n0.next) return;\n    // n0 -&gt; P -&gt; n1\n    const P = n0.next;\n    const n1 = P.next;\n    n0.next = n1;\n}\n</code></pre> linked_list.ts<pre><code>/* Удалить первый узел после узла n0 в связном списке */\nfunction remove(n0: ListNode): void {\n    if (!n0.next) {\n        return;\n    }\n    // n0 -&gt; P -&gt; n1\n    const P = n0.next;\n    const n1 = P.next;\n    n0.next = n1;\n}\n</code></pre> linked_list.dart<pre><code>/* Удалить первый узел после узла n0 в связном списке */\nvoid remove(ListNode n0) {\n  if (n0.next == null) return;\n  // n0 -&gt; P -&gt; n1\n  ListNode P = n0.next!;\n  ListNode? n1 = P.next;\n  n0.next = n1;\n}\n</code></pre> linked_list.rs<pre><code>/* Удалить первый узел после узла n0 в связном списке */\n#[allow(non_snake_case)]\npub fn remove&lt;T&gt;(n0: &amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;) {\n    // n0 -&gt; P -&gt; n1\n    let P = n0.borrow_mut().next.take();\n    if let Some(node) = P {\n        let n1 = node.borrow_mut().next.take();\n        n0.borrow_mut().next = n1;\n    }\n}\n</code></pre> linked_list.c<pre><code>/* Удалить первый узел после узла n0 в связном списке */\n// Внимание: stdio.h уже использует ключевое слово remove\nvoid removeItem(ListNode *n0) {\n    if (!n0-&gt;next)\n        return;\n    // n0 -&gt; P -&gt; n1\n    ListNode *P = n0-&gt;next;\n    ListNode *n1 = P-&gt;next;\n    n0-&gt;next = n1;\n    // Освободить память\n    free(P);\n}\n</code></pre> linked_list.kt<pre><code>/* Удалить первый узел после узла n0 в связном списке */\nfun remove(n0: ListNode?) {\n    if (n0?.next == null)\n        return\n    // n0 -&gt; P -&gt; n1\n    val p = n0.next\n    val n1 = p?.next\n    n0.next = n1\n}\n</code></pre> linked_list.rb<pre><code>### Удаление первого узла после узла n0 в связном списке ###\ndef remove(n0)\n  return if n0.next.nil?\n\n  # n0 -&gt; remove_node -&gt; n1\n  remove_node = n0.next\n  n1 = remove_node.next\n  n0.next = n1\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 4. Массивы и списки","4.2 &nbsp; Связный список"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#4","level":3,"title":"4.   Доступ к узлу","text":"<p>Доступ к узлам в связном списке менее эффективен. Как уже обсуждалось в предыдущем разделе, к любому элементу массива можно обратиться за \\(O(1)\\) времени. Со связным списком это не так: программе нужно начать с головного узла и последовательно двигаться дальше, пока не будет найден целевой узел. То есть для доступа к \\(i\\) -му узлу списка нужно выполнить \\(i - 1\\) итераций, а временная сложность составляет \\(O(n)\\) .</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linked_list.py<pre><code>def access(head: ListNode, index: int) -&gt; ListNode | None:\n    \"\"\"Доступ к узлу связного списка по индексу index\"\"\"\n    for _ in range(index):\n        if not head:\n            return None\n        head = head.next\n    return head\n</code></pre> linked_list.cpp<pre><code>/* Доступ к узлу связного списка по индексу index */\nListNode *access(ListNode *head, int index) {\n    for (int i = 0; i &lt; index; i++) {\n        if (head == nullptr)\n            return nullptr;\n        head = head-&gt;next;\n    }\n    return head;\n}\n</code></pre> linked_list.java<pre><code>/* Доступ к узлу связного списка по индексу index */\nListNode access(ListNode head, int index) {\n    for (int i = 0; i &lt; index; i++) {\n        if (head == null)\n            return null;\n        head = head.next;\n    }\n    return head;\n}\n</code></pre> linked_list.cs<pre><code>/* Доступ к узлу связного списка по индексу index */\nListNode? Access(ListNode? head, int index) {\n    for (int i = 0; i &lt; index; i++) {\n        if (head == null)\n            return null;\n        head = head.next;\n    }\n    return head;\n}\n</code></pre> linked_list.go<pre><code>/* Доступ к узлу связного списка по индексу index */\nfunc access(head *ListNode, index int) *ListNode {\n    for i := 0; i &lt; index; i++ {\n        if head == nil {\n            return nil\n        }\n        head = head.Next\n    }\n    return head\n}\n</code></pre> linked_list.swift<pre><code>/* Доступ к узлу связного списка по индексу index */\nfunc access(head: ListNode, index: Int) -&gt; ListNode? {\n    var head: ListNode? = head\n    for _ in 0 ..&lt; index {\n        if head == nil {\n            return nil\n        }\n        head = head?.next\n    }\n    return head\n}\n</code></pre> linked_list.js<pre><code>/* Доступ к узлу связного списка по индексу index */\nfunction access(head, index) {\n    for (let i = 0; i &lt; index; i++) {\n        if (!head) {\n            return null;\n        }\n        head = head.next;\n    }\n    return head;\n}\n</code></pre> linked_list.ts<pre><code>/* Доступ к узлу связного списка по индексу index */\nfunction access(head: ListNode | null, index: number): ListNode | null {\n    for (let i = 0; i &lt; index; i++) {\n        if (!head) {\n            return null;\n        }\n        head = head.next;\n    }\n    return head;\n}\n</code></pre> linked_list.dart<pre><code>/* Доступ к узлу связного списка по индексу index */\nListNode? access(ListNode? head, int index) {\n  for (var i = 0; i &lt; index; i++) {\n    if (head == null) return null;\n    head = head.next;\n  }\n  return head;\n}\n</code></pre> linked_list.rs<pre><code>/* Доступ к узлу связного списка по индексу index */\npub fn access&lt;T&gt;(head: Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;, index: i32) -&gt; Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt; {\n    fn dfs&lt;T&gt;(\n        head: Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;,\n        index: i32,\n    ) -&gt; Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt; {\n        if index &lt;= 0 {\n            return head.cloned();\n        }\n\n        if let Some(node) = head {\n            dfs(node.borrow().next.as_ref(), index - 1)\n        } else {\n            None\n        }\n    }\n\n    dfs(Some(head).as_ref(), index)\n}\n</code></pre> linked_list.c<pre><code>/* Доступ к узлу связного списка по индексу index */\nListNode *access(ListNode *head, int index) {\n    for (int i = 0; i &lt; index; i++) {\n        if (head == NULL)\n            return NULL;\n        head = head-&gt;next;\n    }\n    return head;\n}\n</code></pre> linked_list.kt<pre><code>/* Доступ к узлу связного списка по индексу index */\nfun access(head: ListNode?, index: Int): ListNode? {\n    var h = head\n    for (i in 0..&lt;index) {\n        if (h == null)\n            return null\n        h = h.next\n    }\n    return h\n}\n</code></pre> linked_list.rb<pre><code>### Доступ к узлу связного списка по индексу index ###\ndef access(head, index)\n  for i in 0...index\n    return nil if head.nil?\n    head = head.next\n  end\n\n  head\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 4. Массивы и списки","4.2 &nbsp; Связный список"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#5","level":3,"title":"5.   Поиск узла","text":"<p>Поиск узла заключается в обходе связного списка, нахождении узла со значением <code>target</code> и возврате его индекса в списке. Этот процесс тоже относится к линейному поиску. Код выглядит следующим образом:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linked_list.py<pre><code>def find(head: ListNode, target: int) -&gt; int:\n    \"\"\"Найти в связном списке первый узел со значением target\"\"\"\n    index = 0\n    while head:\n        if head.val == target:\n            return index\n        head = head.next\n        index += 1\n    return -1\n</code></pre> linked_list.cpp<pre><code>/* Найти в связном списке первый узел со значением target */\nint find(ListNode *head, int target) {\n    int index = 0;\n    while (head != nullptr) {\n        if (head-&gt;val == target)\n            return index;\n        head = head-&gt;next;\n        index++;\n    }\n    return -1;\n}\n</code></pre> linked_list.java<pre><code>/* Найти в связном списке первый узел со значением target */\nint find(ListNode head, int target) {\n    int index = 0;\n    while (head != null) {\n        if (head.val == target)\n            return index;\n        head = head.next;\n        index++;\n    }\n    return -1;\n}\n</code></pre> linked_list.cs<pre><code>/* Найти в связном списке первый узел со значением target */\nint Find(ListNode? head, int target) {\n    int index = 0;\n    while (head != null) {\n        if (head.val == target)\n            return index;\n        head = head.next;\n        index++;\n    }\n    return -1;\n}\n</code></pre> linked_list.go<pre><code>/* Найти в связном списке первый узел со значением target */\nfunc findNode(head *ListNode, target int) int {\n    index := 0\n    for head != nil {\n        if head.Val == target {\n            return index\n        }\n        head = head.Next\n        index++\n    }\n    return -1\n}\n</code></pre> linked_list.swift<pre><code>/* Найти в связном списке первый узел со значением target */\nfunc find(head: ListNode, target: Int) -&gt; Int {\n    var head: ListNode? = head\n    var index = 0\n    while head != nil {\n        if head?.val == target {\n            return index\n        }\n        head = head?.next\n        index += 1\n    }\n    return -1\n}\n</code></pre> linked_list.js<pre><code>/* Найти в связном списке первый узел со значением target */\nfunction find(head, target) {\n    let index = 0;\n    while (head !== null) {\n        if (head.val === target) {\n            return index;\n        }\n        head = head.next;\n        index += 1;\n    }\n    return -1;\n}\n</code></pre> linked_list.ts<pre><code>/* Найти в связном списке первый узел со значением target */\nfunction find(head: ListNode | null, target: number): number {\n    let index = 0;\n    while (head !== null) {\n        if (head.val === target) {\n            return index;\n        }\n        head = head.next;\n        index += 1;\n    }\n    return -1;\n}\n</code></pre> linked_list.dart<pre><code>/* Найти в связном списке первый узел со значением target */\nint find(ListNode? head, int target) {\n  int index = 0;\n  while (head != null) {\n    if (head.val == target) {\n      return index;\n    }\n    head = head.next;\n    index++;\n  }\n  return -1;\n}\n</code></pre> linked_list.rs<pre><code>/* Найти в связном списке первый узел со значением target */\npub fn find&lt;T: PartialEq&gt;(head: Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;, target: T) -&gt; i32 {\n    fn find&lt;T: PartialEq&gt;(head: Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;, target: T, idx: i32) -&gt; i32 {\n        if let Some(node) = head {\n            if node.borrow().val == target {\n                return idx;\n            }\n            return find(node.borrow().next.as_ref(), target, idx + 1);\n        } else {\n            -1\n        }\n    }\n\n    find(Some(head).as_ref(), target, 0)\n}\n</code></pre> linked_list.c<pre><code>/* Найти в связном списке первый узел со значением target */\nint find(ListNode *head, int target) {\n    int index = 0;\n    while (head) {\n        if (head-&gt;val == target)\n            return index;\n        head = head-&gt;next;\n        index++;\n    }\n    return -1;\n}\n</code></pre> linked_list.kt<pre><code>/* Найти в связном списке первый узел со значением target */\nfun find(head: ListNode?, target: Int): Int {\n    var index = 0\n    var h = head\n    while (h != null) {\n        if (h._val == target)\n            return index\n        h = h.next\n        index++\n    }\n    return -1\n}\n</code></pre> linked_list.rb<pre><code>### Поиск первого узла со значением target в связном списке ###\ndef find(head, target)\n  index = 0\n  while head\n    return index if head.val == target\n    head = head.next\n    index += 1\n  end\n\n  -1\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 4. Массивы и списки","4.2 &nbsp; Связный список"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#422","level":2,"title":"4.2.2   Сравнение массива и связного списка","text":"<p>В таблице 4-1 обобщаются свойства массива и связного списка, а также сравнивается эффективность соответствующих операций. Поскольку они используют противоположные стратегии хранения, их свойства и эффективность операций тоже во многом противоположны.</p> <p> Таблица 4-1   Сравнение эффективности массива и связного списка </p> Массив Связный список Способ хранения Непрерывная область памяти Разрозненная область памяти Расширение емкости Длина неизменяема Гибкое расширение Эффективность памяти Элементы занимают меньше памяти, но возможны потери пространства Элементы занимают больше памяти Доступ к элементу \\(O(1)\\) \\(O(n)\\) Добавление элемента \\(O(n)\\) \\(O(1)\\) Удаление элемента \\(O(n)\\) \\(O(1)\\)","path":["Глава 4. Массивы и списки","4.2 &nbsp; Связный список"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#423","level":2,"title":"4.2.3   Основные типы связных списков","text":"<p>Как показано на рисунке 4-8, существует три распространенных типа связных списков.</p> <ul> <li>Односвязный список: это обычный связный список, рассмотренный выше. Узел односвязного списка содержит значение и ссылку на следующий узел. Первый узел называется головным, последний - хвостовым, и хвост указывает на <code>None</code> .</li> <li>Циклический список: если заставить хвостовой узел односвязного списка указывать на головной, то есть соединить хвост с головой, получится циклический список. В циклическом списке любой узел можно рассматривать как головной.</li> <li>Двусвязный список: по сравнению с односвязным списком двусвязный хранит ссылки в двух направлениях. Определение узла двусвязного списка включает как ссылку на следующий узел, так и ссылку на предыдущий узел. По сравнению с односвязным списком двусвязный более гибок и позволяет обходить список в обе стороны, но за это приходится платить дополнительной памятью.</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>class ListNode:\n    \"\"\"Класс узла двусвязного списка\"\"\"\n    def __init__(self, val: int):\n        self.val: int = val                # Значение узла\n        self.next: ListNode | None = None  # Ссылка на следующий узел\n        self.prev: ListNode | None = None  # Ссылка на предыдущий узел\n</code></pre> <pre><code>/* Структура узла двусвязного списка */\nstruct ListNode {\n    int val;         // Значение узла\n    ListNode *next;  // Указатель на следующий узел\n    ListNode *prev;  // Указатель на предыдущий узел\n    ListNode(int x) : val(x), next(nullptr), prev(nullptr) {}  // Конструктор\n};\n</code></pre> <pre><code>/* Класс узла двусвязного списка */\nclass ListNode {\n    int val;        // Значение узла\n    ListNode next;  // Ссылка на следующий узел\n    ListNode prev;  // Ссылка на предыдущий узел\n    ListNode(int x) { val = x; }  // Конструктор\n}\n</code></pre> <pre><code>/* Класс узла двусвязного списка */\nclass ListNode(int x) {  // Конструктор\n    int val = x;    // Значение узла\n    ListNode next;  // Ссылка на следующий узел\n    ListNode prev;  // Ссылка на предыдущий узел\n}\n</code></pre> <pre><code>/* Структура узла двусвязного списка */\ntype DoublyListNode struct {\n    Val  int             // Значение узла\n    Next *DoublyListNode // Указатель на следующий узел\n    Prev *DoublyListNode // Указатель на предыдущий узел\n}\n\n// NewDoublyListNode Инициализация\nfunc NewDoublyListNode(val int) *DoublyListNode {\n    return &amp;DoublyListNode{\n        Val:  val,\n        Next: nil,\n        Prev: nil,\n    }\n}\n</code></pre> <pre><code>/* Класс узла двусвязного списка */\nclass ListNode {\n    var val: Int // Значение узла\n    var next: ListNode? // Ссылка на следующий узел\n    var prev: ListNode? // Ссылка на предыдущий узел\n\n    init(x: Int) { // Конструктор\n        val = x\n    }\n}\n</code></pre> <pre><code>/* Класс узла двусвязного списка */\nclass ListNode {\n    constructor(val, next, prev) {\n        this.val = val  ===  undefined ? 0 : val;        // Значение узла\n        this.next = next  ===  undefined ? null : next;  // Ссылка на следующий узел\n        this.prev = prev  ===  undefined ? null : prev;  // Ссылка на предыдущий узел\n    }\n}\n</code></pre> <pre><code>/* Класс узла двусвязного списка */\nclass ListNode {\n    val: number;\n    next: ListNode | null;\n    prev: ListNode | null;\n    constructor(val?: number, next?: ListNode | null, prev?: ListNode | null) {\n        this.val = val  ===  undefined ? 0 : val;        // Значение узла\n        this.next = next  ===  undefined ? null : next;  // Ссылка на следующий узел\n        this.prev = prev  ===  undefined ? null : prev;  // Ссылка на предыдущий узел\n    }\n}\n</code></pre> <pre><code>/* Класс узла двусвязного списка */\nclass ListNode {\n    int val;        // Значение узла\n    ListNode? next;  // Ссылка на следующий узел\n    ListNode? prev;  // Ссылка на предыдущий узел\n    ListNode(this.val, [this.next, this.prev]);  // Конструктор\n}\n</code></pre> <pre><code>use std::rc::Rc;\nuse std::cell::RefCell;\n\n/* Тип узла двусвязного списка */\n#[derive(Debug)]\nstruct ListNode {\n    val: i32, // Значение узла\n    next: Option&lt;Rc&lt;RefCell&lt;ListNode&gt;&gt;&gt;, // Указатель на следующий узел\n    prev: Option&lt;Rc&lt;RefCell&lt;ListNode&gt;&gt;&gt;, // Указатель на предыдущий узел\n}\n\n/* Конструктор */\nimpl ListNode {\n    fn new(val: i32) -&gt; Self {\n        ListNode {\n            val,\n            next: None,\n            prev: None,\n        }\n    }\n}\n</code></pre> <pre><code>/* Структура узла двусвязного списка */\ntypedef struct ListNode {\n    int val;               // Значение узла\n    struct ListNode *next; // Указатель на следующий узел\n    struct ListNode *prev; // Указатель на предыдущий узел\n} ListNode;\n\n/* Конструктор */\nListNode *newListNode(int val) {\n    ListNode *node;\n    node = (ListNode *) malloc(sizeof(ListNode));\n    node-&gt;val = val;\n    node-&gt;next = NULL;\n    node-&gt;prev = NULL;\n    return node;\n}\n</code></pre> <pre><code>/* Класс узла двусвязного списка */\n// Конструктор\nclass ListNode(x: Int) {\n    val _val: Int = x           // Значение узла\n    val next: ListNode? = null  // Ссылка на следующий узел\n    val prev: ListNode? = null  // Ссылка на предыдущий узел\n}\n</code></pre> <pre><code># Класс узла двусвязного списка\nclass ListNode\n  attr_accessor :val    # Значение узла\n  attr_accessor :next   # Ссылка на следующий узел\n  attr_accessor :prev   # Ссылка на предыдущий узел\n\n  def initialize(val=0, next_node=nil, prev_node=nil)\n    @val = val\n    @next = next_node\n    @prev = prev_node\n  end\nend\n</code></pre> <p></p> <p> Рисунок 4-8   Распространенные типы связных списков </p>","path":["Глава 4. Массивы и списки","4.2 &nbsp; Связный список"],"tags":[]},{"location":"chapter_array_and_linkedlist/linked_list/#424","level":2,"title":"4.2.4   Типичные применения связных списков","text":"<p>Односвязные списки обычно используются для реализации стеков, очередей, хеш-таблиц и графов.</p> <ul> <li>Стеки и очереди: если операции вставки и удаления выполняются на одном конце связного списка, он проявляет свойства LIFO, соответствующие стеку; если вставка происходит на одном конце, а удаление на другом, он проявляет свойства FIFO, соответствующие очереди.</li> <li>Хеш-таблицы: метод цепочек - один из основных способов разрешения коллизий в хеш-таблицах. В этом подходе все конфликтующие элементы помещаются в связный список.</li> <li>Графы: список смежности - это распространенный способ представления графа, при котором каждой вершине графа соответствует связный список, а каждый элемент этого списка представляет другую вершину, соединенную с данной.</li> </ul> <p>Двусвязные списки обычно используются там, где нужен быстрый доступ как к предыдущему, так и к следующему элементу.</p> <ul> <li>Продвинутые структуры данных: например, в красно-черных деревьях и B-деревьях нам нужен доступ к родительскому узлу; этого можно добиться, сохранив в узле ссылку на родителя, по аналогии с двусвязным списком.</li> <li>История браузера: когда пользователь в браузере нажимает кнопки \"вперед\" или \"назад\", браузеру нужно знать предыдущую и следующую посещенные страницы. Свойства двусвязного списка делают такую операцию простой.</li> <li>Алгоритм LRU: в алгоритмах вытеснения из кэша (LRU) нужно быстро находить наименее недавно использованные данные, а также быстро добавлять и удалять узлы. Для этого двусвязный список подходит очень хорошо.</li> </ul> <p>Циклические списки часто применяются в сценариях, требующих циклических операций, например при планировании ресурсов в операционной системе.</p> <ul> <li>Алгоритм циклического распределения кванта времени: в операционных системах round-robin scheduling - это распространенный алгоритм планирования CPU, который циклически обходит набор процессов. Каждому процессу выделяется квант времени, и когда он исчерпан, CPU переключается на следующий процесс. Такую циклическую операцию удобно реализовать с помощью кольцевого списка.</li> <li>Буферы данных: в некоторых реализациях буферов данных также могут использоваться циклические списки. Например, в аудио- и видеоплеерах поток данных может делиться на несколько буферных блоков и помещаться в кольцевой список для обеспечения непрерывного воспроизведения.</li> </ul>","path":["Глава 4. Массивы и списки","4.2 &nbsp; Связный список"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/","level":1,"title":"4.3   Список","text":"<p>Список (list) - это абстрактное понятие структуры данных, обозначающее упорядоченную коллекцию элементов, которая поддерживает доступ к элементам, их изменение, добавление, удаление и обход, не требуя от пользователя учитывать ограничения по емкости. Список может быть реализован как на основе связного списка, так и на основе массива.</p> <ul> <li>Связный список естественным образом можно рассматривать как список: он поддерживает операции добавления, удаления, поиска и изменения элементов и может гибко расширяться динамически.</li> <li>Массив тоже поддерживает операции добавления, удаления, поиска и изменения элементов, но из-за неизменяемости длины его можно считать лишь списком с ограниченной длиной.</li> </ul> <p>Когда список реализуется с помощью массива, неизменяемость длины снижает его практическую полезность. Причина в том, что мы обычно не можем заранее точно знать, сколько данных нужно хранить, а значит, трудно выбрать подходящую длину списка. Если длина слишком мала, она может не покрыть реальные потребности; если слишком велика, будет зря расходоваться память.</p> <p>Чтобы решить эту проблему, можно использовать динамический массив (dynamic array) для реализации списка. Он сохраняет все преимущества массива и при этом может динамически расширяться во время выполнения программы.</p> <p>На практике списки из стандартных библиотек многих языков программирования реализованы именно на основе динамических массивов, например <code>list</code> в Python, <code>ArrayList</code> в Java, <code>vector</code> в C++ и <code>List</code> в C#. В дальнейшем обсуждении мы будем считать понятия \"список\" и \"динамический массив\" эквивалентными.</p>","path":["Глава 4. Массивы и списки","4.3 &nbsp; Список"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#431","level":2,"title":"4.3.1   Основные операции со списком","text":"","path":["Глава 4. Массивы и списки","4.3 &nbsp; Список"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#1","level":3,"title":"1.   Инициализация списка","text":"<p>Обычно используются два способа инициализации: без начальных значений и с начальными значениями:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby list.py<pre><code># Инициализация списка\n# Без начальных значений\nnums1: list[int] = []\n# С начальными значениями\nnums: list[int] = [1, 3, 2, 5, 4]\n</code></pre> list.cpp<pre><code>/* Инициализация списка */\n// Обрати внимание: в C++ vector соответствует описываемому здесь nums\n// Без начальных значений\nvector&lt;int&gt; nums1;\n// С начальными значениями\nvector&lt;int&gt; nums = { 1, 3, 2, 5, 4 };\n</code></pre> list.java<pre><code>/* Инициализация списка */\n// Без начальных значений\nList&lt;Integer&gt; nums1 = new ArrayList&lt;&gt;();\n// С начальными значениями (обрати внимание: элементы массива должны использовать обертку Integer[] вместо int[])\nInteger[] numbers = new Integer[] { 1, 3, 2, 5, 4 };\nList&lt;Integer&gt; nums = new ArrayList&lt;&gt;(Arrays.asList(numbers));\n</code></pre> list.cs<pre><code>/* Инициализация списка */\n// Без начальных значений\nList&lt;int&gt; nums1 = [];\n// С начальными значениями\nint[] numbers = [1, 3, 2, 5, 4];\nList&lt;int&gt; nums = [.. numbers];\n</code></pre> list_test.go<pre><code>/* Инициализация списка */\n// Без начальных значений\nnums1 := []int{}\n// С начальными значениями\nnums := []int{1, 3, 2, 5, 4}\n</code></pre> list.swift<pre><code>/* Инициализация списка */\n// Без начальных значений\nlet nums1: [Int] = []\n// С начальными значениями\nvar nums = [1, 3, 2, 5, 4]\n</code></pre> list.js<pre><code>/* Инициализация списка */\n// Без начальных значений\nconst nums1 = [];\n// С начальными значениями\nconst nums = [1, 3, 2, 5, 4];\n</code></pre> list.ts<pre><code>/* Инициализация списка */\n// Без начальных значений\nconst nums1: number[] = [];\n// С начальными значениями\nconst nums: number[] = [1, 3, 2, 5, 4];\n</code></pre> list.dart<pre><code>/* Инициализация списка */\n// Без начальных значений\nList&lt;int&gt; nums1 = [];\n// С начальными значениями\nList&lt;int&gt; nums = [1, 3, 2, 5, 4];\n</code></pre> list.rs<pre><code>/* Инициализация списка */\n// Без начальных значений\nlet nums1: Vec&lt;i32&gt; = Vec::new();\n// С начальными значениями\nlet nums: Vec&lt;i32&gt; = vec![1, 3, 2, 5, 4];\n</code></pre> list.c<pre><code>// В C нет встроенного динамического массива\n</code></pre> list.kt<pre><code>/* Инициализация списка */\n// Без начальных значений\nvar nums1 = listOf&lt;Int&gt;()\n// С начальными значениями\nvar numbers = arrayOf(1, 3, 2, 5, 4)\nvar nums = numbers.toMutableList()\n</code></pre> list.rb<pre><code># Инициализация списка\n# Без начальных значений\nnums1 = []\n# С начальными значениями\nnums = [1, 3, 2, 5, 4]\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%0A%20%20%20%20%23%20%D0%91%D0%B5%D0%B7%20%D0%BD%D0%B0%D1%87%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B%D1%85%20%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B9%0A%20%20%20%20nums1%20%3D%20%5B%5D%0A%20%20%20%20%23%20%D0%A1%20%D0%BD%D0%B0%D1%87%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B%D0%BC%D0%B8%20%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D1%8F%D0%BC%D0%B8%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D&amp;cumulative=false&amp;curInstr=4&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 4. Массивы и списки","4.3 &nbsp; Список"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#2","level":3,"title":"2.   Доступ к элементам","text":"<p>Поскольку в этом разделе список рассматривается как структура на основе динамического массива, доступ к элементам и их обновление можно выполнять за \\(O(1)\\) времени, что очень эффективно.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby list.py<pre><code># Доступ к элементу\nnum: int = nums[1]  # Доступ к элементу по индексу 1\n\n# Обновление элемента\nnums[1] = 0    # Обновить элемент по индексу 1 значением 0\n</code></pre> list.cpp<pre><code>/* Доступ к элементу */\nint num = nums[1];  // Доступ к элементу по индексу 1\n\n/* Обновление элемента */\nnums[1] = 0;  // Обновить элемент по индексу 1 значением 0\n</code></pre> list.java<pre><code>/* Доступ к элементу */\nint num = nums.get(1);  // Доступ к элементу по индексу 1\n\n/* Обновление элемента */\nnums.set(1, 0);  // Обновить элемент по индексу 1 значением 0\n</code></pre> list.cs<pre><code>/* Доступ к элементу */\nint num = nums[1];  // Доступ к элементу по индексу 1\n\n/* Обновление элемента */\nnums[1] = 0;  // Обновить элемент по индексу 1 значением 0\n</code></pre> list_test.go<pre><code>/* Доступ к элементу */\nnum := nums[1]  // Доступ к элементу по индексу 1\n\n/* Обновление элемента */\nnums[1] = 0     // Обновить элемент по индексу 1 значением 0\n</code></pre> list.swift<pre><code>/* Доступ к элементу */\nlet num = nums[1] // Доступ к элементу по индексу 1\n\n/* Обновление элемента */\nnums[1] = 0 // Обновить элемент по индексу 1 значением 0\n</code></pre> list.js<pre><code>/* Доступ к элементу */\nconst num = nums[1];  // Доступ к элементу по индексу 1\n\n/* Обновление элемента */\nnums[1] = 0;  // Обновить элемент по индексу 1 значением 0\n</code></pre> list.ts<pre><code>/* Доступ к элементу */\nconst num: number = nums[1];  // Доступ к элементу по индексу 1\n\n/* Обновление элемента */\nnums[1] = 0;  // Обновить элемент по индексу 1 значением 0\n</code></pre> list.dart<pre><code>/* Доступ к элементу */\nint num = nums[1];  // Доступ к элементу по индексу 1\n\n/* Обновление элемента */\nnums[1] = 0;  // Обновить элемент по индексу 1 значением 0\n</code></pre> list.rs<pre><code>/* Доступ к элементу */\nlet num: i32 = nums[1];  // Доступ к элементу по индексу 1\n/* Обновление элемента */\nnums[1] = 0;             // Обновить элемент по индексу 1 значением 0\n</code></pre> list.c<pre><code>// В C нет встроенного динамического массива\n</code></pre> list.kt<pre><code>/* Доступ к элементу */\nval num = nums[1]       // Доступ к элементу по индексу 1\n/* Обновление элемента */\nnums[1] = 0             // Обновить элемент по индексу 1 значением 0\n</code></pre> list.rb<pre><code># Доступ к элементу\nnum = nums[1] # Доступ к элементу по индексу 1\n# Обновление элемента\nnums[1] = 0 # Обновить элемент по индексу 1 значением 0\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%0A%20%20%20%20%23%20%D0%9F%D0%BE%D0%BB%D1%83%D1%87%D0%B8%D1%82%D1%8C%20%D0%B4%D0%BE%D1%81%D1%82%D1%83%D0%BF%20%D0%BA%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D1%83%0A%20%20%20%20num%20%3D%20nums%5B1%5D%20%20%23%20%D0%BE%D0%B1%D1%80%D0%B0%D1%82%D0%B8%D1%82%D1%8C%D1%81%D1%8F%20%D0%BA%D0%B8%D0%BD%D0%B4%D0%B5%D0%BA%D1%81%201%20%D0%BF%D0%BE%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%0A%0A%20%20%20%20%23%20%D0%9E%D0%B1%D0%BD%D0%BE%D0%B2%D0%B8%D1%82%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%0A%20%20%20%20nums%5B1%5D%20%3D%200%20%20%20%20%23%20%D0%9E%D0%B1%D0%BD%D0%BE%D0%B2%D0%B8%D1%82%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%BF%D0%BE%20%D0%B8%D0%BD%D0%B4%D0%B5%D0%BA%D1%81%D1%83%201%20%D0%B4%D0%BE%200&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 4. Массивы и списки","4.3 &nbsp; Список"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#3","level":3,"title":"3.   Вставка и удаление элементов","text":"<p>В отличие от массива список позволяет свободно добавлять и удалять элементы. Добавление элемента в конец списка имеет временную сложность \\(O(1)\\) , но операции вставки и удаления по-прежнему имеют ту же эффективность, что и у массива, то есть \\(O(n)\\) .</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby list.py<pre><code># Очистить список\nnums.clear()\n\n# Добавить элементы в конец\nnums.append(1)\nnums.append(3)\nnums.append(2)\nnums.append(5)\nnums.append(4)\n\n# Вставить элемент в середину\nnums.insert(3, 6)  # Вставить число 6 по индексу 3\n\n# Удалить элемент\nnums.pop(3)        # Удалить элемент по индексу 3\n</code></pre> list.cpp<pre><code>/* Очистить список */\nnums.clear();\n\n/* Добавить элементы в конец */\nnums.push_back(1);\nnums.push_back(3);\nnums.push_back(2);\nnums.push_back(5);\nnums.push_back(4);\n\n/* Вставить элемент в середину */\nnums.insert(nums.begin() + 3, 6);  // Вставить число 6 по индексу 3\n\n/* Удалить элемент */\nnums.erase(nums.begin() + 3);      // Удалить элемент по индексу 3\n</code></pre> list.java<pre><code>/* Очистить список */\nnums.clear();\n\n/* Добавить элементы в конец */\nnums.add(1);\nnums.add(3);\nnums.add(2);\nnums.add(5);\nnums.add(4);\n\n/* Вставить элемент в середину */\nnums.add(3, 6);  // Вставить число 6 по индексу 3\n\n/* Удалить элемент */\nnums.remove(3);  // Удалить элемент по индексу 3\n</code></pre> list.cs<pre><code>/* Очистить список */\nnums.Clear();\n\n/* Добавить элементы в конец */\nnums.Add(1);\nnums.Add(3);\nnums.Add(2);\nnums.Add(5);\nnums.Add(4);\n\n/* Вставить элемент в середину */\nnums.Insert(3, 6);  // Вставить число 6 по индексу 3\n\n/* Удалить элемент */\nnums.RemoveAt(3);  // Удалить элемент по индексу 3\n</code></pre> list_test.go<pre><code>/* Очистить список */\nnums = nil\n\n/* Добавить элементы в конец */\nnums = append(nums, 1)\nnums = append(nums, 3)\nnums = append(nums, 2)\nnums = append(nums, 5)\nnums = append(nums, 4)\n\n/* Вставить элемент в середину */\nnums = append(nums[:3], append([]int{6}, nums[3:]...)...) // Вставить число 6 по индексу 3\n\n/* Удалить элемент */\nnums = append(nums[:3], nums[4:]...) // Удалить элемент по индексу 3\n</code></pre> list.swift<pre><code>/* Очистить список */\nnums.removeAll()\n\n/* Добавить элементы в конец */\nnums.append(1)\nnums.append(3)\nnums.append(2)\nnums.append(5)\nnums.append(4)\n\n/* Вставить элемент в середину */\nnums.insert(6, at: 3) // Вставить число 6 по индексу 3\n\n/* Удалить элемент */\nnums.remove(at: 3) // Удалить элемент по индексу 3\n</code></pre> list.js<pre><code>/* Очистить список */\nnums.length = 0;\n\n/* Добавить элементы в конец */\nnums.push(1);\nnums.push(3);\nnums.push(2);\nnums.push(5);\nnums.push(4);\n\n/* Вставить элемент в середину */\nnums.splice(3, 0, 6); // Вставить число 6 по индексу 3\n\n/* Удалить элемент */\nnums.splice(3, 1);  // Удалить элемент по индексу 3\n</code></pre> list.ts<pre><code>/* Очистить список */\nnums.length = 0;\n\n/* Добавить элементы в конец */\nnums.push(1);\nnums.push(3);\nnums.push(2);\nnums.push(5);\nnums.push(4);\n\n/* Вставить элемент в середину */\nnums.splice(3, 0, 6); // Вставить число 6 по индексу 3\n\n/* Удалить элемент */\nnums.splice(3, 1);  // Удалить элемент по индексу 3\n</code></pre> list.dart<pre><code>/* Очистить список */\nnums.clear();\n\n/* Добавить элементы в конец */\nnums.add(1);\nnums.add(3);\nnums.add(2);\nnums.add(5);\nnums.add(4);\n\n/* Вставить элемент в середину */\nnums.insert(3, 6); // Вставить число 6 по индексу 3\n\n/* Удалить элемент */\nnums.removeAt(3); // Удалить элемент по индексу 3\n</code></pre> list.rs<pre><code>/* Очистить список */\nnums.clear();\n\n/* Добавить элементы в конец */\nnums.push(1);\nnums.push(3);\nnums.push(2);\nnums.push(5);\nnums.push(4);\n\n/* Вставить элемент в середину */\nnums.insert(3, 6);  // Вставить число 6 по индексу 3\n\n/* Удалить элемент */\nnums.remove(3);    // Удалить элемент по индексу 3\n</code></pre> list.c<pre><code>// В C нет встроенного динамического массива\n</code></pre> list.kt<pre><code>/* Очистить список */\nnums.clear();\n\n/* Добавить элементы в конец */\nnums.add(1);\nnums.add(3);\nnums.add(2);\nnums.add(5);\nnums.add(4);\n\n/* Вставить элемент в середину */\nnums.add(3, 6);  // Вставить число 6 по индексу 3\n\n/* Удалить элемент */\nnums.remove(3);  // Удалить элемент по индексу 3\n</code></pre> list.rb<pre><code># Очистить список\nnums.clear\n\n# Добавить элементы в конец\nnums &lt;&lt; 1\nnums &lt;&lt; 3\nnums &lt;&lt; 2\nnums &lt;&lt; 5\nnums &lt;&lt; 4\n\n# Вставить элемент в середину\nnums.insert(3, 6) # Вставить число 6 по индексу 3\n\n# Удалить элемент\nnums.delete_at(3) # Удалить элемент по индексу 3\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%A1%20%D0%BD%D0%B0%D1%87%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B%D0%BC%D0%B8%20%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D1%8F%D0%BC%D0%B8%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9E%D1%87%D0%B8%D1%81%D1%82%D0%B8%D1%82%D1%8C%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%0A%20%20%20%20nums.clear%28%29%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%94%D0%BE%D0%B1%D0%B0%D0%B2%D0%B8%D1%82%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%B2%20%D0%BA%D0%BE%D0%BD%D0%B5%D1%86%0A%20%20%20%20nums.append%281%29%0A%20%20%20%20nums.append%283%29%0A%20%20%20%20nums.append%282%29%0A%20%20%20%20nums.append%285%29%0A%20%20%20%20nums.append%284%29%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%92%D1%81%D1%82%D0%B0%D0%B2%D0%B8%D1%82%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%B2%20%D1%81%D0%B5%D1%80%D0%B5%D0%B4%D0%B8%D0%BD%D1%83%0A%20%20%20%20nums.insert%283%2C%206%29%20%20%23%20%D0%92%D1%81%D1%82%D0%B0%D0%B2%D0%B8%D1%82%D1%8C%20%D1%87%D0%B8%D1%81%D0%BB%D0%BE%206%20%D0%BF%D0%BE%20%D0%B8%D0%BD%D0%B4%D0%B5%D0%BA%D1%81%D1%83%203%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%A3%D0%B4%D0%B0%D0%BB%D0%B8%D1%82%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%0A%20%20%20%20nums.pop%283%29%20%20%20%20%20%20%20%20%23%20%D0%A3%D0%B4%D0%B0%D0%BB%D0%B8%D1%82%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%BF%D0%BE%20%D0%B8%D0%BD%D0%B4%D0%B5%D0%BA%D1%81%D1%83%203&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 4. Массивы и списки","4.3 &nbsp; Список"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#4","level":3,"title":"4.   Обход списка","text":"<p>Как и массив, список можно обходить как по индексам, так и напрямую по элементам.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby list.py<pre><code># Обход списка по индексам\ncount = 0\nfor i in range(len(nums)):\n    count += nums[i]\n\n# Прямой обход элементов списка\nfor num in nums:\n    count += num\n</code></pre> list.cpp<pre><code>/* Обход списка по индексам */\nint count = 0;\nfor (int i = 0; i &lt; nums.size(); i++) {\n    count += nums[i];\n}\n\n/* Прямой обход элементов списка */\ncount = 0;\nfor (int num : nums) {\n    count += num;\n}\n</code></pre> list.java<pre><code>/* Обход списка по индексам */\nint count = 0;\nfor (int i = 0; i &lt; nums.size(); i++) {\n    count += nums.get(i);\n}\n\n/* Прямой обход элементов списка */\nfor (int num : nums) {\n    count += num;\n}\n</code></pre> list.cs<pre><code>/* Обход списка по индексам */\nint count = 0;\nfor (int i = 0; i &lt; nums.Count; i++) {\n    count += nums[i];\n}\n\n/* Прямой обход элементов списка */\ncount = 0;\nforeach (int num in nums) {\n    count += num;\n}\n</code></pre> list_test.go<pre><code>/* Обход списка по индексам */\ncount := 0\nfor i := 0; i &lt; len(nums); i++ {\n    count += nums[i]\n}\n\n/* Прямой обход элементов списка */\ncount = 0\nfor _, num := range nums {\n    count += num\n}\n</code></pre> list.swift<pre><code>/* Обход списка по индексам */\nvar count = 0\nfor i in nums.indices {\n    count += nums[i]\n}\n\n/* Прямой обход элементов списка */\ncount = 0\nfor num in nums {\n    count += num\n}\n</code></pre> list.js<pre><code>/* Обход списка по индексам */\nlet count = 0;\nfor (let i = 0; i &lt; nums.length; i++) {\n    count += nums[i];\n}\n\n/* Прямой обход элементов списка */\ncount = 0;\nfor (const num of nums) {\n    count += num;\n}\n</code></pre> list.ts<pre><code>/* Обход списка по индексам */\nlet count = 0;\nfor (let i = 0; i &lt; nums.length; i++) {\n    count += nums[i];\n}\n\n/* Прямой обход элементов списка */\ncount = 0;\nfor (const num of nums) {\n    count += num;\n}\n</code></pre> list.dart<pre><code>/* Обход списка по индексам */\nint count = 0;\nfor (var i = 0; i &lt; nums.length; i++) {\n    count += nums[i];\n}\n\n/* Прямой обход элементов списка */\ncount = 0;\nfor (var num in nums) {\n    count += num;\n}\n</code></pre> list.rs<pre><code>// Обход списка по индексам\nlet mut _count = 0;\nfor i in 0..nums.len() {\n    _count += nums[i];\n}\n\n// Прямой обход элементов списка\n_count = 0;\nfor num in &amp;nums {\n    _count += num;\n}\n</code></pre> list.c<pre><code>// В C нет встроенного динамического массива\n</code></pre> list.kt<pre><code>/* Обход списка по индексам */\nvar count = 0\nfor (i in nums.indices) {\n    count += nums[i]\n}\n\n/* Прямой обход элементов списка */\nfor (num in nums) {\n    count += num\n}\n</code></pre> list.rb<pre><code># Обход списка по индексам\ncount = 0\nfor i in 0...nums.length\n    count += nums[i]\nend\n\n# Прямой обход элементов списка\ncount = 0\nfor num in nums\n    count += num\nend\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9E%D0%B1%D1%85%D0%BE%D0%B4%D0%B8%D1%82%D1%8C%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%20%D0%BF%D0%BE%20%D0%B8%D0%BD%D0%B4%D0%B5%D0%BA%D1%81%D0%B0%D0%BC%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20for%20i%20in%20range%28len%28nums%29%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%20nums%5Bi%5D%0A%0A%20%20%20%20%23%20%D0%9D%D0%B5%D0%BF%D0%BE%D1%81%D1%80%D0%B5%D0%B4%D1%81%D1%82%D0%B2%D0%B5%D0%BD%D0%BD%D0%BE%20%D0%BE%D0%B1%D1%85%D0%BE%D0%B4%D0%B8%D1%82%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D1%8B%20%D1%81%D0%BF%D0%B8%D1%81%D0%BA%D0%B0%0A%20%20%20%20for%20num%20in%20nums%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%20num&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 4. Массивы и списки","4.3 &nbsp; Список"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#5","level":3,"title":"5.   Конкатенация списков","text":"<p>Создав новый список <code>nums1</code> , мы можем присоединить его к хвосту исходного списка.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby list.py<pre><code># Конкатенация двух списков\nnums1: list[int] = [6, 8, 7, 10, 9]\nnums += nums1  # Присоединить список nums1 к концу nums\n</code></pre> list.cpp<pre><code>/* Конкатенация двух списков */\nvector&lt;int&gt; nums1 = { 6, 8, 7, 10, 9 };\n// Присоединить список nums1 к концу nums\nnums.insert(nums.end(), nums1.begin(), nums1.end());\n</code></pre> list.java<pre><code>/* Конкатенация двух списков */\nList&lt;Integer&gt; nums1 = new ArrayList&lt;&gt;(Arrays.asList(new Integer[] { 6, 8, 7, 10, 9 }));\nnums.addAll(nums1);  // Присоединить список nums1 к концу nums\n</code></pre> list.cs<pre><code>/* Конкатенация двух списков */\nList&lt;int&gt; nums1 = [6, 8, 7, 10, 9];\nnums.AddRange(nums1);  // Присоединить список nums1 к концу nums\n</code></pre> list_test.go<pre><code>/* Конкатенация двух списков */\nnums1 := []int{6, 8, 7, 10, 9}\nnums = append(nums, nums1...)  // Присоединить список nums1 к концу nums\n</code></pre> list.swift<pre><code>/* Конкатенация двух списков */\nlet nums1 = [6, 8, 7, 10, 9]\nnums.append(contentsOf: nums1) // Присоединить список nums1 к концу nums\n</code></pre> list.js<pre><code>/* Конкатенация двух списков */\nconst nums1 = [6, 8, 7, 10, 9];\nnums.push(...nums1);  // Присоединить список nums1 к концу nums\n</code></pre> list.ts<pre><code>/* Конкатенация двух списков */\nconst nums1: number[] = [6, 8, 7, 10, 9];\nnums.push(...nums1);  // Присоединить список nums1 к концу nums\n</code></pre> list.dart<pre><code>/* Конкатенация двух списков */\nList&lt;int&gt; nums1 = [6, 8, 7, 10, 9];\nnums.addAll(nums1);  // Присоединить список nums1 к концу nums\n</code></pre> list.rs<pre><code>/* Конкатенация двух списков */\nlet nums1: Vec&lt;i32&gt; = vec![6, 8, 7, 10, 9];\nnums.extend(nums1);\n</code></pre> list.c<pre><code>// В C нет встроенного динамического массива\n</code></pre> list.kt<pre><code>/* Конкатенация двух списков */\nval nums1 = intArrayOf(6, 8, 7, 10, 9).toMutableList()\nnums.addAll(nums1)  // Присоединить список nums1 к концу nums\n</code></pre> list.rb<pre><code># Конкатенация двух списков\nnums1 = [6, 8, 7, 10, 9]\nnums += nums1\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9E%D0%B1%D1%8A%D0%B5%D0%B4%D0%B8%D0%BD%D0%B8%D1%82%D1%8C%20%D0%B4%D0%B2%D0%B0%20%D1%81%D0%BF%D0%B8%D1%81%D0%BA%D0%B0%0A%20%20%20%20nums1%20%3D%20%5B6%2C%208%2C%207%2C%2010%2C%209%5D%0A%20%20%20%20nums%20%2B%3D%20nums1%20%20%23%20%D0%9F%D1%80%D0%B8%D1%81%D0%BE%D0%B5%D0%B4%D0%B8%D0%BD%D0%B8%D1%82%D1%8C%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%20nums1%20%D0%BA%20nums&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 4. Массивы и списки","4.3 &nbsp; Список"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#6","level":3,"title":"6.   Сортировка списка","text":"<p>После сортировки списка мы сможем применять алгоритмы \"двоичный поиск\" и \"два указателя\", которые очень часто встречаются в задачах по массивам.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby list.py<pre><code># Отсортировать список\nnums.sort()  # После сортировки элементы списка идут по возрастанию\n</code></pre> list.cpp<pre><code>/* Отсортировать список */\nsort(nums.begin(), nums.end());  // После сортировки элементы списка идут по возрастанию\n</code></pre> list.java<pre><code>/* Отсортировать список */\nCollections.sort(nums);  // После сортировки элементы списка идут по возрастанию\n</code></pre> list.cs<pre><code>/* Отсортировать список */\nnums.Sort(); // После сортировки элементы списка идут по возрастанию\n</code></pre> list_test.go<pre><code>/* Отсортировать список */\nsort.Ints(nums)  // После сортировки элементы списка идут по возрастанию\n</code></pre> list.swift<pre><code>/* Отсортировать список */\nnums.sort() // После сортировки элементы списка идут по возрастанию\n</code></pre> list.js<pre><code>/* Отсортировать список */\nnums.sort((a, b) =&gt; a - b);  // После сортировки элементы списка идут по возрастанию\n</code></pre> list.ts<pre><code>/* Отсортировать список */\nnums.sort((a, b) =&gt; a - b);  // После сортировки элементы списка идут по возрастанию\n</code></pre> list.dart<pre><code>/* Отсортировать список */\nnums.sort(); // После сортировки элементы списка идут по возрастанию\n</code></pre> list.rs<pre><code>/* Отсортировать список */\nnums.sort(); // После сортировки элементы списка идут по возрастанию\n</code></pre> list.c<pre><code>// В C нет встроенного динамического массива\n</code></pre> list.kt<pre><code>/* Отсортировать список */\nnums.sort() // После сортировки элементы списка идут по возрастанию\n</code></pre> list.rb<pre><code># Отсортировать список\nnums = nums.sort { |a, b| a &lt;=&gt; b } # После сортировки элементы списка идут по возрастанию\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%0A%20%20%20%20nums%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9E%D1%82%D1%81%D0%BE%D1%80%D1%82%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%0A%20%20%20%20nums.sort%28%29%20%20%23%20%D0%A1%D0%BE%D1%80%D1%82%D0%B8%D1%80%D0%BE%D0%B2%D0%BA%D0%B0%D0%BF%D0%BE%D1%81%D0%BB%D0%B5%2C%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D1%80%D0%B0%D1%81%D0%BF%D0%BE%D0%BB%D0%BE%D0%B6%D0%B5%D0%BD%D1%8B%20%D0%BF%D0%BE%20%D0%B2%D0%BE%D0%B7%D1%80%D0%B0%D1%81%D1%82%D0%B0%D0%BD%D0%B8%D1%8E&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 4. Массивы и списки","4.3 &nbsp; Список"],"tags":[]},{"location":"chapter_array_and_linkedlist/list/#432","level":2,"title":"4.3.2   Реализация списка","text":"<p>Во многих языках программирования списки встроены в стандартную библиотеку, например в Java, C++, Python и других языках. Их реализация довольно сложна, а настройки параметров тщательно продуманы: начальная емкость, коэффициент расширения и так далее. Если это интересно, стоит заглянуть в исходный код.</p> <p>Чтобы лучше понять принцип работы списка, попробуем реализовать его упрощенную версию, в которой есть три ключевых аспекта проектирования.</p> <ul> <li>Начальная емкость: выбрать разумную начальную емкость внутреннего массива. В этом примере мы берем 10.</li> <li>Учет количества элементов: объявить переменную <code>size</code> , которая будет хранить текущее число элементов в списке и обновляться в реальном времени при вставке и удалении элементов. С помощью этой переменной можно определять конец списка и понимать, требуется ли расширение.</li> <li>Механизм расширения: если при вставке элементов емкость списка исчерпана, нужно выполнить расширение. Для этого сначала создается больший массив с учетом коэффициента расширения, а затем все элементы текущего массива по порядку переносятся в новый. В этом примере мы считаем, что каждый раз массив расширяется в 2 раза.</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby my_list.py<pre><code>class MyList:\n    \"\"\"Класс списка\"\"\"\n\n    def __init__(self):\n        \"\"\"Конструктор\"\"\"\n        self._capacity: int = 10  # Вместимость списка\n        self._arr: list[int] = [0] * self._capacity  # Массив (для хранения элементов списка)\n        self._size: int = 0  # Длина списка (текущее число элементов)\n        self._extend_ratio: int = 2  # Коэффициент увеличения списка при каждом расширении\n\n    def size(self) -&gt; int:\n        \"\"\"Получить длину списка (текущее число элементов)\"\"\"\n        return self._size\n\n    def capacity(self) -&gt; int:\n        \"\"\"Получить вместимость списка\"\"\"\n        return self._capacity\n\n    def get(self, index: int) -&gt; int:\n        \"\"\"Доступ к элементу\"\"\"\n        # Если индекс выходит за границы, выбрасывается исключение; далее аналогично\n        if index &lt; 0 or index &gt;= self._size:\n            raise IndexError(\"индекс выходит за границы\")\n        return self._arr[index]\n\n    def set(self, num: int, index: int):\n        \"\"\"Обновление элемента\"\"\"\n        if index &lt; 0 or index &gt;= self._size:\n            raise IndexError(\"индекс выходит за границы\")\n        self._arr[index] = num\n\n    def add(self, num: int):\n        \"\"\"Добавление элемента в конец\"\"\"\n        # При превышении вместимости по числу элементов запускается расширение\n        if self.size() == self.capacity():\n            self.extend_capacity()\n        self._arr[self._size] = num\n        self._size += 1\n\n    def insert(self, num: int, index: int):\n        \"\"\"Вставка элемента в середину\"\"\"\n        if index &lt; 0 or index &gt;= self._size:\n            raise IndexError(\"индекс выходит за границы\")\n        # При превышении вместимости по числу элементов запускается расширение\n        if self._size == self.capacity():\n            self.extend_capacity()\n        # Сдвинуть элемент с индексом index и все следующие элементы на одну позицию назад\n        for j in range(self._size - 1, index - 1, -1):\n            self._arr[j + 1] = self._arr[j]\n        self._arr[index] = num\n        # Обновить число элементов\n        self._size += 1\n\n    def remove(self, index: int) -&gt; int:\n        \"\"\"Удаление элемента\"\"\"\n        if index &lt; 0 or index &gt;= self._size:\n            raise IndexError(\"индекс выходит за границы\")\n        num = self._arr[index]\n        # Сдвинуть все элементы после индекса index на одну позицию вперед\n        for j in range(index, self._size - 1):\n            self._arr[j] = self._arr[j + 1]\n        # Обновить число элементов\n        self._size -= 1\n        # Вернуть удаленный элемент\n        return num\n\n    def extend_capacity(self):\n        \"\"\"Расширение списка\"\"\"\n        # Создать новый массив длиной в _extend_ratio раз больше исходного массива и скопировать в него исходный массив\n        self._arr = self._arr + [0] * self.capacity() * (self._extend_ratio - 1)\n        # Обновить вместимость списка\n        self._capacity = len(self._arr)\n\n    def to_array(self) -&gt; list[int]:\n        \"\"\"Вернуть список фактической длины\"\"\"\n        return self._arr[: self._size]\n</code></pre> my_list.cpp<pre><code>/* Класс списка */\nclass MyList {\n  private:\n    int *arr;             // Массив (для хранения элементов списка)\n    int arrCapacity = 10; // Вместимость списка\n    int arrSize = 0;      // Длина списка (текущее число элементов)\n    int extendRatio = 2;   // Коэффициент увеличения списка при каждом расширении\n\n  public:\n    /* Конструктор */\n    MyList() {\n        arr = new int[arrCapacity];\n    }\n\n    /* Метод-деструктор */\n    ~MyList() {\n        delete[] arr;\n    }\n\n    /* Получить длину списка (текущее число элементов) */\n    int size() {\n        return arrSize;\n    }\n\n    /* Получить вместимость списка */\n    int capacity() {\n        return arrCapacity;\n    }\n\n    /* Доступ к элементу */\n    int get(int index) {\n        // Если индекс выходит за границы, выбрасывается исключение; далее аналогично\n        if (index &lt; 0 || index &gt;= size())\n            throw out_of_range(\"индекс выходит за границы\");\n        return arr[index];\n    }\n\n    /* Обновление элемента */\n    void set(int index, int num) {\n        if (index &lt; 0 || index &gt;= size())\n            throw out_of_range(\"индекс выходит за границы\");\n        arr[index] = num;\n    }\n\n    /* Добавление элемента в конец */\n    void add(int num) {\n        // При превышении вместимости по числу элементов запускается расширение\n        if (size() == capacity())\n            extendCapacity();\n        arr[size()] = num;\n        // Обновить число элементов\n        arrSize++;\n    }\n\n    /* Вставка элемента в середину */\n    void insert(int index, int num) {\n        if (index &lt; 0 || index &gt;= size())\n            throw out_of_range(\"индекс выходит за границы\");\n        // При превышении вместимости по числу элементов запускается расширение\n        if (size() == capacity())\n            extendCapacity();\n        // Сдвинуть элемент с индексом index и все следующие элементы на одну позицию назад\n        for (int j = size() - 1; j &gt;= index; j--) {\n            arr[j + 1] = arr[j];\n        }\n        arr[index] = num;\n        // Обновить число элементов\n        arrSize++;\n    }\n\n    /* Удаление элемента */\n    int remove(int index) {\n        if (index &lt; 0 || index &gt;= size())\n            throw out_of_range(\"индекс выходит за границы\");\n        int num = arr[index];\n        // Сдвинуть все элементы после индекса index на одну позицию вперед\n        for (int j = index; j &lt; size() - 1; j++) {\n            arr[j] = arr[j + 1];\n        }\n        // Обновить число элементов\n        arrSize--;\n        // Вернуть удаленный элемент\n        return num;\n    }\n\n    /* Расширение списка */\n    void extendCapacity() {\n        // Создать новый массив длиной в extendRatio раз больше исходного массива\n        int newCapacity = capacity() * extendRatio;\n        int *tmp = arr;\n        arr = new int[newCapacity];\n        // Скопировать все элементы исходного массива в новый массив\n        for (int i = 0; i &lt; size(); i++) {\n            arr[i] = tmp[i];\n        }\n        // Освободить память\n        delete[] tmp;\n        arrCapacity = newCapacity;\n    }\n\n    /* Преобразовать список в Vector для вывода */\n    vector&lt;int&gt; toVector() {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        vector&lt;int&gt; vec(size());\n        for (int i = 0; i &lt; size(); i++) {\n            vec[i] = arr[i];\n        }\n        return vec;\n    }\n};\n</code></pre> my_list.java<pre><code>/* Класс списка */\nclass MyList {\n    private int[] arr; // Массив (для хранения элементов списка)\n    private int capacity = 10; // Вместимость списка\n    private int size = 0; // Длина списка (текущее число элементов)\n    private int extendRatio = 2; // Коэффициент увеличения списка при каждом расширении\n\n    /* Конструктор */\n    public MyList() {\n        arr = new int[capacity];\n    }\n\n    /* Получить длину списка (текущее число элементов) */\n    public int size() {\n        return size;\n    }\n\n    /* Получить вместимость списка */\n    public int capacity() {\n        return capacity;\n    }\n\n    /* Доступ к элементу */\n    public int get(int index) {\n        // Если индекс выходит за границы, выбрасывается исключение; далее аналогично\n        if (index &lt; 0 || index &gt;= size)\n            throw new IndexOutOfBoundsException(\"индекс выходит за границы\");\n        return arr[index];\n    }\n\n    /* Обновление элемента */\n    public void set(int index, int num) {\n        if (index &lt; 0 || index &gt;= size)\n            throw new IndexOutOfBoundsException(\"индекс выходит за границы\");\n        arr[index] = num;\n    }\n\n    /* Добавление элемента в конец */\n    public void add(int num) {\n        // При превышении вместимости по числу элементов запускается расширение\n        if (size == capacity())\n            extendCapacity();\n        arr[size] = num;\n        // Обновить число элементов\n        size++;\n    }\n\n    /* Вставка элемента в середину */\n    public void insert(int index, int num) {\n        if (index &lt; 0 || index &gt;= size)\n            throw new IndexOutOfBoundsException(\"индекс выходит за границы\");\n        // При превышении вместимости по числу элементов запускается расширение\n        if (size == capacity())\n            extendCapacity();\n        // Сдвинуть элемент с индексом index и все следующие элементы на одну позицию назад\n        for (int j = size - 1; j &gt;= index; j--) {\n            arr[j + 1] = arr[j];\n        }\n        arr[index] = num;\n        // Обновить число элементов\n        size++;\n    }\n\n    /* Удаление элемента */\n    public int remove(int index) {\n        if (index &lt; 0 || index &gt;= size)\n            throw new IndexOutOfBoundsException(\"индекс выходит за границы\");\n        int num = arr[index];\n        // Сдвинуть все элементы после индекса index на одну позицию вперед\n        for (int j = index; j &lt; size - 1; j++) {\n            arr[j] = arr[j + 1];\n        }\n        // Обновить число элементов\n        size--;\n        // Вернуть удаленный элемент\n        return num;\n    }\n\n    /* Расширение списка */\n    public void extendCapacity() {\n        // Создать новый массив длиной в extendRatio раз больше исходного и скопировать в него исходный массив\n        arr = Arrays.copyOf(arr, capacity() * extendRatio);\n        // Обновить вместимость списка\n        capacity = arr.length;\n    }\n\n    /* Преобразовать список в массив */\n    public int[] toArray() {\n        int size = size();\n        // Преобразовывать только элементы списка в пределах фактической длины\n        int[] arr = new int[size];\n        for (int i = 0; i &lt; size; i++) {\n            arr[i] = get(i);\n        }\n        return arr;\n    }\n}\n</code></pre> my_list.cs<pre><code>/* Класс списка */\nclass MyList {\n    private int[] arr;           // Массив (для хранения элементов списка)\n    private int arrCapacity = 10;    // Вместимость списка\n    private int arrSize = 0;         // Длина списка (текущее число элементов)\n    private readonly int extendRatio = 2;  // Коэффициент увеличения списка при каждом расширении\n\n    /* Конструктор */\n    public MyList() {\n        arr = new int[arrCapacity];\n    }\n\n    /* Получить длину списка (текущее число элементов) */\n    public int Size() {\n        return arrSize;\n    }\n\n    /* Получить вместимость списка */\n    public int Capacity() {\n        return arrCapacity;\n    }\n\n    /* Доступ к элементу */\n    public int Get(int index) {\n        // Если индекс выходит за границы, выбрасывается исключение; далее аналогично\n        if (index &lt; 0 || index &gt;= arrSize)\n            throw new IndexOutOfRangeException(\"индекс выходит за границы\");\n        return arr[index];\n    }\n\n    /* Обновление элемента */\n    public void Set(int index, int num) {\n        if (index &lt; 0 || index &gt;= arrSize)\n            throw new IndexOutOfRangeException(\"индекс выходит за границы\");\n        arr[index] = num;\n    }\n\n    /* Добавление элемента в конец */\n    public void Add(int num) {\n        // При превышении вместимости по числу элементов запускается расширение\n        if (arrSize == arrCapacity)\n            ExtendCapacity();\n        arr[arrSize] = num;\n        // Обновить число элементов\n        arrSize++;\n    }\n\n    /* Вставка элемента в середину */\n    public void Insert(int index, int num) {\n        if (index &lt; 0 || index &gt;= arrSize)\n            throw new IndexOutOfRangeException(\"индекс выходит за границы\");\n        // При превышении вместимости по числу элементов запускается расширение\n        if (arrSize == arrCapacity)\n            ExtendCapacity();\n        // Сдвинуть элемент с индексом index и все следующие элементы на одну позицию назад\n        for (int j = arrSize - 1; j &gt;= index; j--) {\n            arr[j + 1] = arr[j];\n        }\n        arr[index] = num;\n        // Обновить число элементов\n        arrSize++;\n    }\n\n    /* Удаление элемента */\n    public int Remove(int index) {\n        if (index &lt; 0 || index &gt;= arrSize)\n            throw new IndexOutOfRangeException(\"индекс выходит за границы\");\n        int num = arr[index];\n        // Сдвинуть все элементы после индекса index на одну позицию вперед\n        for (int j = index; j &lt; arrSize - 1; j++) {\n            arr[j] = arr[j + 1];\n        }\n        // Обновить число элементов\n        arrSize--;\n        // Вернуть удаленный элемент\n        return num;\n    }\n\n    /* Расширение списка */\n    public void ExtendCapacity() {\n        // Создать новый массив длиной arrCapacity * extendRatio и скопировать в него исходный массив\n        Array.Resize(ref arr, arrCapacity * extendRatio);\n        // Обновить вместимость списка\n        arrCapacity = arr.Length;\n    }\n\n    /* Преобразовать список в массив */\n    public int[] ToArray() {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        int[] arr = new int[arrSize];\n        for (int i = 0; i &lt; arrSize; i++) {\n            arr[i] = Get(i);\n        }\n        return arr;\n    }\n}\n</code></pre> my_list.go<pre><code>/* Класс списка */\ntype myList struct {\n    arrCapacity int\n    arr         []int\n    arrSize     int\n    extendRatio int\n}\n\n/* Конструктор */\nfunc newMyList() *myList {\n    return &amp;myList{\n        arrCapacity: 10,              // Вместимость списка\n        arr:         make([]int, 10), // Массив (для хранения элементов списка)\n        arrSize:     0,               // Длина списка (текущее число элементов)\n        extendRatio: 2,               // Коэффициент увеличения списка при каждом расширении\n    }\n}\n\n/* Получить длину списка (текущее число элементов) */\nfunc (l *myList) size() int {\n    return l.arrSize\n}\n\n/* Получить вместимость списка */\nfunc (l *myList) capacity() int {\n    return l.arrCapacity\n}\n\n/* Доступ к элементу */\nfunc (l *myList) get(index int) int {\n    // Если индекс выходит за границы, выбрасывается исключение; далее аналогично\n    if index &lt; 0 || index &gt;= l.arrSize {\n        panic(\"индекс выходит за границы\")\n    }\n    return l.arr[index]\n}\n\n/* Обновление элемента */\nfunc (l *myList) set(num, index int) {\n    if index &lt; 0 || index &gt;= l.arrSize {\n        panic(\"индекс выходит за границы\")\n    }\n    l.arr[index] = num\n}\n\n/* Добавление элемента в конец */\nfunc (l *myList) add(num int) {\n    // При превышении вместимости по числу элементов запускается расширение\n    if l.arrSize == l.arrCapacity {\n        l.extendCapacity()\n    }\n    l.arr[l.arrSize] = num\n    // Обновить число элементов\n    l.arrSize++\n}\n\n/* Вставка элемента в середину */\nfunc (l *myList) insert(num, index int) {\n    if index &lt; 0 || index &gt;= l.arrSize {\n        panic(\"индекс выходит за границы\")\n    }\n    // При превышении вместимости по числу элементов запускается расширение\n    if l.arrSize == l.arrCapacity {\n        l.extendCapacity()\n    }\n    // Сдвинуть элемент с индексом index и все следующие элементы на одну позицию назад\n    for j := l.arrSize - 1; j &gt;= index; j-- {\n        l.arr[j+1] = l.arr[j]\n    }\n    l.arr[index] = num\n    // Обновить число элементов\n    l.arrSize++\n}\n\n/* Удаление элемента */\nfunc (l *myList) remove(index int) int {\n    if index &lt; 0 || index &gt;= l.arrSize {\n        panic(\"индекс выходит за границы\")\n    }\n    num := l.arr[index]\n    // Сдвинуть все элементы после индекса index на одну позицию вперед\n    for j := index; j &lt; l.arrSize-1; j++ {\n        l.arr[j] = l.arr[j+1]\n    }\n    // Обновить число элементов\n    l.arrSize--\n    // Вернуть удаленный элемент\n    return num\n}\n\n/* Расширение списка */\nfunc (l *myList) extendCapacity() {\n    // Создать новый массив длиной в extendRatio раз больше исходного и скопировать в него исходный массив\n    l.arr = append(l.arr, make([]int, l.arrCapacity*(l.extendRatio-1))...)\n    // Обновить вместимость списка\n    l.arrCapacity = len(l.arr)\n}\n\n/* Вернуть список фактической длины */\nfunc (l *myList) toArray() []int {\n    // Преобразовывать только элементы списка в пределах фактической длины\n    return l.arr[:l.arrSize]\n}\n</code></pre> my_list.swift<pre><code>/* Класс списка */\nclass MyList {\n    private var arr: [Int] // Массив (для хранения элементов списка)\n    private var _capacity: Int // Вместимость списка\n    private var _size: Int // Длина списка (текущее число элементов)\n    private let extendRatio: Int // Коэффициент увеличения списка при каждом расширении\n\n    /* Конструктор */\n    init() {\n        _capacity = 10\n        _size = 0\n        extendRatio = 2\n        arr = Array(repeating: 0, count: _capacity)\n    }\n\n    /* Получить длину списка (текущее число элементов) */\n    func size() -&gt; Int {\n        _size\n    }\n\n    /* Получить вместимость списка */\n    func capacity() -&gt; Int {\n        _capacity\n    }\n\n    /* Доступ к элементу */\n    func get(index: Int) -&gt; Int {\n        // Если индекс выходит за границы, выбросить ошибку; далее аналогично\n        if index &lt; 0 || index &gt;= size() {\n            fatalError(\"индекс выходит за границы\")\n        }\n        return arr[index]\n    }\n\n    /* Обновление элемента */\n    func set(index: Int, num: Int) {\n        if index &lt; 0 || index &gt;= size() {\n            fatalError(\"индекс выходит за границы\")\n        }\n        arr[index] = num\n    }\n\n    /* Добавление элемента в конец */\n    func add(num: Int) {\n        // При превышении вместимости по числу элементов запускается расширение\n        if size() == capacity() {\n            extendCapacity()\n        }\n        arr[size()] = num\n        // Обновить число элементов\n        _size += 1\n    }\n\n    /* Вставка элемента в середину */\n    func insert(index: Int, num: Int) {\n        if index &lt; 0 || index &gt;= size() {\n            fatalError(\"индекс выходит за границы\")\n        }\n        // При превышении вместимости по числу элементов запускается расширение\n        if size() == capacity() {\n            extendCapacity()\n        }\n        // Сдвинуть элемент с индексом index и все следующие элементы на одну позицию назад\n        for j in (index ..&lt; size()).reversed() {\n            arr[j + 1] = arr[j]\n        }\n        arr[index] = num\n        // Обновить число элементов\n        _size += 1\n    }\n\n    /* Удаление элемента */\n    @discardableResult\n    func remove(index: Int) -&gt; Int {\n        if index &lt; 0 || index &gt;= size() {\n            fatalError(\"индекс выходит за границы\")\n        }\n        let num = arr[index]\n        // Сдвинуть все элементы после индекса index на одну позицию вперед\n        for j in index ..&lt; (size() - 1) {\n            arr[j] = arr[j + 1]\n        }\n        // Обновить число элементов\n        _size -= 1\n        // Вернуть удаленный элемент\n        return num\n    }\n\n    /* Расширение списка */\n    func extendCapacity() {\n        // Создать новый массив длиной в extendRatio раз больше исходного и скопировать в него исходный массив\n        arr = arr + Array(repeating: 0, count: capacity() * (extendRatio - 1))\n        // Обновить вместимость списка\n        _capacity = arr.count\n    }\n\n    /* Преобразовать список в массив */\n    func toArray() -&gt; [Int] {\n        Array(arr.prefix(size()))\n    }\n}\n</code></pre> my_list.js<pre><code>/* Класс списка */\nclass MyList {\n    #arr = new Array(); // Массив (для хранения элементов списка)\n    #capacity = 10; // Вместимость списка\n    #size = 0; // Длина списка (текущее число элементов)\n    #extendRatio = 2; // Коэффициент увеличения списка при каждом расширении\n\n    /* Конструктор */\n    constructor() {\n        this.#arr = new Array(this.#capacity);\n    }\n\n    /* Получить длину списка (текущее число элементов) */\n    size() {\n        return this.#size;\n    }\n\n    /* Получить вместимость списка */\n    capacity() {\n        return this.#capacity;\n    }\n\n    /* Доступ к элементу */\n    get(index) {\n        // Если индекс выходит за границы, выбрасывается исключение; далее аналогично\n        if (index &lt; 0 || index &gt;= this.#size) throw new Error('индекс выходит за границы');\n        return this.#arr[index];\n    }\n\n    /* Обновление элемента */\n    set(index, num) {\n        if (index &lt; 0 || index &gt;= this.#size) throw new Error('индекс выходит за границы');\n        this.#arr[index] = num;\n    }\n\n    /* Добавление элемента в конец */\n    add(num) {\n        // Если длина равна вместимости, требуется расширение\n        if (this.#size === this.#capacity) {\n            this.extendCapacity();\n        }\n        // Добавить новый элемент в конец списка\n        this.#arr[this.#size] = num;\n        this.#size++;\n    }\n\n    /* Вставка элемента в середину */\n    insert(index, num) {\n        if (index &lt; 0 || index &gt;= this.#size) throw new Error('индекс выходит за границы');\n        // При превышении вместимости по числу элементов запускается расширение\n        if (this.#size === this.#capacity) {\n            this.extendCapacity();\n        }\n        // Сдвинуть элемент с индексом index и все следующие элементы на одну позицию назад\n        for (let j = this.#size - 1; j &gt;= index; j--) {\n            this.#arr[j + 1] = this.#arr[j];\n        }\n        // Обновить число элементов\n        this.#arr[index] = num;\n        this.#size++;\n    }\n\n    /* Удаление элемента */\n    remove(index) {\n        if (index &lt; 0 || index &gt;= this.#size) throw new Error('индекс выходит за границы');\n        let num = this.#arr[index];\n        // Сдвинуть все элементы после индекса index на одну позицию вперед\n        for (let j = index; j &lt; this.#size - 1; j++) {\n            this.#arr[j] = this.#arr[j + 1];\n        }\n        // Обновить число элементов\n        this.#size--;\n        // Вернуть удаленный элемент\n        return num;\n    }\n\n    /* Расширение списка */\n    extendCapacity() {\n        // Создать новый массив длиной в extendRatio раз больше исходного и скопировать в него исходный массив\n        this.#arr = this.#arr.concat(\n            new Array(this.capacity() * (this.#extendRatio - 1))\n        );\n        // Обновить вместимость списка\n        this.#capacity = this.#arr.length;\n    }\n\n    /* Преобразовать список в массив */\n    toArray() {\n        let size = this.size();\n        // Преобразовывать только элементы списка в пределах фактической длины\n        const arr = new Array(size);\n        for (let i = 0; i &lt; size; i++) {\n            arr[i] = this.get(i);\n        }\n        return arr;\n    }\n}\n</code></pre> my_list.ts<pre><code>/* Класс списка */\nclass MyList {\n    private arr: Array&lt;number&gt;; // Массив (для хранения элементов списка)\n    private _capacity: number = 10; // Вместимость списка\n    private _size: number = 0; // Длина списка (текущее число элементов)\n    private extendRatio: number = 2; // Коэффициент увеличения списка при каждом расширении\n\n    /* Конструктор */\n    constructor() {\n        this.arr = new Array(this._capacity);\n    }\n\n    /* Получить длину списка (текущее число элементов) */\n    public size(): number {\n        return this._size;\n    }\n\n    /* Получить вместимость списка */\n    public capacity(): number {\n        return this._capacity;\n    }\n\n    /* Доступ к элементу */\n    public get(index: number): number {\n        // Если индекс выходит за границы, выбрасывается исключение; далее аналогично\n        if (index &lt; 0 || index &gt;= this._size) throw new Error('индекс выходит за границы');\n        return this.arr[index];\n    }\n\n    /* Обновление элемента */\n    public set(index: number, num: number): void {\n        if (index &lt; 0 || index &gt;= this._size) throw new Error('индекс выходит за границы');\n        this.arr[index] = num;\n    }\n\n    /* Добавление элемента в конец */\n    public add(num: number): void {\n        // Если длина равна вместимости, требуется расширение\n        if (this._size === this._capacity) this.extendCapacity();\n        // Добавить новый элемент в конец списка\n        this.arr[this._size] = num;\n        this._size++;\n    }\n\n    /* Вставка элемента в середину */\n    public insert(index: number, num: number): void {\n        if (index &lt; 0 || index &gt;= this._size) throw new Error('индекс выходит за границы');\n        // При превышении вместимости по числу элементов запускается расширение\n        if (this._size === this._capacity) {\n            this.extendCapacity();\n        }\n        // Сдвинуть элемент с индексом index и все следующие элементы на одну позицию назад\n        for (let j = this._size - 1; j &gt;= index; j--) {\n            this.arr[j + 1] = this.arr[j];\n        }\n        // Обновить число элементов\n        this.arr[index] = num;\n        this._size++;\n    }\n\n    /* Удаление элемента */\n    public remove(index: number): number {\n        if (index &lt; 0 || index &gt;= this._size) throw new Error('индекс выходит за границы');\n        let num = this.arr[index];\n        // Сдвинуть все элементы после индекса index на одну позицию вперед\n        for (let j = index; j &lt; this._size - 1; j++) {\n            this.arr[j] = this.arr[j + 1];\n        }\n        // Обновить число элементов\n        this._size--;\n        // Вернуть удаленный элемент\n        return num;\n    }\n\n    /* Расширение списка */\n    public extendCapacity(): void {\n        // Создать новый массив длиной size и скопировать в него исходный массив\n        this.arr = this.arr.concat(\n            new Array(this.capacity() * (this.extendRatio - 1))\n        );\n        // Обновить вместимость списка\n        this._capacity = this.arr.length;\n    }\n\n    /* Преобразовать список в массив */\n    public toArray(): number[] {\n        let size = this.size();\n        // Преобразовывать только элементы списка в пределах фактической длины\n        const arr = new Array(size);\n        for (let i = 0; i &lt; size; i++) {\n            arr[i] = this.get(i);\n        }\n        return arr;\n    }\n}\n</code></pre> my_list.dart<pre><code>/* Класс списка */\nclass MyList {\n  late List&lt;int&gt; _arr; // Массив (для хранения элементов списка)\n  int _capacity = 10; // Вместимость списка\n  int _size = 0; // Длина списка (текущее число элементов)\n  int _extendRatio = 2; // Коэффициент увеличения списка при каждом расширении\n\n  /* Конструктор */\n  MyList() {\n    _arr = List.filled(_capacity, 0);\n  }\n\n  /* Получить длину списка (текущее число элементов) */\n  int size() =&gt; _size;\n\n  /* Получить вместимость списка */\n  int capacity() =&gt; _capacity;\n\n  /* Доступ к элементу */\n  int get(int index) {\n    if (index &gt;= _size) throw RangeError('индекс выходит за границы');\n    return _arr[index];\n  }\n\n  /* Обновление элемента */\n  void set(int index, int _num) {\n    if (index &gt;= _size) throw RangeError('индекс выходит за границы');\n    _arr[index] = _num;\n  }\n\n  /* Добавление элемента в конец */\n  void add(int _num) {\n    // При превышении вместимости по числу элементов запускается расширение\n    if (_size == _capacity) extendCapacity();\n    _arr[_size] = _num;\n    // Обновить число элементов\n    _size++;\n  }\n\n  /* Вставка элемента в середину */\n  void insert(int index, int _num) {\n    if (index &gt;= _size) throw RangeError('индекс выходит за границы');\n    // При превышении вместимости по числу элементов запускается расширение\n    if (_size == _capacity) extendCapacity();\n    // Сдвинуть элемент с индексом index и все следующие элементы на одну позицию назад\n    for (var j = _size - 1; j &gt;= index; j--) {\n      _arr[j + 1] = _arr[j];\n    }\n    _arr[index] = _num;\n    // Обновить число элементов\n    _size++;\n  }\n\n  /* Удаление элемента */\n  int remove(int index) {\n    if (index &gt;= _size) throw RangeError('индекс выходит за границы');\n    int _num = _arr[index];\n    // Сдвинуть все элементы после индекса index на одну позицию вперед\n    for (var j = index; j &lt; _size - 1; j++) {\n      _arr[j] = _arr[j + 1];\n    }\n    // Обновить число элементов\n    _size--;\n    // Вернуть удаленный элемент\n    return _num;\n  }\n\n  /* Расширение списка */\n  void extendCapacity() {\n    // Создать новый массив длиной в _extendRatio раз больше исходного массива\n    final _newNums = List.filled(_capacity * _extendRatio, 0);\n    // Скопировать исходный массив в новый массив\n    List.copyRange(_newNums, 0, _arr);\n    // Обновить ссылку на _arr\n    _arr = _newNums;\n    // Обновить вместимость списка\n    _capacity = _arr.length;\n  }\n\n  /* Преобразовать список в массив */\n  List&lt;int&gt; toArray() {\n    List&lt;int&gt; arr = [];\n    for (var i = 0; i &lt; _size; i++) {\n      arr.add(get(i));\n    }\n    return arr;\n  }\n}\n</code></pre> my_list.rs<pre><code>/* Класс списка */\n#[allow(dead_code)]\nstruct MyList {\n    arr: Vec&lt;i32&gt;,       // Массив (для хранения элементов списка)\n    capacity: usize,     // Вместимость списка\n    size: usize,         // Длина списка (текущее число элементов)\n    extend_ratio: usize, // Коэффициент увеличения списка при каждом расширении\n}\n\n#[allow(unused, unused_comparisons)]\nimpl MyList {\n    /* Конструктор */\n    pub fn new(capacity: usize) -&gt; Self {\n        let mut vec = vec![0; capacity];\n        Self {\n            arr: vec,\n            capacity,\n            size: 0,\n            extend_ratio: 2,\n        }\n    }\n\n    /* Получить длину списка (текущее число элементов) */\n    pub fn size(&amp;self) -&gt; usize {\n        return self.size;\n    }\n\n    /* Получить вместимость списка */\n    pub fn capacity(&amp;self) -&gt; usize {\n        return self.capacity;\n    }\n\n    /* Доступ к элементу */\n    pub fn get(&amp;self, index: usize) -&gt; i32 {\n        // Если индекс выходит за границы, выбрасывается исключение; далее аналогично\n        if index &gt;= self.size {\n            panic!(\"индекс выходит за границы\")\n        };\n        return self.arr[index];\n    }\n\n    /* Обновление элемента */\n    pub fn set(&amp;mut self, index: usize, num: i32) {\n        if index &gt;= self.size {\n            panic!(\"индекс выходит за границы\")\n        };\n        self.arr[index] = num;\n    }\n\n    /* Добавление элемента в конец */\n    pub fn add(&amp;mut self, num: i32) {\n        // При превышении вместимости по числу элементов запускается расширение\n        if self.size == self.capacity() {\n            self.extend_capacity();\n        }\n        self.arr[self.size] = num;\n        // Обновить число элементов\n        self.size += 1;\n    }\n\n    /* Вставка элемента в середину */\n    pub fn insert(&amp;mut self, index: usize, num: i32) {\n        if index &gt;= self.size() {\n            panic!(\"индекс выходит за границы\")\n        };\n        // При превышении вместимости по числу элементов запускается расширение\n        if self.size == self.capacity() {\n            self.extend_capacity();\n        }\n        // Сдвинуть элемент с индексом index и все следующие элементы на одну позицию назад\n        for j in (index..self.size).rev() {\n            self.arr[j + 1] = self.arr[j];\n        }\n        self.arr[index] = num;\n        // Обновить число элементов\n        self.size += 1;\n    }\n\n    /* Удаление элемента */\n    pub fn remove(&amp;mut self, index: usize) -&gt; i32 {\n        if index &gt;= self.size() {\n            panic!(\"индекс выходит за границы\")\n        };\n        let num = self.arr[index];\n        // Сдвинуть все элементы после индекса index на одну позицию вперед\n        for j in index..self.size - 1 {\n            self.arr[j] = self.arr[j + 1];\n        }\n        // Обновить число элементов\n        self.size -= 1;\n        // Вернуть удаленный элемент\n        return num;\n    }\n\n    /* Расширение списка */\n    pub fn extend_capacity(&amp;mut self) {\n        // Создать новый массив длиной в extend_ratio раз больше исходного и скопировать в него исходный массив\n        let new_capacity = self.capacity * self.extend_ratio;\n        self.arr.resize(new_capacity, 0);\n        // Обновить вместимость списка\n        self.capacity = new_capacity;\n    }\n\n    /* Преобразовать список в массив */\n    pub fn to_array(&amp;self) -&gt; Vec&lt;i32&gt; {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        let mut arr = Vec::new();\n        for i in 0..self.size {\n            arr.push(self.get(i));\n        }\n        arr\n    }\n}\n</code></pre> my_list.c<pre><code>/* Класс списка */\ntypedef struct {\n    int *arr;        // Массив (для хранения элементов списка)\n    int capacity;    // Вместимость списка\n    int size;        // Размер списка\n    int extendRatio; // Коэффициент расширения списка при каждом увеличении\n} MyList;\n\n/* Конструктор */\nMyList *newMyList() {\n    MyList *nums = malloc(sizeof(MyList));\n    nums-&gt;capacity = 10;\n    nums-&gt;arr = malloc(sizeof(int) * nums-&gt;capacity);\n    nums-&gt;size = 0;\n    nums-&gt;extendRatio = 2;\n    return nums;\n}\n\n/* Деструктор */\nvoid delMyList(MyList *nums) {\n    free(nums-&gt;arr);\n    free(nums);\n}\n\n/* Получить длину списка */\nint size(MyList *nums) {\n    return nums-&gt;size;\n}\n\n/* Получить вместимость списка */\nint capacity(MyList *nums) {\n    return nums-&gt;capacity;\n}\n\n/* Доступ к элементу */\nint get(MyList *nums, int index) {\n    assert(index &gt;= 0 &amp;&amp; index &lt; nums-&gt;size);\n    return nums-&gt;arr[index];\n}\n\n/* Обновление элемента */\nvoid set(MyList *nums, int index, int num) {\n    assert(index &gt;= 0 &amp;&amp; index &lt; nums-&gt;size);\n    nums-&gt;arr[index] = num;\n}\n\n/* Добавление элемента в конец */\nvoid add(MyList *nums, int num) {\n    if (size(nums) == capacity(nums)) {\n        extendCapacity(nums); // Расширение емкости\n    }\n    nums-&gt;arr[size(nums)] = num;\n    nums-&gt;size++;\n}\n\n/* Вставка элемента в середину */\nvoid insert(MyList *nums, int index, int num) {\n    assert(index &gt;= 0 &amp;&amp; index &lt; size(nums));\n    // При превышении вместимости по числу элементов запускается расширение\n    if (size(nums) == capacity(nums)) {\n        extendCapacity(nums); // Расширение емкости\n    }\n    for (int i = size(nums); i &gt; index; --i) {\n        nums-&gt;arr[i] = nums-&gt;arr[i - 1];\n    }\n    nums-&gt;arr[index] = num;\n    nums-&gt;size++;\n}\n\n/* Удаление элемента */\n// Внимание: stdio.h уже использует ключевое слово remove\nint removeItem(MyList *nums, int index) {\n    assert(index &gt;= 0 &amp;&amp; index &lt; size(nums));\n    int num = nums-&gt;arr[index];\n    for (int i = index; i &lt; size(nums) - 1; i++) {\n        nums-&gt;arr[i] = nums-&gt;arr[i + 1];\n    }\n    nums-&gt;size--;\n    return num;\n}\n\n/* Расширение списка */\nvoid extendCapacity(MyList *nums) {\n    // Сначала выделить память\n    int newCapacity = capacity(nums) * nums-&gt;extendRatio;\n    int *extend = (int *)malloc(sizeof(int) * newCapacity);\n    int *temp = nums-&gt;arr;\n\n    // Скопировать старые данные в новые\n    for (int i = 0; i &lt; size(nums); i++)\n        extend[i] = nums-&gt;arr[i];\n\n    // Освободить старые данные\n    free(temp);\n\n    // Обновить новые данные\n    nums-&gt;arr = extend;\n    nums-&gt;capacity = newCapacity;\n}\n\n/* Преобразовать список в Array для вывода */\nint *toArray(MyList *nums) {\n    return nums-&gt;arr;\n}\n</code></pre> my_list.kt<pre><code>/* Класс списка */\nclass MyList {\n    private var arr: IntArray = intArrayOf() // Массив (для хранения элементов списка)\n    private var capacity: Int = 10 // Вместимость списка\n    private var size: Int = 0 // Длина списка (текущее число элементов)\n    private var extendRatio: Int = 2 // Коэффициент увеличения списка при каждом расширении\n\n    /* Конструктор */\n    init {\n        arr = IntArray(capacity)\n    }\n\n    /* Получить длину списка (текущее число элементов) */\n    fun size(): Int {\n        return size\n    }\n\n    /* Получить вместимость списка */\n    fun capacity(): Int {\n        return capacity\n    }\n\n    /* Доступ к элементу */\n    fun get(index: Int): Int {\n        // Если индекс выходит за границы, выбрасывается исключение; далее аналогично\n        if (index &lt; 0 || index &gt;= size)\n            throw IndexOutOfBoundsException(\"индекс выходит за границы\")\n        return arr[index]\n    }\n\n    /* Обновление элемента */\n    fun set(index: Int, num: Int) {\n        if (index &lt; 0 || index &gt;= size)\n            throw IndexOutOfBoundsException(\"индекс выходит за границы\")\n        arr[index] = num\n    }\n\n    /* Добавление элемента в конец */\n    fun add(num: Int) {\n        // При превышении вместимости по числу элементов запускается расширение\n        if (size == capacity())\n            extendCapacity()\n        arr[size] = num\n        // Обновить число элементов\n        size++\n    }\n\n    /* Вставка элемента в середину */\n    fun insert(index: Int, num: Int) {\n        if (index &lt; 0 || index &gt;= size)\n            throw IndexOutOfBoundsException(\"индекс выходит за границы\")\n        // При превышении вместимости по числу элементов запускается расширение\n        if (size == capacity())\n            extendCapacity()\n        // Сдвинуть элемент с индексом index и все следующие элементы на одну позицию назад\n        for (j in size - 1 downTo index)\n            arr[j + 1] = arr[j]\n        arr[index] = num\n        // Обновить число элементов\n        size++\n    }\n\n    /* Удаление элемента */\n    fun remove(index: Int): Int {\n        if (index &lt; 0 || index &gt;= size)\n            throw IndexOutOfBoundsException(\"индекс выходит за границы\")\n        val num = arr[index]\n        // Сдвинуть все элементы после индекса index на одну позицию вперед\n        for (j in index..&lt;size - 1)\n            arr[j] = arr[j + 1]\n        // Обновить число элементов\n        size--\n        // Вернуть удаленный элемент\n        return num\n    }\n\n    /* Расширение списка */\n    fun extendCapacity() {\n        // Создать новый массив длиной в extendRatio раз больше исходного и скопировать в него исходный массив\n        arr = arr.copyOf(capacity() * extendRatio)\n        // Обновить вместимость списка\n        capacity = arr.size\n    }\n\n    /* Преобразовать список в массив */\n    fun toArray(): IntArray {\n        val size = size()\n        // Преобразовывать только элементы списка в пределах фактической длины\n        val arr = IntArray(size)\n        for (i in 0..&lt;size) {\n            arr[i] = get(i)\n        }\n        return arr\n    }\n}\n</code></pre> my_list.rb<pre><code>### Класс списка ###\nclass MyList\n  attr_reader :size       # Получить длину списка (текущее число элементов)\n  attr_reader :capacity   # Получить вместимость списка\n\n  ### Конструктор ###\n  def initialize\n    @capacity = 10\n    @size = 0\n    @extend_ratio = 2\n    @arr = Array.new(capacity)\n  end\n\n  ### Доступ к элементу ###\n  def get(index)\n    # Если индекс выходит за границы, выбрасывается исключение; далее аналогично\n    raise IndexError, \"индекс выходит за границы\" if index &lt; 0 || index &gt;= size\n    @arr[index]\n  end\n\n  ### Доступ к элементу ###\n  def set(index, num)\n    raise IndexError, \"индекс выходит за границы\" if index &lt; 0 || index &gt;= size\n    @arr[index] = num\n  end\n\n  ### Добавление элемента в конец ###\n  def add(num)\n    # При превышении вместимости по числу элементов запускается расширение\n    extend_capacity if size == capacity\n    @arr[size] = num\n\n    # Обновить число элементов\n    @size += 1\n  end\n\n  ### Вставка элемента в середину ###\n  def insert(index, num)\n    raise IndexError, \"индекс выходит за границы\" if index &lt; 0 || index &gt;= size\n\n    # При превышении вместимости по числу элементов запускается расширение\n    extend_capacity if size == capacity\n\n    # Сдвинуть элемент с индексом index и все следующие элементы на одну позицию назад\n    for j in (size - 1).downto(index)\n      @arr[j + 1] = @arr[j]\n    end\n    @arr[index] = num\n\n    # Обновить число элементов\n    @size += 1\n  end\n\n  ### Удаление элемента ###\n  def remove(index)\n    raise IndexError, \"индекс выходит за границы\" if index &lt; 0 || index &gt;= size\n    num = @arr[index]\n\n    # Сдвинуть все элементы после индекса index на одну позицию вперед\n    for j in index...size\n      @arr[j] = @arr[j + 1]\n    end\n\n    # Обновить число элементов\n    @size -= 1\n\n    # Вернуть удаленный элемент\n    num\n  end\n\n  ### Расширение списка ###\n  def extend_capacity\n    # Создать новый массив длиной в extend_ratio раз больше исходного и скопировать в него исходный массив\n    arr = @arr.dup + Array.new(capacity * (@extend_ratio - 1))\n    # Обновить вместимость списка\n    @capacity = arr.length\n  end\n\n  ### Преобразование списка в массив ###\n  def to_array\n    sz = size\n    # Преобразовывать только элементы списка в пределах фактической длины\n    arr = Array.new(sz)\n    for i in 0...sz\n      arr[i] = get(i)\n    end\n    arr\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 4. Массивы и списки","4.3 &nbsp; Список"],"tags":[]},{"location":"chapter_array_and_linkedlist/ram_and_cache/","level":1,"title":"4.4   Оперативная память и кэш *","text":"<p>В первых двух разделах этой главы мы разобрали массивы и связные списки - две базовые и важные структуры данных, которые представляют соответственно непрерывное хранение и разрозненное хранение.</p> <p>На практике физическая структура во многом определяет, насколько эффективно программа использует память и кэш, а это, в свою очередь, влияет на общую производительность алгоритма.</p>","path":["Глава 4. Массивы и списки","4.4 &nbsp; Оперативная память и кэш *"],"tags":[]},{"location":"chapter_array_and_linkedlist/ram_and_cache/#441","level":2,"title":"4.4.1   Устройства хранения данных в компьютере","text":"<p>В компьютере есть три типа устройств хранения данных: жесткий диск (hard disk) , оперативная память (random-access memory, RAM) и кэш-память (cache memory) . В таблице 4-2 показаны их различные роли и характеристики в компьютерной системе.</p> <p> Таблица 4-2   Устройства хранения данных в компьютере </p> Жесткий диск Оперативная память Кэш Назначение Долговременное хранение данных, включая ОС, программы, файлы и т.д. Временное хранение выполняемых программ и обрабатываемых данных Хранение часто используемых данных и инструкций, уменьшающее число обращений CPU к памяти Энергозависимость Данные не теряются после отключения питания Данные теряются после отключения питания Данные теряются после отключения питания Емкость Большая, уровень TB Меньшая, уровень GB Очень малая, уровень MB Скорость Низкая, от сотен до тысяч MB/s Высокая, десятки GB/s Очень высокая, десятки и сотни GB/s Цена Низкая, единицы валюты за GB Высокая, десятки и сотни валютных единиц за GB Очень высокая, входит в стоимость CPU <p>Компьютерную систему хранения можно представить в виде пирамиды, показанной на рисунке 4-9. Чем ближе устройство хранения к вершине пирамиды, тем оно быстрее, тем меньше его емкость и тем выше его стоимость. Такая многоуровневая конструкция возникла не случайно, а стала результатом тщательных инженерных компромиссов.</p> <ul> <li>Жесткий диск трудно заменить оперативной памятью. Во-первых, данные в оперативной памяти исчезают после отключения питания, поэтому она не подходит для долговременного хранения. Во-вторых, память стоит в разы дороже жесткого диска, что мешает ее широкому применению.</li> <li>Кэш не может одновременно быть и очень большим, и очень быстрым. По мере роста емкости кэшей L1, L2 и L3 их физический размер увеличивается, расстояние до ядра CPU становится больше, время передачи данных растет, а задержка доступа к элементам увеличивается. При текущем уровне технологий многоуровневая структура кэша является лучшим балансом между емкостью, скоростью и стоимостью.</li> </ul> <p></p> <p> Рисунок 4-9   Система хранения данных компьютера </p> <p>Tip</p> <p>Иерархия памяти компьютера отражает тонкий баланс между скоростью, емкостью и стоимостью. Подобные компромиссы встречаются почти во всех областях инженерии: приходится искать оптимальный баланс между преимуществами и ограничениями.</p> <p>В итоге жесткий диск используется для долговременного хранения больших объемов данных, оперативная память - для временного хранения данных, с которыми программа работает прямо сейчас, а кэш - для хранения часто используемых данных и инструкций, чтобы ускорять выполнение программ. Все три уровня работают совместно и обеспечивают эффективную работу компьютерной системы.</p> <p>Как показано на рисунке 4-10, во время выполнения программы данные читаются с жесткого диска в оперативную память, а затем используются CPU в вычислениях. Кэш можно рассматривать как часть CPU: он подгружает данные из оперативной памяти, обеспечивая CPU высокоскоростной доступ и тем самым значительно ускоряя выполнение программы и уменьшая зависимость от более медленной RAM.</p> <p></p> <p> Рисунок 4-10   Поток данных между жестким диском, RAM и кэшем </p>","path":["Глава 4. Массивы и списки","4.4 &nbsp; Оперативная память и кэш *"],"tags":[]},{"location":"chapter_array_and_linkedlist/ram_and_cache/#442","level":2,"title":"4.4.2   Эффективность использования памяти структурами данных","text":"<p>С точки зрения использования пространства памяти массивы и связные списки имеют свои преимущества и ограничения.</p> <p>С одной стороны, память ограничена, и один и тот же участок памяти не может совместно использоваться несколькими программами, поэтому нам хочется, чтобы структуры данных использовали пространство как можно эффективнее. Элементы массива расположены плотно и не требуют дополнительного места для хранения ссылок (указателей) между узлами списка, поэтому массивы эффективнее по памяти. Однако массиву нужно сразу выделить достаточно большой непрерывный участок памяти, что может приводить к потерям пространства, а его расширение требует дополнительных затрат времени и памяти. Напротив, связные списки выделяют и освобождают память на уровне узлов, что дает большую гибкость.</p> <p>С другой стороны, во время выполнения программы при многократном выделении и освобождении памяти фрагментация свободной памяти становится все более серьезной, что снижает эффективность ее использования. Массивы из-за непрерывного хранения относительно менее подвержены фрагментации. Напротив, элементы связного списка распределены по памяти, и частые операции вставки и удаления легче приводят к фрагментации.</p>","path":["Глава 4. Массивы и списки","4.4 &nbsp; Оперативная память и кэш *"],"tags":[]},{"location":"chapter_array_and_linkedlist/ram_and_cache/#443","level":2,"title":"4.4.3   Эффективность использования кэша структурами данных","text":"<p>Хотя по объему кэш намного меньше оперативной памяти, он значительно быстрее и играет критически важную роль в скорости выполнения программ. Поскольку объем кэша ограничен и в нем можно хранить только небольшую долю часто используемых данных, когда CPU пытается обратиться к данным, которых в кэше нет, происходит промах кэша (cache miss) , и CPU вынужден загружать нужные данные из более медленной памяти.</p> <p>Очевидно, что чем меньше промахов кэша, тем выше эффективность чтения и записи данных CPU, а значит, тем лучше производительность программы. Долю обращений, при которых CPU успешно получает данные из кэша, называют коэффициентом попадания в кэш (cache hit rate) ; этот показатель обычно используют для оценки эффективности кэша.</p> <p>Чтобы добиться как можно большей эффективности, кэш использует следующие механизмы загрузки данных.</p> <ul> <li>Строки кэша: кэш хранит и загружает данные не по одному байту, а строками кэша. По сравнению с передачей по байтам это гораздо эффективнее.</li> <li>Механизм предвыборки: процессор старается предсказать шаблон доступа к данным (например последовательный доступ, доступ с фиксированным шагом и т.д.) и на основе этого шаблона заранее загружает данные в кэш, повышая вероятность попадания.</li> <li>Пространственная локальность: если к некоторым данным уже обратились, то велика вероятность, что в ближайшее время понадобятся и соседние данные. Поэтому, загружая некоторые данные, кэш часто подгружает и окружающие их данные.</li> <li>Временная локальность: если к данным уже обратились, то высока вероятность, что к ним снова обратятся в ближайшем будущем. Кэш использует это свойство, сохраняя недавно использованные данные.</li> </ul> <p>На практике массивы и связные списки по-разному используют кэш, и это проявляется в нескольких аспектах.</p> <ul> <li>Занимаемое пространство: элементы связного списка занимают больше места, чем элементы массива, поэтому в кэше помещается меньше полезных данных.</li> <li>Строки кэша: данные списка разбросаны по памяти, а кэш загружает данные строками, поэтому доля бесполезно загружаемых данных оказывается выше.</li> <li>Механизм предвыборки: шаблон доступа к данным у массивов более предсказуем, чем у списков, то есть системе легче угадать, какие данные понадобятся следующими.</li> <li>Пространственная локальность: массив хранится в компактной области памяти, поэтому данные рядом с уже загруженными с большей вероятностью скоро будут использованы.</li> </ul> <p>В целом массивы имеют более высокий коэффициент попадания в кэш, поэтому по эффективности операций они обычно превосходят связные списки. Именно поэтому при решении алгоритмических задач структуры данных на основе массивов часто оказываются предпочтительнее.</p> <p>Важно понимать, что высокая эффективность кэша не означает, что массивы во всех случаях лучше связных списков. В реальных приложениях выбор структуры данных должен определяться конкретными требованиями. Например, и массивы, и списки могут использоваться для реализации \"стека\" (подробнее об этом будет рассказано в следующей главе), но подходят они для разных сценариев.</p> <ul> <li>При решении алгоритмических задач мы обычно предпочитаем стек на основе массива, потому что он дает более высокую эффективность операций и поддерживает произвольный доступ, а цена за это - необходимость заранее выделить некоторый объем памяти под массив.</li> <li>Если объем данных очень велик, структура сильно динамична, а ожидаемый размер стека трудно оценить заранее, то более уместен стек на основе связного списка. Список позволяет распределить большой объем данных по разным участкам памяти и избегает накладных расходов, связанных с расширением массива.</li> </ul>","path":["Глава 4. Массивы и списки","4.4 &nbsp; Оперативная память и кэш *"],"tags":[]},{"location":"chapter_array_and_linkedlist/summary/","level":1,"title":"4.5   Резюме","text":"","path":["Глава 4. Массивы и списки","4.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_array_and_linkedlist/summary/#1","level":3,"title":"1.   Ключевые выводы","text":"<ul> <li>Массивы и связные списки - это две базовые структуры данных, представляющие два способа хранения данных в памяти компьютера: хранение в непрерывном пространстве и хранение в разрозненном пространстве. Их свойства во многом взаимно дополняют друг друга.</li> <li>Массив поддерживает произвольный доступ и занимает меньше памяти; однако вставка и удаление элементов в нем неэффективны, а длина после инициализации фиксирована.</li> <li>Связный список позволяет эффективно вставлять и удалять узлы путем изменения ссылок (указателей), а также гибко менять длину; однако доступ к узлам менее эффективен, а памяти он занимает больше. Распространенные типы списков включают односвязные, циклические и двусвязные списки.</li> <li>Список - это упорядоченная коллекция элементов, поддерживающая добавление, удаление, поиск и изменение, и обычно реализуемая на основе динамического массива. Он сохраняет преимущества массива и при этом может гибко менять длину.</li> <li>Появление списка значительно повысило практическую ценность массива, хотя это и может приводить к потере части памяти.</li> <li>Во время работы программы данные в основном хранятся в оперативной памяти. Массив обеспечивает более высокую эффективность использования пространства памяти, а связный список дает большую гибкость в использовании памяти.</li> <li>Кэш, используя строки кэша, механизм предвыборки, а также пространственную и временную локальность, предоставляет CPU быстрый доступ к данным и заметно повышает эффективность выполнения программ.</li> <li>Поскольку массивы обычно имеют более высокий коэффициент попадания в кэш, они в большинстве случаев работают эффективнее списков. При выборе структуры данных нужно исходить из конкретных требований и сценариев.</li> </ul>","path":["Глава 4. Массивы и списки","4.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_array_and_linkedlist/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: Влияет ли хранение массива в стеке или в куче на временную и пространственную эффективность?</p> <p>Массивы, расположенные и в стеке, и в куче, все равно хранятся в непрерывной области памяти, поэтому эффективность операций с данными у них в целом одинакова. Однако у стека и кучи есть собственные особенности, из-за которых возникают следующие различия.</p> <ol> <li>Эффективность выделения и освобождения: стек представляет собой относительно небольшой участок памяти, а выделение в нем обычно выполняется автоматически компилятором; куча же обычно больше, может выделяться динамически из кода и легче фрагментируется. Поэтому выделение и освобождение памяти в куче обычно медленнее, чем в стеке.</li> <li>Ограничение размера: объем стека относительно невелик, а размер кучи обычно ограничивается доступной памятью. Поэтому куча лучше подходит для хранения больших массивов.</li> <li>Гибкость: размер массива в стеке должен быть известен во время компиляции, а размер массива в куче может определяться динамически во время выполнения.</li> </ol> <p>Q: Почему для массива требуется, чтобы все элементы были одного типа, а для связного списка это не подчеркивается?</p> <p>Связный список состоит из узлов, а узлы соединяются между собой через ссылки (указатели), поэтому каждый узел в принципе может хранить данные разного типа, например <code>int</code> , <code>double</code> , <code>string</code> , <code>object</code> и т.д.</p> <p>Напротив, элементы массива должны быть одного типа, иначе нельзя будет вычислять адрес элемента через смещение. Например, если массив одновременно содержит <code>int</code> и <code>long</code> , один элемент занимает 4 байта, а другой - 8 байт ; в этом случае формула ниже уже не позволит вычислить смещение, потому что в массиве будут присутствовать элементы разной длины.</p> <pre><code># Адрес элемента в памяти = адрес массива в памяти (адрес первого элемента) + длина элемента * индекс элемента\n</code></pre> <p>Q: После удаления узла <code>P</code> нужно ли присваивать <code>P.next = None</code> ?</p> <p>Можно и не изменять <code>P.next</code> . С точки зрения данного списка, при обходе от головы к хвосту узел <code>P</code> уже больше не встретится. Это означает, что узел <code>P</code> уже удален из списка, и то, куда он указывает после этого, на сам список больше не влияет.</p> <p>С точки зрения задач по структурам данных и алгоритмам, отсутствие такого разрыва обычно не критично, если логика программы остается корректной. Но с точки зрения стандартной библиотеки разорвать связь безопаснее и логичнее. Если этого не сделать и удаленный узел не будет нормально собран, он может мешать освобождению памяти последующих узлов.</p> <p>Q: Временная сложность вставки и удаления в связном списке равна \\(O(1)\\) . Но до вставки или удаления обычно еще нужно потратить \\(O(n)\\) на поиск элемента. Почему тогда общая сложность не \\(O(n)\\) ?</p> <p>Если сначала искать элемент, а потом удалять его, то временная сложность действительно будет \\(O(n)\\) . Однако преимущество связного списка с \\(O(1)\\) вставкой и удалением проявляется в других сценариях. Например, двустороннюю очередь удобно реализовывать именно на связном списке: мы поддерживаем указатели на голову и хвост, и тогда каждая операция вставки или удаления остается \\(O(1)\\) .</p> <p>Q: На рисунке \"Определение связного списка и способ хранения\" светло-голубой блок с указателем узла - это отдельный адрес памяти? Или он делит память пополам со значением узла?</p> <p>Этот рисунок дает только качественное представление; количественно все зависит от конкретных условий.</p> <ul> <li>Значения узлов разных типов занимают разный объем памяти, например <code>int</code> , <code>long</code> , <code>double</code> и объекты-экземпляры.</li> <li>Размер памяти, занимаемой переменной-указателем, зависит от операционной системы и среды компиляции и обычно составляет 8 байт или 4 байта.</li> </ul> <p>Q: Всегда ли добавление элемента в конец списка имеет сложность \\(O(1)\\) ?</p> <p>Если при добавлении элемента длина списка превышается, то сначала приходится расширять список, а уже затем добавлять новый элемент. Система выделяет новый участок памяти и переносит туда все элементы исходного списка, и в этот момент временная сложность становится \\(O(n)\\) .</p> <p>Q: В утверждении \"появление списка сильно повысило практическую полезность массива, но может приводить к потере части памяти\" под потерями памяти имеется в виду дополнительная память под такие переменные, как емкость, длина и коэффициент расширения?</p> <p>Потери памяти здесь в основном имеют два значения: во-первых, список обычно имеет некоторую начальную емкость, которая может быть нам не нужна целиком; во-вторых, чтобы избежать слишком частых расширений, емкость при расширении обычно умножается на некоторый коэффициент, например \\(\\times 1.5\\) . Из-за этого появляется много пустых слотов, которые обычно нельзя полностью заполнить.</p> <p>Q: В Python после инициализации <code>n = [1, 2, 3]</code> адреса этих трех элементов выглядят непрерывными, но после <code>m = [2, 1, 3]</code> можно заметить, что <code>id</code> элементов не идут подряд, а совпадают с одинаковыми числами из <code>n</code> . Если адреса элементов не непрерывны, остается ли <code>m</code> массивом?</p> <p>Предположим, что элементами списка являются узлы <code>n = [n1, n2, n3, n4, n5]</code> . Обычно эти 5 объектов-узлов тоже будут храниться в разных местах памяти. Однако, имея индекс списка, мы по-прежнему можем за \\(O(1)\\) получить адрес памяти соответствующего узла и обратиться к нему. Это связано с тем, что в массиве хранятся ссылки на узлы, а не сами узлы.</p> <p>В отличие от многих других языков, в Python даже числа обернуты в объекты, и в списке хранятся не сами числа, а ссылки на них. Поэтому мы и наблюдаем, что одинаковые числа в двух массивах имеют один и тот же <code>id</code> , а адреса этих чисел не обязаны быть непрерывными.</p> <p>Q: В C++ STL уже есть двусвязный список <code>std::list</code> , но в некоторых учебниках по алгоритмам им пользуются не так часто. Это связано с какими-то ограничениями?</p> <p>С одной стороны, при разработке алгоритмов мы обычно предпочитаем структуры на основе массива, а к связным спискам прибегаем только при необходимости, по двум главным причинам.</p> <ul> <li>Накладные расходы по памяти: поскольку каждому элементу нужны два дополнительных указателя (на предыдущий и следующий элементы), <code>std::list</code> обычно занимает больше памяти, чем <code>std::vector</code> .</li> <li>Низкая дружелюбность к кэшу: поскольку данные не лежат непрерывно, <code>std::list</code> хуже использует кэш. В большинстве случаев <code>std::vector</code> показывает лучшую производительность.</li> </ul> <p>С другой стороны, случаи, когда связный список действительно необходим, в основном возникают в деревьях и графах. Для стеков и очередей чаще используют предоставляемые языком <code>stack</code> и <code>queue</code> , а не связный список напрямую.</p> <p>Q: Операция <code>res = [[0]] * n</code> создает двумерный список. Каждый <code>[0]</code> в нем независим?</p> <p>Нет, они не независимы. В таком двумерном списке все <code>[0]</code> на самом деле являются ссылками на один и тот же объект. Если изменить один из них, окажется, что меняются и все остальные соответствующие элементы.</p> <p>Если нужно, чтобы каждый <code>[0]</code> был независимым, можно использовать <code>res = [[0] for _ in range(n)]</code> . В этом варианте создаются \\(n\\) независимых объектов-списков <code>[0]</code> .</p> <p>Q: Операция <code>res = [0] * n</code> создает список. Каждый целочисленный <code>0</code> в нем независим?</p> <p>В этом списке все целые числа <code>0</code> являются ссылками на один и тот же объект. Это связано с тем, что Python использует механизм кэш-пула для маленьких целых чисел (обычно от -5 до 256), чтобы максимально переиспользовать объекты и повысить производительность.</p> <p>Хотя все элементы указывают на один и тот же объект, мы все равно можем независимо изменять элементы списка, потому что целые числа в Python - это \"неизменяемые объекты\". Когда мы изменяем некоторый элемент, на самом деле происходит переключение ссылки на другой объект, а не изменение исходного объекта.</p> <p>Однако если элементами списка являются \"изменяемые объекты\" (например списки, словари или экземпляры классов), то изменение одного элемента прямо меняет сам объект, и все элементы, ссылающиеся на него, увидят одно и то же изменение.</p>","path":["Глава 4. Массивы и списки","4.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_backtracking/","level":1,"title":"Глава 13.   Поиск с возвратом","text":"<p>Abstract</p> <p>Мы словно исследователи в лабиринте: на пути вперед могут встречаться тупики и трудности.</p> <p>Сила возврата позволяет нам начать заново, пробовать снова и снова и в конце концов найти выход к свету.</p>","path":["Глава 13. Поиск с возвратом","Глава 13. &nbsp; Поиск с возвратом"],"tags":[]},{"location":"chapter_backtracking/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>13.1   Алгоритм поиска с возвратом</li> <li>13.2   Задача о перестановках</li> <li>13.3   Задача о сумме подмножеств</li> <li>13.4   Задача о n ферзях</li> <li>13.5   Резюме</li> </ul>","path":["Глава 13. Поиск с возвратом","Глава 13. &nbsp; Поиск с возвратом"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/","level":1,"title":"13.1   Алгоритм поиска с возвратом","text":"<p>Алгоритм поиска с возвратом (backtracking algorithm) - это метод решения задач путем полного перебора. Его основная идея состоит в том, чтобы, начиная с некоторого исходного состояния, грубо перебрать все возможные решения, записывать корректные решения и продолжать поиск до тех пор, пока решение не будет найдено или пока не будут исчерпаны все возможные варианты.</p> <p>Обычно алгоритмы поиска с возвратом используют обход в глубину для обхода пространства решений. В главе \"Бинарные деревья\" мы уже упоминали, что прямой, симметричный и обратный обходы относятся к обходу в глубину. Теперь мы на основе прямого обхода построим задачу поиска с возвратом и постепенно разберем принцип работы этого алгоритма.</p> <p>Пример 1</p> <p>Дано двоичное дерево. Найдите и запишите все узлы со значением \\(7\\) ; верните список этих узлов.</p> <p>Для этой задачи мы выполняем прямой обход дерева и проверяем, равно ли значение текущего узла \\(7\\) ; если да, то добавляем значение этого узла в список результатов <code>res</code> . Соответствующий процесс показан на рисунке 13-1 и в коде:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby preorder_traversal_i_compact.py<pre><code>def pre_order(root: TreeNode):\n    \"\"\"Предварительный обход: пример 1\"\"\"\n    if root is None:\n        return\n    if root.val == 7:\n        # Записать решение\n        res.append(root)\n    pre_order(root.left)\n    pre_order(root.right)\n</code></pre> preorder_traversal_i_compact.cpp<pre><code>/* Предварительный обход: пример 1 */\nvoid preOrder(TreeNode *root) {\n    if (root == nullptr) {\n        return;\n    }\n    if (root-&gt;val == 7) {\n        // Записать решение\n        res.push_back(root);\n    }\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n}\n</code></pre> preorder_traversal_i_compact.java<pre><code>/* Предварительный обход: пример 1 */\nvoid preOrder(TreeNode root) {\n    if (root == null) {\n        return;\n    }\n    if (root.val == 7) {\n        // Записать решение\n        res.add(root);\n    }\n    preOrder(root.left);\n    preOrder(root.right);\n}\n</code></pre> preorder_traversal_i_compact.cs<pre><code>/* Предварительный обход: пример 1 */\nvoid PreOrder(TreeNode? root) {\n    if (root == null) {\n        return;\n    }\n    if (root.val == 7) {\n        // Записать решение\n        res.Add(root);\n    }\n    PreOrder(root.left);\n    PreOrder(root.right);\n}\n</code></pre> preorder_traversal_i_compact.go<pre><code>/* Предварительный обход: пример 1 */\nfunc preOrderI(root *TreeNode, res *[]*TreeNode) {\n    if root == nil {\n        return\n    }\n    if (root.Val).(int) == 7 {\n        // Записать решение\n        *res = append(*res, root)\n    }\n    preOrderI(root.Left, res)\n    preOrderI(root.Right, res)\n}\n</code></pre> preorder_traversal_i_compact.swift<pre><code>/* Предварительный обход: пример 1 */\nfunc preOrder(root: TreeNode?) {\n    guard let root = root else {\n        return\n    }\n    if root.val == 7 {\n        // Записать решение\n        res.append(root)\n    }\n    preOrder(root: root.left)\n    preOrder(root: root.right)\n}\n</code></pre> preorder_traversal_i_compact.js<pre><code>/* Предварительный обход: пример 1 */\nfunction preOrder(root, res) {\n    if (root === null) {\n        return;\n    }\n    if (root.val === 7) {\n        // Записать решение\n        res.push(root);\n    }\n    preOrder(root.left, res);\n    preOrder(root.right, res);\n}\n</code></pre> preorder_traversal_i_compact.ts<pre><code>/* Предварительный обход: пример 1 */\nfunction preOrder(root: TreeNode | null, res: TreeNode[]): void {\n    if (root === null) {\n        return;\n    }\n    if (root.val === 7) {\n        // Записать решение\n        res.push(root);\n    }\n    preOrder(root.left, res);\n    preOrder(root.right, res);\n}\n</code></pre> preorder_traversal_i_compact.dart<pre><code>/* Предварительный обход: пример 1 */\nvoid preOrder(TreeNode? root, List&lt;TreeNode&gt; res) {\n  if (root == null) {\n    return;\n  }\n  if (root.val == 7) {\n    // Записать решение\n    res.add(root);\n  }\n  preOrder(root.left, res);\n  preOrder(root.right, res);\n}\n</code></pre> preorder_traversal_i_compact.rs<pre><code>/* Предварительный обход: пример 1 */\nfn pre_order(res: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;, root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;) {\n    if root.is_none() {\n        return;\n    }\n    if let Some(node) = root {\n        if node.borrow().val == 7 {\n            // Записать решение\n            res.push(node.clone());\n        }\n        pre_order(res, node.borrow().left.as_ref());\n        pre_order(res, node.borrow().right.as_ref());\n    }\n}\n</code></pre> preorder_traversal_i_compact.c<pre><code>/* Предварительный обход: пример 1 */\nvoid preOrder(TreeNode *root) {\n    if (root == NULL) {\n        return;\n    }\n    if (root-&gt;val == 7) {\n        // Записать решение\n        res[resSize++] = root;\n    }\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n}\n</code></pre> preorder_traversal_i_compact.kt<pre><code>/* Предварительный обход: пример 1 */\nfun preOrder(root: TreeNode?) {\n    if (root == null) {\n        return\n    }\n    if (root._val == 7) {\n        // Записать решение\n        res!!.add(root)\n    }\n    preOrder(root.left)\n    preOrder(root.right)\n}\n</code></pre> preorder_traversal_i_compact.rb<pre><code>### Предварительный обход: пример 1 ###\ndef pre_order(root)\n  return unless root\n\n  # Записать решение\n  $res &lt;&lt; root if root.val == 7\n\n  pre_order(root.left)\n  pre_order(root.right)\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p></p> <p> Рисунок 13-1   Поиск узлов при прямом обходе </p>","path":["Глава 13. Поиск с возвратом","13.1 &nbsp; Алгоритм поиска с возвратом"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/#1311","level":2,"title":"13.1.1   Попытка и откат","text":"<p>Алгоритм называется поиском с возвратом, потому что при поиске в пространстве решений он использует стратегию \"попытка\" и \"откат\". Когда в процессе поиска алгоритм приходит в состояние, из которого нельзя двигаться дальше или нельзя получить удовлетворяющее условиям решение, он отменяет предыдущий выбор, возвращается к более раннему состоянию и пробует другие возможные варианты.</p> <p>Для примера 1 посещение каждого узла представляет собой \"попытку\", а прохождение листового узла или возврат к родителю через <code>return</code> означает \"откат\".</p> <p>Важно понимать, что откат не сводится только к возврату из функции. Чтобы показать это, слегка расширим пример 1.</p> <p>Пример 2</p> <p>Найдите в двоичном дереве все узлы со значением \\(7\\) и верните пути от корня до этих узлов.</p> <p>Взяв за основу код примера 1, добавим список <code>path</code> для записи пути посещенных узлов. Когда встречается узел со значением \\(7\\) , мы копируем <code>path</code> и добавляем его в список результатов <code>res</code> . После завершения обхода именно <code>res</code> будет содержать все решения. Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby preorder_traversal_ii_compact.py<pre><code>def pre_order(root: TreeNode):\n    \"\"\"Предварительный обход: пример 2\"\"\"\n    if root is None:\n        return\n    # Попытка\n    path.append(root)\n    if root.val == 7:\n        # Записать решение\n        res.append(list(path))\n    pre_order(root.left)\n    pre_order(root.right)\n    # Откат\n    path.pop()\n</code></pre> preorder_traversal_ii_compact.cpp<pre><code>/* Предварительный обход: пример 2 */\nvoid preOrder(TreeNode *root) {\n    if (root == nullptr) {\n        return;\n    }\n    // Попытка\n    path.push_back(root);\n    if (root-&gt;val == 7) {\n        // Записать решение\n        res.push_back(path);\n    }\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n    // Откат\n    path.pop_back();\n}\n</code></pre> preorder_traversal_ii_compact.java<pre><code>/* Предварительный обход: пример 2 */\nvoid preOrder(TreeNode root) {\n    if (root == null) {\n        return;\n    }\n    // Попытка\n    path.add(root);\n    if (root.val == 7) {\n        // Записать решение\n        res.add(new ArrayList&lt;&gt;(path));\n    }\n    preOrder(root.left);\n    preOrder(root.right);\n    // Откат\n    path.remove(path.size() - 1);\n}\n</code></pre> preorder_traversal_ii_compact.cs<pre><code>/* Предварительный обход: пример 2 */\nvoid PreOrder(TreeNode? root) {\n    if (root == null) {\n        return;\n    }\n    // Попытка\n    path.Add(root);\n    if (root.val == 7) {\n        // Записать решение\n        res.Add(new List&lt;TreeNode&gt;(path));\n    }\n    PreOrder(root.left);\n    PreOrder(root.right);\n    // Откат\n    path.RemoveAt(path.Count - 1);\n}\n</code></pre> preorder_traversal_ii_compact.go<pre><code>/* Предварительный обход: пример 2 */\nfunc preOrderII(root *TreeNode, res *[][]*TreeNode, path *[]*TreeNode) {\n    if root == nil {\n        return\n    }\n    // Попытка\n    *path = append(*path, root)\n    if root.Val.(int) == 7 {\n        // Записать решение\n        *res = append(*res, append([]*TreeNode{}, *path...))\n    }\n    preOrderII(root.Left, res, path)\n    preOrderII(root.Right, res, path)\n    // Откат\n    *path = (*path)[:len(*path)-1]\n}\n</code></pre> preorder_traversal_ii_compact.swift<pre><code>/* Предварительный обход: пример 2 */\nfunc preOrder(root: TreeNode?) {\n    guard let root = root else {\n        return\n    }\n    // Попытка\n    path.append(root)\n    if root.val == 7 {\n        // Записать решение\n        res.append(path)\n    }\n    preOrder(root: root.left)\n    preOrder(root: root.right)\n    // Откат\n    path.removeLast()\n}\n</code></pre> preorder_traversal_ii_compact.js<pre><code>/* Предварительный обход: пример 2 */\nfunction preOrder(root, path, res) {\n    if (root === null) {\n        return;\n    }\n    // Попытка\n    path.push(root);\n    if (root.val === 7) {\n        // Записать решение\n        res.push([...path]);\n    }\n    preOrder(root.left, path, res);\n    preOrder(root.right, path, res);\n    // Откат\n    path.pop();\n}\n</code></pre> preorder_traversal_ii_compact.ts<pre><code>/* Предварительный обход: пример 2 */\nfunction preOrder(\n    root: TreeNode | null,\n    path: TreeNode[],\n    res: TreeNode[][]\n): void {\n    if (root === null) {\n        return;\n    }\n    // Попытка\n    path.push(root);\n    if (root.val === 7) {\n        // Записать решение\n        res.push([...path]);\n    }\n    preOrder(root.left, path, res);\n    preOrder(root.right, path, res);\n    // Откат\n    path.pop();\n}\n</code></pre> preorder_traversal_ii_compact.dart<pre><code>/* Предварительный обход: пример 2 */\nvoid preOrder(\n  TreeNode? root,\n  List&lt;TreeNode&gt; path,\n  List&lt;List&lt;TreeNode&gt;&gt; res,\n) {\n  if (root == null) {\n    return;\n  }\n\n  // Попытка\n  path.add(root);\n  if (root.val == 7) {\n    // Записать решение\n    res.add(List.from(path));\n  }\n  preOrder(root.left, path, res);\n  preOrder(root.right, path, res);\n  // Откат\n  path.removeLast();\n}\n</code></pre> preorder_traversal_ii_compact.rs<pre><code>/* Предварительный обход: пример 2 */\nfn pre_order(\n    res: &amp;mut Vec&lt;Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;&gt;,\n    path: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,\n    root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,\n) {\n    if root.is_none() {\n        return;\n    }\n    if let Some(node) = root {\n        // Попытка\n        path.push(node.clone());\n        if node.borrow().val == 7 {\n            // Записать решение\n            res.push(path.clone());\n        }\n        pre_order(res, path, node.borrow().left.as_ref());\n        pre_order(res, path, node.borrow().right.as_ref());\n        // Откат\n        path.pop();\n    }\n}\n</code></pre> preorder_traversal_ii_compact.c<pre><code>/* Предварительный обход: пример 2 */\nvoid preOrder(TreeNode *root) {\n    if (root == NULL) {\n        return;\n    }\n    // Попытка\n    path[pathSize++] = root;\n    if (root-&gt;val == 7) {\n        // Записать решение\n        for (int i = 0; i &lt; pathSize; ++i) {\n            res[resSize][i] = path[i];\n        }\n        resSize++;\n    }\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n    // Откат\n    pathSize--;\n}\n</code></pre> preorder_traversal_ii_compact.kt<pre><code>/* Предварительный обход: пример 2 */\nfun preOrder(root: TreeNode?) {\n    if (root == null) {\n        return\n    }\n    // Попытка\n    path!!.add(root)\n    if (root._val == 7) {\n        // Записать решение\n        res!!.add(path!!.toMutableList())\n    }\n    preOrder(root.left)\n    preOrder(root.right)\n    // Откат\n    path!!.removeAt(path!!.size - 1)\n}\n</code></pre> preorder_traversal_ii_compact.rb<pre><code>### Предварительный обход: пример 2 ###\ndef pre_order(root)\n  return unless root\n\n  # Попытка\n  $path &lt;&lt; root\n\n  # Записать решение\n  $res &lt;&lt; $path.dup if root.val == 7\n\n  pre_order(root.left)\n  pre_order(root.right)\n\n  # Откат\n  $path.pop\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>В каждой \"попытке\" мы добавляем текущий узел в <code>path</code> , чтобы записать путь; а перед \"откатом\" нам нужно удалить этот узел из <code>path</code> , чтобы восстановить состояние, существовавшее до текущей попытки.</p> <p>Если посмотреть на процесс, изображенный на рисунке 13-2, то попытку и откат можно понимать как \"движение вперед\" и \"отмену\": это два взаимно противоположных действия.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 13-2   Попытка и откат </p>","path":["Глава 13. Поиск с возвратом","13.1 &nbsp; Алгоритм поиска с возвратом"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/#1312","level":2,"title":"13.1.2   Обрезка","text":"<p>Сложные задачи поиска с возвратом обычно содержат одно или несколько ограничений, которые часто можно использовать для \"обрезки\".</p> <p>Пример 3</p> <p>Найдите в двоичном дереве все узлы со значением \\(7\\) , верните пути от корня до этих узлов, причем путь не должен содержать узлы со значением \\(3\\).</p> <p>Чтобы выполнить это ограничение, нам нужно добавить операцию обрезки: во время поиска, если встречается узел со значением \\(3\\) , мы сразу возвращаемся и не продолжаем дальнейший поиск. Код выглядит так:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby preorder_traversal_iii_compact.py<pre><code>def pre_order(root: TreeNode):\n    \"\"\"Предварительный обход: пример 3\"\"\"\n    # Отсечение\n    if root is None or root.val == 3:\n        return\n    # Попытка\n    path.append(root)\n    if root.val == 7:\n        # Записать решение\n        res.append(list(path))\n    pre_order(root.left)\n    pre_order(root.right)\n    # Откат\n    path.pop()\n</code></pre> preorder_traversal_iii_compact.cpp<pre><code>/* Предварительный обход: пример 3 */\nvoid preOrder(TreeNode *root) {\n    // Отсечение\n    if (root == nullptr || root-&gt;val == 3) {\n        return;\n    }\n    // Попытка\n    path.push_back(root);\n    if (root-&gt;val == 7) {\n        // Записать решение\n        res.push_back(path);\n    }\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n    // Откат\n    path.pop_back();\n}\n</code></pre> preorder_traversal_iii_compact.java<pre><code>/* Предварительный обход: пример 3 */\nvoid preOrder(TreeNode root) {\n    // Отсечение\n    if (root == null || root.val == 3) {\n        return;\n    }\n    // Попытка\n    path.add(root);\n    if (root.val == 7) {\n        // Записать решение\n        res.add(new ArrayList&lt;&gt;(path));\n    }\n    preOrder(root.left);\n    preOrder(root.right);\n    // Откат\n    path.remove(path.size() - 1);\n}\n</code></pre> preorder_traversal_iii_compact.cs<pre><code>/* Предварительный обход: пример 3 */\nvoid PreOrder(TreeNode? root) {\n    // Отсечение\n    if (root == null || root.val == 3) {\n        return;\n    }\n    // Попытка\n    path.Add(root);\n    if (root.val == 7) {\n        // Записать решение\n        res.Add(new List&lt;TreeNode&gt;(path));\n    }\n    PreOrder(root.left);\n    PreOrder(root.right);\n    // Откат\n    path.RemoveAt(path.Count - 1);\n}\n</code></pre> preorder_traversal_iii_compact.go<pre><code>/* Предварительный обход: пример 3 */\nfunc preOrderIII(root *TreeNode, res *[][]*TreeNode, path *[]*TreeNode) {\n    // Отсечение\n    if root == nil || root.Val == 3 {\n        return\n    }\n    // Попытка\n    *path = append(*path, root)\n    if root.Val.(int) == 7 {\n        // Записать решение\n        *res = append(*res, append([]*TreeNode{}, *path...))\n    }\n    preOrderIII(root.Left, res, path)\n    preOrderIII(root.Right, res, path)\n    // Откат\n    *path = (*path)[:len(*path)-1]\n}\n</code></pre> preorder_traversal_iii_compact.swift<pre><code>/* Предварительный обход: пример 3 */\nfunc preOrder(root: TreeNode?) {\n    // Отсечение\n    guard let root = root, root.val != 3 else {\n        return\n    }\n    // Попытка\n    path.append(root)\n    if root.val == 7 {\n        // Записать решение\n        res.append(path)\n    }\n    preOrder(root: root.left)\n    preOrder(root: root.right)\n    // Откат\n    path.removeLast()\n}\n</code></pre> preorder_traversal_iii_compact.js<pre><code>/* Предварительный обход: пример 3 */\nfunction preOrder(root, path, res) {\n    // Отсечение\n    if (root === null || root.val === 3) {\n        return;\n    }\n    // Попытка\n    path.push(root);\n    if (root.val === 7) {\n        // Записать решение\n        res.push([...path]);\n    }\n    preOrder(root.left, path, res);\n    preOrder(root.right, path, res);\n    // Откат\n    path.pop();\n}\n</code></pre> preorder_traversal_iii_compact.ts<pre><code>/* Предварительный обход: пример 3 */\nfunction preOrder(\n    root: TreeNode | null,\n    path: TreeNode[],\n    res: TreeNode[][]\n): void {\n    // Отсечение\n    if (root === null || root.val === 3) {\n        return;\n    }\n    // Попытка\n    path.push(root);\n    if (root.val === 7) {\n        // Записать решение\n        res.push([...path]);\n    }\n    preOrder(root.left, path, res);\n    preOrder(root.right, path, res);\n    // Откат\n    path.pop();\n}\n</code></pre> preorder_traversal_iii_compact.dart<pre><code>/* Предварительный обход: пример 3 */\nvoid preOrder(\n  TreeNode? root,\n  List&lt;TreeNode&gt; path,\n  List&lt;List&lt;TreeNode&gt;&gt; res,\n) {\n  if (root == null || root.val == 3) {\n    return;\n  }\n\n  // Попытка\n  path.add(root);\n  if (root.val == 7) {\n    // Записать решение\n    res.add(List.from(path));\n  }\n  preOrder(root.left, path, res);\n  preOrder(root.right, path, res);\n  // Откат\n  path.removeLast();\n}\n</code></pre> preorder_traversal_iii_compact.rs<pre><code>/* Предварительный обход: пример 3 */\nfn pre_order(\n    res: &amp;mut Vec&lt;Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;&gt;,\n    path: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,\n    root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,\n) {\n    // Отсечение\n    if root.is_none() || root.as_ref().unwrap().borrow().val == 3 {\n        return;\n    }\n    if let Some(node) = root {\n        // Попытка\n        path.push(node.clone());\n        if node.borrow().val == 7 {\n            // Записать решение\n            res.push(path.clone());\n        }\n        pre_order(res, path, node.borrow().left.as_ref());\n        pre_order(res, path, node.borrow().right.as_ref());\n        // Откат\n        path.pop();\n    }\n}\n</code></pre> preorder_traversal_iii_compact.c<pre><code>/* Предварительный обход: пример 3 */\nvoid preOrder(TreeNode *root) {\n    // Отсечение\n    if (root == NULL || root-&gt;val == 3) {\n        return;\n    }\n    // Попытка\n    path[pathSize++] = root;\n    if (root-&gt;val == 7) {\n        // Записать решение\n        for (int i = 0; i &lt; pathSize; i++) {\n            res[resSize][i] = path[i];\n        }\n        resSize++;\n    }\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n    // Откат\n    pathSize--;\n}\n</code></pre> preorder_traversal_iii_compact.kt<pre><code>/* Предварительный обход: пример 3 */\nfun preOrder(root: TreeNode?) {\n    // Отсечение\n    if (root == null || root._val == 3) {\n        return\n    }\n    // Попытка\n    path!!.add(root)\n    if (root._val == 7) {\n        // Записать решение\n        res!!.add(path!!.toMutableList())\n    }\n    preOrder(root.left)\n    preOrder(root.right)\n    // Откат\n    path!!.removeAt(path!!.size - 1)\n}\n</code></pre> preorder_traversal_iii_compact.rb<pre><code>### Предварительный обход: пример 3 ###\ndef pre_order(root)\n  # Отсечение\n  return if !root || root.val == 3\n\n  # Попытка\n  $path.append(root)\n\n  # Записать решение\n  $res &lt;&lt; $path.dup if root.val == 7\n\n  pre_order(root.left)\n  pre_order(root.right)\n\n  # Откат\n  $path.pop\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Термин \"обрезка\" очень нагляден. Как показано на рисунке 13-3, во время поиска мы отсекаем ветви, не удовлетворяющие ограничениям , тем самым избегая множества бессмысленных попыток и повышая эффективность поиска.</p> <p></p> <p> Рисунок 13-3   Обрезка по условиям задачи </p>","path":["Глава 13. Поиск с возвратом","13.1 &nbsp; Алгоритм поиска с возвратом"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/#1313","level":2,"title":"13.1.3   Каркас кода","text":"<p>Теперь попробуем извлечь общий каркас из действий \"попытка\", \"откат\" и \"обрезка\", чтобы сделать код более универсальным.</p> <p>В следующем каркасе кода <code>state</code> обозначает текущее состояние задачи, а <code>choices</code> - список выборов, доступных в текущем состоянии:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>def backtrack(state: State, choices: list[choice], res: list[state]):\n    \"\"\"Каркас алгоритма поиска с возвратом\"\"\"\n    # Проверка, является ли текущее состояние решением\n    if is_solution(state):\n        # Запись решения\n        record_solution(state, res)\n        # Дальше не продолжаем поиск\n        return\n    # Перебор всех возможных выборов\n    for choice in choices:\n        # Обрезка: проверка допустимости выбора\n        if is_valid(state, choice):\n            # Попытка: сделать выбор и обновить состояние\n            make_choice(state, choice)\n            backtrack(state, choices, res)\n            # Откат: отменить выбор и восстановить предыдущее состояние\n            undo_choice(state, choice)\n</code></pre> <pre><code>/* Каркас алгоритма поиска с возвратом */\nvoid backtrack(State *state, vector&lt;Choice *&gt; &amp;choices, vector&lt;State *&gt; &amp;res) {\n    // Проверка, является ли текущее состояние решением\n    if (isSolution(state)) {\n        // Запись решения\n        recordSolution(state, res);\n        // Дальше не продолжаем поиск\n        return;\n    }\n    // Перебор всех возможных выборов\n    for (Choice choice : choices) {\n        // Обрезка: проверка допустимости выбора\n        if (isValid(state, choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, choice);\n            backtrack(state, choices, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* Каркас алгоритма поиска с возвратом */\nvoid backtrack(State state, List&lt;Choice&gt; choices, List&lt;State&gt; res) {\n    // Проверка, является ли текущее состояние решением\n    if (isSolution(state)) {\n        // Запись решения\n        recordSolution(state, res);\n        // Дальше не продолжаем поиск\n        return;\n    }\n    // Перебор всех возможных выборов\n    for (Choice choice : choices) {\n        // Обрезка: проверка допустимости выбора\n        if (isValid(state, choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, choice);\n            backtrack(state, choices, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* Каркас алгоритма поиска с возвратом */\nvoid Backtrack(State state, List&lt;Choice&gt; choices, List&lt;State&gt; res) {\n    // Проверка, является ли текущее состояние решением\n    if (IsSolution(state)) {\n        // Запись решения\n        RecordSolution(state, res);\n        // Дальше не продолжаем поиск\n        return;\n    }\n    // Перебор всех возможных выборов\n    foreach (Choice choice in choices) {\n        // Обрезка: проверка допустимости выбора\n        if (IsValid(state, choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            MakeChoice(state, choice);\n            Backtrack(state, choices, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            UndoChoice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* Каркас алгоритма поиска с возвратом */\nfunc backtrack(state *State, choices []Choice, res *[]State) {\n    // Проверка, является ли текущее состояние решением\n    if isSolution(state) {\n        // Запись решения\n        recordSolution(state, res)\n        // Дальше не продолжаем поиск\n        return\n    }\n    // Перебор всех возможных выборов\n    for _, choice := range choices {\n        // Обрезка: проверка допустимости выбора\n        if isValid(state, choice) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, choice)\n            backtrack(state, choices, res)\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state, choice)\n        }\n    }\n}\n</code></pre> <pre><code>/* Каркас алгоритма поиска с возвратом */\nfunc backtrack(state: inout State, choices: [Choice], res: inout [State]) {\n    // Проверка, является ли текущее состояние решением\n    if isSolution(state: state) {\n        // Запись решения\n        recordSolution(state: state, res: &amp;res)\n        // Дальше не продолжаем поиск\n        return\n    }\n    // Перебор всех возможных выборов\n    for choice in choices {\n        // Обрезка: проверка допустимости выбора\n        if isValid(state: state, choice: choice) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state: &amp;state, choice: choice)\n            backtrack(state: &amp;state, choices: choices, res: &amp;res)\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state: &amp;state, choice: choice)\n        }\n    }\n}\n</code></pre> <pre><code>/* Каркас алгоритма поиска с возвратом */\nfunction backtrack(state, choices, res) {\n    // Проверка, является ли текущее состояние решением\n    if (isSolution(state)) {\n        // Запись решения\n        recordSolution(state, res);\n        // Дальше не продолжаем поиск\n        return;\n    }\n    // Перебор всех возможных выборов\n    for (let choice of choices) {\n        // Обрезка: проверка допустимости выбора\n        if (isValid(state, choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, choice);\n            backtrack(state, choices, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* Каркас алгоритма поиска с возвратом */\nfunction backtrack(state: State, choices: Choice[], res: State[]): void {\n    // Проверка, является ли текущее состояние решением\n    if (isSolution(state)) {\n        // Запись решения\n        recordSolution(state, res);\n        // Дальше не продолжаем поиск\n        return;\n    }\n    // Перебор всех возможных выборов\n    for (let choice of choices) {\n        // Обрезка: проверка допустимости выбора\n        if (isValid(state, choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, choice);\n            backtrack(state, choices, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* Каркас алгоритма поиска с возвратом */\nvoid backtrack(State state, List&lt;Choice&gt;, List&lt;State&gt; res) {\n  // Проверка, является ли текущее состояние решением\n  if (isSolution(state)) {\n    // Запись решения\n    recordSolution(state, res);\n    // Дальше не продолжаем поиск\n    return;\n  }\n  // Перебор всех возможных выборов\n  for (Choice choice in choices) {\n    // Обрезка: проверка допустимости выбора\n    if (isValid(state, choice)) {\n      // Попытка: сделать выбор и обновить состояние\n      makeChoice(state, choice);\n      backtrack(state, choices, res);\n      // Откат: отменить выбор и восстановить предыдущее состояние\n      undoChoice(state, choice);\n    }\n  }\n}\n</code></pre> <pre><code>/* Каркас алгоритма поиска с возвратом */\nfn backtrack(state: &amp;mut State, choices: &amp;Vec&lt;Choice&gt;, res: &amp;mut Vec&lt;State&gt;) {\n    // Проверка, является ли текущее состояние решением\n    if is_solution(state) {\n        // Запись решения\n        record_solution(state, res);\n        // Дальше не продолжаем поиск\n        return;\n    }\n    // Перебор всех возможных выборов\n    for choice in choices {\n        // Обрезка: проверка допустимости выбора\n        if is_valid(state, choice) {\n            // Попытка: сделать выбор и обновить состояние\n            make_choice(state, choice);\n            backtrack(state, choices, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undo_choice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* Каркас алгоритма поиска с возвратом */\nvoid backtrack(State *state, Choice *choices, int numChoices, State *res, int numRes) {\n    // Проверка, является ли текущее состояние решением\n    if (isSolution(state)) {\n        // Запись решения\n        recordSolution(state, res, numRes);\n        // Дальше не продолжаем поиск\n        return;\n    }\n    // Перебор всех возможных выборов\n    for (int i = 0; i &lt; numChoices; i++) {\n        // Обрезка: проверка допустимости выбора\n        if (isValid(state, &amp;choices[i])) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, &amp;choices[i]);\n            backtrack(state, choices, numChoices, res, numRes);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state, &amp;choices[i]);\n        }\n    }\n}\n</code></pre> <pre><code>/* Каркас алгоритма поиска с возвратом */\nfun backtrack(state: State?, choices: List&lt;Choice?&gt;, res: List&lt;State?&gt;?) {\n    // Проверка, является ли текущее состояние решением\n    if (isSolution(state)) {\n        // Запись решения\n        recordSolution(state, res)\n        // Дальше не продолжаем поиск\n        return\n    }\n    // Перебор всех возможных выборов\n    for (choice in choices) {\n        // Обрезка: проверка допустимости выбора\n        if (isValid(state, choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, choice)\n            backtrack(state, choices, res)\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state, choice)\n        }\n    }\n}\n</code></pre> <pre><code>### Каркас алгоритма поиска с возвратом ###\ndef backtrack(state, choices, res)\n    # Проверка, является ли текущее состояние решением\n    if is_solution?(state)\n        # Запись решения\n        record_solution(state, res)\n        return\n    end\n\n    # Перебор всех возможных выборов\n    for choice in choices\n        # Обрезка: проверка допустимости выбора\n        if is_valid?(state, choice)\n            # Попытка: сделать выбор и обновить состояние\n            make_choice(state, choice)\n            backtrack(state, choices, res)\n            # Откат: отменить выбор и восстановить предыдущее состояние\n            undo_choice(state, choice)\n        end\n    end\nend\n</code></pre> <p>Теперь, опираясь на этот каркас, решим пример 3. Состояние <code>state</code> здесь - это путь обхода узлов, выбор <code>choices</code> - левый и правый потомки текущего узла, а результат <code>res</code> - список путей:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby preorder_traversal_iii_template.py<pre><code>def is_solution(state: list[TreeNode]) -&gt; bool:\n    \"\"\"Проверить, является ли текущее состояние решением\"\"\"\n    return state and state[-1].val == 7\n\ndef record_solution(state: list[TreeNode], res: list[list[TreeNode]]):\n    \"\"\"Записать решение\"\"\"\n    res.append(list(state))\n\ndef is_valid(state: list[TreeNode], choice: TreeNode) -&gt; bool:\n    \"\"\"Проверить, допустим ли этот выбор в текущем состоянии\"\"\"\n    return choice is not None and choice.val != 3\n\ndef make_choice(state: list[TreeNode], choice: TreeNode):\n    \"\"\"Обновить состояние\"\"\"\n    state.append(choice)\n\ndef undo_choice(state: list[TreeNode], choice: TreeNode):\n    \"\"\"Восстановить состояние\"\"\"\n    state.pop()\n\ndef backtrack(\n    state: list[TreeNode], choices: list[TreeNode], res: list[list[TreeNode]]\n):\n    \"\"\"Алгоритм бэктрекинга: пример 3\"\"\"\n    # Проверить, является ли текущее состояние решением\n    if is_solution(state):\n        # Записать решение\n        record_solution(state, res)\n    # Перебор всех вариантов выбора\n    for choice in choices:\n        # Отсечение: проверить допустимость выбора\n        if is_valid(state, choice):\n            # Попытка: сделать выбор и обновить состояние\n            make_choice(state, choice)\n            # Перейти к следующему выбору\n            backtrack(state, [choice.left, choice.right], res)\n            # Откат: отменить выбор и восстановить предыдущее состояние\n            undo_choice(state, choice)\n</code></pre> preorder_traversal_iii_template.cpp<pre><code>/* Проверить, является ли текущее состояние решением */\nbool isSolution(vector&lt;TreeNode *&gt; &amp;state) {\n    return !state.empty() &amp;&amp; state.back()-&gt;val == 7;\n}\n\n/* Записать решение */\nvoid recordSolution(vector&lt;TreeNode *&gt; &amp;state, vector&lt;vector&lt;TreeNode *&gt;&gt; &amp;res) {\n    res.push_back(state);\n}\n\n/* Проверить, допустим ли этот выбор в текущем состоянии */\nbool isValid(vector&lt;TreeNode *&gt; &amp;state, TreeNode *choice) {\n    return choice != nullptr &amp;&amp; choice-&gt;val != 3;\n}\n\n/* Обновить состояние */\nvoid makeChoice(vector&lt;TreeNode *&gt; &amp;state, TreeNode *choice) {\n    state.push_back(choice);\n}\n\n/* Восстановить состояние */\nvoid undoChoice(vector&lt;TreeNode *&gt; &amp;state, TreeNode *choice) {\n    state.pop_back();\n}\n\n/* Алгоритм бэктрекинга: пример 3 */\nvoid backtrack(vector&lt;TreeNode *&gt; &amp;state, vector&lt;TreeNode *&gt; &amp;choices, vector&lt;vector&lt;TreeNode *&gt;&gt; &amp;res) {\n    // Проверить, является ли текущее состояние решением\n    if (isSolution(state)) {\n        // Записать решение\n        recordSolution(state, res);\n    }\n    // Перебор всех вариантов выбора\n    for (TreeNode *choice : choices) {\n        // Отсечение: проверить допустимость выбора\n        if (isValid(state, choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, choice);\n            // Перейти к следующему выбору\n            vector&lt;TreeNode *&gt; nextChoices{choice-&gt;left, choice-&gt;right};\n            backtrack(state, nextChoices, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.java<pre><code>/* Проверить, является ли текущее состояние решением */\nboolean isSolution(List&lt;TreeNode&gt; state) {\n    return !state.isEmpty() &amp;&amp; state.get(state.size() - 1).val == 7;\n}\n\n/* Записать решение */\nvoid recordSolution(List&lt;TreeNode&gt; state, List&lt;List&lt;TreeNode&gt;&gt; res) {\n    res.add(new ArrayList&lt;&gt;(state));\n}\n\n/* Проверить, допустим ли этот выбор в текущем состоянии */\nboolean isValid(List&lt;TreeNode&gt; state, TreeNode choice) {\n    return choice != null &amp;&amp; choice.val != 3;\n}\n\n/* Обновить состояние */\nvoid makeChoice(List&lt;TreeNode&gt; state, TreeNode choice) {\n    state.add(choice);\n}\n\n/* Восстановить состояние */\nvoid undoChoice(List&lt;TreeNode&gt; state, TreeNode choice) {\n    state.remove(state.size() - 1);\n}\n\n/* Алгоритм бэктрекинга: пример 3 */\nvoid backtrack(List&lt;TreeNode&gt; state, List&lt;TreeNode&gt; choices, List&lt;List&lt;TreeNode&gt;&gt; res) {\n    // Проверить, является ли текущее состояние решением\n    if (isSolution(state)) {\n        // Записать решение\n        recordSolution(state, res);\n    }\n    // Перебор всех вариантов выбора\n    for (TreeNode choice : choices) {\n        // Отсечение: проверить допустимость выбора\n        if (isValid(state, choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, choice);\n            // Перейти к следующему выбору\n            backtrack(state, Arrays.asList(choice.left, choice.right), res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.cs<pre><code>/* Проверить, является ли текущее состояние решением */\nbool IsSolution(List&lt;TreeNode&gt; state) {\n    return state.Count != 0 &amp;&amp; state[^1].val == 7;\n}\n\n/* Записать решение */\nvoid RecordSolution(List&lt;TreeNode&gt; state, List&lt;List&lt;TreeNode&gt;&gt; res) {\n    res.Add(new List&lt;TreeNode&gt;(state));\n}\n\n/* Проверить, допустим ли этот выбор в текущем состоянии */\nbool IsValid(List&lt;TreeNode&gt; state, TreeNode choice) {\n    return choice != null &amp;&amp; choice.val != 3;\n}\n\n/* Обновить состояние */\nvoid MakeChoice(List&lt;TreeNode&gt; state, TreeNode choice) {\n    state.Add(choice);\n}\n\n/* Восстановить состояние */\nvoid UndoChoice(List&lt;TreeNode&gt; state, TreeNode choice) {\n    state.RemoveAt(state.Count - 1);\n}\n\n/* Алгоритм бэктрекинга: пример 3 */\nvoid Backtrack(List&lt;TreeNode&gt; state, List&lt;TreeNode&gt; choices, List&lt;List&lt;TreeNode&gt;&gt; res) {\n    // Проверить, является ли текущее состояние решением\n    if (IsSolution(state)) {\n        // Записать решение\n        RecordSolution(state, res);\n    }\n    // Перебор всех вариантов выбора\n    foreach (TreeNode choice in choices) {\n        // Отсечение: проверить допустимость выбора\n        if (IsValid(state, choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            MakeChoice(state, choice);\n            // Перейти к следующему выбору\n            Backtrack(state, [choice.left!, choice.right!], res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            UndoChoice(state, choice);\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.go<pre><code>/* Проверить, является ли текущее состояние решением */\nfunc isSolution(state *[]*TreeNode) bool {\n    return len(*state) != 0 &amp;&amp; (*state)[len(*state)-1].Val == 7\n}\n\n/* Записать решение */\nfunc recordSolution(state *[]*TreeNode, res *[][]*TreeNode) {\n    *res = append(*res, append([]*TreeNode{}, *state...))\n}\n\n/* Проверить, допустим ли этот выбор в текущем состоянии */\nfunc isValid(state *[]*TreeNode, choice *TreeNode) bool {\n    return choice != nil &amp;&amp; choice.Val != 3\n}\n\n/* Обновить состояние */\nfunc makeChoice(state *[]*TreeNode, choice *TreeNode) {\n    *state = append(*state, choice)\n}\n\n/* Восстановить состояние */\nfunc undoChoice(state *[]*TreeNode, choice *TreeNode) {\n    *state = (*state)[:len(*state)-1]\n}\n\n/* Алгоритм бэктрекинга: пример 3 */\nfunc backtrackIII(state *[]*TreeNode, choices *[]*TreeNode, res *[][]*TreeNode) {\n    // Проверить, является ли текущее состояние решением\n    if isSolution(state) {\n        // Записать решение\n        recordSolution(state, res)\n    }\n    // Перебор всех вариантов выбора\n    for _, choice := range *choices {\n        // Отсечение: проверить допустимость выбора\n        if isValid(state, choice) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, choice)\n            // Перейти к следующему выбору\n            temp := make([]*TreeNode, 0)\n            temp = append(temp, choice.Left, choice.Right)\n            backtrackIII(state, &amp;temp, res)\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state, choice)\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.swift<pre><code>/* Проверить, является ли текущее состояние решением */\nfunc isSolution(state: [TreeNode]) -&gt; Bool {\n    !state.isEmpty &amp;&amp; state.last!.val == 7\n}\n\n/* Записать решение */\nfunc recordSolution(state: [TreeNode], res: inout [[TreeNode]]) {\n    res.append(state)\n}\n\n/* Проверить, допустим ли этот выбор в текущем состоянии */\nfunc isValid(state: [TreeNode], choice: TreeNode?) -&gt; Bool {\n    choice != nil &amp;&amp; choice!.val != 3\n}\n\n/* Обновить состояние */\nfunc makeChoice(state: inout [TreeNode], choice: TreeNode) {\n    state.append(choice)\n}\n\n/* Восстановить состояние */\nfunc undoChoice(state: inout [TreeNode], choice: TreeNode) {\n    state.removeLast()\n}\n\n/* Алгоритм бэктрекинга: пример 3 */\nfunc backtrack(state: inout [TreeNode], choices: [TreeNode], res: inout [[TreeNode]]) {\n    // Проверить, является ли текущее состояние решением\n    if isSolution(state: state) {\n        recordSolution(state: state, res: &amp;res)\n    }\n    // Перебор всех вариантов выбора\n    for choice in choices {\n        // Отсечение: проверить допустимость выбора\n        if isValid(state: state, choice: choice) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state: &amp;state, choice: choice)\n            // Перейти к следующему выбору\n            backtrack(state: &amp;state, choices: [choice.left, choice.right].compactMap { $0 }, res: &amp;res)\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state: &amp;state, choice: choice)\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.js<pre><code>/* Проверить, является ли текущее состояние решением */\nfunction isSolution(state) {\n    return state &amp;&amp; state[state.length - 1]?.val === 7;\n}\n\n/* Записать решение */\nfunction recordSolution(state, res) {\n    res.push([...state]);\n}\n\n/* Проверить, допустим ли этот выбор в текущем состоянии */\nfunction isValid(state, choice) {\n    return choice !== null &amp;&amp; choice.val !== 3;\n}\n\n/* Обновить состояние */\nfunction makeChoice(state, choice) {\n    state.push(choice);\n}\n\n/* Восстановить состояние */\nfunction undoChoice(state) {\n    state.pop();\n}\n\n/* Алгоритм бэктрекинга: пример 3 */\nfunction backtrack(state, choices, res) {\n    // Проверить, является ли текущее состояние решением\n    if (isSolution(state)) {\n        // Записать решение\n        recordSolution(state, res);\n    }\n    // Перебор всех вариантов выбора\n    for (const choice of choices) {\n        // Отсечение: проверить допустимость выбора\n        if (isValid(state, choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, choice);\n            // Перейти к следующему выбору\n            backtrack(state, [choice.left, choice.right], res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state);\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.ts<pre><code>/* Проверить, является ли текущее состояние решением */\nfunction isSolution(state: TreeNode[]): boolean {\n    return state &amp;&amp; state[state.length - 1]?.val === 7;\n}\n\n/* Записать решение */\nfunction recordSolution(state: TreeNode[], res: TreeNode[][]): void {\n    res.push([...state]);\n}\n\n/* Проверить, допустим ли этот выбор в текущем состоянии */\nfunction isValid(state: TreeNode[], choice: TreeNode): boolean {\n    return choice !== null &amp;&amp; choice.val !== 3;\n}\n\n/* Обновить состояние */\nfunction makeChoice(state: TreeNode[], choice: TreeNode): void {\n    state.push(choice);\n}\n\n/* Восстановить состояние */\nfunction undoChoice(state: TreeNode[]): void {\n    state.pop();\n}\n\n/* Алгоритм бэктрекинга: пример 3 */\nfunction backtrack(\n    state: TreeNode[],\n    choices: TreeNode[],\n    res: TreeNode[][]\n): void {\n    // Проверить, является ли текущее состояние решением\n    if (isSolution(state)) {\n        // Записать решение\n        recordSolution(state, res);\n    }\n    // Перебор всех вариантов выбора\n    for (const choice of choices) {\n        // Отсечение: проверить допустимость выбора\n        if (isValid(state, choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, choice);\n            // Перейти к следующему выбору\n            backtrack(state, [choice.left, choice.right], res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state);\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.dart<pre><code>/* Проверить, является ли текущее состояние решением */\nbool isSolution(List&lt;TreeNode&gt; state) {\n  return state.isNotEmpty &amp;&amp; state.last.val == 7;\n}\n\n/* Записать решение */\nvoid recordSolution(List&lt;TreeNode&gt; state, List&lt;List&lt;TreeNode&gt;&gt; res) {\n  res.add(List.from(state));\n}\n\n/* Проверить, допустим ли этот выбор в текущем состоянии */\nbool isValid(List&lt;TreeNode&gt; state, TreeNode? choice) {\n  return choice != null &amp;&amp; choice.val != 3;\n}\n\n/* Обновить состояние */\nvoid makeChoice(List&lt;TreeNode&gt; state, TreeNode? choice) {\n  state.add(choice!);\n}\n\n/* Восстановить состояние */\nvoid undoChoice(List&lt;TreeNode&gt; state, TreeNode? choice) {\n  state.removeLast();\n}\n\n/* Алгоритм бэктрекинга: пример 3 */\nvoid backtrack(\n  List&lt;TreeNode&gt; state,\n  List&lt;TreeNode?&gt; choices,\n  List&lt;List&lt;TreeNode&gt;&gt; res,\n) {\n  // Проверить, является ли текущее состояние решением\n  if (isSolution(state)) {\n    // Записать решение\n    recordSolution(state, res);\n  }\n  // Перебор всех вариантов выбора\n  for (TreeNode? choice in choices) {\n    // Отсечение: проверить допустимость выбора\n    if (isValid(state, choice)) {\n      // Попытка: сделать выбор и обновить состояние\n      makeChoice(state, choice);\n      // Перейти к следующему выбору\n      backtrack(state, [choice!.left, choice.right], res);\n      // Откат: отменить выбор и восстановить предыдущее состояние\n      undoChoice(state, choice);\n    }\n  }\n}\n</code></pre> preorder_traversal_iii_template.rs<pre><code>/* Проверить, является ли текущее состояние решением */\nfn is_solution(state: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;) -&gt; bool {\n    return !state.is_empty() &amp;&amp; state.last().unwrap().borrow().val == 7;\n}\n\n/* Записать решение */\nfn record_solution(\n    state: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,\n    res: &amp;mut Vec&lt;Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;&gt;,\n) {\n    res.push(state.clone());\n}\n\n/* Проверить, допустим ли этот выбор в текущем состоянии */\nfn is_valid(_: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;, choice: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;) -&gt; bool {\n    return choice.is_some() &amp;&amp; choice.unwrap().borrow().val != 3;\n}\n\n/* Обновить состояние */\nfn make_choice(state: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;, choice: Rc&lt;RefCell&lt;TreeNode&gt;&gt;) {\n    state.push(choice);\n}\n\n/* Восстановить состояние */\nfn undo_choice(state: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;, _: Rc&lt;RefCell&lt;TreeNode&gt;&gt;) {\n    state.pop();\n}\n\n/* Алгоритм бэктрекинга: пример 3 */\nfn backtrack(\n    state: &amp;mut Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,\n    choices: &amp;Vec&lt;Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;&gt;,\n    res: &amp;mut Vec&lt;Vec&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;&gt;,\n) {\n    // Проверить, является ли текущее состояние решением\n    if is_solution(state) {\n        // Записать решение\n        record_solution(state, res);\n    }\n    // Перебор всех вариантов выбора\n    for &amp;choice in choices.iter() {\n        // Отсечение: проверить допустимость выбора\n        if is_valid(state, choice) {\n            // Попытка: сделать выбор и обновить состояние\n            make_choice(state, choice.unwrap().clone());\n            // Перейти к следующему выбору\n            backtrack(\n                state,\n                &amp;vec![\n                    choice.unwrap().borrow().left.as_ref(),\n                    choice.unwrap().borrow().right.as_ref(),\n                ],\n                res,\n            );\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undo_choice(state, choice.unwrap().clone());\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.c<pre><code>/* Проверить, является ли текущее состояние решением */\nbool isSolution(void) {\n    return pathSize &gt; 0 &amp;&amp; path[pathSize - 1]-&gt;val == 7;\n}\n\n/* Записать решение */\nvoid recordSolution(void) {\n    for (int i = 0; i &lt; pathSize; i++) {\n        res[resSize][i] = path[i];\n    }\n    resSize++;\n}\n\n/* Проверить, допустим ли этот выбор в текущем состоянии */\nbool isValid(TreeNode *choice) {\n    return choice != NULL &amp;&amp; choice-&gt;val != 3;\n}\n\n/* Обновить состояние */\nvoid makeChoice(TreeNode *choice) {\n    path[pathSize++] = choice;\n}\n\n/* Восстановить состояние */\nvoid undoChoice(void) {\n    pathSize--;\n}\n\n/* Алгоритм бэктрекинга: пример 3 */\nvoid backtrack(TreeNode *choices[2]) {\n    // Проверить, является ли текущее состояние решением\n    if (isSolution()) {\n        // Записать решение\n        recordSolution();\n    }\n    // Перебор всех вариантов выбора\n    for (int i = 0; i &lt; 2; i++) {\n        TreeNode *choice = choices[i];\n        // Отсечение: проверить допустимость выбора\n        if (isValid(choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(choice);\n            // Перейти к следующему выбору\n            TreeNode *nextChoices[2] = {choice-&gt;left, choice-&gt;right};\n            backtrack(nextChoices);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice();\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.kt<pre><code>/* Проверить, является ли текущее состояние решением */\nfun isSolution(state: MutableList&lt;TreeNode?&gt;): Boolean {\n    return state.isNotEmpty() &amp;&amp; state[state.size - 1]?._val == 7\n}\n\n/* Записать решение */\nfun recordSolution(state: MutableList&lt;TreeNode?&gt;?, res: MutableList&lt;MutableList&lt;TreeNode?&gt;?&gt;) {\n    res.add(state!!.toMutableList())\n}\n\n/* Проверить, допустим ли этот выбор в текущем состоянии */\nfun isValid(state: MutableList&lt;TreeNode?&gt;?, choice: TreeNode?): Boolean {\n    return choice != null &amp;&amp; choice._val != 3\n}\n\n/* Обновить состояние */\nfun makeChoice(state: MutableList&lt;TreeNode?&gt;, choice: TreeNode?) {\n    state.add(choice)\n}\n\n/* Восстановить состояние */\nfun undoChoice(state: MutableList&lt;TreeNode?&gt;, choice: TreeNode?) {\n    state.removeLast()\n}\n\n/* Алгоритм бэктрекинга: пример 3 */\nfun backtrack(\n    state: MutableList&lt;TreeNode?&gt;,\n    choices: MutableList&lt;TreeNode?&gt;,\n    res: MutableList&lt;MutableList&lt;TreeNode?&gt;?&gt;\n) {\n    // Проверить, является ли текущее состояние решением\n    if (isSolution(state)) {\n        // Записать решение\n        recordSolution(state, res)\n    }\n    // Перебор всех вариантов выбора\n    for (choice in choices) {\n        // Отсечение: проверить допустимость выбора\n        if (isValid(state, choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            makeChoice(state, choice)\n            // Перейти к следующему выбору\n            backtrack(state, mutableListOf(choice!!.left, choice.right), res)\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            undoChoice(state, choice)\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.rb<pre><code>### Проверка, является ли текущее состояние решением ###\ndef is_solution?(state)\n  !state.empty? &amp;&amp; state.last.val == 7\nend\n\n### Записать решение ###\ndef record_solution(state, res)\n  res &lt;&lt; state.dup\nend\n\n### Проверка допустимости этого выбора в текущем состоянии ###\ndef is_valid?(state, choice)\n  choice &amp;&amp; choice.val != 3\nend\n\n### Обновить состояние ###\ndef make_choice(state, choice)\n  state &lt;&lt; choice\nend\n\n### Восстановить состояние ###\ndef undo_choice(state, choice)\n  state.pop\nend\n\n### Алгоритм бэктрекинга: пример 3 ###\ndef backtrack(state, choices, res)\n  # Проверить, является ли текущее состояние решением\n  record_solution(state, res) if is_solution?(state)\n\n  # Перебор всех вариантов выбора\n  for choice in choices\n    # Отсечение: проверить допустимость выбора\n    if is_valid?(state, choice)\n      # Попытка: сделать выбор и обновить состояние\n      make_choice(state, choice)\n      # Перейти к следующему выбору\n      backtrack(state, [choice.left, choice.right], res)\n      # Откат: отменить выбор и восстановить предыдущее состояние\n      undo_choice(state, choice)\n    end\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Согласно условию задачи, после нахождения узла со значением \\(7\\) мы должны продолжать поиск, поэтому оператор <code>return</code> после записи решения нужно удалить. На рисунке 13-4 сравниваются процессы поиска в случаях, когда <code>return</code> сохраняется и когда он удаляется.</p> <p></p> <p> Рисунок 13-4   Сравнение поиска при сохранении и удалении return </p> <p>По сравнению с реализацией на основе прямого обхода, версия на основе общего каркаса поиска с возвратом выглядит более громоздкой, но при этом обладает лучшей универсальностью. На практике многие задачи поиска с возвратом можно решать в рамках этого каркаса. Для этого нужно лишь определить <code>state</code> и <code>choices</code> под конкретную задачу и реализовать соответствующие методы каркаса.</p>","path":["Глава 13. Поиск с возвратом","13.1 &nbsp; Алгоритм поиска с возвратом"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/#1314","level":2,"title":"13.1.4   Часто используемые термины","text":"<p>Чтобы яснее анализировать алгоритмические задачи, подытожим значения часто используемых терминов поиска с возвратом и сопоставим их с примером 3, как показано в таблице 13-1.</p> <p> Таблица 13-1   Часто используемые термины алгоритма поиска с возвратом </p> Термин Определение Пример 3 Решение (solution) Решение - это ответ, удовлетворяющий условиям задачи; решений может быть одно или несколько Все пути от корня до узла \\(7\\) , удовлетворяющие ограничениям Ограничение (constraint) Ограничение определяет допустимость решения и обычно используется для обрезки Путь не содержит узлы со значением \\(3\\) Состояние (state) Состояние описывает ситуацию задачи в некоторый момент времени, включая уже сделанные выборы Текущий путь посещенных узлов, то есть список узлов <code>path</code> Попытка (attempt) Попытка - это исследование пространства решений на основе доступных выборов, включая выбор, обновление состояния и проверку, является ли состояние решением Рекурсивный переход к левому или правому потомку, добавление узла в <code>path</code> и проверка, равно ли значение узла \\(7\\) Откат (backtracking) Откат означает отмену предыдущих выборов и возврат к более раннему состоянию при встрече состояния, не удовлетворяющего ограничениям Завершение поиска при проходе через лист, окончании посещения узла или встрече узла со значением \\(3\\) , то есть возврат из функции Обрезка (pruning) Обрезка - это способ избегать бессмысленных путей поиска на основе свойств задачи и ее ограничений, повышающий эффективность При встрече узла со значением \\(3\\) поиск по этой ветви прекращается <p>Tip</p> <p>Такие понятия, как задача, решение и состояние, являются общими и встречаются не только в поиске с возвратом, но и в \"разделяй и властвуй\", динамическом программировании, жадных алгоритмах и других темах.</p>","path":["Глава 13. Поиск с возвратом","13.1 &nbsp; Алгоритм поиска с возвратом"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/#1315","level":2,"title":"13.1.5   Преимущества и ограничения","text":"<p>Алгоритм поиска с возвратом по своей сути представляет собой алгоритм обхода в глубину, который перебирает все возможные решения, пока не найдет удовлетворяющее условиям. Преимущество этого подхода в том, что он позволяет находить все возможные решения и при разумной обрезке может работать весьма эффективно.</p> <p>Однако при работе с большими или сложными задачами эффективность поиска с возвратом может оказаться неприемлемой.</p> <ul> <li>Время: поиск с возвратом обычно требует обхода всех возможных состояний пространства состояний, и его временная сложность может достигать экспоненциального или факториального порядка.</li> <li>Память: при рекурсивных вызовах нужно хранить текущее состояние (например, путь, вспомогательные переменные для обрезки и т.д.), поэтому при большой глубине рекурсии потребность в памяти может стать значительной.</li> </ul> <p>Тем не менее поиск с возвратом по-прежнему остается лучшим решением для некоторых поисковых задач и задач удовлетворения ограничений. В таких задачах заранее невозможно предсказать, какие выборы приведут к эффективному решению, поэтому приходится перебирать все возможные варианты. В этой ситуации ключевым становится вопрос оптимизации эффективности , и для этого обычно используют две стратегии.</p> <ul> <li>Обрезка: избегать поиска по тем путям, которые заведомо не приведут к решению, тем самым экономя время и память.</li> <li>Эвристический поиск: вводить во время поиска дополнительные стратегии или оценки, чтобы в первую очередь исследовать пути, наиболее вероятно ведущие к эффективному решению.</li> </ul>","path":["Глава 13. Поиск с возвратом","13.1 &nbsp; Алгоритм поиска с возвратом"],"tags":[]},{"location":"chapter_backtracking/backtracking_algorithm/#1316","level":2,"title":"13.1.6   Типичные задачи поиска с возвратом","text":"<p>Алгоритм поиска с возвратом можно использовать для решения множества поисковых задач, задач удовлетворения ограничений и задач комбинаторной оптимизации.</p> <p>Поисковые задачи: целью таких задач является поиск решений, удовлетворяющих определенным условиям.</p> <ul> <li>Задача о перестановках: дано множество, требуется найти все возможные перестановки его элементов.</li> <li>Задача о сумме подмножеств: даны множество и целевая сумма; нужно найти все подмножества, сумма элементов которых равна целевой.</li> <li>Задача о Ханойской башне: даны три стержня и набор дисков разного размера; требуется перенести все диски с одного стержня на другой, перемещая за раз только один диск и не помещая больший диск на меньший.</li> </ul> <p>Задачи удовлетворения ограничений: целью таких задач является поиск решений, удовлетворяющих всем ограничениям.</p> <ul> <li>Задача о \\(n\\) ферзях: разместить \\(n\\) ферзей на шахматной доске размера \\(n \\times n\\) так, чтобы они не атаковали друг друга.</li> <li>Судоку: заполнить сетку \\(9 \\times 9\\) числами от \\(1\\) до \\(9\\) так, чтобы в каждой строке, каждом столбце и каждом блоке \\(3 \\times 3\\) числа не повторялись.</li> <li>Задача раскраски графа: дан неориентированный граф; требуется раскрасить его вершины минимальным числом цветов так, чтобы соседние вершины имели разные цвета.</li> </ul> <p>Задачи комбинаторной оптимизации: целью таких задач является поиск оптимального решения в некотором комбинаторном пространстве при заданных ограничениях.</p> <ul> <li>Задача о рюкзаке 0-1: даны набор предметов и рюкзак; у каждого предмета есть ценность и вес, и нужно выбрать предметы так, чтобы при ограниченной вместимости рюкзака суммарная ценность была максимальной.</li> <li>Задача коммивояжера: начиная из некоторой вершины графа, требуется посетить все остальные вершины ровно по одному разу и вернуться в исходную вершину, найдя при этом кратчайший путь.</li> <li>Задача о максимальной клике: дан неориентированный граф; требуется найти в нем максимальный полный подграф, то есть подграф, в котором любая пара вершин соединена ребром.</li> </ul> <p>Стоит отметить: для многих задач комбинаторной оптимизации поиск с возвратом не является оптимальным способом решения.</p> <ul> <li>Задача о рюкзаке 0-1 обычно решается с помощью динамического программирования, что дает более высокую временную эффективность.</li> <li>Задача коммивояжера является известной NP-Hard задачей; для ее решения часто используют генетические алгоритмы, муравьиные алгоритмы и другие методы.</li> <li>Задача о максимальной клике является классической задачей теории графов и может решаться жадными и другими эвристическими алгоритмами.</li> </ul>","path":["Глава 13. Поиск с возвратом","13.1 &nbsp; Алгоритм поиска с возвратом"],"tags":[]},{"location":"chapter_backtracking/n_queens_problem/","level":1,"title":"13.4   Задача о n ферзях","text":"<p>Question</p> <p>Согласно правилам шахмат ферзь может атаковать фигуры, находящиеся с ним на одной строке, в одном столбце или на одной диагонали. Даны \\(n\\) ферзей и шахматная доска размера \\(n \\times n\\) ; требуется найти такие расстановки, при которых ни одна пара ферзей не может атаковать друг друга.</p> <p>Как показано на рисунке 13-15, при \\(n = 4\\) существует два решения. С точки зрения поиска с возвратом доска размера \\(n \\times n\\) содержит \\(n^2\\) клеток, которые образуют все возможные выборы <code>choices</code> . По мере поочередного размещения ферзей состояние доски непрерывно меняется, и текущее содержимое доски образует состояние <code>state</code> .</p> <p></p> <p> Рисунок 13-15   Решения задачи о 4 ферзях </p> <p>На рисунке 13-16 показаны три ограничения этой задачи: несколько ферзей не могут находиться на одной строке, в одном столбце или на одной диагонали. При этом нужно помнить, что диагонали бывают двух типов: главная <code>\\</code> и побочная <code>/</code> .</p> <p></p> <p> Рисунок 13-16   Ограничения задачи о n ферзях </p>","path":["Глава 13. Поиск с возвратом","13.4 &nbsp; Задача о n ферзях"],"tags":[]},{"location":"chapter_backtracking/n_queens_problem/#1","level":3,"title":"1.   Построчная стратегия размещения","text":"<p>Число ферзей и число строк доски одинаково и равно \\(n\\) , поэтому легко получить следующий вывод: в каждой строке доски разрешено и нужно разместить ровно одного ферзя.</p> <p>Иначе говоря, можно использовать построчную стратегию: начиная с первой строки, размещать по одному ферзю в каждой строке, пока не будет достигнута последняя.</p> <p>На рисунке 13-17 показан процесс построчного размещения для задачи о 4 ферзях. Из-за ограничений размера изображения на нем раскрыта только одна ветвь поиска для первой строки, а все варианты, не удовлетворяющие ограничениям по столбцам и диагоналям, были отсечены.</p> <p></p> <p> Рисунок 13-17   Построчная стратегия размещения </p> <p>По своей сути построчная стратегия сама по себе выполняет роль обрезки , потому что заранее исключает все ветви поиска, в которых в одной строке оказалось бы несколько ферзей.</p>","path":["Глава 13. Поиск с возвратом","13.4 &nbsp; Задача о n ферзях"],"tags":[]},{"location":"chapter_backtracking/n_queens_problem/#2","level":3,"title":"2.   Обрезка по столбцам и диагоналям","text":"<p>Чтобы удовлетворить ограничению по столбцам, можно использовать булев массив <code>cols</code> длины \\(n\\) , который записывает, есть ли ферзь в каждом столбце. Перед каждым размещением мы используем <code>cols</code> для отсечения столбцов, уже занятых ферзями, а затем динамически обновляем состояние <code>cols</code> во время отката.</p> <p>Tip</p> <p>Обратите внимание: начало координат матрицы находится в левом верхнем углу, при этом индексы строк растут сверху вниз, а индексы столбцов - слева направо.</p> <p>Как теперь обработать ограничения по диагоналям? Пусть клетка на доске имеет координаты \\((row, col)\\) . Выбрав некоторую главную диагональ в матрице, можно заметить, что разность индексов строки и столбца одинакова для всех клеток этой диагонали, то есть для всех клеток главной диагонали значение \\(row - col\\) постоянно.</p> <p>Это означает, что если для двух клеток выполняется равенство \\(row_1 - col_1 = row_2 - col_2\\) , то они обязательно лежат на одной и той же главной диагонали. Используя это правило, можно с помощью массива <code>diags1</code> , показанного на рисунке 13-18, отмечать наличие ферзя на каждой главной диагонали.</p> <p>Аналогично для всех клеток побочной диагонали значение \\(row + col\\) является постоянным. Поэтому для обработки ограничений по побочным диагоналям можно использовать еще один массив <code>diags2</code> .</p> <p></p> <p> Рисунок 13-18   Обработка ограничений по столбцам и диагоналям </p>","path":["Глава 13. Поиск с возвратом","13.4 &nbsp; Задача о n ферзях"],"tags":[]},{"location":"chapter_backtracking/n_queens_problem/#3","level":3,"title":"3.   Реализация кода","text":"<p>Заметим, что в квадратной матрице размера \\(n\\) диапазон значений \\(row - col\\) равен \\([-n + 1, n - 1]\\) , а диапазон значений \\(row + col\\) равен \\([0, 2n - 2]\\) . Следовательно, число главных и побочных диагоналей равно \\(2n - 1\\) , а значит, длины массивов <code>diags1</code> и <code>diags2</code> тоже равны \\(2n - 1\\) .</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby n_queens.py<pre><code>def backtrack(\n    row: int,\n    n: int,\n    state: list[list[str]],\n    res: list[list[list[str]]],\n    cols: list[bool],\n    diags1: list[bool],\n    diags2: list[bool],\n):\n    \"\"\"Алгоритм бэктрекинга: n ферзей\"\"\"\n    # Когда все строки уже обработаны, записать решение\n    if row == n:\n        res.append([list(row) for row in state])\n        return\n    # Обойти все столбцы\n    for col in range(n):\n        # Вычислить главную и побочную диагонали, соответствующие этой клетке\n        diag1 = row - col + n - 1\n        diag2 = row + col\n        # Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n        if not cols[col] and not diags1[diag1] and not diags2[diag2]:\n            # Попытка: поставить ферзя в эту клетку\n            state[row][col] = \"Q\"\n            cols[col] = diags1[diag1] = diags2[diag2] = True\n            # Перейти к размещению следующей строки\n            backtrack(row + 1, n, state, res, cols, diags1, diags2)\n            # Откат: восстановить эту клетку как пустую\n            state[row][col] = \"#\"\n            cols[col] = diags1[diag1] = diags2[diag2] = False\n\ndef n_queens(n: int) -&gt; list[list[list[str]]]:\n    \"\"\"Решить задачу о n ферзях\"\"\"\n    # Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n    state = [[\"#\" for _ in range(n)] for _ in range(n)]\n    cols = [False] * n  # Отмечать, есть ли ферзь в столбце\n    diags1 = [False] * (2 * n - 1)  # Отмечать наличие ферзя на главной диагонали\n    diags2 = [False] * (2 * n - 1)  # Отмечать наличие ферзя на побочной диагонали\n    res = []\n    backtrack(0, n, state, res, cols, diags1, diags2)\n\n    return res\n</code></pre> n_queens.cpp<pre><code>/* Алгоритм бэктрекинга: n ферзей */\nvoid backtrack(int row, int n, vector&lt;vector&lt;string&gt;&gt; &amp;state, vector&lt;vector&lt;vector&lt;string&gt;&gt;&gt; &amp;res, vector&lt;bool&gt; &amp;cols,\n               vector&lt;bool&gt; &amp;diags1, vector&lt;bool&gt; &amp;diags2) {\n    // Когда все строки уже обработаны, записать решение\n    if (row == n) {\n        res.push_back(state);\n        return;\n    }\n    // Обойти все столбцы\n    for (int col = 0; col &lt; n; col++) {\n        // Вычислить главную и побочную диагонали, соответствующие этой клетке\n        int diag1 = row - col + n - 1;\n        int diag2 = row + col;\n        // Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n        if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n            // Попытка: поставить ферзя в эту клетку\n            state[row][col] = \"Q\";\n            cols[col] = diags1[diag1] = diags2[diag2] = true;\n            // Перейти к размещению следующей строки\n            backtrack(row + 1, n, state, res, cols, diags1, diags2);\n            // Откат: восстановить эту клетку как пустую\n            state[row][col] = \"#\";\n            cols[col] = diags1[diag1] = diags2[diag2] = false;\n        }\n    }\n}\n\n/* Решить задачу о n ферзях */\nvector&lt;vector&lt;vector&lt;string&gt;&gt;&gt; nQueens(int n) {\n    // Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n    vector&lt;vector&lt;string&gt;&gt; state(n, vector&lt;string&gt;(n, \"#\"));\n    vector&lt;bool&gt; cols(n, false);           // Отмечать, есть ли ферзь в столбце\n    vector&lt;bool&gt; diags1(2 * n - 1, false); // Отмечать наличие ферзя на главной диагонали\n    vector&lt;bool&gt; diags2(2 * n - 1, false); // Отмечать наличие ферзя на побочной диагонали\n    vector&lt;vector&lt;vector&lt;string&gt;&gt;&gt; res;\n\n    backtrack(0, n, state, res, cols, diags1, diags2);\n\n    return res;\n}\n</code></pre> n_queens.java<pre><code>/* Алгоритм бэктрекинга: n ферзей */\nvoid backtrack(int row, int n, List&lt;List&lt;String&gt;&gt; state, List&lt;List&lt;List&lt;String&gt;&gt;&gt; res,\n        boolean[] cols, boolean[] diags1, boolean[] diags2) {\n    // Когда все строки уже обработаны, записать решение\n    if (row == n) {\n        List&lt;List&lt;String&gt;&gt; copyState = new ArrayList&lt;&gt;();\n        for (List&lt;String&gt; sRow : state) {\n            copyState.add(new ArrayList&lt;&gt;(sRow));\n        }\n        res.add(copyState);\n        return;\n    }\n    // Обойти все столбцы\n    for (int col = 0; col &lt; n; col++) {\n        // Вычислить главную и побочную диагонали, соответствующие этой клетке\n        int diag1 = row - col + n - 1;\n        int diag2 = row + col;\n        // Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n        if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n            // Попытка: поставить ферзя в эту клетку\n            state.get(row).set(col, \"Q\");\n            cols[col] = diags1[diag1] = diags2[diag2] = true;\n            // Перейти к размещению следующей строки\n            backtrack(row + 1, n, state, res, cols, diags1, diags2);\n            // Откат: восстановить эту клетку как пустую\n            state.get(row).set(col, \"#\");\n            cols[col] = diags1[diag1] = diags2[diag2] = false;\n        }\n    }\n}\n\n/* Решить задачу о n ферзях */\nList&lt;List&lt;List&lt;String&gt;&gt;&gt; nQueens(int n) {\n    // Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n    List&lt;List&lt;String&gt;&gt; state = new ArrayList&lt;&gt;();\n    for (int i = 0; i &lt; n; i++) {\n        List&lt;String&gt; row = new ArrayList&lt;&gt;();\n        for (int j = 0; j &lt; n; j++) {\n            row.add(\"#\");\n        }\n        state.add(row);\n    }\n    boolean[] cols = new boolean[n]; // Отмечать, есть ли ферзь в столбце\n    boolean[] diags1 = new boolean[2 * n - 1]; // Отмечать наличие ферзя на главной диагонали\n    boolean[] diags2 = new boolean[2 * n - 1]; // Отмечать наличие ферзя на побочной диагонали\n    List&lt;List&lt;List&lt;String&gt;&gt;&gt; res = new ArrayList&lt;&gt;();\n\n    backtrack(0, n, state, res, cols, diags1, diags2);\n\n    return res;\n}\n</code></pre> n_queens.cs<pre><code>/* Алгоритм бэктрекинга: n ферзей */\nvoid Backtrack(int row, int n, List&lt;List&lt;string&gt;&gt; state, List&lt;List&lt;List&lt;string&gt;&gt;&gt; res,\n        bool[] cols, bool[] diags1, bool[] diags2) {\n    // Когда все строки уже обработаны, записать решение\n    if (row == n) {\n        List&lt;List&lt;string&gt;&gt; copyState = [];\n        foreach (List&lt;string&gt; sRow in state) {\n            copyState.Add(new List&lt;string&gt;(sRow));\n        }\n        res.Add(copyState);\n        return;\n    }\n    // Обойти все столбцы\n    for (int col = 0; col &lt; n; col++) {\n        // Вычислить главную и побочную диагонали, соответствующие этой клетке\n        int diag1 = row - col + n - 1;\n        int diag2 = row + col;\n        // Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n        if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n            // Попытка: поставить ферзя в эту клетку\n            state[row][col] = \"Q\";\n            cols[col] = diags1[diag1] = diags2[diag2] = true;\n            // Перейти к размещению следующей строки\n            Backtrack(row + 1, n, state, res, cols, diags1, diags2);\n            // Откат: восстановить эту клетку как пустую\n            state[row][col] = \"#\";\n            cols[col] = diags1[diag1] = diags2[diag2] = false;\n        }\n    }\n}\n\n/* Решить задачу о n ферзях */\nList&lt;List&lt;List&lt;string&gt;&gt;&gt; NQueens(int n) {\n    // Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n    List&lt;List&lt;string&gt;&gt; state = [];\n    for (int i = 0; i &lt; n; i++) {\n        List&lt;string&gt; row = [];\n        for (int j = 0; j &lt; n; j++) {\n            row.Add(\"#\");\n        }\n        state.Add(row);\n    }\n    bool[] cols = new bool[n]; // Отмечать, есть ли ферзь в столбце\n    bool[] diags1 = new bool[2 * n - 1]; // Отмечать наличие ферзя на главной диагонали\n    bool[] diags2 = new bool[2 * n - 1]; // Отмечать наличие ферзя на побочной диагонали\n    List&lt;List&lt;List&lt;string&gt;&gt;&gt; res = [];\n\n    Backtrack(0, n, state, res, cols, diags1, diags2);\n\n    return res;\n}\n</code></pre> n_queens.go<pre><code>/* Алгоритм бэктрекинга: n ферзей */\nfunc backtrack(row, n int, state *[][]string, res *[][][]string, cols, diags1, diags2 *[]bool) {\n    // Когда все строки уже обработаны, записать решение\n    if row == n {\n        newState := make([][]string, len(*state))\n        for i, _ := range newState {\n            newState[i] = make([]string, len((*state)[0]))\n            copy(newState[i], (*state)[i])\n\n        }\n        *res = append(*res, newState)\n        return\n    }\n    // Обойти все столбцы\n    for col := 0; col &lt; n; col++ {\n        // Вычислить главную и побочную диагонали, соответствующие этой клетке\n        diag1 := row - col + n - 1\n        diag2 := row + col\n        // Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n        if !(*cols)[col] &amp;&amp; !(*diags1)[diag1] &amp;&amp; !(*diags2)[diag2] {\n            // Попытка: поставить ферзя в эту клетку\n            (*state)[row][col] = \"Q\"\n            (*cols)[col], (*diags1)[diag1], (*diags2)[diag2] = true, true, true\n            // Перейти к размещению следующей строки\n            backtrack(row+1, n, state, res, cols, diags1, diags2)\n            // Откат: восстановить эту клетку как пустую\n            (*state)[row][col] = \"#\"\n            (*cols)[col], (*diags1)[diag1], (*diags2)[diag2] = false, false, false\n        }\n    }\n}\n\n/* Решить задачу о n ферзях */\nfunc nQueens(n int) [][][]string {\n    // Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n    state := make([][]string, n)\n    for i := 0; i &lt; n; i++ {\n        row := make([]string, n)\n        for i := 0; i &lt; n; i++ {\n            row[i] = \"#\"\n        }\n        state[i] = row\n    }\n    // Отмечать, есть ли ферзь в столбце\n    cols := make([]bool, n)\n    diags1 := make([]bool, 2*n-1)\n    diags2 := make([]bool, 2*n-1)\n    res := make([][][]string, 0)\n    backtrack(0, n, &amp;state, &amp;res, &amp;cols, &amp;diags1, &amp;diags2)\n    return res\n}\n</code></pre> n_queens.swift<pre><code>/* Алгоритм бэктрекинга: n ферзей */\nfunc backtrack(row: Int, n: Int, state: inout [[String]], res: inout [[[String]]], cols: inout [Bool], diags1: inout [Bool], diags2: inout [Bool]) {\n    // Когда все строки уже обработаны, записать решение\n    if row == n {\n        res.append(state)\n        return\n    }\n    // Обойти все столбцы\n    for col in 0 ..&lt; n {\n        // Вычислить главную и побочную диагонали, соответствующие этой клетке\n        let diag1 = row - col + n - 1\n        let diag2 = row + col\n        // Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n        if !cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2] {\n            // Попытка: поставить ферзя в эту клетку\n            state[row][col] = \"Q\"\n            cols[col] = true\n            diags1[diag1] = true\n            diags2[diag2] = true\n            // Перейти к размещению следующей строки\n            backtrack(row: row + 1, n: n, state: &amp;state, res: &amp;res, cols: &amp;cols, diags1: &amp;diags1, diags2: &amp;diags2)\n            // Откат: восстановить эту клетку как пустую\n            state[row][col] = \"#\"\n            cols[col] = false\n            diags1[diag1] = false\n            diags2[diag2] = false\n        }\n    }\n}\n\n/* Решить задачу о n ферзях */\nfunc nQueens(n: Int) -&gt; [[[String]]] {\n    // Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n    var state = Array(repeating: Array(repeating: \"#\", count: n), count: n)\n    var cols = Array(repeating: false, count: n) // Отмечать, есть ли ферзь в столбце\n    var diags1 = Array(repeating: false, count: 2 * n - 1) // Отмечать наличие ферзя на главной диагонали\n    var diags2 = Array(repeating: false, count: 2 * n - 1) // Отмечать наличие ферзя на побочной диагонали\n    var res: [[[String]]] = []\n\n    backtrack(row: 0, n: n, state: &amp;state, res: &amp;res, cols: &amp;cols, diags1: &amp;diags1, diags2: &amp;diags2)\n\n    return res\n}\n</code></pre> n_queens.js<pre><code>/* Алгоритм бэктрекинга: n ферзей */\nfunction backtrack(row, n, state, res, cols, diags1, diags2) {\n    // Когда все строки уже обработаны, записать решение\n    if (row === n) {\n        res.push(state.map((row) =&gt; row.slice()));\n        return;\n    }\n    // Обойти все столбцы\n    for (let col = 0; col &lt; n; col++) {\n        // Вычислить главную и побочную диагонали, соответствующие этой клетке\n        const diag1 = row - col + n - 1;\n        const diag2 = row + col;\n        // Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n        if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n            // Попытка: поставить ферзя в эту клетку\n            state[row][col] = 'Q';\n            cols[col] = diags1[diag1] = diags2[diag2] = true;\n            // Перейти к размещению следующей строки\n            backtrack(row + 1, n, state, res, cols, diags1, diags2);\n            // Откат: восстановить эту клетку как пустую\n            state[row][col] = '#';\n            cols[col] = diags1[diag1] = diags2[diag2] = false;\n        }\n    }\n}\n\n/* Решить задачу о n ферзях */\nfunction nQueens(n) {\n    // Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n    const state = Array.from({ length: n }, () =&gt; Array(n).fill('#'));\n    const cols = Array(n).fill(false); // Отмечать, есть ли ферзь в столбце\n    const diags1 = Array(2 * n - 1).fill(false); // Отмечать наличие ферзя на главной диагонали\n    const diags2 = Array(2 * n - 1).fill(false); // Отмечать наличие ферзя на побочной диагонали\n    const res = [];\n\n    backtrack(0, n, state, res, cols, diags1, diags2);\n    return res;\n}\n</code></pre> n_queens.ts<pre><code>/* Алгоритм бэктрекинга: n ферзей */\nfunction backtrack(\n    row: number,\n    n: number,\n    state: string[][],\n    res: string[][][],\n    cols: boolean[],\n    diags1: boolean[],\n    diags2: boolean[]\n): void {\n    // Когда все строки уже обработаны, записать решение\n    if (row === n) {\n        res.push(state.map((row) =&gt; row.slice()));\n        return;\n    }\n    // Обойти все столбцы\n    for (let col = 0; col &lt; n; col++) {\n        // Вычислить главную и побочную диагонали, соответствующие этой клетке\n        const diag1 = row - col + n - 1;\n        const diag2 = row + col;\n        // Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n        if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n            // Попытка: поставить ферзя в эту клетку\n            state[row][col] = 'Q';\n            cols[col] = diags1[diag1] = diags2[diag2] = true;\n            // Перейти к размещению следующей строки\n            backtrack(row + 1, n, state, res, cols, diags1, diags2);\n            // Откат: восстановить эту клетку как пустую\n            state[row][col] = '#';\n            cols[col] = diags1[diag1] = diags2[diag2] = false;\n        }\n    }\n}\n\n/* Решить задачу о n ферзях */\nfunction nQueens(n: number): string[][][] {\n    // Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n    const state = Array.from({ length: n }, () =&gt; Array(n).fill('#'));\n    const cols = Array(n).fill(false); // Отмечать, есть ли ферзь в столбце\n    const diags1 = Array(2 * n - 1).fill(false); // Отмечать наличие ферзя на главной диагонали\n    const diags2 = Array(2 * n - 1).fill(false); // Отмечать наличие ферзя на побочной диагонали\n    const res: string[][][] = [];\n\n    backtrack(0, n, state, res, cols, diags1, diags2);\n    return res;\n}\n</code></pre> n_queens.dart<pre><code>/* Алгоритм бэктрекинга: n ферзей */\nvoid backtrack(\n  int row,\n  int n,\n  List&lt;List&lt;String&gt;&gt; state,\n  List&lt;List&lt;List&lt;String&gt;&gt;&gt; res,\n  List&lt;bool&gt; cols,\n  List&lt;bool&gt; diags1,\n  List&lt;bool&gt; diags2,\n) {\n  // Когда все строки уже обработаны, записать решение\n  if (row == n) {\n    List&lt;List&lt;String&gt;&gt; copyState = [];\n    for (List&lt;String&gt; sRow in state) {\n      copyState.add(List.from(sRow));\n    }\n    res.add(copyState);\n    return;\n  }\n  // Обойти все столбцы\n  for (int col = 0; col &lt; n; col++) {\n    // Вычислить главную и побочную диагонали, соответствующие этой клетке\n    int diag1 = row - col + n - 1;\n    int diag2 = row + col;\n    // Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n    if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n      // Попытка: поставить ферзя в эту клетку\n      state[row][col] = \"Q\";\n      cols[col] = true;\n      diags1[diag1] = true;\n      diags2[diag2] = true;\n      // Перейти к размещению следующей строки\n      backtrack(row + 1, n, state, res, cols, diags1, diags2);\n      // Откат: восстановить эту клетку как пустую\n      state[row][col] = \"#\";\n      cols[col] = false;\n      diags1[diag1] = false;\n      diags2[diag2] = false;\n    }\n  }\n}\n\n/* Решить задачу о n ферзях */\nList&lt;List&lt;List&lt;String&gt;&gt;&gt; nQueens(int n) {\n  // Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n  List&lt;List&lt;String&gt;&gt; state = List.generate(n, (index) =&gt; List.filled(n, \"#\"));\n  List&lt;bool&gt; cols = List.filled(n, false); // Отмечать, есть ли ферзь в столбце\n  List&lt;bool&gt; diags1 = List.filled(2 * n - 1, false); // Отмечать наличие ферзя на главной диагонали\n  List&lt;bool&gt; diags2 = List.filled(2 * n - 1, false); // Отмечать наличие ферзя на побочной диагонали\n  List&lt;List&lt;List&lt;String&gt;&gt;&gt; res = [];\n\n  backtrack(0, n, state, res, cols, diags1, diags2);\n\n  return res;\n}\n</code></pre> n_queens.rs<pre><code>/* Алгоритм бэктрекинга: n ферзей */\nfn backtrack(\n    row: usize,\n    n: usize,\n    state: &amp;mut Vec&lt;Vec&lt;String&gt;&gt;,\n    res: &amp;mut Vec&lt;Vec&lt;Vec&lt;String&gt;&gt;&gt;,\n    cols: &amp;mut [bool],\n    diags1: &amp;mut [bool],\n    diags2: &amp;mut [bool],\n) {\n    // Когда все строки уже обработаны, записать решение\n    if row == n {\n        res.push(state.clone());\n        return;\n    }\n    // Обойти все столбцы\n    for col in 0..n {\n        // Вычислить главную и побочную диагонали, соответствующие этой клетке\n        let diag1 = row + n - 1 - col;\n        let diag2 = row + col;\n        // Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n        if !cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2] {\n            // Попытка: поставить ферзя в эту клетку\n            state[row][col] = \"Q\".into();\n            (cols[col], diags1[diag1], diags2[diag2]) = (true, true, true);\n            // Перейти к размещению следующей строки\n            backtrack(row + 1, n, state, res, cols, diags1, diags2);\n            // Откат: восстановить эту клетку как пустую\n            state[row][col] = \"#\".into();\n            (cols[col], diags1[diag1], diags2[diag2]) = (false, false, false);\n        }\n    }\n}\n\n/* Решить задачу о n ферзях */\nfn n_queens(n: usize) -&gt; Vec&lt;Vec&lt;Vec&lt;String&gt;&gt;&gt; {\n    // Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n    let mut state: Vec&lt;Vec&lt;String&gt;&gt; = vec![vec![\"#\".to_string(); n]; n];\n    let mut cols = vec![false; n]; // Отмечать, есть ли ферзь в столбце\n    let mut diags1 = vec![false; 2 * n - 1]; // Отмечать наличие ферзя на главной диагонали\n    let mut diags2 = vec![false; 2 * n - 1]; // Отмечать наличие ферзя на побочной диагонали\n    let mut res: Vec&lt;Vec&lt;Vec&lt;String&gt;&gt;&gt; = Vec::new();\n\n    backtrack(\n        0,\n        n,\n        &amp;mut state,\n        &amp;mut res,\n        &amp;mut cols,\n        &amp;mut diags1,\n        &amp;mut diags2,\n    );\n\n    res\n}\n</code></pre> n_queens.c<pre><code>/* Алгоритм бэктрекинга: n ферзей */\nvoid backtrack(int row, int n, char state[MAX_SIZE][MAX_SIZE], char ***res, int *resSize, bool cols[MAX_SIZE],\n               bool diags1[2 * MAX_SIZE - 1], bool diags2[2 * MAX_SIZE - 1]) {\n    // Когда все строки уже обработаны, записать решение\n    if (row == n) {\n        res[*resSize] = (char **)malloc(sizeof(char *) * n);\n        for (int i = 0; i &lt; n; ++i) {\n            res[*resSize][i] = (char *)malloc(sizeof(char) * (n + 1));\n            strcpy(res[*resSize][i], state[i]);\n        }\n        (*resSize)++;\n        return;\n    }\n    // Обойти все столбцы\n    for (int col = 0; col &lt; n; col++) {\n        // Вычислить главную и побочную диагонали, соответствующие этой клетке\n        int diag1 = row - col + n - 1;\n        int diag2 = row + col;\n        // Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n        if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n            // Попытка: поставить ферзя в эту клетку\n            state[row][col] = 'Q';\n            cols[col] = diags1[diag1] = diags2[diag2] = true;\n            // Перейти к размещению следующей строки\n            backtrack(row + 1, n, state, res, resSize, cols, diags1, diags2);\n            // Откат: восстановить эту клетку как пустую\n            state[row][col] = '#';\n            cols[col] = diags1[diag1] = diags2[diag2] = false;\n        }\n    }\n}\n\n/* Решить задачу о n ферзях */\nchar ***nQueens(int n, int *returnSize) {\n    char state[MAX_SIZE][MAX_SIZE];\n    // Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n    for (int i = 0; i &lt; n; ++i) {\n        for (int j = 0; j &lt; n; ++j) {\n            state[i][j] = '#';\n        }\n        state[i][n] = '\\0';\n    }\n    bool cols[MAX_SIZE] = {false};           // Отмечать, есть ли ферзь в столбце\n    bool diags1[2 * MAX_SIZE - 1] = {false}; // Отмечать наличие ферзя на главной диагонали\n    bool diags2[2 * MAX_SIZE - 1] = {false}; // Отмечать наличие ферзя на побочной диагонали\n\n    char ***res = (char ***)malloc(sizeof(char **) * MAX_SIZE);\n    *returnSize = 0;\n    backtrack(0, n, state, res, returnSize, cols, diags1, diags2);\n    return res;\n}\n</code></pre> n_queens.kt<pre><code>/* Алгоритм бэктрекинга: n ферзей */\nfun backtrack(\n    row: Int,\n    n: Int,\n    state: MutableList&lt;MutableList&lt;String&gt;&gt;,\n    res: MutableList&lt;MutableList&lt;MutableList&lt;String&gt;&gt;?&gt;,\n    cols: BooleanArray,\n    diags1: BooleanArray,\n    diags2: BooleanArray\n) {\n    // Когда все строки уже обработаны, записать решение\n    if (row == n) {\n        val copyState = mutableListOf&lt;MutableList&lt;String&gt;&gt;()\n        for (sRow in state) {\n            copyState.add(sRow.toMutableList())\n        }\n        res.add(copyState)\n        return\n    }\n    // Обойти все столбцы\n    for (col in 0..&lt;n) {\n        // Вычислить главную и побочную диагонали, соответствующие этой клетке\n        val diag1 = row - col + n - 1\n        val diag2 = row + col\n        // Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n        if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n            // Попытка: поставить ферзя в эту клетку\n            state[row][col] = \"Q\"\n            diags2[diag2] = true\n            diags1[diag1] = diags2[diag2]\n            cols[col] = diags1[diag1]\n            // Перейти к размещению следующей строки\n            backtrack(row + 1, n, state, res, cols, diags1, diags2)\n            // Откат: восстановить эту клетку как пустую\n            state[row][col] = \"#\"\n            diags2[diag2] = false\n            diags1[diag1] = diags2[diag2]\n            cols[col] = diags1[diag1]\n        }\n    }\n}\n\n/* Решить задачу о n ферзях */\nfun nQueens(n: Int): MutableList&lt;MutableList&lt;MutableList&lt;String&gt;&gt;?&gt; {\n    // Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n    val state = mutableListOf&lt;MutableList&lt;String&gt;&gt;()\n    for (i in 0..&lt;n) {\n        val row = mutableListOf&lt;String&gt;()\n        for (j in 0..&lt;n) {\n            row.add(\"#\")\n        }\n        state.add(row)\n    }\n    val cols = BooleanArray(n) // Отмечать, есть ли ферзь в столбце\n    val diags1 = BooleanArray(2 * n - 1) // Отмечать наличие ферзя на главной диагонали\n    val diags2 = BooleanArray(2 * n - 1) // Отмечать наличие ферзя на побочной диагонали\n    val res = mutableListOf&lt;MutableList&lt;MutableList&lt;String&gt;&gt;?&gt;()\n\n    backtrack(0, n, state, res, cols, diags1, diags2)\n\n    return res\n}\n</code></pre> n_queens.rb<pre><code>### Алгоритм бэктрекинга: n ферзей ###\ndef backtrack(row, n, state, res, cols, diags1, diags2)\n  # Когда все строки уже обработаны, записать решение\n  if row == n\n    res &lt;&lt; state.map { |row| row.dup }\n    return\n  end\n\n  # Обойти все столбцы\n  for col in 0...n\n    # Вычислить главную и побочную диагонали, соответствующие этой клетке\n    diag1 = row - col + n - 1\n    diag2 = row + col\n    # Отсечение: в столбце, главной диагонали и побочной диагонали этой клетки не должно быть ферзей\n    if !cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]\n      # Попытка: поставить ферзя в эту клетку\n      state[row][col] = \"Q\"\n      cols[col] = diags1[diag1] = diags2[diag2] = true\n      # Перейти к размещению следующей строки\n      backtrack(row + 1, n, state, res, cols, diags1, diags2)\n      # Откат: восстановить эту клетку как пустую\n      state[row][col] = \"#\"\n      cols[col] = diags1[diag1] = diags2[diag2] = false\n    end\n  end\nend\n\n### Решить задачу о n ферзях ###\ndef n_queens(n)\n  # Инициализировать доску размера n*n, где 'Q' обозначает ферзя, а '#' — пустую клетку\n  state = Array.new(n) { Array.new(n, \"#\") }\n  cols = Array.new(n, false) # Отмечать, есть ли ферзь в столбце\n  diags1 = Array.new(2 * n - 1, false) # Отмечать наличие ферзя на главной диагонали\n  diags2 = Array.new(2 * n - 1, false) # Отмечать наличие ферзя на побочной диагонали\n  res = []\n  backtrack(0, n, state, res, cols, diags1, diags2)\n\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Если размещать ферзей построчно \\(n\\) раз, учитывая ограничение по столбцам, то начиная с первой строки и заканчивая последней мы получаем соответственно \\(n\\), \\(n-1\\), \\(\\dots\\), \\(2\\), \\(1\\) вариантов выбора, что дает \\(O(n!)\\) времени. При записи решения нужно скопировать матрицу <code>state</code> и добавить ее в <code>res</code> , а копирование требует \\(O(n^2)\\) времени. Следовательно, общая временная сложность равна \\(O(n! \\cdot n^2)\\) . На практике обрезка по диагональным ограничениям дополнительно сильно уменьшает пространство поиска, поэтому фактическая эффективность часто лучше этой оценки.</p> <p>Массив <code>state</code> использует \\(O(n^2)\\) пространства, а массивы <code>cols</code> , <code>diags1</code> и <code>diags2</code> используют по \\(O(n)\\) пространства. Максимальная глубина рекурсии равна \\(n\\) , что требует \\(O(n)\\) памяти стека. Следовательно, пространственная сложность равна \\(O(n^2)\\) .</p>","path":["Глава 13. Поиск с возвратом","13.4 &nbsp; Задача о n ферзях"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/","level":1,"title":"13.2   Задача о перестановках","text":"<p>Задача о перестановках является типичным применением алгоритма поиска с возвратом. Ее определение состоит в том, чтобы для данного множества элементов (например, массива или строки) найти все возможные перестановки этих элементов.</p> <p>В таблице 13-2 приведено несколько примеров входных массивов и соответствующих им перестановок.</p> <p> Таблица 13-2   Примеры перестановок </p> Входной массив Все перестановки \\([1]\\) \\([1]\\) \\([1, 2]\\) \\([1, 2], [2, 1]\\) \\([1, 2, 3]\\) \\([1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]\\)","path":["Глава 13. Поиск с возвратом","13.2 &nbsp; Задача о перестановках"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#1321","level":2,"title":"13.2.1   Случай без равных элементов","text":"<p>Question</p> <p>Дан массив целых чисел, в котором нет повторяющихся элементов. Верните все возможные перестановки.</p> <p>С точки зрения поиска с возвратом процесс построения перестановок можно представить как результат последовательности выборов. Пусть входной массив равен \\([1, 2, 3]\\) ; если мы сначала выберем \\(1\\) , затем \\(3\\) , а потом \\(2\\) , то получим перестановку \\([1, 3, 2]\\) . Откат здесь означает отмену одного из выборов с последующей попыткой других вариантов.</p> <p>С точки зрения кода поиска с возвратом множество кандидатов <code>choices</code> состоит из всех элементов входного массива, а состояние <code>state</code> - из элементов, уже выбранных к текущему моменту. Поскольку каждый элемент разрешено выбирать только один раз, все элементы в <code>state</code> должны быть уникальны.</p> <p>Как показано на рисунке 13-5, процесс поиска можно развернуть в дерево рекурсии, где каждый узел представляет текущее состояние <code>state</code> . Начиная от корня, после трех раундов выбора мы попадаем в листья, и каждый лист соответствует одной перестановке.</p> <p></p> <p> Рисунок 13-5   Дерево рекурсии для перестановок </p>","path":["Глава 13. Поиск с возвратом","13.2 &nbsp; Задача о перестановках"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#1","level":3,"title":"1.   Обрезка повторного выбора","text":"<p>Чтобы гарантировать, что каждый элемент выбирается только один раз, введем булев массив <code>selected</code> , где <code>selected[i]</code> обозначает, был ли уже выбран <code>choices[i]</code> , и на его основе выполним следующую обрезку.</p> <ul> <li>После того как сделан выбор <code>choice[i]</code> , мы присваиваем <code>selected[i]</code> значение \\(\\text{True}\\) , тем самым отмечая, что этот элемент уже выбран.</li> <li>При обходе списка вариантов <code>choices</code> пропускаем все уже выбранные элементы, то есть выполняем обрезку.</li> </ul> <p>Как показано на рисунке 13-6, если в первом раунде мы выберем 1 , во втором - 3 , а в третьем - 2 , то во втором раунде нужно отсечь ветвь элемента 1 , а в третьем - ветви элементов 1 и 3 .</p> <p></p> <p> Рисунок 13-6   Пример обрезки в задаче о перестановках </p> <p>Из рисунка видно, что такая обрезка уменьшает размер пространства поиска с \\(O(n^n)\\) до \\(O(n!)\\) .</p>","path":["Глава 13. Поиск с возвратом","13.2 &nbsp; Задача о перестановках"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#2","level":3,"title":"2.   Реализация кода","text":"<p>После прояснения всей логики можно просто \"заполнить пропуски\" в шаблоне поиска с возвратом. Чтобы сократить общий объем кода, мы не будем отдельно реализовывать каждую функцию из каркаса, а раскроем их прямо внутри <code>backtrack()</code> :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby permutations_i.py<pre><code>def backtrack(\n    state: list[int], choices: list[int], selected: list[bool], res: list[list[int]]\n):\n    \"\"\"Алгоритм бэктрекинга: все перестановки I\"\"\"\n    # Когда длина состояния равна числу элементов, записать решение\n    if len(state) == len(choices):\n        res.append(list(state))\n        return\n    # Перебор всех вариантов выбора\n    for i, choice in enumerate(choices):\n        # Отсечение: нельзя выбирать один и тот же элемент повторно\n        if not selected[i]:\n            # Попытка: сделать выбор и обновить состояние\n            selected[i] = True\n            state.append(choice)\n            # Перейти к следующему выбору\n            backtrack(state, choices, selected, res)\n            # Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = False\n            state.pop()\n\ndef permutations_i(nums: list[int]) -&gt; list[list[int]]:\n    \"\"\"Все перестановки I\"\"\"\n    res = []\n    backtrack(state=[], choices=nums, selected=[False] * len(nums), res=res)\n    return res\n</code></pre> permutations_i.cpp<pre><code>/* Алгоритм бэктрекинга: все перестановки I */\nvoid backtrack(vector&lt;int&gt; &amp;state, const vector&lt;int&gt; &amp;choices, vector&lt;bool&gt; &amp;selected, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (state.size() == choices.size()) {\n        res.push_back(state);\n        return;\n    }\n    // Перебор всех вариантов выбора\n    for (int i = 0; i &lt; choices.size(); i++) {\n        int choice = choices[i];\n        // Отсечение: нельзя выбирать один и тот же элемент повторно\n        if (!selected[i]) {\n            // Попытка: сделать выбор и обновить состояние\n            selected[i] = true;\n            state.push_back(choice);\n            // Перейти к следующему выбору\n            backtrack(state, choices, selected, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n            state.pop_back();\n        }\n    }\n}\n\n/* Все перестановки I */\nvector&lt;vector&lt;int&gt;&gt; permutationsI(vector&lt;int&gt; nums) {\n    vector&lt;int&gt; state;\n    vector&lt;bool&gt; selected(nums.size(), false);\n    vector&lt;vector&lt;int&gt;&gt; res;\n    backtrack(state, nums, selected, res);\n    return res;\n}\n</code></pre> permutations_i.java<pre><code>/* Алгоритм бэктрекинга: все перестановки I */\nvoid backtrack(List&lt;Integer&gt; state, int[] choices, boolean[] selected, List&lt;List&lt;Integer&gt;&gt; res) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (state.size() == choices.length) {\n        res.add(new ArrayList&lt;Integer&gt;(state));\n        return;\n    }\n    // Перебор всех вариантов выбора\n    for (int i = 0; i &lt; choices.length; i++) {\n        int choice = choices[i];\n        // Отсечение: нельзя выбирать один и тот же элемент повторно\n        if (!selected[i]) {\n            // Попытка: сделать выбор и обновить состояние\n            selected[i] = true;\n            state.add(choice);\n            // Перейти к следующему выбору\n            backtrack(state, choices, selected, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n            state.remove(state.size() - 1);\n        }\n    }\n}\n\n/* Все перестановки I */\nList&lt;List&lt;Integer&gt;&gt; permutationsI(int[] nums) {\n    List&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;List&lt;Integer&gt;&gt;();\n    backtrack(new ArrayList&lt;Integer&gt;(), nums, new boolean[nums.length], res);\n    return res;\n}\n</code></pre> permutations_i.cs<pre><code>/* Алгоритм бэктрекинга: все перестановки I */\nvoid Backtrack(List&lt;int&gt; state, int[] choices, bool[] selected, List&lt;List&lt;int&gt;&gt; res) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (state.Count == choices.Length) {\n        res.Add(new List&lt;int&gt;(state));\n        return;\n    }\n    // Перебор всех вариантов выбора\n    for (int i = 0; i &lt; choices.Length; i++) {\n        int choice = choices[i];\n        // Отсечение: нельзя выбирать один и тот же элемент повторно\n        if (!selected[i]) {\n            // Попытка: сделать выбор и обновить состояние\n            selected[i] = true;\n            state.Add(choice);\n            // Перейти к следующему выбору\n            Backtrack(state, choices, selected, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n            state.RemoveAt(state.Count - 1);\n        }\n    }\n}\n\n/* Все перестановки I */\nList&lt;List&lt;int&gt;&gt; PermutationsI(int[] nums) {\n    List&lt;List&lt;int&gt;&gt; res = [];\n    Backtrack([], nums, new bool[nums.Length], res);\n    return res;\n}\n</code></pre> permutations_i.go<pre><code>/* Алгоритм бэктрекинга: все перестановки I */\nfunc backtrackI(state *[]int, choices *[]int, selected *[]bool, res *[][]int) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if len(*state) == len(*choices) {\n        newState := append([]int{}, *state...)\n        *res = append(*res, newState)\n    }\n    // Перебор всех вариантов выбора\n    for i := 0; i &lt; len(*choices); i++ {\n        choice := (*choices)[i]\n        // Отсечение: нельзя выбирать один и тот же элемент повторно\n        if !(*selected)[i] {\n            // Попытка: сделать выбор и обновить состояние\n            (*selected)[i] = true\n            *state = append(*state, choice)\n            // Перейти к следующему выбору\n            backtrackI(state, choices, selected, res)\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            (*selected)[i] = false\n            *state = (*state)[:len(*state)-1]\n        }\n    }\n}\n\n/* Все перестановки I */\nfunc permutationsI(nums []int) [][]int {\n    res := make([][]int, 0)\n    state := make([]int, 0)\n    selected := make([]bool, len(nums))\n    backtrackI(&amp;state, &amp;nums, &amp;selected, &amp;res)\n    return res\n}\n</code></pre> permutations_i.swift<pre><code>/* Алгоритм бэктрекинга: все перестановки I */\nfunc backtrack(state: inout [Int], choices: [Int], selected: inout [Bool], res: inout [[Int]]) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if state.count == choices.count {\n        res.append(state)\n        return\n    }\n    // Перебор всех вариантов выбора\n    for (i, choice) in choices.enumerated() {\n        // Отсечение: нельзя выбирать один и тот же элемент повторно\n        if !selected[i] {\n            // Попытка: сделать выбор и обновить состояние\n            selected[i] = true\n            state.append(choice)\n            // Перейти к следующему выбору\n            backtrack(state: &amp;state, choices: choices, selected: &amp;selected, res: &amp;res)\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false\n            state.removeLast()\n        }\n    }\n}\n\n/* Все перестановки I */\nfunc permutationsI(nums: [Int]) -&gt; [[Int]] {\n    var state: [Int] = []\n    var selected = Array(repeating: false, count: nums.count)\n    var res: [[Int]] = []\n    backtrack(state: &amp;state, choices: nums, selected: &amp;selected, res: &amp;res)\n    return res\n}\n</code></pre> permutations_i.js<pre><code>/* Алгоритм бэктрекинга: все перестановки I */\nfunction backtrack(state, choices, selected, res) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (state.length === choices.length) {\n        res.push([...state]);\n        return;\n    }\n    // Перебор всех вариантов выбора\n    choices.forEach((choice, i) =&gt; {\n        // Отсечение: нельзя выбирать один и тот же элемент повторно\n        if (!selected[i]) {\n            // Попытка: сделать выбор и обновить состояние\n            selected[i] = true;\n            state.push(choice);\n            // Перейти к следующему выбору\n            backtrack(state, choices, selected, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n            state.pop();\n        }\n    });\n}\n\n/* Все перестановки I */\nfunction permutationsI(nums) {\n    const res = [];\n    backtrack([], nums, Array(nums.length).fill(false), res);\n    return res;\n}\n</code></pre> permutations_i.ts<pre><code>/* Алгоритм бэктрекинга: все перестановки I */\nfunction backtrack(\n    state: number[],\n    choices: number[],\n    selected: boolean[],\n    res: number[][]\n): void {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (state.length === choices.length) {\n        res.push([...state]);\n        return;\n    }\n    // Перебор всех вариантов выбора\n    choices.forEach((choice, i) =&gt; {\n        // Отсечение: нельзя выбирать один и тот же элемент повторно\n        if (!selected[i]) {\n            // Попытка: сделать выбор и обновить состояние\n            selected[i] = true;\n            state.push(choice);\n            // Перейти к следующему выбору\n            backtrack(state, choices, selected, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n            state.pop();\n        }\n    });\n}\n\n/* Все перестановки I */\nfunction permutationsI(nums: number[]): number[][] {\n    const res: number[][] = [];\n    backtrack([], nums, Array(nums.length).fill(false), res);\n    return res;\n}\n</code></pre> permutations_i.dart<pre><code>/* Алгоритм бэктрекинга: все перестановки I */\nvoid backtrack(\n  List&lt;int&gt; state,\n  List&lt;int&gt; choices,\n  List&lt;bool&gt; selected,\n  List&lt;List&lt;int&gt;&gt; res,\n) {\n  // Когда длина состояния равна числу элементов, записать решение\n  if (state.length == choices.length) {\n    res.add(List.from(state));\n    return;\n  }\n  // Перебор всех вариантов выбора\n  for (int i = 0; i &lt; choices.length; i++) {\n    int choice = choices[i];\n    // Отсечение: нельзя выбирать один и тот же элемент повторно\n    if (!selected[i]) {\n      // Попытка: сделать выбор и обновить состояние\n      selected[i] = true;\n      state.add(choice);\n      // Перейти к следующему выбору\n      backtrack(state, choices, selected, res);\n      // Откат: отменить выбор и восстановить предыдущее состояние\n      selected[i] = false;\n      state.removeLast();\n    }\n  }\n}\n\n/* Все перестановки I */\nList&lt;List&lt;int&gt;&gt; permutationsI(List&lt;int&gt; nums) {\n  List&lt;List&lt;int&gt;&gt; res = [];\n  backtrack([], nums, List.filled(nums.length, false), res);\n  return res;\n}\n</code></pre> permutations_i.rs<pre><code>/* Алгоритм бэктрекинга: все перестановки I */\nfn backtrack(mut state: Vec&lt;i32&gt;, choices: &amp;[i32], selected: &amp;mut [bool], res: &amp;mut Vec&lt;Vec&lt;i32&gt;&gt;) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if state.len() == choices.len() {\n        res.push(state);\n        return;\n    }\n    // Перебор всех вариантов выбора\n    for i in 0..choices.len() {\n        let choice = choices[i];\n        // Отсечение: нельзя выбирать один и тот же элемент повторно\n        if !selected[i] {\n            // Попытка: сделать выбор и обновить состояние\n            selected[i] = true;\n            state.push(choice);\n            // Перейти к следующему выбору\n            backtrack(state.clone(), choices, selected, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n            state.pop();\n        }\n    }\n}\n\n/* Все перестановки I */\nfn permutations_i(nums: &amp;mut [i32]) -&gt; Vec&lt;Vec&lt;i32&gt;&gt; {\n    let mut res = Vec::new(); // Состояние (подмножество)\n    backtrack(Vec::new(), nums, &amp;mut vec![false; nums.len()], &amp;mut res);\n    res\n}\n</code></pre> permutations_i.c<pre><code>/* Алгоритм бэктрекинга: все перестановки I */\nvoid backtrack(int *state, int stateSize, int *choices, int choicesSize, bool *selected, int **res, int *resSize) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (stateSize == choicesSize) {\n        res[*resSize] = (int *)malloc(choicesSize * sizeof(int));\n        for (int i = 0; i &lt; choicesSize; i++) {\n            res[*resSize][i] = state[i];\n        }\n        (*resSize)++;\n        return;\n    }\n    // Перебор всех вариантов выбора\n    for (int i = 0; i &lt; choicesSize; i++) {\n        int choice = choices[i];\n        // Отсечение: нельзя выбирать один и тот же элемент повторно\n        if (!selected[i]) {\n            // Попытка: сделать выбор и обновить состояние\n            selected[i] = true;\n            state[stateSize] = choice;\n            // Перейти к следующему выбору\n            backtrack(state, stateSize + 1, choices, choicesSize, selected, res, resSize);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n        }\n    }\n}\n\n/* Все перестановки I */\nint **permutationsI(int *nums, int numsSize, int *returnSize) {\n    int *state = (int *)malloc(numsSize * sizeof(int));\n    bool *selected = (bool *)malloc(numsSize * sizeof(bool));\n    for (int i = 0; i &lt; numsSize; i++) {\n        selected[i] = false;\n    }\n    int **res = (int **)malloc(MAX_SIZE * sizeof(int *));\n    *returnSize = 0;\n\n    backtrack(state, 0, nums, numsSize, selected, res, returnSize);\n\n    free(state);\n    free(selected);\n\n    return res;\n}\n</code></pre> permutations_i.kt<pre><code>/* Алгоритм бэктрекинга: все перестановки I */\nfun backtrack(\n    state: MutableList&lt;Int&gt;,\n    choices: IntArray,\n    selected: BooleanArray,\n    res: MutableList&lt;MutableList&lt;Int&gt;?&gt;\n) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (state.size == choices.size) {\n        res.add(state.toMutableList())\n        return\n    }\n    // Перебор всех вариантов выбора\n    for (i in choices.indices) {\n        val choice = choices[i]\n        // Отсечение: нельзя выбирать один и тот же элемент повторно\n        if (!selected[i]) {\n            // Попытка: сделать выбор и обновить состояние\n            selected[i] = true\n            state.add(choice)\n            // Перейти к следующему выбору\n            backtrack(state, choices, selected, res)\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false\n            state.removeAt(state.size - 1)\n        }\n    }\n}\n\n/* Все перестановки I */\nfun permutationsI(nums: IntArray): MutableList&lt;MutableList&lt;Int&gt;?&gt; {\n    val res = mutableListOf&lt;MutableList&lt;Int&gt;?&gt;()\n    backtrack(mutableListOf(), nums, BooleanArray(nums.size), res)\n    return res\n}\n</code></pre> permutations_i.rb<pre><code>### Алгоритм бэктрекинга: все перестановки I ###\ndef backtrack(state, choices, selected, res)\n  # Когда длина состояния равна числу элементов, записать решение\n  if state.length == choices.length\n    res &lt;&lt; state.dup\n    return\n  end\n\n  # Перебор всех вариантов выбора\n  choices.each_with_index do |choice, i|\n    # Отсечение: нельзя выбирать один и тот же элемент повторно\n    unless selected[i]\n      # Попытка: сделать выбор и обновить состояние\n      selected[i] = true\n      state &lt;&lt; choice\n      # Перейти к следующему выбору\n      backtrack(state, choices, selected, res)\n      # Откат: отменить выбор и восстановить предыдущее состояние\n      selected[i] = false\n      state.pop\n    end\n  end\nend\n\n### Все перестановки I ###\ndef permutations_i(nums)\n  res = []\n  backtrack([], nums, Array.new(nums.length, false), res)\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 13. Поиск с возвратом","13.2 &nbsp; Задача о перестановках"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#1322","level":2,"title":"13.2.2   Учет равных элементов","text":"<p>Question</p> <p>Дан массив целых чисел, который может содержать повторяющиеся элементы. Верните все неповторяющиеся перестановки.</p> <p>Пусть входной массив равен \\([1, 1, 2]\\) . Чтобы различать два одинаковых элемента \\(1\\) , будем обозначать второй из них как \\(\\hat{1}\\) .</p> <p>Как показано на рисунке 13-7, описанный выше метод создаст результат, половина которого окажется дублирующейся.</p> <p></p> <p> Рисунок 13-7   Повторяющиеся перестановки </p> <p>Как же убрать повторяющиеся перестановки? Самый прямолинейный способ - воспользоваться хеш-множеством и удалить дубликаты уже после генерации результата. Но это не слишком изящно, потому что ветви поиска, порождающие дубликаты, вообще не нужно посещать: их следует распознавать заранее и отсекать, что дополнительно повышает эффективность алгоритма.</p>","path":["Глава 13. Поиск с возвратом","13.2 &nbsp; Задача о перестановках"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#1_1","level":3,"title":"1.   Обрезка равных элементов","text":"<p>Посмотрите на рисунок 13-8: в первом раунде выбрать \\(1\\) или выбрать \\(\\hat{1}\\) - это одно и то же, а значит, все перестановки, полученные из этих двух выборов, будут дублироваться. Поэтому ветвь \\(\\hat{1}\\) нужно отсечь.</p> <p>Точно так же, если в первом раунде выбрать \\(2\\) , то во втором раунде выборы \\(1\\) и \\(\\hat{1}\\) снова создадут дублирующиеся ветви, поэтому и в этом случае ветвь \\(\\hat{1}\\) нужно отсечь.</p> <p>Иначе говоря, наша цель заключается в том, чтобы на каждом раунде выбора каждый из нескольких равных элементов выбирался только один раз.</p> <p></p> <p> Рисунок 13-8   Обрезка повторяющихся перестановок </p>","path":["Глава 13. Поиск с возвратом","13.2 &nbsp; Задача о перестановках"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#2_1","level":3,"title":"2.   Реализация кода","text":"<p>На основе решения из предыдущей задачи можно на каждом раунде выбора заводить хеш-множество <code>duplicated</code> , которое будет записывать элементы, уже встречавшиеся в этом раунде, и отсекать повторы:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby permutations_ii.py<pre><code>def backtrack(\n    state: list[int], choices: list[int], selected: list[bool], res: list[list[int]]\n):\n    \"\"\"Алгоритм бэктрекинга: все перестановки II\"\"\"\n    # Когда длина состояния равна числу элементов, записать решение\n    if len(state) == len(choices):\n        res.append(list(state))\n        return\n    # Перебор всех вариантов выбора\n    duplicated = set[int]()\n    for i, choice in enumerate(choices):\n        # Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n        if not selected[i] and choice not in duplicated:\n            # Попытка: сделать выбор и обновить состояние\n            duplicated.add(choice)  # Записать значения уже выбранных элементов\n            selected[i] = True\n            state.append(choice)\n            # Перейти к следующему выбору\n            backtrack(state, choices, selected, res)\n            # Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = False\n            state.pop()\n\ndef permutations_ii(nums: list[int]) -&gt; list[list[int]]:\n    \"\"\"Все перестановки II\"\"\"\n    res = []\n    backtrack(state=[], choices=nums, selected=[False] * len(nums), res=res)\n    return res\n</code></pre> permutations_ii.cpp<pre><code>/* Алгоритм бэктрекинга: все перестановки II */\nvoid backtrack(vector&lt;int&gt; &amp;state, const vector&lt;int&gt; &amp;choices, vector&lt;bool&gt; &amp;selected, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (state.size() == choices.size()) {\n        res.push_back(state);\n        return;\n    }\n    // Перебор всех вариантов выбора\n    unordered_set&lt;int&gt; duplicated;\n    for (int i = 0; i &lt; choices.size(); i++) {\n        int choice = choices[i];\n        // Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n        if (!selected[i] &amp;&amp; duplicated.find(choice) == duplicated.end()) {\n            // Попытка: сделать выбор и обновить состояние\n            duplicated.emplace(choice); // Записать значения уже выбранных элементов\n            selected[i] = true;\n            state.push_back(choice);\n            // Перейти к следующему выбору\n            backtrack(state, choices, selected, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n            state.pop_back();\n        }\n    }\n}\n\n/* Все перестановки II */\nvector&lt;vector&lt;int&gt;&gt; permutationsII(vector&lt;int&gt; nums) {\n    vector&lt;int&gt; state;\n    vector&lt;bool&gt; selected(nums.size(), false);\n    vector&lt;vector&lt;int&gt;&gt; res;\n    backtrack(state, nums, selected, res);\n    return res;\n}\n</code></pre> permutations_ii.java<pre><code>/* Алгоритм бэктрекинга: все перестановки II */\nvoid backtrack(List&lt;Integer&gt; state, int[] choices, boolean[] selected, List&lt;List&lt;Integer&gt;&gt; res) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (state.size() == choices.length) {\n        res.add(new ArrayList&lt;Integer&gt;(state));\n        return;\n    }\n    // Перебор всех вариантов выбора\n    Set&lt;Integer&gt; duplicated = new HashSet&lt;Integer&gt;();\n    for (int i = 0; i &lt; choices.length; i++) {\n        int choice = choices[i];\n        // Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n        if (!selected[i] &amp;&amp; !duplicated.contains(choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            duplicated.add(choice); // Записать значения уже выбранных элементов\n            selected[i] = true;\n            state.add(choice);\n            // Перейти к следующему выбору\n            backtrack(state, choices, selected, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n            state.remove(state.size() - 1);\n        }\n    }\n}\n\n/* Все перестановки II */\nList&lt;List&lt;Integer&gt;&gt; permutationsII(int[] nums) {\n    List&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;List&lt;Integer&gt;&gt;();\n    backtrack(new ArrayList&lt;Integer&gt;(), nums, new boolean[nums.length], res);\n    return res;\n}\n</code></pre> permutations_ii.cs<pre><code>/* Алгоритм бэктрекинга: все перестановки II */\nvoid Backtrack(List&lt;int&gt; state, int[] choices, bool[] selected, List&lt;List&lt;int&gt;&gt; res) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (state.Count == choices.Length) {\n        res.Add(new List&lt;int&gt;(state));\n        return;\n    }\n    // Перебор всех вариантов выбора\n    HashSet&lt;int&gt; duplicated = [];\n    for (int i = 0; i &lt; choices.Length; i++) {\n        int choice = choices[i];\n        // Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n        if (!selected[i] &amp;&amp; !duplicated.Contains(choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            duplicated.Add(choice); // Записать значения уже выбранных элементов\n            selected[i] = true;\n            state.Add(choice);\n            // Перейти к следующему выбору\n            Backtrack(state, choices, selected, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n            state.RemoveAt(state.Count - 1);\n        }\n    }\n}\n\n/* Все перестановки II */\nList&lt;List&lt;int&gt;&gt; PermutationsII(int[] nums) {\n    List&lt;List&lt;int&gt;&gt; res = [];\n    Backtrack([], nums, new bool[nums.Length], res);\n    return res;\n}\n</code></pre> permutations_ii.go<pre><code>/* Алгоритм бэктрекинга: все перестановки II */\nfunc backtrackII(state *[]int, choices *[]int, selected *[]bool, res *[][]int) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if len(*state) == len(*choices) {\n        newState := append([]int{}, *state...)\n        *res = append(*res, newState)\n    }\n    // Перебор всех вариантов выбора\n    duplicated := make(map[int]struct{}, 0)\n    for i := 0; i &lt; len(*choices); i++ {\n        choice := (*choices)[i]\n        // Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n        if _, ok := duplicated[choice]; !ok &amp;&amp; !(*selected)[i] {\n            // Попробовать: сделать выбор, обновить состояние\n            // Записать значение уже выбранного элемента\n            duplicated[choice] = struct{}{}\n            (*selected)[i] = true\n            *state = append(*state, choice)\n            // Перейти к следующему выбору\n            backtrackII(state, choices, selected, res)\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            (*selected)[i] = false\n            *state = (*state)[:len(*state)-1]\n        }\n    }\n}\n\n/* Все перестановки II */\nfunc permutationsII(nums []int) [][]int {\n    res := make([][]int, 0)\n    state := make([]int, 0)\n    selected := make([]bool, len(nums))\n    backtrackII(&amp;state, &amp;nums, &amp;selected, &amp;res)\n    return res\n}\n</code></pre> permutations_ii.swift<pre><code>/* Алгоритм бэктрекинга: все перестановки II */\nfunc backtrack(state: inout [Int], choices: [Int], selected: inout [Bool], res: inout [[Int]]) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if state.count == choices.count {\n        res.append(state)\n        return\n    }\n    // Перебор всех вариантов выбора\n    var duplicated: Set&lt;Int&gt; = []\n    for (i, choice) in choices.enumerated() {\n        // Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n        if !selected[i], !duplicated.contains(choice) {\n            // Попытка: сделать выбор и обновить состояние\n            duplicated.insert(choice) // Записать значения уже выбранных элементов\n            selected[i] = true\n            state.append(choice)\n            // Перейти к следующему выбору\n            backtrack(state: &amp;state, choices: choices, selected: &amp;selected, res: &amp;res)\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false\n            state.removeLast()\n        }\n    }\n}\n\n/* Все перестановки II */\nfunc permutationsII(nums: [Int]) -&gt; [[Int]] {\n    var state: [Int] = []\n    var selected = Array(repeating: false, count: nums.count)\n    var res: [[Int]] = []\n    backtrack(state: &amp;state, choices: nums, selected: &amp;selected, res: &amp;res)\n    return res\n}\n</code></pre> permutations_ii.js<pre><code>/* Алгоритм бэктрекинга: все перестановки II */\nfunction backtrack(state, choices, selected, res) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (state.length === choices.length) {\n        res.push([...state]);\n        return;\n    }\n    // Перебор всех вариантов выбора\n    const duplicated = new Set();\n    choices.forEach((choice, i) =&gt; {\n        // Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n        if (!selected[i] &amp;&amp; !duplicated.has(choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            duplicated.add(choice); // Записать значения уже выбранных элементов\n            selected[i] = true;\n            state.push(choice);\n            // Перейти к следующему выбору\n            backtrack(state, choices, selected, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n            state.pop();\n        }\n    });\n}\n\n/* Все перестановки II */\nfunction permutationsII(nums) {\n    const res = [];\n    backtrack([], nums, Array(nums.length).fill(false), res);\n    return res;\n}\n</code></pre> permutations_ii.ts<pre><code>/* Алгоритм бэктрекинга: все перестановки II */\nfunction backtrack(\n    state: number[],\n    choices: number[],\n    selected: boolean[],\n    res: number[][]\n): void {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (state.length === choices.length) {\n        res.push([...state]);\n        return;\n    }\n    // Перебор всех вариантов выбора\n    const duplicated = new Set();\n    choices.forEach((choice, i) =&gt; {\n        // Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n        if (!selected[i] &amp;&amp; !duplicated.has(choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            duplicated.add(choice); // Записать значения уже выбранных элементов\n            selected[i] = true;\n            state.push(choice);\n            // Перейти к следующему выбору\n            backtrack(state, choices, selected, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n            state.pop();\n        }\n    });\n}\n\n/* Все перестановки II */\nfunction permutationsII(nums: number[]): number[][] {\n    const res: number[][] = [];\n    backtrack([], nums, Array(nums.length).fill(false), res);\n    return res;\n}\n</code></pre> permutations_ii.dart<pre><code>/* Алгоритм бэктрекинга: все перестановки II */\nvoid backtrack(\n  List&lt;int&gt; state,\n  List&lt;int&gt; choices,\n  List&lt;bool&gt; selected,\n  List&lt;List&lt;int&gt;&gt; res,\n) {\n  // Когда длина состояния равна числу элементов, записать решение\n  if (state.length == choices.length) {\n    res.add(List.from(state));\n    return;\n  }\n  // Перебор всех вариантов выбора\n  Set&lt;int&gt; duplicated = {};\n  for (int i = 0; i &lt; choices.length; i++) {\n    int choice = choices[i];\n    // Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n    if (!selected[i] &amp;&amp; !duplicated.contains(choice)) {\n      // Попытка: сделать выбор и обновить состояние\n      duplicated.add(choice); // Записать значения уже выбранных элементов\n      selected[i] = true;\n      state.add(choice);\n      // Перейти к следующему выбору\n      backtrack(state, choices, selected, res);\n      // Откат: отменить выбор и восстановить предыдущее состояние\n      selected[i] = false;\n      state.removeLast();\n    }\n  }\n}\n\n/* Все перестановки II */\nList&lt;List&lt;int&gt;&gt; permutationsII(List&lt;int&gt; nums) {\n  List&lt;List&lt;int&gt;&gt; res = [];\n  backtrack([], nums, List.filled(nums.length, false), res);\n  return res;\n}\n</code></pre> permutations_ii.rs<pre><code>/* Алгоритм бэктрекинга: все перестановки II */\nfn backtrack(mut state: Vec&lt;i32&gt;, choices: &amp;[i32], selected: &amp;mut [bool], res: &amp;mut Vec&lt;Vec&lt;i32&gt;&gt;) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if state.len() == choices.len() {\n        res.push(state);\n        return;\n    }\n    // Перебор всех вариантов выбора\n    let mut duplicated = HashSet::&lt;i32&gt;::new();\n    for i in 0..choices.len() {\n        let choice = choices[i];\n        // Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n        if !selected[i] &amp;&amp; !duplicated.contains(&amp;choice) {\n            // Попытка: сделать выбор и обновить состояние\n            duplicated.insert(choice); // Записать значения уже выбранных элементов\n            selected[i] = true;\n            state.push(choice);\n            // Перейти к следующему выбору\n            backtrack(state.clone(), choices, selected, res);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n            state.pop();\n        }\n    }\n}\n\n/* Все перестановки II */\nfn permutations_ii(nums: &amp;mut [i32]) -&gt; Vec&lt;Vec&lt;i32&gt;&gt; {\n    let mut res = Vec::new();\n    backtrack(Vec::new(), nums, &amp;mut vec![false; nums.len()], &amp;mut res);\n    res\n}\n</code></pre> permutations_ii.c<pre><code>/* Алгоритм бэктрекинга: все перестановки II */\nvoid backtrack(int *state, int stateSize, int *choices, int choicesSize, bool *selected, int **res, int *resSize) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (stateSize == choicesSize) {\n        res[*resSize] = (int *)malloc(choicesSize * sizeof(int));\n        for (int i = 0; i &lt; choicesSize; i++) {\n            res[*resSize][i] = state[i];\n        }\n        (*resSize)++;\n        return;\n    }\n    // Перебор всех вариантов выбора\n    bool duplicated[MAX_SIZE] = {false};\n    for (int i = 0; i &lt; choicesSize; i++) {\n        int choice = choices[i];\n        // Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n        if (!selected[i] &amp;&amp; !duplicated[choice]) {\n            // Попытка: сделать выбор и обновить состояние\n            duplicated[choice] = true; // Записать значения уже выбранных элементов\n            selected[i] = true;\n            state[stateSize] = choice;\n            // Перейти к следующему выбору\n            backtrack(state, stateSize + 1, choices, choicesSize, selected, res, resSize);\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false;\n        }\n    }\n}\n\n/* Все перестановки II */\nint **permutationsII(int *nums, int numsSize, int *returnSize) {\n    int *state = (int *)malloc(numsSize * sizeof(int));\n    bool *selected = (bool *)malloc(numsSize * sizeof(bool));\n    for (int i = 0; i &lt; numsSize; i++) {\n        selected[i] = false;\n    }\n    int **res = (int **)malloc(MAX_SIZE * sizeof(int *));\n    *returnSize = 0;\n\n    backtrack(state, 0, nums, numsSize, selected, res, returnSize);\n\n    free(state);\n    free(selected);\n\n    return res;\n}\n</code></pre> permutations_ii.kt<pre><code>/* Алгоритм бэктрекинга: все перестановки II */\nfun backtrack(\n    state: MutableList&lt;Int&gt;,\n    choices: IntArray,\n    selected: BooleanArray,\n    res: MutableList&lt;MutableList&lt;Int&gt;?&gt;\n) {\n    // Когда длина состояния равна числу элементов, записать решение\n    if (state.size == choices.size) {\n        res.add(state.toMutableList())\n        return\n    }\n    // Перебор всех вариантов выбора\n    val duplicated = HashSet&lt;Int&gt;()\n    for (i in choices.indices) {\n        val choice = choices[i]\n        // Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n        if (!selected[i] &amp;&amp; !duplicated.contains(choice)) {\n            // Попытка: сделать выбор и обновить состояние\n            duplicated.add(choice) // Записать значения уже выбранных элементов\n            selected[i] = true\n            state.add(choice)\n            // Перейти к следующему выбору\n            backtrack(state, choices, selected, res)\n            // Откат: отменить выбор и восстановить предыдущее состояние\n            selected[i] = false\n            state.removeAt(state.size - 1)\n        }\n    }\n}\n\n/* Все перестановки II */\nfun permutationsII(nums: IntArray): MutableList&lt;MutableList&lt;Int&gt;?&gt; {\n    val res = mutableListOf&lt;MutableList&lt;Int&gt;?&gt;()\n    backtrack(mutableListOf(), nums, BooleanArray(nums.size), res)\n    return res\n}\n</code></pre> permutations_ii.rb<pre><code>### Алгоритм бэктрекинга: все перестановки II ###\ndef backtrack(state, choices, selected, res)\n  # Когда длина состояния равна числу элементов, записать решение\n  if state.length == choices.length\n    res &lt;&lt; state.dup\n    return\n  end\n\n  # Перебор всех вариантов выбора\n  duplicated = Set.new\n  choices.each_with_index do |choice, i|\n    # Отсечение: нельзя выбирать один и тот же элемент повторно и нельзя повторно выбирать равные элементы\n    if !selected[i] &amp;&amp; !duplicated.include?(choice)\n      # Попытка: сделать выбор и обновить состояние\n      duplicated.add(choice)\n      selected[i] = true\n      state &lt;&lt; choice\n      # Перейти к следующему выбору\n      backtrack(state, choices, selected, res)\n      # Откат: отменить выбор и восстановить предыдущее состояние\n      selected[i] = false\n      state.pop\n    end\n  end\nend\n\n### Все перестановки II ###\ndef permutations_ii(nums)\n  res = []\n  backtrack([], nums, Array.new(nums.length, false), res)\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Если предположить, что все элементы попарно различны, то из \\(n\\) элементов можно получить \\(n!\\) перестановок; при записи результата требуется копировать список длины \\(n\\) , что занимает \\(O(n)\\) времени. Следовательно, временная сложность равна \\(O(n!n)\\) .</p> <p>Максимальная глубина рекурсии равна \\(n\\) , что требует \\(O(n)\\) стековой памяти. Массив <code>selected</code> занимает \\(O(n)\\) пространства. Одновременно может существовать до \\(n\\) хеш-множеств <code>duplicated</code> , что дает \\(O(n^2)\\) памяти. Следовательно, пространственная сложность равна \\(O(n^2)\\) .</p>","path":["Глава 13. Поиск с возвратом","13.2 &nbsp; Задача о перестановках"],"tags":[]},{"location":"chapter_backtracking/permutations_problem/#3","level":3,"title":"3.   Сравнение двух видов обрезки","text":"<p>Обратите внимание: хотя и <code>selected</code> , и <code>duplicated</code> используются для обрезки, их цели различаются.</p> <ul> <li>Обрезка повторного выбора: во всем процессе поиска существует только один <code>selected</code> . Он записывает, какие элементы уже входят в текущее состояние, и нужен для того, чтобы один и тот же элемент не появлялся в <code>state</code> дважды.</li> <li>Обрезка равных элементов: каждый раунд выбора (каждый вызов <code>backtrack</code>) содержит собственный <code>duplicated</code> . Он записывает, какие элементы уже выбирались в текущем раунде (<code>for</code> цикле), и нужен для того, чтобы равные элементы выбирались только один раз.</li> </ul> <p>На рисунке 13-9 показана область действия двух условий обрезки. Помните, что каждый узел дерева соответствует одному выбору, а путь от корня до листа образует одну перестановку.</p> <p></p> <p> Рисунок 13-9   Область действия двух условий обрезки </p>","path":["Глава 13. Поиск с возвратом","13.2 &nbsp; Задача о перестановках"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/","level":1,"title":"13.3   Задача о сумме подмножеств","text":"","path":["Глава 13. Поиск с возвратом","13.3 &nbsp; Задача о сумме подмножеств"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#1331","level":2,"title":"13.3.1   Случай без повторяющихся элементов","text":"<p>Question</p> <p>Дан массив положительных целых чисел <code>nums</code> и целое положительное значение <code>target</code> . Найдите все возможные комбинации, сумма элементов которых равна <code>target</code> . Во входном массиве нет повторяющихся элементов, и каждый элемент можно выбирать неограниченное число раз. Верните эти комбинации в виде списка; в результате не должно быть повторяющихся комбинаций.</p> <p>Например, для входного множества \\(\\{3, 4, 5\\}\\) и целевого значения \\(9\\) решениями будут \\(\\{3, 3, 3\\}\\) и \\(\\{4, 5\\}\\) . При этом важно учитывать два обстоятельства.</p> <ul> <li>Элементы входного множества можно выбирать повторно неограниченное число раз.</li> <li>Подмножество не различает порядок элементов, поэтому \\(\\{4, 5\\}\\) и \\(\\{5, 4\\}\\) считаются одним и тем же подмножеством.</li> </ul>","path":["Глава 13. Поиск с возвратом","13.3 &nbsp; Задача о сумме подмножеств"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#1","level":3,"title":"1.   Отталкиваемся от решения задачи о перестановках","text":"<p>Как и в задаче о перестановках, можно представлять построение подмножеств как результат последовательности выборов и во время выбора динамически обновлять \"сумму элементов\"; когда эта сумма становится равной <code>target</code> , соответствующее подмножество записывается в список результатов.</p> <p>Однако в отличие от задачи о перестановках в этой задаче элементы множества можно выбирать неограниченное число раз, поэтому нам не нужен булев список <code>selected</code> для записи того, был ли выбран элемент. Можно слегка изменить код для перестановок и получить первоначальную версию решения:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby subset_sum_i_naive.py<pre><code>def backtrack(\n    state: list[int],\n    target: int,\n    total: int,\n    choices: list[int],\n    res: list[list[int]],\n):\n    \"\"\"Алгоритм бэктрекинга: сумма подмножеств I\"\"\"\n    # Если сумма подмножества равна target, записать решение\n    if total == target:\n        res.append(list(state))\n        return\n    # Перебор всех вариантов выбора\n    for i in range(len(choices)):\n        # Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n        if total + choices[i] &gt; target:\n            continue\n        # Попытка: сделать выбор и обновить элемент и total\n        state.append(choices[i])\n        # Перейти к следующему выбору\n        backtrack(state, target, total + choices[i], choices, res)\n        # Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop()\n\ndef subset_sum_i_naive(nums: list[int], target: int) -&gt; list[list[int]]:\n    \"\"\"Решить задачу суммы подмножеств I (с повторяющимися подмножествами)\"\"\"\n    state = []  # Состояние (подмножество)\n    total = 0  # Сумма подмножеств\n    res = []  # Список результатов (список подмножеств)\n    backtrack(state, target, total, nums, res)\n    return res\n</code></pre> subset_sum_i_naive.cpp<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nvoid backtrack(vector&lt;int&gt; &amp;state, int target, int total, vector&lt;int&gt; &amp;choices, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n    // Если сумма подмножества равна target, записать решение\n    if (total == target) {\n        res.push_back(state);\n        return;\n    }\n    // Перебор всех вариантов выбора\n    for (size_t i = 0; i &lt; choices.size(); i++) {\n        // Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n        if (total + choices[i] &gt; target) {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить элемент и total\n        state.push_back(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target, total + choices[i], choices, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop_back();\n    }\n}\n\n/* Решить задачу суммы подмножеств I (с повторяющимися подмножествами) */\nvector&lt;vector&lt;int&gt;&gt; subsetSumINaive(vector&lt;int&gt; &amp;nums, int target) {\n    vector&lt;int&gt; state;       // Состояние (подмножество)\n    int total = 0;           // Сумма подмножеств\n    vector&lt;vector&lt;int&gt;&gt; res; // Список результатов (список подмножеств)\n    backtrack(state, target, total, nums, res);\n    return res;\n}\n</code></pre> subset_sum_i_naive.java<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nvoid backtrack(List&lt;Integer&gt; state, int target, int total, int[] choices, List&lt;List&lt;Integer&gt;&gt; res) {\n    // Если сумма подмножества равна target, записать решение\n    if (total == target) {\n        res.add(new ArrayList&lt;&gt;(state));\n        return;\n    }\n    // Перебор всех вариантов выбора\n    for (int i = 0; i &lt; choices.length; i++) {\n        // Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n        if (total + choices[i] &gt; target) {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить элемент и total\n        state.add(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target, total + choices[i], choices, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.remove(state.size() - 1);\n    }\n}\n\n/* Решить задачу суммы подмножеств I (с повторяющимися подмножествами) */\nList&lt;List&lt;Integer&gt;&gt; subsetSumINaive(int[] nums, int target) {\n    List&lt;Integer&gt; state = new ArrayList&lt;&gt;(); // Состояние (подмножество)\n    int total = 0; // Сумма подмножеств\n    List&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;&gt;(); // Список результатов (список подмножеств)\n    backtrack(state, target, total, nums, res);\n    return res;\n}\n</code></pre> subset_sum_i_naive.cs<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nvoid Backtrack(List&lt;int&gt; state, int target, int total, int[] choices, List&lt;List&lt;int&gt;&gt; res) {\n    // Если сумма подмножества равна target, записать решение\n    if (total == target) {\n        res.Add(new List&lt;int&gt;(state));\n        return;\n    }\n    // Перебор всех вариантов выбора\n    for (int i = 0; i &lt; choices.Length; i++) {\n        // Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n        if (total + choices[i] &gt; target) {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить элемент и total\n        state.Add(choices[i]);\n        // Перейти к следующему выбору\n        Backtrack(state, target, total + choices[i], choices, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.RemoveAt(state.Count - 1);\n    }\n}\n\n/* Решить задачу суммы подмножеств I (с повторяющимися подмножествами) */\nList&lt;List&lt;int&gt;&gt; SubsetSumINaive(int[] nums, int target) {\n    List&lt;int&gt; state = []; // Состояние (подмножество)\n    int total = 0; // Сумма подмножеств\n    List&lt;List&lt;int&gt;&gt; res = []; // Список результатов (список подмножеств)\n    Backtrack(state, target, total, nums, res);\n    return res;\n}\n</code></pre> subset_sum_i_naive.go<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nfunc backtrackSubsetSumINaive(total, target int, state, choices *[]int, res *[][]int) {\n    // Если сумма подмножества равна target, записать решение\n    if target == total {\n        newState := append([]int{}, *state...)\n        *res = append(*res, newState)\n        return\n    }\n    // Перебор всех вариантов выбора\n    for i := 0; i &lt; len(*choices); i++ {\n        // Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n        if total+(*choices)[i] &gt; target {\n            continue\n        }\n        // Попытка: сделать выбор и обновить элемент и total\n        *state = append(*state, (*choices)[i])\n        // Перейти к следующему выбору\n        backtrackSubsetSumINaive(total+(*choices)[i], target, state, choices, res)\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        *state = (*state)[:len(*state)-1]\n    }\n}\n\n/* Решить задачу суммы подмножеств I (с повторяющимися подмножествами) */\nfunc subsetSumINaive(nums []int, target int) [][]int {\n    state := make([]int, 0) // Состояние (подмножество)\n    total := 0              // Сумма подмножеств\n    res := make([][]int, 0) // Список результатов (список подмножеств)\n    backtrackSubsetSumINaive(total, target, &amp;state, &amp;nums, &amp;res)\n    return res\n}\n</code></pre> subset_sum_i_naive.swift<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nfunc backtrack(state: inout [Int], target: Int, total: Int, choices: [Int], res: inout [[Int]]) {\n    // Если сумма подмножества равна target, записать решение\n    if total == target {\n        res.append(state)\n        return\n    }\n    // Перебор всех вариантов выбора\n    for i in choices.indices {\n        // Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n        if total + choices[i] &gt; target {\n            continue\n        }\n        // Попытка: сделать выбор и обновить элемент и total\n        state.append(choices[i])\n        // Перейти к следующему выбору\n        backtrack(state: &amp;state, target: target, total: total + choices[i], choices: choices, res: &amp;res)\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.removeLast()\n    }\n}\n\n/* Решить задачу суммы подмножеств I (с повторяющимися подмножествами) */\nfunc subsetSumINaive(nums: [Int], target: Int) -&gt; [[Int]] {\n    var state: [Int] = [] // Состояние (подмножество)\n    let total = 0 // Сумма подмножеств\n    var res: [[Int]] = [] // Список результатов (список подмножеств)\n    backtrack(state: &amp;state, target: target, total: total, choices: nums, res: &amp;res)\n    return res\n}\n</code></pre> subset_sum_i_naive.js<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nfunction backtrack(state, target, total, choices, res) {\n    // Если сумма подмножества равна target, записать решение\n    if (total === target) {\n        res.push([...state]);\n        return;\n    }\n    // Перебор всех вариантов выбора\n    for (let i = 0; i &lt; choices.length; i++) {\n        // Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n        if (total + choices[i] &gt; target) {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить элемент и total\n        state.push(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target, total + choices[i], choices, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop();\n    }\n}\n\n/* Решить задачу суммы подмножеств I (с повторяющимися подмножествами) */\nfunction subsetSumINaive(nums, target) {\n    const state = []; // Состояние (подмножество)\n    const total = 0; // Сумма подмножеств\n    const res = []; // Список результатов (список подмножеств)\n    backtrack(state, target, total, nums, res);\n    return res;\n}\n</code></pre> subset_sum_i_naive.ts<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nfunction backtrack(\n    state: number[],\n    target: number,\n    total: number,\n    choices: number[],\n    res: number[][]\n): void {\n    // Если сумма подмножества равна target, записать решение\n    if (total === target) {\n        res.push([...state]);\n        return;\n    }\n    // Перебор всех вариантов выбора\n    for (let i = 0; i &lt; choices.length; i++) {\n        // Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n        if (total + choices[i] &gt; target) {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить элемент и total\n        state.push(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target, total + choices[i], choices, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop();\n    }\n}\n\n/* Решить задачу суммы подмножеств I (с повторяющимися подмножествами) */\nfunction subsetSumINaive(nums: number[], target: number): number[][] {\n    const state = []; // Состояние (подмножество)\n    const total = 0; // Сумма подмножеств\n    const res = []; // Список результатов (список подмножеств)\n    backtrack(state, target, total, nums, res);\n    return res;\n}\n</code></pre> subset_sum_i_naive.dart<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nvoid backtrack(\n  List&lt;int&gt; state,\n  int target,\n  int total,\n  List&lt;int&gt; choices,\n  List&lt;List&lt;int&gt;&gt; res,\n) {\n  // Если сумма подмножества равна target, записать решение\n  if (total == target) {\n    res.add(List.from(state));\n    return;\n  }\n  // Перебор всех вариантов выбора\n  for (int i = 0; i &lt; choices.length; i++) {\n    // Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n    if (total + choices[i] &gt; target) {\n      continue;\n    }\n    // Попытка: сделать выбор и обновить элемент и total\n    state.add(choices[i]);\n    // Перейти к следующему выбору\n    backtrack(state, target, total + choices[i], choices, res);\n    // Откат: отменить выбор и восстановить предыдущее состояние\n    state.removeLast();\n  }\n}\n\n/* Решить задачу суммы подмножеств I (с повторяющимися подмножествами) */\nList&lt;List&lt;int&gt;&gt; subsetSumINaive(List&lt;int&gt; nums, int target) {\n  List&lt;int&gt; state = []; // Состояние (подмножество)\n  int total = 0; // Сумма элементов\n  List&lt;List&lt;int&gt;&gt; res = []; // Список результатов (список подмножеств)\n  backtrack(state, target, total, nums, res);\n  return res;\n}\n</code></pre> subset_sum_i_naive.rs<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nfn backtrack(\n    state: &amp;mut Vec&lt;i32&gt;,\n    target: i32,\n    total: i32,\n    choices: &amp;[i32],\n    res: &amp;mut Vec&lt;Vec&lt;i32&gt;&gt;,\n) {\n    // Если сумма подмножества равна target, записать решение\n    if total == target {\n        res.push(state.clone());\n        return;\n    }\n    // Перебор всех вариантов выбора\n    for i in 0..choices.len() {\n        // Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n        if total + choices[i] &gt; target {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить элемент и total\n        state.push(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target, total + choices[i], choices, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop();\n    }\n}\n\n/* Решить задачу суммы подмножеств I (с повторяющимися подмножествами) */\nfn subset_sum_i_naive(nums: &amp;[i32], target: i32) -&gt; Vec&lt;Vec&lt;i32&gt;&gt; {\n    let mut state = Vec::new(); // Состояние (подмножество)\n    let total = 0; // Сумма подмножеств\n    let mut res = Vec::new(); // Список результатов (список подмножеств)\n    backtrack(&amp;mut state, target, total, nums, &amp;mut res);\n    res\n}\n</code></pre> subset_sum_i_naive.c<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nvoid backtrack(int target, int total, int *choices, int choicesSize) {\n    // Если сумма подмножества равна target, записать решение\n    if (total == target) {\n        for (int i = 0; i &lt; stateSize; i++) {\n            res[resSize][i] = state[i];\n        }\n        resColSizes[resSize++] = stateSize;\n        return;\n    }\n    // Перебор всех вариантов выбора\n    for (int i = 0; i &lt; choicesSize; i++) {\n        // Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n        if (total + choices[i] &gt; target) {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить элемент и total\n        state[stateSize++] = choices[i];\n        // Перейти к следующему выбору\n        backtrack(target, total + choices[i], choices, choicesSize);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        stateSize--;\n    }\n}\n\n/* Решить задачу суммы подмножеств I (с повторяющимися подмножествами) */\nvoid subsetSumINaive(int *nums, int numsSize, int target) {\n    resSize = 0; // Инициализировать число решений нулем\n    backtrack(target, 0, nums, numsSize);\n}\n</code></pre> subset_sum_i_naive.kt<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nfun backtrack(\n    state: MutableList&lt;Int&gt;,\n    target: Int,\n    total: Int,\n    choices: IntArray,\n    res: MutableList&lt;MutableList&lt;Int&gt;?&gt;\n) {\n    // Если сумма подмножества равна target, записать решение\n    if (total == target) {\n        res.add(state.toMutableList())\n        return\n    }\n    // Перебор всех вариантов выбора\n    for (i in choices.indices) {\n        // Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n        if (total + choices[i] &gt; target) {\n            continue\n        }\n        // Попытка: сделать выбор и обновить элемент и total\n        state.add(choices[i])\n        // Перейти к следующему выбору\n        backtrack(state, target, total + choices[i], choices, res)\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.removeAt(state.size - 1)\n    }\n}\n\n/* Решить задачу суммы подмножеств I (с повторяющимися подмножествами) */\nfun subsetSumINaive(nums: IntArray, target: Int): MutableList&lt;MutableList&lt;Int&gt;?&gt; {\n    val state = mutableListOf&lt;Int&gt;() // Состояние (подмножество)\n    val total = 0 // Сумма подмножеств\n    val res = mutableListOf&lt;MutableList&lt;Int&gt;?&gt;() // Список результатов (список подмножеств)\n    backtrack(state, target, total, nums, res)\n    return res\n}\n</code></pre> subset_sum_i_naive.rb<pre><code>### Алгоритм бэктрекинга: сумма подмножеств I ###\ndef backtrack(state, target, total, choices, res)\n  # Если сумма подмножества равна target, записать решение\n  if total == target\n    res &lt;&lt; state.dup\n    return\n  end\n\n  # Перебор всех вариантов выбора\n  for i in 0...choices.length\n    # Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n    next if total + choices[i] &gt; target\n    # Попытка: сделать выбор и обновить элемент и total\n    state &lt;&lt; choices[i]\n    # Перейти к следующему выбору\n    backtrack(state, target, total + choices[i], choices, res)\n    # Откат: отменить выбор и восстановить предыдущее состояние\n    state.pop\n  end\nend\n\n### Алгоритм бэктрекинга: сумма подмножеств I ###\ndef backtrack(state, target, total, choices, res)\n  # Если сумма подмножества равна target, записать решение\n  if total == target\n    res &lt;&lt; state.dup\n    return\n  end\n\n  # Перебор всех вариантов выбора\n  for i in 0...choices.length\n    # Отсечение: если сумма подмножества превышает target, пропустить этот выбор\n    next if total + choices[i] &gt; target\n    # Попытка: сделать выбор и обновить элемент и total\n    state &lt;&lt; choices[i]\n    # Перейти к следующему выбору\n    backtrack(state, target, total + choices[i], choices, res)\n    # Откат: отменить выбор и восстановить предыдущее состояние\n    state.pop\n  end\nend\n\n# ## Решить задачу суммы подмножеств I (с повторяющимися подмножествами) ###\ndef subset_sum_i_naive(nums, target)\n  state = [] # Состояние (подмножество)\n  total = 0 # Сумма подмножеств\n  res = [] # Список результатов (список подмножеств)\n  backtrack(state, target, total, nums, res)\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Если подать на этот код массив \\([3, 4, 5]\\) и целевое значение \\(9\\) , то на выходе мы получим \\([3, 3, 3], [4, 5], [5, 4]\\) . Хотя все подмножества с суммой \\(9\\) успешно найдены, среди них все же присутствуют дубликаты: \\([4, 5]\\) и \\([5, 4]\\) .</p> <p>Причина в том, что процесс поиска различает порядок выбора, тогда как для подмножеств порядок не важен. Как показано на рисунке 13-10, сначала выбрать \\(4\\) , а затем \\(5\\) , и сначала выбрать \\(5\\) , а затем \\(4\\) - это разные ветви поиска, но им соответствует одно и то же подмножество.</p> <p></p> <p> Рисунок 13-10   Поиск подмножеств и обрезка по выходу за границу </p> <p>Чтобы убрать повторяющиеся подмножества, одна из прямых идей - удалить дубликаты уже из итогового списка результатов. Но это решение малоэффективно по двум причинам.</p> <ul> <li>Когда массив содержит много элементов, а особенно когда <code>target</code> велик, процесс поиска порождает огромное число повторяющихся подмножеств.</li> <li>Сравнение подмножеств (то есть массивов) само по себе довольно затратно: сначала приходится сортировать массивы, а затем поэлементно сравнивать их.</li> </ul>","path":["Глава 13. Поиск с возвратом","13.3 &nbsp; Задача о сумме подмножеств"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#2","level":3,"title":"2.   Обрезка повторяющихся подмножеств","text":"<p>Поэтому стоит выполнять устранение дубликатов прямо во время поиска, с помощью обрезки. Посмотрите на рисунок 13-11: повторяющиеся подмножества возникают тогда, когда элементы массива выбираются в разном порядке, например так.</p> <ol> <li>Если в первом и втором раундах выбрать соответственно \\(3\\) и \\(4\\) , то будут сгенерированы все подмножества, содержащие эти два элемента, и их можно обозначить как \\([3, 4, \\dots]\\) .</li> <li>После этого, если в первом раунде выбрать \\(4\\) , то во втором раунде нужно пропустить \\(3\\) , потому что подмножества \\([4, 3, \\dots]\\) полностью дублируют подмножества, уже построенные на шаге <code>1.</code> .</li> </ol> <p>Во время поиска варианты на каждом уровне пробуются по одному слева направо, поэтому чем правее ветвь, тем больше ветвей оказывается отсечено.</p> <ol> <li>В первых двух раундах выбираются \\(3\\) и \\(5\\) , что дает подмножества \\([3, 5, \\dots]\\) .</li> <li>В первых двух раундах выбираются \\(4\\) и \\(5\\) , что дает подмножества \\([4, 5, \\dots]\\) .</li> <li>Если же в первом раунде выбрать \\(5\\) , то во втором раунде нужно пропустить \\(3\\) и \\(4\\) , потому что подмножества \\([5, 3, \\dots]\\) и \\([5, 4, \\dots]\\) полностью дублируют случаи, описанные в шагах <code>1.</code> и <code>2.</code> .</li> </ol> <p></p> <p> Рисунок 13-11   Повторяющиеся подмножества из-за разного порядка выбора </p> <p>В общем виде, если входной массив имеет вид \\([x_1, x_2, \\dots, x_n]\\) , а последовательность выборов в ходе поиска равна \\([x_{i_1}, x_{i_2}, \\dots, x_{i_m}]\\) , то она должна удовлетворять условию \\(i_1 \\leq i_2 \\leq \\dots \\leq i_m\\) ; все последовательности выборов, не удовлетворяющие этому условию, приводят к дубликатам и должны отсекаться.</p>","path":["Глава 13. Поиск с возвратом","13.3 &nbsp; Задача о сумме подмножеств"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#3","level":3,"title":"3.   Реализация кода","text":"<p>Чтобы реализовать такую обрезку, инициализируем переменную <code>start</code> , которая будет указывать начальную точку обхода. После выбора элемента \\(x_i\\) следующий раунд начинается с индекса \\(i\\). Благодаря этому последовательность выборов всегда удовлетворяет условию \\(i_1 \\leq i_2 \\leq \\dots \\leq i_m\\) , а значит, каждое подмножество создается только один раз.</p> <p>Помимо этого, мы внесем в код еще два улучшения.</p> <ul> <li>Перед началом поиска отсортируем массив <code>nums</code> . Тогда при обходе всех вариантов можно сразу прервать цикл, как только сумма подмножества превысит <code>target</code> , потому что все последующие элементы будут еще больше и их сумма тоже превысит <code>target</code> .</li> <li>Откажемся от отдельной переменной суммы <code>total</code> и будем учитывать сумму через вычитание из <code>target</code> ; когда <code>target</code> станет равным \\(0\\) , решение фиксируется.</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby subset_sum_i.py<pre><code>def backtrack(\n    state: list[int], target: int, choices: list[int], start: int, res: list[list[int]]\n):\n    \"\"\"Алгоритм бэктрекинга: сумма подмножеств I\"\"\"\n    # Если сумма подмножества равна target, записать решение\n    if target == 0:\n        res.append(list(state))\n        return\n    # Обойти все варианты выбора\n    # Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    for i in range(start, len(choices)):\n        # Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        # Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if target - choices[i] &lt; 0:\n            break\n        # Попытка: сделать выбор и обновить target и start\n        state.append(choices[i])\n        # Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i, res)\n        # Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop()\n\ndef subset_sum_i(nums: list[int], target: int) -&gt; list[list[int]]:\n    \"\"\"Решить задачу суммы подмножеств I\"\"\"\n    state = []  # Состояние (подмножество)\n    nums.sort()  # Отсортировать nums\n    start = 0  # Стартовая вершина обхода\n    res = []  # Список результатов (список подмножеств)\n    backtrack(state, target, nums, start, res)\n    return res\n</code></pre> subset_sum_i.cpp<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nvoid backtrack(vector&lt;int&gt; &amp;state, int target, vector&lt;int&gt; &amp;choices, int start, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n    // Если сумма подмножества равна target, записать решение\n    if (target == 0) {\n        res.push_back(state);\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    for (int i = start; i &lt; choices.size(); i++) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.push_back(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop_back();\n    }\n}\n\n/* Решить задачу суммы подмножеств I */\nvector&lt;vector&lt;int&gt;&gt; subsetSumI(vector&lt;int&gt; &amp;nums, int target) {\n    vector&lt;int&gt; state;              // Состояние (подмножество)\n    sort(nums.begin(), nums.end()); // Отсортировать nums\n    int start = 0;                  // Стартовая вершина обхода\n    vector&lt;vector&lt;int&gt;&gt; res;        // Список результатов (список подмножеств)\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_i.java<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nvoid backtrack(List&lt;Integer&gt; state, int target, int[] choices, int start, List&lt;List&lt;Integer&gt;&gt; res) {\n    // Если сумма подмножества равна target, записать решение\n    if (target == 0) {\n        res.add(new ArrayList&lt;&gt;(state));\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    for (int i = start; i &lt; choices.length; i++) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.add(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.remove(state.size() - 1);\n    }\n}\n\n/* Решить задачу суммы подмножеств I */\nList&lt;List&lt;Integer&gt;&gt; subsetSumI(int[] nums, int target) {\n    List&lt;Integer&gt; state = new ArrayList&lt;&gt;(); // Состояние (подмножество)\n    Arrays.sort(nums); // Отсортировать nums\n    int start = 0; // Стартовая вершина обхода\n    List&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;&gt;(); // Список результатов (список подмножеств)\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_i.cs<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nvoid Backtrack(List&lt;int&gt; state, int target, int[] choices, int start, List&lt;List&lt;int&gt;&gt; res) {\n    // Если сумма подмножества равна target, записать решение\n    if (target == 0) {\n        res.Add(new List&lt;int&gt;(state));\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    for (int i = start; i &lt; choices.Length; i++) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.Add(choices[i]);\n        // Перейти к следующему выбору\n        Backtrack(state, target - choices[i], choices, i, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.RemoveAt(state.Count - 1);\n    }\n}\n\n/* Решить задачу суммы подмножеств I */\nList&lt;List&lt;int&gt;&gt; SubsetSumI(int[] nums, int target) {\n    List&lt;int&gt; state = []; // Состояние (подмножество)\n    Array.Sort(nums); // Отсортировать nums\n    int start = 0; // Стартовая вершина обхода\n    List&lt;List&lt;int&gt;&gt; res = []; // Список результатов (список подмножеств)\n    Backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_i.go<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nfunc backtrackSubsetSumI(start, target int, state, choices *[]int, res *[][]int) {\n    // Если сумма подмножества равна target, записать решение\n    if target == 0 {\n        newState := append([]int{}, *state...)\n        *res = append(*res, newState)\n        return\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    for i := start; i &lt; len(*choices); i++ {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if target-(*choices)[i] &lt; 0 {\n            break\n        }\n        // Попытка: сделать выбор и обновить target и start\n        *state = append(*state, (*choices)[i])\n        // Перейти к следующему выбору\n        backtrackSubsetSumI(i, target-(*choices)[i], state, choices, res)\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        *state = (*state)[:len(*state)-1]\n    }\n}\n\n/* Решить задачу суммы подмножеств I */\nfunc subsetSumI(nums []int, target int) [][]int {\n    state := make([]int, 0) // Состояние (подмножество)\n    sort.Ints(nums)         // Отсортировать nums\n    start := 0              // Стартовая вершина обхода\n    res := make([][]int, 0) // Список результатов (список подмножеств)\n    backtrackSubsetSumI(start, target, &amp;state, &amp;nums, &amp;res)\n    return res\n}\n</code></pre> subset_sum_i.swift<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nfunc backtrack(state: inout [Int], target: Int, choices: [Int], start: Int, res: inout [[Int]]) {\n    // Если сумма подмножества равна target, записать решение\n    if target == 0 {\n        res.append(state)\n        return\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    for i in choices.indices.dropFirst(start) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if target - choices[i] &lt; 0 {\n            break\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.append(choices[i])\n        // Перейти к следующему выбору\n        backtrack(state: &amp;state, target: target - choices[i], choices: choices, start: i, res: &amp;res)\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.removeLast()\n    }\n}\n\n/* Решить задачу суммы подмножеств I */\nfunc subsetSumI(nums: [Int], target: Int) -&gt; [[Int]] {\n    var state: [Int] = [] // Состояние (подмножество)\n    let nums = nums.sorted() // Отсортировать nums\n    let start = 0 // Стартовая вершина обхода\n    var res: [[Int]] = [] // Список результатов (список подмножеств)\n    backtrack(state: &amp;state, target: target, choices: nums, start: start, res: &amp;res)\n    return res\n}\n</code></pre> subset_sum_i.js<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nfunction backtrack(state, target, choices, start, res) {\n    // Если сумма подмножества равна target, записать решение\n    if (target === 0) {\n        res.push([...state]);\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    for (let i = start; i &lt; choices.length; i++) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.push(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop();\n    }\n}\n\n/* Решить задачу суммы подмножеств I */\nfunction subsetSumI(nums, target) {\n    const state = []; // Состояние (подмножество)\n    nums.sort((a, b) =&gt; a - b); // Отсортировать nums\n    const start = 0; // Стартовая вершина обхода\n    const res = []; // Список результатов (список подмножеств)\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_i.ts<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nfunction backtrack(\n    state: number[],\n    target: number,\n    choices: number[],\n    start: number,\n    res: number[][]\n): void {\n    // Если сумма подмножества равна target, записать решение\n    if (target === 0) {\n        res.push([...state]);\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    for (let i = start; i &lt; choices.length; i++) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.push(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop();\n    }\n}\n\n/* Решить задачу суммы подмножеств I */\nfunction subsetSumI(nums: number[], target: number): number[][] {\n    const state = []; // Состояние (подмножество)\n    nums.sort((a, b) =&gt; a - b); // Отсортировать nums\n    const start = 0; // Стартовая вершина обхода\n    const res = []; // Список результатов (список подмножеств)\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_i.dart<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nvoid backtrack(\n  List&lt;int&gt; state,\n  int target,\n  List&lt;int&gt; choices,\n  int start,\n  List&lt;List&lt;int&gt;&gt; res,\n) {\n  // Если сумма подмножества равна target, записать решение\n  if (target == 0) {\n    res.add(List.from(state));\n    return;\n  }\n  // Обойти все варианты выбора\n  // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n  for (int i = start; i &lt; choices.length; i++) {\n    // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n    // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n    if (target - choices[i] &lt; 0) {\n      break;\n    }\n    // Попытка: сделать выбор и обновить target и start\n    state.add(choices[i]);\n    // Перейти к следующему выбору\n    backtrack(state, target - choices[i], choices, i, res);\n    // Откат: отменить выбор и восстановить предыдущее состояние\n    state.removeLast();\n  }\n}\n\n/* Решить задачу суммы подмножеств I */\nList&lt;List&lt;int&gt;&gt; subsetSumI(List&lt;int&gt; nums, int target) {\n  List&lt;int&gt; state = []; // Состояние (подмножество)\n  nums.sort(); // Отсортировать nums\n  int start = 0; // Стартовая вершина обхода\n  List&lt;List&lt;int&gt;&gt; res = []; // Список результатов (список подмножеств)\n  backtrack(state, target, nums, start, res);\n  return res;\n}\n</code></pre> subset_sum_i.rs<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nfn backtrack(\n    state: &amp;mut Vec&lt;i32&gt;,\n    target: i32,\n    choices: &amp;[i32],\n    start: usize,\n    res: &amp;mut Vec&lt;Vec&lt;i32&gt;&gt;,\n) {\n    // Если сумма подмножества равна target, записать решение\n    if target == 0 {\n        res.push(state.clone());\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    for i in start..choices.len() {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if target - choices[i] &lt; 0 {\n            break;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.push(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop();\n    }\n}\n\n/* Решить задачу суммы подмножеств I */\nfn subset_sum_i(nums: &amp;mut [i32], target: i32) -&gt; Vec&lt;Vec&lt;i32&gt;&gt; {\n    let mut state = Vec::new(); // Состояние (подмножество)\n    nums.sort(); // Отсортировать nums\n    let start = 0; // Стартовая вершина обхода\n    let mut res = Vec::new(); // Список результатов (список подмножеств)\n    backtrack(&amp;mut state, target, nums, start, &amp;mut res);\n    res\n}\n</code></pre> subset_sum_i.c<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nvoid backtrack(int target, int *choices, int choicesSize, int start) {\n    // Если сумма подмножества равна target, записать решение\n    if (target == 0) {\n        for (int i = 0; i &lt; stateSize; ++i) {\n            res[resSize][i] = state[i];\n        }\n        resColSizes[resSize++] = stateSize;\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    for (int i = start; i &lt; choicesSize; i++) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state[stateSize] = choices[i];\n        stateSize++;\n        // Перейти к следующему выбору\n        backtrack(target - choices[i], choices, choicesSize, i);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        stateSize--;\n    }\n}\n\n/* Решить задачу суммы подмножеств I */\nvoid subsetSumI(int *nums, int numsSize, int target) {\n    qsort(nums, numsSize, sizeof(int), cmp); // Отсортировать nums\n    int start = 0;                           // Стартовая вершина обхода\n    backtrack(target, nums, numsSize, start);\n}\n</code></pre> subset_sum_i.kt<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств I */\nfun backtrack(\n    state: MutableList&lt;Int&gt;,\n    target: Int,\n    choices: IntArray,\n    start: Int,\n    res: MutableList&lt;MutableList&lt;Int&gt;?&gt;\n) {\n    // Если сумма подмножества равна target, записать решение\n    if (target == 0) {\n        res.add(state.toMutableList())\n        return\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    for (i in start..&lt;choices.size) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.add(choices[i])\n        // Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i, res)\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.removeAt(state.size - 1)\n    }\n}\n\n/* Решить задачу суммы подмножеств I */\nfun subsetSumI(nums: IntArray, target: Int): MutableList&lt;MutableList&lt;Int&gt;?&gt; {\n    val state = mutableListOf&lt;Int&gt;() // Состояние (подмножество)\n    nums.sort() // Отсортировать nums\n    val start = 0 // Стартовая вершина обхода\n    val res = mutableListOf&lt;MutableList&lt;Int&gt;?&gt;() // Список результатов (список подмножеств)\n    backtrack(state, target, nums, start, res)\n    return res\n}\n</code></pre> subset_sum_i.rb<pre><code>### Алгоритм бэктрекинга: сумма подмножеств I ###\ndef backtrack(state, target, choices, start, res)\n  # Если сумма подмножества равна target, записать решение\n  if target.zero?\n    res &lt;&lt; state.dup\n    return\n  end\n  # Обойти все варианты выбора\n  # Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n  for i in start...choices.length\n    # Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n    # Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n    break if target - choices[i] &lt; 0\n    # Попытка: сделать выбор и обновить target и start\n    state &lt;&lt; choices[i]\n    # Перейти к следующему выбору\n    backtrack(state, target - choices[i], choices, i, res)\n    # Откат: отменить выбор и восстановить предыдущее состояние\n    state.pop\n  end\nend\n\n### Решить задачу суммы подмножеств I ###\ndef subset_sum_i(nums, target)\n  state = [] # Состояние (подмножество)\n  nums.sort! # Отсортировать nums\n  start = 0 # Стартовая вершина обхода\n  res = [] # Список результатов (список подмножеств)\n  backtrack(state, target, nums, start, res)\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>На рисунке 13-12 показан полный процесс поиска с возвратом для массива \\([3, 4, 5]\\) и целевого значения \\(9\\) .</p> <p></p> <p> Рисунок 13-12   Процесс поиска с возвратом для задачи о сумме подмножеств I </p>","path":["Глава 13. Поиск с возвратом","13.3 &nbsp; Задача о сумме подмножеств"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#1332","level":2,"title":"13.3.2   Учет повторяющихся элементов","text":"<p>Question</p> <p>Дан массив положительных целых чисел <code>nums</code> и целое положительное значение <code>target</code> . Найдите все возможные комбинации, сумма элементов которых равна <code>target</code> . Во входном массиве могут присутствовать повторяющиеся элементы, и каждый элемент разрешено выбирать только один раз. Верните эти комбинации в виде списка; в результате не должно быть повторяющихся комбинаций.</p> <p>По сравнению с предыдущей задачей во входном массиве теперь могут присутствовать повторяющиеся элементы, и это создает новую проблему. Например, если дан массив \\([4, \\hat{4}, 5]\\) и целевое значение \\(9\\) , то существующий код вернет результат \\([4, 5], [\\hat{4}, 5]\\) , то есть с повторяющимся подмножеством.</p> <p>Причина появления дублей в том, что равные элементы выбираются несколько раз в одном и том же раунде. На рисунке 13-13 в первом раунде существует три варианта выбора, и два из них равны \\(4\\) ; из-за этого появляются две дублирующиеся ветви поиска и, соответственно, повторяющиеся подмножества. Точно так же два элемента \\(4\\) во втором раунде тоже порождают дубликаты.</p> <p></p> <p> Рисунок 13-13   Повторяющиеся подмножества из-за равных элементов </p>","path":["Глава 13. Поиск с возвратом","13.3 &nbsp; Задача о сумме подмножеств"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#1_1","level":3,"title":"1.   Обрезка равных элементов","text":"<p>Чтобы решить эту проблему, нужно ограничить выбор равных элементов так, чтобы в каждом раунде каждый из них выбирался только один раз. Реализуется это довольно естественно: поскольку массив отсортирован, равные элементы стоят рядом. Значит, если в текущем раунде текущий элемент равен соседнему слева, то этот вариант уже был рассмотрен, и текущий элемент нужно пропустить.</p> <p>Одновременно по условию этой задачи каждый элемент массива можно выбрать только один раз. К счастью, это ограничение тоже можно реализовать через переменную <code>start</code> : после выбора элемента \\(x_i\\) следующий раунд начинается с индекса \\(i + 1\\) . Так мы одновременно убираем повторяющиеся подмножества и исключаем повторный выбор одного и того же элемента.</p>","path":["Глава 13. Поиск с возвратом","13.3 &nbsp; Задача о сумме подмножеств"],"tags":[]},{"location":"chapter_backtracking/subset_sum_problem/#2_1","level":3,"title":"2.   Реализация кода","text":"PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby subset_sum_ii.py<pre><code>def backtrack(\n    state: list[int], target: int, choices: list[int], start: int, res: list[list[int]]\n):\n    \"\"\"Алгоритм бэктрекинга: сумма подмножеств II\"\"\"\n    # Если сумма подмножества равна target, записать решение\n    if target == 0:\n        res.append(list(state))\n        return\n    # Обойти все варианты выбора\n    # Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    # Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n    for i in range(start, len(choices)):\n        # Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        # Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if target - choices[i] &lt; 0:\n            break\n        # Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n        if i &gt; start and choices[i] == choices[i - 1]:\n            continue\n        # Попытка: сделать выбор и обновить target и start\n        state.append(choices[i])\n        # Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i + 1, res)\n        # Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop()\n\ndef subset_sum_ii(nums: list[int], target: int) -&gt; list[list[int]]:\n    \"\"\"Решить задачу суммы подмножеств II\"\"\"\n    state = []  # Состояние (подмножество)\n    nums.sort()  # Отсортировать nums\n    start = 0  # Стартовая вершина обхода\n    res = []  # Список результатов (список подмножеств)\n    backtrack(state, target, nums, start, res)\n    return res\n</code></pre> subset_sum_ii.cpp<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств II */\nvoid backtrack(vector&lt;int&gt; &amp;state, int target, vector&lt;int&gt; &amp;choices, int start, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n    // Если сумма подмножества равна target, записать решение\n    if (target == 0) {\n        res.push_back(state);\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    // Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n    for (int i = start; i &lt; choices.size(); i++) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n        if (i &gt; start &amp;&amp; choices[i] == choices[i - 1]) {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.push_back(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i + 1, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop_back();\n    }\n}\n\n/* Решить задачу суммы подмножеств II */\nvector&lt;vector&lt;int&gt;&gt; subsetSumII(vector&lt;int&gt; &amp;nums, int target) {\n    vector&lt;int&gt; state;              // Состояние (подмножество)\n    sort(nums.begin(), nums.end()); // Отсортировать nums\n    int start = 0;                  // Стартовая вершина обхода\n    vector&lt;vector&lt;int&gt;&gt; res;        // Список результатов (список подмножеств)\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_ii.java<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств II */\nvoid backtrack(List&lt;Integer&gt; state, int target, int[] choices, int start, List&lt;List&lt;Integer&gt;&gt; res) {\n    // Если сумма подмножества равна target, записать решение\n    if (target == 0) {\n        res.add(new ArrayList&lt;&gt;(state));\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    // Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n    for (int i = start; i &lt; choices.length; i++) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n        if (i &gt; start &amp;&amp; choices[i] == choices[i - 1]) {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.add(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i + 1, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.remove(state.size() - 1);\n    }\n}\n\n/* Решить задачу суммы подмножеств II */\nList&lt;List&lt;Integer&gt;&gt; subsetSumII(int[] nums, int target) {\n    List&lt;Integer&gt; state = new ArrayList&lt;&gt;(); // Состояние (подмножество)\n    Arrays.sort(nums); // Отсортировать nums\n    int start = 0; // Стартовая вершина обхода\n    List&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;&gt;(); // Список результатов (список подмножеств)\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_ii.cs<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств II */\nvoid Backtrack(List&lt;int&gt; state, int target, int[] choices, int start, List&lt;List&lt;int&gt;&gt; res) {\n    // Если сумма подмножества равна target, записать решение\n    if (target == 0) {\n        res.Add(new List&lt;int&gt;(state));\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    // Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n    for (int i = start; i &lt; choices.Length; i++) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n        if (i &gt; start &amp;&amp; choices[i] == choices[i - 1]) {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.Add(choices[i]);\n        // Перейти к следующему выбору\n        Backtrack(state, target - choices[i], choices, i + 1, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.RemoveAt(state.Count - 1);\n    }\n}\n\n/* Решить задачу суммы подмножеств II */\nList&lt;List&lt;int&gt;&gt; SubsetSumII(int[] nums, int target) {\n    List&lt;int&gt; state = []; // Состояние (подмножество)\n    Array.Sort(nums); // Отсортировать nums\n    int start = 0; // Стартовая вершина обхода\n    List&lt;List&lt;int&gt;&gt; res = []; // Список результатов (список подмножеств)\n    Backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_ii.go<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств II */\nfunc backtrackSubsetSumII(start, target int, state, choices *[]int, res *[][]int) {\n    // Если сумма подмножества равна target, записать решение\n    if target == 0 {\n        newState := append([]int{}, *state...)\n        *res = append(*res, newState)\n        return\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    // Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n    for i := start; i &lt; len(*choices); i++ {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if target-(*choices)[i] &lt; 0 {\n            break\n        }\n        // Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n        if i &gt; start &amp;&amp; (*choices)[i] == (*choices)[i-1] {\n            continue\n        }\n        // Попытка: сделать выбор и обновить target и start\n        *state = append(*state, (*choices)[i])\n        // Перейти к следующему выбору\n        backtrackSubsetSumII(i+1, target-(*choices)[i], state, choices, res)\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        *state = (*state)[:len(*state)-1]\n    }\n}\n\n/* Решить задачу суммы подмножеств II */\nfunc subsetSumII(nums []int, target int) [][]int {\n    state := make([]int, 0) // Состояние (подмножество)\n    sort.Ints(nums)         // Отсортировать nums\n    start := 0              // Стартовая вершина обхода\n    res := make([][]int, 0) // Список результатов (список подмножеств)\n    backtrackSubsetSumII(start, target, &amp;state, &amp;nums, &amp;res)\n    return res\n}\n</code></pre> subset_sum_ii.swift<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств II */\nfunc backtrack(state: inout [Int], target: Int, choices: [Int], start: Int, res: inout [[Int]]) {\n    // Если сумма подмножества равна target, записать решение\n    if target == 0 {\n        res.append(state)\n        return\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    // Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n    for i in choices.indices.dropFirst(start) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if target - choices[i] &lt; 0 {\n            break\n        }\n        // Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n        if i &gt; start, choices[i] == choices[i - 1] {\n            continue\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.append(choices[i])\n        // Перейти к следующему выбору\n        backtrack(state: &amp;state, target: target - choices[i], choices: choices, start: i + 1, res: &amp;res)\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.removeLast()\n    }\n}\n\n/* Решить задачу суммы подмножеств II */\nfunc subsetSumII(nums: [Int], target: Int) -&gt; [[Int]] {\n    var state: [Int] = [] // Состояние (подмножество)\n    let nums = nums.sorted() // Отсортировать nums\n    let start = 0 // Стартовая вершина обхода\n    var res: [[Int]] = [] // Список результатов (список подмножеств)\n    backtrack(state: &amp;state, target: target, choices: nums, start: start, res: &amp;res)\n    return res\n}\n</code></pre> subset_sum_ii.js<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств II */\nfunction backtrack(state, target, choices, start, res) {\n    // Если сумма подмножества равна target, записать решение\n    if (target === 0) {\n        res.push([...state]);\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    // Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n    for (let i = start; i &lt; choices.length; i++) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n        if (i &gt; start &amp;&amp; choices[i] === choices[i - 1]) {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.push(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i + 1, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop();\n    }\n}\n\n/* Решить задачу суммы подмножеств II */\nfunction subsetSumII(nums, target) {\n    const state = []; // Состояние (подмножество)\n    nums.sort((a, b) =&gt; a - b); // Отсортировать nums\n    const start = 0; // Стартовая вершина обхода\n    const res = []; // Список результатов (список подмножеств)\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_ii.ts<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств II */\nfunction backtrack(\n    state: number[],\n    target: number,\n    choices: number[],\n    start: number,\n    res: number[][]\n): void {\n    // Если сумма подмножества равна target, записать решение\n    if (target === 0) {\n        res.push([...state]);\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    // Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n    for (let i = start; i &lt; choices.length; i++) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n        if (i &gt; start &amp;&amp; choices[i] === choices[i - 1]) {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.push(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i + 1, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop();\n    }\n}\n\n/* Решить задачу суммы подмножеств II */\nfunction subsetSumII(nums: number[], target: number): number[][] {\n    const state = []; // Состояние (подмножество)\n    nums.sort((a, b) =&gt; a - b); // Отсортировать nums\n    const start = 0; // Стартовая вершина обхода\n    const res = []; // Список результатов (список подмножеств)\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_ii.dart<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств II */\nvoid backtrack(\n  List&lt;int&gt; state,\n  int target,\n  List&lt;int&gt; choices,\n  int start,\n  List&lt;List&lt;int&gt;&gt; res,\n) {\n  // Если сумма подмножества равна target, записать решение\n  if (target == 0) {\n    res.add(List.from(state));\n    return;\n  }\n  // Обойти все варианты выбора\n  // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n  // Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n  for (int i = start; i &lt; choices.length; i++) {\n    // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n    // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n    if (target - choices[i] &lt; 0) {\n      break;\n    }\n    // Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n    if (i &gt; start &amp;&amp; choices[i] == choices[i - 1]) {\n      continue;\n    }\n    // Попытка: сделать выбор и обновить target и start\n    state.add(choices[i]);\n    // Перейти к следующему выбору\n    backtrack(state, target - choices[i], choices, i + 1, res);\n    // Откат: отменить выбор и восстановить предыдущее состояние\n    state.removeLast();\n  }\n}\n\n/* Решить задачу суммы подмножеств II */\nList&lt;List&lt;int&gt;&gt; subsetSumII(List&lt;int&gt; nums, int target) {\n  List&lt;int&gt; state = []; // Состояние (подмножество)\n  nums.sort(); // Отсортировать nums\n  int start = 0; // Стартовая вершина обхода\n  List&lt;List&lt;int&gt;&gt; res = []; // Список результатов (список подмножеств)\n  backtrack(state, target, nums, start, res);\n  return res;\n}\n</code></pre> subset_sum_ii.rs<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств II */\nfn backtrack(\n    state: &amp;mut Vec&lt;i32&gt;,\n    target: i32,\n    choices: &amp;[i32],\n    start: usize,\n    res: &amp;mut Vec&lt;Vec&lt;i32&gt;&gt;,\n) {\n    // Если сумма подмножества равна target, записать решение\n    if target == 0 {\n        res.push(state.clone());\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    // Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n    for i in start..choices.len() {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if target - choices[i] &lt; 0 {\n            break;\n        }\n        // Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n        if i &gt; start &amp;&amp; choices[i] == choices[i - 1] {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.push(choices[i]);\n        // Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i + 1, res);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.pop();\n    }\n}\n\n/* Решить задачу суммы подмножеств II */\nfn subset_sum_ii(nums: &amp;mut [i32], target: i32) -&gt; Vec&lt;Vec&lt;i32&gt;&gt; {\n    let mut state = Vec::new(); // Состояние (подмножество)\n    nums.sort(); // Отсортировать nums\n    let start = 0; // Стартовая вершина обхода\n    let mut res = Vec::new(); // Список результатов (список подмножеств)\n    backtrack(&amp;mut state, target, nums, start, &amp;mut res);\n    res\n}\n</code></pre> subset_sum_ii.c<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств II */\nvoid backtrack(int target, int *choices, int choicesSize, int start) {\n    // Если сумма подмножества равна target, записать решение\n    if (target == 0) {\n        for (int i = 0; i &lt; stateSize; i++) {\n            res[resSize][i] = state[i];\n        }\n        resColSizes[resSize++] = stateSize;\n        return;\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    // Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n    for (int i = start; i &lt; choicesSize; i++) {\n        // Отсечение 1: если сумма подмножества превышает target, сразу пропустить\n        if (target - choices[i] &lt; 0) {\n            continue;\n        }\n        // Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n        if (i &gt; start &amp;&amp; choices[i] == choices[i - 1]) {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state[stateSize] = choices[i];\n        stateSize++;\n        // Перейти к следующему выбору\n        backtrack(target - choices[i], choices, choicesSize, i + 1);\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        stateSize--;\n    }\n}\n\n/* Решить задачу суммы подмножеств II */\nvoid subsetSumII(int *nums, int numsSize, int target) {\n    // Отсортировать nums\n    qsort(nums, numsSize, sizeof(int), cmp);\n    // Начать бэктрекинг\n    backtrack(target, nums, numsSize, 0);\n}\n</code></pre> subset_sum_ii.kt<pre><code>/* Алгоритм бэктрекинга: сумма подмножеств II */\nfun backtrack(\n    state: MutableList&lt;Int&gt;,\n    target: Int,\n    choices: IntArray,\n    start: Int,\n    res: MutableList&lt;MutableList&lt;Int&gt;?&gt;\n) {\n    // Если сумма подмножества равна target, записать решение\n    if (target == 0) {\n        res.add(state.toMutableList())\n        return\n    }\n    // Обойти все варианты выбора\n    // Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n    // Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n    for (i in start..&lt;choices.size) {\n        // Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n        // Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n        if (target - choices[i] &lt; 0) {\n            break\n        }\n        // Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n        if (i &gt; start &amp;&amp; choices[i] == choices[i - 1]) {\n            continue\n        }\n        // Попытка: сделать выбор и обновить target и start\n        state.add(choices[i])\n        // Перейти к следующему выбору\n        backtrack(state, target - choices[i], choices, i + 1, res)\n        // Откат: отменить выбор и восстановить предыдущее состояние\n        state.removeAt(state.size - 1)\n    }\n}\n\n/* Решить задачу суммы подмножеств II */\nfun subsetSumII(nums: IntArray, target: Int): MutableList&lt;MutableList&lt;Int&gt;?&gt; {\n    val state = mutableListOf&lt;Int&gt;() // Состояние (подмножество)\n    nums.sort() // Отсортировать nums\n    val start = 0 // Стартовая вершина обхода\n    val res = mutableListOf&lt;MutableList&lt;Int&gt;?&gt;() // Список результатов (список подмножеств)\n    backtrack(state, target, nums, start, res)\n    return res\n}\n</code></pre> subset_sum_ii.rb<pre><code>### Алгоритм бэктрекинга: сумма подмножеств II ###\ndef backtrack(state, target, choices, start, res)\n  # Если сумма подмножества равна target, записать решение\n  if target.zero?\n    res &lt;&lt; state.dup\n    return\n  end\n\n  # Обойти все варианты выбора\n  # Отсечение 2: начинать обход с start, чтобы избежать генерации повторяющихся подмножеств\n  # Отсечение 3: начинать обход с start, чтобы избежать повторного выбора одного и того же элемента\n  for i in start...choices.length\n    # Отсечение 1: если сумма подмножества превышает target, немедленно завершить цикл\n    # Это связано с тем, что массив уже отсортирован, следующие элементы больше, и сумма подмножества точно превысит target\n    break if target - choices[i] &lt; 0\n    # Отсечение 4: если этот элемент равен элементу слева, значит ветвь поиска повторяется, ее нужно сразу пропустить\n    next if i &gt; start &amp;&amp; choices[i] == choices[i - 1]\n    # Попытка: сделать выбор и обновить target и start\n    state &lt;&lt; choices[i]\n    # Перейти к следующему выбору\n    backtrack(state, target - choices[i], choices, i + 1, res)\n    # Откат: отменить выбор и восстановить предыдущее состояние\n    state.pop\n  end\nend\n\n### Решить задачу суммы подмножеств II ###\ndef subset_sum_ii(nums, target)\n  state = [] # Состояние (подмножество)\n  nums.sort! # Отсортировать nums\n  start = 0 # Стартовая вершина обхода\n  res = [] # Список результатов (список подмножеств)\n  backtrack(state, target, nums, start, res)\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>На рисунке 13-14 показан процесс поиска с возвратом для массива \\([4, 4, 5]\\) и целевого значения \\(9\\) . В нем используются четыре вида обрезки. Попробуйте сопоставить рисунок с комментариями в коде, чтобы понять полный процесс поиска и то, как работает каждый тип обрезки.</p> <p></p> <p> Рисунок 13-14   Процесс поиска с возвратом для задачи о сумме подмножеств II </p>","path":["Глава 13. Поиск с возвратом","13.3 &nbsp; Задача о сумме подмножеств"],"tags":[]},{"location":"chapter_backtracking/summary/","level":1,"title":"13.5   Резюме","text":"","path":["Глава 13. Поиск с возвратом","13.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_backtracking/summary/#1","level":3,"title":"1.   Ключевые выводы","text":"<ul> <li>Алгоритм поиска с возвратом по своей сути является методом полного перебора: он ищет решения путем обхода пространства решений в глубину. Во время поиска он фиксирует решения, удовлетворяющие условиям, пока не найдет все такие решения или пока обход не завершится.</li> <li>Процесс поиска с возвратом состоит из двух частей: попытки и отката. Он с помощью поиска в глубину пробует разные варианты выбора; когда встречается состояние, не удовлетворяющее ограничениям, алгоритм отменяет предыдущий выбор, возвращается к прошлому состоянию и продолжает пробовать другие варианты. Попытка и откат являются двумя противоположными по направлению действиями.</li> <li>Задачи поиска с возвратом обычно содержат несколько ограничений, которые можно использовать для обрезки. Обрезка позволяет заранее завершать ненужные ветви поиска и тем самым значительно повышать эффективность.</li> <li>Алгоритм поиска с возвратом в первую очередь применяется для решения поисковых задач и задач с ограничениями. Задачи комбинаторной оптимизации тоже можно решать с его помощью, но для них часто существуют более эффективные или более подходящие методы.</li> <li>Задача о перестановках нацелена на поиск всех возможных перестановок элементов данного множества. Мы используем массив для записи того, был ли выбран каждый элемент, и отсекаем ветви, где один и тот же элемент выбирается повторно, чтобы гарантировать однократный выбор каждого элемента.</li> <li>В задаче о перестановках, если во множестве присутствуют повторяющиеся элементы, в итоговом результате возникнут повторяющиеся перестановки. Поэтому нужно ограничить выбор равных элементов так, чтобы в каждом раунде каждый из них выбирался только один раз; обычно это реализуется с помощью хеш-множества.</li> <li>Цель задачи о сумме подмножеств - найти все подмножества данного множества, сумма которых равна целевому значению. В множестве порядок элементов не важен, однако процесс поиска порождает результаты во всех возможных порядках, из-за чего появляются повторяющиеся подмножества. Поэтому перед запуском поиска с возвратом мы сортируем данные и вводим переменную, указывающую начальную точку обхода в каждом раунде, чтобы отсечь ветви, создающие дубликаты.</li> <li>В задаче о сумме подмножеств равные элементы массива также порождают повторяющиеся множества. При наличии предварительной сортировки их можно отсекать, проверяя равенство соседних элементов, и тем самым гарантировать, что в каждом раунде равные элементы будут выбираться только один раз.</li> <li>Задача о \\(n\\) ферзях состоит в поиске способов разместить \\(n\\) ферзей на доске размера \\(n \\times n\\) так, чтобы никакие два ферзя не атаковали друг друга. Ограничения этой задачи включают строки, столбцы, главные диагонали и побочные диагонали. Чтобы выполнить ограничение по строкам, используется построчная стратегия размещения, гарантирующая по одному ферзю в каждой строке.</li> <li>Обработка ограничений по столбцам и диагоналям устроена похожим образом. Для ограничения по столбцам используется массив, фиксирующий наличие ферзя в каждом столбце. Для диагоналей используются два массива, записывающие наличие ферзей на главных и побочных диагоналях. Основная сложность здесь состоит в том, чтобы найти закономерность индексов строк и столбцов клеток, лежащих на одной и той же главной или побочной диагонали.</li> </ul>","path":["Глава 13. Поиск с возвратом","13.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_backtracking/summary/#2","level":3,"title":"2.   Вопросы и ответы","text":"<p>Q: Как понять связь между поиском с возвратом и рекурсией?</p> <p>В целом поиск с возвратом - это скорее \"алгоритмическая стратегия\", а рекурсия больше похожа на \"инструмент\".</p> <ul> <li>Алгоритмы поиска с возвратом обычно реализуются на основе рекурсии. Однако поиск с возвратом - это лишь один из вариантов применения рекурсии, а именно ее использование в поисковых задачах.</li> <li>Структура рекурсии отражает парадигму разбиения на подзадачи и часто применяется для решения задач \"разделяй и властвуй\", поиска с возвратом, динамического программирования (мемоизированной рекурсии) и других подобных задач.</li> </ul>","path":["Глава 13. Поиск с возвратом","13.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_computational_complexity/","level":1,"title":"Глава 2.   Анализ сложности","text":"<p>Abstract</p> <p>Анализ сложности подобен пространственно-временному проводнику в необъятной вселенной алгоритмов.</p> <p>Он ведет нас в глубину двух измерений - времени и пространства, помогая искать более изящные решения.</p>","path":["Глава 2. Анализ сложности","Глава 2. &nbsp; Анализ сложности"],"tags":[]},{"location":"chapter_computational_complexity/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>2.1   Оценка эффективности алгоритмов</li> <li>2.2   Итерация и рекурсия</li> <li>2.3   Временная сложность</li> <li>2.4   Пространственная сложность</li> <li>2.5   Резюме</li> </ul>","path":["Глава 2. Анализ сложности","Глава 2. &nbsp; Анализ сложности"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/","level":1,"title":"2.2   Итерация и рекурсия","text":"<p>В алгоритмах часто требуется повторное выполнение определенной задачи, что тесно связано с анализом сложности. Поэтому, прежде чем перейти к обсуждению временной и пространственной сложности, рассмотрим, как реализовать повторное выполнение задач в программе, а именно две основные структуры управления программой: итерацию и рекурсию.</p>","path":["Глава 2. Анализ сложности","2.2 &nbsp; Итерация и рекурсия"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#221","level":2,"title":"2.2.1   Итерация","text":"<p>Итерация (iteration) - это структура управления, которая позволяет повторно выполнять определенную задачу. В итерации программа повторяет выполнение определенного участка кода, пока выполняется определенное условие.</p>","path":["Глава 2. Анализ сложности","2.2 &nbsp; Итерация и рекурсия"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#1-for","level":3,"title":"1.   Цикл for","text":"<p>Цикл <code>for</code> - одна из наиболее распространенных форм итерации, которая подходит для использования, когда количество итераций известно заранее.</p> <p>Следующая функция реализует суммирование \\(1 + 2 + \\dots + n\\) с использованием цикла <code>for</code> , а результат суммирования сохраняется в переменной <code>res</code> . Следует отметить, что в Python диапазон <code>range(a, b)</code> соответствует левому закрытому, правому открытому интервалу, то есть перебираются значения \\(a, a + 1, \\dots, b-1\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby iteration.py<pre><code>def for_loop(n: int) -&gt; int:\n    \"\"\"Цикл for\"\"\"\n    res = 0\n    # Циклическое суммирование 1, 2, ..., n-1, n\n    for i in range(1, n + 1):\n        res += i\n    return res\n</code></pre> iteration.cpp<pre><code>/* Цикл for */\nint forLoop(int n) {\n    int res = 0;\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    for (int i = 1; i &lt;= n; ++i) {\n        res += i;\n    }\n    return res;\n}\n</code></pre> iteration.java<pre><code>/* Цикл for */\nint forLoop(int n) {\n    int res = 0;\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    for (int i = 1; i &lt;= n; i++) {\n        res += i;\n    }\n    return res;\n}\n</code></pre> iteration.cs<pre><code>/* Цикл for */\nint ForLoop(int n) {\n    int res = 0;\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    for (int i = 1; i &lt;= n; i++) {\n        res += i;\n    }\n    return res;\n}\n</code></pre> iteration.go<pre><code>/* Цикл for */\nfunc forLoop(n int) int {\n    res := 0\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    for i := 1; i &lt;= n; i++ {\n        res += i\n    }\n    return res\n}\n</code></pre> iteration.swift<pre><code>/* Цикл for */\nfunc forLoop(n: Int) -&gt; Int {\n    var res = 0\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    for i in 1 ... n {\n        res += i\n    }\n    return res\n}\n</code></pre> iteration.js<pre><code>/* Цикл for */\nfunction forLoop(n) {\n    let res = 0;\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    for (let i = 1; i &lt;= n; i++) {\n        res += i;\n    }\n    return res;\n}\n</code></pre> iteration.ts<pre><code>/* Цикл for */\nfunction forLoop(n: number): number {\n    let res = 0;\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    for (let i = 1; i &lt;= n; i++) {\n        res += i;\n    }\n    return res;\n}\n</code></pre> iteration.dart<pre><code>/* Цикл for */\nint forLoop(int n) {\n  int res = 0;\n  // Циклическое суммирование 1, 2, ..., n-1, n\n  for (int i = 1; i &lt;= n; i++) {\n    res += i;\n  }\n  return res;\n}\n</code></pre> iteration.rs<pre><code>/* Цикл for */\nfn for_loop(n: i32) -&gt; i32 {\n    let mut res = 0;\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    for i in 1..=n {\n        res += i;\n    }\n    res\n}\n</code></pre> iteration.c<pre><code>/* Цикл for */\nint forLoop(int n) {\n    int res = 0;\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    for (int i = 1; i &lt;= n; i++) {\n        res += i;\n    }\n    return res;\n}\n</code></pre> iteration.kt<pre><code>/* Цикл for */\nfun forLoop(n: Int): Int {\n    var res = 0\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    for (i in 1..n) {\n        res += i\n    }\n    return res\n}\n</code></pre> iteration.rb<pre><code>### Цикл for ###\ndef for_loop(n)\n  res = 0\n\n  # Циклическое суммирование 1, 2, ..., n-1, n\n  for i in 1..n\n    res += i\n  end\n\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Ниже представлена блок-схема этой функции суммирования.</p> <p></p> <p> Рисунок 2-1   Блок-схема функции суммирования </p> <p>Количество операций этой функции суммирования пропорционально размеру входных данных \\(n\\) , или, другими словами, линейно зависит от него. На самом деле временная сложность описывает именно эту линейную зависимость. Соответствующий материал будет подробно рассмотрен в следующем разделе.</p>","path":["Глава 2. Анализ сложности","2.2 &nbsp; Итерация и рекурсия"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#2-while","level":3,"title":"2.   Цикл while","text":"<p>Подобно циклу <code>for</code> , цикл <code>while</code> также представляет собой метод реализации итерации. В цикле <code>while</code> программа перед каждой итерацией проверяет условие: если условие истинно, то выполнение продолжается, иначе цикл завершается.</p> <p>Ниже приведен пример реализации суммирования \\(1 + 2 + \\dots + n\\) с использованием цикла <code>while</code> :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby iteration.py<pre><code>def while_loop(n: int) -&gt; int:\n    \"\"\"Цикл while\"\"\"\n    res = 0\n    i = 1  # Инициализация условной переменной\n    # Циклическое суммирование 1, 2, ..., n-1, n\n    while i &lt;= n:\n        res += i\n        i += 1  # Обновить условную переменную\n    return res\n</code></pre> iteration.cpp<pre><code>/* Цикл while */\nint whileLoop(int n) {\n    int res = 0;\n    int i = 1; // Инициализация условной переменной\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    while (i &lt;= n) {\n        res += i;\n        i++; // Обновить условную переменную\n    }\n    return res;\n}\n</code></pre> iteration.java<pre><code>/* Цикл while */\nint whileLoop(int n) {\n    int res = 0;\n    int i = 1; // Инициализация условной переменной\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    while (i &lt;= n) {\n        res += i;\n        i++; // Обновить условную переменную\n    }\n    return res;\n}\n</code></pre> iteration.cs<pre><code>/* Цикл while */\nint WhileLoop(int n) {\n    int res = 0;\n    int i = 1; // Инициализация условной переменной\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    while (i &lt;= n) {\n        res += i;\n        i += 1; // Обновить условную переменную\n    }\n    return res;\n}\n</code></pre> iteration.go<pre><code>/* Цикл while */\nfunc whileLoop(n int) int {\n    res := 0\n    // Инициализация условной переменной\n    i := 1\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    for i &lt;= n {\n        res += i\n        // Обновить условную переменную\n        i++\n    }\n    return res\n}\n</code></pre> iteration.swift<pre><code>/* Цикл while */\nfunc whileLoop(n: Int) -&gt; Int {\n    var res = 0\n    var i = 1 // Инициализация условной переменной\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    while i &lt;= n {\n        res += i\n        i += 1 // Обновить условную переменную\n    }\n    return res\n}\n</code></pre> iteration.js<pre><code>/* Цикл while */\nfunction whileLoop(n) {\n    let res = 0;\n    let i = 1; // Инициализация условной переменной\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    while (i &lt;= n) {\n        res += i;\n        i++; // Обновить условную переменную\n    }\n    return res;\n}\n</code></pre> iteration.ts<pre><code>/* Цикл while */\nfunction whileLoop(n: number): number {\n    let res = 0;\n    let i = 1; // Инициализация условной переменной\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    while (i &lt;= n) {\n        res += i;\n        i++; // Обновить условную переменную\n    }\n    return res;\n}\n</code></pre> iteration.dart<pre><code>/* Цикл while */\nint whileLoop(int n) {\n  int res = 0;\n  int i = 1; // Инициализация условной переменной\n  // Циклическое суммирование 1, 2, ..., n-1, n\n  while (i &lt;= n) {\n    res += i;\n    i++; // Обновить условную переменную\n  }\n  return res;\n}\n</code></pre> iteration.rs<pre><code>/* Цикл while */\nfn while_loop(n: i32) -&gt; i32 {\n    let mut res = 0;\n    let mut i = 1; // Инициализация условной переменной\n\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    while i &lt;= n {\n        res += i;\n        i += 1; // Обновить условную переменную\n    }\n    res\n}\n</code></pre> iteration.c<pre><code>/* Цикл while */\nint whileLoop(int n) {\n    int res = 0;\n    int i = 1; // Инициализация условной переменной\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    while (i &lt;= n) {\n        res += i;\n        i++; // Обновить условную переменную\n    }\n    return res;\n}\n</code></pre> iteration.kt<pre><code>/* Цикл while */\nfun whileLoop(n: Int): Int {\n    var res = 0\n    var i = 1 // Инициализация условной переменной\n    // Циклическое суммирование 1, 2, ..., n-1, n\n    while (i &lt;= n) {\n        res += i\n        i++ // Обновить условную переменную\n    }\n    return res\n}\n</code></pre> iteration.rb<pre><code>### Цикл while ###\ndef while_loop(n)\n  res = 0\n  i = 1 # Инициализация условной переменной\n\n  # Циклическое суммирование 1, 2, ..., n-1, n\n  while i &lt;= n\n    res += i\n    i += 1 # Обновить условную переменную\n  end\n\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>**Цикл <code>while</code> обладает большей степенью свободы по сравнению с циклом <code>for</code> **. В цикле <code>while</code> можно свободно управлять инициализацией и обновлением условной переменной.</p> <p>Например, в следующем коде условная переменная \\(i\\) обновляется дважды на каждой итерации, что затруднительно сделать с использованием цикла <code>for</code> :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby iteration.py<pre><code>def while_loop_ii(n: int) -&gt; int:\n    \"\"\"Цикл while (двойное обновление)\"\"\"\n    res = 0\n    i = 1  # Инициализация условной переменной\n    # Циклическое суммирование 1, 4, 10, ...\n    while i &lt;= n:\n        res += i\n        # Обновить условную переменную\n        i += 1\n        i *= 2\n    return res\n</code></pre> iteration.cpp<pre><code>/* Цикл while (двойное обновление) */\nint whileLoopII(int n) {\n    int res = 0;\n    int i = 1; // Инициализация условной переменной\n    // Циклическое суммирование 1, 4, 10, ...\n    while (i &lt;= n) {\n        res += i;\n        // Обновить условную переменную\n        i++;\n        i *= 2;\n    }\n    return res;\n}\n</code></pre> iteration.java<pre><code>/* Цикл while (двойное обновление) */\nint whileLoopII(int n) {\n    int res = 0;\n    int i = 1; // Инициализация условной переменной\n    // Циклическое суммирование 1, 4, 10, ...\n    while (i &lt;= n) {\n        res += i;\n        // Обновить условную переменную\n        i++;\n        i *= 2;\n    }\n    return res;\n}\n</code></pre> iteration.cs<pre><code>/* Цикл while (двойное обновление) */\nint WhileLoopII(int n) {\n    int res = 0;\n    int i = 1; // Инициализация условной переменной\n    // Циклическое суммирование 1, 4, 10, ...\n    while (i &lt;= n) {\n        res += i;\n        // Обновить условную переменную\n        i += 1; \n        i *= 2;\n    }\n    return res;\n}\n</code></pre> iteration.go<pre><code>/* Цикл while (двойное обновление) */\nfunc whileLoopII(n int) int {\n    res := 0\n    // Инициализация условной переменной\n    i := 1\n    // Циклическое суммирование 1, 4, 10, ...\n    for i &lt;= n {\n        res += i\n        // Обновить условную переменную\n        i++\n        i *= 2\n    }\n    return res\n}\n</code></pre> iteration.swift<pre><code>/* Цикл while (двойное обновление) */\nfunc whileLoopII(n: Int) -&gt; Int {\n    var res = 0\n    var i = 1 // Инициализация условной переменной\n    // Циклическое суммирование 1, 4, 10, ...\n    while i &lt;= n {\n        res += i\n        // Обновить условную переменную\n        i += 1\n        i *= 2\n    }\n    return res\n}\n</code></pre> iteration.js<pre><code>/* Цикл while (двойное обновление) */\nfunction whileLoopII(n) {\n    let res = 0;\n    let i = 1; // Инициализация условной переменной\n    // Циклическое суммирование 1, 4, 10, ...\n    while (i &lt;= n) {\n        res += i;\n        // Обновить условную переменную\n        i++;\n        i *= 2;\n    }\n    return res;\n}\n</code></pre> iteration.ts<pre><code>/* Цикл while (двойное обновление) */\nfunction whileLoopII(n: number): number {\n    let res = 0;\n    let i = 1; // Инициализация условной переменной\n    // Циклическое суммирование 1, 4, 10, ...\n    while (i &lt;= n) {\n        res += i;\n        // Обновить условную переменную\n        i++;\n        i *= 2;\n    }\n    return res;\n}\n</code></pre> iteration.dart<pre><code>/* Цикл while (двойное обновление) */\nint whileLoopII(int n) {\n  int res = 0;\n  int i = 1; // Инициализация условной переменной\n  // Циклическое суммирование 1, 4, 10, ...\n  while (i &lt;= n) {\n    res += i;\n    // Обновить условную переменную\n    i++;\n    i *= 2;\n  }\n  return res;\n}\n</code></pre> iteration.rs<pre><code>/* Цикл while (двойное обновление) */\nfn while_loop_ii(n: i32) -&gt; i32 {\n    let mut res = 0;\n    let mut i = 1; // Инициализация условной переменной\n\n    // Циклическое суммирование 1, 4, 10, ...\n    while i &lt;= n {\n        res += i;\n        // Обновить условную переменную\n        i += 1;\n        i *= 2;\n    }\n    res\n}\n</code></pre> iteration.c<pre><code>/* Цикл while (двойное обновление) */\nint whileLoopII(int n) {\n    int res = 0;\n    int i = 1; // Инициализация условной переменной\n    // Циклическое суммирование 1, 4, 10, ...\n    while (i &lt;= n) {\n        res += i;\n        // Обновить условную переменную\n        i++;\n        i *= 2;\n    }\n    return res;\n}\n</code></pre> iteration.kt<pre><code>/* Цикл while (двойное обновление) */\nfun whileLoopII(n: Int): Int {\n    var res = 0\n    var i = 1 // Инициализация условной переменной\n    // Циклическое суммирование 1, 4, 10, ...\n    while (i &lt;= n) {\n        res += i\n        // Обновить условную переменную\n        i++\n        i *= 2\n    }\n    return res\n}\n</code></pre> iteration.rb<pre><code>### Цикл while ###\ndef while_loop(n)\n  res = 0\n  i = 1 # Инициализация условной переменной\n\n  # Циклическое суммирование 1, 2, ..., n-1, n\n  while i &lt;= n\n    res += i\n    i += 1 # Обновить условную переменную\n  end\n\n  res\nend\n\n# ## Цикл while (двойное обновление) ###\ndef while_loop_ii(n)\n  res = 0\n  i = 1 # Инициализация условной переменной\n\n  # Циклическое суммирование 1, 4, 10, ...\n  while i &lt;= n\n    res += i\n    # Обновить условную переменную\n    i += 1\n    i *= 2\n  end\n\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>В целом код с использованием цикла <code>for</code> более компактный, а цикл <code>while</code> более гибкий. Но они оба могут реализовать итерационную структуру. Выбор между ними определяется требованиями конкретной задачи.</p>","path":["Глава 2. Анализ сложности","2.2 &nbsp; Итерация и рекурсия"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#3","level":3,"title":"3.   Вложенные циклы","text":"<p>Внутрь одной циклической структуры можно вложить другую, например используя два цикла <code>for</code> :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby iteration.py<pre><code>def nested_for_loop(n: int) -&gt; str:\n    \"\"\"Двойной цикл for\"\"\"\n    res = \"\"\n    # Цикл по i = 1, 2, ..., n-1, n\n    for i in range(1, n + 1):\n        # Цикл по j = 1, 2, ..., n-1, n\n        for j in range(1, n + 1):\n            res += f\"({i}, {j}), \"\n    return res\n</code></pre> iteration.cpp<pre><code>/* Двойной цикл for */\nstring nestedForLoop(int n) {\n    ostringstream res;\n    // Цикл по i = 1, 2, ..., n-1, n\n    for (int i = 1; i &lt;= n; ++i) {\n        // Цикл по j = 1, 2, ..., n-1, n\n        for (int j = 1; j &lt;= n; ++j) {\n            res &lt;&lt; \"(\" &lt;&lt; i &lt;&lt; \", \" &lt;&lt; j &lt;&lt; \"), \";\n        }\n    }\n    return res.str();\n}\n</code></pre> iteration.java<pre><code>/* Двойной цикл for */\nString nestedForLoop(int n) {\n    StringBuilder res = new StringBuilder();\n    // Цикл по i = 1, 2, ..., n-1, n\n    for (int i = 1; i &lt;= n; i++) {\n        // Цикл по j = 1, 2, ..., n-1, n\n        for (int j = 1; j &lt;= n; j++) {\n            res.append(\"(\" + i + \", \" + j + \"), \");\n        }\n    }\n    return res.toString();\n}\n</code></pre> iteration.cs<pre><code>/* Двойной цикл for */\nstring NestedForLoop(int n) {\n    StringBuilder res = new();\n    // Цикл по i = 1, 2, ..., n-1, n\n    for (int i = 1; i &lt;= n; i++) {\n        // Цикл по j = 1, 2, ..., n-1, n\n        for (int j = 1; j &lt;= n; j++) {\n            res.Append($\"({i}, {j}), \");\n        }\n    }\n    return res.ToString();\n}\n</code></pre> iteration.go<pre><code>/* Двойной цикл for */\nfunc nestedForLoop(n int) string {\n    res := \"\"\n    // Цикл по i = 1, 2, ..., n-1, n\n    for i := 1; i &lt;= n; i++ {\n        for j := 1; j &lt;= n; j++ {\n            // Цикл по j = 1, 2, ..., n-1, n\n            res += fmt.Sprintf(\"(%d, %d), \", i, j)\n        }\n    }\n    return res\n}\n</code></pre> iteration.swift<pre><code>/* Двойной цикл for */\nfunc nestedForLoop(n: Int) -&gt; String {\n    var res = \"\"\n    // Цикл по i = 1, 2, ..., n-1, n\n    for i in 1 ... n {\n        // Цикл по j = 1, 2, ..., n-1, n\n        for j in 1 ... n {\n            res.append(\"(\\(i), \\(j)), \")\n        }\n    }\n    return res\n}\n</code></pre> iteration.js<pre><code>/* Двойной цикл for */\nfunction nestedForLoop(n) {\n    let res = '';\n    // Цикл по i = 1, 2, ..., n-1, n\n    for (let i = 1; i &lt;= n; i++) {\n        // Цикл по j = 1, 2, ..., n-1, n\n        for (let j = 1; j &lt;= n; j++) {\n            res += `(${i}, ${j}), `;\n        }\n    }\n    return res;\n}\n</code></pre> iteration.ts<pre><code>/* Двойной цикл for */\nfunction nestedForLoop(n: number): string {\n    let res = '';\n    // Цикл по i = 1, 2, ..., n-1, n\n    for (let i = 1; i &lt;= n; i++) {\n        // Цикл по j = 1, 2, ..., n-1, n\n        for (let j = 1; j &lt;= n; j++) {\n            res += `(${i}, ${j}), `;\n        }\n    }\n    return res;\n}\n</code></pre> iteration.dart<pre><code>/* Двойной цикл for */\nString nestedForLoop(int n) {\n  String res = \"\";\n  // Цикл по i = 1, 2, ..., n-1, n\n  for (int i = 1; i &lt;= n; i++) {\n    // Цикл по j = 1, 2, ..., n-1, n\n    for (int j = 1; j &lt;= n; j++) {\n      res += \"($i, $j), \";\n    }\n  }\n  return res;\n}\n</code></pre> iteration.rs<pre><code>/* Двойной цикл for */\nfn nested_for_loop(n: i32) -&gt; String {\n    let mut res = vec![];\n    // Цикл по i = 1, 2, ..., n-1, n\n    for i in 1..=n {\n        // Цикл по j = 1, 2, ..., n-1, n\n        for j in 1..=n {\n            res.push(format!(\"({}, {}), \", i, j));\n        }\n    }\n    res.join(\"\")\n}\n</code></pre> iteration.c<pre><code>/* Двойной цикл for */\nchar *nestedForLoop(int n) {\n    // n * n — это число соответствующих точек, а максимальная длина строки \"(i, j), \" равна 6+10*2, плюс дополнительное место для завершающего нулевого символа \\0\n    int size = n * n * 26 + 1;\n    char *res = malloc(size * sizeof(char));\n    // Цикл по i = 1, 2, ..., n-1, n\n    for (int i = 1; i &lt;= n; i++) {\n        // Цикл по j = 1, 2, ..., n-1, n\n        for (int j = 1; j &lt;= n; j++) {\n            char tmp[26];\n            snprintf(tmp, sizeof(tmp), \"(%d, %d), \", i, j);\n            strncat(res, tmp, size - strlen(res) - 1);\n        }\n    }\n    return res;\n}\n</code></pre> iteration.kt<pre><code>/* Двойной цикл for */\nfun nestedForLoop(n: Int): String {\n    val res = StringBuilder()\n    // Цикл по i = 1, 2, ..., n-1, n\n    for (i in 1..n) {\n        // Цикл по j = 1, 2, ..., n-1, n\n        for (j in 1..n) {\n            res.append(\" ($i, $j), \")\n        }\n    }\n    return res.toString()\n}\n</code></pre> iteration.rb<pre><code>### Двойной цикл for ###\ndef nested_for_loop(n)\n  res = \"\"\n\n  # Цикл по i = 1, 2, ..., n-1, n\n  for i in 1..n\n    # Цикл по j = 1, 2, ..., n-1, n\n    for j in 1..n\n      res += \"(#{i}, #{j}), \"\n    end\n  end\n\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Ниже приведена блок-схема такого вложенного цикла.</p> <p></p> <p> Рисунок 2-2   Блок-схема вложенного цикла </p> <p>В этом случае количество выполненных действий пропорционально \\(n^2\\) , или, другими словами, время выполнения алгоритма и размер входных данных \\(n\\) находятся в квадратичной зависимости.</p> <p>Можно и дальше добавлять вложенные циклы, тогда каждое вложение будет повышать размерность, увеличивая временную сложность до кубической зависимости, зависимости четвертой степени и так далее.</p>","path":["Глава 2. Анализ сложности","2.2 &nbsp; Итерация и рекурсия"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#222","level":2,"title":"2.2.2   Рекурсия","text":"<p>Рекурсия (recursion) - это стратегия алгоритма, при которой функция вызывает саму себя для решения задачи. Она включает два основных этапа.</p> <ol> <li>Вызов: программа постоянно вызывает саму себя, обычно передавая меньшие или более упрощенные параметры, пока не будет достигнуто условие завершения.</li> <li>Возврат: после срабатывания условия завершения программа начинает возвращаться из самой глубокой рекурсивной функции, объединяя результаты каждого уровня.</li> </ol> <p>С точки зрения реализации рекурсивный код включает три основных элемента.</p> <ol> <li>Условие завершения: используется для определения момента перехода от вызова к возврату.</li> <li>Рекурсивный вызов: соответствует вызову, функция вызывает саму себя, обычно с меньшими или упрощенными параметрами.</li> <li>Возврат результата: соответствует возврату, возвращает результат текущего уровня рекурсии на предыдущий уровень.</li> </ol> <p>Рассмотрим следующий код: вызов функции <code>recur(n)</code> позволяет вычислить сумму \\(1 + 2 + \\dots + n\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby recursion.py<pre><code>def recur(n: int) -&gt; int:\n    \"\"\"Рекурсия\"\"\"\n    # Условие завершения\n    if n == 1:\n        return 1\n    # Рекурсия: рекурсивный вызов\n    res = recur(n - 1)\n    # Возврат: вернуть результат\n    return n + res\n</code></pre> recursion.cpp<pre><code>/* Рекурсия */\nint recur(int n) {\n    // Условие завершения\n    if (n == 1)\n        return 1;\n    // Рекурсия: рекурсивный вызов\n    int res = recur(n - 1);\n    // Возврат: вернуть результат\n    return n + res;\n}\n</code></pre> recursion.java<pre><code>/* Рекурсия */\nint recur(int n) {\n    // Условие завершения\n    if (n == 1)\n        return 1;\n    // Рекурсия: рекурсивный вызов\n    int res = recur(n - 1);\n    // Возврат: вернуть результат\n    return n + res;\n}\n</code></pre> recursion.cs<pre><code>/* Рекурсия */\nint Recur(int n) {\n    // Условие завершения\n    if (n == 1)\n        return 1;\n    // Рекурсия: рекурсивный вызов\n    int res = Recur(n - 1);\n    // Возврат: вернуть результат\n    return n + res;\n}\n</code></pre> recursion.go<pre><code>/* Рекурсия */\nfunc recur(n int) int {\n    // Условие завершения\n    if n == 1 {\n        return 1\n    }\n    // Рекурсия: рекурсивный вызов\n    res := recur(n - 1)\n    // Возврат: вернуть результат\n    return n + res\n}\n</code></pre> recursion.swift<pre><code>/* Рекурсия */\nfunc recur(n: Int) -&gt; Int {\n    // Условие завершения\n    if n == 1 {\n        return 1\n    }\n    // Рекурсия: рекурсивный вызов\n    let res = recur(n: n - 1)\n    // Возврат: вернуть результат\n    return n + res\n}\n</code></pre> recursion.js<pre><code>/* Рекурсия */\nfunction recur(n) {\n    // Условие завершения\n    if (n === 1) return 1;\n    // Рекурсия: рекурсивный вызов\n    const res = recur(n - 1);\n    // Возврат: вернуть результат\n    return n + res;\n}\n</code></pre> recursion.ts<pre><code>/* Рекурсия */\nfunction recur(n: number): number {\n    // Условие завершения\n    if (n === 1) return 1;\n    // Рекурсия: рекурсивный вызов\n    const res = recur(n - 1);\n    // Возврат: вернуть результат\n    return n + res;\n}\n</code></pre> recursion.dart<pre><code>/* Рекурсия */\nint recur(int n) {\n  // Условие завершения\n  if (n == 1) return 1;\n  // Рекурсия: рекурсивный вызов\n  int res = recur(n - 1);\n  // Возврат: вернуть результат\n  return n + res;\n}\n</code></pre> recursion.rs<pre><code>/* Рекурсия */\nfn recur(n: i32) -&gt; i32 {\n    // Условие завершения\n    if n == 1 {\n        return 1;\n    }\n    // Рекурсия: рекурсивный вызов\n    let res = recur(n - 1);\n    // Возврат: вернуть результат\n    n + res\n}\n</code></pre> recursion.c<pre><code>/* Рекурсия */\nint recur(int n) {\n    // Условие завершения\n    if (n == 1)\n        return 1;\n    // Рекурсия: рекурсивный вызов\n    int res = recur(n - 1);\n    // Возврат: вернуть результат\n    return n + res;\n}\n</code></pre> recursion.kt<pre><code>/* Рекурсия */\nfun recur(n: Int): Int {\n    // Условие завершения\n    if (n == 1)\n        return 1\n    // Рекурсивный шаг: рекурсивный вызов\n    val res = recur(n - 1)\n    // Возврат: вернуть результат\n    return n + res\n}\n</code></pre> recursion.rb<pre><code>### Рекурсия ###\ndef recur(n)\n  # Условие завершения\n  return 1 if n == 1\n  # Рекурсия: рекурсивный вызов\n  res = recur(n - 1)\n  # Возврат: вернуть результат\n  n + res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Ниже представлен рекурсивный процесс этой функции.</p> <p></p> <p> Рисунок 2-3   Рекурсивный процесс функции суммирования </p> <p>Хотя с точки зрения вычислений итерация и рекурсия могут давать одинаковый результат, они представляют собой совершенно разные парадигмы мышления и решения задач.</p> <ul> <li>Итерация: решение задачи снизу вверх. Начинаем с самых базовых шагов, которые затем повторяются или накапливаются до завершения задачи.</li> <li>Рекурсия: решение задачи сверху вниз. Исходная задача разбивается на более мелкие подзадачи, которые имеют ту же форму, что и исходная задача. Далее подзадачи продолжают делиться на еще более мелкие, пока не достигается базовый случай, решение которого известно.</li> </ul> <p>Рассмотрим в качестве примера вышеупомянутую функцию суммирования, где решается задача \\(f(n) = 1 + 2 + \\dots + n\\) .</p> <ul> <li>Итерация: моделирование процесса суммирования в цикле проходит от \\(1\\) до \\(n\\) , выполняя операцию суммирования на каждом шаге, чтобы получить итоговое значение \\(f(n)\\) .</li> <li>Рекурсия: последовательное разбиение задачи на подзадачи вида \\(f(n) = n + f(n - 1)\\) до достижения базового случая \\(f(1) = 1\\) .</li> </ul>","path":["Глава 2. Анализ сложности","2.2 &nbsp; Итерация и рекурсия"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#1","level":3,"title":"1.   Стек вызовов","text":"<p>Каждый раз, когда рекурсивная функция вызывает саму себя, система выделяет память для нового вызова функции, чтобы хранить локальные переменные, адрес вызова и другую информацию. Это поведение имеет два последствия.</p> <ul> <li>Контекстные данные функции хранятся в области памяти, называемой пространством стекового кадра, и освобождаются только после возврата функции. Поэтому рекурсия обычно требует больше памяти, чем итерация.</li> <li>Рекурсивный вызов функции создает дополнительные накладные расходы. Поэтому рекурсия обычно менее эффективна по времени, чем цикл.</li> </ul> <p>Как показано на рисунке 2-4, до срабатывания условия завершения одновременно существует \\(n\\) невозвращенных рекурсивных функций, а глубина рекурсии равна \\(n\\) .</p> <p></p> <p> Рисунок 2-4   Глубина рекурсивного вызова </p> <p>На практике глубина рекурсии, разрешенная языком программирования, обычно ограничена, и слишком глубокая рекурсия может привести к ошибке переполнения стека.</p>","path":["Глава 2. Анализ сложности","2.2 &nbsp; Итерация и рекурсия"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#2","level":3,"title":"2.   Хвостовая рекурсия","text":"<p>Интересно, что если рекурсивный вызов происходит на последнем шаге перед возвратом функции , то компилятор или интерпретатор может оптимизировать этот вызов, сделав его по эффективности использования памяти сопоставимым с итерацией. Это называется хвостовой рекурсией (tail recursion).</p> <ul> <li>Обычная рекурсия: когда функция возвращается на предыдущий уровень, необходимо продолжить выполнение кода, поэтому системе нужно сохранить контекст предыдущего вызова.</li> <li>Хвостовая рекурсия: рекурсивный вызов является последней операцией перед возвратом функции, что означает, что после возврата на предыдущий уровень не требуется выполнять другие операции, поэтому системе не нужно сохранять контекст предыдущей функции.</li> </ul> <p>В качестве примера вычисления суммы \\(1 + 2 + \\dots + n\\) можно установить переменную результата <code>res</code> в качестве параметра функции, чтобы реализовать хвостовую рекурсию:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby recursion.py<pre><code>def tail_recur(n, res):\n    \"\"\"Хвостовая рекурсия\"\"\"\n    # Условие завершения\n    if n == 0:\n        return res\n    # Хвостовой рекурсивный вызов\n    return tail_recur(n - 1, res + n)\n</code></pre> recursion.cpp<pre><code>/* Хвостовая рекурсия */\nint tailRecur(int n, int res) {\n    // Условие завершения\n    if (n == 0)\n        return res;\n    // Хвостовой рекурсивный вызов\n    return tailRecur(n - 1, res + n);\n}\n</code></pre> recursion.java<pre><code>/* Хвостовая рекурсия */\nint tailRecur(int n, int res) {\n    // Условие завершения\n    if (n == 0)\n        return res;\n    // Хвостовой рекурсивный вызов\n    return tailRecur(n - 1, res + n);\n}\n</code></pre> recursion.cs<pre><code>/* Хвостовая рекурсия */\nint TailRecur(int n, int res) {\n    // Условие завершения\n    if (n == 0)\n        return res;\n    // Хвостовой рекурсивный вызов\n    return TailRecur(n - 1, res + n);\n}\n</code></pre> recursion.go<pre><code>/* Хвостовая рекурсия */\nfunc tailRecur(n int, res int) int {\n    // Условие завершения\n    if n == 0 {\n        return res\n    }\n    // Хвостовой рекурсивный вызов\n    return tailRecur(n-1, res+n)\n}\n</code></pre> recursion.swift<pre><code>/* Хвостовая рекурсия */\nfunc tailRecur(n: Int, res: Int) -&gt; Int {\n    // Условие завершения\n    if n == 0 {\n        return res\n    }\n    // Хвостовой рекурсивный вызов\n    return tailRecur(n: n - 1, res: res + n)\n}\n</code></pre> recursion.js<pre><code>/* Хвостовая рекурсия */\nfunction tailRecur(n, res) {\n    // Условие завершения\n    if (n === 0) return res;\n    // Хвостовой рекурсивный вызов\n    return tailRecur(n - 1, res + n);\n}\n</code></pre> recursion.ts<pre><code>/* Хвостовая рекурсия */\nfunction tailRecur(n: number, res: number): number {\n    // Условие завершения\n    if (n === 0) return res;\n    // Хвостовой рекурсивный вызов\n    return tailRecur(n - 1, res + n);\n}\n</code></pre> recursion.dart<pre><code>/* Хвостовая рекурсия */\nint tailRecur(int n, int res) {\n  // Условие завершения\n  if (n == 0) return res;\n  // Хвостовой рекурсивный вызов\n  return tailRecur(n - 1, res + n);\n}\n</code></pre> recursion.rs<pre><code>/* Хвостовая рекурсия */\nfn tail_recur(n: i32, res: i32) -&gt; i32 {\n    // Условие завершения\n    if n == 0 {\n        return res;\n    }\n    // Хвостовой рекурсивный вызов\n    tail_recur(n - 1, res + n)\n}\n</code></pre> recursion.c<pre><code>/* Хвостовая рекурсия */\nint tailRecur(int n, int res) {\n    // Условие завершения\n    if (n == 0)\n        return res;\n    // Хвостовой рекурсивный вызов\n    return tailRecur(n - 1, res + n);\n}\n</code></pre> recursion.kt<pre><code>/* Хвостовая рекурсия */\ntailrec fun tailRecur(n: Int, res: Int): Int {\n    // Добавить ключевое слово tailrec, чтобы включить оптимизацию хвостовой рекурсии\n    // Условие завершения\n    if (n == 0)\n        return res\n    // Хвостовой рекурсивный вызов\n    return tailRecur(n - 1, res + n)\n}\n</code></pre> recursion.rb<pre><code>### Хвостовая рекурсия ###\ndef tail_recur(n, res)\n  # Условие завершения\n  return res if n == 0\n  # Хвостовой рекурсивный вызов\n  tail_recur(n - 1, res + n)\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Процесс выполнения хвостовой рекурсии показан на рисунке 2-5. Сравнивая обычную и хвостовую рекурсии, можно заметить, что точка выполнения операции суммирования у них различается.</p> <ul> <li>Обычная рекурсия: операция суммирования выполняется в процессе возврата, после каждого возврата необходимо снова выполнить операцию суммирования.</li> <li>Хвостовая рекурсия: операция суммирования выполняется в процессе вызова, а процесс возврата требует только последовательного возврата.</li> </ul> <p></p> <p> Рисунок 2-5   Процесс хвостовой рекурсии </p> <p>Tip</p> <p>Обратите внимание: многие компиляторы и интерпретаторы не поддерживают оптимизацию хвостовой рекурсии. Например, Python по умолчанию такую оптимизацию не выполняет, поэтому даже функция в хвостово-рекурсивной форме все равно может привести к переполнению стека.</p>","path":["Глава 2. Анализ сложности","2.2 &nbsp; Итерация и рекурсия"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#3_1","level":3,"title":"3.   Дерево рекурсии","text":"<p>При решении задач, связанных с алгоритмами типа \"разделяй и властвуй\", рекурсия часто оказывается более интуитивной и читабельной, чем итерация. Рассмотрим в качестве примера последовательность Фибоначчи.</p> <p>Question</p> <p>Дана последовательность Фибоначчи \\(0, 1, 1, 2, 3, 5, 8, 13, \\dots\\) ; найди \\(n\\)-й элемент этой последовательности.</p> <p>Обозначив \\(n\\)-й член последовательности Фибоначчи как \\(f(n)\\) , можно сформулировать два утверждения.</p> <ul> <li>Первые два числа последовательности: \\(f(1) = 0\\) и \\(f(2) = 1\\) .</li> <li>Каждое число последовательности является суммой двух предыдущих чисел, то есть \\(f(n) = f(n - 1) + f(n - 2)\\) .</li> </ul> <p>Используя рекурсивные вызовы в соответствии с рекуррентным соотношением и принимая первые два числа за условия остановки, можно написать рекурсивный код. Вызов <code>fib(n)</code> позволит получить \\(n\\)-й член последовательности Фибоначчи:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby recursion.py<pre><code>def fib(n: int) -&gt; int:\n    \"\"\"Последовательность Фибоначчи: рекурсия\"\"\"\n    # Условие завершения: f(1) = 0, f(2) = 1\n    if n == 1 or n == 2:\n        return n - 1\n    # Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n    res = fib(n - 1) + fib(n - 2)\n    # Вернуть результат f(n)\n    return res\n</code></pre> recursion.cpp<pre><code>/* Последовательность Фибоначчи: рекурсия */\nint fib(int n) {\n    // Условие завершения: f(1) = 0, f(2) = 1\n    if (n == 1 || n == 2)\n        return n - 1;\n    // Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n    int res = fib(n - 1) + fib(n - 2);\n    // Вернуть результат f(n)\n    return res;\n}\n</code></pre> recursion.java<pre><code>/* Последовательность Фибоначчи: рекурсия */\nint fib(int n) {\n    // Условие завершения: f(1) = 0, f(2) = 1\n    if (n == 1 || n == 2)\n        return n - 1;\n    // Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n    int res = fib(n - 1) + fib(n - 2);\n    // Вернуть результат f(n)\n    return res;\n}\n</code></pre> recursion.cs<pre><code>/* Последовательность Фибоначчи: рекурсия */\nint Fib(int n) {\n    // Условие завершения: f(1) = 0, f(2) = 1\n    if (n == 1 || n == 2)\n        return n - 1;\n    // Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n    int res = Fib(n - 1) + Fib(n - 2);\n    // Вернуть результат f(n)\n    return res;\n}\n</code></pre> recursion.go<pre><code>/* Последовательность Фибоначчи: рекурсия */\nfunc fib(n int) int {\n    // Условие завершения: f(1) = 0, f(2) = 1\n    if n == 1 || n == 2 {\n        return n - 1\n    }\n    // Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n    res := fib(n-1) + fib(n-2)\n    // Вернуть результат f(n)\n    return res\n}\n</code></pre> recursion.swift<pre><code>/* Последовательность Фибоначчи: рекурсия */\nfunc fib(n: Int) -&gt; Int {\n    // Условие завершения: f(1) = 0, f(2) = 1\n    if n == 1 || n == 2 {\n        return n - 1\n    }\n    // Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n    let res = fib(n: n - 1) + fib(n: n - 2)\n    // Вернуть результат f(n)\n    return res\n}\n</code></pre> recursion.js<pre><code>/* Последовательность Фибоначчи: рекурсия */\nfunction fib(n) {\n    // Условие завершения: f(1) = 0, f(2) = 1\n    if (n === 1 || n === 2) return n - 1;\n    // Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n    const res = fib(n - 1) + fib(n - 2);\n    // Вернуть результат f(n)\n    return res;\n}\n</code></pre> recursion.ts<pre><code>/* Последовательность Фибоначчи: рекурсия */\nfunction fib(n: number): number {\n    // Условие завершения: f(1) = 0, f(2) = 1\n    if (n === 1 || n === 2) return n - 1;\n    // Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n    const res = fib(n - 1) + fib(n - 2);\n    // Вернуть результат f(n)\n    return res;\n}\n</code></pre> recursion.dart<pre><code>/* Последовательность Фибоначчи: рекурсия */\nint fib(int n) {\n  // Условие завершения: f(1) = 0, f(2) = 1\n  if (n == 1 || n == 2) return n - 1;\n  // Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n  int res = fib(n - 1) + fib(n - 2);\n  // Вернуть результат f(n)\n  return res;\n}\n</code></pre> recursion.rs<pre><code>/* Последовательность Фибоначчи: рекурсия */\nfn fib(n: i32) -&gt; i32 {\n    // Условие завершения: f(1) = 0, f(2) = 1\n    if n == 1 || n == 2 {\n        return n - 1;\n    }\n    // Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n    let res = fib(n - 1) + fib(n - 2);\n    // Вернуть результат\n    res\n}\n</code></pre> recursion.c<pre><code>/* Последовательность Фибоначчи: рекурсия */\nint fib(int n) {\n    // Условие завершения: f(1) = 0, f(2) = 1\n    if (n == 1 || n == 2)\n        return n - 1;\n    // Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n    int res = fib(n - 1) + fib(n - 2);\n    // Вернуть результат f(n)\n    return res;\n}\n</code></pre> recursion.kt<pre><code>/* Последовательность Фибоначчи: рекурсия */\nfun fib(n: Int): Int {\n    // Условие завершения: f(1) = 0, f(2) = 1\n    if (n == 1 || n == 2)\n        return n - 1\n    // Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n    val res = fib(n - 1) + fib(n - 2)\n    // Вернуть результат f(n)\n    return res\n}\n</code></pre> recursion.rb<pre><code>### Последовательность Фибоначчи: рекурсия ###\ndef fib(n)\n  # Условие завершения: f(1) = 0, f(2) = 1\n  return n - 1 if n == 1 || n == 2\n  # Рекурсивный вызов f(n) = f(n-1) + f(n-2)\n  res = fib(n - 1) + fib(n - 2)\n  # Вернуть результат f(n)\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Проанализировав приведенный код, можно заметить, что внутри функции осуществляется рекурсивный вызов двух функций, то есть из одного вызова образуются два ветвления. Как показано на рисунке 2-6, при последующем выполнении рекурсивных вызовов в итоге образуется дерево рекурсии (recursion tree) глубиной \\(n\\) .</p> <p></p> <p> Рисунок 2-6   Дерево рекурсии последовательности Фибоначчи </p> <p>По своей сути рекурсия отражает парадигму мышления \"разбиение задачи на более мелкие подзадачи\", что делает стратегию \"разделяй и властвуй\" крайне важной.</p> <ul> <li>С точки зрения алгоритмов многие важные алгоритмические стратегии, такие как поиск, сортировка, возврат, \"разделяй и властвуй\" и динамическое программирование, прямо или косвенно используют этот подход.</li> <li>С точки зрения структур данных рекурсия естественно подходит для решения задач, связанных со списками, деревьями и графами, поскольку они очень хорошо поддаются анализу с использованием идеи \"разделяй и властвуй\".</li> </ul>","path":["Глава 2. Анализ сложности","2.2 &nbsp; Итерация и рекурсия"],"tags":[]},{"location":"chapter_computational_complexity/iteration_and_recursion/#223","level":2,"title":"2.2.3   Сравнение","text":"<p>Подводя итог, можно сказать, что итерация и рекурсия различаются по реализации, производительности и применимости, как показано в таблице 2-1.</p> <p> Таблица 2-1   Сравнение итерации и рекурсии </p> Итерация Рекурсия Способ реализации Циклическая структура Функция вызывает саму себя Временная эффективность Обычно высокая эффективность, нет затрат на вызов функции Каждый вызов функции создает затраты Использование памяти Обычно используется фиксированный объем памяти Накопление вызовов функции может использовать значительное количество пространства стека Сфера использования Подходит для простых циклических задач, код интуитивно понятен и хорошо читаем Подходит для разбиения на подзадачи, для структур деревья и графы, алгоритмов \"разделяй и властвуй\", возврата и т. д.; структура кода проста и ясна <p>Tip</p> <p>Если дальнейшее содержание кажется сложным, можно вернуться к нему после чтения главы о \"стеке\".</p> <p>Какова же внутренняя связь между итерацией и рекурсией? В рассмотренном примере рекурсивной функции операция сложения выполняется на этапе возврата рекурсии. Это означает, что функция, вызванная первой, фактически завершает операцию сложения последней, что соответствует принципу стека \"первым пришел - последним вышел\".</p> <p>На самом деле такие термины рекурсии, как \"стек вызовов\" и \"пространство стекового кадра\", уже намекают на тесную связь между рекурсией и стеком.</p> <ol> <li>Вызов: когда вызывается функция, система выделяет для нее новый стековый кадр в \"стеке вызовов\" для хранения локальных переменных функции, параметров, адреса возврата и других данных.</li> <li>Возврат: когда функция завершает выполнение и возвращает результат, соответствующий стековый кадр удаляется из \"стека вызовов\", восстанавливая среду выполнения предыдущей функции.</li> </ol> <p>Таким образом, можно использовать явный стек для моделирования поведения стека вызовов, чтобы преобразовать рекурсию в итеративную форму:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby recursion.py<pre><code>def for_loop_recur(n: int) -&gt; int:\n    \"\"\"Имитация рекурсии итерацией\"\"\"\n    # Использовать явный стек для имитации системного стека вызовов\n    stack = []\n    res = 0\n    # Рекурсия: рекурсивный вызов\n    for i in range(n, 0, -1):\n        # Имитировать «рекурсию» с помощью операции помещения в стек\n        stack.append(i)\n    # Возврат: вернуть результат\n    while stack:\n        # Имитировать «возврат» с помощью операции извлечения из стека\n        res += stack.pop()\n    # res = 1+2+3+...+n\n    return res\n</code></pre> recursion.cpp<pre><code>/* Имитация рекурсии итерацией */\nint forLoopRecur(int n) {\n    // Использовать явный стек для имитации системного стека вызовов\n    stack&lt;int&gt; stack;\n    int res = 0;\n    // Рекурсия: рекурсивный вызов\n    for (int i = n; i &gt; 0; i--) {\n        // Имитировать «рекурсию» с помощью операции помещения в стек\n        stack.push(i);\n    }\n    // Возврат: вернуть результат\n    while (!stack.empty()) {\n        // Имитировать «возврат» с помощью операции извлечения из стека\n        res += stack.top();\n        stack.pop();\n    }\n    // res = 1+2+3+...+n\n    return res;\n}\n</code></pre> recursion.java<pre><code>/* Имитация рекурсии итерацией */\nint forLoopRecur(int n) {\n    // Использовать явный стек для имитации системного стека вызовов\n    Stack&lt;Integer&gt; stack = new Stack&lt;&gt;();\n    int res = 0;\n    // Рекурсия: рекурсивный вызов\n    for (int i = n; i &gt; 0; i--) {\n        // Имитировать «рекурсию» с помощью операции помещения в стек\n        stack.push(i);\n    }\n    // Возврат: вернуть результат\n    while (!stack.isEmpty()) {\n        // Имитировать «возврат» с помощью операции извлечения из стека\n        res += stack.pop();\n    }\n    // res = 1+2+3+...+n\n    return res;\n}\n</code></pre> recursion.cs<pre><code>/* Имитация рекурсии итерацией */\nint ForLoopRecur(int n) {\n    // Использовать явный стек для имитации системного стека вызовов\n    Stack&lt;int&gt; stack = new();\n    int res = 0;\n    // Рекурсия: рекурсивный вызов\n    for (int i = n; i &gt; 0; i--) {\n        // Имитировать «рекурсию» с помощью операции помещения в стек\n        stack.Push(i);\n    }\n    // Возврат: вернуть результат\n    while (stack.Count &gt; 0) {\n        // Имитировать «возврат» с помощью операции извлечения из стека\n        res += stack.Pop();\n    }\n    // res = 1+2+3+...+n\n    return res;\n}\n</code></pre> recursion.go<pre><code>/* Имитация рекурсии итерацией */\nfunc forLoopRecur(n int) int {\n    // Использовать явный стек для имитации системного стека вызовов\n    stack := list.New()\n    res := 0\n    // Рекурсия: рекурсивный вызов\n    for i := n; i &gt; 0; i-- {\n        // Имитировать «рекурсию» с помощью операции помещения в стек\n        stack.PushBack(i)\n    }\n    // Возврат: вернуть результат\n    for stack.Len() != 0 {\n        // Имитировать «возврат» с помощью операции извлечения из стека\n        res += stack.Back().Value.(int)\n        stack.Remove(stack.Back())\n    }\n    // res = 1+2+3+...+n\n    return res\n}\n</code></pre> recursion.swift<pre><code>/* Имитация рекурсии итерацией */\nfunc forLoopRecur(n: Int) -&gt; Int {\n    // Использовать явный стек для имитации системного стека вызовов\n    var stack: [Int] = []\n    var res = 0\n    // Рекурсия: рекурсивный вызов\n    for i in (1 ... n).reversed() {\n        // Имитировать «рекурсию» с помощью операции помещения в стек\n        stack.append(i)\n    }\n    // Возврат: вернуть результат\n    while !stack.isEmpty {\n        // Имитировать «возврат» с помощью операции извлечения из стека\n        res += stack.removeLast()\n    }\n    // res = 1+2+3+...+n\n    return res\n}\n</code></pre> recursion.js<pre><code>/* Имитация рекурсии итерацией */\nfunction forLoopRecur(n) {\n    // Использовать явный стек для имитации системного стека вызовов\n    const stack = [];\n    let res = 0;\n    // Рекурсия: рекурсивный вызов\n    for (let i = n; i &gt; 0; i--) {\n        // Имитировать «рекурсию» с помощью операции помещения в стек\n        stack.push(i);\n    }\n    // Возврат: вернуть результат\n    while (stack.length) {\n        // Имитировать «возврат» с помощью операции извлечения из стека\n        res += stack.pop();\n    }\n    // res = 1+2+3+...+n\n    return res;\n}\n</code></pre> recursion.ts<pre><code>/* Имитация рекурсии итерацией */\nfunction forLoopRecur(n: number): number {\n    // Использовать явный стек для имитации системного стека вызовов\n    const stack: number[] = [];\n    let res: number = 0;\n    // Рекурсия: рекурсивный вызов\n    for (let i = n; i &gt; 0; i--) {\n        // Имитировать «рекурсию» с помощью операции помещения в стек\n        stack.push(i);\n    }\n    // Возврат: вернуть результат\n    while (stack.length) {\n        // Имитировать «возврат» с помощью операции извлечения из стека\n        res += stack.pop();\n    }\n    // res = 1+2+3+...+n\n    return res;\n}\n</code></pre> recursion.dart<pre><code>/* Имитация рекурсии итерацией */\nint forLoopRecur(int n) {\n  // Использовать явный стек для имитации системного стека вызовов\n  List&lt;int&gt; stack = [];\n  int res = 0;\n  // Рекурсия: рекурсивный вызов\n  for (int i = n; i &gt; 0; i--) {\n    // Имитировать «рекурсию» с помощью операции помещения в стек\n    stack.add(i);\n  }\n  // Возврат: вернуть результат\n  while (!stack.isEmpty) {\n    // Имитировать «возврат» с помощью операции извлечения из стека\n    res += stack.removeLast();\n  }\n  // res = 1+2+3+...+n\n  return res;\n}\n</code></pre> recursion.rs<pre><code>/* Имитация рекурсии итерацией */\nfn for_loop_recur(n: i32) -&gt; i32 {\n    // Использовать явный стек для имитации системного стека вызовов\n    let mut stack = Vec::new();\n    let mut res = 0;\n    // Рекурсия: рекурсивный вызов\n    for i in (1..=n).rev() {\n        // Имитировать «рекурсию» с помощью операции помещения в стек\n        stack.push(i);\n    }\n    // Возврат: вернуть результат\n    while !stack.is_empty() {\n        // Имитировать «возврат» с помощью операции извлечения из стека\n        res += stack.pop().unwrap();\n    }\n    // res = 1+2+3+...+n\n    res\n}\n</code></pre> recursion.c<pre><code>/* Имитация рекурсии итерацией */\nint forLoopRecur(int n) {\n    int stack[1000]; // Использовать большой массив для имитации стека\n    int top = -1;    // Индекс вершины стека\n    int res = 0;\n    // Рекурсия: рекурсивный вызов\n    for (int i = n; i &gt; 0; i--) {\n        // Имитировать «рекурсию» с помощью операции помещения в стек\n        stack[1 + top++] = i;\n    }\n    // Возврат: вернуть результат\n    while (top &gt;= 0) {\n        // Имитировать «возврат» с помощью операции извлечения из стека\n        res += stack[top--];\n    }\n    // res = 1+2+3+...+n\n    return res;\n}\n</code></pre> recursion.kt<pre><code>/* Имитация рекурсии итерацией */\nfun forLoopRecur(n: Int): Int {\n    // Использовать явный стек для имитации системного стека вызовов\n    val stack = Stack&lt;Int&gt;()\n    var res = 0\n    // Рекурсивный шаг: рекурсивный вызов\n    for (i in n downTo 0) {\n        // Имитировать «рекурсию» с помощью операции помещения в стек\n        stack.push(i)\n    }\n    // Возврат: вернуть результат\n    while (stack.isNotEmpty()) {\n        // Имитировать «возврат» с помощью операции извлечения из стека\n        res += stack.pop()\n    }\n    // res = 1+2+3+...+n\n    return res\n}\n</code></pre> recursion.rb<pre><code>### Имитация рекурсии итерацией ###\ndef for_loop_recur(n)\n  # Использовать явный стек для имитации системного стека вызовов\n  stack = []\n  res = 0\n\n  # Рекурсия: рекурсивный вызов\n  for i in n.downto(0)\n    # Имитировать «рекурсию» с помощью операции помещения в стек\n    stack &lt;&lt; i\n  end\n  # Возврат: вернуть результат\n  while !stack.empty?\n    res += stack.pop\n  end\n\n  # res = 1+2+3+...+n\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Наблюдая за приведенным выше кодом, можно заметить, что после преобразования рекурсии в итерацию код становится более сложным. Хотя во многих случаях итерация и рекурсия действительно могут быть преобразованы друг в друга, это не всегда стоит делать по двум причинам.</p> <ul> <li>Преобразованный код может стать труднее для понимания и менее читаемым.</li> <li>Для некоторых сложных задач моделирование поведения системного стека вызовов может оказаться очень трудным.</li> </ul> <p>Итак, выбор между итерацией и рекурсией зависит от природы конкретной задачи. В практическом программировании крайне важно взвешивать преимущества и недостатки обоих подходов и выбирать подходящий метод с учетом контекста.</p>","path":["Глава 2. Анализ сложности","2.2 &nbsp; Итерация и рекурсия"],"tags":[]},{"location":"chapter_computational_complexity/performance_evaluation/","level":1,"title":"2.1   Оценка эффективности алгоритмов","text":"<p>В процессе разработки алгоритмов мы стремимся к достижению следующих целей.</p> <ol> <li>Найти решение задачи: алгоритм должен надежно находить правильное решение задачи в заданных пределах входных данных.</li> <li>Найти оптимальное решение: для одной и той же задачи может существовать несколько решений, и мы стремимся найти максимально эффективный алгоритм.</li> </ol> <p>Таким образом, при условии возможности решения задачи эффективность алгоритма становится основным критерием его оценки, который включает два аспекта.</p> <ul> <li>Временная эффективность: продолжительность выполнения алгоритма.</li> <li>Пространственная эффективность: объем памяти, занимаемой алгоритмом.</li> </ul> <p>В двух словах, наша цель - разработка быстрых и экономных структур данных и алгоритмов. Эффективная оценка алгоритмов крайне важна, так как только так можно сравнивать различные алгоритмы и управлять процессом их разработки и оптимизации.</p> <p>Методы оценки эффективности делятся на два типа: практическое тестирование и теоретическую оценку.</p>","path":["Глава 2. Анализ сложности","2.1 &nbsp; Оценка эффективности алгоритмов"],"tags":[]},{"location":"chapter_computational_complexity/performance_evaluation/#211","level":2,"title":"2.1.1   Практическое тестирование","text":"<p>Предположим, у нас есть алгоритмы <code>A</code> и <code>B</code>, которые решают одну и ту же задачу, и необходимо сравнить их эффективность. Самый прямой метод - это запустить оба алгоритма на компьютере и зафиксировать время их выполнения и объем используемой памяти. Этот метод отражает реальную ситуацию, но имеет значительные ограничения.</p> <p>С одной стороны, сложно исключить влияние факторов тестовой среды. Аппаратная конфигурация влияет на производительность алгоритма. Например, если алгоритм обладает высокой степенью параллелизма, он будет лучше работать на многоядерных CPU; если алгоритм интенсивно использует память, его производительность будет выше на высокопроизводительной памяти. Это означает, что результаты тестирования на разных машинах могут значительно отличаться, а для получения средней эффективности пришлось бы тестировать на различных платформах, что крайне затруднительно.</p> <p>С другой стороны, проведение полного тестирования требует значительных ресурсов. С изменением объема входных данных алгоритмы демонстрируют разную эффективность. Например, при небольшом объеме данных алгоритм <code>A</code> может работать быстрее, чем алгоритм <code>B</code>, но при большом объеме данных результат может быть противоположным. Следовательно, для получения убедительных выводов необходимо тестировать различные масштабы входных данных, что требует значительных вычислительных ресурсов.</p>","path":["Глава 2. Анализ сложности","2.1 &nbsp; Оценка эффективности алгоритмов"],"tags":[]},{"location":"chapter_computational_complexity/performance_evaluation/#212","level":2,"title":"2.1.2   Теоретическая оценка","text":"<p>Из-за значительных ограничений практического тестирования можно рассмотреть возможность оценки эффективности алгоритмов только с помощью вычислений. Такой метод называется анализом асимптотической сложности (asymptotic complexity analysis), или сокращенно анализом сложности.</p> <p>Анализ сложности позволяет отразить зависимость между ресурсами времени и пространства, необходимыми для выполнения алгоритма, и размером входных данных. Он описывает тенденцию роста времени и пространства, необходимых для выполнения алгоритма, по мере увеличения размера входных данных. Это определение может показаться сложным, но его можно разбить на три ключевых момента.</p> <ul> <li>\"Ресурсы времени и пространства\" соответствуют временной сложности (time complexity) и пространственной сложности (space complexity).</li> <li>\"По мере увеличения размера входных данных\" означает, что сложность отражает зависимость эффективности алгоритма от объема входных данных.</li> <li>\"Тенденция роста времени и пространства\" указывает, что анализ сложности фокусируется не на конкретных значениях времени выполнения или объема занимаемой памяти, а на скорости их роста.</li> </ul> <p>Анализ сложности преодолевает недостатки метода практического тестирования, что выражается в следующих аспектах.</p> <ul> <li>Он не требует фактического выполнения кода, что делает его более экологичным и энергосберегающим.</li> <li>Он независим от тестовой среды, а результаты анализа применимы ко всем платформам выполнения.</li> <li>Он может продемонстрировать эффективность алгоритма при различных объемах данных, особенно при больших объемах.</li> </ul> <p>Tip</p> <p>Если понятие сложности пока все еще кажется вам запутанным, не переживайте: мы подробно разберем его в следующих разделах.</p> <p>Анализ сложности предоставляет нам мерило оценки эффективности алгоритмов, позволяя измерять время и ресурсы, необходимые для выполнения конкретного алгоритма, а также сравнивать эффективность различных алгоритмов.</p> <p>Сложность - это математическое понятие, которое новичкам может показаться абстрактным и сложным для изучения. С этой точки зрения анализ сложности не то, с чего стоит начинать изучение алгоритмов. Однако, обсуждая особенности той или иной структуры данных или алгоритма, невозможно избежать анализа их скорости выполнения и использования памяти.</p> <p>Таким образом, перед погружением в изучение структур данных и алгоритмов рекомендуется получить базовое представление об анализе сложности, чтобы иметь возможность выполнять хотя бы базовую оценку их эффективности.</p>","path":["Глава 2. Анализ сложности","2.1 &nbsp; Оценка эффективности алгоритмов"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/","level":1,"title":"2.4   Пространственная сложность","text":"<p>Пространственная сложность (space complexity) служит для оценки того, как меняется объем памяти, требуемой алгоритму, по мере роста объема данных. Это понятие очень похоже на временную сложность, только вместо времени выполнения рассматривается объем используемой памяти.</p>","path":["Глава 2. Анализ сложности","2.4 &nbsp; Пространственная сложность"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#241","level":2,"title":"2.4.1   Пространство, связанное с алгоритмом","text":"<p>Память, которую использует алгоритм во время работы, в основном делится на следующие части.</p> <ul> <li>Входное пространство: используется для хранения входных данных алгоритма.</li> <li>Временное пространство: используется для хранения переменных, объектов, контекста функций и других данных, возникающих во время выполнения алгоритма.</li> <li>Выходное пространство: используется для хранения выходных данных алгоритма.</li> </ul> <p>Как правило, при анализе пространственной сложности в расчет включают временное пространство и выходное пространство.</p> <p>Временное пространство можно дополнительно разделить на три части.</p> <ul> <li>Временные данные: используются для хранения различных констант, переменных, объектов и т.д., возникающих во время выполнения алгоритма.</li> <li>Пространство кадров стека: используется для хранения контекстных данных вызываемых функций. При каждом вызове функции система создает на вершине стека новый кадр; после возврата функции пространство этого кадра освобождается.</li> <li>Пространство инструкций: используется для хранения скомпилированных инструкций программы и в реальном подсчете обычно не учитывается.</li> </ul> <p>При анализе пространственной сложности программы обычно учитываются временные данные, пространство стека и выходные данные, как показано на рисунке 2-15.</p> <p></p> <p> Рисунок 2-15   Пространство, используемое алгоритмом </p> <p>Ниже приведен соответствующий код:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>class Node:\n    \"\"\"Класс\"\"\"\n    def __init__(self, x: int):\n        self.val: int = x              # Значение узла\n        self.next: Node | None = None  # Ссылка на следующий узел\n\ndef function() -&gt; int:\n    \"\"\"Функция\"\"\"\n    # Выполнить некоторые операции...\n    return 0\n\ndef algorithm(n) -&gt; int:  # Входные данные\n    A = 0                 # Временные данные (константа, обычно обозначается заглавной буквой)\n    b = 0                 # Временные данные (переменная)\n    node = Node(0)        # Временные данные (объект)\n    c = function()        # Пространство кадра стека (вызов функции)\n    return A + b + c      # Выходные данные\n</code></pre> <pre><code>/* Структура */\nstruct Node {\n    int val;\n    Node *next;\n    Node(int x) : val(x), next(nullptr) {}\n};\n\n/* Функция */\nint func() {\n    // Выполнить некоторые операции...\n    return 0;\n}\n\nint algorithm(int n) {        // Входные данные\n    const int a = 0;          // Временные данные (константа)\n    int b = 0;                // Временные данные (переменная)\n    Node* node = new Node(0); // Временные данные (объект)\n    int c = func();           // Пространство кадра стека (вызов функции)\n    return a + b + c;         // Выходные данные\n}\n</code></pre> <pre><code>/* Класс */\nclass Node {\n    int val;\n    Node next;\n    Node(int x) { val = x; }\n}\n\n/* Функция */\nint function() {\n    // Выполнить некоторые операции...\n    return 0;\n}\n\nint algorithm(int n) {        // Входные данные\n    final int a = 0;          // Временные данные (константа)\n    int b = 0;                // Временные данные (переменная)\n    Node node = new Node(0);  // Временные данные (объект)\n    int c = function();       // Пространство кадра стека (вызов функции)\n    return a + b + c;         // Выходные данные\n}\n</code></pre> <pre><code>/* Класс */\nclass Node(int x) {\n    int val = x;\n    Node next;\n}\n\n/* Функция */\nint Function() {\n    // Выполнить некоторые операции...\n    return 0;\n}\n\nint Algorithm(int n) {        // Входные данные\n    const int a = 0;          // Временные данные (константа)\n    int b = 0;                // Временные данные (переменная)\n    Node node = new(0);       // Временные данные (объект)\n    int c = Function();       // Пространство кадра стека (вызов функции)\n    return a + b + c;         // Выходные данные\n}\n</code></pre> <pre><code>/* Структура */\ntype node struct {\n    val  int\n    next *node\n}\n\n/* Создать структуру node */\nfunc newNode(val int) *node {\n    return &amp;node{val: val}\n}\n\n/* Функция */\nfunc function() int {\n    // Выполнить некоторые операции...\n    return 0\n}\n\nfunc algorithm(n int) int { // Входные данные\n    const a = 0             // Временные данные (константа)\n    b := 0                  // Временные данные (переменная)\n    newNode(0)              // Временные данные (объект)\n    c := function()         // Пространство кадра стека (вызов функции)\n    return a + b + c        // Выходные данные\n}\n</code></pre> <pre><code>/* Класс */\nclass Node {\n    var val: Int\n    var next: Node?\n\n    init(x: Int) {\n        val = x\n    }\n}\n\n/* Функция */\nfunc function() -&gt; Int {\n    // Выполнить некоторые операции...\n    return 0\n}\n\nfunc algorithm(n: Int) -&gt; Int { // Входные данные\n    let a = 0             // Временные данные (константа)\n    var b = 0             // Временные данные (переменная)\n    let node = Node(x: 0) // Временные данные (объект)\n    let c = function()    // Пространство кадра стека (вызов функции)\n    return a + b + c      // Выходные данные\n}\n</code></pre> <pre><code>/* Класс */\nclass Node {\n    val;\n    next;\n    constructor(val) {\n        this.val = val === undefined ? 0 : val; // Значение узла\n        this.next = null;                       // Ссылка на следующий узел\n    }\n}\n\n/* Функция */\nfunction constFunc() {\n    // Выполнить некоторые операции\n    return 0;\n}\n\nfunction algorithm(n) {       // Входные данные\n    const a = 0;              // Временные данные (константа)\n    let b = 0;                // Временные данные (переменная)\n    const node = new Node(0); // Временные данные (объект)\n    const c = constFunc();    // Пространство кадра стека (вызов функции)\n    return a + b + c;         // Выходные данные\n}\n</code></pre> <pre><code>/* Класс */\nclass Node {\n    val: number;\n    next: Node | null;\n    constructor(val?: number) {\n        this.val = val === undefined ? 0 : val; // Значение узла\n        this.next = null;                       // Ссылка на следующий узел\n    }\n}\n\n/* Функция */\nfunction constFunc(): number {\n    // Выполнить некоторые операции\n    return 0;\n}\n\nfunction algorithm(n: number): number { // Входные данные\n    const a = 0;                        // Временные данные (константа)\n    let b = 0;                          // Временные данные (переменная)\n    const node = new Node(0);           // Временные данные (объект)\n    const c = constFunc();              // Пространство кадра стека (вызов функции)\n    return a + b + c;                   // Выходные данные\n}\n</code></pre> <pre><code>/* Класс */\nclass Node {\n  int val;\n  Node next;\n  Node(this.val, [this.next]);\n}\n\n/* Функция */\nint function() {\n  // Выполнить некоторые операции...\n  return 0;\n}\n\nint algorithm(int n) {  // Входные данные\n  const int a = 0;      // Временные данные (константа)\n  int b = 0;            // Временные данные (переменная)\n  Node node = Node(0);  // Временные данные (объект)\n  int c = function();   // Пространство кадра стека (вызов функции)\n  return a + b + c;     // Выходные данные\n}\n</code></pre> <pre><code>use std::rc::Rc;\nuse std::cell::RefCell;\n\n/* Структура */\nstruct Node {\n    val: i32,\n    next: Option&lt;Rc&lt;RefCell&lt;Node&gt;&gt;&gt;,\n}\n\n/* Создать структуру Node */\nimpl Node {\n    fn new(val: i32) -&gt; Self {\n        Self { val: val, next: None }\n    }\n}\n\n/* Функция */\nfn function() -&gt; i32 {      \n    // Выполнить некоторые операции...\n    return 0;\n}\n\nfn algorithm(n: i32) -&gt; i32 {       // Входные данные\n    const a: i32 = 0;               // Временные данные (константа)\n    let mut b = 0;                  // Временные данные (переменная)\n    let node = Node::new(0);        // Временные данные (объект)\n    let c = function();             // Пространство кадра стека (вызов функции)\n    return a + b + c;               // Выходные данные\n}\n</code></pre> <pre><code>/* Функция */\nint func() {\n    // Выполнить некоторые операции...\n    return 0;\n}\n\nint algorithm(int n) { // Входные данные\n    const int a = 0;   // Временные данные (константа)\n    int b = 0;         // Временные данные (переменная)\n    int c = func();    // Пространство кадра стека (вызов функции)\n    return a + b + c;  // Выходные данные\n}\n</code></pre> <pre><code>/* Класс */\nclass Node(var _val: Int) {\n    var next: Node? = null\n}\n\n/* Функция */\nfun function(): Int {\n    // Выполнить некоторые операции...\n    return 0\n}\n\nfun algorithm(n: Int): Int { // Входные данные\n    val a = 0                // Временные данные (константа)\n    var b = 0                // Временные данные (переменная)\n    val node = Node(0)       // Временные данные (объект)\n    val c = function()       // Пространство кадра стека (вызов функции)\n    return a + b + c         // Выходные данные\n}\n</code></pre> <pre><code>### Класс ###\nclass Node\n    attr_accessor :val      # Значение узла\n    attr_accessor :next     # Ссылка на следующий узел\n\n    def initialize(x)\n        @val = x\n    end\nend\n\n### Функция ###\ndef function\n    # Выполнить некоторые операции...\n    0\nend\n\n### Алгоритм ###\ndef algorithm(n)        # Входные данные\n    a = 0               # Временные данные (константа)\n    b = 0               # Временные данные (переменная)\n    node = Node.new(0)  # Временные данные (объект)\n    c = function        # Пространство кадра стека (вызов функции)\n    a + b + c           # Выходные данные\nend\n</code></pre>","path":["Глава 2. Анализ сложности","2.4 &nbsp; Пространственная сложность"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#242","level":2,"title":"2.4.2   Метод вывода","text":"<p>Метод вывода пространственной сложности в целом аналогичен выводу временной сложности: меняется только объект подсчета, с количества операций на размер используемого пространства.</p> <p>В отличие от временной сложности, обычно рассматривается только худшая пространственная сложность. Это связано с тем, что память является жестким ограничением: необходимо гарантировать, что для любых входных данных у программы будет достаточно памяти.</p> <p>Рассмотрим следующий код. Понятие худшей пространственной сложности здесь имеет два значения.</p> <ol> <li>Ориентир на худшие входные данные: когда \\(n &lt; 10\\) , пространственная сложность равна \\(O(1)\\) ; но когда \\(n &gt; 10\\) , инициализированный массив <code>nums</code> занимает \\(O(n)\\) пространства, поэтому худшая пространственная сложность равна \\(O(n)\\) .</li> <li>Ориентир на пиковое использование памяти во время выполнения: например, до выполнения последней строки программа занимает \\(O(1)\\) пространства; при инициализации массива <code>nums</code> она занимает \\(O(n)\\) пространства, поэтому худшая пространственная сложность также равна \\(O(n)\\) .</li> </ol> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>def algorithm(n: int):\n    a = 0               # O(1)\n    b = [0] * 10000     # O(1)\n    if n &gt; 10:\n        nums = [0] * n  # O(n)\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 0;               // O(1)\n    vector&lt;int&gt; b(10000);    // O(1)\n    if (n &gt; 10)\n        vector&lt;int&gt; nums(n); // O(n)\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 0;                   // O(1)\n    int[] b = new int[10000];    // O(1)\n    if (n &gt; 10)\n        int[] nums = new int[n]; // O(n)\n}\n</code></pre> <pre><code>void Algorithm(int n) {\n    int a = 0;                   // O(1)\n    int[] b = new int[10000];    // O(1)\n    if (n &gt; 10) {\n        int[] nums = new int[n]; // O(n)\n    }\n}\n</code></pre> <pre><code>func algorithm(n int) {\n    a := 0                      // O(1)\n    b := make([]int, 10000)     // O(1)\n    var nums []int\n    if n &gt; 10 {\n        nums := make([]int, n)  // O(n)\n    }\n    fmt.Println(a, b, nums)\n}\n</code></pre> <pre><code>func algorithm(n: Int) {\n    let a = 0 // O(1)\n    let b = Array(repeating: 0, count: 10000) // O(1)\n    if n &gt; 10 {\n        let nums = Array(repeating: 0, count: n) // O(n)\n    }\n}\n</code></pre> <pre><code>function algorithm(n) {\n    const a = 0;                   // O(1)\n    const b = new Array(10000);    // O(1)\n    if (n &gt; 10) {\n        const nums = new Array(n); // O(n)\n    }\n}\n</code></pre> <pre><code>function algorithm(n: number): void {\n    const a = 0;                   // O(1)\n    const b = new Array(10000);    // O(1)\n    if (n &gt; 10) {\n        const nums = new Array(n); // O(n)\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n  int a = 0;                            // O(1)\n  List&lt;int&gt; b = List.filled(10000, 0);  // O(1)\n  if (n &gt; 10) {\n    List&lt;int&gt; nums = List.filled(n, 0); // O(n)\n  }\n}\n</code></pre> <pre><code>fn algorithm(n: i32) {\n    let a = 0;                              // O(1)\n    let b = [0; 10000];                     // O(1)\n    if n &gt; 10 {\n        let nums = vec![0; n as usize];     // O(n)\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 0;               // O(1)\n    int b[10000];            // O(1)\n    if (n &gt; 10)\n        int nums[n] = {0};   // O(n)\n}\n</code></pre> <pre><code>fun algorithm(n: Int) {\n    val a = 0                    // O(1)\n    val b = IntArray(10000)      // O(1)\n    if (n &gt; 10) {\n        val nums = IntArray(n)   // O(n)\n    }\n}\n</code></pre> <pre><code>def algorithm(n)\n    a = 0                           # O(1)\n    b = Array.new(10000)            # O(1)\n    nums = Array.new(n) if n &gt; 10   # O(n)\nend\n</code></pre> <p>В рекурсивных функциях необходимо учитывать пространство кадров стека. Рассмотрим следующий код:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>def function() -&gt; int:\n    # Выполнить некоторые операции\n    return 0\n\ndef loop(n: int):\n    \"\"\"Пространственная сложность цикла равна O(1)\"\"\"\n    for _ in range(n):\n        function()\n\ndef recur(n: int):\n    \"\"\"Пространственная сложность рекурсии равна O(n)\"\"\"\n    if n == 1:\n        return\n    return recur(n - 1)\n</code></pre> <pre><code>int func() {\n    // Выполнить некоторые операции\n    return 0;\n}\n/* Пространственная сложность цикла равна O(1) */\nvoid loop(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        func();\n    }\n}\n/* Пространственная сложность рекурсии равна O(n) */\nvoid recur(int n) {\n    if (n == 1) return;\n    recur(n - 1);\n}\n</code></pre> <pre><code>int function() {\n    // Выполнить некоторые операции\n    return 0;\n}\n/* Пространственная сложность цикла равна O(1) */\nvoid loop(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        function();\n    }\n}\n/* Пространственная сложность рекурсии равна O(n) */\nvoid recur(int n) {\n    if (n == 1) return;\n    recur(n - 1);\n}\n</code></pre> <pre><code>int Function() {\n    // Выполнить некоторые операции\n    return 0;\n}\n/* Пространственная сложность цикла равна O(1) */\nvoid Loop(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        Function();\n    }\n}\n/* Пространственная сложность рекурсии равна O(n) */\nint Recur(int n) {\n    if (n == 1) return 1;\n    return Recur(n - 1);\n}\n</code></pre> <pre><code>func function() int {\n    // Выполнить некоторые операции\n    return 0\n}\n\n/* Пространственная сложность цикла равна O(1) */\nfunc loop(n int) {\n    for i := 0; i &lt; n; i++ {\n        function()\n    }\n}\n\n/* Пространственная сложность рекурсии равна O(n) */\nfunc recur(n int) {\n    if n == 1 {\n        return\n    }\n    recur(n - 1)\n}\n</code></pre> <pre><code>@discardableResult\nfunc function() -&gt; Int {\n    // Выполнить некоторые операции\n    return 0\n}\n\n/* Пространственная сложность цикла равна O(1) */\nfunc loop(n: Int) {\n    for _ in 0 ..&lt; n {\n        function()\n    }\n}\n\n/* Пространственная сложность рекурсии равна O(n) */\nfunc recur(n: Int) {\n    if n == 1 {\n        return\n    }\n    recur(n: n - 1)\n}\n</code></pre> <pre><code>function constFunc() {\n    // Выполнить некоторые операции\n    return 0;\n}\n/* Пространственная сложность цикла равна O(1) */\nfunction loop(n) {\n    for (let i = 0; i &lt; n; i++) {\n        constFunc();\n    }\n}\n/* Пространственная сложность рекурсии равна O(n) */\nfunction recur(n) {\n    if (n === 1) return;\n    return recur(n - 1);\n}\n</code></pre> <pre><code>function constFunc(): number {\n    // Выполнить некоторые операции\n    return 0;\n}\n/* Пространственная сложность цикла равна O(1) */\nfunction loop(n: number): void {\n    for (let i = 0; i &lt; n; i++) {\n        constFunc();\n    }\n}\n/* Пространственная сложность рекурсии равна O(n) */\nfunction recur(n: number): void {\n    if (n === 1) return;\n    return recur(n - 1);\n}\n</code></pre> <pre><code>int function() {\n  // Выполнить некоторые операции\n  return 0;\n}\n/* Пространственная сложность цикла равна O(1) */\nvoid loop(int n) {\n  for (int i = 0; i &lt; n; i++) {\n    function();\n  }\n}\n/* Пространственная сложность рекурсии равна O(n) */\nvoid recur(int n) {\n  if (n == 1) return;\n  recur(n - 1);\n}\n</code></pre> <pre><code>fn function() -&gt; i32 {\n    // Выполнить некоторые операции\n    return 0;\n}\n/* Пространственная сложность цикла равна O(1) */\nfn loop(n: i32) {\n    for i in 0..n {\n        function();\n    }\n}\n/* Пространственная сложность рекурсии равна O(n) */\nfn recur(n: i32) {\n    if n == 1 {\n        return;\n    }\n    recur(n - 1);\n}\n</code></pre> <pre><code>int func() {\n    // Выполнить некоторые операции\n    return 0;\n}\n/* Пространственная сложность цикла равна O(1) */\nvoid loop(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        func();\n    }\n}\n/* Пространственная сложность рекурсии равна O(n) */\nvoid recur(int n) {\n    if (n == 1) return;\n    recur(n - 1);\n}\n</code></pre> <pre><code>fun function(): Int {\n    // Выполнить некоторые операции\n    return 0\n}\n/* Пространственная сложность цикла равна O(1) */\nfun loop(n: Int) {\n    for (i in 0..&lt;n) {\n        function()\n    }\n}\n/* Пространственная сложность рекурсии равна O(n) */\nfun recur(n: Int) {\n    if (n == 1) return\n    return recur(n - 1)\n}\n</code></pre> <pre><code>def function\n    # Выполнить некоторые операции\n    0\nend\n\n### Пространственная сложность цикла равна O(1) ###\ndef loop(n)\n    (0...n).each { function }\nend\n\n### Пространственная сложность рекурсии равна O(n) ###\ndef recur(n)\n    return if n == 1\n    recur(n - 1)\nend\n</code></pre> <p>Функции <code>loop()</code> и <code>recur()</code> имеют временную сложность \\(O(n)\\) , но их пространственная сложность различается.</p> <ul> <li>Функция <code>loop()</code> вызывает <code>function()</code> в цикле \\(n\\) раз; на каждой итерации <code>function()</code> возвращается и освобождает пространство своего кадра стека, поэтому пространственная сложность по-прежнему равна \\(O(1)\\) .</li> <li>Рекурсивная функция <code>recur()</code> во время выполнения одновременно содержит \\(n\\) еще не завершившихся экземпляров <code>recur()</code> , поэтому занимает \\(O(n)\\) пространства кадров стека.</li> </ul>","path":["Глава 2. Анализ сложности","2.4 &nbsp; Пространственная сложность"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#243","level":2,"title":"2.4.3   Распространенные типы","text":"<p>Пусть размер входных данных равен \\(n\\) . На рисунке 2-16 показаны распространенные типы пространственной сложности в порядке от меньшей к большей.</p> \\[ \\begin{aligned} O(1) &lt; O(\\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \\newline \\text{Постоянная} &lt; \\text{Логарифмическая} &lt; \\text{Линейная} &lt; \\text{Квадратичная} &lt; \\text{Экспоненциальная} \\end{aligned} \\] <p></p> <p> Рисунок 2-16   Распространенные типы пространственной сложности </p>","path":["Глава 2. Анализ сложности","2.4 &nbsp; Пространственная сложность"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#1-o1","level":3,"title":"1.   Постоянная сложность \\(O(1)\\)","text":"<p>Постоянная сложность обычно встречается у констант, переменных и объектов, количество которых не зависит от размера входных данных \\(n\\) .</p> <p>Следует заметить, что память, занятая инициализацией переменных или вызовом функций внутри цикла, освобождается при переходе к следующей итерации, поэтому она не накапливается, и пространственная сложность по-прежнему остается \\(O(1)\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby space_complexity.py<pre><code>def function() -&gt; int:\n    \"\"\"Функция\"\"\"\n    # Выполнить некоторые операции\n    return 0\n\ndef constant(n: int):\n    \"\"\"Постоянная сложность\"\"\"\n    # Константы, переменные и объекты занимают O(1) памяти\n    a = 0\n    nums = [0] * 10000\n    node = ListNode(0)\n    # Переменные в цикле занимают O(1) памяти\n    for _ in range(n):\n        c = 0\n    # Функции в цикле занимают O(1) памяти\n    for _ in range(n):\n        function()\n</code></pre> space_complexity.cpp<pre><code>/* Функция */\nint func() {\n    // Выполнить некоторые операции\n    return 0;\n}\n\n/* Постоянная сложность */\nvoid constant(int n) {\n    // Константы, переменные и объекты занимают O(1) памяти\n    const int a = 0;\n    int b = 0;\n    vector&lt;int&gt; nums(10000);\n    ListNode node(0);\n    // Переменные в цикле занимают O(1) памяти\n    for (int i = 0; i &lt; n; i++) {\n        int c = 0;\n    }\n    // Функции в цикле занимают O(1) памяти\n    for (int i = 0; i &lt; n; i++) {\n        func();\n    }\n}\n</code></pre> space_complexity.java<pre><code>/* Функция */\nint function() {\n    // Выполнить некоторые операции\n    return 0;\n}\n\n/* Постоянная сложность */\nvoid constant(int n) {\n    // Константы, переменные и объекты занимают O(1) памяти\n    final int a = 0;\n    int b = 0;\n    int[] nums = new int[10000];\n    ListNode node = new ListNode(0);\n    // Переменные в цикле занимают O(1) памяти\n    for (int i = 0; i &lt; n; i++) {\n        int c = 0;\n    }\n    // Функции в цикле занимают O(1) памяти\n    for (int i = 0; i &lt; n; i++) {\n        function();\n    }\n}\n</code></pre> space_complexity.cs<pre><code>/* Функция */\nint Function() {\n    // Выполнить некоторые операции\n    return 0;\n}\n\n/* Постоянная сложность */\nvoid Constant(int n) {\n    // Константы, переменные и объекты занимают O(1) памяти\n    int a = 0;\n    int b = 0;\n    int[] nums = new int[10000];\n    ListNode node = new(0);\n    // Переменные в цикле занимают O(1) памяти\n    for (int i = 0; i &lt; n; i++) {\n        int c = 0;\n    }\n    // Функции в цикле занимают O(1) памяти\n    for (int i = 0; i &lt; n; i++) {\n        Function();\n    }\n}\n</code></pre> space_complexity.go<pre><code>/* Функция */\nfunc function() int {\n    // Выполнить некоторые операции...\n    return 0\n}\n\n/* Постоянная сложность */\nfunc spaceConstant(n int) {\n    // Константы, переменные и объекты занимают O(1) памяти\n    const a = 0\n    b := 0\n    nums := make([]int, 10000)\n    node := newNode(0)\n    // Переменные в цикле занимают O(1) памяти\n    var c int\n    for i := 0; i &lt; n; i++ {\n        c = 0\n    }\n    // Функции в цикле занимают O(1) памяти\n    for i := 0; i &lt; n; i++ {\n        function()\n    }\n    b += 0\n    c += 0\n    nums[0] = 0\n    node.val = 0\n}\n</code></pre> space_complexity.swift<pre><code>/* Функция */\n@discardableResult\nfunc function() -&gt; Int {\n    // Выполнить некоторые операции\n    return 0\n}\n\n/* Постоянная сложность */\nfunc constant(n: Int) {\n    // Константы, переменные и объекты занимают O(1) памяти\n    let a = 0\n    var b = 0\n    let nums = Array(repeating: 0, count: 10000)\n    let node = ListNode(x: 0)\n    // Переменные в цикле занимают O(1) памяти\n    for _ in 0 ..&lt; n {\n        let c = 0\n    }\n    // Функции в цикле занимают O(1) памяти\n    for _ in 0 ..&lt; n {\n        function()\n    }\n}\n</code></pre> space_complexity.js<pre><code>/* Функция */\nfunction constFunc() {\n    // Выполнить некоторые операции\n    return 0;\n}\n\n/* Постоянная сложность */\nfunction constant(n) {\n    // Константы, переменные и объекты занимают O(1) памяти\n    const a = 0;\n    const b = 0;\n    const nums = new Array(10000);\n    const node = new ListNode(0);\n    // Переменные в цикле занимают O(1) памяти\n    for (let i = 0; i &lt; n; i++) {\n        const c = 0;\n    }\n    // Функции в цикле занимают O(1) памяти\n    for (let i = 0; i &lt; n; i++) {\n        constFunc();\n    }\n}\n</code></pre> space_complexity.ts<pre><code>/* Функция */\nfunction constFunc(): number {\n    // Выполнить некоторые операции\n    return 0;\n}\n\n/* Постоянная сложность */\nfunction constant(n: number): void {\n    // Константы, переменные и объекты занимают O(1) памяти\n    const a = 0;\n    const b = 0;\n    const nums = new Array(10000);\n    const node = new ListNode(0);\n    // Переменные в цикле занимают O(1) памяти\n    for (let i = 0; i &lt; n; i++) {\n        const c = 0;\n    }\n    // Функции в цикле занимают O(1) памяти\n    for (let i = 0; i &lt; n; i++) {\n        constFunc();\n    }\n}\n</code></pre> space_complexity.dart<pre><code>/* Функция */\nint function() {\n  // Выполнить некоторые операции\n  return 0;\n}\n\n/* Постоянная сложность */\nvoid constant(int n) {\n  // Константы, переменные и объекты занимают O(1) памяти\n  final int a = 0;\n  int b = 0;\n  List&lt;int&gt; nums = List.filled(10000, 0);\n  ListNode node = ListNode(0);\n  // Переменные в цикле занимают O(1) памяти\n  for (var i = 0; i &lt; n; i++) {\n    int c = 0;\n  }\n  // Функции в цикле занимают O(1) памяти\n  for (var i = 0; i &lt; n; i++) {\n    function();\n  }\n}\n</code></pre> space_complexity.rs<pre><code>/* Функция */\nfn function() -&gt; i32 {\n    // Выполнить некоторые операции\n    return 0;\n}\n\n/* Постоянная сложность */\n#[allow(unused)]\nfn constant(n: i32) {\n    // Константы, переменные и объекты занимают O(1) памяти\n    const A: i32 = 0;\n    let b = 0;\n    let nums = vec![0; 10000];\n    let node = ListNode::new(0);\n    // Переменные в цикле занимают O(1) памяти\n    for i in 0..n {\n        let c = 0;\n    }\n    // Функции в цикле занимают O(1) памяти\n    for i in 0..n {\n        function();\n    }\n}\n</code></pre> space_complexity.c<pre><code>/* Функция */\nint func() {\n    // Выполнить некоторые операции\n    return 0;\n}\n\n/* Постоянная сложность */\nvoid constant(int n) {\n    // Константы, переменные и объекты занимают O(1) памяти\n    const int a = 0;\n    int b = 0;\n    int nums[1000];\n    ListNode *node = newListNode(0);\n    free(node);\n    // Переменные в цикле занимают O(1) памяти\n    for (int i = 0; i &lt; n; i++) {\n        int c = 0;\n    }\n    // Функции в цикле занимают O(1) памяти\n    for (int i = 0; i &lt; n; i++) {\n        func();\n    }\n}\n</code></pre> space_complexity.kt<pre><code>/* Функция */\nfun function(): Int {\n    // Выполнить некоторые операции\n    return 0\n}\n\n/* Постоянная сложность */\nfun constant(n: Int) {\n    // Константы, переменные и объекты занимают O(1) памяти\n    val a = 0\n    var b = 0\n    val nums = Array(10000) { 0 }\n    val node = ListNode(0)\n    // Переменные в цикле занимают O(1) памяти\n    for (i in 0..&lt;n) {\n        val c = 0\n    }\n    // Функции в цикле занимают O(1) памяти\n    for (i in 0..&lt;n) {\n        function()\n    }\n}\n</code></pre> space_complexity.rb<pre><code>### Функция ###\ndef function\n  # Выполнить некоторые операции\n  0\nend\n\n### Постоянная сложность ###\ndef constant(n)\n  # Константы, переменные и объекты занимают O(1) памяти\n  a = 0\n  nums = [0] * 10000\n  node = ListNode.new\n\n  # Переменные в цикле занимают O(1) памяти\n  (0...n).each { c = 0 }\n  # Функции в цикле занимают O(1) памяти\n  (0...n).each { function }\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 2. Анализ сложности","2.4 &nbsp; Пространственная сложность"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#2-on","level":3,"title":"2.   Линейная сложность \\(O(n)\\)","text":"<p>Линейная сложность часто встречается у массивов, списков, стеков, очередей и других структур, число элементов в которых пропорционально \\(n\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby space_complexity.py<pre><code>def linear(n: int):\n    \"\"\"Линейная сложность\"\"\"\n    # Список длины n занимает O(n) памяти\n    nums = [0] * n\n    # Хеш-таблица длины n занимает O(n) памяти\n    hmap = dict[int, str]()\n    for i in range(n):\n        hmap[i] = str(i)\n</code></pre> space_complexity.cpp<pre><code>/* Линейная сложность */\nvoid linear(int n) {\n    // Массив длины n занимает O(n) памяти\n    vector&lt;int&gt; nums(n);\n    // Список длины n занимает O(n) памяти\n    vector&lt;ListNode&gt; nodes;\n    for (int i = 0; i &lt; n; i++) {\n        nodes.push_back(ListNode(i));\n    }\n    // Хеш-таблица длины n занимает O(n) памяти\n    unordered_map&lt;int, string&gt; map;\n    for (int i = 0; i &lt; n; i++) {\n        map[i] = to_string(i);\n    }\n}\n</code></pre> space_complexity.java<pre><code>/* Линейная сложность */\nvoid linear(int n) {\n    // Массив длины n занимает O(n) памяти\n    int[] nums = new int[n];\n    // Список длины n занимает O(n) памяти\n    List&lt;ListNode&gt; nodes = new ArrayList&lt;&gt;();\n    for (int i = 0; i &lt; n; i++) {\n        nodes.add(new ListNode(i));\n    }\n    // Хеш-таблица длины n занимает O(n) памяти\n    Map&lt;Integer, String&gt; map = new HashMap&lt;&gt;();\n    for (int i = 0; i &lt; n; i++) {\n        map.put(i, String.valueOf(i));\n    }\n}\n</code></pre> space_complexity.cs<pre><code>/* Линейная сложность */\nvoid Linear(int n) {\n    // Массив длины n занимает O(n) памяти\n    int[] nums = new int[n];\n    // Список длины n занимает O(n) памяти\n    List&lt;ListNode&gt; nodes = [];\n    for (int i = 0; i &lt; n; i++) {\n        nodes.Add(new ListNode(i));\n    }\n    // Хеш-таблица длины n занимает O(n) памяти\n    Dictionary&lt;int, string&gt; map = [];\n    for (int i = 0; i &lt; n; i++) {\n        map.Add(i, i.ToString());\n    }\n}\n</code></pre> space_complexity.go<pre><code>/* Линейная сложность */\nfunc spaceLinear(n int) {\n    // Массив длины n занимает O(n) памяти\n    _ = make([]int, n)\n    // Список длины n занимает O(n) памяти\n    var nodes []*node\n    for i := 0; i &lt; n; i++ {\n        nodes = append(nodes, newNode(i))\n    }\n    // Хеш-таблица длины n занимает O(n) памяти\n    m := make(map[int]string, n)\n    for i := 0; i &lt; n; i++ {\n        m[i] = strconv.Itoa(i)\n    }\n}\n</code></pre> space_complexity.swift<pre><code>/* Линейная сложность */\nfunc linear(n: Int) {\n    // Массив длины n занимает O(n) памяти\n    let nums = Array(repeating: 0, count: n)\n    // Список длины n занимает O(n) памяти\n    let nodes = (0 ..&lt; n).map { ListNode(x: $0) }\n    // Хеш-таблица длины n занимает O(n) памяти\n    let map = Dictionary(uniqueKeysWithValues: (0 ..&lt; n).map { ($0, \"\\($0)\") })\n}\n</code></pre> space_complexity.js<pre><code>/* Линейная сложность */\nfunction linear(n) {\n    // Массив длины n занимает O(n) памяти\n    const nums = new Array(n);\n    // Список длины n занимает O(n) памяти\n    const nodes = [];\n    for (let i = 0; i &lt; n; i++) {\n        nodes.push(new ListNode(i));\n    }\n    // Хеш-таблица длины n занимает O(n) памяти\n    const map = new Map();\n    for (let i = 0; i &lt; n; i++) {\n        map.set(i, i.toString());\n    }\n}\n</code></pre> space_complexity.ts<pre><code>/* Линейная сложность */\nfunction linear(n: number): void {\n    // Массив длины n занимает O(n) памяти\n    const nums = new Array(n);\n    // Список длины n занимает O(n) памяти\n    const nodes: ListNode[] = [];\n    for (let i = 0; i &lt; n; i++) {\n        nodes.push(new ListNode(i));\n    }\n    // Хеш-таблица длины n занимает O(n) памяти\n    const map = new Map();\n    for (let i = 0; i &lt; n; i++) {\n        map.set(i, i.toString());\n    }\n}\n</code></pre> space_complexity.dart<pre><code>/* Линейная сложность */\nvoid linear(int n) {\n  // Массив длины n занимает O(n) памяти\n  List&lt;int&gt; nums = List.filled(n, 0);\n  // Список длины n занимает O(n) памяти\n  List&lt;ListNode&gt; nodes = [];\n  for (var i = 0; i &lt; n; i++) {\n    nodes.add(ListNode(i));\n  }\n  // Хеш-таблица длины n занимает O(n) памяти\n  Map&lt;int, String&gt; map = HashMap();\n  for (var i = 0; i &lt; n; i++) {\n    map.putIfAbsent(i, () =&gt; i.toString());\n  }\n}\n</code></pre> space_complexity.rs<pre><code>/* Линейная сложность */\n#[allow(unused)]\nfn linear(n: i32) {\n    // Массив длины n занимает O(n) памяти\n    let mut nums = vec![0; n as usize];\n    // Список длины n занимает O(n) памяти\n    let mut nodes = Vec::new();\n    for i in 0..n {\n        nodes.push(ListNode::new(i))\n    }\n    // Хеш-таблица длины n занимает O(n) памяти\n    let mut map = HashMap::new();\n    for i in 0..n {\n        map.insert(i, i.to_string());\n    }\n}\n</code></pre> space_complexity.c<pre><code>/* Хеш-таблица */\ntypedef struct {\n    int key;\n    int val;\n    UT_hash_handle hh; // Реализовано на основе uthash.h\n} HashTable;\n\n/* Линейная сложность */\nvoid linear(int n) {\n    // Массив длины n занимает O(n) памяти\n    int *nums = malloc(sizeof(int) * n);\n    free(nums);\n\n    // Список длины n занимает O(n) памяти\n    ListNode **nodes = malloc(sizeof(ListNode *) * n);\n    for (int i = 0; i &lt; n; i++) {\n        nodes[i] = newListNode(i);\n    }\n    // Освобождение памяти\n    for (int i = 0; i &lt; n; i++) {\n        free(nodes[i]);\n    }\n    free(nodes);\n\n    // Хеш-таблица длины n занимает O(n) памяти\n    HashTable *h = NULL;\n    for (int i = 0; i &lt; n; i++) {\n        HashTable *tmp = malloc(sizeof(HashTable));\n        tmp-&gt;key = i;\n        tmp-&gt;val = i;\n        HASH_ADD_INT(h, key, tmp);\n    }\n\n    // Освобождение памяти\n    HashTable *curr, *tmp;\n    HASH_ITER(hh, h, curr, tmp) {\n        HASH_DEL(h, curr);\n        free(curr);\n    }\n}\n</code></pre> space_complexity.kt<pre><code>/* Линейная сложность */\nfun linear(n: Int) {\n    // Массив длины n занимает O(n) памяти\n    val nums = Array(n) { 0 }\n    // Список длины n занимает O(n) памяти\n    val nodes = mutableListOf&lt;ListNode&gt;()\n    for (i in 0..&lt;n) {\n        nodes.add(ListNode(i))\n    }\n    // Хеш-таблица длины n занимает O(n) памяти\n    val map = mutableMapOf&lt;Int, String&gt;()\n    for (i in 0..&lt;n) {\n        map[i] = i.toString()\n    }\n}\n</code></pre> space_complexity.rb<pre><code>### Линейная сложность ###\ndef linear(n)\n  # Список длины n занимает O(n) памяти\n  nums = Array.new(n, 0)\n\n  # Хеш-таблица длины n занимает O(n) памяти\n  hmap = {}\n  for i in 0...n\n    hmap[i] = i.to_s\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Как показано на рисунке 2-17, глубина рекурсии этой функции равна \\(n\\) , то есть одновременно существует \\(n\\) еще не завершившихся функций <code>linear_recur()</code> , которые используют \\(O(n)\\) пространства кадров стека:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby space_complexity.py<pre><code>def linear_recur(n: int):\n    \"\"\"Линейная сложность (рекурсивная реализация)\"\"\"\n    print(\"Рекурсия n =\", n)\n    if n == 1:\n        return\n    linear_recur(n - 1)\n</code></pre> space_complexity.cpp<pre><code>/* Линейная сложность (рекурсивная реализация) */\nvoid linearRecur(int n) {\n    cout &lt;&lt; \"Рекурсия n = \" &lt;&lt; n &lt;&lt; endl;\n    if (n == 1)\n        return;\n    linearRecur(n - 1);\n}\n</code></pre> space_complexity.java<pre><code>/* Линейная сложность (рекурсивная реализация) */\nvoid linearRecur(int n) {\n    System.out.println(\"Рекурсия n = \" + n);\n    if (n == 1)\n        return;\n    linearRecur(n - 1);\n}\n</code></pre> space_complexity.cs<pre><code>/* Линейная сложность (рекурсивная реализация) */\nvoid LinearRecur(int n) {\n    Console.WriteLine(\"Рекурсия n = \" + n);\n    if (n == 1) return;\n    LinearRecur(n - 1);\n}\n</code></pre> space_complexity.go<pre><code>/* Линейная сложность (рекурсивная реализация) */\nfunc spaceLinearRecur(n int) {\n    fmt.Println(\"Рекурсия n =\", n)\n    if n == 1 {\n        return\n    }\n    spaceLinearRecur(n - 1)\n}\n</code></pre> space_complexity.swift<pre><code>/* Линейная сложность (рекурсивная реализация) */\nfunc linearRecur(n: Int) {\n    print(\"Рекурсия n = \\(n)\")\n    if n == 1 {\n        return\n    }\n    linearRecur(n: n - 1)\n}\n</code></pre> space_complexity.js<pre><code>/* Линейная сложность (рекурсивная реализация) */\nfunction linearRecur(n) {\n    console.log(`Рекурсия n = ${n}`);\n    if (n === 1) return;\n    linearRecur(n - 1);\n}\n</code></pre> space_complexity.ts<pre><code>/* Линейная сложность (рекурсивная реализация) */\nfunction linearRecur(n: number): void {\n    console.log(`Рекурсия n = ${n}`);\n    if (n === 1) return;\n    linearRecur(n - 1);\n}\n</code></pre> space_complexity.dart<pre><code>/* Линейная сложность (рекурсивная реализация) */\nvoid linearRecur(int n) {\n  print('Рекурсия n = $n');\n  if (n == 1) return;\n  linearRecur(n - 1);\n}\n</code></pre> space_complexity.rs<pre><code>/* Линейная сложность (рекурсивная реализация) */\nfn linear_recur(n: i32) {\n    println!(\"Рекурсия n = {}\", n);\n    if n == 1 {\n        return;\n    };\n    linear_recur(n - 1);\n}\n</code></pre> space_complexity.c<pre><code>/* Линейная сложность (рекурсивная реализация) */\nvoid linearRecur(int n) {\n    printf(\"Рекурсия n = %d\\r\\n\", n);\n    if (n == 1)\n        return;\n    linearRecur(n - 1);\n}\n</code></pre> space_complexity.kt<pre><code>/* Линейная сложность (рекурсивная реализация) */\nfun linearRecur(n: Int) {\n    println(\"Рекурсия n = $n\")\n    if (n == 1)\n        return\n    linearRecur(n - 1)\n}\n</code></pre> space_complexity.rb<pre><code>### Линейная сложность ###\ndef linear(n)\n  # Список длины n занимает O(n) памяти\n  nums = Array.new(n, 0)\n\n  # Хеш-таблица длины n занимает O(n) памяти\n  hmap = {}\n  for i in 0...n\n    hmap[i] = i.to_s\n  end\nend\n\n# ## Линейная сложность (рекурсивная реализация) ###\ndef linear_recur(n)\n  puts \"Рекурсия n = #{n}\"\n  return if n == 1\n  linear_recur(n - 1)\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p></p> <p> Рисунок 2-17   Линейная пространственная сложность, порождаемая рекурсивной функцией </p>","path":["Глава 2. Анализ сложности","2.4 &nbsp; Пространственная сложность"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#3-on2","level":3,"title":"3.   Квадратичная сложность \\(O(n^2)\\)","text":"<p>Квадратичная сложность часто встречается у матриц и графов, где число элементов связано с \\(n\\) квадратичной зависимостью:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby space_complexity.py<pre><code>def quadratic(n: int):\n    \"\"\"Квадратичная сложность\"\"\"\n    # Двумерный список занимает O(n^2) памяти\n    num_matrix = [[0] * n for _ in range(n)]\n</code></pre> space_complexity.cpp<pre><code>/* Квадратичная сложность */\nvoid quadratic(int n) {\n    // Двумерный список занимает O(n^2) памяти\n    vector&lt;vector&lt;int&gt;&gt; numMatrix;\n    for (int i = 0; i &lt; n; i++) {\n        vector&lt;int&gt; tmp;\n        for (int j = 0; j &lt; n; j++) {\n            tmp.push_back(0);\n        }\n        numMatrix.push_back(tmp);\n    }\n}\n</code></pre> space_complexity.java<pre><code>/* Квадратичная сложность */\nvoid quadratic(int n) {\n    // Матрица занимает O(n^2) памяти\n    int[][] numMatrix = new int[n][n];\n    // Двумерный список занимает O(n^2) памяти\n    List&lt;List&lt;Integer&gt;&gt; numList = new ArrayList&lt;&gt;();\n    for (int i = 0; i &lt; n; i++) {\n        List&lt;Integer&gt; tmp = new ArrayList&lt;&gt;();\n        for (int j = 0; j &lt; n; j++) {\n            tmp.add(0);\n        }\n        numList.add(tmp);\n    }\n}\n</code></pre> space_complexity.cs<pre><code>/* Квадратичная сложность */\nvoid Quadratic(int n) {\n    // Матрица занимает O(n^2) памяти\n    int[,] numMatrix = new int[n, n];\n    // Двумерный список занимает O(n^2) памяти\n    List&lt;List&lt;int&gt;&gt; numList = [];\n    for (int i = 0; i &lt; n; i++) {\n        List&lt;int&gt; tmp = [];\n        for (int j = 0; j &lt; n; j++) {\n            tmp.Add(0);\n        }\n        numList.Add(tmp);\n    }\n}\n</code></pre> space_complexity.go<pre><code>/* Квадратичная сложность */\nfunc spaceQuadratic(n int) {\n    // Матрица занимает O(n^2) памяти\n    numMatrix := make([][]int, n)\n    for i := 0; i &lt; n; i++ {\n        numMatrix[i] = make([]int, n)\n    }\n}\n</code></pre> space_complexity.swift<pre><code>/* Квадратичная сложность */\nfunc quadratic(n: Int) {\n    // Двумерный список занимает O(n^2) памяти\n    let numList = Array(repeating: Array(repeating: 0, count: n), count: n)\n}\n</code></pre> space_complexity.js<pre><code>/* Квадратичная сложность */\nfunction quadratic(n) {\n    // Матрица занимает O(n^2) памяти\n    const numMatrix = Array(n)\n        .fill(null)\n        .map(() =&gt; Array(n).fill(null));\n    // Двумерный список занимает O(n^2) памяти\n    const numList = [];\n    for (let i = 0; i &lt; n; i++) {\n        const tmp = [];\n        for (let j = 0; j &lt; n; j++) {\n            tmp.push(0);\n        }\n        numList.push(tmp);\n    }\n}\n</code></pre> space_complexity.ts<pre><code>/* Квадратичная сложность */\nfunction quadratic(n: number): void {\n    // Матрица занимает O(n^2) памяти\n    const numMatrix = Array(n)\n        .fill(null)\n        .map(() =&gt; Array(n).fill(null));\n    // Двумерный список занимает O(n^2) памяти\n    const numList = [];\n    for (let i = 0; i &lt; n; i++) {\n        const tmp = [];\n        for (let j = 0; j &lt; n; j++) {\n            tmp.push(0);\n        }\n        numList.push(tmp);\n    }\n}\n</code></pre> space_complexity.dart<pre><code>/* Квадратичная сложность */\nvoid quadratic(int n) {\n  // Матрица занимает O(n^2) памяти\n  List&lt;List&lt;int&gt;&gt; numMatrix = List.generate(n, (_) =&gt; List.filled(n, 0));\n  // Двумерный список занимает O(n^2) памяти\n  List&lt;List&lt;int&gt;&gt; numList = [];\n  for (var i = 0; i &lt; n; i++) {\n    List&lt;int&gt; tmp = [];\n    for (int j = 0; j &lt; n; j++) {\n      tmp.add(0);\n    }\n    numList.add(tmp);\n  }\n}\n</code></pre> space_complexity.rs<pre><code>/* Квадратичная сложность */\n#[allow(unused)]\nfn quadratic(n: i32) {\n    // Матрица занимает O(n^2) памяти\n    let num_matrix = vec![vec![0; n as usize]; n as usize];\n    // Двумерный список занимает O(n^2) памяти\n    let mut num_list = Vec::new();\n    for i in 0..n {\n        let mut tmp = Vec::new();\n        for j in 0..n {\n            tmp.push(0);\n        }\n        num_list.push(tmp);\n    }\n}\n</code></pre> space_complexity.c<pre><code>/* Квадратичная сложность */\nvoid quadratic(int n) {\n    // Двумерный список занимает O(n^2) памяти\n    int **numMatrix = malloc(sizeof(int *) * n);\n    for (int i = 0; i &lt; n; i++) {\n        int *tmp = malloc(sizeof(int) * n);\n        for (int j = 0; j &lt; n; j++) {\n            tmp[j] = 0;\n        }\n        numMatrix[i] = tmp;\n    }\n\n    // Освобождение памяти\n    for (int i = 0; i &lt; n; i++) {\n        free(numMatrix[i]);\n    }\n    free(numMatrix);\n}\n</code></pre> space_complexity.kt<pre><code>/* Квадратичная сложность */\nfun quadratic(n: Int) {\n    // Матрица занимает O(n^2) памяти\n    val numMatrix = arrayOfNulls&lt;Array&lt;Int&gt;?&gt;(n)\n    // Двумерный список занимает O(n^2) памяти\n    val numList = mutableListOf&lt;MutableList&lt;Int&gt;&gt;()\n    for (i in 0..&lt;n) {\n        val tmp = mutableListOf&lt;Int&gt;()\n        for (j in 0..&lt;n) {\n            tmp.add(0)\n        }\n        numList.add(tmp)\n    }\n}\n</code></pre> space_complexity.rb<pre><code>### Квадратичная сложность ###\ndef quadratic(n)\n  # Двумерный список занимает O(n^2) памяти\n  Array.new(n) { Array.new(n, 0) }\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Как показано на рисунке 2-18, глубина рекурсии этой функции равна \\(n\\) , и в каждой рекурсивной функции инициализируется массив длины \\(n\\) , \\(n-1\\) , \\(\\dots\\) , \\(2\\) , \\(1\\) ; его средняя длина равна \\(n / 2\\) , поэтому в сумме используется \\(O(n^2)\\) пространства:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby space_complexity.py<pre><code>def quadratic_recur(n: int) -&gt; int:\n    \"\"\"Квадратичная сложность (рекурсивная реализация)\"\"\"\n    if n &lt;= 0:\n        return 0\n    # Длина массива nums равна n, n-1, ..., 2, 1\n    nums = [0] * n\n    return quadratic_recur(n - 1)\n</code></pre> space_complexity.cpp<pre><code>/* Квадратичная сложность (рекурсивная реализация) */\nint quadraticRecur(int n) {\n    if (n &lt;= 0)\n        return 0;\n    vector&lt;int&gt; nums(n);\n    cout &lt;&lt; \"Рекурсия n = \" &lt;&lt; n &lt;&lt; \" , длина nums = \" &lt;&lt; nums.size() &lt;&lt; endl;\n    return quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.java<pre><code>/* Квадратичная сложность (рекурсивная реализация) */\nint quadraticRecur(int n) {\n    if (n &lt;= 0)\n        return 0;\n    // Длина массива nums равна n, n-1, ..., 2, 1\n    int[] nums = new int[n];\n    System.out.println(\"В рекурсии n = \" + n + \", длина nums = \" + nums.length);\n    return quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.cs<pre><code>/* Квадратичная сложность (рекурсивная реализация) */\nint QuadraticRecur(int n) {\n    if (n &lt;= 0) return 0;\n    int[] nums = new int[n];\n    Console.WriteLine(\"В рекурсии n = \" + n + \", длина nums = \" + nums.Length);\n    return QuadraticRecur(n - 1);\n}\n</code></pre> space_complexity.go<pre><code>/* Квадратичная сложность (рекурсивная реализация) */\nfunc spaceQuadraticRecur(n int) int {\n    if n &lt;= 0 {\n        return 0\n    }\n    nums := make([]int, n)\n    fmt.Printf(\"В рекурсии n = %d, длина nums = %d\\n\", n, len(nums))\n    return spaceQuadraticRecur(n - 1)\n}\n</code></pre> space_complexity.swift<pre><code>/* Квадратичная сложность (рекурсивная реализация) */\n@discardableResult\nfunc quadraticRecur(n: Int) -&gt; Int {\n    if n &lt;= 0 {\n        return 0\n    }\n    // Длина массива nums равна n, n-1, ..., 2, 1\n    let nums = Array(repeating: 0, count: n)\n    print(\"В рекурсии n = \\(n), длина nums = \\(nums.count)\")\n    return quadraticRecur(n: n - 1)\n}\n</code></pre> space_complexity.js<pre><code>/* Квадратичная сложность (рекурсивная реализация) */\nfunction quadraticRecur(n) {\n    if (n &lt;= 0) return 0;\n    const nums = new Array(n);\n    console.log(`В рекурсии n = ${n} длина nums = ${nums.length}`);\n    return quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.ts<pre><code>/* Квадратичная сложность (рекурсивная реализация) */\nfunction quadraticRecur(n: number): number {\n    if (n &lt;= 0) return 0;\n    const nums = new Array(n);\n    console.log(`В рекурсии n = ${n} длина nums = ${nums.length}`);\n    return quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.dart<pre><code>/* Квадратичная сложность (рекурсивная реализация) */\nint quadraticRecur(int n) {\n  if (n &lt;= 0) return 0;\n  List&lt;int&gt; nums = List.filled(n, 0);\n  print('В рекурсии n = $n длина nums = ${nums.length}');\n  return quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.rs<pre><code>/* Квадратичная сложность (рекурсивная реализация) */\nfn quadratic_recur(n: i32) -&gt; i32 {\n    if n &lt;= 0 {\n        return 0;\n    };\n    // Длина массива nums равна n, n-1, ..., 2, 1\n    let nums = vec![0; n as usize];\n    println!(\"В рекурсии n = {} , длина nums = {}\", n, nums.len());\n    return quadratic_recur(n - 1);\n}\n</code></pre> space_complexity.c<pre><code>/* Квадратичная сложность (рекурсивная реализация) */\nint quadraticRecur(int n) {\n    if (n &lt;= 0)\n        return 0;\n    int *nums = malloc(sizeof(int) * n);\n    printf(\"Рекурсия n = %d, длина nums = %d\\r\\n\", n, n);\n    int res = quadraticRecur(n - 1);\n    free(nums);\n    return res;\n}\n</code></pre> space_complexity.kt<pre><code>/* Квадратичная сложность (рекурсивная реализация) */\ntailrec fun quadraticRecur(n: Int): Int {\n    if (n &lt;= 0)\n        return 0\n    // Длина массива nums равна n, n-1, ..., 2, 1\n    val nums = Array(n) { 0 }\n    println(\"В рекурсии n = $n длина nums = ${nums.size}\")\n    return quadraticRecur(n - 1)\n}\n</code></pre> space_complexity.rb<pre><code>### Квадратичная сложность ###\ndef quadratic(n)\n  # Двумерный список занимает O(n^2) памяти\n  Array.new(n) { Array.new(n, 0) }\nend\n\n# ## Квадратичная сложность (рекурсивная реализация) ###\ndef quadratic_recur(n)\n  return 0 unless n &gt; 0\n\n  # Длина массива nums равна n, n-1, ..., 2, 1\n  nums = Array.new(n, 0)\n  quadratic_recur(n - 1)\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p></p> <p> Рисунок 2-18   Квадратичная пространственная сложность, порождаемая рекурсивной функцией </p>","path":["Глава 2. Анализ сложности","2.4 &nbsp; Пространственная сложность"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#4-o2n","level":3,"title":"4.   Экспоненциальная сложность \\(O(2^n)\\)","text":"<p>Экспоненциальная сложность часто встречается у бинарных деревьев. Полное бинарное дерево с \\(n\\) уровнями содержит \\(2^n - 1\\) узлов и занимает \\(O(2^n)\\) пространства:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby space_complexity.py<pre><code>def build_tree(n: int) -&gt; TreeNode | None:\n    \"\"\"Экспоненциальная сложность (построение полного двоичного дерева)\"\"\"\n    if n == 0:\n        return None\n    root = TreeNode(0)\n    root.left = build_tree(n - 1)\n    root.right = build_tree(n - 1)\n    return root\n</code></pre> space_complexity.cpp<pre><code>/* Экспоненциальная сложность (построение полного двоичного дерева) */\nTreeNode *buildTree(int n) {\n    if (n == 0)\n        return nullptr;\n    TreeNode *root = new TreeNode(0);\n    root-&gt;left = buildTree(n - 1);\n    root-&gt;right = buildTree(n - 1);\n    return root;\n}\n</code></pre> space_complexity.java<pre><code>/* Экспоненциальная сложность (построение полного двоичного дерева) */\nTreeNode buildTree(int n) {\n    if (n == 0)\n        return null;\n    TreeNode root = new TreeNode(0);\n    root.left = buildTree(n - 1);\n    root.right = buildTree(n - 1);\n    return root;\n}\n</code></pre> space_complexity.cs<pre><code>/* Экспоненциальная сложность (построение полного двоичного дерева) */\nTreeNode? BuildTree(int n) {\n    if (n == 0) return null;\n    TreeNode root = new(0) {\n        left = BuildTree(n - 1),\n        right = BuildTree(n - 1)\n    };\n    return root;\n}\n</code></pre> space_complexity.go<pre><code>/* Экспоненциальная сложность (построение полного двоичного дерева) */\nfunc buildTree(n int) *TreeNode {\n    if n == 0 {\n        return nil\n    }\n    root := NewTreeNode(0)\n    root.Left = buildTree(n - 1)\n    root.Right = buildTree(n - 1)\n    return root\n}\n</code></pre> space_complexity.swift<pre><code>/* Экспоненциальная сложность (построение полного двоичного дерева) */\nfunc buildTree(n: Int) -&gt; TreeNode? {\n    if n == 0 {\n        return nil\n    }\n    let root = TreeNode(x: 0)\n    root.left = buildTree(n: n - 1)\n    root.right = buildTree(n: n - 1)\n    return root\n}\n</code></pre> space_complexity.js<pre><code>/* Экспоненциальная сложность (построение полного двоичного дерева) */\nfunction buildTree(n) {\n    if (n === 0) return null;\n    const root = new TreeNode(0);\n    root.left = buildTree(n - 1);\n    root.right = buildTree(n - 1);\n    return root;\n}\n</code></pre> space_complexity.ts<pre><code>/* Экспоненциальная сложность (построение полного двоичного дерева) */\nfunction buildTree(n: number): TreeNode | null {\n    if (n === 0) return null;\n    const root = new TreeNode(0);\n    root.left = buildTree(n - 1);\n    root.right = buildTree(n - 1);\n    return root;\n}\n</code></pre> space_complexity.dart<pre><code>/* Экспоненциальная сложность (построение полного двоичного дерева) */\nTreeNode? buildTree(int n) {\n  if (n == 0) return null;\n  TreeNode root = TreeNode(0);\n  root.left = buildTree(n - 1);\n  root.right = buildTree(n - 1);\n  return root;\n}\n</code></pre> space_complexity.rs<pre><code>/* Экспоненциальная сложность (построение полного двоичного дерева) */\nfn build_tree(n: i32) -&gt; Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt; {\n    if n == 0 {\n        return None;\n    };\n    let root = TreeNode::new(0);\n    root.borrow_mut().left = build_tree(n - 1);\n    root.borrow_mut().right = build_tree(n - 1);\n    return Some(root);\n}\n</code></pre> space_complexity.c<pre><code>/* Экспоненциальная сложность (построение полного двоичного дерева) */\nTreeNode *buildTree(int n) {\n    if (n == 0)\n        return NULL;\n    TreeNode *root = newTreeNode(0);\n    root-&gt;left = buildTree(n - 1);\n    root-&gt;right = buildTree(n - 1);\n    return root;\n}\n</code></pre> space_complexity.kt<pre><code>/* Экспоненциальная сложность (построение полного двоичного дерева) */\nfun buildTree(n: Int): TreeNode? {\n    if (n == 0)\n        return null\n    val root = TreeNode(0)\n    root.left = buildTree(n - 1)\n    root.right = buildTree(n - 1)\n    return root\n}\n</code></pre> space_complexity.rb<pre><code>### Квадратичная сложность ###\ndef quadratic(n)\n  # Двумерный список занимает O(n^2) памяти\n  Array.new(n) { Array.new(n, 0) }\nend\n\n# ## Квадратичная сложность (рекурсивная реализация) ###\ndef quadratic_recur(n)\n  return 0 unless n &gt; 0\n\n  # Длина массива nums равна n, n-1, ..., 2, 1\n  nums = Array.new(n, 0)\n  quadratic_recur(n - 1)\nend\n\n# ## Экспоненциальная сложность (построение полного двоичного дерева) ###\ndef build_tree(n)\n  return if n == 0\n\n  TreeNode.new.tap do |root|\n    root.left = build_tree(n - 1)\n    root.right = build_tree(n - 1)\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p></p> <p> Рисунок 2-19   Экспоненциальная пространственная сложность, порождаемая полным бинарным деревом </p>","path":["Глава 2. Анализ сложности","2.4 &nbsp; Пространственная сложность"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#5-olog-n","level":3,"title":"5.   Логарифмическая сложность \\(O(\\log n)\\)","text":"<p>Логарифмическая сложность часто встречается в алгоритмах \"разделяй и властвуй\". Например, при сортировке слиянием входной массив длины \\(n\\) на каждом шаге рекурсии делится пополам, образуя рекурсивное дерево высоты \\(\\log n\\) и используя \\(O(\\log n)\\) пространства кадров стека.</p> <p>Еще один пример - преобразование числа в строку. Если задано положительное целое число \\(n\\) , то количество его цифр равно \\(\\lfloor \\log_{10} n \\rfloor + 1\\) , то есть длина соответствующей строки тоже равна \\(\\lfloor \\log_{10} n \\rfloor + 1\\) , следовательно, пространственная сложность составляет \\(O(\\log_{10} n + 1) = O(\\log n)\\) .</p>","path":["Глава 2. Анализ сложности","2.4 &nbsp; Пространственная сложность"],"tags":[]},{"location":"chapter_computational_complexity/space_complexity/#244","level":2,"title":"2.4.4   Компромисс между временем и пространством","text":"<p>В идеальных условиях хотелось бы, чтобы и временная, и пространственная сложность алгоритма были оптимальными. Однако на практике одновременно оптимизировать и время, и память обычно очень трудно.</p> <p>Снижение временной сложности обычно достигается ценой увеличения пространственной сложности, и наоборот. Подход, при котором жертвуют памятью ради ускорения работы алгоритма, называется обменом пространства на время; обратный подход называется обменом времени на пространство.</p> <p>Выбор между этими двумя идеями зависит от того, что важнее в конкретной задаче. В большинстве случаев время ценнее памяти, поэтому стратегия обмена пространства на время используется чаще. Но при очень больших объемах данных контроль пространственной сложности тоже становится крайне важным.</p>","path":["Глава 2. Анализ сложности","2.4 &nbsp; Пространственная сложность"],"tags":[]},{"location":"chapter_computational_complexity/summary/","level":1,"title":"2.5   Резюме","text":"","path":["Глава 2. Анализ сложности","2.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_computational_complexity/summary/#1","level":3,"title":"1.   Ключевые выводы","text":"<p>Оценка эффективности алгоритмов</p> <ul> <li>Временная и пространственная эффективность являются двумя основными критериями для оценки качества алгоритмов.</li> <li>Эффективность алгоритмов можно оценивать с помощью практических тестов, однако это сложно из-за влияния тестовой среды и значительных затрат вычислительных ресурсов.</li> <li>Анализ сложности позволяет устранить недостатки практических тестов, а результаты анализа применимы ко всем платформам и могут выявить эффективность алгоритма при различных объемах данных.</li> </ul> <p>Временная сложность</p> <ul> <li>Временная сложность используется для оценки тенденции изменения времени выполнения алгоритма с увеличением объема данных, что позволяет оценивать его эффективность. Однако в некоторых случаях она может работать не так хорошо, например когда объем входных данных мал или временная сложность одинакова, что не позволяет точно сравнить эффективность алгоритмов.</li> <li>Худшая временная сложность обозначается символом Big \\(O\\) и соответствует асимптотической верхней границе, отражая уровень роста количества операций \\(T(n)\\) при стремлении \\(n\\) к бесконечности.</li> <li>Определение временной сложности включает два этапа: сначала подсчитывается количество операций, затем определяется асимптотическая верхняя граница.</li> <li>Наиболее распространенные временные сложности в порядке возрастания: \\(O(1)\\), \\(O(\\log n)\\), \\(O(n)\\), \\(O(n \\log n)\\), \\(O(n^2)\\), \\(O(2^n)\\) и \\(O(n!)\\).</li> <li>Временная сложность некоторых алгоритмов не является фиксированной и зависит от распределения входных данных. Временная сложность делится на худшую, лучшую и среднюю. Лучшая временная сложность почти не используется, так как для достижения лучшего случая входные данные должны соответствовать строгим критериям.</li> <li>Средняя временная сложность отражает эффективность алгоритма при случайных входных данных и наиболее близка к реальной производительности алгоритма. Для расчета средней временной сложности необходимо учитывать распределение входных данных и математическое ожидание.</li> </ul> <p>Пространственная сложность</p> <ul> <li>Пространственная сложность аналогична временной сложности и используется для оценки тенденции изменения объема памяти, занимаемой алгоритмом, с увеличением объема данных.</li> <li>Память, используемую в процессе выполнения алгоритма, можно разделить на входное пространство, временное пространство и выходное пространство. Обычно при расчете пространственной сложности входное пространство не учитывается. Временное пространство делится на временные данные, пространство стека и пространство инструкций, причем пространство стека обычно влияет на сложность только в рекурсивных функциях.</li> <li>Обычно рассматривается только худшая пространственная сложность, то есть пространственная сложность алгоритма при худших входных данных и в худший момент выполнения.</li> <li>Наиболее распространенные пространственные сложности в порядке возрастания: \\(O(1)\\), \\(O(\\log n)\\), \\(O(n)\\), \\(O(n^2)\\) и \\(O(2^n)\\).</li> </ul>","path":["Глава 2. Анализ сложности","2.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_computational_complexity/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: Является ли пространственная сложность хвостовой рекурсии равной \\(O(1)\\)?</p> <p>Теоретически пространственную сложность хвостово-рекурсивных функций можно оптимизировать до \\(O(1)\\) . Однако большинство языков программирования (например Java, Python, C++, Go, C# и другие) не поддерживают автоматическую оптимизацию хвостовой рекурсии, поэтому на практике пространственная сложность обычно считается равной \\(O(n)\\) .</p> <p>Q: В чем разница между терминами function и method?</p> <p>Функция (function) может выполняться независимо, и все ее параметры передаются явно. Метод (method) связан с объектом, неявно получает объект, который его вызывает, и может работать с данными, содержащимися в экземпляре класса.</p> <p>Ниже это проиллюстрировано на примере нескольких распространенных языков программирования.</p> <ul> <li>C - процедурный язык программирования без объектно-ориентированной модели, поэтому в нем есть только функции. Однако мы можем имитировать объектно-ориентированное программирование через структуры (<code>struct</code>), и функции, связанные со структурами, эквивалентны методам в других языках.</li> <li>Java и C# - объектно-ориентированные языки программирования, в которых блоки кода (методы) обычно являются частью класса. Статические методы по поведению похожи на функции, потому что они привязаны к классу и не могут обращаться к конкретным переменным экземпляра.</li> <li>C++ и Python поддерживают как процедурное программирование (функции), так и объектно-ориентированное программирование (методы).</li> </ul> <p>Q: Отражает ли диаграмма \"распространенных типов пространственной сложности\" абсолютный размер занятой памяти?</p> <p>Нет, эта диаграмма показывает пространственную сложность, а значит отражает именно тенденцию роста, а не абсолютный объем занятого пространства.</p> <p>Если взять \\(n = 8\\) , можно заметить, что значения на кривых не совпадают напрямую с соответствующими функциями. Это связано с тем, что каждая кривая содержит константный член, который сжимает диапазон значений до визуально удобного масштаба.</p> <p>На практике, поскольку мы обычно не знаем, какова \"константная\" сложность каждого метода, только по сложности мы, как правило, не можем выбрать оптимальное решение для случая \\(n = 8\\) . Но для \\(n = 8^5\\) выбор уже очевиден: в этой области доминирует именно тенденция роста.</p> <p>Q: Бывают ли случаи, когда в реальных сценариях алгоритм специально проектируют так, чтобы жертвовать временем ради пространства или пространством ради времени?</p> <p>На практике в большинстве случаев выбирают обмен пространства на время. Например, для индексов в базах данных обычно строят B+ деревья или хеш-индексы, расходуя значительный объем памяти ради эффективных запросов уровня \\(O(\\log n)\\) или даже \\(O(1)\\).</p> <p>В сценариях, где память особенно дорога, наоборот, могут жертвовать временем ради пространства. Например, в embedded-разработке память устройства очень ограничена, поэтому инженеры могут отказаться от хеш-таблиц и выбрать последовательный поиск по массиву, экономя память ценой более медленного поиска.</p>","path":["Глава 2. Анализ сложности","2.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/","level":1,"title":"2.3   Временная сложность","text":"<p>Время выполнения действительно может наглядно и точно отражать эффективность алгоритма. Но если мы захотим точно оценить время работы некоторого фрагмента кода, то столкнемся со следующими шагами.</p> <ol> <li>Определить платформу выполнения, включая конфигурацию оборудования, язык программирования, системную среду и т.д., поскольку все эти факторы влияют на эффективность выполнения кода.</li> <li>Оценить время выполнения различных вычислительных операций, например операция сложения <code>+</code> требует 1 нс , операция умножения <code>*</code> требует 10 нс , операция вывода <code>print()</code> требует 5 нс и т.д.</li> <li>Подсчитать все вычислительные операции в коде и суммировать время выполнения всех операций, чтобы получить общее время работы.</li> </ol> <p>Например, в следующем коде размер входных данных равен \\(n\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code># На некоторой платформе выполнения\ndef algorithm(n: int):\n    a = 2      # 1 нс\n    a = a + 1  # 1 нс\n    a = a * 2  # 10 нс\n    # Цикл выполняется n раз\n    for _ in range(n):  # 1 нс\n        print(0)        # 5 нс\n</code></pre> <pre><code>// На некоторой платформе выполнения\nvoid algorithm(int n) {\n    int a = 2;  // 1 нс\n    a = a + 1;  // 1 нс\n    a = a * 2;  // 10 нс\n    // Цикл выполняется n раз\n    for (int i = 0; i &lt; n; i++) {  // 1 нс\n        cout &lt;&lt; 0 &lt;&lt; endl;         // 5 нс\n    }\n}\n</code></pre> <pre><code>// На некоторой платформе выполнения\nvoid algorithm(int n) {\n    int a = 2;  // 1 нс\n    a = a + 1;  // 1 нс\n    a = a * 2;  // 10 нс\n    // Цикл выполняется n раз\n    for (int i = 0; i &lt; n; i++) {  // 1 нс\n        System.out.println(0);     // 5 нс\n    }\n}\n</code></pre> <pre><code>// На некоторой платформе выполнения\nvoid Algorithm(int n) {\n    int a = 2;  // 1 нс\n    a = a + 1;  // 1 нс\n    a = a * 2;  // 10 нс\n    // Цикл выполняется n раз\n    for (int i = 0; i &lt; n; i++) {  // 1 нс\n        Console.WriteLine(0);      // 5 нс\n    }\n}\n</code></pre> <pre><code>// На некоторой платформе выполнения\nfunc algorithm(n int) {\n    a := 2     // 1 нс\n    a = a + 1  // 1 нс\n    a = a * 2  // 10 нс\n    // Цикл выполняется n раз\n    for i := 0; i &lt; n; i++ {  // 1 нс\n        fmt.Println(a)        // 5 нс\n    }\n}\n</code></pre> <pre><code>// На некоторой платформе выполнения\nfunc algorithm(n: Int) {\n    var a = 2 // 1 нс\n    a = a + 1 // 1 нс\n    a = a * 2 // 10 нс\n    // Цикл выполняется n раз\n    for _ in 0 ..&lt; n { // 1 нс\n        print(0) // 5 нс\n    }\n}\n</code></pre> <pre><code>// На некоторой платформе выполнения\nfunction algorithm(n) {\n    var a = 2; // 1 нс\n    a = a + 1; // 1 нс\n    a = a * 2; // 10 нс\n    // Цикл выполняется n раз\n    for(let i = 0; i &lt; n; i++) { // 1 нс\n        console.log(0); // 5 нс\n    }\n}\n</code></pre> <pre><code>// На некоторой платформе выполнения\nfunction algorithm(n: number): void {\n    var a: number = 2; // 1 нс\n    a = a + 1; // 1 нс\n    a = a * 2; // 10 нс\n    // Цикл выполняется n раз\n    for(let i = 0; i &lt; n; i++) { // 1 нс\n        console.log(0); // 5 нс\n    }\n}\n</code></pre> <pre><code>// На некоторой платформе выполнения\nvoid algorithm(int n) {\n  int a = 2; // 1 нс\n  a = a + 1; // 1 нс\n  a = a * 2; // 10 нс\n  // Цикл выполняется n раз\n  for (int i = 0; i &lt; n; i++) { // 1 нс\n    print(0); // 5 нс\n  }\n}\n</code></pre> <pre><code>// На некоторой платформе выполнения\nfn algorithm(n: i32) {\n    let mut a = 2;      // 1 нс\n    a = a + 1;          // 1 нс\n    a = a * 2;          // 10 нс\n    // Цикл выполняется n раз\n    for _ in 0..n {     // 1 нс\n        println!(\"{}\", 0);  // 5 нс\n    }\n}\n</code></pre> <pre><code>// На некоторой платформе выполнения\nvoid algorithm(int n) {\n    int a = 2;  // 1 нс\n    a = a + 1;  // 1 нс\n    a = a * 2;  // 10 нс\n    // Цикл выполняется n раз\n    for (int i = 0; i &lt; n; i++) {   // 1 нс\n        printf(\"%d\", 0);            // 5 нс\n    }\n}\n</code></pre> <pre><code>// На некоторой платформе выполнения\nfun algorithm(n: Int) {\n    var a = 2 // 1 нс\n    a = a + 1 // 1 нс\n    a = a * 2 // 10 нс\n    // Цикл выполняется n раз\n    for (i in 0..&lt;n) {  // 1 нс\n        println(0)      // 5 нс\n    }\n}\n</code></pre> <pre><code># На некоторой платформе выполнения\ndef algorithm(n)\n    a = 2       # 1 нс\n    a = a + 1   # 1 нс\n    a = a * 2   # 10 нс\n    # Цикл выполняется n раз\n    (0...n).each do # 1 нс\n        puts 0      # 5 нс\n    end\nend\n</code></pre> <p>Согласно приведенному выше методу, время работы алгоритма равно \\((6n + 12)\\) нс :</p> \\[ 1 + 1 + 10 + (1 + 5) \\times n = 6n + 12 \\] <p>Но на практике подсчитывать реальное время выполнения алгоритма и неразумно, и нереалистично. Во-первых, мы не хотим привязывать оценку времени к конкретной платформе, потому что алгоритм должен запускаться на самых разных платформах. Во-вторых, нам трудно определить время выполнения каждого типа операций, а это делает точную оценку крайне затруднительной.</p>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#231","level":2,"title":"2.3.1   Подсчет тенденции роста времени","text":"<p>Анализ временной сложности оценивает не само время выполнения алгоритма, а тенденцию роста этого времени по мере увеличения объема данных.</p> <p>Понятие \"тенденции роста времени\" выглядит довольно абстрактным, поэтому разберем его на примере. Предположим, размер входных данных равен \\(n\\) , и даны три алгоритма <code>A</code> , <code>B</code> и <code>C</code> :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code># Временная сложность алгоритма A: постоянная\ndef algorithm_A(n: int):\n    print(0)\n# Временная сложность алгоритма B: линейная\ndef algorithm_B(n: int):\n    for _ in range(n):\n        print(0)\n# Временная сложность алгоритма C: постоянная\ndef algorithm_C(n: int):\n    for _ in range(1000000):\n        print(0)\n</code></pre> <pre><code>// Временная сложность алгоритма A: постоянная\nvoid algorithm_A(int n) {\n    cout &lt;&lt; 0 &lt;&lt; endl;\n}\n// Временная сложность алгоритма B: линейная\nvoid algorithm_B(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        cout &lt;&lt; 0 &lt;&lt; endl;\n    }\n}\n// Временная сложность алгоритма C: постоянная\nvoid algorithm_C(int n) {\n    for (int i = 0; i &lt; 1000000; i++) {\n        cout &lt;&lt; 0 &lt;&lt; endl;\n    }\n}\n</code></pre> <pre><code>// Временная сложность алгоритма A: постоянная\nvoid algorithm_A(int n) {\n    System.out.println(0);\n}\n// Временная сложность алгоритма B: линейная\nvoid algorithm_B(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        System.out.println(0);\n    }\n}\n// Временная сложность алгоритма C: постоянная\nvoid algorithm_C(int n) {\n    for (int i = 0; i &lt; 1000000; i++) {\n        System.out.println(0);\n    }\n}\n</code></pre> <pre><code>// Временная сложность алгоритма A: постоянная\nvoid AlgorithmA(int n) {\n    Console.WriteLine(0);\n}\n// Временная сложность алгоритма B: линейная\nvoid AlgorithmB(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        Console.WriteLine(0);\n    }\n}\n// Временная сложность алгоритма C: постоянная\nvoid AlgorithmC(int n) {\n    for (int i = 0; i &lt; 1000000; i++) {\n        Console.WriteLine(0);\n    }\n}\n</code></pre> <pre><code>// Временная сложность алгоритма A: постоянная\nfunc algorithm_A(n int) {\n    fmt.Println(0)\n}\n// Временная сложность алгоритма B: линейная\nfunc algorithm_B(n int) {\n    for i := 0; i &lt; n; i++ {\n        fmt.Println(0)\n    }\n}\n// Временная сложность алгоритма C: постоянная\nfunc algorithm_C(n int) {\n    for i := 0; i &lt; 1000000; i++ {\n        fmt.Println(0)\n    }\n}\n</code></pre> <pre><code>// Временная сложность алгоритма A: постоянная\nfunc algorithmA(n: Int) {\n    print(0)\n}\n\n// Временная сложность алгоритма B: линейная\nfunc algorithmB(n: Int) {\n    for _ in 0 ..&lt; n {\n        print(0)\n    }\n}\n\n// Временная сложность алгоритма C: постоянная\nfunc algorithmC(n: Int) {\n    for _ in 0 ..&lt; 1_000_000 {\n        print(0)\n    }\n}\n</code></pre> <pre><code>// Временная сложность алгоритма A: постоянная\nfunction algorithm_A(n) {\n    console.log(0);\n}\n// Временная сложность алгоритма B: линейная\nfunction algorithm_B(n) {\n    for (let i = 0; i &lt; n; i++) {\n        console.log(0);\n    }\n}\n// Временная сложность алгоритма C: постоянная\nfunction algorithm_C(n) {\n    for (let i = 0; i &lt; 1000000; i++) {\n        console.log(0);\n    }\n}\n</code></pre> <pre><code>// Временная сложность алгоритма A: постоянная\nfunction algorithm_A(n: number): void {\n    console.log(0);\n}\n// Временная сложность алгоритма B: линейная\nfunction algorithm_B(n: number): void {\n    for (let i = 0; i &lt; n; i++) {\n        console.log(0);\n    }\n}\n// Временная сложность алгоритма C: постоянная\nfunction algorithm_C(n: number): void {\n    for (let i = 0; i &lt; 1000000; i++) {\n        console.log(0);\n    }\n}\n</code></pre> <pre><code>// Временная сложность алгоритма A: постоянная\nvoid algorithmA(int n) {\n  print(0);\n}\n// Временная сложность алгоритма B: линейная\nvoid algorithmB(int n) {\n  for (int i = 0; i &lt; n; i++) {\n    print(0);\n  }\n}\n// Временная сложность алгоритма C: постоянная\nvoid algorithmC(int n) {\n  for (int i = 0; i &lt; 1000000; i++) {\n    print(0);\n  }\n}\n</code></pre> <pre><code>// Временная сложность алгоритма A: постоянная\nfn algorithm_A(n: i32) {\n    println!(\"{}\", 0);\n}\n// Временная сложность алгоритма B: линейная\nfn algorithm_B(n: i32) {\n    for _ in 0..n {\n        println!(\"{}\", 0);\n    }\n}\n// Временная сложность алгоритма C: постоянная\nfn algorithm_C(n: i32) {\n    for _ in 0..1000000 {\n        println!(\"{}\", 0);\n    }\n}\n</code></pre> <pre><code>// Временная сложность алгоритма A: постоянная\nvoid algorithm_A(int n) {\n    printf(\"%d\", 0);\n}\n// Временная сложность алгоритма B: линейная\nvoid algorithm_B(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        printf(\"%d\", 0);\n    }\n}\n// Временная сложность алгоритма C: постоянная\nvoid algorithm_C(int n) {\n    for (int i = 0; i &lt; 1000000; i++) {\n        printf(\"%d\", 0);\n    }\n}\n</code></pre> <pre><code>// Временная сложность алгоритма A: постоянная\nfun algoritm_A(n: Int) {\n    println(0)\n}\n// Временная сложность алгоритма B: линейная\nfun algorithm_B(n: Int) {\n    for (i in 0..&lt;n){\n        println(0)\n    }\n}\n// Временная сложность алгоритма C: постоянная\nfun algorithm_C(n: Int) {\n    for (i in 0..&lt;1000000) {\n        println(0)\n    }\n}\n</code></pre> <pre><code># Временная сложность алгоритма A: постоянная\ndef algorithm_A(n)\n    puts 0\nend\n\n# Временная сложность алгоритма B: линейная\ndef algorithm_B(n)\n    (0...n).each { puts 0 }\nend\n\n# Временная сложность алгоритма C: постоянная\ndef algorithm_C(n)\n    (0...1_000_000).each { puts 0 }\nend\n</code></pre> <p>Ниже показаны временные сложности трех приведенных выше функций.</p> <ul> <li>У алгоритма <code>A</code> есть только одна операция вывода, и время его работы не растет с увеличением \\(n\\) . Такую временную сложность называют постоянной.</li> <li>В алгоритме <code>B</code> операция вывода выполняется в цикле \\(n\\) раз, поэтому время работы растет линейно по мере увеличения \\(n\\) . Такая временная сложность называется линейной.</li> <li>В алгоритме <code>C</code> операция вывода выполняется \\(1000000\\) раз; хотя время работы велико, оно не зависит от размера входных данных \\(n\\) . Поэтому временная сложность <code>C</code> такая же, как у <code>A</code> , и тоже является постоянной.</li> </ul> <p></p> <p> Рисунок 2-7   Тенденции роста времени для алгоритмов A, B и C </p> <p>Какие особенности имеет анализ временной сложности по сравнению с непосредственным измерением времени работы алгоритма?</p> <ul> <li>Временная сложность позволяет эффективно оценивать эффективность алгоритма. Например, время работы алгоритма <code>B</code> растет линейно: при \\(n &gt; 1\\) он медленнее алгоритма <code>A</code> , а при \\(n &gt; 1000000\\) медленнее алгоритма <code>C</code> . Если размер входных данных достаточно велик, алгоритм с постоянной сложностью обязательно лучше алгоритма с линейной сложностью. В этом и состоит смысл тенденции роста времени.</li> <li>Метод вывода временной сложности проще. Платформа выполнения и тип вычислительных операций не влияют на тенденцию роста времени работы алгоритма. Поэтому в анализе временной сложности можно считать время выполнения всех вычислительных операций одинаковым единичным временем и тем самым упростить подсчет времени выполнения до подсчета количества операций.</li> <li>У временной сложности есть и определенные ограничения. Например, хотя временная сложность алгоритмов <code>A</code> и <code>C</code> одинакова, их реальное время выполнения сильно различается. Точно так же, хотя временная сложность <code>B</code> выше, чем у <code>C</code> , при малых \\(n\\) алгоритм <code>B</code> очевидно лучше <code>C</code> . Несмотря на эти ограничения, анализ сложности все равно остается самым эффективным и самым распространенным способом оценки алгоритмов.</li> </ul>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#232","level":2,"title":"2.3.2   Асимптотическая верхняя граница функции","text":"<p>Для функции с входным размером \\(n\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>def algorithm(n: int):\n    a = 1      # +1\n    a = a + 1  # +1\n    a = a * 2  # +1\n    # Цикл выполняется n раз\n    for i in range(n):  # +1\n        print(0)        # +1\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +1\n    a = a + 1;  // +1\n    a = a * 2;  // +1\n    // Цикл выполняется n раз\n    for (int i = 0; i &lt; n; i++) { // +1 (каждый раз выполняется i ++)\n        cout &lt;&lt; 0 &lt;&lt; endl;    // +1\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +1\n    a = a + 1;  // +1\n    a = a * 2;  // +1\n    // Цикл выполняется n раз\n    for (int i = 0; i &lt; n; i++) { // +1 (каждый раз выполняется i ++)\n        System.out.println(0);    // +1\n    }\n}\n</code></pre> <pre><code>void Algorithm(int n) {\n    int a = 1;  // +1\n    a = a + 1;  // +1\n    a = a * 2;  // +1\n    // Цикл выполняется n раз\n    for (int i = 0; i &lt; n; i++) {   // +1 (каждый раз выполняется i ++)\n        Console.WriteLine(0);   // +1\n    }\n}\n</code></pre> <pre><code>func algorithm(n int) {\n    a := 1      // +1\n    a = a + 1   // +1\n    a = a * 2   // +1\n    // Цикл выполняется n раз\n    for i := 0; i &lt; n; i++ {   // +1\n        fmt.Println(a)         // +1\n    }\n}\n</code></pre> <pre><code>func algorithm(n: Int) {\n    var a = 1 // +1\n    a = a + 1 // +1\n    a = a * 2 // +1\n    // Цикл выполняется n раз\n    for _ in 0 ..&lt; n { // +1\n        print(0) // +1\n    }\n}\n</code></pre> <pre><code>function algorithm(n) {\n    var a = 1; // +1\n    a += 1; // +1\n    a *= 2; // +1\n    // Цикл выполняется n раз\n    for(let i = 0; i &lt; n; i++){ // +1 (каждый раз выполняется i ++)\n        console.log(0); // +1\n    }\n}\n</code></pre> <pre><code>function algorithm(n: number): void{\n    var a: number = 1; // +1\n    a += 1; // +1\n    a *= 2; // +1\n    // Цикл выполняется n раз\n    for(let i = 0; i &lt; n; i++){ // +1 (каждый раз выполняется i ++)\n        console.log(0); // +1\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n  int a = 1; // +1\n  a = a + 1; // +1\n  a = a * 2; // +1\n  // Цикл выполняется n раз\n  for (int i = 0; i &lt; n; i++) { // +1 (каждый раз выполняется i ++)\n    print(0); // +1\n  }\n}\n</code></pre> <pre><code>fn algorithm(n: i32) {\n    let mut a = 1;   // +1\n    a = a + 1;      // +1\n    a = a * 2;      // +1\n\n    // Цикл выполняется n раз\n    for _ in 0..n { // +1 (каждый раз выполняется i ++)\n        println!(\"{}\", 0); // +1\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +1\n    a = a + 1;  // +1\n    a = a * 2;  // +1\n    // Цикл выполняется n раз\n    for (int i = 0; i &lt; n; i++) {   // +1 (каждый раз выполняется i ++)\n        printf(\"%d\", 0);            // +1\n    }\n}\n</code></pre> <pre><code>fun algorithm(n: Int) {\n    var a = 1 // +1\n    a = a + 1 // +1\n    a = a * 2 // +1\n    // Цикл выполняется n раз\n    for (i in 0..&lt;n) { // +1 (каждый раз выполняется i ++)\n        println(0) // +1\n    }\n}\n</code></pre> <pre><code>def algorithm(n)\n    a = 1       # +1\n    a = a + 1   # +1\n    a = a * 2   # +1\n    # Цикл выполняется n раз\n    (0...n).each do # +1\n        puts 0      # +1\n    end\nend\n</code></pre> <p>Пусть количество операций алгоритма является функцией от размера входных данных \\(n\\) и обозначается как \\(T(n)\\) ; тогда для приведенной выше функции число операций равно:</p> \\[ T(n) = 3 + 2n \\] <p>\\(T(n)\\) - линейная функция, а это означает, что тенденция роста времени работы линейна, следовательно, временная сложность здесь тоже линейна.</p> <p>Линейную временную сложность записывают как \\(O(n)\\) ; этот математический символ называется нотацией Big \\(O\\) (big-\\(O\\) notation) и обозначает асимптотическую верхнюю границу (asymptotic upper bound) функции \\(T(n)\\) .</p> <p>Иными словами, анализ временной сложности сводится к определению асимптотической верхней границы числа операций \\(T(n)\\), и у этого понятия есть строгое математическое определение.</p> <p>Асимптотическая верхняя граница функции</p> <p>Если существуют положительное действительное число \\(c\\) и действительное число \\(n_0\\) , такие что для всех \\(n &gt; n_0\\) выполняется \\(T(n) \\leq c \\cdot f(n)\\) , то можно считать, что \\(f(n)\\) задает асимптотическую верхнюю границу для \\(T(n)\\) ; это записывается как \\(T(n) = O(f(n))\\) .</p> <p>Как показано на рисунке 2-8, вычислить асимптотическую верхнюю границу - значит найти такую функцию \\(f(n)\\) , что при стремлении \\(n\\) к бесконечности функции \\(T(n)\\) и \\(f(n)\\) имеют один и тот же порядок роста и отличаются только постоянным коэффициентом \\(c\\).</p> <p></p> <p> Рисунок 2-8   Асимптотическая верхняя граница функции </p>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#233","level":2,"title":"2.3.3   Метод вывода","text":"<p>Математическое определение асимптотической верхней границы выглядит довольно формально, и если оно пока не до конца понятно, переживать не стоит. Сначала можно освоить сам метод вывода, а в процессе дальнейшей практики постепенно почувствовать его математический смысл.</p> <p>Согласно определению, после того как мы определили \\(f(n)\\) , можно получить временную сложность \\(O(f(n))\\) . Но как определить саму асимптотическую верхнюю границу \\(f(n)\\) ? В целом процесс состоит из двух шагов: сначала подсчитать количество операций, затем определить асимптотическую верхнюю границу.</p>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#1-1","level":3,"title":"1.   Шаг 1: подсчет количества операций","text":"<p>Для кода это можно делать построчно сверху вниз. Однако, поскольку в выражении \\(c \\cdot f(n)\\) постоянный коэффициент \\(c\\) может быть сколь угодно большим, различные коэффициенты и постоянные члены в числе операций \\(T(n)\\) можно игнорировать. Исходя из этого принципа, можно сформулировать следующие упрощающие приемы подсчета.</p> <ol> <li>Игнорировать константы в \\(T(n)\\). Они не зависят от \\(n\\) , а значит не влияют на временную сложность.</li> <li>Опускать все коэффициенты. Например, циклы на \\(2n\\) раз или \\(5n + 1\\) раз можно упростить до \\(n\\) раз, потому что коэффициент перед \\(n\\) не влияет на временную сложность.</li> <li>При вложенных циклах использовать умножение. Общее число операций равно произведению числа операций внешнего и внутреннего циклов; при этом для каждого уровня цикла по-прежнему можно применять приемы из пунктов <code>1.</code> и <code>2.</code> .</li> </ol> <p>Для заданной функции мы можем использовать перечисленные выше приемы и подсчитать число операций:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>def algorithm(n: int):\n    a = 1      # +0 (прием 1)\n    a = a + n  # +0 (прием 1)\n    # +n (прием 2)\n    for i in range(5 * n + 1):\n        print(0)\n    # +n*n (прием 3)\n    for i in range(2 * n):\n        for j in range(n + 1):\n            print(0)\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +0 (прием 1)\n    a = a + n;  // +0 (прием 1)\n    // +n (прием 2)\n    for (int i = 0; i &lt; 5 * n + 1; i++) {\n        cout &lt;&lt; 0 &lt;&lt; endl;\n    }\n    // +n*n (прием 3)\n    for (int i = 0; i &lt; 2 * n; i++) {\n        for (int j = 0; j &lt; n + 1; j++) {\n            cout &lt;&lt; 0 &lt;&lt; endl;\n        }\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +0 (прием 1)\n    a = a + n;  // +0 (прием 1)\n    // +n (прием 2)\n    for (int i = 0; i &lt; 5 * n + 1; i++) {\n        System.out.println(0);\n    }\n    // +n*n (прием 3)\n    for (int i = 0; i &lt; 2 * n; i++) {\n        for (int j = 0; j &lt; n + 1; j++) {\n            System.out.println(0);\n        }\n    }\n}\n</code></pre> <pre><code>void Algorithm(int n) {\n    int a = 1;  // +0 (прием 1)\n    a = a + n;  // +0 (прием 1)\n    // +n (прием 2)\n    for (int i = 0; i &lt; 5 * n + 1; i++) {\n        Console.WriteLine(0);\n    }\n    // +n*n (прием 3)\n    for (int i = 0; i &lt; 2 * n; i++) {\n        for (int j = 0; j &lt; n + 1; j++) {\n            Console.WriteLine(0);\n        }\n    }\n}\n</code></pre> <pre><code>func algorithm(n int) {\n    a := 1     // +0 (прием 1)\n    a = a + n  // +0 (прием 1)\n    // +n (прием 2)\n    for i := 0; i &lt; 5 * n + 1; i++ {\n        fmt.Println(0)\n    }\n    // +n*n (прием 3)\n    for i := 0; i &lt; 2 * n; i++ {\n        for j := 0; j &lt; n + 1; j++ {\n            fmt.Println(0)\n        }\n    }\n}\n</code></pre> <pre><code>func algorithm(n: Int) {\n    var a = 1 // +0 (прием 1)\n    a = a + n // +0 (прием 1)\n    // +n (прием 2)\n    for _ in 0 ..&lt; (5 * n + 1) {\n        print(0)\n    }\n    // +n*n (прием 3)\n    for _ in 0 ..&lt; (2 * n) {\n        for _ in 0 ..&lt; (n + 1) {\n            print(0)\n        }\n    }\n}\n</code></pre> <pre><code>function algorithm(n) {\n    let a = 1;  // +0 (прием 1)\n    a = a + n;  // +0 (прием 1)\n    // +n (прием 2)\n    for (let i = 0; i &lt; 5 * n + 1; i++) {\n        console.log(0);\n    }\n    // +n*n (прием 3)\n    for (let i = 0; i &lt; 2 * n; i++) {\n        for (let j = 0; j &lt; n + 1; j++) {\n            console.log(0);\n        }\n    }\n}\n</code></pre> <pre><code>function algorithm(n: number): void {\n    let a = 1;  // +0 (прием 1)\n    a = a + n;  // +0 (прием 1)\n    // +n (прием 2)\n    for (let i = 0; i &lt; 5 * n + 1; i++) {\n        console.log(0);\n    }\n    // +n*n (прием 3)\n    for (let i = 0; i &lt; 2 * n; i++) {\n        for (let j = 0; j &lt; n + 1; j++) {\n            console.log(0);\n        }\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n  int a = 1; // +0 (прием 1)\n  a = a + n; // +0 (прием 1)\n  // +n (прием 2)\n  for (int i = 0; i &lt; 5 * n + 1; i++) {\n    print(0);\n  }\n  // +n*n (прием 3)\n  for (int i = 0; i &lt; 2 * n; i++) {\n    for (int j = 0; j &lt; n + 1; j++) {\n      print(0);\n    }\n  }\n}\n</code></pre> <pre><code>fn algorithm(n: i32) {\n    let mut a = 1;     // +0 (прием 1)\n    a = a + n;        // +0 (прием 1)\n\n    // +n (прием 2)\n    for i in 0..(5 * n + 1) {\n        println!(\"{}\", 0);\n    }\n\n    // +n*n (прием 3)\n    for i in 0..(2 * n) {\n        for j in 0..(n + 1) {\n            println!(\"{}\", 0);\n        }\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +0 (прием 1)\n    a = a + n;  // +0 (прием 1)\n    // +n (прием 2)\n    for (int i = 0; i &lt; 5 * n + 1; i++) {\n        printf(\"%d\", 0);\n    }\n    // +n*n (прием 3)\n    for (int i = 0; i &lt; 2 * n; i++) {\n        for (int j = 0; j &lt; n + 1; j++) {\n            printf(\"%d\", 0);\n        }\n    }\n}\n</code></pre> <pre><code>fun algorithm(n: Int) {\n    var a = 1   // +0 (прием 1)\n    a = a + n   // +0 (прием 1)\n    // +n (прием 2)\n    for (i in 0..&lt;5 * n + 1) {\n        println(0)\n    }\n    // +n*n (прием 3)\n    for (i in 0..&lt;2 * n) {\n        for (j in 0..&lt;n + 1) {\n            println(0)\n        }\n    }\n}\n</code></pre> <pre><code>def algorithm(n)\n    a = 1       # +0 (прием 1)\n    a = a + n   # +0 (прием 1)\n    # +n (прием 2)\n    (0...(5 * n + 1)).each do { puts 0 }\n    # +n*n (прием 3)\n    (0...(2 * n)).each do\n        (0...(n + 1)).each do { puts 0 }\n    end\nend\n</code></pre> <p>Следующая формула показывает результаты подсчета до и после использования перечисленных выше приемов; в обоих случаях выводимая временная сложность равна \\(O(n^2)\\) .</p> \\[ \\begin{aligned} T(n) &amp; = 2n(n + 1) + (5n + 1) + 2 &amp; \\text{полный подсчет (-.-|||)} \\newline &amp; = 2n^2 + 7n + 3 \\newline T(n) &amp; = n^2 + n &amp; \\text{ленивый подсчет (o.O)} \\end{aligned} \\]","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#2-2","level":3,"title":"2.   Шаг 2: определение асимптотической верхней границы","text":"<p>**Временная сложность определяется старшим по степени членом в \\(T(n)\\) **. Это связано с тем, что при стремлении \\(n\\) к бесконечности именно старший член начинает доминировать, а влиянием остальных членов можно пренебречь.</p> <p>В таблице 2-2 приведены несколько примеров. Некоторые значения специально сделаны преувеличенными, чтобы подчеркнуть вывод: коэффициент не способен изменить порядок. Когда \\(n\\) стремится к бесконечности, эти константы становятся несущественными.</p> <p> Таблица 2-2   Временная сложность, соответствующая разному количеству операций </p> Число операций \\(T(n)\\) Временная сложность \\(O(f(n))\\) \\(100000\\) \\(O(1)\\) \\(3n + 2\\) \\(O(n)\\) \\(2n^2 + 3n + 2\\) \\(O(n^2)\\) \\(n^3 + 10000n^2\\) \\(O(n^3)\\) \\(2^n + 10000n^{10000}\\) \\(O(2^n)\\)","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#234","level":2,"title":"2.3.4   Распространенные типы","text":"<p>Пусть размер входных данных равен \\(n\\) ; распространенные типы временной сложности показаны на рисунке 2-9 в порядке от меньшей к большей.</p> \\[ \\begin{aligned} O(1) &lt; O(\\log n) &lt; O(n) &lt; O(n \\log n) &lt; O(n^2) &lt; O(2^n) &lt; O(n!) \\newline \\text{Постоянная} &lt; \\text{Логарифмическая} &lt; \\text{Линейная} &lt; \\text{Линейно-логарифмическая} &lt; \\text{Квадратичная} &lt; \\text{Экспоненциальная} &lt; \\text{Факториальная} \\end{aligned} \\] <p></p> <p> Рисунок 2-9   Распространенные типы временной сложности </p>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#1-o1","level":3,"title":"1.   Постоянная сложность \\(O(1)\\)","text":"<p>Число операций при постоянной сложности не зависит от размера входных данных \\(n\\) , то есть не изменяется вместе с изменением \\(n\\) .</p> <p>В следующей функции, хотя число операций <code>size</code> может быть большим, оно не зависит от размера входных данных \\(n\\) , поэтому временная сложность по-прежнему равна \\(O(1)\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def constant(n: int) -&gt; int:\n    \"\"\"Постоянная сложность\"\"\"\n    count = 0\n    size = 100000\n    for _ in range(size):\n        count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* Постоянная сложность */\nint constant(int n) {\n    int count = 0;\n    int size = 100000;\n    for (int i = 0; i &lt; size; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* Постоянная сложность */\nint constant(int n) {\n    int count = 0;\n    int size = 100000;\n    for (int i = 0; i &lt; size; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* Постоянная сложность */\nint Constant(int n) {\n    int count = 0;\n    int size = 100000;\n    for (int i = 0; i &lt; size; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* Постоянная сложность */\nfunc constant(n int) int {\n    count := 0\n    size := 100000\n    for i := 0; i &lt; size; i++ {\n        count++\n    }\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* Постоянная сложность */\nfunc constant(n: Int) -&gt; Int {\n    var count = 0\n    let size = 100_000\n    for _ in 0 ..&lt; size {\n        count += 1\n    }\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* Постоянная сложность */\nfunction constant(n) {\n    let count = 0;\n    const size = 100000;\n    for (let i = 0; i &lt; size; i++) count++;\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* Постоянная сложность */\nfunction constant(n: number): number {\n    let count = 0;\n    const size = 100000;\n    for (let i = 0; i &lt; size; i++) count++;\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* Постоянная сложность */\nint constant(int n) {\n  int count = 0;\n  int size = 100000;\n  for (var i = 0; i &lt; size; i++) {\n    count++;\n  }\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* Постоянная сложность */\nfn constant(n: i32) -&gt; i32 {\n    _ = n;\n    let mut count = 0;\n    let size = 100_000;\n    for _ in 0..size {\n        count += 1;\n    }\n    count\n}\n</code></pre> time_complexity.c<pre><code>/* Постоянная сложность */\nint constant(int n) {\n    int count = 0;\n    int size = 100000;\n    int i = 0;\n    for (int i = 0; i &lt; size; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* Постоянная сложность */\nfun constant(n: Int): Int {\n    var count = 0\n    val size = 100000\n    for (i in 0..&lt;size)\n        count++\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### Постоянная сложность ###\ndef constant(n)\n  count = 0\n  size = 100000\n\n  (0...size).each { count += 1 }\n\n  count\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#2-on","level":3,"title":"2.   Линейная сложность \\(O(n)\\)","text":"<p>Линейная сложность характеризуется тем, что число операций растет линейно относительно размера входных данных \\(n\\) . Линейная сложность обычно встречается в одноуровневых циклах:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def linear(n: int) -&gt; int:\n    \"\"\"Линейная сложность\"\"\"\n    count = 0\n    for _ in range(n):\n        count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* Линейная сложность */\nint linear(int n) {\n    int count = 0;\n    for (int i = 0; i &lt; n; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* Линейная сложность */\nint linear(int n) {\n    int count = 0;\n    for (int i = 0; i &lt; n; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* Линейная сложность */\nint Linear(int n) {\n    int count = 0;\n    for (int i = 0; i &lt; n; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* Линейная сложность */\nfunc linear(n int) int {\n    count := 0\n    for i := 0; i &lt; n; i++ {\n        count++\n    }\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* Линейная сложность */\nfunc linear(n: Int) -&gt; Int {\n    var count = 0\n    for _ in 0 ..&lt; n {\n        count += 1\n    }\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* Линейная сложность */\nfunction linear(n) {\n    let count = 0;\n    for (let i = 0; i &lt; n; i++) count++;\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* Линейная сложность */\nfunction linear(n: number): number {\n    let count = 0;\n    for (let i = 0; i &lt; n; i++) count++;\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* Линейная сложность */\nint linear(int n) {\n  int count = 0;\n  for (var i = 0; i &lt; n; i++) {\n    count++;\n  }\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* Линейная сложность */\nfn linear(n: i32) -&gt; i32 {\n    let mut count = 0;\n    for _ in 0..n {\n        count += 1;\n    }\n    count\n}\n</code></pre> time_complexity.c<pre><code>/* Линейная сложность */\nint linear(int n) {\n    int count = 0;\n    for (int i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* Линейная сложность */\nfun linear(n: Int): Int {\n    var count = 0\n    for (i in 0..&lt;n)\n        count++\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### Линейная сложность ###\ndef linear(n)\n  count = 0\n  (0...n).each { count += 1 }\n  count\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Операции обхода массива и обхода связного списка имеют временную сложность \\(O(n)\\) , где \\(n\\) - длина массива или списка:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def array_traversal(nums: list[int]) -&gt; int:\n    \"\"\"Линейная сложность (обход массива)\"\"\"\n    count = 0\n    # Число итераций пропорционально длине массива\n    for num in nums:\n        count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* Линейная сложность (обход массива) */\nint arrayTraversal(vector&lt;int&gt; &amp;nums) {\n    int count = 0;\n    // Число итераций пропорционально длине массива\n    for (int num : nums) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* Линейная сложность (обход массива) */\nint arrayTraversal(int[] nums) {\n    int count = 0;\n    // Число итераций пропорционально длине массива\n    for (int num : nums) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* Линейная сложность (обход массива) */\nint ArrayTraversal(int[] nums) {\n    int count = 0;\n    // Число итераций пропорционально длине массива\n    foreach (int num in nums) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* Линейная сложность (обход массива) */\nfunc arrayTraversal(nums []int) int {\n    count := 0\n    // Число итераций пропорционально длине массива\n    for range nums {\n        count++\n    }\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* Линейная сложность (обход массива) */\nfunc arrayTraversal(nums: [Int]) -&gt; Int {\n    var count = 0\n    // Число итераций пропорционально длине массива\n    for _ in nums {\n        count += 1\n    }\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* Линейная сложность (обход массива) */\nfunction arrayTraversal(nums) {\n    let count = 0;\n    // Число итераций пропорционально длине массива\n    for (let i = 0; i &lt; nums.length; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* Линейная сложность (обход массива) */\nfunction arrayTraversal(nums: number[]): number {\n    let count = 0;\n    // Число итераций пропорционально длине массива\n    for (let i = 0; i &lt; nums.length; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* Линейная сложность (обход массива) */\nint arrayTraversal(List&lt;int&gt; nums) {\n  int count = 0;\n  // Число итераций пропорционально длине массива\n  for (var _num in nums) {\n    count++;\n  }\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* Линейная сложность (обход массива) */\nfn array_traversal(nums: &amp;[i32]) -&gt; i32 {\n    let mut count = 0;\n    // Число итераций пропорционально длине массива\n    for _ in nums {\n        count += 1;\n    }\n    count\n}\n</code></pre> time_complexity.c<pre><code>/* Линейная сложность (обход массива) */\nint arrayTraversal(int *nums, int n) {\n    int count = 0;\n    // Число итераций пропорционально длине массива\n    for (int i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* Линейная сложность (обход массива) */\nfun arrayTraversal(nums: IntArray): Int {\n    var count = 0\n    // Число итераций пропорционально длине массива\n    for (num in nums) {\n        count++\n    }\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### Линейная сложность ###\ndef linear(n)\n  count = 0\n  (0...n).each { count += 1 }\n  count\nend\n\n# ## Линейная сложность (обход массива) ###\ndef array_traversal(nums)\n  count = 0\n\n  # Число итераций пропорционально длине массива\n  for num in nums\n    count += 1\n  end\n\n  count\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Стоит отметить, что размер входных данных \\(n\\) нужно определять конкретно в зависимости от типа входа. Например, в первом примере переменная \\(n\\) сама является размером входных данных; во втором примере размером данных служит длина массива.</p>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#3-on2","level":3,"title":"3.   Квадратичная сложность \\(O(n^2)\\)","text":"<p>Квадратичная сложность характеризуется тем, что число операций растет квадратично относительно размера входных данных \\(n\\) . Квадратичная сложность обычно встречается во вложенных циклах: временная сложность внешнего и внутреннего циклов равна \\(O(n)\\) , поэтому общая временная сложность составляет \\(O(n^2)\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def quadratic(n: int) -&gt; int:\n    \"\"\"Квадратичная сложность\"\"\"\n    count = 0\n    # Число итераций квадратично зависит от размера данных n\n    for i in range(n):\n        for j in range(n):\n            count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* Квадратичная сложность */\nint quadratic(int n) {\n    int count = 0;\n    // Число итераций квадратично зависит от размера данных n\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; n; j++) {\n            count++;\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* Квадратичная сложность */\nint quadratic(int n) {\n    int count = 0;\n    // Число итераций квадратично зависит от размера данных n\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; n; j++) {\n            count++;\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* Квадратичная сложность */\nint Quadratic(int n) {\n    int count = 0;\n    // Число итераций квадратично зависит от размера данных n\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; n; j++) {\n            count++;\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* Квадратичная сложность */\nfunc quadratic(n int) int {\n    count := 0\n    // Число итераций квадратично зависит от размера данных n\n    for i := 0; i &lt; n; i++ {\n        for j := 0; j &lt; n; j++ {\n            count++\n        }\n    }\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* Квадратичная сложность */\nfunc quadratic(n: Int) -&gt; Int {\n    var count = 0\n    // Число итераций квадратично зависит от размера данных n\n    for _ in 0 ..&lt; n {\n        for _ in 0 ..&lt; n {\n            count += 1\n        }\n    }\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* Квадратичная сложность */\nfunction quadratic(n) {\n    let count = 0;\n    // Число итераций квадратично зависит от размера данных n\n    for (let i = 0; i &lt; n; i++) {\n        for (let j = 0; j &lt; n; j++) {\n            count++;\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* Квадратичная сложность */\nfunction quadratic(n: number): number {\n    let count = 0;\n    // Число итераций квадратично зависит от размера данных n\n    for (let i = 0; i &lt; n; i++) {\n        for (let j = 0; j &lt; n; j++) {\n            count++;\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* Квадратичная сложность */\nint quadratic(int n) {\n  int count = 0;\n  // Число итераций квадратично зависит от размера данных n\n  for (int i = 0; i &lt; n; i++) {\n    for (int j = 0; j &lt; n; j++) {\n      count++;\n    }\n  }\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* Квадратичная сложность */\nfn quadratic(n: i32) -&gt; i32 {\n    let mut count = 0;\n    // Число итераций квадратично зависит от размера данных n\n    for _ in 0..n {\n        for _ in 0..n {\n            count += 1;\n        }\n    }\n    count\n}\n</code></pre> time_complexity.c<pre><code>/* Квадратичная сложность */\nint quadratic(int n) {\n    int count = 0;\n    // Число итераций квадратично зависит от размера данных n\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; n; j++) {\n            count++;\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* Квадратичная сложность */\nfun quadratic(n: Int): Int {\n    var count = 0\n    // Число итераций квадратично зависит от размера данных n\n    for (i in 0..&lt;n) {\n        for (j in 0..&lt;n) {\n            count++\n        }\n    }\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### Квадратичная сложность ###\ndef quadratic(n)\n  count = 0\n\n  # Число итераций квадратично зависит от размера данных n\n  for i in 0...n\n    for j in 0...n\n      count += 1\n    end\n  end\n\n  count\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>На рисунке 2-10 сравниваются три временные сложности: постоянная, линейная и квадратичная.</p> <p></p> <p> Рисунок 2-10   Постоянная, линейная и квадратичная временная сложность </p> <p>Возьмем в качестве примера пузырьковую сортировку: внешний цикл выполняется \\(n - 1\\) раз, внутренний цикл выполняется \\(n-1\\) , \\(n-2\\) , \\(\\dots\\) , \\(2\\) , \\(1\\) раз, в среднем это \\(n / 2\\) раз, поэтому временная сложность равна \\(O((n - 1)n / 2) = O(n^2)\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def bubble_sort(nums: list[int]) -&gt; int:\n    \"\"\"Квадратичная сложность (пузырьковая сортировка)\"\"\"\n    count = 0  # Счетчик\n    # Внешний цикл: неотсортированный диапазон [0, i]\n    for i in range(len(nums) - 1, 0, -1):\n        # Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for j in range(i):\n            if nums[j] &gt; nums[j + 1]:\n                # Поменять местами nums[j] и nums[j + 1]\n                tmp: int = nums[j]\n                nums[j] = nums[j + 1]\n                nums[j + 1] = tmp\n                count += 3  # Обмен элементов включает 3 элементарные операции\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* Квадратичная сложность (пузырьковая сортировка) */\nint bubbleSort(vector&lt;int&gt; &amp;nums) {\n    int count = 0; // Счетчик\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (int i = nums.size() - 1; i &gt; 0; i--) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                int tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                count += 3; // Обмен элементов включает 3 элементарные операции\n            }\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* Квадратичная сложность (пузырьковая сортировка) */\nint bubbleSort(int[] nums) {\n    int count = 0; // Счетчик\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (int i = nums.length - 1; i &gt; 0; i--) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                int tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                count += 3; // Обмен элементов включает 3 элементарные операции\n            }\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* Квадратичная сложность (пузырьковая сортировка) */\nint BubbleSort(int[] nums) {\n    int count = 0;  // Счетчик\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (int i = nums.Length - 1; i &gt; 0; i--) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                (nums[j + 1], nums[j]) = (nums[j], nums[j + 1]);\n                count += 3;  // Обмен элементов включает 3 элементарные операции\n            }\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* Квадратичная сложность (пузырьковая сортировка) */\nfunc bubbleSort(nums []int) int {\n    count := 0 // Счетчик\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for i := len(nums) - 1; i &gt; 0; i-- {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for j := 0; j &lt; i; j++ {\n            if nums[j] &gt; nums[j+1] {\n                // Поменять местами nums[j] и nums[j + 1]\n                tmp := nums[j]\n                nums[j] = nums[j+1]\n                nums[j+1] = tmp\n                count += 3 // Обмен элементов включает 3 элементарные операции\n            }\n        }\n    }\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* Квадратичная сложность (пузырьковая сортировка) */\nfunc bubbleSort(nums: inout [Int]) -&gt; Int {\n    var count = 0 // Счетчик\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for i in nums.indices.dropFirst().reversed() {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for j in 0 ..&lt; i {\n            if nums[j] &gt; nums[j + 1] {\n                // Поменять местами nums[j] и nums[j + 1]\n                let tmp = nums[j]\n                nums[j] = nums[j + 1]\n                nums[j + 1] = tmp\n                count += 3 // Обмен элементов включает 3 элементарные операции\n            }\n        }\n    }\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* Квадратичная сложность (пузырьковая сортировка) */\nfunction bubbleSort(nums) {\n    let count = 0; // Счетчик\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (let i = nums.length - 1; i &gt; 0; i--) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (let j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                let tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                count += 3; // Обмен элементов включает 3 элементарные операции\n            }\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* Квадратичная сложность (пузырьковая сортировка) */\nfunction bubbleSort(nums: number[]): number {\n    let count = 0; // Счетчик\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (let i = nums.length - 1; i &gt; 0; i--) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (let j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                let tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                count += 3; // Обмен элементов включает 3 элементарные операции\n            }\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* Квадратичная сложность (пузырьковая сортировка) */\nint bubbleSort(List&lt;int&gt; nums) {\n  int count = 0; // Счетчик\n  // Внешний цикл: неотсортированный диапазон [0, i]\n  for (var i = nums.length - 1; i &gt; 0; i--) {\n    // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n    for (var j = 0; j &lt; i; j++) {\n      if (nums[j] &gt; nums[j + 1]) {\n        // Поменять местами nums[j] и nums[j + 1]\n        int tmp = nums[j];\n        nums[j] = nums[j + 1];\n        nums[j + 1] = tmp;\n        count += 3; // Обмен элементов включает 3 элементарные операции\n      }\n    }\n  }\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* Квадратичная сложность (пузырьковая сортировка) */\nfn bubble_sort(nums: &amp;mut [i32]) -&gt; i32 {\n    let mut count = 0; // Счетчик\n\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for i in (1..nums.len()).rev() {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for j in 0..i {\n            if nums[j] &gt; nums[j + 1] {\n                // Поменять местами nums[j] и nums[j + 1]\n                let tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                count += 3; // Обмен элементов включает 3 элементарные операции\n            }\n        }\n    }\n    count\n}\n</code></pre> time_complexity.c<pre><code>/* Квадратичная сложность (пузырьковая сортировка) */\nint bubbleSort(int *nums, int n) {\n    int count = 0; // Счетчик\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (int i = n - 1; i &gt; 0; i--) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                int tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                count += 3; // Обмен элементов включает 3 элементарные операции\n            }\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* Квадратичная сложность (пузырьковая сортировка) */\nfun bubbleSort(nums: IntArray): Int {\n    var count = 0 // Счетчик\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (i in nums.size - 1 downTo 1) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (j in 0..&lt;i) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                val temp = nums[j]\n                nums[j] = nums[j + 1]\n                nums[j + 1] = temp\n                count += 3 // Обмен элементов включает 3 элементарные операции\n            }\n        }\n    }\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### Квадратичная сложность ###\ndef quadratic(n)\n  count = 0\n\n  # Число итераций квадратично зависит от размера данных n\n  for i in 0...n\n    for j in 0...n\n      count += 1\n    end\n  end\n\n  count\nend\n\n# ## Квадратичная сложность (пузырьковая сортировка) ###\ndef bubble_sort(nums)\n  count = 0  # Счетчик\n\n  # Внешний цикл: неотсортированный диапазон [0, i]\n  for i in (nums.length - 1).downto(0)\n    # Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n    for j in 0...i\n      if nums[j] &gt; nums[j + 1]\n        # Поменять местами nums[j] и nums[j + 1]\n        tmp = nums[j]\n        nums[j] = nums[j + 1]\n        nums[j + 1] = tmp\n        count += 3 # Обмен элементов включает 3 элементарные операции\n      end\n    end\n  end\n\n  count\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#4-o2n","level":3,"title":"4.   Экспоненциальная сложность \\(O(2^n)\\)","text":"<p>Типичный пример экспоненциального роста в биологии - деление клеток: в начальном состоянии есть одна клетка, после одного деления их становится 2, после двух делений - 4 и так далее; после \\(n\\) раундов деления клеток становится \\(2^n\\) .</p> <p>На рисунке 2-11 и в следующем коде моделируется процесс деления клеток; временная сложность равна \\(O(2^n)\\) . Здесь входное значение \\(n\\) обозначает число раундов деления, а возвращаемое значение <code>count</code> обозначает общее число делений.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def exponential(n: int) -&gt; int:\n    \"\"\"Экспоненциальная сложность (итеративная реализация)\"\"\"\n    count = 0\n    base = 1\n    # На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n    for _ in range(n):\n        for _ in range(base):\n            count += 1\n        base *= 2\n    # count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* Экспоненциальная сложность (итеративная реализация) */\nint exponential(int n) {\n    int count = 0, base = 1;\n    // На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; base; j++) {\n            count++;\n        }\n        base *= 2;\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* Экспоненциальная сложность (итеративная реализация) */\nint exponential(int n) {\n    int count = 0, base = 1;\n    // На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; base; j++) {\n            count++;\n        }\n        base *= 2;\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* Экспоненциальная сложность (итеративная реализация) */\nint Exponential(int n) {\n    int count = 0, bas = 1;\n    // На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; bas; j++) {\n            count++;\n        }\n        bas *= 2;\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* Экспоненциальная сложность (итеративная реализация) */\nfunc exponential(n int) int {\n    count, base := 0, 1\n    // На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n    for i := 0; i &lt; n; i++ {\n        for j := 0; j &lt; base; j++ {\n            count++\n        }\n        base *= 2\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* Экспоненциальная сложность (итеративная реализация) */\nfunc exponential(n: Int) -&gt; Int {\n    var count = 0\n    var base = 1\n    // На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n    for _ in 0 ..&lt; n {\n        for _ in 0 ..&lt; base {\n            count += 1\n        }\n        base *= 2\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* Экспоненциальная сложность (итеративная реализация) */\nfunction exponential(n) {\n    let count = 0,\n        base = 1;\n    // На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n    for (let i = 0; i &lt; n; i++) {\n        for (let j = 0; j &lt; base; j++) {\n            count++;\n        }\n        base *= 2;\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* Экспоненциальная сложность (итеративная реализация) */\nfunction exponential(n: number): number {\n    let count = 0,\n        base = 1;\n    // На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n    for (let i = 0; i &lt; n; i++) {\n        for (let j = 0; j &lt; base; j++) {\n            count++;\n        }\n        base *= 2;\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* Экспоненциальная сложность (итеративная реализация) */\nint exponential(int n) {\n  int count = 0, base = 1;\n  // На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n  for (var i = 0; i &lt; n; i++) {\n    for (var j = 0; j &lt; base; j++) {\n      count++;\n    }\n    base *= 2;\n  }\n  // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* Экспоненциальная сложность (итеративная реализация) */\nfn exponential(n: i32) -&gt; i32 {\n    let mut count = 0;\n    let mut base = 1;\n    // На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n    for _ in 0..n {\n        for _ in 0..base {\n            count += 1\n        }\n        base *= 2;\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    count\n}\n</code></pre> time_complexity.c<pre><code>/* Экспоненциальная сложность (итеративная реализация) */\nint exponential(int n) {\n    int count = 0;\n    int bas = 1;\n    // На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; bas; j++) {\n            count++;\n        }\n        bas *= 2;\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* Экспоненциальная сложность (итеративная реализация) */\nfun exponential(n: Int): Int {\n    var count = 0\n    var base = 1\n    // На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n    for (i in 0..&lt;n) {\n        for (j in 0..&lt;base) {\n            count++\n        }\n        base *= 2\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### Квадратичная сложность ###\ndef quadratic(n)\n  count = 0\n\n  # Число итераций квадратично зависит от размера данных n\n  for i in 0...n\n    for j in 0...n\n      count += 1\n    end\n  end\n\n  count\nend\n\n# ## Квадратичная сложность (пузырьковая сортировка) ###\ndef bubble_sort(nums)\n  count = 0  # Счетчик\n\n  # Внешний цикл: неотсортированный диапазон [0, i]\n  for i in (nums.length - 1).downto(0)\n    # Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n    for j in 0...i\n      if nums[j] &gt; nums[j + 1]\n        # Поменять местами nums[j] и nums[j + 1]\n        tmp = nums[j]\n        nums[j] = nums[j + 1]\n        nums[j + 1] = tmp\n        count += 3 # Обмен элементов включает 3 элементарные операции\n      end\n    end\n  end\n\n  count\nend\n\n# ## Экспоненциальная сложность (итеративная реализация) ###\ndef exponential(n)\n  count, base = 0, 1\n\n  # На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n  (0...n).each do\n    (0...base).each { count += 1 }\n    base *= 2\n  end\n\n  # count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n  count\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p></p> <p> Рисунок 2-11   Экспоненциальная временная сложность </p> <p>В реальных алгоритмах экспоненциальная сложность также часто встречается в рекурсивных функциях. Например, в следующем коде процесс рекурсивно делится надвое и останавливается после \\(n\\) разбиений:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def exp_recur(n: int) -&gt; int:\n    \"\"\"Экспоненциальная сложность (рекурсивная реализация)\"\"\"\n    if n == 1:\n        return 1\n    return exp_recur(n - 1) + exp_recur(n - 1) + 1\n</code></pre> time_complexity.cpp<pre><code>/* Экспоненциальная сложность (рекурсивная реализация) */\nint expRecur(int n) {\n    if (n == 1)\n        return 1;\n    return expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.java<pre><code>/* Экспоненциальная сложность (рекурсивная реализация) */\nint expRecur(int n) {\n    if (n == 1)\n        return 1;\n    return expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.cs<pre><code>/* Экспоненциальная сложность (рекурсивная реализация) */\nint ExpRecur(int n) {\n    if (n == 1) return 1;\n    return ExpRecur(n - 1) + ExpRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.go<pre><code>/* Экспоненциальная сложность (рекурсивная реализация) */\nfunc expRecur(n int) int {\n    if n == 1 {\n        return 1\n    }\n    return expRecur(n-1) + expRecur(n-1) + 1\n}\n</code></pre> time_complexity.swift<pre><code>/* Экспоненциальная сложность (рекурсивная реализация) */\nfunc expRecur(n: Int) -&gt; Int {\n    if n == 1 {\n        return 1\n    }\n    return expRecur(n: n - 1) + expRecur(n: n - 1) + 1\n}\n</code></pre> time_complexity.js<pre><code>/* Экспоненциальная сложность (рекурсивная реализация) */\nfunction expRecur(n) {\n    if (n === 1) return 1;\n    return expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.ts<pre><code>/* Экспоненциальная сложность (рекурсивная реализация) */\nfunction expRecur(n: number): number {\n    if (n === 1) return 1;\n    return expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.dart<pre><code>/* Экспоненциальная сложность (рекурсивная реализация) */\nint expRecur(int n) {\n  if (n == 1) return 1;\n  return expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.rs<pre><code>/* Экспоненциальная сложность (рекурсивная реализация) */\nfn exp_recur(n: i32) -&gt; i32 {\n    if n == 1 {\n        return 1;\n    }\n    exp_recur(n - 1) + exp_recur(n - 1) + 1\n}\n</code></pre> time_complexity.c<pre><code>/* Экспоненциальная сложность (рекурсивная реализация) */\nint expRecur(int n) {\n    if (n == 1)\n        return 1;\n    return expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.kt<pre><code>/* Экспоненциальная сложность (рекурсивная реализация) */\nfun expRecur(n: Int): Int {\n    if (n == 1) {\n        return 1\n    }\n    return expRecur(n - 1) + expRecur(n - 1) + 1\n}\n</code></pre> time_complexity.rb<pre><code>### Квадратичная сложность ###\ndef quadratic(n)\n  count = 0\n\n  # Число итераций квадратично зависит от размера данных n\n  for i in 0...n\n    for j in 0...n\n      count += 1\n    end\n  end\n\n  count\nend\n\n# ## Квадратичная сложность (пузырьковая сортировка) ###\ndef bubble_sort(nums)\n  count = 0  # Счетчик\n\n  # Внешний цикл: неотсортированный диапазон [0, i]\n  for i in (nums.length - 1).downto(0)\n    # Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n    for j in 0...i\n      if nums[j] &gt; nums[j + 1]\n        # Поменять местами nums[j] и nums[j + 1]\n        tmp = nums[j]\n        nums[j] = nums[j + 1]\n        nums[j + 1] = tmp\n        count += 3 # Обмен элементов включает 3 элементарные операции\n      end\n    end\n  end\n\n  count\nend\n\n# ## Экспоненциальная сложность (итеративная реализация) ###\ndef exponential(n)\n  count, base = 0, 1\n\n  # На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n  (0...n).each do\n    (0...base).each { count += 1 }\n    base *= 2\n  end\n\n  # count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n  count\nend\n\n# ## Экспоненциальная сложность (рекурсивная реализация) ###\ndef exp_recur(n)\n  return 1 if n == 1\n  exp_recur(n - 1) + exp_recur(n - 1) + 1\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Экспоненциальный рост происходит очень быстро и часто встречается в переборных методах, грубой силе, поиске с возвратом и тому подобных подходах. Для задач большого масштаба экспоненциальная сложность неприемлема, и обычно приходится применять динамическое программирование, жадные алгоритмы и другие стратегии.</p>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#5-olog-n","level":3,"title":"5.   Логарифмическая сложность \\(O(\\log n)\\)","text":"<p>В противоположность экспоненциальной, логарифмическая сложность описывает ситуацию, когда в каждом раунде размер задачи уменьшается вдвое. Пусть размер входных данных равен \\(n\\) ; так как на каждом шаге размер уменьшается вдвое, число итераций равно \\(\\log_2 n\\) , то есть является обратной функцией к \\(2^n\\) .</p> <p>На рисунке 2-12 и в следующем коде моделируется процесс, в котором в каждом раунде размер задачи уменьшается вдвое; временная сложность равна \\(O(\\log_2 n)\\) и кратко записывается как \\(O(\\log n)\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def logarithmic(n: int) -&gt; int:\n    \"\"\"Логарифмическая сложность (итеративная реализация)\"\"\"\n    count = 0\n    while n &gt; 1:\n        n = n / 2\n        count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* Логарифмическая сложность (итеративная реализация) */\nint logarithmic(int n) {\n    int count = 0;\n    while (n &gt; 1) {\n        n = n / 2;\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* Логарифмическая сложность (итеративная реализация) */\nint logarithmic(int n) {\n    int count = 0;\n    while (n &gt; 1) {\n        n = n / 2;\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* Логарифмическая сложность (итеративная реализация) */\nint Logarithmic(int n) {\n    int count = 0;\n    while (n &gt; 1) {\n        n /= 2;\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* Логарифмическая сложность (итеративная реализация) */\nfunc logarithmic(n int) int {\n    count := 0\n    for n &gt; 1 {\n        n = n / 2\n        count++\n    }\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* Логарифмическая сложность (итеративная реализация) */\nfunc logarithmic(n: Int) -&gt; Int {\n    var count = 0\n    var n = n\n    while n &gt; 1 {\n        n = n / 2\n        count += 1\n    }\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* Логарифмическая сложность (итеративная реализация) */\nfunction logarithmic(n) {\n    let count = 0;\n    while (n &gt; 1) {\n        n = n / 2;\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* Логарифмическая сложность (итеративная реализация) */\nfunction logarithmic(n: number): number {\n    let count = 0;\n    while (n &gt; 1) {\n        n = n / 2;\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* Логарифмическая сложность (итеративная реализация) */\nint logarithmic(int n) {\n  int count = 0;\n  while (n &gt; 1) {\n    n = n ~/ 2;\n    count++;\n  }\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* Логарифмическая сложность (итеративная реализация) */\nfn logarithmic(mut n: i32) -&gt; i32 {\n    let mut count = 0;\n    while n &gt; 1 {\n        n = n / 2;\n        count += 1;\n    }\n    count\n}\n</code></pre> time_complexity.c<pre><code>/* Логарифмическая сложность (итеративная реализация) */\nint logarithmic(int n) {\n    int count = 0;\n    while (n &gt; 1) {\n        n = n / 2;\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* Логарифмическая сложность (итеративная реализация) */\nfun logarithmic(n: Int): Int {\n    var n1 = n\n    var count = 0\n    while (n1 &gt; 1) {\n        n1 /= 2\n        count++\n    }\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### Квадратичная сложность ###\ndef quadratic(n)\n  count = 0\n\n  # Число итераций квадратично зависит от размера данных n\n  for i in 0...n\n    for j in 0...n\n      count += 1\n    end\n  end\n\n  count\nend\n\n# ## Квадратичная сложность (пузырьковая сортировка) ###\ndef bubble_sort(nums)\n  count = 0  # Счетчик\n\n  # Внешний цикл: неотсортированный диапазон [0, i]\n  for i in (nums.length - 1).downto(0)\n    # Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n    for j in 0...i\n      if nums[j] &gt; nums[j + 1]\n        # Поменять местами nums[j] и nums[j + 1]\n        tmp = nums[j]\n        nums[j] = nums[j + 1]\n        nums[j + 1] = tmp\n        count += 3 # Обмен элементов включает 3 элементарные операции\n      end\n    end\n  end\n\n  count\nend\n\n# ## Экспоненциальная сложность (итеративная реализация) ###\ndef exponential(n)\n  count, base = 0, 1\n\n  # На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n  (0...n).each do\n    (0...base).each { count += 1 }\n    base *= 2\n  end\n\n  # count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n  count\nend\n\n# ## Экспоненциальная сложность (рекурсивная реализация) ###\ndef exp_recur(n)\n  return 1 if n == 1\n  exp_recur(n - 1) + exp_recur(n - 1) + 1\nend\n\n# ## Логарифмическая сложность (итеративная реализация) ###\ndef logarithmic(n)\n  count = 0\n\n  while n &gt; 1\n    n /= 2\n    count += 1\n  end\n\n  count\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p></p> <p> Рисунок 2-12   Логарифмическая временная сложность </p> <p>Подобно экспоненциальной сложности, логарифмическая также часто встречается в рекурсивных функциях. Следующий код формирует рекурсивное дерево высотой \\(\\log_2 n\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def log_recur(n: int) -&gt; int:\n    \"\"\"Логарифмическая сложность (рекурсивная реализация)\"\"\"\n    if n &lt;= 1:\n        return 0\n    return log_recur(n / 2) + 1\n</code></pre> time_complexity.cpp<pre><code>/* Логарифмическая сложность (рекурсивная реализация) */\nint logRecur(int n) {\n    if (n &lt;= 1)\n        return 0;\n    return logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.java<pre><code>/* Логарифмическая сложность (рекурсивная реализация) */\nint logRecur(int n) {\n    if (n &lt;= 1)\n        return 0;\n    return logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.cs<pre><code>/* Логарифмическая сложность (рекурсивная реализация) */\nint LogRecur(int n) {\n    if (n &lt;= 1) return 0;\n    return LogRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.go<pre><code>/* Логарифмическая сложность (рекурсивная реализация) */\nfunc logRecur(n int) int {\n    if n &lt;= 1 {\n        return 0\n    }\n    return logRecur(n/2) + 1\n}\n</code></pre> time_complexity.swift<pre><code>/* Логарифмическая сложность (рекурсивная реализация) */\nfunc logRecur(n: Int) -&gt; Int {\n    if n &lt;= 1 {\n        return 0\n    }\n    return logRecur(n: n / 2) + 1\n}\n</code></pre> time_complexity.js<pre><code>/* Логарифмическая сложность (рекурсивная реализация) */\nfunction logRecur(n) {\n    if (n &lt;= 1) return 0;\n    return logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.ts<pre><code>/* Логарифмическая сложность (рекурсивная реализация) */\nfunction logRecur(n: number): number {\n    if (n &lt;= 1) return 0;\n    return logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.dart<pre><code>/* Логарифмическая сложность (рекурсивная реализация) */\nint logRecur(int n) {\n  if (n &lt;= 1) return 0;\n  return logRecur(n ~/ 2) + 1;\n}\n</code></pre> time_complexity.rs<pre><code>/* Логарифмическая сложность (рекурсивная реализация) */\nfn log_recur(n: i32) -&gt; i32 {\n    if n &lt;= 1 {\n        return 0;\n    }\n    log_recur(n / 2) + 1\n}\n</code></pre> time_complexity.c<pre><code>/* Логарифмическая сложность (рекурсивная реализация) */\nint logRecur(int n) {\n    if (n &lt;= 1)\n        return 0;\n    return logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.kt<pre><code>/* Логарифмическая сложность (рекурсивная реализация) */\nfun logRecur(n: Int): Int {\n    if (n &lt;= 1)\n        return 0\n    return logRecur(n / 2) + 1\n}\n</code></pre> time_complexity.rb<pre><code>### Квадратичная сложность ###\ndef quadratic(n)\n  count = 0\n\n  # Число итераций квадратично зависит от размера данных n\n  for i in 0...n\n    for j in 0...n\n      count += 1\n    end\n  end\n\n  count\nend\n\n# ## Квадратичная сложность (пузырьковая сортировка) ###\ndef bubble_sort(nums)\n  count = 0  # Счетчик\n\n  # Внешний цикл: неотсортированный диапазон [0, i]\n  for i in (nums.length - 1).downto(0)\n    # Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n    for j in 0...i\n      if nums[j] &gt; nums[j + 1]\n        # Поменять местами nums[j] и nums[j + 1]\n        tmp = nums[j]\n        nums[j] = nums[j + 1]\n        nums[j + 1] = tmp\n        count += 3 # Обмен элементов включает 3 элементарные операции\n      end\n    end\n  end\n\n  count\nend\n\n# ## Экспоненциальная сложность (итеративная реализация) ###\ndef exponential(n)\n  count, base = 0, 1\n\n  # На каждом шаге клетка делится надвое, образуя последовательность 1, 2, 4, 8, ..., 2^(n-1)\n  (0...n).each do\n    (0...base).each { count += 1 }\n    base *= 2\n  end\n\n  # count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n  count\nend\n\n# ## Экспоненциальная сложность (рекурсивная реализация) ###\ndef exp_recur(n)\n  return 1 if n == 1\n  exp_recur(n - 1) + exp_recur(n - 1) + 1\nend\n\n# ## Логарифмическая сложность (итеративная реализация) ###\ndef logarithmic(n)\n  count = 0\n\n  while n &gt; 1\n    n /= 2\n    count += 1\n  end\n\n  count\nend\n\n# ## Логарифмическая сложность (рекурсивная реализация) ###\ndef log_recur(n)\n  return 0 unless n &gt; 1\n  log_recur(n / 2) + 1\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Логарифмическая сложность часто встречается в алгоритмах, основанных на стратегии \"разделяй и властвуй\", и отражает идеи разбиения на части и упрощения сложной задачи. Она растет медленно и считается одной из самых желательных временных сложностей после константной.</p> <p>Каково основание у \\(O(\\log n)\\) ?</p> <p>Точнее говоря, \"разделение на \\(m\\) частей\" соответствует временной сложности \\(O(\\log_m n)\\) . А по формуле перехода к другому основанию логарифма мы получаем равные по сложности выражения с разными основаниями:</p> \\[ O(\\log_m n) = O(\\log_k n / \\log_k m) = O(\\log_k n) \\] <p>Иными словами, основание \\(m\\) можно менять без влияния на сложность. Поэтому мы обычно опускаем основание \\(m\\) и напрямую записываем логарифмическую сложность как \\(O(\\log n)\\) .</p>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#6-on-log-n","level":3,"title":"6.   Линейно-логарифмическая сложность \\(O(n \\log n)\\)","text":"<p>Линейно-логарифмическая сложность часто встречается в рекурсивных разбиениях, где временная сложность одного измерения равна \\(O(\\log n)\\) , а другого - \\(O(n)\\) . Соответствующий код выглядит следующим образом:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def linear_log_recur(n: int) -&gt; int:\n    \"\"\"Линейно-логарифмическая сложность\"\"\"\n    if n &lt;= 1:\n        return 1\n    # Разделение надвое: размер подзадачи уменьшается вдвое\n    count = linear_log_recur(n // 2) + linear_log_recur(n // 2)\n    # Текущая подзадача содержит n операций\n    for _ in range(n):\n        count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* Линейно-логарифмическая сложность */\nint linearLogRecur(int n) {\n    if (n &lt;= 1)\n        return 1;\n    int count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\n    for (int i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* Линейно-логарифмическая сложность */\nint linearLogRecur(int n) {\n    if (n &lt;= 1)\n        return 1;\n    int count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\n    for (int i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* Линейно-логарифмическая сложность */\nint LinearLogRecur(int n) {\n    if (n &lt;= 1) return 1;\n    int count = LinearLogRecur(n / 2) + LinearLogRecur(n / 2);\n    for (int i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* Линейно-логарифмическая сложность */\nfunc linearLogRecur(n int) int {\n    if n &lt;= 1 {\n        return 1\n    }\n    count := linearLogRecur(n/2) + linearLogRecur(n/2)\n    for i := 0; i &lt; n; i++ {\n        count++\n    }\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* Линейно-логарифмическая сложность */\nfunc linearLogRecur(n: Int) -&gt; Int {\n    if n &lt;= 1 {\n        return 1\n    }\n    var count = linearLogRecur(n: n / 2) + linearLogRecur(n: n / 2)\n    for _ in stride(from: 0, to: n, by: 1) {\n        count += 1\n    }\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* Линейно-логарифмическая сложность */\nfunction linearLogRecur(n) {\n    if (n &lt;= 1) return 1;\n    let count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\n    for (let i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* Линейно-логарифмическая сложность */\nfunction linearLogRecur(n: number): number {\n    if (n &lt;= 1) return 1;\n    let count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\n    for (let i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* Линейно-логарифмическая сложность */\nint linearLogRecur(int n) {\n  if (n &lt;= 1) return 1;\n  int count = linearLogRecur(n ~/ 2) + linearLogRecur(n ~/ 2);\n  for (var i = 0; i &lt; n; i++) {\n    count++;\n  }\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* Линейно-логарифмическая сложность */\nfn linear_log_recur(n: i32) -&gt; i32 {\n    if n &lt;= 1 {\n        return 1;\n    }\n    let mut count = linear_log_recur(n / 2) + linear_log_recur(n / 2);\n    for _ in 0..n {\n        count += 1;\n    }\n    return count;\n}\n</code></pre> time_complexity.c<pre><code>/* Линейно-логарифмическая сложность */\nint linearLogRecur(int n) {\n    if (n &lt;= 1)\n        return 1;\n    int count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\n    for (int i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* Линейно-логарифмическая сложность */\nfun linearLogRecur(n: Int): Int {\n    if (n &lt;= 1)\n        return 1\n    var count = linearLogRecur(n / 2) + linearLogRecur(n / 2)\n    for (i in 0..&lt;n) {\n        count++\n    }\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### Линейно-логарифмическая сложность ###\ndef linear_log_recur(n)\n  return 1 unless n &gt; 1\n\n  count = linear_log_recur(n / 2) + linear_log_recur(n / 2)\n  (0...n).each { count += 1 }\n\n  count\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>На рисунке 2-13 показано, как возникает линейно-логарифмическая сложность. Общее число операций на каждом уровне бинарного дерева равно \\(n\\) , а дерево имеет \\(\\log_2 n + 1\\) уровней, поэтому временная сложность равна \\(O(n \\log n)\\) .</p> <p></p> <p> Рисунок 2-13   Линейно-логарифмическая временная сложность </p> <p>Временная сложность основных алгоритмов сортировки обычно равна \\(O(n \\log n)\\) , например у быстрой сортировки, сортировки слиянием, пирамидальной сортировки и т.д.</p>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#7-on","level":3,"title":"7.   Факториальная сложность \\(O(n!)\\)","text":"<p>Факториальная сложность соответствует математической задаче полной перестановки. Если даны \\(n\\) попарно различных элементов, то число всех возможных перестановок равно:</p> \\[ n! = n \\times (n - 1) \\times (n - 2) \\times \\dots \\times 2 \\times 1 \\] <p>Факториал обычно реализуют через рекурсию. Как показано на рисунке 2-14 и в следующем коде, на первом уровне происходит ветвление на \\(n\\) подзадач, на втором - на \\(n - 1\\) и так далее, пока на \\(n\\)-м уровне ветвление не прекращается:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby time_complexity.py<pre><code>def factorial_recur(n: int) -&gt; int:\n    \"\"\"Факториальная сложность (рекурсивная реализация)\"\"\"\n    if n == 0:\n        return 1\n    count = 0\n    # Из одного получается n\n    for _ in range(n):\n        count += factorial_recur(n - 1)\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* Факториальная сложность (рекурсивная реализация) */\nint factorialRecur(int n) {\n    if (n == 0)\n        return 1;\n    int count = 0;\n    // Из одного получается n\n    for (int i = 0; i &lt; n; i++) {\n        count += factorialRecur(n - 1);\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* Факториальная сложность (рекурсивная реализация) */\nint factorialRecur(int n) {\n    if (n == 0)\n        return 1;\n    int count = 0;\n    // Из одного получается n\n    for (int i = 0; i &lt; n; i++) {\n        count += factorialRecur(n - 1);\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>/* Факториальная сложность (рекурсивная реализация) */\nint FactorialRecur(int n) {\n    if (n == 0) return 1;\n    int count = 0;\n    // Из одного получается n\n    for (int i = 0; i &lt; n; i++) {\n        count += FactorialRecur(n - 1);\n    }\n    return count;\n}\n</code></pre> time_complexity.go<pre><code>/* Факториальная сложность (рекурсивная реализация) */\nfunc factorialRecur(n int) int {\n    if n == 0 {\n        return 1\n    }\n    count := 0\n    // Из одного получается n\n    for i := 0; i &lt; n; i++ {\n        count += factorialRecur(n - 1)\n    }\n    return count\n}\n</code></pre> time_complexity.swift<pre><code>/* Факториальная сложность (рекурсивная реализация) */\nfunc factorialRecur(n: Int) -&gt; Int {\n    if n == 0 {\n        return 1\n    }\n    var count = 0\n    // Из одного получается n\n    for _ in 0 ..&lt; n {\n        count += factorialRecur(n: n - 1)\n    }\n    return count\n}\n</code></pre> time_complexity.js<pre><code>/* Факториальная сложность (рекурсивная реализация) */\nfunction factorialRecur(n) {\n    if (n === 0) return 1;\n    let count = 0;\n    // Из одного получается n\n    for (let i = 0; i &lt; n; i++) {\n        count += factorialRecur(n - 1);\n    }\n    return count;\n}\n</code></pre> time_complexity.ts<pre><code>/* Факториальная сложность (рекурсивная реализация) */\nfunction factorialRecur(n: number): number {\n    if (n === 0) return 1;\n    let count = 0;\n    // Из одного получается n\n    for (let i = 0; i &lt; n; i++) {\n        count += factorialRecur(n - 1);\n    }\n    return count;\n}\n</code></pre> time_complexity.dart<pre><code>/* Факториальная сложность (рекурсивная реализация) */\nint factorialRecur(int n) {\n  if (n == 0) return 1;\n  int count = 0;\n  // Из одного получается n\n  for (var i = 0; i &lt; n; i++) {\n    count += factorialRecur(n - 1);\n  }\n  return count;\n}\n</code></pre> time_complexity.rs<pre><code>/* Факториальная сложность (рекурсивная реализация) */\nfn factorial_recur(n: i32) -&gt; i32 {\n    if n == 0 {\n        return 1;\n    }\n    let mut count = 0;\n    // Из одного получается n\n    for _ in 0..n {\n        count += factorial_recur(n - 1);\n    }\n    count\n}\n</code></pre> time_complexity.c<pre><code>/* Факториальная сложность (рекурсивная реализация) */\nint factorialRecur(int n) {\n    if (n == 0)\n        return 1;\n    int count = 0;\n    for (int i = 0; i &lt; n; i++) {\n        count += factorialRecur(n - 1);\n    }\n    return count;\n}\n</code></pre> time_complexity.kt<pre><code>/* Факториальная сложность (рекурсивная реализация) */\nfun factorialRecur(n: Int): Int {\n    if (n == 0)\n        return 1\n    var count = 0\n    // Из одного получается n\n    for (i in 0..&lt;n) {\n        count += factorialRecur(n - 1)\n    }\n    return count\n}\n</code></pre> time_complexity.rb<pre><code>### Линейно-логарифмическая сложность ###\ndef linear_log_recur(n)\n  return 1 unless n &gt; 1\n\n  count = linear_log_recur(n / 2) + linear_log_recur(n / 2)\n  (0...n).each { count += 1 }\n\n  count\nend\n\n# ## Факториальная сложность (рекурсивная реализация) ###\ndef factorial_recur(n)\n  return 1 if n == 0\n\n  count = 0\n  # Из одного получается n\n  (0...n).each { count += factorial_recur(n - 1) }\n\n  count\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p></p> <p> Рисунок 2-14   Факториальная временная сложность </p> <p>Следует отметить, что поскольку при \\(n \\geq 4\\) всегда выполняется \\(n! &gt; 2^n\\) , факториальная сложность растет еще быстрее, чем экспоненциальная, и при больших \\(n\\) становится неприемлемой.</p>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_computational_complexity/time_complexity/#235","level":2,"title":"2.3.5   Худшая, лучшая и средняя временная сложность","text":"<p>Временная эффективность алгоритма часто не фиксирована, а зависит от распределения входных данных. Предположим, на вход подается массив <code>nums</code> длины \\(n\\) , состоящий из чисел от \\(1\\) до \\(n\\) , каждое из которых встречается ровно один раз; при этом порядок элементов случайно перемешан. Задача состоит в том, чтобы вернуть индекс элемента \\(1\\) . Тогда можно сделать следующие выводы.</p> <ul> <li>Когда <code>nums = [?, ?, ..., 1]</code> , то есть когда последний элемент равен \\(1\\) , нужно полностью пройти по массиву, что дает худшую временную сложность \\(O(n)\\) .</li> <li>Когда <code>nums = [1, ?, ?, ...]</code> , то есть когда первый элемент равен \\(1\\) , независимо от длины массива продолжать обход не нужно, что дает лучшую временную сложность \\(\\Omega(1)\\) .</li> </ul> <p>Худшая временная сложность соответствует асимптотической верхней границе функции и обозначается нотацией Big \\(O\\) . Соответственно, лучшая временная сложность соответствует асимптотической нижней границе функции и обозначается символом \\(\\Omega\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby worst_best_time_complexity.py<pre><code>def random_numbers(n: int) -&gt; list[int]:\n    \"\"\"Сгенерировать массив с элементами 1, 2, ..., n в случайном порядке\"\"\"\n    # Создать массив nums =: 1, 2, 3, ..., n\n    nums = [i for i in range(1, n + 1)]\n    # Случайно перемешать элементы массива\n    random.shuffle(nums)\n    return nums\n\ndef find_one(nums: list[int]) -&gt; int:\n    \"\"\"Найти индекс числа 1 в массиве nums\"\"\"\n    for i in range(len(nums)):\n        # Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n        # Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n        if nums[i] == 1:\n            return i\n    return -1\n</code></pre> worst_best_time_complexity.cpp<pre><code>/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */\nvector&lt;int&gt; randomNumbers(int n) {\n    vector&lt;int&gt; nums(n);\n    // Создать массив nums = { 1, 2, 3, ..., n }\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = i + 1;\n    }\n    // Использовать системное время для генерации случайного seed\n    unsigned seed = chrono::system_clock::now().time_since_epoch().count();\n    // Случайно перемешать элементы массива\n    shuffle(nums.begin(), nums.end(), default_random_engine(seed));\n    return nums;\n}\n\n/* Найти индекс числа 1 в массиве nums */\nint findOne(vector&lt;int&gt; &amp;nums) {\n    for (int i = 0; i &lt; nums.size(); i++) {\n        // Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n        // Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n        if (nums[i] == 1)\n            return i;\n    }\n    return -1;\n}\n</code></pre> worst_best_time_complexity.java<pre><code>/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */\nint[] randomNumbers(int n) {\n    Integer[] nums = new Integer[n];\n    // Создать массив nums = { 1, 2, 3, ..., n }\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = i + 1;\n    }\n    // Случайно перемешать элементы массива\n    Collections.shuffle(Arrays.asList(nums));\n    // Integer[] -&gt; int[]\n    int[] res = new int[n];\n    for (int i = 0; i &lt; n; i++) {\n        res[i] = nums[i];\n    }\n    return res;\n}\n\n/* Найти индекс числа 1 в массиве nums */\nint findOne(int[] nums) {\n    for (int i = 0; i &lt; nums.length; i++) {\n        // Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n        // Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n        if (nums[i] == 1)\n            return i;\n    }\n    return -1;\n}\n</code></pre> worst_best_time_complexity.cs<pre><code>/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */\nint[] RandomNumbers(int n) {\n    int[] nums = new int[n];\n    // Создать массив nums = { 1, 2, 3, ..., n }\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = i + 1;\n    }\n\n    // Случайно перемешать элементы массива\n    for (int i = 0; i &lt; nums.Length; i++) {\n        int index = new Random().Next(i, nums.Length);\n        (nums[i], nums[index]) = (nums[index], nums[i]);\n    }\n    return nums;\n}\n\n/* Найти индекс числа 1 в массиве nums */\nint FindOne(int[] nums) {\n    for (int i = 0; i &lt; nums.Length; i++) {\n        // Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n        // Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n        if (nums[i] == 1)\n            return i;\n    }\n    return -1;\n}\n</code></pre> worst_best_time_complexity.go<pre><code>/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */\nfunc randomNumbers(n int) []int {\n    nums := make([]int, n)\n    // Создать массив nums = { 1, 2, 3, ..., n }\n    for i := 0; i &lt; n; i++ {\n        nums[i] = i + 1\n    }\n    // Случайно перемешать элементы массива\n    rand.Shuffle(len(nums), func(i, j int) {\n        nums[i], nums[j] = nums[j], nums[i]\n    })\n    return nums\n}\n\n/* Найти индекс числа 1 в массиве nums */\nfunc findOne(nums []int) int {\n    for i := 0; i &lt; len(nums); i++ {\n        // Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n        // Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n        if nums[i] == 1 {\n            return i\n        }\n    }\n    return -1\n}\n</code></pre> worst_best_time_complexity.swift<pre><code>/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */\nfunc randomNumbers(n: Int) -&gt; [Int] {\n    // Создать массив nums = { 1, 2, 3, ..., n }\n    var nums = Array(1 ... n)\n    // Случайно перемешать элементы массива\n    nums.shuffle()\n    return nums\n}\n\n/* Найти индекс числа 1 в массиве nums */\nfunc findOne(nums: [Int]) -&gt; Int {\n    for i in nums.indices {\n        // Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n        // Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n        if nums[i] == 1 {\n            return i\n        }\n    }\n    return -1\n}\n</code></pre> worst_best_time_complexity.js<pre><code>/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */\nfunction randomNumbers(n) {\n    const nums = Array(n);\n    // Создать массив nums = { 1, 2, 3, ..., n }\n    for (let i = 0; i &lt; n; i++) {\n        nums[i] = i + 1;\n    }\n    // Случайно перемешать элементы массива\n    for (let i = 0; i &lt; n; i++) {\n        const r = Math.floor(Math.random() * (i + 1));\n        const temp = nums[i];\n        nums[i] = nums[r];\n        nums[r] = temp;\n    }\n    return nums;\n}\n\n/* Найти индекс числа 1 в массиве nums */\nfunction findOne(nums) {\n    for (let i = 0; i &lt; nums.length; i++) {\n        // Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n        // Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n        if (nums[i] === 1) {\n            return i;\n        }\n    }\n    return -1;\n}\n</code></pre> worst_best_time_complexity.ts<pre><code>/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */\nfunction randomNumbers(n: number): number[] {\n    const nums = Array(n);\n    // Создать массив nums = { 1, 2, 3, ..., n }\n    for (let i = 0; i &lt; n; i++) {\n        nums[i] = i + 1;\n    }\n    // Случайно перемешать элементы массива\n    for (let i = 0; i &lt; n; i++) {\n        const r = Math.floor(Math.random() * (i + 1));\n        const temp = nums[i];\n        nums[i] = nums[r];\n        nums[r] = temp;\n    }\n    return nums;\n}\n\n/* Найти индекс числа 1 в массиве nums */\nfunction findOne(nums: number[]): number {\n    for (let i = 0; i &lt; nums.length; i++) {\n        // Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n        // Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n        if (nums[i] === 1) {\n            return i;\n        }\n    }\n    return -1;\n}\n</code></pre> worst_best_time_complexity.dart<pre><code>/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */\nList&lt;int&gt; randomNumbers(int n) {\n  final nums = List.filled(n, 0);\n  // Создать массив nums = { 1, 2, 3, ..., n }\n  for (var i = 0; i &lt; n; i++) {\n    nums[i] = i + 1;\n  }\n  // Случайно перемешать элементы массива\n  nums.shuffle();\n\n  return nums;\n}\n\n/* Найти индекс числа 1 в массиве nums */\nint findOne(List&lt;int&gt; nums) {\n  for (var i = 0; i &lt; nums.length; i++) {\n    // Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n    // Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n    if (nums[i] == 1) return i;\n  }\n\n  return -1;\n}\n</code></pre> worst_best_time_complexity.rs<pre><code>/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */\nfn random_numbers(n: i32) -&gt; Vec&lt;i32&gt; {\n    // Создать массив nums = { 1, 2, 3, ..., n }\n    let mut nums = (1..=n).collect::&lt;Vec&lt;i32&gt;&gt;();\n    // Случайно перемешать элементы массива\n    nums.shuffle(&amp;mut thread_rng());\n    nums\n}\n\n/* Найти индекс числа 1 в массиве nums */\nfn find_one(nums: &amp;[i32]) -&gt; Option&lt;usize&gt; {\n    for i in 0..nums.len() {\n        // Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n        // Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n        if nums[i] == 1 {\n            return Some(i);\n        }\n    }\n    None\n}\n</code></pre> worst_best_time_complexity.c<pre><code>/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */\nint *randomNumbers(int n) {\n    // Выделить память в куче (создать одномерный массив переменной длины: число элементов равно n, тип элементов — int)\n    int *nums = (int *)malloc(n * sizeof(int));\n    // Создать массив nums = { 1, 2, 3, ..., n }\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = i + 1;\n    }\n    // Случайно перемешать элементы массива\n    for (int i = n - 1; i &gt; 0; i--) {\n        int j = rand() % (i + 1);\n        int temp = nums[i];\n        nums[i] = nums[j];\n        nums[j] = temp;\n    }\n    return nums;\n}\n\n/* Найти индекс числа 1 в массиве nums */\nint findOne(int *nums, int n) {\n    for (int i = 0; i &lt; n; i++) {\n        // Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n        // Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n        if (nums[i] == 1)\n            return i;\n    }\n    return -1;\n}\n</code></pre> worst_best_time_complexity.kt<pre><code>/* Создать массив с элементами { 1, 2, ..., n } в случайном порядке */\nfun randomNumbers(n: Int): Array&lt;Int?&gt; {\n    val nums = IntArray(n)\n    // Создать массив nums = { 1, 2, 3, ..., n }\n    for (i in 0..&lt;n) {\n        nums[i] = i + 1\n    }\n    // Случайно перемешать элементы массива\n    nums.shuffle()\n    val res = arrayOfNulls&lt;Int&gt;(n)\n    for (i in 0..&lt;n) {\n        res[i] = nums[i]\n    }\n    return res\n}\n\n/* Найти индекс числа 1 в массиве nums */\nfun findOne(nums: Array&lt;Int?&gt;): Int {\n    for (i in nums.indices) {\n        // Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n        // Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n        if (nums[i] == 1)\n            return i\n    }\n    return -1\n}\n</code></pre> worst_best_time_complexity.rb<pre><code>### Создать массив с элементами: 1, 2, ..., n в случайном порядке ###\ndef random_numbers(n)\n  # Создать массив nums =: 1, 2, 3, ..., n\n  nums = Array.new(n) { |i| i + 1 }\n  # Случайно перемешать элементы массива\n  nums.shuffle!\nend\n\n### Найти индекс числа 1 в массиве nums ###\ndef find_one(nums)\n  for i in 0...nums.length\n    # Когда элемент 1 находится в начале массива, достигается лучшая временная сложность O(1)\n    # Когда элемент 1 находится в конце массива, достигается худшая временная сложность O(n)\n    return i if nums[i] == 1\n  end\n\n  -1\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Стоит отметить, что на практике лучшая временная сложность используется редко, поскольку обычно она достигается лишь с очень малой вероятностью и может вводить в заблуждение. Худшая временная сложность гораздо практичнее, потому что задает безопасную оценку эффективности и позволяет уверенно использовать алгоритм.</p> <p>Из приведенного выше примера видно, что худшая и лучшая временные сложности возникают только при особых распределениях данных; вероятность таких случаев может быть низкой, и они не всегда реально отражают эффективность алгоритма. Напротив, средняя временная сложность способна показать эффективность алгоритма на случайных входных данных и обозначается символом \\(\\Theta\\) .</p> <p>Для некоторых алгоритмов можно относительно просто вывести средний случай при случайном распределении данных. Например, в приведенном выше примере входной массив перемешан, а вероятность появления элемента \\(1\\) на любом индексе одинакова; следовательно, среднее число итераций алгоритма равно половине длины массива, то есть \\(n / 2\\) , а средняя временная сложность равна \\(\\Theta(n / 2) = \\Theta(n)\\) .</p> <p>Однако для более сложных алгоритмов вычислить среднюю временную сложность часто непросто, потому что трудно проанализировать полное математическое ожидание на заданном распределении данных. В таких случаях обычно используют худшую временную сложность как критерий оценки эффективности алгоритма.</p> <p>Почему символ \\(\\Theta\\) встречается так редко?</p> <p>Возможно, потому что символ \\(O\\) звучит слишком привычно, и мы часто используем его для обозначения средней временной сложности. Но строго говоря, это некорректно. В этой книге и в других материалах, если встретится выражение вроде \"средняя временная сложность \\(O(n)\\)\", просто понимай его как \\(\\Theta(n)\\) .</p>","path":["Глава 2. Анализ сложности","2.3 &nbsp; Временная сложность"],"tags":[]},{"location":"chapter_data_structure/","level":1,"title":"Глава 3.   Структуры данных","text":"<p>Abstract</p> <p>Структуры данных подобны прочному и многообразному каркасу.</p> <p>Они задают схему упорядоченной организации данных, на основе которой оживают алгоритмы.</p>","path":["Глава 3. Структуры данных","Глава 3. &nbsp; Структуры данных"],"tags":[]},{"location":"chapter_data_structure/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>3.1   Классификация структур данных</li> <li>3.2   Базовые типы данных</li> <li>3.3   Кодирование чисел *</li> <li>3.4   Кодирование символов *</li> <li>3.5   Резюме</li> </ul>","path":["Глава 3. Структуры данных","Глава 3. &nbsp; Структуры данных"],"tags":[]},{"location":"chapter_data_structure/basic_data_types/","level":1,"title":"3.2   Базовые типы данных","text":"<p>Когда речь заходит о данных в компьютере, мы в первую очередь вспоминаем текст, изображения, видео, звук, 3D-модели и многие другие формы представления информации. Хотя способы организации этих данных различаются, все они строятся из базовых типов данных.</p> <p>Базовые типы данных - это типы, которые процессор может обрабатывать непосредственно. В алгоритмах они используются напрямую и в основном включают следующее.</p> <ul> <li>Целочисленные типы <code>byte</code> , <code>short</code> , <code>int</code> , <code>long</code> .</li> <li>Типы с плавающей точкой <code>float</code> , <code>double</code> , используемые для представления дробных чисел.</li> <li>Символьный тип <code>char</code> , используемый для представления букв, знаков препинания и даже эмодзи в разных языках.</li> <li>Логический тип <code>bool</code> , используемый для представления суждений \"да\" и \"нет\".</li> </ul> <p>Базовые типы данных хранятся в компьютере в двоичной форме. Один двоичный разряд равен \\(1\\) биту. В большинстве современных операционных систем \\(1\\) байт (byte) состоит из \\(8\\) битов (bit).</p> <p>Диапазон значений базовых типов данных зависит от объема занимаемого ими пространства. Ниже в качестве примера используется Java.</p> <ul> <li>Целочисленный тип <code>byte</code> занимает \\(1\\) байт = \\(8\\) бит и может представлять \\(2^{8}\\) чисел.</li> <li>Целочисленный тип <code>int</code> занимает \\(4\\) байта = \\(32\\) бита и может представлять \\(2^{32}\\) чисел.</li> </ul> <p>В таблице 3-1 перечислены объем памяти, диапазон значений и значения по умолчанию для различных базовых типов данных в Java. Эту таблицу не нужно заучивать наизусть; достаточно иметь общее представление и при необходимости обращаться к ней.</p> <p> Таблица 3-1   Объем памяти и диапазоны значений базовых типов данных </p> Тип Обозначение Объем памяти Минимальное значение Максимальное значение Значение по умолчанию Целые <code>byte</code> 1 байт \\(-2^7\\) (\\(-128\\)) \\(2^7 - 1\\) (\\(127\\)) \\(0\\) <code>short</code> 2 байта \\(-2^{15}\\) \\(2^{15} - 1\\) \\(0\\) <code>int</code> 4 байта \\(-2^{31}\\) \\(2^{31} - 1\\) \\(0\\) <code>long</code> 8 байт \\(-2^{63}\\) \\(2^{63} - 1\\) \\(0\\) Вещественные <code>float</code> 4 байта \\(1.175 \\times 10^{-38}\\) \\(3.403 \\times 10^{38}\\) \\(0.0\\text{f}\\) <code>double</code> 8 байт \\(2.225 \\times 10^{-308}\\) \\(1.798 \\times 10^{308}\\) \\(0.0\\) Символы <code>char</code> 2 байта \\(0\\) \\(2^{16} - 1\\) \\(0\\) Логические <code>bool</code> 1 байт \\(\\text{false}\\) \\(\\text{true}\\) \\(\\text{false}\\) <p>Обрати внимание: приведенная выше таблица относится именно к базовым типам данных Java. В каждом языке программирования свои определения типов, поэтому объем памяти, диапазон значений и значения по умолчанию могут различаться.</p> <ul> <li>В Python целочисленный тип <code>int</code> может иметь произвольный размер, ограниченный только доступной памятью; тип <code>float</code> является 64-битным числом двойной точности; типа <code>char</code> нет, а отдельный символ на деле является строкой <code>str</code> длины 1.</li> <li>В C и C++ размер базовых типов данных явно не зафиксирован и зависит от реализации и платформы. таблица 3-1 соответствует модели данных LP64 data model, используемой в 64-битных Unix-системах, включая Linux и macOS.</li> <li>Размер символа <code>char</code> в C и C++ составляет 1 байт, а в большинстве других языков программирования зависит от конкретного способа кодирования символов; подробнее это рассматривается в разделе \"Кодирование символов\".</li> <li>Хотя для представления логического значения достаточно 1 бита ( \\(0\\) или \\(1\\) ), в памяти оно обычно хранится как 1 байт. Это связано с тем, что современные CPU обычно используют 1 байт как минимальную адресуемую единицу памяти.</li> </ul> <p>Какова же связь между базовыми типами данных и структурами данных? Мы знаем, что структура данных - это способ организации и хранения данных в компьютере. Подлежащее в этой фразе - \"структура\", а не \"данные\".</p> <p>Если мы хотим представить \"ряд чисел\", то естественно подумаем об использовании массива. Это связано с тем, что линейная структура массива может выразить отношения соседства и порядка между числами, а то, что именно хранится внутри - целые <code>int</code> , вещественные <code>float</code> или символы <code>char</code> , - к \"структуре данных\" отношения не имеет.</p> <p>Иными словами, базовые типы данных задают \"тип содержимого\" данных, а структуры данных задают \"способ организации\" данных. Например, в следующем коде мы используем одну и ту же структуру данных (массив) для хранения и представления различных базовых типов данных, включая <code>int</code> , <code>float</code> , <code>char</code> , <code>bool</code> и т.д.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code># Инициализируем массивы с использованием различных базовых типов данных\nnumbers: list[int] = [0] * 5\ndecimals: list[float] = [0.0] * 5\n# В Python символы фактически являются строками длины 1\ncharacters: list[str] = ['0'] * 5\nbools: list[bool] = [False] * 5\n# Списки Python могут свободно хранить различные базовые типы данных и ссылки на объекты\ndata = [0, 0.0, 'a', False, ListNode(0)]\n</code></pre> <pre><code>// Инициализируем массивы с использованием различных базовых типов данных\nint numbers[5];\nfloat decimals[5];\nchar characters[5];\nbool bools[5];\n</code></pre> <pre><code>// Инициализируем массивы с использованием различных базовых типов данных\nint[] numbers = new int[5];\nfloat[] decimals = new float[5];\nchar[] characters = new char[5];\nboolean[] bools = new boolean[5];\n</code></pre> <pre><code>// Инициализируем массивы с использованием различных базовых типов данных\nint[] numbers = new int[5];\nfloat[] decimals = new float[5];\nchar[] characters = new char[5];\nbool[] bools = new bool[5];\n</code></pre> <pre><code>// Инициализируем массивы с использованием различных базовых типов данных\nvar numbers = [5]int{}\nvar decimals = [5]float64{}\nvar characters = [5]byte{}\nvar bools = [5]bool{}\n</code></pre> <pre><code>// Инициализируем массивы с использованием различных базовых типов данных\nlet numbers = Array(repeating: 0, count: 5)\nlet decimals = Array(repeating: 0.0, count: 5)\nlet characters: [Character] = Array(repeating: \"a\", count: 5)\nlet bools = Array(repeating: false, count: 5)\n</code></pre> <pre><code>// Массивы JavaScript могут свободно хранить различные базовые типы данных и объекты\nconst array = [0, 0.0, 'a', false];\n</code></pre> <pre><code>// Инициализируем массивы с использованием различных базовых типов данных\nconst numbers: number[] = [];\nconst characters: string[] = [];\nconst bools: boolean[] = [];\n</code></pre> <pre><code>// Инициализируем массивы с использованием различных базовых типов данных\nList&lt;int&gt; numbers = List.filled(5, 0);\nList&lt;double&gt; decimals = List.filled(5, 0.0);\nList&lt;String&gt; characters = List.filled(5, 'a');\nList&lt;bool&gt; bools = List.filled(5, false);\n</code></pre> <pre><code>// Инициализируем массивы с использованием различных базовых типов данных\nlet numbers: Vec&lt;i32&gt; = vec![0; 5];\nlet decimals: Vec&lt;f32&gt; = vec![0.0; 5];\nlet characters: Vec&lt;char&gt; = vec!['0'; 5];\nlet bools: Vec&lt;bool&gt; = vec![false; 5];\n</code></pre> <pre><code>// Инициализируем массивы с использованием различных базовых типов данных\nint numbers[10];\nfloat decimals[10];\nchar characters[10];\nbool bools[10];\n</code></pre> <pre><code>// Инициализируем массивы с использованием различных базовых типов данных\nval numbers = IntArray(5)\nval decinals = FloatArray(5)\nval characters = CharArray(5)\nval bools = BooleanArray(5)\n</code></pre> <pre><code># Списки Ruby могут свободно хранить различные базовые типы данных и ссылки на объекты\ndata = [0, 0.0, 'a', false, ListNode(0)]\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%D1%81%D0%B2%D1%8F%D0%B7%D0%BD%D1%8B%D0%B9%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%D1%83%D0%B7%D0%B5%D0%BB%D0%BA%D0%BB%D0%B0%D1%81%D1%81%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%D0%97%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%83%D0%B7%D0%BB%D0%B0%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%D0%A1%D1%81%D1%8B%D0%BB%D0%BA%D0%B0%20%D0%BD%D0%B0%20%D1%81%D0%BB%D0%B5%D0%B4%D1%83%D1%8E%D1%89%D0%B8%D0%B9%20%D1%83%D0%B7%D0%B5%D0%BB%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D0%BC%D0%B0%D1%81%D1%81%D0%B8%D0%B2%20%D1%81%20%D0%B8%D1%81%D0%BF%D0%BE%D0%BB%D1%8C%D0%B7%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5%D0%BC%20%D0%BD%D0%B5%D1%81%D0%BA%D0%BE%D0%BB%D1%8C%D0%BA%D0%B8%D1%85%20%D0%B1%D0%B0%D0%B7%D0%BE%D0%B2%D1%8B%D1%85%20%D1%82%D0%B8%D0%BF%D0%BE%D0%B2%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%0A%20%20%20%20numbers%20%3D%20%5B0%5D%20%2A%205%0A%20%20%20%20decimals%20%3D%20%5B0.0%5D%20%2A%205%0A%20%20%20%20%23%20%D0%92%20Python%20%D1%81%D0%B8%D0%BC%D0%B2%D0%BE%D0%BB%D1%8B%20%D0%BD%D0%B0%20%D1%81%D0%B0%D0%BC%D0%BE%D0%BC%20%D0%B4%D0%B5%D0%BB%D0%B5%20%D1%8F%D0%B2%D0%BB%D1%8F%D1%8E%D1%82%D1%81%D1%8F%20%D1%81%D1%82%D1%80%D0%BE%D0%BA%D0%B0%D0%BC%D0%B8%20%D0%B4%D0%BB%D0%B8%D0%BD%D1%8B%201%0A%20%20%20%20characters%20%3D%20%5B%270%27%5D%20%2A%205%0A%20%20%20%20bools%20%3D%20%5BFalse%5D%20%2A%205%0A%20%20%20%20%23%20%D0%A1%D0%BF%D0%B8%D1%81%D0%BA%D0%B8%20%D0%B2%20Python%20%D0%BC%D0%BE%D0%B3%D1%83%D1%82%20%D1%81%D0%B2%D0%BE%D0%B1%D0%BE%D0%B4%D0%BD%D0%BE%20%D1%85%D1%80%D0%B0%D0%BD%D0%B8%D1%82%D1%8C%20%D1%80%D0%B0%D0%B7%D0%BB%D0%B8%D1%87%D0%BD%D1%8B%D0%B5%20%D0%B1%D0%B0%D0%B7%D0%BE%D0%B2%D1%8B%D0%B5%20%D1%82%D0%B8%D0%BF%D1%8B%20%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85%20%D0%B8%20%D1%81%D1%81%D1%8B%D0%BB%D0%BA%D0%B8%20%D0%BD%D0%B0%20%D0%BE%D0%B1%D1%8A%D0%B5%D0%BA%D1%82%D1%8B%0A%20%20%20%20data%20%3D%20%5B0%2C%200.0%2C%20%27a%27%2C%20False%2C%20ListNode%280%29%5D&amp;cumulative=false&amp;curInstr=12&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 3. Структуры данных","3.2 &nbsp; Базовые типы данных"],"tags":[]},{"location":"chapter_data_structure/character_encoding/","level":1,"title":"3.4   Кодирование символов *","text":"<p>В компьютере все данные хранятся в виде двоичных чисел, и символьный тип данных <code>char</code> не является исключением. Для представления символов необходимо задать \"таблицу символов\", которая устанавливает взаимно-однозначное соответствие между каждым символом и двоичным числом. С помощью этой таблицы компьютер может преобразовывать двоичные числа в символы.</p>","path":["Глава 3. Структуры данных","3.4 &nbsp; Кодирование символов *"],"tags":[]},{"location":"chapter_data_structure/character_encoding/#341-ascii","level":2,"title":"3.4.1   Таблица символов ASCII","text":"<p>Код ASCII - это самая ранняя таблица символов; ее полное название - American Standard Code for Information Interchange (американский стандартный код обмена информацией). Для представления символов в ней используются 7 двоичных битов (нижние 7 битов одного байта), что позволяет закодировать до 128 различных символов. Как показано на рисунке 3-6, ASCII включает заглавные и строчные буквы английского алфавита, цифры 0 ~ 9, некоторые знаки препинания, а также некоторые управляющие символы (например перевод строки и табуляцию).</p> <p></p> <p> Рисунок 3-6   Таблица ASCII </p> <p>Однако код ASCII может представлять только английский язык. С развитием компьютерных технологий появилась таблица символов EASCII, способная охватывать больше языков. Она расширяет 7-битную основу ASCII до 8 битов и может представлять 256 различных символов.</p> <p>Во всем мире постепенно появились разные таблицы EASCII, подходящие для разных регионов. Первые 128 символов в этих таблицах одинаковы и соответствуют ASCII, а последние 128 символов определяются по-разному, чтобы удовлетворять потребностям разных языков.</p>","path":["Глава 3. Структуры данных","3.4 &nbsp; Кодирование символов *"],"tags":[]},{"location":"chapter_data_structure/character_encoding/#342-gbk","level":2,"title":"3.4.2   Таблица символов GBK","text":"<p>Позже люди обнаружили, что кодов EASCII все равно недостаточно для количества символов во многих языках. Например, китайских иероглифов существует почти сто тысяч, а в повседневном употреблении нужны тысячи. В 1980 году Государственное управление стандартов Китая выпустило таблицу символов GB2312, включающую 6763 иероглифа, что в основном удовлетворило потребности компьютерной обработки китайского текста.</p> <p>Однако GB2312 не умеет работать с некоторыми редкими иероглифами и традиционными формами письма. Таблица символов GBK представляет собой расширение GB2312 и в общей сложности содержит 21886 иероглифов. В схеме кодирования GBK символы ASCII представляются одним байтом, а китайские иероглифы - двумя байтами.</p>","path":["Глава 3. Структуры данных","3.4 &nbsp; Кодирование символов *"],"tags":[]},{"location":"chapter_data_structure/character_encoding/#343-unicode","level":2,"title":"3.4.3   Таблица символов Unicode","text":"<p>С бурным развитием компьютерной техники таблицы символов и стандарты кодирования начали стремительно множиться, и это породило множество проблем. С одной стороны, такие таблицы обычно определяли символы только для конкретных языков и не могли нормально работать в многоязычной среде. С другой стороны, для одного и того же языка существовало несколько стандартов кодирования; если две машины использовали разные стандарты, при обмене информацией возникали искажения текста.</p> <p>Исследователи той эпохи задумались: если создать достаточно полную таблицу символов, которая включит все языки и знаки мира, разве это не решит проблемы многоязычной среды и искаженного текста? Под влиянием этой идеи и появилась большая и всеобъемлющая таблица символов Unicode.</p> <p>Unicode по-китайски называется \"единый код\" и теоретически способен вместить более миллиона символов. Его цель - собрать символы со всего мира в единую таблицу символов, предоставить универсальный стандарт для обработки и отображения текстов на разных языках и уменьшить количество проблем с искажением текста, вызванных различиями стандартов кодирования.</p> <p>С момента публикации в 1991 году Unicode непрерывно расширялся, добавляя новые языки и символы. По состоянию на сентябрь 2022 года Unicode уже включал 149186 символов, в том числе буквы разных языков, знаки, а также эмодзи. В огромной таблице символов Unicode часто используемые символы занимают 2 байта, а некоторые редкие символы - 3 байта и даже 4 байта.</p> <p>Unicode - это универсальный набор символов, который по сути просто присваивает каждому символу номер (так называемую \"кодовую точку\"), но не определяет, как именно хранить эти кодовые точки в компьютере. Тут неизбежно возникает вопрос: если в одном тексте одновременно встречаются кодовые точки Unicode разной длины, как система должна разбирать символы? Например, если дан код длиной 2 байта, как понять, является ли это одним 2-байтовым символом или двумя 1-байтовыми?</p> <p>Для этой проблемы прямолинейное решение состоит в том, чтобы хранить все символы в кодировке одинаковой длины. Как показано на рисунке 3-7, каждый символ в \"Hello\" занимает 1 байт, а каждый символ в \"алгоритм\" занимает 2 байта. Мы можем дополнить старшие биты нулями и закодировать все символы в \"Hello алгоритм\" в виде 2-байтовых единиц. Тогда система сможет считывать по одному символу каждые 2 байта и восстановить эту фразу.</p> <p></p> <p> Рисунок 3-7   Пример кодирования Unicode </p> <p>Однако ASCII уже показал нам, что для кодирования английского текста достаточно 1 байта. Если использовать описанную выше схему, английский текст будет занимать вдвое больше памяти, чем при ASCII, а это очень неэффективно. Поэтому нам нужен более эффективный способ кодирования Unicode.</p>","path":["Глава 3. Структуры данных","3.4 &nbsp; Кодирование символов *"],"tags":[]},{"location":"chapter_data_structure/character_encoding/#344-utf-8","level":2,"title":"3.4.4   Кодировка UTF-8","text":"<p>Сегодня UTF-8 стала самым широко используемым способом кодирования Unicode в мире. Это кодировка переменной длины, использующая от 1 до 4 байт на символ в зависимости от его сложности. Символам ASCII нужен только 1 байт, латинским и греческим буквам - 2 байта, часто используемым китайским символам - 3 байта, а некоторым редким символам - 4 байта.</p> <p>Правила кодирования UTF-8 не слишком сложны и делятся на два случая.</p> <ul> <li>Для символов длиной 1 байт старший бит устанавливается в \\(0\\) , а оставшиеся 7 битов содержат кодовую точку Unicode. Стоит отметить, что символы ASCII занимают первые 128 кодовых точек в наборе Unicode. Иными словами, кодировка UTF-8 обратно совместима с ASCII. Это означает, что мы можем использовать UTF-8 для разбора очень старых ASCII-текстов.</li> <li>Для символов длиной \\(n\\) байт (где \\(n &gt; 1\\)) старшие \\(n\\) битов первого байта устанавливаются в \\(1\\) , а \\((n + 1)\\)-й бит устанавливается в \\(0\\) ; начиная со второго байта, старшие 2 бита каждого байта устанавливаются в \\(10\\) ; все остальные биты используются для заполнения кодовой точки Unicode соответствующего символа.</li> </ul> <p>На рисунке 3-8 показана UTF-8-кодировка для строки \"Hello алгоритм\". Можно заметить, что поскольку старшие \\(n\\) битов установлены в \\(1\\) , система может определить длину символа как \\(n\\) , подсчитав число ведущих единиц.</p> <p>Но почему старшие 2 бита всех остальных байтов устанавливаются в \\(10\\) ? На самом деле это \\(10\\) играет роль контрольного маркера. Если система начнет разбирать текст с неверного байта, префикс \\(10\\) поможет быстро обнаружить аномалию.</p> <p>Причина выбора \\(10\\) в качестве контрольного маркера в том, что по правилам UTF-8 символ не может иметь старшие два бита, равные \\(10\\) . Это можно доказать от противного: если предположить, что у некоторого символа старшие два бита равны \\(10\\) , то длина такого символа должна быть 1 байт, то есть это ASCII. Но у ASCII старший бит обязан быть \\(0\\) , что противоречит предположению.</p> <p></p> <p> Рисунок 3-8   Пример кодировки UTF-8 </p> <p>Помимо UTF-8, распространены еще два следующих способа кодирования.</p> <ul> <li>Кодировка UTF-16: использует 2 или 4 байта для представления символа. Все символы ASCII и часто используемые неанглийские символы представляются 2 байтами; небольшая часть символов требует 4 байта. Для 2-байтовых символов кодировка UTF-16 совпадает с кодовой точкой Unicode.</li> <li>Кодировка UTF-32: каждый символ занимает 4 байта. Это означает, что UTF-32 требует больше места, чем UTF-8 и UTF-16, особенно в текстах с большой долей ASCII-символов.</li> </ul> <p>С точки зрения занимаемого места UTF-8 очень эффективна для английских символов, потому что им нужен всего 1 байт; а для некоторых неанглийских символов (например китайских) UTF-16 может быть эффективнее, потому что ей требуется только 2 байта, тогда как UTF-8 может потребовать 3 байта.</p> <p>С точки зрения совместимости у UTF-8 наилучшая универсальность, и многие инструменты и библиотеки в первую очередь поддерживают именно UTF-8.</p>","path":["Глава 3. Структуры данных","3.4 &nbsp; Кодирование символов *"],"tags":[]},{"location":"chapter_data_structure/character_encoding/#345","level":2,"title":"3.4.5   Кодирование символов в языках программирования","text":"<p>Для большинства языков программирования прошлого строки во время выполнения программы использовали фиксированные по длине кодировки, такие как UTF-16 или UTF-32. При кодировке фиксированной длины строку можно обрабатывать как массив, и такой подход дает следующие преимущества.</p> <ul> <li>Произвольный доступ: к строкам в UTF-16 легко осуществлять произвольный доступ. UTF-8 же является кодировкой переменной длины, поэтому, чтобы найти \\(i\\) -й символ, нужно пройти от начала строки до этого символа, а это требует \\(O(n)\\) времени.</li> <li>Подсчет длины строки: аналогично произвольному доступу, вычисление длины строки в UTF-16 - это операция \\(O(1)\\) . А вот вычисление длины строки в UTF-8 требует обхода всей строки.</li> <li>Строковые операции: многие операции со строками (разделение, конкатенация, вставка, удаление и т.д.) над строками в UTF-16 реализуются проще. При работе с UTF-8 обычно требуются дополнительные вычисления, чтобы не породить некорректную UTF-8-последовательность.</li> </ul> <p>Вообще говоря, проектирование схем кодирования символов в языках программирования - очень интересная тема, в которой учитывается множество факторов.</p> <ul> <li>Тип <code>String</code> в Java использует кодировку UTF-16, и каждый символ занимает 2 байта. Это связано с тем, что на раннем этапе проектирования Java считалось, что 16 битов достаточно для представления всех возможных символов. Но это оказалось неверным предположением. Позднее Unicode вышел за пределы 16 битов, поэтому символы в Java теперь могут представляться парой 16-битных значений (так называемой \"суррогатной парой\").</li> <li>Строки в JavaScript и TypeScript используют UTF-16 по причинам, похожим на Java. Когда Netscape впервые выпустила JavaScript в 1995 году, Unicode еще находился на ранней стадии развития, и 16-битного кодирования тогда было достаточно для представления всех символов Unicode.</li> <li>C# использует UTF-16 главным образом потому, что платформа .NET была разработана Microsoft, а многие технологии Microsoft (включая Windows) широко используют именно UTF-16.</li> </ul> <p>Из-за недооценки общего числа символов перечисленным выше языкам пришлось использовать \"суррогатные пары\" для представления Unicode-символов длиной больше 16 бит. Это вынужденный компромисс. С одной стороны, в строках с суррогатными парами один символ может занимать 2 байта или 4 байта, из-за чего теряется преимущество кодировки фиксированной длины. С другой стороны, обработка суррогатных пар требует дополнительного кода, что повышает сложность разработки и отладки.</p> <p>По этим причинам некоторые языки программирования предложили иные схемы кодирования.</p> <ul> <li><code>str</code> в Python использует Unicode и гибкое строковое представление, где длина хранимого символа зависит от наибольшей кодовой точки Unicode в строке. Если все символы строки принадлежат ASCII, каждый символ занимает 1 байт; если есть символы за пределами ASCII, но все они лежат в базовой многоязычной плоскости (BMP), каждый символ занимает 2 байта; если встречаются символы за пределами BMP, каждый символ занимает 4 байта.</li> <li>Тип <code>string</code> в Go внутри использует кодировку UTF-8. Язык Go также предоставляет тип <code>rune</code>, предназначенный для представления одной кодовой точки Unicode.</li> <li>Типы <code>str</code> и <code>String</code> в Rust внутри используют UTF-8. В Rust также есть тип <code>char</code>, представляющий одну кодовую точку Unicode.</li> </ul> <p>Следует помнить, что выше обсуждался способ хранения строк внутри языков программирования, а это не то же самое, что хранение строк в файлах или передача их по сети. При файловом хранении и сетевой передаче мы обычно кодируем строки в формате UTF-8, чтобы получить наилучшую совместимость и эффективность по занимаемому месту.</p>","path":["Глава 3. Структуры данных","3.4 &nbsp; Кодирование символов *"],"tags":[]},{"location":"chapter_data_structure/classification_of_data_structure/","level":1,"title":"3.1   Классификация структур данных","text":"<p>К распространенным структурам данных относятся массивы, связные списки, стеки, очереди, хеш-таблицы, деревья, кучи и графы. Их можно классифицировать по двум измерениям: логической структуре и физической структуре.</p>","path":["Глава 3. Структуры данных","3.1 &nbsp; Классификация структур данных"],"tags":[]},{"location":"chapter_data_structure/classification_of_data_structure/#311","level":2,"title":"3.1.1   Логическая структура: линейная и нелинейная","text":"<p>Логическая структура раскрывает логические отношения между элементами данных. В массивах и связных списках данные расположены в определенном порядке, что отражает линейные отношения между элементами. В деревьях данные расположены по уровням сверху вниз, что демонстрирует отношения \"предок\" и \"потомок\". Графы состоят из вершин и ребер, отражая сложные сетевые отношения.</p> <p>Как показано на рисунке 3-1, логические структуры делятся на две большие категории: линейные и нелинейные. Линейные структуры более интуитивны, поскольку в них данные расположены линейно и логически связаны. Нелинейные структуры, напротив, представляют собой нелинейное расположение элементов данных.</p> <ul> <li>Линейные структуры данных: массивы, связные списки, стеки, очереди, хеш-таблицы, в которых элементы связаны отношением \"один к одному\".</li> <li>Нелинейные структуры данных: деревья, кучи, графы, хеш-таблицы.</li> </ul> <p>Нелинейные структуры данных можно дополнительно разделить на древовидные и сетевые.</p> <ul> <li>Древовидные структуры: деревья, кучи, хеш-таблицы, в которых элементы связаны отношением \"один ко многим\".</li> <li>Сетевые структуры: графы, в которых элементы связаны отношением \"многие ко многим\".</li> </ul> <p></p> <p> Рисунок 3-1   Линейные и нелинейные структуры данных </p>","path":["Глава 3. Структуры данных","3.1 &nbsp; Классификация структур данных"],"tags":[]},{"location":"chapter_data_structure/classification_of_data_structure/#312","level":2,"title":"3.1.2   Физическая структура: непрерывная и разрозненная","text":"<p>Во время выполнения программы обрабатываемые данные в основном хранятся в памяти. На рисунке 3-2 показан модуль оперативной памяти компьютера, где каждый черный блок содержит определенный участок памяти. Память можно представить как огромную таблицу Excel, в которой каждая ячейка способна хранить данные определенного размера.</p> <p>Система обращается к данным по адресам памяти соответствующих позиций. Как показано на рисунке 3-2, компьютер по определенным правилам присваивает каждой ячейке в этой таблице номер, чтобы каждый участок памяти имел уникальный адрес. Благодаря этим адресам программа получает доступ к данным, находящимся в памяти.</p> <p></p> <p> Рисунок 3-2   Планка памяти, участок памяти и адрес памяти </p> <p>Tip</p> <p>Стоит отметить, что сравнение памяти с таблицей Excel - это упрощенная аналогия; реальный механизм работы памяти гораздо сложнее и включает такие понятия, как адресное пространство, управление памятью, кэш-механизмы, виртуальная и физическая память.</p> <p>Память - общий ресурс для всех программ. Когда некоторый участок памяти занят одной программой, другие программы обычно не могут использовать его одновременно. Поэтому при проектировании структур данных и алгоритмов память занимает важное место. Например, пиковое потребление памяти алгоритмом не должно превышать объем доступной свободной памяти системы; если не хватает непрерывных крупных участков памяти, выбранная структура данных должна уметь размещаться в разрозненных областях памяти.</p> <p>Как показано на рисунке 3-3, физическая структура отражает способ хранения данных в памяти компьютера. Ее можно разделить на хранение в непрерывном пространстве (массивы) и хранение в разрозненном пространстве (связные списки). Физическая структура на низком уровне определяет способы доступа к данным, их обновления, вставки и удаления. Эти два типа физических структур взаимно дополняют друг друга по временной и пространственной эффективности.</p> <p></p> <p> Рисунок 3-3   Хранение в непрерывном и разрозненном пространстве </p> <p>Стоит отметить, что все структуры данных реализуются на основе массивов, связных списков или их комбинации. Например, стек и очередь можно реализовать как с помощью массивов, так и с помощью связных списков; реализация хеш-таблицы также может одновременно включать массивы и связные списки.</p> <ul> <li>Можно реализовать на основе массивов: стеки, очереди, хеш-таблицы, деревья, кучи, графы, матрицы, тензоры (массивы размерности \\(\\geq 3\\) ) и т.д.</li> <li>Можно реализовать на основе связных списков: стеки, очереди, хеш-таблицы, деревья, кучи, графы и т.д.</li> </ul> <p>После инициализации длину связного списка все еще можно изменять во время выполнения программы, поэтому его также называют \"динамической структурой данных\". Длина массива после инициализации неизменна, поэтому его также называют \"статической структурой данных\". Стоит отметить, что массив может изменять длину за счет повторного выделения памяти, тем самым приобретая определенную \"динамичность\".</p> <p>Tip</p> <p>Если тебе пока трудно понять физическую структуру, рекомендуется сначала прочитать следующую главу, а затем вернуться к этому разделу.</p>","path":["Глава 3. Структуры данных","3.1 &nbsp; Классификация структур данных"],"tags":[]},{"location":"chapter_data_structure/number_encoding/","level":1,"title":"3.3   Кодирование чисел *","text":"<p>Tip</p> <p>В этой книге разделы, помеченные символом <code>*</code>, относятся к дополнительному чтению. Если у тебя мало времени или материал кажется трудным, можно сначала пропустить их и вернуться после изучения обязательных разделов.</p>","path":["Глава 3. Структуры данных","3.3 &nbsp; Кодирование чисел *"],"tags":[]},{"location":"chapter_data_structure/number_encoding/#331","level":2,"title":"3.3.1   Прямой, обратный и дополнительный коды","text":"<p>В таблице из предыдущего раздела можно заметить, что все целочисленные типы могут представлять на одно отрицательное число больше, чем положительных. Например, диапазон <code>byte</code> равен \\([-128, 127]\\) . Это выглядит не слишком интуитивно, и внутренняя причина связана с прямым, обратным и дополнительным кодами.</p> <p>Прежде всего нужно отметить, что числа хранятся в компьютере в виде \"дополнительного кода\". Прежде чем разбирать причины такого решения, сначала дадим определения всем трем способам представления.</p> <ul> <li>Прямой код: старший бит двоичного представления числа рассматривается как знаковый, где \\(0\\) означает положительное число, а \\(1\\) - отрицательное; остальные биты представляют значение числа.</li> <li>Обратный код: для положительного числа обратный код совпадает с прямым; для отрицательного числа он получается инверсией всех битов прямого кода, кроме знакового бита.</li> <li>Дополнительный код: для положительного числа дополнительный код совпадает с прямым; для отрицательного числа он получается добавлением \\(1\\) к его обратному коду.</li> </ul> <p>На рисунке 3-4 показаны способы преобразования между прямым, обратным и дополнительным кодами.</p> <p></p> <p> Рисунок 3-4   Преобразования между прямым, обратным и дополнительным кодами </p> <p>Прямой код (sign-magnitude), хотя и является самым наглядным, имеет определенные ограничения. С одной стороны, прямой код отрицательных чисел нельзя напрямую использовать в вычислениях. Например, при вычислении \\(1 + (-2)\\) в прямом коде результатом будет \\(-3\\) , что, очевидно, неверно.</p> \\[ \\begin{aligned} &amp; 1 + (-2) \\newline &amp; \\rightarrow 0000 \\; 0001 + 1000 \\; 0010 \\newline &amp; = 1000 \\; 0011 \\newline &amp; \\rightarrow -3 \\end{aligned} \\] <p>Чтобы решить эту проблему, компьютеры ввели обратный код (1's complement). Если сначала преобразовать прямой код в обратный и выполнить вычисление \\(1 + (-2)\\) в обратном коде, а затем перевести результат обратно в прямой код, то получится правильный результат \\(-1\\) .</p> \\[ \\begin{aligned} &amp; 1 + (-2) \\newline &amp; \\rightarrow 0000 \\; 0001 \\; \\text{(прямой код)} + 1000 \\; 0010 \\; \\text{(прямой код)} \\newline &amp; = 0000 \\; 0001 \\; \\text{(обратный код)} + 1111  \\; 1101 \\; \\text{(обратный код)} \\newline &amp; = 1111 \\; 1110 \\; \\text{(обратный код)} \\newline &amp; = 1000 \\; 0001 \\; \\text{(прямой код)} \\newline &amp; \\rightarrow -1 \\end{aligned} \\] <p>С другой стороны, **в прямом коде у нуля есть два представления: \\(+0\\) и \\(-0\\) **. Это означает, что числу ноль соответствуют два разных двоичных кода, что может приводить к неоднозначности. Например, если в условном выражении не различать положительный и отрицательный ноль, можно получить ошибочный результат. А если специально обрабатывать такую неоднозначность, придется вводить дополнительные проверки, что может снизить вычислительную эффективность компьютера.</p> \\[ \\begin{aligned} +0 &amp; \\rightarrow 0000 \\; 0000 \\newline -0 &amp; \\rightarrow 1000 \\; 0000 \\end{aligned} \\] <p>Как и прямой код, обратный код тоже страдает от неоднозначности положительного и отрицательного нуля, поэтому компьютеры ввели дополнительный код (2's complement). Сначала посмотрим на процесс преобразования отрицательного нуля из прямого кода в обратный, а затем в дополнительный:</p> \\[ \\begin{aligned} -0 \\rightarrow \\; &amp; 1000 \\; 0000 \\; \\text{(прямой код)} \\newline = \\; &amp; 1111 \\; 1111 \\; \\text{(обратный код)} \\newline = 1 \\; &amp; 0000 \\; 0000 \\; \\text{(дополнительный код)} \\newline \\end{aligned} \\] <p>При добавлении \\(1\\) к обратному коду отрицательного нуля возникает перенос, но длина типа <code>byte</code> составляет всего 8 бит, поэтому переполнившаяся в 9-й бит единица отбрасывается. Иными словами, дополнительный код отрицательного нуля равен \\(0000 \\; 0000\\) и совпадает с дополнительным кодом положительного нуля. Значит, в представлении дополнительного кода существует только один ноль, и проблема неоднозначности положительного и отрицательного нуля тем самым устраняется.</p> <p>Остается последний вопрос: диапазон типа <code>byte</code> равен \\([-128, 127]\\) , откуда берется лишнее отрицательное число \\(-128\\) ? Мы замечаем, что у всех целых чисел из интервала \\([-127, +127]\\) есть соответствующие прямой, обратный и дополнительный коды, а прямой и дополнительный коды можно преобразовывать друг в друга.</p> <p>Однако дополнительный код \\(1000 \\; 0000\\) является исключением: у него нет соответствующего прямого кода. Согласно правилу преобразования, прямой код для этого дополнительного кода должен быть равен \\(0000 \\; 0000\\) . Это очевидное противоречие, потому что такой прямой код обозначает число \\(0\\) , а его дополнительный код должен совпадать с ним самим. Компьютер просто определяет, что этот особый дополнительный код \\(1000 \\; 0000\\) представляет число \\(-128\\) . На самом деле результат вычисления \\((-1) + (-127)\\) в дополнительном коде как раз и равен \\(-128\\) .</p> \\[ \\begin{aligned} &amp; (-127) + (-1) \\newline &amp; \\rightarrow 1111 \\; 1111 \\; \\text{(прямой код)} + 1000 \\; 0001 \\; \\text{(прямой код)} \\newline &amp; = 1000 \\; 0000 \\; \\text{(обратный код)} + 1111  \\; 1110 \\; \\text{(обратный код)} \\newline &amp; = 1000 \\; 0001 \\; \\text{(дополнительный код)} + 1111  \\; 1111 \\; \\text{(дополнительный код)} \\newline &amp; = 1000 \\; 0000 \\; \\text{(дополнительный код)} \\newline &amp; \\rightarrow -128 \\end{aligned} \\] <p>Ты, вероятно, уже заметил, что все приведенные выше вычисления были операциями сложения. Это указывает на важный факт: аппаратные схемы внутри компьютера в основном проектируются на основе операций сложения. Причина в том, что сложение по сравнению с другими операциями (например умножением, делением и вычитанием) проще реализуется на аппаратном уровне, легче распараллеливается и выполняется быстрее.</p> <p>Обрати внимание: это не означает, что компьютер умеет только складывать. Комбинируя сложение с некоторыми базовыми логическими операциями, компьютер может реализовать и другие математические операции. Например, вычитание \\(a - b\\) можно преобразовать в сложение \\(a + (-b)\\) ; умножение и деление можно свести к многократному сложению или вычитанию.</p> <p>Теперь можно подвести итог, почему компьютеры используют дополнительный код: с представлением в дополнительном коде компьютер может использовать одни и те же схемы и операции для сложения положительных и отрицательных чисел, без необходимости проектировать специальные аппаратные схемы для вычитания и без особой обработки неоднозначности положительного и отрицательного нуля. Это значительно упрощает аппаратную архитектуру и повышает эффективность вычислений.</p> <p>Идея дополнительного кода очень изящна; из-за ограничений по объему мы на этом остановимся. Если тебе интересно, стоит изучить эту тему глубже.</p>","path":["Глава 3. Структуры данных","3.3 &nbsp; Кодирование чисел *"],"tags":[]},{"location":"chapter_data_structure/number_encoding/#332","level":2,"title":"3.3.2   Кодирование чисел с плавающей точкой","text":"<p>Внимательный читатель может заметить: <code>int</code> и <code>float</code> имеют одинаковую длину, по 4 байта , но почему диапазон значений у <code>float</code> намного больше, чем у <code>int</code> ? Это выглядит парадоксально, ведь <code>float</code> должен еще представлять дробные числа, а значит диапазон вроде бы должен быть меньше.</p> <p>На самом деле это связано с тем, что число с плавающей точкой <code>float</code> использует другой способ представления. Обозначим двоичное число длиной 32 бита как:</p> \\[ b_{31} b_{30} b_{29} \\ldots b_2 b_1 b_0 \\] <p>Согласно стандарту IEEE 754, 32-битный <code>float</code> состоит из следующих трех частей.</p> <ul> <li>Бит знака \\(\\mathrm{S}\\) : занимает 1 бит и соответствует \\(b_{31}\\) .</li> <li>Биты экспоненты \\(\\mathrm{E}\\) : занимают 8 бит и соответствуют \\(b_{30} b_{29} \\ldots b_{23}\\) .</li> <li>Биты мантиссы \\(\\mathrm{N}\\) : занимают 23 бита и соответствуют \\(b_{22} b_{21} \\ldots b_0\\) .</li> </ul> <p>Формула вычисления значения, соответствующего двоичному числу <code>float</code>, имеет вид:</p> \\[ \\text {val} = (-1)^{b_{31}} \\times 2^{\\left(b_{30} b_{29} \\ldots b_{23}\\right)_2-127} \\times\\left(1 . b_{22} b_{21} \\ldots b_0\\right)_2 \\] <p>Если перейти к десятичной записи, формула вычисления будет такой:</p> \\[ \\text {val}=(-1)^{\\mathrm{S}} \\times 2^{\\mathrm{E} -127} \\times (1 + \\mathrm{N}) \\] <p>Диапазоны значений соответствующих частей таковы:</p> \\[ \\begin{aligned} \\mathrm{S} \\in &amp; \\{ 0, 1\\}, \\quad \\mathrm{E} \\in \\{ 1, 2, \\dots, 254 \\} \\newline (1 + \\mathrm{N}) = &amp; (1 + \\sum_{i=1}^{23} b_{23-i} 2^{-i}) \\subset [1, 2 - 2^{-23}] \\end{aligned} \\] <p></p> <p> Рисунок 3-5   Пример вычисления float по стандарту IEEE 754 </p> <p>Посмотрим на рисунок 3-5: если взять пример \\(\\mathrm{S} = 0\\) , \\(\\mathrm{E} = 124\\) , \\(\\mathrm{N} = 2^{-2} + 2^{-3} = 0.375\\) , то получим:</p> \\[ \\text { val } = (-1)^0 \\times 2^{124 - 127} \\times (1 + 0.375) = 0.171875 \\] <p>Теперь мы можем ответить на исходный вопрос: в представлении <code>float</code> присутствуют биты экспоненты, поэтому его диапазон значений намного больше, чем у <code>int</code>. Согласно приведенным выше вычислениям, максимально возможное положительное число для <code>float</code> равно \\(2^{254 - 127} \\times (2 - 2^{-23}) \\approx 3.4 \\times 10^{38}\\) ; если изменить бит знака, получим минимальное отрицательное число.</p> <p>Хотя число с плавающей точкой <code>float</code> расширяет диапазон значений, побочным эффектом становится потеря точности. Целочисленный тип <code>int</code> использует все 32 бита для представления числа, и числа распределены равномерно; а из-за существования битов экспоненты у <code>float</code> чем больше число, тем больше обычно становится разница между двумя соседними представимыми значениями.</p> <p>Как показано в таблице 3-2, значения экспоненты \\(\\mathrm{E} = 0\\) и \\(\\mathrm{E} = 255\\) имеют специальный смысл и используются для представления нуля, бесконечности, \\(\\mathrm{NaN}\\) и т.д.</p> <p> Таблица 3-2   Значение поля экспоненты </p> Поле экспоненты E Поле мантиссы \\(\\mathrm{N} = 0\\) Поле мантиссы \\(\\mathrm{N} \\ne 0\\) Формула вычисления \\(0\\) \\(\\pm 0\\) Денормализованное число \\((-1)^{\\mathrm{S}} \\times 2^{-126} \\times (0.\\mathrm{N})\\) \\(1, 2, \\dots, 254\\) Нормализованное число Нормализованное число \\((-1)^{\\mathrm{S}} \\times 2^{(\\mathrm{E} -127)} \\times (1.\\mathrm{N})\\) \\(255\\) \\(\\pm \\infty\\) \\(\\mathrm{NaN}\\) <p>Стоит отметить, что денормализованные числа заметно повышают точность чисел с плавающей точкой. Наименьшее положительное нормализованное число равно \\(2^{-126}\\) , а наименьшее положительное денормализованное число равно \\(2^{-126} \\times 2^{-23}\\) .</p> <p>Двойная точность <code>double</code> использует способ представления, аналогичный <code>float</code> , поэтому здесь мы не будем подробно останавливаться на нем.</p>","path":["Глава 3. Структуры данных","3.3 &nbsp; Кодирование чисел *"],"tags":[]},{"location":"chapter_data_structure/summary/","level":1,"title":"3.5   Резюме","text":"","path":["Глава 3. Структуры данных","3.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_data_structure/summary/#1","level":3,"title":"1.   Ключевые выводы","text":"<ul> <li>Структуры данных можно классифицировать с точки зрения логической и физической структуры. Логическая структура описывает логические отношения между элементами данных, а физическая структура описывает способ хранения данных в памяти компьютера.</li> <li>К распространенным логическим структурам относятся линейные, древовидные и сетевые. Обычно структуры данных делятся на линейные (массивы, связные списки, стеки, очереди) и нелинейные (деревья, графы, кучи). Реализация хеш-таблицы может включать как линейные, так и нелинейные структуры данных.</li> <li>При выполнении программы данные хранятся в памяти компьютера. Каждый участок памяти имеет соответствующий адрес, с помощью которого программа получает доступ к данным.</li> <li>Физическая структура делится на хранение в непрерывном пространстве (массивы) и хранение в разрозненном пространстве (связные списки). Все структуры данных реализуются на основе массивов, связных списков или их комбинации.</li> <li>Базовые типы данных в компьютере включают целые <code>byte</code> , <code>short</code> , <code>int</code> , <code>long</code> , числа с плавающей точкой <code>float</code> , <code>double</code> , символы <code>char</code> и логический тип <code>bool</code> . Их диапазон значений зависит от объема занимаемого пространства и способа представления.</li> <li>Прямой код, обратный код и дополнительный код - это три способа кодирования чисел в компьютере, между которыми можно выполнять взаимные преобразования. В прямом коде старший бит целого числа является знаковым, а остальные биты представляют значение числа.</li> <li>Целые числа в компьютере хранятся в виде дополнительного кода. В таком представлении компьютер может одинаково обрабатывать сложение положительных и отрицательных чисел без специальной аппаратной схемы для вычитания, и при этом исчезает неоднозначность положительного и отрицательного нуля.</li> <li>Кодирование числа с плавающей точкой состоит из 1 бита знака, 8 битов экспоненты и 23 битов мантиссы. Благодаря наличию экспоненты диапазон значений у чисел с плавающей точкой намного больше, чем у целых, но это достигается ценой потери точности.</li> <li>ASCII - это самый ранний набор английских символов длиной 1 байт, включающий в общей сложности 127 символов. Набор GBK - распространенный китайский набор символов, включающий более двадцати тысяч иероглифов. Unicode стремится предоставить единый полный стандарт набора символов, включающий символы всех языков мира, чтобы решить проблемы искаженного текста, вызванные несовместимыми способами кодирования.</li> <li>UTF-8 - самый популярный способ кодирования Unicode, обладающий очень хорошей универсальностью. Это кодировка переменной длины, хорошо расширяемая и эффективно использующая память. UTF-16 и UTF-32 относятся к кодировкам фиксированной длины. При кодировании китайского текста UTF-16 занимает меньше места, чем UTF-8. Такие языки программирования, как Java и C#, по умолчанию используют UTF-16.</li> </ul>","path":["Глава 3. Структуры данных","3.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_data_structure/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: Почему хеш-таблица одновременно включает линейные и нелинейные структуры данных?</p> <p>В основе хеш-таблицы лежит массив, а для разрешения коллизий мы можем использовать \"цепочки адресации\" (об этом будет рассказано в последующем разделе \"Хеш-коллизии\"): каждый бакет массива указывает на связный список, а если длина списка превышает некоторый порог, он может быть преобразован в дерево (обычно в красно-черное дерево).</p> <p>С точки зрения хранения данных в основе хеш-таблицы находится массив, где каждый слот бакета может содержать либо отдельное значение, либо связный список, либо дерево. Поэтому хеш-таблица действительно может одновременно включать линейные структуры данных (массивы, списки) и нелинейные структуры данных (деревья).</p> <p>Q: Длина типа <code>char</code> равна 1 байту?</p> <p>Длина типа <code>char</code> определяется используемым в языке программирования способом кодирования. Например, Java, JavaScript, TypeScript и C# используют кодировку UTF-16 (для хранения кодовых точек Unicode), поэтому длина <code>char</code> у них равна 2 байтам.</p> <p>Q: Не является ли двусмысленным утверждение, что структуры данных, реализованные на основе массива, также называются \"статическими структурами данных\"? Ведь стек тоже поддерживает операции push и pop, а они явно \"динамические\".</p> <p>Стек действительно может поддерживать динамические операции над данными, но сама структура данных при этом остается \"статической\" (ее длина неизменна). Хотя структуры на основе массива могут динамически добавлять и удалять элементы, их емкость фиксирована. Если количество данных превышает заранее выделенный размер, приходится создавать новый, более крупный массив и копировать в него содержимое старого.</p> <p>Q: При построении стека (очереди) его размер не задается явно, почему же его относят к \"статическим структурам данных\"?</p> <p>В языках высокого уровня нам не нужно вручную задавать начальную емкость стека (очереди): это автоматически делает сама реализация класса. Например, начальная емкость <code>ArrayList</code> в Java обычно равна 10. Кроме того, автоматом реализуется и расширение емкости. Подробнее это рассматривается в последующем разделе о \"списках\".</p> <p>Q: Если метод преобразования из прямого кода в дополнительный - это \"сначала инвертировать, затем прибавить 1\", то обратное преобразование из дополнительного кода в прямой, по идее, должно быть обратной операцией \"сначала вычесть 1, затем инвертировать\". Почему же дополнительный код также можно перевести в прямой тем же способом \"сначала инвертировать, затем прибавить 1\"?</p> <p>Это связано с тем, что взаимное преобразование прямого и дополнительного кодов по сути является вычислением \"дополнения\". Сначала дадим определение дополнения: если \\(a + b = c\\) , то говорят, что \\(a\\) является дополнением числа \\(b\\) до \\(c\\) ; аналогично, \\(b\\) является дополнением числа \\(a\\) до \\(c\\) .</p> <p>Для двоичного числа длины \\(n = 4\\) со значением \\(0010\\) , если рассматривать его как прямой код (не учитывая знаковый бит), то его дополнительный код получается правилом \"сначала инвертировать, затем прибавить 1\":</p> \\[ 0010 \\rightarrow 1101 \\rightarrow 1110 \\] <p>Мы видим, что сумма прямого и дополнительного кодов равна \\(0010 + 1110 = 10000\\) , то есть дополнительный код \\(1110\\) является \"дополнением\" прямого кода \\(0010\\) до \\(10000\\) . **Это означает, что описанная выше операция \"сначала инвертировать, затем прибавить 1\" на самом деле вычисляет дополнение до \\(10000\\) **.</p> <p>Тогда чему равно \"дополнение\" дополнительного кода \\(1110\\) до \\(10000\\) ? Мы снова можем получить его правилом \"сначала инвертировать, затем прибавить 1\":</p> \\[ 1110 \\rightarrow 0001 \\rightarrow 0010 \\] <p>Иначе говоря, прямой и дополнительный коды являются взаимными \"дополнениями\" друг друга до \\(10000\\) , поэтому и \"прямой код -&gt; дополнительный код\", и \"дополнительный код -&gt; прямой код\" можно реализовать одной и той же операцией (сначала инвертировать, затем прибавить 1).</p> <p>Разумеется, можно получить прямой код из дополнительного кода \\(1110\\) и обратной операцией, то есть \"сначала вычесть 1, затем инвертировать\":</p> \\[ 1110 \\rightarrow 1101 \\rightarrow 0010 \\] <p>В итоге и \"сначала инвертировать, затем прибавить 1\", и \"сначала вычесть 1, затем инвертировать\" - это два эквивалентных способа вычисления дополнения до \\(10000\\) .</p> <p>По сути операция \"инвертировать\" сама по себе вычисляет дополнение до \\(1111\\) (потому что всегда выполняется <code>прямой код + обратный код = 1111</code> ); а дополнительный код, получающийся после добавления 1 к обратному коду, и есть дополнение до \\(10000\\) .</p> <p>Приведенный выше пример использовал \\(n = 4\\) , но его можно обобщить на двоичные числа любой длины.</p>","path":["Глава 3. Структуры данных","3.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_divide_and_conquer/","level":1,"title":"Глава 12.   Разделяй и властвуй","text":"<p>Abstract</p> <p>Сложная задача раскладывается слой за слоем, и каждое новое разбиение делает ее проще.</p> <p>Принцип \"разделяй и властвуй\" показывает важный факт: если начать с простого, многое перестает быть сложным.</p>","path":["Глава 12. Разделяй и властвуй","Глава 12. &nbsp; Разделяй и властвуй"],"tags":[]},{"location":"chapter_divide_and_conquer/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>12.1   Стратегия разделяй и властвуй</li> <li>12.2   Поисковая стратегия разделяй и властвуй</li> <li>12.3   Задача построения двоичного дерева</li> <li>12.4   Задача о Ханойской башне</li> <li>12.5   Резюме</li> </ul>","path":["Глава 12. Разделяй и властвуй","Глава 12. &nbsp; Разделяй и властвуй"],"tags":[]},{"location":"chapter_divide_and_conquer/binary_search_recur/","level":1,"title":"12.2   Поисковая стратегия разделяй и властвуй","text":"<p>Мы уже знаем, что алгоритмы поиска делятся на две большие категории.</p> <ul> <li>Полный перебор: реализуется через обход структуры данных, временная сложность равна \\(O(n)\\) .</li> <li>Адаптивный поиск: использует особую организацию данных или априорную информацию, временная сложность может достигать \\(O(\\log n)\\) и даже \\(O(1)\\) .</li> </ul> <p>На практике алгоритмы поиска с временной сложностью \\(O(\\log n)\\) обычно реализуются на основе стратегии \"разделяй и властвуй\", например двоичный поиск и деревья.</p> <ul> <li>На каждом шаге двоичный поиск раскладывает задачу (поиск целевого элемента в массиве) на более мелкую задачу (поиск целевого элемента в одной половине массива), и этот процесс продолжается, пока массив не станет пустым или пока не будет найден целевой элемент.</li> <li>Деревья являются типичными представителями идей \"разделяй и властвуй\"; в таких структурах данных, как двоичное дерево поиска, AVL-дерево и куча, временная сложность различных операций равна \\(O(\\log n)\\) .</li> </ul> <p>Стратегия \"разделяй и властвуй\" для двоичного поиска выглядит следующим образом.</p> <ul> <li>Задача раскладывается на части: двоичный поиск рекурсивно разбивает исходную задачу (поиск в массиве) на подзадачу (поиск в одной половине массива), и это достигается сравнением среднего элемента с целевым значением.</li> <li>Подзадачи независимы: в двоичном поиске на каждом шаге обрабатывается только одна подзадача, и она не зависит от других подзадач.</li> <li>Решения подзадач не нужно объединять: двоичный поиск нацелен на поиск конкретного элемента, поэтому объединять решения подзадач не требуется. Как только подзадача решена, одновременно считается решенной и исходная задача.</li> </ul> <p>Иными словами, стратегия \"разделяй и властвуй\" повышает эффективность поиска потому, что при полном переборе за один шаг удается исключить только один вариант, тогда как при поиске на основе \"разделяй и властвуй\" за один шаг можно исключить половину вариантов.</p>","path":["Глава 12. Разделяй и властвуй","12.2 &nbsp; Поисковая стратегия разделяй и властвуй"],"tags":[]},{"location":"chapter_divide_and_conquer/binary_search_recur/#1","level":3,"title":"1.   Реализация двоичного поиска на основе \"разделяй и властвуй\"","text":"<p>В предыдущих главах двоичный поиск реализовывался через итерацию. Теперь реализуем его с помощью стратегии \"разделяй и властвуй\", то есть через рекурсию.</p> <p>Question</p> <p>Дан отсортированный массив <code>nums</code> длины \\(n\\) , в котором все элементы уникальны. Найдите элемент <code>target</code> .</p> <p>С точки зрения стратегии \"разделяй и властвуй\" обозначим подзадачу, соответствующую интервалу поиска \\([i, j]\\) , через \\(f(i, j)\\) .</p> <p>Начиная с исходной задачи \\(f(0, n-1)\\) , выполняем двоичный поиск по следующим шагам.</p> <ol> <li>Вычислить середину \\(m\\) интервала поиска \\([i, j]\\) и с ее помощью исключить половину интервала.</li> <li>Рекурсивно решить подзадачу вдвое меньшего размера; это может быть либо \\(f(i, m-1)\\) , либо \\(f(m+1, j)\\) .</li> <li>Повторять шаг <code>1.</code> и шаг <code>2.</code> , пока не будет найден <code>target</code> или пока интервал не станет пустым.</li> </ol> <p>На рисунке 12-4 показан процесс применения стратегии \"разделяй и властвуй\" для поиска элемента \\(6\\) в массиве.</p> <p></p> <p> Рисунок 12-4   Процесс двоичного поиска в стиле разделяй и властвуй </p> <p>В реализации кода мы объявляем рекурсивную функцию <code>dfs()</code> для решения задачи \\(f(i, j)\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_recur.py<pre><code>def dfs(nums: list[int], target: int, i: int, j: int) -&gt; int:\n    \"\"\"Бинарный поиск: задача f(i, j)\"\"\"\n    # Если интервал пуст, целевой элемент отсутствует, вернуть -1\n    if i &gt; j:\n        return -1\n    # Вычислить индекс середины m\n    m = (i + j) // 2\n    if nums[m] &lt; target:\n        # Рекурсивная подзадача f(m+1, j)\n        return dfs(nums, target, m + 1, j)\n    elif nums[m] &gt; target:\n        # Рекурсивная подзадача f(i, m-1)\n        return dfs(nums, target, i, m - 1)\n    else:\n        # Целевой элемент найден, вернуть его индекс\n        return m\n\ndef binary_search(nums: list[int], target: int) -&gt; int:\n    \"\"\"Бинарный поиск\"\"\"\n    n = len(nums)\n    # Решить задачу f(0, n-1)\n    return dfs(nums, target, 0, n - 1)\n</code></pre> binary_search_recur.cpp<pre><code>/* Бинарный поиск: задача f(i, j) */\nint dfs(vector&lt;int&gt; &amp;nums, int target, int i, int j) {\n    // Если интервал пуст, целевой элемент отсутствует, вернуть -1\n    if (i &gt; j) {\n        return -1;\n    }\n    // Вычислить индекс середины m\n    int m = (i + j) / 2;\n    if (nums[m] &lt; target) {\n        // Рекурсивная подзадача f(m+1, j)\n        return dfs(nums, target, m + 1, j);\n    } else if (nums[m] &gt; target) {\n        // Рекурсивная подзадача f(i, m-1)\n        return dfs(nums, target, i, m - 1);\n    } else {\n        // Целевой элемент найден, вернуть его индекс\n        return m;\n    }\n}\n\n/* Бинарный поиск */\nint binarySearch(vector&lt;int&gt; &amp;nums, int target) {\n    int n = nums.size();\n    // Решить задачу f(0, n-1)\n    return dfs(nums, target, 0, n - 1);\n}\n</code></pre> binary_search_recur.java<pre><code>/* Бинарный поиск: задача f(i, j) */\nint dfs(int[] nums, int target, int i, int j) {\n    // Если интервал пуст, целевой элемент отсутствует, вернуть -1\n    if (i &gt; j) {\n        return -1;\n    }\n    // Вычислить индекс середины m\n    int m = (i + j) / 2;\n    if (nums[m] &lt; target) {\n        // Рекурсивная подзадача f(m+1, j)\n        return dfs(nums, target, m + 1, j);\n    } else if (nums[m] &gt; target) {\n        // Рекурсивная подзадача f(i, m-1)\n        return dfs(nums, target, i, m - 1);\n    } else {\n        // Целевой элемент найден, вернуть его индекс\n        return m;\n    }\n}\n\n/* Бинарный поиск */\nint binarySearch(int[] nums, int target) {\n    int n = nums.length;\n    // Решить задачу f(0, n-1)\n    return dfs(nums, target, 0, n - 1);\n}\n</code></pre> binary_search_recur.cs<pre><code>/* Бинарный поиск: задача f(i, j) */\nint DFS(int[] nums, int target, int i, int j) {\n    // Если интервал пуст, целевой элемент отсутствует, вернуть -1\n    if (i &gt; j) {\n        return -1;\n    }\n    // Вычислить индекс середины m\n    int m = (i + j) / 2;\n    if (nums[m] &lt; target) {\n        // Рекурсивная подзадача f(m+1, j)\n        return DFS(nums, target, m + 1, j);\n    } else if (nums[m] &gt; target) {\n        // Рекурсивная подзадача f(i, m-1)\n        return DFS(nums, target, i, m - 1);\n    } else {\n        // Целевой элемент найден, вернуть его индекс\n        return m;\n    }\n}\n\n/* Бинарный поиск */\nint BinarySearch(int[] nums, int target) {\n    int n = nums.Length;\n    // Решить задачу f(0, n-1)\n    return DFS(nums, target, 0, n - 1);\n}\n</code></pre> binary_search_recur.go<pre><code>/* Бинарный поиск: задача f(i, j) */\nfunc dfs(nums []int, target, i, j int) int {\n    // Если интервал пуст, это означает отсутствие целевого элемента, вернуть -1\n    if i &gt; j {\n        return -1\n    }\n    // Вычислить средний индекс\n    m := i + ((j - i) &gt;&gt; 1)\n    // Сравнить середину и целевой элемент\n    if nums[m] &lt; target {\n        // Если меньше, рекурсивно обрабатывать правую половину массива\n        // Рекурсивная подзадача f(m+1, j)\n        return dfs(nums, target, m+1, j)\n    } else if nums[m] &gt; target {\n        // Если больше, рекурсивно обработать левую половину массива\n        // Рекурсивная подзадача f(i, m-1)\n        return dfs(nums, target, i, m-1)\n    } else {\n        // Целевой элемент найден, вернуть его индекс\n        return m\n    }\n}\n\n/* Бинарный поиск */\nfunc binarySearch(nums []int, target int) int {\n    n := len(nums)\n    return dfs(nums, target, 0, n-1)\n}\n</code></pre> binary_search_recur.swift<pre><code>/* Бинарный поиск: задача f(i, j) */\nfunc dfs(nums: [Int], target: Int, i: Int, j: Int) -&gt; Int {\n    // Если интервал пуст, целевой элемент отсутствует, вернуть -1\n    if i &gt; j {\n        return -1\n    }\n    // Вычислить индекс середины m\n    let m = (i + j) / 2\n    if nums[m] &lt; target {\n        // Рекурсивная подзадача f(m+1, j)\n        return dfs(nums: nums, target: target, i: m + 1, j: j)\n    } else if nums[m] &gt; target {\n        // Рекурсивная подзадача f(i, m-1)\n        return dfs(nums: nums, target: target, i: i, j: m - 1)\n    } else {\n        // Целевой элемент найден, вернуть его индекс\n        return m\n    }\n}\n\n/* Бинарный поиск */\nfunc binarySearch(nums: [Int], target: Int) -&gt; Int {\n    // Решить задачу f(0, n-1)\n    dfs(nums: nums, target: target, i: nums.startIndex, j: nums.endIndex - 1)\n}\n</code></pre> binary_search_recur.js<pre><code>/* Бинарный поиск: задача f(i, j) */\nfunction dfs(nums, target, i, j) {\n    // Если интервал пуст, целевой элемент отсутствует, вернуть -1\n    if (i &gt; j) {\n        return -1;\n    }\n    // Вычислить индекс середины m\n    const m = i + ((j - i) &gt;&gt; 1);\n    if (nums[m] &lt; target) {\n        // Рекурсивная подзадача f(m+1, j)\n        return dfs(nums, target, m + 1, j);\n    } else if (nums[m] &gt; target) {\n        // Рекурсивная подзадача f(i, m-1)\n        return dfs(nums, target, i, m - 1);\n    } else {\n        // Целевой элемент найден, вернуть его индекс\n        return m;\n    }\n}\n\n/* Бинарный поиск */\nfunction binarySearch(nums, target) {\n    const n = nums.length;\n    // Решить задачу f(0, n-1)\n    return dfs(nums, target, 0, n - 1);\n}\n</code></pre> binary_search_recur.ts<pre><code>/* Бинарный поиск: задача f(i, j) */\nfunction dfs(nums: number[], target: number, i: number, j: number): number {\n    // Если интервал пуст, целевой элемент отсутствует, вернуть -1\n    if (i &gt; j) {\n        return -1;\n    }\n    // Вычислить индекс середины m\n    const m = i + ((j - i) &gt;&gt; 1);\n    if (nums[m] &lt; target) {\n        // Рекурсивная подзадача f(m+1, j)\n        return dfs(nums, target, m + 1, j);\n    } else if (nums[m] &gt; target) {\n        // Рекурсивная подзадача f(i, m-1)\n        return dfs(nums, target, i, m - 1);\n    } else {\n        // Целевой элемент найден, вернуть его индекс\n        return m;\n    }\n}\n\n/* Бинарный поиск */\nfunction binarySearch(nums: number[], target: number): number {\n    const n = nums.length;\n    // Решить задачу f(0, n-1)\n    return dfs(nums, target, 0, n - 1);\n}\n</code></pre> binary_search_recur.dart<pre><code>/* Бинарный поиск: задача f(i, j) */\nint dfs(List&lt;int&gt; nums, int target, int i, int j) {\n  // Если интервал пуст, целевой элемент отсутствует, вернуть -1\n  if (i &gt; j) {\n    return -1;\n  }\n  // Вычислить индекс середины m\n  int m = (i + j) ~/ 2;\n  if (nums[m] &lt; target) {\n    // Рекурсивная подзадача f(m+1, j)\n    return dfs(nums, target, m + 1, j);\n  } else if (nums[m] &gt; target) {\n    // Рекурсивная подзадача f(i, m-1)\n    return dfs(nums, target, i, m - 1);\n  } else {\n    // Целевой элемент найден, вернуть его индекс\n    return m;\n  }\n}\n\n/* Бинарный поиск */\nint binarySearch(List&lt;int&gt; nums, int target) {\n  int n = nums.length;\n  // Решить задачу f(0, n-1)\n  return dfs(nums, target, 0, n - 1);\n}\n</code></pre> binary_search_recur.rs<pre><code>/* Бинарный поиск: задача f(i, j) */\nfn dfs(nums: &amp;[i32], target: i32, i: i32, j: i32) -&gt; i32 {\n    // Если интервал пуст, целевой элемент отсутствует, вернуть -1\n    if i &gt; j {\n        return -1;\n    }\n    let m: i32 = i + (j - i) / 2;\n    if nums[m as usize] &lt; target {\n        // Рекурсивная подзадача f(m+1, j)\n        return dfs(nums, target, m + 1, j);\n    } else if nums[m as usize] &gt; target {\n        // Рекурсивная подзадача f(i, m-1)\n        return dfs(nums, target, i, m - 1);\n    } else {\n        // Целевой элемент найден, вернуть его индекс\n        return m;\n    }\n}\n\n/* Бинарный поиск */\nfn binary_search(nums: &amp;[i32], target: i32) -&gt; i32 {\n    let n = nums.len() as i32;\n    // Решить задачу f(0, n-1)\n    dfs(nums, target, 0, n - 1)\n}\n</code></pre> binary_search_recur.c<pre><code>/* Бинарный поиск: задача f(i, j) */\nint dfs(int nums[], int target, int i, int j) {\n    // Если интервал пуст, целевой элемент отсутствует, вернуть -1\n    if (i &gt; j) {\n        return -1;\n    }\n    // Вычислить индекс середины m\n    int m = (i + j) / 2;\n    if (nums[m] &lt; target) {\n        // Рекурсивная подзадача f(m+1, j)\n        return dfs(nums, target, m + 1, j);\n    } else if (nums[m] &gt; target) {\n        // Рекурсивная подзадача f(i, m-1)\n        return dfs(nums, target, i, m - 1);\n    } else {\n        // Целевой элемент найден, вернуть его индекс\n        return m;\n    }\n}\n\n/* Бинарный поиск */\nint binarySearch(int nums[], int target, int numsSize) {\n    int n = numsSize;\n    // Решить задачу f(0, n-1)\n    return dfs(nums, target, 0, n - 1);\n}\n</code></pre> binary_search_recur.kt<pre><code>/* Бинарный поиск: задача f(i, j) */\nfun dfs(\n    nums: IntArray,\n    target: Int,\n    i: Int,\n    j: Int\n): Int {\n    // Если интервал пуст, целевой элемент отсутствует, вернуть -1\n    if (i &gt; j) {\n        return -1\n    }\n    // Вычислить индекс середины m\n    val m = (i + j) / 2\n    return if (nums[m] &lt; target) {\n        // Рекурсивная подзадача f(m+1, j)\n        dfs(nums, target, m + 1, j)\n    } else if (nums[m] &gt; target) {\n        // Рекурсивная подзадача f(i, m-1)\n        dfs(nums, target, i, m - 1)\n    } else {\n        // Целевой элемент найден, вернуть его индекс\n        m\n    }\n}\n\n/* Бинарный поиск */\nfun binarySearch(nums: IntArray, target: Int): Int {\n    val n = nums.size\n    // Решить задачу f(0, n-1)\n    return dfs(nums, target, 0, n - 1)\n}\n</code></pre> binary_search_recur.rb<pre><code>### Бинарный поиск: задача f(i, j) ###\ndef dfs(nums, target, i, j)\n  # Если интервал пуст, целевой элемент отсутствует, вернуть -1\n  return -1 if i &gt; j\n\n  # Вычислить индекс середины m\n  m = (i + j) / 2\n\n  if nums[m] &lt; target\n    # Рекурсивная подзадача f(m+1, j)\n    return dfs(nums, target, m + 1, j)\n  elsif nums[m] &gt; target\n    # Рекурсивная подзадача f(i, m-1)\n    return dfs(nums, target, i, m - 1)\n  else\n    # Целевой элемент найден, вернуть его индекс\n    return m\n  end\nend\n\n### Бинарный поиск ###\ndef binary_search(nums, target)\n  n = nums.length\n  # Решить задачу f(0, n-1)\n  dfs(nums, target, 0, n - 1)\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 12. Разделяй и властвуй","12.2 &nbsp; Поисковая стратегия разделяй и властвуй"],"tags":[]},{"location":"chapter_divide_and_conquer/build_binary_tree_problem/","level":1,"title":"12.3   Задача построения двоичного дерева","text":"<p>Question</p> <p>Даны прямой обход <code>preorder</code> и симметричный обход <code>inorder</code> некоторого двоичного дерева. Постройте по ним двоичное дерево и верните его корневой узел. Предполагается, что в дереве нет узлов с одинаковыми значениями (как показано на рисунке 12-5).</p> <p></p> <p> Рисунок 12-5   Пример данных для построения двоичного дерева </p>","path":["Глава 12. Разделяй и властвуй","12.3 &nbsp; Задача построения двоичного дерева"],"tags":[]},{"location":"chapter_divide_and_conquer/build_binary_tree_problem/#1","level":3,"title":"1.   Проверка, является ли это задачей \"разделяй и властвуй\"","text":"<p>Исходная задача - построить двоичное дерево по <code>preorder</code> и <code>inorder</code> - является типичной задачей для стратегии \"разделяй и властвуй\".</p> <ul> <li>Задача раскладывается на части: если смотреть с точки зрения стратегии \"разделяй и властвуй\", исходную задачу можно разбить на две подзадачи: построение левого поддерева и построение правого поддерева, плюс одно действие: инициализация корневого узла. Для каждого поддерева (подзадачи) можно использовать тот же способ разбиения, пока не будет достигнута наименьшая подзадача (пустое поддерево).</li> <li>Подзадачи независимы: левое и правое поддеревья независимы друг от друга и не пересекаются. При построении левого поддерева нам нужно смотреть только на ту часть прямого и симметричного обходов, которая соответствует левому поддереву. Для правого поддерева рассуждение аналогично.</li> <li>Решения подзадач можно объединить: когда левое и правое поддеревья (решения подзадач) уже построены, их можно присоединить к корневому узлу и тем самым получить решение исходной задачи.</li> </ul>","path":["Глава 12. Разделяй и властвуй","12.3 &nbsp; Задача построения двоичного дерева"],"tags":[]},{"location":"chapter_divide_and_conquer/build_binary_tree_problem/#2","level":3,"title":"2.   Как разделить поддеревья","text":"<p>Из анализа выше видно, что эта задача действительно решается через \"разделяй и властвуй\", но как именно, имея прямой обход <code>preorder</code> и симметричный обход <code>inorder</code>, отделить левое и правое поддеревья?</p> <p>По определению и <code>preorder</code> , и <code>inorder</code> можно разбить на три части.</p> <ul> <li>Прямой обход: <code>[ корневой узел | левое поддерево | правое поддерево ]</code> , например для дерева на рисунке 12-5 это <code>[ 3 | 9 | 2 1 7 ]</code> .</li> <li>Симметричный обход: <code>[ левое поддерево | корневой узел | правое поддерево ]</code> , например для дерева на рисунке 12-5 это <code>[ 9 | 3 | 1 2 7 ]</code> .</li> </ul> <p>На примере данных с рисунка можно получить результат разбиения по следующим шагам.</p> <ol> <li>Первый элемент прямого обхода, равный 3, является значением корневого узла.</li> <li>Найти индекс корневого узла 3 в <code>inorder</code> ; используя этот индекс, можно разбить <code>inorder</code> на <code>[ 9 | 3 | 1 2 7 ]</code> .</li> <li>По результату разбиения <code>inorder</code> нетрудно определить, что число узлов в левом и правом поддеревьях равно 1 и 3 соответственно, а значит, <code>preorder</code> можно разбить как <code>[ 3 | 9 | 2 1 7 ]</code> .</li> </ol> <p></p> <p> Рисунок 12-6   Разбиение поддеревьев в прямом и симметричном обходах </p>","path":["Глава 12. Разделяй и властвуй","12.3 &nbsp; Задача построения двоичного дерева"],"tags":[]},{"location":"chapter_divide_and_conquer/build_binary_tree_problem/#3","level":3,"title":"3.   Описание интервалов поддеревьев через переменные","text":"<p>Согласно описанному выше способу разбиения, мы уже получили интервалы индексов корневого узла, левого и правого поддеревьев в <code>preorder</code> и <code>inorder</code>. Чтобы описывать эти интервалы, нам понадобится несколько указателей-переменных.</p> <ul> <li>Обозначим индекс корневого узла текущего дерева в <code>preorder</code> через \\(i\\) .</li> <li>Обозначим индекс корневого узла текущего дерева в <code>inorder</code> через \\(m\\) .</li> <li>Обозначим интервал индексов текущего дерева в <code>inorder</code> через \\([l, r]\\) .</li> </ul> <p>Как показано в таблице 12-1, этих переменных достаточно для описания индекса корневого узла в <code>preorder</code> и интервалов поддеревьев в <code>inorder</code> .</p> <p> Таблица 12-1   Индексы корневого узла и поддеревьев в прямом и симметричном обходах </p> Индекс корневого узла в <code>preorder</code> Интервал индексов поддерева в <code>inorder</code> Текущее дерево \\(i\\) \\([l, r]\\) Левое поддерево \\(i + 1\\) \\([l, m-1]\\) Правое поддерево \\(i + 1 + (m - l)\\) \\([m+1, r]\\) <p>Стоит отметить, что \\((m-l)\\) в индексе корневого узла правого поддерева означает число узлов в левом поддереве; лучше всего понимать это выражение вместе с рисунком ниже.</p> <p></p> <p> Рисунок 12-7   Представление индексных интервалов корня и поддеревьев </p>","path":["Глава 12. Разделяй и властвуй","12.3 &nbsp; Задача построения двоичного дерева"],"tags":[]},{"location":"chapter_divide_and_conquer/build_binary_tree_problem/#4","level":3,"title":"4.   Реализация кода","text":"<p>Чтобы ускорить поиск \\(m\\) , мы используем хеш-таблицу <code>hmap</code> для хранения отображения значений массива <code>inorder</code> в индексы:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby build_tree.py<pre><code>def dfs(\n    preorder: list[int],\n    inorder_map: dict[int, int],\n    i: int,\n    l: int,\n    r: int,\n) -&gt; TreeNode | None:\n    \"\"\"Построить двоичное дерево: разделяй и властвуй\"\"\"\n    # Завершить при пустом диапазоне поддерева\n    if r - l &lt; 0:\n        return None\n    # Инициализировать корневой узел\n    root = TreeNode(preorder[i])\n    # Найти m, чтобы разделить левое и правое поддеревья\n    m = inorder_map[preorder[i]]\n    # Подзадача: построить левое поддерево\n    root.left = dfs(preorder, inorder_map, i + 1, l, m - 1)\n    # Подзадача: построить правое поддерево\n    root.right = dfs(preorder, inorder_map, i + 1 + m - l, m + 1, r)\n    # Вернуть корневой узел\n    return root\n\ndef build_tree(preorder: list[int], inorder: list[int]) -&gt; TreeNode | None:\n    \"\"\"Построить двоичное дерево\"\"\"\n    # Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n    inorder_map = {val: i for i, val in enumerate(inorder)}\n    root = dfs(preorder, inorder_map, 0, 0, len(inorder) - 1)\n    return root\n</code></pre> build_tree.cpp<pre><code>/* Построить двоичное дерево: разделяй и властвуй */\nTreeNode *dfs(vector&lt;int&gt; &amp;preorder, unordered_map&lt;int, int&gt; &amp;inorderMap, int i, int l, int r) {\n    // Завершить при пустом диапазоне поддерева\n    if (r - l &lt; 0)\n        return NULL;\n    // Инициализировать корневой узел\n    TreeNode *root = new TreeNode(preorder[i]);\n    // Найти m, чтобы разделить левое и правое поддеревья\n    int m = inorderMap[preorder[i]];\n    // Подзадача: построить левое поддерево\n    root-&gt;left = dfs(preorder, inorderMap, i + 1, l, m - 1);\n    // Подзадача: построить правое поддерево\n    root-&gt;right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r);\n    // Вернуть корневой узел\n    return root;\n}\n\n/* Построить двоичное дерево */\nTreeNode *buildTree(vector&lt;int&gt; &amp;preorder, vector&lt;int&gt; &amp;inorder) {\n    // Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n    unordered_map&lt;int, int&gt; inorderMap;\n    for (int i = 0; i &lt; inorder.size(); i++) {\n        inorderMap[inorder[i]] = i;\n    }\n    TreeNode *root = dfs(preorder, inorderMap, 0, 0, inorder.size() - 1);\n    return root;\n}\n</code></pre> build_tree.java<pre><code>/* Построить двоичное дерево: разделяй и властвуй */\nTreeNode dfs(int[] preorder, Map&lt;Integer, Integer&gt; inorderMap, int i, int l, int r) {\n    // Завершить при пустом диапазоне поддерева\n    if (r - l &lt; 0)\n        return null;\n    // Инициализировать корневой узел\n    TreeNode root = new TreeNode(preorder[i]);\n    // Найти m, чтобы разделить левое и правое поддеревья\n    int m = inorderMap.get(preorder[i]);\n    // Подзадача: построить левое поддерево\n    root.left = dfs(preorder, inorderMap, i + 1, l, m - 1);\n    // Подзадача: построить правое поддерево\n    root.right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r);\n    // Вернуть корневой узел\n    return root;\n}\n\n/* Построить двоичное дерево */\nTreeNode buildTree(int[] preorder, int[] inorder) {\n    // Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n    Map&lt;Integer, Integer&gt; inorderMap = new HashMap&lt;&gt;();\n    for (int i = 0; i &lt; inorder.length; i++) {\n        inorderMap.put(inorder[i], i);\n    }\n    TreeNode root = dfs(preorder, inorderMap, 0, 0, inorder.length - 1);\n    return root;\n}\n</code></pre> build_tree.cs<pre><code>/* Построить двоичное дерево: разделяй и властвуй */\nTreeNode? DFS(int[] preorder, Dictionary&lt;int, int&gt; inorderMap, int i, int l, int r) {\n    // Завершить при пустом диапазоне поддерева\n    if (r - l &lt; 0)\n        return null;\n    // Инициализировать корневой узел\n    TreeNode root = new(preorder[i]);\n    // Найти m, чтобы разделить левое и правое поддеревья\n    int m = inorderMap[preorder[i]];\n    // Подзадача: построить левое поддерево\n    root.left = DFS(preorder, inorderMap, i + 1, l, m - 1);\n    // Подзадача: построить правое поддерево\n    root.right = DFS(preorder, inorderMap, i + 1 + m - l, m + 1, r);\n    // Вернуть корневой узел\n    return root;\n}\n\n/* Построить двоичное дерево */\nTreeNode? BuildTree(int[] preorder, int[] inorder) {\n    // Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n    Dictionary&lt;int, int&gt; inorderMap = [];\n    for (int i = 0; i &lt; inorder.Length; i++) {\n        inorderMap.TryAdd(inorder[i], i);\n    }\n    TreeNode? root = DFS(preorder, inorderMap, 0, 0, inorder.Length - 1);\n    return root;\n}\n</code></pre> build_tree.go<pre><code>/* Построить двоичное дерево: разделяй и властвуй */\nfunc dfsBuildTree(preorder []int, inorderMap map[int]int, i, l, r int) *TreeNode {\n    // Завершить при пустом диапазоне поддерева\n    if r-l &lt; 0 {\n        return nil\n    }\n    // Инициализировать корневой узел\n    root := NewTreeNode(preorder[i])\n    // Найти m, чтобы разделить левое и правое поддеревья\n    m := inorderMap[preorder[i]]\n    // Подзадача: построить левое поддерево\n    root.Left = dfsBuildTree(preorder, inorderMap, i+1, l, m-1)\n    // Подзадача: построить правое поддерево\n    root.Right = dfsBuildTree(preorder, inorderMap, i+1+m-l, m+1, r)\n    // Вернуть корневой узел\n    return root\n}\n\n/* Построить двоичное дерево */\nfunc buildTree(preorder, inorder []int) *TreeNode {\n    // Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n    inorderMap := make(map[int]int, len(inorder))\n    for i := 0; i &lt; len(inorder); i++ {\n        inorderMap[inorder[i]] = i\n    }\n\n    root := dfsBuildTree(preorder, inorderMap, 0, 0, len(inorder)-1)\n    return root\n}\n</code></pre> build_tree.swift<pre><code>/* Построить двоичное дерево: разделяй и властвуй */\nfunc dfs(preorder: [Int], inorderMap: [Int: Int], i: Int, l: Int, r: Int) -&gt; TreeNode? {\n    // Завершить при пустом диапазоне поддерева\n    if r - l &lt; 0 {\n        return nil\n    }\n    // Инициализировать корневой узел\n    let root = TreeNode(x: preorder[i])\n    // Найти m, чтобы разделить левое и правое поддеревья\n    let m = inorderMap[preorder[i]]!\n    // Подзадача: построить левое поддерево\n    root.left = dfs(preorder: preorder, inorderMap: inorderMap, i: i + 1, l: l, r: m - 1)\n    // Подзадача: построить правое поддерево\n    root.right = dfs(preorder: preorder, inorderMap: inorderMap, i: i + 1 + m - l, l: m + 1, r: r)\n    // Вернуть корневой узел\n    return root\n}\n\n/* Построить двоичное дерево */\nfunc buildTree(preorder: [Int], inorder: [Int]) -&gt; TreeNode? {\n    // Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n    let inorderMap = inorder.enumerated().reduce(into: [:]) { $0[$1.element] = $1.offset }\n    return dfs(preorder: preorder, inorderMap: inorderMap, i: inorder.startIndex, l: inorder.startIndex, r: inorder.endIndex - 1)\n}\n</code></pre> build_tree.js<pre><code>/* Построить двоичное дерево: разделяй и властвуй */\nfunction dfs(preorder, inorderMap, i, l, r) {\n    // Завершить при пустом диапазоне поддерева\n    if (r - l &lt; 0) return null;\n    // Инициализировать корневой узел\n    const root = new TreeNode(preorder[i]);\n    // Найти m, чтобы разделить левое и правое поддеревья\n    const m = inorderMap.get(preorder[i]);\n    // Подзадача: построить левое поддерево\n    root.left = dfs(preorder, inorderMap, i + 1, l, m - 1);\n    // Подзадача: построить правое поддерево\n    root.right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r);\n    // Вернуть корневой узел\n    return root;\n}\n\n/* Построить двоичное дерево */\nfunction buildTree(preorder, inorder) {\n    // Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n    let inorderMap = new Map();\n    for (let i = 0; i &lt; inorder.length; i++) {\n        inorderMap.set(inorder[i], i);\n    }\n    const root = dfs(preorder, inorderMap, 0, 0, inorder.length - 1);\n    return root;\n}\n</code></pre> build_tree.ts<pre><code>/* Построить двоичное дерево: разделяй и властвуй */\nfunction dfs(\n    preorder: number[],\n    inorderMap: Map&lt;number, number&gt;,\n    i: number,\n    l: number,\n    r: number\n): TreeNode | null {\n    // Завершить при пустом диапазоне поддерева\n    if (r - l &lt; 0) return null;\n    // Инициализировать корневой узел\n    const root: TreeNode = new TreeNode(preorder[i]);\n    // Найти m, чтобы разделить левое и правое поддеревья\n    const m = inorderMap.get(preorder[i]);\n    // Подзадача: построить левое поддерево\n    root.left = dfs(preorder, inorderMap, i + 1, l, m - 1);\n    // Подзадача: построить правое поддерево\n    root.right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r);\n    // Вернуть корневой узел\n    return root;\n}\n\n/* Построить двоичное дерево */\nfunction buildTree(preorder: number[], inorder: number[]): TreeNode | null {\n    // Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n    let inorderMap = new Map&lt;number, number&gt;();\n    for (let i = 0; i &lt; inorder.length; i++) {\n        inorderMap.set(inorder[i], i);\n    }\n    const root = dfs(preorder, inorderMap, 0, 0, inorder.length - 1);\n    return root;\n}\n</code></pre> build_tree.dart<pre><code>/* Построить двоичное дерево: разделяй и властвуй */\nTreeNode? dfs(\n  List&lt;int&gt; preorder,\n  Map&lt;int, int&gt; inorderMap,\n  int i,\n  int l,\n  int r,\n) {\n  // Завершить при пустом диапазоне поддерева\n  if (r - l &lt; 0) {\n    return null;\n  }\n  // Инициализировать корневой узел\n  TreeNode? root = TreeNode(preorder[i]);\n  // Найти m, чтобы разделить левое и правое поддеревья\n  int m = inorderMap[preorder[i]]!;\n  // Подзадача: построить левое поддерево\n  root.left = dfs(preorder, inorderMap, i + 1, l, m - 1);\n  // Подзадача: построить правое поддерево\n  root.right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r);\n  // Вернуть корневой узел\n  return root;\n}\n\n/* Построить двоичное дерево */\nTreeNode? buildTree(List&lt;int&gt; preorder, List&lt;int&gt; inorder) {\n  // Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n  Map&lt;int, int&gt; inorderMap = {};\n  for (int i = 0; i &lt; inorder.length; i++) {\n    inorderMap[inorder[i]] = i;\n  }\n  TreeNode? root = dfs(preorder, inorderMap, 0, 0, inorder.length - 1);\n  return root;\n}\n</code></pre> build_tree.rs<pre><code>/* Построить двоичное дерево: разделяй и властвуй */\nfn dfs(\n    preorder: &amp;[i32],\n    inorder_map: &amp;HashMap&lt;i32, i32&gt;,\n    i: i32,\n    l: i32,\n    r: i32,\n) -&gt; Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt; {\n    // Завершить при пустом диапазоне поддерева\n    if r - l &lt; 0 {\n        return None;\n    }\n    // Инициализировать корневой узел\n    let root = TreeNode::new(preorder[i as usize]);\n    // Найти m, чтобы разделить левое и правое поддеревья\n    let m = inorder_map.get(&amp;preorder[i as usize]).unwrap();\n    // Подзадача: построить левое поддерево\n    root.borrow_mut().left = dfs(preorder, inorder_map, i + 1, l, m - 1);\n    // Подзадача: построить правое поддерево\n    root.borrow_mut().right = dfs(preorder, inorder_map, i + 1 + m - l, m + 1, r);\n    // Вернуть корневой узел\n    Some(root)\n}\n\n/* Построить двоичное дерево */\nfn build_tree(preorder: &amp;[i32], inorder: &amp;[i32]) -&gt; Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt; {\n    // Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n    let mut inorder_map: HashMap&lt;i32, i32&gt; = HashMap::new();\n    for i in 0..inorder.len() {\n        inorder_map.insert(inorder[i], i as i32);\n    }\n    let root = dfs(preorder, &amp;inorder_map, 0, 0, inorder.len() as i32 - 1);\n    root\n}\n</code></pre> build_tree.c<pre><code>/* Построить двоичное дерево: разделяй и властвуй */\nTreeNode *dfs(int *preorder, int *inorderMap, int i, int l, int r, int size) {\n    // Завершить при пустом диапазоне поддерева\n    if (r - l &lt; 0)\n        return NULL;\n    // Инициализировать корневой узел\n    TreeNode *root = (TreeNode *)malloc(sizeof(TreeNode));\n    root-&gt;val = preorder[i];\n    root-&gt;left = NULL;\n    root-&gt;right = NULL;\n    // Найти m, чтобы разделить левое и правое поддеревья\n    int m = inorderMap[preorder[i]];\n    // Подзадача: построить левое поддерево\n    root-&gt;left = dfs(preorder, inorderMap, i + 1, l, m - 1, size);\n    // Подзадача: построить правое поддерево\n    root-&gt;right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r, size);\n    // Вернуть корневой узел\n    return root;\n}\n\n/* Построить двоичное дерево */\nTreeNode *buildTree(int *preorder, int preorderSize, int *inorder, int inorderSize) {\n    // Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n    int *inorderMap = (int *)malloc(sizeof(int) * MAX_SIZE);\n    for (int i = 0; i &lt; inorderSize; i++) {\n        inorderMap[inorder[i]] = i;\n    }\n    TreeNode *root = dfs(preorder, inorderMap, 0, 0, inorderSize - 1, inorderSize);\n    free(inorderMap);\n    return root;\n}\n</code></pre> build_tree.kt<pre><code>/* Построить двоичное дерево: разделяй и властвуй */\nfun dfs(\n    preorder: IntArray,\n    inorderMap: Map&lt;Int?, Int?&gt;,\n    i: Int,\n    l: Int,\n    r: Int\n): TreeNode? {\n    // Завершить при пустом диапазоне поддерева\n    if (r - l &lt; 0) return null\n    // Инициализировать корневой узел\n    val root = TreeNode(preorder[i])\n    // Найти m, чтобы разделить левое и правое поддеревья\n    val m = inorderMap[preorder[i]]!!\n    // Подзадача: построить левое поддерево\n    root.left = dfs(preorder, inorderMap, i + 1, l, m - 1)\n    // Подзадача: построить правое поддерево\n    root.right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r)\n    // Вернуть корневой узел\n    return root\n}\n\n/* Построить двоичное дерево */\nfun buildTree(preorder: IntArray, inorder: IntArray): TreeNode? {\n    // Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n    val inorderMap = HashMap&lt;Int?, Int?&gt;()\n    for (i in inorder.indices) {\n        inorderMap[inorder[i]] = i\n    }\n    val root = dfs(preorder, inorderMap, 0, 0, inorder.size - 1)\n    return root\n}\n</code></pre> build_tree.rb<pre><code>### Построить двоичное дерево: разделяй и властвуй ###\ndef dfs(preorder, inorder_map, i, l, r)\n  # Завершить при пустом диапазоне поддерева\n  return if r - l &lt; 0\n\n  # Инициализировать корневой узел\n  root = TreeNode.new(preorder[i])\n  # Найти m, чтобы разделить левое и правое поддеревья\n  m = inorder_map[preorder[i]]\n  # Подзадача: построить левое поддерево\n  root.left = dfs(preorder, inorder_map, i + 1, l, m - 1)\n  # Подзадача: построить правое поддерево\n  root.right = dfs(preorder, inorder_map, i + 1 + m - l, m + 1, r)\n\n  # Вернуть корневой узел\n  root\nend\n\n### Построить двоичное дерево ###\ndef build_tree(preorder, inorder)\n  # Инициализировать хеш-таблицу для хранения соответствия элементов inorder их индексам\n  inorder_map = {}\n  inorder.each_with_index { |val, i| inorder_map[val] = i }\n  dfs(preorder, inorder_map, 0, 0, inorder.length - 1)\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>На рисунке 12-8 показан рекурсивный процесс построения двоичного дерева: каждый узел создается в фазе \"спуска\", а каждое ребро (ссылка) формируется в фазе \"подъема\".</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 12-8   Рекурсивный процесс построения двоичного дерева </p> <p>Результаты разбиения <code>preorder</code> и <code>inorder</code> внутри каждого рекурсивного вызова показаны на рисунке 12-9.</p> <p></p> <p> Рисунок 12-9   Результаты разбиения в каждом рекурсивном вызове </p> <p>Пусть число узлов дерева равно \\(n\\) ; инициализация каждого узла (то есть выполнение одного рекурсивного вызова <code>dfs()</code> ) занимает \\(O(1)\\) времени. Следовательно, общая временная сложность равна \\(O(n)\\) .</p> <p>Хеш-таблица хранит отображение значений <code>inorder</code> в индексы, поэтому ее пространственная сложность равна \\(O(n)\\) . В худшем случае, когда двоичное дерево вырождается в связный список, глубина рекурсии достигает \\(n\\) и требует \\(O(n)\\) памяти стека. Следовательно, общая пространственная сложность также равна \\(O(n)\\) .</p>","path":["Глава 12. Разделяй и властвуй","12.3 &nbsp; Задача построения двоичного дерева"],"tags":[]},{"location":"chapter_divide_and_conquer/divide_and_conquer/","level":1,"title":"12.1   Стратегия разделяй и властвуй","text":"<p>Разделяй и властвуй (divide and conquer) - это очень важная и широко используемая стратегия построения алгоритмов. Обычно она реализуется через рекурсию и включает два этапа: \"разделение\" и \"объединение\".</p> <ol> <li>Разделение (этап декомпозиции): рекурсивно разбить исходную задачу на две или более подзадачи, пока не будет достигнута наименьшая подзадача.</li> <li>Объединение (этап синтеза): начиная с уже известных решений наименьших подзадач, снизу вверх объединять решения подзадач и тем самым получать решение исходной задачи.</li> </ol> <p>Как показано на рисунке 12-1, \"сортировка слиянием\" является одним из типичных примеров применения стратегии \"разделяй и властвуй\".</p> <ol> <li>Разделение: рекурсивно разделить исходный массив (исходную задачу) на два подмассива (подзадачи), пока в подмассиве не останется только один элемент (наименьшая подзадача).</li> <li>Объединение: снизу вверх объединять упорядоченные подмассивы (решения подзадач), чтобы получить упорядоченный исходный массив (решение исходной задачи).</li> </ol> <p></p> <p> Рисунок 12-1   Стратегия разделяй и властвуй в сортировке слиянием </p>","path":["Глава 12. Разделяй и властвуй","12.1 &nbsp; Стратегия разделяй и властвуй"],"tags":[]},{"location":"chapter_divide_and_conquer/divide_and_conquer/#1211","level":2,"title":"12.1.1   Как определить задачу \"разделяй и властвуй\"","text":"<p>Чтобы понять, подходит ли задача для решения методом \"разделяй и властвуй\", обычно можно ориентироваться на следующие критерии.</p> <ol> <li>Задача раскладывается на части: исходную задачу можно разбить на более мелкие и похожие подзадачи, причем такое разбиение можно применять рекурсивно.</li> <li>Подзадачи независимы: подзадачи не пересекаются, не зависят друг от друга и могут решаться независимо.</li> <li>Решения подзадач можно объединить: решение исходной задачи получается объединением решений подзадач.</li> </ol> <p>Очевидно, что сортировка слиянием удовлетворяет всем трем критериям.</p> <ol> <li>Задача раскладывается на части: массив (исходная задача) рекурсивно делится на два подмассива (подзадачи).</li> <li>Подзадачи независимы: каждый подмассив можно сортировать отдельно (то есть каждую подзадачу можно решать независимо).</li> <li>Решения подзадач можно объединить: два упорядоченных подмассива (решения подзадач) можно объединить в один упорядоченный массив (решение исходной задачи).</li> </ol>","path":["Глава 12. Разделяй и властвуй","12.1 &nbsp; Стратегия разделяй и властвуй"],"tags":[]},{"location":"chapter_divide_and_conquer/divide_and_conquer/#1212","level":2,"title":"12.1.2   Повышение эффективности с помощью \"разделяй и властвуй\"","text":"<p>Стратегия \"разделяй и властвуй\" не только позволяет эффективно решать алгоритмические задачи, но и часто повышает эффективность самих алгоритмов. Именно поэтому быстрая сортировка, сортировка слиянием и пирамидальная сортировка обычно работают быстрее, чем сортировка выбором, пузырьком и вставками.</p> <p>Тогда возникает естественный вопрос: почему стратегия \"разделяй и властвуй\" повышает эффективность алгоритма и какова внутренняя логика этого подхода? Иными словами, почему разбиение большой задачи на несколько подзадач, решение этих подзадач и последующее объединение их решений оказывается эффективнее, чем прямое решение исходной задачи? Этот вопрос можно рассмотреть с двух сторон: через число операций и через параллельные вычисления.</p>","path":["Глава 12. Разделяй и властвуй","12.1 &nbsp; Стратегия разделяй и властвуй"],"tags":[]},{"location":"chapter_divide_and_conquer/divide_and_conquer/#1","level":3,"title":"1.   Оптимизация числа операций","text":"<p>Рассмотрим \"сортировку пузырьком\": для массива длины \\(n\\) ей требуется \\(O(n^2)\\) времени. Предположим, что мы разделим массив на два подмассива в середине, как показано на рисунке 12-2. Тогда само разбиение потребует \\(O(n)\\) времени, сортировка каждого подмассива займет \\(O((n / 2)^2)\\) времени, а объединение двух подмассивов потребует еще \\(O(n)\\) времени. Общая временная сложность будет равна:</p> \\[ O(n + (\\frac{n}{2})^2 \\times 2 + n) = O(\\frac{n^2}{2} + 2n) \\] <p></p> <p> Рисунок 12-2   Сортировка пузырьком до и после разбиения массива </p> <p>Теперь рассмотрим следующее неравенство, в котором левая и правая части обозначают общее число операций до разбиения и после него:</p> \\[ \\begin{aligned} n^2 &amp; &gt; \\frac{n^2}{2} + 2n \\newline n^2 - \\frac{n^2}{2} - 2n &amp; &gt; 0 \\newline n(n - 4) &amp; &gt; 0 \\end{aligned} \\] <p>Это означает, что при \\(n &gt; 4\\) число операций после разбиения становится меньше, а значит, сортировка должна работать быстрее. При этом важно заметить, что временная сложность после разбиения все еще остается квадратичной, то есть \\(O(n^2)\\) ; уменьшается лишь константный множитель.</p> <p>Если пойти дальше и продолжать делить каждый подмассив пополам, пока в нем не останется только один элемент, то мы фактически получим \"сортировку слиянием\", чья временная сложность равна \\(O(n \\log n)\\) .</p> <p>Можно пойти еще дальше и спросить: что если задать несколько точек разделения и равномерно разбить исходный массив на \\(k\\) подмассивов? Такая ситуация очень похожа на блочную сортировку, которая особенно хорошо подходит для сортировки очень больших объемов данных и теоретически может достигать временной сложности \\(O(n + k)\\) .</p>","path":["Глава 12. Разделяй и властвуй","12.1 &nbsp; Стратегия разделяй и властвуй"],"tags":[]},{"location":"chapter_divide_and_conquer/divide_and_conquer/#2","level":3,"title":"2.   Оптимизация параллельных вычислений","text":"<p>Мы знаем, что подзадачи, порождаемые стратегией \"разделяй и властвуй\", являются независимыми, а значит, их обычно можно решать параллельно. Иначе говоря, \"разделяй и властвуй\" не только может уменьшить временную сложность алгоритма, но и хорошо сочетается с параллельной оптимизацией на уровне системы.</p> <p>Параллельная оптимизация особенно эффективна в среде с несколькими ядрами или несколькими процессорами, потому что система может одновременно обрабатывать разные подзадачи, лучше загружая вычислительные ресурсы и тем самым заметно сокращая общее время работы.</p> <p>Например, в показанной ниже \"блочной сортировке\" большой объем данных равномерно распределяется по блокам. Тогда сортировку каждого блока можно поручить отдельным вычислительным единицам, а после завершения просто объединить результаты.</p> <p></p> <p> Рисунок 12-3   Параллельные вычисления в блочной сортировке </p>","path":["Глава 12. Разделяй и властвуй","12.1 &nbsp; Стратегия разделяй и властвуй"],"tags":[]},{"location":"chapter_divide_and_conquer/divide_and_conquer/#1213","level":2,"title":"12.1.3   Типичные применения стратегии \"разделяй и властвуй\"","text":"<p>С одной стороны, стратегию \"разделяй и властвуй\" можно использовать для решения многих классических алгоритмических задач.</p> <ul> <li>Поиск ближайшей пары точек: сначала множество точек делится на две части, затем ищется ближайшая пара в каждой части, а затем ближайшая пара, пересекающая границу между двумя частями.</li> <li>Умножение больших чисел: например, алгоритм Карацубы, который раскладывает умножение больших чисел на несколько умножений и сложений меньших чисел.</li> <li>Умножение матриц: например, алгоритм Штрассена, который раскладывает умножение больших матриц на несколько умножений и сложений матриц меньшего размера.</li> <li>Задача о Ханойской башне: задача о Ханойской башне решается рекурсивно и является типичным примером применения стратегии \"разделяй и властвуй\".</li> <li>Подсчет инверсий: если в последовательности предыдущее число больше следующего, то такая пара образует инверсию. Эту задачу можно решить с помощью идей \"разделяй и властвуй\", опираясь на сортировку слиянием.</li> </ul> <p>С другой стороны, стратегия \"разделяй и властвуй\" очень широко применяется при проектировании алгоритмов и структур данных.</p> <ul> <li>Двоичный поиск: двоичный поиск делит отсортированный массив на две части по индексу середины, а затем, в зависимости от результата сравнения целевого значения со средним элементом, исключает одну из половин и повторяет ту же операцию на оставшемся интервале.</li> <li>Сортировка слиянием: она уже была рассмотрена в начале этого раздела, поэтому не будем повторяться.</li> <li>Быстрая сортировка: в ней выбирается опорное значение, после чего массив делится на два подмассива: один содержит элементы меньше опорного, а другой - больше. Затем такая же операция повторяется для обеих частей, пока в подмассиве не останется один элемент.</li> <li>Блочная сортировка: ее основная идея заключается в распределении данных по нескольким блокам, сортировке элементов внутри каждого блока и последующем последовательном извлечении элементов из блоков для построения отсортированного массива.</li> <li>Деревья: например, двоичные деревья поиска, AVL-деревья, красно-черные деревья, B-деревья, B+ деревья и т.д. Их операции поиска, вставки и удаления можно рассматривать как применение стратегии \"разделяй и властвуй\".</li> <li>Кучи: куча является особым видом полного двоичного дерева, а такие операции, как вставка, удаление и упорядочивание, по сути содержат идеи \"разделяй и властвуй\".</li> <li>Хеш-таблицы: хотя хеш-таблицы напрямую не используют стратегию \"разделяй и властвуй\", некоторые способы разрешения коллизий косвенно опираются на эту идею. Например, длинные цепочки в методе цепочек могут преобразовываться в красно-черные деревья для повышения эффективности поиска.</li> </ul> <p>Нетрудно заметить, что \"разделяй и властвуй\" - это \"тихая\" алгоритмическая идея, скрыто присутствующая внутри самых разных алгоритмов и структур данных.</p>","path":["Глава 12. Разделяй и властвуй","12.1 &nbsp; Стратегия разделяй и властвуй"],"tags":[]},{"location":"chapter_divide_and_conquer/hanota_problem/","level":1,"title":"12.4   Задача о Ханойской башне","text":"<p>В задачах сортировки слиянием и построения двоичного дерева мы делили исходную задачу на две подзадачи, каждая из которых имела размер, равный примерно половине исходной задачи. Однако для задачи о Ханойской башне используется другая стратегия разбиения.</p> <p>Question</p> <p>Даны три стержня, обозначенные как <code>A</code> , <code>B</code> и <code>C</code> . В начальном состоянии на стержне <code>A</code> находятся \\(n\\) дисков, расположенных сверху вниз в порядке от меньшего к большему. Нужно переместить эти \\(n\\) дисков на стержень <code>C</code> , сохранив их исходный порядок (как показано на рисунке 12-10). Во время перемещения дисков необходимо соблюдать следующие правила.</p> <ol> <li>Диск можно снять только с вершины одного стержня и положить только на вершину другого стержня.</li> <li>За один раз можно перемещать только один диск.</li> <li>Меньший диск всегда должен лежать на большем.</li> </ol> <p></p> <p> Рисунок 12-10   Пример задачи о Ханойской башне </p> <p>Обозначим задачу о Ханойской башне размера \\(i\\) как \\(f(i)\\) . Например, \\(f(3)\\) означает задачу перемещения 3 дисков со стержня <code>A</code> на стержень <code>C</code> .</p>","path":["Глава 12. Разделяй и властвуй","12.4 &nbsp; Задача о Ханойской башне"],"tags":[]},{"location":"chapter_divide_and_conquer/hanota_problem/#1","level":3,"title":"1.   Рассмотрим базовые случаи","text":"<p>Как показано на рисунке 12-11, для задачи \\(f(1)\\) , то есть когда имеется только один диск, достаточно просто переместить его напрямую со стержня <code>A</code> на стержень <code>C</code> .</p> &lt;1&gt;&lt;2&gt; <p></p> <p></p> <p> Рисунок 12-11   Решение задачи размера 1 </p> <p>Как показано на рисунке 12-12, для задачи \\(f(2)\\) , то есть когда есть два диска, поскольку меньший диск все время должен лежать на большем, приходится использовать <code>B</code> как вспомогательный стержень.</p> <ol> <li>Сначала переместить верхний маленький диск с <code>A</code> на <code>B</code> .</li> <li>Затем переместить большой диск с <code>A</code> на <code>C</code> .</li> <li>Наконец, переместить маленький диск с <code>B</code> на <code>C</code> .</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p> Рисунок 12-12   Решение задачи размера 2 </p> <p>Процесс решения задачи \\(f(2)\\) можно кратко описать так: переместить два диска с <code>A</code> на <code>C</code> с помощью <code>B</code> . Здесь <code>C</code> называется целевым стержнем, а <code>B</code> - буферным стержнем.</p>","path":["Глава 12. Разделяй и властвуй","12.4 &nbsp; Задача о Ханойской башне"],"tags":[]},{"location":"chapter_divide_and_conquer/hanota_problem/#2","level":3,"title":"2.   Разбиение на подзадачи","text":"<p>Для задачи \\(f(3)\\) , то есть когда имеется три диска, ситуация становится сложнее.</p> <p>Поскольку решения \\(f(1)\\) и \\(f(2)\\) уже известны, можно подойти к задаче с точки зрения стратегии \"разделяй и властвуй\" и рассматривать два верхних диска на <code>A</code> как единое целое, выполняя шаги, показанные на рисунке 12-13. Так три диска успешно перемещаются с <code>A</code> на <code>C</code> .</p> <ol> <li>Сделать <code>B</code> целевым стержнем, а <code>C</code> буферным, и переместить два диска с <code>A</code> на <code>B</code> .</li> <li>Переместить оставшийся один диск с <code>A</code> напрямую на <code>C</code> .</li> <li>Сделать <code>C</code> целевым стержнем, а <code>A</code> буферным, и переместить два диска с <code>B</code> на <code>C</code> .</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p> Рисунок 12-13   Решение задачи размера 3 </p> <p>Иначе говоря, мы разбиваем задачу \\(f(3)\\) на две подзадачи \\(f(2)\\) и одну подзадачу \\(f(1)\\) . Если последовательно решить эти три подзадачи, исходная задача тоже будет решена. Это показывает, что подзадачи независимы и что их решения можно объединить.</p> <p>Таким образом, можно сформулировать показанную на рисунке 12-14 стратегию \"разделяй и властвуй\" для задачи о Ханойской башне: исходная задача \\(f(n)\\) разбивается на две подзадачи \\(f(n-1)\\) и одну подзадачу \\(f(1)\\) , которые затем решаются в следующем порядке.</p> <ol> <li>Переместить \\(n-1\\) дисков с <code>A</code> на <code>B</code> с помощью <code>C</code> .</li> <li>Переместить оставшийся \\(1\\) диск напрямую с <code>A</code> на <code>C</code> .</li> <li>Переместить \\(n-1\\) дисков с <code>B</code> на <code>C</code> с помощью <code>A</code> .</li> </ol> <p>Для двух подзадач \\(f(n-1)\\) можно применять тот же способ рекурсивного разбиения, пока не будет достигнута наименьшая подзадача \\(f(1)\\) . А решение для \\(f(1)\\) уже известно и требует всего одного перемещения.</p> <p></p> <p> Рисунок 12-14   Стратегия разделяй и властвуй для решения задачи о Ханойской башне </p>","path":["Глава 12. Разделяй и властвуй","12.4 &nbsp; Задача о Ханойской башне"],"tags":[]},{"location":"chapter_divide_and_conquer/hanota_problem/#3","level":3,"title":"3.   Реализация кода","text":"<p>В коде мы объявляем рекурсивную функцию <code>dfs(i, src, buf, tar)</code> , которая перемещает \\(i\\) верхних дисков со стержня <code>src</code> на целевой стержень <code>tar</code> с помощью буферного стержня <code>buf</code> :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby hanota.py<pre><code>def move(src: list[int], tar: list[int]):\n    \"\"\"Переместить один диск\"\"\"\n    # Снять диск с вершины src\n    pan = src.pop()\n    # Положить диск на вершину tar\n    tar.append(pan)\n\ndef dfs(i: int, src: list[int], buf: list[int], tar: list[int]):\n    \"\"\"Решить задачу Ханойской башни f(i)\"\"\"\n    # Если в src остался только один диск, сразу переместить его в tar\n    if i == 1:\n        move(src, tar)\n        return\n    # Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n    dfs(i - 1, src, tar, buf)\n    # Подзадача f(1): переместить оставшийся один диск из src в tar\n    move(src, tar)\n    # Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n    dfs(i - 1, buf, src, tar)\n\ndef solve_hanota(A: list[int], B: list[int], C: list[int]):\n    \"\"\"Решить задачу Ханойской башни\"\"\"\n    n = len(A)\n    # Переместить верхние n дисков из A в C с помощью B\n    dfs(n, A, B, C)\n</code></pre> hanota.cpp<pre><code>/* Переместить один диск */\nvoid move(vector&lt;int&gt; &amp;src, vector&lt;int&gt; &amp;tar) {\n    // Снять диск с вершины src\n    int pan = src.back();\n    src.pop_back();\n    // Положить диск на вершину tar\n    tar.push_back(pan);\n}\n\n/* Решить задачу Ханойской башни f(i) */\nvoid dfs(int i, vector&lt;int&gt; &amp;src, vector&lt;int&gt; &amp;buf, vector&lt;int&gt; &amp;tar) {\n    // Если в src остался только один диск, сразу переместить его в tar\n    if (i == 1) {\n        move(src, tar);\n        return;\n    }\n    // Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n    dfs(i - 1, src, tar, buf);\n    // Подзадача f(1): переместить оставшийся один диск из src в tar\n    move(src, tar);\n    // Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n    dfs(i - 1, buf, src, tar);\n}\n\n/* Решить задачу Ханойской башни */\nvoid solveHanota(vector&lt;int&gt; &amp;A, vector&lt;int&gt; &amp;B, vector&lt;int&gt; &amp;C) {\n    int n = A.size();\n    // Переместить верхние n дисков из A в C с помощью B\n    dfs(n, A, B, C);\n}\n</code></pre> hanota.java<pre><code>/* Переместить один диск */\nvoid move(List&lt;Integer&gt; src, List&lt;Integer&gt; tar) {\n    // Снять диск с вершины src\n    Integer pan = src.remove(src.size() - 1);\n    // Положить диск на вершину tar\n    tar.add(pan);\n}\n\n/* Решить задачу Ханойской башни f(i) */\nvoid dfs(int i, List&lt;Integer&gt; src, List&lt;Integer&gt; buf, List&lt;Integer&gt; tar) {\n    // Если в src остался только один диск, сразу переместить его в tar\n    if (i == 1) {\n        move(src, tar);\n        return;\n    }\n    // Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n    dfs(i - 1, src, tar, buf);\n    // Подзадача f(1): переместить оставшийся один диск из src в tar\n    move(src, tar);\n    // Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n    dfs(i - 1, buf, src, tar);\n}\n\n/* Решить задачу Ханойской башни */\nvoid solveHanota(List&lt;Integer&gt; A, List&lt;Integer&gt; B, List&lt;Integer&gt; C) {\n    int n = A.size();\n    // Переместить верхние n дисков из A в C с помощью B\n    dfs(n, A, B, C);\n}\n</code></pre> hanota.cs<pre><code>/* Переместить один диск */\nvoid Move(List&lt;int&gt; src, List&lt;int&gt; tar) {\n    // Снять диск с вершины src\n    int pan = src[^1];\n    src.RemoveAt(src.Count - 1);\n    // Положить диск на вершину tar\n    tar.Add(pan);\n}\n\n/* Решить задачу Ханойской башни f(i) */\nvoid DFS(int i, List&lt;int&gt; src, List&lt;int&gt; buf, List&lt;int&gt; tar) {\n    // Если в src остался только один диск, сразу переместить его в tar\n    if (i == 1) {\n        Move(src, tar);\n        return;\n    }\n    // Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n    DFS(i - 1, src, tar, buf);\n    // Подзадача f(1): переместить оставшийся один диск из src в tar\n    Move(src, tar);\n    // Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n    DFS(i - 1, buf, src, tar);\n}\n\n/* Решить задачу Ханойской башни */\nvoid SolveHanota(List&lt;int&gt; A, List&lt;int&gt; B, List&lt;int&gt; C) {\n    int n = A.Count;\n    // Переместить верхние n дисков из A в C с помощью B\n    DFS(n, A, B, C);\n}\n</code></pre> hanota.go<pre><code>/* Переместить один диск */\nfunc move(src, tar *list.List) {\n    // Снять диск с вершины src\n    pan := src.Back()\n    // Положить диск на вершину tar\n    tar.PushBack(pan.Value)\n    // Убрать верхний диск из src\n    src.Remove(pan)\n}\n\n/* Решить задачу Ханойской башни f(i) */\nfunc dfsHanota(i int, src, buf, tar *list.List) {\n    // Если в src остался только один диск, сразу переместить его в tar\n    if i == 1 {\n        move(src, tar)\n        return\n    }\n    // Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n    dfsHanota(i-1, src, tar, buf)\n    // Подзадача f(1): переместить оставшийся один диск из src в tar\n    move(src, tar)\n    // Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n    dfsHanota(i-1, buf, src, tar)\n}\n\n/* Решить задачу Ханойской башни */\nfunc solveHanota(A, B, C *list.List) {\n    n := A.Len()\n    // Переместить верхние n дисков из A в C с помощью B\n    dfsHanota(n, A, B, C)\n}\n</code></pre> hanota.swift<pre><code>/* Переместить один диск */\nfunc move(src: inout [Int], tar: inout [Int]) {\n    // Снять диск с вершины src\n    let pan = src.popLast()!\n    // Положить диск на вершину tar\n    tar.append(pan)\n}\n\n/* Решить задачу Ханойской башни f(i) */\nfunc dfs(i: Int, src: inout [Int], buf: inout [Int], tar: inout [Int]) {\n    // Если в src остался только один диск, сразу переместить его в tar\n    if i == 1 {\n        move(src: &amp;src, tar: &amp;tar)\n        return\n    }\n    // Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n    dfs(i: i - 1, src: &amp;src, buf: &amp;tar, tar: &amp;buf)\n    // Подзадача f(1): переместить оставшийся один диск из src в tar\n    move(src: &amp;src, tar: &amp;tar)\n    // Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n    dfs(i: i - 1, src: &amp;buf, buf: &amp;src, tar: &amp;tar)\n}\n\n/* Решить задачу Ханойской башни */\nfunc solveHanota(A: inout [Int], B: inout [Int], C: inout [Int]) {\n    let n = A.count\n    // Хвост списка соответствует вершине столбца\n    // Переместить верхние n дисков из src в C с помощью B\n    dfs(i: n, src: &amp;A, buf: &amp;B, tar: &amp;C)\n}\n</code></pre> hanota.js<pre><code>/* Переместить один диск */\nfunction move(src, tar) {\n    // Снять диск с вершины src\n    const pan = src.pop();\n    // Положить диск на вершину tar\n    tar.push(pan);\n}\n\n/* Решить задачу Ханойской башни f(i) */\nfunction dfs(i, src, buf, tar) {\n    // Если в src остался только один диск, сразу переместить его в tar\n    if (i === 1) {\n        move(src, tar);\n        return;\n    }\n    // Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n    dfs(i - 1, src, tar, buf);\n    // Подзадача f(1): переместить оставшийся один диск из src в tar\n    move(src, tar);\n    // Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n    dfs(i - 1, buf, src, tar);\n}\n\n/* Решить задачу Ханойской башни */\nfunction solveHanota(A, B, C) {\n    const n = A.length;\n    // Переместить верхние n дисков из A в C с помощью B\n    dfs(n, A, B, C);\n}\n</code></pre> hanota.ts<pre><code>/* Переместить один диск */\nfunction move(src: number[], tar: number[]): void {\n    // Снять диск с вершины src\n    const pan = src.pop();\n    // Положить диск на вершину tar\n    tar.push(pan);\n}\n\n/* Решить задачу Ханойской башни f(i) */\nfunction dfs(i: number, src: number[], buf: number[], tar: number[]): void {\n    // Если в src остался только один диск, сразу переместить его в tar\n    if (i === 1) {\n        move(src, tar);\n        return;\n    }\n    // Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n    dfs(i - 1, src, tar, buf);\n    // Подзадача f(1): переместить оставшийся один диск из src в tar\n    move(src, tar);\n    // Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n    dfs(i - 1, buf, src, tar);\n}\n\n/* Решить задачу Ханойской башни */\nfunction solveHanota(A: number[], B: number[], C: number[]): void {\n    const n = A.length;\n    // Переместить верхние n дисков из A в C с помощью B\n    dfs(n, A, B, C);\n}\n</code></pre> hanota.dart<pre><code>/* Переместить один диск */\nvoid move(List&lt;int&gt; src, List&lt;int&gt; tar) {\n  // Снять диск с вершины src\n  int pan = src.removeLast();\n  // Положить диск на вершину tar\n  tar.add(pan);\n}\n\n/* Решить задачу Ханойской башни f(i) */\nvoid dfs(int i, List&lt;int&gt; src, List&lt;int&gt; buf, List&lt;int&gt; tar) {\n  // Если в src остался только один диск, сразу переместить его в tar\n  if (i == 1) {\n    move(src, tar);\n    return;\n  }\n  // Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n  dfs(i - 1, src, tar, buf);\n  // Подзадача f(1): переместить оставшийся один диск из src в tar\n  move(src, tar);\n  // Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n  dfs(i - 1, buf, src, tar);\n}\n\n/* Решить задачу Ханойской башни */\nvoid solveHanota(List&lt;int&gt; A, List&lt;int&gt; B, List&lt;int&gt; C) {\n  int n = A.length;\n  // Переместить верхние n дисков из A в C с помощью B\n  dfs(n, A, B, C);\n}\n</code></pre> hanota.rs<pre><code>/* Переместить один диск */\nfn move_pan(src: &amp;mut Vec&lt;i32&gt;, tar: &amp;mut Vec&lt;i32&gt;) {\n    // Снять диск с вершины src\n    let pan = src.pop().unwrap();\n    // Положить диск на вершину tar\n    tar.push(pan);\n}\n\n/* Решить задачу Ханойской башни f(i) */\nfn dfs(i: i32, src: &amp;mut Vec&lt;i32&gt;, buf: &amp;mut Vec&lt;i32&gt;, tar: &amp;mut Vec&lt;i32&gt;) {\n    // Если в src остался только один диск, сразу переместить его в tar\n    if i == 1 {\n        move_pan(src, tar);\n        return;\n    }\n    // Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n    dfs(i - 1, src, tar, buf);\n    // Подзадача f(1): переместить оставшийся один диск из src в tar\n    move_pan(src, tar);\n    // Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n    dfs(i - 1, buf, src, tar);\n}\n\n/* Решить задачу Ханойской башни */\nfn solve_hanota(A: &amp;mut Vec&lt;i32&gt;, B: &amp;mut Vec&lt;i32&gt;, C: &amp;mut Vec&lt;i32&gt;) {\n    let n = A.len() as i32;\n    // Переместить верхние n дисков из A в C с помощью B\n    dfs(n, A, B, C);\n}\n</code></pre> hanota.c<pre><code>/* Переместить один диск */\nvoid move(int *src, int *srcSize, int *tar, int *tarSize) {\n    // Снять диск с вершины src\n    int pan = src[*srcSize - 1];\n    src[*srcSize - 1] = 0;\n    (*srcSize)--;\n    // Положить диск на вершину tar\n    tar[*tarSize] = pan;\n    (*tarSize)++;\n}\n\n/* Решить задачу Ханойской башни f(i) */\nvoid dfs(int i, int *src, int *srcSize, int *buf, int *bufSize, int *tar, int *tarSize) {\n    // Если в src остался только один диск, сразу переместить его в tar\n    if (i == 1) {\n        move(src, srcSize, tar, tarSize);\n        return;\n    }\n    // Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n    dfs(i - 1, src, srcSize, tar, tarSize, buf, bufSize);\n    // Подзадача f(1): переместить оставшийся один диск из src в tar\n    move(src, srcSize, tar, tarSize);\n    // Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n    dfs(i - 1, buf, bufSize, src, srcSize, tar, tarSize);\n}\n\n/* Решить задачу Ханойской башни */\nvoid solveHanota(int *A, int *ASize, int *B, int *BSize, int *C, int *CSize) {\n    // Переместить верхние n дисков из A в C с помощью B\n    dfs(*ASize, A, ASize, B, BSize, C, CSize);\n}\n</code></pre> hanota.kt<pre><code>/* Переместить один диск */\nfun move(src: MutableList&lt;Int&gt;, tar: MutableList&lt;Int&gt;) {\n    // Снять диск с вершины src\n    val pan = src.removeAt(src.size - 1)\n    // Положить диск на вершину tar\n    tar.add(pan)\n}\n\n/* Решить задачу Ханойской башни f(i) */\nfun dfs(i: Int, src: MutableList&lt;Int&gt;, buf: MutableList&lt;Int&gt;, tar: MutableList&lt;Int&gt;) {\n    // Если в src остался только один диск, сразу переместить его в tar\n    if (i == 1) {\n        move(src, tar)\n        return\n    }\n    // Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n    dfs(i - 1, src, tar, buf)\n    // Подзадача f(1): переместить оставшийся один диск из src в tar\n    move(src, tar)\n    // Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n    dfs(i - 1, buf, src, tar)\n}\n\n/* Решить задачу Ханойской башни */\nfun solveHanota(A: MutableList&lt;Int&gt;, B: MutableList&lt;Int&gt;, C: MutableList&lt;Int&gt;) {\n    val n = A.size\n    // Переместить верхние n дисков из A в C с помощью B\n    dfs(n, A, B, C)\n}\n</code></pre> hanota.rb<pre><code>### Переместить один диск ###\ndef move(src, tar)\n  # Снять диск с вершины src\n  pan = src.pop\n  # Положить диск на вершину tar\n  tar &lt;&lt; pan\nend\n\n### Решить задачу Ханойской башни f(i) ###\ndef dfs(i, src, buf, tar)\n  # Если в src остался только один диск, сразу переместить его в tar\n  if i == 1\n    move(src, tar)\n    return\n  end\n\n  # Подзадача f(i-1): переместить верхние i-1 дисков из src в buf с помощью tar\n  dfs(i - 1, src, tar, buf)\n  # Подзадача f(1): переместить оставшийся один диск из src в tar\n  move(src, tar)\n  # Подзадача f(i-1): переместить верхние i-1 дисков из buf в tar с помощью src\n  dfs(i - 1, buf, src, tar)\nend\n\n### Решить задачу Ханойской башни ###\ndef solve_hanota(_A, _B, _C)\n  n = _A.length\n  # Переместить верхние n дисков из A в C с помощью B\n  dfs(n, _A, _B, _C)\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Как показано на рисунке 12-15, задача о Ханойской башне формирует дерево рекурсии высоты \\(n\\) , в котором каждый узел представляет подзадачу и соответствует одному открытому вызову <code>dfs()</code> ; поэтому временная сложность равна \\(O(2^n)\\) , а пространственная сложность равна \\(O(n)\\) .</p> <p></p> <p> Рисунок 12-15   Дерево рекурсии задачи о Ханойской башне </p> <p>Quote</p> <p>Задача о Ханойской башне происходит из древней легенды. В одном из храмов древней Индии монахи имели три высоких алмазных стержня и \\(64\\) золотых диска разного размера. Монахи непрерывно перекладывали диски и верили, что в тот момент, когда последний диск будет правильно перенесен, мир подойдет к концу.</p> <p>Однако даже если бы монахи перемещали по одному диску в секунду, им понадобилось бы примерно \\(2^{64} \\approx 1.84×10^{19}\\) секунд, то есть около \\(585\\) миллиардов лет, что намного превышает текущую оценку возраста Вселенной. Поэтому, если легенда и верна, нам, вероятно, пока не о чем беспокоиться.</p>","path":["Глава 12. Разделяй и властвуй","12.4 &nbsp; Задача о Ханойской башне"],"tags":[]},{"location":"chapter_divide_and_conquer/summary/","level":1,"title":"12.5   Резюме","text":"","path":["Глава 12. Разделяй и властвуй","12.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_divide_and_conquer/summary/#1","level":3,"title":"1.   Ключевые выводы","text":"<ul> <li>\"Разделяй и властвуй\" - это распространенная стратегия проектирования алгоритмов, которая включает два этапа: разделение (декомпозицию) и объединение (синтез), и обычно реализуется с помощью рекурсии.</li> <li>Критерии применимости этой стратегии к задаче включают: возможность разложения задачи, независимость подзадач и возможность объединения их решений.</li> <li>Сортировка слиянием является типичным применением стратегии \"разделяй и властвуй\": она рекурсивно делит массив на два равных по длине подмассива, пока не останется массив из одного элемента, после чего начинает поэтапное объединение.</li> <li>Использование стратегии \"разделяй и властвуй\" часто позволяет повысить эффективность алгоритма. С одной стороны, она уменьшает число операций; с другой - после разбиения способствует параллельной оптимизации на уровне системы.</li> <li>\"Разделяй и властвуй\" не только помогает решать многие алгоритмические задачи, но и широко используется при проектировании структур данных и алгоритмов, поэтому его можно встретить буквально повсюду.</li> <li>По сравнению с полным перебором адаптивный поиск работает эффективнее. Алгоритмы поиска со сложностью \\(O(\\log n)\\) обычно реализуются на основе стратегии \"разделяй и властвуй\".</li> <li>Двоичный поиск - еще одно типичное применение стратегии \"разделяй и властвуй\", в котором отсутствует шаг объединения решений подзадач. Его можно реализовать рекурсивно, опираясь на эту стратегию.</li> <li>В задаче построения двоичного дерева исходная задача построения дерева может быть разбита на две подзадачи: построение левого и правого поддеревьев, а реализуется это через разбиение индексных интервалов прямого и симметричного обходов.</li> <li>В задаче о Ханойской башне задача размера \\(n\\) разбивается на две подзадачи размера \\(n-1\\) и одну подзадачу размера \\(1\\) . После последовательного решения этих трех подзадач исходная задача также оказывается решенной.</li> </ul>","path":["Глава 12. Разделяй и властвуй","12.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_dynamic_programming/","level":1,"title":"Глава 14.   Динамическое программирование","text":"<p>Abstract</p> <p>Ручьи впадают в реки, а реки вливаются в море.</p> <p>Динамическое программирование собирает решения малых задач в ответ на большую задачу и шаг за шагом ведет нас к ее решению.</p>","path":["Глава 14. Динамическое программирование","Глава 14. &nbsp; Динамическое программирование"],"tags":[]},{"location":"chapter_dynamic_programming/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>14.1   Первое знакомство с динамическим программированием</li> <li>14.2   Свойства задач динамического программирования</li> <li>14.3   Подход к решению задач динамического программирования</li> <li>14.4   Задача о рюкзаке 0-1</li> <li>14.5   Задача о полном рюкзаке</li> <li>14.6   Задача о расстоянии редактирования</li> <li>14.7   Резюме</li> </ul>","path":["Глава 14. Динамическое программирование","Глава 14. &nbsp; Динамическое программирование"],"tags":[]},{"location":"chapter_dynamic_programming/dp_problem_features/","level":1,"title":"14.2   Свойства задач динамического программирования","text":"<p>В предыдущем разделе мы увидели, как динамическое программирование решает исходную задачу через разложение на подзадачи. На самом деле разложение на подзадачи - это общий алгоритмический подход, но в методе \"разделяй и властвуй\", динамическом программировании и поиске с возвратом акценты расставлены по-разному.</p> <ul> <li>Алгоритмы \"разделяй и властвуй\" рекурсивно раскладывают исходную задачу на несколько независимых подзадач, пока не будет достигнута наименьшая подзадача, а затем в процессе возврата объединяют решения подзадач в решение исходной задачи.</li> <li>Динамическое программирование тоже раскладывает задачу рекурсивно, но его главное отличие от метода \"разделяй и властвуй\" в том, что подзадачи здесь зависят друг от друга и в процессе разложения возникает много перекрывающихся подзадач.</li> <li>Алгоритм поиска с возвратом перебирает все возможные решения через попытки и откат и с помощью обрезки избегает ненужных ветвей поиска. Решение исходной задачи состоит из последовательности решений, и подзадачей можно считать префикс этой последовательности решений.</li> </ul> <p>На практике динамическое программирование часто применяется для задач оптимизации. Такие задачи не только содержат перекрывающиеся подзадачи, но и обладают еще двумя важными свойствами: оптимальной подструктурой и отсутствием последствий.</p>","path":["Глава 14. Динамическое программирование","14.2 &nbsp; Свойства задач динамического программирования"],"tags":[]},{"location":"chapter_dynamic_programming/dp_problem_features/#1421","level":2,"title":"14.2.1   Оптимальная подструктура","text":"<p>Немного изменим задачу о подъеме по лестнице, чтобы нагляднее показать понятие оптимальной подструктуры.</p> <p>Минимальная стоимость подъема по лестнице</p> <p>Дана лестница, по которой можно подниматься на \\(1\\) или на \\(2\\) ступени за раз. На каждой ступени указано неотрицательное целое число, обозначающее цену попадания на эту ступень. Дан массив неотрицательных целых чисел \\(cost\\) , где \\(cost[i]\\) - это цена для ступени \\(i\\) , а \\(cost[0]\\) соответствует земле (начальной позиции). Найдите минимальную суммарную стоимость, необходимую для достижения вершины.</p> <p>Как показано на рисунке 14-6, если цены для ступеней \\(1\\) , \\(2\\) и \\(3\\) равны соответственно \\(1\\) , \\(10\\) и \\(1\\) , то минимальная стоимость подъема с земли на третью ступень равна \\(2\\) .</p> <p></p> <p> Рисунок 14-6   Минимальная стоимость подъема на 3-ю ступень </p> <p>Пусть \\(dp[i]\\) обозначает накопленную стоимость подъема на ступень \\(i\\) . Поскольку на ступень \\(i\\) можно прийти только со ступени \\(i - 1\\) или со ступени \\(i - 2\\) , значение \\(dp[i]\\) может быть либо \\(dp[i - 1] + cost[i]\\) , либо \\(dp[i - 2] + cost[i]\\) . Чтобы минимизировать стоимость, нужно выбрать меньший из этих двух вариантов:</p> \\[ dp[i] = \\min(dp[i-1], dp[i-2]) + cost[i] \\] <p>Отсюда и возникает смысл оптимальной подструктуры: оптимальное решение исходной задачи строится из оптимальных решений подзадач.</p> <p>Очевидно, что эта задача обладает оптимальной подструктурой: мы берем лучшее из двух оптимальных решений подзадач \\(dp[i-1]\\) и \\(dp[i-2]\\) и на его основе строим оптимальное решение исходной задачи \\(dp[i]\\) .</p> <p>А обладает ли оптимальной подструктурой исходная задача о числе способов подъема по лестнице из прошлого раздела? Формально она не про оптимум, а про подсчет количества. Но если переформулировать ее как \"найдите максимальное количество способов\", мы неожиданно увидим, что хотя исходная задача осталась по сути той же, оптимальная подструктура стала явной: максимальное число способов добраться до ступени \\(n\\) равно сумме максимальных чисел способов добраться до ступеней \\(n-1\\) и \\(n-2\\) . То есть объяснение оптимальной подструктуры в разных задачах может быть довольно гибким.</p> <p>Зная уравнение перехода состояния, а также начальные состояния \\(dp[1] = cost[1]\\) и \\(dp[2] = cost[2]\\) , мы можем сразу написать код динамического программирования:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby min_cost_climbing_stairs_dp.py<pre><code>def min_cost_climbing_stairs_dp(cost: list[int]) -&gt; int:\n    \"\"\"Минимальная стоимость подъема по лестнице: динамическое программирование\"\"\"\n    n = len(cost) - 1\n    if n == 1 or n == 2:\n        return cost[n]\n    # Инициализация таблицы dp для хранения решений подзадач\n    dp = [0] * (n + 1)\n    # Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1], dp[2] = cost[1], cost[2]\n    # Переход состояний: постепенное решение больших подзадач через меньшие\n    for i in range(3, n + 1):\n        dp[i] = min(dp[i - 1], dp[i - 2]) + cost[i]\n    return dp[n]\n</code></pre> min_cost_climbing_stairs_dp.cpp<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование */\nint minCostClimbingStairsDP(vector&lt;int&gt; &amp;cost) {\n    int n = cost.size() - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    // Инициализация таблицы dp для хранения решений подзадач\n    vector&lt;int&gt; dp(n + 1);\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = cost[1];\n    dp[2] = cost[2];\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = min(dp[i - 1], dp[i - 2]) + cost[i];\n    }\n    return dp[n];\n}\n</code></pre> min_cost_climbing_stairs_dp.java<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование */\nint minCostClimbingStairsDP(int[] cost) {\n    int n = cost.length - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    // Инициализация таблицы dp для хранения решений подзадач\n    int[] dp = new int[n + 1];\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = cost[1];\n    dp[2] = cost[2];\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = Math.min(dp[i - 1], dp[i - 2]) + cost[i];\n    }\n    return dp[n];\n}\n</code></pre> min_cost_climbing_stairs_dp.cs<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование */\nint MinCostClimbingStairsDP(int[] cost) {\n    int n = cost.Length - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    // Инициализация таблицы dp для хранения решений подзадач\n    int[] dp = new int[n + 1];\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = cost[1];\n    dp[2] = cost[2];\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = Math.Min(dp[i - 1], dp[i - 2]) + cost[i];\n    }\n    return dp[n];\n}\n</code></pre> min_cost_climbing_stairs_dp.go<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование */\nfunc minCostClimbingStairsDP(cost []int) int {\n    n := len(cost) - 1\n    if n == 1 || n == 2 {\n        return cost[n]\n    }\n    min := func(a, b int) int {\n        if a &lt; b {\n            return a\n        }\n        return b\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    dp := make([]int, n+1)\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = cost[1]\n    dp[2] = cost[2]\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for i := 3; i &lt;= n; i++ {\n        dp[i] = min(dp[i-1], dp[i-2]) + cost[i]\n    }\n    return dp[n]\n}\n</code></pre> min_cost_climbing_stairs_dp.swift<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование */\nfunc minCostClimbingStairsDP(cost: [Int]) -&gt; Int {\n    let n = cost.count - 1\n    if n == 1 || n == 2 {\n        return cost[n]\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    var dp = Array(repeating: 0, count: n + 1)\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = cost[1]\n    dp[2] = cost[2]\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for i in 3 ... n {\n        dp[i] = min(dp[i - 1], dp[i - 2]) + cost[i]\n    }\n    return dp[n]\n}\n</code></pre> min_cost_climbing_stairs_dp.js<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование */\nfunction minCostClimbingStairsDP(cost) {\n    const n = cost.length - 1;\n    if (n === 1 || n === 2) {\n        return cost[n];\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    const dp = new Array(n + 1);\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = cost[1];\n    dp[2] = cost[2];\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (let i = 3; i &lt;= n; i++) {\n        dp[i] = Math.min(dp[i - 1], dp[i - 2]) + cost[i];\n    }\n    return dp[n];\n}\n</code></pre> min_cost_climbing_stairs_dp.ts<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование */\nfunction minCostClimbingStairsDP(cost: Array&lt;number&gt;): number {\n    const n = cost.length - 1;\n    if (n === 1 || n === 2) {\n        return cost[n];\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    const dp = new Array(n + 1);\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = cost[1];\n    dp[2] = cost[2];\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (let i = 3; i &lt;= n; i++) {\n        dp[i] = Math.min(dp[i - 1], dp[i - 2]) + cost[i];\n    }\n    return dp[n];\n}\n</code></pre> min_cost_climbing_stairs_dp.dart<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование */\nint minCostClimbingStairsDP(List&lt;int&gt; cost) {\n  int n = cost.length - 1;\n  if (n == 1 || n == 2) return cost[n];\n  // Инициализация таблицы dp для хранения решений подзадач\n  List&lt;int&gt; dp = List.filled(n + 1, 0);\n  // Начальное состояние: заранее задать решения наименьших подзадач\n  dp[1] = cost[1];\n  dp[2] = cost[2];\n  // Переход состояний: постепенное решение больших подзадач через меньшие\n  for (int i = 3; i &lt;= n; i++) {\n    dp[i] = min(dp[i - 1], dp[i - 2]) + cost[i];\n  }\n  return dp[n];\n}\n</code></pre> min_cost_climbing_stairs_dp.rs<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование */\nfn min_cost_climbing_stairs_dp(cost: &amp;[i32]) -&gt; i32 {\n    let n = cost.len() - 1;\n    if n == 1 || n == 2 {\n        return cost[n];\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    let mut dp = vec![-1; n + 1];\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = cost[1];\n    dp[2] = cost[2];\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for i in 3..=n {\n        dp[i] = cmp::min(dp[i - 1], dp[i - 2]) + cost[i];\n    }\n    dp[n]\n}\n</code></pre> min_cost_climbing_stairs_dp.c<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование */\nint minCostClimbingStairsDP(int cost[], int costSize) {\n    int n = costSize - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    // Инициализация таблицы dp для хранения решений подзадач\n    int *dp = calloc(n + 1, sizeof(int));\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = cost[1];\n    dp[2] = cost[2];\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = myMin(dp[i - 1], dp[i - 2]) + cost[i];\n    }\n    int res = dp[n];\n    // Освободить память\n    free(dp);\n    return res;\n}\n</code></pre> min_cost_climbing_stairs_dp.kt<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование */\nfun minCostClimbingStairsDP(cost: IntArray): Int {\n    val n = cost.size - 1\n    if (n == 1 || n == 2) return cost[n]\n    // Инициализация таблицы dp для хранения решений подзадач\n    val dp = IntArray(n + 1)\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = cost[1]\n    dp[2] = cost[2]\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (i in 3..n) {\n        dp[i] = min(dp[i - 1], dp[i - 2]) + cost[i]\n    }\n    return dp[n]\n}\n</code></pre> min_cost_climbing_stairs_dp.rb<pre><code>### Минимальная стоимость подъема по лестнице: динамическое программирование ###\ndef min_cost_climbing_stairs_dp(cost)\n  n = cost.length - 1\n  return cost[n] if n == 1 || n == 2\n  # Инициализация таблицы dp для хранения решений подзадач\n  dp = Array.new(n + 1, 0)\n  # Начальное состояние: заранее задать решения наименьших подзадач\n  dp[1], dp[2] = cost[1], cost[2]\n  # Переход состояний: постепенное решение больших подзадач через меньшие\n  (3...(n + 1)).each { |i| dp[i] = [dp[i - 1], dp[i - 2]].min + cost[i] }\n  dp[n]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>На рисунке 14-7 показан процесс динамического программирования для этой задачи.</p> <p></p> <p> Рисунок 14-7   Процесс динамического программирования для минимальной стоимости подъема </p> <p>В этой задаче тоже можно оптимизировать пространство, сжав одномерное состояние в нулевое измерение и тем самым уменьшив пространственную сложность с \\(O(n)\\) до \\(O(1)\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby min_cost_climbing_stairs_dp.py<pre><code>def min_cost_climbing_stairs_dp_comp(cost: list[int]) -&gt; int:\n    \"\"\"Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти\"\"\"\n    n = len(cost) - 1\n    if n == 1 or n == 2:\n        return cost[n]\n    a, b = cost[1], cost[2]\n    for i in range(3, n + 1):\n        a, b = b, min(a, b) + cost[i]\n    return b\n</code></pre> min_cost_climbing_stairs_dp.cpp<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти */\nint minCostClimbingStairsDPComp(vector&lt;int&gt; &amp;cost) {\n    int n = cost.size() - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    int a = cost[1], b = cost[2];\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = min(a, tmp) + cost[i];\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> min_cost_climbing_stairs_dp.java<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти */\nint minCostClimbingStairsDPComp(int[] cost) {\n    int n = cost.length - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    int a = cost[1], b = cost[2];\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = Math.min(a, tmp) + cost[i];\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> min_cost_climbing_stairs_dp.cs<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти */\nint MinCostClimbingStairsDPComp(int[] cost) {\n    int n = cost.Length - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    int a = cost[1], b = cost[2];\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = Math.Min(a, tmp) + cost[i];\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> min_cost_climbing_stairs_dp.go<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти */\nfunc minCostClimbingStairsDPComp(cost []int) int {\n    n := len(cost) - 1\n    if n == 1 || n == 2 {\n        return cost[n]\n    }\n    min := func(a, b int) int {\n        if a &lt; b {\n            return a\n        }\n        return b\n    }\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    a, b := cost[1], cost[2]\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for i := 3; i &lt;= n; i++ {\n        tmp := b\n        b = min(a, tmp) + cost[i]\n        a = tmp\n    }\n    return b\n}\n</code></pre> min_cost_climbing_stairs_dp.swift<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти */\nfunc minCostClimbingStairsDPComp(cost: [Int]) -&gt; Int {\n    let n = cost.count - 1\n    if n == 1 || n == 2 {\n        return cost[n]\n    }\n    var (a, b) = (cost[1], cost[2])\n    for i in 3 ... n {\n        (a, b) = (b, min(a, b) + cost[i])\n    }\n    return b\n}\n</code></pre> min_cost_climbing_stairs_dp.js<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти */\nfunction minCostClimbingStairsDPComp(cost) {\n    const n = cost.length - 1;\n    if (n === 1 || n === 2) {\n        return cost[n];\n    }\n    let a = cost[1],\n        b = cost[2];\n    for (let i = 3; i &lt;= n; i++) {\n        const tmp = b;\n        b = Math.min(a, tmp) + cost[i];\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> min_cost_climbing_stairs_dp.ts<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти */\nfunction minCostClimbingStairsDPComp(cost: Array&lt;number&gt;): number {\n    const n = cost.length - 1;\n    if (n === 1 || n === 2) {\n        return cost[n];\n    }\n    let a = cost[1],\n        b = cost[2];\n    for (let i = 3; i &lt;= n; i++) {\n        const tmp = b;\n        b = Math.min(a, tmp) + cost[i];\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> min_cost_climbing_stairs_dp.dart<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти */\nint minCostClimbingStairsDPComp(List&lt;int&gt; cost) {\n  int n = cost.length - 1;\n  if (n == 1 || n == 2) return cost[n];\n  int a = cost[1], b = cost[2];\n  for (int i = 3; i &lt;= n; i++) {\n    int tmp = b;\n    b = min(a, tmp) + cost[i];\n    a = tmp;\n  }\n  return b;\n}\n</code></pre> min_cost_climbing_stairs_dp.rs<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти */\nfn min_cost_climbing_stairs_dp_comp(cost: &amp;[i32]) -&gt; i32 {\n    let n = cost.len() - 1;\n    if n == 1 || n == 2 {\n        return cost[n];\n    };\n    let (mut a, mut b) = (cost[1], cost[2]);\n    for i in 3..=n {\n        let tmp = b;\n        b = cmp::min(a, tmp) + cost[i];\n        a = tmp;\n    }\n    b\n}\n</code></pre> min_cost_climbing_stairs_dp.c<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти */\nint minCostClimbingStairsDPComp(int cost[], int costSize) {\n    int n = costSize - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    int a = cost[1], b = cost[2];\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = myMin(a, tmp) + cost[i];\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> min_cost_climbing_stairs_dp.kt<pre><code>/* Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти */\nfun minCostClimbingStairsDPComp(cost: IntArray): Int {\n    val n = cost.size - 1\n    if (n == 1 || n == 2) return cost[n]\n    var a = cost[1]\n    var b = cost[2]\n    for (i in 3..n) {\n        val tmp = b\n        b = min(a, tmp) + cost[i]\n        a = tmp\n    }\n    return b\n}\n</code></pre> min_cost_climbing_stairs_dp.rb<pre><code>### Минимальная стоимость подъема по лестнице: динамическое программирование ###\ndef min_cost_climbing_stairs_dp(cost)\n  n = cost.length - 1\n  return cost[n] if n == 1 || n == 2\n  # Инициализация таблицы dp для хранения решений подзадач\n  dp = Array.new(n + 1, 0)\n  # Начальное состояние: заранее задать решения наименьших подзадач\n  dp[1], dp[2] = cost[1], cost[2]\n  # Переход состояний: постепенное решение больших подзадач через меньшие\n  (3...(n + 1)).each { |i| dp[i] = [dp[i - 1], dp[i - 2]].min + cost[i] }\n  dp[n]\nend\n\n# Минимальная стоимость подъема по лестнице: динамическое программирование с оптимизацией памяти\ndef min_cost_climbing_stairs_dp_comp(cost)\n  n = cost.length - 1\n  return cost[n] if n == 1 || n == 2\n  a, b = cost[1], cost[2]\n  (3...(n + 1)).each { |i| a, b = b, [a, b].min + cost[i] }\n  b\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 14. Динамическое программирование","14.2 &nbsp; Свойства задач динамического программирования"],"tags":[]},{"location":"chapter_dynamic_programming/dp_problem_features/#1422","level":2,"title":"14.2.2   Отсутствие последствий","text":"<p>Отсутствие последствий - одно из ключевых свойств, благодаря которому динамическое программирование вообще может эффективно работать. Его определение таково: если текущее состояние задано однозначно, то его дальнейшее развитие зависит только от него самого и не зависит от всей истории предыдущих состояний.</p> <p>Для примера снова рассмотрим задачу о лестнице. Если дано состояние \\(i\\) , то из него можно перейти в состояния \\(i+1\\) и \\(i+2\\) , соответствующие прыжкам на \\(1\\) и на \\(2\\) ступени. Чтобы сделать один из этих выборов, не нужно знать, какими были состояния до \\(i\\) ; на будущее влияет только текущее состояние \\(i\\) .</p> <p>Однако если добавить в задачу дополнительное ограничение, ситуация изменится.</p> <p>Подъем по лестнице с ограничением</p> <p>Дана лестница из \\(n\\) ступеней. За один шаг можно подняться на \\(1\\) или на \\(2\\) ступени, но нельзя два раунда подряд прыгать на \\(1\\) ступень. Сколькими способами можно добраться до вершины?</p> <p>Как показано на рисунке 14-8, на третью ступень теперь существует только \\(2\\) допустимых способа добраться: вариант с тремя последовательными прыжками на \\(1\\) не удовлетворяет ограничению и потому отбрасывается.</p> <p></p> <p> Рисунок 14-8   Число способов подняться на 3-ю ступень при наличии ограничения </p> <p>В этой задаче, если в предыдущем раунде был сделан прыжок на \\(1\\) ступень, то в следующем раунде уже обязательно нужно прыгнуть на \\(2\\) ступени. Иными словами, следующий выбор уже нельзя определить только по текущему состоянию (текущему номеру ступени) - он зависит еще и от предыдущего состояния (с какой ступени мы пришли в прошлый раз).</p> <p>Нетрудно заметить, что в таком виде задача больше не удовлетворяет свойству отсутствия последствий, а уравнение перехода состояния \\(dp[i] = dp[i-1] + dp[i-2]\\) перестает работать, потому что \\(dp[i-1]\\) соответствует прыжку на \\(1\\) ступень, но при этом включает множество вариантов, где предыдущий раунд тоже был прыжком на \\(1\\) ступень. Такие варианты уже нельзя напрямую учитывать в \\(dp[i]\\) , если мы хотим соблюдать ограничение.</p> <p>Поэтому нам нужно расширить определение состояния: состояние \\([i, j]\\) означает, что мы находимся на ступени \\(i\\) и в предыдущем раунде прыгнули на \\(j\\) ступеней, где \\(j \\in \\{1, 2\\}\\) . Такое определение состояния эффективно различает, был ли в прошлом раунде прыжок на \\(1\\) или на \\(2\\) ступени, и позволяет корректно определить, откуда произошло текущее состояние.</p> <ul> <li>Если в предыдущем раунде был прыжок на \\(1\\) ступень, то в раунде перед ним мог быть только прыжок на \\(2\\) ступени, то есть \\(dp[i, 1]\\) может перейти только из \\(dp[i-1, 2]\\) .</li> <li>Если в предыдущем раунде был прыжок на \\(2\\) ступени, то еще шагом раньше можно было прыгнуть либо на \\(1\\) , либо на \\(2\\) ступени, то есть \\(dp[i, 2]\\) может переходить из \\(dp[i-2, 1]\\) или из \\(dp[i-2, 2]\\) .</li> </ul> <p>Как показано на рисунке 14-9, при таком определении \\(dp[i, j]\\) обозначает число способов для состояния \\([i, j]\\) . Тогда уравнение перехода состояния имеет вид:</p> \\[ \\begin{cases} dp[i, 1] = dp[i-1, 2] \\\\ dp[i, 2] = dp[i-2, 1] + dp[i-2, 2] \\end{cases} \\] <p></p> <p> Рисунок 14-9   Рекуррентная связь с учетом ограничения </p> <p>В конце достаточно вернуть \\(dp[n, 1] + dp[n, 2]\\) ; эта сумма и представляет общее число способов добраться до ступени \\(n\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby climbing_stairs_constraint_dp.py<pre><code>def climbing_stairs_constraint_dp(n: int) -&gt; int:\n    \"\"\"Подъем по лестнице с ограничениями: динамическое программирование\"\"\"\n    if n == 1 or n == 2:\n        return 1\n    # Инициализация таблицы dp для хранения решений подзадач\n    dp = [[0] * 3 for _ in range(n + 1)]\n    # Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1][1], dp[1][2] = 1, 0\n    dp[2][1], dp[2][2] = 0, 1\n    # Переход состояний: постепенное решение больших подзадач через меньшие\n    for i in range(3, n + 1):\n        dp[i][1] = dp[i - 1][2]\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2]\n    return dp[n][1] + dp[n][2]\n</code></pre> climbing_stairs_constraint_dp.cpp<pre><code>/* Подъем по лестнице с ограничениями: динамическое программирование */\nint climbingStairsConstraintDP(int n) {\n    if (n == 1 || n == 2) {\n        return 1;\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(3, 0));\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1][1] = 1;\n    dp[1][2] = 0;\n    dp[2][1] = 0;\n    dp[2][2] = 1;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i][1] = dp[i - 1][2];\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2];\n    }\n    return dp[n][1] + dp[n][2];\n}\n</code></pre> climbing_stairs_constraint_dp.java<pre><code>/* Подъем по лестнице с ограничениями: динамическое программирование */\nint climbingStairsConstraintDP(int n) {\n    if (n == 1 || n == 2) {\n        return 1;\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    int[][] dp = new int[n + 1][3];\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1][1] = 1;\n    dp[1][2] = 0;\n    dp[2][1] = 0;\n    dp[2][2] = 1;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i][1] = dp[i - 1][2];\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2];\n    }\n    return dp[n][1] + dp[n][2];\n}\n</code></pre> climbing_stairs_constraint_dp.cs<pre><code>/* Подъем по лестнице с ограничениями: динамическое программирование */\nint ClimbingStairsConstraintDP(int n) {\n    if (n == 1 || n == 2) {\n        return 1;\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    int[,] dp = new int[n + 1, 3];\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1, 1] = 1;\n    dp[1, 2] = 0;\n    dp[2, 1] = 0;\n    dp[2, 2] = 1;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i, 1] = dp[i - 1, 2];\n        dp[i, 2] = dp[i - 2, 1] + dp[i - 2, 2];\n    }\n    return dp[n, 1] + dp[n, 2];\n}\n</code></pre> climbing_stairs_constraint_dp.go<pre><code>/* Подъем по лестнице с ограничениями: динамическое программирование */\nfunc climbingStairsConstraintDP(n int) int {\n    if n == 1 || n == 2 {\n        return 1\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    dp := make([][3]int, n+1)\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1][1] = 1\n    dp[1][2] = 0\n    dp[2][1] = 0\n    dp[2][2] = 1\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for i := 3; i &lt;= n; i++ {\n        dp[i][1] = dp[i-1][2]\n        dp[i][2] = dp[i-2][1] + dp[i-2][2]\n    }\n    return dp[n][1] + dp[n][2]\n}\n</code></pre> climbing_stairs_constraint_dp.swift<pre><code>/* Подъем по лестнице с ограничениями: динамическое программирование */\nfunc climbingStairsConstraintDP(n: Int) -&gt; Int {\n    if n == 1 || n == 2 {\n        return 1\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    var dp = Array(repeating: Array(repeating: 0, count: 3), count: n + 1)\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1][1] = 1\n    dp[1][2] = 0\n    dp[2][1] = 0\n    dp[2][2] = 1\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for i in 3 ... n {\n        dp[i][1] = dp[i - 1][2]\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2]\n    }\n    return dp[n][1] + dp[n][2]\n}\n</code></pre> climbing_stairs_constraint_dp.js<pre><code>/* Подъем по лестнице с ограничениями: динамическое программирование */\nfunction climbingStairsConstraintDP(n) {\n    if (n === 1 || n === 2) {\n        return 1;\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    const dp = Array.from(new Array(n + 1), () =&gt; new Array(3));\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1][1] = 1;\n    dp[1][2] = 0;\n    dp[2][1] = 0;\n    dp[2][2] = 1;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (let i = 3; i &lt;= n; i++) {\n        dp[i][1] = dp[i - 1][2];\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2];\n    }\n    return dp[n][1] + dp[n][2];\n}\n</code></pre> climbing_stairs_constraint_dp.ts<pre><code>/* Подъем по лестнице с ограничениями: динамическое программирование */\nfunction climbingStairsConstraintDP(n: number): number {\n    if (n === 1 || n === 2) {\n        return 1;\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    const dp = Array.from({ length: n + 1 }, () =&gt; new Array(3));\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1][1] = 1;\n    dp[1][2] = 0;\n    dp[2][1] = 0;\n    dp[2][2] = 1;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (let i = 3; i &lt;= n; i++) {\n        dp[i][1] = dp[i - 1][2];\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2];\n    }\n    return dp[n][1] + dp[n][2];\n}\n</code></pre> climbing_stairs_constraint_dp.dart<pre><code>/* Подъем по лестнице с ограничениями: динамическое программирование */\nint climbingStairsConstraintDP(int n) {\n  if (n == 1 || n == 2) {\n    return 1;\n  }\n  // Инициализация таблицы dp для хранения решений подзадач\n  List&lt;List&lt;int&gt;&gt; dp = List.generate(n + 1, (index) =&gt; List.filled(3, 0));\n  // Начальное состояние: заранее задать решения наименьших подзадач\n  dp[1][1] = 1;\n  dp[1][2] = 0;\n  dp[2][1] = 0;\n  dp[2][2] = 1;\n  // Переход состояний: постепенное решение больших подзадач через меньшие\n  for (int i = 3; i &lt;= n; i++) {\n    dp[i][1] = dp[i - 1][2];\n    dp[i][2] = dp[i - 2][1] + dp[i - 2][2];\n  }\n  return dp[n][1] + dp[n][2];\n}\n</code></pre> climbing_stairs_constraint_dp.rs<pre><code>/* Подъем по лестнице с ограничениями: динамическое программирование */\nfn climbing_stairs_constraint_dp(n: usize) -&gt; i32 {\n    if n == 1 || n == 2 {\n        return 1;\n    };\n    // Инициализация таблицы dp для хранения решений подзадач\n    let mut dp = vec![vec![-1; 3]; n + 1];\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1][1] = 1;\n    dp[1][2] = 0;\n    dp[2][1] = 0;\n    dp[2][2] = 1;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for i in 3..=n {\n        dp[i][1] = dp[i - 1][2];\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2];\n    }\n    dp[n][1] + dp[n][2]\n}\n</code></pre> climbing_stairs_constraint_dp.c<pre><code>/* Подъем по лестнице с ограничениями: динамическое программирование */\nint climbingStairsConstraintDP(int n) {\n    if (n == 1 || n == 2) {\n        return 1;\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    int **dp = malloc((n + 1) * sizeof(int *));\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i] = calloc(3, sizeof(int));\n    }\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1][1] = 1;\n    dp[1][2] = 0;\n    dp[2][1] = 0;\n    dp[2][2] = 1;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i][1] = dp[i - 1][2];\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2];\n    }\n    int res = dp[n][1] + dp[n][2];\n    // Освободить память\n    for (int i = 0; i &lt;= n; i++) {\n        free(dp[i]);\n    }\n    free(dp);\n    return res;\n}\n</code></pre> climbing_stairs_constraint_dp.kt<pre><code>/* Подъем по лестнице с ограничениями: динамическое программирование */\nfun climbingStairsConstraintDP(n: Int): Int {\n    if (n == 1 || n == 2) {\n        return 1\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    val dp = Array(n + 1) { IntArray(3) }\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1][1] = 1\n    dp[1][2] = 0\n    dp[2][1] = 0\n    dp[2][2] = 1\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (i in 3..n) {\n        dp[i][1] = dp[i - 1][2]\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2]\n    }\n    return dp[n][1] + dp[n][2]\n}\n</code></pre> climbing_stairs_constraint_dp.rb<pre><code>### Подъем по лестнице с ограничениями: динамическое программирование ###\ndef climbing_stairs_constraint_dp(n)\n  return 1 if n == 1 || n == 2\n\n  # Инициализация таблицы dp для хранения решений подзадач\n  dp = Array.new(n + 1) { Array.new(3, 0) }\n  # Начальное состояние: заранее задать решения наименьших подзадач\n  dp[1][1], dp[1][2] = 1, 0\n  dp[2][1], dp[2][2] = 0, 1\n  # Переход состояний: постепенное решение больших подзадач через меньшие\n  for i in 3...(n + 1)\n    dp[i][1] = dp[i - 1][2]\n    dp[i][2] = dp[i - 2][1] + dp[i - 2][2]\n  end\n\n  dp[n][1] + dp[n][2]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>В этом примере достаточно дополнительно учитывать только одно предыдущее состояние, поэтому после расширения определения состояния задача снова начинает удовлетворять свойству отсутствия последствий. Однако в некоторых задачах \"зависимость от прошлого\" бывает гораздо серьезнее.</p> <p>Подъем по лестнице с порождением препятствий</p> <p>Дана лестница из \\(n\\) ступеней. За один шаг можно подняться на \\(1\\) или на \\(2\\) ступени. При этом, если вы попали на ступень \\(i\\) , система автоматически создает препятствие на ступени \\(2i\\) , и на всех последующих шагах становиться на ступень \\(2i\\) уже нельзя. Например, если в первых двух раундах вы попали на ступени \\(2\\) и \\(3\\) , то после этого нельзя будет попадать на ступени \\(4\\) и \\(6\\) . Сколько существует способов добраться до вершины?</p> <p>В этой задаче следующий прыжок зависит от всех предыдущих состояний, потому что каждый прыжок порождает новое препятствие на более высокой ступени и тем самым влияет на все будущие прыжки. Для задач такого типа динамическое программирование обычно оказывается непригодным.</p> <p>Вообще, многие сложные задачи комбинаторной оптимизации (например, задача коммивояжера) не обладают свойством отсутствия последствий. Для таких задач обычно выбирают другие методы - например, эвристический поиск, генетические алгоритмы, обучение с подкреплением и т.д., - чтобы за ограниченное время получить пригодное локально оптимальное решение.</p>","path":["Глава 14. Динамическое программирование","14.2 &nbsp; Свойства задач динамического программирования"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/","level":1,"title":"14.3   Подход к решению задач динамического программирования","text":"<p>В двух предыдущих разделах были рассмотрены основные свойства задач динамического программирования. Теперь исследуем два более практических вопроса.</p> <ol> <li>Как определить, является ли некоторая задача задачей динамического программирования?</li> <li>С чего начинать решение такой задачи и как выглядит полный процесс решения?</li> </ol>","path":["Глава 14. Динамическое программирование","14.3 &nbsp; Подход к решению задач динамического программирования"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#1431","level":2,"title":"14.3.1   Определение задачи","text":"<p>В целом, если задача содержит перекрывающиеся подзадачи, оптимальную подструктуру и удовлетворяет свойству отсутствия последствий, то она обычно подходит для решения с помощью динамического программирования. Однако извлечь все эти свойства напрямую из формулировки задачи бывает трудно. Поэтому на практике мы обычно ослабляем требования и сначала смотрим, подходит ли задача для решения методом поиска с возвратом (полного перебора).</p> <p>Задачи, подходящие для поиска с возвратом, обычно удовлетворяют \"модели дерева решений\". Такие задачи можно описать деревом, где каждый узел представляет одно решение, а каждый путь представляет последовательность решений.</p> <p>Иначе говоря, если в задаче есть четко выраженные решения и ответ порождается последовательностью таких решений, то она удовлетворяет модели дерева решений и обычно допускает решение через поиск с возвратом.</p> <p>Поверх этого у задач динамического программирования есть и некоторые дополнительные \"плюсы\".</p> <ul> <li>В условии задачи фигурируют слова \"максимальный\", \"минимальный\", \"наибольший\", \"наименьший\" и другие формулировки оптимизации.</li> <li>Состояния задачи можно описать списком, многомерной матрицей или деревом, и между состоянием и соседними состояниями существует рекуррентная зависимость.</li> </ul> <p>Соответственно, существуют и некоторые \"минусы\".</p> <ul> <li>Цель задачи состоит в поиске всех возможных решений, а не одного оптимального решения.</li> <li>В формулировке явно присутствуют признаки комбинаторного перечисления, и требуется вернуть сразу много конкретных вариантов.</li> </ul> <p>Если задача удовлетворяет модели дерева решений и имеет достаточно явные \"плюсы\", мы можем предположить, что это задача динамического программирования, а затем проверить это предположение уже в процессе решения.</p>","path":["Глава 14. Динамическое программирование","14.3 &nbsp; Подход к решению задач динамического программирования"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#1432","level":2,"title":"14.3.2   Этапы решения задачи","text":"<p>Конкретный процесс решения задач динамического программирования зависит от природы и сложности задачи, но обычно включает следующие шаги: описание решений, определение состояний, построение таблицы \\(dp\\) , вывод уравнения перехода состояния, определение граничных условий и порядка переходов.</p> <p>Чтобы нагляднее показать этот процесс, рассмотрим классическую задачу \"минимальная сумма пути\".</p> <p>Question</p> <p>Дана двумерная сетка <code>grid</code> размера \\(n \\times m\\) , в каждой клетке которой записано неотрицательное целое число, означающее стоимость прохождения через эту клетку. Робот стартует из левой верхней клетки и за один шаг может двигаться только вправо или вниз, пока не достигнет правой нижней клетки. Верните минимальную сумму пути от левой верхней клетки до правой нижней.</p> <p>На рисунке 14-10 показан пример, в котором минимальная сумма пути равна \\(13\\) .</p> <p></p> <p> Рисунок 14-10   Пример данных для задачи о минимальной сумме пути </p> <p>Шаг 1: понять решения на каждом раунде, определить состояние и тем самым получить таблицу \\(dp\\)</p> <p>В этой задаче на каждом раунде решение состоит в том, чтобы из текущей клетки сделать один шаг вниз или вправо. Пусть индексы строки и столбца текущей клетки равны \\([i, j]\\) ; тогда после шага вниз или вправо индексы становятся равными \\([i+1, j]\\) или \\([i, j+1]\\) . Значит, состояние должно включать два переменных индекса: строки и столбца, то есть состояние обозначается как \\([i, j]\\) .</p> <p>Подзадача, соответствующая состоянию \\([i, j]\\) , такова: минимальная сумма пути от стартовой клетки \\([0, 0]\\) до клетки \\([i, j]\\) . Ее решение обозначается через \\(dp[i, j]\\) .</p> <p>На этом этапе мы получаем двумерную матрицу \\(dp\\) , показанную на рисунке 14-11, размер которой совпадает с размером входной сетки <code>grid</code> .</p> <p></p> <p> Рисунок 14-11   Определение состояния и таблицы dp </p> <p>Note</p> <p>Как в динамическом программировании, так и в поиске с возвратом, решение задачи можно описать как последовательность решений, а состояние образуется всеми переменными решений. Оно должно содержать всю информацию, достаточную для вывода следующего состояния.</p> <p>Каждому состоянию соответствует некоторая подзадача, и для хранения решений всех подзадач мы определяем таблицу \\(dp\\) ; каждая независимая переменная состояния становится одним измерением таблицы \\(dp\\) . По сути таблица \\(dp\\) - это отображение от состояния к решению соответствующей подзадачи.</p> <p>Шаг 2: найти оптимальную подструктуру и на ее основе вывести уравнение перехода состояния</p> <p>Для состояния \\([i, j]\\) возможны только два источника: клетка сверху \\([i-1, j]\\) и клетка слева \\([i, j-1]\\) . Следовательно, оптимальная подструктура выглядит так: минимальная сумма пути до \\([i, j]\\) определяется меньшим из двух значений - минимальной суммы пути до \\([i-1, j]\\) и минимальной суммы пути до \\([i, j-1]\\) .</p> <p>По этому рассуждению получается уравнение перехода состояния, показанное на рисунке 14-12:</p> \\[ dp[i, j] = \\min(dp[i-1, j], dp[i, j-1]) + grid[i, j] \\] <p></p> <p> Рисунок 14-12   Оптимальная подструктура и уравнение перехода состояния </p> <p>Note</p> <p>Опираясь на уже определенную таблицу \\(dp\\) , нужно продумать отношение между исходной задачей и подзадачами и найти способ построить оптимальное решение исходной задачи из оптимальных решений подзадач, то есть найти оптимальную подструктуру.</p> <p>Как только оптимальная подструктура найдена, на ее основе можно построить уравнение перехода состояния.</p> <p>Шаг 3: определить граничные условия и порядок переходов</p> <p>В этой задаче состояния в первой строке могут переходить только из клетки слева, а состояния в первом столбце - только из клетки сверху, поэтому первая строка \\(i = 0\\) и первый столбец \\(j = 0\\) образуют граничные условия.</p> <p>Как показано на рисунке 14-13, поскольку каждая клетка получается из клетки слева и клетки сверху, мы можем проходить матрицу циклами: внешний цикл по строкам, внутренний - по столбцам.</p> <p></p> <p> Рисунок 14-13   Граничные условия и порядок перехода состояний </p> <p>Note</p> <p>В динамическом программировании граничные условия используются для инициализации таблицы \\(dp\\) , а в поиске - для обрезки.</p> <p>Смысл порядка перехода состояния в том, чтобы к моменту вычисления текущей подзадачи все более мелкие подзадачи, от которых она зависит, уже были вычислены корректно.</p> <p>После этого анализа мы уже можем напрямую написать код динамического программирования. Однако разложение на подзадачи - это мышление \"сверху вниз\", поэтому с точки зрения мышления более естественно реализовывать задачу в порядке \"полный перебор \\(\\rightarrow\\) поиск с мемоизацией \\(\\rightarrow\\) динамическое программирование\".</p>","path":["Глава 14. Динамическое программирование","14.3 &nbsp; Подход к решению задач динамического программирования"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#1-1","level":3,"title":"1.   Метод 1: полный перебор","text":"<p>Начав со состояния \\([i, j]\\) , мы непрерывно раскладываем его на меньшие состояния \\([i-1, j]\\) и \\([i, j-1]\\) . Рекурсивная функция при этом имеет следующие элементы.</p> <ul> <li>Параметры рекурсии: состояние \\([i, j]\\) .</li> <li>Возвращаемое значение: минимальная сумма пути до \\([i, j]\\) , то есть \\(dp[i, j]\\) .</li> <li>Условие завершения: когда \\(i = 0\\) и \\(j = 0\\) , возвращается стоимость \\(grid[0, 0]\\) .</li> <li>Обрезка: если \\(i &lt; 0\\) или \\(j &lt; 0\\) , индекс выходит за границы, и в этом случае возвращается стоимость \\(+\\infty\\) , обозначающая невозможность.</li> </ul> <p>Код реализации:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby min_path_sum.py<pre><code>def min_path_sum_dfs(grid: list[list[int]], i: int, j: int) -&gt; int:\n    \"\"\"Минимальная сумма пути: полный перебор\"\"\"\n    # Если это верхняя левая ячейка, завершить поиск\n    if i == 0 and j == 0:\n        return grid[0][0]\n    # Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if i &lt; 0 or j &lt; 0:\n        return inf\n    # Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n    up = min_path_sum_dfs(grid, i - 1, j)\n    left = min_path_sum_dfs(grid, i, j - 1)\n    # Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    return min(left, up) + grid[i][j]\n</code></pre> min_path_sum.cpp<pre><code>/* Минимальная сумма пути: полный перебор */\nint minPathSumDFS(vector&lt;vector&lt;int&gt;&gt; &amp;grid, int i, int j) {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return INT_MAX;\n    }\n    // Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n    int up = minPathSumDFS(grid, i - 1, j);\n    int left = minPathSumDFS(grid, i, j - 1);\n    // Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    return min(left, up) != INT_MAX ? min(left, up) + grid[i][j] : INT_MAX;\n}\n</code></pre> min_path_sum.java<pre><code>/* Минимальная сумма пути: полный перебор */\nint minPathSumDFS(int[][] grid, int i, int j) {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return Integer.MAX_VALUE;\n    }\n    // Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n    int up = minPathSumDFS(grid, i - 1, j);\n    int left = minPathSumDFS(grid, i, j - 1);\n    // Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    return Math.min(left, up) + grid[i][j];\n}\n</code></pre> min_path_sum.cs<pre><code>/* Минимальная сумма пути: полный перебор */\nint MinPathSumDFS(int[][] grid, int i, int j) {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return int.MaxValue;\n    }\n    // Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n    int up = MinPathSumDFS(grid, i - 1, j);\n    int left = MinPathSumDFS(grid, i, j - 1);\n    // Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    return Math.Min(left, up) + grid[i][j];\n}\n</code></pre> min_path_sum.go<pre><code>/* Минимальная сумма пути: полный перебор */\nfunc minPathSumDFS(grid [][]int, i, j int) int {\n    // Если это верхняя левая ячейка, завершить поиск\n    if i == 0 &amp;&amp; j == 0 {\n        return grid[0][0]\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if i &lt; 0 || j &lt; 0 {\n        return math.MaxInt\n    }\n    // Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n    up := minPathSumDFS(grid, i-1, j)\n    left := minPathSumDFS(grid, i, j-1)\n    // Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    return int(math.Min(float64(left), float64(up))) + grid[i][j]\n}\n</code></pre> min_path_sum.swift<pre><code>/* Минимальная сумма пути: полный перебор */\nfunc minPathSumDFS(grid: [[Int]], i: Int, j: Int) -&gt; Int {\n    // Если это верхняя левая ячейка, завершить поиск\n    if i == 0, j == 0 {\n        return grid[0][0]\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if i &lt; 0 || j &lt; 0 {\n        return .max\n    }\n    // Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n    let up = minPathSumDFS(grid: grid, i: i - 1, j: j)\n    let left = minPathSumDFS(grid: grid, i: i, j: j - 1)\n    // Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    return min(left, up) + grid[i][j]\n}\n</code></pre> min_path_sum.js<pre><code>/* Минимальная сумма пути: полный перебор */\nfunction minPathSumDFS(grid, i, j) {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i === 0 &amp;&amp; j === 0) {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return Infinity;\n    }\n    // Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n    const up = minPathSumDFS(grid, i - 1, j);\n    const left = minPathSumDFS(grid, i, j - 1);\n    // Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    return Math.min(left, up) + grid[i][j];\n}\n</code></pre> min_path_sum.ts<pre><code>/* Минимальная сумма пути: полный перебор */\nfunction minPathSumDFS(\n    grid: Array&lt;Array&lt;number&gt;&gt;,\n    i: number,\n    j: number\n): number {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i === 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return Infinity;\n    }\n    // Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n    const up = minPathSumDFS(grid, i - 1, j);\n    const left = minPathSumDFS(grid, i, j - 1);\n    // Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    return Math.min(left, up) + grid[i][j];\n}\n</code></pre> min_path_sum.dart<pre><code>/* Минимальная сумма пути: полный перебор */\nint minPathSumDFS(List&lt;List&lt;int&gt;&gt; grid, int i, int j) {\n  // Если это верхняя левая ячейка, завершить поиск\n  if (i == 0 &amp;&amp; j == 0) {\n    return grid[0][0];\n  }\n  // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n  if (i &lt; 0 || j &lt; 0) {\n    // В Dart тип int — целое число фиксированного диапазона; значения, представляющего «бесконечность», не существует\n    return BigInt.from(2).pow(31).toInt();\n  }\n  // Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n  int up = minPathSumDFS(grid, i - 1, j);\n  int left = minPathSumDFS(grid, i, j - 1);\n  // Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n  return min(left, up) + grid[i][j];\n}\n</code></pre> min_path_sum.rs<pre><code>/* Минимальная сумма пути: полный перебор */\nfn min_path_sum_dfs(grid: &amp;Vec&lt;Vec&lt;i32&gt;&gt;, i: i32, j: i32) -&gt; i32 {\n    // Если это верхняя левая ячейка, завершить поиск\n    if i == 0 &amp;&amp; j == 0 {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if i &lt; 0 || j &lt; 0 {\n        return i32::MAX;\n    }\n    // Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n    let up = min_path_sum_dfs(grid, i - 1, j);\n    let left = min_path_sum_dfs(grid, i, j - 1);\n    // Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    std::cmp::min(left, up) + grid[i as usize][j as usize]\n}\n</code></pre> min_path_sum.c<pre><code>/* Минимальная сумма пути: полный перебор */\nint minPathSumDFS(int grid[MAX_SIZE][MAX_SIZE], int i, int j) {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return INT_MAX;\n    }\n    // Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n    int up = minPathSumDFS(grid, i - 1, j);\n    int left = minPathSumDFS(grid, i, j - 1);\n    // Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    return myMin(left, up) != INT_MAX ? myMin(left, up) + grid[i][j] : INT_MAX;\n}\n</code></pre> min_path_sum.kt<pre><code>/* Минимальная сумма пути: полный перебор */\nfun minPathSumDFS(grid: Array&lt;IntArray&gt;, i: Int, j: Int): Int {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0]\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return Int.MAX_VALUE\n    }\n    // Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n    val up = minPathSumDFS(grid, i - 1, j)\n    val left = minPathSumDFS(grid, i, j - 1)\n    // Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    return min(left, up) + grid[i][j]\n}\n</code></pre> min_path_sum.rb<pre><code>### Минимальная сумма пути: полный перебор ###\ndef min_path_sum_dfs(grid, i, j)\n  # Если это верхняя левая ячейка, завершить поиск\n  return grid[i][j] if i == 0 &amp;&amp; j == 0\n  # Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n  return Float::INFINITY if i &lt; 0 || j &lt; 0\n  # Вычислить минимальную стоимость пути из левого верхнего угла до (i-1, j) и (i, j-1)\n  up = min_path_sum_dfs(grid, i - 1, j)\n  left = min_path_sum_dfs(grid, i, j - 1)\n  # Вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n  [left, up].min + grid[i][j]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>На рисунке 14-14 показано дерево рекурсии с корнем в \\(dp[2, 1]\\) ; в нем содержатся перекрывающиеся подзадачи, и их число будет резко расти вместе с размером сетки <code>grid</code> .</p> <p>По своей сути причина появления перекрывающихся подзадач такова: существует много разных путей от левого верхнего угла до одной и той же клетки.</p> <p></p> <p> Рисунок 14-14   Дерево рекурсии полного перебора </p> <p>У каждого состояния есть два выбора - вниз и вправо, а от левого верхнего угла до правого нижнего нужно сделать всего \\(m + n - 2\\) шагов, поэтому худшая временная сложность равна \\(O(2^{m + n})\\) , где \\(n\\) и \\(m\\) - число строк и столбцов сетки соответственно. Заметим, что в этой оценке не учитывается близость к границам сетки: у граничных клеток остается только один выбор, так что фактическое число путей будет несколько меньше.</p>","path":["Глава 14. Динамическое программирование","14.3 &nbsp; Подход к решению задач динамического программирования"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#2-2","level":3,"title":"2.   Метод 2: поиск с мемоизацией","text":"<p>Введем список памяти <code>mem</code> того же размера, что и сетка <code>grid</code> , для хранения решений всех подзадач и отсечения перекрывающихся подзадач:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby min_path_sum.py<pre><code>def min_path_sum_dfs_mem(\n    grid: list[list[int]], mem: list[list[int]], i: int, j: int\n) -&gt; int:\n    \"\"\"Минимальная сумма пути: поиск с мемоизацией\"\"\"\n    # Если это верхняя левая ячейка, завершить поиск\n    if i == 0 and j == 0:\n        return grid[0][0]\n    # Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if i &lt; 0 or j &lt; 0:\n        return inf\n    # Если запись уже есть, вернуть сразу\n    if mem[i][j] != -1:\n        return mem[i][j]\n    # Минимальная стоимость пути для левой и верхней ячеек\n    up = min_path_sum_dfs_mem(grid, mem, i - 1, j)\n    left = min_path_sum_dfs_mem(grid, mem, i, j - 1)\n    # Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    mem[i][j] = min(left, up) + grid[i][j]\n    return mem[i][j]\n</code></pre> min_path_sum.cpp<pre><code>/* Минимальная сумма пути: поиск с мемоизацией */\nint minPathSumDFSMem(vector&lt;vector&lt;int&gt;&gt; &amp;grid, vector&lt;vector&lt;int&gt;&gt; &amp;mem, int i, int j) {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return INT_MAX;\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][j] != -1) {\n        return mem[i][j];\n    }\n    // Минимальная стоимость пути для левой и верхней ячеек\n    int up = minPathSumDFSMem(grid, mem, i - 1, j);\n    int left = minPathSumDFSMem(grid, mem, i, j - 1);\n    // Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    mem[i][j] = min(left, up) != INT_MAX ? min(left, up) + grid[i][j] : INT_MAX;\n    return mem[i][j];\n}\n</code></pre> min_path_sum.java<pre><code>/* Минимальная сумма пути: поиск с мемоизацией */\nint minPathSumDFSMem(int[][] grid, int[][] mem, int i, int j) {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return Integer.MAX_VALUE;\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][j] != -1) {\n        return mem[i][j];\n    }\n    // Минимальная стоимость пути для левой и верхней ячеек\n    int up = minPathSumDFSMem(grid, mem, i - 1, j);\n    int left = minPathSumDFSMem(grid, mem, i, j - 1);\n    // Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    mem[i][j] = Math.min(left, up) + grid[i][j];\n    return mem[i][j];\n}\n</code></pre> min_path_sum.cs<pre><code>/* Минимальная сумма пути: поиск с мемоизацией */\nint MinPathSumDFSMem(int[][] grid, int[][] mem, int i, int j) {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return int.MaxValue;\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][j] != -1) {\n        return mem[i][j];\n    }\n    // Минимальная стоимость пути для левой и верхней ячеек\n    int up = MinPathSumDFSMem(grid, mem, i - 1, j);\n    int left = MinPathSumDFSMem(grid, mem, i, j - 1);\n    // Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    mem[i][j] = Math.Min(left, up) + grid[i][j];\n    return mem[i][j];\n}\n</code></pre> min_path_sum.go<pre><code>/* Минимальная сумма пути: поиск с мемоизацией */\nfunc minPathSumDFSMem(grid, mem [][]int, i, j int) int {\n    // Если это верхняя левая ячейка, завершить поиск\n    if i == 0 &amp;&amp; j == 0 {\n        return grid[0][0]\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if i &lt; 0 || j &lt; 0 {\n        return math.MaxInt\n    }\n    // Если запись уже есть, вернуть сразу\n    if mem[i][j] != -1 {\n        return mem[i][j]\n    }\n    // Минимальная стоимость пути для левой и верхней ячеек\n    up := minPathSumDFSMem(grid, mem, i-1, j)\n    left := minPathSumDFSMem(grid, mem, i, j-1)\n    // Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    mem[i][j] = int(math.Min(float64(left), float64(up))) + grid[i][j]\n    return mem[i][j]\n}\n</code></pre> min_path_sum.swift<pre><code>/* Минимальная сумма пути: поиск с мемоизацией */\nfunc minPathSumDFSMem(grid: [[Int]], mem: inout [[Int]], i: Int, j: Int) -&gt; Int {\n    // Если это верхняя левая ячейка, завершить поиск\n    if i == 0, j == 0 {\n        return grid[0][0]\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if i &lt; 0 || j &lt; 0 {\n        return .max\n    }\n    // Если запись уже есть, вернуть сразу\n    if mem[i][j] != -1 {\n        return mem[i][j]\n    }\n    // Минимальная стоимость пути для левой и верхней ячеек\n    let up = minPathSumDFSMem(grid: grid, mem: &amp;mem, i: i - 1, j: j)\n    let left = minPathSumDFSMem(grid: grid, mem: &amp;mem, i: i, j: j - 1)\n    // Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    mem[i][j] = min(left, up) + grid[i][j]\n    return mem[i][j]\n}\n</code></pre> min_path_sum.js<pre><code>/* Минимальная сумма пути: поиск с мемоизацией */\nfunction minPathSumDFSMem(grid, mem, i, j) {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i === 0 &amp;&amp; j === 0) {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return Infinity;\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][j] !== -1) {\n        return mem[i][j];\n    }\n    // Минимальная стоимость пути для левой и верхней ячеек\n    const up = minPathSumDFSMem(grid, mem, i - 1, j);\n    const left = minPathSumDFSMem(grid, mem, i, j - 1);\n    // Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    mem[i][j] = Math.min(left, up) + grid[i][j];\n    return mem[i][j];\n}\n</code></pre> min_path_sum.ts<pre><code>/* Минимальная сумма пути: поиск с мемоизацией */\nfunction minPathSumDFSMem(\n    grid: Array&lt;Array&lt;number&gt;&gt;,\n    mem: Array&lt;Array&lt;number&gt;&gt;,\n    i: number,\n    j: number\n): number {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i === 0 &amp;&amp; j === 0) {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return Infinity;\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][j] != -1) {\n        return mem[i][j];\n    }\n    // Минимальная стоимость пути для левой и верхней ячеек\n    const up = minPathSumDFSMem(grid, mem, i - 1, j);\n    const left = minPathSumDFSMem(grid, mem, i, j - 1);\n    // Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    mem[i][j] = Math.min(left, up) + grid[i][j];\n    return mem[i][j];\n}\n</code></pre> min_path_sum.dart<pre><code>/* Минимальная сумма пути: поиск с мемоизацией */\nint minPathSumDFSMem(List&lt;List&lt;int&gt;&gt; grid, List&lt;List&lt;int&gt;&gt; mem, int i, int j) {\n  // Если это верхняя левая ячейка, завершить поиск\n  if (i == 0 &amp;&amp; j == 0) {\n    return grid[0][0];\n  }\n  // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n  if (i &lt; 0 || j &lt; 0) {\n    // В Dart тип int — целое число фиксированного диапазона; значения, представляющего «бесконечность», не существует\n    return BigInt.from(2).pow(31).toInt();\n  }\n  // Если запись уже есть, вернуть сразу\n  if (mem[i][j] != -1) {\n    return mem[i][j];\n  }\n  // Минимальная стоимость пути для левой и верхней ячеек\n  int up = minPathSumDFSMem(grid, mem, i - 1, j);\n  int left = minPathSumDFSMem(grid, mem, i, j - 1);\n  // Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n  mem[i][j] = min(left, up) + grid[i][j];\n  return mem[i][j];\n}\n</code></pre> min_path_sum.rs<pre><code>/* Минимальная сумма пути: поиск с мемоизацией */\nfn min_path_sum_dfs_mem(grid: &amp;Vec&lt;Vec&lt;i32&gt;&gt;, mem: &amp;mut Vec&lt;Vec&lt;i32&gt;&gt;, i: i32, j: i32) -&gt; i32 {\n    // Если это верхняя левая ячейка, завершить поиск\n    if i == 0 &amp;&amp; j == 0 {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if i &lt; 0 || j &lt; 0 {\n        return i32::MAX;\n    }\n    // Если запись уже есть, вернуть сразу\n    if mem[i as usize][j as usize] != -1 {\n        return mem[i as usize][j as usize];\n    }\n    // Минимальная стоимость пути для левой и верхней ячеек\n    let up = min_path_sum_dfs_mem(grid, mem, i - 1, j);\n    let left = min_path_sum_dfs_mem(grid, mem, i, j - 1);\n    // Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    mem[i as usize][j as usize] = std::cmp::min(left, up) + grid[i as usize][j as usize];\n    mem[i as usize][j as usize]\n}\n</code></pre> min_path_sum.c<pre><code>/* Минимальная сумма пути: поиск с мемоизацией */\nint minPathSumDFSMem(int grid[MAX_SIZE][MAX_SIZE], int mem[MAX_SIZE][MAX_SIZE], int i, int j) {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return INT_MAX;\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][j] != -1) {\n        return mem[i][j];\n    }\n    // Минимальная стоимость пути для левой и верхней ячеек\n    int up = minPathSumDFSMem(grid, mem, i - 1, j);\n    int left = minPathSumDFSMem(grid, mem, i, j - 1);\n    // Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    mem[i][j] = myMin(left, up) != INT_MAX ? myMin(left, up) + grid[i][j] : INT_MAX;\n    return mem[i][j];\n}\n</code></pre> min_path_sum.kt<pre><code>/* Минимальная сумма пути: поиск с мемоизацией */\nfun minPathSumDFSMem(\n    grid: Array&lt;IntArray&gt;,\n    mem: Array&lt;IntArray&gt;,\n    i: Int,\n    j: Int\n): Int {\n    // Если это верхняя левая ячейка, завершить поиск\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0]\n    }\n    // Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n    if (i &lt; 0 || j &lt; 0) {\n        return Int.MAX_VALUE\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][j] != -1) {\n        return mem[i][j]\n    }\n    // Минимальная стоимость пути для левой и верхней ячеек\n    val up = minPathSumDFSMem(grid, mem, i - 1, j)\n    val left = minPathSumDFSMem(grid, mem, i, j - 1)\n    // Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n    mem[i][j] = min(left, up) + grid[i][j]\n    return mem[i][j]\n}\n</code></pre> min_path_sum.rb<pre><code>### Минимальная сумма пути: поиск с мемоизацией ###\ndef min_path_sum_dfs_mem(grid, mem, i, j)\n  # Если это верхняя левая ячейка, завершить поиск\n  return grid[0][0] if i == 0 &amp;&amp; j == 0\n  # Если индексы строки или столбца выходят за границы, вернуть стоимость +∞\n  return Float::INFINITY if i &lt; 0 || j &lt; 0\n  # Если запись уже есть, вернуть сразу\n  return mem[i][j] if mem[i][j] != -1\n  # Минимальная стоимость пути для левой и верхней ячеек\n  up = min_path_sum_dfs_mem(grid, mem, i - 1, j)\n  left = min_path_sum_dfs_mem(grid, mem, i, j - 1)\n  # Сохранить и вернуть минимальную стоимость пути из левого верхнего угла до (i, j)\n  mem[i][j] = [left, up].min + grid[i][j]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Как показано на рисунке 14-15, после добавления мемоизации решение каждой подзадачи вычисляется только один раз, поэтому временная сложность определяется общим числом состояний, то есть равна \\(O(nm)\\) .</p> <p></p> <p> Рисунок 14-15   Дерево рекурсии для поиска с мемоизацией </p>","path":["Глава 14. Динамическое программирование","14.3 &nbsp; Подход к решению задач динамического программирования"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#3-3","level":3,"title":"3.   Метод 3: динамическое программирование","text":"<p>Итеративная реализация динамического программирования выглядит так:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby min_path_sum.py<pre><code>def min_path_sum_dp(grid: list[list[int]]) -&gt; int:\n    \"\"\"Минимальная сумма пути: динамическое программирование\"\"\"\n    n, m = len(grid), len(grid[0])\n    # Инициализация таблицы dp\n    dp = [[0] * m for _ in range(n)]\n    dp[0][0] = grid[0][0]\n    # Переход состояний: первая строка\n    for j in range(1, m):\n        dp[0][j] = dp[0][j - 1] + grid[0][j]\n    # Переход состояний: первый столбец\n    for i in range(1, n):\n        dp[i][0] = dp[i - 1][0] + grid[i][0]\n    # Переход состояний: остальные строки и столбцы\n    for i in range(1, n):\n        for j in range(1, m):\n            dp[i][j] = min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j]\n    return dp[n - 1][m - 1]\n</code></pre> min_path_sum.cpp<pre><code>/* Минимальная сумма пути: динамическое программирование */\nint minPathSumDP(vector&lt;vector&lt;int&gt;&gt; &amp;grid) {\n    int n = grid.size(), m = grid[0].size();\n    // Инициализация таблицы dp\n    vector&lt;vector&lt;int&gt;&gt; dp(n, vector&lt;int&gt;(m));\n    dp[0][0] = grid[0][0];\n    // Переход состояний: первая строка\n    for (int j = 1; j &lt; m; j++) {\n        dp[0][j] = dp[0][j - 1] + grid[0][j];\n    }\n    // Переход состояний: первый столбец\n    for (int i = 1; i &lt; n; i++) {\n        dp[i][0] = dp[i - 1][0] + grid[i][0];\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (int i = 1; i &lt; n; i++) {\n        for (int j = 1; j &lt; m; j++) {\n            dp[i][j] = min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];\n        }\n    }\n    return dp[n - 1][m - 1];\n}\n</code></pre> min_path_sum.java<pre><code>/* Минимальная сумма пути: динамическое программирование */\nint minPathSumDP(int[][] grid) {\n    int n = grid.length, m = grid[0].length;\n    // Инициализация таблицы dp\n    int[][] dp = new int[n][m];\n    dp[0][0] = grid[0][0];\n    // Переход состояний: первая строка\n    for (int j = 1; j &lt; m; j++) {\n        dp[0][j] = dp[0][j - 1] + grid[0][j];\n    }\n    // Переход состояний: первый столбец\n    for (int i = 1; i &lt; n; i++) {\n        dp[i][0] = dp[i - 1][0] + grid[i][0];\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (int i = 1; i &lt; n; i++) {\n        for (int j = 1; j &lt; m; j++) {\n            dp[i][j] = Math.min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];\n        }\n    }\n    return dp[n - 1][m - 1];\n}\n</code></pre> min_path_sum.cs<pre><code>/* Минимальная сумма пути: динамическое программирование */\nint MinPathSumDP(int[][] grid) {\n    int n = grid.Length, m = grid[0].Length;\n    // Инициализация таблицы dp\n    int[,] dp = new int[n, m];\n    dp[0, 0] = grid[0][0];\n    // Переход состояний: первая строка\n    for (int j = 1; j &lt; m; j++) {\n        dp[0, j] = dp[0, j - 1] + grid[0][j];\n    }\n    // Переход состояний: первый столбец\n    for (int i = 1; i &lt; n; i++) {\n        dp[i, 0] = dp[i - 1, 0] + grid[i][0];\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (int i = 1; i &lt; n; i++) {\n        for (int j = 1; j &lt; m; j++) {\n            dp[i, j] = Math.Min(dp[i, j - 1], dp[i - 1, j]) + grid[i][j];\n        }\n    }\n    return dp[n - 1, m - 1];\n}\n</code></pre> min_path_sum.go<pre><code>/* Минимальная сумма пути: динамическое программирование */\nfunc minPathSumDP(grid [][]int) int {\n    n, m := len(grid), len(grid[0])\n    // Инициализация таблицы dp\n    dp := make([][]int, n)\n    for i := 0; i &lt; n; i++ {\n        dp[i] = make([]int, m)\n    }\n    dp[0][0] = grid[0][0]\n    // Переход состояний: первая строка\n    for j := 1; j &lt; m; j++ {\n        dp[0][j] = dp[0][j-1] + grid[0][j]\n    }\n    // Переход состояний: первый столбец\n    for i := 1; i &lt; n; i++ {\n        dp[i][0] = dp[i-1][0] + grid[i][0]\n    }\n    // Переход состояний: остальные строки и столбцы\n    for i := 1; i &lt; n; i++ {\n        for j := 1; j &lt; m; j++ {\n            dp[i][j] = int(math.Min(float64(dp[i][j-1]), float64(dp[i-1][j]))) + grid[i][j]\n        }\n    }\n    return dp[n-1][m-1]\n}\n</code></pre> min_path_sum.swift<pre><code>/* Минимальная сумма пути: динамическое программирование */\nfunc minPathSumDP(grid: [[Int]]) -&gt; Int {\n    let n = grid.count\n    let m = grid[0].count\n    // Инициализация таблицы dp\n    var dp = Array(repeating: Array(repeating: 0, count: m), count: n)\n    dp[0][0] = grid[0][0]\n    // Переход состояний: первая строка\n    for j in 1 ..&lt; m {\n        dp[0][j] = dp[0][j - 1] + grid[0][j]\n    }\n    // Переход состояний: первый столбец\n    for i in 1 ..&lt; n {\n        dp[i][0] = dp[i - 1][0] + grid[i][0]\n    }\n    // Переход состояний: остальные строки и столбцы\n    for i in 1 ..&lt; n {\n        for j in 1 ..&lt; m {\n            dp[i][j] = min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j]\n        }\n    }\n    return dp[n - 1][m - 1]\n}\n</code></pre> min_path_sum.js<pre><code>/* Минимальная сумма пути: динамическое программирование */\nfunction minPathSumDP(grid) {\n    const n = grid.length,\n        m = grid[0].length;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: n }, () =&gt;\n        Array.from({ length: m }, () =&gt; 0)\n    );\n    dp[0][0] = grid[0][0];\n    // Переход состояний: первая строка\n    for (let j = 1; j &lt; m; j++) {\n        dp[0][j] = dp[0][j - 1] + grid[0][j];\n    }\n    // Переход состояний: первый столбец\n    for (let i = 1; i &lt; n; i++) {\n        dp[i][0] = dp[i - 1][0] + grid[i][0];\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (let i = 1; i &lt; n; i++) {\n        for (let j = 1; j &lt; m; j++) {\n            dp[i][j] = Math.min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];\n        }\n    }\n    return dp[n - 1][m - 1];\n}\n</code></pre> min_path_sum.ts<pre><code>/* Минимальная сумма пути: динамическое программирование */\nfunction minPathSumDP(grid: Array&lt;Array&lt;number&gt;&gt;): number {\n    const n = grid.length,\n        m = grid[0].length;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: n }, () =&gt;\n        Array.from({ length: m }, () =&gt; 0)\n    );\n    dp[0][0] = grid[0][0];\n    // Переход состояний: первая строка\n    for (let j = 1; j &lt; m; j++) {\n        dp[0][j] = dp[0][j - 1] + grid[0][j];\n    }\n    // Переход состояний: первый столбец\n    for (let i = 1; i &lt; n; i++) {\n        dp[i][0] = dp[i - 1][0] + grid[i][0];\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (let i = 1; i &lt; n; i++) {\n        for (let j: number = 1; j &lt; m; j++) {\n            dp[i][j] = Math.min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];\n        }\n    }\n    return dp[n - 1][m - 1];\n}\n</code></pre> min_path_sum.dart<pre><code>/* Минимальная сумма пути: динамическое программирование */\nint minPathSumDP(List&lt;List&lt;int&gt;&gt; grid) {\n  int n = grid.length, m = grid[0].length;\n  // Инициализация таблицы dp\n  List&lt;List&lt;int&gt;&gt; dp = List.generate(n, (i) =&gt; List.filled(m, 0));\n  dp[0][0] = grid[0][0];\n  // Переход состояний: первая строка\n  for (int j = 1; j &lt; m; j++) {\n    dp[0][j] = dp[0][j - 1] + grid[0][j];\n  }\n  // Переход состояний: первый столбец\n  for (int i = 1; i &lt; n; i++) {\n    dp[i][0] = dp[i - 1][0] + grid[i][0];\n  }\n  // Переход состояний: остальные строки и столбцы\n  for (int i = 1; i &lt; n; i++) {\n    for (int j = 1; j &lt; m; j++) {\n      dp[i][j] = min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];\n    }\n  }\n  return dp[n - 1][m - 1];\n}\n</code></pre> min_path_sum.rs<pre><code>/* Минимальная сумма пути: динамическое программирование */\nfn min_path_sum_dp(grid: &amp;Vec&lt;Vec&lt;i32&gt;&gt;) -&gt; i32 {\n    let (n, m) = (grid.len(), grid[0].len());\n    // Инициализация таблицы dp\n    let mut dp = vec![vec![0; m]; n];\n    dp[0][0] = grid[0][0];\n    // Переход состояний: первая строка\n    for j in 1..m {\n        dp[0][j] = dp[0][j - 1] + grid[0][j];\n    }\n    // Переход состояний: первый столбец\n    for i in 1..n {\n        dp[i][0] = dp[i - 1][0] + grid[i][0];\n    }\n    // Переход состояний: остальные строки и столбцы\n    for i in 1..n {\n        for j in 1..m {\n            dp[i][j] = std::cmp::min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];\n        }\n    }\n    dp[n - 1][m - 1]\n}\n</code></pre> min_path_sum.c<pre><code>/* Минимальная сумма пути: динамическое программирование */\nint minPathSumDP(int grid[MAX_SIZE][MAX_SIZE], int n, int m) {\n    // Инициализация таблицы dp\n    int **dp = malloc(n * sizeof(int *));\n    for (int i = 0; i &lt; n; i++) {\n        dp[i] = calloc(m, sizeof(int));\n    }\n    dp[0][0] = grid[0][0];\n    // Переход состояний: первая строка\n    for (int j = 1; j &lt; m; j++) {\n        dp[0][j] = dp[0][j - 1] + grid[0][j];\n    }\n    // Переход состояний: первый столбец\n    for (int i = 1; i &lt; n; i++) {\n        dp[i][0] = dp[i - 1][0] + grid[i][0];\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (int i = 1; i &lt; n; i++) {\n        for (int j = 1; j &lt; m; j++) {\n            dp[i][j] = myMin(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];\n        }\n    }\n    int res = dp[n - 1][m - 1];\n    // Освободить память\n    for (int i = 0; i &lt; n; i++) {\n        free(dp[i]);\n    }\n    return res;\n}\n</code></pre> min_path_sum.kt<pre><code>/* Минимальная сумма пути: динамическое программирование */\nfun minPathSumDP(grid: Array&lt;IntArray&gt;): Int {\n    val n = grid.size\n    val m = grid[0].size\n    // Инициализация таблицы dp\n    val dp = Array(n) { IntArray(m) }\n    dp[0][0] = grid[0][0]\n    // Переход состояний: первая строка\n    for (j in 1..&lt;m) {\n        dp[0][j] = dp[0][j - 1] + grid[0][j]\n    }\n    // Переход состояний: первый столбец\n    for (i in 1..&lt;n) {\n        dp[i][0] = dp[i - 1][0] + grid[i][0]\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (i in 1..&lt;n) {\n        for (j in 1..&lt;m) {\n            dp[i][j] = min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j]\n        }\n    }\n    return dp[n - 1][m - 1]\n}\n</code></pre> min_path_sum.rb<pre><code>### Минимальная сумма пути: динамическое программирование ###\ndef min_path_sum_dp(grid)\n  n, m = grid.length, grid.first.length\n  # Инициализация таблицы dp\n  dp = Array.new(n) { Array.new(m, 0) }\n  dp[0][0] = grid[0][0]\n  # Переход состояний: первая строка\n  (1...m).each { |j| dp[0][j] = dp[0][j - 1] + grid[0][j] }\n  # Переход состояний: первый столбец\n  (1...n).each { |i| dp[i][0] = dp[i - 1][0] + grid[i][0] }\n  # Переход состояний: остальные строки и столбцы\n  for i in 1...n\n    for j in 1...m\n      dp[i][j] = [dp[i][j - 1], dp[i - 1][j]].min + grid[i][j]\n    end\n  end\n  dp[n -1][m -1]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>На рисунке 14-16 показан процесс переходов состояний в задаче о минимальной сумме пути. Он проходит по всей сетке, поэтому временная сложность равна \\(O(nm)\\) .</p> <p>Размер массива <code>dp</code> равен \\(n \\times m\\) , поэтому пространственная сложность равна \\(O(nm)\\) .</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 14-16   Процесс динамического программирования для минимальной суммы пути </p>","path":["Глава 14. Динамическое программирование","14.3 &nbsp; Подход к решению задач динамического программирования"],"tags":[]},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#4","level":3,"title":"4.   Оптимизация пространства","text":"<p>Поскольку каждая клетка зависит только от клетки слева и клетки сверху, таблицу \\(dp\\) можно реализовать с помощью одномерного массива, соответствующего одной строке.</p> <p>Обратите внимание: поскольку массив <code>dp</code> теперь может представлять только одну строку состояний, мы не можем заранее инициализировать состояния первого столбца, а должны обновлять их по мере обхода каждой строки:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby min_path_sum.py<pre><code>def min_path_sum_dp_comp(grid: list[list[int]]) -&gt; int:\n    \"\"\"Минимальная сумма пути: динамическое программирование с оптимизацией памяти\"\"\"\n    n, m = len(grid), len(grid[0])\n    # Инициализация таблицы dp\n    dp = [0] * m\n    # Переход состояний: первая строка\n    dp[0] = grid[0][0]\n    for j in range(1, m):\n        dp[j] = dp[j - 1] + grid[0][j]\n    # Переход состояний: остальные строки\n    for i in range(1, n):\n        # Переход состояний: первый столбец\n        dp[0] = dp[0] + grid[i][0]\n        # Переход состояний: остальные столбцы\n        for j in range(1, m):\n            dp[j] = min(dp[j - 1], dp[j]) + grid[i][j]\n    return dp[m - 1]\n</code></pre> min_path_sum.cpp<pre><code>/* Минимальная сумма пути: динамическое программирование с оптимизацией памяти */\nint minPathSumDPComp(vector&lt;vector&lt;int&gt;&gt; &amp;grid) {\n    int n = grid.size(), m = grid[0].size();\n    // Инициализация таблицы dp\n    vector&lt;int&gt; dp(m);\n    // Переход состояний: первая строка\n    dp[0] = grid[0][0];\n    for (int j = 1; j &lt; m; j++) {\n        dp[j] = dp[j - 1] + grid[0][j];\n    }\n    // Переход состояний: остальные строки\n    for (int i = 1; i &lt; n; i++) {\n        // Переход состояний: первый столбец\n        dp[0] = dp[0] + grid[i][0];\n        // Переход состояний: остальные столбцы\n        for (int j = 1; j &lt; m; j++) {\n            dp[j] = min(dp[j - 1], dp[j]) + grid[i][j];\n        }\n    }\n    return dp[m - 1];\n}\n</code></pre> min_path_sum.java<pre><code>/* Минимальная сумма пути: динамическое программирование с оптимизацией памяти */\nint minPathSumDPComp(int[][] grid) {\n    int n = grid.length, m = grid[0].length;\n    // Инициализация таблицы dp\n    int[] dp = new int[m];\n    // Переход состояний: первая строка\n    dp[0] = grid[0][0];\n    for (int j = 1; j &lt; m; j++) {\n        dp[j] = dp[j - 1] + grid[0][j];\n    }\n    // Переход состояний: остальные строки\n    for (int i = 1; i &lt; n; i++) {\n        // Переход состояний: первый столбец\n        dp[0] = dp[0] + grid[i][0];\n        // Переход состояний: остальные столбцы\n        for (int j = 1; j &lt; m; j++) {\n            dp[j] = Math.min(dp[j - 1], dp[j]) + grid[i][j];\n        }\n    }\n    return dp[m - 1];\n}\n</code></pre> min_path_sum.cs<pre><code>/* Минимальная сумма пути: динамическое программирование с оптимизацией памяти */\nint MinPathSumDPComp(int[][] grid) {\n    int n = grid.Length, m = grid[0].Length;\n    // Инициализация таблицы dp\n    int[] dp = new int[m];\n    dp[0] = grid[0][0];\n    // Переход состояний: первая строка\n    for (int j = 1; j &lt; m; j++) {\n        dp[j] = dp[j - 1] + grid[0][j];\n    }\n    // Переход состояний: остальные строки\n    for (int i = 1; i &lt; n; i++) {\n        // Переход состояний: первый столбец\n        dp[0] = dp[0] + grid[i][0];\n        // Переход состояний: остальные столбцы\n        for (int j = 1; j &lt; m; j++) {\n            dp[j] = Math.Min(dp[j - 1], dp[j]) + grid[i][j];\n        }\n    }\n    return dp[m - 1];\n}\n</code></pre> min_path_sum.go<pre><code>/* Минимальная сумма пути: динамическое программирование с оптимизацией памяти */\nfunc minPathSumDPComp(grid [][]int) int {\n    n, m := len(grid), len(grid[0])\n    // Инициализация таблицы dp\n    dp := make([]int, m)\n    // Переход состояний: первая строка\n    dp[0] = grid[0][0]\n    for j := 1; j &lt; m; j++ {\n        dp[j] = dp[j-1] + grid[0][j]\n    }\n    // Переход состояний: остальные строки и столбцы\n    for i := 1; i &lt; n; i++ {\n        // Переход состояний: первый столбец\n        dp[0] = dp[0] + grid[i][0]\n        // Переход состояний: остальные столбцы\n        for j := 1; j &lt; m; j++ {\n            dp[j] = int(math.Min(float64(dp[j-1]), float64(dp[j]))) + grid[i][j]\n        }\n    }\n    return dp[m-1]\n}\n</code></pre> min_path_sum.swift<pre><code>/* Минимальная сумма пути: динамическое программирование с оптимизацией памяти */\nfunc minPathSumDPComp(grid: [[Int]]) -&gt; Int {\n    let n = grid.count\n    let m = grid[0].count\n    // Инициализация таблицы dp\n    var dp = Array(repeating: 0, count: m)\n    // Переход состояний: первая строка\n    dp[0] = grid[0][0]\n    for j in 1 ..&lt; m {\n        dp[j] = dp[j - 1] + grid[0][j]\n    }\n    // Переход состояний: остальные строки\n    for i in 1 ..&lt; n {\n        // Переход состояний: первый столбец\n        dp[0] = dp[0] + grid[i][0]\n        // Переход состояний: остальные столбцы\n        for j in 1 ..&lt; m {\n            dp[j] = min(dp[j - 1], dp[j]) + grid[i][j]\n        }\n    }\n    return dp[m - 1]\n}\n</code></pre> min_path_sum.js<pre><code>/* Минимальная сумма пути: динамическое программирование с оптимизацией памяти */\nfunction minPathSumDPComp(grid) {\n    const n = grid.length,\n        m = grid[0].length;\n    // Инициализация таблицы dp\n    const dp = new Array(m);\n    // Переход состояний: первая строка\n    dp[0] = grid[0][0];\n    for (let j = 1; j &lt; m; j++) {\n        dp[j] = dp[j - 1] + grid[0][j];\n    }\n    // Переход состояний: остальные строки\n    for (let i = 1; i &lt; n; i++) {\n        // Переход состояний: первый столбец\n        dp[0] = dp[0] + grid[i][0];\n        // Переход состояний: остальные столбцы\n        for (let j = 1; j &lt; m; j++) {\n            dp[j] = Math.min(dp[j - 1], dp[j]) + grid[i][j];\n        }\n    }\n    return dp[m - 1];\n}\n</code></pre> min_path_sum.ts<pre><code>/* Минимальная сумма пути: динамическое программирование с оптимизацией памяти */\nfunction minPathSumDPComp(grid: Array&lt;Array&lt;number&gt;&gt;): number {\n    const n = grid.length,\n        m = grid[0].length;\n    // Инициализация таблицы dp\n    const dp = new Array(m);\n    // Переход состояний: первая строка\n    dp[0] = grid[0][0];\n    for (let j = 1; j &lt; m; j++) {\n        dp[j] = dp[j - 1] + grid[0][j];\n    }\n    // Переход состояний: остальные строки\n    for (let i = 1; i &lt; n; i++) {\n        // Переход состояний: первый столбец\n        dp[0] = dp[0] + grid[i][0];\n        // Переход состояний: остальные столбцы\n        for (let j = 1; j &lt; m; j++) {\n            dp[j] = Math.min(dp[j - 1], dp[j]) + grid[i][j];\n        }\n    }\n    return dp[m - 1];\n}\n</code></pre> min_path_sum.dart<pre><code>/* Минимальная сумма пути: динамическое программирование с оптимизацией памяти */\nint minPathSumDPComp(List&lt;List&lt;int&gt;&gt; grid) {\n  int n = grid.length, m = grid[0].length;\n  // Инициализация таблицы dp\n  List&lt;int&gt; dp = List.filled(m, 0);\n  dp[0] = grid[0][0];\n  for (int j = 1; j &lt; m; j++) {\n    dp[j] = dp[j - 1] + grid[0][j];\n  }\n  // Переход состояний: остальные строки\n  for (int i = 1; i &lt; n; i++) {\n    // Переход состояний: первый столбец\n    dp[0] = dp[0] + grid[i][0];\n    // Переход состояний: остальные столбцы\n    for (int j = 1; j &lt; m; j++) {\n      dp[j] = min(dp[j - 1], dp[j]) + grid[i][j];\n    }\n  }\n  return dp[m - 1];\n}\n</code></pre> min_path_sum.rs<pre><code>/* Минимальная сумма пути: динамическое программирование с оптимизацией памяти */\nfn min_path_sum_dp_comp(grid: &amp;Vec&lt;Vec&lt;i32&gt;&gt;) -&gt; i32 {\n    let (n, m) = (grid.len(), grid[0].len());\n    // Инициализация таблицы dp\n    let mut dp = vec![0; m];\n    // Переход состояний: первая строка\n    dp[0] = grid[0][0];\n    for j in 1..m {\n        dp[j] = dp[j - 1] + grid[0][j];\n    }\n    // Переход состояний: остальные строки\n    for i in 1..n {\n        // Переход состояний: первый столбец\n        dp[0] = dp[0] + grid[i][0];\n        // Переход состояний: остальные столбцы\n        for j in 1..m {\n            dp[j] = std::cmp::min(dp[j - 1], dp[j]) + grid[i][j];\n        }\n    }\n    dp[m - 1]\n}\n</code></pre> min_path_sum.c<pre><code>/* Минимальная сумма пути: динамическое программирование с оптимизацией памяти */\nint minPathSumDPComp(int grid[MAX_SIZE][MAX_SIZE], int n, int m) {\n    // Инициализация таблицы dp\n    int *dp = calloc(m, sizeof(int));\n    // Переход состояний: первая строка\n    dp[0] = grid[0][0];\n    for (int j = 1; j &lt; m; j++) {\n        dp[j] = dp[j - 1] + grid[0][j];\n    }\n    // Переход состояний: остальные строки\n    for (int i = 1; i &lt; n; i++) {\n        // Переход состояний: первый столбец\n        dp[0] = dp[0] + grid[i][0];\n        // Переход состояний: остальные столбцы\n        for (int j = 1; j &lt; m; j++) {\n            dp[j] = myMin(dp[j - 1], dp[j]) + grid[i][j];\n        }\n    }\n    int res = dp[m - 1];\n    // Освободить память\n    free(dp);\n    return res;\n}\n</code></pre> min_path_sum.kt<pre><code>/* Минимальная сумма пути: динамическое программирование с оптимизацией памяти */\nfun minPathSumDPComp(grid: Array&lt;IntArray&gt;): Int {\n    val n = grid.size\n    val m = grid[0].size\n    // Инициализация таблицы dp\n    val dp = IntArray(m)\n    // Переход состояний: первая строка\n    dp[0] = grid[0][0]\n    for (j in 1..&lt;m) {\n        dp[j] = dp[j - 1] + grid[0][j]\n    }\n    // Переход состояний: остальные строки\n    for (i in 1..&lt;n) {\n        // Переход состояний: первый столбец\n        dp[0] = dp[0] + grid[i][0]\n        // Переход состояний: остальные столбцы\n        for (j in 1..&lt;m) {\n            dp[j] = min(dp[j - 1], dp[j]) + grid[i][j]\n        }\n    }\n    return dp[m - 1]\n}\n</code></pre> min_path_sum.rb<pre><code>### Минимальная сумма пути: динамическое программирование с оптимизацией памяти ###\ndef min_path_sum_dp_comp(grid)\n  n, m = grid.length, grid.first.length\n  # Инициализация таблицы dp\n  dp = Array.new(m, 0)\n  # Переход состояний: первая строка\n  dp[0] = grid[0][0]\n  (1...m).each { |j| dp[j] = dp[j - 1] + grid[0][j] }\n  # Переход состояний: остальные строки\n  for i in 1...n\n    # Переход состояний: первый столбец\n    dp[0] = dp[0] + grid[i][0]\n    # Переход состояний: остальные столбцы\n    (1...m).each { |j| dp[j] = [dp[j - 1], dp[j]].min + grid[i][j] }\n  end\n  dp[m - 1]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 14. Динамическое программирование","14.3 &nbsp; Подход к решению задач динамического программирования"],"tags":[]},{"location":"chapter_dynamic_programming/edit_distance_problem/","level":1,"title":"14.6   Задача о расстоянии редактирования","text":"<p>Расстояние редактирования, также называемое расстоянием Левенштейна, - это минимальное количество изменений, необходимых для преобразования одной строки в другую. Обычно оно используется для измерения сходства двух последовательностей в информационном поиске и обработке естественного языка.</p> <p>Question</p> <p>Даны две строки \\(s\\) и \\(t\\) . Верните минимальное число шагов редактирования, необходимое для преобразования \\(s\\) в \\(t\\) .</p> <p>Для строки допускаются три операции редактирования: вставка одного символа, удаление одного символа и замена одного символа на произвольный другой символ.</p> <p>Как показано на рисунке 14-27, для преобразования <code>kitten</code> в <code>sitting</code> требуется 3 шага редактирования: 2 операции замены и 1 операция вставки; для преобразования <code>hello</code> в <code>algo</code> также требуется 3 шага: 2 замены и 1 удаление.</p> <p></p> <p> Рисунок 14-27   Пример данных для задачи о расстоянии редактирования </p> <p>Задачу о расстоянии редактирования можно естественным образом объяснить с помощью модели дерева решений. Строки соответствуют узлам дерева, а один шаг решения, то есть одна операция редактирования, соответствует одному ребру дерева.</p> <p>Как показано на рисунке 14-28, если не ограничивать число операций, то каждый узел может порождать множество ребер, и каждое из них соответствует одному из вариантов преобразования. Это означает, что преобразовать <code>hello</code> в <code>algo</code> можно множеством разных путей.</p> <p>С точки зрения дерева решений цель этой задачи - найти кратчайший путь между узлом <code>hello</code> и узлом <code>algo</code> .</p> <p></p> <p> Рисунок 14-28   Представление задачи о расстоянии редактирования через дерево решений </p>","path":["Глава 14. Динамическое программирование","14.6 &nbsp; Задача о расстоянии редактирования"],"tags":[]},{"location":"chapter_dynamic_programming/edit_distance_problem/#1","level":3,"title":"1.   Идея динамического программирования","text":"<p>Шаг 1: продумать решения на каждом раунде, определить состояние и тем самым получить таблицу \\(dp\\)</p> <p>На каждом раунде решение состоит в выполнении одной операции редактирования над строкой \\(s\\) .</p> <p>Нам нужно, чтобы в ходе выполнения операций размер задачи постепенно уменьшался; только тогда можно строить подзадачи. Пусть длины строк \\(s\\) и \\(t\\) равны соответственно \\(n\\) и \\(m\\) ; сначала рассмотрим последние символы этих строк, то есть \\(s[n-1]\\) и \\(t[m-1]\\) .</p> <ul> <li>Если \\(s[n-1]\\) и \\(t[m-1]\\) совпадают, их можно просто пропустить и сразу перейти к сравнению \\(s[n-2]\\) и \\(t[m-2]\\) .</li> <li>Если \\(s[n-1]\\) и \\(t[m-1]\\) различны, нужно выполнить над \\(s\\) одну операцию редактирования (вставку, удаление или замену), чтобы последние символы стали одинаковыми, после чего можно перейти к задаче меньшего размера.</li> </ul> <p>Иначе говоря, каждый шаг решения, то есть операция редактирования над строкой \\(s\\) , меняет те символы, которые еще необходимо сопоставить в строках \\(s\\) и \\(t\\) . Поэтому состояние определяется текущими позициями рассматриваемых символов в \\(s\\) и \\(t\\) , то есть состоянием \\([i, j]\\) .</p> <p>Подзадача, соответствующая состоянию \\([i, j]\\) , такова: минимальное число операций редактирования, необходимое для преобразования первых \\(i\\) символов строки \\(s\\) в первые \\(j\\) символов строки \\(t\\).</p> <p>Отсюда получается двумерная таблица \\(dp\\) размера \\((i+1) \\times (j+1)\\) .</p> <p>Шаг 2: найти оптимальную подструктуру и на ее основе вывести уравнение перехода состояния</p> <p>Рассмотрим подзадачу \\(dp[i, j]\\) . Ее последние символы - это \\(s[i-1]\\) и \\(t[j-1]\\) . В зависимости от операции редактирования возможны три случая, показанные на рисунке 14-29.</p> <ol> <li>Вставить после \\(s[i-1]\\) символ \\(t[j-1]\\) ; тогда остается подзадача \\(dp[i, j-1]\\) .</li> <li>Удалить \\(s[i-1]\\) ; тогда остается подзадача \\(dp[i-1, j]\\) .</li> <li>Заменить \\(s[i-1]\\) на \\(t[j-1]\\) ; тогда остается подзадача \\(dp[i-1, j-1]\\) .</li> </ol> <p></p> <p> Рисунок 14-29   Переходы состояния в задаче о расстоянии редактирования </p> <p>Согласно этому анализу оптимальная подструктура такова: минимальное число шагов редактирования для \\(dp[i, j]\\) равно минимуму из трех значений - \\(dp[i, j-1]\\) , \\(dp[i-1, j]\\) и \\(dp[i-1, j-1]\\) - плюс \\(1\\) шаг за текущее редактирование. Значит, уравнение перехода состояния имеет вид:</p> \\[ dp[i, j] = \\min(dp[i, j-1], dp[i-1, j], dp[i-1, j-1]) + 1 \\] <p>Заметим, что если символы \\(s[i-1]\\) и \\(t[j-1]\\) совпадают, то редактировать текущий символ не нужно. В этом случае уравнение перехода состояния имеет вид:</p> \\[ dp[i, j] = dp[i-1, j-1] \\] <p>Шаг 3: определить граничные условия и порядок переходов</p> <p>Когда обе строки пусты, число операций редактирования равно \\(0\\) , то есть \\(dp[0, 0] = 0\\) . Когда строка \\(s\\) пуста, а строка \\(t\\) непуста, минимальное число операций равно длине строки \\(t\\) , то есть вся первая строка инициализируется как \\(dp[0, j] = j\\) . Когда строка \\(s\\) непуста, а строка \\(t\\) пуста, минимальное число операций равно длине строки \\(s\\) , то есть весь первый столбец инициализируется как \\(dp[i, 0] = i\\) .</p> <p>Из уравнения перехода видно, что решение \\(dp[i, j]\\) зависит от значений слева, сверху и слева сверху, поэтому всю таблицу \\(dp\\) можно обходить двумя вложенными циклами в прямом порядке.</p>","path":["Глава 14. Динамическое программирование","14.6 &nbsp; Задача о расстоянии редактирования"],"tags":[]},{"location":"chapter_dynamic_programming/edit_distance_problem/#2","level":3,"title":"2.   Реализация кода","text":"PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby edit_distance.py<pre><code>def edit_distance_dp(s: str, t: str) -&gt; int:\n    \"\"\"Редакционное расстояние: динамическое программирование\"\"\"\n    n, m = len(s), len(t)\n    dp = [[0] * (m + 1) for _ in range(n + 1)]\n    # Переход состояний: первая строка и первый столбец\n    for i in range(1, n + 1):\n        dp[i][0] = i\n    for j in range(1, m + 1):\n        dp[0][j] = j\n    # Переход состояний: остальные строки и столбцы\n    for i in range(1, n + 1):\n        for j in range(1, m + 1):\n            if s[i - 1] == t[j - 1]:\n                # Если два символа равны, сразу пропустить их\n                dp[i][j] = dp[i - 1][j - 1]\n            else:\n                # Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[i][j] = min(dp[i][j - 1], dp[i - 1][j], dp[i - 1][j - 1]) + 1\n    return dp[n][m]\n</code></pre> edit_distance.cpp<pre><code>/* Редакционное расстояние: динамическое программирование */\nint editDistanceDP(string s, string t) {\n    int n = s.length(), m = t.length();\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(m + 1, 0));\n    // Переход состояний: первая строка и первый столбец\n    for (int i = 1; i &lt;= n; i++) {\n        dp[i][0] = i;\n    }\n    for (int j = 1; j &lt;= m; j++) {\n        dp[0][j] = j;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (int i = 1; i &lt;= n; i++) {\n        for (int j = 1; j &lt;= m; j++) {\n            if (s[i - 1] == t[j - 1]) {\n                // Если два символа равны, сразу пропустить их\n                dp[i][j] = dp[i - 1][j - 1];\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[i][j] = min(min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;\n            }\n        }\n    }\n    return dp[n][m];\n}\n</code></pre> edit_distance.java<pre><code>/* Редакционное расстояние: динамическое программирование */\nint editDistanceDP(String s, String t) {\n    int n = s.length(), m = t.length();\n    int[][] dp = new int[n + 1][m + 1];\n    // Переход состояний: первая строка и первый столбец\n    for (int i = 1; i &lt;= n; i++) {\n        dp[i][0] = i;\n    }\n    for (int j = 1; j &lt;= m; j++) {\n        dp[0][j] = j;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (int i = 1; i &lt;= n; i++) {\n        for (int j = 1; j &lt;= m; j++) {\n            if (s.charAt(i - 1) == t.charAt(j - 1)) {\n                // Если два символа равны, сразу пропустить их\n                dp[i][j] = dp[i - 1][j - 1];\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[i][j] = Math.min(Math.min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;\n            }\n        }\n    }\n    return dp[n][m];\n}\n</code></pre> edit_distance.cs<pre><code>/* Редакционное расстояние: динамическое программирование */\nint EditDistanceDP(string s, string t) {\n    int n = s.Length, m = t.Length;\n    int[,] dp = new int[n + 1, m + 1];\n    // Переход состояний: первая строка и первый столбец\n    for (int i = 1; i &lt;= n; i++) {\n        dp[i, 0] = i;\n    }\n    for (int j = 1; j &lt;= m; j++) {\n        dp[0, j] = j;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (int i = 1; i &lt;= n; i++) {\n        for (int j = 1; j &lt;= m; j++) {\n            if (s[i - 1] == t[j - 1]) {\n                // Если два символа равны, сразу пропустить их\n                dp[i, j] = dp[i - 1, j - 1];\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[i, j] = Math.Min(Math.Min(dp[i, j - 1], dp[i - 1, j]), dp[i - 1, j - 1]) + 1;\n            }\n        }\n    }\n    return dp[n, m];\n}\n</code></pre> edit_distance.go<pre><code>/* Редакционное расстояние: динамическое программирование */\nfunc editDistanceDP(s string, t string) int {\n    n := len(s)\n    m := len(t)\n    dp := make([][]int, n+1)\n    for i := 0; i &lt;= n; i++ {\n        dp[i] = make([]int, m+1)\n    }\n    // Переход состояний: первая строка и первый столбец\n    for i := 1; i &lt;= n; i++ {\n        dp[i][0] = i\n    }\n    for j := 1; j &lt;= m; j++ {\n        dp[0][j] = j\n    }\n    // Переход состояний: остальные строки и столбцы\n    for i := 1; i &lt;= n; i++ {\n        for j := 1; j &lt;= m; j++ {\n            if s[i-1] == t[j-1] {\n                // Если два символа равны, сразу пропустить их\n                dp[i][j] = dp[i-1][j-1]\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[i][j] = MinInt(MinInt(dp[i][j-1], dp[i-1][j]), dp[i-1][j-1]) + 1\n            }\n        }\n    }\n    return dp[n][m]\n}\n</code></pre> edit_distance.swift<pre><code>/* Редакционное расстояние: динамическое программирование */\nfunc editDistanceDP(s: String, t: String) -&gt; Int {\n    let n = s.utf8CString.count\n    let m = t.utf8CString.count\n    var dp = Array(repeating: Array(repeating: 0, count: m + 1), count: n + 1)\n    // Переход состояний: первая строка и первый столбец\n    for i in 1 ... n {\n        dp[i][0] = i\n    }\n    for j in 1 ... m {\n        dp[0][j] = j\n    }\n    // Переход состояний: остальные строки и столбцы\n    for i in 1 ... n {\n        for j in 1 ... m {\n            if s.utf8CString[i - 1] == t.utf8CString[j - 1] {\n                // Если два символа равны, сразу пропустить их\n                dp[i][j] = dp[i - 1][j - 1]\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[i][j] = min(min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1\n            }\n        }\n    }\n    return dp[n][m]\n}\n</code></pre> edit_distance.js<pre><code>/* Редакционное расстояние: динамическое программирование */\nfunction editDistanceDP(s, t) {\n    const n = s.length,\n        m = t.length;\n    const dp = Array.from({ length: n + 1 }, () =&gt; new Array(m + 1).fill(0));\n    // Переход состояний: первая строка и первый столбец\n    for (let i = 1; i &lt;= n; i++) {\n        dp[i][0] = i;\n    }\n    for (let j = 1; j &lt;= m; j++) {\n        dp[0][j] = j;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (let i = 1; i &lt;= n; i++) {\n        for (let j = 1; j &lt;= m; j++) {\n            if (s.charAt(i - 1) === t.charAt(j - 1)) {\n                // Если два символа равны, сразу пропустить их\n                dp[i][j] = dp[i - 1][j - 1];\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[i][j] =\n                    Math.min(dp[i][j - 1], dp[i - 1][j], dp[i - 1][j - 1]) + 1;\n            }\n        }\n    }\n    return dp[n][m];\n}\n</code></pre> edit_distance.ts<pre><code>/* Редакционное расстояние: динамическое программирование */\nfunction editDistanceDP(s: string, t: string): number {\n    const n = s.length,\n        m = t.length;\n    const dp = Array.from({ length: n + 1 }, () =&gt;\n        Array.from({ length: m + 1 }, () =&gt; 0)\n    );\n    // Переход состояний: первая строка и первый столбец\n    for (let i = 1; i &lt;= n; i++) {\n        dp[i][0] = i;\n    }\n    for (let j = 1; j &lt;= m; j++) {\n        dp[0][j] = j;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (let i = 1; i &lt;= n; i++) {\n        for (let j = 1; j &lt;= m; j++) {\n            if (s.charAt(i - 1) === t.charAt(j - 1)) {\n                // Если два символа равны, сразу пропустить их\n                dp[i][j] = dp[i - 1][j - 1];\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[i][j] =\n                    Math.min(dp[i][j - 1], dp[i - 1][j], dp[i - 1][j - 1]) + 1;\n            }\n        }\n    }\n    return dp[n][m];\n}\n</code></pre> edit_distance.dart<pre><code>/* Редакционное расстояние: динамическое программирование */\nint editDistanceDP(String s, String t) {\n  int n = s.length, m = t.length;\n  List&lt;List&lt;int&gt;&gt; dp = List.generate(n + 1, (_) =&gt; List.filled(m + 1, 0));\n  // Переход состояний: первая строка и первый столбец\n  for (int i = 1; i &lt;= n; i++) {\n    dp[i][0] = i;\n  }\n  for (int j = 1; j &lt;= m; j++) {\n    dp[0][j] = j;\n  }\n  // Переход состояний: остальные строки и столбцы\n  for (int i = 1; i &lt;= n; i++) {\n    for (int j = 1; j &lt;= m; j++) {\n      if (s[i - 1] == t[j - 1]) {\n        // Если два символа равны, сразу пропустить их\n        dp[i][j] = dp[i - 1][j - 1];\n      } else {\n        // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n        dp[i][j] = min(min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;\n      }\n    }\n  }\n  return dp[n][m];\n}\n</code></pre> edit_distance.rs<pre><code>/* Редакционное расстояние: динамическое программирование */\nfn edit_distance_dp(s: &amp;str, t: &amp;str) -&gt; i32 {\n    let (n, m) = (s.len(), t.len());\n    let mut dp = vec![vec![0; m + 1]; n + 1];\n    // Переход состояний: первая строка и первый столбец\n    for i in 1..=n {\n        dp[i][0] = i as i32;\n    }\n    for j in 1..m {\n        dp[0][j] = j as i32;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for i in 1..=n {\n        for j in 1..=m {\n            if s.chars().nth(i - 1) == t.chars().nth(j - 1) {\n                // Если два символа равны, сразу пропустить их\n                dp[i][j] = dp[i - 1][j - 1];\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[i][j] =\n                    std::cmp::min(std::cmp::min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;\n            }\n        }\n    }\n    dp[n][m]\n}\n</code></pre> edit_distance.c<pre><code>/* Редакционное расстояние: динамическое программирование */\nint editDistanceDP(char *s, char *t, int n, int m) {\n    int **dp = malloc((n + 1) * sizeof(int *));\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i] = calloc(m + 1, sizeof(int));\n    }\n    // Переход состояний: первая строка и первый столбец\n    for (int i = 1; i &lt;= n; i++) {\n        dp[i][0] = i;\n    }\n    for (int j = 1; j &lt;= m; j++) {\n        dp[0][j] = j;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (int i = 1; i &lt;= n; i++) {\n        for (int j = 1; j &lt;= m; j++) {\n            if (s[i - 1] == t[j - 1]) {\n                // Если два символа равны, сразу пропустить их\n                dp[i][j] = dp[i - 1][j - 1];\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[i][j] = myMin(myMin(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;\n            }\n        }\n    }\n    int res = dp[n][m];\n    // Освободить память\n    for (int i = 0; i &lt;= n; i++) {\n        free(dp[i]);\n    }\n    return res;\n}\n</code></pre> edit_distance.kt<pre><code>/* Редакционное расстояние: динамическое программирование */\nfun editDistanceDP(s: String, t: String): Int {\n    val n = s.length\n    val m = t.length\n    val dp = Array(n + 1) { IntArray(m + 1) }\n    // Переход состояний: первая строка и первый столбец\n    for (i in 1..n) {\n        dp[i][0] = i\n    }\n    for (j in 1..m) {\n        dp[0][j] = j\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (i in 1..n) {\n        for (j in 1..m) {\n            if (s[i - 1] == t[j - 1]) {\n                // Если два символа равны, сразу пропустить их\n                dp[i][j] = dp[i - 1][j - 1]\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[i][j] = min(min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1\n            }\n        }\n    }\n    return dp[n][m]\n}\n</code></pre> edit_distance.rb<pre><code>### Редакционное расстояние: динамическое программирование ###\ndef edit_distance_dp(s, t)\n  n, m = s.length, t.length\n  dp = Array.new(n + 1) { Array.new(m + 1, 0) }\n  # Переход состояний: первая строка и первый столбец\n  (1...(n + 1)).each { |i| dp[i][0] = i }\n  (1...(m + 1)).each { |j| dp[0][j] = j }\n  # Переход состояний: остальные строки и столбцы\n  for i in 1...(n + 1)\n    for j in 1...(m +1)\n      if s[i - 1] == t[j - 1]\n        # Если два символа равны, сразу пропустить их\n        dp[i][j] = dp[i - 1][j - 1]\n      else\n        # Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n        dp[i][j] = [dp[i][j - 1], dp[i - 1][j], dp[i - 1][j - 1]].min + 1\n      end\n    end\n  end\n  dp[n][m]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Как показано на рисунке 14-30, процесс переходов состояния в задаче о расстоянии редактирования очень похож на задачи о рюкзаке: и там и здесь его можно рассматривать как заполнение двумерной сетки.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt;&lt;13&gt;&lt;14&gt;&lt;15&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 14-30   Процесс динамического программирования для расстояния редактирования </p>","path":["Глава 14. Динамическое программирование","14.6 &nbsp; Задача о расстоянии редактирования"],"tags":[]},{"location":"chapter_dynamic_programming/edit_distance_problem/#3","level":3,"title":"3.   Оптимизация пространства","text":"<p>Поскольку \\(dp[i,j]\\) зависит от значения сверху \\(dp[i-1, j]\\) , слева \\(dp[i, j-1]\\) и слева сверху \\(dp[i-1, j-1]\\) , прямой обход после оптимизации памяти теряет значение слева сверху, а обратный обход не позволяет заранее построить значение слева \\(dp[i, j-1]\\) . Значит, оба наивных варианта обхода здесь непригодны.</p> <p>Чтобы решить эту проблему, можно использовать переменную <code>leftup</code> для временного сохранения значения слева сверху \\(dp[i-1, j-1]\\) ; после этого остается учитывать только верхнее и левое значения. Тогда ситуация становится аналогичной задаче о полном рюкзаке, и можно выполнять прямой обход. Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby edit_distance.py<pre><code>def edit_distance_dp_comp(s: str, t: str) -&gt; int:\n    \"\"\"Редакционное расстояние: динамическое программирование с оптимизацией памяти\"\"\"\n    n, m = len(s), len(t)\n    dp = [0] * (m + 1)\n    # Переход состояний: первая строка\n    for j in range(1, m + 1):\n        dp[j] = j\n    # Переход состояний: остальные строки\n    for i in range(1, n + 1):\n        # Переход состояний: первый столбец\n        leftup = dp[0]  # Временно сохранить dp[i-1, j-1]\n        dp[0] += 1\n        # Переход состояний: остальные столбцы\n        for j in range(1, m + 1):\n            temp = dp[j]\n            if s[i - 1] == t[j - 1]:\n                # Если два символа равны, сразу пропустить их\n                dp[j] = leftup\n            else:\n                # Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[j] = min(dp[j - 1], dp[j], leftup) + 1\n            leftup = temp  # Обновить до значения dp[i-1, j-1] для следующей итерации\n    return dp[m]\n</code></pre> edit_distance.cpp<pre><code>/* Редакционное расстояние: динамическое программирование с оптимизацией памяти */\nint editDistanceDPComp(string s, string t) {\n    int n = s.length(), m = t.length();\n    vector&lt;int&gt; dp(m + 1, 0);\n    // Переход состояний: первая строка\n    for (int j = 1; j &lt;= m; j++) {\n        dp[j] = j;\n    }\n    // Переход состояний: остальные строки\n    for (int i = 1; i &lt;= n; i++) {\n        // Переход состояний: первый столбец\n        int leftup = dp[0]; // Временно сохранить dp[i-1, j-1]\n        dp[0] = i;\n        // Переход состояний: остальные столбцы\n        for (int j = 1; j &lt;= m; j++) {\n            int temp = dp[j];\n            if (s[i - 1] == t[j - 1]) {\n                // Если два символа равны, сразу пропустить их\n                dp[j] = leftup;\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[j] = min(min(dp[j - 1], dp[j]), leftup) + 1;\n            }\n            leftup = temp; // Обновить до значения dp[i-1, j-1] для следующей итерации\n        }\n    }\n    return dp[m];\n}\n</code></pre> edit_distance.java<pre><code>/* Редакционное расстояние: динамическое программирование с оптимизацией памяти */\nint editDistanceDPComp(String s, String t) {\n    int n = s.length(), m = t.length();\n    int[] dp = new int[m + 1];\n    // Переход состояний: первая строка\n    for (int j = 1; j &lt;= m; j++) {\n        dp[j] = j;\n    }\n    // Переход состояний: остальные строки\n    for (int i = 1; i &lt;= n; i++) {\n        // Переход состояний: первый столбец\n        int leftup = dp[0]; // Временно сохранить dp[i-1, j-1]\n        dp[0] = i;\n        // Переход состояний: остальные столбцы\n        for (int j = 1; j &lt;= m; j++) {\n            int temp = dp[j];\n            if (s.charAt(i - 1) == t.charAt(j - 1)) {\n                // Если два символа равны, сразу пропустить их\n                dp[j] = leftup;\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[j] = Math.min(Math.min(dp[j - 1], dp[j]), leftup) + 1;\n            }\n            leftup = temp; // Обновить до значения dp[i-1, j-1] для следующей итерации\n        }\n    }\n    return dp[m];\n}\n</code></pre> edit_distance.cs<pre><code>/* Редакционное расстояние: динамическое программирование с оптимизацией памяти */\nint EditDistanceDPComp(string s, string t) {\n    int n = s.Length, m = t.Length;\n    int[] dp = new int[m + 1];\n    // Переход состояний: первая строка\n    for (int j = 1; j &lt;= m; j++) {\n        dp[j] = j;\n    }\n    // Переход состояний: остальные строки\n    for (int i = 1; i &lt;= n; i++) {\n        // Переход состояний: первый столбец\n        int leftup = dp[0]; // Временно сохранить dp[i-1, j-1]\n        dp[0] = i;\n        // Переход состояний: остальные столбцы\n        for (int j = 1; j &lt;= m; j++) {\n            int temp = dp[j];\n            if (s[i - 1] == t[j - 1]) {\n                // Если два символа равны, сразу пропустить их\n                dp[j] = leftup;\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[j] = Math.Min(Math.Min(dp[j - 1], dp[j]), leftup) + 1;\n            }\n            leftup = temp; // Обновить до значения dp[i-1, j-1] для следующей итерации\n        }\n    }\n    return dp[m];\n}\n</code></pre> edit_distance.go<pre><code>/* Редакционное расстояние: динамическое программирование с оптимизацией памяти */\nfunc editDistanceDPComp(s string, t string) int {\n    n := len(s)\n    m := len(t)\n    dp := make([]int, m+1)\n    // Переход состояний: первая строка\n    for j := 1; j &lt;= m; j++ {\n        dp[j] = j\n    }\n    // Переход состояний: остальные строки\n    for i := 1; i &lt;= n; i++ {\n        // Переход состояний: первый столбец\n        leftUp := dp[0] // Временно сохранить dp[i-1, j-1]\n        dp[0] = i\n        // Переход состояний: остальные столбцы\n        for j := 1; j &lt;= m; j++ {\n            temp := dp[j]\n            if s[i-1] == t[j-1] {\n                // Если два символа равны, сразу пропустить их\n                dp[j] = leftUp\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[j] = MinInt(MinInt(dp[j-1], dp[j]), leftUp) + 1\n            }\n            leftUp = temp // Обновить до значения dp[i-1, j-1] для следующей итерации\n        }\n    }\n    return dp[m]\n}\n</code></pre> edit_distance.swift<pre><code>/* Редакционное расстояние: динамическое программирование с оптимизацией памяти */\nfunc editDistanceDPComp(s: String, t: String) -&gt; Int {\n    let n = s.utf8CString.count\n    let m = t.utf8CString.count\n    var dp = Array(repeating: 0, count: m + 1)\n    // Переход состояний: первая строка\n    for j in 1 ... m {\n        dp[j] = j\n    }\n    // Переход состояний: остальные строки\n    for i in 1 ... n {\n        // Переход состояний: первый столбец\n        var leftup = dp[0] // Временно сохранить dp[i-1, j-1]\n        dp[0] = i\n        // Переход состояний: остальные столбцы\n        for j in 1 ... m {\n            let temp = dp[j]\n            if s.utf8CString[i - 1] == t.utf8CString[j - 1] {\n                // Если два символа равны, сразу пропустить их\n                dp[j] = leftup\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[j] = min(min(dp[j - 1], dp[j]), leftup) + 1\n            }\n            leftup = temp // Обновить до значения dp[i-1, j-1] для следующей итерации\n        }\n    }\n    return dp[m]\n}\n</code></pre> edit_distance.js<pre><code>/* Редакционное расстояние: динамическое программирование с оптимизацией памяти */\nfunction editDistanceDPComp(s, t) {\n    const n = s.length,\n        m = t.length;\n    const dp = new Array(m + 1).fill(0);\n    // Переход состояний: первая строка\n    for (let j = 1; j &lt;= m; j++) {\n        dp[j] = j;\n    }\n    // Переход состояний: остальные строки\n    for (let i = 1; i &lt;= n; i++) {\n        // Переход состояний: первый столбец\n        let leftup = dp[0]; // Временно сохранить dp[i-1, j-1]\n        dp[0] = i;\n        // Переход состояний: остальные столбцы\n        for (let j = 1; j &lt;= m; j++) {\n            const temp = dp[j];\n            if (s.charAt(i - 1) === t.charAt(j - 1)) {\n                // Если два символа равны, сразу пропустить их\n                dp[j] = leftup;\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[j] = Math.min(dp[j - 1], dp[j], leftup) + 1;\n            }\n            leftup = temp; // Обновить до значения dp[i-1, j-1] для следующей итерации\n        }\n    }\n    return dp[m];\n}\n</code></pre> edit_distance.ts<pre><code>/* Редакционное расстояние: динамическое программирование с оптимизацией памяти */\nfunction editDistanceDPComp(s: string, t: string): number {\n    const n = s.length,\n        m = t.length;\n    const dp = new Array(m + 1).fill(0);\n    // Переход состояний: первая строка\n    for (let j = 1; j &lt;= m; j++) {\n        dp[j] = j;\n    }\n    // Переход состояний: остальные строки\n    for (let i = 1; i &lt;= n; i++) {\n        // Переход состояний: первый столбец\n        let leftup = dp[0]; // Временно сохранить dp[i-1, j-1]\n        dp[0] = i;\n        // Переход состояний: остальные столбцы\n        for (let j = 1; j &lt;= m; j++) {\n            const temp = dp[j];\n            if (s.charAt(i - 1) === t.charAt(j - 1)) {\n                // Если два символа равны, сразу пропустить их\n                dp[j] = leftup;\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[j] = Math.min(dp[j - 1], dp[j], leftup) + 1;\n            }\n            leftup = temp; // Обновить до значения dp[i-1, j-1] для следующей итерации\n        }\n    }\n    return dp[m];\n}\n</code></pre> edit_distance.dart<pre><code>/* Редакционное расстояние: динамическое программирование с оптимизацией памяти */\nint editDistanceDPComp(String s, String t) {\n  int n = s.length, m = t.length;\n  List&lt;int&gt; dp = List.filled(m + 1, 0);\n  // Переход состояний: первая строка\n  for (int j = 1; j &lt;= m; j++) {\n    dp[j] = j;\n  }\n  // Переход состояний: остальные строки\n  for (int i = 1; i &lt;= n; i++) {\n    // Переход состояний: первый столбец\n    int leftup = dp[0]; // Временно сохранить dp[i-1, j-1]\n    dp[0] = i;\n    // Переход состояний: остальные столбцы\n    for (int j = 1; j &lt;= m; j++) {\n      int temp = dp[j];\n      if (s[i - 1] == t[j - 1]) {\n        // Если два символа равны, сразу пропустить их\n        dp[j] = leftup;\n      } else {\n        // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n        dp[j] = min(min(dp[j - 1], dp[j]), leftup) + 1;\n      }\n      leftup = temp; // Обновить до значения dp[i-1, j-1] для следующей итерации\n    }\n  }\n  return dp[m];\n}\n</code></pre> edit_distance.rs<pre><code>/* Редакционное расстояние: динамическое программирование с оптимизацией памяти */\nfn edit_distance_dp_comp(s: &amp;str, t: &amp;str) -&gt; i32 {\n    let (n, m) = (s.len(), t.len());\n    let mut dp = vec![0; m + 1];\n    // Переход состояний: первая строка\n    for j in 1..m {\n        dp[j] = j as i32;\n    }\n    // Переход состояний: остальные строки\n    for i in 1..=n {\n        // Переход состояний: первый столбец\n        let mut leftup = dp[0]; // Временно сохранить dp[i-1, j-1]\n        dp[0] = i as i32;\n        // Переход состояний: остальные столбцы\n        for j in 1..=m {\n            let temp = dp[j];\n            if s.chars().nth(i - 1) == t.chars().nth(j - 1) {\n                // Если два символа равны, сразу пропустить их\n                dp[j] = leftup;\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[j] = std::cmp::min(std::cmp::min(dp[j - 1], dp[j]), leftup) + 1;\n            }\n            leftup = temp; // Обновить до значения dp[i-1, j-1] для следующей итерации\n        }\n    }\n    dp[m]\n}\n</code></pre> edit_distance.c<pre><code>/* Редакционное расстояние: динамическое программирование с оптимизацией памяти */\nint editDistanceDPComp(char *s, char *t, int n, int m) {\n    int *dp = calloc(m + 1, sizeof(int));\n    // Переход состояний: первая строка\n    for (int j = 1; j &lt;= m; j++) {\n        dp[j] = j;\n    }\n    // Переход состояний: остальные строки\n    for (int i = 1; i &lt;= n; i++) {\n        // Переход состояний: первый столбец\n        int leftup = dp[0]; // Временно сохранить dp[i-1, j-1]\n        dp[0] = i;\n        // Переход состояний: остальные столбцы\n        for (int j = 1; j &lt;= m; j++) {\n            int temp = dp[j];\n            if (s[i - 1] == t[j - 1]) {\n                // Если два символа равны, сразу пропустить их\n                dp[j] = leftup;\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[j] = myMin(myMin(dp[j - 1], dp[j]), leftup) + 1;\n            }\n            leftup = temp; // Обновить до значения dp[i-1, j-1] для следующей итерации\n        }\n    }\n    int res = dp[m];\n    // Освободить память\n    free(dp);\n    return res;\n}\n</code></pre> edit_distance.kt<pre><code>/* Редакционное расстояние: динамическое программирование с оптимизацией памяти */\nfun editDistanceDPComp(s: String, t: String): Int {\n    val n = s.length\n    val m = t.length\n    val dp = IntArray(m + 1)\n    // Переход состояний: первая строка\n    for (j in 1..m) {\n        dp[j] = j\n    }\n    // Переход состояний: остальные строки\n    for (i in 1..n) {\n        // Переход состояний: первый столбец\n        var leftup = dp[0] // Временно сохранить dp[i-1, j-1]\n        dp[0] = i\n        // Переход состояний: остальные столбцы\n        for (j in 1..m) {\n            val temp = dp[j]\n            if (s[i - 1] == t[j - 1]) {\n                // Если два символа равны, сразу пропустить их\n                dp[j] = leftup\n            } else {\n                // Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n                dp[j] = min(min(dp[j - 1], dp[j]), leftup) + 1\n            }\n            leftup = temp // Обновить до значения dp[i-1, j-1] для следующей итерации\n        }\n    }\n    return dp[m]\n}\n</code></pre> edit_distance.rb<pre><code>### Редакционное расстояние: динамическое программирование с оптимизацией памяти ###\ndef edit_distance_dp_comp(s, t)\n  n, m = s.length, t.length\n  dp = Array.new(m + 1, 0)\n  # Переход состояний: первая строка\n  (1...(m + 1)).each { |j| dp[j] = j }\n  # Переход состояний: остальные строки\n  for i in 1...(n + 1)\n    # Переход состояний: первый столбец\n    leftup = dp.first # Временно сохранить dp[i-1, j-1]\n    dp[0] += 1\n    # Переход состояний: остальные столбцы\n    for j in 1...(m + 1)\n      temp = dp[j]\n      if s[i - 1] == t[j - 1]\n        # Если два символа равны, сразу пропустить их\n        dp[j] = leftup\n      else\n        # Минимальное число шагов редактирования = минимальное число шагов для вставки, удаления и замены + 1\n        dp[j] = [dp[j - 1], dp[j], leftup].min + 1\n      end\n      leftup = temp # Обновить до значения dp[i-1, j-1] для следующей итерации\n    end\n  end\n  dp[m]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 14. Динамическое программирование","14.6 &nbsp; Задача о расстоянии редактирования"],"tags":[]},{"location":"chapter_dynamic_programming/intro_to_dynamic_programming/","level":1,"title":"14.1   Первое знакомство с динамическим программированием","text":"<p>Динамическое программирование (dynamic programming) - это важная алгоритмическая парадигма, которая разбивает задачу на последовательность более мелких подзадач и за счет хранения их решений избегает повторных вычислений, тем самым резко повышая эффективность по времени.</p> <p>В этом разделе мы начнем с классического примера: сначала представим его грубое решение методом поиска с возвратом, увидим в нем перекрывающиеся подзадачи, а затем постепенно выведем более эффективное решение на основе динамического программирования.</p> <p>Подъем по лестнице</p> <p>Дана лестница из \\(n\\) ступеней. За один шаг можно подняться на \\(1\\) или на \\(2\\) ступени. Сколькими способами можно добраться до вершины?</p> <p>Как показано на рисунке 14-1, для лестницы из \\(3\\) ступеней существует \\(3\\) способа добраться до вершины.</p> <p></p> <p> Рисунок 14-1   Число способов подняться на 3-ю ступень </p> <p>Цель этой задачи - вычислить количество способов. Поэтому можно попробовать использовать для ее решения метод поиска с возвратом. Если представить подъем по лестнице как последовательность решений, то мы начинаем от земли и на каждом раунде выбираем прыжок на \\(1\\) или на \\(2\\) ступени; всякий раз, когда достигаем вершины, увеличиваем число способов на \\(1\\) , а если перескакиваем вершину, обрезаем эту ветвь. Код выглядит так:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby climbing_stairs_backtrack.py<pre><code>def backtrack(choices: list[int], state: int, n: int, res: list[int]) -&gt; int:\n    \"\"\"Бэктрекинг\"\"\"\n    # Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n    if state == n:\n        res[0] += 1\n    # Перебор всех вариантов выбора\n    for choice in choices:\n        # Отсечение: нельзя выходить за n-ю ступень\n        if state + choice &gt; n:\n            continue\n        # Попытка: сделать выбор и обновить состояние\n        backtrack(choices, state + choice, n, res)\n        # Откат\n\ndef climbing_stairs_backtrack(n: int) -&gt; int:\n    \"\"\"Подъем по лестнице: бэктрекинг\"\"\"\n    choices = [1, 2]  # Можно подняться на 1 или 2 ступени\n    state = 0  # Начать подъем с 0-й ступени\n    res = [0]  # Использовать res[0] для хранения числа решений\n    backtrack(choices, state, n, res)\n    return res[0]\n</code></pre> climbing_stairs_backtrack.cpp<pre><code>/* Бэктрекинг */\nvoid backtrack(vector&lt;int&gt; &amp;choices, int state, int n, vector&lt;int&gt; &amp;res) {\n    // Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n    if (state == n)\n        res[0]++;\n    // Перебор всех вариантов выбора\n    for (auto &amp;choice : choices) {\n        // Отсечение: нельзя выходить за n-ю ступень\n        if (state + choice &gt; n)\n            continue;\n        // Попытка: сделать выбор и обновить состояние\n        backtrack(choices, state + choice, n, res);\n        // Откат\n    }\n}\n\n/* Подъем по лестнице: бэктрекинг */\nint climbingStairsBacktrack(int n) {\n    vector&lt;int&gt; choices = {1, 2}; // Можно подняться на 1 или 2 ступени\n    int state = 0;                // Начать подъем с 0-й ступени\n    vector&lt;int&gt; res = {0};        // Использовать res[0] для хранения числа решений\n    backtrack(choices, state, n, res);\n    return res[0];\n}\n</code></pre> climbing_stairs_backtrack.java<pre><code>/* Бэктрекинг */\nvoid backtrack(List&lt;Integer&gt; choices, int state, int n, List&lt;Integer&gt; res) {\n    // Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n    if (state == n)\n        res.set(0, res.get(0) + 1);\n    // Перебор всех вариантов выбора\n    for (Integer choice : choices) {\n        // Отсечение: нельзя выходить за n-ю ступень\n        if (state + choice &gt; n)\n            continue;\n        // Попытка: сделать выбор и обновить состояние\n        backtrack(choices, state + choice, n, res);\n        // Откат\n    }\n}\n\n/* Подъем по лестнице: бэктрекинг */\nint climbingStairsBacktrack(int n) {\n    List&lt;Integer&gt; choices = Arrays.asList(1, 2); // Можно подняться на 1 или 2 ступени\n    int state = 0; // Начать подъем с 0-й ступени\n    List&lt;Integer&gt; res = new ArrayList&lt;&gt;();\n    res.add(0); // Использовать res[0] для хранения числа решений\n    backtrack(choices, state, n, res);\n    return res.get(0);\n}\n</code></pre> climbing_stairs_backtrack.cs<pre><code>/* Бэктрекинг */\nvoid Backtrack(List&lt;int&gt; choices, int state, int n, List&lt;int&gt; res) {\n    // Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n    if (state == n)\n        res[0]++;\n    // Перебор всех вариантов выбора\n    foreach (int choice in choices) {\n        // Отсечение: нельзя выходить за n-ю ступень\n        if (state + choice &gt; n)\n            continue;\n        // Попытка: сделать выбор и обновить состояние\n        Backtrack(choices, state + choice, n, res);\n        // Откат\n    }\n}\n\n/* Подъем по лестнице: бэктрекинг */\nint ClimbingStairsBacktrack(int n) {\n    List&lt;int&gt; choices = [1, 2]; // Можно подняться на 1 или 2 ступени\n    int state = 0; // Начать подъем с 0-й ступени\n    List&lt;int&gt; res = [0]; // Использовать res[0] для хранения числа решений\n    Backtrack(choices, state, n, res);\n    return res[0];\n}\n</code></pre> climbing_stairs_backtrack.go<pre><code>/* Бэктрекинг */\nfunc backtrack(choices []int, state, n int, res []int) {\n    // Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n    if state == n {\n        res[0] = res[0] + 1\n    }\n    // Перебор всех вариантов выбора\n    for _, choice := range choices {\n        // Отсечение: нельзя выходить за n-ю ступень\n        if state+choice &gt; n {\n            continue\n        }\n        // Попытка: сделать выбор и обновить состояние\n        backtrack(choices, state+choice, n, res)\n        // Откат\n    }\n}\n\n/* Подъем по лестнице: бэктрекинг */\nfunc climbingStairsBacktrack(n int) int {\n    // Можно подняться на 1 или 2 ступени\n    choices := []int{1, 2}\n    // Начать подъем с 0-й ступени\n    state := 0\n    res := make([]int, 1)\n    // Использовать res[0] для хранения числа решений\n    res[0] = 0\n    backtrack(choices, state, n, res)\n    return res[0]\n}\n</code></pre> climbing_stairs_backtrack.swift<pre><code>/* Бэктрекинг */\nfunc backtrack(choices: [Int], state: Int, n: Int, res: inout [Int]) {\n    // Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n    if state == n {\n        res[0] += 1\n    }\n    // Перебор всех вариантов выбора\n    for choice in choices {\n        // Отсечение: нельзя выходить за n-ю ступень\n        if state + choice &gt; n {\n            continue\n        }\n        // Попытка: сделать выбор и обновить состояние\n        backtrack(choices: choices, state: state + choice, n: n, res: &amp;res)\n        // Откат\n    }\n}\n\n/* Подъем по лестнице: бэктрекинг */\nfunc climbingStairsBacktrack(n: Int) -&gt; Int {\n    let choices = [1, 2] // Можно подняться на 1 или 2 ступени\n    let state = 0 // Начать подъем с 0-й ступени\n    var res: [Int] = []\n    res.append(0) // Использовать res[0] для хранения числа решений\n    backtrack(choices: choices, state: state, n: n, res: &amp;res)\n    return res[0]\n}\n</code></pre> climbing_stairs_backtrack.js<pre><code>/* Бэктрекинг */\nfunction backtrack(choices, state, n, res) {\n    // Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n    if (state === n) res.set(0, res.get(0) + 1);\n    // Перебор всех вариантов выбора\n    for (const choice of choices) {\n        // Отсечение: нельзя выходить за n-ю ступень\n        if (state + choice &gt; n) continue;\n        // Попытка: сделать выбор и обновить состояние\n        backtrack(choices, state + choice, n, res);\n        // Откат\n    }\n}\n\n/* Подъем по лестнице: бэктрекинг */\nfunction climbingStairsBacktrack(n) {\n    const choices = [1, 2]; // Можно подняться на 1 или 2 ступени\n    const state = 0; // Начать подъем с 0-й ступени\n    const res = new Map();\n    res.set(0, 0); // Использовать res[0] для хранения числа решений\n    backtrack(choices, state, n, res);\n    return res.get(0);\n}\n</code></pre> climbing_stairs_backtrack.ts<pre><code>/* Бэктрекинг */\nfunction backtrack(\n    choices: number[],\n    state: number,\n    n: number,\n    res: Map&lt;0, any&gt;\n): void {\n    // Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n    if (state === n) res.set(0, res.get(0) + 1);\n    // Перебор всех вариантов выбора\n    for (const choice of choices) {\n        // Отсечение: нельзя выходить за n-ю ступень\n        if (state + choice &gt; n) continue;\n        // Попытка: сделать выбор и обновить состояние\n        backtrack(choices, state + choice, n, res);\n        // Откат\n    }\n}\n\n/* Подъем по лестнице: бэктрекинг */\nfunction climbingStairsBacktrack(n: number): number {\n    const choices = [1, 2]; // Можно подняться на 1 или 2 ступени\n    const state = 0; // Начать подъем с 0-й ступени\n    const res = new Map();\n    res.set(0, 0); // Использовать res[0] для хранения числа решений\n    backtrack(choices, state, n, res);\n    return res.get(0);\n}\n</code></pre> climbing_stairs_backtrack.dart<pre><code>/* Бэктрекинг */\nvoid backtrack(List&lt;int&gt; choices, int state, int n, List&lt;int&gt; res) {\n  // Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n  if (state == n) {\n    res[0]++;\n  }\n  // Перебор всех вариантов выбора\n  for (int choice in choices) {\n    // Отсечение: нельзя выходить за n-ю ступень\n    if (state + choice &gt; n) continue;\n    // Попытка: сделать выбор и обновить состояние\n    backtrack(choices, state + choice, n, res);\n    // Откат\n  }\n}\n\n/* Подъем по лестнице: бэктрекинг */\nint climbingStairsBacktrack(int n) {\n  List&lt;int&gt; choices = [1, 2]; // Можно подняться на 1 или 2 ступени\n  int state = 0; // Начать подъем с 0-й ступени\n  List&lt;int&gt; res = [];\n  res.add(0); // Использовать res[0] для хранения числа решений\n  backtrack(choices, state, n, res);\n  return res[0];\n}\n</code></pre> climbing_stairs_backtrack.rs<pre><code>/* Бэктрекинг */\nfn backtrack(choices: &amp;[i32], state: i32, n: i32, res: &amp;mut [i32]) {\n    // Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n    if state == n {\n        res[0] = res[0] + 1;\n    }\n    // Перебор всех вариантов выбора\n    for &amp;choice in choices {\n        // Отсечение: нельзя выходить за n-ю ступень\n        if state + choice &gt; n {\n            continue;\n        }\n        // Попытка: сделать выбор и обновить состояние\n        backtrack(choices, state + choice, n, res);\n        // Откат\n    }\n}\n\n/* Подъем по лестнице: бэктрекинг */\nfn climbing_stairs_backtrack(n: usize) -&gt; i32 {\n    let choices = vec![1, 2]; // Можно подняться на 1 или 2 ступени\n    let state = 0; // Начать подъем с 0-й ступени\n    let mut res = Vec::new();\n    res.push(0); // Использовать res[0] для хранения числа решений\n    backtrack(&amp;choices, state, n as i32, &amp;mut res);\n    res[0]\n}\n</code></pre> climbing_stairs_backtrack.c<pre><code>/* Бэктрекинг */\nvoid backtrack(int *choices, int state, int n, int *res, int len) {\n    // Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n    if (state == n)\n        res[0]++;\n    // Перебор всех вариантов выбора\n    for (int i = 0; i &lt; len; i++) {\n        int choice = choices[i];\n        // Отсечение: нельзя выходить за n-ю ступень\n        if (state + choice &gt; n)\n            continue;\n        // Попытка: сделать выбор и обновить состояние\n        backtrack(choices, state + choice, n, res, len);\n        // Откат\n    }\n}\n\n/* Подъем по лестнице: бэктрекинг */\nint climbingStairsBacktrack(int n) {\n    int choices[2] = {1, 2}; // Можно подняться на 1 или 2 ступени\n    int state = 0;           // Начать подъем с 0-й ступени\n    int *res = (int *)malloc(sizeof(int));\n    *res = 0; // Использовать res[0] для хранения числа решений\n    int len = sizeof(choices) / sizeof(int);\n    backtrack(choices, state, n, res, len);\n    int result = *res;\n    free(res);\n    return result;\n}\n</code></pre> climbing_stairs_backtrack.kt<pre><code>/* Бэктрекинг */\nfun backtrack(\n    choices: MutableList&lt;Int&gt;,\n    state: Int,\n    n: Int,\n    res: MutableList&lt;Int&gt;\n) {\n    // Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n    if (state == n)\n        res[0] = res[0] + 1\n    // Перебор всех вариантов выбора\n    for (choice in choices) {\n        // Отсечение: нельзя выходить за n-ю ступень\n        if (state + choice &gt; n) continue\n        // Попытка: сделать выбор и обновить состояние\n        backtrack(choices, state + choice, n, res)\n        // Откат\n    }\n}\n\n/* Подъем по лестнице: бэктрекинг */\nfun climbingStairsBacktrack(n: Int): Int {\n    val choices = mutableListOf(1, 2) // Можно подняться на 1 или 2 ступени\n    val state = 0 // Начать подъем с 0-й ступени\n    val res = mutableListOf&lt;Int&gt;()\n    res.add(0) // Использовать res[0] для хранения числа решений\n    backtrack(choices, state, n, res)\n    return res[0]\n}\n</code></pre> climbing_stairs_backtrack.rb<pre><code>### Бэктрекинг ###\ndef backtrack(choices, state, n, res)\n  # Когда подъем достигает n-й ступени, число вариантов увеличивается на 1\n  res[0] += 1 if state == n\n  # Перебор всех вариантов выбора\n  for choice in choices\n    # Отсечение: нельзя выходить за n-ю ступень\n    next if state + choice &gt; n\n\n    # Попытка: сделать выбор и обновить состояние\n    backtrack(choices, state + choice, n, res)\n  end\n  # Откат\nend\n\n### Подъем по лестнице: бэктрекинг ###\ndef climbing_stairs_backtrack(n)\n  choices = [1, 2] # Можно подняться на 1 или 2 ступени\n  state = 0 # Начать подъем с 0-й ступени\n  res = [0] # Использовать res[0] для хранения числа решений\n  backtrack(choices, state, n, res)\n  res.first\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 14. Динамическое программирование","14.1 &nbsp; Первое знакомство с динамическим программированием"],"tags":[]},{"location":"chapter_dynamic_programming/intro_to_dynamic_programming/#1411-1","level":2,"title":"14.1.1   Метод 1: полный перебор","text":"<p>Алгоритм поиска с возвратом обычно не раскладывает задачу явно на подзадачи; вместо этого он рассматривает решение как последовательность решений, используя попытки и обрезку для поиска всех возможных ответов.</p> <p>Попробуем посмотреть на задачу именно как на разложение подзадач. Пусть число способов добраться до ступени \\(i\\) равно \\(dp[i]\\) ; тогда \\(dp[i]\\) - это исходная задача, а ее подзадачи включают:</p> \\[ dp[i-1], dp[i-2], \\dots, dp[2], dp[1] \\] <p>Поскольку за один раунд можно подняться только на \\(1\\) или на \\(2\\) ступени, стоя на ступени \\(i\\) , в предыдущий раунд мы могли находиться только на ступени \\(i - 1\\) или на ступени \\(i - 2\\) . Иначе говоря, на ступень \\(i\\) можно попасть только со ступени \\(i -1\\) или со ступени \\(i - 2\\) .</p> <p>Отсюда получается важный вывод: число способов добраться до ступени \\(i - 1\\) плюс число способов добраться до ступени \\(i - 2\\) равно числу способов добраться до ступени \\(i\\). Формула имеет вид:</p> \\[ dp[i] = dp[i-1] + dp[i-2] \\] <p>Это означает, что в задаче о подъеме по лестнице между подзадачами существует рекуррентная зависимость, и решение исходной задачи может быть построено на основе решений подзадач. Эта связь показана на рисунке 14-2.</p> <p></p> <p> Рисунок 14-2   Рекуррентная связь числа способов </p> <p>По рекуррентной формуле можно получить решение полного перебора. Начиная с \\(dp[n]\\) , мы рекурсивно разлагаем большую задачу в сумму двух меньших задач , пока не дойдем до наименьших подзадач \\(dp[1]\\) и \\(dp[2]\\) . Их решения уже известны: \\(dp[1] = 1\\) и \\(dp[2] = 2\\) , что означает \\(1\\) и \\(2\\) способа подняться соответственно на \\(1\\)-ю и \\(2\\)-ю ступени.</p> <p>Посмотрите на следующий код: как и стандартный поиск с возвратом, он относится к поиску в глубину, но выглядит более компактно:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby climbing_stairs_dfs.py<pre><code>def dfs(i: int) -&gt; int:\n    \"\"\"Поиск\"\"\"\n    # dp[1] и dp[2] уже известны, вернуть их\n    if i == 1 or i == 2:\n        return i\n    # dp[i] = dp[i-1] + dp[i-2]\n    count = dfs(i - 1) + dfs(i - 2)\n    return count\n\ndef climbing_stairs_dfs(n: int) -&gt; int:\n    \"\"\"Подъем по лестнице: поиск\"\"\"\n    return dfs(n)\n</code></pre> climbing_stairs_dfs.cpp<pre><code>/* Поиск */\nint dfs(int i) {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i == 1 || i == 2)\n        return i;\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1) + dfs(i - 2);\n    return count;\n}\n\n/* Подъем по лестнице: поиск */\nint climbingStairsDFS(int n) {\n    return dfs(n);\n}\n</code></pre> climbing_stairs_dfs.java<pre><code>/* Поиск */\nint dfs(int i) {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i == 1 || i == 2)\n        return i;\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1) + dfs(i - 2);\n    return count;\n}\n\n/* Подъем по лестнице: поиск */\nint climbingStairsDFS(int n) {\n    return dfs(n);\n}\n</code></pre> climbing_stairs_dfs.cs<pre><code>/* Поиск */\nint DFS(int i) {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i == 1 || i == 2)\n        return i;\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = DFS(i - 1) + DFS(i - 2);\n    return count;\n}\n\n/* Подъем по лестнице: поиск */\nint ClimbingStairsDFS(int n) {\n    return DFS(n);\n}\n</code></pre> climbing_stairs_dfs.go<pre><code>/* Поиск */\nfunc dfs(i int) int {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if i == 1 || i == 2 {\n        return i\n    }\n    // dp[i] = dp[i-1] + dp[i-2]\n    count := dfs(i-1) + dfs(i-2)\n    return count\n}\n\n/* Подъем по лестнице: поиск */\nfunc climbingStairsDFS(n int) int {\n    return dfs(n)\n}\n</code></pre> climbing_stairs_dfs.swift<pre><code>/* Поиск */\nfunc dfs(i: Int) -&gt; Int {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if i == 1 || i == 2 {\n        return i\n    }\n    // dp[i] = dp[i-1] + dp[i-2]\n    let count = dfs(i: i - 1) + dfs(i: i - 2)\n    return count\n}\n\n/* Подъем по лестнице: поиск */\nfunc climbingStairsDFS(n: Int) -&gt; Int {\n    dfs(i: n)\n}\n</code></pre> climbing_stairs_dfs.js<pre><code>/* Поиск */\nfunction dfs(i) {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i === 1 || i === 2) return i;\n    // dp[i] = dp[i-1] + dp[i-2]\n    const count = dfs(i - 1) + dfs(i - 2);\n    return count;\n}\n\n/* Подъем по лестнице: поиск */\nfunction climbingStairsDFS(n) {\n    return dfs(n);\n}\n</code></pre> climbing_stairs_dfs.ts<pre><code>/* Поиск */\nfunction dfs(i: number): number {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i === 1 || i === 2) return i;\n    // dp[i] = dp[i-1] + dp[i-2]\n    const count = dfs(i - 1) + dfs(i - 2);\n    return count;\n}\n\n/* Подъем по лестнице: поиск */\nfunction climbingStairsDFS(n: number): number {\n    return dfs(n);\n}\n</code></pre> climbing_stairs_dfs.dart<pre><code>/* Поиск */\nint dfs(int i) {\n  // dp[1] и dp[2] уже известны, вернуть их\n  if (i == 1 || i == 2) return i;\n  // dp[i] = dp[i-1] + dp[i-2]\n  int count = dfs(i - 1) + dfs(i - 2);\n  return count;\n}\n\n/* Подъем по лестнице: поиск */\nint climbingStairsDFS(int n) {\n  return dfs(n);\n}\n</code></pre> climbing_stairs_dfs.rs<pre><code>/* Поиск */\nfn dfs(i: usize) -&gt; i32 {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if i == 1 || i == 2 {\n        return i as i32;\n    }\n    // dp[i] = dp[i-1] + dp[i-2]\n    let count = dfs(i - 1) + dfs(i - 2);\n    count\n}\n\n/* Подъем по лестнице: поиск */\nfn climbing_stairs_dfs(n: usize) -&gt; i32 {\n    dfs(n)\n}\n</code></pre> climbing_stairs_dfs.c<pre><code>/* Поиск */\nint dfs(int i) {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i == 1 || i == 2)\n        return i;\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1) + dfs(i - 2);\n    return count;\n}\n\n/* Подъем по лестнице: поиск */\nint climbingStairsDFS(int n) {\n    return dfs(n);\n}\n</code></pre> climbing_stairs_dfs.kt<pre><code>/* Поиск */\nfun dfs(i: Int): Int {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i == 1 || i == 2) return i\n    // dp[i] = dp[i-1] + dp[i-2]\n    val count = dfs(i - 1) + dfs(i - 2)\n    return count\n}\n\n/* Подъем по лестнице: поиск */\nfun climbingStairsDFS(n: Int): Int {\n    return dfs(n)\n}\n</code></pre> climbing_stairs_dfs.rb<pre><code>### Поиск ###\ndef dfs(i)\n  # dp[1] и dp[2] уже известны, вернуть их\n  return i if i == 1 || i == 2\n  # dp[i] = dp[i-1] + dp[i-2]\n  dfs(i - 1) + dfs(i - 2)\nend\n\n### Подъем по лестнице: поиск ###\ndef climbing_stairs_dfs(n)\n  dfs(n)\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>На рисунке 14-3 показано дерево рекурсии, возникающее при полном переборе. Для задачи \\(dp[n]\\) глубина дерева рекурсии равна \\(n\\) , а временная сложность равна \\(O(2^n)\\) . Экспоненциальный рост взрывообразен: если подать на вход достаточно большое значение \\(n\\) , ожидание станет очень долгим.</p> <p></p> <p> Рисунок 14-3   Дерево рекурсии для подъема по лестнице </p> <p>Если посмотреть на рисунок 14-3, то видно, что экспоненциальная временная сложность порождается \"перекрывающимися подзадачами\". Например, \\(dp[9]\\) раскладывается в \\(dp[8]\\) и \\(dp[7]\\) , а \\(dp[8]\\) - в \\(dp[7]\\) и \\(dp[6]\\) ; обе ветви содержат подзадачу \\(dp[7]\\) .</p> <p>Продолжая это рассуждение, мы видим, что подзадачи порождают все более мелкие перекрывающиеся подзадачи без конца. Подавляющая часть вычислительных ресурсов уходит именно на них.</p>","path":["Глава 14. Динамическое программирование","14.1 &nbsp; Первое знакомство с динамическим программированием"],"tags":[]},{"location":"chapter_dynamic_programming/intro_to_dynamic_programming/#1412-2","level":2,"title":"14.1.2   Метод 2: поиск с мемоизацией","text":"<p>Чтобы ускорить алгоритм, мы хотим, чтобы каждая перекрывающаяся подзадача вычислялась только один раз. Для этого объявим массив <code>mem</code> для хранения решения каждой подзадачи и будем обрезать повторные вычисления в процессе поиска.</p> <ol> <li>Когда \\(dp[i]\\) вычисляется впервые, мы сохраняем его в <code>mem[i]</code> для последующего использования.</li> <li>Когда значение \\(dp[i]\\) требуется снова, мы просто берем его напрямую из <code>mem[i]</code> и тем самым избегаем повторного вычисления подзадачи.</li> </ol> <p>Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby climbing_stairs_dfs_mem.py<pre><code>def dfs(i: int, mem: list[int]) -&gt; int:\n    \"\"\"Поиск с мемоизацией\"\"\"\n    # dp[1] и dp[2] уже известны, вернуть их\n    if i == 1 or i == 2:\n        return i\n    # Если запись dp[i] существует, сразу вернуть ее\n    if mem[i] != -1:\n        return mem[i]\n    # dp[i] = dp[i-1] + dp[i-2]\n    count = dfs(i - 1, mem) + dfs(i - 2, mem)\n    # Сохранить dp[i]\n    mem[i] = count\n    return count\n\ndef climbing_stairs_dfs_mem(n: int) -&gt; int:\n    \"\"\"Подъем по лестнице: поиск с мемоизацией\"\"\"\n    # mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n    mem = [-1] * (n + 1)\n    return dfs(n, mem)\n</code></pre> climbing_stairs_dfs_mem.cpp<pre><code>/* Поиск с мемоизацией */\nint dfs(int i, vector&lt;int&gt; &amp;mem) {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i == 1 || i == 2)\n        return i;\n    // Если запись dp[i] существует, сразу вернуть ее\n    if (mem[i] != -1)\n        return mem[i];\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1, mem) + dfs(i - 2, mem);\n    // Сохранить dp[i]\n    mem[i] = count;\n    return count;\n}\n\n/* Подъем по лестнице: поиск с мемоизацией */\nint climbingStairsDFSMem(int n) {\n    // mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n    vector&lt;int&gt; mem(n + 1, -1);\n    return dfs(n, mem);\n}\n</code></pre> climbing_stairs_dfs_mem.java<pre><code>/* Поиск с мемоизацией */\nint dfs(int i, int[] mem) {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i == 1 || i == 2)\n        return i;\n    // Если запись dp[i] существует, сразу вернуть ее\n    if (mem[i] != -1)\n        return mem[i];\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1, mem) + dfs(i - 2, mem);\n    // Сохранить dp[i]\n    mem[i] = count;\n    return count;\n}\n\n/* Подъем по лестнице: поиск с мемоизацией */\nint climbingStairsDFSMem(int n) {\n    // mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n    int[] mem = new int[n + 1];\n    Arrays.fill(mem, -1);\n    return dfs(n, mem);\n}\n</code></pre> climbing_stairs_dfs_mem.cs<pre><code>/* Поиск с мемоизацией */\nint DFS(int i, int[] mem) {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i == 1 || i == 2)\n        return i;\n    // Если запись dp[i] существует, сразу вернуть ее\n    if (mem[i] != -1)\n        return mem[i];\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = DFS(i - 1, mem) + DFS(i - 2, mem);\n    // Сохранить dp[i]\n    mem[i] = count;\n    return count;\n}\n\n/* Подъем по лестнице: поиск с мемоизацией */\nint ClimbingStairsDFSMem(int n) {\n    // mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n    int[] mem = new int[n + 1];\n    Array.Fill(mem, -1);\n    return DFS(n, mem);\n}\n</code></pre> climbing_stairs_dfs_mem.go<pre><code>/* Поиск с мемоизацией */\nfunc dfsMem(i int, mem []int) int {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if i == 1 || i == 2 {\n        return i\n    }\n    // Если запись dp[i] существует, сразу вернуть ее\n    if mem[i] != -1 {\n        return mem[i]\n    }\n    // dp[i] = dp[i-1] + dp[i-2]\n    count := dfsMem(i-1, mem) + dfsMem(i-2, mem)\n    // Сохранить dp[i]\n    mem[i] = count\n    return count\n}\n\n/* Подъем по лестнице: поиск с мемоизацией */\nfunc climbingStairsDFSMem(n int) int {\n    // mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n    mem := make([]int, n+1)\n    for i := range mem {\n        mem[i] = -1\n    }\n    return dfsMem(n, mem)\n}\n</code></pre> climbing_stairs_dfs_mem.swift<pre><code>/* Поиск с мемоизацией */\nfunc dfs(i: Int, mem: inout [Int]) -&gt; Int {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if i == 1 || i == 2 {\n        return i\n    }\n    // Если запись dp[i] существует, сразу вернуть ее\n    if mem[i] != -1 {\n        return mem[i]\n    }\n    // dp[i] = dp[i-1] + dp[i-2]\n    let count = dfs(i: i - 1, mem: &amp;mem) + dfs(i: i - 2, mem: &amp;mem)\n    // Сохранить dp[i]\n    mem[i] = count\n    return count\n}\n\n/* Подъем по лестнице: поиск с мемоизацией */\nfunc climbingStairsDFSMem(n: Int) -&gt; Int {\n    // mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n    var mem = Array(repeating: -1, count: n + 1)\n    return dfs(i: n, mem: &amp;mem)\n}\n</code></pre> climbing_stairs_dfs_mem.js<pre><code>/* Поиск с мемоизацией */\nfunction dfs(i, mem) {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i === 1 || i === 2) return i;\n    // Если запись dp[i] существует, сразу вернуть ее\n    if (mem[i] != -1) return mem[i];\n    // dp[i] = dp[i-1] + dp[i-2]\n    const count = dfs(i - 1, mem) + dfs(i - 2, mem);\n    // Сохранить dp[i]\n    mem[i] = count;\n    return count;\n}\n\n/* Подъем по лестнице: поиск с мемоизацией */\nfunction climbingStairsDFSMem(n) {\n    // mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n    const mem = new Array(n + 1).fill(-1);\n    return dfs(n, mem);\n}\n</code></pre> climbing_stairs_dfs_mem.ts<pre><code>/* Поиск с мемоизацией */\nfunction dfs(i: number, mem: number[]): number {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i === 1 || i === 2) return i;\n    // Если запись dp[i] существует, сразу вернуть ее\n    if (mem[i] != -1) return mem[i];\n    // dp[i] = dp[i-1] + dp[i-2]\n    const count = dfs(i - 1, mem) + dfs(i - 2, mem);\n    // Сохранить dp[i]\n    mem[i] = count;\n    return count;\n}\n\n/* Подъем по лестнице: поиск с мемоизацией */\nfunction climbingStairsDFSMem(n: number): number {\n    // mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n    const mem = new Array(n + 1).fill(-1);\n    return dfs(n, mem);\n}\n</code></pre> climbing_stairs_dfs_mem.dart<pre><code>/* Поиск с мемоизацией */\nint dfs(int i, List&lt;int&gt; mem) {\n  // dp[1] и dp[2] уже известны, вернуть их\n  if (i == 1 || i == 2) return i;\n  // Если запись dp[i] существует, сразу вернуть ее\n  if (mem[i] != -1) return mem[i];\n  // dp[i] = dp[i-1] + dp[i-2]\n  int count = dfs(i - 1, mem) + dfs(i - 2, mem);\n  // Сохранить dp[i]\n  mem[i] = count;\n  return count;\n}\n\n/* Подъем по лестнице: поиск с мемоизацией */\nint climbingStairsDFSMem(int n) {\n  // mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n  List&lt;int&gt; mem = List.filled(n + 1, -1);\n  return dfs(n, mem);\n}\n</code></pre> climbing_stairs_dfs_mem.rs<pre><code>/* Поиск с мемоизацией */\nfn dfs(i: usize, mem: &amp;mut [i32]) -&gt; i32 {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if i == 1 || i == 2 {\n        return i as i32;\n    }\n    // Если запись dp[i] существует, сразу вернуть ее\n    if mem[i] != -1 {\n        return mem[i];\n    }\n    // dp[i] = dp[i-1] + dp[i-2]\n    let count = dfs(i - 1, mem) + dfs(i - 2, mem);\n    // Сохранить dp[i]\n    mem[i] = count;\n    count\n}\n\n/* Подъем по лестнице: поиск с мемоизацией */\nfn climbing_stairs_dfs_mem(n: usize) -&gt; i32 {\n    // mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n    let mut mem = vec![-1; n + 1];\n    dfs(n, &amp;mut mem)\n}\n</code></pre> climbing_stairs_dfs_mem.c<pre><code>/* Поиск с мемоизацией */\nint dfs(int i, int *mem) {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i == 1 || i == 2)\n        return i;\n    // Если запись dp[i] существует, сразу вернуть ее\n    if (mem[i] != -1)\n        return mem[i];\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1, mem) + dfs(i - 2, mem);\n    // Сохранить dp[i]\n    mem[i] = count;\n    return count;\n}\n\n/* Подъем по лестнице: поиск с мемоизацией */\nint climbingStairsDFSMem(int n) {\n    // mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n    int *mem = (int *)malloc((n + 1) * sizeof(int));\n    for (int i = 0; i &lt;= n; i++) {\n        mem[i] = -1;\n    }\n    int result = dfs(n, mem);\n    free(mem);\n    return result;\n}\n</code></pre> climbing_stairs_dfs_mem.kt<pre><code>/* Поиск с мемоизацией */\nfun dfs(i: Int, mem: IntArray): Int {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if (i == 1 || i == 2) return i\n    // Если запись dp[i] существует, сразу вернуть ее\n    if (mem[i] != -1) return mem[i]\n    // dp[i] = dp[i-1] + dp[i-2]\n    val count = dfs(i - 1, mem) + dfs(i - 2, mem)\n    // Сохранить dp[i]\n    mem[i] = count\n    return count\n}\n\n/* Подъем по лестнице: поиск с мемоизацией */\nfun climbingStairsDFSMem(n: Int): Int {\n    // mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n    val mem = IntArray(n + 1)\n    mem.fill(-1)\n    return dfs(n, mem)\n}\n</code></pre> climbing_stairs_dfs_mem.rb<pre><code>### Поиск с мемоизацией ###\ndef dfs(i, mem)\n  # dp[1] и dp[2] уже известны, вернуть их\n  return i if i == 1 || i == 2\n  # Если запись dp[i] существует, сразу вернуть ее\n  return mem[i] if mem[i] != -1\n\n  # dp[i] = dp[i-1] + dp[i-2]\n  count = dfs(i - 1, mem) + dfs(i - 2, mem)\n  # Сохранить dp[i]\n  mem[i] = count\nend\n\n### Подъем по лестнице: поиск с мемоизацией ###\ndef climbing_stairs_dfs_mem(n)\n  # mem[i] хранит число способов подняться на i-ю ступень, -1 означает отсутствие записи\n  mem = Array.new(n + 1, -1)\n  dfs(n, mem)\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Как показано на рисунке 14-4, после введения мемоизации каждая перекрывающаяся подзадача вычисляется только один раз, и временная сложность оптимизируется до \\(O(n)\\) . Это огромный скачок в эффективности.</p> <p></p> <p> Рисунок 14-4   Дерево рекурсии для поиска с мемоизацией </p>","path":["Глава 14. Динамическое программирование","14.1 &nbsp; Первое знакомство с динамическим программированием"],"tags":[]},{"location":"chapter_dynamic_programming/intro_to_dynamic_programming/#1413-3","level":2,"title":"14.1.3   Метод 3: динамическое программирование","text":"<p>Поиск с мемоизацией - это метод \"сверху вниз\" : мы начинаем с исходной задачи (корня), рекурсивно раскладываем более крупные подзадачи на меньшие, пока не достигнем наименьших подзадач с уже известным ответом (листьев). Затем в процессе возврата постепенно собираем решения подзадач и тем самым получаем решение исходной задачи.</p> <p>Напротив, динамическое программирование - это метод \"снизу вверх\" : начиная с решений наименьших подзадач, мы итеративно строим решения для более крупных подзадач, пока не получим ответ на исходную задачу.</p> <p>Поскольку в динамическом программировании нет этапа возврата, для его реализации достаточно обычных циклов, без рекурсии. В приведенном ниже коде мы инициализируем массив <code>dp</code> для хранения решений подзадач; он выполняет ту же роль, что и массив <code>mem</code> в мемоизированном поиске:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby climbing_stairs_dp.py<pre><code>def climbing_stairs_dp(n: int) -&gt; int:\n    \"\"\"Подъем по лестнице: динамическое программирование\"\"\"\n    if n == 1 or n == 2:\n        return n\n    # Инициализация таблицы dp для хранения решений подзадач\n    dp = [0] * (n + 1)\n    # Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1], dp[2] = 1, 2\n    # Переход состояний: постепенное решение больших подзадач через меньшие\n    for i in range(3, n + 1):\n        dp[i] = dp[i - 1] + dp[i - 2]\n    return dp[n]\n</code></pre> climbing_stairs_dp.cpp<pre><code>/* Подъем по лестнице: динамическое программирование */\nint climbingStairsDP(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    // Инициализация таблицы dp для хранения решений подзадач\n    vector&lt;int&gt; dp(n + 1);\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = 1;\n    dp[2] = 2;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    return dp[n];\n}\n</code></pre> climbing_stairs_dp.java<pre><code>/* Подъем по лестнице: динамическое программирование */\nint climbingStairsDP(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    // Инициализация таблицы dp для хранения решений подзадач\n    int[] dp = new int[n + 1];\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = 1;\n    dp[2] = 2;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    return dp[n];\n}\n</code></pre> climbing_stairs_dp.cs<pre><code>/* Подъем по лестнице: динамическое программирование */\nint ClimbingStairsDP(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    // Инициализация таблицы dp для хранения решений подзадач\n    int[] dp = new int[n + 1];\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = 1;\n    dp[2] = 2;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    return dp[n];\n}\n</code></pre> climbing_stairs_dp.go<pre><code>/* Подъем по лестнице: динамическое программирование */\nfunc climbingStairsDP(n int) int {\n    if n == 1 || n == 2 {\n        return n\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    dp := make([]int, n+1)\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = 1\n    dp[2] = 2\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for i := 3; i &lt;= n; i++ {\n        dp[i] = dp[i-1] + dp[i-2]\n    }\n    return dp[n]\n}\n</code></pre> climbing_stairs_dp.swift<pre><code>/* Подъем по лестнице: динамическое программирование */\nfunc climbingStairsDP(n: Int) -&gt; Int {\n    if n == 1 || n == 2 {\n        return n\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    var dp = Array(repeating: 0, count: n + 1)\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = 1\n    dp[2] = 2\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for i in 3 ... n {\n        dp[i] = dp[i - 1] + dp[i - 2]\n    }\n    return dp[n]\n}\n</code></pre> climbing_stairs_dp.js<pre><code>/* Подъем по лестнице: динамическое программирование */\nfunction climbingStairsDP(n) {\n    if (n === 1 || n === 2) return n;\n    // Инициализация таблицы dp для хранения решений подзадач\n    const dp = new Array(n + 1).fill(-1);\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = 1;\n    dp[2] = 2;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (let i = 3; i &lt;= n; i++) {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    return dp[n];\n}\n</code></pre> climbing_stairs_dp.ts<pre><code>/* Подъем по лестнице: динамическое программирование */\nfunction climbingStairsDP(n: number): number {\n    if (n === 1 || n === 2) return n;\n    // Инициализация таблицы dp для хранения решений подзадач\n    const dp = new Array(n + 1).fill(-1);\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = 1;\n    dp[2] = 2;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (let i = 3; i &lt;= n; i++) {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    return dp[n];\n}\n</code></pre> climbing_stairs_dp.dart<pre><code>/* Подъем по лестнице: динамическое программирование */\nint climbingStairsDP(int n) {\n  if (n == 1 || n == 2) return n;\n  // Инициализация таблицы dp для хранения решений подзадач\n  List&lt;int&gt; dp = List.filled(n + 1, 0);\n  // Начальное состояние: заранее задать решения наименьших подзадач\n  dp[1] = 1;\n  dp[2] = 2;\n  // Переход состояний: постепенное решение больших подзадач через меньшие\n  for (int i = 3; i &lt;= n; i++) {\n    dp[i] = dp[i - 1] + dp[i - 2];\n  }\n  return dp[n];\n}\n</code></pre> climbing_stairs_dp.rs<pre><code>/* Подъем по лестнице: динамическое программирование */\nfn climbing_stairs_dp(n: usize) -&gt; i32 {\n    // dp[1] и dp[2] уже известны, вернуть их\n    if n == 1 || n == 2 {\n        return n as i32;\n    }\n    // Инициализация таблицы dp для хранения решений подзадач\n    let mut dp = vec![-1; n + 1];\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = 1;\n    dp[2] = 2;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for i in 3..=n {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    dp[n]\n}\n</code></pre> climbing_stairs_dp.c<pre><code>/* Подъем по лестнице: динамическое программирование */\nint climbingStairsDP(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    // Инициализация таблицы dp для хранения решений подзадач\n    int *dp = (int *)malloc((n + 1) * sizeof(int));\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = 1;\n    dp[2] = 2;\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    int result = dp[n];\n    free(dp);\n    return result;\n}\n</code></pre> climbing_stairs_dp.kt<pre><code>/* Подъем по лестнице: динамическое программирование */\nfun climbingStairsDP(n: Int): Int {\n    if (n == 1 || n == 2) return n\n    // Инициализация таблицы dp для хранения решений подзадач\n    val dp = IntArray(n + 1)\n    // Начальное состояние: заранее задать решения наименьших подзадач\n    dp[1] = 1\n    dp[2] = 2\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for (i in 3..n) {\n        dp[i] = dp[i - 1] + dp[i - 2]\n    }\n    return dp[n]\n}\n</code></pre> climbing_stairs_dp.rb<pre><code>### Подъем по лестнице: динамическое программирование ###\ndef climbing_stairs_dp(n)\n  return n  if n == 1 || n == 2\n\n  # Инициализация таблицы dp для хранения решений подзадач\n  dp = Array.new(n + 1, 0)\n  # Начальное состояние: заранее задать решения наименьших подзадач\n  dp[1], dp[2] = 1, 2\n  # Переход состояний: постепенное решение больших подзадач через меньшие\n  (3...(n + 1)).each { |i| dp[i] = dp[i - 1] + dp[i - 2] }\n\n  dp[n]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>На рисунке 14-5 смоделирован процесс выполнения этого кода.</p> <p></p> <p> Рисунок 14-5   Процесс динамического программирования для подъема по лестнице </p> <p>Как и в поиске с возвратом, в динамическом программировании используется понятие \"состояние\" для обозначения некоторого этапа решения задачи; каждое состояние соответствует одной подзадаче и ее локально оптимальному решению. Например, в задаче о лестнице состояние определяется текущим номером ступени \\(i\\) .</p> <p>На основе сказанного можно подвести несколько часто используемых терминов динамического программирования.</p> <ul> <li>Массив <code>dp</code> называют таблицей dp, а \\(dp[i]\\) обозначает решение подзадачи, соответствующей состоянию \\(i\\) .</li> <li>Состояния, соответствующие наименьшим подзадачам (первая и вторая ступени), называют начальными состояниями.</li> <li>Рекуррентную формулу \\(dp[i] = dp[i-1] + dp[i-2]\\) называют уравнением перехода состояния.</li> </ul>","path":["Глава 14. Динамическое программирование","14.1 &nbsp; Первое знакомство с динамическим программированием"],"tags":[]},{"location":"chapter_dynamic_programming/intro_to_dynamic_programming/#1414","level":2,"title":"14.1.4   Оптимизация пространства","text":"<p>Внимательный читатель мог заметить, что поскольку \\(dp[i]\\) зависит только от \\(dp[i-1]\\) и \\(dp[i-2]\\) , нам не нужен весь массив <code>dp</code> для хранения ответов всех подзадач ; достаточно двух переменных, которые будут \"перекатываться\" вперед. Код имеет вид:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby climbing_stairs_dp.py<pre><code>def climbing_stairs_dp_comp(n: int) -&gt; int:\n    \"\"\"Подъем по лестнице: динамическое программирование с оптимизацией памяти\"\"\"\n    if n == 1 or n == 2:\n        return n\n    a, b = 1, 2\n    for _ in range(3, n + 1):\n        a, b = b, a + b\n    return b\n</code></pre> climbing_stairs_dp.cpp<pre><code>/* Подъем по лестнице: динамическое программирование с оптимизацией памяти */\nint climbingStairsDPComp(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    int a = 1, b = 2;\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = a + b;\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> climbing_stairs_dp.java<pre><code>/* Подъем по лестнице: динамическое программирование с оптимизацией памяти */\nint climbingStairsDPComp(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    int a = 1, b = 2;\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = a + b;\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> climbing_stairs_dp.cs<pre><code>/* Подъем по лестнице: динамическое программирование с оптимизацией памяти */\nint ClimbingStairsDPComp(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    int a = 1, b = 2;\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = a + b;\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> climbing_stairs_dp.go<pre><code>/* Подъем по лестнице: динамическое программирование с оптимизацией памяти */\nfunc climbingStairsDPComp(n int) int {\n    if n == 1 || n == 2 {\n        return n\n    }\n    a, b := 1, 2\n    // Переход состояний: постепенное решение больших подзадач через меньшие\n    for i := 3; i &lt;= n; i++ {\n        a, b = b, a+b\n    }\n    return b\n}\n</code></pre> climbing_stairs_dp.swift<pre><code>/* Подъем по лестнице: динамическое программирование с оптимизацией памяти */\nfunc climbingStairsDPComp(n: Int) -&gt; Int {\n    if n == 1 || n == 2 {\n        return n\n    }\n    var a = 1\n    var b = 2\n    for _ in 3 ... n {\n        (a, b) = (b, a + b)\n    }\n    return b\n}\n</code></pre> climbing_stairs_dp.js<pre><code>/* Подъем по лестнице: динамическое программирование с оптимизацией памяти */\nfunction climbingStairsDPComp(n) {\n    if (n === 1 || n === 2) return n;\n    let a = 1,\n        b = 2;\n    for (let i = 3; i &lt;= n; i++) {\n        const tmp = b;\n        b = a + b;\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> climbing_stairs_dp.ts<pre><code>/* Подъем по лестнице: динамическое программирование с оптимизацией памяти */\nfunction climbingStairsDPComp(n: number): number {\n    if (n === 1 || n === 2) return n;\n    let a = 1,\n        b = 2;\n    for (let i = 3; i &lt;= n; i++) {\n        const tmp = b;\n        b = a + b;\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> climbing_stairs_dp.dart<pre><code>/* Подъем по лестнице: динамическое программирование с оптимизацией памяти */\nint climbingStairsDPComp(int n) {\n  if (n == 1 || n == 2) return n;\n  int a = 1, b = 2;\n  for (int i = 3; i &lt;= n; i++) {\n    int tmp = b;\n    b = a + b;\n    a = tmp;\n  }\n  return b;\n}\n</code></pre> climbing_stairs_dp.rs<pre><code>/* Подъем по лестнице: динамическое программирование с оптимизацией памяти */\nfn climbing_stairs_dp_comp(n: usize) -&gt; i32 {\n    if n == 1 || n == 2 {\n        return n as i32;\n    }\n    let (mut a, mut b) = (1, 2);\n    for _ in 3..=n {\n        let tmp = b;\n        b = a + b;\n        a = tmp;\n    }\n    b\n}\n</code></pre> climbing_stairs_dp.c<pre><code>/* Подъем по лестнице: динамическое программирование с оптимизацией памяти */\nint climbingStairsDPComp(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    int a = 1, b = 2;\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = a + b;\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> climbing_stairs_dp.kt<pre><code>/* Подъем по лестнице: динамическое программирование с оптимизацией памяти */\nfun climbingStairsDPComp(n: Int): Int {\n    if (n == 1 || n == 2) return n\n    var a = 1\n    var b = 2\n    for (i in 3..n) {\n        val temp = b\n        b += a\n        a = temp\n    }\n    return b\n}\n</code></pre> climbing_stairs_dp.rb<pre><code>### Подъем по лестнице: динамическое программирование с оптимизацией памяти ###\ndef climbing_stairs_dp_comp(n)\n  return n if n == 1 || n == 2\n\n  a, b = 1, 2\n  (3...(n + 1)).each { a, b = b, a + b }\n\n  b\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Из кода видно, что после отказа от массива <code>dp</code> пространственная сложность уменьшается с \\(O(n)\\) до \\(O(1)\\) .</p> <p>Во многих задачах динамического программирования текущее состояние зависит лишь от ограниченного числа предыдущих состояний. Тогда можно сохранять только действительно нужные состояния и за счет \"уменьшения размерности\" экономить память. Этот прием оптимизации памяти называют \"скользящими переменными\" или \"скользящим массивом\".</p>","path":["Глава 14. Динамическое программирование","14.1 &nbsp; Первое знакомство с динамическим программированием"],"tags":[]},{"location":"chapter_dynamic_programming/knapsack_problem/","level":1,"title":"14.4   Задача о рюкзаке 0-1","text":"<p>Задача о рюкзаке является отличным примером для начала изучения динамического программирования и представляет собой одну из наиболее распространенных форм этой задачи. У нее существует множество вариантов, например задача о рюкзаке 0-1, задача о полном рюкзаке, задача о многократном рюкзаке и т.д.</p> <p>В этом разделе сначала разберем самый распространенный вариант - задачу о рюкзаке 0-1.</p> <p>Question</p> <p>Даны \\(n\\) предметов. Вес \\(i\\)-го предмета равен \\(wgt[i-1]\\) , стоимость равна \\(val[i-1]\\) . Также дан рюкзак вместимости \\(cap\\) . Каждый предмет можно выбрать только один раз. Найдите максимальную суммарную стоимость, которую можно поместить в рюкзак при заданной вместимости.</p> <p>Как видно на рисунке 14-17, поскольку номер предмета \\(i\\) начинается с \\(1\\) , а индексы массива начинаются с \\(0\\) , предмету \\(i\\) соответствуют вес \\(wgt[i-1]\\) и стоимость \\(val[i-1]\\) .</p> <p></p> <p> Рисунок 14-17   Пример данных для задачи о рюкзаке 0-1 </p> <p>Задачу о рюкзаке 0-1 можно рассматривать как процесс из \\(n\\) раундов принятия решений: для каждого предмета есть два решения - не класть его в рюкзак или положить в рюкзак. Поэтому задача удовлетворяет модели дерева решений.</p> <p>Цель задачи - найти \"максимальную суммарную стоимость при ограниченной вместимости рюкзака\", а это с большой вероятностью указывает на задачу динамического программирования.</p> <p>Шаг 1: продумать решения на каждом раунде, определить состояние и тем самым получить таблицу \\(dp\\)</p> <p>Для каждого предмета возможны два случая: не класть его в рюкзак, тогда вместимость не меняется; или положить его в рюкзак, тогда оставшаяся вместимость уменьшается. Отсюда получается определение состояния: текущий номер предмета \\(i\\) и текущая вместимость рюкзака \\(c\\) , то есть состояние обозначается как \\([i, c]\\) .</p> <p>Подзадача, соответствующая состоянию \\([i, c]\\) , такова: максимальная стоимость, которую можно получить, используя первые \\(i\\) предметов и рюкзак вместимости \\(c\\). Ее решение обозначается через \\(dp[i, c]\\) .</p> <p>Искомым значением является \\(dp[n, cap]\\) , значит, нам нужна двумерная таблица \\(dp\\) размера \\((n+1) \\times (cap+1)\\) .</p> <p>Шаг 2: найти оптимальную подструктуру и на ее основе вывести уравнение перехода состояния</p> <p>После того как мы принимаем решение по предмету \\(i\\) , остается подзадача, связанная с первыми \\(i-1\\) предметами. Здесь возможны два случая.</p> <ul> <li>Не класть предмет \\(i\\) : вместимость рюкзака не меняется, и состояние переходит в \\([i-1, c]\\) .</li> <li>Положить предмет \\(i\\) : вместимость рюкзака уменьшается на \\(wgt[i-1]\\) , а стоимость увеличивается на \\(val[i-1]\\) , и состояние переходит в \\([i-1, c-wgt[i-1]]\\) .</li> </ul> <p>Этот анализ и раскрывает оптимальную подструктуру задачи: максимальная стоимость \\(dp[i, c]\\) равна лучшему из двух вариантов - не брать предмет \\(i\\) или взять предмет \\(i\\). Отсюда получается уравнение перехода состояния:</p> \\[ dp[i, c] = \\max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1]) \\] <p>Нужно учитывать, что если вес текущего предмета \\(wgt[i - 1]\\) превышает оставшуюся вместимость \\(c\\) , то предмет можно только не брать.</p> <p>Шаг 3: определить граничные условия и порядок переходов</p> <p>Когда предметов нет или вместимость рюкзака равна \\(0\\) , максимальная стоимость равна \\(0\\) ; то есть весь первый столбец \\(dp[i, 0]\\) и вся первая строка \\(dp[0, c]\\) заполняются нулями.</p> <p>Текущее состояние \\([i, c]\\) зависит от состояния сверху \\([i-1, c]\\) и состояния слева сверху \\([i-1, c-wgt[i-1]]\\) , поэтому достаточно двумя вложенными циклами пройти по всей таблице \\(dp\\) в прямом порядке.</p> <p>После этого анализа реализуем по порядку: полный перебор, поиск с мемоизацией и динамическое программирование.</p>","path":["Глава 14. Динамическое программирование","14.4 &nbsp; Задача о рюкзаке 0-1"],"tags":[]},{"location":"chapter_dynamic_programming/knapsack_problem/#1-1","level":3,"title":"1.   Метод 1: полный перебор","text":"<p>Код поиска содержит следующие элементы.</p> <ul> <li>Параметры рекурсии: состояние \\([i, c]\\) .</li> <li>Возвращаемое значение: решение подзадачи \\(dp[i, c]\\) .</li> <li>Условие завершения: когда номер предмета выходит за границу, то есть \\(i = 0\\) , или оставшаяся вместимость равна \\(0\\) , рекурсия завершается и возвращается стоимость \\(0\\) .</li> <li>Обрезка: если вес текущего предмета превышает оставшуюся вместимость рюкзака, то можно только не класть этот предмет.</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby knapsack.py<pre><code>def knapsack_dfs(wgt: list[int], val: list[int], i: int, c: int) -&gt; int:\n    \"\"\"Рюкзак 0-1: полный перебор\"\"\"\n    # Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if i == 0 or c == 0:\n        return 0\n    # Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if wgt[i - 1] &gt; c:\n        return knapsack_dfs(wgt, val, i - 1, c)\n    # Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    no = knapsack_dfs(wgt, val, i - 1, c)\n    yes = knapsack_dfs(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1]\n    # Вернуть вариант с большей стоимостью из двух возможных\n    return max(no, yes)\n</code></pre> knapsack.cpp<pre><code>/* Рюкзак 0-1: полный перебор */\nint knapsackDFS(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int i, int c) {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFS(wgt, val, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    int no = knapsackDFS(wgt, val, i - 1, c);\n    int yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // Вернуть вариант с большей стоимостью из двух возможных\n    return max(no, yes);\n}\n</code></pre> knapsack.java<pre><code>/* Рюкзак 0-1: полный перебор */\nint knapsackDFS(int[] wgt, int[] val, int i, int c) {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFS(wgt, val, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    int no = knapsackDFS(wgt, val, i - 1, c);\n    int yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // Вернуть вариант с большей стоимостью из двух возможных\n    return Math.max(no, yes);\n}\n</code></pre> knapsack.cs<pre><code>/* Рюкзак 0-1: полный перебор */\nint KnapsackDFS(int[] weight, int[] val, int i, int c) {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (weight[i - 1] &gt; c) {\n        return KnapsackDFS(weight, val, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    int no = KnapsackDFS(weight, val, i - 1, c);\n    int yes = KnapsackDFS(weight, val, i - 1, c - weight[i - 1]) + val[i - 1];\n    // Вернуть вариант с большей стоимостью из двух возможных\n    return Math.Max(no, yes);\n}\n</code></pre> knapsack.go<pre><code>/* Рюкзак 0-1: полный перебор */\nfunc knapsackDFS(wgt, val []int, i, c int) int {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if i == 0 || c == 0 {\n        return 0\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if wgt[i-1] &gt; c {\n        return knapsackDFS(wgt, val, i-1, c)\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    no := knapsackDFS(wgt, val, i-1, c)\n    yes := knapsackDFS(wgt, val, i-1, c-wgt[i-1]) + val[i-1]\n    // Вернуть вариант с большей стоимостью из двух возможных\n    return int(math.Max(float64(no), float64(yes)))\n}\n</code></pre> knapsack.swift<pre><code>/* Рюкзак 0-1: полный перебор */\nfunc knapsackDFS(wgt: [Int], val: [Int], i: Int, c: Int) -&gt; Int {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if i == 0 || c == 0 {\n        return 0\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if wgt[i - 1] &gt; c {\n        return knapsackDFS(wgt: wgt, val: val, i: i - 1, c: c)\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    let no = knapsackDFS(wgt: wgt, val: val, i: i - 1, c: c)\n    let yes = knapsackDFS(wgt: wgt, val: val, i: i - 1, c: c - wgt[i - 1]) + val[i - 1]\n    // Вернуть вариант с большей стоимостью из двух возможных\n    return max(no, yes)\n}\n</code></pre> knapsack.js<pre><code>/* Рюкзак 0-1: полный перебор */\nfunction knapsackDFS(wgt, val, i, c) {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i === 0 || c === 0) {\n        return 0;\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFS(wgt, val, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    const no = knapsackDFS(wgt, val, i - 1, c);\n    const yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // Вернуть вариант с большей стоимостью из двух возможных\n    return Math.max(no, yes);\n}\n</code></pre> knapsack.ts<pre><code>/* Рюкзак 0-1: полный перебор */\nfunction knapsackDFS(\n    wgt: Array&lt;number&gt;,\n    val: Array&lt;number&gt;,\n    i: number,\n    c: number\n): number {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i === 0 || c === 0) {\n        return 0;\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFS(wgt, val, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    const no = knapsackDFS(wgt, val, i - 1, c);\n    const yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // Вернуть вариант с большей стоимостью из двух возможных\n    return Math.max(no, yes);\n}\n</code></pre> knapsack.dart<pre><code>/* Рюкзак 0-1: полный перебор */\nint knapsackDFS(List&lt;int&gt; wgt, List&lt;int&gt; val, int i, int c) {\n  // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n  if (i == 0 || c == 0) {\n    return 0;\n  }\n  // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n  if (wgt[i - 1] &gt; c) {\n    return knapsackDFS(wgt, val, i - 1, c);\n  }\n  // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n  int no = knapsackDFS(wgt, val, i - 1, c);\n  int yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];\n  // Вернуть вариант с большей стоимостью из двух возможных\n  return max(no, yes);\n}\n</code></pre> knapsack.rs<pre><code>/* Рюкзак 0-1: полный перебор */\nfn knapsack_dfs(wgt: &amp;[i32], val: &amp;[i32], i: usize, c: usize) -&gt; i32 {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if i == 0 || c == 0 {\n        return 0;\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if wgt[i - 1] &gt; c as i32 {\n        return knapsack_dfs(wgt, val, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    let no = knapsack_dfs(wgt, val, i - 1, c);\n    let yes = knapsack_dfs(wgt, val, i - 1, c - wgt[i - 1] as usize) + val[i - 1];\n    // Вернуть вариант с большей стоимостью из двух возможных\n    std::cmp::max(no, yes)\n}\n</code></pre> knapsack.c<pre><code>/* Рюкзак 0-1: полный перебор */\nint knapsackDFS(int wgt[], int val[], int i, int c) {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFS(wgt, val, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    int no = knapsackDFS(wgt, val, i - 1, c);\n    int yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // Вернуть вариант с большей стоимостью из двух возможных\n    return myMax(no, yes);\n}\n</code></pre> knapsack.kt<pre><code>/* Рюкзак 0-1: полный перебор */\nfun knapsackDFS(\n    wgt: IntArray,\n    _val: IntArray,\n    i: Int,\n    c: Int\n): Int {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i == 0 || c == 0) {\n        return 0\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFS(wgt, _val, i - 1, c)\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    val no = knapsackDFS(wgt, _val, i - 1, c)\n    val yes = knapsackDFS(wgt, _val, i - 1, c - wgt[i - 1]) + _val[i - 1]\n    // Вернуть вариант с большей стоимостью из двух возможных\n    return max(no, yes)\n}\n</code></pre> knapsack.rb<pre><code>### Рюкзак 0-1: полный перебор ###\ndef knapsack_dfs(wgt, val, i, c)\n  # Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n  return 0 if i == 0 || c == 0\n  # Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n  return knapsack_dfs(wgt, val, i - 1, c) if wgt[i - 1] &gt; c\n  # Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n  no = knapsack_dfs(wgt, val, i - 1, c)\n  yes = knapsack_dfs(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1]\n  # Вернуть вариант с большей стоимостью из двух возможных\n  [no, yes].max\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Как показано на рисунке 14-18, поскольку каждый предмет создает две ветви поиска - \"не брать\" и \"брать\", временная сложность равна \\(O(2^n)\\) .</p> <p>Посмотрев на дерево рекурсии, легко заметить наличие перекрывающихся подзадач, например \\(dp[1, 10]\\) и подобных. Когда число предметов растет, вместимость рюкзака велика, а особенно когда много предметов с одинаковым весом, количество перекрывающихся подзадач быстро увеличивается.</p> <p></p> <p> Рисунок 14-18   Дерево полного перебора для задачи о рюкзаке 0-1 </p>","path":["Глава 14. Динамическое программирование","14.4 &nbsp; Задача о рюкзаке 0-1"],"tags":[]},{"location":"chapter_dynamic_programming/knapsack_problem/#2-2","level":3,"title":"2.   Метод 2: мемоизация","text":"<p>Чтобы каждая перекрывающаяся подзадача вычислялась только один раз, используем таблицу памяти <code>mem</code> для хранения решений подзадач, где <code>mem[i][c]</code> соответствует \\(dp[i, c]\\) .</p> <p>После введения мемоизации временная сложность определяется числом подзадач , то есть равна \\(O(n \\times cap)\\) . Код выглядит так:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby knapsack.py<pre><code>def knapsack_dfs_mem(\n    wgt: list[int], val: list[int], mem: list[list[int]], i: int, c: int\n) -&gt; int:\n    \"\"\"Рюкзак 0-1: поиск с мемоизацией\"\"\"\n    # Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if i == 0 or c == 0:\n        return 0\n    # Если запись уже есть, вернуть сразу\n    if mem[i][c] != -1:\n        return mem[i][c]\n    # Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if wgt[i - 1] &gt; c:\n        return knapsack_dfs_mem(wgt, val, mem, i - 1, c)\n    # Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    no = knapsack_dfs_mem(wgt, val, mem, i - 1, c)\n    yes = knapsack_dfs_mem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1]\n    # Сохранить и вернуть вариант с большей стоимостью из двух решений\n    mem[i][c] = max(no, yes)\n    return mem[i][c]\n</code></pre> knapsack.cpp<pre><code>/* Рюкзак 0-1: поиск с мемоизацией */\nint knapsackDFSMem(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, vector&lt;vector&lt;int&gt;&gt; &amp;mem, int i, int c) {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][c] != -1) {\n        return mem[i][c];\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFSMem(wgt, val, mem, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    int no = knapsackDFSMem(wgt, val, mem, i - 1, c);\n    int yes = knapsackDFSMem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // Сохранить и вернуть вариант с большей стоимостью из двух решений\n    mem[i][c] = max(no, yes);\n    return mem[i][c];\n}\n</code></pre> knapsack.java<pre><code>/* Рюкзак 0-1: поиск с мемоизацией */\nint knapsackDFSMem(int[] wgt, int[] val, int[][] mem, int i, int c) {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][c] != -1) {\n        return mem[i][c];\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFSMem(wgt, val, mem, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    int no = knapsackDFSMem(wgt, val, mem, i - 1, c);\n    int yes = knapsackDFSMem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // Сохранить и вернуть вариант с большей стоимостью из двух решений\n    mem[i][c] = Math.max(no, yes);\n    return mem[i][c];\n}\n</code></pre> knapsack.cs<pre><code>/* Рюкзак 0-1: поиск с мемоизацией */\nint KnapsackDFSMem(int[] weight, int[] val, int[][] mem, int i, int c) {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][c] != -1) {\n        return mem[i][c];\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (weight[i - 1] &gt; c) {\n        return KnapsackDFSMem(weight, val, mem, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    int no = KnapsackDFSMem(weight, val, mem, i - 1, c);\n    int yes = KnapsackDFSMem(weight, val, mem, i - 1, c - weight[i - 1]) + val[i - 1];\n    // Сохранить и вернуть вариант с большей стоимостью из двух решений\n    mem[i][c] = Math.Max(no, yes);\n    return mem[i][c];\n}\n</code></pre> knapsack.go<pre><code>/* Рюкзак 0-1: поиск с мемоизацией */\nfunc knapsackDFSMem(wgt, val []int, mem [][]int, i, c int) int {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if i == 0 || c == 0 {\n        return 0\n    }\n    // Если запись уже есть, вернуть сразу\n    if mem[i][c] != -1 {\n        return mem[i][c]\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if wgt[i-1] &gt; c {\n        return knapsackDFSMem(wgt, val, mem, i-1, c)\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    no := knapsackDFSMem(wgt, val, mem, i-1, c)\n    yes := knapsackDFSMem(wgt, val, mem, i-1, c-wgt[i-1]) + val[i-1]\n    // Вернуть вариант с большей стоимостью из двух возможных\n    mem[i][c] = int(math.Max(float64(no), float64(yes)))\n    return mem[i][c]\n}\n</code></pre> knapsack.swift<pre><code>/* Рюкзак 0-1: поиск с мемоизацией */\nfunc knapsackDFSMem(wgt: [Int], val: [Int], mem: inout [[Int]], i: Int, c: Int) -&gt; Int {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if i == 0 || c == 0 {\n        return 0\n    }\n    // Если запись уже есть, вернуть сразу\n    if mem[i][c] != -1 {\n        return mem[i][c]\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if wgt[i - 1] &gt; c {\n        return knapsackDFSMem(wgt: wgt, val: val, mem: &amp;mem, i: i - 1, c: c)\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    let no = knapsackDFSMem(wgt: wgt, val: val, mem: &amp;mem, i: i - 1, c: c)\n    let yes = knapsackDFSMem(wgt: wgt, val: val, mem: &amp;mem, i: i - 1, c: c - wgt[i - 1]) + val[i - 1]\n    // Сохранить и вернуть вариант с большей стоимостью из двух решений\n    mem[i][c] = max(no, yes)\n    return mem[i][c]\n}\n</code></pre> knapsack.js<pre><code>/* Рюкзак 0-1: поиск с мемоизацией */\nfunction knapsackDFSMem(wgt, val, mem, i, c) {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i === 0 || c === 0) {\n        return 0;\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][c] !== -1) {\n        return mem[i][c];\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFSMem(wgt, val, mem, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    const no = knapsackDFSMem(wgt, val, mem, i - 1, c);\n    const yes =\n        knapsackDFSMem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // Сохранить и вернуть вариант с большей стоимостью из двух решений\n    mem[i][c] = Math.max(no, yes);\n    return mem[i][c];\n}\n</code></pre> knapsack.ts<pre><code>/* Рюкзак 0-1: поиск с мемоизацией */\nfunction knapsackDFSMem(\n    wgt: Array&lt;number&gt;,\n    val: Array&lt;number&gt;,\n    mem: Array&lt;Array&lt;number&gt;&gt;,\n    i: number,\n    c: number\n): number {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i === 0 || c === 0) {\n        return 0;\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][c] !== -1) {\n        return mem[i][c];\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFSMem(wgt, val, mem, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    const no = knapsackDFSMem(wgt, val, mem, i - 1, c);\n    const yes =\n        knapsackDFSMem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // Сохранить и вернуть вариант с большей стоимостью из двух решений\n    mem[i][c] = Math.max(no, yes);\n    return mem[i][c];\n}\n</code></pre> knapsack.dart<pre><code>/* Рюкзак 0-1: поиск с мемоизацией */\nint knapsackDFSMem(\n  List&lt;int&gt; wgt,\n  List&lt;int&gt; val,\n  List&lt;List&lt;int&gt;&gt; mem,\n  int i,\n  int c,\n) {\n  // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n  if (i == 0 || c == 0) {\n    return 0;\n  }\n  // Если запись уже есть, вернуть сразу\n  if (mem[i][c] != -1) {\n    return mem[i][c];\n  }\n  // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n  if (wgt[i - 1] &gt; c) {\n    return knapsackDFSMem(wgt, val, mem, i - 1, c);\n  }\n  // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n  int no = knapsackDFSMem(wgt, val, mem, i - 1, c);\n  int yes = knapsackDFSMem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1];\n  // Сохранить и вернуть вариант с большей стоимостью из двух решений\n  mem[i][c] = max(no, yes);\n  return mem[i][c];\n}\n</code></pre> knapsack.rs<pre><code>/* Рюкзак 0-1: поиск с мемоизацией */\nfn knapsack_dfs_mem(wgt: &amp;[i32], val: &amp;[i32], mem: &amp;mut Vec&lt;Vec&lt;i32&gt;&gt;, i: usize, c: usize) -&gt; i32 {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if i == 0 || c == 0 {\n        return 0;\n    }\n    // Если запись уже есть, вернуть сразу\n    if mem[i][c] != -1 {\n        return mem[i][c];\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if wgt[i - 1] &gt; c as i32 {\n        return knapsack_dfs_mem(wgt, val, mem, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    let no = knapsack_dfs_mem(wgt, val, mem, i - 1, c);\n    let yes = knapsack_dfs_mem(wgt, val, mem, i - 1, c - wgt[i - 1] as usize) + val[i - 1];\n    // Сохранить и вернуть вариант с большей стоимостью из двух решений\n    mem[i][c] = std::cmp::max(no, yes);\n    mem[i][c]\n}\n</code></pre> knapsack.c<pre><code>/* Рюкзак 0-1: поиск с мемоизацией */\nint knapsackDFSMem(int wgt[], int val[], int memCols, int **mem, int i, int c) {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][c] != -1) {\n        return mem[i][c];\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFSMem(wgt, val, memCols, mem, i - 1, c);\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    int no = knapsackDFSMem(wgt, val, memCols, mem, i - 1, c);\n    int yes = knapsackDFSMem(wgt, val, memCols, mem, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // Сохранить и вернуть вариант с большей стоимостью из двух решений\n    mem[i][c] = myMax(no, yes);\n    return mem[i][c];\n}\n</code></pre> knapsack.kt<pre><code>/* Рюкзак 0-1: поиск с мемоизацией */\nfun knapsackDFSMem(\n    wgt: IntArray,\n    _val: IntArray,\n    mem: Array&lt;IntArray&gt;,\n    i: Int,\n    c: Int\n): Int {\n    // Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n    if (i == 0 || c == 0) {\n        return 0\n    }\n    // Если запись уже есть, вернуть сразу\n    if (mem[i][c] != -1) {\n        return mem[i][c]\n    }\n    // Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFSMem(wgt, _val, mem, i - 1, c)\n    }\n    // Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n    val no = knapsackDFSMem(wgt, _val, mem, i - 1, c)\n    val yes = knapsackDFSMem(wgt, _val, mem, i - 1, c - wgt[i - 1]) + _val[i - 1]\n    // Сохранить и вернуть вариант с большей стоимостью из двух решений\n    mem[i][c] = max(no, yes)\n    return mem[i][c]\n}\n</code></pre> knapsack.rb<pre><code>### Рюкзак 0-1: поиск с мемоизацией ###\ndef knapsack_dfs_mem(wgt, val, mem, i, c)\n  # Если все предметы уже рассмотрены или в рюкзаке не осталось места, вернуть стоимость 0\n  return 0 if i == 0 || c == 0\n  # Если запись уже есть, вернуть сразу\n  return mem[i][c] if mem[i][c] != -1\n  # Если вместимость рюкзака превышена, можно только не класть предмет в рюкзак\n  return knapsack_dfs_mem(wgt, val, mem, i - 1, c) if wgt[i - 1] &gt; c\n  # Вычислить максимальную стоимость для случаев, когда предмет i не кладут и кладут\n  no = knapsack_dfs_mem(wgt, val, mem, i - 1, c)\n  yes = knapsack_dfs_mem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1]\n  # Сохранить и вернуть вариант с большей стоимостью из двух решений\n  mem[i][c] = [no, yes].max\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>На рисунке 14-19 показаны ветви поиска, которые были отсечены благодаря мемоизации.</p> <p></p> <p> Рисунок 14-19   Дерево поиска с мемоизацией для задачи о рюкзаке 0-1 </p>","path":["Глава 14. Динамическое программирование","14.4 &nbsp; Задача о рюкзаке 0-1"],"tags":[]},{"location":"chapter_dynamic_programming/knapsack_problem/#3-3","level":3,"title":"3.   Метод 3: динамическое программирование","text":"<p>По своей сути динамическое программирование здесь - это процесс последовательного заполнения таблицы \\(dp\\) в соответствии с переходами состояний. Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby knapsack.py<pre><code>def knapsack_dp(wgt: list[int], val: list[int], cap: int) -&gt; int:\n    \"\"\"Рюкзак 0-1: динамическое программирование\"\"\"\n    n = len(wgt)\n    # Инициализация таблицы dp\n    dp = [[0] * (cap + 1) for _ in range(n + 1)]\n    # Переход состояний\n    for i in range(1, n + 1):\n        for c in range(1, cap + 1):\n            if wgt[i - 1] &gt; c:\n                # Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c]\n            else:\n                # Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1])\n    return dp[n][cap]\n</code></pre> knapsack.cpp<pre><code>/* Рюкзак 0-1: динамическое программирование */\nint knapsackDP(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int cap) {\n    int n = wgt.size();\n    // Инициализация таблицы dp\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(cap + 1, 0));\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> knapsack.java<pre><code>/* Рюкзак 0-1: динамическое программирование */\nint knapsackDP(int[] wgt, int[] val, int cap) {\n    int n = wgt.length;\n    // Инициализация таблицы dp\n    int[][] dp = new int[n + 1][cap + 1];\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = Math.max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> knapsack.cs<pre><code>/* Рюкзак 0-1: динамическое программирование */\nint KnapsackDP(int[] weight, int[] val, int cap) {\n    int n = weight.Length;\n    // Инициализация таблицы dp\n    int[,] dp = new int[n + 1, cap + 1];\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (weight[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i, c] = dp[i - 1, c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i, c] = Math.Max(dp[i - 1, c - weight[i - 1]] + val[i - 1], dp[i - 1, c]);\n            }\n        }\n    }\n    return dp[n, cap];\n}\n</code></pre> knapsack.go<pre><code>/* Рюкзак 0-1: динамическое программирование */\nfunc knapsackDP(wgt, val []int, cap int) int {\n    n := len(wgt)\n    // Инициализация таблицы dp\n    dp := make([][]int, n+1)\n    for i := 0; i &lt;= n; i++ {\n        dp[i] = make([]int, cap+1)\n    }\n    // Переход состояний\n    for i := 1; i &lt;= n; i++ {\n        for c := 1; c &lt;= cap; c++ {\n            if wgt[i-1] &gt; c {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i-1][c]\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = int(math.Max(float64(dp[i-1][c]), float64(dp[i-1][c-wgt[i-1]]+val[i-1])))\n            }\n        }\n    }\n    return dp[n][cap]\n}\n</code></pre> knapsack.swift<pre><code>/* Рюкзак 0-1: динамическое программирование */\nfunc knapsackDP(wgt: [Int], val: [Int], cap: Int) -&gt; Int {\n    let n = wgt.count\n    // Инициализация таблицы dp\n    var dp = Array(repeating: Array(repeating: 0, count: cap + 1), count: n + 1)\n    // Переход состояний\n    for i in 1 ... n {\n        for c in 1 ... cap {\n            if wgt[i - 1] &gt; c {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c]\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1])\n            }\n        }\n    }\n    return dp[n][cap]\n}\n</code></pre> knapsack.js<pre><code>/* Рюкзак 0-1: динамическое программирование */\nfunction knapsackDP(wgt, val, cap) {\n    const n = wgt.length;\n    // Инициализация таблицы dp\n    const dp = Array(n + 1)\n        .fill(0)\n        .map(() =&gt; Array(cap + 1).fill(0));\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        for (let c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = Math.max(\n                    dp[i - 1][c],\n                    dp[i - 1][c - wgt[i - 1]] + val[i - 1]\n                );\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> knapsack.ts<pre><code>/* Рюкзак 0-1: динамическое программирование */\nfunction knapsackDP(\n    wgt: Array&lt;number&gt;,\n    val: Array&lt;number&gt;,\n    cap: number\n): number {\n    const n = wgt.length;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: n + 1 }, () =&gt;\n        Array.from({ length: cap + 1 }, () =&gt; 0)\n    );\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        for (let c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = Math.max(\n                    dp[i - 1][c],\n                    dp[i - 1][c - wgt[i - 1]] + val[i - 1]\n                );\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> knapsack.dart<pre><code>/* Рюкзак 0-1: динамическое программирование */\nint knapsackDP(List&lt;int&gt; wgt, List&lt;int&gt; val, int cap) {\n  int n = wgt.length;\n  // Инициализация таблицы dp\n  List&lt;List&lt;int&gt;&gt; dp = List.generate(n + 1, (index) =&gt; List.filled(cap + 1, 0));\n  // Переход состояний\n  for (int i = 1; i &lt;= n; i++) {\n    for (int c = 1; c &lt;= cap; c++) {\n      if (wgt[i - 1] &gt; c) {\n        // Если вместимость рюкзака превышена, предмет i не выбирать\n        dp[i][c] = dp[i - 1][c];\n      } else {\n        // Большее из двух решений: не брать или взять предмет i\n        dp[i][c] = max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1]);\n      }\n    }\n  }\n  return dp[n][cap];\n}\n</code></pre> knapsack.rs<pre><code>/* Рюкзак 0-1: динамическое программирование */\nfn knapsack_dp(wgt: &amp;[i32], val: &amp;[i32], cap: usize) -&gt; i32 {\n    let n = wgt.len();\n    // Инициализация таблицы dp\n    let mut dp = vec![vec![0; cap + 1]; n + 1];\n    // Переход состояний\n    for i in 1..=n {\n        for c in 1..=cap {\n            if wgt[i - 1] &gt; c as i32 {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = std::cmp::max(\n                    dp[i - 1][c],\n                    dp[i - 1][c - wgt[i - 1] as usize] + val[i - 1],\n                );\n            }\n        }\n    }\n    dp[n][cap]\n}\n</code></pre> knapsack.c<pre><code>/* Рюкзак 0-1: динамическое программирование */\nint knapsackDP(int wgt[], int val[], int cap, int wgtSize) {\n    int n = wgtSize;\n    // Инициализация таблицы dp\n    int **dp = malloc((n + 1) * sizeof(int *));\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i] = calloc(cap + 1, sizeof(int));\n    }\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = myMax(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    int res = dp[n][cap];\n    // Освободить память\n    for (int i = 0; i &lt;= n; i++) {\n        free(dp[i]);\n    }\n    return res;\n}\n</code></pre> knapsack.kt<pre><code>/* Рюкзак 0-1: динамическое программирование */\nfun knapsackDP(wgt: IntArray, _val: IntArray, cap: Int): Int {\n    val n = wgt.size\n    // Инициализация таблицы dp\n    val dp = Array(n + 1) { IntArray(cap + 1) }\n    // Переход состояний\n    for (i in 1..n) {\n        for (c in 1..cap) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c]\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + _val[i - 1])\n            }\n        }\n    }\n    return dp[n][cap]\n}\n</code></pre> knapsack.rb<pre><code>### Рюкзак 0-1: динамическое программирование ###\ndef knapsack_dp(wgt, val, cap)\n  n = wgt.length\n  # Инициализация таблицы dp\n  dp = Array.new(n + 1) { Array.new(cap + 1, 0) }\n  # Переход состояний\n  for i in 1...(n + 1)\n    for c in 1...(cap + 1)\n      if wgt[i - 1] &gt; c\n        # Если вместимость рюкзака превышена, предмет i не выбирать\n        dp[i][c] = dp[i - 1][c]\n      else\n        # Большее из двух решений: не брать или взять предмет i\n        dp[i][c] = [dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1]].max\n      end\n    end\n  end\n  dp[n][cap]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Как показано на рисунке 14-20, и временная сложность, и пространственная сложность определяются размером массива <code>dp</code> , то есть равны \\(O(n \\times cap)\\) .</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt;&lt;13&gt;&lt;14&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 14-20   Процесс динамического программирования для задачи о рюкзаке 0-1 </p>","path":["Глава 14. Динамическое программирование","14.4 &nbsp; Задача о рюкзаке 0-1"],"tags":[]},{"location":"chapter_dynamic_programming/knapsack_problem/#4","level":3,"title":"4.   Оптимизация пространства","text":"<p>Поскольку каждое состояние зависит только от состояния в предыдущей строке, можно использовать два массива, которые будут продвигаться вперед по очереди, и тем самым уменьшить пространственную сложность с \\(O(n^2)\\) до \\(O(n)\\) .</p> <p>Если пойти дальше, можно спросить: можно ли оптимизировать память так, чтобы использовать только один массив? Наблюдение показывает, что каждое состояние зависит от клетки прямо сверху и клетки слева сверху. Предположим, что у нас есть только один массив, и в момент начала обхода строки \\(i\\) он еще хранит состояния строки \\(i-1\\) .</p> <ul> <li>Если обходить массив слева направо, то к моменту вычисления \\(dp[i, j]\\) значения слева сверху \\(dp[i-1, 1]\\) ~ \\(dp[i-1, j-1]\\) могут уже быть перезаписаны, и правильный результат перехода состояния получить не удастся.</li> <li>Если же обходить массив справа налево, проблема перезаписи не возникает, и переход состояния вычисляется корректно.</li> </ul> <p>На рисунке 14-21 показан процесс перехода от строки \\(i = 1\\) к строке \\(i = 2\\) при использовании одного массива. С его помощью удобно понять различие между прямым и обратным обходом.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 14-21   Процесс динамического программирования после оптимизации памяти для рюкзака 0-1 </p> <p>В коде для этого достаточно удалить первое измерение массива <code>dp</code> , а внутренний цикл заменить на обратный обход:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby knapsack.py<pre><code>def knapsack_dp_comp(wgt: list[int], val: list[int], cap: int) -&gt; int:\n    \"\"\"Рюкзак 0-1: динамическое программирование с оптимизацией памяти\"\"\"\n    n = len(wgt)\n    # Инициализация таблицы dp\n    dp = [0] * (cap + 1)\n    # Переход состояний\n    for i in range(1, n + 1):\n        # Обход в обратном порядке\n        for c in range(cap, 0, -1):\n            if wgt[i - 1] &gt; c:\n                # Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c]\n            else:\n                # Большее из двух решений: не брать или взять предмет i\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1])\n    return dp[cap]\n</code></pre> knapsack.cpp<pre><code>/* Рюкзак 0-1: динамическое программирование с оптимизацией памяти */\nint knapsackDPComp(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int cap) {\n    int n = wgt.size();\n    // Инициализация таблицы dp\n    vector&lt;int&gt; dp(cap + 1, 0);\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        // Обход в обратном порядке\n        for (int c = cap; c &gt;= 1; c--) {\n            if (wgt[i - 1] &lt;= c) {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> knapsack.java<pre><code>/* Рюкзак 0-1: динамическое программирование с оптимизацией памяти */\nint knapsackDPComp(int[] wgt, int[] val, int cap) {\n    int n = wgt.length;\n    // Инициализация таблицы dp\n    int[] dp = new int[cap + 1];\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        // Обход в обратном порядке\n        for (int c = cap; c &gt;= 1; c--) {\n            if (wgt[i - 1] &lt;= c) {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> knapsack.cs<pre><code>/* Рюкзак 0-1: динамическое программирование с оптимизацией памяти */\nint KnapsackDPComp(int[] weight, int[] val, int cap) {\n    int n = weight.Length;\n    // Инициализация таблицы dp\n    int[] dp = new int[cap + 1];\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        // Обход в обратном порядке\n        for (int c = cap; c &gt; 0; c--) {\n            if (weight[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = Math.Max(dp[c], dp[c - weight[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> knapsack.go<pre><code>/* Рюкзак 0-1: динамическое программирование с оптимизацией памяти */\nfunc knapsackDPComp(wgt, val []int, cap int) int {\n    n := len(wgt)\n    // Инициализация таблицы dp\n    dp := make([]int, cap+1)\n    // Переход состояний\n    for i := 1; i &lt;= n; i++ {\n        // Обход в обратном порядке\n        for c := cap; c &gt;= 1; c-- {\n            if wgt[i-1] &lt;= c {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = int(math.Max(float64(dp[c]), float64(dp[c-wgt[i-1]]+val[i-1])))\n            }\n        }\n    }\n    return dp[cap]\n}\n</code></pre> knapsack.swift<pre><code>/* Рюкзак 0-1: динамическое программирование с оптимизацией памяти */\nfunc knapsackDPComp(wgt: [Int], val: [Int], cap: Int) -&gt; Int {\n    let n = wgt.count\n    // Инициализация таблицы dp\n    var dp = Array(repeating: 0, count: cap + 1)\n    // Переход состояний\n    for i in 1 ... n {\n        // Обход в обратном порядке\n        for c in (1 ... cap).reversed() {\n            if wgt[i - 1] &lt;= c {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1])\n            }\n        }\n    }\n    return dp[cap]\n}\n</code></pre> knapsack.js<pre><code>/* Рюкзак 0-1: динамическое программирование с оптимизацией памяти */\nfunction knapsackDPComp(wgt, val, cap) {\n    const n = wgt.length;\n    // Инициализация таблицы dp\n    const dp = Array(cap + 1).fill(0);\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        // Обход в обратном порядке\n        for (let c = cap; c &gt;= 1; c--) {\n            if (wgt[i - 1] &lt;= c) {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> knapsack.ts<pre><code>/* Рюкзак 0-1: динамическое программирование с оптимизацией памяти */\nfunction knapsackDPComp(\n    wgt: Array&lt;number&gt;,\n    val: Array&lt;number&gt;,\n    cap: number\n): number {\n    const n = wgt.length;\n    // Инициализация таблицы dp\n    const dp = Array(cap + 1).fill(0);\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        // Обход в обратном порядке\n        for (let c = cap; c &gt;= 1; c--) {\n            if (wgt[i - 1] &lt;= c) {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> knapsack.dart<pre><code>/* Рюкзак 0-1: динамическое программирование с оптимизацией памяти */\nint knapsackDPComp(List&lt;int&gt; wgt, List&lt;int&gt; val, int cap) {\n  int n = wgt.length;\n  // Инициализация таблицы dp\n  List&lt;int&gt; dp = List.filled(cap + 1, 0);\n  // Переход состояний\n  for (int i = 1; i &lt;= n; i++) {\n    // Обход в обратном порядке\n    for (int c = cap; c &gt;= 1; c--) {\n      if (wgt[i - 1] &lt;= c) {\n        // Большее из двух решений: не брать или взять предмет i\n        dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n      }\n    }\n  }\n  return dp[cap];\n}\n</code></pre> knapsack.rs<pre><code>/* Рюкзак 0-1: динамическое программирование с оптимизацией памяти */\nfn knapsack_dp_comp(wgt: &amp;[i32], val: &amp;[i32], cap: usize) -&gt; i32 {\n    let n = wgt.len();\n    // Инициализация таблицы dp\n    let mut dp = vec![0; cap + 1];\n    // Переход состояний\n    for i in 1..=n {\n        // Обход в обратном порядке\n        for c in (1..=cap).rev() {\n            if wgt[i - 1] &lt;= c as i32 {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = std::cmp::max(dp[c], dp[c - wgt[i - 1] as usize] + val[i - 1]);\n            }\n        }\n    }\n    dp[cap]\n}\n</code></pre> knapsack.c<pre><code>/* Рюкзак 0-1: динамическое программирование с оптимизацией памяти */\nint knapsackDPComp(int wgt[], int val[], int cap, int wgtSize) {\n    int n = wgtSize;\n    // Инициализация таблицы dp\n    int *dp = calloc(cap + 1, sizeof(int));\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        // Обход в обратном порядке\n        for (int c = cap; c &gt;= 1; c--) {\n            if (wgt[i - 1] &lt;= c) {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = myMax(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    int res = dp[cap];\n    // Освободить память\n    free(dp);\n    return res;\n}\n</code></pre> knapsack.kt<pre><code>/* Рюкзак 0-1: динамическое программирование с оптимизацией памяти */\nfun knapsackDPComp(wgt: IntArray, _val: IntArray, cap: Int): Int {\n    val n = wgt.size\n    // Инициализация таблицы dp\n    val dp = IntArray(cap + 1)\n    // Переход состояний\n    for (i in 1..n) {\n        // Обход в обратном порядке\n        for (c in cap downTo 1) {\n            if (wgt[i - 1] &lt;= c) {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + _val[i - 1])\n            }\n        }\n    }\n    return dp[cap]\n}\n</code></pre> knapsack.rb<pre><code>### Рюкзак 0-1: динамическое программирование с оптимизацией памяти ###\ndef knapsack_dp_comp(wgt, val, cap)\n  n = wgt.length\n  # Инициализация таблицы dp\n  dp = Array.new(cap + 1, 0)\n  # Переход состояний\n  for i in 1...(n + 1)\n    # Обход в обратном порядке\n    for c in cap.downto(1)\n      if wgt[i - 1] &gt; c\n        # Если вместимость рюкзака превышена, предмет i не выбирать\n        dp[c] = dp[c]\n      else\n        # Большее из двух решений: не брать или взять предмет i\n        dp[c] = [dp[c], dp[c - wgt[i - 1]] + val[i - 1]].max\n      end\n    end\n  end\n  dp[cap]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 14. Динамическое программирование","14.4 &nbsp; Задача о рюкзаке 0-1"],"tags":[]},{"location":"chapter_dynamic_programming/summary/","level":1,"title":"14.7   Резюме","text":"","path":["Глава 14. Динамическое программирование","14.7 &nbsp; Резюме"],"tags":[]},{"location":"chapter_dynamic_programming/summary/#1","level":3,"title":"1.   Ключевые выводы","text":"<ul> <li>Динамическое программирование раскладывает задачу на подзадачи и повышает вычислительную эффективность за счет хранения решений этих подзадач и устранения повторных вычислений.</li> <li>Если не учитывать затраты времени, то любую задачу динамического программирования можно решить с помощью поиска с возвратом (полного перебора), однако в дереве рекурсии возникает множество перекрывающихся подзадач, из-за чего эффективность крайне низка. После введения таблицы памяти можно хранить решения всех уже вычисленных подзадач и гарантировать, что каждая перекрывающаяся подзадача будет вычисляться только один раз.</li> <li>Поиск с мемоизацией - это рекурсивный метод \"сверху вниз\", а соответствующее ему динамическое программирование - это итеративный метод \"снизу вверх\", похожий на заполнение таблицы. Поскольку текущее состояние обычно зависит только от части локальных состояний, можно убрать одно измерение таблицы \\(dp\\) и тем самым снизить пространственную сложность.</li> <li>Разложение на подзадачи - это общий алгоритмический подход, но в методе \"разделяй и властвуй\", динамическом программировании и поиске с возвратом он имеет разные свойства.</li> <li>Для задач динамического программирования характерны три главных свойства: перекрывающиеся подзадачи, оптимальная подструктура и отсутствие последствий.</li> <li>Если оптимальное решение исходной задачи можно построить из оптимальных решений подзадач, то задача обладает оптимальной подструктурой.</li> <li>Отсутствие последствий означает, что для данного состояния его дальнейшее развитие определяется только этим состоянием и не зависит от всех прошлых состояний. Многие задачи комбинаторной оптимизации этим свойством не обладают и потому не могут эффективно решаться с помощью динамического программирования.</li> </ul> <p>Задачи о рюкзаке</p> <ul> <li>Задача о рюкзаке - один из самых типичных классов задач динамического программирования; она включает варианты 0-1 рюкзака, полного рюкзака, многократного рюкзака и другие.</li> <li>В задаче о рюкзаке 0-1 состояние определяется как максимальная стоимость первых \\(i\\) предметов в рюкзаке вместимости \\(c\\) . Рассматривая два решения - не брать предмет и брать предмет, - можно получить оптимальную подструктуру и вывести уравнение перехода состояния. При оптимизации памяти, поскольку каждое состояние зависит от значения сверху и слева сверху, внутренний цикл нужно выполнять в обратном порядке, чтобы не перезаписать нужное значение.</li> <li>В задаче о полном рюкзаке число экземпляров каждого предмета не ограничено, поэтому при выборе предмета переход состояния отличается от варианта 0-1. Поскольку состояние зависит от значения сверху и слева, после оптимизации памяти внутренний цикл следует выполнять в прямом порядке.</li> <li>Задача о размене монет - это вариант задачи о полном рюкзаке. Здесь вместо \"максимальной стоимости\" ищется \"минимальное число монет\", поэтому в уравнении перехода \\(\\max()\\) заменяется на \\(\\min()\\) . Кроме того, вместо условия \"не превышать вместимость рюкзака\" нужно ровно набрать целевую сумму, поэтому значение \\(amt + 1\\) используется как обозначение недопустимого решения \"сумму набрать нельзя\".</li> <li>В задаче о размене монет II вместо \"минимального числа монет\" требуется найти \"число комбинаций монет\", поэтому в уравнении перехода оператор \\(\\min()\\) заменяется на суммирование.</li> </ul> <p>Задача о расстоянии редактирования</p> <ul> <li>Расстояние редактирования (расстояние Левенштейна) используется для измерения сходства двух строк и определяется как минимальное число операций редактирования, необходимых для преобразования одной строки в другую; допустимые операции - вставка, удаление и замена.</li> <li>В задаче о расстоянии редактирования состояние определяется как минимальное число шагов редактирования, необходимых для преобразования первых \\(i\\) символов строки \\(s\\) в первые \\(j\\) символов строки \\(t\\) . Если \\(s[i] \\ne t[j]\\) , то существуют три решения: вставка, удаление и замена, и каждому из них соответствует своя остаточная подзадача. На этой основе выводятся оптимальная подструктура и уравнение перехода состояния. Если же \\(s[i] = t[j]\\) , то редактировать текущий символ не нужно.</li> <li>В задаче о расстоянии редактирования состояние зависит от значений сверху, слева и слева сверху. Поэтому после оптимизации памяти ни прямой, ни обратный обход сам по себе не дает корректного перехода состояния. Для решения этой проблемы значение слева сверху временно сохраняется в отдельной переменной, что делает ситуацию эквивалентной задаче о полном рюкзаке и позволяет использовать прямой обход.</li> </ul>","path":["Глава 14. Динамическое программирование","14.7 &nbsp; Резюме"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/","level":1,"title":"14.5   Задача о полном рюкзаке","text":"<p>В этом разделе сначала решим еще одну распространенную задачу о рюкзаке - задачу о полном рюкзаке, а затем рассмотрим один из ее типичных частных случаев: задачу о размене монет.</p>","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1451","level":2,"title":"14.5.1   Задача о полном рюкзаке","text":"<p>Question</p> <p>Даны \\(n\\) предметов. Вес \\(i\\)-го предмета равен \\(wgt[i-1]\\) , стоимость равна \\(val[i-1]\\) . Также дан рюкзак вместимости \\(cap\\) . Каждый предмет можно выбирать многократно. Найдите максимальную суммарную стоимость, которую можно поместить в рюкзак при заданной вместимости. Пример показан на рисунке 14-22.</p> <p></p> <p> Рисунок 14-22   Пример данных для задачи о полном рюкзаке </p>","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1","level":3,"title":"1.   Идея динамического программирования","text":"<p>Задача о полном рюкзаке очень похожа на задачу о рюкзаке 0-1; разница состоит только в том, что количество выборов каждого предмета не ограничено.</p> <ul> <li>В задаче о рюкзаке 0-1 каждого предмета существует только один экземпляр, поэтому после того как предмет \\(i\\) помещен в рюкзак, выбирать можно только из первых \\(i-1\\) предметов.</li> <li>В задаче о полном рюкзаке количество предметов не ограничено, поэтому после того как предмет \\(i\\) помещен в рюкзак, можно продолжать выбирать из первых \\(i\\) предметов.</li> </ul> <p>При этом состояние \\([i, c]\\) в задаче о полном рюкзаке может изменяться двумя способами.</p> <ul> <li>Не брать предмет \\(i\\) : как и в задаче о рюкзаке 0-1, переход осуществляется в \\([i-1, c]\\) .</li> <li>Взять предмет \\(i\\) : в отличие от рюкзака 0-1 переход происходит в \\([i, c-wgt[i-1]]\\) .</li> </ul> <p>Следовательно, уравнение перехода состояния принимает вид:</p> \\[ dp[i, c] = \\max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1]) \\]","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#2","level":3,"title":"2.   Реализация кода","text":"<p>Если сравнить код этой задачи с кодом задачи о рюкзаке 0-1, то окажется, что в переходе состояний меняется только одна деталь: вместо \\(i-1\\) появляется \\(i\\) ; все остальное остается таким же:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby unbounded_knapsack.py<pre><code>def unbounded_knapsack_dp(wgt: list[int], val: list[int], cap: int) -&gt; int:\n    \"\"\"Полный рюкзак: динамическое программирование\"\"\"\n    n = len(wgt)\n    # Инициализация таблицы dp\n    dp = [[0] * (cap + 1) for _ in range(n + 1)]\n    # Переход состояний\n    for i in range(1, n + 1):\n        for c in range(1, cap + 1):\n            if wgt[i - 1] &gt; c:\n                # Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c]\n            else:\n                # Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1])\n    return dp[n][cap]\n</code></pre> unbounded_knapsack.cpp<pre><code>/* Полный рюкзак: динамическое программирование */\nint unboundedKnapsackDP(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int cap) {\n    int n = wgt.size();\n    // Инициализация таблицы dp\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(cap + 1, 0));\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> unbounded_knapsack.java<pre><code>/* Полный рюкзак: динамическое программирование */\nint unboundedKnapsackDP(int[] wgt, int[] val, int cap) {\n    int n = wgt.length;\n    // Инициализация таблицы dp\n    int[][] dp = new int[n + 1][cap + 1];\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = Math.max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> unbounded_knapsack.cs<pre><code>/* Полный рюкзак: динамическое программирование */\nint UnboundedKnapsackDP(int[] wgt, int[] val, int cap) {\n    int n = wgt.Length;\n    // Инициализация таблицы dp\n    int[,] dp = new int[n + 1, cap + 1];\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i, c] = dp[i - 1, c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i, c] = Math.Max(dp[i - 1, c], dp[i, c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n, cap];\n}\n</code></pre> unbounded_knapsack.go<pre><code>/* Полный рюкзак: динамическое программирование */\nfunc unboundedKnapsackDP(wgt, val []int, cap int) int {\n    n := len(wgt)\n    // Инициализация таблицы dp\n    dp := make([][]int, n+1)\n    for i := 0; i &lt;= n; i++ {\n        dp[i] = make([]int, cap+1)\n    }\n    // Переход состояний\n    for i := 1; i &lt;= n; i++ {\n        for c := 1; c &lt;= cap; c++ {\n            if wgt[i-1] &gt; c {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i-1][c]\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = int(math.Max(float64(dp[i-1][c]), float64(dp[i][c-wgt[i-1]]+val[i-1])))\n            }\n        }\n    }\n    return dp[n][cap]\n}\n</code></pre> unbounded_knapsack.swift<pre><code>/* Полный рюкзак: динамическое программирование */\nfunc unboundedKnapsackDP(wgt: [Int], val: [Int], cap: Int) -&gt; Int {\n    let n = wgt.count\n    // Инициализация таблицы dp\n    var dp = Array(repeating: Array(repeating: 0, count: cap + 1), count: n + 1)\n    // Переход состояний\n    for i in 1 ... n {\n        for c in 1 ... cap {\n            if wgt[i - 1] &gt; c {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c]\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1])\n            }\n        }\n    }\n    return dp[n][cap]\n}\n</code></pre> unbounded_knapsack.js<pre><code>/* Полный рюкзак: динамическое программирование */\nfunction unboundedKnapsackDP(wgt, val, cap) {\n    const n = wgt.length;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: n + 1 }, () =&gt;\n        Array.from({ length: cap + 1 }, () =&gt; 0)\n    );\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        for (let c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = Math.max(\n                    dp[i - 1][c],\n                    dp[i][c - wgt[i - 1]] + val[i - 1]\n                );\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> unbounded_knapsack.ts<pre><code>/* Полный рюкзак: динамическое программирование */\nfunction unboundedKnapsackDP(\n    wgt: Array&lt;number&gt;,\n    val: Array&lt;number&gt;,\n    cap: number\n): number {\n    const n = wgt.length;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: n + 1 }, () =&gt;\n        Array.from({ length: cap + 1 }, () =&gt; 0)\n    );\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        for (let c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = Math.max(\n                    dp[i - 1][c],\n                    dp[i][c - wgt[i - 1]] + val[i - 1]\n                );\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> unbounded_knapsack.dart<pre><code>/* Полный рюкзак: динамическое программирование */\nint unboundedKnapsackDP(List&lt;int&gt; wgt, List&lt;int&gt; val, int cap) {\n  int n = wgt.length;\n  // Инициализация таблицы dp\n  List&lt;List&lt;int&gt;&gt; dp = List.generate(n + 1, (index) =&gt; List.filled(cap + 1, 0));\n  // Переход состояний\n  for (int i = 1; i &lt;= n; i++) {\n    for (int c = 1; c &lt;= cap; c++) {\n      if (wgt[i - 1] &gt; c) {\n        // Если вместимость рюкзака превышена, предмет i не выбирать\n        dp[i][c] = dp[i - 1][c];\n      } else {\n        // Большее из двух решений: не брать или взять предмет i\n        dp[i][c] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]);\n      }\n    }\n  }\n  return dp[n][cap];\n}\n</code></pre> unbounded_knapsack.rs<pre><code>/* Полный рюкзак: динамическое программирование */\nfn unbounded_knapsack_dp(wgt: &amp;[i32], val: &amp;[i32], cap: usize) -&gt; i32 {\n    let n = wgt.len();\n    // Инициализация таблицы dp\n    let mut dp = vec![vec![0; cap + 1]; n + 1];\n    // Переход состояний\n    for i in 1..=n {\n        for c in 1..=cap {\n            if wgt[i - 1] &gt; c as i32 {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = std::cmp::max(dp[i - 1][c], dp[i][c - wgt[i - 1] as usize] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> unbounded_knapsack.c<pre><code>/* Полный рюкзак: динамическое программирование */\nint unboundedKnapsackDP(int wgt[], int val[], int cap, int wgtSize) {\n    int n = wgtSize;\n    // Инициализация таблицы dp\n    int **dp = malloc((n + 1) * sizeof(int *));\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i] = calloc(cap + 1, sizeof(int));\n    }\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = myMax(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    int res = dp[n][cap];\n    // Освободить память\n    for (int i = 0; i &lt;= n; i++) {\n        free(dp[i]);\n    }\n    return res;\n}\n</code></pre> unbounded_knapsack.kt<pre><code>/* Полный рюкзак: динамическое программирование */\nfun unboundedKnapsackDP(wgt: IntArray, _val: IntArray, cap: Int): Int {\n    val n = wgt.size\n    // Инициализация таблицы dp\n    val dp = Array(n + 1) { IntArray(cap + 1) }\n    // Переход состояний\n    for (i in 1..n) {\n        for (c in 1..cap) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[i][c] = dp[i - 1][c]\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[i][c] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + _val[i - 1])\n            }\n        }\n    }\n    return dp[n][cap]\n}\n</code></pre> unbounded_knapsack.rb<pre><code>### Полный рюкзак: динамическое программирование ###\ndef unbounded_knapsack_dp(wgt, val, cap)\n  n = wgt.length\n  # Инициализация таблицы dp\n  dp = Array.new(n + 1) { Array.new(cap + 1, 0) }\n  # Переход состояний\n  for i in 1...(n + 1)\n    for c in 1...(cap + 1)\n      if wgt[i - 1] &gt; c\n        # Если вместимость рюкзака превышена, предмет i не выбирать\n        dp[i][c] = dp[i - 1][c]\n      else\n        # Большее из двух решений: не брать или взять предмет i\n        dp[i][c] = [dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]].max\n      end\n    end\n  end\n  dp[n][cap]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#3","level":3,"title":"3.   Оптимизация пространства","text":"<p>Поскольку текущее состояние переходит из состояния слева и состояния сверху, после оптимизации памяти каждую строку таблицы \\(dp\\) нужно обходить слева направо.</p> <p>Этот порядок обхода как раз противоположен задаче о рюкзаке 0-1. Разницу удобно понять по рисунку ниже.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 14-23   Процесс динамического программирования после оптимизации памяти для полного рюкзака </p> <p>Код реализации здесь довольно прост: достаточно просто убрать первое измерение массива <code>dp</code> :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby unbounded_knapsack.py<pre><code>def unbounded_knapsack_dp_comp(wgt: list[int], val: list[int], cap: int) -&gt; int:\n    \"\"\"Полный рюкзак: динамическое программирование с оптимизацией памяти\"\"\"\n    n = len(wgt)\n    # Инициализация таблицы dp\n    dp = [0] * (cap + 1)\n    # Переход состояний\n    for i in range(1, n + 1):\n        # Прямой обход\n        for c in range(1, cap + 1):\n            if wgt[i - 1] &gt; c:\n                # Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c]\n            else:\n                # Большее из двух решений: не брать или взять предмет i\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1])\n    return dp[cap]\n</code></pre> unbounded_knapsack.cpp<pre><code>/* Полный рюкзак: динамическое программирование с оптимизацией памяти */\nint unboundedKnapsackDPComp(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int cap) {\n    int n = wgt.size();\n    // Инициализация таблицы dp\n    vector&lt;int&gt; dp(cap + 1, 0);\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> unbounded_knapsack.java<pre><code>/* Полный рюкзак: динамическое программирование с оптимизацией памяти */\nint unboundedKnapsackDPComp(int[] wgt, int[] val, int cap) {\n    int n = wgt.length;\n    // Инициализация таблицы dp\n    int[] dp = new int[cap + 1];\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> unbounded_knapsack.cs<pre><code>/* Полный рюкзак: динамическое программирование с оптимизацией памяти */\nint UnboundedKnapsackDPComp(int[] wgt, int[] val, int cap) {\n    int n = wgt.Length;\n    // Инициализация таблицы dp\n    int[] dp = new int[cap + 1];\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = Math.Max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> unbounded_knapsack.go<pre><code>/* Полный рюкзак: динамическое программирование с оптимизацией памяти */\nfunc unboundedKnapsackDPComp(wgt, val []int, cap int) int {\n    n := len(wgt)\n    // Инициализация таблицы dp\n    dp := make([]int, cap+1)\n    // Переход состояний\n    for i := 1; i &lt;= n; i++ {\n        for c := 1; c &lt;= cap; c++ {\n            if wgt[i-1] &gt; c {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c]\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = int(math.Max(float64(dp[c]), float64(dp[c-wgt[i-1]]+val[i-1])))\n            }\n        }\n    }\n    return dp[cap]\n}\n</code></pre> unbounded_knapsack.swift<pre><code>/* Полный рюкзак: динамическое программирование с оптимизацией памяти */\nfunc unboundedKnapsackDPComp(wgt: [Int], val: [Int], cap: Int) -&gt; Int {\n    let n = wgt.count\n    // Инициализация таблицы dp\n    var dp = Array(repeating: 0, count: cap + 1)\n    // Переход состояний\n    for i in 1 ... n {\n        for c in 1 ... cap {\n            if wgt[i - 1] &gt; c {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c]\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1])\n            }\n        }\n    }\n    return dp[cap]\n}\n</code></pre> unbounded_knapsack.js<pre><code>/* Полный рюкзак: динамическое программирование с оптимизацией памяти */\nfunction unboundedKnapsackDPComp(wgt, val, cap) {\n    const n = wgt.length;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: cap + 1 }, () =&gt; 0);\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        for (let c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> unbounded_knapsack.ts<pre><code>/* Полный рюкзак: динамическое программирование с оптимизацией памяти */\nfunction unboundedKnapsackDPComp(\n    wgt: Array&lt;number&gt;,\n    val: Array&lt;number&gt;,\n    cap: number\n): number {\n    const n = wgt.length;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: cap + 1 }, () =&gt; 0);\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        for (let c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> unbounded_knapsack.dart<pre><code>/* Полный рюкзак: динамическое программирование с оптимизацией памяти */\nint unboundedKnapsackDPComp(List&lt;int&gt; wgt, List&lt;int&gt; val, int cap) {\n  int n = wgt.length;\n  // Инициализация таблицы dp\n  List&lt;int&gt; dp = List.filled(cap + 1, 0);\n  // Переход состояний\n  for (int i = 1; i &lt;= n; i++) {\n    for (int c = 1; c &lt;= cap; c++) {\n      if (wgt[i - 1] &gt; c) {\n        // Если вместимость рюкзака превышена, предмет i не выбирать\n        dp[c] = dp[c];\n      } else {\n        // Большее из двух решений: не брать или взять предмет i\n        dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n      }\n    }\n  }\n  return dp[cap];\n}\n</code></pre> unbounded_knapsack.rs<pre><code>/* Полный рюкзак: динамическое программирование с оптимизацией памяти */\nfn unbounded_knapsack_dp_comp(wgt: &amp;[i32], val: &amp;[i32], cap: usize) -&gt; i32 {\n    let n = wgt.len();\n    // Инициализация таблицы dp\n    let mut dp = vec![0; cap + 1];\n    // Переход состояний\n    for i in 1..=n {\n        for c in 1..=cap {\n            if wgt[i - 1] &gt; c as i32 {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = std::cmp::max(dp[c], dp[c - wgt[i - 1] as usize] + val[i - 1]);\n            }\n        }\n    }\n    dp[cap]\n}\n</code></pre> unbounded_knapsack.c<pre><code>/* Полный рюкзак: динамическое программирование с оптимизацией памяти */\nint unboundedKnapsackDPComp(int wgt[], int val[], int cap, int wgtSize) {\n    int n = wgtSize;\n    // Инициализация таблицы dp\n    int *dp = calloc(cap + 1, sizeof(int));\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c];\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = myMax(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    int res = dp[cap];\n    // Освободить память\n    free(dp);\n    return res;\n}\n</code></pre> unbounded_knapsack.kt<pre><code>/* Полный рюкзак: динамическое программирование с оптимизацией памяти */\nfun unboundedKnapsackDPComp(\n    wgt: IntArray,\n    _val: IntArray,\n    cap: Int\n): Int {\n    val n = wgt.size\n    // Инициализация таблицы dp\n    val dp = IntArray(cap + 1)\n    // Переход состояний\n    for (i in 1..n) {\n        for (c in 1..cap) {\n            if (wgt[i - 1] &gt; c) {\n                // Если вместимость рюкзака превышена, предмет i не выбирать\n                dp[c] = dp[c]\n            } else {\n                // Большее из двух решений: не брать или взять предмет i\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + _val[i - 1])\n            }\n        }\n    }\n    return dp[cap]\n}\n</code></pre> unbounded_knapsack.rb<pre><code>### Полный рюкзак: динамическое программирование ###\ndef unbounded_knapsack_dp(wgt, val, cap)\n  n = wgt.length\n  # Инициализация таблицы dp\n  dp = Array.new(n + 1) { Array.new(cap + 1, 0) }\n  # Переход состояний\n  for i in 1...(n + 1)\n    for c in 1...(cap + 1)\n      if wgt[i - 1] &gt; c\n        # Если вместимость рюкзака превышена, предмет i не выбирать\n        dp[i][c] = dp[i - 1][c]\n      else\n        # Большее из двух решений: не брать или взять предмет i\n        dp[i][c] = [dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]].max\n      end\n    end\n  end\n  dp[n][cap]\nend\n\n# ## Полный рюкзак: динамическое программирование с оптимизацией памяти ##3\ndef unbounded_knapsack_dp_comp(wgt, val, cap)\n  n = wgt.length\n  # Инициализация таблицы dp\n  dp = Array.new(cap + 1, 0)\n  # Переход состояний\n  for i in 1...(n + 1)\n    # Прямой обход\n    for c in 1...(cap + 1)\n      if wgt[i -1] &gt; c\n        # Если вместимость рюкзака превышена, предмет i не выбирать\n        dp[c] = dp[c]\n      else\n        # Большее из двух решений: не брать или взять предмет i\n        dp[c] = [dp[c], dp[c - wgt[i - 1]] + val[i - 1]].max\n      end\n    end\n  end\n  dp[cap]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1452","level":2,"title":"14.5.2   Задача о размене монет","text":"<p>Задача о рюкзаке представляет собой целый класс задач динамического программирования, у которого есть множество вариантов, и одной из таких вариаций является задача о размене монет.</p> <p>Question</p> <p>Даны \\(n\\) видов монет, номинал монеты \\(i\\) равен \\(coins[i - 1]\\) , а целевая сумма равна \\(amt\\) . Монеты каждого вида можно брать многократно. Требуется найти минимальное число монет, которыми можно набрать целевую сумму. Если набрать сумму невозможно, верните \\(-1\\) . Пример показан на рисунке 14-24.</p> <p></p> <p> Рисунок 14-24   Пример данных для задачи о размене монет </p>","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1_1","level":3,"title":"1.   Идея динамического программирования","text":"<p>Задачу о размене монет можно рассматривать как частный случай задачи о полном рюкзаке ; между ними существуют следующие соответствия и различия.</p> <ul> <li>Эти две задачи можно взаимно преобразовать: \"предмет\" соответствует \"монете\", \"вес предмета\" соответствует \"номиналу монеты\", а \"вместимость рюкзака\" соответствует \"целевой сумме\".</li> <li>Цель оптимизации противоположна: в задаче о полном рюкзаке нужно максимизировать стоимость предметов, а в задаче о размене монет - минимизировать число монет.</li> <li>В задаче о полном рюкзаке ищется решение, не превышающее вместимость, а в задаче о размене монет требуется ровно набрать целевую сумму.</li> </ul> <p>Шаг 1: продумать решения на каждом раунде, определить состояние и тем самым получить таблицу \\(dp\\)</p> <p>Подзадача, соответствующая состоянию \\([i, a]\\) , выглядит так: минимальное число монет из первых \\(i\\) видов, которыми можно набрать сумму \\(a\\). Решение этой подзадачи обозначается как \\(dp[i, a]\\) .</p> <p>Размер двумерной таблицы \\(dp\\) равен \\((n+1) \\times (amt+1)\\) .</p> <p>Шаг 2: найти оптимальную подструктуру и на ее основе вывести уравнение перехода состояния</p> <p>По сравнению с задачей о полном рюкзаке здесь есть два отличия в уравнении перехода состояния.</p> <ul> <li>Нужно искать минимум, а не максимум, поэтому оператор \\(\\max()\\) заменяется на \\(\\min()\\) .</li> <li>Оптимизируемое значение - это число монет, а не суммарная стоимость, поэтому при выборе монеты нужно просто прибавить \\(1\\) .</li> </ul> \\[ dp[i, a] = \\min(dp[i-1, a], dp[i, a - coins[i-1]] + 1) \\] <p>Шаг 3: определить граничные условия и порядок переходов</p> <p>Когда целевая сумма равна \\(0\\) , минимальное число монет для ее набора равно \\(0\\) , то есть весь первый столбец \\(dp[i, 0]\\) заполняется нулями.</p> <p>Когда монет нет, невозможно набрать никакую целевую сумму \\(&gt; 0\\) ; это и есть недопустимое решение. Чтобы функция \\(\\min()\\) в уравнении перехода состояния могла распознавать и отбрасывать такие недопустимые решения, удобно использовать значение \\(+ \\infty\\) ; то есть всю первую строку \\(dp[0, a]\\) нужно инициализировать значением \\(+ \\infty\\) .</p>","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#2_1","level":3,"title":"2.   Реализация кода","text":"<p>Большинство языков программирования не предоставляет представление для \\(+ \\infty\\) в целочисленном виде, поэтому обычно приходится заменять его на максимальное значение типа <code>int</code> . Но тогда возникает риск переполнения: операция \\(+ 1\\) в уравнении перехода может переполнить большое число.</p> <p>Поэтому здесь мы используем число \\(amt + 1\\) как обозначение недопустимого решения, потому что для набора суммы \\(amt\\) максимум нужно не больше чем \\(amt\\) монет. Перед возвратом результата проверяем, равно ли \\(dp[n, amt]\\) значению \\(amt + 1\\) ; если да, то возвращаем \\(-1\\) , что означает невозможность набрать целевую сумму. Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby coin_change.py<pre><code>def coin_change_dp(coins: list[int], amt: int) -&gt; int:\n    \"\"\"Размен монет: динамическое программирование\"\"\"\n    n = len(coins)\n    MAX = amt + 1\n    # Инициализация таблицы dp\n    dp = [[0] * (amt + 1) for _ in range(n + 1)]\n    # Переход состояний: первая строка и первый столбец\n    for a in range(1, amt + 1):\n        dp[0][a] = MAX\n    # Переход состояний: остальные строки и столбцы\n    for i in range(1, n + 1):\n        for a in range(1, amt + 1):\n            if coins[i - 1] &gt; a:\n                # Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a]\n            else:\n                # Меньшее из двух решений: не брать или взять монету i\n                dp[i][a] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1)\n    return dp[n][amt] if dp[n][amt] != MAX else -1\n</code></pre> coin_change.cpp<pre><code>/* Размен монет: динамическое программирование */\nint coinChangeDP(vector&lt;int&gt; &amp;coins, int amt) {\n    int n = coins.size();\n    int MAX = amt + 1;\n    // Инициализация таблицы dp\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(amt + 1, 0));\n    // Переход состояний: первая строка и первый столбец\n    for (int a = 1; a &lt;= amt; a++) {\n        dp[0][a] = MAX;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[i][a] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[n][amt] != MAX ? dp[n][amt] : -1;\n}\n</code></pre> coin_change.java<pre><code>/* Размен монет: динамическое программирование */\nint coinChangeDP(int[] coins, int amt) {\n    int n = coins.length;\n    int MAX = amt + 1;\n    // Инициализация таблицы dp\n    int[][] dp = new int[n + 1][amt + 1];\n    // Переход состояний: первая строка и первый столбец\n    for (int a = 1; a &lt;= amt; a++) {\n        dp[0][a] = MAX;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[i][a] = Math.min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[n][amt] != MAX ? dp[n][amt] : -1;\n}\n</code></pre> coin_change.cs<pre><code>/* Размен монет: динамическое программирование */\nint CoinChangeDP(int[] coins, int amt) {\n    int n = coins.Length;\n    int MAX = amt + 1;\n    // Инициализация таблицы dp\n    int[,] dp = new int[n + 1, amt + 1];\n    // Переход состояний: первая строка и первый столбец\n    for (int a = 1; a &lt;= amt; a++) {\n        dp[0, a] = MAX;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i, a] = dp[i - 1, a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[i, a] = Math.Min(dp[i - 1, a], dp[i, a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[n, amt] != MAX ? dp[n, amt] : -1;\n}\n</code></pre> coin_change.go<pre><code>/* Размен монет: динамическое программирование */\nfunc coinChangeDP(coins []int, amt int) int {\n    n := len(coins)\n    max := amt + 1\n    // Инициализация таблицы dp\n    dp := make([][]int, n+1)\n    for i := 0; i &lt;= n; i++ {\n        dp[i] = make([]int, amt+1)\n    }\n    // Переход состояний: первая строка и первый столбец\n    for a := 1; a &lt;= amt; a++ {\n        dp[0][a] = max\n    }\n    // Переход состояний: остальные строки и столбцы\n    for i := 1; i &lt;= n; i++ {\n        for a := 1; a &lt;= amt; a++ {\n            if coins[i-1] &gt; a {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i-1][a]\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[i][a] = int(math.Min(float64(dp[i-1][a]), float64(dp[i][a-coins[i-1]]+1)))\n            }\n        }\n    }\n    if dp[n][amt] != max {\n        return dp[n][amt]\n    }\n    return -1\n}\n</code></pre> coin_change.swift<pre><code>/* Размен монет: динамическое программирование */\nfunc coinChangeDP(coins: [Int], amt: Int) -&gt; Int {\n    let n = coins.count\n    let MAX = amt + 1\n    // Инициализация таблицы dp\n    var dp = Array(repeating: Array(repeating: 0, count: amt + 1), count: n + 1)\n    // Переход состояний: первая строка и первый столбец\n    for a in 1 ... amt {\n        dp[0][a] = MAX\n    }\n    // Переход состояний: остальные строки и столбцы\n    for i in 1 ... n {\n        for a in 1 ... amt {\n            if coins[i - 1] &gt; a {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a]\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[i][a] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1)\n            }\n        }\n    }\n    return dp[n][amt] != MAX ? dp[n][amt] : -1\n}\n</code></pre> coin_change.js<pre><code>/* Размен монет: динамическое программирование */\nfunction coinChangeDP(coins, amt) {\n    const n = coins.length;\n    const MAX = amt + 1;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: n + 1 }, () =&gt;\n        Array.from({ length: amt + 1 }, () =&gt; 0)\n    );\n    // Переход состояний: первая строка и первый столбец\n    for (let a = 1; a &lt;= amt; a++) {\n        dp[0][a] = MAX;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (let i = 1; i &lt;= n; i++) {\n        for (let a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[i][a] = Math.min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[n][amt] !== MAX ? dp[n][amt] : -1;\n}\n</code></pre> coin_change.ts<pre><code>/* Размен монет: динамическое программирование */\nfunction coinChangeDP(coins: Array&lt;number&gt;, amt: number): number {\n    const n = coins.length;\n    const MAX = amt + 1;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: n + 1 }, () =&gt;\n        Array.from({ length: amt + 1 }, () =&gt; 0)\n    );\n    // Переход состояний: первая строка и первый столбец\n    for (let a = 1; a &lt;= amt; a++) {\n        dp[0][a] = MAX;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (let i = 1; i &lt;= n; i++) {\n        for (let a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[i][a] = Math.min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[n][amt] !== MAX ? dp[n][amt] : -1;\n}\n</code></pre> coin_change.dart<pre><code>/* Размен монет: динамическое программирование */\nint coinChangeDP(List&lt;int&gt; coins, int amt) {\n  int n = coins.length;\n  int MAX = amt + 1;\n  // Инициализация таблицы dp\n  List&lt;List&lt;int&gt;&gt; dp = List.generate(n + 1, (index) =&gt; List.filled(amt + 1, 0));\n  // Переход состояний: первая строка и первый столбец\n  for (int a = 1; a &lt;= amt; a++) {\n    dp[0][a] = MAX;\n  }\n  // Переход состояний: остальные строки и столбцы\n  for (int i = 1; i &lt;= n; i++) {\n    for (int a = 1; a &lt;= amt; a++) {\n      if (coins[i - 1] &gt; a) {\n        // Если целевая сумма превышена, монету i не выбирать\n        dp[i][a] = dp[i - 1][a];\n      } else {\n        // Меньшее из двух решений: не брать или взять монету i\n        dp[i][a] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);\n      }\n    }\n  }\n  return dp[n][amt] != MAX ? dp[n][amt] : -1;\n}\n</code></pre> coin_change.rs<pre><code>/* Размен монет: динамическое программирование */\nfn coin_change_dp(coins: &amp;[i32], amt: usize) -&gt; i32 {\n    let n = coins.len();\n    let max = amt + 1;\n    // Инициализация таблицы dp\n    let mut dp = vec![vec![0; amt + 1]; n + 1];\n    // Переход состояний: первая строка и первый столбец\n    for a in 1..=amt {\n        dp[0][a] = max;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for i in 1..=n {\n        for a in 1..=amt {\n            if coins[i - 1] &gt; a as i32 {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[i][a] = std::cmp::min(dp[i - 1][a], dp[i][a - coins[i - 1] as usize] + 1);\n            }\n        }\n    }\n    if dp[n][amt] != max {\n        return dp[n][amt] as i32;\n    } else {\n        -1\n    }\n}\n</code></pre> coin_change.c<pre><code>/* Размен монет: динамическое программирование */\nint coinChangeDP(int coins[], int amt, int coinsSize) {\n    int n = coinsSize;\n    int MAX = amt + 1;\n    // Инициализация таблицы dp\n    int **dp = malloc((n + 1) * sizeof(int *));\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i] = calloc(amt + 1, sizeof(int));\n    }\n    // Переход состояний: первая строка и первый столбец\n    for (int a = 1; a &lt;= amt; a++) {\n        dp[0][a] = MAX;\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[i][a] = myMin(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    int res = dp[n][amt] != MAX ? dp[n][amt] : -1;\n    // Освободить память\n    for (int i = 0; i &lt;= n; i++) {\n        free(dp[i]);\n    }\n    free(dp);\n    return res;\n}\n</code></pre> coin_change.kt<pre><code>/* Размен монет: динамическое программирование */\nfun coinChangeDP(coins: IntArray, amt: Int): Int {\n    val n = coins.size\n    val MAX = amt + 1\n    // Инициализация таблицы dp\n    val dp = Array(n + 1) { IntArray(amt + 1) }\n    // Переход состояний: первая строка и первый столбец\n    for (a in 1..amt) {\n        dp[0][a] = MAX\n    }\n    // Переход состояний: остальные строки и столбцы\n    for (i in 1..n) {\n        for (a in 1..amt) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a]\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[i][a] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1)\n            }\n        }\n    }\n    return if (dp[n][amt] != MAX) dp[n][amt] else -1\n}\n</code></pre> coin_change.rb<pre><code>### Размен монет: динамическое программирование ###\ndef coin_change_dp(coins, amt)\n  n = coins.length\n  _MAX = amt + 1\n  # Инициализация таблицы dp\n  dp = Array.new(n + 1) { Array.new(amt + 1, 0) }\n  # Переход состояний: первая строка и первый столбец\n  (1...(amt + 1)).each { |a| dp[0][a] = _MAX }\n  # Переход состояний: остальные строки и столбцы\n  for i in 1...(n + 1)\n    for a in 1...(amt + 1)\n      if coins[i - 1] &gt; a\n        # Если целевая сумма превышена, монету i не выбирать\n        dp[i][a] = dp[i - 1][a]\n      else\n        # Меньшее из двух решений: не брать или взять монету i\n        dp[i][a] = [dp[i - 1][a], dp[i][a - coins[i - 1]] + 1].min\n      end\n    end\n  end\n  dp[n][amt] != _MAX ? dp[n][amt] : -1\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Как показано на рисунке 14-25, процесс динамического программирования для задачи о размене монет очень похож на задачу о полном рюкзаке.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt;&lt;13&gt;&lt;14&gt;&lt;15&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 14-25   Процесс динамического программирования для задачи о размене монет </p>","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#3_1","level":3,"title":"3.   Оптимизация пространства","text":"<p>Оптимизация пространства для задачи о размене монет выполняется так же, как и для полного рюкзака:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby coin_change.py<pre><code>def coin_change_dp_comp(coins: list[int], amt: int) -&gt; int:\n    \"\"\"Размен монет: динамическое программирование с оптимизацией памяти\"\"\"\n    n = len(coins)\n    MAX = amt + 1\n    # Инициализация таблицы dp\n    dp = [MAX] * (amt + 1)\n    dp[0] = 0\n    # Переход состояний\n    for i in range(1, n + 1):\n        # Прямой обход\n        for a in range(1, amt + 1):\n            if coins[i - 1] &gt; a:\n                # Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a]\n            else:\n                # Меньшее из двух решений: не брать или взять монету i\n                dp[a] = min(dp[a], dp[a - coins[i - 1]] + 1)\n    return dp[amt] if dp[amt] != MAX else -1\n</code></pre> coin_change.cpp<pre><code>/* Размен монет: динамическое программирование с оптимизацией памяти */\nint coinChangeDPComp(vector&lt;int&gt; &amp;coins, int amt) {\n    int n = coins.size();\n    int MAX = amt + 1;\n    // Инициализация таблицы dp\n    vector&lt;int&gt; dp(amt + 1, MAX);\n    dp[0] = 0;\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[a] = min(dp[a], dp[a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[amt] != MAX ? dp[amt] : -1;\n}\n</code></pre> coin_change.java<pre><code>/* Размен монет: динамическое программирование с оптимизацией памяти */\nint coinChangeDPComp(int[] coins, int amt) {\n    int n = coins.length;\n    int MAX = amt + 1;\n    // Инициализация таблицы dp\n    int[] dp = new int[amt + 1];\n    Arrays.fill(dp, MAX);\n    dp[0] = 0;\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[a] = Math.min(dp[a], dp[a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[amt] != MAX ? dp[amt] : -1;\n}\n</code></pre> coin_change.cs<pre><code>/* Размен монет: динамическое программирование с оптимизацией памяти */\nint CoinChangeDPComp(int[] coins, int amt) {\n    int n = coins.Length;\n    int MAX = amt + 1;\n    // Инициализация таблицы dp\n    int[] dp = new int[amt + 1];\n    Array.Fill(dp, MAX);\n    dp[0] = 0;\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[a] = Math.Min(dp[a], dp[a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[amt] != MAX ? dp[amt] : -1;\n}\n</code></pre> coin_change.go<pre><code>/* Размен монет: динамическое программирование */\nfunc coinChangeDPComp(coins []int, amt int) int {\n    n := len(coins)\n    max := amt + 1\n    // Инициализация таблицы dp\n    dp := make([]int, amt+1)\n    for i := 1; i &lt;= amt; i++ {\n        dp[i] = max\n    }\n    // Переход состояний\n    for i := 1; i &lt;= n; i++ {\n        // Прямой обход\n        for a := 1; a &lt;= amt; a++ {\n            if coins[i-1] &gt; a {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a]\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[a] = int(math.Min(float64(dp[a]), float64(dp[a-coins[i-1]]+1)))\n            }\n        }\n    }\n    if dp[amt] != max {\n        return dp[amt]\n    }\n    return -1\n}\n</code></pre> coin_change.swift<pre><code>/* Размен монет: динамическое программирование с оптимизацией памяти */\nfunc coinChangeDPComp(coins: [Int], amt: Int) -&gt; Int {\n    let n = coins.count\n    let MAX = amt + 1\n    // Инициализация таблицы dp\n    var dp = Array(repeating: MAX, count: amt + 1)\n    dp[0] = 0\n    // Переход состояний\n    for i in 1 ... n {\n        for a in 1 ... amt {\n            if coins[i - 1] &gt; a {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a]\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[a] = min(dp[a], dp[a - coins[i - 1]] + 1)\n            }\n        }\n    }\n    return dp[amt] != MAX ? dp[amt] : -1\n}\n</code></pre> coin_change.js<pre><code>/* Размен монет: динамическое программирование с оптимизацией памяти */\nfunction coinChangeDPComp(coins, amt) {\n    const n = coins.length;\n    const MAX = amt + 1;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: amt + 1 }, () =&gt; MAX);\n    dp[0] = 0;\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        for (let a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[a] = Math.min(dp[a], dp[a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[amt] !== MAX ? dp[amt] : -1;\n}\n</code></pre> coin_change.ts<pre><code>/* Размен монет: динамическое программирование с оптимизацией памяти */\nfunction coinChangeDPComp(coins: Array&lt;number&gt;, amt: number): number {\n    const n = coins.length;\n    const MAX = amt + 1;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: amt + 1 }, () =&gt; MAX);\n    dp[0] = 0;\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        for (let a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[a] = Math.min(dp[a], dp[a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[amt] !== MAX ? dp[amt] : -1;\n}\n</code></pre> coin_change.dart<pre><code>/* Размен монет: динамическое программирование с оптимизацией памяти */\nint coinChangeDPComp(List&lt;int&gt; coins, int amt) {\n  int n = coins.length;\n  int MAX = amt + 1;\n  // Инициализация таблицы dp\n  List&lt;int&gt; dp = List.filled(amt + 1, MAX);\n  dp[0] = 0;\n  // Переход состояний\n  for (int i = 1; i &lt;= n; i++) {\n    for (int a = 1; a &lt;= amt; a++) {\n      if (coins[i - 1] &gt; a) {\n        // Если целевая сумма превышена, монету i не выбирать\n        dp[a] = dp[a];\n      } else {\n        // Меньшее из двух решений: не брать или взять монету i\n        dp[a] = min(dp[a], dp[a - coins[i - 1]] + 1);\n      }\n    }\n  }\n  return dp[amt] != MAX ? dp[amt] : -1;\n}\n</code></pre> coin_change.rs<pre><code>/* Размен монет: динамическое программирование с оптимизацией памяти */\nfn coin_change_dp_comp(coins: &amp;[i32], amt: usize) -&gt; i32 {\n    let n = coins.len();\n    let max = amt + 1;\n    // Инициализация таблицы dp\n    let mut dp = vec![0; amt + 1];\n    dp.fill(max);\n    dp[0] = 0;\n    // Переход состояний\n    for i in 1..=n {\n        for a in 1..=amt {\n            if coins[i - 1] &gt; a as i32 {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[a] = std::cmp::min(dp[a], dp[a - coins[i - 1] as usize] + 1);\n            }\n        }\n    }\n    if dp[amt] != max {\n        return dp[amt] as i32;\n    } else {\n        -1\n    }\n}\n</code></pre> coin_change.c<pre><code>/* Размен монет: динамическое программирование с оптимизацией памяти */\nint coinChangeDPComp(int coins[], int amt, int coinsSize) {\n    int n = coinsSize;\n    int MAX = amt + 1;\n    // Инициализация таблицы dp\n    int *dp = malloc((amt + 1) * sizeof(int));\n    for (int j = 1; j &lt;= amt; j++) {\n        dp[j] = MAX;\n    } \n    dp[0] = 0;\n\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[a] = myMin(dp[a], dp[a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    int res = dp[amt] != MAX ? dp[amt] : -1;\n    // Освободить память\n    free(dp);\n    return res;\n}\n</code></pre> coin_change.kt<pre><code>/* Размен монет: динамическое программирование с оптимизацией памяти */\nfun coinChangeDPComp(coins: IntArray, amt: Int): Int {\n    val n = coins.size\n    val MAX = amt + 1\n    // Инициализация таблицы dp\n    val dp = IntArray(amt + 1)\n    dp.fill(MAX)\n    dp[0] = 0\n    // Переход состояний\n    for (i in 1..n) {\n        for (a in 1..amt) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a]\n            } else {\n                // Меньшее из двух решений: не брать или взять монету i\n                dp[a] = min(dp[a], dp[a - coins[i - 1]] + 1)\n            }\n        }\n    }\n    return if (dp[amt] != MAX) dp[amt] else -1\n}\n</code></pre> coin_change.rb<pre><code>### Размен монет: динамическое программирование с оптимизацией памяти ###\ndef coin_change_dp_comp(coins, amt)\n  n = coins.length\n  _MAX = amt + 1\n  # Инициализация таблицы dp\n  dp = Array.new(amt + 1, _MAX)\n  dp[0] = 0\n  # Переход состояний\n  for i in 1...(n + 1)\n    # Прямой обход\n    for a in 1...(amt + 1)\n      if coins[i - 1] &gt; a\n        # Если целевая сумма превышена, монету i не выбирать\n        dp[a] = dp[a]\n      else\n        # Меньшее из двух решений: не брать или взять монету i\n        dp[a] = [dp[a], dp[a - coins[i - 1]] + 1].min\n      end\n    end\n  end\n  dp[amt] != _MAX ? dp[amt] : -1\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1453-ii","level":2,"title":"14.5.3   Задача о размене монет II","text":"<p>Question</p> <p>Даны \\(n\\) видов монет, номинал монеты \\(i\\) равен \\(coins[i - 1]\\) , а целевая сумма равна \\(amt\\) . Монеты каждого вида можно брать многократно. Найдите число различных комбинаций монет, которыми можно набрать целевую сумму. Пример показан на рисунке 14-26.</p> <p></p> <p> Рисунок 14-26   Пример данных для задачи о размене монет II </p>","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1_2","level":3,"title":"1.   Идея динамического программирования","text":"<p>По сравнению с предыдущей задачей здесь целью является число комбинаций. Поэтому подзадача меняется на следующую: число комбинаций из первых \\(i\\) видов монет, которыми можно набрать сумму \\(a\\). При этом таблица \\(dp\\) по-прежнему остается двумерной матрицей размера \\((n+1) \\times (amt + 1)\\) .</p> <p>Число комбинаций для текущего состояния равно сумме числа комбинаций для двух решений: не брать текущую монету и брать текущую монету. Поэтому уравнение перехода состояния принимает вид:</p> \\[ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]] \\] <p>Когда целевая сумма равна \\(0\\) , ее можно набрать, не выбирая ни одной монеты, поэтому весь первый столбец \\(dp[i, 0]\\) нужно инициализировать единицами. Когда монет нет, невозможно набрать никакую сумму \\(&gt;0\\) , поэтому вся первая строка \\(dp[0, a]\\) должна быть заполнена нулями.</p>","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#2_2","level":3,"title":"2.   Реализация кода","text":"PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby coin_change_ii.py<pre><code>def coin_change_ii_dp(coins: list[int], amt: int) -&gt; int:\n    \"\"\"Размен монет II: динамическое программирование\"\"\"\n    n = len(coins)\n    # Инициализация таблицы dp\n    dp = [[0] * (amt + 1) for _ in range(n + 1)]\n    # Инициализация первого столбца\n    for i in range(n + 1):\n        dp[i][0] = 1\n    # Переход состояний\n    for i in range(1, n + 1):\n        for a in range(1, amt + 1):\n            if coins[i - 1] &gt; a:\n                # Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a]\n            else:\n                # Сумма двух решений: не брать или взять монету i\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]]\n    return dp[n][amt]\n</code></pre> coin_change_ii.cpp<pre><code>/* Размен монет II: динамическое программирование */\nint coinChangeIIDP(vector&lt;int&gt; &amp;coins, int amt) {\n    int n = coins.size();\n    // Инициализация таблицы dp\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(amt + 1, 0));\n    // Инициализация первого столбца\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i][0] = 1;\n    }\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[n][amt];\n}\n</code></pre> coin_change_ii.java<pre><code>/* Размен монет II: динамическое программирование */\nint coinChangeIIDP(int[] coins, int amt) {\n    int n = coins.length;\n    // Инициализация таблицы dp\n    int[][] dp = new int[n + 1][amt + 1];\n    // Инициализация первого столбца\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i][0] = 1;\n    }\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[n][amt];\n}\n</code></pre> coin_change_ii.cs<pre><code>/* Размен монет II: динамическое программирование */\nint CoinChangeIIDP(int[] coins, int amt) {\n    int n = coins.Length;\n    // Инициализация таблицы dp\n    int[,] dp = new int[n + 1, amt + 1];\n    // Инициализация первого столбца\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i, 0] = 1;\n    }\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i, a] = dp[i - 1, a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[i, a] = dp[i - 1, a] + dp[i, a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[n, amt];\n}\n</code></pre> coin_change_ii.go<pre><code>/* Размен монет II: динамическое программирование */\nfunc coinChangeIIDP(coins []int, amt int) int {\n    n := len(coins)\n    // Инициализация таблицы dp\n    dp := make([][]int, n+1)\n    for i := 0; i &lt;= n; i++ {\n        dp[i] = make([]int, amt+1)\n    }\n    // Инициализация первого столбца\n    for i := 0; i &lt;= n; i++ {\n        dp[i][0] = 1\n    }\n    // Переход состояний: остальные строки и столбцы\n    for i := 1; i &lt;= n; i++ {\n        for a := 1; a &lt;= amt; a++ {\n            if coins[i-1] &gt; a {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i-1][a]\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[i][a] = dp[i-1][a] + dp[i][a-coins[i-1]]\n            }\n        }\n    }\n    return dp[n][amt]\n}\n</code></pre> coin_change_ii.swift<pre><code>/* Размен монет II: динамическое программирование */\nfunc coinChangeIIDP(coins: [Int], amt: Int) -&gt; Int {\n    let n = coins.count\n    // Инициализация таблицы dp\n    var dp = Array(repeating: Array(repeating: 0, count: amt + 1), count: n + 1)\n    // Инициализация первого столбца\n    for i in 0 ... n {\n        dp[i][0] = 1\n    }\n    // Переход состояний\n    for i in 1 ... n {\n        for a in 1 ... amt {\n            if coins[i - 1] &gt; a {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a]\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]]\n            }\n        }\n    }\n    return dp[n][amt]\n}\n</code></pre> coin_change_ii.js<pre><code>/* Размен монет II: динамическое программирование */\nfunction coinChangeIIDP(coins, amt) {\n    const n = coins.length;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: n + 1 }, () =&gt;\n        Array.from({ length: amt + 1 }, () =&gt; 0)\n    );\n    // Инициализация первого столбца\n    for (let i = 0; i &lt;= n; i++) {\n        dp[i][0] = 1;\n    }\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        for (let a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[n][amt];\n}\n</code></pre> coin_change_ii.ts<pre><code>/* Размен монет II: динамическое программирование */\nfunction coinChangeIIDP(coins: Array&lt;number&gt;, amt: number): number {\n    const n = coins.length;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: n + 1 }, () =&gt;\n        Array.from({ length: amt + 1 }, () =&gt; 0)\n    );\n    // Инициализация первого столбца\n    for (let i = 0; i &lt;= n; i++) {\n        dp[i][0] = 1;\n    }\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        for (let a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[n][amt];\n}\n</code></pre> coin_change_ii.dart<pre><code>/* Размен монет II: динамическое программирование */\nint coinChangeIIDP(List&lt;int&gt; coins, int amt) {\n  int n = coins.length;\n  // Инициализация таблицы dp\n  List&lt;List&lt;int&gt;&gt; dp = List.generate(n + 1, (index) =&gt; List.filled(amt + 1, 0));\n  // Инициализация первого столбца\n  for (int i = 0; i &lt;= n; i++) {\n    dp[i][0] = 1;\n  }\n  // Переход состояний\n  for (int i = 1; i &lt;= n; i++) {\n    for (int a = 1; a &lt;= amt; a++) {\n      if (coins[i - 1] &gt; a) {\n        // Если целевая сумма превышена, монету i не выбирать\n        dp[i][a] = dp[i - 1][a];\n      } else {\n        // Сумма двух решений: не брать или взять монету i\n        dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];\n      }\n    }\n  }\n  return dp[n][amt];\n}\n</code></pre> coin_change_ii.rs<pre><code>/* Размен монет II: динамическое программирование */\nfn coin_change_ii_dp(coins: &amp;[i32], amt: usize) -&gt; i32 {\n    let n = coins.len();\n    // Инициализация таблицы dp\n    let mut dp = vec![vec![0; amt + 1]; n + 1];\n    // Инициализация первого столбца\n    for i in 0..=n {\n        dp[i][0] = 1;\n    }\n    // Переход состояний\n    for i in 1..=n {\n        for a in 1..=amt {\n            if coins[i - 1] &gt; a as i32 {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1] as usize];\n            }\n        }\n    }\n    dp[n][amt]\n}\n</code></pre> coin_change_ii.c<pre><code>/* Размен монет II: динамическое программирование */\nint coinChangeIIDP(int coins[], int amt, int coinsSize) {\n    int n = coinsSize;\n    // Инициализация таблицы dp\n    int **dp = malloc((n + 1) * sizeof(int *));\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i] = calloc(amt + 1, sizeof(int));\n    }\n    // Инициализация первого столбца\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i][0] = 1;\n    }\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];\n            }\n        }\n    }\n    int res = dp[n][amt];\n    // Освободить память\n    for (int i = 0; i &lt;= n; i++) {\n        free(dp[i]);\n    }\n    free(dp);\n    return res;\n}\n</code></pre> coin_change_ii.kt<pre><code>/* Размен монет II: динамическое программирование */\nfun coinChangeIIDP(coins: IntArray, amt: Int): Int {\n    val n = coins.size\n    // Инициализация таблицы dp\n    val dp = Array(n + 1) { IntArray(amt + 1) }\n    // Инициализация первого столбца\n    for (i in 0..n) {\n        dp[i][0] = 1\n    }\n    // Переход состояний\n    for (i in 1..n) {\n        for (a in 1..amt) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[i][a] = dp[i - 1][a]\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]]\n            }\n        }\n    }\n    return dp[n][amt]\n}\n</code></pre> coin_change_ii.rb<pre><code>### Размен монет II: динамическое программирование ###\ndef coin_change_ii_dp(coins, amt)\n  n = coins.length\n  # Инициализация таблицы dp\n  dp = Array.new(n + 1) { Array.new(amt + 1, 0) }\n  # Инициализация первого столбца\n  (0...(n + 1)).each { |i| dp[i][0] = 1 }\n  # Переход состояний\n  for i in 1...(n + 1)\n    for a in 1...(amt + 1)\n      if coins[i - 1] &gt; a\n        # Если целевая сумма превышена, монету i не выбирать\n        dp[i][a] = dp[i - 1][a]\n      else\n        # Сумма двух решений: не брать или взять монету i\n        dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]]\n      end\n    end\n  end\n  dp[n][amt]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#3_2","level":3,"title":"3.   Оптимизация пространства","text":"<p>При оптимизации памяти способ остается тем же самым: достаточно убрать измерение, отвечающее за виды монет:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby coin_change_ii.py<pre><code>def coin_change_ii_dp_comp(coins: list[int], amt: int) -&gt; int:\n    \"\"\"Размен монет II: динамическое программирование с оптимизацией памяти\"\"\"\n    n = len(coins)\n    # Инициализация таблицы dp\n    dp = [0] * (amt + 1)\n    dp[0] = 1\n    # Переход состояний\n    for i in range(1, n + 1):\n        # Прямой обход\n        for a in range(1, amt + 1):\n            if coins[i - 1] &gt; a:\n                # Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a]\n            else:\n                # Сумма двух решений: не брать или взять монету i\n                dp[a] = dp[a] + dp[a - coins[i - 1]]\n    return dp[amt]\n</code></pre> coin_change_ii.cpp<pre><code>/* Размен монет II: динамическое программирование с оптимизацией памяти */\nint coinChangeIIDPComp(vector&lt;int&gt; &amp;coins, int amt) {\n    int n = coins.size();\n    // Инициализация таблицы dp\n    vector&lt;int&gt; dp(amt + 1, 0);\n    dp[0] = 1;\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[a] = dp[a] + dp[a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[amt];\n}\n</code></pre> coin_change_ii.java<pre><code>/* Размен монет II: динамическое программирование с оптимизацией памяти */\nint coinChangeIIDPComp(int[] coins, int amt) {\n    int n = coins.length;\n    // Инициализация таблицы dp\n    int[] dp = new int[amt + 1];\n    dp[0] = 1;\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[a] = dp[a] + dp[a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[amt];\n}\n</code></pre> coin_change_ii.cs<pre><code>/* Размен монет II: динамическое программирование с оптимизацией памяти */\nint CoinChangeIIDPComp(int[] coins, int amt) {\n    int n = coins.Length;\n    // Инициализация таблицы dp\n    int[] dp = new int[amt + 1];\n    dp[0] = 1;\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[a] = dp[a] + dp[a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[amt];\n}\n</code></pre> coin_change_ii.go<pre><code>/* Размен монет II: динамическое программирование с оптимизацией памяти */\nfunc coinChangeIIDPComp(coins []int, amt int) int {\n    n := len(coins)\n    // Инициализация таблицы dp\n    dp := make([]int, amt+1)\n    dp[0] = 1\n    // Переход состояний\n    for i := 1; i &lt;= n; i++ {\n        // Прямой обход\n        for a := 1; a &lt;= amt; a++ {\n            if coins[i-1] &gt; a {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a]\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[a] = dp[a] + dp[a-coins[i-1]]\n            }\n        }\n    }\n    return dp[amt]\n}\n</code></pre> coin_change_ii.swift<pre><code>/* Размен монет II: динамическое программирование с оптимизацией памяти */\nfunc coinChangeIIDPComp(coins: [Int], amt: Int) -&gt; Int {\n    let n = coins.count\n    // Инициализация таблицы dp\n    var dp = Array(repeating: 0, count: amt + 1)\n    dp[0] = 1\n    // Переход состояний\n    for i in 1 ... n {\n        for a in 1 ... amt {\n            if coins[i - 1] &gt; a {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a]\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[a] = dp[a] + dp[a - coins[i - 1]]\n            }\n        }\n    }\n    return dp[amt]\n}\n</code></pre> coin_change_ii.js<pre><code>/* Размен монет II: динамическое программирование с оптимизацией памяти */\nfunction coinChangeIIDPComp(coins, amt) {\n    const n = coins.length;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: amt + 1 }, () =&gt; 0);\n    dp[0] = 1;\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        for (let a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[a] = dp[a] + dp[a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[amt];\n}\n</code></pre> coin_change_ii.ts<pre><code>/* Размен монет II: динамическое программирование с оптимизацией памяти */\nfunction coinChangeIIDPComp(coins: Array&lt;number&gt;, amt: number): number {\n    const n = coins.length;\n    // Инициализация таблицы dp\n    const dp = Array.from({ length: amt + 1 }, () =&gt; 0);\n    dp[0] = 1;\n    // Переход состояний\n    for (let i = 1; i &lt;= n; i++) {\n        for (let a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[a] = dp[a] + dp[a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[amt];\n}\n</code></pre> coin_change_ii.dart<pre><code>/* Размен монет II: динамическое программирование с оптимизацией памяти */\nint coinChangeIIDPComp(List&lt;int&gt; coins, int amt) {\n  int n = coins.length;\n  // Инициализация таблицы dp\n  List&lt;int&gt; dp = List.filled(amt + 1, 0);\n  dp[0] = 1;\n  // Переход состояний\n  for (int i = 1; i &lt;= n; i++) {\n    for (int a = 1; a &lt;= amt; a++) {\n      if (coins[i - 1] &gt; a) {\n        // Если целевая сумма превышена, монету i не выбирать\n        dp[a] = dp[a];\n      } else {\n        // Сумма двух решений: не брать или взять монету i\n        dp[a] = dp[a] + dp[a - coins[i - 1]];\n      }\n    }\n  }\n  return dp[amt];\n}\n</code></pre> coin_change_ii.rs<pre><code>/* Размен монет II: динамическое программирование с оптимизацией памяти */\nfn coin_change_ii_dp_comp(coins: &amp;[i32], amt: usize) -&gt; i32 {\n    let n = coins.len();\n    // Инициализация таблицы dp\n    let mut dp = vec![0; amt + 1];\n    dp[0] = 1;\n    // Переход состояний\n    for i in 1..=n {\n        for a in 1..=amt {\n            if coins[i - 1] &gt; a as i32 {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[a] = dp[a] + dp[a - coins[i - 1] as usize];\n            }\n        }\n    }\n    dp[amt]\n}\n</code></pre> coin_change_ii.c<pre><code>/* Размен монет II: динамическое программирование с оптимизацией памяти */\nint coinChangeIIDPComp(int coins[], int amt, int coinsSize) {\n    int n = coinsSize;\n    // Инициализация таблицы dp\n    int *dp = calloc(amt + 1, sizeof(int));\n    dp[0] = 1;\n    // Переход состояний\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a];\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[a] = dp[a] + dp[a - coins[i - 1]];\n            }\n        }\n    }\n    int res = dp[amt];\n    // Освободить память\n    free(dp);\n    return res;\n}\n</code></pre> coin_change_ii.kt<pre><code>/* Размен монет II: динамическое программирование с оптимизацией памяти */\nfun coinChangeIIDPComp(coins: IntArray, amt: Int): Int {\n    val n = coins.size\n    // Инициализация таблицы dp\n    val dp = IntArray(amt + 1)\n    dp[0] = 1\n    // Переход состояний\n    for (i in 1..n) {\n        for (a in 1..amt) {\n            if (coins[i - 1] &gt; a) {\n                // Если целевая сумма превышена, монету i не выбирать\n                dp[a] = dp[a]\n            } else {\n                // Сумма двух решений: не брать или взять монету i\n                dp[a] = dp[a] + dp[a - coins[i - 1]]\n            }\n        }\n    }\n    return dp[amt]\n}\n</code></pre> coin_change_ii.rb<pre><code>### Размен монет II: динамическое программирование с оптимизацией памяти ###\ndef coin_change_ii_dp_comp(coins, amt)\n  n = coins.length\n  # Инициализация таблицы dp\n  dp = Array.new(amt + 1, 0)\n  dp[0] = 1\n  # Переход состояний\n  for i in 1...(n + 1)\n    # Прямой обход\n    for a in 1...(amt + 1)\n      if coins[i - 1] &gt; a\n        # Если целевая сумма превышена, монету i не выбирать\n        dp[a] = dp[a]\n      else\n        # Сумма двух решений: не брать или взять монету i\n        dp[a] = dp[a] + dp[a - coins[i - 1]]\n      end\n    end\n  end\n  dp[amt]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 14. Динамическое программирование","14.5 &nbsp; Задача о полном рюкзаке"],"tags":[]},{"location":"chapter_graph/","level":1,"title":"Глава 9.   Графы","text":"<p>Abstract</p> <p>В жизни мы похожи на вершины, соединенные множеством невидимых ребер.</p> <p>Каждая встреча и каждое расставание оставляют в этой огромной сети свой след.</p>","path":["Глава 9. Графы","Глава 9. &nbsp; Графы"],"tags":[]},{"location":"chapter_graph/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>9.1   Граф</li> <li>9.2   Базовые операции графа</li> <li>9.3   Обход графа</li> <li>9.4   Краткие итоги</li> </ul>","path":["Глава 9. Графы","Глава 9. &nbsp; Графы"],"tags":[]},{"location":"chapter_graph/graph/","level":1,"title":"9.1   Граф","text":"<p>Граф (graph) - это нелинейная структура данных, состоящая из вершин (vertex) и ребер (edge). Граф \\(G\\) можно абстрактно представить как множество вершин \\(V\\) и множество ребер \\(E\\) . Ниже приведен пример графа, содержащего 5 вершин и 7 ребер.</p> \\[ \\begin{aligned} V &amp; = \\{ 1, 2, 3, 4, 5 \\} \\newline E &amp; = \\{ (1,2), (1,3), (1,5), (2,3), (2,4), (2,5), (4,5) \\} \\newline G &amp; = \\{ V, E \\} \\newline \\end{aligned} \\] <p>Если рассматривать вершины как узлы, а ребра как ссылки, соединяющие узлы, граф можно считать структурой данных, расширяющей связный список. Как показано на рисунке 9-1, по сравнению с линейными отношениями (связный список) и отношениями разделения (дерево), сетевые отношения (граф) обладают большей свободой и потому являются более сложными.</p> <p></p> <p> Рисунок 9-1   Связь между связным списком, деревом и графом </p>","path":["Глава 9. Графы","9.1 &nbsp; Граф"],"tags":[]},{"location":"chapter_graph/graph/#911","level":2,"title":"9.1.1   Распространенные типы и термины графов","text":"<p>В зависимости от наличия направления у ребер графы делятся на неориентированные графы (undirected graph) и ориентированные графы (directed graph) , как показано на рисунке 9-2.</p> <ul> <li>В неориентированном графе ребро представляет двустороннюю связь между двумя вершинами, например дружеские отношения в социальных сетях.</li> <li>В ориентированном графе ребро имеет направление, то есть ребра \\(A \\rightarrow B\\) и \\(A \\leftarrow B\\) независимы друг от друга, например отношения подписки и подписчиков.</li> </ul> <p></p> <p> Рисунок 9-2   Ориентированный и неориентированный графы </p> <p>В зависимости от того, связаны ли все вершины между собой, граф делится на связный граф (connected graph) и несвязный граф (disconnected graph) , как показано на рисунке 9-3.</p> <ul> <li>В связном графе из любой вершины можно достичь любой другой вершины.</li> <li>В несвязном графе существует по крайней мере одна вершина, недостижимая из текущей.</li> </ul> <p></p> <p> Рисунок 9-3   Связный и несвязный графы </p> <p>Мы также можем добавить к ребрам переменную \"вес\" и получить показанный ниже взвешенный граф (weighted graph). Например, в мобильных играх вроде Honor of Kings система рассчитывает \"близость\" между игроками по времени совместной игры, и такую сеть близости можно представить взвешенным графом.</p> <p></p> <p> Рисунок 9-4   Взвешенный и невзвешенный графы </p> <p>Со структурой данных \"граф\" связаны следующие основные термины.</p> <ul> <li>Смежность (adjacency): если между двумя вершинами существует ребро, то такие вершины называются смежными. На рисунке 9-4 с вершиной 1 смежны вершины 2, 3 и 5.</li> <li>Путь (path): последовательность ребер от вершины A до вершины B называется путем из A в B. На рисунке 9-4 последовательность ребер 1-5-2-4 является одним из путей от вершины 1 к вершине 4.</li> <li>Степень (degree): количество ребер, принадлежащих вершине. Для ориентированного графа входящая степень (in-degree) показывает, сколько ребер входит в вершину, а исходящая степень (out-degree) показывает, сколько ребер из нее выходит.</li> </ul>","path":["Глава 9. Графы","9.1 &nbsp; Граф"],"tags":[]},{"location":"chapter_graph/graph/#912","level":2,"title":"9.1.2   Представление графа","text":"<p>Распространенные способы представления графа включают \"матрицу смежности\" и \"список смежности\". Ниже для примера рассматривается неориентированный граф.</p>","path":["Глава 9. Графы","9.1 &nbsp; Граф"],"tags":[]},{"location":"chapter_graph/graph/#1","level":3,"title":"1.   Матрица смежности","text":"<p>Пусть число вершин графа равно \\(n\\) ; тогда матрица смежности (adjacency matrix) использует матрицу размера \\(n \\times n\\) для представления графа, где каждая строка и каждый столбец соответствуют вершине, а элементы матрицы показывают наличие или отсутствие ребра.</p> <p>Как показано на рисунке 9-5, обозначим матрицу смежности через \\(M\\) , а список вершин через \\(V\\) ; тогда элемент матрицы \\(M[i, j] = 1\\) означает наличие ребра между вершинами \\(V[i]\\) и \\(V[j]\\) , а элемент \\(M[i, j] = 0\\) означает отсутствие ребра.</p> <p></p> <p> Рисунок 9-5   Представление графа матрицей смежности </p> <p>Матрица смежности обладает следующими особенностями.</p> <ul> <li>В простом графе вершина не может соединяться сама с собой, поэтому элементы на главной диагонали матрицы смежности не имеют значения.</li> <li>Для неориентированного графа ребра в обоих направлениях эквивалентны, поэтому матрица смежности симметрична относительно главной диагонали.</li> <li>Если заменить в матрице смежности значения \\(1\\) и \\(0\\) на веса, то можно представить взвешенный граф.</li> </ul> <p>При представлении графа матрицей смежности можно напрямую обращаться к элементам матрицы и получать сведения о ребрах, поэтому операции добавления, удаления, поиска и изменения обладают высокой эффективностью и выполняются за \\(O(1)\\) . Однако пространственная сложность матрицы составляет \\(O(n^2)\\) , поэтому она требует значительных затрат памяти.</p>","path":["Глава 9. Графы","9.1 &nbsp; Граф"],"tags":[]},{"location":"chapter_graph/graph/#2","level":3,"title":"2.   Список смежности","text":"<p>Список смежности (adjacency list) использует \\(n\\) списков для представления графа, где узлы списка обозначают вершины. \\(i\\)-й список соответствует вершине \\(i\\) и хранит все смежные с ней вершины, то есть все вершины, соединенные с данной вершиной. На рисунке 9-6 показан пример графа, представленного списком смежности.</p> <p></p> <p> Рисунок 9-6   Представление графа списком смежности </p> <p>Список смежности хранит только реально существующие ребра, а общее число ребер обычно значительно меньше \\(n^2\\) , поэтому он лучше экономит память. Однако для поиска ребра в списке смежности требуется обходить список, поэтому по времени он уступает матрице смежности.</p> <p>Если посмотреть на рисунок 9-6, можно заметить, что структура списка смежности очень похожа на цепную адресацию в хеш-таблицах, поэтому здесь можно использовать похожие методы оптимизации эффективности. Например, если список слишком длинный, его можно преобразовать в AVL-дерево или красно-черное дерево, чтобы снизить временную сложность с \\(O(n)\\) до \\(O(\\log n)\\) ; также список можно преобразовать в хеш-таблицу, чтобы довести временную сложность до \\(O(1)\\) .</p>","path":["Глава 9. Графы","9.1 &nbsp; Граф"],"tags":[]},{"location":"chapter_graph/graph/#913","level":2,"title":"9.1.3   Типичные применения графов","text":"<p>Как показано в таблице 9-1, многие реальные системы можно моделировать с помощью графов, а соответствующие задачи затем сводить к задачам вычислений на графах.</p> <p> Таблица 9-1   Распространенные графы в реальной жизни </p> Вершина Ребро Задача вычислений на графе Социальные сети Пользователь Дружеская связь Рекомендация потенциальных друзей Линии метро Станция Связь между станциями Рекомендация кратчайшего маршрута Солнечная система Небесное тело Гравитационное взаимодействие между телами Вычисление орбит планет","path":["Глава 9. Графы","9.1 &nbsp; Граф"],"tags":[]},{"location":"chapter_graph/graph_operations/","level":1,"title":"9.2   Базовые операции графа","text":"<p>Базовые операции графа можно разделить на операции над \"ребрами\" и операции над \"вершинами\". При двух способах представления, \"матрице смежности\" и \"списке смежности\", реализация этих операций различается.</p>","path":["Глава 9. Графы","9.2 &nbsp; Базовые операции графа"],"tags":[]},{"location":"chapter_graph/graph_operations/#921","level":2,"title":"9.2.1   Реализация на основе матрицы смежности","text":"<p>Пусть дан неориентированный граф с числом вершин \\(n\\) . Тогда способы реализации различных операций показаны на рисунках ниже.</p> <ul> <li>Добавление или удаление ребра: достаточно изменить соответствующее ребро в матрице смежности, что требует \\(O(1)\\) времени. Поскольку граф неориентированный, необходимо одновременно обновить ребра в обоих направлениях.</li> <li>Добавление вершины: в конец матрицы смежности добавляется строка и столбец, полностью заполненные нулями; это требует \\(O(n)\\) времени.</li> <li>Удаление вершины: из матрицы смежности удаляется строка и столбец. При удалении первой строки и первого столбца достигается худший случай, когда требуется \"сдвинуть влево вверх\" \\((n-1)^2\\) элементов, поэтому используется \\(O(n^2)\\) времени.</li> <li>Инициализация: передаются \\(n\\) вершин, затем инициализируется список вершин <code>vertices</code> длины \\(n\\) , что требует \\(O(n)\\) времени; после этого инициализируется матрица смежности <code>adjMat</code> размера \\(n \\times n\\) , что требует \\(O(n^2)\\) времени.</li> </ul> Инициализация матрицы смежностиДобавление ребраУдаление ребраДобавление вершиныУдаление вершины <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 9-7   Инициализация матрицы смежности, добавление и удаление ребер и вершин </p> <p>Ниже приведен код реализации графа на основе матрицы смежности:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby graph_adjacency_matrix.py<pre><code>class GraphAdjMat:\n    \"\"\"Класс неориентированного графа на основе матрицы смежности\"\"\"\n\n    def __init__(self, vertices: list[int], edges: list[list[int]]):\n        \"\"\"Конструктор\"\"\"\n        # Список вершин: элементы представляют «значения вершин», а индексы — «индексы вершин»\n        self.vertices: list[int] = []\n        # Матрица смежности, где индексы строк и столбцов соответствуют «индексам вершин»\n        self.adj_mat: list[list[int]] = []\n        # Добавление вершины\n        for val in vertices:\n            self.add_vertex(val)\n        # Добавить ребра\n        # Обратите внимание: элементы edges представляют собой индексы вершин, то есть соответствуют индексам элементов vertices\n        for e in edges:\n            self.add_edge(e[0], e[1])\n\n    def size(self) -&gt; int:\n        \"\"\"Получить число вершин\"\"\"\n        return len(self.vertices)\n\n    def add_vertex(self, val: int):\n        \"\"\"Добавление вершины\"\"\"\n        n = self.size()\n        # Добавить значение новой вершины в список вершин\n        self.vertices.append(val)\n        # Добавить строку в матрицу смежности\n        new_row = [0] * n\n        self.adj_mat.append(new_row)\n        # Добавить столбец в матрицу смежности\n        for row in self.adj_mat:\n            row.append(0)\n\n    def remove_vertex(self, index: int):\n        \"\"\"Удаление вершины\"\"\"\n        if index &gt;= self.size():\n            raise IndexError()\n        # Удалить вершину с индексом index из списка вершин\n        self.vertices.pop(index)\n        # Удалить строку с индексом index из матрицы смежности\n        self.adj_mat.pop(index)\n        # Удалить столбец с индексом index из матрицы смежности\n        for row in self.adj_mat:\n            row.pop(index)\n\n    def add_edge(self, i: int, j: int):\n        \"\"\"Добавление ребра\"\"\"\n        # Параметры i и j соответствуют индексам элементов vertices\n        # Обработка выхода индекса за границы и случая равенства\n        if i &lt; 0 or j &lt; 0 or i &gt;= self.size() or j &gt;= self.size() or i == j:\n            raise IndexError()\n        # В неориентированном графе матрица смежности симметрична относительно главной диагонали, то есть выполняется (i, j) == (j, i)\n        self.adj_mat[i][j] = 1\n        self.adj_mat[j][i] = 1\n\n    def remove_edge(self, i: int, j: int):\n        \"\"\"Удаление ребра\"\"\"\n        # Параметры i и j соответствуют индексам элементов vertices\n        # Обработка выхода индекса за границы и случая равенства\n        if i &lt; 0 or j &lt; 0 or i &gt;= self.size() or j &gt;= self.size() or i == j:\n            raise IndexError()\n        self.adj_mat[i][j] = 0\n        self.adj_mat[j][i] = 0\n\n    def print(self):\n        \"\"\"Вывести матрицу смежности\"\"\"\n        print(\"Список вершин =\", self.vertices)\n        print(\"Матрица смежности =\")\n        print_matrix(self.adj_mat)\n</code></pre> graph_adjacency_matrix.cpp<pre><code>/* Класс неориентированного графа на основе матрицы смежности */\nclass GraphAdjMat {\n    vector&lt;int&gt; vertices;       // Список вершин: элементы представляют «значения вершин», а индексы — «индексы вершин»\n    vector&lt;vector&lt;int&gt;&gt; adjMat; // Матрица смежности, где индексы строк и столбцов соответствуют «индексам вершин»\n\n  public:\n    /* Конструктор */\n    GraphAdjMat(const vector&lt;int&gt; &amp;vertices, const vector&lt;vector&lt;int&gt;&gt; &amp;edges) {\n        // Добавление вершины\n        for (int val : vertices) {\n            addVertex(val);\n        }\n        // Добавить ребра\n        // Обратите внимание: элементы edges представляют собой индексы вершин, то есть соответствуют индексам элементов vertices\n        for (const vector&lt;int&gt; &amp;edge : edges) {\n            addEdge(edge[0], edge[1]);\n        }\n    }\n\n    /* Получить число вершин */\n    int size() const {\n        return vertices.size();\n    }\n\n    /* Добавление вершины */\n    void addVertex(int val) {\n        int n = size();\n        // Добавить значение новой вершины в список вершин\n        vertices.push_back(val);\n        // Добавить строку в матрицу смежности\n        adjMat.emplace_back(vector&lt;int&gt;(n, 0));\n        // Добавить столбец в матрицу смежности\n        for (vector&lt;int&gt; &amp;row : adjMat) {\n            row.push_back(0);\n        }\n    }\n\n    /* Удаление вершины */\n    void removeVertex(int index) {\n        if (index &gt;= size()) {\n            throw out_of_range(\"вершина не существует\");\n        }\n        // Удалить вершину с индексом index из списка вершин\n        vertices.erase(vertices.begin() + index);\n        // Удалить строку с индексом index из матрицы смежности\n        adjMat.erase(adjMat.begin() + index);\n        // Удалить столбец с индексом index из матрицы смежности\n        for (vector&lt;int&gt; &amp;row : adjMat) {\n            row.erase(row.begin() + index);\n        }\n    }\n\n    /* Добавление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    void addEdge(int i, int j) {\n        // Обработка выхода индекса за границы и случая равенства\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j) {\n            throw out_of_range(\"вершина не существует\");\n        }\n        // В неориентированном графе матрица смежности симметрична относительно главной диагонали, то есть выполняется (i, j) == (j, i)\n        adjMat[i][j] = 1;\n        adjMat[j][i] = 1;\n    }\n\n    /* Удаление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    void removeEdge(int i, int j) {\n        // Обработка выхода индекса за границы и случая равенства\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j) {\n            throw out_of_range(\"вершина не существует\");\n        }\n        adjMat[i][j] = 0;\n        adjMat[j][i] = 0;\n    }\n\n    /* Вывести матрицу смежности */\n    void print() {\n        cout &lt;&lt; \"Список вершин = \";\n        printVector(vertices);\n        cout &lt;&lt; \"Матрица смежности =\" &lt;&lt; endl;\n        printVectorMatrix(adjMat);\n    }\n};\n</code></pre> graph_adjacency_matrix.java<pre><code>/* Класс неориентированного графа на основе матрицы смежности */\nclass GraphAdjMat {\n    List&lt;Integer&gt; vertices; // Список вершин: элементы представляют «значения вершин», а индексы — «индексы вершин»\n    List&lt;List&lt;Integer&gt;&gt; adjMat; // Матрица смежности, где индексы строк и столбцов соответствуют «индексам вершин»\n\n    /* Конструктор */\n    public GraphAdjMat(int[] vertices, int[][] edges) {\n        this.vertices = new ArrayList&lt;&gt;();\n        this.adjMat = new ArrayList&lt;&gt;();\n        // Добавление вершины\n        for (int val : vertices) {\n            addVertex(val);\n        }\n        // Добавить ребра\n        // Обратите внимание: элементы edges представляют собой индексы вершин, то есть соответствуют индексам элементов vertices\n        for (int[] e : edges) {\n            addEdge(e[0], e[1]);\n        }\n    }\n\n    /* Получить число вершин */\n    public int size() {\n        return vertices.size();\n    }\n\n    /* Добавление вершины */\n    public void addVertex(int val) {\n        int n = size();\n        // Добавить значение новой вершины в список вершин\n        vertices.add(val);\n        // Добавить строку в матрицу смежности\n        List&lt;Integer&gt; newRow = new ArrayList&lt;&gt;(n);\n        for (int j = 0; j &lt; n; j++) {\n            newRow.add(0);\n        }\n        adjMat.add(newRow);\n        // Добавить столбец в матрицу смежности\n        for (List&lt;Integer&gt; row : adjMat) {\n            row.add(0);\n        }\n    }\n\n    /* Удаление вершины */\n    public void removeVertex(int index) {\n        if (index &gt;= size())\n            throw new IndexOutOfBoundsException();\n        // Удалить вершину с индексом index из списка вершин\n        vertices.remove(index);\n        // Удалить строку с индексом index из матрицы смежности\n        adjMat.remove(index);\n        // Удалить столбец с индексом index из матрицы смежности\n        for (List&lt;Integer&gt; row : adjMat) {\n            row.remove(index);\n        }\n    }\n\n    /* Добавление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    public void addEdge(int i, int j) {\n        // Обработка выхода индекса за границы и случая равенства\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j)\n            throw new IndexOutOfBoundsException();\n        // В неориентированном графе матрица смежности симметрична относительно главной диагонали, то есть выполняется (i, j) == (j, i)\n        adjMat.get(i).set(j, 1);\n        adjMat.get(j).set(i, 1);\n    }\n\n    /* Удаление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    public void removeEdge(int i, int j) {\n        // Обработка выхода индекса за границы и случая равенства\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j)\n            throw new IndexOutOfBoundsException();\n        adjMat.get(i).set(j, 0);\n        adjMat.get(j).set(i, 0);\n    }\n\n    /* Вывести матрицу смежности */\n    public void print() {\n        System.out.print(\"Список вершин = \");\n        System.out.println(vertices);\n        System.out.println(\"Матрица смежности =\");\n        PrintUtil.printMatrix(adjMat);\n    }\n}\n</code></pre> graph_adjacency_matrix.cs<pre><code>/* Класс неориентированного графа на основе матрицы смежности */\nclass GraphAdjMat {\n    List&lt;int&gt; vertices;     // Список вершин: элементы представляют «значения вершин», а индексы — «индексы вершин»\n    List&lt;List&lt;int&gt;&gt; adjMat; // Матрица смежности, где индексы строк и столбцов соответствуют «индексам вершин»\n\n    /* Конструктор */\n    public GraphAdjMat(int[] vertices, int[][] edges) {\n        this.vertices = [];\n        this.adjMat = [];\n        // Добавление вершины\n        foreach (int val in vertices) {\n            AddVertex(val);\n        }\n        // Добавить ребра\n        // Обратите внимание: элементы edges представляют собой индексы вершин, то есть соответствуют индексам элементов vertices\n        foreach (int[] e in edges) {\n            AddEdge(e[0], e[1]);\n        }\n    }\n\n    /* Получить число вершин */\n    int Size() {\n        return vertices.Count;\n    }\n\n    /* Добавление вершины */\n    public void AddVertex(int val) {\n        int n = Size();\n        // Добавить значение новой вершины в список вершин\n        vertices.Add(val);\n        // Добавить строку в матрицу смежности\n        List&lt;int&gt; newRow = new(n);\n        for (int j = 0; j &lt; n; j++) {\n            newRow.Add(0);\n        }\n        adjMat.Add(newRow);\n        // Добавить столбец в матрицу смежности\n        foreach (List&lt;int&gt; row in adjMat) {\n            row.Add(0);\n        }\n    }\n\n    /* Удаление вершины */\n    public void RemoveVertex(int index) {\n        if (index &gt;= Size())\n            throw new IndexOutOfRangeException();\n        // Удалить вершину с индексом index из списка вершин\n        vertices.RemoveAt(index);\n        // Удалить строку с индексом index из матрицы смежности\n        adjMat.RemoveAt(index);\n        // Удалить столбец с индексом index из матрицы смежности\n        foreach (List&lt;int&gt; row in adjMat) {\n            row.RemoveAt(index);\n        }\n    }\n\n    /* Добавление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    public void AddEdge(int i, int j) {\n        // Обработка выхода индекса за границы и случая равенства\n        if (i &lt; 0 || j &lt; 0 || i &gt;= Size() || j &gt;= Size() || i == j)\n            throw new IndexOutOfRangeException();\n        // В неориентированном графе матрица смежности симметрична относительно главной диагонали, то есть выполняется (i, j) == (j, i)\n        adjMat[i][j] = 1;\n        adjMat[j][i] = 1;\n    }\n\n    /* Удаление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    public void RemoveEdge(int i, int j) {\n        // Обработка выхода индекса за границы и случая равенства\n        if (i &lt; 0 || j &lt; 0 || i &gt;= Size() || j &gt;= Size() || i == j)\n            throw new IndexOutOfRangeException();\n        adjMat[i][j] = 0;\n        adjMat[j][i] = 0;\n    }\n\n    /* Вывести матрицу смежности */\n    public void Print() {\n        Console.Write(\"Список вершин = \");\n        PrintUtil.PrintList(vertices);\n        Console.WriteLine(\"Матрица смежности =\");\n        PrintUtil.PrintMatrix(adjMat);\n    }\n}\n</code></pre> graph_adjacency_matrix.go<pre><code>/* Класс неориентированного графа на основе матрицы смежности */\ntype graphAdjMat struct {\n    // Список вершин: элементы представляют «значения вершин», а индексы — «индексы вершин»\n    vertices []int\n    // Матрица смежности, где индексы строк и столбцов соответствуют «индексам вершин»\n    adjMat [][]int\n}\n\n/* Конструктор */\nfunc newGraphAdjMat(vertices []int, edges [][]int) *graphAdjMat {\n    // Добавление вершины\n    n := len(vertices)\n    adjMat := make([][]int, n)\n    for i := range adjMat {\n        adjMat[i] = make([]int, n)\n    }\n    // Инициализировать граф\n    g := &amp;graphAdjMat{\n        vertices: vertices,\n        adjMat:   adjMat,\n    }\n    // Добавить ребра\n    // Обратите внимание: элементы edges представляют собой индексы вершин, то есть соответствуют индексам элементов vertices\n    for i := range edges {\n        g.addEdge(edges[i][0], edges[i][1])\n    }\n    return g\n}\n\n/* Получить число вершин */\nfunc (g *graphAdjMat) size() int {\n    return len(g.vertices)\n}\n\n/* Добавление вершины */\nfunc (g *graphAdjMat) addVertex(val int) {\n    n := g.size()\n    // Добавить значение новой вершины в список вершин\n    g.vertices = append(g.vertices, val)\n    // Добавить строку в матрицу смежности\n    newRow := make([]int, n)\n    g.adjMat = append(g.adjMat, newRow)\n    // Добавить столбец в матрицу смежности\n    for i := range g.adjMat {\n        g.adjMat[i] = append(g.adjMat[i], 0)\n    }\n}\n\n/* Удаление вершины */\nfunc (g *graphAdjMat) removeVertex(index int) {\n    if index &gt;= g.size() {\n        return\n    }\n    // Удалить вершину с индексом index из списка вершин\n    g.vertices = append(g.vertices[:index], g.vertices[index+1:]...)\n    // Удалить строку с индексом index из матрицы смежности\n    g.adjMat = append(g.adjMat[:index], g.adjMat[index+1:]...)\n    // Удалить столбец с индексом index из матрицы смежности\n    for i := range g.adjMat {\n        g.adjMat[i] = append(g.adjMat[i][:index], g.adjMat[i][index+1:]...)\n    }\n}\n\n/* Добавление ребра */\n// Параметры i и j соответствуют индексам элементов vertices\nfunc (g *graphAdjMat) addEdge(i, j int) {\n    // Обработка выхода индекса за границы и случая равенства\n    if i &lt; 0 || j &lt; 0 || i &gt;= g.size() || j &gt;= g.size() || i == j {\n        fmt.Errorf(\"%s\", \"Index Out Of Bounds Exception\")\n    }\n    // В неориентированном графе матрица смежности симметрична относительно главной диагонали, то есть выполняется (i, j) == (j, i)\n    g.adjMat[i][j] = 1\n    g.adjMat[j][i] = 1\n}\n\n/* Удаление ребра */\n// Параметры i и j соответствуют индексам элементов vertices\nfunc (g *graphAdjMat) removeEdge(i, j int) {\n    // Обработка выхода индекса за границы и случая равенства\n    if i &lt; 0 || j &lt; 0 || i &gt;= g.size() || j &gt;= g.size() || i == j {\n        fmt.Errorf(\"%s\", \"Index Out Of Bounds Exception\")\n    }\n    g.adjMat[i][j] = 0\n    g.adjMat[j][i] = 0\n}\n\n/* Вывести матрицу смежности */\nfunc (g *graphAdjMat) print() {\n    fmt.Printf(\"\\tСписок вершин = %v\\n\", g.vertices)\n    fmt.Printf(\"\\tМатрица смежности = \\n\")\n    for i := range g.adjMat {\n        fmt.Printf(\"\\t\\t\\t%v\\n\", g.adjMat[i])\n    }\n}\n</code></pre> graph_adjacency_matrix.swift<pre><code>/* Класс неориентированного графа на основе матрицы смежности */\nclass GraphAdjMat {\n    private var vertices: [Int] // Список вершин: элементы представляют «значения вершин», а индексы — «индексы вершин»\n    private var adjMat: [[Int]] // Матрица смежности, где индексы строк и столбцов соответствуют «индексам вершин»\n\n    /* Конструктор */\n    init(vertices: [Int], edges: [[Int]]) {\n        self.vertices = []\n        adjMat = []\n        // Добавление вершины\n        for val in vertices {\n            addVertex(val: val)\n        }\n        // Добавить ребра\n        // Обратите внимание: элементы edges представляют собой индексы вершин, то есть соответствуют индексам элементов vertices\n        for e in edges {\n            addEdge(i: e[0], j: e[1])\n        }\n    }\n\n    /* Получить число вершин */\n    func size() -&gt; Int {\n        vertices.count\n    }\n\n    /* Добавление вершины */\n    func addVertex(val: Int) {\n        let n = size()\n        // Добавить значение новой вершины в список вершин\n        vertices.append(val)\n        // Добавить строку в матрицу смежности\n        let newRow = Array(repeating: 0, count: n)\n        adjMat.append(newRow)\n        // Добавить столбец в матрицу смежности\n        for i in adjMat.indices {\n            adjMat[i].append(0)\n        }\n    }\n\n    /* Удаление вершины */\n    func removeVertex(index: Int) {\n        if index &gt;= size() {\n            fatalError(\"Выход за границы диапазона\")\n        }\n        // Удалить вершину с индексом index из списка вершин\n        vertices.remove(at: index)\n        // Удалить строку с индексом index из матрицы смежности\n        adjMat.remove(at: index)\n        // Удалить столбец с индексом index из матрицы смежности\n        for i in adjMat.indices {\n            adjMat[i].remove(at: index)\n        }\n    }\n\n    /* Добавление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    func addEdge(i: Int, j: Int) {\n        // Обработка выхода индекса за границы и случая равенства\n        if i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j {\n            fatalError(\"Выход за границы диапазона\")\n        }\n        // В неориентированном графе матрица смежности симметрична относительно главной диагонали, то есть выполняется (i, j) == (j, i)\n        adjMat[i][j] = 1\n        adjMat[j][i] = 1\n    }\n\n    /* Удаление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    func removeEdge(i: Int, j: Int) {\n        // Обработка выхода индекса за границы и случая равенства\n        if i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j {\n            fatalError(\"Выход за границы диапазона\")\n        }\n        adjMat[i][j] = 0\n        adjMat[j][i] = 0\n    }\n\n    /* Вывести матрицу смежности */\n    func print() {\n        Swift.print(\"Список вершин = \", terminator: \"\")\n        Swift.print(vertices)\n        Swift.print(\"Матрица смежности =\")\n        PrintUtil.printMatrix(matrix: adjMat)\n    }\n}\n</code></pre> graph_adjacency_matrix.js<pre><code>/* Класс неориентированного графа на основе матрицы смежности */\nclass GraphAdjMat {\n    vertices; // Список вершин: элементы представляют «значения вершин», а индексы — «индексы вершин»\n    adjMat; // Матрица смежности, где индексы строк и столбцов соответствуют «индексам вершин»\n\n    /* Конструктор */\n    constructor(vertices, edges) {\n        this.vertices = [];\n        this.adjMat = [];\n        // Добавление вершины\n        for (const val of vertices) {\n            this.addVertex(val);\n        }\n        // Добавить ребра\n        // Обратите внимание: элементы edges представляют собой индексы вершин, то есть соответствуют индексам элементов vertices\n        for (const e of edges) {\n            this.addEdge(e[0], e[1]);\n        }\n    }\n\n    /* Получить число вершин */\n    size() {\n        return this.vertices.length;\n    }\n\n    /* Добавление вершины */\n    addVertex(val) {\n        const n = this.size();\n        // Добавить значение новой вершины в список вершин\n        this.vertices.push(val);\n        // Добавить строку в матрицу смежности\n        const newRow = [];\n        for (let j = 0; j &lt; n; j++) {\n            newRow.push(0);\n        }\n        this.adjMat.push(newRow);\n        // Добавить столбец в матрицу смежности\n        for (const row of this.adjMat) {\n            row.push(0);\n        }\n    }\n\n    /* Удаление вершины */\n    removeVertex(index) {\n        if (index &gt;= this.size()) {\n            throw new RangeError('Index Out Of Bounds Exception');\n        }\n        // Удалить вершину с индексом index из списка вершин\n        this.vertices.splice(index, 1);\n\n        // Удалить строку с индексом index из матрицы смежности\n        this.adjMat.splice(index, 1);\n        // Удалить столбец с индексом index из матрицы смежности\n        for (const row of this.adjMat) {\n            row.splice(index, 1);\n        }\n    }\n\n    /* Добавление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    addEdge(i, j) {\n        // Обработка выхода индекса за границы и случая равенства\n        if (i &lt; 0 || j &lt; 0 || i &gt;= this.size() || j &gt;= this.size() || i === j) {\n            throw new RangeError('Index Out Of Bounds Exception');\n        }\n        // В неориентированном графе матрица смежности симметрична относительно главной диагонали, то есть выполняется (i, j) === (j, i)\n        this.adjMat[i][j] = 1;\n        this.adjMat[j][i] = 1;\n    }\n\n    /* Удаление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    removeEdge(i, j) {\n        // Обработка выхода индекса за границы и случая равенства\n        if (i &lt; 0 || j &lt; 0 || i &gt;= this.size() || j &gt;= this.size() || i === j) {\n            throw new RangeError('Index Out Of Bounds Exception');\n        }\n        this.adjMat[i][j] = 0;\n        this.adjMat[j][i] = 0;\n    }\n\n    /* Вывести матрицу смежности */\n    print() {\n        console.log('Список вершин = ', this.vertices);\n        console.log('Матрица смежности =', this.adjMat);\n    }\n}\n</code></pre> graph_adjacency_matrix.ts<pre><code>/* Класс неориентированного графа на основе матрицы смежности */\nclass GraphAdjMat {\n    vertices: number[]; // Список вершин: элементы представляют «значения вершин», а индексы — «индексы вершин»\n    adjMat: number[][]; // Матрица смежности, где индексы строк и столбцов соответствуют «индексам вершин»\n\n    /* Конструктор */\n    constructor(vertices: number[], edges: number[][]) {\n        this.vertices = [];\n        this.adjMat = [];\n        // Добавление вершины\n        for (const val of vertices) {\n            this.addVertex(val);\n        }\n        // Добавить ребра\n        // Обратите внимание: элементы edges представляют собой индексы вершин, то есть соответствуют индексам элементов vertices\n        for (const e of edges) {\n            this.addEdge(e[0], e[1]);\n        }\n    }\n\n    /* Получить число вершин */\n    size(): number {\n        return this.vertices.length;\n    }\n\n    /* Добавление вершины */\n    addVertex(val: number): void {\n        const n: number = this.size();\n        // Добавить значение новой вершины в список вершин\n        this.vertices.push(val);\n        // Добавить строку в матрицу смежности\n        const newRow: number[] = [];\n        for (let j: number = 0; j &lt; n; j++) {\n            newRow.push(0);\n        }\n        this.adjMat.push(newRow);\n        // Добавить столбец в матрицу смежности\n        for (const row of this.adjMat) {\n            row.push(0);\n        }\n    }\n\n    /* Удаление вершины */\n    removeVertex(index: number): void {\n        if (index &gt;= this.size()) {\n            throw new RangeError('Index Out Of Bounds Exception');\n        }\n        // Удалить вершину с индексом index из списка вершин\n        this.vertices.splice(index, 1);\n\n        // Удалить строку с индексом index из матрицы смежности\n        this.adjMat.splice(index, 1);\n        // Удалить столбец с индексом index из матрицы смежности\n        for (const row of this.adjMat) {\n            row.splice(index, 1);\n        }\n    }\n\n    /* Добавление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    addEdge(i: number, j: number): void {\n        // Обработка выхода индекса за границы и случая равенства\n        if (i &lt; 0 || j &lt; 0 || i &gt;= this.size() || j &gt;= this.size() || i === j) {\n            throw new RangeError('Index Out Of Bounds Exception');\n        }\n        // В неориентированном графе матрица смежности симметрична относительно главной диагонали, то есть выполняется (i, j) === (j, i)\n        this.adjMat[i][j] = 1;\n        this.adjMat[j][i] = 1;\n    }\n\n    /* Удаление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    removeEdge(i: number, j: number): void {\n        // Обработка выхода индекса за границы и случая равенства\n        if (i &lt; 0 || j &lt; 0 || i &gt;= this.size() || j &gt;= this.size() || i === j) {\n            throw new RangeError('Index Out Of Bounds Exception');\n        }\n        this.adjMat[i][j] = 0;\n        this.adjMat[j][i] = 0;\n    }\n\n    /* Вывести матрицу смежности */\n    print(): void {\n        console.log('Список вершин = ', this.vertices);\n        console.log('Матрица смежности =', this.adjMat);\n    }\n}\n</code></pre> graph_adjacency_matrix.dart<pre><code>/* Класс неориентированного графа на основе матрицы смежности */\nclass GraphAdjMat {\n  List&lt;int&gt; vertices = []; // Элемент вершины: элемент представляет «значение вершины», индекс представляет «индекс вершины»\n  List&lt;List&lt;int&gt;&gt; adjMat = []; // Матрица смежности, где индексы строк и столбцов соответствуют «индексам вершин»\n\n  /* Конструктор */\n  GraphAdjMat(List&lt;int&gt; vertices, List&lt;List&lt;int&gt;&gt; edges) {\n    this.vertices = [];\n    this.adjMat = [];\n    // Добавление вершины\n    for (int val in vertices) {\n      addVertex(val);\n    }\n    // Добавить ребра\n    // Обратите внимание: элементы edges представляют собой индексы вершин, то есть соответствуют индексам элементов vertices\n    for (List&lt;int&gt; e in edges) {\n      addEdge(e[0], e[1]);\n    }\n  }\n\n  /* Получить число вершин */\n  int size() {\n    return vertices.length;\n  }\n\n  /* Добавление вершины */\n  void addVertex(int val) {\n    int n = size();\n    // Добавить значение новой вершины в список вершин\n    vertices.add(val);\n    // Добавить строку в матрицу смежности\n    List&lt;int&gt; newRow = List.filled(n, 0, growable: true);\n    adjMat.add(newRow);\n    // Добавить столбец в матрицу смежности\n    for (List&lt;int&gt; row in adjMat) {\n      row.add(0);\n    }\n  }\n\n  /* Удаление вершины */\n  void removeVertex(int index) {\n    if (index &gt;= size()) {\n      throw IndexError;\n    }\n    // Удалить вершину с индексом index из списка вершин\n    vertices.removeAt(index);\n    // Удалить строку с индексом index из матрицы смежности\n    adjMat.removeAt(index);\n    // Удалить столбец с индексом index из матрицы смежности\n    for (List&lt;int&gt; row in adjMat) {\n      row.removeAt(index);\n    }\n  }\n\n  /* Добавление ребра */\n  // Параметры i и j соответствуют индексам элементов vertices\n  void addEdge(int i, int j) {\n    // Обработка выхода индекса за границы и случая равенства\n    if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j) {\n      throw IndexError;\n    }\n    // В неориентированном графе матрица смежности симметрична относительно главной диагонали, то есть выполняется (i, j) == (j, i)\n    adjMat[i][j] = 1;\n    adjMat[j][i] = 1;\n  }\n\n  /* Удаление ребра */\n  // Параметры i и j соответствуют индексам элементов vertices\n  void removeEdge(int i, int j) {\n    // Обработка выхода индекса за границы и случая равенства\n    if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j) {\n      throw IndexError;\n    }\n    adjMat[i][j] = 0;\n    adjMat[j][i] = 0;\n  }\n\n  /* Вывести матрицу смежности */\n  void printAdjMat() {\n    print(\"Список вершин = $vertices\");\n    print(\"Матрица смежности = \");\n    printMatrix(adjMat);\n  }\n}\n</code></pre> graph_adjacency_matrix.rs<pre><code>/* Тип неориентированного графа на основе матрицы смежности */\npub struct GraphAdjMat {\n    // Список вершин: элементы представляют «значения вершин», а индексы — «индексы вершин»\n    pub vertices: Vec&lt;i32&gt;,\n    // Матрица смежности, где индексы строк и столбцов соответствуют «индексам вершин»\n    pub adj_mat: Vec&lt;Vec&lt;i32&gt;&gt;,\n}\n\nimpl GraphAdjMat {\n    /* Конструктор */\n    pub fn new(vertices: Vec&lt;i32&gt;, edges: Vec&lt;[usize; 2]&gt;) -&gt; Self {\n        let mut graph = GraphAdjMat {\n            vertices: vec![],\n            adj_mat: vec![],\n        };\n        // Добавление вершины\n        for val in vertices {\n            graph.add_vertex(val);\n        }\n        // Добавить ребра\n        // Обратите внимание: элементы edges представляют собой индексы вершин, то есть соответствуют индексам элементов vertices\n        for edge in edges {\n            graph.add_edge(edge[0], edge[1])\n        }\n\n        graph\n    }\n\n    /* Получить число вершин */\n    pub fn size(&amp;self) -&gt; usize {\n        self.vertices.len()\n    }\n\n    /* Добавление вершины */\n    pub fn add_vertex(&amp;mut self, val: i32) {\n        let n = self.size();\n        // Добавить значение новой вершины в список вершин\n        self.vertices.push(val);\n        // Добавить строку в матрицу смежности\n        self.adj_mat.push(vec![0; n]);\n        // Добавить столбец в матрицу смежности\n        for row in self.adj_mat.iter_mut() {\n            row.push(0);\n        }\n    }\n\n    /* Удаление вершины */\n    pub fn remove_vertex(&amp;mut self, index: usize) {\n        if index &gt;= self.size() {\n            panic!(\"index error\")\n        }\n        // Удалить вершину с индексом index из списка вершин\n        self.vertices.remove(index);\n        // Удалить строку с индексом index из матрицы смежности\n        self.adj_mat.remove(index);\n        // Удалить столбец с индексом index из матрицы смежности\n        for row in self.adj_mat.iter_mut() {\n            row.remove(index);\n        }\n    }\n\n    /* Добавление ребра */\n    pub fn add_edge(&amp;mut self, i: usize, j: usize) {\n        // Параметры i и j соответствуют индексам элементов vertices\n        // Обработка выхода индекса за границы и случая равенства\n        if i &gt;= self.size() || j &gt;= self.size() || i == j {\n            panic!(\"index error\")\n        }\n        // В неориентированном графе матрица смежности симметрична относительно главной диагонали, то есть выполняется (i, j) == (j, i)\n        self.adj_mat[i][j] = 1;\n        self.adj_mat[j][i] = 1;\n    }\n\n    /* Удаление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    pub fn remove_edge(&amp;mut self, i: usize, j: usize) {\n        // Параметры i и j соответствуют индексам элементов vertices\n        // Обработка выхода индекса за границы и случая равенства\n        if i &gt;= self.size() || j &gt;= self.size() || i == j {\n            panic!(\"index error\")\n        }\n        self.adj_mat[i][j] = 0;\n        self.adj_mat[j][i] = 0;\n    }\n\n    /* Вывести матрицу смежности */\n    pub fn print(&amp;self) {\n        println!(\"Список вершин = {:?}\", self.vertices);\n        println!(\"Матрица смежности =\");\n        println!(\"[\");\n        for row in &amp;self.adj_mat {\n            println!(\"  {:?},\", row);\n        }\n        println!(\"]\")\n    }\n}\n</code></pre> graph_adjacency_matrix.c<pre><code>/* Структура неориентированного графа на основе матрицы смежности */\ntypedef struct {\n    int vertices[MAX_SIZE];\n    int adjMat[MAX_SIZE][MAX_SIZE];\n    int size;\n} GraphAdjMat;\n\n/* Конструктор */\nGraphAdjMat *newGraphAdjMat() {\n    GraphAdjMat *graph = (GraphAdjMat *)malloc(sizeof(GraphAdjMat));\n    graph-&gt;size = 0;\n    for (int i = 0; i &lt; MAX_SIZE; i++) {\n        for (int j = 0; j &lt; MAX_SIZE; j++) {\n            graph-&gt;adjMat[i][j] = 0;\n        }\n    }\n    return graph;\n}\n\n/* Деструктор */\nvoid delGraphAdjMat(GraphAdjMat *graph) {\n    free(graph);\n}\n\n/* Добавление вершины */\nvoid addVertex(GraphAdjMat *graph, int val) {\n    if (graph-&gt;size == MAX_SIZE) {\n        fprintf(stderr, \"Количество вершин графа уже достигло максимума\\n\");\n        return;\n    }\n    // Добавить n-ю вершину и обнулить n-ю строку и столбец\n    int n = graph-&gt;size;\n    graph-&gt;vertices[n] = val;\n    for (int i = 0; i &lt;= n; i++) {\n        graph-&gt;adjMat[n][i] = graph-&gt;adjMat[i][n] = 0;\n    }\n    graph-&gt;size++;\n}\n\n/* Удаление вершины */\nvoid removeVertex(GraphAdjMat *graph, int index) {\n    if (index &lt; 0 || index &gt;= graph-&gt;size) {\n        fprintf(stderr, \"индекс вершины выходит за границы\\n\");\n        return;\n    }\n    // Удалить вершину с индексом index из списка вершин\n    for (int i = index; i &lt; graph-&gt;size - 1; i++) {\n        graph-&gt;vertices[i] = graph-&gt;vertices[i + 1];\n    }\n    // Удалить строку с индексом index из матрицы смежности\n    for (int i = index; i &lt; graph-&gt;size - 1; i++) {\n        for (int j = 0; j &lt; graph-&gt;size; j++) {\n            graph-&gt;adjMat[i][j] = graph-&gt;adjMat[i + 1][j];\n        }\n    }\n    // Удалить столбец с индексом index из матрицы смежности\n    for (int i = 0; i &lt; graph-&gt;size; i++) {\n        for (int j = index; j &lt; graph-&gt;size - 1; j++) {\n            graph-&gt;adjMat[i][j] = graph-&gt;adjMat[i][j + 1];\n        }\n    }\n    graph-&gt;size--;\n}\n\n/* Добавление ребра */\n// Параметры i и j соответствуют индексам элементов vertices\nvoid addEdge(GraphAdjMat *graph, int i, int j) {\n    if (i &lt; 0 || j &lt; 0 || i &gt;= graph-&gt;size || j &gt;= graph-&gt;size || i == j) {\n        fprintf(stderr, \"индексы ребра выходят за границы или совпадают\\n\");\n        return;\n    }\n    graph-&gt;adjMat[i][j] = 1;\n    graph-&gt;adjMat[j][i] = 1;\n}\n\n/* Удаление ребра */\n// Параметры i и j соответствуют индексам элементов vertices\nvoid removeEdge(GraphAdjMat *graph, int i, int j) {\n    if (i &lt; 0 || j &lt; 0 || i &gt;= graph-&gt;size || j &gt;= graph-&gt;size || i == j) {\n        fprintf(stderr, \"индексы ребра выходят за границы или совпадают\\n\");\n        return;\n    }\n    graph-&gt;adjMat[i][j] = 0;\n    graph-&gt;adjMat[j][i] = 0;\n}\n\n/* Вывести матрицу смежности */\nvoid printGraphAdjMat(GraphAdjMat *graph) {\n    printf(\"Список вершин = \");\n    printArray(graph-&gt;vertices, graph-&gt;size);\n    printf(\"Матрица смежности =\\n\");\n    for (int i = 0; i &lt; graph-&gt;size; i++) {\n        printArray(graph-&gt;adjMat[i], graph-&gt;size);\n    }\n}\n</code></pre> graph_adjacency_matrix.kt<pre><code>/* Класс неориентированного графа на основе матрицы смежности */\nclass GraphAdjMat(vertices: IntArray, edges: Array&lt;IntArray&gt;) {\n    val vertices = mutableListOf&lt;Int&gt;() // Список вершин: элементы представляют «значения вершин», а индексы — «индексы вершин»\n    val adjMat = mutableListOf&lt;MutableList&lt;Int&gt;&gt;() // Матрица смежности, где индексы строк и столбцов соответствуют «индексам вершин»\n\n    /* Конструктор */\n    init {\n        // Добавление вершины\n        for (vertex in vertices) {\n            addVertex(vertex)\n        }\n        // Добавить ребра\n        // Обратите внимание: элементы edges представляют собой индексы вершин, то есть соответствуют индексам элементов vertices\n        for (edge in edges) {\n            addEdge(edge[0], edge[1])\n        }\n    }\n\n    /* Получить число вершин */\n    fun size(): Int {\n        return vertices.size\n    }\n\n    /* Добавление вершины */\n    fun addVertex(_val: Int) {\n        val n = size()\n        // Добавить значение новой вершины в список вершин\n        vertices.add(_val)\n        // Добавить строку в матрицу смежности\n        val newRow = mutableListOf&lt;Int&gt;()\n        for (j in 0..&lt;n) {\n            newRow.add(0)\n        }\n        adjMat.add(newRow)\n        // Добавить столбец в матрицу смежности\n        for (row in adjMat) {\n            row.add(0)\n        }\n    }\n\n    /* Удаление вершины */\n    fun removeVertex(index: Int) {\n        if (index &gt;= size())\n            throw IndexOutOfBoundsException()\n        // Удалить вершину с индексом index из списка вершин\n        vertices.removeAt(index)\n        // Удалить строку с индексом index из матрицы смежности\n        adjMat.removeAt(index)\n        // Удалить столбец с индексом index из матрицы смежности\n        for (row in adjMat) {\n            row.removeAt(index)\n        }\n    }\n\n    /* Добавление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    fun addEdge(i: Int, j: Int) {\n        // Обработка выхода индекса за границы и случая равенства\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j)\n            throw IndexOutOfBoundsException()\n        // В неориентированном графе матрица смежности симметрична относительно главной диагонали, то есть выполняется (i, j) == (j, i)\n        adjMat[i][j] = 1\n        adjMat[j][i] = 1\n    }\n\n    /* Удаление ребра */\n    // Параметры i и j соответствуют индексам элементов vertices\n    fun removeEdge(i: Int, j: Int) {\n        // Обработка выхода индекса за границы и случая равенства\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j)\n            throw IndexOutOfBoundsException()\n        adjMat[i][j] = 0\n        adjMat[j][i] = 0\n    }\n\n    /* Вывести матрицу смежности */\n    fun print() {\n        print(\"Список вершин = \")\n        println(vertices)\n        println(\"Матрица смежности =\")\n        printMatrix(adjMat)\n    }\n}\n</code></pre> graph_adjacency_matrix.rb<pre><code>### Класс неориентированного графа на основе матрицы смежности ###\nclass GraphAdjMat\n  def initialize(vertices, edges)\n    ### Конструктор ###\n    # Список вершин: элементы представляют «значения вершин», а индексы — «индексы вершин»\n    @vertices = []\n    # Матрица смежности, где индексы строк и столбцов соответствуют «индексам вершин»\n    @adj_mat = []\n    # Добавление вершины\n    vertices.each { |val| add_vertex(val) }\n    # Добавить ребра\n    # Обратите внимание: элементы edges представляют собой индексы вершин, то есть соответствуют индексам элементов vertices\n    edges.each { |e| add_edge(e[0], e[1]) }\n  end\n\n  ### Получение числа вершин ###\n  def size\n    @vertices.length\n  end\n\n  ### Добавление вершины ###\n  def add_vertex(val)\n    n = size\n    # Добавить значение новой вершины в список вершин\n    @vertices &lt;&lt; val\n    # Добавить строку в матрицу смежности\n    new_row = Array.new(n, 0)\n    @adj_mat &lt;&lt; new_row\n    # Добавить столбец в матрицу смежности\n    @adj_mat.each { |row| row &lt;&lt; 0 }\n  end\n\n  ### Удаление вершины ###\n  def remove_vertex(index)\n    raise IndexError if index &gt;= size\n\n    # Удалить вершину с индексом index из списка вершин\n    @vertices.delete_at(index)\n    # Удалить строку с индексом index из матрицы смежности\n    @adj_mat.delete_at(index)\n    # Удалить столбец с индексом index из матрицы смежности\n    @adj_mat.each { |row| row.delete_at(index) }\n  end\n\n  ### Добавление ребра ###\n  def add_edge(i, j)\n    # Параметры i и j соответствуют индексам элементов vertices\n    # Обработка выхода индекса за границы и случая равенства\n    if i &lt; 0 || j &lt; 0 || i &gt;= size || j &gt;= size || i == j\n      raise IndexError\n    end\n    # В неориентированном графе матрица смежности симметрична относительно главной диагонали, то есть выполняется (i, j) == (j, i)\n    @adj_mat[i][j] = 1\n    @adj_mat[j][i] = 1\n  end\n\n  ### Удаление ребра ###\n  def remove_edge(i, j)\n    # Параметры i и j соответствуют индексам элементов vertices\n    # Обработка выхода индекса за границы и случая равенства\n    if i &lt; 0 || j &lt; 0 || i &gt;= size || j &gt;= size || i == j\n      raise IndexError\n    end\n    @adj_mat[i][j] = 0\n    @adj_mat[j][i] = 0\n  end\n\n  ### Вывести матрицу смежности ###\n  def __print__\n    puts \"Список вершин = #{@vertices}\"\n    puts 'Матрица смежности ='\n    print_matrix(@adj_mat)\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 9. Графы","9.2 &nbsp; Базовые операции графа"],"tags":[]},{"location":"chapter_graph/graph_operations/#922","level":2,"title":"9.2.2   Реализация на основе списка смежности","text":"<p>Пусть неориентированный граф содержит в сумме \\(n\\) вершин и \\(m\\) ребер. Тогда различные операции можно реализовать способом, показанным на рисунках ниже.</p> <ul> <li>Добавление ребра: достаточно добавить ребро в конец списка, соответствующего вершине; это требует \\(O(1)\\) времени. Поскольку граф неориентированный, необходимо одновременно добавить ребра в обоих направлениях.</li> <li>Удаление ребра: нужно найти и удалить указанное ребро в списке, соответствующем вершине; это требует \\(O(m)\\) времени. В неориентированном графе необходимо удалить ребра в обоих направлениях.</li> <li>Добавление вершины: в список смежности добавляется еще один список, а новая вершина становится его головным узлом; это требует \\(O(1)\\) времени.</li> <li>Удаление вершины: требуется пройти по всему списку смежности и удалить все ребра, содержащие указанную вершину; это требует \\(O(n + m)\\) времени.</li> <li>Инициализация: в списке смежности создаются \\(n\\) вершин и \\(2m\\) ребер; это требует \\(O(n + m)\\) времени.</li> </ul> Инициализация списка смежностиДобавление ребраУдаление ребраДобавление вершиныУдаление вершины <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 9-8   Инициализация списка смежности, добавление и удаление ребер и вершин </p> <p>Ниже приведен код списка смежности. По сравнению с рисунками выше, реальная реализация имеет следующие отличия.</p> <ul> <li>Чтобы упростить добавление и удаление вершин, а также сделать код проще, мы используем список, то есть динамический массив, вместо связного списка.</li> <li>Для хранения списка смежности используется хеш-таблица, где <code>key</code> - это экземпляр вершины, а <code>value</code> - список смежных вершин данной вершины.</li> </ul> <p>Кроме того, в списке смежности используется класс <code>Vertex</code> для представления вершины. Причина в том, что если, как и в матрице смежности, различать вершины по индексам списка, то при удалении вершины с индексом \\(i\\) пришлось бы обходить весь список смежности и уменьшать на \\(1\\) все индексы, большие \\(i\\) , что крайне неэффективно. Если же каждая вершина является уникальным экземпляром <code>Vertex</code> , то после удаления одной вершины остальные вершины менять уже не требуется.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby graph_adjacency_list.py<pre><code>class GraphAdjList:\n    \"\"\"Класс неориентированного графа на основе списка смежности\"\"\"\n\n    def __init__(self, edges: list[list[Vertex]]):\n        \"\"\"Конструктор\"\"\"\n        # Список смежности, где key — вершина, а value — все смежные ей вершины\n        self.adj_list = dict[Vertex, list[Vertex]]()\n        # Добавить все вершины и ребра\n        for edge in edges:\n            self.add_vertex(edge[0])\n            self.add_vertex(edge[1])\n            self.add_edge(edge[0], edge[1])\n\n    def size(self) -&gt; int:\n        \"\"\"Получить число вершин\"\"\"\n        return len(self.adj_list)\n\n    def add_edge(self, vet1: Vertex, vet2: Vertex):\n        \"\"\"Добавление ребра\"\"\"\n        if vet1 not in self.adj_list or vet2 not in self.adj_list or vet1 == vet2:\n            raise ValueError()\n        # Добавить ребро vet1 - vet2\n        self.adj_list[vet1].append(vet2)\n        self.adj_list[vet2].append(vet1)\n\n    def remove_edge(self, vet1: Vertex, vet2: Vertex):\n        \"\"\"Удаление ребра\"\"\"\n        if vet1 not in self.adj_list or vet2 not in self.adj_list or vet1 == vet2:\n            raise ValueError()\n        # Удалить ребро vet1 - vet2\n        self.adj_list[vet1].remove(vet2)\n        self.adj_list[vet2].remove(vet1)\n\n    def add_vertex(self, vet: Vertex):\n        \"\"\"Добавление вершины\"\"\"\n        if vet in self.adj_list:\n            return\n        # Добавить новый список в список смежности\n        self.adj_list[vet] = []\n\n    def remove_vertex(self, vet: Vertex):\n        \"\"\"Удаление вершины\"\"\"\n        if vet not in self.adj_list:\n            raise ValueError()\n        # Удалить из списка смежности список, соответствующий вершине vet\n        self.adj_list.pop(vet)\n        # Обойти списки других вершин и удалить все ребра, содержащие vet\n        for vertex in self.adj_list:\n            if vet in self.adj_list[vertex]:\n                self.adj_list[vertex].remove(vet)\n\n    def print(self):\n        \"\"\"Вывести список смежности\"\"\"\n        print(\"Список смежности =\")\n        for vertex in self.adj_list:\n            tmp = [v.val for v in self.adj_list[vertex]]\n            print(f\"{vertex.val}: {tmp},\")\n</code></pre> graph_adjacency_list.cpp<pre><code>/* Класс неориентированного графа на основе списка смежности */\nclass GraphAdjList {\n  public:\n    // Список смежности, где key — вершина, а value — все смежные ей вершины\n    unordered_map&lt;Vertex *, vector&lt;Vertex *&gt;&gt; adjList;\n\n    /* Удалить указанный узел из vector */\n    void remove(vector&lt;Vertex *&gt; &amp;vec, Vertex *vet) {\n        for (int i = 0; i &lt; vec.size(); i++) {\n            if (vec[i] == vet) {\n                vec.erase(vec.begin() + i);\n                break;\n            }\n        }\n    }\n\n    /* Конструктор */\n    GraphAdjList(const vector&lt;vector&lt;Vertex *&gt;&gt; &amp;edges) {\n        // Добавить все вершины и ребра\n        for (const vector&lt;Vertex *&gt; &amp;edge : edges) {\n            addVertex(edge[0]);\n            addVertex(edge[1]);\n            addEdge(edge[0], edge[1]);\n        }\n    }\n\n    /* Получить число вершин */\n    int size() {\n        return adjList.size();\n    }\n\n    /* Добавление ребра */\n    void addEdge(Vertex *vet1, Vertex *vet2) {\n        if (!adjList.count(vet1) || !adjList.count(vet2) || vet1 == vet2)\n            throw invalid_argument(\"вершина не существует\");\n        // Добавить ребро vet1 - vet2\n        adjList[vet1].push_back(vet2);\n        adjList[vet2].push_back(vet1);\n    }\n\n    /* Удаление ребра */\n    void removeEdge(Vertex *vet1, Vertex *vet2) {\n        if (!adjList.count(vet1) || !adjList.count(vet2) || vet1 == vet2)\n            throw invalid_argument(\"вершина не существует\");\n        // Удалить ребро vet1 - vet2\n        remove(adjList[vet1], vet2);\n        remove(adjList[vet2], vet1);\n    }\n\n    /* Добавление вершины */\n    void addVertex(Vertex *vet) {\n        if (adjList.count(vet))\n            return;\n        // Добавить новый список в список смежности\n        adjList[vet] = vector&lt;Vertex *&gt;();\n    }\n\n    /* Удаление вершины */\n    void removeVertex(Vertex *vet) {\n        if (!adjList.count(vet))\n            throw invalid_argument(\"вершина не существует\");\n        // Удалить из списка смежности список, соответствующий вершине vet\n        adjList.erase(vet);\n        // Обойти списки других вершин и удалить все ребра, содержащие vet\n        for (auto &amp;adj : adjList) {\n            remove(adj.second, vet);\n        }\n    }\n\n    /* Вывести список смежности */\n    void print() {\n        cout &lt;&lt; \"Список смежности =\" &lt;&lt; endl;\n        for (auto &amp;adj : adjList) {\n            const auto &amp;key = adj.first;\n            const auto &amp;vec = adj.second;\n            cout &lt;&lt; key-&gt;val &lt;&lt; \": \";\n            printVector(vetsToVals(vec));\n        }\n    }\n};\n</code></pre> graph_adjacency_list.java<pre><code>/* Класс неориентированного графа на основе списка смежности */\nclass GraphAdjList {\n    // Список смежности, где key — вершина, а value — все смежные ей вершины\n    Map&lt;Vertex, List&lt;Vertex&gt;&gt; adjList;\n\n    /* Конструктор */\n    public GraphAdjList(Vertex[][] edges) {\n        this.adjList = new HashMap&lt;&gt;();\n        // Добавить все вершины и ребра\n        for (Vertex[] edge : edges) {\n            addVertex(edge[0]);\n            addVertex(edge[1]);\n            addEdge(edge[0], edge[1]);\n        }\n    }\n\n    /* Получить число вершин */\n    public int size() {\n        return adjList.size();\n    }\n\n    /* Добавление ребра */\n    public void addEdge(Vertex vet1, Vertex vet2) {\n        if (!adjList.containsKey(vet1) || !adjList.containsKey(vet2) || vet1 == vet2)\n            throw new IllegalArgumentException();\n        // Добавить ребро vet1 - vet2\n        adjList.get(vet1).add(vet2);\n        adjList.get(vet2).add(vet1);\n    }\n\n    /* Удаление ребра */\n    public void removeEdge(Vertex vet1, Vertex vet2) {\n        if (!adjList.containsKey(vet1) || !adjList.containsKey(vet2) || vet1 == vet2)\n            throw new IllegalArgumentException();\n        // Удалить ребро vet1 - vet2\n        adjList.get(vet1).remove(vet2);\n        adjList.get(vet2).remove(vet1);\n    }\n\n    /* Добавление вершины */\n    public void addVertex(Vertex vet) {\n        if (adjList.containsKey(vet))\n            return;\n        // Добавить новый список в список смежности\n        adjList.put(vet, new ArrayList&lt;&gt;());\n    }\n\n    /* Удаление вершины */\n    public void removeVertex(Vertex vet) {\n        if (!adjList.containsKey(vet))\n            throw new IllegalArgumentException();\n        // Удалить из списка смежности список, соответствующий вершине vet\n        adjList.remove(vet);\n        // Обойти списки других вершин и удалить все ребра, содержащие vet\n        for (List&lt;Vertex&gt; list : adjList.values()) {\n            list.remove(vet);\n        }\n    }\n\n    /* Вывести список смежности */\n    public void print() {\n        System.out.println(\"Список смежности =\");\n        for (Map.Entry&lt;Vertex, List&lt;Vertex&gt;&gt; pair : adjList.entrySet()) {\n            List&lt;Integer&gt; tmp = new ArrayList&lt;&gt;();\n            for (Vertex vertex : pair.getValue())\n                tmp.add(vertex.val);\n            System.out.println(pair.getKey().val + \": \" + tmp + \",\");\n        }\n    }\n}\n</code></pre> graph_adjacency_list.cs<pre><code>/* Класс неориентированного графа на основе списка смежности */\nclass GraphAdjList {\n    // Список смежности, где key — вершина, а value — все смежные ей вершины\n    public Dictionary&lt;Vertex, List&lt;Vertex&gt;&gt; adjList;\n\n    /* Конструктор */\n    public GraphAdjList(Vertex[][] edges) {\n        adjList = [];\n        // Добавить все вершины и ребра\n        foreach (Vertex[] edge in edges) {\n            AddVertex(edge[0]);\n            AddVertex(edge[1]);\n            AddEdge(edge[0], edge[1]);\n        }\n    }\n\n    /* Получить число вершин */\n    int Size() {\n        return adjList.Count;\n    }\n\n    /* Добавление ребра */\n    public void AddEdge(Vertex vet1, Vertex vet2) {\n        if (!adjList.ContainsKey(vet1) || !adjList.ContainsKey(vet2) || vet1 == vet2)\n            throw new InvalidOperationException();\n        // Добавить ребро vet1 - vet2\n        adjList[vet1].Add(vet2);\n        adjList[vet2].Add(vet1);\n    }\n\n    /* Удаление ребра */\n    public void RemoveEdge(Vertex vet1, Vertex vet2) {\n        if (!adjList.ContainsKey(vet1) || !adjList.ContainsKey(vet2) || vet1 == vet2)\n            throw new InvalidOperationException();\n        // Удалить ребро vet1 - vet2\n        adjList[vet1].Remove(vet2);\n        adjList[vet2].Remove(vet1);\n    }\n\n    /* Добавление вершины */\n    public void AddVertex(Vertex vet) {\n        if (adjList.ContainsKey(vet))\n            return;\n        // Добавить новый список в список смежности\n        adjList.Add(vet, []);\n    }\n\n    /* Удаление вершины */\n    public void RemoveVertex(Vertex vet) {\n        if (!adjList.ContainsKey(vet))\n            throw new InvalidOperationException();\n        // Удалить из списка смежности список, соответствующий вершине vet\n        adjList.Remove(vet);\n        // Обойти списки других вершин и удалить все ребра, содержащие vet\n        foreach (List&lt;Vertex&gt; list in adjList.Values) {\n            list.Remove(vet);\n        }\n    }\n\n    /* Вывести список смежности */\n    public void Print() {\n        Console.WriteLine(\"Список смежности =\");\n        foreach (KeyValuePair&lt;Vertex, List&lt;Vertex&gt;&gt; pair in adjList) {\n            List&lt;int&gt; tmp = [];\n            foreach (Vertex vertex in pair.Value)\n                tmp.Add(vertex.val);\n            Console.WriteLine(pair.Key.val + \": [\" + string.Join(\", \", tmp) + \"],\");\n        }\n    }\n}\n</code></pre> graph_adjacency_list.go<pre><code>/* Класс неориентированного графа на основе списка смежности */\ntype graphAdjList struct {\n    // Список смежности, где key — вершина, а value — все смежные ей вершины\n    adjList map[Vertex][]Vertex\n}\n\n/* Конструктор */\nfunc newGraphAdjList(edges [][]Vertex) *graphAdjList {\n    g := &amp;graphAdjList{\n        adjList: make(map[Vertex][]Vertex),\n    }\n    // Добавить все вершины и ребра\n    for _, edge := range edges {\n        g.addVertex(edge[0])\n        g.addVertex(edge[1])\n        g.addEdge(edge[0], edge[1])\n    }\n    return g\n}\n\n/* Получить число вершин */\nfunc (g *graphAdjList) size() int {\n    return len(g.adjList)\n}\n\n/* Добавление ребра */\nfunc (g *graphAdjList) addEdge(vet1 Vertex, vet2 Vertex) {\n    _, ok1 := g.adjList[vet1]\n    _, ok2 := g.adjList[vet2]\n    if !ok1 || !ok2 || vet1 == vet2 {\n        panic(\"error\")\n    }\n    // Добавить ребро vet1 - vet2, добавив анонимную struct{}\n    g.adjList[vet1] = append(g.adjList[vet1], vet2)\n    g.adjList[vet2] = append(g.adjList[vet2], vet1)\n}\n\n/* Удаление ребра */\nfunc (g *graphAdjList) removeEdge(vet1 Vertex, vet2 Vertex) {\n    _, ok1 := g.adjList[vet1]\n    _, ok2 := g.adjList[vet2]\n    if !ok1 || !ok2 || vet1 == vet2 {\n        panic(\"error\")\n    }\n    // Удалить ребро vet1 - vet2\n    g.adjList[vet1] = DeleteSliceElms(g.adjList[vet1], vet2)\n    g.adjList[vet2] = DeleteSliceElms(g.adjList[vet2], vet1)\n}\n\n/* Добавление вершины */\nfunc (g *graphAdjList) addVertex(vet Vertex) {\n    _, ok := g.adjList[vet]\n    if ok {\n        return\n    }\n    // Добавить новый список в список смежности\n    g.adjList[vet] = make([]Vertex, 0)\n}\n\n/* Удаление вершины */\nfunc (g *graphAdjList) removeVertex(vet Vertex) {\n    _, ok := g.adjList[vet]\n    if !ok {\n        panic(\"error\")\n    }\n    // Удалить из списка смежности список, соответствующий вершине vet\n    delete(g.adjList, vet)\n    // Обойти списки других вершин и удалить все ребра, содержащие vet\n    for v, list := range g.adjList {\n        g.adjList[v] = DeleteSliceElms(list, vet)\n    }\n}\n\n/* Вывести список смежности */\nfunc (g *graphAdjList) print() {\n    var builder strings.Builder\n    fmt.Printf(\"Список смежности = \\n\")\n    for k, v := range g.adjList {\n        builder.WriteString(\"\\t\\t\" + strconv.Itoa(k.Val) + \": \")\n        for _, vet := range v {\n            builder.WriteString(strconv.Itoa(vet.Val) + \" \")\n        }\n        fmt.Println(builder.String())\n        builder.Reset()\n    }\n}\n</code></pre> graph_adjacency_list.swift<pre><code>/* Класс неориентированного графа на основе списка смежности */\nclass GraphAdjList {\n    // Список смежности, где key — вершина, а value — все смежные ей вершины\n    public private(set) var adjList: [Vertex: [Vertex]]\n\n    /* Конструктор */\n    public init(edges: [[Vertex]]) {\n        adjList = [:]\n        // Добавить все вершины и ребра\n        for edge in edges {\n            addVertex(vet: edge[0])\n            addVertex(vet: edge[1])\n            addEdge(vet1: edge[0], vet2: edge[1])\n        }\n    }\n\n    /* Получить число вершин */\n    public func size() -&gt; Int {\n        adjList.count\n    }\n\n    /* Добавление ребра */\n    public func addEdge(vet1: Vertex, vet2: Vertex) {\n        if adjList[vet1] == nil || adjList[vet2] == nil || vet1 == vet2 {\n            fatalError(\"Неверный аргумент\")\n        }\n        // Добавить ребро vet1 - vet2\n        adjList[vet1]?.append(vet2)\n        adjList[vet2]?.append(vet1)\n    }\n\n    /* Удаление ребра */\n    public func removeEdge(vet1: Vertex, vet2: Vertex) {\n        if adjList[vet1] == nil || adjList[vet2] == nil || vet1 == vet2 {\n            fatalError(\"Неверный аргумент\")\n        }\n        // Удалить ребро vet1 - vet2\n        adjList[vet1]?.removeAll { $0 == vet2 }\n        adjList[vet2]?.removeAll { $0 == vet1 }\n    }\n\n    /* Добавление вершины */\n    public func addVertex(vet: Vertex) {\n        if adjList[vet] != nil {\n            return\n        }\n        // Добавить новый список в список смежности\n        adjList[vet] = []\n    }\n\n    /* Удаление вершины */\n    public func removeVertex(vet: Vertex) {\n        if adjList[vet] == nil {\n            fatalError(\"Неверный аргумент\")\n        }\n        // Удалить из списка смежности список, соответствующий вершине vet\n        adjList.removeValue(forKey: vet)\n        // Обойти списки других вершин и удалить все ребра, содержащие vet\n        for key in adjList.keys {\n            adjList[key]?.removeAll { $0 == vet }\n        }\n    }\n\n    /* Вывести список смежности */\n    public func print() {\n        Swift.print(\"Список смежности =\")\n        for (vertex, list) in adjList {\n            let list = list.map { $0.val }\n            Swift.print(\"\\(vertex.val): \\(list),\")\n        }\n    }\n}\n</code></pre> graph_adjacency_list.js<pre><code>/* Класс неориентированного графа на основе списка смежности */\nclass GraphAdjList {\n    // Список смежности, где key — вершина, а value — все смежные ей вершины\n    adjList;\n\n    /* Конструктор */\n    constructor(edges) {\n        this.adjList = new Map();\n        // Добавить все вершины и ребра\n        for (const edge of edges) {\n            this.addVertex(edge[0]);\n            this.addVertex(edge[1]);\n            this.addEdge(edge[0], edge[1]);\n        }\n    }\n\n    /* Получить число вершин */\n    size() {\n        return this.adjList.size;\n    }\n\n    /* Добавление ребра */\n    addEdge(vet1, vet2) {\n        if (\n            !this.adjList.has(vet1) ||\n            !this.adjList.has(vet2) ||\n            vet1 === vet2\n        ) {\n            throw new Error('Illegal Argument Exception');\n        }\n        // Добавить ребро vet1 - vet2\n        this.adjList.get(vet1).push(vet2);\n        this.adjList.get(vet2).push(vet1);\n    }\n\n    /* Удаление ребра */\n    removeEdge(vet1, vet2) {\n        if (\n            !this.adjList.has(vet1) ||\n            !this.adjList.has(vet2) ||\n            vet1 === vet2 ||\n            this.adjList.get(vet1).indexOf(vet2) === -1\n        ) {\n            throw new Error('Illegal Argument Exception');\n        }\n        // Удалить ребро vet1 - vet2\n        this.adjList.get(vet1).splice(this.adjList.get(vet1).indexOf(vet2), 1);\n        this.adjList.get(vet2).splice(this.adjList.get(vet2).indexOf(vet1), 1);\n    }\n\n    /* Добавление вершины */\n    addVertex(vet) {\n        if (this.adjList.has(vet)) return;\n        // Добавить новый список в список смежности\n        this.adjList.set(vet, []);\n    }\n\n    /* Удаление вершины */\n    removeVertex(vet) {\n        if (!this.adjList.has(vet)) {\n            throw new Error('Illegal Argument Exception');\n        }\n        // Удалить из списка смежности список, соответствующий вершине vet\n        this.adjList.delete(vet);\n        // Обойти списки других вершин и удалить все ребра, содержащие vet\n        for (const set of this.adjList.values()) {\n            const index = set.indexOf(vet);\n            if (index &gt; -1) {\n                set.splice(index, 1);\n            }\n        }\n    }\n\n    /* Вывести список смежности */\n    print() {\n        console.log('Список смежности =');\n        for (const [key, value] of this.adjList) {\n            const tmp = [];\n            for (const vertex of value) {\n                tmp.push(vertex.val);\n            }\n            console.log(key.val + ': ' + tmp.join());\n        }\n    }\n}\n</code></pre> graph_adjacency_list.ts<pre><code>/* Класс неориентированного графа на основе списка смежности */\nclass GraphAdjList {\n    // Список смежности, где key — вершина, а value — все смежные ей вершины\n    adjList: Map&lt;Vertex, Vertex[]&gt;;\n\n    /* Конструктор */\n    constructor(edges: Vertex[][]) {\n        this.adjList = new Map();\n        // Добавить все вершины и ребра\n        for (const edge of edges) {\n            this.addVertex(edge[0]);\n            this.addVertex(edge[1]);\n            this.addEdge(edge[0], edge[1]);\n        }\n    }\n\n    /* Получить число вершин */\n    size(): number {\n        return this.adjList.size;\n    }\n\n    /* Добавление ребра */\n    addEdge(vet1: Vertex, vet2: Vertex): void {\n        if (\n            !this.adjList.has(vet1) ||\n            !this.adjList.has(vet2) ||\n            vet1 === vet2\n        ) {\n            throw new Error('Illegal Argument Exception');\n        }\n        // Добавить ребро vet1 - vet2\n        this.adjList.get(vet1).push(vet2);\n        this.adjList.get(vet2).push(vet1);\n    }\n\n    /* Удаление ребра */\n    removeEdge(vet1: Vertex, vet2: Vertex): void {\n        if (\n            !this.adjList.has(vet1) ||\n            !this.adjList.has(vet2) ||\n            vet1 === vet2 ||\n            this.adjList.get(vet1).indexOf(vet2) === -1\n        ) {\n            throw new Error('Illegal Argument Exception');\n        }\n        // Удалить ребро vet1 - vet2\n        this.adjList.get(vet1).splice(this.adjList.get(vet1).indexOf(vet2), 1);\n        this.adjList.get(vet2).splice(this.adjList.get(vet2).indexOf(vet1), 1);\n    }\n\n    /* Добавление вершины */\n    addVertex(vet: Vertex): void {\n        if (this.adjList.has(vet)) return;\n        // Добавить новый список в список смежности\n        this.adjList.set(vet, []);\n    }\n\n    /* Удаление вершины */\n    removeVertex(vet: Vertex): void {\n        if (!this.adjList.has(vet)) {\n            throw new Error('Illegal Argument Exception');\n        }\n        // Удалить из списка смежности список, соответствующий вершине vet\n        this.adjList.delete(vet);\n        // Обойти списки других вершин и удалить все ребра, содержащие vet\n        for (const set of this.adjList.values()) {\n            const index: number = set.indexOf(vet);\n            if (index &gt; -1) {\n                set.splice(index, 1);\n            }\n        }\n    }\n\n    /* Вывести список смежности */\n    print(): void {\n        console.log('Список смежности =');\n        for (const [key, value] of this.adjList.entries()) {\n            const tmp = [];\n            for (const vertex of value) {\n                tmp.push(vertex.val);\n            }\n            console.log(key.val + ': ' + tmp.join());\n        }\n    }\n}\n</code></pre> graph_adjacency_list.dart<pre><code>/* Класс неориентированного графа на основе списка смежности */\nclass GraphAdjList {\n  // Список смежности, где key — вершина, а value — все смежные ей вершины\n  Map&lt;Vertex, List&lt;Vertex&gt;&gt; adjList = {};\n\n  /* Конструктор */\n  GraphAdjList(List&lt;List&lt;Vertex&gt;&gt; edges) {\n    for (List&lt;Vertex&gt; edge in edges) {\n      addVertex(edge[0]);\n      addVertex(edge[1]);\n      addEdge(edge[0], edge[1]);\n    }\n  }\n\n  /* Получить число вершин */\n  int size() {\n    return adjList.length;\n  }\n\n  /* Добавление ребра */\n  void addEdge(Vertex vet1, Vertex vet2) {\n    if (!adjList.containsKey(vet1) ||\n        !adjList.containsKey(vet2) ||\n        vet1 == vet2) {\n      throw ArgumentError;\n    }\n    // Добавить ребро vet1 - vet2\n    adjList[vet1]!.add(vet2);\n    adjList[vet2]!.add(vet1);\n  }\n\n  /* Удаление ребра */\n  void removeEdge(Vertex vet1, Vertex vet2) {\n    if (!adjList.containsKey(vet1) ||\n        !adjList.containsKey(vet2) ||\n        vet1 == vet2) {\n      throw ArgumentError;\n    }\n    // Удалить ребро vet1 - vet2\n    adjList[vet1]!.remove(vet2);\n    adjList[vet2]!.remove(vet1);\n  }\n\n  /* Добавление вершины */\n  void addVertex(Vertex vet) {\n    if (adjList.containsKey(vet)) return;\n    // Добавить новый список в список смежности\n    adjList[vet] = [];\n  }\n\n  /* Удаление вершины */\n  void removeVertex(Vertex vet) {\n    if (!adjList.containsKey(vet)) {\n      throw ArgumentError;\n    }\n    // Удалить из списка смежности список, соответствующий вершине vet\n    adjList.remove(vet);\n    // Обойти списки других вершин и удалить все ребра, содержащие vet\n    adjList.forEach((key, value) {\n      value.remove(vet);\n    });\n  }\n\n  /* Вывести список смежности */\n  void printAdjList() {\n    print(\"Список смежности =\");\n    adjList.forEach((key, value) {\n      List&lt;int&gt; tmp = [];\n      for (Vertex vertex in value) {\n        tmp.add(vertex.val);\n      }\n      print(\"${key.val}: $tmp,\");\n    });\n  }\n}\n</code></pre> graph_adjacency_list.rs<pre><code>/* Тип неориентированного графа на основе списка смежности */\npub struct GraphAdjList {\n    // Список смежности, где key — вершина, а value — все смежные ей вершины\n    pub adj_list: HashMap&lt;Vertex, Vec&lt;Vertex&gt;&gt;, // maybe HashSet&lt;Vertex&gt; for value part is better?\n}\n\nimpl GraphAdjList {\n    /* Конструктор */\n    pub fn new(edges: Vec&lt;[Vertex; 2]&gt;) -&gt; Self {\n        let mut graph = GraphAdjList {\n            adj_list: HashMap::new(),\n        };\n        // Добавить все вершины и ребра\n        for edge in edges {\n            graph.add_vertex(edge[0]);\n            graph.add_vertex(edge[1]);\n            graph.add_edge(edge[0], edge[1]);\n        }\n\n        graph\n    }\n\n    /* Получить число вершин */\n    #[allow(unused)]\n    pub fn size(&amp;self) -&gt; usize {\n        self.adj_list.len()\n    }\n\n    /* Добавление ребра */\n    pub fn add_edge(&amp;mut self, vet1: Vertex, vet2: Vertex) {\n        if vet1 == vet2 {\n            panic!(\"value error\");\n        }\n        // Добавить ребро vet1 - vet2\n        self.adj_list.entry(vet1).or_default().push(vet2);\n        self.adj_list.entry(vet2).or_default().push(vet1);\n    }\n\n    /* Удаление ребра */\n    #[allow(unused)]\n    pub fn remove_edge(&amp;mut self, vet1: Vertex, vet2: Vertex) {\n        if vet1 == vet2 {\n            panic!(\"value error\");\n        }\n        // Удалить ребро vet1 - vet2\n        self.adj_list\n            .entry(vet1)\n            .and_modify(|v| v.retain(|&amp;e| e != vet2));\n        self.adj_list\n            .entry(vet2)\n            .and_modify(|v| v.retain(|&amp;e| e != vet1));\n    }\n\n    /* Добавление вершины */\n    pub fn add_vertex(&amp;mut self, vet: Vertex) {\n        if self.adj_list.contains_key(&amp;vet) {\n            return;\n        }\n        // Добавить новый список в список смежности\n        self.adj_list.insert(vet, vec![]);\n    }\n\n    /* Удаление вершины */\n    #[allow(unused)]\n    pub fn remove_vertex(&amp;mut self, vet: Vertex) {\n        // Удалить из списка смежности список, соответствующий вершине vet\n        self.adj_list.remove(&amp;vet);\n        // Обойти списки других вершин и удалить все ребра, содержащие vet\n        for list in self.adj_list.values_mut() {\n            list.retain(|&amp;v| v != vet);\n        }\n    }\n\n    /* Вывести список смежности */\n    pub fn print(&amp;self) {\n        println!(\"Список смежности =\");\n        for (vertex, list) in &amp;self.adj_list {\n            let list = list.iter().map(|vertex| vertex.val).collect::&lt;Vec&lt;i32&gt;&gt;();\n            println!(\"{}: {:?},\", vertex.val, list);\n        }\n    }\n}\n</code></pre> graph_adjacency_list.c<pre><code>/* Структура узла */\ntypedef struct AdjListNode {\n    Vertex *vertex;           // Вершина\n    struct AdjListNode *next; // Узел-преемник\n} AdjListNode;\n\n/* Найти узел, соответствующий вершине */\nAdjListNode *findNode(GraphAdjList *graph, Vertex *vet) {\n    for (int i = 0; i &lt; graph-&gt;size; i++) {\n        if (graph-&gt;heads[i]-&gt;vertex == vet) {\n            return graph-&gt;heads[i];\n        }\n    }\n    return NULL;\n}\n\n/* Вспомогательная функция добавления ребра */\nvoid addEdgeHelper(AdjListNode *head, Vertex *vet) {\n    AdjListNode *node = (AdjListNode *)malloc(sizeof(AdjListNode));\n    node-&gt;vertex = vet;\n    // Вставка в голову\n    node-&gt;next = head-&gt;next;\n    head-&gt;next = node;\n}\n\n/* Вспомогательная функция удаления ребра */\nvoid removeEdgeHelper(AdjListNode *head, Vertex *vet) {\n    AdjListNode *pre = head;\n    AdjListNode *cur = head-&gt;next;\n    // Искать в связном списке узел, соответствующий vet\n    while (cur != NULL &amp;&amp; cur-&gt;vertex != vet) {\n        pre = cur;\n        cur = cur-&gt;next;\n    }\n    if (cur == NULL)\n        return;\n    // Удалить из связного списка узел, соответствующий vet\n    pre-&gt;next = cur-&gt;next;\n    // Освободить память\n    free(cur);\n}\n\n/* Класс неориентированного графа на основе списка смежности */\ntypedef struct {\n    AdjListNode *heads[MAX_SIZE]; // Массив узлов\n    int size;                     // Количество узлов\n} GraphAdjList;\n\n/* Конструктор */\nGraphAdjList *newGraphAdjList() {\n    GraphAdjList *graph = (GraphAdjList *)malloc(sizeof(GraphAdjList));\n    if (!graph) {\n        return NULL;\n    }\n    graph-&gt;size = 0;\n    for (int i = 0; i &lt; MAX_SIZE; i++) {\n        graph-&gt;heads[i] = NULL;\n    }\n    return graph;\n}\n\n/* Деструктор */\nvoid delGraphAdjList(GraphAdjList *graph) {\n    for (int i = 0; i &lt; graph-&gt;size; i++) {\n        AdjListNode *cur = graph-&gt;heads[i];\n        while (cur != NULL) {\n            AdjListNode *next = cur-&gt;next;\n            if (cur != graph-&gt;heads[i]) {\n                free(cur);\n            }\n            cur = next;\n        }\n        free(graph-&gt;heads[i]-&gt;vertex);\n        free(graph-&gt;heads[i]);\n    }\n    free(graph);\n}\n\n/* Найти узел, соответствующий вершине */\nAdjListNode *findNode(GraphAdjList *graph, Vertex *vet) {\n    for (int i = 0; i &lt; graph-&gt;size; i++) {\n        if (graph-&gt;heads[i]-&gt;vertex == vet) {\n            return graph-&gt;heads[i];\n        }\n    }\n    return NULL;\n}\n\n/* Добавление ребра */\nvoid addEdge(GraphAdjList *graph, Vertex *vet1, Vertex *vet2) {\n    AdjListNode *head1 = findNode(graph, vet1);\n    AdjListNode *head2 = findNode(graph, vet2);\n    assert(head1 != NULL &amp;&amp; head2 != NULL &amp;&amp; head1 != head2);\n    // Добавить ребро vet1 - vet2\n    addEdgeHelper(head1, vet2);\n    addEdgeHelper(head2, vet1);\n}\n\n/* Удаление ребра */\nvoid removeEdge(GraphAdjList *graph, Vertex *vet1, Vertex *vet2) {\n    AdjListNode *head1 = findNode(graph, vet1);\n    AdjListNode *head2 = findNode(graph, vet2);\n    assert(head1 != NULL &amp;&amp; head2 != NULL);\n    // Удалить ребро vet1 - vet2\n    removeEdgeHelper(head1, head2-&gt;vertex);\n    removeEdgeHelper(head2, head1-&gt;vertex);\n}\n\n/* Добавление вершины */\nvoid addVertex(GraphAdjList *graph, Vertex *vet) {\n    assert(graph != NULL &amp;&amp; graph-&gt;size &lt; MAX_SIZE);\n    AdjListNode *head = (AdjListNode *)malloc(sizeof(AdjListNode));\n    head-&gt;vertex = vet;\n    head-&gt;next = NULL;\n    // Добавить новый список в список смежности\n    graph-&gt;heads[graph-&gt;size++] = head;\n}\n\n/* Удаление вершины */\nvoid removeVertex(GraphAdjList *graph, Vertex *vet) {\n    AdjListNode *node = findNode(graph, vet);\n    assert(node != NULL);\n    // Удалить из списка смежности список, соответствующий вершине vet\n    AdjListNode *cur = node, *pre = NULL;\n    while (cur) {\n        pre = cur;\n        cur = cur-&gt;next;\n        free(pre);\n    }\n    // Обойти списки других вершин и удалить все ребра, содержащие vet\n    for (int i = 0; i &lt; graph-&gt;size; i++) {\n        cur = graph-&gt;heads[i];\n        pre = NULL;\n        while (cur) {\n            pre = cur;\n            cur = cur-&gt;next;\n            if (cur &amp;&amp; cur-&gt;vertex == vet) {\n                pre-&gt;next = cur-&gt;next;\n                free(cur);\n                break;\n            }\n        }\n    }\n    // Сдвинуть вершины после данной вперед, чтобы заполнить образовавшийся пробел\n    int i;\n    for (i = 0; i &lt; graph-&gt;size; i++) {\n        if (graph-&gt;heads[i] == node)\n            break;\n    }\n    for (int j = i; j &lt; graph-&gt;size - 1; j++) {\n        graph-&gt;heads[j] = graph-&gt;heads[j + 1];\n    }\n    graph-&gt;size--;\n    free(vet);\n}\n</code></pre> graph_adjacency_list.kt<pre><code>/* Класс неориентированного графа на основе списка смежности */\nclass GraphAdjList(edges: Array&lt;Array&lt;Vertex?&gt;&gt;) {\n    // Список смежности, где key — вершина, а value — все смежные ей вершины\n    val adjList = HashMap&lt;Vertex, MutableList&lt;Vertex&gt;&gt;()\n\n    /* Конструктор */\n    init {\n        // Добавить все вершины и ребра\n        for (edge in edges) {\n            addVertex(edge[0]!!)\n            addVertex(edge[1]!!)\n            addEdge(edge[0]!!, edge[1]!!)\n        }\n    }\n\n    /* Получить число вершин */\n    fun size(): Int {\n        return adjList.size\n    }\n\n    /* Добавление ребра */\n    fun addEdge(vet1: Vertex, vet2: Vertex) {\n        if (!adjList.containsKey(vet1) || !adjList.containsKey(vet2) || vet1 == vet2)\n            throw IllegalArgumentException()\n        // Добавить ребро vet1 - vet2\n        adjList[vet1]?.add(vet2)\n        adjList[vet2]?.add(vet1)\n    }\n\n    /* Удаление ребра */\n    fun removeEdge(vet1: Vertex, vet2: Vertex) {\n        if (!adjList.containsKey(vet1) || !adjList.containsKey(vet2) || vet1 == vet2)\n            throw IllegalArgumentException()\n        // Удалить ребро vet1 - vet2\n        adjList[vet1]?.remove(vet2)\n        adjList[vet2]?.remove(vet1)\n    }\n\n    /* Добавление вершины */\n    fun addVertex(vet: Vertex) {\n        if (adjList.containsKey(vet))\n            return\n        // Добавить новый список в список смежности\n        adjList[vet] = mutableListOf()\n    }\n\n    /* Удаление вершины */\n    fun removeVertex(vet: Vertex) {\n        if (!adjList.containsKey(vet))\n            throw IllegalArgumentException()\n        // Удалить из списка смежности список, соответствующий вершине vet\n        adjList.remove(vet)\n        // Обойти списки других вершин и удалить все ребра, содержащие vet\n        for (list in adjList.values) {\n            list.remove(vet)\n        }\n    }\n\n    /* Вывести список смежности */\n    fun print() {\n        println(\"Список смежности =\")\n        for (pair in adjList.entries) {\n            val tmp = mutableListOf&lt;Int&gt;()\n            for (vertex in pair.value) {\n                tmp.add(vertex._val)\n            }\n            println(\"${pair.key._val}: $tmp,\")\n        }\n    }\n}\n</code></pre> graph_adjacency_list.rb<pre><code>### Класс неориентированного графа на основе списка смежности ###\nclass GraphAdjList\n  attr_reader :adj_list\n\n  ### Конструктор ###\n  def initialize(edges)\n    # Список смежности, где key — вершина, а value — все смежные ей вершины\n    @adj_list = {}\n    # Добавить все вершины и ребра\n    for edge in edges\n      add_vertex(edge[0])\n      add_vertex(edge[1])\n      add_edge(edge[0], edge[1])\n    end\n  end\n\n  ### Получение числа вершин ###\n  def size\n    @adj_list.length\n  end\n\n  ### Добавление ребра ###\n  def add_edge(vet1, vet2)\n    raise ArgumentError if !@adj_list.include?(vet1) || !@adj_list.include?(vet2)\n\n    @adj_list[vet1] &lt;&lt; vet2\n    @adj_list[vet2] &lt;&lt; vet1\n  end\n\n  ### Удаление ребра ###\n  def remove_edge(vet1, vet2)\n    raise ArgumentError if !@adj_list.include?(vet1) || !@adj_list.include?(vet2)\n\n    # Удалить ребро vet1 - vet2\n    @adj_list[vet1].delete(vet2)\n    @adj_list[vet2].delete(vet1)\n  end\n\n  ### Добавление вершины ###\n  def add_vertex(vet)\n    return if @adj_list.include?(vet)\n\n    # Добавить новый список в список смежности\n    @adj_list[vet] = []\n  end\n\n  ### Удаление вершины ###\n  def remove_vertex(vet)\n    raise ArgumentError unless @adj_list.include?(vet)\n\n    # Удалить из списка смежности список, соответствующий вершине vet\n    @adj_list.delete(vet)\n    # Обойти списки других вершин и удалить все ребра, содержащие vet\n    for vertex in @adj_list\n      @adj_list[vertex.first].delete(vet) if @adj_list[vertex.first].include?(vet)\n    end\n  end\n\n  ### Вывести список смежности ###\n  def __print__\n    puts 'Список смежности ='\n    for vertex in @adj_list\n      tmp = @adj_list[vertex.first].map { |v| v.val }\n      puts \"#{vertex.first.val}: #{tmp},\"\n    end\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 9. Графы","9.2 &nbsp; Базовые операции графа"],"tags":[]},{"location":"chapter_graph/graph_operations/#923","level":2,"title":"9.2.3   Сравнение эффективности","text":"<p>Пусть в графе имеется \\(n\\) вершин и \\(m\\) ребер. В таблице 9-2 сравниваются временная и пространственная эффективность матрицы смежности и списка смежности. Обратите внимание: список смежности (связный список) соответствует реализации из этой статьи, а список смежности (хеш-таблица) означает вариант, в котором все списки заменены хеш-таблицами.</p> <p> Таблица 9-2   Сравнение матрицы смежности и списка смежности </p> Матрица смежности Список смежности (связный список) Список смежности (хеш-таблица) Проверка смежности \\(O(1)\\) \\(O(n)\\) \\(O(1)\\) Добавление ребра \\(O(1)\\) \\(O(1)\\) \\(O(1)\\) Удаление ребра \\(O(1)\\) \\(O(n)\\) \\(O(1)\\) Добавление вершины \\(O(n)\\) \\(O(1)\\) \\(O(1)\\) Удаление вершины \\(O(n^2)\\) \\(O(n + m)\\) \\(O(n)\\) Занимаемая память \\(O(n^2)\\) \\(O(n + m)\\) \\(O(n + m)\\) <p>Если смотреть только на таблицу, может показаться, что список смежности на основе хеш-таблицы является лучшим и по времени, и по памяти. Но на практике операции над ребрами в матрице смежности обычно выполняются быстрее, потому что там нужен лишь один доступ к массиву или одно присваивание. В целом матрица смежности воплощает принцип \"обмена пространства на время\", а список смежности - принцип \"обмена времени на пространство\".</p>","path":["Глава 9. Графы","9.2 &nbsp; Базовые операции графа"],"tags":[]},{"location":"chapter_graph/graph_traversal/","level":1,"title":"9.3   Обход графа","text":"<p>Дерево представляет отношение \"один ко многим\", тогда как граф обладает большей свободой и может выражать произвольные отношения \"многие ко многим\". Поэтому дерево можно рассматривать как частный случай графа. Очевидно, что операции обхода дерева также являются частным случаем операций обхода графа.</p> <p>И графы, и деревья требуют применения алгоритмов обхода. Способы обхода графа также делятся на два типа: обход в ширину и обход в глубину.</p>","path":["Глава 9. Графы","9.3 &nbsp; Обход графа"],"tags":[]},{"location":"chapter_graph/graph_traversal/#931","level":2,"title":"9.3.1   Обход в ширину","text":"<p>Обход в ширину - это способ обхода от ближнего к дальнему, при котором начиная с некоторого узла сначала посещают ближайшие вершины, а затем слой за слоем расширяются наружу. Как показано на рисунке 9-9, начиная с вершины в левом верхнем углу, мы сначала обходим все смежные вершины этой вершины, затем все смежные вершины следующей вершины и так далее, пока не будут посещены все вершины.</p> <p></p> <p> Рисунок 9-9   Обход графа в ширину </p>","path":["Глава 9. Графы","9.3 &nbsp; Обход графа"],"tags":[]},{"location":"chapter_graph/graph_traversal/#1","level":3,"title":"1.   Реализация алгоритма","text":"<p>BFS обычно реализуется с помощью очереди, код приведен ниже. Очередь обладает свойством \"первым пришел - первым вышел\", что хорошо соответствует идее BFS \"от ближнего к дальнему\".</p> <ol> <li>Поместить стартовую вершину обхода <code>startVet</code> в очередь и запустить цикл.</li> <li>На каждой итерации цикла извлекать вершину из головы очереди и записывать ее посещение, после чего добавлять все смежные вершины этой вершины в хвост очереди.</li> <li>Повторять шаг <code>2.</code> до тех пор, пока не будут посещены все вершины.</li> </ol> <p>Чтобы предотвратить повторный обход вершин, нам нужно хеш-множество <code>visited</code> , в котором записывается, какие вершины уже посещены.</p> <p>Tip</p> <p>Хеш-множество можно рассматривать как хеш-таблицу, которая хранит только <code>key</code> и не хранит <code>value</code> . Оно позволяет выполнять добавление, удаление и проверку наличия <code>key</code> за \\(O(1)\\) времени. Благодаря уникальности <code>key</code> хеш-множество обычно используется, например, для устранения повторов.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby graph_bfs.py<pre><code>def graph_bfs(graph: GraphAdjList, start_vet: Vertex) -&gt; list[Vertex]:\n    \"\"\"Обход в ширину\"\"\"\n    # Использовать список смежности для представления графа, чтобы получать все смежные вершины заданной вершины\n    # Последовательность обхода вершин\n    res = []\n    # Хеш-множество для хранения уже посещенных вершин\n    visited = set[Vertex]([start_vet])\n    # Очередь используется для реализации BFS\n    que = deque[Vertex]([start_vet])\n    # Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n    while len(que) &gt; 0:\n        vet = que.popleft()  # Извлечь головную вершину из очереди\n        res.append(vet)  # Отметить посещенную вершину\n        # Обойти все смежные вершины данной вершины\n        for adj_vet in graph.adj_list[vet]:\n            if adj_vet in visited:\n                continue  # Пропустить уже посещенную вершину\n            que.append(adj_vet)  # Помещать в очередь только непосещенные вершины\n            visited.add(adj_vet)  # Отметить эту вершину как посещенную\n    # Вернуть последовательность обхода вершин\n    return res\n</code></pre> graph_bfs.cpp<pre><code>/* Обход в ширину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nvector&lt;Vertex *&gt; graphBFS(GraphAdjList &amp;graph, Vertex *startVet) {\n    // Последовательность обхода вершин\n    vector&lt;Vertex *&gt; res;\n    // Хеш-множество для хранения уже посещенных вершин\n    unordered_set&lt;Vertex *&gt; visited = {startVet};\n    // Очередь используется для реализации BFS\n    queue&lt;Vertex *&gt; que;\n    que.push(startVet);\n    // Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n    while (!que.empty()) {\n        Vertex *vet = que.front();\n        que.pop();          // Извлечь головную вершину из очереди\n        res.push_back(vet); // Отметить посещенную вершину\n        // Обойти все смежные вершины данной вершины\n        for (auto adjVet : graph.adjList[vet]) {\n            if (visited.count(adjVet))\n                continue;            // Пропустить уже посещенную вершину\n            que.push(adjVet);        // Помещать в очередь только непосещенные вершины\n            visited.emplace(adjVet); // Отметить эту вершину как посещенную\n        }\n    }\n    // Вернуть последовательность обхода вершин\n    return res;\n}\n</code></pre> graph_bfs.java<pre><code>/* Обход в ширину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nList&lt;Vertex&gt; graphBFS(GraphAdjList graph, Vertex startVet) {\n    // Последовательность обхода вершин\n    List&lt;Vertex&gt; res = new ArrayList&lt;&gt;();\n    // Хеш-множество для хранения уже посещенных вершин\n    Set&lt;Vertex&gt; visited = new HashSet&lt;&gt;();\n    visited.add(startVet);\n    // Очередь используется для реализации BFS\n    Queue&lt;Vertex&gt; que = new LinkedList&lt;&gt;();\n    que.offer(startVet);\n    // Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n    while (!que.isEmpty()) {\n        Vertex vet = que.poll(); // Извлечь головную вершину из очереди\n        res.add(vet);            // Отметить посещенную вершину\n        // Обойти все смежные вершины данной вершины\n        for (Vertex adjVet : graph.adjList.get(vet)) {\n            if (visited.contains(adjVet))\n                continue;        // Пропустить уже посещенную вершину\n            que.offer(adjVet);   // Помещать в очередь только непосещенные вершины\n            visited.add(adjVet); // Отметить эту вершину как посещенную\n        }\n    }\n    // Вернуть последовательность обхода вершин\n    return res;\n}\n</code></pre> graph_bfs.cs<pre><code>/* Обход в ширину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nList&lt;Vertex&gt; GraphBFS(GraphAdjList graph, Vertex startVet) {\n    // Последовательность обхода вершин\n    List&lt;Vertex&gt; res = [];\n    // Хеш-множество для хранения уже посещенных вершин\n    HashSet&lt;Vertex&gt; visited = [startVet];\n    // Очередь используется для реализации BFS\n    Queue&lt;Vertex&gt; que = new();\n    que.Enqueue(startVet);\n    // Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n    while (que.Count &gt; 0) {\n        Vertex vet = que.Dequeue(); // Извлечь головную вершину из очереди\n        res.Add(vet);               // Отметить посещенную вершину\n        foreach (Vertex adjVet in graph.adjList[vet]) {\n            if (visited.Contains(adjVet)) {\n                continue;          // Пропустить уже посещенную вершину\n            }\n            que.Enqueue(adjVet);   // Помещать в очередь только непосещенные вершины\n            visited.Add(adjVet);   // Отметить эту вершину как посещенную\n        }\n    }\n\n    // Вернуть последовательность обхода вершин\n    return res;\n}\n</code></pre> graph_bfs.go<pre><code>/* Обход в ширину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfunc graphBFS(g *graphAdjList, startVet Vertex) []Vertex {\n    // Последовательность обхода вершин\n    res := make([]Vertex, 0)\n    // Хеш-множество для хранения уже посещенных вершин\n    visited := make(map[Vertex]struct{})\n    visited[startVet] = struct{}{}\n    // Очередь используется для реализации BFS, срез используется для имитации очереди\n    queue := make([]Vertex, 0)\n    queue = append(queue, startVet)\n    // Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n    for len(queue) &gt; 0 {\n        // Извлечь головную вершину из очереди\n        vet := queue[0]\n        queue = queue[1:]\n        // Отметить посещенную вершину\n        res = append(res, vet)\n        // Обойти все смежные вершины данной вершины\n        for _, adjVet := range g.adjList[vet] {\n            _, isExist := visited[adjVet]\n            // Помещать в очередь только непосещенные вершины\n            if !isExist {\n                queue = append(queue, adjVet)\n                visited[adjVet] = struct{}{}\n            }\n        }\n    }\n    // Вернуть последовательность обхода вершин\n    return res\n}\n</code></pre> graph_bfs.swift<pre><code>/* Обход в ширину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfunc graphBFS(graph: GraphAdjList, startVet: Vertex) -&gt; [Vertex] {\n    // Последовательность обхода вершин\n    var res: [Vertex] = []\n    // Хеш-множество для хранения уже посещенных вершин\n    var visited: Set&lt;Vertex&gt; = [startVet]\n    // Очередь используется для реализации BFS\n    var que: [Vertex] = [startVet]\n    // Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n    while !que.isEmpty {\n        let vet = que.removeFirst() // Извлечь головную вершину из очереди\n        res.append(vet) // Отметить посещенную вершину\n        // Обойти все смежные вершины данной вершины\n        for adjVet in graph.adjList[vet] ?? [] {\n            if visited.contains(adjVet) {\n                continue // Пропустить уже посещенную вершину\n            }\n            que.append(adjVet) // Помещать в очередь только непосещенные вершины\n            visited.insert(adjVet) // Отметить эту вершину как посещенную\n        }\n    }\n    // Вернуть последовательность обхода вершин\n    return res\n}\n</code></pre> graph_bfs.js<pre><code>/* Обход в ширину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfunction graphBFS(graph, startVet) {\n    // Последовательность обхода вершин\n    const res = [];\n    // Хеш-множество для хранения уже посещенных вершин\n    const visited = new Set();\n    visited.add(startVet);\n    // Очередь используется для реализации BFS\n    const que = [startVet];\n    // Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n    while (que.length) {\n        const vet = que.shift(); // Извлечь головную вершину из очереди\n        res.push(vet); // Отметить посещенную вершину\n        // Обойти все смежные вершины данной вершины\n        for (const adjVet of graph.adjList.get(vet) ?? []) {\n            if (visited.has(adjVet)) {\n                continue; // Пропустить уже посещенную вершину\n            }\n            que.push(adjVet); // Помещать в очередь только непосещенные вершины\n            visited.add(adjVet); // Отметить эту вершину как посещенную\n        }\n    }\n    // Вернуть последовательность обхода вершин\n    return res;\n}\n</code></pre> graph_bfs.ts<pre><code>/* Обход в ширину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfunction graphBFS(graph: GraphAdjList, startVet: Vertex): Vertex[] {\n    // Последовательность обхода вершин\n    const res: Vertex[] = [];\n    // Хеш-множество для хранения уже посещенных вершин\n    const visited: Set&lt;Vertex&gt; = new Set();\n    visited.add(startVet);\n    // Очередь используется для реализации BFS\n    const que = [startVet];\n    // Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n    while (que.length) {\n        const vet = que.shift(); // Извлечь головную вершину из очереди\n        res.push(vet); // Отметить посещенную вершину\n        // Обойти все смежные вершины данной вершины\n        for (const adjVet of graph.adjList.get(vet) ?? []) {\n            if (visited.has(adjVet)) {\n                continue; // Пропустить уже посещенную вершину\n            }\n            que.push(adjVet); // Помещать в очередь только непосещенные вершины\n            visited.add(adjVet); // Отметить эту вершину как посещенную\n        }\n    }\n    // Вернуть последовательность обхода вершин\n    return res;\n}\n</code></pre> graph_bfs.dart<pre><code>/* Обход в ширину */\nList&lt;Vertex&gt; graphBFS(GraphAdjList graph, Vertex startVet) {\n  // Использовать список смежности для представления графа, чтобы получать все смежные вершины заданной вершины\n  // Последовательность обхода вершин\n  List&lt;Vertex&gt; res = [];\n  // Хеш-множество для хранения уже посещенных вершин\n  Set&lt;Vertex&gt; visited = {};\n  visited.add(startVet);\n  // Очередь используется для реализации BFS\n  Queue&lt;Vertex&gt; que = Queue();\n  que.add(startVet);\n  // Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n  while (que.isNotEmpty) {\n    Vertex vet = que.removeFirst(); // Извлечь головную вершину из очереди\n    res.add(vet); // Отметить посещенную вершину\n    // Обойти все смежные вершины данной вершины\n    for (Vertex adjVet in graph.adjList[vet]!) {\n      if (visited.contains(adjVet)) {\n        continue; // Пропустить уже посещенную вершину\n      }\n      que.add(adjVet); // Помещать в очередь только непосещенные вершины\n      visited.add(adjVet); // Отметить эту вершину как посещенную\n    }\n  }\n  // Вернуть последовательность обхода вершин\n  return res;\n}\n</code></pre> graph_bfs.rs<pre><code>/* Обход в ширину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfn graph_bfs(graph: GraphAdjList, start_vet: Vertex) -&gt; Vec&lt;Vertex&gt; {\n    // Последовательность обхода вершин\n    let mut res = vec![];\n    // Хеш-множество для хранения уже посещенных вершин\n    let mut visited = HashSet::new();\n    visited.insert(start_vet);\n    // Очередь используется для реализации BFS\n    let mut que = VecDeque::new();\n    que.push_back(start_vet);\n    // Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n    while let Some(vet) = que.pop_front() {\n        res.push(vet); // Отметить посещенную вершину\n\n        // Обойти все смежные вершины данной вершины\n        if let Some(adj_vets) = graph.adj_list.get(&amp;vet) {\n            for &amp;adj_vet in adj_vets {\n                if visited.contains(&amp;adj_vet) {\n                    continue; // Пропустить уже посещенную вершину\n                }\n                que.push_back(adj_vet); // Помещать в очередь только непосещенные вершины\n                visited.insert(adj_vet); // Отметить эту вершину как посещенную\n            }\n        }\n    }\n    // Вернуть последовательность обхода вершин\n    res\n}\n</code></pre> graph_bfs.c<pre><code>/* Структура очереди узлов */\ntypedef struct {\n    Vertex *vertices[MAX_SIZE];\n    int front, rear, size;\n} Queue;\n\n/* Конструктор */\nQueue *newQueue() {\n    Queue *q = (Queue *)malloc(sizeof(Queue));\n    q-&gt;front = q-&gt;rear = q-&gt;size = 0;\n    return q;\n}\n\n/* Проверка, пуста ли очередь */\nint isEmpty(Queue *q) {\n    return q-&gt;size == 0;\n}\n\n/* Операция добавления в очередь */\nvoid enqueue(Queue *q, Vertex *vet) {\n    q-&gt;vertices[q-&gt;rear] = vet;\n    q-&gt;rear = (q-&gt;rear + 1) % MAX_SIZE;\n    q-&gt;size++;\n}\n\n/* Операция извлечения из очереди */\nVertex *dequeue(Queue *q) {\n    Vertex *vet = q-&gt;vertices[q-&gt;front];\n    q-&gt;front = (q-&gt;front + 1) % MAX_SIZE;\n    q-&gt;size--;\n    return vet;\n}\n\n/* Проверить, была ли вершина уже посещена */\nint isVisited(Vertex **visited, int size, Vertex *vet) {\n    // Искать узел обходом за O(n) времени\n    for (int i = 0; i &lt; size; i++) {\n        if (visited[i] == vet)\n            return 1;\n    }\n    return 0;\n}\n\n/* Обход в ширину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nvoid graphBFS(GraphAdjList *graph, Vertex *startVet, Vertex **res, int *resSize, Vertex **visited, int *visitedSize) {\n    // Очередь используется для реализации BFS\n    Queue *queue = newQueue();\n    enqueue(queue, startVet);\n    visited[(*visitedSize)++] = startVet;\n    // Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n    while (!isEmpty(queue)) {\n        Vertex *vet = dequeue(queue); // Извлечь головную вершину из очереди\n        res[(*resSize)++] = vet;      // Отметить посещенную вершину\n        // Обойти все смежные вершины данной вершины\n        AdjListNode *node = findNode(graph, vet);\n        while (node != NULL) {\n            // Пропустить уже посещенную вершину\n            if (!isVisited(visited, *visitedSize, node-&gt;vertex)) {\n                enqueue(queue, node-&gt;vertex);             // Помещать в очередь только непосещенные вершины\n                visited[(*visitedSize)++] = node-&gt;vertex; // Отметить эту вершину как посещенную\n            }\n            node = node-&gt;next;\n        }\n    }\n    // Освободить память\n    free(queue);\n}\n</code></pre> graph_bfs.kt<pre><code>/* Обход в ширину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfun graphBFS(graph: GraphAdjList, startVet: Vertex): MutableList&lt;Vertex?&gt; {\n    // Последовательность обхода вершин\n    val res = mutableListOf&lt;Vertex?&gt;()\n    // Хеш-множество для хранения уже посещенных вершин\n    val visited = HashSet&lt;Vertex&gt;()\n    visited.add(startVet)\n    // Очередь используется для реализации BFS\n    val que = LinkedList&lt;Vertex&gt;()\n    que.offer(startVet)\n    // Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n    while (!que.isEmpty()) {\n        val vet = que.poll() // Извлечь головную вершину из очереди\n        res.add(vet)         // Отметить посещенную вершину\n        // Обойти все смежные вершины данной вершины\n        for (adjVet in graph.adjList[vet]!!) {\n            if (visited.contains(adjVet))\n                continue        // Пропустить уже посещенную вершину\n            que.offer(adjVet)   // Помещать в очередь только непосещенные вершины\n            visited.add(adjVet) // Отметить эту вершину как посещенную\n        }\n    }\n    // Вернуть последовательность обхода вершин\n    return res\n}\n</code></pre> graph_bfs.rb<pre><code>### Обход в ширину ###\ndef graph_bfs(graph, start_vet)\n  # Использовать список смежности для представления графа, чтобы получать все смежные вершины заданной вершины\n  # Последовательность обхода вершин\n  res = []\n  # Хеш-множество для хранения уже посещенных вершин\n  visited = Set.new([start_vet])\n  # Очередь используется для реализации BFS\n  que = [start_vet]\n  # Начиная с вершины vet, продолжать цикл, пока не будут посещены все вершины\n  while que.length &gt; 0\n    vet = que.shift # Извлечь головную вершину из очереди\n    res &lt;&lt; vet # Отметить посещенную вершину\n    # Обойти все смежные вершины данной вершины\n    for adj_vet in graph.adj_list[vet]\n      next if visited.include?(adj_vet) # Пропустить уже посещенную вершину\n      que &lt;&lt; adj_vet # Помещать в очередь только непосещенные вершины\n      visited.add(adj_vet) # Отметить эту вершину как посещенную\n    end\n  end\n  # Вернуть последовательность обхода вершин\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Код сравнительно абстрактен, поэтому рекомендуется сверяться с рисунками ниже для лучшего понимания.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 9-10   Шаги обхода графа в ширину </p> <p>Является ли последовательность обхода в ширину единственной?</p> <p>Нет. Обход в ширину требует только соблюдения порядка \"от ближнего к дальнему\", а порядок обхода нескольких вершин на одинаковом расстоянии может произвольно меняться. Например, на рисунке 9-10 можно поменять местами порядок посещения вершин \\(1\\) и \\(3\\) , а вершины \\(2\\), \\(4\\), \\(6\\) также можно переставлять произвольно.</p>","path":["Глава 9. Графы","9.3 &nbsp; Обход графа"],"tags":[]},{"location":"chapter_graph/graph_traversal/#2","level":3,"title":"2.   Анализ сложности","text":"<p>Временная сложность: все вершины по одному разу помещаются в очередь и извлекаются из нее, что требует \\(O(|V|)\\) времени; при обходе смежных вершин, поскольку граф неориентированный, все ребра будут посещены по \\(2\\) раза, что требует \\(O(2|E|)\\) времени; в сумме получается \\(O(|V| + |E|)\\) .</p> <p>Пространственная сложность: список <code>res</code> , хеш-множество <code>visited</code> и очередь <code>que</code> в худшем случае могут содержать до \\(|V|\\) вершин, поэтому требуется \\(O(|V|)\\) памяти.</p>","path":["Глава 9. Графы","9.3 &nbsp; Обход графа"],"tags":[]},{"location":"chapter_graph/graph_traversal/#932","level":2,"title":"9.3.2   Обход в глубину","text":"<p>Обход в глубину - это способ обхода, при котором сначала идут до самого конца, а когда дальше идти нельзя, возвращаются назад. Как показано на рисунке 9-11, начиная с вершины в левом верхнем углу, мы выбираем некоторую смежную вершину текущей вершины, идем до упора, затем возвращаемся назад, снова идем до упора и так далее, пока не будут посещены все вершины.</p> <p></p> <p> Рисунок 9-11   Обход графа в глубину </p>","path":["Глава 9. Графы","9.3 &nbsp; Обход графа"],"tags":[]},{"location":"chapter_graph/graph_traversal/#1_1","level":3,"title":"1.   Реализация алгоритма","text":"<p>Такой алгоритмический шаблон \"дойти до конца и вернуться\" обычно реализуется через рекурсию. Подобно обходу в ширину, в обходе в глубину мы также используем хеш-множество <code>visited</code> для записи уже посещенных вершин и тем самым избегаем повторного посещения.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby graph_dfs.py<pre><code>def dfs(graph: GraphAdjList, visited: set[Vertex], res: list[Vertex], vet: Vertex):\n    \"\"\"Вспомогательная функция обхода в глубину\"\"\"\n    res.append(vet)  # Отметить посещенную вершину\n    visited.add(vet)  # Отметить эту вершину как посещенную\n    # Обойти все смежные вершины данной вершины\n    for adjVet in graph.adj_list[vet]:\n        if adjVet in visited:\n            continue  # Пропустить уже посещенную вершину\n        # Рекурсивно обходить смежные вершины\n        dfs(graph, visited, res, adjVet)\n\ndef graph_dfs(graph: GraphAdjList, start_vet: Vertex) -&gt; list[Vertex]:\n    \"\"\"Обход в глубину\"\"\"\n    # Использовать список смежности для представления графа, чтобы получать все смежные вершины заданной вершины\n    # Последовательность обхода вершин\n    res = []\n    # Хеш-множество для хранения уже посещенных вершин\n    visited = set[Vertex]()\n    dfs(graph, visited, res, start_vet)\n    return res\n</code></pre> graph_dfs.cpp<pre><code>/* Вспомогательная функция обхода в глубину */\nvoid dfs(GraphAdjList &amp;graph, unordered_set&lt;Vertex *&gt; &amp;visited, vector&lt;Vertex *&gt; &amp;res, Vertex *vet) {\n    res.push_back(vet);   // Отметить посещенную вершину\n    visited.emplace(vet); // Отметить эту вершину как посещенную\n    // Обойти все смежные вершины данной вершины\n    for (Vertex *adjVet : graph.adjList[vet]) {\n        if (visited.count(adjVet))\n            continue; // Пропустить уже посещенную вершину\n        // Рекурсивно обходить смежные вершины\n        dfs(graph, visited, res, adjVet);\n    }\n}\n\n/* Обход в глубину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nvector&lt;Vertex *&gt; graphDFS(GraphAdjList &amp;graph, Vertex *startVet) {\n    // Последовательность обхода вершин\n    vector&lt;Vertex *&gt; res;\n    // Хеш-множество для хранения уже посещенных вершин\n    unordered_set&lt;Vertex *&gt; visited;\n    dfs(graph, visited, res, startVet);\n    return res;\n}\n</code></pre> graph_dfs.java<pre><code>/* Вспомогательная функция обхода в глубину */\nvoid dfs(GraphAdjList graph, Set&lt;Vertex&gt; visited, List&lt;Vertex&gt; res, Vertex vet) {\n    res.add(vet);     // Отметить посещенную вершину\n    visited.add(vet); // Отметить эту вершину как посещенную\n    // Обойти все смежные вершины данной вершины\n    for (Vertex adjVet : graph.adjList.get(vet)) {\n        if (visited.contains(adjVet))\n            continue; // Пропустить уже посещенную вершину\n        // Рекурсивно обходить смежные вершины\n        dfs(graph, visited, res, adjVet);\n    }\n}\n\n/* Обход в глубину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nList&lt;Vertex&gt; graphDFS(GraphAdjList graph, Vertex startVet) {\n    // Последовательность обхода вершин\n    List&lt;Vertex&gt; res = new ArrayList&lt;&gt;();\n    // Хеш-множество для хранения уже посещенных вершин\n    Set&lt;Vertex&gt; visited = new HashSet&lt;&gt;();\n    dfs(graph, visited, res, startVet);\n    return res;\n}\n</code></pre> graph_dfs.cs<pre><code>/* Вспомогательная функция обхода в глубину */\nvoid DFS(GraphAdjList graph, HashSet&lt;Vertex&gt; visited, List&lt;Vertex&gt; res, Vertex vet) {\n    res.Add(vet);     // Отметить посещенную вершину\n    visited.Add(vet); // Отметить эту вершину как посещенную\n    // Обойти все смежные вершины данной вершины\n    foreach (Vertex adjVet in graph.adjList[vet]) {\n        if (visited.Contains(adjVet)) {\n            continue; // Пропустить уже посещенную вершину\n        }\n        // Рекурсивно обходить смежные вершины\n        DFS(graph, visited, res, adjVet);\n    }\n}\n\n/* Обход в глубину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nList&lt;Vertex&gt; GraphDFS(GraphAdjList graph, Vertex startVet) {\n    // Последовательность обхода вершин\n    List&lt;Vertex&gt; res = [];\n    // Хеш-множество для хранения уже посещенных вершин\n    HashSet&lt;Vertex&gt; visited = [];\n    DFS(graph, visited, res, startVet);\n    return res;\n}\n</code></pre> graph_dfs.go<pre><code>/* Вспомогательная функция обхода в глубину */\nfunc dfs(g *graphAdjList, visited map[Vertex]struct{}, res *[]Vertex, vet Vertex) {\n    // Операция append возвращает новую ссылку, поэтому исходную ссылку нужно заново присвоить новому срезу\n    *res = append(*res, vet)\n    visited[vet] = struct{}{}\n    // Обойти все смежные вершины данной вершины\n    for _, adjVet := range g.adjList[vet] {\n        _, isExist := visited[adjVet]\n        // Рекурсивно обходить смежные вершины\n        if !isExist {\n            dfs(g, visited, res, adjVet)\n        }\n    }\n}\n\n/* Обход в глубину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfunc graphDFS(g *graphAdjList, startVet Vertex) []Vertex {\n    // Последовательность обхода вершин\n    res := make([]Vertex, 0)\n    // Хеш-множество для хранения уже посещенных вершин\n    visited := make(map[Vertex]struct{})\n    dfs(g, visited, &amp;res, startVet)\n    // Вернуть последовательность обхода вершин\n    return res\n}\n</code></pre> graph_dfs.swift<pre><code>/* Вспомогательная функция обхода в глубину */\nfunc dfs(graph: GraphAdjList, visited: inout Set&lt;Vertex&gt;, res: inout [Vertex], vet: Vertex) {\n    res.append(vet) // Отметить посещенную вершину\n    visited.insert(vet) // Отметить эту вершину как посещенную\n    // Обойти все смежные вершины данной вершины\n    for adjVet in graph.adjList[vet] ?? [] {\n        if visited.contains(adjVet) {\n            continue // Пропустить уже посещенную вершину\n        }\n        // Рекурсивно обходить смежные вершины\n        dfs(graph: graph, visited: &amp;visited, res: &amp;res, vet: adjVet)\n    }\n}\n\n/* Обход в глубину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfunc graphDFS(graph: GraphAdjList, startVet: Vertex) -&gt; [Vertex] {\n    // Последовательность обхода вершин\n    var res: [Vertex] = []\n    // Хеш-множество для хранения уже посещенных вершин\n    var visited: Set&lt;Vertex&gt; = []\n    dfs(graph: graph, visited: &amp;visited, res: &amp;res, vet: startVet)\n    return res\n}\n</code></pre> graph_dfs.js<pre><code>/* Обход в глубину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfunction dfs(graph, visited, res, vet) {\n    res.push(vet); // Отметить посещенную вершину\n    visited.add(vet); // Отметить эту вершину как посещенную\n    // Обойти все смежные вершины данной вершины\n    for (const adjVet of graph.adjList.get(vet)) {\n        if (visited.has(adjVet)) {\n            continue; // Пропустить уже посещенную вершину\n        }\n        // Рекурсивно обходить смежные вершины\n        dfs(graph, visited, res, adjVet);\n    }\n}\n\n/* Обход в глубину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfunction graphDFS(graph, startVet) {\n    // Последовательность обхода вершин\n    const res = [];\n    // Хеш-множество для хранения уже посещенных вершин\n    const visited = new Set();\n    dfs(graph, visited, res, startVet);\n    return res;\n}\n</code></pre> graph_dfs.ts<pre><code>/* Вспомогательная функция обхода в глубину */\nfunction dfs(\n    graph: GraphAdjList,\n    visited: Set&lt;Vertex&gt;,\n    res: Vertex[],\n    vet: Vertex\n): void {\n    res.push(vet); // Отметить посещенную вершину\n    visited.add(vet); // Отметить эту вершину как посещенную\n    // Обойти все смежные вершины данной вершины\n    for (const adjVet of graph.adjList.get(vet)) {\n        if (visited.has(adjVet)) {\n            continue; // Пропустить уже посещенную вершину\n        }\n        // Рекурсивно обходить смежные вершины\n        dfs(graph, visited, res, adjVet);\n    }\n}\n\n/* Обход в глубину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfunction graphDFS(graph: GraphAdjList, startVet: Vertex): Vertex[] {\n    // Последовательность обхода вершин\n    const res: Vertex[] = [];\n    // Хеш-множество для хранения уже посещенных вершин\n    const visited: Set&lt;Vertex&gt; = new Set();\n    dfs(graph, visited, res, startVet);\n    return res;\n}\n</code></pre> graph_dfs.dart<pre><code>/* Вспомогательная функция обхода в глубину */\nvoid dfs(\n  GraphAdjList graph,\n  Set&lt;Vertex&gt; visited,\n  List&lt;Vertex&gt; res,\n  Vertex vet,\n) {\n  res.add(vet); // Отметить посещенную вершину\n  visited.add(vet); // Отметить эту вершину как посещенную\n  // Обойти все смежные вершины данной вершины\n  for (Vertex adjVet in graph.adjList[vet]!) {\n    if (visited.contains(adjVet)) {\n      continue; // Пропустить уже посещенную вершину\n    }\n    // Рекурсивно обходить смежные вершины\n    dfs(graph, visited, res, adjVet);\n  }\n}\n\n/* Обход в глубину */\nList&lt;Vertex&gt; graphDFS(GraphAdjList graph, Vertex startVet) {\n  // Последовательность обхода вершин\n  List&lt;Vertex&gt; res = [];\n  // Хеш-множество для хранения уже посещенных вершин\n  Set&lt;Vertex&gt; visited = {};\n  dfs(graph, visited, res, startVet);\n  return res;\n}\n</code></pre> graph_dfs.rs<pre><code>/* Вспомогательная функция обхода в глубину */\nfn dfs(graph: &amp;GraphAdjList, visited: &amp;mut HashSet&lt;Vertex&gt;, res: &amp;mut Vec&lt;Vertex&gt;, vet: Vertex) {\n    res.push(vet); // Отметить посещенную вершину\n    visited.insert(vet); // Отметить эту вершину как посещенную\n                         // Обойти все смежные вершины данной вершины\n    if let Some(adj_vets) = graph.adj_list.get(&amp;vet) {\n        for &amp;adj_vet in adj_vets {\n            if visited.contains(&amp;adj_vet) {\n                continue; // Пропустить уже посещенную вершину\n            }\n            // Рекурсивно обходить смежные вершины\n            dfs(graph, visited, res, adj_vet);\n        }\n    }\n}\n\n/* Обход в глубину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfn graph_dfs(graph: GraphAdjList, start_vet: Vertex) -&gt; Vec&lt;Vertex&gt; {\n    // Последовательность обхода вершин\n    let mut res = vec![];\n    // Хеш-множество для хранения уже посещенных вершин\n    let mut visited = HashSet::new();\n    dfs(&amp;graph, &amp;mut visited, &amp;mut res, start_vet);\n\n    res\n}\n</code></pre> graph_dfs.c<pre><code>/* Проверить, была ли вершина уже посещена */\nint isVisited(Vertex **res, int size, Vertex *vet) {\n    // Искать узел обходом за O(n) времени\n    for (int i = 0; i &lt; size; i++) {\n        if (res[i] == vet) {\n            return 1;\n        }\n    }\n    return 0;\n}\n\n/* Вспомогательная функция обхода в глубину */\nvoid dfs(GraphAdjList *graph, Vertex **res, int *resSize, Vertex *vet) {\n    // Отметить посещенную вершину\n    res[(*resSize)++] = vet;\n    // Обойти все смежные вершины данной вершины\n    AdjListNode *node = findNode(graph, vet);\n    while (node != NULL) {\n        // Пропустить уже посещенную вершину\n        if (!isVisited(res, *resSize, node-&gt;vertex)) {\n            // Рекурсивно обходить смежные вершины\n            dfs(graph, res, resSize, node-&gt;vertex);\n        }\n        node = node-&gt;next;\n    }\n}\n\n/* Обход в глубину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nvoid graphDFS(GraphAdjList *graph, Vertex *startVet, Vertex **res, int *resSize) {\n    dfs(graph, res, resSize, startVet);\n}\n</code></pre> graph_dfs.kt<pre><code>/* Вспомогательная функция обхода в глубину */\nfun dfs(\n    graph: GraphAdjList,\n    visited: MutableSet&lt;Vertex?&gt;,\n    res: MutableList&lt;Vertex?&gt;,\n    vet: Vertex?\n) {\n    res.add(vet)     // Отметить посещенную вершину\n    visited.add(vet) // Отметить эту вершину как посещенную\n    // Обойти все смежные вершины данной вершины\n    for (adjVet in graph.adjList[vet]!!) {\n        if (visited.contains(adjVet))\n            continue  // Пропустить уже посещенную вершину\n        // Рекурсивно обходить смежные вершины\n        dfs(graph, visited, res, adjVet)\n    }\n}\n\n/* Обход в глубину */\n// Использовать список смежности для представления графа, чтобы получить все смежные вершины заданной вершины\nfun graphDFS(graph: GraphAdjList, startVet: Vertex?): MutableList&lt;Vertex?&gt; {\n    // Последовательность обхода вершин\n    val res = mutableListOf&lt;Vertex?&gt;()\n    // Хеш-множество для хранения уже посещенных вершин\n    val visited = HashSet&lt;Vertex?&gt;()\n    dfs(graph, visited, res, startVet)\n    return res\n}\n</code></pre> graph_dfs.rb<pre><code>### Вспомогательная функция обхода в глубину ###\ndef dfs(graph, visited, res, vet)\n  res &lt;&lt; vet # Отметить посещенную вершину\n  visited.add(vet) # Отметить эту вершину как посещенную\n  # Обойти все смежные вершины данной вершины\n  for adj_vet in graph.adj_list[vet]\n    next if visited.include?(adj_vet) # Пропустить уже посещенную вершину\n    # Рекурсивно обходить смежные вершины\n    dfs(graph, visited, res, adj_vet)\n  end\nend\n\n### Обход в глубину ###\ndef graph_dfs(graph, start_vet)\n  # Использовать список смежности для представления графа, чтобы получать все смежные вершины заданной вершины\n  # Последовательность обхода вершин\n  res = []\n  # Хеш-множество для хранения уже посещенных вершин\n  visited = Set.new\n  dfs(graph, visited, res, start_vet)\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Алгоритмический процесс обхода в глубину показан на рисунках ниже.</p> <ul> <li>Прямая пунктирная линия обозначает нисходящую рекурсию , то есть запуск нового рекурсивного метода для посещения новой вершины.</li> <li>Изогнутая пунктирная линия обозначает восходящую рекурсию , то есть данный рекурсивный метод завершился и управление вернулось туда, откуда он был вызван.</li> </ul> <p>Чтобы лучше понять алгоритм, рекомендуется совместить рисунки ниже с кодом и мысленно проследить весь процесс DFS, включая моменты запуска и возврата каждого рекурсивного вызова.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 9-12   Шаги обхода графа в глубину </p> <p>Является ли последовательность обхода в глубину единственной?</p> <p>Как и в случае обхода в ширину, последовательность DFS тоже не является единственной. Для заданной вершины допустимо сначала углубиться в любое направление, то есть порядок смежных вершин может быть произвольным, и все такие варианты будут корректными обходами в глубину.</p> <p>Если взять в качестве примера обход дерева, то варианты \"корень \\(\\rightarrow\\) лево \\(\\rightarrow\\) право\", \"лево \\(\\rightarrow\\) корень \\(\\rightarrow\\) право\" и \"лево \\(\\rightarrow\\) право \\(\\rightarrow\\) корень\" соответствуют прямому, симметричному и обратному обходам соответственно. Они показывают три разных приоритета обхода, но все они относятся к обходу в глубину.</p>","path":["Глава 9. Графы","9.3 &nbsp; Обход графа"],"tags":[]},{"location":"chapter_graph/graph_traversal/#2_1","level":3,"title":"2.   Анализ сложности","text":"<p>Временная сложность: все вершины будут посещены по \\(1\\) разу, что требует \\(O(|V|)\\) времени; все ребра будут посещены по \\(2\\) раза, что требует \\(O(2|E|)\\) времени; суммарно получается \\(O(|V| + |E|)\\) .</p> <p>Пространственная сложность: число вершин в списке <code>res</code> и хеш-множестве <code>visited</code> в худшем случае достигает \\(|V|\\) , максимальная глубина рекурсии тоже равна \\(|V|\\) , поэтому требуется \\(O(|V|)\\) памяти.</p>","path":["Глава 9. Графы","9.3 &nbsp; Обход графа"],"tags":[]},{"location":"chapter_graph/summary/","level":1,"title":"9.4   Краткие итоги","text":"","path":["Глава 9. Графы","9.4 &nbsp; Краткие итоги"],"tags":[]},{"location":"chapter_graph/summary/#1","level":3,"title":"1.   Основные моменты","text":"<ul> <li>Граф состоит из вершин и ребер и может быть задан как множество вершин и множество ребер.</li> <li>По сравнению с линейными отношениями (связный список) и отношениями разделения (дерево), сетевые отношения (граф) обладают большей свободой и потому более сложны.</li> <li>Ребра ориентированного графа имеют направление, в связном графе любые вершины достижимы, а во взвешенном графе каждое ребро содержит переменную веса.</li> <li>Матрица смежности использует матрицу для представления графа: каждая строка и каждый столбец соответствуют вершине, а элементы матрицы показывают, есть между двумя вершинами ребро или нет. Матрица смежности эффективна в операциях добавления, удаления, поиска и изменения, но расходует больше памяти.</li> <li>Список смежности использует несколько списков для представления графа; \\(i\\)-й список соответствует вершине \\(i\\) и хранит все ее смежные вершины. По сравнению с матрицей смежности список смежности экономит пространство, но для поиска ребра в нем приходится обходить список, поэтому по времени он уступает.</li> <li>Когда списки в списке смежности становятся слишком длинными, их можно преобразовать в красно-черное дерево или хеш-таблицу, чтобы повысить эффективность поиска.</li> <li>С точки зрения алгоритмической идеи матрица смежности отражает принцип \"обмена пространства на время\", а список смежности - принцип \"обмена времени на пространство\".</li> <li>Графы можно использовать для моделирования различных реальных систем, таких как социальные сети, линии метро и так далее.</li> <li>Дерево является частным случаем графа, а обход дерева - частным случаем обхода графа.</li> <li>Обход графа в ширину представляет собой способ поиска, который расширяется от ближнего к дальнему и обычно реализуется с помощью очереди.</li> <li>Обход графа в глубину представляет собой способ поиска, который сначала идет до самого конца, а затем возвращается назад, когда путь исчерпан; обычно он реализуется на основе рекурсии.</li> </ul>","path":["Глава 9. Графы","9.4 &nbsp; Краткие итоги"],"tags":[]},{"location":"chapter_graph/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: Что считается путем: последовательность вершин или последовательность ребер?</p> <p>Определение в разных языковых версиях Википедии различается: в английской версии путь определяется как \"последовательность ребер\", а в русской версии - как \"последовательность вершин\". В английской версии исходная формулировка выглядит так: In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices.</p> <p>В этой книге путь рассматривается как последовательность ребер, а не как последовательность вершин. Причина в том, что между двумя вершинами может существовать несколько ребер, и в таком случае каждому ребру соответствует свой путь.</p> <p>Q: Есть ли в несвязном графе вершины, до которых нельзя дойти?</p> <p>В несвязном графе, начиная из некоторой вершины, по крайней мере одна вершина оказывается недостижимой. Чтобы обойти весь несвязный граф, нужно задать несколько стартовых точек и обойти все связные компоненты графа.</p> <p>Q: Есть ли требования к порядку вершин в списке \"всех вершин, соединенных с данной вершиной\" в списке смежности?</p> <p>Порядок может быть произвольным. Но на практике может понадобиться сортировка по определенному правилу, например по порядку добавления вершин или по возрастанию значений вершин; это помогает быстро находить вершины с некоторым экстремальным свойством.</p>","path":["Глава 9. Графы","9.4 &nbsp; Краткие итоги"],"tags":[]},{"location":"chapter_greedy/","level":1,"title":"Глава 15.   Жадность","text":"<p>Abstract</p> <p>Подсолнух поворачивается к солнцу, постоянно стремясь к наилучшим условиям для роста.</p> <p>Жадная стратегия через цепочку простых выборов постепенно приводит к наилучшему ответу.</p>","path":["Глава 15. Жадность","Глава 15. &nbsp; Жадность"],"tags":[]},{"location":"chapter_greedy/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>15.1   Жадный алгоритм</li> <li>15.2   Задача о дробном рюкзаке</li> <li>15.3   Задача о максимальной вместимости</li> <li>15.4   Задача о максимальном произведении разбиения</li> <li>15.5   Резюме</li> </ul>","path":["Глава 15. Жадность","Глава 15. &nbsp; Жадность"],"tags":[]},{"location":"chapter_greedy/fractional_knapsack_problem/","level":1,"title":"15.2   Задача о дробном рюкзаке","text":"<p>Question</p> <p>Дано \\(n\\) предметов. Вес предмета \\(i\\) равен \\(wgt[i-1]\\), ценность равна \\(val[i-1]\\), также дан рюкзак вместимостью \\(cap\\). Каждый предмет можно выбрать только один раз, но разрешается взять лишь часть предмета, а ценность вычисляется пропорционально взятому весу. Требуется найти максимальную ценность предметов в рюкзаке при ограниченной вместимости. Пример показан на рисунке 15-3.</p> <p></p> <p> Рисунок 15-3   Пример данных для задачи о дробном рюкзаке </p> <p>Задача о дробном рюкзаке в целом очень похожа на задачу о рюкзаке 0-1: состояние включает текущий предмет \\(i\\) и вместимость \\(c\\), а цель состоит в нахождении максимальной ценности при заданной вместимости рюкзака.</p> <p>Отличие в том, что здесь разрешено брать только часть предмета. Как показано на рисунке 15-4, мы можем произвольно делить предмет и вычислять соответствующую ценность пропорционально весу.</p> <ol> <li>Для предмета \\(i\\) его ценность на единицу веса равна \\(val[i-1] / wgt[i-1]\\), сокращенно - удельная ценность.</li> <li>Если взять часть предмета \\(i\\) весом \\(w\\), то ценность рюкзака увеличится на \\(w \\times val[i-1] / wgt[i-1]\\).</li> </ol> <p></p> <p> Рисунок 15-4   Ценность предмета на единицу веса </p>","path":["Глава 15. Жадность","15.2 &nbsp; Задача о дробном рюкзаке"],"tags":[]},{"location":"chapter_greedy/fractional_knapsack_problem/#1","level":3,"title":"1.   Определение жадной стратегии","text":"<p>Максимизация общей ценности предметов в рюкзаке по сути равносильна максимизации ценности на единицу веса. Отсюда естественно выводится следующая жадная стратегия.</p> <ol> <li>Отсортировать предметы по убыванию удельной ценности.</li> <li>Перебирать все предметы и на каждом шаге жадно выбирать предмет с наибольшей удельной ценностью.</li> <li>Если оставшейся вместимости рюкзака недостаточно, взять часть текущего предмета, чтобы заполнить рюкзак.</li> </ol> <p></p> <p> Рисунок 15-5   Жадная стратегия для задачи о дробном рюкзаке </p>","path":["Глава 15. Жадность","15.2 &nbsp; Задача о дробном рюкзаке"],"tags":[]},{"location":"chapter_greedy/fractional_knapsack_problem/#2","level":3,"title":"2.   Код реализации","text":"<p>Мы вводим класс <code>Item</code>, чтобы можно было сортировать предметы по удельной ценности. Далее циклически выполняем жадный выбор и, когда рюкзак заполнен, выходим и возвращаем ответ:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby fractional_knapsack.py<pre><code>class Item:\n    \"\"\"Предмет\"\"\"\n\n    def __init__(self, w: int, v: int):\n        self.w = w  # Вес предмета\n        self.v = v  # Стоимость предмета\n\ndef fractional_knapsack(wgt: list[int], val: list[int], cap: int) -&gt; int:\n    \"\"\"Дробный рюкзак: жадный алгоритм\"\"\"\n    # Создать список предметов с двумя свойствами: вес и стоимость\n    items = [Item(w, v) for w, v in zip(wgt, val)]\n    # Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n    items.sort(key=lambda item: item.v / item.w, reverse=True)\n    # Циклический жадный выбор\n    res = 0\n    for item in items:\n        if item.w &lt;= cap:\n            # Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n            res += item.v\n            cap -= item.w\n        else:\n            # Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n            res += (item.v / item.w) * cap\n            # Свободной вместимости больше не осталось, поэтому выйти из цикла\n            break\n    return res\n</code></pre> fractional_knapsack.cpp<pre><code>/* Предмет */\nclass Item {\n  public:\n    int w; // Вес предмета\n    int v; // Стоимость предмета\n\n    Item(int w, int v) : w(w), v(v) {\n    }\n};\n\n/* Дробный рюкзак: жадный алгоритм */\ndouble fractionalKnapsack(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int cap) {\n    // Создать список предметов с двумя свойствами: вес и стоимость\n    vector&lt;Item&gt; items;\n    for (int i = 0; i &lt; wgt.size(); i++) {\n        items.push_back(Item(wgt[i], val[i]));\n    }\n    // Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n    sort(items.begin(), items.end(), [](Item &amp;a, Item &amp;b) { return (double)a.v / a.w &gt; (double)b.v / b.w; });\n    // Циклический жадный выбор\n    double res = 0;\n    for (auto &amp;item : items) {\n        if (item.w &lt;= cap) {\n            // Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n            res += item.v;\n            cap -= item.w;\n        } else {\n            // Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n            res += (double)item.v / item.w * cap;\n            // Свободной вместимости больше не осталось, поэтому выйти из цикла\n            break;\n        }\n    }\n    return res;\n}\n</code></pre> fractional_knapsack.java<pre><code>/* Предмет */\nclass Item {\n    int w; // Вес предмета\n    int v; // Стоимость предмета\n\n    public Item(int w, int v) {\n        this.w = w;\n        this.v = v;\n    }\n}\n\n/* Дробный рюкзак: жадный алгоритм */\ndouble fractionalKnapsack(int[] wgt, int[] val, int cap) {\n    // Создать список предметов с двумя свойствами: вес и стоимость\n    Item[] items = new Item[wgt.length];\n    for (int i = 0; i &lt; wgt.length; i++) {\n        items[i] = new Item(wgt[i], val[i]);\n    }\n    // Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n    Arrays.sort(items, Comparator.comparingDouble(item -&gt; -((double) item.v / item.w)));\n    // Циклический жадный выбор\n    double res = 0;\n    for (Item item : items) {\n        if (item.w &lt;= cap) {\n            // Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n            res += item.v;\n            cap -= item.w;\n        } else {\n            // Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n            res += (double) item.v / item.w * cap;\n            // Свободной вместимости больше не осталось, поэтому выйти из цикла\n            break;\n        }\n    }\n    return res;\n}\n</code></pre> fractional_knapsack.cs<pre><code>/* Предмет */\nclass Item(int w, int v) {\n    public int w = w; // Вес предмета\n    public int v = v; // Стоимость предмета\n}\n\n/* Дробный рюкзак: жадный алгоритм */\ndouble FractionalKnapsack(int[] wgt, int[] val, int cap) {\n    // Создать список предметов с двумя свойствами: вес и стоимость\n    Item[] items = new Item[wgt.Length];\n    for (int i = 0; i &lt; wgt.Length; i++) {\n        items[i] = new Item(wgt[i], val[i]);\n    }\n    // Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n    Array.Sort(items, (x, y) =&gt; (y.v / y.w).CompareTo(x.v / x.w));\n    // Циклический жадный выбор\n    double res = 0;\n    foreach (Item item in items) {\n        if (item.w &lt;= cap) {\n            // Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n            res += item.v;\n            cap -= item.w;\n        } else {\n            // Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n            res += (double)item.v / item.w * cap;\n            // Свободной вместимости больше не осталось, поэтому выйти из цикла\n            break;\n        }\n    }\n    return res;\n}\n</code></pre> fractional_knapsack.go<pre><code>/* Предмет */\ntype Item struct {\n    w int // Вес предмета\n    v int // Стоимость предмета\n}\n\n/* Дробный рюкзак: жадный алгоритм */\nfunc fractionalKnapsack(wgt []int, val []int, cap int) float64 {\n    // Создать список предметов с двумя свойствами: вес и стоимость\n    items := make([]Item, len(wgt))\n    for i := 0; i &lt; len(wgt); i++ {\n        items[i] = Item{wgt[i], val[i]}\n    }\n    // Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n    sort.Slice(items, func(i, j int) bool {\n        return float64(items[i].v)/float64(items[i].w) &gt; float64(items[j].v)/float64(items[j].w)\n    })\n    // Циклический жадный выбор\n    res := 0.0\n    for _, item := range items {\n        if item.w &lt;= cap {\n            // Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n            res += float64(item.v)\n            cap -= item.w\n        } else {\n            // Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n            res += float64(item.v) / float64(item.w) * float64(cap)\n            // Свободной вместимости больше не осталось, поэтому выйти из цикла\n            break\n        }\n    }\n    return res\n}\n</code></pre> fractional_knapsack.swift<pre><code>/* Предмет */\nclass Item {\n    var w: Int // Вес предмета\n    var v: Int // Стоимость предмета\n\n    init(w: Int, v: Int) {\n        self.w = w\n        self.v = v\n    }\n}\n\n/* Дробный рюкзак: жадный алгоритм */\nfunc fractionalKnapsack(wgt: [Int], val: [Int], cap: Int) -&gt; Double {\n    // Создать список предметов с двумя свойствами: вес и стоимость\n    var items = zip(wgt, val).map { Item(w: $0, v: $1) }\n    // Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n    items.sort { -(Double($0.v) / Double($0.w)) &lt; -(Double($1.v) / Double($1.w)) }\n    // Циклический жадный выбор\n    var res = 0.0\n    var cap = cap\n    for item in items {\n        if item.w &lt;= cap {\n            // Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n            res += Double(item.v)\n            cap -= item.w\n        } else {\n            // Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n            res += Double(item.v) / Double(item.w) * Double(cap)\n            // Свободной вместимости больше не осталось, поэтому выйти из цикла\n            break\n        }\n    }\n    return res\n}\n</code></pre> fractional_knapsack.js<pre><code>/* Предмет */\nclass Item {\n    constructor(w, v) {\n        this.w = w; // Вес предмета\n        this.v = v; // Стоимость предмета\n    }\n}\n\n/* Дробный рюкзак: жадный алгоритм */\nfunction fractionalKnapsack(wgt, val, cap) {\n    // Создать список предметов с двумя свойствами: вес и стоимость\n    const items = wgt.map((w, i) =&gt; new Item(w, val[i]));\n    // Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n    items.sort((a, b) =&gt; b.v / b.w - a.v / a.w);\n    // Циклический жадный выбор\n    let res = 0;\n    for (const item of items) {\n        if (item.w &lt;= cap) {\n            // Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n            res += item.v;\n            cap -= item.w;\n        } else {\n            // Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n            res += (item.v / item.w) * cap;\n            // Свободной вместимости больше не осталось, поэтому выйти из цикла\n            break;\n        }\n    }\n    return res;\n}\n</code></pre> fractional_knapsack.ts<pre><code>/* Предмет */\nclass Item {\n    w: number; // Вес предмета\n    v: number; // Стоимость предмета\n\n    constructor(w: number, v: number) {\n        this.w = w;\n        this.v = v;\n    }\n}\n\n/* Дробный рюкзак: жадный алгоритм */\nfunction fractionalKnapsack(wgt: number[], val: number[], cap: number): number {\n    // Создать список предметов с двумя свойствами: вес и стоимость\n    const items: Item[] = wgt.map((w, i) =&gt; new Item(w, val[i]));\n    // Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n    items.sort((a, b) =&gt; b.v / b.w - a.v / a.w);\n    // Циклический жадный выбор\n    let res = 0;\n    for (const item of items) {\n        if (item.w &lt;= cap) {\n            // Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n            res += item.v;\n            cap -= item.w;\n        } else {\n            // Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n            res += (item.v / item.w) * cap;\n            // Свободной вместимости больше не осталось, поэтому выйти из цикла\n            break;\n        }\n    }\n    return res;\n}\n</code></pre> fractional_knapsack.dart<pre><code>/* Предмет */\nclass Item {\n  int w; // Вес предмета\n  int v; // Стоимость предмета\n\n  Item(this.w, this.v);\n}\n\n/* Дробный рюкзак: жадный алгоритм */\ndouble fractionalKnapsack(List&lt;int&gt; wgt, List&lt;int&gt; val, int cap) {\n  // Создать список предметов с двумя свойствами: вес и стоимость\n  List&lt;Item&gt; items = List.generate(wgt.length, (i) =&gt; Item(wgt[i], val[i]));\n  // Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n  items.sort((a, b) =&gt; (b.v / b.w).compareTo(a.v / a.w));\n  // Циклический жадный выбор\n  double res = 0;\n  for (Item item in items) {\n    if (item.w &lt;= cap) {\n      // Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n      res += item.v;\n      cap -= item.w;\n    } else {\n      // Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n      res += item.v / item.w * cap;\n      // Свободной вместимости больше не осталось, поэтому выйти из цикла\n      break;\n    }\n  }\n  return res;\n}\n</code></pre> fractional_knapsack.rs<pre><code>/* Предмет */\nstruct Item {\n    w: i32, // Вес предмета\n    v: i32, // Стоимость предмета\n}\n\nimpl Item {\n    fn new(w: i32, v: i32) -&gt; Self {\n        Self { w, v }\n    }\n}\n\n/* Дробный рюкзак: жадный алгоритм */\nfn fractional_knapsack(wgt: &amp;[i32], val: &amp;[i32], mut cap: i32) -&gt; f64 {\n    // Создать список предметов с двумя свойствами: вес и стоимость\n    let mut items = wgt\n        .iter()\n        .zip(val.iter())\n        .map(|(&amp;w, &amp;v)| Item::new(w, v))\n        .collect::&lt;Vec&lt;Item&gt;&gt;();\n    // Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n    items.sort_by(|a, b| {\n        (b.v as f64 / b.w as f64)\n            .partial_cmp(&amp;(a.v as f64 / a.w as f64))\n            .unwrap()\n    });\n    // Циклический жадный выбор\n    let mut res = 0.0;\n    for item in &amp;items {\n        if item.w &lt;= cap {\n            // Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n            res += item.v as f64;\n            cap -= item.w;\n        } else {\n            // Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n            res += item.v as f64 / item.w as f64 * cap as f64;\n            // Свободной вместимости больше не осталось, поэтому выйти из цикла\n            break;\n        }\n    }\n    res\n}\n</code></pre> fractional_knapsack.c<pre><code>/* Предмет */\ntypedef struct {\n    int w; // Вес предмета\n    int v; // Стоимость предмета\n} Item;\n\n/* Дробный рюкзак: жадный алгоритм */\nfloat fractionalKnapsack(int wgt[], int val[], int itemCount, int cap) {\n    // Создать список предметов с двумя свойствами: вес и стоимость\n    Item *items = malloc(sizeof(Item) * itemCount);\n    for (int i = 0; i &lt; itemCount; i++) {\n        items[i] = (Item){.w = wgt[i], .v = val[i]};\n    }\n    // Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n    qsort(items, (size_t)itemCount, sizeof(Item), sortByValueDensity);\n    // Циклический жадный выбор\n    float res = 0.0;\n    for (int i = 0; i &lt; itemCount; i++) {\n        if (items[i].w &lt;= cap) {\n            // Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n            res += items[i].v;\n            cap -= items[i].w;\n        } else {\n            // Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n            res += (float)cap / items[i].w * items[i].v;\n            cap = 0;\n            break;\n        }\n    }\n    free(items);\n    return res;\n}\n</code></pre> fractional_knapsack.kt<pre><code>/* Предмет */\nclass Item(\n    val w: Int, // Предмет\n    val v: Int  // Стоимость предмета\n)\n\n/* Дробный рюкзак: жадный алгоритм */\nfun fractionalKnapsack(wgt: IntArray, _val: IntArray, c: Int): Double {\n    // Создать список предметов с двумя свойствами: вес и стоимость\n    var cap = c\n    val items = arrayOfNulls&lt;Item&gt;(wgt.size)\n    for (i in wgt.indices) {\n        items[i] = Item(wgt[i], _val[i])\n    }\n    // Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n    items.sortBy { item: Item? -&gt; -(item!!.v.toDouble() / item.w) }\n    // Циклический жадный выбор\n    var res = 0.0\n    for (item in items) {\n        if (item!!.w &lt;= cap) {\n            // Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n            res += item.v\n            cap -= item.w\n        } else {\n            // Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n            res += item.v.toDouble() / item.w * cap\n            // Свободной вместимости больше не осталось, поэтому выйти из цикла\n            break\n        }\n    }\n    return res\n}\n</code></pre> fractional_knapsack.rb<pre><code>### Предмет ###\nclass Item\n  attr_accessor :w # Вес предмета\n  attr_accessor :v # Стоимость предмета\n\n  def initialize(w, v)\n    @w = w\n    @v = v\n  end\nend\n\n### Дробный рюкзак: жадный алгоритм ###\ndef fractional_knapsack(wgt, val, cap)\n  # Создать список предметов с двумя свойствами: вес и стоимость\n  items = wgt.each_with_index.map { |w, i| Item.new(w, val[i]) }\n  # Отсортировать по удельной стоимости item.v / item.w в порядке убывания\n  items.sort! { |a, b| (b.v.to_f / b.w) &lt;=&gt; (a.v.to_f / a.w) }\n  # Циклический жадный выбор\n  res = 0\n  for item in items\n    if item.w &lt;= cap\n      # Если оставшейся вместимости достаточно, положить в рюкзак текущий предмет целиком\n      res += item.v\n      cap -= item.w\n    else\n      # Если оставшейся вместимости недостаточно, положить в рюкзак часть текущего предмета\n      res += (item.v.to_f / item.w) * cap\n      # Свободной вместимости больше не осталось, поэтому выйти из цикла\n      break\n    end\n  end\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Встроенный алгоритм сортировки обычно имеет временную сложность \\(O(n \\log n)\\), а пространственная сложность обычно равна \\(O(\\log n)\\) или \\(O(n)\\), в зависимости от конкретной реализации в языке программирования.</p> <p>Помимо сортировки, в худшем случае потребуется пройти весь список предметов, но это не меняет асимптотику, поэтому итоговая временная сложность равна \\(O(n \\log n)\\), где \\(n\\) - число предметов.</p> <p>Поскольку инициализируется список объектов <code>Item</code>, пространственная сложность равна \\(O(n)\\).</p>","path":["Глава 15. Жадность","15.2 &nbsp; Задача о дробном рюкзаке"],"tags":[]},{"location":"chapter_greedy/fractional_knapsack_problem/#3","level":3,"title":"3.   Доказательство корректности","text":"<p>Используем доказательство от противного. Предположим, что предмет \\(x\\) имеет наибольшую удельную ценность, некоторый алгоритм получил максимальную ценность <code>res</code>, но в найденном решении предмет \\(x\\) отсутствует.</p> <p>Теперь вынем из рюкзака произвольный предмет единичного веса и заменим его на предмет \\(x\\) того же веса. Поскольку предмет \\(x\\) имеет наибольшую удельную ценность, общая ценность после замены обязательно станет больше <code>res</code>. Это противоречит тому, что <code>res</code> является оптимальным решением, а значит оптимальное решение обязательно содержит предмет \\(x\\).</p> <p>Для других предметов в этом решении можно построить аналогичное противоречие. Иными словами, предметы с большей удельной ценностью всегда являются более выгодным выбором, а значит жадная стратегия корректна.</p> <p>Как показано на рисунке 15-6, если рассматривать вес предметов и их удельную ценность как горизонтальную и вертикальную оси двумерной диаграммы, то задачу о дробном рюкзаке можно интерпретировать как «поиск максимальной площади, ограниченной конечным отрезком по горизонтали». Эта аналогия помогает понять корректность жадной стратегии с геометрической точки зрения.</p> <p></p> <p> Рисунок 15-6   Геометрическая интерпретация задачи о дробном рюкзаке </p>","path":["Глава 15. Жадность","15.2 &nbsp; Задача о дробном рюкзаке"],"tags":[]},{"location":"chapter_greedy/greedy_algorithm/","level":1,"title":"15.1   Жадный алгоритм","text":"<p>Жадный алгоритм (greedy algorithm) - это распространенный метод решения задач оптимизации. Его основная идея состоит в том, чтобы на каждом этапе принятия решения выбирать вариант, который выглядит наилучшим прямо сейчас, то есть жадно принимать локально оптимальные решения в надежде получить глобально оптимальный результат. Жадные алгоритмы просты и эффективны, поэтому широко применяются во многих практических задачах.</p> <p>Жадные алгоритмы и динамическое программирование часто используются для решения задач оптимизации. У них есть некоторое сходство, например оба метода опираются на свойство оптимальной подструктуры, но принципы работы различаются.</p> <ul> <li>Динамическое программирование при получении текущего решения учитывает все предыдущие решения и использует ответы для прошлых подзадач, чтобы построить ответ для текущей подзадачи.</li> <li>Жадный алгоритм не учитывает предыдущие решения, а просто движется вперед, каждый раз делая жадный выбор и постепенно сужая область задачи, пока она не будет решена.</li> </ul> <p>Чтобы лучше понять принцип работы жадного алгоритма, разберем его на примере задачи «размен монет». Эта задача уже встречалась в разделе «задача о полном рюкзаке», поэтому она наверняка вам знакома.</p> <p>Question</p> <p>Дано \\(n\\) видов монет. Номинал монеты \\(i\\) равен \\(coins[i - 1]\\), целевая сумма равна \\(amt\\), причем каждую монету можно брать неограниченное число раз. Требуется найти минимальное число монет, которыми можно набрать целевую сумму. Если набрать сумму невозможно, верните \\(-1\\).</p> <p>Жадная стратегия для этой задачи показана на рисунке 15-1. Для заданной целевой суммы мы жадно выбираем монету, которая не превышает ее и находится к ней ближе всего, и повторяем этот шаг, пока не получим нужную сумму.</p> <p></p> <p> Рисунок 15-1   Жадная стратегия для задачи о размене монет </p> <p>Ниже приведен код реализации.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby coin_change_greedy.py<pre><code>def coin_change_greedy(coins: list[int], amt: int) -&gt; int:\n    \"\"\"Размен монет: жадный алгоритм\"\"\"\n    # Предположить, что список coins упорядочен\n    i = len(coins) - 1\n    count = 0\n    # Циклически выполнять жадный выбор, пока не останется суммы\n    while amt &gt; 0:\n        # Найти монету, которая меньше остатка суммы и наиболее к нему близка\n        while i &gt; 0 and coins[i] &gt; amt:\n            i -= 1\n        # Выбрать coins[i]\n        amt -= coins[i]\n        count += 1\n    # Если допустимое решение не найдено, вернуть -1\n    return count if amt == 0 else -1\n</code></pre> coin_change_greedy.cpp<pre><code>/* Размен монет: жадный алгоритм */\nint coinChangeGreedy(vector&lt;int&gt; &amp;coins, int amt) {\n    // Предположить, что список coins упорядочен\n    int i = coins.size() - 1;\n    int count = 0;\n    // Циклически выполнять жадный выбор, пока не останется суммы\n    while (amt &gt; 0) {\n        // Найти монету, которая меньше остатка суммы и наиболее к нему близка\n        while (i &gt; 0 &amp;&amp; coins[i] &gt; amt) {\n            i--;\n        }\n        // Выбрать coins[i]\n        amt -= coins[i];\n        count++;\n    }\n    // Если допустимое решение не найдено, вернуть -1\n    return amt == 0 ? count : -1;\n}\n</code></pre> coin_change_greedy.java<pre><code>/* Размен монет: жадный алгоритм */\nint coinChangeGreedy(int[] coins, int amt) {\n    // Предположить, что список coins упорядочен\n    int i = coins.length - 1;\n    int count = 0;\n    // Циклически выполнять жадный выбор, пока не останется суммы\n    while (amt &gt; 0) {\n        // Найти монету, которая меньше остатка суммы и наиболее к нему близка\n        while (i &gt; 0 &amp;&amp; coins[i] &gt; amt) {\n            i--;\n        }\n        // Выбрать coins[i]\n        amt -= coins[i];\n        count++;\n    }\n    // Если допустимое решение не найдено, вернуть -1\n    return amt == 0 ? count : -1;\n}\n</code></pre> coin_change_greedy.cs<pre><code>/* Размен монет: жадный алгоритм */\nint CoinChangeGreedy(int[] coins, int amt) {\n    // Предположить, что список coins упорядочен\n    int i = coins.Length - 1;\n    int count = 0;\n    // Циклически выполнять жадный выбор, пока не останется суммы\n    while (amt &gt; 0) {\n        // Найти монету, которая меньше остатка суммы и наиболее к нему близка\n        while (i &gt; 0 &amp;&amp; coins[i] &gt; amt) {\n            i--;\n        }\n        // Выбрать coins[i]\n        amt -= coins[i];\n        count++;\n    }\n    // Если допустимое решение не найдено, вернуть -1\n    return amt == 0 ? count : -1;\n}\n</code></pre> coin_change_greedy.go<pre><code>/* Размен монет: жадный алгоритм */\nfunc coinChangeGreedy(coins []int, amt int) int {\n    // Предположить, что список coins упорядочен\n    i := len(coins) - 1\n    count := 0\n    // Циклически выполнять жадный выбор, пока не останется суммы\n    for amt &gt; 0 {\n        // Найти монету, которая меньше остатка суммы и наиболее к нему близка\n        for i &gt; 0 &amp;&amp; coins[i] &gt; amt {\n            i--\n        }\n        // Выбрать coins[i]\n        amt -= coins[i]\n        count++\n    }\n    // Если допустимое решение не найдено, вернуть -1\n    if amt != 0 {\n        return -1\n    }\n    return count\n}\n</code></pre> coin_change_greedy.swift<pre><code>/* Размен монет: жадный алгоритм */\nfunc coinChangeGreedy(coins: [Int], amt: Int) -&gt; Int {\n    // Предположить, что список coins упорядочен\n    var i = coins.count - 1\n    var count = 0\n    var amt = amt\n    // Циклически выполнять жадный выбор, пока не останется суммы\n    while amt &gt; 0 {\n        // Найти монету, которая меньше остатка суммы и наиболее к нему близка\n        while i &gt; 0 &amp;&amp; coins[i] &gt; amt {\n            i -= 1\n        }\n        // Выбрать coins[i]\n        amt -= coins[i]\n        count += 1\n    }\n    // Если допустимое решение не найдено, вернуть -1\n    return amt == 0 ? count : -1\n}\n</code></pre> coin_change_greedy.js<pre><code>/* Размен монет: жадный алгоритм */\nfunction coinChangeGreedy(coins, amt) {\n    // Предположить, что массив coins упорядочен\n    let i = coins.length - 1;\n    let count = 0;\n    // Циклически выполнять жадный выбор, пока не останется суммы\n    while (amt &gt; 0) {\n        // Найти монету, которая меньше остатка суммы и наиболее к нему близка\n        while (i &gt; 0 &amp;&amp; coins[i] &gt; amt) {\n            i--;\n        }\n        // Выбрать coins[i]\n        amt -= coins[i];\n        count++;\n    }\n    // Если допустимое решение не найдено, вернуть -1\n    return amt === 0 ? count : -1;\n}\n</code></pre> coin_change_greedy.ts<pre><code>/* Размен монет: жадный алгоритм */\nfunction coinChangeGreedy(coins: number[], amt: number): number {\n    // Предположить, что массив coins упорядочен\n    let i = coins.length - 1;\n    let count = 0;\n    // Циклически выполнять жадный выбор, пока не останется суммы\n    while (amt &gt; 0) {\n        // Найти монету, которая меньше остатка суммы и наиболее к нему близка\n        while (i &gt; 0 &amp;&amp; coins[i] &gt; amt) {\n            i--;\n        }\n        // Выбрать coins[i]\n        amt -= coins[i];\n        count++;\n    }\n    // Если допустимое решение не найдено, вернуть -1\n    return amt === 0 ? count : -1;\n}\n</code></pre> coin_change_greedy.dart<pre><code>/* Размен монет: жадный алгоритм */\nint coinChangeGreedy(List&lt;int&gt; coins, int amt) {\n  // Предположить, что список coins упорядочен\n  int i = coins.length - 1;\n  int count = 0;\n  // Циклически выполнять жадный выбор, пока не останется суммы\n  while (amt &gt; 0) {\n    // Найти монету, которая меньше остатка суммы и наиболее к нему близка\n    while (i &gt; 0 &amp;&amp; coins[i] &gt; amt) {\n      i--;\n    }\n    // Выбрать coins[i]\n    amt -= coins[i];\n    count++;\n  }\n  // Если допустимое решение не найдено, вернуть -1\n  return amt == 0 ? count : -1;\n}\n</code></pre> coin_change_greedy.rs<pre><code>/* Размен монет: жадный алгоритм */\nfn coin_change_greedy(coins: &amp;[i32], mut amt: i32) -&gt; i32 {\n    // Предположить, что список coins упорядочен\n    let mut i = coins.len() - 1;\n    let mut count = 0;\n    // Циклически выполнять жадный выбор, пока не останется суммы\n    while amt &gt; 0 {\n        // Найти монету, которая меньше остатка суммы и наиболее к нему близка\n        while i &gt; 0 &amp;&amp; coins[i] &gt; amt {\n            i -= 1;\n        }\n        // Выбрать coins[i]\n        amt -= coins[i];\n        count += 1;\n    }\n    // Если допустимое решение не найдено, вернуть -1\n    if amt == 0 {\n        count\n    } else {\n        -1\n    }\n}\n</code></pre> coin_change_greedy.c<pre><code>/* Размен монет: жадный алгоритм */\nint coinChangeGreedy(int *coins, int size, int amt) {\n    // Предположить, что список coins упорядочен\n    int i = size - 1;\n    int count = 0;\n    // Циклически выполнять жадный выбор, пока не останется суммы\n    while (amt &gt; 0) {\n        // Найти монету, которая меньше остатка суммы и наиболее к нему близка\n        while (i &gt; 0 &amp;&amp; coins[i] &gt; amt) {\n            i--;\n        }\n        // Выбрать coins[i]\n        amt -= coins[i];\n        count++;\n    }\n    // Если допустимое решение не найдено, вернуть -1\n    return amt == 0 ? count : -1;\n}\n</code></pre> coin_change_greedy.kt<pre><code>/* Размен монет: жадный алгоритм */\nfun coinChangeGreedy(coins: IntArray, amt: Int): Int {\n    // Предположить, что список coins упорядочен\n    var am = amt\n    var i = coins.size - 1\n    var count = 0\n    // Циклически выполнять жадный выбор, пока не останется суммы\n    while (am &gt; 0) {\n        // Найти монету, которая меньше остатка суммы и наиболее к нему близка\n        while (i &gt; 0 &amp;&amp; coins[i] &gt; am) {\n            i--\n        }\n        // Выбрать coins[i]\n        am -= coins[i]\n        count++\n    }\n    // Если допустимое решение не найдено, вернуть -1\n    return if (am == 0) count else -1\n}\n</code></pre> coin_change_greedy.rb<pre><code>### Размен монет: жадный алгоритм ###\ndef coin_change_greedy(coins, amt)\n  # Предположить, что список coins упорядочен\n  i = coins.length - 1\n  count = 0\n  # Циклически выполнять жадный выбор, пока не останется суммы\n  while amt &gt; 0\n    # Найти монету, которая меньше остатка суммы и наиболее к нему близка\n    while i &gt; 0 &amp;&amp; coins[i] &gt; amt\n      i -= 1\n    end\n    # Выбрать coins[i]\n    amt -= coins[i]\n    count += 1\n  end\n  # Если допустимое решение не найдено, вернуть -1\n  amt == 0 ? count : -1\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>У вас может невольно вырваться: «Эврика!» Жадный алгоритм решает задачу размена монет всего примерно десятью строками кода.</p>","path":["Глава 15. Жадность","15.1 &nbsp; Жадный алгоритм"],"tags":[]},{"location":"chapter_greedy/greedy_algorithm/#1511","level":2,"title":"15.1.1   Преимущества и ограничения жадного алгоритма","text":"<p>Жадный алгоритм не только прост в реализации, но и обычно очень эффективен. В приведенном выше коде обозначим минимальный номинал монеты через \\(\\min(coins)\\), тогда жадный выбор выполняется не более чем \\(amt / \\min(coins)\\) раз, а временная сложность равна \\(O(amt / \\min(coins))\\). Это на порядок меньше, чем временная сложность решения через динамическое программирование \\(O(n \\times amt)\\).</p> <p>Однако для некоторых наборов номиналов монет жадный алгоритм не может найти оптимальный ответ. Ниже показаны два примера.</p> <ul> <li>Положительный пример \\(coins = [1, 5, 10, 20, 50, 100]\\): для такого набора монет при любом \\(amt\\) жадный алгоритм находит оптимальное решение.</li> <li>Отрицательный пример \\(coins = [1, 20, 50]\\): пусть \\(amt = 60\\). Жадный алгоритм найдет только комбинацию \\(50 + 1 \\times 10\\), то есть всего \\(11\\) монет, тогда как динамическое программирование находит оптимум \\(20 + 20 + 20\\), где требуется лишь \\(3\\) монеты.</li> <li>Отрицательный пример \\(coins = [1, 49, 50]\\): пусть \\(amt = 98\\). Жадный алгоритм найдет только комбинацию \\(50 + 1 \\times 48\\), то есть всего \\(49\\) монет, тогда как динамическое программирование находит оптимум \\(49 + 49\\), где требуется лишь \\(2\\) монеты.</li> </ul> <p></p> <p> Рисунок 15-2   Примеры, где жадный алгоритм не находит оптимального решения </p> <p>Иными словами, в задаче о размене монет жадный алгоритм не гарантирует нахождение глобально оптимального решения и иногда может приводить к очень плохому ответу. Для этой задачи больше подходит динамическое программирование.</p> <p>В общем случае жадный алгоритм применим в двух следующих ситуациях.</p> <ol> <li>Можно гарантировать нахождение оптимального решения: в таком случае жадный алгоритм часто является лучшим выбором, поскольку обычно он эффективнее, чем поиск с возвратом и динамическое программирование.</li> <li>Можно найти приближенно оптимальное решение: в таком случае жадный алгоритм тоже полезен. Для многих сложных задач поиск глобального оптимума очень труден, и возможность быстро найти субоптимальный ответ уже весьма ценна.</li> </ol>","path":["Глава 15. Жадность","15.1 &nbsp; Жадный алгоритм"],"tags":[]},{"location":"chapter_greedy/greedy_algorithm/#1512","level":2,"title":"15.1.2   Свойства жадного алгоритма","text":"<p>Тогда возникает вопрос: какие задачи подходят для решения жадным алгоритмом? Или, другими словами, в каких случаях жадный алгоритм может гарантировать оптимальный ответ?</p> <p>По сравнению с динамическим программированием условия применения жадного алгоритма более строгие. В основном нас интересуют два свойства задачи.</p> <ul> <li>Свойство жадного выбора: только когда локально оптимальный выбор всегда может привести к глобально оптимальному решению, жадный алгоритм способен гарантировать оптимум.</li> <li>Оптимальная подструктура: оптимальное решение исходной задачи содержит оптимальные решения подзадач.</li> </ul> <p>Оптимальная подструктура уже обсуждалась в главе «Динамическое программирование», поэтому здесь не будем повторяться. Стоит отметить, что у некоторых задач оптимальная подструктура не столь очевидна, но их все равно можно решать жадным алгоритмом.</p> <p>Основное внимание мы уделяем тому, как определить свойство жадного выбора. Хотя формулировка выглядит довольно простой, на практике для многих задач доказать свойство жадного выбора совсем не легко.</p> <p>Например, в задаче о размене монет легко привести контрпример и опровергнуть свойство жадного выбора, но вот доказать его истинность намного сложнее. Если спросить: для каких наборов монет можно использовать жадный алгоритм? - обычно удается дать лишь интуитивный или примерный ответ, а не строгое математическое доказательство.</p> <p>Quote</p> <p>Существует статья, в которой приводится алгоритм со временной сложностью \\(O(n^3)\\) для определения того, можно ли с помощью жадного алгоритма находить оптимальный размен для любой суммы в заданной системе монет.</p> <p>Pearson, D. A polynomial-time algorithm for the change-making problem[J]. Operations Research Letters, 2005, 33(3): 231-234.</p>","path":["Глава 15. Жадность","15.1 &nbsp; Жадный алгоритм"],"tags":[]},{"location":"chapter_greedy/greedy_algorithm/#1513","level":2,"title":"15.1.3   Этапы решения задач жадным алгоритмом","text":"<p>Процесс решения жадной задачи в общем виде можно разбить на три шага.</p> <ol> <li>Анализ задачи: разобраться в свойствах задачи, включая определение состояний, целевой функции и ограничений. Этот этап присутствует и в поиске с возвратом, и в динамическом программировании.</li> <li>Определение жадной стратегии: определить, какой жадный выбор следует делать на каждом шаге. Эта стратегия должна уменьшать размер задачи на каждом этапе и в итоге привести к решению всей задачи.</li> <li>Доказательство корректности: обычно требуется доказать, что задача обладает свойством жадного выбора и оптимальной подструктурой. На этом этапе может понадобиться математическое доказательство, например индукция или доказательство от противного.</li> </ol> <p>Определение жадной стратегии - это ключевой этап решения, но на практике он часто оказывается непростым по следующим причинам.</p> <ul> <li>Жадные стратегии для разных задач сильно различаются. Для многих задач стратегия довольно очевидна, и до нее можно дойти за счет общих рассуждений и нескольких проб. Но в более сложных задачах жадная стратегия может быть очень скрытой, и тут уже многое зависит от опыта решения задач и алгоритмической подготовки.</li> <li>Некоторые жадные стратегии выглядят убедительно, но оказываются обманчивыми. Бывает, что мы с уверенностью придумали жадную стратегию, написали код и отправили его на проверку, а часть тестов не проходит. Причина в том, что спроектированная стратегия лишь «частично верна», и описанная выше задача о размене монет - типичный пример.</li> </ul> <p>Чтобы гарантировать корректность, нужно дать строгое математическое доказательство жадной стратегии, обычно с использованием доказательства от противного или математической индукции.</p> <p>Однако и доказательство корректности может оказаться непростой задачей. Если идей нет, мы обычно начинаем отлаживать код на тестовых примерах, постепенно меняя и проверяя жадную стратегию.</p>","path":["Глава 15. Жадность","15.1 &nbsp; Жадный алгоритм"],"tags":[]},{"location":"chapter_greedy/greedy_algorithm/#1514","level":2,"title":"15.1.4   Типичные задачи для жадного алгоритма","text":"<p>Жадные алгоритмы часто применяются в задачах оптимизации, обладающих свойством жадного выбора и оптимальной подструктурой. Ниже приведены некоторые типичные задачи, решаемые жадным подходом.</p> <ul> <li>Задача о размене монет: при некоторых системах монет жадный алгоритм всегда дает оптимальный ответ.</li> <li>Задача о расписании интервалов: пусть есть несколько задач, каждая выполняется в некотором временном интервале, и требуется завершить как можно больше задач. Если каждый раз выбирать задачу с самым ранним временем окончания, то жадный алгоритм дает оптимальный ответ.</li> <li>Задача о дробном рюкзаке: дана группа предметов и грузоподъемность. Требуется выбрать предметы так, чтобы их общий вес не превышал ограничение, а общая ценность была максимальной. Если каждый раз выбирать предмет с наилучшим отношением стоимости к весу, то в некоторых случаях жадный алгоритм дает оптимальный ответ.</li> <li>Задача о покупке и продаже акций: дана история цен акции. Можно совершать несколько сделок, но если акция уже куплена, то до продажи покупать снова нельзя. Цель - получить максимальную прибыль.</li> <li>Код Хаффмана: это жадный алгоритм для сжатия данных без потерь. Построив дерево Хаффмана и каждый раз объединяя два узла с наименьшей частотой, мы получаем дерево с минимальной взвешенной длиной пути, то есть минимальной длиной кодирования.</li> <li>Алгоритм Дейкстры: это жадный алгоритм решения задачи о кратчайших путях от заданной исходной вершины до всех остальных вершин.</li> </ul>","path":["Глава 15. Жадность","15.1 &nbsp; Жадный алгоритм"],"tags":[]},{"location":"chapter_greedy/max_capacity_problem/","level":1,"title":"15.3   Задача о максимальной вместимости","text":"<p>Question</p> <p>Дан массив \\(ht\\), где каждый элемент обозначает высоту вертикальной перегородки. Любые две перегородки в массиве вместе с пространством между ними образуют контейнер.</p> <p>Вместимость контейнера равна произведению высоты и ширины (площади), где высота определяется более короткой перегородкой, а ширина - разностью индексов двух перегородок в массиве.</p> <p>Требуется выбрать две перегородки так, чтобы образованный ими контейнер имел максимальную вместимость. Пример показан на рисунке 15-7.</p> <p></p> <p> Рисунок 15-7   Пример данных для задачи о максимальной вместимости </p> <p>Контейнер образуется произвольными двумя перегородками, поэтому состоянием задачи служит пара индексов этих перегородок, обозначим ее как \\([i, j]\\).</p> <p>Согласно условию, вместимость равна произведению высоты на ширину, где высота определяется короткой перегородкой, а ширина - разностью индексов двух перегородок. Обозначим вместимость через \\(cap[i, j]\\), тогда формула принимает вид:</p> \\[ cap[i, j] = \\min(ht[i], ht[j]) \\times (j - i) \\] <p>Пусть длина массива равна \\(n\\). Тогда число пар перегородок, то есть общее число состояний, равно \\(C_n^2 = \\frac{n(n - 1)}{2}\\). Самый прямолинейный подход - перебрать все состояния, после чего найти максимальную вместимость. Его временная сложность равна \\(O(n^2)\\).</p>","path":["Глава 15. Жадность","15.3 &nbsp; Задача о максимальной вместимости"],"tags":[]},{"location":"chapter_greedy/max_capacity_problem/#1","level":3,"title":"1.   Определение жадной стратегии","text":"<p>У этой задачи есть и более эффективное решение. Как показано на рисунке 15-8, рассмотрим состояние \\([i, j]\\), где индексы удовлетворяют \\(i &lt; j\\), а высоты - условию \\(ht[i] &lt; ht[j]\\), то есть \\(i\\) - короткая перегородка, а \\(j\\) - длинная.</p> <p></p> <p> Рисунок 15-8   Начальное состояние </p> <p>Как показано на рисунке 15-9, если в этот момент сдвинуть длинную перегородку \\(j\\) ближе к короткой перегородке \\(i\\), то вместимость обязательно уменьшится.</p> <p>Причина в том, что после смещения длинной перегородки \\(j\\) ширина \\(j-i\\) обязательно станет меньше, а высота определяется короткой перегородкой, поэтому высота либо останется прежней (если \\(i\\) останется короткой перегородкой), либо уменьшится (если сдвинутая \\(j\\) станет короткой перегородкой).</p> <p></p> <p> Рисунок 15-9   Состояние после перемещения длинной перегородки внутрь </p> <p>Рассуждая в обратную сторону, только сдвигая короткую перегородку \\(i\\) внутрь, мы можем получить шанс увеличить вместимость. Хотя ширина при этом обязательно уменьшится, высота может возрасти (если после перемещения короткая перегородка \\(i\\) станет выше). Например, на рисунке 15-10 после перемещения короткой перегородки площадь увеличивается.</p> <p></p> <p> Рисунок 15-10   Состояние после перемещения короткой перегородки внутрь </p> <p>Отсюда и выводится жадная стратегия для этой задачи: инициализировать два указателя по краям контейнера и на каждом шаге сдвигать внутрь указатель, соответствующий короткой перегородке, пока указатели не встретятся.</p> <p>На рисунках ниже показан процесс выполнения этой жадной стратегии.</p> <ol> <li>В начальном состоянии указатели \\(i\\) и \\(j\\) стоят на двух концах массива.</li> <li>Вычислить вместимость текущего состояния \\(cap[i, j]\\) и обновить максимальную вместимость.</li> <li>Сравнить высоты перегородок \\(i\\) и \\(j\\), после чего сдвинуть короткую перегородку на одну позицию внутрь.</li> <li>Повторять шаги <code>2.</code> и <code>3.</code> до тех пор, пока \\(i\\) и \\(j\\) не встретятся.</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 15-11   Жадный процесс решения задачи о максимальной вместимости </p>","path":["Глава 15. Жадность","15.3 &nbsp; Задача о максимальной вместимости"],"tags":[]},{"location":"chapter_greedy/max_capacity_problem/#2","level":3,"title":"2.   Код реализации","text":"<p>Цикл в коде выполняется не более \\(n\\) раз, поэтому временная сложность равна \\(O(n)\\).</p> <p>Переменные \\(i\\), \\(j\\), \\(res\\) используют дополнительную память постоянного размера, поэтому пространственная сложность равна \\(O(1)\\).</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby max_capacity.py<pre><code>def max_capacity(ht: list[int]) -&gt; int:\n    \"\"\"Максимальная вместимость: жадный алгоритм\"\"\"\n    # Инициализировать i и j так, чтобы они располагались по двум концам массива\n    i, j = 0, len(ht) - 1\n    # Начальная максимальная вместимость равна 0\n    res = 0\n    # Выполнять жадный выбор в цикле, пока две доски не встретятся\n    while i &lt; j:\n        # Обновить максимальную вместимость\n        cap = min(ht[i], ht[j]) * (j - i)\n        res = max(res, cap)\n        # Сдвигать внутрь более короткую сторону\n        if ht[i] &lt; ht[j]:\n            i += 1\n        else:\n            j -= 1\n    return res\n</code></pre> max_capacity.cpp<pre><code>/* Максимальная вместимость: жадный алгоритм */\nint maxCapacity(vector&lt;int&gt; &amp;ht) {\n    // Инициализировать i и j так, чтобы они располагались по двум концам массива\n    int i = 0, j = ht.size() - 1;\n    // Начальная максимальная вместимость равна 0\n    int res = 0;\n    // Выполнять жадный выбор в цикле, пока две доски не встретятся\n    while (i &lt; j) {\n        // Обновить максимальную вместимость\n        int cap = min(ht[i], ht[j]) * (j - i);\n        res = max(res, cap);\n        // Сдвигать внутрь более короткую сторону\n        if (ht[i] &lt; ht[j]) {\n            i++;\n        } else {\n            j--;\n        }\n    }\n    return res;\n}\n</code></pre> max_capacity.java<pre><code>/* Максимальная вместимость: жадный алгоритм */\nint maxCapacity(int[] ht) {\n    // Инициализировать i и j так, чтобы они располагались по двум концам массива\n    int i = 0, j = ht.length - 1;\n    // Начальная максимальная вместимость равна 0\n    int res = 0;\n    // Выполнять жадный выбор в цикле, пока две доски не встретятся\n    while (i &lt; j) {\n        // Обновить максимальную вместимость\n        int cap = Math.min(ht[i], ht[j]) * (j - i);\n        res = Math.max(res, cap);\n        // Сдвигать внутрь более короткую сторону\n        if (ht[i] &lt; ht[j]) {\n            i++;\n        } else {\n            j--;\n        }\n    }\n    return res;\n}\n</code></pre> max_capacity.cs<pre><code>/* Максимальная вместимость: жадный алгоритм */\nint MaxCapacity(int[] ht) {\n    // Инициализировать i и j так, чтобы они располагались по двум концам массива\n    int i = 0, j = ht.Length - 1;\n    // Начальная максимальная вместимость равна 0\n    int res = 0;\n    // Выполнять жадный выбор в цикле, пока две доски не встретятся\n    while (i &lt; j) {\n        // Обновить максимальную вместимость\n        int cap = Math.Min(ht[i], ht[j]) * (j - i);\n        res = Math.Max(res, cap);\n        // Сдвигать внутрь более короткую сторону\n        if (ht[i] &lt; ht[j]) {\n            i++;\n        } else {\n            j--;\n        }\n    }\n    return res;\n}\n</code></pre> max_capacity.go<pre><code>/* Максимальная вместимость: жадный алгоритм */\nfunc maxCapacity(ht []int) int {\n    // Инициализировать i и j так, чтобы они располагались по двум концам массива\n    i, j := 0, len(ht)-1\n    // Начальная максимальная вместимость равна 0\n    res := 0\n    // Выполнять жадный выбор в цикле, пока две доски не встретятся\n    for i &lt; j {\n        // Обновить максимальную вместимость\n        capacity := int(math.Min(float64(ht[i]), float64(ht[j]))) * (j - i)\n        res = int(math.Max(float64(res), float64(capacity)))\n        // Сдвигать внутрь более короткую сторону\n        if ht[i] &lt; ht[j] {\n            i++\n        } else {\n            j--\n        }\n    }\n    return res\n}\n</code></pre> max_capacity.swift<pre><code>/* Максимальная вместимость: жадный алгоритм */\nfunc maxCapacity(ht: [Int]) -&gt; Int {\n    // Инициализировать i и j так, чтобы они располагались по двум концам массива\n    var i = ht.startIndex, j = ht.endIndex - 1\n    // Начальная максимальная вместимость равна 0\n    var res = 0\n    // Выполнять жадный выбор в цикле, пока две доски не встретятся\n    while i &lt; j {\n        // Обновить максимальную вместимость\n        let cap = min(ht[i], ht[j]) * (j - i)\n        res = max(res, cap)\n        // Сдвигать внутрь более короткую сторону\n        if ht[i] &lt; ht[j] {\n            i += 1\n        } else {\n            j -= 1\n        }\n    }\n    return res\n}\n</code></pre> max_capacity.js<pre><code>/* Максимальная вместимость: жадный алгоритм */\nfunction maxCapacity(ht) {\n    // Инициализировать i и j так, чтобы они располагались по двум концам массива\n    let i = 0,\n        j = ht.length - 1;\n    // Начальная максимальная вместимость равна 0\n    let res = 0;\n    // Выполнять жадный выбор в цикле, пока две доски не встретятся\n    while (i &lt; j) {\n        // Обновить максимальную вместимость\n        const cap = Math.min(ht[i], ht[j]) * (j - i);\n        res = Math.max(res, cap);\n        // Сдвигать внутрь более короткую сторону\n        if (ht[i] &lt; ht[j]) {\n            i += 1;\n        } else {\n            j -= 1;\n        }\n    }\n    return res;\n}\n</code></pre> max_capacity.ts<pre><code>/* Максимальная вместимость: жадный алгоритм */\nfunction maxCapacity(ht: number[]): number {\n    // Инициализировать i и j так, чтобы они располагались по двум концам массива\n    let i = 0,\n        j = ht.length - 1;\n    // Начальная максимальная вместимость равна 0\n    let res = 0;\n    // Выполнять жадный выбор в цикле, пока две доски не встретятся\n    while (i &lt; j) {\n        // Обновить максимальную вместимость\n        const cap: number = Math.min(ht[i], ht[j]) * (j - i);\n        res = Math.max(res, cap);\n        // Сдвигать внутрь более короткую сторону\n        if (ht[i] &lt; ht[j]) {\n            i += 1;\n        } else {\n            j -= 1;\n        }\n    }\n    return res;\n}\n</code></pre> max_capacity.dart<pre><code>/* Максимальная вместимость: жадный алгоритм */\nint maxCapacity(List&lt;int&gt; ht) {\n  // Инициализировать i и j так, чтобы они располагались по двум концам массива\n  int i = 0, j = ht.length - 1;\n  // Начальная максимальная вместимость равна 0\n  int res = 0;\n  // Выполнять жадный выбор в цикле, пока две доски не встретятся\n  while (i &lt; j) {\n    // Обновить максимальную вместимость\n    int cap = min(ht[i], ht[j]) * (j - i);\n    res = max(res, cap);\n    // Сдвигать внутрь более короткую сторону\n    if (ht[i] &lt; ht[j]) {\n      i++;\n    } else {\n      j--;\n    }\n  }\n  return res;\n}\n</code></pre> max_capacity.rs<pre><code>/* Максимальная вместимость: жадный алгоритм */\nfn max_capacity(ht: &amp;[i32]) -&gt; i32 {\n    // Инициализировать i и j так, чтобы они располагались по двум концам массива\n    let mut i = 0;\n    let mut j = ht.len() - 1;\n    // Начальная максимальная вместимость равна 0\n    let mut res = 0;\n    // Выполнять жадный выбор в цикле, пока две доски не встретятся\n    while i &lt; j {\n        // Обновить максимальную вместимость\n        let cap = std::cmp::min(ht[i], ht[j]) * (j - i) as i32;\n        res = std::cmp::max(res, cap);\n        // Сдвигать внутрь более короткую сторону\n        if ht[i] &lt; ht[j] {\n            i += 1;\n        } else {\n            j -= 1;\n        }\n    }\n    res\n}\n</code></pre> max_capacity.c<pre><code>/* Максимальная вместимость: жадный алгоритм */\nint maxCapacity(int ht[], int htLength) {\n    // Инициализировать i и j так, чтобы они располагались по двум концам массива\n    int i = 0;\n    int j = htLength - 1;\n    // Начальная максимальная вместимость равна 0\n    int res = 0;\n    // Выполнять жадный выбор в цикле, пока две доски не встретятся\n    while (i &lt; j) {\n        // Обновить максимальную вместимость\n        int capacity = myMin(ht[i], ht[j]) * (j - i);\n        res = myMax(res, capacity);\n        // Сдвигать внутрь более короткую сторону\n        if (ht[i] &lt; ht[j]) {\n            i++;\n        } else {\n            j--;\n        }\n    }\n    return res;\n}\n</code></pre> max_capacity.kt<pre><code>/* Максимальная вместимость: жадный алгоритм */\nfun maxCapacity(ht: IntArray): Int {\n    // Инициализировать i и j так, чтобы они располагались по двум концам массива\n    var i = 0\n    var j = ht.size - 1\n    // Начальная максимальная вместимость равна 0\n    var res = 0\n    // Выполнять жадный выбор в цикле, пока две доски не встретятся\n    while (i &lt; j) {\n        // Обновить максимальную вместимость\n        val cap = min(ht[i], ht[j]) * (j - i)\n        res = max(res, cap)\n        // Сдвигать внутрь более короткую сторону\n        if (ht[i] &lt; ht[j]) {\n            i++\n        } else {\n            j--\n        }\n    }\n    return res\n}\n</code></pre> max_capacity.rb<pre><code>### Максимальная вместимость: жадный алгоритм ###\ndef max_capacity(ht)\n  # Инициализировать i и j так, чтобы они располагались по двум концам массива\n  i, j = 0, ht.length - 1\n  # Начальная максимальная вместимость равна 0\n  res = 0\n\n  # Выполнять жадный выбор в цикле, пока две доски не встретятся\n  while i &lt; j\n    # Обновить максимальную вместимость\n    cap = [ht[i], ht[j]].min * (j - i)\n    res = [res, cap].max\n    # Сдвигать внутрь более короткую сторону\n    if ht[i] &lt; ht[j]\n      i += 1\n    else\n      j -= 1\n    end\n  end\n\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 15. Жадность","15.3 &nbsp; Задача о максимальной вместимости"],"tags":[]},{"location":"chapter_greedy/max_capacity_problem/#3","level":3,"title":"3.   Доказательство корректности","text":"<p>Жадный алгоритм быстрее полного перебора именно потому, что каждый жадный шаг «пропускает» часть состояний.</p> <p>Например, в состоянии \\(cap[i, j]\\) перегородка \\(i\\) является короткой, а \\(j\\) - длинной. Если жадно сдвинуть короткую перегородку \\(i\\) на одну позицию внутрь, то состояния, показанные на рисунке 15-12, будут «пропущены». Это означает, что позже мы уже не сможем проверить вместимость этих состояний.</p> \\[ cap[i, i+1], cap[i, i+2], \\dots, cap[i, j-2], cap[i, j-1] \\] <p></p> <p> Рисунок 15-12   Состояния, пропущенные из-за смещения короткой перегородки </p> <p>Нетрудно заметить, что эти пропущенные состояния на самом деле и есть все состояния, в которых длинная перегородка \\(j\\) сдвигается внутрь. Ранее мы уже доказали, что перемещение длинной перегородки внутрь обязательно уменьшает вместимость. Иными словами, пропущенные состояния не могут быть оптимальным решением, поэтому их пропуск не приводит к потере оптимума.</p> <p>Приведенный анализ показывает, что операция перемещения короткой перегородки является «безопасной», а жадная стратегия действительно корректна.</p>","path":["Глава 15. Жадность","15.3 &nbsp; Задача о максимальной вместимости"],"tags":[]},{"location":"chapter_greedy/max_product_cutting_problem/","level":1,"title":"15.4   Задача о максимальном произведении разбиения","text":"<p>Question</p> <p>Дан положительный целый \\(n\\). Требуется разложить его в сумму как минимум двух положительных целых чисел и найти максимально возможное произведение всех полученных чисел, как показано на рисунке 15-13.</p> <p></p> <p> Рисунок 15-13   Определение задачи о максимальном произведении разбиения </p> <p>Предположим, что мы разбили \\(n\\) на \\(m\\) целочисленных множителей, где \\(i\\)-й множитель обозначим через \\(n_i\\), то есть</p> \\[ n = \\sum_{i=1}^{m}n_i \\] <p>Цель задачи - найти максимальное произведение всех целочисленных множителей, то есть</p> \\[ \\max(\\prod_{i=1}^{m}n_i) \\] <p>Нужно понять: каким должно быть число частей \\(m\\) и какими должны быть значения каждого \\(n_i\\)?</p>","path":["Глава 15. Жадность","15.4 &nbsp; Задача о максимальном произведении разбиения"],"tags":[]},{"location":"chapter_greedy/max_product_cutting_problem/#1","level":3,"title":"1.   Определение жадной стратегии","text":"<p>Из опыта известно, что произведение двух целых чисел часто больше их суммы. Предположим, что мы выделяем из \\(n\\) множитель \\(2\\), тогда произведение равно \\(2(n-2)\\). Сравним это выражение с \\(n\\):</p> \\[ \\begin{aligned} 2(n-2) &amp; \\geq n \\newline 2n - n - 4 &amp; \\geq 0 \\newline n &amp; \\geq 4 \\end{aligned} \\] <p>Как показано на рисунке 15-14, когда \\(n \\geq 4\\), выделение множителя \\(2\\) увеличивает произведение. Это означает, что все целые числа, большие либо равные \\(4\\), следует продолжать разбивать.</p> <p>Жадная стратегия 1: если в схеме разбиения присутствует множитель \\(\\geq 4\\), то его нужно дальше разбивать. В конечной схеме разбиения должны остаться только множители \\(1\\), \\(2\\), \\(3\\).</p> <p></p> <p> Рисунок 15-14   Разбиение увеличивает произведение </p> <p>Теперь подумаем, какой множитель является наилучшим. Среди \\(1\\), \\(2\\), \\(3\\) очевидно худшим является \\(1\\), потому что всегда выполняется \\(1 \\times (n-1) &lt; n\\), то есть выделение \\(1\\) уменьшает произведение.</p> <p>Как показано на рисунке 15-15, при \\(n = 6\\) имеем \\(3 \\times 3 &gt; 2 \\times 2 \\times 2\\). Это означает, что выделять \\(3\\) выгоднее, чем выделять \\(2\\).</p> <p>Жадная стратегия 2: в схеме разбиения должно быть не более двух множителей \\(2\\). Потому что три двойки всегда можно заменить двумя тройками и получить большее произведение.</p> <p></p> <p> Рисунок 15-15   Оптимальные множители разбиения </p> <p>Итак, получаем следующую жадную стратегию.</p> <ol> <li>Для заданного целого \\(n\\) непрерывно выделять из него множитель \\(3\\), пока остаток не станет равным \\(0\\), \\(1\\) или \\(2\\).</li> <li>Если остаток равен \\(0\\), это означает, что \\(n\\) кратно \\(3\\), и больше ничего делать не нужно.</li> <li>Если остаток равен \\(2\\), дальнейшее разбиение не требуется, его нужно сохранить.</li> <li>Если остаток равен \\(1\\), то поскольку \\(2 \\times 2 &gt; 1 \\times 3\\), последний множитель \\(3\\) следует заменить на \\(2\\).</li> </ol>","path":["Глава 15. Жадность","15.4 &nbsp; Задача о максимальном произведении разбиения"],"tags":[]},{"location":"chapter_greedy/max_product_cutting_problem/#2","level":3,"title":"2.   Код реализации","text":"<p>Как показано на рисунке 15-16, нам не нужен цикл, чтобы выполнять разбиение числа. Можно использовать целочисленное деление, чтобы получить число троек \\(a\\), и операцию взятия остатка, чтобы получить остаток \\(b\\). Тогда имеем:</p> \\[ n = 3 a + b \\] <p>Обратите внимание, что для граничного случая \\(n \\leq 3\\) необходимо выделить множитель \\(1\\), и тогда произведение равно \\(1 \\times (n - 1)\\).</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby max_product_cutting.py<pre><code>def max_product_cutting(n: int) -&gt; int:\n    \"\"\"Максимальное произведение разрезания: жадный алгоритм\"\"\"\n    # Когда n &lt;= 3, обязательно нужно выделить одну 1\n    if n &lt;= 3:\n        return 1 * (n - 1)\n    # Жадно выделить множители 3, где a — число троек, а b — остаток\n    a, b = n // 3, n % 3\n    if b == 1:\n        # Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n        return int(math.pow(3, a - 1)) * 2 * 2\n    if b == 2:\n        # Если остаток равен 2, ничего не делать\n        return int(math.pow(3, a)) * 2\n    # Если остаток равен 0, ничего не делать\n    return int(math.pow(3, a))\n</code></pre> max_product_cutting.cpp<pre><code>/* Максимальное произведение разрезания: жадный алгоритм */\nint maxProductCutting(int n) {\n    // Когда n &lt;= 3, обязательно нужно выделить одну 1\n    if (n &lt;= 3) {\n        return 1 * (n - 1);\n    }\n    // Жадно выделить множители 3, где a — число троек, а b — остаток\n    int a = n / 3;\n    int b = n % 3;\n    if (b == 1) {\n        // Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n        return (int)pow(3, a - 1) * 2 * 2;\n    }\n    if (b == 2) {\n        // Если остаток равен 2, ничего не делать\n        return (int)pow(3, a) * 2;\n    }\n    // Если остаток равен 0, ничего не делать\n    return (int)pow(3, a);\n}\n</code></pre> max_product_cutting.java<pre><code>/* Максимальное произведение разрезания: жадный алгоритм */\nint maxProductCutting(int n) {\n    // Когда n &lt;= 3, обязательно нужно выделить одну 1\n    if (n &lt;= 3) {\n        return 1 * (n - 1);\n    }\n    // Жадно выделить множители 3, где a — число троек, а b — остаток\n    int a = n / 3;\n    int b = n % 3;\n    if (b == 1) {\n        // Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n        return (int) Math.pow(3, a - 1) * 2 * 2;\n    }\n    if (b == 2) {\n        // Если остаток равен 2, ничего не делать\n        return (int) Math.pow(3, a) * 2;\n    }\n    // Если остаток равен 0, ничего не делать\n    return (int) Math.pow(3, a);\n}\n</code></pre> max_product_cutting.cs<pre><code>/* Максимальное произведение разрезания: жадный алгоритм */\nint MaxProductCutting(int n) {\n    // Когда n &lt;= 3, обязательно нужно выделить одну 1\n    if (n &lt;= 3) {\n        return 1 * (n - 1);\n    }\n    // Жадно выделить множители 3, где a — число троек, а b — остаток\n    int a = n / 3;\n    int b = n % 3;\n    if (b == 1) {\n        // Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n        return (int)Math.Pow(3, a - 1) * 2 * 2;\n    }\n    if (b == 2) {\n        // Если остаток равен 2, ничего не делать\n        return (int)Math.Pow(3, a) * 2;\n    }\n    // Если остаток равен 0, ничего не делать\n    return (int)Math.Pow(3, a);\n}\n</code></pre> max_product_cutting.go<pre><code>/* Максимальное произведение разрезания: жадный алгоритм */\nfunc maxProductCutting(n int) int {\n    // Когда n &lt;= 3, обязательно нужно выделить одну 1\n    if n &lt;= 3 {\n        return 1 * (n - 1)\n    }\n    // Жадно выделить множители 3, где a — число троек, а b — остаток\n    a := n / 3\n    b := n % 3\n    if b == 1 {\n        // Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n        return int(math.Pow(3, float64(a-1))) * 2 * 2\n    }\n    if b == 2 {\n        // Если остаток равен 2, ничего не делать\n        return int(math.Pow(3, float64(a))) * 2\n    }\n    // Если остаток равен 0, ничего не делать\n    return int(math.Pow(3, float64(a)))\n}\n</code></pre> max_product_cutting.swift<pre><code>/* Максимальное произведение разрезания: жадный алгоритм */\nfunc maxProductCutting(n: Int) -&gt; Int {\n    // Когда n &lt;= 3, обязательно нужно выделить одну 1\n    if n &lt;= 3 {\n        return 1 * (n - 1)\n    }\n    // Жадно выделить множители 3, где a — число троек, а b — остаток\n    let a = n / 3\n    let b = n % 3\n    if b == 1 {\n        // Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n        return pow(3, a - 1) * 2 * 2\n    }\n    if b == 2 {\n        // Если остаток равен 2, ничего не делать\n        return pow(3, a) * 2\n    }\n    // Если остаток равен 0, ничего не делать\n    return pow(3, a)\n}\n</code></pre> max_product_cutting.js<pre><code>/* Максимальное произведение разрезания: жадный алгоритм */\nfunction maxProductCutting(n) {\n    // Когда n &lt;= 3, обязательно нужно выделить одну 1\n    if (n &lt;= 3) {\n        return 1 * (n - 1);\n    }\n    // Жадно выделить множители 3, где a — число троек, а b — остаток\n    let a = Math.floor(n / 3);\n    let b = n % 3;\n    if (b === 1) {\n        // Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n        return Math.pow(3, a - 1) * 2 * 2;\n    }\n    if (b === 2) {\n        // Если остаток равен 2, ничего не делать\n        return Math.pow(3, a) * 2;\n    }\n    // Если остаток равен 0, ничего не делать\n    return Math.pow(3, a);\n}\n</code></pre> max_product_cutting.ts<pre><code>/* Максимальное произведение разрезания: жадный алгоритм */\nfunction maxProductCutting(n: number): number {\n    // Когда n &lt;= 3, обязательно нужно выделить одну 1\n    if (n &lt;= 3) {\n        return 1 * (n - 1);\n    }\n    // Жадно выделить множители 3, где a — число троек, а b — остаток\n    let a: number = Math.floor(n / 3);\n    let b: number = n % 3;\n    if (b === 1) {\n        // Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n        return Math.pow(3, a - 1) * 2 * 2;\n    }\n    if (b === 2) {\n        // Если остаток равен 2, ничего не делать\n        return Math.pow(3, a) * 2;\n    }\n    // Если остаток равен 0, ничего не делать\n    return Math.pow(3, a);\n}\n</code></pre> max_product_cutting.dart<pre><code>/* Максимальное произведение разрезания: жадный алгоритм */\nint maxProductCutting(int n) {\n  // Когда n &lt;= 3, обязательно нужно выделить одну 1\n  if (n &lt;= 3) {\n    return 1 * (n - 1);\n  }\n  // Жадно выделить множители 3, где a — число троек, а b — остаток\n  int a = n ~/ 3;\n  int b = n % 3;\n  if (b == 1) {\n    // Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n    return (pow(3, a - 1) * 2 * 2).toInt();\n  }\n  if (b == 2) {\n    // Если остаток равен 2, ничего не делать\n    return (pow(3, a) * 2).toInt();\n  }\n  // Если остаток равен 0, ничего не делать\n  return pow(3, a).toInt();\n}\n</code></pre> max_product_cutting.rs<pre><code>/* Максимальное произведение разрезания: жадный алгоритм */\nfn max_product_cutting(n: i32) -&gt; i32 {\n    // Когда n &lt;= 3, обязательно нужно выделить одну 1\n    if n &lt;= 3 {\n        return 1 * (n - 1);\n    }\n    // Жадно выделить множители 3, где a — число троек, а b — остаток\n    let a = n / 3;\n    let b = n % 3;\n    if b == 1 {\n        // Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n        3_i32.pow(a as u32 - 1) * 2 * 2\n    } else if b == 2 {\n        // Если остаток равен 2, ничего не делать\n        3_i32.pow(a as u32) * 2\n    } else {\n        // Если остаток равен 0, ничего не делать\n        3_i32.pow(a as u32)\n    }\n}\n</code></pre> max_product_cutting.c<pre><code>/* Максимальное произведение разрезания: жадный алгоритм */\nint maxProductCutting(int n) {\n    // Когда n &lt;= 3, обязательно нужно выделить одну 1\n    if (n &lt;= 3) {\n        return 1 * (n - 1);\n    }\n    // Жадно выделить множители 3, где a — число троек, а b — остаток\n    int a = n / 3;\n    int b = n % 3;\n    if (b == 1) {\n        // Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n        return pow(3, a - 1) * 2 * 2;\n    }\n    if (b == 2) {\n        // Если остаток равен 2, ничего не делать\n        return pow(3, a) * 2;\n    }\n    // Если остаток равен 0, ничего не делать\n    return pow(3, a);\n}\n</code></pre> max_product_cutting.kt<pre><code>/* Максимальное произведение разрезания: жадный алгоритм */\nfun maxProductCutting(n: Int): Int {\n    // Когда n &lt;= 3, обязательно нужно выделить одну 1\n    if (n &lt;= 3) {\n        return 1 * (n - 1)\n    }\n    // Жадно выделить множители 3, где a — число троек, а b — остаток\n    val a = n / 3\n    val b = n % 3\n    if (b == 1) {\n        // Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n        return 3.0.pow((a - 1)).toInt() * 2 * 2\n    }\n    if (b == 2) {\n        // Если остаток равен 2, ничего не делать\n        return 3.0.pow(a).toInt() * 2 * 2\n    }\n    // Если остаток равен 0, ничего не делать\n    return 3.0.pow(a).toInt()\n}\n</code></pre> max_product_cutting.rb<pre><code>### Максимальное произведение разрезания: жадный алгоритм ###\ndef max_product_cutting(n)\n  # Когда n &lt;= 3, обязательно нужно выделить одну 1\n  return 1 * (n - 1) if n &lt;= 3\n  # Жадно выделить множители 3, где a — число троек, а b — остаток\n  a, b = n / 3, n % 3\n  # Если остаток равен 1, преобразовать одну пару 1 * 3 в 2 * 2\n  return (3.pow(a - 1) * 2 * 2).to_i if b == 1\n  # Если остаток равен 2, ничего не делать\n  return (3.pow(a) * 2).to_i if b == 2\n  # Если остаток равен 0, ничего не делать\n  3.pow(a).to_i\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p></p> <p> Рисунок 15-16   Метод вычисления максимального произведения разбиения </p> <p>Временная сложность зависит от того, как в языке программирования реализовано возведение в степень. Если взять Python, то обычно используются три распространенные функции для вычисления степени.</p> <ul> <li>Оператор <code>**</code> и функция <code>pow()</code> имеют временную сложность \\(O(\\log⁡ a)\\).</li> <li>Функция <code>math.pow()</code> внутри вызывает функцию <code>pow()</code> из библиотеки C, выполняющую возведение в степень с плавающей точкой, и ее временная сложность равна \\(O(1)\\).</li> </ul> <p>Переменные \\(a\\) и \\(b\\) занимают дополнительную память постоянного размера, поэтому пространственная сложность равна \\(O(1)\\).</p>","path":["Глава 15. Жадность","15.4 &nbsp; Задача о максимальном произведении разбиения"],"tags":[]},{"location":"chapter_greedy/max_product_cutting_problem/#3","level":3,"title":"3.   Доказательство корректности","text":"<p>Используем доказательство от противного и рассмотрим только случай \\(n \\geq 4\\).</p> <ol> <li>Все множители \\(\\leq 3\\): предположим, что в оптимальной схеме разбиения существует множитель \\(x \\geq 4\\). Тогда его можно дальше разложить в \\(2(x-2)\\) и получить большее или равное произведение. Это противоречит предположению.</li> <li>Схема разбиения не содержит \\(1\\): предположим, что в оптимальной схеме присутствует множитель \\(1\\). Тогда его можно объединить с другим множителем и получить большее произведение. Это противоречит предположению.</li> <li>Схема разбиения содержит не более двух \\(2\\): предположим, что в оптимальной схеме присутствуют три двойки. Тогда их можно заменить двумя тройками и получить большее произведение. Это противоречит предположению.</li> </ol>","path":["Глава 15. Жадность","15.4 &nbsp; Задача о максимальном произведении разбиения"],"tags":[]},{"location":"chapter_greedy/summary/","level":1,"title":"15.5   Резюме","text":"","path":["Глава 15. Жадность","15.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_greedy/summary/#1","level":3,"title":"1.   Ключевые моменты","text":"<ul> <li>Жадный алгоритм обычно используется для решения задач оптимизации. Его принцип состоит в том, чтобы на каждом этапе принятия решения делать локально оптимальный выбор в надежде получить глобально оптимальный ответ.</li> <li>Жадный алгоритм итеративно делает один жадный выбор за другим, на каждом шаге превращая задачу в подзадачу меньшего размера, пока задача не будет полностью решена.</li> <li>Жадный алгоритм не только прост в реализации, но и часто обладает высокой эффективностью. По сравнению с динамическим программированием его временная сложность обычно ниже.</li> <li>В задаче о размене монет для некоторых наборов монет жадный алгоритм способен гарантировать оптимальный ответ, а для других наборов - нет: он может дать очень плохое решение.</li> <li>Задачи, подходящие для жадного алгоритма, обладают двумя ключевыми свойствами: свойством жадного выбора и оптимальной подструктурой. Свойство жадного выбора отражает корректность жадной стратегии.</li> <li>Для некоторых сложных задач доказать свойство жадного выбора непросто. Относительно легче найти контрпример и опровергнуть его, как это видно на примере задачи о размене монет.</li> <li>Решение жадной задачи обычно состоит из трех шагов: анализ задачи, определение жадной стратегии и доказательство корректности. Из них ключевым является выбор жадной стратегии, а доказательство корректности часто оказывается самым трудным.</li> <li>В задаче о дробном рюкзаке, в отличие от задачи о рюкзаке 0-1, разрешено брать часть предмета, поэтому ее можно решать жадным алгоритмом. Корректность жадной стратегии доказывается методом от противного.</li> <li>Задачу о максимальной вместимости можно решать полным перебором со временной сложностью \\(O(n^2)\\). Разработав жадную стратегию со сдвигом короткой перегородки внутрь на каждом шаге, временную сложность можно оптимизировать до \\(O(n)\\).</li> <li>В задаче о максимальном произведении разбиения мы последовательно выводим две жадные стратегии: все целые числа \\(\\geq 4\\) следует дальше разбивать, а оптимальным множителем разбиения является \\(3\\). В коде присутствуют операции возведения в степень, поэтому временная сложность зависит от способа их реализации и обычно равна \\(O(1)\\) или \\(O(\\log n)\\).</li> </ul>","path":["Глава 15. Жадность","15.5 &nbsp; Резюме"],"tags":[]},{"location":"chapter_hashing/","level":1,"title":"Глава 6.   Хеш-таблицы","text":"<p>Abstract</p> <p>Хеш-таблица устанавливает соответствие между ключом и значением.</p> <p>Благодаря этому она позволяет получать нужное значение по ключу за очень короткое время.</p>","path":["Глава 6. Хеш-таблицы","Глава 6. &nbsp; Хеш-таблицы"],"tags":[]},{"location":"chapter_hashing/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>6.1   Хеш-таблица</li> <li>6.2   Хеш-коллизии</li> <li>6.3   Алгоритмы хеширования</li> <li>6.4   Резюме</li> </ul>","path":["Глава 6. Хеш-таблицы","Глава 6. &nbsp; Хеш-таблицы"],"tags":[]},{"location":"chapter_hashing/hash_algorithm/","level":1,"title":"6.3   Алгоритмы хеширования","text":"<p>В двух предыдущих разделах мы рассмотрели принципы работы хеш-таблицы и способы обработки хеш-коллизий. Однако и открытая адресация, и метод цепочек лишь позволяют хеш-таблице корректно работать при возникновении коллизий, но не уменьшают вероятность появления самих коллизий.</p> <p>Если хеш-коллизии происходят слишком часто, производительность хеш-таблицы резко деградирует. Как показано на рисунке 6-8, для хеш-таблицы с методом цепочек в идеальном случае пары ключ-значение равномерно распределены по всем бакетам, и это дает наилучшую эффективность поиска; в худшем же случае все пары ключ-значение оказываются в одном бакете, и временная сложность вырождается до \\(O(n)\\) .</p> <p></p> <p> Рисунок 6-8   Лучший и худший случаи хеш-коллизий </p> <p>Распределение пар ключ-значение определяется хеш-функцией. Вспомним этапы вычисления хеш-функции: сначала вычисляется хеш-значение, затем оно берется по модулю длины массива:</p> <pre><code>index = hash(key) % capacity\n</code></pre> <p>Из этой формулы видно: при фиксированной емкости хеш-таблицы <code>capacity</code> **выходное значение определяет именно хеш-алгоритм <code>hash()</code> **, а значит, именно он определяет распределение пар ключ-значение в хеш-таблице.</p> <p>Это означает, что для уменьшения вероятности хеш-коллизий нам следует сосредоточиться на проектировании хеш-алгоритма <code>hash()</code> .</p>","path":["Глава 6. Хеш-таблицы","6.3 &nbsp; Алгоритмы хеширования"],"tags":[]},{"location":"chapter_hashing/hash_algorithm/#631-","level":2,"title":"6.3.1   Цели хеш-алгоритма","text":"<p>Чтобы получить структуру данных хеш-таблицы, которая будет одновременно быстрой и надежной, хеш-алгоритм должен обладать следующими свойствами.</p> <ul> <li>Детерминированность: для одинакового входа хеш-алгоритм всегда должен выдавать одинаковый результат. Только так хеш-таблица остается надежной.</li> <li>Высокая эффективность: вычисление хеш-значения должно быть достаточно быстрым. Чем меньше вычислительные затраты, тем выше практическая ценность хеш-таблицы.</li> <li>Равномерное распределение: хеш-алгоритм должен стараться распределять пары ключ-значение в хеш-таблице равномерно. Чем равномернее распределение, тем ниже вероятность хеш-коллизий.</li> </ul> <p>На практике хеш-алгоритмы используются не только для реализации хеш-таблиц, но и во многих других областях.</p> <ul> <li>Хранение паролей: чтобы защищать пароли пользователей, система обычно хранит не сами пароли в открытом виде, а их хеш-значения. Когда пользователь вводит пароль, система вычисляет хеш-значение введенного пароля и сравнивает его с сохраненным значением. Если они совпадают, пароль считается правильным.</li> <li>Проверка целостности данных: отправитель может вычислить хеш-значение данных и отправить его вместе с самими данными; получатель затем вычисляет хеш-значение повторно и сравнивает его с полученным. Если они совпадают, данные считаются целостными.</li> </ul> <p>Для приложений, связанных с криптографией, чтобы не допустить восстановления исходного пароля по хеш-значению и иных форм обратного анализа, хеш-алгоритм должен обладать более строгими свойствами безопасности.</p> <ul> <li>Односторонность: по хеш-значению нельзя восстановить какую-либо информацию о входных данных.</li> <li>Устойчивость к коллизиям: должно быть крайне трудно найти два разных входа, имеющих одинаковое хеш-значение.</li> <li>Эффект лавины: даже небольшое изменение во входных данных должно приводить к заметному и непредсказуемому изменению результата.</li> </ul> <p>Обрати внимание: \"равномерное распределение\" и \"устойчивость к коллизиям\" - это два независимых понятия , и выполнение первого не означает автоматического выполнения второго. Например, при случайном распределении входных <code>key</code> хеш-функция <code>key % 100</code> может выдавать достаточно равномерное распределение. Однако этот хеш-алгоритм слишком прост: все <code>key</code> с одинаковыми двумя последними цифрами будут иметь одинаковый результат, а значит, по хеш-значению можно легко подобрать подходящие <code>key</code> и, например, взломать пароль.</p>","path":["Глава 6. Хеш-таблицы","6.3 &nbsp; Алгоритмы хеширования"],"tags":[]},{"location":"chapter_hashing/hash_algorithm/#632-","level":2,"title":"6.3.2   Проектирование хеш-алгоритма","text":"<p>Разработка хеш-алгоритма - это сложная задача, в которой нужно учитывать множество факторов. Однако для некоторых нетребовательных сценариев мы можем спроектировать и несколько простых хеш-алгоритмов.</p> <ul> <li>Аддитивный хеш: складываем ASCII-коды всех символов входной строки и используем полученную сумму как хеш-значение.</li> <li>Мультипликативный хеш: используем \"некоррелированность\" умножения; на каждом шаге умножаем текущее значение на константу и добавляем ASCII-код очередного символа.</li> <li>XOR-хеш: последовательно накапливаем элементы входных данных в одном хеш-значении через операцию XOR.</li> <li>Ротационный хеш: последовательно накапливаем ASCII-коды символов, причем перед каждым накоплением выполняем циклический сдвиг хеш-значения.</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby simple_hash.py<pre><code>def add_hash(key: str) -&gt; int:\n    \"\"\"Аддитивное хеширование\"\"\"\n    hash = 0\n    modulus = 1000000007\n    for c in key:\n        hash += ord(c)\n    return hash % modulus\n\ndef mul_hash(key: str) -&gt; int:\n    \"\"\"Мультипликативное хеширование\"\"\"\n    hash = 0\n    modulus = 1000000007\n    for c in key:\n        hash = 31 * hash + ord(c)\n    return hash % modulus\n\ndef xor_hash(key: str) -&gt; int:\n    \"\"\"XOR-хеширование\"\"\"\n    hash = 0\n    modulus = 1000000007\n    for c in key:\n        hash ^= ord(c)\n    return hash % modulus\n\ndef rot_hash(key: str) -&gt; int:\n    \"\"\"Хеширование с циклическим сдвигом\"\"\"\n    hash = 0\n    modulus = 1000000007\n    for c in key:\n        hash = (hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ ord(c)\n    return hash % modulus\n</code></pre> simple_hash.cpp<pre><code>/* Аддитивное хеширование */\nint addHash(string key) {\n    long long hash = 0;\n    const int MODULUS = 1000000007;\n    for (unsigned char c : key) {\n        hash = (hash + (int)c) % MODULUS;\n    }\n    return (int)hash;\n}\n\n/* Мультипликативное хеширование */\nint mulHash(string key) {\n    long long hash = 0;\n    const int MODULUS = 1000000007;\n    for (unsigned char c : key) {\n        hash = (31 * hash + (int)c) % MODULUS;\n    }\n    return (int)hash;\n}\n\n/* XOR-хеширование */\nint xorHash(string key) {\n    int hash = 0;\n    const int MODULUS = 1000000007;\n    for (unsigned char c : key) {\n        hash ^= (int)c;\n    }\n    return hash &amp; MODULUS;\n}\n\n/* Хеширование с циклическим сдвигом */\nint rotHash(string key) {\n    long long hash = 0;\n    const int MODULUS = 1000000007;\n    for (unsigned char c : key) {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ (int)c) % MODULUS;\n    }\n    return (int)hash;\n}\n</code></pre> simple_hash.java<pre><code>/* Аддитивное хеширование */\nint addHash(String key) {\n    long hash = 0;\n    final int MODULUS = 1000000007;\n    for (char c : key.toCharArray()) {\n        hash = (hash + (int) c) % MODULUS;\n    }\n    return (int) hash;\n}\n\n/* Мультипликативное хеширование */\nint mulHash(String key) {\n    long hash = 0;\n    final int MODULUS = 1000000007;\n    for (char c : key.toCharArray()) {\n        hash = (31 * hash + (int) c) % MODULUS;\n    }\n    return (int) hash;\n}\n\n/* XOR-хеширование */\nint xorHash(String key) {\n    int hash = 0;\n    final int MODULUS = 1000000007;\n    for (char c : key.toCharArray()) {\n        hash ^= (int) c;\n    }\n    return hash &amp; MODULUS;\n}\n\n/* Хеширование с циклическим сдвигом */\nint rotHash(String key) {\n    long hash = 0;\n    final int MODULUS = 1000000007;\n    for (char c : key.toCharArray()) {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ (int) c) % MODULUS;\n    }\n    return (int) hash;\n}\n</code></pre> simple_hash.cs<pre><code>/* Аддитивное хеширование */\nint AddHash(string key) {\n    long hash = 0;\n    const int MODULUS = 1000000007;\n    foreach (char c in key) {\n        hash = (hash + c) % MODULUS;\n    }\n    return (int)hash;\n}\n\n/* Мультипликативное хеширование */\nint MulHash(string key) {\n    long hash = 0;\n    const int MODULUS = 1000000007;\n    foreach (char c in key) {\n        hash = (31 * hash + c) % MODULUS;\n    }\n    return (int)hash;\n}\n\n/* XOR-хеширование */\nint XorHash(string key) {\n    int hash = 0;\n    const int MODULUS = 1000000007;\n    foreach (char c in key) {\n        hash ^= c;\n    }\n    return hash &amp; MODULUS;\n}\n\n/* Хеширование с циклическим сдвигом */\nint RotHash(string key) {\n    long hash = 0;\n    const int MODULUS = 1000000007;\n    foreach (char c in key) {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ c) % MODULUS;\n    }\n    return (int)hash;\n}\n</code></pre> simple_hash.go<pre><code>/* Аддитивное хеширование */\nfunc addHash(key string) int {\n    var hash int64\n    var modulus int64\n\n    modulus = 1000000007\n    for _, b := range []byte(key) {\n        hash = (hash + int64(b)) % modulus\n    }\n    return int(hash)\n}\n\n/* Мультипликативное хеширование */\nfunc mulHash(key string) int {\n    var hash int64\n    var modulus int64\n\n    modulus = 1000000007\n    for _, b := range []byte(key) {\n        hash = (31*hash + int64(b)) % modulus\n    }\n    return int(hash)\n}\n\n/* XOR-хеширование */\nfunc xorHash(key string) int {\n    hash := 0\n    modulus := 1000000007\n    for _, b := range []byte(key) {\n        fmt.Println(int(b))\n        hash ^= int(b)\n        hash = (31*hash + int(b)) % modulus\n    }\n    return hash &amp; modulus\n}\n\n/* Хеширование с циклическим сдвигом */\nfunc rotHash(key string) int {\n    var hash int64\n    var modulus int64\n\n    modulus = 1000000007\n    for _, b := range []byte(key) {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ int64(b)) % modulus\n    }\n    return int(hash)\n}\n</code></pre> simple_hash.swift<pre><code>/* Аддитивное хеширование */\nfunc addHash(key: String) -&gt; Int {\n    var hash = 0\n    let MODULUS = 1_000_000_007\n    for c in key {\n        for scalar in c.unicodeScalars {\n            hash = (hash + Int(scalar.value)) % MODULUS\n        }\n    }\n    return hash\n}\n\n/* Мультипликативное хеширование */\nfunc mulHash(key: String) -&gt; Int {\n    var hash = 0\n    let MODULUS = 1_000_000_007\n    for c in key {\n        for scalar in c.unicodeScalars {\n            hash = (31 * hash + Int(scalar.value)) % MODULUS\n        }\n    }\n    return hash\n}\n\n/* XOR-хеширование */\nfunc xorHash(key: String) -&gt; Int {\n    var hash = 0\n    let MODULUS = 1_000_000_007\n    for c in key {\n        for scalar in c.unicodeScalars {\n            hash ^= Int(scalar.value)\n        }\n    }\n    return hash &amp; MODULUS\n}\n\n/* Хеширование с циклическим сдвигом */\nfunc rotHash(key: String) -&gt; Int {\n    var hash = 0\n    let MODULUS = 1_000_000_007\n    for c in key {\n        for scalar in c.unicodeScalars {\n            hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ Int(scalar.value)) % MODULUS\n        }\n    }\n    return hash\n}\n</code></pre> simple_hash.js<pre><code>/* Аддитивное хеширование */\nfunction addHash(key) {\n    let hash = 0;\n    const MODULUS = 1000000007;\n    for (const c of key) {\n        hash = (hash + c.charCodeAt(0)) % MODULUS;\n    }\n    return hash;\n}\n\n/* Мультипликативное хеширование */\nfunction mulHash(key) {\n    let hash = 0;\n    const MODULUS = 1000000007;\n    for (const c of key) {\n        hash = (31 * hash + c.charCodeAt(0)) % MODULUS;\n    }\n    return hash;\n}\n\n/* XOR-хеширование */\nfunction xorHash(key) {\n    let hash = 0;\n    const MODULUS = 1000000007;\n    for (const c of key) {\n        hash ^= c.charCodeAt(0);\n    }\n    return hash % MODULUS;\n}\n\n/* Хеширование с циклическим сдвигом */\nfunction rotHash(key) {\n    let hash = 0;\n    const MODULUS = 1000000007;\n    for (const c of key) {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ c.charCodeAt(0)) % MODULUS;\n    }\n    return hash;\n}\n</code></pre> simple_hash.ts<pre><code>/* Аддитивное хеширование */\nfunction addHash(key: string): number {\n    let hash = 0;\n    const MODULUS = 1000000007;\n    for (const c of key) {\n        hash = (hash + c.charCodeAt(0)) % MODULUS;\n    }\n    return hash;\n}\n\n/* Мультипликативное хеширование */\nfunction mulHash(key: string): number {\n    let hash = 0;\n    const MODULUS = 1000000007;\n    for (const c of key) {\n        hash = (31 * hash + c.charCodeAt(0)) % MODULUS;\n    }\n    return hash;\n}\n\n/* XOR-хеширование */\nfunction xorHash(key: string): number {\n    let hash = 0;\n    const MODULUS = 1000000007;\n    for (const c of key) {\n        hash ^= c.charCodeAt(0);\n    }\n    return hash % MODULUS;\n}\n\n/* Хеширование с циклическим сдвигом */\nfunction rotHash(key: string): number {\n    let hash = 0;\n    const MODULUS = 1000000007;\n    for (const c of key) {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ c.charCodeAt(0)) % MODULUS;\n    }\n    return hash;\n}\n</code></pre> simple_hash.dart<pre><code>/* Аддитивное хеширование */\nint addHash(String key) {\n  int hash = 0;\n  final int MODULUS = 1000000007;\n  for (int i = 0; i &lt; key.length; i++) {\n    hash = (hash + key.codeUnitAt(i)) % MODULUS;\n  }\n  return hash;\n}\n\n/* Мультипликативное хеширование */\nint mulHash(String key) {\n  int hash = 0;\n  final int MODULUS = 1000000007;\n  for (int i = 0; i &lt; key.length; i++) {\n    hash = (31 * hash + key.codeUnitAt(i)) % MODULUS;\n  }\n  return hash;\n}\n\n/* XOR-хеширование */\nint xorHash(String key) {\n  int hash = 0;\n  final int MODULUS = 1000000007;\n  for (int i = 0; i &lt; key.length; i++) {\n    hash ^= key.codeUnitAt(i);\n  }\n  return hash &amp; MODULUS;\n}\n\n/* Хеширование с циклическим сдвигом */\nint rotHash(String key) {\n  int hash = 0;\n  final int MODULUS = 1000000007;\n  for (int i = 0; i &lt; key.length; i++) {\n    hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ key.codeUnitAt(i)) % MODULUS;\n  }\n  return hash;\n}\n</code></pre> simple_hash.rs<pre><code>/* Аддитивное хеширование */\nfn add_hash(key: &amp;str) -&gt; i32 {\n    let mut hash = 0_i64;\n    const MODULUS: i64 = 1000000007;\n\n    for c in key.chars() {\n        hash = (hash + c as i64) % MODULUS;\n    }\n\n    hash as i32\n}\n\n/* Мультипликативное хеширование */\nfn mul_hash(key: &amp;str) -&gt; i32 {\n    let mut hash = 0_i64;\n    const MODULUS: i64 = 1000000007;\n\n    for c in key.chars() {\n        hash = (31 * hash + c as i64) % MODULUS;\n    }\n\n    hash as i32\n}\n\n/* XOR-хеширование */\nfn xor_hash(key: &amp;str) -&gt; i32 {\n    let mut hash = 0_i64;\n    const MODULUS: i64 = 1000000007;\n\n    for c in key.chars() {\n        hash ^= c as i64;\n    }\n\n    (hash &amp; MODULUS) as i32\n}\n\n/* Хеширование с циклическим сдвигом */\nfn rot_hash(key: &amp;str) -&gt; i32 {\n    let mut hash = 0_i64;\n    const MODULUS: i64 = 1000000007;\n\n    for c in key.chars() {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ c as i64) % MODULUS;\n    }\n\n    hash as i32\n}\n</code></pre> simple_hash.c<pre><code>/* Аддитивное хеширование */\nint addHash(char *key) {\n    long long hash = 0;\n    const int MODULUS = 1000000007;\n    for (int i = 0; i &lt; strlen(key); i++) {\n        hash = (hash + (unsigned char)key[i]) % MODULUS;\n    }\n    return (int)hash;\n}\n\n/* Мультипликативное хеширование */\nint mulHash(char *key) {\n    long long hash = 0;\n    const int MODULUS = 1000000007;\n    for (int i = 0; i &lt; strlen(key); i++) {\n        hash = (31 * hash + (unsigned char)key[i]) % MODULUS;\n    }\n    return (int)hash;\n}\n\n/* XOR-хеширование */\nint xorHash(char *key) {\n    int hash = 0;\n    const int MODULUS = 1000000007;\n\n    for (int i = 0; i &lt; strlen(key); i++) {\n        hash ^= (unsigned char)key[i];\n    }\n    return hash &amp; MODULUS;\n}\n\n/* Хеширование с циклическим сдвигом */\nint rotHash(char *key) {\n    long long hash = 0;\n    const int MODULUS = 1000000007;\n    for (int i = 0; i &lt; strlen(key); i++) {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ (unsigned char)key[i]) % MODULUS;\n    }\n\n    return (int)hash;\n}\n</code></pre> simple_hash.kt<pre><code>/* Аддитивное хеширование */\nfun addHash(key: String): Int {\n    var hash = 0L\n    val MODULUS = 1000000007\n    for (c in key.toCharArray()) {\n        hash = (hash + c.code) % MODULUS\n    }\n    return hash.toInt()\n}\n\n/* Мультипликативное хеширование */\nfun mulHash(key: String): Int {\n    var hash = 0L\n    val MODULUS = 1000000007\n    for (c in key.toCharArray()) {\n        hash = (31 * hash + c.code) % MODULUS\n    }\n    return hash.toInt()\n}\n\n/* XOR-хеширование */\nfun xorHash(key: String): Int {\n    var hash = 0\n    val MODULUS = 1000000007\n    for (c in key.toCharArray()) {\n        hash = hash xor c.code\n    }\n    return hash and MODULUS\n}\n\n/* Хеширование с циклическим сдвигом */\nfun rotHash(key: String): Int {\n    var hash = 0L\n    val MODULUS = 1000000007\n    for (c in key.toCharArray()) {\n        hash = ((hash shl 4) xor (hash shr 28) xor c.code.toLong()) % MODULUS\n    }\n    return hash.toInt()\n}\n</code></pre> simple_hash.rb<pre><code>### Аддитивное хеширование ###\ndef add_hash(key)\n  hash = 0\n  modulus = 1_000_000_007\n\n  key.each_char { |c| hash += c.ord }\n\n  hash % modulus\nend\n\n### Мультипликативное хеширование ###\ndef mul_hash(key)\n  hash = 0\n  modulus = 1_000_000_007\n\n  key.each_char { |c| hash = 31 * hash + c.ord }\n\n  hash % modulus\nend\n\n### XOR-хеширование ###\ndef xor_hash(key)\n  hash = 0\n  modulus = 1_000_000_007\n\n  key.each_char { |c| hash ^= c.ord }\n\n  hash % modulus\nend\n\n### Хеширование с циклическим сдвигом ###\ndef rot_hash(key)\n  hash = 0\n  modulus = 1_000_000_007\n\n  key.each_char { |c| hash = (hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ c.ord }\n\n  hash % modulus\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Нетрудно заметить, что последний шаг каждого из этих хеш-алгоритмов - взятие по модулю большого простого числа \\(1000000007\\) , чтобы гарантировать, что хеш-значение остается в разумных границах. Стоит задуматься: почему подчеркивается именно взятие по модулю простого числа, и какие недостатки возникают при использовании составного модуля? Это интересный вопрос.</p> <p>Сначала дадим вывод: использование большого простого числа в качестве модуля позволяет в максимальной степени обеспечивать равномерное распределение хеш-значений. Поскольку простое число не имеет общих делителей с другими числами, это помогает уменьшить периодические закономерности, возникающие из-за операции взятия остатка, и тем самым снизить число хеш-коллизий.</p> <p>Рассмотрим пример. Предположим, мы выбрали составное число \\(9\\) в качестве модуля. Оно делится на \\(3\\) , поэтому все <code>key</code> , которые делятся на \\(3\\) , будут отображаться только в три хеш-значения: \\(0\\) , \\(3\\) , \\(6\\) .</p> \\[ \\begin{aligned} \\text{modulus} &amp; = 9 \\newline \\text{key} &amp; = \\{ 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, \\dots \\} \\newline \\text{hash} &amp; = \\{ 0, 3, 6, 0, 3, 6, 0, 3, 6, 0, 3, 6,\\dots \\} \\end{aligned} \\] <p>Если входные <code>key</code> как раз удовлетворяют такому распределению в виде арифметической прогрессии, то хеш-значения начнут скучиваться, а это усугубит хеш-коллизии. Теперь предположим, что мы заменили <code>modulus</code> на простое число \\(13\\) ; поскольку между <code>key</code> и <code>modulus</code> нет общих делителей, равномерность распределения хеш-значений заметно улучшится.</p> \\[ \\begin{aligned} \\text{modulus} &amp; = 13 \\newline \\text{key} &amp; = \\{ 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, \\dots \\} \\newline \\text{hash} &amp; = \\{ 0, 3, 6, 9, 12, 2, 5, 8, 11, 1, 4, 7, \\dots \\} \\end{aligned} \\] <p>Следует отметить: если можно гарантировать, что <code>key</code> распределены случайно и равномерно, то выбор простого или составного числа в качестве модуля не так важен - оба варианта способны дать равномерное распределение хеш-значений. Но если в распределении <code>key</code> присутствует периодичность, то взятие по модулю составного числа гораздо легче приводит к кластеризации.</p> <p>Итак, на практике мы обычно выбираем простое число в качестве модуля, причем это простое число желательно брать достаточно большим, чтобы по возможности убрать периодические закономерности и повысить устойчивость хеш-алгоритма.</p>","path":["Глава 6. Хеш-таблицы","6.3 &nbsp; Алгоритмы хеширования"],"tags":[]},{"location":"chapter_hashing/hash_algorithm/#633-","level":2,"title":"6.3.3   Распространенные хеш-алгоритмы","text":"<p>Нетрудно заметить, что описанные выше простые хеш-алгоритмы довольно хрупкие и далеки от поставленных целей. Например, сложение и XOR подчиняются коммутативному закону, поэтому аддитивный хеш и XOR-хеш не различают строки, состоящие из одних и тех же символов, но в разном порядке. Это может усиливать хеш-коллизии и даже создавать некоторые проблемы безопасности.</p> <p>На практике мы обычно используем стандартные хеш-алгоритмы, такие как MD5, SHA-1, SHA-2 и SHA-3. Они могут отображать входные данные произвольной длины в хеш-значения фиксированной длины.</p> <p>На протяжении почти ста лет хеш-алгоритмы непрерывно развивались и оптимизировались. Одни исследователи старались повысить их производительность, а другие исследователи и хакеры сосредоточивались на поиске уязвимостей в их безопасности. В таблице 6-2 приведены распространенные хеш-алгоритмы, которые часто встречаются в реальных приложениях.</p> <ul> <li>MD5 и SHA-1 уже многократно были успешно атакованы, поэтому они выведены из большинства сценариев, где требуется безопасность.</li> <li>SHA-256 из семейства SHA-2 является одним из самых надежных хеш-алгоритмов; на сегодняшний день не известно успешных практических атак, поэтому он широко используется в самых разных протоколах и системах безопасности.</li> <li>SHA-3 по сравнению с SHA-2 требует меньших затрат на реализацию и обеспечивает более высокую вычислительную эффективность, но на данный момент распространен слабее, чем семейство SHA-2.</li> </ul> <p> Таблица 6-2   Распространенные хеш-алгоритмы </p> MD5 SHA-1 SHA-2 SHA-3 Год появления 1992 1995 2002 2008 Длина вывода 128 bit 160 bit 256/512 bit 224/256/384/512 bit Хеш-коллизии Частые Частые Редкие Редкие Уровень безопасности Низкий, успешно атакован Низкий, успешно атакован Высокий Высокий Применение Устарел, но еще используется для проверки целостности данных Устарел Проверка криптовалютных транзакций, цифровые подписи и т. д. Может использоваться как замена SHA-2","path":["Глава 6. Хеш-таблицы","6.3 &nbsp; Алгоритмы хеширования"],"tags":[]},{"location":"chapter_hashing/hash_algorithm/#634-","level":2,"title":"6.3.4   Хеш-значения структур данных","text":"<p>Мы знаем, что <code>key</code> в хеш-таблице могут быть целыми числами, вещественными числами, строками и другими типами данных. Языки программирования обычно предоставляют встроенные хеш-алгоритмы для этих типов, чтобы вычислять индексы бакетов в хеш-таблице. Возьмем Python: в нем можно вызвать функцию <code>hash()</code> , чтобы вычислить хеш-значения для различных типов данных.</p> <ul> <li>Хеш-значение целого числа и булева значения совпадает с самим значением.</li> <li>Вычисление хеш-значений для вещественных чисел и строк устроено сложнее; интересующиеся читатели могут изучить это самостоятельно.</li> <li>Хеш-значение кортежа получается путем хеширования каждого элемента, а затем объединения этих хеш-значений в одно итоговое значение.</li> <li>Хеш-значение объекта обычно строится на основе его адреса в памяти. Если переопределить метод хеширования объекта, можно реализовать вычисление хеша по содержимому.</li> </ul> <p>Tip</p> <p>Обрати внимание: определения и способы вычисления встроенных хеш-значений в разных языках программирования отличаются.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby built_in_hash.py<pre><code>num = 3\nhash_num = hash(num)\n# Хеш-значение целого числа 3 равно 3\n\nbol = True\nhash_bol = hash(bol)\n# Хеш-значение булевого значения True равно 1\n\ndec = 3.14159\nhash_dec = hash(dec)\n# Хеш-значение числа 3.14159 равно 326484311674566659\n\nstr = \"Hello Algo\"\nhash_str = hash(str)\n# Хеш-значение строки \"Hello Algo\" равно 4617003410720528961\n\ntup = (12836, \"Сяо Ха\")\nhash_tup = hash(tup)\n# Хеш-значение кортежа (12836, \"Сяо Ха\") равно 1029005403108185979\n\nobj = ListNode(0)\nhash_obj = hash(obj)\n# Хеш-значение объекта узла &lt;ListNode object at 0x1058fd810&gt; равно 274267521\n</code></pre> built_in_hash.cpp<pre><code>int num = 3;\nsize_t hashNum = hash&lt;int&gt;()(num);\n// Хеш-значение целого числа 3 равно 3\n\nbool bol = true;\nsize_t hashBol = hash&lt;bool&gt;()(bol);\n// Хеш-значение булевого значения 1 равно 1\n\ndouble dec = 3.14159;\nsize_t hashDec = hash&lt;double&gt;()(dec);\n// Хеш-значение числа 3.14159 равно 4614256650576692846\n\nstring str = \"Hello Algo\";\nsize_t hashStr = hash&lt;string&gt;()(str);\n// Хеш-значение строки \"Hello Algo\" равно 15466937326284535026\n\n// В C++ встроенный std::hash() предоставляет вычисление хеша только для базовых типов данных\n// Для массивов и объектов хеш-значение обычно приходится реализовывать самостоятельно\n</code></pre> built_in_hash.java<pre><code>int num = 3;\nint hashNum = Integer.hashCode(num);\n// Хеш-значение целого числа 3 равно 3\n\nboolean bol = true;\nint hashBol = Boolean.hashCode(bol);\n// Хеш-значение булевого значения true равно 1231\n\ndouble dec = 3.14159;\nint hashDec = Double.hashCode(dec);\n// Хеш-значение числа 3.14159 равно -1340954729\n\nString str = \"Hello Algo\";\nint hashStr = str.hashCode();\n// Хеш-значение строки \"Hello Algo\" равно -727081396\n\nObject[] arr = { 12836, \"Сяо Ха\" };\nint hashTup = Arrays.hashCode(arr);\n// Хеш-значение массива [12836, Сяо Ха] равно 1151158\n\nListNode obj = new ListNode(0);\nint hashObj = obj.hashCode();\n// Хеш-значение объекта узла utils.ListNode@7dc5e7b4 равно 2110121908\n</code></pre> built_in_hash.cs<pre><code>int num = 3;\nint hashNum = num.GetHashCode();\n// Хеш-значение целого числа 3 равно 3;\n\nbool bol = true;\nint hashBol = bol.GetHashCode();\n// Хеш-значение булевого значения true равно 1;\n\ndouble dec = 3.14159;\nint hashDec = dec.GetHashCode();\n// Хеш-значение числа 3.14159 равно -1340954729;\n\nstring str = \"Hello Algo\";\nint hashStr = str.GetHashCode();\n// Хеш-значение строки \"Hello Algo\" равно -586107568;\n\nobject[] arr = [12836, \"Сяо Ха\"];\nint hashTup = arr.GetHashCode();\n// Хеш-значение массива [12836, Сяо Ха] равно 42931033;\n\nListNode obj = new(0);\nint hashObj = obj.GetHashCode();\n// Хеш-значение объекта узла 0 равно 39053774;\n</code></pre> built_in_hash.go<pre><code>// В Go нет встроенной функции hash code\n</code></pre> built_in_hash.swift<pre><code>let num = 3\nlet hashNum = num.hashValue\n// Хеш-значение целого числа 3 равно 9047044699613009734\n\nlet bol = true\nlet hashBol = bol.hashValue\n// Хеш-значение булевого значения true равно -4431640247352757451\n\nlet dec = 3.14159\nlet hashDec = dec.hashValue\n// Хеш-значение числа 3.14159 равно -2465384235396674631\n\nlet str = \"Hello Algo\"\nlet hashStr = str.hashValue\n// Хеш-значение строки \"Hello Algo\" равно -7850626797806988787\n\nlet arr = [AnyHashable(12836), AnyHashable(\"Сяо Ха\")]\nlet hashTup = arr.hashValue\n// Хеш-значение массива [AnyHashable(12836), AnyHashable(\"Сяо Ха\")] равно -2308633508154532996\n\nlet obj = ListNode(x: 0)\nlet hashObj = obj.hashValue\n// Хеш-значение объекта узла utils.ListNode равно -2434780518035996159\n</code></pre> built_in_hash.js<pre><code>// В JavaScript нет встроенной функции hash code\n</code></pre> built_in_hash.ts<pre><code>// В TypeScript нет встроенной функции hash code\n</code></pre> built_in_hash.dart<pre><code>int num = 3;\nint hashNum = num.hashCode;\n// Хеш-значение целого числа 3 равно 34803\n\nbool bol = true;\nint hashBol = bol.hashCode;\n// Хеш-значение булевого значения true равно 1231\n\ndouble dec = 3.14159;\nint hashDec = dec.hashCode;\n// Хеш-значение числа 3.14159 равно 2570631074981783\n\nString str = \"Hello Algo\";\nint hashStr = str.hashCode;\n// Хеш-значение строки \"Hello Algo\" равно 468167534\n\nList arr = [12836, \"Сяо Ха\"];\nint hashArr = arr.hashCode;\n// Хеш-значение массива [12836, Сяо Ха] равно 976512528\n\nListNode obj = new ListNode(0);\nint hashObj = obj.hashCode;\n// Хеш-значение объекта Instance of 'ListNode' равно 1033450432\n</code></pre> built_in_hash.rs<pre><code>use std::collections::hash_map::DefaultHasher;\nuse std::hash::{Hash, Hasher};\n\nlet num = 3;\nlet mut num_hasher = DefaultHasher::new();\nnum.hash(&amp;mut num_hasher);\nlet hash_num = num_hasher.finish();\n// Хеш-значение целого числа 3 равно 568126464209439262\n\nlet bol = true;\nlet mut bol_hasher = DefaultHasher::new();\nbol.hash(&amp;mut bol_hasher);\nlet hash_bol = bol_hasher.finish();\n// Хеш-значение булевого значения true равно 4952851536318644461\n\nlet dec: f32 = 3.14159;\nlet mut dec_hasher = DefaultHasher::new();\ndec.to_bits().hash(&amp;mut dec_hasher);\nlet hash_dec = dec_hasher.finish();\n// Хеш-значение числа 3.14159 равно 2566941990314602357\n\nlet str = \"Hello Algo\";\nlet mut str_hasher = DefaultHasher::new();\nstr.hash(&amp;mut str_hasher);\nlet hash_str = str_hasher.finish();\n// Хеш-значение строки \"Hello Algo\" равно 16092673739211250988\n\nlet arr = (&amp;12836, &amp;\"Сяо Ха\");\nlet mut tup_hasher = DefaultHasher::new();\narr.hash(&amp;mut tup_hasher);\nlet hash_tup = tup_hasher.finish();\n// Хеш-значение кортежа (12836, \"Сяо Ха\") равно 1885128010422702749\n\nlet node = ListNode::new(42);\nlet mut hasher = DefaultHasher::new();\nnode.borrow().val.hash(&amp;mut hasher);\nlet hash = hasher.finish();\n// Хеш-значение объекта RefCell { value: ListNode { val: 42, next: None } } равно 15387811073369036852\n</code></pre> built_in_hash.c<pre><code>// В C нет встроенной функции hash code\n</code></pre> built_in_hash.kt<pre><code>val num = 3\nval hashNum = num.hashCode()\n// Хеш-значение целого числа 3 равно 3\n\nval bol = true\nval hashBol = bol.hashCode()\n// Хеш-значение булевого значения true равно 1231\n\nval dec = 3.14159\nval hashDec = dec.hashCode()\n// Хеш-значение числа 3.14159 равно -1340954729\n\nval str = \"Hello Algo\"\nval hashStr = str.hashCode()\n// Хеш-значение строки \"Hello Algo\" равно -727081396\n\nval arr = arrayOf&lt;Any&gt;(12836, \"Сяо Ха\")\nval hashTup = arr.hashCode()\n// Хеш-значение массива [12836, Сяо Ха] равно 189568618\n\nval obj = ListNode(0)\nval hashObj = obj.hashCode()\n// Хеш-значение объекта узла utils.ListNode@1d81eb93 равно 495053715\n</code></pre> built_in_hash.rb<pre><code>num = 3\nhash_num = num.hash\n# Хеш-значение целого числа 3 равно -4385856518450339636\n\nbol = true\nhash_bol = bol.hash\n# Хеш-значение булевого значения true равно -1617938112149317027\n\ndec = 3.14159\nhash_dec = dec.hash\n# Хеш-значение числа 3.14159 равно -1479186995943067893\n\nstr = \"Hello Algo\"\nhash_str = str.hash\n# Хеш-значение строки \"Hello Algo\" равно -4075943250025831763\n\ntup = [12836, 'Сяо Ха']\nhash_tup = tup.hash\n# Хеш-значение кортежа (12836, 'Сяо Ха') равно 1999544809202288822\n\nobj = ListNode.new(0)\nhash_obj = obj.hash\n# Хеш-значение объекта #&lt;ListNode:0x000078133140ab70&gt; равно 4302940560806366381\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%D1%81%D0%B2%D1%8F%D0%B7%D0%BD%D1%8B%D0%B9%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%D1%83%D0%B7%D0%B5%D0%BB%D0%BA%D0%BB%D0%B0%D1%81%D1%81%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%D0%97%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%83%D0%B7%D0%BB%D0%B0%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%D0%A1%D1%81%D1%8B%D0%BB%D0%BA%D0%B0%20%D0%BD%D0%B0%20%D1%81%D0%BB%D0%B5%D0%B4%D1%83%D1%8E%D1%89%D0%B8%D0%B9%20%D1%83%D0%B7%D0%B5%D0%BB%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20num%20%3D%203%0A%20%20%20%20hash_num%20%3D%20hash%28num%29%0A%20%20%20%20%23%20%D0%A5%D0%B5%D1%88-%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%86%D0%B5%D0%BB%D0%BE%D0%B3%D0%BE%20%D1%87%D0%B8%D1%81%D0%BB%D0%B0%203%20%D1%80%D0%B0%D0%B2%D0%BD%D0%BE%203%0A%0A%20%20%20%20bol%20%3D%20True%0A%20%20%20%20hash_bol%20%3D%20hash%28bol%29%0A%20%20%20%20%23%20%D0%A5%D0%B5%D1%88-%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D0%B1%D1%83%D0%BB%D0%B5%D0%B2%D0%B0%20%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D1%8F%20True%20%D1%80%D0%B0%D0%B2%D0%BD%D0%BE%201%0A%0A%20%20%20%20dec%20%3D%203.14159%0A%20%20%20%20hash_dec%20%3D%20hash%28dec%29%0A%20%20%20%20%23%20%D0%A5%D0%B5%D1%88-%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%87%D0%B8%D1%81%D0%BB%D0%B0%203.14159%20%D1%80%D0%B0%D0%B2%D0%BD%D0%BE%20326484311674566659%0A%0A%20%20%20%20str%20%3D%20%22Hello%20Algo%22%0A%20%20%20%20hash_str%20%3D%20hash%28str%29%0A%20%20%20%20%23%20%D0%A5%D0%B5%D1%88-%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%81%D1%82%D1%80%D0%BE%D0%BA%D0%B8%20%22Hello%20Algo%22%20%D1%80%D0%B0%D0%B2%D0%BD%D0%BE%204617003410720528961%0A%0A%20%20%20%20tup%20%3D%20%2812836%2C%20%22%D0%A1%D1%8F%D0%BE%20%D0%A5%D0%B0%22%29%0A%20%20%20%20hash_tup%20%3D%20hash%28tup%29%0A%20%20%20%20%23%20%D0%A5%D0%B5%D1%88-%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D0%BA%D0%BE%D1%80%D1%82%D0%B5%D0%B6%D0%B0%20%2812836%2C%20%27%D0%A1%D1%8F%D0%BE%20%D0%A5%D0%B0%27%29%20%D1%80%D0%B0%D0%B2%D0%BD%D0%BE%201029005403108185979%0A%0A%20%20%20%20obj%20%3D%20ListNode%280%29%0A%20%20%20%20hash_obj%20%3D%20hash%28obj%29%0A%20%20%20%20%23%20%D0%A5%D0%B5%D1%88-%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D0%BE%D0%B1%D1%8A%D0%B5%D0%BA%D1%82%D0%B0%20%D1%83%D0%B7%D0%BB%D0%B0%20%3CListNode%20object%20at%200x1058fd810%3E%20%D1%80%D0%B0%D0%B2%D0%BD%D0%BE%20274267521&amp;cumulative=false&amp;curInstr=19&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p> <p>Во многих языках программирования в качестве <code>key</code> хеш-таблицы можно использовать только неизменяемые объекты . Если, например, использовать список (динамический массив) как <code>key</code> , то после изменения содержимого списка изменится и его хеш-значение, из-за чего мы уже не сможем найти прежнее <code>value</code> в хеш-таблице.</p> <p>Хотя у пользовательских объектов (например, у узла связного списка) поля являются изменяемыми, сам объект все же может быть хешируемым. Причина в том, что хеш-значение объекта обычно строится на основе адреса в памяти : даже если содержимое объекта меняется, его адрес памяти остается прежним, а значит, и хеш-значение не меняется.</p> <p>Внимательный читатель мог заметить, что при запуске программы в разных консолях выводимые хеш-значения отличаются. Это связано с тем, что интерпретатор Python при каждом запуске добавляет в хеш-функцию строк случайную соль (salt). Такой подход эффективно защищает от атак типа HashDoS и повышает безопасность хеш-алгоритма.</p>","path":["Глава 6. Хеш-таблицы","6.3 &nbsp; Алгоритмы хеширования"],"tags":[]},{"location":"chapter_hashing/hash_collision/","level":1,"title":"6.2   Хеш-коллизии","text":"<p>Как уже говорилось в предыдущем разделе, в обычных условиях входное пространство хеш-функции намного больше выходного пространства , поэтому теоретически хеш-коллизии неизбежны. Например, если входное пространство состоит из всех целых чисел, а выходное пространство ограничено размером массива, то неизбежно несколько целых чисел будут отображаться в один и тот же индекс бакета.</p> <p>Хеш-коллизии могут приводить к ошибочным результатам поиска и серьезно влиять на работоспособность хеш-таблицы. Чтобы решить эту проблему, можно при каждом конфликте выполнять расширение хеш-таблицы, пока конфликт не исчезнет. Этот метод понятен и прост, но слишком неэффективен, потому что расширение хеш-таблицы требует большого объема переноса данных и вычислений хеш-значений. Чтобы повысить эффективность, можно использовать следующие стратегии.</p> <ol> <li>Улучшить структуру данных хеш-таблицы, чтобы она могла корректно работать даже при возникновении хеш-коллизий.</li> <li>Выполнять расширение только тогда, когда это действительно необходимо, то есть когда хеш-коллизии становятся достаточно серьезными.</li> </ol> <p>Основные способы улучшения структуры хеш-таблицы включают метод цепочек и открытую адресацию.</p>","path":["Глава 6. Хеш-таблицы","6.2 &nbsp; Хеш-коллизии"],"tags":[]},{"location":"chapter_hashing/hash_collision/#621","level":2,"title":"6.2.1   Метод цепочек","text":"<p>В исходной хеш-таблице каждый бакет может хранить только одну пару ключ-значение. Метод цепочек (separate chaining) превращает отдельный элемент в связный список: пары ключ-значение становятся узлами списка, и все конфликтующие пары ключ-значение хранятся в одном и том же списке. На рисунке 6-5 показан пример хеш-таблицы, реализованной методом цепочек.</p> <p></p> <p> Рисунок 6-5   Хеш-таблица с методом цепочек </p> <p>Методы работы с хеш-таблицей, построенной на основе метода цепочек, меняются следующим образом.</p> <ul> <li>Поиск элемента: передаем <code>key</code> , по хеш-функции получаем индекс бакета, после чего обращаемся к голове списка и обходим список, сравнивая <code>key</code> , пока не найдем целевую пару ключ-значение.</li> <li>Добавление элемента: сначала через хеш-функцию получаем голову списка, затем добавляем узел (пару ключ-значение) в этот список.</li> <li>Удаление элемента: по результату хеш-функции обращаемся к голове списка, затем обходим список, находим целевой узел и удаляем его.</li> </ul> <p>Метод цепочек имеет следующие ограничения.</p> <ul> <li>Рост потребления памяти: связный список содержит указатели на узлы, поэтому по сравнению с массивом он требует больше памяти.</li> <li>Снижение эффективности поиска: для нахождения нужного элемента нужно линейно обходить связный список.</li> </ul> <p>Ниже приведена простая реализация хеш-таблицы методом цепочек. Следует обратить внимание на два момента.</p> <ul> <li>Для упрощения кода вместо связного списка используется список (динамический массив). В этой реализации хеш-таблица (массив) содержит несколько бакетов, и каждый бакет представляет собой список.</li> <li>Ниже включен метод расширения хеш-таблицы. Когда коэффициент загрузки превышает \\(\\frac{2}{3}\\) , мы расширяем хеш-таблицу до \\(2\\) раз от прежней емкости.</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby hash_map_chaining.py<pre><code>class HashMapChaining:\n    \"\"\"Хеш-таблица с цепочками\"\"\"\n\n    def __init__(self):\n        \"\"\"Конструктор\"\"\"\n        self.size = 0  # Число пар ключ-значение\n        self.capacity = 4  # Вместимость хеш-таблицы\n        self.load_thres = 2.0 / 3.0  # Порог коэффициента загрузки для запуска расширения\n        self.extend_ratio = 2  # Коэффициент расширения\n        self.buckets = [[] for _ in range(self.capacity)]  # Массив корзин\n\n    def hash_func(self, key: int) -&gt; int:\n        \"\"\"Хеш-функция\"\"\"\n        return key % self.capacity\n\n    def load_factor(self) -&gt; float:\n        \"\"\"Коэффициент загрузки\"\"\"\n        return self.size / self.capacity\n\n    def get(self, key: int) -&gt; str | None:\n        \"\"\"Операция поиска\"\"\"\n        index = self.hash_func(key)\n        bucket = self.buckets[index]\n        # Обойти корзину; если найден key, вернуть соответствующее val\n        for pair in bucket:\n            if pair.key == key:\n                return pair.val\n        # Если key не найден, вернуть None\n        return None\n\n    def put(self, key: int, val: str):\n        \"\"\"Операция добавления\"\"\"\n        # Когда коэффициент загрузки превышает порог, выполнить расширение\n        if self.load_factor() &gt; self.load_thres:\n            self.extend()\n        index = self.hash_func(key)\n        bucket = self.buckets[index]\n        # Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n        for pair in bucket:\n            if pair.key == key:\n                pair.val = val\n                return\n        # Если такого key нет, добавить пару ключ-значение в конец\n        pair = Pair(key, val)\n        bucket.append(pair)\n        self.size += 1\n\n    def remove(self, key: int):\n        \"\"\"Операция удаления\"\"\"\n        index = self.hash_func(key)\n        bucket = self.buckets[index]\n        # Обойти корзину и удалить из нее пару ключ-значение\n        for pair in bucket:\n            if pair.key == key:\n                bucket.remove(pair)\n                self.size -= 1\n                break\n\n    def extend(self):\n        \"\"\"Расширить хеш-таблицу\"\"\"\n        # Временно сохранить исходную хеш-таблицу\n        buckets = self.buckets\n        # Инициализация новой хеш-таблицы после расширения\n        self.capacity *= self.extend_ratio\n        self.buckets = [[] for _ in range(self.capacity)]\n        self.size = 0\n        # Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for bucket in buckets:\n            for pair in bucket:\n                self.put(pair.key, pair.val)\n\n    def print(self):\n        \"\"\"Вывести хеш-таблицу\"\"\"\n        for bucket in self.buckets:\n            res = []\n            for pair in bucket:\n                res.append(str(pair.key) + \" -&gt; \" + pair.val)\n            print(res)\n</code></pre> hash_map_chaining.cpp<pre><code>/* Хеш-таблица с цепочками */\nclass HashMapChaining {\n  private:\n    int size;                       // Число пар ключ-значение\n    int capacity;                   // Вместимость хеш-таблицы\n    double loadThres;               // Порог коэффициента загрузки для запуска расширения\n    int extendRatio;                // Коэффициент расширения\n    vector&lt;vector&lt;Pair *&gt;&gt; buckets; // Массив корзин\n\n  public:\n    /* Конструктор */\n    HashMapChaining() : size(0), capacity(4), loadThres(2.0 / 3.0), extendRatio(2) {\n        buckets.resize(capacity);\n    }\n\n    /* Метод-деструктор */\n    ~HashMapChaining() {\n        for (auto &amp;bucket : buckets) {\n            for (Pair *pair : bucket) {\n                // Освободить память\n                delete pair;\n            }\n        }\n    }\n\n    /* Хеш-функция */\n    int hashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* Коэффициент загрузки */\n    double loadFactor() {\n        return (double)size / (double)capacity;\n    }\n\n    /* Операция поиска */\n    string get(int key) {\n        int index = hashFunc(key);\n        // Обойти корзину; если найден key, вернуть соответствующее val\n        for (Pair *pair : buckets[index]) {\n            if (pair-&gt;key == key) {\n                return pair-&gt;val;\n            }\n        }\n        // Если key не найден, вернуть пустую строку\n        return \"\";\n    }\n\n    /* Операция добавления */\n    void put(int key, string val) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if (loadFactor() &gt; loadThres) {\n            extend();\n        }\n        int index = hashFunc(key);\n        // Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n        for (Pair *pair : buckets[index]) {\n            if (pair-&gt;key == key) {\n                pair-&gt;val = val;\n                return;\n            }\n        }\n        // Если такого key нет, добавить пару ключ-значение в конец\n        buckets[index].push_back(new Pair(key, val));\n        size++;\n    }\n\n    /* Операция удаления */\n    void remove(int key) {\n        int index = hashFunc(key);\n        auto &amp;bucket = buckets[index];\n        // Обойти корзину и удалить из нее пару ключ-значение\n        for (int i = 0; i &lt; bucket.size(); i++) {\n            if (bucket[i]-&gt;key == key) {\n                Pair *tmp = bucket[i];\n                bucket.erase(bucket.begin() + i); // Удалить из него пару ключ-значение\n                delete tmp;                       // Освободить память\n                size--;\n                return;\n            }\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    void extend() {\n        // Временно сохранить исходную хеш-таблицу\n        vector&lt;vector&lt;Pair *&gt;&gt; bucketsTmp = buckets;\n        // Инициализация новой хеш-таблицы после расширения\n        capacity *= extendRatio;\n        buckets.clear();\n        buckets.resize(capacity);\n        size = 0;\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for (auto &amp;bucket : bucketsTmp) {\n            for (Pair *pair : bucket) {\n                put(pair-&gt;key, pair-&gt;val);\n                // Освободить память\n                delete pair;\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    void print() {\n        for (auto &amp;bucket : buckets) {\n            cout &lt;&lt; \"[\";\n            for (Pair *pair : bucket) {\n                cout &lt;&lt; pair-&gt;key &lt;&lt; \" -&gt; \" &lt;&lt; pair-&gt;val &lt;&lt; \", \";\n            }\n            cout &lt;&lt; \"]\\n\";\n        }\n    }\n};\n</code></pre> hash_map_chaining.java<pre><code>/* Хеш-таблица с цепочками */\nclass HashMapChaining {\n    int size; // Число пар ключ-значение\n    int capacity; // Вместимость хеш-таблицы\n    double loadThres; // Порог коэффициента загрузки для запуска расширения\n    int extendRatio; // Коэффициент расширения\n    List&lt;List&lt;Pair&gt;&gt; buckets; // Массив корзин\n\n    /* Конструктор */\n    public HashMapChaining() {\n        size = 0;\n        capacity = 4;\n        loadThres = 2.0 / 3.0;\n        extendRatio = 2;\n        buckets = new ArrayList&lt;&gt;(capacity);\n        for (int i = 0; i &lt; capacity; i++) {\n            buckets.add(new ArrayList&lt;&gt;());\n        }\n    }\n\n    /* Хеш-функция */\n    int hashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* Коэффициент загрузки */\n    double loadFactor() {\n        return (double) size / capacity;\n    }\n\n    /* Операция поиска */\n    String get(int key) {\n        int index = hashFunc(key);\n        List&lt;Pair&gt; bucket = buckets.get(index);\n        // Обойти корзину; если найден key, вернуть соответствующее val\n        for (Pair pair : bucket) {\n            if (pair.key == key) {\n                return pair.val;\n            }\n        }\n        // Если key не найден, вернуть null\n        return null;\n    }\n\n    /* Операция добавления */\n    void put(int key, String val) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if (loadFactor() &gt; loadThres) {\n            extend();\n        }\n        int index = hashFunc(key);\n        List&lt;Pair&gt; bucket = buckets.get(index);\n        // Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n        for (Pair pair : bucket) {\n            if (pair.key == key) {\n                pair.val = val;\n                return;\n            }\n        }\n        // Если такого key нет, добавить пару ключ-значение в конец\n        Pair pair = new Pair(key, val);\n        bucket.add(pair);\n        size++;\n    }\n\n    /* Операция удаления */\n    void remove(int key) {\n        int index = hashFunc(key);\n        List&lt;Pair&gt; bucket = buckets.get(index);\n        // Обойти корзину и удалить из нее пару ключ-значение\n        for (Pair pair : bucket) {\n            if (pair.key == key) {\n                bucket.remove(pair);\n                size--;\n                break;\n            }\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    void extend() {\n        // Временно сохранить исходную хеш-таблицу\n        List&lt;List&lt;Pair&gt;&gt; bucketsTmp = buckets;\n        // Инициализация новой хеш-таблицы после расширения\n        capacity *= extendRatio;\n        buckets = new ArrayList&lt;&gt;(capacity);\n        for (int i = 0; i &lt; capacity; i++) {\n            buckets.add(new ArrayList&lt;&gt;());\n        }\n        size = 0;\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for (List&lt;Pair&gt; bucket : bucketsTmp) {\n            for (Pair pair : bucket) {\n                put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    void print() {\n        for (List&lt;Pair&gt; bucket : buckets) {\n            List&lt;String&gt; res = new ArrayList&lt;&gt;();\n            for (Pair pair : bucket) {\n                res.add(pair.key + \" -&gt; \" + pair.val);\n            }\n            System.out.println(res);\n        }\n    }\n}\n</code></pre> hash_map_chaining.cs<pre><code>/* Хеш-таблица с цепочками */\nclass HashMapChaining {\n    int size; // Число пар ключ-значение\n    int capacity; // Вместимость хеш-таблицы\n    double loadThres; // Порог коэффициента загрузки для запуска расширения\n    int extendRatio; // Коэффициент расширения\n    List&lt;List&lt;Pair&gt;&gt; buckets; // Массив корзин\n\n    /* Конструктор */\n    public HashMapChaining() {\n        size = 0;\n        capacity = 4;\n        loadThres = 2.0 / 3.0;\n        extendRatio = 2;\n        buckets = new List&lt;List&lt;Pair&gt;&gt;(capacity);\n        for (int i = 0; i &lt; capacity; i++) {\n            buckets.Add([]);\n        }\n    }\n\n    /* Хеш-функция */\n    int HashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* Коэффициент загрузки */\n    double LoadFactor() {\n        return (double)size / capacity;\n    }\n\n    /* Операция поиска */\n    public string? Get(int key) {\n        int index = HashFunc(key);\n        // Обойти корзину; если найден key, вернуть соответствующее val\n        foreach (Pair pair in buckets[index]) {\n            if (pair.key == key) {\n                return pair.val;\n            }\n        }\n        // Если key не найден, вернуть null\n        return null;\n    }\n\n    /* Операция добавления */\n    public void Put(int key, string val) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if (LoadFactor() &gt; loadThres) {\n            Extend();\n        }\n        int index = HashFunc(key);\n        // Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n        foreach (Pair pair in buckets[index]) {\n            if (pair.key == key) {\n                pair.val = val;\n                return;\n            }\n        }\n        // Если такого key нет, добавить пару ключ-значение в конец\n        buckets[index].Add(new Pair(key, val));\n        size++;\n    }\n\n    /* Операция удаления */\n    public void Remove(int key) {\n        int index = HashFunc(key);\n        // Обойти корзину и удалить из нее пару ключ-значение\n        foreach (Pair pair in buckets[index].ToList()) {\n            if (pair.key == key) {\n                buckets[index].Remove(pair);\n                size--;\n                break;\n            }\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    void Extend() {\n        // Временно сохранить исходную хеш-таблицу\n        List&lt;List&lt;Pair&gt;&gt; bucketsTmp = buckets;\n        // Инициализация новой хеш-таблицы после расширения\n        capacity *= extendRatio;\n        buckets = new List&lt;List&lt;Pair&gt;&gt;(capacity);\n        for (int i = 0; i &lt; capacity; i++) {\n            buckets.Add([]);\n        }\n        size = 0;\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        foreach (List&lt;Pair&gt; bucket in bucketsTmp) {\n            foreach (Pair pair in bucket) {\n                Put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    public void Print() {\n        foreach (List&lt;Pair&gt; bucket in buckets) {\n            List&lt;string&gt; res = [];\n            foreach (Pair pair in bucket) {\n                res.Add(pair.key + \" -&gt; \" + pair.val);\n            }\n            foreach (string kv in res) {\n                Console.WriteLine(kv);\n            }\n        }\n    }\n}\n</code></pre> hash_map_chaining.go<pre><code>/* Хеш-таблица с цепочками */\ntype hashMapChaining struct {\n    size        int      // Число пар ключ-значение\n    capacity    int      // Вместимость хеш-таблицы\n    loadThres   float64  // Порог коэффициента загрузки для запуска расширения\n    extendRatio int      // Коэффициент расширения\n    buckets     [][]pair // Массив корзин\n}\n\n/* Конструктор */\nfunc newHashMapChaining() *hashMapChaining {\n    buckets := make([][]pair, 4)\n    for i := 0; i &lt; 4; i++ {\n        buckets[i] = make([]pair, 0)\n    }\n    return &amp;hashMapChaining{\n        size:        0,\n        capacity:    4,\n        loadThres:   2.0 / 3.0,\n        extendRatio: 2,\n        buckets:     buckets,\n    }\n}\n\n/* Хеш-функция */\nfunc (m *hashMapChaining) hashFunc(key int) int {\n    return key % m.capacity\n}\n\n/* Коэффициент загрузки */\nfunc (m *hashMapChaining) loadFactor() float64 {\n    return float64(m.size) / float64(m.capacity)\n}\n\n/* Операция поиска */\nfunc (m *hashMapChaining) get(key int) string {\n    idx := m.hashFunc(key)\n    bucket := m.buckets[idx]\n    // Обойти корзину; если найден key, вернуть соответствующее val\n    for _, p := range bucket {\n        if p.key == key {\n            return p.val\n        }\n    }\n    // Если key не найден, вернуть пустую строку\n    return \"\"\n}\n\n/* Операция добавления */\nfunc (m *hashMapChaining) put(key int, val string) {\n    // Когда коэффициент загрузки превышает порог, выполнить расширение\n    if m.loadFactor() &gt; m.loadThres {\n        m.extend()\n    }\n    idx := m.hashFunc(key)\n    // Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n    for i := range m.buckets[idx] {\n        if m.buckets[idx][i].key == key {\n            m.buckets[idx][i].val = val\n            return\n        }\n    }\n    // Если такого key нет, добавить пару ключ-значение в конец\n    p := pair{\n        key: key,\n        val: val,\n    }\n    m.buckets[idx] = append(m.buckets[idx], p)\n    m.size += 1\n}\n\n/* Операция удаления */\nfunc (m *hashMapChaining) remove(key int) {\n    idx := m.hashFunc(key)\n    // Обойти корзину и удалить из нее пару ключ-значение\n    for i, p := range m.buckets[idx] {\n        if p.key == key {\n            // Удаление из среза\n            m.buckets[idx] = append(m.buckets[idx][:i], m.buckets[idx][i+1:]...)\n            m.size -= 1\n            break\n        }\n    }\n}\n\n/* Расширить хеш-таблицу */\nfunc (m *hashMapChaining) extend() {\n    // Временно сохранить исходную хеш-таблицу\n    tmpBuckets := make([][]pair, len(m.buckets))\n    for i := 0; i &lt; len(m.buckets); i++ {\n        tmpBuckets[i] = make([]pair, len(m.buckets[i]))\n        copy(tmpBuckets[i], m.buckets[i])\n    }\n    // Инициализация новой хеш-таблицы после расширения\n    m.capacity *= m.extendRatio\n    m.buckets = make([][]pair, m.capacity)\n    for i := 0; i &lt; m.capacity; i++ {\n        m.buckets[i] = make([]pair, 0)\n    }\n    m.size = 0\n    // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n    for _, bucket := range tmpBuckets {\n        for _, p := range bucket {\n            m.put(p.key, p.val)\n        }\n    }\n}\n\n/* Вывести хеш-таблицу */\nfunc (m *hashMapChaining) print() {\n    var builder strings.Builder\n\n    for _, bucket := range m.buckets {\n        builder.WriteString(\"[\")\n        for _, p := range bucket {\n            builder.WriteString(strconv.Itoa(p.key) + \" -&gt; \" + p.val + \" \")\n        }\n        builder.WriteString(\"]\")\n        fmt.Println(builder.String())\n        builder.Reset()\n    }\n}\n</code></pre> hash_map_chaining.swift<pre><code>/* Хеш-таблица с цепочками */\nclass HashMapChaining {\n    var size: Int // Число пар ключ-значение\n    var capacity: Int // Вместимость хеш-таблицы\n    var loadThres: Double // Порог коэффициента загрузки для запуска расширения\n    var extendRatio: Int // Коэффициент расширения\n    var buckets: [[Pair]] // Массив корзин\n\n    /* Конструктор */\n    init() {\n        size = 0\n        capacity = 4\n        loadThres = 2.0 / 3.0\n        extendRatio = 2\n        buckets = Array(repeating: [], count: capacity)\n    }\n\n    /* Хеш-функция */\n    func hashFunc(key: Int) -&gt; Int {\n        key % capacity\n    }\n\n    /* Коэффициент загрузки */\n    func loadFactor() -&gt; Double {\n        Double(size) / Double(capacity)\n    }\n\n    /* Операция поиска */\n    func get(key: Int) -&gt; String? {\n        let index = hashFunc(key: key)\n        let bucket = buckets[index]\n        // Обойти корзину; если найден key, вернуть соответствующее val\n        for pair in bucket {\n            if pair.key == key {\n                return pair.val\n            }\n        }\n        // Если key не найден, вернуть nil\n        return nil\n    }\n\n    /* Операция добавления */\n    func put(key: Int, val: String) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if loadFactor() &gt; loadThres {\n            extend()\n        }\n        let index = hashFunc(key: key)\n        let bucket = buckets[index]\n        // Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n        for pair in bucket {\n            if pair.key == key {\n                pair.val = val\n                return\n            }\n        }\n        // Если такого key нет, добавить пару ключ-значение в конец\n        let pair = Pair(key: key, val: val)\n        buckets[index].append(pair)\n        size += 1\n    }\n\n    /* Операция удаления */\n    func remove(key: Int) {\n        let index = hashFunc(key: key)\n        let bucket = buckets[index]\n        // Обойти корзину и удалить из нее пару ключ-значение\n        for (pairIndex, pair) in bucket.enumerated() {\n            if pair.key == key {\n                buckets[index].remove(at: pairIndex)\n                size -= 1\n                break\n            }\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    func extend() {\n        // Временно сохранить исходную хеш-таблицу\n        let bucketsTmp = buckets\n        // Инициализация новой хеш-таблицы после расширения\n        capacity *= extendRatio\n        buckets = Array(repeating: [], count: capacity)\n        size = 0\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for bucket in bucketsTmp {\n            for pair in bucket {\n                put(key: pair.key, val: pair.val)\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    func print() {\n        for bucket in buckets {\n            let res = bucket.map { \"\\($0.key) -&gt; \\($0.val)\" }\n            Swift.print(res)\n        }\n    }\n}\n</code></pre> hash_map_chaining.js<pre><code>/* Хеш-таблица с цепочками */\nclass HashMapChaining {\n    #size; // Число пар ключ-значение\n    #capacity; // Вместимость хеш-таблицы\n    #loadThres; // Порог коэффициента загрузки для запуска расширения\n    #extendRatio; // Коэффициент расширения\n    #buckets; // Массив корзин\n\n    /* Конструктор */\n    constructor() {\n        this.#size = 0;\n        this.#capacity = 4;\n        this.#loadThres = 2.0 / 3.0;\n        this.#extendRatio = 2;\n        this.#buckets = new Array(this.#capacity).fill(null).map((x) =&gt; []);\n    }\n\n    /* Хеш-функция */\n    #hashFunc(key) {\n        return key % this.#capacity;\n    }\n\n    /* Коэффициент загрузки */\n    #loadFactor() {\n        return this.#size / this.#capacity;\n    }\n\n    /* Операция поиска */\n    get(key) {\n        const index = this.#hashFunc(key);\n        const bucket = this.#buckets[index];\n        // Обойти корзину; если найден key, вернуть соответствующее val\n        for (const pair of bucket) {\n            if (pair.key === key) {\n                return pair.val;\n            }\n        }\n        // Если key не найден, вернуть null\n        return null;\n    }\n\n    /* Операция добавления */\n    put(key, val) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if (this.#loadFactor() &gt; this.#loadThres) {\n            this.#extend();\n        }\n        const index = this.#hashFunc(key);\n        const bucket = this.#buckets[index];\n        // Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n        for (const pair of bucket) {\n            if (pair.key === key) {\n                pair.val = val;\n                return;\n            }\n        }\n        // Если такого key нет, добавить пару ключ-значение в конец\n        const pair = new Pair(key, val);\n        bucket.push(pair);\n        this.#size++;\n    }\n\n    /* Операция удаления */\n    remove(key) {\n        const index = this.#hashFunc(key);\n        let bucket = this.#buckets[index];\n        // Обойти корзину и удалить из нее пару ключ-значение\n        for (let i = 0; i &lt; bucket.length; i++) {\n            if (bucket[i].key === key) {\n                bucket.splice(i, 1);\n                this.#size--;\n                break;\n            }\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    #extend() {\n        // Временно сохранить исходную хеш-таблицу\n        const bucketsTmp = this.#buckets;\n        // Инициализация новой хеш-таблицы после расширения\n        this.#capacity *= this.#extendRatio;\n        this.#buckets = new Array(this.#capacity).fill(null).map((x) =&gt; []);\n        this.#size = 0;\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for (const bucket of bucketsTmp) {\n            for (const pair of bucket) {\n                this.put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    print() {\n        for (const bucket of this.#buckets) {\n            let res = [];\n            for (const pair of bucket) {\n                res.push(pair.key + ' -&gt; ' + pair.val);\n            }\n            console.log(res);\n        }\n    }\n}\n</code></pre> hash_map_chaining.ts<pre><code>/* Хеш-таблица с цепочками */\nclass HashMapChaining {\n    #size: number; // Число пар ключ-значение\n    #capacity: number; // Вместимость хеш-таблицы\n    #loadThres: number; // Порог коэффициента загрузки для запуска расширения\n    #extendRatio: number; // Коэффициент расширения\n    #buckets: Pair[][]; // Массив корзин\n\n    /* Конструктор */\n    constructor() {\n        this.#size = 0;\n        this.#capacity = 4;\n        this.#loadThres = 2.0 / 3.0;\n        this.#extendRatio = 2;\n        this.#buckets = new Array(this.#capacity).fill(null).map((x) =&gt; []);\n    }\n\n    /* Хеш-функция */\n    #hashFunc(key: number): number {\n        return key % this.#capacity;\n    }\n\n    /* Коэффициент загрузки */\n    #loadFactor(): number {\n        return this.#size / this.#capacity;\n    }\n\n    /* Операция поиска */\n    get(key: number): string | null {\n        const index = this.#hashFunc(key);\n        const bucket = this.#buckets[index];\n        // Обойти корзину; если найден key, вернуть соответствующее val\n        for (const pair of bucket) {\n            if (pair.key === key) {\n                return pair.val;\n            }\n        }\n        // Если key не найден, вернуть null\n        return null;\n    }\n\n    /* Операция добавления */\n    put(key: number, val: string): void {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if (this.#loadFactor() &gt; this.#loadThres) {\n            this.#extend();\n        }\n        const index = this.#hashFunc(key);\n        const bucket = this.#buckets[index];\n        // Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n        for (const pair of bucket) {\n            if (pair.key === key) {\n                pair.val = val;\n                return;\n            }\n        }\n        // Если такого key нет, добавить пару ключ-значение в конец\n        const pair = new Pair(key, val);\n        bucket.push(pair);\n        this.#size++;\n    }\n\n    /* Операция удаления */\n    remove(key: number): void {\n        const index = this.#hashFunc(key);\n        let bucket = this.#buckets[index];\n        // Обойти корзину и удалить из нее пару ключ-значение\n        for (let i = 0; i &lt; bucket.length; i++) {\n            if (bucket[i].key === key) {\n                bucket.splice(i, 1);\n                this.#size--;\n                break;\n            }\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    #extend(): void {\n        // Временно сохранить исходную хеш-таблицу\n        const bucketsTmp = this.#buckets;\n        // Инициализация новой хеш-таблицы после расширения\n        this.#capacity *= this.#extendRatio;\n        this.#buckets = new Array(this.#capacity).fill(null).map((x) =&gt; []);\n        this.#size = 0;\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for (const bucket of bucketsTmp) {\n            for (const pair of bucket) {\n                this.put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    print(): void {\n        for (const bucket of this.#buckets) {\n            let res = [];\n            for (const pair of bucket) {\n                res.push(pair.key + ' -&gt; ' + pair.val);\n            }\n            console.log(res);\n        }\n    }\n}\n</code></pre> hash_map_chaining.dart<pre><code>/* Хеш-таблица с цепочками */\nclass HashMapChaining {\n  late int size; // Число пар ключ-значение\n  late int capacity; // Вместимость хеш-таблицы\n  late double loadThres; // Порог коэффициента загрузки для запуска расширения\n  late int extendRatio; // Коэффициент расширения\n  late List&lt;List&lt;Pair&gt;&gt; buckets; // Массив корзин\n\n  /* Конструктор */\n  HashMapChaining() {\n    size = 0;\n    capacity = 4;\n    loadThres = 2.0 / 3.0;\n    extendRatio = 2;\n    buckets = List.generate(capacity, (_) =&gt; []);\n  }\n\n  /* Хеш-функция */\n  int hashFunc(int key) {\n    return key % capacity;\n  }\n\n  /* Коэффициент загрузки */\n  double loadFactor() {\n    return size / capacity;\n  }\n\n  /* Операция поиска */\n  String? get(int key) {\n    int index = hashFunc(key);\n    List&lt;Pair&gt; bucket = buckets[index];\n    // Обойти корзину; если найден key, вернуть соответствующее val\n    for (Pair pair in bucket) {\n      if (pair.key == key) {\n        return pair.val;\n      }\n    }\n    // Если key не найден, вернуть null\n    return null;\n  }\n\n  /* Операция добавления */\n  void put(int key, String val) {\n    // Когда коэффициент загрузки превышает порог, выполнить расширение\n    if (loadFactor() &gt; loadThres) {\n      extend();\n    }\n    int index = hashFunc(key);\n    List&lt;Pair&gt; bucket = buckets[index];\n    // Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n    for (Pair pair in bucket) {\n      if (pair.key == key) {\n        pair.val = val;\n        return;\n      }\n    }\n    // Если такого key нет, добавить пару ключ-значение в конец\n    Pair pair = Pair(key, val);\n    bucket.add(pair);\n    size++;\n  }\n\n  /* Операция удаления */\n  void remove(int key) {\n    int index = hashFunc(key);\n    List&lt;Pair&gt; bucket = buckets[index];\n    // Обойти корзину и удалить из нее пару ключ-значение\n    for (Pair pair in bucket) {\n      if (pair.key == key) {\n        bucket.remove(pair);\n        size--;\n        break;\n      }\n    }\n  }\n\n  /* Расширить хеш-таблицу */\n  void extend() {\n    // Временно сохранить исходную хеш-таблицу\n    List&lt;List&lt;Pair&gt;&gt; bucketsTmp = buckets;\n    // Инициализация новой хеш-таблицы после расширения\n    capacity *= extendRatio;\n    buckets = List.generate(capacity, (_) =&gt; []);\n    size = 0;\n    // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n    for (List&lt;Pair&gt; bucket in bucketsTmp) {\n      for (Pair pair in bucket) {\n        put(pair.key, pair.val);\n      }\n    }\n  }\n\n  /* Вывести хеш-таблицу */\n  void printHashMap() {\n    for (List&lt;Pair&gt; bucket in buckets) {\n      List&lt;String&gt; res = [];\n      for (Pair pair in bucket) {\n        res.add(\"${pair.key} -&gt; ${pair.val}\");\n      }\n      print(res);\n    }\n  }\n}\n</code></pre> hash_map_chaining.rs<pre><code>/* Хеш-таблица с цепочками */\nstruct HashMapChaining {\n    size: usize,\n    capacity: usize,\n    load_thres: f32,\n    extend_ratio: usize,\n    buckets: Vec&lt;Vec&lt;Pair&gt;&gt;,\n}\n\nimpl HashMapChaining {\n    /* Конструктор */\n    fn new() -&gt; Self {\n        Self {\n            size: 0,\n            capacity: 4,\n            load_thres: 2.0 / 3.0,\n            extend_ratio: 2,\n            buckets: vec![vec![]; 4],\n        }\n    }\n\n    /* Хеш-функция */\n    fn hash_func(&amp;self, key: i32) -&gt; usize {\n        key as usize % self.capacity\n    }\n\n    /* Коэффициент загрузки */\n    fn load_factor(&amp;self) -&gt; f32 {\n        self.size as f32 / self.capacity as f32\n    }\n\n    /* Операция удаления */\n    fn remove(&amp;mut self, key: i32) -&gt; Option&lt;String&gt; {\n        let index = self.hash_func(key);\n\n        // Обойти корзину и удалить из нее пару ключ-значение\n        for (i, p) in self.buckets[index].iter_mut().enumerate() {\n            if p.key == key {\n                let pair = self.buckets[index].remove(i);\n                self.size -= 1;\n                return Some(pair.val);\n            }\n        }\n\n        // Если key не найден, вернуть None\n        None\n    }\n\n    /* Расширить хеш-таблицу */\n    fn extend(&amp;mut self) {\n        // Временно сохранить исходную хеш-таблицу\n        let buckets_tmp = std::mem::take(&amp;mut self.buckets);\n\n        // Инициализация новой хеш-таблицы после расширения\n        self.capacity *= self.extend_ratio;\n        self.buckets = vec![Vec::new(); self.capacity as usize];\n        self.size = 0;\n\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for bucket in buckets_tmp {\n            for pair in bucket {\n                self.put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    fn print(&amp;self) {\n        for bucket in &amp;self.buckets {\n            let mut res = Vec::new();\n            for pair in bucket {\n                res.push(format!(\"{} -&gt; {}\", pair.key, pair.val));\n            }\n            println!(\"{:?}\", res);\n        }\n    }\n\n    /* Операция добавления */\n    fn put(&amp;mut self, key: i32, val: String) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if self.load_factor() &gt; self.load_thres {\n            self.extend();\n        }\n\n        let index = self.hash_func(key);\n\n        // Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n        for pair in self.buckets[index].iter_mut() {\n            if pair.key == key {\n                pair.val = val;\n                return;\n            }\n        }\n\n        // Если такого key нет, добавить пару ключ-значение в конец\n        let pair = Pair { key, val };\n        self.buckets[index].push(pair);\n        self.size += 1;\n    }\n\n    /* Операция поиска */\n    fn get(&amp;self, key: i32) -&gt; Option&lt;&amp;str&gt; {\n        let index = self.hash_func(key);\n\n        // Обойти корзину; если найден key, вернуть соответствующее val\n        for pair in self.buckets[index].iter() {\n            if pair.key == key {\n                return Some(&amp;pair.val);\n            }\n        }\n\n        // Если key не найден, вернуть None\n        None\n    }\n}\n</code></pre> hash_map_chaining.c<pre><code>/* Узел связного списка */\ntypedef struct Node {\n    Pair *pair;\n    struct Node *next;\n} Node;\n\n/* Хеш-таблица с цепочками */\ntypedef struct {\n    int size;         // Число пар ключ-значение\n    int capacity;     // Вместимость хеш-таблицы\n    double loadThres; // Порог коэффициента загрузки для запуска расширения\n    int extendRatio;  // Коэффициент расширения\n    Node **buckets;   // Массив корзин\n} HashMapChaining;\n\n/* Конструктор */\nHashMapChaining *newHashMapChaining() {\n    HashMapChaining *hashMap = (HashMapChaining *)malloc(sizeof(HashMapChaining));\n    hashMap-&gt;size = 0;\n    hashMap-&gt;capacity = 4;\n    hashMap-&gt;loadThres = 2.0 / 3.0;\n    hashMap-&gt;extendRatio = 2;\n    hashMap-&gt;buckets = (Node **)malloc(hashMap-&gt;capacity * sizeof(Node *));\n    for (int i = 0; i &lt; hashMap-&gt;capacity; i++) {\n        hashMap-&gt;buckets[i] = NULL;\n    }\n    return hashMap;\n}\n\n/* Деструктор */\nvoid delHashMapChaining(HashMapChaining *hashMap) {\n    for (int i = 0; i &lt; hashMap-&gt;capacity; i++) {\n        Node *cur = hashMap-&gt;buckets[i];\n        while (cur) {\n            Node *tmp = cur;\n            cur = cur-&gt;next;\n            free(tmp-&gt;pair);\n            free(tmp);\n        }\n    }\n    free(hashMap-&gt;buckets);\n    free(hashMap);\n}\n\n/* Хеш-функция */\nint hashFunc(HashMapChaining *hashMap, int key) {\n    return key % hashMap-&gt;capacity;\n}\n\n/* Коэффициент загрузки */\ndouble loadFactor(HashMapChaining *hashMap) {\n    return (double)hashMap-&gt;size / (double)hashMap-&gt;capacity;\n}\n\n/* Операция поиска */\nchar *get(HashMapChaining *hashMap, int key) {\n    int index = hashFunc(hashMap, key);\n    // Обойти корзину; если найден key, вернуть соответствующее val\n    Node *cur = hashMap-&gt;buckets[index];\n    while (cur) {\n        if (cur-&gt;pair-&gt;key == key) {\n            return cur-&gt;pair-&gt;val;\n        }\n        cur = cur-&gt;next;\n    }\n    return \"\"; // Если key не найден, вернуть пустую строку\n}\n\n/* Операция добавления */\nvoid put(HashMapChaining *hashMap, int key, const char *val) {\n    // Когда коэффициент загрузки превышает порог, выполнить расширение\n    if (loadFactor(hashMap) &gt; hashMap-&gt;loadThres) {\n        extend(hashMap);\n    }\n    int index = hashFunc(hashMap, key);\n    // Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n    Node *cur = hashMap-&gt;buckets[index];\n    while (cur) {\n        if (cur-&gt;pair-&gt;key == key) {\n            strcpy(cur-&gt;pair-&gt;val, val); // Если встретился указанный key, обновить соответствующий val и вернуть\n            return;\n        }\n        cur = cur-&gt;next;\n    }\n    // Если такого key нет, добавить пару ключ-значение в голову связного списка\n    Pair *newPair = (Pair *)malloc(sizeof(Pair));\n    newPair-&gt;key = key;\n    strcpy(newPair-&gt;val, val);\n    Node *newNode = (Node *)malloc(sizeof(Node));\n    newNode-&gt;pair = newPair;\n    newNode-&gt;next = hashMap-&gt;buckets[index];\n    hashMap-&gt;buckets[index] = newNode;\n    hashMap-&gt;size++;\n}\n\n/* Расширить хеш-таблицу */\nvoid extend(HashMapChaining *hashMap) {\n    // Временно сохранить исходную хеш-таблицу\n    int oldCapacity = hashMap-&gt;capacity;\n    Node **oldBuckets = hashMap-&gt;buckets;\n    // Инициализация новой хеш-таблицы после расширения\n    hashMap-&gt;capacity *= hashMap-&gt;extendRatio;\n    hashMap-&gt;buckets = (Node **)malloc(hashMap-&gt;capacity * sizeof(Node *));\n    for (int i = 0; i &lt; hashMap-&gt;capacity; i++) {\n        hashMap-&gt;buckets[i] = NULL;\n    }\n    hashMap-&gt;size = 0;\n    // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n    for (int i = 0; i &lt; oldCapacity; i++) {\n        Node *cur = oldBuckets[i];\n        while (cur) {\n            put(hashMap, cur-&gt;pair-&gt;key, cur-&gt;pair-&gt;val);\n            Node *temp = cur;\n            cur = cur-&gt;next;\n            // Освободить память\n            free(temp-&gt;pair);\n            free(temp);\n        }\n    }\n\n    free(oldBuckets);\n}\n\n/* Операция удаления */\nvoid removeItem(HashMapChaining *hashMap, int key) {\n    int index = hashFunc(hashMap, key);\n    Node *cur = hashMap-&gt;buckets[index];\n    Node *pre = NULL;\n    while (cur) {\n        if (cur-&gt;pair-&gt;key == key) {\n            // Удалить из него пару ключ-значение\n            if (pre) {\n                pre-&gt;next = cur-&gt;next;\n            } else {\n                hashMap-&gt;buckets[index] = cur-&gt;next;\n            }\n            // Освободить память\n            free(cur-&gt;pair);\n            free(cur);\n            hashMap-&gt;size--;\n            return;\n        }\n        pre = cur;\n        cur = cur-&gt;next;\n    }\n}\n\n/* Вывести хеш-таблицу */\nvoid print(HashMapChaining *hashMap) {\n    for (int i = 0; i &lt; hashMap-&gt;capacity; i++) {\n        Node *cur = hashMap-&gt;buckets[i];\n        printf(\"[\");\n        while (cur) {\n            printf(\"%d -&gt; %s, \", cur-&gt;pair-&gt;key, cur-&gt;pair-&gt;val);\n            cur = cur-&gt;next;\n        }\n        printf(\"]\\n\");\n    }\n}\n</code></pre> hash_map_chaining.kt<pre><code>/* Хеш-таблица с цепочками */\nclass HashMapChaining {\n    var size: Int // Число пар ключ-значение\n    var capacity: Int // Вместимость хеш-таблицы\n    val loadThres: Double // Порог коэффициента загрузки для запуска расширения\n    val extendRatio: Int // Коэффициент расширения\n    var buckets: MutableList&lt;MutableList&lt;Pair&gt;&gt; // Массив корзин\n\n    /* Конструктор */\n    init {\n        size = 0\n        capacity = 4\n        loadThres = 2.0 / 3.0\n        extendRatio = 2\n        buckets = mutableListOf()\n        for (i in 0..&lt;capacity) {\n            buckets.add(mutableListOf())\n        }\n    }\n\n    /* Хеш-функция */\n    fun hashFunc(key: Int): Int {\n        return key % capacity\n    }\n\n    /* Коэффициент загрузки */\n    fun loadFactor(): Double {\n        return (size / capacity).toDouble()\n    }\n\n    /* Операция поиска */\n    fun get(key: Int): String? {\n        val index = hashFunc(key)\n        val bucket = buckets[index]\n        // Обойти корзину; если найден key, вернуть соответствующее val\n        for (pair in bucket) {\n            if (pair.key == key) return pair._val\n        }\n        // Если key не найден, вернуть null\n        return null\n    }\n\n    /* Операция добавления */\n    fun put(key: Int, _val: String) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if (loadFactor() &gt; loadThres) {\n            extend()\n        }\n        val index = hashFunc(key)\n        val bucket = buckets[index]\n        // Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n        for (pair in bucket) {\n            if (pair.key == key) {\n                pair._val = _val\n                return\n            }\n        }\n        // Если такого key нет, добавить пару ключ-значение в конец\n        val pair = Pair(key, _val)\n        bucket.add(pair)\n        size++\n    }\n\n    /* Операция удаления */\n    fun remove(key: Int) {\n        val index = hashFunc(key)\n        val bucket = buckets[index]\n        // Обойти корзину и удалить из нее пару ключ-значение\n        for (pair in bucket) {\n            if (pair.key == key) {\n                bucket.remove(pair)\n                size--\n                break\n            }\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    fun extend() {\n        // Временно сохранить исходную хеш-таблицу\n        val bucketsTmp = buckets\n        // Инициализация новой хеш-таблицы после расширения\n        capacity *= extendRatio\n        // mutablelist не имеет фиксированного размера\n        buckets = mutableListOf()\n        for (i in 0..&lt;capacity) {\n            buckets.add(mutableListOf())\n        }\n        size = 0\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for (bucket in bucketsTmp) {\n            for (pair in bucket) {\n                put(pair.key, pair._val)\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    fun print() {\n        for (bucket in buckets) {\n            val res = mutableListOf&lt;String&gt;()\n            for (pair in bucket) {\n                val k = pair.key\n                val v = pair._val\n                res.add(\"$k -&gt; $v\")\n            }\n            println(res)\n        }\n    }\n}\n</code></pre> hash_map_chaining.rb<pre><code>### Хеш-таблица с цепочками ###\nclass HashMapChaining\n  ### Конструктор ###\n  def initialize\n    @size = 0 # Число пар ключ-значение\n    @capacity = 4 # Вместимость хеш-таблицы\n    @load_thres = 2.0 / 3.0 # Порог коэффициента загрузки для запуска расширения\n    @extend_ratio = 2 # Коэффициент расширения\n    @buckets = Array.new(@capacity) { [] } # Массив корзин\n  end\n\n  ### Хеш-функция ###\n  def hash_func(key)\n    key % @capacity\n  end\n\n  ### Коэффициент загрузки ###\n  def load_factor\n    @size / @capacity\n  end\n\n  ### Операция поиска ###\n  def get(key)\n    index = hash_func(key)\n    bucket = @buckets[index]\n    # Обойти корзину; если найден key, вернуть соответствующее val\n    for pair in bucket\n      return pair.val if pair.key == key\n    end\n    # Если key не найден, вернуть nil\n    nil\n  end\n\n  ### Операция добавления ###\n  def put(key, val)\n    # Когда коэффициент загрузки превышает порог, выполнить расширение\n    extend if load_factor &gt; @load_thres\n    index = hash_func(key)\n    bucket = @buckets[index]\n    # Обойти корзину; если встретился указанный key, обновить соответствующее val и вернуть\n    for pair in bucket\n      if pair.key == key\n        pair.val = val\n        return\n      end\n    end\n    # Если такого key нет, добавить пару ключ-значение в конец\n    pair = Pair.new(key, val)\n    bucket &lt;&lt; pair\n    @size += 1\n  end\n\n  ### Операция удаления ###\n  def remove(key)\n    index = hash_func(key)\n    bucket = @buckets[index]\n    # Обойти корзину и удалить из нее пару ключ-значение\n    for pair in bucket\n      if pair.key == key\n        bucket.delete(pair)\n        @size -= 1\n        break\n      end\n    end\n  end\n\n  ### Расширение хеш-таблицы ###\n  def extend\n    # Временно сохранить исходную хеш-таблицу\n    buckets = @buckets\n    # Инициализация новой хеш-таблицы после расширения\n    @capacity *= @extend_ratio\n    @buckets = Array.new(@capacity) { [] }\n    @size = 0\n    # Перенести пары ключ-значение из исходной хеш-таблицы в новую\n    for bucket in buckets\n      for pair in bucket\n        put(pair.key, pair.val)\n      end\n    end\n  end\n\n  ### Вывести хеш-таблицу ###\n  def print\n    for bucket in @buckets\n      res = []\n      for pair in bucket\n        res &lt;&lt; \"#{pair.key} -&gt; #{pair.val}\"\n      end\n      pp res\n    end\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Следует отметить, что когда связный список становится очень длинным, эффективность поиска \\(O(n)\\) оказывается низкой. В этом случае список можно преобразовать в AVL-дерево или красно-черное дерево , чтобы оптимизировать временную сложность поиска до \\(O(\\log n)\\) .</p>","path":["Глава 6. Хеш-таблицы","6.2 &nbsp; Хеш-коллизии"],"tags":[]},{"location":"chapter_hashing/hash_collision/#622","level":2,"title":"6.2.2   Открытая адресация","text":"<p>Открытая адресация (open addressing) не вводит дополнительных структур данных, а обрабатывает хеш-коллизии с помощью многократного пробирования; основные варианты пробирования включают линейное пробирование, квадратичное пробирование и повторное хеширование.</p> <p>Ниже на примере линейного пробирования рассмотрим механизм работы хеш-таблицы с открытой адресацией.</p>","path":["Глава 6. Хеш-таблицы","6.2 &nbsp; Хеш-коллизии"],"tags":[]},{"location":"chapter_hashing/hash_collision/#1","level":3,"title":"1.   Линейное пробирование","text":"<p>Линейное пробирование использует линейный поиск с фиксированным шагом. Его методы работы отличаются от обычной хеш-таблицы.</p> <ul> <li>Вставка элемента: по хеш-функции вычисляется индекс бакета; если бакет уже занят, то от места конфликта выполняется линейный обход вперед (шаг обычно равен \\(1\\) ), пока не будет найден пустой бакет, после чего элемент вставляется туда.</li> <li>Поиск элемента: если возник конфликт, то с тем же шагом продолжается линейный обход вперед, пока не будет найден целевой элемент и возвращено <code>value</code> ; если встречается пустой бакет, это означает, что искомого элемента в хеш-таблице нет, и возвращается <code>None</code> .</li> </ul> <p>На рисунке 6-6 показано распределение пар ключ-значение в хеш-таблице с открытой адресацией (линейное пробирование). Для этой хеш-функции все <code>key</code> с одинаковыми двумя последними цифрами отображаются в один и тот же бакет. Благодаря линейному пробированию они по очереди сохраняются в этом бакете и в следующих за ним бакетах.</p> <p></p> <p> Рисунок 6-6   Распределение пар ключ-значение в хеш-таблице с открытой адресацией (линейное пробирование) </p> <p>Однако линейное пробирование легко приводит к кластеризации. Иначе говоря, чем длиннее непрерывная занятая область в массиве, тем выше вероятность новых коллизий в этой области, что еще сильнее способствует росту этой группы и в итоге ухудшает эффективность операций добавления, удаления, поиска и обновления.</p> <p>Стоит заметить, что мы не можем напрямую удалять элементы из хеш-таблицы с открытой адресацией. Причина в том, что удаление создаст внутри массива пустой бакет <code>None</code> , а при поиске элемента линейное пробирование остановится на этом пустом бакете и вернет результат, из-за чего элементы ниже этого бакета уже не смогут быть найдены, и программа может ошибочно посчитать, что их не существует, как показано на рисунке 6-7.</p> <p></p> <p> Рисунок 6-7   Проблема поиска после удаления элемента в открытой адресации </p> <p>Чтобы решить эту проблему, можно использовать механизм ленивого удаления (lazy deletion): он не удаляет элемент из хеш-таблицы напрямую, **а помечает этот бакет специальной константой <code>TOMBSTONE</code> **. В этом механизме и <code>None</code> , и <code>TOMBSTONE</code> означают пустой бакет, и оба могут быть использованы для размещения пары ключ-значение. Но есть важное различие: при линейном пробировании, встретив <code>TOMBSTONE</code> , нужно продолжать обход, потому что ниже него все еще могут существовать пары ключ-значение.</p> <p>Однако ленивое удаление может ускорять деградацию производительности хеш-таблицы. Это связано с тем, что каждая операция удаления создает новую метку удаления; по мере роста числа <code>TOMBSTONE</code> время поиска тоже увеличивается, потому что линейное пробирование может быть вынуждено перескакивать через множество <code>TOMBSTONE</code> , прежде чем найдет целевой элемент.</p> <p>Поэтому имеет смысл при линейном пробировании запоминать индекс первого встреченного <code>TOMBSTONE</code> и затем менять найденный целевой элемент местами с этим <code>TOMBSTONE</code> . Преимущество такого подхода в том, что при каждом поиске или добавлении элемент будет перемещаться в бакет, расположенный ближе к его идеальной позиции (начальной точке пробирования), а значит, эффективность поиска улучшится.</p> <p>Ниже приведена реализация хеш-таблицы с открытой адресацией, то есть с линейным пробированием, включающая ленивое удаление. Чтобы пространство хеш-таблицы использовалось более полно, мы рассматриваем ее как кольцевой массив: когда обход выходит за конец массива, он возвращается к началу и продолжается.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby hash_map_open_addressing.py<pre><code>class HashMapOpenAddressing:\n    \"\"\"Хеш-таблица с открытой адресацией\"\"\"\n\n    def __init__(self):\n        \"\"\"Конструктор\"\"\"\n        self.size = 0  # Число пар ключ-значение\n        self.capacity = 4  # Вместимость хеш-таблицы\n        self.load_thres = 2.0 / 3.0  # Порог коэффициента загрузки для запуска расширения\n        self.extend_ratio = 2  # Коэффициент расширения\n        self.buckets: list[Pair | None] = [None] * self.capacity  # Массив корзин\n        self.TOMBSTONE = Pair(-1, \"-1\")  # Удалить метку\n\n    def hash_func(self, key: int) -&gt; int:\n        \"\"\"Хеш-функция\"\"\"\n        return key % self.capacity\n\n    def load_factor(self) -&gt; float:\n        \"\"\"Коэффициент загрузки\"\"\"\n        return self.size / self.capacity\n\n    def find_bucket(self, key: int) -&gt; int:\n        \"\"\"Найти индекс корзины, соответствующий key\"\"\"\n        index = self.hash_func(key)\n        first_tombstone = -1\n        # Выполнять линейное пробирование и завершить при встрече с пустой корзиной\n        while self.buckets[index] is not None:\n            # Если встретился key, вернуть соответствующий индекс корзины\n            if self.buckets[index].key == key:\n                # Если ранее встретилась метка удаления, переместить пару ключ-значение на этот индекс\n                if first_tombstone != -1:\n                    self.buckets[first_tombstone] = self.buckets[index]\n                    self.buckets[index] = self.TOMBSTONE\n                    return first_tombstone  # Вернуть индекс корзины после перемещения\n                return index  # Вернуть индекс корзины\n            # Записать первую встретившуюся метку удаления\n            if first_tombstone == -1 and self.buckets[index] is self.TOMBSTONE:\n                first_tombstone = index\n            # Вычислить индекс корзины; при выходе за конец вернуться к началу\n            index = (index + 1) % self.capacity\n        # Если key не существует, вернуть индекс точки добавления\n        return index if first_tombstone == -1 else first_tombstone\n\n    def get(self, key: int) -&gt; str:\n        \"\"\"Операция поиска\"\"\"\n        # Найти индекс корзины, соответствующий key\n        index = self.find_bucket(key)\n        # Если пара ключ-значение найдена, вернуть соответствующее val\n        if self.buckets[index] not in [None, self.TOMBSTONE]:\n            return self.buckets[index].val\n        # Если пара ключ-значение не существует, вернуть None\n        return None\n\n    def put(self, key: int, val: str):\n        \"\"\"Операция добавления\"\"\"\n        # Когда коэффициент загрузки превышает порог, выполнить расширение\n        if self.load_factor() &gt; self.load_thres:\n            self.extend()\n        # Найти индекс корзины, соответствующий key\n        index = self.find_bucket(key)\n        # Если пара ключ-значение найдена, перезаписать val и вернуть\n        if self.buckets[index] not in [None, self.TOMBSTONE]:\n            self.buckets[index].val = val\n            return\n        # Если пары ключ-значение нет, добавить ее\n        self.buckets[index] = Pair(key, val)\n        self.size += 1\n\n    def remove(self, key: int):\n        \"\"\"Операция удаления\"\"\"\n        # Найти индекс корзины, соответствующий key\n        index = self.find_bucket(key)\n        # Если пара ключ-значение найдена, заменить ее меткой удаления\n        if self.buckets[index] not in [None, self.TOMBSTONE]:\n            self.buckets[index] = self.TOMBSTONE\n            self.size -= 1\n\n    def extend(self):\n        \"\"\"Расширить хеш-таблицу\"\"\"\n        # Временно сохранить исходную хеш-таблицу\n        buckets_tmp = self.buckets\n        # Инициализация новой хеш-таблицы после расширения\n        self.capacity *= self.extend_ratio\n        self.buckets = [None] * self.capacity\n        self.size = 0\n        # Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for pair in buckets_tmp:\n            if pair not in [None, self.TOMBSTONE]:\n                self.put(pair.key, pair.val)\n\n    def print(self):\n        \"\"\"Вывести хеш-таблицу\"\"\"\n        for pair in self.buckets:\n            if pair is None:\n                print(\"None\")\n            elif pair is self.TOMBSTONE:\n                print(\"TOMBSTONE\")\n            else:\n                print(pair.key, \"-&gt;\", pair.val)\n</code></pre> hash_map_open_addressing.cpp<pre><code>/* Хеш-таблица с открытой адресацией */\nclass HashMapOpenAddressing {\n  private:\n    int size;                             // Число пар ключ-значение\n    int capacity = 4;                     // Вместимость хеш-таблицы\n    const double loadThres = 2.0 / 3.0;     // Порог коэффициента загрузки для запуска расширения\n    const int extendRatio = 2;            // Коэффициент расширения\n    vector&lt;Pair *&gt; buckets;               // Массив корзин\n    Pair *TOMBSTONE = new Pair(-1, \"-1\"); // Удалить метку\n\n  public:\n    /* Конструктор */\n    HashMapOpenAddressing() : size(0), buckets(capacity, nullptr) {\n    }\n\n    /* Метод-деструктор */\n    ~HashMapOpenAddressing() {\n        for (Pair *pair : buckets) {\n            if (pair != nullptr &amp;&amp; pair != TOMBSTONE) {\n                delete pair;\n            }\n        }\n        delete TOMBSTONE;\n    }\n\n    /* Хеш-функция */\n    int hashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* Коэффициент загрузки */\n    double loadFactor() {\n        return (double)size / capacity;\n    }\n\n    /* Найти индекс корзины, соответствующий key */\n    int findBucket(int key) {\n        int index = hashFunc(key);\n        int firstTombstone = -1;\n        // Выполнять линейное пробирование и завершить при встрече с пустой корзиной\n        while (buckets[index] != nullptr) {\n            // Если встретился key, вернуть соответствующий индекс корзины\n            if (buckets[index]-&gt;key == key) {\n                // Если ранее встретилась метка удаления, переместить пару ключ-значение на этот индекс\n                if (firstTombstone != -1) {\n                    buckets[firstTombstone] = buckets[index];\n                    buckets[index] = TOMBSTONE;\n                    return firstTombstone; // Вернуть индекс корзины после перемещения\n                }\n                return index; // Вернуть индекс корзины\n            }\n            // Записать первую встретившуюся метку удаления\n            if (firstTombstone == -1 &amp;&amp; buckets[index] == TOMBSTONE) {\n                firstTombstone = index;\n            }\n            // Вычислить индекс корзины; при выходе за конец вернуться к началу\n            index = (index + 1) % capacity;\n        }\n        // Если key не существует, вернуть индекс точки добавления\n        return firstTombstone == -1 ? index : firstTombstone;\n    }\n\n    /* Операция поиска */\n    string get(int key) {\n        // Найти индекс корзины, соответствующий key\n        int index = findBucket(key);\n        // Если пара ключ-значение найдена, вернуть соответствующее val\n        if (buckets[index] != nullptr &amp;&amp; buckets[index] != TOMBSTONE) {\n            return buckets[index]-&gt;val;\n        }\n        // Если пары ключ-значение не существует, вернуть пустую строку\n        return \"\";\n    }\n\n    /* Операция добавления */\n    void put(int key, string val) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if (loadFactor() &gt; loadThres) {\n            extend();\n        }\n        // Найти индекс корзины, соответствующий key\n        int index = findBucket(key);\n        // Если пара ключ-значение найдена, перезаписать val и вернуть\n        if (buckets[index] != nullptr &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index]-&gt;val = val;\n            return;\n        }\n        // Если пары ключ-значение нет, добавить ее\n        buckets[index] = new Pair(key, val);\n        size++;\n    }\n\n    /* Операция удаления */\n    void remove(int key) {\n        // Найти индекс корзины, соответствующий key\n        int index = findBucket(key);\n        // Если пара ключ-значение найдена, заменить ее меткой удаления\n        if (buckets[index] != nullptr &amp;&amp; buckets[index] != TOMBSTONE) {\n            delete buckets[index];\n            buckets[index] = TOMBSTONE;\n            size--;\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    void extend() {\n        // Временно сохранить исходную хеш-таблицу\n        vector&lt;Pair *&gt; bucketsTmp = buckets;\n        // Инициализация новой хеш-таблицы после расширения\n        capacity *= extendRatio;\n        buckets = vector&lt;Pair *&gt;(capacity, nullptr);\n        size = 0;\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for (Pair *pair : bucketsTmp) {\n            if (pair != nullptr &amp;&amp; pair != TOMBSTONE) {\n                put(pair-&gt;key, pair-&gt;val);\n                delete pair;\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    void print() {\n        for (Pair *pair : buckets) {\n            if (pair == nullptr) {\n                cout &lt;&lt; \"nullptr\" &lt;&lt; endl;\n            } else if (pair == TOMBSTONE) {\n                cout &lt;&lt; \"TOMBSTONE\" &lt;&lt; endl;\n            } else {\n                cout &lt;&lt; pair-&gt;key &lt;&lt; \" -&gt; \" &lt;&lt; pair-&gt;val &lt;&lt; endl;\n            }\n        }\n    }\n};\n</code></pre> hash_map_open_addressing.java<pre><code>/* Хеш-таблица с открытой адресацией */\nclass HashMapOpenAddressing {\n    private int size; // Число пар ключ-значение\n    private int capacity = 4; // Вместимость хеш-таблицы\n    private final double loadThres = 2.0 / 3.0; // Порог коэффициента загрузки для запуска расширения\n    private final int extendRatio = 2; // Коэффициент расширения\n    private Pair[] buckets; // Массив корзин\n    private final Pair TOMBSTONE = new Pair(-1, \"-1\"); // Удалить метку\n\n    /* Конструктор */\n    public HashMapOpenAddressing() {\n        size = 0;\n        buckets = new Pair[capacity];\n    }\n\n    /* Хеш-функция */\n    private int hashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* Коэффициент загрузки */\n    private double loadFactor() {\n        return (double) size / capacity;\n    }\n\n    /* Найти индекс корзины, соответствующий key */\n    private int findBucket(int key) {\n        int index = hashFunc(key);\n        int firstTombstone = -1;\n        // Выполнять линейное пробирование и завершить при встрече с пустой корзиной\n        while (buckets[index] != null) {\n            // Если встретился key, вернуть соответствующий индекс корзины\n            if (buckets[index].key == key) {\n                // Если ранее встретилась метка удаления, переместить пару ключ-значение на этот индекс\n                if (firstTombstone != -1) {\n                    buckets[firstTombstone] = buckets[index];\n                    buckets[index] = TOMBSTONE;\n                    return firstTombstone; // Вернуть индекс корзины после перемещения\n                }\n                return index; // Вернуть индекс корзины\n            }\n            // Записать первую встретившуюся метку удаления\n            if (firstTombstone == -1 &amp;&amp; buckets[index] == TOMBSTONE) {\n                firstTombstone = index;\n            }\n            // Вычислить индекс корзины; при выходе за конец вернуться к началу\n            index = (index + 1) % capacity;\n        }\n        // Если key не существует, вернуть индекс точки добавления\n        return firstTombstone == -1 ? index : firstTombstone;\n    }\n\n    /* Операция поиска */\n    public String get(int key) {\n        // Найти индекс корзины, соответствующий key\n        int index = findBucket(key);\n        // Если пара ключ-значение найдена, вернуть соответствующее val\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            return buckets[index].val;\n        }\n        // Если пары ключ-значение не существует, вернуть null\n        return null;\n    }\n\n    /* Операция добавления */\n    public void put(int key, String val) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if (loadFactor() &gt; loadThres) {\n            extend();\n        }\n        // Найти индекс корзины, соответствующий key\n        int index = findBucket(key);\n        // Если пара ключ-значение найдена, перезаписать val и вернуть\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index].val = val;\n            return;\n        }\n        // Если пары ключ-значение нет, добавить ее\n        buckets[index] = new Pair(key, val);\n        size++;\n    }\n\n    /* Операция удаления */\n    public void remove(int key) {\n        // Найти индекс корзины, соответствующий key\n        int index = findBucket(key);\n        // Если пара ключ-значение найдена, заменить ее меткой удаления\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index] = TOMBSTONE;\n            size--;\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    private void extend() {\n        // Временно сохранить исходную хеш-таблицу\n        Pair[] bucketsTmp = buckets;\n        // Инициализация новой хеш-таблицы после расширения\n        capacity *= extendRatio;\n        buckets = new Pair[capacity];\n        size = 0;\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for (Pair pair : bucketsTmp) {\n            if (pair != null &amp;&amp; pair != TOMBSTONE) {\n                put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    public void print() {\n        for (Pair pair : buckets) {\n            if (pair == null) {\n                System.out.println(\"null\");\n            } else if (pair == TOMBSTONE) {\n                System.out.println(\"TOMBSTONE\");\n            } else {\n                System.out.println(pair.key + \" -&gt; \" + pair.val);\n            }\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.cs<pre><code>/* Хеш-таблица с открытой адресацией */\nclass HashMapOpenAddressing {\n    int size; // Число пар ключ-значение\n    int capacity = 4; // Вместимость хеш-таблицы\n    double loadThres = 2.0 / 3.0; // Порог коэффициента загрузки для запуска расширения\n    int extendRatio = 2; // Коэффициент расширения\n    Pair[] buckets; // Массив корзин\n    Pair TOMBSTONE = new(-1, \"-1\"); // Удалить метку\n\n    /* Конструктор */\n    public HashMapOpenAddressing() {\n        size = 0;\n        buckets = new Pair[capacity];\n    }\n\n    /* Хеш-функция */\n    int HashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* Коэффициент загрузки */\n    double LoadFactor() {\n        return (double)size / capacity;\n    }\n\n    /* Найти индекс корзины, соответствующий key */\n    int FindBucket(int key) {\n        int index = HashFunc(key);\n        int firstTombstone = -1;\n        // Выполнять линейное пробирование и завершить при встрече с пустой корзиной\n        while (buckets[index] != null) {\n            // Если встретился key, вернуть соответствующий индекс корзины\n            if (buckets[index].key == key) {\n                // Если ранее встретилась метка удаления, переместить пару ключ-значение на этот индекс\n                if (firstTombstone != -1) {\n                    buckets[firstTombstone] = buckets[index];\n                    buckets[index] = TOMBSTONE;\n                    return firstTombstone; // Вернуть индекс корзины после перемещения\n                }\n                return index; // Вернуть индекс корзины\n            }\n            // Записать первую встретившуюся метку удаления\n            if (firstTombstone == -1 &amp;&amp; buckets[index] == TOMBSTONE) {\n                firstTombstone = index;\n            }\n            // Вычислить индекс корзины; при выходе за конец вернуться к началу\n            index = (index + 1) % capacity;\n        }\n        // Если key не существует, вернуть индекс точки добавления\n        return firstTombstone == -1 ? index : firstTombstone;\n    }\n\n    /* Операция поиска */\n    public string? Get(int key) {\n        // Найти индекс корзины, соответствующий key\n        int index = FindBucket(key);\n        // Если пара ключ-значение найдена, вернуть соответствующее val\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            return buckets[index].val;\n        }\n        // Если пары ключ-значение не существует, вернуть null\n        return null;\n    }\n\n    /* Операция добавления */\n    public void Put(int key, string val) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if (LoadFactor() &gt; loadThres) {\n            Extend();\n        }\n        // Найти индекс корзины, соответствующий key\n        int index = FindBucket(key);\n        // Если пара ключ-значение найдена, перезаписать val и вернуть\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index].val = val;\n            return;\n        }\n        // Если пары ключ-значение нет, добавить ее\n        buckets[index] = new Pair(key, val);\n        size++;\n    }\n\n    /* Операция удаления */\n    public void Remove(int key) {\n        // Найти индекс корзины, соответствующий key\n        int index = FindBucket(key);\n        // Если пара ключ-значение найдена, заменить ее меткой удаления\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index] = TOMBSTONE;\n            size--;\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    void Extend() {\n        // Временно сохранить исходную хеш-таблицу\n        Pair[] bucketsTmp = buckets;\n        // Инициализация новой хеш-таблицы после расширения\n        capacity *= extendRatio;\n        buckets = new Pair[capacity];\n        size = 0;\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        foreach (Pair pair in bucketsTmp) {\n            if (pair != null &amp;&amp; pair != TOMBSTONE) {\n                Put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    public void Print() {\n        foreach (Pair pair in buckets) {\n            if (pair == null) {\n                Console.WriteLine(\"null\");\n            } else if (pair == TOMBSTONE) {\n                Console.WriteLine(\"TOMBSTONE\");\n            } else {\n                Console.WriteLine(pair.key + \" -&gt; \" + pair.val);\n            }\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.go<pre><code>/* Хеш-таблица с открытой адресацией */\ntype hashMapOpenAddressing struct {\n    size        int     // Число пар ключ-значение\n    capacity    int     // Вместимость хеш-таблицы\n    loadThres   float64 // Порог коэффициента загрузки для запуска расширения\n    extendRatio int     // Коэффициент расширения\n    buckets     []*pair // Массив корзин\n    TOMBSTONE   *pair   // Удалить метку\n}\n\n/* Конструктор */\nfunc newHashMapOpenAddressing() *hashMapOpenAddressing {\n    return &amp;hashMapOpenAddressing{\n        size:        0,\n        capacity:    4,\n        loadThres:   2.0 / 3.0,\n        extendRatio: 2,\n        buckets:     make([]*pair, 4),\n        TOMBSTONE:   &amp;pair{-1, \"-1\"},\n    }\n}\n\n/* Хеш-функция */\nfunc (h *hashMapOpenAddressing) hashFunc(key int) int {\n    return key % h.capacity // Вычислить хеш-значение по ключу\n}\n\n/* Коэффициент загрузки */\nfunc (h *hashMapOpenAddressing) loadFactor() float64 {\n    return float64(h.size) / float64(h.capacity) // Вычислить текущий коэффициент загрузки\n}\n\n/* Найти индекс корзины, соответствующий key */\nfunc (h *hashMapOpenAddressing) findBucket(key int) int {\n    index := h.hashFunc(key) // Получить начальный индекс\n    firstTombstone := -1     // Запомнить положение первого TOMBSTONE\n    for h.buckets[index] != nil {\n        if h.buckets[index].key == key {\n            if firstTombstone != -1 {\n                // Если ранее встретилась метка удаления, переместить пару ключ-значение на этот индекс\n                h.buckets[firstTombstone] = h.buckets[index]\n                h.buckets[index] = h.TOMBSTONE\n                return firstTombstone // Вернуть индекс корзины после перемещения\n            }\n            return index // Вернуть найденный индекс\n        }\n        if firstTombstone == -1 &amp;&amp; h.buckets[index] == h.TOMBSTONE {\n            firstTombstone = index // Запомнить положение первой метки удаления\n        }\n        index = (index + 1) % h.capacity // Линейное пробирование: при выходе за хвост вернуться к началу\n    }\n    // Если key не существует, вернуть индекс точки добавления\n    if firstTombstone != -1 {\n        return firstTombstone\n    }\n    return index\n}\n\n/* Операция поиска */\nfunc (h *hashMapOpenAddressing) get(key int) string {\n    index := h.findBucket(key) // Найти индекс корзины, соответствующий key\n    if h.buckets[index] != nil &amp;&amp; h.buckets[index] != h.TOMBSTONE {\n        return h.buckets[index].val // Если пара ключ-значение найдена, вернуть соответствующее val\n    }\n    return \"\" // Если пара ключ-значение не существует, вернуть \"\"\n}\n\n/* Операция добавления */\nfunc (h *hashMapOpenAddressing) put(key int, val string) {\n    if h.loadFactor() &gt; h.loadThres {\n        h.extend() // Когда коэффициент загрузки превышает порог, выполнить расширение\n    }\n    index := h.findBucket(key) // Найти индекс корзины, соответствующий key\n    if h.buckets[index] == nil || h.buckets[index] == h.TOMBSTONE {\n        h.buckets[index] = &amp;pair{key, val} // Если пары ключ-значение нет, добавить ее\n        h.size++\n    } else {\n        h.buckets[index].val = val // Если пара ключ-значение найдена, перезаписать val\n    }\n}\n\n/* Операция удаления */\nfunc (h *hashMapOpenAddressing) remove(key int) {\n    index := h.findBucket(key) // Найти индекс корзины, соответствующий key\n    if h.buckets[index] != nil &amp;&amp; h.buckets[index] != h.TOMBSTONE {\n        h.buckets[index] = h.TOMBSTONE // Если пара ключ-значение найдена, заменить ее меткой удаления\n        h.size--\n    }\n}\n\n/* Расширить хеш-таблицу */\nfunc (h *hashMapOpenAddressing) extend() {\n    oldBuckets := h.buckets               // Временно сохранить исходную хеш-таблицу\n    h.capacity *= h.extendRatio           // Обновить емкость\n    h.buckets = make([]*pair, h.capacity) // Инициализация новой хеш-таблицы после расширения\n    h.size = 0                            // Сбросить размер\n    // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n    for _, pair := range oldBuckets {\n        if pair != nil &amp;&amp; pair != h.TOMBSTONE {\n            h.put(pair.key, pair.val)\n        }\n    }\n}\n\n/* Вывести хеш-таблицу */\nfunc (h *hashMapOpenAddressing) print() {\n    for _, pair := range h.buckets {\n        if pair == nil {\n            fmt.Println(\"nil\")\n        } else if pair == h.TOMBSTONE {\n            fmt.Println(\"TOMBSTONE\")\n        } else {\n            fmt.Printf(\"%d -&gt; %s\\n\", pair.key, pair.val)\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.swift<pre><code>/* Хеш-таблица с открытой адресацией */\nclass HashMapOpenAddressing {\n    var size: Int // Число пар ключ-значение\n    var capacity: Int // Вместимость хеш-таблицы\n    var loadThres: Double // Порог коэффициента загрузки для запуска расширения\n    var extendRatio: Int // Коэффициент расширения\n    var buckets: [Pair?] // Массив корзин\n    var TOMBSTONE: Pair // Удалить метку\n\n    /* Конструктор */\n    init() {\n        size = 0\n        capacity = 4\n        loadThres = 2.0 / 3.0\n        extendRatio = 2\n        buckets = Array(repeating: nil, count: capacity)\n        TOMBSTONE = Pair(key: -1, val: \"-1\")\n    }\n\n    /* Хеш-функция */\n    func hashFunc(key: Int) -&gt; Int {\n        key % capacity\n    }\n\n    /* Коэффициент загрузки */\n    func loadFactor() -&gt; Double {\n        Double(size) / Double(capacity)\n    }\n\n    /* Найти индекс корзины, соответствующий key */\n    func findBucket(key: Int) -&gt; Int {\n        var index = hashFunc(key: key)\n        var firstTombstone = -1\n        // Выполнять линейное пробирование и завершить при встрече с пустой корзиной\n        while buckets[index] != nil {\n            // Если встретился key, вернуть соответствующий индекс корзины\n            if buckets[index]!.key == key {\n                // Если ранее встретилась метка удаления, переместить пару ключ-значение на этот индекс\n                if firstTombstone != -1 {\n                    buckets[firstTombstone] = buckets[index]\n                    buckets[index] = TOMBSTONE\n                    return firstTombstone // Вернуть индекс корзины после перемещения\n                }\n                return index // Вернуть индекс корзины\n            }\n            // Записать первую встретившуюся метку удаления\n            if firstTombstone == -1 &amp;&amp; buckets[index] == TOMBSTONE {\n                firstTombstone = index\n            }\n            // Вычислить индекс корзины; при выходе за конец вернуться к началу\n            index = (index + 1) % capacity\n        }\n        // Если key не существует, вернуть индекс точки добавления\n        return firstTombstone == -1 ? index : firstTombstone\n    }\n\n    /* Операция поиска */\n    func get(key: Int) -&gt; String? {\n        // Найти индекс корзины, соответствующий key\n        let index = findBucket(key: key)\n        // Если пара ключ-значение найдена, вернуть соответствующее val\n        if buckets[index] != nil, buckets[index] != TOMBSTONE {\n            return buckets[index]!.val\n        }\n        // Если пары ключ-значение не существует, вернуть null\n        return nil\n    }\n\n    /* Операция добавления */\n    func put(key: Int, val: String) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if loadFactor() &gt; loadThres {\n            extend()\n        }\n        // Найти индекс корзины, соответствующий key\n        let index = findBucket(key: key)\n        // Если пара ключ-значение найдена, перезаписать val и вернуть\n        if buckets[index] != nil, buckets[index] != TOMBSTONE {\n            buckets[index]!.val = val\n            return\n        }\n        // Если пары ключ-значение нет, добавить ее\n        buckets[index] = Pair(key: key, val: val)\n        size += 1\n    }\n\n    /* Операция удаления */\n    func remove(key: Int) {\n        // Найти индекс корзины, соответствующий key\n        let index = findBucket(key: key)\n        // Если пара ключ-значение найдена, заменить ее меткой удаления\n        if buckets[index] != nil, buckets[index] != TOMBSTONE {\n            buckets[index] = TOMBSTONE\n            size -= 1\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    func extend() {\n        // Временно сохранить исходную хеш-таблицу\n        let bucketsTmp = buckets\n        // Инициализация новой хеш-таблицы после расширения\n        capacity *= extendRatio\n        buckets = Array(repeating: nil, count: capacity)\n        size = 0\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for pair in bucketsTmp {\n            if let pair, pair != TOMBSTONE {\n                put(key: pair.key, val: pair.val)\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    func print() {\n        for pair in buckets {\n            if pair == nil {\n                Swift.print(\"null\")\n            } else if pair == TOMBSTONE {\n                Swift.print(\"TOMBSTONE\")\n            } else {\n                Swift.print(\"\\(pair!.key) -&gt; \\(pair!.val)\")\n            }\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.js<pre><code>/* Хеш-таблица с открытой адресацией */\nclass HashMapOpenAddressing {\n    #size; // Число пар ключ-значение\n    #capacity; // Вместимость хеш-таблицы\n    #loadThres; // Порог коэффициента загрузки для запуска расширения\n    #extendRatio; // Коэффициент расширения\n    #buckets; // Массив корзин\n    #TOMBSTONE; // Удалить метку\n\n    /* Конструктор */\n    constructor() {\n        this.#size = 0; // Число пар ключ-значение\n        this.#capacity = 4; // Вместимость хеш-таблицы\n        this.#loadThres = 2.0 / 3.0; // Порог коэффициента загрузки для запуска расширения\n        this.#extendRatio = 2; // Коэффициент расширения\n        this.#buckets = Array(this.#capacity).fill(null); // Массив корзин\n        this.#TOMBSTONE = new Pair(-1, '-1'); // Удалить метку\n    }\n\n    /* Хеш-функция */\n    #hashFunc(key) {\n        return key % this.#capacity;\n    }\n\n    /* Коэффициент загрузки */\n    #loadFactor() {\n        return this.#size / this.#capacity;\n    }\n\n    /* Найти индекс корзины, соответствующий key */\n    #findBucket(key) {\n        let index = this.#hashFunc(key);\n        let firstTombstone = -1;\n        // Выполнять линейное пробирование и завершить при встрече с пустой корзиной\n        while (this.#buckets[index] !== null) {\n            // Если встретился key, вернуть соответствующий индекс корзины\n            if (this.#buckets[index].key === key) {\n                // Если ранее встретилась метка удаления, переместить пару ключ-значение на этот индекс\n                if (firstTombstone !== -1) {\n                    this.#buckets[firstTombstone] = this.#buckets[index];\n                    this.#buckets[index] = this.#TOMBSTONE;\n                    return firstTombstone; // Вернуть индекс корзины после перемещения\n                }\n                return index; // Вернуть индекс корзины\n            }\n            // Записать первую встретившуюся метку удаления\n            if (\n                firstTombstone === -1 &amp;&amp;\n                this.#buckets[index] === this.#TOMBSTONE\n            ) {\n                firstTombstone = index;\n            }\n            // Вычислить индекс корзины; при выходе за конец вернуться к началу\n            index = (index + 1) % this.#capacity;\n        }\n        // Если key не существует, вернуть индекс точки добавления\n        return firstTombstone === -1 ? index : firstTombstone;\n    }\n\n    /* Операция поиска */\n    get(key) {\n        // Найти индекс корзины, соответствующий key\n        const index = this.#findBucket(key);\n        // Если пара ключ-значение найдена, вернуть соответствующее val\n        if (\n            this.#buckets[index] !== null &amp;&amp;\n            this.#buckets[index] !== this.#TOMBSTONE\n        ) {\n            return this.#buckets[index].val;\n        }\n        // Если пары ключ-значение не существует, вернуть null\n        return null;\n    }\n\n    /* Операция добавления */\n    put(key, val) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if (this.#loadFactor() &gt; this.#loadThres) {\n            this.#extend();\n        }\n        // Найти индекс корзины, соответствующий key\n        const index = this.#findBucket(key);\n        // Если пара ключ-значение найдена, перезаписать val и вернуть\n        if (\n            this.#buckets[index] !== null &amp;&amp;\n            this.#buckets[index] !== this.#TOMBSTONE\n        ) {\n            this.#buckets[index].val = val;\n            return;\n        }\n        // Если пары ключ-значение нет, добавить ее\n        this.#buckets[index] = new Pair(key, val);\n        this.#size++;\n    }\n\n    /* Операция удаления */\n    remove(key) {\n        // Найти индекс корзины, соответствующий key\n        const index = this.#findBucket(key);\n        // Если пара ключ-значение найдена, заменить ее меткой удаления\n        if (\n            this.#buckets[index] !== null &amp;&amp;\n            this.#buckets[index] !== this.#TOMBSTONE\n        ) {\n            this.#buckets[index] = this.#TOMBSTONE;\n            this.#size--;\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    #extend() {\n        // Временно сохранить исходную хеш-таблицу\n        const bucketsTmp = this.#buckets;\n        // Инициализация новой хеш-таблицы после расширения\n        this.#capacity *= this.#extendRatio;\n        this.#buckets = Array(this.#capacity).fill(null);\n        this.#size = 0;\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for (const pair of bucketsTmp) {\n            if (pair !== null &amp;&amp; pair !== this.#TOMBSTONE) {\n                this.put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    print() {\n        for (const pair of this.#buckets) {\n            if (pair === null) {\n                console.log('null');\n            } else if (pair === this.#TOMBSTONE) {\n                console.log('TOMBSTONE');\n            } else {\n                console.log(pair.key + ' -&gt; ' + pair.val);\n            }\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.ts<pre><code>/* Хеш-таблица с открытой адресацией */\nclass HashMapOpenAddressing {\n    private size: number; // Число пар ключ-значение\n    private capacity: number; // Вместимость хеш-таблицы\n    private loadThres: number; // Порог коэффициента загрузки для запуска расширения\n    private extendRatio: number; // Коэффициент расширения\n    private buckets: Array&lt;Pair | null&gt;; // Массив корзин\n    private TOMBSTONE: Pair; // Удалить метку\n\n    /* Конструктор */\n    constructor() {\n        this.size = 0; // Число пар ключ-значение\n        this.capacity = 4; // Вместимость хеш-таблицы\n        this.loadThres = 2.0 / 3.0; // Порог коэффициента загрузки для запуска расширения\n        this.extendRatio = 2; // Коэффициент расширения\n        this.buckets = Array(this.capacity).fill(null); // Массив корзин\n        this.TOMBSTONE = new Pair(-1, '-1'); // Удалить метку\n    }\n\n    /* Хеш-функция */\n    private hashFunc(key: number): number {\n        return key % this.capacity;\n    }\n\n    /* Коэффициент загрузки */\n    private loadFactor(): number {\n        return this.size / this.capacity;\n    }\n\n    /* Найти индекс корзины, соответствующий key */\n    private findBucket(key: number): number {\n        let index = this.hashFunc(key);\n        let firstTombstone = -1;\n        // Выполнять линейное пробирование и завершить при встрече с пустой корзиной\n        while (this.buckets[index] !== null) {\n            // Если встретился key, вернуть соответствующий индекс корзины\n            if (this.buckets[index]!.key === key) {\n                // Если ранее встретилась метка удаления, переместить пару ключ-значение на этот индекс\n                if (firstTombstone !== -1) {\n                    this.buckets[firstTombstone] = this.buckets[index];\n                    this.buckets[index] = this.TOMBSTONE;\n                    return firstTombstone; // Вернуть индекс корзины после перемещения\n                }\n                return index; // Вернуть индекс корзины\n            }\n            // Записать первую встретившуюся метку удаления\n            if (\n                firstTombstone === -1 &amp;&amp;\n                this.buckets[index] === this.TOMBSTONE\n            ) {\n                firstTombstone = index;\n            }\n            // Вычислить индекс корзины; при выходе за конец вернуться к началу\n            index = (index + 1) % this.capacity;\n        }\n        // Если key не существует, вернуть индекс точки добавления\n        return firstTombstone === -1 ? index : firstTombstone;\n    }\n\n    /* Операция поиска */\n    get(key: number): string | null {\n        // Найти индекс корзины, соответствующий key\n        const index = this.findBucket(key);\n        // Если пара ключ-значение найдена, вернуть соответствующее val\n        if (\n            this.buckets[index] !== null &amp;&amp;\n            this.buckets[index] !== this.TOMBSTONE\n        ) {\n            return this.buckets[index]!.val;\n        }\n        // Если пары ключ-значение не существует, вернуть null\n        return null;\n    }\n\n    /* Операция добавления */\n    put(key: number, val: string): void {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if (this.loadFactor() &gt; this.loadThres) {\n            this.extend();\n        }\n        // Найти индекс корзины, соответствующий key\n        const index = this.findBucket(key);\n        // Если пара ключ-значение найдена, перезаписать val и вернуть\n        if (\n            this.buckets[index] !== null &amp;&amp;\n            this.buckets[index] !== this.TOMBSTONE\n        ) {\n            this.buckets[index]!.val = val;\n            return;\n        }\n        // Если пары ключ-значение нет, добавить ее\n        this.buckets[index] = new Pair(key, val);\n        this.size++;\n    }\n\n    /* Операция удаления */\n    remove(key: number): void {\n        // Найти индекс корзины, соответствующий key\n        const index = this.findBucket(key);\n        // Если пара ключ-значение найдена, заменить ее меткой удаления\n        if (\n            this.buckets[index] !== null &amp;&amp;\n            this.buckets[index] !== this.TOMBSTONE\n        ) {\n            this.buckets[index] = this.TOMBSTONE;\n            this.size--;\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    private extend(): void {\n        // Временно сохранить исходную хеш-таблицу\n        const bucketsTmp = this.buckets;\n        // Инициализация новой хеш-таблицы после расширения\n        this.capacity *= this.extendRatio;\n        this.buckets = Array(this.capacity).fill(null);\n        this.size = 0;\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for (const pair of bucketsTmp) {\n            if (pair !== null &amp;&amp; pair !== this.TOMBSTONE) {\n                this.put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    print(): void {\n        for (const pair of this.buckets) {\n            if (pair === null) {\n                console.log('null');\n            } else if (pair === this.TOMBSTONE) {\n                console.log('TOMBSTONE');\n            } else {\n                console.log(pair.key + ' -&gt; ' + pair.val);\n            }\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.dart<pre><code>/* Хеш-таблица с открытой адресацией */\nclass HashMapOpenAddressing {\n  late int _size; // Число пар ключ-значение\n  int _capacity = 4; // Вместимость хеш-таблицы\n  double _loadThres = 2.0 / 3.0; // Порог коэффициента загрузки для запуска расширения\n  int _extendRatio = 2; // Коэффициент расширения\n  late List&lt;Pair?&gt; _buckets; // Массив корзин\n  Pair _TOMBSTONE = Pair(-1, \"-1\"); // Удалить метку\n\n  /* Конструктор */\n  HashMapOpenAddressing() {\n    _size = 0;\n    _buckets = List.generate(_capacity, (index) =&gt; null);\n  }\n\n  /* Хеш-функция */\n  int hashFunc(int key) {\n    return key % _capacity;\n  }\n\n  /* Коэффициент загрузки */\n  double loadFactor() {\n    return _size / _capacity;\n  }\n\n  /* Найти индекс корзины, соответствующий key */\n  int findBucket(int key) {\n    int index = hashFunc(key);\n    int firstTombstone = -1;\n    // Выполнять линейное пробирование и завершить при встрече с пустой корзиной\n    while (_buckets[index] != null) {\n      // Если встретился key, вернуть соответствующий индекс корзины\n      if (_buckets[index]!.key == key) {\n        // Если ранее встретилась метка удаления, переместить пару ключ-значение на этот индекс\n        if (firstTombstone != -1) {\n          _buckets[firstTombstone] = _buckets[index];\n          _buckets[index] = _TOMBSTONE;\n          return firstTombstone; // Вернуть индекс корзины после перемещения\n        }\n        return index; // Вернуть индекс корзины\n      }\n      // Записать первую встретившуюся метку удаления\n      if (firstTombstone == -1 &amp;&amp; _buckets[index] == _TOMBSTONE) {\n        firstTombstone = index;\n      }\n      // Вычислить индекс корзины; при выходе за конец вернуться к началу\n      index = (index + 1) % _capacity;\n    }\n    // Если key не существует, вернуть индекс точки добавления\n    return firstTombstone == -1 ? index : firstTombstone;\n  }\n\n  /* Операция поиска */\n  String? get(int key) {\n    // Найти индекс корзины, соответствующий key\n    int index = findBucket(key);\n    // Если пара ключ-значение найдена, вернуть соответствующее val\n    if (_buckets[index] != null &amp;&amp; _buckets[index] != _TOMBSTONE) {\n      return _buckets[index]!.val;\n    }\n    // Если пары ключ-значение не существует, вернуть null\n    return null;\n  }\n\n  /* Операция добавления */\n  void put(int key, String val) {\n    // Когда коэффициент загрузки превышает порог, выполнить расширение\n    if (loadFactor() &gt; _loadThres) {\n      extend();\n    }\n    // Найти индекс корзины, соответствующий key\n    int index = findBucket(key);\n    // Если пара ключ-значение найдена, перезаписать val и вернуть\n    if (_buckets[index] != null &amp;&amp; _buckets[index] != _TOMBSTONE) {\n      _buckets[index]!.val = val;\n      return;\n    }\n    // Если пары ключ-значение нет, добавить ее\n    _buckets[index] = new Pair(key, val);\n    _size++;\n  }\n\n  /* Операция удаления */\n  void remove(int key) {\n    // Найти индекс корзины, соответствующий key\n    int index = findBucket(key);\n    // Если пара ключ-значение найдена, заменить ее меткой удаления\n    if (_buckets[index] != null &amp;&amp; _buckets[index] != _TOMBSTONE) {\n      _buckets[index] = _TOMBSTONE;\n      _size--;\n    }\n  }\n\n  /* Расширить хеш-таблицу */\n  void extend() {\n    // Временно сохранить исходную хеш-таблицу\n    List&lt;Pair?&gt; bucketsTmp = _buckets;\n    // Инициализация новой хеш-таблицы после расширения\n    _capacity *= _extendRatio;\n    _buckets = List.generate(_capacity, (index) =&gt; null);\n    _size = 0;\n    // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n    for (Pair? pair in bucketsTmp) {\n      if (pair != null &amp;&amp; pair != _TOMBSTONE) {\n        put(pair.key, pair.val);\n      }\n    }\n  }\n\n  /* Вывести хеш-таблицу */\n  void printHashMap() {\n    for (Pair? pair in _buckets) {\n      if (pair == null) {\n        print(\"null\");\n      } else if (pair == _TOMBSTONE) {\n        print(\"TOMBSTONE\");\n      } else {\n        print(\"${pair.key} -&gt; ${pair.val}\");\n      }\n    }\n  }\n}\n</code></pre> hash_map_open_addressing.rs<pre><code>/* Хеш-таблица с открытой адресацией */\nstruct HashMapOpenAddressing {\n    size: usize,                // Число пар ключ-значение\n    capacity: usize,            // Вместимость хеш-таблицы\n    load_thres: f64,            // Порог коэффициента загрузки для запуска расширения\n    extend_ratio: usize,        // Коэффициент расширения\n    buckets: Vec&lt;Option&lt;Pair&gt;&gt;, // Массив корзин\n    TOMBSTONE: Option&lt;Pair&gt;,    // Удалить метку\n}\n\nimpl HashMapOpenAddressing {\n    /* Конструктор */\n    fn new() -&gt; Self {\n        Self {\n            size: 0,\n            capacity: 4,\n            load_thres: 2.0 / 3.0,\n            extend_ratio: 2,\n            buckets: vec![None; 4],\n            TOMBSTONE: Some(Pair {\n                key: -1,\n                val: \"-1\".to_string(),\n            }),\n        }\n    }\n\n    /* Хеш-функция */\n    fn hash_func(&amp;self, key: i32) -&gt; usize {\n        (key % self.capacity as i32) as usize\n    }\n\n    /* Коэффициент загрузки */\n    fn load_factor(&amp;self) -&gt; f64 {\n        self.size as f64 / self.capacity as f64\n    }\n\n    /* Найти индекс корзины, соответствующий key */\n    fn find_bucket(&amp;mut self, key: i32) -&gt; usize {\n        let mut index = self.hash_func(key);\n        let mut first_tombstone = -1;\n        // Выполнять линейное пробирование и завершить при встрече с пустой корзиной\n        while self.buckets[index].is_some() {\n            // Если встретился key, вернуть соответствующий индекс корзины\n            if self.buckets[index].as_ref().unwrap().key == key {\n                // Если ранее встретилась метка удаления, переместить пару ключ-значение в этот индекс\n                if first_tombstone != -1 {\n                    self.buckets[first_tombstone as usize] = self.buckets[index].take();\n                    self.buckets[index] = self.TOMBSTONE.clone();\n                    return first_tombstone as usize; // Вернуть индекс корзины после перемещения\n                }\n                return index; // Вернуть индекс корзины\n            }\n            // Записать первую встретившуюся метку удаления\n            if first_tombstone == -1 &amp;&amp; self.buckets[index] == self.TOMBSTONE {\n                first_tombstone = index as i32;\n            }\n            // Вычислить индекс корзины; при выходе за конец вернуться к началу\n            index = (index + 1) % self.capacity;\n        }\n        // Если key не существует, вернуть индекс точки добавления\n        if first_tombstone == -1 {\n            index\n        } else {\n            first_tombstone as usize\n        }\n    }\n\n    /* Операция поиска */\n    fn get(&amp;mut self, key: i32) -&gt; Option&lt;&amp;str&gt; {\n        // Найти индекс корзины, соответствующий key\n        let index = self.find_bucket(key);\n        // Если пара ключ-значение найдена, вернуть соответствующее val\n        if self.buckets[index].is_some() &amp;&amp; self.buckets[index] != self.TOMBSTONE {\n            return self.buckets[index].as_ref().map(|pair| &amp;pair.val as &amp;str);\n        }\n        // Если пары ключ-значение не существует, вернуть null\n        None\n    }\n\n    /* Операция добавления */\n    fn put(&amp;mut self, key: i32, val: String) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if self.load_factor() &gt; self.load_thres {\n            self.extend();\n        }\n        // Найти индекс корзины, соответствующий key\n        let index = self.find_bucket(key);\n        // Если пара ключ-значение найдена, перезаписать val и вернуть\n        if self.buckets[index].is_some() &amp;&amp; self.buckets[index] != self.TOMBSTONE {\n            self.buckets[index].as_mut().unwrap().val = val;\n            return;\n        }\n        // Если пары ключ-значение нет, добавить ее\n        self.buckets[index] = Some(Pair { key, val });\n        self.size += 1;\n    }\n\n    /* Операция удаления */\n    fn remove(&amp;mut self, key: i32) {\n        // Найти индекс корзины, соответствующий key\n        let index = self.find_bucket(key);\n        // Если пара ключ-значение найдена, заменить ее меткой удаления\n        if self.buckets[index].is_some() &amp;&amp; self.buckets[index] != self.TOMBSTONE {\n            self.buckets[index] = self.TOMBSTONE.clone();\n            self.size -= 1;\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    fn extend(&amp;mut self) {\n        // Временно сохранить исходную хеш-таблицу\n        let buckets_tmp = self.buckets.clone();\n        // Инициализация новой хеш-таблицы после расширения\n        self.capacity *= self.extend_ratio;\n        self.buckets = vec![None; self.capacity];\n        self.size = 0;\n\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for pair in buckets_tmp {\n            if pair.is_none() || pair == self.TOMBSTONE {\n                continue;\n            }\n            let pair = pair.unwrap();\n\n            self.put(pair.key, pair.val);\n        }\n    }\n    /* Вывести хеш-таблицу */\n    fn print(&amp;self) {\n        for pair in &amp;self.buckets {\n            if pair.is_none() {\n                println!(\"null\");\n            } else if pair == &amp;self.TOMBSTONE {\n                println!(\"TOMBSTONE\");\n            } else {\n                let pair = pair.as_ref().unwrap();\n                println!(\"{} -&gt; {}\", pair.key, pair.val);\n            }\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.c<pre><code>/* Хеш-таблица с открытой адресацией */\ntypedef struct {\n    int size;         // Число пар ключ-значение\n    int capacity;     // Вместимость хеш-таблицы\n    double loadThres; // Порог коэффициента загрузки для запуска расширения\n    int extendRatio;  // Коэффициент расширения\n    Pair **buckets;   // Массив корзин\n    Pair *TOMBSTONE;  // Удалить метку\n} HashMapOpenAddressing;\n\n/* Конструктор */\nHashMapOpenAddressing *newHashMapOpenAddressing() {\n    HashMapOpenAddressing *hashMap = (HashMapOpenAddressing *)malloc(sizeof(HashMapOpenAddressing));\n    hashMap-&gt;size = 0;\n    hashMap-&gt;capacity = 4;\n    hashMap-&gt;loadThres = 2.0 / 3.0;\n    hashMap-&gt;extendRatio = 2;\n    hashMap-&gt;buckets = (Pair **)calloc(hashMap-&gt;capacity, sizeof(Pair *));\n    hashMap-&gt;TOMBSTONE = (Pair *)malloc(sizeof(Pair));\n    hashMap-&gt;TOMBSTONE-&gt;key = -1;\n    hashMap-&gt;TOMBSTONE-&gt;val = \"-1\";\n\n    return hashMap;\n}\n\n/* Деструктор */\nvoid delHashMapOpenAddressing(HashMapOpenAddressing *hashMap) {\n    for (int i = 0; i &lt; hashMap-&gt;capacity; i++) {\n        Pair *pair = hashMap-&gt;buckets[i];\n        if (pair != NULL &amp;&amp; pair != hashMap-&gt;TOMBSTONE) {\n            free(pair-&gt;val);\n            free(pair);\n        }\n    }\n    free(hashMap-&gt;buckets);\n    free(hashMap-&gt;TOMBSTONE);\n    free(hashMap);\n}\n\n/* Хеш-функция */\nint hashFunc(HashMapOpenAddressing *hashMap, int key) {\n    return key % hashMap-&gt;capacity;\n}\n\n/* Коэффициент загрузки */\ndouble loadFactor(HashMapOpenAddressing *hashMap) {\n    return (double)hashMap-&gt;size / (double)hashMap-&gt;capacity;\n}\n\n/* Найти индекс корзины, соответствующий key */\nint findBucket(HashMapOpenAddressing *hashMap, int key) {\n    int index = hashFunc(hashMap, key);\n    int firstTombstone = -1;\n    // Выполнять линейное пробирование и завершить при встрече с пустой корзиной\n    while (hashMap-&gt;buckets[index] != NULL) {\n        // Если встретился key, вернуть соответствующий индекс корзины\n        if (hashMap-&gt;buckets[index]-&gt;key == key) {\n            // Если ранее встретилась метка удаления, переместить пару ключ-значение на этот индекс\n            if (firstTombstone != -1) {\n                hashMap-&gt;buckets[firstTombstone] = hashMap-&gt;buckets[index];\n                hashMap-&gt;buckets[index] = hashMap-&gt;TOMBSTONE;\n                return firstTombstone; // Вернуть индекс корзины после перемещения\n            }\n            return index; // Вернуть индекс корзины\n        }\n        // Записать первую встретившуюся метку удаления\n        if (firstTombstone == -1 &amp;&amp; hashMap-&gt;buckets[index] == hashMap-&gt;TOMBSTONE) {\n            firstTombstone = index;\n        }\n        // Вычислить индекс корзины; при выходе за конец вернуться к началу\n        index = (index + 1) % hashMap-&gt;capacity;\n    }\n    // Если key не существует, вернуть индекс точки добавления\n    return firstTombstone == -1 ? index : firstTombstone;\n}\n\n/* Операция поиска */\nchar *get(HashMapOpenAddressing *hashMap, int key) {\n    // Найти индекс корзины, соответствующий key\n    int index = findBucket(hashMap, key);\n    // Если пара ключ-значение найдена, вернуть соответствующее val\n    if (hashMap-&gt;buckets[index] != NULL &amp;&amp; hashMap-&gt;buckets[index] != hashMap-&gt;TOMBSTONE) {\n        return hashMap-&gt;buckets[index]-&gt;val;\n    }\n    // Если пары ключ-значение не существует, вернуть пустую строку\n    return \"\";\n}\n\n/* Операция добавления */\nvoid put(HashMapOpenAddressing *hashMap, int key, char *val) {\n    // Когда коэффициент загрузки превышает порог, выполнить расширение\n    if (loadFactor(hashMap) &gt; hashMap-&gt;loadThres) {\n        extend(hashMap);\n    }\n    // Найти индекс корзины, соответствующий key\n    int index = findBucket(hashMap, key);\n    // Если пара ключ-значение найдена, перезаписать val и вернуть\n    if (hashMap-&gt;buckets[index] != NULL &amp;&amp; hashMap-&gt;buckets[index] != hashMap-&gt;TOMBSTONE) {\n        free(hashMap-&gt;buckets[index]-&gt;val);\n        hashMap-&gt;buckets[index]-&gt;val = (char *)malloc(sizeof(strlen(val) + 1));\n        strcpy(hashMap-&gt;buckets[index]-&gt;val, val);\n        hashMap-&gt;buckets[index]-&gt;val[strlen(val)] = '\\0';\n        return;\n    }\n    // Если пары ключ-значение нет, добавить ее\n    Pair *pair = (Pair *)malloc(sizeof(Pair));\n    pair-&gt;key = key;\n    pair-&gt;val = (char *)malloc(sizeof(strlen(val) + 1));\n    strcpy(pair-&gt;val, val);\n    pair-&gt;val[strlen(val)] = '\\0';\n\n    hashMap-&gt;buckets[index] = pair;\n    hashMap-&gt;size++;\n}\n\n/* Операция удаления */\nvoid removeItem(HashMapOpenAddressing *hashMap, int key) {\n    // Найти индекс корзины, соответствующий key\n    int index = findBucket(hashMap, key);\n    // Если пара ключ-значение найдена, заменить ее меткой удаления\n    if (hashMap-&gt;buckets[index] != NULL &amp;&amp; hashMap-&gt;buckets[index] != hashMap-&gt;TOMBSTONE) {\n        Pair *pair = hashMap-&gt;buckets[index];\n        free(pair-&gt;val);\n        free(pair);\n        hashMap-&gt;buckets[index] = hashMap-&gt;TOMBSTONE;\n        hashMap-&gt;size--;\n    }\n}\n\n/* Расширить хеш-таблицу */\nvoid extend(HashMapOpenAddressing *hashMap) {\n    // Временно сохранить исходную хеш-таблицу\n    Pair **bucketsTmp = hashMap-&gt;buckets;\n    int oldCapacity = hashMap-&gt;capacity;\n    // Инициализация новой хеш-таблицы после расширения\n    hashMap-&gt;capacity *= hashMap-&gt;extendRatio;\n    hashMap-&gt;buckets = (Pair **)calloc(hashMap-&gt;capacity, sizeof(Pair *));\n    hashMap-&gt;size = 0;\n    // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n    for (int i = 0; i &lt; oldCapacity; i++) {\n        Pair *pair = bucketsTmp[i];\n        if (pair != NULL &amp;&amp; pair != hashMap-&gt;TOMBSTONE) {\n            put(hashMap, pair-&gt;key, pair-&gt;val);\n            free(pair-&gt;val);\n            free(pair);\n        }\n    }\n    free(bucketsTmp);\n}\n\n/* Вывести хеш-таблицу */\nvoid print(HashMapOpenAddressing *hashMap) {\n    for (int i = 0; i &lt; hashMap-&gt;capacity; i++) {\n        Pair *pair = hashMap-&gt;buckets[i];\n        if (pair == NULL) {\n            printf(\"NULL\\n\");\n        } else if (pair == hashMap-&gt;TOMBSTONE) {\n            printf(\"TOMBSTONE\\n\");\n        } else {\n            printf(\"%d -&gt; %s\\n\", pair-&gt;key, pair-&gt;val);\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.kt<pre><code>/* Хеш-таблица с открытой адресацией */\nclass HashMapOpenAddressing {\n    private var size: Int               // Число пар ключ-значение\n    private var capacity: Int           // Вместимость хеш-таблицы\n    private val loadThres: Double       // Порог коэффициента загрузки для запуска расширения\n    private val extendRatio: Int        // Коэффициент расширения\n    private var buckets: Array&lt;Pair?&gt;   // Массив корзин\n    private val TOMBSTONE: Pair         // Удалить метку\n\n    /* Конструктор */\n    init {\n        size = 0\n        capacity = 4\n        loadThres = 2.0 / 3.0\n        extendRatio = 2\n        buckets = arrayOfNulls(capacity)\n        TOMBSTONE = Pair(-1, \"-1\")\n    }\n\n    /* Хеш-функция */\n    fun hashFunc(key: Int): Int {\n        return key % capacity\n    }\n\n    /* Коэффициент загрузки */\n    fun loadFactor(): Double {\n        return (size / capacity).toDouble()\n    }\n\n    /* Найти индекс корзины, соответствующий key */\n    fun findBucket(key: Int): Int {\n        var index = hashFunc(key)\n        var firstTombstone = -1\n        // Выполнять линейное пробирование и завершить при встрече с пустой корзиной\n        while (buckets[index] != null) {\n            // Если встретился key, вернуть соответствующий индекс корзины\n            if (buckets[index]?.key == key) {\n                // Если ранее встретилась метка удаления, переместить пару ключ-значение на этот индекс\n                if (firstTombstone != -1) {\n                    buckets[firstTombstone] = buckets[index]\n                    buckets[index] = TOMBSTONE\n                    return firstTombstone // Вернуть индекс корзины после перемещения\n                }\n                return index // Вернуть индекс корзины\n            }\n            // Записать первую встретившуюся метку удаления\n            if (firstTombstone == -1 &amp;&amp; buckets[index] == TOMBSTONE) {\n                firstTombstone = index\n            }\n            // Вычислить индекс корзины; при выходе за конец вернуться к началу\n            index = (index + 1) % capacity\n        }\n        // Если key не существует, вернуть индекс точки добавления\n        return if (firstTombstone == -1) index else firstTombstone\n    }\n\n    /* Операция поиска */\n    fun get(key: Int): String? {\n        // Найти индекс корзины, соответствующий key\n        val index = findBucket(key)\n        // Если пара ключ-значение найдена, вернуть соответствующее val\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            return buckets[index]?._val\n        }\n        // Если пары ключ-значение не существует, вернуть null\n        return null\n    }\n\n    /* Операция добавления */\n    fun put(key: Int, _val: String) {\n        // Когда коэффициент загрузки превышает порог, выполнить расширение\n        if (loadFactor() &gt; loadThres) {\n            extend()\n        }\n        // Найти индекс корзины, соответствующий key\n        val index = findBucket(key)\n        // Если пара ключ-значение найдена, перезаписать val и вернуть\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index]!!._val = _val\n            return\n        }\n        // Если пары ключ-значение нет, добавить ее\n        buckets[index] = Pair(key, _val)\n        size++\n    }\n\n    /* Операция удаления */\n    fun remove(key: Int) {\n        // Найти индекс корзины, соответствующий key\n        val index = findBucket(key)\n        // Если пара ключ-значение найдена, заменить ее меткой удаления\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index] = TOMBSTONE\n            size--\n        }\n    }\n\n    /* Расширить хеш-таблицу */\n    fun extend() {\n        // Временно сохранить исходную хеш-таблицу\n        val bucketsTmp = buckets\n        // Инициализация новой хеш-таблицы после расширения\n        capacity *= extendRatio\n        buckets = arrayOfNulls(capacity)\n        size = 0\n        // Перенести пары ключ-значение из исходной хеш-таблицы в новую\n        for (pair in bucketsTmp) {\n            if (pair != null &amp;&amp; pair != TOMBSTONE) {\n                put(pair.key, pair._val)\n            }\n        }\n    }\n\n    /* Вывести хеш-таблицу */\n    fun print() {\n        for (pair in buckets) {\n            if (pair == null) {\n                println(\"null\")\n            } else if (pair == TOMBSTONE) {\n                println(\"TOMESTOME\")\n            } else {\n                println(\"${pair.key} -&gt; ${pair._val}\")\n            }\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.rb<pre><code>### Хеш-таблица с открытой адресацией ###\nclass HashMapOpenAddressing\n  TOMBSTONE = Pair.new(-1, '-1') # Удалить метку\n\n  ### Конструктор ###\n  def initialize\n    @size = 0 # Число пар ключ-значение\n    @capacity = 4 # Вместимость хеш-таблицы\n    @load_thres = 2.0 / 3.0 # Порог коэффициента загрузки для запуска расширения\n    @extend_ratio = 2 # Коэффициент расширения\n    @buckets = Array.new(@capacity) # Массив корзин\n  end\n\n  ### Хеш-функция ###\n  def hash_func(key)\n    key % @capacity\n  end\n\n  ### Коэффициент загрузки ###\n  def load_factor\n    @size / @capacity\n  end\n\n  ### Найти индекс корзины, соответствующий key ###\n  def find_bucket(key)\n    index = hash_func(key)\n    first_tombstone = -1\n    # Выполнять линейное пробирование и завершить при встрече с пустой корзиной\n    while !@buckets[index].nil?\n      # Если встретился key, вернуть соответствующий индекс корзины\n      if @buckets[index].key == key\n        # Если ранее встретилась метка удаления, переместить пару ключ-значение на этот индекс\n        if first_tombstone != -1\n          @buckets[first_tombstone] = @buckets[index]\n          @buckets[index] = TOMBSTONE\n          return first_tombstone # Вернуть индекс корзины после перемещения\n        end\n        return index # Вернуть индекс корзины\n      end\n      # Записать первую встретившуюся метку удаления\n      first_tombstone = index if first_tombstone == -1 &amp;&amp; @buckets[index] == TOMBSTONE\n      # Вычислить индекс корзины; при выходе за конец вернуться к началу\n      index = (index + 1) % @capacity\n    end\n    # Если key не существует, вернуть индекс точки добавления\n    first_tombstone == -1 ? index : first_tombstone\n  end\n\n  ### Операция поиска ###\n  def get(key)\n    # Найти индекс корзины, соответствующий key\n    index = find_bucket(key)\n    # Если пара ключ-значение найдена, вернуть соответствующее val\n    return @buckets[index].val unless [nil, TOMBSTONE].include?(@buckets[index])\n    # Если пара ключ-значение не существует, вернуть nil\n    nil\n  end\n\n  ### Операция добавления ###\n  def put(key, val)\n    # Когда коэффициент загрузки превышает порог, выполнить расширение\n    extend if load_factor &gt; @load_thres\n    # Найти индекс корзины, соответствующий key\n    index = find_bucket(key)\n    # Если пара ключ-значение найдена, перезаписать val и вернуть\n    unless [nil, TOMBSTONE].include?(@buckets[index])\n      @buckets[index].val = val\n      return\n    end\n    # Если пары ключ-значение нет, добавить ее\n    @buckets[index] = Pair.new(key, val)\n    @size += 1\n  end\n\n  ### Операция удаления ###\n  def remove(key)\n    # Найти индекс корзины, соответствующий key\n    index = find_bucket(key)\n    # Если пара ключ-значение найдена, заменить ее меткой удаления\n    unless [nil, TOMBSTONE].include?(@buckets[index])\n      @buckets[index] = TOMBSTONE\n      @size -= 1\n    end\n  end\n\n  ### Расширение хеш-таблицы ###\n  def extend\n    # Временно сохранить исходную хеш-таблицу\n    buckets_tmp = @buckets\n    # Инициализация новой хеш-таблицы после расширения\n    @capacity *= @extend_ratio\n    @buckets = Array.new(@capacity)\n    @size = 0\n    # Перенести пары ключ-значение из исходной хеш-таблицы в новую\n    for pair in buckets_tmp\n      put(pair.key, pair.val) unless [nil, TOMBSTONE].include?(pair)\n    end\n  end\n\n  ### Вывести хеш-таблицу ###\n  def print\n    for pair in @buckets\n      if pair.nil?\n        puts \"Nil\"\n      elsif pair == TOMBSTONE\n        puts \"TOMBSTONE\"\n      else\n        puts \"#{pair.key} -&gt; #{pair.val}\"\n      end\n    end\n  end\nend\n</code></pre>","path":["Глава 6. Хеш-таблицы","6.2 &nbsp; Хеш-коллизии"],"tags":[]},{"location":"chapter_hashing/hash_collision/#2","level":3,"title":"2.   Квадратичное пробирование","text":"<p>Квадратичное пробирование похоже на линейное пробирование и тоже является одной из распространенных стратегий открытой адресации. При возникновении конфликта оно не пропускает фиксированное число шагов, а переходит на расстояние, равное \"квадрату числа попыток\", то есть на \\(1, 4, 9, \\dots\\) шагов.</p> <p>Квадратичное пробирование имеет следующие основные преимущества.</p> <ul> <li>Квадратичное пробирование пытается смягчить эффект кластеризации линейного пробирования, так как пропускает расстояния, равные квадрату номера попытки.</li> <li>Квадратичное пробирование перепрыгивает на более дальние позиции в поисках свободного места, что помогает распределять данные более равномерно.</li> </ul> <p>Однако квадратичное пробирование не является идеальным.</p> <ul> <li>Кластеризация все равно существует: некоторые позиции по-прежнему занимают чаще других.</li> <li>Из-за быстрого роста квадрата квадратичное пробирование может не охватить всю хеш-таблицу, а это означает, что даже при наличии пустых бакетов оно может так до них и не добраться.</li> </ul>","path":["Глава 6. Хеш-таблицы","6.2 &nbsp; Хеш-коллизии"],"tags":[]},{"location":"chapter_hashing/hash_collision/#3","level":3,"title":"3.   Повторное хеширование","text":"<p>Как видно из названия, метод повторного хеширования использует для пробирования несколько хеш-функций \\(f_1(x)\\), \\(f_2(x)\\), \\(f_3(x)\\), \\(\\dots\\) .</p> <ul> <li>Вставка элемента: если хеш-функция \\(f_1(x)\\) вызывает конфликт, то пробуем \\(f_2(x)\\) , и так далее, пока не будет найдено пустое место для вставки элемента.</li> <li>Поиск элемента: поиск идет в том же порядке хеш-функций, пока не будет найден целевой элемент; если встречается пустая позиция или уже были опробованы все хеш-функции, это означает, что элемента в хеш-таблице нет, и возвращается <code>None</code> .</li> </ul> <p>По сравнению с линейным пробированием метод повторного хеширования меньше подвержен кластеризации, но несколько хеш-функций приносят дополнительные вычислительные затраты.</p> <p>Tip</p> <p>Обрати внимание: у хеш-таблиц с открытой адресацией (линейное пробирование, квадратичное пробирование и повторное хеширование) есть общая проблема: в них нельзя напрямую удалять элементы.</p>","path":["Глава 6. Хеш-таблицы","6.2 &nbsp; Хеш-коллизии"],"tags":[]},{"location":"chapter_hashing/hash_collision/#623","level":2,"title":"6.2.3   Выбор в языках программирования","text":"<p>Разные языки программирования используют разные стратегии реализации хеш-таблиц. Ниже приведено несколько примеров.</p> <ul> <li>Python использует открытую адресацию. В словаре <code>dict</code> для пробирования применяются псевдослучайные числа.</li> <li>Java использует метод цепочек. Начиная с JDK 1.8, когда длина массива внутри <code>HashMap</code> достигает 64, а длина списка достигает 8, этот список преобразуется в красно-черное дерево для повышения производительности поиска.</li> <li>Go использует метод цепочек. В Go установлено, что каждый бакет может хранить не более 8 пар ключ-значение; при переполнении подключается overflow-бакет, а когда таких бакетов становится слишком много, выполняется специальное расширение того же масштаба, чтобы сохранить производительность.</li> </ul>","path":["Глава 6. Хеш-таблицы","6.2 &nbsp; Хеш-коллизии"],"tags":[]},{"location":"chapter_hashing/hash_map/","level":1,"title":"6.1   Хеш-таблица","text":"<p>Хеш-таблица (hash table), также называемая таблицей рассеяния, реализует эффективный поиск элементов за счет установления соответствия между ключом <code>key</code> и значением <code>value</code> . Иначе говоря, если передать в хеш-таблицу ключ <code>key</code> , то можно за \\(O(1)\\) времени получить соответствующее значение <code>value</code> .</p> <p>Как показано на рисунке 6-1, пусть есть \\(n\\) студентов, и у каждого из них есть два поля данных: имя и номер студенческого билета. Если мы хотим реализовать запрос вида \"ввести номер студенческого билета и вернуть соответствующее имя\", то для этого можно использовать показанную ниже хеш-таблицу.</p> <p></p> <p> Рисунок 6-1   Абстрактное представление хеш-таблицы </p> <p>Помимо хеш-таблицы, функцией поиска также обладают массив и связный список. Сравнение их эффективности приведено в таблице 6-1.</p> <ul> <li>Добавление элемента: нужно лишь добавить элемент в конец массива (или списка), что занимает \\(O(1)\\) времени.</li> <li>Поиск элемента: так как массив (или список) неупорядочен, приходится обходить все элементы, что занимает \\(O(n)\\) времени.</li> <li>Удаление элемента: сначала нужно найти элемент, затем удалить его из массива (или списка), что занимает \\(O(n)\\) времени.</li> </ul> <p> Таблица 6-1   Сравнение эффективности поиска элементов </p> Массив Связный список Хеш-таблица Поиск элемента \\(O(n)\\) \\(O(n)\\) \\(O(1)\\) Добавление элемента \\(O(1)\\) \\(O(1)\\) \\(O(1)\\) Удаление элемента \\(O(n)\\) \\(O(n)\\) \\(O(1)\\) <p>Нетрудно заметить, что операции поиска, добавления и удаления в хеш-таблице имеют временную сложность \\(O(1)\\) , то есть выполняются очень эффективно.</p>","path":["Глава 6. Хеш-таблицы","6.1 &nbsp; Хеш-таблица"],"tags":[]},{"location":"chapter_hashing/hash_map/#611-","level":2,"title":"6.1.1   Основные операции с хеш-таблицей","text":"<p>К базовым операциям хеш-таблицы относятся инициализация, поиск, добавление пар ключ-значение и удаление пар ключ-значение. Пример кода приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby hash_map.py<pre><code># Инициализация хеш-таблицы\nhmap: dict = {}\n\n# Операция добавления\n# Добавить пару ключ-значение (key, value) в хеш-таблицу\nhmap[12836] = \"Сяо Ха\"\nhmap[15937] = \"Сяо Ло\"\nhmap[16750] = \"Сяо Суань\"\nhmap[13276] = \"Сяо Фа\"\nhmap[10583] = \"Сяо Я\"\n\n# Операция поиска\n# Передать в хеш-таблицу ключ key и получить значение value\nname: str = hmap[15937]\n\n# Операция удаления\n# Удалить пару ключ-значение (key, value) из хеш-таблицы\nhmap.pop(10583)\n</code></pre> hash_map.cpp<pre><code>/* Инициализация хеш-таблицы */\nunordered_map&lt;int, string&gt; map;\n\n/* Операция добавления */\n// Добавить пару ключ-значение (key, value) в хеш-таблицу\nmap[12836] = \"Сяо Ха\";\nmap[15937] = \"Сяо Ло\";\nmap[16750] = \"Сяо Суань\";\nmap[13276] = \"Сяо Фа\";\nmap[10583] = \"Сяо Я\";\n\n/* Операция поиска */\n// Передать в хеш-таблицу ключ key и получить значение value\nstring name = map[15937];\n\n/* Операция удаления */\n// Удалить пару ключ-значение (key, value) из хеш-таблицы\nmap.erase(10583);\n</code></pre> hash_map.java<pre><code>/* Инициализация хеш-таблицы */\nMap&lt;Integer, String&gt; map = new HashMap&lt;&gt;();\n\n/* Операция добавления */\n// Добавить пару ключ-значение (key, value) в хеш-таблицу\nmap.put(12836, \"Сяо Ха\");\nmap.put(15937, \"Сяо Ло\");\nmap.put(16750, \"Сяо Суань\");\nmap.put(13276, \"Сяо Фа\");\nmap.put(10583, \"Сяо Я\");\n\n/* Операция поиска */\n// Передать в хеш-таблицу ключ key и получить значение value\nString name = map.get(15937);\n\n/* Операция удаления */\n// Удалить пару ключ-значение (key, value) из хеш-таблицы\nmap.remove(10583);\n</code></pre> hash_map.cs<pre><code>/* Инициализация хеш-таблицы */\nDictionary&lt;int, string&gt; map = new() {\n    /* Операция добавления */\n    // Добавить пару ключ-значение (key, value) в хеш-таблицу\n    { 12836, \"Сяо Ха\" },\n    { 15937, \"Сяо Ло\" },\n    { 16750, \"Сяо Суань\" },\n    { 13276, \"Сяо Фа\" },\n    { 10583, \"Сяо Я\" }\n};\n\n/* Операция поиска */\n// Передать в хеш-таблицу ключ key и получить значение value\nstring name = map[15937];\n\n/* Операция удаления */\n// Удалить пару ключ-значение (key, value) из хеш-таблицы\nmap.Remove(10583);\n</code></pre> hash_map_test.go<pre><code>/* Инициализация хеш-таблицы */\nhmap := make(map[int]string)\n\n/* Операция добавления */\n// Добавить пару ключ-значение (key, value) в хеш-таблицу\nhmap[12836] = \"Сяо Ха\"\nhmap[15937] = \"Сяо Ло\"\nhmap[16750] = \"Сяо Суань\"\nhmap[13276] = \"Сяо Фа\"\nhmap[10583] = \"Сяо Я\"\n\n/* Операция поиска */\n// Передать в хеш-таблицу ключ key и получить значение value\nname := hmap[15937]\n\n/* Операция удаления */\n// Удалить пару ключ-значение (key, value) из хеш-таблицы\ndelete(hmap, 10583)\n</code></pre> hash_map.swift<pre><code>/* Инициализация хеш-таблицы */\nvar map: [Int: String] = [:]\n\n/* Операция добавления */\n// Добавить пару ключ-значение (key, value) в хеш-таблицу\nmap[12836] = \"Сяо Ха\"\nmap[15937] = \"Сяо Ло\"\nmap[16750] = \"Сяо Суань\"\nmap[13276] = \"Сяо Фа\"\nmap[10583] = \"Сяо Я\"\n\n/* Операция поиска */\n// Передать в хеш-таблицу ключ key и получить значение value\nlet name = map[15937]!\n\n/* Операция удаления */\n// Удалить пару ключ-значение (key, value) из хеш-таблицы\nmap.removeValue(forKey: 10583)\n</code></pre> hash_map.js<pre><code>/* Инициализация хеш-таблицы */\nconst map = new Map();\n/* Операция добавления */\n// Добавить пару ключ-значение (key, value) в хеш-таблицу\nmap.set(12836, 'Сяо Ха');\nmap.set(15937, 'Сяо Ло');\nmap.set(16750, 'Сяо Суань');\nmap.set(13276, 'Сяо Фа');\nmap.set(10583, 'Сяо Я');\n\n/* Операция поиска */\n// Передать в хеш-таблицу ключ key и получить значение value\nlet name = map.get(15937);\n\n/* Операция удаления */\n// Удалить пару ключ-значение (key, value) из хеш-таблицы\nmap.delete(10583);\n</code></pre> hash_map.ts<pre><code>/* Инициализация хеш-таблицы */\nconst map = new Map&lt;number, string&gt;();\n/* Операция добавления */\n// Добавить пару ключ-значение (key, value) в хеш-таблицу\nmap.set(12836, 'Сяо Ха');\nmap.set(15937, 'Сяо Ло');\nmap.set(16750, 'Сяо Суань');\nmap.set(13276, 'Сяо Фа');\nmap.set(10583, 'Сяо Я');\nconsole.info('\\nПосле добавления хеш-таблица имеет вид\\nKey -&gt; Value');\nconsole.info(map);\n\n/* Операция поиска */\n// Передать в хеш-таблицу ключ key и получить значение value\nlet name = map.get(15937);\nconsole.info('\\nПо номеру 15937 найдено имя ' + name);\n\n/* Операция удаления */\n// Удалить пару ключ-значение (key, value) из хеш-таблицы\nmap.delete(10583);\nconsole.info('\\nПосле удаления 10583 хеш-таблица имеет вид\\nKey -&gt; Value');\nconsole.info(map);\n</code></pre> hash_map.dart<pre><code>/* Инициализация хеш-таблицы */\nMap&lt;int, String&gt; map = {};\n\n/* Операция добавления */\n// Добавить пару ключ-значение (key, value) в хеш-таблицу\nmap[12836] = \"Сяо Ха\";\nmap[15937] = \"Сяо Ло\";\nmap[16750] = \"Сяо Суань\";\nmap[13276] = \"Сяо Фа\";\nmap[10583] = \"Сяо Я\";\n\n/* Операция поиска */\n// Передать в хеш-таблицу ключ key и получить значение value\nString name = map[15937];\n\n/* Операция удаления */\n// Удалить пару ключ-значение (key, value) из хеш-таблицы\nmap.remove(10583);\n</code></pre> hash_map.rs<pre><code>use std::collections::HashMap;\n\n/* Инициализация хеш-таблицы */\nlet mut map: HashMap&lt;i32, String&gt; = HashMap::new();\n\n/* Операция добавления */\n// Добавить пару ключ-значение (key, value) в хеш-таблицу\nmap.insert(12836, \"Сяо Ха\".to_string());\nmap.insert(15937, \"Сяо Ло\".to_string());\nmap.insert(16750, \"Сяо Суань\".to_string());\nmap.insert(13279, \"Сяо Фа\".to_string());\nmap.insert(10583, \"Сяо Я\".to_string());\n\n/* Операция поиска */\n// Передать в хеш-таблицу ключ key и получить значение value\nlet _name: Option&lt;&amp;String&gt; = map.get(&amp;15937);\n\n/* Операция удаления */\n// Удалить пару ключ-значение (key, value) из хеш-таблицы\nlet _removed_value: Option&lt;String&gt; = map.remove(&amp;10583);\n</code></pre> hash_map.c<pre><code>// В C нет встроенной хеш-таблицы\n</code></pre> hash_map.kt<pre><code>/* Инициализация хеш-таблицы */\nval map = HashMap&lt;Int,String&gt;()\n\n/* Операция добавления */\n// Добавить пару ключ-значение (key, value) в хеш-таблицу\nmap[12836] = \"Сяо Ха\"\nmap[15937] = \"Сяо Ло\"\nmap[16750] = \"Сяо Суань\"\nmap[13276] = \"Сяо Фа\"\nmap[10583] = \"Сяо Я\"\n\n/* Операция поиска */\n// Передать в хеш-таблицу ключ key и получить значение value\nval name = map[15937]\n\n/* Операция удаления */\n// Удалить пару ключ-значение (key, value) из хеш-таблицы\nmap.remove(10583)\n</code></pre> hash_map.rb<pre><code># Инициализация хеш-таблицы\nhmap = {}\n\n# Операция добавления\n# Добавить пару ключ-значение (key, value) в хеш-таблицу\nhmap[12836] = \"Сяо Ха\"\nhmap[15937] = \"Сяо Ло\"\nhmap[16750] = \"Сяо Суань\"\nhmap[13276] = \"Сяо Фа\"\nhmap[10583] = \"Сяо Я\"\n\n# Операция поиска\n# Передать в хеш-таблицу ключ key и получить значение value\nname = hmap[15937]\n\n# Операция удаления\n# Удалить пару ключ-значение (key, value) из хеш-таблицы\nhmap.delete(10583)\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%85%D0%B5%D1%88-%D1%82%D0%B0%D0%B1%D0%BB%D0%B8%D1%86%D1%83%0A%20%20%20%20hmap%20%3D%20%7B%7D%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9E%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%8F%20%D0%B4%D0%BE%D0%B1%D0%B0%D0%B2%D0%BB%D0%B5%D0%BD%D0%B8%D1%8F%0A%20%20%20%20%23%20%D0%94%D0%BE%D0%B1%D0%B0%D0%B2%D0%B8%D1%82%D1%8C%20%D0%B2%20%D1%85%D0%B5%D1%88-%D1%82%D0%B0%D0%B1%D0%BB%D0%B8%D1%86%D1%83%20%D0%BF%D0%B0%D1%80%D1%83%20%D0%BA%D0%BB%D1%8E%D1%87-%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%28key%2C%20value%29%0A%20%20%20%20hmap%5B12836%5D%20%3D%20%22%D0%A1%D1%8F%D0%BE%20%D0%A5%D0%B0%22%0A%20%20%20%20hmap%5B15937%5D%20%3D%20%22%D0%A1%D1%8F%D0%BE%20%D0%9B%D0%BE%22%0A%20%20%20%20hmap%5B16750%5D%20%3D%20%22%D0%A1%D1%8F%D0%BE%20%D0%A1%D1%83%D0%B0%D0%BD%D1%8C%22%0A%20%20%20%20hmap%5B13276%5D%20%3D%20%22%D0%A1%D1%8F%D0%BE%20%D0%A4%D0%B0%22%0A%20%20%20%20hmap%5B10583%5D%20%3D%20%22%D0%A3%D1%82%D0%B5%D0%BD%D0%BE%D0%BA%22%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9E%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%8F%20%D0%BF%D0%BE%D0%B8%D1%81%D0%BA%D0%B0%0A%20%20%20%20%23%20%D0%9F%D0%B5%D1%80%D0%B5%D0%B4%D0%B0%D1%82%D1%8C%20%D0%BA%D0%BB%D1%8E%D1%87%20key%20%D0%B2%20%D1%85%D0%B5%D1%88-%D1%82%D0%B0%D0%B1%D0%BB%D0%B8%D1%86%D1%83%20%D0%B8%20%D0%BF%D0%BE%D0%BB%D1%83%D1%87%D0%B8%D1%82%D1%8C%20%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20value%0A%20%20%20%20name%20%3D%20hmap%5B15937%5D%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9E%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%8F%20%D1%83%D0%B4%D0%B0%D0%BB%D0%B5%D0%BD%D0%B8%D1%8F%0A%20%20%20%20%23%20%D0%A3%D0%B4%D0%B0%D0%BB%D0%B8%D1%82%D1%8C%20%D0%B8%D0%B7%20%D1%85%D0%B5%D1%88-%D1%82%D0%B0%D0%B1%D0%BB%D0%B8%D1%86%D1%8B%20%D0%BF%D0%B0%D1%80%D1%83%20%D0%BA%D0%BB%D1%8E%D1%87-%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%28key%2C%20value%29%0A%20%20%20%20hmap.pop%2810583%29&amp;cumulative=false&amp;curInstr=2&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p> <p>Существует три распространенных способа обхода хеш-таблицы: обход пар ключ-значение, обход ключей и обход значений. Примеры кода приведены ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby hash_map.py<pre><code># Обход хеш-таблицы\n# Обход пар ключ-значение key-&gt;value\nfor key, value in hmap.items():\n    print(key, \"-&gt;\", value)\n# Обход только ключей key\nfor key in hmap.keys():\n    print(key)\n# Обход только значений value\nfor value in hmap.values():\n    print(value)\n</code></pre> hash_map.cpp<pre><code>/* Обход хеш-таблицы */\n// Обход пар ключ-значение key-&gt;value\nfor (auto kv: map) {\n    cout &lt;&lt; kv.first &lt;&lt; \" -&gt; \" &lt;&lt; kv.second &lt;&lt; endl;\n}\n// Обход key-&gt;value с помощью итератора\nfor (auto iter = map.begin(); iter != map.end(); iter++) {\n    cout &lt;&lt; iter-&gt;first &lt;&lt; \"-&gt;\" &lt;&lt; iter-&gt;second &lt;&lt; endl;\n}\n</code></pre> hash_map.java<pre><code>/* Обход хеш-таблицы */\n// Обход пар ключ-значение key-&gt;value\nfor (Map.Entry &lt;Integer, String&gt; kv: map.entrySet()) {\n    System.out.println(kv.getKey() + \" -&gt; \" + kv.getValue());\n}\n// Обход только ключей key\nfor (int key: map.keySet()) {\n    System.out.println(key);\n}\n// Обход только значений value\nfor (String val: map.values()) {\n    System.out.println(val);\n}\n</code></pre> hash_map.cs<pre><code>/* Обход хеш-таблицы */\n// Обход пар ключ-значение Key-&gt;Value\nforeach (var kv in map) {\n    Console.WriteLine(kv.Key + \" -&gt; \" + kv.Value);\n}\n// Обход только ключей key\nforeach (int key in map.Keys) {\n    Console.WriteLine(key);\n}\n// Обход только значений value\nforeach (string val in map.Values) {\n    Console.WriteLine(val);\n}\n</code></pre> hash_map_test.go<pre><code>/* Обход хеш-таблицы */\n// Обход пар ключ-значение key-&gt;value\nfor key, value := range hmap {\n    fmt.Println(key, \"-&gt;\", value)\n}\n// Обход только ключей key\nfor key := range hmap {\n    fmt.Println(key)\n}\n// Обход только значений value\nfor _, value := range hmap {\n    fmt.Println(value)\n}\n</code></pre> hash_map.swift<pre><code>/* Обход хеш-таблицы */\n// Обход пар ключ-значение Key-&gt;Value\nfor (key, value) in map {\n    print(\"\\(key) -&gt; \\(value)\")\n}\n// Обход только ключей Key\nfor key in map.keys {\n    print(key)\n}\n// Обход только значений Value\nfor value in map.values {\n    print(value)\n}\n</code></pre> hash_map.js<pre><code>/* Обход хеш-таблицы */\nconsole.info('\\nОбход пар ключ-значение Key-&gt;Value');\nfor (const [k, v] of map.entries()) {\n    console.info(k + ' -&gt; ' + v);\n}\nconsole.info('\\nОбход только ключей Key');\nfor (const k of map.keys()) {\n    console.info(k);\n}\nconsole.info('\\nОбход только значений Value');\nfor (const v of map.values()) {\n    console.info(v);\n}\n</code></pre> hash_map.ts<pre><code>/* Обход хеш-таблицы */\nconsole.info('\\nОбход пар ключ-значение Key-&gt;Value');\nfor (const [k, v] of map.entries()) {\n    console.info(k + ' -&gt; ' + v);\n}\nconsole.info('\\nОбход только ключей Key');\nfor (const k of map.keys()) {\n    console.info(k);\n}\nconsole.info('\\nОбход только значений Value');\nfor (const v of map.values()) {\n    console.info(v);\n}\n</code></pre> hash_map.dart<pre><code>/* Обход хеш-таблицы */\n// Обход пар ключ-значение Key-&gt;Value\nmap.forEach((key, value) {\n  print('$key -&gt; $value');\n});\n\n// Обход только ключей Key\nmap.keys.forEach((key) {\n  print(key);\n});\n\n// Обход только значений Value\nmap.values.forEach((value) {\n  print(value);\n});\n</code></pre> hash_map.rs<pre><code>/* Обход хеш-таблицы */\n// Обход пар ключ-значение Key-&gt;Value\nfor (key, value) in &amp;map {\n    println!(\"{key} -&gt; {value}\");\n}\n\n// Обход только ключей Key\nfor key in map.keys() {\n    println!(\"{key}\");\n}\n\n// Обход только значений Value\nfor value in map.values() {\n    println!(\"{value}\");\n}\n</code></pre> hash_map.c<pre><code>// В C нет встроенной хеш-таблицы\n</code></pre> hash_map.kt<pre><code>/* Обход хеш-таблицы */\n// Обход пар ключ-значение key-&gt;value\nfor ((key, value) in map) {\n    println(\"$key -&gt; $value\")\n}\n// Обход только ключей key\nfor (key in map.keys) {\n    println(key)\n}\n// Обход только значений value\nfor (_val in map.values) {\n    println(_val)\n}\n</code></pre> hash_map.rb<pre><code># Обход хеш-таблицы\n# Обход пар ключ-значение key-&gt;value\nhmap.entries.each { |key, value| puts \"#{key} -&gt; #{value}\" }\n\n# Обход только ключей key\nhmap.keys.each { |key| puts key }\n\n# Обход только значений value\nhmap.values.each { |val| puts val }\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%85%D0%B5%D1%88-%D1%82%D0%B0%D0%B1%D0%BB%D0%B8%D1%86%D1%83%0A%20%20%20%20hmap%20%3D%20%7B%7D%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9E%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%8F%20%D0%B4%D0%BE%D0%B1%D0%B0%D0%B2%D0%BB%D0%B5%D0%BD%D0%B8%D1%8F%0A%20%20%20%20%23%20%D0%94%D0%BE%D0%B1%D0%B0%D0%B2%D0%B8%D1%82%D1%8C%20%D0%B2%20%D1%85%D0%B5%D1%88-%D1%82%D0%B0%D0%B1%D0%BB%D0%B8%D1%86%D1%83%20%D0%BF%D0%B0%D1%80%D1%83%20%D0%BA%D0%BB%D1%8E%D1%87-%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%28key%2C%20value%29%0A%20%20%20%20hmap%5B12836%5D%20%3D%20%22%D0%A1%D1%8F%D0%BE%20%D0%A5%D0%B0%22%0A%20%20%20%20hmap%5B15937%5D%20%3D%20%22%D0%A1%D1%8F%D0%BE%20%D0%9B%D0%BE%22%0A%20%20%20%20hmap%5B16750%5D%20%3D%20%22%D0%A1%D1%8F%D0%BE%20%D0%A1%D1%83%D0%B0%D0%BD%D1%8C%22%0A%20%20%20%20hmap%5B13276%5D%20%3D%20%22%D0%A1%D1%8F%D0%BE%20%D0%A4%D0%B0%22%0A%20%20%20%20hmap%5B10583%5D%20%3D%20%22%D0%A3%D1%82%D0%B5%D0%BD%D0%BE%D0%BA%22%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9F%D0%B5%D1%80%D0%B5%D0%B1%D1%80%D0%B0%D1%82%D1%8C%20%D1%85%D0%B5%D1%88-%D1%82%D0%B0%D0%B1%D0%BB%D0%B8%D1%86%D1%83%0A%20%20%20%20%23%20%D0%9E%D0%B1%D0%BE%D0%B9%D1%82%D0%B8%D0%BF%D0%B0%D1%80%D0%B0%20%D0%BA%D0%BB%D1%8E%D1%87-%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20key-%3Evalue%0A%20%20%20%20for%20key%2C%20value%20in%20hmap.items%28%29%3A%0A%20%20%20%20%20%20%20%20print%28key%2C%20%22-%3E%22%2C%20value%29%0A%20%20%20%20%23%20%D0%BE%D1%82%D0%B4%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D0%9E%D0%B1%D0%BE%D0%B9%D1%82%D0%B8%D0%BA%D0%BB%D1%8E%D1%87%20key%0A%20%20%20%20for%20key%20in%20hmap.keys%28%29%3A%0A%20%20%20%20%20%20%20%20print%28key%29%0A%20%20%20%20%23%20%D0%BE%D1%82%D0%B4%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D0%9E%D0%B1%D0%BE%D0%B9%D1%82%D0%B8%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20value%0A%20%20%20%20for%20value%20in%20hmap.values%28%29%3A%0A%20%20%20%20%20%20%20%20print%28value%29&amp;cumulative=false&amp;curInstr=8&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 6. Хеш-таблицы","6.1 &nbsp; Хеш-таблица"],"tags":[]},{"location":"chapter_hashing/hash_map/#612-","level":2,"title":"6.1.2   Простая реализация хеш-таблицы","text":"<p>Сначала рассмотрим самый простой случай: реализуем хеш-таблицу только с помощью одного массива. В хеш-таблице каждую пустую ячейку массива мы называем бакетом (bucket), и каждый бакет может хранить одну пару ключ-значение. Следовательно, операция поиска сводится к тому, чтобы найти бакет, соответствующий <code>key</code> , и получить из него <code>value</code> .</p> <p>Но как определить бакет, соответствующий заданному <code>key</code> ? Это делается с помощью хеш-функции (hash function). Назначение хеш-функции - отображать большое входное пространство в меньшее выходное пространство. В хеш-таблице входным пространством являются все <code>key</code> , а выходным - все бакеты, то есть индексы массива. Иначе говоря, передав <code>key</code> на вход, мы можем с помощью хеш-функции получить позицию хранения соответствующей пары ключ-значение в массиве.</p> <p>Процесс вычисления хеш-функции для одного <code>key</code> включает два шага.</p> <ol> <li>Сначала с помощью некоторого хеш-алгоритма <code>hash()</code> вычисляется хеш-значение.</li> <li>Затем хеш-значение берется по модулю числа бакетов (длины массива) <code>capacity</code> , чтобы получить бакет (индекс массива) <code>index</code> , соответствующий этому <code>key</code> .</li> </ol> <pre><code>index = hash(key) % capacity\n</code></pre> <p>После этого можно использовать <code>index</code> для доступа к соответствующему бакету в хеш-таблице и получения <code>value</code> .</p> <p>Пусть длина массива <code>capacity = 100</code> , а хеш-алгоритм <code>hash(key) = key</code> . Тогда легко получить хеш-функцию <code>key % 100</code> . На рисунке 6-2 на примере <code>key</code> \"номер студенческого билета\" и <code>value</code> \"имя\" показан принцип работы хеш-функции.</p> <p></p> <p> Рисунок 6-2   Принцип работы хеш-функции </p> <p>Ниже приведен код простой реализации хеш-таблицы. В нем мы инкапсулируем <code>key</code> и <code>value</code> в класс <code>Pair</code> , чтобы представить пару ключ-значение.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array_hash_map.py<pre><code>class Pair:\n    \"\"\"Пара ключ-значение\"\"\"\n\n    def __init__(self, key: int, val: str):\n        self.key = key\n        self.val = val\n\nclass ArrayHashMap:\n    \"\"\"Хеш-таблица на основе массива\"\"\"\n\n    def __init__(self):\n        \"\"\"Конструктор\"\"\"\n        # Инициализировать массив, содержащий 100 корзин\n        self.buckets: list[Pair | None] = [None] * 100\n\n    def hash_func(self, key: int) -&gt; int:\n        \"\"\"Хеш-функция\"\"\"\n        index = key % 100\n        return index\n\n    def get(self, key: int) -&gt; str | None:\n        \"\"\"Операция поиска\"\"\"\n        index: int = self.hash_func(key)\n        pair: Pair = self.buckets[index]\n        if pair is None:\n            return None\n        return pair.val\n\n    def put(self, key: int, val: str):\n        \"\"\"Операции добавления и обновления\"\"\"\n        pair = Pair(key, val)\n        index: int = self.hash_func(key)\n        self.buckets[index] = pair\n\n    def remove(self, key: int):\n        \"\"\"Операция удаления\"\"\"\n        index: int = self.hash_func(key)\n        # Присвоить None, что означает удаление\n        self.buckets[index] = None\n\n    def entry_set(self) -&gt; list[Pair]:\n        \"\"\"Получить все пары ключ-значение\"\"\"\n        result: list[Pair] = []\n        for pair in self.buckets:\n            if pair is not None:\n                result.append(pair)\n        return result\n\n    def key_set(self) -&gt; list[int]:\n        \"\"\"Получить все ключи\"\"\"\n        result = []\n        for pair in self.buckets:\n            if pair is not None:\n                result.append(pair.key)\n        return result\n\n    def value_set(self) -&gt; list[str]:\n        \"\"\"Получить все значения\"\"\"\n        result = []\n        for pair in self.buckets:\n            if pair is not None:\n                result.append(pair.val)\n        return result\n\n    def print(self):\n        \"\"\"Вывести хеш-таблицу\"\"\"\n        for pair in self.buckets:\n            if pair is not None:\n                print(pair.key, \"-&gt;\", pair.val)\n</code></pre> array_hash_map.cpp<pre><code>/* Пара ключ-значение */\nstruct Pair {\n  public:\n    int key;\n    string val;\n    Pair(int key, string val) {\n        this-&gt;key = key;\n        this-&gt;val = val;\n    }\n};\n\n/* Хеш-таблица на основе массива */\nclass ArrayHashMap {\n  private:\n    vector&lt;Pair *&gt; buckets;\n\n  public:\n    ArrayHashMap() {\n        // Инициализировать массив, содержащий 100 корзин\n        buckets = vector&lt;Pair *&gt;(100);\n    }\n\n    ~ArrayHashMap() {\n        // Освободить память\n        for (const auto &amp;bucket : buckets) {\n            delete bucket;\n        }\n        buckets.clear();\n    }\n\n    /* Хеш-функция */\n    int hashFunc(int key) {\n        int index = key % 100;\n        return index;\n    }\n\n    /* Операция поиска */\n    string get(int key) {\n        int index = hashFunc(key);\n        Pair *pair = buckets[index];\n        if (pair == nullptr)\n            return \"\";\n        return pair-&gt;val;\n    }\n\n    /* Операция добавления */\n    void put(int key, string val) {\n        Pair *pair = new Pair(key, val);\n        int index = hashFunc(key);\n        buckets[index] = pair;\n    }\n\n    /* Операция удаления */\n    void remove(int key) {\n        int index = hashFunc(key);\n        // Освободить память и присвоить nullptr\n        delete buckets[index];\n        buckets[index] = nullptr;\n    }\n\n    /* Получить все пары ключ-значение */\n    vector&lt;Pair *&gt; pairSet() {\n        vector&lt;Pair *&gt; pairSet;\n        for (Pair *pair : buckets) {\n            if (pair != nullptr) {\n                pairSet.push_back(pair);\n            }\n        }\n        return pairSet;\n    }\n\n    /* Получить все ключи */\n    vector&lt;int&gt; keySet() {\n        vector&lt;int&gt; keySet;\n        for (Pair *pair : buckets) {\n            if (pair != nullptr) {\n                keySet.push_back(pair-&gt;key);\n            }\n        }\n        return keySet;\n    }\n\n    /* Получить все значения */\n    vector&lt;string&gt; valueSet() {\n        vector&lt;string&gt; valueSet;\n        for (Pair *pair : buckets) {\n            if (pair != nullptr) {\n                valueSet.push_back(pair-&gt;val);\n            }\n        }\n        return valueSet;\n    }\n\n    /* Вывести хеш-таблицу */\n    void print() {\n        for (Pair *kv : pairSet()) {\n            cout &lt;&lt; kv-&gt;key &lt;&lt; \" -&gt; \" &lt;&lt; kv-&gt;val &lt;&lt; endl;\n        }\n    }\n};\n</code></pre> array_hash_map.java<pre><code>/* Пара ключ-значение */\nclass Pair {\n    public int key;\n    public String val;\n\n    public Pair(int key, String val) {\n        this.key = key;\n        this.val = val;\n    }\n}\n\n/* Хеш-таблица на основе массива */\nclass ArrayHashMap {\n    private List&lt;Pair&gt; buckets;\n\n    public ArrayHashMap() {\n        // Инициализировать массив, содержащий 100 корзин\n        buckets = new ArrayList&lt;&gt;();\n        for (int i = 0; i &lt; 100; i++) {\n            buckets.add(null);\n        }\n    }\n\n    /* Хеш-функция */\n    private int hashFunc(int key) {\n        int index = key % 100;\n        return index;\n    }\n\n    /* Операция поиска */\n    public String get(int key) {\n        int index = hashFunc(key);\n        Pair pair = buckets.get(index);\n        if (pair == null)\n            return null;\n        return pair.val;\n    }\n\n    /* Операция добавления */\n    public void put(int key, String val) {\n        Pair pair = new Pair(key, val);\n        int index = hashFunc(key);\n        buckets.set(index, pair);\n    }\n\n    /* Операция удаления */\n    public void remove(int key) {\n        int index = hashFunc(key);\n        // Присвоить null, что означает удаление\n        buckets.set(index, null);\n    }\n\n    /* Получить все пары ключ-значение */\n    public List&lt;Pair&gt; pairSet() {\n        List&lt;Pair&gt; pairSet = new ArrayList&lt;&gt;();\n        for (Pair pair : buckets) {\n            if (pair != null)\n                pairSet.add(pair);\n        }\n        return pairSet;\n    }\n\n    /* Получить все ключи */\n    public List&lt;Integer&gt; keySet() {\n        List&lt;Integer&gt; keySet = new ArrayList&lt;&gt;();\n        for (Pair pair : buckets) {\n            if (pair != null)\n                keySet.add(pair.key);\n        }\n        return keySet;\n    }\n\n    /* Получить все значения */\n    public List&lt;String&gt; valueSet() {\n        List&lt;String&gt; valueSet = new ArrayList&lt;&gt;();\n        for (Pair pair : buckets) {\n            if (pair != null)\n                valueSet.add(pair.val);\n        }\n        return valueSet;\n    }\n\n    /* Вывести хеш-таблицу */\n    public void print() {\n        for (Pair kv : pairSet()) {\n            System.out.println(kv.key + \" -&gt; \" + kv.val);\n        }\n    }\n}\n</code></pre> array_hash_map.cs<pre><code>/* Пара ключ-значение int-&gt;string */\nclass Pair(int key, string val) {\n    public int key = key;\n    public string val = val;\n}\n\n/* Хеш-таблица на основе массива */\nclass ArrayHashMap {\n    List&lt;Pair?&gt; buckets;\n    public ArrayHashMap() {\n        // Инициализировать массив, содержащий 100 корзин\n        buckets = [];\n        for (int i = 0; i &lt; 100; i++) {\n            buckets.Add(null);\n        }\n    }\n\n    /* Хеш-функция */\n    int HashFunc(int key) {\n        int index = key % 100;\n        return index;\n    }\n\n    /* Операция поиска */\n    public string? Get(int key) {\n        int index = HashFunc(key);\n        Pair? pair = buckets[index];\n        if (pair == null) return null;\n        return pair.val;\n    }\n\n    /* Операция добавления */\n    public void Put(int key, string val) {\n        Pair pair = new(key, val);\n        int index = HashFunc(key);\n        buckets[index] = pair;\n    }\n\n    /* Операция удаления */\n    public void Remove(int key) {\n        int index = HashFunc(key);\n        // Присвоить null, что означает удаление\n        buckets[index] = null;\n    }\n\n    /* Получить все пары ключ-значение */\n    public List&lt;Pair&gt; PairSet() {\n        List&lt;Pair&gt; pairSet = [];\n        foreach (Pair? pair in buckets) {\n            if (pair != null)\n                pairSet.Add(pair);\n        }\n        return pairSet;\n    }\n\n    /* Получить все ключи */\n    public List&lt;int&gt; KeySet() {\n        List&lt;int&gt; keySet = [];\n        foreach (Pair? pair in buckets) {\n            if (pair != null)\n                keySet.Add(pair.key);\n        }\n        return keySet;\n    }\n\n    /* Получить все значения */\n    public List&lt;string&gt; ValueSet() {\n        List&lt;string&gt; valueSet = [];\n        foreach (Pair? pair in buckets) {\n            if (pair != null)\n                valueSet.Add(pair.val);\n        }\n        return valueSet;\n    }\n\n    /* Вывести хеш-таблицу */\n    public void Print() {\n        foreach (Pair kv in PairSet()) {\n            Console.WriteLine(kv.key + \" -&gt; \" + kv.val);\n        }\n    }\n}\n</code></pre> array_hash_map.go<pre><code>/* Пара ключ-значение */\ntype pair struct {\n    key int\n    val string\n}\n\n/* Хеш-таблица на основе массива */\ntype arrayHashMap struct {\n    buckets []*pair\n}\n\n/* Инициализация хеш-таблицы */\nfunc newArrayHashMap() *arrayHashMap {\n    // Инициализировать массив, содержащий 100 корзин\n    buckets := make([]*pair, 100)\n    return &amp;arrayHashMap{buckets: buckets}\n}\n\n/* Хеш-функция */\nfunc (a *arrayHashMap) hashFunc(key int) int {\n    index := key % 100\n    return index\n}\n\n/* Операция поиска */\nfunc (a *arrayHashMap) get(key int) string {\n    index := a.hashFunc(key)\n    pair := a.buckets[index]\n    if pair == nil {\n        return \"Not Found\"\n    }\n    return pair.val\n}\n\n/* Операция добавления */\nfunc (a *arrayHashMap) put(key int, val string) {\n    pair := &amp;pair{key: key, val: val}\n    index := a.hashFunc(key)\n    a.buckets[index] = pair\n}\n\n/* Операция удаления */\nfunc (a *arrayHashMap) remove(key int) {\n    index := a.hashFunc(key)\n    // Присвоить nil, что означает удаление\n    a.buckets[index] = nil\n}\n\n/* Получить все ключи */\nfunc (a *arrayHashMap) pairSet() []*pair {\n    var pairs []*pair\n    for _, pair := range a.buckets {\n        if pair != nil {\n            pairs = append(pairs, pair)\n        }\n    }\n    return pairs\n}\n\n/* Получить все ключи */\nfunc (a *arrayHashMap) keySet() []int {\n    var keys []int\n    for _, pair := range a.buckets {\n        if pair != nil {\n            keys = append(keys, pair.key)\n        }\n    }\n    return keys\n}\n\n/* Получить все значения */\nfunc (a *arrayHashMap) valueSet() []string {\n    var values []string\n    for _, pair := range a.buckets {\n        if pair != nil {\n            values = append(values, pair.val)\n        }\n    }\n    return values\n}\n\n/* Вывести хеш-таблицу */\nfunc (a *arrayHashMap) print() {\n    for _, pair := range a.buckets {\n        if pair != nil {\n            fmt.Println(pair.key, \"-&gt;\", pair.val)\n        }\n    }\n}\n</code></pre> array_hash_map.swift<pre><code>/* Пара ключ-значение */\nclass Pair: Equatable {\n    public var key: Int\n    public var val: String\n\n    public init(key: Int, val: String) {\n        self.key = key\n        self.val = val\n    }\n\n    public static func == (lhs: Pair, rhs: Pair) -&gt; Bool {\n        lhs.key == rhs.key &amp;&amp; lhs.val == rhs.val\n    }\n}\n\n/* Хеш-таблица на основе массива */\nclass ArrayHashMap {\n    private var buckets: [Pair?]\n\n    init() {\n        // Инициализировать массив, содержащий 100 корзин\n        buckets = Array(repeating: nil, count: 100)\n    }\n\n    /* Хеш-функция */\n    private func hashFunc(key: Int) -&gt; Int {\n        let index = key % 100\n        return index\n    }\n\n    /* Операция поиска */\n    func get(key: Int) -&gt; String? {\n        let index = hashFunc(key: key)\n        let pair = buckets[index]\n        return pair?.val\n    }\n\n    /* Операция добавления */\n    func put(key: Int, val: String) {\n        let pair = Pair(key: key, val: val)\n        let index = hashFunc(key: key)\n        buckets[index] = pair\n    }\n\n    /* Операция удаления */\n    func remove(key: Int) {\n        let index = hashFunc(key: key)\n        // Присвоить nil, что означает удаление\n        buckets[index] = nil\n    }\n\n    /* Получить все пары ключ-значение */\n    func pairSet() -&gt; [Pair] {\n        buckets.compactMap { $0 }\n    }\n\n    /* Получить все ключи */\n    func keySet() -&gt; [Int] {\n        buckets.compactMap { $0?.key }\n    }\n\n    /* Получить все значения */\n    func valueSet() -&gt; [String] {\n        buckets.compactMap { $0?.val }\n    }\n\n    /* Вывести хеш-таблицу */\n    func print() {\n        for pair in pairSet() {\n            Swift.print(\"\\(pair.key) -&gt; \\(pair.val)\")\n        }\n    }\n}\n</code></pre> array_hash_map.js<pre><code>/* Пара ключ-значение Number -&gt; String */\nclass Pair {\n    constructor(key, val) {\n        this.key = key;\n        this.val = val;\n    }\n}\n\n/* Хеш-таблица на основе массива */\nclass ArrayHashMap {\n    #buckets;\n    constructor() {\n        // Инициализировать массив, содержащий 100 корзин\n        this.#buckets = new Array(100).fill(null);\n    }\n\n    /* Хеш-функция */\n    #hashFunc(key) {\n        return key % 100;\n    }\n\n    /* Операция поиска */\n    get(key) {\n        let index = this.#hashFunc(key);\n        let pair = this.#buckets[index];\n        if (pair === null) return null;\n        return pair.val;\n    }\n\n    /* Операция добавления */\n    set(key, val) {\n        let index = this.#hashFunc(key);\n        this.#buckets[index] = new Pair(key, val);\n    }\n\n    /* Операция удаления */\n    delete(key) {\n        let index = this.#hashFunc(key);\n        // Присвоить null, что означает удаление\n        this.#buckets[index] = null;\n    }\n\n    /* Получить все пары ключ-значение */\n    entries() {\n        let arr = [];\n        for (let i = 0; i &lt; this.#buckets.length; i++) {\n            if (this.#buckets[i]) {\n                arr.push(this.#buckets[i]);\n            }\n        }\n        return arr;\n    }\n\n    /* Получить все ключи */\n    keys() {\n        let arr = [];\n        for (let i = 0; i &lt; this.#buckets.length; i++) {\n            if (this.#buckets[i]) {\n                arr.push(this.#buckets[i].key);\n            }\n        }\n        return arr;\n    }\n\n    /* Получить все значения */\n    values() {\n        let arr = [];\n        for (let i = 0; i &lt; this.#buckets.length; i++) {\n            if (this.#buckets[i]) {\n                arr.push(this.#buckets[i].val);\n            }\n        }\n        return arr;\n    }\n\n    /* Вывести хеш-таблицу */\n    print() {\n        let pairSet = this.entries();\n        for (const pair of pairSet) {\n            console.info(`${pair.key} -&gt; ${pair.val}`);\n        }\n    }\n}\n</code></pre> array_hash_map.ts<pre><code>/* Пара ключ-значение Number -&gt; String */\nclass Pair {\n    public key: number;\n    public val: string;\n\n    constructor(key: number, val: string) {\n        this.key = key;\n        this.val = val;\n    }\n}\n\n/* Хеш-таблица на основе массива */\nclass ArrayHashMap {\n    private readonly buckets: (Pair | null)[];\n\n    constructor() {\n        // Инициализировать массив, содержащий 100 корзин\n        this.buckets = new Array(100).fill(null);\n    }\n\n    /* Хеш-функция */\n    private hashFunc(key: number): number {\n        return key % 100;\n    }\n\n    /* Операция поиска */\n    public get(key: number): string | null {\n        let index = this.hashFunc(key);\n        let pair = this.buckets[index];\n        if (pair === null) return null;\n        return pair.val;\n    }\n\n    /* Операция добавления */\n    public set(key: number, val: string) {\n        let index = this.hashFunc(key);\n        this.buckets[index] = new Pair(key, val);\n    }\n\n    /* Операция удаления */\n    public delete(key: number) {\n        let index = this.hashFunc(key);\n        // Присвоить null, что означает удаление\n        this.buckets[index] = null;\n    }\n\n    /* Получить все пары ключ-значение */\n    public entries(): (Pair | null)[] {\n        let arr: (Pair | null)[] = [];\n        for (let i = 0; i &lt; this.buckets.length; i++) {\n            if (this.buckets[i]) {\n                arr.push(this.buckets[i]);\n            }\n        }\n        return arr;\n    }\n\n    /* Получить все ключи */\n    public keys(): (number | undefined)[] {\n        let arr: (number | undefined)[] = [];\n        for (let i = 0; i &lt; this.buckets.length; i++) {\n            if (this.buckets[i]) {\n                arr.push(this.buckets[i].key);\n            }\n        }\n        return arr;\n    }\n\n    /* Получить все значения */\n    public values(): (string | undefined)[] {\n        let arr: (string | undefined)[] = [];\n        for (let i = 0; i &lt; this.buckets.length; i++) {\n            if (this.buckets[i]) {\n                arr.push(this.buckets[i].val);\n            }\n        }\n        return arr;\n    }\n\n    /* Вывести хеш-таблицу */\n    public print() {\n        let pairSet = this.entries();\n        for (const pair of pairSet) {\n            console.info(`${pair.key} -&gt; ${pair.val}`);\n        }\n    }\n}\n</code></pre> array_hash_map.dart<pre><code>/* Пара ключ-значение */\nclass Pair {\n  int key;\n  String val;\n  Pair(this.key, this.val);\n}\n\n/* Хеш-таблица на основе массива */\nclass ArrayHashMap {\n  late List&lt;Pair?&gt; _buckets;\n\n  ArrayHashMap() {\n    // Инициализировать массив, содержащий 100 корзин\n    _buckets = List.filled(100, null);\n  }\n\n  /* Хеш-функция */\n  int _hashFunc(int key) {\n    final int index = key % 100;\n    return index;\n  }\n\n  /* Операция поиска */\n  String? get(int key) {\n    final int index = _hashFunc(key);\n    final Pair? pair = _buckets[index];\n    if (pair == null) {\n      return null;\n    }\n    return pair.val;\n  }\n\n  /* Операция добавления */\n  void put(int key, String val) {\n    final Pair pair = Pair(key, val);\n    final int index = _hashFunc(key);\n    _buckets[index] = pair;\n  }\n\n  /* Операция удаления */\n  void remove(int key) {\n    final int index = _hashFunc(key);\n    _buckets[index] = null;\n  }\n\n  /* Получить все пары ключ-значение */\n  List&lt;Pair&gt; pairSet() {\n    List&lt;Pair&gt; pairSet = [];\n    for (final Pair? pair in _buckets) {\n      if (pair != null) {\n        pairSet.add(pair);\n      }\n    }\n    return pairSet;\n  }\n\n  /* Получить все ключи */\n  List&lt;int&gt; keySet() {\n    List&lt;int&gt; keySet = [];\n    for (final Pair? pair in _buckets) {\n      if (pair != null) {\n        keySet.add(pair.key);\n      }\n    }\n    return keySet;\n  }\n\n  /* Получить все значения */\n  List&lt;String&gt; values() {\n    List&lt;String&gt; valueSet = [];\n    for (final Pair? pair in _buckets) {\n      if (pair != null) {\n        valueSet.add(pair.val);\n      }\n    }\n    return valueSet;\n  }\n\n  /* Вывести хеш-таблицу */\n  void printHashMap() {\n    for (final Pair kv in pairSet()) {\n      print(\"${kv.key} -&gt; ${kv.val}\");\n    }\n  }\n}\n</code></pre> array_hash_map.rs<pre><code>/* Пара ключ-значение */\n#[derive(Debug, Clone, PartialEq)]\npub struct Pair {\n    pub key: i32,\n    pub val: String,\n}\n\n/* Хеш-таблица на основе массива */\npub struct ArrayHashMap {\n    buckets: Vec&lt;Option&lt;Pair&gt;&gt;,\n}\n\nimpl ArrayHashMap {\n    pub fn new() -&gt; ArrayHashMap {\n        // Инициализировать массив, содержащий 100 корзин\n        Self {\n            buckets: vec![None; 100],\n        }\n    }\n\n    /* Хеш-функция */\n    fn hash_func(&amp;self, key: i32) -&gt; usize {\n        key as usize % 100\n    }\n\n    /* Операция поиска */\n    pub fn get(&amp;self, key: i32) -&gt; Option&lt;&amp;String&gt; {\n        let index = self.hash_func(key);\n        self.buckets[index].as_ref().map(|pair| &amp;pair.val)\n    }\n\n    /* Операция добавления */\n    pub fn put(&amp;mut self, key: i32, val: &amp;str) {\n        let index = self.hash_func(key);\n        self.buckets[index] = Some(Pair {\n            key,\n            val: val.to_string(),\n        });\n    }\n\n    /* Операция удаления */\n    pub fn remove(&amp;mut self, key: i32) {\n        let index = self.hash_func(key);\n        // Присвоить None, что означает удаление\n        self.buckets[index] = None;\n    }\n\n    /* Получить все пары ключ-значение */\n    pub fn entry_set(&amp;self) -&gt; Vec&lt;&amp;Pair&gt; {\n        self.buckets\n            .iter()\n            .filter_map(|pair| pair.as_ref())\n            .collect()\n    }\n\n    /* Получить все ключи */\n    pub fn key_set(&amp;self) -&gt; Vec&lt;&amp;i32&gt; {\n        self.buckets\n            .iter()\n            .filter_map(|pair| pair.as_ref().map(|pair| &amp;pair.key))\n            .collect()\n    }\n\n    /* Получить все значения */\n    pub fn value_set(&amp;self) -&gt; Vec&lt;&amp;String&gt; {\n        self.buckets\n            .iter()\n            .filter_map(|pair| pair.as_ref().map(|pair| &amp;pair.val))\n            .collect()\n    }\n\n    /* Вывести хеш-таблицу */\n    pub fn print(&amp;self) {\n        for pair in self.entry_set() {\n            println!(\"{} -&gt; {}\", pair.key, pair.val);\n        }\n    }\n}\n</code></pre> array_hash_map.c<pre><code>/* Пара ключ-значение int-&gt;string */\ntypedef struct {\n    int key;\n    char *val;\n} Pair;\n\n/* Хеш-таблица на основе массива */\ntypedef struct {\n    Pair *buckets[MAX_SIZE];\n} ArrayHashMap;\n\n/* Конструктор */\nArrayHashMap *newArrayHashMap() {\n    ArrayHashMap *hmap = malloc(sizeof(ArrayHashMap));\n    for (int i=0; i &lt; MAX_SIZE; i++) {\n        hmap-&gt;buckets[i] = NULL;\n    }\n    return hmap;\n}\n\n/* Деструктор */\nvoid delArrayHashMap(ArrayHashMap *hmap) {\n    for (int i = 0; i &lt; MAX_SIZE; i++) {\n        if (hmap-&gt;buckets[i] != NULL) {\n            free(hmap-&gt;buckets[i]-&gt;val);\n            free(hmap-&gt;buckets[i]);\n        }\n    }\n    free(hmap);\n}\n\n/* Операция добавления */\nvoid put(ArrayHashMap *hmap, const int key, const char *val) {\n    Pair *Pair = malloc(sizeof(Pair));\n    Pair-&gt;key = key;\n    Pair-&gt;val = malloc(strlen(val) + 1);\n    strcpy(Pair-&gt;val, val);\n\n    int index = hashFunc(key);\n    hmap-&gt;buckets[index] = Pair;\n}\n\n/* Операция удаления */\nvoid removeItem(ArrayHashMap *hmap, const int key) {\n    int index = hashFunc(key);\n    free(hmap-&gt;buckets[index]-&gt;val);\n    free(hmap-&gt;buckets[index]);\n    hmap-&gt;buckets[index] = NULL;\n}\n\n/* Получить все пары ключ-значение */\nvoid pairSet(ArrayHashMap *hmap, MapSet *set) {\n    Pair *entries;\n    int i = 0, index = 0;\n    int total = 0;\n    /* Подсчитать число действительных пар ключ-значение */\n    for (i = 0; i &lt; MAX_SIZE; i++) {\n        if (hmap-&gt;buckets[i] != NULL) {\n            total++;\n        }\n    }\n    entries = malloc(sizeof(Pair) * total);\n    for (i = 0; i &lt; MAX_SIZE; i++) {\n        if (hmap-&gt;buckets[i] != NULL) {\n            entries[index].key = hmap-&gt;buckets[i]-&gt;key;\n            entries[index].val = malloc(strlen(hmap-&gt;buckets[i]-&gt;val) + 1);\n            strcpy(entries[index].val, hmap-&gt;buckets[i]-&gt;val);\n            index++;\n        }\n    }\n    set-&gt;set = entries;\n    set-&gt;len = total;\n}\n\n/* Получить все ключи */\nvoid keySet(ArrayHashMap *hmap, MapSet *set) {\n    int *keys;\n    int i = 0, index = 0;\n    int total = 0;\n    /* Подсчитать число действительных пар ключ-значение */\n    for (i = 0; i &lt; MAX_SIZE; i++) {\n        if (hmap-&gt;buckets[i] != NULL) {\n            total++;\n        }\n    }\n    keys = malloc(total * sizeof(int));\n    for (i = 0; i &lt; MAX_SIZE; i++) {\n        if (hmap-&gt;buckets[i] != NULL) {\n            keys[index] = hmap-&gt;buckets[i]-&gt;key;\n            index++;\n        }\n    }\n    set-&gt;set = keys;\n    set-&gt;len = total;\n}\n\n/* Получить все значения */\nvoid valueSet(ArrayHashMap *hmap, MapSet *set) {\n    char **vals;\n    int i = 0, index = 0;\n    int total = 0;\n    /* Подсчитать число действительных пар ключ-значение */\n    for (i = 0; i &lt; MAX_SIZE; i++) {\n        if (hmap-&gt;buckets[i] != NULL) {\n            total++;\n        }\n    }\n    vals = malloc(total * sizeof(char *));\n    for (i = 0; i &lt; MAX_SIZE; i++) {\n        if (hmap-&gt;buckets[i] != NULL) {\n            vals[index] = hmap-&gt;buckets[i]-&gt;val;\n            index++;\n        }\n    }\n    set-&gt;set = vals;\n    set-&gt;len = total;\n}\n\n/* Вывести хеш-таблицу */\nvoid print(ArrayHashMap *hmap) {\n    int i;\n    MapSet set;\n    pairSet(hmap, &amp;set);\n    Pair *entries = (Pair *)set.set;\n    for (i = 0; i &lt; set.len; i++) {\n        printf(\"%d -&gt; %s\\n\", entries[i].key, entries[i].val);\n    }\n    free(set.set);\n}\n</code></pre> array_hash_map.kt<pre><code>/* Пара ключ-значение */\nclass Pair(\n    var key: Int,\n    var _val: String\n)\n\n/* Хеш-таблица на основе массива */\nclass ArrayHashMap {\n    // Инициализировать массив, содержащий 100 корзин\n    private val buckets = arrayOfNulls&lt;Pair&gt;(100)\n\n    /* Хеш-функция */\n    fun hashFunc(key: Int): Int {\n        val index = key % 100\n        return index\n    }\n\n    /* Операция поиска */\n    fun get(key: Int): String? {\n        val index = hashFunc(key)\n        val pair = buckets[index] ?: return null\n        return pair._val\n    }\n\n    /* Операция добавления */\n    fun put(key: Int, _val: String) {\n        val pair = Pair(key, _val)\n        val index = hashFunc(key)\n        buckets[index] = pair\n    }\n\n    /* Операция удаления */\n    fun remove(key: Int) {\n        val index = hashFunc(key)\n        // Присвоить null, что означает удаление\n        buckets[index] = null\n    }\n\n    /* Получить все пары ключ-значение */\n    fun pairSet(): MutableList&lt;Pair&gt; {\n        val pairSet = mutableListOf&lt;Pair&gt;()\n        for (pair in buckets) {\n            if (pair != null)\n                pairSet.add(pair)\n        }\n        return pairSet\n    }\n\n    /* Получить все ключи */\n    fun keySet(): MutableList&lt;Int&gt; {\n        val keySet = mutableListOf&lt;Int&gt;()\n        for (pair in buckets) {\n            if (pair != null)\n                keySet.add(pair.key)\n        }\n        return keySet\n    }\n\n    /* Получить все значения */\n    fun valueSet(): MutableList&lt;String&gt; {\n        val valueSet = mutableListOf&lt;String&gt;()\n        for (pair in buckets) {\n            if (pair != null)\n                valueSet.add(pair._val)\n        }\n        return valueSet\n    }\n\n    /* Вывести хеш-таблицу */\n    fun print() {\n        for (kv in pairSet()) {\n            val key = kv.key\n            val _val = kv._val\n            println(\"$key -&gt; $_val\")\n        }\n    }\n}\n</code></pre> array_hash_map.rb<pre><code>### Пара ключ-значение ###\nclass Pair\n  attr_accessor :key, :val\n\n  def initialize(key, val)\n    @key = key\n    @val = val\n  end\nend\n\n### Хеш-таблица на основе массива ###\nclass ArrayHashMap\n  ### Конструктор ###\n  def initialize\n    # Инициализировать массив, содержащий 100 корзин\n    @buckets = Array.new(100)\n  end\n\n  ### Хеш-функция ###\n  def hash_func(key)\n    index = key % 100\n  end\n\n  ### Операция поиска ###\n  def get(key)\n    index = hash_func(key)\n    pair = @buckets[index]\n\n    return if pair.nil?\n    pair.val\n  end\n\n  ### Операция добавления ###\n  def put(key, val)\n    pair = Pair.new(key, val)\n    index = hash_func(key)\n    @buckets[index] = pair\n  end\n\n  ### Операция удаления ###\n  def remove(key)\n    index = hash_func(key)\n    # Присвоить nil, что означает удаление\n    @buckets[index] = nil\n  end\n\n  ### Получить все пары ключ-значение ###\n  def entry_set\n    result = []\n    @buckets.each { |pair| result &lt;&lt; pair unless pair.nil? }\n    result\n  end\n\n  ### Получить все ключи ###\n  def key_set\n    result = []\n    @buckets.each { |pair| result &lt;&lt; pair.key unless pair.nil? }\n    result\n  end\n\n  ### Получить все значения ###\n  def value_set\n    result = []\n    @buckets.each { |pair| result &lt;&lt; pair.val unless pair.nil? }\n    result\n  end\n\n  ### Вывести хеш-таблицу ###\n  def print\n    @buckets.each { |pair| puts \"#{pair.key} -&gt; #{pair.val}\" unless pair.nil? }\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 6. Хеш-таблицы","6.1 &nbsp; Хеш-таблица"],"tags":[]},{"location":"chapter_hashing/hash_map/#613-","level":2,"title":"6.1.3   Хеш-коллизии и расширение","text":"<p>По сути, хеш-функция отображает входное пространство, состоящее из всех <code>key</code> , в выходное пространство, состоящее из всех индексов массива, а входное пространство обычно значительно больше выходного. Поэтому теоретически неизбежно существование ситуации \"несколько входов соответствуют одному выходу\".</p> <p>Для хеш-функции из приведенного выше примера, если последние две цифры <code>key</code> совпадают, то совпадает и результат хеш-функции. Например, если искать студентов с номерами 12836 и 20336, то получим:</p> <pre><code>12836 % 100 = 36\n20336 % 100 = 36\n</code></pre> <p>Как показано на рисунке 6-3, два номера указывают на одно и то же имя, что, очевидно, неверно. Такую ситуацию, когда нескольким входам соответствует один и тот же выход, называют хеш-коллизией (hash collision).</p> <p></p> <p> Рисунок 6-3   Пример хеш-коллизии </p> <p>Легко понять, что чем больше емкость хеш-таблицы \\(n\\) , тем ниже вероятность того, что несколько <code>key</code> попадут в один и тот же бакет, а значит, тем меньше коллизий. Поэтому мы можем уменьшать число хеш-коллизий путем расширения хеш-таблицы.</p> <p>Как показано на рисунке 6-4, до расширения пары ключ-значение <code>(136, A)</code> и <code>(236, D)</code> конфликтовали, а после расширения коллизия исчезла.</p> <p></p> <p> Рисунок 6-4   Расширение хеш-таблицы </p> <p>Подобно расширению массива, расширение хеш-таблицы требует перенести все пары ключ-значение из старой таблицы в новую, а это очень затратно по времени; кроме того, поскольку емкость хеш-таблицы <code>capacity</code> изменилась, нам приходится с помощью хеш-функции заново вычислять позиции хранения всех пар ключ-значение, что дополнительно увеличивает вычислительные расходы процесса расширения. Поэтому языки программирования обычно заранее резервируют достаточно большую емкость хеш-таблицы, чтобы избежать частых расширений.</p> <p>Коэффициент загрузки (load factor) - важное понятие хеш-таблицы. Он определяется как отношение числа элементов в хеш-таблице к числу бакетов и используется для оценки степени серьезности хеш-коллизий, а также часто служит условием срабатывания расширения хеш-таблицы. Например, в Java, когда коэффициент загрузки превышает \\(0.75\\) , система расширяет хеш-таблицу до \\(2\\) раз от исходной емкости.</p>","path":["Глава 6. Хеш-таблицы","6.1 &nbsp; Хеш-таблица"],"tags":[]},{"location":"chapter_hashing/summary/","level":1,"title":"6.4   Резюме","text":"","path":["Глава 6. Хеш-таблицы","6.4 &nbsp; Резюме"],"tags":[]},{"location":"chapter_hashing/summary/#1","level":3,"title":"1.   Ключевые выводы","text":"<ul> <li>Передав <code>key</code> , мы можем получить <code>value</code> из хеш-таблицы за \\(O(1)\\) времени, поэтому она очень эффективна.</li> <li>К типичным операциям хеш-таблицы относятся поиск, добавление пары ключ-значение, удаление пары ключ-значение и обход хеш-таблицы.</li> <li>Хеш-функция отображает <code>key</code> в индекс массива, после чего можно обратиться к соответствующему бакету и получить <code>value</code> .</li> <li>Два разных <code>key</code> после хеш-функции могут дать один и тот же индекс массива, что приводит к ошибочному результату поиска; это явление называется хеш-коллизией.</li> <li>Чем больше емкость хеш-таблицы, тем ниже вероятность хеш-коллизий. Поэтому хеш-коллизии можно смягчать путем расширения хеш-таблицы. Как и у массива, операция расширения у хеш-таблицы очень затратна.</li> <li>Коэффициент загрузки определяется как отношение числа элементов в хеш-таблице к числу бакетов, отражает степень серьезности хеш-коллизий и часто используется как условие запуска расширения хеш-таблицы.</li> <li>Метод цепочек превращает одиночный элемент в связный список и хранит все конфликтующие элементы в одном списке. Однако слишком длинный список снижает эффективность поиска, поэтому его можно дополнительно преобразовать в красно-черное дерево.</li> <li>Открытая адресация обрабатывает хеш-коллизии за счет многократного пробирования. Линейное пробирование использует фиксированный шаг, его недостатки - невозможность прямого удаления элементов и склонность к кластеризации. Повторное хеширование использует несколько хеш-функций и по сравнению с линейным пробированием меньше подвержено кластеризации, но требует больше вычислений.</li> <li>Разные языки программирования выбирают разные стратегии реализации хеш-таблиц. Например, <code>HashMap</code> в Java использует метод цепочек, а <code>Dict</code> в Python - открытую адресацию.</li> <li>Для хеш-таблицы желательно, чтобы хеш-алгоритм был детерминированным, быстрым и обеспечивал равномерное распределение. В криптографии от него дополнительно требуют устойчивости к коллизиям и эффекта лавины.</li> <li>В качестве модуля хеш-алгоритмы обычно используют большое простое число, чтобы максимально обеспечить равномерность распределения хеш-значений и снизить число хеш-коллизий.</li> <li>К распространенным хеш-алгоритмам относятся MD5, SHA-1, SHA-2 и SHA-3. MD5 часто применяли для проверки целостности файлов, а SHA-2 широко используется в протоколах и приложениях, связанных с безопасностью.</li> <li>Языки программирования обычно предоставляют для типов данных встроенные хеш-алгоритмы, чтобы вычислять индексы бакетов в хеш-таблице. Как правило, хешируемыми могут быть только неизменяемые объекты.</li> </ul>","path":["Глава 6. Хеш-таблицы","6.4 &nbsp; Резюме"],"tags":[]},{"location":"chapter_hashing/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: В каких случаях временная сложность хеш-таблицы становится \\(O(n)\\) ?</p> <p>Когда хеш-коллизии становятся достаточно серьезными, временная сложность хеш-таблицы деградирует до \\(O(n)\\) . Если хеш-функция спроектирована хорошо, емкость выбрана разумно, а конфликты распределены достаточно равномерно, то временная сложность обычно считается \\(O(1)\\) . При использовании встроенной хеш-таблицы языка программирования мы, как правило, и принимаем ее за \\(O(1)\\) .</p> <p>Q: Почему бы не использовать хеш-функцию \\(f(x) = x\\) ? Тогда ведь коллизий не будет.</p> <p>При хеш-функции \\(f(x) = x\\) каждому элементу соответствует уникальный индекс бакета, и такая структура становится эквивалентна массиву. Однако входное пространство обычно намного больше выходного пространства (длины массива), поэтому последним шагом хеш-функции обычно выступает взятие по модулю длины массива. Иначе говоря, цель хеш-таблицы состоит в том, чтобы отобразить большее пространство состояний в меньшее пространство и при этом обеспечить \\(O(1)\\) поиска.</p> <p>Q: В основе хеш-таблицы лежат массив, связный список и двоичное дерево. Почему же она может быть быстрее них?</p> <p>Во-первых, у хеш-таблицы повышается временная эффективность, но снижается пространственная эффективность. Значительная часть ее памяти остается неиспользованной.</p> <p>Во-вторых, она быстрее только в определенных сценариях. Если одну и ту же задачу можно реализовать на массиве или связном списке с той же асимптотикой, то часто такая реализация окажется быстрее, чем хеш-таблица. Причина в том, что вычисление хеш-функции само по себе стоит времени, то есть константа в сложности получается выше.</p> <p>Наконец, временная сложность хеш-таблицы тоже может деградировать. Например, при методе цепочек мы все равно выполняем поиск в связном списке или красно-черном дереве, поэтому риск деградации до \\(O(n)\\) сохраняется.</p> <p>Q: Есть ли у повторного хеширования недостаток \"нельзя напрямую удалять элементы\"? Можно ли повторно использовать место, помеченное как удаленное?</p> <p>Повторное хеширование - это разновидность открытой адресации, а у всех методов открытой адресации есть недостаток: элементы нельзя удалять напрямую, поэтому приходится использовать метку удаления. Пространство, помеченное как удаленное, можно использовать повторно. Когда новый элемент вставляется в хеш-таблицу и в процессе пробирования попадает на такую отмеченную позицию, эта позиция может быть занята новым элементом. Такой подход сохраняет последовательность пробирования и одновременно поддерживает приемлемую эффективность использования памяти.</p> <p>Q: Почему при линейном пробировании во время поиска элемента вообще возникает хеш-коллизия?</p> <p>Во время поиска мы через хеш-функцию находим соответствующий бакет и соответствующую пару ключ-значение, но видим, что <code>key</code> не совпадает, а это и означает наличие хеш-коллизии. Поэтому метод линейного пробирования в соответствии с заранее заданным шагом последовательно движется дальше, пока не найдет правильную пару ключ-значение или не убедится, что поиск завершился неудачей.</p> <p>Q: Почему расширение хеш-таблицы помогает смягчать хеш-коллизии?</p> <p>Последний шаг хеш-функции обычно состоит во взятии по модулю длины массива \\(n\\) , чтобы результат попадал в диапазон индексов массива; после расширения длина массива \\(n\\) меняется, а значит, может измениться и индекс, соответствующий данному <code>key</code> . Несколько <code>key</code> , которые раньше попадали в один бакет, после расширения могут распределиться по нескольким бакетам, и тем самым хеш-коллизии будут ослаблены.</p> <p>Q: Если нам нужен быстрый доступ, почему бы просто не использовать массив?</p> <p>Когда <code>key</code> данных - это непрерывные целые числа из маленького диапазона, действительно можно напрямую использовать массив: это просто и эффективно. Но если <code>key</code> имеют другой тип данных (например, строки), тогда нужен хеш-алгоритм, который отобразит <code>key</code> в индекс массива, а хранение элементов будет выполняться через массив бакетов. Такая структура и называется хеш-таблицей.</p>","path":["Глава 6. Хеш-таблицы","6.4 &nbsp; Резюме"],"tags":[]},{"location":"chapter_heap/","level":1,"title":"Глава 8.   Куча","text":"<p>Abstract</p> <p>Куча - это полное двоичное дерево, удовлетворяющее определенным условиям.</p> <p>В максимальной и минимальной куче элемент на вершине всегда обладает самым выраженным приоритетом.</p>","path":["Глава 8. Куча","Глава 8. &nbsp; Куча"],"tags":[]},{"location":"chapter_heap/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>8.1   Куча</li> <li>8.2   Построение кучи</li> <li>8.3   Задача Top-k</li> <li>8.4   Резюме</li> </ul>","path":["Глава 8. Куча","Глава 8. &nbsp; Куча"],"tags":[]},{"location":"chapter_heap/build_heap/","level":1,"title":"8.2   Построение кучи","text":"<p>В некоторых случаях требуется построить кучу, используя сразу все элементы списка. Этот процесс называется построением кучи.</p>","path":["Глава 8. Куча","8.2 &nbsp; Построение кучи"],"tags":[]},{"location":"chapter_heap/build_heap/#821","level":2,"title":"8.2.1   Реализация через операцию добавления в кучу","text":"<p>Сначала мы создаем пустую кучу, затем обходим список и для каждого элемента по очереди выполняем операцию добавления в кучу: сначала помещаем элемент в хвост кучи, а затем выполняем для него упорядочивание снизу вверх.</p> <p>Каждый раз, когда элемент добавляется в кучу, ее длина увеличивается на единицу. Поскольку узлы последовательно добавляются в двоичное дерево сверху вниз, куча строится сверху вниз.</p> <p>Пусть число элементов равно \\(n\\) ; так как каждая операция добавления требует \\(O(\\log{n})\\) времени, временная сложность такого построения кучи составляет \\(O(n \\log n)\\) .</p>","path":["Глава 8. Куча","8.2 &nbsp; Построение кучи"],"tags":[]},{"location":"chapter_heap/build_heap/#822","level":2,"title":"8.2.2   Реализация через обход и упорядочивание","text":"<p>На самом деле можно реализовать и более эффективный способ построения кучи, который состоит из двух шагов.</p> <ol> <li>Без изменений добавить все элементы списка в кучу; в этот момент свойства кучи еще не выполняются.</li> <li>Обойти кучу в обратном порядке, то есть в порядке, обратном обходу по уровням, и по очереди выполнить упорядочивание сверху вниз для каждого нелистового узла.</li> </ol> <p>После того как некоторый узел был упорядочен, поддерево с этим узлом в качестве корня становится корректной подкучей. А поскольку обход выполняется в обратном порядке, куча строится снизу вверх.</p> <p>Причина выбора обратного обхода в том, что он гарантирует: поддеревья ниже текущего узла уже являются корректными подкучами, а значит, упорядочивание текущего узла действительно будет эффективным.</p> <p>Стоит отметить, что листовые узлы не имеют дочерних узлов, поэтому они естественным образом являются корректными подкучами и не требуют упорядочивания. Как показано в коде ниже, последний нелистовой узел является родителем последнего узла, и именно с него мы начинаем обратный обход и упорядочивание:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby my_heap.py<pre><code>def __init__(self, nums: list[int]):\n    \"\"\"Конструктор, строящий кучу по входному списку\"\"\"\n    # Добавить элементы списка в кучу без изменений\n    self.max_heap = nums\n    # Выполнить heapify для всех узлов, кроме листовых\n    for i in range(self.parent(self.size() - 1), -1, -1):\n        self.sift_down(i)\n</code></pre> my_heap.cpp<pre><code>/* Конструктор, строящий кучу по входному списку */\nMaxHeap(vector&lt;int&gt; nums) {\n    // Добавить элементы списка в кучу без изменений\n    maxHeap = nums;\n    // Выполнить heapify для всех узлов, кроме листовых\n    for (int i = parent(size() - 1); i &gt;= 0; i--) {\n        siftDown(i);\n    }\n}\n</code></pre> my_heap.java<pre><code>/* Конструктор, строящий кучу по входному списку */\nMaxHeap(List&lt;Integer&gt; nums) {\n    // Добавить элементы списка в кучу без изменений\n    maxHeap = new ArrayList&lt;&gt;(nums);\n    // Выполнить heapify для всех узлов, кроме листовых\n    for (int i = parent(size() - 1); i &gt;= 0; i--) {\n        siftDown(i);\n    }\n}\n</code></pre> my_heap.cs<pre><code>/* Конструктор: построить кучу по входному списку */\nMaxHeap(IEnumerable&lt;int&gt; nums) {\n    // Добавить элементы списка в кучу без изменений\n    maxHeap = new List&lt;int&gt;(nums);\n    // Выполнить heapify для всех узлов, кроме листовых\n    var size = Parent(this.Size() - 1);\n    for (int i = size; i &gt;= 0; i--) {\n        SiftDown(i);\n    }\n}\n</code></pre> my_heap.go<pre><code>/* Конструктор, строящий кучу по срезу */\nfunc newMaxHeap(nums []any) *maxHeap {\n    // Добавить элементы списка в кучу без изменений\n    h := &amp;maxHeap{data: nums}\n    for i := h.parent(len(h.data) - 1); i &gt;= 0; i-- {\n        // Выполнить heapify для всех узлов, кроме листовых\n        h.siftDown(i)\n    }\n    return h\n}\n</code></pre> my_heap.swift<pre><code>/* Конструктор, строящий кучу по входному списку */\ninit(nums: [Int]) {\n    // Добавить элементы списка в кучу без изменений\n    maxHeap = nums\n    // Выполнить heapify для всех узлов, кроме листовых\n    for i in (0 ... parent(i: size() - 1)).reversed() {\n        siftDown(i: i)\n    }\n}\n</code></pre> my_heap.js<pre><code>/* Конструктор, создающий пустую кучу или строящий кучу по входному списку */\nconstructor(nums) {\n    // Добавить элементы списка в кучу без изменений\n    this.#maxHeap = nums === undefined ? [] : [...nums];\n    // Выполнить heapify для всех узлов, кроме листовых\n    for (let i = this.#parent(this.size() - 1); i &gt;= 0; i--) {\n        this.#siftDown(i);\n    }\n}\n</code></pre> my_heap.ts<pre><code>/* Конструктор, создающий пустую кучу или строящий кучу по входному списку */\nconstructor(nums?: number[]) {\n    // Добавить элементы списка в кучу без изменений\n    this.maxHeap = nums === undefined ? [] : [...nums];\n    // Выполнить heapify для всех узлов, кроме листовых\n    for (let i = this.parent(this.size() - 1); i &gt;= 0; i--) {\n        this.siftDown(i);\n    }\n}\n</code></pre> my_heap.dart<pre><code>/* Конструктор, строящий кучу по входному списку */\nMaxHeap(List&lt;int&gt; nums) {\n  // Добавить элементы списка в кучу без изменений\n  _maxHeap = nums;\n  // Выполнить heapify для всех узлов, кроме листовых\n  for (int i = _parent(size() - 1); i &gt;= 0; i--) {\n    siftDown(i);\n  }\n}\n</code></pre> my_heap.rs<pre><code>/* Конструктор, строящий кучу по входному списку */\nfn new(nums: Vec&lt;i32&gt;) -&gt; Self {\n    // Добавить элементы списка в кучу без изменений\n    let mut heap = MaxHeap { max_heap: nums };\n    // Выполнить heapify для всех узлов, кроме листовых\n    for i in (0..=Self::parent(heap.size() - 1)).rev() {\n        heap.sift_down(i);\n    }\n    heap\n}\n</code></pre> my_heap.c<pre><code>/* Конструктор, строящий кучу по срезу */\nMaxHeap *newMaxHeap(int nums[], int size) {\n    // Поместить все элементы в кучу\n    MaxHeap *maxHeap = (MaxHeap *)malloc(sizeof(MaxHeap));\n    maxHeap-&gt;size = size;\n    memcpy(maxHeap-&gt;data, nums, size * sizeof(int));\n    for (int i = parent(maxHeap, size - 1); i &gt;= 0; i--) {\n        // Выполнить heapify для всех узлов, кроме листовых\n        siftDown(maxHeap, i);\n    }\n    return maxHeap;\n}\n</code></pre> my_heap.kt<pre><code>/* Максимальная куча */\nclass MaxHeap(nums: MutableList&lt;Int&gt;?) {\n    // Использовать список вместо массива, чтобы не учитывать проблему расширения\n    private val maxHeap = mutableListOf&lt;Int&gt;()\n\n    /* Конструктор, строящий кучу по входному списку */\n    init {\n        // Добавить элементы списка в кучу без изменений\n        maxHeap.addAll(nums!!)\n        // Выполнить heapify для всех узлов, кроме листовых\n        for (i in parent(size() - 1) downTo 0) {\n            siftDown(i)\n        }\n    }\n\n    /* Получить индекс левого дочернего узла */\n    private fun left(i: Int): Int {\n        return 2 * i + 1\n    }\n\n    /* Получить индекс правого дочернего узла */\n    private fun right(i: Int): Int {\n        return 2 * i + 2\n    }\n\n    /* Получить индекс родительского узла */\n    private fun parent(i: Int): Int {\n        return (i - 1) / 2 // Округление вниз при делении\n    }\n\n    /* Поменять элементы местами */\n    private fun swap(i: Int, j: Int) {\n        val temp = maxHeap[i]\n        maxHeap[i] = maxHeap[j]\n        maxHeap[j] = temp\n    }\n\n    /* Получение размера кучи */\n    fun size(): Int {\n        return maxHeap.size\n    }\n\n    /* Проверка, пуста ли куча */\n    fun isEmpty(): Boolean {\n        /* Проверка, пуста ли куча */\n        return size() == 0\n    }\n\n    /* Доступ к элементу на вершине кучи */\n    fun peek(): Int {\n        return maxHeap[0]\n    }\n\n    /* Добавление элемента в кучу */\n    fun push(_val: Int) {\n        // Добавление узла\n        maxHeap.add(_val)\n        // Просеивание снизу вверх\n        siftUp(size() - 1)\n    }\n\n    /* Начиная с узла i, выполнить просеивание снизу вверх */\n    private fun siftUp(it: Int) {\n        // Параметры функций в Kotlin неизменяемы, поэтому создается временная переменная\n        var i = it\n        while (true) {\n            // Получение родительского узла для узла i\n            val p = parent(i)\n            // Завершить heapify, когда «корневой узел уже пройден» или «узел не требует исправления»\n            if (p &lt; 0 || maxHeap[i] &lt;= maxHeap[p]) break\n            // Поменять два узла местами\n            swap(i, p)\n            // Циклическое просеивание вверх\n            i = p\n        }\n    }\n\n    /* Извлечение элемента из кучи */\n    fun pop(): Int {\n        // Обработка пустого случая\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n        swap(0, size() - 1)\n        // Удаление узла\n        val _val = maxHeap.removeAt(size() - 1)\n        // Просеивание сверху вниз\n        siftDown(0)\n        // Вернуть элемент с вершины кучи\n        return _val\n    }\n\n    /* Начиная с узла i, выполнить просеивание сверху вниз */\n    private fun siftDown(it: Int) {\n        // Параметры функций в Kotlin неизменяемы, поэтому создается временная переменная\n        var i = it\n        while (true) {\n            // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n            val l = left(i)\n            val r = right(i)\n            var ma = i\n            if (l &lt; size() &amp;&amp; maxHeap[l] &gt; maxHeap[ma]) ma = l\n            if (r &lt; size() &amp;&amp; maxHeap[r] &gt; maxHeap[ma]) ma = r\n            // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n            if (ma == i) break\n            // Поменять два узла местами\n            swap(i, ma)\n            // Циклическое просеивание вниз\n            i = ma\n        }\n    }\n\n    /* Вывести кучу (двоичное дерево) */\n    fun print() {\n        val queue = PriorityQueue { a: Int, b: Int -&gt; b - a }\n        queue.addAll(maxHeap)\n        printHeap(queue)\n    }\n}\n</code></pre> my_heap.rb<pre><code>### Конструктор, строящий кучу по входному списку ###\ndef initialize(nums)\n  # Добавить элементы списка в кучу без изменений\n  @max_heap = nums\n  # Выполнить heapify для всех узлов, кроме листовых\n  parent(size - 1).downto(0) do |i|\n    sift_down(i)\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 8. Куча","8.2 &nbsp; Построение кучи"],"tags":[]},{"location":"chapter_heap/build_heap/#823","level":2,"title":"8.2.3   Анализ сложности","text":"<p>Теперь попробуем оценить временную сложность второго способа построения кучи.</p> <ul> <li>Пусть число узлов полного двоичного дерева равно \\(n\\) , тогда число листовых узлов равно \\((n + 1) / 2\\) , где \\(/\\) означает целочисленное деление вниз. Следовательно, число узлов, которые нужно упорядочивать, равно \\((n - 1) / 2\\) .</li> <li>В процессе упорядочивания сверху вниз каждый узел в худшем случае может просеяться до листа, поэтому максимальное число итераций равно высоте двоичного дерева \\(\\log n\\) .</li> </ul> <p>Перемножив эти два значения, можно получить временную сложность построения кучи \\(O(n \\log n)\\) . Но эта оценка неточна, потому что мы не учли свойство двоичного дерева: на нижних уровнях узлов гораздо больше, чем на верхних.</p> <p>Далее выполним более точный расчет. Чтобы упростить вычисления, предположим, что дано \"идеальное двоичное дерево\" высоты \\(h\\) с числом узлов \\(n\\) ; это предположение не повлияет на корректность результата.</p> <p></p> <p> Рисунок 8-5   Число узлов на каждом уровне идеального двоичного дерева </p> <p>Как показано на рисунке 8-5, максимальное число итераций упорядочивания сверху вниз для некоторого узла равно расстоянию от этого узла до листового узла, а это расстояние как раз и есть высота узла. Поэтому мы можем просуммировать для каждого уровня выражение \"число узлов \\(\\times\\) высота узла\" и получить суммарное число итераций упорядочивания для всех узлов.</p> \\[ T(h) = 2^0h + 2^1(h-1) + 2^2(h-2) + \\dots + 2^{(h-1)}\\times1 \\] <p>Чтобы упростить это выражение, воспользуемся школьными знаниями о последовательностях и сначала умножим \\(T(h)\\) на \\(2\\) :</p> \\[ \\begin{aligned} T(h) &amp; = 2^0h + 2^1(h-1) + 2^2(h-2) + \\dots + 2^{h-1}\\times1 \\newline 2 T(h) &amp; = 2^1h + 2^2(h-1) + 2^3(h-2) + \\dots + 2^{h}\\times1 \\newline \\end{aligned} \\] <p>Используя метод вычитания со сдвигом, вычтем из нижней строки \\(2 T(h)\\) верхнюю строку \\(T(h)\\) , тогда получим:</p> \\[ 2T(h) - T(h) = T(h) = -2^0h + 2^1 + 2^2 + \\dots + 2^{h-1} + 2^h \\] <p>Из этого выражения видно, что \\(T(h)\\) представляет собой геометрическую прогрессию, поэтому можно напрямую применить формулу суммы и получить временную сложность:</p> \\[ \\begin{aligned} T(h) &amp; = 2 \\frac{1 - 2^h}{1 - 2} - h \\newline &amp; = 2^{h+1} - h - 2 \\newline &amp; = O(2^h) \\end{aligned} \\] <p>Далее, число узлов идеального двоичного дерева высоты \\(h\\) равно \\(n = 2^{h+1} - 1\\) , поэтому несложно получить сложность \\(O(2^h) = O(n)\\) . Из этого вывода следует, что построение кучи из входного списка имеет временную сложность \\(O(n)\\) , то есть выполняется очень эффективно.</p>","path":["Глава 8. Куча","8.2 &nbsp; Построение кучи"],"tags":[]},{"location":"chapter_heap/heap/","level":1,"title":"8.1   Куча","text":"<p>Куча (heap) - это полное двоичное дерево, удовлетворяющее определенным условиям. Основных типов кучи два, как показано на рисунке 8-1.</p> <ul> <li>Минимальная куча (min heap): значение любого узла \\(\\leq\\) значения его дочерних узлов.</li> <li>Максимальная куча (max heap): значение любого узла \\(\\geq\\) значения его дочерних узлов.</li> </ul> <p></p> <p> Рисунок 8-1   Минимальная куча и максимальная куча </p> <p>Куча, являясь частным случаем полного двоичного дерева, обладает следующими свойствами.</p> <ul> <li>Узлы самого нижнего уровня заполняются слева, а все остальные уровни заполнены полностью.</li> <li>Корневой узел двоичного дерева мы называем вершиной кучи, а самый правый узел нижнего уровня - основанием кучи.</li> <li>Для максимальной (минимальной) кучи значение элемента на вершине, то есть у корневого узла, является максимальным (минимальным).</li> </ul>","path":["Глава 8. Куча","8.1 &nbsp; Куча"],"tags":[]},{"location":"chapter_heap/heap/#811","level":2,"title":"8.1.1   Распространенные операции с кучей","text":"<p>Нужно отметить, что многие языки программирования предоставляют не саму кучу, а очередь с приоритетом (priority queue) - абстрактную структуру данных, определяемую как очередь, в которой элементы извлекаются в соответствии с приоритетом.</p> <p>На практике куча обычно используется для реализации очереди с приоритетом, а максимальная куча эквивалентна очереди с приоритетом, в которой элементы извлекаются по убыванию. С точки зрения использования очередь с приоритетом и куча могут считаться эквивалентными структурами данных. Поэтому в этой книге мы не будем специально различать их и в дальнейшем будем единообразно называть кучей.</p> <p>Распространенные операции с кучей приведены в таблице 8-1. Конкретные имена методов зависят от языка программирования.</p> <p> Таблица 8-1   Эффективность операций с кучей </p> Имя метода Описание Временная сложность <code>push()</code> Поместить элемент в кучу \\(O(\\log n)\\) <code>pop()</code> Извлечь элемент с вершины кучи \\(O(\\log n)\\) <code>peek()</code> Получить доступ к вершине кучи (для max / min кучи это соответственно максимум / минимум) \\(O(1)\\) <code>size()</code> Получить число элементов в куче \\(O(1)\\) <code>isEmpty()</code> Проверить, пуста ли куча \\(O(1)\\) <p>В реальных приложениях мы можем напрямую использовать классы кучи, предоставляемые языком программирования, или классы очереди с приоритетом.</p> <p>Подобно сортировкам \"по возрастанию\" и \"по убыванию\", мы можем переключаться между \"минимальной кучей\" и \"максимальной кучей\", изменяя <code>flag</code> или модифицируя <code>Comparator</code> . Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby heap.py<pre><code># Инициализация минимальной кучи\nmin_heap, flag = [], 1\n# Инициализация максимальной кучи\nmax_heap, flag = [], -1\n\n# Модуль heapq в Python по умолчанию реализует минимальную кучу\n# Если инвертировать знак элемента перед добавлением, то отношение порядка перевернется и так реализуется максимальная куча\n# В этом примере flag = 1 соответствует минимальной куче, а flag = -1 - максимальной\n\n# Добавление элементов в кучу\nheapq.heappush(max_heap, flag * 1)\nheapq.heappush(max_heap, flag * 3)\nheapq.heappush(max_heap, flag * 2)\nheapq.heappush(max_heap, flag * 5)\nheapq.heappush(max_heap, flag * 4)\n\n# Получение элемента на вершине кучи\npeek: int = flag * max_heap[0] # 5\n\n# Извлечение элемента с вершины кучи\n# Извлеченные элементы образуют последовательность по убыванию\nval = flag * heapq.heappop(max_heap) # 5\nval = flag * heapq.heappop(max_heap) # 4\nval = flag * heapq.heappop(max_heap) # 3\nval = flag * heapq.heappop(max_heap) # 2\nval = flag * heapq.heappop(max_heap) # 1\n\n# Получение размера кучи\nsize: int = len(max_heap)\n\n# Проверка, пуста ли куча\nis_empty: bool = not max_heap\n\n# Построение кучи из входного списка\nmin_heap: list[int] = [1, 3, 2, 5, 4]\nheapq.heapify(min_heap)\n</code></pre> heap.cpp<pre><code>/* Инициализация кучи */\n// Инициализация минимальной кучи\npriority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; minHeap;\n// Инициализация максимальной кучи\npriority_queue&lt;int, vector&lt;int&gt;, less&lt;int&gt;&gt; maxHeap;\n\n/* Добавление элементов в кучу */\nmaxHeap.push(1);\nmaxHeap.push(3);\nmaxHeap.push(2);\nmaxHeap.push(5);\nmaxHeap.push(4);\n\n/* Получение элемента на вершине кучи */\nint peek = maxHeap.top(); // 5\n\n/* Извлечение элемента с вершины кучи */\n// Извлеченные элементы образуют последовательность по убыванию\nmaxHeap.pop(); // 5\nmaxHeap.pop(); // 4\nmaxHeap.pop(); // 3\nmaxHeap.pop(); // 2\nmaxHeap.pop(); // 1\n\n/* Получение размера кучи */\nint size = maxHeap.size();\n\n/* Проверка, пуста ли куча */\nbool isEmpty = maxHeap.empty();\n\n/* Построение кучи из входного списка */\nvector&lt;int&gt; input{1, 3, 2, 5, 4};\npriority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; minHeap(input.begin(), input.end());\n</code></pre> heap.java<pre><code>/* Инициализация кучи */\n// Инициализация минимальной кучи\nQueue&lt;Integer&gt; minHeap = new PriorityQueue&lt;&gt;();\n// Инициализация максимальной кучи (достаточно изменить Comparator через lambda)\nQueue&lt;Integer&gt; maxHeap = new PriorityQueue&lt;&gt;((a, b) -&gt; b - a);\n\n/* Добавление элементов в кучу */\nmaxHeap.offer(1);\nmaxHeap.offer(3);\nmaxHeap.offer(2);\nmaxHeap.offer(5);\nmaxHeap.offer(4);\n\n/* Получение элемента на вершине кучи */\nint peek = maxHeap.peek(); // 5\n\n/* Извлечение элемента с вершины кучи */\n// Извлеченные элементы образуют последовательность по убыванию\npeek = maxHeap.poll(); // 5\npeek = maxHeap.poll(); // 4\npeek = maxHeap.poll(); // 3\npeek = maxHeap.poll(); // 2\npeek = maxHeap.poll(); // 1\n\n/* Получение размера кучи */\nint size = maxHeap.size();\n\n/* Проверка, пуста ли куча */\nboolean isEmpty = maxHeap.isEmpty();\n\n/* Построение кучи из входного списка */\nminHeap = new PriorityQueue&lt;&gt;(Arrays.asList(1, 3, 2, 5, 4));\n</code></pre> heap.cs<pre><code>/* Инициализация кучи */\n// Инициализация минимальной кучи\nPriorityQueue&lt;int, int&gt; minHeap = new();\n// Инициализация максимальной кучи (достаточно изменить Comparer через lambda)\nPriorityQueue&lt;int, int&gt; maxHeap = new(Comparer&lt;int&gt;.Create((x, y) =&gt; y.CompareTo(x)));\n\n/* Добавление элементов в кучу */\nmaxHeap.Enqueue(1, 1);\nmaxHeap.Enqueue(3, 3);\nmaxHeap.Enqueue(2, 2);\nmaxHeap.Enqueue(5, 5);\nmaxHeap.Enqueue(4, 4);\n\n/* Получение элемента на вершине кучи */\nint peek = maxHeap.Peek();//5\n\n/* Извлечение элемента с вершины кучи */\n// Извлеченные элементы образуют последовательность по убыванию\npeek = maxHeap.Dequeue();  // 5\npeek = maxHeap.Dequeue();  // 4\npeek = maxHeap.Dequeue();  // 3\npeek = maxHeap.Dequeue();  // 2\npeek = maxHeap.Dequeue();  // 1\n\n/* Получение размера кучи */\nint size = maxHeap.Count;\n\n/* Проверка, пуста ли куча */\nbool isEmpty = maxHeap.Count == 0;\n\n/* Построение кучи из входного списка */\nminHeap = new PriorityQueue&lt;int, int&gt;([(1, 1), (3, 3), (2, 2), (5, 5), (4, 4)]);\n</code></pre> heap.go<pre><code>// В Go можно построить целочисленную максимальную кучу, реализовав heap.Interface\n// Для реализации heap.Interface также нужно реализовать sort.Interface\ntype intHeap []any\n\n// Метод Push из heap.Interface, реализует добавление элемента в кучу\nfunc (h *intHeap) Push(x any) {\n    // Push и Pop используют pointer receiver\n    // Потому что они не только изменяют содержимое среза, но и его длину\n    *h = append(*h, x.(int))\n}\n\n// Метод Pop из heap.Interface, реализует извлечение элемента с вершины кучи\nfunc (h *intHeap) Pop() any {\n    // Извлекаемый элемент хранится в конце\n    last := (*h)[len(*h)-1]\n    *h = (*h)[:len(*h)-1]\n    return last\n}\n\n// Метод Len из sort.Interface\nfunc (h *intHeap) Len() int {\n    return len(*h)\n}\n\n// Метод Less из sort.Interface\nfunc (h *intHeap) Less(i, j int) bool {\n    // Для минимальной кучи здесь нужно заменить сравнение на &lt;\n    return (*h)[i].(int) &gt; (*h)[j].(int)\n}\n\n// Метод Swap из sort.Interface\nfunc (h *intHeap) Swap(i, j int) {\n    (*h)[i], (*h)[j] = (*h)[j], (*h)[i]\n}\n\n// Top получает элемент на вершине кучи\nfunc (h *intHeap) Top() any {\n    return (*h)[0]\n}\n\n/* Driver Code */\nfunc TestHeap(t *testing.T) {\n    /* Инициализация кучи */\n    // Инициализация максимальной кучи\n    maxHeap := &amp;intHeap{}\n    heap.Init(maxHeap)\n    /* Добавление элементов в кучу */\n    // Вызываем методы heap.Interface для добавления элементов\n    heap.Push(maxHeap, 1)\n    heap.Push(maxHeap, 3)\n    heap.Push(maxHeap, 2)\n    heap.Push(maxHeap, 4)\n    heap.Push(maxHeap, 5)\n\n    /* Получение элемента на вершине кучи */\n    top := maxHeap.Top()\n    fmt.Printf(\"Элемент на вершине кучи: %d\\n\", top)\n\n    /* Извлечение элемента с вершины кучи */\n    // Вызываем методы heap.Interface для удаления элементов\n    heap.Pop(maxHeap) // 5\n    heap.Pop(maxHeap) // 4\n    heap.Pop(maxHeap) // 3\n    heap.Pop(maxHeap) // 2\n    heap.Pop(maxHeap) // 1\n\n    /* Получение размера кучи */\n    size := len(*maxHeap)\n    fmt.Printf(\"Число элементов в куче: %d\\n\", size)\n\n    /* Проверка, пуста ли куча */\n    isEmpty := len(*maxHeap) == 0\n    fmt.Printf(\"Пуста ли куча: %t\\n\", isEmpty)\n}\n</code></pre> heap.swift<pre><code>/* Инициализация кучи */\n// Тип Heap в Swift поддерживает и max-heap, и min-heap, но требует swift-collections\nvar heap = Heap&lt;Int&gt;()\n\n/* Добавление элементов в кучу */\nheap.insert(1)\nheap.insert(3)\nheap.insert(2)\nheap.insert(5)\nheap.insert(4)\n\n/* Получение элемента на вершине кучи */\nvar peek = heap.max()!\n\n/* Извлечение элемента с вершины кучи */\npeek = heap.removeMax() // 5\npeek = heap.removeMax() // 4\npeek = heap.removeMax() // 3\npeek = heap.removeMax() // 2\npeek = heap.removeMax() // 1\n\n/* Получение размера кучи */\nlet size = heap.count\n\n/* Проверка, пуста ли куча */\nlet isEmpty = heap.isEmpty\n\n/* Построение кучи из входного списка */\nlet heap2 = Heap([1, 3, 2, 5, 4])\n</code></pre> heap.js<pre><code>// В JavaScript нет встроенного класса Heap\n</code></pre> heap.ts<pre><code>// В TypeScript нет встроенного класса Heap\n</code></pre> heap.dart<pre><code>// В Dart нет встроенного класса Heap\n</code></pre> heap.rs<pre><code>use std::collections::BinaryHeap;\nuse std::cmp::Reverse;\n\n/* Инициализация кучи */\n// Инициализация минимальной кучи\nlet mut min_heap = BinaryHeap::&lt;Reverse&lt;i32&gt;&gt;::new();\n// Инициализация максимальной кучи\nlet mut max_heap = BinaryHeap::new();\n\n/* Добавление элементов в кучу */\nmax_heap.push(1);\nmax_heap.push(3);\nmax_heap.push(2);\nmax_heap.push(5);\nmax_heap.push(4);\n\n/* Получение элемента на вершине кучи */\nlet peek = max_heap.peek().unwrap();  // 5\n\n/* Извлечение элемента с вершины кучи */\n// Извлеченные элементы образуют последовательность по убыванию\nlet peek = max_heap.pop().unwrap();   // 5\nlet peek = max_heap.pop().unwrap();   // 4\nlet peek = max_heap.pop().unwrap();   // 3\nlet peek = max_heap.pop().unwrap();   // 2\nlet peek = max_heap.pop().unwrap();   // 1\n\n/* Получение размера кучи */\nlet size = max_heap.len();\n\n/* Проверка, пуста ли куча */\nlet is_empty = max_heap.is_empty();\n\n/* Построение кучи из входного списка */\nlet min_heap = BinaryHeap::from(vec![Reverse(1), Reverse(3), Reverse(2), Reverse(5), Reverse(4)]);\n</code></pre> heap.c<pre><code>// В C нет встроенного класса Heap\n</code></pre> heap.kt<pre><code>/* Инициализация кучи */\n// Инициализация минимальной кучи\nvar minHeap = PriorityQueue&lt;Int&gt;()\n// Инициализация максимальной кучи (достаточно изменить Comparator через lambda)\nval maxHeap = PriorityQueue { a: Int, b: Int -&gt; b - a }\n\n/* Добавление элементов в кучу */\nmaxHeap.offer(1)\nmaxHeap.offer(3)\nmaxHeap.offer(2)\nmaxHeap.offer(5)\nmaxHeap.offer(4)\n\n/* Получение элемента на вершине кучи */\nvar peek = maxHeap.peek() // 5\n\n/* Извлечение элемента с вершины кучи */\n// Извлеченные элементы образуют последовательность по убыванию\npeek = maxHeap.poll() // 5\npeek = maxHeap.poll() // 4\npeek = maxHeap.poll() // 3\npeek = maxHeap.poll() // 2\npeek = maxHeap.poll() // 1\n\n/* Получение размера кучи */\nval size = maxHeap.size\n\n/* Проверка, пуста ли куча */\nval isEmpty = maxHeap.isEmpty()\n\n/* Построение кучи из входного списка */\nminHeap = PriorityQueue(mutableListOf(1, 3, 2, 5, 4))\n</code></pre> heap.rb<pre><code># В Ruby нет встроенного класса Heap\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=import%20heapq%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20min-%D0%BA%D1%83%D1%87%D1%83%0A%20%20%20%20min_heap%2C%20flag%20%3D%20%5B%5D%2C%201%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20max-%D0%BA%D1%83%D1%87%D1%83%0A%20%20%20%20max_heap%2C%20flag%20%3D%20%5B%5D%2C%20-1%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8C%20heapq%20%D0%B2%20Python%20%D0%BF%D0%BE%20%D1%83%D0%BC%D0%BE%D0%BB%D1%87%D0%B0%D0%BD%D0%B8%D1%8E%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D1%83%D0%B5%D1%82%20min-%D0%BA%D1%83%D1%87%D1%83%0A%20%20%20%20%23%20%D0%95%D1%81%D0%BB%D0%B8%20%D0%BF%D0%B5%D1%80%D0%B5%D0%B4%20%D0%BF%D0%BE%D0%BC%D0%B5%D1%89%D0%B5%D0%BD%D0%B8%D0%B5%D0%BC%20%D0%B2%20%D0%BA%D1%83%D1%87%D1%83%20%D0%B1%D1%80%D0%B0%D1%82%D1%8C%20%D0%BE%D1%82%D1%80%D0%B8%D1%86%D0%B0%D0%BD%D0%B8%D0%B5%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D0%B0%2C%20%D0%BC%D0%BE%D0%B6%D0%BD%D0%BE%20%D0%BE%D0%B1%D1%80%D0%B0%D1%82%D0%B8%D1%82%D1%8C%20%D0%BE%D1%82%D0%BD%D0%BE%D1%88%D0%B5%D0%BD%D0%B8%D0%B5%20%D0%BF%D0%BE%D1%80%D1%8F%D0%B4%D0%BA%D0%B0%20%D0%B8%20%D1%82%D0%B5%D0%BC%20%D1%81%D0%B0%D0%BC%D1%8B%D0%BC%20%D1%80%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20max-%D0%BA%D1%83%D1%87%D1%83%0A%20%20%20%20%23%20%D0%92%20%D1%8D%D1%82%D0%BE%D0%BC%20%D0%BF%D1%80%D0%B8%D0%BC%D0%B5%D1%80%D0%B5%20flag%20%3D%201%20%D1%81%D0%BE%D0%BE%D1%82%D0%B2%D0%B5%D1%82%D1%81%D1%82%D0%B2%D1%83%D0%B5%D1%82%20min-%D0%BA%D1%83%D1%87%D0%B5%2C%20%D0%B0%20flag%20%3D%20-1%20%D1%81%D0%BE%D0%BE%D1%82%D0%B2%D0%B5%D1%82%D1%81%D1%82%D0%B2%D1%83%D0%B5%D1%82%20max-%D0%BA%D1%83%D1%87%D0%B5%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%94%D0%BE%D0%B1%D0%B0%D0%B2%D0%B8%D1%82%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%B2%20%D0%BA%D1%83%D1%87%D1%83%0A%20%20%20%20heapq.heappush%28max_heap%2C%20flag%20%2A%201%29%0A%20%20%20%20heapq.heappush%28max_heap%2C%20flag%20%2A%203%29%0A%20%20%20%20heapq.heappush%28max_heap%2C%20flag%20%2A%202%29%0A%20%20%20%20heapq.heappush%28max_heap%2C%20flag%20%2A%205%29%0A%20%20%20%20heapq.heappush%28max_heap%2C%20flag%20%2A%204%29%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9F%D0%BE%D0%BB%D1%83%D1%87%D0%B8%D1%82%D1%8C%20%D0%B2%D0%B5%D1%80%D1%85%D0%BD%D0%B8%D0%B9%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%BA%D1%83%D1%87%D0%B8%0A%20%20%20%20peek%20%3D%20flag%20%2A%20max_heap%5B0%5D%20%23%205%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%98%D0%B7%D0%B2%D0%BB%D0%B5%D1%87%D1%8C%20%D0%B2%D0%B5%D1%80%D1%85%D0%BD%D0%B8%D0%B9%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%B8%D0%B7%20%D0%BA%D1%83%D1%87%D0%B8%0A%20%20%20%20%23%20%D0%98%D0%B7%D0%B2%D0%BB%D0%B5%D1%87%D0%B5%D0%BD%D0%BD%D1%8B%D0%B5%20%D0%B8%D0%B7%20%D0%BA%D1%83%D1%87%D0%B8%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D1%8B%20%D0%BE%D0%B1%D1%80%D0%B0%D0%B7%D1%83%D1%8E%D1%82%20%D0%BF%D0%BE%D1%81%D0%BB%D0%B5%D0%B4%D0%BE%D0%B2%D0%B0%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D1%81%D1%82%D1%8C%20%D0%BE%D1%82%20%D0%B1%D0%BE%D0%BB%D1%8C%D1%88%D0%B5%D0%B3%D0%BE%20%D0%BA%20%D0%BC%D0%B5%D0%BD%D1%8C%D1%88%D0%B5%D0%BC%D1%83%0A%20%20%20%20val%20%3D%20flag%20%2A%20heapq.heappop%28max_heap%29%20%23%205%0A%20%20%20%20val%20%3D%20flag%20%2A%20heapq.heappop%28max_heap%29%20%23%204%0A%20%20%20%20val%20%3D%20flag%20%2A%20heapq.heappop%28max_heap%29%20%23%203%0A%20%20%20%20val%20%3D%20flag%20%2A%20heapq.heappop%28max_heap%29%20%23%202%0A%20%20%20%20val%20%3D%20flag%20%2A%20heapq.heappop%28max_heap%29%20%23%201%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9F%D0%BE%D0%BB%D1%83%D1%87%D0%B8%D1%82%D1%8C%20%D1%80%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%20%D0%BA%D1%83%D1%87%D0%B8%0A%20%20%20%20size%20%3D%20len%28max_heap%29%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%9F%D1%80%D0%BE%D0%B2%D0%B5%D1%80%D0%B8%D1%82%D1%8C%2C%20%D0%BF%D1%83%D1%81%D1%82%D0%B0%20%D0%BB%D0%B8%20%D0%BA%D1%83%D1%87%D0%B0%0A%20%20%20%20is_empty%20%3D%20not%20max_heap%0A%20%20%20%20%0A%20%20%20%20%23%20%D0%92%D1%85%D0%BE%D0%B4%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%D0%B8%D0%BF%D0%BE%D1%81%D1%82%D1%80%D0%BE%D0%B5%D0%BD%D0%B8%D0%B5%20%D0%BA%D1%83%D1%87%D0%B8%0A%20%20%20%20min_heap%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20heapq.heapify%28min_heap%29&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 8. Куча","8.1 &nbsp; Куча"],"tags":[]},{"location":"chapter_heap/heap/#812","level":2,"title":"8.1.2   Реализация кучи","text":"<p>Ниже реализуется максимальная куча. Чтобы преобразовать ее в минимальную кучу, достаточно инвертировать всю логику сравнений по величине, например заменить \\(\\geq\\) на \\(\\leq\\) . Заинтересованные читатели могут попробовать реализовать это самостоятельно.</p>","path":["Глава 8. Куча","8.1 &nbsp; Куча"],"tags":[]},{"location":"chapter_heap/heap/#1","level":3,"title":"1.   Хранение и представление кучи","text":"<p>В разделе \"Двоичные деревья\" мы уже говорили, что полное двоичное дерево очень удобно представлять массивом. Поскольку куча как раз и является полным двоичным деревом, для хранения кучи мы также будем использовать массив.</p> <p>Когда двоичное дерево представляется массивом, элементы массива соответствуют значениям узлов, а индексы - положениям этих узлов в двоичном дереве. Указатели на узлы реализуются через формулы отображения индексов.</p> <p>Как показано на рисунке 8-2, для заданного индекса \\(i\\) индекс левого дочернего узла равен \\(2i + 1\\) , правого дочернего узла - \\(2i + 2\\) , а родительского узла - \\((i - 1) / 2\\) с округлением вниз. Если индекс выходит за допустимые границы, это означает пустой узел или отсутствие узла.</p> <p></p> <p> Рисунок 8-2   Представление и хранение кучи </p> <p>Мы можем инкапсулировать формулы отображения индексов в функции, чтобы потом было удобнее ими пользоваться:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby my_heap.py<pre><code>def left(self, i: int) -&gt; int:\n    \"\"\"Получить индекс левого дочернего узла\"\"\"\n    return 2 * i + 1\n\ndef right(self, i: int) -&gt; int:\n    \"\"\"Получить индекс правого дочернего узла\"\"\"\n    return 2 * i + 2\n\ndef parent(self, i: int) -&gt; int:\n    \"\"\"Получить индекс родительского узла\"\"\"\n    return (i - 1) // 2  # Округление вниз при делении\n</code></pre> my_heap.cpp<pre><code>/* Получить индекс левого дочернего узла */\nint left(int i) {\n    return 2 * i + 1;\n}\n\n/* Получить индекс правого дочернего узла */\nint right(int i) {\n    return 2 * i + 2;\n}\n\n/* Получить индекс родительского узла */\nint parent(int i) {\n    return (i - 1) / 2; // Округление вниз при делении\n}\n</code></pre> my_heap.java<pre><code>/* Получить индекс левого дочернего узла */\nint left(int i) {\n    return 2 * i + 1;\n}\n\n/* Получить индекс правого дочернего узла */\nint right(int i) {\n    return 2 * i + 2;\n}\n\n/* Получить индекс родительского узла */\nint parent(int i) {\n    return (i - 1) / 2; // Округление вниз при делении\n}\n</code></pre> my_heap.cs<pre><code>/* Получить индекс левого дочернего узла */\nint Left(int i) {\n    return 2 * i + 1;\n}\n\n/* Получить индекс правого дочернего узла */\nint Right(int i) {\n    return 2 * i + 2;\n}\n\n/* Получить индекс родительского узла */\nint Parent(int i) {\n    return (i - 1) / 2; // Округление вниз при делении\n}\n</code></pre> my_heap.go<pre><code>/* Получить индекс левого дочернего узла */\nfunc (h *maxHeap) left(i int) int {\n    return 2*i + 1\n}\n\n/* Получить индекс правого дочернего узла */\nfunc (h *maxHeap) right(i int) int {\n    return 2*i + 2\n}\n\n/* Получить индекс родительского узла */\nfunc (h *maxHeap) parent(i int) int {\n    // Округление вниз при делении\n    return (i - 1) / 2\n}\n</code></pre> my_heap.swift<pre><code>/* Получить индекс левого дочернего узла */\nfunc left(i: Int) -&gt; Int {\n    2 * i + 1\n}\n\n/* Получить индекс правого дочернего узла */\nfunc right(i: Int) -&gt; Int {\n    2 * i + 2\n}\n\n/* Получить индекс родительского узла */\nfunc parent(i: Int) -&gt; Int {\n    (i - 1) / 2 // Округление вниз при делении\n}\n</code></pre> my_heap.js<pre><code>/* Получить индекс левого дочернего узла */\n#left(i) {\n    return 2 * i + 1;\n}\n\n/* Получить индекс правого дочернего узла */\n#right(i) {\n    return 2 * i + 2;\n}\n\n/* Получить индекс родительского узла */\n#parent(i) {\n    return Math.floor((i - 1) / 2); // Округление вниз при делении\n}\n</code></pre> my_heap.ts<pre><code>/* Получить индекс левого дочернего узла */\nleft(i: number): number {\n    return 2 * i + 1;\n}\n\n/* Получить индекс правого дочернего узла */\nright(i: number): number {\n    return 2 * i + 2;\n}\n\n/* Получить индекс родительского узла */\nparent(i: number): number {\n    return Math.floor((i - 1) / 2); // Округление вниз при делении\n}\n</code></pre> my_heap.dart<pre><code>/* Получить индекс левого дочернего узла */\nint _left(int i) {\n  return 2 * i + 1;\n}\n\n/* Получить индекс правого дочернего узла */\nint _right(int i) {\n  return 2 * i + 2;\n}\n\n/* Получить индекс родительского узла */\nint _parent(int i) {\n  return (i - 1) ~/ 2; // Округление вниз при делении\n}\n</code></pre> my_heap.rs<pre><code>/* Получить индекс левого дочернего узла */\nfn left(i: usize) -&gt; usize {\n    2 * i + 1\n}\n\n/* Получить индекс правого дочернего узла */\nfn right(i: usize) -&gt; usize {\n    2 * i + 2\n}\n\n/* Получить индекс родительского узла */\nfn parent(i: usize) -&gt; usize {\n    (i - 1) / 2 // Округление вниз при делении\n}\n</code></pre> my_heap.c<pre><code>/* Получить индекс левого дочернего узла */\nint left(MaxHeap *maxHeap, int i) {\n    return 2 * i + 1;\n}\n\n/* Получить индекс правого дочернего узла */\nint right(MaxHeap *maxHeap, int i) {\n    return 2 * i + 2;\n}\n\n/* Получить индекс родительского узла */\nint parent(MaxHeap *maxHeap, int i) {\n    return (i - 1) / 2; // Округление вниз\n}\n</code></pre> my_heap.kt<pre><code>/* Получить индекс левого дочернего узла */\nfun left(i: Int): Int {\n    return 2 * i + 1\n}\n\n/* Получить индекс правого дочернего узла */\nfun right(i: Int): Int {\n    return 2 * i + 2\n}\n\n/* Получить индекс родительского узла */\nfun parent(i: Int): Int {\n    return (i - 1) / 2 // Округление вниз при делении\n}\n</code></pre> my_heap.rb<pre><code>### Получить индекс левого дочернего узла ###\ndef left(i)\n  2 * i + 1\nend\n\n### Получить индекс правого дочернего узла ###\ndef right(i)\n  2 * i + 2\nend\n\n### Получить индекс родительского узла ###\ndef parent(i)\n  (i - 1) / 2     # Округление вниз при делении\nend\n</code></pre>","path":["Глава 8. Куча","8.1 &nbsp; Куча"],"tags":[]},{"location":"chapter_heap/heap/#2","level":3,"title":"2.   Доступ к элементу на вершине кучи","text":"<p>Элемент на вершине кучи - это корневой узел двоичного дерева, то есть первый элемент списка:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby my_heap.py<pre><code>def peek(self) -&gt; int:\n    \"\"\"Доступ к элементу на вершине кучи\"\"\"\n    return self.max_heap[0]\n</code></pre> my_heap.cpp<pre><code>/* Доступ к элементу на вершине кучи */\nint peek() {\n    return maxHeap[0];\n}\n</code></pre> my_heap.java<pre><code>/* Доступ к элементу на вершине кучи */\nint peek() {\n    return maxHeap.get(0);\n}\n</code></pre> my_heap.cs<pre><code>/* Доступ к элементу на вершине кучи */\nint Peek() {\n    return maxHeap[0];\n}\n</code></pre> my_heap.go<pre><code>/* Доступ к элементу на вершине кучи */\nfunc (h *maxHeap) peek() any {\n    return h.data[0]\n}\n</code></pre> my_heap.swift<pre><code>/* Доступ к элементу на вершине кучи */\nfunc peek() -&gt; Int {\n    maxHeap[0]\n}\n</code></pre> my_heap.js<pre><code>/* Доступ к элементу на вершине кучи */\npeek() {\n    return this.#maxHeap[0];\n}\n</code></pre> my_heap.ts<pre><code>/* Доступ к элементу на вершине кучи */\npeek(): number {\n    return this.maxHeap[0];\n}\n</code></pre> my_heap.dart<pre><code>/* Доступ к элементу на вершине кучи */\nint peek() {\n  return _maxHeap[0];\n}\n</code></pre> my_heap.rs<pre><code>/* Доступ к элементу на вершине кучи */\nfn peek(&amp;self) -&gt; Option&lt;i32&gt; {\n    self.max_heap.first().copied()\n}\n</code></pre> my_heap.c<pre><code>/* Доступ к элементу на вершине кучи */\nint peek(MaxHeap *maxHeap) {\n    return maxHeap-&gt;data[0];\n}\n</code></pre> my_heap.kt<pre><code>/* Доступ к элементу на вершине кучи */\nfun peek(): Int {\n    return maxHeap[0]\n}\n</code></pre> my_heap.rb<pre><code>### Доступ к элементу на вершине кучи ###\ndef peek\n  @max_heap[0]\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 8. Куча","8.1 &nbsp; Куча"],"tags":[]},{"location":"chapter_heap/heap/#3","level":3,"title":"3.   Добавление элемента в кучу","text":"<p>Пусть дан элемент <code>val</code> . Сначала мы помещаем его в основание кучи. После добавления свойства кучи могут нарушиться, потому что <code>val</code> может оказаться больше, чем другие элементы в куче. Поэтому необходимо восстановить порядок на пути от вставленного узла к корню ; эта операция называется упорядочиванием кучи.</p> <p>Рассмотрим ситуацию, когда упорядочивание выполняется снизу вверх, начиная от только что вставленного узла. Как показано на рисунках ниже, мы сравниваем значение вставленного узла со значением его родителя; если вставленный узел больше, то меняем их местами. Затем продолжаем выполнять ту же операцию и последовательно восстанавливать корректность всех узлов по пути снизу вверх, пока не выйдем за корень или не встретим узел, для которого обмен не требуется.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 8-3   Шаги добавления элемента в кучу </p> <p>Пусть общее число узлов равно \\(n\\) , тогда высота дерева равна \\(O(\\log n)\\) . Следовательно, максимальное число итераций операции упорядочивания кучи тоже не превышает \\(O(\\log n)\\) . Отсюда временная сложность добавления элемента в кучу равна \\(O(\\log n)\\) . Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby my_heap.py<pre><code>def push(self, val: int):\n    \"\"\"Добавление элемента в кучу\"\"\"\n    # Добавление узла\n    self.max_heap.append(val)\n    # Просеивание снизу вверх\n    self.sift_up(self.size() - 1)\n\ndef sift_up(self, i: int):\n    \"\"\"Начиная с узла i, выполнить просеивание снизу вверх\"\"\"\n    while True:\n        # Получение родительского узла для узла i\n        p = self.parent(i)\n        # Завершить heapify, когда «корневой узел уже пройден» или «узел не требует исправления»\n        if p &lt; 0 or self.max_heap[i] &lt;= self.max_heap[p]:\n            break\n        # Поменять два узла местами\n        self.swap(i, p)\n        # Циклическое просеивание вверх\n        i = p\n</code></pre> my_heap.cpp<pre><code>/* Добавление элемента в кучу */\nvoid push(int val) {\n    // Добавление узла\n    maxHeap.push_back(val);\n    // Просеивание снизу вверх\n    siftUp(size() - 1);\n}\n\n/* Начиная с узла i, выполнить просеивание снизу вверх */\nvoid siftUp(int i) {\n    while (true) {\n        // Получение родительского узла для узла i\n        int p = parent(i);\n        // Завершить heapify, когда «корневой узел уже пройден» или «узел не требует исправления»\n        if (p &lt; 0 || maxHeap[i] &lt;= maxHeap[p])\n            break;\n        // Поменять два узла местами\n        swap(maxHeap[i], maxHeap[p]);\n        // Циклическое просеивание вверх\n        i = p;\n    }\n}\n</code></pre> my_heap.java<pre><code>/* Добавление элемента в кучу */\nvoid push(int val) {\n    // Добавление узла\n    maxHeap.add(val);\n    // Просеивание снизу вверх\n    siftUp(size() - 1);\n}\n\n/* Начиная с узла i, выполнить просеивание снизу вверх */\nvoid siftUp(int i) {\n    while (true) {\n        // Получение родительского узла для узла i\n        int p = parent(i);\n        // Завершить heapify, когда «корневой узел уже пройден» или «узел не требует исправления»\n        if (p &lt; 0 || maxHeap.get(i) &lt;= maxHeap.get(p))\n            break;\n        // Поменять два узла местами\n        swap(i, p);\n        // Циклическое просеивание вверх\n        i = p;\n    }\n}\n</code></pre> my_heap.cs<pre><code>/* Добавление элемента в кучу */\nvoid Push(int val) {\n    // Добавление узла\n    maxHeap.Add(val);\n    // Просеивание снизу вверх\n    SiftUp(Size() - 1);\n}\n\n/* Начиная с узла i, выполнить просеивание снизу вверх */\nvoid SiftUp(int i) {\n    while (true) {\n        // Получение родительского узла для узла i\n        int p = Parent(i);\n        // Если «выход за пределы корневого узла» или «узел не требует исправления», завершить просеивание\n        if (p &lt; 0 || maxHeap[i] &lt;= maxHeap[p])\n            break;\n        // Поменять два узла местами\n        Swap(i, p);\n        // Циклическое просеивание вверх\n        i = p;\n    }\n}\n</code></pre> my_heap.go<pre><code>/* Добавление элемента в кучу */\nfunc (h *maxHeap) push(val any) {\n    // Добавление узла\n    h.data = append(h.data, val)\n    // Просеивание снизу вверх\n    h.siftUp(len(h.data) - 1)\n}\n\n/* Начиная с узла i, выполнить просеивание снизу вверх */\nfunc (h *maxHeap) siftUp(i int) {\n    for true {\n        // Получение родительского узла для узла i\n        p := h.parent(i)\n        // Завершить heapify, когда «корневой узел уже пройден» или «узел не требует исправления»\n        if p &lt; 0 || h.data[i].(int) &lt;= h.data[p].(int) {\n            break\n        }\n        // Поменять два узла местами\n        h.swap(i, p)\n        // Циклическое просеивание вверх\n        i = p\n    }\n}\n</code></pre> my_heap.swift<pre><code>/* Добавление элемента в кучу */\nfunc push(val: Int) {\n    // Добавление узла\n    maxHeap.append(val)\n    // Просеивание снизу вверх\n    siftUp(i: size() - 1)\n}\n\n/* Начиная с узла i, выполнить просеивание снизу вверх */\nfunc siftUp(i: Int) {\n    var i = i\n    while true {\n        // Получение родительского узла для узла i\n        let p = parent(i: i)\n        // Завершить heapify, когда «корневой узел уже пройден» или «узел не требует исправления»\n        if p &lt; 0 || maxHeap[i] &lt;= maxHeap[p] {\n            break\n        }\n        // Поменять два узла местами\n        swap(i: i, j: p)\n        // Циклическое просеивание вверх\n        i = p\n    }\n}\n</code></pre> my_heap.js<pre><code>/* Добавление элемента в кучу */\npush(val) {\n    // Добавление узла\n    this.#maxHeap.push(val);\n    // Просеивание снизу вверх\n    this.#siftUp(this.size() - 1);\n}\n\n/* Начиная с узла i, выполнить просеивание снизу вверх */\n#siftUp(i) {\n    while (true) {\n        // Получение родительского узла для узла i\n        const p = this.#parent(i);\n        // Завершить heapify, когда «корневой узел уже пройден» или «узел не требует исправления»\n        if (p &lt; 0 || this.#maxHeap[i] &lt;= this.#maxHeap[p]) break;\n        // Поменять два узла местами\n        this.#swap(i, p);\n        // Циклическое просеивание вверх\n        i = p;\n    }\n}\n</code></pre> my_heap.ts<pre><code>/* Добавление элемента в кучу */\npush(val: number): void {\n    // Добавление узла\n    this.maxHeap.push(val);\n    // Просеивание снизу вверх\n    this.siftUp(this.size() - 1);\n}\n\n/* Начиная с узла i, выполнить просеивание снизу вверх */\nsiftUp(i: number): void {\n    while (true) {\n        // Получение родительского узла для узла i\n        const p = this.parent(i);\n        // Завершить heapify, когда «корневой узел уже пройден» или «узел не требует исправления»\n        if (p &lt; 0 || this.maxHeap[i] &lt;= this.maxHeap[p]) break;\n        // Поменять два узла местами\n        this.swap(i, p);\n        // Циклическое просеивание вверх\n        i = p;\n    }\n}\n</code></pre> my_heap.dart<pre><code>/* Добавление элемента в кучу */\nvoid push(int val) {\n  // Добавление узла\n  _maxHeap.add(val);\n  // Просеивание снизу вверх\n  siftUp(size() - 1);\n}\n\n/* Начиная с узла i, выполнить просеивание снизу вверх */\nvoid siftUp(int i) {\n  while (true) {\n    // Получение родительского узла для узла i\n    int p = _parent(i);\n    // Завершить heapify, когда «корневой узел уже пройден» или «узел не требует исправления»\n    if (p &lt; 0 || _maxHeap[i] &lt;= _maxHeap[p]) {\n      break;\n    }\n    // Поменять два узла местами\n    _swap(i, p);\n    // Циклическое просеивание вверх\n    i = p;\n  }\n}\n</code></pre> my_heap.rs<pre><code>/* Добавление элемента в кучу */\nfn push(&amp;mut self, val: i32) {\n    // Добавление узла\n    self.max_heap.push(val);\n    // Просеивание снизу вверх\n    self.sift_up(self.size() - 1);\n}\n\n/* Начиная с узла i, выполнить просеивание снизу вверх */\nfn sift_up(&amp;mut self, mut i: usize) {\n    loop {\n        // Если узел i уже является вершиной кучи, завершить просеивание\n        if i == 0 {\n            break;\n        }\n        // Получение родительского узла для узла i\n        let p = Self::parent(i);\n        // Когда «узел не требует исправления», завершить просеивание\n        if self.max_heap[i] &lt;= self.max_heap[p] {\n            break;\n        }\n        // Поменять два узла местами\n        self.swap(i, p);\n        // Циклическое просеивание вверх\n        i = p;\n    }\n}\n</code></pre> my_heap.c<pre><code>/* Добавление элемента в кучу */\nvoid push(MaxHeap *maxHeap, int val) {\n    // По умолчанию не следует добавлять так много узлов\n    if (maxHeap-&gt;size == MAX_SIZE) {\n        printf(\"heap is full!\");\n        return;\n    }\n    // Добавление узла\n    maxHeap-&gt;data[maxHeap-&gt;size] = val;\n    maxHeap-&gt;size++;\n\n    // Просеивание снизу вверх\n    siftUp(maxHeap, maxHeap-&gt;size - 1);\n}\n\n/* Начиная с узла i, выполнить просеивание снизу вверх */\nvoid siftUp(MaxHeap *maxHeap, int i) {\n    while (true) {\n        // Получение родительского узла для узла i\n        int p = parent(maxHeap, i);\n        // Завершить heapify, когда «корневой узел уже пройден» или «узел не требует исправления»\n        if (p &lt; 0 || maxHeap-&gt;data[i] &lt;= maxHeap-&gt;data[p]) {\n            break;\n        }\n        // Поменять два узла местами\n        swap(maxHeap, i, p);\n        // Циклическое просеивание вверх\n        i = p;\n    }\n}\n</code></pre> my_heap.kt<pre><code>/* Добавление элемента в кучу */\nfun push(_val: Int) {\n    // Добавление узла\n    maxHeap.add(_val)\n    // Просеивание снизу вверх\n    siftUp(size() - 1)\n}\n\n/* Начиная с узла i, выполнить просеивание снизу вверх */\nfun siftUp(it: Int) {\n    // Параметры функций в Kotlin неизменяемы, поэтому создается временная переменная\n    var i = it\n    while (true) {\n        // Получение родительского узла для узла i\n        val p = parent(i)\n        // Завершить heapify, когда «корневой узел уже пройден» или «узел не требует исправления»\n        if (p &lt; 0 || maxHeap[i] &lt;= maxHeap[p]) break\n        // Поменять два узла местами\n        swap(i, p)\n        // Циклическое просеивание вверх\n        i = p\n    }\n}\n</code></pre> my_heap.rb<pre><code>### Добавление элемента в кучу ###\ndef push(val)\n  # Добавление узла\n  @max_heap &lt;&lt; val\n  # Просеивание снизу вверх\n  sift_up(size - 1)\nend\n\n### Начиная с узла i, выполнить просеивание снизу вверх ###\ndef sift_up(i)\n  loop do\n    # Получение родительского узла для узла i\n    p = parent(i)\n    # Завершить heapify, когда «корневой узел уже пройден» или «узел не требует исправления»\n    break if p &lt; 0 || @max_heap[i] &lt;= @max_heap[p]\n    # Поменять два узла местами\n    swap(i, p)\n    # Циклическое просеивание вверх\n    i = p\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 8. Куча","8.1 &nbsp; Куча"],"tags":[]},{"location":"chapter_heap/heap/#4","level":3,"title":"4.   Извлечение элемента с вершины кучи","text":"<p>Элемент на вершине кучи - это корневой узел двоичного дерева, то есть первый элемент списка. Если просто удалить первый элемент списка, то индексы всех узлов двоичного дерева изменятся, и это сильно затруднит последующее восстановление структуры при помощи упорядочивания кучи. Чтобы по возможности минимизировать изменение индексов элементов, мы используем следующий порядок действий.</p> <ol> <li>Поменять местами элемент на вершине кучи и элемент у основания кучи, то есть поменять корневой узел с самым правым листовым узлом.</li> <li>После обмена удалить основание кучи из списка. Стоит отметить, что, поскольку обмен уже выполнен, фактически удаляется исходный элемент вершины кучи.</li> <li>Начиная от корневого узла, выполнить упорядочивание кучи сверху вниз.</li> </ol> <p>Как показано на рисунках ниже, направление операции упорядочивания кучи сверху вниз противоположно операции упорядочивания кучи снизу вверх. Мы сравниваем значение корневого узла со значениями двух дочерних узлов, выбираем больший дочерний узел и меняем его местами с корневым узлом. Затем циклически повторяем ту же операцию, пока не выйдем за листовой узел или не встретим узел, который уже не требует обмена.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 8-4   Шаги извлечения элемента с вершины кучи </p> <p>Как и операция добавления в кучу, операция извлечения элемента с вершины кучи также имеет временную сложность \\(O(\\log n)\\) . Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby my_heap.py<pre><code>def pop(self) -&gt; int:\n    \"\"\"Извлечение элемента из кучи\"\"\"\n    # Обработка пустого случая\n    if self.is_empty():\n        raise IndexError(\"куча пуста\")\n    # Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    self.swap(0, self.size() - 1)\n    # Удаление узла\n    val = self.max_heap.pop()\n    # Просеивание сверху вниз\n    self.sift_down(0)\n    # Вернуть элемент с вершины кучи\n    return val\n\ndef sift_down(self, i: int):\n    \"\"\"Начиная с узла i, выполнить просеивание сверху вниз\"\"\"\n    while True:\n        # Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        l, r, ma = self.left(i), self.right(i), i\n        if l &lt; self.size() and self.max_heap[l] &gt; self.max_heap[ma]:\n            ma = l\n        if r &lt; self.size() and self.max_heap[r] &gt; self.max_heap[ma]:\n            ma = r\n        # Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if ma == i:\n            break\n        # Поменять два узла местами\n        self.swap(i, ma)\n        # Циклическое просеивание вниз\n        i = ma\n</code></pre> my_heap.cpp<pre><code>/* Извлечение элемента из кучи */\nvoid pop() {\n    // Обработка пустого случая\n    if (isEmpty()) {\n        throw out_of_range(\"куча пуста\");\n    }\n    // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    swap(maxHeap[0], maxHeap[size() - 1]);\n    // Удаление узла\n    maxHeap.pop_back();\n    // Просеивание сверху вниз\n    siftDown(0);\n}\n\n/* Начиная с узла i, выполнить просеивание сверху вниз */\nvoid siftDown(int i) {\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        int l = left(i), r = right(i), ma = i;\n        if (l &lt; size() &amp;&amp; maxHeap[l] &gt; maxHeap[ma])\n            ma = l;\n        if (r &lt; size() &amp;&amp; maxHeap[r] &gt; maxHeap[ma])\n            ma = r;\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (ma == i)\n            break;\n        swap(maxHeap[i], maxHeap[ma]);\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n</code></pre> my_heap.java<pre><code>/* Извлечение элемента из кучи */\nint pop() {\n    // Обработка пустого случая\n    if (isEmpty())\n        throw new IndexOutOfBoundsException();\n    // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    swap(0, size() - 1);\n    // Удаление узла\n    int val = maxHeap.remove(size() - 1);\n    // Просеивание сверху вниз\n    siftDown(0);\n    // Вернуть элемент с вершины кучи\n    return val;\n}\n\n/* Начиная с узла i, выполнить просеивание сверху вниз */\nvoid siftDown(int i) {\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        int l = left(i), r = right(i), ma = i;\n        if (l &lt; size() &amp;&amp; maxHeap.get(l) &gt; maxHeap.get(ma))\n            ma = l;\n        if (r &lt; size() &amp;&amp; maxHeap.get(r) &gt; maxHeap.get(ma))\n            ma = r;\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (ma == i)\n            break;\n        // Поменять два узла местами\n        swap(i, ma);\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n</code></pre> my_heap.cs<pre><code>/* Извлечение элемента из кучи */\nint Pop() {\n    // Обработка пустого случая\n    if (IsEmpty())\n        throw new IndexOutOfRangeException();\n    // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    Swap(0, Size() - 1);\n    // Удаление узла\n    int val = maxHeap.Last();\n    maxHeap.RemoveAt(Size() - 1);\n    // Просеивание сверху вниз\n    SiftDown(0);\n    // Вернуть элемент с вершины кучи\n    return val;\n}\n\n/* Начиная с узла i, выполнить просеивание сверху вниз */\nvoid SiftDown(int i) {\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        int l = Left(i), r = Right(i), ma = i;\n        if (l &lt; Size() &amp;&amp; maxHeap[l] &gt; maxHeap[ma])\n            ma = l;\n        if (r &lt; Size() &amp;&amp; maxHeap[r] &gt; maxHeap[ma])\n            ma = r;\n        // Если «узел i максимален» или «выход за пределы листовых узлов», завершить просеивание\n        if (ma == i) break;\n        // Поменять два узла местами\n        Swap(i, ma);\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n</code></pre> my_heap.go<pre><code>/* Извлечение элемента из кучи */\nfunc (h *maxHeap) pop() any {\n    // Обработка пустого случая\n    if h.isEmpty() {\n        fmt.Println(\"error\")\n        return nil\n    }\n    // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    h.swap(0, h.size()-1)\n    // Удаление узла\n    val := h.data[len(h.data)-1]\n    h.data = h.data[:len(h.data)-1]\n    // Просеивание сверху вниз\n    h.siftDown(0)\n\n    // Вернуть элемент с вершины кучи\n    return val\n}\n\n/* Начиная с узла i, выполнить просеивание сверху вниз */\nfunc (h *maxHeap) siftDown(i int) {\n    for true {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как max\n        l, r, max := h.left(i), h.right(i), i\n        if l &lt; h.size() &amp;&amp; h.data[l].(int) &gt; h.data[max].(int) {\n            max = l\n        }\n        if r &lt; h.size() &amp;&amp; h.data[r].(int) &gt; h.data[max].(int) {\n            max = r\n        }\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if max == i {\n            break\n        }\n        // Поменять два узла местами\n        h.swap(i, max)\n        // Циклическое просеивание вниз\n        i = max\n    }\n}\n</code></pre> my_heap.swift<pre><code>/* Извлечение элемента из кучи */\nfunc pop() -&gt; Int {\n    // Обработка пустого случая\n    if isEmpty() {\n        fatalError(\"куча пуста\")\n    }\n    // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    swap(i: 0, j: size() - 1)\n    // Удаление узла\n    let val = maxHeap.remove(at: size() - 1)\n    // Просеивание сверху вниз\n    siftDown(i: 0)\n    // Вернуть элемент с вершины кучи\n    return val\n}\n\n/* Начиная с узла i, выполнить просеивание сверху вниз */\nfunc siftDown(i: Int) {\n    var i = i\n    while true {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        let l = left(i: i)\n        let r = right(i: i)\n        var ma = i\n        if l &lt; size(), maxHeap[l] &gt; maxHeap[ma] {\n            ma = l\n        }\n        if r &lt; size(), maxHeap[r] &gt; maxHeap[ma] {\n            ma = r\n        }\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if ma == i {\n            break\n        }\n        // Поменять два узла местами\n        swap(i: i, j: ma)\n        // Циклическое просеивание вниз\n        i = ma\n    }\n}\n</code></pre> my_heap.js<pre><code>/* Извлечение элемента из кучи */\npop() {\n    // Обработка пустого случая\n    if (this.isEmpty()) throw new Error('куча пуста');\n    // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    this.#swap(0, this.size() - 1);\n    // Удаление узла\n    const val = this.#maxHeap.pop();\n    // Просеивание сверху вниз\n    this.#siftDown(0);\n    // Вернуть элемент с вершины кучи\n    return val;\n}\n\n/* Начиная с узла i, выполнить просеивание сверху вниз */\n#siftDown(i) {\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        const l = this.#left(i),\n            r = this.#right(i);\n        let ma = i;\n        if (l &lt; this.size() &amp;&amp; this.#maxHeap[l] &gt; this.#maxHeap[ma]) ma = l;\n        if (r &lt; this.size() &amp;&amp; this.#maxHeap[r] &gt; this.#maxHeap[ma]) ma = r;\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (ma === i) break;\n        // Поменять два узла местами\n        this.#swap(i, ma);\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n</code></pre> my_heap.ts<pre><code>/* Извлечение элемента из кучи */\npop(): number {\n    // Обработка пустого случая\n    if (this.isEmpty()) throw new RangeError('Heap is empty.');\n    // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    this.swap(0, this.size() - 1);\n    // Удаление узла\n    const val = this.maxHeap.pop();\n    // Просеивание сверху вниз\n    this.siftDown(0);\n    // Вернуть элемент с вершины кучи\n    return val;\n}\n\n/* Начиная с узла i, выполнить просеивание сверху вниз */\nsiftDown(i: number): void {\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        const l = this.left(i),\n            r = this.right(i);\n        let ma = i;\n        if (l &lt; this.size() &amp;&amp; this.maxHeap[l] &gt; this.maxHeap[ma]) ma = l;\n        if (r &lt; this.size() &amp;&amp; this.maxHeap[r] &gt; this.maxHeap[ma]) ma = r;\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (ma === i) break;\n        // Поменять два узла местами\n        this.swap(i, ma);\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n</code></pre> my_heap.dart<pre><code>/* Извлечение элемента из кучи */\nint pop() {\n  // Обработка пустого случая\n  if (isEmpty()) throw Exception('куча пуста');\n  // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n  _swap(0, size() - 1);\n  // Удаление узла\n  int val = _maxHeap.removeLast();\n  // Просеивание сверху вниз\n  siftDown(0);\n  // Вернуть элемент с вершины кучи\n  return val;\n}\n\n/* Начиная с узла i, выполнить просеивание сверху вниз */\nvoid siftDown(int i) {\n  while (true) {\n    // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n    int l = _left(i);\n    int r = _right(i);\n    int ma = i;\n    if (l &lt; size() &amp;&amp; _maxHeap[l] &gt; _maxHeap[ma]) ma = l;\n    if (r &lt; size() &amp;&amp; _maxHeap[r] &gt; _maxHeap[ma]) ma = r;\n    // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n    if (ma == i) break;\n    // Поменять два узла местами\n    _swap(i, ma);\n    // Циклическое просеивание вниз\n    i = ma;\n  }\n}\n</code></pre> my_heap.rs<pre><code>/* Извлечение элемента из кучи */\nfn pop(&amp;mut self) -&gt; i32 {\n    // Обработка пустого случая\n    if self.is_empty() {\n        panic!(\"index out of bounds\");\n    }\n    // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    self.swap(0, self.size() - 1);\n    // Удаление узла\n    let val = self.max_heap.pop().unwrap();\n    // Просеивание сверху вниз\n    self.sift_down(0);\n    // Вернуть элемент с вершины кучи\n    val\n}\n\n/* Начиная с узла i, выполнить просеивание сверху вниз */\nfn sift_down(&amp;mut self, mut i: usize) {\n    loop {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        let (l, r, mut ma) = (Self::left(i), Self::right(i), i);\n        if l &lt; self.size() &amp;&amp; self.max_heap[l] &gt; self.max_heap[ma] {\n            ma = l;\n        }\n        if r &lt; self.size() &amp;&amp; self.max_heap[r] &gt; self.max_heap[ma] {\n            ma = r;\n        }\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if ma == i {\n            break;\n        }\n        // Поменять два узла местами\n        self.swap(i, ma);\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n</code></pre> my_heap.c<pre><code>/* Извлечение элемента из кучи */\nint pop(MaxHeap *maxHeap) {\n    // Обработка пустого случая\n    if (isEmpty(maxHeap)) {\n        printf(\"heap is empty!\");\n        return INT_MAX;\n    }\n    // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    swap(maxHeap, 0, size(maxHeap) - 1);\n    // Удаление узла\n    int val = maxHeap-&gt;data[maxHeap-&gt;size - 1];\n    maxHeap-&gt;size--;\n    // Просеивание сверху вниз\n    siftDown(maxHeap, 0);\n\n    // Вернуть элемент с вершины кучи\n    return val;\n}\n\n/* Начиная с узла i, выполнить просеивание сверху вниз */\nvoid siftDown(MaxHeap *maxHeap, int i) {\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как max\n        int l = left(maxHeap, i);\n        int r = right(maxHeap, i);\n        int max = i;\n        if (l &lt; size(maxHeap) &amp;&amp; maxHeap-&gt;data[l] &gt; maxHeap-&gt;data[max]) {\n            max = l;\n        }\n        if (r &lt; size(maxHeap) &amp;&amp; maxHeap-&gt;data[r] &gt; maxHeap-&gt;data[max]) {\n            max = r;\n        }\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (max == i) {\n            break;\n        }\n        // Поменять два узла местами\n        swap(maxHeap, i, max);\n        // Циклическое просеивание вниз\n        i = max;\n    }\n}\n</code></pre> my_heap.kt<pre><code>/* Извлечение элемента из кучи */\nfun pop(): Int {\n    // Обработка пустого случая\n    if (isEmpty()) throw IndexOutOfBoundsException()\n    // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    swap(0, size() - 1)\n    // Удаление узла\n    val _val = maxHeap.removeAt(size() - 1)\n    // Просеивание сверху вниз\n    siftDown(0)\n    // Вернуть элемент с вершины кучи\n    return _val\n}\n\n/* Начиная с узла i, выполнить просеивание сверху вниз */\nfun siftDown(it: Int) {\n    // Параметры функций в Kotlin неизменяемы, поэтому создается временная переменная\n    var i = it\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        val l = left(i)\n        val r = right(i)\n        var ma = i\n        if (l &lt; size() &amp;&amp; maxHeap[l] &gt; maxHeap[ma]) ma = l\n        if (r &lt; size() &amp;&amp; maxHeap[r] &gt; maxHeap[ma]) ma = r\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (ma == i) break\n        // Поменять два узла местами\n        swap(i, ma)\n        // Циклическое просеивание вниз\n        i = ma\n    }\n}\n</code></pre> my_heap.rb<pre><code>### Извлечение элемента из кучи ###\ndef pop\n  # Обработка пустого случая\n  raise IndexError, \"куча пуста\" if is_empty?\n  # Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n  swap(0, size - 1)\n  # Удаление узла\n  val = @max_heap.pop\n  # Просеивание сверху вниз\n  sift_down(0)\n  # Вернуть элемент с вершины кучи\n  val\nend\n\n### Начиная с узла i, выполнить просеивание сверху вниз ###\ndef sift_down(i)\n  loop do\n    # Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n    l, r, ma = left(i), right(i), i\n    ma = l if l &lt; size &amp;&amp; @max_heap[l] &gt; @max_heap[ma]\n    ma = r if r &lt; size &amp;&amp; @max_heap[r] &gt; @max_heap[ma]\n\n    # Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n    break if ma == i\n\n    # Поменять два узла местами\n    swap(i, ma)\n    # Циклическое просеивание вниз\n    i = ma\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 8. Куча","8.1 &nbsp; Куча"],"tags":[]},{"location":"chapter_heap/heap/#813","level":2,"title":"8.1.3   Типичные применения кучи","text":"<ul> <li>Очередь с приоритетом: куча обычно является предпочтительной структурой данных для реализации очереди с приоритетом; добавление и извлечение элементов имеют временную сложность \\(O(\\log n)\\) , а построение кучи - \\(O(n)\\) , и все эти операции выполняются очень эффективно.</li> <li>Пирамидальная сортировка: для заданного набора данных можно построить кучу, а затем непрерывно извлекать из нее элементы, получая отсортированные данные. Однако на практике мы обычно используем более изящную реализацию пирамидальной сортировки; подробности см. в разделе \"Пирамидальная сортировка\".</li> <li>Получение наибольших \\(k\\) элементов: это классическая алгоритмическая задача и одновременно типичное применение кучи. Например, выбор 10 самых горячих новостей для списка популярных тем или выбор 10 самых продаваемых товаров.</li> </ul>","path":["Глава 8. Куча","8.1 &nbsp; Куча"],"tags":[]},{"location":"chapter_heap/summary/","level":1,"title":"8.4   Резюме","text":"","path":["Глава 8. Куча","8.4 &nbsp; Резюме"],"tags":[]},{"location":"chapter_heap/summary/#1","level":3,"title":"1.   Ключевые выводы","text":"<ul> <li>Куча представляет собой полное двоичное дерево и делится на максимальную кучу и минимальную кучу. Элемент на вершине максимальной (минимальной) кучи является наибольшим (наименьшим).</li> <li>Очередь с приоритетом определяется как очередь, элементы которой извлекаются в соответствии с приоритетом; обычно ее реализуют с помощью кучи.</li> <li>К основным операциям кучи и их временным сложностям относятся: добавление элемента в кучу \\(O(\\log n)\\) , извлечение элемента с вершины кучи \\(O(\\log n)\\) и доступ к вершине кучи \\(O(1)\\) .</li> <li>Полное двоичное дерево очень удобно представлять массивом, поэтому кучу обычно тоже хранят в массиве.</li> <li>Операция упорядочивания кучи используется для поддержания свойств кучи и применяется как при добавлении элемента, так и при извлечении элемента.</li> <li>Временную сложность построения кучи из \\(n\\) элементов можно оптимизировать до \\(O(n)\\) , что очень эффективно.</li> <li>Top-k - это классическая алгоритмическая задача, которую можно эффективно решать с помощью кучи за \\(O(n \\log k)\\) .</li> </ul>","path":["Глава 8. Куча","8.4 &nbsp; Резюме"],"tags":[]},{"location":"chapter_heap/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: Является ли \"куча\" как структура данных тем же самым понятием, что и \"куча\" в управлении памятью?</p> <p>Это не одно и то же, просто у них случайно совпало название. Куча в памяти компьютерной системы является частью динамического распределения памяти: во время выполнения программы она используется для хранения данных. Программа может запросить определенный объем памяти в куче для хранения сложных структур, таких как объекты и массивы. Когда эти данные больше не нужны, память нужно освободить, чтобы не допустить утечек. По сравнению со стековой памятью управление памятью в куче требует большей осторожности, а неправильное использование может привести к утечкам памяти и проблемам с указателями.</p>","path":["Глава 8. Куча","8.4 &nbsp; Резюме"],"tags":[]},{"location":"chapter_heap/top_k/","level":1,"title":"8.3   Задача Top-k","text":"<p>Question</p> <p>Дан неупорядоченный массив <code>nums</code> длины \\(n\\) . Требуется вернуть наибольшие \\(k\\) элементов массива.</p> <p>Для этой задачи мы сначала покажем два относительно прямолинейных способа решения, а затем более эффективный способ на основе кучи.</p>","path":["Глава 8. Куча","8.3 &nbsp; Задача Top-k"],"tags":[]},{"location":"chapter_heap/top_k/#831-1","level":2,"title":"8.3.1   Метод 1: выбор через обход","text":"<p>Как показано на рисунке 8-6, можно выполнить \\(k\\) проходов по массиву и на каждом проходе извлекать соответственно \\(1\\)-й, \\(2\\)-й, \\(\\dots\\) , \\(k\\)-й по величине элемент; временная сложность такого подхода равна \\(O(nk)\\) .</p> <p>Этот метод подходит только для случая \\(k \\ll n\\) , потому что когда \\(k\\) приближается к \\(n\\) , его временная сложность стремится к \\(O(n^2)\\) , а это уже очень затратно.</p> <p></p> <p> Рисунок 8-6   Поиск наибольших k элементов через обход </p> <p>Tip</p> <p>Когда \\(k = n\\) , мы получаем полную упорядоченную последовательность, и в этот момент задача становится эквивалентной алгоритму \"сортировка выбором\".</p>","path":["Глава 8. Куча","8.3 &nbsp; Задача Top-k"],"tags":[]},{"location":"chapter_heap/top_k/#832-2","level":2,"title":"8.3.2   Метод 2: сортировка","text":"<p>Как показано на рисунке 8-7, можно сначала отсортировать массив <code>nums</code> , а затем вернуть его крайние правые \\(k\\) элементов; временная сложность такого метода равна \\(O(n \\log n)\\) .</p> <p>Очевидно, что этот способ делает слишком много, потому что нам нужно только найти наибольшие \\(k\\) элементов, а сортировать остальные элементы совсем не обязательно.</p> <p></p> <p> Рисунок 8-7   Поиск наибольших k элементов через сортировку </p>","path":["Глава 8. Куча","8.3 &nbsp; Задача Top-k"],"tags":[]},{"location":"chapter_heap/top_k/#833-3","level":2,"title":"8.3.3   Метод 3: куча","text":"<p>Задачу Top-k можно решить гораздо эффективнее с помощью кучи, как показано на рисунках ниже.</p> <ol> <li>Инициализировать минимальную кучу, у которой вершина содержит наименьший элемент.</li> <li>Сначала по очереди поместить в кучу первые \\(k\\) элементов массива.</li> <li>Начиная с элемента номер \\(k + 1\\) , если текущий элемент больше элемента на вершине кучи, то извлечь вершину кучи и поместить в кучу текущий элемент.</li> <li>После завершения обхода в куче будут храниться как раз наибольшие \\(k\\) элементов.</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 8-8   Поиск наибольших k элементов с помощью кучи </p> <p>Пример кода приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby top_k.py<pre><code>def top_k_heap(nums: list[int], k: int) -&gt; list[int]:\n    \"\"\"Найти k наибольших элементов массива с помощью кучи\"\"\"\n    # Инициализация минимальной кучи\n    heap = []\n    # Поместить первые k элементов массива в кучу\n    for i in range(k):\n        heapq.heappush(heap, nums[i])\n    # Начиная с элемента k+1, поддерживать длину кучи равной k\n    for i in range(k, len(nums)):\n        # Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n        if nums[i] &gt; heap[0]:\n            heapq.heappop(heap)\n            heapq.heappush(heap, nums[i])\n    return heap\n</code></pre> top_k.cpp<pre><code>/* Найти k наибольших элементов массива с помощью кучи */\npriority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; topKHeap(vector&lt;int&gt; &amp;nums, int k) {\n    // Инициализация минимальной кучи\n    priority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; heap;\n    // Поместить первые k элементов массива в кучу\n    for (int i = 0; i &lt; k; i++) {\n        heap.push(nums[i]);\n    }\n    // Начиная с элемента k+1, поддерживать длину кучи равной k\n    for (int i = k; i &lt; nums.size(); i++) {\n        // Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n        if (nums[i] &gt; heap.top()) {\n            heap.pop();\n            heap.push(nums[i]);\n        }\n    }\n    return heap;\n}\n</code></pre> top_k.java<pre><code>/* Найти k наибольших элементов массива с помощью кучи */\nQueue&lt;Integer&gt; topKHeap(int[] nums, int k) {\n    // Инициализация минимальной кучи\n    Queue&lt;Integer&gt; heap = new PriorityQueue&lt;Integer&gt;();\n    // Поместить первые k элементов массива в кучу\n    for (int i = 0; i &lt; k; i++) {\n        heap.offer(nums[i]);\n    }\n    // Начиная с элемента k+1, поддерживать длину кучи равной k\n    for (int i = k; i &lt; nums.length; i++) {\n        // Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n        if (nums[i] &gt; heap.peek()) {\n            heap.poll();\n            heap.offer(nums[i]);\n        }\n    }\n    return heap;\n}\n</code></pre> top_k.cs<pre><code>/* Найти k наибольших элементов массива с помощью кучи */\nPriorityQueue&lt;int, int&gt; TopKHeap(int[] nums, int k) {\n    // Инициализация минимальной кучи\n    PriorityQueue&lt;int, int&gt; heap = new();\n    // Поместить первые k элементов массива в кучу\n    for (int i = 0; i &lt; k; i++) {\n        heap.Enqueue(nums[i], nums[i]);\n    }\n    // Начиная с элемента k+1, поддерживать длину кучи равной k\n    for (int i = k; i &lt; nums.Length; i++) {\n        // Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n        if (nums[i] &gt; heap.Peek()) {\n            heap.Dequeue();\n            heap.Enqueue(nums[i], nums[i]);\n        }\n    }\n    return heap;\n}\n</code></pre> top_k.go<pre><code>/* Найти k наибольших элементов массива с помощью кучи */\nfunc topKHeap(nums []int, k int) *minHeap {\n    // Инициализация минимальной кучи\n    h := &amp;minHeap{}\n    heap.Init(h)\n    // Поместить первые k элементов массива в кучу\n    for i := 0; i &lt; k; i++ {\n        heap.Push(h, nums[i])\n    }\n    // Начиная с элемента k+1, поддерживать длину кучи равной k\n    for i := k; i &lt; len(nums); i++ {\n        // Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n        if nums[i] &gt; h.Top().(int) {\n            heap.Pop(h)\n            heap.Push(h, nums[i])\n        }\n    }\n    return h\n}\n</code></pre> top_k.swift<pre><code>/* Найти k наибольших элементов массива с помощью кучи */\nfunc topKHeap(nums: [Int], k: Int) -&gt; [Int] {\n    // Инициализировать минимальную кучу и построить ее по первым k элементам\n    var heap = Heap(nums.prefix(k))\n    // Начиная с элемента k+1, поддерживать длину кучи равной k\n    for i in nums.indices.dropFirst(k) {\n        // Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n        if nums[i] &gt; heap.min()! {\n            _ = heap.removeMin()\n            heap.insert(nums[i])\n        }\n    }\n    return heap.unordered\n}\n</code></pre> top_k.js<pre><code>/* Добавление элемента в кучу */\nfunction pushMinHeap(maxHeap, val) {\n    // Инвертировать знак элемента\n    maxHeap.push(-val);\n}\n\n/* Извлечение элемента из кучи */\nfunction popMinHeap(maxHeap) {\n    // Инвертировать знак элемента\n    return -maxHeap.pop();\n}\n\n/* Доступ к элементу на вершине кучи */\nfunction peekMinHeap(maxHeap) {\n    // Инвертировать знак элемента\n    return -maxHeap.peek();\n}\n\n/* Извлечь элементы из кучи */\nfunction getMinHeap(maxHeap) {\n    // Инвертировать знак элемента\n    return maxHeap.getMaxHeap().map((num) =&gt; -num);\n}\n\n/* Найти k наибольших элементов массива с помощью кучи */\nfunction topKHeap(nums, k) {\n    // Инициализация минимальной кучи\n    // Обратите внимание: мы инвертируем все элементы кучи, чтобы с помощью максимальной кучи имитировать минимальную\n    const maxHeap = new MaxHeap([]);\n    // Поместить первые k элементов массива в кучу\n    for (let i = 0; i &lt; k; i++) {\n        pushMinHeap(maxHeap, nums[i]);\n    }\n    // Начиная с элемента k+1, поддерживать длину кучи равной k\n    for (let i = k; i &lt; nums.length; i++) {\n        // Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n        if (nums[i] &gt; peekMinHeap(maxHeap)) {\n            popMinHeap(maxHeap);\n            pushMinHeap(maxHeap, nums[i]);\n        }\n    }\n    // Вернуть элементы кучи\n    return getMinHeap(maxHeap);\n}\n</code></pre> top_k.ts<pre><code>/* Добавление элемента в кучу */\nfunction pushMinHeap(maxHeap: MaxHeap, val: number): void {\n    // Инвертировать знак элемента\n    maxHeap.push(-val);\n}\n\n/* Извлечение элемента из кучи */\nfunction popMinHeap(maxHeap: MaxHeap): number {\n    // Инвертировать знак элемента\n    return -maxHeap.pop();\n}\n\n/* Доступ к элементу на вершине кучи */\nfunction peekMinHeap(maxHeap: MaxHeap): number {\n    // Инвертировать знак элемента\n    return -maxHeap.peek();\n}\n\n/* Извлечь элементы из кучи */\nfunction getMinHeap(maxHeap: MaxHeap): number[] {\n    // Инвертировать знак элемента\n    return maxHeap.getMaxHeap().map((num: number) =&gt; -num);\n}\n\n/* Найти k наибольших элементов массива с помощью кучи */\nfunction topKHeap(nums: number[], k: number): number[] {\n    // Инициализация минимальной кучи\n    // Обратите внимание: мы инвертируем все элементы кучи, чтобы с помощью максимальной кучи имитировать минимальную\n    const maxHeap = new MaxHeap([]);\n    // Поместить первые k элементов массива в кучу\n    for (let i = 0; i &lt; k; i++) {\n        pushMinHeap(maxHeap, nums[i]);\n    }\n    // Начиная с элемента k+1, поддерживать длину кучи равной k\n    for (let i = k; i &lt; nums.length; i++) {\n        // Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n        if (nums[i] &gt; peekMinHeap(maxHeap)) {\n            popMinHeap(maxHeap);\n            pushMinHeap(maxHeap, nums[i]);\n        }\n    }\n    // Вернуть элементы кучи\n    return getMinHeap(maxHeap);\n}\n</code></pre> top_k.dart<pre><code>/* Найти k наибольших элементов массива с помощью кучи */\nMinHeap topKHeap(List&lt;int&gt; nums, int k) {\n  // Инициализировать минимальную кучу, поместив в нее первые k элементов массива\n  MinHeap heap = MinHeap(nums.sublist(0, k));\n  // Начиная с элемента k+1, поддерживать длину кучи равной k\n  for (int i = k; i &lt; nums.length; i++) {\n    // Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n    if (nums[i] &gt; heap.peek()) {\n      heap.pop();\n      heap.push(nums[i]);\n    }\n  }\n  return heap;\n}\n</code></pre> top_k.rs<pre><code>/* Найти k наибольших элементов массива с помощью кучи */\nfn top_k_heap(nums: Vec&lt;i32&gt;, k: usize) -&gt; BinaryHeap&lt;Reverse&lt;i32&gt;&gt; {\n    // BinaryHeap — это максимальная куча; с помощью Reverse элементы инвертируются, чтобы реализовать минимальную кучу\n    let mut heap = BinaryHeap::&lt;Reverse&lt;i32&gt;&gt;::new();\n    // Поместить первые k элементов массива в кучу\n    for &amp;num in nums.iter().take(k) {\n        heap.push(Reverse(num));\n    }\n    // Начиная с элемента k+1, поддерживать длину кучи равной k\n    for &amp;num in nums.iter().skip(k) {\n        // Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n        if num &gt; heap.peek().unwrap().0 {\n            heap.pop();\n            heap.push(Reverse(num));\n        }\n    }\n    heap\n}\n</code></pre> top_k.c<pre><code>/* Добавление элемента в кучу */\nvoid pushMinHeap(MaxHeap *maxHeap, int val) {\n    // Инвертировать знак элемента\n    push(maxHeap, -val);\n}\n\n/* Извлечение элемента из кучи */\nint popMinHeap(MaxHeap *maxHeap) {\n    // Инвертировать знак элемента\n    return -pop(maxHeap);\n}\n\n/* Доступ к элементу на вершине кучи */\nint peekMinHeap(MaxHeap *maxHeap) {\n    // Инвертировать знак элемента\n    return -peek(maxHeap);\n}\n\n/* Извлечь элементы из кучи */\nint *getMinHeap(MaxHeap *maxHeap) {\n    // Инвертировать все элементы кучи и записать их в массив res\n    int *res = (int *)malloc(maxHeap-&gt;size * sizeof(int));\n    for (int i = 0; i &lt; maxHeap-&gt;size; i++) {\n        res[i] = -maxHeap-&gt;data[i];\n    }\n    return res;\n}\n\n/* Извлечь элементы из кучи */\nint *getMinHeap(MaxHeap *maxHeap) {\n    // Инвертировать все элементы кучи и записать их в массив res\n    int *res = (int *)malloc(maxHeap-&gt;size * sizeof(int));\n    for (int i = 0; i &lt; maxHeap-&gt;size; i++) {\n        res[i] = -maxHeap-&gt;data[i];\n    }\n    return res;\n}\n\n// Функция поиска k наибольших элементов массива на основе кучи\nint *topKHeap(int *nums, int sizeNums, int k) {\n    // Инициализация минимальной кучи\n    // Обратите внимание: мы инвертируем все элементы кучи, чтобы с помощью максимальной кучи имитировать минимальную\n    int *empty = (int *)malloc(0);\n    MaxHeap *maxHeap = newMaxHeap(empty, 0);\n    // Поместить первые k элементов массива в кучу\n    for (int i = 0; i &lt; k; i++) {\n        pushMinHeap(maxHeap, nums[i]);\n    }\n    // Начиная с элемента k+1, поддерживать длину кучи равной k\n    for (int i = k; i &lt; sizeNums; i++) {\n        // Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n        if (nums[i] &gt; peekMinHeap(maxHeap)) {\n            popMinHeap(maxHeap);\n            pushMinHeap(maxHeap, nums[i]);\n        }\n    }\n    int *res = getMinHeap(maxHeap);\n    // Освободить память\n    delMaxHeap(maxHeap);\n    return res;\n}\n</code></pre> top_k.kt<pre><code>/* Найти k наибольших элементов массива с помощью кучи */\nfun topKHeap(nums: IntArray, k: Int): Queue&lt;Int&gt; {\n    // Инициализация минимальной кучи\n    val heap = PriorityQueue&lt;Int&gt;()\n    // Поместить первые k элементов массива в кучу\n    for (i in 0..&lt;k) {\n        heap.offer(nums[i])\n    }\n    // Начиная с элемента k+1, поддерживать длину кучи равной k\n    for (i in k..&lt;nums.size) {\n        // Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n        if (nums[i] &gt; heap.peek()) {\n            heap.poll()\n            heap.offer(nums[i])\n        }\n    }\n    return heap\n}\n</code></pre> top_k.rb<pre><code>### Поиск k наибольших элементов массива с помощью кучи ###\ndef top_k_heap(nums, k)\n  # Инициализация минимальной кучи\n  # Обратите внимание: мы инвертируем все элементы кучи, чтобы с помощью максимальной кучи имитировать минимальную\n  max_heap = MaxHeap.new([])\n\n  # Поместить первые k элементов массива в кучу\n  for i in 0...k\n    push_min_heap(max_heap, nums[i])\n  end\n\n  # Начиная с элемента k+1, поддерживать длину кучи равной k\n  for i in k...nums.length\n    # Если текущий элемент больше элемента на вершине кучи, извлечь вершину кучи и добавить текущий элемент в кучу\n    if nums[i] &gt; peek_min_heap(max_heap)\n      pop_min_heap(max_heap)\n      push_min_heap(max_heap, nums[i])\n    end\n  end\n\n  get_min_heap(max_heap)\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Всего выполняется \\(n\\) операций добавления и извлечения из кучи, а максимальная длина кучи равна \\(k\\) , поэтому временная сложность равна \\(O(n \\log k)\\) . Этот метод очень эффективен: когда \\(k\\) мало, временная сложность стремится к \\(O(n)\\) ; когда \\(k\\) велико, она все равно не превышает \\(O(n \\log n)\\) .</p> <p>Кроме того, этот метод подходит и для сценариев с динамическим потоком данных. При непрерывном поступлении новых данных мы можем продолжать поддерживать содержимое кучи, тем самым динамически обновляя наибольшие \\(k\\) элементов.</p>","path":["Глава 8. Куча","8.3 &nbsp; Задача Top-k"],"tags":[]},{"location":"chapter_hello_algo/","level":1,"title":"Перед началом","text":"<p>Несколько лет назад я публиковал на LeetCode разборы серии задач \"Sword for Offer\" и получил поддержку и ободрение от многих читателей. Во время общения с ними мне чаще всего задавали один и тот же вопрос: \"как начать изучать алгоритмы?\" Постепенно этот вопрос начал меня по-настоящему занимать.</p> <p>Слепо бросаться в решение задач кажется самым популярным способом: он прост, прямолинеен и действительно работает. Но решение задач похоже на игру в \"Сапера\": люди с сильными навыками самообучения способны обезвредить мины одну за другой, а тем, у кого не хватает базы, легко набить себе шишки и шаг за шагом отступить под давлением неудач. Полностью проходить учебники тоже принято часто, но для тех, кто готовится к поиску работы, диплом, резюме, письменные тесты и собеседования уже отнимают большую часть сил, и потому толстые книги нередко превращаются в тяжелое испытание.</p> <p>Если ты тоже сталкиваешься с такими трудностями, то можно сказать, что эта книга сама \"нашла\" тебя. Она стала моим ответом на этот вопрос: пусть и не идеальным, но как минимум честной и активной попыткой. Эта книга сама по себе не гарантирует предложения о работе, но поможет тебе увидеть \"карту знаний\" по структурам данных и алгоритмам, понять форму, размер и расположение разных \"мин\" и освоить разные \"способы разминирования\". Освоив это, ты сможешь увереннее решать задачи и читать технические материалы, шаг за шагом выстраивая целостную систему знаний.</p> <p>Я глубоко согласен со словами профессора Фейнмана: \"Knowledge isn't free. You have to pay attention.\" В этом смысле книга не совсем \"бесплатна\". Чтобы не подвести то драгоценное \"внимание\", которое ты ей уделишь, я постараюсь вложить в ее создание максимум собственного \"внимания\".</p> <p>Я хорошо понимаю пределы собственных знаний. Хотя материал этой книги уже довольно долго шлифовался, в нем наверняка все еще осталось немало ошибок, поэтому я искренне прошу преподавателей и читателей указывать на неточности и недоработки.</p> <p></p> Hello, алгоритмы! <p>Появление компьютеров радикально изменило мир. Благодаря высокой скорости вычислений и отличной программируемости они стали идеальной средой для исполнения алгоритмов и обработки данных. Реалистичная графика в играх, интеллектуальные решения в автономном вождении, впечатляющие партии AlphaGo и естественное взаимодействие ChatGPT: все это изящные проявления алгоритмов на компьютере.</p> <p>На самом деле еще до появления компьютеров алгоритмы и структуры данных уже существовали во всех уголках мира. Ранние алгоритмы были сравнительно простыми: например, древние способы счета или последовательности действий при изготовлении инструментов. По мере развития цивилизации алгоритмы становились тоньше и сложнее. За мастерством ремесленников, промышленными продуктами, освобождающими производительные силы, и даже за научными законами движения Вселенной почти всегда стоит изобретательная алгоритмическая мысль.</p> <p>Точно так же структуры данных встречаются повсюду: от социальных сетей до схем метро многие системы можно моделировать как \"граф\"; от государства до семьи основные формы общественной организации обладают свойствами \"дерева\"; зимняя одежда похожа на \"стек\", где то, что надевают первым, снимают последним; тубус для бадминтонных воланов похож на \"очередь\", где элементы добавляются с одного конца и извлекаются с другого; словарь похож на \"хеш-таблицу\", позволяющую быстро находить нужную статью.</p> <p>Эта книга стремится с помощью понятных анимированных иллюстраций и исполняемых примеров кода помочь читателю понять ключевые идеи алгоритмов и структур данных и научиться реализовывать их программно. На этой основе книга также пытается показать живые проявления алгоритмов в сложном мире и раскрыть их красоту. Надеюсь, она окажется для тебя полезной.</p>","path":["Перед началом"],"tags":[]},{"location":"chapter_introduction/","level":1,"title":"Глава 1.   Введение в алгоритмы","text":"<p>Abstract</p> <p>Юная девушка кружится в танце, переплетаясь с данными, а по подолу ее платья струится мелодия алгоритмов.</p> <p>Она приглашает вас присоединиться к танцу: следуйте за ее шагами и войдите в мир алгоритмов, полный логики и красоты.</p>","path":["Глава 1. Введение в алгоритмы","Глава 1. &nbsp; Введение в алгоритмы"],"tags":[]},{"location":"chapter_introduction/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>1.1   Алгоритмы повсюду</li> <li>1.2   Что такое алгоритм</li> <li>1.3   Резюме</li> </ul>","path":["Глава 1. Введение в алгоритмы","Глава 1. &nbsp; Введение в алгоритмы"],"tags":[]},{"location":"chapter_introduction/algorithms_are_everywhere/","level":1,"title":"1.1   Алгоритмы повсюду","text":"<p>Говоря об алгоритмах, естественно вспомнить о математике. Однако на самом деле многие алгоритмы не связаны со сложной математикой, а больше полагаются на базовую логику, которая повсеместно встречается в нашей повседневной жизни.</p> <p>Прежде чем углубиться в обсуждение алгоритмов, стоит упомянуть интересный факт: вы уже точно освоили множество алгоритмов и привыкли применять их в повседневной жизни. Далее приведем несколько конкретных примеров, чтобы подтвердить этот факт.</p> <p>Пример 1: поиск в словаре. В словаре все слова упорядочены по алфавиту. Предположим, нам нужно найти слово, начинающееся на букву \\(r\\); обычно для этого нужно выполнить следующие действия.</p> <ol> <li>Откройте словарь примерно на половине страниц и посмотрите, какая буква является первой на этой странице; предположим, это буква \\(m\\).</li> <li>Поскольку в алфавите буква \\(r\\) идет после \\(m\\), исключаем первую половину словаря, и область поиска сужается до второй половины.</li> <li>Продолжайте повторять шаги <code>1.</code> и <code>2.</code> , пока не найдете страницу, где первой буквой слов будет \\(r\\).</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 1-1   Этапы поиска в словаре. Шаг 1 </p> <p>Навык поиска в словаре, которым владеет каждый школьник, на самом деле является известным алгоритмом двоичного поиска. С точки зрения структуры данных словарь можно рассматривать как отсортированный массив; с точки зрения алгоритма последовательность операций по поиску в словаре можно считать двоичным поиском.</p> <p>Пример 2: упорядочивание карт. Во время игры в карты необходимо каждый раз упорядочивать карты в руке от меньшего к большему. Для этого нужно выполнить следующие действия.</p> <ol> <li>Разделите карты на упорядоченную и неупорядоченную части, предполагая, что изначально самая левая карта уже упорядочена.</li> <li>Из неупорядоченной части извлеките одну карту и вставьте ее в правильное место в упорядоченной части; после этого две самые левые карты станут упорядоченными.</li> <li>Повторяйте шаг <code>2.</code> , каждый раз перемещая одну карту из неупорядоченной части в упорядоченную, пока все карты не станут упорядоченными.</li> </ol> <p></p> <p> Рисунок 1-2   Этапы упорядочивания карт </p> <p>Метод упорядочивания карт по своей сути является алгоритмом сортировки вставками, который весьма эффективен при обработке небольших наборов данных. Многие функции сортировки в библиотеках программирования используют именно этот алгоритм.</p> <p>Пример 3: сдача. Предположим, что в супермаркете мы купили товар стоимостью \\(69\\) руб. и дали кассиру купюру в \\(100\\) руб. Кассир должен вернуть нам \\(31\\) руб. Для этого ему нужно выполнить следующие действия.</p> <ol> <li>Варианты выбора - это купюры номиналом меньше \\(31\\) руб. Пусть у нас имеются номиналы \\(1\\) , \\(5\\) , \\(10\\) и \\(20\\) руб.</li> <li>Возьмем самую крупную доступную купюру в \\(20\\) руб. Остаток сдачи составит \\(31 - 20 = 11\\) руб.</li> <li>Возьмем самую крупную из оставшихся купюр в \\(10\\) руб. Остаток составит \\(11 - 10 = 1\\) руб.</li> <li>Возьмем самую крупную из оставшихся купюр в \\(1\\) руб. Остаток составит \\(1 - 1 = 0\\) руб.</li> <li>Завершим выдачу сдачи, схема: \\(20 + 10 + 1 = 31\\) руб.</li> </ol> <p></p> <p> Рисунок 1-3   Этапы выдачи сдачи </p> <p>В этих шагах мы на каждом этапе выбираем наилучший вариант, используя купюры наибольшего номинала, и в итоге получаем рабочую схему сдачи. С точки зрения структуры данных и алгоритмов этот метод по своей сути является жадным алгоритмом.</p> <p>От приготовления блюда до межзвездных путешествий решение практически любой задачи неразрывно связано с алгоритмами. Появление компьютеров позволило нам с помощью программирования хранить структуры данных в памяти, а также писать код для вызовов к CPU и GPU для выполнения алгоритмов. Таким образом, мы можем переносить задачи из реальной жизни в компьютер и решать различные сложные проблемы более эффективно.</p> <p>Tip</p> <p>Если представление о структурах данных, алгоритмах, массивах и двоичном поиске пока остается расплывчатым, просто продолжайте читать. Эта книга постепенно введет вас в мир структур данных и алгоритмов.</p>","path":["Глава 1. Введение в алгоритмы","1.1 &nbsp; Алгоритмы повсюду"],"tags":[]},{"location":"chapter_introduction/summary/","level":1,"title":"1.3   Резюме","text":"","path":["Глава 1. Введение в алгоритмы","1.3 &nbsp; Резюме"],"tags":[]},{"location":"chapter_introduction/summary/#1","level":3,"title":"1.   Ключевые выводы","text":"<ul> <li>Алгоритмы повсеместно присутствуют в нашей повседневной жизни и не являются недосягаемыми сложными знаниями. На самом деле мы уже освоили множество алгоритмов, которые помогают решать различные жизненные задачи.</li> <li>Принцип поиска в словаре соответствует алгоритму двоичного поиска. Двоичный поиск иллюстрирует важную идею алгоритмов \"разделяй и властвуй\".</li> <li>Процесс сортировки карт в колоде очень похож на алгоритм сортировки вставками, который хорошо подходит для сортировки небольших наборов данных.</li> <li>Процесс размена по своей сути является жадным алгоритмом, в котором на каждом этапе принимается наилучшее на данный момент решение.</li> <li>Алгоритм представляет собой набор инструкций или шагов, предназначенных для решения конкретной задачи в ограниченное время, а структура данных - это способ организации и хранения данных в компьютере.</li> <li>Структуры данных и алгоритмы тесно связаны. Структуры данных являются основой для алгоритмов, а алгоритмы оживляют структуры данных.</li> <li>Структуры данных и алгоритмы можно сравнить с конструктором: детали конструктора представляют данные, их форма и способы соединения - структуры данных, а этапы сборки конструктора соответствуют алгоритмам.</li> </ul>","path":["Глава 1. Введение в алгоритмы","1.3 &nbsp; Резюме"],"tags":[]},{"location":"chapter_introduction/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: Я программист и в повседневной работе никогда не использовал алгоритмы для решения задач, поскольку часто используемые алгоритмы уже встроены в языки программирования и ими можно пользоваться напрямую. Значит ли это, что рабочие задачи еще не требуют применения алгоритмов?</p> <p>Если сравнить конкретные профессиональные навыки с приемами в боевых искусствах, то базовые дисциплины скорее напоминают \"внутреннюю силу\".</p> <p>Я считаю, что изучение алгоритмов и других базовых дисциплин важно не для того, чтобы реализовывать их с нуля в работе, а для того, чтобы на основе полученных знаний принимать профессиональные решения и оценки при решении задач, тем самым повышая общее качество работы. Простой пример: каждый язык программирования имеет встроенные функции сортировки.</p> <ul> <li>Если бы мы не изучали структуры данных и алгоритмы, то, получив любые данные, возможно, просто передали бы их этой функции сортировки. Все работает гладко, производительность хорошая, и на первый взгляд проблем нет.</li> <li>Однако если мы изучили алгоритмы, то знаем, что временная сложность встроенной функции сортировки составляет \\(O(n \\log n)\\) ; если же данные представлены целыми числами фиксированной разрядности, например номерами студентов, то можно использовать более эффективный метод поразрядной сортировки, снизив временную сложность до \\(O(nk)\\) , где \\(k\\) - это количество разрядов, а при больших объемах данных выиграть во времени, затратах и пользовательском опыте.</li> </ul> <p>В инженерной практике множество задач трудно решить оптимальным образом, и многие из них решаются \"как-то\". Сложность задачи зависит как от ее природы, так и от уровня знаний и опыта человека, который ее анализирует. Чем более полными знаниями и большим опытом обладает человек, тем глубже он может проанализировать проблему и тем изящнее может быть ее решение.</p>","path":["Глава 1. Введение в алгоритмы","1.3 &nbsp; Резюме"],"tags":[]},{"location":"chapter_introduction/what_is_dsa/","level":1,"title":"1.2   Что такое алгоритм","text":"","path":["Глава 1. Введение в алгоритмы","1.2 &nbsp; Что такое алгоритм"],"tags":[]},{"location":"chapter_introduction/what_is_dsa/#121","level":2,"title":"1.2.1   Определение алгоритма","text":"<p>Алгоритм (algorithm) - это набор инструкций или шагов, предназначенных для решения конкретной задачи за ограниченное время. Он обладает следующими свойствами.</p> <ul> <li>Задача четко определена и включает ясные определения входных и выходных данных.</li> <li>Обладает осуществимостью и может быть выполнен за ограниченное количество шагов, времени и памяти.</li> <li>Каждый шаг имеет определенное значение, и при одинаковых входных данных и условиях выполнения результат всегда будет одинаковым.</li> </ul>","path":["Глава 1. Введение в алгоритмы","1.2 &nbsp; Что такое алгоритм"],"tags":[]},{"location":"chapter_introduction/what_is_dsa/#122","level":2,"title":"1.2.2   Определение структуры данных","text":"<p>Структура данных (data structure) - это способ организации и хранения данных, включающий содержимое данных, их взаимосвязи и методы операций с ними. Структура данных преследует следующие цели.</p> <ul> <li>Минимизировать занимаемое пространство для экономии памяти компьютера.</li> <li>Обеспечивать максимально быструю обработку данных, включая доступ, добавление, удаление и обновление данных.</li> <li>Обеспечивать простое представление данных и логическую информацию для эффективного выполнения алгоритмов.</li> </ul> <p>Проектирование структуры данных - это процесс, полный компромиссов. Если вы хотите улучшить один аспект, часто приходится идти на уступки в другом. Приведем два примера.</p> <ul> <li>Связный список, по сравнению с массивом, более удобен для добавления и удаления данных, но имеет проблемы со скоростью доступа к данным.</li> <li>Граф, по сравнению со связным списком, предоставляет более богатую логическую информацию, но требует большего объема памяти.</li> </ul>","path":["Глава 1. Введение в алгоритмы","1.2 &nbsp; Что такое алгоритм"],"tags":[]},{"location":"chapter_introduction/what_is_dsa/#123","level":2,"title":"1.2.3   Связь между структурами данных и алгоритмами","text":"<p>Как показано на рисунке 1-4, структуры данных и алгоритмы тесно взаимосвязаны, что проявляется в следующих трех аспектах.</p> <ul> <li>Структуры данных являются основой алгоритмов. Они обеспечивают структурированное хранение данных и методы их обработки.</li> <li>Алгоритмы оживляют структуры данных. Сами по себе структуры данных лишь хранят информацию, но в сочетании с алгоритмами они позволяют решать конкретные задачи.</li> <li>Алгоритмы можно реализовать на основе различных структур данных, однако эффективность их выполнения может значительно различаться, поэтому выбор подходящей структуры данных является ключевым фактором.</li> </ul> <p></p> <p> Рисунок 1-4   Связь между структурами данных и алгоритмами </p> <p>Структуры данных и алгоритмы подобны конструктору, как показано на рисунке 1-5. Комплект конструктора, помимо множества деталей, содержит также подробную инструкцию по сборке. Следуя этой инструкции шаг за шагом, можно собрать красивую модель.</p> <p></p> <p> Рисунок 1-5   Сборка конструктора </p> <p>Подробное описание аналогии с конструктором представлено в таблице 1-1.</p> <p> Таблица 1-1   Сравнение структур данных и алгоритмов с конструктором </p> Структуры данных и алгоритмы Конструктор Входные данные Несобранные детали конструктора Структура данных Организация деталей конструктора, включая форму, размер, способы соединения и т. д. Алгоритм Последовательность действий по сборке деталей в целевую модель Выходные данные Собранная модель конструктора <p>Стоит отметить, что структуры данных и алгоритмы не зависят от языка программирования. Именно поэтому данная книга предлагает их реализации на различных языках.</p> <p>Принятое сокращение</p> <p>В реальных обсуждениях выражение \"структуры данных и алгоритмы\" обычно сокращают до просто \"алгоритмы\". Например, хорошо известные задачи LeetCode на деле одновременно проверяют знания и по структурам данных, и по алгоритмам.</p>","path":["Глава 1. Введение в алгоритмы","1.2 &nbsp; Что такое алгоритм"],"tags":[]},{"location":"chapter_preface/","level":1,"title":"Глава 0.   Предисловие","text":"<p>Abstract</p> <p>Алгоритмы подобны прекрасной симфонии, а каждая строка кода льется подобно мелодии.</p> <p>Пусть эта книга тихо зазвучит в вашем сознании и оставит после себя особую и глубокую мелодию.</p>","path":["Глава 0. Предисловие","Глава 0. &nbsp; Предисловие"],"tags":[]},{"location":"chapter_preface/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>0.1   Об этой книге</li> <li>0.2   Как пользоваться этой книгой</li> <li>0.3   Резюме</li> </ul>","path":["Глава 0. Предисловие","Глава 0. &nbsp; Предисловие"],"tags":[]},{"location":"chapter_preface/about_the_book/","level":1,"title":"0.1   Об этой книге","text":"<p>Этот проект задуман как открытое, бесплатное и дружелюбное к новичкам введение в структуры данных и алгоритмы.</p> <ul> <li>В книге используются анимированные иллюстрации: материал изложен ясно и последовательно, что облегчает освоение и помогает начинающим выстроить карту знаний по структурам данных и алгоритмам.</li> <li>Исходный код можно запустить одним нажатием, что позволяет тренироваться, развивать навыки программирования и понимать принципы работы алгоритмов и реализации структур данных на фундаментальном уровне.</li> <li>Мы призываем читателей к взаимопомощи: задавайте вопросы и делитесь идеями в комментариях. Обсуждения помогают двигаться вперед всем вместе.</li> </ul>","path":["Глава 0. Предисловие","0.1 &nbsp; Об этой книге"],"tags":[]},{"location":"chapter_preface/about_the_book/#011","level":2,"title":"0.1.1   Целевая аудитория","text":"<p>Если вы новичок в алгоритмах, никогда с ними не сталкивались или уже имеете некоторый опыт решения задач, но еще не обладаете четким пониманием структур данных и алгоритмов, эта книга создана специально для вас!</p> <p>Если у вас уже есть определенный опыт решения задач и вы знакомы с большинством типов задач, эта книга поможет вам освежить и систематизировать знания об алгоритмах, а исходный код может служить набором инструментов для решения задач или алгоритмическим словарем.</p> <p>Если вы владеете алгоритмами на экспертном уровне, мы будем рады вашим ценным советам или совместному участию в создании книги.</p> <p>Предварительные требования</p> <p>Необходимо иметь хотя бы базовую подготовку в одном из языков программирования, чтобы читать и писать простой код.</p>","path":["Глава 0. Предисловие","0.1 &nbsp; Об этой книге"],"tags":[]},{"location":"chapter_preface/about_the_book/#012","level":2,"title":"0.1.2   Структура содержания","text":"<p>Основное содержание книги представлено на рисунке 0-1.</p> <ul> <li>Анализ сложности: критерии и методы оценки структур данных и алгоритмов. Методы расчета временной и пространственной сложности, распространенные типы, примеры и т. д.</li> <li>Структуры данных: классификация основных типов данных и структур данных. Определение, преимущества и недостатки, основные операции, распространенные типы, типичные приложения и методы реализации массивов, списков, стеков, очередей, хеш-таблиц, деревьев, куч и графов.</li> <li>Алгоритмы: определение, преимущества и недостатки, эффективность, области применения, этапы решения и примеры задач для поиска, сортировки, алгоритма \"разделяй и властвуй\", поиска с возвратом, динамического программирования и жадных алгоритмов.</li> </ul> <p></p> <p> Рисунок 0-1   Основное содержание книги </p>","path":["Глава 0. Предисловие","0.1 &nbsp; Об этой книге"],"tags":[]},{"location":"chapter_preface/about_the_book/#013","level":2,"title":"0.1.3   Благодарности","text":"<p>Эта книга постоянно совершенствуется благодаря совместным усилиям множества участников открытого сообщества. Благодарим каждого автора, вложившего свое время и силы; их имена перечислены в порядке, автоматически сгенерированном GitHub: krahets, coderonion, Gonglja, nuomi1, Reanon, justin-tse, hpstory, danielsss, curtishd, night-cruise, S-N-O-R-L-A-X, rongyi, msk397, gvenusleo, khoaxuantu, rivertwilight, K3v123, gyt95, zhuoqinyue, yuelinxin, Zuoxun, mingXta, Phoenix0415, FangYuan33, GN-Yu, longsizhuo, IsChristina, xBLACKICEx, guowei-gong, Cathay-Chen, pengchzn, QiLOL, magentaqin, hello-ikun, JoseHung, qualifier1024, thomasq0, sunshinesDL, L-Super, Guanngxu, Transmigration-zhou, WSL0809, Slone123c, lhxsm, yuan0221, what-is-me, Shyam-Chen, theNefelibatas, longranger2, codeberg-user, xiongsp, JeffersonHuang, prinpal, seven1240, Wonderdch, malone6, xiaomiusa87, gaofer, bluebean-cloud, a16su, SamJin98, hongyun-robot, nanlei, XiaChuerwu, yd-j, iron-irax, mgisr, steventimes, junminhong, heshuyue, danny900714, MolDuM, Nigh, Dr-XYZ, XC-Zero, reeswell, PXG-XPG, NI-SW, Horbin-Magician, Enlightenus, YangXuanyi, beatrix-chan, DullSword, xjr7670, jiaxianhua, qq909244296, iStig, boloboloda, hts0000, gledfish, wenjianmin, keshida, kilikilikid, lclc6, lwbaptx, linyejoe2, liuxjerry, llql1211, fbigm, echo1937, szu17dmy, dshlstarr, Yucao-cy, coderlef, czruby, bongbongbakudan, beintentional, ZongYangL, ZhongYuuu, ZhongGuanbin, hezhizhen, linzeyan, ZJKung, luluxia, xb534, ztkuaikuai, yw-1021, ElaBosak233, baagod, zhouLion, yishangzhang, yi427, yanedie, yabo083, weibk, wangwang105, th1nk3r-ing, tao363, 4yDX3906, syd168, sslmj2020, smilelsb, siqyka, selear, sdshaoda, Xi-Row, popozhu, nuquist19, noobcodemaker, XiaoK29, chadyi, lyl625760, lucaswangdev, 0130w, shanghai-Jerry, EJackYang, Javesun99, eltociear, lipusheng, KNChiu, BlindTerran, ShiMaRing, lovelock, FreddieLi, FloranceYeh, fanchenggang, gltianwen, goerll, nedchu, curly210102, CuB3y0nd, KraHsu, CarrotDLaw, youshaoXG, bubble9um, Asashishi, Asa0oo0o0o, fanenr, eagleanurag, akshiterate, 52coder, foursevenlove, KorsChen, GaochaoZhu, hopkings2008, yang-le, realwujing, Evilrabbit520, Umer-Jahangir, Turing-1024-Lee, Suremotoo, paoxiaomooo, Chieko-Seren, Allen-Scai, ymmmas, Risuntsy, Richard-Zhang1019, RafaelCaso, qingpeng9802, primexiao, Urbaner3, zhongfq, nidhoggfgg, MwumLi, CreatorMetaSky, martinx, ZnYang2018, hugtyftg, logan-qiu, psychelzh, Keynman, KeiichiKasai и KawaiiAsh.</p> <p>Рецензирование кода книги выполнили coderonion, curtishd, Gonglja, gvenusleo, hpstory, justin-tse, khoaxuantu, krahets, night-cruise, nuomi1, Reanon и rongyi (в алфавитном порядке). Благодарим их за потраченное время и силы, которые обеспечили стандартизацию и единообразие кода на различных языках.</p> <p>Традиционную китайскую версию книги вычитали Shyam-Chen и Dr-XYZ, английскую версию - yuelinxin, K3v123, QiLOL, Phoenix0415, SamJin98, yanedie, RafaelCaso, pengchzn, thomasq0 и magentaqin, а японскую версию - eltociear. Именно благодаря их постоянному вкладу эта книга может служить более широкому кругу читателей, и мы искренне благодарим их.</p> <p>Инструмент генерации ePub-версии этой книги разработал zhongfq. Благодарим его за вклад, который дал читателям более свободный способ чтения.</p> <p>В процессе создания этой книги мне помогало много людей.</p> <ul> <li>Благодарю моего наставника в компании, доктора Ли Си: в одной из бесед вы вдохновили меня быстрее начать, что укрепило мою решимость написать эту книгу;</li> <li>Благодарю мою девушку Bubble, первого читателя этой книги: с позиции новичка в алгоритмах она дала много ценных советов, благодаря которым книга стала более понятной и доступной;</li> <li>Благодарю Tengbao, Qibao и Feibao за креативное название книги, которое навевает приятные воспоминания о первой строке кода \"Hello World!\";</li> <li>Благодарю Xiaoquan за профессиональную помощь в вопросах интеллектуальной собственности, что сыграло важную роль в совершенствовании этой открытой книги;</li> <li>Благодарю Sutong за дизайн обложки и логотипа книги, а также за терпение при многочисленных исправлениях по моим просьбам;</li> <li>Благодарю @squidfunk за советы по оформлению и за разработку открытой темы документации Material-for-MkDocs.</li> </ul> <p>В процессе написания книги я ознакомился с множеством учебников и статей по структурам данных и алгоритмам. Эти работы послужили отличным образцом для этой книги, обеспечив ее точность и качество. Я искренне благодарю всех преподавателей и предшественников за их выдающийся вклад!</p> <p>Эта книга пропагандирует метод обучения, сочетающий умственную и практическую деятельность; в этом отношении на меня сильно повлияла Dive into Deep Learning. Я настоятельно рекомендую эту замечательную работу всем читателям.</p> <p>Сердечно благодарю моих родителей: именно ваша постоянная поддержка и ободрение дали мне возможность заняться этим увлекательным делом.</p>","path":["Глава 0. Предисловие","0.1 &nbsp; Об этой книге"],"tags":[]},{"location":"chapter_preface/suggestions/","level":1,"title":"0.2   Как пользоваться этой книгой","text":"<p>Tip</p> <p>Для получения наилучшего опыта чтения рекомендуется полностью прочитать этот раздел.</p>","path":["Глава 0. Предисловие","0.2 &nbsp; Как пользоваться этой книгой"],"tags":[]},{"location":"chapter_preface/suggestions/#021","level":2,"title":"0.2.1   Соглашения о стиле изложения","text":"<ul> <li>Главы, помеченные <code>*</code> в заголовке, являются дополнительными и содержат более сложный материал. Если времени мало, их можно пропустить.</li> <li>Профессиональные термины выделяются полужирным шрифтом в печатной и PDF-версии или подчеркиванием в веб-версии, например массив (array). Рекомендуется запоминать их для удобства чтения литературы.</li> <li>Важные моменты и обобщающие фразы будут выделяться полужирным шрифтом, и на такие тексты следует обращать особое внимание.</li> <li>Слова и выражения со специальным смыслом будут отмечаться \"кавычками\", чтобы избежать неоднозначности.</li> <li>Когда термины различаются между языками программирования, в качестве стандарта используется Python; например, <code>None</code> применяется для обозначения \"пустого\" значения.</li> <li>В некоторых местах книга отходит от стандартов комментирования программного кода ради более компактного оформления. Комментарии в основном делятся на три типа: заголовочные, содержательные и многострочные.</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>\"\"\"Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п.\"\"\"\n\n# Содержательный комментарий: подробно поясняет код\n\n\"\"\"\nМногострочный\nкомментарий\n\"\"\"\n</code></pre> <pre><code>/* Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п. */\n\n// Содержательный комментарий: подробно поясняет код\n\n/**\n * Многострочный\n * комментарий\n */\n</code></pre> <pre><code>/* Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п. */\n\n// Содержательный комментарий: подробно поясняет код\n\n/**\n * Многострочный\n * комментарий\n */\n</code></pre> <pre><code>/* Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п. */\n\n// Содержательный комментарий: подробно поясняет код\n\n/**\n * Многострочный\n * комментарий\n */\n</code></pre> <pre><code>/* Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п. */\n\n// Содержательный комментарий: подробно поясняет код\n\n/**\n * Многострочный\n * комментарий\n */\n</code></pre> <pre><code>/* Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п. */\n\n// Содержательный комментарий: подробно поясняет код\n\n/**\n * Многострочный\n * комментарий\n */\n</code></pre> <pre><code>/* Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п. */\n\n// Содержательный комментарий: подробно поясняет код\n\n/**\n * Многострочный\n * комментарий\n */\n</code></pre> <pre><code>/* Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п. */\n\n// Содержательный комментарий: подробно поясняет код\n\n/**\n * Многострочный\n * комментарий\n */\n</code></pre> <pre><code>/* Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п. */\n\n// Содержательный комментарий: подробно поясняет код\n\n/**\n * Многострочный\n * комментарий\n */\n</code></pre> <pre><code>/* Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п. */\n\n// Содержательный комментарий: подробно поясняет код\n\n/**\n * Многострочный\n * комментарий\n */\n</code></pre> <pre><code>/* Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п. */\n\n// Содержательный комментарий: подробно поясняет код\n\n/**\n * Многострочный\n * комментарий\n */\n</code></pre> <pre><code>/* Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п. */\n\n// Содержательный комментарий: подробно поясняет код\n\n/**\n * Многострочный\n * комментарий\n */\n</code></pre> <pre><code>### Комментарий-заголовок: используется для обозначения функций, классов, тестовых примеров и т. п. ###\n\n# Содержательный комментарий: подробно поясняет код\n\n# Многострочный\n# комментарий\n</code></pre>","path":["Глава 0. Предисловие","0.2 &nbsp; Как пользоваться этой книгой"],"tags":[]},{"location":"chapter_preface/suggestions/#022","level":2,"title":"0.2.2   Эффективное обучение с помощью анимированных иллюстраций","text":"<p>По сравнению с текстом видео и изображения обладают более высокой плотностью информации и более четкой структурой, поэтому их легче воспринимать. В этой книге ключевые и сложные моменты в основном представлены в виде анимированных иллюстраций, а текст служит пояснением и дополнением.</p> <p>Если во время чтения вы встречаете фрагмент с анимированной иллюстрацией, как на рисунке 0-2, используйте иллюстрацию в качестве основного источника информации, а текст - в качестве вспомогательного, объединяя оба источника для понимания материала.</p> <p></p> <p> Рисунок 0-2   Пример анимированной иллюстрации </p>","path":["Глава 0. Предисловие","0.2 &nbsp; Как пользоваться этой книгой"],"tags":[]},{"location":"chapter_preface/suggestions/#023","level":2,"title":"0.2.3   Углубление понимания через практику кода","text":"<p>Сопроводительный код этой книги размещен в репозитории GitHub. Как показано ниже, исходный код содержит тестовые примеры и может быть запущен одним нажатием кнопки.</p> <p>Если позволяет время, рекомендуется самостоятельно набирать код. Если времени на обучение мало, по крайней мере просмотрите и выполните весь код.</p> <p>Процесс написания кода приносит больше пользы, чем его чтение. Настоящее обучение - это обучение на практике.</p> <p></p> <p> Рисунок 0-3   Пример запуска кода </p> <p>Подготовка к запуску кода в основном состоит из трех этапов.</p> <p>Шаг 1: установка локальной среды программирования. Воспользуйтесь руководством из приложения. Если среда уже установлена, этот шаг можно пропустить.</p> <p>Шаг 2: клонирование или загрузка репозитория кода. Перейдите в репозиторий GitHub. Если у вас уже установлен Git, репозиторий можно клонировать следующей командой:</p> <pre><code>git clone https://github.com/krahets/hello-algo.git\n</code></pre> <p>Также можно нажать кнопку \"Download ZIP\" в месте, показанном на рисунке 0-4, напрямую скачать архив с кодом и затем распаковать его локально.</p> <p></p> <p> Рисунок 0-4   Клонирование репозитория и загрузка кода </p> <p>Шаг 3: запуск исходного кода. Как показано на рисунке 0-5, для блоков кода, у которых сверху указано имя файла, соответствующий исходный файл можно найти в папке <code>codes</code> репозитория. Исходные файлы запускаются одним нажатием, что помогает не тратить лишнее время на отладку и сосредоточиться на изучении материала.</p> <p></p> <p> Рисунок 0-5   Блоки кода и соответствующие исходные файлы </p> <p>Помимо локального запуска, веб-версия также поддерживает визуальное выполнение Python-кода (на базе pythontutor). Как показано ниже, можно нажать \"Визуализировать выполнение\" под блоком кода, чтобы раскрыть окно и наблюдать за выполнением алгоритма; также можно нажать \"Полноэкранный режим\" для более удобного просмотра.</p> <p></p> <p> Рисунок 0-6   Визуальный запуск Python-кода </p>","path":["Глава 0. Предисловие","0.2 &nbsp; Как пользоваться этой книгой"],"tags":[]},{"location":"chapter_preface/suggestions/#024","level":2,"title":"0.2.4   Совместный рост через вопросы и обсуждения","text":"<p>Во время чтения книги не стоит пропускать те места, которые остались непонятными. Мы призываем вас задавать вопросы в разделе комментариев: я и мои коллеги постараемся ответить вам как можно тщательнее, обычно в течение двух дней.</p> <p>Как показано на рисунке 0-7, в веб-версии у каждой главы внизу есть раздел комментариев. Рекомендуется уделять внимание его содержанию. С одной стороны, это поможет увидеть, с какими трудностями сталкиваются другие читатели, восполнить пробелы и подтолкнуть себя к более глубокому пониманию. С другой стороны, мы надеемся, что вы будете отвечать на вопросы других участников и делиться своими мнениями.</p> <p></p> <p> Рисунок 0-7   Пример раздела комментариев </p>","path":["Глава 0. Предисловие","0.2 &nbsp; Как пользоваться этой книгой"],"tags":[]},{"location":"chapter_preface/suggestions/#025","level":2,"title":"0.2.5   Дорожная карта изучения алгоритмов","text":"<p>В целом процесс изучения структур данных и алгоритмов можно разделить на три этапа.</p> <ol> <li>Этап 1: введение в алгоритмы. Необходимо познакомиться с особенностями и применением различных структур данных, изучить принципы, процессы, назначение и эффективность различных алгоритмов.</li> <li>Этап 2: решение алгоритмических задач. Рекомендуется начинать с популярных задач и решить не менее 100 из них, чтобы познакомиться с основными алгоритмическими проблемами. При первых попытках \"забывание знаний\" может стать испытанием, но это нормально. Следуйте при повторении задач \"кривой забывания Эббингауза\", и обычно после 3-5 циклов повторения материал хорошо запоминается. Рекомендуемые списки задач и планы практики см. в этом репозитории GitHub.</li> <li>Этап 3: построение системы знаний. В процессе обучения можно читать статьи по алгоритмам, изучать каркасы решений и учебники, чтобы постоянно обогащать свою систему знаний. В решении задач можно применять продвинутые стратегии, например классификацию по темам, несколько решений одной задачи или одно решение для нескольких задач; соответствующий опыт можно найти в различных сообществах.</li> </ol> <p>Как показано на рисунке 0-8, содержание этой книги в основном охватывает \"этап 1\" и призвано помочь вам более эффективно перейти к обучению на этапах 2 и 3.</p> <p></p> <p> Рисунок 0-8   Дорожная карта изучения алгоритмов </p>","path":["Глава 0. Предисловие","0.2 &nbsp; Как пользоваться этой книгой"],"tags":[]},{"location":"chapter_preface/summary/","level":1,"title":"0.3   Резюме","text":"","path":["Глава 0. Предисловие","0.3 &nbsp; Резюме"],"tags":[]},{"location":"chapter_preface/summary/#1","level":3,"title":"1.   Ключевые выводы","text":"<ul> <li>Основная аудитория этой книги - новички в изучении алгоритмов. Если у вас уже есть определенная база, книга поможет систематизировать знания, а исходный код послужит инструментальной библиотекой для решения задач.</li> <li>Содержание книги включает три основные части - анализ сложности, структуры данных и алгоритмы - и охватывает большинство тем в этой области.</li> <li>Для новичков в алгоритмах крайне важно изучить начальные разделы книги, чтобы избежать множества ошибок в будущем.</li> <li>Анимированные иллюстрации в книге обычно используются для представления ключевых и сложных аспектов. При чтении книги следует уделять этим материалам больше внимания.</li> <li>Практика - лучший способ изучения программирования. Настоятельно рекомендуется запускать исходный код и самостоятельно писать программы.</li> <li>В веб-версии книги каждая глава имеет область комментариев, где можно задавать вопросы и делиться своими мыслями.</li> </ul>","path":["Глава 0. Предисловие","0.3 &nbsp; Резюме"],"tags":[]},{"location":"chapter_reference/","level":1,"title":"Список литературы","text":"<p>[1] Thomas H. Cormen и др. Introduction to Algorithms (3<sup>rd</sup> Edition).</p> <p>[2] Aditya Bhargava. Grokking Algorithms: An Illustrated Guide for Programmers and Other Curious People (1<sup>st</sup> Edition).</p> <p>[3] Robert Sedgewick и др. Algorithms (4<sup>th</sup> Edition).</p> <p>[4] Yan Weimin. Data Structures (C Language Edition).</p> <p>[5] Deng Junhui. Data Structures (C++ Language Edition, 3<sup>rd</sup> Edition).</p> <p>[6] Mark Allen Weiss; пер. Chen Yue. Data Structures and Algorithm Analysis: Java Description (3<sup>rd</sup> Edition).</p> <p>[7] Cheng Jie. A Plainspoken Guide to Data Structures.</p> <p>[8] Wang Zheng. The Beauty of Data Structures and Algorithms.</p> <p>[9] Gayle Laakmann McDowell. Cracking the Coding Interview: 189 Programming Questions and Solutions (6<sup>th</sup> Edition).</p> <p>[10] Aston Zhang и др. Dive into Deep Learning.</p>","path":["Список литературы"],"tags":[]},{"location":"chapter_searching/","level":1,"title":"Глава 10.   Поиск","text":"<p>Abstract</p> <p>Поиск - это движение в неизвестность: иногда приходится пройти каждый уголок пространства, а иногда удается быстро найти цель.</p> <p>В этом пути каждый новый шаг может привести к ответу, которого мы не ожидали.</p>","path":["Глава 10. Поиск","Глава 10. &nbsp; Поиск"],"tags":[]},{"location":"chapter_searching/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>10.1   Двоичный поиск</li> <li>10.2   Двоичный поиск точки вставки</li> <li>10.3   Двоичный поиск границ</li> <li>10.4   Стратегии оптимизации хеширования</li> <li>10.5   Переосмысление алгоритмов поиска</li> <li>10.6   Резюме</li> </ul>","path":["Глава 10. Поиск","Глава 10. &nbsp; Поиск"],"tags":[]},{"location":"chapter_searching/binary_search/","level":1,"title":"10.1   Двоичный поиск","text":"<p>Двоичный поиск (binary search) - это эффективный алгоритм поиска, основанный на стратегии \"разделяй и властвуй\". Он использует упорядоченность данных, сокращая на каждом шаге область поиска вдвое, пока не будет найден целевой элемент или пока интервал поиска не опустеет.</p> <p>Question</p> <p>Дан массив <code>nums</code> длины \\(n\\), элементы которого расположены в порядке возрастания и не повторяются. Найдите и верните индекс элемента <code>target</code> в этом массиве. Если массив не содержит этого элемента, верните \\(-1\\) . Пример показан на рисунке 10-1.</p> <p></p> <p> Рисунок 10-1   Пример данных для двоичного поиска </p> <p>Как показано на рисунке 10-2, сначала инициализируем указатели \\(i = 0\\) и \\(j = n - 1\\) , которые указывают на первый и последний элементы массива и задают интервал поиска \\([0, n - 1]\\) . Обратите внимание: квадратные скобки обозначают замкнутый интервал и включают граничные значения.</p> <p>Далее в цикле выполняются следующие два шага.</p> <ol> <li>Вычислить индекс середины \\(m = \\lfloor {(i + j) / 2} \\rfloor\\) , где \\(\\lfloor \\: \\rfloor\\) означает операцию округления вниз.</li> <li>Сравнить <code>nums[m]</code> и <code>target</code> , после чего возможны три случая.<ol> <li>Если <code>nums[m] &lt; target</code> , это означает, что <code>target</code> находится в интервале \\([m + 1, j]\\) , поэтому выполняется \\(i = m + 1\\) .</li> <li>Если <code>nums[m] &gt; target</code> , это означает, что <code>target</code> находится в интервале \\([i, m - 1]\\) , поэтому выполняется \\(j = m - 1\\) .</li> <li>Если <code>nums[m] = target</code> , значит, элемент <code>target</code> найден, поэтому возвращается индекс \\(m\\) .</li> </ol> </li> </ol> <p>Если массив не содержит целевой элемент, область поиска в итоге сузится до пустого интервала. В этом случае возвращается \\(-1\\) .</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 10-2   Процесс двоичного поиска </p> <p>Стоит отметить, что поскольку и \\(i\\) , и \\(j\\) имеют тип <code>int</code> , то сумма \\(i + j\\) может выйти за пределы диапазона типа <code>int</code>. Чтобы избежать переполнения, обычно используют формулу \\(m = \\lfloor {i + (j - i) / 2} \\rfloor\\) для вычисления середины.</p> <p>Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search.py<pre><code>def binary_search(nums: list[int], target: int) -&gt; int:\n    \"\"\"Бинарный поиск (двусторонне замкнутый интервал)\"\"\"\n    # Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n    i, j = 0, len(nums) - 1\n    # Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n    while i &lt;= j:\n        # Теоретически числа в Python могут быть сколь угодно большими (ограничены только объемом памяти), поэтому не нужно учитывать переполнение больших чисел\n        m = (i + j) // 2  # Вычислить индекс середины m\n        if nums[m] &lt; target:\n            i = m + 1  # Это означает, что target находится в интервале [m+1, j]\n        elif nums[m] &gt; target:\n            j = m - 1  # Это означает, что target находится в интервале [i, m-1]\n        else:\n            return m  # Целевой элемент найден, вернуть его индекс\n    return -1  # Целевой элемент не найден, вернуть -1\n</code></pre> binary_search.cpp<pre><code>/* Бинарный поиск (двусторонне замкнутый интервал) */\nint binarySearch(vector&lt;int&gt; &amp;nums, int target) {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n    int i = 0, j = nums.size() - 1;\n    // Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target)    // Это означает, что target находится в интервале [m+1, j]\n            i = m + 1;\n        else if (nums[m] &gt; target) // Это означает, что target находится в интервале [i, m-1]\n            j = m - 1;\n        else // Целевой элемент найден, вернуть его индекс\n            return m;\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1;\n}\n</code></pre> binary_search.java<pre><code>/* Бинарный поиск (двусторонне замкнутый интервал) */\nint binarySearch(int[] nums, int target) {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n    int i = 0, j = nums.length - 1;\n    // Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target) // Это означает, что target находится в интервале [m+1, j]\n            i = m + 1;\n        else if (nums[m] &gt; target) // Это означает, что target находится в интервале [i, m-1]\n            j = m - 1;\n        else // Целевой элемент найден, вернуть его индекс\n            return m;\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1;\n}\n</code></pre> binary_search.cs<pre><code>/* Бинарный поиск (двусторонне замкнутый интервал) */\nint BinarySearch(int[] nums, int target) {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n    int i = 0, j = nums.Length - 1;\n    // Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2;   // Вычислить индекс середины m\n        if (nums[m] &lt; target)      // Это означает, что target находится в интервале [m+1, j]\n            i = m + 1;\n        else if (nums[m] &gt; target) // Это означает, что target находится в интервале [i, m-1]\n            j = m - 1;\n        else                       // Целевой элемент найден, вернуть его индекс\n            return m;\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1;\n}\n</code></pre> binary_search.go<pre><code>/* Бинарный поиск (двусторонне замкнутый интервал) */\nfunc binarySearch(nums []int, target int) int {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n    i, j := 0, len(nums)-1\n    // Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n    for i &lt;= j {\n        m := i + (j-i)/2      // Вычислить индекс середины m\n        if nums[m] &lt; target { // Это означает, что target находится в интервале [m+1, j]\n            i = m + 1\n        } else if nums[m] &gt; target { // Это означает, что target находится в интервале [i, m-1]\n            j = m - 1\n        } else { // Целевой элемент найден, вернуть его индекс\n            return m\n        }\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1\n}\n</code></pre> binary_search.swift<pre><code>/* Бинарный поиск (двусторонне замкнутый интервал) */\nfunc binarySearch(nums: [Int], target: Int) -&gt; Int {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n    var i = nums.startIndex\n    var j = nums.endIndex - 1\n    // Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n    while i &lt;= j {\n        let m = i + (j - i) / 2 // Вычислить индекс середины m\n        if nums[m] &lt; target { // Это означает, что target находится в интервале [m+1, j]\n            i = m + 1\n        } else if nums[m] &gt; target { // Это означает, что target находится в интервале [i, m-1]\n            j = m - 1\n        } else { // Целевой элемент найден, вернуть его индекс\n            return m\n        }\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1\n}\n</code></pre> binary_search.js<pre><code>/* Бинарный поиск (двусторонне замкнутый интервал) */\nfunction binarySearch(nums, target) {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n    let i = 0,\n        j = nums.length - 1;\n    // Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n    while (i &lt;= j) {\n        // Вычислить индекс середины m, используя parseInt() для округления вниз\n        const m = parseInt(i + (j - i) / 2);\n        if (nums[m] &lt; target)\n            // Это означает, что target находится в интервале [m+1, j]\n            i = m + 1;\n        else if (nums[m] &gt; target)\n            // Это означает, что target находится в интервале [i, m-1]\n            j = m - 1;\n        else return m; // Целевой элемент найден, вернуть его индекс\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1;\n}\n</code></pre> binary_search.ts<pre><code>/* Бинарный поиск (двусторонне замкнутый интервал) */\nfunction binarySearch(nums: number[], target: number): number {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n    let i = 0,\n        j = nums.length - 1;\n    // Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n    while (i &lt;= j) {\n        // Вычислить индекс середины m\n        const m = Math.floor(i + (j - i) / 2);\n        if (nums[m] &lt; target) {\n            // Это означает, что target находится в интервале [m+1, j]\n            i = m + 1;\n        } else if (nums[m] &gt; target) {\n            // Это означает, что target находится в интервале [i, m-1]\n            j = m - 1;\n        } else {\n            // Целевой элемент найден, вернуть его индекс\n            return m;\n        }\n    }\n    return -1; // Целевой элемент не найден, вернуть -1\n}\n</code></pre> binary_search.dart<pre><code>/* Бинарный поиск (двусторонне замкнутый интервал) */\nint binarySearch(List&lt;int&gt; nums, int target) {\n  // Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n  int i = 0, j = nums.length - 1;\n  // Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n  while (i &lt;= j) {\n    int m = i + (j - i) ~/ 2; // Вычислить индекс середины m\n    if (nums[m] &lt; target) {\n      // Это означает, что target находится в интервале [m+1, j]\n      i = m + 1;\n    } else if (nums[m] &gt; target) {\n      // Это означает, что target находится в интервале [i, m-1]\n      j = m - 1;\n    } else {\n      // Целевой элемент найден, вернуть его индекс\n      return m;\n    }\n  }\n  // Целевой элемент не найден, вернуть -1\n  return -1;\n}\n</code></pre> binary_search.rs<pre><code>/* Бинарный поиск (двусторонне замкнутый интервал) */\nfn binary_search(nums: &amp;[i32], target: i32) -&gt; i32 {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n    let mut i = 0;\n    let mut j = nums.len() as i32 - 1;\n    // Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n    while i &lt;= j {\n        let m = i + (j - i) / 2; // Вычислить индекс середины m\n        if nums[m as usize] &lt; target {\n            // Это означает, что target находится в интервале [m+1, j]\n            i = m + 1;\n        } else if nums[m as usize] &gt; target {\n            // Это означает, что target находится в интервале [i, m-1]\n            j = m - 1;\n        } else {\n            // Целевой элемент найден, вернуть его индекс\n            return m;\n        }\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1;\n}\n</code></pre> binary_search.c<pre><code>/* Бинарный поиск (двусторонне замкнутый интервал) */\nint binarySearch(int *nums, int len, int target) {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n    int i = 0, j = len - 1;\n    // Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target)    // Это означает, что target находится в интервале [m+1, j]\n            i = m + 1;\n        else if (nums[m] &gt; target) // Это означает, что target находится в интервале [i, m-1]\n            j = m - 1;\n        else // Целевой элемент найден, вернуть его индекс\n            return m;\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1;\n}\n</code></pre> binary_search.kt<pre><code>/* Бинарный поиск (двусторонне замкнутый интервал) */\nfun binarySearch(nums: IntArray, target: Int): Int {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n    var i = 0\n    var j = nums.size - 1\n    // Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n    while (i &lt;= j) {\n        val m = i + (j - i) / 2 // Вычислить индекс середины m\n        if (nums[m] &lt; target) // Это означает, что target находится в интервале [m+1, j]\n            i = m + 1\n        else if (nums[m] &gt; target) // Это означает, что target находится в интервале [i, m-1]\n            j = m - 1\n        else  // Целевой элемент найден, вернуть его индекс\n            return m\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1\n}\n</code></pre> binary_search.rb<pre><code>### Бинарный поиск (двусторонне замкнутый интервал) ###\ndef binary_search(nums, target)\n  # Инициализировать двусторонне замкнутый интервал [0, n-1], то есть i и j указывают на первый и последний элементы массива соответственно\n  i, j = 0, nums.length - 1\n\n  # Цикл завершается, когда диапазон поиска пуст (при i &gt; j диапазон пуст)\n  while i &lt;= j\n    # Теоретически числа в Ruby могут быть сколь угодно большими (ограничены только объемом памяти), поэтому не нужно учитывать переполнение больших чисел\n    m = (i + j) / 2   # Вычислить индекс середины m\n\n    if nums[m] &lt; target\n      i = m + 1 # Это означает, что target находится в интервале [m+1, j]\n    elsif nums[m] &gt; target\n      j = m - 1 # Это означает, что target находится в интервале [i, m-1]\n    else\n      return m  # Целевой элемент найден, вернуть его индекс\n    end\n  end\n\n  -1  # Целевой элемент не найден, вернуть -1\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Временная сложность равна \\(O(\\log n)\\) : в цикле двоичного поиска интервал каждый раз сокращается вдвое, поэтому число итераций равно \\(\\log_2 n\\) .</p> <p>Пространственная сложность равна \\(O(1)\\) : указатели \\(i\\) и \\(j\\) занимают константный объем памяти.</p>","path":["Глава 10. Поиск","10.1 &nbsp; Двоичный поиск"],"tags":[]},{"location":"chapter_searching/binary_search/#1011","level":2,"title":"10.1.1   Методы представления интервалов","text":"<p>Помимо описанного выше двойного замкнутого интервала, часто используется и левозамкнутый правооткрытый интервал, который задается как \\([0, n)\\) , то есть левая граница включается, а правая - нет. В этом представлении интервал \\([i, j)\\) пуст, когда \\(i = j\\) .</p> <p>На основе этого представления можно реализовать двоичный поиск с той же функциональностью:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search.py<pre><code>def binary_search_lcro(nums: list[int], target: int) -&gt; int:\n    \"\"\"Бинарный поиск (лево замкнутый, право открытый интервал)\"\"\"\n    # Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n    i, j = 0, len(nums)\n    # Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n    while i &lt; j:\n        m = (i + j) // 2  # Вычислить индекс середины m\n        if nums[m] &lt; target:\n            i = m + 1  # Это означает, что target находится в интервале [m+1, j)\n        elif nums[m] &gt; target:\n            j = m  # Это означает, что target находится в интервале [i, m)\n        else:\n            return m  # Целевой элемент найден, вернуть его индекс\n    return -1  # Целевой элемент не найден, вернуть -1\n</code></pre> binary_search.cpp<pre><code>/* Бинарный поиск (лево замкнутый, право открытый интервал) */\nint binarySearchLCRO(vector&lt;int&gt; &amp;nums, int target) {\n    // Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n    int i = 0, j = nums.size();\n    // Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n    while (i &lt; j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target)    // Это означает, что target находится в интервале [m+1, j)\n            i = m + 1;\n        else if (nums[m] &gt; target) // Это означает, что target находится в интервале [i, m)\n            j = m;\n        else // Целевой элемент найден, вернуть его индекс\n            return m;\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1;\n}\n</code></pre> binary_search.java<pre><code>/* Бинарный поиск (лево замкнутый, право открытый интервал) */\nint binarySearchLCRO(int[] nums, int target) {\n    // Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n    int i = 0, j = nums.length;\n    // Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n    while (i &lt; j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target) // Это означает, что target находится в интервале [m+1, j)\n            i = m + 1;\n        else if (nums[m] &gt; target) // Это означает, что target находится в интервале [i, m)\n            j = m;\n        else // Целевой элемент найден, вернуть его индекс\n            return m;\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1;\n}\n</code></pre> binary_search.cs<pre><code>/* Бинарный поиск (лево замкнутый, право открытый интервал) */\nint BinarySearchLCRO(int[] nums, int target) {\n    // Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n    int i = 0, j = nums.Length;\n    // Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n    while (i &lt; j) {\n        int m = i + (j - i) / 2;   // Вычислить индекс середины m\n        if (nums[m] &lt; target)      // Это означает, что target находится в интервале [m+1, j)\n            i = m + 1;\n        else if (nums[m] &gt; target) // Это означает, что target находится в интервале [i, m)\n            j = m;\n        else                       // Целевой элемент найден, вернуть его индекс\n            return m;\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1;\n}\n</code></pre> binary_search.go<pre><code>/* Бинарный поиск (лево замкнутый, право открытый интервал) */\nfunc binarySearchLCRO(nums []int, target int) int {\n    // Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n    i, j := 0, len(nums)\n    // Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n    for i &lt; j {\n        m := i + (j-i)/2      // Вычислить индекс середины m\n        if nums[m] &lt; target { // Это означает, что target находится в интервале [m+1, j)\n            i = m + 1\n        } else if nums[m] &gt; target { // Это означает, что target находится в интервале [i, m)\n            j = m\n        } else { // Целевой элемент найден, вернуть его индекс\n            return m\n        }\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1\n}\n</code></pre> binary_search.swift<pre><code>/* Бинарный поиск (лево замкнутый, право открытый интервал) */\nfunc binarySearchLCRO(nums: [Int], target: Int) -&gt; Int {\n    // Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n    var i = nums.startIndex\n    var j = nums.endIndex\n    // Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n    while i &lt; j {\n        let m = i + (j - i) / 2 // Вычислить индекс середины m\n        if nums[m] &lt; target { // Это означает, что target находится в интервале [m+1, j)\n            i = m + 1\n        } else if nums[m] &gt; target { // Это означает, что target находится в интервале [i, m)\n            j = m\n        } else { // Целевой элемент найден, вернуть его индекс\n            return m\n        }\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1\n}\n</code></pre> binary_search.js<pre><code>/* Бинарный поиск (лево замкнутый, право открытый интервал) */\nfunction binarySearchLCRO(nums, target) {\n    // Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n    let i = 0,\n        j = nums.length;\n    // Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n    while (i &lt; j) {\n        // Вычислить индекс середины m, используя parseInt() для округления вниз\n        const m = parseInt(i + (j - i) / 2);\n        if (nums[m] &lt; target)\n            // Это означает, что target находится в интервале [m+1, j)\n            i = m + 1;\n        else if (nums[m] &gt; target)\n            // Это означает, что target находится в интервале [i, m)\n            j = m;\n        // Целевой элемент найден, вернуть его индекс\n        else return m;\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1;\n}\n</code></pre> binary_search.ts<pre><code>/* Бинарный поиск (лево замкнутый, право открытый интервал) */\nfunction binarySearchLCRO(nums: number[], target: number): number {\n    // Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n    let i = 0,\n        j = nums.length;\n    // Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n    while (i &lt; j) {\n        // Вычислить индекс середины m\n        const m = Math.floor(i + (j - i) / 2);\n        if (nums[m] &lt; target) {\n            // Это означает, что target находится в интервале [m+1, j)\n            i = m + 1;\n        } else if (nums[m] &gt; target) {\n            // Это означает, что target находится в интервале [i, m)\n            j = m;\n        } else {\n            // Целевой элемент найден, вернуть его индекс\n            return m;\n        }\n    }\n    return -1; // Целевой элемент не найден, вернуть -1\n}\n</code></pre> binary_search.dart<pre><code>/* Бинарный поиск (лево замкнутый, право открытый интервал) */\nint binarySearchLCRO(List&lt;int&gt; nums, int target) {\n  // Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n  int i = 0, j = nums.length;\n  // Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n  while (i &lt; j) {\n    int m = i + (j - i) ~/ 2; // Вычислить индекс середины m\n    if (nums[m] &lt; target) {\n      // Это означает, что target находится в интервале [m+1, j)\n      i = m + 1;\n    } else if (nums[m] &gt; target) {\n      // Это означает, что target находится в интервале [i, m)\n      j = m;\n    } else {\n      // Целевой элемент найден, вернуть его индекс\n      return m;\n    }\n  }\n  // Целевой элемент не найден, вернуть -1\n  return -1;\n}\n</code></pre> binary_search.rs<pre><code>/* Бинарный поиск (лево замкнутый, право открытый интервал) */\nfn binary_search_lcro(nums: &amp;[i32], target: i32) -&gt; i32 {\n    // Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n    let mut i = 0;\n    let mut j = nums.len() as i32;\n    // Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n    while i &lt; j {\n        let m = i + (j - i) / 2; // Вычислить индекс середины m\n        if nums[m as usize] &lt; target {\n            // Это означает, что target находится в интервале [m+1, j)\n            i = m + 1;\n        } else if nums[m as usize] &gt; target {\n            // Это означает, что target находится в интервале [i, m)\n            j = m;\n        } else {\n            // Целевой элемент найден, вернуть его индекс\n            return m;\n        }\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1;\n}\n</code></pre> binary_search.c<pre><code>/* Бинарный поиск (лево замкнутый, право открытый интервал) */\nint binarySearchLCRO(int *nums, int len, int target) {\n    // Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n    int i = 0, j = len;\n    // Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n    while (i &lt; j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target)    // Это означает, что target находится в интервале [m+1, j)\n            i = m + 1;\n        else if (nums[m] &gt; target) // Это означает, что target находится в интервале [i, m)\n            j = m;\n        else // Целевой элемент найден, вернуть его индекс\n            return m;\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1;\n}\n</code></pre> binary_search.kt<pre><code>/* Бинарный поиск (лево замкнутый, право открытый интервал) */\nfun binarySearchLCRO(nums: IntArray, target: Int): Int {\n    // Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n    var i = 0\n    var j = nums.size\n    // Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n    while (i &lt; j) {\n        val m = i + (j - i) / 2 // Вычислить индекс середины m\n        if (nums[m] &lt; target) // Это означает, что target находится в интервале [m+1, j)\n            i = m + 1\n        else if (nums[m] &gt; target) // Это означает, что target находится в интервале [i, m)\n            j = m\n        else  // Целевой элемент найден, вернуть его индекс\n            return m\n    }\n    // Целевой элемент не найден, вернуть -1\n    return -1\n}\n</code></pre> binary_search.rb<pre><code>### Бинарный поиск (лево замкнутый, право открытый интервал) ###\ndef binary_search_lcro(nums, target)\n  # Инициализировать лево замкнутый, право открытый интервал [0, n), то есть i и j указывают на первый элемент массива и позицию сразу за последним элементом соответственно\n  i, j = 0, nums.length\n\n  # Цикл завершается, когда диапазон поиска пуст (при i = j диапазон пуст)\n  while i &lt; j\n    # Вычислить индекс середины m\n    m = (i + j) / 2\n\n    if nums[m] &lt; target\n      i = m + 1 # Это означает, что target находится в интервале [m+1, j)\n    elsif nums[m] &gt; target\n      j = m - 1 # Это означает, что target находится в интервале [i, m)\n    else\n      return m  # Целевой элемент найден, вернуть его индекс\n    end\n  end\n\n  -1  # Целевой элемент не найден, вернуть -1\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Как показано на рисунке 10-3, в этих двух вариантах представления интервала различаются инициализация, условие цикла и операция сужения интервала в алгоритме двоичного поиска.</p> <p>Поскольку в записи \"двойной замкнутый интервал\" обе границы являются закрытыми, операции сужения интервала при помощи указателей \\(i\\) и \\(j\\) тоже получаются симметричными. Из-за этого в таком варианте сложнее допустить ошибку, поэтому обычно рекомендуется использовать именно запись \"двойной замкнутый интервал\".</p> <p></p> <p> Рисунок 10-3   Два определения интервалов </p>","path":["Глава 10. Поиск","10.1 &nbsp; Двоичный поиск"],"tags":[]},{"location":"chapter_searching/binary_search/#1012","level":2,"title":"10.1.2   Преимущества и ограничения","text":"<p>Двоичный поиск показывает хорошие результаты и по времени, и по памяти.</p> <ul> <li>Двоичный поиск очень эффективен по времени. На больших объемах данных логарифмическая временная сложность дает заметное преимущество. Например, когда размер данных \\(n = 2^{20}\\) , линейный поиск потребует \\(2^{20} = 1048576\\) итераций, тогда как двоичный поиск выполнится всего за \\(\\log_2 2^{20} = 20\\) итераций.</li> <li>Двоичный поиск не требует дополнительной памяти. По сравнению с алгоритмами поиска, которым нужно внешнее пространство (например, с хеш-поиском), двоичный поиск заметно экономнее по памяти.</li> </ul> <p>Однако двоичный поиск подходит не для всех ситуаций, и основные причины таковы.</p> <ul> <li>Двоичный поиск применим только к упорядоченным данным. Если входные данные неупорядочены, специально сортировать их ради двоичного поиска невыгодно. Это связано с тем, что временная сложность алгоритмов сортировки обычно составляет \\(O(n \\log n)\\) , что выше, чем у линейного и двоичного поиска. Если элементы приходится часто вставлять, то для сохранения порядка в массиве их нужно помещать в конкретные позиции, а это требует \\(O(n)\\) времени и тоже обходится дорого.</li> <li>Двоичный поиск применим только к массивам. Для него нужен скачкообразный доступ к элементам, а в связном списке такой доступ малоэффективен, поэтому двоичный поиск не подходит для списков и структур данных, построенных на их основе.</li> <li>При малом объеме данных линейный поиск работает лучше. В линейном поиске на каждом шаге нужна всего одна операция сравнения; в двоичном поиске требуется 1 сложение, 1 деление, от 1 до 3 сравнений и еще 1 сложение или вычитание, то есть всего от 4 до 6 элементарных операций. Поэтому при небольшом \\(n\\) линейный поиск может оказаться быстрее двоичного.</li> </ul>","path":["Глава 10. Поиск","10.1 &nbsp; Двоичный поиск"],"tags":[]},{"location":"chapter_searching/binary_search_edge/","level":1,"title":"10.3   Двоичный поиск границ","text":"","path":["Глава 10. Поиск","10.3 &nbsp; Двоичный поиск границ"],"tags":[]},{"location":"chapter_searching/binary_search_edge/#1031","level":2,"title":"10.3.1   Поиск левой границы","text":"<p>Question</p> <p>Дан упорядоченный массив <code>nums</code> длины \\(n\\), который может содержать повторяющиеся элементы. Верните индекс самого левого элемента <code>target</code> в массиве. Если массив не содержит этот элемент, верните \\(-1\\) .</p> <p>Вспомним метод поиска точки вставки при двоичном поиске: после завершения поиска указатель \\(i\\) указывает на самый левый <code>target</code> , поэтому поиск точки вставки по сути является поиском индекса самого левого <code>target</code>.</p> <p>Рассмотрим реализацию поиска левой границы через функцию поиска точки вставки. Обратите внимание: массив может не содержать <code>target</code> , и тогда возможны две ситуации.</p> <ul> <li>Индекс точки вставки \\(i\\) выходит за границы массива.</li> <li>Элемент <code>nums[i]</code> не равен <code>target</code> .</li> </ul> <p>Если возникает любая из этих ситуаций, достаточно сразу вернуть \\(-1\\) . Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_edge.py<pre><code>def binary_search_left_edge(nums: list[int], target: int) -&gt; int:\n    \"\"\"Бинарный поиск самого левого target\"\"\"\n    # Эквивалентно поиску точки вставки target\n    i = binary_search_insertion(nums, target)\n    # target не найден, вернуть -1\n    if i == len(nums) or nums[i] != target:\n        return -1\n    # Найти target и вернуть индекс i\n    return i\n</code></pre> binary_search_edge.cpp<pre><code>/* Бинарный поиск самого левого target */\nint binarySearchLeftEdge(vector&lt;int&gt; &amp;nums, int target) {\n    // Эквивалентно поиску точки вставки target\n    int i = binarySearchInsertion(nums, target);\n    // target не найден, вернуть -1\n    if (i == nums.size() || nums[i] != target) {\n        return -1;\n    }\n    // Найти target и вернуть индекс i\n    return i;\n}\n</code></pre> binary_search_edge.java<pre><code>/* Бинарный поиск самого левого target */\nint binarySearchLeftEdge(int[] nums, int target) {\n    // Эквивалентно поиску точки вставки target\n    int i = binary_search_insertion.binarySearchInsertion(nums, target);\n    // target не найден, вернуть -1\n    if (i == nums.length || nums[i] != target) {\n        return -1;\n    }\n    // Найти target и вернуть индекс i\n    return i;\n}\n</code></pre> binary_search_edge.cs<pre><code>/* Бинарный поиск самого левого target */\nint BinarySearchLeftEdge(int[] nums, int target) {\n    // Эквивалентно поиску точки вставки target\n    int i = binary_search_insertion.BinarySearchInsertion(nums, target);\n    // target не найден, вернуть -1\n    if (i == nums.Length || nums[i] != target) {\n        return -1;\n    }\n    // Найти target и вернуть индекс i\n    return i;\n}\n</code></pre> binary_search_edge.go<pre><code>/* Бинарный поиск самого левого target */\nfunc binarySearchLeftEdge(nums []int, target int) int {\n    // Эквивалентно поиску точки вставки target\n    i := binarySearchInsertion(nums, target)\n    // target не найден, вернуть -1\n    if i == len(nums) || nums[i] != target {\n        return -1\n    }\n    // Найти target и вернуть индекс i\n    return i\n}\n</code></pre> binary_search_edge.swift<pre><code>/* Бинарный поиск самого левого target */\nfunc binarySearchLeftEdge(nums: [Int], target: Int) -&gt; Int {\n    // Эквивалентно поиску точки вставки target\n    let i = binarySearchInsertion(nums: nums, target: target)\n    // target не найден, вернуть -1\n    if i == nums.endIndex || nums[i] != target {\n        return -1\n    }\n    // Найти target и вернуть индекс i\n    return i\n}\n</code></pre> binary_search_edge.js<pre><code>/* Бинарный поиск самого левого target */\nfunction binarySearchLeftEdge(nums, target) {\n    // Эквивалентно поиску точки вставки target\n    const i = binarySearchInsertion(nums, target);\n    // target не найден, вернуть -1\n    if (i === nums.length || nums[i] !== target) {\n        return -1;\n    }\n    // Найти target и вернуть индекс i\n    return i;\n}\n</code></pre> binary_search_edge.ts<pre><code>/* Бинарный поиск самого левого target */\nfunction binarySearchLeftEdge(nums: Array&lt;number&gt;, target: number): number {\n    // Эквивалентно поиску точки вставки target\n    const i = binarySearchInsertion(nums, target);\n    // target не найден, вернуть -1\n    if (i === nums.length || nums[i] !== target) {\n        return -1;\n    }\n    // Найти target и вернуть индекс i\n    return i;\n}\n</code></pre> binary_search_edge.dart<pre><code>/* Бинарный поиск самого левого target */\nint binarySearchLeftEdge(List&lt;int&gt; nums, int target) {\n  // Эквивалентно поиску точки вставки target\n  int i = binarySearchInsertion(nums, target);\n  // target не найден, вернуть -1\n  if (i == nums.length || nums[i] != target) {\n    return -1;\n  }\n  // Найти target и вернуть индекс i\n  return i;\n}\n</code></pre> binary_search_edge.rs<pre><code>/* Бинарный поиск самого левого target */\nfn binary_search_left_edge(nums: &amp;[i32], target: i32) -&gt; i32 {\n    // Эквивалентно поиску точки вставки target\n    let i = binary_search_insertion(nums, target);\n    // target не найден, вернуть -1\n    if i == nums.len() as i32 || nums[i as usize] != target {\n        return -1;\n    }\n    // Найти target и вернуть индекс i\n    i\n}\n</code></pre> binary_search_edge.c<pre><code>/* Бинарный поиск самого левого target */\nint binarySearchLeftEdge(int *nums, int numSize, int target) {\n    // Эквивалентно поиску точки вставки target\n    int i = binarySearchInsertion(nums, numSize, target);\n    // target не найден, вернуть -1\n    if (i == numSize || nums[i] != target) {\n        return -1;\n    }\n    // Найти target и вернуть индекс i\n    return i;\n}\n</code></pre> binary_search_edge.kt<pre><code>/* Бинарный поиск самого левого target */\nfun binarySearchLeftEdge(nums: IntArray, target: Int): Int {\n    // Эквивалентно поиску точки вставки target\n    val i = binarySearchInsertion(nums, target)\n    // target не найден, вернуть -1\n    if (i == nums.size || nums[i] != target) {\n        return -1\n    }\n    // Найти target и вернуть индекс i\n    return i\n}\n</code></pre> binary_search_edge.rb<pre><code>### Бинарный поиск самого левого target ###\ndef binary_search_left_edge(nums, target)\n  # Эквивалентно поиску точки вставки target\n  i = binary_search_insertion(nums, target)\n\n  # target не найден, вернуть -1\n  return -1 if i == nums.length || nums[i] != target\n\n  i # Найти target и вернуть индекс i\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 10. Поиск","10.3 &nbsp; Двоичный поиск границ"],"tags":[]},{"location":"chapter_searching/binary_search_edge/#1032","level":2,"title":"10.3.2   Поиск правой границы","text":"<p>Как тогда найти самый правый <code>target</code> ? Самый прямой способ - изменить код, заменив операцию сужения указателя в случае <code>nums[m] == target</code> . Мы не будем приводить этот код, заинтересованные читатели могут реализовать его самостоятельно.</p> <p>Ниже представлены два более изящных способа.</p>","path":["Глава 10. Поиск","10.3 &nbsp; Двоичный поиск границ"],"tags":[]},{"location":"chapter_searching/binary_search_edge/#1","level":3,"title":"1.   Повторное использование поиска левой границы","text":"<p>На самом деле функцию поиска самого левого элемента можно использовать и для поиска самого правого элемента. Конкретная идея такова: преобразовать поиск самого правого <code>target</code> в поиск самого левого <code>target + 1</code>.</p> <p>Как показано на рисунке 10-7, после завершения поиска указатель \\(i\\) указывает на самый левый <code>target + 1</code> (если он существует), а указатель \\(j\\) указывает на самый правый <code>target</code> , поэтому достаточно вернуть \\(j\\).</p> <p></p> <p> Рисунок 10-7   Преобразование поиска правой границы в поиск левой </p> <p>Обратите внимание: функция возвращает точку вставки \\(i\\) , поэтому из нее нужно вычесть \\(1\\) , чтобы получить \\(j\\) :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_edge.py<pre><code>def binary_search_right_edge(nums: list[int], target: int) -&gt; int:\n    \"\"\"Бинарный поиск самого правого target\"\"\"\n    # Преобразовать задачу в поиск самого левого target + 1\n    i = binary_search_insertion(nums, target + 1)\n    # j указывает на самый правый target, а i — на первый элемент больше target\n    j = i - 1\n    # target не найден, вернуть -1\n    if j == -1 or nums[j] != target:\n        return -1\n    # Найти target и вернуть индекс j\n    return j\n</code></pre> binary_search_edge.cpp<pre><code>/* Бинарный поиск самого правого target */\nint binarySearchRightEdge(vector&lt;int&gt; &amp;nums, int target) {\n    // Преобразовать задачу в поиск самого левого target + 1\n    int i = binarySearchInsertion(nums, target + 1);\n    // j указывает на самый правый target, а i — на первый элемент больше target\n    int j = i - 1;\n    // target не найден, вернуть -1\n    if (j == -1 || nums[j] != target) {\n        return -1;\n    }\n    // Найти target и вернуть индекс j\n    return j;\n}\n</code></pre> binary_search_edge.java<pre><code>/* Бинарный поиск самого правого target */\nint binarySearchRightEdge(int[] nums, int target) {\n    // Преобразовать задачу в поиск самого левого target + 1\n    int i = binary_search_insertion.binarySearchInsertion(nums, target + 1);\n    // j указывает на самый правый target, а i — на первый элемент больше target\n    int j = i - 1;\n    // target не найден, вернуть -1\n    if (j == -1 || nums[j] != target) {\n        return -1;\n    }\n    // Найти target и вернуть индекс j\n    return j;\n}\n</code></pre> binary_search_edge.cs<pre><code>/* Бинарный поиск самого правого target */\nint BinarySearchRightEdge(int[] nums, int target) {\n    // Преобразовать задачу в поиск самого левого target + 1\n    int i = binary_search_insertion.BinarySearchInsertion(nums, target + 1);\n    // j указывает на самый правый target, а i — на первый элемент больше target\n    int j = i - 1;\n    // target не найден, вернуть -1\n    if (j == -1 || nums[j] != target) {\n        return -1;\n    }\n    // Найти target и вернуть индекс j\n    return j;\n}\n</code></pre> binary_search_edge.go<pre><code>/* Бинарный поиск самого правого target */\nfunc binarySearchRightEdge(nums []int, target int) int {\n    // Преобразовать задачу в поиск самого левого target + 1\n    i := binarySearchInsertion(nums, target+1)\n    // j указывает на самый правый target, а i — на первый элемент больше target\n    j := i - 1\n    // target не найден, вернуть -1\n    if j == -1 || nums[j] != target {\n        return -1\n    }\n    // Найти target и вернуть индекс j\n    return j\n}\n</code></pre> binary_search_edge.swift<pre><code>/* Бинарный поиск самого правого target */\nfunc binarySearchRightEdge(nums: [Int], target: Int) -&gt; Int {\n    // Преобразовать задачу в поиск самого левого target + 1\n    let i = binarySearchInsertion(nums: nums, target: target + 1)\n    // j указывает на самый правый target, а i — на первый элемент больше target\n    let j = i - 1\n    // target не найден, вернуть -1\n    if j == -1 || nums[j] != target {\n        return -1\n    }\n    // Найти target и вернуть индекс j\n    return j\n}\n</code></pre> binary_search_edge.js<pre><code>/* Бинарный поиск самого правого target */\nfunction binarySearchRightEdge(nums, target) {\n    // Преобразовать задачу в поиск самого левого target + 1\n    const i = binarySearchInsertion(nums, target + 1);\n    // j указывает на самый правый target, а i — на первый элемент больше target\n    const j = i - 1;\n    // target не найден, вернуть -1\n    if (j === -1 || nums[j] !== target) {\n        return -1;\n    }\n    // Найти target и вернуть индекс j\n    return j;\n}\n</code></pre> binary_search_edge.ts<pre><code>/* Бинарный поиск самого правого target */\nfunction binarySearchRightEdge(nums: Array&lt;number&gt;, target: number): number {\n    // Преобразовать задачу в поиск самого левого target + 1\n    const i = binarySearchInsertion(nums, target + 1);\n    // j указывает на самый правый target, а i — на первый элемент больше target\n    const j = i - 1;\n    // target не найден, вернуть -1\n    if (j === -1 || nums[j] !== target) {\n        return -1;\n    }\n    // Найти target и вернуть индекс j\n    return j;\n}\n</code></pre> binary_search_edge.dart<pre><code>/* Бинарный поиск самого правого target */\nint binarySearchRightEdge(List&lt;int&gt; nums, int target) {\n  // Преобразовать задачу в поиск самого левого target + 1\n  int i = binarySearchInsertion(nums, target + 1);\n  // j указывает на самый правый target, а i — на первый элемент больше target\n  int j = i - 1;\n  // target не найден, вернуть -1\n  if (j == -1 || nums[j] != target) {\n    return -1;\n  }\n  // Найти target и вернуть индекс j\n  return j;\n}\n</code></pre> binary_search_edge.rs<pre><code>/* Бинарный поиск самого правого target */\nfn binary_search_right_edge(nums: &amp;[i32], target: i32) -&gt; i32 {\n    // Преобразовать задачу в поиск самого левого target + 1\n    let i = binary_search_insertion(nums, target + 1);\n    // j указывает на самый правый target, а i — на первый элемент больше target\n    let j = i - 1;\n    // target не найден, вернуть -1\n    if j == -1 || nums[j as usize] != target {\n        return -1;\n    }\n    // Найти target и вернуть индекс j\n    j\n}\n</code></pre> binary_search_edge.c<pre><code>/* Бинарный поиск самого правого target */\nint binarySearchRightEdge(int *nums, int numSize, int target) {\n    // Преобразовать задачу в поиск самого левого target + 1\n    int i = binarySearchInsertion(nums, numSize, target + 1);\n    // j указывает на самый правый target, а i — на первый элемент больше target\n    int j = i - 1;\n    // target не найден, вернуть -1\n    if (j == -1 || nums[j] != target) {\n        return -1;\n    }\n    // Найти target и вернуть индекс j\n    return j;\n}\n</code></pre> binary_search_edge.kt<pre><code>/* Бинарный поиск самого правого target */\nfun binarySearchRightEdge(nums: IntArray, target: Int): Int {\n    // Преобразовать задачу в поиск самого левого target + 1\n    val i = binarySearchInsertion(nums, target + 1)\n    // j указывает на самый правый target, а i — на первый элемент больше target\n    val j = i - 1\n    // target не найден, вернуть -1\n    if (j == -1 || nums[j] != target) {\n        return -1\n    }\n    // Найти target и вернуть индекс j\n    return j\n}\n</code></pre> binary_search_edge.rb<pre><code>### Бинарный поиск самого правого target ###\ndef binary_search_right_edge(nums, target)\n  # Преобразовать задачу в поиск самого левого target + 1\n  i = binary_search_insertion(nums, target + 1)\n\n  # j указывает на самый правый target, а i — на первый элемент больше target\n  j = i - 1\n\n  # target не найден, вернуть -1\n  return -1 if j == -1 || nums[j] != target\n\n  j # Найти target и вернуть индекс j\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 10. Поиск","10.3 &nbsp; Двоичный поиск границ"],"tags":[]},{"location":"chapter_searching/binary_search_edge/#2","level":3,"title":"2.   Преобразование в поиск элемента","text":"<p>Мы знаем, что если массив не содержит <code>target</code> , то в конце поиска указатели \\(i\\) и \\(j\\) будут указывать соответственно на первый элемент, больший <code>target</code> , и на первый элемент, меньший <code>target</code> .</p> <p>Следовательно, как показано на рисунке 10-8, для поиска левой и правой границы можно сконструировать элемент, которого нет в массиве.</p> <ul> <li>Поиск самого левого <code>target</code> : можно преобразовать в поиск <code>target - 0.5</code> и вернуть указатель \\(i\\) .</li> <li>Поиск самого правого <code>target</code> : можно преобразовать в поиск <code>target + 0.5</code> и вернуть указатель \\(j\\) .</li> </ul> <p></p> <p> Рисунок 10-8   Преобразование поиска границ в поиск элемента </p> <p>Код здесь опущен, но стоит обратить внимание на два момента.</p> <ul> <li>По условию массив не содержит дробных чисел, поэтому нам не нужно беспокоиться о том, как обрабатывать случай равенства другим элементам массива.</li> <li>Поскольку этот метод вводит дробные числа, переменную <code>target</code> в функции нужно изменить на тип с плавающей запятой (в Python менять ничего не требуется).</li> </ul>","path":["Глава 10. Поиск","10.3 &nbsp; Двоичный поиск границ"],"tags":[]},{"location":"chapter_searching/binary_search_insertion/","level":1,"title":"10.2   Двоичный поиск точки вставки","text":"<p>Двоичный поиск можно использовать не только для поиска целевого элемента, но и для решения многих вариаций задачи, например для поиска позиции вставки целевого элемента.</p>","path":["Глава 10. Поиск","10.2 &nbsp; Двоичный поиск точки вставки"],"tags":[]},{"location":"chapter_searching/binary_search_insertion/#1021","level":2,"title":"10.2.1   Случай без повторяющихся элементов","text":"<p>Question</p> <p>Дан упорядоченный массив <code>nums</code> длины \\(n\\) и элемент <code>target</code> , причем в массиве нет повторяющихся элементов. Нужно вставить <code>target</code> в массив <code>nums</code> , сохранив порядок. Если элемент <code>target</code> уже присутствует в массиве, вставьте его слева от него. Верните индекс, который будет иметь <code>target</code> после вставки. Пример показан на рисунке 10-4.</p> <p></p> <p> Рисунок 10-4   Пример данных для точки вставки </p> <p>Если мы хотим переиспользовать код двоичного поиска из предыдущего раздела, нужно ответить на два вопроса.</p> <p>Вопрос 1: если массив содержит <code>target</code> , будет ли индекс вставки совпадать с индексом этого элемента?</p> <p>По условию <code>target</code> нужно вставить слева от равного элемента, а это означает, что новый <code>target</code> занимает место старого <code>target</code> . Иначе говоря, если массив содержит <code>target</code> , то индекс вставки совпадает с индексом этого <code>target</code>.</p> <p>Вопрос 2: если массив не содержит <code>target</code> , индекс какого элемента будет точкой вставки?</p> <p>Рассмотрим процесс двоичного поиска подробнее: когда <code>nums[m] &lt; target</code> , указатель \\(i\\) сдвигается вправо и тем самым приближается к элементу, который больше либо равен <code>target</code> . Аналогично указатель \\(j\\) постепенно приближается к элементу, который меньше либо равен <code>target</code> .</p> <p>Следовательно, после завершения двоичного поиска обязательно выполняется следующее: указатель \\(i\\) указывает на первый элемент, больший <code>target</code> , а указатель \\(j\\) указывает на первый элемент, меньший <code>target</code> . Нетрудно сделать вывод, что если массив не содержит <code>target</code> , то индекс вставки равен \\(i\\) . Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_insertion.py<pre><code>def binary_search_insertion_simple(nums: list[int], target: int) -&gt; int:\n    \"\"\"Бинарный поиск точки вставки (без повторяющихся элементов)\"\"\"\n    i, j = 0, len(nums) - 1  # Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while i &lt;= j:\n        m = (i + j) // 2  # Вычислить индекс середины m\n        if nums[m] &lt; target:\n            i = m + 1  # target находится в интервале [m+1, j]\n        elif nums[m] &gt; target:\n            j = m - 1  # target находится в интервале [i, m-1]\n        else:\n            return m  # Найти target и вернуть точку вставки m\n    # target не найден, вернуть точку вставки i\n    return i\n</code></pre> binary_search_insertion.cpp<pre><code>/* Бинарный поиск точки вставки (без повторяющихся элементов) */\nint binarySearchInsertionSimple(vector&lt;int&gt; &amp;nums, int target) {\n    int i = 0, j = nums.size() - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target) {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            return m; // Найти target и вернуть точку вставки m\n        }\n    }\n    // target не найден, вернуть точку вставки i\n    return i;\n}\n</code></pre> binary_search_insertion.java<pre><code>/* Бинарный поиск точки вставки (без повторяющихся элементов) */\nint binarySearchInsertionSimple(int[] nums, int target) {\n    int i = 0, j = nums.length - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target) {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            return m; // Найти target и вернуть точку вставки m\n        }\n    }\n    // target не найден, вернуть точку вставки i\n    return i;\n}\n</code></pre> binary_search_insertion.cs<pre><code>/* Бинарный поиск точки вставки (без повторяющихся элементов) */\nint BinarySearchInsertionSimple(int[] nums, int target) {\n    int i = 0, j = nums.Length - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target) {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            return m; // Найти target и вернуть точку вставки m\n        }\n    }\n    // target не найден, вернуть точку вставки i\n    return i;\n}\n</code></pre> binary_search_insertion.go<pre><code>/* Бинарный поиск точки вставки (без повторяющихся элементов) */\nfunc binarySearchInsertionSimple(nums []int, target int) int {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    i, j := 0, len(nums)-1\n    for i &lt;= j {\n        // Вычислить индекс середины m\n        m := i + (j-i)/2\n        if nums[m] &lt; target {\n            // target находится в интервале [m+1, j]\n            i = m + 1\n        } else if nums[m] &gt; target {\n            // target находится в интервале [i, m-1]\n            j = m - 1\n        } else {\n            // Найти target и вернуть точку вставки m\n            return m\n        }\n    }\n    // target не найден, вернуть точку вставки i\n    return i\n}\n</code></pre> binary_search_insertion.swift<pre><code>/* Бинарный поиск точки вставки (без повторяющихся элементов) */\nfunc binarySearchInsertionSimple(nums: [Int], target: Int) -&gt; Int {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    var i = nums.startIndex\n    var j = nums.endIndex - 1\n    while i &lt;= j {\n        let m = i + (j - i) / 2 // Вычислить индекс середины m\n        if nums[m] &lt; target {\n            i = m + 1 // target находится в интервале [m+1, j]\n        } else if nums[m] &gt; target {\n            j = m - 1 // target находится в интервале [i, m-1]\n        } else {\n            return m // Найти target и вернуть точку вставки m\n        }\n    }\n    // target не найден, вернуть точку вставки i\n    return i\n}\n</code></pre> binary_search_insertion.js<pre><code>/* Бинарный поиск точки вставки (без повторяющихся элементов) */\nfunction binarySearchInsertionSimple(nums, target) {\n    let i = 0,\n        j = nums.length - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        const m = Math.floor(i + (j - i) / 2); // Вычислить индекс середины m, используя Math.floor() для округления вниз\n        if (nums[m] &lt; target) {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            return m; // Найти target и вернуть точку вставки m\n        }\n    }\n    // target не найден, вернуть точку вставки i\n    return i;\n}\n</code></pre> binary_search_insertion.ts<pre><code>/* Бинарный поиск точки вставки (без повторяющихся элементов) */\nfunction binarySearchInsertionSimple(\n    nums: Array&lt;number&gt;,\n    target: number\n): number {\n    let i = 0,\n        j = nums.length - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        const m = Math.floor(i + (j - i) / 2); // Вычислить индекс середины m, используя Math.floor() для округления вниз\n        if (nums[m] &lt; target) {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            return m; // Найти target и вернуть точку вставки m\n        }\n    }\n    // target не найден, вернуть точку вставки i\n    return i;\n}\n</code></pre> binary_search_insertion.dart<pre><code>/* Бинарный поиск точки вставки (без повторяющихся элементов) */\nint binarySearchInsertionSimple(List&lt;int&gt; nums, int target) {\n  int i = 0, j = nums.length - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n  while (i &lt;= j) {\n    int m = i + (j - i) ~/ 2; // Вычислить индекс середины m\n    if (nums[m] &lt; target) {\n      i = m + 1; // target находится в интервале [m+1, j]\n    } else if (nums[m] &gt; target) {\n      j = m - 1; // target находится в интервале [i, m-1]\n    } else {\n      return m; // Найти target и вернуть точку вставки m\n    }\n  }\n  // target не найден, вернуть точку вставки i\n  return i;\n}\n</code></pre> binary_search_insertion.rs<pre><code>/* Бинарный поиск точки вставки (без повторяющихся элементов) */\nfn binary_search_insertion_simple(nums: &amp;[i32], target: i32) -&gt; i32 {\n    let (mut i, mut j) = (0, nums.len() as i32 - 1); // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while i &lt;= j {\n        let m = i + (j - i) / 2; // Вычислить индекс середины m\n        if nums[m as usize] &lt; target {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if nums[m as usize] &gt; target {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            return m;\n        }\n    }\n    // target не найден, вернуть точку вставки i\n    i\n}\n</code></pre> binary_search_insertion.c<pre><code>/* Бинарный поиск точки вставки (без повторяющихся элементов) */\nint binarySearchInsertionSimple(int *nums, int numSize, int target) {\n    int i = 0, j = numSize - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target) {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            return m; // Найти target и вернуть точку вставки m\n        }\n    }\n    // target не найден, вернуть точку вставки i\n    return i;\n}\n</code></pre> binary_search_insertion.kt<pre><code>/* Бинарный поиск точки вставки (без повторяющихся элементов) */\nfun binarySearchInsertionSimple(nums: IntArray, target: Int): Int {\n    var i = 0\n    var j = nums.size - 1 // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        val m = i + (j - i) / 2 // Вычислить индекс середины m\n        if (nums[m] &lt; target) {\n            i = m + 1 // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1 // target находится в интервале [i, m-1]\n        } else {\n            return m // Найти target и вернуть точку вставки m\n        }\n    }\n    // target не найден, вернуть точку вставки i\n    return i\n}\n</code></pre> binary_search_insertion.rb<pre><code>### Бинарный поиск точки вставки (без повторяющихся элементов) ###\ndef binary_search_insertion_simple(nums, target)\n  # Инициализировать двусторонне замкнутый интервал [0, n-1]\n  i, j = 0, nums.length - 1\n\n  while i &lt;= j\n    # Вычислить индекс середины m\n    m = (i + j) / 2\n\n    if nums[m] &lt; target\n      i = m + 1 # target находится в интервале [m+1, j]\n    elsif nums[m] &gt; target\n      j = m - 1 # target находится в интервале [i, m-1]\n    else\n      return m  # Найти target и вернуть точку вставки m\n    end\n  end\n\n  i # target не найден, вернуть точку вставки i\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 10. Поиск","10.2 &nbsp; Двоичный поиск точки вставки"],"tags":[]},{"location":"chapter_searching/binary_search_insertion/#1022","level":2,"title":"10.2.2   Случай с повторяющимися элементами","text":"<p>Question</p> <p>В предыдущей задаче теперь допускается, что массив может содержать повторяющиеся элементы, а все остальные условия остаются без изменений.</p> <p>Если в массиве есть несколько элементов <code>target</code> , то обычный двоичный поиск сможет вернуть индекс только одного из них, но не позволит определить, сколько элементов <code>target</code> находится слева и справа от него.</p> <p>По условию целевой элемент нужно вставить в самую левую позицию, поэтому нам нужно найти индекс самого левого <code>target</code> в массиве. На первом этапе можно рассмотреть решение, показанное на рисунке 10-5.</p> <ol> <li>Выполнить двоичный поиск и получить индекс любого элемента <code>target</code> , обозначив его как \\(k\\) .</li> <li>Начиная с индекса \\(k\\) , линейно двигаться влево и вернуть результат, когда будет найден самый левый <code>target</code> .</li> </ol> <p></p> <p> Рисунок 10-5   Линейный поиск точки вставки среди повторяющихся элементов </p> <p>Этот метод применим на практике, однако в нем есть линейный поиск, поэтому его временная сложность равна \\(O(n)\\) . Когда в массиве имеется много повторяющихся <code>target</code> , такой подход работает неэффективно.</p> <p>Теперь рассмотрим расширение кода двоичного поиска. Как показано на рисунке 10-6, общий процесс остается прежним: на каждом шаге мы сначала вычисляем индекс середины \\(m\\) , а затем сравниваем <code>target</code> и <code>nums[m]</code> , после чего возможны следующие случаи.</p> <ul> <li>Когда <code>nums[m] &lt; target</code> или <code>nums[m] &gt; target</code> , это означает, что <code>target</code> еще не найден, поэтому используется стандартная операция сужения интервала в двоичном поиске, благодаря чему указатели \\(i\\) и \\(j\\) приближаются к <code>target</code>.</li> <li>Когда <code>nums[m] == target</code> , это означает, что элементы меньше <code>target</code> находятся в интервале \\([i, m - 1]\\) , поэтому мы используем \\(j = m - 1\\) для сужения интервала, тем самым приближая указатель \\(j\\) к элементам, меньшим <code>target</code>.</li> </ul> <p>После завершения цикла указатель \\(i\\) будет указывать на самый левый <code>target</code> , а указатель \\(j\\) - на первый элемент, меньший <code>target</code> , поэтому индекс \\(i\\) и является точкой вставки.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 10-6   Шаги поиска точки вставки для повторяющихся элементов </p> <p>Если посмотреть на следующий код, то видно, что действия в ветвях <code>nums[m] &gt; target</code> и <code>nums[m] == target</code> совпадают, поэтому эти две ветви можно объединить.</p> <p>Даже в этом случае можно оставить условия развернутыми, потому что так логика выглядит более ясной и код легче читать.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_insertion.py<pre><code>def binary_search_insertion(nums: list[int], target: int) -&gt; int:\n    \"\"\"Бинарный поиск точки вставки (с повторяющимися элементами)\"\"\"\n    i, j = 0, len(nums) - 1  # Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while i &lt;= j:\n        m = (i + j) // 2  # Вычислить индекс середины m\n        if nums[m] &lt; target:\n            i = m + 1  # target находится в интервале [m+1, j]\n        elif nums[m] &gt; target:\n            j = m - 1  # target находится в интервале [i, m-1]\n        else:\n            j = m - 1  # Первый элемент меньше target находится в интервале [i, m-1]\n    # Вернуть точку вставки i\n    return i\n</code></pre> binary_search_insertion.cpp<pre><code>/* Бинарный поиск точки вставки (с повторяющимися элементами) */\nint binarySearchInsertion(vector&lt;int&gt; &amp;nums, int target) {\n    int i = 0, j = nums.size() - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target) {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            j = m - 1; // Первый элемент меньше target находится в интервале [i, m-1]\n        }\n    }\n    // Вернуть точку вставки i\n    return i;\n}\n</code></pre> binary_search_insertion.java<pre><code>/* Бинарный поиск точки вставки (с повторяющимися элементами) */\nint binarySearchInsertion(int[] nums, int target) {\n    int i = 0, j = nums.length - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target) {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            j = m - 1; // Первый элемент меньше target находится в интервале [i, m-1]\n        }\n    }\n    // Вернуть точку вставки i\n    return i;\n}\n</code></pre> binary_search_insertion.cs<pre><code>/* Бинарный поиск точки вставки (с повторяющимися элементами) */\nint BinarySearchInsertion(int[] nums, int target) {\n    int i = 0, j = nums.Length - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target) {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            j = m - 1; // Первый элемент меньше target находится в интервале [i, m-1]\n        }\n    }\n    // Вернуть точку вставки i\n    return i;\n}\n</code></pre> binary_search_insertion.go<pre><code>/* Бинарный поиск точки вставки (с повторяющимися элементами) */\nfunc binarySearchInsertion(nums []int, target int) int {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    i, j := 0, len(nums)-1\n    for i &lt;= j {\n        // Вычислить индекс середины m\n        m := i + (j-i)/2\n        if nums[m] &lt; target {\n            // target находится в интервале [m+1, j]\n            i = m + 1\n        } else if nums[m] &gt; target {\n            // target находится в интервале [i, m-1]\n            j = m - 1\n        } else {\n            // Первый элемент меньше target находится в интервале [i, m-1]\n            j = m - 1\n        }\n    }\n    // Вернуть точку вставки i\n    return i\n}\n</code></pre> binary_search_insertion.swift<pre><code>/* Бинарный поиск точки вставки (с повторяющимися элементами) */\nfunc binarySearchInsertion(nums: [Int], target: Int) -&gt; Int {\n    // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    var i = nums.startIndex\n    var j = nums.endIndex - 1\n    while i &lt;= j {\n        let m = i + (j - i) / 2 // Вычислить индекс середины m\n        if nums[m] &lt; target {\n            i = m + 1 // target находится в интервале [m+1, j]\n        } else if nums[m] &gt; target {\n            j = m - 1 // target находится в интервале [i, m-1]\n        } else {\n            j = m - 1 // Первый элемент меньше target находится в интервале [i, m-1]\n        }\n    }\n    // Вернуть точку вставки i\n    return i\n}\n</code></pre> binary_search_insertion.js<pre><code>/* Бинарный поиск точки вставки (с повторяющимися элементами) */\nfunction binarySearchInsertion(nums, target) {\n    let i = 0,\n        j = nums.length - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        const m = Math.floor(i + (j - i) / 2); // Вычислить индекс середины m, используя Math.floor() для округления вниз\n        if (nums[m] &lt; target) {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            j = m - 1; // Первый элемент меньше target находится в интервале [i, m-1]\n        }\n    }\n    // Вернуть точку вставки i\n    return i;\n}\n</code></pre> binary_search_insertion.ts<pre><code>/* Бинарный поиск точки вставки (с повторяющимися элементами) */\nfunction binarySearchInsertion(nums: Array&lt;number&gt;, target: number): number {\n    let i = 0,\n        j = nums.length - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        const m = Math.floor(i + (j - i) / 2); // Вычислить индекс середины m, используя Math.floor() для округления вниз\n        if (nums[m] &lt; target) {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            j = m - 1; // Первый элемент меньше target находится в интервале [i, m-1]\n        }\n    }\n    // Вернуть точку вставки i\n    return i;\n}\n</code></pre> binary_search_insertion.dart<pre><code>/* Бинарный поиск точки вставки (с повторяющимися элементами) */\nint binarySearchInsertion(List&lt;int&gt; nums, int target) {\n  int i = 0, j = nums.length - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n  while (i &lt;= j) {\n    int m = i + (j - i) ~/ 2; // Вычислить индекс середины m\n    if (nums[m] &lt; target) {\n      i = m + 1; // target находится в интервале [m+1, j]\n    } else if (nums[m] &gt; target) {\n      j = m - 1; // target находится в интервале [i, m-1]\n    } else {\n      j = m - 1; // Первый элемент меньше target находится в интервале [i, m-1]\n    }\n  }\n  // Вернуть точку вставки i\n  return i;\n}\n</code></pre> binary_search_insertion.rs<pre><code>/* Бинарный поиск точки вставки (с повторяющимися элементами) */\npub fn binary_search_insertion(nums: &amp;[i32], target: i32) -&gt; i32 {\n    let (mut i, mut j) = (0, nums.len() as i32 - 1); // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while i &lt;= j {\n        let m = i + (j - i) / 2; // Вычислить индекс середины m\n        if nums[m as usize] &lt; target {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if nums[m as usize] &gt; target {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            j = m - 1; // Первый элемент меньше target находится в интервале [i, m-1]\n        }\n    }\n    // Вернуть точку вставки i\n    i\n}\n</code></pre> binary_search_insertion.c<pre><code>/* Бинарный поиск точки вставки (с повторяющимися элементами) */\nint binarySearchInsertion(int *nums, int numSize, int target) {\n    int i = 0, j = numSize - 1; // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // Вычислить индекс середины m\n        if (nums[m] &lt; target) {\n            i = m + 1; // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target находится в интервале [i, m-1]\n        } else {\n            j = m - 1; // Первый элемент меньше target находится в интервале [i, m-1]\n        }\n    }\n    // Вернуть точку вставки i\n    return i;\n}\n</code></pre> binary_search_insertion.kt<pre><code>/* Бинарный поиск точки вставки (с повторяющимися элементами) */\nfun binarySearchInsertion(nums: IntArray, target: Int): Int {\n    var i = 0\n    var j = nums.size - 1 // Инициализировать двусторонне замкнутый интервал [0, n-1]\n    while (i &lt;= j) {\n        val m = i + (j - i) / 2 // Вычислить индекс середины m\n        if (nums[m] &lt; target) {\n            i = m + 1 // target находится в интервале [m+1, j]\n        } else if (nums[m] &gt; target) {\n            j = m - 1 // target находится в интервале [i, m-1]\n        } else {\n            j = m - 1 // Первый элемент меньше target находится в интервале [i, m-1]\n        }\n    }\n    // Вернуть точку вставки i\n    return i\n}\n</code></pre> binary_search_insertion.rb<pre><code>### Бинарный поиск точки вставки (с повторяющимися элементами) ###\ndef binary_search_insertion(nums, target)\n  # Инициализировать двусторонне замкнутый интервал [0, n-1]\n  i, j = 0, nums.length - 1\n\n  while i &lt;= j\n    # Вычислить индекс середины m\n    m = (i + j) / 2\n\n    if nums[m] &lt; target\n      i = m + 1 # target находится в интервале [m+1, j]\n    elsif nums[m] &gt; target\n      j = m - 1 # target находится в интервале [i, m-1]\n    else\n      j = m - 1 # Первый элемент меньше target находится в интервале [i, m-1]\n    end\n  end\n\n  i # Вернуть точку вставки i\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Tip</p> <p>Код в этом разделе записан в стиле \"двойного замкнутого интервала\". При желании можно самостоятельно реализовать вариант \"слева закрыт, справа открыт\".</p> <p>Если смотреть в целом, суть двоичного поиска сводится к тому, что для указателей \\(i\\) и \\(j\\) заранее задаются ориентиры поиска; целью может быть конкретный элемент, например <code>target</code> , а может быть и диапазон элементов, например все элементы, меньшие <code>target</code> .</p> <p>В ходе непрерывного двоичного деления указатели \\(i\\) и \\(j\\) постепенно приближаются к заранее заданной цели. В конце они либо успешно находят ответ, либо останавливаются после выхода за границы.</p>","path":["Глава 10. Поиск","10.2 &nbsp; Двоичный поиск точки вставки"],"tags":[]},{"location":"chapter_searching/replace_linear_by_hashing/","level":1,"title":"10.4   Стратегии оптимизации хеширования","text":"<p>В алгоритмических задачах мы часто заменяем линейный поиск на хеш-поиск, чтобы уменьшить временную сложность алгоритма. Разберем одну задачу, чтобы лучше понять этот прием.</p> <p>Question</p> <p>Дан массив целых чисел <code>nums</code> и целевой элемент <code>target</code> . Найдите в массиве два элемента, сумма которых равна <code>target</code> , и верните их индексы. Подойдет любой корректный ответ.</p>","path":["Глава 10. Поиск","10.4 &nbsp; Стратегии оптимизации хеширования"],"tags":[]},{"location":"chapter_searching/replace_linear_by_hashing/#1041","level":2,"title":"10.4.1   Линейный поиск: обмен времени на пространство","text":"<p>Рассмотрим прямой перебор всех возможных комбинаций. Как показано на рисунке 10-9, мы запускаем два вложенных цикла и на каждом шаге проверяем, равна ли сумма двух целых чисел <code>target</code> ; если да, то возвращаем их индексы.</p> <p></p> <p> Рисунок 10-9   Линейный поиск для задачи о двух суммах </p> <p>Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby two_sum.py<pre><code>def two_sum_brute_force(nums: list[int], target: int) -&gt; list[int]:\n    \"\"\"Метод 1: полный перебор\"\"\"\n    # Два вложенных цикла, временная сложность O(n^2)\n    for i in range(len(nums) - 1):\n        for j in range(i + 1, len(nums)):\n            if nums[i] + nums[j] == target:\n                return [i, j]\n    return []\n</code></pre> two_sum.cpp<pre><code>/* Метод 1: полный перебор */\nvector&lt;int&gt; twoSumBruteForce(vector&lt;int&gt; &amp;nums, int target) {\n    int size = nums.size();\n    // Два вложенных цикла, временная сложность O(n^2)\n    for (int i = 0; i &lt; size - 1; i++) {\n        for (int j = i + 1; j &lt; size; j++) {\n            if (nums[i] + nums[j] == target)\n                return {i, j};\n        }\n    }\n    return {};\n}\n</code></pre> two_sum.java<pre><code>/* Метод 1: полный перебор */\nint[] twoSumBruteForce(int[] nums, int target) {\n    int size = nums.length;\n    // Два вложенных цикла, временная сложность O(n^2)\n    for (int i = 0; i &lt; size - 1; i++) {\n        for (int j = i + 1; j &lt; size; j++) {\n            if (nums[i] + nums[j] == target)\n                return new int[] { i, j };\n        }\n    }\n    return new int[0];\n}\n</code></pre> two_sum.cs<pre><code>/* Метод 1: полный перебор */\nint[] TwoSumBruteForce(int[] nums, int target) {\n    int size = nums.Length;\n    // Два вложенных цикла, временная сложность O(n^2)\n    for (int i = 0; i &lt; size - 1; i++) {\n        for (int j = i + 1; j &lt; size; j++) {\n            if (nums[i] + nums[j] == target)\n                return [i, j];\n        }\n    }\n    return [];\n}\n</code></pre> two_sum.go<pre><code>/* Метод 1: полный перебор */\nfunc twoSumBruteForce(nums []int, target int) []int {\n    size := len(nums)\n    // Два вложенных цикла, временная сложность O(n^2)\n    for i := 0; i &lt; size-1; i++ {\n        for j := i + 1; j &lt; size; j++ {\n            if nums[i]+nums[j] == target {\n                return []int{i, j}\n            }\n        }\n    }\n    return nil\n}\n</code></pre> two_sum.swift<pre><code>/* Метод 1: полный перебор */\nfunc twoSumBruteForce(nums: [Int], target: Int) -&gt; [Int] {\n    // Два вложенных цикла, временная сложность O(n^2)\n    for i in nums.indices.dropLast() {\n        for j in nums.indices.dropFirst(i + 1) {\n            if nums[i] + nums[j] == target {\n                return [i, j]\n            }\n        }\n    }\n    return [0]\n}\n</code></pre> two_sum.js<pre><code>/* Метод 1: полный перебор */\nfunction twoSumBruteForce(nums, target) {\n    const n = nums.length;\n    // Два вложенных цикла, временная сложность O(n^2)\n    for (let i = 0; i &lt; n; i++) {\n        for (let j = i + 1; j &lt; n; j++) {\n            if (nums[i] + nums[j] === target) {\n                return [i, j];\n            }\n        }\n    }\n    return [];\n}\n</code></pre> two_sum.ts<pre><code>/* Метод 1: полный перебор */\nfunction twoSumBruteForce(nums: number[], target: number): number[] {\n    const n = nums.length;\n    // Два вложенных цикла, временная сложность O(n^2)\n    for (let i = 0; i &lt; n; i++) {\n        for (let j = i + 1; j &lt; n; j++) {\n            if (nums[i] + nums[j] === target) {\n                return [i, j];\n            }\n        }\n    }\n    return [];\n}\n</code></pre> two_sum.dart<pre><code>/* Способ 1: полный перебор */\nList&lt;int&gt; twoSumBruteForce(List&lt;int&gt; nums, int target) {\n  int size = nums.length;\n  // Два вложенных цикла, временная сложность O(n^2)\n  for (var i = 0; i &lt; size - 1; i++) {\n    for (var j = i + 1; j &lt; size; j++) {\n      if (nums[i] + nums[j] == target) return [i, j];\n    }\n  }\n  return [0];\n}\n</code></pre> two_sum.rs<pre><code>/* Метод 1: полный перебор */\npub fn two_sum_brute_force(nums: &amp;Vec&lt;i32&gt;, target: i32) -&gt; Option&lt;Vec&lt;i32&gt;&gt; {\n    let size = nums.len();\n    // Два вложенных цикла, временная сложность O(n^2)\n    for i in 0..size - 1 {\n        for j in i + 1..size {\n            if nums[i] + nums[j] == target {\n                return Some(vec![i as i32, j as i32]);\n            }\n        }\n    }\n    None\n}\n</code></pre> two_sum.c<pre><code>/* Метод 1: полный перебор */\nint *twoSumBruteForce(int *nums, int numsSize, int target, int *returnSize) {\n    for (int i = 0; i &lt; numsSize; ++i) {\n        for (int j = i + 1; j &lt; numsSize; ++j) {\n            if (nums[i] + nums[j] == target) {\n                int *res = malloc(sizeof(int) * 2);\n                res[0] = i, res[1] = j;\n                *returnSize = 2;\n                return res;\n            }\n        }\n    }\n    *returnSize = 0;\n    return NULL;\n}\n</code></pre> two_sum.kt<pre><code>/* Метод 1: полный перебор */\nfun twoSumBruteForce(nums: IntArray, target: Int): IntArray {\n    val size = nums.size\n    // Два вложенных цикла, временная сложность O(n^2)\n    for (i in 0..&lt;size - 1) {\n        for (j in i + 1..&lt;size) {\n            if (nums[i] + nums[j] == target) return intArrayOf(i, j)\n        }\n    }\n    return IntArray(0)\n}\n</code></pre> two_sum.rb<pre><code>### Метод 1: полный перебор ###\ndef two_sum_brute_force(nums, target)\n  # Два вложенных цикла, временная сложность O(n^2)\n  for i in 0...(nums.length - 1)\n    for j in (i + 1)...nums.length\n      return [i, j] if nums[i] + nums[j] == target\n    end\n  end\n\n  []\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Временная сложность этого метода равна \\(O(n^2)\\) , а пространственная сложность равна \\(O(1)\\) , поэтому на больших объемах данных он очень медленный.</p>","path":["Глава 10. Поиск","10.4 &nbsp; Стратегии оптимизации хеширования"],"tags":[]},{"location":"chapter_searching/replace_linear_by_hashing/#1042-","level":2,"title":"10.4.2   Хеш-поиск: обмен пространства на время","text":"<p>Рассмотрим вариант с использованием хеш-таблицы, где ключами и значениями будут элементы массива и их индексы. При циклическом обходе массива на каждом шаге выполняются действия, показанные на рисунке 10-10.</p> <ol> <li>Проверить, находится ли число <code>target - nums[i]</code> в хеш-таблице; если да, то сразу вернуть индексы этих двух элементов.</li> <li>Добавить в хеш-таблицу пару из ключа <code>nums[i]</code> и индекса <code>i</code> .</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt; <p></p> <p></p> <p></p> <p> Рисунок 10-10   Вспомогательная хеш-таблица для задачи о двух суммах </p> <p>Код реализации показан ниже, и для него достаточно одного цикла:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby two_sum.py<pre><code>def two_sum_hash_table(nums: list[int], target: int) -&gt; list[int]:\n    \"\"\"Метод 2: вспомогательная хеш-таблица\"\"\"\n    # Вспомогательная хеш-таблица, пространственная сложность O(n)\n    dic = {}\n    # Один цикл, временная сложность O(n)\n    for i in range(len(nums)):\n        if target - nums[i] in dic:\n            return [dic[target - nums[i]], i]\n        dic[nums[i]] = i\n    return []\n</code></pre> two_sum.cpp<pre><code>/* Метод 2: вспомогательная хеш-таблица */\nvector&lt;int&gt; twoSumHashTable(vector&lt;int&gt; &amp;nums, int target) {\n    int size = nums.size();\n    // Вспомогательная хеш-таблица, пространственная сложность O(n)\n    unordered_map&lt;int, int&gt; dic;\n    // Один цикл, временная сложность O(n)\n    for (int i = 0; i &lt; size; i++) {\n        if (dic.find(target - nums[i]) != dic.end()) {\n            return {dic[target - nums[i]], i};\n        }\n        dic.emplace(nums[i], i);\n    }\n    return {};\n}\n</code></pre> two_sum.java<pre><code>/* Метод 2: вспомогательная хеш-таблица */\nint[] twoSumHashTable(int[] nums, int target) {\n    int size = nums.length;\n    // Вспомогательная хеш-таблица, пространственная сложность O(n)\n    Map&lt;Integer, Integer&gt; dic = new HashMap&lt;&gt;();\n    // Один цикл, временная сложность O(n)\n    for (int i = 0; i &lt; size; i++) {\n        if (dic.containsKey(target - nums[i])) {\n            return new int[] { dic.get(target - nums[i]), i };\n        }\n        dic.put(nums[i], i);\n    }\n    return new int[0];\n}\n</code></pre> two_sum.cs<pre><code>/* Метод 2: вспомогательная хеш-таблица */\nint[] TwoSumHashTable(int[] nums, int target) {\n    int size = nums.Length;\n    // Вспомогательная хеш-таблица, пространственная сложность O(n)\n    Dictionary&lt;int, int&gt; dic = [];\n    // Один цикл, временная сложность O(n)\n    for (int i = 0; i &lt; size; i++) {\n        if (dic.ContainsKey(target - nums[i])) {\n            return [dic[target - nums[i]], i];\n        }\n        dic.Add(nums[i], i);\n    }\n    return [];\n}\n</code></pre> two_sum.go<pre><code>/* Метод 2: вспомогательная хеш-таблица */\nfunc twoSumHashTable(nums []int, target int) []int {\n    // Вспомогательная хеш-таблица, пространственная сложность O(n)\n    hashTable := map[int]int{}\n    // Один цикл, временная сложность O(n)\n    for idx, val := range nums {\n        if preIdx, ok := hashTable[target-val]; ok {\n            return []int{preIdx, idx}\n        }\n        hashTable[val] = idx\n    }\n    return nil\n}\n</code></pre> two_sum.swift<pre><code>/* Метод 2: вспомогательная хеш-таблица */\nfunc twoSumHashTable(nums: [Int], target: Int) -&gt; [Int] {\n    // Вспомогательная хеш-таблица, пространственная сложность O(n)\n    var dic: [Int: Int] = [:]\n    // Один цикл, временная сложность O(n)\n    for i in nums.indices {\n        if let j = dic[target - nums[i]] {\n            return [j, i]\n        }\n        dic[nums[i]] = i\n    }\n    return [0]\n}\n</code></pre> two_sum.js<pre><code>/* Метод 2: вспомогательная хеш-таблица */\nfunction twoSumHashTable(nums, target) {\n    // Вспомогательная хеш-таблица, пространственная сложность O(n)\n    let m = {};\n    // Один цикл, временная сложность O(n)\n    for (let i = 0; i &lt; nums.length; i++) {\n        if (m[target - nums[i]] !== undefined) {\n            return [m[target - nums[i]], i];\n        } else {\n            m[nums[i]] = i;\n        }\n    }\n    return [];\n}\n</code></pre> two_sum.ts<pre><code>/* Метод 2: вспомогательная хеш-таблица */\nfunction twoSumHashTable(nums: number[], target: number): number[] {\n    // Вспомогательная хеш-таблица, пространственная сложность O(n)\n    let m: Map&lt;number, number&gt; = new Map();\n    // Один цикл, временная сложность O(n)\n    for (let i = 0; i &lt; nums.length; i++) {\n        let index = m.get(target - nums[i]);\n        if (index !== undefined) {\n            return [index, i];\n        } else {\n            m.set(nums[i], i);\n        }\n    }\n    return [];\n}\n</code></pre> two_sum.dart<pre><code>/* Способ 2: вспомогательная хеш-таблица */\nList&lt;int&gt; twoSumHashTable(List&lt;int&gt; nums, int target) {\n  int size = nums.length;\n  // Вспомогательная хеш-таблица, пространственная сложность O(n)\n  Map&lt;int, int&gt; dic = HashMap();\n  // Один цикл, временная сложность O(n)\n  for (var i = 0; i &lt; size; i++) {\n    if (dic.containsKey(target - nums[i])) {\n      return [dic[target - nums[i]]!, i];\n    }\n    dic.putIfAbsent(nums[i], () =&gt; i);\n  }\n  return [0];\n}\n</code></pre> two_sum.rs<pre><code>/* Метод 2: вспомогательная хеш-таблица */\npub fn two_sum_hash_table(nums: &amp;Vec&lt;i32&gt;, target: i32) -&gt; Option&lt;Vec&lt;i32&gt;&gt; {\n    // Вспомогательная хеш-таблица, пространственная сложность O(n)\n    let mut dic = HashMap::new();\n    // Один цикл, временная сложность O(n)\n    for (i, num) in nums.iter().enumerate() {\n        match dic.get(&amp;(target - num)) {\n            Some(v) =&gt; return Some(vec![*v as i32, i as i32]),\n            None =&gt; dic.insert(num, i as i32),\n        };\n    }\n    None\n}\n</code></pre> two_sum.c<pre><code>/* Хеш-таблица */\ntypedef struct {\n    int key;\n    int val;\n    UT_hash_handle hh; // Реализовано на основе uthash.h\n} HashTable;\n\n/* Поиск в хеш-таблице */\nHashTable *find(HashTable *h, int key) {\n    HashTable *tmp;\n    HASH_FIND_INT(h, &amp;key, tmp);\n    return tmp;\n}\n\n/* Вставка элемента в хеш-таблицу */\nvoid insert(HashTable **h, int key, int val) {\n    HashTable *t = find(*h, key);\n    if (t == NULL) {\n        HashTable *tmp = malloc(sizeof(HashTable));\n        tmp-&gt;key = key, tmp-&gt;val = val;\n        HASH_ADD_INT(*h, key, tmp);\n    } else {\n        t-&gt;val = val;\n    }\n}\n\n/* Метод 2: вспомогательная хеш-таблица */\nint *twoSumHashTable(int *nums, int numsSize, int target, int *returnSize) {\n    HashTable *hashtable = NULL;\n    for (int i = 0; i &lt; numsSize; i++) {\n        HashTable *t = find(hashtable, target - nums[i]);\n        if (t != NULL) {\n            int *res = malloc(sizeof(int) * 2);\n            res[0] = t-&gt;val, res[1] = i;\n            *returnSize = 2;\n            return res;\n        }\n        insert(&amp;hashtable, nums[i], i);\n    }\n    *returnSize = 0;\n    return NULL;\n}\n</code></pre> two_sum.kt<pre><code>/* Метод 2: вспомогательная хеш-таблица */\nfun twoSumHashTable(nums: IntArray, target: Int): IntArray {\n    val size = nums.size\n    // Вспомогательная хеш-таблица, пространственная сложность O(n)\n    val dic = HashMap&lt;Int, Int&gt;()\n    // Один цикл, временная сложность O(n)\n    for (i in 0..&lt;size) {\n        if (dic.containsKey(target - nums[i])) {\n            return intArrayOf(dic[target - nums[i]]!!, i)\n        }\n        dic[nums[i]] = i\n    }\n    return IntArray(0)\n}\n</code></pre> two_sum.rb<pre><code>### Метод 2: вспомогательная хеш-таблица ###\ndef two_sum_hash_table(nums, target)\n  # Вспомогательная хеш-таблица, пространственная сложность O(n)\n  dic = {}\n  # Один цикл, временная сложность O(n)\n  for i in 0...nums.length\n    return [dic[target - nums[i]], i] if dic.has_key?(target - nums[i])\n\n    dic[nums[i]] = i\n  end\n\n  []\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Благодаря хеш-поиску этот метод снижает временную сложность с \\(O(n^2)\\) до \\(O(n)\\) , существенно повышая эффективность работы.</p> <p>Поскольку требуется поддерживать дополнительную хеш-таблицу, пространственная сложность составляет \\(O(n)\\) . Несмотря на это, в целом данный метод лучше сбалансирован по времени и памяти, поэтому именно он является оптимальным решением этой задачи.</p>","path":["Глава 10. Поиск","10.4 &nbsp; Стратегии оптимизации хеширования"],"tags":[]},{"location":"chapter_searching/searching_algorithm_revisited/","level":1,"title":"10.5   Переосмысление алгоритмов поиска","text":"<p>Алгоритмы поиска (searching algorithm) используются для того, чтобы находить один или несколько элементов, удовлетворяющих определенным условиям, в структурах данных, таких как массивы, списки, деревья или графы.</p> <p>Алгоритмы поиска можно разделить на две категории по способу реализации.</p> <ul> <li>Поиск целевого элемента путем обхода структуры данных, например обход массива, списка, дерева или графа.</li> <li>Эффективный поиск элементов с использованием структуры организации данных или априорной информации, например двоичный поиск, хеш-поиск и поиск в двоичном дереве поиска.</li> </ul> <p>Нетрудно заметить, что эти темы уже рассматривались в предыдущих главах, поэтому алгоритмы поиска нам уже знакомы. В этом разделе мы систематизируем полученные ранее знания и еще раз посмотрим на них как на единую группу методов.</p>","path":["Глава 10. Поиск","10.5 &nbsp; Переосмысление алгоритмов поиска"],"tags":[]},{"location":"chapter_searching/searching_algorithm_revisited/#1051","level":2,"title":"10.5.1   Полный перебор","text":"<p>Полный перебор заключается в том, что мы обходим каждый элемент структуры данных, чтобы найти целевой элемент.</p> <ul> <li>\"Линейный поиск\" применяется к линейным структурам данных, таким как массивы и списки. Он начинается с одного конца структуры данных и последовательно проверяет элементы, пока не найдет целевой элемент или пока не достигнет другого конца структуры данных.</li> <li>\"Обход в ширину\" и \"обход в глубину\" - это две стратегии обхода графов и деревьев. Обход в ширину стартует из начального узла и исследует все узлы текущего уровня, прежде чем переходить к следующему. Обход в глубину стартует из начального узла, проходит один путь до конца, затем возвращается назад и пробует другие пути, пока не будет полностью пройдена вся структура данных.</li> </ul> <p>Преимущество полного перебора состоит в его простоте и универсальности, поскольку он не требует предварительной обработки данных и использования дополнительных структур данных.</p> <p>Однако временная сложность таких алгоритмов равна \\(O(n)\\) , где \\(n\\) - число элементов, поэтому при больших объемах данных их производительность невысока.</p>","path":["Глава 10. Поиск","10.5 &nbsp; Переосмысление алгоритмов поиска"],"tags":[]},{"location":"chapter_searching/searching_algorithm_revisited/#1052","level":2,"title":"10.5.2   Адаптивный поиск","text":"<p>Адаптивный поиск использует специфические свойства данных (например, упорядоченность), чтобы оптимизировать процесс поиска и тем самым эффективнее находить целевой элемент.</p> <ul> <li>\"Двоичный поиск\" использует упорядоченность данных для эффективного поиска и применим только к массивам.</li> <li>\"Хеш-поиск\" использует хеш-таблицу для построения отображения между поисковыми данными и целевыми данными, благодаря чему запросы выполняются эффективно.</li> <li>\"Поиск в дереве\" ведется в конкретной древовидной структуре (например, в двоичном дереве поиска) и позволяет быстро отсекать узлы на основе сравнения значений, чтобы найти цель.</li> </ul> <p>Преимущество этих алгоритмов заключается в высокой эффективности: их временная сложность может достигать \\(O(\\log n)\\) и даже \\(O(1)\\) .</p> <p>Однако для использования таких алгоритмов обычно требуется предварительная обработка данных. Например, для двоичного поиска нужно заранее отсортировать массив, а хеш-поиск и поиск в дереве требуют дополнительных структур данных, поддержание которых тоже отнимает время и память.</p> <p>Tip</p> <p>Адаптивные алгоритмы поиска часто называют алгоритмами поиска в узком смысле, поскольку они в основном предназначены для быстрого нахождения целевого элемента в конкретной структуре данных.</p>","path":["Глава 10. Поиск","10.5 &nbsp; Переосмысление алгоритмов поиска"],"tags":[]},{"location":"chapter_searching/searching_algorithm_revisited/#1053","level":2,"title":"10.5.3   Выбор метода поиска","text":"<p>Для поиска целевого элемента в наборе данных размера \\(n\\) можно использовать линейный поиск, двоичный поиск, поиск в дереве, хеш-поиск и другие методы. Принципы работы этих методов показаны на рисунке 10-11.</p> <p></p> <p> Рисунок 10-11   Различные стратегии поиска </p> <p>Эффективность и особенности перечисленных методов приведены в таблице 10-1.</p> <p> Таблица 10-1   Сравнение эффективности алгоритмов поиска </p> Линейный поиск Двоичный поиск Поиск в дереве Хеш-поиск Поиск элемента \\(O(n)\\) \\(O(\\log n)\\) \\(O(\\log n)\\) \\(O(1)\\) Вставка элемента \\(O(1)\\) \\(O(n)\\) \\(O(\\log n)\\) \\(O(1)\\) Удаление элемента \\(O(n)\\) \\(O(n)\\) \\(O(\\log n)\\) \\(O(1)\\) Дополнительное пространство \\(O(1)\\) \\(O(1)\\) \\(O(n)\\) \\(O(n)\\) Предварительная обработка / Сортировка \\(O(n \\log n)\\) Построение дерева \\(O(n \\log n)\\) Построение хеш-таблицы \\(O(n)\\) Упорядоченность данных Не требуется Требуется Требуется Не требуется <p>Выбор алгоритма поиска также зависит от масштаба данных, требований к производительности поиска, а также частоты запросов и обновлений данных.</p> <p>Линейный поиск</p> <ul> <li>Обладает хорошей универсальностью и не требует никакой предварительной обработки данных. Если нужно выполнить только один запрос, то время предварительной обработки для остальных трех методов окажется больше, чем время линейного поиска.</li> <li>Подходит для небольших объемов данных, потому что в этом случае влияние временной сложности на эффективность невелико.</li> <li>Подходит для сценариев с высокой частотой обновления данных, поскольку этот метод не требует никакого дополнительного обслуживания данных.</li> </ul> <p>Двоичный поиск</p> <ul> <li>Подходит для больших наборов данных и демонстрирует стабильную эффективность; его худшая временная сложность равна \\(O(\\log n)\\) .</li> <li>Объем данных не должен быть слишком большим, потому что массив требует непрерывного участка памяти.</li> <li>Не подходит для сценариев с частыми вставками и удалениями данных, так как поддержание массива в отсортированном виде требует больших затрат.</li> </ul> <p>Хеш-поиск</p> <ul> <li>Подходит для сценариев, в которых требования к скорости запросов очень высоки; средняя временная сложность равна \\(O(1)\\) .</li> <li>Не подходит для сценариев, где требуется упорядоченность данных или поиск по диапазону, потому что хеш-таблица не умеет поддерживать порядок данных.</li> <li>Сильно зависит от хеш-функции и стратегии обработки коллизий, поэтому риск деградации производительности сравнительно велик.</li> <li>Не подходит для слишком больших объемов данных, так как хеш-таблице требуется дополнительное пространство, чтобы максимально снизить число коллизий и обеспечить хорошую производительность поиска.</li> </ul> <p>Поиск в дереве</p> <ul> <li>Подходит для очень больших объемов данных, потому что узлы дерева распределены в памяти и не требуют непрерывного хранения.</li> <li>Подходит для сценариев, где нужно поддерживать упорядоченные данные или выполнять поиск по диапазону.</li> <li>В процессе постоянных вставок и удалений узлов двоичное дерево поиска может перекоситься, и тогда временная сложность деградирует до \\(O(n)\\) .</li> <li>Если использовать AVL-дерево или красно-черное дерево, то все операции могут стабильно выполняться за \\(O(\\log n)\\) , но поддержание баланса дерева увеличивает дополнительные накладные расходы.</li> </ul>","path":["Глава 10. Поиск","10.5 &nbsp; Переосмысление алгоритмов поиска"],"tags":[]},{"location":"chapter_searching/summary/","level":1,"title":"10.6   Резюме","text":"","path":["Глава 10. Поиск","10.6 &nbsp; Резюме"],"tags":[]},{"location":"chapter_searching/summary/#1","level":3,"title":"1.   Ключевые выводы","text":"<ul> <li>Двоичный поиск опирается на упорядоченность данных и выполняет поиск путем циклического сокращения интервала вдвое. Он требует упорядоченных входных данных и подходит только для массивов или структур данных, реализованных на их основе.</li> <li>Полный перебор находит данные путем обхода структуры данных. Линейный поиск подходит для массивов и списков, а обход в ширину и обход в глубину подходят для графов и деревьев. Эти алгоритмы универсальны и не требуют предварительной обработки данных, но их временная сложность \\(O(n)\\) сравнительно велика.</li> <li>Хеш-поиск, поиск в дереве и двоичный поиск относятся к эффективным методам поиска и позволяют быстро находить целевой элемент в конкретных структурах данных. Такие алгоритмы обладают высокой эффективностью, их временная сложность может достигать \\(O(\\log n)\\) и даже \\(O(1)\\) , но обычно им нужны дополнительные структуры данных.</li> <li>На практике нужно анализировать размер данных, требования к производительности поиска, а также частоту запросов и обновлений данных, чтобы выбрать подходящий метод поиска.</li> <li>Линейный поиск подходит для небольших или часто обновляемых наборов данных; двоичный поиск - для больших отсортированных данных; хеш-поиск - для сценариев с высокими требованиями к скорости запросов и без необходимости поиска по диапазону; поиск в дереве - для больших динамических данных, где нужно поддерживать порядок и выполнять диапазонные запросы.</li> <li>Замена линейного поиска на хеш-поиск - это распространенная стратегия ускорения, которая позволяет снизить временную сложность с \\(O(n)\\) до \\(O(1)\\) .</li> </ul>","path":["Глава 10. Поиск","10.6 &nbsp; Резюме"],"tags":[]},{"location":"chapter_sorting/","level":1,"title":"Глава 11.   Сортировка","text":"<p>Abstract</p> <p>Сортировка упорядочивает хаотичные данные и позволяет быстрее находить закономерности.</p> <p>За кажущейся простотой скрывается целая группа алгоритмов с разными достоинствами и ограничениями.</p>","path":["Глава 11. Сортировка","Глава 11. &nbsp; Сортировка"],"tags":[]},{"location":"chapter_sorting/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>11.1   Алгоритмы сортировки</li> <li>11.2   Сортировка выбором</li> <li>11.3   Сортировка пузырьком</li> <li>11.4   Сортировка вставками</li> <li>11.5   Быстрая сортировка</li> <li>11.6   Сортировка слиянием</li> <li>11.7   Пирамидальная сортировка</li> <li>11.8   Блочная сортировка</li> <li>11.9   Сортировка подсчетом</li> <li>11.10   Поразрядная сортировка</li> <li>11.11   Резюме</li> </ul>","path":["Глава 11. Сортировка","Глава 11. &nbsp; Сортировка"],"tags":[]},{"location":"chapter_sorting/bubble_sort/","level":1,"title":"11.3   Сортировка пузырьком","text":"<p>Сортировка пузырьком (bubble sort) реализует сортировку путем последовательного сравнения и обмена соседних элементов. Этот процесс напоминает всплытие пузырьков снизу вверх, откуда и произошло название алгоритма.</p> <p>Как показано на рисунке 11-4, процесс \"всплытия\" можно смоделировать через операцию обмена элементов: начиная от левого края массива и двигаясь вправо, мы последовательно сравниваем соседние элементы и, если \"левый элемент &gt; правый элемент\", меняем их местами. После завершения прохода максимальный элемент будет перемещен в самый правый конец массива.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 11-4   Моделирование пузырька через обмен элементов </p>","path":["Глава 11. Сортировка","11.3 &nbsp; Сортировка пузырьком"],"tags":[]},{"location":"chapter_sorting/bubble_sort/#1131","level":2,"title":"11.3.1   Алгоритм","text":"<p>Пусть длина массива равна \\(n\\) ; тогда шаги сортировки пузырьком показаны на рисунке 11-5.</p> <ol> <li>Сначала выполнить один проход \"всплытия\" по \\(n\\) элементам, переместив максимальный элемент массива на правильную позицию.</li> <li>Затем выполнить \"всплытие\" по оставшимся \\(n - 1\\) элементам, переместив второй по величине элемент на правильную позицию.</li> <li>Продолжать по аналогии; после \\(n - 1\\) раундов \"всплытия\" первые \\(n - 1\\) по величине элементы окажутся на правильных позициях.</li> <li>Оставшийся единственный элемент обязательно является минимальным, сортировать его уже не нужно, поэтому сортировка завершена.</li> </ol> <p></p> <p> Рисунок 11-5   Процесс сортировки пузырьком </p> <p>Пример кода:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby bubble_sort.py<pre><code>def bubble_sort(nums: list[int]):\n    \"\"\"Пузырьковая сортировка\"\"\"\n    n = len(nums)\n    # Внешний цикл: неотсортированный диапазон [0, i]\n    for i in range(n - 1, 0, -1):\n        # Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for j in range(i):\n            if nums[j] &gt; nums[j + 1]:\n                # Поменять местами nums[j] и nums[j + 1]\n                nums[j], nums[j + 1] = nums[j + 1], nums[j]\n</code></pre> bubble_sort.cpp<pre><code>/* Пузырьковая сортировка */\nvoid bubbleSort(vector&lt;int&gt; &amp;nums) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (int i = nums.size() - 1; i &gt; 0; i--) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                // Здесь используется функция std::swap()\n                swap(nums[j], nums[j + 1]);\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.java<pre><code>/* Пузырьковая сортировка */\nvoid bubbleSort(int[] nums) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (int i = nums.length - 1; i &gt; 0; i--) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                int tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.cs<pre><code>/* Пузырьковая сортировка */\nvoid BubbleSort(int[] nums) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (int i = nums.Length - 1; i &gt; 0; i--) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                (nums[j + 1], nums[j]) = (nums[j], nums[j + 1]);\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.go<pre><code>/* Пузырьковая сортировка */\nfunc bubbleSort(nums []int) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for i := len(nums) - 1; i &gt; 0; i-- {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for j := 0; j &lt; i; j++ {\n            if nums[j] &gt; nums[j+1] {\n                // Поменять местами nums[j] и nums[j + 1]\n                nums[j], nums[j+1] = nums[j+1], nums[j]\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.swift<pre><code>/* Пузырьковая сортировка */\nfunc bubbleSort(nums: inout [Int]) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for i in nums.indices.dropFirst().reversed() {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for j in 0 ..&lt; i {\n            if nums[j] &gt; nums[j + 1] {\n                // Поменять местами nums[j] и nums[j + 1]\n                nums.swapAt(j, j + 1)\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.js<pre><code>/* Пузырьковая сортировка */\nfunction bubbleSort(nums) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (let i = nums.length - 1; i &gt; 0; i--) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (let j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                let tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.ts<pre><code>/* Пузырьковая сортировка */\nfunction bubbleSort(nums: number[]): void {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (let i = nums.length - 1; i &gt; 0; i--) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (let j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                let tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.dart<pre><code>/* Пузырьковая сортировка */\nvoid bubbleSort(List&lt;int&gt; nums) {\n  // Внешний цикл: неотсортированный диапазон [0, i]\n  for (int i = nums.length - 1; i &gt; 0; i--) {\n    // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n    for (int j = 0; j &lt; i; j++) {\n      if (nums[j] &gt; nums[j + 1]) {\n        // Поменять местами nums[j] и nums[j + 1]\n        int tmp = nums[j];\n        nums[j] = nums[j + 1];\n        nums[j + 1] = tmp;\n      }\n    }\n  }\n}\n</code></pre> bubble_sort.rs<pre><code>/* Пузырьковая сортировка */\nfn bubble_sort(nums: &amp;mut [i32]) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for i in (1..nums.len()).rev() {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for j in 0..i {\n            if nums[j] &gt; nums[j + 1] {\n                // Поменять местами nums[j] и nums[j + 1]\n                nums.swap(j, j + 1);\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.c<pre><code>/* Пузырьковая сортировка */\nvoid bubbleSort(int nums[], int size) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (int i = size - 1; i &gt; 0; i--) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                int temp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = temp;\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.kt<pre><code>/* Пузырьковая сортировка */\nfun bubbleSort(nums: IntArray) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (i in nums.size - 1 downTo 1) {\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (j in 0..&lt;i) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                val temp = nums[j]\n                nums[j] = nums[j + 1]\n                nums[j + 1] = temp\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.rb<pre><code>### Пузырьковая сортировка ###\ndef bubble_sort(nums)\n  n = nums.length\n  # Внешний цикл: неотсортированный диапазон [0, i]\n  for i in (n - 1).downto(1)\n    # Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n    for j in 0...i\n      if nums[j] &gt; nums[j + 1]\n        # Поменять местами nums[j] и nums[j + 1]\n        nums[j], nums[j + 1] = nums[j + 1], nums[j]\n      end\n    end\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 11. Сортировка","11.3 &nbsp; Сортировка пузырьком"],"tags":[]},{"location":"chapter_sorting/bubble_sort/#1132","level":2,"title":"11.3.2   Оптимизация эффективности","text":"<p>Если в каком-либо раунде \"всплытия\" не произошло ни одного обмена, значит, массив уже отсортирован и можно сразу вернуть результат. Поэтому можно добавить флаг <code>flag</code> для отслеживания этой ситуации и немедленного выхода.</p> <p>После такой оптимизации худшая и средняя временные сложности сортировки пузырьком по-прежнему равны \\(O(n^2)\\) ; однако если входной массив уже полностью упорядочен, достигается лучшая временная сложность \\(O(n)\\) .</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby bubble_sort.py<pre><code>def bubble_sort_with_flag(nums: list[int]):\n    \"\"\"Пузырьковая сортировка (оптимизация флагом)\"\"\"\n    n = len(nums)\n    # Внешний цикл: неотсортированный диапазон [0, i]\n    for i in range(n - 1, 0, -1):\n        flag = False  # Инициализировать флаг\n        # Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for j in range(i):\n            if nums[j] &gt; nums[j + 1]:\n                # Поменять местами nums[j] и nums[j + 1]\n                nums[j], nums[j + 1] = nums[j + 1], nums[j]\n                flag = True  # Записать обмен элементов\n        if not flag:\n            break  # На этой итерации «всплытия» не было ни одного обмена, сразу выйти\n</code></pre> bubble_sort.cpp<pre><code>/* Пузырьковая сортировка (оптимизация флагом) */\nvoid bubbleSortWithFlag(vector&lt;int&gt; &amp;nums) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (int i = nums.size() - 1; i &gt; 0; i--) {\n        bool flag = false; // Инициализировать флаг\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                // Здесь используется функция std::swap()\n                swap(nums[j], nums[j + 1]);\n                flag = true; // Записать обмен элементов\n            }\n        }\n        if (!flag)\n            break; // На этой итерации «всплытия» не было ни одного обмена, сразу выйти\n    }\n}\n</code></pre> bubble_sort.java<pre><code>/* Пузырьковая сортировка (оптимизация флагом) */\nvoid bubbleSortWithFlag(int[] nums) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (int i = nums.length - 1; i &gt; 0; i--) {\n        boolean flag = false; // Инициализировать флаг\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                int tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                flag = true; // Записать обмен элементов\n            }\n        }\n        if (!flag)\n            break; // На этой итерации «всплытия» не было ни одного обмена, сразу выйти\n    }\n}\n</code></pre> bubble_sort.cs<pre><code>/* Пузырьковая сортировка (оптимизация флагом) */\nvoid BubbleSortWithFlag(int[] nums) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (int i = nums.Length - 1; i &gt; 0; i--) {\n        bool flag = false; // Инициализировать флаг\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                (nums[j + 1], nums[j]) = (nums[j], nums[j + 1]);\n                flag = true;  // Записать обмен элементов\n            }\n        }\n        if (!flag) break;     // На этой итерации «всплытия» не было ни одного обмена, сразу выйти\n    }\n}\n</code></pre> bubble_sort.go<pre><code>/* Пузырьковая сортировка (оптимизация флагом) */\nfunc bubbleSortWithFlag(nums []int) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for i := len(nums) - 1; i &gt; 0; i-- {\n        flag := false // Инициализировать флаг\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for j := 0; j &lt; i; j++ {\n            if nums[j] &gt; nums[j+1] {\n                // Поменять местами nums[j] и nums[j + 1]\n                nums[j], nums[j+1] = nums[j+1], nums[j]\n                flag = true // Записать обмен элементов\n            }\n        }\n        if flag == false { // На этой итерации «всплытия» не было ни одного обмена, сразу выйти\n            break\n        }\n    }\n}\n</code></pre> bubble_sort.swift<pre><code>/* Пузырьковая сортировка (оптимизация флагом) */\nfunc bubbleSortWithFlag(nums: inout [Int]) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for i in nums.indices.dropFirst().reversed() {\n        var flag = false // Инициализировать флаг\n        for j in 0 ..&lt; i {\n            if nums[j] &gt; nums[j + 1] {\n                // Поменять местами nums[j] и nums[j + 1]\n                nums.swapAt(j, j + 1)\n                flag = true // Записать обмен элементов\n            }\n        }\n        if !flag { // На этой итерации «всплытия» не было ни одного обмена, сразу выйти\n            break\n        }\n    }\n}\n</code></pre> bubble_sort.js<pre><code>/* Пузырьковая сортировка (оптимизация флагом) */\nfunction bubbleSortWithFlag(nums) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (let i = nums.length - 1; i &gt; 0; i--) {\n        let flag = false; // Инициализировать флаг\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (let j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                let tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                flag = true; // Записать обмен элементов\n            }\n        }\n        if (!flag) break; // На этой итерации «всплытия» не было ни одного обмена, сразу выйти\n    }\n}\n</code></pre> bubble_sort.ts<pre><code>/* Пузырьковая сортировка (оптимизация флагом) */\nfunction bubbleSortWithFlag(nums: number[]): void {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (let i = nums.length - 1; i &gt; 0; i--) {\n        let flag = false; // Инициализировать флаг\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (let j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                let tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                flag = true; // Записать обмен элементов\n            }\n        }\n        if (!flag) break; // На этой итерации «всплытия» не было ни одного обмена, сразу выйти\n    }\n}\n</code></pre> bubble_sort.dart<pre><code>/* Пузырьковая сортировка (оптимизация флагом) */\nvoid bubbleSortWithFlag(List&lt;int&gt; nums) {\n  // Внешний цикл: неотсортированный диапазон [0, i]\n  for (int i = nums.length - 1; i &gt; 0; i--) {\n    bool flag = false; // Инициализировать флаг\n    // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n    for (int j = 0; j &lt; i; j++) {\n      if (nums[j] &gt; nums[j + 1]) {\n        // Поменять местами nums[j] и nums[j + 1]\n        int tmp = nums[j];\n        nums[j] = nums[j + 1];\n        nums[j + 1] = tmp;\n        flag = true; // Записать обмен элементов\n      }\n    }\n    if (!flag) break; // На этой итерации «всплытия» не было ни одного обмена, сразу выйти\n  }\n}\n</code></pre> bubble_sort.rs<pre><code>/* Пузырьковая сортировка (оптимизация флагом) */\nfn bubble_sort_with_flag(nums: &amp;mut [i32]) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for i in (1..nums.len()).rev() {\n        let mut flag = false; // Инициализировать флаг\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for j in 0..i {\n            if nums[j] &gt; nums[j + 1] {\n                // Поменять местами nums[j] и nums[j + 1]\n                nums.swap(j, j + 1);\n                flag = true; // Записать обмен элементов\n            }\n        }\n        if !flag {\n            break; // На этой итерации «всплытия» не было ни одного обмена, сразу выйти\n        };\n    }\n}\n</code></pre> bubble_sort.c<pre><code>/* Пузырьковая сортировка (оптимизация флагом) */\nvoid bubbleSortWithFlag(int nums[], int size) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (int i = size - 1; i &gt; 0; i--) {\n        bool flag = false;\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                int temp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = temp;\n                flag = true;\n            }\n        }\n        if (!flag)\n            break;\n    }\n}\n</code></pre> bubble_sort.kt<pre><code>/* Пузырьковая сортировка (оптимизация флагом) */\nfun bubbleSortWithFlag(nums: IntArray) {\n    // Внешний цикл: неотсортированный диапазон [0, i]\n    for (i in nums.size - 1 downTo 1) {\n        var flag = false // Инициализировать флаг\n        // Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n        for (j in 0..&lt;i) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // Поменять местами nums[j] и nums[j + 1]\n                val temp = nums[j]\n                nums[j] = nums[j + 1]\n                nums[j + 1] = temp\n                flag = true // Записать обмен элементов\n            }\n        }\n        if (!flag) break // На этой итерации «всплытия» не было ни одного обмена, сразу выйти\n    }\n}\n</code></pre> bubble_sort.rb<pre><code>### Пузырьковая сортировка ###\ndef bubble_sort(nums)\n  n = nums.length\n  # Внешний цикл: неотсортированный диапазон [0, i]\n  for i in (n - 1).downto(1)\n    # Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n    for j in 0...i\n      if nums[j] &gt; nums[j + 1]\n        # Поменять местами nums[j] и nums[j + 1]\n        nums[j], nums[j + 1] = nums[j + 1], nums[j]\n      end\n    end\n  end\nend\n\n# ## Пузырьковая сортировка (оптимизация флагом) ###\ndef bubble_sort_with_flag(nums)\n  n = nums.length\n  # Внешний цикл: неотсортированный диапазон [0, i]\n  for i in (n - 1).downto(1)\n    flag = false # Инициализировать флаг\n\n    # Внутренний цикл: переместить максимальный элемент неотсортированного диапазона [0, i] в его правый конец\n    for j in 0...i\n      if nums[j] &gt; nums[j + 1]\n        # Поменять местами nums[j] и nums[j + 1]\n        nums[j], nums[j + 1] = nums[j + 1], nums[j]\n        flag = true # Записать обмен элементов\n      end\n    end\n\n    break unless flag # На этой итерации «всплытия» не было ни одного обмена, сразу выйти\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 11. Сортировка","11.3 &nbsp; Сортировка пузырьком"],"tags":[]},{"location":"chapter_sorting/bubble_sort/#1133","level":2,"title":"11.3.3   Характеристики алгоритма","text":"<ul> <li>Временная сложность равна \\(O(n^2)\\), алгоритм адаптивен: длины диапазонов, проходящих \"всплытие\" в разных раундах, последовательно равны \\(n - 1\\), \\(n - 2\\), \\(\\dots\\), \\(2\\), \\(1\\) , а их сумма равна \\((n - 1) n / 2\\) . После добавления оптимизации с <code>flag</code> лучшая временная сложность может достигать \\(O(n)\\) .</li> <li>Пространственная сложность равна \\(O(1)\\), сортировка выполняется на месте: указатели \\(i\\) и \\(j\\) используют константный объем дополнительной памяти.</li> <li>Стабильная сортировка: поскольку при \"всплытии\" равные элементы не обмениваются местами.</li> </ul>","path":["Глава 11. Сортировка","11.3 &nbsp; Сортировка пузырьком"],"tags":[]},{"location":"chapter_sorting/bucket_sort/","level":1,"title":"11.8   Блочная сортировка","text":"<p>Рассмотренные выше алгоритмы сортировки относятся к \"сортировкам на основе сравнений\": они упорядочивают данные, сравнивая элементы друг с другом. Временная сложность таких алгоритмов не может быть лучше \\(O(n \\log n)\\) . Далее мы рассмотрим несколько \"сортировок без сравнений\", чья временная сложность может достигать линейного порядка.</p> <p>Блочная сортировка (bucket sort) является типичным применением стратегии \"разделяй и властвуй\". Она создает набор упорядоченных по величине блоков, где каждый блок соответствует определенному диапазону данных; затем элементы равномерно распределяются по этим блокам, внутри каждого блока отдельно выполняется сортировка, а в конце результаты объединяются в порядке блоков.</p>","path":["Глава 11. Сортировка","11.8 &nbsp; Блочная сортировка"],"tags":[]},{"location":"chapter_sorting/bucket_sort/#1181","level":2,"title":"11.8.1   Алгоритм","text":"<p>Рассмотрим массив длины \\(n\\), элементы которого являются числами с плавающей запятой из диапазона \\([0, 1)\\) . Процесс блочной сортировки показан на рисунке 11-13.</p> <ol> <li>Инициализировать \\(k\\) блоков и распределить \\(n\\) элементов по этим \\(k\\) блокам.</li> <li>Отсортировать каждый блок по отдельности (здесь используется встроенная функция сортировки языка программирования).</li> <li>Объединить результаты в порядке следования блоков от меньшего к большему.</li> </ol> <p></p> <p> Рисунок 11-13   Процесс блочной сортировки </p> <p>Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby bucket_sort.py<pre><code>def bucket_sort(nums: list[float]):\n    \"\"\"Сортировка корзинами\"\"\"\n    # Инициализировать k = n/2 корзин, предполагая распределение 2 элементов в каждую корзину\n    k = len(nums) // 2\n    buckets = [[] for _ in range(k)]\n    # 1. Распределить элементы массива по корзинам\n    for num in nums:\n        # Входные данные лежат в диапазоне [0, 1); использовать num * k для отображения в диапазон индексов [0, k-1]\n        i = int(num * k)\n        # Добавить num в корзину i\n        buckets[i].append(num)\n    # 2. Выполнить сортировку внутри каждой корзины\n    for bucket in buckets:\n        # Использовать встроенную функцию сортировки; ее также можно заменить другим алгоритмом сортировки\n        bucket.sort()\n    # 3. Обойти корзины и объединить результаты\n    i = 0\n    for bucket in buckets:\n        for num in bucket:\n            nums[i] = num\n            i += 1\n</code></pre> bucket_sort.cpp<pre><code>/* Сортировка корзинами */\nvoid bucketSort(vector&lt;float&gt; &amp;nums) {\n    // Инициализировать k = n/2 корзин, предполагая распределение 2 элементов в каждую корзину\n    int k = nums.size() / 2;\n    vector&lt;vector&lt;float&gt;&gt; buckets(k);\n    // 1. Распределить элементы массива по корзинам\n    for (float num : nums) {\n        // Входные данные лежат в диапазоне [0, 1); использовать num * k для отображения в диапазон индексов [0, k-1]\n        int i = num * k;\n        // Добавить num в корзину bucket_idx\n        buckets[i].push_back(num);\n    }\n    // 2. Выполнить сортировку внутри каждой корзины\n    for (vector&lt;float&gt; &amp;bucket : buckets) {\n        // Использовать встроенную функцию сортировки; ее также можно заменить другим алгоритмом сортировки\n        sort(bucket.begin(), bucket.end());\n    }\n    // 3. Обойти корзины и объединить результаты\n    int i = 0;\n    for (vector&lt;float&gt; &amp;bucket : buckets) {\n        for (float num : bucket) {\n            nums[i++] = num;\n        }\n    }\n}\n</code></pre> bucket_sort.java<pre><code>/* Сортировка корзинами */\nvoid bucketSort(float[] nums) {\n    // Инициализировать k = n/2 корзин, предполагая распределение 2 элементов в каждую корзину\n    int k = nums.length / 2;\n    List&lt;List&lt;Float&gt;&gt; buckets = new ArrayList&lt;&gt;();\n    for (int i = 0; i &lt; k; i++) {\n        buckets.add(new ArrayList&lt;&gt;());\n    }\n    // 1. Распределить элементы массива по корзинам\n    for (float num : nums) {\n        // Входные данные лежат в диапазоне [0, 1); использовать num * k для отображения в диапазон индексов [0, k-1]\n        int i = (int) (num * k);\n        // Добавить num в корзину i\n        buckets.get(i).add(num);\n    }\n    // 2. Выполнить сортировку внутри каждой корзины\n    for (List&lt;Float&gt; bucket : buckets) {\n        // Использовать встроенную функцию сортировки; ее также можно заменить другим алгоритмом сортировки\n        Collections.sort(bucket);\n    }\n    // 3. Обойти корзины и объединить результаты\n    int i = 0;\n    for (List&lt;Float&gt; bucket : buckets) {\n        for (float num : bucket) {\n            nums[i++] = num;\n        }\n    }\n}\n</code></pre> bucket_sort.cs<pre><code>/* Сортировка корзинами */\nvoid BucketSort(float[] nums) {\n    // Инициализировать k = n/2 корзин, предполагая распределение 2 элементов в каждую корзину\n    int k = nums.Length / 2;\n    List&lt;List&lt;float&gt;&gt; buckets = [];\n    for (int i = 0; i &lt; k; i++) {\n        buckets.Add([]);\n    }\n    // 1. Распределить элементы массива по корзинам\n    foreach (float num in nums) {\n        // Входные данные лежат в диапазоне [0, 1); использовать num * k для отображения в диапазон индексов [0, k-1]\n        int i = (int)(num * k);\n        // Добавить num в корзину i\n        buckets[i].Add(num);\n    }\n    // 2. Выполнить сортировку внутри каждой корзины\n    foreach (List&lt;float&gt; bucket in buckets) {\n        // Использовать встроенную функцию сортировки; ее также можно заменить другим алгоритмом сортировки\n        bucket.Sort();\n    }\n    // 3. Обойти корзины и объединить результаты\n    int j = 0;\n    foreach (List&lt;float&gt; bucket in buckets) {\n        foreach (float num in bucket) {\n            nums[j++] = num;\n        }\n    }\n}\n</code></pre> bucket_sort.go<pre><code>/* Сортировка корзинами */\nfunc bucketSort(nums []float64) {\n    // Инициализировать k = n/2 корзин, предполагая распределение 2 элементов в каждую корзину\n    k := len(nums) / 2\n    buckets := make([][]float64, k)\n    for i := 0; i &lt; k; i++ {\n        buckets[i] = make([]float64, 0)\n    }\n    // 1. Распределить элементы массива по корзинам\n    for _, num := range nums {\n        // Входные данные лежат в диапазоне [0, 1); использовать num * k для отображения в диапазон индексов [0, k-1]\n        i := int(num * float64(k))\n        // Добавить num в корзину i\n        buckets[i] = append(buckets[i], num)\n    }\n    // 2. Выполнить сортировку внутри каждой корзины\n    for i := 0; i &lt; k; i++ {\n        // Использовать встроенную функцию сортировки среза; ее также можно заменить другим алгоритмом сортировки\n        sort.Float64s(buckets[i])\n    }\n    // 3. Обойти корзины и объединить результаты\n    i := 0\n    for _, bucket := range buckets {\n        for _, num := range bucket {\n            nums[i] = num\n            i++\n        }\n    }\n}\n</code></pre> bucket_sort.swift<pre><code>/* Сортировка корзинами */\nfunc bucketSort(nums: inout [Double]) {\n    // Инициализировать k = n/2 корзин, предполагая распределение 2 элементов в каждую корзину\n    let k = nums.count / 2\n    var buckets = (0 ..&lt; k).map { _ in [Double]() }\n    // 1. Распределить элементы массива по корзинам\n    for num in nums {\n        // Входные данные лежат в диапазоне [0, 1); использовать num * k для отображения в диапазон индексов [0, k-1]\n        let i = Int(num * Double(k))\n        // Добавить num в корзину i\n        buckets[i].append(num)\n    }\n    // 2. Выполнить сортировку внутри каждой корзины\n    for i in buckets.indices {\n        // Использовать встроенную функцию сортировки; ее также можно заменить другим алгоритмом сортировки\n        buckets[i].sort()\n    }\n    // 3. Обойти корзины и объединить результаты\n    var i = nums.startIndex\n    for bucket in buckets {\n        for num in bucket {\n            nums[i] = num\n            i += 1\n        }\n    }\n}\n</code></pre> bucket_sort.js<pre><code>/* Сортировка корзинами */\nfunction bucketSort(nums) {\n    // Инициализировать k = n/2 корзин, предполагая распределение 2 элементов в каждую корзину\n    const k = nums.length / 2;\n    const buckets = [];\n    for (let i = 0; i &lt; k; i++) {\n        buckets.push([]);\n    }\n    // 1. Распределить элементы массива по корзинам\n    for (const num of nums) {\n        // Входные данные лежат в диапазоне [0, 1); использовать num * k для отображения в диапазон индексов [0, k-1]\n        const i = Math.floor(num * k);\n        // Добавить num в корзину i\n        buckets[i].push(num);\n    }\n    // 2. Выполнить сортировку внутри каждой корзины\n    for (const bucket of buckets) {\n        // Использовать встроенную функцию сортировки; ее также можно заменить другим алгоритмом сортировки\n        bucket.sort((a, b) =&gt; a - b);\n    }\n    // 3. Обойти корзины и объединить результаты\n    let i = 0;\n    for (const bucket of buckets) {\n        for (const num of bucket) {\n            nums[i++] = num;\n        }\n    }\n}\n</code></pre> bucket_sort.ts<pre><code>/* Сортировка корзинами */\nfunction bucketSort(nums: number[]): void {\n    // Инициализировать k = n/2 корзин, предполагая распределение 2 элементов в каждую корзину\n    const k = nums.length / 2;\n    const buckets: number[][] = [];\n    for (let i = 0; i &lt; k; i++) {\n        buckets.push([]);\n    }\n    // 1. Распределить элементы массива по корзинам\n    for (const num of nums) {\n        // Входные данные лежат в диапазоне [0, 1); использовать num * k для отображения в диапазон индексов [0, k-1]\n        const i = Math.floor(num * k);\n        // Добавить num в корзину i\n        buckets[i].push(num);\n    }\n    // 2. Выполнить сортировку внутри каждой корзины\n    for (const bucket of buckets) {\n        // Использовать встроенную функцию сортировки; ее также можно заменить другим алгоритмом сортировки\n        bucket.sort((a, b) =&gt; a - b);\n    }\n    // 3. Обойти корзины и объединить результаты\n    let i = 0;\n    for (const bucket of buckets) {\n        for (const num of bucket) {\n            nums[i++] = num;\n        }\n    }\n}\n</code></pre> bucket_sort.dart<pre><code>/* Сортировка корзинами */\nvoid bucketSort(List&lt;double&gt; nums) {\n  // Инициализировать k = n/2 корзин, предполагая распределение 2 элементов в каждую корзину\n  int k = nums.length ~/ 2;\n  List&lt;List&lt;double&gt;&gt; buckets = List.generate(k, (index) =&gt; []);\n\n  // 1. Распределить элементы массива по корзинам\n  for (double _num in nums) {\n    // Входные данные находятся в диапазоне [0, 1), используем _num * k для отображения в диапазон индексов [0, k-1]\n    int i = (_num * k).toInt();\n    // Добавить _num в корзину bucket_idx\n    buckets[i].add(_num);\n  }\n  // 2. Выполнить сортировку внутри каждой корзины\n  for (List&lt;double&gt; bucket in buckets) {\n    bucket.sort();\n  }\n  // 3. Обойти корзины и объединить результаты\n  int i = 0;\n  for (List&lt;double&gt; bucket in buckets) {\n    for (double _num in bucket) {\n      nums[i++] = _num;\n    }\n  }\n}\n</code></pre> bucket_sort.rs<pre><code>/* Сортировка корзинами */\nfn bucket_sort(nums: &amp;mut [f64]) {\n    // Инициализировать k = n/2 корзин, предполагая распределение 2 элементов в каждую корзину\n    let k = nums.len() / 2;\n    let mut buckets = vec![vec![]; k];\n    // 1. Распределить элементы массива по корзинам\n    for &amp;num in nums.iter() {\n        // Входные данные лежат в диапазоне [0, 1); использовать num * k для отображения в диапазон индексов [0, k-1]\n        let i = (num * k as f64) as usize;\n        // Добавить num в корзину i\n        buckets[i].push(num);\n    }\n    // 2. Выполнить сортировку внутри каждой корзины\n    for bucket in &amp;mut buckets {\n        // Использовать встроенную функцию сортировки; ее также можно заменить другим алгоритмом сортировки\n        bucket.sort_by(|a, b| a.partial_cmp(b).unwrap());\n    }\n    // 3. Обойти корзины и объединить результаты\n    let mut i = 0;\n    for bucket in buckets.iter() {\n        for &amp;num in bucket.iter() {\n            nums[i] = num;\n            i += 1;\n        }\n    }\n}\n</code></pre> bucket_sort.c<pre><code>/* Сортировка корзинами */\nvoid bucketSort(float nums[], int n) {\n    int k = n / 2;                                 // Инициализировать k = n/2 корзин\n    int *sizes = malloc(k * sizeof(int));          // Записать размер каждой корзины\n    float **buckets = malloc(k * sizeof(float *)); // Массив динамических массивов (корзины)\n    // Предварительно выделить достаточно места для каждой корзины\n    for (int i = 0; i &lt; k; ++i) {\n        buckets[i] = (float *)malloc(n * sizeof(float));\n        sizes[i] = 0;\n    }\n    // 1. Распределить элементы массива по корзинам\n    for (int i = 0; i &lt; n; ++i) {\n        int idx = (int)(nums[i] * k);\n        buckets[idx][sizes[idx]++] = nums[i];\n    }\n    // 2. Выполнить сортировку внутри каждой корзины\n    for (int i = 0; i &lt; k; ++i) {\n        qsort(buckets[i], sizes[i], sizeof(float), compare);\n    }\n    // 3. Объединить отсортированные корзины\n    int idx = 0;\n    for (int i = 0; i &lt; k; ++i) {\n        for (int j = 0; j &lt; sizes[i]; ++j) {\n            nums[idx++] = buckets[i][j];\n        }\n        // Освободить память\n        free(buckets[i]);\n    }\n}\n</code></pre> bucket_sort.kt<pre><code>/* Сортировка корзинами */\nfun bucketSort(nums: FloatArray) {\n    // Инициализировать k = n/2 корзин, предполагая распределение 2 элементов в каждую корзину\n    val k = nums.size / 2\n    val buckets = mutableListOf&lt;MutableList&lt;Float&gt;&gt;()\n    for (i in 0..&lt;k) {\n        buckets.add(mutableListOf())\n    }\n    // 1. Распределить элементы массива по корзинам\n    for (num in nums) {\n        // Входные данные лежат в диапазоне [0, 1); использовать num * k для отображения в диапазон индексов [0, k-1]\n        val i = (num * k).toInt()\n        // Добавить num в корзину i\n        buckets[i].add(num)\n    }\n    // 2. Выполнить сортировку внутри каждой корзины\n    for (bucket in buckets) {\n        // Использовать встроенную функцию сортировки; ее также можно заменить другим алгоритмом сортировки\n        bucket.sort()\n    }\n    // 3. Обойти корзины и объединить результаты\n    var i = 0\n    for (bucket in buckets) {\n        for (num in bucket) {\n            nums[i++] = num\n        }\n    }\n}\n</code></pre> bucket_sort.rb<pre><code>### Сортировка корзинами ###\ndef bucket_sort(nums)\n  # Инициализировать k = n/2 корзин, предполагая распределение 2 элементов в каждую корзину\n  k = nums.length / 2\n  buckets = Array.new(k) { [] }\n\n  # 1. Распределить элементы массива по корзинам\n  nums.each do |num|\n    # Входные данные лежат в диапазоне [0, 1); использовать num * k для отображения в диапазон индексов [0, k-1]\n    i = (num * k).to_i\n    # Добавить num в корзину i\n    buckets[i] &lt;&lt; num\n  end\n\n  # 2. Выполнить сортировку внутри каждой корзины\n  buckets.each do |bucket|\n    # Использовать встроенную функцию сортировки; ее также можно заменить другим алгоритмом сортировки\n    bucket.sort!\n  end\n\n  # 3. Обойти корзины и объединить результаты\n  i = 0\n  buckets.each do |bucket|\n    bucket.each do |num|\n      nums[i] = num\n      i += 1\n    end\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 11. Сортировка","11.8 &nbsp; Блочная сортировка"],"tags":[]},{"location":"chapter_sorting/bucket_sort/#1182","level":2,"title":"11.8.2   Характеристики алгоритма","text":"<p>Блочная сортировка подходит для обработки очень больших объемов данных. Например, если вход содержит 1 миллион элементов и из-за ограничений памяти система не может загрузить их все сразу, можно разбить данные на 1000 блоков, отсортировать каждый блок отдельно, а затем объединить результаты.</p> <ul> <li>Временная сложность равна \\(O(n + k)\\) : если элементы распределены по блокам равномерно, то в каждом блоке будет \\(\\frac{n}{k}\\) элементов. Если сортировка одного блока требует \\(O(\\frac{n}{k} \\log\\frac{n}{k})\\) времени, то сортировка всех блоков потребует \\(O(n \\log\\frac{n}{k})\\) времени. Когда число блоков \\(k\\) достаточно велико, временная сложность приближается к \\(O(n)\\) . На объединение результатов требуется \\(O(n + k)\\) времени, потому что нужно пройти по всем блокам и элементам. В худшем случае все данные попадут в один блок, и если сортировка этого блока использует \\(O(n^2)\\) времени, общая сложность также станет \\(O(n^2)\\) .</li> <li>Пространственная сложность равна \\(O(n + k)\\), сортировка не выполняется на месте: требуются дополнительные блоки в количестве \\(k\\) и место для всех \\(n\\) элементов внутри них.</li> <li>Является ли блочная сортировка стабильной, зависит от того, стабилен ли алгоритм сортировки внутри каждого блока.</li> </ul>","path":["Глава 11. Сортировка","11.8 &nbsp; Блочная сортировка"],"tags":[]},{"location":"chapter_sorting/bucket_sort/#1183","level":2,"title":"11.8.3   Как добиться равномерного распределения","text":"<p>Теоретически временная сложность блочной сортировки может достигать \\(O(n)\\) ; ключ к этому - как можно более равномерно распределить элементы по блокам. На практике данные часто распределены неравномерно. Например, если нужно распределить все товары на маркетплейсе по 10 ценовым блокам, количество товаров дешевле 100 рублей может быть очень большим, а товаров дороже 1000 рублей - очень маленьким. Если просто разбить диапазон цен на 10 равных частей, число товаров в каждом блоке будет сильно различаться.</p> <p>Чтобы добиться более равномерного распределения, можно сначала задать грубую линию раздела и приблизительно распределить данные по 3 блокам. После этого блоки с большим числом товаров можно снова делить на 3 блока и продолжать процесс до тех пор, пока число элементов в каждом блоке не станет примерно одинаковым.</p> <p>Как показано на рисунке 11-14, по сути этот метод строит рекурсивное дерево, цель которого - сделать значения в листьях как можно более равномерными. Конечно, совсем не обязательно каждый раз делить данные именно на 3 блока; конкретную схему разбиения можно выбирать в зависимости от свойств данных.</p> <p></p> <p> Рисунок 11-14   Рекурсивное разбиение по блокам </p> <p>Если нам заранее известна вероятностная модель распределения цен товаров, то границы цен для каждого блока можно задавать в соответствии с этим распределением. Важно отметить, что фактическое распределение данных не обязательно специально измерять - его можно приблизить некоторой вероятностной моделью исходя из свойств данных.</p> <p>Как показано на рисунке 11-15, если предположить, что цены товаров подчиняются нормальному распределению, то можно разумно задать интервалы цен и тем самым распределить товары по блокам достаточно равномерно.</p> <p></p> <p> Рисунок 11-15   Разбиение блоков по вероятностному распределению </p>","path":["Глава 11. Сортировка","11.8 &nbsp; Блочная сортировка"],"tags":[]},{"location":"chapter_sorting/counting_sort/","level":1,"title":"11.9   Сортировка подсчетом","text":"<p>Сортировка подсчетом (counting sort) реализует сортировку за счет подсчета количества вхождений элементов и обычно используется для массивов целых чисел.</p>","path":["Глава 11. Сортировка","11.9 &nbsp; Сортировка подсчетом"],"tags":[]},{"location":"chapter_sorting/counting_sort/#1191","level":2,"title":"11.9.1   Простая реализация","text":"<p>Сначала рассмотрим простой пример. Дан массив <code>nums</code> длины \\(n\\) , элементы которого являются \"неотрицательными целыми числами\". Общий процесс сортировки подсчетом показан на рисунке 11-16.</p> <ol> <li>Пройти по массиву, найти в нем максимальное число, обозначить его как \\(m\\) , а затем создать вспомогательный массив <code>counter</code> длины \\(m + 1\\) .</li> <li>С помощью <code>counter</code> подсчитать, сколько раз каждое число встречается в <code>nums</code>; при этом <code>counter[num]</code> хранит число вхождений значения <code>num</code> . Делается это просто: достаточно пройти по <code>nums</code> (пусть текущее число равно <code>num</code> ) и на каждом шаге увеличить <code>counter[num]</code> на \\(1\\) .</li> <li>Поскольку индексы массива <code>counter</code> изначально упорядочены, можно считать, что все числа уже отсортированы. Далее остается пройти по <code>counter</code> и в соответствии с числом вхождений записать значения обратно в <code>nums</code> в порядке возрастания.</li> </ol> <p></p> <p> Рисунок 11-16   Процесс сортировки подсчетом </p> <p>Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby counting_sort.py<pre><code>def counting_sort_naive(nums: list[int]):\n    \"\"\"Сортировка подсчетом\"\"\"\n    # Простая реализация, не подходит для сортировки объектов\n    # 1. Найти максимальный элемент массива m\n    m = max(nums)\n    # 2. Подсчитать число появлений каждой цифры\n    # counter[num] обозначает число появлений num\n    counter = [0] * (m + 1)\n    for num in nums:\n        counter[num] += 1\n    # 3. Обойти counter и заполнить исходный массив nums элементами\n    i = 0\n    for num in range(m + 1):\n        for _ in range(counter[num]):\n            nums[i] = num\n            i += 1\n</code></pre> counting_sort.cpp<pre><code>/* Сортировка подсчетом */\n// Простая реализация, не подходит для сортировки объектов\nvoid countingSortNaive(vector&lt;int&gt; &amp;nums) {\n    // 1. Найти максимальный элемент массива m\n    int m = 0;\n    for (int num : nums) {\n        m = max(m, num);\n    }\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    vector&lt;int&gt; counter(m + 1, 0);\n    for (int num : nums) {\n        counter[num]++;\n    }\n    // 3. Обойти counter и заполнить исходный массив nums элементами\n    int i = 0;\n    for (int num = 0; num &lt; m + 1; num++) {\n        for (int j = 0; j &lt; counter[num]; j++, i++) {\n            nums[i] = num;\n        }\n    }\n}\n</code></pre> counting_sort.java<pre><code>/* Сортировка подсчетом */\n// Простая реализация, не подходит для сортировки объектов\nvoid countingSortNaive(int[] nums) {\n    // 1. Найти максимальный элемент массива m\n    int m = 0;\n    for (int num : nums) {\n        m = Math.max(m, num);\n    }\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    int[] counter = new int[m + 1];\n    for (int num : nums) {\n        counter[num]++;\n    }\n    // 3. Обойти counter и заполнить исходный массив nums элементами\n    int i = 0;\n    for (int num = 0; num &lt; m + 1; num++) {\n        for (int j = 0; j &lt; counter[num]; j++, i++) {\n            nums[i] = num;\n        }\n    }\n}\n</code></pre> counting_sort.cs<pre><code>/* Сортировка подсчетом */\n// Простая реализация, не подходит для сортировки объектов\nvoid CountingSortNaive(int[] nums) {\n    // 1. Найти максимальный элемент массива m\n    int m = 0;\n    foreach (int num in nums) {\n        m = Math.Max(m, num);\n    }\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    int[] counter = new int[m + 1];\n    foreach (int num in nums) {\n        counter[num]++;\n    }\n    // 3. Обойти counter и заполнить исходный массив nums элементами\n    int i = 0;\n    for (int num = 0; num &lt; m + 1; num++) {\n        for (int j = 0; j &lt; counter[num]; j++, i++) {\n            nums[i] = num;\n        }\n    }\n}\n</code></pre> counting_sort.go<pre><code>/* Сортировка подсчетом */\n// Простая реализация, не подходит для сортировки объектов\nfunc countingSortNaive(nums []int) {\n    // 1. Найти максимальный элемент массива m\n    m := 0\n    for _, num := range nums {\n        if num &gt; m {\n            m = num\n        }\n    }\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    counter := make([]int, m+1)\n    for _, num := range nums {\n        counter[num]++\n    }\n    // 3. Обойти counter и заполнить исходный массив nums элементами\n    for i, num := 0, 0; num &lt; m+1; num++ {\n        for j := 0; j &lt; counter[num]; j++ {\n            nums[i] = num\n            i++\n        }\n    }\n}\n</code></pre> counting_sort.swift<pre><code>/* Сортировка подсчетом */\n// Простая реализация, не подходит для сортировки объектов\nfunc countingSortNaive(nums: inout [Int]) {\n    // 1. Найти максимальный элемент массива m\n    let m = nums.max()!\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    var counter = Array(repeating: 0, count: m + 1)\n    for num in nums {\n        counter[num] += 1\n    }\n    // 3. Обойти counter и заполнить исходный массив nums элементами\n    var i = 0\n    for num in 0 ..&lt; m + 1 {\n        for _ in 0 ..&lt; counter[num] {\n            nums[i] = num\n            i += 1\n        }\n    }\n}\n</code></pre> counting_sort.js<pre><code>/* Сортировка подсчетом */\n// Простая реализация, не подходит для сортировки объектов\nfunction countingSortNaive(nums) {\n    // 1. Найти максимальный элемент массива m\n    let m = Math.max(...nums);\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    const counter = new Array(m + 1).fill(0);\n    for (const num of nums) {\n        counter[num]++;\n    }\n    // 3. Обойти counter и заполнить исходный массив nums элементами\n    let i = 0;\n    for (let num = 0; num &lt; m + 1; num++) {\n        for (let j = 0; j &lt; counter[num]; j++, i++) {\n            nums[i] = num;\n        }\n    }\n}\n</code></pre> counting_sort.ts<pre><code>/* Сортировка подсчетом */\n// Простая реализация, не подходит для сортировки объектов\nfunction countingSortNaive(nums: number[]): void {\n    // 1. Найти максимальный элемент массива m\n    let m: number = Math.max(...nums);\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    const counter: number[] = new Array&lt;number&gt;(m + 1).fill(0);\n    for (const num of nums) {\n        counter[num]++;\n    }\n    // 3. Обойти counter и заполнить исходный массив nums элементами\n    let i = 0;\n    for (let num = 0; num &lt; m + 1; num++) {\n        for (let j = 0; j &lt; counter[num]; j++, i++) {\n            nums[i] = num;\n        }\n    }\n}\n</code></pre> counting_sort.dart<pre><code>/* Сортировка подсчетом */\n// Простая реализация, не подходит для сортировки объектов\nvoid countingSortNaive(List&lt;int&gt; nums) {\n  // 1. Найти максимальный элемент массива m\n  int m = 0;\n  for (int _num in nums) {\n    m = max(m, _num);\n  }\n  // 2. Подсчитать число появлений каждой цифры\n  // counter[_num] обозначает число появлений _num\n  List&lt;int&gt; counter = List.filled(m + 1, 0);\n  for (int _num in nums) {\n    counter[_num]++;\n  }\n  // 3. Обойти counter и заполнить исходный массив nums элементами\n  int i = 0;\n  for (int _num = 0; _num &lt; m + 1; _num++) {\n    for (int j = 0; j &lt; counter[_num]; j++, i++) {\n      nums[i] = _num;\n    }\n  }\n}\n</code></pre> counting_sort.rs<pre><code>/* Сортировка подсчетом */\n// Простая реализация, не подходит для сортировки объектов\nfn counting_sort_naive(nums: &amp;mut [i32]) {\n    // 1. Найти максимальный элемент массива m\n    let m = *nums.iter().max().unwrap();\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    let mut counter = vec![0; m as usize + 1];\n    for &amp;num in nums.iter() {\n        counter[num as usize] += 1;\n    }\n    // 3. Обойти counter и заполнить исходный массив nums элементами\n    let mut i = 0;\n    for num in 0..m + 1 {\n        for _ in 0..counter[num as usize] {\n            nums[i] = num;\n            i += 1;\n        }\n    }\n}\n</code></pre> counting_sort.c<pre><code>/* Сортировка подсчетом */\n// Простая реализация, не подходит для сортировки объектов\nvoid countingSortNaive(int nums[], int size) {\n    // 1. Найти максимальный элемент массива m\n    int m = 0;\n    for (int i = 0; i &lt; size; i++) {\n        if (nums[i] &gt; m) {\n            m = nums[i];\n        }\n    }\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    int *counter = calloc(m + 1, sizeof(int));\n    for (int i = 0; i &lt; size; i++) {\n        counter[nums[i]]++;\n    }\n    // 3. Обойти counter и заполнить исходный массив nums элементами\n    int i = 0;\n    for (int num = 0; num &lt; m + 1; num++) {\n        for (int j = 0; j &lt; counter[num]; j++, i++) {\n            nums[i] = num;\n        }\n    }\n    // 4. Освободить память\n    free(counter);\n}\n</code></pre> counting_sort.kt<pre><code>/* Сортировка подсчетом */\n// Простая реализация, не подходит для сортировки объектов\nfun countingSortNaive(nums: IntArray) {\n    // 1. Найти максимальный элемент массива m\n    var m = 0\n    for (num in nums) {\n        m = max(m, num)\n    }\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    val counter = IntArray(m + 1)\n    for (num in nums) {\n        counter[num]++\n    }\n    // 3. Обойти counter и заполнить исходный массив nums элементами\n    var i = 0\n    for (num in 0..&lt;m + 1) {\n        var j = 0\n        while (j &lt; counter[num]) {\n            nums[i] = num\n            j++\n            i++\n        }\n    }\n}\n</code></pre> counting_sort.rb<pre><code>### Сортировка подсчетом ###\ndef counting_sort_naive(nums)\n  # Простая реализация, не подходит для сортировки объектов\n  # 1. Найти максимальный элемент массива m\n  m = 0\n  nums.each { |num| m = [m, num].max }\n  # 2. Подсчитать число появлений каждой цифры\n  # counter[num] обозначает число появлений num\n  counter = Array.new(m + 1, 0)\n  nums.each { |num| counter[num] += 1 }\n  # 3. Обойти counter и заполнить исходный массив nums элементами\n  i = 0\n  for num in 0...(m + 1)\n    (0...counter[num]).each do\n      nums[i] = num\n      i += 1\n    end\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Связь между сортировкой подсчетом и блочной сортировкой</p> <p>Если посмотреть на сортировку подсчетом с точки зрения блочной сортировки, то каждый индекс массива <code>counter</code> можно рассматривать как отдельный блок, а процесс подсчета - как распределение элементов по соответствующим блокам. Иными словами, сортировка подсчетом является частным случаем блочной сортировки для целочисленных данных.</p>","path":["Глава 11. Сортировка","11.9 &nbsp; Сортировка подсчетом"],"tags":[]},{"location":"chapter_sorting/counting_sort/#1192","level":2,"title":"11.9.2   Полная реализация","text":"<p>Внимательный читатель мог заметить, что если входные данные представлены объектами, то описанный выше шаг <code>3.</code> перестает работать. Например, если входными данными являются объекты товаров и мы хотим отсортировать их по цене (полю класса), то описанный алгоритм сможет выдать только отсортированный ряд цен, но не исходные объекты в нужном порядке.</p> <p>Как же получить корректный порядок исходных данных? Сначала вычислим \"префиксную сумму\" массива <code>counter</code> . Как следует из названия, префиксная сумма в индексе <code>i</code> , обозначаемая как <code>prefix[i]</code> , равна сумме первых <code>i</code> элементов массива:</p> \\[ \\text{prefix}[i] = \\sum_{j=0}^i \\text{counter[j]} \\] <p>Префиксная сумма имеет четкий смысл: <code>prefix[num] - 1</code> обозначает индекс последнего вхождения элемента <code>num</code> в результирующем массиве <code>res</code>. Это очень важная информация, потому что она указывает, в какую позицию результирующего массива должен попасть каждый элемент. Далее мы проходим исходный массив <code>nums</code> в обратном порядке и на каждой итерации для очередного элемента <code>num</code> выполняем два действия.</p> <ol> <li>Записать <code>num</code> в массив <code>res</code> по индексу <code>prefix[num] - 1</code> .</li> <li>Уменьшить префиксную сумму <code>prefix[num]</code> на \\(1\\) , чтобы получить индекс следующего размещения элемента <code>num</code> .</li> </ol> <p>После завершения прохода массив <code>res</code> будет содержать отсортированный результат; остается только переписать <code>res</code> обратно в <code>nums</code> . Полный процесс сортировки подсчетом показан на рисунке 11-17.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 11-17   Шаги сортировки подсчетом </p> <p>Код реализации сортировки подсчетом приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby counting_sort.py<pre><code>def counting_sort(nums: list[int]):\n    \"\"\"Сортировка подсчетом\"\"\"\n    # Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\n    # 1. Найти максимальный элемент массива m\n    m = max(nums)\n    # 2. Подсчитать число появлений каждой цифры\n    # counter[num] обозначает число появлений num\n    counter = [0] * (m + 1)\n    for num in nums:\n        counter[num] += 1\n    # 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n    # То есть counter[num]-1 — это индекс последнего появления num в res\n    for i in range(m):\n        counter[i + 1] += counter[i]\n    # 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n    # Инициализировать массив res для хранения результата\n    n = len(nums)\n    res = [0] * n\n    for i in range(n - 1, -1, -1):\n        num = nums[i]\n        res[counter[num] - 1] = num  # Поместить num по соответствующему индексу\n        counter[num] -= 1  # Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения num\n    # Перезаписать исходный массив nums массивом результата res\n    for i in range(n):\n        nums[i] = res[i]\n</code></pre> counting_sort.cpp<pre><code>/* Сортировка подсчетом */\n// Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\nvoid countingSort(vector&lt;int&gt; &amp;nums) {\n    // 1. Найти максимальный элемент массива m\n    int m = 0;\n    for (int num : nums) {\n        m = max(m, num);\n    }\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    vector&lt;int&gt; counter(m + 1, 0);\n    for (int num : nums) {\n        counter[num]++;\n    }\n    // 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n    // То есть counter[num]-1 — это индекс последнего появления num в res\n    for (int i = 0; i &lt; m; i++) {\n        counter[i + 1] += counter[i];\n    }\n    // 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n    // Инициализировать массив res для хранения результата\n    int n = nums.size();\n    vector&lt;int&gt; res(n);\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int num = nums[i];\n        res[counter[num] - 1] = num; // Поместить num по соответствующему индексу\n        counter[num]--;              // Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения num\n    }\n    // Перезаписать исходный массив nums массивом результата res\n    nums = res;\n}\n</code></pre> counting_sort.java<pre><code>/* Сортировка подсчетом */\n// Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\nvoid countingSort(int[] nums) {\n    // 1. Найти максимальный элемент массива m\n    int m = 0;\n    for (int num : nums) {\n        m = Math.max(m, num);\n    }\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    int[] counter = new int[m + 1];\n    for (int num : nums) {\n        counter[num]++;\n    }\n    // 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n    // То есть counter[num]-1 — это индекс последнего появления num в res\n    for (int i = 0; i &lt; m; i++) {\n        counter[i + 1] += counter[i];\n    }\n    // 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n    // Инициализировать массив res для хранения результата\n    int n = nums.length;\n    int[] res = new int[n];\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int num = nums[i];\n        res[counter[num] - 1] = num; // Поместить num по соответствующему индексу\n        counter[num]--; // Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения num\n    }\n    // Перезаписать исходный массив nums массивом результата res\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = res[i];\n    }\n}\n</code></pre> counting_sort.cs<pre><code>/* Сортировка подсчетом */\n// Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\nvoid CountingSort(int[] nums) {\n    // 1. Найти максимальный элемент массива m\n    int m = 0;\n    foreach (int num in nums) {\n        m = Math.Max(m, num);\n    }\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    int[] counter = new int[m + 1];\n    foreach (int num in nums) {\n        counter[num]++;\n    }\n    // 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n    // То есть counter[num]-1 — это индекс последнего появления num в res\n    for (int i = 0; i &lt; m; i++) {\n        counter[i + 1] += counter[i];\n    }\n    // 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n    // Инициализировать массив res для хранения результата\n    int n = nums.Length;\n    int[] res = new int[n];\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int num = nums[i];\n        res[counter[num] - 1] = num; // Поместить num по соответствующему индексу\n        counter[num]--; // Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения num\n    }\n    // Перезаписать исходный массив nums массивом результата res\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = res[i];\n    }\n}\n</code></pre> counting_sort.go<pre><code>/* Сортировка подсчетом */\n// Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\nfunc countingSort(nums []int) {\n    // 1. Найти максимальный элемент массива m\n    m := 0\n    for _, num := range nums {\n        if num &gt; m {\n            m = num\n        }\n    }\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    counter := make([]int, m+1)\n    for _, num := range nums {\n        counter[num]++\n    }\n    // 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n    // То есть counter[num]-1 — это индекс последнего появления num в res\n    for i := 0; i &lt; m; i++ {\n        counter[i+1] += counter[i]\n    }\n    // 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n    // Инициализировать массив res для хранения результата\n    n := len(nums)\n    res := make([]int, n)\n    for i := n - 1; i &gt;= 0; i-- {\n        num := nums[i]\n        // Поместить num по соответствующему индексу\n        res[counter[num]-1] = num\n        // Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения num\n        counter[num]--\n    }\n    // Перезаписать исходный массив nums массивом результата res\n    copy(nums, res)\n}\n</code></pre> counting_sort.swift<pre><code>/* Сортировка подсчетом */\n// Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\nfunc countingSort(nums: inout [Int]) {\n    // 1. Найти максимальный элемент массива m\n    let m = nums.max()!\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    var counter = Array(repeating: 0, count: m + 1)\n    for num in nums {\n        counter[num] += 1\n    }\n    // 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n    // То есть counter[num]-1 — это индекс последнего появления num в res\n    for i in 0 ..&lt; m {\n        counter[i + 1] += counter[i]\n    }\n    // 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n    // Инициализировать массив res для хранения результата\n    var res = Array(repeating: 0, count: nums.count)\n    for i in nums.indices.reversed() {\n        let num = nums[i]\n        res[counter[num] - 1] = num // Поместить num по соответствующему индексу\n        counter[num] -= 1 // Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения num\n    }\n    // Перезаписать исходный массив nums массивом результата res\n    for i in nums.indices {\n        nums[i] = res[i]\n    }\n}\n</code></pre> counting_sort.js<pre><code>/* Сортировка подсчетом */\n// Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\nfunction countingSort(nums) {\n    // 1. Найти максимальный элемент массива m\n    let m = Math.max(...nums);\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    const counter = new Array(m + 1).fill(0);\n    for (const num of nums) {\n        counter[num]++;\n    }\n    // 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n    // То есть counter[num]-1 — это индекс последнего появления num в res\n    for (let i = 0; i &lt; m; i++) {\n        counter[i + 1] += counter[i];\n    }\n    // 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n    // Инициализировать массив res для хранения результата\n    const n = nums.length;\n    const res = new Array(n);\n    for (let i = n - 1; i &gt;= 0; i--) {\n        const num = nums[i];\n        res[counter[num] - 1] = num; // Поместить num по соответствующему индексу\n        counter[num]--; // Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения num\n    }\n    // Перезаписать исходный массив nums массивом результата res\n    for (let i = 0; i &lt; n; i++) {\n        nums[i] = res[i];\n    }\n}\n</code></pre> counting_sort.ts<pre><code>/* Сортировка подсчетом */\n// Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\nfunction countingSort(nums: number[]): void {\n    // 1. Найти максимальный элемент массива m\n    let m: number = Math.max(...nums);\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    const counter: number[] = new Array&lt;number&gt;(m + 1).fill(0);\n    for (const num of nums) {\n        counter[num]++;\n    }\n    // 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n    // То есть counter[num]-1 — это индекс последнего появления num в res\n    for (let i = 0; i &lt; m; i++) {\n        counter[i + 1] += counter[i];\n    }\n    // 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n    // Инициализировать массив res для хранения результата\n    const n = nums.length;\n    const res: number[] = new Array&lt;number&gt;(n);\n    for (let i = n - 1; i &gt;= 0; i--) {\n        const num = nums[i];\n        res[counter[num] - 1] = num; // Поместить num по соответствующему индексу\n        counter[num]--; // Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения num\n    }\n    // Перезаписать исходный массив nums массивом результата res\n    for (let i = 0; i &lt; n; i++) {\n        nums[i] = res[i];\n    }\n}\n</code></pre> counting_sort.dart<pre><code>/* Сортировка подсчетом */\n// Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\nvoid countingSort(List&lt;int&gt; nums) {\n  // 1. Найти максимальный элемент массива m\n  int m = 0;\n  for (int _num in nums) {\n    m = max(m, _num);\n  }\n  // 2. Подсчитать число появлений каждой цифры\n  // counter[_num] обозначает число появлений _num\n  List&lt;int&gt; counter = List.filled(m + 1, 0);\n  for (int _num in nums) {\n    counter[_num]++;\n  }\n  // 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n  // То есть counter[_num]-1 — это индекс последнего появления _num в res\n  for (int i = 0; i &lt; m; i++) {\n    counter[i + 1] += counter[i];\n  }\n  // 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n  // Инициализировать массив res для хранения результата\n  int n = nums.length;\n  List&lt;int&gt; res = List.filled(n, 0);\n  for (int i = n - 1; i &gt;= 0; i--) {\n    int _num = nums[i];\n    res[counter[_num] - 1] = _num; // Поместить _num по соответствующему индексу\n    counter[_num]--; // Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения _num\n  }\n  // Перезаписать исходный массив nums массивом результата res\n  nums.setAll(0, res);\n}\n</code></pre> counting_sort.rs<pre><code>/* Сортировка подсчетом */\n// Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\nfn counting_sort(nums: &amp;mut [i32]) {\n    // 1. Найти максимальный элемент массива m\n    let m = *nums.iter().max().unwrap() as usize;\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    let mut counter = vec![0; m + 1];\n    for &amp;num in nums.iter() {\n        counter[num as usize] += 1;\n    }\n    // 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n    // То есть counter[num]-1 — это индекс последнего появления num в res\n    for i in 0..m {\n        counter[i + 1] += counter[i];\n    }\n    // 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n    // Инициализировать массив res для хранения результата\n    let n = nums.len();\n    let mut res = vec![0; n];\n    for i in (0..n).rev() {\n        let num = nums[i];\n        res[counter[num as usize] - 1] = num; // Поместить num по соответствующему индексу\n        counter[num as usize] -= 1; // Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения num\n    }\n    // Перезаписать исходный массив nums массивом результата res\n    nums.copy_from_slice(&amp;res)\n}\n</code></pre> counting_sort.c<pre><code>/* Сортировка подсчетом */\n// Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\nvoid countingSort(int nums[], int size) {\n    // 1. Найти максимальный элемент массива m\n    int m = 0;\n    for (int i = 0; i &lt; size; i++) {\n        if (nums[i] &gt; m) {\n            m = nums[i];\n        }\n    }\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    int *counter = calloc(m, sizeof(int));\n    for (int i = 0; i &lt; size; i++) {\n        counter[nums[i]]++;\n    }\n    // 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n    // То есть counter[num]-1 — это индекс последнего появления num в res\n    for (int i = 0; i &lt; m; i++) {\n        counter[i + 1] += counter[i];\n    }\n    // 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n    // Инициализировать массив res для хранения результата\n    int *res = malloc(sizeof(int) * size);\n    for (int i = size - 1; i &gt;= 0; i--) {\n        int num = nums[i];\n        res[counter[num] - 1] = num; // Поместить num по соответствующему индексу\n        counter[num]--;              // Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения num\n    }\n    // Перезаписать исходный массив nums массивом результата res\n    memcpy(nums, res, size * sizeof(int));\n    // 5. Освободить память\n    free(res);\n    free(counter);\n}\n</code></pre> counting_sort.kt<pre><code>/* Сортировка подсчетом */\n// Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\nfun countingSort(nums: IntArray) {\n    // 1. Найти максимальный элемент массива m\n    var m = 0\n    for (num in nums) {\n        m = max(m, num)\n    }\n    // 2. Подсчитать число появлений каждой цифры\n    // counter[num] обозначает число появлений num\n    val counter = IntArray(m + 1)\n    for (num in nums) {\n        counter[num]++\n    }\n    // 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n    // То есть counter[num]-1 — это индекс последнего появления num в res\n    for (i in 0..&lt;m) {\n        counter[i + 1] += counter[i]\n    }\n    // 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n    // Инициализировать массив res для хранения результата\n    val n = nums.size\n    val res = IntArray(n)\n    for (i in n - 1 downTo 0) {\n        val num = nums[i]\n        res[counter[num] - 1] = num // Поместить num по соответствующему индексу\n        counter[num]-- // Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения num\n    }\n    // Перезаписать исходный массив nums массивом результата res\n    for (i in 0..&lt;n) {\n        nums[i] = res[i]\n    }\n}\n</code></pre> counting_sort.rb<pre><code>### Сортировка подсчетом ###\ndef counting_sort(nums)\n  # Полная реализация, позволяет сортировать объекты и является стабильной сортировкой\n  # 1. Найти максимальный элемент массива m\n  m = nums.max\n  # 2. Подсчитать число появлений каждой цифры\n  # counter[num] обозначает число появлений num\n  counter = Array.new(m + 1, 0)\n  nums.each { |num| counter[num] += 1 }\n  # 3. Вычислить префиксные суммы counter и преобразовать «число появлений» в «конечный индекс»\n  # То есть counter[num]-1 — это индекс последнего появления num в res\n  (0...m).each { |i| counter[i + 1] += counter[i] }\n  # 4. Обойти nums в обратном порядке и поместить элементы в результирующий массив res\n  # Инициализировать массив res для хранения результата\n  n = nums.length\n  res = Array.new(n, 0)\n  (n - 1).downto(0).each do |i|\n    num = nums[i]\n    res[counter[num] - 1] = num # Поместить num по соответствующему индексу\n    counter[num] -= 1 # Уменьшить префиксную сумму на 1, чтобы получить индекс следующего размещения num\n  end\n  # Перезаписать исходный массив nums массивом результата res\n  (0...n).each { |i| nums[i] = res[i] }\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 11. Сортировка","11.9 &nbsp; Сортировка подсчетом"],"tags":[]},{"location":"chapter_sorting/counting_sort/#1193","level":2,"title":"11.9.3   Характеристики алгоритма","text":"<ul> <li>Временная сложность равна \\(O(n + m)\\), алгоритм не является адаптивным : необходимо пройти по <code>nums</code> и по <code>counter</code> , а оба этих прохода занимают линейное время. Обычно выполняется \\(n \\gg m\\) , поэтому временная сложность стремится к \\(O(n)\\) .</li> <li>Пространственная сложность равна \\(O(n + m)\\), сортировка не выполняется на месте: используются массивы <code>res</code> и <code>counter</code> длины \\(n\\) и \\(m\\) соответственно.</li> <li>Стабильная сортировка: порядок заполнения <code>res</code> идет \"справа налево\", поэтому обратный проход по <code>nums</code> позволяет сохранить относительный порядок равных элементов и тем самым реализовать стабильную сортировку. Вообще говоря, прямой проход по <code>nums</code> тоже даст правильный результат сортировки, но он будет нестабильным.</li> </ul>","path":["Глава 11. Сортировка","11.9 &nbsp; Сортировка подсчетом"],"tags":[]},{"location":"chapter_sorting/counting_sort/#1194","level":2,"title":"11.9.4   Ограничения","text":"<p>На этом этапе сортировка подсчетом может показаться очень изящной: она позволяет эффективно сортировать данные, опираясь только на подсчет числа вхождений. Однако условия ее применения довольно строгие.</p> <p>Сортировка подсчетом применима только к неотрицательным целым числам. Чтобы использовать ее для других типов данных, нужно убедиться, что эти данные можно преобразовать в неотрицательные целые числа и что при преобразовании относительный порядок элементов не изменится. Например, для массива целых чисел с отрицательными значениями можно сначала прибавить ко всем числам константу, превратив их в положительные, затем выполнить сортировку и после этого преобразовать значения обратно.</p> <p>Сортировка подсчетом подходит для случаев, когда объем данных велик, но диапазон значений невелик. Например, в приведенном выше примере \\(m\\) не должно быть слишком большим, иначе будет занято слишком много памяти. А когда \\(n \\ll m\\) , сортировка подсчетом использует \\(O(m)\\) времени и может оказаться медленнее, чем алгоритмы сортировки с \\(O(n \\log n)\\) .</p>","path":["Глава 11. Сортировка","11.9 &nbsp; Сортировка подсчетом"],"tags":[]},{"location":"chapter_sorting/heap_sort/","level":1,"title":"11.7   Пирамидальная сортировка","text":"<p>Tip</p> <p>Перед чтением этого раздела убедитесь, что вы уже изучили главу \"Куча\".</p> <p>Пирамидальная сортировка (heap sort) - это эффективный алгоритм сортировки, основанный на структуре данных \"куча\". Для его реализации можно использовать уже изученные нами \"построение кучи\" и \"извлечение элементов из кучи\".</p> <ol> <li>Подать на вход массив и построить из него мин-кучу; в этот момент минимальный элемент будет находиться в вершине кучи.</li> <li>Непрерывно выполнять извлечение из кучи и по порядку записывать извлеченные элементы - так получится последовательность, отсортированная по возрастанию.</li> </ol> <p>Хотя этот метод и работоспособен, он требует дополнительного массива для хранения извлеченных элементов и потому расходует лишнюю память. На практике обычно используют более изящную реализацию.</p>","path":["Глава 11. Сортировка","11.7 &nbsp; Пирамидальная сортировка"],"tags":[]},{"location":"chapter_sorting/heap_sort/#1171","level":2,"title":"11.7.1   Алгоритм","text":"<p>Пусть длина массива равна \\(n\\) ; тогда процесс пирамидальной сортировки показан на рисунке 11-12.</p> <ol> <li>Подать на вход массив и построить из него макс-кучу. После этого максимальный элемент окажется в вершине кучи.</li> <li>Обменять элемент в вершине кучи (первый элемент) с элементом внизу кучи (последний элемент). После обмена длина кучи уменьшается на \\(1\\) , а число уже отсортированных элементов увеличивается на \\(1\\) .</li> <li>Начиная с вершины, выполнить операцию просеивания сверху вниз. После этого свойство кучи будет восстановлено.</li> <li>Циклически повторять шаг <code>2.</code> и шаг <code>3.</code> . После \\(n - 1\\) раундов массив будет полностью отсортирован.</li> </ol> <p>Tip</p> <p>На самом деле операция извлечения из кучи тоже включает шаг <code>2.</code> и шаг <code>3.</code> , только дополнительно содержит действие по удалению элемента.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 11-12   Шаги пирамидальной сортировки </p> <p>В коде используется та же функция просеивания сверху вниз <code>sift_down()</code>, что и в главе \"Куча\". Важно помнить, что длина кучи уменьшается по мере извлечения максимального элемента, поэтому функции <code>sift_down()</code> нужно передавать параметр длины \\(n\\) , чтобы указать текущую действительную длину кучи. Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby heap_sort.py<pre><code>def sift_down(nums: list[int], n: int, i: int):\n    \"\"\"Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз\"\"\"\n    while True:\n        # Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        l = 2 * i + 1\n        r = 2 * i + 2\n        ma = i\n        if l &lt; n and nums[l] &gt; nums[ma]:\n            ma = l\n        if r &lt; n and nums[r] &gt; nums[ma]:\n            ma = r\n        # Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if ma == i:\n            break\n        # Поменять два узла местами\n        nums[i], nums[ma] = nums[ma], nums[i]\n        # Циклическое просеивание вниз\n        i = ma\n\ndef heap_sort(nums: list[int]):\n    \"\"\"Сортировка кучей\"\"\"\n    # Построение кучи: выполнить heapify для всех узлов, кроме листовых\n    for i in range(len(nums) // 2 - 1, -1, -1):\n        sift_down(nums, len(nums), i)\n    # Извлекать максимальный элемент из кучи в течение n-1 итераций\n    for i in range(len(nums) - 1, 0, -1):\n        # Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n        nums[0], nums[i] = nums[i], nums[0]\n        # Начиная с корневого узла, выполнить просеивание сверху вниз\n        sift_down(nums, i, 0)\n</code></pre> heap_sort.cpp<pre><code>/* Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз */\nvoid siftDown(vector&lt;int&gt; &amp;nums, int n, int i) {\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        int l = 2 * i + 1;\n        int r = 2 * i + 2;\n        int ma = i;\n        if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma])\n            ma = l;\n        if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma])\n            ma = r;\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (ma == i) {\n            break;\n        }\n        // Поменять два узла местами\n        swap(nums[i], nums[ma]);\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n\n/* Сортировка кучей */\nvoid heapSort(vector&lt;int&gt; &amp;nums) {\n    // Построение кучи: выполнить heapify для всех узлов, кроме листовых\n    for (int i = nums.size() / 2 - 1; i &gt;= 0; --i) {\n        siftDown(nums, nums.size(), i);\n    }\n    // Извлекать максимальный элемент из кучи в течение n-1 итераций\n    for (int i = nums.size() - 1; i &gt; 0; --i) {\n        // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n        swap(nums[0], nums[i]);\n        // Начиная с корневого узла, выполнить просеивание сверху вниз\n        siftDown(nums, i, 0);\n    }\n}\n</code></pre> heap_sort.java<pre><code>/* Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз */\nvoid siftDown(int[] nums, int n, int i) {\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        int l = 2 * i + 1;\n        int r = 2 * i + 2;\n        int ma = i;\n        if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma])\n            ma = l;\n        if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma])\n            ma = r;\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (ma == i)\n            break;\n        // Поменять два узла местами\n        int temp = nums[i];\n        nums[i] = nums[ma];\n        nums[ma] = temp;\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n\n/* Сортировка кучей */\nvoid heapSort(int[] nums) {\n    // Построение кучи: выполнить heapify для всех узлов, кроме листовых\n    for (int i = nums.length / 2 - 1; i &gt;= 0; i--) {\n        siftDown(nums, nums.length, i);\n    }\n    // Извлекать максимальный элемент из кучи в течение n-1 итераций\n    for (int i = nums.length - 1; i &gt; 0; i--) {\n        // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n        int tmp = nums[0];\n        nums[0] = nums[i];\n        nums[i] = tmp;\n        // Начиная с корневого узла, выполнить просеивание сверху вниз\n        siftDown(nums, i, 0);\n    }\n}\n</code></pre> heap_sort.cs<pre><code>/* Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз */\nvoid SiftDown(int[] nums, int n, int i) {\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        int l = 2 * i + 1;\n        int r = 2 * i + 2;\n        int ma = i;\n        if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma])\n            ma = l;\n        if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma])\n            ma = r;\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (ma == i)\n            break;\n        // Поменять два узла местами\n        (nums[ma], nums[i]) = (nums[i], nums[ma]);\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n\n/* Сортировка кучей */\nvoid HeapSort(int[] nums) {\n    // Построение кучи: выполнить heapify для всех узлов, кроме листовых\n    for (int i = nums.Length / 2 - 1; i &gt;= 0; i--) {\n        SiftDown(nums, nums.Length, i);\n    }\n    // Извлекать максимальный элемент из кучи в течение n-1 итераций\n    for (int i = nums.Length - 1; i &gt; 0; i--) {\n        // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n        (nums[i], nums[0]) = (nums[0], nums[i]);\n        // Начиная с корневого узла, выполнить просеивание сверху вниз\n        SiftDown(nums, i, 0);\n    }\n}\n</code></pre> heap_sort.go<pre><code>/* Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз */\nfunc siftDown(nums *[]int, n, i int) {\n    for true {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        l := 2*i + 1\n        r := 2*i + 2\n        ma := i\n        if l &lt; n &amp;&amp; (*nums)[l] &gt; (*nums)[ma] {\n            ma = l\n        }\n        if r &lt; n &amp;&amp; (*nums)[r] &gt; (*nums)[ma] {\n            ma = r\n        }\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if ma == i {\n            break\n        }\n        // Поменять два узла местами\n        (*nums)[i], (*nums)[ma] = (*nums)[ma], (*nums)[i]\n        // Циклическое просеивание вниз\n        i = ma\n    }\n}\n\n/* Сортировка кучей */\nfunc heapSort(nums *[]int) {\n    // Построение кучи: выполнить heapify для всех узлов, кроме листовых\n    for i := len(*nums)/2 - 1; i &gt;= 0; i-- {\n        siftDown(nums, len(*nums), i)\n    }\n    // Извлекать максимальный элемент из кучи в течение n-1 итераций\n    for i := len(*nums) - 1; i &gt; 0; i-- {\n        // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n        (*nums)[0], (*nums)[i] = (*nums)[i], (*nums)[0]\n        // Начиная с корневого узла, выполнить просеивание сверху вниз\n        siftDown(nums, i, 0)\n    }\n}\n</code></pre> heap_sort.swift<pre><code>/* Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз */\nfunc siftDown(nums: inout [Int], n: Int, i: Int) {\n    var i = i\n    while true {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        let l = 2 * i + 1\n        let r = 2 * i + 2\n        var ma = i\n        if l &lt; n, nums[l] &gt; nums[ma] {\n            ma = l\n        }\n        if r &lt; n, nums[r] &gt; nums[ma] {\n            ma = r\n        }\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if ma == i {\n            break\n        }\n        // Поменять два узла местами\n        nums.swapAt(i, ma)\n        // Циклическое просеивание вниз\n        i = ma\n    }\n}\n\n/* Сортировка кучей */\nfunc heapSort(nums: inout [Int]) {\n    // Построение кучи: выполнить heapify для всех узлов, кроме листовых\n    for i in stride(from: nums.count / 2 - 1, through: 0, by: -1) {\n        siftDown(nums: &amp;nums, n: nums.count, i: i)\n    }\n    // Извлекать максимальный элемент из кучи в течение n-1 итераций\n    for i in nums.indices.dropFirst().reversed() {\n        // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n        nums.swapAt(0, i)\n        // Начиная с корневого узла, выполнить просеивание сверху вниз\n        siftDown(nums: &amp;nums, n: i, i: 0)\n    }\n}\n</code></pre> heap_sort.js<pre><code>/* Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз */\nfunction siftDown(nums, n, i) {\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        let l = 2 * i + 1;\n        let r = 2 * i + 2;\n        let ma = i;\n        if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma]) {\n            ma = l;\n        }\n        if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma]) {\n            ma = r;\n        }\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (ma === i) {\n            break;\n        }\n        // Поменять два узла местами\n        [nums[i], nums[ma]] = [nums[ma], nums[i]];\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n\n/* Сортировка кучей */\nfunction heapSort(nums) {\n    // Построение кучи: выполнить heapify для всех узлов, кроме листовых\n    for (let i = Math.floor(nums.length / 2) - 1; i &gt;= 0; i--) {\n        siftDown(nums, nums.length, i);\n    }\n    // Извлекать максимальный элемент из кучи в течение n-1 итераций\n    for (let i = nums.length - 1; i &gt; 0; i--) {\n        // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n        [nums[0], nums[i]] = [nums[i], nums[0]];\n        // Начиная с корневого узла, выполнить просеивание сверху вниз\n        siftDown(nums, i, 0);\n    }\n}\n</code></pre> heap_sort.ts<pre><code>/* Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз */\nfunction siftDown(nums: number[], n: number, i: number): void {\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        let l = 2 * i + 1;\n        let r = 2 * i + 2;\n        let ma = i;\n        if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma]) {\n            ma = l;\n        }\n        if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma]) {\n            ma = r;\n        }\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (ma === i) {\n            break;\n        }\n        // Поменять два узла местами\n        [nums[i], nums[ma]] = [nums[ma], nums[i]];\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n\n/* Сортировка кучей */\nfunction heapSort(nums: number[]): void {\n    // Построение кучи: выполнить heapify для всех узлов, кроме листовых\n    for (let i = Math.floor(nums.length / 2) - 1; i &gt;= 0; i--) {\n        siftDown(nums, nums.length, i);\n    }\n    // Извлекать максимальный элемент из кучи в течение n-1 итераций\n    for (let i = nums.length - 1; i &gt; 0; i--) {\n        // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n        [nums[0], nums[i]] = [nums[i], nums[0]];\n        // Начиная с корневого узла, выполнить просеивание сверху вниз\n        siftDown(nums, i, 0);\n    }\n}\n</code></pre> heap_sort.dart<pre><code>/* Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз */\nvoid siftDown(List&lt;int&gt; nums, int n, int i) {\n  while (true) {\n    // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n    int l = 2 * i + 1;\n    int r = 2 * i + 2;\n    int ma = i;\n    if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma]) ma = l;\n    if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma]) ma = r;\n    // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n    if (ma == i) break;\n    // Поменять два узла местами\n    int temp = nums[i];\n    nums[i] = nums[ma];\n    nums[ma] = temp;\n    // Циклическое просеивание вниз\n    i = ma;\n  }\n}\n\n/* Сортировка кучей */\nvoid heapSort(List&lt;int&gt; nums) {\n  // Построение кучи: выполнить heapify для всех узлов, кроме листовых\n  for (int i = nums.length ~/ 2 - 1; i &gt;= 0; i--) {\n    siftDown(nums, nums.length, i);\n  }\n  // Извлекать максимальный элемент из кучи в течение n-1 итераций\n  for (int i = nums.length - 1; i &gt; 0; i--) {\n    // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    int tmp = nums[0];\n    nums[0] = nums[i];\n    nums[i] = tmp;\n    // Начиная с корневого узла, выполнить просеивание сверху вниз\n    siftDown(nums, i, 0);\n  }\n}\n</code></pre> heap_sort.rs<pre><code>/* Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз */\nfn sift_down(nums: &amp;mut [i32], n: usize, mut i: usize) {\n    loop {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        let l = 2 * i + 1;\n        let r = 2 * i + 2;\n        let mut ma = i;\n        if l &lt; n &amp;&amp; nums[l] &gt; nums[ma] {\n            ma = l;\n        }\n        if r &lt; n &amp;&amp; nums[r] &gt; nums[ma] {\n            ma = r;\n        }\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if ma == i {\n            break;\n        }\n        // Поменять два узла местами\n        nums.swap(i, ma);\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n\n/* Сортировка кучей */\nfn heap_sort(nums: &amp;mut [i32]) {\n    // Построение кучи: выполнить heapify для всех узлов, кроме листовых\n    for i in (0..nums.len() / 2).rev() {\n        sift_down(nums, nums.len(), i);\n    }\n    // Извлекать максимальный элемент из кучи в течение n-1 итераций\n    for i in (1..nums.len()).rev() {\n        // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n        nums.swap(0, i);\n        // Начиная с корневого узла, выполнить просеивание сверху вниз\n        sift_down(nums, i, 0);\n    }\n}\n</code></pre> heap_sort.c<pre><code>/* Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз */\nvoid siftDown(int nums[], int n, int i) {\n    while (1) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        int l = 2 * i + 1;\n        int r = 2 * i + 2;\n        int ma = i;\n        if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma])\n            ma = l;\n        if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma])\n            ma = r;\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (ma == i) {\n            break;\n        }\n        // Поменять два узла местами\n        int temp = nums[i];\n        nums[i] = nums[ma];\n        nums[ma] = temp;\n        // Циклическое просеивание вниз\n        i = ma;\n    }\n}\n\n/* Сортировка кучей */\nvoid heapSort(int nums[], int n) {\n    // Построение кучи: выполнить heapify для всех узлов, кроме листовых\n    for (int i = n / 2 - 1; i &gt;= 0; --i) {\n        siftDown(nums, n, i);\n    }\n    // Извлекать максимальный элемент из кучи в течение n-1 итераций\n    for (int i = n - 1; i &gt; 0; --i) {\n        // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n        int tmp = nums[0];\n        nums[0] = nums[i];\n        nums[i] = tmp;\n        // Начиная с корневого узла, выполнить просеивание сверху вниз\n        siftDown(nums, i, 0);\n    }\n}\n</code></pre> heap_sort.kt<pre><code>/* Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз */\nfun siftDown(nums: IntArray, n: Int, li: Int) {\n    var i = li\n    while (true) {\n        // Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n        val l = 2 * i + 1\n        val r = 2 * i + 2\n        var ma = i\n        if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma]) \n            ma = l\n        if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma]) \n            ma = r\n        // Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n        if (ma == i) \n            break\n        // Поменять два узла местами\n        val temp = nums[i]\n        nums[i] = nums[ma]\n        nums[ma] = temp\n        // Циклическое просеивание вниз\n        i = ma\n    }\n}\n\n/* Сортировка кучей */\nfun heapSort(nums: IntArray) {\n    // Построение кучи: выполнить heapify для всех узлов, кроме листовых\n    for (i in nums.size / 2 - 1 downTo 0) {\n        siftDown(nums, nums.size, i)\n    }\n    // Извлекать максимальный элемент из кучи в течение n-1 итераций\n    for (i in nums.size - 1 downTo 1) {\n        // Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n        val temp = nums[0]\n        nums[0] = nums[i]\n        nums[i] = temp\n        // Начиная с корневого узла, выполнить просеивание сверху вниз\n        siftDown(nums, i, 0)\n    }\n}\n</code></pre> heap_sort.rb<pre><code>### Длина кучи равна n; начиная с узла i, выполнить просеивание сверху вниз ###\ndef sift_down(nums, n, i)\n  while true\n    # Определить узел с максимальным значением среди i, l и r и обозначить его как ma\n    l = 2 * i + 1\n    r = 2 * i + 2\n    ma = i\n    ma = l if l &lt; n &amp;&amp; nums[l] &gt; nums[ma]\n    ma = r if r &lt; n &amp;&amp; nums[r] &gt; nums[ma]\n    # Если узел i уже максимален или индексы l и r вне границ, дальнейшее просеивание не требуется, выйти\n    break if ma == i\n    # Поменять два узла местами\n    nums[i], nums[ma] = nums[ma], nums[i]\n    # Циклическое просеивание вниз\n    i = ma\n  end\nend\n\n### Сортировка кучей ###\ndef heap_sort(nums)\n  # Построение кучи: выполнить heapify для всех узлов, кроме листовых\n  (nums.length / 2 - 1).downto(0) do |i|\n    sift_down(nums, nums.length, i)\n  end\n  # Извлекать максимальный элемент из кучи в течение n-1 итераций\n  (nums.length - 1).downto(1) do |i|\n    # Поменять корневой узел с самым правым листом местами (поменять первый и последний элементы)\n    nums[0], nums[i] = nums[i], nums[0]\n    # Начиная с корневого узла, выполнить просеивание сверху вниз\n    sift_down(nums, i, 0)\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 11. Сортировка","11.7 &nbsp; Пирамидальная сортировка"],"tags":[]},{"location":"chapter_sorting/heap_sort/#1172","level":2,"title":"11.7.2   Характеристики алгоритма","text":"<ul> <li>Временная сложность равна \\(O(n \\log n)\\), алгоритм не является адаптивным: построение кучи занимает \\(O(n)\\) времени. Извлечение максимального элемента из кучи имеет временную сложность \\(O(\\log n)\\) и выполняется \\(n - 1\\) раз.</li> <li>Пространственная сложность равна \\(O(1)\\), сортировка выполняется на месте: несколько переменных-указателей используют \\(O(1)\\) памяти. Обмен элементов и операции просеивания выполняются прямо в исходном массиве.</li> <li>Нестабильная сортировка: при обмене вершины кучи и нижнего элемента относительный порядок равных элементов может измениться.</li> </ul>","path":["Глава 11. Сортировка","11.7 &nbsp; Пирамидальная сортировка"],"tags":[]},{"location":"chapter_sorting/insertion_sort/","level":1,"title":"11.4   Сортировка вставками","text":"<p>Сортировка вставками (insertion sort) - это простой алгоритм сортировки, принцип которого очень похож на ручную сортировку карт в колоде.</p> <p>Точнее говоря, в неотсортированном диапазоне выбирается опорный элемент, после чего он сравнивается с элементами слева в уже отсортированном диапазоне и вставляется в правильную позицию.</p> <p>На рисунке 11-6 показан процесс вставки элемента в массив. Пусть опорный элемент обозначен как <code>base</code> ; нам нужно сдвинуть все элементы от целевого индекса до <code>base</code> на одну позицию вправо, а затем записать <code>base</code> в целевой индекс.</p> <p></p> <p> Рисунок 11-6   Одна операция вставки </p>","path":["Глава 11. Сортировка","11.4 &nbsp; Сортировка вставками"],"tags":[]},{"location":"chapter_sorting/insertion_sort/#1141","level":2,"title":"11.4.1   Алгоритм","text":"<p>Общий процесс сортировки вставками показан на рисунке 11-7.</p> <ol> <li>В начальном состоянии отсортирован только первый элемент массива.</li> <li>Выбрать второй элемент массива как <code>base</code> ; после вставки в правильную позицию первые два элемента массива окажутся отсортированными.</li> <li>Выбрать третий элемент как <code>base</code> ; после вставки в правильную позицию первые три элемента массива окажутся отсортированными.</li> <li>Продолжать по аналогии; в последнем раунде в качестве <code>base</code> берется последний элемент, и после его вставки все элементы массива будут отсортированы.</li> </ol> <p></p> <p> Рисунок 11-7   Процесс сортировки вставками </p> <p>Пример кода:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby insertion_sort.py<pre><code>def insertion_sort(nums: list[int]):\n    \"\"\"Сортировка вставками\"\"\"\n    # Внешний цикл: отсортированный диапазон [0, i-1]\n    for i in range(1, len(nums)):\n        base = nums[i]\n        j = i - 1\n        # Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n        while j &gt;= 0 and nums[j] &gt; base:\n            nums[j + 1] = nums[j]  # Сдвинуть nums[j] на одну позицию вправо\n            j -= 1\n        nums[j + 1] = base  # Поместить base в правильную позицию\n</code></pre> insertion_sort.cpp<pre><code>/* Сортировка вставками */\nvoid insertionSort(vector&lt;int&gt; &amp;nums) {\n    // Внешний цикл: отсортированный диапазон [0, i-1]\n    for (int i = 1; i &lt; nums.size(); i++) {\n        int base = nums[i], j = i - 1;\n        // Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n        while (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n            nums[j + 1] = nums[j]; // Сдвинуть nums[j] на одну позицию вправо\n            j--;\n        }\n        nums[j + 1] = base; // Поместить base в правильную позицию\n    }\n}\n</code></pre> insertion_sort.java<pre><code>/* Сортировка вставками */\nvoid insertionSort(int[] nums) {\n    // Внешний цикл: отсортированный диапазон [0, i-1]\n    for (int i = 1; i &lt; nums.length; i++) {\n        int base = nums[i], j = i - 1;\n        // Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n        while (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n            nums[j + 1] = nums[j]; // Сдвинуть nums[j] на одну позицию вправо\n            j--;\n        }\n        nums[j + 1] = base;        // Поместить base в правильную позицию\n    }\n}\n</code></pre> insertion_sort.cs<pre><code>/* Сортировка вставками */\nvoid InsertionSort(int[] nums) {\n    // Внешний цикл: отсортированный диапазон [0, i-1]\n    for (int i = 1; i &lt; nums.Length; i++) {\n        int bas = nums[i], j = i - 1;\n        // Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n        while (j &gt;= 0 &amp;&amp; nums[j] &gt; bas) {\n            nums[j + 1] = nums[j]; // Сдвинуть nums[j] на одну позицию вправо\n            j--;\n        }\n        nums[j + 1] = bas;         // Поместить base в правильную позицию\n    }\n}\n</code></pre> insertion_sort.go<pre><code>/* Сортировка вставками */\nfunc insertionSort(nums []int) {\n    // Внешний цикл: отсортированный диапазон [0, i-1]\n    for i := 1; i &lt; len(nums); i++ {\n        base := nums[i]\n        j := i - 1\n        // Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n        for j &gt;= 0 &amp;&amp; nums[j] &gt; base {\n            nums[j+1] = nums[j] // Сдвинуть nums[j] на одну позицию вправо\n            j--\n        }\n        nums[j+1] = base // Поместить base в правильную позицию\n    }\n}\n</code></pre> insertion_sort.swift<pre><code>/* Сортировка вставками */\nfunc insertionSort(nums: inout [Int]) {\n    // Внешний цикл: отсортированный диапазон [0, i-1]\n    for i in nums.indices.dropFirst() {\n        let base = nums[i]\n        var j = i - 1\n        // Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n        while j &gt;= 0, nums[j] &gt; base {\n            nums[j + 1] = nums[j] // Сдвинуть nums[j] на одну позицию вправо\n            j -= 1\n        }\n        nums[j + 1] = base // Поместить base в правильную позицию\n    }\n}\n</code></pre> insertion_sort.js<pre><code>/* Сортировка вставками */\nfunction insertionSort(nums) {\n    // Внешний цикл: отсортированный диапазон [0, i-1]\n    for (let i = 1; i &lt; nums.length; i++) {\n        let base = nums[i],\n            j = i - 1;\n        // Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n        while (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n            nums[j + 1] = nums[j]; // Сдвинуть nums[j] на одну позицию вправо\n            j--;\n        }\n        nums[j + 1] = base; // Поместить base в правильную позицию\n    }\n}\n</code></pre> insertion_sort.ts<pre><code>/* Сортировка вставками */\nfunction insertionSort(nums: number[]): void {\n    // Внешний цикл: отсортированный диапазон [0, i-1]\n    for (let i = 1; i &lt; nums.length; i++) {\n        const base = nums[i];\n        let j = i - 1;\n        // Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n        while (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n            nums[j + 1] = nums[j]; // Сдвинуть nums[j] на одну позицию вправо\n            j--;\n        }\n        nums[j + 1] = base; // Поместить base в правильную позицию\n    }\n}\n</code></pre> insertion_sort.dart<pre><code>/* Сортировка вставками */\nvoid insertionSort(List&lt;int&gt; nums) {\n  // Внешний цикл: отсортированный диапазон [0, i-1]\n  for (int i = 1; i &lt; nums.length; i++) {\n    int base = nums[i], j = i - 1;\n    // Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n    while (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n      nums[j + 1] = nums[j]; // Сдвинуть nums[j] на одну позицию вправо\n      j--;\n    }\n    nums[j + 1] = base; // Поместить base в правильную позицию\n  }\n}\n</code></pre> insertion_sort.rs<pre><code>/* Сортировка вставками */\nfn insertion_sort(nums: &amp;mut [i32]) {\n    // Внешний цикл: отсортированный диапазон [0, i-1]\n    for i in 1..nums.len() {\n        let (base, mut j) = (nums[i], (i - 1) as i32);\n        // Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n        while j &gt;= 0 &amp;&amp; nums[j as usize] &gt; base {\n            nums[(j + 1) as usize] = nums[j as usize]; // Сдвинуть nums[j] на одну позицию вправо\n            j -= 1;\n        }\n        nums[(j + 1) as usize] = base; // Поместить base в правильную позицию\n    }\n}\n</code></pre> insertion_sort.c<pre><code>/* Сортировка вставками */\nvoid insertionSort(int nums[], int size) {\n    // Внешний цикл: отсортированный диапазон [0, i-1]\n    for (int i = 1; i &lt; size; i++) {\n        int base = nums[i], j = i - 1;\n        // Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n        while (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n            // Сдвинуть nums[j] на одну позицию вправо\n            nums[j + 1] = nums[j];\n            j--;\n        }\n        // Поместить base в правильную позицию\n        nums[j + 1] = base;\n    }\n}\n</code></pre> insertion_sort.kt<pre><code>/* Сортировка вставками */\nfun insertionSort(nums: IntArray) {\n    // Внешний цикл: отсортированные элементы равны 1, 2, ..., n\n    for (i in nums.indices) {\n        val base = nums[i]\n        var j = i - 1\n        // Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n        while (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n            nums[j + 1] = nums[j] // Сдвинуть nums[j] на одну позицию вправо\n            j--\n        }\n        nums[j + 1] = base        // Поместить base в правильную позицию\n    }\n}\n</code></pre> insertion_sort.rb<pre><code>### Сортировка вставками ###\ndef insertion_sort(nums)\n  n = nums.length\n  # Внешний цикл: отсортированный диапазон [0, i-1]\n  for i in 1...n\n    base = nums[i]\n    j = i - 1\n    # Внутренний цикл: вставить base в правильную позицию отсортированного диапазона [0, i-1]\n    while j &gt;= 0 &amp;&amp; nums[j] &gt; base\n      nums[j + 1] = nums[j] # Сдвинуть nums[j] на одну позицию вправо\n      j -= 1\n    end\n    nums[j + 1] = base # Поместить base в правильную позицию\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 11. Сортировка","11.4 &nbsp; Сортировка вставками"],"tags":[]},{"location":"chapter_sorting/insertion_sort/#1142","level":2,"title":"11.4.2   Характеристики алгоритма","text":"<ul> <li>Временная сложность равна \\(O(n^2)\\), алгоритм адаптивен: в худшем случае каждой операции вставки требуется соответственно \\(n - 1\\), \\(n-2\\), \\(\\dots\\), \\(2\\), \\(1\\) итераций, а их сумма равна \\((n - 1) n / 2\\) , поэтому временная сложность равна \\(O(n^2)\\) . Если входные данные уже упорядочены, операция вставки завершается раньше. Когда входной массив полностью отсортирован, сортировка вставками достигает лучшей временной сложности \\(O(n)\\) .</li> <li>Пространственная сложность равна \\(O(1)\\), сортировка выполняется на месте: указатели \\(i\\) и \\(j\\) используют константный объем дополнительной памяти.</li> <li>Стабильная сортировка: в процессе вставки элементы помещаются справа от равных им элементов, поэтому их относительный порядок не меняется.</li> </ul>","path":["Глава 11. Сортировка","11.4 &nbsp; Сортировка вставками"],"tags":[]},{"location":"chapter_sorting/insertion_sort/#1143","level":2,"title":"11.4.3   Преимущества сортировки вставками","text":"<p>Временная сложность сортировки вставками равна \\(O(n^2)\\) , а у быстрой сортировки, которую мы скоро изучим, временная сложность равна \\(O(n \\log n)\\) . Несмотря на более высокую асимптотическую сложность, на малых объемах данных сортировка вставками обычно работает быстрее.</p> <p>Этот вывод похож на сравнение линейного и двоичного поиска. Алгоритмы уровня \\(O(n \\log n)\\) , такие как быстрая сортировка, относятся к алгоритмам на основе стратегии \"разделяй и властвуй\" и обычно включают больше элементарных вычислений. Когда объем данных мал, значения \\(n^2\\) и \\(n \\log n\\) близки друг к другу, поэтому асимптотика не доминирует, а решающим становится число элементарных операций в каждом раунде.</p> <p>На практике встроенные функции сортировки во многих языках программирования (например, в Java) используют сортировку вставками. Общая идея такова: для длинных массивов применять алгоритмы сортировки на основе стратегии \"разделяй и властвуй\", например быструю сортировку; для коротких массивов сразу использовать сортировку вставками.</p> <p>Хотя сортировка пузырьком, выбором и вставками имеют одинаковую временную сложность \\(O(n^2)\\) , в реальных задачах сортировка вставками используется заметно чаще, чем сортировка пузырьком и сортировка выбором. Основные причины таковы.</p> <ul> <li>Сортировка пузырьком основана на обмене элементов, для чего нужна временная переменная и суммарно выполняются 3 элементарные операции; сортировка вставками основана на присваивании элементов и требует всего 1 элементарной операции. Поэтому вычислительные затраты сортировки пузырьком обычно выше, чем у сортировки вставками.</li> <li>Временная сложность сортировки выбором в любом случае равна \\(O(n^2)\\) . Если входные данные уже частично упорядочены, сортировка вставками обычно эффективнее сортировки выбором.</li> <li>Сортировка выбором нестабильна, поэтому ее нельзя использовать для многоуровневой сортировки.</li> </ul>","path":["Глава 11. Сортировка","11.4 &nbsp; Сортировка вставками"],"tags":[]},{"location":"chapter_sorting/merge_sort/","level":1,"title":"11.6   Сортировка слиянием","text":"<p>Сортировка слиянием (merge sort) - это алгоритм сортировки, основанный на стратегии \"разделяй и властвуй\", который включает этапы \"разделения\" и \"слияния\", показанные на рисунке 11-10.</p> <ol> <li>Этап разделения: массив рекурсивно делится пополам, и задача сортировки длинного массива превращается в задачи сортировки более коротких массивов.</li> <li>Этап слияния: когда длина подмассива становится равной 1, разделение завершается и начинается слияние; два коротких упорядоченных массива непрерывно объединяются в один более длинный упорядоченный массив, пока процесс не завершится.</li> </ol> <p></p> <p> Рисунок 11-10   Этапы разделения и слияния в сортировке слиянием </p>","path":["Глава 11. Сортировка","11.6 &nbsp; Сортировка слиянием"],"tags":[]},{"location":"chapter_sorting/merge_sort/#1161","level":2,"title":"11.6.1   Алгоритм","text":"<p>Как показано на рисунке 11-11, на этапе \"разделения\" массив рекурсивно разбивается сверху вниз по середине на два подмассива.</p> <ol> <li>Вычислить середину массива <code>mid</code> и рекурсивно разделить левый подмассив (интервал <code>[left, mid]</code> ) и правый подмассив (интервал <code>[mid + 1, right]</code> ).</li> <li>Рекурсивно повторять шаг <code>1.</code> , пока длина подмассива не станет равной 1.</li> </ol> <p>Этап \"слияния\" снизу вверх объединяет левый и правый подмассивы в один упорядоченный массив. Следует заметить, что начиная с подмассивов длины 1, каждый подмассив в фазе слияния уже является упорядоченным.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 11-11   Шаги сортировки слиянием </p> <p>Нетрудно заметить, что порядок рекурсии в сортировке слиянием совпадает с порядком обхода в глубину двоичного дерева.</p> <ul> <li>Обход в глубину: сначала рекурсивно обходится левое поддерево, затем правое поддерево, а в конце обрабатывается корневой узел.</li> <li>Сортировка слиянием: сначала рекурсивно разделяется левый подмассив, затем правый подмассив, а в конце выполняется слияние.</li> </ul> <p>Реализация сортировки слиянием показана в коде ниже. Обратите внимание: в <code>nums</code> объединяемый интервал равен <code>[left, right]</code> , а соответствующий интервал в <code>tmp</code> равен <code>[0, right - left]</code> .</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby merge_sort.py<pre><code>def merge(nums: list[int], left: int, mid: int, right: int):\n    \"\"\"Объединить левый и правый подмассивы\"\"\"\n    # Диапазон левого подмассива: [left, mid], диапазон правого подмассива: [mid+1, right]\n    # Создать временный массив tmp для хранения результата слияния\n    tmp = [0] * (right - left + 1)\n    # Инициализировать начальные индексы левого и правого подмассивов\n    i, j, k = left, mid + 1, 0\n    # Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n    while i &lt;= mid and j &lt;= right:\n        if nums[i] &lt;= nums[j]:\n            tmp[k] = nums[i]\n            i += 1\n        else:\n            tmp[k] = nums[j]\n            j += 1\n        k += 1\n    # Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n    while i &lt;= mid:\n        tmp[k] = nums[i]\n        i += 1\n        k += 1\n    while j &lt;= right:\n        tmp[k] = nums[j]\n        j += 1\n        k += 1\n    # Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n    for k in range(0, len(tmp)):\n        nums[left + k] = tmp[k]\n\ndef merge_sort(nums: list[int], left: int, right: int):\n    \"\"\"Сортировка слиянием\"\"\"\n    # Условие завершения\n    if left &gt;= right:\n        return  # Завершить рекурсию, когда длина подмассива равна 1\n    # Этап разбиения\n    mid = (left + right) // 2 # Вычислить середину\n    merge_sort(nums, left, mid)  # Рекурсивно обработать левый подмассив\n    merge_sort(nums, mid + 1, right)  # Рекурсивно обработать правый подмассив\n    # Этап слияния\n    merge(nums, left, mid, right)\n</code></pre> merge_sort.cpp<pre><code>/* Объединить левый и правый подмассивы */\nvoid merge(vector&lt;int&gt; &amp;nums, int left, int mid, int right) {\n    // Диапазон левого подмассива: [left, mid], диапазон правого подмассива: [mid+1, right]\n    // Создать временный массив tmp для хранения результата слияния\n    vector&lt;int&gt; tmp(right - left + 1);\n    // Инициализировать начальные индексы левого и правого подмассивов\n    int i = left, j = mid + 1, k = 0;\n    // Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n    while (i &lt;= mid &amp;&amp; j &lt;= right) {\n        if (nums[i] &lt;= nums[j])\n            tmp[k++] = nums[i++];\n        else\n            tmp[k++] = nums[j++];\n    }\n    // Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n    while (i &lt;= mid) {\n        tmp[k++] = nums[i++];\n    }\n    while (j &lt;= right) {\n        tmp[k++] = nums[j++];\n    }\n    // Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n    for (k = 0; k &lt; tmp.size(); k++) {\n        nums[left + k] = tmp[k];\n    }\n}\n\n/* Сортировка слиянием */\nvoid mergeSort(vector&lt;int&gt; &amp;nums, int left, int right) {\n    // Условие завершения\n    if (left &gt;= right)\n        return; // Завершить рекурсию, когда длина подмассива равна 1\n    // Этап разбиения\n    int mid = left + (right - left) / 2;    // Вычислить середину\n    mergeSort(nums, left, mid);      // Рекурсивно обработать левый подмассив\n    mergeSort(nums, mid + 1, right); // Рекурсивно обработать правый подмассив\n    // Этап слияния\n    merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.java<pre><code>/* Объединить левый и правый подмассивы */\nvoid merge(int[] nums, int left, int mid, int right) {\n    // Диапазон левого подмассива: [left, mid], диапазон правого подмассива: [mid+1, right]\n    // Создать временный массив tmp для хранения результата слияния\n    int[] tmp = new int[right - left + 1];\n    // Инициализировать начальные индексы левого и правого подмассивов\n    int i = left, j = mid + 1, k = 0;\n    // Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n    while (i &lt;= mid &amp;&amp; j &lt;= right) {\n        if (nums[i] &lt;= nums[j])\n            tmp[k++] = nums[i++];\n        else\n            tmp[k++] = nums[j++];\n    }\n    // Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n    while (i &lt;= mid) {\n        tmp[k++] = nums[i++];\n    }\n    while (j &lt;= right) {\n        tmp[k++] = nums[j++];\n    }\n    // Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n    for (k = 0; k &lt; tmp.length; k++) {\n        nums[left + k] = tmp[k];\n    }\n}\n\n/* Сортировка слиянием */\nvoid mergeSort(int[] nums, int left, int right) {\n    // Условие завершения\n    if (left &gt;= right)\n        return; // Завершить рекурсию, когда длина подмассива равна 1\n    // Этап разбиения\n    int mid = left + (right - left) / 2; // Вычислить середину\n    mergeSort(nums, left, mid); // Рекурсивно обработать левый подмассив\n    mergeSort(nums, mid + 1, right); // Рекурсивно обработать правый подмассив\n    // Этап слияния\n    merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.cs<pre><code>/* Объединить левый и правый подмассивы */\nvoid Merge(int[] nums, int left, int mid, int right) {\n    // Диапазон левого подмассива: [left, mid], диапазон правого подмассива: [mid+1, right]\n    // Создать временный массив tmp для хранения результата слияния\n    int[] tmp = new int[right - left + 1];\n    // Инициализировать начальные индексы левого и правого подмассивов\n    int i = left, j = mid + 1, k = 0;\n    // Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n    while (i &lt;= mid &amp;&amp; j &lt;= right) {\n        if (nums[i] &lt;= nums[j])\n            tmp[k++] = nums[i++];\n        else\n            tmp[k++] = nums[j++];\n    }\n    // Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n    while (i &lt;= mid) {\n        tmp[k++] = nums[i++];\n    }\n    while (j &lt;= right) {\n        tmp[k++] = nums[j++];\n    }\n    // Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n    for (k = 0; k &lt; tmp.Length; ++k) {\n        nums[left + k] = tmp[k];\n    }\n}\n\n/* Сортировка слиянием */\nvoid MergeSort(int[] nums, int left, int right) {\n    // Условие завершения\n    if (left &gt;= right) return;       // Завершить рекурсию, когда длина подмассива равна 1\n    // Этап разбиения\n    int mid = left + (right - left) / 2;    // Вычислить середину\n    MergeSort(nums, left, mid);      // Рекурсивно обработать левый подмассив\n    MergeSort(nums, mid + 1, right); // Рекурсивно обработать правый подмассив\n    // Этап слияния\n    Merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.go<pre><code>/* Объединить левый и правый подмассивы */\nfunc merge(nums []int, left, mid, right int) {\n    // Диапазон левого подмассива: [left, mid], диапазон правого подмассива: [mid+1, right]\n    // Создать временный массив tmp для хранения результата слияния\n    tmp := make([]int, right-left+1)\n    // Инициализировать начальные индексы левого и правого подмассивов\n    i, j, k := left, mid+1, 0\n    // Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n    for i &lt;= mid &amp;&amp; j &lt;= right {\n        if nums[i] &lt;= nums[j] {\n            tmp[k] = nums[i]\n            i++\n        } else {\n            tmp[k] = nums[j]\n            j++\n        }\n        k++\n    }\n    // Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n    for i &lt;= mid {\n        tmp[k] = nums[i]\n        i++\n        k++\n    }\n    for j &lt;= right {\n        tmp[k] = nums[j]\n        j++\n        k++\n    }\n    // Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n    for k := 0; k &lt; len(tmp); k++ {\n        nums[left+k] = tmp[k]\n    }\n}\n\n/* Сортировка слиянием */\nfunc mergeSort(nums []int, left, right int) {\n    // Условие завершения\n    if left &gt;= right {\n        return\n    }\n    // Этап разбиения\n    mid := left + (right - left) / 2\n    mergeSort(nums, left, mid)\n    mergeSort(nums, mid+1, right)\n    // Этап слияния\n    merge(nums, left, mid, right)\n}\n</code></pre> merge_sort.swift<pre><code>/* Объединить левый и правый подмассивы */\nfunc merge(nums: inout [Int], left: Int, mid: Int, right: Int) {\n    // Диапазон левого подмассива: [left, mid], диапазон правого подмассива: [mid+1, right]\n    // Создать временный массив tmp для хранения результата слияния\n    var tmp = Array(repeating: 0, count: right - left + 1)\n    // Инициализировать начальные индексы левого и правого подмассивов\n    var i = left, j = mid + 1, k = 0\n    // Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n    while i &lt;= mid, j &lt;= right {\n        if nums[i] &lt;= nums[j] {\n            tmp[k] = nums[i]\n            i += 1\n        } else {\n            tmp[k] = nums[j]\n            j += 1\n        }\n        k += 1\n    }\n    // Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n    while i &lt;= mid {\n        tmp[k] = nums[i]\n        i += 1\n        k += 1\n    }\n    while j &lt;= right {\n        tmp[k] = nums[j]\n        j += 1\n        k += 1\n    }\n    // Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n    for k in tmp.indices {\n        nums[left + k] = tmp[k]\n    }\n}\n\n/* Сортировка слиянием */\nfunc mergeSort(nums: inout [Int], left: Int, right: Int) {\n    // Условие завершения\n    if left &gt;= right { // Завершить рекурсию, когда длина подмассива равна 1\n        return\n    }\n    // Этап разбиения\n    let mid = left + (right - left) / 2 // Вычислить середину\n    mergeSort(nums: &amp;nums, left: left, right: mid) // Рекурсивно обработать левый подмассив\n    mergeSort(nums: &amp;nums, left: mid + 1, right: right) // Рекурсивно обработать правый подмассив\n    // Этап слияния\n    merge(nums: &amp;nums, left: left, mid: mid, right: right)\n}\n</code></pre> merge_sort.js<pre><code>/* Объединить левый и правый подмассивы */\nfunction merge(nums, left, mid, right) {\n    // Диапазон левого подмассива: [left, mid], диапазон правого подмассива: [mid+1, right]\n    // Создать временный массив tmp для хранения результата слияния\n    const tmp = new Array(right - left + 1);\n    // Инициализировать начальные индексы левого и правого подмассивов\n    let i = left,\n        j = mid + 1,\n        k = 0;\n    // Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n    while (i &lt;= mid &amp;&amp; j &lt;= right) {\n        if (nums[i] &lt;= nums[j]) {\n            tmp[k++] = nums[i++];\n        } else {\n            tmp[k++] = nums[j++];\n        }\n    }\n    // Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n    while (i &lt;= mid) {\n        tmp[k++] = nums[i++];\n    }\n    while (j &lt;= right) {\n        tmp[k++] = nums[j++];\n    }\n    // Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n    for (k = 0; k &lt; tmp.length; k++) {\n        nums[left + k] = tmp[k];\n    }\n}\n\n/* Сортировка слиянием */\nfunction mergeSort(nums, left, right) {\n    // Условие завершения\n    if (left &gt;= right) return; // Завершить рекурсию, когда длина подмассива равна 1\n    // Этап разбиения\n    let mid = Math.floor(left + (right - left) / 2); // Вычислить середину\n    mergeSort(nums, left, mid); // Рекурсивно обработать левый подмассив\n    mergeSort(nums, mid + 1, right); // Рекурсивно обработать правый подмассив\n    // Этап слияния\n    merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.ts<pre><code>/* Объединить левый и правый подмассивы */\nfunction merge(nums: number[], left: number, mid: number, right: number): void {\n    // Диапазон левого подмассива: [left, mid], диапазон правого подмассива: [mid+1, right]\n    // Создать временный массив tmp для хранения результата слияния\n    const tmp = new Array(right - left + 1);\n    // Инициализировать начальные индексы левого и правого подмассивов\n    let i = left,\n        j = mid + 1,\n        k = 0;\n    // Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n    while (i &lt;= mid &amp;&amp; j &lt;= right) {\n        if (nums[i] &lt;= nums[j]) {\n            tmp[k++] = nums[i++];\n        } else {\n            tmp[k++] = nums[j++];\n        }\n    }\n    // Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n    while (i &lt;= mid) {\n        tmp[k++] = nums[i++];\n    }\n    while (j &lt;= right) {\n        tmp[k++] = nums[j++];\n    }\n    // Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n    for (k = 0; k &lt; tmp.length; k++) {\n        nums[left + k] = tmp[k];\n    }\n}\n\n/* Сортировка слиянием */\nfunction mergeSort(nums: number[], left: number, right: number): void {\n    // Условие завершения\n    if (left &gt;= right) return; // Завершить рекурсию, когда длина подмассива равна 1\n    // Этап разбиения\n    let mid = Math.floor(left + (right - left) / 2); // Вычислить середину\n    mergeSort(nums, left, mid); // Рекурсивно обработать левый подмассив\n    mergeSort(nums, mid + 1, right); // Рекурсивно обработать правый подмассив\n    // Этап слияния\n    merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.dart<pre><code>/* Объединить левый и правый подмассивы */\nvoid merge(List&lt;int&gt; nums, int left, int mid, int right) {\n  // Диапазон левого подмассива: [left, mid], диапазон правого подмассива: [mid+1, right]\n  // Создать временный массив tmp для хранения результата слияния\n  List&lt;int&gt; tmp = List.filled(right - left + 1, 0);\n  // Инициализировать начальные индексы левого и правого подмассивов\n  int i = left, j = mid + 1, k = 0;\n  // Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n  while (i &lt;= mid &amp;&amp; j &lt;= right) {\n    if (nums[i] &lt;= nums[j])\n      tmp[k++] = nums[i++];\n    else\n      tmp[k++] = nums[j++];\n  }\n  // Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n  while (i &lt;= mid) {\n    tmp[k++] = nums[i++];\n  }\n  while (j &lt;= right) {\n    tmp[k++] = nums[j++];\n  }\n  // Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n  for (k = 0; k &lt; tmp.length; k++) {\n    nums[left + k] = tmp[k];\n  }\n}\n\n/* Сортировка слиянием */\nvoid mergeSort(List&lt;int&gt; nums, int left, int right) {\n  // Условие завершения\n  if (left &gt;= right) return; // Завершить рекурсию, когда длина подмассива равна 1\n  // Этап разбиения\n  int mid = left + (right - left) ~/ 2; // Вычислить середину\n  mergeSort(nums, left, mid); // Рекурсивно обработать левый подмассив\n  mergeSort(nums, mid + 1, right); // Рекурсивно обработать правый подмассив\n  // Этап слияния\n  merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.rs<pre><code>/* Объединить левый и правый подмассивы */\nfn merge(nums: &amp;mut [i32], left: usize, mid: usize, right: usize) {\n    // Диапазон левого подмассива: [left, mid], диапазон правого подмассива: [mid+1, right]\n    // Создать временный массив tmp для хранения результата слияния\n    let tmp_size = right - left + 1;\n    let mut tmp = vec![0; tmp_size];\n    // Инициализировать начальные индексы левого и правого подмассивов\n    let (mut i, mut j, mut k) = (left, mid + 1, 0);\n    // Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n    while i &lt;= mid &amp;&amp; j &lt;= right {\n        if nums[i] &lt;= nums[j] {\n            tmp[k] = nums[i];\n            i += 1;\n        } else {\n            tmp[k] = nums[j];\n            j += 1;\n        }\n        k += 1;\n    }\n    // Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n    while i &lt;= mid {\n        tmp[k] = nums[i];\n        k += 1;\n        i += 1;\n    }\n    while j &lt;= right {\n        tmp[k] = nums[j];\n        k += 1;\n        j += 1;\n    }\n    // Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n    for k in 0..tmp_size {\n        nums[left + k] = tmp[k];\n    }\n}\n\n/* Сортировка слиянием */\nfn merge_sort(nums: &amp;mut [i32], left: usize, right: usize) {\n    // Условие завершения\n    if left &gt;= right {\n        return; // Завершить рекурсию, когда длина подмассива равна 1\n    }\n\n    // Этап разбиения\n    let mid = left + (right - left) / 2; // Вычислить середину\n    merge_sort(nums, left, mid); // Рекурсивно обработать левый подмассив\n    merge_sort(nums, mid + 1, right); // Рекурсивно обработать правый подмассив\n\n    // Этап слияния\n    merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.c<pre><code>/* Объединить левый и правый подмассивы */\nvoid merge(int *nums, int left, int mid, int right) {\n    // Диапазон левого подмассива: [left, mid], диапазон правого подмассива: [mid+1, right]\n    // Создать временный массив tmp для хранения результата слияния\n    int tmpSize = right - left + 1;\n    int *tmp = (int *)malloc(tmpSize * sizeof(int));\n    // Инициализировать начальные индексы левого и правого подмассивов\n    int i = left, j = mid + 1, k = 0;\n    // Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n    while (i &lt;= mid &amp;&amp; j &lt;= right) {\n        if (nums[i] &lt;= nums[j]) {\n            tmp[k++] = nums[i++];\n        } else {\n            tmp[k++] = nums[j++];\n        }\n    }\n    // Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n    while (i &lt;= mid) {\n        tmp[k++] = nums[i++];\n    }\n    while (j &lt;= right) {\n        tmp[k++] = nums[j++];\n    }\n    // Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n    for (k = 0; k &lt; tmpSize; ++k) {\n        nums[left + k] = tmp[k];\n    }\n    // Освободить память\n    free(tmp);\n}\n\n/* Сортировка слиянием */\nvoid mergeSort(int *nums, int left, int right) {\n    // Условие завершения\n    if (left &gt;= right)\n        return; // Завершить рекурсию, когда длина подмассива равна 1\n    // Этап разбиения\n    int mid = left + (right - left) / 2;    // Вычислить середину\n    mergeSort(nums, left, mid);      // Рекурсивно обработать левый подмассив\n    mergeSort(nums, mid + 1, right); // Рекурсивно обработать правый подмассив\n    // Этап слияния\n    merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.kt<pre><code>/* Объединить левый и правый подмассивы */\nfun merge(nums: IntArray, left: Int, mid: Int, right: Int) {\n    // Диапазон левого подмассива: [left, mid], диапазон правого подмассива: [mid+1, right]\n    // Создать временный массив tmp для хранения результата слияния\n    val tmp = IntArray(right - left + 1)\n    // Инициализировать начальные индексы левого и правого подмассивов\n    var i = left\n    var j = mid + 1\n    var k = 0\n    // Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n    while (i &lt;= mid &amp;&amp; j &lt;= right) {\n        if (nums[i] &lt;= nums[j])\n            tmp[k++] = nums[i++]\n        else\n            tmp[k++] = nums[j++]\n    }\n    // Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n    while (i &lt;= mid) {\n        tmp[k++] = nums[i++]\n    }\n    while (j &lt;= right) {\n        tmp[k++] = nums[j++]\n    }\n    // Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n    for (l in tmp.indices) {\n        nums[left + l] = tmp[l]\n    }\n}\n\n/* Сортировка слиянием */\nfun mergeSort(nums: IntArray, left: Int, right: Int) {\n    // Условие завершения\n    if (left &gt;= right) return  // Завершить рекурсию, когда длина подмассива равна 1\n    // Этап разбиения\n    val mid = left + (right - left) / 2 // Вычислить середину\n    mergeSort(nums, left, mid) // Рекурсивно обработать левый подмассив\n    mergeSort(nums, mid + 1, right) // Рекурсивно обработать правый подмассив\n    // Этап слияния\n    merge(nums, left, mid, right)\n}\n</code></pre> merge_sort.rb<pre><code>### Слияние левого и правого подмассивов ###\ndef merge(nums, left, mid, right)\n  # Интервал левого подмассива: [left, mid], правого подмассива: [mid+1, right]\n  # Создать временный массив tmp для хранения результата слияния\n  tmp = Array.new(right - left + 1, 0)\n  # Инициализировать начальные индексы левого и правого подмассивов\n  i, j, k = left, mid + 1, 0\n  # Пока в левом и правом подмассивах еще есть элементы, сравнивать их и копировать меньший во временный массив\n  while i &lt;= mid &amp;&amp; j &lt;= right\n    if nums[i] &lt;= nums[j]\n      tmp[k] = nums[i]\n      i += 1\n    else\n      tmp[k] = nums[j]\n      j += 1\n    end\n    k += 1\n  end\n  # Скопировать оставшиеся элементы левого и правого подмассивов во временный массив\n  while i &lt;= mid\n    tmp[k] = nums[i]\n    i += 1\n    k += 1\n  end\n  while j &lt;= right\n    tmp[k] = nums[j]\n    j += 1\n    k += 1\n  end\n  # Скопировать элементы временного массива tmp обратно в соответствующий диапазон исходного массива nums\n  (0...tmp.length).each do |k|\n    nums[left + k] = tmp[k]\n  end\nend\n\n### Сортировка слиянием ###\ndef merge_sort(nums, left, right)\n  # Условие завершения\n  # Когда длина подмассива равна 1, рекурсия завершается\n  return if left &gt;= right\n  # Этап разбиения\n  mid = left + (right - left) / 2 # Вычислить середину\n  merge_sort(nums, left, mid) # Рекурсивно обработать левый подмассив\n  merge_sort(nums, mid + 1, right) # Рекурсивно обработать правый подмассив\n  # Этап слияния\n  merge(nums, left, mid, right)\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 11. Сортировка","11.6 &nbsp; Сортировка слиянием"],"tags":[]},{"location":"chapter_sorting/merge_sort/#1162","level":2,"title":"11.6.2   Характеристики алгоритма","text":"<ul> <li>Временная сложность равна \\(O(n \\log n)\\), алгоритм не является адаптивным: этап разделения создает дерево рекурсии высоты \\(\\log n\\) , а суммарное число операций слияния на каждом уровне равно \\(n\\) , поэтому общая временная сложность составляет \\(O(n \\log n)\\) .</li> <li>Пространственная сложность равна \\(O(n)\\), сортировка не выполняется на месте: глубина рекурсии равна \\(\\log n\\) , из-за чего требуется \\(O(\\log n)\\) памяти под стек вызовов. Для этапа слияния нужен вспомогательный массив, поэтому дополнительно используется \\(O(n)\\) памяти.</li> <li>Стабильная сортировка: в процессе слияния относительный порядок равных элементов не меняется.</li> </ul>","path":["Глава 11. Сортировка","11.6 &nbsp; Сортировка слиянием"],"tags":[]},{"location":"chapter_sorting/merge_sort/#1163","level":2,"title":"11.6.3   Сортировка связного списка","text":"<p>Для связных списков сортировка слиянием имеет заметное преимущество перед другими алгоритмами сортировки: пространственную сложность задачи сортировки списка можно оптимизировать до \\(O(1)\\).</p> <ul> <li>Этап разделения: работу по разбиению списка можно реализовать с помощью \"итерации\" вместо \"рекурсии\", тем самым устранив расход памяти на стек вызовов.</li> <li>Этап слияния: в связном списке добавление и удаление узлов требует только изменения ссылок (указателей), поэтому при слиянии двух коротких упорядоченных списков в один длинный упорядоченный список не нужно создавать дополнительный список.</li> </ul> <p>Детали реализации достаточно сложны; заинтересованные читатели могут обратиться к соответствующим материалам самостоятельно.</p>","path":["Глава 11. Сортировка","11.6 &nbsp; Сортировка слиянием"],"tags":[]},{"location":"chapter_sorting/quick_sort/","level":1,"title":"11.5   Быстрая сортировка","text":"<p>Быстрая сортировка (quick sort) - это алгоритм сортировки, основанный на стратегии \"разделяй и властвуй\"; он работает эффективно и применяется очень широко.</p> <p>Ключевая операция быстрой сортировки - это \"разделение с опорным элементом\". Ее цель такова: выбрать некоторый элемент массива в качестве \"опорного\" и переместить все элементы меньше опорного влево от него, а все элементы больше опорного - вправо. Конкретный процесс показан на рисунке 11-8.</p> <ol> <li>Выбрать самый левый элемент массива как опорный и инициализировать два указателя <code>i</code> и <code>j</code> , направленные на левую и правую границы массива.</li> <li>Запустить цикл, в котором <code>i</code> и <code>j</code> ищут соответственно первый элемент, больший опорного, и первый элемент, меньший опорного, после чего эти два элемента меняются местами.</li> <li>Повторять шаг <code>2.</code> , пока указатели <code>i</code> и <code>j</code> не встретятся, а затем обменять опорный элемент с элементом на границе двух подмассивов.</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 11-8   Шаги разделения с опорным элементом </p> <p>После завершения разделения исходный массив разбивается на три части: левый подмассив, опорный элемент и правый подмассив; при этом выполняется условие \"любой элемент левого подмассива \\(\\leq\\) опорный элемент \\(\\leq\\) любой элемент правого подмассива\". Следовательно, далее нам нужно лишь отсортировать эти два подмассива.</p> <p>Стратегия разделяй и властвуй в быстрой сортировке</p> <p>Иными словами, разделение с опорным элементом сводит задачу сортировки длинного массива к двум задачам сортировки более коротких массивов.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby quick_sort.py<pre><code>def partition(self, nums: list[int], left: int, right: int) -&gt; int:\n    \"\"\"Разбиение с опорными указателями\"\"\"\n    # Взять nums[left] в качестве опорного элемента\n    i, j = left, right\n    while i &lt; j:\n        while i &lt; j and nums[j] &gt;= nums[left]:\n            j -= 1  # Идти справа налево в поисках первого элемента меньше опорного\n        while i &lt; j and nums[i] &lt;= nums[left]:\n            i += 1  # Идти слева направо в поисках первого элемента больше опорного\n        # Обмен элементов\n        nums[i], nums[j] = nums[j], nums[i]\n    # Переместить опорный элемент на границу двух подмассивов\n    nums[i], nums[left] = nums[left], nums[i]\n    return i  # Вернуть индекс опорного элемента\n</code></pre> quick_sort.cpp<pre><code>/* Разбиение с опорными указателями */\nint partition(vector&lt;int&gt; &amp;nums, int left, int right) {\n    // Взять nums[left] в качестве опорного элемента\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--;                // Идти справа налево в поисках первого элемента меньше опорного\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;                // Идти слева направо в поисках первого элемента больше опорного\n        swap(nums[i], nums[j]); // Поменять эти два элемента местами\n    }\n    swap(nums[i], nums[left]);  // Переместить опорный элемент на границу двух подмассивов\n    return i;                   // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.java<pre><code>/* Обмен элементов */\nvoid swap(int[] nums, int i, int j) {\n    int tmp = nums[i];\n    nums[i] = nums[j];\n    nums[j] = tmp;\n}\n\n/* Разбиение с опорными указателями */\nint partition(int[] nums, int left, int right) {\n    // Взять nums[left] в качестве опорного элемента\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--;          // Идти справа налево в поисках первого элемента меньше опорного\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;          // Идти слева направо в поисках первого элемента больше опорного\n        swap(nums, i, j); // Поменять эти два элемента местами\n    }\n    swap(nums, i, left);  // Переместить опорный элемент на границу двух подмассивов\n    return i;             // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.cs<pre><code>/* Обмен элементов */\nvoid Swap(int[] nums, int i, int j) {\n    (nums[j], nums[i]) = (nums[i], nums[j]);\n}\n\n/* Разбиение с опорными указателями */\nint Partition(int[] nums, int left, int right) {\n    // Взять nums[left] в качестве опорного элемента\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--;          // Идти справа налево в поисках первого элемента меньше опорного\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;          // Идти слева направо в поисках первого элемента больше опорного\n        Swap(nums, i, j); // Поменять эти два элемента местами\n    }\n    Swap(nums, i, left);  // Переместить опорный элемент на границу двух подмассивов\n    return i;             // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.go<pre><code>/* Разбиение с опорными указателями */\nfunc (q *quickSort) partition(nums []int, left, right int) int {\n    // Взять nums[left] в качестве опорного элемента\n    i, j := left, right\n    for i &lt; j {\n        for i &lt; j &amp;&amp; nums[j] &gt;= nums[left] {\n            j-- // Идти справа налево в поисках первого элемента меньше опорного\n        }\n        for i &lt; j &amp;&amp; nums[i] &lt;= nums[left] {\n            i++ // Идти слева направо в поисках первого элемента больше опорного\n        }\n        // Обмен элементов\n        nums[i], nums[j] = nums[j], nums[i]\n    }\n    // Переместить опорный элемент на границу двух подмассивов\n    nums[i], nums[left] = nums[left], nums[i]\n    return i // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.swift<pre><code>/* Разбиение с опорными указателями */\nfunc partition(nums: inout [Int], left: Int, right: Int) -&gt; Int {\n    // Взять nums[left] в качестве опорного элемента\n    var i = left\n    var j = right\n    while i &lt; j {\n        while i &lt; j, nums[j] &gt;= nums[left] {\n            j -= 1 // Идти справа налево в поисках первого элемента меньше опорного\n        }\n        while i &lt; j, nums[i] &lt;= nums[left] {\n            i += 1 // Идти слева направо в поисках первого элемента больше опорного\n        }\n        nums.swapAt(i, j) // Поменять эти два элемента местами\n    }\n    nums.swapAt(i, left) // Переместить опорный элемент на границу двух подмассивов\n    return i // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.js<pre><code>/* Обмен элементов */\nswap(nums, i, j) {\n    let tmp = nums[i];\n    nums[i] = nums[j];\n    nums[j] = tmp;\n}\n\n/* Разбиение с опорными указателями */\npartition(nums, left, right) {\n    // Взять nums[left] в качестве опорного элемента\n    let i = left,\n        j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) {\n            j -= 1; // Идти справа налево в поисках первого элемента меньше опорного\n        }\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) {\n            i += 1; // Идти слева направо в поисках первого элемента больше опорного\n        }\n        // Обмен элементов\n        this.swap(nums, i, j); // Поменять эти два элемента местами\n    }\n    this.swap(nums, i, left); // Переместить опорный элемент на границу двух подмассивов\n    return i; // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.ts<pre><code>/* Обмен элементов */\nswap(nums: number[], i: number, j: number): void {\n    let tmp = nums[i];\n    nums[i] = nums[j];\n    nums[j] = tmp;\n}\n\n/* Разбиение с опорными указателями */\npartition(nums: number[], left: number, right: number): number {\n    // Взять nums[left] в качестве опорного элемента\n    let i = left,\n        j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) {\n            j -= 1; // Идти справа налево в поисках первого элемента меньше опорного\n        }\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) {\n            i += 1; // Идти слева направо в поисках первого элемента больше опорного\n        }\n        // Обмен элементов\n        this.swap(nums, i, j); // Поменять эти два элемента местами\n    }\n    this.swap(nums, i, left); // Переместить опорный элемент на границу двух подмассивов\n    return i; // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.dart<pre><code>/* Обмен элементов */\nvoid _swap(List&lt;int&gt; nums, int i, int j) {\n  int tmp = nums[i];\n  nums[i] = nums[j];\n  nums[j] = tmp;\n}\n\n/* Разбиение с опорными указателями */\nint _partition(List&lt;int&gt; nums, int left, int right) {\n  // Взять nums[left] в качестве опорного элемента\n  int i = left, j = right;\n  while (i &lt; j) {\n    while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) j--; // Идти справа налево в поисках первого элемента меньше опорного\n    while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) i++; // Идти слева направо в поисках первого элемента больше опорного\n    _swap(nums, i, j); // Поменять эти два элемента местами\n  }\n  _swap(nums, i, left); // Переместить опорный элемент на границу двух подмассивов\n  return i; // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.rs<pre><code>/* Разбиение с опорными указателями */\nfn partition(nums: &amp;mut [i32], left: usize, right: usize) -&gt; usize {\n    // Взять nums[left] в качестве опорного элемента\n    let (mut i, mut j) = (left, right);\n    while i &lt; j {\n        while i &lt; j &amp;&amp; nums[j] &gt;= nums[left] {\n            j -= 1; // Идти справа налево в поисках первого элемента меньше опорного\n        }\n        while i &lt; j &amp;&amp; nums[i] &lt;= nums[left] {\n            i += 1; // Идти слева направо в поисках первого элемента больше опорного\n        }\n        nums.swap(i, j); // Поменять эти два элемента местами\n    }\n    nums.swap(i, left); // Переместить опорный элемент на границу двух подмассивов\n    i // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.c<pre><code>/* Обмен элементов */\nvoid swap(int nums[], int i, int j) {\n    int tmp = nums[i];\n    nums[i] = nums[j];\n    nums[j] = tmp;\n}\n\n/* Разбиение с опорными указателями */\nint partition(int nums[], int left, int right) {\n    // Взять nums[left] в качестве опорного элемента\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) {\n            j--; // Идти справа налево в поисках первого элемента меньше опорного\n        }\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) {\n            i++; // Идти слева направо в поисках первого элемента больше опорного\n        }\n        // Поменять эти два элемента местами\n        swap(nums, i, j);\n    }\n    // Переместить опорный элемент на границу двух подмассивов\n    swap(nums, i, left);\n    // Вернуть индекс опорного элемента\n    return i;\n}\n</code></pre> quick_sort.kt<pre><code>/* Обмен элементов */\nfun swap(nums: IntArray, i: Int, j: Int) {\n    val temp = nums[i]\n    nums[i] = nums[j]\n    nums[j] = temp\n}\n\n/* Разбиение с опорными указателями */\nfun partition(nums: IntArray, left: Int, right: Int): Int {\n    // Взять nums[left] в качестве опорного элемента\n    var i = left\n    var j = right\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--           // Идти справа налево в поисках первого элемента меньше опорного\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++           // Идти слева направо в поисках первого элемента больше опорного\n        swap(nums, i, j)  // Поменять эти два элемента местами\n    }\n    swap(nums, i, left)   // Переместить опорный элемент на границу двух подмассивов\n    return i              // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.rb<pre><code>### Разбиение с опорными указателями ###\ndef partition(nums, left, right)\n  # Взять nums[left] в качестве опорного элемента\n  i, j = left, right\n  while i &lt; j\n    while i &lt; j &amp;&amp; nums[j] &gt;= nums[left]\n      j -= 1 # Идти справа налево в поисках первого элемента меньше опорного\n    end\n    while i &lt; j &amp;&amp; nums[i] &lt;= nums[left]\n      i += 1 # Идти слева направо в поисках первого элемента больше опорного\n    end\n    # Обмен элементов\n    nums[i], nums[j] = nums[j], nums[i]\n  end\n  # Переместить опорный элемент на границу двух подмассивов\n  nums[i], nums[left] = nums[left], nums[i]\n  i # Вернуть индекс опорного элемента\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 11. Сортировка","11.5 &nbsp; Быстрая сортировка"],"tags":[]},{"location":"chapter_sorting/quick_sort/#1151","level":2,"title":"11.5.1   Алгоритм","text":"<p>Общий процесс быстрой сортировки показан на рисунке 11-9.</p> <ol> <li>Сначала выполнить \"разделение с опорным элементом\" для исходного массива и получить неотсортированные левый и правый подмассивы.</li> <li>Затем рекурсивно выполнить \"разделение с опорным элементом\" для левого и правого подмассивов.</li> <li>Продолжать рекурсию до тех пор, пока длина подмассива не станет равной 1; после этого сортировка всего массива будет завершена.</li> </ol> <p></p> <p> Рисунок 11-9   Процесс быстрой сортировки </p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby quick_sort.py<pre><code>def quick_sort(self, nums: list[int], left: int, right: int):\n    \"\"\"Быстрая сортировка\"\"\"\n    # Завершить рекурсию, когда длина подмассива равна 1\n    if left &gt;= right:\n        return\n    # Разбиение с опорными указателями\n    pivot = self.partition(nums, left, right)\n    # Рекурсивно обработать левый и правый подмассивы\n    self.quick_sort(nums, left, pivot - 1)\n    self.quick_sort(nums, pivot + 1, right)\n</code></pre> quick_sort.cpp<pre><code>/* Быстрая сортировка */\nvoid quickSort(vector&lt;int&gt; &amp;nums, int left, int right) {\n    // Завершить рекурсию, когда длина подмассива равна 1\n    if (left &gt;= right)\n        return;\n    // Разбиение с опорными указателями\n    int pivot = partition(nums, left, right);\n    // Рекурсивно обработать левый и правый подмассивы\n    quickSort(nums, left, pivot - 1);\n    quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.java<pre><code>/* Быстрая сортировка */\nvoid quickSort(int[] nums, int left, int right) {\n    // Завершить рекурсию, когда длина подмассива равна 1\n    if (left &gt;= right)\n        return;\n    // Разбиение с опорными указателями\n    int pivot = partition(nums, left, right);\n    // Рекурсивно обработать левый и правый подмассивы\n    quickSort(nums, left, pivot - 1);\n    quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.cs<pre><code>/* Быстрая сортировка */\nvoid QuickSort(int[] nums, int left, int right) {\n    // Завершить рекурсию, когда длина подмассива равна 1\n    if (left &gt;= right)\n        return;\n    // Разбиение с опорными указателями\n    int pivot = Partition(nums, left, right);\n    // Рекурсивно обработать левый и правый подмассивы\n    QuickSort(nums, left, pivot - 1);\n    QuickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.go<pre><code>/* Быстрая сортировка */\nfunc (q *quickSort) quickSort(nums []int, left, right int) {\n    // Завершить рекурсию, когда длина подмассива равна 1\n    if left &gt;= right {\n        return\n    }\n    // Разбиение с опорными указателями\n    pivot := q.partition(nums, left, right)\n    // Рекурсивно обработать левый и правый подмассивы\n    q.quickSort(nums, left, pivot-1)\n    q.quickSort(nums, pivot+1, right)\n}\n</code></pre> quick_sort.swift<pre><code>/* Быстрая сортировка */\nfunc quickSort(nums: inout [Int], left: Int, right: Int) {\n    // Завершить рекурсию, когда длина подмассива равна 1\n    if left &gt;= right {\n        return\n    }\n    // Разбиение с опорными указателями\n    let pivot = partition(nums: &amp;nums, left: left, right: right)\n    // Рекурсивно обработать левый и правый подмассивы\n    quickSort(nums: &amp;nums, left: left, right: pivot - 1)\n    quickSort(nums: &amp;nums, left: pivot + 1, right: right)\n}\n</code></pre> quick_sort.js<pre><code>/* Быстрая сортировка */\nquickSort(nums, left, right) {\n    // Завершить рекурсию, когда длина подмассива равна 1\n    if (left &gt;= right) return;\n    // Разбиение с опорными указателями\n    const pivot = this.partition(nums, left, right);\n    // Рекурсивно обработать левый и правый подмассивы\n    this.quickSort(nums, left, pivot - 1);\n    this.quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.ts<pre><code>/* Быстрая сортировка */\nquickSort(nums: number[], left: number, right: number): void {\n    // Завершить рекурсию, когда длина подмассива равна 1\n    if (left &gt;= right) {\n        return;\n    }\n    // Разбиение с опорными указателями\n    const pivot = this.partition(nums, left, right);\n    // Рекурсивно обработать левый и правый подмассивы\n    this.quickSort(nums, left, pivot - 1);\n    this.quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.dart<pre><code>/* Быстрая сортировка */\nvoid quickSort(List&lt;int&gt; nums, int left, int right) {\n  // Завершить рекурсию, когда длина подмассива равна 1\n  if (left &gt;= right) return;\n  // Разбиение с опорными указателями\n  int pivot = _partition(nums, left, right);\n  // Рекурсивно обработать левый и правый подмассивы\n  quickSort(nums, left, pivot - 1);\n  quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.rs<pre><code>/* Быстрая сортировка */\npub fn quick_sort(left: i32, right: i32, nums: &amp;mut [i32]) {\n    // Завершить рекурсию, когда длина подмассива равна 1\n    if left &gt;= right {\n        return;\n    }\n    // Разбиение с опорными указателями\n    let pivot = Self::partition(nums, left as usize, right as usize) as i32;\n    // Рекурсивно обработать левый и правый подмассивы\n    Self::quick_sort(left, pivot - 1, nums);\n    Self::quick_sort(pivot + 1, right, nums);\n}\n</code></pre> quick_sort.c<pre><code>/* Быстрая сортировка */\nvoid quickSort(int nums[], int left, int right) {\n    // Завершить рекурсию, когда длина подмассива равна 1\n    if (left &gt;= right) {\n        return;\n    }\n    // Разбиение с опорными указателями\n    int pivot = partition(nums, left, right);\n    // Рекурсивно обработать левый и правый подмассивы\n    quickSort(nums, left, pivot - 1);\n    quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.kt<pre><code>/* Быстрая сортировка */\nfun quickSort(nums: IntArray, left: Int, right: Int) {\n    // Завершить рекурсию, когда длина подмассива равна 1\n    if (left &gt;= right) return\n    // Разбиение с опорными указателями\n    val pivot = partition(nums, left, right)\n    // Рекурсивно обработать левый и правый подмассивы\n    quickSort(nums, left, pivot - 1)\n    quickSort(nums, pivot + 1, right)\n}\n</code></pre> quick_sort.rb<pre><code>### Класс быстрой сортировки ###\ndef quick_sort(nums, left, right)\n  # Рекурсивно обрабатывать, пока длина подмассива не станет равной 1\n  if left &lt; right\n    # Разбиение с опорными указателями\n    pivot = partition(nums, left, right)\n    # Рекурсивно обработать левый и правый подмассивы\n    quick_sort(nums, left, pivot - 1)\n    quick_sort(nums, pivot + 1, right)\n  end\n  nums\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 11. Сортировка","11.5 &nbsp; Быстрая сортировка"],"tags":[]},{"location":"chapter_sorting/quick_sort/#1152","level":2,"title":"11.5.2   Характеристики алгоритма","text":"<ul> <li>Временная сложность равна \\(O(n \\log n)\\), алгоритм не является адаптивным: в среднем глубина рекурсии при разделении равна \\(\\log n\\) , а суммарное число циклов на каждом уровне равно \\(n\\) , поэтому общая сложность составляет \\(O(n \\log n)\\) . В худшем случае каждое разделение делит массив длины \\(n\\) на подмассивы длины \\(0\\) и \\(n - 1\\) ; тогда глубина рекурсии достигает \\(n\\) , на каждом уровне выполняется \\(n\\) операций, и общая временная сложность вырождается в \\(O(n^2)\\) .</li> <li>Пространственная сложность равна \\(O(n)\\), сортировка выполняется на месте: если входной массив полностью отсортирован в обратном порядке, глубина рекурсии достигает худшего случая \\(n\\) , что требует \\(O(n)\\) памяти под стек вызовов. При этом сама сортировка выполняется в исходном массиве без дополнительного массива.</li> <li>Нестабильная сортировка: на последнем шаге разделения опорный элемент может быть обменян вправо от равного ему элемента.</li> </ul>","path":["Глава 11. Сортировка","11.5 &nbsp; Быстрая сортировка"],"tags":[]},{"location":"chapter_sorting/quick_sort/#1153","level":2,"title":"11.5.3   Почему быстрая сортировка быстрая","text":"<p>Уже по названию понятно, что быстрая сортировка должна иметь преимущества по эффективности. Хотя ее средняя временная сложность совпадает со сложностью \"сортировки слиянием\" и \"пирамидальной сортировки\", на практике быстрая сортировка обычно работает быстрее. Основные причины таковы.</p> <ul> <li>Вероятность худшего случая очень мала: хотя худшая временная сложность быстрой сортировки равна \\(O(n^2)\\) и она не так стабильна, как сортировка слиянием, в подавляющем большинстве случаев она работает за \\(O(n \\log n)\\) .</li> <li>Высокая эффективность использования кэша: при выполнении разделения система может загрузить весь подмассив в кэш, поэтому доступ к элементам оказывается быстрым. Алгоритмы вроде \"пирамидальной сортировки\" требуют скачкообразного доступа к элементам и таким свойством не обладают.</li> <li>Небольшой константный множитель в сложности: среди трех перечисленных алгоритмов у быстрой сортировки обычно меньше всего сравнений, присваиваний и обменов. Это похоже на причину, по которой \"сортировка вставками\" часто быстрее \"сортировки пузырьком\".</li> </ul>","path":["Глава 11. Сортировка","11.5 &nbsp; Быстрая сортировка"],"tags":[]},{"location":"chapter_sorting/quick_sort/#1154","level":2,"title":"11.5.4   Оптимизация выбора опорного элемента","text":"<p>На некоторых входных данных временная эффективность быстрой сортировки может ухудшаться. Рассмотрим крайний случай: входной массив полностью отсортирован в обратном порядке. Поскольку в качестве опорного мы выбираем самый левый элемент, после разделения он будет обменян в самый правый конец массива, из-за чего длина левого подмассива станет \\(n - 1\\) , а длина правого - \\(0\\) . Если рекурсия будет продолжаться таким образом, то после каждого разделения один из подмассивов будет иметь длину \\(0\\) , стратегия \"разделяй и властвуй\" потеряет смысл, а быстрая сортировка выродится в нечто близкое к \"сортировке пузырьком\".</p> <p>Чтобы по возможности избежать такого сценария, можно улучшить стратегию выбора опорного элемента в процедуре разделения. Например, можно выбирать случайный элемент массива как опорный. Однако если не повезет и каждый раз будет выбираться неудачный опорный элемент, производительность все равно останется неудовлетворительной.</p> <p>Стоит учитывать, что языки программирования обычно генерируют псевдослучайные числа. Если специально построить тестовый пример под такую последовательность, эффективность быстрой сортировки все равно может деградировать.</p> <p>Чтобы улучшить ситуацию, можно взять три кандидата (обычно первый, последний и средний элементы массива) и использовать медиану этих трех значений как опорный элемент. Благодаря этому вероятность того, что опорный элемент окажется \"не слишком маленьким и не слишком большим\", заметно возрастает. Конечно, можно брать и большее число кандидатов, чтобы еще сильнее повысить устойчивость алгоритма. После этого вероятность деградации временной сложности до \\(O(n^2)\\) существенно уменьшается.</p> <p>Пример кода:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby quick_sort.py<pre><code>def median_three(self, nums: list[int], left: int, mid: int, right: int) -&gt; int:\n    \"\"\"Выбрать медиану из трех кандидатов\"\"\"\n    l, m, r = nums[left], nums[mid], nums[right]\n    if (l &lt;= m &lt;= r) or (r &lt;= m &lt;= l):\n        return mid  # m находится между l и r\n    if (m &lt;= l &lt;= r) or (r &lt;= l &lt;= m):\n        return left  # l находится между m и r\n    return right\n\ndef partition(self, nums: list[int], left: int, right: int) -&gt; int:\n    \"\"\"Разбиение с опорными указателями (медиана трех)\"\"\"\n    # Взять nums[left] в качестве опорного элемента\n    med = self.median_three(nums, left, (left + right) // 2, right)\n    # Переместить медиану в крайний левый элемент массива\n    nums[left], nums[med] = nums[med], nums[left]\n    # Взять nums[left] в качестве опорного элемента\n    i, j = left, right\n    while i &lt; j:\n        while i &lt; j and nums[j] &gt;= nums[left]:\n            j -= 1  # Идти справа налево в поисках первого элемента меньше опорного\n        while i &lt; j and nums[i] &lt;= nums[left]:\n            i += 1  # Идти слева направо в поисках первого элемента больше опорного\n        # Обмен элементов\n        nums[i], nums[j] = nums[j], nums[i]\n    # Переместить опорный элемент на границу двух подмассивов\n    nums[i], nums[left] = nums[left], nums[i]\n    return i  # Вернуть индекс опорного элемента\n</code></pre> quick_sort.cpp<pre><code>/* Выбрать медиану из трех кандидатов */\nint medianThree(vector&lt;int&gt; &amp;nums, int left, int mid, int right) {\n    int l = nums[left], m = nums[mid], r = nums[right];\n    if ((l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l))\n        return mid; // m находится между l и r\n    if ((m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m))\n        return left; // l находится между m и r\n    return right;\n}\n\n/* Разбиение с опорными указателями (медиана трех) */\nint partition(vector&lt;int&gt; &amp;nums, int left, int right) {\n    // Выбрать медиану из трех кандидатов\n    int med = medianThree(nums, left, (left + right) / 2, right);\n    // Переместить медиану в крайний левый элемент массива\n    swap(nums[left], nums[med]);\n    // Взять nums[left] в качестве опорного элемента\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--;                // Идти справа налево в поисках первого элемента меньше опорного\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;                // Идти слева направо в поисках первого элемента больше опорного\n        swap(nums[i], nums[j]); // Поменять эти два элемента местами\n    }\n    swap(nums[i], nums[left]);  // Переместить опорный элемент на границу двух подмассивов\n    return i;                   // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.java<pre><code>/* Выбрать медиану из трех кандидатов */\nint medianThree(int[] nums, int left, int mid, int right) {\n    int l = nums[left], m = nums[mid], r = nums[right];\n    if ((l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l))\n        return mid; // m находится между l и r\n    if ((m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m))\n        return left; // l находится между m и r\n    return right;\n}\n\n/* Разбиение с опорными указателями (медиана трех) */\nint partition(int[] nums, int left, int right) {\n    // Выбрать медиану из трех кандидатов\n    int med = medianThree(nums, left, (left + right) / 2, right);\n    // Переместить медиану в крайний левый элемент массива\n    swap(nums, left, med);\n    // Взять nums[left] в качестве опорного элемента\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--;          // Идти справа налево в поисках первого элемента меньше опорного\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;          // Идти слева направо в поисках первого элемента больше опорного\n        swap(nums, i, j); // Поменять эти два элемента местами\n    }\n    swap(nums, i, left);  // Переместить опорный элемент на границу двух подмассивов\n    return i;             // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.cs<pre><code>/* Выбрать медиану из трех кандидатов */\nint MedianThree(int[] nums, int left, int mid, int right) {\n    int l = nums[left], m = nums[mid], r = nums[right];\n    if ((l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l))\n        return mid; // m находится между l и r\n    if ((m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m))\n        return left; // l находится между m и r\n    return right;\n}\n\n/* Разбиение с опорными указателями (медиана трех) */\nint Partition(int[] nums, int left, int right) {\n    // Выбрать медиану из трех кандидатов\n    int med = MedianThree(nums, left, (left + right) / 2, right);\n    // Переместить медиану в крайний левый элемент массива\n    Swap(nums, left, med);\n    // Взять nums[left] в качестве опорного элемента\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--;          // Идти справа налево в поисках первого элемента меньше опорного\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;          // Идти слева направо в поисках первого элемента больше опорного\n        Swap(nums, i, j); // Поменять эти два элемента местами\n    }\n    Swap(nums, i, left);  // Переместить опорный элемент на границу двух подмассивов\n    return i;             // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.go<pre><code>/* Выбрать медиану из трех кандидатов */\nfunc (q *quickSortMedian) medianThree(nums []int, left, mid, right int) int {\n    l, m, r := nums[left], nums[mid], nums[right]\n    if (l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l) {\n        return mid // m находится между l и r\n    }\n    if (m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m) {\n        return left // l находится между m и r\n    }\n    return right\n}\n\n/* Разбиение с опорными указателями (медиана трех) */\nfunc (q *quickSortMedian) partition(nums []int, left, right int) int {\n    // Взять nums[left] в качестве опорного элемента\n    med := q.medianThree(nums, left, (left+right)/2, right)\n    // Переместить медиану в крайний левый элемент массива\n    nums[left], nums[med] = nums[med], nums[left]\n    // Взять nums[left] в качестве опорного элемента\n    i, j := left, right\n    for i &lt; j {\n        for i &lt; j &amp;&amp; nums[j] &gt;= nums[left] {\n            j-- // Идти справа налево в поисках первого элемента меньше опорного\n        }\n        for i &lt; j &amp;&amp; nums[i] &lt;= nums[left] {\n            i++ // Идти слева направо в поисках первого элемента больше опорного\n        }\n        // Обмен элементов\n        nums[i], nums[j] = nums[j], nums[i]\n    }\n    // Переместить опорный элемент на границу двух подмассивов\n    nums[i], nums[left] = nums[left], nums[i]\n    return i // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.swift<pre><code>/* Выбрать медиану из трех кандидатов */\nfunc medianThree(nums: [Int], left: Int, mid: Int, right: Int) -&gt; Int {\n    let l = nums[left]\n    let m = nums[mid]\n    let r = nums[right]\n    if (l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l) {\n        return mid // m находится между l и r\n    }\n    if (m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m) {\n        return left // l находится между m и r\n    }\n    return right\n}\n\n/* Разбиение с опорными указателями (медиана трех) */\nfunc partitionMedian(nums: inout [Int], left: Int, right: Int) -&gt; Int {\n    // Выбрать медиану из трех кандидатов\n    let med = medianThree(nums: nums, left: left, mid: left + (right - left) / 2, right: right)\n    // Переместить медиану в крайний левый элемент массива\n    nums.swapAt(left, med)\n    return partition(nums: &amp;nums, left: left, right: right)\n}\n</code></pre> quick_sort.js<pre><code>/* Выбрать медиану из трех кандидатов */\nmedianThree(nums, left, mid, right) {\n    let l = nums[left],\n        m = nums[mid],\n        r = nums[right];\n    // m находится между l и r\n    if ((l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l)) return mid;\n    // l находится между m и r\n    if ((m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m)) return left;\n    return right;\n}\n\n/* Разбиение с опорными указателями (медиана трех) */\npartition(nums, left, right) {\n    // Выбрать медиану из трех кандидатов\n    let med = this.medianThree(\n        nums,\n        left,\n        Math.floor((left + right) / 2),\n        right\n    );\n    // Переместить медиану в крайний левый элемент массива\n    this.swap(nums, left, med);\n    // Взять nums[left] в качестве опорного элемента\n    let i = left,\n        j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) j--; // Идти справа налево в поисках первого элемента меньше опорного\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) i++; // Идти слева направо в поисках первого элемента больше опорного\n        this.swap(nums, i, j); // Поменять эти два элемента местами\n    }\n    this.swap(nums, i, left); // Переместить опорный элемент на границу двух подмассивов\n    return i; // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.ts<pre><code>/* Выбрать медиану из трех кандидатов */\nmedianThree(\n    nums: number[],\n    left: number,\n    mid: number,\n    right: number\n): number {\n    let l = nums[left],\n        m = nums[mid],\n        r = nums[right];\n    // m находится между l и r\n    if ((l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l)) return mid;\n    // l находится между m и r\n    if ((m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m)) return left;\n    return right;\n}\n\n/* Разбиение с опорными указателями (медиана трех) */\npartition(nums: number[], left: number, right: number): number {\n    // Выбрать медиану из трех кандидатов\n    let med = this.medianThree(\n        nums,\n        left,\n        Math.floor((left + right) / 2),\n        right\n    );\n    // Переместить медиану в крайний левый элемент массива\n    this.swap(nums, left, med);\n    // Взять nums[left] в качестве опорного элемента\n    let i = left,\n        j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) {\n            j--; // Идти справа налево в поисках первого элемента меньше опорного\n        }\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) {\n            i++; // Идти слева направо в поисках первого элемента больше опорного\n        }\n        this.swap(nums, i, j); // Поменять эти два элемента местами\n    }\n    this.swap(nums, i, left); // Переместить опорный элемент на границу двух подмассивов\n    return i; // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.dart<pre><code>/* Выбрать медиану из трех кандидатов */\nint _medianThree(List&lt;int&gt; nums, int left, int mid, int right) {\n  int l = nums[left], m = nums[mid], r = nums[right];\n  if ((l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l))\n    return mid; // m находится между l и r\n  if ((m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m))\n    return left; // l находится между m и r\n  return right;\n}\n\n/* Разбиение с опорными указателями (медиана трех) */\nint _partition(List&lt;int&gt; nums, int left, int right) {\n  // Выбрать медиану из трех кандидатов\n  int med = _medianThree(nums, left, (left + right) ~/ 2, right);\n  // Переместить медиану в крайний левый элемент массива\n  _swap(nums, left, med);\n  // Взять nums[left] в качестве опорного элемента\n  int i = left, j = right;\n  while (i &lt; j) {\n    while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) j--; // Идти справа налево в поисках первого элемента меньше опорного\n    while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) i++; // Идти слева направо в поисках первого элемента больше опорного\n    _swap(nums, i, j); // Поменять эти два элемента местами\n  }\n  _swap(nums, i, left); // Переместить опорный элемент на границу двух подмассивов\n  return i; // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.rs<pre><code>/* Выбрать медиану из трех кандидатов */\nfn median_three(nums: &amp;mut [i32], left: usize, mid: usize, right: usize) -&gt; usize {\n    let (l, m, r) = (nums[left], nums[mid], nums[right]);\n    if (l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l) {\n        return mid; // m находится между l и r\n    }\n    if (m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m) {\n        return left; // l находится между m и r\n    }\n    right\n}\n\n/* Разбиение с опорными указателями (медиана трех) */\nfn partition(nums: &amp;mut [i32], left: usize, right: usize) -&gt; usize {\n    // Выбрать медиану из трех кандидатов\n    let med = Self::median_three(nums, left, (left + right) / 2, right);\n    // Переместить медиану в крайний левый элемент массива\n    nums.swap(left, med);\n    // Взять nums[left] в качестве опорного элемента\n    let (mut i, mut j) = (left, right);\n    while i &lt; j {\n        while i &lt; j &amp;&amp; nums[j] &gt;= nums[left] {\n            j -= 1; // Идти справа налево в поисках первого элемента меньше опорного\n        }\n        while i &lt; j &amp;&amp; nums[i] &lt;= nums[left] {\n            i += 1; // Идти слева направо в поисках первого элемента больше опорного\n        }\n        nums.swap(i, j); // Поменять эти два элемента местами\n    }\n    nums.swap(i, left); // Переместить опорный элемент на границу двух подмассивов\n    i // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.c<pre><code>/* Выбрать медиану из трех кандидатов */\nint medianThree(int nums[], int left, int mid, int right) {\n    int l = nums[left], m = nums[mid], r = nums[right];\n    if ((l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l))\n        return mid; // m находится между l и r\n    if ((m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m))\n        return left; // l находится между m и r\n    return right;\n}\n\n/* Разбиение с опорными указателями (медиана трех) */\nint partitionMedian(int nums[], int left, int right) {\n    // Выбрать медиану из трех кандидатов\n    int med = medianThree(nums, left, (left + right) / 2, right);\n    // Переместить медиану в крайний левый элемент массива\n    swap(nums, left, med);\n    // Взять nums[left] в качестве опорного элемента\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--; // Идти справа налево в поисках первого элемента меньше опорного\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;          // Идти слева направо в поисках первого элемента больше опорного\n        swap(nums, i, j); // Поменять эти два элемента местами\n    }\n    swap(nums, i, left); // Переместить опорный элемент на границу двух подмассивов\n    return i;            // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.kt<pre><code>/* Выбрать медиану из трех кандидатов */\nfun medianThree(nums: IntArray, left: Int, mid: Int, right: Int): Int {\n    val l = nums[left]\n    val m = nums[mid]\n    val r = nums[right]\n    if ((m in l..r) || (m in r..l))\n        return mid  // m находится между l и r\n    if ((l in m..r) || (l in r..m))\n        return left // l находится между m и r\n    return right\n}\n\n/* Разбиение с опорными указателями (медиана трех) */\nfun partitionMedian(nums: IntArray, left: Int, right: Int): Int {\n    // Выбрать медиану из трех кандидатов\n    val med = medianThree(nums, left, (left + right) / 2, right)\n    // Переместить медиану в крайний левый элемент массива\n    swap(nums, left, med)\n    // Взять nums[left] в качестве опорного элемента\n    var i = left\n    var j = right\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--                      // Идти справа налево в поисках первого элемента меньше опорного\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++                      // Идти слева направо в поисках первого элемента больше опорного\n        swap(nums, i, j)             // Поменять эти два элемента местами\n    }\n    swap(nums, i, left)              // Переместить опорный элемент на границу двух подмассивов\n    return i                         // Вернуть индекс опорного элемента\n}\n</code></pre> quick_sort.rb<pre><code>### Выбрать медиану из трех кандидатов ###\ndef median_three(nums, left, mid, right)\n  # Выбрать медиану из трех кандидатов\n  _l, _m, _r = nums[left], nums[mid], nums[right]\n  # m находится между l и r\n  return mid if (_l &lt;= _m &amp;&amp; _m &lt;= _r) || (_r &lt;= _m &amp;&amp; _m &lt;= _l)\n  # l находится между m и r\n  return left if (_m &lt;= _l &amp;&amp; _l &lt;= _r) || (_r &lt;= _l &amp;&amp; _l &lt;= _m)\n  return right\nend\n\n### Выбрать медиану из трех кандидатов ###\ndef median_three(nums, left, mid, right)\n  # Выбрать медиану из трех кандидатов\n  _l, _m, _r = nums[left], nums[mid], nums[right]\n  # m находится между l и r\n  return mid if (_l &lt;= _m &amp;&amp; _m &lt;= _r) || (_r &lt;= _m &amp;&amp; _m &lt;= _l)\n  # l находится между m и r\n  return left if (_m &lt;= _l &amp;&amp; _l &lt;= _r) || (_r &lt;= _l &amp;&amp; _l &lt;= _m)\n  return right\nend\n\n# ## Разбиение с опорными указателями (медиана трех) ###\ndef partition(nums, left, right)\n  # ## Использовать nums[left] как опорный элемент\n  med = median_three(nums, left, (left + right) / 2, right)\n  # Переместить медиану в крайний левый элемент массива\n  nums[left], nums[med] = nums[med], nums[left]\n  i, j = left, right\n  while i &lt; j\n    while i &lt; j &amp;&amp; nums[j] &gt;= nums[left]\n      j -= 1 # Идти справа налево в поисках первого элемента меньше опорного\n    end\n    while i &lt; j &amp;&amp; nums[i] &lt;= nums[left]\n      i += 1 # Идти слева направо в поисках первого элемента больше опорного\n    end\n    # Обмен элементов\n    nums[i], nums[j] = nums[j], nums[i]\n  end\n  # Переместить опорный элемент на границу двух подмассивов\n  nums[i], nums[left] = nums[left], nums[i]\n  i # Вернуть индекс опорного элемента\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 11. Сортировка","11.5 &nbsp; Быстрая сортировка"],"tags":[]},{"location":"chapter_sorting/quick_sort/#1155","level":2,"title":"11.5.5   Оптимизация глубины рекурсии","text":"<p>На некоторых входных данных быстрая сортировка может занимать слишком много памяти. Рассмотрим полностью отсортированный входной массив. Пусть длина текущего подмассива в рекурсии равна \\(m\\) ; тогда после каждого разделения будут получаться левый подмассив длины \\(0\\) и правый подмассив длины \\(m - 1\\) . Это означает, что на каждом уровне размер задачи уменьшается совсем немного (лишь на один элемент), а высота дерева рекурсии достигает \\(n - 1\\) , поэтому требуется \\(O(n)\\) памяти под стек вызовов.</p> <p>Чтобы избежать накопления стековых кадров, после каждого разделения можно сравнивать длины двух подмассивов и рекурсивно обрабатывать только более короткий из них. Поскольку длина короткого подмассива не превысит \\(n / 2\\) , такой подход гарантирует, что глубина рекурсии не превысит \\(\\log n\\) , а худшая пространственная сложность будет оптимизирована до \\(O(\\log n)\\) . Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby quick_sort.py<pre><code>def quick_sort(self, nums: list[int], left: int, right: int):\n    \"\"\"Быстрая сортировка (оптимизация глубины рекурсии)\"\"\"\n    # Завершить, когда длина подмассива равна 1\n    while left &lt; right:\n        # Операция разбиения с опорными указателями\n        pivot = self.partition(nums, left, right)\n        # Выполнить быструю сортировку для более короткого из двух подмассивов\n        if pivot - left &lt; right - pivot:\n            self.quick_sort(nums, left, pivot - 1)  # Рекурсивно отсортировать левый подмассив\n            left = pivot + 1  # Оставшийся неотсортированный диапазон: [pivot + 1, right]\n        else:\n            self.quick_sort(nums, pivot + 1, right)  # Рекурсивно отсортировать правый подмассив\n            right = pivot - 1  # Оставшийся неотсортированный диапазон: [left, pivot - 1]\n</code></pre> quick_sort.cpp<pre><code>/* Быстрая сортировка (оптимизация глубины рекурсии) */\nvoid quickSort(vector&lt;int&gt; &amp;nums, int left, int right) {\n    // Завершить, когда длина подмассива равна 1\n    while (left &lt; right) {\n        // Операция разбиения с опорными указателями\n        int pivot = partition(nums, left, right);\n        // Выполнить быструю сортировку для более короткого из двух подмассивов\n        if (pivot - left &lt; right - pivot) {\n            quickSort(nums, left, pivot - 1); // Рекурсивно отсортировать левый подмассив\n            left = pivot + 1;                 // Оставшийся неотсортированный диапазон: [pivot + 1, right]\n        } else {\n            quickSort(nums, pivot + 1, right); // Рекурсивно отсортировать правый подмассив\n            right = pivot - 1;                 // Оставшийся неотсортированный диапазон: [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.java<pre><code>/* Быстрая сортировка (оптимизация глубины рекурсии) */\nvoid quickSort(int[] nums, int left, int right) {\n    // Завершить, когда длина подмассива равна 1\n    while (left &lt; right) {\n        // Операция разбиения с опорными указателями\n        int pivot = partition(nums, left, right);\n        // Выполнить быструю сортировку для более короткого из двух подмассивов\n        if (pivot - left &lt; right - pivot) {\n            quickSort(nums, left, pivot - 1); // Рекурсивно отсортировать левый подмассив\n            left = pivot + 1; // Оставшийся неотсортированный диапазон: [pivot + 1, right]\n        } else {\n            quickSort(nums, pivot + 1, right); // Рекурсивно отсортировать правый подмассив\n            right = pivot - 1; // Оставшийся неотсортированный диапазон: [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.cs<pre><code>/* Быстрая сортировка (оптимизация глубины рекурсии) */\nvoid QuickSort(int[] nums, int left, int right) {\n    // Завершить, когда длина подмассива равна 1\n    while (left &lt; right) {\n        // Операция разбиения с опорными указателями\n        int pivot = Partition(nums, left, right);\n        // Выполнить быструю сортировку для более короткого из двух подмассивов\n        if (pivot - left &lt; right - pivot) {\n            QuickSort(nums, left, pivot - 1);  // Рекурсивно отсортировать левый подмассив\n            left = pivot + 1;  // Оставшийся неотсортированный диапазон: [pivot + 1, right]\n        } else {\n            QuickSort(nums, pivot + 1, right); // Рекурсивно отсортировать правый подмассив\n            right = pivot - 1; // Оставшийся неотсортированный диапазон: [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.go<pre><code>/* Быстрая сортировка (оптимизация глубины рекурсии) */\nfunc (q *quickSortTailCall) quickSort(nums []int, left, right int) {\n    // Завершить, когда длина подмассива равна 1\n    for left &lt; right {\n        // Операция разбиения с опорными указателями\n        pivot := q.partition(nums, left, right)\n        // Выполнить быструю сортировку для более короткого из двух подмассивов\n        if pivot-left &lt; right-pivot {\n            q.quickSort(nums, left, pivot-1) // Рекурсивно отсортировать левый подмассив\n            left = pivot + 1                 // Оставшийся неотсортированный диапазон: [pivot + 1, right]\n        } else {\n            q.quickSort(nums, pivot+1, right) // Рекурсивно отсортировать правый подмассив\n            right = pivot - 1                 // Оставшийся неотсортированный диапазон: [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.swift<pre><code>/* Быстрая сортировка (оптимизация глубины рекурсии) */\nfunc quickSortTailCall(nums: inout [Int], left: Int, right: Int) {\n    var left = left\n    var right = right\n    // Завершить, когда длина подмассива равна 1\n    while left &lt; right {\n        // Операция разбиения с опорными указателями\n        let pivot = partition(nums: &amp;nums, left: left, right: right)\n        // Выполнить быструю сортировку для более короткого из двух подмассивов\n        if (pivot - left) &lt; (right - pivot) {\n            quickSortTailCall(nums: &amp;nums, left: left, right: pivot - 1) // Рекурсивно отсортировать левый подмассив\n            left = pivot + 1 // Оставшийся неотсортированный диапазон: [pivot + 1, right]\n        } else {\n            quickSortTailCall(nums: &amp;nums, left: pivot + 1, right: right) // Рекурсивно отсортировать правый подмассив\n            right = pivot - 1 // Оставшийся неотсортированный диапазон: [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.js<pre><code>/* Быстрая сортировка (оптимизация глубины рекурсии) */\nquickSort(nums, left, right) {\n    // Завершить, когда длина подмассива равна 1\n    while (left &lt; right) {\n        // Операция разбиения с опорными указателями\n        let pivot = this.partition(nums, left, right);\n        // Выполнить быструю сортировку для более короткого из двух подмассивов\n        if (pivot - left &lt; right - pivot) {\n            this.quickSort(nums, left, pivot - 1); // Рекурсивно отсортировать левый подмассив\n            left = pivot + 1; // Оставшийся неотсортированный диапазон: [pivot + 1, right]\n        } else {\n            this.quickSort(nums, pivot + 1, right); // Рекурсивно отсортировать правый подмассив\n            right = pivot - 1; // Оставшийся неотсортированный диапазон: [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.ts<pre><code>/* Быстрая сортировка (оптимизация глубины рекурсии) */\nquickSort(nums: number[], left: number, right: number): void {\n    // Завершить, когда длина подмассива равна 1\n    while (left &lt; right) {\n        // Операция разбиения с опорными указателями\n        let pivot = this.partition(nums, left, right);\n        // Выполнить быструю сортировку для более короткого из двух подмассивов\n        if (pivot - left &lt; right - pivot) {\n            this.quickSort(nums, left, pivot - 1); // Рекурсивно отсортировать левый подмассив\n            left = pivot + 1; // Оставшийся неотсортированный диапазон: [pivot + 1, right]\n        } else {\n            this.quickSort(nums, pivot + 1, right); // Рекурсивно отсортировать правый подмассив\n            right = pivot - 1; // Оставшийся неотсортированный диапазон: [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.dart<pre><code>/* Быстрая сортировка (оптимизация глубины рекурсии) */\nvoid quickSort(List&lt;int&gt; nums, int left, int right) {\n  // Завершить, когда длина подмассива равна 1\n  while (left &lt; right) {\n    // Операция разбиения с опорными указателями\n    int pivot = _partition(nums, left, right);\n    // Выполнить быструю сортировку для более короткого из двух подмассивов\n    if (pivot - left &lt; right - pivot) {\n      quickSort(nums, left, pivot - 1); // Рекурсивно отсортировать левый подмассив\n      left = pivot + 1; // Оставшийся неотсортированный диапазон: [pivot + 1, right]\n    } else {\n      quickSort(nums, pivot + 1, right); // Рекурсивно отсортировать правый подмассив\n      right = pivot - 1; // Оставшийся неотсортированный диапазон: [left, pivot - 1]\n    }\n  }\n}\n</code></pre> quick_sort.rs<pre><code>/* Быстрая сортировка (оптимизация глубины рекурсии) */\npub fn quick_sort(mut left: i32, mut right: i32, nums: &amp;mut [i32]) {\n    // Завершить, когда длина подмассива равна 1\n    while left &lt; right {\n        // Операция разбиения с опорными указателями\n        let pivot = Self::partition(nums, left as usize, right as usize) as i32;\n        // Выполнить быструю сортировку для более короткого из двух подмассивов\n        if pivot - left &lt; right - pivot {\n            Self::quick_sort(left, pivot - 1, nums); // Рекурсивно отсортировать левый подмассив\n            left = pivot + 1; // Оставшийся неотсортированный диапазон: [pivot + 1, right]\n        } else {\n            Self::quick_sort(pivot + 1, right, nums); // Рекурсивно отсортировать правый подмассив\n            right = pivot - 1; // Оставшийся неотсортированный диапазон: [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.c<pre><code>/* Быстрая сортировка (оптимизация глубины рекурсии) */\nvoid quickSortTailCall(int nums[], int left, int right) {\n    // Завершить, когда длина подмассива равна 1\n    while (left &lt; right) {\n        // Операция разбиения с опорными указателями\n        int pivot = partition(nums, left, right);\n        // Выполнить быструю сортировку для более короткого из двух подмассивов\n        if (pivot - left &lt; right - pivot) {\n            // Рекурсивно отсортировать левый подмассив\n            quickSortTailCall(nums, left, pivot - 1);\n            // Оставшийся неотсортированный диапазон: [pivot + 1, right]\n            left = pivot + 1;\n        } else {\n            // Рекурсивно отсортировать правый подмассив\n            quickSortTailCall(nums, pivot + 1, right);\n            // Оставшийся неотсортированный диапазон: [left, pivot - 1]\n            right = pivot - 1;\n        }\n    }\n}\n</code></pre> quick_sort.kt<pre><code>/* Быстрая сортировка (оптимизация глубины рекурсии) */\nfun quickSortTailCall(nums: IntArray, left: Int, right: Int) {\n    // Завершить, когда длина подмассива равна 1\n    var l = left\n    var r = right\n    while (l &lt; r) {\n        // Операция разбиения с опорными указателями\n        val pivot = partition(nums, l, r)\n        // Выполнить быструю сортировку для более короткого из двух подмассивов\n        if (pivot - l &lt; r - pivot) {\n            quickSort(nums, l, pivot - 1) // Рекурсивно отсортировать левый подмассив\n            l = pivot + 1 // Оставшийся неотсортированный диапазон: [pivot + 1, right]\n        } else {\n            quickSort(nums, pivot + 1, r) // Рекурсивно отсортировать правый подмассив\n            r = pivot - 1 // Оставшийся неотсортированный диапазон: [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.rb<pre><code>### Разбиение с опорными указателями ###\ndef partition(nums, left, right)\n  # Использовать nums[left] как опорный элемент\n  i = left\n  j = right\n  while i &lt; j\n    while i &lt; j &amp;&amp; nums[j] &gt;= nums[left]\n      j -= 1 # Идти справа налево в поисках первого элемента меньше опорного\n    end\n    while i &lt; j &amp;&amp; nums[i] &lt;= nums[left]\n      i += 1 # Идти слева направо в поисках первого элемента больше опорного\n    end\n    # Обмен элементов\n    nums[i], nums[j] = nums[j], nums[i]\n  end\n  # Переместить опорный элемент на границу двух подмассивов\n  nums[i], nums[left] = nums[left], nums[i]\n  i # Вернуть индекс опорного элемента\nend\n\n# ## Быстрая сортировка (оптимизация глубины рекурсии) ###\ndef quick_sort(nums, left, right)\n  # Рекурсивно обрабатывать, пока длина подмассива не станет равной 1\n  while left &lt; right\n    # Разбиение с опорными указателями\n    pivot = partition(nums, left, right)\n    # Выполнить быструю сортировку для более короткого из двух подмассивов\n    if pivot - left &lt; right - pivot\n      quick_sort(nums, left, pivot - 1)\n      left = pivot + 1 # Оставшийся неотсортированный диапазон: [pivot + 1, right]\n    else\n      quick_sort(nums, pivot + 1, right)\n      right = pivot - 1 # Оставшийся неотсортированный диапазон: [left, pivot - 1]\n    end\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 11. Сортировка","11.5 &nbsp; Быстрая сортировка"],"tags":[]},{"location":"chapter_sorting/radix_sort/","level":1,"title":"11.10   Поразрядная сортировка","text":"<p>В предыдущем разделе была рассмотрена сортировка подсчетом: она хорошо подходит для случаев, когда объем данных \\(n\\) велик, а диапазон значений \\(m\\) сравнительно мал. Предположим теперь, что нужно отсортировать \\(n = 10^6\\) номеров студентов, причем каждый номер представляет собой \\(8\\)-значное число. Тогда диапазон данных \\(m = 10^8\\) оказывается очень большим; сортировка подсчетом потребует огромного объема памяти, а поразрядная сортировка позволяет этого избежать.</p> <p>Поразрядная сортировка (radix sort) по своей основной идее совпадает с сортировкой подсчетом и тоже реализует сортировку через подсчет количества. При этом поразрядная сортировка использует соотношение между разрядами числа и последовательно сортирует данные по каждому разряду, получая итоговый упорядоченный результат.</p>","path":["Глава 11. Сортировка","11.10 &nbsp; Поразрядная сортировка"],"tags":[]},{"location":"chapter_sorting/radix_sort/#11101","level":2,"title":"11.10.1   Алгоритм","text":"<p>Рассмотрим пример со студенческими номерами: будем считать, что младший разряд имеет номер \\(1\\) , а старший - номер \\(8\\) . Тогда процесс поразрядной сортировки показан на рисунке 11-18.</p> <ol> <li>Инициализировать номер разряда \\(k = 1\\) .</li> <li>Выполнить \"сортировку подсчетом\" по \\(k\\)-му разряду студенческого номера. После этого данные будут упорядочены по \\(k\\)-му разряду по возрастанию.</li> <li>Увеличить \\(k\\) на \\(1\\) и вернуться к шагу <code>2.</code> , продолжая процесс, пока сортировка не будет выполнена для всех разрядов.</li> </ol> <p></p> <p> Рисунок 11-18   Процесс поразрядной сортировки </p> <p>Ниже разберем реализацию кода. Для числа \\(x\\) в системе счисления с основанием \\(d\\) получить его \\(k\\)-й разряд \\(x_k\\) можно по формуле:</p> \\[ x_k = \\lfloor\\frac{x}{d^{k-1}}\\rfloor \\bmod d \\] <p>где \\(\\lfloor a \\rfloor\\) обозначает округление числа \\(a\\) вниз, а \\(\\bmod \\: d\\) означает взятие остатка по модулю \\(d\\) . Для студенческих номеров выполняется \\(d = 10\\) и \\(k \\in [1, 8]\\) .</p> <p>Кроме того, нам нужно слегка изменить код сортировки подсчетом, чтобы он мог сортировать числа по их \\(k\\)-му разряду:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby radix_sort.py<pre><code>def digit(num: int, exp: int) -&gt; int:\n    \"\"\"Получить k-й разряд элемента num, где exp = 10^(k-1)\"\"\"\n    # Передача exp вместо k позволяет избежать повторного дорогостоящего вычисления степени\n    return (num // exp) % 10\n\ndef counting_sort_digit(nums: list[int], exp: int):\n    \"\"\"Сортировка подсчетом (сортировка по k-му разряду nums)\"\"\"\n    # Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n    counter = [0] * 10\n    n = len(nums)\n    # Подсчитать число появлений каждой цифры от 0 до 9\n    for i in range(n):\n        d = digit(nums[i], exp)  # Получить k-й разряд nums[i], обозначив его как d\n        counter[d] += 1  # Подсчитать число появлений цифры d\n    # Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n    for i in range(1, 10):\n        counter[i] += counter[i - 1]\n    # Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n    res = [0] * n\n    for i in range(n - 1, -1, -1):\n        d = digit(nums[i], exp)\n        j = counter[d] - 1  # Получить индекс j цифры d в массиве\n        res[j] = nums[i]  # Поместить текущий элемент по индексу j\n        counter[d] -= 1  # Уменьшить количество d на 1\n    # Перезаписать исходный массив nums результатом\n    for i in range(n):\n        nums[i] = res[i]\n\ndef radix_sort(nums: list[int]):\n    \"\"\"Поразрядная сортировка\"\"\"\n    # Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n    m = max(nums)\n    # Проходить разряды от младшего к старшему\n    exp = 1\n    while exp &lt;= m:\n        # Выполнить сортировку подсчетом по k-му разряду элементов массива\n        # k = 1 -&gt; exp = 1\n        # k = 2 -&gt; exp = 10\n        # то есть exp = 10^(k-1)\n        counting_sort_digit(nums, exp)\n        exp *= 10\n</code></pre> radix_sort.cpp<pre><code>/* Получить k-й разряд элемента num, где exp = 10^(k-1) */\nint digit(int num, int exp) {\n    // Передача exp вместо k позволяет избежать повторного дорогостоящего вычисления степени\n    return (num / exp) % 10;\n}\n\n/* Сортировка подсчетом (сортировка по k-му разряду nums) */\nvoid countingSortDigit(vector&lt;int&gt; &amp;nums, int exp) {\n    // Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n    vector&lt;int&gt; counter(10, 0);\n    int n = nums.size();\n    // Подсчитать число появлений каждой цифры от 0 до 9\n    for (int i = 0; i &lt; n; i++) {\n        int d = digit(nums[i], exp); // Получить k-й разряд nums[i], обозначив его как d\n        counter[d]++;                // Подсчитать число появлений цифры d\n    }\n    // Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n    for (int i = 1; i &lt; 10; i++) {\n        counter[i] += counter[i - 1];\n    }\n    // Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n    vector&lt;int&gt; res(n, 0);\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int d = digit(nums[i], exp);\n        int j = counter[d] - 1; // Получить индекс j цифры d в массиве\n        res[j] = nums[i];       // Поместить текущий элемент по индексу j\n        counter[d]--;           // Уменьшить количество d на 1\n    }\n    // Перезаписать исходный массив nums результатом\n    for (int i = 0; i &lt; n; i++)\n        nums[i] = res[i];\n}\n\n/* Поразрядная сортировка */\nvoid radixSort(vector&lt;int&gt; &amp;nums) {\n    // Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n    int m = *max_element(nums.begin(), nums.end());\n    // Проходить разряды от младшего к старшему\n    for (int exp = 1; exp &lt;= m; exp *= 10)\n        // Выполнить сортировку подсчетом по k-му разряду элементов массива\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // то есть exp = 10^(k-1)\n        countingSortDigit(nums, exp);\n}\n</code></pre> radix_sort.java<pre><code>/* Получить k-й разряд элемента num, где exp = 10^(k-1) */\nint digit(int num, int exp) {\n    // Передача exp вместо k позволяет избежать повторного дорогостоящего вычисления степени\n    return (num / exp) % 10;\n}\n\n/* Сортировка подсчетом (сортировка по k-му разряду nums) */\nvoid countingSortDigit(int[] nums, int exp) {\n    // Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n    int[] counter = new int[10];\n    int n = nums.length;\n    // Подсчитать число появлений каждой цифры от 0 до 9\n    for (int i = 0; i &lt; n; i++) {\n        int d = digit(nums[i], exp); // Получить k-й разряд nums[i], обозначив его как d\n        counter[d]++;                // Подсчитать число появлений цифры d\n    }\n    // Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n    for (int i = 1; i &lt; 10; i++) {\n        counter[i] += counter[i - 1];\n    }\n    // Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n    int[] res = new int[n];\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int d = digit(nums[i], exp);\n        int j = counter[d] - 1; // Получить индекс j цифры d в массиве\n        res[j] = nums[i];       // Поместить текущий элемент по индексу j\n        counter[d]--;           // Уменьшить количество d на 1\n    }\n    // Перезаписать исходный массив nums результатом\n    for (int i = 0; i &lt; n; i++)\n        nums[i] = res[i];\n}\n\n/* Поразрядная сортировка */\nvoid radixSort(int[] nums) {\n    // Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n    int m = Integer.MIN_VALUE;\n    for (int num : nums)\n        if (num &gt; m)\n            m = num;\n    // Проходить разряды от младшего к старшему\n    for (int exp = 1; exp &lt;= m; exp *= 10) {\n        // Выполнить сортировку подсчетом по k-му разряду элементов массива\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // то есть exp = 10^(k-1)\n        countingSortDigit(nums, exp);\n    }\n}\n</code></pre> radix_sort.cs<pre><code>/* Получить k-й разряд элемента num, где exp = 10^(k-1) */\nint Digit(int num, int exp) {\n    // Передача exp вместо k позволяет избежать повторного дорогостоящего вычисления степени\n    return (num / exp) % 10;\n}\n\n/* Сортировка подсчетом (сортировка по k-му разряду nums) */\nvoid CountingSortDigit(int[] nums, int exp) {\n    // Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n    int[] counter = new int[10];\n    int n = nums.Length;\n    // Подсчитать число появлений каждой цифры от 0 до 9\n    for (int i = 0; i &lt; n; i++) {\n        int d = Digit(nums[i], exp); // Получить k-й разряд nums[i], обозначив его как d\n        counter[d]++;                // Подсчитать число появлений цифры d\n    }\n    // Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n    for (int i = 1; i &lt; 10; i++) {\n        counter[i] += counter[i - 1];\n    }\n    // Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n    int[] res = new int[n];\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int d = Digit(nums[i], exp);\n        int j = counter[d] - 1; // Получить индекс j цифры d в массиве\n        res[j] = nums[i];       // Поместить текущий элемент по индексу j\n        counter[d]--;           // Уменьшить количество d на 1\n    }\n    // Перезаписать исходный массив nums результатом\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = res[i];\n    }\n}\n\n/* Поразрядная сортировка */\nvoid RadixSort(int[] nums) {\n    // Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n    int m = int.MinValue;\n    foreach (int num in nums) {\n        if (num &gt; m) m = num;\n    }\n    // Проходить разряды от младшего к старшему\n    for (int exp = 1; exp &lt;= m; exp *= 10) {\n        // Выполнить сортировку подсчетом по k-му разряду элементов массива\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // то есть exp = 10^(k-1)\n        CountingSortDigit(nums, exp);\n    }\n}\n</code></pre> radix_sort.go<pre><code>/* Получить k-й разряд элемента num, где exp = 10^(k-1) */\nfunc digit(num, exp int) int {\n    // Передача exp вместо k позволяет избежать повторного дорогостоящего вычисления степени\n    return (num / exp) % 10\n}\n\n/* Сортировка подсчетом (сортировка по k-му разряду nums) */\nfunc countingSortDigit(nums []int, exp int) {\n    // Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n    counter := make([]int, 10)\n    n := len(nums)\n    // Подсчитать число появлений каждой цифры от 0 до 9\n    for i := 0; i &lt; n; i++ {\n        d := digit(nums[i], exp) // Получить k-й разряд nums[i], обозначив его как d\n        counter[d]++             // Подсчитать число появлений цифры d\n    }\n    // Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n    for i := 1; i &lt; 10; i++ {\n        counter[i] += counter[i-1]\n    }\n    // Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n    res := make([]int, n)\n    for i := n - 1; i &gt;= 0; i-- {\n        d := digit(nums[i], exp)\n        j := counter[d] - 1 // Получить индекс j цифры d в массиве\n        res[j] = nums[i]    // Поместить текущий элемент по индексу j\n        counter[d]--        // Уменьшить количество d на 1\n    }\n    // Перезаписать исходный массив nums результатом\n    for i := 0; i &lt; n; i++ {\n        nums[i] = res[i]\n    }\n}\n\n/* Поразрядная сортировка */\nfunc radixSort(nums []int) {\n    // Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n    max := math.MinInt\n    for _, num := range nums {\n        if num &gt; max {\n            max = num\n        }\n    }\n    // Проходить разряды от младшего к старшему\n    for exp := 1; max &gt;= exp; exp *= 10 {\n        // Выполнить сортировку подсчетом по k-му разряду элементов массива\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // то есть exp = 10^(k-1)\n        countingSortDigit(nums, exp)\n    }\n}\n</code></pre> radix_sort.swift<pre><code>/* Получить k-й разряд элемента num, где exp = 10^(k-1) */\nfunc digit(num: Int, exp: Int) -&gt; Int {\n    // Передача exp вместо k позволяет избежать повторного дорогостоящего вычисления степени\n    (num / exp) % 10\n}\n\n/* Сортировка подсчетом (сортировка по k-му разряду nums) */\nfunc countingSortDigit(nums: inout [Int], exp: Int) {\n    // Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n    var counter = Array(repeating: 0, count: 10)\n    // Подсчитать число появлений каждой цифры от 0 до 9\n    for i in nums.indices {\n        let d = digit(num: nums[i], exp: exp) // Получить k-й разряд nums[i], обозначив его как d\n        counter[d] += 1 // Подсчитать число появлений цифры d\n    }\n    // Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n    for i in 1 ..&lt; 10 {\n        counter[i] += counter[i - 1]\n    }\n    // Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n    var res = Array(repeating: 0, count: nums.count)\n    for i in nums.indices.reversed() {\n        let d = digit(num: nums[i], exp: exp)\n        let j = counter[d] - 1 // Получить индекс j цифры d в массиве\n        res[j] = nums[i] // Поместить текущий элемент по индексу j\n        counter[d] -= 1 // Уменьшить количество d на 1\n    }\n    // Перезаписать исходный массив nums результатом\n    for i in nums.indices {\n        nums[i] = res[i]\n    }\n}\n\n/* Поразрядная сортировка */\nfunc radixSort(nums: inout [Int]) {\n    // Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n    var m = Int.min\n    for num in nums {\n        if num &gt; m {\n            m = num\n        }\n    }\n    // Проходить разряды от младшего к старшему\n    for exp in sequence(first: 1, next: { m &gt;= ($0 * 10) ? $0 * 10 : nil }) {\n        // Выполнить сортировку подсчетом по k-му разряду элементов массива\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // то есть exp = 10^(k-1)\n        countingSortDigit(nums: &amp;nums, exp: exp)\n    }\n}\n</code></pre> radix_sort.js<pre><code>/* Получить k-й разряд элемента num, где exp = 10^(k-1) */\nfunction digit(num, exp) {\n    // Передача exp вместо k позволяет избежать повторного дорогостоящего вычисления степени\n    return Math.floor(num / exp) % 10;\n}\n\n/* Сортировка подсчетом (сортировка по k-му разряду nums) */\nfunction countingSortDigit(nums, exp) {\n    // Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n    const counter = new Array(10).fill(0);\n    const n = nums.length;\n    // Подсчитать число появлений каждой цифры от 0 до 9\n    for (let i = 0; i &lt; n; i++) {\n        const d = digit(nums[i], exp); // Получить k-й разряд nums[i], обозначив его как d\n        counter[d]++; // Подсчитать число появлений цифры d\n    }\n    // Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n    for (let i = 1; i &lt; 10; i++) {\n        counter[i] += counter[i - 1];\n    }\n    // Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n    const res = new Array(n).fill(0);\n    for (let i = n - 1; i &gt;= 0; i--) {\n        const d = digit(nums[i], exp);\n        const j = counter[d] - 1; // Получить индекс j цифры d в массиве\n        res[j] = nums[i]; // Поместить текущий элемент по индексу j\n        counter[d]--; // Уменьшить количество d на 1\n    }\n    // Перезаписать исходный массив nums результатом\n    for (let i = 0; i &lt; n; i++) {\n        nums[i] = res[i];\n    }\n}\n\n/* Поразрядная сортировка */\nfunction radixSort(nums) {\n    // Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n    let m = Math.max(... nums);\n    // Проходить разряды от младшего к старшему\n    for (let exp = 1; exp &lt;= m; exp *= 10) {\n        // Выполнить сортировку подсчетом по k-му разряду элементов массива\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // то есть exp = 10^(k-1)\n        countingSortDigit(nums, exp);\n    }\n}\n</code></pre> radix_sort.ts<pre><code>/* Получить k-й разряд элемента num, где exp = 10^(k-1) */\nfunction digit(num: number, exp: number): number {\n    // Передача exp вместо k позволяет избежать повторного дорогостоящего вычисления степени\n    return Math.floor(num / exp) % 10;\n}\n\n/* Сортировка подсчетом (сортировка по k-му разряду nums) */\nfunction countingSortDigit(nums: number[], exp: number): void {\n    // Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n    const counter = new Array(10).fill(0);\n    const n = nums.length;\n    // Подсчитать число появлений каждой цифры от 0 до 9\n    for (let i = 0; i &lt; n; i++) {\n        const d = digit(nums[i], exp); // Получить k-й разряд nums[i], обозначив его как d\n        counter[d]++; // Подсчитать число появлений цифры d\n    }\n    // Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n    for (let i = 1; i &lt; 10; i++) {\n        counter[i] += counter[i - 1];\n    }\n    // Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n    const res = new Array(n).fill(0);\n    for (let i = n - 1; i &gt;= 0; i--) {\n        const d = digit(nums[i], exp);\n        const j = counter[d] - 1; // Получить индекс j цифры d в массиве\n        res[j] = nums[i]; // Поместить текущий элемент по индексу j\n        counter[d]--; // Уменьшить количество d на 1\n    }\n    // Перезаписать исходный массив nums результатом\n    for (let i = 0; i &lt; n; i++) {\n        nums[i] = res[i];\n    }\n}\n\n/* Поразрядная сортировка */\nfunction radixSort(nums: number[]): void {\n    // Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n    let m: number = Math.max(... nums);\n    // Проходить разряды от младшего к старшему\n    for (let exp = 1; exp &lt;= m; exp *= 10) {\n        // Выполнить сортировку подсчетом по k-му разряду элементов массива\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // то есть exp = 10^(k-1)\n        countingSortDigit(nums, exp);\n    }\n}\n</code></pre> radix_sort.dart<pre><code>/* Получить k-й разряд элемента _num, где exp = 10^(k-1) */\nint digit(int _num, int exp) {\n  // Передача exp вместо k позволяет избежать повторного дорогостоящего вычисления степени\n  return (_num ~/ exp) % 10;\n}\n\n/* Сортировка подсчетом (сортировка по k-му разряду nums) */\nvoid countingSortDigit(List&lt;int&gt; nums, int exp) {\n  // Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n  List&lt;int&gt; counter = List&lt;int&gt;.filled(10, 0);\n  int n = nums.length;\n  // Подсчитать число появлений каждой цифры от 0 до 9\n  for (int i = 0; i &lt; n; i++) {\n    int d = digit(nums[i], exp); // Получить k-й разряд nums[i], обозначив его как d\n    counter[d]++; // Подсчитать число появлений цифры d\n  }\n  // Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n  for (int i = 1; i &lt; 10; i++) {\n    counter[i] += counter[i - 1];\n  }\n  // Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n  List&lt;int&gt; res = List&lt;int&gt;.filled(n, 0);\n  for (int i = n - 1; i &gt;= 0; i--) {\n    int d = digit(nums[i], exp);\n    int j = counter[d] - 1; // Получить индекс j цифры d в массиве\n    res[j] = nums[i]; // Поместить текущий элемент по индексу j\n    counter[d]--; // Уменьшить количество d на 1\n  }\n  // Перезаписать исходный массив nums результатом\n  for (int i = 0; i &lt; n; i++) nums[i] = res[i];\n}\n\n/* Поразрядная сортировка */\nvoid radixSort(List&lt;int&gt; nums) {\n  // Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n  // В dart длина int составляет 64 бита\n  int m = -1 &lt;&lt; 63;\n  for (int _num in nums) if (_num &gt; m) m = _num;\n  // Проходить разряды от младшего к старшему\n  for (int exp = 1; exp &lt;= m; exp *= 10)\n    // Выполнить сортировку подсчетом по k-му разряду элементов массива\n    // k = 1 -&gt; exp = 1\n    // k = 2 -&gt; exp = 10\n    // то есть exp = 10^(k-1)\n    countingSortDigit(nums, exp);\n}\n</code></pre> radix_sort.rs<pre><code>/* Получить k-й разряд элемента num, где exp = 10^(k-1) */\nfn digit(num: i32, exp: i32) -&gt; usize {\n    // Передача exp вместо k позволяет избежать повторного дорогостоящего вычисления степени\n    return ((num / exp) % 10) as usize;\n}\n\n/* Сортировка подсчетом (сортировка по k-му разряду nums) */\nfn counting_sort_digit(nums: &amp;mut [i32], exp: i32) {\n    // Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n    let mut counter = [0; 10];\n    let n = nums.len();\n    // Подсчитать число появлений каждой цифры от 0 до 9\n    for i in 0..n {\n        let d = digit(nums[i], exp); // Получить k-й разряд nums[i], обозначив его как d\n        counter[d] += 1; // Подсчитать число появлений цифры d\n    }\n    // Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n    for i in 1..10 {\n        counter[i] += counter[i - 1];\n    }\n    // Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n    let mut res = vec![0; n];\n    for i in (0..n).rev() {\n        let d = digit(nums[i], exp);\n        let j = counter[d] - 1; // Получить индекс j цифры d в массиве\n        res[j] = nums[i]; // Поместить текущий элемент по индексу j\n        counter[d] -= 1; // Уменьшить количество d на 1\n    }\n    // Перезаписать исходный массив nums результатом\n    nums.copy_from_slice(&amp;res);\n}\n\n/* Поразрядная сортировка */\nfn radix_sort(nums: &amp;mut [i32]) {\n    // Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n    let m = *nums.into_iter().max().unwrap();\n    // Проходить разряды от младшего к старшему\n    let mut exp = 1;\n    while exp &lt;= m {\n        counting_sort_digit(nums, exp);\n        exp *= 10;\n    }\n}\n</code></pre> radix_sort.c<pre><code>/* Получить k-й разряд элемента num, где exp = 10^(k-1) */\nint digit(int num, int exp) {\n    // Передача exp вместо k позволяет избежать повторного дорогостоящего вычисления степени\n    return (num / exp) % 10;\n}\n\n/* Сортировка подсчетом (сортировка по k-му разряду nums) */\nvoid countingSortDigit(int nums[], int size, int exp) {\n    // Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n    int *counter = (int *)malloc((sizeof(int) * 10));\n    memset(counter, 0, sizeof(int) * 10); // Инициализировать нулем для последующего освобождения памяти\n    // Подсчитать число появлений каждой цифры от 0 до 9\n    for (int i = 0; i &lt; size; i++) {\n        // Получить k-й разряд nums[i], обозначив его как d\n        int d = digit(nums[i], exp);\n        // Подсчитать число появлений цифры d\n        counter[d]++;\n    }\n    // Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n    for (int i = 1; i &lt; 10; i++) {\n        counter[i] += counter[i - 1];\n    }\n    // Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n    int *res = (int *)malloc(sizeof(int) * size);\n    for (int i = size - 1; i &gt;= 0; i--) {\n        int d = digit(nums[i], exp);\n        int j = counter[d] - 1; // Получить индекс j цифры d в массиве\n        res[j] = nums[i];       // Поместить текущий элемент по индексу j\n        counter[d]--;           // Уменьшить количество d на 1\n    }\n    // Перезаписать исходный массив nums результатом\n    for (int i = 0; i &lt; size; i++) {\n        nums[i] = res[i];\n    }\n    // Освободить память\n    free(res);\n    free(counter);\n}\n\n/* Поразрядная сортировка */\nvoid radixSort(int nums[], int size) {\n    // Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n    int max = INT32_MIN;\n    for (int i = 0; i &lt; size; i++) {\n        if (nums[i] &gt; max) {\n            max = nums[i];\n        }\n    }\n    // Проходить разряды от младшего к старшему\n    for (int exp = 1; max &gt;= exp; exp *= 10)\n        // Выполнить сортировку подсчетом по k-му разряду элементов массива\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // то есть exp = 10^(k-1)\n        countingSortDigit(nums, size, exp);\n}\n</code></pre> radix_sort.kt<pre><code>/* Получить k-й разряд элемента num, где exp = 10^(k-1) */\nfun digit(num: Int, exp: Int): Int {\n    // Передача exp вместо k позволяет избежать повторного дорогостоящего вычисления степени\n    return (num / exp) % 10\n}\n\n/* Сортировка подсчетом (сортировка по k-му разряду nums) */\nfun countingSortDigit(nums: IntArray, exp: Int) {\n    // Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n    val counter = IntArray(10)\n    val n = nums.size\n    // Подсчитать число появлений каждой цифры от 0 до 9\n    for (i in 0..&lt;n) {\n        val d = digit(nums[i], exp) // Получить k-й разряд nums[i], обозначив его как d\n        counter[d]++                // Подсчитать число появлений цифры d\n    }\n    // Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n    for (i in 1..9) {\n        counter[i] += counter[i - 1]\n    }\n    // Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n    val res = IntArray(n)\n    for (i in n - 1 downTo 0) {\n        val d = digit(nums[i], exp)\n        val j = counter[d] - 1 // Получить индекс j цифры d в массиве\n        res[j] = nums[i]       // Поместить текущий элемент по индексу j\n        counter[d]--           // Уменьшить количество d на 1\n    }\n    // Перезаписать исходный массив nums результатом\n    for (i in 0..&lt;n)\n        nums[i] = res[i]\n}\n\n/* Поразрядная сортировка */\nfun radixSort(nums: IntArray) {\n    // Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n    var m = Int.MIN_VALUE\n    for (num in nums) if (num &gt; m) m = num\n    var exp = 1\n    // Проходить разряды от младшего к старшему\n    while (exp &lt;= m) {\n        // Выполнить сортировку подсчетом по k-му разряду элементов массива\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // то есть exp = 10^(k-1)\n        countingSortDigit(nums, exp)\n        exp *= 10\n    }\n}\n</code></pre> radix_sort.rb<pre><code>### Получить k-й разряд элемента num, где exp = 10^(k-1) ###\ndef digit(num, exp)\n  # Передача exp вместо k позволяет избежать повторного выполнения дорогостоящих вычислений степени\n  (num / exp) % 10\nend\n\n### Получить k-й разряд элемента num, где exp = 10^(k-1) ###\ndef digit(num, exp)\n  # Передача exp вместо k позволяет избежать повторного выполнения дорогостоящих вычислений степени\n  (num / exp) % 10\nend\n\n# ## Сортировка подсчетом (сортировка по k-му разряду nums) ###\ndef counting_sort_digit(nums, exp)\n  # Разряды десятичной системы лежат в диапазоне 0~9, поэтому нужен массив корзин длины 10\n  counter = Array.new(10, 0)\n  n = nums.length\n  # Подсчитать число появлений каждой цифры от 0 до 9\n  for i in 0...n\n    d = digit(nums[i], exp) # Получить k-й разряд nums[i], обозначив его как d\n    counter[d] += 1 # Подсчитать число появлений цифры d\n  end\n  # Вычислить префиксные суммы и преобразовать «число появлений» в «индекс массива»\n  (1...10).each { |i| counter[i] += counter[i - 1] }\n  # Выполняя обратный проход, заполнить res элементами по статистике в корзинах\n  res = Array.new(n, 0)\n  for i in (n - 1).downto(0)\n    d = digit(nums[i], exp)\n    j = counter[d] - 1 # Получить индекс j цифры d в массиве\n    res[j] = nums[i] # Поместить текущий элемент по индексу j\n    counter[d] -= 1 # Уменьшить количество d на 1\n  end\n  # Перезаписать исходный массив nums результатом\n  (0...n).each { |i| nums[i] = res[i] }\nend\n\n### Поразрядная сортировка ###\ndef radix_sort(nums)\n  # Получить максимальный элемент массива, чтобы определить максимальное число разрядов\n  m = nums.max\n  # Проходить разряды от младшего к старшему\n  exp = 1\n  while exp &lt;= m\n    # Выполнить сортировку подсчетом по k-му разряду элементов массива\n    # k = 1 -&gt; exp = 1\n    # k = 2 -&gt; exp = 10\n    # то есть exp = 10^(k-1)\n    counting_sort_digit(nums, exp)\n    exp *= 10\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Почему сортировка выполняется от младшего разряда к старшему?</p> <p>В последовательных раундах сортировки результаты более позднего раунда перекрывают результаты предыдущего. Например, если после первого раунда получилось \\(a &lt; b\\) , а после второго - \\(a &gt; b\\) , то именно результат второго раунда станет окончательным. Поскольку старшие разряды имеют более высокий приоритет, сначала нужно сортировать по младшим разрядам, а затем по старшим.</p>","path":["Глава 11. Сортировка","11.10 &nbsp; Поразрядная сортировка"],"tags":[]},{"location":"chapter_sorting/radix_sort/#11102","level":2,"title":"11.10.2   Характеристики алгоритма","text":"<p>По сравнению с сортировкой подсчетом поразрядная сортировка подходит для случаев с большим диапазоном чисел, но только при условии, что данные можно представить в виде чисел фиксированной длины и число разрядов не слишком велико. Например, числа с плавающей запятой плохо подходят для поразрядной сортировки, потому что число разрядов \\(k\\) слишком велико и может привести к ситуации \\(O(nk) \\gg O(n^2)\\) .</p> <ul> <li>Временная сложность равна \\(O(nk)\\), алгоритм не является адаптивным: пусть объем данных равен \\(n\\) , числа записаны в системе счисления с основанием \\(d\\) , а максимальное число разрядов равно \\(k\\) . Тогда выполнение сортировки подсчетом для одного разряда требует \\(O(n + d)\\) времени, а сортировка по всем \\(k\\) разрядам требует \\(O((n + d)k)\\) времени. Обычно \\(d\\) и \\(k\\) сравнительно малы, поэтому временная сложность стремится к \\(O(n)\\) .</li> <li>Пространственная сложность равна \\(O(n + d)\\), сортировка не выполняется на месте: как и в сортировке подсчетом, здесь требуются массивы <code>res</code> и <code>counter</code> длины \\(n\\) и \\(d\\) .</li> <li>Стабильная сортировка: если сортировка подсчетом стабильна, то и поразрядная сортировка стабильна; если же сортировка подсчетом нестабильна, поразрядная сортировка не может гарантировать корректный результат.</li> </ul>","path":["Глава 11. Сортировка","11.10 &nbsp; Поразрядная сортировка"],"tags":[]},{"location":"chapter_sorting/selection_sort/","level":1,"title":"11.2   Сортировка выбором","text":"<p>Сортировка выбором (selection sort) работает очень просто: запускается цикл, и на каждом шаге из неотсортированного диапазона выбирается минимальный элемент, после чего он переносится в конец уже отсортированного диапазона.</p> <p>Пусть длина массива равна \\(n\\) ; тогда процесс сортировки выбором выглядит так, как показано на рисунке 11-2.</p> <ol> <li>В начальном состоянии все элементы не отсортированы, то есть неотсортированный диапазон индексов равен \\([0, n-1]\\) .</li> <li>Выбрать минимальный элемент из диапазона \\([0, n-1]\\) и поменять его местами с элементом в позиции \\(0\\) . После этого первый элемент массива отсортирован.</li> <li>Выбрать минимальный элемент из диапазона \\([1, n-1]\\) и поменять его местами с элементом в позиции \\(1\\) . После этого первые два элемента массива отсортированы.</li> <li>Продолжать по аналогии. После \\(n - 1\\) раундов выбора и обмена первые \\(n - 1\\) элементов массива будут отсортированы.</li> <li>Оставшийся элемент обязательно является максимальным, сортировать его не нужно, поэтому массив считается отсортированным.</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 11-2   Шаги сортировки выбором </p> <p>В коде мы используем \\(k\\) для записи минимального элемента в пределах неотсортированного диапазона:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby selection_sort.py<pre><code>def selection_sort(nums: list[int]):\n    \"\"\"Сортировка выбором\"\"\"\n    n = len(nums)\n    # Внешний цикл: неотсортированный диапазон [i, n-1]\n    for i in range(n - 1):\n        # Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n        k = i\n        for j in range(i + 1, n):\n            if nums[j] &lt; nums[k]:\n                k = j  # Записать индекс минимального элемента\n        # Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n        nums[i], nums[k] = nums[k], nums[i]\n</code></pre> selection_sort.cpp<pre><code>/* Сортировка выбором */\nvoid selectionSort(vector&lt;int&gt; &amp;nums) {\n    int n = nums.size();\n    // Внешний цикл: неотсортированный диапазон [i, n-1]\n    for (int i = 0; i &lt; n - 1; i++) {\n        // Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n        int k = i;\n        for (int j = i + 1; j &lt; n; j++) {\n            if (nums[j] &lt; nums[k])\n                k = j; // Записать индекс минимального элемента\n        }\n        // Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n        swap(nums[i], nums[k]);\n    }\n}\n</code></pre> selection_sort.java<pre><code>/* Сортировка выбором */\nvoid selectionSort(int[] nums) {\n    int n = nums.length;\n    // Внешний цикл: неотсортированный диапазон [i, n-1]\n    for (int i = 0; i &lt; n - 1; i++) {\n        // Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n        int k = i;\n        for (int j = i + 1; j &lt; n; j++) {\n            if (nums[j] &lt; nums[k])\n                k = j; // Записать индекс минимального элемента\n        }\n        // Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n        int temp = nums[i];\n        nums[i] = nums[k];\n        nums[k] = temp;\n    }\n}\n</code></pre> selection_sort.cs<pre><code>/* Сортировка выбором */\nvoid SelectionSort(int[] nums) {\n    int n = nums.Length;\n    // Внешний цикл: неотсортированный диапазон [i, n-1]\n    for (int i = 0; i &lt; n - 1; i++) {\n        // Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n        int k = i;\n        for (int j = i + 1; j &lt; n; j++) {\n            if (nums[j] &lt; nums[k])\n                k = j; // Записать индекс минимального элемента\n        }\n        // Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n        (nums[k], nums[i]) = (nums[i], nums[k]);\n    }\n}\n</code></pre> selection_sort.go<pre><code>/* Сортировка выбором */\nfunc selectionSort(nums []int) {\n    n := len(nums)\n    // Внешний цикл: неотсортированный диапазон [i, n-1]\n    for i := 0; i &lt; n-1; i++ {\n        // Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n        k := i\n        for j := i + 1; j &lt; n; j++ {\n            if nums[j] &lt; nums[k] {\n                // Записать индекс минимального элемента\n                k = j\n            }\n        }\n        // Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n        nums[i], nums[k] = nums[k], nums[i]\n\n    }\n}\n</code></pre> selection_sort.swift<pre><code>/* Сортировка выбором */\nfunc selectionSort(nums: inout [Int]) {\n    // Внешний цикл: неотсортированный диапазон [i, n-1]\n    for i in nums.indices.dropLast() {\n        // Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n        var k = i\n        for j in nums.indices.dropFirst(i + 1) {\n            if nums[j] &lt; nums[k] {\n                k = j // Записать индекс минимального элемента\n            }\n        }\n        // Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n        nums.swapAt(i, k)\n    }\n}\n</code></pre> selection_sort.js<pre><code>/* Сортировка выбором */\nfunction selectionSort(nums) {\n    let n = nums.length;\n    // Внешний цикл: неотсортированный диапазон [i, n-1]\n    for (let i = 0; i &lt; n - 1; i++) {\n        // Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n        let k = i;\n        for (let j = i + 1; j &lt; n; j++) {\n            if (nums[j] &lt; nums[k]) {\n                k = j; // Записать индекс минимального элемента\n            }\n        }\n        // Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n        [nums[i], nums[k]] = [nums[k], nums[i]];\n    }\n}\n</code></pre> selection_sort.ts<pre><code>/* Сортировка выбором */\nfunction selectionSort(nums: number[]): void {\n    let n = nums.length;\n    // Внешний цикл: неотсортированный диапазон [i, n-1]\n    for (let i = 0; i &lt; n - 1; i++) {\n        // Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n        let k = i;\n        for (let j = i + 1; j &lt; n; j++) {\n            if (nums[j] &lt; nums[k]) {\n                k = j; // Записать индекс минимального элемента\n            }\n        }\n        // Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n        [nums[i], nums[k]] = [nums[k], nums[i]];\n    }\n}\n</code></pre> selection_sort.dart<pre><code>/* Сортировка выбором */\nvoid selectionSort(List&lt;int&gt; nums) {\n  int n = nums.length;\n  // Внешний цикл: неотсортированный диапазон [i, n-1]\n  for (int i = 0; i &lt; n - 1; i++) {\n    // Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n    int k = i;\n    for (int j = i + 1; j &lt; n; j++) {\n      if (nums[j] &lt; nums[k]) k = j; // Записать индекс минимального элемента\n    }\n    // Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n    int temp = nums[i];\n    nums[i] = nums[k];\n    nums[k] = temp;\n  }\n}\n</code></pre> selection_sort.rs<pre><code>/* Сортировка выбором */\nfn selection_sort(nums: &amp;mut [i32]) {\n    if nums.is_empty() {\n        return;\n    }\n    let n = nums.len();\n    // Внешний цикл: неотсортированный диапазон [i, n-1]\n    for i in 0..n - 1 {\n        // Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n        let mut k = i;\n        for j in i + 1..n {\n            if nums[j] &lt; nums[k] {\n                k = j; // Записать индекс минимального элемента\n            }\n        }\n        // Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n        nums.swap(i, k);\n    }\n}\n</code></pre> selection_sort.c<pre><code>/* Сортировка выбором */\nvoid selectionSort(int nums[], int n) {\n    // Внешний цикл: неотсортированный диапазон [i, n-1]\n    for (int i = 0; i &lt; n - 1; i++) {\n        // Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n        int k = i;\n        for (int j = i + 1; j &lt; n; j++) {\n            if (nums[j] &lt; nums[k])\n                k = j; // Записать индекс минимального элемента\n        }\n        // Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n        int temp = nums[i];\n        nums[i] = nums[k];\n        nums[k] = temp;\n    }\n}\n</code></pre> selection_sort.kt<pre><code>/* Сортировка выбором */\nfun selectionSort(nums: IntArray) {\n    val n = nums.size\n    // Внешний цикл: неотсортированный диапазон [i, n-1]\n    for (i in 0..&lt;n - 1) {\n        var k = i\n        // Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n        for (j in i + 1..&lt;n) {\n            if (nums[j] &lt; nums[k])\n                k = j // Записать индекс минимального элемента\n        }\n        // Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n        val temp = nums[i]\n        nums[i] = nums[k]\n        nums[k] = temp\n    }\n}\n</code></pre> selection_sort.rb<pre><code>### Сортировка выбором ###\ndef selection_sort(nums)\n  n = nums.length\n  # Внешний цикл: неотсортированный диапазон [i, n-1]\n  for i in 0...(n - 1)\n    # Внутренний цикл: найти минимальный элемент в неотсортированном диапазоне\n    k = i\n    for j in (i + 1)...n\n      if nums[j] &lt; nums[k]\n        k = j # Записать индекс минимального элемента\n      end\n    end\n    # Поменять этот минимальный элемент местами с первым элементом неотсортированного диапазона\n    nums[i], nums[k] = nums[k], nums[i]\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 11. Сортировка","11.2 &nbsp; Сортировка выбором"],"tags":[]},{"location":"chapter_sorting/selection_sort/#1121","level":2,"title":"11.2.1   Характеристики алгоритма","text":"<ul> <li>Временная сложность равна \\(O(n^2)\\), сортировка не является адаптивной: внешний цикл выполняется \\(n - 1\\) раз; в первом раунде длина неотсортированного диапазона равна \\(n\\) , а в последнем - \\(2\\) , то есть отдельные раунды содержат \\(n\\), \\(n - 1\\), \\(\\dots\\), \\(3\\), \\(2\\) проходов внутреннего цикла, их сумма равна \\(\\frac{(n - 1)(n + 2)}{2}\\) .</li> <li>Пространственная сложность равна \\(O(1)\\), сортировка выполняется на месте: указатели \\(i\\) и \\(j\\) используют константный объем дополнительной памяти.</li> <li>Нестабильная сортировка: как показано на рисунке 11-3, элемент <code>nums[i]</code> может быть переставлен вправо от другого равного ему элемента, из-за чего их относительный порядок изменится.</li> </ul> <p> Рисунок 11-3   Пример нестабильности сортировки выбором </p>","path":["Глава 11. Сортировка","11.2 &nbsp; Сортировка выбором"],"tags":[]},{"location":"chapter_sorting/sorting_algorithm/","level":1,"title":"11.1   Алгоритмы сортировки","text":"<p>Алгоритмы сортировки (sorting algorithm) используются для упорядочивания набора данных по определенному правилу. Они применяются очень широко, потому что упорядоченные данные обычно проще анализировать, обрабатывать и искать в них нужные элементы.</p> <p>Как показано на рисунке 11-1, данными в алгоритмах сортировки могут быть целые числа, числа с плавающей запятой, символы, строки и другие типы. Критерий сравнения тоже можно задать по-разному, например по величине чисел, по порядку ASCII-кодов символов или по пользовательскому правилу.</p> <p></p> <p> Рисунок 11-1   Примеры типов данных и правил сравнения </p>","path":["Глава 11. Сортировка","11.1 &nbsp; Алгоритмы сортировки"],"tags":[]},{"location":"chapter_sorting/sorting_algorithm/#1111","level":2,"title":"11.1.1   Критерии оценки","text":"<p>Скорость выполнения: мы ожидаем, что временная сложность алгоритма сортировки будет как можно ниже, а общее число операций будет как можно меньше (то есть константа во временной сложности будет небольшой). Для больших объемов данных этот критерий особенно важен.</p> <p>Сортировка на месте: как следует из названия, сортировка на месте выполняется прямо в исходном массиве и не требует дополнительного вспомогательного массива, что позволяет экономить память. Обычно при сортировке на месте переносов данных меньше, а скорость работы выше.</p> <p>Стабильность: стабильная сортировка после завершения не меняет относительный порядок одинаковых элементов в массиве.</p> <p>Стабильность является необходимым условием для многоуровневой сортировки. Предположим, у нас есть таблица со сведениями о студентах, где в первом и втором столбцах записаны имя и возраст. В этом случае нестабильная сортировка может разрушить уже существующий порядок входных данных:</p> <pre><code># Входные данные уже отсортированы по имени\n# (name, age)\n  ('A', 19)\n  ('B', 18)\n  ('C', 21)\n  ('D', 19)\n  ('E', 23)\n\n# Если затем нестабильным алгоритмом отсортировать список по возрасту,\n# относительный порядок ('D', 19) и ('A', 19) изменится,\n# и свойство упорядоченности по имени будет потеряно\n  ('B', 18)\n  ('D', 19)\n  ('A', 19)\n  ('C', 21)\n  ('E', 23)\n</code></pre> <p>Адаптивность: адаптивная сортировка умеет использовать уже существующий порядок входных данных, чтобы сократить вычисления и добиться лучшей эффективности. Лучшая временная сложность адаптивных алгоритмов обычно лучше их средней временной сложности.</p> <p>Основанность на сравнении: сортировка на основе сравнений использует операторы сравнения (\\(&lt;\\), \\(=\\), \\(&gt;\\)), чтобы определить относительный порядок элементов и отсортировать массив; ее теоретически лучшая временная сложность равна \\(O(n \\log n)\\) . А вот сортировка без сравнений не опирается на операторы сравнения, поэтому может достигать \\(O(n)\\) , но универсальность у нее ниже.</p>","path":["Глава 11. Сортировка","11.1 &nbsp; Алгоритмы сортировки"],"tags":[]},{"location":"chapter_sorting/sorting_algorithm/#1112","level":2,"title":"11.1.2   Идеальный алгоритм сортировки","text":"<p>Быстрый, выполняющийся на месте, стабильный, адаптивный и универсальный. Очевидно, что на сегодняшний день не существует алгоритма сортировки, который одновременно обладал бы всеми этими свойствами. Поэтому при выборе алгоритма сортировки нужно исходить из конкретных особенностей данных и требований задачи.</p> <p>Далее мы последовательно изучим разные алгоритмы сортировки и на основании приведенных выше критериев разберем их преимущества и недостатки.</p>","path":["Глава 11. Сортировка","11.1 &nbsp; Алгоритмы сортировки"],"tags":[]},{"location":"chapter_sorting/summary/","level":1,"title":"11.11   Резюме","text":"","path":["Глава 11. Сортировка","11.11 &nbsp; Резюме"],"tags":[]},{"location":"chapter_sorting/summary/#1","level":3,"title":"1.   Ключевые выводы","text":"<ul> <li>Сортировка пузырьком выполняет сортировку за счет обмена соседних элементов. Если добавить флаг для досрочного выхода, лучшую временную сложность пузырьковой сортировки можно оптимизировать до \\(O(n)\\) .</li> <li>Сортировка вставками на каждом раунде вставляет элемент из неотсортированного диапазона в правильную позицию внутри отсортированного диапазона. Хотя ее временная сложность равна \\(O(n^2)\\) , она очень популярна для задач сортировки небольших массивов, поскольку число элементарных операций у нее сравнительно невелико.</li> <li>Быстрая сортировка основана на операции разделения с опорным элементом. При неудачном выборе опорного элемента на каждом раунде ее временная сложность может деградировать до \\(O(n^2)\\) . Использование медианы трех элементов или случайного опорного элемента уменьшает вероятность этой деградации. Если всегда рекурсивно обрабатывать более короткий поддиапазон первым, можно эффективно уменьшить глубину рекурсии и оптимизировать пространственную сложность до \\(O(\\log n)\\) .</li> <li>Сортировка слиянием включает этапы разделения и слияния и служит типичным проявлением стратегии \"разделяй и властвуй\". Для сортировки массива ей требуется вспомогательный массив, поэтому пространственная сложность равна \\(O(n)\\) ; однако при сортировке связного списка пространственную сложность можно оптимизировать до \\(O(1)\\) .</li> <li>Блочная сортировка включает три этапа: распределение данных по блокам, сортировку внутри блоков и объединение результатов. Она тоже отражает стратегию \"разделяй и властвуй\" и подходит для очень больших объемов данных. Ключ к эффективности блочной сортировки - равномерное распределение данных.</li> <li>Сортировка подсчетом является частным случаем блочной сортировки; она реализует сортировку через подсчет числа вхождений данных. Сортировка подсчетом подходит для случаев, когда объем данных велик, но диапазон значений ограничен, и при этом данные можно преобразовать в положительные целые числа.</li> <li>Поразрядная сортировка выполняет сортировку данных путем последовательной сортировки по каждому разряду и требует, чтобы данные можно было представить в виде чисел фиксированной разрядности.</li> <li>В общем случае нам хотелось бы найти алгоритм сортировки, который одновременно обладал бы высокой эффективностью, стабильностью, выполнением на месте и адаптивностью. Но, как и в других разделах алгоритмов и структур данных, не существует одного алгоритма сортировки, способного удовлетворить всем этим требованиям одновременно. На практике приходится выбирать подходящий алгоритм в зависимости от свойств данных.</li> <li>На рисунке 11-19 сравниваются эффективность, стабильность, выполнение на месте и адаптивность основных алгоритмов сортировки.</li> </ul> <p> Рисунок 11-19   Сравнение алгоритмов сортировки </p>","path":["Глава 11. Сортировка","11.11 &nbsp; Резюме"],"tags":[]},{"location":"chapter_sorting/summary/#2","level":3,"title":"2.   Вопросы и ответы","text":"<p>В: В каких случаях стабильность алгоритма сортировки является обязательной?</p> <p>В реальных задачах нам может понадобиться сортировать объекты по некоторому атрибуту. Например, у студентов есть два атрибута: имя и рост. Мы хотим выполнить многоуровневую сортировку: сначала отсортировать по имени и получить <code>(A, 180) (B, 185) (C, 170) (D, 170)</code> , а затем отсортировать по росту. Если используемый алгоритм сортировки нестабилен, то мы можем получить <code>(D, 170) (C, 170) (A, 180) (B, 185)</code> .</p> <p>Нетрудно увидеть, что в этом случае студенты D и C поменялись местами, порядок по имени разрушился, а именно этого мы и не хотим.</p> <p>В: Можно ли поменять местами порядок \"поиска справа налево\" и \"поиска слева направо\" в разделении с опорным элементом?</p> <p>Нет. Если в качестве опорного элемента выбирается самый левый элемент, необходимо сначала выполнять \"поиск справа налево\", а уже затем - \"поиск слева направо\". Этот вывод кажется немного неочевидным, поэтому разберем его подробнее.</p> <p>Последний шаг <code>partition()</code> - это обмен <code>nums[left]</code> и <code>nums[i]</code> . После обмена все элементы слева от опорного должны быть <code>&lt;=</code> опорного, а значит, перед этим обменом должно выполняться условие <code>nums[left] &gt;= nums[i]</code>. Если сначала выполнять \"поиск слева направо\", то в случае, когда не удается найти элемент больше опорного, цикл завершится в состоянии <code>i == j</code> , и при этом может оказаться, что <code>nums[j] == nums[i] &gt; nums[left]</code>. Иными словами, на последнем шаге обмена элемент, больший опорного, будет помещен в начало массива, из-за чего разделение завершится неверно.</p> <p>Например, для массива <code>[0, 0, 0, 0, 1]</code> , если сначала выполнять \"поиск слева направо\", после разделения получится <code>[1, 0, 0, 0, 0]</code> , а это неправильный результат.</p> <p>Если же выбрать <code>nums[right]</code> в качестве опорного элемента, то ситуация станет противоположной, и тогда сначала нужно выполнять \"поиск слева направо\".</p> <p>В: Почему при оптимизации глубины рекурсии в быстрой сортировке выбор короткого массива гарантирует, что глубина рекурсии не превысит \\(\\log n\\) ?</p> <p>Глубина рекурсии - это число текущих рекурсивных вызовов, которые еще не завершились. На каждом раунде разделения исходный массив разбивается на два подмассива. После оптимизации глубины рекурсии длина подмассива, в который мы продолжаем рекурсивный спуск, не превышает половины длины исходного массива. Если рассматривать худший случай, когда длина каждый раз становится ровно вдвое меньше, итоговая глубина рекурсии и будет равна \\(\\log n\\) .</p> <p>В исходной версии быстрой сортировки может происходить последовательный рекурсивный вызов для более длинных массивов; в худшем случае это будут длины \\(n\\) , \\(n - 1\\) , \\(\\dots\\) , \\(2\\) , \\(1\\) , а глубина рекурсии окажется равной \\(n\\) . Оптимизация глубины рекурсии как раз и позволяет избежать такого сценария.</p> <p>В: Если все элементы массива равны, будет ли временная сложность быстрой сортировки равна \\(O(n^2)\\) ? Как справиться с таким вырождением?</p> <p>Да. Для этого случая можно рассмотреть разделение массива на три части: элементы меньше опорного, равные опорному и большие опорного. Рекурсию нужно продолжать только для частей меньше и больше опорного. При таком подходе массив, целиком состоящий из одинаковых элементов, будет отсортирован всего за один раунд разделения.</p> <p>В: Почему худшая временная сложность блочной сортировки равна \\(O(n^2)\\) ?</p> <p>В худшем случае все элементы попадут в один и тот же блок. Если затем сортировать этот блок алгоритмом со сложностью \\(O(n^2)\\) , то общая временная сложность тоже станет \\(O(n^2)\\) .</p>","path":["Глава 11. Сортировка","11.11 &nbsp; Резюме"],"tags":[]},{"location":"chapter_stack_and_queue/","level":1,"title":"Глава 5.   Стек и очередь","text":"<p>Abstract</p> <p>Стек и очередь - две базовые линейные структуры данных.</p> <p>Они соответственно воплощают принципы \"последним пришел - первым вышел\" и \"первым пришел - первым вышел\".</p>","path":["Глава 5. Стек и очередь","Глава 5. &nbsp; Стек и очередь"],"tags":[]},{"location":"chapter_stack_and_queue/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>5.1   Стек</li> <li>5.2   Очередь</li> <li>5.3   Двусторонняя очередь</li> <li>5.4   Резюме</li> </ul>","path":["Глава 5. Стек и очередь","Глава 5. &nbsp; Стек и очередь"],"tags":[]},{"location":"chapter_stack_and_queue/deque/","level":1,"title":"5.3   Двусторонняя очередь","text":"<p>В обычной очереди мы можем удалять элементы только из головы и добавлять их только в хвост. Как показано на рисунке 5-7, двусторонняя очередь (double-ended queue) обеспечивает большую гибкость и позволяет выполнять добавление и удаление элементов как с головы, так и с хвоста.</p> <p></p> <p> Рисунок 5-7   Операции двусторонней очереди </p>","path":["Глава 5. Стек и очередь","5.3 &nbsp; Двусторонняя очередь"],"tags":[]},{"location":"chapter_stack_and_queue/deque/#531","level":2,"title":"5.3.1   Основные операции с двусторонней очередью","text":"<p>Распространенные операции двусторонней очереди приведены в таблице 5-3. Конкретные названия методов зависят от используемого языка программирования.</p> <p> Таблица 5-3   Эффективность операций двусторонней очереди </p> Имя метода Описание Временная сложность <code>push_first()</code> Добавить элемент в голову очереди \\(O(1)\\) <code>push_last()</code> Добавить элемент в хвост очереди \\(O(1)\\) <code>pop_first()</code> Удалить элемент из головы очереди \\(O(1)\\) <code>pop_last()</code> Удалить элемент из хвоста очереди \\(O(1)\\) <code>peek_first()</code> Просмотреть элемент в голове очереди \\(O(1)\\) <code>peek_last()</code> Просмотреть элемент в хвосте очереди \\(O(1)\\) <p>Точно так же мы можем напрямую использовать уже реализованные в языках программирования классы двусторонней очереди:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby deque.py<pre><code>from collections import deque\n\n# Инициализация двусторонней очереди\ndeq: deque[int] = deque()\n\n# Поместить элементы в очередь\ndeq.append(2)      # Добавить в хвост\ndeq.append(5)\ndeq.append(4)\ndeq.appendleft(3)  # Добавить в голову\ndeq.appendleft(1)\n\n# Просмотреть элементы\nfront: int = deq[0]  # Элемент в голове\nrear: int = deq[-1]  # Элемент в хвосте\n\n# Извлечь элементы из очереди\npop_front: int = deq.popleft()  # Извлечь элемент из головы\npop_rear: int = deq.pop()       # Извлечь элемент из хвоста\n\n# Получить длину двусторонней очереди\nsize: int = len(deq)\n\n# Проверить, пуста ли двусторонняя очередь\nis_empty: bool = len(deq) == 0\n</code></pre> deque.cpp<pre><code>/* Инициализация двусторонней очереди */\ndeque&lt;int&gt; deque;\n\n/* Поместить элементы в очередь */\ndeque.push_back(2);   // Добавить в хвост\ndeque.push_back(5);\ndeque.push_back(4);\ndeque.push_front(3);  // Добавить в голову\ndeque.push_front(1);\n\n/* Просмотреть элементы */\nint front = deque.front(); // Элемент в голове\nint back = deque.back();   // Элемент в хвосте\n\n/* Извлечь элементы из очереди */\ndeque.pop_front();  // Извлечь элемент из головы\ndeque.pop_back();   // Извлечь элемент из хвоста\n\n/* Получить длину двусторонней очереди */\nint size = deque.size();\n\n/* Проверить, пуста ли двусторонняя очередь */\nbool empty = deque.empty();\n</code></pre> deque.java<pre><code>/* Инициализация двусторонней очереди */\nDeque&lt;Integer&gt; deque = new LinkedList&lt;&gt;();\n\n/* Поместить элементы в очередь */\ndeque.offerLast(2);   // Добавить в хвост\ndeque.offerLast(5);\ndeque.offerLast(4);\ndeque.offerFirst(3);  // Добавить в голову\ndeque.offerFirst(1);\n\n/* Просмотреть элементы */\nint peekFirst = deque.peekFirst();  // Элемент в голове\nint peekLast = deque.peekLast();    // Элемент в хвосте\n\n/* Извлечь элементы из очереди */\nint popFirst = deque.pollFirst();  // Извлечь элемент из головы\nint popLast = deque.pollLast();    // Извлечь элемент из хвоста\n\n/* Получить длину двусторонней очереди */\nint size = deque.size();\n\n/* Проверить, пуста ли двусторонняя очередь */\nboolean isEmpty = deque.isEmpty();\n</code></pre> deque.cs<pre><code>/* Инициализация двусторонней очереди */\n// В C# двустороннюю очередь обычно моделируют через связный список LinkedList\nLinkedList&lt;int&gt; deque = new();\n\n/* Поместить элементы в очередь */\ndeque.AddLast(2);   // Добавить в хвост\ndeque.AddLast(5);\ndeque.AddLast(4);\ndeque.AddFirst(3);  // Добавить в голову\ndeque.AddFirst(1);\n\n/* Просмотреть элементы */\nint peekFirst = deque.First.Value;  // Элемент в голове\nint peekLast = deque.Last.Value;    // Элемент в хвосте\n\n/* Извлечь элементы из очереди */\ndeque.RemoveFirst();  // Извлечь элемент из головы\ndeque.RemoveLast();   // Извлечь элемент из хвоста\n\n/* Получить длину двусторонней очереди */\nint size = deque.Count;\n\n/* Проверить, пуста ли двусторонняя очередь */\nbool isEmpty = deque.Count == 0;\n</code></pre> deque_test.go<pre><code>/* Инициализация двусторонней очереди */\n// В Go list обычно используется как двусторонняя очередь\ndeque := list.New()\n\n/* Поместить элементы в очередь */\ndeque.PushBack(2)      // Добавить в хвост\ndeque.PushBack(5)\ndeque.PushBack(4)\ndeque.PushFront(3)     // Добавить в голову\ndeque.PushFront(1)\n\n/* Просмотреть элементы */\nfront := deque.Front() // Элемент в голове\nrear := deque.Back()   // Элемент в хвосте\n\n/* Извлечь элементы из очереди */\ndeque.Remove(front)    // Извлечь элемент из головы\ndeque.Remove(rear)     // Извлечь элемент из хвоста\n\n/* Получить длину двусторонней очереди */\nsize := deque.Len()\n\n/* Проверить, пуста ли двусторонняя очередь */\nisEmpty := deque.Len() == 0\n</code></pre> deque.swift<pre><code>/* Инициализация двусторонней очереди */\n// В Swift нет встроенного класса двусторонней очереди, поэтому можно использовать Array как двустороннюю очередь\nvar deque: [Int] = []\n\n/* Поместить элементы в очередь */\ndeque.append(2) // Добавить в хвост\ndeque.append(5)\ndeque.append(4)\ndeque.insert(3, at: 0) // Добавить в голову\ndeque.insert(1, at: 0)\n\n/* Просмотреть элементы */\nlet peekFirst = deque.first! // Элемент в голове\nlet peekLast = deque.last! // Элемент в хвосте\n\n/* Извлечь элементы из очереди */\n// При моделировании через Array сложность popFirst равна O(n)\nlet popFirst = deque.removeFirst() // Извлечь элемент из головы\nlet popLast = deque.removeLast() // Извлечь элемент из хвоста\n\n/* Получить длину двусторонней очереди */\nlet size = deque.count\n\n/* Проверить, пуста ли двусторонняя очередь */\nlet isEmpty = deque.isEmpty\n</code></pre> deque.js<pre><code>/* Инициализация двусторонней очереди */\n// В JavaScript нет встроенной двусторонней очереди, поэтому можно использовать Array как двустороннюю очередь\nconst deque = [];\n\n/* Поместить элементы в очередь */\ndeque.push(2);\ndeque.push(5);\ndeque.push(4);\n// Обрати внимание: поскольку это массив, метод unshift() имеет сложность O(n)\ndeque.unshift(3);\ndeque.unshift(1);\n\n/* Просмотреть элементы */\nconst peekFirst = deque[0];\nconst peekLast = deque[deque.length - 1];\n\n/* Извлечь элементы из очереди */\n// Обрати внимание: поскольку это массив, метод shift() имеет сложность O(n)\nconst popFront = deque.shift();\nconst popBack = deque.pop();\n\n/* Получить длину двусторонней очереди */\nconst size = deque.length;\n\n/* Проверить, пуста ли двусторонняя очередь */\nconst isEmpty = size === 0;\n</code></pre> deque.ts<pre><code>/* Инициализация двусторонней очереди */\n// В TypeScript нет встроенной двусторонней очереди, поэтому можно использовать Array как двустороннюю очередь\nconst deque: number[] = [];\n\n/* Поместить элементы в очередь */\ndeque.push(2);\ndeque.push(5);\ndeque.push(4);\n// Обрати внимание: поскольку это массив, метод unshift() имеет сложность O(n)\ndeque.unshift(3);\ndeque.unshift(1);\n\n/* Просмотреть элементы */\nconst peekFirst: number = deque[0];\nconst peekLast: number = deque[deque.length - 1];\n\n/* Извлечь элементы из очереди */\n// Обрати внимание: поскольку это массив, метод shift() имеет сложность O(n)\nconst popFront: number = deque.shift() as number;\nconst popBack: number = deque.pop() as number;\n\n/* Получить длину двусторонней очереди */\nconst size: number = deque.length;\n\n/* Проверить, пуста ли двусторонняя очередь */\nconst isEmpty: boolean = size === 0;\n</code></pre> deque.dart<pre><code>/* Инициализация двусторонней очереди */\n// В Dart Queue определена как двусторонняя очередь\nQueue&lt;int&gt; deque = Queue&lt;int&gt;();\n\n/* Поместить элементы в очередь */\ndeque.addLast(2);  // Добавить в хвост\ndeque.addLast(5);\ndeque.addLast(4);\ndeque.addFirst(3); // Добавить в голову\ndeque.addFirst(1);\n\n/* Просмотреть элементы */\nint peekFirst = deque.first; // Элемент в голове\nint peekLast = deque.last;   // Элемент в хвосте\n\n/* Извлечь элементы из очереди */\nint popFirst = deque.removeFirst(); // Извлечь элемент из головы\nint popLast = deque.removeLast();   // Извлечь элемент из хвоста\n\n/* Получить длину двусторонней очереди */\nint size = deque.length;\n\n/* Проверить, пуста ли двусторонняя очередь */\nbool isEmpty = deque.isEmpty;\n</code></pre> deque.rs<pre><code>/* Инициализация двусторонней очереди */\nlet mut deque: VecDeque&lt;u32&gt; = VecDeque::new();\n\n/* Поместить элементы в очередь */\ndeque.push_back(2);  // Добавить в хвост\ndeque.push_back(5);\ndeque.push_back(4);\ndeque.push_front(3); // Добавить в голову\ndeque.push_front(1);\n\n/* Просмотреть элементы */\nif let Some(front) = deque.front() { // Элемент в голове\n}\nif let Some(rear) = deque.back() {   // Элемент в хвосте\n}\n\n/* Извлечь элементы из очереди */\nif let Some(pop_front) = deque.pop_front() { // Извлечь элемент из головы\n}\nif let Some(pop_rear) = deque.pop_back() {   // Извлечь элемент из хвоста\n}\n\n/* Получить длину двусторонней очереди */\nlet size = deque.len();\n\n/* Проверить, пуста ли двусторонняя очередь */\nlet is_empty = deque.is_empty();\n</code></pre> deque.c<pre><code>// В C нет встроенной двусторонней очереди\n</code></pre> deque.kt<pre><code>/* Инициализация двусторонней очереди */\nval deque = LinkedList&lt;Int&gt;()\n\n/* Поместить элементы в очередь */\ndeque.offerLast(2)  // Добавить в хвост\ndeque.offerLast(5)\ndeque.offerLast(4)\ndeque.offerFirst(3) // Добавить в голову\ndeque.offerFirst(1)\n\n/* Просмотреть элементы */\nval peekFirst = deque.peekFirst() // Элемент в голове\nval peekLast = deque.peekLast()   // Элемент в хвосте\n\n/* Извлечь элементы из очереди */\nval popFirst = deque.pollFirst() // Извлечь элемент из головы\nval popLast = deque.pollLast()   // Извлечь элемент из хвоста\n\n/* Получить длину двусторонней очереди */\nval size = deque.size\n\n/* Проверить, пуста ли двусторонняя очередь */\nval isEmpty = deque.isEmpty()\n</code></pre> deque.rb<pre><code># Инициализация двусторонней очереди\n# В Ruby нет встроенной двусторонней очереди, поэтому можно использовать Array как двустороннюю очередь\ndeque = []\n\n# Поместить элементы в очередь\ndeque &lt;&lt; 2\ndeque &lt;&lt; 5\ndeque &lt;&lt; 4\n# Обрати внимание: поскольку это массив, метод Array#unshift имеет сложность O(n)\ndeque.unshift(3)\ndeque.unshift(1)\n\n# Просмотреть элементы\npeek_first = deque.first\npeek_last = deque.last\n\n# Извлечь элементы из очереди\n# Обрати внимание: поскольку это массив, метод Array#shift имеет сложность O(n)\npop_front = deque.shift\npop_back = deque.pop\n\n# Получить длину двусторонней очереди\nsize = deque.length\n\n# Проверить, пуста ли двусторонняя очередь\nis_empty = size.zero?\n</code></pre> Визуализация выполнения 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rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 5. Стек и очередь","5.3 &nbsp; Двусторонняя очередь"],"tags":[]},{"location":"chapter_stack_and_queue/deque/#532","level":2,"title":"5.3.2   Реализация двусторонней очереди *","text":"<p>Реализация двусторонней очереди похожа на реализацию обычной очереди: в качестве базовой структуры данных можно выбрать связный список или массив.</p>","path":["Глава 5. Стек и очередь","5.3 &nbsp; Двусторонняя очередь"],"tags":[]},{"location":"chapter_stack_and_queue/deque/#1","level":3,"title":"1.   Реализация на основе двусвязного списка","text":"<p>Вспомним предыдущий раздел: там мы использовали обычный односвязный список для реализации очереди, потому что он позволяет удобно удалять головной узел, что соответствует операции <code>dequeue</code> , и добавлять новый узел после хвостового узла, что соответствует операции <code>enqueue</code> .</p> <p>Для двусторонней очереди и голова, и хвост допускают операции добавления и удаления элементов. Иначе говоря, двусторонняя очередь требует реализации еще одного симметричного направления операций. Поэтому в качестве базовой структуры данных двусторонней очереди удобно использовать двусвязный список.</p> <p>Как показано на рисунках ниже, мы рассматриваем головной и хвостовой узлы двусвязного списка как голову и хвост двусторонней очереди и одновременно реализуем функции добавления и удаления узлов с обеих сторон.</p> LinkedListDequepush_last()push_first()pop_last()pop_first() <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 5-8   Операции enqueue и dequeue для двусторонней очереди на связном списке </p> <p>Код реализации приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linkedlist_deque.py<pre><code>class ListNode:\n    \"\"\"Узел двусвязного списка\"\"\"\n\n    def __init__(self, val: int):\n        \"\"\"Конструктор\"\"\"\n        self.val: int = val\n        self.next: ListNode | None = None  # Ссылка на узел-преемник\n        self.prev: ListNode | None = None  # Ссылка на узел-предшественник\n\nclass LinkedListDeque:\n    \"\"\"Двусторонняя очередь на основе двусвязного списка\"\"\"\n\n    def __init__(self):\n        \"\"\"Конструктор\"\"\"\n        self._front: ListNode | None = None  # Головной узел front\n        self._rear: ListNode | None = None  # Хвостовой узел rear\n        self._size: int = 0  # Длина двусторонней очереди\n\n    def size(self) -&gt; int:\n        \"\"\"Получение длины двусторонней очереди\"\"\"\n        return self._size\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"Проверка, пуста ли двусторонняя очередь\"\"\"\n        return self._size == 0\n\n    def push(self, num: int, is_front: bool):\n        \"\"\"Операция добавления в очередь\"\"\"\n        node = ListNode(num)\n        # Если связный список пуст, сделать так, чтобы и front, и rear указывали на node\n        if self.is_empty():\n            self._front = self._rear = node\n        # Операция добавления в голову очереди\n        elif is_front:\n            # Добавить node в голову списка\n            self._front.prev = node\n            node.next = self._front\n            self._front = node  # Обновить головной узел\n        # Операция добавления в хвост очереди\n        else:\n            # Добавить node в хвост списка\n            self._rear.next = node\n            node.prev = self._rear\n            self._rear = node  # Обновить хвостовой узел\n        self._size += 1  # Обновить длину очереди\n\n    def push_first(self, num: int):\n        \"\"\"Добавление в голову очереди\"\"\"\n        self.push(num, True)\n\n    def push_last(self, num: int):\n        \"\"\"Добавление в хвост очереди\"\"\"\n        self.push(num, False)\n\n    def pop(self, is_front: bool) -&gt; int:\n        \"\"\"Операция извлечения из очереди\"\"\"\n        if self.is_empty():\n            raise IndexError(\"двусторонняя очередь пуста\")\n        # Операция извлечения из головы очереди\n        if is_front:\n            val: int = self._front.val  # Временно сохранить значение головного узла\n            # Удалить головной узел\n            fnext: ListNode | None = self._front.next\n            if fnext is not None:\n                fnext.prev = None\n                self._front.next = None\n            self._front = fnext  # Обновить головной узел\n        # Операция извлечения из хвоста очереди\n        else:\n            val: int = self._rear.val  # Временно сохранить значение хвостового узла\n            # Удалить хвостовой узел\n            rprev: ListNode | None = self._rear.prev\n            if rprev is not None:\n                rprev.next = None\n                self._rear.prev = None\n            self._rear = rprev  # Обновить хвостовой узел\n        self._size -= 1  # Обновить длину очереди\n        return val\n\n    def pop_first(self) -&gt; int:\n        \"\"\"Извлечение из головы очереди\"\"\"\n        return self.pop(True)\n\n    def pop_last(self) -&gt; int:\n        \"\"\"Извлечение из хвоста очереди\"\"\"\n        return self.pop(False)\n\n    def peek_first(self) -&gt; int:\n        \"\"\"Доступ к элементу в начале очереди\"\"\"\n        if self.is_empty():\n            raise IndexError(\"двусторонняя очередь пуста\")\n        return self._front.val\n\n    def peek_last(self) -&gt; int:\n        \"\"\"Доступ к элементу в конце очереди\"\"\"\n        if self.is_empty():\n            raise IndexError(\"двусторонняя очередь пуста\")\n        return self._rear.val\n\n    def to_array(self) -&gt; list[int]:\n        \"\"\"Вернуть массив для вывода\"\"\"\n        node = self._front\n        res = [0] * self.size()\n        for i in range(self.size()):\n            res[i] = node.val\n            node = node.next\n        return res\n</code></pre> linkedlist_deque.cpp<pre><code>/* Узел двусвязного списка */\nstruct DoublyListNode {\n    int val;              // Значение узла\n    DoublyListNode *next; // Указатель на узел-преемник\n    DoublyListNode *prev; // Указатель на узел-предшественник\n    DoublyListNode(int val) : val(val), prev(nullptr), next(nullptr) {\n    }\n};\n\n/* Двусторонняя очередь на основе двусвязного списка */\nclass LinkedListDeque {\n  private:\n    DoublyListNode *front, *rear; // Головной узел front, хвостовой узел rear\n    int queSize = 0;              // Длина двусторонней очереди\n\n  public:\n    /* Конструктор */\n    LinkedListDeque() : front(nullptr), rear(nullptr) {\n    }\n\n    /* Метод-деструктор */\n    ~LinkedListDeque() {\n        // Обходить связный список, удалять узлы и освобождать память\n        DoublyListNode *pre, *cur = front;\n        while (cur != nullptr) {\n            pre = cur;\n            cur = cur-&gt;next;\n            delete pre;\n        }\n    }\n\n    /* Получение длины двусторонней очереди */\n    int size() {\n        return queSize;\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    bool isEmpty() {\n        return size() == 0;\n    }\n\n    /* Операция добавления в очередь */\n    void push(int num, bool isFront) {\n        DoublyListNode *node = new DoublyListNode(num);\n        // Если связный список пуст, сделать так, чтобы и front, и rear указывали на node\n        if (isEmpty())\n            front = rear = node;\n        // Операция добавления в голову очереди\n        else if (isFront) {\n            // Добавить node в голову списка\n            front-&gt;prev = node;\n            node-&gt;next = front;\n            front = node; // Обновить головной узел\n        // Операция добавления в хвост очереди\n        } else {\n            // Добавить node в хвост списка\n            rear-&gt;next = node;\n            node-&gt;prev = rear;\n            rear = node; // Обновить хвостовой узел\n        }\n        queSize++; // Обновить длину очереди\n    }\n\n    /* Добавление в голову очереди */\n    void pushFirst(int num) {\n        push(num, true);\n    }\n\n    /* Добавление в хвост очереди */\n    void pushLast(int num) {\n        push(num, false);\n    }\n\n    /* Операция извлечения из очереди */\n    int pop(bool isFront) {\n        if (isEmpty())\n            throw out_of_range(\"очередь пуста\");\n        int val;\n        // Операция извлечения из головы очереди\n        if (isFront) {\n            val = front-&gt;val; // Временно сохранить значение головного узла\n            // Удалить головной узел\n            DoublyListNode *fNext = front-&gt;next;\n            if (fNext != nullptr) {\n                fNext-&gt;prev = nullptr;\n                front-&gt;next = nullptr;\n            }\n            delete front;\n            front = fNext; // Обновить головной узел\n        // Операция извлечения из хвоста очереди\n        } else {\n            val = rear-&gt;val; // Временно сохранить значение хвостового узла\n            // Удалить хвостовой узел\n            DoublyListNode *rPrev = rear-&gt;prev;\n            if (rPrev != nullptr) {\n                rPrev-&gt;next = nullptr;\n                rear-&gt;prev = nullptr;\n            }\n            delete rear;\n            rear = rPrev; // Обновить хвостовой узел\n        }\n        queSize--; // Обновить длину очереди\n        return val;\n    }\n\n    /* Извлечение из головы очереди */\n    int popFirst() {\n        return pop(true);\n    }\n\n    /* Извлечение из хвоста очереди */\n    int popLast() {\n        return pop(false);\n    }\n\n    /* Доступ к элементу в начале очереди */\n    int peekFirst() {\n        if (isEmpty())\n            throw out_of_range(\"двусторонняя очередь пуста\");\n        return front-&gt;val;\n    }\n\n    /* Доступ к элементу в конце очереди */\n    int peekLast() {\n        if (isEmpty())\n            throw out_of_range(\"двусторонняя очередь пуста\");\n        return rear-&gt;val;\n    }\n\n    /* Вернуть массив для вывода */\n    vector&lt;int&gt; toVector() {\n        DoublyListNode *node = front;\n        vector&lt;int&gt; res(size());\n        for (int i = 0; i &lt; res.size(); i++) {\n            res[i] = node-&gt;val;\n            node = node-&gt;next;\n        }\n        return res;\n    }\n};\n</code></pre> linkedlist_deque.java<pre><code>/* Узел двусвязного списка */\nclass ListNode {\n    int val; // Значение узла\n    ListNode next; // Ссылка на узел-преемник\n    ListNode prev; // Ссылка на узел-предшественник\n\n    ListNode(int val) {\n        this.val = val;\n        prev = next = null;\n    }\n}\n\n/* Двусторонняя очередь на основе двусвязного списка */\nclass LinkedListDeque {\n    private ListNode front, rear; // Головной узел front, хвостовой узел rear\n    private int queSize = 0; // Длина двусторонней очереди\n\n    public LinkedListDeque() {\n        front = rear = null;\n    }\n\n    /* Получение длины двусторонней очереди */\n    public int size() {\n        return queSize;\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    public boolean isEmpty() {\n        return size() == 0;\n    }\n\n    /* Операция добавления в очередь */\n    private void push(int num, boolean isFront) {\n        ListNode node = new ListNode(num);\n        // Если связный список пуст, сделать так, чтобы и front, и rear указывали на node\n        if (isEmpty())\n            front = rear = node;\n        // Операция добавления в голову очереди\n        else if (isFront) {\n            // Добавить node в голову списка\n            front.prev = node;\n            node.next = front;\n            front = node; // Обновить головной узел\n        // Операция добавления в хвост очереди\n        } else {\n            // Добавить node в хвост списка\n            rear.next = node;\n            node.prev = rear;\n            rear = node; // Обновить хвостовой узел\n        }\n        queSize++; // Обновить длину очереди\n    }\n\n    /* Добавление в голову очереди */\n    public void pushFirst(int num) {\n        push(num, true);\n    }\n\n    /* Добавление в хвост очереди */\n    public void pushLast(int num) {\n        push(num, false);\n    }\n\n    /* Операция извлечения из очереди */\n    private int pop(boolean isFront) {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        int val;\n        // Операция извлечения из головы очереди\n        if (isFront) {\n            val = front.val; // Временно сохранить значение головного узла\n            // Удалить головной узел\n            ListNode fNext = front.next;\n            if (fNext != null) {\n                fNext.prev = null;\n                front.next = null;\n            }\n            front = fNext; // Обновить головной узел\n        // Операция извлечения из хвоста очереди\n        } else {\n            val = rear.val; // Временно сохранить значение хвостового узла\n            // Удалить хвостовой узел\n            ListNode rPrev = rear.prev;\n            if (rPrev != null) {\n                rPrev.next = null;\n                rear.prev = null;\n            }\n            rear = rPrev; // Обновить хвостовой узел\n        }\n        queSize--; // Обновить длину очереди\n        return val;\n    }\n\n    /* Извлечение из головы очереди */\n    public int popFirst() {\n        return pop(true);\n    }\n\n    /* Извлечение из хвоста очереди */\n    public int popLast() {\n        return pop(false);\n    }\n\n    /* Доступ к элементу в начале очереди */\n    public int peekFirst() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return front.val;\n    }\n\n    /* Доступ к элементу в конце очереди */\n    public int peekLast() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return rear.val;\n    }\n\n    /* Вернуть массив для вывода */\n    public int[] toArray() {\n        ListNode node = front;\n        int[] res = new int[size()];\n        for (int i = 0; i &lt; res.length; i++) {\n            res[i] = node.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_deque.cs<pre><code>/* Узел двусвязного списка */\nclass ListNode(int val) {\n    public int val = val;       // Значение узла\n    public ListNode? next = null; // Ссылка на узел-преемник\n    public ListNode? prev = null; // Ссылка на узел-предшественник\n}\n\n/* Двусторонняя очередь на основе двусвязного списка */\nclass LinkedListDeque {\n    ListNode? front, rear; // Головной узел front, хвостовой узел rear\n    int queSize = 0;      // Длина двусторонней очереди\n\n    public LinkedListDeque() {\n        front = null;\n        rear = null;\n    }\n\n    /* Получение длины двусторонней очереди */\n    public int Size() {\n        return queSize;\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    public bool IsEmpty() {\n        return Size() == 0;\n    }\n\n    /* Операция добавления в очередь */\n    void Push(int num, bool isFront) {\n        ListNode node = new(num);\n        // Если связный список пуст, сделать так, чтобы и front, и rear указывали на node\n        if (IsEmpty()) {\n            front = node;\n            rear = node;\n        }\n        // Операция добавления в голову очереди\n        else if (isFront) {\n            // Добавить node в голову списка\n            front!.prev = node;\n            node.next = front;\n            front = node; // Обновить головной узел\n        }\n        // Операция добавления в хвост очереди\n        else {\n            // Добавить node в хвост списка\n            rear!.next = node;\n            node.prev = rear;\n            rear = node;  // Обновить хвостовой узел\n        }\n\n        queSize++; // Обновить длину очереди\n    }\n\n    /* Добавление в голову очереди */\n    public void PushFirst(int num) {\n        Push(num, true);\n    }\n\n    /* Добавление в хвост очереди */\n    public void PushLast(int num) {\n        Push(num, false);\n    }\n\n    /* Операция извлечения из очереди */\n    int? Pop(bool isFront) {\n        if (IsEmpty())\n            throw new Exception();\n        int? val;\n        // Операция извлечения из головы очереди\n        if (isFront) {\n            val = front?.val; // Временно сохранить значение головного узла\n            // Удалить головной узел\n            ListNode? fNext = front?.next;\n            if (fNext != null) {\n                fNext.prev = null;\n                front!.next = null;\n            }\n            front = fNext;   // Обновить головной узел\n        }\n        // Операция извлечения из хвоста очереди\n        else {\n            val = rear?.val;  // Временно сохранить значение хвостового узла\n            // Удалить хвостовой узел\n            ListNode? rPrev = rear?.prev;\n            if (rPrev != null) {\n                rPrev.next = null;\n                rear!.prev = null;\n            }\n            rear = rPrev;    // Обновить хвостовой узел\n        }\n\n        queSize--; // Обновить длину очереди\n        return val;\n    }\n\n    /* Извлечение из головы очереди */\n    public int? PopFirst() {\n        return Pop(true);\n    }\n\n    /* Извлечение из хвоста очереди */\n    public int? PopLast() {\n        return Pop(false);\n    }\n\n    /* Доступ к элементу в начале очереди */\n    public int? PeekFirst() {\n        if (IsEmpty())\n            throw new Exception();\n        return front?.val;\n    }\n\n    /* Доступ к элементу в конце очереди */\n    public int? PeekLast() {\n        if (IsEmpty())\n            throw new Exception();\n        return rear?.val;\n    }\n\n    /* Вернуть массив для вывода */\n    public int?[] ToArray() {\n        ListNode? node = front;\n        int?[] res = new int?[Size()];\n        for (int i = 0; i &lt; res.Length; i++) {\n            res[i] = node?.val;\n            node = node?.next;\n        }\n\n        return res;\n    }\n}\n</code></pre> linkedlist_deque.go<pre><code>/* Двусторонняя очередь на основе двусвязного списка */\ntype linkedListDeque struct {\n    // Использовать встроенный пакет list\n    data *list.List\n}\n\n/* Инициализировать двустороннюю очередь */\nfunc newLinkedListDeque() *linkedListDeque {\n    return &amp;linkedListDeque{\n        data: list.New(),\n    }\n}\n\n/* Поместить элемент в голову очереди */\nfunc (s *linkedListDeque) pushFirst(value any) {\n    s.data.PushFront(value)\n}\n\n/* Поместить элемент в хвост очереди */\nfunc (s *linkedListDeque) pushLast(value any) {\n    s.data.PushBack(value)\n}\n\n/* Извлечь элемент из головы очереди */\nfunc (s *linkedListDeque) popFirst() any {\n    if s.isEmpty() {\n        return nil\n    }\n    e := s.data.Front()\n    s.data.Remove(e)\n    return e.Value\n}\n\n/* Извлечь элемент из хвоста очереди */\nfunc (s *linkedListDeque) popLast() any {\n    if s.isEmpty() {\n        return nil\n    }\n    e := s.data.Back()\n    s.data.Remove(e)\n    return e.Value\n}\n\n/* Доступ к элементу в начале очереди */\nfunc (s *linkedListDeque) peekFirst() any {\n    if s.isEmpty() {\n        return nil\n    }\n    e := s.data.Front()\n    return e.Value\n}\n\n/* Доступ к элементу в конце очереди */\nfunc (s *linkedListDeque) peekLast() any {\n    if s.isEmpty() {\n        return nil\n    }\n    e := s.data.Back()\n    return e.Value\n}\n\n/* Получение длины очереди */\nfunc (s *linkedListDeque) size() int {\n    return s.data.Len()\n}\n\n/* Проверка, пуста ли очередь */\nfunc (s *linkedListDeque) isEmpty() bool {\n    return s.data.Len() == 0\n}\n\n/* Получить List для вывода */\nfunc (s *linkedListDeque) toList() *list.List {\n    return s.data\n}\n</code></pre> linkedlist_deque.swift<pre><code>/* Узел двусвязного списка */\nclass ListNode {\n    var val: Int // Значение узла\n    var next: ListNode? // Ссылка на узел-преемник\n    weak var prev: ListNode? // Ссылка на узел-предшественник\n\n    init(val: Int) {\n        self.val = val\n    }\n}\n\n/* Двусторонняя очередь на основе двусвязного списка */\nclass LinkedListDeque {\n    private var front: ListNode? // Головной узел front\n    private var rear: ListNode? // Хвостовой узел rear\n    private var _size: Int // Длина двусторонней очереди\n\n    init() {\n        _size = 0\n    }\n\n    /* Получение длины двусторонней очереди */\n    func size() -&gt; Int {\n        _size\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    func isEmpty() -&gt; Bool {\n        size() == 0\n    }\n\n    /* Операция добавления в очередь */\n    private func push(num: Int, isFront: Bool) {\n        let node = ListNode(val: num)\n        // Если связный список пуст, сделать так, чтобы и front, и rear указывали на node\n        if isEmpty() {\n            front = node\n            rear = node\n        }\n        // Операция добавления в голову очереди\n        else if isFront {\n            // Добавить node в голову списка\n            front?.prev = node\n            node.next = front\n            front = node // Обновить головной узел\n        }\n        // Операция добавления в хвост очереди\n        else {\n            // Добавить node в хвост списка\n            rear?.next = node\n            node.prev = rear\n            rear = node // Обновить хвостовой узел\n        }\n        _size += 1 // Обновить длину очереди\n    }\n\n    /* Добавление в голову очереди */\n    func pushFirst(num: Int) {\n        push(num: num, isFront: true)\n    }\n\n    /* Добавление в хвост очереди */\n    func pushLast(num: Int) {\n        push(num: num, isFront: false)\n    }\n\n    /* Операция извлечения из очереди */\n    private func pop(isFront: Bool) -&gt; Int {\n        if isEmpty() {\n            fatalError(\"двусторонняя очередь пуста\")\n        }\n        let val: Int\n        // Операция извлечения из головы очереди\n        if isFront {\n            val = front!.val // Временно сохранить значение головного узла\n            // Удалить головной узел\n            let fNext = front?.next\n            if fNext != nil {\n                fNext?.prev = nil\n                front?.next = nil\n            }\n            front = fNext // Обновить головной узел\n        }\n        // Операция извлечения из хвоста очереди\n        else {\n            val = rear!.val // Временно сохранить значение хвостового узла\n            // Удалить хвостовой узел\n            let rPrev = rear?.prev\n            if rPrev != nil {\n                rPrev?.next = nil\n                rear?.prev = nil\n            }\n            rear = rPrev // Обновить хвостовой узел\n        }\n        _size -= 1 // Обновить длину очереди\n        return val\n    }\n\n    /* Извлечение из головы очереди */\n    func popFirst() -&gt; Int {\n        pop(isFront: true)\n    }\n\n    /* Извлечение из хвоста очереди */\n    func popLast() -&gt; Int {\n        pop(isFront: false)\n    }\n\n    /* Доступ к элементу в начале очереди */\n    func peekFirst() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"двусторонняя очередь пуста\")\n        }\n        return front!.val\n    }\n\n    /* Доступ к элементу в конце очереди */\n    func peekLast() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"двусторонняя очередь пуста\")\n        }\n        return rear!.val\n    }\n\n    /* Вернуть массив для вывода */\n    func toArray() -&gt; [Int] {\n        var node = front\n        var res = Array(repeating: 0, count: size())\n        for i in res.indices {\n            res[i] = node!.val\n            node = node?.next\n        }\n        return res\n    }\n}\n</code></pre> linkedlist_deque.js<pre><code>/* Узел двусвязного списка */\nclass ListNode {\n    prev; // Ссылка на узел-предшественник (указатель)\n    next; // Ссылка на узел-преемник (указатель)\n    val; // Значение узла\n\n    constructor(val) {\n        this.val = val;\n        this.next = null;\n        this.prev = null;\n    }\n}\n\n/* Двусторонняя очередь на основе двусвязного списка */\nclass LinkedListDeque {\n    #front; // Головной узел front\n    #rear; // Хвостовой узел rear\n    #queSize; // Длина двусторонней очереди\n\n    constructor() {\n        this.#front = null;\n        this.#rear = null;\n        this.#queSize = 0;\n    }\n\n    /* Операция добавления в хвост очереди */\n    pushLast(val) {\n        const node = new ListNode(val);\n        // Если связный список пуст, сделать так, чтобы и front, и rear указывали на node\n        if (this.#queSize === 0) {\n            this.#front = node;\n            this.#rear = node;\n        } else {\n            // Добавить node в хвост списка\n            this.#rear.next = node;\n            node.prev = this.#rear;\n            this.#rear = node; // Обновить хвостовой узел\n        }\n        this.#queSize++;\n    }\n\n    /* Операция добавления в голову очереди */\n    pushFirst(val) {\n        const node = new ListNode(val);\n        // Если связный список пуст, сделать так, чтобы и front, и rear указывали на node\n        if (this.#queSize === 0) {\n            this.#front = node;\n            this.#rear = node;\n        } else {\n            // Добавить node в голову списка\n            this.#front.prev = node;\n            node.next = this.#front;\n            this.#front = node; // Обновить головной узел\n        }\n        this.#queSize++;\n    }\n\n    /* Операция извлечения из хвоста очереди */\n    popLast() {\n        if (this.#queSize === 0) {\n            return null;\n        }\n        const value = this.#rear.val; // Сохранить значение хвостового узла\n        // Удалить хвостовой узел\n        let temp = this.#rear.prev;\n        if (temp !== null) {\n            temp.next = null;\n            this.#rear.prev = null;\n        }\n        this.#rear = temp; // Обновить хвостовой узел\n        this.#queSize--;\n        return value;\n    }\n\n    /* Операция извлечения из головы очереди */\n    popFirst() {\n        if (this.#queSize === 0) {\n            return null;\n        }\n        const value = this.#front.val; // Сохранить значение хвостового узла\n        // Удалить головной узел\n        let temp = this.#front.next;\n        if (temp !== null) {\n            temp.prev = null;\n            this.#front.next = null;\n        }\n        this.#front = temp; // Обновить головной узел\n        this.#queSize--;\n        return value;\n    }\n\n    /* Доступ к элементу в конце очереди */\n    peekLast() {\n        return this.#queSize === 0 ? null : this.#rear.val;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    peekFirst() {\n        return this.#queSize === 0 ? null : this.#front.val;\n    }\n\n    /* Получение длины двусторонней очереди */\n    size() {\n        return this.#queSize;\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    isEmpty() {\n        return this.#queSize === 0;\n    }\n\n    /* Вывести двустороннюю очередь */\n    print() {\n        const arr = [];\n        let temp = this.#front;\n        while (temp !== null) {\n            arr.push(temp.val);\n            temp = temp.next;\n        }\n        console.log('[' + arr.join(', ') + ']');\n    }\n}\n</code></pre> linkedlist_deque.ts<pre><code>/* Узел двусвязного списка */\nclass ListNode {\n    prev: ListNode; // Ссылка на узел-предшественник (указатель)\n    next: ListNode; // Ссылка на узел-преемник (указатель)\n    val: number; // Значение узла\n\n    constructor(val: number) {\n        this.val = val;\n        this.next = null;\n        this.prev = null;\n    }\n}\n\n/* Двусторонняя очередь на основе двусвязного списка */\nclass LinkedListDeque {\n    private front: ListNode; // Головной узел front\n    private rear: ListNode; // Хвостовой узел rear\n    private queSize: number; // Длина двусторонней очереди\n\n    constructor() {\n        this.front = null;\n        this.rear = null;\n        this.queSize = 0;\n    }\n\n    /* Операция добавления в хвост очереди */\n    pushLast(val: number): void {\n        const node: ListNode = new ListNode(val);\n        // Если связный список пуст, сделать так, чтобы и front, и rear указывали на node\n        if (this.queSize === 0) {\n            this.front = node;\n            this.rear = node;\n        } else {\n            // Добавить node в хвост списка\n            this.rear.next = node;\n            node.prev = this.rear;\n            this.rear = node; // Обновить хвостовой узел\n        }\n        this.queSize++;\n    }\n\n    /* Операция добавления в голову очереди */\n    pushFirst(val: number): void {\n        const node: ListNode = new ListNode(val);\n        // Если связный список пуст, сделать так, чтобы и front, и rear указывали на node\n        if (this.queSize === 0) {\n            this.front = node;\n            this.rear = node;\n        } else {\n            // Добавить node в голову списка\n            this.front.prev = node;\n            node.next = this.front;\n            this.front = node; // Обновить головной узел\n        }\n        this.queSize++;\n    }\n\n    /* Операция извлечения из хвоста очереди */\n    popLast(): number {\n        if (this.queSize === 0) {\n            return null;\n        }\n        const value: number = this.rear.val; // Сохранить значение хвостового узла\n        // Удалить хвостовой узел\n        let temp: ListNode = this.rear.prev;\n        if (temp !== null) {\n            temp.next = null;\n            this.rear.prev = null;\n        }\n        this.rear = temp; // Обновить хвостовой узел\n        this.queSize--;\n        return value;\n    }\n\n    /* Операция извлечения из головы очереди */\n    popFirst(): number {\n        if (this.queSize === 0) {\n            return null;\n        }\n        const value: number = this.front.val; // Сохранить значение хвостового узла\n        // Удалить головной узел\n        let temp: ListNode = this.front.next;\n        if (temp !== null) {\n            temp.prev = null;\n            this.front.next = null;\n        }\n        this.front = temp; // Обновить головной узел\n        this.queSize--;\n        return value;\n    }\n\n    /* Доступ к элементу в конце очереди */\n    peekLast(): number {\n        return this.queSize === 0 ? null : this.rear.val;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    peekFirst(): number {\n        return this.queSize === 0 ? null : this.front.val;\n    }\n\n    /* Получение длины двусторонней очереди */\n    size(): number {\n        return this.queSize;\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    isEmpty(): boolean {\n        return this.queSize === 0;\n    }\n\n    /* Вывести двустороннюю очередь */\n    print(): void {\n        const arr: number[] = [];\n        let temp: ListNode = this.front;\n        while (temp !== null) {\n            arr.push(temp.val);\n            temp = temp.next;\n        }\n        console.log('[' + arr.join(', ') + ']');\n    }\n}\n</code></pre> linkedlist_deque.dart<pre><code>/* Узел двусвязного списка */\nclass ListNode {\n  int val; // Значение узла\n  ListNode? next; // Ссылка на узел-преемник\n  ListNode? prev; // Ссылка на узел-предшественник\n\n  ListNode(this.val, {this.next, this.prev});\n}\n\n/* Двусторонняя очередь на основе двусвязного списка */\nclass LinkedListDeque {\n  late ListNode? _front; // Головной узел _front\n  late ListNode? _rear; // Хвостовой узел _rear\n  int _queSize = 0; // Длина двусторонней очереди\n\n  LinkedListDeque() {\n    this._front = null;\n    this._rear = null;\n  }\n\n  /* Получить длину двусторонней очереди */\n  int size() {\n    return this._queSize;\n  }\n\n  /* Проверка, пуста ли двусторонняя очередь */\n  bool isEmpty() {\n    return size() == 0;\n  }\n\n  /* Операция добавления в очередь */\n  void push(int _num, bool isFront) {\n    final ListNode node = ListNode(_num);\n    if (isEmpty()) {\n      // Если связный список пуст, пусть _front и _rear оба указывают на node\n      _front = _rear = node;\n    } else if (isFront) {\n      // Операция добавления в голову очереди\n      // Добавить node в начало связного списка\n      _front!.prev = node;\n      node.next = _front;\n      _front = node; // Обновить головной узел\n    } else {\n      // Операция добавления в хвост очереди\n      // Добавить node в конец связного списка\n      _rear!.next = node;\n      node.prev = _rear;\n      _rear = node; // Обновить хвостовой узел\n    }\n    _queSize++; // Обновить длину очереди\n  }\n\n  /* Добавление в голову очереди */\n  void pushFirst(int _num) {\n    push(_num, true);\n  }\n\n  /* Добавление в хвост очереди */\n  void pushLast(int _num) {\n    push(_num, false);\n  }\n\n  /* Операция извлечения из очереди */\n  int? pop(bool isFront) {\n    // Если очередь пуста, сразу вернуть null\n    if (isEmpty()) {\n      return null;\n    }\n    final int val;\n    if (isFront) {\n      // Операция извлечения из головы очереди\n      val = _front!.val; // Временно сохранить значение головного узла\n      // Удалить головной узел\n      ListNode? fNext = _front!.next;\n      if (fNext != null) {\n        fNext.prev = null;\n        _front!.next = null;\n      }\n      _front = fNext; // Обновить головной узел\n    } else {\n      // Операция извлечения из хвоста очереди\n      val = _rear!.val; // Временно сохранить значение хвостового узла\n      // Удалить хвостовой узел\n      ListNode? rPrev = _rear!.prev;\n      if (rPrev != null) {\n        rPrev.next = null;\n        _rear!.prev = null;\n      }\n      _rear = rPrev; // Обновить хвостовой узел\n    }\n    _queSize--; // Обновить длину очереди\n    return val;\n  }\n\n  /* Извлечение из головы очереди */\n  int? popFirst() {\n    return pop(true);\n  }\n\n  /* Извлечение из хвоста очереди */\n  int? popLast() {\n    return pop(false);\n  }\n\n  /* Доступ к элементу в начале очереди */\n  int? peekFirst() {\n    return _front?.val;\n  }\n\n  /* Доступ к элементу в конце очереди */\n  int? peekLast() {\n    return _rear?.val;\n  }\n\n  /* Вернуть массив для вывода */\n  List&lt;int&gt; toArray() {\n    ListNode? node = _front;\n    final List&lt;int&gt; res = [];\n    for (int i = 0; i &lt; _queSize; i++) {\n      res.add(node!.val);\n      node = node.next;\n    }\n    return res;\n  }\n}\n</code></pre> linkedlist_deque.rs<pre><code>/* Узел двусвязного списка */\npub struct ListNode&lt;T&gt; {\n    pub val: T,                                 // Значение узла\n    pub next: Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;, // Указатель на узел-преемник\n    pub prev: Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;, // Указатель на узел-предшественник\n}\n\nimpl&lt;T&gt; ListNode&lt;T&gt; {\n    pub fn new(val: T) -&gt; Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt; {\n        Rc::new(RefCell::new(ListNode {\n            val,\n            next: None,\n            prev: None,\n        }))\n    }\n}\n\n/* Двусторонняя очередь на основе двусвязного списка */\n#[allow(dead_code)]\npub struct LinkedListDeque&lt;T&gt; {\n    front: Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;, // Головной узел front\n    rear: Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;,  // Хвостовой узел rear\n    que_size: usize,                         // Длина двусторонней очереди\n}\n\nimpl&lt;T: Copy&gt; LinkedListDeque&lt;T&gt; {\n    pub fn new() -&gt; Self {\n        Self {\n            front: None,\n            rear: None,\n            que_size: 0,\n        }\n    }\n\n    /* Получение длины двусторонней очереди */\n    pub fn size(&amp;self) -&gt; usize {\n        return self.que_size;\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    pub fn is_empty(&amp;self) -&gt; bool {\n        return self.que_size == 0;\n    }\n\n    /* Операция добавления в очередь */\n    fn push(&amp;mut self, num: T, is_front: bool) {\n        let node = ListNode::new(num);\n        // Операция добавления в голову очереди\n        if is_front {\n            match self.front.take() {\n                // Если связный список пуст, сделать так, чтобы и front, и rear указывали на node\n                None =&gt; {\n                    self.rear = Some(node.clone());\n                    self.front = Some(node);\n                }\n                // Добавить node в голову списка\n                Some(old_front) =&gt; {\n                    old_front.borrow_mut().prev = Some(node.clone());\n                    node.borrow_mut().next = Some(old_front);\n                    self.front = Some(node); // Обновить головной узел\n                }\n            }\n        }\n        // Операция добавления в хвост очереди\n        else {\n            match self.rear.take() {\n                // Если связный список пуст, сделать так, чтобы и front, и rear указывали на node\n                None =&gt; {\n                    self.front = Some(node.clone());\n                    self.rear = Some(node);\n                }\n                // Добавить node в хвост списка\n                Some(old_rear) =&gt; {\n                    old_rear.borrow_mut().next = Some(node.clone());\n                    node.borrow_mut().prev = Some(old_rear);\n                    self.rear = Some(node); // Обновить хвостовой узел\n                }\n            }\n        }\n        self.que_size += 1; // Обновить длину очереди\n    }\n\n    /* Добавление в голову очереди */\n    pub fn push_first(&amp;mut self, num: T) {\n        self.push(num, true);\n    }\n\n    /* Добавление в хвост очереди */\n    pub fn push_last(&amp;mut self, num: T) {\n        self.push(num, false);\n    }\n\n    /* Операция извлечения из очереди */\n    fn pop(&amp;mut self, is_front: bool) -&gt; Option&lt;T&gt; {\n        // Если очередь пуста, сразу вернуть None\n        if self.is_empty() {\n            return None;\n        };\n        // Операция извлечения из головы очереди\n        if is_front {\n            self.front.take().map(|old_front| {\n                match old_front.borrow_mut().next.take() {\n                    Some(new_front) =&gt; {\n                        new_front.borrow_mut().prev.take();\n                        self.front = Some(new_front); // Обновить головной узел\n                    }\n                    None =&gt; {\n                        self.rear.take();\n                    }\n                }\n                self.que_size -= 1; // Обновить длину очереди\n                old_front.borrow().val\n            })\n        }\n        // Операция извлечения из хвоста очереди\n        else {\n            self.rear.take().map(|old_rear| {\n                match old_rear.borrow_mut().prev.take() {\n                    Some(new_rear) =&gt; {\n                        new_rear.borrow_mut().next.take();\n                        self.rear = Some(new_rear); // Обновить хвостовой узел\n                    }\n                    None =&gt; {\n                        self.front.take();\n                    }\n                }\n                self.que_size -= 1; // Обновить длину очереди\n                old_rear.borrow().val\n            })\n        }\n    }\n\n    /* Извлечение из головы очереди */\n    pub fn pop_first(&amp;mut self) -&gt; Option&lt;T&gt; {\n        return self.pop(true);\n    }\n\n    /* Извлечение из хвоста очереди */\n    pub fn pop_last(&amp;mut self) -&gt; Option&lt;T&gt; {\n        return self.pop(false);\n    }\n\n    /* Доступ к элементу в начале очереди */\n    pub fn peek_first(&amp;self) -&gt; Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt; {\n        self.front.as_ref()\n    }\n\n    /* Доступ к элементу в конце очереди */\n    pub fn peek_last(&amp;self) -&gt; Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt; {\n        self.rear.as_ref()\n    }\n\n    /* Вернуть массив для вывода */\n    pub fn to_array(&amp;self, head: Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;) -&gt; Vec&lt;T&gt; {\n        let mut res: Vec&lt;T&gt; = Vec::new();\n        fn recur&lt;T: Copy&gt;(cur: Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;, res: &amp;mut Vec&lt;T&gt;) {\n            if let Some(cur) = cur {\n                res.push(cur.borrow().val);\n                recur(cur.borrow().next.as_ref(), res);\n            }\n        }\n\n        recur(head, &amp;mut res);\n        res\n    }\n}\n</code></pre> linkedlist_deque.c<pre><code>/* Узел двусвязного списка */\ntypedef struct DoublyListNode {\n    int val;                     // Значение узла\n    struct DoublyListNode *next; // Узел-преемник\n    struct DoublyListNode *prev; // Узел-предшественник\n} DoublyListNode;\n\n/* Конструктор */\nDoublyListNode *newDoublyListNode(int num) {\n    DoublyListNode *new = (DoublyListNode *)malloc(sizeof(DoublyListNode));\n    new-&gt;val = num;\n    new-&gt;next = NULL;\n    new-&gt;prev = NULL;\n    return new;\n}\n\n/* Деструктор */\nvoid delDoublyListNode(DoublyListNode *node) {\n    free(node);\n}\n\n/* Двусторонняя очередь на основе двусвязного списка */\ntypedef struct {\n    DoublyListNode *front, *rear; // Головной узел front, хвостовой узел rear\n    int queSize;                  // Длина двусторонней очереди\n} LinkedListDeque;\n\n/* Конструктор */\nLinkedListDeque *newLinkedListDeque() {\n    LinkedListDeque *deque = (LinkedListDeque *)malloc(sizeof(LinkedListDeque));\n    deque-&gt;front = NULL;\n    deque-&gt;rear = NULL;\n    deque-&gt;queSize = 0;\n    return deque;\n}\n\n/* Деструктор */\nvoid delLinkedListdeque(LinkedListDeque *deque) {\n    // Освободить все узлы\n    for (int i = 0; i &lt; deque-&gt;queSize &amp;&amp; deque-&gt;front != NULL; i++) {\n        DoublyListNode *tmp = deque-&gt;front;\n        deque-&gt;front = deque-&gt;front-&gt;next;\n        free(tmp);\n    }\n    // Освободить структуру deque\n    free(deque);\n}\n\n/* Получение длины очереди */\nint size(LinkedListDeque *deque) {\n    return deque-&gt;queSize;\n}\n\n/* Проверка, пуста ли очередь */\nbool empty(LinkedListDeque *deque) {\n    return (size(deque) == 0);\n}\n\n/* Поместить в очередь */\nvoid push(LinkedListDeque *deque, int num, bool isFront) {\n    DoublyListNode *node = newDoublyListNode(num);\n    // Если связный список пуст, пусть front и rear оба указывают на node\n    if (empty(deque)) {\n        deque-&gt;front = deque-&gt;rear = node;\n    }\n    // Операция добавления в голову очереди\n    else if (isFront) {\n        // Добавить node в голову списка\n        deque-&gt;front-&gt;prev = node;\n        node-&gt;next = deque-&gt;front;\n        deque-&gt;front = node; // Обновить головной узел\n    }\n    // Операция добавления в хвост очереди\n    else {\n        // Добавить node в хвост списка\n        deque-&gt;rear-&gt;next = node;\n        node-&gt;prev = deque-&gt;rear;\n        deque-&gt;rear = node;\n    }\n    deque-&gt;queSize++; // Обновить длину очереди\n}\n\n/* Добавление в голову очереди */\nvoid pushFirst(LinkedListDeque *deque, int num) {\n    push(deque, num, true);\n}\n\n/* Добавление в хвост очереди */\nvoid pushLast(LinkedListDeque *deque, int num) {\n    push(deque, num, false);\n}\n\n/* Доступ к элементу в начале очереди */\nint peekFirst(LinkedListDeque *deque) {\n    assert(size(deque) &amp;&amp; deque-&gt;front);\n    return deque-&gt;front-&gt;val;\n}\n\n/* Доступ к элементу в конце очереди */\nint peekLast(LinkedListDeque *deque) {\n    assert(size(deque) &amp;&amp; deque-&gt;rear);\n    return deque-&gt;rear-&gt;val;\n}\n\n/* Извлечь из очереди */\nint pop(LinkedListDeque *deque, bool isFront) {\n    if (empty(deque))\n        return -1;\n    int val;\n    // Операция извлечения из головы очереди\n    if (isFront) {\n        val = peekFirst(deque); // Временно сохранить значение головного узла\n        DoublyListNode *fNext = deque-&gt;front-&gt;next;\n        if (fNext) {\n            fNext-&gt;prev = NULL;\n            deque-&gt;front-&gt;next = NULL;\n        }\n        delDoublyListNode(deque-&gt;front);\n        deque-&gt;front = fNext; // Обновить головной узел\n    }\n    // Операция извлечения из хвоста очереди\n    else {\n        val = peekLast(deque); // Временно сохранить значение хвостового узла\n        DoublyListNode *rPrev = deque-&gt;rear-&gt;prev;\n        if (rPrev) {\n            rPrev-&gt;next = NULL;\n            deque-&gt;rear-&gt;prev = NULL;\n        }\n        delDoublyListNode(deque-&gt;rear);\n        deque-&gt;rear = rPrev; // Обновить хвостовой узел\n    }\n    deque-&gt;queSize--; // Обновить длину очереди\n    return val;\n}\n\n/* Извлечение из головы очереди */\nint popFirst(LinkedListDeque *deque) {\n    return pop(deque, true);\n}\n\n/* Извлечение из хвоста очереди */\nint popLast(LinkedListDeque *deque) {\n    return pop(deque, false);\n}\n\n/* Вывести очередь */\nvoid printLinkedListDeque(LinkedListDeque *deque) {\n    int *arr = malloc(sizeof(int) * deque-&gt;queSize);\n    // Скопировать данные связного списка в массив\n    int i;\n    DoublyListNode *node;\n    for (i = 0, node = deque-&gt;front; i &lt; deque-&gt;queSize; i++) {\n        arr[i] = node-&gt;val;\n        node = node-&gt;next;\n    }\n    printArray(arr, deque-&gt;queSize);\n    free(arr);\n}\n</code></pre> linkedlist_deque.kt<pre><code>/* Узел двусвязного списка */\nclass ListNode(var _val: Int) {\n    // Значение узла\n    var next: ListNode? = null // Ссылка на узел-преемник\n    var prev: ListNode? = null // Ссылка на узел-предшественник\n}\n\n/* Двусторонняя очередь на основе двусвязного списка */\nclass LinkedListDeque {\n    private var front: ListNode? = null // Головной узел front\n    private var rear: ListNode? = null // Хвостовой узел rear\n    private var queSize: Int = 0 // Длина двусторонней очереди\n\n    /* Получение длины двусторонней очереди */\n    fun size(): Int {\n        return queSize\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    fun isEmpty(): Boolean {\n        return size() == 0\n    }\n\n    /* Операция добавления в очередь */\n    fun push(num: Int, isFront: Boolean) {\n        val node = ListNode(num)\n        // Если связный список пуст, сделать так, чтобы и front, и rear указывали на node\n        if (isEmpty()) {\n            rear = node\n            front = rear\n            // Операция добавления в голову очереди\n        } else if (isFront) {\n            // Добавить node в голову списка\n            front?.prev = node\n            node.next = front\n            front = node // Обновить головной узел\n            // Операция добавления в хвост очереди\n        } else {\n            // Добавить node в хвост списка\n            rear?.next = node\n            node.prev = rear\n            rear = node // Обновить хвостовой узел\n        }\n        queSize++ // Обновить длину очереди\n    }\n\n    /* Добавление в голову очереди */\n    fun pushFirst(num: Int) {\n        push(num, true)\n    }\n\n    /* Добавление в хвост очереди */\n    fun pushLast(num: Int) {\n        push(num, false)\n    }\n\n    /* Операция извлечения из очереди */\n    fun pop(isFront: Boolean): Int {\n        if (isEmpty()) \n            throw IndexOutOfBoundsException()\n        val _val: Int\n        // Операция извлечения из головы очереди\n        if (isFront) {\n            _val = front!!._val // Временно сохранить значение головного узла\n            // Удалить головной узел\n            val fNext = front!!.next\n            if (fNext != null) {\n                fNext.prev = null\n                front!!.next = null\n            }\n            front = fNext // Обновить головной узел\n            // Операция извлечения из хвоста очереди\n        } else {\n            _val = rear!!._val // Временно сохранить значение хвостового узла\n            // Удалить хвостовой узел\n            val rPrev = rear!!.prev\n            if (rPrev != null) {\n                rPrev.next = null\n                rear!!.prev = null\n            }\n            rear = rPrev // Обновить хвостовой узел\n        }\n        queSize-- // Обновить длину очереди\n        return _val\n    }\n\n    /* Извлечение из головы очереди */\n    fun popFirst(): Int {\n        return pop(true)\n    }\n\n    /* Извлечение из хвоста очереди */\n    fun popLast(): Int {\n        return pop(false)\n    }\n\n    /* Доступ к элементу в начале очереди */\n    fun peekFirst(): Int {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        return front!!._val\n    }\n\n    /* Доступ к элементу в конце очереди */\n    fun peekLast(): Int {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        return rear!!._val\n    }\n\n    /* Вернуть массив для вывода */\n    fun toArray(): IntArray {\n        var node = front\n        val res = IntArray(size())\n        for (i in res.indices) {\n            res[i] = node!!._val\n            node = node.next\n        }\n        return res\n    }\n}\n</code></pre> linkedlist_deque.rb<pre><code>=begin\nFile: linkedlist_deque.rb\nCreated Time: 2024-04-06\nAuthor: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)\n=end\n\n# ## Узел двусвязного списка\nclass ListNode\n  attr_accessor :val\n  attr_accessor :next # Ссылка на узел-преемник\n  attr_accessor :prev # Ссылка на узел-предшественник\n\n  ### Конструктор ###\n  def initialize(val)\n    @val = val\n  end\nend\n\n### Двусторонняя очередь на основе двусвязного списка ###\nclass LinkedListDeque\n  ### Получение длины двусторонней очереди ###\n  attr_reader :size\n\n  ### Конструктор ###\n  def initialize\n    @front = nil  # Головной узел front\n    @rear = nil   # Хвостовой узел rear\n    @size = 0     # Длина двусторонней очереди\n  end\n\n  ### Проверка, пуста ли двусторонняя очередь ###\n  def is_empty?\n    size.zero?\n  end\n\n  ### Операция добавления в очередь ###\n  def push(num, is_front)\n    node = ListNode.new(num)\n    # Если связный список пуст, пусть front и rear оба указывают на node\n    if is_empty?\n      @front = @rear = node\n    # Операция добавления в голову очереди\n    elsif is_front\n      # Добавить node в голову списка\n      @front.prev = node\n      node.next = @front\n      @front = node # Обновить головной узел\n    # Операция добавления в хвост очереди\n    else\n      # Добавить node в хвост списка\n      @rear.next = node\n      node.prev = @rear\n      @rear = node # Обновить хвостовой узел\n    end\n    @size += 1 # Обновить длину очереди\n  end\n\n  ### Добавление в голову очереди ###\n  def push_first(num)\n    push(num, true)\n  end\n\n  ### Добавление в хвост очереди ###\n  def push_last(num)\n    push(num, false)\n  end\n\n  ### Операция извлечения из очереди ###\n  def pop(is_front)\n    raise IndexError, 'двусторонняя очередь пуста' if is_empty?\n\n    # Операция извлечения из головы очереди\n    if is_front\n      val = @front.val # Временно сохранить значение головного узла\n      # Удалить головной узел\n      fnext = @front.next\n      unless fnext.nil?\n        fnext.prev = nil\n        @front.next = nil\n      end\n      @front = fnext # Обновить головной узел\n    # Операция извлечения из хвоста очереди\n    else\n      val = @rear.val # Временно сохранить значение хвостового узла\n      # Удалить хвостовой узел\n      rprev = @rear.prev\n      unless rprev.nil?\n        rprev.next = nil\n        @rear.prev = nil\n      end\n      @rear = rprev # Обновить хвостовой узел\n    end\n    @size -= 1 # Обновить длину очереди\n\n    val\n  end\n\n  ### Извлечение из головы очереди ###\n  def pop_first\n    pop(true)\n  end\n\n  ### Извлечение из головы очереди ###\n  def pop_last\n    pop(false)\n  end\n\n  ### Доступ к элементу в начале очереди ###\n  def peek_first\n    raise IndexError, 'двусторонняя очередь пуста' if is_empty?\n\n    @front.val\n  end\n\n  ### Доступ к элементу в хвосте очереди ###\n  def peek_last\n    raise IndexError, 'двусторонняя очередь пуста' if is_empty?\n\n    @rear.val\n  end\n\n  ### Вернуть массив для вывода ###\n  def to_array\n    node = @front\n    res = Array.new(size, 0)\n    for i in 0...size\n      res[i] = node.val\n      node = node.next\n    end\n    res\n  end\nend\n</code></pre>","path":["Глава 5. Стек и очередь","5.3 &nbsp; Двусторонняя очередь"],"tags":[]},{"location":"chapter_stack_and_queue/deque/#2","level":3,"title":"2.   Реализация на основе массива","text":"<p>Как показано на рисунках ниже, аналогично реализации обычной очереди на массиве мы также можем использовать кольцевой массив для реализации двусторонней очереди.</p> ArrayDequepush_last()push_first()pop_last()pop_first() <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 5-9   Операции enqueue и dequeue для двусторонней очереди на массиве </p> <p>На основе реализации обычной очереди нужно лишь добавить методы добавления в голову очереди и удаления из хвоста:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array_deque.py<pre><code>class ArrayDeque:\n    \"\"\"Двусторонняя очередь на основе кольцевого массива\"\"\"\n\n    def __init__(self, capacity: int):\n        \"\"\"Конструктор\"\"\"\n        self._nums: list[int] = [0] * capacity\n        self._front: int = 0\n        self._size: int = 0\n\n    def capacity(self) -&gt; int:\n        \"\"\"Получить вместимость двусторонней очереди\"\"\"\n        return len(self._nums)\n\n    def size(self) -&gt; int:\n        \"\"\"Получение длины двусторонней очереди\"\"\"\n        return self._size\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"Проверка, пуста ли двусторонняя очередь\"\"\"\n        return self._size == 0\n\n    def index(self, i: int) -&gt; int:\n        \"\"\"Вычислить индекс в кольцевом массиве\"\"\"\n        # С помощью операции взятия по модулю соединить начало и конец массива\n        # Когда i выходит за конец массива, он возвращается в начало\n        # Когда i выходит за начало массива, он возвращается в конец\n        return (i + self.capacity()) % self.capacity()\n\n    def push_first(self, num: int):\n        \"\"\"Добавление в голову очереди\"\"\"\n        if self._size == self.capacity():\n            print(\"Двусторонняя очередь заполнена\")\n            return\n        # Указатель головы сдвигается на одну позицию влево\n        # С помощью операции взятия по модулю front после выхода за начало массива возвращается в хвост\n        self._front = self.index(self._front - 1)\n        # Добавить num в голову очереди\n        self._nums[self._front] = num\n        self._size += 1\n\n    def push_last(self, num: int):\n        \"\"\"Добавление в хвост очереди\"\"\"\n        if self._size == self.capacity():\n            print(\"Двусторонняя очередь заполнена\")\n            return\n        # Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        rear = self.index(self._front + self._size)\n        # Добавить num в хвост очереди\n        self._nums[rear] = num\n        self._size += 1\n\n    def pop_first(self) -&gt; int:\n        \"\"\"Извлечение из головы очереди\"\"\"\n        num = self.peek_first()\n        # Указатель головы сдвигается на одну позицию назад\n        self._front = self.index(self._front + 1)\n        self._size -= 1\n        return num\n\n    def pop_last(self) -&gt; int:\n        \"\"\"Извлечение из хвоста очереди\"\"\"\n        num = self.peek_last()\n        self._size -= 1\n        return num\n\n    def peek_first(self) -&gt; int:\n        \"\"\"Доступ к элементу в начале очереди\"\"\"\n        if self.is_empty():\n            raise IndexError(\"двусторонняя очередь пуста\")\n        return self._nums[self._front]\n\n    def peek_last(self) -&gt; int:\n        \"\"\"Доступ к элементу в конце очереди\"\"\"\n        if self.is_empty():\n            raise IndexError(\"двусторонняя очередь пуста\")\n        # Вычислить индекс хвостового элемента\n        last = self.index(self._front + self._size - 1)\n        return self._nums[last]\n\n    def to_array(self) -&gt; list[int]:\n        \"\"\"Вернуть массив для вывода\"\"\"\n        # Преобразовывать только элементы списка в пределах фактической длины\n        res = []\n        for i in range(self._size):\n            res.append(self._nums[self.index(self._front + i)])\n        return res\n</code></pre> array_deque.cpp<pre><code>/* Двусторонняя очередь на основе кольцевого массива */\nclass ArrayDeque {\n  private:\n    vector&lt;int&gt; nums; // Массив для хранения элементов двусторонней очереди\n    int front;        // Указатель head, указывающий на первый элемент очереди\n    int queSize;      // Длина двусторонней очереди\n\n  public:\n    /* Конструктор */\n    ArrayDeque(int capacity) {\n        nums.resize(capacity);\n        front = queSize = 0;\n    }\n\n    /* Получить вместимость двусторонней очереди */\n    int capacity() {\n        return nums.size();\n    }\n\n    /* Получение длины двусторонней очереди */\n    int size() {\n        return queSize;\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    bool isEmpty() {\n        return queSize == 0;\n    }\n\n    /* Вычислить индекс в кольцевом массиве */\n    int index(int i) {\n        // С помощью операции взятия по модулю соединить начало и конец массива\n        // Когда i выходит за конец массива, он возвращается в начало\n        // Когда i выходит за начало массива, он возвращается в конец\n        return (i + capacity()) % capacity();\n    }\n\n    /* Добавление в голову очереди */\n    void pushFirst(int num) {\n        if (queSize == capacity()) {\n            cout &lt;&lt; \"Двусторонняя очередь заполнена\" &lt;&lt; endl;\n            return;\n        }\n        // Указатель головы сдвигается на одну позицию влево\n        // С помощью операции взятия по модулю front после выхода за начало массива возвращается в хвост\n        front = index(front - 1);\n        // Добавить num в голову очереди\n        nums[front] = num;\n        queSize++;\n    }\n\n    /* Добавление в хвост очереди */\n    void pushLast(int num) {\n        if (queSize == capacity()) {\n            cout &lt;&lt; \"Двусторонняя очередь заполнена\" &lt;&lt; endl;\n            return;\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        int rear = index(front + queSize);\n        // Добавить num в хвост очереди\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* Извлечение из головы очереди */\n    int popFirst() {\n        int num = peekFirst();\n        // Указатель головы сдвигается на одну позицию назад\n        front = index(front + 1);\n        queSize--;\n        return num;\n    }\n\n    /* Извлечение из хвоста очереди */\n    int popLast() {\n        int num = peekLast();\n        queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    int peekFirst() {\n        if (isEmpty())\n            throw out_of_range(\"двусторонняя очередь пуста\");\n        return nums[front];\n    }\n\n    /* Доступ к элементу в конце очереди */\n    int peekLast() {\n        if (isEmpty())\n            throw out_of_range(\"двусторонняя очередь пуста\");\n        // Вычислить индекс хвостового элемента\n        int last = index(front + queSize - 1);\n        return nums[last];\n    }\n\n    /* Вернуть массив для вывода */\n    vector&lt;int&gt; toVector() {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        vector&lt;int&gt; res(queSize);\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            res[i] = nums[index(j)];\n        }\n        return res;\n    }\n};\n</code></pre> array_deque.java<pre><code>/* Двусторонняя очередь на основе кольцевого массива */\nclass ArrayDeque {\n    private int[] nums; // Массив для хранения элементов двусторонней очереди\n    private int front; // Указатель head, указывающий на первый элемент очереди\n    private int queSize; // Длина двусторонней очереди\n\n    /* Конструктор */\n    public ArrayDeque(int capacity) {\n        this.nums = new int[capacity];\n        front = queSize = 0;\n    }\n\n    /* Получить вместимость двусторонней очереди */\n    public int capacity() {\n        return nums.length;\n    }\n\n    /* Получение длины двусторонней очереди */\n    public int size() {\n        return queSize;\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    public boolean isEmpty() {\n        return queSize == 0;\n    }\n\n    /* Вычислить индекс в кольцевом массиве */\n    private int index(int i) {\n        // С помощью операции взятия по модулю соединить начало и конец массива\n        // Когда i выходит за конец массива, он возвращается в начало\n        // Когда i выходит за начало массива, он возвращается в конец\n        return (i + capacity()) % capacity();\n    }\n\n    /* Добавление в голову очереди */\n    public void pushFirst(int num) {\n        if (queSize == capacity()) {\n            System.out.println(\"Двусторонняя очередь заполнена\");\n            return;\n        }\n        // Указатель головы сдвигается на одну позицию влево\n        // С помощью операции взятия по модулю front после выхода за начало массива возвращается в хвост\n        front = index(front - 1);\n        // Добавить num в голову очереди\n        nums[front] = num;\n        queSize++;\n    }\n\n    /* Добавление в хвост очереди */\n    public void pushLast(int num) {\n        if (queSize == capacity()) {\n            System.out.println(\"Двусторонняя очередь заполнена\");\n            return;\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        int rear = index(front + queSize);\n        // Добавить num в хвост очереди\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* Извлечение из головы очереди */\n    public int popFirst() {\n        int num = peekFirst();\n        // Указатель головы сдвигается на одну позицию назад\n        front = index(front + 1);\n        queSize--;\n        return num;\n    }\n\n    /* Извлечение из хвоста очереди */\n    public int popLast() {\n        int num = peekLast();\n        queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    public int peekFirst() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return nums[front];\n    }\n\n    /* Доступ к элементу в конце очереди */\n    public int peekLast() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        // Вычислить индекс хвостового элемента\n        int last = index(front + queSize - 1);\n        return nums[last];\n    }\n\n    /* Вернуть массив для вывода */\n    public int[] toArray() {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        int[] res = new int[queSize];\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            res[i] = nums[index(j)];\n        }\n        return res;\n    }\n}\n</code></pre> array_deque.cs<pre><code>/* Двусторонняя очередь на основе кольцевого массива */\nclass ArrayDeque {\n    int[] nums;  // Массив для хранения элементов двусторонней очереди\n    int front;   // Указатель head, указывающий на первый элемент очереди\n    int queSize; // Длина двусторонней очереди\n\n    /* Конструктор */\n    public ArrayDeque(int capacity) {\n        nums = new int[capacity];\n        front = queSize = 0;\n    }\n\n    /* Получить вместимость двусторонней очереди */\n    int Capacity() {\n        return nums.Length;\n    }\n\n    /* Получение длины двусторонней очереди */\n    public int Size() {\n        return queSize;\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    public bool IsEmpty() {\n        return queSize == 0;\n    }\n\n    /* Вычислить индекс в кольцевом массиве */\n    int Index(int i) {\n        // С помощью операции взятия по модулю соединить начало и конец массива\n        // Когда i выходит за конец массива, он возвращается в начало\n        // Когда i выходит за начало массива, он возвращается в конец\n        return (i + Capacity()) % Capacity();\n    }\n\n    /* Добавление в голову очереди */\n    public void PushFirst(int num) {\n        if (queSize == Capacity()) {\n            Console.WriteLine(\"Двусторонняя очередь заполнена\");\n            return;\n        }\n        // Указатель головы сдвигается на одну позицию влево\n        // С помощью операции взятия по модулю front после выхода за начало массива возвращается в хвост\n        front = Index(front - 1);\n        // Добавить num в голову очереди\n        nums[front] = num;\n        queSize++;\n    }\n\n    /* Добавление в хвост очереди */\n    public void PushLast(int num) {\n        if (queSize == Capacity()) {\n            Console.WriteLine(\"Двусторонняя очередь заполнена\");\n            return;\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        int rear = Index(front + queSize);\n        // Добавить num в хвост очереди\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* Извлечение из головы очереди */\n    public int PopFirst() {\n        int num = PeekFirst();\n        // Указатель головы сдвигается на одну позицию назад\n        front = Index(front + 1);\n        queSize--;\n        return num;\n    }\n\n    /* Извлечение из хвоста очереди */\n    public int PopLast() {\n        int num = PeekLast();\n        queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    public int PeekFirst() {\n        if (IsEmpty()) {\n            throw new InvalidOperationException();\n        }\n        return nums[front];\n    }\n\n    /* Доступ к элементу в конце очереди */\n    public int PeekLast() {\n        if (IsEmpty()) {\n            throw new InvalidOperationException();\n        }\n        // Вычислить индекс хвостового элемента\n        int last = Index(front + queSize - 1);\n        return nums[last];\n    }\n\n    /* Вернуть массив для вывода */\n    public int[] ToArray() {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        int[] res = new int[queSize];\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            res[i] = nums[Index(j)];\n        }\n        return res;\n    }\n}\n</code></pre> array_deque.go<pre><code>/* Двусторонняя очередь на основе кольцевого массива */\ntype arrayDeque struct {\n    nums        []int // Массив для хранения элементов двусторонней очереди\n    front       int   // Указатель head, указывающий на первый элемент очереди\n    queSize     int   // Длина двусторонней очереди\n    queCapacity int   // Вместимость очереди (то есть максимальное число элементов)\n}\n\n/* Инициализация очереди */\nfunc newArrayDeque(queCapacity int) *arrayDeque {\n    return &amp;arrayDeque{\n        nums:        make([]int, queCapacity),\n        queCapacity: queCapacity,\n        front:       0,\n        queSize:     0,\n    }\n}\n\n/* Получение длины двусторонней очереди */\nfunc (q *arrayDeque) size() int {\n    return q.queSize\n}\n\n/* Проверка, пуста ли двусторонняя очередь */\nfunc (q *arrayDeque) isEmpty() bool {\n    return q.queSize == 0\n}\n\n/* Вычислить индекс в кольцевом массиве */\nfunc (q *arrayDeque) index(i int) int {\n    // С помощью операции взятия по модулю соединить начало и конец массива\n    // Когда i выходит за конец массива, он возвращается в начало\n    // Когда i выходит за начало массива, он возвращается в конец\n    return (i + q.queCapacity) % q.queCapacity\n}\n\n/* Добавление в голову очереди */\nfunc (q *arrayDeque) pushFirst(num int) {\n    if q.queSize == q.queCapacity {\n        fmt.Println(\"Двусторонняя очередь заполнена\")\n        return\n    }\n    // Указатель головы сдвигается на одну позицию влево\n    // С помощью операции взятия по модулю front после выхода за начало массива возвращается в хвост\n    q.front = q.index(q.front - 1)\n    // Добавить num в голову очереди\n    q.nums[q.front] = num\n    q.queSize++\n}\n\n/* Добавление в хвост очереди */\nfunc (q *arrayDeque) pushLast(num int) {\n    if q.queSize == q.queCapacity {\n        fmt.Println(\"Двусторонняя очередь заполнена\")\n        return\n    }\n    // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n    rear := q.index(q.front + q.queSize)\n    // Добавить num в хвост очереди\n    q.nums[rear] = num\n    q.queSize++\n}\n\n/* Извлечение из головы очереди */\nfunc (q *arrayDeque) popFirst() any {\n    num := q.peekFirst()\n    if num == nil {\n        return nil\n    }\n    // Указатель головы сдвигается на одну позицию назад\n    q.front = q.index(q.front + 1)\n    q.queSize--\n    return num\n}\n\n/* Извлечение из хвоста очереди */\nfunc (q *arrayDeque) popLast() any {\n    num := q.peekLast()\n    if num == nil {\n        return nil\n    }\n    q.queSize--\n    return num\n}\n\n/* Доступ к элементу в начале очереди */\nfunc (q *arrayDeque) peekFirst() any {\n    if q.isEmpty() {\n        return nil\n    }\n    return q.nums[q.front]\n}\n\n/* Доступ к элементу в конце очереди */\nfunc (q *arrayDeque) peekLast() any {\n    if q.isEmpty() {\n        return nil\n    }\n    // Вычислить индекс хвостового элемента\n    last := q.index(q.front + q.queSize - 1)\n    return q.nums[last]\n}\n\n/* Получить Slice для вывода */\nfunc (q *arrayDeque) toSlice() []int {\n    // Преобразовывать только элементы списка в пределах фактической длины\n    res := make([]int, q.queSize)\n    for i, j := 0, q.front; i &lt; q.queSize; i++ {\n        res[i] = q.nums[q.index(j)]\n        j++\n    }\n    return res\n}\n</code></pre> array_deque.swift<pre><code>/* Двусторонняя очередь на основе кольцевого массива */\nclass ArrayDeque {\n    private var nums: [Int] // Массив для хранения элементов двусторонней очереди\n    private var front: Int // Указатель head, указывающий на первый элемент очереди\n    private var _size: Int // Длина двусторонней очереди\n\n    /* Конструктор */\n    init(capacity: Int) {\n        nums = Array(repeating: 0, count: capacity)\n        front = 0\n        _size = 0\n    }\n\n    /* Получить вместимость двусторонней очереди */\n    func capacity() -&gt; Int {\n        nums.count\n    }\n\n    /* Получение длины двусторонней очереди */\n    func size() -&gt; Int {\n        _size\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    func isEmpty() -&gt; Bool {\n        size() == 0\n    }\n\n    /* Вычислить индекс в кольцевом массиве */\n    private func index(i: Int) -&gt; Int {\n        // С помощью операции взятия по модулю соединить начало и конец массива\n        // Когда i выходит за конец массива, он возвращается в начало\n        // Когда i выходит за начало массива, он возвращается в конец\n        (i + capacity()) % capacity()\n    }\n\n    /* Добавление в голову очереди */\n    func pushFirst(num: Int) {\n        if size() == capacity() {\n            print(\"Двусторонняя очередь заполнена\")\n            return\n        }\n        // Указатель головы сдвигается на одну позицию влево\n        // С помощью операции взятия по модулю front после выхода за начало массива возвращается в хвост\n        front = index(i: front - 1)\n        // Добавить num в голову очереди\n        nums[front] = num\n        _size += 1\n    }\n\n    /* Добавление в хвост очереди */\n    func pushLast(num: Int) {\n        if size() == capacity() {\n            print(\"Двусторонняя очередь заполнена\")\n            return\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        let rear = index(i: front + size())\n        // Добавить num в хвост очереди\n        nums[rear] = num\n        _size += 1\n    }\n\n    /* Извлечение из головы очереди */\n    func popFirst() -&gt; Int {\n        let num = peekFirst()\n        // Указатель головы сдвигается на одну позицию назад\n        front = index(i: front + 1)\n        _size -= 1\n        return num\n    }\n\n    /* Извлечение из хвоста очереди */\n    func popLast() -&gt; Int {\n        let num = peekLast()\n        _size -= 1\n        return num\n    }\n\n    /* Доступ к элементу в начале очереди */\n    func peekFirst() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"двусторонняя очередь пуста\")\n        }\n        return nums[front]\n    }\n\n    /* Доступ к элементу в конце очереди */\n    func peekLast() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"двусторонняя очередь пуста\")\n        }\n        // Вычислить индекс хвостового элемента\n        let last = index(i: front + size() - 1)\n        return nums[last]\n    }\n\n    /* Вернуть массив для вывода */\n    func toArray() -&gt; [Int] {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        (front ..&lt; front + size()).map { nums[index(i: $0)] }\n    }\n}\n</code></pre> array_deque.js<pre><code>/* Двусторонняя очередь на основе кольцевого массива */\nclass ArrayDeque {\n    #nums; // Массив для хранения элементов двусторонней очереди\n    #front; // Указатель head, указывающий на первый элемент очереди\n    #queSize; // Длина двусторонней очереди\n\n    /* Конструктор */\n    constructor(capacity) {\n        this.#nums = new Array(capacity);\n        this.#front = 0;\n        this.#queSize = 0;\n    }\n\n    /* Получить вместимость двусторонней очереди */\n    capacity() {\n        return this.#nums.length;\n    }\n\n    /* Получение длины двусторонней очереди */\n    size() {\n        return this.#queSize;\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    isEmpty() {\n        return this.#queSize === 0;\n    }\n\n    /* Вычислить индекс в кольцевом массиве */\n    index(i) {\n        // С помощью операции взятия по модулю соединить начало и конец массива\n        // Когда i выходит за конец массива, он возвращается в начало\n        // Когда i выходит за начало массива, он возвращается в конец\n        return (i + this.capacity()) % this.capacity();\n    }\n\n    /* Добавление в голову очереди */\n    pushFirst(num) {\n        if (this.#queSize === this.capacity()) {\n            console.log('Двусторонняя очередь заполнена');\n            return;\n        }\n        // Указатель головы сдвигается на одну позицию влево\n        // С помощью операции взятия по модулю front после выхода за начало массива возвращается в хвост\n        this.#front = this.index(this.#front - 1);\n        // Добавить num в голову очереди\n        this.#nums[this.#front] = num;\n        this.#queSize++;\n    }\n\n    /* Добавление в хвост очереди */\n    pushLast(num) {\n        if (this.#queSize === this.capacity()) {\n            console.log('Двусторонняя очередь заполнена');\n            return;\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        const rear = this.index(this.#front + this.#queSize);\n        // Добавить num в хвост очереди\n        this.#nums[rear] = num;\n        this.#queSize++;\n    }\n\n    /* Извлечение из головы очереди */\n    popFirst() {\n        const num = this.peekFirst();\n        // Указатель головы сдвигается на одну позицию назад\n        this.#front = this.index(this.#front + 1);\n        this.#queSize--;\n        return num;\n    }\n\n    /* Извлечение из хвоста очереди */\n    popLast() {\n        const num = this.peekLast();\n        this.#queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    peekFirst() {\n        if (this.isEmpty()) throw new Error('The Deque Is Empty.');\n        return this.#nums[this.#front];\n    }\n\n    /* Доступ к элементу в конце очереди */\n    peekLast() {\n        if (this.isEmpty()) throw new Error('The Deque Is Empty.');\n        // Вычислить индекс хвостового элемента\n        const last = this.index(this.#front + this.#queSize - 1);\n        return this.#nums[last];\n    }\n\n    /* Вернуть массив для вывода */\n    toArray() {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        const res = [];\n        for (let i = 0, j = this.#front; i &lt; this.#queSize; i++, j++) {\n            res[i] = this.#nums[this.index(j)];\n        }\n        return res;\n    }\n}\n</code></pre> array_deque.ts<pre><code>/* Двусторонняя очередь на основе кольцевого массива */\nclass ArrayDeque {\n    private nums: number[]; // Массив для хранения элементов двусторонней очереди\n    private front: number; // Указатель head, указывающий на первый элемент очереди\n    private queSize: number; // Длина двусторонней очереди\n\n    /* Конструктор */\n    constructor(capacity: number) {\n        this.nums = new Array(capacity);\n        this.front = 0;\n        this.queSize = 0;\n    }\n\n    /* Получить вместимость двусторонней очереди */\n    capacity(): number {\n        return this.nums.length;\n    }\n\n    /* Получение длины двусторонней очереди */\n    size(): number {\n        return this.queSize;\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    isEmpty(): boolean {\n        return this.queSize === 0;\n    }\n\n    /* Вычислить индекс в кольцевом массиве */\n    index(i: number): number {\n        // С помощью операции взятия по модулю соединить начало и конец массива\n        // Когда i выходит за конец массива, он возвращается в начало\n        // Когда i выходит за начало массива, он возвращается в конец\n        return (i + this.capacity()) % this.capacity();\n    }\n\n    /* Добавление в голову очереди */\n    pushFirst(num: number): void {\n        if (this.queSize === this.capacity()) {\n            console.log('Двусторонняя очередь заполнена');\n            return;\n        }\n        // Указатель головы сдвигается на одну позицию влево\n        // С помощью операции взятия по модулю front после выхода за начало массива возвращается в хвост\n        this.front = this.index(this.front - 1);\n        // Добавить num в голову очереди\n        this.nums[this.front] = num;\n        this.queSize++;\n    }\n\n    /* Добавление в хвост очереди */\n    pushLast(num: number): void {\n        if (this.queSize === this.capacity()) {\n            console.log('Двусторонняя очередь заполнена');\n            return;\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        const rear: number = this.index(this.front + this.queSize);\n        // Добавить num в хвост очереди\n        this.nums[rear] = num;\n        this.queSize++;\n    }\n\n    /* Извлечение из головы очереди */\n    popFirst(): number {\n        const num: number = this.peekFirst();\n        // Указатель головы сдвигается на одну позицию назад\n        this.front = this.index(this.front + 1);\n        this.queSize--;\n        return num;\n    }\n\n    /* Извлечение из хвоста очереди */\n    popLast(): number {\n        const num: number = this.peekLast();\n        this.queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    peekFirst(): number {\n        if (this.isEmpty()) throw new Error('The Deque Is Empty.');\n        return this.nums[this.front];\n    }\n\n    /* Доступ к элементу в конце очереди */\n    peekLast(): number {\n        if (this.isEmpty()) throw new Error('The Deque Is Empty.');\n        // Вычислить индекс хвостового элемента\n        const last = this.index(this.front + this.queSize - 1);\n        return this.nums[last];\n    }\n\n    /* Вернуть массив для вывода */\n    toArray(): number[] {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        const res: number[] = [];\n        for (let i = 0, j = this.front; i &lt; this.queSize; i++, j++) {\n            res[i] = this.nums[this.index(j)];\n        }\n        return res;\n    }\n}\n</code></pre> array_deque.dart<pre><code>/* Двусторонняя очередь на основе кольцевого массива */\nclass ArrayDeque {\n  late List&lt;int&gt; _nums; // Массив для хранения элементов двусторонней очереди\n  late int _front; // Указатель head, указывающий на первый элемент очереди\n  late int _queSize; // Длина двусторонней очереди\n\n  /* Конструктор */\n  ArrayDeque(int capacity) {\n    this._nums = List.filled(capacity, 0);\n    this._front = this._queSize = 0;\n  }\n\n  /* Получить вместимость двусторонней очереди */\n  int capacity() {\n    return _nums.length;\n  }\n\n  /* Получение длины двусторонней очереди */\n  int size() {\n    return _queSize;\n  }\n\n  /* Проверка, пуста ли двусторонняя очередь */\n  bool isEmpty() {\n    return _queSize == 0;\n  }\n\n  /* Вычислить индекс в кольцевом массиве */\n  int index(int i) {\n    // С помощью операции взятия по модулю соединить начало и конец массива\n    // Когда i выходит за конец массива, он возвращается в начало\n    // Когда i выходит за начало массива, он возвращается в конец\n    return (i + capacity()) % capacity();\n  }\n\n  /* Добавление в голову очереди */\n  void pushFirst(int _num) {\n    if (_queSize == capacity()) {\n      throw Exception(\"Двусторонняя очередь заполнена\");\n    }\n    // Указатель головы сместить влево на одну позицию\n    // С помощью операции взятия остатка реализовать возврат _front к хвосту после выхода за начало массива\n    _front = index(_front - 1);\n    // Добавить _num в голову очереди\n    _nums[_front] = _num;\n    _queSize++;\n  }\n\n  /* Добавление в хвост очереди */\n  void pushLast(int _num) {\n    if (_queSize == capacity()) {\n      throw Exception(\"Двусторонняя очередь заполнена\");\n    }\n    // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n    int rear = index(_front + _queSize);\n    // Добавить _num в хвост очереди\n    _nums[rear] = _num;\n    _queSize++;\n  }\n\n  /* Извлечение из головы очереди */\n  int popFirst() {\n    int _num = peekFirst();\n    // Указатель головы сместить вправо на одну позицию\n    _front = index(_front + 1);\n    _queSize--;\n    return _num;\n  }\n\n  /* Извлечение из хвоста очереди */\n  int popLast() {\n    int _num = peekLast();\n    _queSize--;\n    return _num;\n  }\n\n  /* Доступ к элементу в начале очереди */\n  int peekFirst() {\n    if (isEmpty()) {\n      throw Exception(\"двусторонняя очередь пуста\");\n    }\n    return _nums[_front];\n  }\n\n  /* Доступ к элементу в конце очереди */\n  int peekLast() {\n    if (isEmpty()) {\n      throw Exception(\"двусторонняя очередь пуста\");\n    }\n    // Вычислить индекс хвостового элемента\n    int last = index(_front + _queSize - 1);\n    return _nums[last];\n  }\n\n  /* Вернуть массив для вывода */\n  List&lt;int&gt; toArray() {\n    // Преобразовывать только элементы списка в пределах фактической длины\n    List&lt;int&gt; res = List.filled(_queSize, 0);\n    for (int i = 0, j = _front; i &lt; _queSize; i++, j++) {\n      res[i] = _nums[index(j)];\n    }\n    return res;\n  }\n}\n</code></pre> array_deque.rs<pre><code>/* Двусторонняя очередь на основе кольцевого массива */\nstruct ArrayDeque&lt;T&gt; {\n    nums: Vec&lt;T&gt;,    // Массив для хранения элементов двусторонней очереди\n    front: usize,    // Указатель head, указывающий на первый элемент очереди\n    que_size: usize, // Длина двусторонней очереди\n}\n\nimpl&lt;T: Copy + Default&gt; ArrayDeque&lt;T&gt; {\n    /* Конструктор */\n    pub fn new(capacity: usize) -&gt; Self {\n        Self {\n            nums: vec![T::default(); capacity],\n            front: 0,\n            que_size: 0,\n        }\n    }\n\n    /* Получить вместимость двусторонней очереди */\n    pub fn capacity(&amp;self) -&gt; usize {\n        self.nums.len()\n    }\n\n    /* Получение длины двусторонней очереди */\n    pub fn size(&amp;self) -&gt; usize {\n        self.que_size\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    pub fn is_empty(&amp;self) -&gt; bool {\n        self.que_size == 0\n    }\n\n    /* Вычислить индекс в кольцевом массиве */\n    fn index(&amp;self, i: i32) -&gt; usize {\n        // С помощью операции взятия по модулю соединить начало и конец массива\n        // Когда i выходит за конец массива, он возвращается в начало\n        // Когда i выходит за начало массива, он возвращается в конец\n        ((i + self.capacity() as i32) % self.capacity() as i32) as usize\n    }\n\n    /* Добавление в голову очереди */\n    pub fn push_first(&amp;mut self, num: T) {\n        if self.que_size == self.capacity() {\n            println!(\"Двусторонняя очередь заполнена\");\n            return;\n        }\n        // Указатель головы сдвигается на одну позицию влево\n        // С помощью операции взятия по модулю front после выхода за начало массива возвращается в хвост\n        self.front = self.index(self.front as i32 - 1);\n        // Добавить num в голову очереди\n        self.nums[self.front] = num;\n        self.que_size += 1;\n    }\n\n    /* Добавление в хвост очереди */\n    pub fn push_last(&amp;mut self, num: T) {\n        if self.que_size == self.capacity() {\n            println!(\"Двусторонняя очередь заполнена\");\n            return;\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        let rear = self.index(self.front as i32 + self.que_size as i32);\n        // Добавить num в хвост очереди\n        self.nums[rear] = num;\n        self.que_size += 1;\n    }\n\n    /* Извлечение из головы очереди */\n    fn pop_first(&amp;mut self) -&gt; T {\n        let num = self.peek_first();\n        // Указатель головы сдвигается на одну позицию назад\n        self.front = self.index(self.front as i32 + 1);\n        self.que_size -= 1;\n        num\n    }\n\n    /* Извлечение из хвоста очереди */\n    fn pop_last(&amp;mut self) -&gt; T {\n        let num = self.peek_last();\n        self.que_size -= 1;\n        num\n    }\n\n    /* Доступ к элементу в начале очереди */\n    fn peek_first(&amp;self) -&gt; T {\n        if self.is_empty() {\n            panic!(\"двусторонняя очередь пуста\")\n        };\n        self.nums[self.front]\n    }\n\n    /* Доступ к элементу в конце очереди */\n    fn peek_last(&amp;self) -&gt; T {\n        if self.is_empty() {\n            panic!(\"двусторонняя очередь пуста\")\n        };\n        // Вычислить индекс хвостового элемента\n        let last = self.index(self.front as i32 + self.que_size as i32 - 1);\n        self.nums[last]\n    }\n\n    /* Вернуть массив для вывода */\n    fn to_array(&amp;self) -&gt; Vec&lt;T&gt; {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        let mut res = vec![T::default(); self.que_size];\n        let mut j = self.front;\n        for i in 0..self.que_size {\n            res[i] = self.nums[self.index(j as i32)];\n            j += 1;\n        }\n        res\n    }\n}\n</code></pre> array_deque.c<pre><code>/* Двусторонняя очередь на основе кольцевого массива */\ntypedef struct {\n    int *nums;       // Массив для хранения элементов очереди\n    int front;       // Указатель head, указывающий на первый элемент очереди\n    int queSize;     // Указатель хвоста, указывающий на позицию после хвоста\n    int queCapacity; // Вместимость очереди\n} ArrayDeque;\n\n/* Конструктор */\nArrayDeque *newArrayDeque(int capacity) {\n    ArrayDeque *deque = (ArrayDeque *)malloc(sizeof(ArrayDeque));\n    // Инициализация массива\n    deque-&gt;queCapacity = capacity;\n    deque-&gt;nums = (int *)malloc(sizeof(int) * deque-&gt;queCapacity);\n    deque-&gt;front = deque-&gt;queSize = 0;\n    return deque;\n}\n\n/* Деструктор */\nvoid delArrayDeque(ArrayDeque *deque) {\n    free(deque-&gt;nums);\n    free(deque);\n}\n\n/* Получить вместимость двусторонней очереди */\nint capacity(ArrayDeque *deque) {\n    return deque-&gt;queCapacity;\n}\n\n/* Получение длины двусторонней очереди */\nint size(ArrayDeque *deque) {\n    return deque-&gt;queSize;\n}\n\n/* Проверка, пуста ли двусторонняя очередь */\nbool empty(ArrayDeque *deque) {\n    return deque-&gt;queSize == 0;\n}\n\n/* Вычислить индекс в кольцевом массиве */\nint dequeIndex(ArrayDeque *deque, int i) {\n    // С помощью операции взятия остатка соединить начало и конец массива\n    // Когда i выходит за хвост массива, вернуться к началу\n    // Когда i выходит за голову массива, вернуться к концу\n    return ((i + capacity(deque)) % capacity(deque));\n}\n\n/* Добавление в голову очереди */\nvoid pushFirst(ArrayDeque *deque, int num) {\n    if (deque-&gt;queSize == capacity(deque)) {\n        printf(\"Дек заполнен\\r\\n\");\n        return;\n    }\n    // Указатель головы сместить влево на одну позицию\n    // С помощью операции взятия остатка реализовать возврат front к хвосту после выхода за начало массива\n    deque-&gt;front = dequeIndex(deque, deque-&gt;front - 1);\n    // Добавить num в голову очереди\n    deque-&gt;nums[deque-&gt;front] = num;\n    deque-&gt;queSize++;\n}\n\n/* Добавление в хвост очереди */\nvoid pushLast(ArrayDeque *deque, int num) {\n    if (deque-&gt;queSize == capacity(deque)) {\n        printf(\"Дек заполнен\\r\\n\");\n        return;\n    }\n    // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n    int rear = dequeIndex(deque, deque-&gt;front + deque-&gt;queSize);\n    // Добавить num в хвост очереди\n    deque-&gt;nums[rear] = num;\n    deque-&gt;queSize++;\n}\n\n/* Доступ к элементу в начале очереди */\nint peekFirst(ArrayDeque *deque) {\n    // Ошибка доступа: двусторонняя очередь пуста\n    assert(empty(deque) == 0);\n    return deque-&gt;nums[deque-&gt;front];\n}\n\n/* Доступ к элементу в конце очереди */\nint peekLast(ArrayDeque *deque) {\n    // Ошибка доступа: двусторонняя очередь пуста\n    assert(empty(deque) == 0);\n    int last = dequeIndex(deque, deque-&gt;front + deque-&gt;queSize - 1);\n    return deque-&gt;nums[last];\n}\n\n/* Извлечение из головы очереди */\nint popFirst(ArrayDeque *deque) {\n    int num = peekFirst(deque);\n    // Указатель головы сдвигается на одну позицию назад\n    deque-&gt;front = dequeIndex(deque, deque-&gt;front + 1);\n    deque-&gt;queSize--;\n    return num;\n}\n\n/* Извлечение из хвоста очереди */\nint popLast(ArrayDeque *deque) {\n    int num = peekLast(deque);\n    deque-&gt;queSize--;\n    return num;\n}\n\n/* Вернуть массив для вывода */\nint *toArray(ArrayDeque *deque, int *queSize) {\n    *queSize = deque-&gt;queSize;\n    int *res = (int *)calloc(deque-&gt;queSize, sizeof(int));\n    int j = deque-&gt;front;\n    for (int i = 0; i &lt; deque-&gt;queSize; i++) {\n        res[i] = deque-&gt;nums[j % deque-&gt;queCapacity];\n        j++;\n    }\n    return res;\n}\n</code></pre> array_deque.kt<pre><code>/* Конструктор */\nclass ArrayDeque(capacity: Int) {\n    private var nums: IntArray = IntArray(capacity) // Массив для хранения элементов двусторонней очереди\n    private var front: Int = 0 // Указатель head, указывающий на первый элемент очереди\n    private var queSize: Int = 0 // Длина двусторонней очереди\n\n    /* Получить вместимость двусторонней очереди */\n    fun capacity(): Int {\n        return nums.size\n    }\n\n    /* Получение длины двусторонней очереди */\n    fun size(): Int {\n        return queSize\n    }\n\n    /* Проверка, пуста ли двусторонняя очередь */\n    fun isEmpty(): Boolean {\n        return queSize == 0\n    }\n\n    /* Вычислить индекс в кольцевом массиве */\n    private fun index(i: Int): Int {\n        // С помощью операции взятия по модулю соединить начало и конец массива\n        // Когда i выходит за конец массива, он возвращается в начало\n        // Когда i выходит за начало массива, он возвращается в конец\n        return (i + capacity()) % capacity()\n    }\n\n    /* Добавление в голову очереди */\n    fun pushFirst(num: Int) {\n        if (queSize == capacity()) {\n            println(\"Двусторонняя очередь заполнена\")\n            return\n        }\n        // Указатель головы сдвигается на одну позицию влево\n        // С помощью операции взятия по модулю front после выхода за начало массива возвращается в хвост\n        front = index(front - 1)\n        // Добавить num в голову очереди\n        nums[front] = num\n        queSize++\n    }\n\n    /* Добавление в хвост очереди */\n    fun pushLast(num: Int) {\n        if (queSize == capacity()) {\n            println(\"Двусторонняя очередь заполнена\")\n            return\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        val rear = index(front + queSize)\n        // Добавить num в хвост очереди\n        nums[rear] = num\n        queSize++\n    }\n\n    /* Извлечение из головы очереди */\n    fun popFirst(): Int {\n        val num = peekFirst()\n        // Указатель головы сдвигается на одну позицию назад\n        front = index(front + 1)\n        queSize--\n        return num\n    }\n\n    /* Извлечение из хвоста очереди */\n    fun popLast(): Int {\n        val num = peekLast()\n        queSize--\n        return num\n    }\n\n    /* Доступ к элементу в начале очереди */\n    fun peekFirst(): Int {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        return nums[front]\n    }\n\n    /* Доступ к элементу в конце очереди */\n    fun peekLast(): Int {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        // Вычислить индекс хвостового элемента\n        val last = index(front + queSize - 1)\n        return nums[last]\n    }\n\n    /* Вернуть массив для вывода */\n    fun toArray(): IntArray {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        val res = IntArray(queSize)\n        var i = 0\n        var j = front\n        while (i &lt; queSize) {\n            res[i] = nums[index(j)]\n            i++\n            j++\n        }\n        return res\n    }\n}\n</code></pre> array_deque.rb<pre><code>### Двусторонняя очередь на основе кольцевого массива ###\nclass ArrayDeque\n  ### Получение длины двусторонней очереди ###\n  attr_reader :size\n\n  ### Конструктор ###\n  def initialize(capacity)\n    @nums = Array.new(capacity, 0)\n    @front = 0\n    @size = 0\n  end\n\n  ### Получить вместимость двусторонней очереди ###\n  def capacity\n    @nums.length\n  end\n\n  ### Проверка, пуста ли двусторонняя очередь ###\n  def is_empty?\n    size.zero?\n  end\n\n  ### Добавление в голову очереди ###\n  def push_first(num)\n    if size == capacity\n      puts 'Двусторонняя очередь заполнена'\n      return\n    end\n\n    # Указатель головы сдвигается на одну позицию влево\n    # С помощью операции взятия по модулю front после выхода за начало массива возвращается в хвост\n    @front = index(@front - 1)\n    # Добавить num в голову очереди\n    @nums[@front] = num\n    @size += 1\n  end\n\n  ### Добавление в хвост очереди ###\n  def push_last(num)\n    if size == capacity\n      puts 'Двусторонняя очередь заполнена'\n      return\n    end\n\n    # Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n    rear = index(@front + size)\n    # Добавить num в хвост очереди\n    @nums[rear] = num\n    @size += 1\n  end\n\n  ### Извлечение из головы очереди ###\n  def pop_first\n    num = peek_first\n    # Указатель головы сдвигается на одну позицию назад\n    @front = index(@front + 1)\n    @size -= 1\n    num\n  end\n\n  ### Извлечение из хвоста очереди ###\n  def pop_last\n    num = peek_last\n    @size -= 1\n    num\n  end\n\n  ### Доступ к элементу в начале очереди ###\n  def peek_first\n    raise IndexError, 'двусторонняя очередь пуста' if is_empty?\n\n    @nums[@front]\n  end\n\n  ### Доступ к элементу в хвосте очереди ###\n  def peek_last\n    raise IndexError, 'двусторонняя очередь пуста' if is_empty?\n\n    # Вычислить индекс хвостового элемента\n    last = index(@front + size - 1)\n    @nums[last]\n  end\n\n  ### Вернуть массив для вывода ###\n  def to_array\n    # Преобразовывать только элементы списка в пределах фактической длины\n    res = []\n    for i in 0...size\n      res &lt;&lt; @nums[index(@front + i)]\n    end\n    res\n  end\n\n  private\n\n  ### Вычислить индекс в кольцевом массиве ###\n  def index(i)\n    # С помощью операции взятия по модулю соединить начало и конец массива\n    # Когда i выходит за конец массива, он возвращается в начало\n    # Когда i выходит за начало массива, он возвращается в конец\n    (i + capacity) % capacity\n  end\nend\n</code></pre>","path":["Глава 5. Стек и очередь","5.3 &nbsp; Двусторонняя очередь"],"tags":[]},{"location":"chapter_stack_and_queue/deque/#533","level":2,"title":"5.3.3   Применение двусторонней очереди","text":"<p>Двусторонняя очередь сочетает в себе логику стека и очереди, поэтому она может покрыть все сценарии применения обеих структур и при этом предоставляет более высокую степень свободы.</p> <p>Мы знаем, что функция \"undo\" в программном обеспечении обычно реализуется с помощью стека: система помещает каждое изменение в стек с помощью <code>push</code> , а затем использует <code>pop</code> для отмены. Однако, учитывая ограниченность системных ресурсов, программы обычно ограничивают число шагов отмены, например разрешают хранить только \\(50\\) шагов. Когда длина стека превышает этот предел, программе нужно удалить элемент с дна стека, то есть с головы очереди. Но стек не может реализовать такую операцию, и в этом случае его приходится заменять двусторонней очередью. Обрати внимание: основная логика \"undo\" по-прежнему следует стековому правилу LIFO, просто двусторонняя очередь позволяет более гибко реализовать некоторые дополнительные механизмы.</p>","path":["Глава 5. Стек и очередь","5.3 &nbsp; Двусторонняя очередь"],"tags":[]},{"location":"chapter_stack_and_queue/queue/","level":1,"title":"5.2   Очередь","text":"<p>Очередь (queue) - это линейная структура данных, подчиняющаяся правилу \"первым пришел - первым вышел\". Как видно из названия, очередь моделирует обычную ситуацию ожидания: новые люди непрерывно присоединяются к хвосту очереди, а стоящие в начале по одному уходят.</p> <p>Как показано на рисунке 5-4, начало очереди называется головой очереди, а конец - хвостом очереди; операцию добавления элемента в хвост называют <code>enqueue</code>, а операцию удаления элемента из головы - <code>dequeue</code>.</p> <p></p> <p> Рисунок 5-4   Правило FIFO для очереди </p>","path":["Глава 5. Стек и очередь","5.2 &nbsp; Очередь"],"tags":[]},{"location":"chapter_stack_and_queue/queue/#521","level":2,"title":"5.2.1   Основные операции с очередью","text":"<p>Распространенные операции с очередью показаны в таблице 5-2. Следует учитывать, что названия методов в разных языках могут различаться. Здесь мы используем те же названия, что и для стека.</p> <p> Таблица 5-2   Эффективность операций с очередью </p> Имя метода Описание Временная сложность <code>push()</code> Поместить элемент в очередь, то есть добавить его в хвост \\(O(1)\\) <code>pop()</code> Извлечь элемент из головы очереди \\(O(1)\\) <code>peek()</code> Просмотреть элемент в голове очереди \\(O(1)\\) <p>Обычно достаточно использовать готовые классы очереди, предоставляемые языками программирования:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby queue.py<pre><code>from collections import deque\n\n# Инициализация очереди\n# В Python обычно используют двустороннюю очередь deque как обычную очередь\n# Хотя queue.Queue() является \"чистой\" очередью, она не слишком удобна, поэтому ее не рекомендуют\nque: deque[int] = deque()\n\n# Поместить элементы в очередь\nque.append(1)\nque.append(3)\nque.append(2)\nque.append(5)\nque.append(4)\n\n# Просмотреть элемент в голове очереди\nfront: int = que[0]\n\n# Извлечь элемент из очереди\npop: int = que.popleft()\n\n# Получить длину очереди\nsize: int = len(que)\n\n# Проверить, пуста ли очередь\nis_empty: bool = len(que) == 0\n</code></pre> queue.cpp<pre><code>/* Инициализация очереди */\nqueue&lt;int&gt; queue;\n\n/* Поместить элементы в очередь */\nqueue.push(1);\nqueue.push(3);\nqueue.push(2);\nqueue.push(5);\nqueue.push(4);\n\n/* Просмотреть элемент в голове очереди */\nint front = queue.front();\n\n/* Извлечь элемент из очереди */\nqueue.pop();\n\n/* Получить длину очереди */\nint size = queue.size();\n\n/* Проверить, пуста ли очередь */\nbool empty = queue.empty();\n</code></pre> queue.java<pre><code>/* Инициализация очереди */\nQueue&lt;Integer&gt; queue = new LinkedList&lt;&gt;();\n\n/* Поместить элементы в очередь */\nqueue.offer(1);\nqueue.offer(3);\nqueue.offer(2);\nqueue.offer(5);\nqueue.offer(4);\n\n/* Просмотреть элемент в голове очереди */\nint peek = queue.peek();\n\n/* Извлечь элемент из очереди */\nint pop = queue.poll();\n\n/* Получить длину очереди */\nint size = queue.size();\n\n/* Проверить, пуста ли очередь */\nboolean isEmpty = queue.isEmpty();\n</code></pre> queue.cs<pre><code>/* Инициализация очереди */\nQueue&lt;int&gt; queue = new();\n\n/* Поместить элементы в очередь */\nqueue.Enqueue(1);\nqueue.Enqueue(3);\nqueue.Enqueue(2);\nqueue.Enqueue(5);\nqueue.Enqueue(4);\n\n/* Просмотреть элемент в голове очереди */\nint peek = queue.Peek();\n\n/* Извлечь элемент из очереди */\nint pop = queue.Dequeue();\n\n/* Получить длину очереди */\nint size = queue.Count;\n\n/* Проверить, пуста ли очередь */\nbool isEmpty = queue.Count == 0;\n</code></pre> queue_test.go<pre><code>/* Инициализация очереди */\n// В Go очередь обычно реализуют через list\nqueue := list.New()\n\n/* Поместить элементы в очередь */\nqueue.PushBack(1)\nqueue.PushBack(3)\nqueue.PushBack(2)\nqueue.PushBack(5)\nqueue.PushBack(4)\n\n/* Просмотреть элемент в голове очереди */\npeek := queue.Front()\n\n/* Извлечь элемент из очереди */\npop := queue.Front()\nqueue.Remove(pop)\n\n/* Получить длину очереди */\nsize := queue.Len()\n\n/* Проверить, пуста ли очередь */\nisEmpty := queue.Len() == 0\n</code></pre> queue.swift<pre><code>/* Инициализация очереди */\n// В Swift нет встроенного класса очереди, поэтому можно использовать Array как очередь\nvar queue: [Int] = []\n\n/* Поместить элементы в очередь */\nqueue.append(1)\nqueue.append(3)\nqueue.append(2)\nqueue.append(5)\nqueue.append(4)\n\n/* Просмотреть элемент в голове очереди */\nlet peek = queue.first!\n\n/* Извлечь элемент из очереди */\n// Поскольку в основе лежит массив, removeFirst имеет сложность O(n)\nlet pool = queue.removeFirst()\n\n/* Получить длину очереди */\nlet size = queue.count\n\n/* Проверить, пуста ли очередь */\nlet isEmpty = queue.isEmpty\n</code></pre> queue.js<pre><code>/* Инициализация очереди */\n// В JavaScript нет встроенной очереди, поэтому можно использовать Array как очередь\nconst queue = [];\n\n/* Поместить элементы в очередь */\nqueue.push(1);\nqueue.push(3);\nqueue.push(2);\nqueue.push(5);\nqueue.push(4);\n\n/* Просмотреть элемент в голове очереди */\nconst peek = queue[0];\n\n/* Извлечь элемент из очереди */\n// В основе лежит массив, поэтому shift() имеет сложность O(n)\nconst pop = queue.shift();\n\n/* Получить длину очереди */\nconst size = queue.length;\n\n/* Проверить, пуста ли очередь */\nconst empty = queue.length === 0;\n</code></pre> queue.ts<pre><code>/* Инициализация очереди */\n// В TypeScript нет встроенной очереди, поэтому можно использовать Array как очередь\nconst queue: number[] = [];\n\n/* Поместить элементы в очередь */\nqueue.push(1);\nqueue.push(3);\nqueue.push(2);\nqueue.push(5);\nqueue.push(4);\n\n/* Просмотреть элемент в голове очереди */\nconst peek = queue[0];\n\n/* Извлечь элемент из очереди */\n// В основе лежит массив, поэтому shift() имеет сложность O(n)\nconst pop = queue.shift();\n\n/* Получить длину очереди */\nconst size = queue.length;\n\n/* Проверить, пуста ли очередь */\nconst empty = queue.length === 0;\n</code></pre> queue.dart<pre><code>/* Инициализация очереди */\n// В Dart класс Queue является двусторонней очередью и может использоваться как обычная очередь\nQueue&lt;int&gt; queue = Queue();\n\n/* Поместить элементы в очередь */\nqueue.add(1);\nqueue.add(3);\nqueue.add(2);\nqueue.add(5);\nqueue.add(4);\n\n/* Просмотреть элемент в голове очереди */\nint peek = queue.first;\n\n/* Извлечь элемент из очереди */\nint pop = queue.removeFirst();\n\n/* Получить длину очереди */\nint size = queue.length;\n\n/* Проверить, пуста ли очередь */\nbool isEmpty = queue.isEmpty;\n</code></pre> queue.rs<pre><code>/* Инициализация двусторонней очереди */\n// В Rust двусторонняя очередь может использоваться как обычная очередь\nlet mut deque: VecDeque&lt;u32&gt; = VecDeque::new();\n\n/* Поместить элементы в очередь */\ndeque.push_back(1);\ndeque.push_back(3);\ndeque.push_back(2);\ndeque.push_back(5);\ndeque.push_back(4);\n\n/* Просмотреть элемент в голове очереди */\nif let Some(front) = deque.front() {\n}\n\n/* Извлечь элемент из очереди */\nif let Some(pop) = deque.pop_front() {\n}\n\n/* Получить длину очереди */\nlet size = deque.len();\n\n/* Проверить, пуста ли очередь */\nlet is_empty = deque.is_empty();\n</code></pre> queue.c<pre><code>// В C нет встроенной очереди\n</code></pre> queue.kt<pre><code>/* Инициализация очереди */\nval queue = LinkedList&lt;Int&gt;()\n\n/* Поместить элементы в очередь */\nqueue.offer(1)\nqueue.offer(3)\nqueue.offer(2)\nqueue.offer(5)\nqueue.offer(4)\n\n/* Просмотреть элемент в голове очереди */\nval peek = queue.peek()\n\n/* Извлечь элемент из очереди */\nval pop = queue.poll()\n\n/* Получить длину очереди */\nval size = queue.size\n\n/* Проверить, пуста ли очередь */\nval isEmpty = queue.isEmpty()\n</code></pre> queue.rb<pre><code># Инициализация очереди\n# Встроенная очередь в Ruby (Thread::Queue) не имеет методов peek и traverse, поэтому можно использовать Array как очередь\nqueue = []\n\n# Поместить элементы в очередь\nqueue.push(1)\nqueue.push(3)\nqueue.push(2)\nqueue.push(5)\nqueue.push(4)\n\n# Просмотреть элемент очереди\npeek = queue.first\n\n# Извлечь элемент из очереди\n# Обрати внимание: поскольку это массив, метод Array#shift имеет сложность O(n)\npop = queue.shift\n\n# Получить длину очереди\nsize = queue.length\n\n# Проверить, пуста ли очередь\nis_empty = queue.empty?\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=from%20collections%20import%20deque%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D1%8C%0A%20%20%20%20%23%20%D0%92%20Python%20%D0%B4%D0%B2%D1%83%D1%81%D1%82%D0%BE%D1%80%D0%BE%D0%BD%D0%BD%D1%8E%D1%8E%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D1%8C%20deque%20%D0%BE%D0%B1%D1%8B%D1%87%D0%BD%D0%BE%20%D0%B8%D1%81%D0%BF%D0%BE%D0%BB%D1%8C%D0%B7%D1%83%D1%8E%D1%82%20%D0%BA%D0%B0%D0%BA%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D1%8C%0A%20%20%20%20%23%20%D0%A5%D0%BE%D1%82%D1%8F%20queue.Queue%28%29%20%D1%8F%D0%B2%D0%BB%D1%8F%D0%B5%D1%82%D1%81%D1%8F%20%D0%BD%D0%B0%D1%81%D1%82%D0%BE%D1%8F%D1%89%D0%B8%D0%BC%20%D0%BA%D0%BB%D0%B0%D1%81%D1%81%D0%BE%D0%BC%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D0%B8%2C%20%D0%BF%D0%BE%D0%BB%D1%8C%D0%B7%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%D1%81%D1%8F%20%D0%B8%D0%BC%20%D0%BD%D0%B5%20%D1%81%D0%BB%D0%B8%D1%88%D0%BA%D0%BE%D0%BC%20%D1%83%D0%B4%D0%BE%D0%B1%D0%BD%D0%BE%0A%20%20%20%20que%20%3D%20deque%28%29%0A%0A%20%20%20%20%23%20%D0%9F%D0%BE%D0%BC%D0%B5%D1%81%D1%82%D0%B8%D1%82%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%B2%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D1%8C%0A%20%20%20%20que.append%281%29%0A%20%20%20%20que.append%283%29%0A%20%20%20%20que.append%282%29%0A%20%20%20%20que.append%285%29%0A%20%20%20%20que.append%284%29%0A%20%20%20%20print%28%22%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D1%8C%20que%20%3D%22%2C%20que%29%0A%0A%20%20%20%20%23%20%D0%9F%D0%BE%D0%BB%D1%83%D1%87%D0%B8%D1%82%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%B2%20%D0%BD%D0%B0%D1%87%D0%B0%D0%BB%D0%B5%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D0%B8%0A%20%20%20%20front%20%3D%20que%5B0%5D%0A%20%20%20%20print%28%22%D0%AD%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%B2%20%D0%BD%D0%B0%D1%87%D0%B0%D0%BB%D0%B5%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D0%B8%20front%20%3D%22%2C%20front%29%0A%0A%20%20%20%20%23%20%D0%98%D0%B7%D0%B2%D0%BB%D0%B5%D1%87%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%B8%D0%B7%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D0%B8%0A%20%20%20%20pop%20%3D%20que.popleft%28%29%0A%20%20%20%20print%28%22%D0%98%D0%B7%D0%B2%D0%BB%D0%B5%D1%87%D0%B5%D0%BD%D0%BD%D1%8B%D0%B9%20%D0%B8%D0%B7%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D0%B8%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20pop%20%3D%22%2C%20pop%29%0A%20%20%20%20print%28%22que%20%D0%BF%D0%BE%D1%81%D0%BB%D0%B5%20%D0%B8%D0%B7%D0%B2%D0%BB%D0%B5%D1%87%D0%B5%D0%BD%D0%B8%D1%8F%20%3D%22%2C%20que%29%0A%0A%20%20%20%20%23%20%D0%9F%D0%BE%D0%BB%D1%83%D1%87%D0%B8%D1%82%D1%8C%20%D0%B4%D0%BB%D0%B8%D0%BD%D1%83%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D0%B8%0A%20%20%20%20size%20%3D%20len%28que%29%0A%20%20%20%20print%28%22%D0%94%D0%BB%D0%B8%D0%BD%D0%B0%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D0%B8%20size%20%3D%22%2C%20size%29%0A%0A%20%20%20%20%23%20%D0%9F%D1%80%D0%BE%D0%B2%D0%B5%D1%80%D0%B8%D1%82%D1%8C%2C%20%D0%BF%D1%83%D1%81%D1%82%D0%B0%20%D0%BB%D0%B8%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D1%8C%0A%20%20%20%20is_empty%20%3D%20len%28que%29%20%3D%3D%200%0A%20%20%20%20print%28%22%D0%9F%D1%83%D1%81%D1%82%D0%B0%20%D0%BB%D0%B8%20%D0%BE%D1%87%D0%B5%D1%80%D0%B5%D0%B4%D1%8C%20%3D%22%2C%20is_empty%29&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 5. Стек и очередь","5.2 &nbsp; Очередь"],"tags":[]},{"location":"chapter_stack_and_queue/queue/#522","level":2,"title":"5.2.2   Реализация очереди","text":"<p>Чтобы реализовать очередь, нам нужна такая структура данных, которая позволяет добавлять элементы с одного конца и удалять их с другого; и связный список, и массив этим требованиям удовлетворяют.</p>","path":["Глава 5. Стек и очередь","5.2 &nbsp; Очередь"],"tags":[]},{"location":"chapter_stack_and_queue/queue/#1","level":3,"title":"1.   Реализация на основе связного списка","text":"<p>Как показано на рисунке 5-5, мы можем рассматривать головной узел и хвостовой узел связного списка как голову очереди и хвост очереди соответственно, договорившись, что добавлять узлы можно только в хвост, а удалять - только из головы.</p> LinkedListQueuepush()pop() <p></p> <p></p> <p></p> <p> Рисунок 5-5   Операции enqueue и dequeue в реализации очереди на связном списке </p> <p>Ниже приведен код реализации очереди на связном списке:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linkedlist_queue.py<pre><code>class LinkedListQueue:\n    \"\"\"Очередь на основе связного списка\"\"\"\n\n    def __init__(self):\n        \"\"\"Конструктор\"\"\"\n        self._front: ListNode | None = None  # Головной узел front\n        self._rear: ListNode | None = None  # Хвостовой узел rear\n        self._size: int = 0\n\n    def size(self) -&gt; int:\n        \"\"\"Получение длины очереди\"\"\"\n        return self._size\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"Проверка, пуста ли очередь\"\"\"\n        return self._size == 0\n\n    def push(self, num: int):\n        \"\"\"Поместить в очередь\"\"\"\n        # Добавить num после хвостового узла\n        node = ListNode(num)\n        # Если очередь пуста, сделать так, чтобы и head, и tail указывали на этот узел\n        if self._front is None:\n            self._front = node\n            self._rear = node\n        # Если очередь не пуста, добавить этот узел после хвостового узла\n        else:\n            self._rear.next = node\n            self._rear = node\n        self._size += 1\n\n    def pop(self) -&gt; int:\n        \"\"\"Извлечь из очереди\"\"\"\n        num = self.peek()\n        # Удалить головной узел\n        self._front = self._front.next\n        self._size -= 1\n        return num\n\n    def peek(self) -&gt; int:\n        \"\"\"Доступ к элементу в начале очереди\"\"\"\n        if self.is_empty():\n            raise IndexError(\"очередь пуста\")\n        return self._front.val\n\n    def to_list(self) -&gt; list[int]:\n        \"\"\"Преобразовать в список для вывода\"\"\"\n        queue = []\n        temp = self._front\n        while temp:\n            queue.append(temp.val)\n            temp = temp.next\n        return queue\n</code></pre> linkedlist_queue.cpp<pre><code>/* Очередь на основе связного списка */\nclass LinkedListQueue {\n  private:\n    ListNode *front, *rear; // Головной узел front, хвостовой узел rear\n    int queSize;\n\n  public:\n    LinkedListQueue() {\n        front = nullptr;\n        rear = nullptr;\n        queSize = 0;\n    }\n\n    ~LinkedListQueue() {\n        // Обходить связный список, удалять узлы и освобождать память\n        freeMemoryLinkedList(front);\n    }\n\n    /* Получение длины очереди */\n    int size() {\n        return queSize;\n    }\n\n    /* Проверка, пуста ли очередь */\n    bool isEmpty() {\n        return queSize == 0;\n    }\n\n    /* Поместить в очередь */\n    void push(int num) {\n        // Добавить num после хвостового узла\n        ListNode *node = new ListNode(num);\n        // Если очередь пуста, сделать так, чтобы и head, и tail указывали на этот узел\n        if (front == nullptr) {\n            front = node;\n            rear = node;\n        }\n        // Если очередь не пуста, добавить этот узел после хвостового узла\n        else {\n            rear-&gt;next = node;\n            rear = node;\n        }\n        queSize++;\n    }\n\n    /* Извлечь из очереди */\n    int pop() {\n        int num = peek();\n        // Удалить головной узел\n        ListNode *tmp = front;\n        front = front-&gt;next;\n        // Освободить память\n        delete tmp;\n        queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    int peek() {\n        if (size() == 0)\n            throw out_of_range(\"очередь пуста\");\n        return front-&gt;val;\n    }\n\n    /* Преобразовать связный список в Vector и вернуть */\n    vector&lt;int&gt; toVector() {\n        ListNode *node = front;\n        vector&lt;int&gt; res(size());\n        for (int i = 0; i &lt; res.size(); i++) {\n            res[i] = node-&gt;val;\n            node = node-&gt;next;\n        }\n        return res;\n    }\n};\n</code></pre> linkedlist_queue.java<pre><code>/* Очередь на основе связного списка */\nclass LinkedListQueue {\n    private ListNode front, rear; // Головной узел front, хвостовой узел rear\n    private int queSize = 0;\n\n    public LinkedListQueue() {\n        front = null;\n        rear = null;\n    }\n\n    /* Получение длины очереди */\n    public int size() {\n        return queSize;\n    }\n\n    /* Проверка, пуста ли очередь */\n    public boolean isEmpty() {\n        return size() == 0;\n    }\n\n    /* Поместить в очередь */\n    public void push(int num) {\n        // Добавить num после хвостового узла\n        ListNode node = new ListNode(num);\n        // Если очередь пуста, сделать так, чтобы и head, и tail указывали на этот узел\n        if (front == null) {\n            front = node;\n            rear = node;\n        // Если очередь не пуста, добавить этот узел после хвостового узла\n        } else {\n            rear.next = node;\n            rear = node;\n        }\n        queSize++;\n    }\n\n    /* Извлечь из очереди */\n    public int pop() {\n        int num = peek();\n        // Удалить головной узел\n        front = front.next;\n        queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    public int peek() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return front.val;\n    }\n\n    /* Преобразовать связный список в Array и вернуть */\n    public int[] toArray() {\n        ListNode node = front;\n        int[] res = new int[size()];\n        for (int i = 0; i &lt; res.length; i++) {\n            res[i] = node.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_queue.cs<pre><code>/* Очередь на основе связного списка */\nclass LinkedListQueue {\n    ListNode? front, rear;  // Головной узел front, хвостовой узел rear\n    int queSize = 0;\n\n    public LinkedListQueue() {\n        front = null;\n        rear = null;\n    }\n\n    /* Получение длины очереди */\n    public int Size() {\n        return queSize;\n    }\n\n    /* Проверка, пуста ли очередь */\n    public bool IsEmpty() {\n        return Size() == 0;\n    }\n\n    /* Поместить в очередь */\n    public void Push(int num) {\n        // Добавить num после хвостового узла\n        ListNode node = new(num);\n        // Если очередь пуста, сделать так, чтобы и head, и tail указывали на этот узел\n        if (front == null) {\n            front = node;\n            rear = node;\n            // Если очередь не пуста, добавить этот узел после хвостового узла\n        } else if (rear != null) {\n            rear.next = node;\n            rear = node;\n        }\n        queSize++;\n    }\n\n    /* Извлечь из очереди */\n    public int Pop() {\n        int num = Peek();\n        // Удалить головной узел\n        front = front?.next;\n        queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    public int Peek() {\n        if (IsEmpty())\n            throw new Exception();\n        return front!.val;\n    }\n\n    /* Преобразовать связный список в Array и вернуть */\n    public int[] ToArray() {\n        if (front == null)\n            return [];\n\n        ListNode? node = front;\n        int[] res = new int[Size()];\n        for (int i = 0; i &lt; res.Length; i++) {\n            res[i] = node!.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_queue.go<pre><code>/* Очередь на основе связного списка */\ntype linkedListQueue struct {\n    // Использовать встроенный пакет list для реализации очереди\n    data *list.List\n}\n\n/* Инициализация очереди */\nfunc newLinkedListQueue() *linkedListQueue {\n    return &amp;linkedListQueue{\n        data: list.New(),\n    }\n}\n\n/* Поместить в очередь */\nfunc (s *linkedListQueue) push(value any) {\n    s.data.PushBack(value)\n}\n\n/* Извлечь из очереди */\nfunc (s *linkedListQueue) pop() any {\n    if s.isEmpty() {\n        return nil\n    }\n    e := s.data.Front()\n    s.data.Remove(e)\n    return e.Value\n}\n\n/* Доступ к элементу в начале очереди */\nfunc (s *linkedListQueue) peek() any {\n    if s.isEmpty() {\n        return nil\n    }\n    e := s.data.Front()\n    return e.Value\n}\n\n/* Получение длины очереди */\nfunc (s *linkedListQueue) size() int {\n    return s.data.Len()\n}\n\n/* Проверка, пуста ли очередь */\nfunc (s *linkedListQueue) isEmpty() bool {\n    return s.data.Len() == 0\n}\n\n/* Получить List для вывода */\nfunc (s *linkedListQueue) toList() *list.List {\n    return s.data\n}\n</code></pre> linkedlist_queue.swift<pre><code>/* Очередь на основе связного списка */\nclass LinkedListQueue {\n    private var front: ListNode? // Головной узел\n    private var rear: ListNode? // Хвостовой узел\n    private var _size: Int\n\n    init() {\n        _size = 0\n    }\n\n    /* Получение длины очереди */\n    func size() -&gt; Int {\n        _size\n    }\n\n    /* Проверка, пуста ли очередь */\n    func isEmpty() -&gt; Bool {\n        size() == 0\n    }\n\n    /* Поместить в очередь */\n    func push(num: Int) {\n        // Добавить num после хвостового узла\n        let node = ListNode(x: num)\n        // Если очередь пуста, сделать так, чтобы и head, и tail указывали на этот узел\n        if front == nil {\n            front = node\n            rear = node\n        }\n        // Если очередь не пуста, добавить этот узел после хвостового узла\n        else {\n            rear?.next = node\n            rear = node\n        }\n        _size += 1\n    }\n\n    /* Извлечь из очереди */\n    @discardableResult\n    func pop() -&gt; Int {\n        let num = peek()\n        // Удалить головной узел\n        front = front?.next\n        _size -= 1\n        return num\n    }\n\n    /* Доступ к элементу в начале очереди */\n    func peek() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"очередь пуста\")\n        }\n        return front!.val\n    }\n\n    /* Преобразовать связный список в Array и вернуть */\n    func toArray() -&gt; [Int] {\n        var node = front\n        var res = Array(repeating: 0, count: size())\n        for i in res.indices {\n            res[i] = node!.val\n            node = node?.next\n        }\n        return res\n    }\n}\n</code></pre> linkedlist_queue.js<pre><code>/* Очередь на основе связного списка */\nclass LinkedListQueue {\n    #front; // Головной узел #front\n    #rear; // Хвостовой узел #rear\n    #queSize = 0;\n\n    constructor() {\n        this.#front = null;\n        this.#rear = null;\n    }\n\n    /* Получение длины очереди */\n    get size() {\n        return this.#queSize;\n    }\n\n    /* Проверка, пуста ли очередь */\n    isEmpty() {\n        return this.size === 0;\n    }\n\n    /* Поместить в очередь */\n    push(num) {\n        // Добавить num после хвостового узла\n        const node = new ListNode(num);\n        // Если очередь пуста, сделать так, чтобы и head, и tail указывали на этот узел\n        if (!this.#front) {\n            this.#front = node;\n            this.#rear = node;\n            // Если очередь не пуста, добавить этот узел после хвостового узла\n        } else {\n            this.#rear.next = node;\n            this.#rear = node;\n        }\n        this.#queSize++;\n    }\n\n    /* Извлечь из очереди */\n    pop() {\n        const num = this.peek();\n        // Удалить головной узел\n        this.#front = this.#front.next;\n        this.#queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    peek() {\n        if (this.size === 0) throw new Error('очередь пуста');\n        return this.#front.val;\n    }\n\n    /* Преобразовать связный список в Array и вернуть */\n    toArray() {\n        let node = this.#front;\n        const res = new Array(this.size);\n        for (let i = 0; i &lt; res.length; i++) {\n            res[i] = node.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_queue.ts<pre><code>/* Очередь на основе связного списка */\nclass LinkedListQueue {\n    private front: ListNode | null; // Головной узел front\n    private rear: ListNode | null; // Хвостовой узел rear\n    private queSize: number = 0;\n\n    constructor() {\n        this.front = null;\n        this.rear = null;\n    }\n\n    /* Получение длины очереди */\n    get size(): number {\n        return this.queSize;\n    }\n\n    /* Проверка, пуста ли очередь */\n    isEmpty(): boolean {\n        return this.size === 0;\n    }\n\n    /* Поместить в очередь */\n    push(num: number): void {\n        // Добавить num после хвостового узла\n        const node = new ListNode(num);\n        // Если очередь пуста, сделать так, чтобы и head, и tail указывали на этот узел\n        if (!this.front) {\n            this.front = node;\n            this.rear = node;\n            // Если очередь не пуста, добавить этот узел после хвостового узла\n        } else {\n            this.rear!.next = node;\n            this.rear = node;\n        }\n        this.queSize++;\n    }\n\n    /* Извлечь из очереди */\n    pop(): number {\n        const num = this.peek();\n        if (!this.front) throw new Error('очередь пуста');\n        // Удалить головной узел\n        this.front = this.front.next;\n        this.queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    peek(): number {\n        if (this.size === 0) throw new Error('очередь пуста');\n        return this.front!.val;\n    }\n\n    /* Преобразовать связный список в Array и вернуть */\n    toArray(): number[] {\n        let node = this.front;\n        const res = new Array&lt;number&gt;(this.size);\n        for (let i = 0; i &lt; res.length; i++) {\n            res[i] = node!.val;\n            node = node!.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_queue.dart<pre><code>/* Очередь на основе связного списка */\nclass LinkedListQueue {\n  ListNode? _front; // Головной узел _front\n  ListNode? _rear; // Хвостовой узел _rear\n  int _queSize = 0; // Длина очереди\n\n  LinkedListQueue() {\n    _front = null;\n    _rear = null;\n  }\n\n  /* Получение длины очереди */\n  int size() {\n    return _queSize;\n  }\n\n  /* Проверка, пуста ли очередь */\n  bool isEmpty() {\n    return _queSize == 0;\n  }\n\n  /* Поместить в очередь */\n  void push(int _num) {\n    // Добавить _num после хвостового узла\n    final node = ListNode(_num);\n    // Если очередь пуста, сделать так, чтобы и head, и tail указывали на этот узел\n    if (_front == null) {\n      _front = node;\n      _rear = node;\n    } else {\n      // Если очередь не пуста, добавить этот узел после хвостового узла\n      _rear!.next = node;\n      _rear = node;\n    }\n    _queSize++;\n  }\n\n  /* Извлечь из очереди */\n  int pop() {\n    final int _num = peek();\n    // Удалить головной узел\n    _front = _front!.next;\n    _queSize--;\n    return _num;\n  }\n\n  /* Доступ к элементу в начале очереди */\n  int peek() {\n    if (_queSize == 0) {\n      throw Exception('очередь пуста');\n    }\n    return _front!.val;\n  }\n\n  /* Преобразовать связный список в Array и вернуть */\n  List&lt;int&gt; toArray() {\n    ListNode? node = _front;\n    final List&lt;int&gt; queue = [];\n    while (node != null) {\n      queue.add(node.val);\n      node = node.next;\n    }\n    return queue;\n  }\n}\n</code></pre> linkedlist_queue.rs<pre><code>/* Очередь на основе связного списка */\n#[allow(dead_code)]\npub struct LinkedListQueue&lt;T&gt; {\n    front: Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;, // Головной узел front\n    rear: Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;,  // Хвостовой узел rear\n    que_size: usize,                         // Длина очереди\n}\n\nimpl&lt;T: Copy&gt; LinkedListQueue&lt;T&gt; {\n    pub fn new() -&gt; Self {\n        Self {\n            front: None,\n            rear: None,\n            que_size: 0,\n        }\n    }\n\n    /* Получение длины очереди */\n    pub fn size(&amp;self) -&gt; usize {\n        return self.que_size;\n    }\n\n    /* Проверка, пуста ли очередь */\n    pub fn is_empty(&amp;self) -&gt; bool {\n        return self.que_size == 0;\n    }\n\n    /* Поместить в очередь */\n    pub fn push(&amp;mut self, num: T) {\n        // Добавить num после хвостового узла\n        let new_rear = ListNode::new(num);\n        match self.rear.take() {\n            // Если очередь не пуста, добавить этот узел после хвостового узла\n            Some(old_rear) =&gt; {\n                old_rear.borrow_mut().next = Some(new_rear.clone());\n                self.rear = Some(new_rear);\n            }\n            // Если очередь пуста, сделать так, чтобы и head, и tail указывали на этот узел\n            None =&gt; {\n                self.front = Some(new_rear.clone());\n                self.rear = Some(new_rear);\n            }\n        }\n        self.que_size += 1;\n    }\n\n    /* Извлечь из очереди */\n    pub fn pop(&amp;mut self) -&gt; Option&lt;T&gt; {\n        self.front.take().map(|old_front| {\n            match old_front.borrow_mut().next.take() {\n                Some(new_front) =&gt; {\n                    self.front = Some(new_front);\n                }\n                None =&gt; {\n                    self.rear.take();\n                }\n            }\n            self.que_size -= 1;\n            old_front.borrow().val\n        })\n    }\n\n    /* Доступ к элементу в начале очереди */\n    pub fn peek(&amp;self) -&gt; Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt; {\n        self.front.as_ref()\n    }\n\n    /* Преобразовать связный список в Array и вернуть */\n    pub fn to_array(&amp;self, head: Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;) -&gt; Vec&lt;T&gt; {\n        let mut res: Vec&lt;T&gt; = Vec::new();\n\n        fn recur&lt;T: Copy&gt;(cur: Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;, res: &amp;mut Vec&lt;T&gt;) {\n            if let Some(cur) = cur {\n                res.push(cur.borrow().val);\n                recur(cur.borrow().next.as_ref(), res);\n            }\n        }\n\n        recur(head, &amp;mut res);\n\n        res\n    }\n}\n</code></pre> linkedlist_queue.c<pre><code>/* Очередь на основе связного списка */\ntypedef struct {\n    ListNode *front, *rear;\n    int queSize;\n} LinkedListQueue;\n\n/* Конструктор */\nLinkedListQueue *newLinkedListQueue() {\n    LinkedListQueue *queue = (LinkedListQueue *)malloc(sizeof(LinkedListQueue));\n    queue-&gt;front = NULL;\n    queue-&gt;rear = NULL;\n    queue-&gt;queSize = 0;\n    return queue;\n}\n\n/* Деструктор */\nvoid delLinkedListQueue(LinkedListQueue *queue) {\n    // Освободить все узлы\n    while (queue-&gt;front != NULL) {\n        ListNode *tmp = queue-&gt;front;\n        queue-&gt;front = queue-&gt;front-&gt;next;\n        free(tmp);\n    }\n    // Освободить структуру queue\n    free(queue);\n}\n\n/* Получение длины очереди */\nint size(LinkedListQueue *queue) {\n    return queue-&gt;queSize;\n}\n\n/* Проверка, пуста ли очередь */\nbool empty(LinkedListQueue *queue) {\n    return (size(queue) == 0);\n}\n\n/* Поместить в очередь */\nvoid push(LinkedListQueue *queue, int num) {\n    // Добавить node в хвост\n    ListNode *node = newListNode(num);\n    // Если очередь пуста, сделать так, чтобы и head, и tail указывали на этот узел\n    if (queue-&gt;front == NULL) {\n        queue-&gt;front = node;\n        queue-&gt;rear = node;\n    }\n    // Если очередь не пуста, добавить этот узел после хвостового узла\n    else {\n        queue-&gt;rear-&gt;next = node;\n        queue-&gt;rear = node;\n    }\n    queue-&gt;queSize++;\n}\n\n/* Доступ к элементу в начале очереди */\nint peek(LinkedListQueue *queue) {\n    assert(size(queue) &amp;&amp; queue-&gt;front);\n    return queue-&gt;front-&gt;val;\n}\n\n/* Извлечь из очереди */\nint pop(LinkedListQueue *queue) {\n    int num = peek(queue);\n    ListNode *tmp = queue-&gt;front;\n    queue-&gt;front = queue-&gt;front-&gt;next;\n    free(tmp);\n    queue-&gt;queSize--;\n    return num;\n}\n\n/* Вывести очередь */\nvoid printLinkedListQueue(LinkedListQueue *queue) {\n    int *arr = malloc(sizeof(int) * queue-&gt;queSize);\n    // Скопировать данные связного списка в массив\n    int i;\n    ListNode *node;\n    for (i = 0, node = queue-&gt;front; i &lt; queue-&gt;queSize; i++) {\n        arr[i] = node-&gt;val;\n        node = node-&gt;next;\n    }\n    printArray(arr, queue-&gt;queSize);\n    free(arr);\n}\n</code></pre> linkedlist_queue.kt<pre><code>/* Очередь на основе связного списка */\nclass LinkedListQueue(\n    // Головной узел front, хвостовой узел rear\n    private var front: ListNode? = null,\n    private var rear: ListNode? = null,\n    private var queSize: Int = 0\n) {\n\n    /* Получение длины очереди */\n    fun size(): Int {\n        return queSize\n    }\n\n    /* Проверка, пуста ли очередь */\n    fun isEmpty(): Boolean {\n        return size() == 0\n    }\n\n    /* Поместить в очередь */\n    fun push(num: Int) {\n        // Добавить num после хвостового узла\n        val node = ListNode(num)\n        // Если очередь пуста, сделать так, чтобы и head, и tail указывали на этот узел\n        if (front == null) {\n            front = node\n            rear = node\n            // Если очередь не пуста, добавить этот узел после хвостового узла\n        } else {\n            rear?.next = node\n            rear = node\n        }\n        queSize++\n    }\n\n    /* Извлечь из очереди */\n    fun pop(): Int {\n        val num = peek()\n        // Удалить головной узел\n        front = front?.next\n        queSize--\n        return num\n    }\n\n    /* Доступ к элементу в начале очереди */\n    fun peek(): Int {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        return front!!._val\n    }\n\n    /* Преобразовать связный список в Array и вернуть */\n    fun toArray(): IntArray {\n        var node = front\n        val res = IntArray(size())\n        for (i in res.indices) {\n            res[i] = node!!._val\n            node = node.next\n        }\n        return res\n    }\n}\n</code></pre> linkedlist_queue.rb<pre><code>### Очередь на основе связного списка ###\nclass LinkedListQueue\n  ### Получение длины очереди ###\n  attr_reader :size\n\n  ### Конструктор ###\n  def initialize\n    @front = nil  # Головной узел front\n    @rear = nil   # Хвостовой узел rear\n    @size = 0\n  end\n\n  ### Проверка, пуста ли очередь ###\n  def is_empty?\n    @front.nil?\n  end\n\n  ### Добавление в очередь ###\n  def push(num)\n    # Добавить num после хвостового узла\n    node = ListNode.new(num)\n\n    # Если очередь пуста, сделать так, чтобы и head, и tail указывали на этот узел\n    if @front.nil?\n      @front = node\n      @rear = node\n    # Если очередь не пуста, добавить этот узел после хвостового узла\n    else\n      @rear.next = node\n      @rear = node\n    end\n\n    @size += 1\n  end\n\n  ### Извлечение из очереди ###\n  def pop\n    num = peek\n    # Удалить головной узел\n    @front = @front.next\n    @size -= 1\n    num\n  end\n\n  ### Доступ к элементу в начале очереди ###\n  def peek\n    raise IndexError, 'очередь пуста' if is_empty?\n\n    @front.val\n  end\n\n  ### Преобразовать связный список в Array и вернуть ###\n  def to_array\n    queue = []\n    temp = @front\n    while temp\n      queue &lt;&lt; temp.val\n      temp = temp.next\n    end\n    queue\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 5. Стек и очередь","5.2 &nbsp; Очередь"],"tags":[]},{"location":"chapter_stack_and_queue/queue/#2","level":3,"title":"2.   Реализация на основе массива","text":"<p>Удаление первого элемента из массива имеет временную сложность \\(O(n)\\) , из-за чего операция <code>dequeue</code> оказывается неэффективной. Однако этого можно избежать с помощью следующего приема.</p> <p>Мы можем использовать переменную <code>front</code> , указывающую на индекс элемента в голове очереди, и поддерживать переменную <code>size</code> , которая хранит длину очереди. Определим <code>rear = front + size</code> ; эта формула дает позицию <code>rear</code>, указывающую на ячейку сразу после хвоста очереди.</p> <p>Исходя из этого, эффективный диапазон элементов массива равен <code>[front, rear - 1]</code>, а различные операции реализуются, как показано на рисунке 5-6.</p> <ul> <li>Операция <code>enqueue</code>: записать входной элемент по индексу <code>rear</code> и увеличить <code>size</code> на 1.</li> <li>Операция <code>dequeue</code>: просто увеличить <code>front</code> на 1 и уменьшить <code>size</code> на 1.</li> </ul> <p>Можно увидеть, что и <code>enqueue</code> , и <code>dequeue</code> требуют всего одной операции, а значит обе имеют временную сложность \\(O(1)\\) .</p> ArrayQueuepush()pop() <p></p> <p></p> <p></p> <p> Рисунок 5-6   Операции enqueue и dequeue в реализации очереди на массиве </p> <p>Ты можешь заметить еще одну проблему: при непрерывных операциях <code>enqueue</code> и <code>dequeue</code> значения <code>front</code> и <code>rear</code> оба движутся вправо, и когда они доходят до конца массива, дальше сдвигаться уже нельзя. Чтобы решить эту проблему, можно рассматривать массив как кольцевой массив, у которого начало и конец соединены.</p> <p>Для кольцевого массива нужно сделать так, чтобы <code>front</code> или <code>rear</code>, перешагнув конец массива, сразу возвращались к его началу и продолжали движение. Такую периодичность удобно реализовать с помощью операции взятия остатка, как показано в коде ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array_queue.py<pre><code>class ArrayQueue:\n    \"\"\"Очередь на основе кольцевого массива\"\"\"\n\n    def __init__(self, size: int):\n        \"\"\"Конструктор\"\"\"\n        self._nums: list[int] = [0] * size  # Массив для хранения элементов очереди\n        self._front: int = 0  # Указатель head, указывающий на первый элемент очереди\n        self._size: int = 0  # Длина очереди\n\n    def capacity(self) -&gt; int:\n        \"\"\"Получить вместимость очереди\"\"\"\n        return len(self._nums)\n\n    def size(self) -&gt; int:\n        \"\"\"Получение длины очереди\"\"\"\n        return self._size\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"Проверка, пуста ли очередь\"\"\"\n        return self._size == 0\n\n    def push(self, num: int):\n        \"\"\"Поместить в очередь\"\"\"\n        if self._size == self.capacity():\n            raise IndexError(\"очередь заполнена\")\n        # Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        # С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n        rear: int = (self._front + self._size) % self.capacity()\n        # Добавить num в хвост очереди\n        self._nums[rear] = num\n        self._size += 1\n\n    def pop(self) -&gt; int:\n        \"\"\"Извлечь из очереди\"\"\"\n        num: int = self.peek()\n        # Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n        self._front = (self._front + 1) % self.capacity()\n        self._size -= 1\n        return num\n\n    def peek(self) -&gt; int:\n        \"\"\"Доступ к элементу в начале очереди\"\"\"\n        if self.is_empty():\n            raise IndexError(\"очередь пуста\")\n        return self._nums[self._front]\n\n    def to_list(self) -&gt; list[int]:\n        \"\"\"Вернуть список для вывода\"\"\"\n        res = [0] * self.size()\n        j: int = self._front\n        for i in range(self.size()):\n            res[i] = self._nums[(j % self.capacity())]\n            j += 1\n        return res\n</code></pre> array_queue.cpp<pre><code>/* Очередь на основе кольцевого массива */\nclass ArrayQueue {\n  private:\n    int *nums;       // Массив для хранения элементов очереди\n    int front;       // Указатель head, указывающий на первый элемент очереди\n    int queSize;     // Длина очереди\n    int queCapacity; // Вместимость очереди\n\n  public:\n    ArrayQueue(int capacity) {\n        // Инициализация массива\n        nums = new int[capacity];\n        queCapacity = capacity;\n        front = queSize = 0;\n    }\n\n    ~ArrayQueue() {\n        delete[] nums;\n    }\n\n    /* Получить вместимость очереди */\n    int capacity() {\n        return queCapacity;\n    }\n\n    /* Получение длины очереди */\n    int size() {\n        return queSize;\n    }\n\n    /* Проверка, пуста ли очередь */\n    bool isEmpty() {\n        return size() == 0;\n    }\n\n    /* Поместить в очередь */\n    void push(int num) {\n        if (queSize == queCapacity) {\n            cout &lt;&lt; \"Очередь заполнена\" &lt;&lt; endl;\n            return;\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        // С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n        int rear = (front + queSize) % queCapacity;\n        // Добавить num в хвост очереди\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* Извлечь из очереди */\n    int pop() {\n        int num = peek();\n        // Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n        front = (front + 1) % queCapacity;\n        queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    int peek() {\n        if (isEmpty())\n            throw out_of_range(\"очередь пуста\");\n        return nums[front];\n    }\n\n    /* Преобразовать массив в Vector и вернуть */\n    vector&lt;int&gt; toVector() {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        vector&lt;int&gt; arr(queSize);\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            arr[i] = nums[j % queCapacity];\n        }\n        return arr;\n    }\n};\n</code></pre> array_queue.java<pre><code>/* Очередь на основе кольцевого массива */\nclass ArrayQueue {\n    private int[] nums; // Массив для хранения элементов очереди\n    private int front; // Указатель head, указывающий на первый элемент очереди\n    private int queSize; // Длина очереди\n\n    public ArrayQueue(int capacity) {\n        nums = new int[capacity];\n        front = queSize = 0;\n    }\n\n    /* Получить вместимость очереди */\n    public int capacity() {\n        return nums.length;\n    }\n\n    /* Получение длины очереди */\n    public int size() {\n        return queSize;\n    }\n\n    /* Проверка, пуста ли очередь */\n    public boolean isEmpty() {\n        return queSize == 0;\n    }\n\n    /* Поместить в очередь */\n    public void push(int num) {\n        if (queSize == capacity()) {\n            System.out.println(\"Очередь заполнена\");\n            return;\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        // С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n        int rear = (front + queSize) % capacity();\n        // Добавить num в хвост очереди\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* Извлечь из очереди */\n    public int pop() {\n        int num = peek();\n        // Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n        front = (front + 1) % capacity();\n        queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    public int peek() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return nums[front];\n    }\n\n    /* Вернуть массив */\n    public int[] toArray() {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        int[] res = new int[queSize];\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            res[i] = nums[j % capacity()];\n        }\n        return res;\n    }\n}\n</code></pre> array_queue.cs<pre><code>/* Очередь на основе кольцевого массива */\nclass ArrayQueue {\n    int[] nums;  // Массив для хранения элементов очереди\n    int front;   // Указатель head, указывающий на первый элемент очереди\n    int queSize; // Длина очереди\n\n    public ArrayQueue(int capacity) {\n        nums = new int[capacity];\n        front = queSize = 0;\n    }\n\n    /* Получить вместимость очереди */\n    int Capacity() {\n        return nums.Length;\n    }\n\n    /* Получение длины очереди */\n    public int Size() {\n        return queSize;\n    }\n\n    /* Проверка, пуста ли очередь */\n    public bool IsEmpty() {\n        return queSize == 0;\n    }\n\n    /* Поместить в очередь */\n    public void Push(int num) {\n        if (queSize == Capacity()) {\n            Console.WriteLine(\"Очередь заполнена\");\n            return;\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        // С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n        int rear = (front + queSize) % Capacity();\n        // Добавить num в хвост очереди\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* Извлечь из очереди */\n    public int Pop() {\n        int num = Peek();\n        // Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n        front = (front + 1) % Capacity();\n        queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    public int Peek() {\n        if (IsEmpty())\n            throw new Exception();\n        return nums[front];\n    }\n\n    /* Вернуть массив */\n    public int[] ToArray() {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        int[] res = new int[queSize];\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            res[i] = nums[j % this.Capacity()];\n        }\n        return res;\n    }\n}\n</code></pre> array_queue.go<pre><code>/* Очередь на основе кольцевого массива */\ntype arrayQueue struct {\n    nums        []int // Массив для хранения элементов очереди\n    front       int   // Указатель head, указывающий на первый элемент очереди\n    queSize     int   // Длина очереди\n    queCapacity int   // Вместимость очереди (то есть максимальное число элементов)\n}\n\n/* Инициализация очереди */\nfunc newArrayQueue(queCapacity int) *arrayQueue {\n    return &amp;arrayQueue{\n        nums:        make([]int, queCapacity),\n        queCapacity: queCapacity,\n        front:       0,\n        queSize:     0,\n    }\n}\n\n/* Получение длины очереди */\nfunc (q *arrayQueue) size() int {\n    return q.queSize\n}\n\n/* Проверка, пуста ли очередь */\nfunc (q *arrayQueue) isEmpty() bool {\n    return q.queSize == 0\n}\n\n/* Поместить в очередь */\nfunc (q *arrayQueue) push(num int) {\n    // Когда rear == queCapacity, очередь заполнена\n    if q.queSize == q.queCapacity {\n        return\n    }\n    // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n    // С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n    rear := (q.front + q.queSize) % q.queCapacity\n    // Добавить num в хвост очереди\n    q.nums[rear] = num\n    q.queSize++\n}\n\n/* Извлечь из очереди */\nfunc (q *arrayQueue) pop() any {\n    num := q.peek()\n    if num == nil {\n        return nil\n    }\n\n    // Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n    q.front = (q.front + 1) % q.queCapacity\n    q.queSize--\n    return num\n}\n\n/* Доступ к элементу в начале очереди */\nfunc (q *arrayQueue) peek() any {\n    if q.isEmpty() {\n        return nil\n    }\n    return q.nums[q.front]\n}\n\n/* Получить Slice для вывода */\nfunc (q *arrayQueue) toSlice() []int {\n    rear := (q.front + q.queSize)\n    if rear &gt;= q.queCapacity {\n        rear %= q.queCapacity\n        return append(q.nums[q.front:], q.nums[:rear]...)\n    }\n    return q.nums[q.front:rear]\n}\n</code></pre> array_queue.swift<pre><code>/* Очередь на основе кольцевого массива */\nclass ArrayQueue {\n    private var nums: [Int] // Массив для хранения элементов очереди\n    private var front: Int // Указатель head, указывающий на первый элемент очереди\n    private var _size: Int // Длина очереди\n\n    init(capacity: Int) {\n        // Инициализация массива\n        nums = Array(repeating: 0, count: capacity)\n        front = 0\n        _size = 0\n    }\n\n    /* Получить вместимость очереди */\n    func capacity() -&gt; Int {\n        nums.count\n    }\n\n    /* Получение длины очереди */\n    func size() -&gt; Int {\n        _size\n    }\n\n    /* Проверка, пуста ли очередь */\n    func isEmpty() -&gt; Bool {\n        size() == 0\n    }\n\n    /* Поместить в очередь */\n    func push(num: Int) {\n        if size() == capacity() {\n            print(\"Очередь заполнена\")\n            return\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        // С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n        let rear = (front + size()) % capacity()\n        // Добавить num в хвост очереди\n        nums[rear] = num\n        _size += 1\n    }\n\n    /* Извлечь из очереди */\n    @discardableResult\n    func pop() -&gt; Int {\n        let num = peek()\n        // Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n        front = (front + 1) % capacity()\n        _size -= 1\n        return num\n    }\n\n    /* Доступ к элементу в начале очереди */\n    func peek() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"очередь пуста\")\n        }\n        return nums[front]\n    }\n\n    /* Вернуть массив */\n    func toArray() -&gt; [Int] {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        (front ..&lt; front + size()).map { nums[$0 % capacity()] }\n    }\n}\n</code></pre> array_queue.js<pre><code>/* Очередь на основе кольцевого массива */\nclass ArrayQueue {\n    #nums; // Массив для хранения элементов очереди\n    #front = 0; // Указатель head, указывающий на первый элемент очереди\n    #queSize = 0; // Длина очереди\n\n    constructor(capacity) {\n        this.#nums = new Array(capacity);\n    }\n\n    /* Получить вместимость очереди */\n    get capacity() {\n        return this.#nums.length;\n    }\n\n    /* Получение длины очереди */\n    get size() {\n        return this.#queSize;\n    }\n\n    /* Проверка, пуста ли очередь */\n    isEmpty() {\n        return this.#queSize === 0;\n    }\n\n    /* Поместить в очередь */\n    push(num) {\n        if (this.size === this.capacity) {\n            console.log('Очередь заполнена');\n            return;\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        // С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n        const rear = (this.#front + this.size) % this.capacity;\n        // Добавить num в хвост очереди\n        this.#nums[rear] = num;\n        this.#queSize++;\n    }\n\n    /* Извлечь из очереди */\n    pop() {\n        const num = this.peek();\n        // Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n        this.#front = (this.#front + 1) % this.capacity;\n        this.#queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    peek() {\n        if (this.isEmpty()) throw new Error('очередь пуста');\n        return this.#nums[this.#front];\n    }\n\n    /* Вернуть Array */\n    toArray() {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        const arr = new Array(this.size);\n        for (let i = 0, j = this.#front; i &lt; this.size; i++, j++) {\n            arr[i] = this.#nums[j % this.capacity];\n        }\n        return arr;\n    }\n}\n</code></pre> array_queue.ts<pre><code>/* Очередь на основе кольцевого массива */\nclass ArrayQueue {\n    private nums: number[]; // Массив для хранения элементов очереди\n    private front: number; // Указатель head, указывающий на первый элемент очереди\n    private queSize: number; // Длина очереди\n\n    constructor(capacity: number) {\n        this.nums = new Array(capacity);\n        this.front = this.queSize = 0;\n    }\n\n    /* Получить вместимость очереди */\n    get capacity(): number {\n        return this.nums.length;\n    }\n\n    /* Получение длины очереди */\n    get size(): number {\n        return this.queSize;\n    }\n\n    /* Проверка, пуста ли очередь */\n    isEmpty(): boolean {\n        return this.queSize === 0;\n    }\n\n    /* Поместить в очередь */\n    push(num: number): void {\n        if (this.size === this.capacity) {\n            console.log('Очередь заполнена');\n            return;\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        // С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n        const rear = (this.front + this.queSize) % this.capacity;\n        // Добавить num в хвост очереди\n        this.nums[rear] = num;\n        this.queSize++;\n    }\n\n    /* Извлечь из очереди */\n    pop(): number {\n        const num = this.peek();\n        // Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n        this.front = (this.front + 1) % this.capacity;\n        this.queSize--;\n        return num;\n    }\n\n    /* Доступ к элементу в начале очереди */\n    peek(): number {\n        if (this.isEmpty()) throw new Error('очередь пуста');\n        return this.nums[this.front];\n    }\n\n    /* Вернуть Array */\n    toArray(): number[] {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        const arr = new Array(this.size);\n        for (let i = 0, j = this.front; i &lt; this.size; i++, j++) {\n            arr[i] = this.nums[j % this.capacity];\n        }\n        return arr;\n    }\n}\n</code></pre> array_queue.dart<pre><code>/* Очередь на основе кольцевого массива */\nclass ArrayQueue {\n  late List&lt;int&gt; _nums; // Массив для хранения элементов очереди\n  late int _front; // Указатель head, указывающий на первый элемент очереди\n  late int _queSize; // Длина очереди\n\n  ArrayQueue(int capacity) {\n    _nums = List.filled(capacity, 0);\n    _front = _queSize = 0;\n  }\n\n  /* Получить вместимость очереди */\n  int capaCity() {\n    return _nums.length;\n  }\n\n  /* Получение длины очереди */\n  int size() {\n    return _queSize;\n  }\n\n  /* Проверка, пуста ли очередь */\n  bool isEmpty() {\n    return _queSize == 0;\n  }\n\n  /* Поместить в очередь */\n  void push(int _num) {\n    if (_queSize == capaCity()) {\n      throw Exception(\"Очередь заполнена\");\n    }\n    // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n    // С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n    int rear = (_front + _queSize) % capaCity();\n    // Добавить _num в хвост очереди\n    _nums[rear] = _num;\n    _queSize++;\n  }\n\n  /* Извлечь из очереди */\n  int pop() {\n    int _num = peek();\n    // Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n    _front = (_front + 1) % capaCity();\n    _queSize--;\n    return _num;\n  }\n\n  /* Доступ к элементу в начале очереди */\n  int peek() {\n    if (isEmpty()) {\n      throw Exception(\"очередь пуста\");\n    }\n    return _nums[_front];\n  }\n\n  /* Вернуть Array */\n  List&lt;int&gt; toArray() {\n    // Преобразовывать только элементы списка в пределах фактической длины\n    final List&lt;int&gt; res = List.filled(_queSize, 0);\n    for (int i = 0, j = _front; i &lt; _queSize; i++, j++) {\n      res[i] = _nums[j % capaCity()];\n    }\n    return res;\n  }\n}\n</code></pre> array_queue.rs<pre><code>/* Очередь на основе кольцевого массива */\nstruct ArrayQueue&lt;T&gt; {\n    nums: Vec&lt;T&gt;,      // Массив для хранения элементов очереди\n    front: i32,        // Указатель head, указывающий на первый элемент очереди\n    que_size: i32,     // Длина очереди\n    que_capacity: i32, // Вместимость очереди\n}\n\nimpl&lt;T: Copy + Default&gt; ArrayQueue&lt;T&gt; {\n    /* Конструктор */\n    fn new(capacity: i32) -&gt; ArrayQueue&lt;T&gt; {\n        ArrayQueue {\n            nums: vec![T::default(); capacity as usize],\n            front: 0,\n            que_size: 0,\n            que_capacity: capacity,\n        }\n    }\n\n    /* Получить вместимость очереди */\n    fn capacity(&amp;self) -&gt; i32 {\n        self.que_capacity\n    }\n\n    /* Получение длины очереди */\n    fn size(&amp;self) -&gt; i32 {\n        self.que_size\n    }\n\n    /* Проверка, пуста ли очередь */\n    fn is_empty(&amp;self) -&gt; bool {\n        self.que_size == 0\n    }\n\n    /* Поместить в очередь */\n    fn push(&amp;mut self, num: T) {\n        if self.que_size == self.capacity() {\n            println!(\"Очередь заполнена\");\n            return;\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        // С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n        let rear = (self.front + self.que_size) % self.que_capacity;\n        // Добавить num в хвост очереди\n        self.nums[rear as usize] = num;\n        self.que_size += 1;\n    }\n\n    /* Извлечь из очереди */\n    fn pop(&amp;mut self) -&gt; T {\n        let num = self.peek();\n        // Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n        self.front = (self.front + 1) % self.que_capacity;\n        self.que_size -= 1;\n        num\n    }\n\n    /* Доступ к элементу в начале очереди */\n    fn peek(&amp;self) -&gt; T {\n        if self.is_empty() {\n            panic!(\"index out of bounds\");\n        }\n        self.nums[self.front as usize]\n    }\n\n    /* Вернуть массив */\n    fn to_vector(&amp;self) -&gt; Vec&lt;T&gt; {\n        let cap = self.que_capacity;\n        let mut j = self.front;\n        let mut arr = vec![T::default(); cap as usize];\n        for i in 0..self.que_size {\n            arr[i as usize] = self.nums[(j % cap) as usize];\n            j += 1;\n        }\n        arr\n    }\n}\n</code></pre> array_queue.c<pre><code>/* Очередь на основе кольцевого массива */\ntypedef struct {\n    int *nums;       // Массив для хранения элементов очереди\n    int front;       // Указатель head, указывающий на первый элемент очереди\n    int queSize;     // Указатель хвоста, указывающий на позицию после хвоста\n    int queCapacity; // Вместимость очереди\n} ArrayQueue;\n\n/* Конструктор */\nArrayQueue *newArrayQueue(int capacity) {\n    ArrayQueue *queue = (ArrayQueue *)malloc(sizeof(ArrayQueue));\n    // Инициализация массива\n    queue-&gt;queCapacity = capacity;\n    queue-&gt;nums = (int *)malloc(sizeof(int) * queue-&gt;queCapacity);\n    queue-&gt;front = queue-&gt;queSize = 0;\n    return queue;\n}\n\n/* Деструктор */\nvoid delArrayQueue(ArrayQueue *queue) {\n    free(queue-&gt;nums);\n    free(queue);\n}\n\n/* Получить вместимость очереди */\nint capacity(ArrayQueue *queue) {\n    return queue-&gt;queCapacity;\n}\n\n/* Получение длины очереди */\nint size(ArrayQueue *queue) {\n    return queue-&gt;queSize;\n}\n\n/* Проверка, пуста ли очередь */\nbool empty(ArrayQueue *queue) {\n    return queue-&gt;queSize == 0;\n}\n\n/* Доступ к элементу в начале очереди */\nint peek(ArrayQueue *queue) {\n    assert(size(queue) != 0);\n    return queue-&gt;nums[queue-&gt;front];\n}\n\n/* Поместить в очередь */\nvoid push(ArrayQueue *queue, int num) {\n    if (size(queue) == capacity(queue)) {\n        printf(\"Очередь заполнена\\r\\n\");\n        return;\n    }\n    // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n    // С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n    int rear = (queue-&gt;front + queue-&gt;queSize) % queue-&gt;queCapacity;\n    // Добавить num в хвост очереди\n    queue-&gt;nums[rear] = num;\n    queue-&gt;queSize++;\n}\n\n/* Извлечь из очереди */\nint pop(ArrayQueue *queue) {\n    int num = peek(queue);\n    // Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n    queue-&gt;front = (queue-&gt;front + 1) % queue-&gt;queCapacity;\n    queue-&gt;queSize--;\n    return num;\n}\n\n/* Вернуть массив для вывода */\nint *toArray(ArrayQueue *queue, int *queSize) {\n    *queSize = queue-&gt;queSize;\n    int *res = (int *)calloc(queue-&gt;queSize, sizeof(int));\n    int j = queue-&gt;front;\n    for (int i = 0; i &lt; queue-&gt;queSize; i++) {\n        res[i] = queue-&gt;nums[j % queue-&gt;queCapacity];\n        j++;\n    }\n    return res;\n}\n</code></pre> array_queue.kt<pre><code>/* Очередь на основе кольцевого массива */\nclass ArrayQueue(capacity: Int) {\n    private val nums: IntArray = IntArray(capacity) // Массив для хранения элементов очереди\n    private var front: Int = 0 // Указатель head, указывающий на первый элемент очереди\n    private var queSize: Int = 0 // Длина очереди\n\n    /* Получить вместимость очереди */\n    fun capacity(): Int {\n        return nums.size\n    }\n\n    /* Получение длины очереди */\n    fun size(): Int {\n        return queSize\n    }\n\n    /* Проверка, пуста ли очередь */\n    fun isEmpty(): Boolean {\n        return queSize == 0\n    }\n\n    /* Поместить в очередь */\n    fun push(num: Int) {\n        if (queSize == capacity()) {\n            println(\"Очередь заполнена\")\n            return\n        }\n        // Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n        // С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n        val rear = (front + queSize) % capacity()\n        // Добавить num в хвост очереди\n        nums[rear] = num\n        queSize++\n    }\n\n    /* Извлечь из очереди */\n    fun pop(): Int {\n        val num = peek()\n        // Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n        front = (front + 1) % capacity()\n        queSize--\n        return num\n    }\n\n    /* Доступ к элементу в начале очереди */\n    fun peek(): Int {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        return nums[front]\n    }\n\n    /* Вернуть массив */\n    fun toArray(): IntArray {\n        // Преобразовывать только элементы списка в пределах фактической длины\n        val res = IntArray(queSize)\n        var i = 0\n        var j = front\n        while (i &lt; queSize) {\n            res[i] = nums[j % capacity()]\n            i++\n            j++\n        }\n        return res\n    }\n}\n</code></pre> array_queue.rb<pre><code>### Очередь на основе кольцевого массива ###\nclass ArrayQueue\n  ### Получение длины очереди ###\n  attr_reader :size\n\n  ### Конструктор ###\n  def initialize(size)\n    @nums = Array.new(size, 0) # Массив для хранения элементов очереди\n    @front = 0 # Указатель head, указывающий на первый элемент очереди\n    @size = 0 # Длина очереди\n  end\n\n  ### Получить вместимость очереди ###\n  def capacity\n    @nums.length\n  end\n\n  ### Проверка, пуста ли очередь ###\n  def is_empty?\n    size.zero?\n  end\n\n  ### Добавление в очередь ###\n  def push(num)\n    raise IndexError, 'очередь заполнена' if size == capacity\n\n    # Вычислить указатель хвоста, указывающий на индекс хвоста + 1\n    # С помощью операции взятия по модулю вернуть rear к началу после выхода за конец массива\n    rear = (@front + size) % capacity\n    # Добавить num в хвост очереди\n    @nums[rear] = num\n    @size += 1\n  end\n\n  ### Извлечение из очереди ###\n  def pop\n    num = peek\n    # Указатель head сдвигается на одну позицию назад; если он выходит за конец, то возвращается в начало массива\n    @front = (@front + 1) % capacity\n    @size -= 1\n    num\n  end\n\n  ### Доступ к элементу в начале очереди ###\n  def peek\n    raise IndexError, 'очередь пуста' if is_empty?\n\n    @nums[@front]\n  end\n\n  ### Вернуть список для вывода ###\n  def to_array\n    res = Array.new(size, 0)\n    j = @front\n\n    for i in 0...size\n      res[i] = @nums[j % capacity]\n      j += 1\n    end\n\n    res\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Даже такая реализация очереди остается ограниченной: ее длина неизменяема. Однако это несложно исправить, заменив массив на динамический массив и тем самым введя механизм расширения. Заинтересованные читатели могут попробовать реализовать это самостоятельно.</p> <p>Выводы сравнения двух реализаций в целом такие же, как и для стека, поэтому здесь мы не будем повторяться.</p>","path":["Глава 5. Стек и очередь","5.2 &nbsp; Очередь"],"tags":[]},{"location":"chapter_stack_and_queue/queue/#523","level":2,"title":"5.2.3   Типичные применения очереди","text":"<ul> <li>Очереди заказов. После оформления заказа покупателем заказ попадает в очередь, а затем система обрабатывает заказы по порядку. Во время крупных распродаж за короткое время возникает огромный поток заказов, и высокая конкурентная нагрузка становится ключевой инженерной проблемой.</li> <li>Различные отложенные задачи. Любой сценарий, где нужно реализовать принцип \"кто раньше пришел, тот раньше обслуживается\", например очередь заданий принтера или очередь блюд на кухне ресторана, хорошо моделируется очередью, которая эффективно поддерживает нужный порядок обработки.</li> </ul>","path":["Глава 5. Стек и очередь","5.2 &nbsp; Очередь"],"tags":[]},{"location":"chapter_stack_and_queue/stack/","level":1,"title":"5.1   Стек","text":"<p>Стек (stack) - это линейная структура данных, подчиняющаяся логике \"последним пришел - первым вышел\".</p> <p>Стек можно сравнить со стопкой тарелок на столе. Если разрешено перемещать только одну тарелку за раз, то, чтобы достать тарелку снизу, сначала придется по одной убрать все тарелки сверху. Если заменить тарелки различными элементами, например целыми числами, символами, объектами и т.д., получится структура данных \"стек\".</p> <p>Как показано на рисунке 5-1, верхнюю часть стопки элементов мы называем вершиной стека, а нижнюю - основанием стека. Операция добавления элемента на вершину называется <code>push</code>, а операция удаления верхнего элемента - <code>pop</code>.</p> <p></p> <p> Рисунок 5-1   Правило LIFO для стека </p>","path":["Глава 5. Стек и очередь","5.1 &nbsp; Стек"],"tags":[]},{"location":"chapter_stack_and_queue/stack/#511","level":2,"title":"5.1.1   Основные операции со стеком","text":"<p>Основные операции со стеком показаны в таблице 5-1. Конкретные имена методов зависят от используемого языка программирования. Здесь в качестве примера используются распространенные названия <code>push()</code> , <code>pop()</code> и <code>peek()</code> .</p> <p> Таблица 5-1   Эффективность операций со стеком </p> Метод Описание Временная сложность <code>push()</code> Поместить элемент в стек (на вершину) \\(O(1)\\) <code>pop()</code> Извлечь верхний элемент стека \\(O(1)\\) <code>peek()</code> Просмотреть верхний элемент \\(O(1)\\) <p>Обычно достаточно использовать встроенный стек, предоставляемый языком программирования. Однако в некоторых языках специальный класс стека может отсутствовать. В таком случае можно использовать массив или связный список как стек и в логике программы игнорировать операции, не относящиеся к стеку.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby stack.py<pre><code># Инициализация стека\n# В Python нет встроенного класса стека, поэтому можно использовать list как стек\nstack: list[int] = []\n\n# Поместить элементы в стек\nstack.append(1)\nstack.append(3)\nstack.append(2)\nstack.append(5)\nstack.append(4)\n\n# Просмотреть верхний элемент\npeek: int = stack[-1]\n\n# Извлечь элемент\npop: int = stack.pop()\n\n# Получить длину стека\nsize: int = len(stack)\n\n# Проверить, пуст ли стек\nis_empty: bool = len(stack) == 0\n</code></pre> stack.cpp<pre><code>/* Инициализация стека */\nstack&lt;int&gt; stack;\n\n/* Поместить элементы в стек */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n\n/* Просмотреть верхний элемент */\nint top = stack.top();\n\n/* Извлечь элемент */\nstack.pop(); // Без возвращаемого значения\n\n/* Получить длину стека */\nint size = stack.size();\n\n/* Проверить, пуст ли стек */\nbool empty = stack.empty();\n</code></pre> stack.java<pre><code>/* Инициализация стека */\nStack&lt;Integer&gt; stack = new Stack&lt;&gt;();\n\n/* Поместить элементы в стек */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n\n/* Просмотреть верхний элемент */\nint peek = stack.peek();\n\n/* Извлечь элемент */\nint pop = stack.pop();\n\n/* Получить длину стека */\nint size = stack.size();\n\n/* Проверить, пуст ли стек */\nboolean isEmpty = stack.isEmpty();\n</code></pre> stack.cs<pre><code>/* Инициализация стека */\nStack&lt;int&gt; stack = new();\n\n/* Поместить элементы в стек */\nstack.Push(1);\nstack.Push(3);\nstack.Push(2);\nstack.Push(5);\nstack.Push(4);\n\n/* Просмотреть верхний элемент */\nint peek = stack.Peek();\n\n/* Извлечь элемент */\nint pop = stack.Pop();\n\n/* Получить длину стека */\nint size = stack.Count;\n\n/* Проверить, пуст ли стек */\nbool isEmpty = stack.Count == 0;\n</code></pre> stack_test.go<pre><code>/* Инициализация стека */\n// В Go рекомендуется использовать Slice как стек\nvar stack []int\n\n/* Поместить элементы в стек */\nstack = append(stack, 1)\nstack = append(stack, 3)\nstack = append(stack, 2)\nstack = append(stack, 5)\nstack = append(stack, 4)\n\n/* Просмотреть верхний элемент */\npeek := stack[len(stack)-1]\n\n/* Извлечь элемент */\npop := stack[len(stack)-1]\nstack = stack[:len(stack)-1]\n\n/* Получить длину стека */\nsize := len(stack)\n\n/* Проверить, пуст ли стек */\nisEmpty := len(stack) == 0\n</code></pre> stack.swift<pre><code>/* Инициализация стека */\n// В Swift нет встроенного класса стека, поэтому можно использовать Array как стек\nvar stack: [Int] = []\n\n/* Поместить элементы в стек */\nstack.append(1)\nstack.append(3)\nstack.append(2)\nstack.append(5)\nstack.append(4)\n\n/* Просмотреть верхний элемент */\nlet peek = stack.last!\n\n/* Извлечь элемент */\nlet pop = stack.removeLast()\n\n/* Получить длину стека */\nlet size = stack.count\n\n/* Проверить, пуст ли стек */\nlet isEmpty = stack.isEmpty\n</code></pre> stack.js<pre><code>/* Инициализация стека */\n// В JavaScript нет встроенного класса стека, поэтому можно использовать Array как стек\nconst stack = [];\n\n/* Поместить элементы в стек */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n\n/* Просмотреть верхний элемент */\nconst peek = stack[stack.length-1];\n\n/* Извлечь элемент */\nconst pop = stack.pop();\n\n/* Получить длину стека */\nconst size = stack.length;\n\n/* Проверить, пуст ли стек */\nconst is_empty = stack.length === 0;\n</code></pre> stack.ts<pre><code>/* Инициализация стека */\n// В TypeScript нет встроенного класса стека, поэтому можно использовать Array как стек\nconst stack: number[] = [];\n\n/* Поместить элементы в стек */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n\n/* Просмотреть верхний элемент */\nconst peek = stack[stack.length - 1];\n\n/* Извлечь элемент */\nconst pop = stack.pop();\n\n/* Получить длину стека */\nconst size = stack.length;\n\n/* Проверить, пуст ли стек */\nconst is_empty = stack.length === 0;\n</code></pre> stack.dart<pre><code>/* Инициализация стека */\n// В Dart нет встроенного класса стека, поэтому можно использовать List как стек\nList&lt;int&gt; stack = [];\n\n/* Поместить элементы в стек */\nstack.add(1);\nstack.add(3);\nstack.add(2);\nstack.add(5);\nstack.add(4);\n\n/* Просмотреть верхний элемент */\nint peek = stack.last;\n\n/* Извлечь элемент */\nint pop = stack.removeLast();\n\n/* Получить длину стека */\nint size = stack.length;\n\n/* Проверить, пуст ли стек */\nbool isEmpty = stack.isEmpty;\n</code></pre> stack.rs<pre><code>/* Инициализация стека */\n// Используем Vec как стек\nlet mut stack: Vec&lt;i32&gt; = Vec::new();\n\n/* Поместить элементы в стек */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n\n/* Просмотреть верхний элемент */\nlet top = stack.last().unwrap();\n\n/* Извлечь элемент */\nlet pop = stack.pop().unwrap();\n\n/* Получить длину стека */\nlet size = stack.len();\n\n/* Проверить, пуст ли стек */\nlet is_empty = stack.is_empty();\n</code></pre> stack.c<pre><code>// В C нет встроенного стека\n</code></pre> stack.kt<pre><code>/* Инициализация стека */\nval stack = Stack&lt;Int&gt;()\n\n/* Поместить элементы в стек */\nstack.push(1)\nstack.push(3)\nstack.push(2)\nstack.push(5)\nstack.push(4)\n\n/* Просмотреть верхний элемент */\nval peek = stack.peek()\n\n/* Извлечь элемент */\nval pop = stack.pop()\n\n/* Получить длину стека */\nval size = stack.size\n\n/* Проверить, пуст ли стек */\nval isEmpty = stack.isEmpty()\n</code></pre> stack.rb<pre><code># Инициализация стека\n# В Ruby нет встроенного класса стека, поэтому можно использовать Array как стек\nstack = []\n\n# Поместить элементы в стек\nstack &lt;&lt; 1\nstack &lt;&lt; 3\nstack &lt;&lt; 2\nstack &lt;&lt; 5\nstack &lt;&lt; 4\n\n# Просмотреть верхний элемент\npeek = stack.last\n\n# Извлечь элемент\npop = stack.pop\n\n# Получить длину стека\nsize = stack.length\n\n# Проверить, пуст ли стек\nis_empty = stack.empty?\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%81%D1%82%D0%B5%D0%BA%0A%20%20%20%20%23%20%D0%92%20Python%20%D0%BD%D0%B5%D1%82%20%D0%B2%D1%81%D1%82%D1%80%D0%BE%D0%B5%D0%BD%D0%BD%D0%BE%D0%B3%D0%BE%20%D0%BA%D0%BB%D0%B0%D1%81%D1%81%D0%B0%20%D1%81%D1%82%D0%B5%D0%BA%D0%B0%2C%20%D0%BF%D0%BE%D1%8D%D1%82%D0%BE%D0%BC%D1%83%20list%20%D0%BC%D0%BE%D0%B6%D0%BD%D0%BE%20%D0%B8%D1%81%D0%BF%D0%BE%D0%BB%D1%8C%D0%B7%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D0%BA%D0%B0%D0%BA%20%D1%81%D1%82%D0%B5%D0%BA%0A%20%20%20%20stack%20%3D%20%5B%5D%0A%0A%20%20%20%20%23%20%D0%9F%D0%BE%D0%BC%D0%B5%D1%81%D1%82%D0%B8%D1%82%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%B2%20%D1%81%D1%82%D0%B5%D0%BA%0A%20%20%20%20stack.append%281%29%0A%20%20%20%20stack.append%283%29%0A%20%20%20%20stack.append%282%29%0A%20%20%20%20stack.append%285%29%0A%20%20%20%20stack.append%284%29%0A%20%20%20%20print%28%22%D1%81%D1%82%D0%B5%D0%BA%20stack%20%3D%22%2C%20stack%29%0A%0A%20%20%20%20%23%20%D0%9F%D0%BE%D0%BB%D1%83%D1%87%D0%B8%D1%82%D1%8C%20%D0%B2%D0%B5%D1%80%D1%85%D0%BD%D0%B8%D0%B9%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D1%81%D1%82%D0%B5%D0%BA%D0%B0%0A%20%20%20%20peek%20%3D%20stack%5B-1%5D%0A%20%20%20%20print%28%22%D0%92%D0%B5%D1%80%D1%85%D0%BD%D0%B8%D0%B9%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D1%81%D1%82%D0%B5%D0%BA%D0%B0%20peek%20%3D%22%2C%20peek%29%0A%0A%20%20%20%20%23%20%D0%98%D0%B7%D0%B2%D0%BB%D0%B5%D1%87%D1%8C%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20%D0%B8%D0%B7%20%D1%81%D1%82%D0%B5%D0%BA%D0%B0%0A%20%20%20%20pop%20%3D%20stack.pop%28%29%0A%20%20%20%20print%28%22%D0%98%D0%B7%D0%B2%D0%BB%D0%B5%D1%87%D0%B5%D0%BD%D0%BD%D1%8B%D0%B9%20%D0%B8%D0%B7%20%D1%81%D1%82%D0%B5%D0%BA%D0%B0%20%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%20pop%20%3D%22%2C%20pop%29%0A%20%20%20%20print%28%22%D0%9F%D0%BE%D1%81%D0%BB%D0%B5%20%D0%B8%D0%B7%D0%B2%D0%BB%D0%B5%D1%87%D0%B5%D0%BD%D0%B8%D1%8F%20stack%20%3D%22%2C%20stack%29%0A%0A%20%20%20%20%23%20%D0%9F%D0%BE%D0%BB%D1%83%D1%87%D0%B8%D1%82%D1%8C%20%D0%B4%D0%BB%D0%B8%D0%BD%D1%83%20%D1%81%D1%82%D0%B5%D0%BA%D0%B0%0A%20%20%20%20size%20%3D%20len%28stack%29%0A%20%20%20%20print%28%22%D0%94%D0%BB%D0%B8%D0%BD%D0%B0%20%D1%81%D1%82%D0%B5%D0%BA%D0%B0%20size%20%3D%22%2C%20size%29%0A%0A%20%20%20%20%23%20%D0%9F%D1%80%D0%BE%D0%B2%D0%B5%D1%80%D0%B8%D1%82%D1%8C%2C%20%D0%BF%D1%83%D1%81%D1%82%D0%B0%20%D0%BB%D0%B8%20%D1%81%D1%82%D1%80%D1%83%D0%BA%D1%82%D1%83%D1%80%D0%B0%0A%20%20%20%20is_empty%20%3D%20len%28stack%29%20%3D%3D%200%0A%20%20%20%20print%28%22%D0%9F%D1%83%D1%81%D1%82%20%D0%BB%D0%B8%20%D1%81%D1%82%D0%B5%D0%BA%20%3D%22%2C%20is_empty%29&amp;cumulative=false&amp;curInstr=2&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 5. Стек и очередь","5.1 &nbsp; Стек"],"tags":[]},{"location":"chapter_stack_and_queue/stack/#512","level":2,"title":"5.1.2   Реализация стека","text":"<p>Чтобы глубже понять механизм работы стека, попробуем самостоятельно реализовать класс стека.</p> <p>Стек подчиняется принципу LIFO, поэтому мы можем добавлять и удалять элементы только на вершине. Однако и массив, и связный список позволяют добавлять и удалять элементы в произвольном месте. Следовательно, стек можно рассматривать как ограниченный массив или связный список. Иными словами, мы можем скрыть часть нерелевантных операций массива или списка, так чтобы внешняя логика соответствовала свойствам стека.</p>","path":["Глава 5. Стек и очередь","5.1 &nbsp; Стек"],"tags":[]},{"location":"chapter_stack_and_queue/stack/#1","level":3,"title":"1.   Реализация на основе связного списка","text":"<p>Если реализовывать стек на основе связного списка, то головной узел списка можно рассматривать как вершину стека, а хвостовой - как основание.</p> <p>Как показано на рисунке 5-2, для операции <code>push</code> достаточно вставить элемент в голову связного списка. Такой способ вставки называется вставкой в голову. Для операции <code>pop</code> достаточно удалить головной узел из списка.</p> LinkedListStackpush()pop() <p></p> <p></p> <p></p> <p> Рисунок 5-2   Операции push и pop в реализации стека на связном списке </p> <p>Ниже приведен пример кода реализации стека на основе связного списка:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby linkedlist_stack.py<pre><code>class LinkedListStack:\n    \"\"\"Стек на основе связного списка\"\"\"\n\n    def __init__(self):\n        \"\"\"Конструктор\"\"\"\n        self._peek: ListNode | None = None\n        self._size: int = 0\n\n    def size(self) -&gt; int:\n        \"\"\"Получение длины стека\"\"\"\n        return self._size\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"Проверка, пуст ли стек\"\"\"\n        return self._size == 0\n\n    def push(self, val: int):\n        \"\"\"Поместить в стек\"\"\"\n        node = ListNode(val)\n        node.next = self._peek\n        self._peek = node\n        self._size += 1\n\n    def pop(self) -&gt; int:\n        \"\"\"Извлечь из стека\"\"\"\n        num = self.peek()\n        self._peek = self._peek.next\n        self._size -= 1\n        return num\n\n    def peek(self) -&gt; int:\n        \"\"\"Доступ к верхнему элементу стека\"\"\"\n        if self.is_empty():\n            raise IndexError(\"стек пуст\")\n        return self._peek.val\n\n    def to_list(self) -&gt; list[int]:\n        \"\"\"Преобразовать в список для вывода\"\"\"\n        arr = []\n        node = self._peek\n        while node:\n            arr.append(node.val)\n            node = node.next\n        arr.reverse()\n        return arr\n</code></pre> linkedlist_stack.cpp<pre><code>/* Стек на основе связного списка */\nclass LinkedListStack {\n  private:\n    ListNode *stackTop; // Использовать головной узел как вершину стека\n    int stkSize;        // Длина стека\n\n  public:\n    LinkedListStack() {\n        stackTop = nullptr;\n        stkSize = 0;\n    }\n\n    ~LinkedListStack() {\n        // Обходить связный список, удалять узлы и освобождать память\n        freeMemoryLinkedList(stackTop);\n    }\n\n    /* Получение длины стека */\n    int size() {\n        return stkSize;\n    }\n\n    /* Проверка, пуст ли стек */\n    bool isEmpty() {\n        return size() == 0;\n    }\n\n    /* Поместить в стек */\n    void push(int num) {\n        ListNode *node = new ListNode(num);\n        node-&gt;next = stackTop;\n        stackTop = node;\n        stkSize++;\n    }\n\n    /* Извлечь из стека */\n    int pop() {\n        int num = top();\n        ListNode *tmp = stackTop;\n        stackTop = stackTop-&gt;next;\n        // Освободить память\n        delete tmp;\n        stkSize--;\n        return num;\n    }\n\n    /* Доступ к верхнему элементу стека */\n    int top() {\n        if (isEmpty())\n            throw out_of_range(\"стек пуст\");\n        return stackTop-&gt;val;\n    }\n\n    /* Преобразовать List в Array и вернуть */\n    vector&lt;int&gt; toVector() {\n        ListNode *node = stackTop;\n        vector&lt;int&gt; res(size());\n        for (int i = res.size() - 1; i &gt;= 0; i--) {\n            res[i] = node-&gt;val;\n            node = node-&gt;next;\n        }\n        return res;\n    }\n};\n</code></pre> linkedlist_stack.java<pre><code>/* Стек на основе связного списка */\nclass LinkedListStack {\n    private ListNode stackPeek; // Использовать головной узел как вершину стека\n    private int stkSize = 0; // Длина стека\n\n    public LinkedListStack() {\n        stackPeek = null;\n    }\n\n    /* Получение длины стека */\n    public int size() {\n        return stkSize;\n    }\n\n    /* Проверка, пуст ли стек */\n    public boolean isEmpty() {\n        return size() == 0;\n    }\n\n    /* Поместить в стек */\n    public void push(int num) {\n        ListNode node = new ListNode(num);\n        node.next = stackPeek;\n        stackPeek = node;\n        stkSize++;\n    }\n\n    /* Извлечь из стека */\n    public int pop() {\n        int num = peek();\n        stackPeek = stackPeek.next;\n        stkSize--;\n        return num;\n    }\n\n    /* Доступ к верхнему элементу стека */\n    public int peek() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return stackPeek.val;\n    }\n\n    /* Преобразовать List в Array и вернуть */\n    public int[] toArray() {\n        ListNode node = stackPeek;\n        int[] res = new int[size()];\n        for (int i = res.length - 1; i &gt;= 0; i--) {\n            res[i] = node.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_stack.cs<pre><code>/* Стек на основе связного списка */\nclass LinkedListStack {\n    ListNode? stackPeek;  // Использовать головной узел как вершину стека\n    int stkSize = 0;   // Длина стека\n\n    public LinkedListStack() {\n        stackPeek = null;\n    }\n\n    /* Получение длины стека */\n    public int Size() {\n        return stkSize;\n    }\n\n    /* Проверка, пуст ли стек */\n    public bool IsEmpty() {\n        return Size() == 0;\n    }\n\n    /* Поместить в стек */\n    public void Push(int num) {\n        ListNode node = new(num) {\n            next = stackPeek\n        };\n        stackPeek = node;\n        stkSize++;\n    }\n\n    /* Извлечь из стека */\n    public int Pop() {\n        int num = Peek();\n        stackPeek = stackPeek!.next;\n        stkSize--;\n        return num;\n    }\n\n    /* Доступ к верхнему элементу стека */\n    public int Peek() {\n        if (IsEmpty())\n            throw new Exception();\n        return stackPeek!.val;\n    }\n\n    /* Преобразовать List в Array и вернуть */\n    public int[] ToArray() {\n        if (stackPeek == null)\n            return [];\n\n        ListNode? node = stackPeek;\n        int[] res = new int[Size()];\n        for (int i = res.Length - 1; i &gt;= 0; i--) {\n            res[i] = node!.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_stack.go<pre><code>/* Стек на основе связного списка */\ntype linkedListStack struct {\n    // Использовать встроенный пакет list для реализации стека\n    data *list.List\n}\n\n/* Инициализация стека */\nfunc newLinkedListStack() *linkedListStack {\n    return &amp;linkedListStack{\n        data: list.New(),\n    }\n}\n\n/* Поместить в стек */\nfunc (s *linkedListStack) push(value int) {\n    s.data.PushBack(value)\n}\n\n/* Извлечь из стека */\nfunc (s *linkedListStack) pop() any {\n    if s.isEmpty() {\n        return nil\n    }\n    e := s.data.Back()\n    s.data.Remove(e)\n    return e.Value\n}\n\n/* Доступ к верхнему элементу стека */\nfunc (s *linkedListStack) peek() any {\n    if s.isEmpty() {\n        return nil\n    }\n    e := s.data.Back()\n    return e.Value\n}\n\n/* Получение длины стека */\nfunc (s *linkedListStack) size() int {\n    return s.data.Len()\n}\n\n/* Проверка, пуст ли стек */\nfunc (s *linkedListStack) isEmpty() bool {\n    return s.data.Len() == 0\n}\n\n/* Получить List для вывода */\nfunc (s *linkedListStack) toList() *list.List {\n    return s.data\n}\n</code></pre> linkedlist_stack.swift<pre><code>/* Стек на основе связного списка */\nclass LinkedListStack {\n    private var _peek: ListNode? // Использовать головной узел как вершину стека\n    private var _size: Int // Длина стека\n\n    init() {\n        _size = 0\n    }\n\n    /* Получение длины стека */\n    func size() -&gt; Int {\n        _size\n    }\n\n    /* Проверка, пуст ли стек */\n    func isEmpty() -&gt; Bool {\n        size() == 0\n    }\n\n    /* Поместить в стек */\n    func push(num: Int) {\n        let node = ListNode(x: num)\n        node.next = _peek\n        _peek = node\n        _size += 1\n    }\n\n    /* Извлечь из стека */\n    @discardableResult\n    func pop() -&gt; Int {\n        let num = peek()\n        _peek = _peek?.next\n        _size -= 1\n        return num\n    }\n\n    /* Доступ к верхнему элементу стека */\n    func peek() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"стек пуст\")\n        }\n        return _peek!.val\n    }\n\n    /* Преобразовать List в Array и вернуть */\n    func toArray() -&gt; [Int] {\n        var node = _peek\n        var res = Array(repeating: 0, count: size())\n        for i in res.indices.reversed() {\n            res[i] = node!.val\n            node = node?.next\n        }\n        return res\n    }\n}\n</code></pre> linkedlist_stack.js<pre><code>/* Стек на основе связного списка */\nclass LinkedListStack {\n    #stackPeek; // Использовать головной узел как вершину стека\n    #stkSize = 0; // Длина стека\n\n    constructor() {\n        this.#stackPeek = null;\n    }\n\n    /* Получение длины стека */\n    get size() {\n        return this.#stkSize;\n    }\n\n    /* Проверка, пуст ли стек */\n    isEmpty() {\n        return this.size === 0;\n    }\n\n    /* Поместить в стек */\n    push(num) {\n        const node = new ListNode(num);\n        node.next = this.#stackPeek;\n        this.#stackPeek = node;\n        this.#stkSize++;\n    }\n\n    /* Извлечь из стека */\n    pop() {\n        const num = this.peek();\n        this.#stackPeek = this.#stackPeek.next;\n        this.#stkSize--;\n        return num;\n    }\n\n    /* Доступ к верхнему элементу стека */\n    peek() {\n        if (!this.#stackPeek) throw new Error('стек пуст');\n        return this.#stackPeek.val;\n    }\n\n    /* Преобразовать связный список в Array и вернуть */\n    toArray() {\n        let node = this.#stackPeek;\n        const res = new Array(this.size);\n        for (let i = res.length - 1; i &gt;= 0; i--) {\n            res[i] = node.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_stack.ts<pre><code>/* Стек на основе связного списка */\nclass LinkedListStack {\n    private stackPeek: ListNode | null; // Использовать головной узел как вершину стека\n    private stkSize: number = 0; // Длина стека\n\n    constructor() {\n        this.stackPeek = null;\n    }\n\n    /* Получение длины стека */\n    get size(): number {\n        return this.stkSize;\n    }\n\n    /* Проверка, пуст ли стек */\n    isEmpty(): boolean {\n        return this.size === 0;\n    }\n\n    /* Поместить в стек */\n    push(num: number): void {\n        const node = new ListNode(num);\n        node.next = this.stackPeek;\n        this.stackPeek = node;\n        this.stkSize++;\n    }\n\n    /* Извлечь из стека */\n    pop(): number {\n        const num = this.peek();\n        if (!this.stackPeek) throw new Error('стек пуст');\n        this.stackPeek = this.stackPeek.next;\n        this.stkSize--;\n        return num;\n    }\n\n    /* Доступ к верхнему элементу стека */\n    peek(): number {\n        if (!this.stackPeek) throw new Error('стек пуст');\n        return this.stackPeek.val;\n    }\n\n    /* Преобразовать связный список в Array и вернуть */\n    toArray(): number[] {\n        let node = this.stackPeek;\n        const res = new Array&lt;number&gt;(this.size);\n        for (let i = res.length - 1; i &gt;= 0; i--) {\n            res[i] = node!.val;\n            node = node!.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_stack.dart<pre><code>/* Стек на основе класса связного списка */\nclass LinkedListStack {\n  ListNode? _stackPeek; // Использовать головной узел как вершину стека\n  int _stkSize = 0; // Длина стека\n\n  LinkedListStack() {\n    _stackPeek = null;\n  }\n\n  /* Получение длины стека */\n  int size() {\n    return _stkSize;\n  }\n\n  /* Проверка, пуст ли стек */\n  bool isEmpty() {\n    return _stkSize == 0;\n  }\n\n  /* Поместить в стек */\n  void push(int _num) {\n    final ListNode node = ListNode(_num);\n    node.next = _stackPeek;\n    _stackPeek = node;\n    _stkSize++;\n  }\n\n  /* Извлечь из стека */\n  int pop() {\n    final int _num = peek();\n    _stackPeek = _stackPeek!.next;\n    _stkSize--;\n    return _num;\n  }\n\n  /* Доступ к верхнему элементу стека */\n  int peek() {\n    if (_stackPeek == null) {\n      throw Exception(\"стек пуст\");\n    }\n    return _stackPeek!.val;\n  }\n\n  /* Преобразовать связный список в List и вернуть */\n  List&lt;int&gt; toList() {\n    ListNode? node = _stackPeek;\n    List&lt;int&gt; list = [];\n    while (node != null) {\n      list.add(node.val);\n      node = node.next;\n    }\n    list = list.reversed.toList();\n    return list;\n  }\n}\n</code></pre> linkedlist_stack.rs<pre><code>/* Стек на основе связного списка */\n#[allow(dead_code)]\npub struct LinkedListStack&lt;T&gt; {\n    stack_peek: Option&lt;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;, // Использовать головной узел как вершину стека\n    stk_size: usize,                              // Длина стека\n}\n\nimpl&lt;T: Copy&gt; LinkedListStack&lt;T&gt; {\n    pub fn new() -&gt; Self {\n        Self {\n            stack_peek: None,\n            stk_size: 0,\n        }\n    }\n\n    /* Получение длины стека */\n    pub fn size(&amp;self) -&gt; usize {\n        return self.stk_size;\n    }\n\n    /* Проверка, пуст ли стек */\n    pub fn is_empty(&amp;self) -&gt; bool {\n        return self.size() == 0;\n    }\n\n    /* Поместить в стек */\n    pub fn push(&amp;mut self, num: T) {\n        let node = ListNode::new(num);\n        node.borrow_mut().next = self.stack_peek.take();\n        self.stack_peek = Some(node);\n        self.stk_size += 1;\n    }\n\n    /* Извлечь из стека */\n    pub fn pop(&amp;mut self) -&gt; Option&lt;T&gt; {\n        self.stack_peek.take().map(|old_head| {\n            self.stack_peek = old_head.borrow_mut().next.take();\n            self.stk_size -= 1;\n\n            old_head.borrow().val\n        })\n    }\n\n    /* Доступ к верхнему элементу стека */\n    pub fn peek(&amp;self) -&gt; Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt; {\n        self.stack_peek.as_ref()\n    }\n\n    /* Преобразовать List в Array и вернуть */\n    pub fn to_array(&amp;self) -&gt; Vec&lt;T&gt; {\n        fn _to_array&lt;T: Sized + Copy&gt;(head: Option&lt;&amp;Rc&lt;RefCell&lt;ListNode&lt;T&gt;&gt;&gt;&gt;) -&gt; Vec&lt;T&gt; {\n            if let Some(node) = head {\n                let mut nums = _to_array(node.borrow().next.as_ref());\n                nums.push(node.borrow().val);\n                return nums;\n            }\n            return Vec::new();\n        }\n\n        _to_array(self.peek())\n    }\n}\n</code></pre> linkedlist_stack.c<pre><code>/* Стек на основе связного списка */\ntypedef struct {\n    ListNode *top; // Использовать головной узел как вершину стека\n    int size;      // Длина стека\n} LinkedListStack;\n\n/* Конструктор */\nLinkedListStack *newLinkedListStack() {\n    LinkedListStack *s = malloc(sizeof(LinkedListStack));\n    s-&gt;top = NULL;\n    s-&gt;size = 0;\n    return s;\n}\n\n/* Деструктор */\nvoid delLinkedListStack(LinkedListStack *s) {\n    while (s-&gt;top) {\n        ListNode *n = s-&gt;top-&gt;next;\n        free(s-&gt;top);\n        s-&gt;top = n;\n    }\n    free(s);\n}\n\n/* Получение длины стека */\nint size(LinkedListStack *s) {\n    return s-&gt;size;\n}\n\n/* Проверка, пуст ли стек */\nbool isEmpty(LinkedListStack *s) {\n    return size(s) == 0;\n}\n\n/* Поместить в стек */\nvoid push(LinkedListStack *s, int num) {\n    ListNode *node = (ListNode *)malloc(sizeof(ListNode));\n    node-&gt;next = s-&gt;top; // Обновить поле указателя нового узла\n    node-&gt;val = num;     // Обновить поле данных нового узла\n    s-&gt;top = node;       // Обновить вершину стека\n    s-&gt;size++;           // Обновить размер стека\n}\n\n/* Доступ к верхнему элементу стека */\nint peek(LinkedListStack *s) {\n    if (s-&gt;size == 0) {\n        printf(\"стек пуст\\n\");\n        return INT_MAX;\n    }\n    return s-&gt;top-&gt;val;\n}\n\n/* Извлечь из стека */\nint pop(LinkedListStack *s) {\n    int val = peek(s);\n    ListNode *tmp = s-&gt;top;\n    s-&gt;top = s-&gt;top-&gt;next;\n    // Освободить память\n    free(tmp);\n    s-&gt;size--;\n    return val;\n}\n</code></pre> linkedlist_stack.kt<pre><code>/* Стек на основе связного списка */\nclass LinkedListStack(\n    private var stackPeek: ListNode? = null, // Использовать головной узел как вершину стека\n    private var stkSize: Int = 0 // Длина стека\n) {\n\n    /* Получение длины стека */\n    fun size(): Int {\n        return stkSize\n    }\n\n    /* Проверка, пуст ли стек */\n    fun isEmpty(): Boolean {\n        return size() == 0\n    }\n\n    /* Поместить в стек */\n    fun push(num: Int) {\n        val node = ListNode(num)\n        node.next = stackPeek\n        stackPeek = node\n        stkSize++\n    }\n\n    /* Извлечь из стека */\n    fun pop(): Int? {\n        val num = peek()\n        stackPeek = stackPeek?.next\n        stkSize--\n        return num\n    }\n\n    /* Доступ к верхнему элементу стека */\n    fun peek(): Int? {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        return stackPeek?._val\n    }\n\n    /* Преобразовать List в Array и вернуть */\n    fun toArray(): IntArray {\n        var node = stackPeek\n        val res = IntArray(size())\n        for (i in res.size - 1 downTo 0) {\n            res[i] = node?._val!!\n            node = node.next\n        }\n        return res\n    }\n}\n</code></pre> linkedlist_stack.rb<pre><code>### Стек на основе связного списка ###\nclass LinkedListStack\n  attr_reader :size\n\n  ### Конструктор ###\n  def initialize\n    @size = 0\n  end\n\n  ### Проверка, пуст ли стек ###\n  def is_empty?\n    @peek.nil?\n  end\n\n  ### Помещение в стек ###\n  def push(val)\n    node = ListNode.new(val)\n    node.next = @peek\n    @peek = node\n    @size += 1\n  end\n\n  ### Извлечение из стека ###\n  def pop\n    num = peek\n    @peek = @peek.next\n    @size -= 1\n    num\n  end\n\n  ### Доступ к верхнему элементу стека ###\n  def peek\n    raise IndexError, 'стек пуст' if is_empty?\n\n    @peek.val\n  end\n\n  ### Преобразовать связный список в Array и вернуть ###\n  def to_array\n    arr = []\n    node = @peek\n    while node\n      arr &lt;&lt; node.val\n      node = node.next\n    end\n    arr.reverse\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 5. Стек и очередь","5.1 &nbsp; Стек"],"tags":[]},{"location":"chapter_stack_and_queue/stack/#2","level":3,"title":"2.   Реализация на основе массива","text":"<p>Если реализовывать стек на основе массива, то хвост массива можно рассматривать как вершину стека. Как показано на рисунке 5-3, операции <code>push</code> и <code>pop</code> соответствуют добавлению элемента в конец массива и удалению элемента из конца, обе имеют временную сложность \\(O(1)\\) .</p> ArrayStackpush()pop() <p></p> <p></p> <p></p> <p> Рисунок 5-3   Операции push и pop в реализации стека на массиве </p> <p>Поскольку количество элементов, помещаемых в стек, может непрерывно расти, мы можем использовать динамический массив и тем самым не заниматься расширением массива вручную. Ниже приведен пример кода:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array_stack.py<pre><code>class ArrayStack:\n    \"\"\"Стек на основе массива\"\"\"\n\n    def __init__(self):\n        \"\"\"Конструктор\"\"\"\n        self._stack: list[int] = []\n\n    def size(self) -&gt; int:\n        \"\"\"Получение длины стека\"\"\"\n        return len(self._stack)\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"Проверка, пуст ли стек\"\"\"\n        return self.size() == 0\n\n    def push(self, item: int):\n        \"\"\"Поместить в стек\"\"\"\n        self._stack.append(item)\n\n    def pop(self) -&gt; int:\n        \"\"\"Извлечь из стека\"\"\"\n        if self.is_empty():\n            raise IndexError(\"стек пуст\")\n        return self._stack.pop()\n\n    def peek(self) -&gt; int:\n        \"\"\"Доступ к верхнему элементу стека\"\"\"\n        if self.is_empty():\n            raise IndexError(\"стек пуст\")\n        return self._stack[-1]\n\n    def to_list(self) -&gt; list[int]:\n        \"\"\"Вернуть список для вывода\"\"\"\n        return self._stack\n</code></pre> array_stack.cpp<pre><code>/* Стек на основе массива */\nclass ArrayStack {\n  private:\n    vector&lt;int&gt; stack;\n\n  public:\n    /* Получение длины стека */\n    int size() {\n        return stack.size();\n    }\n\n    /* Проверка, пуст ли стек */\n    bool isEmpty() {\n        return stack.size() == 0;\n    }\n\n    /* Поместить в стек */\n    void push(int num) {\n        stack.push_back(num);\n    }\n\n    /* Извлечь из стека */\n    int pop() {\n        int num = top();\n        stack.pop_back();\n        return num;\n    }\n\n    /* Доступ к верхнему элементу стека */\n    int top() {\n        if (isEmpty())\n            throw out_of_range(\"стек пуст\");\n        return stack.back();\n    }\n\n    /* Вернуть Vector */\n    vector&lt;int&gt; toVector() {\n        return stack;\n    }\n};\n</code></pre> array_stack.java<pre><code>/* Стек на основе массива */\nclass ArrayStack {\n    private ArrayList&lt;Integer&gt; stack;\n\n    public ArrayStack() {\n        // Инициализация списка (динамического массива)\n        stack = new ArrayList&lt;&gt;();\n    }\n\n    /* Получение длины стека */\n    public int size() {\n        return stack.size();\n    }\n\n    /* Проверка, пуст ли стек */\n    public boolean isEmpty() {\n        return size() == 0;\n    }\n\n    /* Поместить в стек */\n    public void push(int num) {\n        stack.add(num);\n    }\n\n    /* Извлечь из стека */\n    public int pop() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return stack.remove(size() - 1);\n    }\n\n    /* Доступ к верхнему элементу стека */\n    public int peek() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return stack.get(size() - 1);\n    }\n\n    /* Преобразовать List в Array и вернуть */\n    public Object[] toArray() {\n        return stack.toArray();\n    }\n}\n</code></pre> array_stack.cs<pre><code>/* Стек на основе массива */\nclass ArrayStack {\n    List&lt;int&gt; stack;\n    public ArrayStack() {\n        // Инициализация списка (динамического массива)\n        stack = [];\n    }\n\n    /* Получение длины стека */\n    public int Size() {\n        return stack.Count;\n    }\n\n    /* Проверка, пуст ли стек */\n    public bool IsEmpty() {\n        return Size() == 0;\n    }\n\n    /* Поместить в стек */\n    public void Push(int num) {\n        stack.Add(num);\n    }\n\n    /* Извлечь из стека */\n    public int Pop() {\n        if (IsEmpty())\n            throw new Exception();\n        var val = Peek();\n        stack.RemoveAt(Size() - 1);\n        return val;\n    }\n\n    /* Доступ к верхнему элементу стека */\n    public int Peek() {\n        if (IsEmpty())\n            throw new Exception();\n        return stack[Size() - 1];\n    }\n\n    /* Преобразовать List в Array и вернуть */\n    public int[] ToArray() {\n        return [.. stack];\n    }\n}\n</code></pre> array_stack.go<pre><code>/* Стек на основе массива */\ntype arrayStack struct {\n    data []int // Данные\n}\n\n/* Инициализация стека */\nfunc newArrayStack() *arrayStack {\n    return &amp;arrayStack{\n        // Установить длину стека равной 0, а емкость равной 16\n        data: make([]int, 0, 16),\n    }\n}\n\n/* Длина стека */\nfunc (s *arrayStack) size() int {\n    return len(s.data)\n}\n\n/* Пуст ли стек */\nfunc (s *arrayStack) isEmpty() bool {\n    return s.size() == 0\n}\n\n/* Поместить в стек */\nfunc (s *arrayStack) push(v int) {\n    // Срез автоматически расширяется\n    s.data = append(s.data, v)\n}\n\n/* Извлечь из стека */\nfunc (s *arrayStack) pop() any {\n    val := s.peek()\n    s.data = s.data[:len(s.data)-1]\n    return val\n}\n\n/* Получить элемент на вершине стека */\nfunc (s *arrayStack) peek() any {\n    if s.isEmpty() {\n        return nil\n    }\n    val := s.data[len(s.data)-1]\n    return val\n}\n\n/* Получить Slice для вывода */\nfunc (s *arrayStack) toSlice() []int {\n    return s.data\n}\n</code></pre> array_stack.swift<pre><code>/* Стек на основе массива */\nclass ArrayStack {\n    private var stack: [Int]\n\n    init() {\n        // Инициализация списка (динамического массива)\n        stack = []\n    }\n\n    /* Получение длины стека */\n    func size() -&gt; Int {\n        stack.count\n    }\n\n    /* Проверка, пуст ли стек */\n    func isEmpty() -&gt; Bool {\n        stack.isEmpty\n    }\n\n    /* Поместить в стек */\n    func push(num: Int) {\n        stack.append(num)\n    }\n\n    /* Извлечь из стека */\n    @discardableResult\n    func pop() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"стек пуст\")\n        }\n        return stack.removeLast()\n    }\n\n    /* Доступ к верхнему элементу стека */\n    func peek() -&gt; Int {\n        if isEmpty() {\n            fatalError(\"стек пуст\")\n        }\n        return stack.last!\n    }\n\n    /* Преобразовать List в Array и вернуть */\n    func toArray() -&gt; [Int] {\n        stack\n    }\n}\n</code></pre> array_stack.js<pre><code>/* Стек на основе массива */\nclass ArrayStack {\n    #stack;\n    constructor() {\n        this.#stack = [];\n    }\n\n    /* Получение длины стека */\n    get size() {\n        return this.#stack.length;\n    }\n\n    /* Проверка, пуст ли стек */\n    isEmpty() {\n        return this.#stack.length === 0;\n    }\n\n    /* Поместить в стек */\n    push(num) {\n        this.#stack.push(num);\n    }\n\n    /* Извлечь из стека */\n    pop() {\n        if (this.isEmpty()) throw new Error('стек пуст');\n        return this.#stack.pop();\n    }\n\n    /* Доступ к верхнему элементу стека */\n    top() {\n        if (this.isEmpty()) throw new Error('стек пуст');\n        return this.#stack[this.#stack.length - 1];\n    }\n\n    /* Вернуть Array */\n    toArray() {\n        return this.#stack;\n    }\n}\n</code></pre> array_stack.ts<pre><code>/* Стек на основе массива */\nclass ArrayStack {\n    private stack: number[];\n    constructor() {\n        this.stack = [];\n    }\n\n    /* Получение длины стека */\n    get size(): number {\n        return this.stack.length;\n    }\n\n    /* Проверка, пуст ли стек */\n    isEmpty(): boolean {\n        return this.stack.length === 0;\n    }\n\n    /* Поместить в стек */\n    push(num: number): void {\n        this.stack.push(num);\n    }\n\n    /* Извлечь из стека */\n    pop(): number | undefined {\n        if (this.isEmpty()) throw new Error('стек пуст');\n        return this.stack.pop();\n    }\n\n    /* Доступ к верхнему элементу стека */\n    top(): number | undefined {\n        if (this.isEmpty()) throw new Error('стек пуст');\n        return this.stack[this.stack.length - 1];\n    }\n\n    /* Вернуть Array */\n    toArray() {\n        return this.stack;\n    }\n}\n</code></pre> array_stack.dart<pre><code>/* Стек на основе массива */\nclass ArrayStack {\n  late List&lt;int&gt; _stack;\n  ArrayStack() {\n    _stack = [];\n  }\n\n  /* Получение длины стека */\n  int size() {\n    return _stack.length;\n  }\n\n  /* Проверка, пуст ли стек */\n  bool isEmpty() {\n    return _stack.isEmpty;\n  }\n\n  /* Поместить в стек */\n  void push(int _num) {\n    _stack.add(_num);\n  }\n\n  /* Извлечь из стека */\n  int pop() {\n    if (isEmpty()) {\n      throw Exception(\"стек пуст\");\n    }\n    return _stack.removeLast();\n  }\n\n  /* Доступ к верхнему элементу стека */\n  int peek() {\n    if (isEmpty()) {\n      throw Exception(\"стек пуст\");\n    }\n    return _stack.last;\n  }\n\n  /* Преобразовать стек в Array и вернуть */\n  List&lt;int&gt; toArray() =&gt; _stack;\n}\n</code></pre> array_stack.rs<pre><code>/* Стек на основе массива */\nstruct ArrayStack&lt;T&gt; {\n    stack: Vec&lt;T&gt;,\n}\n\nimpl&lt;T&gt; ArrayStack&lt;T&gt; {\n    /* Инициализация стека */\n    fn new() -&gt; ArrayStack&lt;T&gt; {\n        ArrayStack::&lt;T&gt; {\n            stack: Vec::&lt;T&gt;::new(),\n        }\n    }\n\n    /* Получение длины стека */\n    fn size(&amp;self) -&gt; usize {\n        self.stack.len()\n    }\n\n    /* Проверка, пуст ли стек */\n    fn is_empty(&amp;self) -&gt; bool {\n        self.size() == 0\n    }\n\n    /* Поместить в стек */\n    fn push(&amp;mut self, num: T) {\n        self.stack.push(num);\n    }\n\n    /* Извлечь из стека */\n    fn pop(&amp;mut self) -&gt; Option&lt;T&gt; {\n        self.stack.pop()\n    }\n\n    /* Доступ к верхнему элементу стека */\n    fn peek(&amp;self) -&gt; Option&lt;&amp;T&gt; {\n        if self.is_empty() {\n            panic!(\"стек пуст\")\n        };\n        self.stack.last()\n    }\n\n    /* Вернуть &amp;Vec */\n    fn to_array(&amp;self) -&gt; &amp;Vec&lt;T&gt; {\n        &amp;self.stack\n    }\n}\n</code></pre> array_stack.c<pre><code>/* Стек на основе массива */\ntypedef struct {\n    int *data;\n    int size;\n} ArrayStack;\n\n/* Конструктор */\nArrayStack *newArrayStack() {\n    ArrayStack *stack = malloc(sizeof(ArrayStack));\n    // Инициализировать большую вместимость, чтобы избежать расширения\n    stack-&gt;data = malloc(sizeof(int) * MAX_SIZE);\n    stack-&gt;size = 0;\n    return stack;\n}\n\n/* Деструктор */\nvoid delArrayStack(ArrayStack *stack) {\n    free(stack-&gt;data);\n    free(stack);\n}\n\n/* Получение длины стека */\nint size(ArrayStack *stack) {\n    return stack-&gt;size;\n}\n\n/* Проверка, пуст ли стек */\nbool isEmpty(ArrayStack *stack) {\n    return stack-&gt;size == 0;\n}\n\n/* Поместить в стек */\nvoid push(ArrayStack *stack, int num) {\n    if (stack-&gt;size == MAX_SIZE) {\n        printf(\"Стек заполнен\\n\");\n        return;\n    }\n    stack-&gt;data[stack-&gt;size] = num;\n    stack-&gt;size++;\n}\n\n/* Доступ к верхнему элементу стека */\nint peek(ArrayStack *stack) {\n    if (stack-&gt;size == 0) {\n        printf(\"стек пуст\\n\");\n        return INT_MAX;\n    }\n    return stack-&gt;data[stack-&gt;size - 1];\n}\n\n/* Извлечь из стека */\nint pop(ArrayStack *stack) {\n    int val = peek(stack);\n    stack-&gt;size--;\n    return val;\n}\n</code></pre> array_stack.kt<pre><code>/* Стек на основе массива */\nclass ArrayStack {\n    // Инициализация списка (динамического массива)\n    private val stack = mutableListOf&lt;Int&gt;()\n\n    /* Получение длины стека */\n    fun size(): Int {\n        return stack.size\n    }\n\n    /* Проверка, пуст ли стек */\n    fun isEmpty(): Boolean {\n        return size() == 0\n    }\n\n    /* Поместить в стек */\n    fun push(num: Int) {\n        stack.add(num)\n    }\n\n    /* Извлечь из стека */\n    fun pop(): Int {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        return stack.removeAt(size() - 1)\n    }\n\n    /* Доступ к верхнему элементу стека */\n    fun peek(): Int {\n        if (isEmpty()) throw IndexOutOfBoundsException()\n        return stack[size() - 1]\n    }\n\n    /* Преобразовать List в Array и вернуть */\n    fun toArray(): Array&lt;Any&gt; {\n        return stack.toTypedArray()\n    }\n}\n</code></pre> array_stack.rb<pre><code>### Стек на основе массива ###\nclass ArrayStack\n  ### Конструктор ###\n  def initialize\n    @stack = []\n  end\n\n  ### Получить длину стека ###\n  def size\n    @stack.length\n  end\n\n  ### Проверка, пуст ли стек ###\n  def is_empty?\n    @stack.empty?\n  end\n\n  ### Помещение в стек ###\n  def push(item)\n    @stack &lt;&lt; item\n  end\n\n  ### Извлечение из стека ###\n  def pop\n    raise IndexError, 'стек пуст' if is_empty?\n\n    @stack.pop\n  end\n\n  ### Доступ к верхнему элементу стека ###\n  def peek\n    raise IndexError, 'стек пуст' if is_empty?\n\n    @stack.last\n  end\n\n  ### Вернуть список для вывода ###\n  def to_array\n    @stack\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 5. Стек и очередь","5.1 &nbsp; Стек"],"tags":[]},{"location":"chapter_stack_and_queue/stack/#513","level":2,"title":"5.1.3   Сравнение двух реализаций","text":"<p>Поддерживаемые операции</p> <p>Обе реализации поддерживают все операции, определенные для стека. Реализация на массиве дополнительно позволяет выполнять произвольный доступ, но это уже выходит за рамки определения стека и обычно не используется.</p> <p>Временная эффективность</p> <p>В реализации на массиве и <code>push</code> , и <code>pop</code> выполняются в заранее выделенной непрерывной памяти, которая хорошо использует локальность кэша, поэтому такие операции обычно эффективнее. Однако если при <code>push</code> емкость массива оказывается превышена, включается механизм расширения, и временная сложность именно этой операции становится \\(O(n)\\) .</p> <p>В реализации на связном списке расширение выполняется очень гибко, и проблемы падения эффективности из-за расширения массива здесь нет. Но сама операция <code>push</code> требует инициализации объекта-узла и изменения указателей, поэтому в среднем она немного менее эффективна. Впрочем, если помещаемые в стек элементы уже сами являются объектами-узлами, шаг инициализации можно пропустить и тем самым повысить эффективность.</p> <p>Итак, когда элементами, помещаемыми и извлекаемыми из стека, являются базовые типы данных, например <code>int</code> или <code>double</code> , можно сделать следующие выводы.</p> <ul> <li>Стек на основе массива теряет в эффективности в моменты расширения, но поскольку расширение происходит редко, его средняя эффективность выше.</li> <li>Стек на основе связного списка может обеспечивать более стабильную производительность.</li> </ul> <p>Пространственная эффективность</p> <p>При инициализации массива система выделяет начальную емкость, которая может превышать реальную потребность. Кроме того, механизм расширения обычно увеличивает емкость по некоторому коэффициенту, например в 2 раза, и расширенная емкость тоже может оказаться больше фактически необходимой. Поэтому реализация стека на основе массива может приводить к некоторым потерям памяти.</p> <p>Однако, поскольку узлы связного списка должны дополнительно хранить указатели, узлы списка сами по себе занимают больше пространства.</p> <p>В итоге нельзя просто сказать, какая из реализаций более экономна по памяти; это нужно анализировать в контексте конкретной задачи.</p>","path":["Глава 5. Стек и очередь","5.1 &nbsp; Стек"],"tags":[]},{"location":"chapter_stack_and_queue/stack/#514","level":2,"title":"5.1.4   Типичные применения стека","text":"<ul> <li>Кнопки \"назад\" и \"вперед\" в браузере, undo и redo в программах. Каждый раз, когда мы открываем новую страницу, браузер помещает предыдущую страницу в стек, чтобы по операции \"назад\" можно было вернуться к ней. Операция \"назад\" по сути является <code>pop</code> . Если нужно одновременно поддерживать и \"назад\", и \"вперед\", то обычно используются два стека.</li> <li>Управление памятью программы. Каждый раз при вызове функции система помещает на вершину стека стековый кадр, в котором хранится контекст функции. В рекурсивной функции на этапе углубления рекурсии непрерывно выполняются операции <code>push</code> , а на этапе возврата - операции <code>pop</code> .</li> </ul>","path":["Глава 5. Стек и очередь","5.1 &nbsp; Стек"],"tags":[]},{"location":"chapter_stack_and_queue/summary/","level":1,"title":"5.4   Резюме","text":"","path":["Глава 5. Стек и очередь","5.4 &nbsp; Резюме"],"tags":[]},{"location":"chapter_stack_and_queue/summary/#1","level":3,"title":"1.   Основные выводы","text":"<ul> <li>Стек - это структура данных, следующая правилу \"последним пришел - первым вышел\", и его можно реализовать с помощью массива или связного списка.</li> <li>С точки зрения временной эффективности реализация стека на массиве обычно работает быстрее в среднем, но во время расширения емкости временная сложность отдельной операции <code>push</code> может ухудшаться до \\(O(n)\\) . Напротив, реализация стека на связном списке дает более стабильные характеристики.</li> <li>С точки зрения использования памяти реализация стека на массиве может приводить к некоторой потере пространства. Однако следует учитывать, что узлы связного списка занимают больше памяти, чем элементы массива.</li> <li>Очередь - это структура данных, следующая правилу \"первым пришел - первым вышел\", и ее также можно реализовать с помощью массива или связного списка. Сравнение временной и пространственной эффективности для очереди в целом приводит к тем же выводам, что и для стека.</li> <li>Двусторонняя очередь - это очередь с более высокой степенью свободы, которая позволяет добавлять и удалять элементы с обоих концов.</li> </ul>","path":["Глава 5. Стек и очередь","5.4 &nbsp; Резюме"],"tags":[]},{"location":"chapter_stack_and_queue/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: Реализованы ли кнопки \"вперед\" и \"назад\" в браузере с помощью двусвязного списка?</p> <p>По сути, функция переходов \"вперед/назад\" в браузере отражает логику стека. Когда пользователь открывает новую страницу, она помещается на вершину стека; когда пользователь нажимает кнопку \"назад\", эта страница снимается с вершины стека. Двусторонняя очередь позволяет удобно реализовать некоторые дополнительные операции, об этом уже упоминалось в разделе \"Двусторонняя очередь\".</p> <p>Q: Нужно ли освобождать память узла после извлечения его из стека?</p> <p>Если извлеченный узел еще понадобится, память освобождать не нужно. Если он больше не нужен, то в языках <code>Java</code> и <code>Python</code> есть автоматический сборщик мусора, поэтому ручное освобождение памяти не требуется; в <code>C</code> и <code>C++</code> память нужно освобождать вручную.</p> <p>Q: Двусторонняя очередь выглядит как два соединенных стека. Для чего она нужна?</p> <p>Двусторонняя очередь похожа на комбинацию стека и очереди или на два соединенных стека. Она объединяет логику обеих структур, поэтому может покрыть все их применения и при этом остается более гибкой.</p> <p>Q: Как именно реализуются отмена (undo) и повтор (redo)?</p> <p>Используются два стека: стек <code>A</code> для отмены и стек <code>B</code> для повтора.</p> <ol> <li>Каждый раз, когда пользователь выполняет действие, это действие помещается в стек <code>A</code> , а стек <code>B</code> очищается.</li> <li>Когда пользователь выполняет \"undo\", последнее действие извлекается из стека <code>A</code> и помещается в стек <code>B</code> .</li> <li>Когда пользователь выполняет \"redo\", последнее действие извлекается из стека <code>B</code> и помещается обратно в стек <code>A</code> .</li> </ol>","path":["Глава 5. Стек и очередь","5.4 &nbsp; Резюме"],"tags":[]},{"location":"chapter_tree/","level":1,"title":"Глава 7.   Деревья","text":"<p>Abstract</p> <p>Высокое дерево полно жизни: мощные корни, густая листва и раскидистые ветви.</p> <p>Оно наглядно показывает нам живую форму данных, построенную на принципе \"разделяй и властвуй\".</p>","path":["Глава 7. Деревья","Глава 7. &nbsp; Деревья"],"tags":[]},{"location":"chapter_tree/#_1","level":2,"title":"Содержание главы","text":"<ul> <li>7.1   Двоичное дерево</li> <li>7.2   Обход двоичного дерева</li> <li>7.3   Представление двоичного дерева массивом</li> <li>7.4   Двоичное дерево поиска</li> <li>7.5   AVL-дерево *</li> <li>7.6   Краткие итоги</li> </ul>","path":["Глава 7. Деревья","Глава 7. &nbsp; Деревья"],"tags":[]},{"location":"chapter_tree/array_representation_of_tree/","level":1,"title":"7.3   Представление двоичного дерева массивом","text":"<p>В представлении через связную структуру единицей хранения двоичного дерева является узел <code>TreeNode</code> , а между узлами существуют связи через указатели. В предыдущем разделе были рассмотрены основные операции двоичного дерева в таком представлении.</p> <p>Возникает вопрос: можно ли представить двоичное дерево с помощью массива? Ответ: да.</p>","path":["Глава 7. Деревья","7.3 &nbsp; Представление двоичного дерева массивом"],"tags":[]},{"location":"chapter_tree/array_representation_of_tree/#731","level":2,"title":"7.3.1   Представление идеального двоичного дерева","text":"<p>Сначала разберем простой случай. Если дана идеальная двоичная структура и все ее узлы хранятся в массиве в порядке обхода по уровням, то каждому узлу будет соответствовать единственный индекс массива.</p> <p>Из свойств обхода по уровням можно вывести формулу соответствия между индексом родителя и индексами дочерних узлов: если индекс некоторого узла равен \\(i\\) , то индекс его левого дочернего узла равен \\(2i + 1\\) , а правого - \\(2i + 2\\) . На рисунке 7-12 показано соответствие между индексами разных узлов.</p> <p></p> <p> Рисунок 7-12   Представление идеального двоичного дерева массивом </p> <p>Эта формула соответствия играет ту же роль, что и ссылки на узлы в связной структуре . Имея любой узел в массиве, мы можем с ее помощью получить доступ к его левому и правому дочерним узлам.</p>","path":["Глава 7. Деревья","7.3 &nbsp; Представление двоичного дерева массивом"],"tags":[]},{"location":"chapter_tree/array_representation_of_tree/#732","level":2,"title":"7.3.2   Представление произвольного двоичного дерева","text":"<p>Идеальное двоичное дерево - лишь частный случай; в обычной двоичной структуре на промежуточных уровнях часто существует множество <code>None</code> . Поскольку последовательность обхода по уровням не содержит этих <code>None</code> , мы не можем по одной лишь этой последовательности определить их количество и расположение. Это означает, что одному и тому же обходу по уровням может соответствовать сразу несколько различных структур двоичного дерева.</p> <p>Как показано на рисунке 7-13, для неполной двоичной структуры описанный выше способ представления массивом уже перестает работать.</p> <p></p> <p> Рисунок 7-13   Одной последовательности обхода по уровням соответствуют разные двоичные структуры </p> <p>Чтобы решить эту проблему, мы можем явно записывать все <code>None</code> в последовательности обхода по уровням . Как показано на рисунке 7-14, после такой обработки последовательность обхода по уровням уже сможет однозначно задавать двоичное дерево. Пример кода приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code># Представление двоичного дерева массивом\n# Используем None для обозначения пустых позиций\ntree = [1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, None, None, 15]\n</code></pre> <pre><code>/* Представление двоичного дерева массивом */\n// Используем максимальное значение int, INT_MAX, для обозначения пустых позиций\nvector&lt;int&gt; tree = {1, 2, 3, 4, INT_MAX, 6, 7, 8, 9, INT_MAX, INT_MAX, 12, INT_MAX, INT_MAX, 15};\n</code></pre> <pre><code>/* Представление двоичного дерева массивом */\n// Используя обертку Integer для int, можно применять null для обозначения пустых позиций\nInteger[] tree = { 1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15 };\n</code></pre> <pre><code>/* Представление двоичного дерева массивом */\n// Используя nullable-тип int? , можно применять null для обозначения пустых позиций\nint?[] tree = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <pre><code>/* Представление двоичного дерева массивом */\n// Используем срез типа any, чтобы можно было применять nil для обозначения пустых позиций\ntree := []any{1, 2, 3, 4, nil, 6, 7, 8, 9, nil, nil, 12, nil, nil, 15}\n</code></pre> <pre><code>/* Представление двоичного дерева массивом */\n// Используя nullable-тип Int? , можно применять nil для обозначения пустых позиций\nlet tree: [Int?] = [1, 2, 3, 4, nil, 6, 7, 8, 9, nil, nil, 12, nil, nil, 15]\n</code></pre> <pre><code>/* Представление двоичного дерева массивом */\n// Используем null для обозначения пустых позиций\nlet tree = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <pre><code>/* Представление двоичного дерева массивом */\n// Используем null для обозначения пустых позиций\nlet tree: (number | null)[] = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <pre><code>/* Представление двоичного дерева массивом */\n// Используя nullable-тип int? , можно применять null для обозначения пустых позиций\nList&lt;int?&gt; tree = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <pre><code>/* Представление двоичного дерева массивом */\n// Используем None для обозначения пустых позиций\nlet tree = [Some(1), Some(2), Some(3), Some(4), None, Some(6), Some(7), Some(8), Some(9), None, None, Some(12), None, None, Some(15)];\n</code></pre> <pre><code>/* Представление двоичного дерева массивом */\n// Используем максимальное значение int для обозначения пустых позиций, поэтому узлы не должны принимать значение INT_MAX\nint tree[] = {1, 2, 3, 4, INT_MAX, 6, 7, 8, 9, INT_MAX, INT_MAX, 12, INT_MAX, INT_MAX, 15};\n</code></pre> <pre><code>/* Представление двоичного дерева массивом */\n// Используем null для обозначения пустых позиций\nval tree = arrayOf( 1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15 )\n</code></pre> <pre><code>### Представление двоичного дерева массивом ###\n# Используем nil для обозначения пустых позиций\ntree = [1, 2, 3, 4, nil, 6, 7, 8, 9, nil, nil, 12, nil, nil, 15]\n</code></pre> <p></p> <p> Рисунок 7-14   Представление произвольного двоичного дерева массивом </p> <p>Стоит отметить, что полное двоичное дерево очень удобно представлять массивом . Если вспомнить определение полного двоичного дерева, то <code>None</code> появляются только на самом нижнем уровне и справа, а значит, все <code>None</code> обязательно находятся в конце последовательности обхода по уровням.</p> <p>Это означает, что при представлении полного двоичного дерева массивом можно не хранить все <code>None</code> , что очень удобно. На рисунке 7-15 приведен пример.</p> <p></p> <p> Рисунок 7-15   Представление полного двоичного дерева массивом </p> <p>Ниже приведен код реализации двоичного дерева, представленного массивом. Он включает следующие операции.</p> <ul> <li>Для заданного узла получить его значение, левого дочернего узла, правого дочернего узла и родительский узел.</li> <li>Получить последовательности прямого, симметричного, обратного обходов и обхода по уровням.</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby array_binary_tree.py<pre><code>class ArrayBinaryTree:\n    \"\"\"Класс двоичного дерева в массивном представлении\"\"\"\n\n    def __init__(self, arr: list[int | None]):\n        \"\"\"Конструктор\"\"\"\n        self._tree = list(arr)\n\n    def size(self):\n        \"\"\"Вместимость списка\"\"\"\n        return len(self._tree)\n\n    def val(self, i: int) -&gt; int | None:\n        \"\"\"Получить значение узла с индексом i\"\"\"\n        # Если индекс выходит за границы, вернуть None, обозначающий пустую позицию\n        if i &lt; 0 or i &gt;= self.size():\n            return None\n        return self._tree[i]\n\n    def left(self, i: int) -&gt; int | None:\n        \"\"\"Получить индекс левого дочернего узла узла с индексом i\"\"\"\n        return 2 * i + 1\n\n    def right(self, i: int) -&gt; int | None:\n        \"\"\"Получить индекс правого дочернего узла узла с индексом i\"\"\"\n        return 2 * i + 2\n\n    def parent(self, i: int) -&gt; int | None:\n        \"\"\"Получить индекс родительского узла узла с индексом i\"\"\"\n        return (i - 1) // 2\n\n    def level_order(self) -&gt; list[int]:\n        \"\"\"Обход в ширину\"\"\"\n        self.res = []\n        # Непосредственно обходить массив\n        for i in range(self.size()):\n            if self.val(i) is not None:\n                self.res.append(self.val(i))\n        return self.res\n\n    def dfs(self, i: int, order: str):\n        \"\"\"Обход в глубину\"\"\"\n        if self.val(i) is None:\n            return\n        # Предварительный обход\n        if order == \"pre\":\n            self.res.append(self.val(i))\n        self.dfs(self.left(i), order)\n        # Симметричный обход\n        if order == \"in\":\n            self.res.append(self.val(i))\n        self.dfs(self.right(i), order)\n        # Обратный обход\n        if order == \"post\":\n            self.res.append(self.val(i))\n\n    def pre_order(self) -&gt; list[int]:\n        \"\"\"Предварительный обход\"\"\"\n        self.res = []\n        self.dfs(0, order=\"pre\")\n        return self.res\n\n    def in_order(self) -&gt; list[int]:\n        \"\"\"Симметричный обход\"\"\"\n        self.res = []\n        self.dfs(0, order=\"in\")\n        return self.res\n\n    def post_order(self) -&gt; list[int]:\n        \"\"\"Обратный обход\"\"\"\n        self.res = []\n        self.dfs(0, order=\"post\")\n        return self.res\n</code></pre> array_binary_tree.cpp<pre><code>/* Класс двоичного дерева в массивном представлении */\nclass ArrayBinaryTree {\n  public:\n    /* Конструктор */\n    ArrayBinaryTree(vector&lt;int&gt; arr) {\n        tree = arr;\n    }\n\n    /* Вместимость списка */\n    int size() {\n        return tree.size();\n    }\n\n    /* Получить значение узла с индексом i */\n    int val(int i) {\n        // Если индекс выходит за границы, вернуть INT_MAX, обозначающий пустую позицию\n        if (i &lt; 0 || i &gt;= size())\n            return INT_MAX;\n        return tree[i];\n    }\n\n    /* Получить индекс левого дочернего узла узла с индексом i */\n    int left(int i) {\n        return 2 * i + 1;\n    }\n\n    /* Получить индекс правого дочернего узла узла с индексом i */\n    int right(int i) {\n        return 2 * i + 2;\n    }\n\n    /* Получить индекс родительского узла узла с индексом i */\n    int parent(int i) {\n        return (i - 1) / 2;\n    }\n\n    /* Обход в ширину */\n    vector&lt;int&gt; levelOrder() {\n        vector&lt;int&gt; res;\n        // Непосредственно обходить массив\n        for (int i = 0; i &lt; size(); i++) {\n            if (val(i) != INT_MAX)\n                res.push_back(val(i));\n        }\n        return res;\n    }\n\n    /* Предварительный обход */\n    vector&lt;int&gt; preOrder() {\n        vector&lt;int&gt; res;\n        dfs(0, \"pre\", res);\n        return res;\n    }\n\n    /* Симметричный обход */\n    vector&lt;int&gt; inOrder() {\n        vector&lt;int&gt; res;\n        dfs(0, \"in\", res);\n        return res;\n    }\n\n    /* Обратный обход */\n    vector&lt;int&gt; postOrder() {\n        vector&lt;int&gt; res;\n        dfs(0, \"post\", res);\n        return res;\n    }\n\n  private:\n    vector&lt;int&gt; tree;\n\n    /* Обход в глубину */\n    void dfs(int i, string order, vector&lt;int&gt; &amp;res) {\n        // Если это пустая позиция, вернуть\n        if (val(i) == INT_MAX)\n            return;\n        // Предварительный обход\n        if (order == \"pre\")\n            res.push_back(val(i));\n        dfs(left(i), order, res);\n        // Симметричный обход\n        if (order == \"in\")\n            res.push_back(val(i));\n        dfs(right(i), order, res);\n        // Обратный обход\n        if (order == \"post\")\n            res.push_back(val(i));\n    }\n};\n</code></pre> array_binary_tree.java<pre><code>/* Класс двоичного дерева в массивном представлении */\nclass ArrayBinaryTree {\n    private List&lt;Integer&gt; tree;\n\n    /* Конструктор */\n    public ArrayBinaryTree(List&lt;Integer&gt; arr) {\n        tree = new ArrayList&lt;&gt;(arr);\n    }\n\n    /* Вместимость списка */\n    public int size() {\n        return tree.size();\n    }\n\n    /* Получить значение узла с индексом i */\n    public Integer val(int i) {\n        // Если индекс выходит за границы, вернуть null, обозначающий пустую позицию\n        if (i &lt; 0 || i &gt;= size())\n            return null;\n        return tree.get(i);\n    }\n\n    /* Получить индекс левого дочернего узла узла с индексом i */\n    public Integer left(int i) {\n        return 2 * i + 1;\n    }\n\n    /* Получить индекс правого дочернего узла узла с индексом i */\n    public Integer right(int i) {\n        return 2 * i + 2;\n    }\n\n    /* Получить индекс родительского узла узла с индексом i */\n    public Integer parent(int i) {\n        return (i - 1) / 2;\n    }\n\n    /* Обход в ширину */\n    public List&lt;Integer&gt; levelOrder() {\n        List&lt;Integer&gt; res = new ArrayList&lt;&gt;();\n        // Непосредственно обходить массив\n        for (int i = 0; i &lt; size(); i++) {\n            if (val(i) != null)\n                res.add(val(i));\n        }\n        return res;\n    }\n\n    /* Обход в глубину */\n    private void dfs(Integer i, String order, List&lt;Integer&gt; res) {\n        // Если это пустая позиция, вернуть\n        if (val(i) == null)\n            return;\n        // Предварительный обход\n        if (\"pre\".equals(order))\n            res.add(val(i));\n        dfs(left(i), order, res);\n        // Симметричный обход\n        if (\"in\".equals(order))\n            res.add(val(i));\n        dfs(right(i), order, res);\n        // Обратный обход\n        if (\"post\".equals(order))\n            res.add(val(i));\n    }\n\n    /* Предварительный обход */\n    public List&lt;Integer&gt; preOrder() {\n        List&lt;Integer&gt; res = new ArrayList&lt;&gt;();\n        dfs(0, \"pre\", res);\n        return res;\n    }\n\n    /* Симметричный обход */\n    public List&lt;Integer&gt; inOrder() {\n        List&lt;Integer&gt; res = new ArrayList&lt;&gt;();\n        dfs(0, \"in\", res);\n        return res;\n    }\n\n    /* Обратный обход */\n    public List&lt;Integer&gt; postOrder() {\n        List&lt;Integer&gt; res = new ArrayList&lt;&gt;();\n        dfs(0, \"post\", res);\n        return res;\n    }\n}\n</code></pre> array_binary_tree.cs<pre><code>/* Класс двоичного дерева в массивном представлении */\nclass ArrayBinaryTree(List&lt;int?&gt; arr) {\n    List&lt;int?&gt; tree = new(arr);\n\n    /* Вместимость списка */\n    public int Size() {\n        return tree.Count;\n    }\n\n    /* Получить значение узла с индексом i */\n    public int? Val(int i) {\n        // Если индекс выходит за границы, вернуть null, обозначающий пустую позицию\n        if (i &lt; 0 || i &gt;= Size())\n            return null;\n        return tree[i];\n    }\n\n    /* Получить индекс левого дочернего узла узла с индексом i */\n    public int Left(int i) {\n        return 2 * i + 1;\n    }\n\n    /* Получить индекс правого дочернего узла узла с индексом i */\n    public int Right(int i) {\n        return 2 * i + 2;\n    }\n\n    /* Получить индекс родительского узла узла с индексом i */\n    public int Parent(int i) {\n        return (i - 1) / 2;\n    }\n\n    /* Обход в ширину */\n    public List&lt;int&gt; LevelOrder() {\n        List&lt;int&gt; res = [];\n        // Непосредственно обходить массив\n        for (int i = 0; i &lt; Size(); i++) {\n            if (Val(i).HasValue)\n                res.Add(Val(i)!.Value);\n        }\n        return res;\n    }\n\n    /* Обход в глубину */\n    void DFS(int i, string order, List&lt;int&gt; res) {\n        // Если это пустая позиция, вернуть\n        if (!Val(i).HasValue)\n            return;\n        // Предварительный обход\n        if (order == \"pre\")\n            res.Add(Val(i)!.Value);\n        DFS(Left(i), order, res);\n        // Симметричный обход\n        if (order == \"in\")\n            res.Add(Val(i)!.Value);\n        DFS(Right(i), order, res);\n        // Обратный обход\n        if (order == \"post\")\n            res.Add(Val(i)!.Value);\n    }\n\n    /* Предварительный обход */\n    public List&lt;int&gt; PreOrder() {\n        List&lt;int&gt; res = [];\n        DFS(0, \"pre\", res);\n        return res;\n    }\n\n    /* Симметричный обход */\n    public List&lt;int&gt; InOrder() {\n        List&lt;int&gt; res = [];\n        DFS(0, \"in\", res);\n        return res;\n    }\n\n    /* Обратный обход */\n    public List&lt;int&gt; PostOrder() {\n        List&lt;int&gt; res = [];\n        DFS(0, \"post\", res);\n        return res;\n    }\n}\n</code></pre> array_binary_tree.go<pre><code>/* Класс двоичного дерева в массивном представлении */\ntype arrayBinaryTree struct {\n    tree []any\n}\n\n/* Конструктор */\nfunc newArrayBinaryTree(arr []any) *arrayBinaryTree {\n    return &amp;arrayBinaryTree{\n        tree: arr,\n    }\n}\n\n/* Вместимость списка */\nfunc (abt *arrayBinaryTree) size() int {\n    return len(abt.tree)\n}\n\n/* Получить значение узла с индексом i */\nfunc (abt *arrayBinaryTree) val(i int) any {\n    // Если индекс выходит за границы, вернуть null, обозначающий пустую позицию\n    if i &lt; 0 || i &gt;= abt.size() {\n        return nil\n    }\n    return abt.tree[i]\n}\n\n/* Получить индекс левого дочернего узла узла с индексом i */\nfunc (abt *arrayBinaryTree) left(i int) int {\n    return 2*i + 1\n}\n\n/* Получить индекс правого дочернего узла узла с индексом i */\nfunc (abt *arrayBinaryTree) right(i int) int {\n    return 2*i + 2\n}\n\n/* Получить индекс родительского узла узла с индексом i */\nfunc (abt *arrayBinaryTree) parent(i int) int {\n    return (i - 1) / 2\n}\n\n/* Обход в ширину */\nfunc (abt *arrayBinaryTree) levelOrder() []any {\n    var res []any\n    // Непосредственно обходить массив\n    for i := 0; i &lt; abt.size(); i++ {\n        if abt.val(i) != nil {\n            res = append(res, abt.val(i))\n        }\n    }\n    return res\n}\n\n/* Обход в глубину */\nfunc (abt *arrayBinaryTree) dfs(i int, order string, res *[]any) {\n    // Если это пустая позиция, вернуть\n    if abt.val(i) == nil {\n        return\n    }\n    // Предварительный обход\n    if order == \"pre\" {\n        *res = append(*res, abt.val(i))\n    }\n    abt.dfs(abt.left(i), order, res)\n    // Симметричный обход\n    if order == \"in\" {\n        *res = append(*res, abt.val(i))\n    }\n    abt.dfs(abt.right(i), order, res)\n    // Обратный обход\n    if order == \"post\" {\n        *res = append(*res, abt.val(i))\n    }\n}\n\n/* Предварительный обход */\nfunc (abt *arrayBinaryTree) preOrder() []any {\n    var res []any\n    abt.dfs(0, \"pre\", &amp;res)\n    return res\n}\n\n/* Симметричный обход */\nfunc (abt *arrayBinaryTree) inOrder() []any {\n    var res []any\n    abt.dfs(0, \"in\", &amp;res)\n    return res\n}\n\n/* Обратный обход */\nfunc (abt *arrayBinaryTree) postOrder() []any {\n    var res []any\n    abt.dfs(0, \"post\", &amp;res)\n    return res\n}\n</code></pre> array_binary_tree.swift<pre><code>/* Класс двоичного дерева в массивном представлении */\nclass ArrayBinaryTree {\n    private var tree: [Int?]\n\n    /* Конструктор */\n    init(arr: [Int?]) {\n        tree = arr\n    }\n\n    /* Вместимость списка */\n    func size() -&gt; Int {\n        tree.count\n    }\n\n    /* Получить значение узла с индексом i */\n    func val(i: Int) -&gt; Int? {\n        // Если индекс выходит за границы, вернуть null, обозначающий пустую позицию\n        if i &lt; 0 || i &gt;= size() {\n            return nil\n        }\n        return tree[i]\n    }\n\n    /* Получить индекс левого дочернего узла узла с индексом i */\n    func left(i: Int) -&gt; Int {\n        2 * i + 1\n    }\n\n    /* Получить индекс правого дочернего узла узла с индексом i */\n    func right(i: Int) -&gt; Int {\n        2 * i + 2\n    }\n\n    /* Получить индекс родительского узла узла с индексом i */\n    func parent(i: Int) -&gt; Int {\n        (i - 1) / 2\n    }\n\n    /* Обход в ширину */\n    func levelOrder() -&gt; [Int] {\n        var res: [Int] = []\n        // Непосредственно обходить массив\n        for i in 0 ..&lt; size() {\n            if let val = val(i: i) {\n                res.append(val)\n            }\n        }\n        return res\n    }\n\n    /* Обход в глубину */\n    private func dfs(i: Int, order: String, res: inout [Int]) {\n        // Если это пустая позиция, вернуть\n        guard let val = val(i: i) else {\n            return\n        }\n        // Предварительный обход\n        if order == \"pre\" {\n            res.append(val)\n        }\n        dfs(i: left(i: i), order: order, res: &amp;res)\n        // Симметричный обход\n        if order == \"in\" {\n            res.append(val)\n        }\n        dfs(i: right(i: i), order: order, res: &amp;res)\n        // Обратный обход\n        if order == \"post\" {\n            res.append(val)\n        }\n    }\n\n    /* Предварительный обход */\n    func preOrder() -&gt; [Int] {\n        var res: [Int] = []\n        dfs(i: 0, order: \"pre\", res: &amp;res)\n        return res\n    }\n\n    /* Симметричный обход */\n    func inOrder() -&gt; [Int] {\n        var res: [Int] = []\n        dfs(i: 0, order: \"in\", res: &amp;res)\n        return res\n    }\n\n    /* Обратный обход */\n    func postOrder() -&gt; [Int] {\n        var res: [Int] = []\n        dfs(i: 0, order: \"post\", res: &amp;res)\n        return res\n    }\n}\n</code></pre> array_binary_tree.js<pre><code>/* Класс двоичного дерева в массивном представлении */\nclass ArrayBinaryTree {\n    #tree;\n\n    /* Конструктор */\n    constructor(arr) {\n        this.#tree = arr;\n    }\n\n    /* Вместимость списка */\n    size() {\n        return this.#tree.length;\n    }\n\n    /* Получить значение узла с индексом i */\n    val(i) {\n        // Если индекс выходит за границы, вернуть null, обозначающий пустую позицию\n        if (i &lt; 0 || i &gt;= this.size()) return null;\n        return this.#tree[i];\n    }\n\n    /* Получить индекс левого дочернего узла узла с индексом i */\n    left(i) {\n        return 2 * i + 1;\n    }\n\n    /* Получить индекс правого дочернего узла узла с индексом i */\n    right(i) {\n        return 2 * i + 2;\n    }\n\n    /* Получить индекс родительского узла узла с индексом i */\n    parent(i) {\n        return Math.floor((i - 1) / 2); // Округление вниз при делении\n    }\n\n    /* Обход в ширину */\n    levelOrder() {\n        let res = [];\n        // Непосредственно обходить массив\n        for (let i = 0; i &lt; this.size(); i++) {\n            if (this.val(i) !== null) res.push(this.val(i));\n        }\n        return res;\n    }\n\n    /* Обход в глубину */\n    #dfs(i, order, res) {\n        // Если это пустая позиция, вернуть\n        if (this.val(i) === null) return;\n        // Предварительный обход\n        if (order === 'pre') res.push(this.val(i));\n        this.#dfs(this.left(i), order, res);\n        // Симметричный обход\n        if (order === 'in') res.push(this.val(i));\n        this.#dfs(this.right(i), order, res);\n        // Обратный обход\n        if (order === 'post') res.push(this.val(i));\n    }\n\n    /* Предварительный обход */\n    preOrder() {\n        const res = [];\n        this.#dfs(0, 'pre', res);\n        return res;\n    }\n\n    /* Симметричный обход */\n    inOrder() {\n        const res = [];\n        this.#dfs(0, 'in', res);\n        return res;\n    }\n\n    /* Обратный обход */\n    postOrder() {\n        const res = [];\n        this.#dfs(0, 'post', res);\n        return res;\n    }\n}\n</code></pre> array_binary_tree.ts<pre><code>/* Класс двоичного дерева в массивном представлении */\nclass ArrayBinaryTree {\n    #tree: (number | null)[];\n\n    /* Конструктор */\n    constructor(arr: (number | null)[]) {\n        this.#tree = arr;\n    }\n\n    /* Вместимость списка */\n    size(): number {\n        return this.#tree.length;\n    }\n\n    /* Получить значение узла с индексом i */\n    val(i: number): number | null {\n        // Если индекс выходит за границы, вернуть null, обозначающий пустую позицию\n        if (i &lt; 0 || i &gt;= this.size()) return null;\n        return this.#tree[i];\n    }\n\n    /* Получить индекс левого дочернего узла узла с индексом i */\n    left(i: number): number {\n        return 2 * i + 1;\n    }\n\n    /* Получить индекс правого дочернего узла узла с индексом i */\n    right(i: number): number {\n        return 2 * i + 2;\n    }\n\n    /* Получить индекс родительского узла узла с индексом i */\n    parent(i: number): number {\n        return Math.floor((i - 1) / 2); // Округление вниз при делении\n    }\n\n    /* Обход в ширину */\n    levelOrder(): number[] {\n        let res = [];\n        // Непосредственно обходить массив\n        for (let i = 0; i &lt; this.size(); i++) {\n            if (this.val(i) !== null) res.push(this.val(i));\n        }\n        return res;\n    }\n\n    /* Обход в глубину */\n    #dfs(i: number, order: Order, res: (number | null)[]): void {\n        // Если это пустая позиция, вернуть\n        if (this.val(i) === null) return;\n        // Предварительный обход\n        if (order === 'pre') res.push(this.val(i));\n        this.#dfs(this.left(i), order, res);\n        // Симметричный обход\n        if (order === 'in') res.push(this.val(i));\n        this.#dfs(this.right(i), order, res);\n        // Обратный обход\n        if (order === 'post') res.push(this.val(i));\n    }\n\n    /* Предварительный обход */\n    preOrder(): (number | null)[] {\n        const res = [];\n        this.#dfs(0, 'pre', res);\n        return res;\n    }\n\n    /* Симметричный обход */\n    inOrder(): (number | null)[] {\n        const res = [];\n        this.#dfs(0, 'in', res);\n        return res;\n    }\n\n    /* Обратный обход */\n    postOrder(): (number | null)[] {\n        const res = [];\n        this.#dfs(0, 'post', res);\n        return res;\n    }\n}\n</code></pre> array_binary_tree.dart<pre><code>/* Класс двоичного дерева в массивном представлении */\nclass ArrayBinaryTree {\n  late List&lt;int?&gt; _tree;\n\n  /* Конструктор */\n  ArrayBinaryTree(this._tree);\n\n  /* Вместимость списка */\n  int size() {\n    return _tree.length;\n  }\n\n  /* Получить значение узла с индексом i */\n  int? val(int i) {\n    // Если индекс выходит за границы, вернуть null, обозначающий пустую позицию\n    if (i &lt; 0 || i &gt;= size()) {\n      return null;\n    }\n    return _tree[i];\n  }\n\n  /* Получить индекс левого дочернего узла узла с индексом i */\n  int? left(int i) {\n    return 2 * i + 1;\n  }\n\n  /* Получить индекс правого дочернего узла узла с индексом i */\n  int? right(int i) {\n    return 2 * i + 2;\n  }\n\n  /* Получить индекс родительского узла узла с индексом i */\n  int? parent(int i) {\n    return (i - 1) ~/ 2;\n  }\n\n  /* Обход в ширину */\n  List&lt;int&gt; levelOrder() {\n    List&lt;int&gt; res = [];\n    for (int i = 0; i &lt; size(); i++) {\n      if (val(i) != null) {\n        res.add(val(i)!);\n      }\n    }\n    return res;\n  }\n\n  /* Обход в глубину */\n  void dfs(int i, String order, List&lt;int?&gt; res) {\n    // Если это пустая позиция, вернуть\n    if (val(i) == null) {\n      return;\n    }\n    // Предварительный обход\n    if (order == 'pre') {\n      res.add(val(i));\n    }\n    dfs(left(i)!, order, res);\n    // Симметричный обход\n    if (order == 'in') {\n      res.add(val(i));\n    }\n    dfs(right(i)!, order, res);\n    // Обратный обход\n    if (order == 'post') {\n      res.add(val(i));\n    }\n  }\n\n  /* Предварительный обход */\n  List&lt;int?&gt; preOrder() {\n    List&lt;int?&gt; res = [];\n    dfs(0, 'pre', res);\n    return res;\n  }\n\n  /* Симметричный обход */\n  List&lt;int?&gt; inOrder() {\n    List&lt;int?&gt; res = [];\n    dfs(0, 'in', res);\n    return res;\n  }\n\n  /* Обратный обход */\n  List&lt;int?&gt; postOrder() {\n    List&lt;int?&gt; res = [];\n    dfs(0, 'post', res);\n    return res;\n  }\n}\n</code></pre> array_binary_tree.rs<pre><code>/* Класс двоичного дерева в массивном представлении */\nstruct ArrayBinaryTree {\n    tree: Vec&lt;Option&lt;i32&gt;&gt;,\n}\n\nimpl ArrayBinaryTree {\n    /* Конструктор */\n    fn new(arr: Vec&lt;Option&lt;i32&gt;&gt;) -&gt; Self {\n        Self { tree: arr }\n    }\n\n    /* Вместимость списка */\n    fn size(&amp;self) -&gt; i32 {\n        self.tree.len() as i32\n    }\n\n    /* Получить значение узла с индексом i */\n    fn val(&amp;self, i: i32) -&gt; Option&lt;i32&gt; {\n        // Если индекс выходит за границы, вернуть None, обозначающий пустую позицию\n        if i &lt; 0 || i &gt;= self.size() {\n            None\n        } else {\n            self.tree[i as usize]\n        }\n    }\n\n    /* Получить индекс левого дочернего узла узла с индексом i */\n    fn left(&amp;self, i: i32) -&gt; i32 {\n        2 * i + 1\n    }\n\n    /* Получить индекс правого дочернего узла узла с индексом i */\n    fn right(&amp;self, i: i32) -&gt; i32 {\n        2 * i + 2\n    }\n\n    /* Получить индекс родительского узла узла с индексом i */\n    fn parent(&amp;self, i: i32) -&gt; i32 {\n        (i - 1) / 2\n    }\n\n    /* Обход в ширину */\n    fn level_order(&amp;self) -&gt; Vec&lt;i32&gt; {\n        self.tree.iter().filter_map(|&amp;x| x).collect()\n    }\n\n    /* Обход в глубину */\n    fn dfs(&amp;self, i: i32, order: &amp;'static str, res: &amp;mut Vec&lt;i32&gt;) {\n        if self.val(i).is_none() {\n            return;\n        }\n        let val = self.val(i).unwrap();\n        // Предварительный обход\n        if order == \"pre\" {\n            res.push(val);\n        }\n        self.dfs(self.left(i), order, res);\n        // Симметричный обход\n        if order == \"in\" {\n            res.push(val);\n        }\n        self.dfs(self.right(i), order, res);\n        // Обратный обход\n        if order == \"post\" {\n            res.push(val);\n        }\n    }\n\n    /* Предварительный обход */\n    fn pre_order(&amp;self) -&gt; Vec&lt;i32&gt; {\n        let mut res = vec![];\n        self.dfs(0, \"pre\", &amp;mut res);\n        res\n    }\n\n    /* Симметричный обход */\n    fn in_order(&amp;self) -&gt; Vec&lt;i32&gt; {\n        let mut res = vec![];\n        self.dfs(0, \"in\", &amp;mut res);\n        res\n    }\n\n    /* Обратный обход */\n    fn post_order(&amp;self) -&gt; Vec&lt;i32&gt; {\n        let mut res = vec![];\n        self.dfs(0, \"post\", &amp;mut res);\n        res\n    }\n}\n</code></pre> array_binary_tree.c<pre><code>/* Структура двоичного дерева в представлении массивом */\ntypedef struct {\n    int *tree;\n    int size;\n} ArrayBinaryTree;\n\n/* Конструктор */\nArrayBinaryTree *newArrayBinaryTree(int *arr, int arrSize) {\n    ArrayBinaryTree *abt = (ArrayBinaryTree *)malloc(sizeof(ArrayBinaryTree));\n    abt-&gt;tree = malloc(sizeof(int) * arrSize);\n    memcpy(abt-&gt;tree, arr, sizeof(int) * arrSize);\n    abt-&gt;size = arrSize;\n    return abt;\n}\n\n/* Деструктор */\nvoid delArrayBinaryTree(ArrayBinaryTree *abt) {\n    free(abt-&gt;tree);\n    free(abt);\n}\n\n/* Вместимость списка */\nint size(ArrayBinaryTree *abt) {\n    return abt-&gt;size;\n}\n\n/* Получить значение узла с индексом i */\nint val(ArrayBinaryTree *abt, int i) {\n    // Если индекс выходит за границы, вернуть INT_MAX, обозначающий пустую позицию\n    if (i &lt; 0 || i &gt;= size(abt))\n        return INT_MAX;\n    return abt-&gt;tree[i];\n}\n\n/* Обход в ширину */\nint *levelOrder(ArrayBinaryTree *abt, int *returnSize) {\n    int *res = (int *)malloc(sizeof(int) * size(abt));\n    int index = 0;\n    // Непосредственно обходить массив\n    for (int i = 0; i &lt; size(abt); i++) {\n        if (val(abt, i) != INT_MAX)\n            res[index++] = val(abt, i);\n    }\n    *returnSize = index;\n    return res;\n}\n\n/* Обход в глубину */\nvoid dfs(ArrayBinaryTree *abt, int i, char *order, int *res, int *index) {\n    // Если это пустая позиция, вернуть\n    if (val(abt, i) == INT_MAX)\n        return;\n    // Предварительный обход\n    if (strcmp(order, \"pre\") == 0)\n        res[(*index)++] = val(abt, i);\n    dfs(abt, left(i), order, res, index);\n    // Симметричный обход\n    if (strcmp(order, \"in\") == 0)\n        res[(*index)++] = val(abt, i);\n    dfs(abt, right(i), order, res, index);\n    // Обратный обход\n    if (strcmp(order, \"post\") == 0)\n        res[(*index)++] = val(abt, i);\n}\n\n/* Предварительный обход */\nint *preOrder(ArrayBinaryTree *abt, int *returnSize) {\n    int *res = (int *)malloc(sizeof(int) * size(abt));\n    int index = 0;\n    dfs(abt, 0, \"pre\", res, &amp;index);\n    *returnSize = index;\n    return res;\n}\n\n/* Симметричный обход */\nint *inOrder(ArrayBinaryTree *abt, int *returnSize) {\n    int *res = (int *)malloc(sizeof(int) * size(abt));\n    int index = 0;\n    dfs(abt, 0, \"in\", res, &amp;index);\n    *returnSize = index;\n    return res;\n}\n\n/* Обратный обход */\nint *postOrder(ArrayBinaryTree *abt, int *returnSize) {\n    int *res = (int *)malloc(sizeof(int) * size(abt));\n    int index = 0;\n    dfs(abt, 0, \"post\", res, &amp;index);\n    *returnSize = index;\n    return res;\n}\n</code></pre> array_binary_tree.kt<pre><code>/* Класс двоичного дерева в массивном представлении */\nclass ArrayBinaryTree(val tree: MutableList&lt;Int?&gt;) {\n    /* Вместимость списка */\n    fun size(): Int {\n        return tree.size\n    }\n\n    /* Получить значение узла с индексом i */\n    fun _val(i: Int): Int? {\n        // Если индекс выходит за границы, вернуть null, обозначающий пустую позицию\n        if (i &lt; 0 || i &gt;= size()) return null\n        return tree[i]\n    }\n\n    /* Получить индекс левого дочернего узла узла с индексом i */\n    fun left(i: Int): Int {\n        return 2 * i + 1\n    }\n\n    /* Получить индекс правого дочернего узла узла с индексом i */\n    fun right(i: Int): Int {\n        return 2 * i + 2\n    }\n\n    /* Получить индекс родительского узла узла с индексом i */\n    fun parent(i: Int): Int {\n        return (i - 1) / 2\n    }\n\n    /* Обход в ширину */\n    fun levelOrder(): MutableList&lt;Int?&gt; {\n        val res = mutableListOf&lt;Int?&gt;()\n        // Непосредственно обходить массив\n        for (i in 0..&lt;size()) {\n            if (_val(i) != null)\n                res.add(_val(i))\n        }\n        return res\n    }\n\n    /* Обход в глубину */\n    fun dfs(i: Int, order: String, res: MutableList&lt;Int?&gt;) {\n        // Если это пустая позиция, вернуть\n        if (_val(i) == null)\n            return\n        // Предварительный обход\n        if (\"pre\" == order)\n            res.add(_val(i))\n        dfs(left(i), order, res)\n        // Симметричный обход\n        if (\"in\" == order)\n            res.add(_val(i))\n        dfs(right(i), order, res)\n        // Обратный обход\n        if (\"post\" == order)\n            res.add(_val(i))\n    }\n\n    /* Предварительный обход */\n    fun preOrder(): MutableList&lt;Int?&gt; {\n        val res = mutableListOf&lt;Int?&gt;()\n        dfs(0, \"pre\", res)\n        return res\n    }\n\n    /* Симметричный обход */\n    fun inOrder(): MutableList&lt;Int?&gt; {\n        val res = mutableListOf&lt;Int?&gt;()\n        dfs(0, \"in\", res)\n        return res\n    }\n\n    /* Обратный обход */\n    fun postOrder(): MutableList&lt;Int?&gt; {\n        val res = mutableListOf&lt;Int?&gt;()\n        dfs(0, \"post\", res)\n        return res\n    }\n}\n</code></pre> array_binary_tree.rb<pre><code>### Класс двоичного дерева в массивном представлении ###\nclass ArrayBinaryTree\n  ### Конструктор ###\n  def initialize(arr)\n    @tree = arr.to_a\n  end\n\n  ### Вместимость списка ###\n  def size\n    @tree.length\n  end\n\n  ### Получить значение узла с индексом i ###\n  def val(i)\n    # Если индекс выходит за границы, вернуть nil, обозначающий пустую ячейку\n    return if i &lt; 0 || i &gt;= size\n\n    @tree[i]\n  end\n\n  ### Получить индекс левого дочернего узла узла с индексом i ###\n  def left(i)\n    2 * i + 1\n  end\n\n  ### Получить индекс правого дочернего узла узла с индексом i ###\n  def right(i)\n    2 * i + 2\n  end\n\n  ### Получить индекс родительского узла узла с индексом i ###\n  def parent(i)\n    (i - 1) / 2\n  end\n\n  ### Обход в ширину ###\n  def level_order\n    @res = []\n\n    # Непосредственно обходить массив\n    for i in 0...size\n      @res &lt;&lt; val(i) unless val(i).nil?\n    end\n\n    @res\n  end\n\n  ### Обход в глубину ###\n  def dfs(i, order)\n    return if val(i).nil?\n    # Предварительный обход\n    @res &lt;&lt; val(i) if order == :pre\n    dfs(left(i), order)\n    # Симметричный обход\n    @res &lt;&lt; val(i) if order == :in\n    dfs(right(i), order)\n    # Обратный обход\n    @res &lt;&lt; val(i) if order == :post\n  end\n\n  ### Предварительный обход ###\n  def pre_order\n    @res = []\n    dfs(0, :pre)\n    @res\n  end\n\n  ### Симметричный обход ###\n  def in_order\n    @res = []\n    dfs(0, :in)\n    @res\n  end\n\n  ### Обратный обход ###\n  def post_order\n    @res = []\n    dfs(0, :post)\n    @res\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 7. Деревья","7.3 &nbsp; Представление двоичного дерева массивом"],"tags":[]},{"location":"chapter_tree/array_representation_of_tree/#733","level":2,"title":"7.3.3   Преимущества и ограничения","text":"<p>Представление двоичного дерева массивом имеет в основном следующие преимущества.</p> <ul> <li>Массив хранится в непрерывной области памяти, хорошо работает с кешем и обеспечивает высокую скорость доступа и обхода.</li> <li>Не нужно хранить указатели, поэтому память расходуется экономнее.</li> <li>Разрешается произвольный доступ к узлам.</li> </ul> <p>Однако у представления массивом есть и некоторые ограничения.</p> <ul> <li>Для хранения массива требуется непрерывная область памяти, поэтому такой способ не подходит для деревьев с очень большим объемом данных.</li> <li>Добавление и удаление узлов приходится реализовывать через вставку и удаление элементов массива, а это не слишком эффективно.</li> <li>Когда в двоичном дереве имеется большое число <code>None</code> , доля действительно полезных данных в массиве оказывается низкой, и эффективность использования пространства падает.</li> </ul>","path":["Глава 7. Деревья","7.3 &nbsp; Представление двоичного дерева массивом"],"tags":[]},{"location":"chapter_tree/avl_tree/","level":1,"title":"7.5   AVL-дерево *","text":"<p>В разделе \"Двоичное дерево поиска\" мы упоминали, что после многократных операций вставки и удаления узлов двоичное дерево поиска может выродиться в связный список. В таком случае временная сложность всех операций ухудшается с \\(O(\\log n)\\) до \\(O(n)\\) .</p> <p>Как показано на рисунке 7-24, после двух операций удаления узлов это двоичное дерево поиска вырождается в связный список.</p> <p></p> <p> Рисунок 7-24   Деградация AVL-дерева после удаления узлов </p> <p>Другой пример: если в идеальное двоичное дерево, показанное на рисунке 7-25, вставить два узла, то дерево сильно наклонится влево, а временная сложность поиска тоже ухудшится.</p> <p></p> <p> Рисунок 7-25   Деградация AVL-дерева после вставки узлов </p> <p>В 1962 году Г. М. Adelson-Velsky и Е. М. Landis в статье \"An algorithm for the organization of information\" предложили AVL-дерево. В статье подробно описан набор операций, гарантирующий, что при непрерывном добавлении и удалении узлов AVL-дерево не вырождается, благодаря чему временная сложность различных операций сохраняется на уровне \\(O(\\log n)\\) . Иначе говоря, в сценариях, где часто выполняются вставка, удаление, поиск и изменение, AVL-дерево всегда поддерживает эффективную работу с данными и потому имеет высокую практическую ценность.</p>","path":["Глава 7. Деревья","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#751-avl-","level":2,"title":"7.5.1   Распространенные термины AVL-дерева","text":"<p>AVL-дерево одновременно является и двоичным деревом поиска, и сбалансированным двоичным деревом, то есть одновременно удовлетворяет всем свойствам обеих этих структур. Поэтому AVL-дерево является разновидностью сбалансированного двоичного дерева поиска (balanced binary search tree).</p>","path":["Глава 7. Деревья","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#1","level":3,"title":"1.   Высота узла","text":"<p>Поскольку операции AVL-дерева требуют получать высоту узла, нам нужно добавить в класс узла переменную <code>height</code> :</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>class TreeNode:\n    \"\"\"Класс узла AVL-дерева\"\"\"\n    def __init__(self, val: int):\n        self.val: int = val                 # Значение узла\n        self.height: int = 0                # Высота узла\n        self.left: TreeNode | None = None   # Ссылка на левого дочернего узла\n        self.right: TreeNode | None = None  # Ссылка на правого дочернего узла\n</code></pre> <pre><code>/* Класс узла AVL-дерева */\nstruct TreeNode {\n    int val{};          // Значение узла\n    int height = 0;     // Высота узла\n    TreeNode *left{};   // Левый дочерний узел\n    TreeNode *right{};  // Правый дочерний узел\n    TreeNode() = default;\n    explicit TreeNode(int x) : val(x){}\n};\n</code></pre> <pre><code>/* Класс узла AVL-дерева */\nclass TreeNode {\n    public int val;        // Значение узла\n    public int height;     // Высота узла\n    public TreeNode left;  // Левый дочерний узел\n    public TreeNode right; // Правый дочерний узел\n    public TreeNode(int x) { val = x; }\n}\n</code></pre> <pre><code>/* Класс узла AVL-дерева */\nclass TreeNode(int? x) {\n    public int? val = x;    // Значение узла\n    public int height;      // Высота узла\n    public TreeNode? left;  // Ссылка на левого дочернего узла\n    public TreeNode? right; // Ссылка на правого дочернего узла\n}\n</code></pre> <pre><code>/* Структура узла AVL-дерева */\ntype TreeNode struct {\n    Val    int       // Значение узла\n    Height int       // Высота узла\n    Left   *TreeNode // Ссылка на левого дочернего узла\n    Right  *TreeNode // Ссылка на правого дочернего узла\n}\n</code></pre> <pre><code>/* Класс узла AVL-дерева */\nclass TreeNode {\n    var val: Int // Значение узла\n    var height: Int // Высота узла\n    var left: TreeNode? // Левый дочерний узел\n    var right: TreeNode? // Правый дочерний узел\n\n    init(x: Int) {\n        val = x\n        height = 0\n    }\n}\n</code></pre> <pre><code>/* Класс узла AVL-дерева */\nclass TreeNode {\n    val; // Значение узла\n    height; // Высота узла\n    left; // Указатель на левого дочернего узла\n    right; // Указатель на правого дочернего узла\n    constructor(val, left, right, height) {\n        this.val = val === undefined ? 0 : val;\n        this.height = height === undefined ? 0 : height;\n        this.left = left === undefined ? null : left;\n        this.right = right === undefined ? null : right;\n    }\n}\n</code></pre> <pre><code>/* Класс узла AVL-дерева */\nclass TreeNode {\n    val: number;            // Значение узла\n    height: number;         // Высота узла\n    left: TreeNode | null;  // Указатель на левого дочернего узла\n    right: TreeNode | null; // Указатель на правого дочернего узла\n    constructor(val?: number, height?: number, left?: TreeNode | null, right?: TreeNode | null) {\n        this.val = val === undefined ? 0 : val;\n        this.height = height === undefined ? 0 : height;\n        this.left = left === undefined ? null : left;\n        this.right = right === undefined ? null : right;\n    }\n}\n</code></pre> <pre><code>/* Класс узла AVL-дерева */\nclass TreeNode {\n  int val;         // Значение узла\n  int height;      // Высота узла\n  TreeNode? left;  // Левый дочерний узел\n  TreeNode? right; // Правый дочерний узел\n  TreeNode(this.val, [this.height = 0, this.left, this.right]);\n}\n</code></pre> <pre><code>use std::rc::Rc;\nuse std::cell::RefCell;\n\n/* Структура узла AVL-дерева */\nstruct TreeNode {\n    val: i32,                               // Значение узла\n    height: i32,                            // Высота узла\n    left: Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,    // Левый дочерний узел\n    right: Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,   // Правый дочерний узел\n}\n\nimpl TreeNode {\n    /* Конструктор */\n    fn new(val: i32) -&gt; Rc&lt;RefCell&lt;Self&gt;&gt; {\n        Rc::new(RefCell::new(Self {\n            val,\n            height: 0,\n            left: None,\n            right: None\n        }))\n    }\n}\n</code></pre> <pre><code>/* Структура узла AVL-дерева */\ntypedef struct TreeNode {\n    int val;\n    int height;\n    struct TreeNode *left;\n    struct TreeNode *right;\n} TreeNode;\n\n/* Конструктор */\nTreeNode *newTreeNode(int val) {\n    TreeNode *node;\n\n    node = (TreeNode *)malloc(sizeof(TreeNode));\n    node-&gt;val = val;\n    node-&gt;height = 0;\n    node-&gt;left = NULL;\n    node-&gt;right = NULL;\n    return node;\n}\n</code></pre> <pre><code>/* Класс узла AVL-дерева */\nclass TreeNode(val _val: Int) {  // Значение узла\n    val height: Int = 0          // Высота узла\n    val left: TreeNode? = null   // Левый дочерний узел\n    val right: TreeNode? = null  // Правый дочерний узел\n}\n</code></pre> <pre><code>### Класс узла AVL-дерева ###\nclass TreeNode\n  attr_accessor :val    # Значение узла\n  attr_accessor :height # Высота узла\n  attr_accessor :left   # Ссылка на левого дочернего узла\n  attr_accessor :right  # Ссылка на правого дочернего узла\n\n  def initialize(val)\n    @val = val\n    @height = 0\n  end\nend\n</code></pre> <p>\"Высота узла\" означает расстояние от этого узла до самого удаленного листового узла, то есть число пройденных \"ребер\". Особенно важно помнить, что высота листового узла равна \\(0\\) , а высота пустого узла равна \\(-1\\) . Мы создадим две вспомогательные функции: одну для получения высоты узла, другую для ее обновления:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def height(self, node: TreeNode | None) -&gt; int:\n    \"\"\"Получить высоту узла\"\"\"\n    # Высота пустого узла равна -1, высота листового узла равна 0\n    if node is not None:\n        return node.height\n    return -1\n\ndef update_height(self, node: TreeNode | None):\n    \"\"\"Обновить высоту узла\"\"\"\n    # Высота узла равна высоте более высокого поддерева + 1\n    node.height = max([self.height(node.left), self.height(node.right)]) + 1\n</code></pre> avl_tree.cpp<pre><code>/* Получить высоту узла */\nint height(TreeNode *node) {\n    // Высота пустого узла равна -1, высота листового узла равна 0\n    return node == nullptr ? -1 : node-&gt;height;\n}\n\n/* Обновить высоту узла */\nvoid updateHeight(TreeNode *node) {\n    // Высота узла равна высоте более высокого поддерева + 1\n    node-&gt;height = max(height(node-&gt;left), height(node-&gt;right)) + 1;\n}\n</code></pre> avl_tree.java<pre><code>/* Получить высоту узла */\nint height(TreeNode node) {\n    // Высота пустого узла равна -1, высота листового узла равна 0\n    return node == null ? -1 : node.height;\n}\n\n/* Обновить высоту узла */\nvoid updateHeight(TreeNode node) {\n    // Высота узла равна высоте более высокого поддерева + 1\n    node.height = Math.max(height(node.left), height(node.right)) + 1;\n}\n</code></pre> avl_tree.cs<pre><code>/* Получить высоту узла */\nint Height(TreeNode? node) {\n    // Высота пустого узла равна -1, высота листового узла равна 0\n    return node == null ? -1 : node.height;\n}\n\n/* Обновить высоту узла */\nvoid UpdateHeight(TreeNode node) {\n    // Высота узла равна высоте более высокого поддерева + 1\n    node.height = Math.Max(Height(node.left), Height(node.right)) + 1;\n}\n</code></pre> avl_tree.go<pre><code>/* Получить высоту узла */\nfunc (t *aVLTree) height(node *TreeNode) int {\n    // Высота пустого узла равна -1, высота листового узла равна 0\n    if node != nil {\n        return node.Height\n    }\n    return -1\n}\n\n/* Обновить высоту узла */\nfunc (t *aVLTree) updateHeight(node *TreeNode) {\n    lh := t.height(node.Left)\n    rh := t.height(node.Right)\n    // Высота узла равна высоте более высокого поддерева + 1\n    if lh &gt; rh {\n        node.Height = lh + 1\n    } else {\n        node.Height = rh + 1\n    }\n}\n</code></pre> avl_tree.swift<pre><code>/* Получить высоту узла */\nfunc height(node: TreeNode?) -&gt; Int {\n    // Высота пустого узла равна -1, высота листового узла равна 0\n    node?.height ?? -1\n}\n\n/* Обновить высоту узла */\nfunc updateHeight(node: TreeNode?) {\n    // Высота узла равна высоте более высокого поддерева + 1\n    node?.height = max(height(node: node?.left), height(node: node?.right)) + 1\n}\n</code></pre> avl_tree.js<pre><code>/* Получить высоту узла */\nheight(node) {\n    // Высота пустого узла равна -1, высота листового узла равна 0\n    return node === null ? -1 : node.height;\n}\n\n/* Обновить высоту узла */\n#updateHeight(node) {\n    // Высота узла равна высоте более высокого поддерева + 1\n    node.height =\n        Math.max(this.height(node.left), this.height(node.right)) + 1;\n}\n</code></pre> avl_tree.ts<pre><code>/* Получить высоту узла */\nheight(node: TreeNode): number {\n    // Высота пустого узла равна -1, высота листового узла равна 0\n    return node === null ? -1 : node.height;\n}\n\n/* Обновить высоту узла */\nupdateHeight(node: TreeNode): void {\n    // Высота узла равна высоте более высокого поддерева + 1\n    node.height =\n        Math.max(this.height(node.left), this.height(node.right)) + 1;\n}\n</code></pre> avl_tree.dart<pre><code>/* Получить высоту узла */\nint height(TreeNode? node) {\n  // Высота пустого узла равна -1, высота листового узла равна 0\n  return node == null ? -1 : node.height;\n}\n\n/* Обновить высоту узла */\nvoid updateHeight(TreeNode? node) {\n  // Высота узла равна высоте более высокого поддерева + 1\n  node!.height = max(height(node.left), height(node.right)) + 1;\n}\n</code></pre> avl_tree.rs<pre><code>/* Получить высоту узла */\nfn height(node: OptionTreeNodeRc) -&gt; i32 {\n    // Высота пустого узла равна -1, высота листового узла равна 0\n    match node {\n        Some(node) =&gt; node.borrow().height,\n        None =&gt; -1,\n    }\n}\n\n/* Обновить высоту узла */\nfn update_height(node: OptionTreeNodeRc) {\n    if let Some(node) = node {\n        let left = node.borrow().left.clone();\n        let right = node.borrow().right.clone();\n        // Высота узла равна высоте более высокого поддерева + 1\n        node.borrow_mut().height = std::cmp::max(Self::height(left), Self::height(right)) + 1;\n    }\n}\n</code></pre> avl_tree.c<pre><code>/* Получить высоту узла */\nint height(TreeNode *node) {\n    // Высота пустого узла равна -1, высота листового узла равна 0\n    if (node != NULL) {\n        return node-&gt;height;\n    }\n    return -1;\n}\n\n/* Обновить высоту узла */\nvoid updateHeight(TreeNode *node) {\n    int lh = height(node-&gt;left);\n    int rh = height(node-&gt;right);\n    // Высота узла равна высоте более высокого поддерева + 1\n    if (lh &gt; rh) {\n        node-&gt;height = lh + 1;\n    } else {\n        node-&gt;height = rh + 1;\n    }\n}\n</code></pre> avl_tree.kt<pre><code>/* Получить высоту узла */\nfun height(node: TreeNode?): Int {\n    // Высота пустого узла равна -1, высота листового узла равна 0\n    return node?.height ?: -1\n}\n\n/* Обновить высоту узла */\nfun updateHeight(node: TreeNode?) {\n    // Высота узла равна высоте более высокого поддерева + 1\n    node?.height = max(height(node?.left), height(node?.right)) + 1\n}\n</code></pre> avl_tree.rb<pre><code>### Получить высоту узла ###\ndef height(node)\n  # Высота пустого узла равна -1, высота листового узла равна 0\n  return node.height unless node.nil?\n\n  -1\nend\n\n### Обновить высоту узла ###\ndef update_height(node)\n  # Высота узла равна высоте более высокого поддерева + 1\n  node.height = [height(node.left), height(node.right)].max + 1\nend\n</code></pre>","path":["Глава 7. Деревья","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#2-","level":3,"title":"2.   Баланс-фактор узла","text":"<p>Баланс-фактор (balance factor) узла определяется как высота левого поддерева минус высота правого поддерева; при этом баланс-фактор пустого узла считается равным \\(0\\) . Мы также инкапсулируем получение баланс-фактора в отдельную функцию, чтобы потом было удобнее ее использовать:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def balance_factor(self, node: TreeNode | None) -&gt; int:\n    \"\"\"Получить коэффициент баланса\"\"\"\n    # Коэффициент баланса пустого узла равен 0\n    if node is None:\n        return 0\n    # Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n    return self.height(node.left) - self.height(node.right)\n</code></pre> avl_tree.cpp<pre><code>/* Получить коэффициент баланса */\nint balanceFactor(TreeNode *node) {\n    // Коэффициент баланса пустого узла равен 0\n    if (node == nullptr)\n        return 0;\n    // Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n    return height(node-&gt;left) - height(node-&gt;right);\n}\n</code></pre> avl_tree.java<pre><code>/* Получить коэффициент баланса */\nint balanceFactor(TreeNode node) {\n    // Коэффициент баланса пустого узла равен 0\n    if (node == null)\n        return 0;\n    // Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n    return height(node.left) - height(node.right);\n}\n</code></pre> avl_tree.cs<pre><code>/* Получить коэффициент баланса */\nint BalanceFactor(TreeNode? node) {\n    // Коэффициент баланса пустого узла равен 0\n    if (node == null) return 0;\n    // Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n    return Height(node.left) - Height(node.right);\n}\n</code></pre> avl_tree.go<pre><code>/* Получить коэффициент баланса */\nfunc (t *aVLTree) balanceFactor(node *TreeNode) int {\n    // Коэффициент баланса пустого узла равен 0\n    if node == nil {\n        return 0\n    }\n    // Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n    return t.height(node.Left) - t.height(node.Right)\n}\n</code></pre> avl_tree.swift<pre><code>/* Получить коэффициент баланса */\nfunc balanceFactor(node: TreeNode?) -&gt; Int {\n    // Коэффициент баланса пустого узла равен 0\n    guard let node = node else { return 0 }\n    // Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n    return height(node: node.left) - height(node: node.right)\n}\n</code></pre> avl_tree.js<pre><code>/* Получить коэффициент баланса */\nbalanceFactor(node) {\n    // Коэффициент баланса пустого узла равен 0\n    if (node === null) return 0;\n    // Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n    return this.height(node.left) - this.height(node.right);\n}\n</code></pre> avl_tree.ts<pre><code>/* Получить коэффициент баланса */\nbalanceFactor(node: TreeNode): number {\n    // Коэффициент баланса пустого узла равен 0\n    if (node === null) return 0;\n    // Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n    return this.height(node.left) - this.height(node.right);\n}\n</code></pre> avl_tree.dart<pre><code>/* Получить коэффициент баланса */\nint balanceFactor(TreeNode? node) {\n  // Коэффициент баланса пустого узла равен 0\n  if (node == null) return 0;\n  // Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n  return height(node.left) - height(node.right);\n}\n</code></pre> avl_tree.rs<pre><code>/* Получить коэффициент баланса */\nfn balance_factor(node: OptionTreeNodeRc) -&gt; i32 {\n    match node {\n        // Коэффициент баланса пустого узла равен 0\n        None =&gt; 0,\n        // Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n        Some(node) =&gt; {\n            Self::height(node.borrow().left.clone()) - Self::height(node.borrow().right.clone())\n        }\n    }\n}\n</code></pre> avl_tree.c<pre><code>/* Получить коэффициент баланса */\nint balanceFactor(TreeNode *node) {\n    // Коэффициент баланса пустого узла равен 0\n    if (node == NULL) {\n        return 0;\n    }\n    // Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n    return height(node-&gt;left) - height(node-&gt;right);\n}\n</code></pre> avl_tree.kt<pre><code>/* Получить коэффициент баланса */\nfun balanceFactor(node: TreeNode?): Int {\n    // Коэффициент баланса пустого узла равен 0\n    if (node == null) return 0\n    // Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n    return height(node.left) - height(node.right)\n}\n</code></pre> avl_tree.rb<pre><code>### Получить коэффициент баланса ###\ndef balance_factor(node)\n  # Коэффициент баланса пустого узла равен 0\n  return 0 if node.nil?\n\n  # Коэффициент баланса узла = высота левого поддерева - высота правого поддерева\n  height(node.left) - height(node.right)\nend\n</code></pre> <p>Tip</p> <p>Пусть баланс-фактор равен \\(f\\) ; тогда для любого узла AVL-дерева выполняется \\(-1 \\le f \\le 1\\) .</p>","path":["Глава 7. Деревья","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#752-avl-","level":2,"title":"7.5.2   Вращения AVL-дерева","text":"<p>Особенность AVL-дерева заключается в операции \"вращения\", которая позволяет заново сбалансировать разбалансированный узел, не нарушая последовательность симметричного обхода двоичного дерева. Иначе говоря, операция вращения одновременно сохраняет свойство \"двоичного дерева поиска\" и возвращает дерево в состояние \"сбалансированного двоичного дерева\".</p> <p>Узлы, для которых абсолютное значение баланс-фактора больше \\(1\\) , мы называем \"разбалансированными узлами\". В зависимости от вида разбаланса вращения делятся на четыре типа: правое вращение, левое вращение, сначала левое затем правое, и сначала правое затем левое. Ниже разберем их подробно.</p>","path":["Глава 7. Деревья","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#1_1","level":3,"title":"1.   Правое вращение","text":"<p>Как показано на рисунках ниже, под узлом указан его баланс-фактор. Если двигаться снизу вверх, то первым разбалансированным узлом в двоичном дереве будет \"узел 3\". Рассмотрим поддерево с этим узлом в качестве корня, обозначим данный узел как <code>node</code> , его левого дочернего узла как <code>child</code> и выполним \"правое вращение\". После завершения правого вращения поддерево снова станет сбалансированным и при этом сохранит свойство двоичного дерева поиска.</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p> Рисунок 7-26   Шаги правого вращения </p> <p>Как показано на рисунке 7-27, когда у узла <code>child</code> есть правый дочерний узел, который мы обозначим как <code>grand_child</code> , в правое вращение нужно добавить еще один шаг: сделать <code>grand_child</code> левым дочерним узлом <code>node</code> .</p> <p></p> <p> Рисунок 7-27   Правое вращение при наличии grand_child </p> <p>\"Поворот вправо\" - это лишь образное описание; в реальности он реализуется через изменение указателей узлов. Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def right_rotate(self, node: TreeNode | None) -&gt; TreeNode | None:\n    \"\"\"Операция правого вращения\"\"\"\n    child = node.left\n    grand_child = child.right\n    # Выполнить правое вращение узла node вокруг child\n    child.right = node\n    node.left = grand_child\n    # Обновить высоту узла\n    self.update_height(node)\n    self.update_height(child)\n    # Вернуть корневой узел поддерева после вращения\n    return child\n</code></pre> avl_tree.cpp<pre><code>/* Операция правого вращения */\nTreeNode *rightRotate(TreeNode *node) {\n    TreeNode *child = node-&gt;left;\n    TreeNode *grandChild = child-&gt;right;\n    // Выполнить правое вращение узла node вокруг child\n    child-&gt;right = node;\n    node-&gt;left = grandChild;\n    // Обновить высоту узла\n    updateHeight(node);\n    updateHeight(child);\n    // Вернуть корневой узел поддерева после вращения\n    return child;\n}\n</code></pre> avl_tree.java<pre><code>/* Операция правого вращения */\nTreeNode rightRotate(TreeNode node) {\n    TreeNode child = node.left;\n    TreeNode grandChild = child.right;\n    // Выполнить правое вращение узла node вокруг child\n    child.right = node;\n    node.left = grandChild;\n    // Обновить высоту узла\n    updateHeight(node);\n    updateHeight(child);\n    // Вернуть корневой узел поддерева после вращения\n    return child;\n}\n</code></pre> avl_tree.cs<pre><code>/* Операция правого вращения */\nTreeNode? RightRotate(TreeNode? node) {\n    TreeNode? child = node?.left;\n    TreeNode? grandChild = child?.right;\n    // Выполнить правое вращение узла node вокруг child\n    child.right = node;\n    node.left = grandChild;\n    // Обновить высоту узла\n    UpdateHeight(node);\n    UpdateHeight(child);\n    // Вернуть корневой узел поддерева после вращения\n    return child;\n}\n</code></pre> avl_tree.go<pre><code>/* Операция правого вращения */\nfunc (t *aVLTree) rightRotate(node *TreeNode) *TreeNode {\n    child := node.Left\n    grandChild := child.Right\n    // Выполнить правое вращение узла node вокруг child\n    child.Right = node\n    node.Left = grandChild\n    // Обновить высоту узла\n    t.updateHeight(node)\n    t.updateHeight(child)\n    // Вернуть корневой узел поддерева после вращения\n    return child\n}\n</code></pre> avl_tree.swift<pre><code>/* Операция правого вращения */\nfunc rightRotate(node: TreeNode?) -&gt; TreeNode? {\n    let child = node?.left\n    let grandChild = child?.right\n    // Выполнить правое вращение узла node вокруг child\n    child?.right = node\n    node?.left = grandChild\n    // Обновить высоту узла\n    updateHeight(node: node)\n    updateHeight(node: child)\n    // Вернуть корневой узел поддерева после вращения\n    return child\n}\n</code></pre> avl_tree.js<pre><code>/* Операция правого вращения */\n#rightRotate(node) {\n    const child = node.left;\n    const grandChild = child.right;\n    // Выполнить правое вращение узла node вокруг child\n    child.right = node;\n    node.left = grandChild;\n    // Обновить высоту узла\n    this.#updateHeight(node);\n    this.#updateHeight(child);\n    // Вернуть корневой узел поддерева после вращения\n    return child;\n}\n</code></pre> avl_tree.ts<pre><code>/* Операция правого вращения */\nrightRotate(node: TreeNode): TreeNode {\n    const child = node.left;\n    const grandChild = child.right;\n    // Выполнить правое вращение узла node вокруг child\n    child.right = node;\n    node.left = grandChild;\n    // Обновить высоту узла\n    this.updateHeight(node);\n    this.updateHeight(child);\n    // Вернуть корневой узел поддерева после вращения\n    return child;\n}\n</code></pre> avl_tree.dart<pre><code>/* Операция правого вращения */\nTreeNode? rightRotate(TreeNode? node) {\n  TreeNode? child = node!.left;\n  TreeNode? grandChild = child!.right;\n  // Выполнить правое вращение узла node вокруг child\n  child.right = node;\n  node.left = grandChild;\n  // Обновить высоту узла\n  updateHeight(node);\n  updateHeight(child);\n  // Вернуть корневой узел поддерева после вращения\n  return child;\n}\n</code></pre> avl_tree.rs<pre><code>/* Операция правого вращения */\nfn right_rotate(node: OptionTreeNodeRc) -&gt; OptionTreeNodeRc {\n    match node {\n        Some(node) =&gt; {\n            let child = node.borrow().left.clone().unwrap();\n            let grand_child = child.borrow().right.clone();\n            // Выполнить правое вращение узла node вокруг child\n            child.borrow_mut().right = Some(node.clone());\n            node.borrow_mut().left = grand_child;\n            // Обновить высоту узла\n            Self::update_height(Some(node));\n            Self::update_height(Some(child.clone()));\n            // Вернуть корневой узел поддерева после вращения\n            Some(child)\n        }\n        None =&gt; None,\n    }\n}\n</code></pre> avl_tree.c<pre><code>/* Операция правого вращения */\nTreeNode *rightRotate(TreeNode *node) {\n    TreeNode *child, *grandChild;\n    child = node-&gt;left;\n    grandChild = child-&gt;right;\n    // Выполнить правое вращение узла node вокруг child\n    child-&gt;right = node;\n    node-&gt;left = grandChild;\n    // Обновить высоту узла\n    updateHeight(node);\n    updateHeight(child);\n    // Вернуть корневой узел поддерева после вращения\n    return child;\n}\n</code></pre> avl_tree.kt<pre><code>/* Операция правого вращения */\nfun rightRotate(node: TreeNode?): TreeNode {\n    val child = node!!.left\n    val grandChild = child!!.right\n    // Выполнить правое вращение узла node вокруг child\n    child.right = node\n    node.left = grandChild\n    // Обновить высоту узла\n    updateHeight(node)\n    updateHeight(child)\n    // Вернуть корневой узел поддерева после вращения\n    return child\n}\n</code></pre> avl_tree.rb<pre><code>### Операция правого вращения ###\ndef right_rotate(node)\n  child = node.left\n  grand_child = child.right\n  # Выполнить правое вращение узла node вокруг child\n  child.right = node\n  node.left = grand_child\n  # Обновить высоту узла\n  update_height(node)\n  update_height(child)\n  # Вернуть корневой узел поддерева после вращения\n  child\nend\n</code></pre>","path":["Глава 7. Деревья","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#2","level":3,"title":"2.   Левое вращение","text":"<p>Соответственно, если рассмотреть \"зеркальную\" версию приведенного выше разбалансированного двоичного дерева, то понадобится выполнить \"левое вращение\", показанное на рисунке 7-28.</p> <p></p> <p> Рисунок 7-28   Левое вращение </p> <p>По той же причине, когда у узла <code>child</code> есть левый дочерний узел, который обозначим как <code>grand_child</code> , в левое вращение также требуется добавить шаг: сделать <code>grand_child</code> правым дочерним узлом <code>node</code> .</p> <p></p> <p> Рисунок 7-29   Левое вращение при наличии grand_child </p> <p>Можно заметить, что операции правого и левого вращения логически зеркально симметричны, и два вида разбаланса, которые они исправляют, тоже симметричны. Поэтому, опираясь на эту симметрию, достаточно заменить в коде правого вращения все <code>left</code> на <code>right</code> , а все <code>right</code> на <code>left</code> , чтобы получить реализацию левого вращения:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def left_rotate(self, node: TreeNode | None) -&gt; TreeNode | None:\n    \"\"\"Операция левого вращения\"\"\"\n    child = node.right\n    grand_child = child.left\n    # Выполнить левое вращение узла node вокруг child\n    child.left = node\n    node.right = grand_child\n    # Обновить высоту узла\n    self.update_height(node)\n    self.update_height(child)\n    # Вернуть корневой узел поддерева после вращения\n    return child\n</code></pre> avl_tree.cpp<pre><code>/* Операция левого вращения */\nTreeNode *leftRotate(TreeNode *node) {\n    TreeNode *child = node-&gt;right;\n    TreeNode *grandChild = child-&gt;left;\n    // Выполнить левое вращение узла node вокруг child\n    child-&gt;left = node;\n    node-&gt;right = grandChild;\n    // Обновить высоту узла\n    updateHeight(node);\n    updateHeight(child);\n    // Вернуть корневой узел поддерева после вращения\n    return child;\n}\n</code></pre> avl_tree.java<pre><code>/* Операция левого вращения */\nTreeNode leftRotate(TreeNode node) {\n    TreeNode child = node.right;\n    TreeNode grandChild = child.left;\n    // Выполнить левое вращение узла node вокруг child\n    child.left = node;\n    node.right = grandChild;\n    // Обновить высоту узла\n    updateHeight(node);\n    updateHeight(child);\n    // Вернуть корневой узел поддерева после вращения\n    return child;\n}\n</code></pre> avl_tree.cs<pre><code>/* Операция левого вращения */\nTreeNode? LeftRotate(TreeNode? node) {\n    TreeNode? child = node?.right;\n    TreeNode? grandChild = child?.left;\n    // Выполнить левое вращение узла node вокруг child\n    child.left = node;\n    node.right = grandChild;\n    // Обновить высоту узла\n    UpdateHeight(node);\n    UpdateHeight(child);\n    // Вернуть корневой узел поддерева после вращения\n    return child;\n}\n</code></pre> avl_tree.go<pre><code>/* Операция левого вращения */\nfunc (t *aVLTree) leftRotate(node *TreeNode) *TreeNode {\n    child := node.Right\n    grandChild := child.Left\n    // Выполнить левое вращение узла node вокруг child\n    child.Left = node\n    node.Right = grandChild\n    // Обновить высоту узла\n    t.updateHeight(node)\n    t.updateHeight(child)\n    // Вернуть корневой узел поддерева после вращения\n    return child\n}\n</code></pre> avl_tree.swift<pre><code>/* Операция левого вращения */\nfunc leftRotate(node: TreeNode?) -&gt; TreeNode? {\n    let child = node?.right\n    let grandChild = child?.left\n    // Выполнить левое вращение узла node вокруг child\n    child?.left = node\n    node?.right = grandChild\n    // Обновить высоту узла\n    updateHeight(node: node)\n    updateHeight(node: child)\n    // Вернуть корневой узел поддерева после вращения\n    return child\n}\n</code></pre> avl_tree.js<pre><code>/* Операция левого вращения */\n#leftRotate(node) {\n    const child = node.right;\n    const grandChild = child.left;\n    // Выполнить левое вращение узла node вокруг child\n    child.left = node;\n    node.right = grandChild;\n    // Обновить высоту узла\n    this.#updateHeight(node);\n    this.#updateHeight(child);\n    // Вернуть корневой узел поддерева после вращения\n    return child;\n}\n</code></pre> avl_tree.ts<pre><code>/* Операция левого вращения */\nleftRotate(node: TreeNode): TreeNode {\n    const child = node.right;\n    const grandChild = child.left;\n    // Выполнить левое вращение узла node вокруг child\n    child.left = node;\n    node.right = grandChild;\n    // Обновить высоту узла\n    this.updateHeight(node);\n    this.updateHeight(child);\n    // Вернуть корневой узел поддерева после вращения\n    return child;\n}\n</code></pre> avl_tree.dart<pre><code>/* Операция левого вращения */\nTreeNode? leftRotate(TreeNode? node) {\n  TreeNode? child = node!.right;\n  TreeNode? grandChild = child!.left;\n  // Выполнить левое вращение узла node вокруг child\n  child.left = node;\n  node.right = grandChild;\n  // Обновить высоту узла\n  updateHeight(node);\n  updateHeight(child);\n  // Вернуть корневой узел поддерева после вращения\n  return child;\n}\n</code></pre> avl_tree.rs<pre><code>/* Операция левого вращения */\nfn left_rotate(node: OptionTreeNodeRc) -&gt; OptionTreeNodeRc {\n    match node {\n        Some(node) =&gt; {\n            let child = node.borrow().right.clone().unwrap();\n            let grand_child = child.borrow().left.clone();\n            // Выполнить левое вращение узла node вокруг child\n            child.borrow_mut().left = Some(node.clone());\n            node.borrow_mut().right = grand_child;\n            // Обновить высоту узла\n            Self::update_height(Some(node));\n            Self::update_height(Some(child.clone()));\n            // Вернуть корневой узел поддерева после вращения\n            Some(child)\n        }\n        None =&gt; None,\n    }\n}\n</code></pre> avl_tree.c<pre><code>/* Операция левого вращения */\nTreeNode *leftRotate(TreeNode *node) {\n    TreeNode *child, *grandChild;\n    child = node-&gt;right;\n    grandChild = child-&gt;left;\n    // Выполнить левое вращение узла node вокруг child\n    child-&gt;left = node;\n    node-&gt;right = grandChild;\n    // Обновить высоту узла\n    updateHeight(node);\n    updateHeight(child);\n    // Вернуть корневой узел поддерева после вращения\n    return child;\n}\n</code></pre> avl_tree.kt<pre><code>/* Операция левого вращения */\nfun leftRotate(node: TreeNode?): TreeNode {\n    val child = node!!.right\n    val grandChild = child!!.left\n    // Выполнить левое вращение узла node вокруг child\n    child.left = node\n    node.right = grandChild\n    // Обновить высоту узла\n    updateHeight(node)\n    updateHeight(child)\n    // Вернуть корневой узел поддерева после вращения\n    return child\n}\n</code></pre> avl_tree.rb<pre><code>### Операция левого вращения ###\ndef left_rotate(node)\n  child = node.right\n  grand_child = child.left\n  # Выполнить левое вращение узла node вокруг child\n  child.left = node\n  node.right = grand_child\n  # Обновить высоту узла\n  update_height(node)\n  update_height(child)\n  # Вернуть корневой узел поддерева после вращения\n  child\nend\n</code></pre>","path":["Глава 7. Деревья","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#3","level":3,"title":"3.   Сначала левое, затем правое вращение","text":"<p>Для разбалансированного узла 3 на рисунке 7-30 ни одно лишь левое вращение, ни одно лишь правое вращение не способны вернуть поддерево в баланс. В этом случае нужно сначала выполнить \"левое вращение\" для <code>child</code> , а затем выполнить \"правое вращение\" для <code>node</code> .</p> <p></p> <p> Рисунок 7-30   Сначала левое, затем правое вращение </p>","path":["Глава 7. Деревья","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#4","level":3,"title":"4.   Сначала правое, затем левое вращение","text":"<p>Как показано на рисунке 7-31, для зеркальной ситуации предыдущего разбалансированного двоичного дерева нужно сначала выполнить \"правое вращение\" для <code>child</code> , а затем \"левое вращение\" для <code>node</code> .</p> <p></p> <p> Рисунок 7-31   Сначала правое, затем левое вращение </p>","path":["Глава 7. Деревья","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#5","level":3,"title":"5.   Выбор вращения","text":"<p>Четыре вида разбаланса, показанные на рисунке 7-32, по одному соответствуют рассмотренным выше случаям; для них соответственно требуются правое вращение, сначала левое затем правое, сначала правое затем левое и левое вращение.</p> <p></p> <p> Рисунок 7-32   Четыре случая вращений AVL-дерева </p> <p>Как показано в таблице 7-3, мы определяем, какому из этих четырех случаев соответствует разбалансированный узел, по знаку баланс-фактора самого разбалансированного узла и по знаку баланс-фактора дочернего узла на более высокой стороне.</p> <p> Таблица 7-3   Условия выбора для четырех случаев вращений </p> Баланс-фактор разбалансированного узла Баланс-фактор дочернего узла Какое вращение использовать \\(&gt; 1\\) (левостороннее дерево) \\(\\geq 0\\) Правое вращение \\(&gt; 1\\) (левостороннее дерево) \\(&lt;0\\) Сначала левое, затем правое \\(&lt; -1\\) (правостороннее дерево) \\(\\leq 0\\) Левое вращение \\(&lt; -1\\) (правостороннее дерево) \\(&gt;0\\) Сначала правое, затем левое <p>Для удобства мы инкапсулируем операцию вращения в отдельную функцию. С помощью этой функции можно выполнить корректное вращение для любой ситуации разбаланса и снова привести узел в сбалансированное состояние. Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def rotate(self, node: TreeNode | None) -&gt; TreeNode | None:\n    \"\"\"Выполнить вращение, чтобы снова сбалансировать поддерево\"\"\"\n    # Получить коэффициент баланса узла node\n    balance_factor = self.balance_factor(node)\n    # Левосторонне перекошенное дерево\n    if balance_factor &gt; 1:\n        if self.balance_factor(node.left) &gt;= 0:\n            # Правое вращение\n            return self.right_rotate(node)\n        else:\n            # Сначала левое вращение, затем правое\n            node.left = self.left_rotate(node.left)\n            return self.right_rotate(node)\n    # Правосторонне перекошенное дерево\n    elif balance_factor &lt; -1:\n        if self.balance_factor(node.right) &lt;= 0:\n            # Левое вращение\n            return self.left_rotate(node)\n        else:\n            # Сначала правое вращение, затем левое\n            node.right = self.right_rotate(node.right)\n            return self.left_rotate(node)\n    # Дерево сбалансировано, вращение не требуется, вернуть сразу\n    return node\n</code></pre> avl_tree.cpp<pre><code>/* Выполнить вращение, чтобы снова сбалансировать поддерево */\nTreeNode *rotate(TreeNode *node) {\n    // Получить коэффициент баланса узла node\n    int _balanceFactor = balanceFactor(node);\n    // Левосторонне перекошенное дерево\n    if (_balanceFactor &gt; 1) {\n        if (balanceFactor(node-&gt;left) &gt;= 0) {\n            // Правое вращение\n            return rightRotate(node);\n        } else {\n            // Сначала левое вращение, затем правое\n            node-&gt;left = leftRotate(node-&gt;left);\n            return rightRotate(node);\n        }\n    }\n    // Правосторонне перекошенное дерево\n    if (_balanceFactor &lt; -1) {\n        if (balanceFactor(node-&gt;right) &lt;= 0) {\n            // Левое вращение\n            return leftRotate(node);\n        } else {\n            // Сначала правое вращение, затем левое\n            node-&gt;right = rightRotate(node-&gt;right);\n            return leftRotate(node);\n        }\n    }\n    // Дерево сбалансировано, вращение не требуется, вернуть сразу\n    return node;\n}\n</code></pre> avl_tree.java<pre><code>/* Выполнить вращение, чтобы снова сбалансировать поддерево */\nTreeNode rotate(TreeNode node) {\n    // Получить коэффициент баланса узла node\n    int balanceFactor = balanceFactor(node);\n    // Левосторонне перекошенное дерево\n    if (balanceFactor &gt; 1) {\n        if (balanceFactor(node.left) &gt;= 0) {\n            // Правое вращение\n            return rightRotate(node);\n        } else {\n            // Сначала левое вращение, затем правое\n            node.left = leftRotate(node.left);\n            return rightRotate(node);\n        }\n    }\n    // Правосторонне перекошенное дерево\n    if (balanceFactor &lt; -1) {\n        if (balanceFactor(node.right) &lt;= 0) {\n            // Левое вращение\n            return leftRotate(node);\n        } else {\n            // Сначала правое вращение, затем левое\n            node.right = rightRotate(node.right);\n            return leftRotate(node);\n        }\n    }\n    // Дерево сбалансировано, вращение не требуется, вернуть сразу\n    return node;\n}\n</code></pre> avl_tree.cs<pre><code>/* Выполнить вращение, чтобы снова сбалансировать поддерево */\nTreeNode? Rotate(TreeNode? node) {\n    // Получить коэффициент баланса узла node\n    int balanceFactorInt = BalanceFactor(node);\n    // Левосторонне перекошенное дерево\n    if (balanceFactorInt &gt; 1) {\n        if (BalanceFactor(node?.left) &gt;= 0) {\n            // Правое вращение\n            return RightRotate(node);\n        } else {\n            // Сначала левое вращение, затем правое\n            node!.left = LeftRotate(node!.left);\n            return RightRotate(node);\n        }\n    }\n    // Правосторонне перекошенное дерево\n    if (balanceFactorInt &lt; -1) {\n        if (BalanceFactor(node?.right) &lt;= 0) {\n            // Левое вращение\n            return LeftRotate(node);\n        } else {\n            // Сначала правое вращение, затем левое\n            node!.right = RightRotate(node!.right);\n            return LeftRotate(node);\n        }\n    }\n    // Дерево сбалансировано, вращение не требуется, вернуть сразу\n    return node;\n}\n</code></pre> avl_tree.go<pre><code>/* Выполнить вращение, чтобы снова сбалансировать поддерево */\nfunc (t *aVLTree) rotate(node *TreeNode) *TreeNode {\n    // Получить коэффициент баланса узла node\n    // В Go рекомендуется использовать короткие имена переменных, здесь bf обозначает t.balanceFactor\n    bf := t.balanceFactor(node)\n    // Левосторонне перекошенное дерево\n    if bf &gt; 1 {\n        if t.balanceFactor(node.Left) &gt;= 0 {\n            // Правое вращение\n            return t.rightRotate(node)\n        } else {\n            // Сначала левое вращение, затем правое\n            node.Left = t.leftRotate(node.Left)\n            return t.rightRotate(node)\n        }\n    }\n    // Правосторонне перекошенное дерево\n    if bf &lt; -1 {\n        if t.balanceFactor(node.Right) &lt;= 0 {\n            // Левое вращение\n            return t.leftRotate(node)\n        } else {\n            // Сначала правое вращение, затем левое\n            node.Right = t.rightRotate(node.Right)\n            return t.leftRotate(node)\n        }\n    }\n    // Дерево сбалансировано, вращение не требуется, вернуть сразу\n    return node\n}\n</code></pre> avl_tree.swift<pre><code>/* Выполнить вращение, чтобы снова сбалансировать поддерево */\nfunc rotate(node: TreeNode?) -&gt; TreeNode? {\n    // Получить коэффициент баланса узла node\n    let balanceFactor = balanceFactor(node: node)\n    // Левосторонне перекошенное дерево\n    if balanceFactor &gt; 1 {\n        if self.balanceFactor(node: node?.left) &gt;= 0 {\n            // Правое вращение\n            return rightRotate(node: node)\n        } else {\n            // Сначала левое вращение, затем правое\n            node?.left = leftRotate(node: node?.left)\n            return rightRotate(node: node)\n        }\n    }\n    // Правосторонне перекошенное дерево\n    if balanceFactor &lt; -1 {\n        if self.balanceFactor(node: node?.right) &lt;= 0 {\n            // Левое вращение\n            return leftRotate(node: node)\n        } else {\n            // Сначала правое вращение, затем левое\n            node?.right = rightRotate(node: node?.right)\n            return leftRotate(node: node)\n        }\n    }\n    // Дерево сбалансировано, вращение не требуется, вернуть сразу\n    return node\n}\n</code></pre> avl_tree.js<pre><code>/* Выполнить вращение, чтобы снова сбалансировать поддерево */\n#rotate(node) {\n    // Получить коэффициент баланса узла node\n    const balanceFactor = this.balanceFactor(node);\n    // Левосторонне перекошенное дерево\n    if (balanceFactor &gt; 1) {\n        if (this.balanceFactor(node.left) &gt;= 0) {\n            // Правое вращение\n            return this.#rightRotate(node);\n        } else {\n            // Сначала левое вращение, затем правое\n            node.left = this.#leftRotate(node.left);\n            return this.#rightRotate(node);\n        }\n    }\n    // Правосторонне перекошенное дерево\n    if (balanceFactor &lt; -1) {\n        if (this.balanceFactor(node.right) &lt;= 0) {\n            // Левое вращение\n            return this.#leftRotate(node);\n        } else {\n            // Сначала правое вращение, затем левое\n            node.right = this.#rightRotate(node.right);\n            return this.#leftRotate(node);\n        }\n    }\n    // Дерево сбалансировано, вращение не требуется, вернуть сразу\n    return node;\n}\n</code></pre> avl_tree.ts<pre><code>/* Выполнить вращение, чтобы снова сбалансировать поддерево */\nrotate(node: TreeNode): TreeNode {\n    // Получить коэффициент баланса узла node\n    const balanceFactor = this.balanceFactor(node);\n    // Левосторонне перекошенное дерево\n    if (balanceFactor &gt; 1) {\n        if (this.balanceFactor(node.left) &gt;= 0) {\n            // Правое вращение\n            return this.rightRotate(node);\n        } else {\n            // Сначала левое вращение, затем правое\n            node.left = this.leftRotate(node.left);\n            return this.rightRotate(node);\n        }\n    }\n    // Правосторонне перекошенное дерево\n    if (balanceFactor &lt; -1) {\n        if (this.balanceFactor(node.right) &lt;= 0) {\n            // Левое вращение\n            return this.leftRotate(node);\n        } else {\n            // Сначала правое вращение, затем левое\n            node.right = this.rightRotate(node.right);\n            return this.leftRotate(node);\n        }\n    }\n    // Дерево сбалансировано, вращение не требуется, вернуть сразу\n    return node;\n}\n</code></pre> avl_tree.dart<pre><code>/* Выполнить вращение, чтобы снова сбалансировать поддерево */\nTreeNode? rotate(TreeNode? node) {\n  // Получить коэффициент баланса узла node\n  int factor = balanceFactor(node);\n  // Левосторонне перекошенное дерево\n  if (factor &gt; 1) {\n    if (balanceFactor(node!.left) &gt;= 0) {\n      // Правое вращение\n      return rightRotate(node);\n    } else {\n      // Сначала левое вращение, затем правое\n      node.left = leftRotate(node.left);\n      return rightRotate(node);\n    }\n  }\n  // Правосторонне перекошенное дерево\n  if (factor &lt; -1) {\n    if (balanceFactor(node!.right) &lt;= 0) {\n      // Левое вращение\n      return leftRotate(node);\n    } else {\n      // Сначала правое вращение, затем левое\n      node.right = rightRotate(node.right);\n      return leftRotate(node);\n    }\n  }\n  // Дерево сбалансировано, вращение не требуется, вернуть сразу\n  return node;\n}\n</code></pre> avl_tree.rs<pre><code>/* Выполнить вращение, чтобы снова сбалансировать поддерево */\nfn rotate(node: OptionTreeNodeRc) -&gt; OptionTreeNodeRc {\n    // Получить коэффициент баланса узла node\n    let balance_factor = Self::balance_factor(node.clone());\n    // Левосторонне перекошенное дерево\n    if balance_factor &gt; 1 {\n        let node = node.unwrap();\n        if Self::balance_factor(node.borrow().left.clone()) &gt;= 0 {\n            // Правое вращение\n            Self::right_rotate(Some(node))\n        } else {\n            // Сначала левое вращение, затем правое\n            let left = node.borrow().left.clone();\n            node.borrow_mut().left = Self::left_rotate(left);\n            Self::right_rotate(Some(node))\n        }\n    }\n    // Правосторонне перекошенное дерево\n    else if balance_factor &lt; -1 {\n        let node = node.unwrap();\n        if Self::balance_factor(node.borrow().right.clone()) &lt;= 0 {\n            // Левое вращение\n            Self::left_rotate(Some(node))\n        } else {\n            // Сначала правое вращение, затем левое\n            let right = node.borrow().right.clone();\n            node.borrow_mut().right = Self::right_rotate(right);\n            Self::left_rotate(Some(node))\n        }\n    } else {\n        // Дерево сбалансировано, вращение не требуется, вернуть сразу\n        node\n    }\n}\n</code></pre> avl_tree.c<pre><code>/* Выполнить вращение, чтобы снова сбалансировать поддерево */\nTreeNode *rotate(TreeNode *node) {\n    // Получить коэффициент баланса узла node\n    int bf = balanceFactor(node);\n    // Левосторонне перекошенное дерево\n    if (bf &gt; 1) {\n        if (balanceFactor(node-&gt;left) &gt;= 0) {\n            // Правое вращение\n            return rightRotate(node);\n        } else {\n            // Сначала левое вращение, затем правое\n            node-&gt;left = leftRotate(node-&gt;left);\n            return rightRotate(node);\n        }\n    }\n    // Правосторонне перекошенное дерево\n    if (bf &lt; -1) {\n        if (balanceFactor(node-&gt;right) &lt;= 0) {\n            // Левое вращение\n            return leftRotate(node);\n        } else {\n            // Сначала правое вращение, затем левое\n            node-&gt;right = rightRotate(node-&gt;right);\n            return leftRotate(node);\n        }\n    }\n    // Дерево сбалансировано, вращение не требуется, вернуть сразу\n    return node;\n}\n</code></pre> avl_tree.kt<pre><code>/* Выполнить вращение, чтобы снова сбалансировать поддерево */\nfun rotate(node: TreeNode): TreeNode {\n    // Получить коэффициент баланса узла node\n    val balanceFactor = balanceFactor(node)\n    // Левосторонне перекошенное дерево\n    if (balanceFactor &gt; 1) {\n        if (balanceFactor(node.left) &gt;= 0) {\n            // Правое вращение\n            return rightRotate(node)\n        } else {\n            // Сначала левое вращение, затем правое\n            node.left = leftRotate(node.left)\n            return rightRotate(node)\n        }\n    }\n    // Правосторонне перекошенное дерево\n    if (balanceFactor &lt; -1) {\n        if (balanceFactor(node.right) &lt;= 0) {\n            // Левое вращение\n            return leftRotate(node)\n        } else {\n            // Сначала правое вращение, затем левое\n            node.right = rightRotate(node.right)\n            return leftRotate(node)\n        }\n    }\n    // Дерево сбалансировано, вращение не требуется, вернуть сразу\n    return node\n}\n</code></pre> avl_tree.rb<pre><code>### Выполнить вращение, чтобы снова сбалансировать поддерево ###\ndef rotate(node)\n  # Получить коэффициент баланса узла node\n  balance_factor = balance_factor(node)\n  # Обойти левое поддерево\n  if balance_factor &gt; 1\n    if balance_factor(node.left) &gt;= 0\n      # Правое вращение\n      return right_rotate(node)\n    else\n      # Сначала левое вращение, затем правое\n      node.left = left_rotate(node.left)\n      return right_rotate(node)\n    end\n  # Правостороннее дерево обхода\n  elsif balance_factor &lt; -1\n    if balance_factor(node.right) &lt;= 0\n      # Левое вращение\n      return left_rotate(node)\n    else\n      # Сначала правое вращение, затем левое\n      node.right = right_rotate(node.right)\n      return left_rotate(node)\n    end\n  end\n  # Дерево сбалансировано, вращение не требуется, вернуть сразу\n  node\nend\n</code></pre>","path":["Глава 7. Деревья","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#753-avl-","level":2,"title":"7.5.3   Распространенные операции AVL-дерева","text":"","path":["Глава 7. Деревья","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#1_2","level":3,"title":"1.   Вставка узла","text":"<p>Операция вставки узла в AVL-дерево по основному процессу похожа на вставку в двоичное дерево поиска. Единственная разница состоит в том, что после вставки в AVL-дерево на пути от вставленного узла к корню может появиться цепочка разбалансированных узлов. Поэтому начиная от этого узла, мы должны выполнять вращения снизу вверх, чтобы вернуть в баланс все разбалансированные узлы. Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def insert(self, val):\n    \"\"\"Вставка узла\"\"\"\n    self._root = self.insert_helper(self._root, val)\n\ndef insert_helper(self, node: TreeNode | None, val: int) -&gt; TreeNode:\n    \"\"\"Рекурсивная вставка узла (вспомогательный метод)\"\"\"\n    if node is None:\n        return TreeNode(val)\n    # 1. Найти позицию вставки и вставить узел\n    if val &lt; node.val:\n        node.left = self.insert_helper(node.left, val)\n    elif val &gt; node.val:\n        node.right = self.insert_helper(node.right, val)\n    else:\n        # Повторяющийся узел не вставлять, сразу вернуть\n        return node\n    # Обновить высоту узла\n    self.update_height(node)\n    # 2. Выполнить вращение, чтобы снова сбалансировать поддерево\n    return self.rotate(node)\n</code></pre> avl_tree.cpp<pre><code>/* Вставка узла */\nvoid insert(int val) {\n    root = insertHelper(root, val);\n}\n\n/* Рекурсивная вставка узла (вспомогательный метод) */\nTreeNode *insertHelper(TreeNode *node, int val) {\n    if (node == nullptr)\n        return new TreeNode(val);\n    /* 1. Найти позицию вставки и вставить узел */\n    if (val &lt; node-&gt;val)\n        node-&gt;left = insertHelper(node-&gt;left, val);\n    else if (val &gt; node-&gt;val)\n        node-&gt;right = insertHelper(node-&gt;right, val);\n    else\n        return node;    // Повторяющийся узел не вставлять, сразу вернуть\n    updateHeight(node); // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = rotate(node);\n    // Вернуть корневой узел поддерева\n    return node;\n}\n</code></pre> avl_tree.java<pre><code>/* Вставка узла */\nvoid insert(int val) {\n    root = insertHelper(root, val);\n}\n\n/* Рекурсивная вставка узла (вспомогательный метод) */\nTreeNode insertHelper(TreeNode node, int val) {\n    if (node == null)\n        return new TreeNode(val);\n    /* 1. Найти позицию вставки и вставить узел */\n    if (val &lt; node.val)\n        node.left = insertHelper(node.left, val);\n    else if (val &gt; node.val)\n        node.right = insertHelper(node.right, val);\n    else\n        return node; // Повторяющийся узел не вставлять, сразу вернуть\n    updateHeight(node); // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = rotate(node);\n    // Вернуть корневой узел поддерева\n    return node;\n}\n</code></pre> avl_tree.cs<pre><code>/* Вставка узла */\nvoid Insert(int val) {\n    root = InsertHelper(root, val);\n}\n\n/* Рекурсивная вставка узла (вспомогательный метод) */\nTreeNode? InsertHelper(TreeNode? node, int val) {\n    if (node == null) return new TreeNode(val);\n    /* 1. Найти позицию вставки и вставить узел */\n    if (val &lt; node.val)\n        node.left = InsertHelper(node.left, val);\n    else if (val &gt; node.val)\n        node.right = InsertHelper(node.right, val);\n    else\n        return node;     // Повторяющийся узел не вставлять, сразу вернуть\n    UpdateHeight(node);  // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = Rotate(node);\n    // Вернуть корневой узел поддерева\n    return node;\n}\n</code></pre> avl_tree.go<pre><code>/* Вставка узла */\nfunc (t *aVLTree) insert(val int) {\n    t.root = t.insertHelper(t.root, val)\n}\n\n/* Рекурсивная вставка узла (вспомогательная функция) */\nfunc (t *aVLTree) insertHelper(node *TreeNode, val int) *TreeNode {\n    if node == nil {\n        return NewTreeNode(val)\n    }\n    /* 1. Найти позицию вставки и вставить узел */\n    if val &lt; node.Val.(int) {\n        node.Left = t.insertHelper(node.Left, val)\n    } else if val &gt; node.Val.(int) {\n        node.Right = t.insertHelper(node.Right, val)\n    } else {\n        // Повторяющийся узел не вставлять, сразу вернуть\n        return node\n    }\n    // Обновить высоту узла\n    t.updateHeight(node)\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = t.rotate(node)\n    // Вернуть корневой узел поддерева\n    return node\n}\n</code></pre> avl_tree.swift<pre><code>/* Вставка узла */\nfunc insert(val: Int) {\n    root = insertHelper(node: root, val: val)\n}\n\n/* Рекурсивная вставка узла (вспомогательный метод) */\nfunc insertHelper(node: TreeNode?, val: Int) -&gt; TreeNode? {\n    var node = node\n    if node == nil {\n        return TreeNode(x: val)\n    }\n    /* 1. Найти позицию вставки и вставить узел */\n    if val &lt; node!.val {\n        node?.left = insertHelper(node: node?.left, val: val)\n    } else if val &gt; node!.val {\n        node?.right = insertHelper(node: node?.right, val: val)\n    } else {\n        return node // Повторяющийся узел не вставлять, сразу вернуть\n    }\n    updateHeight(node: node) // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = rotate(node: node)\n    // Вернуть корневой узел поддерева\n    return node\n}\n</code></pre> avl_tree.js<pre><code>/* Вставка узла */\ninsert(val) {\n    this.root = this.#insertHelper(this.root, val);\n}\n\n/* Рекурсивная вставка узла (вспомогательный метод) */\n#insertHelper(node, val) {\n    if (node === null) return new TreeNode(val);\n    /* 1. Найти позицию вставки и вставить узел */\n    if (val &lt; node.val) node.left = this.#insertHelper(node.left, val);\n    else if (val &gt; node.val)\n        node.right = this.#insertHelper(node.right, val);\n    else return node; // Повторяющийся узел не вставлять, сразу вернуть\n    this.#updateHeight(node); // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = this.#rotate(node);\n    // Вернуть корневой узел поддерева\n    return node;\n}\n</code></pre> avl_tree.ts<pre><code>/* Вставка узла */\ninsert(val: number): void {\n    this.root = this.insertHelper(this.root, val);\n}\n\n/* Рекурсивная вставка узла (вспомогательный метод) */\ninsertHelper(node: TreeNode, val: number): TreeNode {\n    if (node === null) return new TreeNode(val);\n    /* 1. Найти позицию вставки и вставить узел */\n    if (val &lt; node.val) {\n        node.left = this.insertHelper(node.left, val);\n    } else if (val &gt; node.val) {\n        node.right = this.insertHelper(node.right, val);\n    } else {\n        return node; // Повторяющийся узел не вставлять, сразу вернуть\n    }\n    this.updateHeight(node); // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = this.rotate(node);\n    // Вернуть корневой узел поддерева\n    return node;\n}\n</code></pre> avl_tree.dart<pre><code>/* Вставка узла */\nvoid insert(int val) {\n  root = insertHelper(root, val);\n}\n\n/* Рекурсивная вставка узла (вспомогательный метод) */\nTreeNode? insertHelper(TreeNode? node, int val) {\n  if (node == null) return TreeNode(val);\n  /* 1. Найти позицию вставки и вставить узел */\n  if (val &lt; node.val)\n    node.left = insertHelper(node.left, val);\n  else if (val &gt; node.val)\n    node.right = insertHelper(node.right, val);\n  else\n    return node; // Повторяющийся узел не вставлять, сразу вернуть\n  updateHeight(node); // Обновить высоту узла\n  /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n  node = rotate(node);\n  // Вернуть корневой узел поддерева\n  return node;\n}\n</code></pre> avl_tree.rs<pre><code>/* Вставка узла */\nfn insert(&amp;mut self, val: i32) {\n    self.root = Self::insert_helper(self.root.clone(), val);\n}\n\n/* Рекурсивная вставка узла (вспомогательный метод) */\nfn insert_helper(node: OptionTreeNodeRc, val: i32) -&gt; OptionTreeNodeRc {\n    match node {\n        Some(mut node) =&gt; {\n            /* 1. Найти позицию вставки и вставить узел */\n            match {\n                let node_val = node.borrow().val;\n                node_val\n            }\n            .cmp(&amp;val)\n            {\n                Ordering::Greater =&gt; {\n                    let left = node.borrow().left.clone();\n                    node.borrow_mut().left = Self::insert_helper(left, val);\n                }\n                Ordering::Less =&gt; {\n                    let right = node.borrow().right.clone();\n                    node.borrow_mut().right = Self::insert_helper(right, val);\n                }\n                Ordering::Equal =&gt; {\n                    return Some(node); // Повторяющийся узел не вставлять, сразу вернуть\n                }\n            }\n            Self::update_height(Some(node.clone())); // Обновить высоту узла\n\n            /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n            node = Self::rotate(Some(node)).unwrap();\n            // Вернуть корневой узел поддерева\n            Some(node)\n        }\n        None =&gt; Some(TreeNode::new(val)),\n    }\n}\n</code></pre> avl_tree.c<pre><code>/* Вставка узла */\nvoid insert(AVLTree *tree, int val) {\n    tree-&gt;root = insertHelper(tree-&gt;root, val);\n}\n\n/* Рекурсивная вставка узла (вспомогательная функция) */\nTreeNode *insertHelper(TreeNode *node, int val) {\n    if (node == NULL) {\n        return newTreeNode(val);\n    }\n    /* 1. Найти позицию вставки и вставить узел */\n    if (val &lt; node-&gt;val) {\n        node-&gt;left = insertHelper(node-&gt;left, val);\n    } else if (val &gt; node-&gt;val) {\n        node-&gt;right = insertHelper(node-&gt;right, val);\n    } else {\n        // Повторяющийся узел не вставлять, сразу вернуть\n        return node;\n    }\n    // Обновить высоту узла\n    updateHeight(node);\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = rotate(node);\n    // Вернуть корневой узел поддерева\n    return node;\n}\n</code></pre> avl_tree.kt<pre><code>/* Вставка узла */\nfun insert(_val: Int) {\n    root = insertHelper(root, _val)\n}\n\n/* Рекурсивная вставка узла (вспомогательный метод) */\nfun insertHelper(n: TreeNode?, _val: Int): TreeNode {\n    if (n == null)\n        return TreeNode(_val)\n    var node = n\n    /* 1. Найти позицию вставки и вставить узел */\n    if (_val &lt; node._val)\n        node.left = insertHelper(node.left, _val)\n    else if (_val &gt; node._val)\n        node.right = insertHelper(node.right, _val)\n    else\n        return node // Повторяющийся узел не вставлять, сразу вернуть\n    updateHeight(node) // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = rotate(node)\n    // Вернуть корневой узел поддерева\n    return node\n}\n</code></pre> avl_tree.rb<pre><code>### Вставка узла ###\ndef insert(val)\n  @root = insert_helper(@root, val)\nend\n\n### Вставка узла ###\ndef insert(val)\n  @root = insert_helper(@root, val)\nend\n\n# ## Рекурсивная вставка узла (вспомогательный метод) ###\ndef insert_helper(node, val)\n  return TreeNode.new(val) if node.nil?\n  # 1. Найти позицию вставки и вставить узел\n  if val &lt; node.val\n    node.left = insert_helper(node.left, val)\n  elsif val &gt; node.val\n    node.right = insert_helper(node.right, val)\n  else\n    # Повторяющийся узел не вставлять, сразу вернуть\n    return node\n  end\n  # Обновить высоту узла\n  update_height(node)\n  # 2. Выполнить вращение, чтобы снова сбалансировать поддерево\n  rotate(node)\nend\n</code></pre>","path":["Глава 7. Деревья","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#2_1","level":3,"title":"2.   Удаление узла","text":"<p>Аналогично, на основе метода удаления узла из двоичного дерева поиска нужно добавить вращения снизу вверх, чтобы восстановить баланс всех разбалансированных узлов. Код приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby avl_tree.py<pre><code>def remove(self, val: int):\n    \"\"\"Удаление узла\"\"\"\n    self._root = self.remove_helper(self._root, val)\n\ndef remove_helper(self, node: TreeNode | None, val: int) -&gt; TreeNode | None:\n    \"\"\"Рекурсивное удаление узла (вспомогательный метод)\"\"\"\n    if node is None:\n        return None\n    # 1. Найти узел и удалить его\n    if val &lt; node.val:\n        node.left = self.remove_helper(node.left, val)\n    elif val &gt; node.val:\n        node.right = self.remove_helper(node.right, val)\n    else:\n        if node.left is None or node.right is None:\n            child = node.left or node.right\n            # Число дочерних узлов = 0, удалить node и сразу вернуть\n            if child is None:\n                return None\n            # Число дочерних узлов = 1, удалить node напрямую\n            else:\n                node = child\n        else:\n            # Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n            temp = node.right\n            while temp.left is not None:\n                temp = temp.left\n            node.right = self.remove_helper(node.right, temp.val)\n            node.val = temp.val\n    # Обновить высоту узла\n    self.update_height(node)\n    # 2. Выполнить вращение, чтобы снова сбалансировать поддерево\n    return self.rotate(node)\n</code></pre> avl_tree.cpp<pre><code>/* Удаление узла */\nvoid remove(int val) {\n    root = removeHelper(root, val);\n}\n\n/* Рекурсивное удаление узла (вспомогательный метод) */\nTreeNode *removeHelper(TreeNode *node, int val) {\n    if (node == nullptr)\n        return nullptr;\n    /* 1. Найти узел и удалить его */\n    if (val &lt; node-&gt;val)\n        node-&gt;left = removeHelper(node-&gt;left, val);\n    else if (val &gt; node-&gt;val)\n        node-&gt;right = removeHelper(node-&gt;right, val);\n    else {\n        if (node-&gt;left == nullptr || node-&gt;right == nullptr) {\n            TreeNode *child = node-&gt;left != nullptr ? node-&gt;left : node-&gt;right;\n            // Число дочерних узлов = 0, удалить node и сразу вернуть\n            if (child == nullptr) {\n                delete node;\n                return nullptr;\n            }\n            // Число дочерних узлов = 1, удалить node напрямую\n            else {\n                delete node;\n                node = child;\n            }\n        } else {\n            // Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n            TreeNode *temp = node-&gt;right;\n            while (temp-&gt;left != nullptr) {\n                temp = temp-&gt;left;\n            }\n            int tempVal = temp-&gt;val;\n            node-&gt;right = removeHelper(node-&gt;right, temp-&gt;val);\n            node-&gt;val = tempVal;\n        }\n    }\n    updateHeight(node); // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = rotate(node);\n    // Вернуть корневой узел поддерева\n    return node;\n}\n</code></pre> avl_tree.java<pre><code>/* Удаление узла */\nvoid remove(int val) {\n    root = removeHelper(root, val);\n}\n\n/* Рекурсивное удаление узла (вспомогательный метод) */\nTreeNode removeHelper(TreeNode node, int val) {\n    if (node == null)\n        return null;\n    /* 1. Найти узел и удалить его */\n    if (val &lt; node.val)\n        node.left = removeHelper(node.left, val);\n    else if (val &gt; node.val)\n        node.right = removeHelper(node.right, val);\n    else {\n        if (node.left == null || node.right == null) {\n            TreeNode child = node.left != null ? node.left : node.right;\n            // Число дочерних узлов = 0, удалить node и сразу вернуть\n            if (child == null)\n                return null;\n            // Число дочерних узлов = 1, удалить node напрямую\n            else\n                node = child;\n        } else {\n            // Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n            TreeNode temp = node.right;\n            while (temp.left != null) {\n                temp = temp.left;\n            }\n            node.right = removeHelper(node.right, temp.val);\n            node.val = temp.val;\n        }\n    }\n    updateHeight(node); // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = rotate(node);\n    // Вернуть корневой узел поддерева\n    return node;\n}\n</code></pre> avl_tree.cs<pre><code>/* Удаление узла */\nvoid Remove(int val) {\n    root = RemoveHelper(root, val);\n}\n\n/* Рекурсивное удаление узла (вспомогательный метод) */\nTreeNode? RemoveHelper(TreeNode? node, int val) {\n    if (node == null) return null;\n    /* 1. Найти узел и удалить его */\n    if (val &lt; node.val)\n        node.left = RemoveHelper(node.left, val);\n    else if (val &gt; node.val)\n        node.right = RemoveHelper(node.right, val);\n    else {\n        if (node.left == null || node.right == null) {\n            TreeNode? child = node.left ?? node.right;\n            // Число дочерних узлов = 0, удалить node и сразу вернуть\n            if (child == null)\n                return null;\n            // Число дочерних узлов = 1, удалить node напрямую\n            else\n                node = child;\n        } else {\n            // Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n            TreeNode? temp = node.right;\n            while (temp.left != null) {\n                temp = temp.left;\n            }\n            node.right = RemoveHelper(node.right, temp.val!.Value);\n            node.val = temp.val;\n        }\n    }\n    UpdateHeight(node);  // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = Rotate(node);\n    // Вернуть корневой узел поддерева\n    return node;\n}\n</code></pre> avl_tree.go<pre><code>/* Удаление узла */\nfunc (t *aVLTree) remove(val int) {\n    t.root = t.removeHelper(t.root, val)\n}\n\n/* Рекурсивное удаление узла (вспомогательная функция) */\nfunc (t *aVLTree) removeHelper(node *TreeNode, val int) *TreeNode {\n    if node == nil {\n        return nil\n    }\n    /* 1. Найти узел и удалить его */\n    if val &lt; node.Val.(int) {\n        node.Left = t.removeHelper(node.Left, val)\n    } else if val &gt; node.Val.(int) {\n        node.Right = t.removeHelper(node.Right, val)\n    } else {\n        if node.Left == nil || node.Right == nil {\n            child := node.Left\n            if node.Right != nil {\n                child = node.Right\n            }\n            if child == nil {\n                // Число дочерних узлов = 0, удалить node и сразу вернуть\n                return nil\n            } else {\n                // Число дочерних узлов = 1, удалить node напрямую\n                node = child\n            }\n        } else {\n            // Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n            temp := node.Right\n            for temp.Left != nil {\n                temp = temp.Left\n            }\n            node.Right = t.removeHelper(node.Right, temp.Val.(int))\n            node.Val = temp.Val\n        }\n    }\n    // Обновить высоту узла\n    t.updateHeight(node)\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = t.rotate(node)\n    // Вернуть корневой узел поддерева\n    return node\n}\n</code></pre> avl_tree.swift<pre><code>/* Удаление узла */\nfunc remove(val: Int) {\n    root = removeHelper(node: root, val: val)\n}\n\n/* Рекурсивное удаление узла (вспомогательный метод) */\nfunc removeHelper(node: TreeNode?, val: Int) -&gt; TreeNode? {\n    var node = node\n    if node == nil {\n        return nil\n    }\n    /* 1. Найти узел и удалить его */\n    if val &lt; node!.val {\n        node?.left = removeHelper(node: node?.left, val: val)\n    } else if val &gt; node!.val {\n        node?.right = removeHelper(node: node?.right, val: val)\n    } else {\n        if node?.left == nil || node?.right == nil {\n            let child = node?.left ?? node?.right\n            // Число дочерних узлов = 0, удалить node и сразу вернуть\n            if child == nil {\n                return nil\n            }\n            // Число дочерних узлов = 1, удалить node напрямую\n            else {\n                node = child\n            }\n        } else {\n            // Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n            var temp = node?.right\n            while temp?.left != nil {\n                temp = temp?.left\n            }\n            node?.right = removeHelper(node: node?.right, val: temp!.val)\n            node?.val = temp!.val\n        }\n    }\n    updateHeight(node: node) // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = rotate(node: node)\n    // Вернуть корневой узел поддерева\n    return node\n}\n</code></pre> avl_tree.js<pre><code>/* Удаление узла */\nremove(val) {\n    this.root = this.#removeHelper(this.root, val);\n}\n\n/* Рекурсивное удаление узла (вспомогательный метод) */\n#removeHelper(node, val) {\n    if (node === null) return null;\n    /* 1. Найти узел и удалить его */\n    if (val &lt; node.val) node.left = this.#removeHelper(node.left, val);\n    else if (val &gt; node.val)\n        node.right = this.#removeHelper(node.right, val);\n    else {\n        if (node.left === null || node.right === null) {\n            const child = node.left !== null ? node.left : node.right;\n            // Число дочерних узлов = 0, удалить node и сразу вернуть\n            if (child === null) return null;\n            // Число дочерних узлов = 1, удалить node напрямую\n            else node = child;\n        } else {\n            // Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n            let temp = node.right;\n            while (temp.left !== null) {\n                temp = temp.left;\n            }\n            node.right = this.#removeHelper(node.right, temp.val);\n            node.val = temp.val;\n        }\n    }\n    this.#updateHeight(node); // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = this.#rotate(node);\n    // Вернуть корневой узел поддерева\n    return node;\n}\n</code></pre> avl_tree.ts<pre><code>/* Удаление узла */\nremove(val: number): void {\n    this.root = this.removeHelper(this.root, val);\n}\n\n/* Рекурсивное удаление узла (вспомогательный метод) */\nremoveHelper(node: TreeNode, val: number): TreeNode {\n    if (node === null) return null;\n    /* 1. Найти узел и удалить его */\n    if (val &lt; node.val) {\n        node.left = this.removeHelper(node.left, val);\n    } else if (val &gt; node.val) {\n        node.right = this.removeHelper(node.right, val);\n    } else {\n        if (node.left === null || node.right === null) {\n            const child = node.left !== null ? node.left : node.right;\n            // Число дочерних узлов = 0, удалить node и сразу вернуть\n            if (child === null) {\n                return null;\n            } else {\n                // Число дочерних узлов = 1, удалить node напрямую\n                node = child;\n            }\n        } else {\n            // Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n            let temp = node.right;\n            while (temp.left !== null) {\n                temp = temp.left;\n            }\n            node.right = this.removeHelper(node.right, temp.val);\n            node.val = temp.val;\n        }\n    }\n    this.updateHeight(node); // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = this.rotate(node);\n    // Вернуть корневой узел поддерева\n    return node;\n}\n</code></pre> avl_tree.dart<pre><code>/* Удаление узла */\nvoid remove(int val) {\n  root = removeHelper(root, val);\n}\n\n/* Рекурсивное удаление узла (вспомогательный метод) */\nTreeNode? removeHelper(TreeNode? node, int val) {\n  if (node == null) return null;\n  /* 1. Найти узел и удалить его */\n  if (val &lt; node.val)\n    node.left = removeHelper(node.left, val);\n  else if (val &gt; node.val)\n    node.right = removeHelper(node.right, val);\n  else {\n    if (node.left == null || node.right == null) {\n      TreeNode? child = node.left ?? node.right;\n      // Число дочерних узлов = 0, удалить node и сразу вернуть\n      if (child == null)\n        return null;\n      // Число дочерних узлов = 1, удалить node напрямую\n      else\n        node = child;\n    } else {\n      // Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n      TreeNode? temp = node.right;\n      while (temp!.left != null) {\n        temp = temp.left;\n      }\n      node.right = removeHelper(node.right, temp.val);\n      node.val = temp.val;\n    }\n  }\n  updateHeight(node); // Обновить высоту узла\n  /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n  node = rotate(node);\n  // Вернуть корневой узел поддерева\n  return node;\n}\n</code></pre> avl_tree.rs<pre><code>/* Удаление узла */\nfn remove(&amp;self, val: i32) {\n    Self::remove_helper(self.root.clone(), val);\n}\n\n/* Рекурсивное удаление узла (вспомогательный метод) */\nfn remove_helper(node: OptionTreeNodeRc, val: i32) -&gt; OptionTreeNodeRc {\n    match node {\n        Some(mut node) =&gt; {\n            /* 1. Найти узел и удалить его */\n            if val &lt; node.borrow().val {\n                let left = node.borrow().left.clone();\n                node.borrow_mut().left = Self::remove_helper(left, val);\n            } else if val &gt; node.borrow().val {\n                let right = node.borrow().right.clone();\n                node.borrow_mut().right = Self::remove_helper(right, val);\n            } else if node.borrow().left.is_none() || node.borrow().right.is_none() {\n                let child = if node.borrow().left.is_some() {\n                    node.borrow().left.clone()\n                } else {\n                    node.borrow().right.clone()\n                };\n                match child {\n                    // Число дочерних узлов = 0, удалить node и сразу вернуть\n                    None =&gt; {\n                        return None;\n                    }\n                    // Число дочерних узлов = 1, удалить node напрямую\n                    Some(child) =&gt; node = child,\n                }\n            } else {\n                // Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n                let mut temp = node.borrow().right.clone().unwrap();\n                loop {\n                    let temp_left = temp.borrow().left.clone();\n                    if temp_left.is_none() {\n                        break;\n                    }\n                    temp = temp_left.unwrap();\n                }\n                let right = node.borrow().right.clone();\n                node.borrow_mut().right = Self::remove_helper(right, temp.borrow().val);\n                node.borrow_mut().val = temp.borrow().val;\n            }\n            Self::update_height(Some(node.clone())); // Обновить высоту узла\n\n            /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n            node = Self::rotate(Some(node)).unwrap();\n            // Вернуть корневой узел поддерева\n            Some(node)\n        }\n        None =&gt; None,\n    }\n}\n</code></pre> avl_tree.c<pre><code>/* Удаление узла */\n// Из-за подключения stdio.h здесь нельзя использовать ключевое слово remove\nvoid removeItem(AVLTree *tree, int val) {\n    TreeNode *root = removeHelper(tree-&gt;root, val);\n}\n\n/* Рекурсивное удаление узла (вспомогательная функция) */\nTreeNode *removeHelper(TreeNode *node, int val) {\n    TreeNode *child, *grandChild;\n    if (node == NULL) {\n        return NULL;\n    }\n    /* 1. Найти узел и удалить его */\n    if (val &lt; node-&gt;val) {\n        node-&gt;left = removeHelper(node-&gt;left, val);\n    } else if (val &gt; node-&gt;val) {\n        node-&gt;right = removeHelper(node-&gt;right, val);\n    } else {\n        if (node-&gt;left == NULL || node-&gt;right == NULL) {\n            child = node-&gt;left;\n            if (node-&gt;right != NULL) {\n                child = node-&gt;right;\n            }\n            // Число дочерних узлов = 0, удалить node и сразу вернуть\n            if (child == NULL) {\n                return NULL;\n            } else {\n                // Число дочерних узлов = 1, удалить node напрямую\n                node = child;\n            }\n        } else {\n            // Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n            TreeNode *temp = node-&gt;right;\n            while (temp-&gt;left != NULL) {\n                temp = temp-&gt;left;\n            }\n            int tempVal = temp-&gt;val;\n            node-&gt;right = removeHelper(node-&gt;right, temp-&gt;val);\n            node-&gt;val = tempVal;\n        }\n    }\n    // Обновить высоту узла\n    updateHeight(node);\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = rotate(node);\n    // Вернуть корневой узел поддерева\n    return node;\n}\n</code></pre> avl_tree.kt<pre><code>/* Удаление узла */\nfun remove(_val: Int) {\n    root = removeHelper(root, _val)\n}\n\n/* Рекурсивное удаление узла (вспомогательный метод) */\nfun removeHelper(n: TreeNode?, _val: Int): TreeNode? {\n    var node = n ?: return null\n    /* 1. Найти узел и удалить его */\n    if (_val &lt; node._val)\n        node.left = removeHelper(node.left, _val)\n    else if (_val &gt; node._val)\n        node.right = removeHelper(node.right, _val)\n    else {\n        if (node.left == null || node.right == null) {\n            val child = if (node.left != null)\n                node.left\n            else\n                node.right\n            // Число дочерних узлов = 0, удалить node и сразу вернуть\n            if (child == null)\n                return null\n            // Число дочерних узлов = 1, удалить node напрямую\n            else\n                node = child\n        } else {\n            // Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n            var temp = node.right\n            while (temp!!.left != null) {\n                temp = temp.left\n            }\n            node.right = removeHelper(node.right, temp._val)\n            node._val = temp._val\n        }\n    }\n    updateHeight(node) // Обновить высоту узла\n    /* 2. Выполнить вращение, чтобы снова сбалансировать поддерево */\n    node = rotate(node)\n    // Вернуть корневой узел поддерева\n    return node\n}\n</code></pre> avl_tree.rb<pre><code>### Удаление узла ###\ndef remove(val)\n  @root = remove_helper(@root, val)\nend\n\n### Удаление узла ###\ndef remove(val)\n  @root = remove_helper(@root, val)\nend\n\n# ## Рекурсивное удаление узла (вспомогательный метод) ###\ndef remove_helper(node, val)\n  return if node.nil?\n  # 1. Найти узел и удалить его\n  if val &lt; node.val\n    node.left = remove_helper(node.left, val)\n  elsif val &gt; node.val\n    node.right = remove_helper(node.right, val)\n  else\n    if node.left.nil? || node.right.nil?\n      child = node.left || node.right\n      # Число дочерних узлов = 0, удалить node и сразу вернуть\n      return if child.nil?\n      # Число дочерних узлов = 1, удалить node напрямую\n      node = child\n    else\n      # Число дочерних узлов = 2, удалить следующий по симметричному обходу узел и заменить им текущий узел\n      temp = node.right\n      while !temp.left.nil?\n        temp = temp.left\n      end\n      node.right = remove_helper(node.right, temp.val)\n      node.val = temp.val\n    end\n  end\n  # Обновить высоту узла\n  update_height(node)\n  # 2. Выполнить вращение, чтобы снова сбалансировать поддерево\n  rotate(node)\nend\n</code></pre>","path":["Глава 7. Деревья","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#3_1","level":3,"title":"3.   Поиск узла","text":"<p>Операция поиска узла в AVL-дереве совпадает с поиском в двоичном дереве поиска, поэтому здесь она повторно не рассматривается.</p>","path":["Глава 7. Деревья","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/avl_tree/#754-avl-","level":2,"title":"7.5.4   Типичные применения AVL-дерева","text":"<ul> <li>Организация и хранение больших массивов данных, особенно в сценариях с частым поиском и относительно редкими вставками и удалениями.</li> <li>Использование при построении индексных систем в базах данных.</li> <li>Красно-черное дерево тоже является распространенным видом сбалансированного двоичного дерева поиска. По сравнению с AVL-деревом условия баланса у красно-черного дерева мягче, поэтому при вставке и удалении требуется меньше вращений, а средняя эффективность операций добавления и удаления выше.</li> </ul>","path":["Глава 7. Деревья","7.5 &nbsp; AVL-дерево *"],"tags":[]},{"location":"chapter_tree/binary_search_tree/","level":1,"title":"7.4   Двоичное дерево поиска","text":"<p>Как показано на рисунке 7-16, двоичное дерево поиска (binary search tree) удовлетворяет следующим условиям.</p> <ol> <li>Для корневого узла все значения в левом поддереве меньше значения корневого узла, а все значения в правом поддереве больше значения корневого узла.</li> <li>Левое и правое поддеревья любого узла также являются двоичными деревьями поиска, то есть тоже удовлетворяют условию <code>1.</code> .</li> </ol> <p></p> <p> Рисунок 7-16   Двоичное дерево поиска </p>","path":["Глава 7. Деревья","7.4 &nbsp; Двоичное дерево поиска"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#741","level":2,"title":"7.4.1   Операции с двоичным деревом поиска","text":"<p>Мы инкапсулируем двоичное дерево поиска в класс <code>BinarySearchTree</code> и объявляем переменную-член <code>root</code> , которая указывает на корневой узел дерева.</p>","path":["Глава 7. Деревья","7.4 &nbsp; Двоичное дерево поиска"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#1","level":3,"title":"1.   Поиск узла","text":"<p>Для заданного целевого значения узла <code>num</code> можно выполнить поиск, опираясь на свойства двоичного дерева поиска. Как показано на рисунках ниже, мы объявляем узел <code>cur</code> , стартуем от корня дерева <code>root</code> и циклически сравниваем значения <code>cur.val</code> и <code>num</code> .</p> <ul> <li>Если <code>cur.val &lt; num</code> , это означает, что целевой узел находится в правом поддереве <code>cur</code> , поэтому выполняем <code>cur = cur.right</code> .</li> <li>Если <code>cur.val &gt; num</code> , это означает, что целевой узел находится в левом поддереве <code>cur</code> , поэтому выполняем <code>cur = cur.left</code> .</li> <li>Если <code>cur.val = num</code> , это означает, что целевой узел найден, и мы выходим из цикла, возвращая этот узел.</li> </ul> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p> Рисунок 7-17   Пример поиска узла в двоичном дереве поиска </p> <p>Операция поиска в двоичном дереве поиска работает по тому же принципу, что и двоичный поиск: на каждом шаге она отбрасывает половину вариантов. Число итераций не превосходит высоты двоичного дерева, а когда дерево сбалансировано, требуется \\(O(\\log n)\\) времени. Пример кода приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_tree.py<pre><code>def search(self, num: int) -&gt; TreeNode | None:\n    \"\"\"Поиск узла\"\"\"\n    cur = self._root\n    # Искать в цикле и выйти после прохода за листовой узел\n    while cur is not None:\n        # Целевой узел находится в правом поддереве cur\n        if cur.val &lt; num:\n            cur = cur.right\n        # Целевой узел находится в левом поддереве cur\n        elif cur.val &gt; num:\n            cur = cur.left\n        # Найти целевой узел и выйти из цикла\n        else:\n            break\n    return cur\n</code></pre> binary_search_tree.cpp<pre><code>/* Поиск узла */\nTreeNode *search(int num) {\n    TreeNode *cur = root;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != nullptr) {\n        // Целевой узел находится в правом поддереве cur\n        if (cur-&gt;val &lt; num)\n            cur = cur-&gt;right;\n        // Целевой узел находится в левом поддереве cur\n        else if (cur-&gt;val &gt; num)\n            cur = cur-&gt;left;\n        // Найти целевой узел и выйти из цикла\n        else\n            break;\n    }\n    // Вернуть целевой узел\n    return cur;\n}\n</code></pre> binary_search_tree.java<pre><code>/* Поиск узла */\nTreeNode search(int num) {\n    TreeNode cur = root;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != null) {\n        // Целевой узел находится в правом поддереве cur\n        if (cur.val &lt; num)\n            cur = cur.right;\n        // Целевой узел находится в левом поддереве cur\n        else if (cur.val &gt; num)\n            cur = cur.left;\n        // Найти целевой узел и выйти из цикла\n        else\n            break;\n    }\n    // Вернуть целевой узел\n    return cur;\n}\n</code></pre> binary_search_tree.cs<pre><code>/* Поиск узла */\nTreeNode? Search(int num) {\n    TreeNode? cur = root;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != null) {\n        // Целевой узел находится в правом поддереве cur\n        if (cur.val &lt; num) cur =\n            cur.right;\n        // Целевой узел находится в левом поддереве cur\n        else if (cur.val &gt; num)\n            cur = cur.left;\n        // Найти целевой узел и выйти из цикла\n        else\n            break;\n    }\n    // Вернуть целевой узел\n    return cur;\n}\n</code></pre> binary_search_tree.go<pre><code>/* Поиск узла */\nfunc (bst *binarySearchTree) search(num int) *TreeNode {\n    node := bst.root\n    // Искать в цикле и выйти после прохода за листовой узел\n    for node != nil {\n        if node.Val.(int) &lt; num {\n            // Целевой узел находится в правом поддереве cur\n            node = node.Right\n        } else if node.Val.(int) &gt; num {\n            // Целевой узел находится в левом поддереве cur\n            node = node.Left\n        } else {\n            // Найти целевой узел и выйти из цикла\n            break\n        }\n    }\n    // Вернуть целевой узел\n    return node\n}\n</code></pre> binary_search_tree.swift<pre><code>/* Поиск узла */\nfunc search(num: Int) -&gt; TreeNode? {\n    var cur = root\n    // Искать в цикле и выйти после прохода за листовой узел\n    while cur != nil {\n        // Целевой узел находится в правом поддереве cur\n        if cur!.val &lt; num {\n            cur = cur?.right\n        }\n        // Целевой узел находится в левом поддереве cur\n        else if cur!.val &gt; num {\n            cur = cur?.left\n        }\n        // Найти целевой узел и выйти из цикла\n        else {\n            break\n        }\n    }\n    // Вернуть целевой узел\n    return cur\n}\n</code></pre> binary_search_tree.js<pre><code>/* Поиск узла */\nsearch(num) {\n    let cur = this.root;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur !== null) {\n        // Целевой узел находится в правом поддереве cur\n        if (cur.val &lt; num) cur = cur.right;\n        // Целевой узел находится в левом поддереве cur\n        else if (cur.val &gt; num) cur = cur.left;\n        // Найти целевой узел и выйти из цикла\n        else break;\n    }\n    // Вернуть целевой узел\n    return cur;\n}\n</code></pre> binary_search_tree.ts<pre><code>/* Поиск узла */\nsearch(num: number): TreeNode | null {\n    let cur = this.root;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur !== null) {\n        // Целевой узел находится в правом поддереве cur\n        if (cur.val &lt; num) cur = cur.right;\n        // Целевой узел находится в левом поддереве cur\n        else if (cur.val &gt; num) cur = cur.left;\n        // Найти целевой узел и выйти из цикла\n        else break;\n    }\n    // Вернуть целевой узел\n    return cur;\n}\n</code></pre> binary_search_tree.dart<pre><code>/* Поиск узла */\nTreeNode? search(int _num) {\n  TreeNode? cur = _root;\n  // Искать в цикле и выйти после прохода за листовой узел\n  while (cur != null) {\n    // Целевой узел находится в правом поддереве cur\n    if (cur.val &lt; _num)\n      cur = cur.right;\n    // Целевой узел находится в левом поддереве cur\n    else if (cur.val &gt; _num)\n      cur = cur.left;\n    // Найти целевой узел и выйти из цикла\n    else\n      break;\n  }\n  // Вернуть целевой узел\n  return cur;\n}\n</code></pre> binary_search_tree.rs<pre><code>/* Поиск узла */\npub fn search(&amp;self, num: i32) -&gt; OptionTreeNodeRc {\n    let mut cur = self.root.clone();\n    // Искать в цикле и выйти после прохода за листовой узел\n    while let Some(node) = cur.clone() {\n        match num.cmp(&amp;node.borrow().val) {\n            // Целевой узел находится в правом поддереве cur\n            Ordering::Greater =&gt; cur = node.borrow().right.clone(),\n            // Целевой узел находится в левом поддереве cur\n            Ordering::Less =&gt; cur = node.borrow().left.clone(),\n            // Найти целевой узел и выйти из цикла\n            Ordering::Equal =&gt; break,\n        }\n    }\n\n    // Вернуть целевой узел\n    cur\n}\n</code></pre> binary_search_tree.c<pre><code>/* Поиск узла */\nTreeNode *search(BinarySearchTree *bst, int num) {\n    TreeNode *cur = bst-&gt;root;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != NULL) {\n        if (cur-&gt;val &lt; num) {\n            // Целевой узел находится в правом поддереве cur\n            cur = cur-&gt;right;\n        } else if (cur-&gt;val &gt; num) {\n            // Целевой узел находится в левом поддереве cur\n            cur = cur-&gt;left;\n        } else {\n            // Найти целевой узел и выйти из цикла\n            break;\n        }\n    }\n    // Вернуть целевой узел\n    return cur;\n}\n</code></pre> binary_search_tree.kt<pre><code>/* Поиск узла */\nfun search(num: Int): TreeNode? {\n    var cur = root\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != null) {\n        // Целевой узел находится в правом поддереве cur\n        cur = if (cur._val &lt; num)\n            cur.right\n        // Целевой узел находится в левом поддереве cur\n        else if (cur._val &gt; num)\n            cur.left\n        // Найти целевой узел и выйти из цикла\n        else\n            break\n    }\n    // Вернуть целевой узел\n    return cur\n}\n</code></pre> binary_search_tree.rb<pre><code>### Поиск узла ###\ndef search(num)\n  cur = @root\n\n  # Искать в цикле и выйти после прохода за листовой узел\n  while !cur.nil?\n    # Целевой узел находится в правом поддереве cur\n    if cur.val &lt; num\n      cur = cur.right\n    # Целевой узел находится в левом поддереве cur\n    elsif cur.val &gt; num\n      cur = cur.left\n    # Найти целевой узел и выйти из цикла\n    else\n      break\n    end\n  end\n\n  cur\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 7. Деревья","7.4 &nbsp; Двоичное дерево поиска"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#2","level":3,"title":"2.   Вставка узла","text":"<p>Пусть дан элемент <code>num</code> , который нужно вставить. Чтобы сохранить свойство двоичного дерева поиска \"левое поддерево &lt; корень &lt; правое поддерево\", процесс вставки выглядит следующим образом.</p> <ol> <li>Найти позицию для вставки: как и в операции поиска, начиная от корня, мы циклически спускаемся вниз в зависимости от соотношения между текущим значением узла и <code>num</code> , пока не выйдем за листовой узел (то есть не дойдем до <code>None</code> ).</li> <li>Вставить узел в найденную позицию: инициализировать узел <code>num</code> и поставить его на место этого <code>None</code> .</li> </ol> <p></p> <p> Рисунок 7-18   Вставка узла в двоичное дерево поиска </p> <p>В реализации кода нужно обратить внимание на следующие два момента.</p> <ul> <li>Двоичное дерево поиска не допускает дублирующихся узлов, иначе его определение будет нарушено. Поэтому если вставляемый узел уже существует в дереве, вставка не выполняется и функция сразу возвращается.</li> <li>Чтобы реализовать вставку, нам нужно использовать узел <code>pre</code> для сохранения узла предыдущей итерации цикла. Тогда, когда обход дойдет до <code>None</code> , мы сможем получить его родителя и завершить вставку.</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_tree.py<pre><code>def insert(self, num: int):\n    \"\"\"Вставка узла\"\"\"\n    # Если дерево пусто, инициализировать корневой узел\n    if self._root is None:\n        self._root = TreeNode(num)\n        return\n    # Искать в цикле и выйти после прохода за листовой узел\n    cur, pre = self._root, None\n    while cur is not None:\n        # Найти повторяющийся узел и сразу вернуть\n        if cur.val == num:\n            return\n        pre = cur\n        # Позиция вставки находится в правом поддереве cur\n        if cur.val &lt; num:\n            cur = cur.right\n        # Позиция вставки находится в левом поддереве cur\n        else:\n            cur = cur.left\n    # Вставка узла\n    node = TreeNode(num)\n    if pre.val &lt; num:\n        pre.right = node\n    else:\n        pre.left = node\n</code></pre> binary_search_tree.cpp<pre><code>/* Вставка узла */\nvoid insert(int num) {\n    // Если дерево пусто, инициализировать корневой узел\n    if (root == nullptr) {\n        root = new TreeNode(num);\n        return;\n    }\n    TreeNode *cur = root, *pre = nullptr;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != nullptr) {\n        // Найти повторяющийся узел и сразу вернуть\n        if (cur-&gt;val == num)\n            return;\n        pre = cur;\n        // Позиция вставки находится в правом поддереве cur\n        if (cur-&gt;val &lt; num)\n            cur = cur-&gt;right;\n        // Позиция вставки находится в левом поддереве cur\n        else\n            cur = cur-&gt;left;\n    }\n    // Вставка узла\n    TreeNode *node = new TreeNode(num);\n    if (pre-&gt;val &lt; num)\n        pre-&gt;right = node;\n    else\n        pre-&gt;left = node;\n}\n</code></pre> binary_search_tree.java<pre><code>/* Вставка узла */\nvoid insert(int num) {\n    // Если дерево пусто, инициализировать корневой узел\n    if (root == null) {\n        root = new TreeNode(num);\n        return;\n    }\n    TreeNode cur = root, pre = null;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != null) {\n        // Найти повторяющийся узел и сразу вернуть\n        if (cur.val == num)\n            return;\n        pre = cur;\n        // Позиция вставки находится в правом поддереве cur\n        if (cur.val &lt; num)\n            cur = cur.right;\n        // Позиция вставки находится в левом поддереве cur\n        else\n            cur = cur.left;\n    }\n    // Вставка узла\n    TreeNode node = new TreeNode(num);\n    if (pre.val &lt; num)\n        pre.right = node;\n    else\n        pre.left = node;\n}\n</code></pre> binary_search_tree.cs<pre><code>/* Вставка узла */\nvoid Insert(int num) {\n    // Если дерево пусто, инициализировать корневой узел\n    if (root == null) {\n        root = new TreeNode(num);\n        return;\n    }\n    TreeNode? cur = root, pre = null;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != null) {\n        // Найти повторяющийся узел и сразу вернуть\n        if (cur.val == num)\n            return;\n        pre = cur;\n        // Позиция вставки находится в правом поддереве cur\n        if (cur.val &lt; num)\n            cur = cur.right;\n        // Позиция вставки находится в левом поддереве cur\n        else\n            cur = cur.left;\n    }\n\n    // Вставка узла\n    TreeNode node = new(num);\n    if (pre != null) {\n        if (pre.val &lt; num)\n            pre.right = node;\n        else\n            pre.left = node;\n    }\n}\n</code></pre> binary_search_tree.go<pre><code>/* Вставка узла */\nfunc (bst *binarySearchTree) insert(num int) {\n    cur := bst.root\n    // Если дерево пусто, инициализировать корневой узел\n    if cur == nil {\n        bst.root = NewTreeNode(num)\n        return\n    }\n    // Позиция узла, предшествующего вставляемому\n    var pre *TreeNode = nil\n    // Искать в цикле и выйти после прохода за листовой узел\n    for cur != nil {\n        if cur.Val == num {\n            return\n        }\n        pre = cur\n        if cur.Val.(int) &lt; num {\n            cur = cur.Right\n        } else {\n            cur = cur.Left\n        }\n    }\n    // Вставка узла\n    node := NewTreeNode(num)\n    if pre.Val.(int) &lt; num {\n        pre.Right = node\n    } else {\n        pre.Left = node\n    }\n}\n</code></pre> binary_search_tree.swift<pre><code>/* Вставка узла */\nfunc insert(num: Int) {\n    // Если дерево пусто, инициализировать корневой узел\n    if root == nil {\n        root = TreeNode(x: num)\n        return\n    }\n    var cur = root\n    var pre: TreeNode?\n    // Искать в цикле и выйти после прохода за листовой узел\n    while cur != nil {\n        // Найти повторяющийся узел и сразу вернуть\n        if cur!.val == num {\n            return\n        }\n        pre = cur\n        // Позиция вставки находится в правом поддереве cur\n        if cur!.val &lt; num {\n            cur = cur?.right\n        }\n        // Позиция вставки находится в левом поддереве cur\n        else {\n            cur = cur?.left\n        }\n    }\n    // Вставка узла\n    let node = TreeNode(x: num)\n    if pre!.val &lt; num {\n        pre?.right = node\n    } else {\n        pre?.left = node\n    }\n}\n</code></pre> binary_search_tree.js<pre><code>/* Вставка узла */\ninsert(num) {\n    // Если дерево пусто, инициализировать корневой узел\n    if (this.root === null) {\n        this.root = new TreeNode(num);\n        return;\n    }\n    let cur = this.root,\n        pre = null;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur !== null) {\n        // Найти повторяющийся узел и сразу вернуть\n        if (cur.val === num) return;\n        pre = cur;\n        // Позиция вставки находится в правом поддереве cur\n        if (cur.val &lt; num) cur = cur.right;\n        // Позиция вставки находится в левом поддереве cur\n        else cur = cur.left;\n    }\n    // Вставка узла\n    const node = new TreeNode(num);\n    if (pre.val &lt; num) pre.right = node;\n    else pre.left = node;\n}\n</code></pre> binary_search_tree.ts<pre><code>/* Вставка узла */\ninsert(num: number): void {\n    // Если дерево пусто, инициализировать корневой узел\n    if (this.root === null) {\n        this.root = new TreeNode(num);\n        return;\n    }\n    let cur: TreeNode | null = this.root,\n        pre: TreeNode | null = null;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur !== null) {\n        // Найти повторяющийся узел и сразу вернуть\n        if (cur.val === num) return;\n        pre = cur;\n        // Позиция вставки находится в правом поддереве cur\n        if (cur.val &lt; num) cur = cur.right;\n        // Позиция вставки находится в левом поддереве cur\n        else cur = cur.left;\n    }\n    // Вставка узла\n    const node = new TreeNode(num);\n    if (pre!.val &lt; num) pre!.right = node;\n    else pre!.left = node;\n}\n</code></pre> binary_search_tree.dart<pre><code>/* Вставка узла */\nvoid insert(int _num) {\n  // Если дерево пусто, инициализировать корневой узел\n  if (_root == null) {\n    _root = TreeNode(_num);\n    return;\n  }\n  TreeNode? cur = _root;\n  TreeNode? pre = null;\n  // Искать в цикле и выйти после прохода за листовой узел\n  while (cur != null) {\n    // Найти повторяющийся узел и сразу вернуть\n    if (cur.val == _num) return;\n    pre = cur;\n    // Позиция вставки находится в правом поддереве cur\n    if (cur.val &lt; _num)\n      cur = cur.right;\n    // Позиция вставки находится в левом поддереве cur\n    else\n      cur = cur.left;\n  }\n  // Вставка узла\n  TreeNode? node = TreeNode(_num);\n  if (pre!.val &lt; _num)\n    pre.right = node;\n  else\n    pre.left = node;\n}\n</code></pre> binary_search_tree.rs<pre><code>/* Вставка узла */\npub fn insert(&amp;mut self, num: i32) {\n    // Если дерево пусто, инициализировать корневой узел\n    if self.root.is_none() {\n        self.root = Some(TreeNode::new(num));\n        return;\n    }\n    let mut cur = self.root.clone();\n    let mut pre = None;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while let Some(node) = cur.clone() {\n        match num.cmp(&amp;node.borrow().val) {\n            // Найти повторяющийся узел и сразу вернуть\n            Ordering::Equal =&gt; return,\n            // Позиция вставки находится в правом поддереве cur\n            Ordering::Greater =&gt; {\n                pre = cur.clone();\n                cur = node.borrow().right.clone();\n            }\n            // Позиция вставки находится в левом поддереве cur\n            Ordering::Less =&gt; {\n                pre = cur.clone();\n                cur = node.borrow().left.clone();\n            }\n        }\n    }\n    // Вставка узла\n    let pre = pre.unwrap();\n    let node = Some(TreeNode::new(num));\n    if num &gt; pre.borrow().val {\n        pre.borrow_mut().right = node;\n    } else {\n        pre.borrow_mut().left = node;\n    }\n}\n</code></pre> binary_search_tree.c<pre><code>/* Вставка узла */\nvoid insert(BinarySearchTree *bst, int num) {\n    // Если дерево пусто, инициализировать корневой узел\n    if (bst-&gt;root == NULL) {\n        bst-&gt;root = newTreeNode(num);\n        return;\n    }\n    TreeNode *cur = bst-&gt;root, *pre = NULL;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != NULL) {\n        // Найти повторяющийся узел и сразу вернуть\n        if (cur-&gt;val == num) {\n            return;\n        }\n        pre = cur;\n        if (cur-&gt;val &lt; num) {\n            // Позиция вставки находится в правом поддереве cur\n            cur = cur-&gt;right;\n        } else {\n            // Позиция вставки находится в левом поддереве cur\n            cur = cur-&gt;left;\n        }\n    }\n    // Вставка узла\n    TreeNode *node = newTreeNode(num);\n    if (pre-&gt;val &lt; num) {\n        pre-&gt;right = node;\n    } else {\n        pre-&gt;left = node;\n    }\n}\n</code></pre> binary_search_tree.kt<pre><code>/* Вставка узла */\nfun insert(num: Int) {\n    // Если дерево пусто, инициализировать корневой узел\n    if (root == null) {\n        root = TreeNode(num)\n        return\n    }\n    var cur = root\n    var pre: TreeNode? = null\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != null) {\n        // Найти повторяющийся узел и сразу вернуть\n        if (cur._val == num)\n            return\n        pre = cur\n        // Позиция вставки находится в правом поддереве cur\n        cur = if (cur._val &lt; num)\n            cur.right\n        // Позиция вставки находится в левом поддереве cur\n        else\n            cur.left\n    }\n    // Вставка узла\n    val node = TreeNode(num)\n    if (pre?._val!! &lt; num)\n        pre.right = node\n    else\n        pre.left = node\n}\n</code></pre> binary_search_tree.rb<pre><code>### Вставка узла ###\ndef insert(num)\n  # Если дерево пусто, инициализировать корневой узел\n  if @root.nil?\n    @root = TreeNode.new(num)\n    return\n  end\n\n  # Искать в цикле и выйти после прохода за листовой узел\n  cur, pre = @root, nil\n  while !cur.nil?\n    # Найти повторяющийся узел и сразу вернуть\n    return if cur.val == num\n\n    pre = cur\n    # Позиция вставки находится в правом поддереве cur\n    if cur.val &lt; num\n      cur = cur.right\n    # Позиция вставки находится в левом поддереве cur\n    else\n      cur = cur.left\n    end\n  end\n\n  # Вставка узла\n  node = TreeNode.new(num)\n  if pre.val &lt; num\n    pre.right = node\n  else\n    pre.left = node\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Как и поиск узла, вставка узла требует \\(O(\\log n)\\) времени.</p>","path":["Глава 7. Деревья","7.4 &nbsp; Двоичное дерево поиска"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#3","level":3,"title":"3.   Удаление узла","text":"<p>Сначала нужно найти в двоичном дереве целевой узел, а затем удалить его. Как и при вставке, после удаления необходимо сохранить свойство двоичного дерева поиска: \"левое поддерево &lt; корень &lt; правое поддерево\". Поэтому в зависимости от числа дочерних узлов у удаляемого узла, то есть для случаев со степенью 0, 1 и 2, выполняются разные операции удаления.</p> <p>Как показано на рисунке 7-19, когда степень удаляемого узла равна \\(0\\) , это значит, что узел является листом и может быть удален напрямую.</p> <p></p> <p> Рисунок 7-19   Удаление узла в двоичном дереве поиска (степень 0) </p> <p>Как показано на рисунке 7-20, когда степень удаляемого узла равна \\(1\\) , достаточно заменить удаляемый узел его дочерним узлом.</p> <p></p> <p> Рисунок 7-20   Удаление узла в двоичном дереве поиска (степень 1) </p> <p>Когда степень удаляемого узла равна \\(2\\) , мы уже не можем удалить его напрямую и должны использовать для замены другой узел. Чтобы сохранить свойство двоичного дерева поиска \"левое поддерево \\(&lt;\\) корень \\(&lt;\\) правое поддерево\", этим узлом может быть минимальный узел правого поддерева или максимальный узел левого поддерева.</p> <p>Предположим, мы выбираем минимальный узел правого поддерева, то есть следующий узел в симметричном обходе. Тогда процесс удаления выглядит так.</p> <ol> <li>Найти следующий узел в \"последовательности симметричного обхода\" для удаляемого узла и обозначить его как <code>tmp</code> .</li> <li>Значением <code>tmp</code> перезаписать значение удаляемого узла, а затем рекурсивно удалить узел <code>tmp</code> из дерева.</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p> Рисунок 7-21   Удаление узла в двоичном дереве поиска (степень 2) </p> <p>Операция удаления узла также требует \\(O(\\log n)\\) времени, где поиск удаляемого узла стоит \\(O(\\log n)\\) , а получение следующего узла симметричного обхода также требует \\(O(\\log n)\\) . Пример кода приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_search_tree.py<pre><code>def remove(self, num: int):\n    \"\"\"Удаление узла\"\"\"\n    # Если дерево пусто, сразу вернуть\n    if self._root is None:\n        return\n    # Искать в цикле и выйти после прохода за листовой узел\n    cur, pre = self._root, None\n    while cur is not None:\n        # Найти узел для удаления и выйти из цикла\n        if cur.val == num:\n            break\n        pre = cur\n        # Узел для удаления находится в правом поддереве cur\n        if cur.val &lt; num:\n            cur = cur.right\n        # Узел для удаления находится в левом поддереве cur\n        else:\n            cur = cur.left\n    # Если узел для удаления отсутствует, сразу вернуть\n    if cur is None:\n        return\n\n    # Число дочерних узлов = 0 или 1\n    if cur.left is None or cur.right is None:\n        # Когда число дочерних узлов = 0 / 1, child = null / этот дочерний узел\n        child = cur.left or cur.right\n        # Удалить узел cur\n        if cur != self._root:\n            if pre.left == cur:\n                pre.left = child\n            else:\n                pre.right = child\n        else:\n            # Если удаляемый узел является корнем, заново назначить корневой узел\n            self._root = child\n    # Число дочерних узлов = 2\n    else:\n        # Получить следующий узел после cur в симметричном обходе\n        tmp: TreeNode = cur.right\n        while tmp.left is not None:\n            tmp = tmp.left\n        # Рекурсивно удалить узел tmp\n        self.remove(tmp.val)\n        # Перезаписать cur значением tmp\n        cur.val = tmp.val\n</code></pre> binary_search_tree.cpp<pre><code>/* Удаление узла */\nvoid remove(int num) {\n    // Если дерево пусто, сразу вернуть\n    if (root == nullptr)\n        return;\n    TreeNode *cur = root, *pre = nullptr;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != nullptr) {\n        // Найти узел для удаления и выйти из цикла\n        if (cur-&gt;val == num)\n            break;\n        pre = cur;\n        // Узел для удаления находится в правом поддереве cur\n        if (cur-&gt;val &lt; num)\n            cur = cur-&gt;right;\n        // Узел для удаления находится в левом поддереве cur\n        else\n            cur = cur-&gt;left;\n    }\n    // Если узел для удаления отсутствует, сразу вернуть\n    if (cur == nullptr)\n        return;\n    // Число дочерних узлов = 0 или 1\n    if (cur-&gt;left == nullptr || cur-&gt;right == nullptr) {\n        // Когда число дочерних узлов = 0 / 1, child = nullptr / этот дочерний узел\n        TreeNode *child = cur-&gt;left != nullptr ? cur-&gt;left : cur-&gt;right;\n        // Удалить узел cur\n        if (cur != root) {\n            if (pre-&gt;left == cur)\n                pre-&gt;left = child;\n            else\n                pre-&gt;right = child;\n        } else {\n            // Если удаляемый узел является корнем, заново назначить корневой узел\n            root = child;\n        }\n        // Освободить память\n        delete cur;\n    }\n    // Число дочерних узлов = 2\n    else {\n        // Получить следующий узел после cur в симметричном обходе\n        TreeNode *tmp = cur-&gt;right;\n        while (tmp-&gt;left != nullptr) {\n            tmp = tmp-&gt;left;\n        }\n        int tmpVal = tmp-&gt;val;\n        // Рекурсивно удалить узел tmp\n        remove(tmp-&gt;val);\n        // Перезаписать cur значением tmp\n        cur-&gt;val = tmpVal;\n    }\n}\n</code></pre> binary_search_tree.java<pre><code>/* Удаление узла */\nvoid remove(int num) {\n    // Если дерево пусто, сразу вернуть\n    if (root == null)\n        return;\n    TreeNode cur = root, pre = null;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != null) {\n        // Найти узел для удаления и выйти из цикла\n        if (cur.val == num)\n            break;\n        pre = cur;\n        // Узел для удаления находится в правом поддереве cur\n        if (cur.val &lt; num)\n            cur = cur.right;\n        // Узел для удаления находится в левом поддереве cur\n        else\n            cur = cur.left;\n    }\n    // Если узел для удаления отсутствует, сразу вернуть\n    if (cur == null)\n        return;\n    // Число дочерних узлов = 0 или 1\n    if (cur.left == null || cur.right == null) {\n        // Когда число дочерних узлов = 0 / 1, child = null / этот дочерний узел\n        TreeNode child = cur.left != null ? cur.left : cur.right;\n        // Удалить узел cur\n        if (cur != root) {\n            if (pre.left == cur)\n                pre.left = child;\n            else\n                pre.right = child;\n        } else {\n            // Если удаляемый узел является корнем, заново назначить корневой узел\n            root = child;\n        }\n    }\n    // Число дочерних узлов = 2\n    else {\n        // Получить следующий узел после cur в симметричном обходе\n        TreeNode tmp = cur.right;\n        while (tmp.left != null) {\n            tmp = tmp.left;\n        }\n        // Рекурсивно удалить узел tmp\n        remove(tmp.val);\n        // Перезаписать cur значением tmp\n        cur.val = tmp.val;\n    }\n}\n</code></pre> binary_search_tree.cs<pre><code>/* Удаление узла */\nvoid Remove(int num) {\n    // Если дерево пусто, сразу вернуть\n    if (root == null)\n        return;\n    TreeNode? cur = root, pre = null;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != null) {\n        // Найти узел для удаления и выйти из цикла\n        if (cur.val == num)\n            break;\n        pre = cur;\n        // Узел для удаления находится в правом поддереве cur\n        if (cur.val &lt; num)\n            cur = cur.right;\n        // Узел для удаления находится в левом поддереве cur\n        else\n            cur = cur.left;\n    }\n    // Если узел для удаления отсутствует, сразу вернуть\n    if (cur == null)\n        return;\n    // Число дочерних узлов = 0 или 1\n    if (cur.left == null || cur.right == null) {\n        // Когда число дочерних узлов = 0 / 1, child = null / этот дочерний узел\n        TreeNode? child = cur.left ?? cur.right;\n        // Удалить узел cur\n        if (cur != root) {\n            if (pre!.left == cur)\n                pre.left = child;\n            else\n                pre.right = child;\n        } else {\n            // Если удаляемый узел является корнем, заново назначить корневой узел\n            root = child;\n        }\n    }\n    // Число дочерних узлов = 2\n    else {\n        // Получить следующий узел после cur в симметричном обходе\n        TreeNode? tmp = cur.right;\n        while (tmp.left != null) {\n            tmp = tmp.left;\n        }\n        // Рекурсивно удалить узел tmp\n        Remove(tmp.val!.Value);\n        // Перезаписать cur значением tmp\n        cur.val = tmp.val;\n    }\n}\n</code></pre> binary_search_tree.go<pre><code>/* Удаление узла */\nfunc (bst *binarySearchTree) remove(num int) {\n    cur := bst.root\n    // Если дерево пусто, сразу вернуть\n    if cur == nil {\n        return\n    }\n    // Позиция узла, предшествующего удаляемому\n    var pre *TreeNode = nil\n    // Искать в цикле и выйти после прохода за листовой узел\n    for cur != nil {\n        if cur.Val == num {\n            break\n        }\n        pre = cur\n        if cur.Val.(int) &lt; num {\n            // Удаляемый узел находится в правом поддереве\n            cur = cur.Right\n        } else {\n            // Удаляемый узел находится в левом поддереве\n            cur = cur.Left\n        }\n    }\n    // Если узел для удаления отсутствует, сразу вернуть\n    if cur == nil {\n        return\n    }\n    // Число дочерних узлов равно 0 или 1\n    if cur.Left == nil || cur.Right == nil {\n        var child *TreeNode = nil\n        // Извлечь дочерний узел удаляемого узла\n        if cur.Left != nil {\n            child = cur.Left\n        } else {\n            child = cur.Right\n        }\n        // Удалить узел cur\n        if cur != bst.root {\n            if pre.Left == cur {\n                pre.Left = child\n            } else {\n                pre.Right = child\n            }\n        } else {\n            // Если удаляемый узел является корнем, заново назначить корневой узел\n            bst.root = child\n        }\n        // Число дочерних узлов равно 2\n    } else {\n        // Получить следующий после cur узел в симметричном обходе для удаляемого узла\n        tmp := cur.Right\n        for tmp.Left != nil {\n            tmp = tmp.Left\n        }\n        // Рекурсивно удалить узел tmp\n        bst.remove(tmp.Val.(int))\n        // Перезаписать cur значением tmp\n        cur.Val = tmp.Val\n    }\n}\n</code></pre> binary_search_tree.swift<pre><code>/* Удаление узла */\nfunc remove(num: Int) {\n    // Если дерево пусто, сразу вернуть\n    if root == nil {\n        return\n    }\n    var cur = root\n    var pre: TreeNode?\n    // Искать в цикле и выйти после прохода за листовой узел\n    while cur != nil {\n        // Найти узел для удаления и выйти из цикла\n        if cur!.val == num {\n            break\n        }\n        pre = cur\n        // Узел для удаления находится в правом поддереве cur\n        if cur!.val &lt; num {\n            cur = cur?.right\n        }\n        // Узел для удаления находится в левом поддереве cur\n        else {\n            cur = cur?.left\n        }\n    }\n    // Если узел для удаления отсутствует, сразу вернуть\n    if cur == nil {\n        return\n    }\n    // Число дочерних узлов = 0 или 1\n    if cur?.left == nil || cur?.right == nil {\n        // Когда число дочерних узлов = 0 / 1, child = null / этот дочерний узел\n        let child = cur?.left ?? cur?.right\n        // Удалить узел cur\n        if cur !== root {\n            if pre?.left === cur {\n                pre?.left = child\n            } else {\n                pre?.right = child\n            }\n        } else {\n            // Если удаляемый узел является корнем, заново назначить корневой узел\n            root = child\n        }\n    }\n    // Число дочерних узлов = 2\n    else {\n        // Получить следующий узел после cur в симметричном обходе\n        var tmp = cur?.right\n        while tmp?.left != nil {\n            tmp = tmp?.left\n        }\n        // Рекурсивно удалить узел tmp\n        remove(num: tmp!.val)\n        // Перезаписать cur значением tmp\n        cur?.val = tmp!.val\n    }\n}\n</code></pre> binary_search_tree.js<pre><code>/* Удаление узла */\nremove(num) {\n    // Если дерево пусто, сразу вернуть\n    if (this.root === null) return;\n    let cur = this.root,\n        pre = null;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur !== null) {\n        // Найти узел для удаления и выйти из цикла\n        if (cur.val === num) break;\n        pre = cur;\n        // Узел для удаления находится в правом поддереве cur\n        if (cur.val &lt; num) cur = cur.right;\n        // Узел для удаления находится в левом поддереве cur\n        else cur = cur.left;\n    }\n    // Если узел для удаления отсутствует, сразу вернуть\n    if (cur === null) return;\n    // Число дочерних узлов = 0 или 1\n    if (cur.left === null || cur.right === null) {\n        // Когда число дочерних узлов = 0 / 1, child = null / этот дочерний узел\n        const child = cur.left !== null ? cur.left : cur.right;\n        // Удалить узел cur\n        if (cur !== this.root) {\n            if (pre.left === cur) pre.left = child;\n            else pre.right = child;\n        } else {\n            // Если удаляемый узел является корнем, заново назначить корневой узел\n            this.root = child;\n        }\n    }\n    // Число дочерних узлов = 2\n    else {\n        // Получить следующий узел после cur в симметричном обходе\n        let tmp = cur.right;\n        while (tmp.left !== null) {\n            tmp = tmp.left;\n        }\n        // Рекурсивно удалить узел tmp\n        this.remove(tmp.val);\n        // Перезаписать cur значением tmp\n        cur.val = tmp.val;\n    }\n}\n</code></pre> binary_search_tree.ts<pre><code>/* Удаление узла */\nremove(num: number): void {\n    // Если дерево пусто, сразу вернуть\n    if (this.root === null) return;\n    let cur: TreeNode | null = this.root,\n        pre: TreeNode | null = null;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur !== null) {\n        // Найти узел для удаления и выйти из цикла\n        if (cur.val === num) break;\n        pre = cur;\n        // Узел для удаления находится в правом поддереве cur\n        if (cur.val &lt; num) cur = cur.right;\n        // Узел для удаления находится в левом поддереве cur\n        else cur = cur.left;\n    }\n    // Если узел для удаления отсутствует, сразу вернуть\n    if (cur === null) return;\n    // Число дочерних узлов = 0 или 1\n    if (cur.left === null || cur.right === null) {\n        // Когда число дочерних узлов = 0 / 1, child = null / этот дочерний узел\n        const child: TreeNode | null =\n            cur.left !== null ? cur.left : cur.right;\n        // Удалить узел cur\n        if (cur !== this.root) {\n            if (pre!.left === cur) pre!.left = child;\n            else pre!.right = child;\n        } else {\n            // Если удаляемый узел является корнем, заново назначить корневой узел\n            this.root = child;\n        }\n    }\n    // Число дочерних узлов = 2\n    else {\n        // Получить следующий узел после cur в симметричном обходе\n        let tmp: TreeNode | null = cur.right;\n        while (tmp!.left !== null) {\n            tmp = tmp!.left;\n        }\n        // Рекурсивно удалить узел tmp\n        this.remove(tmp!.val);\n        // Перезаписать cur значением tmp\n        cur.val = tmp!.val;\n    }\n}\n</code></pre> binary_search_tree.dart<pre><code>/* Удаление узла */\nvoid remove(int _num) {\n  // Если дерево пусто, сразу вернуть\n  if (_root == null) return;\n  TreeNode? cur = _root;\n  TreeNode? pre = null;\n  // Искать в цикле и выйти после прохода за листовой узел\n  while (cur != null) {\n    // Найти узел для удаления и выйти из цикла\n    if (cur.val == _num) break;\n    pre = cur;\n    // Узел для удаления находится в правом поддереве cur\n    if (cur.val &lt; _num)\n      cur = cur.right;\n    // Узел для удаления находится в левом поддереве cur\n    else\n      cur = cur.left;\n  }\n  // Если удаляемого узла нет, сразу вернуть\n  if (cur == null) return;\n  // Число дочерних узлов = 0 или 1\n  if (cur.left == null || cur.right == null) {\n    // Когда число дочерних узлов = 0 / 1, child = null / этот дочерний узел\n    TreeNode? child = cur.left ?? cur.right;\n    // Удалить узел cur\n    if (cur != _root) {\n      if (pre!.left == cur)\n        pre.left = child;\n      else\n        pre.right = child;\n    } else {\n      // Если удаляемый узел является корнем, заново назначить корневой узел\n      _root = child;\n    }\n  } else {\n    // Число дочерних узлов = 2\n    // Получить следующий узел после cur в симметричном обходе\n    TreeNode? tmp = cur.right;\n    while (tmp!.left != null) {\n      tmp = tmp.left;\n    }\n    // Рекурсивно удалить узел tmp\n    remove(tmp.val);\n    // Перезаписать cur значением tmp\n    cur.val = tmp.val;\n  }\n}\n</code></pre> binary_search_tree.rs<pre><code>/* Удаление узла */\npub fn remove(&amp;mut self, num: i32) {\n    // Если дерево пусто, сразу вернуть\n    if self.root.is_none() {\n        return;\n    }\n    let mut cur = self.root.clone();\n    let mut pre = None;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while let Some(node) = cur.clone() {\n        match num.cmp(&amp;node.borrow().val) {\n            // Найти узел для удаления и выйти из цикла\n            Ordering::Equal =&gt; break,\n            // Узел для удаления находится в правом поддереве cur\n            Ordering::Greater =&gt; {\n                pre = cur.clone();\n                cur = node.borrow().right.clone();\n            }\n            // Узел для удаления находится в левом поддереве cur\n            Ordering::Less =&gt; {\n                pre = cur.clone();\n                cur = node.borrow().left.clone();\n            }\n        }\n    }\n    // Если узел для удаления отсутствует, сразу вернуть\n    if cur.is_none() {\n        return;\n    }\n    let cur = cur.unwrap();\n    let (left_child, right_child) = (cur.borrow().left.clone(), cur.borrow().right.clone());\n    match (left_child.clone(), right_child.clone()) {\n        // Число дочерних узлов = 0 или 1\n        (None, None) | (Some(_), None) | (None, Some(_)) =&gt; {\n            // Когда число дочерних узлов = 0 / 1, child = nullptr / этот дочерний узел\n            let child = left_child.or(right_child);\n            let pre = pre.unwrap();\n            // Удалить узел cur\n            if !Rc::ptr_eq(&amp;cur, self.root.as_ref().unwrap()) {\n                let left = pre.borrow().left.clone();\n                if left.is_some() &amp;&amp; Rc::ptr_eq(left.as_ref().unwrap(), &amp;cur) {\n                    pre.borrow_mut().left = child;\n                } else {\n                    pre.borrow_mut().right = child;\n                }\n            } else {\n                // Если удаляемый узел является корнем, заново назначить корневой узел\n                self.root = child;\n            }\n        }\n        // Число дочерних узлов = 2\n        (Some(_), Some(_)) =&gt; {\n            // Получить следующий узел после cur в симметричном обходе\n            let mut tmp = cur.borrow().right.clone();\n            while let Some(node) = tmp.clone() {\n                if node.borrow().left.is_some() {\n                    tmp = node.borrow().left.clone();\n                } else {\n                    break;\n                }\n            }\n            let tmp_val = tmp.unwrap().borrow().val;\n            // Рекурсивно удалить узел tmp\n            self.remove(tmp_val);\n            // Перезаписать cur значением tmp\n            cur.borrow_mut().val = tmp_val;\n        }\n    }\n}\n</code></pre> binary_search_tree.c<pre><code>/* Удаление узла */\n// Из-за подключения stdio.h здесь нельзя использовать ключевое слово remove\nvoid removeItem(BinarySearchTree *bst, int num) {\n    // Если дерево пусто, сразу вернуть\n    if (bst-&gt;root == NULL)\n        return;\n    TreeNode *cur = bst-&gt;root, *pre = NULL;\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != NULL) {\n        // Найти узел для удаления и выйти из цикла\n        if (cur-&gt;val == num)\n            break;\n        pre = cur;\n        if (cur-&gt;val &lt; num) {\n            // Удаляемый узел находится в правом поддереве root\n            cur = cur-&gt;right;\n        } else {\n            // Удаляемый узел находится в левом поддереве root\n            cur = cur-&gt;left;\n        }\n    }\n    // Если узел для удаления отсутствует, сразу вернуть\n    if (cur == NULL)\n        return;\n    // Проверить, есть ли дочерние узлы у удаляемого узла\n    if (cur-&gt;left == NULL || cur-&gt;right == NULL) {\n        /* Число дочерних узлов = 0 или 1 */\n        // Когда число дочерних узлов = 0 / 1, child = nullptr / этот дочерний узел\n        TreeNode *child = cur-&gt;left != NULL ? cur-&gt;left : cur-&gt;right;\n        // Удалить узел cur\n        if (pre-&gt;left == cur) {\n            pre-&gt;left = child;\n        } else {\n            pre-&gt;right = child;\n        }\n        // Освободить память\n        free(cur);\n    } else {\n        /* Число дочерних узлов = 2 */\n        // Получить следующий узел после cur в симметричном обходе\n        TreeNode *tmp = cur-&gt;right;\n        while (tmp-&gt;left != NULL) {\n            tmp = tmp-&gt;left;\n        }\n        int tmpVal = tmp-&gt;val;\n        // Рекурсивно удалить узел tmp\n        removeItem(bst, tmp-&gt;val);\n        // Перезаписать cur значением tmp\n        cur-&gt;val = tmpVal;\n    }\n}\n</code></pre> binary_search_tree.kt<pre><code>/* Удаление узла */\nfun remove(num: Int) {\n    // Если дерево пусто, сразу вернуть\n    if (root == null)\n        return\n    var cur = root\n    var pre: TreeNode? = null\n    // Искать в цикле и выйти после прохода за листовой узел\n    while (cur != null) {\n        // Найти узел для удаления и выйти из цикла\n        if (cur._val == num)\n            break\n        pre = cur\n        // Узел для удаления находится в правом поддереве cur\n        cur = if (cur._val &lt; num)\n            cur.right\n        // Узел для удаления находится в левом поддереве cur\n        else\n            cur.left\n    }\n    // Если узел для удаления отсутствует, сразу вернуть\n    if (cur == null)\n        return\n    // Число дочерних узлов = 0 или 1\n    if (cur.left == null || cur.right == null) {\n        // Когда число дочерних узлов = 0 / 1, child = null / этот дочерний узел\n        val child = if (cur.left != null)\n            cur.left\n        else\n            cur.right\n        // Удалить узел cur\n        if (cur != root) {\n            if (pre!!.left == cur)\n                pre.left = child\n            else\n                pre.right = child\n        } else {\n            // Если удаляемый узел является корнем, заново назначить корневой узел\n            root = child\n        }\n        // Число дочерних узлов = 2\n    } else {\n        // Получить следующий узел после cur в симметричном обходе\n        var tmp = cur.right\n        while (tmp!!.left != null) {\n            tmp = tmp.left\n        }\n        // Рекурсивно удалить узел tmp\n        remove(tmp._val)\n        // Перезаписать cur значением tmp\n        cur._val = tmp._val\n    }\n}\n</code></pre> binary_search_tree.rb<pre><code>### Удаление узла ###\ndef remove(num)\n  # Если дерево пусто, сразу вернуть\n  return if @root.nil?\n\n  # Искать в цикле и выйти после прохода за листовой узел\n  cur, pre = @root, nil\n  while !cur.nil?\n    # Найти узел для удаления и выйти из цикла\n    break if cur.val == num\n\n    pre = cur\n    # Узел для удаления находится в правом поддереве cur\n    if cur.val &lt; num\n      cur = cur.right\n    # Узел для удаления находится в левом поддереве cur\n    else\n      cur = cur.left\n    end\n  end\n  # Если узел для удаления отсутствует, сразу вернуть\n  return if cur.nil?\n\n  # Число дочерних узлов = 0 или 1\n  if cur.left.nil? || cur.right.nil?\n    # Когда число дочерних узлов = 0 / 1, child = null / этот дочерний узел\n    child = cur.left || cur.right\n    # Удалить узел cur\n    if cur != @root\n      if pre.left == cur\n        pre.left = child\n      else\n        pre.right = child\n      end\n    else\n      # Если удаляемый узел является корнем, заново назначить корневой узел\n      @root = child\n    end\n  # Число дочерних узлов = 2\n  else\n    # Получить следующий узел после cur в симметричном обходе\n    tmp = cur.right\n    while !tmp.left.nil?\n      tmp = tmp.left\n    end\n    # Рекурсивно удалить узел tmp\n    remove(tmp.val)\n    # Перезаписать cur значением tmp\n    cur.val = tmp.val\n  end\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 7. Деревья","7.4 &nbsp; Двоичное дерево поиска"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#4","level":3,"title":"4.   Упорядоченность симметричного обхода","text":"<p>Как показано на рисунке 7-22, симметричный обход двоичного дерева следует порядку \"лево \\(\\rightarrow\\) корень \\(\\rightarrow\\) право\", а двоичное дерево поиска удовлетворяет соотношению \"левый дочерний узел \\(&lt;\\) корень \\(&lt;\\) правый дочерний узел\".</p> <p>Это означает, что при симметричном обходе двоичного дерева поиска мы всегда сначала будем посещать следующий минимальный узел, и отсюда получается важное свойство: последовательность симметричного обхода двоичного дерева поиска является возрастающей.</p> <p>Используя это свойство возрастающей последовательности симметричного обхода, мы можем получить отсортированные данные из двоичного дерева поиска всего за \\(O(n)\\) времени, без дополнительной сортировки, что очень эффективно.</p> <p></p> <p> Рисунок 7-22   Последовательность симметричного обхода двоичного дерева поиска </p>","path":["Глава 7. Деревья","7.4 &nbsp; Двоичное дерево поиска"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#742","level":2,"title":"7.4.2   Эффективность двоичного дерева поиска","text":"<p>Для заданного набора данных можно рассмотреть хранение либо в массиве, либо в двоичном дереве поиска. Из таблицы ниже видно, что временная сложность операций двоичного дерева поиска имеет логарифмический порядок и обеспечивает стабильную высокую производительность. Только в сценариях с очень частыми вставками и редкими поисками и удалениями массив может быть эффективнее, чем двоичное дерево поиска.</p> <p> Таблица 7-2   Сравнение эффективности массива и дерева поиска </p> Неупорядоченный массив Двоичное дерево поиска Поиск элемента \\(O(n)\\) \\(O(\\log n)\\) Вставка элемента \\(O(1)\\) \\(O(\\log n)\\) Удаление элемента \\(O(n)\\) \\(O(\\log n)\\) <p>В идеальном случае двоичное дерево поиска является \"сбалансированным\", и тогда любой узел можно найти за \\(\\log n\\) итераций.</p> <p>Однако если в двоичное дерево поиска непрерывно вставлять и удалять узлы, оно может выродиться в связный список, как показано на рисунке 7-23. Тогда временная сложность различных операций тоже вырождается до \\(O(n)\\) .</p> <p></p> <p> Рисунок 7-23   Деградация двоичного дерева поиска </p>","path":["Глава 7. Деревья","7.4 &nbsp; Двоичное дерево поиска"],"tags":[]},{"location":"chapter_tree/binary_search_tree/#743","level":2,"title":"7.4.3   Типичные применения двоичного дерева поиска","text":"<ul> <li>Используется как многоуровневый индекс в системах, обеспечивая эффективный поиск, вставку и удаление.</li> <li>Служит базовой структурой данных для некоторых поисковых алгоритмов.</li> <li>Применяется для хранения потока данных в отсортированном состоянии.</li> </ul>","path":["Глава 7. Деревья","7.4 &nbsp; Двоичное дерево поиска"],"tags":[]},{"location":"chapter_tree/binary_tree/","level":1,"title":"7.1   Двоичное дерево","text":"<p>Двоичное дерево (binary tree) - это нелинейная структура данных, представляющая отношения между \"предками\" и \"потомками\" и отражающая логику \"разделяй и властвуй\". Подобно связному списку, базовой единицей двоичного дерева является узел; каждый узел содержит значение, ссылку на левого дочернего узла и ссылку на правого дочернего узла.</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby <pre><code>class TreeNode:\n    \"\"\"Класс узла двоичного дерева\"\"\"\n    def __init__(self, val: int):\n        self.val: int = val                # Значение узла\n        self.left: TreeNode | None = None  # Ссылка на левого дочернего узла\n        self.right: TreeNode | None = None # Ссылка на правого дочернего узла\n</code></pre> <pre><code>/* Структура узла двоичного дерева */\nstruct TreeNode {\n    int val;          // Значение узла\n    TreeNode *left;   // Указатель на левого дочернего узла\n    TreeNode *right;  // Указатель на правого дочернего узла\n    TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}\n};\n</code></pre> <pre><code>/* Класс узла двоичного дерева */\nclass TreeNode {\n    int val;         // Значение узла\n    TreeNode left;   // Ссылка на левого дочернего узла\n    TreeNode right;  // Ссылка на правого дочернего узла\n    TreeNode(int x) { val = x; }\n}\n</code></pre> <pre><code>/* Класс узла двоичного дерева */\nclass TreeNode(int? x) {\n    public int? val = x;    // Значение узла\n    public TreeNode? left;  // Ссылка на левого дочернего узла\n    public TreeNode? right; // Ссылка на правого дочернего узла\n}\n</code></pre> <pre><code>/* Структура узла двоичного дерева */\ntype TreeNode struct {\n    Val   int\n    Left  *TreeNode\n    Right *TreeNode\n}\n/* Конструктор */\nfunc NewTreeNode(v int) *TreeNode {\n    return &amp;TreeNode{\n        Left:  nil, // Указатель на левого дочернего узла\n        Right: nil, // Указатель на правого дочернего узла\n        Val:   v,   // Значение узла\n    }\n}\n</code></pre> <pre><code>/* Класс узла двоичного дерева */\nclass TreeNode {\n    var val: Int // Значение узла\n    var left: TreeNode? // Ссылка на левого дочернего узла\n    var right: TreeNode? // Ссылка на правого дочернего узла\n\n    init(x: Int) {\n        val = x\n    }\n}\n</code></pre> <pre><code>/* Класс узла двоичного дерева */\nclass TreeNode {\n    val; // Значение узла\n    left; // Указатель на левого дочернего узла\n    right; // Указатель на правого дочернего узла\n    constructor(val, left, right) {\n        this.val = val === undefined ? 0 : val;\n        this.left = left === undefined ? null : left;\n        this.right = right === undefined ? null : right;\n    }\n}\n</code></pre> <pre><code>/* Класс узла двоичного дерева */\nclass TreeNode {\n    val: number;\n    left: TreeNode | null;\n    right: TreeNode | null;\n\n    constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {\n        this.val = val === undefined ? 0 : val; // Значение узла\n        this.left = left === undefined ? null : left; // Ссылка на левого дочернего узла\n        this.right = right === undefined ? null : right; // Ссылка на правого дочернего узла\n    }\n}\n</code></pre> <pre><code>/* Класс узла двоичного дерева */\nclass TreeNode {\n  int val;         // Значение узла\n  TreeNode? left;  // Ссылка на левого дочернего узла\n  TreeNode? right; // Ссылка на правого дочернего узла\n  TreeNode(this.val, [this.left, this.right]);\n}\n</code></pre> <pre><code>use std::rc::Rc;\nuse std::cell::RefCell;\n\n/* Структура узла двоичного дерева */\nstruct TreeNode {\n    val: i32,                               // Значение узла\n    left: Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,    // Ссылка на левого дочернего узла\n    right: Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,   // Ссылка на правого дочернего узла\n}\n\nimpl TreeNode {\n    /* Конструктор */\n    fn new(val: i32) -&gt; Rc&lt;RefCell&lt;Self&gt;&gt; {\n        Rc::new(RefCell::new(Self {\n            val,\n            left: None,\n            right: None\n        }))\n    }\n}\n</code></pre> <pre><code>/* Структура узла двоичного дерева */\ntypedef struct TreeNode {\n    int val;                // Значение узла\n    int height;             // Высота узла\n    struct TreeNode *left;  // Указатель на левого дочернего узла\n    struct TreeNode *right; // Указатель на правого дочернего узла\n} TreeNode;\n\n/* Конструктор */\nTreeNode *newTreeNode(int val) {\n    TreeNode *node;\n\n    node = (TreeNode *)malloc(sizeof(TreeNode));\n    node-&gt;val = val;\n    node-&gt;height = 0;\n    node-&gt;left = NULL;\n    node-&gt;right = NULL;\n    return node;\n}\n</code></pre> <pre><code>/* Класс узла двоичного дерева */\nclass TreeNode(val _val: Int) {  // Значение узла\n    val left: TreeNode? = null   // Ссылка на левого дочернего узла\n    val right: TreeNode? = null  // Ссылка на правого дочернего узла\n}\n</code></pre> <pre><code>### Класс узла двоичного дерева ###\nclass TreeNode\n  attr_accessor :val    # Значение узла\n  attr_accessor :left   # Ссылка на левого дочернего узла\n  attr_accessor :right  # Ссылка на правого дочернего узла\n\n  def initialize(val)\n    @val = val\n  end\nend\n</code></pre> <p>Каждый узел имеет две ссылки (указателя), которые соответственно указывают на левого дочернего узла (left-child node) и правого дочернего узла (right-child node); данный узел называется родительским узлом (parent node) для этих двух дочерних узлов. Если задан некоторый узел двоичного дерева, то дерево, образованное его левым дочерним узлом и всеми узлами ниже него, называется левым поддеревом (left subtree) этого узла; аналогично определяется правое поддерево (right subtree).</p> <p>Узлы, не имеющие дочерних узлов, называют листьями, а все остальные узлы содержат дочерние узлы и непустые поддеревья. Как показано на рисунке 7-1, если рассматривать \"узел 2\" как родительский, то его левым и правым дочерними узлами будут \"узел 4\" и \"узел 5\"; левое поддерево - это \"узел 4 и дерево ниже него\", а правое поддерево - это \"узел 5 и дерево ниже него\".</p> <p></p> <p> Рисунок 7-1   Родительский узел, дочерние узлы и поддеревья </p>","path":["Глава 7. Деревья","7.1 &nbsp; Двоичное дерево"],"tags":[]},{"location":"chapter_tree/binary_tree/#711","level":2,"title":"7.1.1   Распространенные термины двоичного дерева","text":"<p>Распространенные термины двоичного дерева показаны на рисунке 7-2.</p> <ul> <li>Корневой узел (root node): узел, расположенный на верхнем уровне двоичного дерева и не имеющий родительского узла.</li> <li>Листовой узел (leaf node): узел без дочерних узлов; оба его указателя направлены на <code>None</code> .</li> <li>Ребро (edge): отрезок, соединяющий два узла, то есть ссылка (указатель) между узлами.</li> <li>Уровень (level) узла: увеличивается сверху вниз; уровень корневого узла равен 1 .</li> <li>Степень (degree) узла: число дочерних узлов данного узла. В двоичном дереве возможны степени 0, 1, 2 .</li> <li>Высота (height) двоичного дерева: число ребер от корневого узла до самого удаленного листового узла.</li> <li>Глубина (depth) узла: число ребер от корневого узла до данного узла.</li> <li>Высота (height) узла: число ребер от самого удаленного листового узла до данного узла.</li> </ul> <p></p> <p> Рисунок 7-2   Распространенные термины двоичного дерева </p> <p>Tip</p> <p>Обычно под \"высотой\" и \"глубиной\" понимают \"число пройденных ребер\", но в некоторых задачах или учебниках их могут определять как \"число пройденных узлов\". В таком случае и высоту, и глубину нужно увеличить на 1 .</p>","path":["Глава 7. Деревья","7.1 &nbsp; Двоичное дерево"],"tags":[]},{"location":"chapter_tree/binary_tree/#712","level":2,"title":"7.1.2   Базовые операции двоичного дерева","text":"","path":["Глава 7. Деревья","7.1 &nbsp; Двоичное дерево"],"tags":[]},{"location":"chapter_tree/binary_tree/#1","level":3,"title":"1.   Инициализация двоичного дерева","text":"<p>Как и в связном списке, сначала инициализируются узлы, а затем между ними строятся ссылки (указатели).</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_tree.py<pre><code># Инициализация двоичного дерева\n# Инициализация узлов\nn1 = TreeNode(val=1)\nn2 = TreeNode(val=2)\nn3 = TreeNode(val=3)\nn4 = TreeNode(val=4)\nn5 = TreeNode(val=5)\n# Построение ссылок (указателей) между узлами\nn1.left = n2\nn1.right = n3\nn2.left = n4\nn2.right = n5\n</code></pre> binary_tree.cpp<pre><code>/* Инициализация двоичного дерева */\n// Инициализация узлов\nTreeNode* n1 = new TreeNode(1);\nTreeNode* n2 = new TreeNode(2);\nTreeNode* n3 = new TreeNode(3);\nTreeNode* n4 = new TreeNode(4);\nTreeNode* n5 = new TreeNode(5);\n// Построение ссылок (указателей) между узлами\nn1-&gt;left = n2;\nn1-&gt;right = n3;\nn2-&gt;left = n4;\nn2-&gt;right = n5;\n</code></pre> binary_tree.java<pre><code>// Инициализация узлов\nTreeNode n1 = new TreeNode(1);\nTreeNode n2 = new TreeNode(2);\nTreeNode n3 = new TreeNode(3);\nTreeNode n4 = new TreeNode(4);\nTreeNode n5 = new TreeNode(5);\n// Построение ссылок (указателей) между узлами\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.cs<pre><code>/* Инициализация двоичного дерева */\n// Инициализация узлов\nTreeNode n1 = new(1);\nTreeNode n2 = new(2);\nTreeNode n3 = new(3);\nTreeNode n4 = new(4);\nTreeNode n5 = new(5);\n// Построение ссылок (указателей) между узлами\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.go<pre><code>/* Инициализация двоичного дерева */\n// Инициализация узлов\nn1 := NewTreeNode(1)\nn2 := NewTreeNode(2)\nn3 := NewTreeNode(3)\nn4 := NewTreeNode(4)\nn5 := NewTreeNode(5)\n// Построение ссылок (указателей) между узлами\nn1.Left = n2\nn1.Right = n3\nn2.Left = n4\nn2.Right = n5\n</code></pre> binary_tree.swift<pre><code>// Инициализация узлов\nlet n1 = TreeNode(x: 1)\nlet n2 = TreeNode(x: 2)\nlet n3 = TreeNode(x: 3)\nlet n4 = TreeNode(x: 4)\nlet n5 = TreeNode(x: 5)\n// Построение ссылок (указателей) между узлами\nn1.left = n2\nn1.right = n3\nn2.left = n4\nn2.right = n5\n</code></pre> binary_tree.js<pre><code>/* Инициализация двоичного дерева */\n// Инициализация узлов\nlet n1 = new TreeNode(1),\n    n2 = new TreeNode(2),\n    n3 = new TreeNode(3),\n    n4 = new TreeNode(4),\n    n5 = new TreeNode(5);\n// Построение ссылок (указателей) между узлами\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.ts<pre><code>/* Инициализация двоичного дерева */\n// Инициализация узлов\nlet n1 = new TreeNode(1),\n    n2 = new TreeNode(2),\n    n3 = new TreeNode(3),\n    n4 = new TreeNode(4),\n    n5 = new TreeNode(5);\n// Построение ссылок (указателей) между узлами\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.dart<pre><code>/* Инициализация двоичного дерева */\n// Инициализация узлов\nTreeNode n1 = new TreeNode(1);\nTreeNode n2 = new TreeNode(2);\nTreeNode n3 = new TreeNode(3);\nTreeNode n4 = new TreeNode(4);\nTreeNode n5 = new TreeNode(5);\n// Построение ссылок (указателей) между узлами\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.rs<pre><code>// Инициализация узлов\nlet n1 = TreeNode::new(1);\nlet n2 = TreeNode::new(2);\nlet n3 = TreeNode::new(3);\nlet n4 = TreeNode::new(4);\nlet n5 = TreeNode::new(5);\n// Построение ссылок (указателей) между узлами\nn1.borrow_mut().left = Some(n2.clone());\nn1.borrow_mut().right = Some(n3);\nn2.borrow_mut().left = Some(n4);\nn2.borrow_mut().right = Some(n5);\n</code></pre> binary_tree.c<pre><code>/* Инициализация двоичного дерева */\n// Инициализация узлов\nTreeNode *n1 = newTreeNode(1);\nTreeNode *n2 = newTreeNode(2);\nTreeNode *n3 = newTreeNode(3);\nTreeNode *n4 = newTreeNode(4);\nTreeNode *n5 = newTreeNode(5);\n// Построение ссылок (указателей) между узлами\nn1-&gt;left = n2;\nn1-&gt;right = n3;\nn2-&gt;left = n4;\nn2-&gt;right = n5;\n</code></pre> binary_tree.kt<pre><code>// Инициализация узлов\nval n1 = TreeNode(1)\nval n2 = TreeNode(2)\nval n3 = TreeNode(3)\nval n4 = TreeNode(4)\nval n5 = TreeNode(5)\n// Построение ссылок (указателей) между узлами\nn1.left = n2\nn1.right = n3\nn2.left = n4\nn2.right = n5\n</code></pre> binary_tree.rb<pre><code># Инициализация двоичного дерева\n# Инициализация узлов\nn1 = TreeNode.new(1)\nn2 = TreeNode.new(2)\nn3 = TreeNode.new(3)\nn4 = TreeNode.new(4)\nn5 = TreeNode.new(5)\n# Построение ссылок (указателей) между узлами\nn1.left = n2\nn1.right = n3\nn2.left = n4\nn2.right = n5\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%D0%9A%D0%BB%D0%B0%D1%81%D1%81%20%D1%83%D0%B7%D0%BB%D0%B0%20%D0%B4%D0%B2%D0%BE%D0%B8%D1%87%D0%BD%D0%BE%D0%B3%D0%BE%20%D0%B4%D0%B5%D1%80%D0%B5%D0%B2%D0%B0%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%D0%97%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%83%D0%B7%D0%BB%D0%B0%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%D0%A1%D1%81%D1%8B%D0%BB%D0%BA%D0%B0%20%D0%BD%D0%B0%20%D0%BB%D0%B5%D0%B2%D1%8B%D0%B9%20%D0%B4%D0%BE%D1%87%D0%B5%D1%80%D0%BD%D0%B8%D0%B9%20%D1%83%D0%B7%D0%B5%D0%BB%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%23%20%D0%A1%D1%81%D1%8B%D0%BB%D0%BA%D0%B0%20%D0%BD%D0%B0%20%D0%BF%D1%80%D0%B0%D0%B2%D1%8B%D0%B9%20%D0%B4%D0%BE%D1%87%D0%B5%D1%80%D0%BD%D0%B8%D0%B9%20%D1%83%D0%B7%D0%B5%D0%BB%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D0%B4%D0%B2%D0%BE%D0%B8%D1%87%D0%BD%D0%BE%D0%B5%20%D0%B4%D0%B5%D1%80%D0%B5%D0%B2%D0%BE%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%83%D0%B7%D0%B5%D0%BB%0A%20%20%20%20n1%20%3D%20TreeNode%28val%3D1%29%0A%20%20%20%20n2%20%3D%20TreeNode%28val%3D2%29%0A%20%20%20%20n3%20%3D%20TreeNode%28val%3D3%29%0A%20%20%20%20n4%20%3D%20TreeNode%28val%3D4%29%0A%20%20%20%20n5%20%3D%20TreeNode%28val%3D5%29%0A%20%20%20%20%23%20%D0%9F%D0%BE%D1%81%D1%82%D1%80%D0%BE%D0%B8%D1%82%D1%8C%20%D1%81%D1%81%D1%8B%D0%BB%D0%BA%D0%B8%20%D0%BC%D0%B5%D0%B6%D0%B4%D1%83%20%D1%83%D0%B7%D0%BB%D0%B0%D0%BC%D0%B8%20%28%D1%83%D0%BA%D0%B0%D0%B7%D0%B0%D1%82%D0%B5%D0%BB%D0%B8%29%0A%20%20%20%20n1.left%20%3D%20n2%0A%20%20%20%20n1.right%20%3D%20n3%0A%20%20%20%20n2.left%20%3D%20n4%0A%20%20%20%20n2.right%20%3D%20n5&amp;cumulative=false&amp;curInstr=3&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p>","path":["Глава 7. Деревья","7.1 &nbsp; Двоичное дерево"],"tags":[]},{"location":"chapter_tree/binary_tree/#2","level":3,"title":"2.   Вставка и удаление узлов","text":"<p>Как и в связном списке, вставка и удаление узлов в двоичном дереве могут выполняться через изменение указателей. На рисунке 7-3 приведен пример.</p> <p></p> <p> Рисунок 7-3   Вставка и удаление узлов в двоичном дереве </p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_tree.py<pre><code># Вставка и удаление узлов\np = TreeNode(0)\n# Вставить узел P между n1 -&gt; n2\nn1.left = p\np.left = n2\n# Удалить узел P\nn1.left = n2\n</code></pre> binary_tree.cpp<pre><code>/* Вставка и удаление узлов */\nTreeNode* P = new TreeNode(0);\n// Вставить узел P между n1 -&gt; n2\nn1-&gt;left = P;\nP-&gt;left = n2;\n// Удалить узел P\nn1-&gt;left = n2;\n// Освободить память\ndelete P;\n</code></pre> binary_tree.java<pre><code>TreeNode P = new TreeNode(0);\n// Вставить узел P между n1 -&gt; n2\nn1.left = P;\nP.left = n2;\n// Удалить узел P\nn1.left = n2;\n</code></pre> binary_tree.cs<pre><code>/* Вставка и удаление узлов */\nTreeNode P = new(0);\n// Вставить узел P между n1 -&gt; n2\nn1.left = P;\nP.left = n2;\n// Удалить узел P\nn1.left = n2;\n</code></pre> binary_tree.go<pre><code>/* Вставка и удаление узлов */\n// Вставить узел P между n1 -&gt; n2\np := NewTreeNode(0)\nn1.Left = p\np.Left = n2\n// Удалить узел P\nn1.Left = n2\n</code></pre> binary_tree.swift<pre><code>let P = TreeNode(x: 0)\n// Вставить узел P между n1 -&gt; n2\nn1.left = P\nP.left = n2\n// Удалить узел P\nn1.left = n2\n</code></pre> binary_tree.js<pre><code>/* Вставка и удаление узлов */\nlet P = new TreeNode(0);\n// Вставить узел P между n1 -&gt; n2\nn1.left = P;\nP.left = n2;\n// Удалить узел P\nn1.left = n2;\n</code></pre> binary_tree.ts<pre><code>/* Вставка и удаление узлов */\nconst P = new TreeNode(0);\n// Вставить узел P между n1 -&gt; n2\nn1.left = P;\nP.left = n2;\n// Удалить узел P\nn1.left = n2;\n</code></pre> binary_tree.dart<pre><code>/* Вставка и удаление узлов */\nTreeNode P = new TreeNode(0);\n// Вставить узел P между n1 -&gt; n2\nn1.left = P;\nP.left = n2;\n// Удалить узел P\nn1.left = n2;\n</code></pre> binary_tree.rs<pre><code>let p = TreeNode::new(0);\n// Вставить узел P между n1 -&gt; n2\nn1.borrow_mut().left = Some(p.clone());\np.borrow_mut().left = Some(n2.clone());\n// Удалить узел p\nn1.borrow_mut().left = Some(n2);\n</code></pre> binary_tree.c<pre><code>/* Вставка и удаление узлов */\nTreeNode *P = newTreeNode(0);\n// Вставить узел P между n1 -&gt; n2\nn1-&gt;left = P;\nP-&gt;left = n2;\n// Удалить узел P\nn1-&gt;left = n2;\n// Освободить память\nfree(P);\n</code></pre> binary_tree.kt<pre><code>val P = TreeNode(0)\n// Вставить узел P между n1 -&gt; n2\nn1.left = P\nP.left = n2\n// Удалить узел P\nn1.left = n2\n</code></pre> binary_tree.rb<pre><code># Вставка и удаление узлов\n_p = TreeNode.new(0)\n# Вставить узел _p между n1 -&gt; n2\nn1.left = _p\n_p.left = n2\n# Удалить узел\nn1.left = n2\n</code></pre> Визуализация выполнения <p>https://pythontutor.com/render.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%D0%9A%D0%BB%D0%B0%D1%81%D1%81%20%D1%83%D0%B7%D0%BB%D0%B0%20%D0%B4%D0%B2%D0%BE%D0%B8%D1%87%D0%BD%D0%BE%D0%B3%D0%BE%20%D0%B4%D0%B5%D1%80%D0%B5%D0%B2%D0%B0%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%D0%97%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%83%D0%B7%D0%BB%D0%B0%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%D0%A1%D1%81%D1%8B%D0%BB%D0%BA%D0%B0%20%D0%BD%D0%B0%20%D0%BB%D0%B5%D0%B2%D1%8B%D0%B9%20%D0%B4%D0%BE%D1%87%D0%B5%D1%80%D0%BD%D0%B8%D0%B9%20%D1%83%D0%B7%D0%B5%D0%BB%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%23%20%D0%A1%D1%81%D1%8B%D0%BB%D0%BA%D0%B0%20%D0%BD%D0%B0%20%D0%BF%D1%80%D0%B0%D0%B2%D1%8B%D0%B9%20%D0%B4%D0%BE%D1%87%D0%B5%D1%80%D0%BD%D0%B8%D0%B9%20%D1%83%D0%B7%D0%B5%D0%BB%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D0%B4%D0%B2%D0%BE%D0%B8%D1%87%D0%BD%D0%BE%D0%B5%20%D0%B4%D0%B5%D1%80%D0%B5%D0%B2%D0%BE%0A%20%20%20%20%23%20%D0%98%D0%BD%D0%B8%D1%86%D0%B8%D0%B0%D0%BB%D0%B8%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D1%82%D1%8C%20%D1%83%D0%B7%D0%B5%D0%BB%0A%20%20%20%20n1%20%3D%20TreeNode%28val%3D1%29%0A%20%20%20%20n2%20%3D%20TreeNode%28val%3D2%29%0A%20%20%20%20n3%20%3D%20TreeNode%28val%3D3%29%0A%20%20%20%20n4%20%3D%20TreeNode%28val%3D4%29%0A%20%20%20%20n5%20%3D%20TreeNode%28val%3D5%29%0A%20%20%20%20%23%20%D0%9F%D0%BE%D1%81%D1%82%D1%80%D0%BE%D0%B8%D1%82%D1%8C%20%D1%81%D1%81%D1%8B%D0%BB%D0%BA%D0%B8%20%D0%BC%D0%B5%D0%B6%D0%B4%D1%83%20%D1%83%D0%B7%D0%BB%D0%B0%D0%BC%D0%B8%20%28%D1%83%D0%BA%D0%B0%D0%B7%D0%B0%D1%82%D0%B5%D0%BB%D0%B8%29%0A%20%20%20%20n1.left%20%3D%20n2%0A%20%20%20%20n1.right%20%3D%20n3%0A%20%20%20%20n2.left%20%3D%20n4%0A%20%20%20%20n2.right%20%3D%20n5%0A%0A%20%20%20%20%23%20%D0%92%D1%81%D1%82%D0%B0%D0%B2%D0%BA%D0%B0%20%D0%B8%20%D1%83%D0%B4%D0%B0%D0%BB%D0%B5%D0%BD%D0%B8%D0%B5%20%D1%83%D0%B7%D0%BB%D0%BE%D0%B2%0A%20%20%20%20p%20%3D%20TreeNode%280%29%0A%20%20%20%20%23%20%D0%92%D1%81%D1%82%D0%B0%D0%B2%D0%B8%D1%82%D1%8C%20%D1%83%D0%B7%D0%B5%D0%BB%20P%20%D0%BC%D0%B5%D0%B6%D0%B4%D1%83%20n1%20-%3E%20n2%0A%20%20%20%20n1.left%20%3D%20p%0A%20%20%20%20p.left%20%3D%20n2%0A%20%20%20%20%23%20%D0%A3%D0%B4%D0%B0%D0%BB%D0%B8%D1%82%D1%8C%20%D1%83%D0%B7%D0%B5%D0%BB%20P%0A%20%20%20%20n1.left%20%3D%20n2&amp;cumulative=false&amp;curInstr=37&amp;heapPrimitives=nevernest&amp;mode=display&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false</p> <p>Tip</p> <p>Стоит помнить, что вставка узла может изменить исходную логическую структуру двоичного дерева, а удаление узла обычно означает удаление этого узла вместе со всеми его поддеревьями. Поэтому в двоичном дереве операции вставки и удаления обычно являются частью более крупного набора операций, который и реализует осмысленное действие.</p>","path":["Глава 7. Деревья","7.1 &nbsp; Двоичное дерево"],"tags":[]},{"location":"chapter_tree/binary_tree/#713","level":2,"title":"7.1.3   Распространенные типы двоичных деревьев","text":"","path":["Глава 7. Деревья","7.1 &nbsp; Двоичное дерево"],"tags":[]},{"location":"chapter_tree/binary_tree/#1_1","level":3,"title":"1.   Идеальное двоичное дерево","text":"<p>Как показано на рисунке 7-4, идеальное двоичное дерево (perfect binary tree) полностью заполнено на всех уровнях. В идеальном двоичном дереве степень листовых узлов равна \\(0\\) , а у всех остальных узлов степень равна \\(2\\) ; если высота дерева равна \\(h\\) , то общее число узлов равно \\(2^{h+1} - 1\\) , что образует стандартную экспоненциальную зависимость и отражает часто встречающееся в природе явление клеточного деления.</p> <p>Tip</p> <p>В китайскоязычном сообществе идеальное двоичное дерево часто называют полностью заполненным двоичным деревом.</p> <p></p> <p> Рисунок 7-4   Идеальное двоичное дерево </p>","path":["Глава 7. Деревья","7.1 &nbsp; Двоичное дерево"],"tags":[]},{"location":"chapter_tree/binary_tree/#2_1","level":3,"title":"2.   Полное двоичное дерево","text":"<p>Как показано на рисунке 7-5, полное двоичное дерево (complete binary tree) допускает неполное заполнение только на самом нижнем уровне, причем узлы этого уровня должны непрерывно заполняться слева направо. Стоит отметить, что идеальное двоичное дерево тоже является полным двоичным деревом.</p> <p></p> <p> Рисунок 7-5   Полное двоичное дерево </p>","path":["Глава 7. Деревья","7.1 &nbsp; Двоичное дерево"],"tags":[]},{"location":"chapter_tree/binary_tree/#3","level":3,"title":"3.   Строгое двоичное дерево","text":"<p>Как показано на рисунке 7-6, строгое двоичное дерево (full binary tree) имеет у всех нелистовых узлов ровно двух дочерних узлов.</p> <p></p> <p> Рисунок 7-6   Строгое двоичное дерево </p>","path":["Глава 7. Деревья","7.1 &nbsp; Двоичное дерево"],"tags":[]},{"location":"chapter_tree/binary_tree/#4","level":3,"title":"4.   Сбалансированное двоичное дерево","text":"<p>Как показано на рисунке 7-7, в сбалансированном двоичном дереве (balanced binary tree) для любого узла абсолютное значение разности высот левого и правого поддеревьев не превышает 1 .</p> <p></p> <p> Рисунок 7-7   Сбалансированное двоичное дерево </p>","path":["Глава 7. Деревья","7.1 &nbsp; Двоичное дерево"],"tags":[]},{"location":"chapter_tree/binary_tree/#714","level":2,"title":"7.1.4   Вырождение двоичного дерева","text":"<p>На рисунке 7-8 показаны идеальная структура двоичного дерева и вырожденная структура. Когда каждый уровень двоичного дерева полностью заполнен узлами, мы получаем \"идеальное двоичное дерево\"; когда же все узлы смещаются к одной стороне, двоичное дерево вырождается в \"связный список\".</p> <ul> <li>Идеальное двоичное дерево соответствует лучшему случаю и позволяет в полной мере раскрыть преимущества подхода \"разделяй и властвуй\".</li> <li>Связный список представляет противоположную крайность: все операции становятся линейными, а временная сложность деградирует до \\(O(n)\\) .</li> </ul> <p></p> <p> Рисунок 7-8   Лучший и худший случаи структуры двоичного дерева </p> <p>Как показано в таблице 7-1, в лучшем и худшем случаях число листовых узлов, общее число узлов, высота и другие характеристики двоичного дерева достигают максимума или минимума.</p> <p> Таблица 7-1   Лучший и худший случаи структуры двоичного дерева </p> Идеальное двоичное дерево Связный список Число узлов на уровне \\(i\\) \\(2^{i-1}\\) \\(1\\) Число листьев у дерева высоты \\(h\\) \\(2^h\\) \\(1\\) Общее число узлов у дерева высоты \\(h\\) \\(2^{h+1} - 1\\) \\(h + 1\\) Высота дерева с \\(n\\) узлами \\(\\log_2 (n+1) - 1\\) \\(n - 1\\)","path":["Глава 7. Деревья","7.1 &nbsp; Двоичное дерево"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/","level":1,"title":"7.2   Обход двоичного дерева","text":"<p>С точки зрения физической структуры дерево представляет собой разновидность структуры данных на основе связей, поэтому его обход выполняется через последовательный доступ к узлам по указателям. Однако дерево является нелинейной структурой данных, а значит, его обход сложнее, чем обход связного списка, и для него требуется использовать поисковые алгоритмы.</p> <p>К распространенным способам обхода двоичного дерева относятся обход по уровням, прямой обход, симметричный обход и обратный обход.</p>","path":["Глава 7. Деревья","7.2 &nbsp; Обход двоичного дерева"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/#721","level":2,"title":"7.2.1   Обход по уровням","text":"<p>Как показано на рисунке 7-9, обход по уровням (level-order traversal) проходит двоичное дерево сверху вниз по уровням и на каждом уровне посещает узлы слева направо.</p> <p>По своей сути обход по уровням относится к обходу в ширину (breadth-first traversal), также называемому поиском в ширину (breadth-first search, BFS); он отражает идею \"расширяться от центра к периферии слой за слоем\".</p> <p></p> <p> Рисунок 7-9   Обход двоичного дерева по уровням </p>","path":["Глава 7. Деревья","7.2 &nbsp; Обход двоичного дерева"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/#1","level":3,"title":"1.   Код реализации","text":"<p>Обход в ширину обычно реализуется с помощью \"очереди\". Очередь подчиняется правилу \"первым пришел - первым вышел\", а обход в ширину подчиняется правилу \"продвигаться по уровням\", поэтому стоящая за ними идея согласована. Код реализации приведен ниже:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_tree_bfs.py<pre><code>def level_order(root: TreeNode | None) -&gt; list[int]:\n    \"\"\"Обход в ширину\"\"\"\n    # Инициализировать очередь и добавить корневой узел\n    queue: deque[TreeNode] = deque()\n    queue.append(root)\n    # Инициализировать список для хранения последовательности обхода\n    res = []\n    while queue:\n        node: TreeNode = queue.popleft()  # Извлечение из очереди\n        res.append(node.val)  # Сохранить значение узла\n        if node.left is not None:\n            queue.append(node.left)  # Поместить левый дочерний узел в очередь\n        if node.right is not None:\n            queue.append(node.right)  # Поместить правый дочерний узел в очередь\n    return res\n</code></pre> binary_tree_bfs.cpp<pre><code>/* Обход в ширину */\nvector&lt;int&gt; levelOrder(TreeNode *root) {\n    // Инициализировать очередь и добавить корневой узел\n    queue&lt;TreeNode *&gt; queue;\n    queue.push(root);\n    // Инициализировать список для хранения последовательности обхода\n    vector&lt;int&gt; vec;\n    while (!queue.empty()) {\n        TreeNode *node = queue.front();\n        queue.pop();              // Извлечение из очереди\n        vec.push_back(node-&gt;val); // Сохранить значение узла\n        if (node-&gt;left != nullptr)\n            queue.push(node-&gt;left); // Поместить левый дочерний узел в очередь\n        if (node-&gt;right != nullptr)\n            queue.push(node-&gt;right); // Поместить правый дочерний узел в очередь\n    }\n    return vec;\n}\n</code></pre> binary_tree_bfs.java<pre><code>/* Обход в ширину */\nList&lt;Integer&gt; levelOrder(TreeNode root) {\n    // Инициализировать очередь и добавить корневой узел\n    Queue&lt;TreeNode&gt; queue = new LinkedList&lt;&gt;();\n    queue.add(root);\n    // Инициализировать список для хранения последовательности обхода\n    List&lt;Integer&gt; list = new ArrayList&lt;&gt;();\n    while (!queue.isEmpty()) {\n        TreeNode node = queue.poll(); // Извлечение из очереди\n        list.add(node.val);           // Сохранить значение узла\n        if (node.left != null)\n            queue.offer(node.left);   // Поместить левый дочерний узел в очередь\n        if (node.right != null)\n            queue.offer(node.right);  // Поместить правый дочерний узел в очередь\n    }\n    return list;\n}\n</code></pre> binary_tree_bfs.cs<pre><code>/* Обход в ширину */\nList&lt;int&gt; LevelOrder(TreeNode root) {\n    // Инициализировать очередь и добавить корневой узел\n    Queue&lt;TreeNode&gt; queue = new();\n    queue.Enqueue(root);\n    // Инициализировать список для хранения последовательности обхода\n    List&lt;int&gt; list = [];\n    while (queue.Count != 0) {\n        TreeNode node = queue.Dequeue(); // Извлечение из очереди\n        list.Add(node.val!.Value);       // Сохранить значение узла\n        if (node.left != null)\n            queue.Enqueue(node.left);    // Поместить левый дочерний узел в очередь\n        if (node.right != null)\n            queue.Enqueue(node.right);   // Поместить правый дочерний узел в очередь\n    }\n    return list;\n}\n</code></pre> binary_tree_bfs.go<pre><code>/* Обход в ширину */\nfunc levelOrder(root *TreeNode) []any {\n    // Инициализировать очередь и добавить корневой узел\n    queue := list.New()\n    queue.PushBack(root)\n    // Инициализировать срез для хранения последовательности обхода\n    nums := make([]any, 0)\n    for queue.Len() &gt; 0 {\n        // Извлечение из очереди\n        node := queue.Remove(queue.Front()).(*TreeNode)\n        // Сохранить значение узла\n        nums = append(nums, node.Val)\n        if node.Left != nil {\n            // Поместить левый дочерний узел в очередь\n            queue.PushBack(node.Left)\n        }\n        if node.Right != nil {\n            // Поместить правый дочерний узел в очередь\n            queue.PushBack(node.Right)\n        }\n    }\n    return nums\n}\n</code></pre> binary_tree_bfs.swift<pre><code>/* Обход в ширину */\nfunc levelOrder(root: TreeNode) -&gt; [Int] {\n    // Инициализировать очередь и добавить корневой узел\n    var queue: [TreeNode] = [root]\n    // Инициализировать список для хранения последовательности обхода\n    var list: [Int] = []\n    while !queue.isEmpty {\n        let node = queue.removeFirst() // Извлечение из очереди\n        list.append(node.val) // Сохранить значение узла\n        if let left = node.left {\n            queue.append(left) // Поместить левый дочерний узел в очередь\n        }\n        if let right = node.right {\n            queue.append(right) // Поместить правый дочерний узел в очередь\n        }\n    }\n    return list\n}\n</code></pre> binary_tree_bfs.js<pre><code>/* Обход в ширину */\nfunction levelOrder(root) {\n    // Инициализировать очередь и добавить корневой узел\n    const queue = [root];\n    // Инициализировать список для хранения последовательности обхода\n    const list = [];\n    while (queue.length) {\n        let node = queue.shift(); // Извлечение из очереди\n        list.push(node.val); // Сохранить значение узла\n        if (node.left) queue.push(node.left); // Поместить левый дочерний узел в очередь\n        if (node.right) queue.push(node.right); // Поместить правый дочерний узел в очередь\n    }\n    return list;\n}\n</code></pre> binary_tree_bfs.ts<pre><code>/* Обход в ширину */\nfunction levelOrder(root: TreeNode | null): number[] {\n    // Инициализировать очередь и добавить корневой узел\n    const queue = [root];\n    // Инициализировать список для хранения последовательности обхода\n    const list: number[] = [];\n    while (queue.length) {\n        let node = queue.shift() as TreeNode; // Извлечение из очереди\n        list.push(node.val); // Сохранить значение узла\n        if (node.left) {\n            queue.push(node.left); // Поместить левый дочерний узел в очередь\n        }\n        if (node.right) {\n            queue.push(node.right); // Поместить правый дочерний узел в очередь\n        }\n    }\n    return list;\n}\n</code></pre> binary_tree_bfs.dart<pre><code>/* Обход в ширину */\nList&lt;int&gt; levelOrder(TreeNode? root) {\n  // Инициализировать очередь и добавить корневой узел\n  Queue&lt;TreeNode?&gt; queue = Queue();\n  queue.add(root);\n  // Инициализировать список для хранения последовательности обхода\n  List&lt;int&gt; res = [];\n  while (queue.isNotEmpty) {\n    TreeNode? node = queue.removeFirst(); // Извлечение из очереди\n    res.add(node!.val); // Сохранить значение узла\n    if (node.left != null) queue.add(node.left); // Поместить левый дочерний узел в очередь\n    if (node.right != null) queue.add(node.right); // Поместить правый дочерний узел в очередь\n  }\n  return res;\n}\n</code></pre> binary_tree_bfs.rs<pre><code>/* Обход в ширину */\nfn level_order(root: &amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;) -&gt; Vec&lt;i32&gt; {\n    // Инициализировать очередь и добавить корневой узел\n    let mut que = VecDeque::new();\n    que.push_back(root.clone());\n    // Инициализировать список для хранения последовательности обхода\n    let mut vec = Vec::new();\n\n    while let Some(node) = que.pop_front() {\n        // Извлечение из очереди\n        vec.push(node.borrow().val); // Сохранить значение узла\n        if let Some(left) = node.borrow().left.as_ref() {\n            que.push_back(left.clone()); // Поместить левый дочерний узел в очередь\n        }\n        if let Some(right) = node.borrow().right.as_ref() {\n            que.push_back(right.clone()); // Поместить правый дочерний узел в очередь\n        };\n    }\n    vec\n}\n</code></pre> binary_tree_bfs.c<pre><code>/* Обход в ширину */\nint *levelOrder(TreeNode *root, int *size) {\n    /* Вспомогательная очередь */\n    int front, rear;\n    int index, *arr;\n    TreeNode *node;\n    TreeNode **queue;\n\n    /* Вспомогательная очередь */\n    queue = (TreeNode **)malloc(sizeof(TreeNode *) * MAX_SIZE);\n    // Указатель очереди\n    front = 0, rear = 0;\n    // Добавить корневой узел\n    queue[rear++] = root;\n    // Инициализировать список для хранения последовательности обхода\n    /* Вспомогательный массив */\n    arr = (int *)malloc(sizeof(int) * MAX_SIZE);\n    // Указатель на массив\n    index = 0;\n    while (front &lt; rear) {\n        // Извлечение из очереди\n        node = queue[front++];\n        // Сохранить значение узла\n        arr[index++] = node-&gt;val;\n        if (node-&gt;left != NULL) {\n            // Поместить левый дочерний узел в очередь\n            queue[rear++] = node-&gt;left;\n        }\n        if (node-&gt;right != NULL) {\n            // Поместить правый дочерний узел в очередь\n            queue[rear++] = node-&gt;right;\n        }\n    }\n    // Обновить значение длины массива\n    *size = index;\n    arr = realloc(arr, sizeof(int) * (*size));\n\n    // Освободить память вспомогательного массива\n    free(queue);\n    return arr;\n}\n</code></pre> binary_tree_bfs.kt<pre><code>/* Обход в ширину */\nfun levelOrder(root: TreeNode?): MutableList&lt;Int&gt; {\n    // Инициализировать очередь и добавить корневой узел\n    val queue = LinkedList&lt;TreeNode?&gt;()\n    queue.add(root)\n    // Инициализировать список для хранения последовательности обхода\n    val list = mutableListOf&lt;Int&gt;()\n    while (queue.isNotEmpty()) {\n        val node = queue.poll()      // Извлечение из очереди\n        list.add(node?._val!!)       // Сохранить значение узла\n        if (node.left != null)\n            queue.offer(node.left)   // Поместить левый дочерний узел в очередь\n        if (node.right != null)\n            queue.offer(node.right)  // Поместить правый дочерний узел в очередь\n    }\n    return list\n}\n</code></pre> binary_tree_bfs.rb<pre><code>### Обход в ширину ###\ndef level_order(root)\n  # Инициализировать очередь и добавить корневой узел\n  queue = [root]\n  # Инициализировать список для хранения последовательности обхода\n  res = []\n  while !queue.empty?\n    node = queue.shift # Извлечение из очереди\n    res &lt;&lt; node.val # Сохранить значение узла\n    queue &lt;&lt; node.left unless node.left.nil? # Поместить левый дочерний узел в очередь\n    queue &lt;&lt; node.right unless node.right.nil? # Поместить правый дочерний узел в очередь\n  end\n  res\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p>","path":["Глава 7. Деревья","7.2 &nbsp; Обход двоичного дерева"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/#2","level":3,"title":"2.   Анализ сложности","text":"<ul> <li>Временная сложность равна \\(O(n)\\) : все узлы посещаются по одному разу, поэтому требуется \\(O(n)\\) времени, где \\(n\\) - число узлов.</li> <li>Пространственная сложность равна \\(O(n)\\) : в худшем случае, то есть для полной двоичной деревообразной структуры, до достижения самого нижнего уровня в очереди одновременно может находиться до \\((n + 1) / 2\\) узлов, что требует \\(O(n)\\) памяти.</li> </ul>","path":["Глава 7. Деревья","7.2 &nbsp; Обход двоичного дерева"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/#722","level":2,"title":"7.2.2   Прямой, симметричный и обратный обходы","text":"<p>Соответственно, прямой, симметричный и обратный обходы относятся к обходу в глубину (depth-first traversal), также называемому поиском в глубину (depth-first search, DFS); он отражает идею \"сначала идти до конца, затем возвращаться и продолжать\".</p> <p>На рисунке 7-10 показан принцип работы обхода двоичного дерева в глубину. Обход в глубину можно представить как обход всей двоичной структуры по внешнему контуру , и у каждого узла встречаются три позиции, соответствующие прямому, симметричному и обратному обходам.</p> <p></p> <p> Рисунок 7-10   Прямой, симметричный и обратный обходы двоичного дерева поиска </p>","path":["Глава 7. Деревья","7.2 &nbsp; Обход двоичного дерева"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/#1_1","level":3,"title":"1.   Код реализации","text":"<p>Поиск в глубину обычно реализуется через рекурсию:</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRuby binary_tree_dfs.py<pre><code>def pre_order(root: TreeNode | None):\n    \"\"\"Предварительный обход\"\"\"\n    if root is None:\n        return\n    # Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n    res.append(root.val)\n    pre_order(root=root.left)\n    pre_order(root=root.right)\n\ndef in_order(root: TreeNode | None):\n    \"\"\"Симметричный обход\"\"\"\n    if root is None:\n        return\n    # Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n    in_order(root=root.left)\n    res.append(root.val)\n    in_order(root=root.right)\n\ndef post_order(root: TreeNode | None):\n    \"\"\"Обратный обход\"\"\"\n    if root is None:\n        return\n    # Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n    post_order(root=root.left)\n    post_order(root=root.right)\n    res.append(root.val)\n</code></pre> binary_tree_dfs.cpp<pre><code>/* Предварительный обход */\nvoid preOrder(TreeNode *root) {\n    if (root == nullptr)\n        return;\n    // Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n    vec.push_back(root-&gt;val);\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n}\n\n/* Симметричный обход */\nvoid inOrder(TreeNode *root) {\n    if (root == nullptr)\n        return;\n    // Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n    inOrder(root-&gt;left);\n    vec.push_back(root-&gt;val);\n    inOrder(root-&gt;right);\n}\n\n/* Обратный обход */\nvoid postOrder(TreeNode *root) {\n    if (root == nullptr)\n        return;\n    // Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n    postOrder(root-&gt;left);\n    postOrder(root-&gt;right);\n    vec.push_back(root-&gt;val);\n}\n</code></pre> binary_tree_dfs.java<pre><code>/* Предварительный обход */\nvoid preOrder(TreeNode root) {\n    if (root == null)\n        return;\n    // Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n    list.add(root.val);\n    preOrder(root.left);\n    preOrder(root.right);\n}\n\n/* Симметричный обход */\nvoid inOrder(TreeNode root) {\n    if (root == null)\n        return;\n    // Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n    inOrder(root.left);\n    list.add(root.val);\n    inOrder(root.right);\n}\n\n/* Обратный обход */\nvoid postOrder(TreeNode root) {\n    if (root == null)\n        return;\n    // Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n    postOrder(root.left);\n    postOrder(root.right);\n    list.add(root.val);\n}\n</code></pre> binary_tree_dfs.cs<pre><code>/* Предварительный обход */\nvoid PreOrder(TreeNode? root) {\n    if (root == null) return;\n    // Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n    list.Add(root.val!.Value);\n    PreOrder(root.left);\n    PreOrder(root.right);\n}\n\n/* Симметричный обход */\nvoid InOrder(TreeNode? root) {\n    if (root == null) return;\n    // Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n    InOrder(root.left);\n    list.Add(root.val!.Value);\n    InOrder(root.right);\n}\n\n/* Обратный обход */\nvoid PostOrder(TreeNode? root) {\n    if (root == null) return;\n    // Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n    PostOrder(root.left);\n    PostOrder(root.right);\n    list.Add(root.val!.Value);\n}\n</code></pre> binary_tree_dfs.go<pre><code>/* Предварительный обход */\nfunc preOrder(node *TreeNode) {\n    if node == nil {\n        return\n    }\n    // Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n    nums = append(nums, node.Val)\n    preOrder(node.Left)\n    preOrder(node.Right)\n}\n\n/* Симметричный обход */\nfunc inOrder(node *TreeNode) {\n    if node == nil {\n        return\n    }\n    // Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n    inOrder(node.Left)\n    nums = append(nums, node.Val)\n    inOrder(node.Right)\n}\n\n/* Обратный обход */\nfunc postOrder(node *TreeNode) {\n    if node == nil {\n        return\n    }\n    // Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n    postOrder(node.Left)\n    postOrder(node.Right)\n    nums = append(nums, node.Val)\n}\n</code></pre> binary_tree_dfs.swift<pre><code>/* Предварительный обход */\nfunc preOrder(root: TreeNode?) {\n    guard let root = root else {\n        return\n    }\n    // Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n    list.append(root.val)\n    preOrder(root: root.left)\n    preOrder(root: root.right)\n}\n\n/* Симметричный обход */\nfunc inOrder(root: TreeNode?) {\n    guard let root = root else {\n        return\n    }\n    // Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n    inOrder(root: root.left)\n    list.append(root.val)\n    inOrder(root: root.right)\n}\n\n/* Обратный обход */\nfunc postOrder(root: TreeNode?) {\n    guard let root = root else {\n        return\n    }\n    // Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n    postOrder(root: root.left)\n    postOrder(root: root.right)\n    list.append(root.val)\n}\n</code></pre> binary_tree_dfs.js<pre><code>/* Предварительный обход */\nfunction preOrder(root) {\n    if (root === null) return;\n    // Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n    list.push(root.val);\n    preOrder(root.left);\n    preOrder(root.right);\n}\n\n/* Симметричный обход */\nfunction inOrder(root) {\n    if (root === null) return;\n    // Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n    inOrder(root.left);\n    list.push(root.val);\n    inOrder(root.right);\n}\n\n/* Обратный обход */\nfunction postOrder(root) {\n    if (root === null) return;\n    // Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n    postOrder(root.left);\n    postOrder(root.right);\n    list.push(root.val);\n}\n</code></pre> binary_tree_dfs.ts<pre><code>/* Предварительный обход */\nfunction preOrder(root: TreeNode | null): void {\n    if (root === null) {\n        return;\n    }\n    // Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n    list.push(root.val);\n    preOrder(root.left);\n    preOrder(root.right);\n}\n\n/* Симметричный обход */\nfunction inOrder(root: TreeNode | null): void {\n    if (root === null) {\n        return;\n    }\n    // Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n    inOrder(root.left);\n    list.push(root.val);\n    inOrder(root.right);\n}\n\n/* Обратный обход */\nfunction postOrder(root: TreeNode | null): void {\n    if (root === null) {\n        return;\n    }\n    // Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n    postOrder(root.left);\n    postOrder(root.right);\n    list.push(root.val);\n}\n</code></pre> binary_tree_dfs.dart<pre><code>/* Предварительный обход */\nvoid preOrder(TreeNode? node) {\n  if (node == null) return;\n  // Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n  list.add(node.val);\n  preOrder(node.left);\n  preOrder(node.right);\n}\n\n/* Симметричный обход */\nvoid inOrder(TreeNode? node) {\n  if (node == null) return;\n  // Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n  inOrder(node.left);\n  list.add(node.val);\n  inOrder(node.right);\n}\n\n/* Обратный обход */\nvoid postOrder(TreeNode? node) {\n  if (node == null) return;\n  // Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n  postOrder(node.left);\n  postOrder(node.right);\n  list.add(node.val);\n}\n</code></pre> binary_tree_dfs.rs<pre><code>/* Предварительный обход */\nfn pre_order(root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;) -&gt; Vec&lt;i32&gt; {\n    let mut result = vec![];\n\n    fn dfs(root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;, res: &amp;mut Vec&lt;i32&gt;) {\n        if let Some(node) = root {\n            // Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n            let node = node.borrow();\n            res.push(node.val);\n            dfs(node.left.as_ref(), res);\n            dfs(node.right.as_ref(), res);\n        }\n    }\n    dfs(root, &amp;mut result);\n\n    result\n}\n\n/* Симметричный обход */\nfn in_order(root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;) -&gt; Vec&lt;i32&gt; {\n    let mut result = vec![];\n\n    fn dfs(root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;, res: &amp;mut Vec&lt;i32&gt;) {\n        if let Some(node) = root {\n            // Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n            let node = node.borrow();\n            dfs(node.left.as_ref(), res);\n            res.push(node.val);\n            dfs(node.right.as_ref(), res);\n        }\n    }\n    dfs(root, &amp;mut result);\n\n    result\n}\n\n/* Обратный обход */\nfn post_order(root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;) -&gt; Vec&lt;i32&gt; {\n    let mut result = vec![];\n\n    fn dfs(root: Option&lt;&amp;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;, res: &amp;mut Vec&lt;i32&gt;) {\n        if let Some(node) = root {\n            // Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n            let node = node.borrow();\n            dfs(node.left.as_ref(), res);\n            dfs(node.right.as_ref(), res);\n            res.push(node.val);\n        }\n    }\n\n    dfs(root, &amp;mut result);\n\n    result\n}\n</code></pre> binary_tree_dfs.c<pre><code>/* Предварительный обход */\nvoid preOrder(TreeNode *root, int *size) {\n    if (root == NULL)\n        return;\n    // Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n    arr[(*size)++] = root-&gt;val;\n    preOrder(root-&gt;left, size);\n    preOrder(root-&gt;right, size);\n}\n\n/* Симметричный обход */\nvoid inOrder(TreeNode *root, int *size) {\n    if (root == NULL)\n        return;\n    // Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n    inOrder(root-&gt;left, size);\n    arr[(*size)++] = root-&gt;val;\n    inOrder(root-&gt;right, size);\n}\n\n/* Обратный обход */\nvoid postOrder(TreeNode *root, int *size) {\n    if (root == NULL)\n        return;\n    // Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n    postOrder(root-&gt;left, size);\n    postOrder(root-&gt;right, size);\n    arr[(*size)++] = root-&gt;val;\n}\n</code></pre> binary_tree_dfs.kt<pre><code>/* Предварительный обход */\nfun preOrder(root: TreeNode?) {\n    if (root == null) return\n    // Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n    list.add(root._val)\n    preOrder(root.left)\n    preOrder(root.right)\n}\n\n/* Симметричный обход */\nfun inOrder(root: TreeNode?) {\n    if (root == null) return\n    // Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n    inOrder(root.left)\n    list.add(root._val)\n    inOrder(root.right)\n}\n\n/* Обратный обход */\nfun postOrder(root: TreeNode?) {\n    if (root == null) return\n    // Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n    postOrder(root.left)\n    postOrder(root.right)\n    list.add(root._val)\n}\n</code></pre> binary_tree_dfs.rb<pre><code>### Предварительный обход ###\ndef pre_order(root)\n  return if root.nil?\n\n  # Порядок обхода: корень -&gt; левое поддерево -&gt; правое поддерево\n  $res &lt;&lt; root.val\n  pre_order(root.left)\n  pre_order(root.right)\nend\n\n### Симметричный обход ###\ndef in_order(root)\n  return if root.nil?\n\n  # Порядок обхода: левое поддерево -&gt; корень -&gt; правое поддерево\n  in_order(root.left)\n  $res &lt;&lt; root.val\n  in_order(root.right)\nend\n\n### Обратный обход ###\ndef post_order(root)\n  return if root.nil?\n\n  # Порядок обхода: левое поддерево -&gt; правое поддерево -&gt; корень\n  post_order(root.left)\n  post_order(root.right)\n  $res &lt;&lt; root.val\nend\n</code></pre> Визуализация кода <p> Во весь экран &gt;</p> <p>Tip</p> <p>Поиск в глубину можно реализовать и итеративно; заинтересованные читатели могут изучить это самостоятельно.</p> <p>На рисунках ниже показан рекурсивный процесс прямого обхода двоичного дерева. Его можно разделить на две противоположные части: \"вход в рекурсию\" и \"возврат\".</p> <ol> <li>\"Вход в рекурсию\" означает запуск нового вызова функции; в этом процессе программа переходит к следующему узлу.</li> <li>\"Возврат\" означает завершение вызова функции и возврат назад, то есть текущий узел уже полностью обработан.</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> Рисунок 7-11   Рекурсивный процесс прямого обхода </p>","path":["Глава 7. Деревья","7.2 &nbsp; Обход двоичного дерева"],"tags":[]},{"location":"chapter_tree/binary_tree_traversal/#2_1","level":3,"title":"2.   Анализ сложности","text":"<ul> <li>Временная сложность равна \\(O(n)\\) : все узлы посещаются по одному разу, поэтому требуется \\(O(n)\\) времени.</li> <li>Пространственная сложность равна \\(O(n)\\) : в худшем случае, когда дерево вырождается в связный список, глубина рекурсии достигает \\(n\\) , и система тратит \\(O(n)\\) памяти на стек вызовов.</li> </ul>","path":["Глава 7. Деревья","7.2 &nbsp; Обход двоичного дерева"],"tags":[]},{"location":"chapter_tree/summary/","level":1,"title":"7.6   Краткие итоги","text":"","path":["Глава 7. Деревья","7.6 &nbsp; Краткие итоги"],"tags":[]},{"location":"chapter_tree/summary/#1","level":3,"title":"1.   Основные моменты","text":"<ul> <li>Двоичное дерево - это нелинейная структура данных, отражающая логику \"разделяй и властвуй\". Каждый узел двоичного дерева содержит значение и два указателя, которые соответственно ведут к левому и правому дочерним узлам.</li> <li>Для любого узла двоичного дерева дерево, образованное его левым (правым) дочерним узлом и всеми нижележащими узлами, называется левым (правым) поддеревом этого узла.</li> <li>К связанным с двоичным деревом терминам относятся корневой узел, листовой узел, уровень, степень, ребро, высота, глубина и так далее.</li> <li>Инициализация двоичного дерева, вставка узлов и удаление узлов аналогичны операциям со связным списком.</li> <li>К распространенным видам двоичного дерева относятся идеальное двоичное дерево, полное двоичное дерево, строгое двоичное дерево и сбалансированное двоичное дерево. Идеальное двоичное дерево - наиболее желательное состояние, а связный список - худший случай после вырождения.</li> <li>Двоичное дерево можно представить массивом: значения узлов и пустые позиции располагаются в порядке обхода по уровням, а связи между родителем и детьми реализуются через индексацию.</li> <li>Обход двоичного дерева по уровням является методом поиска в ширину; он отражает идею \"расширяться от центра к периферии слой за слоем\" и обычно реализуется через очередь.</li> <li>Прямой, симметричный и обратный обходы относятся к поиску в глубину; они отражают идею \"сначала дойти до конца, затем вернуться и продолжить\" и обычно реализуются рекурсивно.</li> <li>Двоичное дерево поиска - это эффективная структура данных для поиска элементов; его поиск, вставка и удаление имеют временную сложность \\(O(\\log n)\\) . Когда двоичное дерево поиска вырождается в связный список, все эти сложности деградируют до \\(O(n)\\) .</li> <li>AVL-дерево, также называемое сбалансированным двоичным деревом поиска, с помощью вращений гарантирует, что после постоянных вставок и удалений узлов дерево остается сбалансированным.</li> <li>Вращения AVL-дерева включают правое вращение, левое вращение, сначала правое затем левое и сначала левое затем правое. После вставки или удаления узла AVL-дерево выполняет вращения снизу вверх, чтобы снова восстановить баланс.</li> </ul>","path":["Глава 7. Деревья","7.6 &nbsp; Краткие итоги"],"tags":[]},{"location":"chapter_tree/summary/#2-q-a","level":3,"title":"2.   Q &amp; A","text":"<p>Q: Для двоичного дерева, состоящего из одного узла, высота дерева и глубина корня обе равны \\(0\\) ?</p> <p>Да, потому что высота и глубина обычно определяются как \"число пройденных ребер\".</p> <p>Q: Вставка и удаление в двоичном дереве обычно выполняются в составе набора операций. Что именно означает этот \"набор операций\"? Можно ли понимать это как освобождение ресурсов у дочерних узлов ресурса?</p> <p>Возьмем в качестве примера двоичное дерево поиска: операция удаления узла делится на три случая, и каждый из этих случаев требует нескольких последовательных шагов работы с узлами.</p> <p>Q: Почему у DFS для двоичного дерева есть три порядка: прямой, симметричный и обратный? Для чего они нужны?</p> <p>Подобно прямому и обратному обходу массива, прямой, симметричный и обратный обходы - это три способа обхода двоичного дерева, с помощью которых можно получить результаты в определенном порядке. Например, в двоичном дереве поиска, где соблюдается отношение <code>значение левого дочернего узла &lt; значение корня &lt; значение правого дочернего узла</code> , если обходить дерево с приоритетом \"лево \\(\\rightarrow\\) корень \\(\\rightarrow\\) право\", то получится упорядоченная последовательность узлов.</p> <p>Q: Правое вращение работает с отношениями между <code>node</code> , <code>child</code> и <code>grand_child</code> . А связь между <code>node</code> и его исходным родителем разве не нужно поддерживать? После правого вращения она ведь не оборвется?</p> <p>На это нужно смотреть с точки зрения рекурсии. В правое вращение <code>right_rotate(root)</code> передается корень поддерева, а затем через <code>return child</code> возвращается корень этого поддерева уже после вращения. Соединение между новым корнем поддерева и его родителем восстанавливается после возврата функции и не входит в обязанности самой операции правого вращения.</p> <p>Q: В C++ функции делятся на <code>private</code> и <code>public</code> . Какая логика стоит за этим? Почему <code>height()</code> и <code>updateHeight()</code> помещают в разные области видимости?</p> <p>Главный критерий - область использования метода. Если метод нужен только внутри класса, его следует проектировать как <code>private</code> . Например, самостоятельный вызов <code>updateHeight()</code> пользователем не имеет смысла: это лишь один из шагов внутри вставки или удаления. А <code>height()</code> используется для чтения высоты узла, подобно <code>vector.size()</code> , поэтому его разумно делать <code>public</code> .</p> <p>Q: Как построить двоичное дерево поиска из набора входных данных? Важен ли выбор корневого узла?</p> <p>Да, важен. Способ построения дерева уже показан в методе <code>build_tree()</code> в коде двоичного дерева поиска. Что касается выбора корня, обычно входные данные сортируют, берут средний элемент как корень, а затем рекурсивно строят левое и правое поддеревья. Это позволяет в наибольшей степени сохранить баланс дерева.</p> <p>Q: Нужно ли в Java всегда использовать <code>equals()</code> для сравнения строк?</p> <p>В Java для базовых типов <code>==</code> используется, чтобы сравнивать, равны ли значения двух переменных. Для ссылочных типов логика у этих двух способов уже разная.</p> <ul> <li><code>==</code> : сравнивает, ссылаются ли две переменные на один и тот же объект, то есть совпадает ли их адрес в памяти.</li> <li><code>equals()</code>: сравнивает, равны ли значения двух объектов.</li> </ul> <p>Поэтому если нужно сравнить значения, то следует использовать <code>equals()</code> . Но строки, инициализированные как <code>String a = \"hi\"; String b = \"hi\";</code> , хранятся в строковом пуле констант и указывают на один и тот же объект, поэтому в таком случае <code>a == b</code> тоже может дать истинный результат при сравнении содержимого.</p> <p>Q: До достижения самого нижнего уровня при обходе в ширину число узлов в очереди равно \\(2^h\\) ?</p> <p>Да. Например, для полного двоичного дерева высоты \\(h = 2\\) общее число узлов равно \\(n = 7\\) , а число узлов на нижнем уровне равно \\(4 = 2^h = (n + 1) / 2\\) .</p>","path":["Глава 7. Деревья","7.6 &nbsp; Краткие итоги"],"tags":[]}]}
\ No newline at end of file
diff --git a/ru/stylesheets/extra.css b/ru/stylesheets/extra.css
index dc5453f01..8805cdf77 100644
--- a/ru/stylesheets/extra.css
+++ b/ru/stylesheets/extra.css
@@ -375,6 +375,14 @@ a:hover .text-button span {
   font-weight: normal;
 }
 
+.hero-div--en {
+  font-size: min(1.65vh, 2.3vw);
+}
+
+.hero-div--ru {
+  font-size: min(1.45vh, 2vw);
+}
+
 .hero-bg {
   height: 100%;
   width: 100%;
@@ -487,6 +495,11 @@ a:hover .text-button span {
   text-align: center;
 }
 
+.profile-cell a:hover b,
+.profile-cell a:focus-visible b {
+  text-decoration: underline;
+}
+
 .profile-img {
   width: 5em;
   border-radius: 50%;
@@ -768,4 +781,4 @@ html:has(body[data-md-color-scheme="default"]) {
 .md-typeset a:not(.md-button):focus-visible {
   text-decoration: underline;
 }
-/*! update cache: 20260329054803 */
+/*! update cache: 20260330081625 */
diff --git a/stylesheets/extra.css b/stylesheets/extra.css
index 7b10b6e8e..94c236f4b 100644
--- a/stylesheets/extra.css
+++ b/stylesheets/extra.css
@@ -375,6 +375,14 @@ a:hover .text-button span {
   font-weight: normal;
 }
 
+.hero-div--en {
+  font-size: min(1.65vh, 2.3vw);
+}
+
+.hero-div--ru {
+  font-size: min(1.45vh, 2vw);
+}
+
 .hero-bg {
   height: 100%;
   width: 100%;
@@ -487,6 +495,11 @@ a:hover .text-button span {
   text-align: center;
 }
 
+.profile-cell a:hover b,
+.profile-cell a:focus-visible b {
+  text-decoration: underline;
+}
+
 .profile-img {
   width: 5em;
   border-radius: 50%;
@@ -768,4 +781,4 @@ html:has(body[data-md-color-scheme="default"]) {
 .md-typeset a:not(.md-button):focus-visible {
   text-decoration: underline;
 }
-/*! update cache: 20260329054721 */
+/*! update cache: 20260330081538 */
diff --git a/zh-hant/404.html b/zh-hant/404.html
index 16193fbdd..29c66d31d 100644
--- a/zh-hant/404.html
+++ b/zh-hant/404.html
@@ -59,8 +59,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+SC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans SC";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+TC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Noto Sans TC";--md-code-font:"JetBrains Mono"}</style>
       
     
     
diff --git a/zh-hant/assets/javascripts/bundle.c2b142ea.min.js b/zh-hant/assets/javascripts/bundle.c2b142ea.min.js
index 88c1fd753..edc6fe418 100644
--- a/zh-hant/assets/javascripts/bundle.c2b142ea.min.js
+++ b/zh-hant/assets/javascripts/bundle.c2b142ea.min.js
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rect{fill:var(--md-mermaid-edge-color)!important;stroke:none!important}.statediagram-cluster.statediagram-cluster .inner{fill:var(--md-default-bg-color)}.statediagram-cluster rect{fill:var(--md-mermaid-node-bg-color);stroke:var(--md-mermaid-node-fg-color)}.statediagram-state rect.divider{fill:var(--md-default-fg-color--lightest);stroke:var(--md-default-fg-color--lighter)}defs #statediagram-barbEnd{stroke:var(--md-mermaid-edge-color)}[id^=entity] path,[id^=entity] rect{fill:var(--md-default-bg-color)}.relationshipLine{stroke:var(--md-mermaid-edge-color)}defs .marker.oneOrMore.er *,defs .marker.onlyOne.er *,defs .marker.zeroOrMore.er *,defs .marker.zeroOrOne.er 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t.pipe(g(r=>R(Y(!0),Y(!1).pipe(It(2e3))).pipe(f(n=>({message:r,active:n})))))}function Fs(e,t){let r=G(".md-typeset",e);return j(()=>{let n=new I;return n.subscribe(({message:o,active:i})=>{e.classList.toggle("md-dialog--active",i),r.textContent=o}),dp(e,t).pipe($(o=>n.next(o)),V(()=>n.complete()),f(o=>H({ref:e},o)))})}function hp({viewport$:e}){if(!X("header.autohide"))return Y(!1);let t=e.pipe(f(({offset:{y:o}})=>o),Pt(2,1),f(([o,i])=>[o<i,i]),fe(0)),r=re([e,t]).pipe(L(([{offset:o},[,i]])=>Math.abs(i-o.y)>100),f(([,[o]])=>o),ie()),n=Tn("search");return re([e,n]).pipe(f(([{offset:o},i])=>o.y>400&&!i),ie(),g(o=>o?r:Y(!1)),J(!1))}function Us(e,t){return j(()=>re([Re(e),hp(t)])).pipe(f(([{height:r},n])=>({height:r,hidden:n})),ie((r,n)=>r.height===n.height&&r.hidden===n.hidden),se(1))}function Ns(e,{viewport$:t,header$:r,main$:n}){return j(()=>{let o=new 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-        <style>:root{--md-text-font:"Noto Sans SC";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+TC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
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+        <style>:root{--md-text-font:"Noto Sans TC";--md-code-font:"JetBrains Mono"}</style>
       
     
     
diff --git a/zh-hant/chapter_appendix/installation/index.html b/zh-hant/chapter_appendix/installation/index.html
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-        <style>:root{--md-text-font:"Noto Sans SC";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+TC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Noto Sans TC";--md-code-font:"JetBrains Mono"}</style>
       
     
     
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index 03f954ef6..4d3968aa9 100644
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-        <style>:root{--md-text-font:"Noto Sans SC";--md-code-font:"JetBrains Mono"}</style>
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+        <style>:root{--md-text-font:"Noto Sans TC";--md-code-font:"JetBrains Mono"}</style>
       
     
     
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+        <style>:root{--md-text-font:"Noto Sans TC";--md-code-font:"JetBrains Mono"}</style>
       
     
     
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index 5e26fc8b4..f86867dec 100644
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-        <style>:root{--md-text-font:"Noto Sans SC";--md-code-font:"JetBrains Mono"}</style>
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+        <style>:root{--md-text-font:"Noto Sans TC";--md-code-font:"JetBrains Mono"}</style>
       
     
     
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index f7471ad32..5f0147f54 100644
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+        <style>:root{--md-text-font:"Noto Sans TC";--md-code-font:"JetBrains Mono"}</style>
       
     
     
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diff --git a/zh-hant/chapter_stack_and_queue/queue/index.html b/zh-hant/chapter_stack_and_queue/queue/index.html
index e57113377..c08ac3e43 100644
--- a/zh-hant/chapter_stack_and_queue/queue/index.html
+++ b/zh-hant/chapter_stack_and_queue/queue/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+SC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans SC";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+TC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Noto Sans TC";--md-code-font:"JetBrains Mono"}</style>
       
     
     
diff --git a/zh-hant/chapter_stack_and_queue/stack/index.html b/zh-hant/chapter_stack_and_queue/stack/index.html
index 473c0bda5..6b5eb04d9 100644
--- a/zh-hant/chapter_stack_and_queue/stack/index.html
+++ b/zh-hant/chapter_stack_and_queue/stack/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+SC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans SC";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+TC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Noto Sans TC";--md-code-font:"JetBrains Mono"}</style>
       
     
     
diff --git a/zh-hant/chapter_stack_and_queue/summary/index.html b/zh-hant/chapter_stack_and_queue/summary/index.html
index b899355af..5f3b8b7b2 100644
--- a/zh-hant/chapter_stack_and_queue/summary/index.html
+++ b/zh-hant/chapter_stack_and_queue/summary/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+SC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans SC";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+TC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Noto Sans TC";--md-code-font:"JetBrains Mono"}</style>
       
     
     
diff --git a/zh-hant/chapter_tree/array_representation_of_tree/index.html b/zh-hant/chapter_tree/array_representation_of_tree/index.html
index c14a53901..4e738f95a 100644
--- a/zh-hant/chapter_tree/array_representation_of_tree/index.html
+++ b/zh-hant/chapter_tree/array_representation_of_tree/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+SC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans SC";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+TC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Noto Sans TC";--md-code-font:"JetBrains Mono"}</style>
       
     
     
diff --git a/zh-hant/chapter_tree/avl_tree/index.html b/zh-hant/chapter_tree/avl_tree/index.html
index 9b716cb7e..6940878ab 100644
--- a/zh-hant/chapter_tree/avl_tree/index.html
+++ b/zh-hant/chapter_tree/avl_tree/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+SC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans SC";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+TC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Noto Sans TC";--md-code-font:"JetBrains Mono"}</style>
       
     
     
diff --git a/zh-hant/chapter_tree/binary_search_tree/index.html b/zh-hant/chapter_tree/binary_search_tree/index.html
index df64e6017..fe8f13907 100644
--- a/zh-hant/chapter_tree/binary_search_tree/index.html
+++ b/zh-hant/chapter_tree/binary_search_tree/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+SC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans SC";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+TC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Noto Sans TC";--md-code-font:"JetBrains Mono"}</style>
       
     
     
diff --git a/zh-hant/chapter_tree/binary_tree/index.html b/zh-hant/chapter_tree/binary_tree/index.html
index 4849b6b4f..3f8523171 100644
--- a/zh-hant/chapter_tree/binary_tree/index.html
+++ b/zh-hant/chapter_tree/binary_tree/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+SC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans SC";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+TC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Noto Sans TC";--md-code-font:"JetBrains Mono"}</style>
       
     
     
diff --git a/zh-hant/chapter_tree/binary_tree_traversal/index.html b/zh-hant/chapter_tree/binary_tree_traversal/index.html
index fcf2c3d27..69ac4a2d4 100644
--- a/zh-hant/chapter_tree/binary_tree_traversal/index.html
+++ b/zh-hant/chapter_tree/binary_tree_traversal/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+SC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans SC";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+TC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Noto Sans TC";--md-code-font:"JetBrains Mono"}</style>
       
     
     
diff --git a/zh-hant/chapter_tree/index.html b/zh-hant/chapter_tree/index.html
index 16f214df3..55d2da84c 100644
--- a/zh-hant/chapter_tree/index.html
+++ b/zh-hant/chapter_tree/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+SC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans SC";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+TC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Noto Sans TC";--md-code-font:"JetBrains Mono"}</style>
       
     
     
diff --git a/zh-hant/chapter_tree/summary/index.html b/zh-hant/chapter_tree/summary/index.html
index bfbe6a024..5fc62714a 100644
--- a/zh-hant/chapter_tree/summary/index.html
+++ b/zh-hant/chapter_tree/summary/index.html
@@ -65,8 +65,8 @@
         
         
         <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
-        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+SC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
-        <style>:root{--md-text-font:"Noto Sans SC";--md-code-font:"JetBrains Mono"}</style>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+TC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Noto Sans TC";--md-code-font:"JetBrains Mono"}</style>
       
     
     
diff --git a/zh-hant/index.html b/zh-hant/index.html
index ff6207214..968582282 100644
--- a/zh-hant/index.html
+++ b/zh-hant/index.html
@@ -19,9 +19,9 @@
     <link href="./assets/stylesheets/modern/main.6f2fbb28.min.css" rel="stylesheet"/>
     <link href="./assets/stylesheets/modern/palette.dfe2e883.min.css" rel="stylesheet"/>
     <link crossorigin="" href="https://fonts.gstatic.com" rel="preconnect"/>
-    <link href="https://fonts.googleapis.com/css?family=Noto+Sans+SC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&amp;display=fallback" rel="stylesheet"/>
+    <link href="https://fonts.googleapis.com/css?family=Noto+Sans+TC:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&amp;display=fallback" rel="stylesheet"/>
     <style>
-      :root{--md-text-font:"Noto Sans SC";--md-code-font:"JetBrains Mono"}
+      :root{--md-text-font:"Noto Sans TC";--md-code-font:"JetBrains Mono"}
     </style>
     <link href="./stylesheets/extra.css" rel="stylesheet"/>
     <script>
diff --git a/zh-hant/javascripts/katex.js b/zh-hant/javascripts/katex.js
index 6876c4d54..0602e2390 100644
--- a/zh-hant/javascripts/katex.js
+++ b/zh-hant/javascripts/katex.js
@@ -8,4 +8,4 @@ document$.subscribe(({ body }) => {
     ],
   });
 });
-/*! update cache: 20260329054733 */
+/*! update cache: 20260330081550 */
diff --git a/zh-hant/javascripts/mathjax.js b/zh-hant/javascripts/mathjax.js
index f21530892..c45574a6b 100644
--- a/zh-hant/javascripts/mathjax.js
+++ b/zh-hant/javascripts/mathjax.js
@@ -15,4 +15,4 @@ window.MathJax = {
 document$.subscribe(() => {
   MathJax.typesetPromise();
 });
-/*! update cache: 20260329054733 */
+/*! update cache: 20260330081550 */
diff --git a/zh-hant/javascripts/starfield.js b/zh-hant/javascripts/starfield.js
index cf854d6d5..b351113f6 100644
--- a/zh-hant/javascripts/starfield.js
+++ b/zh-hant/javascripts/starfield.js
@@ -469,4 +469,4 @@
 
   return Starfield;
 });
-/*! update cache: 20260329054733 */
+/*! update cache: 20260330081550 */
diff --git a/zh-hant/stylesheets/extra.css b/zh-hant/stylesheets/extra.css
index ff77b0d93..e91ff7908 100644
--- a/zh-hant/stylesheets/extra.css
+++ b/zh-hant/stylesheets/extra.css
@@ -375,6 +375,14 @@ a:hover .text-button span {
   font-weight: normal;
 }
 
+.hero-div--en {
+  font-size: min(1.65vh, 2.3vw);
+}
+
+.hero-div--ru {
+  font-size: min(1.45vh, 2vw);
+}
+
 .hero-bg {
   height: 100%;
   width: 100%;
@@ -487,6 +495,11 @@ a:hover .text-button span {
   text-align: center;
 }
 
+.profile-cell a:hover b,
+.profile-cell a:focus-visible b {
+  text-decoration: underline;
+}
+
 .profile-img {
   width: 5em;
   border-radius: 50%;
@@ -768,4 +781,4 @@ html:has(body[data-md-color-scheme="default"]) {
 .md-typeset a:not(.md-button):focus-visible {
   text-decoration: underline;
 }
-/*! update cache: 20260329054733 */
+/*! update cache: 20260330081550 */